%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : ALG141+1 : TPTP v8.1.2. Released v2.7.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n013.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed Aug 30 16:37:08 EDT 2023

% Result   : Unsatisfiable 25.55s 4.20s
% Output   : Proof 232.32s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : ALG141+1 : TPTP v8.1.2. Released v2.7.0.
% 0.00/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.16/0.34  % Computer : n013.cluster.edu
% 0.16/0.34  % Model    : x86_64 x86_64
% 0.16/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34  % Memory   : 8042.1875MB
% 0.16/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34  % CPULimit : 300
% 0.16/0.34  % WCLimit  : 300
% 0.16/0.34  % DateTime : Mon Aug 28 04:16:46 EDT 2023
% 0.16/0.34  % CPUTime  : 
% 0.20/0.59  ________       _____
% 0.20/0.59  ___  __ \_________(_)________________________________
% 0.20/0.59  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.20/0.59  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.20/0.59  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.20/0.59  
% 0.20/0.59  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.59  (2023-06-19)
% 0.20/0.59  
% 0.20/0.59  (c) Philipp Rümmer, 2009-2023
% 0.20/0.59  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.59                Amanda Stjerna.
% 0.20/0.59  Free software under BSD-3-Clause.
% 0.20/0.59  
% 0.20/0.59  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.59  
% 0.20/0.59  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.60  Running up to 7 provers in parallel.
% 0.20/0.62  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.62  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.62  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.62  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.62  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.62  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.62  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.83/1.33  Prover 1: Preprocessing ...
% 3.83/1.33  Prover 4: Preprocessing ...
% 3.83/1.37  Prover 6: Preprocessing ...
% 3.83/1.37  Prover 5: Preprocessing ...
% 3.83/1.37  Prover 3: Preprocessing ...
% 3.83/1.37  Prover 2: Preprocessing ...
% 3.83/1.37  Prover 0: Preprocessing ...
% 7.38/1.76  Prover 2: Constructing countermodel ...
% 7.38/1.76  Prover 3: Constructing countermodel ...
% 7.79/1.80  Prover 4: Constructing countermodel ...
% 7.79/1.81  Prover 6: Constructing countermodel ...
% 7.79/1.81  Prover 0: Constructing countermodel ...
% 7.79/1.81  Prover 1: Constructing countermodel ...
% 8.63/2.07  Prover 5: Constructing countermodel ...
% 25.55/4.19  Prover 3: proved (3574ms)
% 25.55/4.19  
% 25.55/4.20  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 25.55/4.20  
% 25.55/4.20  Prover 6: stopped
% 25.55/4.20  Prover 0: stopped
% 25.55/4.20  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 25.55/4.20  Prover 2: stopped
% 25.55/4.20  Prover 5: stopped
% 25.55/4.21  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 25.55/4.21  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 25.55/4.21  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 25.55/4.21  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 26.84/4.43  Prover 7: Preprocessing ...
% 27.13/4.44  Prover 8: Preprocessing ...
% 27.13/4.44  Prover 11: Preprocessing ...
% 27.13/4.45  Prover 10: Preprocessing ...
% 27.22/4.47  Prover 13: Preprocessing ...
% 28.71/4.66  Prover 8: Constructing countermodel ...
% 28.97/4.73  Prover 10: Constructing countermodel ...
% 29.37/4.74  Prover 11: Constructing countermodel ...
% 29.37/4.74  Prover 7: Constructing countermodel ...
% 29.37/4.75  Prover 13: Constructing countermodel ...
% 65.70/9.56  Prover 13: stopped
% 66.31/9.58  Prover 16: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 66.74/9.67  Prover 16: Preprocessing ...
% 68.64/9.89  Prover 16: Constructing countermodel ...
% 110.43/15.39  Prover 16: stopped
% 110.70/15.41  Prover 19: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 110.94/15.47  Prover 19: Preprocessing ...
% 111.70/15.54  Prover 19: Constructing countermodel ...
% 114.75/15.95  Prover 1: stopped
% 138.31/19.16  Prover 19: stopped
% 186.16/26.86  Prover 7: stopped
% 190.58/27.94  Prover 4: stopped
% 212.60/34.70  Prover 10: Found proof (size 18581326)
% 212.60/34.70  Prover 10: proved (30496ms)
% 212.60/34.70  Prover 11: stopped
% 212.60/34.71  Prover 8: stopped
% 212.60/34.71  
% 212.60/34.71  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 212.60/34.71  
% 215.75/36.07  % SZS output start Proof for theBenchmark
% 216.00/36.25  Assumptions after simplification:
% 216.00/36.25  ---------------------------------
% 216.00/36.25  
% 216.00/36.25    (ax1)
% 216.29/36.31    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : 
% 216.29/36.31    ? [v3: $i] :  ? [v4: $i] :  ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i] :  ? [v8:
% 216.29/36.31      $i] :  ? [v9: $i] :  ? [v10: $i] :  ? [v11: $i] :  ? [v12: $i] :  ? [v13:
% 216.29/36.31      $i] :  ? [v14: $i] :  ? [v15: $i] : (op(e3, e3) = v15 & op(e3, e2) = v14 &
% 216.29/36.31      op(e3, e1) = v13 & op(e3, e0) = v12 & op(e2, e3) = v11 & op(e2, e2) = v10 &
% 216.29/36.31      op(e2, e1) = v9 & op(e2, e0) = v8 & op(e1, e3) = v7 & op(e1, e2) = v6 &
% 216.29/36.31      op(e1, e1) = v5 & op(e1, e0) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 &
% 216.29/36.31      op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) & $i(v12) &
% 216.29/36.31      $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) &
% 216.29/36.31      $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v15 = e3 | v15 = e2 | v15 = e1 | v15 =
% 216.29/36.31        e0) & (v14 = e3 | v14 = e2 | v14 = e1 | v14 = e0) & (v13 = e3 | v13 = e2 |
% 216.29/36.31        v13 = e1 | v13 = e0) & (v12 = e3 | v12 = e2 | v12 = e1 | v12 = e0) & (v11
% 216.29/36.31        = e3 | v11 = e2 | v11 = e1 | v11 = e0) & (v10 = e3 | v10 = e2 | v10 = e1 |
% 216.29/36.31        v10 = e0) & (v9 = e3 | v9 = e2 | v9 = e1 | v9 = e0) & (v8 = e3 | v8 = e2 |
% 216.29/36.31        v8 = e1 | v8 = e0) & (v7 = e3 | v7 = e2 | v7 = e1 | v7 = e0) & (v6 = e3 |
% 216.29/36.31        v6 = e2 | v6 = e1 | v6 = e0) & (v5 = e3 | v5 = e2 | v5 = e1 | v5 = e0) &
% 216.29/36.31      (v4 = e3 | v4 = e2 | v4 = e1 | v4 = e0) & (v3 = e3 | v3 = e2 | v3 = e1 | v3
% 216.29/36.31        = e0) & (v2 = e3 | v2 = e2 | v2 = e1 | v2 = e0) & (v1 = e3 | v1 = e2 | v1
% 216.29/36.31        = e1 | v1 = e0) & (v0 = e3 | v0 = e2 | v0 = e1 | v0 = e0))
% 216.29/36.31  
% 216.29/36.31    (ax10)
% 216.29/36.31    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 216.29/36.31    (op(e2, e2) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e1) & op(v1, e2) = v2 &
% 216.29/36.31          op(e2, e3) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e2, e3) = v1 &
% 216.29/36.31          $i(v1))))
% 216.29/36.31  
% 216.29/36.31    (ax11)
% 216.29/36.31    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 216.29/36.31    (op(e1, e1) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e2) & op(v1, e1) = v2 &
% 216.29/36.31          op(e1, e3) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e1, e3) = v1 &
% 216.29/36.31          $i(v1))))
% 216.29/36.31  
% 216.29/36.31    (ax12)
% 216.29/36.31    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 216.29/36.31    (op(e3, e3) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e2) & op(v1, e3) = v2 &
% 216.29/36.31          op(e3, e0) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e3, e0) = v1 &
% 216.29/36.31          $i(v1))))
% 216.29/36.31  
% 216.29/36.31    (ax13)
% 216.29/36.32    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 216.29/36.32    (op(e2, e2) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e3) & op(v1, e2) = v2 &
% 216.29/36.32          op(e2, e0) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e2, e0) = v1 &
% 216.29/36.32          $i(v1))))
% 216.29/36.32  
% 216.29/36.32    (ax14)
% 216.29/36.32    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 216.29/36.32    (op(e3, e3) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e0) & op(v1, e3) = v2 &
% 216.29/36.32          op(e3, e2) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e3, e2) = v1 &
% 216.29/36.32          $i(v1))))
% 216.29/36.32  
% 216.29/36.32    (ax15)
% 216.29/36.32    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 216.29/36.32    (op(e0, e0) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e3) & op(v1, e0) = v2 &
% 216.29/36.32          op(e0, e2) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e0, e2) = v1 &
% 216.29/36.32          $i(v1))))
% 216.29/36.32  
% 216.29/36.32    (ax16)
% 216.29/36.32    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 216.29/36.32    (op(e2, e2) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e0) & op(v1, e2) = v2 &
% 216.29/36.32          op(e2, e3) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e2, e3) = v1 &
% 216.29/36.32          $i(v1))))
% 216.29/36.32  
% 216.29/36.32    (ax17)
% 216.29/36.32    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 216.29/36.32    (op(e0, e0) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e2) & op(v1, e0) = v2 &
% 216.29/36.32          op(e0, e3) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e0, e3) = v1 &
% 216.29/36.32          $i(v1))))
% 216.29/36.32  
% 216.29/36.32    (ax18)
% 216.29/36.33    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 216.29/36.33    (op(e3, e3) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e1) & op(v1, e3) = v2 &
% 216.29/36.33          op(e3, e0) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e3, e0) = v1 &
% 216.29/36.33          $i(v1))))
% 216.29/36.33  
% 216.29/36.33    (ax19)
% 216.29/36.33    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 216.29/36.33    (op(e1, e1) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e3) & op(v1, e1) = v2 &
% 216.29/36.33          op(e1, e0) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e1, e0) = v1 &
% 216.29/36.33          $i(v1))))
% 216.29/36.33  
% 216.29/36.33    (ax2)
% 216.29/36.35    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : 
% 216.29/36.35    ? [v3: $i] :  ? [v4: $i] :  ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i] :  ? [v8:
% 216.29/36.35      $i] :  ? [v9: $i] :  ? [v10: $i] :  ? [v11: $i] :  ? [v12: $i] :  ? [v13:
% 216.29/36.35      $i] :  ? [v14: $i] :  ? [v15: $i] : (((v15 = e3 & op(e3, e3) = e3) | (v14 =
% 216.29/36.35          e3 & op(e3, e2) = e3) | (v11 = e3 & op(e3, e1) = e3) | (v6 = e3 & op(e3,
% 216.29/36.35            e0) = e3)) & ((v15 = e3 & op(e3, e3) = e3) | (v13 = e3 & op(e2, e3) =
% 216.29/36.35          e3) | (v9 = e3 & op(e1, e3) = e3) | (v3 = e3 & op(e0, e3) = e3)) & ((v15
% 216.29/36.35          = e2 & op(e3, e3) = e2) | (v14 = e2 & op(e3, e2) = e2) | (v11 = e2 &
% 216.29/36.35          op(e3, e1) = e2) | (v6 = e2 & op(e3, e0) = e2)) & ((v15 = e2 & op(e3,
% 216.29/36.35            e3) = e2) | (v13 = e2 & op(e2, e3) = e2) | (v9 = e2 & op(e1, e3) = e2)
% 216.29/36.35        | (v3 = e2 & op(e0, e3) = e2)) & ((v15 = e1 & op(e3, e3) = e1) | (v14 = e1
% 216.29/36.35          & op(e3, e2) = e1) | (v11 = e1 & op(e3, e1) = e1) | (v6 = e1 & op(e3,
% 216.29/36.35            e0) = e1)) & ((v15 = e1 & op(e3, e3) = e1) | (v13 = e1 & op(e2, e3) =
% 216.29/36.35          e1) | (v9 = e1 & op(e1, e3) = e1) | (v3 = e1 & op(e0, e3) = e1)) & ((v15
% 216.29/36.35          = e0 & op(e3, e3) = e0) | (v14 = e0 & op(e3, e2) = e0) | (v11 = e0 &
% 216.29/36.35          op(e3, e1) = e0) | (v6 = e0 & op(e3, e0) = e0)) & ((v15 = e0 & op(e3,
% 216.29/36.35            e3) = e0) | (v13 = e0 & op(e2, e3) = e0) | (v9 = e0 & op(e1, e3) = e0)
% 216.29/36.35        | (v3 = e0 & op(e0, e3) = e0)) & ((v14 = e3 & op(e3, e2) = e3) | (v12 = e3
% 216.29/36.35          & op(e2, e2) = e3) | (v8 = e3 & op(e1, e2) = e3) | (v2 = e3 & op(e0, e2)
% 216.29/36.35          = e3)) & ((v14 = e2 & op(e3, e2) = e2) | (v12 = e2 & op(e2, e2) = e2) |
% 216.29/36.35        (v8 = e2 & op(e1, e2) = e2) | (v2 = e2 & op(e0, e2) = e2)) & ((v14 = e1 &
% 216.29/36.35          op(e3, e2) = e1) | (v12 = e1 & op(e2, e2) = e1) | (v8 = e1 & op(e1, e2)
% 216.29/36.35          = e1) | (v2 = e1 & op(e0, e2) = e1)) & ((v14 = e0 & op(e3, e2) = e0) |
% 216.29/36.35        (v12 = e0 & op(e2, e2) = e0) | (v8 = e0 & op(e1, e2) = e0) | (v2 = e0 &
% 216.29/36.35          op(e0, e2) = e0)) & ((v13 = e3 & op(e2, e3) = e3) | (v12 = e3 & op(e2,
% 216.29/36.35            e2) = e3) | (v10 = e3 & op(e2, e1) = e3) | (v5 = e3 & op(e2, e0) =
% 216.29/36.35          e3)) & ((v13 = e2 & op(e2, e3) = e2) | (v12 = e2 & op(e2, e2) = e2) |
% 216.29/36.35        (v10 = e2 & op(e2, e1) = e2) | (v5 = e2 & op(e2, e0) = e2)) & ((v13 = e1 &
% 216.29/36.35          op(e2, e3) = e1) | (v12 = e1 & op(e2, e2) = e1) | (v10 = e1 & op(e2, e1)
% 216.29/36.35          = e1) | (v5 = e1 & op(e2, e0) = e1)) & ((v13 = e0 & op(e2, e3) = e0) |
% 216.29/36.35        (v12 = e0 & op(e2, e2) = e0) | (v10 = e0 & op(e2, e1) = e0) | (v5 = e0 &
% 216.29/36.35          op(e2, e0) = e0)) & ((v11 = e3 & op(e3, e1) = e3) | (v10 = e3 & op(e2,
% 216.29/36.35            e1) = e3) | (v7 = e3 & op(e1, e1) = e3) | (v1 = e3 & op(e0, e1) = e3))
% 216.29/36.35      & ((v11 = e2 & op(e3, e1) = e2) | (v10 = e2 & op(e2, e1) = e2) | (v7 = e2 &
% 216.29/36.35          op(e1, e1) = e2) | (v1 = e2 & op(e0, e1) = e2)) & ((v11 = e1 & op(e3,
% 216.29/36.35            e1) = e1) | (v10 = e1 & op(e2, e1) = e1) | (v7 = e1 & op(e1, e1) = e1)
% 216.29/36.35        | (v1 = e1 & op(e0, e1) = e1)) & ((v11 = e0 & op(e3, e1) = e0) | (v10 = e0
% 216.29/36.35          & op(e2, e1) = e0) | (v7 = e0 & op(e1, e1) = e0) | (v1 = e0 & op(e0, e1)
% 216.29/36.35          = e0)) & ((v9 = e3 & op(e1, e3) = e3) | (v8 = e3 & op(e1, e2) = e3) |
% 216.29/36.35        (v7 = e3 & op(e1, e1) = e3) | (v4 = e3 & op(e1, e0) = e3)) & ((v9 = e2 &
% 216.29/36.35          op(e1, e3) = e2) | (v8 = e2 & op(e1, e2) = e2) | (v7 = e2 & op(e1, e1) =
% 216.29/36.35          e2) | (v4 = e2 & op(e1, e0) = e2)) & ((v9 = e1 & op(e1, e3) = e1) | (v8
% 216.29/36.35          = e1 & op(e1, e2) = e1) | (v7 = e1 & op(e1, e1) = e1) | (v4 = e1 &
% 216.29/36.35          op(e1, e0) = e1)) & ((v9 = e0 & op(e1, e3) = e0) | (v8 = e0 & op(e1, e2)
% 216.29/36.35          = e0) | (v7 = e0 & op(e1, e1) = e0) | (v4 = e0 & op(e1, e0) = e0)) &
% 216.29/36.35      ((v6 = e3 & op(e3, e0) = e3) | (v5 = e3 & op(e2, e0) = e3) | (v4 = e3 &
% 216.29/36.35          op(e1, e0) = e3) | (v0 = e3 & op(e0, e0) = e3)) & ((v6 = e2 & op(e3, e0)
% 216.29/36.35          = e2) | (v5 = e2 & op(e2, e0) = e2) | (v4 = e2 & op(e1, e0) = e2) | (v0
% 216.29/36.35          = e2 & op(e0, e0) = e2)) & ((v6 = e1 & op(e3, e0) = e1) | (v5 = e1 &
% 216.29/36.35          op(e2, e0) = e1) | (v4 = e1 & op(e1, e0) = e1) | (v0 = e1 & op(e0, e0) =
% 216.29/36.35          e1)) & ((v3 = e3 & op(e0, e3) = e3) | (v2 = e3 & op(e0, e2) = e3) | (v1
% 216.29/36.35          = e3 & op(e0, e1) = e3) | (v0 = e3 & op(e0, e0) = e3)) & ((v3 = e2 &
% 216.29/36.35          op(e0, e3) = e2) | (v2 = e2 & op(e0, e2) = e2) | (v1 = e2 & op(e0, e1) =
% 216.29/36.35          e2) | (v0 = e2 & op(e0, e0) = e2)) & ((v3 = e1 & op(e0, e3) = e1) | (v2
% 216.29/36.35          = e1 & op(e0, e2) = e1) | (v1 = e1 & op(e0, e1) = e1) | (v0 = e1 &
% 216.29/36.35          op(e0, e0) = e1)) & ((v0 = e0 & op(e0, e0) = e0) | (((v6 = e0 & op(e3,
% 216.29/36.35                e0) = e0) | (v5 = e0 & op(e2, e0) = e0) | (v4 = e0 & op(e1, e0) =
% 216.29/36.35              e0)) & ((v3 = e0 & op(e0, e3) = e0) | (v2 = e0 & op(e0, e2) = e0) |
% 216.29/36.35            (v1 = e0 & op(e0, e1) = e0)))))
% 216.29/36.35  
% 216.29/36.35    (ax20)
% 216.29/36.36    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 216.29/36.36    (op(e3, e3) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e0) & op(v1, e3) = v2 &
% 216.29/36.36          op(e3, e1) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e3, e1) = v1 &
% 216.29/36.36          $i(v1))))
% 216.29/36.36  
% 216.29/36.36    (ax21)
% 216.29/36.36    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 216.29/36.36    (op(e0, e0) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e3) & op(v1, e0) = v2 &
% 216.29/36.36          op(e0, e1) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e0, e1) = v1 &
% 216.29/36.36          $i(v1))))
% 216.29/36.36  
% 216.29/36.36    (ax22)
% 216.29/36.36    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 216.29/36.36    (op(e1, e1) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e0) & op(v1, e1) = v2 &
% 216.29/36.36          op(e1, e3) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e1, e3) = v1 &
% 216.29/36.36          $i(v1))))
% 216.29/36.36  
% 216.29/36.36    (ax23)
% 216.29/36.36    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 216.29/36.36    (op(e0, e0) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e1) & op(v1, e0) = v2 &
% 216.29/36.36          op(e0, e3) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e0, e3) = v1 &
% 216.29/36.36          $i(v1))))
% 216.29/36.36  
% 216.29/36.36    (ax24)
% 216.29/36.36    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 216.29/36.36    (op(e2, e2) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e1) & op(v1, e2) = v2 &
% 216.29/36.36          op(e2, e0) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e2, e0) = v1 &
% 216.29/36.36          $i(v1))))
% 216.29/36.36  
% 216.29/36.36    (ax25)
% 216.29/36.36    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 216.29/36.36    (op(e1, e1) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e2) & op(v1, e1) = v2 &
% 216.29/36.36          op(e1, e0) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e1, e0) = v1 &
% 216.29/36.36          $i(v1))))
% 216.29/36.36  
% 216.29/36.36    (ax26)
% 216.29/36.36    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 216.29/36.36    (op(e2, e2) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e0) & op(v1, e2) = v2 &
% 216.29/36.37          op(e2, e1) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e2, e1) = v1 &
% 216.29/36.37          $i(v1))))
% 216.29/36.37  
% 216.29/36.37    (ax27)
% 216.29/36.37    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 216.29/36.37    (op(e0, e0) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e2) & op(v1, e0) = v2 &
% 216.29/36.37          op(e0, e1) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e0, e1) = v1 &
% 216.29/36.37          $i(v1))))
% 216.29/36.37  
% 216.29/36.37    (ax28)
% 216.29/36.37    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 216.29/36.37    (op(e1, e1) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e0) & op(v1, e1) = v2 &
% 216.29/36.37          op(e1, e2) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e1, e2) = v1 &
% 216.29/36.37          $i(v1))))
% 216.29/36.37  
% 216.29/36.37    (ax29)
% 216.29/36.37    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 216.29/36.37    (op(e0, e0) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e1) & op(v1, e0) = v2 &
% 216.29/36.37          op(e0, e2) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e0, e2) = v1 &
% 216.29/36.37          $i(v1))))
% 216.29/36.37  
% 216.29/36.37    (ax3)
% 216.29/36.38    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : 
% 216.29/36.38    ? [v3: $i] :  ? [v4: $i] :  ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i] :  ? [v8:
% 216.29/36.38      $i] :  ? [v9: $i] :  ? [v10: $i] :  ? [v11: $i] :  ? [v12: $i] :  ? [v13:
% 216.29/36.38      $i] :  ? [v14: $i] :  ? [v15: $i] : ( ~ (v15 = v14) &  ~ (v15 = v13) &  ~
% 216.29/36.38      (v15 = v12) &  ~ (v15 = v11) &  ~ (v15 = v7) &  ~ (v15 = v3) &  ~ (v14 =
% 216.29/36.38        v13) &  ~ (v14 = v12) &  ~ (v14 = v10) &  ~ (v14 = v6) &  ~ (v14 = v2) & 
% 216.29/36.38      ~ (v13 = v12) &  ~ (v13 = v9) &  ~ (v13 = v5) &  ~ (v13 = v1) &  ~ (v12 =
% 216.29/36.38        v8) &  ~ (v12 = v4) &  ~ (v12 = v0) &  ~ (v11 = v10) &  ~ (v11 = v9) &  ~
% 216.29/36.38      (v11 = v8) &  ~ (v11 = v7) &  ~ (v11 = v3) &  ~ (v10 = v9) &  ~ (v10 = v8) &
% 216.29/36.38       ~ (v10 = v6) &  ~ (v10 = v2) &  ~ (v9 = v8) &  ~ (v9 = v5) &  ~ (v9 = v1) &
% 216.29/36.38       ~ (v8 = v4) &  ~ (v8 = v0) &  ~ (v7 = v6) &  ~ (v7 = v5) &  ~ (v7 = v4) & 
% 216.29/36.38      ~ (v7 = v3) &  ~ (v6 = v5) &  ~ (v6 = v4) &  ~ (v6 = v2) &  ~ (v5 = v4) &  ~
% 216.29/36.38      (v5 = v1) &  ~ (v4 = v0) &  ~ (v3 = v2) &  ~ (v3 = v1) &  ~ (v3 = v0) &  ~
% 216.29/36.38      (v2 = v1) &  ~ (v2 = v0) &  ~ (v1 = v0) & op(e3, e3) = v15 & op(e3, e2) =
% 216.29/36.38      v11 & op(e3, e1) = v7 & op(e3, e0) = v3 & op(e2, e3) = v14 & op(e2, e2) =
% 216.29/36.38      v10 & op(e2, e1) = v6 & op(e2, e0) = v2 & op(e1, e3) = v13 & op(e1, e2) = v9
% 216.29/36.38      & op(e1, e1) = v5 & op(e1, e0) = v1 & op(e0, e3) = v12 & op(e0, e2) = v8 &
% 216.29/36.38      op(e0, e1) = v4 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) & $i(v12) &
% 216.29/36.38      $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) &
% 216.29/36.38      $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 216.29/36.38  
% 216.29/36.38    (ax4)
% 216.29/36.38     ~ (e3 = e2) &  ~ (e3 = e1) &  ~ (e3 = e0) &  ~ (e2 = e1) &  ~ (e2 = e0) &  ~
% 216.29/36.38    (e1 = e0) & $i(e3) & $i(e2) & $i(e1) & $i(e0)
% 216.29/36.38  
% 216.29/36.38    (ax5)
% 216.29/36.38    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : 
% 216.29/36.38    ? [v3: $i] :  ? [v4: $i] :  ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i] :  ? [v8:
% 216.29/36.38      $i] :  ? [v9: $i] :  ? [v10: $i] :  ? [v11: $i] :  ? [v12: $i] :  ? [v13:
% 216.29/36.38      $i] :  ? [v14: $i] :  ? [v15: $i] :  ? [v16: $i] :  ? [v17: $i] :  ? [v18:
% 216.29/36.38      $i] :  ? [v19: $i] :  ? [v20: $i] :  ? [v21: $i] :  ? [v22: $i] :  ? [v23:
% 216.29/36.38      $i] :  ? [v24: $i] :  ? [v25: $i] :  ? [v26: $i] :  ? [v27: $i] :  ? [v28:
% 216.29/36.38      $i] :  ? [v29: $i] :  ? [v30: $i] :  ? [v31: $i] : ((v31 = e3 & v29 = e2 &
% 216.29/36.38        v27 = e1 & v25 = e0 & op(v30, v30) = e3 & op(v28, v28) = e2 & op(v26, v26)
% 216.29/36.38        = e1 & op(v24, v24) = e0 & op(e3, e3) = v30 & op(e3, e2) = v28 & op(e3,
% 216.29/36.38          e1) = v26 & op(e3, e0) = v24 & $i(v30) & $i(v28) & $i(v26) & $i(v24)) |
% 216.29/36.38      (v23 = e3 & v21 = e2 & v19 = e1 & v17 = e0 & op(v22, v22) = e3 & op(v20,
% 216.29/36.38          v20) = e2 & op(v18, v18) = e1 & op(v16, v16) = e0 & op(e2, e3) = v22 &
% 216.29/36.38        op(e2, e2) = v20 & op(e2, e1) = v18 & op(e2, e0) = v16 & $i(v22) & $i(v20)
% 216.29/36.38        & $i(v18) & $i(v16)) | (v15 = e3 & v13 = e2 & v11 = e1 & v9 = e0 & op(v14,
% 216.29/36.38          v14) = e3 & op(v12, v12) = e2 & op(v10, v10) = e1 & op(v8, v8) = e0 &
% 216.29/36.38        op(e1, e3) = v14 & op(e1, e2) = v12 & op(e1, e1) = v10 & op(e1, e0) = v8 &
% 216.29/36.38        $i(v14) & $i(v12) & $i(v10) & $i(v8)) | (v7 = e3 & v5 = e2 & v3 = e1 & v1
% 216.29/36.38        = e0 & op(v6, v6) = e3 & op(v4, v4) = e2 & op(v2, v2) = e1 & op(v0, v0) =
% 216.29/36.38        e0 & op(e0, e3) = v6 & op(e0, e2) = v4 & op(e0, e1) = v2 & op(e0, e0) = v0
% 216.29/36.38        & $i(v6) & $i(v4) & $i(v2) & $i(v0)))
% 216.29/36.38  
% 216.29/36.38    (ax6)
% 216.29/36.38    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 216.29/36.38    (op(e3, e3) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e2) & op(v1, e3) = v2 &
% 216.29/36.38          op(e3, e1) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e3, e1) = v1 &
% 216.29/36.38          $i(v1))))
% 216.29/36.38  
% 216.29/36.38    (ax7)
% 216.29/36.39    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 216.29/36.39    (op(e2, e2) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e3) & op(v1, e2) = v2 &
% 216.29/36.39          op(e2, e1) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e2, e1) = v1 &
% 216.29/36.39          $i(v1))))
% 216.29/36.39  
% 216.29/36.39    (ax8)
% 216.29/36.39    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 216.29/36.39    (op(e3, e3) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e1) & op(v1, e3) = v2 &
% 216.29/36.39          op(e3, e2) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e3, e2) = v1 &
% 216.29/36.39          $i(v1))))
% 216.29/36.39  
% 216.29/36.39    (ax9)
% 216.29/36.39    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 216.29/36.39    (op(e1, e1) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e3) & op(v1, e1) = v2 &
% 216.29/36.39          op(e1, e2) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e1, e2) = v1 &
% 216.29/36.39          $i(v1))))
% 216.29/36.39  
% 216.29/36.39    (function-axioms)
% 216.29/36.39     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (op(v3,
% 216.29/36.39          v2) = v1) |  ~ (op(v3, v2) = v0))
% 216.29/36.39  
% 216.29/36.39  Those formulas are unsatisfiable:
% 216.29/36.39  ---------------------------------
% 216.29/36.39  
% 216.29/36.39  Begin of proof
% 216.29/36.39  | 
% 216.29/36.39  | ALPHA: (ax1) implies:
% 216.74/36.40  |   (1)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: $i] : 
% 216.74/36.40  |        ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i] :  ? [v8: $i] :  ? [v9: $i] :  ?
% 216.74/36.40  |        [v10: $i] :  ? [v11: $i] :  ? [v12: $i] :  ? [v13: $i] :  ? [v14: $i] :
% 216.74/36.40  |         ? [v15: $i] : (op(e3, e3) = v15 & op(e3, e2) = v14 & op(e3, e1) = v13
% 216.74/36.40  |          & op(e3, e0) = v12 & op(e2, e3) = v11 & op(e2, e2) = v10 & op(e2, e1)
% 216.74/36.40  |          = v9 & op(e2, e0) = v8 & op(e1, e3) = v7 & op(e1, e2) = v6 & op(e1,
% 216.74/36.40  |            e1) = v5 & op(e1, e0) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 &
% 216.74/36.40  |          op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) &
% 216.74/36.40  |          $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) &
% 216.74/36.40  |          $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v15 = e3 | v15
% 216.74/36.40  |            = e2 | v15 = e1 | v15 = e0) & (v14 = e3 | v14 = e2 | v14 = e1 | v14
% 216.74/36.40  |            = e0) & (v13 = e3 | v13 = e2 | v13 = e1 | v13 = e0) & (v12 = e3 |
% 216.74/36.40  |            v12 = e2 | v12 = e1 | v12 = e0) & (v11 = e3 | v11 = e2 | v11 = e1 |
% 216.74/36.40  |            v11 = e0) & (v10 = e3 | v10 = e2 | v10 = e1 | v10 = e0) & (v9 = e3
% 216.74/36.40  |            | v9 = e2 | v9 = e1 | v9 = e0) & (v8 = e3 | v8 = e2 | v8 = e1 | v8
% 216.74/36.40  |            = e0) & (v7 = e3 | v7 = e2 | v7 = e1 | v7 = e0) & (v6 = e3 | v6 =
% 216.74/36.40  |            e2 | v6 = e1 | v6 = e0) & (v5 = e3 | v5 = e2 | v5 = e1 | v5 = e0) &
% 216.74/36.40  |          (v4 = e3 | v4 = e2 | v4 = e1 | v4 = e0) & (v3 = e3 | v3 = e2 | v3 =
% 216.74/36.40  |            e1 | v3 = e0) & (v2 = e3 | v2 = e2 | v2 = e1 | v2 = e0) & (v1 = e3
% 216.74/36.40  |            | v1 = e2 | v1 = e1 | v1 = e0) & (v0 = e3 | v0 = e2 | v0 = e1 | v0
% 216.74/36.40  |            = e0))
% 216.74/36.40  | 
% 216.74/36.40  | ALPHA: (ax2) implies:
% 216.74/36.42  |   (2)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: $i] : 
% 216.74/36.42  |        ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i] :  ? [v8: $i] :  ? [v9: $i] :  ?
% 216.74/36.42  |        [v10: $i] :  ? [v11: $i] :  ? [v12: $i] :  ? [v13: $i] :  ? [v14: $i] :
% 216.74/36.42  |         ? [v15: $i] : (((v15 = e3 & op(e3, e3) = e3) | (v14 = e3 & op(e3, e2)
% 216.74/36.42  |              = e3) | (v11 = e3 & op(e3, e1) = e3) | (v6 = e3 & op(e3, e0) =
% 216.74/36.42  |              e3)) & ((v15 = e3 & op(e3, e3) = e3) | (v13 = e3 & op(e2, e3) =
% 216.74/36.42  |              e3) | (v9 = e3 & op(e1, e3) = e3) | (v3 = e3 & op(e0, e3) = e3))
% 216.74/36.42  |          & ((v15 = e2 & op(e3, e3) = e2) | (v14 = e2 & op(e3, e2) = e2) | (v11
% 216.74/36.42  |              = e2 & op(e3, e1) = e2) | (v6 = e2 & op(e3, e0) = e2)) & ((v15 =
% 216.74/36.42  |              e2 & op(e3, e3) = e2) | (v13 = e2 & op(e2, e3) = e2) | (v9 = e2 &
% 216.74/36.42  |              op(e1, e3) = e2) | (v3 = e2 & op(e0, e3) = e2)) & ((v15 = e1 &
% 216.74/36.42  |              op(e3, e3) = e1) | (v14 = e1 & op(e3, e2) = e1) | (v11 = e1 &
% 216.74/36.42  |              op(e3, e1) = e1) | (v6 = e1 & op(e3, e0) = e1)) & ((v15 = e1 &
% 216.74/36.42  |              op(e3, e3) = e1) | (v13 = e1 & op(e2, e3) = e1) | (v9 = e1 &
% 216.74/36.42  |              op(e1, e3) = e1) | (v3 = e1 & op(e0, e3) = e1)) & ((v15 = e0 &
% 216.74/36.42  |              op(e3, e3) = e0) | (v14 = e0 & op(e3, e2) = e0) | (v11 = e0 &
% 216.74/36.42  |              op(e3, e1) = e0) | (v6 = e0 & op(e3, e0) = e0)) & ((v15 = e0 &
% 216.74/36.42  |              op(e3, e3) = e0) | (v13 = e0 & op(e2, e3) = e0) | (v9 = e0 &
% 216.74/36.42  |              op(e1, e3) = e0) | (v3 = e0 & op(e0, e3) = e0)) & ((v14 = e3 &
% 216.74/36.42  |              op(e3, e2) = e3) | (v12 = e3 & op(e2, e2) = e3) | (v8 = e3 &
% 216.74/36.42  |              op(e1, e2) = e3) | (v2 = e3 & op(e0, e2) = e3)) & ((v14 = e2 &
% 216.74/36.42  |              op(e3, e2) = e2) | (v12 = e2 & op(e2, e2) = e2) | (v8 = e2 &
% 216.74/36.42  |              op(e1, e2) = e2) | (v2 = e2 & op(e0, e2) = e2)) & ((v14 = e1 &
% 216.74/36.42  |              op(e3, e2) = e1) | (v12 = e1 & op(e2, e2) = e1) | (v8 = e1 &
% 216.74/36.42  |              op(e1, e2) = e1) | (v2 = e1 & op(e0, e2) = e1)) & ((v14 = e0 &
% 216.74/36.42  |              op(e3, e2) = e0) | (v12 = e0 & op(e2, e2) = e0) | (v8 = e0 &
% 216.74/36.42  |              op(e1, e2) = e0) | (v2 = e0 & op(e0, e2) = e0)) & ((v13 = e3 &
% 216.74/36.42  |              op(e2, e3) = e3) | (v12 = e3 & op(e2, e2) = e3) | (v10 = e3 &
% 216.74/36.42  |              op(e2, e1) = e3) | (v5 = e3 & op(e2, e0) = e3)) & ((v13 = e2 &
% 216.74/36.42  |              op(e2, e3) = e2) | (v12 = e2 & op(e2, e2) = e2) | (v10 = e2 &
% 216.74/36.42  |              op(e2, e1) = e2) | (v5 = e2 & op(e2, e0) = e2)) & ((v13 = e1 &
% 216.74/36.42  |              op(e2, e3) = e1) | (v12 = e1 & op(e2, e2) = e1) | (v10 = e1 &
% 216.74/36.42  |              op(e2, e1) = e1) | (v5 = e1 & op(e2, e0) = e1)) & ((v13 = e0 &
% 216.74/36.42  |              op(e2, e3) = e0) | (v12 = e0 & op(e2, e2) = e0) | (v10 = e0 &
% 216.74/36.42  |              op(e2, e1) = e0) | (v5 = e0 & op(e2, e0) = e0)) & ((v11 = e3 &
% 216.74/36.42  |              op(e3, e1) = e3) | (v10 = e3 & op(e2, e1) = e3) | (v7 = e3 &
% 216.74/36.42  |              op(e1, e1) = e3) | (v1 = e3 & op(e0, e1) = e3)) & ((v11 = e2 &
% 216.74/36.42  |              op(e3, e1) = e2) | (v10 = e2 & op(e2, e1) = e2) | (v7 = e2 &
% 216.74/36.42  |              op(e1, e1) = e2) | (v1 = e2 & op(e0, e1) = e2)) & ((v11 = e1 &
% 216.74/36.42  |              op(e3, e1) = e1) | (v10 = e1 & op(e2, e1) = e1) | (v7 = e1 &
% 216.74/36.42  |              op(e1, e1) = e1) | (v1 = e1 & op(e0, e1) = e1)) & ((v11 = e0 &
% 216.74/36.42  |              op(e3, e1) = e0) | (v10 = e0 & op(e2, e1) = e0) | (v7 = e0 &
% 216.74/36.42  |              op(e1, e1) = e0) | (v1 = e0 & op(e0, e1) = e0)) & ((v9 = e3 &
% 216.74/36.42  |              op(e1, e3) = e3) | (v8 = e3 & op(e1, e2) = e3) | (v7 = e3 &
% 216.74/36.42  |              op(e1, e1) = e3) | (v4 = e3 & op(e1, e0) = e3)) & ((v9 = e2 &
% 216.74/36.42  |              op(e1, e3) = e2) | (v8 = e2 & op(e1, e2) = e2) | (v7 = e2 &
% 216.74/36.42  |              op(e1, e1) = e2) | (v4 = e2 & op(e1, e0) = e2)) & ((v9 = e1 &
% 216.74/36.42  |              op(e1, e3) = e1) | (v8 = e1 & op(e1, e2) = e1) | (v7 = e1 &
% 216.74/36.42  |              op(e1, e1) = e1) | (v4 = e1 & op(e1, e0) = e1)) & ((v9 = e0 &
% 216.74/36.42  |              op(e1, e3) = e0) | (v8 = e0 & op(e1, e2) = e0) | (v7 = e0 &
% 216.74/36.42  |              op(e1, e1) = e0) | (v4 = e0 & op(e1, e0) = e0)) & ((v6 = e3 &
% 216.74/36.42  |              op(e3, e0) = e3) | (v5 = e3 & op(e2, e0) = e3) | (v4 = e3 &
% 216.74/36.42  |              op(e1, e0) = e3) | (v0 = e3 & op(e0, e0) = e3)) & ((v6 = e2 &
% 216.74/36.42  |              op(e3, e0) = e2) | (v5 = e2 & op(e2, e0) = e2) | (v4 = e2 &
% 216.74/36.42  |              op(e1, e0) = e2) | (v0 = e2 & op(e0, e0) = e2)) & ((v6 = e1 &
% 216.74/36.42  |              op(e3, e0) = e1) | (v5 = e1 & op(e2, e0) = e1) | (v4 = e1 &
% 216.74/36.42  |              op(e1, e0) = e1) | (v0 = e1 & op(e0, e0) = e1)) & ((v3 = e3 &
% 216.74/36.42  |              op(e0, e3) = e3) | (v2 = e3 & op(e0, e2) = e3) | (v1 = e3 &
% 216.74/36.42  |              op(e0, e1) = e3) | (v0 = e3 & op(e0, e0) = e3)) & ((v3 = e2 &
% 216.74/36.42  |              op(e0, e3) = e2) | (v2 = e2 & op(e0, e2) = e2) | (v1 = e2 &
% 216.74/36.42  |              op(e0, e1) = e2) | (v0 = e2 & op(e0, e0) = e2)) & ((v3 = e1 &
% 216.74/36.42  |              op(e0, e3) = e1) | (v2 = e1 & op(e0, e2) = e1) | (v1 = e1 &
% 216.74/36.42  |              op(e0, e1) = e1) | (v0 = e1 & op(e0, e0) = e1)) & ((v0 = e0 &
% 216.74/36.42  |              op(e0, e0) = e0) | (((v6 = e0 & op(e3, e0) = e0) | (v5 = e0 &
% 216.74/36.42  |                  op(e2, e0) = e0) | (v4 = e0 & op(e1, e0) = e0)) & ((v3 = e0 &
% 216.74/36.42  |                  op(e0, e3) = e0) | (v2 = e0 & op(e0, e2) = e0) | (v1 = e0 &
% 216.74/36.42  |                  op(e0, e1) = e0)))))
% 216.74/36.42  | 
% 216.74/36.42  | ALPHA: (ax3) implies:
% 216.74/36.43  |   (3)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: $i] : 
% 216.74/36.43  |        ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i] :  ? [v8: $i] :  ? [v9: $i] :  ?
% 216.74/36.43  |        [v10: $i] :  ? [v11: $i] :  ? [v12: $i] :  ? [v13: $i] :  ? [v14: $i] :
% 216.74/36.43  |         ? [v15: $i] : ( ~ (v15 = v14) &  ~ (v15 = v13) &  ~ (v15 = v12) &  ~
% 216.74/36.43  |          (v15 = v11) &  ~ (v15 = v7) &  ~ (v15 = v3) &  ~ (v14 = v13) &  ~
% 216.74/36.43  |          (v14 = v12) &  ~ (v14 = v10) &  ~ (v14 = v6) &  ~ (v14 = v2) &  ~
% 216.74/36.43  |          (v13 = v12) &  ~ (v13 = v9) &  ~ (v13 = v5) &  ~ (v13 = v1) &  ~ (v12
% 216.74/36.43  |            = v8) &  ~ (v12 = v4) &  ~ (v12 = v0) &  ~ (v11 = v10) &  ~ (v11 =
% 216.74/36.43  |            v9) &  ~ (v11 = v8) &  ~ (v11 = v7) &  ~ (v11 = v3) &  ~ (v10 = v9)
% 216.74/36.43  |          &  ~ (v10 = v8) &  ~ (v10 = v6) &  ~ (v10 = v2) &  ~ (v9 = v8) &  ~
% 216.74/36.43  |          (v9 = v5) &  ~ (v9 = v1) &  ~ (v8 = v4) &  ~ (v8 = v0) &  ~ (v7 = v6)
% 216.74/36.43  |          &  ~ (v7 = v5) &  ~ (v7 = v4) &  ~ (v7 = v3) &  ~ (v6 = v5) &  ~ (v6
% 216.74/36.43  |            = v4) &  ~ (v6 = v2) &  ~ (v5 = v4) &  ~ (v5 = v1) &  ~ (v4 = v0) &
% 216.74/36.43  |           ~ (v3 = v2) &  ~ (v3 = v1) &  ~ (v3 = v0) &  ~ (v2 = v1) &  ~ (v2 =
% 216.74/36.43  |            v0) &  ~ (v1 = v0) & op(e3, e3) = v15 & op(e3, e2) = v11 & op(e3,
% 216.74/36.43  |            e1) = v7 & op(e3, e0) = v3 & op(e2, e3) = v14 & op(e2, e2) = v10 &
% 216.74/36.43  |          op(e2, e1) = v6 & op(e2, e0) = v2 & op(e1, e3) = v13 & op(e1, e2) =
% 216.74/36.43  |          v9 & op(e1, e1) = v5 & op(e1, e0) = v1 & op(e0, e3) = v12 & op(e0,
% 216.74/36.43  |            e2) = v8 & op(e0, e1) = v4 & op(e0, e0) = v0 & $i(v15) & $i(v14) &
% 216.74/36.43  |          $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) &
% 216.74/36.43  |          $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 216.74/36.43  | 
% 216.74/36.43  | ALPHA: (ax4) implies:
% 216.74/36.43  |   (4)   ~ (e1 = e0)
% 216.74/36.43  |   (5)   ~ (e2 = e0)
% 216.74/36.43  |   (6)   ~ (e2 = e1)
% 216.74/36.43  |   (7)   ~ (e3 = e0)
% 216.74/36.43  |   (8)   ~ (e3 = e1)
% 216.74/36.43  |   (9)   ~ (e3 = e2)
% 216.74/36.43  | 
% 216.74/36.43  | ALPHA: (ax5) implies:
% 216.74/36.44  |   (10)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: $i] : 
% 216.74/36.44  |         ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i] :  ? [v8: $i] :  ? [v9: $i] : 
% 216.74/36.44  |         ? [v10: $i] :  ? [v11: $i] :  ? [v12: $i] :  ? [v13: $i] :  ? [v14:
% 216.74/36.44  |           $i] :  ? [v15: $i] :  ? [v16: $i] :  ? [v17: $i] :  ? [v18: $i] :  ?
% 216.74/36.44  |         [v19: $i] :  ? [v20: $i] :  ? [v21: $i] :  ? [v22: $i] :  ? [v23: $i]
% 216.74/36.44  |         :  ? [v24: $i] :  ? [v25: $i] :  ? [v26: $i] :  ? [v27: $i] :  ? [v28:
% 216.74/36.44  |           $i] :  ? [v29: $i] :  ? [v30: $i] :  ? [v31: $i] : ((v31 = e3 & v29
% 216.74/36.44  |             = e2 & v27 = e1 & v25 = e0 & op(v30, v30) = e3 & op(v28, v28) = e2
% 216.74/36.44  |             & op(v26, v26) = e1 & op(v24, v24) = e0 & op(e3, e3) = v30 &
% 216.74/36.44  |             op(e3, e2) = v28 & op(e3, e1) = v26 & op(e3, e0) = v24 & $i(v30) &
% 216.74/36.44  |             $i(v28) & $i(v26) & $i(v24)) | (v23 = e3 & v21 = e2 & v19 = e1 &
% 216.74/36.44  |             v17 = e0 & op(v22, v22) = e3 & op(v20, v20) = e2 & op(v18, v18) =
% 216.74/36.44  |             e1 & op(v16, v16) = e0 & op(e2, e3) = v22 & op(e2, e2) = v20 &
% 216.74/36.44  |             op(e2, e1) = v18 & op(e2, e0) = v16 & $i(v22) & $i(v20) & $i(v18)
% 216.74/36.44  |             & $i(v16)) | (v15 = e3 & v13 = e2 & v11 = e1 & v9 = e0 & op(v14,
% 216.74/36.44  |               v14) = e3 & op(v12, v12) = e2 & op(v10, v10) = e1 & op(v8, v8) =
% 216.74/36.44  |             e0 & op(e1, e3) = v14 & op(e1, e2) = v12 & op(e1, e1) = v10 &
% 216.74/36.44  |             op(e1, e0) = v8 & $i(v14) & $i(v12) & $i(v10) & $i(v8)) | (v7 = e3
% 216.74/36.44  |             & v5 = e2 & v3 = e1 & v1 = e0 & op(v6, v6) = e3 & op(v4, v4) = e2
% 216.74/36.44  |             & op(v2, v2) = e1 & op(v0, v0) = e0 & op(e0, e3) = v6 & op(e0, e2)
% 216.74/36.44  |             = v4 & op(e0, e1) = v2 & op(e0, e0) = v0 & $i(v6) & $i(v4) &
% 216.74/36.44  |             $i(v2) & $i(v0)))
% 216.74/36.44  | 
% 216.74/36.44  | ALPHA: (ax6) implies:
% 216.74/36.44  |   (11)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e3, e3) = v0 & $i(v0) &
% 216.74/36.44  |           ( ~ (v0 = e1) | ( ~ (v2 = e2) & op(v1, e3) = v2 & op(e3, e1) = v1 &
% 216.74/36.44  |               $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e3, e1) = v1 & $i(v1))))
% 216.74/36.44  | 
% 216.74/36.44  | ALPHA: (ax7) implies:
% 216.74/36.44  |   (12)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e2, e2) = v0 & $i(v0) &
% 216.74/36.44  |           ( ~ (v0 = e1) | ( ~ (v2 = e3) & op(v1, e2) = v2 & op(e2, e1) = v1 &
% 216.74/36.44  |               $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e2, e1) = v1 & $i(v1))))
% 216.74/36.44  | 
% 216.74/36.44  | ALPHA: (ax8) implies:
% 216.74/36.44  |   (13)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e3, e3) = v0 & $i(v0) &
% 216.74/36.44  |           ( ~ (v0 = e2) | ( ~ (v2 = e1) & op(v1, e3) = v2 & op(e3, e2) = v1 &
% 216.74/36.44  |               $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e3, e2) = v1 & $i(v1))))
% 216.74/36.44  | 
% 216.74/36.44  | ALPHA: (ax9) implies:
% 216.74/36.45  |   (14)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e1, e1) = v0 & $i(v0) &
% 216.74/36.45  |           ( ~ (v0 = e2) | ( ~ (v2 = e3) & op(v1, e1) = v2 & op(e1, e2) = v1 &
% 216.74/36.45  |               $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e1, e2) = v1 & $i(v1))))
% 216.74/36.45  | 
% 216.74/36.45  | ALPHA: (ax10) implies:
% 216.74/36.45  |   (15)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e2, e2) = v0 & $i(v0) &
% 216.74/36.45  |           ( ~ (v0 = e3) | ( ~ (v2 = e1) & op(v1, e2) = v2 & op(e2, e3) = v1 &
% 216.74/36.45  |               $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e2, e3) = v1 & $i(v1))))
% 216.74/36.45  | 
% 216.74/36.45  | ALPHA: (ax11) implies:
% 216.74/36.45  |   (16)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e1, e1) = v0 & $i(v0) &
% 216.74/36.45  |           ( ~ (v0 = e3) | ( ~ (v2 = e2) & op(v1, e1) = v2 & op(e1, e3) = v1 &
% 216.74/36.45  |               $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e1, e3) = v1 & $i(v1))))
% 216.74/36.45  | 
% 216.74/36.45  | ALPHA: (ax12) implies:
% 216.74/36.45  |   (17)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e3, e3) = v0 & $i(v0) &
% 216.74/36.45  |           ( ~ (v0 = e0) | ( ~ (v2 = e2) & op(v1, e3) = v2 & op(e3, e0) = v1 &
% 216.74/36.45  |               $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e3, e0) = v1 & $i(v1))))
% 216.74/36.45  | 
% 216.74/36.45  | ALPHA: (ax13) implies:
% 216.74/36.45  |   (18)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e2, e2) = v0 & $i(v0) &
% 216.74/36.45  |           ( ~ (v0 = e0) | ( ~ (v2 = e3) & op(v1, e2) = v2 & op(e2, e0) = v1 &
% 216.74/36.45  |               $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e2, e0) = v1 & $i(v1))))
% 216.74/36.45  | 
% 216.74/36.45  | ALPHA: (ax14) implies:
% 216.74/36.45  |   (19)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e3, e3) = v0 & $i(v0) &
% 216.74/36.45  |           ( ~ (v0 = e2) | ( ~ (v2 = e0) & op(v1, e3) = v2 & op(e3, e2) = v1 &
% 216.74/36.45  |               $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e3, e2) = v1 & $i(v1))))
% 216.74/36.45  | 
% 216.74/36.45  | ALPHA: (ax15) implies:
% 216.74/36.45  |   (20)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e0, e0) = v0 & $i(v0) &
% 216.74/36.45  |           ( ~ (v0 = e2) | ( ~ (v2 = e3) & op(v1, e0) = v2 & op(e0, e2) = v1 &
% 216.74/36.45  |               $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e0, e2) = v1 & $i(v1))))
% 216.74/36.45  | 
% 216.74/36.45  | ALPHA: (ax16) implies:
% 216.74/36.45  |   (21)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e2, e2) = v0 & $i(v0) &
% 216.74/36.45  |           ( ~ (v0 = e3) | ( ~ (v2 = e0) & op(v1, e2) = v2 & op(e2, e3) = v1 &
% 216.74/36.45  |               $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e2, e3) = v1 & $i(v1))))
% 216.74/36.45  | 
% 216.74/36.45  | ALPHA: (ax17) implies:
% 216.74/36.45  |   (22)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e0, e0) = v0 & $i(v0) &
% 216.74/36.45  |           ( ~ (v0 = e3) | ( ~ (v2 = e2) & op(v1, e0) = v2 & op(e0, e3) = v1 &
% 216.74/36.45  |               $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e0, e3) = v1 & $i(v1))))
% 216.74/36.45  | 
% 216.74/36.45  | ALPHA: (ax18) implies:
% 216.74/36.46  |   (23)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e3, e3) = v0 & $i(v0) &
% 216.74/36.46  |           ( ~ (v0 = e0) | ( ~ (v2 = e1) & op(v1, e3) = v2 & op(e3, e0) = v1 &
% 216.74/36.46  |               $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e3, e0) = v1 & $i(v1))))
% 216.74/36.46  | 
% 216.74/36.46  | ALPHA: (ax19) implies:
% 216.74/36.46  |   (24)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e1, e1) = v0 & $i(v0) &
% 216.74/36.46  |           ( ~ (v0 = e0) | ( ~ (v2 = e3) & op(v1, e1) = v2 & op(e1, e0) = v1 &
% 216.74/36.46  |               $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e1, e0) = v1 & $i(v1))))
% 216.74/36.46  | 
% 216.74/36.46  | ALPHA: (ax20) implies:
% 216.74/36.46  |   (25)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e3, e3) = v0 & $i(v0) &
% 216.74/36.46  |           ( ~ (v0 = e1) | ( ~ (v2 = e0) & op(v1, e3) = v2 & op(e3, e1) = v1 &
% 216.74/36.46  |               $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e3, e1) = v1 & $i(v1))))
% 216.74/36.46  | 
% 216.74/36.46  | ALPHA: (ax21) implies:
% 216.74/36.46  |   (26)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e0, e0) = v0 & $i(v0) &
% 216.74/36.46  |           ( ~ (v0 = e1) | ( ~ (v2 = e3) & op(v1, e0) = v2 & op(e0, e1) = v1 &
% 216.74/36.46  |               $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e0, e1) = v1 & $i(v1))))
% 216.74/36.46  | 
% 216.74/36.46  | ALPHA: (ax22) implies:
% 216.74/36.46  |   (27)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e1, e1) = v0 & $i(v0) &
% 216.74/36.46  |           ( ~ (v0 = e3) | ( ~ (v2 = e0) & op(v1, e1) = v2 & op(e1, e3) = v1 &
% 216.74/36.46  |               $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e1, e3) = v1 & $i(v1))))
% 216.74/36.46  | 
% 216.74/36.46  | ALPHA: (ax23) implies:
% 216.74/36.46  |   (28)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e0, e0) = v0 & $i(v0) &
% 216.74/36.46  |           ( ~ (v0 = e3) | ( ~ (v2 = e1) & op(v1, e0) = v2 & op(e0, e3) = v1 &
% 216.74/36.46  |               $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e0, e3) = v1 & $i(v1))))
% 216.74/36.46  | 
% 216.74/36.46  | ALPHA: (ax24) implies:
% 216.74/36.46  |   (29)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e2, e2) = v0 & $i(v0) &
% 216.74/36.46  |           ( ~ (v0 = e0) | ( ~ (v2 = e1) & op(v1, e2) = v2 & op(e2, e0) = v1 &
% 216.74/36.46  |               $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e2, e0) = v1 & $i(v1))))
% 216.74/36.46  | 
% 216.74/36.46  | ALPHA: (ax25) implies:
% 216.74/36.46  |   (30)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e1, e1) = v0 & $i(v0) &
% 216.74/36.46  |           ( ~ (v0 = e0) | ( ~ (v2 = e2) & op(v1, e1) = v2 & op(e1, e0) = v1 &
% 216.74/36.46  |               $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e1, e0) = v1 & $i(v1))))
% 216.74/36.46  | 
% 216.74/36.46  | ALPHA: (ax26) implies:
% 216.74/36.46  |   (31)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e2, e2) = v0 & $i(v0) &
% 216.74/36.46  |           ( ~ (v0 = e1) | ( ~ (v2 = e0) & op(v1, e2) = v2 & op(e2, e1) = v1 &
% 216.74/36.46  |               $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e2, e1) = v1 & $i(v1))))
% 216.74/36.46  | 
% 216.74/36.46  | ALPHA: (ax27) implies:
% 216.74/36.46  |   (32)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e0, e0) = v0 & $i(v0) &
% 216.74/36.46  |           ( ~ (v0 = e1) | ( ~ (v2 = e2) & op(v1, e0) = v2 & op(e0, e1) = v1 &
% 216.74/36.46  |               $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e0, e1) = v1 & $i(v1))))
% 216.74/36.46  | 
% 216.74/36.46  | ALPHA: (ax28) implies:
% 216.74/36.47  |   (33)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e1, e1) = v0 & $i(v0) &
% 216.74/36.47  |           ( ~ (v0 = e2) | ( ~ (v2 = e0) & op(v1, e1) = v2 & op(e1, e2) = v1 &
% 216.74/36.47  |               $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e1, e2) = v1 & $i(v1))))
% 216.74/36.47  | 
% 216.74/36.47  | ALPHA: (ax29) implies:
% 216.74/36.47  |   (34)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e0, e0) = v0 & $i(v0) &
% 216.74/36.47  |           ( ~ (v0 = e2) | ( ~ (v2 = e1) & op(v1, e0) = v2 & op(e0, e2) = v1 &
% 216.74/36.47  |               $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e0, e2) = v1 & $i(v1))))
% 216.74/36.47  | 
% 216.74/36.47  | DELTA: instantiating (20) with fresh symbols all_4_0, all_4_1, all_4_2 gives:
% 216.74/36.47  |   (35)  op(e0, e0) = all_4_2 & $i(all_4_2) & ( ~ (all_4_2 = e2) | ( ~ (all_4_0
% 216.74/36.47  |               = e3) & op(all_4_1, e0) = all_4_0 & op(e0, e2) = all_4_1 &
% 216.74/36.47  |             $i(all_4_0) & $i(all_4_1)) | ( ~ (all_4_1 = e1) & op(e0, e2) =
% 216.74/36.47  |             all_4_1 & $i(all_4_1)))
% 216.74/36.47  | 
% 216.74/36.47  | ALPHA: (35) implies:
% 216.74/36.47  |   (36)  op(e0, e0) = all_4_2
% 216.74/36.47  |   (37)   ~ (all_4_2 = e2) | ( ~ (all_4_0 = e3) & op(all_4_1, e0) = all_4_0 &
% 216.74/36.47  |           op(e0, e2) = all_4_1 & $i(all_4_0) & $i(all_4_1)) | ( ~ (all_4_1 =
% 216.74/36.47  |             e1) & op(e0, e2) = all_4_1 & $i(all_4_1))
% 216.74/36.47  | 
% 216.74/36.47  | DELTA: instantiating (27) with fresh symbols all_6_0, all_6_1, all_6_2 gives:
% 216.74/36.47  |   (38)  op(e1, e1) = all_6_2 & $i(all_6_2) & ( ~ (all_6_2 = e3) | ( ~ (all_6_0
% 216.74/36.47  |               = e0) & op(all_6_1, e1) = all_6_0 & op(e1, e3) = all_6_1 &
% 216.74/36.47  |             $i(all_6_0) & $i(all_6_1)) | ( ~ (all_6_1 = e2) & op(e1, e3) =
% 216.74/36.47  |             all_6_1 & $i(all_6_1)))
% 216.74/36.47  | 
% 216.74/36.47  | ALPHA: (38) implies:
% 216.74/36.47  |   (39)  op(e1, e1) = all_6_2
% 216.74/36.47  |   (40)   ~ (all_6_2 = e3) | ( ~ (all_6_0 = e0) & op(all_6_1, e1) = all_6_0 &
% 216.74/36.47  |           op(e1, e3) = all_6_1 & $i(all_6_0) & $i(all_6_1)) | ( ~ (all_6_1 =
% 216.74/36.47  |             e2) & op(e1, e3) = all_6_1 & $i(all_6_1))
% 216.74/36.47  | 
% 216.74/36.47  | DELTA: instantiating (21) with fresh symbols all_8_0, all_8_1, all_8_2 gives:
% 216.74/36.47  |   (41)  op(e2, e2) = all_8_2 & $i(all_8_2) & ( ~ (all_8_2 = e3) | ( ~ (all_8_0
% 216.74/36.47  |               = e0) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 216.74/36.47  |             $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e1) & op(e2, e3) =
% 216.74/36.47  |             all_8_1 & $i(all_8_1)))
% 216.74/36.47  | 
% 216.74/36.47  | ALPHA: (41) implies:
% 216.74/36.47  |   (42)  op(e2, e2) = all_8_2
% 216.74/36.47  |   (43)   ~ (all_8_2 = e3) | ( ~ (all_8_0 = e0) & op(all_8_1, e2) = all_8_0 &
% 216.74/36.47  |           op(e2, e3) = all_8_1 & $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 =
% 216.74/36.47  |             e1) & op(e2, e3) = all_8_1 & $i(all_8_1))
% 216.74/36.47  | 
% 216.74/36.47  | DELTA: instantiating (11) with fresh symbols all_10_0, all_10_1, all_10_2
% 216.74/36.47  |        gives:
% 216.74/36.47  |   (44)  op(e3, e3) = all_10_2 & $i(all_10_2) & ( ~ (all_10_2 = e1) | ( ~
% 216.74/36.47  |             (all_10_0 = e2) & op(all_10_1, e3) = all_10_0 & op(e3, e1) =
% 216.74/36.47  |             all_10_1 & $i(all_10_0) & $i(all_10_1)) | ( ~ (all_10_1 = e0) &
% 216.74/36.47  |             op(e3, e1) = all_10_1 & $i(all_10_1)))
% 216.74/36.47  | 
% 216.74/36.47  | ALPHA: (44) implies:
% 216.74/36.47  |   (45)  op(e3, e3) = all_10_2
% 216.74/36.47  |   (46)   ~ (all_10_2 = e1) | ( ~ (all_10_0 = e2) & op(all_10_1, e3) = all_10_0
% 216.74/36.47  |           & op(e3, e1) = all_10_1 & $i(all_10_0) & $i(all_10_1)) | ( ~
% 216.74/36.47  |           (all_10_1 = e0) & op(e3, e1) = all_10_1 & $i(all_10_1))
% 216.74/36.47  | 
% 216.74/36.47  | DELTA: instantiating (22) with fresh symbols all_12_0, all_12_1, all_12_2
% 216.74/36.47  |        gives:
% 216.74/36.47  |   (47)  op(e0, e0) = all_12_2 & $i(all_12_2) & ( ~ (all_12_2 = e3) | ( ~
% 216.74/36.47  |             (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 216.74/36.47  |             all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) &
% 216.74/36.47  |             op(e0, e3) = all_12_1 & $i(all_12_1)))
% 216.74/36.47  | 
% 216.74/36.47  | ALPHA: (47) implies:
% 216.74/36.48  |   (48)  op(e0, e0) = all_12_2
% 216.74/36.48  |   (49)   ~ (all_12_2 = e3) | ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0
% 216.74/36.48  |           & op(e0, e3) = all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~
% 216.74/36.48  |           (all_12_1 = e1) & op(e0, e3) = all_12_1 & $i(all_12_1))
% 216.74/36.48  | 
% 216.74/36.48  | DELTA: instantiating (29) with fresh symbols all_14_0, all_14_1, all_14_2
% 216.74/36.48  |        gives:
% 216.74/36.48  |   (50)  op(e2, e2) = all_14_2 & $i(all_14_2) & ( ~ (all_14_2 = e0) | ( ~
% 216.74/36.48  |             (all_14_0 = e1) & op(all_14_1, e2) = all_14_0 & op(e2, e0) =
% 216.74/36.48  |             all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e3) &
% 216.74/36.48  |             op(e2, e0) = all_14_1 & $i(all_14_1)))
% 216.74/36.48  | 
% 216.74/36.48  | ALPHA: (50) implies:
% 216.74/36.48  |   (51)  op(e2, e2) = all_14_2
% 216.74/36.48  |   (52)   ~ (all_14_2 = e0) | ( ~ (all_14_0 = e1) & op(all_14_1, e2) = all_14_0
% 216.74/36.48  |           & op(e2, e0) = all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~
% 216.74/36.48  |           (all_14_1 = e3) & op(e2, e0) = all_14_1 & $i(all_14_1))
% 216.74/36.48  | 
% 216.74/36.48  | DELTA: instantiating (31) with fresh symbols all_16_0, all_16_1, all_16_2
% 216.74/36.48  |        gives:
% 216.74/36.48  |   (53)  op(e2, e2) = all_16_2 & $i(all_16_2) & ( ~ (all_16_2 = e1) | ( ~
% 216.74/36.48  |             (all_16_0 = e0) & op(all_16_1, e2) = all_16_0 & op(e2, e1) =
% 216.74/36.48  |             all_16_1 & $i(all_16_0) & $i(all_16_1)) | ( ~ (all_16_1 = e3) &
% 216.74/36.48  |             op(e2, e1) = all_16_1 & $i(all_16_1)))
% 216.74/36.48  | 
% 216.74/36.48  | ALPHA: (53) implies:
% 216.74/36.48  |   (54)  op(e2, e2) = all_16_2
% 216.74/36.48  |   (55)   ~ (all_16_2 = e1) | ( ~ (all_16_0 = e0) & op(all_16_1, e2) = all_16_0
% 216.74/36.48  |           & op(e2, e1) = all_16_1 & $i(all_16_0) & $i(all_16_1)) | ( ~
% 216.74/36.48  |           (all_16_1 = e3) & op(e2, e1) = all_16_1 & $i(all_16_1))
% 216.74/36.48  | 
% 216.74/36.48  | DELTA: instantiating (23) with fresh symbols all_18_0, all_18_1, all_18_2
% 216.74/36.48  |        gives:
% 216.74/36.48  |   (56)  op(e3, e3) = all_18_2 & $i(all_18_2) & ( ~ (all_18_2 = e0) | ( ~
% 216.74/36.48  |             (all_18_0 = e1) & op(all_18_1, e3) = all_18_0 & op(e3, e0) =
% 216.74/36.48  |             all_18_1 & $i(all_18_0) & $i(all_18_1)) | ( ~ (all_18_1 = e2) &
% 216.74/36.48  |             op(e3, e0) = all_18_1 & $i(all_18_1)))
% 216.74/36.48  | 
% 216.74/36.48  | ALPHA: (56) implies:
% 216.74/36.48  |   (57)  op(e3, e3) = all_18_2
% 216.74/36.48  |   (58)   ~ (all_18_2 = e0) | ( ~ (all_18_0 = e1) & op(all_18_1, e3) = all_18_0
% 216.74/36.48  |           & op(e3, e0) = all_18_1 & $i(all_18_0) & $i(all_18_1)) | ( ~
% 216.74/36.48  |           (all_18_1 = e2) & op(e3, e0) = all_18_1 & $i(all_18_1))
% 216.74/36.48  | 
% 216.74/36.48  | DELTA: instantiating (13) with fresh symbols all_20_0, all_20_1, all_20_2
% 216.74/36.48  |        gives:
% 216.74/36.48  |   (59)  op(e3, e3) = all_20_2 & $i(all_20_2) & ( ~ (all_20_2 = e2) | ( ~
% 216.74/36.48  |             (all_20_0 = e1) & op(all_20_1, e3) = all_20_0 & op(e3, e2) =
% 216.74/36.48  |             all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e0) &
% 216.74/36.48  |             op(e3, e2) = all_20_1 & $i(all_20_1)))
% 216.74/36.48  | 
% 216.74/36.48  | ALPHA: (59) implies:
% 216.74/36.48  |   (60)  op(e3, e3) = all_20_2
% 216.74/36.48  |   (61)   ~ (all_20_2 = e2) | ( ~ (all_20_0 = e1) & op(all_20_1, e3) = all_20_0
% 216.74/36.48  |           & op(e3, e2) = all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~
% 216.74/36.48  |           (all_20_1 = e0) & op(e3, e2) = all_20_1 & $i(all_20_1))
% 216.74/36.48  | 
% 216.74/36.48  | DELTA: instantiating (28) with fresh symbols all_22_0, all_22_1, all_22_2
% 216.74/36.48  |        gives:
% 216.74/36.48  |   (62)  op(e0, e0) = all_22_2 & $i(all_22_2) & ( ~ (all_22_2 = e3) | ( ~
% 216.74/36.48  |             (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 216.74/36.48  |             all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) &
% 216.74/36.48  |             op(e0, e3) = all_22_1 & $i(all_22_1)))
% 216.74/36.48  | 
% 216.74/36.48  | ALPHA: (62) implies:
% 216.74/36.48  |   (63)  op(e0, e0) = all_22_2
% 216.74/36.48  |   (64)   ~ (all_22_2 = e3) | ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0
% 216.74/36.48  |           & op(e0, e3) = all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~
% 216.74/36.48  |           (all_22_1 = e2) & op(e0, e3) = all_22_1 & $i(all_22_1))
% 216.74/36.48  | 
% 216.74/36.48  | DELTA: instantiating (30) with fresh symbols all_24_0, all_24_1, all_24_2
% 216.74/36.48  |        gives:
% 216.74/36.48  |   (65)  op(e1, e1) = all_24_2 & $i(all_24_2) & ( ~ (all_24_2 = e0) | ( ~
% 216.74/36.48  |             (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 & op(e1, e0) =
% 216.74/36.48  |             all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 = e3) &
% 216.74/36.48  |             op(e1, e0) = all_24_1 & $i(all_24_1)))
% 216.74/36.48  | 
% 216.74/36.48  | ALPHA: (65) implies:
% 216.74/36.48  |   (66)  op(e1, e1) = all_24_2
% 216.74/36.48  |   (67)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0
% 216.74/36.48  |           & op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~
% 216.74/36.48  |           (all_24_1 = e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 216.74/36.48  | 
% 216.74/36.48  | DELTA: instantiating (12) with fresh symbols all_26_0, all_26_1, all_26_2
% 216.74/36.48  |        gives:
% 216.74/36.48  |   (68)  op(e2, e2) = all_26_2 & $i(all_26_2) & ( ~ (all_26_2 = e1) | ( ~
% 216.74/36.48  |             (all_26_0 = e3) & op(all_26_1, e2) = all_26_0 & op(e2, e1) =
% 216.74/36.48  |             all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 = e0) &
% 216.74/36.48  |             op(e2, e1) = all_26_1 & $i(all_26_1)))
% 216.74/36.48  | 
% 216.74/36.48  | ALPHA: (68) implies:
% 216.74/36.48  |   (69)  op(e2, e2) = all_26_2
% 216.74/36.49  |   (70)   ~ (all_26_2 = e1) | ( ~ (all_26_0 = e3) & op(all_26_1, e2) = all_26_0
% 216.74/36.49  |           & op(e2, e1) = all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~
% 216.74/36.49  |           (all_26_1 = e0) & op(e2, e1) = all_26_1 & $i(all_26_1))
% 216.74/36.49  | 
% 216.74/36.49  | DELTA: instantiating (19) with fresh symbols all_28_0, all_28_1, all_28_2
% 216.74/36.49  |        gives:
% 216.74/36.49  |   (71)  op(e3, e3) = all_28_2 & $i(all_28_2) & ( ~ (all_28_2 = e2) | ( ~
% 216.74/36.49  |             (all_28_0 = e0) & op(all_28_1, e3) = all_28_0 & op(e3, e2) =
% 216.74/36.49  |             all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 = e1) &
% 216.74/36.49  |             op(e3, e2) = all_28_1 & $i(all_28_1)))
% 216.74/36.49  | 
% 216.74/36.49  | ALPHA: (71) implies:
% 216.74/36.49  |   (72)  op(e3, e3) = all_28_2
% 216.74/36.49  |   (73)   ~ (all_28_2 = e2) | ( ~ (all_28_0 = e0) & op(all_28_1, e3) = all_28_0
% 216.74/36.49  |           & op(e3, e2) = all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~
% 216.74/36.49  |           (all_28_1 = e1) & op(e3, e2) = all_28_1 & $i(all_28_1))
% 216.74/36.49  | 
% 216.74/36.49  | DELTA: instantiating (32) with fresh symbols all_30_0, all_30_1, all_30_2
% 216.74/36.49  |        gives:
% 217.18/36.49  |   (74)  op(e0, e0) = all_30_2 & $i(all_30_2) & ( ~ (all_30_2 = e1) | ( ~
% 217.18/36.49  |             (all_30_0 = e2) & op(all_30_1, e0) = all_30_0 & op(e0, e1) =
% 217.18/36.49  |             all_30_1 & $i(all_30_0) & $i(all_30_1)) | ( ~ (all_30_1 = e3) &
% 217.18/36.49  |             op(e0, e1) = all_30_1 & $i(all_30_1)))
% 217.18/36.49  | 
% 217.18/36.49  | ALPHA: (74) implies:
% 217.18/36.49  |   (75)  op(e0, e0) = all_30_2
% 217.18/36.49  |   (76)   ~ (all_30_2 = e1) | ( ~ (all_30_0 = e2) & op(all_30_1, e0) = all_30_0
% 217.18/36.49  |           & op(e0, e1) = all_30_1 & $i(all_30_0) & $i(all_30_1)) | ( ~
% 217.18/36.49  |           (all_30_1 = e3) & op(e0, e1) = all_30_1 & $i(all_30_1))
% 217.18/36.49  | 
% 217.18/36.49  | DELTA: instantiating (34) with fresh symbols all_32_0, all_32_1, all_32_2
% 217.18/36.49  |        gives:
% 217.18/36.49  |   (77)  op(e0, e0) = all_32_2 & $i(all_32_2) & ( ~ (all_32_2 = e2) | ( ~
% 217.18/36.49  |             (all_32_0 = e1) & op(all_32_1, e0) = all_32_0 & op(e0, e2) =
% 217.18/36.49  |             all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 = e3) &
% 217.18/36.49  |             op(e0, e2) = all_32_1 & $i(all_32_1)))
% 217.18/36.49  | 
% 217.18/36.49  | ALPHA: (77) implies:
% 217.18/36.49  |   (78)  op(e0, e0) = all_32_2
% 217.18/36.49  |   (79)   ~ (all_32_2 = e2) | ( ~ (all_32_0 = e1) & op(all_32_1, e0) = all_32_0
% 217.18/36.49  |           & op(e0, e2) = all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~
% 217.18/36.49  |           (all_32_1 = e3) & op(e0, e2) = all_32_1 & $i(all_32_1))
% 217.18/36.49  | 
% 217.18/36.49  | DELTA: instantiating (24) with fresh symbols all_34_0, all_34_1, all_34_2
% 217.18/36.49  |        gives:
% 217.18/36.49  |   (80)  op(e1, e1) = all_34_2 & $i(all_34_2) & ( ~ (all_34_2 = e0) | ( ~
% 217.18/36.49  |             (all_34_0 = e3) & op(all_34_1, e1) = all_34_0 & op(e1, e0) =
% 217.18/36.49  |             all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 = e2) &
% 217.18/36.49  |             op(e1, e0) = all_34_1 & $i(all_34_1)))
% 217.18/36.49  | 
% 217.18/36.49  | ALPHA: (80) implies:
% 217.18/36.49  |   (81)  op(e1, e1) = all_34_2
% 217.18/36.49  |   (82)   ~ (all_34_2 = e0) | ( ~ (all_34_0 = e3) & op(all_34_1, e1) = all_34_0
% 217.18/36.49  |           & op(e1, e0) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~
% 217.18/36.49  |           (all_34_1 = e2) & op(e1, e0) = all_34_1 & $i(all_34_1))
% 217.18/36.49  | 
% 217.18/36.49  | DELTA: instantiating (25) with fresh symbols all_36_0, all_36_1, all_36_2
% 217.18/36.49  |        gives:
% 217.18/36.49  |   (83)  op(e3, e3) = all_36_2 & $i(all_36_2) & ( ~ (all_36_2 = e1) | ( ~
% 217.18/36.49  |             (all_36_0 = e0) & op(all_36_1, e3) = all_36_0 & op(e3, e1) =
% 217.18/36.49  |             all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e2) &
% 217.18/36.49  |             op(e3, e1) = all_36_1 & $i(all_36_1)))
% 217.18/36.49  | 
% 217.18/36.49  | ALPHA: (83) implies:
% 217.18/36.49  |   (84)  op(e3, e3) = all_36_2
% 217.18/36.49  |   (85)   ~ (all_36_2 = e1) | ( ~ (all_36_0 = e0) & op(all_36_1, e3) = all_36_0
% 217.18/36.49  |           & op(e3, e1) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~
% 217.18/36.49  |           (all_36_1 = e2) & op(e3, e1) = all_36_1 & $i(all_36_1))
% 217.18/36.49  | 
% 217.18/36.49  | DELTA: instantiating (33) with fresh symbols all_38_0, all_38_1, all_38_2
% 217.18/36.49  |        gives:
% 217.18/36.49  |   (86)  op(e1, e1) = all_38_2 & $i(all_38_2) & ( ~ (all_38_2 = e2) | ( ~
% 217.18/36.49  |             (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 & op(e1, e2) =
% 217.18/36.49  |             all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 = e3) &
% 217.18/36.49  |             op(e1, e2) = all_38_1 & $i(all_38_1)))
% 217.18/36.49  | 
% 217.18/36.49  | ALPHA: (86) implies:
% 217.18/36.49  |   (87)  op(e1, e1) = all_38_2
% 217.18/36.49  |   (88)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0
% 217.18/36.49  |           & op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~
% 217.18/36.49  |           (all_38_1 = e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 217.18/36.49  | 
% 217.18/36.49  | DELTA: instantiating (26) with fresh symbols all_40_0, all_40_1, all_40_2
% 217.18/36.49  |        gives:
% 217.18/36.49  |   (89)  op(e0, e0) = all_40_2 & $i(all_40_2) & ( ~ (all_40_2 = e1) | ( ~
% 217.18/36.49  |             (all_40_0 = e3) & op(all_40_1, e0) = all_40_0 & op(e0, e1) =
% 217.18/36.49  |             all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 = e2) &
% 217.18/36.49  |             op(e0, e1) = all_40_1 & $i(all_40_1)))
% 217.18/36.49  | 
% 217.18/36.49  | ALPHA: (89) implies:
% 217.18/36.49  |   (90)  op(e0, e0) = all_40_2
% 217.18/36.49  |   (91)   ~ (all_40_2 = e1) | ( ~ (all_40_0 = e3) & op(all_40_1, e0) = all_40_0
% 217.18/36.49  |           & op(e0, e1) = all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~
% 217.18/36.49  |           (all_40_1 = e2) & op(e0, e1) = all_40_1 & $i(all_40_1))
% 217.18/36.49  | 
% 217.18/36.49  | DELTA: instantiating (14) with fresh symbols all_42_0, all_42_1, all_42_2
% 217.18/36.49  |        gives:
% 217.18/36.49  |   (92)  op(e1, e1) = all_42_2 & $i(all_42_2) & ( ~ (all_42_2 = e2) | ( ~
% 217.18/36.49  |             (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 & op(e1, e2) =
% 217.18/36.49  |             all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e0) &
% 217.18/36.49  |             op(e1, e2) = all_42_1 & $i(all_42_1)))
% 217.18/36.49  | 
% 217.18/36.49  | ALPHA: (92) implies:
% 217.18/36.49  |   (93)  op(e1, e1) = all_42_2
% 217.18/36.50  |   (94)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0
% 217.18/36.50  |           & op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~
% 217.18/36.50  |           (all_42_1 = e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 217.18/36.50  | 
% 217.18/36.50  | DELTA: instantiating (15) with fresh symbols all_44_0, all_44_1, all_44_2
% 217.18/36.50  |        gives:
% 217.18/36.50  |   (95)  op(e2, e2) = all_44_2 & $i(all_44_2) & ( ~ (all_44_2 = e3) | ( ~
% 217.18/36.50  |             (all_44_0 = e1) & op(all_44_1, e2) = all_44_0 & op(e2, e3) =
% 217.18/36.50  |             all_44_1 & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 = e0) &
% 217.18/36.50  |             op(e2, e3) = all_44_1 & $i(all_44_1)))
% 217.18/36.50  | 
% 217.18/36.50  | ALPHA: (95) implies:
% 217.18/36.50  |   (96)  op(e2, e2) = all_44_2
% 217.18/36.50  |   (97)   ~ (all_44_2 = e3) | ( ~ (all_44_0 = e1) & op(all_44_1, e2) = all_44_0
% 217.18/36.50  |           & op(e2, e3) = all_44_1 & $i(all_44_0) & $i(all_44_1)) | ( ~
% 217.18/36.50  |           (all_44_1 = e0) & op(e2, e3) = all_44_1 & $i(all_44_1))
% 217.18/36.50  | 
% 217.18/36.50  | DELTA: instantiating (16) with fresh symbols all_46_0, all_46_1, all_46_2
% 217.18/36.50  |        gives:
% 217.18/36.50  |   (98)  op(e1, e1) = all_46_2 & $i(all_46_2) & ( ~ (all_46_2 = e3) | ( ~
% 217.18/36.50  |             (all_46_0 = e2) & op(all_46_1, e1) = all_46_0 & op(e1, e3) =
% 217.18/36.50  |             all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 = e0) &
% 217.18/36.50  |             op(e1, e3) = all_46_1 & $i(all_46_1)))
% 217.18/36.50  | 
% 217.18/36.50  | ALPHA: (98) implies:
% 217.18/36.50  |   (99)  op(e1, e1) = all_46_2
% 217.18/36.50  |   (100)   ~ (all_46_2 = e3) | ( ~ (all_46_0 = e2) & op(all_46_1, e1) =
% 217.18/36.50  |            all_46_0 & op(e1, e3) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | (
% 217.18/36.50  |            ~ (all_46_1 = e0) & op(e1, e3) = all_46_1 & $i(all_46_1))
% 217.18/36.50  | 
% 217.18/36.50  | DELTA: instantiating (17) with fresh symbols all_48_0, all_48_1, all_48_2
% 217.18/36.50  |        gives:
% 217.18/36.50  |   (101)  op(e3, e3) = all_48_2 & $i(all_48_2) & ( ~ (all_48_2 = e0) | ( ~
% 217.18/36.50  |              (all_48_0 = e2) & op(all_48_1, e3) = all_48_0 & op(e3, e0) =
% 217.18/36.50  |              all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 = e1) &
% 217.18/36.50  |              op(e3, e0) = all_48_1 & $i(all_48_1)))
% 217.18/36.50  | 
% 217.18/36.50  | ALPHA: (101) implies:
% 217.18/36.50  |   (102)  op(e3, e3) = all_48_2
% 217.18/36.50  |   (103)   ~ (all_48_2 = e0) | ( ~ (all_48_0 = e2) & op(all_48_1, e3) =
% 217.18/36.50  |            all_48_0 & op(e3, e0) = all_48_1 & $i(all_48_0) & $i(all_48_1)) | (
% 217.18/36.50  |            ~ (all_48_1 = e1) & op(e3, e0) = all_48_1 & $i(all_48_1))
% 217.18/36.50  | 
% 217.18/36.50  | DELTA: instantiating (18) with fresh symbols all_50_0, all_50_1, all_50_2
% 217.18/36.50  |        gives:
% 217.18/36.50  |   (104)  op(e2, e2) = all_50_2 & $i(all_50_2) & ( ~ (all_50_2 = e0) | ( ~
% 217.18/36.50  |              (all_50_0 = e3) & op(all_50_1, e2) = all_50_0 & op(e2, e0) =
% 217.18/36.50  |              all_50_1 & $i(all_50_0) & $i(all_50_1)) | ( ~ (all_50_1 = e1) &
% 217.18/36.50  |              op(e2, e0) = all_50_1 & $i(all_50_1)))
% 217.18/36.50  | 
% 217.18/36.50  | ALPHA: (104) implies:
% 217.18/36.50  |   (105)  op(e2, e2) = all_50_2
% 217.18/36.50  |   (106)   ~ (all_50_2 = e0) | ( ~ (all_50_0 = e3) & op(all_50_1, e2) =
% 217.18/36.50  |            all_50_0 & op(e2, e0) = all_50_1 & $i(all_50_0) & $i(all_50_1)) | (
% 217.18/36.50  |            ~ (all_50_1 = e1) & op(e2, e0) = all_50_1 & $i(all_50_1))
% 217.18/36.50  | 
% 217.18/36.50  | DELTA: instantiating (10) with fresh symbols all_52_0, all_52_1, all_52_2,
% 217.18/36.50  |        all_52_3, all_52_4, all_52_5, all_52_6, all_52_7, all_52_8, all_52_9,
% 217.18/36.50  |        all_52_10, all_52_11, all_52_12, all_52_13, all_52_14, all_52_15,
% 217.18/36.50  |        all_52_16, all_52_17, all_52_18, all_52_19, all_52_20, all_52_21,
% 217.18/36.50  |        all_52_22, all_52_23, all_52_24, all_52_25, all_52_26, all_52_27,
% 217.18/36.50  |        all_52_28, all_52_29, all_52_30, all_52_31 gives:
% 217.18/36.50  |   (107)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 217.18/36.50  |            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 217.18/36.50  |            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3,
% 217.18/36.50  |              e3) = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 &
% 217.18/36.50  |            op(e3, e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5)
% 217.18/36.50  |            & $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1
% 217.18/36.50  |            & all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 217.18/36.50  |              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 217.18/36.50  |              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11
% 217.18/36.50  |            & op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 217.18/36.50  |            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 217.18/36.50  |            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 217.18/36.50  |              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 217.18/36.50  |              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 217.18/36.50  |            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 &
% 217.18/36.50  |            op(e1, e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 217.18/36.50  |            $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 &
% 217.18/36.50  |            all_52_28 = e1 & all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 217.18/36.50  |            op(all_52_27, all_52_27) = e2 & op(all_52_29, all_52_29) = e1 &
% 217.18/36.50  |            op(all_52_31, all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2)
% 217.18/36.50  |            = all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 &
% 217.18/36.50  |            $i(all_52_25) & $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 217.18/36.50  | 
% 217.18/36.50  | DELTA: instantiating (3) with fresh symbols all_53_0, all_53_1, all_53_2,
% 217.18/36.50  |        all_53_3, all_53_4, all_53_5, all_53_6, all_53_7, all_53_8, all_53_9,
% 217.18/36.50  |        all_53_10, all_53_11, all_53_12, all_53_13, all_53_14, all_53_15 gives:
% 217.18/36.51  |   (108)   ~ (all_53_0 = all_53_1) &  ~ (all_53_0 = all_53_2) &  ~ (all_53_0 =
% 217.18/36.51  |            all_53_3) &  ~ (all_53_0 = all_53_4) &  ~ (all_53_0 = all_53_8) & 
% 217.18/36.51  |          ~ (all_53_0 = all_53_12) &  ~ (all_53_1 = all_53_2) &  ~ (all_53_1 =
% 217.18/36.51  |            all_53_3) &  ~ (all_53_1 = all_53_5) &  ~ (all_53_1 = all_53_9) & 
% 217.18/36.51  |          ~ (all_53_1 = all_53_13) &  ~ (all_53_2 = all_53_3) &  ~ (all_53_2 =
% 217.18/36.51  |            all_53_6) &  ~ (all_53_2 = all_53_10) &  ~ (all_53_2 = all_53_14) &
% 217.18/36.51  |           ~ (all_53_3 = all_53_7) &  ~ (all_53_3 = all_53_11) &  ~ (all_53_3 =
% 217.18/36.51  |            all_53_15) &  ~ (all_53_4 = all_53_5) &  ~ (all_53_4 = all_53_6) & 
% 217.18/36.51  |          ~ (all_53_4 = all_53_7) &  ~ (all_53_4 = all_53_8) &  ~ (all_53_4 =
% 217.18/36.51  |            all_53_12) &  ~ (all_53_5 = all_53_6) &  ~ (all_53_5 = all_53_7) & 
% 217.18/36.51  |          ~ (all_53_5 = all_53_9) &  ~ (all_53_5 = all_53_13) &  ~ (all_53_6 =
% 217.18/36.51  |            all_53_7) &  ~ (all_53_6 = all_53_10) &  ~ (all_53_6 = all_53_14) &
% 217.18/36.51  |           ~ (all_53_7 = all_53_11) &  ~ (all_53_7 = all_53_15) &  ~ (all_53_8
% 217.18/36.51  |            = all_53_9) &  ~ (all_53_8 = all_53_10) &  ~ (all_53_8 = all_53_11)
% 217.18/36.51  |          &  ~ (all_53_8 = all_53_12) &  ~ (all_53_9 = all_53_10) &  ~
% 217.18/36.51  |          (all_53_9 = all_53_11) &  ~ (all_53_9 = all_53_13) &  ~ (all_53_10 =
% 217.18/36.51  |            all_53_11) &  ~ (all_53_10 = all_53_14) &  ~ (all_53_11 =
% 217.18/36.51  |            all_53_15) &  ~ (all_53_12 = all_53_13) &  ~ (all_53_12 =
% 217.18/36.51  |            all_53_14) &  ~ (all_53_12 = all_53_15) &  ~ (all_53_13 =
% 217.18/36.51  |            all_53_14) &  ~ (all_53_13 = all_53_15) &  ~ (all_53_14 =
% 217.18/36.51  |            all_53_15) & op(e3, e3) = all_53_0 & op(e3, e2) = all_53_4 & op(e3,
% 217.18/36.51  |            e1) = all_53_8 & op(e3, e0) = all_53_12 & op(e2, e3) = all_53_1 &
% 217.18/36.51  |          op(e2, e2) = all_53_5 & op(e2, e1) = all_53_9 & op(e2, e0) =
% 217.18/36.51  |          all_53_13 & op(e1, e3) = all_53_2 & op(e1, e2) = all_53_6 & op(e1,
% 217.18/36.51  |            e1) = all_53_10 & op(e1, e0) = all_53_14 & op(e0, e3) = all_53_3 &
% 217.18/36.51  |          op(e0, e2) = all_53_7 & op(e0, e1) = all_53_11 & op(e0, e0) =
% 217.18/36.51  |          all_53_15 & $i(all_53_0) & $i(all_53_1) & $i(all_53_2) & $i(all_53_3)
% 217.18/36.51  |          & $i(all_53_4) & $i(all_53_5) & $i(all_53_6) & $i(all_53_7) &
% 217.18/36.51  |          $i(all_53_8) & $i(all_53_9) & $i(all_53_10) & $i(all_53_11) &
% 217.18/36.51  |          $i(all_53_12) & $i(all_53_13) & $i(all_53_14) & $i(all_53_15)
% 217.18/36.51  | 
% 217.18/36.51  | ALPHA: (108) implies:
% 217.18/36.51  |   (109)   ~ (all_53_14 = all_53_15)
% 217.18/36.51  |   (110)   ~ (all_53_13 = all_53_15)
% 217.18/36.51  |   (111)   ~ (all_53_13 = all_53_14)
% 217.18/36.51  |   (112)   ~ (all_53_12 = all_53_15)
% 217.18/36.51  |   (113)   ~ (all_53_12 = all_53_14)
% 217.18/36.51  |   (114)   ~ (all_53_12 = all_53_13)
% 217.18/36.51  |   (115)   ~ (all_53_11 = all_53_15)
% 217.18/36.51  |   (116)   ~ (all_53_10 = all_53_14)
% 217.18/36.51  |   (117)   ~ (all_53_10 = all_53_11)
% 217.18/36.51  |   (118)   ~ (all_53_9 = all_53_13)
% 217.18/36.51  |   (119)   ~ (all_53_9 = all_53_11)
% 217.18/36.51  |   (120)   ~ (all_53_9 = all_53_10)
% 217.18/36.51  |   (121)   ~ (all_53_8 = all_53_12)
% 217.18/36.51  |   (122)   ~ (all_53_8 = all_53_11)
% 217.18/36.51  |   (123)   ~ (all_53_8 = all_53_10)
% 217.18/36.51  |   (124)   ~ (all_53_8 = all_53_9)
% 217.18/36.51  |   (125)   ~ (all_53_7 = all_53_15)
% 217.18/36.51  |   (126)   ~ (all_53_7 = all_53_11)
% 217.18/36.51  |   (127)   ~ (all_53_6 = all_53_14)
% 217.18/36.51  |   (128)   ~ (all_53_6 = all_53_10)
% 217.18/36.51  |   (129)   ~ (all_53_6 = all_53_7)
% 217.18/36.51  |   (130)   ~ (all_53_5 = all_53_13)
% 217.18/36.51  |   (131)   ~ (all_53_5 = all_53_9)
% 217.18/36.51  |   (132)   ~ (all_53_5 = all_53_7)
% 217.18/36.51  |   (133)   ~ (all_53_5 = all_53_6)
% 217.18/36.51  |   (134)   ~ (all_53_4 = all_53_12)
% 217.18/36.51  |   (135)   ~ (all_53_4 = all_53_8)
% 217.18/36.51  |   (136)   ~ (all_53_4 = all_53_7)
% 217.18/36.51  |   (137)   ~ (all_53_4 = all_53_6)
% 217.18/36.51  |   (138)   ~ (all_53_4 = all_53_5)
% 217.18/36.51  |   (139)   ~ (all_53_3 = all_53_15)
% 217.18/36.51  |   (140)   ~ (all_53_3 = all_53_11)
% 217.18/36.51  |   (141)   ~ (all_53_3 = all_53_7)
% 217.18/36.51  |   (142)   ~ (all_53_2 = all_53_14)
% 217.18/36.51  |   (143)   ~ (all_53_2 = all_53_10)
% 217.18/36.51  |   (144)   ~ (all_53_2 = all_53_6)
% 217.18/36.51  |   (145)   ~ (all_53_2 = all_53_3)
% 217.18/36.51  |   (146)   ~ (all_53_1 = all_53_13)
% 217.18/36.51  |   (147)   ~ (all_53_1 = all_53_9)
% 217.18/36.51  |   (148)   ~ (all_53_1 = all_53_5)
% 217.18/36.51  |   (149)   ~ (all_53_1 = all_53_3)
% 217.18/36.51  |   (150)   ~ (all_53_1 = all_53_2)
% 217.18/36.51  |   (151)   ~ (all_53_0 = all_53_12)
% 217.18/36.51  |   (152)   ~ (all_53_0 = all_53_8)
% 217.18/36.51  |   (153)   ~ (all_53_0 = all_53_4)
% 217.18/36.51  |   (154)   ~ (all_53_0 = all_53_3)
% 217.18/36.51  |   (155)   ~ (all_53_0 = all_53_2)
% 217.18/36.51  |   (156)   ~ (all_53_0 = all_53_1)
% 217.18/36.51  |   (157)  op(e0, e0) = all_53_15
% 217.18/36.51  |   (158)  op(e0, e1) = all_53_11
% 217.18/36.51  |   (159)  op(e0, e2) = all_53_7
% 217.18/36.51  |   (160)  op(e0, e3) = all_53_3
% 217.18/36.51  |   (161)  op(e1, e0) = all_53_14
% 217.18/36.51  |   (162)  op(e1, e1) = all_53_10
% 217.18/36.51  |   (163)  op(e1, e2) = all_53_6
% 217.18/36.51  |   (164)  op(e1, e3) = all_53_2
% 217.18/36.51  |   (165)  op(e2, e0) = all_53_13
% 217.18/36.51  |   (166)  op(e2, e1) = all_53_9
% 217.18/36.51  |   (167)  op(e2, e2) = all_53_5
% 217.18/36.51  |   (168)  op(e2, e3) = all_53_1
% 217.18/36.51  |   (169)  op(e3, e0) = all_53_12
% 217.18/36.51  |   (170)  op(e3, e1) = all_53_8
% 217.18/36.51  |   (171)  op(e3, e2) = all_53_4
% 217.18/36.51  |   (172)  op(e3, e3) = all_53_0
% 217.18/36.51  | 
% 217.18/36.51  | DELTA: instantiating (1) with fresh symbols all_55_0, all_55_1, all_55_2,
% 217.18/36.51  |        all_55_3, all_55_4, all_55_5, all_55_6, all_55_7, all_55_8, all_55_9,
% 217.18/36.51  |        all_55_10, all_55_11, all_55_12, all_55_13, all_55_14, all_55_15 gives:
% 217.18/36.51  |   (173)  op(e3, e3) = all_55_0 & op(e3, e2) = all_55_1 & op(e3, e1) = all_55_2
% 217.18/36.51  |          & op(e3, e0) = all_55_3 & op(e2, e3) = all_55_4 & op(e2, e2) =
% 217.18/36.51  |          all_55_5 & op(e2, e1) = all_55_6 & op(e2, e0) = all_55_7 & op(e1, e3)
% 217.18/36.51  |          = all_55_8 & op(e1, e2) = all_55_9 & op(e1, e1) = all_55_10 & op(e1,
% 217.18/36.51  |            e0) = all_55_11 & op(e0, e3) = all_55_12 & op(e0, e2) = all_55_13 &
% 217.18/36.51  |          op(e0, e1) = all_55_14 & op(e0, e0) = all_55_15 & $i(all_55_0) &
% 217.18/36.51  |          $i(all_55_1) & $i(all_55_2) & $i(all_55_3) & $i(all_55_4) &
% 217.18/36.51  |          $i(all_55_5) & $i(all_55_6) & $i(all_55_7) & $i(all_55_8) &
% 217.18/36.51  |          $i(all_55_9) & $i(all_55_10) & $i(all_55_11) & $i(all_55_12) &
% 217.18/36.51  |          $i(all_55_13) & $i(all_55_14) & $i(all_55_15) & (all_55_0 = e3 |
% 217.18/36.51  |            all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0) & (all_55_1 = e3 |
% 217.18/36.51  |            all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0) & (all_55_2 = e3 |
% 217.18/36.52  |            all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0) & (all_55_3 = e3 |
% 217.18/36.52  |            all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0) & (all_55_4 = e3 |
% 217.18/36.52  |            all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0) & (all_55_5 = e3 |
% 217.18/36.52  |            all_55_5 = e2 | all_55_5 = e1 | all_55_5 = e0) & (all_55_6 = e3 |
% 217.18/36.52  |            all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0) & (all_55_7 = e3 |
% 217.18/36.52  |            all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0) & (all_55_8 = e3 |
% 217.18/36.52  |            all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0) & (all_55_9 = e3 |
% 217.18/36.52  |            all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0) & (all_55_10 = e3 |
% 217.18/36.52  |            all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0) & (all_55_11 = e3
% 217.18/36.52  |            | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0) & (all_55_12 =
% 217.18/36.52  |            e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0) & (all_55_13
% 217.18/36.52  |            = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0) &
% 217.18/36.52  |          (all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0) &
% 217.18/36.52  |          (all_55_15 = e3 | all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0)
% 217.18/36.52  | 
% 217.18/36.52  | ALPHA: (173) implies:
% 217.18/36.52  |   (174)  op(e0, e0) = all_55_15
% 217.18/36.52  |   (175)  op(e0, e1) = all_55_14
% 217.18/36.52  |   (176)  op(e0, e2) = all_55_13
% 217.18/36.52  |   (177)  op(e0, e3) = all_55_12
% 217.18/36.52  |   (178)  op(e1, e0) = all_55_11
% 217.18/36.52  |   (179)  op(e1, e1) = all_55_10
% 217.18/36.52  |   (180)  op(e1, e2) = all_55_9
% 217.18/36.52  |   (181)  op(e1, e3) = all_55_8
% 217.18/36.52  |   (182)  op(e2, e0) = all_55_7
% 217.18/36.52  |   (183)  op(e2, e1) = all_55_6
% 217.18/36.52  |   (184)  op(e2, e2) = all_55_5
% 217.18/36.52  |   (185)  op(e2, e3) = all_55_4
% 217.18/36.52  |   (186)  op(e3, e0) = all_55_3
% 217.18/36.52  |   (187)  op(e3, e1) = all_55_2
% 217.18/36.52  |   (188)  op(e3, e2) = all_55_1
% 217.18/36.52  |   (189)  op(e3, e3) = all_55_0
% 217.18/36.52  |   (190)  all_55_15 = e3 | all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 217.18/36.52  |   (191)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 217.18/36.52  |   (192)  all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 217.18/36.52  |   (193)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 217.18/36.52  |   (194)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 217.18/36.52  |   (195)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 217.18/36.52  |   (196)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 217.18/36.52  |   (197)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 217.18/36.52  |   (198)  all_55_7 = e3 | all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 217.18/36.52  |   (199)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 217.18/36.52  |   (200)  all_55_5 = e3 | all_55_5 = e2 | all_55_5 = e1 | all_55_5 = e0
% 217.18/36.52  |   (201)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 217.18/36.52  |   (202)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 217.18/36.52  |   (203)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 217.18/36.52  |   (204)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 217.18/36.52  |   (205)  all_55_0 = e3 | all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 217.18/36.52  | 
% 217.18/36.52  | DELTA: instantiating (2) with fresh symbols all_57_0, all_57_1, all_57_2,
% 217.18/36.52  |        all_57_3, all_57_4, all_57_5, all_57_6, all_57_7, all_57_8, all_57_9,
% 217.18/36.52  |        all_57_10, all_57_11, all_57_12, all_57_13, all_57_14, all_57_15 gives:
% 217.18/36.53  |   (206)  ((all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) =
% 217.18/36.53  |              e3) | (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3,
% 217.18/36.53  |                e0) = e3)) & ((all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 =
% 217.18/36.53  |              e3 & op(e2, e3) = e3) | (all_57_6 = e3 & op(e1, e3) = e3) |
% 217.18/36.53  |            (all_57_12 = e3 & op(e0, e3) = e3)) & ((all_57_0 = e2 & op(e3, e3)
% 217.18/36.53  |              = e2) | (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_4 = e2 &
% 217.18/36.53  |              op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)) &
% 217.18/36.53  |          ((all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) =
% 217.18/36.53  |              e2) | (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 &
% 217.18/36.53  |              op(e0, e3) = e2)) & ((all_57_0 = e1 & op(e3, e3) = e1) |
% 217.18/36.53  |            (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_4 = e1 & op(e3, e1) =
% 217.18/36.53  |              e1) | (all_57_9 = e1 & op(e3, e0) = e1)) & ((all_57_0 = e1 &
% 217.18/36.53  |              op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_6
% 217.18/36.53  |              = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)) &
% 217.18/36.53  |          ((all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) =
% 217.18/36.53  |              e0) | (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3,
% 217.18/36.53  |                e0) = e0)) & ((all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 =
% 217.18/36.53  |              e0 & op(e2, e3) = e0) | (all_57_6 = e0 & op(e1, e3) = e0) |
% 217.18/36.53  |            (all_57_12 = e0 & op(e0, e3) = e0)) & ((all_57_1 = e3 & op(e3, e2)
% 217.18/36.53  |              = e3) | (all_57_3 = e3 & op(e2, e2) = e3) | (all_57_7 = e3 &
% 217.18/36.53  |              op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)) &
% 217.18/36.53  |          ((all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 217.18/36.53  |              e2) | (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 &
% 217.18/36.53  |              op(e0, e2) = e2)) & ((all_57_1 = e1 & op(e3, e2) = e1) |
% 217.18/36.53  |            (all_57_3 = e1 & op(e2, e2) = e1) | (all_57_7 = e1 & op(e1, e2) =
% 217.18/36.53  |              e1) | (all_57_13 = e1 & op(e0, e2) = e1)) & ((all_57_1 = e0 &
% 217.18/36.53  |              op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) | (all_57_7
% 217.18/36.53  |              = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)) &
% 217.18/36.53  |          ((all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 217.18/36.53  |              e3) | (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 &
% 217.18/36.53  |              op(e2, e0) = e3)) & ((all_57_2 = e2 & op(e2, e3) = e2) |
% 217.18/36.53  |            (all_57_3 = e2 & op(e2, e2) = e2) | (all_57_5 = e2 & op(e2, e1) =
% 217.18/36.53  |              e2) | (all_57_10 = e2 & op(e2, e0) = e2)) & ((all_57_2 = e1 &
% 217.18/36.53  |              op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) | (all_57_5
% 217.18/36.53  |              = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)) &
% 217.18/36.53  |          ((all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) =
% 217.18/36.53  |              e0) | (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 &
% 217.18/36.53  |              op(e2, e0) = e0)) & ((all_57_4 = e3 & op(e3, e1) = e3) |
% 217.18/36.53  |            (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_8 = e3 & op(e1, e1) =
% 217.18/36.53  |              e3) | (all_57_14 = e3 & op(e0, e1) = e3)) & ((all_57_4 = e2 &
% 217.18/36.53  |              op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_8
% 217.18/36.53  |              = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)) &
% 217.18/36.53  |          ((all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) =
% 217.18/36.53  |              e1) | (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 &
% 217.18/36.53  |              op(e0, e1) = e1)) & ((all_57_4 = e0 & op(e3, e1) = e0) |
% 217.18/36.53  |            (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_8 = e0 & op(e1, e1) =
% 217.18/36.53  |              e0) | (all_57_14 = e0 & op(e0, e1) = e0)) & ((all_57_6 = e3 &
% 217.18/36.53  |              op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_8
% 217.18/36.53  |              = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)) &
% 217.18/36.53  |          ((all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) =
% 217.18/36.53  |              e2) | (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 &
% 217.18/36.53  |              op(e1, e0) = e2)) & ((all_57_6 = e1 & op(e1, e3) = e1) |
% 217.18/36.53  |            (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_8 = e1 & op(e1, e1) =
% 217.18/36.53  |              e1) | (all_57_11 = e1 & op(e1, e0) = e1)) & ((all_57_6 = e0 &
% 217.18/36.53  |              op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_8
% 217.18/36.53  |              = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) &
% 217.18/36.53  |          ((all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 217.18/36.53  |              e3) | (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 &
% 217.18/36.53  |              op(e0, e0) = e3)) & ((all_57_9 = e2 & op(e3, e0) = e2) |
% 217.18/36.53  |            (all_57_10 = e2 & op(e2, e0) = e2) | (all_57_11 = e2 & op(e1, e0) =
% 217.18/36.53  |              e2) | (all_57_15 = e2 & op(e0, e0) = e2)) & ((all_57_9 = e1 &
% 217.18/36.53  |              op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 217.18/36.53  |            (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 217.18/36.53  |              e1)) & ((all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 &
% 217.18/36.53  |              op(e0, e2) = e3) | (all_57_14 = e3 & op(e0, e1) = e3) |
% 217.18/36.53  |            (all_57_15 = e3 & op(e0, e0) = e3)) & ((all_57_12 = e2 & op(e0, e3)
% 217.18/36.53  |              = e2) | (all_57_13 = e2 & op(e0, e2) = e2) | (all_57_14 = e2 &
% 217.18/36.53  |              op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)) &
% 217.18/36.53  |          ((all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 217.18/36.53  |              e1) | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 &
% 217.18/36.53  |              op(e0, e0) = e1)) & ((all_57_15 = e0 & op(e0, e0) = e0) |
% 217.18/36.53  |            (((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0)
% 217.18/36.53  |                  = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 =
% 217.18/36.53  |                  e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 217.18/36.53  |                (all_57_14 = e0 & op(e0, e1) = e0))))
% 217.18/36.53  | 
% 217.18/36.53  | ALPHA: (206) implies:
% 217.18/36.53  |   (207)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) =
% 217.18/36.53  |                e0) | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 217.18/36.53  |                op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) |
% 217.18/36.53  |              (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1)
% 217.18/36.53  |                = e0)))
% 217.18/36.53  |   (208)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 217.18/36.53  |            e1) | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0,
% 217.18/36.53  |              e0) = e1)
% 217.18/36.53  |   (209)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 217.18/36.53  |            e2) | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0,
% 217.18/36.53  |              e0) = e2)
% 217.18/36.53  |   (210)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 217.18/36.53  |            e3) | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0,
% 217.18/36.53  |              e0) = e3)
% 217.18/36.53  |   (211)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) =
% 217.18/36.53  |            e1) | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0,
% 217.18/36.53  |              e0) = e1)
% 217.18/36.53  |   (212)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 217.18/36.53  |            e2) | (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0,
% 217.18/36.53  |              e0) = e2)
% 217.18/36.53  |   (213)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 217.18/36.53  |            e3) | (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0,
% 217.18/36.53  |              e0) = e3)
% 217.18/36.53  |   (214)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0)
% 217.18/36.53  |          | (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 217.18/36.53  |            e0)
% 217.18/36.54  |   (215)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1)
% 217.18/36.54  |          | (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) =
% 217.18/36.54  |            e1)
% 217.18/36.54  |   (216)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2)
% 217.18/36.54  |          | (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) =
% 217.18/36.54  |            e2)
% 217.18/36.54  |   (217)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3)
% 217.18/36.54  |          | (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 217.18/36.54  |            e3)
% 217.18/36.54  |   (218)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0)
% 217.18/36.54  |          | (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 217.18/36.54  |            e0)
% 217.18/36.54  |   (219)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1)
% 217.18/36.54  |          | (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) =
% 217.18/36.54  |            e1)
% 217.18/36.54  |   (220)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2)
% 217.18/36.54  |          | (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) =
% 217.18/36.54  |            e2)
% 217.18/36.54  |   (221)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3)
% 217.18/36.54  |          | (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) =
% 217.18/36.54  |            e3)
% 217.18/36.54  |   (222)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0)
% 217.18/36.54  |          | (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 217.18/36.54  |            e0)
% 217.18/36.54  |   (223)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1)
% 217.18/36.54  |          | (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) =
% 217.18/36.54  |            e1)
% 217.18/36.54  |   (224)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2)
% 217.18/36.54  |          | (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 217.18/36.54  |            e2)
% 217.18/36.54  |   (225)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3)
% 217.18/36.54  |          | (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 217.18/36.54  |            e3)
% 217.18/36.54  |   (226)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0)
% 217.18/36.54  |          | (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 217.18/36.54  |            e0)
% 217.18/36.54  |   (227)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1)
% 217.18/36.54  |          | (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 217.18/36.54  |            e1)
% 217.18/36.54  |   (228)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2)
% 217.18/36.54  |          | (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 217.18/36.54  |            e2)
% 217.18/36.54  |   (229)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3)
% 217.18/36.54  |          | (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 217.18/36.54  |            e3)
% 217.18/36.54  |   (230)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0)
% 217.18/36.54  |          | (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) =
% 217.18/36.54  |            e0)
% 217.18/36.54  |   (231)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0)
% 217.18/36.54  |          | (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) =
% 217.18/36.54  |            e0)
% 217.18/36.54  |   (232)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1)
% 217.18/36.54  |          | (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) =
% 217.18/36.54  |            e1)
% 217.18/36.54  |   (233)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1)
% 217.18/36.54  |          | (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) =
% 217.18/36.54  |            e1)
% 217.18/36.54  |   (234)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2)
% 217.18/36.54  |          | (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) =
% 217.18/36.54  |            e2)
% 217.18/36.54  |   (235)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2)
% 217.18/36.54  |          | (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) =
% 217.18/36.54  |            e2)
% 217.18/36.54  |   (236)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3)
% 217.18/36.54  |          | (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) =
% 217.18/36.54  |            e3)
% 217.18/36.54  |   (237)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3)
% 217.18/36.54  |          | (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) =
% 217.18/36.54  |            e3)
% 217.18/36.54  | 
% 217.18/36.55  | GROUND_INST: instantiating (function-axioms) with all_12_2, all_30_2, e0, e0,
% 217.18/36.55  |              simplifying with (48), (75) gives:
% 217.18/36.55  |   (238)  all_30_2 = all_12_2
% 217.18/36.55  | 
% 217.18/36.55  | GROUND_INST: instantiating (function-axioms) with all_30_2, all_32_2, e0, e0,
% 217.18/36.55  |              simplifying with (75), (78) gives:
% 217.18/36.55  |   (239)  all_32_2 = all_30_2
% 217.18/36.55  | 
% 217.18/36.55  | GROUND_INST: instantiating (function-axioms) with all_22_2, all_32_2, e0, e0,
% 217.18/36.55  |              simplifying with (63), (78) gives:
% 217.18/36.55  |   (240)  all_32_2 = all_22_2
% 217.18/36.55  | 
% 217.18/36.55  | GROUND_INST: instantiating (function-axioms) with all_40_2, all_53_15, e0, e0,
% 217.18/36.55  |              simplifying with (90), (157) gives:
% 217.18/36.55  |   (241)  all_53_15 = all_40_2
% 217.18/36.55  | 
% 217.80/36.63  | GROUND_INST: instantiating (function-axioms) with all_32_2, all_53_15, e0, e0,
% 217.80/36.63  |              simplifying with (78), (157) gives:
% 217.80/36.63  |   (242)  all_53_15 = all_32_2
% 217.80/36.63  | 
% 217.80/36.63  | GROUND_INST: instantiating (function-axioms) with all_53_15, all_55_15, e0,
% 217.80/36.63  |              e0, simplifying with (157), (174) gives:
% 217.80/36.63  |   (243)  all_55_15 = all_53_15
% 217.80/36.63  | 
% 217.80/36.63  | GROUND_INST: instantiating (function-axioms) with all_4_2, all_55_15, e0, e0,
% 217.80/36.63  |              simplifying with (36), (174) gives:
% 217.80/36.63  |   (244)  all_55_15 = all_4_2
% 217.80/36.63  | 
% 217.80/36.63  | GROUND_INST: instantiating (function-axioms) with all_53_11, all_55_14, e1,
% 217.80/36.63  |              e0, simplifying with (158), (175) gives:
% 217.80/36.63  |   (245)  all_55_14 = all_53_11
% 217.80/36.63  | 
% 217.80/36.63  | GROUND_INST: instantiating (function-axioms) with all_53_7, all_55_13, e2, e0,
% 217.80/36.63  |              simplifying with (159), (176) gives:
% 217.80/36.63  |   (246)  all_55_13 = all_53_7
% 217.80/36.63  | 
% 217.80/36.63  | GROUND_INST: instantiating (function-axioms) with all_53_3, all_55_12, e3, e0,
% 217.80/36.63  |              simplifying with (160), (177) gives:
% 217.80/36.63  |   (247)  all_55_12 = all_53_3
% 217.80/36.63  | 
% 217.80/36.63  | GROUND_INST: instantiating (function-axioms) with all_53_14, all_55_11, e0,
% 217.80/36.63  |              e1, simplifying with (161), (178) gives:
% 217.80/36.63  |   (248)  all_55_11 = all_53_14
% 217.80/36.63  | 
% 217.80/36.64  | GROUND_INST: instantiating (function-axioms) with all_6_2, all_38_2, e1, e1,
% 217.80/36.64  |              simplifying with (39), (87) gives:
% 217.80/36.64  |   (249)  all_38_2 = all_6_2
% 217.80/36.64  | 
% 217.80/36.64  | GROUND_INST: instantiating (function-axioms) with all_46_2, all_53_10, e1, e1,
% 217.80/36.64  |              simplifying with (99), (162) gives:
% 217.80/36.64  |   (250)  all_53_10 = all_46_2
% 217.80/36.64  | 
% 217.80/36.64  | GROUND_INST: instantiating (function-axioms) with all_38_2, all_53_10, e1, e1,
% 217.80/36.64  |              simplifying with (87), (162) gives:
% 217.80/36.64  |   (251)  all_53_10 = all_38_2
% 217.80/36.64  | 
% 217.80/36.64  | GROUND_INST: instantiating (function-axioms) with all_34_2, all_53_10, e1, e1,
% 217.80/36.64  |              simplifying with (81), (162) gives:
% 217.80/36.64  |   (252)  all_53_10 = all_34_2
% 217.80/36.64  | 
% 217.80/36.64  | GROUND_INST: instantiating (function-axioms) with all_53_10, all_55_10, e1,
% 217.80/36.64  |              e1, simplifying with (162), (179) gives:
% 217.80/36.64  |   (253)  all_55_10 = all_53_10
% 217.80/36.64  | 
% 217.80/36.64  | GROUND_INST: instantiating (function-axioms) with all_42_2, all_55_10, e1, e1,
% 217.80/36.64  |              simplifying with (93), (179) gives:
% 217.80/36.64  |   (254)  all_55_10 = all_42_2
% 217.80/36.64  | 
% 217.80/36.64  | GROUND_INST: instantiating (function-axioms) with all_24_2, all_55_10, e1, e1,
% 217.80/36.64  |              simplifying with (66), (179) gives:
% 217.80/36.64  |   (255)  all_55_10 = all_24_2
% 217.80/36.64  | 
% 217.80/36.64  | GROUND_INST: instantiating (function-axioms) with all_53_6, all_55_9, e2, e1,
% 217.80/36.64  |              simplifying with (163), (180) gives:
% 217.80/36.64  |   (256)  all_55_9 = all_53_6
% 217.80/36.64  | 
% 217.80/36.64  | GROUND_INST: instantiating (function-axioms) with all_53_2, all_55_8, e3, e1,
% 217.80/36.64  |              simplifying with (164), (181) gives:
% 217.80/36.64  |   (257)  all_55_8 = all_53_2
% 217.80/36.64  | 
% 217.80/36.64  | GROUND_INST: instantiating (function-axioms) with all_53_13, all_55_7, e0, e2,
% 217.80/36.64  |              simplifying with (165), (182) gives:
% 217.80/36.64  |   (258)  all_55_7 = all_53_13
% 217.80/36.64  | 
% 217.80/36.64  | GROUND_INST: instantiating (function-axioms) with all_53_9, all_55_6, e1, e2,
% 217.80/36.64  |              simplifying with (166), (183) gives:
% 217.80/36.64  |   (259)  all_55_6 = all_53_9
% 217.80/36.64  | 
% 217.80/36.64  | GROUND_INST: instantiating (function-axioms) with all_14_2, all_16_2, e2, e2,
% 217.80/36.64  |              simplifying with (51), (54) gives:
% 217.80/36.64  |   (260)  all_16_2 = all_14_2
% 217.80/36.64  | 
% 217.80/36.64  | GROUND_INST: instantiating (function-axioms) with all_16_2, all_26_2, e2, e2,
% 217.80/36.64  |              simplifying with (54), (69) gives:
% 217.80/36.64  |   (261)  all_26_2 = all_16_2
% 217.80/36.64  | 
% 217.80/36.64  | GROUND_INST: instantiating (function-axioms) with all_26_2, all_44_2, e2, e2,
% 217.80/36.64  |              simplifying with (69), (96) gives:
% 217.80/36.64  |   (262)  all_44_2 = all_26_2
% 217.80/36.64  | 
% 217.80/36.64  | GROUND_INST: instantiating (function-axioms) with all_50_2, all_53_5, e2, e2,
% 217.80/36.64  |              simplifying with (105), (167) gives:
% 217.80/36.64  |   (263)  all_53_5 = all_50_2
% 217.80/36.64  | 
% 217.80/36.64  | GROUND_INST: instantiating (function-axioms) with all_44_2, all_53_5, e2, e2,
% 217.80/36.64  |              simplifying with (96), (167) gives:
% 217.80/36.64  |   (264)  all_53_5 = all_44_2
% 217.80/36.64  | 
% 217.80/36.64  | GROUND_INST: instantiating (function-axioms) with all_53_5, all_55_5, e2, e2,
% 217.80/36.64  |              simplifying with (167), (184) gives:
% 217.80/36.64  |   (265)  all_55_5 = all_53_5
% 217.80/36.64  | 
% 217.80/36.64  | GROUND_INST: instantiating (function-axioms) with all_8_2, all_55_5, e2, e2,
% 217.80/36.64  |              simplifying with (42), (184) gives:
% 217.80/36.64  |   (266)  all_55_5 = all_8_2
% 217.80/36.64  | 
% 217.80/36.64  | GROUND_INST: instantiating (function-axioms) with all_53_1, all_55_4, e3, e2,
% 217.80/36.64  |              simplifying with (168), (185) gives:
% 217.80/36.64  |   (267)  all_55_4 = all_53_1
% 217.80/36.64  | 
% 217.80/36.64  | GROUND_INST: instantiating (function-axioms) with all_53_12, all_55_3, e0, e3,
% 217.80/36.64  |              simplifying with (169), (186) gives:
% 217.80/36.64  |   (268)  all_55_3 = all_53_12
% 217.80/36.64  | 
% 217.80/36.64  | GROUND_INST: instantiating (function-axioms) with all_53_8, all_55_2, e1, e3,
% 217.80/36.64  |              simplifying with (170), (187) gives:
% 217.80/36.64  |   (269)  all_55_2 = all_53_8
% 217.80/36.64  | 
% 217.80/36.64  | GROUND_INST: instantiating (function-axioms) with all_53_4, all_55_1, e2, e3,
% 217.80/36.64  |              simplifying with (171), (188) gives:
% 217.80/36.64  |   (270)  all_55_1 = all_53_4
% 217.80/36.64  | 
% 217.80/36.64  | GROUND_INST: instantiating (function-axioms) with all_28_2, all_36_2, e3, e3,
% 217.80/36.64  |              simplifying with (72), (84) gives:
% 217.80/36.64  |   (271)  all_36_2 = all_28_2
% 217.80/36.64  | 
% 217.80/36.64  | GROUND_INST: instantiating (function-axioms) with all_20_2, all_36_2, e3, e3,
% 217.80/36.64  |              simplifying with (60), (84) gives:
% 217.80/36.64  |   (272)  all_36_2 = all_20_2
% 217.80/36.64  | 
% 217.80/36.64  | GROUND_INST: instantiating (function-axioms) with all_20_2, all_48_2, e3, e3,
% 217.80/36.64  |              simplifying with (60), (102) gives:
% 217.80/36.64  |   (273)  all_48_2 = all_20_2
% 217.80/36.64  | 
% 217.80/36.64  | GROUND_INST: instantiating (function-axioms) with all_36_2, all_53_0, e3, e3,
% 217.80/36.64  |              simplifying with (84), (172) gives:
% 217.80/36.64  |   (274)  all_53_0 = all_36_2
% 217.80/36.64  | 
% 217.80/36.64  | GROUND_INST: instantiating (function-axioms) with all_18_2, all_53_0, e3, e3,
% 217.80/36.64  |              simplifying with (57), (172) gives:
% 217.80/36.64  |   (275)  all_53_0 = all_18_2
% 217.80/36.64  | 
% 217.80/36.64  | GROUND_INST: instantiating (function-axioms) with all_48_2, all_55_0, e3, e3,
% 217.80/36.64  |              simplifying with (102), (189) gives:
% 217.80/36.64  |   (276)  all_55_0 = all_48_2
% 217.80/36.64  | 
% 217.80/36.64  | GROUND_INST: instantiating (function-axioms) with all_10_2, all_55_0, e3, e3,
% 217.80/36.64  |              simplifying with (45), (189) gives:
% 217.80/36.64  |   (277)  all_55_0 = all_10_2
% 217.80/36.64  | 
% 217.80/36.64  | COMBINE_EQS: (276), (277) imply:
% 217.80/36.64  |   (278)  all_48_2 = all_10_2
% 217.80/36.64  | 
% 217.80/36.64  | SIMP: (278) implies:
% 217.80/36.64  |   (279)  all_48_2 = all_10_2
% 217.80/36.64  | 
% 217.80/36.64  | COMBINE_EQS: (265), (266) imply:
% 217.80/36.64  |   (280)  all_53_5 = all_8_2
% 217.80/36.64  | 
% 217.80/36.64  | SIMP: (280) implies:
% 217.80/36.64  |   (281)  all_53_5 = all_8_2
% 217.80/36.64  | 
% 217.80/36.64  | COMBINE_EQS: (254), (255) imply:
% 217.80/36.64  |   (282)  all_42_2 = all_24_2
% 217.80/36.64  | 
% 217.80/36.64  | COMBINE_EQS: (253), (254) imply:
% 217.80/36.64  |   (283)  all_53_10 = all_42_2
% 217.80/36.64  | 
% 217.80/36.64  | SIMP: (283) implies:
% 217.80/36.64  |   (284)  all_53_10 = all_42_2
% 217.80/36.64  | 
% 217.80/36.64  | COMBINE_EQS: (243), (244) imply:
% 217.80/36.64  |   (285)  all_53_15 = all_4_2
% 217.80/36.64  | 
% 217.80/36.64  | SIMP: (285) implies:
% 217.80/36.64  |   (286)  all_53_15 = all_4_2
% 217.80/36.64  | 
% 217.80/36.64  | COMBINE_EQS: (274), (275) imply:
% 217.80/36.64  |   (287)  all_36_2 = all_18_2
% 217.80/36.64  | 
% 217.80/36.64  | SIMP: (287) implies:
% 217.80/36.64  |   (288)  all_36_2 = all_18_2
% 217.80/36.64  | 
% 217.80/36.64  | COMBINE_EQS: (263), (264) imply:
% 217.80/36.64  |   (289)  all_50_2 = all_44_2
% 217.80/36.64  | 
% 217.80/36.64  | COMBINE_EQS: (263), (281) imply:
% 217.80/36.64  |   (290)  all_50_2 = all_8_2
% 217.80/36.64  | 
% 217.80/36.64  | COMBINE_EQS: (250), (251) imply:
% 217.80/36.64  |   (291)  all_46_2 = all_38_2
% 217.80/36.64  | 
% 217.80/36.64  | COMBINE_EQS: (250), (252) imply:
% 217.80/36.64  |   (292)  all_46_2 = all_34_2
% 217.80/36.64  | 
% 217.80/36.64  | COMBINE_EQS: (250), (284) imply:
% 217.80/36.64  |   (293)  all_46_2 = all_42_2
% 217.80/36.65  | 
% 217.80/36.65  | COMBINE_EQS: (241), (242) imply:
% 217.80/36.65  |   (294)  all_40_2 = all_32_2
% 217.80/36.65  | 
% 217.80/36.65  | COMBINE_EQS: (241), (286) imply:
% 217.80/36.65  |   (295)  all_40_2 = all_4_2
% 217.80/36.65  | 
% 217.80/36.65  | COMBINE_EQS: (289), (290) imply:
% 217.80/36.65  |   (296)  all_44_2 = all_8_2
% 217.80/36.65  | 
% 217.80/36.65  | SIMP: (296) implies:
% 217.80/36.65  |   (297)  all_44_2 = all_8_2
% 217.80/36.65  | 
% 217.80/36.65  | COMBINE_EQS: (273), (279) imply:
% 217.80/36.65  |   (298)  all_20_2 = all_10_2
% 217.80/36.65  | 
% 217.80/36.65  | SIMP: (298) implies:
% 217.80/36.65  |   (299)  all_20_2 = all_10_2
% 217.80/36.65  | 
% 217.80/36.65  | COMBINE_EQS: (292), (293) imply:
% 217.80/36.65  |   (300)  all_42_2 = all_34_2
% 217.80/36.65  | 
% 217.80/36.65  | SIMP: (300) implies:
% 217.80/36.65  |   (301)  all_42_2 = all_34_2
% 217.80/36.65  | 
% 217.80/36.65  | COMBINE_EQS: (291), (292) imply:
% 217.80/36.65  |   (302)  all_38_2 = all_34_2
% 217.80/36.65  | 
% 217.80/36.65  | SIMP: (302) implies:
% 217.80/36.65  |   (303)  all_38_2 = all_34_2
% 217.80/36.65  | 
% 217.80/36.65  | COMBINE_EQS: (262), (297) imply:
% 217.80/36.65  |   (304)  all_26_2 = all_8_2
% 217.80/36.65  | 
% 217.80/36.65  | SIMP: (304) implies:
% 217.80/36.65  |   (305)  all_26_2 = all_8_2
% 217.80/36.65  | 
% 217.80/36.65  | COMBINE_EQS: (282), (301) imply:
% 217.80/36.65  |   (306)  all_34_2 = all_24_2
% 217.80/36.65  | 
% 217.80/36.65  | SIMP: (306) implies:
% 217.80/36.65  |   (307)  all_34_2 = all_24_2
% 217.80/36.65  | 
% 217.80/36.65  | COMBINE_EQS: (294), (295) imply:
% 217.80/36.65  |   (308)  all_32_2 = all_4_2
% 217.80/36.65  | 
% 217.80/36.65  | SIMP: (308) implies:
% 217.80/36.65  |   (309)  all_32_2 = all_4_2
% 217.80/36.65  | 
% 217.80/36.65  | COMBINE_EQS: (249), (303) imply:
% 217.80/36.65  |   (310)  all_34_2 = all_6_2
% 217.80/36.65  | 
% 217.80/36.65  | SIMP: (310) implies:
% 217.80/36.65  |   (311)  all_34_2 = all_6_2
% 217.80/36.65  | 
% 217.80/36.65  | COMBINE_EQS: (271), (272) imply:
% 217.80/36.65  |   (312)  all_28_2 = all_20_2
% 217.80/36.65  | 
% 217.80/36.65  | COMBINE_EQS: (271), (288) imply:
% 217.80/36.65  |   (313)  all_28_2 = all_18_2
% 217.80/36.65  | 
% 217.80/36.65  | COMBINE_EQS: (307), (311) imply:
% 217.80/36.65  |   (314)  all_24_2 = all_6_2
% 217.80/36.65  | 
% 217.80/36.65  | SIMP: (314) implies:
% 217.80/36.65  |   (315)  all_24_2 = all_6_2
% 217.80/36.65  | 
% 217.80/36.65  | COMBINE_EQS: (239), (240) imply:
% 217.80/36.65  |   (316)  all_30_2 = all_22_2
% 217.80/36.65  | 
% 217.80/36.65  | SIMP: (316) implies:
% 217.80/36.65  |   (317)  all_30_2 = all_22_2
% 217.80/36.65  | 
% 217.80/36.65  | COMBINE_EQS: (240), (309) imply:
% 217.80/36.65  |   (318)  all_22_2 = all_4_2
% 217.80/36.65  | 
% 217.80/36.65  | COMBINE_EQS: (238), (317) imply:
% 217.80/36.65  |   (319)  all_22_2 = all_12_2
% 217.80/36.65  | 
% 217.80/36.65  | SIMP: (319) implies:
% 217.80/36.65  |   (320)  all_22_2 = all_12_2
% 217.80/36.65  | 
% 217.80/36.65  | COMBINE_EQS: (312), (313) imply:
% 217.80/36.65  |   (321)  all_20_2 = all_18_2
% 217.80/36.65  | 
% 217.80/36.65  | SIMP: (321) implies:
% 217.80/36.65  |   (322)  all_20_2 = all_18_2
% 217.80/36.65  | 
% 217.80/36.65  | COMBINE_EQS: (261), (305) imply:
% 217.80/36.65  |   (323)  all_16_2 = all_8_2
% 217.80/36.65  | 
% 217.80/36.65  | SIMP: (323) implies:
% 217.80/36.65  |   (324)  all_16_2 = all_8_2
% 217.80/36.65  | 
% 217.80/36.65  | COMBINE_EQS: (318), (320) imply:
% 217.80/36.65  |   (325)  all_12_2 = all_4_2
% 217.80/36.65  | 
% 217.80/36.65  | COMBINE_EQS: (299), (322) imply:
% 217.80/36.65  |   (326)  all_18_2 = all_10_2
% 217.80/36.65  | 
% 217.80/36.65  | SIMP: (326) implies:
% 217.80/36.65  |   (327)  all_18_2 = all_10_2
% 217.80/36.65  | 
% 217.80/36.65  | COMBINE_EQS: (260), (324) imply:
% 217.80/36.65  |   (328)  all_14_2 = all_8_2
% 217.80/36.65  | 
% 217.80/36.65  | COMBINE_EQS: (313), (327) imply:
% 217.80/36.65  |   (329)  all_28_2 = all_10_2
% 217.80/36.65  | 
% 217.80/36.65  | COMBINE_EQS: (238), (325) imply:
% 217.80/36.65  |   (330)  all_30_2 = all_4_2
% 217.80/36.65  | 
% 217.80/36.65  | COMBINE_EQS: (271), (329) imply:
% 217.80/36.65  |   (331)  all_36_2 = all_10_2
% 217.80/36.65  | 
% 217.80/36.65  | COMBINE_EQS: (282), (315) imply:
% 217.80/36.65  |   (332)  all_42_2 = all_6_2
% 217.80/36.65  | 
% 217.80/36.65  | COMBINE_EQS: (292), (311) imply:
% 217.80/36.65  |   (333)  all_46_2 = all_6_2
% 217.80/36.65  | 
% 217.80/36.65  | COMBINE_EQS: (250), (333) imply:
% 217.80/36.65  |   (334)  all_53_10 = all_6_2
% 217.80/36.65  | 
% 217.80/36.65  | COMBINE_EQS: (275), (327) imply:
% 217.80/36.65  |   (335)  all_53_0 = all_10_2
% 217.80/36.65  | 
% 217.80/36.65  | COMBINE_EQS: (254), (332) imply:
% 217.80/36.65  |   (336)  all_55_10 = all_6_2
% 217.80/36.65  | 
% 217.80/36.65  | REDUCE: (156), (335) imply:
% 217.80/36.65  |   (337)   ~ (all_53_1 = all_10_2)
% 217.80/36.65  | 
% 217.80/36.65  | SIMP: (337) implies:
% 217.80/36.65  |   (338)   ~ (all_53_1 = all_10_2)
% 217.80/36.65  | 
% 217.80/36.65  | REDUCE: (155), (335) imply:
% 217.80/36.65  |   (339)   ~ (all_53_2 = all_10_2)
% 217.80/36.65  | 
% 217.80/36.65  | SIMP: (339) implies:
% 217.80/36.65  |   (340)   ~ (all_53_2 = all_10_2)
% 217.80/36.65  | 
% 217.80/36.65  | REDUCE: (154), (335) imply:
% 217.80/36.65  |   (341)   ~ (all_53_3 = all_10_2)
% 217.80/36.65  | 
% 217.80/36.65  | SIMP: (341) implies:
% 217.80/36.65  |   (342)   ~ (all_53_3 = all_10_2)
% 217.80/36.65  | 
% 217.80/36.65  | REDUCE: (153), (335) imply:
% 217.80/36.65  |   (343)   ~ (all_53_4 = all_10_2)
% 217.80/36.65  | 
% 217.80/36.65  | SIMP: (343) implies:
% 217.80/36.65  |   (344)   ~ (all_53_4 = all_10_2)
% 217.80/36.65  | 
% 217.80/36.65  | REDUCE: (152), (335) imply:
% 217.80/36.65  |   (345)   ~ (all_53_8 = all_10_2)
% 217.80/36.65  | 
% 217.80/36.65  | SIMP: (345) implies:
% 217.80/36.65  |   (346)   ~ (all_53_8 = all_10_2)
% 217.80/36.65  | 
% 217.80/36.65  | REDUCE: (151), (335) imply:
% 217.80/36.65  |   (347)   ~ (all_53_12 = all_10_2)
% 217.80/36.65  | 
% 217.80/36.65  | SIMP: (347) implies:
% 217.80/36.65  |   (348)   ~ (all_53_12 = all_10_2)
% 217.80/36.65  | 
% 217.80/36.65  | REDUCE: (148), (281) imply:
% 217.80/36.65  |   (349)   ~ (all_53_1 = all_8_2)
% 217.80/36.65  | 
% 217.80/36.65  | REDUCE: (143), (334) imply:
% 217.80/36.65  |   (350)   ~ (all_53_2 = all_6_2)
% 217.80/36.65  | 
% 217.80/36.65  | REDUCE: (139), (286) imply:
% 217.80/36.65  |   (351)   ~ (all_53_3 = all_4_2)
% 217.80/36.65  | 
% 217.80/36.65  | REDUCE: (138), (281) imply:
% 217.80/36.65  |   (352)   ~ (all_53_4 = all_8_2)
% 217.80/36.65  | 
% 217.80/36.65  | REDUCE: (133), (281) imply:
% 217.80/36.65  |   (353)   ~ (all_53_6 = all_8_2)
% 217.80/36.65  | 
% 217.80/36.65  | SIMP: (353) implies:
% 217.80/36.65  |   (354)   ~ (all_53_6 = all_8_2)
% 217.80/36.65  | 
% 217.80/36.65  | REDUCE: (132), (281) imply:
% 217.80/36.65  |   (355)   ~ (all_53_7 = all_8_2)
% 217.80/36.65  | 
% 217.80/36.65  | SIMP: (355) implies:
% 217.80/36.65  |   (356)   ~ (all_53_7 = all_8_2)
% 217.80/36.65  | 
% 217.80/36.65  | REDUCE: (131), (281) imply:
% 217.80/36.65  |   (357)   ~ (all_53_9 = all_8_2)
% 217.80/36.65  | 
% 217.80/36.65  | SIMP: (357) implies:
% 217.80/36.65  |   (358)   ~ (all_53_9 = all_8_2)
% 217.80/36.65  | 
% 217.80/36.65  | REDUCE: (130), (281) imply:
% 217.80/36.65  |   (359)   ~ (all_53_13 = all_8_2)
% 217.80/36.65  | 
% 217.80/36.65  | SIMP: (359) implies:
% 217.80/36.66  |   (360)   ~ (all_53_13 = all_8_2)
% 217.80/36.66  | 
% 217.80/36.66  | REDUCE: (128), (334) imply:
% 217.80/36.66  |   (361)   ~ (all_53_6 = all_6_2)
% 217.80/36.66  | 
% 217.80/36.66  | REDUCE: (125), (286) imply:
% 217.80/36.66  |   (362)   ~ (all_53_7 = all_4_2)
% 217.80/36.66  | 
% 217.80/36.66  | REDUCE: (123), (334) imply:
% 217.80/36.66  |   (363)   ~ (all_53_8 = all_6_2)
% 217.80/36.66  | 
% 217.80/36.66  | REDUCE: (120), (334) imply:
% 217.80/36.66  |   (364)   ~ (all_53_9 = all_6_2)
% 217.80/36.66  | 
% 217.80/36.66  | REDUCE: (117), (334) imply:
% 217.80/36.66  |   (365)   ~ (all_53_11 = all_6_2)
% 217.80/36.66  | 
% 217.80/36.66  | SIMP: (365) implies:
% 217.80/36.66  |   (366)   ~ (all_53_11 = all_6_2)
% 217.80/36.66  | 
% 217.80/36.66  | REDUCE: (116), (334) imply:
% 217.80/36.66  |   (367)   ~ (all_53_14 = all_6_2)
% 217.80/36.66  | 
% 217.80/36.66  | SIMP: (367) implies:
% 217.80/36.66  |   (368)   ~ (all_53_14 = all_6_2)
% 217.80/36.66  | 
% 217.80/36.66  | REDUCE: (115), (286) imply:
% 217.80/36.66  |   (369)   ~ (all_53_11 = all_4_2)
% 217.80/36.66  | 
% 217.80/36.66  | REDUCE: (112), (286) imply:
% 217.80/36.66  |   (370)   ~ (all_53_12 = all_4_2)
% 217.80/36.66  | 
% 217.80/36.66  | REDUCE: (110), (286) imply:
% 217.80/36.66  |   (371)   ~ (all_53_13 = all_4_2)
% 217.80/36.66  | 
% 217.80/36.66  | REDUCE: (109), (286) imply:
% 217.80/36.66  |   (372)   ~ (all_53_14 = all_4_2)
% 217.80/36.66  | 
% 217.80/36.66  | BETA: splitting (37) gives:
% 217.80/36.66  | 
% 217.80/36.66  | Case 1:
% 217.80/36.66  | | 
% 217.80/36.66  | |   (373)   ~ (all_4_2 = e2)
% 217.80/36.66  | | 
% 217.80/36.66  | | BETA: splitting (40) gives:
% 217.80/36.66  | | 
% 217.80/36.66  | | Case 1:
% 217.80/36.66  | | | 
% 217.80/36.66  | | |   (374)   ~ (all_6_2 = e3)
% 217.80/36.66  | | | 
% 217.80/36.66  | | | BETA: splitting (43) gives:
% 217.80/36.66  | | | 
% 217.80/36.66  | | | Case 1:
% 217.80/36.66  | | | | 
% 217.80/36.66  | | | |   (375)   ~ (all_8_2 = e3)
% 217.80/36.66  | | | | 
% 217.80/36.66  | | | | BETA: splitting (46) gives:
% 217.80/36.66  | | | | 
% 217.80/36.66  | | | | Case 1:
% 217.80/36.66  | | | | | 
% 217.80/36.66  | | | | |   (376)   ~ (all_10_2 = e1)
% 217.80/36.66  | | | | | 
% 217.80/36.66  | | | | | BETA: splitting (49) gives:
% 217.80/36.66  | | | | | 
% 217.80/36.66  | | | | | Case 1:
% 217.80/36.66  | | | | | | 
% 217.80/36.66  | | | | | |   (377)   ~ (all_12_2 = e3)
% 217.80/36.66  | | | | | | 
% 217.80/36.66  | | | | | | REDUCE: (325), (377) imply:
% 217.80/36.66  | | | | | |   (378)   ~ (all_4_2 = e3)
% 217.80/36.66  | | | | | | 
% 217.80/36.66  | | | | | | BETA: splitting (52) gives:
% 217.80/36.66  | | | | | | 
% 217.80/36.66  | | | | | | Case 1:
% 217.80/36.66  | | | | | | | 
% 217.80/36.66  | | | | | | |   (379)   ~ (all_14_2 = e0)
% 217.80/36.66  | | | | | | | 
% 217.80/36.66  | | | | | | | REDUCE: (328), (379) imply:
% 217.80/36.66  | | | | | | |   (380)   ~ (all_8_2 = e0)
% 217.80/36.66  | | | | | | | 
% 217.80/36.66  | | | | | | | BETA: splitting (55) gives:
% 217.80/36.66  | | | | | | | 
% 217.80/36.66  | | | | | | | Case 1:
% 217.80/36.66  | | | | | | | | 
% 217.80/36.66  | | | | | | | |   (381)   ~ (all_16_2 = e1)
% 217.80/36.66  | | | | | | | | 
% 217.80/36.66  | | | | | | | | REDUCE: (324), (381) imply:
% 217.80/36.66  | | | | | | | |   (382)   ~ (all_8_2 = e1)
% 217.80/36.66  | | | | | | | | 
% 217.80/36.66  | | | | | | | | BETA: splitting (200) gives:
% 217.80/36.66  | | | | | | | | 
% 217.80/36.66  | | | | | | | | Case 1:
% 217.80/36.66  | | | | | | | | | 
% 217.80/36.66  | | | | | | | | |   (383)  all_55_5 = e3
% 217.80/36.66  | | | | | | | | | 
% 217.80/36.66  | | | | | | | | | COMBINE_EQS: (266), (383) imply:
% 217.80/36.66  | | | | | | | | |   (384)  all_8_2 = e3
% 217.80/36.66  | | | | | | | | | 
% 217.80/36.66  | | | | | | | | | REDUCE: (375), (384) imply:
% 217.80/36.66  | | | | | | | | |   (385)  $false
% 217.80/36.66  | | | | | | | | | 
% 217.80/36.66  | | | | | | | | | CLOSE: (385) is inconsistent.
% 217.80/36.66  | | | | | | | | | 
% 217.80/36.66  | | | | | | | | Case 2:
% 217.80/36.66  | | | | | | | | | 
% 217.80/36.66  | | | | | | | | |   (386)   ~ (all_55_5 = e3)
% 217.80/36.66  | | | | | | | | |   (387)  all_55_5 = e2 | all_55_5 = e1 | all_55_5 = e0
% 217.80/36.66  | | | | | | | | | 
% 217.80/36.66  | | | | | | | | | BETA: splitting (387) gives:
% 217.80/36.66  | | | | | | | | | 
% 217.80/36.66  | | | | | | | | | Case 1:
% 217.80/36.66  | | | | | | | | | | 
% 217.80/36.66  | | | | | | | | | |   (388)  all_55_5 = e2
% 217.80/36.66  | | | | | | | | | | 
% 217.80/36.66  | | | | | | | | | | COMBINE_EQS: (266), (388) imply:
% 217.80/36.66  | | | | | | | | | |   (389)  all_8_2 = e2
% 217.80/36.66  | | | | | | | | | | 
% 217.80/36.66  | | | | | | | | | | REDUCE: (349), (389) imply:
% 217.80/36.66  | | | | | | | | | |   (390)   ~ (all_53_1 = e2)
% 217.80/36.66  | | | | | | | | | | 
% 217.80/36.66  | | | | | | | | | | REDUCE: (352), (389) imply:
% 217.80/36.66  | | | | | | | | | |   (391)   ~ (all_53_4 = e2)
% 217.80/36.66  | | | | | | | | | | 
% 217.80/36.66  | | | | | | | | | | REDUCE: (354), (389) imply:
% 217.80/36.66  | | | | | | | | | |   (392)   ~ (all_53_6 = e2)
% 217.80/36.66  | | | | | | | | | | 
% 217.80/36.66  | | | | | | | | | | REDUCE: (356), (389) imply:
% 217.80/36.66  | | | | | | | | | |   (393)   ~ (all_53_7 = e2)
% 217.80/36.66  | | | | | | | | | | 
% 217.80/36.66  | | | | | | | | | | REDUCE: (358), (389) imply:
% 217.80/36.66  | | | | | | | | | |   (394)   ~ (all_53_9 = e2)
% 217.80/36.66  | | | | | | | | | | 
% 217.80/36.66  | | | | | | | | | | REDUCE: (360), (389) imply:
% 217.80/36.66  | | | | | | | | | |   (395)   ~ (all_53_13 = e2)
% 217.80/36.66  | | | | | | | | | | 
% 217.80/36.66  | | | | | | | | | | REDUCE: (375), (389) imply:
% 217.80/36.66  | | | | | | | | | |   (396)   ~ (e3 = e2)
% 217.80/36.66  | | | | | | | | | | 
% 217.80/36.66  | | | | | | | | | | BETA: splitting (224) gives:
% 217.80/36.66  | | | | | | | | | | 
% 217.80/36.66  | | | | | | | | | | Case 1:
% 217.80/36.66  | | | | | | | | | | | 
% 217.80/36.66  | | | | | | | | | | |   (397)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 217.80/36.66  | | | | | | | | | | |            & op(e2, e2) = e2)
% 217.80/36.66  | | | | | | | | | | | 
% 217.80/36.66  | | | | | | | | | | | BETA: splitting (397) gives:
% 217.80/36.66  | | | | | | | | | | | 
% 217.80/36.66  | | | | | | | | | | | Case 1:
% 217.80/36.66  | | | | | | | | | | | | 
% 217.80/36.66  | | | | | | | | | | | |   (398)  all_57_2 = e2 & op(e2, e3) = e2
% 217.80/36.66  | | | | | | | | | | | | 
% 217.80/36.66  | | | | | | | | | | | | REF_CLOSE: (168), (390), (398), (function-axioms) are
% 217.80/36.66  | | | | | | | | | | | |            inconsistent by sub-proof #2504.
% 217.80/36.66  | | | | | | | | | | | | 
% 217.80/36.66  | | | | | | | | | | | Case 2:
% 217.80/36.66  | | | | | | | | | | | | 
% 217.80/36.66  | | | | | | | | | | | |   (399)  all_57_3 = e2 & op(e2, e2) = e2
% 217.80/36.66  | | | | | | | | | | | | 
% 217.80/36.66  | | | | | | | | | | | | ALPHA: (399) implies:
% 217.80/36.66  | | | | | | | | | | | |   (400)  all_57_3 = e2
% 217.80/36.66  | | | | | | | | | | | |   (401)  op(e2, e2) = e2
% 217.80/36.66  | | | | | | | | | | | | 
% 217.80/36.66  | | | | | | | | | | | | BETA: splitting (58) gives:
% 217.80/36.66  | | | | | | | | | | | | 
% 217.80/36.66  | | | | | | | | | | | | Case 1:
% 217.80/36.66  | | | | | | | | | | | | | 
% 217.80/36.66  | | | | | | | | | | | | |   (402)   ~ (all_18_2 = e0)
% 217.80/36.66  | | | | | | | | | | | | | 
% 217.80/36.66  | | | | | | | | | | | | | REDUCE: (327), (402) imply:
% 217.80/36.66  | | | | | | | | | | | | |   (403)   ~ (all_10_2 = e0)
% 217.80/36.66  | | | | | | | | | | | | | 
% 217.80/36.66  | | | | | | | | | | | | | BETA: splitting (61) gives:
% 217.80/36.66  | | | | | | | | | | | | | 
% 217.80/36.66  | | | | | | | | | | | | | Case 1:
% 217.80/36.66  | | | | | | | | | | | | | | 
% 217.80/36.66  | | | | | | | | | | | | | |   (404)   ~ (all_20_2 = e2)
% 217.80/36.66  | | | | | | | | | | | | | | 
% 217.80/36.66  | | | | | | | | | | | | | | REDUCE: (299), (404) imply:
% 217.80/36.67  | | | | | | | | | | | | | |   (405)   ~ (all_10_2 = e2)
% 217.80/36.67  | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | BETA: splitting (205) gives:
% 217.80/36.67  | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | Case 1:
% 217.80/36.67  | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | |   (406)  all_55_0 = e3
% 217.80/36.67  | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | COMBINE_EQS: (277), (406) imply:
% 217.80/36.67  | | | | | | | | | | | | | | |   (407)  all_10_2 = e3
% 217.80/36.67  | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | REDUCE: (338), (407) imply:
% 217.80/36.67  | | | | | | | | | | | | | | |   (408)   ~ (all_53_1 = e3)
% 217.80/36.67  | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | REDUCE: (340), (407) imply:
% 217.80/36.67  | | | | | | | | | | | | | | |   (409)   ~ (all_53_2 = e3)
% 217.80/36.67  | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | REDUCE: (342), (407) imply:
% 217.80/36.67  | | | | | | | | | | | | | | |   (410)   ~ (all_53_3 = e3)
% 217.80/36.67  | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | REDUCE: (344), (407) imply:
% 217.80/36.67  | | | | | | | | | | | | | | |   (411)   ~ (all_53_4 = e3)
% 217.80/36.67  | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | REDUCE: (346), (407) imply:
% 217.80/36.67  | | | | | | | | | | | | | | |   (412)   ~ (all_53_8 = e3)
% 217.80/36.67  | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | REDUCE: (348), (407) imply:
% 217.80/36.67  | | | | | | | | | | | | | | |   (413)   ~ (all_53_12 = e3)
% 217.80/36.67  | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | REDUCE: (45), (407) imply:
% 217.80/36.67  | | | | | | | | | | | | | | |   (414)  op(e3, e3) = e3
% 217.80/36.67  | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 217.80/36.67  | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | Case 1:
% 217.80/36.67  | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | |   (415)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 217.80/36.67  | | | | | | | | | | | | | | | |            & op(e3, e2) = e3)
% 217.80/36.67  | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | BETA: splitting (415) gives:
% 217.80/36.67  | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.67  | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | |   (416)  all_57_0 = e3 & op(e3, e3) = e3
% 217.80/36.67  | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | ALPHA: (416) implies:
% 217.80/36.67  | | | | | | | | | | | | | | | | |   (417)  all_57_0 = e3
% 217.80/36.67  | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 217.80/36.67  | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.67  | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | |   (418)   ~ (all_24_2 = e0)
% 217.80/36.67  | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | REDUCE: (315), (418) imply:
% 217.80/36.67  | | | | | | | | | | | | | | | | | |   (419)   ~ (all_6_2 = e0)
% 217.80/36.67  | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | BETA: splitting (76) gives:
% 217.80/36.67  | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | |   (420)   ~ (all_30_2 = e1)
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | REDUCE: (330), (420) imply:
% 217.80/36.67  | | | | | | | | | | | | | | | | | | |   (421)   ~ (all_4_2 = e1)
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | |   (422)  all_55_15 = e3
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (378), (422) are inconsistent by sub-proof
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | |            #2503.
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | Case 2:
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | |   (423)   ~ (all_55_15 = e3)
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | |   (424)  all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | BETA: splitting (424) gives:
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | |   (425)  all_55_15 = e2
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (373), (425) are inconsistent by sub-proof
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | |            #2502.
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | Case 2:
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | |   (426)   ~ (all_55_15 = e2)
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | |   (427)  all_55_15 = e1 | all_55_15 = e0
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (427) gives:
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | |   (428)  all_55_15 = e1
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (421), (428) are inconsistent by sub-proof
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | |            #2501.
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | |   (429)  all_55_15 = e0
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (429) imply:
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | |   (430)  all_4_2 = e0
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | SIMP: (430) implies:
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | |   (431)  all_4_2 = e0
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (362), (431) imply:
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | |   (432)   ~ (all_53_7 = e0)
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (369), (431) imply:
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | |   (433)   ~ (all_53_11 = e0)
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (370), (431) imply:
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | |   (434)   ~ (all_53_12 = e0)
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (371), (431) imply:
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | |   (435)   ~ (all_53_13 = e0)
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (372), (431) imply:
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | |   (436)   ~ (all_53_14 = e0)
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (378), (431) imply:
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | |   (437)   ~ (e3 = e0)
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (373), (431) imply:
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | |   (438)   ~ (e2 = e0)
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (421), (431) imply:
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | |   (439)   ~ (e1 = e0)
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | |   (440)  all_57_15 = e0 & op(e0, e0) = e0
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (440) implies:
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | |   (441)  all_57_15 = e0
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | |   (442)  op(e0, e0) = e0
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (88) gives:
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | |   (443)   ~ (all_38_2 = e2)
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (249), (443) imply:
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | |   (444)   ~ (all_6_2 = e2)
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | |   (445)  all_55_10 = e3
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (374), (445) are inconsistent by sub-proof
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | |            #2500.
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | |   (446)   ~ (all_55_10 = e3)
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | |   (447)  all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (447) gives:
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | |   (448)  all_55_10 = e2
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (444), (448) are inconsistent by sub-proof
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | |            #2499.
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | |   (449)   ~ (all_55_10 = e2)
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | |   (450)  all_55_10 = e1 | all_55_10 = e0
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (450) gives:
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (451)  all_55_10 = e1
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (336), (451) imply:
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (452)  all_6_2 = e1
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (452) implies:
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (453)  all_6_2 = e1
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (350), (453) imply:
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (454)   ~ (all_53_2 = e1)
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (361), (453) imply:
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (455)   ~ (all_53_6 = e1)
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (364), (453) imply:
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (456)   ~ (all_53_9 = e1)
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (366), (453) imply:
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (457)   ~ (all_53_11 = e1)
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (368), (453) imply:
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (458)   ~ (all_53_14 = e1)
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (374), (453) imply:
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (459)   ~ (e3 = e1)
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (444), (453) imply:
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (460)   ~ (e2 = e1)
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (453) imply:
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (461)  op(e1, e1) = e1
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (462)  all_55_7 = e3
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (462) imply:
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (463)  all_53_13 = e3
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (463) implies:
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (464)  all_53_13 = e3
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (464) imply:
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (465)   ~ (all_53_9 = e3)
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (111), (464) imply:
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (466)   ~ (all_53_14 = e3)
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (466) implies:
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (467)   ~ (all_53_14 = e3)
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (468)  all_55_6 = e3
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (465), (468) are inconsistent by sub-proof
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2498.
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (469)   ~ (all_55_6 = e3)
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (470)  all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (471)  all_55_11 = e3
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (467), (471) are inconsistent by sub-proof
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2497.
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (472)   ~ (all_55_11 = e3)
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (473)  all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (474)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (474) gives:
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (475)  all_57_2 = e1 & op(e2, e3) = e1
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (475) implies:
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (476)  all_57_2 = e1
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (473) gives:
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (477)  all_55_11 = e2
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (477) imply:
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (478)  all_53_14 = e2
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (478) implies:
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (479)  all_53_14 = e2
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (142), (479) imply:
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (480)   ~ (all_53_2 = e2)
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (479) imply:
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (481)   ~ (all_53_12 = e2)
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (482)  all_55_8 = e3
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (409), (482) are inconsistent by sub-proof
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2496.
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (483)  all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (484)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e3)
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (484) gives:
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (485)  all_57_4 = e3 & op(e3, e1) = e3
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (485) implies:
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (486)  all_57_4 = e3
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (235),
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (414), (486), (function-axioms) are inconsistent
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2474.
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (487)  all_57_5 = e3 & op(e2, e1) = e3
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (487) implies:
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (488)  all_57_5 = e3
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (165), (222), (401), (435), (476),
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (488), (function-axioms) are inconsistent by
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2469.
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (489)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e1) = e3)
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (489) gives:
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (490)  all_57_8 = e3 & op(e1, e1) = e3
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (490) implies:
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (491)  op(e1, e1) = e3
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (374), (491), (function-axioms) are
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2468.
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (492)  all_57_14 = e3 & op(e0, e1) = e3
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (492) implies:
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (493)  all_57_14 = e3
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (494)  op(e0, e1) = e3
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (495)  all_55_3 = e3
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (495) imply:
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (496)  all_53_12 = e3
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (413), (496) imply:
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (497)  $false
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (497) is inconsistent.
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (498)   ~ (all_55_3 = e3)
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (499)  all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (500)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e3)
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (500) gives:
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (501)  all_57_6 = e3 & op(e1, e3) = e3
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (501) implies:
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (502)  all_57_6 = e3
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (230), (234), (414),
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (476), (502), (function-axioms) are inconsistent
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2459.
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (503)  all_57_7 = e3 & op(e1, e2) = e3
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (503) implies:
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (504)  all_57_7 = e3
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (505)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e2, e0) = e3)
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (505) gives:
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (506)  all_57_9 = e3 & op(e3, e0) = e3
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (506) implies:
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (507)  op(e3, e0) = e3
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (413), (507), (function-axioms) are
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2458.
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (508)  all_57_10 = e3 & op(e2, e0) = e3
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (508) implies:
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (509)  all_57_10 = e3
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (510)  op(e2, e0) = e3
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (511)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e0)
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (401), (476), (511), (function-axioms)
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2457.
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (512)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e2, e0) = e0)
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (512) gives:
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (513)  all_57_5 = e0 & op(e2, e1) = e0
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (513) implies:
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (514)  all_57_5 = e0
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (515)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e2)
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (171), (391), (414), (515), (function-axioms)
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2455.
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (516)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e2)
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (516) gives:
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (517)  all_57_4 = e2 & op(e3, e1) = e2
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (517) implies:
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (518)  all_57_4 = e2
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (519)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (169), (231),
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (235), (237), (395), (413), (414), (434),
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (518), (519), (function-axioms) are inconsistent
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2431.
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (520)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (520) gives:
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (521)  all_57_11 = e2 & op(e1, e0) = e2
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (521) implies:
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (522)  all_57_11 = e2
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (523)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (523) gives:
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (524)  all_57_12 = e2 & op(e0, e3) = e2
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (524) implies:
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (525)  all_57_12 = e2
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (526)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e0)
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (526) gives:
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (527)  all_57_1 = e0 & op(e3, e2) = e0
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (527) implies:
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (528)  all_57_1 = e0
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (529)  op(e3, e2) = e0
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (530)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e1)
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (414), (528), (530), (function-axioms)
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2445.
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (531)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e1)
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (531) gives:
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (532)  all_57_4 = e1 & op(e3, e1) = e1
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (532) implies:
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (533)  all_57_4 = e1
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (218), (220),
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (221), (374), (419), (461), (533),
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2407.
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (534)  all_57_9 = e1 & op(e3, e0) = e1
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (534) implies:
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (535)  all_57_9 = e1
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (483) gives:
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (536)  all_55_8 = e2
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (480), (536) are inconsistent by sub-proof
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2406.
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (537)  all_55_8 = e1 | all_55_8 = e0
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (538)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e0)
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (538) gives:
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (539)  all_57_0 = e0 & op(e3, e3) = e0
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (539) implies:
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (540)  op(e3, e3) = e0
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (9), (169), (235), (237), (413),
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (528), (535), (540), (function-axioms) are
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2400.
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (541)  all_57_2 = e0 & op(e2, e3) = e0
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (476), (541) are inconsistent by sub-proof
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2467.
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (542)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e3) = e0)
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (542) gives:
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (543)  all_57_6 = e0 & op(e1, e3) = e0
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (543) implies:
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (544)  all_57_6 = e0
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (545)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (545) gives:
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (546)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_52_7)
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (546) implies:
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (547)  op(e3, e2) = all_52_3
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (548)  op(all_52_3, all_52_3) = e2
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (442), (529), (547), (548), (function-axioms)
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2399.
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (549)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 217.80/36.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_52_15)
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (549) implies:
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (550)  op(e2, e0) = all_52_15
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (551)  op(all_52_15, all_52_15) = e0
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (470) gives:
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (552)  all_55_6 = e2
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (394), (552) are inconsistent by sub-proof
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2398.
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (553)   ~ (all_55_6 = e2)
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (554)  all_55_6 = e1 | all_55_6 = e0
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (554) gives:
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (555)  all_55_6 = e1
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (555) imply:
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (556)  all_53_9 = e1
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (456), (556) imply:
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (557)  $false
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (557) is inconsistent.
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (558)  all_55_6 = e0
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (558) imply:
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (559)  all_53_9 = e0
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3,
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_15, e0, e2, simplifying with (510), (550)
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (560)  all_52_15 = e3
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (551), (560) imply:
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (561)  op(e3, e3) = e0
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (234), (236), (476),
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (544), (561), (function-axioms) are inconsistent
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2390.
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (562)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_21) = e1 & op(all_52_23, all_52_23) =
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(all_52_25, all_52_25) = e3 &
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_29) = e1 & op(all_52_31, all_52_31) =
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_29) & $i(all_52_31))
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (562) gives:
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (563)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_52_23)
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (563) implies:
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (564)  op(e1, e0) = all_52_23
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (565)  op(all_52_23, all_52_23) = e0
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (216), (218),
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (219), (220), (221), (230), (232), (374), (401),
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (414), (461), (493), (504), (518), (525), (564),
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (565), (function-axioms) are inconsistent by
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2368.
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (566)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_52_31)
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (566) implies:
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (567)  op(e0, e1) = all_52_29
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (568)  op(all_52_29, all_52_29) = e1
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (499) gives:
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (569)  all_55_3 = e2
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (569) imply:
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (570)  all_53_12 = e2
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (481), (570) imply:
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (571)  $false
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (571) is inconsistent.
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (572)  all_55_3 = e1 | all_55_3 = e0
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (572) gives:
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (573)  all_55_3 = e1
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (573) imply:
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (574)  all_53_12 = e1
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3,
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_29, e1, e0, simplifying with (494), (567)
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (575)  all_52_29 = e3
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (568), (575) imply:
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (576)  op(e3, e3) = e1
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (414), (576), (function-axioms) are
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2495.
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (577)  all_55_3 = e0
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (577) imply:
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (578)  all_53_12 = e0
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (434), (578) imply:
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (579)  $false
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (579) is inconsistent.
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (580)  all_57_12 = e0 & op(e0, e3) = e0
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (580) implies:
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (581)  op(e0, e3) = e0
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (145), (160), (257), (454), (537), (581),
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2365.
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (582)  all_57_3 = e0 & op(e2, e2) = e0
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (582) implies:
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (583)  all_57_3 = e0
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (584)  op(e2, e2) = e0
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (509), (514), (583), (584), (function-axioms) are
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2348.
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (585)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0)
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (585) gives:
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (586)  all_57_7 = e0 & op(e1, e2) = e0
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (586) implies:
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (587)  all_57_7 = e0
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (504), (587) imply:
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (588)  e3 = e0
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (493), (588) imply:
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (589)  all_57_14 = e0
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (523) gives:
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (161), (165),
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (214), (217), (221), (222), (231), (232), (233),
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (235), (374), (401), (414), (419), (435), (436),
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (522), (525), (589), (function-axioms) are
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2336.
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (590)  all_57_13 = e2 & op(e0, e2) = e2
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (590) implies:
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (591)  op(e0, e2) = e2
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (393), (591), (function-axioms) are
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2335.
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (592)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (39), (218),
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (219), (220), (221), (373), (374), (518), (592),
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2333.
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (593)  all_57_13 = e0 & op(e0, e2) = e0
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (593) implies:
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (594)  op(e0, e2) = e0
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (432), (594), (function-axioms) are
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2332.
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (595)  all_57_13 = e2 & op(e0, e2) = e2
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (595) implies:
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (596)  op(e0, e2) = e2
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (393), (596), (function-axioms) are
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2335.
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (597)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (39), (218),
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (219), (220), (221), (373), (374), (518), (597),
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2333.
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (598)  all_57_15 = e2 & op(e0, e0) = e2
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (598) implies:
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (599)  op(e0, e0) = e2
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (373), (599), (function-axioms) are
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2334.
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (600)  all_57_9 = e2 & op(e3, e0) = e2
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (600) implies:
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (601)  op(e3, e0) = e2
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (481), (601), (function-axioms) are
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2331.
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (602)  all_57_10 = e0 & op(e2, e0) = e0
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (602) implies:
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (603)  op(e2, e0) = e0
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (435), (603), (function-axioms) are
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2470.
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (604)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e0) = e3)
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (161), (207), (208),
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (209), (467), (493), (604), (function-axioms) are
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2311.
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (605)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e1, e0) = e3)
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (161), (374), (467), (605),
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2310.
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (606)  all_55_11 = e1 | all_55_11 = e0
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (436), (458), (606) are inconsistent by
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2307.
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (607)  all_57_3 = e1 & op(e2, e2) = e1
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (607) implies:
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (608)  op(e2, e2) = e1
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (401), (608), (function-axioms) are
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2306.
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (609)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (609) gives:
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (610)  all_57_5 = e1 & op(e2, e1) = e1
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (456), (610), (function-axioms) are
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2305.
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (611)  all_57_10 = e1 & op(e2, e0) = e1
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (611) implies:
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (612)  all_57_10 = e1
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (161), (169), (213), (413), (442),
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (467), (612), (function-axioms) are inconsistent
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2302.
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (613)   ~ (all_55_7 = e3)
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (614)  all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (258), (613) imply:
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (615)   ~ (all_53_13 = e3)
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (616)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e2, e0) = e3)
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (169), (413), (615), (616),
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2300.
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (617)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e0) = e3)
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (617) gives:
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (618)  all_57_11 = e3 & op(e1, e0) = e3
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (618) implies:
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (619)  all_57_11 = e3
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (620)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e3)
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (168), (401), (408), (620), (function-axioms)
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2297.
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (621)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e2, e0) = e3)
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (621) gives:
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (622)  all_57_5 = e3 & op(e2, e1) = e3
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (622) implies:
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (623)  all_57_5 = e3
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (624)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (624) gives:
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (625)  all_57_9 = e2 & op(e3, e0) = e2
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (625) implies:
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (626)  all_57_9 = e2
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (627)  op(e3, e0) = e2
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (628)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e0)
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (628) gives:
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (629)  all_57_4 = e0 & op(e3, e1) = e0
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (629) implies:
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (630)  all_57_4 = e0
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (631)  op(e3, e1) = e0
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (632)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e2)
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (632) gives:
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (633)  all_57_4 = e2 & op(e3, e1) = e2
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (633) implies:
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (634)  all_57_4 = e2
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (169), (231), (233),
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (235), (237), (413), (414), (434), (626), (634),
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2433.
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (635)  all_57_5 = e2 & op(e2, e1) = e2
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (623), (635) are inconsistent by sub-proof
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2425.
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (636)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e1) = e2)
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (636) gives:
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (637)  all_57_8 = e2 & op(e1, e1) = e2
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (637) implies:
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (638)  op(e1, e1) = e2
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (39), (107),
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (111), (113), (114), (119), (126), (127), (129),
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (134), (135), (136), (137), (140), (141), (159),
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (160), (161), (163), (165), (166), (169), (170),
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (171), (191), (192), (194), (196), (198), (199),
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (204), (207), (208), (209), (210), (213), (214),
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (215), (218), (219), (221), (222), (223), (224),
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (225), (226), (227), (228), (229), (230), (231),
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (232), (233), (234), (235), (237), (245), (246),
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (248), (256), (258), (259), (270), (373), (374),
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (392), (393), (394), (400), (401), (411), (413),
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (414), (419), (432), (433), (434), (435), (436),
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (442), (626), (627), (638), (function-axioms) are
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2172.
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (639)  all_57_14 = e2 & op(e0, e1) = e2
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (639) implies:
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (640)  all_57_14 = e2
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (614) gives:
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (641)  all_55_7 = e2
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (395), (641) are inconsistent by sub-proof
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2171.
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (642)  all_55_7 = e1 | all_55_7 = e0
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (642) gives:
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (643)  all_55_7 = e1
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (643) imply:
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (644)  all_53_13 = e1
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (644) implies:
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (645)  all_53_13 = e1
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (645) imply:
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (646)   ~ (all_53_1 = e1)
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (114), (645) imply:
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (647)   ~ (all_53_12 = e1)
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (111), (645) imply:
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (648)   ~ (all_53_14 = e1)
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (165), (645) imply:
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (649)  op(e2, e0) = e1
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (650)  all_55_4 = e3
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (408), (650) are inconsistent by sub-proof
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2170.
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (651)  all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (652)  all_55_3 = e3
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (413), (652) are inconsistent by sub-proof
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2169.
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (653)  all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (654)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e1)
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (654) gives:
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (655)  all_57_0 = e1 & op(e3, e3) = e1
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (655) implies:
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (656)  op(e3, e3) = e1
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (414), (656), (function-axioms) are
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2495.
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (657)  all_57_1 = e1 & op(e3, e2) = e1
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (657) implies:
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (658)  all_57_1 = e1
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (653) gives:
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (659)  all_55_3 = e2
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (659) imply:
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (660)  all_53_12 = e2
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (660) implies:
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (661)  all_53_12 = e2
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (661) imply:
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (662)   ~ (all_53_14 = e2)
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (662) implies:
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (663)   ~ (all_53_14 = e2)
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (664)  all_55_11 = e3
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (664) imply:
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (665)  all_53_14 = e3
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (665) implies:
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (666)  all_53_14 = e3
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (127), (666) imply:
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (667)   ~ (all_53_6 = e3)
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (651) gives:
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (668)  all_55_4 = e2
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (390), (668) are inconsistent by sub-proof
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2168.
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (669)  all_55_4 = e1 | all_55_4 = e0
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (670)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (670) gives:
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (671)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_52_7)
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (671) implies:
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (672)  op(e3, e1) = all_52_5
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (673)  op(all_52_5, all_52_5) = e1
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (442), (631), (672), (673), (function-axioms)
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2167.
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (674)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_52_15)
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (674) implies:
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (675)  op(e2, e0) = all_52_15
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (676)  op(all_52_15, all_52_15) = e0
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (669) gives:
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (677)  all_55_4 = e1
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (646), (677) are inconsistent by sub-proof
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2166.
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (678)  all_55_4 = e0
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (678) imply:
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (679)  all_53_1 = e0
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (679) implies:
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (680)  all_53_1 = e0
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (147), (680) imply:
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (681)   ~ (all_53_9 = e0)
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (681) implies:
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (682)   ~ (all_53_9 = e0)
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (683)  all_55_6 = e3
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (683) imply:
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (684)  all_53_9 = e3
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (684) implies:
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (685)  all_53_9 = e3
% 217.80/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (119), (685) imply:
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (686)   ~ (all_53_11 = e3)
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (686) implies:
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (687)   ~ (all_53_11 = e3)
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (688)  all_55_14 = e3
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (687), (688) are inconsistent by sub-proof
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2294.
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (689)  all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (689) gives:
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_15, e0, e2, simplifying with (649), (675)
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (690)  all_52_15 = e1
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (676), (690) imply:
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (691)  op(e1, e1) = e0
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (461), (691), (function-axioms) are
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2427.
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (692)  all_55_14 = e1 | all_55_14 = e0
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (122), (170), (245), (457), (631), (692),
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2164.
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (693)  all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (394), (456), (682), (693) are inconsistent
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2160.
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (694)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_21) = e1 & op(all_52_23, all_52_23) =
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(all_52_25, all_52_25) = e3 &
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_29) = e1 & op(all_52_31, all_52_31) =
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_29) & $i(all_52_31))
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (694) gives:
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (695)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_52_23)
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (695) implies:
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (696)  op(e1, e2) = all_52_19
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (697)  op(all_52_19, all_52_19) = e2
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (698)  all_55_9 = e3
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (667), (698) are inconsistent by sub-proof
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2159.
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (699)  all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (256), (392), (442), (455), (696), (697),
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (699), (function-axioms) are inconsistent by
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2157.
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (700)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_52_31)
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (700) implies:
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (701)  op(e0, e1) = all_52_29
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (702)  op(all_52_29, all_52_29) = e1
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (703)  all_55_9 = e3
% 218.45/36.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (667), (703) are inconsistent by sub-proof
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2159.
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (704)   ~ (all_55_9 = e3)
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (705)  all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (705) gives:
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (706)  all_55_9 = e2
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (392), (706) are inconsistent by sub-proof
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2274.
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (707)   ~ (all_55_9 = e2)
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (708)  all_55_9 = e1 | all_55_9 = e0
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (708) gives:
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (709)  all_55_9 = e1
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (455), (709) are inconsistent by sub-proof
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2273.
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (710)  all_55_9 = e0
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (710) imply:
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (711)  all_53_6 = e0
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (711) implies:
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (712)  all_53_6 = e0
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (712) imply:
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (713)   ~ (all_53_2 = e0)
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (714)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (714) gives:
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (715)  all_57_12 = e3 & op(e0, e3) = e3
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (715) implies:
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (716)  all_57_12 = e3
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (717)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e1)
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (168), (414), (646), (717), (function-axioms)
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2155.
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (718)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e3) = e1)
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (718) gives:
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (719)  all_57_6 = e1 & op(e1, e3) = e1
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (719) implies:
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (720)  all_57_6 = e1
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (9), (164), (230), (234), (414),
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (713), (716), (720), (function-axioms) are
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2152.
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (721)  all_57_12 = e1 & op(e0, e3) = e1
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (721) implies:
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (722)  all_57_12 = e1
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (716), (722) are inconsistent by sub-proof
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2151.
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (723)  all_57_13 = e3 & op(e0, e2) = e3
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (723) implies:
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (724)  all_57_13 = e3
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (669) gives:
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (725)  all_55_4 = e1
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (646), (725) are inconsistent by sub-proof
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2166.
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (726)  all_55_4 = e0
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (726) imply:
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (727)  all_53_1 = e0
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (727) implies:
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (728)  all_53_1 = e0
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (147), (728) imply:
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (729)   ~ (all_53_9 = e0)
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (729) implies:
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (730)   ~ (all_53_9 = e0)
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (731)  all_55_6 = e3
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (731) imply:
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (732)  all_53_9 = e3
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (732) implies:
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (733)  all_53_9 = e3
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (119), (733) imply:
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (734)   ~ (all_53_11 = e3)
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (734) implies:
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (735)   ~ (all_53_11 = e3)
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (736)  all_55_14 = e3
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (735), (736) are inconsistent by sub-proof
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2294.
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (737)   ~ (all_55_14 = e3)
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (738)  all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (738) gives:
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (739)  all_55_14 = e2
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (739) imply:
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (740)  all_53_11 = e2
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (740) implies:
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (741)  all_53_11 = e2
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (158), (741) imply:
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (742)  op(e0, e1) = e2
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_29, e1, e0, simplifying with (701), (742)
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (743)  all_52_29 = e2
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (702), (743) imply:
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (744)  op(e2, e2) = e1
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (226), (228), (658),
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (724), (744), (function-axioms) are inconsistent
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2145.
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (745)  all_55_14 = e1 | all_55_14 = e0
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (122), (170), (245), (457), (631), (745),
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2164.
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (746)  all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (394), (456), (730), (746) are inconsistent
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2160.
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (747)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e0) = e3)
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (747) gives:
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (748)  all_57_14 = e3 & op(e0, e1) = e3
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (748) implies:
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (749)  all_57_14 = e3
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (640), (749) imply:
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (750)  e3 = e2
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (623), (750) imply:
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (751)  all_57_5 = e2
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (39), (221), (374), (630), (640), (751),
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2188.
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (752)  all_57_15 = e3 & op(e0, e0) = e3
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (752) implies:
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (753)  all_57_15 = e3
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (207), (211), (212),
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (619), (753) are inconsistent by sub-proof #2134.
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (754)  all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (436), (458), (663), (754) are inconsistent
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2133.
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (755)  all_55_3 = e1 | all_55_3 = e0
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (434), (647), (755) are inconsistent by
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2132.
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (756)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e1)
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (756) gives:
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (757)  all_57_4 = e1 & op(e3, e1) = e1
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (757) implies:
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (758)  all_57_4 = e1
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (39), (218), (221),
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (374), (419), (640), (758), (function-axioms) are
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2408.
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (759)  all_57_9 = e1 & op(e3, e0) = e1
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (647), (759), (function-axioms) are
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2131.
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (760)  all_55_7 = e0
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (435), (760) are inconsistent by sub-proof
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2130.
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (761)  all_57_5 = e0 & op(e2, e1) = e0
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (761) implies:
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (762)  all_57_5 = e0
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (165), (168), (225), (401), (408),
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (615), (762), (function-axioms) are inconsistent
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2129.
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (763)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (763) gives:
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (764)  all_57_8 = e0 & op(e1, e1) = e0
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (764) implies:
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (765)  op(e1, e1) = e0
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (461), (765), (function-axioms) are
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2427.
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (766)  all_57_14 = e0 & op(e0, e1) = e0
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (766) implies:
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (767)  all_57_14 = e0
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (159), (208),
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (209), (210), (373), (393), (441), (442), (767),
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2120.
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (768)  all_57_10 = e2 & op(e2, e0) = e2
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (395), (768), (function-axioms) are
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2432.
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (769)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (769) gives:
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (770)  all_57_11 = e2 & op(e1, e0) = e2
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (770) implies:
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (771)  all_57_11 = e2
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (619), (771) are inconsistent by sub-proof
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2119.
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (772)  all_57_15 = e2 & op(e0, e0) = e2
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (772) implies:
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (773)  op(e0, e0) = e2
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (373), (773), (function-axioms) are
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2334.
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (774)  all_57_10 = e3 & op(e2, e0) = e3
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (774) implies:
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (775)  op(e2, e0) = e3
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (615), (775), (function-axioms) are
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2301.
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (776)  all_57_15 = e3 & op(e0, e0) = e3
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (776) implies:
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (777)  op(e0, e0) = e3
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (442), (777), (function-axioms) are
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2304.
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (778)  all_55_10 = e0
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (419), (778) are inconsistent by sub-proof
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2118.
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | |   (779)  all_38_2 = e2
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (779) imply:
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | |   (780)  all_6_2 = e2
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (780) imply:
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | |   (781)  op(e1, e1) = e2
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | |   (782)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e2)
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (171), (391), (414), (782), (function-axioms)
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2455.
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | |   (783)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e2)
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (783) gives:
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | |   (784)  all_57_4 = e2 & op(e3, e1) = e2
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (784) implies:
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | |   (785)  all_57_4 = e2
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (786)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (169), (231),
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (235), (237), (395), (413), (414), (434),
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (785), (786), (function-axioms) are inconsistent
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2431.
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (787)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (787) gives:
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (788)  all_57_11 = e2 & op(e1, e0) = e2
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (788) implies:
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (789)  all_57_11 = e2
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (790)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (790) gives:
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (791)  all_57_12 = e2 & op(e0, e3) = e2
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (791) implies:
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (792)  all_57_12 = e2
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (793)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e3)
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (161), (165),
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (214), (217), (222), (231), (232), (233), (235),
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (374), (401), (414), (419), (435), (436), (789),
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (792), (793), (function-axioms) are inconsistent
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2339.
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (794)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e1) = e3)
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (794) gives:
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (795)  all_57_8 = e3 & op(e1, e1) = e3
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (795) implies:
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (796)  op(e1, e1) = e3
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (374), (796), (function-axioms) are
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2468.
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (797)  all_57_14 = e3 & op(e0, e1) = e3
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (797) implies:
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (798)  all_57_14 = e3
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (799)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e3)
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (799) gives:
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (800)  all_57_6 = e3 & op(e1, e3) = e3
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (800) implies:
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (801)  all_57_6 = e3
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (230), (232), (234),
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (414), (792), (801), (function-axioms) are
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2116.
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (802)  all_57_7 = e3 & op(e1, e2) = e3
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (802) implies:
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (803)  all_57_7 = e3
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (804)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e0)
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (804) gives:
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (805)  all_57_6 = e0 & op(e1, e3) = e0
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (805) implies:
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (806)  all_57_6 = e0
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (807)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e1)
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (807) gives:
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (808)  all_57_6 = e1 & op(e1, e3) = e1
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (808) implies:
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (809)  all_57_6 = e1
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (9), (39), (161), (214), (217),
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (374), (419), (436), (789), (809),
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2340.
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (810)  all_57_7 = e1 & op(e1, e2) = e1
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (810) implies:
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (811)  all_57_7 = e1
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (39), (217), (374), (789), (806),
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (811), (function-axioms) are inconsistent by
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2114.
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (812)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e1, e0) = e1)
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (812) gives:
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (813)  all_57_8 = e1 & op(e1, e1) = e1
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (813) implies:
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (814)  op(e1, e1) = e1
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (781), (814), (function-axioms) are
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2423.
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (815)  all_57_11 = e1 & op(e1, e0) = e1
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (815) implies:
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (816)  all_57_11 = e1
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (789), (816) are inconsistent by sub-proof
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2113.
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (817)  all_57_7 = e0 & op(e1, e2) = e0
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (817) implies:
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (818)  all_57_7 = e0
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (803), (818) imply:
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (819)  e3 = e0
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (798), (819) imply:
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (820)  all_57_14 = e0
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (161), (165),
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (214), (217), (221), (222), (231), (232), (233),
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (235), (374), (401), (414), (419), (435), (436),
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (789), (792), (820), (function-axioms) are
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2336.
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (821)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (821) gives:
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (822)  all_57_8 = e0 & op(e1, e1) = e0
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (419), (822), (function-axioms) are
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2412.
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (823)  all_57_11 = e0 & op(e1, e0) = e0
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (436), (823), (function-axioms) are
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2341.
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (824)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e1, e0) = e3)
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (824) gives:
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (825)  all_57_8 = e3 & op(e1, e1) = e3
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (825) implies:
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (826)  op(e1, e1) = e3
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (374), (826), (function-axioms) are
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2468.
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (827)  all_57_11 = e3 & op(e1, e0) = e3
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (827) implies:
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (828)  all_57_11 = e3
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (789), (828) imply:
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (829)  e3 = e2
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (829) implies:
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (830)  e3 = e2
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (798), (830) imply:
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (831)  all_57_14 = e2
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (218), (219),
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (220), (221), (374), (785), (831),
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2370.
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (832)  all_57_13 = e2 & op(e0, e2) = e2
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (832) implies:
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (833)  op(e0, e2) = e2
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (393), (833), (function-axioms) are
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2335.
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (834)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (39), (218),
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (219), (220), (221), (373), (374), (785), (834),
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2333.
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (835)  all_57_15 = e2 & op(e0, e0) = e2
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (835) implies:
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (836)  op(e0, e0) = e2
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (373), (836), (function-axioms) are
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2334.
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | |   (837)  all_57_9 = e2 & op(e3, e0) = e2
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (837) implies:
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | |   (838)  all_57_9 = e2
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | |   (839)  op(e3, e0) = e2
% 218.45/36.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (39), (107),
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | |            (111), (113), (114), (119), (126), (127), (129),
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | |            (134), (135), (136), (137), (140), (141), (159),
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | |            (160), (161), (163), (165), (166), (169), (170),
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | |            (171), (191), (192), (194), (196), (198), (199),
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | |            (204), (207), (208), (209), (210), (213), (214),
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | |            (215), (218), (219), (221), (222), (223), (224),
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | |            (225), (226), (227), (228), (229), (230), (231),
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | |            (232), (233), (234), (235), (237), (245), (246),
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | |            (248), (256), (258), (259), (270), (373), (374),
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | |            (392), (393), (394), (400), (401), (411), (413),
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | |            (414), (419), (432), (433), (434), (435), (436),
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | |            (442), (781), (838), (839), (function-axioms) are
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2172.
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | |   (840)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | |                e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (165), (169), (434), (435), (436), (840),
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | |            #2112.
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | |   (841)  all_30_2 = e1
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (330), (841) imply:
% 218.45/36.77  | | | | | | | | | | | | | | | | | | |   (842)  all_4_2 = e1
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | SIMP: (842) implies:
% 218.45/36.77  | | | | | | | | | | | | | | | | | | |   (843)  all_4_2 = e1
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | REDUCE: (362), (843) imply:
% 218.45/36.77  | | | | | | | | | | | | | | | | | | |   (844)   ~ (all_53_7 = e1)
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | REDUCE: (369), (843) imply:
% 218.45/36.77  | | | | | | | | | | | | | | | | | | |   (845)   ~ (all_53_11 = e1)
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | REDUCE: (370), (843) imply:
% 218.45/36.77  | | | | | | | | | | | | | | | | | | |   (846)   ~ (all_53_12 = e1)
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | REDUCE: (371), (843) imply:
% 218.45/36.77  | | | | | | | | | | | | | | | | | | |   (847)   ~ (all_53_13 = e1)
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | REDUCE: (372), (843) imply:
% 218.45/36.77  | | | | | | | | | | | | | | | | | | |   (848)   ~ (all_53_14 = e1)
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | REDUCE: (378), (843) imply:
% 218.45/36.77  | | | | | | | | | | | | | | | | | | |   (849)   ~ (e3 = e1)
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | REDUCE: (373), (843) imply:
% 218.45/36.77  | | | | | | | | | | | | | | | | | | |   (850)   ~ (e2 = e1)
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | REDUCE: (36), (843) imply:
% 218.45/36.77  | | | | | | | | | | | | | | | | | | |   (851)  op(e0, e0) = e1
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | BETA: splitting (88) gives:
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | |   (852)   ~ (all_38_2 = e2)
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | REDUCE: (249), (852) imply:
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | |   (853)   ~ (all_6_2 = e2)
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | |   (854)  all_55_10 = e3
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (374), (854) are inconsistent by sub-proof
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | |            #2500.
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | |   (855)   ~ (all_55_10 = e3)
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | |   (856)  all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (856) gives:
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | |   (857)  all_55_10 = e2
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (853), (857) are inconsistent by sub-proof
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | |            #2499.
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | |   (858)   ~ (all_55_10 = e2)
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | |   (859)  all_55_10 = e1 | all_55_10 = e0
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (859) gives:
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | |   (860)  all_55_10 = e1
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (336), (860) imply:
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | |   (861)  all_6_2 = e1
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (861) implies:
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | |   (862)  all_6_2 = e1
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (364), (862) imply:
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | |   (863)   ~ (all_53_9 = e1)
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (862) imply:
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | |   (864)  op(e1, e1) = e1
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | |   (865)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (865) gives:
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | |   (866)  all_57_2 = e1 & op(e2, e3) = e1
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (866) implies:
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | |   (867)  all_57_2 = e1
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | |   (868)  op(e2, e3) = e1
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | |   (869)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e1)
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (869) gives:
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (870)  all_57_0 = e1 & op(e3, e3) = e1
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (870) implies:
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (871)  op(e3, e3) = e1
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (414), (871), (function-axioms) are
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2495.
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (872)  all_57_1 = e1 & op(e3, e2) = e1
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (872) implies:
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (873)  op(e3, e2) = e1
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_1, e1,
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (168), (868) gives:
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (874)  all_53_1 = e1
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_4, e1,
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (171), (873) gives:
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (875)  all_53_4 = e1
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (147), (874) imply:
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (876)   ~ (all_53_9 = e1)
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (874) imply:
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (877)   ~ (all_53_13 = e1)
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (875) imply:
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (878)   ~ (all_53_12 = e1)
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (879)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (879) gives:
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (880)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_52_7)
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (864), (873), (880), (function-axioms) are
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2111.
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (881)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 218.45/36.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_52_15)
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (374), (868), (881), (function-axioms) are
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2110.
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (882)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_21) = e1 & op(all_52_23, all_52_23) =
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(all_52_25, all_52_25) = e3 &
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_29) = e1 & op(all_52_31, all_52_31) =
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_29) & $i(all_52_31))
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (882) gives:
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (883)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_52_23)
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (883) implies:
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (884)  op(e1, e0) = all_52_23
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (885)  op(e1, e1) = all_52_21
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (886)  op(all_52_23, all_52_23) = e0
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_14,
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_23, e0, e1, simplifying with (161), (884)
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (887)  all_53_14 = all_52_23
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_21, e1, e1, simplifying with (864), (885)
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (888)  all_52_21 = e1
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (887) imply:
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (889)  all_55_11 = all_52_23
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (887) imply:
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (890)   ~ (all_53_12 = all_52_23)
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (111), (887) imply:
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (891)   ~ (all_53_13 = all_52_23)
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (848), (887) imply:
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (892)   ~ (all_52_23 = e1)
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (893)  all_55_6 = e3
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (893) imply:
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (894)  all_53_9 = e3
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (894) implies:
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (895)  all_53_9 = e3
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (895) imply:
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (896)   ~ (all_53_13 = e3)
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (896) implies:
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (897)   ~ (all_53_13 = e3)
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (898)  all_55_7 = e3
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (897), (898) are inconsistent by sub-proof
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2109.
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (899)  all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (899) gives:
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (900)  all_55_7 = e2
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (395), (900) are inconsistent by sub-proof
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2171.
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (901)  all_55_7 = e1 | all_55_7 = e0
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (901) gives:
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (902)  all_55_7 = e1
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (902) imply:
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (903)  all_53_13 = e1
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (847), (903) imply:
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (904)  $false
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (904) is inconsistent.
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (905)  all_55_7 = e0
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (905) imply:
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (906)  all_53_13 = e0
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (114), (906) imply:
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (907)   ~ (all_53_12 = e0)
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (891), (906) imply:
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (908)   ~ (all_52_23 = e0)
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (908) implies:
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (909)   ~ (all_52_23 = e0)
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (910)  all_55_3 = e3
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (413), (910) are inconsistent by sub-proof
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2169.
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (911)  all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (911) gives:
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (912)  all_55_3 = e2
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (912) imply:
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (913)  all_53_12 = e2
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (913) implies:
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (914)  all_53_12 = e2
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (890), (914) imply:
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (915)   ~ (all_52_23 = e2)
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (915) implies:
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (916)   ~ (all_52_23 = e2)
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (194), (414), (886), (889), (892), (909), (916),
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2105.
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (917)  all_55_3 = e1 | all_55_3 = e0
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (846), (907), (917) are inconsistent by
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2132.
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (918)   ~ (all_55_6 = e3)
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (919)  all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (259), (918) imply:
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (920)   ~ (all_53_9 = e3)
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (919) gives:
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (921)  all_55_6 = e2
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (394), (921) are inconsistent by sub-proof
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2398.
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (922)   ~ (all_55_6 = e2)
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (923)  all_55_6 = e1 | all_55_6 = e0
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (924)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e3)
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (924) gives:
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (925)  all_57_4 = e3 & op(e3, e1) = e3
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (925) implies:
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (926)  all_57_4 = e3
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (235),
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (414), (926), (function-axioms) are inconsistent
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2474.
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (927)  all_57_5 = e3 & op(e2, e1) = e3
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (927) implies:
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (928)  all_57_5 = e3
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (923) gives:
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (929)  all_55_6 = e1
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (863), (929) are inconsistent by sub-proof
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2163.
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (930)  all_55_6 = e0
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (930) imply:
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (931)  all_53_9 = e0
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (931) implies:
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (932)  all_53_9 = e0
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (932) imply:
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (933)   ~ (all_53_13 = e0)
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (933) implies:
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (934)   ~ (all_53_13 = e0)
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (920), (932) imply:
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (935)   ~ (e3 = e0)
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (394), (932) imply:
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (936)   ~ (e2 = e0)
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (863), (932) imply:
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (937)   ~ (e1 = e0)
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (165), (222), (401), (867), (928),
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (934), (function-axioms) are inconsistent by
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2469.
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (938)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e1) = e3)
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (938) gives:
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (939)  all_57_8 = e3 & op(e1, e1) = e3
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (939) implies:
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (940)  op(e1, e1) = e3
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (374), (940), (function-axioms) are
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2468.
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (941)  all_57_14 = e3 & op(e0, e1) = e3
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (941) implies:
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (942)  all_57_14 = e3
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (943)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (943) gives:
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (944)  all_57_12 = e2 & op(e0, e3) = e2
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (944) implies:
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (945)  all_57_12 = e2
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (946)  all_57_15 = e0 & op(e0, e0) = e0
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (946) implies:
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (947)  op(e0, e0) = e0
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (851), (947), (function-axioms) are
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2290.
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (948)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (948) implies:
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (949)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e0)
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (949) gives:
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (950)  all_57_12 = e0 & op(e0, e3) = e0
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (950) implies:
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (951)  all_57_12 = e0
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (945), (951) are inconsistent by sub-proof
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2385.
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (952)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (952) gives:
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (953)  all_57_13 = e0 & op(e0, e2) = e0
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (953) implies:
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (954)  all_57_13 = e0
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (955)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e3)
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (171), (401), (411), (955), (function-axioms)
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2285.
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (956)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (956) gives:
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (957)  all_57_7 = e3 & op(e1, e2) = e3
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (957) implies:
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (958)  all_57_7 = e3
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (959)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e2)
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (959) gives:
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (960)  all_57_4 = e2 & op(e3, e1) = e2
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (960) implies:
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (961)  all_57_4 = e2
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (216), (218),
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (219), (220), (221), (230), (232), (374), (401),
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (414), (864), (884), (886), (942), (945), (958),
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (961), (function-axioms) are inconsistent by
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2368.
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (962)  all_57_5 = e2 & op(e2, e1) = e2
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (962) implies:
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (963)  all_57_5 = e2
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (964)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e0)
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (964) gives:
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (965)  all_57_2 = e0 & op(e2, e3) = e0
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (965) implies:
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (966)  all_57_2 = e0
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (867), (966) are inconsistent by sub-proof
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2473.
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (967)  all_57_3 = e0 & op(e2, e2) = e0
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (967) implies:
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (968)  all_57_3 = e0
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (227), (228), (231),
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (235), (414), (954), (958), (968),
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2091.
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (969)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e2, e0) = e0)
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (969) gives:
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (970)  all_57_5 = e0 & op(e2, e1) = e0
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (970) implies:
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (971)  all_57_5 = e0
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (963), (971) imply:
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (972)  e2 = e0
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (400), (972) imply:
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (973)  all_57_3 = e0
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (227), (228), (231),
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (235), (414), (954), (958), (973),
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2091.
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (974)  all_57_10 = e0 & op(e2, e0) = e0
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (118), (165), (259), (863), (923), (974),
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2090.
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (975)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e1) = e2)
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (864), (942), (975), (function-axioms)
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2089.
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (976)  all_57_13 = e3 & op(e0, e2) = e3
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (976) implies:
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (977)  all_57_13 = e3
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (942), (945), (949), (977) are
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2088.
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (978)  all_57_14 = e0 & op(e0, e1) = e0
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (978) implies:
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (979)  all_57_14 = e0
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (942), (979) are inconsistent by sub-proof
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2420.
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (980)  all_57_13 = e2 & op(e0, e2) = e2
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (980) implies:
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (981)  op(e0, e2) = e2
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (393), (981), (function-axioms) are
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2335.
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (982)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (851), (942), (982), (function-axioms)
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2087.
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (983)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_52_31)
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (983) implies:
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (984)  op(e0, e0) = all_52_31
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (985)  op(all_52_31, all_52_31) = e0
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (419), (851), (984), (985),
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2086.
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | |   (986)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e1)
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (169), (218),
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | |            (220), (221), (374), (419), (846), (864), (986),
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | |            #2085.
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | |   (987)  all_57_3 = e1 & op(e2, e2) = e1
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (987) implies:
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | |   (988)  op(e2, e2) = e1
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (401), (988), (function-axioms) are
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2306.
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | |   (989)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (989) gives:
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | |   (990)  all_57_5 = e1 & op(e2, e1) = e1
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (863), (990), (function-axioms) are
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2305.
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | |   (991)  all_57_10 = e1 & op(e2, e0) = e1
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (847), (991), (function-axioms) are
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2084.
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | |   (992)  all_55_10 = e0
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (419), (992) are inconsistent by sub-proof
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | |            #2118.
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | |   (993)  all_38_2 = e2
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (993) imply:
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | |   (994)  all_6_2 = e2
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (994) imply:
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | |   (995)  op(e1, e1) = e2
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | |   (996)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (996) gives:
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | |   (997)  all_57_9 = e2 & op(e3, e0) = e2
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (997) implies:
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | |   (998)  all_57_9 = e2
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | |   (999)  op(e3, e0) = e2
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | |   (1000)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2)
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (168), (390), (414), (1000),
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | |            #2083.
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | |   (1001)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e3) = e2)
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1001) gives:
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | |   (1002)  all_57_6 = e2 & op(e1, e3) = e2
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1002) implies:
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | |   (1003)  all_57_6 = e2
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (159), (207),
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | |            (209), (210), (218), (219), (221), (230), (231),
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | |            (232), (233), (235), (374), (393), (414), (419),
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | |            (851), (995), (1003), (function-axioms) are
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2081.
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | |   (1004)  all_57_12 = e2 & op(e0, e3) = e2
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1004) implies:
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | |   (1005)  all_57_12 = e2
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | |   (1006)  op(e0, e3) = e2
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (39), (107), (111), (113),
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | |            (114), (122), (126), (127), (129), (134), (136),
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | |            (137), (140), (141), (159), (160), (161), (165),
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | |            (169), (170), (171), (191), (192), (194), (196),
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | |            (198), (204), (207), (208), (209), (210), (212),
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | |            (213), (215), (221), (222), (223), (224), (227),
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | |            (228), (229), (230), (231), (233), (235), (245),
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | |            (246), (248), (256), (258), (270), (374), (392),
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | |            (400), (401), (411), (413), (414), (419), (844),
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | |            (845), (846), (847), (848), (851), (995), (998),
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | |            (999), (1005), (1006), (function-axioms) are
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2046.
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | |   (1007)  all_57_10 = e2 & op(e2, e0) = e2
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (395), (1007), (function-axioms) are
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2432.
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | |   (1008)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1008) gives:
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | |   (1009)  all_57_11 = e2 & op(e1, e0) = e2
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1009) implies:
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | |   (1010)  all_57_11 = e2
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | |   (1011)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2)
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (168), (390), (414), (1011),
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | |            #2083.
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.80  | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | |   (1012)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e3) = e2)
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1012) gives:
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | |   (1013)  all_57_6 = e2 & op(e1, e3) = e2
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1013) implies:
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | |   (1014)  all_57_6 = e2
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (159), (207),
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | |            (209), (210), (218), (219), (221), (230), (231),
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | |            (232), (233), (235), (374), (393), (414), (419),
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | |            (851), (995), (1014), (function-axioms) are
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2081.
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | |   (1015)  all_57_12 = e2 & op(e0, e3) = e2
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1015) implies:
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | |   (1016)  all_57_12 = e2
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | |   (1017)  op(e0, e3) = e2
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | |   (1018)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e2)
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (171), (391), (414), (1018),
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | |            #2455.
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | |   (1019)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e2)
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1019) gives:
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1020)  all_57_4 = e2 & op(e3, e1) = e2
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1020) implies:
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1021)  all_57_4 = e2
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1022)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1022) gives:
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1023)  all_57_6 = e3 & op(e1, e3) = e3
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1023) implies:
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1024)  all_57_6 = e3
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (230), (232), (234),
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (414), (1016), (1024), (function-axioms) are
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2116.
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1025)  all_57_7 = e3 & op(e1, e2) = e3
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1025) implies:
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1026)  all_57_7 = e3
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1027)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e1)
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1027) gives:
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1028)  all_57_0 = e1 & op(e3, e3) = e1
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1028) implies:
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1029)  op(e3, e3) = e1
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (414), (1029), (function-axioms) are
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2495.
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1030)  all_57_1 = e1 & op(e3, e2) = e1
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1030) implies:
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1031)  all_57_1 = e1
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1032)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e0)
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1032) gives:
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1033)  all_57_6 = e0 & op(e1, e3) = e0
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1033) implies:
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1034)  all_57_6 = e0
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1035)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (414), (1031), (1035), (function-axioms)
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2492.
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1036)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1036) gives:
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1037)  all_57_4 = e0 & op(e3, e1) = e0
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1021), (1037) are inconsistent by sub-proof
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2045.
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1038)  all_57_9 = e0 & op(e3, e0) = e0
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1038) implies:
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1039)  all_57_9 = e0
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1040)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1040) gives:
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1041)  all_57_6 = e1 & op(e1, e3) = e1
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1034), (1041) are inconsistent by sub-proof
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2044.
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1042)  all_57_7 = e1 & op(e1, e2) = e1
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1042) implies:
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1043)  all_57_7 = e1
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (39), (217), (374), (1010), (1034),
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1043), (function-axioms) are inconsistent by
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2114.
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1044)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (212), (213), (851),
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (995), (1039), (1044), (function-axioms) are
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2043.
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1045)  all_57_7 = e0 & op(e1, e2) = e0
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1026), (1045) are inconsistent by sub-proof
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2042.
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1046)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1046) gives:
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1047)  all_57_8 = e0 & op(e1, e1) = e0
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (419), (1047), (function-axioms) are
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2412.
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1048)  all_57_11 = e0 & op(e1, e0) = e0
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1010), (1048) are inconsistent by sub-proof
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2041.
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1049)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e1)
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1049) gives:
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1050)  all_57_4 = e1 & op(e3, e1) = e1
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1021), (1050) are inconsistent by sub-proof
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2452.
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1051)  all_57_9 = e1 & op(e3, e0) = e1
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (846), (1051), (function-axioms) are
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2131.
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1052)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (39), (374), (1010), (1052),
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2040.
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1053)  all_57_9 = e2 & op(e3, e0) = e2
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1053) implies:
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1054)  all_57_9 = e2
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1055)  op(e3, e0) = e2
% 218.45/36.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (39), (107), (111), (113),
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | |            (114), (122), (126), (127), (129), (134), (136),
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | |            (137), (140), (141), (159), (160), (161), (165),
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | |            (169), (170), (171), (191), (192), (194), (196),
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | |            (198), (204), (207), (208), (209), (210), (212),
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | |            (213), (215), (221), (222), (223), (224), (227),
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | |            (228), (229), (230), (231), (233), (235), (245),
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | |            (246), (248), (256), (258), (270), (374), (392),
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | |            (400), (401), (411), (413), (414), (419), (844),
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | |            (845), (846), (847), (848), (851), (995), (1016),
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | |            (1017), (1054), (1055), (function-axioms) are
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2046.
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | |   (1056)  all_57_15 = e2 & op(e0, e0) = e2
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1056) implies:
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | |   (1057)  op(e0, e0) = e2
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (851), (1057), (function-axioms) are
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2177.
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | End of split
% 218.45/36.82  | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.82  | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | |   (1058)  all_24_2 = e0
% 218.45/36.82  | | | | | | | | | | | | | | | | | |   (1059)  ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0
% 218.45/36.82  | | | | | | | | | | | | | | | | | |             & op(e1, e0) = all_24_1 & $i(all_24_0) &
% 218.45/36.82  | | | | | | | | | | | | | | | | | |             $i(all_24_1)) | ( ~ (all_24_1 = e3) & op(e1, e0)
% 218.45/36.82  | | | | | | | | | | | | | | | | | |             = all_24_1 & $i(all_24_1))
% 218.45/36.82  | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (315), (1058) imply:
% 218.45/36.82  | | | | | | | | | | | | | | | | | |   (1060)  all_6_2 = e0
% 218.45/36.82  | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | SIMP: (1060) implies:
% 218.45/36.82  | | | | | | | | | | | | | | | | | |   (1061)  all_6_2 = e0
% 218.45/36.82  | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (311), (1061) imply:
% 218.45/36.82  | | | | | | | | | | | | | | | | | |   (1062)  all_34_2 = e0
% 218.45/36.82  | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | REDUCE: (350), (1061) imply:
% 218.45/36.82  | | | | | | | | | | | | | | | | | |   (1063)   ~ (all_53_2 = e0)
% 218.45/36.82  | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | REDUCE: (361), (1061) imply:
% 218.45/36.82  | | | | | | | | | | | | | | | | | |   (1064)   ~ (all_53_6 = e0)
% 218.45/36.82  | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | REDUCE: (363), (1061) imply:
% 218.45/36.82  | | | | | | | | | | | | | | | | | |   (1065)   ~ (all_53_8 = e0)
% 218.45/36.82  | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | REDUCE: (364), (1061) imply:
% 218.45/36.82  | | | | | | | | | | | | | | | | | |   (1066)   ~ (all_53_9 = e0)
% 218.45/36.82  | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | REDUCE: (368), (1061) imply:
% 218.45/36.82  | | | | | | | | | | | | | | | | | |   (1067)   ~ (all_53_14 = e0)
% 218.45/36.82  | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | REDUCE: (374), (1061) imply:
% 218.45/36.82  | | | | | | | | | | | | | | | | | |   (1068)   ~ (e3 = e0)
% 218.45/36.82  | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 218.45/36.82  | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | |   (1069)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 218.45/36.82  | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e0)
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (164), (1063), (1064), (1069),
% 218.45/36.82  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 218.45/36.82  | | | | | | | | | | | | | | | | | | |            #2038.
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | |   (1070)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 218.45/36.82  | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | BETA: splitting (1070) gives:
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | |   (1071)  all_57_8 = e0 & op(e1, e1) = e0
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | ALPHA: (1071) implies:
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | |   (1072)  all_57_8 = e0
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | |   (1073)  op(e1, e1) = e0
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | BETA: splitting (76) gives:
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | |   (1074)   ~ (all_30_2 = e1)
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | REDUCE: (330), (1074) imply:
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | |   (1075)   ~ (all_4_2 = e1)
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | |   (1076)  all_55_15 = e3
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (1076) imply:
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | |   (1077)  all_4_2 = e3
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (378), (1077) imply:
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | |   (1078)  $false
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1078) is inconsistent.
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | |   (1079)   ~ (all_55_15 = e3)
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | |   (1080)  all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1080) gives:
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | |   (1081)  all_55_15 = e2
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (1081) imply:
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | |   (1082)  all_4_2 = e2
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (373), (1082) imply:
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | |   (1083)  $false
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1083) is inconsistent.
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | |   (1084)   ~ (all_55_15 = e2)
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | |   (1085)  all_55_15 = e1 | all_55_15 = e0
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1085) gives:
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | |   (1086)  all_55_15 = e1
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (1086) imply:
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | |   (1087)  all_4_2 = e1
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1075), (1087) imply:
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | |   (1088)  $false
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1088) is inconsistent.
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | |   (1089)  all_55_15 = e0
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (1089) imply:
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | |   (1090)  all_4_2 = e0
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (362), (1090) imply:
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | |   (1091)   ~ (all_53_7 = e0)
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (369), (1090) imply:
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | |   (1092)   ~ (all_53_11 = e0)
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (371), (1090) imply:
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | |   (1093)   ~ (all_53_13 = e0)
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (373), (1090) imply:
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | |   (1094)   ~ (e2 = e0)
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1075), (1090) imply:
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | |   (1095)   ~ (e1 = e0)
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (1090) imply:
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | |   (1096)  op(e0, e0) = e0
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | |   (1097)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1097) gives:
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1098)  all_57_2 = e0 & op(e2, e3) = e0
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1098) implies:
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1099)  all_57_2 = e0
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1100)  op(e2, e3) = e0
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1101)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1101) gives:
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1102)  all_57_1 = e0 & op(e3, e2) = e0
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1102) implies:
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1103)  op(e3, e2) = e0
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_1, e0,
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (168), (1100) gives:
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1104)  all_53_1 = e0
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_4, e0,
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (171), (1103) gives:
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1105)  all_53_4 = e0
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (147), (1104) imply:
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1106)   ~ (all_53_9 = e0)
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (1104) imply:
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1107)   ~ (all_53_13 = e0)
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (1105) imply:
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1108)   ~ (all_53_8 = e0)
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (1105) imply:
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1109)   ~ (all_53_12 = e0)
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1109) implies:
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1110)   ~ (all_53_12 = e0)
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1111)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 218.45/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 218.45/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 218.45/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 218.45/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 218.45/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 218.45/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 218.45/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 218.45/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 218.45/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 218.45/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 218.45/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 218.45/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 218.45/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 218.45/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 218.45/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (1096), (1100), (1103), (1111),
% 218.45/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 218.45/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2037.
% 218.45/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1112)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 218.45/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 218.45/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 218.45/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_52_21) = e1 & op(all_52_23, all_52_23) =
% 218.45/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 218.45/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 218.45/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 218.45/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 218.45/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 218.45/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(all_52_25, all_52_25) = e3 &
% 218.45/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 218.45/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_52_29) = e1 & op(all_52_31, all_52_31) =
% 218.45/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 218.45/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 218.45/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 218.45/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_29) & $i(all_52_31))
% 218.45/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1112) gives:
% 218.45/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.45/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1113)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 218.45/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 218.45/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 218.45/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 218.45/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 218.45/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 218.45/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 218.45/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_23)
% 218.45/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1073), (1096), (1113), (function-axioms) are
% 218.45/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2036.
% 218.45/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.45/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.45/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1114)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_31)
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1114) implies:
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1115)  op(e0, e1) = all_52_29
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1116)  op(all_52_29, all_52_29) = e1
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_11,
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_29, e1, e0, simplifying with (158), (1115)
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1117)  all_53_11 = all_52_29
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (1117) imply:
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1118)  all_55_14 = all_52_29
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (122), (1117) imply:
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1119)   ~ (all_53_8 = all_52_29)
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (119), (1117) imply:
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1120)   ~ (all_53_9 = all_52_29)
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1092), (1117) imply:
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1121)   ~ (all_52_29 = e0)
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1122)  all_55_7 = e3
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (1122) imply:
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1123)  all_53_13 = e3
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1123) implies:
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1124)  all_53_13 = e3
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (1124) imply:
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1125)   ~ (all_53_9 = e3)
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1126)  all_55_6 = e3
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (1125), (1126) are inconsistent by
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2498.
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1127)  all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1127) gives:
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1128)  all_55_6 = e2
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (394), (1128) are inconsistent by sub-proof
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2398.
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1129)  all_55_6 = e1 | all_55_6 = e0
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1129) gives:
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1130)  all_55_6 = e1
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (1130) imply:
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1131)  all_53_9 = e1
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1131) implies:
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1132)  all_53_9 = e1
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (124), (1132) imply:
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1133)   ~ (all_53_8 = e1)
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1120), (1132) imply:
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1134)   ~ (all_52_29 = e1)
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1134) implies:
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1135)   ~ (all_52_29 = e1)
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (191), (203), (269), (412), (414), (1065), (1116),
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1118), (1119), (1121), (1133), (1135),
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2029.
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1136)  all_55_6 = e0
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (1066), (1136) are inconsistent by
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2162.
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1137)  all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1137) gives:
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1138)  all_55_7 = e2
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (395), (1138) are inconsistent by sub-proof
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2171.
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1139)  all_55_7 = e1 | all_55_7 = e0
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1139) gives:
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1140)  all_55_7 = e1
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (1140) imply:
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1141)  all_53_13 = e1
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1141) implies:
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1142)  all_53_13 = e1
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (1142) imply:
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1143)   ~ (all_53_9 = e1)
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (114), (1142) imply:
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1144)   ~ (all_53_12 = e1)
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1145)  all_55_6 = e3
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (1145) imply:
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1146)  all_53_9 = e3
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1120), (1146) imply:
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1147)   ~ (all_52_29 = e3)
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1147) implies:
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1148)   ~ (all_52_29 = e3)
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1149)  all_55_3 = e3
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (413), (1149) are inconsistent by sub-proof
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2169.
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1150)  all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1150) gives:
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1151)  all_55_3 = e2
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (1151) imply:
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1152)  all_53_12 = e2
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1152) implies:
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1153)  all_53_12 = e2
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (1153) imply:
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1154)   ~ (all_53_8 = e2)
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1155)  all_55_2 = e3
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (412), (1155) are inconsistent by sub-proof
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2028.
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1156)  all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1156) gives:
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1157)  all_55_2 = e2
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (1154), (1157) are inconsistent by
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2027.
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1158)  all_55_2 = e1 | all_55_2 = e0
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1158) gives:
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1159)  all_55_2 = e1
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (1159) imply:
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1160)  all_53_8 = e1
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1160) implies:
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1161)  all_53_8 = e1
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1119), (1161) imply:
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1162)   ~ (all_52_29 = e1)
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1162) implies:
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1163)   ~ (all_52_29 = e1)
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (191), (401), (1116), (1118), (1121), (1148),
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1163), (function-axioms) are inconsistent by
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2025.
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1164)  all_55_2 = e0
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (1065), (1164) are inconsistent by
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2031.
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1165)  all_55_3 = e1 | all_55_3 = e0
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (1110), (1144), (1165) are inconsistent by
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2132.
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1166)  all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (394), (1066), (1143), (1166) are
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2160.
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1167)  all_55_7 = e0
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (1093), (1167) are inconsistent by
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2130.
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1168)  all_57_3 = e0 & op(e2, e2) = e0
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1168) implies:
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1169)  all_57_3 = e0
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1099), (1169) are inconsistent by sub-proof
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2246.
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1170)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0)
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (163), (1064), (1091), (1170),
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2024.
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1171)  all_57_3 = e0 & op(e2, e2) = e0
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1171) implies:
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1172)  op(e2, e2) = e0
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (401), (1172), (function-axioms) are
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2472.
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | |   (1173)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0)
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (166), (1066), (1093), (1173),
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | |            #2022.
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | |   (1174)  all_30_2 = e1
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | |   (1175)  ( ~ (all_30_0 = e2) & op(all_30_1, e0) = all_30_0
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | |             & op(e0, e1) = all_30_1 & $i(all_30_0) &
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | |             $i(all_30_1)) | ( ~ (all_30_1 = e3) & op(e0, e1)
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | |             = all_30_1 & $i(all_30_1))
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (330), (1174) imply:
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | |   (1176)  all_4_2 = e1
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (295), (1176) imply:
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | |   (1177)  all_40_2 = e1
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | REDUCE: (351), (1176) imply:
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | |   (1178)   ~ (all_53_3 = e1)
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | REDUCE: (362), (1176) imply:
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | |   (1179)   ~ (all_53_7 = e1)
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | REDUCE: (370), (1176) imply:
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | |   (1180)   ~ (all_53_12 = e1)
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | REDUCE: (371), (1176) imply:
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | |   (1181)   ~ (all_53_13 = e1)
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | REDUCE: (372), (1176) imply:
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | |   (1182)   ~ (all_53_14 = e1)
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | REDUCE: (378), (1176) imply:
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | |   (1183)   ~ (e3 = e1)
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | REDUCE: (373), (1176) imply:
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | |   (1184)   ~ (e2 = e1)
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (1176) imply:
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | |   (1185)  op(e0, e0) = e1
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (82) gives:
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | |   (1186)   ~ (all_34_2 = e0)
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1062), (1186) imply:
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | |   (1187)  $false
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1187) is inconsistent.
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | |   (1188)  ( ~ (all_34_0 = e3) & op(all_34_1, e1) = all_34_0
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = all_34_1 & $i(all_34_0) &
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | |             $i(all_34_1)) | ( ~ (all_34_1 = e2) & op(e1, e0)
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | |             = all_34_1 & $i(all_34_1))
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (91) gives:
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | |   (1189)   ~ (all_40_2 = e1)
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1177), (1189) imply:
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | |   (1190)  $false
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1190) is inconsistent.
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | |   (1191)  ( ~ (all_40_0 = e3) & op(all_40_1, e0) = all_40_0
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | |             & op(e0, e1) = all_40_1 & $i(all_40_0) &
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_40_1)) | ( ~ (all_40_1 = e2) & op(e0, e1)
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | |             = all_40_1 & $i(all_40_1))
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | |   (1192)  all_55_9 = e3
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (1192) imply:
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | |   (1193)  all_53_6 = e3
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1193) implies:
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | |   (1194)  all_53_6 = e3
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (129), (1194) imply:
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | |   (1195)   ~ (all_53_7 = e3)
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1195) implies:
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | |   (1196)   ~ (all_53_7 = e3)
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (127), (1194) imply:
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | |   (1197)   ~ (all_53_14 = e3)
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1197) implies:
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | |   (1198)   ~ (all_53_14 = e3)
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | |   (1199)  all_55_13 = e3
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (1199) imply:
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | |   (1200)  all_53_7 = e3
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1196), (1200) imply:
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | |   (1201)  $false
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1201) is inconsistent.
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | |   (1202)  all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1202) gives:
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1203)  all_55_13 = e2
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (1203) imply:
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1204)  all_53_7 = e2
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (393), (1204) imply:
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1205)  $false
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1205) is inconsistent.
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1206)   ~ (all_55_13 = e2)
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1207)  all_55_13 = e1 | all_55_13 = e0
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1208)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1208) gives:
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1209)  all_57_6 = e3 & op(e1, e3) = e3
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1209) implies:
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1210)  all_57_6 = e3
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (230), (232), (234),
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (417), (1210) are inconsistent by sub-proof #2010.
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1211)  all_57_7 = e3 & op(e1, e2) = e3
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1211) implies:
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1212)  all_57_7 = e3
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1213)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1213) gives:
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1214)  all_57_9 = e3 & op(e3, e0) = e3
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1214) implies:
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1215)  op(e3, e0) = e3
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (413), (1215), (function-axioms) are
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2458.
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1216)  all_57_10 = e3 & op(e2, e0) = e3
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1216) implies:
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1217)  all_57_10 = e3
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1218)  op(e2, e0) = e3
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1219)  all_57_15 = e0 & op(e0, e0) = e0
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1219) implies:
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1220)  op(e0, e0) = e0
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1185), (1220), (function-axioms) are
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2290.
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1221)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1221) implies:
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1222)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0)
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1222) gives:
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1223)  all_57_9 = e0 & op(e3, e0) = e0
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1223) implies:
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1224)  all_57_9 = e0
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1225)  op(e3, e0) = e0
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1226)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e2)
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (171), (391), (414), (1226),
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2455.
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1227)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e2)
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1227) gives:
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1228)  all_57_4 = e2 & op(e3, e1) = e2
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1228) implies:
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1229)  all_57_4 = e2
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1230)  all_55_11 = e3
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (1198), (1230) are inconsistent by
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2497.
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1231)  all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1232)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1232) gives:
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1233)  all_57_12 = e3 & op(e0, e3) = e3
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1233) implies:
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1234)  all_57_12 = e3
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1235)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1235) gives:
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1236)  all_57_6 = e1 & op(e1, e3) = e1
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1236) implies:
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1237)  all_57_6 = e1
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (9), (164), (230), (234), (414),
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1063), (1234), (1237), (function-axioms) are
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2152.
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1238)  all_57_7 = e1 & op(e1, e2) = e1
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1212), (1238) are inconsistent by sub-proof
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2104.
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1239)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (212), (213),
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1073), (1185), (1224), (1239), (function-axioms)
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2009.
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1240)  all_57_13 = e3 & op(e0, e2) = e3
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1240) implies:
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1241)  all_57_13 = e3
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1242)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1242) gives:
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1243)  all_57_9 = e2 & op(e3, e0) = e2
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1243) implies:
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1244)  all_57_9 = e2
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1224), (1244) imply:
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1245)  e2 = e0
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1229), (1245) imply:
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1246)  all_57_4 = e0
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (233), (235), (414),
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1224), (1246), (function-axioms) are inconsistent
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2436.
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1247)  all_57_10 = e2 & op(e2, e0) = e2
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (395), (1247), (function-axioms) are
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2432.
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1248)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1248) gives:
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1249)  all_57_11 = e2 & op(e1, e0) = e2
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1249) implies:
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1250)  all_57_11 = e2
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1251)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1251) gives:
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1252)  all_57_6 = e1 & op(e1, e3) = e1
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1252) implies:
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1253)  all_57_6 = e1
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1254)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e1)
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1254) gives:
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1255)  all_57_0 = e1 & op(e3, e3) = e1
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1255) implies:
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1256)  op(e3, e3) = e1
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (414), (1256), (function-axioms) are
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2495.
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1257)  all_57_1 = e1 & op(e3, e2) = e1
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1257) implies:
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1258)  all_57_1 = e1
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1259)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1259) gives:
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1260)  all_57_1 = e0 & op(e3, e2) = e0
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1258), (1260) are inconsistent by sub-proof
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2493.
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1261)  all_57_3 = e0 & op(e2, e2) = e0
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1261) implies:
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1262)  all_57_3 = e0
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1263)  op(e2, e2) = e0
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (227), (228), (1212),
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1241), (1262), (1263), (function-axioms) are
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2007.
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1264)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0)
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1264) gives:
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1265)  all_57_7 = e0 & op(e1, e2) = e0
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1265) implies:
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1266)  all_57_7 = e0
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (39), (217), (374), (1250), (1253),
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1266), (function-axioms) are inconsistent by
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2343.
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1267)  all_57_13 = e0 & op(e0, e2) = e0
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1267) implies:
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1268)  all_57_13 = e0
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1241), (1268) imply:
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1269)  e3 = e0
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1212), (1269) imply:
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1270)  all_57_7 = e0
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (39), (217), (374), (1250), (1253),
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1270), (function-axioms) are inconsistent by
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2343.
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1271)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e1)
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1271) gives:
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1272)  all_57_4 = e1 & op(e3, e1) = e1
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1272) implies:
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1273)  all_57_4 = e1
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1229), (1273) imply:
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1274)  e2 = e1
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1250), (1274) imply:
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1275)  all_57_11 = e1
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (8), (9), (39), (216), (217), (374),
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1072), (1253), (1275), (function-axioms) are
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2003.
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1276)  all_57_9 = e1 & op(e3, e0) = e1
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (1180), (1276), (function-axioms) are
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2131.
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1277)  all_57_7 = e1 & op(e1, e2) = e1
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1212), (1277) are inconsistent by sub-proof
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2104.
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1278)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (212), (213),
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1073), (1185), (1224), (1278), (function-axioms)
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2009.
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1279)  all_57_15 = e2 & op(e0, e0) = e2
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1279) implies:
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1280)  op(e0, e0) = e2
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1185), (1280), (function-axioms) are
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2177.
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1281)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1281) gives:
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1282)  all_57_14 = e3 & op(e0, e1) = e3
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1282) implies:
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1283)  all_57_14 = e3
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1284)  op(e0, e1) = e3
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1285)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1285) gives:
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1286)  all_57_6 = e1 & op(e1, e3) = e1
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1286) implies:
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1287)  op(e1, e3) = e1
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1207) gives:
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1288)  all_55_13 = e1
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (1179), (1288) are inconsistent by
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2002.
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1289)  all_55_13 = e0
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (1289) imply:
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1290)  all_53_7 = e0
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1290) implies:
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1291)  all_53_7 = e0
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (141), (1291) imply:
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1292)   ~ (all_53_3 = e0)
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1179), (1291) imply:
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1293)   ~ (e1 = e0)
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1294)  all_55_12 = e3
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (247), (410), (1294) are inconsistent by sub-proof
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2001.
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1295)  all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1295) gives:
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1296)  all_55_12 = e2
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (1296) imply:
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1297)  all_53_3 = e2
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1297) implies:
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1298)  all_53_3 = e2
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (1298) imply:
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1299)   ~ (all_53_2 = e2)
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1300)  all_55_8 = e3
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (1300) imply:
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1301)  all_53_2 = e3
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (409), (1301) imply:
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1302)  $false
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1302) is inconsistent.
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1303)   ~ (all_55_8 = e3)
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1304)  all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1305)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1305) gives:
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1306)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_7)
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1306) implies:
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1307)  op(e3, e0) = all_52_7
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1308)  op(all_52_7, all_52_7) = e0
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1185), (1225), (1307), (1308),
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2000.
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1309)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_15)
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1309) implies:
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1310)  op(e2, e0) = all_52_15
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1311)  op(all_52_15, all_52_15) = e0
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1231) gives:
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1312)  all_55_11 = e2
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (1312) imply:
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1313)  all_53_14 = e2
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1313) implies:
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1314)  all_53_14 = e2
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (1314) imply:
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1315)   ~ (all_53_12 = e2)
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (202), (268), (413), (414), (1180), (1218),
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1310), (1311), (1315), (function-axioms) are
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1999.
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1316)  all_55_11 = e1 | all_55_11 = e0
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (1067), (1182), (1316) are inconsistent by
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2307.
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1317)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_52_21) = e1 & op(all_52_23, all_52_23) =
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(all_52_25, all_52_25) = e3 &
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_52_29) = e1 & op(all_52_31, all_52_31) =
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_29) & $i(all_52_31))
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1317) gives:
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1318)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_23)
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1318) implies:
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1319)  op(e1, e3) = all_52_17
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1320)  op(all_52_17, all_52_17) = e3
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (195), (336), (374), (1287), (1319), (1320),
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1998.
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1321)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_31)
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1321) implies:
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1322)  op(e0, e1) = all_52_29
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1323)  op(all_52_29, all_52_29) = e1
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1175) gives:
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1324)   ~ (all_30_0 = e2) & op(all_30_1, e0) = all_30_0 &
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e1) = all_30_1 & $i(all_30_0) &
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_30_1)
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1324) implies:
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1325)  op(e0, e1) = all_30_1
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1191) gives:
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1326)   ~ (all_40_0 = e3) & op(all_40_1, e0) = all_40_0 &
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e1) = all_40_1 & $i(all_40_0) &
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_40_1)
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1326) implies:
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1327)  op(e0, e1) = all_40_1
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (409), (414), (1063), (1284), (1299),
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1304), (1322), (1323), (1325), (1327),
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1996.
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1328)   ~ (all_40_1 = e2) & op(e0, e1) = all_40_1 &
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_40_1)
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1328) implies:
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1329)  op(e0, e1) = all_40_1
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (409), (414), (1063), (1284), (1299),
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1304), (1322), (1323), (1325), (1329),
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1996.
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1330)   ~ (all_30_1 = e3) & op(e0, e1) = all_30_1 &
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_30_1)
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1330) implies:
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1331)   ~ (all_30_1 = e3)
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1332)  op(e0, e1) = all_30_1
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1191) gives:
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1333)   ~ (all_40_0 = e3) & op(all_40_1, e0) = all_40_0 &
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e1) = all_40_1 & $i(all_40_0) &
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_40_1)
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1333) implies:
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1334)  op(e0, e1) = all_40_1
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1284), (1331), (1332), (1334), (function-axioms)
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1995.
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1335)   ~ (all_40_1 = e2) & op(e0, e1) = all_40_1 &
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_40_1)
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1335) implies:
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1336)  op(e0, e1) = all_40_1
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1284), (1331), (1332), (1336), (function-axioms)
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1995.
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1337)  all_55_12 = e1 | all_55_12 = e0
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (247), (1178), (1292), (1337) are inconsistent by
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1992.
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1338)  all_57_7 = e1 & op(e1, e2) = e1
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1338) implies:
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1339)  all_57_7 = e1
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1212), (1339) imply:
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1340)  e3 = e1
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1283), (1340) imply:
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1341)  all_57_14 = e1
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (159), (207), (209),
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (210), (393), (1185), (1341), (function-axioms)
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2175.
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1342)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (212), (213),
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1073), (1185), (1224), (1342), (function-axioms)
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2009.
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1343)  all_57_15 = e3 & op(e0, e0) = e3
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1343) implies:
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1344)  all_57_15 = e3
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (207), (211), (212),
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1217), (1224), (1344) are inconsistent by
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1982.
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1345)  all_57_9 = e2 & op(e3, e0) = e2
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1345) implies:
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1346)  all_57_9 = e2
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1224), (1346) are inconsistent by sub-proof
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2440.
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1347)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 =
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1347) gives:
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1348)  all_57_10 = e0 & op(e2, e0) = e0
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1217), (1348) are inconsistent by sub-proof
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1981.
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1349)  all_57_11 = e0 & op(e1, e0) = e0
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (1067), (1349), (function-axioms) are
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2341.
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1350)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1350) gives:
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1351)  all_57_11 = e3 & op(e1, e0) = e3
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1351) implies:
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1352)  op(e1, e0) = e3
% 218.89/36.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (1198), (1352), (function-axioms) are
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2330.
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1353)  all_57_15 = e3 & op(e0, e0) = e3
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1353) implies:
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1354)  op(e0, e0) = e3
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1185), (1354), (function-axioms) are
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2183.
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1355)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (161), (374), (1198), (1355),
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2310.
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | |   (1356)   ~ (all_55_9 = e3)
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | |   (1357)  all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (256), (1356) imply:
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | |   (1358)   ~ (all_53_6 = e3)
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1357) gives:
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | |   (1359)  all_55_9 = e2
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (392), (1359) are inconsistent by sub-proof
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | |            #2274.
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | |   (1360)  all_55_9 = e1 | all_55_9 = e0
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1361)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1361) gives:
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1362)  all_57_6 = e3 & op(e1, e3) = e3
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1362) implies:
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1363)  all_57_6 = e3
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (230), (232), (234),
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (417), (1363) are inconsistent by sub-proof #2010.
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1364)  all_57_7 = e3 & op(e1, e2) = e3
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1364) implies:
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1365)  all_57_7 = e3
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1366)  all_57_15 = e0 & op(e0, e0) = e0
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1366) implies:
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1367)  op(e0, e0) = e0
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1185), (1367), (function-axioms) are
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2290.
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1368)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1368) implies:
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1369)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0)
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1360) gives:
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1370)  all_55_9 = e1
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (1370) imply:
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1371)  all_53_6 = e1
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1371) implies:
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1372)  all_53_6 = e1
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (1372) imply:
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1373)   ~ (all_53_2 = e1)
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1374)  all_55_8 = e3
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (409), (1374) are inconsistent by sub-proof
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2496.
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1375)   ~ (all_55_8 = e3)
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1376)  all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1376) gives:
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1377)  all_55_8 = e2
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (1377) imply:
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1378)  all_53_2 = e2
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1378) implies:
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1379)  all_53_2 = e2
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (1379) imply:
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1380)   ~ (all_53_3 = e2)
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1380) implies:
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1381)   ~ (all_53_3 = e2)
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1382)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (160), (393), (1381), (1382),
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1979.
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1383)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1383) gives:
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1384)  all_57_14 = e2 & op(e0, e1) = e2
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1384) implies:
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1385)  all_57_14 = e2
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1386)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e2)
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (171), (391), (414), (1386),
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2455.
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1387)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e2)
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1387) gives:
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1388)  all_57_4 = e2 & op(e3, e1) = e2
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1388) implies:
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1389)  all_57_4 = e2
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (218), (219),
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (220), (221), (374), (1385), (1389),
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2370.
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1390)  all_57_9 = e2 & op(e3, e0) = e2
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1390) implies:
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1391)  all_57_9 = e2
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (144), (145), (160),
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (169), (170), (197), (209), (210), (227), (231),
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (256), (257), (401), (409), (414), (1063),
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1064), (1065), (1180), (1185), (1358), (1360),
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1365), (1369), (1391), (function-axioms) are
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1971.
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1392)  all_57_15 = e2 & op(e0, e0) = e2
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1392) implies:
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1393)  op(e0, e0) = e2
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1185), (1393), (function-axioms) are
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2177.
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1394)  all_55_8 = e1 | all_55_8 = e0
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (1063), (1373), (1394) are inconsistent by
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1974.
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1395)  all_55_9 = e0
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (1064), (1395) are inconsistent by
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2272.
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1396)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1396) gives:
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1397)  all_57_8 = e3 & op(e1, e1) = e3
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1397) implies:
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1398)  op(e1, e1) = e3
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (374), (1398), (function-axioms) are
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2468.
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1399)  all_57_11 = e3 & op(e1, e0) = e3
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1399) implies:
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1400)  all_57_11 = e3
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1401)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (171), (401), (411), (1401),
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2285.
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1402)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1402) gives:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1403)  all_57_7 = e3 & op(e1, e2) = e3
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1403) implies:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1404)  all_57_7 = e3
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1405)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1405) gives:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1406)  all_57_9 = e2 & op(e3, e0) = e2
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1406) implies:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1407)  all_57_9 = e2
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1408)  all_57_15 = e0 & op(e0, e0) = e0
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1408) implies:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1409)  op(e0, e0) = e0
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1185), (1409), (function-axioms) are
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2290.
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1410)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1410) implies:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1411)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0)
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (144), (145), (160),
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (169), (170), (197), (209), (210), (227), (231),
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (256), (257), (401), (409), (414), (1063),
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1064), (1065), (1180), (1185), (1358), (1360),
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1404), (1407), (1411), (function-axioms) are
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1971.
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1412)  all_57_10 = e2 & op(e2, e0) = e2
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (395), (1412), (function-axioms) are
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2432.
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1413)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1413) gives:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1414)  all_57_11 = e2 & op(e1, e0) = e2
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1414) implies:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1415)  all_57_11 = e2
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1400), (1415) are inconsistent by sub-proof
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2119.
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1416)  all_57_15 = e2 & op(e0, e0) = e2
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1416) implies:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1417)  op(e0, e0) = e2
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1185), (1417), (function-axioms) are
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2177.
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1418)  all_57_13 = e3 & op(e0, e2) = e3
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1418) implies:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1419)  all_57_13 = e3
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1420)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1420) gives:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1421)  all_57_9 = e2 & op(e3, e0) = e2
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1421) implies:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1422)  op(e3, e0) = e2
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1423)  all_57_15 = e0 & op(e0, e0) = e0
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1423) implies:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1424)  op(e0, e0) = e0
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1185), (1424), (function-axioms) are
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2290.
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1425)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1425) implies:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1426)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0)
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1427)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1427) gives:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1428)  all_57_1 = e0 & op(e3, e2) = e0
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1428) implies:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1429)  all_57_1 = e0
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1430)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e2)
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1430) gives:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1431)  all_57_6 = e2 & op(e1, e3) = e2
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1431) implies:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1432)  all_57_6 = e2
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1360) gives:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1433)  all_55_9 = e1
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (1433) imply:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1434)  all_53_6 = e1
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (1434) imply:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1435)   ~ (all_53_2 = e1)
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (127), (1434) imply:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1436)   ~ (all_53_14 = e1)
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1437)  all_55_8 = e3
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (409), (1437) are inconsistent by sub-proof
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2496.
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1438)  all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1439)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e1)
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (414), (1429), (1439), (function-axioms)
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2445.
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1440)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e1)
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1440) gives:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1441)  all_57_4 = e1 & op(e3, e1) = e1
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1441) implies:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1442)  all_57_4 = e1
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1438) gives:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1443)  all_55_8 = e2
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (1443) imply:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1444)  all_53_2 = e2
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1444) implies:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1445)  all_53_2 = e2
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (1445) imply:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1446)   ~ (all_53_3 = e2)
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1446) implies:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1447)   ~ (all_53_3 = e2)
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (142), (1445) imply:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1448)   ~ (all_53_14 = e2)
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1448) implies:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1449)   ~ (all_53_14 = e2)
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1450)  all_55_11 = e3
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (1450) imply:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1451)  all_53_14 = e3
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1451) implies:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1452)  all_53_14 = e3
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (111), (1452) imply:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1453)   ~ (all_53_13 = e3)
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (161), (1452) imply:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1454)  op(e1, e0) = e3
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1455)  all_55_7 = e3
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (1453), (1455) are inconsistent by
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2109.
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1456)   ~ (all_55_7 = e3)
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1457)  all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 218.89/36.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1188) gives:
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1458)   ~ (all_34_0 = e3) & op(all_34_1, e1) = all_34_0 &
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_34_1 & $i(all_34_0) &
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_34_1)
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1458) implies:
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1459)  op(e1, e0) = all_34_1
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (107), (159), (160),
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (165), (168), (169), (208), (209), (210), (225),
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (232), (237), (258), (393), (395), (401),
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (408), (413), (414), (1059), (1181), (1185),
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1419), (1422), (1426), (1429), (1432), (1442),
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1447), (1453), (1454), (1457), (1459),
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1959.
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1460)   ~ (all_34_1 = e2) & op(e1, e0) = all_34_1 &
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_34_1)
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1460) implies:
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1461)  op(e1, e0) = all_34_1
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (107), (159), (160),
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (165), (168), (169), (208), (209), (210), (225),
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (232), (237), (258), (393), (395), (401),
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (408), (413), (414), (1059), (1181), (1185),
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1419), (1422), (1426), (1429), (1432), (1442),
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1447), (1453), (1454), (1457), (1461),
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1959.
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1462)  all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (1067), (1182), (1449), (1462) are
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2133.
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1463)  all_55_8 = e1 | all_55_8 = e0
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (1063), (1435), (1463) are inconsistent by
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1974.
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1464)  all_57_9 = e1 & op(e3, e0) = e1
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (1180), (1464), (function-axioms) are
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2131.
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1465)  all_55_9 = e0
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (1465) imply:
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1466)  all_53_6 = e0
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1064), (1466) imply:
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1467)  $false
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1467) is inconsistent.
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1468)  all_57_7 = e2 & op(e1, e2) = e2
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1468) implies:
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1469)  all_57_7 = e2
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (227), (401), (1419), (1429),
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1469), (function-axioms) are inconsistent by
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1958.
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1470)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e0) = e2)
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1470) gives:
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1471)  all_57_8 = e2 & op(e1, e1) = e2
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1471) implies:
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1472)  all_57_8 = e2
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1072), (1472) are inconsistent by sub-proof
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1957.
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1473)  all_57_11 = e2 & op(e1, e0) = e2
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1473) implies:
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1474)  all_57_11 = e2
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1400), (1474) are inconsistent by sub-proof
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2119.
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1475)  all_57_3 = e0 & op(e2, e2) = e0
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1475) implies:
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1476)  op(e2, e2) = e0
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (401), (1476), (function-axioms) are
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2472.
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1477)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0)
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1477) gives:
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1478)  all_57_7 = e0 & op(e1, e2) = e0
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (1064), (1478), (function-axioms) are
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2039.
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1479)  all_57_13 = e0 & op(e0, e2) = e0
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1479) implies:
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1480)  all_57_13 = e0
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1419), (1480) are inconsistent by sub-proof
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2184.
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1481)  all_57_10 = e2 & op(e2, e0) = e2
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (395), (1481), (function-axioms) are
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2432.
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1482)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (1185), (1400), (1482),
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1956.
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | |   (1483)  all_57_11 = e0 & op(e1, e0) = e0
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (1067), (1483), (function-axioms) are
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2341.
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.90  | | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.90  | | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | End of split
% 218.89/36.90  | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.90  | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | |   (1484)  all_57_1 = e3 & op(e3, e2) = e3
% 218.89/36.90  | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | | REF_CLOSE: (171), (411), (1484), (function-axioms) are
% 218.89/36.90  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2286.
% 218.89/36.90  | | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | End of split
% 218.89/36.90  | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | Case 2:
% 218.89/36.90  | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | |   (1485)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 218.89/36.90  | | | | | | | | | | | | | | | |             & op(e3, e0) = e3)
% 218.89/36.90  | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (169), (231), (233),
% 218.89/36.90  | | | | | | | | | | | | | | | |            (235), (413), (414), (1485), (function-axioms) are
% 218.89/36.90  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1955.
% 218.89/36.90  | | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | End of split
% 218.89/36.90  | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | Case 2:
% 218.89/36.90  | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | |   (1486)  all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 218.89/36.90  | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | | REF_CLOSE: (277), (376), (403), (405), (1486) are
% 218.89/36.90  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1953.
% 218.89/36.90  | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | End of split
% 218.89/36.90  | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | Case 2:
% 218.89/36.90  | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | |   (1487)  all_20_2 = e2
% 218.89/36.90  | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | COMBINE_EQS: (299), (1487) imply:
% 218.89/36.90  | | | | | | | | | | | | | |   (1488)  all_10_2 = e2
% 218.89/36.90  | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | SIMP: (1488) implies:
% 218.89/36.90  | | | | | | | | | | | | | |   (1489)  all_10_2 = e2
% 218.89/36.90  | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | REDUCE: (342), (1489) imply:
% 218.89/36.90  | | | | | | | | | | | | | |   (1490)   ~ (all_53_3 = e2)
% 218.89/36.90  | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | REDUCE: (348), (1489) imply:
% 218.89/36.90  | | | | | | | | | | | | | |   (1491)   ~ (all_53_12 = e2)
% 218.89/36.90  | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | REDUCE: (45), (1489) imply:
% 218.89/36.90  | | | | | | | | | | | | | |   (1492)  op(e3, e3) = e2
% 218.89/36.90  | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 218.89/36.90  | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | Case 1:
% 218.89/36.90  | | | | | | | | | | | | | | | 
% 218.89/36.90  | | | | | | | | | | | | | | |   (1493)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 218.89/36.91  | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 218.89/36.91  | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | REF_CLOSE: (165), (169), (395), (1491), (1493),
% 218.89/36.91  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 218.89/36.91  | | | | | | | | | | | | | | |            #1952.
% 218.89/36.91  | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | Case 2:
% 218.89/36.91  | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | |   (1494)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 218.89/36.91  | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 218.89/36.91  | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | BETA: splitting (1494) gives:
% 218.89/36.91  | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | Case 1:
% 218.89/36.91  | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | |   (1495)  all_57_11 = e2 & op(e1, e0) = e2
% 218.89/36.91  | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | ALPHA: (1495) implies:
% 218.89/36.91  | | | | | | | | | | | | | | | |   (1496)  all_57_11 = e2
% 218.89/36.91  | | | | | | | | | | | | | | | |   (1497)  op(e1, e0) = e2
% 218.89/36.91  | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 218.89/36.91  | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.91  | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | |   (1498)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 218.89/36.91  | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 218.89/36.91  | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (160), (393), (1490), (1498),
% 218.89/36.91  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 218.89/36.91  | | | | | | | | | | | | | | | | |            #1979.
% 218.89/36.91  | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.91  | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | |   (1499)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 218.89/36.91  | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 218.89/36.91  | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | BETA: splitting (1499) gives:
% 218.89/36.91  | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.91  | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | |   (1500)  all_57_14 = e2 & op(e0, e1) = e2
% 218.89/36.91  | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | ALPHA: (1500) implies:
% 218.89/36.91  | | | | | | | | | | | | | | | | | |   (1501)  op(e0, e1) = e2
% 218.89/36.91  | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_11,
% 218.89/36.91  | | | | | | | | | | | | | | | | | |              e2, e1, e0, simplifying with (158), (1501) gives:
% 218.89/36.91  | | | | | | | | | | | | | | | | | |   (1502)  all_53_11 = e2
% 218.89/36.91  | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_14,
% 218.89/36.91  | | | | | | | | | | | | | | | | | |              e2, e0, e1, simplifying with (161), (1497) gives:
% 218.89/36.91  | | | | | | | | | | | | | | | | | |   (1503)  all_53_14 = e2
% 218.89/36.91  | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | REDUCE: (368), (1503) imply:
% 218.89/36.91  | | | | | | | | | | | | | | | | | |   (1504)   ~ (all_6_2 = e2)
% 218.89/36.91  | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | SIMP: (1504) implies:
% 218.89/36.91  | | | | | | | | | | | | | | | | | |   (1505)   ~ (all_6_2 = e2)
% 218.89/36.91  | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | REDUCE: (372), (1503) imply:
% 218.89/36.91  | | | | | | | | | | | | | | | | | |   (1506)   ~ (all_4_2 = e2)
% 218.89/36.91  | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 218.89/36.91  | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | |   (1507)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 218.89/36.91  | | | | | | | | | | | | | | | | | | |             all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 218.89/36.91  | | | | | | | | | | | | | | | | | | |             op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 218.89/36.91  | | | | | | | | | | | | | | | | | | |               all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 218.89/36.91  | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 218.89/36.91  | | | | | | | | | | | | | | | | | | |             op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 218.89/36.91  | | | | | | | | | | | | | | | | | | |             $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 218.89/36.91  | | | | | | | | | | | | | | | | | | |             $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 218.89/36.91  | | | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 218.89/36.91  | | | | | | | | | | | | | | | | | | |               all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 218.89/36.91  | | | | | | | | | | | | | | | | | | |             & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 218.89/36.91  | | | | | | | | | | | | | | | | | | |               all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 218.89/36.91  | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 218.89/36.91  | | | | | | | | | | | | | | | | | | |             & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 218.89/36.91  | | | | | | | | | | | | | | | | | | |             $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | BETA: splitting (1507) gives:
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | |   (1508)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | |           all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | |           op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | |             all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | |           $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | |           $i(all_52_7)
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | ALPHA: (1508) implies:
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | |   (1509)  op(e3, e3) = all_52_1
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | |   (1510)  op(all_52_1, all_52_1) = e3
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (401), (1492), (1509), (1510),
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | |            #1951.
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | |   (1511)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | |           all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | |           op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | |             all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | |           & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | |           $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | |           $i(all_52_15)
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | ALPHA: (1511) implies:
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | |   (1512)  op(e2, e1) = all_52_13
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | |   (1513)  op(e2, e3) = all_52_9
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | |   (1514)  op(all_52_13, all_52_13) = e1
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | |   (1515)  op(all_52_9, all_52_9) = e3
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_9,
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | |              all_52_13, e1, e2, simplifying with (166), (1512)
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | |              gives:
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | |   (1516)  all_53_9 = all_52_13
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_1,
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | |              all_52_9, e3, e2, simplifying with (168), (1513)
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | |              gives:
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | |   (1517)  all_53_1 = all_52_9
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (1516) imply:
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | |   (1518)  all_55_6 = all_52_13
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | REDUCE: (364), (1516) imply:
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | |   (1519)   ~ (all_52_13 = all_6_2)
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | REDUCE: (394), (1516) imply:
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | |   (1520)   ~ (all_52_13 = e2)
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | |   (1521)   ~ (all_24_2 = e0)
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | REDUCE: (315), (1521) imply:
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | |   (1522)   ~ (all_6_2 = e0)
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | |   (1523)  all_55_10 = e3
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (374), (1523) are inconsistent by sub-proof
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | |            #2500.
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | |   (1524)   ~ (all_55_10 = e3)
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | |   (1525)  all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1525) gives:
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | |   (1526)  all_55_10 = e2
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (1505), (1526) are inconsistent by
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2499.
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | |   (1527)   ~ (all_55_10 = e2)
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | |   (1528)  all_55_10 = e1 | all_55_10 = e0
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1528) gives:
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | |   (1529)  all_55_10 = e1
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (336), (1529) imply:
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | |   (1530)  all_6_2 = e1
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1530) implies:
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | |   (1531)  all_6_2 = e1
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1519), (1531) imply:
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | |   (1532)   ~ (all_52_13 = e1)
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1505), (1531) imply:
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | |   (1533)   ~ (e2 = e1)
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (1531) imply:
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | |   (1534)  op(e1, e1) = e1
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (76) gives:
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | |   (1535)   ~ (all_30_2 = e1)
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (330), (1535) imply:
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | |   (1536)   ~ (all_4_2 = e1)
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1537)  all_55_15 = e3
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (378), (1537) are inconsistent by sub-proof
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | | |            #2503.
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1538)  all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1538) gives:
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1539)  all_55_15 = e2
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (373), (1539) are inconsistent by sub-proof
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2502.
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1540)  all_55_15 = e1 | all_55_15 = e0
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1540) gives:
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1541)  all_55_15 = e1
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (1536), (1541) are inconsistent by
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2501.
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1542)  all_55_15 = e0
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (1542) imply:
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1543)  all_4_2 = e0
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1543) implies:
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1544)  all_4_2 = e0
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (1544) imply:
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1545)  op(e0, e0) = e0
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1546)  all_55_6 = e3
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1518), (1546) imply:
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1547)  all_52_13 = e3
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1514), (1547) imply:
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1548)  op(e3, e3) = e1
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1492), (1548), (function-axioms) are
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1950.
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1549)  all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1514), (1518), (1520), (1532), (1545), (1549),
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2289.
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (1550)  all_30_2 = e1
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (330), (1550) imply:
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (1551)  all_4_2 = e1
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (351), (1551) imply:
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (1552)   ~ (all_53_3 = e1)
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (378), (1551) imply:
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (1553)   ~ (e3 = e1)
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1554)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e1)
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1554) gives:
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1555)  all_57_0 = e1 & op(e3, e3) = e1
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1555) implies:
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1556)  op(e3, e3) = e1
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1492), (1556), (function-axioms) are
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1950.
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1557)  all_57_2 = e1 & op(e2, e3) = e1
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1557) implies:
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1558)  op(e2, e3) = e1
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e1,
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (1513), (1558) gives:
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1559)  all_52_9 = e1
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1515), (1559) imply:
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1560)  op(e1, e1) = e3
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (374), (1560), (function-axioms) are
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2468.
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1561)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e3) = e1)
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1561) gives:
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1562)  all_57_6 = e1 & op(e1, e3) = e1
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1562) implies:
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1563)  all_57_6 = e1
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1564)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1564) gives:
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1565)  all_57_6 = e3 & op(e1, e3) = e3
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1565) implies:
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1566)  all_57_6 = e3
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1563), (1566) are inconsistent by sub-proof
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2017.
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1567)  all_57_7 = e3 & op(e1, e2) = e3
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1567) implies:
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1568)  all_57_7 = e3
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1569)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e0)
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (9), (39), (217), (374), (1496),
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1563), (1569), (function-axioms) are inconsistent
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2342.
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1570)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1570) gives:
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1571)  all_57_8 = e0 & op(e1, e1) = e0
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1571) implies:
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1572)  op(e1, e1) = e0
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1534), (1572), (function-axioms) are
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2427.
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1573)  all_57_11 = e0 & op(e1, e0) = e0
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1573) implies:
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1574)  all_57_11 = e0
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (216), (1534), (1563), (1568),
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1574), (function-axioms) are inconsistent by
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1948.
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1575)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (39), (374), (1496), (1575),
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2344.
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1576)  all_57_12 = e1 & op(e0, e3) = e1
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (1552), (1576), (function-axioms) are
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1947.
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | |   (1577)  all_55_10 = e0
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (1522), (1577) are inconsistent by
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2118.
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | |   (1578)  all_24_2 = e0
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | |   (1579)  ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = all_24_1 & $i(all_24_0) &
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | |             $i(all_24_1)) | ( ~ (all_24_1 = e3) & op(e1, e0)
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | |             = all_24_1 & $i(all_24_1))
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (315), (1578) imply:
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | |   (1580)  all_6_2 = e0
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | SIMP: (1580) implies:
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | |   (1581)  all_6_2 = e0
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (311), (1581) imply:
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | |   (1582)  all_34_2 = e0
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | REDUCE: (1519), (1581) imply:
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | |   (1583)   ~ (all_52_13 = e0)
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (1581) imply:
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | |   (1584)  op(e1, e1) = e0
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (82), (199), (1497), (1512), (1514), (1518),
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | |            (1520), (1579), (1582), (1583), (1584),
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | |            #1945.
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | End of split
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | 
% 218.89/36.92  | | | | | | | | | | | | | | | | | | Case 2:
% 218.89/36.92  | | | | | | | | | | | | | | | | | | | 
% 219.27/36.92  | | | | | | | | | | | | | | | | | | |   (1585)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 219.27/36.92  | | | | | | | | | | | | | | | | | | |             & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 219.27/36.92  | | | | | | | | | | | | | | | | | | |             & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 219.27/36.92  | | | | | | | | | | | | | | | | | | |               all_52_21) = e1 & op(all_52_23, all_52_23) =
% 219.27/36.92  | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 219.27/36.92  | | | | | | | | | | | | | | | | | | |             all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 219.27/36.92  | | | | | | | | | | | | | | | | | | |             = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 219.27/36.92  | | | | | | | | | | | | | | | | | | |             $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 219.27/36.92  | | | | | | | | | | | | | | | | | | |             & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 219.27/36.92  | | | | | | | | | | | | | | | | | | |             e0 & op(all_52_25, all_52_25) = e3 &
% 219.27/36.92  | | | | | | | | | | | | | | | | | | |             op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 219.27/36.92  | | | | | | | | | | | | | | | | | | |               all_52_29) = e1 & op(all_52_31, all_52_31) =
% 219.27/36.92  | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 219.27/36.92  | | | | | | | | | | | | | | | | | | |             all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 219.27/36.92  | | | | | | | | | | | | | | | | | | |             = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 219.27/36.92  | | | | | | | | | | | | | | | | | | |             $i(all_52_29) & $i(all_52_31))
% 219.27/36.92  | | | | | | | | | | | | | | | | | | | 
% 219.27/36.92  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (401), (1497), (1501), (1585),
% 219.27/36.92  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 219.27/36.92  | | | | | | | | | | | | | | | | | | |            #1944.
% 219.27/36.92  | | | | | | | | | | | | | | | | | | | 
% 219.27/36.92  | | | | | | | | | | | | | | | | | | End of split
% 219.27/36.92  | | | | | | | | | | | | | | | | | | 
% 219.27/36.92  | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.92  | | | | | | | | | | | | | | | | | | 
% 219.27/36.92  | | | | | | | | | | | | | | | | | |   (1586)  all_57_15 = e2 & op(e0, e0) = e2
% 219.27/36.92  | | | | | | | | | | | | | | | | | | 
% 219.27/36.92  | | | | | | | | | | | | | | | | | | ALPHA: (1586) implies:
% 219.27/36.92  | | | | | | | | | | | | | | | | | |   (1587)  op(e0, e0) = e2
% 219.27/36.92  | | | | | | | | | | | | | | | | | | 
% 219.27/36.92  | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (373), (1587), (function-axioms) are
% 219.27/36.92  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2334.
% 219.27/36.92  | | | | | | | | | | | | | | | | | | 
% 219.27/36.92  | | | | | | | | | | | | | | | | | End of split
% 219.27/36.92  | | | | | | | | | | | | | | | | | 
% 219.27/36.92  | | | | | | | | | | | | | | | | End of split
% 219.27/36.92  | | | | | | | | | | | | | | | | 
% 219.27/36.92  | | | | | | | | | | | | | | | Case 2:
% 219.27/36.92  | | | | | | | | | | | | | | | | 
% 219.27/36.92  | | | | | | | | | | | | | | | |   (1588)  all_57_15 = e2 & op(e0, e0) = e2
% 219.27/36.92  | | | | | | | | | | | | | | | | 
% 219.27/36.92  | | | | | | | | | | | | | | | | ALPHA: (1588) implies:
% 219.27/36.92  | | | | | | | | | | | | | | | |   (1589)  op(e0, e0) = e2
% 219.27/36.92  | | | | | | | | | | | | | | | | 
% 219.27/36.92  | | | | | | | | | | | | | | | | REF_CLOSE: (36), (373), (1589), (function-axioms) are
% 219.27/36.92  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2334.
% 219.27/36.92  | | | | | | | | | | | | | | | | 
% 219.27/36.92  | | | | | | | | | | | | | | | End of split
% 219.27/36.92  | | | | | | | | | | | | | | | 
% 219.27/36.92  | | | | | | | | | | | | | | End of split
% 219.27/36.92  | | | | | | | | | | | | | | 
% 219.27/36.92  | | | | | | | | | | | | | End of split
% 219.27/36.92  | | | | | | | | | | | | | 
% 219.27/36.92  | | | | | | | | | | | | Case 2:
% 219.27/36.92  | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | |   (1590)  all_18_2 = e0
% 219.27/36.93  | | | | | | | | | | | | |   (1591)  ( ~ (all_18_0 = e1) & op(all_18_1, e3) = all_18_0
% 219.27/36.93  | | | | | | | | | | | | |             & op(e3, e0) = all_18_1 & $i(all_18_0) &
% 219.27/36.93  | | | | | | | | | | | | |             $i(all_18_1)) | ( ~ (all_18_1 = e2) & op(e3, e0)
% 219.27/36.93  | | | | | | | | | | | | |             = all_18_1 & $i(all_18_1))
% 219.27/36.93  | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | COMBINE_EQS: (327), (1590) imply:
% 219.27/36.93  | | | | | | | | | | | | |   (1592)  all_10_2 = e0
% 219.27/36.93  | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | SIMP: (1592) implies:
% 219.27/36.93  | | | | | | | | | | | | |   (1593)  all_10_2 = e0
% 219.27/36.93  | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | COMBINE_EQS: (279), (1593) imply:
% 219.27/36.93  | | | | | | | | | | | | |   (1594)  all_48_2 = e0
% 219.27/36.93  | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | REDUCE: (338), (1593) imply:
% 219.27/36.93  | | | | | | | | | | | | |   (1595)   ~ (all_53_1 = e0)
% 219.27/36.93  | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | REDUCE: (340), (1593) imply:
% 219.27/36.93  | | | | | | | | | | | | |   (1596)   ~ (all_53_2 = e0)
% 219.27/36.93  | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | REDUCE: (342), (1593) imply:
% 219.27/36.93  | | | | | | | | | | | | |   (1597)   ~ (all_53_3 = e0)
% 219.27/36.93  | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | REDUCE: (344), (1593) imply:
% 219.27/36.93  | | | | | | | | | | | | |   (1598)   ~ (all_53_4 = e0)
% 219.27/36.93  | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | REDUCE: (346), (1593) imply:
% 219.27/36.93  | | | | | | | | | | | | |   (1599)   ~ (all_53_8 = e0)
% 219.27/36.93  | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | REDUCE: (348), (1593) imply:
% 219.27/36.93  | | | | | | | | | | | | |   (1600)   ~ (all_53_12 = e0)
% 219.27/36.93  | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | REDUCE: (376), (1593) imply:
% 219.27/36.93  | | | | | | | | | | | | |   (1601)   ~ (e1 = e0)
% 219.27/36.93  | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | BETA: splitting (230) gives:
% 219.27/36.93  | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | Case 1:
% 219.27/36.93  | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | |   (1602)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 219.27/36.93  | | | | | | | | | | | | | |             & op(e2, e3) = e0)
% 219.27/36.93  | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | BETA: splitting (1602) gives:
% 219.27/36.93  | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | Case 1:
% 219.27/36.93  | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | |   (1603)  all_57_0 = e0 & op(e3, e3) = e0
% 219.27/36.93  | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | ALPHA: (1603) implies:
% 219.27/36.93  | | | | | | | | | | | | | | |   (1604)  all_57_0 = e0
% 219.27/36.93  | | | | | | | | | | | | | | |   (1605)  op(e3, e3) = e0
% 219.27/36.93  | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 219.27/36.93  | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | Case 1:
% 219.27/36.93  | | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | |   (1606)   ~ (all_24_2 = e0)
% 219.27/36.93  | | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | | REDUCE: (315), (1606) imply:
% 219.27/36.93  | | | | | | | | | | | | | | | |   (1607)   ~ (all_6_2 = e0)
% 219.27/36.93  | | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | | BETA: splitting (76) gives:
% 219.27/36.93  | | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.93  | | | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | | |   (1608)   ~ (all_30_2 = e1)
% 219.27/36.93  | | | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | | | REDUCE: (330), (1608) imply:
% 219.27/36.93  | | | | | | | | | | | | | | | | |   (1609)   ~ (all_4_2 = e1)
% 219.27/36.93  | | | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 219.27/36.93  | | | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.93  | | | | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | | | |   (1610)  all_55_15 = e3
% 219.27/36.93  | | | | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (1610) imply:
% 219.27/36.93  | | | | | | | | | | | | | | | | | |   (1611)  all_4_2 = e3
% 219.27/36.93  | | | | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | | | | REDUCE: (378), (1611) imply:
% 219.27/36.93  | | | | | | | | | | | | | | | | | |   (1612)  $false
% 219.27/36.93  | | | | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | | | | CLOSE: (1612) is inconsistent.
% 219.27/36.93  | | | | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.93  | | | | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | | | |   (1613)   ~ (all_55_15 = e3)
% 219.27/36.93  | | | | | | | | | | | | | | | | | |   (1614)  all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 219.27/36.93  | | | | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | | | | BETA: splitting (1614) gives:
% 219.27/36.93  | | | | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | | | | |   (1615)  all_55_15 = e2
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (1615) imply:
% 219.27/36.93  | | | | | | | | | | | | | | | | | | |   (1616)  all_4_2 = e2
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | REDUCE: (373), (1616) imply:
% 219.27/36.93  | | | | | | | | | | | | | | | | | | |   (1617)  $false
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | CLOSE: (1617) is inconsistent.
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | | | | |   (1618)   ~ (all_55_15 = e2)
% 219.27/36.93  | | | | | | | | | | | | | | | | | | |   (1619)  all_55_15 = e1 | all_55_15 = e0
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | BETA: splitting (1619) gives:
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | |   (1620)  all_55_15 = e1
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (1620) imply:
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | |   (1621)  all_4_2 = e1
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | REDUCE: (1609), (1621) imply:
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | |   (1622)  $false
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | CLOSE: (1622) is inconsistent.
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | |   (1623)  all_55_15 = e0
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (1623) imply:
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | |   (1624)  all_4_2 = e0
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | REDUCE: (362), (1624) imply:
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | |   (1625)   ~ (all_53_7 = e0)
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | REDUCE: (371), (1624) imply:
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | |   (1626)   ~ (all_53_13 = e0)
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | REDUCE: (378), (1624) imply:
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | |   (1627)   ~ (e3 = e0)
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | REDUCE: (373), (1624) imply:
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | |   (1628)   ~ (e2 = e0)
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (1624) imply:
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | |   (1629)  op(e0, e0) = e0
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | |   (1630)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (168), (401), (1595), (1630),
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | |            #1942.
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | |   (1631)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0)
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1631) gives:
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | |   (1632)  all_57_5 = e0 & op(e2, e1) = e0
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1632) implies:
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | |   (1633)  all_57_5 = e0
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | |   (1634)  op(e2, e1) = e0
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | |   (1635)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (171), (401), (1598), (1635),
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | |            #1940.
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | |   (1636)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0)
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1636) gives:
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | | |   (1637)  all_57_7 = e0 & op(e1, e2) = e0
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1637) implies:
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | | |   (1638)  all_57_7 = e0
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | | |   (1639)  op(e1, e2) = e0
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_6, e0,
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | | |              e2, e1, simplifying with (163), (1639) gives:
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | | |   (1640)  all_53_6 = e0
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_9, e0,
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (166), (1634) gives:
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | | |   (1641)  all_53_9 = e0
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (127), (1640) imply:
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | | |   (1642)   ~ (all_53_14 = e0)
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1642) implies:
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | | |   (1643)   ~ (all_53_14 = e0)
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (119), (1641) imply:
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | | |   (1644)   ~ (all_53_11 = e0)
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1644) implies:
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | | |   (1645)   ~ (all_53_11 = e0)
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (1641) imply:
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | | |   (1646)   ~ (all_53_13 = e0)
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (364), (1641) imply:
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | | |   (1647)   ~ (all_6_2 = e0)
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | | | |   (1648)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | | | |             op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | | | |               all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | | | |               all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | | | |               all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (1605), (1629), (1634), (1648),
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | | | |            #1938.
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | |   (1649)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | |             & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | |               all_52_21) = e1 & op(all_52_23, all_52_23) =
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | |             = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | |             & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(all_52_25, all_52_25) = e3 &
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | |             op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | |               all_52_29) = e1 & op(all_52_31, all_52_31) =
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | |             = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_29) & $i(all_52_31))
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1649) gives:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1650)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | |           all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | |           & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | |           & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | |           & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_23)
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1650) implies:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1651)  op(e1, e2) = all_52_19
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1652)  op(all_52_19, all_52_19) = e2
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1629), (1639), (1651), (1652),
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | |            #2158.
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1653)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | |           all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | |           & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | |           & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | |           & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_31)
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1653) implies:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1654)  op(e0, e0) = all_52_31
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1655)  op(e0, e1) = all_52_29
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1656)  op(e0, e3) = all_52_25
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1657)  op(all_52_31, all_52_31) = e0
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1658)  op(all_52_29, all_52_29) = e1
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1659)  op(all_52_25, all_52_25) = e3
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_11,
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_29, e1, e0, simplifying with (158), (1655)
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1660)  all_53_11 = all_52_29
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_3,
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_25, e3, e0, simplifying with (160), (1656)
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1661)  all_53_3 = all_52_25
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (1660) imply:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1662)  all_55_14 = all_52_29
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (122), (1660) imply:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1663)   ~ (all_53_8 = all_52_29)
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (366), (1660) imply:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1664)   ~ (all_52_29 = all_6_2)
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1645), (1660) imply:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1665)   ~ (all_52_29 = e0)
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (88) gives:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1666)   ~ (all_38_2 = e2)
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (249), (1666) imply:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1667)   ~ (all_6_2 = e2)
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1668)  all_55_10 = e3
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (374), (1668) are inconsistent by sub-proof
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2500.
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1669)   ~ (all_55_10 = e3)
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1670)  all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1670) gives:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1671)  all_55_10 = e2
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (1667), (1671) are inconsistent by
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2499.
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1672)   ~ (all_55_10 = e2)
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1673)  all_55_10 = e1 | all_55_10 = e0
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1673) gives:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1674)  all_55_10 = e1
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (336), (1674) imply:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1675)  all_6_2 = e1
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1675) implies:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1676)  all_6_2 = e1
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (350), (1676) imply:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1677)   ~ (all_53_2 = e1)
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (363), (1676) imply:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1678)   ~ (all_53_8 = e1)
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (368), (1676) imply:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1679)   ~ (all_53_14 = e1)
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1664), (1676) imply:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1680)   ~ (all_52_29 = e1)
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (374), (1676) imply:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1681)   ~ (e3 = e1)
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1667), (1676) imply:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1682)   ~ (e2 = e1)
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (1676) imply:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1683)  op(e1, e1) = e1
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1684)  all_55_4 = e3
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (1684) imply:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1685)  all_53_1 = e3
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1685) implies:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1686)  all_53_1 = e3
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (150), (1686) imply:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1687)   ~ (all_53_2 = e3)
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1687) implies:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1688)   ~ (all_53_2 = e3)
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (1686) imply:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1689)   ~ (all_53_13 = e3)
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1689) implies:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1690)   ~ (all_53_13 = e3)
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1691)  all_55_7 = e3
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (1690), (1691) are inconsistent by
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2109.
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1692)  all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1693)  all_55_8 = e3
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (1688), (1693) are inconsistent by
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2496.
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1694)  all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1692) gives:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1695)  all_55_7 = e2
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (1695) imply:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1696)  all_53_13 = e2
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (395), (1696) imply:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1697)  $false
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1697) is inconsistent.
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1698)  all_55_7 = e1 | all_55_7 = e0
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1694) gives:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1699)  all_55_8 = e2
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (1699) imply:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1700)  all_53_2 = e2
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (142), (1700) imply:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1701)   ~ (all_53_14 = e2)
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1701) implies:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1702)   ~ (all_53_14 = e2)
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1703)  all_55_11 = e3
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (1703) imply:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1704)  all_53_14 = e3
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1704) implies:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1705)  all_53_14 = e3
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (1705) imply:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1706)   ~ (all_53_12 = e3)
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1698) gives:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1707)  all_55_7 = e1
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (1707) imply:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1708)  all_53_13 = e1
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1708) implies:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1709)  all_53_13 = e1
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (114), (1709) imply:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1710)   ~ (all_53_12 = e1)
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1711)  all_55_3 = e3
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (1706), (1711) are inconsistent by
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2169.
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1712)  all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1712) gives:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1713)  all_55_3 = e2
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (1713) imply:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1714)  all_53_12 = e2
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1714) implies:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1715)  all_53_12 = e2
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (1715) imply:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1716)   ~ (all_53_8 = e2)
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1717)  all_55_2 = e3
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (1717) imply:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1718)  all_53_8 = e3
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1718) implies:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1719)  all_53_8 = e3
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1663), (1719) imply:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1720)   ~ (all_52_29 = e3)
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1720) implies:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1721)   ~ (all_52_29 = e3)
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (191), (401), (1658), (1662), (1665), (1680),
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1721), (function-axioms) are inconsistent by
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2025.
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1722)  all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (1599), (1678), (1716), (1722) are
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1937.
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1723)  all_55_3 = e1 | all_55_3 = e0
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (1600), (1710), (1723) are inconsistent by
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2132.
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1724)  all_55_7 = e0
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (1626), (1724) are inconsistent by
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2130.
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1725)  all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (1643), (1679), (1702), (1725) are
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2133.
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1726)  all_55_8 = e1 | all_55_8 = e0
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (1596), (1677), (1726) are inconsistent by
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1974.
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1727)   ~ (all_55_4 = e3)
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (267), (1727) imply:
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1728)   ~ (all_53_1 = e3)
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1729)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (168), (401), (1728), (1729),
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2297.
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1730)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1730) gives:
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1731)  all_57_5 = e3 & op(e2, e1) = e3
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1633), (1731) are inconsistent by sub-proof
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1936.
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1732)  all_57_10 = e3 & op(e2, e0) = e3
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1732) implies:
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1733)  all_57_10 = e3
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1734)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1734) gives:
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1735)  all_57_2 = e1 & op(e2, e3) = e1
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1735) implies:
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1736)  all_57_2 = e1
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1737)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1737) gives:
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1738)  all_57_9 = e1 & op(e3, e0) = e1
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1738) implies:
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1739)  all_57_9 = e1
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1740)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e2)
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (171), (391), (1605), (1740),
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1935.
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1741)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e2)
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1741) gives:
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1742)  all_57_4 = e2 & op(e3, e1) = e2
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1742) implies:
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1743)  all_57_4 = e2
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1744)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e3)
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1744) gives:
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1745)  all_57_4 = e3 & op(e3, e1) = e3
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1745) implies:
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1746)  all_57_4 = e3
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1743), (1746) are inconsistent by sub-proof
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2482.
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1747)  all_57_5 = e3 & op(e2, e1) = e3
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1747) implies:
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1748)  all_57_5 = e3
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (165), (222), (401), (1626),
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1736), (1748), (function-axioms) are inconsistent
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2469.
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1749)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e1) = e3)
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (39), (374), (1605), (1655), (1658), (1749),
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1933.
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1750)  all_57_9 = e2 & op(e3, e0) = e2
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1739), (1750) are inconsistent by sub-proof
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2481.
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1751)  all_57_10 = e1 & op(e2, e0) = e1
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1751) implies:
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1752)  all_57_10 = e1
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1733), (1752) are inconsistent by sub-proof
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2248.
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1753)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1753) gives:
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1754)  all_57_11 = e1 & op(e1, e0) = e1
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1754) implies:
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1755)  all_57_11 = e1
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (39), (216), (217),
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (374), (1638), (1683), (1755), (function-axioms)
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1931.
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1756)  all_57_15 = e1 & op(e0, e0) = e1
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1756) implies:
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1757)  op(e0, e0) = e1
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (1607), (1654), (1657), (1757),
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2086.
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1758)  all_57_3 = e1 & op(e2, e2) = e1
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1758) implies:
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1759)  op(e2, e2) = e1
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (401), (1759), (function-axioms) are
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2306.
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1760)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1760) gives:
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1761)  all_57_5 = e1 & op(e2, e1) = e1
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1633), (1761) are inconsistent by sub-proof
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2361.
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1762)  all_57_10 = e1 & op(e2, e0) = e1
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1762) implies:
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1763)  all_57_10 = e1
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1733), (1763) are inconsistent by sub-proof
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2248.
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1764)  all_55_10 = e0
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (1607), (1764) are inconsistent by
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2118.
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1765)  all_38_2 = e2
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (1765) imply:
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1766)  all_6_2 = e2
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (1766) imply:
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1767)  op(e1, e1) = e2
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1768)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e2)
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (171), (391), (1605), (1768),
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1935.
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1769)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e2)
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1769) gives:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1770)  all_57_4 = e2 & op(e3, e1) = e2
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (9), (39), (221), (374), (1605), (1633),
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1655), (1658), (1770), (function-axioms) are
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1930.
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1771)  all_57_9 = e2 & op(e3, e0) = e2
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1771) implies:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1772)  all_57_9 = e2
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1773)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2)
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (168), (390), (1605), (1773),
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1929.
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1774)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e3) = e2)
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1774) gives:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1775)  all_57_6 = e2 & op(e1, e3) = e2
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1775) implies:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1776)  all_57_6 = e2
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1777)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1777) gives:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1778)  all_57_12 = e2 & op(e0, e3) = e2
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1778) implies:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1779)  all_57_12 = e2
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (230), (232), (236),
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1604), (1776), (1779), (function-axioms) are
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1926.
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1780)  all_57_13 = e2 & op(e0, e2) = e2
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1780) implies:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1781)  op(e0, e2) = e2
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (393), (1781), (function-axioms) are
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2335.
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1782)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1782) gives:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1783)  all_57_14 = e2 & op(e0, e1) = e2
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1783) implies:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1784)  all_57_14 = e2
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1785)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e3)
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1785) gives:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1786)  all_57_4 = e3 & op(e3, e1) = e3
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1786) implies:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1787)  all_57_4 = e3
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1788)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1788) gives:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1789)  all_57_6 = e3 & op(e1, e3) = e3
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1789) implies:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1790)  all_57_6 = e3
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1776), (1790) imply:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1791)  e3 = e2
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1791) implies:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1792)  e3 = e2
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1787), (1792) imply:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1793)  all_57_4 = e2
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (218), (219),
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (220), (221), (374), (1784), (1793),
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2370.
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1794)  all_57_7 = e3 & op(e1, e2) = e3
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1794) implies:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1795)  all_57_7 = e3
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1638), (1795) are inconsistent by sub-proof
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2269.
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1796)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1796) gives:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1797)  all_57_8 = e3 & op(e1, e1) = e3
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1797) implies:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1798)  op(e1, e1) = e3
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (374), (1798), (function-axioms) are
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2468.
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1799)  all_57_11 = e3 & op(e1, e0) = e3
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1799) implies:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1800)  all_57_11 = e3
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1801)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1801) gives:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1802)  all_57_9 = e1 & op(e3, e0) = e1
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1772), (1802) are inconsistent by sub-proof
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2451.
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1803)  all_57_10 = e1 & op(e2, e0) = e1
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1803) implies:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1804)  all_57_10 = e1
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1805)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1805) gives:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1806)  all_57_2 = e3 & op(e2, e3) = e3
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1806) implies:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1807)  all_57_2 = e3
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1808)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e1)
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1808) gives:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1809)  all_57_0 = e1 & op(e3, e3) = e1
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1604), (1809) are inconsistent by sub-proof
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2454.
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1810)  all_57_2 = e1 & op(e2, e3) = e1
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1810) implies:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1811)  all_57_2 = e1
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1807), (1811) imply:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1812)  e3 = e1
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1787), (1812) imply:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1813)  all_57_4 = e1
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (39), (218), (221),
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (374), (1607), (1784), (1813), (function-axioms)
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2408.
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1814)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e3) = e1)
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1814) gives:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1815)  all_57_6 = e1 & op(e1, e3) = e1
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1776), (1815) are inconsistent by sub-proof
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2389.
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1816)  all_57_12 = e1 & op(e0, e3) = e1
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1816) implies:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1817)  all_57_12 = e1
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1818)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1818) gives:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1819)  all_57_6 = e1 & op(e1, e3) = e1
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1819) implies:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1820)  all_57_6 = e1
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (234), (1605), (1807), (1817),
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1820), (function-axioms) are inconsistent by
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1923.
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1821)  all_57_7 = e1 & op(e1, e2) = e1
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1821) implies:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1822)  all_57_7 = e1
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1638), (1822) are inconsistent by sub-proof
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2211.
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1823)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1823) gives:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1824)  all_57_8 = e1 & op(e1, e1) = e1
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1824) implies:
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1825)  op(e1, e1) = e1
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1767), (1825), (function-axioms) are
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2423.
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1826)  all_57_11 = e1 & op(e1, e0) = e1
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1826) implies:
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1827)  all_57_11 = e1
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1800), (1827) imply:
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1828)  e3 = e1
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1828) implies:
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1829)  e3 = e1
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1787), (1829) imply:
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1830)  all_57_4 = e1
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (39), (218), (221),
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (374), (1607), (1784), (1830), (function-axioms)
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2408.
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1831)  all_57_3 = e3 & op(e2, e2) = e3
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1831) implies:
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1832)  op(e2, e2) = e3
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (401), (1832), (function-axioms) are
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2298.
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1833)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1833) gives:
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1834)  all_57_5 = e3 & op(e2, e1) = e3
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1834) implies:
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1835)  all_57_5 = e3
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1633), (1835) are inconsistent by sub-proof
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2471.
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1836)  all_57_10 = e3 & op(e2, e0) = e3
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1836) implies:
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1837)  all_57_10 = e3
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1804), (1837) imply:
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1838)  e3 = e1
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1838) implies:
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1839)  e3 = e1
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1787), (1839) imply:
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1840)  all_57_4 = e1
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (39), (218), (221),
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (374), (1607), (1784), (1840), (function-axioms)
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2408.
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1841)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1841) gives:
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1842)  all_57_11 = e1 & op(e1, e0) = e1
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1842) implies:
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1843)  all_57_11 = e1
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1800), (1843) imply:
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1844)  e3 = e1
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1787), (1844) imply:
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1845)  all_57_4 = e1
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (39), (218), (221),
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (374), (1607), (1784), (1845), (function-axioms)
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2408.
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1846)  all_57_15 = e1 & op(e0, e0) = e1
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1846) implies:
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1847)  op(e0, e0) = e1
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (1607), (1654), (1657), (1847),
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2086.
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1848)  all_57_5 = e3 & op(e2, e1) = e3
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1848) implies:
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1849)  all_57_5 = e3
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1633), (1849) are inconsistent by sub-proof
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2471.
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1850)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e1) = e3)
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (39), (374), (1605), (1655), (1658), (1850),
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1933.
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1851)  all_57_15 = e2 & op(e0, e0) = e2
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1851) implies:
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1852)  op(e0, e0) = e2
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (373), (1852), (function-axioms) are
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2334.
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1853)  all_57_12 = e2 & op(e0, e3) = e2
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1853) implies:
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1854)  all_57_12 = e2
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1855)  op(e0, e3) = e2
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1856)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e2)
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1856) gives:
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1857)  all_57_6 = e2 & op(e1, e3) = e2
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1857) implies:
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1858)  all_57_6 = e2
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (230), (232), (236),
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1604), (1854), (1858), (function-axioms) are
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1926.
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1859)  all_57_7 = e2 & op(e1, e2) = e2
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1859) implies:
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1860)  all_57_7 = e2
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1638), (1860) are inconsistent by sub-proof
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2207.
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1861)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e0) = e2)
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1861) gives:
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_25,
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, e0, simplifying with (1656), (1855) gives:
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1862)  all_52_25 = e2
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1659), (1862) imply:
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1863)  op(e2, e2) = e3
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (401), (1863), (function-axioms) are
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2298.
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1864)  all_57_11 = e2 & op(e1, e0) = e2
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1864) implies:
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1865)  all_57_11 = e2
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1866)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1866) gives:
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1867)  all_57_6 = e3 & op(e1, e3) = e3
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1867) implies:
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1868)  all_57_6 = e3
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1869)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1869) gives:
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1870)  all_57_6 = e1 & op(e1, e3) = e1
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1870) implies:
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1871)  all_57_6 = e1
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (9), (39), (161), (214), (217),
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (374), (1607), (1643), (1865), (1871),
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2340.
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1872)  all_57_7 = e1 & op(e1, e2) = e1
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1872) implies:
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1873)  all_57_7 = e1
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1638), (1873) are inconsistent by sub-proof
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2211.
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1874)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1874) gives:
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1875)  all_57_8 = e1 & op(e1, e1) = e1
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1875) implies:
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1876)  op(e1, e1) = e1
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1767), (1876), (function-axioms) are
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2423.
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1877)  all_57_11 = e1 & op(e1, e0) = e1
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1877) implies:
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1878)  all_57_11 = e1
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1865), (1878) imply:
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1879)  e2 = e1
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1879) implies:
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1880)  e2 = e1
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1854), (1880) imply:
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1881)  all_57_12 = e1
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (168), (234), (390), (1605),
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1868), (1881), (function-axioms) are inconsistent
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1921.
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1882)  all_57_7 = e3 & op(e1, e2) = e3
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1882) implies:
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1883)  all_57_7 = e3
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1638), (1883) are inconsistent by sub-proof
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2269.
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1884)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (39), (374), (1865), (1884),
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2040.
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | |   (1885)  all_57_13 = e0 & op(e0, e2) = e0
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1885) implies:
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | |   (1886)  op(e0, e2) = e0
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (1625), (1886), (function-axioms) are
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2332.
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | |   (1887)  all_57_10 = e0 & op(e2, e0) = e0
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1887) implies:
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | |   (1888)  op(e2, e0) = e0
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (1626), (1888), (function-axioms) are
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2470.
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | End of split
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | End of split
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | End of split
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | End of split
% 219.27/36.98  | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | End of split
% 219.27/36.98  | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.98  | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | |   (1889)  all_30_2 = e1
% 219.27/36.98  | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | COMBINE_EQS: (330), (1889) imply:
% 219.27/36.98  | | | | | | | | | | | | | | | | |   (1890)  all_4_2 = e1
% 219.27/36.98  | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | SIMP: (1890) implies:
% 219.27/36.98  | | | | | | | | | | | | | | | | |   (1891)  all_4_2 = e1
% 219.27/36.98  | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | REDUCE: (351), (1891) imply:
% 219.27/36.98  | | | | | | | | | | | | | | | | |   (1892)   ~ (all_53_3 = e1)
% 219.27/36.98  | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | REDUCE: (370), (1891) imply:
% 219.27/36.98  | | | | | | | | | | | | | | | | |   (1893)   ~ (all_53_12 = e1)
% 219.27/36.98  | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | REDUCE: (371), (1891) imply:
% 219.27/36.98  | | | | | | | | | | | | | | | | |   (1894)   ~ (all_53_13 = e1)
% 219.27/36.98  | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | REDUCE: (378), (1891) imply:
% 219.27/36.98  | | | | | | | | | | | | | | | | |   (1895)   ~ (e3 = e1)
% 219.27/36.98  | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | REDUCE: (373), (1891) imply:
% 219.27/36.98  | | | | | | | | | | | | | | | | |   (1896)   ~ (e2 = e1)
% 219.27/36.98  | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | REDUCE: (36), (1891) imply:
% 219.27/36.98  | | | | | | | | | | | | | | | | |   (1897)  op(e0, e0) = e1
% 219.27/36.98  | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | BETA: splitting (88) gives:
% 219.27/36.98  | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.98  | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | |   (1898)   ~ (all_38_2 = e2)
% 219.27/36.98  | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | REDUCE: (249), (1898) imply:
% 219.27/36.98  | | | | | | | | | | | | | | | | | |   (1899)   ~ (all_6_2 = e2)
% 219.27/36.98  | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 219.27/36.98  | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | |   (1900)  all_55_10 = e3
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (374), (1900) are inconsistent by sub-proof
% 219.27/36.98  | | | | | | | | | | | | | | | | | | |            #2500.
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | |   (1901)   ~ (all_55_10 = e3)
% 219.27/36.98  | | | | | | | | | | | | | | | | | | |   (1902)  all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | BETA: splitting (1902) gives:
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | |   (1903)  all_55_10 = e2
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (1899), (1903) are inconsistent by
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | |            sub-proof #2499.
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | |   (1904)   ~ (all_55_10 = e2)
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | |   (1905)  all_55_10 = e1 | all_55_10 = e0
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | BETA: splitting (1905) gives:
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | |   (1906)  all_55_10 = e1
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (336), (1906) imply:
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | |   (1907)  all_6_2 = e1
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | SIMP: (1907) implies:
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | |   (1908)  all_6_2 = e1
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | REDUCE: (361), (1908) imply:
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | |   (1909)   ~ (all_53_6 = e1)
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | REDUCE: (364), (1908) imply:
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | |   (1910)   ~ (all_53_9 = e1)
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | REDUCE: (368), (1908) imply:
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | |   (1911)   ~ (all_53_14 = e1)
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (1908) imply:
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | |   (1912)  op(e1, e1) = e1
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | |   (1913)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1913) gives:
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | |   (1914)  all_57_1 = e1 & op(e3, e2) = e1
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1914) implies:
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | |   (1915)  all_57_1 = e1
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | |   (1916)  op(e3, e2) = e1
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | |   (1917)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e1)
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1917) gives:
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | |   (1918)  all_57_0 = e1 & op(e3, e3) = e1
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1604), (1918) are inconsistent by sub-proof
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | |            #2454.
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | |   (1919)  all_57_2 = e1 & op(e2, e3) = e1
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1919) implies:
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | |   (1920)  op(e2, e3) = e1
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_1, e1,
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (168), (1920) gives:
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | |   (1921)  all_53_1 = e1
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_4, e1,
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (171), (1916) gives:
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | |   (1922)  all_53_4 = e1
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (1921) imply:
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | |   (1923)   ~ (all_53_3 = e1)
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (147), (1921) imply:
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | |   (1924)   ~ (all_53_9 = e1)
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (1921) imply:
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | |   (1925)   ~ (all_53_13 = e1)
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (1922) imply:
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | |   (1926)   ~ (all_53_12 = e1)
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1927)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | |               all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | |               all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | |               all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1927) gives:
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1928)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_7)
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1928) implies:
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1929)  op(e3, e3) = all_52_1
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1930)  op(all_52_1, all_52_1) = e3
% 219.27/36.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (159), (160), (207),
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (208), (209), (210), (393), (1597), (1605),
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1892), (1897), (1929), (1930), (function-axioms)
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1915.
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1931)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |           & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_15)
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (374), (1920), (1931), (function-axioms) are
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2110.
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1932)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | |               all_52_21) = e1 & op(all_52_23, all_52_23) =
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(all_52_25, all_52_25) = e3 &
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | |               all_52_29) = e1 & op(all_52_31, all_52_31) =
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_29) & $i(all_52_31))
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1932) gives:
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1933)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |           & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |           & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |           & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_23)
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1933) implies:
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1934)  op(e1, e0) = all_52_23
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1935)  op(e1, e1) = all_52_21
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1936)  op(all_52_23, all_52_23) = e0
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_14,
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_23, e0, e1, simplifying with (161), (1934)
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1937)  all_53_14 = all_52_23
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_21, e1, e1, simplifying with (1912), (1935)
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1938)  all_52_21 = e1
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (1937) imply:
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1939)  all_55_11 = all_52_23
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (1937) imply:
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1940)   ~ (all_53_12 = all_52_23)
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (111), (1937) imply:
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1941)   ~ (all_53_13 = all_52_23)
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1911), (1937) imply:
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1942)   ~ (all_52_23 = e1)
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1943)  all_55_7 = e3
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (1943) imply:
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1944)  all_53_13 = e3
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1944) implies:
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1945)  all_53_13 = e3
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (114), (1945) imply:
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1946)   ~ (all_53_12 = e3)
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1941), (1945) imply:
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1947)   ~ (all_52_23 = e3)
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1947) implies:
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1948)   ~ (all_52_23 = e3)
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (194), (202), (268), (1600), (1893), (1897),
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1936), (1939), (1940), (1942), (1946), (1948),
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1913.
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1949)   ~ (all_55_7 = e3)
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (258), (1949) imply:
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1950)   ~ (all_53_13 = e3)
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1951)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1951) gives:
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1952)  all_57_2 = e3 & op(e2, e3) = e3
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1952) implies:
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1953)  all_57_2 = e3
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (166), (223),
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (226), (228), (229), (1894), (1910), (1915),
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1953), (function-axioms) are inconsistent by
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1907.
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.27/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1954)  all_57_3 = e3 & op(e2, e2) = e3
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1954) implies:
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1955)  op(e2, e2) = e3
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (401), (1955), (function-axioms) are
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2298.
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1956)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1956) gives:
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1957)  all_57_5 = e3 & op(e2, e1) = e3
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1957) implies:
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1958)  all_57_5 = e3
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1959)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e0)
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (170), (1599), (1958), (1959),
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1906.
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1960)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1960) gives:
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1961)  all_57_8 = e0 & op(e1, e1) = e0
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1961) implies:
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1962)  op(e1, e1) = e0
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1912), (1962), (function-axioms) are
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2427.
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1963)  all_57_14 = e0 & op(e0, e1) = e0
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1963) implies:
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1964)  all_57_14 = e0
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1965)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1965) gives:
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1966)  all_57_12 = e2 & op(e0, e3) = e2
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1966) implies:
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1967)  all_57_12 = e2
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1968)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1968) gives:
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1969)  all_57_12 = e3 & op(e0, e3) = e3
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1969) implies:
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1970)  all_57_12 = e3
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1967), (1970) are inconsistent by sub-proof
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2392.
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1971)  all_57_13 = e3 & op(e0, e2) = e3
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1971) implies:
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1972)  all_57_13 = e3
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1973)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e3)
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1973) gives:
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1974)  all_57_0 = e3 & op(e3, e3) = e3
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1974) implies:
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1975)  op(e3, e3) = e3
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1605), (1975), (function-axioms) are
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2494.
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1976)  all_57_1 = e3 & op(e3, e2) = e3
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1976) implies:
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1977)  all_57_1 = e3
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1915), (1977) imply:
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1978)  e3 = e1
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1978) implies:
% 219.56/36.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1979)  e3 = e1
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1972), (1979) imply:
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1980)  all_57_13 = e1
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (209), (210), (1897),
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1964), (1980), (function-axioms) are inconsistent
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2068.
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1981)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e3)
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1981) gives:
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1982)  all_57_4 = e3 & op(e3, e1) = e3
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (218), (219),
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (220), (1599), (1912), (1958), (1982),
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1903.
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1983)  all_57_9 = e3 & op(e3, e0) = e3
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (165), (212), (395), (401), (1897),
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1934), (1936), (1983), (function-axioms) are
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1901.
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1984)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1984) gives:
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1985)  all_57_14 = e3 & op(e0, e1) = e3
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1985) implies:
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1986)  all_57_14 = e3
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1964), (1986) are inconsistent by sub-proof
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2420.
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1987)  all_57_15 = e3 & op(e0, e0) = e3
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1987) implies:
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1988)  op(e0, e0) = e3
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1897), (1988), (function-axioms) are
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2183.
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1989)  all_57_13 = e2 & op(e0, e2) = e2
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1989) implies:
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1990)  op(e0, e2) = e2
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (393), (1990), (function-axioms) are
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2335.
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1991)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (1897), (1964), (1991),
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2073.
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1992)  all_57_10 = e3 & op(e2, e0) = e3
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1992) implies:
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1993)  op(e2, e0) = e3
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (1950), (1993), (function-axioms) are
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2301.
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1994)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |           & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |           & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |           & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_31)
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1994) implies:
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1995)  op(e0, e0) = all_52_31
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1996)  op(all_52_31, all_52_31) = e0
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (1607), (1897), (1995), (1996),
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2086.
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | |   (1997)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e3) = e1)
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1997) gives:
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | |   (1998)  all_57_6 = e1 & op(e1, e3) = e1
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1998) implies:
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | |   (1999)  all_57_6 = e1
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2000)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2)
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (168), (390), (1605), (2000),
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | |            #1929.
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2001)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e3) = e2)
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2001) gives:
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2002)  all_57_6 = e2 & op(e1, e3) = e2
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2002) implies:
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2003)  all_57_6 = e2
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1999), (2003) are inconsistent by sub-proof
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2233.
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2004)  all_57_12 = e2 & op(e0, e3) = e2
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2004) implies:
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2005)  all_57_12 = e2
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2006)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e3)
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2006) gives:
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2007)  all_57_0 = e3 & op(e3, e3) = e3
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2007) implies:
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2008)  op(e3, e3) = e3
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1605), (2008), (function-axioms) are
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2494.
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2009)  all_57_2 = e3 & op(e2, e3) = e3
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2009) implies:
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2010)  all_57_2 = e3
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (166), (223),
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (226), (228), (229), (1894), (1910), (1915),
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2010), (function-axioms) are inconsistent by
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1907.
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2011)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e3) = e3)
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2011) gives:
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2012)  all_57_6 = e3 & op(e1, e3) = e3
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2012) implies:
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2013)  all_57_6 = e3
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1999), (2013) are inconsistent by sub-proof
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2017.
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2014)  all_57_12 = e3 & op(e0, e3) = e3
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2014) implies:
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2015)  all_57_12 = e3
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2005), (2015) are inconsistent by sub-proof
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2392.
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | |   (2016)  all_57_12 = e1 & op(e0, e3) = e1
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (1892), (2016), (function-axioms) are
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1947.
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | |   (2017)  all_57_3 = e1 & op(e2, e2) = e1
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2017) implies:
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | |   (2018)  op(e2, e2) = e1
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (401), (2018), (function-axioms) are
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2306.
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | |   (2019)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2019) gives:
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | |   (2020)  all_57_7 = e1 & op(e1, e2) = e1
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (1909), (2020), (function-axioms) are
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2265.
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | |   (2021)  all_57_13 = e1 & op(e0, e2) = e1
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2021) implies:
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | |   (2022)  all_57_13 = e1
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (207), (209),
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | |            (210), (1597), (1897), (2022), (function-axioms)
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1918.
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | |   (2023)  all_55_10 = e0
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (1607), (2023) are inconsistent by
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | |            sub-proof #2118.
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.01  | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.01  | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | |   (2024)  all_38_2 = e2
% 219.56/37.01  | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (2024) imply:
% 219.56/37.01  | | | | | | | | | | | | | | | | | |   (2025)  all_6_2 = e2
% 219.56/37.01  | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | | REDUCE: (350), (2025) imply:
% 219.56/37.01  | | | | | | | | | | | | | | | | | |   (2026)   ~ (all_53_2 = e2)
% 219.56/37.01  | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | | REDUCE: (39), (2025) imply:
% 219.56/37.01  | | | | | | | | | | | | | | | | | |   (2027)  op(e1, e1) = e2
% 219.56/37.01  | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 219.56/37.01  | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | | |   (2028)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 219.56/37.01  | | | | | | | | | | | | | | | | | | |             all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 219.56/37.01  | | | | | | | | | | | | | | | | | | |             op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 219.56/37.01  | | | | | | | | | | | | | | | | | | |               all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 219.56/37.01  | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 219.56/37.01  | | | | | | | | | | | | | | | | | | |             op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 219.56/37.01  | | | | | | | | | | | | | | | | | | |             $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 219.56/37.01  | | | | | | | | | | | | | | | | | | |             $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 219.56/37.01  | | | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 219.56/37.01  | | | | | | | | | | | | | | | | | | |               all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 219.56/37.01  | | | | | | | | | | | | | | | | | | |             & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 219.56/37.01  | | | | | | | | | | | | | | | | | | |               all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 219.56/37.01  | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 219.56/37.01  | | | | | | | | | | | | | | | | | | |             & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 219.56/37.01  | | | | | | | | | | | | | | | | | | |             $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | BETA: splitting (2028) gives:
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | |   (2029)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | |           all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | |           op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | |             all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | |           $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | |           $i(all_52_7)
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | ALPHA: (2029) implies:
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | |   (2030)  op(e3, e3) = all_52_1
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | |   (2031)  op(all_52_1, all_52_1) = e3
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (159), (160), (207),
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | |            (208), (209), (210), (393), (1597), (1605),
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | |            (1892), (1897), (2030), (2031), (function-axioms)
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1915.
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | |   (2032)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | |           all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | |           op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | |             all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | |           & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | |           $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | |           $i(all_52_15)
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | ALPHA: (2032) implies:
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | |   (2033)  op(e2, e0) = all_52_15
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | |   (2034)  op(e2, e3) = all_52_9
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | |   (2035)  op(all_52_15, all_52_15) = e0
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | |   (2036)  op(all_52_9, all_52_9) = e3
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (103), (159), (160),
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | |            (165), (168), (169), (201), (207), (208), (209),
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | |            (210), (212), (267), (390), (393), (395), (1591),
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | |            (1594), (1595), (1597), (1600), (1605), (1892),
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | |            (1897), (2033), (2034), (2035), (2036),
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | |            #1894.
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | | |   (2037)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 219.56/37.01  | | | | | | | | | | | | | | | | | | |             & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 219.56/37.01  | | | | | | | | | | | | | | | | | | |             & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 219.56/37.01  | | | | | | | | | | | | | | | | | | |               all_52_21) = e1 & op(all_52_23, all_52_23) =
% 219.56/37.01  | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 219.56/37.01  | | | | | | | | | | | | | | | | | | |             all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 219.56/37.01  | | | | | | | | | | | | | | | | | | |             = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 219.56/37.01  | | | | | | | | | | | | | | | | | | |             $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 219.56/37.01  | | | | | | | | | | | | | | | | | | |             & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 219.56/37.01  | | | | | | | | | | | | | | | | | | |             e0 & op(all_52_25, all_52_25) = e3 &
% 219.56/37.01  | | | | | | | | | | | | | | | | | | |             op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 219.56/37.01  | | | | | | | | | | | | | | | | | | |               all_52_29) = e1 & op(all_52_31, all_52_31) =
% 219.56/37.01  | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 219.56/37.01  | | | | | | | | | | | | | | | | | | |             all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 219.56/37.01  | | | | | | | | | | | | | | | | | | |             = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 219.56/37.01  | | | | | | | | | | | | | | | | | | |             $i(all_52_29) & $i(all_52_31))
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | BETA: splitting (2037) gives:
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | |   (2038)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | |           all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | |           op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | |             all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | |           & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | |           & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | |           & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | |           $i(all_52_23)
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | ALPHA: (2038) implies:
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | |   (2039)  op(e1, e0) = all_52_23
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | |   (2040)  op(e1, e1) = all_52_21
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | |   (2041)  op(e1, e3) = all_52_17
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | |   (2042)  op(all_52_23, all_52_23) = e0
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | |   (2043)  op(all_52_21, all_52_21) = e1
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | |   (2044)  op(all_52_17, all_52_17) = e3
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | |   (2045)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2045) gives:
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | |   (2046)  all_57_9 = e2 & op(e3, e0) = e2
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2046) implies:
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | |   (2047)  all_57_9 = e2
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | |   (2048)  op(e3, e0) = e2
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | |   (2049)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2049) gives:
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | |   (2050)  all_57_12 = e2 & op(e0, e3) = e2
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2050) implies:
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | |   (2051)  all_57_12 = e2
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (2052)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e2)
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2052) gives:
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2053)  all_57_4 = e2 & op(e3, e1) = e2
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2053) implies:
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2054)  all_57_4 = e2
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2055)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e3)
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (233), (1604), (1605), (2047),
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2054), (2055), (function-axioms) are inconsistent
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2449.
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2056)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e3)
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2056) gives:
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2057)  all_57_4 = e3 & op(e3, e1) = e3
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2057) implies:
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2058)  all_57_4 = e3
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2054), (2058) are inconsistent by sub-proof
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2482.
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2059)  all_57_9 = e3 & op(e3, e0) = e3
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (165), (212), (395), (401), (1897),
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2039), (2042), (2059), (function-axioms) are
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1901.
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2060)  all_57_5 = e2 & op(e2, e1) = e2
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2060) implies:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2061)  all_57_5 = e2
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2062)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e1)
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2062) gives:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2063)  all_57_4 = e1 & op(e3, e1) = e1
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2063) implies:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2064)  all_57_4 = e1
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2065)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (168), (401), (1595), (2065),
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1942.
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2066)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0)
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2066) gives:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2067)  all_57_5 = e0 & op(e2, e1) = e0
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2061), (2067) are inconsistent by sub-proof
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2428.
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2068)  all_57_10 = e0 & op(e2, e0) = e0
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2068) implies:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2069)  all_57_10 = e0
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2070)  op(e2, e0) = e0
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2071)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2071) gives:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2072)  all_57_9 = e3 & op(e3, e0) = e3
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (165), (212), (395), (401), (1897),
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2039), (2042), (2072), (function-axioms) are
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1901.
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2073)  all_57_10 = e3 & op(e2, e0) = e3
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2073) implies:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2074)  all_57_10 = e3
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2069), (2074) are inconsistent by sub-proof
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1989.
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2075)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2075) gives:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2076)  all_57_11 = e3 & op(e1, e0) = e3
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2076) implies:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2077)  all_57_11 = e3
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2078)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e0)
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2078) gives:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2079)  all_57_4 = e0 & op(e3, e1) = e0
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2079) implies:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2080)  op(e3, e1) = e0
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (1599), (2080), (function-axioms) are
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2267.
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2081)  all_57_5 = e0 & op(e2, e1) = e0
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2061), (2081) are inconsistent by sub-proof
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2428.
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2082)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2082) gives:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2083)  all_57_8 = e0 & op(e1, e1) = e0
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2083) implies:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2084)  op(e1, e1) = e0
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2085)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2085) gives:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2086)  all_57_2 = e1 & op(e2, e3) = e1
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2086) implies:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2087)  all_57_2 = e1
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2062) gives:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (159), (207),
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (209), (210), (221), (225), (374), (393), (401),
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1897), (2061), (2064), (2069), (2087),
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1887.
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2088)  all_57_5 = e1 & op(e2, e1) = e1
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2061), (2088) are inconsistent by sub-proof
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1886.
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2089)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e1)
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2089) gives:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2090)  all_57_8 = e1 & op(e1, e1) = e1
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2090) implies:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2091)  op(e1, e1) = e1
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2084), (2091), (function-axioms) are
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2427.
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2092)  all_57_14 = e1 & op(e0, e1) = e1
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2092) implies:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2093)  all_57_14 = e1
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (159), (207), (209),
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (210), (393), (1897), (2093), (function-axioms)
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2175.
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2094)  all_57_3 = e1 & op(e2, e2) = e1
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2094) implies:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2095)  op(e2, e2) = e1
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (401), (2095), (function-axioms) are
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2306.
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2096)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2096) gives:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2097)  all_57_5 = e1 & op(e2, e1) = e1
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2097) implies:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2098)  all_57_5 = e1
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2061), (2098) are inconsistent by sub-proof
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1885.
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2099)  all_57_10 = e1 & op(e2, e0) = e1
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2069), (2099) are inconsistent by sub-proof
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2242.
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2100)  all_57_14 = e0 & op(e0, e1) = e0
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2100) implies:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2101)  all_57_14 = e0
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2102)  all_57_15 = e0 & op(e0, e0) = e0
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2102) implies:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2103)  all_57_15 = e0
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2104)  op(e0, e0) = e0
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (159), (208),
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (209), (210), (373), (393), (2101), (2103),
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2104), (function-axioms) are inconsistent by
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2120.
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2105)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2105) implies:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2106)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0)
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2107)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2107) gives:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2108)  all_57_12 = e3 & op(e0, e3) = e3
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2108) implies:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2109)  all_57_12 = e3
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2051), (2109) are inconsistent by sub-proof
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2392.
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2110)  all_57_13 = e3 & op(e0, e2) = e3
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2110) implies:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2111)  all_57_13 = e3
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2112)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 219.56/37.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (171), (401), (1598), (2112),
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1940.
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2113)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0)
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2113) gives:
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2114)  all_57_7 = e0 & op(e1, e2) = e0
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2114) implies:
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2115)  all_57_7 = e0
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2116)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2116) gives:
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2117)  all_57_1 = e1 & op(e3, e2) = e1
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2117) implies:
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2118)  all_57_1 = e1
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2119)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2119) gives:
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2120)  all_57_2 = e1 & op(e2, e3) = e1
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2120) implies:
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2121)  all_57_2 = e1
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (159), (207),
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (209), (210), (221), (225), (374), (393), (401),
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1897), (2061), (2064), (2069), (2121),
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1887.
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2122)  all_57_3 = e1 & op(e2, e2) = e1
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2122) implies:
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2123)  op(e2, e2) = e1
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (226), (228), (229),
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2118), (2123), (function-axioms) are inconsistent
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1908.
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2124)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2124) gives:
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2125)  all_57_5 = e1 & op(e2, e1) = e1
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2125) implies:
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2126)  all_57_5 = e1
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2061), (2126) imply:
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2127)  e2 = e1
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2127) implies:
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2128)  e2 = e1
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2051), (2128) imply:
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2129)  all_57_12 = e1
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (209), (1897), (2101), (2111),
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2129), (function-axioms) are inconsistent by
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2072.
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2130)  all_57_10 = e1 & op(e2, e0) = e1
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (1894), (2130), (function-axioms) are
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2084.
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2131)  all_57_3 = e1 & op(e2, e2) = e1
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2131) implies:
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2132)  op(e2, e2) = e1
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (401), (2132), (function-axioms) are
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2306.
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2133)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2133) gives:
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2134)  all_57_7 = e1 & op(e1, e2) = e1
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2134) implies:
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2135)  all_57_7 = e1
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2115), (2135) imply:
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2136)  e1 = e0
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2064), (2136) imply:
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2137)  all_57_4 = e0
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (219), (220),
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (221), (374), (2101), (2137), (function-axioms)
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2371.
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2138)  all_57_13 = e1 & op(e0, e2) = e1
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2138) implies:
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2139)  all_57_13 = e1
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (209), (210),
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1597), (1897), (2106), (2139), (function-axioms)
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1919.
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2140)  all_57_13 = e0 & op(e0, e2) = e0
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2140) implies:
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2141)  op(e0, e2) = e0
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (36), (107), (111), (113), (114), (127),
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (129), (134), (136), (137), (141), (142), (144),
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (159), (160), (161), (163), (164), (165), (190),
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (194), (196), (197), (202), (204), (207), (208),
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (209), (210), (244), (248), (256), (257), (268),
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (270), (351), (370), (371), (372), (373), (378),
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (391), (392), (393), (395), (401), (1596), (1605),
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2070), (2141), (function-axioms) are inconsistent
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1875.
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2142)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2142) gives:
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2143)  all_57_14 = e3 & op(e0, e1) = e3
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2101), (2143) are inconsistent by sub-proof
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2338.
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2144)  all_57_15 = e3 & op(e0, e0) = e3
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2144) implies:
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2145)  all_57_15 = e3
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (211), (212), (2069),
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2077), (2145) are inconsistent by sub-proof
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2137.
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2146)  all_57_15 = e3 & op(e0, e0) = e3
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2146) implies:
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2147)  op(e0, e0) = e3
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1897), (2147), (function-axioms) are
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2183.
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2148)  all_57_5 = e1 & op(e2, e1) = e1
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2061), (2148) are inconsistent by sub-proof
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1886.
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2149)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e1)
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2149) gives:
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2150)  all_57_8 = e1 & op(e1, e1) = e1
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2150) implies:
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2151)  op(e1, e1) = e1
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2027), (2151), (function-axioms) are
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2423.
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2152)  all_57_14 = e1 & op(e0, e1) = e1
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2152) implies:
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2153)  all_57_14 = e1
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (207), (210), (1897),
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2051), (2153), (function-axioms) are inconsistent
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2179.
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | |   (2154)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e1) = e2)
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2154) gives:
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2155)  all_57_8 = e2 & op(e1, e1) = e2
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (401), (1893), (2027), (2040), (2043),
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | |            (2048), (function-axioms) are inconsistent by
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1874.
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2156)  all_57_14 = e2 & op(e0, e1) = e2
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2156) implies:
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2157)  all_57_14 = e2
% 219.56/37.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (159), (160),
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | |            (207), (209), (210), (218), (219), (220), (221),
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | |            (374), (393), (1597), (1607), (1897), (2027),
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | |            (2051), (2157), (function-axioms) are inconsistent
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1870.
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | |   (2158)  all_57_13 = e2 & op(e0, e2) = e2
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2158) implies:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | |   (2159)  op(e0, e2) = e2
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (393), (2159), (function-axioms) are
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2335.
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | |   (2160)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2160) gives:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | |   (2161)  all_57_14 = e2 & op(e0, e1) = e2
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2161) implies:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | |   (2162)  all_57_14 = e2
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | |   (2163)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2)
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2163) gives:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2164)  all_57_0 = e2 & op(e3, e3) = e2
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2164) implies:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2165)  op(e3, e3) = e2
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (150), (164), (190), (197), (201), (244),
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | |            (257), (267), (374), (378), (390), (1595), (1596),
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | |            (2026), (2041), (2044), (2165), (function-axioms)
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1864.
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2166)  all_57_2 = e2 & op(e2, e3) = e2
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (390), (2166), (function-axioms) are
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2504.
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | |   (2167)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e3) = e2)
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2167) gives:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2168)  all_57_6 = e2 & op(e1, e3) = e2
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2168) implies:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2169)  all_57_6 = e2
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2170)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e1)
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2170) gives:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2171)  all_57_0 = e1 & op(e3, e3) = e1
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1604), (2171) are inconsistent by sub-proof
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2454.
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2172)  all_57_2 = e1 & op(e2, e3) = e1
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2172) implies:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2173)  all_57_2 = e1
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2174)  all_57_15 = e0 & op(e0, e0) = e0
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2174) implies:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2175)  op(e0, e0) = e0
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1897), (2175), (function-axioms) are
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2290.
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2176)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2176) implies:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2177)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0)
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2178)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0)
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2177) gives:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2179)  all_57_12 = e0 & op(e0, e3) = e0
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2179) implies:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2180)  op(e0, e3) = e0
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (1597), (2180), (function-axioms) are
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2366.
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2181)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2181) gives:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2182)  all_57_13 = e0 & op(e0, e2) = e0
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2182) implies:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2183)  op(e0, e2) = e0
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2184)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e3)
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2184) gives:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2185)  all_57_0 = e3 & op(e3, e3) = e3
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2185) implies:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2186)  op(e3, e3) = e3
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (159), (207),
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (209), (210), (218), (219), (221), (230), (231),
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (232), (233), (235), (374), (393), (1607), (1897),
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2027), (2169), (2186), (function-axioms) are
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2081.
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2187)  all_57_2 = e3 & op(e2, e3) = e3
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2187) implies:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2188)  all_57_2 = e3
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2173), (2188) are inconsistent by sub-proof
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2397.
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2189)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e3) = e3)
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2189) gives:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2190)  all_57_6 = e3 & op(e1, e3) = e3
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2190) implies:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2191)  all_57_6 = e3
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2169), (2191) are inconsistent by sub-proof
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2463.
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2192)  all_57_12 = e3 & op(e0, e3) = e3
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2192) implies:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2193)  all_57_12 = e3
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2178) gives:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2194)  all_57_9 = e0 & op(e3, e0) = e0
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (1600), (2194), (function-axioms) are
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2434.
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2195)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 =
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2195) gives:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2196)  all_57_10 = e0 & op(e2, e0) = e0
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2196) implies:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2197)  op(e2, e0) = e0
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (36), (107), (111), (113), (114), (127),
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (129), (134), (136), (137), (141), (142), (144),
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (159), (160), (161), (163), (164), (165), (190),
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (194), (196), (197), (202), (204), (207), (208),
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (209), (210), (244), (248), (256), (257), (268),
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (270), (351), (370), (371), (372), (373), (378),
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (391), (392), (393), (395), (401), (1596), (1605),
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2183), (2197), (function-axioms) are inconsistent
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1875.
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2198)  all_57_11 = e0 & op(e1, e0) = e0
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2198) implies:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2199)  all_57_11 = e0
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2200)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2200) gives:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2201)  all_57_6 = e1 & op(e1, e3) = e1
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2201) implies:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2202)  op(e1, e3) = e1
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (195), (336), (374), (2041), (2044), (2202),
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1998.
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2203)  all_57_7 = e1 & op(e1, e2) = e1
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2203) implies:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2204)  all_57_7 = e1
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2205)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e3)
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2205) gives:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2206)  all_57_4 = e3 & op(e3, e1) = e3
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2206) implies:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2207)  all_57_4 = e3
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2208)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2208) gives:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2209)  all_57_6 = e3 & op(e1, e3) = e3
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2209) implies:
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2210)  all_57_6 = e3
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2169), (2210) imply:
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2211)  e3 = e2
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2207), (2211) imply:
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2212)  all_57_4 = e2
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (218), (219),
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (220), (221), (374), (2162), (2212),
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2370.
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2213)  all_57_7 = e3 & op(e1, e2) = e3
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2213) implies:
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2214)  all_57_7 = e3
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2204), (2214) imply:
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2215)  e3 = e1
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2207), (2215) imply:
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2216)  all_57_4 = e1
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (39), (218), (221),
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (374), (1607), (2162), (2216), (function-axioms)
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2408.
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2217)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (39), (374), (2199), (2217),
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1863.
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2218)  all_57_5 = e3 & op(e2, e1) = e3
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2218) implies:
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2219)  all_57_5 = e3
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (159), (207),
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (209), (210), (218), (219), (393), (1607), (1897),
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2027), (2162), (2219), (function-axioms) are
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2174.
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2220)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e1) = e3)
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2220) gives:
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2221)  all_57_8 = e3 & op(e1, e1) = e3
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2221) implies:
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2222)  op(e1, e1) = e3
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (374), (2222), (function-axioms) are
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2468.
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2223)  all_57_14 = e3 & op(e0, e1) = e3
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2223) implies:
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2224)  all_57_14 = e3
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2162), (2224) imply:
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2225)  e3 = e2
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2193), (2225) imply:
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2226)  all_57_12 = e2
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (230), (232), (236),
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1604), (2169), (2226), (function-axioms) are
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1926.
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2227)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (2027), (2199), (2227),
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1861.
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2228)  all_57_14 = e0 & op(e0, e1) = e0
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2228) implies:
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2229)  all_57_14 = e0
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2162), (2229) imply:
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2230)  e2 = e0
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2169), (2230) imply:
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2231)  all_57_6 = e0
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (234), (236), (1605),
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2173), (2231), (function-axioms) are inconsistent
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2390.
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2232)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e3) = e1)
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (160), (195), (336), (374), (1892), (2041),
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2044), (2232), (function-axioms) are inconsistent
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1860.
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2233)  all_57_12 = e2 & op(e0, e3) = e2
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2233) implies:
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2234)  all_57_12 = e2
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (159), (160),
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | |            (207), (209), (210), (218), (219), (220), (221),
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | |            (374), (393), (1597), (1607), (1897), (2027),
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | |            (2162), (2234), (function-axioms) are inconsistent
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1870.
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | |   (2235)  all_57_15 = e2 & op(e0, e0) = e2
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2235) implies:
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | |   (2236)  op(e0, e0) = e2
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1897), (2236), (function-axioms) are
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2177.
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | |   (2237)  all_57_10 = e2 & op(e2, e0) = e2
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (395), (2237), (function-axioms) are
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2432.
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | |   (2238)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (401), (1897), (2039), (2042), (2238),
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | |            #1902.
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | |   (2239)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | |           all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | |           op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | |             all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | |           & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | |           & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | |           & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | |           $i(all_52_31)
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | ALPHA: (2239) implies:
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | |   (2240)  op(e0, e0) = all_52_31
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | |   (2241)  op(all_52_31, all_52_31) = e0
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (1607), (1897), (2240), (2241),
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | |            #2086.
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.05  | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | End of split
% 219.56/37.05  | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | End of split
% 219.56/37.05  | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | Case 2:
% 219.56/37.05  | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | |   (2242)  all_24_2 = e0
% 219.56/37.05  | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | COMBINE_EQS: (315), (2242) imply:
% 219.56/37.05  | | | | | | | | | | | | | | | |   (2243)  all_6_2 = e0
% 219.56/37.05  | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | REDUCE: (361), (2243) imply:
% 219.56/37.05  | | | | | | | | | | | | | | | |   (2244)   ~ (all_53_6 = e0)
% 219.56/37.05  | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | REDUCE: (364), (2243) imply:
% 219.56/37.05  | | | | | | | | | | | | | | | |   (2245)   ~ (all_53_9 = e0)
% 219.56/37.05  | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | REDUCE: (374), (2243) imply:
% 219.56/37.05  | | | | | | | | | | | | | | | |   (2246)   ~ (e3 = e0)
% 219.56/37.05  | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 219.56/37.05  | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.05  | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | |   (2247)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 219.56/37.05  | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 219.56/37.05  | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (168), (401), (1595), (2247),
% 219.56/37.05  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 219.56/37.05  | | | | | | | | | | | | | | | | |            #1942.
% 219.56/37.05  | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.05  | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | |   (2248)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 219.56/37.05  | | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0)
% 219.56/37.05  | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | BETA: splitting (2248) gives:
% 219.56/37.05  | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.05  | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | |   (2249)  all_57_5 = e0 & op(e2, e1) = e0
% 219.56/37.05  | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (2245), (2249), (function-axioms) are
% 219.56/37.05  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2023.
% 219.56/37.05  | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.05  | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | |   (2250)  all_57_10 = e0 & op(e2, e0) = e0
% 219.56/37.05  | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | ALPHA: (2250) implies:
% 219.56/37.05  | | | | | | | | | | | | | | | | | |   (2251)  op(e2, e0) = e0
% 219.56/37.05  | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 219.56/37.05  | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | |   (2252)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 219.56/37.05  | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (171), (401), (1598), (2252),
% 219.56/37.05  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 219.56/37.05  | | | | | | | | | | | | | | | | | | |            #1940.
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | |   (2253)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 219.56/37.05  | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0)
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | BETA: splitting (2253) gives:
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | |   (2254)  all_57_7 = e0 & op(e1, e2) = e0
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (2244), (2254), (function-axioms) are
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2039.
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | |   (2255)  all_57_13 = e0 & op(e0, e2) = e0
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | ALPHA: (2255) implies:
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | |   (2256)  op(e0, e2) = e0
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (36), (107), (111), (113), (114), (127),
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | |            (129), (134), (136), (137), (141), (142), (144),
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | |            (159), (160), (161), (163), (164), (165), (190),
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | |            (194), (196), (197), (202), (204), (207), (208),
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | |            (209), (210), (244), (248), (256), (257), (268),
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | |            (270), (351), (370), (371), (372), (373), (378),
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | |            (391), (392), (393), (395), (401), (1596), (1605),
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | |            (2251), (2256), (function-axioms) are inconsistent
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | |            by sub-proof #1875.
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.05  | | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.05  | | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | | End of split
% 219.56/37.05  | | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | | End of split
% 219.56/37.05  | | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | End of split
% 219.56/37.05  | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | Case 2:
% 219.56/37.05  | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | |   (2257)  all_57_2 = e0 & op(e2, e3) = e0
% 219.56/37.05  | | | | | | | | | | | | | | | 
% 219.56/37.05  | | | | | | | | | | | | | | | ALPHA: (2257) implies:
% 219.56/37.05  | | | | | | | | | | | | | | |   (2258)  op(e2, e3) = e0
% 219.56/37.05  | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | REF_CLOSE: (168), (1595), (2258), (function-axioms) are
% 219.56/37.06  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1943.
% 219.56/37.06  | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | End of split
% 219.56/37.06  | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | Case 2:
% 219.56/37.06  | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | |   (2259)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 219.56/37.06  | | | | | | | | | | | | | |             e0 & op(e0, e3) = e0)
% 219.56/37.06  | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | REF_CLOSE: (160), (164), (1596), (1597), (2259),
% 219.56/37.06  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 219.56/37.06  | | | | | | | | | | | | | |            #1859.
% 219.56/37.06  | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | End of split
% 219.56/37.06  | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | End of split
% 219.56/37.06  | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | End of split
% 219.56/37.06  | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | Case 2:
% 219.56/37.06  | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | |   (2260)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 219.56/37.06  | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 219.56/37.06  | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | BETA: splitting (2260) gives:
% 219.56/37.06  | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | Case 1:
% 219.56/37.06  | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | |   (2261)  all_57_5 = e2 & op(e2, e1) = e2
% 219.56/37.06  | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | REF_CLOSE: (166), (394), (2261), (function-axioms) are
% 219.56/37.06  | | | | | | | | | | | |            inconsistent by sub-proof #1858.
% 219.56/37.06  | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | Case 2:
% 219.56/37.06  | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | |   (2262)  all_57_10 = e2 & op(e2, e0) = e2
% 219.56/37.06  | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | REF_CLOSE: (165), (395), (2262), (function-axioms) are
% 219.56/37.06  | | | | | | | | | | | |            inconsistent by sub-proof #2432.
% 219.56/37.06  | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | End of split
% 219.56/37.06  | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | End of split
% 219.56/37.06  | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | Case 2:
% 219.56/37.06  | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | |   (2263)  all_55_5 = e1 | all_55_5 = e0
% 219.56/37.06  | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | REF_CLOSE: (266), (380), (382), (2263) are inconsistent by
% 219.56/37.06  | | | | | | | | | |            sub-proof #1857.
% 219.56/37.06  | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | End of split
% 219.56/37.06  | | | | | | | | | 
% 219.56/37.06  | | | | | | | | End of split
% 219.56/37.06  | | | | | | | | 
% 219.56/37.06  | | | | | | | Case 2:
% 219.56/37.06  | | | | | | | | 
% 219.56/37.06  | | | | | | | |   (2264)  all_16_2 = e1
% 219.56/37.06  | | | | | | | |   (2265)  ( ~ (all_16_0 = e0) & op(all_16_1, e2) = all_16_0 &
% 219.56/37.06  | | | | | | | |             op(e2, e1) = all_16_1 & $i(all_16_0) & $i(all_16_1))
% 219.56/37.06  | | | | | | | |           | ( ~ (all_16_1 = e3) & op(e2, e1) = all_16_1 &
% 219.56/37.06  | | | | | | | |             $i(all_16_1))
% 219.56/37.06  | | | | | | | | 
% 219.56/37.06  | | | | | | | | COMBINE_EQS: (324), (2264) imply:
% 219.56/37.06  | | | | | | | |   (2266)  all_8_2 = e1
% 219.56/37.06  | | | | | | | | 
% 219.56/37.06  | | | | | | | | SIMP: (2266) implies:
% 219.56/37.06  | | | | | | | |   (2267)  all_8_2 = e1
% 219.56/37.06  | | | | | | | | 
% 219.56/37.06  | | | | | | | | COMBINE_EQS: (305), (2267) imply:
% 219.56/37.06  | | | | | | | |   (2268)  all_26_2 = e1
% 219.56/37.06  | | | | | | | | 
% 219.56/37.06  | | | | | | | | REDUCE: (349), (2267) imply:
% 219.56/37.06  | | | | | | | |   (2269)   ~ (all_53_1 = e1)
% 219.56/37.06  | | | | | | | | 
% 219.56/37.06  | | | | | | | | REDUCE: (352), (2267) imply:
% 219.56/37.06  | | | | | | | |   (2270)   ~ (all_53_4 = e1)
% 219.56/37.06  | | | | | | | | 
% 219.56/37.06  | | | | | | | | REDUCE: (354), (2267) imply:
% 219.56/37.06  | | | | | | | |   (2271)   ~ (all_53_6 = e1)
% 219.56/37.06  | | | | | | | | 
% 219.56/37.06  | | | | | | | | REDUCE: (356), (2267) imply:
% 219.56/37.06  | | | | | | | |   (2272)   ~ (all_53_7 = e1)
% 219.56/37.06  | | | | | | | | 
% 219.56/37.06  | | | | | | | | REDUCE: (358), (2267) imply:
% 219.56/37.06  | | | | | | | |   (2273)   ~ (all_53_9 = e1)
% 219.56/37.06  | | | | | | | | 
% 219.56/37.06  | | | | | | | | REDUCE: (360), (2267) imply:
% 219.56/37.06  | | | | | | | |   (2274)   ~ (all_53_13 = e1)
% 219.56/37.06  | | | | | | | | 
% 219.56/37.06  | | | | | | | | REDUCE: (375), (2267) imply:
% 219.56/37.06  | | | | | | | |   (2275)   ~ (e3 = e1)
% 219.56/37.06  | | | | | | | | 
% 219.56/37.06  | | | | | | | | BETA: splitting (223) gives:
% 219.56/37.06  | | | | | | | | 
% 219.56/37.06  | | | | | | | | Case 1:
% 219.56/37.06  | | | | | | | | | 
% 219.56/37.06  | | | | | | | | |   (2276)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 &
% 219.56/37.06  | | | | | | | | |             op(e2, e2) = e1)
% 219.56/37.06  | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | BETA: splitting (2276) gives:
% 219.56/37.06  | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | Case 1:
% 219.56/37.06  | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | |   (2277)  all_57_2 = e1 & op(e2, e3) = e1
% 219.56/37.06  | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | REF_CLOSE: (168), (2269), (2277), (function-axioms) are
% 219.56/37.06  | | | | | | | | | |            inconsistent by sub-proof #2156.
% 219.56/37.06  | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | Case 2:
% 219.56/37.06  | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | |   (2278)  all_57_3 = e1 & op(e2, e2) = e1
% 219.56/37.06  | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | ALPHA: (2278) implies:
% 219.56/37.06  | | | | | | | | | |   (2279)  all_57_3 = e1
% 219.56/37.06  | | | | | | | | | |   (2280)  op(e2, e2) = e1
% 219.56/37.06  | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | BETA: splitting (58) gives:
% 219.56/37.06  | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | Case 1:
% 219.56/37.06  | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | |   (2281)   ~ (all_18_2 = e0)
% 219.56/37.06  | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | REDUCE: (327), (2281) imply:
% 219.56/37.06  | | | | | | | | | | |   (2282)   ~ (all_10_2 = e0)
% 219.56/37.06  | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | BETA: splitting (61) gives:
% 219.56/37.06  | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | Case 1:
% 219.56/37.06  | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | |   (2283)   ~ (all_20_2 = e2)
% 219.56/37.06  | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | REDUCE: (299), (2283) imply:
% 219.56/37.06  | | | | | | | | | | | |   (2284)   ~ (all_10_2 = e2)
% 219.56/37.06  | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | BETA: splitting (205) gives:
% 219.56/37.06  | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | Case 1:
% 219.56/37.06  | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | |   (2285)  all_55_0 = e3
% 219.56/37.06  | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | COMBINE_EQS: (277), (2285) imply:
% 219.56/37.06  | | | | | | | | | | | | |   (2286)  all_10_2 = e3
% 219.56/37.06  | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | REDUCE: (342), (2286) imply:
% 219.56/37.06  | | | | | | | | | | | | |   (2287)   ~ (all_53_3 = e3)
% 219.56/37.06  | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | REDUCE: (344), (2286) imply:
% 219.56/37.06  | | | | | | | | | | | | |   (2288)   ~ (all_53_4 = e3)
% 219.56/37.06  | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | REDUCE: (346), (2286) imply:
% 219.56/37.06  | | | | | | | | | | | | |   (2289)   ~ (all_53_8 = e3)
% 219.56/37.06  | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | REDUCE: (348), (2286) imply:
% 219.56/37.06  | | | | | | | | | | | | |   (2290)   ~ (all_53_12 = e3)
% 219.56/37.06  | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | REDUCE: (45), (2286) imply:
% 219.56/37.06  | | | | | | | | | | | | |   (2291)  op(e3, e3) = e3
% 219.56/37.06  | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | BETA: splitting (237) gives:
% 219.56/37.06  | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | Case 1:
% 219.56/37.06  | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | |   (2292)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 219.56/37.06  | | | | | | | | | | | | | |             & op(e3, e2) = e3)
% 219.56/37.06  | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | BETA: splitting (2292) gives:
% 219.56/37.06  | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | Case 1:
% 219.56/37.06  | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | |   (2293)  all_57_0 = e3 & op(e3, e3) = e3
% 219.56/37.06  | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | ALPHA: (2293) implies:
% 219.56/37.06  | | | | | | | | | | | | | | |   (2294)  all_57_0 = e3
% 219.56/37.06  | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 219.56/37.06  | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | Case 1:
% 219.56/37.06  | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | |   (2295)   ~ (all_24_2 = e0)
% 219.56/37.06  | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | REDUCE: (315), (2295) imply:
% 219.56/37.06  | | | | | | | | | | | | | | | |   (2296)   ~ (all_6_2 = e0)
% 219.56/37.06  | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | BETA: splitting (70) gives:
% 219.56/37.06  | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.06  | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | |   (2297)   ~ (all_26_2 = e1)
% 219.56/37.06  | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | REDUCE: (2268), (2297) imply:
% 219.56/37.06  | | | | | | | | | | | | | | | | |   (2298)  $false
% 219.56/37.06  | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | CLOSE: (2298) is inconsistent.
% 219.56/37.06  | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.06  | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | |   (2299)  ( ~ (all_26_0 = e3) & op(all_26_1, e2) = all_26_0
% 219.56/37.06  | | | | | | | | | | | | | | | | |             & op(e2, e1) = all_26_1 & $i(all_26_0) &
% 219.56/37.06  | | | | | | | | | | | | | | | | |             $i(all_26_1)) | ( ~ (all_26_1 = e0) & op(e2, e1)
% 219.56/37.06  | | | | | | | | | | | | | | | | |             = all_26_1 & $i(all_26_1))
% 219.56/37.06  | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | BETA: splitting (76) gives:
% 219.56/37.06  | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.06  | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | |   (2300)   ~ (all_30_2 = e1)
% 219.56/37.06  | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | | REDUCE: (330), (2300) imply:
% 219.56/37.06  | | | | | | | | | | | | | | | | | |   (2301)   ~ (all_4_2 = e1)
% 219.56/37.06  | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 219.56/37.06  | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | | |   (2302)  all_55_15 = e3
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (378), (2302) are inconsistent by sub-proof
% 219.56/37.06  | | | | | | | | | | | | | | | | | | |            #2503.
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | | |   (2303)   ~ (all_55_15 = e3)
% 219.56/37.06  | | | | | | | | | | | | | | | | | | |   (2304)  all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | BETA: splitting (2304) gives:
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | |   (2305)  all_55_15 = e2
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (373), (2305) are inconsistent by sub-proof
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | |            #2502.
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | |   (2306)   ~ (all_55_15 = e2)
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | |   (2307)  all_55_15 = e1 | all_55_15 = e0
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | BETA: splitting (2307) gives:
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | |   (2308)  all_55_15 = e1
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (2301), (2308) are inconsistent by
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | |            sub-proof #2501.
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | |   (2309)  all_55_15 = e0
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (2309) imply:
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | |   (2310)  all_4_2 = e0
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | SIMP: (2310) implies:
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | |   (2311)  all_4_2 = e0
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | REDUCE: (351), (2311) imply:
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | |   (2312)   ~ (all_53_3 = e0)
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | REDUCE: (362), (2311) imply:
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | |   (2313)   ~ (all_53_7 = e0)
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | REDUCE: (369), (2311) imply:
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | |   (2314)   ~ (all_53_11 = e0)
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | REDUCE: (370), (2311) imply:
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | |   (2315)   ~ (all_53_12 = e0)
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | REDUCE: (371), (2311) imply:
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | |   (2316)   ~ (all_53_13 = e0)
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | REDUCE: (372), (2311) imply:
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | |   (2317)   ~ (all_53_14 = e0)
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | REDUCE: (378), (2311) imply:
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | |   (2318)   ~ (e3 = e0)
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | REDUCE: (373), (2311) imply:
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | |   (2319)   ~ (e2 = e0)
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | REDUCE: (2301), (2311) imply:
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | |   (2320)   ~ (e1 = e0)
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | |   (2321)  all_57_15 = e0 & op(e0, e0) = e0
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2321) implies:
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | |   (2322)  all_57_15 = e0
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | |   (2323)  op(e0, e0) = e0
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (88) gives:
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | |   (2324)   ~ (all_38_2 = e2)
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (249), (2324) imply:
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | |   (2325)   ~ (all_6_2 = e2)
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | |   (2326)  all_55_10 = e3
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (374), (2326) are inconsistent by sub-proof
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | |            #2500.
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | |   (2327)   ~ (all_55_10 = e3)
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | |   (2328)  all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2328) gives:
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | | |   (2329)  all_55_10 = e2
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (2325), (2329) are inconsistent by
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2499.
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | | |   (2330)   ~ (all_55_10 = e2)
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | | |   (2331)  all_55_10 = e1 | all_55_10 = e0
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2331) gives:
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2332)  all_55_10 = e1
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (336), (2332) imply:
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2333)  all_6_2 = e1
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2333) implies:
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2334)  all_6_2 = e1
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2325), (2334) imply:
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2335)   ~ (e2 = e1)
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (2334) imply:
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2336)  op(e1, e1) = e1
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2337)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e1)
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (226), (228), (229),
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2280), (2291), (2337), (function-axioms) are
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1856.
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2338)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e1)
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2338) gives:
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2339)  all_57_4 = e1 & op(e3, e1) = e1
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2339) implies:
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2340)  all_57_4 = e1
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2341)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2341) gives:
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2342)  all_57_9 = e1 & op(e3, e0) = e1
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (113),
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (160), (161), (165), (168), (169), (171), (194),
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (208), (214), (216), (217), (218), (220), (221),
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (222), (223), (224), (225), (226), (228), (229),
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (232), (233), (235), (248), (374), (2269),
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2279), (2280), (2288), (2291), (2296), (2315),
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2316), (2317), (2323), (2336), (2342),
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1847.
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2343)  all_57_10 = e1 & op(e2, e0) = e1
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (2274), (2343), (function-axioms) are
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2084.
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2344)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2344) gives:
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2345)  all_57_11 = e1 & op(e1, e0) = e1
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2345) implies:
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2346)  all_57_11 = e1
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2347)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2347) gives:
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2348)  all_57_6 = e3 & op(e1, e3) = e3
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2348) implies:
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2349)  all_57_6 = e3
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (230), (232), (234),
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2294), (2349) are inconsistent by sub-proof
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2010.
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2350)  all_57_7 = e3 & op(e1, e2) = e3
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2350) implies:
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2351)  all_57_7 = e3
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2352)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2352) gives:
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2353)  all_57_0 = e0 & op(e3, e3) = e0
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2353) implies:
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2354)  op(e3, e3) = e0
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2291), (2354), (function-axioms) are
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2494.
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2355)  all_57_1 = e0 & op(e3, e2) = e0
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2355) implies:
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2356)  op(e3, e2) = e0
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2357)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e0)
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2357) gives:
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.56/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2358)  all_57_6 = e0 & op(e1, e3) = e0
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2358) implies:
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2359)  all_57_6 = e0
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (216), (2336), (2346), (2351),
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2359), (function-axioms) are inconsistent by
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1844.
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2360)  all_57_7 = e0 & op(e1, e2) = e0
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2351), (2360) are inconsistent by sub-proof
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2042.
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2361)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2361) gives:
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2362)  all_57_8 = e0 & op(e1, e1) = e0
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2362) implies:
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2363)  op(e1, e1) = e0
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (36), (107), (129), (136), (137), (159),
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (161), (165), (169), (171), (190), (192), (196),
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (207), (226), (244), (246), (256), (362), (370),
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (371), (372), (373), (378), (2270), (2271),
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2272), (2280), (2291), (2301), (2323), (2356),
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2363), (function-axioms) are inconsistent by
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1834.
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2364)  all_57_11 = e0 & op(e1, e0) = e0
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (2317), (2364), (function-axioms) are
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2341.
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2365)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2365) gives:
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2366)  all_57_4 = e0 & op(e3, e1) = e0
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2340), (2366) are inconsistent by sub-proof
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2429.
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2367)  all_57_9 = e0 & op(e3, e0) = e0
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (2315), (2367), (function-axioms) are
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2434.
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2368)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (39), (374), (2346), (2368),
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2004.
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2369)  all_57_15 = e1 & op(e0, e0) = e1
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2369) implies:
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2370)  op(e0, e0) = e1
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2323), (2370), (function-axioms) are
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2290.
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2371)  all_57_9 = e1 & op(e3, e0) = e1
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (113),
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (160), (161), (165), (168), (169), (171), (194),
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (208), (214), (216), (217), (218), (220), (221),
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (222), (223), (224), (225), (226), (228), (229),
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (232), (233), (235), (248), (374), (2269),
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2279), (2280), (2288), (2291), (2296), (2315),
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2316), (2317), (2323), (2336), (2371),
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1847.
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2372)  all_55_10 = e0
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (2296), (2372) are inconsistent by
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2118.
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | |   (2373)  all_38_2 = e2
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (2373) imply:
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | |   (2374)  all_6_2 = e2
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (361), (2374) imply:
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | |   (2375)   ~ (all_53_6 = e2)
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (363), (2374) imply:
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | |   (2376)   ~ (all_53_8 = e2)
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (364), (2374) imply:
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | |   (2377)   ~ (all_53_9 = e2)
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (366), (2374) imply:
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | |   (2378)   ~ (all_53_11 = e2)
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (368), (2374) imply:
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | |   (2379)   ~ (all_53_14 = e2)
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (374), (2374) imply:
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | |   (2380)   ~ (e3 = e2)
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (2374) imply:
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | |   (2381)  op(e1, e1) = e2
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | |   (2382)  all_55_1 = e3
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (2288), (2382) are inconsistent by
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2295.
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | |   (2383)  all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | |   (2384)  all_55_13 = e3
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (2384) imply:
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | |   (2385)  all_53_7 = e3
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2385) implies:
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | |   (2386)  all_53_7 = e3
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (129), (2386) imply:
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | |   (2387)   ~ (all_53_6 = e3)
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (126), (2386) imply:
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | |   (2388)   ~ (all_53_11 = e3)
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2388) implies:
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | |   (2389)   ~ (all_53_11 = e3)
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.87/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2390)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 219.90/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 219.90/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2390) gives:
% 219.90/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.90/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2391)  all_57_6 = e3 & op(e1, e3) = e3
% 219.90/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2391) implies:
% 219.90/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2392)  all_57_6 = e3
% 219.90/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (230), (232), (234),
% 219.90/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2294), (2392) are inconsistent by sub-proof
% 219.90/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2010.
% 219.90/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.90/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2393)  all_57_7 = e3 & op(e1, e2) = e3
% 219.90/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2393) implies:
% 219.90/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2394)  all_57_7 = e3
% 219.90/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 219.90/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.90/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2395)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 219.90/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 219.90/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2395) gives:
% 219.90/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.90/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2396)  all_57_12 = e3 & op(e0, e3) = e3
% 219.90/37.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (168), (223),
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (225), (230), (232), (234), (2269), (2279),
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2291), (2312), (2396), (function-axioms) are
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1833.
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2397)  all_57_13 = e3 & op(e0, e2) = e3
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2397) implies:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2398)  all_57_13 = e3
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2399)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2399) gives:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2400)  all_57_1 = e2 & op(e3, e2) = e2
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2400) implies:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2401)  all_57_1 = e2
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2402)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e1)
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2402) gives:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2403)  all_57_4 = e1 & op(e3, e1) = e1
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2403) implies:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2404)  all_57_4 = e1
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (137), (169), (171), (196), (231),
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (256), (2271), (2291), (2315), (2375), (2387),
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2404), (function-axioms) are inconsistent by
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1830.
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2405)  all_57_5 = e1 & op(e2, e1) = e1
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (2273), (2405), (function-axioms) are
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2305.
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2406)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e1)
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2406) gives:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2407)  all_57_8 = e1 & op(e1, e1) = e1
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2407) implies:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2408)  op(e1, e1) = e1
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2381), (2408), (function-axioms) are
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2423.
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2409)  all_57_14 = e1 & op(e0, e1) = e1
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2409) implies:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2410)  all_57_14 = e1
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2411)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e3)
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2411) gives:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2412)  all_57_4 = e3 & op(e3, e1) = e3
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (235),
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2291), (2401), (2412), (function-axioms) are
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1829.
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2413)  all_57_5 = e3 & op(e2, e1) = e3
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2413) implies:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2414)  all_57_5 = e3
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2415)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2415) gives:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2416)  all_57_12 = e2 & op(e0, e3) = e2
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2416) implies:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2417)  all_57_12 = e2
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2418)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e1)
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2418) gives:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2419)  all_57_0 = e1 & op(e3, e3) = e1
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2419) implies:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2420)  op(e3, e3) = e1
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2291), (2420), (function-axioms) are
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2495.
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2421)  all_57_2 = e1 & op(e2, e3) = e1
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2421) implies:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2422)  all_57_2 = e1
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (222), (224), (2280),
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2414), (2422), (function-axioms) are inconsistent
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1825.
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2423)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e3) = e1)
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2423) gives:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2424)  all_57_6 = e1 & op(e1, e3) = e1
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2424) implies:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2425)  all_57_6 = e1
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2426)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2426) gives:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2427)  all_57_2 = e0 & op(e2, e3) = e0
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2427) implies:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2428)  all_57_2 = e0
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2429)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e0)
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2429) gives:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2430)  all_57_6 = e0 & op(e1, e3) = e0
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2430) implies:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2431)  all_57_6 = e0
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2425), (2431) imply:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2432)  e1 = e0
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2279), (2428), (2432) are inconsistent by
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1824.
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2433)  all_57_7 = e0 & op(e1, e2) = e0
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2433) implies:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2434)  all_57_7 = e0
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2394), (2434) imply:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2435)  e3 = e0
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2414), (2435) imply:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2436)  all_57_5 = e0
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (224), (225), (2280),
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2428), (2436), (function-axioms) are inconsistent
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1848.
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2437)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2437) gives:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2438)  all_57_8 = e0 & op(e1, e1) = e0
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (2296), (2438), (function-axioms) are
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2412.
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2439)  all_57_11 = e0 & op(e1, e0) = e0
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (2317), (2439), (function-axioms) are
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2341.
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2440)  all_57_3 = e0 & op(e2, e2) = e0
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2440) implies:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2441)  all_57_3 = e0
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (227), (2394), (2398), (2401),
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2441) are inconsistent by sub-proof #2008.
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2442)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0)
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (165), (2316), (2414), (2442),
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2222.
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2443)  all_57_12 = e1 & op(e0, e3) = e1
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (226), (228), (229),
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2280), (2401), (2417), (2443), (function-axioms)
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1823.
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2444)  all_57_13 = e2 & op(e0, e2) = e2
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (161), (163),
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (214), (215), (217), (374), (2271), (2296),
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2317), (2381), (2394), (2398), (2444),
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1816.
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2445)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2445) gives:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2446)  all_57_14 = e2 & op(e0, e1) = e2
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (226), (228), (229),
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2280), (2401), (2410), (2446), (function-axioms)
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1850.
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2447)  all_57_15 = e2 & op(e0, e0) = e2
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2447) implies:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2448)  all_57_15 = e2
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2322), (2448) are inconsistent by sub-proof
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2126.
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2449)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e1) = e3)
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (39), (137), (166), (169),
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (171), (196), (219), (231), (256), (374), (2271),
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2273), (2291), (2315), (2375), (2381), (2387),
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2449), (function-axioms) are inconsistent by
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1813.
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2450)  all_57_3 = e2 & op(e2, e2) = e2
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2450) implies:
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2451)  op(e2, e2) = e2
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2280), (2451), (function-axioms) are
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2306.
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2452)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2452) gives:
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2453)  all_57_7 = e2 & op(e1, e2) = e2
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2453) implies:
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2454)  all_57_7 = e2
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (161), (163),
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (214), (215), (217), (374), (2271), (2296),
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2317), (2381), (2454), (function-axioms) are
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1817.
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2455)  all_57_13 = e2 & op(e0, e2) = e2
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (161), (163),
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (214), (215), (217), (374), (2271), (2296),
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2317), (2381), (2394), (2398), (2455),
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1816.
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2456)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2456) gives:
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2457)  all_57_14 = e3 & op(e0, e1) = e3
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (137), (166), (169), (171),
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (196), (219), (231), (256), (2271), (2273),
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2291), (2315), (2375), (2381), (2387), (2457),
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1814.
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2458)  all_57_15 = e3 & op(e0, e0) = e3
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2458) implies:
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2459)  all_57_15 = e3
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2460)  op(e0, e0) = e3
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (70), (107),
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (137), (163), (166), (171), (204), (207), (208),
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (209), (211), (212), (217), (221), (222), (223),
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (225), (226), (227), (228), (229), (230),
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (232), (233), (234), (235), (236), (270),
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (374), (2265), (2268), (2270), (2273), (2279),
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2280), (2291), (2459), (2460), (function-axioms)
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1732.
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2461)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2461) gives:
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2462)  all_57_8 = e3 & op(e1, e1) = e3
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2462) implies:
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2463)  op(e1, e1) = e3
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (374), (2463), (function-axioms) are
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2468.
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2464)  all_57_11 = e3 & op(e1, e0) = e3
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2464) implies:
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2465)  all_57_11 = e3
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2466)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2466) gives:
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2467)  all_57_12 = e3 & op(e0, e3) = e3
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (168), (223),
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (225), (230), (232), (234), (2269), (2279),
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2291), (2312), (2467), (function-axioms) are
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1833.
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2468)  all_57_13 = e3 & op(e0, e2) = e3
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2468) implies:
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2469)  all_57_13 = e3
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2470)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2470) gives:
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2471)  all_57_1 = e2 & op(e3, e2) = e2
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2471) implies:
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2472)  all_57_1 = e2
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2473)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2473) gives:
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2474)  all_57_9 = e1 & op(e3, e0) = e1
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2474) implies:
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2475)  all_57_9 = e1
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2476)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e3)
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2476) gives:
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2477)  all_57_4 = e3 & op(e3, e1) = e3
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (235),
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2291), (2472), (2477), (function-axioms) are
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1829.
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2478)  all_57_5 = e3 & op(e2, e1) = e3
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2478) implies:
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2479)  all_57_5 = e3
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2480)  op(e2, e1) = e3
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2481)  all_55_9 = e3
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (2387), (2481) are inconsistent by
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2159.
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2482)  all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2482) gives:
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2483)  all_55_9 = e2
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (2375), (2483) are inconsistent by
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2274.
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2484)  all_55_9 = e1 | all_55_9 = e0
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2485)  all_55_14 = e3
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (2389), (2485) are inconsistent by
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2294.
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2486)   ~ (all_55_14 = e3)
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2487)  all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2487) gives:
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2488)  all_55_14 = e2
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (2378), (2488) are inconsistent by
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2293.
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2489)   ~ (all_55_14 = e2)
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2490)  all_55_14 = e1 | all_55_14 = e0
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2490) gives:
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2491)  all_55_14 = e1
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (2491) imply:
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2492)  all_53_11 = e1
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2492) implies:
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2493)  all_53_11 = e1
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (122), (2493) imply:
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2494)   ~ (all_53_8 = e1)
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2378), (2493) imply:
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2495)   ~ (e2 = e1)
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2496)  all_55_2 = e3
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (2289), (2496) are inconsistent by
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2028.
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2497)  all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2498)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2498) gives:
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2499)  all_57_0 = e0 & op(e3, e3) = e0
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2499) implies:
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2500)  op(e3, e3) = e0
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2291), (2500), (function-axioms) are
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2494.
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2501)  all_57_1 = e0 & op(e3, e2) = e0
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2501) implies:
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2502)  op(e3, e2) = e0
% 219.90/37.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (137), (171), (256), (2271), (2484), (2502),
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1832.
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2503)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2503) gives:
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2504)  all_57_4 = e0 & op(e3, e1) = e0
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2504) implies:
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2505)  all_57_4 = e0
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2497) gives:
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2506)  all_55_2 = e2
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (2376), (2506) are inconsistent by
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2027.
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2507)   ~ (all_55_2 = e2)
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2508)  all_55_2 = e1 | all_55_2 = e0
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2508) gives:
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2509)  all_55_2 = e1
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (2494), (2509) are inconsistent by
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2032.
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2510)  all_55_2 = e0
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (2510) imply:
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2511)  all_53_8 = e0
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2511) implies:
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2512)  all_53_8 = e0
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (2512) imply:
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2513)   ~ (all_53_4 = e0)
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (170), (2512) imply:
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2514)  op(e3, e1) = e0
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2515)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2515) gives:
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2516)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_7)
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2516) implies:
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2517)  op(e3, e1) = all_52_5
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2518)  op(all_52_5, all_52_5) = e1
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2323), (2514), (2517), (2518),
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2167.
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2519)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_15)
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2519) implies:
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2520)  op(e2, e1) = all_52_13
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2521)  op(all_52_13, all_52_13) = e1
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (70), (2268), (2291), (2480), (2520), (2521),
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1791.
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2522)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_52_21) = e1 & op(all_52_23, all_52_23) =
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(all_52_25, all_52_25) = e3 &
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_52_29) = e1 & op(all_52_31, all_52_31) =
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_29) & $i(all_52_31))
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2522) gives:
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2523)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_23)
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2523) implies:
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2524)  op(e1, e3) = all_52_17
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2525)  op(all_52_17, all_52_17) = e3
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (39), (163), (195), (215), (336), (374),
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2271), (2381), (2465), (2524), (2525),
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1731.
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2526)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_31)
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2526) implies:
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2527)  op(e0, e1) = all_52_29
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2528)  op(all_52_29, all_52_29) = e1
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (204), (219), (233),
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (235), (270), (2270), (2288), (2291), (2381),
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2475), (2479), (2505), (2513), (2527), (2528),
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1728.
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 219.90/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.01/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2529)  all_57_9 = e0 & op(e3, e0) = e0
% 220.01/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (2315), (2529), (function-axioms) are
% 220.01/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2434.
% 220.01/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.01/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.01/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.01/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.01/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2530)  all_55_14 = e0
% 220.01/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (2314), (2530) are inconsistent by
% 220.01/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2288.
% 220.01/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.01/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.01/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.01/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.01/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.01/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.01/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.01/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2531)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 220.01/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e1) = e3)
% 220.01/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (39), (137), (166), (169),
% 220.01/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (171), (196), (219), (231), (256), (374), (2271),
% 220.01/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2273), (2291), (2315), (2375), (2381), (2387),
% 220.01/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2531), (function-axioms) are inconsistent by
% 220.01/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1813.
% 220.01/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.01/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.01/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2532)  all_57_10 = e1 & op(e2, e0) = e1
% 220.01/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (2274), (2532), (function-axioms) are
% 220.01/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2084.
% 220.01/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.01/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.01/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2533)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 220.01/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 220.01/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (2323), (2465), (2533),
% 220.01/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.01/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1727.
% 220.01/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.01/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.01/37.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2534)  all_57_3 = e2 & op(e2, e2) = e2
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2534) implies:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2535)  op(e2, e2) = e2
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2280), (2535), (function-axioms) are
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2306.
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2536)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2536) gives:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2537)  all_57_7 = e2 & op(e1, e2) = e2
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2537) implies:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2538)  all_57_7 = e2
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (161), (163),
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (214), (215), (217), (374), (2271), (2296),
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2317), (2381), (2538), (function-axioms) are
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1817.
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2539)  all_57_13 = e2 & op(e0, e2) = e2
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2539) implies:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2540)  all_57_13 = e2
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2469), (2540) imply:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2541)  e3 = e2
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2465), (2541) imply:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2542)  all_57_11 = e2
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (39), (161), (163),
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (214), (215), (217), (374), (2271), (2296),
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2317), (2381), (2542), (function-axioms) are
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1724.
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2543)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2543) gives:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2544)  all_57_14 = e3 & op(e0, e1) = e3
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (137), (166), (169), (171),
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (196), (219), (231), (256), (2271), (2273),
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2291), (2315), (2375), (2381), (2387), (2544),
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1814.
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2545)  all_57_15 = e3 & op(e0, e0) = e3
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2545) implies:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2546)  all_57_15 = e3
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (207), (211), (212),
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2465), (2546) are inconsistent by sub-proof
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2134.
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | |   (2547)  all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2548)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2548) gives:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2549)  all_57_12 = e3 & op(e0, e3) = e3
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (168), (223),
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (225), (230), (232), (234), (2269), (2279),
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2291), (2312), (2549), (function-axioms) are
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1833.
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2550)  all_57_13 = e3 & op(e0, e2) = e3
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2550) implies:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2551)  all_57_13 = e3
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2552)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2552) gives:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2553)  all_57_1 = e2 & op(e3, e2) = e2
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2553) implies:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2554)  all_57_1 = e2
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2555)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (2291), (2554), (2555),
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1722.
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2556)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (119), (124), (126), (140), (141), (169), (170),
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (191), (193), (199), (245), (246), (247), (259),
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2272), (2273), (2287), (2312), (2313), (2314),
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2315), (2377), (2547), (2556), (function-axioms)
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1718.
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2557)  all_57_3 = e2 & op(e2, e2) = e2
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2557) implies:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2558)  op(e2, e2) = e2
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2280), (2558), (function-axioms) are
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2306.
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2559)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2559) gives:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2560)  all_57_7 = e2 & op(e1, e2) = e2
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2560) implies:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2561)  all_57_7 = e2
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (161), (163),
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (214), (215), (217), (374), (2271), (2296),
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2317), (2381), (2561), (function-axioms) are
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1817.
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2562)  all_57_13 = e2 & op(e0, e2) = e2
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2551), (2562) are inconsistent by sub-proof
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2146.
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2563)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2563) gives:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2564)  all_57_14 = e3 & op(e0, e1) = e3
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2564) implies:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2565)  all_57_14 = e3
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2566)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e1)
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2566) gives:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2567)  all_57_4 = e1 & op(e3, e1) = e1
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2567) implies:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2568)  all_57_4 = e1
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2569)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (218), (223),
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (225), (2279), (2280), (2296), (2565),
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2568), (2569), (function-axioms) are inconsistent
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1715.
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2570)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0)
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2570) gives:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2571)  all_57_5 = e0 & op(e2, e1) = e0
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2571) implies:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2572)  op(e2, e1) = e0
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2573)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2573) gives:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2574)  all_57_0 = e0 & op(e3, e3) = e0
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2574) implies:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2575)  op(e3, e3) = e0
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2291), (2575), (function-axioms) are
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2494.
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2576)  all_57_1 = e0 & op(e3, e2) = e0
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2547) gives:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2577)  all_55_13 = e2
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (2577) imply:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2578)  all_53_7 = e2
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2578) implies:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2579)  all_53_7 = e2
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (136), (2579) imply:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2580)   ~ (all_53_4 = e2)
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2383) gives:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2581)  all_55_1 = e2
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (2580), (2581) are inconsistent by
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2284.
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2582)   ~ (all_55_1 = e2)
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2583)  all_55_1 = e1 | all_55_1 = e0
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2583) gives:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2584)  all_55_1 = e1
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (2270), (2584) are inconsistent by
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2283.
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2585)  all_55_1 = e0
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (2585) imply:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2586)  all_53_4 = e0
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2586) implies:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2587)  all_53_4 = e0
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (137), (2587) imply:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2588)   ~ (all_53_6 = e0)
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2588) implies:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2589)   ~ (all_53_6 = e0)
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (2587) imply:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2590)   ~ (all_53_12 = e0)
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (171), (2587) imply:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2591)  op(e3, e2) = e0
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2592)  all_55_9 = e3
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (2592) imply:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2593)  all_53_6 = e3
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2593) implies:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2594)  all_53_6 = e3
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (127), (2594) imply:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2595)   ~ (all_53_14 = e3)
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2595) implies:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2596)   ~ (all_53_14 = e3)
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2597)  all_55_11 = e3
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (2597) imply:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2598)  all_53_14 = e3
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2596), (2598) imply:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2599)  $false
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2599) is inconsistent.
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2600)  all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.01/37.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2601)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2601) gives:
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2602)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_7)
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2602) implies:
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2603)  op(e3, e2) = all_52_3
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2604)  op(all_52_3, all_52_3) = e2
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2323), (2591), (2603), (2604),
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2399.
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2605)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_15)
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2605) implies:
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2606)  op(e2, e1) = all_52_13
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2607)  op(all_52_13, all_52_13) = e1
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2299) gives:
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2608)   ~ (all_26_0 = e3) & op(all_26_1, e2) = all_26_0 &
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_26_1 & $i(all_26_0) &
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_26_1)
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2608) implies:
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2609)  op(e2, e1) = all_26_1
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2265), (2323), (2572), (2606), (2607),
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2609), (function-axioms) are inconsistent by
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1713.
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2610)   ~ (all_26_1 = e0) & op(e2, e1) = all_26_1 &
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_26_1)
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2610) implies:
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2611)  op(e2, e1) = all_26_1
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2265), (2323), (2572), (2606), (2607),
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2611), (function-axioms) are inconsistent by
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1713.
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2612)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_52_21) = e1 & op(all_52_23, all_52_23) =
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(all_52_25, all_52_25) = e3 &
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_52_29) = e1 & op(all_52_31, all_52_31) =
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_29) & $i(all_52_31))
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2612) gives:
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2613)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_23)
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2613) implies:
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2614)  op(e1, e0) = all_52_23
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2615)  op(e1, e1) = all_52_21
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2616)  op(all_52_23, all_52_23) = e0
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2617)  op(all_52_21, all_52_21) = e1
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2600) gives:
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2618)  all_55_11 = e2
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (2379), (2618) are inconsistent by
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2282.
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2619)  all_55_11 = e1 | all_55_11 = e0
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2619) gives:
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2620)  all_55_11 = e1
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (2620) imply:
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2621)  all_53_14 = e1
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2621) implies:
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2622)  all_53_14 = e1
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (2622) imply:
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2623)   ~ (all_53_12 = e1)
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (161), (2622) imply:
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2624)  op(e1, e0) = e1
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2625)  all_55_3 = e3
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (2290), (2625) are inconsistent by
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2169.
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2626)  all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2626) gives:
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_23, e0, e1, simplifying with (2614), (2624)
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2627)  all_52_23 = e1
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2616), (2627) imply:
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2628)  op(e1, e1) = e0
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (165), (169), (171), (207), (2270), (2315),
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2316), (2317), (2576), (2615), (2617), (2628),
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1842.
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2629)  all_55_3 = e1 | all_55_3 = e0
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (2315), (2623), (2629) are inconsistent by
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2132.
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2630)  all_55_11 = e0
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (2317), (2630) are inconsistent by
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2308.
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2631)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_31)
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2631) implies:
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2632)  op(e0, e2) = all_52_27
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2633)  op(all_52_27, all_52_27) = e2
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (192), (246), (2265), (2272), (2280),
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2299), (2313), (2572), (2632), (2633),
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1709.
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2634)  all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (2271), (2375), (2589), (2634) are
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2271.
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2635)  all_55_13 = e1 | all_55_13 = e0
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (2272), (2313), (2635) are inconsistent by
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1837.
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2636)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (119), (124), (126), (140), (141), (169), (170),
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (191), (193), (199), (245), (246), (247), (259),
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2272), (2273), (2287), (2312), (2313), (2314),
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2315), (2377), (2547), (2636), (function-axioms)
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1718.
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2637)  all_57_10 = e0 & op(e2, e0) = e0
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2637) implies:
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2638)  op(e2, e0) = e0
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (2316), (2638), (function-axioms) are
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2470.
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2639)  all_57_5 = e1 & op(e2, e1) = e1
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (2273), (2639), (function-axioms) are
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2305.
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.01/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2640)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 220.09/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e1)
% 220.09/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (2381), (2565), (2640),
% 220.09/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.09/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1815.
% 220.09/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2641)  all_57_15 = e3 & op(e0, e0) = e3
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2641) implies:
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2642)  all_57_15 = e3
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2643)  op(e0, e0) = e3
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (70), (107),
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (137), (163), (166), (171), (204), (207), (208),
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (209), (211), (212), (217), (221), (222), (223),
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (225), (226), (227), (228), (229), (230),
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (232), (233), (234), (235), (236), (270),
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (374), (2265), (2268), (2270), (2273), (2279),
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2280), (2291), (2642), (2643), (function-axioms)
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1732.
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | |   (2644)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (165), (169), (2315), (2316), (2317),
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | |            (2644), (function-axioms) are inconsistent by
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2112.
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.13  | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.13  | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | |   (2645)  all_30_2 = e1
% 220.09/37.13  | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (330), (2645) imply:
% 220.09/37.13  | | | | | | | | | | | | | | | | | |   (2646)  all_4_2 = e1
% 220.09/37.13  | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | SIMP: (2646) implies:
% 220.09/37.13  | | | | | | | | | | | | | | | | | |   (2647)  all_4_2 = e1
% 220.09/37.13  | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | REDUCE: (351), (2647) imply:
% 220.09/37.13  | | | | | | | | | | | | | | | | | |   (2648)   ~ (all_53_3 = e1)
% 220.09/37.13  | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | REDUCE: (370), (2647) imply:
% 220.09/37.13  | | | | | | | | | | | | | | | | | |   (2649)   ~ (all_53_12 = e1)
% 220.09/37.13  | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | REDUCE: (373), (2647) imply:
% 220.09/37.13  | | | | | | | | | | | | | | | | | |   (2650)   ~ (e2 = e1)
% 220.09/37.13  | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | REDUCE: (36), (2647) imply:
% 220.09/37.13  | | | | | | | | | | | | | | | | | |   (2651)  op(e0, e0) = e1
% 220.09/37.13  | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 220.09/37.13  | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | |   (2652)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 220.09/37.13  | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e1)
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (226), (228), (229),
% 220.09/37.13  | | | | | | | | | | | | | | | | | | |            (2280), (2291), (2652), (function-axioms) are
% 220.09/37.13  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1856.
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | |   (2653)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 220.09/37.13  | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e1)
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | BETA: splitting (2653) gives:
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | |   (2654)  all_57_4 = e1 & op(e3, e1) = e1
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | ALPHA: (2654) implies:
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | |   (2655)  all_57_4 = e1
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | |   (2656)  op(e3, e1) = e1
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | |   (2657)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e1)
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (168), (2269), (2291), (2657),
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | |            #2155.
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | |   (2658)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e3) = e1)
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2658) gives:
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | |   (2659)  all_57_6 = e1 & op(e1, e3) = e1
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2659) implies:
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | |   (2660)  all_57_6 = e1
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | |   (2661)  op(e1, e3) = e1
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_2, e1,
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | |              e3, e1, simplifying with (164), (2661) gives:
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | |   (2662)  all_53_2 = e1
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_8, e1,
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (170), (2656) gives:
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | |   (2663)  all_53_8 = e1
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (2662) imply:
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | |   (2664)   ~ (all_53_6 = e1)
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (142), (2662) imply:
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | |   (2665)   ~ (all_53_14 = e1)
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | SIMP: (2665) implies:
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | |   (2666)   ~ (all_53_14 = e1)
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (124), (2663) imply:
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | |   (2667)   ~ (all_53_9 = e1)
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (2663) imply:
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | |   (2668)   ~ (all_53_12 = e1)
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (363), (2663) imply:
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | |   (2669)   ~ (all_6_2 = e1)
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | SIMP: (2669) implies:
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | |   (2670)   ~ (all_6_2 = e1)
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | |   (2671)  all_55_10 = e3
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (374), (2671) are inconsistent by sub-proof
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | |            #2500.
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | |   (2672)   ~ (all_55_10 = e3)
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | |   (2673)  all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2673) gives:
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | |   (2674)  all_55_10 = e2
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (336), (2674) imply:
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | |   (2675)  all_6_2 = e2
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2675) implies:
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | |   (2676)  all_6_2 = e2
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (361), (2676) imply:
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | |   (2677)   ~ (all_53_6 = e2)
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (368), (2676) imply:
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | |   (2678)   ~ (all_53_14 = e2)
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (2676) imply:
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | |   (2679)  op(e1, e1) = e2
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | |   (2680)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | |             op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | |               all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | |               all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | |               all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2680) gives:
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2681)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | |           all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_7)
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2681) implies:
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2682)  op(e3, e1) = all_52_5
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2683)  op(all_52_5, all_52_5) = e1
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_52_5,
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (2656), (2682) gives:
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2684)  all_52_5 = e1
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2683), (2684) imply:
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2685)  op(e1, e1) = e1
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2679), (2685), (function-axioms) are
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2423.
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2686)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | |           all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | |           & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_15)
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2686) implies:
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2687)  op(e2, e0) = all_52_15
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2688)  op(e2, e1) = all_52_13
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2689)  op(e2, e2) = all_52_11
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2690)  op(all_52_15, all_52_15) = e0
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2691)  op(all_52_13, all_52_13) = e1
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2692)  op(all_52_11, all_52_11) = e2
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_13,
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_15, e0, e2, simplifying with (165), (2687)
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2693)  all_53_13 = all_52_15
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_9,
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_13, e1, e2, simplifying with (166), (2688)
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2694)  all_53_9 = all_52_13
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_11, e2, e2, simplifying with (2280), (2689)
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2695)  all_52_11 = e1
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (2693) imply:
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2696)  all_55_7 = all_52_15
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (114), (2693) imply:
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2697)   ~ (all_53_12 = all_52_15)
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (111), (2693) imply:
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2698)   ~ (all_53_14 = all_52_15)
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2698) implies:
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2699)   ~ (all_53_14 = all_52_15)
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.13  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2274), (2693) imply:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2700)   ~ (all_52_15 = e1)
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2701)  all_55_3 = e3
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (2290), (2701) are inconsistent by
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2169.
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2702)   ~ (all_55_3 = e3)
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2703)  all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2704)  all_55_9 = e3
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (2704) imply:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2705)  all_53_6 = e3
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2705) implies:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2706)  all_53_6 = e3
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (127), (2706) imply:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2707)   ~ (all_53_14 = e3)
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2707) implies:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2708)   ~ (all_53_14 = e3)
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2709)  all_55_11 = e3
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (2708), (2709) are inconsistent by
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2497.
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2710)   ~ (all_55_11 = e3)
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2711)  all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2712)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2712) gives:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2713)  all_57_12 = e3 & op(e0, e3) = e3
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2713) implies:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2714)  all_57_12 = e3
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2715)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2715) gives:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2716)  all_57_9 = e3 & op(e3, e0) = e3
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2716) implies:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2717)  op(e3, e0) = e3
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (2290), (2717), (function-axioms) are
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2458.
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2718)  all_57_10 = e3 & op(e2, e0) = e3
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2718) implies:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2719)  all_57_10 = e3
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2720)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2720) gives:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2721)  all_57_6 = e3 & op(e1, e3) = e3
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2721) implies:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2722)  all_57_6 = e3
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (230), (232), (234),
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2294), (2722) are inconsistent by sub-proof
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2010.
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2723)  all_57_7 = e3 & op(e1, e2) = e3
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2723) implies:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2724)  all_57_7 = e3
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2725)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2725) gives:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2726)  all_57_2 = e2 & op(e2, e3) = e2
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2726) implies:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2727)  all_57_2 = e2
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2728)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e3)
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2728) gives:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2729)  all_57_4 = e3 & op(e3, e1) = e3
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2729) implies:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2730)  all_57_4 = e3
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (235),
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2291), (2730), (function-axioms) are inconsistent
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2474.
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2731)  all_57_5 = e3 & op(e2, e1) = e3
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2731) implies:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2732)  op(e2, e1) = e3
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (70), (2268), (2291), (2688), (2691), (2732),
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1791.
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2733)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e1) = e3)
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2733) gives:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2734)  all_57_8 = e3 & op(e1, e1) = e3
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2734) implies:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2735)  op(e1, e1) = e3
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (374), (2735), (function-axioms) are
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2468.
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2736)  all_57_14 = e3 & op(e0, e1) = e3
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2736) implies:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2737)  all_57_14 = e3
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2738)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2738) gives:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2739)  all_57_9 = e2 & op(e3, e0) = e2
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2739) implies:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2740)  all_57_9 = e2
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2741)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2741) gives:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2742)  all_57_0 = e0 & op(e3, e3) = e0
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2742) implies:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2743)  op(e3, e3) = e0
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2291), (2743), (function-axioms) are
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2494.
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2744)  all_57_1 = e0 & op(e3, e2) = e0
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2744) implies:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2745)  all_57_1 = e0
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2746)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e0)
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2746) gives:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2747)  all_57_0 = e0 & op(e3, e3) = e0
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2747) implies:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2748)  all_57_0 = e0
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2749)  op(e3, e3) = e0
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (169), (226), (227),
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (228), (233), (235), (237), (2279), (2280),
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2290), (2724), (2745), (2748), (2749),
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1706.
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2750)  all_57_2 = e0 & op(e2, e3) = e0
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2750) implies:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2751)  all_57_2 = e0
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (218), (223),
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (225), (2279), (2280), (2296), (2655),
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2737), (2751), (function-axioms) are inconsistent
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1716.
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2752)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = e0)
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2752) gives:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2753)  all_57_6 = e0 & op(e1, e3) = e0
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (232), (2291), (2714), (2727),
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2753), (function-axioms) are inconsistent by
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2225.
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2754)  all_57_12 = e0 & op(e0, e3) = e0
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2714), (2754) are inconsistent by sub-proof
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2237.
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2755)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2755) gives:
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2756)  all_57_4 = e0 & op(e3, e1) = e0
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2756) implies:
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2757)  all_57_4 = e0
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2655), (2757) imply:
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2758)  e1 = e0
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2279), (2758) imply:
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2759)  all_57_3 = e0
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (232), (2291), (2714), (2727), (2759),
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2224.
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2760)  all_57_9 = e0 & op(e3, e0) = e0
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (218), (223),
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (225), (2279), (2280), (2296), (2655),
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2727), (2737), (2740), (2760), (function-axioms)
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1705.
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2761)  all_57_10 = e2 & op(e2, e0) = e2
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (39), (218), (221),
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (374), (2296), (2655), (2719), (2737), (2761),
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1704.
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2762)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2762) gives:
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2763)  all_57_11 = e2 & op(e1, e0) = e2
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2763) implies:
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2764)  all_57_11 = e2
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2765)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e0)
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (218), (223),
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (225), (2279), (2280), (2291), (2296),
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2655), (2737), (2765), (function-axioms) are
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1703.
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2766)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = e0)
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2766) gives:
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2767)  all_57_6 = e0 & op(e1, e3) = e0
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (232), (2291), (2714), (2727),
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2767), (function-axioms) are inconsistent by
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2225.
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2768)  all_57_12 = e0 & op(e0, e3) = e0
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (39), (217), (374), (2660), (2714),
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2724), (2764), (2768), (function-axioms) are
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1702.
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2769)  all_57_15 = e2 & op(e0, e0) = e2
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2769) implies:
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2770)  op(e0, e0) = e2
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2651), (2770), (function-axioms) are
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2177.
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2771)  all_57_3 = e2 & op(e2, e2) = e2
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2771) implies:
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2772)  op(e2, e2) = e2
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2280), (2772), (function-axioms) are
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2306.
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2773)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2773) gives:
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2774)  all_57_5 = e2 & op(e2, e1) = e2
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2774) implies:
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2775)  all_57_5 = e2
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2776)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2776) gives:
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2777)  all_57_2 = e0 & op(e2, e3) = e0
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (218), (221),
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (223), (224), (225), (374), (2279), (2280),
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2296), (2655), (2775), (2777), (function-axioms)
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1701.
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2778)  all_57_3 = e0 & op(e2, e2) = e0
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2778) implies:
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2779)  all_57_3 = e0
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (232), (234), (2291), (2714), (2779),
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2223.
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2780)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0)
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2780) gives:
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2781)  all_57_5 = e0 & op(e2, e1) = e0
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2775), (2781) are inconsistent by sub-proof
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2428.
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2782)  all_57_10 = e0 & op(e2, e0) = e0
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2719), (2782) are inconsistent by sub-proof
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1981.
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2783)  all_57_10 = e2 & op(e2, e0) = e2
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2783) implies:
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2784)  all_57_10 = e2
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2719), (2784) are inconsistent by sub-proof
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2356.
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2785)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (161), (374), (2708), (2785),
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2310.
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2786)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2786) gives:
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2787)  all_57_11 = e3 & op(e1, e0) = e3
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2787) implies:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2788)  op(e1, e0) = e3
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (2708), (2788), (function-axioms) are
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2330.
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2789)  all_57_15 = e3 & op(e0, e0) = e3
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2789) implies:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2790)  all_57_15 = e3
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2791)  op(e0, e0) = e3
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (70), (107),
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (137), (163), (166), (171), (204), (207), (208),
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (209), (211), (212), (217), (221), (222), (223),
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (225), (226), (227), (228), (229), (230),
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (232), (233), (234), (235), (236), (270),
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (374), (2265), (2268), (2270), (2273), (2279),
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2280), (2291), (2790), (2791), (function-axioms)
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1732.
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2792)  all_57_13 = e3 & op(e0, e2) = e3
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2792) implies:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2793)  all_57_13 = e3
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2794)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2794) gives:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2795)  all_57_9 = e3 & op(e3, e0) = e3
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2795) implies:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2796)  op(e3, e0) = e3
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (2290), (2796), (function-axioms) are
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2458.
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2797)  all_57_10 = e3 & op(e2, e0) = e3
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2797) implies:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2798)  all_57_10 = e3
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2799)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2799) gives:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2800)  all_57_6 = e3 & op(e1, e3) = e3
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2800) implies:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2801)  all_57_6 = e3
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (230), (232), (234),
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2294), (2801) are inconsistent by sub-proof
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2010.
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2802)  all_57_7 = e3 & op(e1, e2) = e3
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2802) implies:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2803)  all_57_7 = e3
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2804)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2804) gives:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2805)  all_57_2 = e2 & op(e2, e3) = e2
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2805) implies:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2806)  all_57_2 = e2
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2807)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e0)
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2807) gives:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2808)  all_57_0 = e0 & op(e3, e3) = e0
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2808) implies:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2809)  op(e3, e3) = e0
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2291), (2809), (function-axioms) are
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2494.
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2810)  all_57_2 = e0 & op(e2, e3) = e0
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2806), (2810) are inconsistent by sub-proof
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1700.
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2811)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = e0)
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2811) gives:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2812)  all_57_6 = e0 & op(e1, e3) = e0
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2812) implies:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2813)  all_57_6 = e0
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2660), (2813) imply:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2814)  e1 = e0
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2279), (2814) imply:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2815)  all_57_3 = e0
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (223), (224), (227),
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (228), (2793), (2798), (2803), (2806), (2815) are
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1699.
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2816)  all_57_12 = e0 & op(e0, e3) = e0
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2816) implies:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2817)  all_57_12 = e0
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2818)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2818) gives:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2819)  all_57_12 = e2 & op(e0, e3) = e2
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2819) implies:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2820)  all_57_12 = e2
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2817), (2820) are inconsistent by sub-proof
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2385.
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2821)  all_57_13 = e2 & op(e0, e2) = e2
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2821) implies:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2822)  all_57_13 = e2
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2793), (2822) imply:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2823)  e3 = e2
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2823) implies:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2824)  e3 = e2
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2803), (2824) imply:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2825)  all_57_7 = e2
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (226), (227), (228),
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (229), (2280), (2822), (2825), (function-axioms)
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1696.
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2826)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (218), (221),
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (374), (2296), (2651), (2655), (2826),
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1695.
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2827)  all_57_3 = e2 & op(e2, e2) = e2
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2827) implies:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2828)  op(e2, e2) = e2
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2280), (2828), (function-axioms) are
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2306.
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2829)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2829) gives:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2830)  all_57_5 = e2 & op(e2, e1) = e2
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2830) implies:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2831)  all_57_5 = e2
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2832)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2832) gives:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2833)  all_57_1 = e2 & op(e3, e2) = e2
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2833) implies:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2834)  all_57_1 = e2
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2835)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e3)
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2835) gives:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2836)  all_57_4 = e3 & op(e3, e1) = e3
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (235),
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2291), (2834), (2836), (function-axioms) are
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1829.
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2837)  all_57_5 = e3 & op(e2, e1) = e3
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2837) implies:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2838)  op(e2, e1) = e3
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (70), (2268), (2291), (2688), (2691), (2838),
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1791.
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2839)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e1) = e3)
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2839) gives:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2840)  all_57_8 = e3 & op(e1, e1) = e3
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2840) implies:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2841)  op(e1, e1) = e3
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (374), (2841), (function-axioms) are
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2468.
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2842)  all_57_14 = e3 & op(e0, e1) = e3
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2842) implies:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2843)  all_57_14 = e3
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2844)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2844) gives:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2845)  all_57_9 = e2 & op(e3, e0) = e2
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2845) implies:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2846)  all_57_9 = e2
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2847)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 220.09/37.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (2291), (2834), (2847),
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1722.
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2848)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2848) gives:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2849)  all_57_4 = e0 & op(e3, e1) = e0
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2849) implies:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2850)  all_57_4 = e0
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2655), (2850) imply:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2851)  e1 = e0
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2279), (2851) imply:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2852)  all_57_3 = e0
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (219), (221),
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (223), (224), (231), (233), (235), (374), (2291),
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2679), (2798), (2831), (2850), (2852),
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1691.
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2853)  all_57_9 = e0 & op(e3, e0) = e0
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2846), (2853) are inconsistent by sub-proof
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1973.
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2854)  all_57_10 = e2 & op(e2, e0) = e2
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2854) implies:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2855)  all_57_10 = e2
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2798), (2855) imply:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2856)  e3 = e2
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2793), (2856) imply:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2857)  all_57_13 = e2
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2803), (2856) imply:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2858)  all_57_7 = e2
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (226), (227), (228),
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (229), (2280), (2857), (2858), (function-axioms)
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1696.
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2859)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2859) gives:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2860)  all_57_11 = e2 & op(e1, e0) = e2
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2860) implies:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2861)  all_57_11 = e2
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (39), (217), (218),
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (374), (2296), (2655), (2660), (2803), (2831),
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2843), (2861), (function-axioms) are inconsistent
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1690.
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2862)  all_57_15 = e2 & op(e0, e0) = e2
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2862) implies:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2863)  op(e0, e0) = e2
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2651), (2863), (function-axioms) are
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2177.
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2864)  all_57_3 = e2 & op(e2, e2) = e2
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2864) implies:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2865)  op(e2, e2) = e2
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2280), (2865), (function-axioms) are
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2306.
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2866)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2866) gives:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2867)  all_57_7 = e2 & op(e1, e2) = e2
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2867) implies:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2868)  all_57_7 = e2
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2803), (2868) imply:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2869)  e3 = e2
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2869) implies:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2870)  e3 = e2
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2793), (2870) imply:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2871)  all_57_13 = e2
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (226), (227), (228),
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (229), (2280), (2868), (2871), (function-axioms)
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1696.
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2872)  all_57_13 = e2 & op(e0, e2) = e2
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2872) implies:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2873)  all_57_13 = e2
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2793), (2873) imply:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2874)  e3 = e2
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2803), (2874) imply:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2875)  all_57_7 = e2
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (226), (227), (228),
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (229), (2280), (2873), (2875), (function-axioms)
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1696.
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2876)  all_57_10 = e2 & op(e2, e0) = e2
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2876) implies:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2877)  all_57_10 = e2
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2798), (2877) imply:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2878)  e3 = e2
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2878) implies:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2879)  e3 = e2
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2793), (2879) imply:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2880)  all_57_13 = e2
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2803), (2879) imply:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2881)  all_57_7 = e2
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (226), (227), (228),
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (229), (2280), (2880), (2881), (function-axioms)
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1696.
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2882)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (161), (374), (2708), (2882),
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2310.
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2883)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2883) gives:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2884)  all_57_11 = e3 & op(e1, e0) = e3
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2884) implies:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2885)  op(e1, e0) = e3
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (2708), (2885), (function-axioms) are
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2330.
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2886)  all_57_15 = e3 & op(e0, e0) = e3
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2886) implies:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2887)  all_57_15 = e3
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2888)  op(e0, e0) = e3
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (207), (208), (209),
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2793), (2887), (2888), (function-axioms) are
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1792.
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2889)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2889) gives:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2890)  all_57_14 = e3 & op(e0, e1) = e3
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2890) implies:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2891)  all_57_14 = e3
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2892)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2892) gives:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2893)  all_57_9 = e3 & op(e3, e0) = e3
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2893) implies:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2894)  op(e3, e0) = e3
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (2290), (2894), (function-axioms) are
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2458.
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2895)  all_57_10 = e3 & op(e2, e0) = e3
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2895) implies:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2896)  all_57_10 = e3
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2897)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2897) gives:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2898)  all_57_6 = e3 & op(e1, e3) = e3
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2898) implies:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2899)  all_57_6 = e3
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (230), (232), (234),
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2294), (2899) are inconsistent by sub-proof
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2010.
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2900)  all_57_7 = e3 & op(e1, e2) = e3
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2900) implies:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2901)  all_57_7 = e3
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2902)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2902) gives:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2903)  all_57_2 = e2 & op(e2, e3) = e2
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2903) implies:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2904)  all_57_2 = e2
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2905)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (218), (223),
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (225), (2279), (2280), (2296), (2655),
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2891), (2905), (function-axioms) are inconsistent
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1715.
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2906)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0)
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2906) gives:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2907)  all_57_5 = e0 & op(e2, e1) = e0
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2907) implies:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2908)  all_57_5 = e0
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2909)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2909) gives:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2910)  all_57_9 = e2 & op(e3, e0) = e2
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2910) implies:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2911)  all_57_9 = e2
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2711) gives:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2912)  all_55_11 = e2
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (2678), (2912) are inconsistent by
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2282.
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2913)  all_55_11 = e1 | all_55_11 = e0
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2914)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2914) gives:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2915)  all_57_0 = e0 & op(e3, e3) = e0
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2915) implies:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2916)  op(e3, e3) = e0
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2291), (2916), (function-axioms) are
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2494.
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2917)  all_57_1 = e0 & op(e3, e2) = e0
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2917) implies:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2918)  all_57_1 = e0
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2913) gives:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2919)  all_55_11 = e1
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (2666), (2919) are inconsistent by
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2309.
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2920)  all_55_11 = e0
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (2920) imply:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2921)  all_53_14 = e0
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2921) implies:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2922)  all_53_14 = e0
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (2922) imply:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2923)   ~ (all_53_12 = e0)
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2699), (2922) imply:
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2924)   ~ (all_52_15 = e0)
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2924) implies:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2925)   ~ (all_52_15 = e0)
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2703) gives:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2926)  all_55_3 = e2
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (2926) imply:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2927)  all_53_12 = e2
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2927) implies:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2928)  all_53_12 = e2
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2697), (2928) imply:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2929)   ~ (all_52_15 = e2)
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2929) implies:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2930)   ~ (all_52_15 = e2)
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2931)  all_55_7 = e3
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (237), (2290), (2655), (2690), (2696),
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2700), (2918), (2925), (2931), (function-axioms)
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2279.
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2932)  all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2651), (2690), (2696), (2700), (2930), (2932),
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2078.
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2933)  all_55_3 = e1 | all_55_3 = e0
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (2649), (2923), (2933) are inconsistent by
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2132.
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2934)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2934) gives:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2935)  all_57_4 = e0 & op(e3, e1) = e0
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2655), (2935) are inconsistent by sub-proof
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2429.
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2936)  all_57_9 = e0 & op(e3, e0) = e0
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (218), (223),
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (225), (2279), (2280), (2296), (2655),
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2891), (2904), (2911), (2936), (function-axioms)
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1705.
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2937)  all_57_10 = e2 & op(e2, e0) = e2
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (39), (218), (221),
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (374), (2296), (2655), (2891), (2896), (2937),
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1704.
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2938)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2938) gives:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2939)  all_57_11 = e2 & op(e1, e0) = e2
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2939) implies:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2940)  all_57_11 = e2
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2941)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e0)
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (218), (223),
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (225), (2279), (2280), (2291), (2296),
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2655), (2891), (2941), (function-axioms) are
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1703.
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2942)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = e0)
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2942) gives:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2943)  all_57_6 = e0 & op(e1, e3) = e0
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2660), (2943) are inconsistent by sub-proof
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2347.
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2944)  all_57_12 = e0 & op(e0, e3) = e0
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2944) implies:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2945)  all_57_12 = e0
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2946)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2946) gives:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2947)  all_57_12 = e2 & op(e0, e3) = e2
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2947) implies:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2948)  all_57_12 = e2
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2945), (2948) imply:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2949)  e2 = e0
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2949) implies:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2950)  e2 = e0
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2904), (2950) imply:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2951)  all_57_2 = e0
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (218), (223),
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (225), (2279), (2280), (2296), (2655),
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2891), (2951), (function-axioms) are inconsistent
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1716.
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2952)  all_57_13 = e2 & op(e0, e2) = e2
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2952) implies:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2953)  all_57_13 = e2
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2954)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2954) gives:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2955)  all_57_1 = e0 & op(e3, e2) = e0
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2955) implies:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2956)  all_57_1 = e0
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2957)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e0)
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2957) gives:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2958)  all_57_6 = e0 & op(e1, e3) = e0
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2958) implies:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2959)  all_57_6 = e0
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2660), (2959) imply:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2960)  e1 = e0
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2279), (2960) imply:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2961)  all_57_3 = e0
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (227), (228), (2901),
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2956), (2961) are inconsistent by sub-proof
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2098.
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2962)  all_57_7 = e0 & op(e1, e2) = e0
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2962) implies:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2963)  all_57_7 = e0
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (39), (217), (374), (2660), (2940),
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2963), (function-axioms) are inconsistent by
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2343.
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2964)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2964) gives:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2965)  all_57_8 = e0 & op(e1, e1) = e0
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2965) implies:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2966)  op(e1, e1) = e0
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2280), (2689), (2692), (2966),
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1843.
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2967)  all_57_11 = e0 & op(e1, e0) = e0
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2967) implies:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2968)  all_57_11 = e0
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2940), (2968) imply:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2969)  e2 = e0
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2904), (2969) imply:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2970)  all_57_2 = e0
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (218), (223),
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (225), (2279), (2280), (2296), (2655),
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2891), (2970), (function-axioms) are inconsistent
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1716.
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2971)  all_57_3 = e0 & op(e2, e2) = e0
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2971) implies:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2972)  all_57_3 = e0
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2973)  op(e2, e2) = e0
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (223), (224),
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (225), (2274), (2908), (2972), (2973),
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1689.
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2974)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0)
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2974) gives:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2975)  all_57_7 = e0 & op(e1, e2) = e0
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2975) implies:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2976)  all_57_7 = e0
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (39), (217), (374), (2660), (2940),
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2976), (function-axioms) are inconsistent by
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2343.
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2977)  all_57_13 = e0 & op(e0, e2) = e0
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2977) implies:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2978)  all_57_13 = e0
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2953), (2978) imply:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2979)  e2 = e0
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2904), (2979) imply:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2980)  all_57_2 = e0
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (218), (223),
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (225), (2279), (2280), (2296), (2655),
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2891), (2980), (function-axioms) are inconsistent
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1716.
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2981)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (218), (221),
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (374), (2296), (2651), (2655), (2981),
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1695.
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2982)  all_57_15 = e2 & op(e0, e0) = e2
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2982) implies:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2983)  op(e0, e0) = e2
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2651), (2983), (function-axioms) are
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2177.
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2984)  all_57_10 = e0 & op(e2, e0) = e0
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2896), (2984) are inconsistent by sub-proof
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1981.
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2985)  all_57_3 = e2 & op(e2, e2) = e2
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2985) implies:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2986)  op(e2, e2) = e2
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2280), (2986), (function-axioms) are
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2306.
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2987)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2987) gives:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2988)  all_57_5 = e2 & op(e2, e1) = e2
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2988) implies:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2989)  all_57_5 = e2
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2990)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2990) gives:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2991)  all_57_2 = e0 & op(e2, e3) = e0
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (218), (221),
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (223), (224), (225), (374), (2279), (2280),
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2296), (2655), (2989), (2991), (function-axioms)
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1701.
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2992)  all_57_3 = e0 & op(e2, e2) = e0
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2992) implies:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2993)  op(e2, e2) = e0
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2280), (2993), (function-axioms) are
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2352.
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2994)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0)
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2994) gives:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2995)  all_57_5 = e0 & op(e2, e1) = e0
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2989), (2995) are inconsistent by sub-proof
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2428.
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2996)  all_57_10 = e0 & op(e2, e0) = e0
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2896), (2996) are inconsistent by sub-proof
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1981.
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2997)  all_57_10 = e2 & op(e2, e0) = e2
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2997) implies:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2998)  all_57_10 = e2
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2896), (2998) imply:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2999)  e3 = e2
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2999) implies:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3000)  e3 = e2
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2891), (3000) imply:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3001)  all_57_14 = e2
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (39), (218), (221),
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (374), (2296), (2655), (3001), (function-axioms)
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2408.
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3002)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (161), (374), (2708), (3002),
% 220.09/37.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2310.
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3003)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (161), (207), (208),
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (209), (2708), (2891), (3003), (function-axioms)
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2311.
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3004)  all_57_15 = e3 & op(e0, e0) = e3
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3004) implies:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3005)  all_57_15 = e3
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3006)  op(e0, e0) = e3
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (70), (107),
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (137), (163), (166), (171), (204), (207), (208),
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (209), (211), (212), (217), (221), (222), (223),
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (225), (226), (227), (228), (229), (230),
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (232), (233), (234), (235), (236), (270),
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (374), (2265), (2268), (2270), (2273), (2279),
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2280), (2291), (3005), (3006), (function-axioms)
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1732.
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3007)  all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3007) gives:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3008)  all_55_9 = e2
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (2677), (3008) are inconsistent by
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2274.
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3009)  all_55_9 = e1 | all_55_9 = e0
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3009) gives:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3010)  all_55_9 = e1
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (2271), (3010) are inconsistent by
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2273.
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3011)  all_55_9 = e0
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (3011) imply:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3012)  all_53_6 = e0
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3012) implies:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3013)  all_53_6 = e0
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (127), (3013) imply:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3014)   ~ (all_53_14 = e0)
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3014) implies:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3015)   ~ (all_53_14 = e0)
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2271), (3013) imply:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3016)   ~ (e1 = e0)
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3017)  all_55_11 = e3
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (3017) imply:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3018)  all_53_14 = e3
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3018) implies:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3019)  all_53_14 = e3
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2699), (3019) imply:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3020)   ~ (all_52_15 = e3)
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (198), (2280), (2651), (2690), (2696),
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2700), (3020), (function-axioms) are inconsistent
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1687.
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3021)  all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3021) gives:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3022)  all_55_11 = e2
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (2678), (3022) are inconsistent by
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2282.
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3023)  all_55_11 = e1 | all_55_11 = e0
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (2666), (3015), (3023) are inconsistent by
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2307.
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | |   (3024)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | |             & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | |               all_52_21) = e1 & op(all_52_23, all_52_23) =
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | |             = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | |             & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(all_52_25, all_52_25) = e3 &
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | |             op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | |               all_52_29) = e1 & op(all_52_31, all_52_31) =
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | |             = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_29) & $i(all_52_31))
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (195), (336), (374), (2296), (2651), (2661),
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | |            (3024), (function-axioms) are inconsistent by
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1686.
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | |   (3025)  all_55_10 = e1 | all_55_10 = e0
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (2296), (2670), (3025) are inconsistent by
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1685.
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | |   (3026)  all_57_12 = e1 & op(e0, e3) = e1
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (2648), (3026), (function-axioms) are
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1947.
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | |   (3027)  all_57_9 = e1 & op(e3, e0) = e1
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (2649), (3027), (function-axioms) are
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2131.
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.19  | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | End of split
% 220.09/37.19  | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | End of split
% 220.09/37.19  | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | Case 2:
% 220.09/37.19  | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | |   (3028)  all_24_2 = e0
% 220.09/37.19  | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | COMBINE_EQS: (315), (3028) imply:
% 220.09/37.19  | | | | | | | | | | | | | | | |   (3029)  all_6_2 = e0
% 220.09/37.19  | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | REDUCE: (350), (3029) imply:
% 220.09/37.19  | | | | | | | | | | | | | | | |   (3030)   ~ (all_53_2 = e0)
% 220.09/37.19  | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | REDUCE: (361), (3029) imply:
% 220.09/37.19  | | | | | | | | | | | | | | | |   (3031)   ~ (all_53_6 = e0)
% 220.09/37.19  | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | REDUCE: (363), (3029) imply:
% 220.09/37.19  | | | | | | | | | | | | | | | |   (3032)   ~ (all_53_8 = e0)
% 220.09/37.19  | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | REDUCE: (364), (3029) imply:
% 220.09/37.19  | | | | | | | | | | | | | | | |   (3033)   ~ (all_53_9 = e0)
% 220.09/37.19  | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | REDUCE: (366), (3029) imply:
% 220.09/37.19  | | | | | | | | | | | | | | | |   (3034)   ~ (all_53_11 = e0)
% 220.09/37.19  | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | REDUCE: (368), (3029) imply:
% 220.09/37.19  | | | | | | | | | | | | | | | |   (3035)   ~ (all_53_14 = e0)
% 220.09/37.19  | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | REDUCE: (374), (3029) imply:
% 220.09/37.19  | | | | | | | | | | | | | | | |   (3036)   ~ (e3 = e0)
% 220.09/37.19  | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 220.09/37.19  | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.19  | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | |   (3037)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 220.09/37.19  | | | | | | | | | | | | | | | | |             & op(e1, e2) = e0)
% 220.09/37.19  | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (164), (3030), (3031), (3037),
% 220.09/37.19  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.09/37.19  | | | | | | | | | | | | | | | | |            #2038.
% 220.09/37.19  | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.19  | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | |   (3038)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 220.09/37.19  | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 220.09/37.19  | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | BETA: splitting (3038) gives:
% 220.09/37.19  | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | |   (3039)  all_57_8 = e0 & op(e1, e1) = e0
% 220.09/37.19  | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | ALPHA: (3039) implies:
% 220.09/37.19  | | | | | | | | | | | | | | | | | |   (3040)  all_57_8 = e0
% 220.09/37.19  | | | | | | | | | | | | | | | | | |   (3041)  op(e1, e1) = e0
% 220.09/37.19  | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | BETA: splitting (76) gives:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | |   (3042)   ~ (all_30_2 = e1)
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | REDUCE: (330), (3042) imply:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | |   (3043)   ~ (all_4_2 = e1)
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | |   (3044)  all_55_15 = e3
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (3044) imply:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | |   (3045)  all_4_2 = e3
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | REDUCE: (378), (3045) imply:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | |   (3046)  $false
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | CLOSE: (3046) is inconsistent.
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | |   (3047)   ~ (all_55_15 = e3)
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | |   (3048)  all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | BETA: splitting (3048) gives:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | |   (3049)  all_55_15 = e2
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (3049) imply:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | |   (3050)  all_4_2 = e2
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | REDUCE: (373), (3050) imply:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | |   (3051)  $false
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | CLOSE: (3051) is inconsistent.
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | |   (3052)   ~ (all_55_15 = e2)
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | |   (3053)  all_55_15 = e1 | all_55_15 = e0
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3053) gives:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | |   (3054)  all_55_15 = e1
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (3054) imply:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | |   (3055)  all_4_2 = e1
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3043), (3055) imply:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | |   (3056)  $false
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3056) is inconsistent.
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | |   (3057)  all_55_15 = e0
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (3057) imply:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | |   (3058)  all_4_2 = e0
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (362), (3058) imply:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | |   (3059)   ~ (all_53_7 = e0)
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (373), (3058) imply:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | |   (3060)   ~ (e2 = e0)
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3043), (3058) imply:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | |   (3061)   ~ (e1 = e0)
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (3058) imply:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | |   (3062)  op(e0, e0) = e0
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | |   (3063)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3063) gives:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | |   (3064)  all_57_1 = e0 & op(e3, e2) = e0
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3064) implies:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | |   (3065)  op(e3, e2) = e0
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (36), (107), (129), (136), (137), (159),
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | |            (161), (165), (169), (171), (190), (192), (196),
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | |            (207), (226), (244), (246), (256), (362), (370),
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | |            (371), (372), (373), (378), (2270), (2271),
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | |            (2272), (2280), (2291), (3041), (3043), (3062),
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | |            (3065), (function-axioms) are inconsistent by
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1834.
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | |   (3066)  all_57_3 = e0 & op(e2, e2) = e0
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3066) implies:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | |   (3067)  op(e2, e2) = e0
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2280), (3067), (function-axioms) are
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2352.
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | |   (3068)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0)
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (163), (3031), (3059), (3068),
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | |            #2024.
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | |   (3069)  all_30_2 = e1
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (330), (3069) imply:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | |   (3070)  all_4_2 = e1
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | REDUCE: (351), (3070) imply:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | |   (3071)   ~ (all_53_3 = e1)
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | REDUCE: (370), (3070) imply:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | |   (3072)   ~ (all_53_12 = e1)
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | REDUCE: (373), (3070) imply:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | |   (3073)   ~ (e2 = e1)
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | REDUCE: (36), (3070) imply:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | |   (3074)  op(e0, e0) = e1
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | |   (3075)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | BETA: splitting (3075) gives:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | |   (3076)  all_57_6 = e1 & op(e1, e3) = e1
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | ALPHA: (3076) implies:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | |   (3077)  all_57_6 = e1
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | |   (3078)  op(e1, e3) = e1
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | |   (3079)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e1)
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3079) gives:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | |   (3080)  all_57_4 = e1 & op(e3, e1) = e1
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3080) implies:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | |   (3081)  op(e3, e1) = e1
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_2, e1,
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | |              e3, e1, simplifying with (164), (3078) gives:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | |   (3082)  all_53_2 = e1
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_8, e1,
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (170), (3081) gives:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | |   (3083)  all_53_8 = e1
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (3082) imply:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | |   (3084)   ~ (all_53_3 = e1)
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (3082) imply:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | |   (3085)   ~ (all_53_6 = e1)
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (124), (3083) imply:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | |   (3086)   ~ (all_53_9 = e1)
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (122), (3083) imply:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | |   (3087)   ~ (all_53_11 = e1)
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3087) implies:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | |   (3088)   ~ (all_53_11 = e1)
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.19  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | |   (3089)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | |             all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | |             op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | |               all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | |               all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | |             & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | |               all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3089) gives:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |   (3090)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |           all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |           op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_7)
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3090) implies:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |   (3091)  op(e3, e1) = all_52_5
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |   (3092)  op(all_52_5, all_52_5) = e1
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (39), (163), (170),
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |            (215), (216), (217), (374), (2271), (3032),
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |            (3040), (3041), (3077), (3080), (3091), (3092),
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |            #1684.
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |   (3093)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |           all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |           op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |           & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_15)
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3093) implies:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |   (3094)  op(e2, e2) = all_52_11
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |   (3095)  op(all_52_11, all_52_11) = e2
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2280), (3041), (3094), (3095),
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |            #1843.
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | |   (3096)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | |             & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | |             & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | |               all_52_21) = e1 & op(all_52_23, all_52_23) =
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | |             all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | |             = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | |             & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(all_52_25, all_52_25) = e3 &
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | |             op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | |               all_52_29) = e1 & op(all_52_31, all_52_31) =
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | |             all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | |             = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_29) & $i(all_52_31))
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3096) gives:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |   (3097)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |           all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |           op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |           & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |           & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |           & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_23)
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3097) implies:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |   (3098)  op(e1, e3) = all_52_17
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |   (3099)  op(all_52_17, all_52_17) = e3
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (195), (336), (374), (3078), (3098), (3099),
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |            #1998.
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |   (3100)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |           all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |           op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |           & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |           & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |           & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_31)
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3100) implies:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |   (3101)  op(e0, e0) = all_52_31
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |   (3102)  op(e0, e1) = all_52_29
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |   (3103)  op(e0, e3) = all_52_25
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |   (3104)  op(all_52_31, all_52_31) = e0
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |   (3105)  op(all_52_29, all_52_29) = e1
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |   (3106)  op(all_52_25, all_52_25) = e3
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_11,
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_29, e1, e0, simplifying with (158), (3102)
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |   (3107)  all_53_11 = all_52_29
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_3,
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_25, e3, e0, simplifying with (160), (3103)
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |   (3108)  all_53_3 = all_52_25
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (3107) imply:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |   (3109)  all_55_14 = all_52_29
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (3108) imply:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |   (3110)  all_55_12 = all_52_25
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (3107), (3108) imply:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |   (3111)   ~ (all_52_25 = all_52_29)
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2287), (3108) imply:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |   (3112)   ~ (all_52_25 = e3)
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3071), (3108) imply:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |   (3113)   ~ (all_52_25 = e1)
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (119), (3107) imply:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |   (3114)   ~ (all_53_9 = all_52_29)
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3088), (3107) imply:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |   (3115)   ~ (all_52_29 = e1)
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3034), (3107) imply:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |   (3116)   ~ (all_52_29 = e0)
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3117)  all_55_6 = e3
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (3117) imply:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3118)  all_53_9 = e3
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3118) implies:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3119)  all_53_9 = e3
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3114), (3119) imply:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3120)   ~ (all_52_29 = e3)
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3120) implies:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3121)   ~ (all_52_29 = e3)
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3122)  all_55_14 = e3
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3109), (3122) imply:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3123)  all_52_29 = e3
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3121), (3123) imply:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3124)  $false
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3124) is inconsistent.
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3125)  all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3125) gives:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3126)  all_55_14 = e2
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3109), (3126) imply:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3127)  all_52_29 = e2
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3127) implies:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3128)  all_52_29 = e2
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3111), (3128) imply:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3129)   ~ (all_52_25 = e2)
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3130)  all_55_12 = e3
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3110), (3112), (3130) are inconsistent by
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1683.
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3131)   ~ (all_55_12 = e3)
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3132)  all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3132) gives:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3133)  all_55_12 = e2
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3110), (3129), (3133) are inconsistent by
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1682.
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3134)  all_55_12 = e1 | all_55_12 = e0
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3134) gives:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3135)  all_55_12 = e1
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3110), (3113), (3135) are inconsistent by
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1681.
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3136)  all_55_12 = e0
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3110), (3136) imply:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3137)  all_52_25 = e0
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3137) implies:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3138)  all_52_25 = e0
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3106), (3138) imply:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3139)  op(e0, e0) = e3
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (70), (2268), (2291), (3101), (3104), (3139),
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1789.
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3140)  all_55_14 = e1 | all_55_14 = e0
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (3034), (3088), (3140) are inconsistent by
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1720.
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3141)  all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (191), (259), (2273), (2291), (3033), (3105),
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | |            (3109), (3114), (3115), (3116), (3141),
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | |            #1680.
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | |   (3142)  all_57_5 = e1 & op(e2, e1) = e1
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (2273), (3142), (function-axioms) are
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2305.
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | |   (3143)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e1)
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3143) gives:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | |   (3144)  all_57_8 = e1 & op(e1, e1) = e1
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3144) implies:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | |   (3145)  op(e1, e1) = e1
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3041), (3145), (function-axioms) are
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2427.
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | |   (3146)  all_57_14 = e1 & op(e0, e1) = e1
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3146) implies:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | |   (3147)  all_57_14 = e1
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | |   (3148)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e3)
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3148) gives:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |   (3149)  all_57_4 = e3 & op(e3, e1) = e3
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3149) implies:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |   (3150)  all_57_4 = e3
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (235),
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |            (2291), (3150), (function-axioms) are inconsistent
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2474.
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |   (3151)  all_57_5 = e3 & op(e2, e1) = e3
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3151) implies:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |   (3152)  all_57_5 = e3
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | |   (3153)  op(e2, e1) = e3
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3154)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e1)
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (226), (228), (229),
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | |            (2280), (2291), (3154), (function-axioms) are
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1856.
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3155)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e1)
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3155) gives:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3156)  all_57_4 = e1 & op(e3, e1) = e1
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3156) implies:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3157)  all_57_4 = e1
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3158)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3158) gives:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3159)  all_57_12 = e3 & op(e0, e3) = e3
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3159) implies:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3160)  all_57_12 = e3
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (9), (164), (230), (234), (2291),
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3030), (3077), (3160), (function-axioms) are
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2152.
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3161)  all_57_13 = e3 & op(e0, e2) = e3
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3161) implies:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3162)  all_57_13 = e3
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3163)  all_57_15 = e0 & op(e0, e0) = e0
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3163) implies:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3164)  op(e0, e0) = e0
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3074), (3164), (function-axioms) are
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2290.
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3165)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3165) implies:
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3166)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0)
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3166) gives:
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3167)  all_57_12 = e0 & op(e0, e3) = e0
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3167) implies:
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3168)  all_57_12 = e0
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3169)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (3162), (3168), (3169) are inconsistent
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2061.
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3170)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3074), (3147), (3170), (function-axioms) are
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2176.
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3171)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3171) gives:
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3172)  all_57_13 = e0 & op(e0, e2) = e0
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3172) implies:
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3173)  all_57_13 = e0
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3162), (3173) are inconsistent by sub-proof
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2184.
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3174)  all_57_14 = e0 & op(e0, e1) = e0
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3174) implies:
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3175)  all_57_14 = e0
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3147), (3175) imply:
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3176)  e1 = e0
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3157), (3176) imply:
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3177)  all_57_4 = e0
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (219), (220), (3152),
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3175), (3177), (function-axioms) are inconsistent
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2378.
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3178)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3178) gives:
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3179)  all_57_14 = e3 & op(e0, e1) = e3
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (3147), (3179) are inconsistent by sub-proof
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1966.
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3180)  all_57_15 = e3 & op(e0, e0) = e3
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3180) implies:
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3181)  all_57_15 = e3
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3182)  op(e0, e0) = e3
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (70), (107),
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (137), (163), (166), (171), (204), (207), (211),
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (217), (230), (232), (234), (270), (374),
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2265), (2268), (2270), (2273), (2280), (2291),
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2294), (3153), (3181), (3182), (function-axioms)
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1785.
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3183)  all_57_9 = e1 & op(e3, e0) = e1
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (3072), (3183), (function-axioms) are
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2131.
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | |   (3184)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e1) = e3)
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (39), (374), (3147), (3184),
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | |            #2263.
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | |   (3185)  all_57_7 = e1 & op(e1, e2) = e1
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (2271), (3185), (function-axioms) are
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2265.
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | |   (3186)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | BETA: splitting (3186) gives:
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | |   (3187)  all_57_8 = e1 & op(e1, e1) = e1
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | ALPHA: (3187) implies:
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | |   (3188)  op(e1, e1) = e1
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3041), (3188), (function-axioms) are
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2427.
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | |   (3189)  all_57_11 = e1 & op(e1, e0) = e1
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | ALPHA: (3189) implies:
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | |   (3190)  all_57_11 = e1
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | |   (3191)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3191) gives:
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | |   (3192)  all_57_9 = e3 & op(e3, e0) = e3
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3192) implies:
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | |   (3193)  op(e3, e0) = e3
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (2290), (3193), (function-axioms) are
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2458.
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | |   (3194)  all_57_10 = e3 & op(e2, e0) = e3
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3194) implies:
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | |   (3195)  all_57_10 = e3
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | |   (3196)  all_57_15 = e0 & op(e0, e0) = e0
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3196) implies:
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | |   (3197)  op(e0, e0) = e0
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3074), (3197), (function-axioms) are
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2290.
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | |   (3198)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3198) implies:
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | |   (3199)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0)
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3199) gives:
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | |   (3200)  all_57_9 = e0 & op(e3, e0) = e0
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3200) implies:
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | |   (3201)  all_57_9 = e0
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (212), (213), (3074),
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | |            (3190), (3201), (function-axioms) are inconsistent
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2047.
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | |   (3202)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 =
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3202) gives:
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3203)  all_57_10 = e0 & op(e2, e0) = e0
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3203) implies:
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3204)  all_57_10 = e0
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3195), (3204) imply:
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3205)  e3 = e0
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2294), (3205) imply:
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3206)  all_57_0 = e0
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (39), (160), (168),
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | |            (216), (217), (232), (374), (2269), (3040),
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | |            (3071), (3190), (3206), (function-axioms) are
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1678.
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3207)  all_57_11 = e0 & op(e1, e0) = e0
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (3035), (3207), (function-axioms) are
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2341.
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | |   (3208)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3208) gives:
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | |   (3209)  all_57_11 = e3 & op(e1, e0) = e3
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3209) implies:
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | |   (3210)  all_57_11 = e3
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (3190), (3210) are inconsistent by sub-proof
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | |            #2218.
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | |   (3211)  all_57_15 = e3 & op(e0, e0) = e3
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3211) implies:
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | |   (3212)  all_57_15 = e3
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | |   (3213)  op(e0, e0) = e3
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (70), (107),
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | |            (137), (163), (166), (171), (204), (207), (208),
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | |            (209), (211), (212), (217), (221), (222), (223),
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | |            (224), (225), (226), (227), (228), (229), (230),
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | |            (231), (232), (233), (234), (235), (236), (270),
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | |            (374), (2265), (2268), (2270), (2273), (2279),
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | |            (2280), (2291), (3212), (3213), (function-axioms)
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1732.
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.21  | | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.21  | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.21  | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | |   (3214)  all_57_11 = e0 & op(e1, e0) = e0
% 220.09/37.21  | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (3035), (3214), (function-axioms) are
% 220.09/37.21  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2341.
% 220.09/37.21  | | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | End of split
% 220.09/37.21  | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | End of split
% 220.09/37.21  | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | End of split
% 220.09/37.21  | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | Case 2:
% 220.09/37.21  | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | |   (3215)  all_57_1 = e3 & op(e3, e2) = e3
% 220.09/37.21  | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | REF_CLOSE: (171), (2288), (3215), (function-axioms) are
% 220.09/37.21  | | | | | | | | | | | | | | |            inconsistent by sub-proof #2286.
% 220.09/37.21  | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | End of split
% 220.09/37.21  | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | Case 2:
% 220.09/37.21  | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | |   (3216)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 220.09/37.21  | | | | | | | | | | | | | |             & op(e3, e0) = e3)
% 220.09/37.21  | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (169), (231), (233),
% 220.09/37.21  | | | | | | | | | | | | | |            (235), (2290), (2291), (3216), (function-axioms)
% 220.09/37.21  | | | | | | | | | | | | | |            are inconsistent by sub-proof #1955.
% 220.09/37.21  | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | End of split
% 220.09/37.21  | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | Case 2:
% 220.09/37.21  | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | |   (3217)  all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 220.09/37.21  | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | REF_CLOSE: (277), (376), (2282), (2284), (3217) are
% 220.09/37.21  | | | | | | | | | | | | |            inconsistent by sub-proof #1953.
% 220.09/37.21  | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | End of split
% 220.09/37.21  | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | Case 2:
% 220.09/37.21  | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | |   (3218)  all_20_2 = e2
% 220.09/37.21  | | | | | | | | | | | |   (3219)  ( ~ (all_20_0 = e1) & op(all_20_1, e3) = all_20_0
% 220.09/37.21  | | | | | | | | | | | |             & op(e3, e2) = all_20_1 & $i(all_20_0) &
% 220.09/37.21  | | | | | | | | | | | |             $i(all_20_1)) | ( ~ (all_20_1 = e0) & op(e3, e2)
% 220.09/37.21  | | | | | | | | | | | |             = all_20_1 & $i(all_20_1))
% 220.09/37.21  | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | COMBINE_EQS: (299), (3218) imply:
% 220.09/37.21  | | | | | | | | | | | |   (3220)  all_10_2 = e2
% 220.09/37.21  | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | COMBINE_EQS: (329), (3220) imply:
% 220.09/37.21  | | | | | | | | | | | |   (3221)  all_28_2 = e2
% 220.09/37.21  | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | REDUCE: (338), (3220) imply:
% 220.09/37.21  | | | | | | | | | | | |   (3222)   ~ (all_53_1 = e2)
% 220.09/37.21  | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | REDUCE: (342), (3220) imply:
% 220.09/37.21  | | | | | | | | | | | |   (3223)   ~ (all_53_3 = e2)
% 220.09/37.21  | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | REDUCE: (344), (3220) imply:
% 220.09/37.21  | | | | | | | | | | | |   (3224)   ~ (all_53_4 = e2)
% 220.09/37.21  | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | REDUCE: (346), (3220) imply:
% 220.09/37.21  | | | | | | | | | | | |   (3225)   ~ (all_53_8 = e2)
% 220.09/37.21  | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | REDUCE: (348), (3220) imply:
% 220.09/37.21  | | | | | | | | | | | |   (3226)   ~ (all_53_12 = e2)
% 220.09/37.21  | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | REDUCE: (45), (3220) imply:
% 220.09/37.21  | | | | | | | | | | | |   (3227)  op(e3, e3) = e2
% 220.09/37.21  | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | BETA: splitting (67) gives:
% 220.09/37.21  | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | Case 1:
% 220.09/37.21  | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | |   (3228)   ~ (all_24_2 = e0)
% 220.09/37.21  | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | REDUCE: (315), (3228) imply:
% 220.09/37.21  | | | | | | | | | | | | |   (3229)   ~ (all_6_2 = e0)
% 220.09/37.21  | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | BETA: splitting (76) gives:
% 220.09/37.21  | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | Case 1:
% 220.09/37.21  | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | |   (3230)   ~ (all_30_2 = e1)
% 220.09/37.21  | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | REDUCE: (330), (3230) imply:
% 220.09/37.21  | | | | | | | | | | | | | |   (3231)   ~ (all_4_2 = e1)
% 220.09/37.21  | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 220.09/37.21  | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | Case 1:
% 220.09/37.21  | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | |   (3232)  all_55_15 = e3
% 220.09/37.21  | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | REF_CLOSE: (244), (378), (3232) are inconsistent by sub-proof
% 220.09/37.21  | | | | | | | | | | | | | | |            #2503.
% 220.09/37.21  | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | Case 2:
% 220.09/37.21  | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | |   (3233)   ~ (all_55_15 = e3)
% 220.09/37.21  | | | | | | | | | | | | | | |   (3234)  all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 220.09/37.21  | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | BETA: splitting (3234) gives:
% 220.09/37.21  | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | Case 1:
% 220.09/37.21  | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | |   (3235)  all_55_15 = e2
% 220.09/37.21  | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | REF_CLOSE: (244), (373), (3235) are inconsistent by sub-proof
% 220.09/37.21  | | | | | | | | | | | | | | | |            #2502.
% 220.09/37.21  | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | Case 2:
% 220.09/37.21  | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | |   (3236)   ~ (all_55_15 = e2)
% 220.09/37.21  | | | | | | | | | | | | | | | |   (3237)  all_55_15 = e1 | all_55_15 = e0
% 220.09/37.21  | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | BETA: splitting (3237) gives:
% 220.09/37.21  | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.21  | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | |   (3238)  all_55_15 = e1
% 220.09/37.21  | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (3231), (3238) are inconsistent by
% 220.09/37.21  | | | | | | | | | | | | | | | | |            sub-proof #2501.
% 220.09/37.21  | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.21  | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | |   (3239)  all_55_15 = e0
% 220.09/37.21  | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (3239) imply:
% 220.09/37.21  | | | | | | | | | | | | | | | | |   (3240)  all_4_2 = e0
% 220.09/37.21  | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | SIMP: (3240) implies:
% 220.09/37.21  | | | | | | | | | | | | | | | | |   (3241)  all_4_2 = e0
% 220.09/37.21  | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | REDUCE: (351), (3241) imply:
% 220.09/37.21  | | | | | | | | | | | | | | | | |   (3242)   ~ (all_53_3 = e0)
% 220.09/37.21  | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | REDUCE: (362), (3241) imply:
% 220.09/37.21  | | | | | | | | | | | | | | | | |   (3243)   ~ (all_53_7 = e0)
% 220.09/37.21  | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | REDUCE: (369), (3241) imply:
% 220.09/37.21  | | | | | | | | | | | | | | | | |   (3244)   ~ (all_53_11 = e0)
% 220.09/37.21  | | | | | | | | | | | | | | | | | 
% 220.09/37.21  | | | | | | | | | | | | | | | | | REDUCE: (370), (3241) imply:
% 220.09/37.21  | | | | | | | | | | | | | | | | |   (3245)   ~ (all_53_12 = e0)
% 220.09/37.21  | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | REDUCE: (371), (3241) imply:
% 220.09/37.22  | | | | | | | | | | | | | | | | |   (3246)   ~ (all_53_13 = e0)
% 220.09/37.22  | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | REDUCE: (372), (3241) imply:
% 220.09/37.22  | | | | | | | | | | | | | | | | |   (3247)   ~ (all_53_14 = e0)
% 220.09/37.22  | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | REDUCE: (378), (3241) imply:
% 220.09/37.22  | | | | | | | | | | | | | | | | |   (3248)   ~ (e3 = e0)
% 220.09/37.22  | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | REDUCE: (373), (3241) imply:
% 220.09/37.22  | | | | | | | | | | | | | | | | |   (3249)   ~ (e2 = e0)
% 220.09/37.22  | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | REDUCE: (3231), (3241) imply:
% 220.09/37.22  | | | | | | | | | | | | | | | | |   (3250)   ~ (e1 = e0)
% 220.09/37.22  | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 220.09/37.22  | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.22  | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | |   (3251)  all_57_15 = e0 & op(e0, e0) = e0
% 220.09/37.22  | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | ALPHA: (3251) implies:
% 220.09/37.22  | | | | | | | | | | | | | | | | | |   (3252)  all_57_15 = e0
% 220.09/37.22  | | | | | | | | | | | | | | | | | |   (3253)  op(e0, e0) = e0
% 220.09/37.22  | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | BETA: splitting (88) gives:
% 220.09/37.22  | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | |   (3254)   ~ (all_38_2 = e2)
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | REDUCE: (249), (3254) imply:
% 220.09/37.22  | | | | | | | | | | | | | | | | | | |   (3255)   ~ (all_6_2 = e2)
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | |   (3256)  all_55_10 = e3
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (374), (3256) are inconsistent by sub-proof
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | |            #2500.
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | |   (3257)   ~ (all_55_10 = e3)
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | |   (3258)  all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | BETA: splitting (3258) gives:
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | |   (3259)  all_55_10 = e2
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (3255), (3259) are inconsistent by
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | |            sub-proof #2499.
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | |   (3260)   ~ (all_55_10 = e2)
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | |   (3261)  all_55_10 = e1 | all_55_10 = e0
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3261) gives:
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | |   (3262)  all_55_10 = e1
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (336), (3262) imply:
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | |   (3263)  all_6_2 = e1
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | SIMP: (3263) implies:
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | |   (3264)  all_6_2 = e1
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3255), (3264) imply:
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | |   (3265)   ~ (e2 = e1)
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (3264) imply:
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | |   (3266)  op(e1, e1) = e1
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | |   (3267)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e1)
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (226), (228), (229),
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | |            (2280), (3227), (3267), (function-axioms) are
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1677.
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | |   (3268)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e1)
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3268) gives:
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | |   (3269)  all_57_4 = e1 & op(e3, e1) = e1
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3269) implies:
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | |   (3270)  all_57_4 = e1
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | |   (3271)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e0)
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3271) gives:
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3272)  all_57_4 = e0 & op(e3, e1) = e0
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3272) implies:
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3273)  all_57_4 = e0
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3270), (3273) are inconsistent by sub-proof
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | |            #2438.
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3274)  all_57_5 = e0 & op(e2, e1) = e0
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3274) implies:
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3275)  all_57_5 = e0
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3276)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3276) gives:
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3277)  all_57_9 = e1 & op(e3, e0) = e1
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3277) implies:
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3278)  all_57_9 = e1
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (231), (237), (3227),
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3270), (3278), (function-axioms) are inconsistent
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1672.
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3279)  all_57_10 = e1 & op(e2, e0) = e1
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (2274), (3279), (function-axioms) are
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2084.
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3280)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3280) gives:
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3281)  all_57_11 = e1 & op(e1, e0) = e1
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3281) implies:
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3282)  all_57_11 = e1
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3283)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3283) gives:
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3284)  all_57_9 = e2 & op(e3, e0) = e2
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3284) implies:
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3285)  op(e3, e0) = e2
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (3226), (3285), (function-axioms) are
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2331.
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3286)  all_57_10 = e2 & op(e2, e0) = e2
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3286) implies:
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3287)  all_57_10 = e2
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3288)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e2)
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3288) gives:
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3289)  all_57_6 = e2 & op(e1, e3) = e2
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3289) implies:
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3290)  all_57_6 = e2
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3291)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e0)
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (224), (225), (2280),
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3227), (3275), (3291), (function-axioms) are
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1671.
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3292)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = e0)
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (160), (3242), (3290), (3292),
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1670.
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3293)  all_57_7 = e2 & op(e1, e2) = e2
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3293) implies:
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3294)  all_57_7 = e2
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.09/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3295)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e0)
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (224), (225), (2280),
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3227), (3275), (3295), (function-axioms) are
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1671.
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3296)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = e0)
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3296) gives:
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3297)  all_57_6 = e0 & op(e1, e3) = e0
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3297) implies:
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3298)  all_57_6 = e0
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (39), (217), (374), (3282), (3294),
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3298), (function-axioms) are inconsistent by
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1818.
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3299)  all_57_12 = e0 & op(e0, e3) = e0
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3299) implies:
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3300)  op(e0, e3) = e0
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (3242), (3300), (function-axioms) are
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2366.
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3301)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e0) = e2)
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3301) gives:
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3302)  all_57_8 = e2 & op(e1, e1) = e2
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3302) implies:
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3303)  op(e1, e1) = e2
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3266), (3303), (function-axioms) are
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2423.
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3304)  all_57_11 = e2 & op(e1, e0) = e2
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3304) implies:
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3305)  all_57_11 = e2
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3306)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3306) gives:
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3307)  all_57_9 = e3 & op(e3, e0) = e3
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3307) implies:
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3308)  all_57_9 = e3
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (211), (3252), (3287), (3305),
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3308) are inconsistent by sub-proof #1668.
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3309)  all_57_10 = e3 & op(e2, e0) = e3
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (3287), (3309) are inconsistent by sub-proof
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2051.
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3310)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (3253), (3305), (3310),
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1667.
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3311)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (3252), (3282), (3311) are inconsistent
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1666.
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3312)  all_57_15 = e1 & op(e0, e0) = e1
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3312) implies:
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3313)  op(e0, e0) = e1
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3253), (3313), (function-axioms) are
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2290.
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | |   (3314)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (220), (221),
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | |            (374), (3266), (3270), (3314), (function-axioms)
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2417.
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | |   (3315)  all_57_9 = e1 & op(e3, e0) = e1
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3315) implies:
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | |   (3316)  all_57_9 = e1
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | |   (3317)  op(e3, e0) = e1
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | |   (3318)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3318) gives:
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3319)  all_57_12 = e1 & op(e0, e3) = e1
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (88), (107), (113), (121), (122), (124),
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | |            (126), (127), (129), (134), (135), (136), (137),
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | |            (140), (141), (142), (144), (159), (160), (161),
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | |            (163), (164), (165), (166), (169), (170), (171),
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | |            (191), (192), (194), (195), (196), (202), (203),
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | |            (204), (207), (208), (209), (210), (211), (212),
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | |            (214), (215), (216), (217), (218), (219), (220),
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | |            (221), (222), (223), (224), (225), (226), (227),
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | |            (228), (229), (230), (231), (232), (233), (236),
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | |            (237), (245), (246), (248), (249), (256), (268),
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | |            (269), (270), (336), (361), (363), (368), (374),
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | |            (2271), (2280), (3223), (3224), (3225), (3226),
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | |            (3227), (3242), (3243), (3244), (3245), (3246),
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | |            (3247), (3252), (3253), (3266), (3316), (3317),
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | |            (3319), (function-axioms) are inconsistent by
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1599.
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3320)  all_57_13 = e1 & op(e0, e2) = e1
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3320) implies:
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3321)  all_57_13 = e1
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3322)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 220.47/37.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (39), (88),
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (107), (111), (113), (121), (122), (124), (126),
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (127), (129), (134), (135), (136), (137), (140),
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (141), (142), (144), (159), (160), (161), (163),
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (165), (166), (168), (169), (170), (171),
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (191), (192), (194), (195), (196), (202), (203),
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (204), (207), (208), (209), (210), (211), (212),
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (213), (214), (215), (216), (217), (218), (219),
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (220), (221), (222), (223), (224), (225), (226),
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (227), (228), (229), (230), (231), (232), (233),
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (236), (237), (244), (245), (246), (248), (249),
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (256), (268), (269), (270), (336), (361), (362),
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (363), (368), (370), (371), (372), (373), (374),
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2269), (2270), (2271), (2274), (2280), (3223),
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3224), (3225), (3226), (3227), (3229), (3231),
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3237), (3242), (3243), (3244), (3245), (3246),
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3247), (3252), (3253), (3266), (3316), (3317),
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3322), (function-axioms) are inconsistent by
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1592.
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3323)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3323) gives:
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3324)  all_57_14 = e2 & op(e0, e1) = e2
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3324) implies:
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3325)  all_57_14 = e2
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3326)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (237),
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2280), (3227), (3326), (function-axioms) are
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1591.
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3327)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3327) gives:
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3328)  all_57_7 = e2 & op(e1, e2) = e2
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3328) implies:
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3329)  all_57_7 = e2
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3330)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3330) gives:
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3331)  all_57_1 = e3 & op(e3, e2) = e3
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3331) implies:
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3332)  all_57_1 = e3
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3333)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e1)
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (226), (2279), (2280), (3227), (3321), (3329),
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3332), (3333), (function-axioms) are inconsistent
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1588.
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3334)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e3) = e1)
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3334) gives:
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3335)  all_57_6 = e1 & op(e1, e3) = e1
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3335) implies:
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3336)  all_57_6 = e1
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3337)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e0)
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3337) gives:
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3338)  all_57_6 = e0 & op(e1, e3) = e0
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3338) implies:
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3339)  all_57_6 = e0
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3336), (3339) imply:
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3340)  e1 = e0
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (227), (2279), (3321), (3329),
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3332), (3340) are inconsistent by sub-proof
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1587.
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3341)  all_57_7 = e0 & op(e1, e2) = e0
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3341) implies:
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3342)  all_57_7 = e0
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3329), (3342) imply:
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3343)  e2 = e0
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3325), (3343) imply:
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3344)  all_57_14 = e0
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (209), (210), (3252),
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3253), (3321), (3344), (function-axioms) are
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2123.
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3345)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3345) gives:
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3346)  all_57_8 = e0 & op(e1, e1) = e0
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3346) implies:
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3347)  op(e1, e1) = e0
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3266), (3347), (function-axioms) are
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2427.
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3348)  all_57_11 = e0 & op(e1, e0) = e0
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (39), (217), (374), (3329), (3336),
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3348), (function-axioms) are inconsistent by
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1586.
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3349)  all_57_12 = e1 & op(e0, e3) = e1
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (88), (107), (113), (121), (122), (124),
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (126), (127), (129), (134), (135), (136), (137),
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (140), (141), (142), (144), (159), (160), (161),
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (163), (164), (165), (166), (169), (170), (171),
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (191), (192), (194), (195), (196), (202), (203),
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (204), (207), (208), (209), (210), (211), (212),
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (214), (215), (216), (217), (218), (219), (220),
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (221), (222), (223), (224), (225), (226), (227),
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (228), (229), (230), (231), (232), (233), (236),
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (237), (245), (246), (248), (249), (256), (268),
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (269), (270), (336), (361), (363), (368), (374),
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2271), (2280), (3223), (3224), (3225), (3226),
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3227), (3242), (3243), (3244), (3245), (3246),
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3247), (3252), (3253), (3266), (3316), (3317),
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3349), (function-axioms) are inconsistent by
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1599.
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3350)  all_57_3 = e3 & op(e2, e2) = e3
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3350) implies:
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3351)  op(e2, e2) = e3
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2280), (3351), (function-axioms) are
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1912.
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3352)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3352) gives:
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3353)  all_57_7 = e3 & op(e1, e2) = e3
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3353) implies:
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3354)  all_57_7 = e3
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (3329), (3354) are inconsistent by sub-proof
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2102.
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3355)  all_57_13 = e3 & op(e0, e2) = e3
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3355) implies:
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3356)  all_57_13 = e3
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (3321), (3356) are inconsistent by sub-proof
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2268.
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3357)  all_57_13 = e2 & op(e0, e2) = e2
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3357) implies:
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3358)  all_57_13 = e2
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (207), (208), (210),
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3253), (3325), (3358), (function-axioms) are
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1581.
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3359)  all_57_15 = e2 & op(e0, e0) = e2
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3359) implies:
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3360)  all_57_15 = e2
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3252), (3360) are inconsistent by sub-proof
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2126.
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | |   (3361)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3361) gives:
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3362)  all_57_14 = e1 & op(e0, e1) = e1
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3362) implies:
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3363)  all_57_14 = e1
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3364)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (39), (88),
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (107), (111), (113), (121), (122), (124), (126),
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (127), (129), (134), (135), (136), (137), (140),
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (141), (142), (144), (159), (160), (161), (163),
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (165), (166), (168), (169), (170), (171),
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (191), (192), (194), (195), (196), (202), (203),
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (204), (207), (208), (209), (210), (211), (212),
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (213), (214), (215), (216), (217), (218), (219),
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (220), (221), (222), (223), (224), (225), (226),
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (227), (228), (229), (230), (231), (232), (233),
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (236), (237), (244), (245), (246), (248), (249),
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (256), (268), (269), (270), (336), (361), (362),
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (363), (368), (370), (371), (372), (373), (374),
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2269), (2270), (2271), (2274), (2280), (3223),
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3224), (3225), (3226), (3227), (3229), (3231),
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3237), (3242), (3243), (3244), (3245), (3246),
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3247), (3252), (3253), (3266), (3316), (3317),
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3364), (function-axioms) are inconsistent by
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1592.
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3365)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3365) gives:
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3366)  all_57_14 = e2 & op(e0, e1) = e2
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3366) implies:
% 220.47/37.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3367)  all_57_14 = e2
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3363), (3367) are inconsistent by sub-proof
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2178.
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3368)  all_57_15 = e2 & op(e0, e0) = e2
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3368) implies:
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3369)  all_57_15 = e2
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3252), (3369) are inconsistent by sub-proof
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2126.
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3370)  all_57_15 = e1 & op(e0, e0) = e1
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3370) implies:
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3371)  op(e0, e0) = e1
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3253), (3371), (function-axioms) are
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2290.
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | |   (3372)  all_55_10 = e0
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (3229), (3372) are inconsistent by
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2118.
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | |   (3373)  all_38_2 = e2
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (3373) imply:
% 220.47/37.24  | | | | | | | | | | | | | | | | | | |   (3374)  all_6_2 = e2
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | REDUCE: (374), (3374) imply:
% 220.47/37.24  | | | | | | | | | | | | | | | | | | |   (3375)   ~ (e3 = e2)
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | REDUCE: (39), (3374) imply:
% 220.47/37.24  | | | | | | | | | | | | | | | | | | |   (3376)  op(e1, e1) = e2
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | |   (3377)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (237),
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | |            (2280), (3227), (3377), (function-axioms) are
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1591.
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | |   (3378)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | BETA: splitting (3378) gives:
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | |   (3379)  all_57_7 = e2 & op(e1, e2) = e2
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | ALPHA: (3379) implies:
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | |   (3380)  all_57_7 = e2
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (161), (163),
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | |            (214), (215), (217), (374), (2271), (3229),
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | |            (3247), (3376), (3380), (function-axioms) are
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1817.
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | |   (3381)  all_57_13 = e2 & op(e0, e2) = e2
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | ALPHA: (3381) implies:
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | |   (3382)  op(e0, e2) = e2
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (39), (107),
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | |            (111), (113), (159), (161), (163), (164), (165),
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | |            (169), (171), (194), (195), (202), (207), (212),
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | |            (213), (214), (215), (217), (226), (244), (248),
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | |            (268), (336), (362), (370), (371), (372), (373),
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | |            (374), (2270), (2271), (2274), (2280), (3226),
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | |            (3227), (3229), (3231), (3237), (3246), (3247),
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | |            (3252), (3253), (3376), (3382), (function-axioms)
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1596.
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.24  | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.24  | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | |   (3383)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 220.47/37.24  | | | | | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 220.47/37.24  | | | | | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 220.47/37.24  | | | | | | | | | | | | | | | | | |                 e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 220.47/37.24  | | | | | | | | | | | | | | | | | |               e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 220.47/37.24  | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (165), (169), (3245), (3246), (3247),
% 220.47/37.24  | | | | | | | | | | | | | | | | | |            (3383), (function-axioms) are inconsistent by
% 220.47/37.24  | | | | | | | | | | | | | | | | | |            sub-proof #2112.
% 220.47/37.24  | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | End of split
% 220.47/37.24  | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | End of split
% 220.47/37.24  | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | End of split
% 220.47/37.24  | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | End of split
% 220.47/37.24  | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | Case 2:
% 220.47/37.24  | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | |   (3384)  all_30_2 = e1
% 220.47/37.24  | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | COMBINE_EQS: (330), (3384) imply:
% 220.47/37.24  | | | | | | | | | | | | | |   (3385)  all_4_2 = e1
% 220.47/37.24  | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | SIMP: (3385) implies:
% 220.47/37.24  | | | | | | | | | | | | | |   (3386)  all_4_2 = e1
% 220.47/37.24  | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | REDUCE: (351), (3386) imply:
% 220.47/37.24  | | | | | | | | | | | | | |   (3387)   ~ (all_53_3 = e1)
% 220.47/37.24  | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | REDUCE: (370), (3386) imply:
% 220.47/37.24  | | | | | | | | | | | | | |   (3388)   ~ (all_53_12 = e1)
% 220.47/37.24  | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | REDUCE: (373), (3386) imply:
% 220.47/37.24  | | | | | | | | | | | | | |   (3389)   ~ (e2 = e1)
% 220.47/37.24  | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | REDUCE: (36), (3386) imply:
% 220.47/37.24  | | | | | | | | | | | | | |   (3390)  op(e0, e0) = e1
% 220.47/37.24  | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 220.47/37.24  | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | Case 1:
% 220.47/37.24  | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | |   (3391)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 220.47/37.24  | | | | | | | | | | | | | | |             & op(e3, e2) = e1)
% 220.47/37.24  | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (226), (228), (229),
% 220.47/37.24  | | | | | | | | | | | | | | |            (2280), (3227), (3391), (function-axioms) are
% 220.47/37.24  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1677.
% 220.47/37.24  | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | Case 2:
% 220.47/37.24  | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | |   (3392)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 220.47/37.24  | | | | | | | | | | | | | | |             & op(e3, e0) = e1)
% 220.47/37.24  | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | BETA: splitting (3392) gives:
% 220.47/37.24  | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | Case 1:
% 220.47/37.24  | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | |   (3393)  all_57_4 = e1 & op(e3, e1) = e1
% 220.47/37.24  | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | ALPHA: (3393) implies:
% 220.47/37.24  | | | | | | | | | | | | | | | |   (3394)  all_57_4 = e1
% 220.47/37.24  | | | | | | | | | | | | | | | |   (3395)  op(e3, e1) = e1
% 220.47/37.24  | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 220.47/37.24  | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.24  | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | |   (3396)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 220.47/37.24  | | | | | | | | | | | | | | | | |             & op(e2, e3) = e1)
% 220.47/37.24  | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (168), (2269), (3227), (3396),
% 220.47/37.24  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.47/37.24  | | | | | | | | | | | | | | | | |            #1598.
% 220.47/37.24  | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.24  | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | |   (3397)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 220.47/37.24  | | | | | | | | | | | | | | | | |             e1 & op(e0, e3) = e1)
% 220.47/37.24  | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | BETA: splitting (3397) gives:
% 220.47/37.24  | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.24  | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | |   (3398)  all_57_6 = e1 & op(e1, e3) = e1
% 220.47/37.24  | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | ALPHA: (3398) implies:
% 220.47/37.24  | | | | | | | | | | | | | | | | | |   (3399)  all_57_6 = e1
% 220.47/37.24  | | | | | | | | | | | | | | | | | |   (3400)  op(e1, e3) = e1
% 220.47/37.24  | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_2, e1,
% 220.47/37.24  | | | | | | | | | | | | | | | | | |              e3, e1, simplifying with (164), (3400) gives:
% 220.47/37.24  | | | | | | | | | | | | | | | | | |   (3401)  all_53_2 = e1
% 220.47/37.24  | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_8, e1,
% 220.47/37.24  | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (170), (3395) gives:
% 220.47/37.24  | | | | | | | | | | | | | | | | | |   (3402)  all_53_8 = e1
% 220.47/37.24  | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | REDUCE: (363), (3402) imply:
% 220.47/37.24  | | | | | | | | | | | | | | | | | |   (3403)   ~ (all_6_2 = e1)
% 220.47/37.24  | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | SIMP: (3403) implies:
% 220.47/37.24  | | | | | | | | | | | | | | | | | |   (3404)   ~ (all_6_2 = e1)
% 220.47/37.24  | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 220.47/37.24  | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | |   (3405)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 220.47/37.24  | | | | | | | | | | | | | | | | | | |             all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 220.47/37.24  | | | | | | | | | | | | | | | | | | |             op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 220.47/37.24  | | | | | | | | | | | | | | | | | | |               all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 220.47/37.24  | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 220.47/37.24  | | | | | | | | | | | | | | | | | | |             op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 220.47/37.24  | | | | | | | | | | | | | | | | | | |             $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 220.47/37.24  | | | | | | | | | | | | | | | | | | |             $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 220.47/37.24  | | | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 220.47/37.24  | | | | | | | | | | | | | | | | | | |               all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 220.47/37.24  | | | | | | | | | | | | | | | | | | |             & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 220.47/37.24  | | | | | | | | | | | | | | | | | | |               all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 220.47/37.24  | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 220.47/37.24  | | | | | | | | | | | | | | | | | | |             & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 220.47/37.24  | | | | | | | | | | | | | | | | | | |             $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | BETA: splitting (3405) gives:
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | |   (3406)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | |           all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | |           op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | |             all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | |           $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | |           $i(all_52_7)
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | ALPHA: (3406) implies:
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | |   (3407)  op(e3, e1) = all_52_5
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | |   (3408)  op(e3, e3) = all_52_1
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | |   (3409)  op(all_52_5, all_52_5) = e1
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | |   (3410)  op(all_52_1, all_52_1) = e3
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | |   (3411)  all_55_10 = e3
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (336), (3411) imply:
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | |   (3412)  all_6_2 = e3
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | REDUCE: (374), (3412) imply:
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | |   (3413)  $false
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | CLOSE: (3413) is inconsistent.
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | |   (3414)   ~ (all_55_10 = e3)
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | |   (3415)  all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3415) gives:
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | |   (3416)  all_55_10 = e2
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (336), (3416) imply:
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | |   (3417)  all_6_2 = e2
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (374), (3417) imply:
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | |   (3418)   ~ (e3 = e2)
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (3417) imply:
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | |   (3419)  op(e1, e1) = e2
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | |   (3420)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3420) gives:
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | |   (3421)  all_57_9 = e2 & op(e3, e0) = e2
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3421) implies:
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | |   (3422)  op(e3, e0) = e2
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (3226), (3422), (function-axioms) are
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2331.
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | |   (3423)  all_57_10 = e2 & op(e2, e0) = e2
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (160), (165),
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | |            (209), (218), (221), (226), (227), (228), (229),
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | |            (231), (233), (237), (374), (2274), (2280),
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | |            (3223), (3227), (3229), (3390), (3394), (3395),
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | |            (3407), (3408), (3409), (3410), (3419), (3423),
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | |            #1578.
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | |   (3424)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3424) gives:
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | |   (3425)  all_57_11 = e2 & op(e1, e0) = e2
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3425) implies:
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | |   (3426)  all_57_11 = e2
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | |   (3427)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (237),
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | |            (3227), (3408), (3410), (3427), (function-axioms)
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1580.
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | |   (3428)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3428) gives:
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3429)  all_57_7 = e2 & op(e1, e2) = e2
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (160), (209),
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | |            (218), (221), (226), (227), (228), (229), (374),
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | |            (2280), (3223), (3229), (3390), (3394), (3429),
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | |            #1579.
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3430)  all_57_13 = e2 & op(e0, e2) = e2
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3430) implies:
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3431)  all_57_13 = e2
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3432)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3432) gives:
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3433)  all_57_2 = e2 & op(e2, e3) = e2
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (209),
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (210), (217), (221), (223), (224), (226), (227),
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (228), (229), (230), (232), (236), (374), (2279),
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2280), (3227), (3390), (3394), (3399), (3426),
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3431), (3433), (function-axioms) are inconsistent
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1574.
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3434)  all_57_3 = e2 & op(e2, e2) = e2
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3434) implies:
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3435)  op(e2, e2) = e2
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (3227), (3408), (3410), (3435),
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1951.
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3436)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3436) gives:
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3437)  all_57_5 = e2 & op(e2, e1) = e2
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (39), (217), (218),
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (221), (374), (3229), (3394), (3399), (3426),
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3437), (function-axioms) are inconsistent by
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1573.
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3438)  all_57_10 = e2 & op(e2, e0) = e2
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (160), (165),
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (209), (218), (221), (226), (227), (228), (229),
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (233), (237), (374), (2274), (2280),
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3223), (3227), (3229), (3390), (3394), (3395),
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3407), (3408), (3409), (3410), (3419), (3438),
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1578.
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | |   (3439)  all_57_15 = e2 & op(e0, e0) = e2
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3439) implies:
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | |   (3440)  op(e0, e0) = e2
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3390), (3440), (function-axioms) are
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2177.
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | |   (3441)  all_55_10 = e1 | all_55_10 = e0
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (3229), (3404), (3441) are inconsistent by
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1685.
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | |   (3442)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | |           all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | |           op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | |             all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | |           & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | |           $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | |           $i(all_52_15)
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | ALPHA: (3442) implies:
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | |   (3443)  op(e2, e0) = all_52_15
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | |   (3444)  op(e2, e2) = all_52_11
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | |   (3445)  op(all_52_15, all_52_15) = e0
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | |   (3446)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3446) gives:
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | |   (3447)  all_57_9 = e2 & op(e3, e0) = e2
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3447) implies:
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | |   (3448)  op(e3, e0) = e2
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (3226), (3448), (function-axioms) are
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2331.
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | |   (3449)  all_57_10 = e2 & op(e2, e0) = e2
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (160), (165),
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | |            (209), (218), (221), (226), (227), (228), (229),
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | |            (231), (233), (237), (374), (2280), (3223),
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | |            (3227), (3229), (3390), (3394), (3443), (3444),
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | |            (3445), (3449), (function-axioms) are inconsistent
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1572.
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | |   (3450)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3450) gives:
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | |   (3451)  all_57_11 = e2 & op(e1, e0) = e2
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3451) implies:
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | |   (3452)  all_57_11 = e2
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | |   (3453)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (237),
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | |            (2280), (3227), (3453), (function-axioms) are
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1591.
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | |   (3454)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3454) gives:
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | |   (3455)  all_57_7 = e2 & op(e1, e2) = e2
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (160), (209),
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | |            (218), (221), (226), (227), (228), (229), (374),
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | |            (2280), (3223), (3229), (3390), (3394), (3455),
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | |            #1579.
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | |   (3456)  all_57_13 = e2 & op(e0, e2) = e2
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3456) implies:
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | |   (3457)  all_57_13 = e2
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | |   (3458)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3458) gives:
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3459)  all_57_2 = e2 & op(e2, e3) = e2
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (209),
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | |            (210), (217), (221), (223), (224), (226), (227),
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | |            (228), (229), (230), (232), (236), (374), (2279),
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | |            (2280), (3227), (3390), (3394), (3399), (3452),
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | |            (3457), (3459), (function-axioms) are inconsistent
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1574.
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3460)  all_57_3 = e2 & op(e2, e2) = e2
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3460) implies:
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3461)  op(e2, e2) = e2
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2280), (3461), (function-axioms) are
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2306.
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | |   (3462)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3462) gives:
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3463)  all_57_5 = e2 & op(e2, e1) = e2
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (39), (217), (218),
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | |            (221), (374), (3229), (3394), (3399), (3452),
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | |            (3463), (function-axioms) are inconsistent by
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1573.
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3464)  all_57_10 = e2 & op(e2, e0) = e2
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (160), (165),
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | |            (209), (218), (221), (226), (227), (228), (229),
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (233), (237), (374), (2280), (3223),
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | |            (3227), (3229), (3390), (3394), (3443), (3444),
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | |            (3445), (3464), (function-axioms) are inconsistent
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1572.
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | |   (3465)  all_57_15 = e2 & op(e0, e0) = e2
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3465) implies:
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | |   (3466)  op(e0, e0) = e2
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3390), (3466), (function-axioms) are
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2177.
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | |   (3467)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 220.47/37.25  | | | | | | | | | | | | | | | | | | |             & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 220.47/37.25  | | | | | | | | | | | | | | | | | | |             & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 220.47/37.25  | | | | | | | | | | | | | | | | | | |               all_52_21) = e1 & op(all_52_23, all_52_23) =
% 220.47/37.25  | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 220.47/37.25  | | | | | | | | | | | | | | | | | | |             all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 220.47/37.25  | | | | | | | | | | | | | | | | | | |             = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 220.47/37.25  | | | | | | | | | | | | | | | | | | |             $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 220.47/37.25  | | | | | | | | | | | | | | | | | | |             & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 220.47/37.25  | | | | | | | | | | | | | | | | | | |             e0 & op(all_52_25, all_52_25) = e3 &
% 220.47/37.25  | | | | | | | | | | | | | | | | | | |             op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 220.47/37.25  | | | | | | | | | | | | | | | | | | |               all_52_29) = e1 & op(all_52_31, all_52_31) =
% 220.47/37.25  | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 220.47/37.25  | | | | | | | | | | | | | | | | | | |             all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 220.47/37.25  | | | | | | | | | | | | | | | | | | |             = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 220.47/37.25  | | | | | | | | | | | | | | | | | | |             $i(all_52_29) & $i(all_52_31))
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (195), (336), (374), (3229), (3390), (3400),
% 220.47/37.25  | | | | | | | | | | | | | | | | | | |            (3467), (function-axioms) are inconsistent by
% 220.47/37.25  | | | | | | | | | | | | | | | | | | |            sub-proof #1686.
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.25  | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.25  | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | |   (3468)  all_57_12 = e1 & op(e0, e3) = e1
% 220.47/37.25  | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (3387), (3468), (function-axioms) are
% 220.47/37.25  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1947.
% 220.47/37.25  | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | End of split
% 220.47/37.25  | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | End of split
% 220.47/37.25  | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | Case 2:
% 220.47/37.25  | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | |   (3469)  all_57_9 = e1 & op(e3, e0) = e1
% 220.47/37.25  | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | REF_CLOSE: (169), (3388), (3469), (function-axioms) are
% 220.47/37.25  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2131.
% 220.47/37.25  | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | End of split
% 220.47/37.25  | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | End of split
% 220.47/37.25  | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | End of split
% 220.47/37.25  | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | Case 2:
% 220.47/37.25  | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | |   (3470)  all_24_2 = e0
% 220.47/37.25  | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | COMBINE_EQS: (315), (3470) imply:
% 220.47/37.25  | | | | | | | | | | | | |   (3471)  all_6_2 = e0
% 220.47/37.25  | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | REDUCE: (350), (3471) imply:
% 220.47/37.25  | | | | | | | | | | | | |   (3472)   ~ (all_53_2 = e0)
% 220.47/37.25  | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | REDUCE: (361), (3471) imply:
% 220.47/37.25  | | | | | | | | | | | | |   (3473)   ~ (all_53_6 = e0)
% 220.47/37.25  | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | REDUCE: (363), (3471) imply:
% 220.47/37.25  | | | | | | | | | | | | |   (3474)   ~ (all_53_8 = e0)
% 220.47/37.25  | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | REDUCE: (364), (3471) imply:
% 220.47/37.25  | | | | | | | | | | | | |   (3475)   ~ (all_53_9 = e0)
% 220.47/37.25  | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | REDUCE: (366), (3471) imply:
% 220.47/37.25  | | | | | | | | | | | | |   (3476)   ~ (all_53_11 = e0)
% 220.47/37.25  | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | REDUCE: (368), (3471) imply:
% 220.47/37.25  | | | | | | | | | | | | |   (3477)   ~ (all_53_14 = e0)
% 220.47/37.25  | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | REDUCE: (374), (3471) imply:
% 220.47/37.25  | | | | | | | | | | | | |   (3478)   ~ (e3 = e0)
% 220.47/37.25  | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | BETA: splitting (214) gives:
% 220.47/37.25  | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | Case 1:
% 220.47/37.25  | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | |   (3479)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 220.47/37.25  | | | | | | | | | | | | | |             & op(e1, e2) = e0)
% 220.47/37.25  | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | REF_CLOSE: (163), (164), (3472), (3473), (3479),
% 220.47/37.25  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.47/37.25  | | | | | | | | | | | | | |            #2038.
% 220.47/37.25  | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | Case 2:
% 220.47/37.25  | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | |   (3480)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 220.47/37.25  | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 220.47/37.25  | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | BETA: splitting (3480) gives:
% 220.47/37.25  | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | Case 1:
% 220.47/37.25  | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | |   (3481)  all_57_8 = e0 & op(e1, e1) = e0
% 220.47/37.25  | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | ALPHA: (3481) implies:
% 220.47/37.25  | | | | | | | | | | | | | | |   (3482)  all_57_8 = e0
% 220.47/37.25  | | | | | | | | | | | | | | |   (3483)  op(e1, e1) = e0
% 220.47/37.25  | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | BETA: splitting (73) gives:
% 220.47/37.25  | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | Case 1:
% 220.47/37.25  | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | |   (3484)   ~ (all_28_2 = e2)
% 220.47/37.25  | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | REDUCE: (3221), (3484) imply:
% 220.47/37.25  | | | | | | | | | | | | | | | |   (3485)  $false
% 220.47/37.25  | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | CLOSE: (3485) is inconsistent.
% 220.47/37.25  | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | Case 2:
% 220.47/37.25  | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | |   (3486)  ( ~ (all_28_0 = e0) & op(all_28_1, e3) = all_28_0
% 220.47/37.25  | | | | | | | | | | | | | | | |             & op(e3, e2) = all_28_1 & $i(all_28_0) &
% 220.47/37.25  | | | | | | | | | | | | | | | |             $i(all_28_1)) | ( ~ (all_28_1 = e1) & op(e3, e2)
% 220.47/37.25  | | | | | | | | | | | | | | | |             = all_28_1 & $i(all_28_1))
% 220.47/37.25  | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | BETA: splitting (76) gives:
% 220.47/37.25  | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.25  | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | |   (3487)   ~ (all_30_2 = e1)
% 220.47/37.25  | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | REDUCE: (330), (3487) imply:
% 220.47/37.25  | | | | | | | | | | | | | | | | |   (3488)   ~ (all_4_2 = e1)
% 220.47/37.25  | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 220.47/37.25  | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.25  | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | |   (3489)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 220.47/37.25  | | | | | | | | | | | | | | | | | |             all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 220.47/37.25  | | | | | | | | | | | | | | | | | |             op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 220.47/37.25  | | | | | | | | | | | | | | | | | |               all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 220.47/37.25  | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 220.47/37.25  | | | | | | | | | | | | | | | | | |             op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 220.47/37.25  | | | | | | | | | | | | | | | | | |             $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 220.47/37.25  | | | | | | | | | | | | | | | | | |             $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 220.47/37.25  | | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 220.47/37.25  | | | | | | | | | | | | | | | | | |               all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 220.47/37.25  | | | | | | | | | | | | | | | | | |             & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 220.47/37.25  | | | | | | | | | | | | | | | | | |               all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 220.47/37.25  | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 220.47/37.25  | | | | | | | | | | | | | | | | | |             & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 220.47/37.25  | | | | | | | | | | | | | | | | | |             $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 220.47/37.25  | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | BETA: splitting (3489) gives:
% 220.47/37.25  | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | |   (3490)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 220.47/37.25  | | | | | | | | | | | | | | | | | | |           all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 220.47/37.25  | | | | | | | | | | | | | | | | | | |           op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 220.47/37.25  | | | | | | | | | | | | | | | | | | |             all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 220.47/37.25  | | | | | | | | | | | | | | | | | | |           op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 220.47/37.25  | | | | | | | | | | | | | | | | | | |           op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 220.47/37.25  | | | | | | | | | | | | | | | | | | |           $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 220.47/37.25  | | | | | | | | | | | | | | | | | | |           $i(all_52_7)
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | ALPHA: (3490) implies:
% 220.47/37.25  | | | | | | | | | | | | | | | | | | |   (3491)  op(e3, e3) = all_52_1
% 220.47/37.25  | | | | | | | | | | | | | | | | | | |   (3492)  op(all_52_1, all_52_1) = e3
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | |   (3493)  all_55_15 = e3
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (378), (3493) are inconsistent by sub-proof
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | |            #2503.
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | |   (3494)   ~ (all_55_15 = e3)
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | |   (3495)  all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | BETA: splitting (3495) gives:
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | |   (3496)  all_55_15 = e2
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (373), (3496) are inconsistent by sub-proof
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | |            #2502.
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | |   (3497)  all_55_15 = e1 | all_55_15 = e0
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3497) gives:
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | |   (3498)  all_55_15 = e1
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (3488), (3498) are inconsistent by
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2501.
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | |   (3499)  all_55_15 = e0
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (3499) imply:
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | |   (3500)  all_4_2 = e0
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.25  | | | | | | | | | | | | | | | | | | | | | | SIMP: (3500) implies:
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | |   (3501)  all_4_2 = e0
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (362), (3501) imply:
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | |   (3502)   ~ (all_53_7 = e0)
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | |   (3503)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3503) gives:
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_52_1,
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (3227), (3491) gives:
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | |   (3504)  all_52_1 = e2
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3492), (3504) imply:
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | |   (3505)  op(e2, e2) = e3
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2280), (3505), (function-axioms) are
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1912.
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | |   (3506)  all_57_3 = e0 & op(e2, e2) = e0
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3506) implies:
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | |   (3507)  op(e2, e2) = e0
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3227), (3491), (3492), (3507),
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | |            #1653.
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | |   (3508)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0)
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (163), (3473), (3502), (3508),
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | |            #2024.
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | |   (3509)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 220.47/37.26  | | | | | | | | | | | | | | | | | | |           all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 220.47/37.26  | | | | | | | | | | | | | | | | | | |           op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 220.47/37.26  | | | | | | | | | | | | | | | | | | |             all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 220.47/37.26  | | | | | | | | | | | | | | | | | | |           & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 220.47/37.26  | | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 220.47/37.26  | | | | | | | | | | | | | | | | | | |           $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 220.47/37.26  | | | | | | | | | | | | | | | | | | |           $i(all_52_15)
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | ALPHA: (3509) implies:
% 220.47/37.26  | | | | | | | | | | | | | | | | | | |   (3510)  op(e2, e3) = all_52_9
% 220.47/37.26  | | | | | | | | | | | | | | | | | | |   (3511)  op(all_52_9, all_52_9) = e3
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (160), (164), (168), (190), (230), (244),
% 220.47/37.26  | | | | | | | | | | | | | | | | | | |            (351), (373), (378), (3227), (3472), (3488),
% 220.47/37.26  | | | | | | | | | | | | | | | | | | |            (3510), (3511), (function-axioms) are inconsistent
% 220.47/37.26  | | | | | | | | | | | | | | | | | | |            by sub-proof #1570.
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.26  | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.26  | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | |   (3512)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 220.47/37.26  | | | | | | | | | | | | | | | | | |             & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 220.47/37.26  | | | | | | | | | | | | | | | | | |             & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 220.47/37.26  | | | | | | | | | | | | | | | | | |               all_52_21) = e1 & op(all_52_23, all_52_23) =
% 220.47/37.26  | | | | | | | | | | | | | | | | | |             e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 220.47/37.26  | | | | | | | | | | | | | | | | | |             all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 220.47/37.26  | | | | | | | | | | | | | | | | | |             = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 220.47/37.26  | | | | | | | | | | | | | | | | | |             $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 220.47/37.26  | | | | | | | | | | | | | | | | | |             & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 220.47/37.26  | | | | | | | | | | | | | | | | | |             e0 & op(all_52_25, all_52_25) = e3 &
% 220.47/37.26  | | | | | | | | | | | | | | | | | |             op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 220.47/37.26  | | | | | | | | | | | | | | | | | |               all_52_29) = e1 & op(all_52_31, all_52_31) =
% 220.47/37.26  | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 220.47/37.26  | | | | | | | | | | | | | | | | | |             all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 220.47/37.26  | | | | | | | | | | | | | | | | | |             = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 220.47/37.26  | | | | | | | | | | | | | | | | | |             $i(all_52_29) & $i(all_52_31))
% 220.47/37.26  | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | BETA: splitting (3512) gives:
% 220.47/37.26  | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | |   (3513)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 220.47/37.26  | | | | | | | | | | | | | | | | | | |           all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 220.47/37.26  | | | | | | | | | | | | | | | | | | |           op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 220.47/37.26  | | | | | | | | | | | | | | | | | | |             all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 220.47/37.26  | | | | | | | | | | | | | | | | | | |           & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 220.47/37.26  | | | | | | | | | | | | | | | | | | |           & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 220.47/37.26  | | | | | | | | | | | | | | | | | | |           & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 220.47/37.26  | | | | | | | | | | | | | | | | | | |           $i(all_52_23)
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | ALPHA: (3513) implies:
% 220.47/37.26  | | | | | | | | | | | | | | | | | | |   (3514)  op(e1, e1) = all_52_21
% 220.47/37.26  | | | | | | | | | | | | | | | | | | |   (3515)  op(e1, e2) = all_52_19
% 220.47/37.26  | | | | | | | | | | | | | | | | | | |   (3516)  op(all_52_21, all_52_21) = e1
% 220.47/37.26  | | | | | | | | | | | | | | | | | | |   (3517)  op(all_52_19, all_52_19) = e2
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (159), (161), (165), (169), (171), (190),
% 220.47/37.26  | | | | | | | | | | | | | | | | | | |            (207), (226), (244), (362), (370), (371), (372),
% 220.47/37.26  | | | | | | | | | | | | | | | | | | |            (373), (378), (2270), (2280), (3483), (3488),
% 220.47/37.26  | | | | | | | | | | | | | | | | | | |            (3514), (3515), (3516), (3517), (function-axioms)
% 220.47/37.26  | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1838.
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | |   (3518)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 220.47/37.26  | | | | | | | | | | | | | | | | | | |           all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 220.47/37.26  | | | | | | | | | | | | | | | | | | |           op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 220.47/37.26  | | | | | | | | | | | | | | | | | | |             all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 220.47/37.26  | | | | | | | | | | | | | | | | | | |           & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 220.47/37.26  | | | | | | | | | | | | | | | | | | |           & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 220.47/37.26  | | | | | | | | | | | | | | | | | | |           & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 220.47/37.26  | | | | | | | | | | | | | | | | | | |           $i(all_52_31)
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | ALPHA: (3518) implies:
% 220.47/37.26  | | | | | | | | | | | | | | | | | | |   (3519)  op(e0, e3) = all_52_25
% 220.47/37.26  | | | | | | | | | | | | | | | | | | |   (3520)  op(all_52_25, all_52_25) = e3
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | |   (3521)  all_55_15 = e3
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (378), (3521) are inconsistent by sub-proof
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | |            #2503.
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | |   (3522)  all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (160), (163), (171), (193), (226), (244),
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | |            (247), (351), (362), (373), (2280), (3219),
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | |            (3223), (3227), (3473), (3486), (3488), (3519),
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | |            (3520), (3522), (function-axioms) are inconsistent
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | |            by sub-proof #1566.
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.26  | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | End of split
% 220.47/37.26  | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.26  | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | |   (3523)  all_30_2 = e1
% 220.47/37.26  | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | COMBINE_EQS: (330), (3523) imply:
% 220.47/37.26  | | | | | | | | | | | | | | | | |   (3524)  all_4_2 = e1
% 220.47/37.26  | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | REDUCE: (351), (3524) imply:
% 220.47/37.26  | | | | | | | | | | | | | | | | |   (3525)   ~ (all_53_3 = e1)
% 220.47/37.26  | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | REDUCE: (370), (3524) imply:
% 220.47/37.26  | | | | | | | | | | | | | | | | |   (3526)   ~ (all_53_12 = e1)
% 220.47/37.26  | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | REDUCE: (373), (3524) imply:
% 220.47/37.26  | | | | | | | | | | | | | | | | |   (3527)   ~ (e2 = e1)
% 220.47/37.26  | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 220.47/37.26  | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.26  | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | |   (3528)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 220.47/37.26  | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 220.47/37.26  | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | BETA: splitting (3528) gives:
% 220.47/37.26  | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | |   (3529)  all_57_6 = e1 & op(e1, e3) = e1
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | ALPHA: (3529) implies:
% 220.47/37.26  | | | | | | | | | | | | | | | | | | |   (3530)  all_57_6 = e1
% 220.47/37.26  | | | | | | | | | | | | | | | | | | |   (3531)  op(e1, e3) = e1
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | |   (3532)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e1)
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (226), (228), (229),
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | |            (2280), (3227), (3532), (function-axioms) are
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1677.
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | |   (3533)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e1)
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | BETA: splitting (3533) gives:
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | |   (3534)  all_57_4 = e1 & op(e3, e1) = e1
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | ALPHA: (3534) implies:
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | |   (3535)  op(e3, e1) = e1
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_2, e1,
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | |              e3, e1, simplifying with (164), (3531) gives:
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | |   (3536)  all_53_2 = e1
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_8, e1,
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (170), (3535) gives:
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | |   (3537)  all_53_8 = e1
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (3536) imply:
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | |   (3538)   ~ (all_53_3 = e1)
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (3536) imply:
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | |   (3539)   ~ (all_53_6 = e1)
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | REDUCE: (124), (3537) imply:
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | |   (3540)   ~ (all_53_9 = e1)
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | REDUCE: (122), (3537) imply:
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | |   (3541)   ~ (all_53_11 = e1)
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | SIMP: (3541) implies:
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | |   (3542)   ~ (all_53_11 = e1)
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | |   (3543)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | |             all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | |             op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | |               all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | |               all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | |             & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | |               all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3543) gives:
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | |   (3544)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | |           all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | |           op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | |             all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_7)
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3544) implies:
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | |   (3545)  op(e3, e1) = all_52_5
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | |   (3546)  op(all_52_5, all_52_5) = e1
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (39), (163), (170),
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | |            (215), (216), (217), (374), (2271), (3474),
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | |            (3482), (3483), (3530), (3534), (3545), (3546),
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | |            #1684.
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | |   (3547)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | |           all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | |           op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | |             all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | |           & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_15)
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3547) implies:
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | |   (3548)  op(e2, e2) = all_52_11
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | |   (3549)  op(all_52_11, all_52_11) = e2
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2280), (3483), (3548), (3549),
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | |            #1843.
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | |   (3550)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | |             & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | |             & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | |               all_52_21) = e1 & op(all_52_23, all_52_23) =
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | |             all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | |             = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | |             & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | |             e0 & op(all_52_25, all_52_25) = e3 &
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | |             op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | |               all_52_29) = e1 & op(all_52_31, all_52_31) =
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | |             all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | |             = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_29) & $i(all_52_31))
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3550) gives:
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | |   (3551)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | |           all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | |           op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | |             all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | |           & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | |           & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | |           & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_23)
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3551) implies:
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | |   (3552)  op(e1, e3) = all_52_17
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | |   (3553)  op(all_52_17, all_52_17) = e3
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (195), (336), (374), (3531), (3552), (3553),
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | |            #1998.
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | |   (3554)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | |           all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | |           op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | |             all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | |           & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | |           & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | |           & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_31)
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3554) implies:
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | |   (3555)  op(e0, e1) = all_52_29
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | |   (3556)  op(e0, e3) = all_52_25
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | |   (3557)  op(all_52_29, all_52_29) = e1
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | |   (3558)  op(all_52_25, all_52_25) = e3
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_11,
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | |              all_52_29, e1, e0, simplifying with (158), (3555)
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | |   (3559)  all_53_11 = all_52_29
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_3,
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | |              all_52_25, e3, e0, simplifying with (160), (3556)
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | |   (3560)  all_53_3 = all_52_25
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (3559) imply:
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | |   (3561)  all_55_14 = all_52_29
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (3560) imply:
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | |   (3562)  all_55_12 = all_52_25
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (3560) imply:
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | |   (3563)   ~ (all_53_1 = all_52_25)
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3223), (3560) imply:
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | |   (3564)   ~ (all_52_25 = e2)
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3525), (3560) imply:
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | |   (3565)   ~ (all_52_25 = e1)
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (119), (3559) imply:
% 220.47/37.26  | | | | | | | | | | | | | | | | | | | | | | |   (3566)   ~ (all_53_9 = all_52_29)
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3542), (3559) imply:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | |   (3567)   ~ (all_52_29 = e1)
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3476), (3559) imply:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | |   (3568)   ~ (all_52_29 = e0)
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | |   (3569)  all_55_4 = e3
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (3569) imply:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | |   (3570)  all_53_1 = e3
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3570) implies:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | |   (3571)  all_53_1 = e3
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (147), (3571) imply:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | |   (3572)   ~ (all_53_9 = e3)
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3572) implies:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | |   (3573)   ~ (all_53_9 = e3)
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | |   (3574)  all_55_6 = e3
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (3573), (3574) are inconsistent by
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2498.
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | |   (3575)  all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3575) gives:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3576)  all_55_6 = e2
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (3576) imply:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3577)  all_53_9 = e2
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3577) implies:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3578)  all_53_9 = e2
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3566), (3578) imply:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3579)   ~ (all_52_29 = e2)
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3579) implies:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3580)   ~ (all_52_29 = e2)
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (191), (3227), (3557), (3561), (3567),
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | |            (3568), (3580), (function-axioms) are inconsistent
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1565.
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3581)  all_55_6 = e1 | all_55_6 = e0
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (2273), (3475), (3581) are inconsistent by
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2161.
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | |   (3582)  all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3582) gives:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | |   (3583)  all_55_4 = e2
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (3222), (3583) are inconsistent by
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2168.
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | |   (3584)  all_55_4 = e1 | all_55_4 = e0
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3584) gives:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3585)  all_55_4 = e1
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (2269), (3585) are inconsistent by
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2166.
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3586)  all_55_4 = e0
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (3586) imply:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3587)  all_53_1 = e0
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3587) implies:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3588)  all_53_1 = e0
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3563), (3588) imply:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3589)   ~ (all_52_25 = e0)
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3589) implies:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3590)   ~ (all_52_25 = e0)
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (193), (3227), (3558), (3562), (3564), (3565),
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | |            (3590), (function-axioms) are inconsistent by
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1562.
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | |   (3591)  all_57_9 = e1 & op(e3, e0) = e1
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (3526), (3591), (function-axioms) are
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2131.
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | |   (3592)  all_57_7 = e1 & op(e1, e2) = e1
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (2271), (3592), (function-axioms) are
% 220.47/37.27  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2265.
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.27  | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | |   (3593)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 220.47/37.27  | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 220.47/37.27  | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | BETA: splitting (3593) gives:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | |   (3594)  all_57_8 = e1 & op(e1, e1) = e1
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | ALPHA: (3594) implies:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | |   (3595)  op(e1, e1) = e1
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3483), (3595), (function-axioms) are
% 220.47/37.27  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2427.
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | |   (3596)  all_57_11 = e1 & op(e1, e0) = e1
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | ALPHA: (3596) implies:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | |   (3597)  all_57_11 = e1
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | |   (3598)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e1)
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (168), (2269), (3227), (3598),
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | |            #1598.
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | |   (3599)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e3) = e1)
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (8), (9), (39), (160), (216), (217),
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | |            (374), (3482), (3525), (3597), (3599),
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | |            #1679.
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.27  | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | End of split
% 220.47/37.27  | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | End of split
% 220.47/37.27  | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | End of split
% 220.47/37.27  | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | Case 2:
% 220.47/37.27  | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | |   (3600)  all_57_11 = e0 & op(e1, e0) = e0
% 220.47/37.27  | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | REF_CLOSE: (161), (3477), (3600), (function-axioms) are
% 220.47/37.27  | | | | | | | | | | | | | | |            inconsistent by sub-proof #2341.
% 220.47/37.27  | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | End of split
% 220.47/37.27  | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | End of split
% 220.47/37.27  | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | End of split
% 220.47/37.27  | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | End of split
% 220.47/37.27  | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | Case 2:
% 220.47/37.27  | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | |   (3601)  all_18_2 = e0
% 220.47/37.27  | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | COMBINE_EQS: (327), (3601) imply:
% 220.47/37.27  | | | | | | | | | | |   (3602)  all_10_2 = e0
% 220.47/37.27  | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | SIMP: (3602) implies:
% 220.47/37.27  | | | | | | | | | | |   (3603)  all_10_2 = e0
% 220.47/37.27  | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | REDUCE: (338), (3603) imply:
% 220.47/37.27  | | | | | | | | | | |   (3604)   ~ (all_53_1 = e0)
% 220.47/37.27  | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | REDUCE: (340), (3603) imply:
% 220.47/37.27  | | | | | | | | | | |   (3605)   ~ (all_53_2 = e0)
% 220.47/37.27  | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | REDUCE: (344), (3603) imply:
% 220.47/37.27  | | | | | | | | | | |   (3606)   ~ (all_53_4 = e0)
% 220.47/37.27  | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | REDUCE: (346), (3603) imply:
% 220.47/37.27  | | | | | | | | | | |   (3607)   ~ (all_53_8 = e0)
% 220.47/37.27  | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | REDUCE: (348), (3603) imply:
% 220.47/37.27  | | | | | | | | | | |   (3608)   ~ (all_53_12 = e0)
% 220.47/37.27  | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | REDUCE: (376), (3603) imply:
% 220.47/37.27  | | | | | | | | | | |   (3609)   ~ (e1 = e0)
% 220.47/37.27  | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | BETA: splitting (231) gives:
% 220.47/37.27  | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | Case 1:
% 220.47/37.27  | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | |   (3610)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 220.47/37.27  | | | | | | | | | | | |             & op(e3, e2) = e0)
% 220.47/37.27  | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | BETA: splitting (3610) gives:
% 220.47/37.27  | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | Case 1:
% 220.47/37.27  | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | |   (3611)  all_57_0 = e0 & op(e3, e3) = e0
% 220.47/37.27  | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | ALPHA: (3611) implies:
% 220.47/37.27  | | | | | | | | | | | | |   (3612)  all_57_0 = e0
% 220.47/37.27  | | | | | | | | | | | | |   (3613)  op(e3, e3) = e0
% 220.47/37.27  | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | BETA: splitting (67) gives:
% 220.47/37.27  | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | Case 1:
% 220.47/37.27  | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | |   (3614)   ~ (all_24_2 = e0)
% 220.47/37.27  | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | REDUCE: (315), (3614) imply:
% 220.47/37.27  | | | | | | | | | | | | | |   (3615)   ~ (all_6_2 = e0)
% 220.47/37.27  | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | BETA: splitting (70) gives:
% 220.47/37.27  | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | Case 1:
% 220.47/37.27  | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | |   (3616)   ~ (all_26_2 = e1)
% 220.47/37.27  | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | REDUCE: (2268), (3616) imply:
% 220.47/37.27  | | | | | | | | | | | | | | |   (3617)  $false
% 220.47/37.27  | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | CLOSE: (3617) is inconsistent.
% 220.47/37.27  | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | Case 2:
% 220.47/37.27  | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | |   (3618)  ( ~ (all_26_0 = e3) & op(all_26_1, e2) = all_26_0
% 220.47/37.27  | | | | | | | | | | | | | | |             & op(e2, e1) = all_26_1 & $i(all_26_0) &
% 220.47/37.27  | | | | | | | | | | | | | | |             $i(all_26_1)) | ( ~ (all_26_1 = e0) & op(e2, e1)
% 220.47/37.27  | | | | | | | | | | | | | | |             = all_26_1 & $i(all_26_1))
% 220.47/37.27  | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | BETA: splitting (76) gives:
% 220.47/37.27  | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | Case 1:
% 220.47/37.27  | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | |   (3619)   ~ (all_30_2 = e1)
% 220.47/37.27  | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | REDUCE: (330), (3619) imply:
% 220.47/37.27  | | | | | | | | | | | | | | | |   (3620)   ~ (all_4_2 = e1)
% 220.47/37.27  | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 220.47/37.27  | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.27  | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | |   (3621)  all_55_15 = e3
% 220.47/37.27  | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (3621) imply:
% 220.47/37.27  | | | | | | | | | | | | | | | | |   (3622)  all_4_2 = e3
% 220.47/37.27  | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | REDUCE: (378), (3622) imply:
% 220.47/37.27  | | | | | | | | | | | | | | | | |   (3623)  $false
% 220.47/37.27  | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | CLOSE: (3623) is inconsistent.
% 220.47/37.27  | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.27  | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | |   (3624)   ~ (all_55_15 = e3)
% 220.47/37.27  | | | | | | | | | | | | | | | | |   (3625)  all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 220.47/37.27  | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | BETA: splitting (3625) gives:
% 220.47/37.27  | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | |   (3626)  all_55_15 = e2
% 220.47/37.27  | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (3626) imply:
% 220.47/37.27  | | | | | | | | | | | | | | | | | |   (3627)  all_4_2 = e2
% 220.47/37.27  | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | REDUCE: (373), (3627) imply:
% 220.47/37.27  | | | | | | | | | | | | | | | | | |   (3628)  $false
% 220.47/37.27  | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | CLOSE: (3628) is inconsistent.
% 220.47/37.27  | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | |   (3629)   ~ (all_55_15 = e2)
% 220.47/37.27  | | | | | | | | | | | | | | | | | |   (3630)  all_55_15 = e1 | all_55_15 = e0
% 220.47/37.27  | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | BETA: splitting (3630) gives:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | |   (3631)  all_55_15 = e1
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (3631) imply:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | |   (3632)  all_4_2 = e1
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | REDUCE: (3620), (3632) imply:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | |   (3633)  $false
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | CLOSE: (3633) is inconsistent.
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | |   (3634)  all_55_15 = e0
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (3634) imply:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | |   (3635)  all_4_2 = e0
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | REDUCE: (362), (3635) imply:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | |   (3636)   ~ (all_53_7 = e0)
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | REDUCE: (371), (3635) imply:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | |   (3637)   ~ (all_53_13 = e0)
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | REDUCE: (372), (3635) imply:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | |   (3638)   ~ (all_53_14 = e0)
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | REDUCE: (378), (3635) imply:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | |   (3639)   ~ (e3 = e0)
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | REDUCE: (373), (3635) imply:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | |   (3640)   ~ (e2 = e0)
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | |   (3641)  all_57_15 = e0 & op(e0, e0) = e0
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | ALPHA: (3641) implies:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | |   (3642)  all_57_15 = e0
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | |   (3643)  op(e0, e0) = e0
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | |   (3644)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (171), (2280), (3606), (3644),
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | |            #1561.
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | |   (3645)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0)
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3645) gives:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | |   (3646)  all_57_7 = e0 & op(e1, e2) = e0
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3646) implies:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | |   (3647)  all_57_7 = e0
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | |   (3648)  op(e1, e2) = e0
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | |   (3649)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3649) gives:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | |   (3650)  all_57_2 = e0 & op(e2, e3) = e0
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3650) implies:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | |   (3651)  all_57_2 = e0
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | |   (3652)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e0)
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3652) gives:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3653)  all_57_4 = e0 & op(e3, e1) = e0
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3653) implies:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3654)  op(e3, e1) = e0
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (3607), (3654), (function-axioms) are
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2267.
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3655)  all_57_5 = e0 & op(e2, e1) = e0
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3655) implies:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3656)  all_57_5 = e0
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (224), (225), (2280),
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | |            (3651), (3656), (function-axioms) are inconsistent
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1848.
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | |   (3657)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3657) gives:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3658)  all_57_8 = e0 & op(e1, e1) = e0
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (3615), (3658), (function-axioms) are
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2412.
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3659)  all_57_14 = e0 & op(e0, e1) = e0
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3659) implies:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3660)  all_57_14 = e0
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3661)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3661) gives:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3662)  all_57_12 = e1 & op(e0, e3) = e1
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3662) implies:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3663)  all_57_12 = e1
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (208), (209), (210),
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (226), (228), (229), (234), (236), (2280), (3613),
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3642), (3647), (3651), (3660), (3663),
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1554.
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3664)  all_57_13 = e1 & op(e0, e2) = e1
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3664) implies:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3665)  all_57_13 = e1
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (209), (210), (3642),
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3643), (3660), (3665), (function-axioms) are
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2123.
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3666)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3666) gives:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3667)  all_57_14 = e1 & op(e0, e1) = e1
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3667) implies:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3668)  all_57_14 = e1
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3660), (3668) imply:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3669)  e1 = e0
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2279), (3651), (3669) are inconsistent by
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1824.
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3670)  all_57_15 = e1 & op(e0, e0) = e1
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3670) implies:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3671)  op(e0, e0) = e1
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3643), (3671), (function-axioms) are
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2290.
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.27  | | | | | | | | | | | | | | | | | | | | | | | |   (3672)  all_57_3 = e0 & op(e2, e2) = e0
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3672) implies:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | |   (3673)  op(e2, e2) = e0
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2280), (3673), (function-axioms) are
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2352.
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | |   (3674)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0)
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (107), (129), (159), (163), (165),
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | |            (166), (192), (246), (2265), (2272), (2273),
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | |            (2280), (3613), (3618), (3637), (3643), (3648),
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | |            (3674), (function-axioms) are inconsistent by
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1552.
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | |   (3675)  all_57_13 = e0 & op(e0, e2) = e0
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3675) implies:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | |   (3676)  op(e0, e2) = e0
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (3636), (3676), (function-axioms) are
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2332.
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | |   (3677)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | |                 e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (165), (169), (3608), (3637), (3638),
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | |            (3677), (function-axioms) are inconsistent by
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | |            sub-proof #2112.
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.28  | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | End of split
% 220.47/37.28  | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | End of split
% 220.47/37.28  | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | Case 2:
% 220.47/37.28  | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | |   (3678)  all_30_2 = e1
% 220.47/37.28  | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | COMBINE_EQS: (330), (3678) imply:
% 220.47/37.28  | | | | | | | | | | | | | | | |   (3679)  all_4_2 = e1
% 220.47/37.28  | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | SIMP: (3679) implies:
% 220.47/37.28  | | | | | | | | | | | | | | | |   (3680)  all_4_2 = e1
% 220.47/37.28  | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | REDUCE: (351), (3680) imply:
% 220.47/37.28  | | | | | | | | | | | | | | | |   (3681)   ~ (all_53_3 = e1)
% 220.47/37.28  | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | REDUCE: (370), (3680) imply:
% 220.47/37.28  | | | | | | | | | | | | | | | |   (3682)   ~ (all_53_12 = e1)
% 220.47/37.28  | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | REDUCE: (373), (3680) imply:
% 220.47/37.28  | | | | | | | | | | | | | | | |   (3683)   ~ (e2 = e1)
% 220.47/37.28  | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | REDUCE: (36), (3680) imply:
% 220.47/37.28  | | | | | | | | | | | | | | | |   (3684)  op(e0, e0) = e1
% 220.47/37.28  | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 220.47/37.28  | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.28  | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | |   (3685)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 220.47/37.28  | | | | | | | | | | | | | | | | |             & op(e3, e2) = e1)
% 220.47/37.28  | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (226), (228), (229),
% 220.47/37.28  | | | | | | | | | | | | | | | | |            (2280), (3612), (3685), (function-axioms) are
% 220.47/37.28  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1551.
% 220.47/37.28  | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.28  | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | |   (3686)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 220.47/37.28  | | | | | | | | | | | | | | | | |             & op(e3, e0) = e1)
% 220.47/37.28  | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | BETA: splitting (3686) gives:
% 220.47/37.28  | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | |   (3687)  all_57_4 = e1 & op(e3, e1) = e1
% 220.47/37.28  | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | ALPHA: (3687) implies:
% 220.47/37.28  | | | | | | | | | | | | | | | | | |   (3688)  all_57_4 = e1
% 220.47/37.28  | | | | | | | | | | | | | | | | | |   (3689)  op(e3, e1) = e1
% 220.47/37.28  | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | |   (3690)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 220.47/37.28  | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e1)
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | BETA: splitting (3690) gives:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | |   (3691)  all_57_0 = e1 & op(e3, e3) = e1
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3612), (3691) are inconsistent by sub-proof
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | |            #2454.
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | |   (3692)  all_57_2 = e1 & op(e2, e3) = e1
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | ALPHA: (3692) implies:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | |   (3693)  op(e2, e3) = e1
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_1, e1,
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (168), (3693) gives:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | |   (3694)  all_53_1 = e1
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | REDUCE: (2269), (3694) imply:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | |   (3695)  $false
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | CLOSE: (3695) is inconsistent.
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | |   (3696)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 220.47/37.28  | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e3) = e1)
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | BETA: splitting (3696) gives:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | |   (3697)  all_57_6 = e1 & op(e1, e3) = e1
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | ALPHA: (3697) implies:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | |   (3698)  all_57_6 = e1
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | |   (3699)  op(e1, e3) = e1
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_2, e1,
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | |              e3, e1, simplifying with (164), (3699) gives:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | |   (3700)  all_53_2 = e1
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_8, e1,
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (170), (3689) gives:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | |   (3701)  all_53_8 = e1
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (3700) imply:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | |   (3702)   ~ (all_53_6 = e1)
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (3701) imply:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | |   (3703)   ~ (all_53_12 = e1)
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | REDUCE: (363), (3701) imply:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | |   (3704)   ~ (all_6_2 = e1)
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | SIMP: (3704) implies:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | |   (3705)   ~ (all_6_2 = e1)
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | |   (3706)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | |             all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | |             op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | |               all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | |             $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | |             $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | |               all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | |             & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | |               all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | |             & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | |             $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3706) gives:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | |   (3707)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | |           all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | |           op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | |             all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_7)
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3707) implies:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | |   (3708)  op(e3, e1) = all_52_5
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | |   (3709)  op(all_52_5, all_52_5) = e1
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | |   (3710)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e2)
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3710) gives:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | |   (3711)  all_57_6 = e2 & op(e1, e3) = e2
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3711) implies:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | |   (3712)  all_57_6 = e2
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3698), (3712) are inconsistent by sub-proof
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | |            #2233.
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | |   (3713)  all_57_7 = e2 & op(e1, e2) = e2
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3713) implies:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | |   (3714)  all_57_7 = e2
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (9), (39), (164), (214), (217),
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | |            (374), (3605), (3615), (3698), (3714),
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | |            #1550.
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | |   (3715)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e0) = e2)
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3715) gives:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | |   (3716)  all_57_8 = e2 & op(e1, e1) = e2
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3716) implies:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | |   (3717)  op(e1, e1) = e2
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_52_5,
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (3689), (3708) gives:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | |   (3718)  all_52_5 = e1
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3709), (3718) imply:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | |   (3719)  op(e1, e1) = e1
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3717), (3719), (function-axioms) are
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2423.
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | |   (3720)  all_57_11 = e2 & op(e1, e0) = e2
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3720) implies:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | |   (3721)  all_57_11 = e2
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | |   (3722)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e0)
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3722) gives:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3723)  all_57_6 = e0 & op(e1, e3) = e0
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3723) implies:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3724)  op(e1, e3) = e0
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (3605), (3724), (function-axioms) are
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2154.
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3725)  all_57_7 = e0 & op(e1, e2) = e0
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3725) implies:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3726)  all_57_7 = e0
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (39), (217), (374), (3698), (3721),
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | |            (3726), (function-axioms) are inconsistent by
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2343.
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | |   (3727)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3727) gives:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3728)  all_57_8 = e0 & op(e1, e1) = e0
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (3615), (3728), (function-axioms) are
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2412.
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3729)  all_57_11 = e0 & op(e1, e0) = e0
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3729) implies:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3730)  all_57_11 = e0
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3721), (3730) are inconsistent by sub-proof
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | |            #1949.
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | |   (3731)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | |           all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | |           op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | |             all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | |           & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_15)
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3731) implies:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | |   (3732)  op(e2, e0) = all_52_15
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | |   (3733)  op(e2, e2) = all_52_11
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | |   (3734)  op(all_52_15, all_52_15) = e0
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | |   (3735)  all_55_10 = e3
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (374), (3735) are inconsistent by sub-proof
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | |            #2500.
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | |   (3736)   ~ (all_55_10 = e3)
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | |   (3737)  all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3737) gives:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | |   (3738)  all_55_10 = e2
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (336), (3738) imply:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | |   (3739)  all_6_2 = e2
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3739) implies:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | |   (3740)  all_6_2 = e2
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (361), (3740) imply:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | |   (3741)   ~ (all_53_6 = e2)
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_13,
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | |              all_52_15, e0, e2, simplifying with (165), (3732)
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | |   (3742)  all_53_13 = all_52_15
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | |              all_52_11, e2, e2, simplifying with (2280), (3733)
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | |   (3743)  all_52_11 = e1
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (3742) imply:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | |   (3744)  all_55_7 = all_52_15
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (114), (3742) imply:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | |   (3745)   ~ (all_53_12 = all_52_15)
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (111), (3742) imply:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | |   (3746)   ~ (all_53_14 = all_52_15)
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3746) implies:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | |   (3747)   ~ (all_53_14 = all_52_15)
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2274), (3742) imply:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | |   (3748)   ~ (all_52_15 = e1)
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | |   (3749)  all_55_1 = e3
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (3749) imply:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | |   (3750)  all_53_4 = e3
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3750) implies:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | |   (3751)  all_53_4 = e3
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (137), (3751) imply:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | |   (3752)   ~ (all_53_6 = e3)
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3752) implies:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | |   (3753)   ~ (all_53_6 = e3)
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (3751) imply:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | |   (3754)   ~ (all_53_12 = e3)
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3754) implies:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | |   (3755)   ~ (all_53_12 = e3)
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (171), (3751) imply:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | |   (3756)  op(e3, e2) = e3
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3757)  all_55_3 = e3
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (3757) imply:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3758)  all_53_12 = e3
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3755), (3758) imply:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3759)  $false
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3759) is inconsistent.
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3760)   ~ (all_55_3 = e3)
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3761)  all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3761) gives:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3762)  all_55_3 = e2
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (3762) imply:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3763)  all_53_12 = e2
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3763) implies:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3764)  all_53_12 = e2
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3745), (3764) imply:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3765)   ~ (all_52_15 = e2)
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3765) implies:
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3766)   ~ (all_52_15 = e2)
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3755), (3764) imply:
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3767)   ~ (e3 = e2)
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3768)  all_55_9 = e3
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (3753), (3768) are inconsistent by
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2159.
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3769)  all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3770)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3770) gives:
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3771)  all_57_1 = e2 & op(e3, e2) = e2
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3771) implies:
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3772)  op(e3, e2) = e2
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (3756), (3772), (function-axioms) are
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1549.
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3773)  all_57_3 = e2 & op(e2, e2) = e2
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3773) implies:
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3774)  op(e2, e2) = e2
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2280), (3774), (function-axioms) are
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2306.
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3775)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3775) gives:
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3776)  all_57_7 = e2 & op(e1, e2) = e2
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3776) implies:
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3777)  all_57_7 = e2
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (9), (39), (164), (214), (217),
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (374), (3605), (3615), (3698), (3777),
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1550.
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3778)  all_57_13 = e2 & op(e0, e2) = e2
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3778) implies:
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3779)  all_57_13 = e2
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3780)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e3)
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3780) gives:
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3781)  all_57_0 = e3 & op(e3, e3) = e3
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3781) implies:
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3782)  op(e3, e3) = e3
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3613), (3782), (function-axioms) are
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2494.
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3783)  all_57_1 = e3 & op(e3, e2) = e3
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3783) implies:
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3784)  all_57_1 = e3
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3785)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3785) gives:
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3786)  all_57_6 = e3 & op(e1, e3) = e3
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3786) implies:
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3787)  all_57_6 = e3
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (226), (228), (229),
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2280), (3698), (3784), (3787), (function-axioms)
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1548.
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3788)  all_57_7 = e3 & op(e1, e2) = e3
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3788) implies:
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3789)  all_57_7 = e3
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3790)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3790) gives:
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3791)  all_57_1 = e0 & op(e3, e2) = e0
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3791) implies:
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3792)  all_57_1 = e0
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (169), (226), (227),
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (228), (233), (235), (237), (2279), (2280),
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3612), (3613), (3755), (3779), (3789), (3792),
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1707.
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3793)  all_57_3 = e0 & op(e2, e2) = e0
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3793) implies:
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3794)  all_57_3 = e0
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (227), (3779), (3784), (3789),
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3794) are inconsistent by sub-proof #1779.
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3795)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0)
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3795) gives:
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3796)  all_57_7 = e0 & op(e1, e2) = e0
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3796) implies:
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3797)  all_57_7 = e0
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (169), (226), (227),
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (228), (233), (235), (237), (2279), (2280),
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3612), (3613), (3755), (3779), (3784), (3789),
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3797), (function-axioms) are inconsistent by
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1547.
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3798)  all_57_13 = e0 & op(e0, e2) = e0
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3798) implies:
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3799)  op(e0, e2) = e0
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (129), (159), (256), (2271), (3741), (3769),
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3799), (function-axioms) are inconsistent by
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2077.
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3800)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3800) gives:
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3801)  all_57_8 = e3 & op(e1, e1) = e3
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3801) implies:
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3802)  op(e1, e1) = e3
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (374), (3802), (function-axioms) are
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2468.
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3803)  all_57_11 = e3 & op(e1, e0) = e3
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (194), (198), (248), (3684), (3734),
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3744), (3747), (3748), (3766), (3803),
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2062.
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3804)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e3)
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (169), (3688), (3755), (3804),
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2281.
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3805)  all_55_3 = e1 | all_55_3 = e0
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (3608), (3682), (3805) are inconsistent by
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2132.
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | |   (3806)  all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3806) gives:
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3807)  all_55_1 = e2
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (3807) imply:
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3808)  all_53_4 = e2
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3808) implies:
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3809)  all_53_4 = e2
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (3809) imply:
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3810)   ~ (all_53_12 = e2)
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3810) implies:
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3811)   ~ (all_53_12 = e2)
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3812)  all_55_3 = e3
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (3812) imply:
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3813)  all_53_12 = e3
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3813) implies:
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3814)  all_53_12 = e3
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3745), (3814) imply:
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3815)   ~ (all_52_15 = e3)
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (198), (2280), (3684), (3734), (3744),
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3748), (3815), (function-axioms) are inconsistent
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1687.
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3816)  all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (3608), (3682), (3811), (3816) are
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1546.
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3817)  all_55_1 = e1 | all_55_1 = e0
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (2270), (3606), (3817) are inconsistent by
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1730.
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | |   (3818)  all_55_10 = e1 | all_55_10 = e0
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (3615), (3705), (3818) are inconsistent by
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1685.
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | End of split
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | 
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.47/37.29  | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | | |   (3819)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | | |             & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | | |             & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | | |               all_52_21) = e1 & op(all_52_23, all_52_23) =
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | | |             all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | | |             = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | | |             $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | | |             & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | | |             e0 & op(all_52_25, all_52_25) = e3 &
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | | |             op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | | |               all_52_29) = e1 & op(all_52_31, all_52_31) =
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | | |             all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | | |             = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | | |             $i(all_52_29) & $i(all_52_31))
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3819) gives:
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | | | |   (3820)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | | | |           all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | | | |           op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | | | |             all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | | | |           & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | | | |           & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | | | |           & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_23)
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3820) implies:
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | | | |   (3821)  op(e1, e3) = all_52_17
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | | | |   (3822)  op(all_52_17, all_52_17) = e3
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (195), (336), (374), (3699), (3821), (3822),
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | | | |            #1998.
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | | | |   (3823)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | | | |           all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | | | |           op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | | | |             all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | | | |           & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | | | |           & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | | | |           & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_31)
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3823) implies:
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | | | |   (3824)  op(e0, e0) = all_52_31
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | | | |   (3825)  op(all_52_31, all_52_31) = e0
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (3615), (3684), (3824), (3825),
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | | | |            #2086.
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | |   (3826)  all_57_12 = e1 & op(e0, e3) = e1
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (3681), (3826), (function-axioms) are
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1947.
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | 
% 220.76/37.29  | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.29  | | | | | | | | | | | | | | | | | | 
% 220.76/37.29  | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.29  | | | | | | | | | | | | | | | | | | 
% 220.76/37.29  | | | | | | | | | | | | | | | | | |   (3827)  all_57_9 = e1 & op(e3, e0) = e1
% 220.76/37.29  | | | | | | | | | | | | | | | | | | 
% 220.76/37.29  | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (3682), (3827), (function-axioms) are
% 220.76/37.29  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2131.
% 220.76/37.29  | | | | | | | | | | | | | | | | | | 
% 220.76/37.29  | | | | | | | | | | | | | | | | | End of split
% 220.76/37.29  | | | | | | | | | | | | | | | | | 
% 220.76/37.29  | | | | | | | | | | | | | | | | End of split
% 220.76/37.29  | | | | | | | | | | | | | | | | 
% 220.76/37.29  | | | | | | | | | | | | | | | End of split
% 220.76/37.29  | | | | | | | | | | | | | | | 
% 220.76/37.29  | | | | | | | | | | | | | | End of split
% 220.76/37.29  | | | | | | | | | | | | | | 
% 220.76/37.29  | | | | | | | | | | | | | Case 2:
% 220.76/37.29  | | | | | | | | | | | | | | 
% 220.76/37.29  | | | | | | | | | | | | | |   (3828)  all_24_2 = e0
% 220.76/37.29  | | | | | | | | | | | | | | 
% 220.76/37.29  | | | | | | | | | | | | | | COMBINE_EQS: (315), (3828) imply:
% 220.76/37.29  | | | | | | | | | | | | | |   (3829)  all_6_2 = e0
% 220.76/37.29  | | | | | | | | | | | | | | 
% 220.76/37.29  | | | | | | | | | | | | | | SIMP: (3829) implies:
% 220.76/37.29  | | | | | | | | | | | | | |   (3830)  all_6_2 = e0
% 220.76/37.29  | | | | | | | | | | | | | | 
% 220.76/37.29  | | | | | | | | | | | | | | REDUCE: (361), (3830) imply:
% 220.76/37.29  | | | | | | | | | | | | | |   (3831)   ~ (all_53_6 = e0)
% 220.76/37.29  | | | | | | | | | | | | | | 
% 220.76/37.29  | | | | | | | | | | | | | | REDUCE: (364), (3830) imply:
% 220.76/37.29  | | | | | | | | | | | | | |   (3832)   ~ (all_53_9 = e0)
% 220.76/37.29  | | | | | | | | | | | | | | 
% 220.76/37.29  | | | | | | | | | | | | | | REDUCE: (368), (3830) imply:
% 220.76/37.29  | | | | | | | | | | | | | |   (3833)   ~ (all_53_14 = e0)
% 220.76/37.29  | | | | | | | | | | | | | | 
% 220.76/37.29  | | | | | | | | | | | | | | REDUCE: (374), (3830) imply:
% 220.76/37.29  | | | | | | | | | | | | | |   (3834)   ~ (e3 = e0)
% 220.76/37.29  | | | | | | | | | | | | | | 
% 220.76/37.29  | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 220.76/37.29  | | | | | | | | | | | | | | 
% 220.76/37.29  | | | | | | | | | | | | | | Case 1:
% 220.76/37.29  | | | | | | | | | | | | | | | 
% 220.76/37.29  | | | | | | | | | | | | | | |   (3835)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 220.76/37.29  | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 220.76/37.29  | | | | | | | | | | | | | | | 
% 220.76/37.29  | | | | | | | | | | | | | | | REF_CLOSE: (4), (171), (2280), (3606), (3835),
% 220.76/37.29  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.76/37.29  | | | | | | | | | | | | | | |            #1561.
% 220.76/37.29  | | | | | | | | | | | | | | | 
% 220.76/37.29  | | | | | | | | | | | | | | Case 2:
% 220.76/37.29  | | | | | | | | | | | | | | | 
% 220.76/37.29  | | | | | | | | | | | | | | |   (3836)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 220.76/37.29  | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0)
% 220.76/37.29  | | | | | | | | | | | | | | | 
% 220.76/37.29  | | | | | | | | | | | | | | | BETA: splitting (3836) gives:
% 220.76/37.29  | | | | | | | | | | | | | | | 
% 220.76/37.29  | | | | | | | | | | | | | | | Case 1:
% 220.76/37.29  | | | | | | | | | | | | | | | | 
% 220.76/37.29  | | | | | | | | | | | | | | | |   (3837)  all_57_7 = e0 & op(e1, e2) = e0
% 220.76/37.29  | | | | | | | | | | | | | | | | 
% 220.76/37.29  | | | | | | | | | | | | | | | | REF_CLOSE: (163), (3831), (3837), (function-axioms) are
% 220.76/37.29  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2039.
% 220.76/37.29  | | | | | | | | | | | | | | | | 
% 220.76/37.29  | | | | | | | | | | | | | | | Case 2:
% 220.76/37.29  | | | | | | | | | | | | | | | | 
% 220.76/37.29  | | | | | | | | | | | | | | | |   (3838)  all_57_13 = e0 & op(e0, e2) = e0
% 220.76/37.29  | | | | | | | | | | | | | | | | 
% 220.76/37.29  | | | | | | | | | | | | | | | | ALPHA: (3838) implies:
% 220.76/37.29  | | | | | | | | | | | | | | | |   (3839)  op(e0, e2) = e0
% 220.76/37.29  | | | | | | | | | | | | | | | | 
% 220.76/37.29  | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 220.76/37.29  | | | | | | | | | | | | | | | | 
% 220.76/37.29  | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.29  | | | | | | | | | | | | | | | | | 
% 220.76/37.29  | | | | | | | | | | | | | | | | |   (3840)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 220.76/37.29  | | | | | | | | | | | | | | | | |             & op(e1, e2) = e0)
% 220.76/37.29  | | | | | | | | | | | | | | | | | 
% 220.76/37.29  | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (164), (3605), (3831), (3840),
% 220.76/37.29  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.76/37.29  | | | | | | | | | | | | | | | | |            #2038.
% 220.76/37.29  | | | | | | | | | | | | | | | | | 
% 220.76/37.29  | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.29  | | | | | | | | | | | | | | | | | 
% 220.76/37.29  | | | | | | | | | | | | | | | | |   (3841)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 220.76/37.29  | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 220.76/37.29  | | | | | | | | | | | | | | | | | 
% 220.76/37.29  | | | | | | | | | | | | | | | | | BETA: splitting (3841) gives:
% 220.76/37.29  | | | | | | | | | | | | | | | | | 
% 220.76/37.29  | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.29  | | | | | | | | | | | | | | | | | | 
% 220.76/37.29  | | | | | | | | | | | | | | | | | |   (3842)  all_57_8 = e0 & op(e1, e1) = e0
% 220.76/37.29  | | | | | | | | | | | | | | | | | | 
% 220.76/37.29  | | | | | | | | | | | | | | | | | | ALPHA: (3842) implies:
% 220.76/37.29  | | | | | | | | | | | | | | | | | |   (3843)  all_57_8 = e0
% 220.76/37.29  | | | | | | | | | | | | | | | | | |   (3844)  op(e1, e1) = e0
% 220.76/37.29  | | | | | | | | | | | | | | | | | | 
% 220.76/37.29  | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 220.76/37.29  | | | | | | | | | | | | | | | | | | 
% 220.76/37.29  | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.29  | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | |   (3845)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 220.76/37.30  | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | BETA: splitting (3845) gives:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | |   (3846)  all_57_2 = e0 & op(e2, e3) = e0
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | ALPHA: (3846) implies:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | |   (3847)  op(e2, e3) = e0
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_1, e0,
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (168), (3847) gives:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | |   (3848)  all_53_1 = e0
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | REDUCE: (3604), (3848) imply:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | |   (3849)  $false
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | CLOSE: (3849) is inconsistent.
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | |   (3850)  all_57_3 = e0 & op(e2, e2) = e0
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | ALPHA: (3850) implies:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | |   (3851)  op(e2, e2) = e0
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2280), (3851), (function-axioms) are
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2352.
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | |   (3852)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 220.76/37.30  | | | | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0)
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | BETA: splitting (3852) gives:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | |   (3853)  all_57_5 = e0 & op(e2, e1) = e0
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (3832), (3853), (function-axioms) are
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2023.
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | |   (3854)  all_57_10 = e0 & op(e2, e0) = e0
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | ALPHA: (3854) implies:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | |   (3855)  op(e2, e0) = e0
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_7, e0,
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (159), (3839) gives:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | |   (3856)  all_53_7 = e0
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_13,
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | |              e0, e0, e2, simplifying with (165), (3855) gives:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | |   (3857)  all_53_13 = e0
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | REDUCE: (371), (3857) imply:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | |   (3858)   ~ (all_4_2 = e0)
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | SIMP: (3858) implies:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | |   (3859)   ~ (all_4_2 = e0)
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | |   (3860)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | |             all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | |             op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | |               all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | |             $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | |             $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | |               all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | |             & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | |               all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | |             & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | |             $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3860) gives:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | |   (3861)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | |           all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | |           op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | |             all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_7)
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3861) implies:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | |   (3862)  op(e3, e1) = all_52_5
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | |   (3863)  op(all_52_5, all_52_5) = e1
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | |   (3864)  all_55_15 = e3
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (378), (3864) are inconsistent by sub-proof
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | |            #2503.
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | |   (3865)   ~ (all_55_15 = e3)
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | |   (3866)  all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3866) gives:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | |   (3867)  all_55_15 = e2
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (373), (3867) are inconsistent by sub-proof
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | |            #2502.
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | |   (3868)   ~ (all_55_15 = e2)
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | |   (3869)  all_55_15 = e1 | all_55_15 = e0
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3869) gives:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (3870)  all_55_15 = e1
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (3870) imply:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (3871)  all_4_2 = e1
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3871) implies:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (3872)  all_4_2 = e1
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (351), (3872) imply:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (3873)   ~ (all_53_3 = e1)
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (370), (3872) imply:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (3874)   ~ (all_53_12 = e1)
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (373), (3872) imply:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (3875)   ~ (e2 = e1)
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3876)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e1)
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3876) gives:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3877)  all_57_0 = e1 & op(e3, e3) = e1
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3612), (3877) are inconsistent by sub-proof
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2454.
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3878)  all_57_2 = e1 & op(e2, e3) = e1
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (2269), (3878), (function-axioms) are
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2156.
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3879)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e3) = e1)
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3879) gives:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3880)  all_57_6 = e1 & op(e1, e3) = e1
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3880) implies:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3881)  all_57_6 = e1
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3882)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e1)
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (226), (228), (229),
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2280), (3612), (3882), (function-axioms) are
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1551.
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3883)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e1)
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3883) gives:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3884)  all_57_4 = e1 & op(e3, e1) = e1
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (39), (163), (170),
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (215), (216), (217), (374), (2271), (3607),
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3843), (3844), (3862), (3863), (3881), (3884),
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1684.
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3885)  all_57_9 = e1 & op(e3, e0) = e1
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (3874), (3885), (function-axioms) are
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2131.
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3886)  all_57_12 = e1 & op(e0, e3) = e1
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (3873), (3886), (function-axioms) are
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1947.
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (3887)  all_55_15 = e0
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (3859), (3887) are inconsistent by
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1884.
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | |   (3888)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | |           all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | |           op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | |             all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | |           & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_15)
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3888) implies:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | |   (3889)  op(e2, e0) = all_52_15
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | |   (3890)  op(all_52_15, all_52_15) = e0
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | |   (3891)  all_55_15 = e3
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (378), (3891) are inconsistent by sub-proof
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | |            #2503.
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | |   (3892)   ~ (all_55_15 = e3)
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | |   (3893)  all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3893) gives:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | |   (3894)  all_55_15 = e2
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (373), (3894) are inconsistent by sub-proof
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | |            #2502.
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | |   (3895)   ~ (all_55_15 = e2)
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | |   (3896)  all_55_15 = e1 | all_55_15 = e0
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3896) gives:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (3897)  all_55_15 = e1
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (3897) imply:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (3898)  all_4_2 = e1
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3898) implies:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (3899)  all_4_2 = e1
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (370), (3899) imply:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (3900)   ~ (all_53_12 = e1)
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (373), (3899) imply:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (3901)   ~ (e2 = e1)
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (3899) imply:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (3902)  op(e0, e0) = e1
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3903)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e1)
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (226), (228), (229),
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | |            (2280), (3612), (3903), (function-axioms) are
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1551.
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3904)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e1)
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3904) gives:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3905)  all_57_4 = e1 & op(e3, e1) = e1
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3905) implies:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3906)  op(e3, e1) = e1
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_15, e0, e2, simplifying with (3855), (3889)
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3907)  all_52_15 = e0
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_8, e1,
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (170), (3906) gives:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3908)  all_53_8 = e1
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3890), (3907) imply:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3909)  op(e0, e0) = e0
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3902), (3909), (function-axioms) are
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2290.
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3910)  all_57_9 = e1 & op(e3, e0) = e1
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (3900), (3910), (function-axioms) are
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2131.
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (3911)  all_55_15 = e0
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (3859), (3911) are inconsistent by
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1884.
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | |   (3912)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | |             & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | |             & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | |               all_52_21) = e1 & op(all_52_23, all_52_23) =
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | |             all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | |             = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | |             $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | |             & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | |             e0 & op(all_52_25, all_52_25) = e3 &
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | |             op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | |               all_52_29) = e1 & op(all_52_31, all_52_31) =
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | |             all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | |             = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | |             $i(all_52_29) & $i(all_52_31))
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3912) gives:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | |   (3913)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | |           all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | |           op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | |             all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | |           & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | |           & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | |           & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_23)
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3913) implies:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | |   (3914)  op(e1, e3) = all_52_17
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | |   (3915)  op(all_52_17, all_52_17) = e3
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | |   (3916)  all_55_15 = e3
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (378), (3916) are inconsistent by sub-proof
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | |            #2503.
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | |   (3917)  all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3917) gives:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | |   (3918)  all_55_15 = e2
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (373), (3918) are inconsistent by sub-proof
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | |            #2502.
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | |   (3919)  all_55_15 = e1 | all_55_15 = e0
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3919) gives:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (3920)  all_55_15 = e1
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (3920) imply:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (3921)  all_4_2 = e1
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3921) implies:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (3922)  all_4_2 = e1
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (351), (3922) imply:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (3923)   ~ (all_53_3 = e1)
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (39), (160), (168), (195), (232), (336),
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | |            (374), (2269), (3612), (3914), (3915), (3923),
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | |            #1545.
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (3924)  all_55_15 = e0
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (3859), (3924) are inconsistent by
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1884.
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | |   (3925)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | |           all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | |           op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | |             all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | |           & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | |           & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | |           & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_31)
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3925) implies:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | |   (3926)  op(e0, e0) = all_52_31
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | |   (3927)  op(e0, e2) = all_52_27
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | |   (3928)  op(all_52_27, all_52_27) = e2
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | |   (3929)  all_55_15 = e3
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (378), (3929) are inconsistent by sub-proof
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | |            #2503.
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.30  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | |   (3930)   ~ (all_55_15 = e3)
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | |   (3931)  all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3931) gives:
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | |   (3932)  all_55_15 = e2
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (373), (3932) are inconsistent by sub-proof
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | |            #2502.
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | |   (3933)   ~ (all_55_15 = e2)
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | |   (3934)  all_55_15 = e1 | all_55_15 = e0
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3934) gives:
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (3935)  all_55_15 = e1
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (3935) imply:
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (3936)  all_4_2 = e1
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3936) implies:
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (3937)  all_4_2 = e1
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (351), (3937) imply:
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (3938)   ~ (all_53_3 = e1)
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (370), (3937) imply:
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (3939)   ~ (all_53_12 = e1)
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (373), (3937) imply:
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (3940)   ~ (e2 = e1)
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3941)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3941) gives:
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3942)  all_57_9 = e1 & op(e3, e0) = e1
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (3939), (3942), (function-axioms) are
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2131.
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3943)  all_57_10 = e1 & op(e2, e0) = e1
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (2274), (3943), (function-axioms) are
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2084.
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3944)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3944) gives:
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3945)  all_57_11 = e1 & op(e1, e0) = e1
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3945) implies:
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3946)  all_57_11 = e1
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (39), (160), (168),
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (216), (217), (232), (374), (2269), (3612),
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3843), (3938), (3946), (function-axioms) are
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1678.
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3947)  all_57_15 = e1 & op(e0, e0) = e1
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3839), (3926), (3927), (3928), (3947),
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1877.
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (3948)  all_55_15 = e0
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (3859), (3948) are inconsistent by
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1884.
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.31  | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.31  | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | |   (3949)  all_57_11 = e0 & op(e1, e0) = e0
% 220.76/37.31  | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (3833), (3949), (function-axioms) are
% 220.76/37.31  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2341.
% 220.76/37.31  | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | End of split
% 220.76/37.31  | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | End of split
% 220.76/37.31  | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | End of split
% 220.76/37.31  | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | End of split
% 220.76/37.31  | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | End of split
% 220.76/37.31  | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | Case 2:
% 220.76/37.31  | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | |   (3950)  all_57_1 = e0 & op(e3, e2) = e0
% 220.76/37.31  | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | ALPHA: (3950) implies:
% 220.76/37.31  | | | | | | | | | | | | |   (3951)  op(e3, e2) = e0
% 220.76/37.31  | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | REF_CLOSE: (171), (3606), (3951), (function-axioms) are
% 220.76/37.31  | | | | | | | | | | | | |            inconsistent by sub-proof #1941.
% 220.76/37.31  | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | End of split
% 220.76/37.31  | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | Case 2:
% 220.76/37.31  | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | |   (3952)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 220.76/37.31  | | | | | | | | | | | |             & op(e3, e0) = e0)
% 220.76/37.31  | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | REF_CLOSE: (169), (170), (3607), (3608), (3952),
% 220.76/37.31  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.76/37.31  | | | | | | | | | | | |            #1544.
% 220.76/37.31  | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | End of split
% 220.76/37.31  | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | End of split
% 220.76/37.31  | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | End of split
% 220.76/37.31  | | | | | | | | | 
% 220.76/37.31  | | | | | | | | Case 2:
% 220.76/37.31  | | | | | | | | | 
% 220.76/37.31  | | | | | | | | |   (3953)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1
% 220.76/37.31  | | | | | | | | |             & op(e2, e0) = e1)
% 220.76/37.31  | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | BETA: splitting (3953) gives:
% 220.76/37.31  | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | Case 1:
% 220.76/37.31  | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | |   (3954)  all_57_5 = e1 & op(e2, e1) = e1
% 220.76/37.31  | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | REF_CLOSE: (166), (2273), (3954), (function-axioms) are
% 220.76/37.31  | | | | | | | | | |            inconsistent by sub-proof #2305.
% 220.76/37.31  | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | Case 2:
% 220.76/37.31  | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | |   (3955)  all_57_10 = e1 & op(e2, e0) = e1
% 220.76/37.31  | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | REF_CLOSE: (165), (2274), (3955), (function-axioms) are
% 220.76/37.31  | | | | | | | | | |            inconsistent by sub-proof #2084.
% 220.76/37.31  | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | End of split
% 220.76/37.31  | | | | | | | | | 
% 220.76/37.31  | | | | | | | | End of split
% 220.76/37.31  | | | | | | | | 
% 220.76/37.31  | | | | | | | End of split
% 220.76/37.31  | | | | | | | 
% 220.76/37.31  | | | | | | Case 2:
% 220.76/37.31  | | | | | | | 
% 220.76/37.31  | | | | | | |   (3956)  all_14_2 = e0
% 220.76/37.31  | | | | | | |   (3957)  ( ~ (all_14_0 = e1) & op(all_14_1, e2) = all_14_0 &
% 220.76/37.31  | | | | | | |             op(e2, e0) = all_14_1 & $i(all_14_0) & $i(all_14_1)) |
% 220.76/37.31  | | | | | | |           ( ~ (all_14_1 = e3) & op(e2, e0) = all_14_1 &
% 220.76/37.31  | | | | | | |             $i(all_14_1))
% 220.76/37.31  | | | | | | | 
% 220.76/37.31  | | | | | | | COMBINE_EQS: (328), (3956) imply:
% 220.76/37.31  | | | | | | |   (3958)  all_8_2 = e0
% 220.76/37.31  | | | | | | | 
% 220.76/37.31  | | | | | | | COMBINE_EQS: (290), (3958) imply:
% 220.76/37.31  | | | | | | |   (3959)  all_50_2 = e0
% 220.76/37.31  | | | | | | | 
% 220.76/37.31  | | | | | | | REDUCE: (352), (3958) imply:
% 220.76/37.31  | | | | | | |   (3960)   ~ (all_53_4 = e0)
% 220.76/37.31  | | | | | | | 
% 220.76/37.31  | | | | | | | REDUCE: (354), (3958) imply:
% 220.76/37.31  | | | | | | |   (3961)   ~ (all_53_6 = e0)
% 220.76/37.31  | | | | | | | 
% 220.76/37.31  | | | | | | | REDUCE: (356), (3958) imply:
% 220.76/37.31  | | | | | | |   (3962)   ~ (all_53_7 = e0)
% 220.76/37.31  | | | | | | | 
% 220.76/37.31  | | | | | | | REDUCE: (358), (3958) imply:
% 220.76/37.31  | | | | | | |   (3963)   ~ (all_53_9 = e0)
% 220.76/37.31  | | | | | | | 
% 220.76/37.31  | | | | | | | REDUCE: (360), (3958) imply:
% 220.76/37.31  | | | | | | |   (3964)   ~ (all_53_13 = e0)
% 220.76/37.31  | | | | | | | 
% 220.76/37.31  | | | | | | | REDUCE: (375), (3958) imply:
% 220.76/37.31  | | | | | | |   (3965)   ~ (e3 = e0)
% 220.76/37.31  | | | | | | | 
% 220.76/37.31  | | | | | | | BETA: splitting (226) gives:
% 220.76/37.31  | | | | | | | 
% 220.76/37.31  | | | | | | | Case 1:
% 220.76/37.31  | | | | | | | | 
% 220.76/37.31  | | | | | | | |   (3966)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 &
% 220.76/37.31  | | | | | | | |             op(e2, e2) = e0)
% 220.76/37.31  | | | | | | | | 
% 220.76/37.31  | | | | | | | | BETA: splitting (3966) gives:
% 220.76/37.31  | | | | | | | | 
% 220.76/37.31  | | | | | | | | Case 1:
% 220.76/37.31  | | | | | | | | | 
% 220.76/37.31  | | | | | | | | |   (3967)  all_57_1 = e0 & op(e3, e2) = e0
% 220.76/37.31  | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | ALPHA: (3967) implies:
% 220.76/37.31  | | | | | | | | |   (3968)  op(e3, e2) = e0
% 220.76/37.31  | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | REF_CLOSE: (171), (3960), (3968), (function-axioms) are
% 220.76/37.31  | | | | | | | | |            inconsistent by sub-proof #1941.
% 220.76/37.31  | | | | | | | | | 
% 220.76/37.31  | | | | | | | | Case 2:
% 220.76/37.31  | | | | | | | | | 
% 220.76/37.31  | | | | | | | | |   (3969)  all_57_3 = e0 & op(e2, e2) = e0
% 220.76/37.31  | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | ALPHA: (3969) implies:
% 220.76/37.31  | | | | | | | | |   (3970)  all_57_3 = e0
% 220.76/37.31  | | | | | | | | |   (3971)  op(e2, e2) = e0
% 220.76/37.31  | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | BETA: splitting (58) gives:
% 220.76/37.31  | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | Case 1:
% 220.76/37.31  | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | |   (3972)   ~ (all_18_2 = e0)
% 220.76/37.31  | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | REDUCE: (327), (3972) imply:
% 220.76/37.31  | | | | | | | | | |   (3973)   ~ (all_10_2 = e0)
% 220.76/37.31  | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | BETA: splitting (61) gives:
% 220.76/37.31  | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | Case 1:
% 220.76/37.31  | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | |   (3974)   ~ (all_20_2 = e2)
% 220.76/37.31  | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | REDUCE: (299), (3974) imply:
% 220.76/37.31  | | | | | | | | | | |   (3975)   ~ (all_10_2 = e2)
% 220.76/37.31  | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | BETA: splitting (205) gives:
% 220.76/37.31  | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | Case 1:
% 220.76/37.31  | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | |   (3976)  all_55_0 = e3
% 220.76/37.31  | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | COMBINE_EQS: (277), (3976) imply:
% 220.76/37.31  | | | | | | | | | | | |   (3977)  all_10_2 = e3
% 220.76/37.31  | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | REDUCE: (340), (3977) imply:
% 220.76/37.31  | | | | | | | | | | | |   (3978)   ~ (all_53_2 = e3)
% 220.76/37.31  | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | REDUCE: (342), (3977) imply:
% 220.76/37.31  | | | | | | | | | | | |   (3979)   ~ (all_53_3 = e3)
% 220.76/37.31  | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | REDUCE: (344), (3977) imply:
% 220.76/37.31  | | | | | | | | | | | |   (3980)   ~ (all_53_4 = e3)
% 220.76/37.31  | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | REDUCE: (346), (3977) imply:
% 220.76/37.31  | | | | | | | | | | | |   (3981)   ~ (all_53_8 = e3)
% 220.76/37.31  | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | REDUCE: (348), (3977) imply:
% 220.76/37.31  | | | | | | | | | | | |   (3982)   ~ (all_53_12 = e3)
% 220.76/37.31  | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | REDUCE: (45), (3977) imply:
% 220.76/37.31  | | | | | | | | | | | |   (3983)  op(e3, e3) = e3
% 220.76/37.31  | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | BETA: splitting (237) gives:
% 220.76/37.31  | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | Case 1:
% 220.76/37.31  | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | |   (3984)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 220.76/37.31  | | | | | | | | | | | | |             & op(e3, e2) = e3)
% 220.76/37.31  | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | BETA: splitting (3984) gives:
% 220.76/37.31  | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | Case 1:
% 220.76/37.31  | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | |   (3985)  all_57_0 = e3 & op(e3, e3) = e3
% 220.76/37.31  | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | ALPHA: (3985) implies:
% 220.76/37.31  | | | | | | | | | | | | | |   (3986)  all_57_0 = e3
% 220.76/37.31  | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 220.76/37.31  | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | Case 1:
% 220.76/37.31  | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | |   (3987)   ~ (all_24_2 = e0)
% 220.76/37.31  | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | REDUCE: (315), (3987) imply:
% 220.76/37.31  | | | | | | | | | | | | | | |   (3988)   ~ (all_6_2 = e0)
% 220.76/37.31  | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | BETA: splitting (76) gives:
% 220.76/37.31  | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | Case 1:
% 220.76/37.31  | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | |   (3989)   ~ (all_30_2 = e1)
% 220.76/37.31  | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | REDUCE: (330), (3989) imply:
% 220.76/37.31  | | | | | | | | | | | | | | | |   (3990)   ~ (all_4_2 = e1)
% 220.76/37.31  | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 220.76/37.31  | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.31  | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | |   (3991)  all_55_15 = e3
% 220.76/37.31  | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (3991) imply:
% 220.76/37.31  | | | | | | | | | | | | | | | | |   (3992)  all_4_2 = e3
% 220.76/37.31  | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | REDUCE: (378), (3992) imply:
% 220.76/37.31  | | | | | | | | | | | | | | | | |   (3993)  $false
% 220.76/37.31  | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | CLOSE: (3993) is inconsistent.
% 220.76/37.31  | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.31  | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | |   (3994)   ~ (all_55_15 = e3)
% 220.76/37.31  | | | | | | | | | | | | | | | | |   (3995)  all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 220.76/37.31  | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | BETA: splitting (3995) gives:
% 220.76/37.31  | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.31  | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | |   (3996)  all_55_15 = e2
% 220.76/37.31  | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (3996) imply:
% 220.76/37.31  | | | | | | | | | | | | | | | | | |   (3997)  all_4_2 = e2
% 220.76/37.31  | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | REDUCE: (373), (3997) imply:
% 220.76/37.31  | | | | | | | | | | | | | | | | | |   (3998)  $false
% 220.76/37.31  | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | CLOSE: (3998) is inconsistent.
% 220.76/37.31  | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.31  | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | |   (3999)   ~ (all_55_15 = e2)
% 220.76/37.31  | | | | | | | | | | | | | | | | | |   (4000)  all_55_15 = e1 | all_55_15 = e0
% 220.76/37.31  | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | BETA: splitting (4000) gives:
% 220.76/37.31  | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | |   (4001)  all_55_15 = e1
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (4001) imply:
% 220.76/37.31  | | | | | | | | | | | | | | | | | | |   (4002)  all_4_2 = e1
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | REDUCE: (3990), (4002) imply:
% 220.76/37.31  | | | | | | | | | | | | | | | | | | |   (4003)  $false
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | CLOSE: (4003) is inconsistent.
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | |   (4004)  all_55_15 = e0
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (4004) imply:
% 220.76/37.31  | | | | | | | | | | | | | | | | | | |   (4005)  all_4_2 = e0
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | REDUCE: (351), (4005) imply:
% 220.76/37.31  | | | | | | | | | | | | | | | | | | |   (4006)   ~ (all_53_3 = e0)
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | REDUCE: (370), (4005) imply:
% 220.76/37.31  | | | | | | | | | | | | | | | | | | |   (4007)   ~ (all_53_12 = e0)
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | REDUCE: (373), (4005) imply:
% 220.76/37.31  | | | | | | | | | | | | | | | | | | |   (4008)   ~ (e2 = e0)
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | REDUCE: (3990), (4005) imply:
% 220.76/37.31  | | | | | | | | | | | | | | | | | | |   (4009)   ~ (e1 = e0)
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | |   (4010)  all_57_15 = e0 & op(e0, e0) = e0
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | ALPHA: (4010) implies:
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | |   (4011)  all_57_15 = e0
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | |   (4012)  op(e0, e0) = e0
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | |   (4013)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e0)
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | |            (3970), (3983), (4013), (function-axioms) are
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2229.
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | |   (4014)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = e0)
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4014) gives:
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | |   (4015)  all_57_6 = e0 & op(e1, e3) = e0
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4015) implies:
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | |   (4016)  all_57_6 = e0
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | |   (4017)  op(e1, e3) = e0
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | |   (4018)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (171), (3960), (3983), (4018),
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | |            #1543.
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | |   (4019)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4019) gives:
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | |   (4020)  all_57_4 = e0 & op(e3, e1) = e0
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4020) implies:
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | |   (4021)  all_57_4 = e0
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | |   (4022)  op(e3, e1) = e0
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (39), (45), (67), (88), (94),
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | |            (107), (111), (113), (119), (121), (122), (124),
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | |            (127), (129), (134), (135), (136), (137), (142),
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | |            (144), (158), (159), (161), (163), (164), (165),
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | |            (166), (169), (170), (171), (191), (192), (194),
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | |            (195), (196), (199), (202), (203), (204), (205),
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | |            (207), (208), (209), (210), (211), (212), (213),
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | |            (214), (215), (216), (217), (218), (219), (220),
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | |            (221), (223), (224), (225), (227), (228), (229),
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | |            (230), (231), (232), (233), (234), (235), (236),
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | |            (237), (245), (246), (248), (249), (256), (259),
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | |            (268), (269), (270), (277), (315), (332), (336),
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | |            (348), (361), (363), (364), (366), (368), (374),
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | |            (376), (3962), (3970), (3971), (3973), (3975),
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | |            (3980), (3981), (3982), (3983), (3986), (4011),
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | |            (4012), (4016), (4017), (4021), (4022),
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | |            #1410.
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | |   (4023)  all_57_9 = e0 & op(e3, e0) = e0
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (4007), (4023), (function-axioms) are
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2434.
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | |   (4024)  all_57_12 = e0 & op(e0, e3) = e0
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4024) implies:
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | |   (4025)  op(e0, e3) = e0
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (4006), (4025), (function-axioms) are
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2366.
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | |   (4026)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | |                 e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | ALPHA: (4026) implies:
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | |   (4027)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | |               e1) = e0)
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | |   (4028)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | |               e0) = e0)
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | BETA: splitting (4027) gives:
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | |   (4029)  all_57_12 = e0 & op(e0, e3) = e0
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.31  | | | | | | | | | | | | | | | | | | | | | ALPHA: (4029) implies:
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | |   (4030)  op(e0, e3) = e0
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (4006), (4030), (function-axioms) are
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2366.
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | |   (4031)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4031) gives:
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | |   (4032)  all_57_13 = e0 & op(e0, e2) = e0
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4032) implies:
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | |   (4033)  op(e0, e2) = e0
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (3962), (4033), (function-axioms) are
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2332.
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | |   (4034)  all_57_14 = e0 & op(e0, e1) = e0
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4034) implies:
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | |   (4035)  all_57_14 = e0
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | |   (4036)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4036) gives:
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | |   (4037)  all_57_12 = e3 & op(e0, e3) = e3
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4037) implies:
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | |   (4038)  all_57_12 = e3
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | |   (4039)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e3)
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4039) gives:
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4040)  all_57_4 = e3 & op(e3, e1) = e3
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4040) implies:
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4041)  all_57_4 = e3
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (235),
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | |            (3983), (4041), (function-axioms) are inconsistent
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2474.
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4042)  all_57_5 = e3 & op(e2, e1) = e3
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4042) implies:
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4043)  all_57_5 = e3
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4028) gives:
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4044)  all_57_9 = e0 & op(e3, e0) = e0
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (4007), (4044), (function-axioms) are
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2434.
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4045)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 =
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4045) gives:
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4046)  all_57_10 = e0 & op(e2, e0) = e0
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4046) implies:
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4047)  all_57_10 = e0
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (223), (224), (3970),
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4043), (4047) are inconsistent by sub-proof
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1518.
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4048)  all_57_11 = e0 & op(e1, e0) = e0
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4048) implies:
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4049)  all_57_11 = e0
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4050)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (169), (223), (224),
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3970), (3982), (4043), (4050), (function-axioms)
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1409.
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4051)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4051) gives:
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4052)  all_57_11 = e3 & op(e1, e0) = e3
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4052) implies:
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4053)  all_57_11 = e3
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4049), (4053) are inconsistent by sub-proof
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1595.
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4054)  all_57_15 = e3 & op(e0, e0) = e3
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4054) implies:
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4055)  all_57_15 = e3
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (208), (209), (4035),
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4038), (4055) are inconsistent by sub-proof
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1763.
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | |   (4056)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e1) = e3)
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (39), (374), (4035), (4056),
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | |            #2419.
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | |   (4057)  all_57_13 = e3 & op(e0, e2) = e3
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4057) implies:
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | |   (4058)  all_57_13 = e3
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | |   (4059)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e3)
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4059) gives:
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4060)  all_57_4 = e3 & op(e3, e1) = e3
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4060) implies:
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4061)  all_57_4 = e3
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (235),
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | |            (3983), (4061), (function-axioms) are inconsistent
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2474.
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4062)  all_57_5 = e3 & op(e2, e1) = e3
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4062) implies:
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4063)  all_57_5 = e3
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4064)  op(e2, e1) = e3
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4028) gives:
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4065)  all_57_9 = e0 & op(e3, e0) = e0
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (4007), (4065), (function-axioms) are
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2434.
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4066)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 =
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4066) gives:
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4067)  all_57_10 = e0 & op(e2, e0) = e0
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4067) implies:
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4068)  all_57_10 = e0
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (223), (224), (3970),
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4063), (4068) are inconsistent by sub-proof
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1518.
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4069)  all_57_11 = e0 & op(e1, e0) = e0
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4069) implies:
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4070)  all_57_11 = e0
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (67), (88),
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (94), (107), (121), (124), (134), (135), (137),
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (163), (166), (169), (170), (171), (195), (202),
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (203), (204), (207), (208), (209), (211), (212),
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (213), (214), (215), (216), (217), (218), (219),
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (220), (223), (224), (227), (228), (229), (230),
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (232), (233), (234), (235), (249), (268),
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (269), (270), (315), (332), (336), (363), (364),
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (374), (3960), (3963), (3970), (3971), (3982),
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3983), (3986), (4058), (4063), (4064), (4070),
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1408.
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | |   (4071)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e1) = e3)
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (39), (374), (4035), (4071),
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | |            #2419.
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | |   (4072)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4072) gives:
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | |   (4073)  all_57_14 = e3 & op(e0, e1) = e3
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4073) implies:
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | |   (4074)  all_57_14 = e3
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4035), (4074) are inconsistent by sub-proof
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | |            #2420.
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | |   (4075)  all_57_15 = e3 & op(e0, e0) = e3
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4075) implies:
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | |   (4076)  all_57_15 = e3
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | |   (4077)  op(e0, e0) = e3
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (39), (45), (67), (88), (94),
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | |            (107), (121), (124), (134), (135), (137), (163),
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | |            (166), (169), (170), (171), (195), (202), (203),
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | |            (204), (205), (207), (208), (209), (211), (212),
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | |            (214), (215), (216), (217), (218), (219), (220),
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | |            (221), (223), (224), (225), (227), (228), (229),
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | |            (230), (231), (232), (233), (234), (235), (236),
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | |            (237), (249), (268), (269), (270), (277), (315),
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | |            (332), (336), (348), (363), (364), (374), (376),
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | |            (3960), (3963), (3970), (3973), (3975), (4076),
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | |            (4077), (function-axioms) are inconsistent by
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1414.
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.32  | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | End of split
% 220.76/37.32  | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | End of split
% 220.76/37.32  | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | Case 2:
% 220.76/37.32  | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | |   (4078)  all_30_2 = e1
% 220.76/37.32  | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | COMBINE_EQS: (330), (4078) imply:
% 220.76/37.32  | | | | | | | | | | | | | | | |   (4079)  all_4_2 = e1
% 220.76/37.32  | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | SIMP: (4079) implies:
% 220.76/37.32  | | | | | | | | | | | | | | | |   (4080)  all_4_2 = e1
% 220.76/37.32  | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | REDUCE: (351), (4080) imply:
% 220.76/37.32  | | | | | | | | | | | | | | | |   (4081)   ~ (all_53_3 = e1)
% 220.76/37.32  | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | REDUCE: (362), (4080) imply:
% 220.76/37.32  | | | | | | | | | | | | | | | |   (4082)   ~ (all_53_7 = e1)
% 220.76/37.32  | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | REDUCE: (371), (4080) imply:
% 220.76/37.32  | | | | | | | | | | | | | | | |   (4083)   ~ (all_53_13 = e1)
% 220.76/37.32  | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | REDUCE: (378), (4080) imply:
% 220.76/37.32  | | | | | | | | | | | | | | | |   (4084)   ~ (e3 = e1)
% 220.76/37.32  | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | REDUCE: (373), (4080) imply:
% 220.76/37.32  | | | | | | | | | | | | | | | |   (4085)   ~ (e2 = e1)
% 220.76/37.32  | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | REDUCE: (36), (4080) imply:
% 220.76/37.32  | | | | | | | | | | | | | | | |   (4086)  op(e0, e0) = e1
% 220.76/37.32  | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 220.76/37.32  | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.32  | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | |   (4087)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 220.76/37.32  | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 220.76/37.32  | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | BETA: splitting (4087) gives:
% 220.76/37.32  | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.32  | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | |   (4088)  all_57_9 = e1 & op(e3, e0) = e1
% 220.76/37.32  | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | ALPHA: (4088) implies:
% 220.76/37.32  | | | | | | | | | | | | | | | | | |   (4089)  all_57_9 = e1
% 220.76/37.32  | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (45), (67),
% 220.76/37.32  | | | | | | | | | | | | | | | | | |            (88), (94), (107), (111), (113), (119), (121),
% 220.76/37.32  | | | | | | | | | | | | | | | | | |            (122), (124), (127), (129), (134), (135), (136),
% 220.76/37.32  | | | | | | | | | | | | | | | | | |            (137), (142), (144), (158), (159), (161), (163),
% 220.76/37.32  | | | | | | | | | | | | | | | | | |            (164), (165), (166), (169), (170), (171), (191),
% 220.76/37.32  | | | | | | | | | | | | | | | | | |            (192), (194), (195), (196), (199), (202), (203),
% 220.76/37.32  | | | | | | | | | | | | | | | | | |            (204), (205), (207), (208), (209), (210), (211),
% 220.76/37.32  | | | | | | | | | | | | | | | | | |            (212), (213), (214), (215), (216), (217), (218),
% 220.76/37.32  | | | | | | | | | | | | | | | | | |            (219), (220), (221), (223), (224), (225), (227),
% 220.76/37.32  | | | | | | | | | | | | | | | | | |            (228), (229), (230), (231), (232), (233), (234),
% 220.76/37.32  | | | | | | | | | | | | | | | | | |            (235), (236), (237), (245), (246), (248), (249),
% 220.76/37.32  | | | | | | | | | | | | | | | | | |            (256), (259), (268), (269), (270), (277), (315),
% 220.76/37.32  | | | | | | | | | | | | | | | | | |            (332), (336), (348), (361), (363), (364), (366),
% 220.76/37.32  | | | | | | | | | | | | | | | | | |            (368), (374), (376), (3960), (3962), (3963),
% 220.76/37.32  | | | | | | | | | | | | | | | | | |            (3964), (3970), (3971), (3973), (3975), (3980),
% 220.76/37.32  | | | | | | | | | | | | | | | | | |            (3981), (3982), (3983), (3986), (4086), (4089),
% 220.76/37.32  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.76/37.32  | | | | | | | | | | | | | | | | | |            #1384.
% 220.76/37.32  | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.32  | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | |   (4090)  all_57_10 = e1 & op(e2, e0) = e1
% 220.76/37.32  | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (4083), (4090), (function-axioms) are
% 220.76/37.32  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2084.
% 220.76/37.32  | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | End of split
% 220.76/37.32  | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.32  | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | |   (4091)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 220.76/37.32  | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 220.76/37.32  | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | BETA: splitting (4091) gives:
% 220.76/37.32  | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.32  | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | |   (4092)  all_57_11 = e1 & op(e1, e0) = e1
% 220.76/37.32  | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | ALPHA: (4092) implies:
% 220.76/37.32  | | | | | | | | | | | | | | | | | |   (4093)  all_57_11 = e1
% 220.76/37.32  | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (45), (67),
% 220.76/37.32  | | | | | | | | | | | | | | | | | |            (88), (94), (107), (111), (113), (119), (121),
% 220.76/37.32  | | | | | | | | | | | | | | | | | |            (122), (124), (127), (129), (134), (135), (136),
% 220.76/37.32  | | | | | | | | | | | | | | | | | |            (137), (142), (144), (158), (159), (161), (163),
% 220.76/37.32  | | | | | | | | | | | | | | | | | |            (164), (165), (166), (169), (170), (171), (191),
% 220.76/37.32  | | | | | | | | | | | | | | | | | |            (192), (194), (195), (196), (199), (202), (203),
% 220.76/37.32  | | | | | | | | | | | | | | | | | |            (204), (205), (207), (208), (209), (210), (211),
% 220.76/37.32  | | | | | | | | | | | | | | | | | |            (212), (213), (214), (215), (216), (217), (218),
% 220.76/37.32  | | | | | | | | | | | | | | | | | |            (219), (220), (221), (223), (224), (225), (227),
% 220.76/37.32  | | | | | | | | | | | | | | | | | |            (228), (229), (230), (231), (232), (233), (234),
% 220.76/37.32  | | | | | | | | | | | | | | | | | |            (235), (236), (237), (245), (246), (248), (249),
% 220.76/37.32  | | | | | | | | | | | | | | | | | |            (256), (259), (268), (269), (270), (277), (315),
% 220.76/37.32  | | | | | | | | | | | | | | | | | |            (332), (336), (348), (361), (363), (364), (366),
% 220.76/37.32  | | | | | | | | | | | | | | | | | |            (368), (374), (376), (3960), (3962), (3963),
% 220.76/37.32  | | | | | | | | | | | | | | | | | |            (3964), (3970), (3971), (3973), (3975), (3980),
% 220.76/37.32  | | | | | | | | | | | | | | | | | |            (3981), (3982), (3983), (3986), (3988), (4086),
% 220.76/37.32  | | | | | | | | | | | | | | | | | |            (4093), (function-axioms) are inconsistent by
% 220.76/37.32  | | | | | | | | | | | | | | | | | |            sub-proof #1373.
% 220.76/37.32  | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.32  | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | |   (4094)  all_57_15 = e1 & op(e0, e0) = e1
% 220.76/37.32  | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | ALPHA: (4094) implies:
% 220.76/37.32  | | | | | | | | | | | | | | | | | |   (4095)  all_57_15 = e1
% 220.76/37.32  | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | BETA: splitting (88) gives:
% 220.76/37.32  | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.32  | | | | | | | | | | | | | | | | | | | 
% 220.76/37.32  | | | | | | | | | | | | | | | | | | |   (4096)   ~ (all_38_2 = e2)
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | REDUCE: (249), (4096) imply:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | |   (4097)   ~ (all_6_2 = e2)
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | |   (4098)  all_55_10 = e3
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (374), (4098) are inconsistent by sub-proof
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | |            #2500.
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | |   (4099)   ~ (all_55_10 = e3)
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | |   (4100)  all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | BETA: splitting (4100) gives:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | |   (4101)  all_55_10 = e2
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (4097), (4101) are inconsistent by
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | |            sub-proof #2499.
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | |   (4102)   ~ (all_55_10 = e2)
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | |   (4103)  all_55_10 = e1 | all_55_10 = e0
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4103) gives:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | |   (4104)  all_55_10 = e1
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (336), (4104) imply:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | |   (4105)  all_6_2 = e1
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | SIMP: (4105) implies:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | |   (4106)  all_6_2 = e1
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (4106) imply:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | |   (4107)  op(e1, e1) = e1
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | |   (4108)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e1)
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4108) gives:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | |   (4109)  all_57_0 = e1 & op(e3, e3) = e1
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4109) implies:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | |   (4110)  op(e3, e3) = e1
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (3983), (4110), (function-axioms) are
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2495.
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | |   (4111)  all_57_1 = e1 & op(e3, e2) = e1
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4111) implies:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | |   (4112)  op(e3, e2) = e1
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_4, e1,
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (171), (4112) gives:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | |   (4113)  all_53_4 = e1
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (137), (4113) imply:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | |   (4114)   ~ (all_53_6 = e1)
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4114) implies:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | |   (4115)   ~ (all_53_6 = e1)
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (136), (4113) imply:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | |   (4116)   ~ (all_53_7 = e1)
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | |   (4117)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | |             op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | |               all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | |               all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | |               all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4117) gives:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4118)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | |           all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_7)
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4107), (4112), (4118), (function-axioms) are
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2111.
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4119)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | |           all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | |           & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_15)
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3971), (4086), (4119), (function-axioms) are
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1372.
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | |   (4120)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | |             & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | |               all_52_21) = e1 & op(all_52_23, all_52_23) =
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | |             = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | |             & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(all_52_25, all_52_25) = e3 &
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | |             op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | |               all_52_29) = e1 & op(all_52_31, all_52_31) =
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | |             = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_29) & $i(all_52_31))
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4120) gives:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4121)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | |           all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | |           & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | |           & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | |           & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_23)
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4121) implies:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4122)  op(e1, e2) = all_52_19
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4123)  op(all_52_19, all_52_19) = e2
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_6,
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_19, e2, e1, simplifying with (163), (4122)
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4124)  all_53_6 = all_52_19
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (4124) imply:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4125)  all_55_9 = all_52_19
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (129), (4124) imply:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4126)   ~ (all_53_7 = all_52_19)
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4126) implies:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4127)   ~ (all_53_7 = all_52_19)
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4115), (4124) imply:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4128)   ~ (all_52_19 = e1)
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3961), (4124) imply:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4129)   ~ (all_52_19 = e0)
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4130)  all_55_13 = e3
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (4130) imply:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4131)  all_53_7 = e3
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4131) implies:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4132)  all_53_7 = e3
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4127), (4132) imply:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4133)   ~ (all_52_19 = e3)
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4133) implies:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4134)   ~ (all_52_19 = e3)
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4135)  all_55_9 = e3
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4125), (4135) imply:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4136)  all_52_19 = e3
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4134), (4136) imply:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4137)  $false
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4137) is inconsistent.
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4138)  all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3971), (4123), (4125), (4128), (4129), (4138),
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1371.
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4139)  all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4139) gives:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4140)  all_55_13 = e2
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (4140) imply:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4141)  all_53_7 = e2
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4141) implies:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4142)  all_53_7 = e2
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4127), (4142) imply:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4143)   ~ (all_52_19 = e2)
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4143) implies:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4144)   ~ (all_52_19 = e2)
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (196), (3983), (4123), (4125), (4128), (4129),
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4144), (function-axioms) are inconsistent by
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1370.
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4145)  all_55_13 = e1 | all_55_13 = e0
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (3962), (4082), (4145) are inconsistent by
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1837.
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4146)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | |           all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | |           & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | |           & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | |           & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_31)
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4146) implies:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4147)  op(e0, e0) = all_52_31
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4148)  op(all_52_31, all_52_31) = e0
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (3988), (4086), (4147), (4148),
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | |            #2086.
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | |   (4149)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e1)
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4149) gives:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | |   (4150)  all_57_4 = e1 & op(e3, e1) = e1
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4150) implies:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | |   (4151)  all_57_4 = e1
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | |   (4152)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (171), (3960), (3983), (4152),
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | |            #1543.
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | |   (4153)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4153) gives:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4154)  all_57_4 = e0 & op(e3, e1) = e0
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4154) implies:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4155)  all_57_4 = e0
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4151), (4155) are inconsistent by sub-proof
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | |            #2438.
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4156)  all_57_9 = e0 & op(e3, e0) = e0
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4156) implies:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4157)  all_57_9 = e0
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4158)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e0)
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4158) gives:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4159)  all_57_4 = e0 & op(e3, e1) = e0
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4159) implies:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4160)  all_57_4 = e0
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (233), (235), (3983),
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4157), (4160), (function-axioms) are inconsistent
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2436.
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4161)  all_57_5 = e0 & op(e2, e1) = e0
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4161) implies:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4162)  all_57_5 = e0
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (223), (224),
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (225), (3970), (3971), (4083), (4162),
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1689.
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4163)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (220), (221),
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (374), (4107), (4151), (4163), (function-axioms)
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2417.
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | |   (4164)  all_57_9 = e1 & op(e3, e0) = e1
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4164) implies:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | |   (4165)  all_57_9 = e1
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (45), (67),
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | |            (88), (94), (107), (111), (113), (119), (121),
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | |            (122), (124), (127), (129), (134), (135), (136),
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | |            (137), (142), (144), (158), (159), (161), (163),
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | |            (164), (165), (166), (169), (170), (171), (191),
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | |            (192), (194), (195), (196), (199), (202), (203),
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | |            (204), (205), (207), (208), (209), (210), (211),
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | |            (212), (213), (214), (215), (216), (217), (218),
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | |            (219), (220), (221), (223), (224), (225), (227),
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | |            (228), (229), (230), (231), (232), (233), (234),
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | |            (235), (236), (237), (245), (246), (248), (249),
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | |            (256), (259), (268), (269), (270), (277), (315),
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | |            (332), (336), (348), (361), (363), (364), (366),
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | |            (368), (374), (376), (3960), (3962), (3963),
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | |            (3964), (3970), (3971), (3973), (3975), (3980),
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | |            (3981), (3982), (3983), (3986), (4086), (4165),
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | |            #1384.
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | |   (4166)  all_55_10 = e0
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (3988), (4166) are inconsistent by
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2118.
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | |   (4167)  all_38_2 = e2
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (4167) imply:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | |   (4168)  all_6_2 = e2
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | REDUCE: (350), (4168) imply:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | |   (4169)   ~ (all_53_2 = e2)
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | REDUCE: (361), (4168) imply:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | |   (4170)   ~ (all_53_6 = e2)
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | REDUCE: (374), (4168) imply:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | |   (4171)   ~ (e3 = e2)
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | REDUCE: (39), (4168) imply:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | |   (4172)  op(e1, e1) = e2
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | |   (4173)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | |             all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | |             op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | |               all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | |             $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | |             $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | |               all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | |             & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | |               all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | |             & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | |             $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | BETA: splitting (4173) gives:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.33  | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | |   (4174)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | |           all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | |           op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | |             all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | |           $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | |           $i(all_52_7)
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | ALPHA: (4174) implies:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | |   (4175)  op(e3, e0) = all_52_7
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | |   (4176)  op(e3, e1) = all_52_5
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | |   (4177)  op(e3, e3) = all_52_1
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | |   (4178)  op(all_52_7, all_52_7) = e0
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | |   (4179)  op(all_52_5, all_52_5) = e1
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | |   (4180)  op(all_52_1, all_52_1) = e3
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (106) gives:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | |   (4181)   ~ (all_50_2 = e0)
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3959), (4181) imply:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | |   (4182)  $false
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4182) is inconsistent.
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | |   (4183)  ( ~ (all_50_0 = e3) & op(all_50_1, e2) = all_50_0
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e0) = all_50_1 & $i(all_50_0) &
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | |             $i(all_50_1)) | ( ~ (all_50_1 = e1) & op(e2, e0)
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | |             = all_50_1 & $i(all_50_1))
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | |   (4184)  all_55_13 = e3
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (4184) imply:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | |   (4185)  all_53_7 = e3
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4185) implies:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | |   (4186)  all_53_7 = e3
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (129), (4186) imply:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | |   (4187)   ~ (all_53_6 = e3)
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | |   (4188)  all_55_9 = e3
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (4187), (4188) are inconsistent by
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2159.
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | |   (4189)   ~ (all_55_9 = e3)
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | |   (4190)  all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4190) gives:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | |   (4191)  all_55_9 = e2
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (4170), (4191) are inconsistent by
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2274.
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | |   (4192)   ~ (all_55_9 = e2)
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | |   (4193)  all_55_9 = e1 | all_55_9 = e0
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4194)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e3)
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4194) gives:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4195)  all_57_4 = e3 & op(e3, e1) = e3
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4195) implies:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4196)  all_57_4 = e3
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (235),
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3983), (4196), (function-axioms) are inconsistent
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2474.
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4197)  all_57_5 = e3 & op(e2, e1) = e3
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4197) implies:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4198)  all_57_5 = e3
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4199)  op(e2, e1) = e3
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4200)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4200) gives:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4201)  all_57_12 = e3 & op(e0, e3) = e3
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4201) implies:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4202)  all_57_12 = e3
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4203)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (144), (145),
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (160), (165), (171), (197), (207), (218), (219),
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (220), (221), (223), (224), (225), (227), (228),
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (231), (232), (233), (234), (235), (256),
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (257), (374), (3960), (3961), (3970), (3971),
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3978), (3983), (3988), (4083), (4086), (4169),
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4170), (4175), (4176), (4178), (4179), (4187),
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4193), (4198), (4203), (function-axioms) are
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1364.
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4204)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4204) gives:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4205)  all_57_8 = e3 & op(e1, e1) = e3
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4205) implies:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4206)  op(e1, e1) = e3
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (374), (4206), (function-axioms) are
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2468.
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4207)  all_57_11 = e3 & op(e1, e0) = e3
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4207) implies:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4208)  all_57_11 = e3
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4209)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4209) gives:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4210)  all_57_12 = e2 & op(e0, e3) = e2
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4210) implies:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4211)  all_57_12 = e2
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4202), (4211) are inconsistent by sub-proof
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2392.
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4212)  all_57_13 = e2 & op(e0, e2) = e2
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4212) implies:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4213)  all_57_13 = e2
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (45), (67),
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (88), (94), (107), (111), (113), (119), (121),
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (122), (124), (127), (129), (134), (135), (136),
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (137), (142), (144), (145), (158), (159), (160),
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (161), (163), (164), (165), (166), (169), (170),
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (171), (191), (192), (194), (195), (196), (197),
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (199), (202), (203), (204), (205), (207), (208),
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (209), (210), (211), (212), (213), (214), (215),
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (216), (217), (218), (219), (220), (221), (223),
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (225), (227), (228), (229), (230), (231),
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (232), (233), (234), (235), (236), (237), (245),
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (246), (248), (249), (256), (257), (259), (268),
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (269), (270), (277), (315), (332), (336), (348),
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (361), (363), (364), (366), (368), (374), (376),
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3960), (3961), (3962), (3963), (3964), (3970),
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3971), (3973), (3975), (3978), (3980), (3981),
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3982), (3983), (3986), (3988), (4083), (4086),
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4169), (4170), (4175), (4176), (4177), (4178),
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4179), (4180), (4187), (4193), (4198), (4208),
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4213), (function-axioms) are inconsistent by
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1357.
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4214)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4214) gives:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4215)  all_57_14 = e2 & op(e0, e1) = e2
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4215) implies:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4216)  all_57_14 = e2
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (171), (219),
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (220), (221), (223), (224), (225), (230), (231),
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (232), (233), (234), (235), (374), (3960), (3970),
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3971), (3983), (4086), (4175), (4177), (4178),
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4180), (4202), (4216), (function-axioms) are
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1356.
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4217)  all_57_15 = e2 & op(e0, e0) = e2
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4217) implies:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4218)  op(e0, e0) = e2
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4086), (4218), (function-axioms) are
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2177.
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4219)  all_57_13 = e3 & op(e0, e2) = e3
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4219) implies:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4220)  all_57_13 = e3
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4221)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (144), (145),
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (160), (165), (171), (197), (207), (218), (219),
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (220), (221), (223), (224), (225), (227), (228),
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (231), (232), (233), (234), (235), (256),
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (257), (374), (3960), (3961), (3970), (3971),
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3978), (3983), (3988), (4083), (4086), (4169),
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4170), (4175), (4176), (4178), (4179), (4187),
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4193), (4198), (4221), (function-axioms) are
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1364.
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4222)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4222) gives:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4223)  all_57_8 = e3 & op(e1, e1) = e3
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4223) implies:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4224)  op(e1, e1) = e3
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (374), (4224), (function-axioms) are
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2468.
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4225)  all_57_11 = e3 & op(e1, e0) = e3
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4225) implies:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4226)  all_57_11 = e3
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4227)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4227) gives:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4228)  all_57_12 = e2 & op(e0, e3) = e2
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4228) implies:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4229)  all_57_12 = e2
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4230)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e1)
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4230) gives:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4231)  all_57_4 = e1 & op(e3, e1) = e1
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4231) implies:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4232)  all_57_4 = e1
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4233)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4233) gives:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4234)  all_57_2 = e1 & op(e2, e3) = e1
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4234) implies:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4235)  all_57_2 = e1
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4236)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e0)
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4236) gives:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4237)  all_57_4 = e0 & op(e3, e1) = e0
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (223), (224), (3970),
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4198), (4232), (4235), (4237) are inconsistent by
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1355.
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4238)  all_57_5 = e0 & op(e2, e1) = e0
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4238) implies:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4239)  all_57_5 = e0
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3970), (3971), (4235), (4239), (function-axioms)
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2353.
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4240)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (171), (219),
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (220), (231), (3960), (3983), (3988), (4086),
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4175), (4178), (4198), (4240), (function-axioms)
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1354.
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4241)  all_57_3 = e1 & op(e2, e2) = e1
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4241) implies:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4242)  op(e2, e2) = e1
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3971), (4242), (function-axioms) are
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2352.
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4243)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4243) gives:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4244)  all_57_5 = e1 & op(e2, e1) = e1
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4244) implies:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4245)  all_57_5 = e1
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4198), (4245) imply:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4246)  e3 = e1
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4226), (4246) imply:
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4247)  all_57_11 = e1
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (45), (67),
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (88), (94), (107), (111), (113), (119), (121),
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (122), (124), (127), (129), (134), (135), (136),
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (137), (142), (144), (158), (159), (161), (163),
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (165), (166), (169), (170), (171), (191),
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (192), (194), (195), (196), (199), (202), (203),
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (204), (205), (207), (208), (209), (210), (211),
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (213), (214), (215), (216), (217), (218),
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (219), (220), (221), (223), (224), (225), (227),
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (228), (229), (230), (231), (232), (233), (234),
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (235), (236), (237), (245), (246), (248), (249),
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (256), (259), (268), (269), (270), (277), (315),
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (332), (336), (348), (361), (363), (364), (366),
% 220.76/37.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (368), (374), (376), (3960), (3962), (3963),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3964), (3970), (3971), (3973), (3975), (3980),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3981), (3982), (3983), (3986), (3988), (4086),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4247), (function-axioms) are inconsistent by
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1373.
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4248)  all_57_10 = e1 & op(e2, e0) = e1
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (4083), (4248), (function-axioms) are
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2084.
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4249)  all_57_5 = e1 & op(e2, e1) = e1
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (45), (67),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (88), (94), (107), (111), (113), (119), (121),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (122), (124), (127), (129), (134), (135), (136),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (137), (142), (144), (158), (159), (161), (163),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (165), (166), (169), (170), (171), (191),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (192), (194), (195), (196), (199), (202), (203),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (204), (205), (207), (208), (209), (210), (211),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (213), (214), (215), (216), (217), (218),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (219), (220), (221), (223), (224), (225), (227),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (228), (229), (230), (231), (232), (233), (234),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (235), (236), (237), (245), (246), (248), (249),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (256), (259), (268), (269), (270), (277), (315),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (332), (336), (348), (361), (363), (364), (366),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (368), (374), (376), (3960), (3962), (3963),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3964), (3970), (3971), (3973), (3975), (3980),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3981), (3982), (3983), (3986), (3988), (4086),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4198), (4226), (4249), (function-axioms) are
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1353.
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4250)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e1)
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4250) gives:
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4251)  all_57_8 = e1 & op(e1, e1) = e1
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4251) implies:
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4252)  op(e1, e1) = e1
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4172), (4252), (function-axioms) are
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2423.
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4253)  all_57_14 = e1 & op(e0, e1) = e1
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4253) implies:
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4254)  all_57_14 = e1
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4255)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4255) gives:
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4256)  all_57_2 = e1 & op(e2, e3) = e1
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4256) implies:
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4257)  all_57_2 = e1
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4258)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e0)
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4258) gives:
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4259)  all_57_4 = e0 & op(e3, e1) = e0
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4259) implies:
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4260)  all_57_4 = e0
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4261)  op(e3, e1) = e0
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4262)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e0)
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3970), (3983), (4198), (4262), (function-axioms)
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1784.
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4263)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = e0)
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4263) gives:
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4264)  all_57_6 = e0 & op(e1, e3) = e0
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4264) implies:
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4265)  all_57_6 = e0
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4266)  op(e1, e3) = e0
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4267)  all_57_15 = e0 & op(e0, e0) = e0
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4267) implies:
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4268)  all_57_15 = e0
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4269)  op(e0, e0) = e0
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (39), (45), (67), (88), (94),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (107), (111), (113), (119), (121), (122), (124),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (127), (129), (134), (135), (136), (137), (142),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (144), (158), (159), (161), (163), (164), (165),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (166), (169), (170), (171), (191), (192), (194),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (195), (196), (199), (202), (203), (204), (205),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (207), (208), (209), (210), (211), (212), (213),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (214), (215), (216), (217), (218), (219), (220),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (221), (223), (224), (225), (227), (228), (229),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (231), (232), (233), (234), (235), (236),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (237), (245), (246), (248), (249), (256), (259),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (268), (269), (270), (277), (315), (332), (336),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (348), (361), (363), (364), (366), (368), (374),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (376), (3962), (3970), (3971), (3973), (3975),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3980), (3981), (3982), (3983), (3986), (4260),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4261), (4265), (4266), (4268), (4269),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1410.
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4270)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4270) implies:
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4271)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0)
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4272)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0)
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (45), (67),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (88), (94), (107), (121), (124), (134), (135),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (137), (159), (163), (165), (166), (169), (170),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (171), (195), (202), (203), (204), (205), (207),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (208), (209), (210), (211), (212), (213), (214),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (215), (216), (217), (218), (219), (220), (221),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (223), (224), (225), (227), (228), (229), (230),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (232), (233), (234), (235), (236), (237),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (249), (268), (269), (270), (277), (315), (332),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (336), (348), (363), (364), (374), (376), (3960),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3962), (3963), (3964), (3970), (3973), (3975),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3982), (3983), (4254), (4260), (4271), (4272),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1386.
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4273)  all_57_12 = e0 & op(e0, e3) = e0
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4229), (4273) are inconsistent by sub-proof
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2185.
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4274)  all_57_5 = e0 & op(e2, e1) = e0
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4274) implies:
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4275)  all_57_5 = e0
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3970), (3971), (4257), (4275), (function-axioms)
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2353.
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4276)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (171), (219),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (220), (231), (3960), (3983), (3988), (4086),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4175), (4178), (4198), (4276), (function-axioms)
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1354.
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4277)  all_57_3 = e1 & op(e2, e2) = e1
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4277) implies:
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4278)  op(e2, e2) = e1
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3971), (4278), (function-axioms) are
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2352.
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4279)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4279) gives:
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4280)  all_57_5 = e1 & op(e2, e1) = e1
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (45), (67),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (88), (94), (107), (111), (113), (119), (121),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (122), (124), (127), (129), (134), (135), (136),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (137), (142), (144), (158), (159), (161), (163),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (165), (166), (169), (170), (171), (191),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (192), (194), (195), (196), (199), (202), (203),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (204), (205), (207), (208), (209), (210), (211),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (213), (214), (215), (216), (217), (218),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (219), (220), (221), (223), (224), (225), (227),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (228), (229), (230), (231), (232), (233), (234),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (235), (236), (237), (245), (246), (248), (249),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (256), (259), (268), (269), (270), (277), (315),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (332), (336), (348), (361), (363), (364), (366),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (368), (374), (376), (3960), (3962), (3963),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3964), (3970), (3971), (3973), (3975), (3980),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3981), (3982), (3983), (3986), (3988), (4086),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4198), (4226), (4280), (function-axioms) are
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1353.
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4281)  all_57_10 = e1 & op(e2, e0) = e1
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (4083), (4281), (function-axioms) are
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2084.
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4282)  all_57_13 = e2 & op(e0, e2) = e2
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4282) implies:
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4283)  all_57_13 = e2
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (45), (67),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (88), (94), (107), (111), (113), (119), (121),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (122), (124), (127), (129), (134), (135), (136),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (137), (142), (144), (145), (158), (159), (160),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (161), (163), (164), (165), (166), (169), (170),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (171), (191), (192), (194), (195), (196), (197),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (199), (202), (203), (204), (205), (207), (208),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (209), (210), (211), (212), (213), (214), (215),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (216), (217), (218), (219), (220), (221), (223),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (225), (227), (228), (229), (230), (231),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (232), (233), (234), (235), (236), (237), (245),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (246), (248), (249), (256), (257), (259), (268),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (269), (270), (277), (315), (332), (336), (348),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (361), (363), (364), (366), (368), (374), (376),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3960), (3961), (3962), (3963), (3964), (3970),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3971), (3973), (3975), (3978), (3980), (3981),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3982), (3983), (3986), (3988), (4083), (4086),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4169), (4170), (4175), (4176), (4177), (4178),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4179), (4180), (4187), (4193), (4198), (4226),
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4283), (function-axioms) are inconsistent by
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1357.
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4284)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 220.76/37.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (45), (67),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (88), (94), (107), (111), (113), (119), (121),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (122), (124), (127), (129), (134), (135), (136),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (137), (142), (144), (158), (159), (161), (163),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (165), (166), (169), (170), (171), (191),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (192), (194), (195), (196), (199), (202), (203),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (204), (205), (207), (208), (209), (210), (211),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (213), (214), (215), (216), (217), (218),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (219), (220), (221), (223), (224), (225), (226),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (227), (228), (229), (230), (231), (232), (233),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (234), (235), (236), (237), (245), (246), (248),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (249), (256), (259), (268), (269), (270), (277),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (315), (332), (336), (348), (361), (363), (364),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (366), (368), (374), (376), (3960), (3962),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3963), (3964), (3970), (3971), (3973), (3975),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3980), (3981), (3982), (3983), (3986), (3988),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4083), (4086), (4095), (4172), (4175), (4177),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4178), (4180), (4220), (4284), (function-axioms)
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1347.
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4285)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4285) gives:
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4286)  all_57_14 = e3 & op(e0, e1) = e3
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (45), (67),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (88), (94), (107), (111), (113), (119), (121),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (122), (124), (127), (129), (134), (135), (136),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (137), (142), (144), (145), (158), (159), (160),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (161), (163), (164), (165), (166), (169), (170),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (171), (191), (192), (194), (195), (196), (197),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (199), (202), (203), (204), (205), (207), (208),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (209), (210), (211), (212), (213), (214), (215),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (216), (217), (218), (219), (220), (221), (223),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (225), (226), (227), (228), (229), (230),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (232), (233), (234), (235), (236), (237),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (245), (246), (248), (249), (256), (257), (259),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (268), (269), (270), (277), (315), (332), (336),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (348), (361), (363), (364), (366), (368), (374),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (376), (3960), (3961), (3962), (3963), (3964),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3970), (3971), (3973), (3975), (3978), (3980),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3981), (3982), (3983), (3986), (3988), (4083),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4086), (4095), (4169), (4170), (4172), (4175),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4176), (4177), (4178), (4179), (4180), (4187),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4193), (4286), (function-axioms) are inconsistent
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1338.
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4287)  all_57_15 = e3 & op(e0, e0) = e3
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4287) implies:
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4288)  all_57_15 = e3
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4289)  op(e0, e0) = e3
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (67), (88),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (94), (107), (121), (124), (134), (135), (137),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (163), (166), (169), (170), (171), (195), (202),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (203), (204), (207), (208), (209), (211), (212),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (214), (215), (216), (217), (218), (219), (220),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (223), (224), (227), (228), (230), (231), (232),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (234), (235), (237), (249), (268), (269),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (270), (315), (332), (336), (363), (364), (374),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3960), (3963), (3970), (3982), (3983), (4198),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4199), (4288), (4289), (function-axioms) are
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1438.
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4290)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e1) = e3)
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4290) gives:
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4291)  all_57_8 = e3 & op(e1, e1) = e3
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4291) implies:
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4292)  op(e1, e1) = e3
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (374), (4292), (function-axioms) are
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2468.
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4293)  all_57_14 = e3 & op(e0, e1) = e3
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (45), (67),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (88), (94), (107), (111), (113), (119), (121),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (122), (124), (127), (129), (134), (135), (136),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (137), (142), (144), (145), (158), (159), (160),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (161), (163), (164), (165), (166), (169), (170),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (171), (191), (192), (194), (195), (196), (197),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (199), (202), (203), (204), (205), (207), (208),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (209), (210), (211), (212), (213), (214), (215),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (216), (217), (218), (219), (220), (221), (223),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (225), (226), (227), (228), (229), (230),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (232), (233), (234), (235), (236), (237),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (245), (246), (248), (249), (256), (257), (259),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (268), (269), (270), (277), (315), (332), (336),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (348), (361), (363), (364), (366), (368), (374),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (376), (3960), (3961), (3962), (3963), (3964),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3970), (3971), (3973), (3975), (3978), (3980),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3981), (3982), (3983), (3986), (3988), (4083),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4086), (4095), (4169), (4170), (4172), (4175),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4176), (4177), (4178), (4179), (4180), (4187),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4193), (4293), (function-axioms) are inconsistent
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1338.
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | |   (4294)   ~ (all_55_13 = e3)
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | |   (4295)  all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (246), (4294) imply:
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | |   (4296)   ~ (all_53_7 = e3)
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | |   (4297)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4297) gives:
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | |   (4298)  all_57_12 = e3 & op(e0, e3) = e3
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4298) implies:
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | |   (4299)  all_57_12 = e3
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4300)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e0)
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | |            (3970), (3983), (4300), (function-axioms) are
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2229.
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4301)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = e0)
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4301) gives:
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4302)  all_57_6 = e0 & op(e1, e3) = e0
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4302) implies:
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4303)  op(e1, e3) = e0
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (141), (145), (164), (193), (246), (247), (3962),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3979), (4081), (4082), (4295), (4303),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1335.
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4304)  all_57_12 = e0 & op(e0, e3) = e0
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4299), (4304) are inconsistent by sub-proof
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2237.
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | |   (4305)  all_57_13 = e3 & op(e0, e2) = e3
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4305) implies:
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | |   (4306)  all_57_13 = e3
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4307)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4307) gives:
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4308)  all_57_12 = e2 & op(e0, e3) = e2
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4308) implies:
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4309)  all_57_12 = e2
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4310)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e0)
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3970), (3983), (4310), (function-axioms) are
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2229.
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4311)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = e0)
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4311) gives:
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4312)  all_57_6 = e0 & op(e1, e3) = e0
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4312) implies:
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4313)  op(e1, e3) = e0
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (141), (145), (164), (193), (246), (247), (3962),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3979), (4081), (4082), (4295), (4313),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1335.
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4314)  all_57_12 = e0 & op(e0, e3) = e0
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4309), (4314) are inconsistent by sub-proof
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2185.
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4315)  all_57_13 = e2 & op(e0, e2) = e2
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4306), (4315) are inconsistent by sub-proof
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2146.
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4316)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (45), (67),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | |            (88), (94), (107), (111), (113), (119), (121),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | |            (122), (124), (127), (129), (134), (135), (136),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | |            (137), (142), (144), (158), (159), (161), (163),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (165), (166), (169), (170), (171), (191),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | |            (192), (194), (195), (196), (199), (202), (203),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | |            (204), (205), (207), (208), (209), (210), (211),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (213), (214), (215), (216), (217), (218),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | |            (219), (220), (221), (223), (224), (225), (226),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | |            (227), (228), (229), (230), (231), (232), (233),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | |            (234), (235), (236), (237), (245), (246), (248),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | |            (249), (256), (259), (268), (269), (270), (277),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | |            (315), (332), (336), (348), (361), (363), (364),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | |            (366), (368), (374), (376), (3960), (3962),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | |            (3963), (3964), (3970), (3971), (3973), (3975),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | |            (3980), (3981), (3982), (3983), (3986), (3988),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | |            (4083), (4086), (4095), (4172), (4175), (4177),
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | |            (4178), (4180), (4306), (4316), (function-axioms)
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1347.
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.36  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | |   (4317)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4317) gives:
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | |   (4318)  all_57_14 = e3 & op(e0, e1) = e3
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4318) implies:
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | |   (4319)  all_57_14 = e3
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4320)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e0)
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4320) gives:
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4321)  all_57_4 = e0 & op(e3, e1) = e0
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4321) implies:
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4322)  all_57_4 = e0
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4323)  op(e3, e1) = e0
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4324)  all_57_15 = e0 & op(e0, e0) = e0
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4324) implies:
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4325)  op(e0, e0) = e0
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4176), (4179), (4323), (4325),
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2167.
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4326)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4326) implies:
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4327)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0)
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4328)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0)
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4327) gives:
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4329)  all_57_12 = e0 & op(e0, e3) = e0
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4329) implies:
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4330)  all_57_12 = e0
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4331)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e1)
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4331) gives:
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4332)  all_57_0 = e1 & op(e3, e3) = e1
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4332) implies:
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4333)  op(e3, e3) = e1
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (3983), (4333), (function-axioms) are
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2495.
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4334)  all_57_1 = e1 & op(e3, e2) = e1
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4334) implies:
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4335)  all_57_1 = e1
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4336)  op(e3, e2) = e1
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4337)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e2)
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (3971), (4177), (4180), (4335), (4337),
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1342.
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4338)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e2)
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4338) gives:
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4339)  all_57_4 = e2 & op(e3, e1) = e2
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (165), (171),
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (218), (219), (220), (221), (223), (224), (225),
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (233), (235), (374), (3960), (3970),
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3971), (3983), (3988), (4083), (4086), (4175),
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4178), (4339), (function-axioms) are inconsistent
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1361.
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4340)  all_57_9 = e2 & op(e3, e0) = e2
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4340) implies:
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4341)  all_57_9 = e2
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4342)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4342) gives:
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4343)  all_57_1 = e3 & op(e3, e2) = e3
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4343) implies:
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4344)  all_57_1 = e3
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4335), (4344) imply:
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4345)  e3 = e1
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4345) implies:
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4346)  e3 = e1
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4319), (4346) imply:
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4347)  all_57_14 = e1
% 220.76/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (45), (67),
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (88), (94), (107), (121), (124), (134), (135),
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (137), (163), (165), (166), (169), (170), (171),
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (195), (202), (203), (204), (205), (207), (208),
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (209), (210), (211), (212), (213), (214), (215),
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (216), (217), (218), (219), (220), (221), (223),
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (225), (227), (228), (229), (230), (231),
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (232), (233), (234), (235), (236), (237), (249),
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (268), (269), (270), (277), (315), (332), (336),
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (348), (363), (364), (374), (376), (3960), (3963),
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3964), (3970), (3973), (3975), (3982), (3983),
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4322), (4328), (4330), (4347), (function-axioms)
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1387.
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4348)  all_57_3 = e3 & op(e2, e2) = e3
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4348) implies:
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4349)  all_57_3 = e3
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3970), (4349) imply:
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4350)  e3 = e0
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4319), (4350) imply:
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4351)  all_57_14 = e0
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (219), (220),
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (221), (374), (4322), (4351), (function-axioms)
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2371.
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4352)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4352) gives:
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4353)  all_57_7 = e3 & op(e1, e2) = e3
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4353) implies:
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4354)  all_57_7 = e3
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4295) gives:
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4355)  all_55_13 = e2
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (4355) imply:
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4356)  all_53_7 = e2
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4356) implies:
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4357)  all_53_7 = e2
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (141), (4357) imply:
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4358)   ~ (all_53_3 = e2)
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4359)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e1)
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4359) gives:
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4360)  all_57_4 = e1 & op(e3, e1) = e1
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4360) implies:
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4361)  all_57_4 = e1
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4322), (4361) imply:
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4362)  e1 = e0
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4362) implies:
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4363)  e1 = e0
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4335), (4363) imply:
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4364)  all_57_1 = e0
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (233), (3983), (4322), (4341),
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4364), (function-axioms) are inconsistent by
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2219.
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4365)  all_57_5 = e1 & op(e2, e1) = e1
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4365) implies:
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4366)  all_57_5 = e1
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4367)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4367) gives:
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4368)  all_57_2 = e3 & op(e2, e3) = e3
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4368) implies:
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4369)  all_57_2 = e3
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4370)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e0)
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4370) gives:
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4371)  all_57_6 = e0 & op(e1, e3) = e0
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4371) implies:
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4372)  all_57_6 = e0
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (45), (67),
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (88), (94), (107), (111), (113), (119), (121),
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (122), (124), (127), (129), (134), (135), (136),
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (137), (142), (144), (158), (159), (161), (163),
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (165), (166), (169), (170), (171), (191),
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (192), (194), (195), (196), (199), (202), (203),
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (204), (205), (207), (208), (209), (210), (211),
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (213), (214), (215), (216), (217), (218),
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (219), (220), (221), (223), (224), (225), (227),
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (228), (229), (230), (231), (232), (233), (234),
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (235), (236), (237), (245), (246), (248), (249),
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (256), (259), (268), (269), (270), (277), (315),
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (332), (336), (348), (361), (363), (364), (366),
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (368), (374), (376), (3960), (3962), (3963),
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3964), (3970), (3971), (3973), (3975), (3980),
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3981), (3982), (3983), (3986), (3988), (4086),
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4172), (4322), (4335), (4341), (4354), (4372),
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1341.
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4373)  all_57_7 = e0 & op(e1, e2) = e0
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4373) implies:
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4374)  all_57_7 = e0
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (227), (228), (229),
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3970), (3971), (4335), (4374), (function-axioms)
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1378.
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4375)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4375) gives:
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4376)  all_57_8 = e0 & op(e1, e1) = e0
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (3988), (4376), (function-axioms) are
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2412.
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4377)  all_57_11 = e0 & op(e1, e0) = e0
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4377) implies:
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4378)  all_57_11 = e0
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (169), (207),
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (208), (209), (213), (221), (222), (223), (224),
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (225), (226), (228), (231), (233), (235), (374),
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3970), (3982), (3983), (4354), (4369), (4378),
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1329.
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4379)  all_57_3 = e3 & op(e2, e2) = e3
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4379) implies:
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4380)  all_57_3 = e3
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3970), (4380) imply:
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4381)  e3 = e0
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4381) implies:
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4382)  e3 = e0
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4354), (4382) imply:
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4383)  all_57_7 = e0
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (227), (228), (229),
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3970), (3971), (4335), (4383), (function-axioms)
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1378.
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4384)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4384) gives:
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4385)  all_57_5 = e3 & op(e2, e1) = e3
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4385) implies:
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4386)  all_57_5 = e3
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4366), (4386) imply:
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4387)  e3 = e1
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4387) implies:
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4388)  e3 = e1
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4319), (4388) imply:
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4389)  all_57_14 = e1
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (8), (9), (160), (209), (210), (4086),
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4330), (4358), (4389), (function-axioms) are
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1964.
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4390)  all_57_10 = e3 & op(e2, e0) = e3
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4390) implies:
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4391)  op(e2, e0) = e3
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3957) gives:
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4392)   ~ (all_14_0 = e1) & op(all_14_1, e2) = all_14_0 &
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_14_1 & $i(all_14_0) &
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_14_1)
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4392) implies:
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4393)   ~ (all_14_0 = e1)
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4394)  op(e2, e0) = all_14_1
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4395)  op(all_14_1, e2) = all_14_0
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4183) gives:
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4396)   ~ (all_50_0 = e3) & op(all_50_1, e2) = all_50_0 &
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_50_1 & $i(all_50_0) &
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_50_1)
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4396) implies:
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4397)  op(e2, e0) = all_50_1
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4336), (4391), (4393), (4394), (4395), (4397),
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1328.
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4398)   ~ (all_50_1 = e1) & op(e2, e0) = all_50_1 &
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_50_1)
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4398) implies:
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4399)  op(e2, e0) = all_50_1
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4336), (4391), (4393), (4394), (4395), (4399),
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1328.
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4400)   ~ (all_14_1 = e3) & op(e2, e0) = all_14_1 &
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_14_1)
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4183), (4391), (4400), (function-axioms) are
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1326.
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4401)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e1)
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4401) gives:
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4402)  all_57_8 = e1 & op(e1, e1) = e1
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4402) implies:
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4403)  op(e1, e1) = e1
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4172), (4403), (function-axioms) are
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2423.
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4404)  all_57_14 = e1 & op(e0, e1) = e1
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4404) implies:
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4405)  all_57_14 = e1
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (8), (9), (160), (209), (210), (4086),
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4330), (4358), (4405), (function-axioms) are
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1964.
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4406)  all_55_13 = e1 | all_55_13 = e0
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (3962), (4082), (4406) are inconsistent by
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1837.
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4407)  all_57_13 = e3 & op(e0, e2) = e3
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (45), (67),
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (88), (94), (107), (111), (113), (119), (121),
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (122), (124), (127), (129), (134), (135), (136),
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (137), (142), (144), (158), (159), (161), (163),
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (165), (166), (169), (170), (171), (191),
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (192), (194), (195), (196), (199), (202), (203),
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (204), (205), (207), (208), (209), (210), (211),
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (213), (214), (215), (216), (217), (218),
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (219), (220), (221), (223), (224), (225), (226),
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (227), (228), (229), (230), (231), (232), (233),
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (234), (235), (236), (237), (245), (246), (248),
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (249), (256), (259), (268), (269), (270), (277),
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (315), (332), (336), (348), (361), (363), (364),
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (366), (368), (374), (376), (3960), (3962),
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3963), (3964), (3970), (3971), (3973), (3975),
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3980), (3981), (3982), (3983), (3986), (3988),
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4083), (4086), (4095), (4172), (4175), (4177),
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4178), (4180), (4319), (4407), (function-axioms)
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1339.
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4408)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e1)
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4408) gives:
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4409)  all_57_4 = e1 & op(e3, e1) = e1
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4322), (4409) are inconsistent by sub-proof
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1411.
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4410)  all_57_9 = e1 & op(e3, e0) = e1
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4410) implies:
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4411)  all_57_9 = e1
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (45), (67),
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (88), (94), (107), (111), (113), (119), (121),
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (122), (124), (127), (129), (134), (135), (136),
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (137), (142), (144), (158), (159), (161), (163),
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (165), (166), (169), (170), (171), (191),
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (192), (194), (195), (196), (199), (202), (203),
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (204), (205), (207), (208), (209), (210), (211),
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (213), (214), (215), (216), (217), (218),
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (219), (220), (221), (223), (224), (225), (227),
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (228), (229), (230), (231), (232), (233), (234),
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (235), (236), (237), (245), (246), (248), (249),
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (256), (259), (268), (269), (270), (277), (315),
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (332), (336), (348), (361), (363), (364), (366),
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (368), (374), (376), (3960), (3962), (3963),
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3964), (3970), (3971), (3973), (3975), (3980),
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3981), (3982), (3983), (3986), (4086), (4322),
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4323), (4411), (function-axioms) are inconsistent
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1385.
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4412)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (159), (219),
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (220), (221), (374), (3962), (4322), (4412),
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1399.
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4413)  all_57_5 = e0 & op(e2, e1) = e0
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4413) implies:
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4414)  all_57_5 = e0
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (223), (224),
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (225), (3970), (3971), (4083), (4414),
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1689.
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4415)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (171), (219),
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | |            (220), (221), (231), (233), (235), (374), (3960),
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | |            (3983), (3988), (4086), (4175), (4178), (4415),
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | |            #1366.
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | |   (4416)  all_57_15 = e3 & op(e0, e0) = e3
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4416) implies:
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | |   (4417)  all_57_15 = e3
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | |   (4418)  op(e0, e0) = e3
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (39), (45), (67), (88), (94),
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | |            (107), (121), (124), (134), (135), (137), (163),
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | |            (166), (169), (170), (171), (195), (202), (203),
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | |            (204), (205), (207), (208), (209), (211), (212),
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | |            (214), (215), (216), (217), (218), (219), (220),
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | |            (221), (223), (224), (225), (227), (228), (229),
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (231), (232), (233), (234), (235), (236),
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | |            (237), (249), (268), (269), (270), (277), (315),
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | |            (332), (336), (348), (363), (364), (374), (376),
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | |            (3960), (3963), (3970), (3973), (3975), (4417),
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | |            (4418), (function-axioms) are inconsistent by
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1414.
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | |   (4419)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | |           all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | |           op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | |             all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | |           & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | |           $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | |           $i(all_52_15)
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3971), (4086), (4419), (function-axioms) are
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1372.
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | |   (4420)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | |             & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | |             & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | |               all_52_21) = e1 & op(all_52_23, all_52_23) =
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | |             all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | |             = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | |             $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | |             & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | |             e0 & op(all_52_25, all_52_25) = e3 &
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | |             op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | |               all_52_29) = e1 & op(all_52_31, all_52_31) =
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | |             all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | |             = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | |             $i(all_52_29) & $i(all_52_31))
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | BETA: splitting (4420) gives:
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | |   (4421)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | |           all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | |           op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | |             all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | |           & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | |           & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | |           & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | |           $i(all_52_23)
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | ALPHA: (4421) implies:
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | |   (4422)  op(e1, e1) = all_52_21
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | |   (4423)  op(all_52_21, all_52_21) = e1
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | |   (4424)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e2)
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4424) gives:
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | |   (4425)  all_57_4 = e2 & op(e3, e1) = e2
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4425) implies:
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | |   (4426)  all_57_4 = e2
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | |   (4427)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e1)
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4427) gives:
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | |   (4428)  all_57_0 = e1 & op(e3, e3) = e1
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4428) implies:
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | |   (4429)  op(e3, e3) = e1
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (3983), (4429), (function-axioms) are
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2495.
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | |   (4430)  all_57_1 = e1 & op(e3, e2) = e1
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4430) implies:
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | |   (4431)  all_57_1 = e1
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4432)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e0)
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (223), (224),
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | |            (225), (3970), (3971), (4083), (4426), (4432),
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | |            #1362.
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4433)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4433) gives:
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4434)  all_57_8 = e0 & op(e1, e1) = e0
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (3988), (4434), (function-axioms) are
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2412.
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4435)  all_57_14 = e0 & op(e0, e1) = e0
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4435) implies:
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4436)  all_57_14 = e0
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4437)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e3)
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4437) gives:
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4438)  all_57_4 = e3 & op(e3, e1) = e3
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4438) implies:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4439)  all_57_4 = e3
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (235),
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3983), (4439), (function-axioms) are inconsistent
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2474.
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4440)  all_57_5 = e3 & op(e2, e1) = e3
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4440) implies:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4441)  all_57_5 = e3
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4442)  op(e2, e1) = e3
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4443)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4443) gives:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4444)  all_57_12 = e3 & op(e0, e3) = e3
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4444) implies:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4445)  all_57_12 = e3
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (232), (234), (3970), (3983), (4445),
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2223.
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4446)  all_57_13 = e3 & op(e0, e2) = e3
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4446) implies:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4447)  all_57_13 = e3
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4448)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4448) gives:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4449)  all_57_12 = e2 & op(e0, e3) = e2
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4449) implies:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4450)  all_57_12 = e2
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4451)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (3971), (4431), (4451),
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2208.
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4452)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4452) gives:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4453)  all_57_7 = e2 & op(e1, e2) = e2
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4453) implies:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4454)  all_57_7 = e2
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4455)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (171), (3960), (3983), (4455),
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1543.
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4456)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4456) gives:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4457)  all_57_4 = e0 & op(e3, e1) = e0
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4457) implies:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4458)  all_57_4 = e0
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (219), (220), (4436),
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4441), (4458), (function-axioms) are inconsistent
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2378.
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4459)  all_57_9 = e0 & op(e3, e0) = e0
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4459) implies:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4460)  all_57_9 = e0
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4461)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e0)
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224),
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3970), (3983), (4441), (4461), (function-axioms)
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1784.
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4462)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = e0)
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4462) gives:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4463)  all_57_6 = e0 & op(e1, e3) = e0
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4463) implies:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4464)  all_57_6 = e0
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4465)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e1)
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4465) gives:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4466)  all_57_0 = e1 & op(e3, e3) = e1
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4466) implies:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4467)  op(e3, e3) = e1
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (3983), (4467), (function-axioms) are
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2495.
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4468)  all_57_2 = e1 & op(e2, e3) = e1
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4468) implies:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4469)  all_57_2 = e1
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4470)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4470) gives:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4471)  all_57_6 = e1 & op(e1, e3) = e1
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4471) implies:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4472)  all_57_6 = e1
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4464), (4472) imply:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4473)  e1 = e0
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4469), (4473) imply:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4474)  all_57_2 = e0
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (223), (224), (3970),
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4441), (4474) are inconsistent by sub-proof
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2253.
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4475)  all_57_7 = e1 & op(e1, e2) = e1
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4454), (4475) are inconsistent by sub-proof
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2190.
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4476)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (212), (213), (4086),
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4172), (4460), (4476), (function-axioms) are
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2043.
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4477)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e3) = e1)
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4477) gives:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4478)  all_57_6 = e1 & op(e1, e3) = e1
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4464), (4478) are inconsistent by sub-proof
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2044.
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4479)  all_57_12 = e1 & op(e0, e3) = e1
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4479) implies:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4480)  all_57_12 = e1
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4450), (4480) are inconsistent by sub-proof
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2321.
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4481)  all_57_12 = e0 & op(e0, e3) = e0
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4481) implies:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4482)  all_57_12 = e0
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4450), (4482) imply:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4483)  e2 = e0
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4426), (4483) imply:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4484)  all_57_4 = e0
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (233), (235), (3983),
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4460), (4484), (function-axioms) are inconsistent
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2436.
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4485)  all_57_13 = e2 & op(e0, e2) = e2
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (39), (45),
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (67), (88), (94), (107), (111), (113), (114),
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (118), (119), (121), (122), (124), (126), (129),
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (134), (135), (136), (137), (140), (141), (159),
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (160), (161), (163), (165), (166), (169), (170),
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (171), (190), (191), (192), (194), (195), (196),
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (198), (199), (202), (203), (204), (205), (207),
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (208), (209), (210), (211), (212), (213), (214),
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (215), (216), (217), (218), (219), (220), (221),
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (223), (224), (225), (227), (228), (229), (230),
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (232), (233), (234), (235), (236), (237),
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (244), (245), (246), (248), (249), (256), (258),
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (259), (268), (269), (270), (277), (315), (332),
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (336), (348), (362), (363), (364), (369), (370),
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (371), (372), (373), (374), (376), (378), (3960),
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3961), (3962), (3963), (3970), (3971), (3973),
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3975), (3980), (3981), (3982), (3983), (3986),
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4083), (4095), (4172), (4441), (4447), (4485),
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1299.
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4486)  all_57_13 = e2 & op(e0, e2) = e2
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (39), (45),
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (67), (88), (94), (107), (111), (113), (114),
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (118), (119), (121), (122), (124), (126), (129),
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (134), (135), (136), (137), (140), (141), (159),
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (160), (161), (163), (165), (166), (169), (170),
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (171), (190), (191), (192), (194), (195), (196),
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (198), (199), (202), (203), (204), (205), (207),
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (208), (209), (210), (211), (212), (213), (214),
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (215), (216), (217), (218), (219), (220), (221),
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (223), (224), (225), (227), (228), (229), (230),
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (232), (233), (234), (235), (236), (237),
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (244), (245), (246), (248), (249), (256), (258),
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (259), (268), (269), (270), (277), (315), (332),
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (336), (348), (362), (363), (364), (369), (370),
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (371), (372), (373), (374), (376), (378), (3960),
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3961), (3962), (3963), (3970), (3971), (3973),
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3975), (3980), (3981), (3982), (3983), (3986),
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4083), (4095), (4172), (4441), (4447), (4486),
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1299.
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4487)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4487) gives:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4488)  all_57_14 = e2 & op(e0, e1) = e2
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4488) implies:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4489)  all_57_14 = e2
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (45), (67),
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (88), (94), (107), (111), (113), (119), (121),
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (122), (124), (127), (129), (134), (135), (136),
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (137), (142), (144), (158), (159), (161), (163),
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (165), (166), (169), (170), (171), (191),
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (192), (194), (195), (196), (199), (202), (203),
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (204), (205), (207), (208), (209), (210), (211),
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (213), (214), (215), (216), (217), (218),
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (219), (220), (221), (223), (224), (225), (226),
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (227), (228), (229), (230), (231), (232), (233),
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (234), (235), (236), (237), (245), (246), (248),
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (249), (256), (259), (268), (269), (270), (277),
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (315), (332), (336), (348), (361), (363), (364),
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (366), (368), (374), (376), (3960), (3962),
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3963), (3964), (3970), (3971), (3973), (3975),
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3980), (3981), (3982), (3983), (3986), (3988),
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4083), (4086), (4095), (4172), (4447), (4489),
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1298.
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4490)  all_57_15 = e2 & op(e0, e0) = e2
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4490) implies:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4491)  op(e0, e0) = e2
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4086), (4491), (function-axioms) are
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2177.
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4492)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4492) gives:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4493)  all_57_14 = e3 & op(e0, e1) = e3
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4493) implies:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4494)  all_57_14 = e3
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4436), (4494) imply:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4495)  e3 = e0
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4495) implies:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4496)  e3 = e0
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4441), (4496) imply:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4497)  all_57_5 = e0
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (223), (224),
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (225), (3970), (3971), (4083), (4497),
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1689.
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4498)  all_57_15 = e3 & op(e0, e0) = e3
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4498) implies:
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4499)  all_57_15 = e3
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4500)  op(e0, e0) = e3
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (67), (88),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (94), (107), (121), (124), (134), (135), (137),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (163), (166), (169), (170), (171), (195), (202),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (203), (204), (207), (208), (209), (211), (212),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (214), (215), (216), (217), (218), (219), (220),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (223), (224), (227), (228), (230), (231), (232),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (234), (235), (237), (249), (268), (269),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (270), (315), (332), (336), (363), (364), (374),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3960), (3963), (3970), (3982), (3983), (4441),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4442), (4499), (4500), (function-axioms) are
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1438.
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4501)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e1) = e3)
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (39), (374), (4436), (4501),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2419.
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | |   (4502)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e1)
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4502) gives:
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | |   (4503)  all_57_4 = e1 & op(e3, e1) = e1
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4426), (4503) are inconsistent by sub-proof
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | |            #2452.
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | |   (4504)  all_57_9 = e1 & op(e3, e0) = e1
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4504) implies:
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | |   (4505)  all_57_9 = e1
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (45), (67),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | |            (88), (94), (107), (111), (113), (119), (121),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | |            (122), (124), (127), (129), (134), (135), (136),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | |            (137), (142), (144), (158), (159), (161), (163),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (165), (166), (169), (170), (171), (191),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | |            (192), (194), (195), (196), (199), (202), (203),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | |            (204), (205), (207), (208), (209), (210), (211),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (213), (214), (215), (216), (217), (218),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | |            (219), (220), (221), (223), (224), (225), (227),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | |            (228), (229), (230), (231), (232), (233), (234),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | |            (235), (236), (237), (245), (246), (248), (249),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | |            (256), (259), (268), (269), (270), (277), (315),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | |            (332), (336), (348), (361), (363), (364), (366),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | |            (368), (374), (376), (3960), (3962), (3963),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | |            (3964), (3970), (3971), (3973), (3975), (3980),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | |            (3981), (3982), (3983), (3986), (4086), (4505),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | |            #1384.
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | |   (4506)  all_57_5 = e2 & op(e2, e1) = e2
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4506) implies:
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | |   (4507)  all_57_5 = e2
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (39), (45),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | |            (67), (88), (94), (107), (111), (113), (114),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | |            (118), (119), (121), (122), (124), (126), (129),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | |            (134), (135), (136), (137), (140), (141), (159),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | |            (160), (161), (163), (165), (166), (169), (170),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | |            (171), (190), (191), (192), (194), (195), (196),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | |            (198), (199), (202), (203), (204), (205), (207),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | |            (208), (209), (210), (211), (212), (213), (214),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | |            (215), (216), (217), (218), (219), (220), (221),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | |            (223), (224), (225), (227), (228), (229), (230),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | |            (231), (232), (233), (234), (235), (236), (237),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | |            (244), (245), (246), (248), (249), (256), (258),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | |            (259), (268), (269), (270), (277), (315), (332),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | |            (336), (348), (362), (363), (364), (369), (370),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | |            (371), (372), (373), (374), (376), (378), (3960),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | |            (3961), (3962), (3963), (3970), (3971), (3973),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | |            (3975), (3980), (3981), (3982), (3983), (3986),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | |            (4083), (4095), (4172), (4507), (function-axioms)
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1300.
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | |   (4508)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e1) = e2)
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4508) gives:
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | |   (4509)  all_57_8 = e2 & op(e1, e1) = e2
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | |              all_52_21, e1, e1, simplifying with (4172), (4422)
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | |   (4510)  all_52_21 = e2
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4423), (4510) imply:
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | |   (4511)  op(e2, e2) = e1
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3971), (4511), (function-axioms) are
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2352.
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | |   (4512)  all_57_14 = e2 & op(e0, e1) = e2
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4512) implies:
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | |   (4513)  all_57_14 = e2
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | |   (4514)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4514) gives:
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | |   (4515)  all_57_12 = e3 & op(e0, e3) = e3
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4515) implies:
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | |   (4516)  all_57_12 = e3
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (232), (234), (3970), (3983), (4516),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | |            #2223.
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | |   (4517)  all_57_13 = e3 & op(e0, e2) = e3
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4517) implies:
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | |   (4518)  all_57_13 = e3
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (45), (67),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | |            (88), (94), (107), (111), (113), (119), (121),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | |            (122), (124), (127), (129), (134), (135), (136),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | |            (137), (142), (144), (158), (159), (161), (163),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (165), (166), (169), (170), (171), (191),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | |            (192), (194), (195), (196), (199), (202), (203),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | |            (204), (205), (207), (208), (209), (210), (211),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (213), (214), (215), (216), (217), (218),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | |            (219), (220), (221), (223), (224), (225), (226),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | |            (227), (228), (229), (230), (231), (232), (233),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | |            (234), (235), (236), (237), (245), (246), (248),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | |            (249), (256), (259), (268), (269), (270), (277),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | |            (315), (332), (336), (348), (361), (363), (364),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | |            (366), (368), (374), (376), (3960), (3962),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | |            (3963), (3964), (3970), (3971), (3973), (3975),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | |            (3980), (3981), (3982), (3983), (3986), (3988),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | |            (4083), (4086), (4095), (4172), (4513), (4518),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | |            #1298.
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | |   (4519)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (9), (39), (45), (67), (88), (94),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | |            (107), (121), (124), (134), (135), (137), (163),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | |            (166), (169), (170), (171), (195), (202), (203),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | |            (204), (205), (207), (208), (209), (211), (212),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | |            (214), (215), (216), (217), (218), (219), (220),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | |            (221), (223), (224), (225), (227), (228), (229),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | |            (230), (231), (232), (233), (234), (235), (236),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | |            (237), (249), (268), (269), (270), (277), (315),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | |            (332), (336), (348), (363), (364), (374), (376),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | |            (3960), (3963), (3970), (3973), (3975), (4513),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | |            (4519), (function-axioms) are inconsistent by
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1413.
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | |   (4520)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | |           all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | |           op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | |             all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | |           & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | |           & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | |           & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | |           $i(all_52_31)
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | ALPHA: (4520) implies:
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | |   (4521)  op(e0, e0) = all_52_31
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | |   (4522)  op(all_52_31, all_52_31) = e0
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (3988), (4086), (4521), (4522),
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | |            #2086.
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.40  | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | End of split
% 221.08/37.40  | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | End of split
% 221.08/37.40  | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | End of split
% 221.08/37.40  | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | Case 2:
% 221.08/37.40  | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | |   (4523)  all_24_2 = e0
% 221.08/37.40  | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | COMBINE_EQS: (315), (4523) imply:
% 221.08/37.40  | | | | | | | | | | | | | | |   (4524)  all_6_2 = e0
% 221.08/37.40  | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | REDUCE: (350), (4524) imply:
% 221.08/37.40  | | | | | | | | | | | | | | |   (4525)   ~ (all_53_2 = e0)
% 221.08/37.40  | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | REDUCE: (363), (4524) imply:
% 221.08/37.40  | | | | | | | | | | | | | | |   (4526)   ~ (all_53_8 = e0)
% 221.08/37.40  | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | REDUCE: (39), (4524) imply:
% 221.08/37.40  | | | | | | | | | | | | | | |   (4527)  op(e1, e1) = e0
% 221.08/37.40  | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 221.08/37.40  | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | Case 1:
% 221.08/37.40  | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | |   (4528)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 221.08/37.40  | | | | | | | | | | | | | | | |             & op(e1, e2) = e0)
% 221.08/37.40  | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | BETA: splitting (4528) gives:
% 221.08/37.40  | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.40  | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | |   (4529)  all_57_6 = e0 & op(e1, e3) = e0
% 221.08/37.40  | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | ALPHA: (4529) implies:
% 221.08/37.40  | | | | | | | | | | | | | | | | |   (4530)  op(e1, e3) = e0
% 221.08/37.40  | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (4525), (4530), (function-axioms) are
% 221.08/37.40  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2154.
% 221.08/37.40  | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.40  | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | |   (4531)  all_57_7 = e0 & op(e1, e2) = e0
% 221.08/37.40  | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | ALPHA: (4531) implies:
% 221.08/37.40  | | | | | | | | | | | | | | | | |   (4532)  all_57_7 = e0
% 221.08/37.40  | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 221.08/37.40  | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.40  | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | |   (4533)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 221.08/37.40  | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e0)
% 221.08/37.40  | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 221.08/37.40  | | | | | | | | | | | | | | | | | |            (3970), (3983), (4533), (function-axioms) are
% 221.08/37.40  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2229.
% 221.08/37.40  | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.40  | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | |   (4534)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 221.08/37.40  | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = e0)
% 221.08/37.40  | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | BETA: splitting (4534) gives:
% 221.08/37.40  | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | |   (4535)  all_57_6 = e0 & op(e1, e3) = e0
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | ALPHA: (4535) implies:
% 221.08/37.40  | | | | | | | | | | | | | | | | | | |   (4536)  op(e1, e3) = e0
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (4525), (4536), (function-axioms) are
% 221.08/37.40  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2154.
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | |   (4537)  all_57_12 = e0 & op(e0, e3) = e0
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | ALPHA: (4537) implies:
% 221.08/37.40  | | | | | | | | | | | | | | | | | | |   (4538)  all_57_12 = e0
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | |   (4539)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | BETA: splitting (4539) gives:
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.40  | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | |   (4540)  all_57_6 = e3 & op(e1, e3) = e3
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | ALPHA: (4540) implies:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | |   (4541)  all_57_6 = e3
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (232), (234), (3986),
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | |            (4538), (4541) are inconsistent by sub-proof
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | |            #2011.
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | |   (4542)  all_57_7 = e3 & op(e1, e2) = e3
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | ALPHA: (4542) implies:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | |   (4543)  all_57_7 = e3
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4532), (4543) are inconsistent by sub-proof
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | |            #2269.
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | |   (4544)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | BETA: splitting (4544) gives:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | |   (4545)  all_57_8 = e3 & op(e1, e1) = e3
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | ALPHA: (4545) implies:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | |   (4546)  op(e1, e1) = e3
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (374), (4546), (function-axioms) are
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2468.
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | |   (4547)  all_57_11 = e3 & op(e1, e0) = e3
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | ALPHA: (4547) implies:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | |   (4548)  all_57_11 = e3
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | |   (4549)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (171), (3960), (3983), (4549),
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | |            #1543.
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | |   (4550)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4550) gives:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | |   (4551)  all_57_4 = e0 & op(e3, e1) = e0
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4551) implies:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | |   (4552)  op(e3, e1) = e0
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (4526), (4552), (function-axioms) are
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2267.
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | |   (4553)  all_57_9 = e0 & op(e3, e0) = e0
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4553) implies:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | |   (4554)  all_57_9 = e0
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | |   (4555)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4555) gives:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | |   (4556)  all_57_1 = e3 & op(e3, e2) = e3
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4556) implies:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | |   (4557)  all_57_1 = e3
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4558)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e2)
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4558) gives:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4559)  all_57_0 = e2 & op(e3, e3) = e2
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4559) implies:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4560)  op(e3, e3) = e2
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (227), (228), (229),
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (233), (237), (3970), (3971), (4532),
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4560), (function-axioms) are inconsistent by
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1296.
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4561)  all_57_1 = e2 & op(e3, e2) = e2
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4561) implies:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4562)  all_57_1 = e2
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4557), (4562) imply:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4563)  e3 = e2
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4548), (4563) imply:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4564)  all_57_11 = e2
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (39), (215), (217),
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (374), (4527), (4532), (4564), (function-axioms)
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1314.
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4565)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e2)
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4565) gives:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4566)  all_57_4 = e2 & op(e3, e1) = e2
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4566) implies:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4567)  all_57_4 = e2
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4568)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e1)
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4568) gives:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4569)  all_57_0 = e1 & op(e3, e3) = e1
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4569) implies:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4570)  op(e3, e3) = e1
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (3983), (4570), (function-axioms) are
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2495.
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4571)  all_57_1 = e1 & op(e3, e2) = e1
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4571) implies:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4572)  all_57_1 = e1
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (227), (228), (229),
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3970), (3971), (4532), (4572), (function-axioms)
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1378.
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4573)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e1)
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4573) gives:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4574)  all_57_4 = e1 & op(e3, e1) = e1
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4567), (4574) are inconsistent by sub-proof
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2452.
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4575)  all_57_9 = e1 & op(e3, e0) = e1
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4554), (4575) are inconsistent by sub-proof
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2437.
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4576)  all_57_9 = e2 & op(e3, e0) = e2
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4554), (4576) are inconsistent by sub-proof
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2486.
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | |   (4577)  all_57_3 = e3 & op(e2, e2) = e3
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4577) implies:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | |   (4578)  all_57_3 = e3
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3970), (4578) imply:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | |   (4579)  e3 = e0
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4579) implies:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | |   (4580)  e3 = e0
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4548), (4580) imply:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | |   (4581)  all_57_11 = e0
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (45), (67),
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | |            (88), (94), (107), (121), (124), (134), (135),
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | |            (137), (163), (166), (169), (170), (171), (195),
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | |            (202), (203), (204), (205), (207), (208), (209),
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | |            (210), (211), (212), (213), (214), (215), (216),
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | |            (217), (218), (219), (220), (221), (223), (224),
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | |            (225), (227), (228), (229), (230), (231), (232),
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (234), (235), (236), (237), (249), (268),
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | |            (269), (270), (277), (315), (332), (336), (348),
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | |            (363), (364), (374), (376), (3960), (3963),
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | |            (3970), (3971), (3973), (3975), (3982), (3983),
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | |            (3986), (4526), (4527), (4538), (4581),
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | |            #1295.
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | |   (4582)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4582) gives:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | |   (4583)  all_57_7 = e3 & op(e1, e2) = e3
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4583) implies:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | |   (4584)  all_57_7 = e3
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4532), (4584) imply:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | |   (4585)  e3 = e0
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4585) implies:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | |   (4586)  e3 = e0
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4548), (4586) imply:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | |   (4587)  all_57_11 = e0
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (45), (67),
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | |            (88), (94), (107), (121), (124), (134), (135),
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | |            (137), (163), (166), (169), (170), (171), (195),
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | |            (202), (203), (204), (205), (207), (208), (209),
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | |            (210), (211), (212), (213), (214), (215), (216),
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | |            (217), (218), (219), (220), (221), (223), (224),
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | |            (225), (227), (228), (229), (230), (231), (232),
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (234), (235), (236), (237), (249), (268),
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | |            (269), (270), (277), (315), (332), (336), (348),
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | |            (363), (364), (374), (376), (3960), (3963),
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | |            (3970), (3971), (3973), (3975), (3982), (3983),
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | |            (4526), (4527), (4538), (4584), (4587),
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | |            #1311.
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | |   (4588)  all_57_13 = e3 & op(e0, e2) = e3
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4588) implies:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | |   (4589)  all_57_13 = e3
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (227), (228), (229),
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | |            (3970), (3971), (4532), (4589), (function-axioms)
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2199.
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.41  | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | End of split
% 221.08/37.41  | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | End of split
% 221.08/37.41  | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | Case 2:
% 221.08/37.41  | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | |   (4590)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 221.08/37.41  | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 221.08/37.41  | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | BETA: splitting (4590) gives:
% 221.08/37.41  | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.41  | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | |   (4591)  all_57_8 = e0 & op(e1, e1) = e0
% 221.08/37.41  | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | ALPHA: (4591) implies:
% 221.08/37.41  | | | | | | | | | | | | | | | | |   (4592)  all_57_8 = e0
% 221.08/37.41  | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 221.08/37.41  | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | |   (4593)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 221.08/37.41  | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e0)
% 221.08/37.41  | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 221.08/37.41  | | | | | | | | | | | | | | | | | |            (3970), (3983), (4593), (function-axioms) are
% 221.08/37.41  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2229.
% 221.08/37.41  | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | |   (4594)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 221.08/37.41  | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = e0)
% 221.08/37.41  | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | BETA: splitting (4594) gives:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | |   (4595)  all_57_6 = e0 & op(e1, e3) = e0
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | ALPHA: (4595) implies:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | |   (4596)  op(e1, e3) = e0
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (4525), (4596), (function-axioms) are
% 221.08/37.41  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2154.
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | |   (4597)  all_57_12 = e0 & op(e0, e3) = e0
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | ALPHA: (4597) implies:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | |   (4598)  all_57_12 = e0
% 221.08/37.41  | | | | | | | | | | | | | | | | | | |   (4599)  op(e0, e3) = e0
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | |   (4600)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (171), (3960), (3983), (4600),
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | |            #1543.
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | |   (4601)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | BETA: splitting (4601) gives:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | |   (4602)  all_57_4 = e0 & op(e3, e1) = e0
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | ALPHA: (4602) implies:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | |   (4603)  op(e3, e1) = e0
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (4526), (4603), (function-axioms) are
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2267.
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | |   (4604)  all_57_9 = e0 & op(e3, e0) = e0
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | ALPHA: (4604) implies:
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | |   (4605)  all_57_9 = e0
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | |   (4606)  op(e3, e0) = e0
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (36), (39), (45), (67), (88), (94),
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | |            (107), (111), (113), (114), (118), (119), (121),
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | |            (122), (124), (126), (129), (134), (135), (136),
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | |            (137), (140), (141), (160), (161), (163), (165),
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | |            (166), (169), (170), (171), (190), (191), (192),
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | |            (194), (195), (196), (198), (199), (202), (203),
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | |            (204), (205), (207), (208), (209), (210), (211),
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | |            (212), (213), (214), (215), (216), (217), (218),
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | |            (219), (220), (221), (223), (224), (225), (227),
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | |            (228), (229), (230), (231), (232), (233), (234),
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | |            (235), (236), (237), (244), (245), (246), (248),
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | |            (249), (256), (258), (259), (268), (269), (270),
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | |            (277), (315), (332), (336), (348), (362), (363),
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | |            (364), (369), (370), (371), (372), (373), (374),
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | |            (376), (378), (3961), (3963), (3970), (3971),
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | |            (3973), (3975), (3980), (3981), (3982), (3983),
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | |            (3986), (4527), (4592), (4598), (4599), (4605),
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | |            (4606), (function-axioms) are inconsistent by
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | |            sub-proof #1301.
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.41  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.41  | | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | End of split
% 221.08/37.41  | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.41  | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | |   (4607)  all_57_11 = e0 & op(e1, e0) = e0
% 221.08/37.41  | | | | | | | | | | | | | | | | | 
% 221.08/37.41  | | | | | | | | | | | | | | | | | ALPHA: (4607) implies:
% 221.08/37.41  | | | | | | | | | | | | | | | | |   (4608)  all_57_11 = e0
% 221.08/37.41  | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (45), (67),
% 221.08/37.42  | | | | | | | | | | | | | | | | |            (88), (94), (107), (121), (124), (134), (135),
% 221.08/37.42  | | | | | | | | | | | | | | | | |            (137), (163), (164), (166), (169), (170), (171),
% 221.08/37.42  | | | | | | | | | | | | | | | | |            (195), (202), (203), (204), (205), (207), (208),
% 221.08/37.42  | | | | | | | | | | | | | | | | |            (209), (210), (211), (212), (213), (214), (215),
% 221.08/37.42  | | | | | | | | | | | | | | | | |            (216), (217), (218), (219), (220), (221), (223),
% 221.08/37.42  | | | | | | | | | | | | | | | | |            (224), (225), (227), (228), (229), (230), (231),
% 221.08/37.42  | | | | | | | | | | | | | | | | |            (232), (233), (234), (235), (236), (237), (249),
% 221.08/37.42  | | | | | | | | | | | | | | | | |            (268), (269), (270), (277), (315), (332), (336),
% 221.08/37.42  | | | | | | | | | | | | | | | | |            (348), (363), (364), (374), (376), (3960), (3963),
% 221.08/37.42  | | | | | | | | | | | | | | | | |            (3970), (3971), (3973), (3975), (3982), (3983),
% 221.08/37.42  | | | | | | | | | | | | | | | | |            (3986), (4525), (4526), (4527), (4608),
% 221.08/37.42  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.08/37.42  | | | | | | | | | | | | | | | | |            #1294.
% 221.08/37.42  | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | End of split
% 221.08/37.42  | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | End of split
% 221.08/37.42  | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | End of split
% 221.08/37.42  | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | Case 2:
% 221.08/37.42  | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | |   (4609)  all_57_1 = e3 & op(e3, e2) = e3
% 221.08/37.42  | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | REF_CLOSE: (171), (3980), (4609), (function-axioms) are
% 221.08/37.42  | | | | | | | | | | | | | |            inconsistent by sub-proof #2286.
% 221.08/37.42  | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | End of split
% 221.08/37.42  | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | Case 2:
% 221.08/37.42  | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | |   (4610)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 221.08/37.42  | | | | | | | | | | | | |             & op(e3, e0) = e3)
% 221.08/37.42  | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (169), (231), (233),
% 221.08/37.42  | | | | | | | | | | | | |            (235), (3982), (3983), (4610), (function-axioms)
% 221.08/37.42  | | | | | | | | | | | | |            are inconsistent by sub-proof #1955.
% 221.08/37.42  | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | End of split
% 221.08/37.42  | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | Case 2:
% 221.08/37.42  | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | |   (4611)  all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 221.08/37.42  | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | REF_CLOSE: (277), (376), (3973), (3975), (4611) are
% 221.08/37.42  | | | | | | | | | | | |            inconsistent by sub-proof #1953.
% 221.08/37.42  | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | End of split
% 221.08/37.42  | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | Case 2:
% 221.08/37.42  | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | |   (4612)  all_20_2 = e2
% 221.08/37.42  | | | | | | | | | | |   (4613)  ( ~ (all_20_0 = e1) & op(all_20_1, e3) = all_20_0
% 221.08/37.42  | | | | | | | | | | |             & op(e3, e2) = all_20_1 & $i(all_20_0) &
% 221.08/37.42  | | | | | | | | | | |             $i(all_20_1)) | ( ~ (all_20_1 = e0) & op(e3, e2)
% 221.08/37.42  | | | | | | | | | | |             = all_20_1 & $i(all_20_1))
% 221.08/37.42  | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | COMBINE_EQS: (299), (4612) imply:
% 221.08/37.42  | | | | | | | | | | |   (4614)  all_10_2 = e2
% 221.08/37.42  | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | COMBINE_EQS: (329), (4614) imply:
% 221.08/37.42  | | | | | | | | | | |   (4615)  all_28_2 = e2
% 221.08/37.42  | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | REDUCE: (338), (4614) imply:
% 221.08/37.42  | | | | | | | | | | |   (4616)   ~ (all_53_1 = e2)
% 221.08/37.42  | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | REDUCE: (340), (4614) imply:
% 221.08/37.42  | | | | | | | | | | |   (4617)   ~ (all_53_2 = e2)
% 221.08/37.42  | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | REDUCE: (342), (4614) imply:
% 221.08/37.42  | | | | | | | | | | |   (4618)   ~ (all_53_3 = e2)
% 221.08/37.42  | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | REDUCE: (344), (4614) imply:
% 221.08/37.42  | | | | | | | | | | |   (4619)   ~ (all_53_4 = e2)
% 221.08/37.42  | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | REDUCE: (346), (4614) imply:
% 221.08/37.42  | | | | | | | | | | |   (4620)   ~ (all_53_8 = e2)
% 221.08/37.42  | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | REDUCE: (348), (4614) imply:
% 221.08/37.42  | | | | | | | | | | |   (4621)   ~ (all_53_12 = e2)
% 221.08/37.42  | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | REDUCE: (45), (4614) imply:
% 221.08/37.42  | | | | | | | | | | |   (4622)  op(e3, e3) = e2
% 221.08/37.42  | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | BETA: splitting (235) gives:
% 221.08/37.42  | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | Case 1:
% 221.08/37.42  | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | |   (4623)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 221.08/37.42  | | | | | | | | | | | |             & op(e3, e2) = e2)
% 221.08/37.42  | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | BETA: splitting (4623) gives:
% 221.08/37.42  | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | Case 1:
% 221.08/37.42  | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | |   (4624)  all_57_0 = e2 & op(e3, e3) = e2
% 221.08/37.42  | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | ALPHA: (4624) implies:
% 221.08/37.42  | | | | | | | | | | | | |   (4625)  all_57_0 = e2
% 221.08/37.42  | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | BETA: splitting (67) gives:
% 221.08/37.42  | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | Case 1:
% 221.08/37.42  | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | |   (4626)   ~ (all_24_2 = e0)
% 221.08/37.42  | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | REDUCE: (315), (4626) imply:
% 221.08/37.42  | | | | | | | | | | | | | |   (4627)   ~ (all_6_2 = e0)
% 221.08/37.42  | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | BETA: splitting (73) gives:
% 221.08/37.42  | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | Case 1:
% 221.08/37.42  | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | |   (4628)   ~ (all_28_2 = e2)
% 221.08/37.42  | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | REDUCE: (4615), (4628) imply:
% 221.08/37.42  | | | | | | | | | | | | | | |   (4629)  $false
% 221.08/37.42  | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | CLOSE: (4629) is inconsistent.
% 221.08/37.42  | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | Case 2:
% 221.08/37.42  | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | |   (4630)  ( ~ (all_28_0 = e0) & op(all_28_1, e3) = all_28_0
% 221.08/37.42  | | | | | | | | | | | | | | |             & op(e3, e2) = all_28_1 & $i(all_28_0) &
% 221.08/37.42  | | | | | | | | | | | | | | |             $i(all_28_1)) | ( ~ (all_28_1 = e1) & op(e3, e2)
% 221.08/37.42  | | | | | | | | | | | | | | |             = all_28_1 & $i(all_28_1))
% 221.08/37.42  | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | BETA: splitting (76) gives:
% 221.08/37.42  | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | Case 1:
% 221.08/37.42  | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | |   (4631)   ~ (all_30_2 = e1)
% 221.08/37.42  | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | REDUCE: (330), (4631) imply:
% 221.08/37.42  | | | | | | | | | | | | | | | |   (4632)   ~ (all_4_2 = e1)
% 221.08/37.42  | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 221.08/37.42  | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.42  | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | |   (4633)  all_55_15 = e3
% 221.08/37.42  | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (4633) imply:
% 221.08/37.42  | | | | | | | | | | | | | | | | |   (4634)  all_4_2 = e3
% 221.08/37.42  | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | REDUCE: (378), (4634) imply:
% 221.08/37.42  | | | | | | | | | | | | | | | | |   (4635)  $false
% 221.08/37.42  | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | CLOSE: (4635) is inconsistent.
% 221.08/37.42  | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.42  | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | |   (4636)   ~ (all_55_15 = e3)
% 221.08/37.42  | | | | | | | | | | | | | | | | |   (4637)  all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 221.08/37.42  | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | BETA: splitting (4637) gives:
% 221.08/37.42  | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.42  | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | |   (4638)  all_55_15 = e2
% 221.08/37.42  | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (4638) imply:
% 221.08/37.42  | | | | | | | | | | | | | | | | | |   (4639)  all_4_2 = e2
% 221.08/37.42  | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | REDUCE: (373), (4639) imply:
% 221.08/37.42  | | | | | | | | | | | | | | | | | |   (4640)  $false
% 221.08/37.42  | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | CLOSE: (4640) is inconsistent.
% 221.08/37.42  | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.42  | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | |   (4641)   ~ (all_55_15 = e2)
% 221.08/37.42  | | | | | | | | | | | | | | | | | |   (4642)  all_55_15 = e1 | all_55_15 = e0
% 221.08/37.42  | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | BETA: splitting (4642) gives:
% 221.08/37.42  | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | |   (4643)  all_55_15 = e1
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (4643) imply:
% 221.08/37.42  | | | | | | | | | | | | | | | | | | |   (4644)  all_4_2 = e1
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | REDUCE: (4632), (4644) imply:
% 221.08/37.42  | | | | | | | | | | | | | | | | | | |   (4645)  $false
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | CLOSE: (4645) is inconsistent.
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | |   (4646)  all_55_15 = e0
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (4646) imply:
% 221.08/37.42  | | | | | | | | | | | | | | | | | | |   (4647)  all_4_2 = e0
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | REDUCE: (351), (4647) imply:
% 221.08/37.42  | | | | | | | | | | | | | | | | | | |   (4648)   ~ (all_53_3 = e0)
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | REDUCE: (370), (4647) imply:
% 221.08/37.42  | | | | | | | | | | | | | | | | | | |   (4649)   ~ (all_53_12 = e0)
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | REDUCE: (373), (4647) imply:
% 221.08/37.42  | | | | | | | | | | | | | | | | | | |   (4650)   ~ (e2 = e0)
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | REDUCE: (4632), (4647) imply:
% 221.08/37.42  | | | | | | | | | | | | | | | | | | |   (4651)   ~ (e1 = e0)
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | |   (4652)  all_57_15 = e0 & op(e0, e0) = e0
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | ALPHA: (4652) implies:
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | |   (4653)  all_57_15 = e0
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | |   (4654)  op(e0, e0) = e0
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | |   (4655)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (171), (3960), (4622), (4655),
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | |            #1321.
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | |   (4656)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4656) gives:
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | |   (4657)  all_57_4 = e0 & op(e3, e1) = e0
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4657) implies:
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | |   (4658)  all_57_4 = e0
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | |   (4659)  op(e3, e1) = e0
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (88), (107),
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | |            (113), (121), (127), (129), (134), (135), (136),
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | |            (137), (142), (144), (159), (160), (164), (169),
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | |            (170), (192), (194), (195), (196), (202), (204),
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | |            (207), (208), (209), (210), (211), (212), (214),
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | |            (215), (216), (217), (219), (220), (221), (222),
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | |            (223), (224), (225), (227), (228), (229), (230),
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | |            (231), (232), (233), (236), (237), (246), (248),
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | |            (249), (256), (268), (270), (336), (361), (363),
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | |            (368), (374), (3962), (3970), (3971), (4618),
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | |            (4619), (4620), (4621), (4622), (4648), (4653),
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | |            (4654), (4658), (4659), (function-axioms) are
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1611.
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | |   (4660)  all_57_9 = e0 & op(e3, e0) = e0
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (4649), (4660), (function-axioms) are
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2434.
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | |   (4661)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | |                 e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | ALPHA: (4661) implies:
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | |   (4662)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | |               e1) = e0)
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | BETA: splitting (4662) gives:
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | |   (4663)  all_57_12 = e0 & op(e0, e3) = e0
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | ALPHA: (4663) implies:
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | |   (4664)  op(e0, e3) = e0
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (4648), (4664), (function-axioms) are
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2366.
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | |   (4665)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4665) gives:
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | |   (4666)  all_57_13 = e0 & op(e0, e2) = e0
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4666) implies:
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | |   (4667)  op(e0, e2) = e0
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (3962), (4667), (function-axioms) are
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2332.
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | |   (4668)  all_57_14 = e0 & op(e0, e1) = e0
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4668) implies:
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | |   (4669)  all_57_14 = e0
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (169), (171),
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | |            (219), (220), (221), (231), (374), (3960), (4622),
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | |            (4649), (4669), (function-axioms) are inconsistent
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1293.
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.42  | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | End of split
% 221.08/37.42  | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | End of split
% 221.08/37.42  | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | Case 2:
% 221.08/37.42  | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | |   (4670)  all_30_2 = e1
% 221.08/37.42  | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | COMBINE_EQS: (330), (4670) imply:
% 221.08/37.42  | | | | | | | | | | | | | | | |   (4671)  all_4_2 = e1
% 221.08/37.42  | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | SIMP: (4671) implies:
% 221.08/37.42  | | | | | | | | | | | | | | | |   (4672)  all_4_2 = e1
% 221.08/37.42  | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | REDUCE: (371), (4672) imply:
% 221.08/37.42  | | | | | | | | | | | | | | | |   (4673)   ~ (all_53_13 = e1)
% 221.08/37.42  | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | REDUCE: (378), (4672) imply:
% 221.08/37.42  | | | | | | | | | | | | | | | |   (4674)   ~ (e3 = e1)
% 221.08/37.42  | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | REDUCE: (373), (4672) imply:
% 221.08/37.42  | | | | | | | | | | | | | | | |   (4675)   ~ (e2 = e1)
% 221.08/37.42  | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | REDUCE: (36), (4672) imply:
% 221.08/37.42  | | | | | | | | | | | | | | | |   (4676)  op(e0, e0) = e1
% 221.08/37.42  | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 221.08/37.42  | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.42  | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | |   (4677)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 221.08/37.42  | | | | | | | | | | | | | | | | |             all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 221.08/37.42  | | | | | | | | | | | | | | | | |             op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 221.08/37.42  | | | | | | | | | | | | | | | | |               all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 221.08/37.42  | | | | | | | | | | | | | | | | |             op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 221.08/37.42  | | | | | | | | | | | | | | | | |             op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 221.08/37.42  | | | | | | | | | | | | | | | | |             $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 221.08/37.42  | | | | | | | | | | | | | | | | |             $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 221.08/37.42  | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 221.08/37.42  | | | | | | | | | | | | | | | | |               all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 221.08/37.42  | | | | | | | | | | | | | | | | |             & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 221.08/37.42  | | | | | | | | | | | | | | | | |               all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 221.08/37.42  | | | | | | | | | | | | | | | | |             op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 221.08/37.42  | | | | | | | | | | | | | | | | |             & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 221.08/37.42  | | | | | | | | | | | | | | | | |             $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 221.08/37.42  | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | BETA: splitting (4677) gives:
% 221.08/37.42  | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.42  | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | |   (4678)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 221.08/37.42  | | | | | | | | | | | | | | | | | |           all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 221.08/37.42  | | | | | | | | | | | | | | | | | |           op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 221.08/37.42  | | | | | | | | | | | | | | | | | |             all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 221.08/37.42  | | | | | | | | | | | | | | | | | |           op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 221.08/37.42  | | | | | | | | | | | | | | | | | |           op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 221.08/37.42  | | | | | | | | | | | | | | | | | |           $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 221.08/37.42  | | | | | | | | | | | | | | | | | |           $i(all_52_7)
% 221.08/37.42  | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | ALPHA: (4678) implies:
% 221.08/37.42  | | | | | | | | | | | | | | | | | |   (4679)  op(e3, e3) = all_52_1
% 221.08/37.42  | | | | | | | | | | | | | | | | | |   (4680)  op(all_52_1, all_52_1) = e3
% 221.08/37.42  | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3971), (4622), (4679), (4680),
% 221.08/37.42  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.08/37.42  | | | | | | | | | | | | | | | | | |            #1653.
% 221.08/37.42  | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.42  | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | |   (4681)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 221.08/37.42  | | | | | | | | | | | | | | | | | |           all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 221.08/37.42  | | | | | | | | | | | | | | | | | |           op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 221.08/37.42  | | | | | | | | | | | | | | | | | |             all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 221.08/37.42  | | | | | | | | | | | | | | | | | |           & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 221.08/37.42  | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 221.08/37.42  | | | | | | | | | | | | | | | | | |           $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 221.08/37.42  | | | | | | | | | | | | | | | | | |           $i(all_52_15)
% 221.08/37.42  | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | ALPHA: (4681) implies:
% 221.08/37.42  | | | | | | | | | | | | | | | | | |   (4682)  op(e2, e2) = all_52_11
% 221.08/37.42  | | | | | | | | | | | | | | | | | |   (4683)  op(all_52_11, all_52_11) = e2
% 221.08/37.42  | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 221.08/37.42  | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | |   (4684)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 221.08/37.42  | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | BETA: splitting (4684) gives:
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | |   (4685)  all_57_9 = e1 & op(e3, e0) = e1
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | ALPHA: (4685) implies:
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | |   (4686)  all_57_9 = e1
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (160), (165),
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | |            (169), (171), (207), (208), (209), (210), (211),
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | |            (212), (213), (214), (216), (217), (219), (220),
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | |            (221), (223), (224), (225), (227), (228), (229),
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | |            (230), (231), (232), (233), (234), (236), (237),
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | |            (374), (3960), (3964), (3970), (3971), (4618),
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | |            (4621), (4622), (4625), (4673), (4676), (4686),
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | |            #1266.
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | |   (4687)  all_57_10 = e1 & op(e2, e0) = e1
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (4673), (4687), (function-axioms) are
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2084.
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | |   (4688)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 221.08/37.42  | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | BETA: splitting (4688) gives:
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | |   (4689)  all_57_11 = e1 & op(e1, e0) = e1
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | ALPHA: (4689) implies:
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | |   (4690)  all_57_11 = e1
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (160), (165),
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | |            (169), (171), (207), (208), (209), (210), (211),
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | |            (212), (213), (214), (216), (217), (219), (220),
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | |            (221), (222), (223), (224), (225), (227), (228),
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | |            (229), (230), (231), (232), (233), (234), (236),
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | |            (237), (374), (3960), (3964), (3970), (3971),
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | |            (4618), (4621), (4622), (4625), (4673), (4676),
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | |            (4690), (function-axioms) are inconsistent by
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | |            sub-proof #1250.
% 221.08/37.42  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | |   (4691)  all_57_15 = e1 & op(e0, e0) = e1
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3971), (4682), (4683), (4691),
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | |            #2066.
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.43  | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | End of split
% 221.08/37.43  | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.43  | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | |   (4692)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 221.08/37.43  | | | | | | | | | | | | | | | | |             & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 221.08/37.43  | | | | | | | | | | | | | | | | |             & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 221.08/37.43  | | | | | | | | | | | | | | | | |               all_52_21) = e1 & op(all_52_23, all_52_23) =
% 221.08/37.43  | | | | | | | | | | | | | | | | |             e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 221.08/37.43  | | | | | | | | | | | | | | | | |             all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 221.08/37.43  | | | | | | | | | | | | | | | | |             = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 221.08/37.43  | | | | | | | | | | | | | | | | |             $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 221.08/37.43  | | | | | | | | | | | | | | | | |             & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 221.08/37.43  | | | | | | | | | | | | | | | | |             e0 & op(all_52_25, all_52_25) = e3 &
% 221.08/37.43  | | | | | | | | | | | | | | | | |             op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 221.08/37.43  | | | | | | | | | | | | | | | | |               all_52_29) = e1 & op(all_52_31, all_52_31) =
% 221.08/37.43  | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 221.08/37.43  | | | | | | | | | | | | | | | | |             all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 221.08/37.43  | | | | | | | | | | | | | | | | |             = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 221.08/37.43  | | | | | | | | | | | | | | | | |             $i(all_52_29) & $i(all_52_31))
% 221.08/37.43  | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | BETA: splitting (4692) gives:
% 221.08/37.43  | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | |   (4693)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 221.08/37.43  | | | | | | | | | | | | | | | | | |           all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 221.08/37.43  | | | | | | | | | | | | | | | | | |           op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 221.08/37.43  | | | | | | | | | | | | | | | | | |             all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 221.08/37.43  | | | | | | | | | | | | | | | | | |           & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 221.08/37.43  | | | | | | | | | | | | | | | | | |           & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 221.08/37.43  | | | | | | | | | | | | | | | | | |           & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 221.08/37.43  | | | | | | | | | | | | | | | | | |           $i(all_52_23)
% 221.08/37.43  | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | ALPHA: (4693) implies:
% 221.08/37.43  | | | | | | | | | | | | | | | | | |   (4694)  op(e1, e1) = all_52_21
% 221.08/37.43  | | | | | | | | | | | | | | | | | |   (4695)  op(e1, e3) = all_52_17
% 221.08/37.43  | | | | | | | | | | | | | | | | | |   (4696)  op(all_52_21, all_52_21) = e1
% 221.08/37.43  | | | | | | | | | | | | | | | | | |   (4697)  op(all_52_17, all_52_17) = e3
% 221.08/37.43  | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | |   (4698)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 221.08/37.43  | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | BETA: splitting (4698) gives:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | |   (4699)  all_57_9 = e1 & op(e3, e0) = e1
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | ALPHA: (4699) implies:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | |   (4700)  all_57_9 = e1
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (160), (165),
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | |            (169), (171), (207), (208), (209), (210), (211),
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | |            (212), (213), (214), (216), (217), (219), (220),
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | |            (221), (223), (224), (225), (227), (228), (229),
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | |            (230), (231), (232), (233), (234), (236), (237),
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | |            (374), (3960), (3964), (3970), (3971), (4618),
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | |            (4621), (4622), (4625), (4673), (4676), (4700),
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | |            #1266.
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | |   (4701)  all_57_10 = e1 & op(e2, e0) = e1
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (4673), (4701), (function-axioms) are
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2084.
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | |   (4702)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 221.08/37.43  | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | BETA: splitting (4702) gives:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | |   (4703)  all_57_11 = e1 & op(e1, e0) = e1
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | ALPHA: (4703) implies:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | |   (4704)  all_57_11 = e1
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (160), (165),
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | |            (169), (171), (207), (208), (209), (210), (211),
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | |            (212), (213), (214), (216), (217), (219), (220),
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | |            (221), (222), (223), (224), (225), (227), (228),
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | |            (229), (230), (231), (232), (233), (234), (236),
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | |            (237), (374), (3960), (3964), (3970), (3971),
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | |            (4618), (4621), (4622), (4625), (4673), (4676),
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | |            (4704), (function-axioms) are inconsistent by
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | |            sub-proof #1250.
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | |   (4705)  all_57_15 = e1 & op(e0, e0) = e1
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | ALPHA: (4705) implies:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | |   (4706)  all_57_15 = e1
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | |              all_52_21, e1, e1, simplifying with (39), (4694)
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | |              gives:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | |   (4707)  all_52_21 = all_6_2
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_2,
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | |              all_52_17, e3, e1, simplifying with (164), (4695)
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | |              gives:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | |   (4708)  all_53_2 = all_52_17
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (4708) imply:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | |   (4709)  all_55_8 = all_52_17
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | REDUCE: (150), (4708) imply:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | |   (4710)   ~ (all_53_1 = all_52_17)
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | REDUCE: (4617), (4708) imply:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | |   (4711)   ~ (all_52_17 = e2)
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | REDUCE: (4696), (4707) imply:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | |   (4712)  op(all_6_2, all_6_2) = e1
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | BETA: splitting (88) gives:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | |   (4713)   ~ (all_38_2 = e2)
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | REDUCE: (249), (4713) imply:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | |   (4714)   ~ (all_6_2 = e2)
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | |   (4715)  all_55_10 = e3
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (374), (4715) are inconsistent by sub-proof
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | |            #2500.
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | |   (4716)   ~ (all_55_10 = e3)
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | |   (4717)  all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4717) gives:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | |   (4718)  all_55_10 = e2
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (4714), (4718) are inconsistent by
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2499.
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | |   (4719)   ~ (all_55_10 = e2)
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | |   (4720)  all_55_10 = e1 | all_55_10 = e0
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4720) gives:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | |   (4721)  all_55_10 = e1
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (336), (4721) imply:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | |   (4722)  all_6_2 = e1
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4722) implies:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | |   (4723)  all_6_2 = e1
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (4723) imply:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | |   (4724)  op(e1, e1) = e1
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | |   (4725)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e1)
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4725) gives:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4726)  all_57_0 = e1 & op(e3, e3) = e1
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4726) implies:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4727)  op(e3, e3) = e1
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4622), (4727), (function-axioms) are
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1950.
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4728)  all_57_2 = e1 & op(e2, e3) = e1
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (160), (165),
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | |            (168), (169), (171), (197), (207), (208), (209),
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | |            (210), (211), (212), (213), (214), (216), (217),
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | |            (218), (219), (220), (221), (223), (224), (225),
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | |            (227), (228), (229), (230), (231), (232), (233),
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | |            (234), (236), (237), (374), (3960), (3964),
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | |            (3970), (3971), (4613), (4618), (4621), (4622),
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | |            (4625), (4630), (4673), (4676), (4695), (4697),
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | |            (4709), (4710), (4711), (4724), (4728),
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | |            #1240.
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | |   (4729)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e3) = e1)
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4729) gives:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4730)  all_57_6 = e1 & op(e1, e3) = e1
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4730) implies:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4731)  all_57_6 = e1
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (214), (216),
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | |            (217), (227), (228), (229), (231), (233), (237),
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | |            (374), (3970), (3971), (4622), (4724), (4731),
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | |            #1239.
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4732)  all_57_12 = e1 & op(e0, e3) = e1
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4732) implies:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4733)  all_57_12 = e1
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4734)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4734) gives:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4735)  all_57_1 = e1 & op(e3, e2) = e1
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4735) implies:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4736)  all_57_1 = e1
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4737)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4737) gives:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4738)  all_57_2 = e1 & op(e2, e3) = e1
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (160), (165),
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (168), (169), (171), (197), (207), (208), (209),
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (210), (211), (212), (213), (214), (216), (217),
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (218), (219), (220), (221), (223), (224), (225),
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (227), (228), (229), (230), (231), (232), (233),
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (234), (236), (237), (374), (3960), (3964),
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3970), (3971), (4613), (4618), (4621), (4622),
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4625), (4630), (4673), (4676), (4695), (4697),
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4709), (4710), (4711), (4724), (4738),
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1240.
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4739)  all_57_3 = e1 & op(e2, e2) = e1
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4739) implies:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4740)  op(e2, e2) = e1
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3971), (4740), (function-axioms) are
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2352.
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4741)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4741) gives:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4742)  all_57_5 = e1 & op(e2, e1) = e1
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4742) implies:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4743)  all_57_5 = e1
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4744)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4744) gives:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4745)  all_57_2 = e2 & op(e2, e3) = e2
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4745) implies:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4746)  all_57_2 = e2
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (236), (3970), (4622), (4733), (4746),
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1629.
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4747)  all_57_3 = e2 & op(e2, e2) = e2
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4747) implies:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4748)  op(e2, e2) = e2
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3971), (4748), (function-axioms) are
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2472.
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4749)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4749) gives:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4750)  all_57_5 = e2 & op(e2, e1) = e2
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4750) implies:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4751)  all_57_5 = e2
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4743), (4751) are inconsistent by sub-proof
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1885.
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4752)  all_57_10 = e2 & op(e2, e0) = e2
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4752) implies:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4753)  all_57_10 = e2
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4754)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e0)
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3970), (4622), (4754), (function-axioms) are
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1654.
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4755)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = e0)
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4755) gives:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4756)  all_57_6 = e0 & op(e1, e3) = e0
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4756) implies:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4757)  all_57_6 = e0
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4758)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e2)
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4758) gives:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4759)  all_57_4 = e2 & op(e3, e1) = e2
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4759) implies:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4760)  all_57_4 = e2
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4761)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e0)
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4761) gives:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4762)  all_57_4 = e0 & op(e3, e1) = e0
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4762) implies:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4763)  all_57_4 = e0
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (159), (207),
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (221), (223), (224), (225), (236), (374), (3962),
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3970), (4622), (4706), (4733), (4743), (4753),
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4757), (4763), (function-axioms) are inconsistent
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1238.
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4764)  all_57_5 = e0 & op(e2, e1) = e0
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4764) implies:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4765)  all_57_5 = e0
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (223), (225), (3970),
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4753), (4765) are inconsistent by sub-proof
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2355.
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4766)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4766) gives:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4767)  all_57_8 = e0 & op(e1, e1) = e0
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4767) implies:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4768)  op(e1, e1) = e0
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4724), (4768), (function-axioms) are
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2427.
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4769)  all_57_14 = e0 & op(e0, e1) = e0
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4769) implies:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4770)  all_57_14 = e0
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4771)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e3)
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4771) gives:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4772)  all_57_0 = e3 & op(e3, e3) = e3
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4772) implies:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4773)  op(e3, e3) = e3
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4622), (4773), (function-axioms) are
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2490.
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4774)  all_57_2 = e3 & op(e2, e3) = e3
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4774) implies:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4775)  all_57_2 = e3
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4776)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4776) gives:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4777)  all_57_12 = e3 & op(e0, e3) = e3
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4777) implies:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4778)  all_57_12 = e3
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4733), (4778) imply:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4779)  e3 = e1
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4779) implies:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4780)  e3 = e1
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4775), (4780) imply:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4781)  all_57_2 = e1
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4758) gives:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4782)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4782) gives:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4783)  all_57_2 = e2 & op(e2, e3) = e2
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4783) implies:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4784)  all_57_2 = e2
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4781), (4784) imply:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4785)  e2 = e1
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4785) implies:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4786)  e2 = e1
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4760), (4786) imply:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4787)  all_57_4 = e1
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (218), (220),
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (221), (223), (224), (225), (374), (3970), (3971),
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4724), (4781), (4787), (function-axioms) are
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1242.
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4788)  all_57_3 = e2 & op(e2, e2) = e2
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4788) implies:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4789)  op(e2, e2) = e2
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3971), (4789), (function-axioms) are
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2472.
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4749) gives:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4790)  all_57_5 = e2 & op(e2, e1) = e2
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4790) implies:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4791)  all_57_5 = e2
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4743), (4791) imply:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4792)  e2 = e1
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4792) implies:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4793)  e2 = e1
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4760), (4793) imply:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4794)  all_57_4 = e1
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (218), (220),
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (221), (223), (224), (225), (374), (3970), (3971),
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4724), (4781), (4794), (function-axioms) are
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1242.
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (225), (3970), (4743), (4753),
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4781) are inconsistent by sub-proof #1645.
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4795)  all_57_5 = e2 & op(e2, e1) = e2
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4795) implies:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4796)  all_57_5 = e2
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4743), (4796) are inconsistent by sub-proof
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1885.
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4797)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e1) = e2)
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4797) gives:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4798)  all_57_8 = e2 & op(e1, e1) = e2
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4798) implies:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4799)  op(e1, e1) = e2
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4724), (4799), (function-axioms) are
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2423.
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4800)  all_57_14 = e2 & op(e0, e1) = e2
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4800) implies:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4801)  all_57_14 = e2
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4802)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4802) gives:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4803)  all_57_2 = e2 & op(e2, e3) = e2
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4803) implies:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4804)  all_57_2 = e2
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4781), (4804) imply:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4805)  e2 = e1
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (159), (160), (207),
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (209), (210), (227), (229), (3962), (3970),
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3971), (4618), (4676), (4706), (4736), (4801),
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4805), (function-axioms) are inconsistent by
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1236.
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4806)  all_57_3 = e2 & op(e2, e2) = e2
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4806) implies:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4807)  op(e2, e2) = e2
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3971), (4807), (function-axioms) are
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2472.
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4749) gives:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4808)  all_57_5 = e2 & op(e2, e1) = e2
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4808) implies:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4809)  all_57_5 = e2
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4743), (4809) imply:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4810)  e2 = e1
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (159), (160), (207),
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (209), (210), (227), (229), (3962), (3970),
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3971), (4618), (4676), (4706), (4736), (4801),
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4810), (function-axioms) are inconsistent by
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1236.
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (225), (3970), (4743), (4753),
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4781) are inconsistent by sub-proof #1645.
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4811)  all_57_13 = e3 & op(e0, e2) = e3
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4811) implies:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4812)  all_57_13 = e3
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4813)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4813) gives:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4814)  all_57_12 = e2 & op(e0, e3) = e2
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4814) implies:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4815)  op(e0, e3) = e2
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (4618), (4815), (function-axioms) are
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1980.
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4816)  all_57_13 = e2 & op(e0, e2) = e2
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4812), (4816) are inconsistent by sub-proof
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2146.
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4817)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4817) gives:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4818)  all_57_14 = e2 & op(e0, e1) = e2
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4818) implies:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4819)  all_57_14 = e2
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (159), (207),
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (218), (221), (223), (224), (225), (236), (374),
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3962), (3970), (4622), (4706), (4724), (4733),
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4743), (4753), (4757), (4819), (function-axioms)
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1235.
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4820)  all_57_15 = e2 & op(e0, e0) = e2
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4820) implies:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4821)  op(e0, e0) = e2
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4676), (4821), (function-axioms) are
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2177.
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4822)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4822) gives:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4823)  all_57_14 = e3 & op(e0, e1) = e3
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4823) implies:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4824)  all_57_14 = e3
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (218), (223), (225),
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3970), (4724), (4753), (4760), (4824),
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1233.
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4825)  all_57_15 = e3 & op(e0, e0) = e3
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4825) implies:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4826)  all_57_15 = e3
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (208),
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (209), (220), (221), (374), (4724), (4743),
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4770), (4826), (function-axioms) are inconsistent
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1230.
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4827)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e3) = e3)
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (4733), (4757), (4827) are inconsistent
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1631.
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4828)  all_57_5 = e2 & op(e2, e1) = e2
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4828) implies:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4829)  all_57_5 = e2
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4743), (4829) are inconsistent by sub-proof
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1885.
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4830)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e1) = e2)
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4830) gives:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4831)  all_57_8 = e2 & op(e1, e1) = e2
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4831) implies:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4832)  op(e1, e1) = e2
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4724), (4832), (function-axioms) are
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2423.
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4833)  all_57_14 = e2 & op(e0, e1) = e2
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4833) implies:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4834)  all_57_14 = e2
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (159), (207),
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (218), (221), (223), (224), (225), (236), (374),
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3962), (3970), (4622), (4706), (4724), (4733),
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4743), (4753), (4757), (4834), (function-axioms)
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1235.
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4835)  all_57_12 = e0 & op(e0, e3) = e0
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4835) implies:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4836)  all_57_12 = e0
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4733), (4836) imply:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4837)  e1 = e0
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4837) implies:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4838)  e1 = e0
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4743), (4838) imply:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4839)  all_57_5 = e0
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (223), (225), (3970),
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4753), (4839) are inconsistent by sub-proof
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2355.
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4840)  all_57_10 = e1 & op(e2, e0) = e1
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (4673), (4840), (function-axioms) are
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2084.
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4841)  all_57_3 = e1 & op(e2, e2) = e1
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4841) implies:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4842)  op(e2, e2) = e1
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3971), (4842), (function-axioms) are
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2352.
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4843)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4843) gives:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4844)  all_57_7 = e1 & op(e1, e2) = e1
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4844) implies:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4845)  all_57_7 = e1
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4846)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (237),
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3971), (4622), (4846), (function-axioms) are
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1297.
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4847)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4847) gives:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4848)  all_57_7 = e2 & op(e1, e2) = e2
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4848) implies:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4849)  all_57_7 = e2
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4845), (4849) are inconsistent by sub-proof
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1761.
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4850)  all_57_13 = e2 & op(e0, e2) = e2
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4850) implies:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4851)  all_57_13 = e2
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4852)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e2)
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4852) gives:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4853)  all_57_6 = e2 & op(e1, e3) = e2
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4853) implies:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4854)  all_57_6 = e2
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4855)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4855) gives:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4856)  all_57_12 = e3 & op(e0, e3) = e3
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4856) implies:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4857)  all_57_12 = e3
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4733), (4857) are inconsistent by sub-proof
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2151.
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4858)  all_57_13 = e3 & op(e0, e2) = e3
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4851), (4858) are inconsistent by sub-proof
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1358.
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4859)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4859) gives:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4860)  all_57_14 = e3 & op(e0, e1) = e3
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4860) implies:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4861)  all_57_14 = e3
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4862)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e2)
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4862) gives:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4863)  all_57_4 = e2 & op(e3, e1) = e2
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4863) implies:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4864)  all_57_4 = e2
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4865)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4865) gives:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4866)  all_57_9 = e2 & op(e3, e0) = e2
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4866) implies:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4867)  op(e3, e0) = e2
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (4621), (4867), (function-axioms) are
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2331.
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4868)  all_57_10 = e2 & op(e2, e0) = e2
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4868) implies:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4869)  all_57_10 = e2
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (218), (223), (225),
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3970), (4724), (4861), (4864), (4869),
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1233.
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4870)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4870) gives:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4871)  all_57_11 = e2 & op(e1, e0) = e2
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4871) implies:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4872)  all_57_11 = e2
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (214), (217),
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (227), (229), (374), (3970), (3971), (4724),
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4845), (4851), (4872), (function-axioms) are
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1621.
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4873)  all_57_15 = e2 & op(e0, e0) = e2
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4873) implies:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4874)  op(e0, e0) = e2
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4676), (4874), (function-axioms) are
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2177.
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4875)  all_57_5 = e2 & op(e2, e1) = e2
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4875) implies:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4876)  all_57_5 = e2
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4877)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4877) gives:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4878)  all_57_2 = e1 & op(e2, e3) = e1
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4878) implies:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4879)  all_57_2 = e1
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (160), (165),
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (169), (171), (207), (208), (209), (210), (211),
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (213), (214), (216), (217), (219), (220),
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (221), (223), (224), (225), (227), (228), (229),
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (231), (232), (233), (234), (236), (237),
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (374), (3960), (3964), (3970), (3971), (4618),
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4621), (4622), (4625), (4673), (4676), (4724),
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4845), (4851), (4854), (4879), (function-axioms)
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1244.
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4880)  all_57_3 = e1 & op(e2, e2) = e1
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4880) implies:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4881)  op(e2, e2) = e1
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3971), (4881), (function-axioms) are
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2352.
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4882)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4882) gives:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4883)  all_57_5 = e1 & op(e2, e1) = e1
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4883) implies:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4884)  all_57_5 = e1
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4876), (4884) imply:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4885)  e2 = e1
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4854), (4885) imply:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4886)  all_57_6 = e1
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (214), (216),
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (217), (227), (228), (229), (231), (233), (237),
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (374), (3970), (3971), (4622), (4724), (4886),
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1239.
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4887)  all_57_10 = e1 & op(e2, e0) = e1
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (4673), (4887), (function-axioms) are
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2084.
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4888)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e1) = e2)
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (4724), (4861), (4888),
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2089.
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4889)  all_57_15 = e3 & op(e0, e0) = e3
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4889) implies:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4890)  all_57_15 = e3
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (217), (374), (4845), (4854), (4890),
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1245.
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4891)  all_57_7 = e2 & op(e1, e2) = e2
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4891) implies:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4892)  all_57_7 = e2
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4845), (4892) are inconsistent by sub-proof
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1761.
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4893)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e0) = e2)
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4893) gives:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4894)  all_57_8 = e2 & op(e1, e1) = e2
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4894) implies:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4895)  op(e1, e1) = e2
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4724), (4895), (function-axioms) are
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2423.
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4896)  all_57_11 = e2 & op(e1, e0) = e2
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4896) implies:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4897)  all_57_11 = e2
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (214), (217),
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (227), (229), (374), (3970), (3971), (4724),
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4845), (4851), (4897), (function-axioms) are
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1621.
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4898)  all_57_13 = e1 & op(e0, e2) = e1
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4898) implies:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4899)  all_57_13 = e1
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4900)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4900) gives:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4901)  all_57_12 = e3 & op(e0, e3) = e3
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4901) implies:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4902)  all_57_12 = e3
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4733), (4902) are inconsistent by sub-proof
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2151.
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4903)  all_57_13 = e3 & op(e0, e2) = e3
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4903) implies:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4904)  all_57_13 = e3
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4899), (4904) are inconsistent by sub-proof
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2268.
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4905)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4905) gives:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4906)  all_57_14 = e3 & op(e0, e1) = e3
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4906) implies:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4907)  all_57_14 = e3
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (160), (209), (4618), (4676), (4899),
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4907), (function-axioms) are inconsistent by
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1976.
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4908)  all_57_15 = e3 & op(e0, e0) = e3
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4908) implies:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4909)  op(e0, e0) = e3
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4676), (4909), (function-axioms) are
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2183.
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | |   (4910)  all_55_10 = e0
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (4627), (4910) are inconsistent by
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2118.
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | |   (4911)  all_38_2 = e2
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (4911) imply:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | |   (4912)  all_6_2 = e2
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | REDUCE: (4712), (4912) imply:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | |   (4913)  op(e2, e2) = e1
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3971), (4913), (function-axioms) are
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2352.
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.45  | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | |   (4914)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 221.08/37.45  | | | | | | | | | | | | | | | | | |           all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 221.08/37.45  | | | | | | | | | | | | | | | | | |           op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 221.08/37.45  | | | | | | | | | | | | | | | | | |             all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 221.08/37.45  | | | | | | | | | | | | | | | | | |           & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 221.08/37.45  | | | | | | | | | | | | | | | | | |           & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 221.08/37.45  | | | | | | | | | | | | | | | | | |           & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 221.08/37.45  | | | | | | | | | | | | | | | | | |           $i(all_52_31)
% 221.08/37.45  | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | ALPHA: (4914) implies:
% 221.08/37.45  | | | | | | | | | | | | | | | | | |   (4915)  op(e0, e0) = all_52_31
% 221.08/37.45  | | | | | | | | | | | | | | | | | |   (4916)  op(all_52_31, all_52_31) = e0
% 221.08/37.45  | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (4627), (4676), (4915), (4916),
% 221.08/37.45  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.08/37.45  | | | | | | | | | | | | | | | | | |            #2086.
% 221.08/37.45  | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | End of split
% 221.08/37.45  | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | End of split
% 221.08/37.45  | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | End of split
% 221.08/37.45  | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | End of split
% 221.08/37.45  | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | Case 2:
% 221.08/37.45  | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | |   (4917)  all_24_2 = e0
% 221.08/37.45  | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | COMBINE_EQS: (315), (4917) imply:
% 221.08/37.45  | | | | | | | | | | | | | |   (4918)  all_6_2 = e0
% 221.08/37.45  | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | SIMP: (4918) implies:
% 221.08/37.45  | | | | | | | | | | | | | |   (4919)  all_6_2 = e0
% 221.08/37.45  | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | REDUCE: (350), (4919) imply:
% 221.08/37.45  | | | | | | | | | | | | | |   (4920)   ~ (all_53_2 = e0)
% 221.08/37.45  | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | REDUCE: (363), (4919) imply:
% 221.08/37.45  | | | | | | | | | | | | | |   (4921)   ~ (all_53_8 = e0)
% 221.08/37.45  | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 221.08/37.45  | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | Case 1:
% 221.08/37.45  | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | |   (4922)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 221.08/37.45  | | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 221.08/37.45  | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | REF_CLOSE: (5), (171), (3960), (4622), (4922),
% 221.08/37.45  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.08/37.45  | | | | | | | | | | | | | | |            #1321.
% 221.08/37.45  | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | Case 2:
% 221.08/37.45  | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | |   (4923)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 221.08/37.45  | | | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 221.08/37.45  | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | BETA: splitting (4923) gives:
% 221.08/37.45  | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | Case 1:
% 221.08/37.45  | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | |   (4924)  all_57_4 = e0 & op(e3, e1) = e0
% 221.08/37.45  | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | ALPHA: (4924) implies:
% 221.08/37.45  | | | | | | | | | | | | | | | |   (4925)  op(e3, e1) = e0
% 221.08/37.45  | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | REF_CLOSE: (170), (4921), (4925), (function-axioms) are
% 221.08/37.45  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2267.
% 221.08/37.45  | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | Case 2:
% 221.08/37.45  | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | |   (4926)  all_57_9 = e0 & op(e3, e0) = e0
% 221.08/37.45  | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | ALPHA: (4926) implies:
% 221.08/37.45  | | | | | | | | | | | | | | | |   (4927)  op(e3, e0) = e0
% 221.08/37.45  | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 221.08/37.45  | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.45  | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | |   (4928)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 221.08/37.45  | | | | | | | | | | | | | | | | |             & op(e2, e3) = e0)
% 221.08/37.45  | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 221.08/37.45  | | | | | | | | | | | | | | | | |            (3970), (4622), (4928), (function-axioms) are
% 221.08/37.45  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1654.
% 221.08/37.45  | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.45  | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | |   (4929)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 221.08/37.45  | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = e0)
% 221.08/37.45  | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | BETA: splitting (4929) gives:
% 221.08/37.45  | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | |   (4930)  all_57_6 = e0 & op(e1, e3) = e0
% 221.08/37.45  | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | ALPHA: (4930) implies:
% 221.08/37.45  | | | | | | | | | | | | | | | | | |   (4931)  op(e1, e3) = e0
% 221.08/37.45  | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_2, e0,
% 221.08/37.45  | | | | | | | | | | | | | | | | | |              e3, e1, simplifying with (164), (4931) gives:
% 221.08/37.45  | | | | | | | | | | | | | | | | | |   (4932)  all_53_2 = e0
% 221.08/37.45  | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | REDUCE: (4920), (4932) imply:
% 221.08/37.45  | | | | | | | | | | | | | | | | | |   (4933)  $false
% 221.08/37.45  | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | CLOSE: (4933) is inconsistent.
% 221.08/37.45  | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | |   (4934)  all_57_12 = e0 & op(e0, e3) = e0
% 221.08/37.45  | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | ALPHA: (4934) implies:
% 221.08/37.45  | | | | | | | | | | | | | | | | | |   (4935)  all_57_12 = e0
% 221.08/37.45  | | | | | | | | | | | | | | | | | |   (4936)  op(e0, e3) = e0
% 221.08/37.45  | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_3, e0,
% 221.08/37.45  | | | | | | | | | | | | | | | | | |              e3, e0, simplifying with (160), (4936) gives:
% 221.08/37.45  | | | | | | | | | | | | | | | | | |   (4937)  all_53_3 = e0
% 221.08/37.45  | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_12,
% 221.08/37.45  | | | | | | | | | | | | | | | | | |              e0, e0, e3, simplifying with (169), (4927) gives:
% 221.08/37.45  | | | | | | | | | | | | | | | | | |   (4938)  all_53_12 = e0
% 221.08/37.45  | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | REDUCE: (149), (4937) imply:
% 221.08/37.45  | | | | | | | | | | | | | | | | | |   (4939)   ~ (all_53_1 = e0)
% 221.08/37.45  | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | REDUCE: (370), (4938) imply:
% 221.08/37.45  | | | | | | | | | | | | | | | | | |   (4940)   ~ (all_4_2 = e0)
% 221.08/37.45  | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | SIMP: (4940) implies:
% 221.08/37.45  | | | | | | | | | | | | | | | | | |   (4941)   ~ (all_4_2 = e0)
% 221.08/37.45  | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | |   (4942)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 221.08/37.45  | | | | | | | | | | | | | | | | | | |             all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 221.08/37.45  | | | | | | | | | | | | | | | | | | |             op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 221.08/37.45  | | | | | | | | | | | | | | | | | | |               all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 221.08/37.45  | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 221.08/37.45  | | | | | | | | | | | | | | | | | | |             op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 221.08/37.45  | | | | | | | | | | | | | | | | | | |             $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 221.08/37.45  | | | | | | | | | | | | | | | | | | |             $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 221.08/37.45  | | | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 221.08/37.45  | | | | | | | | | | | | | | | | | | |               all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 221.08/37.45  | | | | | | | | | | | | | | | | | | |             & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 221.08/37.45  | | | | | | | | | | | | | | | | | | |               all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 221.08/37.45  | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 221.08/37.45  | | | | | | | | | | | | | | | | | | |             & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 221.08/37.45  | | | | | | | | | | | | | | | | | | |             $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | BETA: splitting (4942) gives:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | |   (4943)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | |           all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | |           op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | |             all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | |           $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | |           $i(all_52_7)
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | ALPHA: (4943) implies:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | |   (4944)  op(e3, e3) = all_52_1
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | |   (4945)  op(all_52_1, all_52_1) = e3
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3971), (4622), (4944), (4945),
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | |            #1653.
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | |   (4946)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | |           all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | |           op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | |             all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | |           & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | |           $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | |           $i(all_52_15)
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | ALPHA: (4946) implies:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | |   (4947)  op(e2, e2) = all_52_11
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | |   (4948)  op(all_52_11, all_52_11) = e2
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | |   (4949)  all_55_15 = e3
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (378), (4949) are inconsistent by sub-proof
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | |            #2503.
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | |   (4950)   ~ (all_55_15 = e3)
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | |   (4951)  all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4951) gives:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | |   (4952)  all_55_15 = e2
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (373), (4952) are inconsistent by sub-proof
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | |            #2502.
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | |   (4953)   ~ (all_55_15 = e2)
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | |   (4954)  all_55_15 = e1 | all_55_15 = e0
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4954) gives:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.45  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | |   (4955)  all_55_15 = e1
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (4955) imply:
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | |   (4956)  all_4_2 = e1
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4956) implies:
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | |   (4957)  all_4_2 = e1
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (378), (4957) imply:
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | |   (4958)   ~ (e3 = e1)
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (373), (4957) imply:
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | |   (4959)   ~ (e2 = e1)
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (4957) imply:
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | |   (4960)  op(e0, e0) = e1
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (160), (208), (209),
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | |            (210), (3971), (4618), (4935), (4947), (4948),
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | |            (4960), (function-axioms) are inconsistent by
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1228.
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | |   (4961)  all_55_15 = e0
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (4941), (4961) are inconsistent by
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1884.
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | | |   (4962)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 221.08/37.46  | | | | | | | | | | | | | | | | | | |             & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 221.08/37.46  | | | | | | | | | | | | | | | | | | |             & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 221.08/37.46  | | | | | | | | | | | | | | | | | | |               all_52_21) = e1 & op(all_52_23, all_52_23) =
% 221.08/37.46  | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 221.08/37.46  | | | | | | | | | | | | | | | | | | |             all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 221.08/37.46  | | | | | | | | | | | | | | | | | | |             = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 221.08/37.46  | | | | | | | | | | | | | | | | | | |             $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 221.08/37.46  | | | | | | | | | | | | | | | | | | |             & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 221.08/37.46  | | | | | | | | | | | | | | | | | | |             e0 & op(all_52_25, all_52_25) = e3 &
% 221.08/37.46  | | | | | | | | | | | | | | | | | | |             op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 221.08/37.46  | | | | | | | | | | | | | | | | | | |               all_52_29) = e1 & op(all_52_31, all_52_31) =
% 221.08/37.46  | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 221.08/37.46  | | | | | | | | | | | | | | | | | | |             all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 221.08/37.46  | | | | | | | | | | | | | | | | | | |             = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 221.08/37.46  | | | | | | | | | | | | | | | | | | |             $i(all_52_29) & $i(all_52_31))
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | BETA: splitting (4962) gives:
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | |   (4963)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | |           all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | |           op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | |             all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | |           & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | |           & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | |           & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | |           $i(all_52_23)
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | ALPHA: (4963) implies:
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | |   (4964)  op(e1, e3) = all_52_17
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | |   (4965)  op(all_52_17, all_52_17) = e3
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (150), (164), (190), (197), (201), (244),
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | |            (257), (267), (374), (378), (4616), (4617),
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | |            (4622), (4920), (4939), (4964), (4965),
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | |            #1864.
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | |   (4966)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | |           all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | |           op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | |             all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | |           & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | |           & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | |           & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | |           $i(all_52_31)
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | ALPHA: (4966) implies:
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | |   (4967)  op(e0, e0) = all_52_31
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | |   (4968)  op(e0, e3) = all_52_25
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | |   (4969)  op(all_52_25, all_52_25) = e3
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | |   (4970)  all_55_15 = e3
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (378), (4970) are inconsistent by sub-proof
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | |            #2503.
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | |   (4971)   ~ (all_55_15 = e3)
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | |   (4972)  all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4972) gives:
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | |   (4973)  all_55_15 = e2
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (373), (4973) are inconsistent by sub-proof
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | |            #2502.
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | |   (4974)   ~ (all_55_15 = e2)
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | |   (4975)  all_55_15 = e1 | all_55_15 = e0
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4975) gives:
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | |   (4976)  all_55_15 = e1
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (4976) imply:
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | |   (4977)  all_4_2 = e1
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4977) implies:
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | |   (4978)  all_4_2 = e1
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (378), (4978) imply:
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | |   (4979)   ~ (e3 = e1)
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (373), (4978) imply:
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | |   (4980)   ~ (e2 = e1)
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (4978) imply:
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | |   (4981)  op(e0, e0) = e1
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (160), (208), (209),
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | |            (210), (4618), (4935), (4936), (4967), (4968),
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | |            (4969), (4981), (function-axioms) are inconsistent
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1962.
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | |   (4982)  all_55_15 = e0
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (4941), (4982) are inconsistent by
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1884.
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.46  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.46  | | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | End of split
% 221.08/37.46  | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | End of split
% 221.08/37.46  | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | End of split
% 221.08/37.46  | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | End of split
% 221.08/37.46  | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | End of split
% 221.08/37.46  | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | Case 2:
% 221.08/37.46  | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | |   (4983)  all_57_1 = e2 & op(e3, e2) = e2
% 221.08/37.46  | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | ALPHA: (4983) implies:
% 221.08/37.46  | | | | | | | | | | | | |   (4984)  all_57_1 = e2
% 221.08/37.46  | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (237),
% 221.08/37.46  | | | | | | | | | | | | |            (4622), (4984), (function-axioms) are inconsistent
% 221.08/37.46  | | | | | | | | | | | | |            by sub-proof #1655.
% 221.08/37.46  | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | End of split
% 221.08/37.46  | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | Case 2:
% 221.08/37.46  | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | |   (4985)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 221.08/37.46  | | | | | | | | | | | |             & op(e3, e0) = e2)
% 221.08/37.46  | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | BETA: splitting (4985) gives:
% 221.08/37.46  | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | Case 1:
% 221.08/37.46  | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | |   (4986)  all_57_4 = e2 & op(e3, e1) = e2
% 221.08/37.46  | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | ALPHA: (4986) implies:
% 221.08/37.46  | | | | | | | | | | | | |   (4987)  all_57_4 = e2
% 221.08/37.46  | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | BETA: splitting (231) gives:
% 221.08/37.46  | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | Case 1:
% 221.08/37.46  | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | |   (4988)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 221.08/37.46  | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 221.08/37.46  | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | REF_CLOSE: (5), (171), (3960), (4622), (4988),
% 221.08/37.46  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.08/37.46  | | | | | | | | | | | | | |            #1321.
% 221.08/37.46  | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | Case 2:
% 221.08/37.46  | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | |   (4989)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 221.08/37.46  | | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 221.08/37.46  | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (233), (237),
% 221.08/37.46  | | | | | | | | | | | | | |            (4622), (4987), (4989), (function-axioms) are
% 221.08/37.46  | | | | | | | | | | | | | |            inconsistent by sub-proof #1605.
% 221.08/37.46  | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | End of split
% 221.08/37.46  | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | Case 2:
% 221.08/37.46  | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | |   (4990)  all_57_9 = e2 & op(e3, e0) = e2
% 221.08/37.46  | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | ALPHA: (4990) implies:
% 221.08/37.46  | | | | | | | | | | | | |   (4991)  op(e3, e0) = e2
% 221.08/37.46  | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | REF_CLOSE: (169), (4621), (4991), (function-axioms) are
% 221.08/37.46  | | | | | | | | | | | | |            inconsistent by sub-proof #2331.
% 221.08/37.46  | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | End of split
% 221.08/37.46  | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | End of split
% 221.08/37.46  | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | End of split
% 221.08/37.46  | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | Case 2:
% 221.08/37.46  | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | |   (4992)  all_18_2 = e0
% 221.08/37.46  | | | | | | | | | |   (4993)  ( ~ (all_18_0 = e1) & op(all_18_1, e3) = all_18_0
% 221.08/37.46  | | | | | | | | | |             & op(e3, e0) = all_18_1 & $i(all_18_0) &
% 221.08/37.46  | | | | | | | | | |             $i(all_18_1)) | ( ~ (all_18_1 = e2) & op(e3, e0)
% 221.08/37.46  | | | | | | | | | |             = all_18_1 & $i(all_18_1))
% 221.08/37.46  | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | COMBINE_EQS: (327), (4992) imply:
% 221.08/37.46  | | | | | | | | | |   (4994)  all_10_2 = e0
% 221.08/37.46  | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | SIMP: (4994) implies:
% 221.08/37.46  | | | | | | | | | |   (4995)  all_10_2 = e0
% 221.08/37.46  | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | COMBINE_EQS: (279), (4995) imply:
% 221.08/37.46  | | | | | | | | | |   (4996)  all_48_2 = e0
% 221.08/37.46  | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | REDUCE: (338), (4995) imply:
% 221.08/37.46  | | | | | | | | | |   (4997)   ~ (all_53_1 = e0)
% 221.08/37.46  | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | REDUCE: (340), (4995) imply:
% 221.08/37.46  | | | | | | | | | |   (4998)   ~ (all_53_2 = e0)
% 221.08/37.46  | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | REDUCE: (342), (4995) imply:
% 221.08/37.46  | | | | | | | | | |   (4999)   ~ (all_53_3 = e0)
% 221.08/37.46  | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | REDUCE: (346), (4995) imply:
% 221.08/37.46  | | | | | | | | | |   (5000)   ~ (all_53_8 = e0)
% 221.08/37.46  | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | REDUCE: (348), (4995) imply:
% 221.08/37.46  | | | | | | | | | |   (5001)   ~ (all_53_12 = e0)
% 221.08/37.46  | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | REDUCE: (376), (4995) imply:
% 221.08/37.46  | | | | | | | | | |   (5002)   ~ (e1 = e0)
% 221.08/37.46  | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | BETA: splitting (231) gives:
% 221.08/37.46  | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | Case 1:
% 221.08/37.46  | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | |   (5003)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 221.08/37.46  | | | | | | | | | | |             & op(e3, e2) = e0)
% 221.08/37.46  | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | BETA: splitting (5003) gives:
% 221.08/37.46  | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | Case 1:
% 221.08/37.46  | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | |   (5004)  all_57_0 = e0 & op(e3, e3) = e0
% 221.08/37.46  | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | ALPHA: (5004) implies:
% 221.08/37.46  | | | | | | | | | | | |   (5005)  all_57_0 = e0
% 221.08/37.46  | | | | | | | | | | | |   (5006)  op(e3, e3) = e0
% 221.08/37.46  | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | BETA: splitting (67) gives:
% 221.08/37.46  | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | Case 1:
% 221.08/37.46  | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | |   (5007)   ~ (all_24_2 = e0)
% 221.08/37.46  | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | REDUCE: (315), (5007) imply:
% 221.08/37.46  | | | | | | | | | | | | |   (5008)   ~ (all_6_2 = e0)
% 221.08/37.46  | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | BETA: splitting (214) gives:
% 221.08/37.46  | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | Case 1:
% 221.08/37.46  | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | |   (5009)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 221.08/37.46  | | | | | | | | | | | | | |             & op(e1, e2) = e0)
% 221.08/37.46  | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | REF_CLOSE: (163), (164), (3961), (4998), (5009),
% 221.08/37.46  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.08/37.46  | | | | | | | | | | | | | |            #2038.
% 221.08/37.46  | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | Case 2:
% 221.08/37.46  | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | |   (5010)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 221.08/37.46  | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 221.08/37.46  | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | BETA: splitting (5010) gives:
% 221.08/37.46  | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | Case 1:
% 221.08/37.46  | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | |   (5011)  all_57_8 = e0 & op(e1, e1) = e0
% 221.08/37.46  | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | REF_CLOSE: (39), (5008), (5011), (function-axioms) are
% 221.08/37.46  | | | | | | | | | | | | | | |            inconsistent by sub-proof #2412.
% 221.08/37.46  | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | Case 2:
% 221.08/37.46  | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | |   (5012)  all_57_11 = e0 & op(e1, e0) = e0
% 221.08/37.46  | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | ALPHA: (5012) implies:
% 221.08/37.46  | | | | | | | | | | | | | | |   (5013)  op(e1, e0) = e0
% 221.08/37.46  | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 221.08/37.46  | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | Case 1:
% 221.08/37.46  | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | |   (5014)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 221.08/37.46  | | | | | | | | | | | | | | | |             & op(e2, e1) = e0)
% 221.08/37.46  | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | BETA: splitting (5014) gives:
% 221.08/37.46  | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.46  | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | |   (5015)  all_57_4 = e0 & op(e3, e1) = e0
% 221.08/37.46  | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | ALPHA: (5015) implies:
% 221.08/37.46  | | | | | | | | | | | | | | | | |   (5016)  op(e3, e1) = e0
% 221.08/37.46  | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (5000), (5016), (function-axioms) are
% 221.08/37.46  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2267.
% 221.08/37.46  | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.46  | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | |   (5017)  all_57_5 = e0 & op(e2, e1) = e0
% 221.08/37.46  | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | ALPHA: (5017) implies:
% 221.08/37.46  | | | | | | | | | | | | | | | | |   (5018)  op(e2, e1) = e0
% 221.08/37.46  | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_9, e0,
% 221.08/37.46  | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (166), (5018) gives:
% 221.08/37.46  | | | | | | | | | | | | | | | | |   (5019)  all_53_9 = e0
% 221.08/37.46  | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | REDUCE: (3963), (5019) imply:
% 221.08/37.46  | | | | | | | | | | | | | | | | |   (5020)  $false
% 221.08/37.46  | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | CLOSE: (5020) is inconsistent.
% 221.08/37.46  | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | End of split
% 221.08/37.46  | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | Case 2:
% 221.08/37.46  | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | |   (5021)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 221.08/37.46  | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 221.08/37.46  | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | BETA: splitting (5021) gives:
% 221.08/37.46  | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.46  | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | |   (5022)  all_57_8 = e0 & op(e1, e1) = e0
% 221.08/37.46  | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (5008), (5022), (function-axioms) are
% 221.08/37.46  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2412.
% 221.08/37.46  | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.46  | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | |   (5023)  all_57_14 = e0 & op(e0, e1) = e0
% 221.08/37.46  | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | ALPHA: (5023) implies:
% 221.08/37.46  | | | | | | | | | | | | | | | | |   (5024)  all_57_14 = e0
% 221.08/37.46  | | | | | | | | | | | | | | | | |   (5025)  op(e0, e1) = e0
% 221.08/37.46  | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (9), (36), (39), (91), (107), (158),
% 221.08/37.46  | | | | | | | | | | | | | | | | |            (161), (190), (208), (209), (210), (244), (295),
% 221.08/37.46  | | | | | | | | | | | | | | | | |            (368), (372), (373), (378), (3971), (5006),
% 221.08/37.46  | | | | | | | | | | | | | | | | |            (5013), (5024), (5025), (function-axioms) are
% 221.08/37.46  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1226.
% 221.08/37.46  | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | End of split
% 221.08/37.46  | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | End of split
% 221.08/37.46  | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | End of split
% 221.08/37.46  | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | End of split
% 221.08/37.46  | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | Case 2:
% 221.08/37.46  | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | |   (5026)  all_24_2 = e0
% 221.08/37.46  | | | | | | | | | | | | |   (5027)  ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0
% 221.08/37.46  | | | | | | | | | | | | |             & op(e1, e0) = all_24_1 & $i(all_24_0) &
% 221.08/37.46  | | | | | | | | | | | | |             $i(all_24_1)) | ( ~ (all_24_1 = e3) & op(e1, e0)
% 221.08/37.46  | | | | | | | | | | | | |             = all_24_1 & $i(all_24_1))
% 221.08/37.46  | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | COMBINE_EQS: (315), (5026) imply:
% 221.08/37.46  | | | | | | | | | | | | |   (5028)  all_6_2 = e0
% 221.08/37.46  | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | SIMP: (5028) implies:
% 221.08/37.46  | | | | | | | | | | | | |   (5029)  all_6_2 = e0
% 221.08/37.46  | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | COMBINE_EQS: (311), (5029) imply:
% 221.08/37.46  | | | | | | | | | | | | |   (5030)  all_34_2 = e0
% 221.08/37.46  | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | REDUCE: (368), (5029) imply:
% 221.08/37.46  | | | | | | | | | | | | |   (5031)   ~ (all_53_14 = e0)
% 221.08/37.46  | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | BETA: splitting (214) gives:
% 221.08/37.46  | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | Case 1:
% 221.08/37.46  | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | |   (5032)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 221.08/37.46  | | | | | | | | | | | | | |             & op(e1, e2) = e0)
% 221.08/37.46  | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | REF_CLOSE: (163), (164), (3961), (4998), (5032),
% 221.08/37.46  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.08/37.46  | | | | | | | | | | | | | |            #2038.
% 221.08/37.46  | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | Case 2:
% 221.08/37.46  | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | |   (5033)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 221.08/37.46  | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 221.08/37.46  | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | BETA: splitting (5033) gives:
% 221.08/37.46  | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | Case 1:
% 221.08/37.46  | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | |   (5034)  all_57_8 = e0 & op(e1, e1) = e0
% 221.08/37.46  | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | ALPHA: (5034) implies:
% 221.08/37.46  | | | | | | | | | | | | | | |   (5035)  all_57_8 = e0
% 221.08/37.46  | | | | | | | | | | | | | | |   (5036)  op(e1, e1) = e0
% 221.08/37.46  | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 221.08/37.46  | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | Case 1:
% 221.08/37.46  | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | |   (5037)  all_57_15 = e0 & op(e0, e0) = e0
% 221.08/37.46  | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | ALPHA: (5037) implies:
% 221.08/37.46  | | | | | | | | | | | | | | | |   (5038)  all_57_15 = e0
% 221.08/37.46  | | | | | | | | | | | | | | | |   (5039)  op(e0, e0) = e0
% 221.08/37.46  | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, e0,
% 221.08/37.46  | | | | | | | | | | | | | | | |              e0, e0, simplifying with (36), (5039) gives:
% 221.08/37.46  | | | | | | | | | | | | | | | |   (5040)  all_4_2 = e0
% 221.08/37.46  | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | REDUCE: (369), (5040) imply:
% 221.08/37.46  | | | | | | | | | | | | | | | |   (5041)   ~ (all_53_11 = e0)
% 221.08/37.46  | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | REDUCE: (373), (5040) imply:
% 221.08/37.46  | | | | | | | | | | | | | | | |   (5042)   ~ (e2 = e0)
% 221.08/37.46  | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 221.08/37.46  | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.46  | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | |   (5043)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 221.08/37.46  | | | | | | | | | | | | | | | | |             all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 221.08/37.46  | | | | | | | | | | | | | | | | |             op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 221.08/37.46  | | | | | | | | | | | | | | | | |               all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 221.08/37.46  | | | | | | | | | | | | | | | | |             op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 221.08/37.46  | | | | | | | | | | | | | | | | |             op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 221.08/37.46  | | | | | | | | | | | | | | | | |             $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 221.08/37.46  | | | | | | | | | | | | | | | | |             $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 221.08/37.46  | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 221.08/37.46  | | | | | | | | | | | | | | | | |               all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 221.08/37.46  | | | | | | | | | | | | | | | | |             & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 221.08/37.46  | | | | | | | | | | | | | | | | |               all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 221.08/37.46  | | | | | | | | | | | | | | | | |             op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 221.08/37.46  | | | | | | | | | | | | | | | | |             & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 221.08/37.46  | | | | | | | | | | | | | | | | |             $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 221.08/37.46  | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | BETA: splitting (5043) gives:
% 221.08/37.46  | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.46  | | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | |   (5044)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 221.08/37.46  | | | | | | | | | | | | | | | | | |           all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 221.08/37.46  | | | | | | | | | | | | | | | | | |           op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 221.08/37.46  | | | | | | | | | | | | | | | | | |             all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 221.08/37.46  | | | | | | | | | | | | | | | | | |           op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 221.08/37.46  | | | | | | | | | | | | | | | | | |           op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 221.08/37.46  | | | | | | | | | | | | | | | | | |           $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 221.08/37.46  | | | | | | | | | | | | | | | | | |           $i(all_52_7)
% 221.08/37.46  | | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5006), (5039), (5044), (function-axioms) are
% 221.08/37.46  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1939.
% 221.08/37.46  | | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.46  | | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | |   (5045)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 221.08/37.46  | | | | | | | | | | | | | | | | | |           all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 221.08/37.46  | | | | | | | | | | | | | | | | | |           op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 221.08/37.46  | | | | | | | | | | | | | | | | | |             all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 221.08/37.46  | | | | | | | | | | | | | | | | | |           & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 221.08/37.46  | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 221.08/37.46  | | | | | | | | | | | | | | | | | |           $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 221.08/37.46  | | | | | | | | | | | | | | | | | |           $i(all_52_15)
% 221.08/37.46  | | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | | ALPHA: (5045) implies:
% 221.08/37.46  | | | | | | | | | | | | | | | | | |   (5046)  op(e2, e2) = all_52_11
% 221.08/37.46  | | | | | | | | | | | | | | | | | |   (5047)  op(all_52_11, all_52_11) = e2
% 221.08/37.46  | | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3971), (5039), (5046), (5047),
% 221.08/37.46  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.08/37.46  | | | | | | | | | | | | | | | | | |            #2270.
% 221.08/37.46  | | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | | End of split
% 221.08/37.46  | | | | | | | | | | | | | | | | | 
% 221.08/37.46  | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.46  | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | |   (5048)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 221.08/37.47  | | | | | | | | | | | | | | | | |             & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 221.08/37.47  | | | | | | | | | | | | | | | | |             & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 221.08/37.47  | | | | | | | | | | | | | | | | |               all_52_21) = e1 & op(all_52_23, all_52_23) =
% 221.08/37.47  | | | | | | | | | | | | | | | | |             e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 221.08/37.47  | | | | | | | | | | | | | | | | |             all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 221.08/37.47  | | | | | | | | | | | | | | | | |             = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 221.08/37.47  | | | | | | | | | | | | | | | | |             $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 221.08/37.47  | | | | | | | | | | | | | | | | |             & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 221.08/37.47  | | | | | | | | | | | | | | | | |             e0 & op(all_52_25, all_52_25) = e3 &
% 221.08/37.47  | | | | | | | | | | | | | | | | |             op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 221.08/37.47  | | | | | | | | | | | | | | | | |               all_52_29) = e1 & op(all_52_31, all_52_31) =
% 221.08/37.47  | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 221.08/37.47  | | | | | | | | | | | | | | | | |             all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 221.08/37.47  | | | | | | | | | | | | | | | | |             = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 221.08/37.47  | | | | | | | | | | | | | | | | |             $i(all_52_29) & $i(all_52_31))
% 221.08/37.47  | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | BETA: splitting (5048) gives:
% 221.08/37.47  | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | |   (5049)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 221.08/37.47  | | | | | | | | | | | | | | | | | |           all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 221.08/37.47  | | | | | | | | | | | | | | | | | |           op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 221.08/37.47  | | | | | | | | | | | | | | | | | |             all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 221.08/37.47  | | | | | | | | | | | | | | | | | |           & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 221.08/37.47  | | | | | | | | | | | | | | | | | |           & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 221.08/37.47  | | | | | | | | | | | | | | | | | |           & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 221.08/37.47  | | | | | | | | | | | | | | | | | |           $i(all_52_23)
% 221.08/37.47  | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5036), (5039), (5049), (function-axioms) are
% 221.08/37.47  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2036.
% 221.08/37.47  | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | |   (5050)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 221.08/37.47  | | | | | | | | | | | | | | | | | |           all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 221.08/37.47  | | | | | | | | | | | | | | | | | |           op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 221.08/37.47  | | | | | | | | | | | | | | | | | |             all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 221.08/37.47  | | | | | | | | | | | | | | | | | |           & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 221.08/37.47  | | | | | | | | | | | | | | | | | |           & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 221.08/37.47  | | | | | | | | | | | | | | | | | |           & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 221.08/37.47  | | | | | | | | | | | | | | | | | |           $i(all_52_31)
% 221.08/37.47  | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | ALPHA: (5050) implies:
% 221.08/37.47  | | | | | | | | | | | | | | | | | |   (5051)  op(e0, e0) = all_52_31
% 221.08/37.47  | | | | | | | | | | | | | | | | | |   (5052)  op(e0, e1) = all_52_29
% 221.08/37.47  | | | | | | | | | | | | | | | | | |   (5053)  op(e0, e2) = all_52_27
% 221.08/37.47  | | | | | | | | | | | | | | | | | |   (5054)  op(e0, e3) = all_52_25
% 221.08/37.47  | | | | | | | | | | | | | | | | | |   (5055)  op(all_52_29, all_52_29) = e1
% 221.08/37.47  | | | | | | | | | | | | | | | | | |   (5056)  op(all_52_27, all_52_27) = e2
% 221.08/37.47  | | | | | | | | | | | | | | | | | |   (5057)  op(all_52_25, all_52_25) = e3
% 221.08/37.47  | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 221.08/37.47  | | | | | | | | | | | | | | | | | |              all_52_31, e0, e0, simplifying with (5039), (5051)
% 221.08/37.47  | | | | | | | | | | | | | | | | | |              gives:
% 221.08/37.47  | | | | | | | | | | | | | | | | | |   (5058)  all_52_31 = e0
% 221.08/37.47  | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_11,
% 221.08/37.47  | | | | | | | | | | | | | | | | | |              all_52_29, e1, e0, simplifying with (158), (5052)
% 221.08/37.47  | | | | | | | | | | | | | | | | | |              gives:
% 221.08/37.47  | | | | | | | | | | | | | | | | | |   (5059)  all_53_11 = all_52_29
% 221.08/37.47  | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_7,
% 221.08/37.47  | | | | | | | | | | | | | | | | | |              all_52_27, e2, e0, simplifying with (159), (5053)
% 221.08/37.47  | | | | | | | | | | | | | | | | | |              gives:
% 221.08/37.47  | | | | | | | | | | | | | | | | | |   (5060)  all_53_7 = all_52_27
% 221.08/37.47  | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_3,
% 221.08/37.47  | | | | | | | | | | | | | | | | | |              all_52_25, e3, e0, simplifying with (160), (5054)
% 221.08/37.47  | | | | | | | | | | | | | | | | | |              gives:
% 221.08/37.47  | | | | | | | | | | | | | | | | | |   (5061)  all_53_3 = all_52_25
% 221.08/37.47  | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (5059) imply:
% 221.08/37.47  | | | | | | | | | | | | | | | | | |   (5062)  all_55_14 = all_52_29
% 221.08/37.47  | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (5060) imply:
% 221.08/37.47  | | | | | | | | | | | | | | | | | |   (5063)  all_55_13 = all_52_27
% 221.08/37.47  | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (5061) imply:
% 221.08/37.47  | | | | | | | | | | | | | | | | | |   (5064)  all_55_12 = all_52_25
% 221.08/37.47  | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | REDUCE: (149), (5061) imply:
% 221.08/37.47  | | | | | | | | | | | | | | | | | |   (5065)   ~ (all_53_1 = all_52_25)
% 221.08/37.47  | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | REDUCE: (145), (5061) imply:
% 221.08/37.47  | | | | | | | | | | | | | | | | | |   (5066)   ~ (all_53_2 = all_52_25)
% 221.08/37.47  | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | REDUCE: (4999), (5061) imply:
% 221.08/37.47  | | | | | | | | | | | | | | | | | |   (5067)   ~ (all_52_25 = e0)
% 221.08/37.47  | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | REDUCE: (136), (5060) imply:
% 221.08/37.47  | | | | | | | | | | | | | | | | | |   (5068)   ~ (all_53_4 = all_52_27)
% 221.08/37.47  | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | REDUCE: (129), (5060) imply:
% 221.08/37.47  | | | | | | | | | | | | | | | | | |   (5069)   ~ (all_53_6 = all_52_27)
% 221.08/37.47  | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | REDUCE: (126), (5059), (5060) imply:
% 221.08/37.47  | | | | | | | | | | | | | | | | | |   (5070)   ~ (all_52_27 = all_52_29)
% 221.08/37.47  | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | REDUCE: (3962), (5060) imply:
% 221.08/37.47  | | | | | | | | | | | | | | | | | |   (5071)   ~ (all_52_27 = e0)
% 221.08/37.47  | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | REDUCE: (122), (5059) imply:
% 221.08/37.47  | | | | | | | | | | | | | | | | | |   (5072)   ~ (all_53_8 = all_52_29)
% 221.08/37.47  | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | REDUCE: (119), (5059) imply:
% 221.08/37.47  | | | | | | | | | | | | | | | | | |   (5073)   ~ (all_53_9 = all_52_29)
% 221.08/37.47  | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | REDUCE: (5041), (5059) imply:
% 221.08/37.47  | | | | | | | | | | | | | | | | | |   (5074)   ~ (all_52_29 = e0)
% 221.08/37.47  | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | BETA: splitting (82) gives:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | |   (5075)   ~ (all_34_2 = e0)
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | REDUCE: (5030), (5075) imply:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | |   (5076)  $false
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | CLOSE: (5076) is inconsistent.
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | |   (5077)  ( ~ (all_34_0 = e3) & op(all_34_1, e1) = all_34_0
% 221.08/37.47  | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = all_34_1 & $i(all_34_0) &
% 221.08/37.47  | | | | | | | | | | | | | | | | | | |             $i(all_34_1)) | ( ~ (all_34_1 = e2) & op(e1, e0)
% 221.08/37.47  | | | | | | | | | | | | | | | | | | |             = all_34_1 & $i(all_34_1))
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | BETA: splitting (103) gives:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | |   (5078)   ~ (all_48_2 = e0)
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | REDUCE: (4996), (5078) imply:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | |   (5079)  $false
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | CLOSE: (5079) is inconsistent.
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | |   (5080)  ( ~ (all_48_0 = e2) & op(all_48_1, e3) = all_48_0
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_48_1 & $i(all_48_0) &
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | |             $i(all_48_1)) | ( ~ (all_48_1 = e1) & op(e3, e0)
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | |             = all_48_1 & $i(all_48_1))
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | BETA: splitting (106) gives:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | |   (5081)   ~ (all_50_2 = e0)
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | REDUCE: (3959), (5081) imply:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | |   (5082)  $false
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | CLOSE: (5082) is inconsistent.
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | |   (5083)  ( ~ (all_50_0 = e3) & op(all_50_1, e2) = all_50_0
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | |             & op(e2, e0) = all_50_1 & $i(all_50_0) &
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | |             $i(all_50_1)) | ( ~ (all_50_1 = e1) & op(e2, e0)
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | |             = all_50_1 & $i(all_50_1))
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | |   (5084)  all_55_7 = e3
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (5084) imply:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | |   (5085)  all_53_13 = e3
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | SIMP: (5085) implies:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | |   (5086)  all_53_13 = e3
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (114), (5086) imply:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | |   (5087)   ~ (all_53_12 = e3)
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (111), (5086) imply:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | |   (5088)   ~ (all_53_14 = e3)
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | SIMP: (5088) implies:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | |   (5089)   ~ (all_53_14 = e3)
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | |   (5090)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5090) gives:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | |   (5091)  all_57_2 = e3 & op(e2, e3) = e3
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5091) implies:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | |   (5092)  all_57_2 = e3
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | |   (5093)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (169), (223), (224),
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | |            (3970), (5087), (5092), (5093), (function-axioms)
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1334.
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | |   (5094)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (161), (5039), (5089), (5094),
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | |            #2303.
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | |   (5095)  all_57_3 = e3 & op(e2, e2) = e3
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5095) implies:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | |   (5096)  all_57_3 = e3
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3970), (5096) are inconsistent by sub-proof
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | |            #2358.
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | |   (5097)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5097) gives:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | |   (5098)  all_57_5 = e3 & op(e2, e1) = e3
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5098) implies:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | |   (5099)  all_57_5 = e3
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | |   (5100)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (169), (223), (224),
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | |            (3970), (5087), (5099), (5100), (function-axioms)
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1409.
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | |   (5101)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (161), (5039), (5089), (5101),
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | |            #2303.
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | |   (5102)  all_57_10 = e3 & op(e2, e0) = e3
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5102) implies:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | |   (5103)  all_57_10 = e3
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | |   (5104)  op(e2, e0) = e3
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3957) gives:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | |   (5105)   ~ (all_14_0 = e1) & op(all_14_1, e2) = all_14_0 &
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_14_1 & $i(all_14_0) &
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_14_1)
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5105) implies:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | |   (5106)   ~ (all_14_0 = e1)
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | |   (5107)  op(e2, e0) = all_14_1
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | |   (5108)  op(all_14_1, e2) = all_14_0
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5083) gives:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5109)   ~ (all_50_0 = e3) & op(all_50_1, e2) = all_50_0 &
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_50_1 & $i(all_50_0) &
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_50_1)
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5109) implies:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5110)   ~ (all_50_0 = e3)
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5111)  op(e2, e0) = all_50_1
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5112)  op(all_50_1, e2) = all_50_0
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | |              all_50_1, e0, e2, simplifying with (5107), (5111)
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5113)  all_50_1 = all_14_1
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_50_1,
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e2, simplifying with (5104), (5111) gives:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5114)  all_50_1 = e3
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5113), (5114) imply:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5115)  all_14_1 = e3
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5112), (5114) imply:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5116)  op(e3, e2) = all_50_0
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5108), (5115) imply:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5117)  op(e3, e2) = all_14_0
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_4,
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | |              all_14_0, e2, e3, simplifying with (171), (5117)
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5118)  all_53_4 = all_14_0
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_4,
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | |              all_50_0, e2, e3, simplifying with (171), (5116)
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5119)  all_53_4 = all_50_0
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5118), (5119) imply:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5120)  all_50_0 = all_14_0
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5120) implies:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5121)  all_50_0 = all_14_0
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (5118) imply:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5122)  all_55_1 = all_14_0
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (137), (5118) imply:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5123)   ~ (all_53_6 = all_14_0)
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5123) implies:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5124)   ~ (all_53_6 = all_14_0)
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (5118) imply:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5125)   ~ (all_53_8 = all_14_0)
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5125) implies:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5126)   ~ (all_53_8 = all_14_0)
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (5118) imply:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5127)   ~ (all_53_12 = all_14_0)
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5127) implies:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5128)   ~ (all_53_12 = all_14_0)
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5068), (5118) imply:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5129)   ~ (all_52_27 = all_14_0)
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5129) implies:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5130)   ~ (all_52_27 = all_14_0)
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3960), (5118) imply:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5131)   ~ (all_14_0 = e0)
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5110), (5121) imply:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5132)   ~ (all_14_0 = e3)
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5133)  all_55_1 = e3
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5122), (5132), (5133) are inconsistent by
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1225.
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5134)   ~ (all_55_1 = e3)
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5135)  all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (39), (121), (144), (161), (164), (169),
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (191), (192), (196), (197), (202), (203), (209),
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (211), (212), (214), (215), (216), (217), (219),
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (221), (223), (224), (225), (226), (227), (228),
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (229), (230), (231), (232), (233), (234), (235),
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (236), (237), (256), (257), (268), (269), (374),
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3961), (3970), (3971), (4993), (4998), (5000),
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5001), (5005), (5006), (5035), (5036), (5038),
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5039), (5055), (5056), (5062), (5063), (5069),
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5070), (5071), (5072), (5074), (5080), (5087),
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5089), (5103), (5104), (5106), (5107), (5108),
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5111), (5117), (5122), (5124), (5126), (5128),
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5130), (5131), (5132), (5135), (function-axioms)
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1196.
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5136)   ~ (all_50_1 = e1) & op(e2, e0) = all_50_1 &
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_50_1)
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5136) implies:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5137)  op(e2, e0) = all_50_1
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | |              all_50_1, e0, e2, simplifying with (5107), (5137)
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5138)  all_50_1 = all_14_1
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_50_1,
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e2, simplifying with (5104), (5137) gives:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5139)  all_50_1 = e3
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5138), (5139) imply:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5140)  all_14_1 = e3
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5108), (5140) imply:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5141)  op(e3, e2) = all_14_0
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_4,
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | |              all_14_0, e2, e3, simplifying with (171), (5141)
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5142)  all_53_4 = all_14_0
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (5142) imply:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5143)  all_55_1 = all_14_0
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (137), (5142) imply:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5144)   ~ (all_53_6 = all_14_0)
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5144) implies:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5145)   ~ (all_53_6 = all_14_0)
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (5142) imply:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5146)   ~ (all_53_8 = all_14_0)
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5146) implies:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5147)   ~ (all_53_8 = all_14_0)
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (5142) imply:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5148)   ~ (all_53_12 = all_14_0)
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5148) implies:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5149)   ~ (all_53_12 = all_14_0)
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5068), (5142) imply:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5150)   ~ (all_52_27 = all_14_0)
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5150) implies:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5151)   ~ (all_52_27 = all_14_0)
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3960), (5142) imply:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5152)   ~ (all_14_0 = e0)
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5153)  all_55_1 = e3
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5143), (5153) imply:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5154)  all_14_0 = e3
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5154) implies:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5155)  all_14_0 = e3
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5141), (5155) imply:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5156)  op(e3, e2) = e3
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5157)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e3)
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5157) gives:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5158)  all_57_4 = e3 & op(e3, e1) = e3
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5158) implies:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5159)  all_57_4 = e3
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5160)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e2)
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (5006), (5156), (5160),
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1195.
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5161)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e2)
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5161) gives:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5162)  all_57_4 = e2 & op(e3, e1) = e2
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5162) implies:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5163)  all_57_4 = e2
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5159), (5163) are inconsistent by sub-proof
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2482.
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5164)  all_57_9 = e2 & op(e3, e0) = e2
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5164) implies:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5165)  all_57_9 = e2
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5166)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e1)
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5166) gives:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5167)  all_57_0 = e1 & op(e3, e3) = e1
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5005), (5167) are inconsistent by sub-proof
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2454.
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5168)  all_57_1 = e1 & op(e3, e2) = e1
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5168) implies:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5169)  op(e3, e2) = e1
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5104), (5106), (5107), (5108), (5137), (5169),
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1328.
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5170)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e1)
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (5159), (5165), (5170) are inconsistent
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1194.
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5171)  all_57_5 = e3 & op(e2, e1) = e3
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5171) implies:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5172)  all_57_5 = e3
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (223), (224), (3970),
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5103), (5172) are inconsistent by sub-proof
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1693.
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5173)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e1) = e3)
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (39), (374), (5006), (5052), (5055), (5173),
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1933.
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5174)   ~ (all_55_1 = e3)
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5175)  all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5143), (5174) imply:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5176)   ~ (all_14_0 = e3)
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (39), (121), (144), (161), (164), (169),
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (191), (192), (196), (197), (202), (203), (209),
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (211), (212), (214), (215), (216), (217), (219),
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (221), (223), (224), (225), (226), (227), (228),
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (229), (230), (231), (232), (233), (234), (235),
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (236), (237), (256), (257), (268), (269), (374),
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3961), (3970), (3971), (4993), (4998), (5000),
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5001), (5005), (5006), (5035), (5036), (5038),
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5039), (5055), (5056), (5062), (5063), (5069),
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5070), (5071), (5072), (5074), (5080), (5087),
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5089), (5103), (5104), (5106), (5107), (5108),
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5137), (5141), (5143), (5145), (5147), (5149),
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5151), (5152), (5175), (5176), (function-axioms)
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1196.
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | |   (5177)   ~ (all_14_1 = e3) & op(e2, e0) = all_14_1 &
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_14_1)
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5083), (5104), (5177), (function-axioms) are
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1326.
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | |   (5178)   ~ (all_55_7 = e3)
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (258), (5178) imply:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | |   (5179)   ~ (all_53_13 = e3)
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | |   (5180)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5180) gives:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | |   (5181)  all_57_2 = e3 & op(e2, e3) = e3
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5181) implies:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | |   (5182)  all_57_2 = e3
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | |   (5183)  op(e2, e3) = e3
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_1, e3,
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (168), (5183) gives:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | |   (5184)  all_53_1 = e3
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (147), (5184) imply:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | |   (5185)   ~ (all_53_9 = e3)
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5185) implies:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | |   (5186)   ~ (all_53_9 = e3)
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | |   (5187)  all_55_6 = e3
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (5186), (5187) are inconsistent by
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2498.
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | |   (5188)  all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5189)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5189) gives:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5190)  all_57_9 = e3 & op(e3, e0) = e3
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5190) implies:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5191)  all_57_9 = e3
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5192)  op(e3, e0) = e3
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_12,
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, e3, simplifying with (169), (5192) gives:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5193)  all_53_12 = e3
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (5193) imply:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5194)   ~ (all_53_14 = e3)
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5194) implies:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5195)   ~ (all_53_14 = e3)
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5196)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e3)
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5196) gives:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5197)  all_57_4 = e3 & op(e3, e1) = e3
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5197) implies:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5198)  all_57_4 = e3
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5199)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e2)
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5199) gives:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5200)  all_57_0 = e2 & op(e3, e3) = e2
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5200) implies:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5201)  op(e3, e3) = e2
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5006), (5201), (function-axioms) are
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2403.
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5202)  all_57_1 = e2 & op(e3, e2) = e2
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5202) implies:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5203)  all_57_1 = e2
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5204)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5204) gives:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5205)  all_57_6 = e3 & op(e1, e3) = e3
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5205) implies:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5206)  all_57_6 = e3
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (232), (234), (5005),
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5006), (5182), (5206), (function-axioms) are
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1287.
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5207)  all_57_7 = e3 & op(e1, e2) = e3
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5207) implies:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5208)  all_57_7 = e3
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5209)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (3971), (5203), (5209),
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2209.
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5210)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5210) gives:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5211)  all_57_7 = e1 & op(e1, e2) = e1
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5211) implies:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5212)  all_57_7 = e1
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5208), (5212) are inconsistent by sub-proof
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2115.
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5213)  all_57_13 = e1 & op(e0, e2) = e1
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5213) implies:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5214)  all_57_13 = e1
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5215)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e1)
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5215) gives:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5216)  all_57_0 = e1 & op(e3, e3) = e1
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5005), (5216) are inconsistent by sub-proof
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2454.
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5217)  all_57_1 = e1 & op(e3, e2) = e1
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5217) implies:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5218)  all_57_1 = e1
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (228), (229), (3970),
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3971), (5214), (5218), (function-axioms) are
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1193.
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5219)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e1)
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5219) gives:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5220)  all_57_4 = e1 & op(e3, e1) = e1
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5198), (5220) are inconsistent by sub-proof
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2484.
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5221)  all_57_9 = e1 & op(e3, e0) = e1
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5191), (5221) are inconsistent by sub-proof
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1669.
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5222)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (161), (374), (5195), (5222),
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2310.
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5223)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e2)
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5223) gives:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5224)  all_57_4 = e2 & op(e3, e1) = e2
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5198), (5224) are inconsistent by sub-proof
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2487.
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5225)  all_57_9 = e2 & op(e3, e0) = e2
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5225) implies:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5226)  all_57_9 = e2
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5191), (5226) are inconsistent by sub-proof
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1192.
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5227)  all_57_5 = e3 & op(e2, e1) = e3
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5227) implies:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5228)  all_57_5 = e3
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (223), (224), (3970),
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5182), (5228) are inconsistent by sub-proof
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1802.
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5229)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e1) = e3)
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (39), (374), (5006), (5052), (5055), (5229),
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1933.
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5230)  all_57_10 = e3 & op(e2, e0) = e3
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5230) implies:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5231)  all_57_10 = e3
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (223), (224), (3970),
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5182), (5231) are inconsistent by sub-proof
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1433.
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5232)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5232) gives:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5233)  all_57_11 = e3 & op(e1, e0) = e3
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5233) implies:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5234)  all_57_11 = e3
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5235)  op(e1, e0) = e3
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_14,
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, e1, simplifying with (161), (5235) gives:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5236)  all_53_14 = e3
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5077) gives:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5237)   ~ (all_34_0 = e3) & op(all_34_1, e1) = all_34_0 &
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_34_1 & $i(all_34_0) &
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_34_1)
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5237) implies:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5238)   ~ (all_34_0 = e3)
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5239)  op(e1, e0) = all_34_1
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5240)  op(all_34_1, e1) = all_34_0
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5027) gives:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5241)   ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_24_1 & $i(all_24_0) &
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_24_1)
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5241) implies:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5242)   ~ (all_24_0 = e2)
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5243)  op(e1, e0) = all_24_1
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5244)  op(all_24_1, e1) = all_24_0
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_34_1,
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e1, simplifying with (5235), (5239) gives:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5245)  all_34_1 = e3
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_24_1,
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_34_1, e0, e1, simplifying with (5239), (5243)
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5246)  all_34_1 = all_24_1
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5245), (5246) imply:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5247)  all_24_1 = e3
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5247) implies:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5248)  all_24_1 = e3
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5240), (5245) imply:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5249)  op(e3, e1) = all_34_0
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5244), (5248) imply:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5250)  op(e3, e1) = all_24_0
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_8,
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_24_0, e1, e3, simplifying with (170), (5250)
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5251)  all_53_8 = all_24_0
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_8,
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_34_0, e1, e3, simplifying with (170), (5249)
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5252)  all_53_8 = all_34_0
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5251), (5252) imply:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5253)  all_34_0 = all_24_0
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5253) implies:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5254)  all_34_0 = all_24_0
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (5251) imply:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5255)  all_55_2 = all_24_0
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (124), (5251) imply:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5256)   ~ (all_53_9 = all_24_0)
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5256) implies:
% 221.08/37.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5257)   ~ (all_53_9 = all_24_0)
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5072), (5251) imply:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5258)   ~ (all_52_29 = all_24_0)
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5258) implies:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5259)   ~ (all_52_29 = all_24_0)
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5000), (5251) imply:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5260)   ~ (all_24_0 = e0)
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5238), (5254) imply:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5261)   ~ (all_24_0 = e3)
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5262)  all_55_2 = e3
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5255), (5262) imply:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5263)  all_24_0 = e3
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5261), (5263) imply:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5264)  $false
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5264) is inconsistent.
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5265)  all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5265) gives:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5266)  all_55_2 = e2
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5255), (5266) imply:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5267)  all_24_0 = e2
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5242), (5267) imply:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5268)  $false
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5268) is inconsistent.
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5269)  all_55_2 = e1 | all_55_2 = e0
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5269) gives:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5270)  all_55_2 = e1
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5255), (5270) imply:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5271)  all_24_0 = e1
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5257), (5271) imply:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5272)   ~ (all_53_9 = e1)
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5259), (5271) imply:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5273)   ~ (all_52_29 = e1)
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5188) gives:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5274)  all_55_6 = e2
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (5274) imply:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5275)  all_53_9 = e2
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5073), (5275) imply:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5276)   ~ (all_52_29 = e2)
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (191), (5006), (5052), (5055), (5062),
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5074), (5273), (5276), (function-axioms) are
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1191.
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5277)  all_55_6 = e1 | all_55_6 = e0
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (3963), (5272), (5277) are inconsistent by
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2161.
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5278)  all_55_2 = e0
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5255), (5278) imply:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5279)  all_24_0 = e0
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5260), (5279) imply:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5280)  $false
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5280) is inconsistent.
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5281)   ~ (all_24_1 = e3) & op(e1, e0) = all_24_1 &
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_24_1)
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5281) implies:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5282)   ~ (all_24_1 = e3)
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5283)  op(e1, e0) = all_24_1
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5235), (5239), (5282), (5283), (function-axioms)
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1961.
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5284)   ~ (all_34_1 = e2) & op(e1, e0) = all_34_1 &
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_34_1)
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5284) implies:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5285)   ~ (all_34_1 = e2)
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5286)  op(e1, e0) = all_34_1
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5287)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e3)
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5287) gives:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5288)  all_57_4 = e3 & op(e3, e1) = e3
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5288) implies:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5289)  all_57_4 = e3
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5290)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5290) gives:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5291)  all_57_12 = e3 & op(e0, e3) = e3
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5291) implies:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5292)  all_57_12 = e3
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5293)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e1)
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5293) gives:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5294)  all_57_0 = e1 & op(e3, e3) = e1
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5005), (5294) are inconsistent by sub-proof
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2454.
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5295)  all_57_2 = e1 & op(e2, e3) = e1
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5182), (5295) are inconsistent by sub-proof
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1928.
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5296)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e3) = e1)
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5296) gives:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5297)  all_57_6 = e1 & op(e1, e3) = e1
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5297) implies:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5298)  all_57_6 = e1
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5299)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5299) gives:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5300)  all_57_1 = e3 & op(e3, e2) = e3
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5300) implies:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5301)  all_57_1 = e3
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (235),
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5006), (5289), (5301), (function-axioms) are
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1220.
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5302)  all_57_3 = e3 & op(e2, e2) = e3
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5302) implies:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5303)  all_57_3 = e3
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3970), (5303) imply:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5304)  e3 = e0
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5182), (5304) imply:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5305)  all_57_2 = e0
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3970), (5305) are inconsistent by sub-proof
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2246.
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5306)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5306) gives:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5307)  all_57_7 = e3 & op(e1, e2) = e3
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5307) implies:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5308)  all_57_7 = e3
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5309)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e2)
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5309) gives:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5310)  all_57_6 = e2 & op(e1, e3) = e2
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5310) implies:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5311)  all_57_6 = e2
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5298), (5311) are inconsistent by sub-proof
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2233.
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5312)  all_57_7 = e2 & op(e1, e2) = e2
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5312) implies:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5313)  all_57_7 = e2
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5308), (5313) are inconsistent by sub-proof
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2102.
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5314)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e0) = e2)
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5035), (5285), (5286), (5314),
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1189.
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5315)  all_57_13 = e3 & op(e0, e2) = e3
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5315) implies:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5316)  all_57_13 = e3
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5317)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e2)
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5317) gives:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5318)  all_57_6 = e2 & op(e1, e3) = e2
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5318) implies:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5319)  all_57_6 = e2
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5298), (5319) are inconsistent by sub-proof
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2233.
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5320)  all_57_7 = e2 & op(e1, e2) = e2
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5320) implies:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5321)  all_57_7 = e2
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5322)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5322) gives:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5323)  all_57_12 = e2 & op(e0, e3) = e2
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5292), (5323) are inconsistent by sub-proof
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2232.
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5324)  all_57_13 = e2 & op(e0, e2) = e2
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5316), (5324) are inconsistent by sub-proof
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2146.
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5325)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5325) gives:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5326)  all_57_14 = e2 & op(e0, e1) = e2
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5326) implies:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5327)  all_57_14 = e2
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5328)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e1)
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5328) gives:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5329)  all_57_4 = e1 & op(e3, e1) = e1
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5329) implies:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5330)  all_57_4 = e1
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5289), (5330) imply:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5331)  e3 = e1
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5292), (5331) imply:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5332)  all_57_12 = e1
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (234), (236), (5006),
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5298), (5332), (function-axioms) are inconsistent
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1205.
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5333)  all_57_5 = e1 & op(e2, e1) = e1
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5333) implies:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5334)  all_57_5 = e1
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5335)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5335) gives:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5336)  all_57_12 = e1 & op(e0, e3) = e1
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5336) implies:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5337)  all_57_12 = e1
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5292), (5337) are inconsistent by sub-proof
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2151.
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5338)  all_57_13 = e1 & op(e0, e2) = e1
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5338) implies:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5339)  all_57_13 = e1
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5316), (5339) are inconsistent by sub-proof
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2268.
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5340)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5340) gives:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5341)  all_57_14 = e1 & op(e0, e1) = e1
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5341) implies:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5342)  all_57_14 = e1
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (220), (5035), (5289), (5334),
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5342) are inconsistent by sub-proof #1187.
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5343)  all_57_15 = e1 & op(e0, e0) = e1
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5343) implies:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5344)  op(e0, e0) = e1
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5039), (5344), (function-axioms) are
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2290.
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5345)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e1)
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (5036), (5327), (5345),
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2374.
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5346)  all_57_15 = e2 & op(e0, e0) = e2
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5346) implies:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5347)  all_57_15 = e2
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5038), (5347) imply:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5348)  e2 = e0
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5321), (5348) imply:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5349)  all_57_7 = e0
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (227), (228), (229),
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3970), (3971), (5316), (5349), (function-axioms)
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2199.
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5350)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e0) = e2)
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5035), (5285), (5286), (5350),
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1189.
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5351)  all_57_12 = e1 & op(e0, e3) = e1
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5351) implies:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5352)  all_57_12 = e1
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5292), (5352) are inconsistent by sub-proof
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2151.
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5353)  all_57_13 = e3 & op(e0, e2) = e3
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5353) implies:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5354)  op(e0, e2) = e3
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_27,
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e2, e0, simplifying with (5053), (5354) gives:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5355)  all_52_27 = e3
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5056), (5355) imply:
% 221.08/37.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5356)  op(e3, e3) = e2
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5006), (5356), (function-axioms) are
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2403.
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5357)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (207), (211), (212),
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5006), (5052), (5055), (5234), (5357),
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1186.
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5358)  all_57_5 = e3 & op(e2, e1) = e3
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5358) implies:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5359)  all_57_5 = e3
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (223), (224), (3970),
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5182), (5359) are inconsistent by sub-proof
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1802.
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5360)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e1) = e3)
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (39), (374), (5006), (5052), (5055), (5360),
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1933.
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5361)  all_57_15 = e3 & op(e0, e0) = e3
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5361) implies:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5362)  op(e0, e0) = e3
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5039), (5362), (function-axioms) are
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2304.
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | |   (5363)  all_57_3 = e3 & op(e2, e2) = e3
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5363) implies:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | |   (5364)  all_57_3 = e3
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3970), (5364) are inconsistent by sub-proof
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | |            #2358.
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | |   (5365)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5365) gives:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | |   (5366)  all_57_5 = e3 & op(e2, e1) = e3
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5366) implies:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | |   (5367)  all_57_5 = e3
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | |   (5368)  op(e2, e1) = e3
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_9, e3,
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (166), (5368) gives:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | |   (5369)  all_53_9 = e3
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | |   (5370)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e3)
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5370) gives:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5371)  all_57_0 = e3 & op(e3, e3) = e3
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5371) implies:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5372)  op(e3, e3) = e3
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5006), (5372), (function-axioms) are
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2494.
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5373)  all_57_1 = e3 & op(e3, e2) = e3
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5373) implies:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5374)  all_57_1 = e3
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5375)  op(e3, e2) = e3
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_4, e3,
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (171), (5375) gives:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5376)  all_53_4 = e3
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (5376) imply:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5377)   ~ (all_53_12 = e3)
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5377) implies:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5378)   ~ (all_53_12 = e3)
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5379)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (169), (223), (224),
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3970), (5367), (5378), (5379), (function-axioms)
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1409.
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5380)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5380) gives:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5381)  all_57_11 = e3 & op(e1, e0) = e3
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5381) implies:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5382)  all_57_11 = e3
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5383)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5383) gives:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5384)  all_57_12 = e3 & op(e0, e3) = e3
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5384) implies:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5385)  all_57_12 = e3
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5386)  op(e0, e3) = e3
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_25,
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e3, e0, simplifying with (5054), (5386) gives:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5387)  all_52_25 = e3
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (223), (224), (225),
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (232), (234), (3970), (5057), (5067),
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5385), (5387), (function-axioms) are inconsistent
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1185.
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5388)  all_57_13 = e3 & op(e0, e2) = e3
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5388) implies:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5389)  all_57_13 = e3
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5390)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (3971), (5375), (5390),
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1184.
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5391)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5391) gives:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5392)  all_57_7 = e2 & op(e1, e2) = e2
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5392) implies:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5393)  all_57_7 = e2
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5394)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5394) gives:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5395)  all_57_6 = e1 & op(e1, e3) = e1
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5395) implies:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5396)  all_57_6 = e1
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5397)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e3)
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5397) gives:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5398)  all_57_0 = e3 & op(e3, e3) = e3
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5398) implies:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5399)  op(e3, e3) = e3
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5006), (5399), (function-axioms) are
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2494.
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5400)  all_57_2 = e3 & op(e2, e3) = e3
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5400) implies:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5401)  all_57_2 = e3
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (223), (224), (3970),
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5367), (5401) are inconsistent by sub-proof
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1802.
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5402)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e3) = e3)
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5402) gives:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5403)  all_57_6 = e3 & op(e1, e3) = e3
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5403) implies:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5404)  all_57_6 = e3
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5396), (5404) imply:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5405)  e3 = e1
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (229), (3970), (5374), (5389),
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5393), (5405) are inconsistent by sub-proof
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1183.
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5406)  all_57_12 = e3 & op(e0, e3) = e3
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5406) implies:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5407)  all_57_12 = e3
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5408)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5408) gives:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5409)  all_57_1 = e1 & op(e3, e2) = e1
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (234), (236), (5006),
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5374), (5396), (5407), (5409), (function-axioms)
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1182.
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5410)  all_57_3 = e1 & op(e2, e2) = e1
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5410) implies:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5411)  op(e2, e2) = e1
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3971), (5411), (function-axioms) are
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2352.
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5412)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5412) gives:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5413)  all_57_7 = e1 & op(e1, e2) = e1
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5413) implies:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5414)  all_57_7 = e1
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5393), (5414) are inconsistent by sub-proof
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1761.
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5415)  all_57_13 = e1 & op(e0, e2) = e1
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5415) implies:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5416)  all_57_13 = e1
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5389), (5416) imply:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5417)  e3 = e1
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5374), (5417) imply:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5418)  all_57_1 = e1
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (228), (229), (3970),
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3971), (5416), (5418), (function-axioms) are
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1193.
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5419)  all_57_7 = e1 & op(e1, e2) = e1
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5393), (5419) are inconsistent by sub-proof
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2190.
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5420)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5420) gives:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5421)  all_57_8 = e1 & op(e1, e1) = e1
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5421) implies:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5422)  op(e1, e1) = e1
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5036), (5422), (function-axioms) are
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2427.
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5423)  all_57_11 = e1 & op(e1, e0) = e1
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5423) implies:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5424)  all_57_11 = e1
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5382), (5424) imply:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5425)  e3 = e1
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (229), (3970), (5374), (5389),
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5393), (5425) are inconsistent by sub-proof
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1183.
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5426)  all_57_13 = e2 & op(e0, e2) = e2
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5426) implies:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5427)  all_57_13 = e2
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5389), (5427) are inconsistent by sub-proof
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2203.
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5428)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (207), (211), (212),
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5006), (5052), (5055), (5382), (5428),
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1186.
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5429)  all_57_15 = e3 & op(e0, e0) = e3
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5429) implies:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5430)  op(e0, e0) = e3
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5039), (5430), (function-axioms) are
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2304.
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | |   (5431)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e3)
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5431) gives:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5432)  all_57_4 = e3 & op(e3, e1) = e3
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5432) implies:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5433)  all_57_4 = e3
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (219), (220), (5035),
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | |            (5036), (5367), (5433), (function-axioms) are
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1181.
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5434)  all_57_9 = e3 & op(e3, e0) = e3
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5434) implies:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5435)  all_57_9 = e3
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5436)  op(e3, e0) = e3
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_12,
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, e3, simplifying with (169), (5436) gives:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5437)  all_53_12 = e3
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (5437) imply:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5438)   ~ (all_53_4 = e3)
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (114), (5437) imply:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5439)   ~ (all_53_13 = e3)
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4993) gives:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5440)   ~ (all_18_0 = e1) & op(all_18_1, e3) = all_18_0 &
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e0) = all_18_1 & $i(all_18_0) &
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_18_1)
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5440) implies:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5441)   ~ (all_18_0 = e1)
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5442)  op(e3, e0) = all_18_1
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5443)  op(all_18_1, e3) = all_18_0
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5080) gives:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5444)   ~ (all_48_0 = e2) & op(all_48_1, e3) = all_48_0 &
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e0) = all_48_1 & $i(all_48_0) &
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_48_1)
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5444) implies:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5445)   ~ (all_48_0 = e2)
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5446)  op(e3, e0) = all_48_1
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5447)  op(all_48_1, e3) = all_48_0
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_48_1,
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e3, simplifying with (5436), (5446) gives:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5448)  all_48_1 = e3
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_18_1,
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_48_1, e0, e3, simplifying with (5442), (5446)
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5449)  all_48_1 = all_18_1
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5448), (5449) imply:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5450)  all_18_1 = e3
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5450) implies:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5451)  all_18_1 = e3
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5447), (5448) imply:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5452)  op(e3, e3) = all_48_0
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5443), (5451) imply:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5453)  op(e3, e3) = all_18_0
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_48_0,
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (5006), (5452) gives:
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5454)  all_48_0 = e0
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_18_0,
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_48_0, e3, e3, simplifying with (5452), (5453)
% 221.08/37.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5455)  all_48_0 = all_18_0
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5454), (5455) imply:
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5456)  all_18_0 = e0
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (8), (9), (111), (127), (137), (142),
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (144), (161), (165), (168), (192), (193), (196),
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (197), (204), (208), (209), (210), (211), (212),
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (223), (224), (225), (230), (232), (234), (236),
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (256), (257), (270), (3957), (3960), (3961),
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3964), (3970), (3971), (4998), (5031), (5038),
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5039), (5052), (5055), (5056), (5057), (5063),
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5064), (5065), (5066), (5067), (5068), (5071),
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5077), (5083), (5179), (5367), (5368), (5435),
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5438), (5441), (5453), (5456), (function-axioms)
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1171.
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5457)   ~ (all_48_1 = e1) & op(e3, e0) = all_48_1 &
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_48_1)
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5457) implies:
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5458)   ~ (all_48_1 = e1)
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5459)  op(e3, e0) = all_48_1
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_48_1,
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e3, simplifying with (5436), (5459) gives:
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5460)  all_48_1 = e3
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_18_1,
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_48_1, e0, e3, simplifying with (5442), (5459)
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5461)  all_48_1 = all_18_1
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5460), (5461) imply:
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5462)  all_18_1 = e3
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5462) implies:
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5463)  all_18_1 = e3
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5443), (5463) imply:
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5464)  op(e3, e3) = all_18_0
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_18_0,
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (5006), (5464) gives:
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5465)  all_18_0 = e0
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (8), (9), (111), (127), (137), (142),
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (144), (161), (165), (168), (192), (193), (196),
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (197), (204), (208), (209), (210), (211), (212),
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (223), (224), (225), (230), (232), (234), (236),
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (256), (257), (270), (3957), (3960), (3961),
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3964), (3970), (3971), (4998), (5031), (5038),
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5039), (5052), (5055), (5056), (5057), (5063),
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5064), (5065), (5066), (5067), (5068), (5071),
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5077), (5083), (5179), (5367), (5368), (5435),
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5438), (5441), (5464), (5465), (function-axioms)
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1171.
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5466)   ~ (all_18_1 = e2) & op(e3, e0) = all_18_1 &
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_18_1)
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5466) implies:
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5467)   ~ (all_18_1 = e2)
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5468)  op(e3, e0) = all_18_1
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5080) gives:
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5469)   ~ (all_48_0 = e2) & op(all_48_1, e3) = all_48_0 &
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e0) = all_48_1 & $i(all_48_0) &
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_48_1)
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5469) implies:
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5470)   ~ (all_48_0 = e2)
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5471)  op(e3, e0) = all_48_1
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5472)  op(all_48_1, e3) = all_48_0
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_48_1,
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e3, simplifying with (5436), (5471) gives:
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5473)  all_48_1 = e3
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_18_1,
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_48_1, e0, e3, simplifying with (5468), (5471)
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5474)  all_48_1 = all_18_1
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5473), (5474) imply:
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5475)  all_18_1 = e3
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5475) implies:
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5476)  all_18_1 = e3
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5472), (5473) imply:
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5477)  op(e3, e3) = all_48_0
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_48_0,
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (5006), (5477) gives:
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5478)  all_48_0 = e0
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (111), (127), (137),
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (142), (144), (161), (165), (168), (192), (193),
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (196), (197), (204), (208), (209), (210), (211),
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (223), (224), (225), (230), (232), (234),
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (236), (256), (257), (270), (3957), (3960),
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3961), (3964), (3970), (3971), (4998), (5006),
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5031), (5038), (5039), (5052), (5055), (5056),
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5057), (5063), (5064), (5065), (5066), (5067),
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5068), (5071), (5077), (5083), (5179), (5367),
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5368), (5435), (5438), (5467), (5468), (5471),
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1170.
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5479)   ~ (all_48_1 = e1) & op(e3, e0) = all_48_1 &
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_48_1)
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5479) implies:
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5480)   ~ (all_48_1 = e1)
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5481)  op(e3, e0) = all_48_1
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_48_1,
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e3, simplifying with (5436), (5481) gives:
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5482)  all_48_1 = e3
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_18_1,
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_48_1, e0, e3, simplifying with (5468), (5481)
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5483)  all_48_1 = all_18_1
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5482), (5483) imply:
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5484)  all_18_1 = e3
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5484) implies:
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5485)  all_18_1 = e3
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (111), (127), (137),
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (142), (144), (161), (165), (168), (192), (193),
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (196), (197), (204), (208), (209), (210), (211),
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (223), (224), (225), (230), (232), (234),
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (236), (256), (257), (270), (3957), (3960),
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3961), (3964), (3970), (3971), (4998), (5006),
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5031), (5038), (5039), (5052), (5055), (5056),
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5057), (5063), (5064), (5065), (5066), (5067),
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5068), (5071), (5077), (5083), (5179), (5367),
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5368), (5435), (5438), (5467), (5468), (5481),
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1170.
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | |   (5486)  all_57_10 = e3 & op(e2, e0) = e3
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5486) implies:
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | |   (5487)  op(e2, e0) = e3
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (5179), (5487), (function-axioms) are
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2301.
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.51  | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | End of split
% 221.08/37.51  | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | End of split
% 221.08/37.51  | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | Case 2:
% 221.08/37.51  | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | |   (5488)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 221.08/37.51  | | | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 221.08/37.51  | | | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 221.08/37.51  | | | | | | | | | | | | | | | |                 e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 221.08/37.51  | | | | | | | | | | | | | | | |               e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 221.08/37.51  | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | ALPHA: (5488) implies:
% 221.08/37.51  | | | | | | | | | | | | | | | |   (5489)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 221.08/37.51  | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 221.08/37.51  | | | | | | | | | | | | | | | |               e1) = e0)
% 221.08/37.51  | | | | | | | | | | | | | | | |   (5490)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 221.08/37.51  | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 221.08/37.51  | | | | | | | | | | | | | | | |               e0) = e0)
% 221.08/37.51  | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | BETA: splitting (5489) gives:
% 221.08/37.51  | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.51  | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | |   (5491)  all_57_12 = e0 & op(e0, e3) = e0
% 221.08/37.51  | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | ALPHA: (5491) implies:
% 221.08/37.51  | | | | | | | | | | | | | | | | |   (5492)  op(e0, e3) = e0
% 221.08/37.51  | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (4999), (5492), (function-axioms) are
% 221.08/37.51  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2366.
% 221.08/37.51  | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.51  | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | |   (5493)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 221.08/37.51  | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 221.08/37.51  | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | BETA: splitting (5493) gives:
% 221.08/37.51  | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.51  | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | |   (5494)  all_57_13 = e0 & op(e0, e2) = e0
% 221.08/37.51  | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | | ALPHA: (5494) implies:
% 221.08/37.51  | | | | | | | | | | | | | | | | | |   (5495)  op(e0, e2) = e0
% 221.08/37.51  | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (3962), (5495), (function-axioms) are
% 221.08/37.51  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2332.
% 221.08/37.51  | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.51  | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | |   (5496)  all_57_14 = e0 & op(e0, e1) = e0
% 221.08/37.51  | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | | ALPHA: (5496) implies:
% 221.08/37.51  | | | | | | | | | | | | | | | | | |   (5497)  all_57_14 = e0
% 221.08/37.51  | | | | | | | | | | | | | | | | | |   (5498)  op(e0, e1) = e0
% 221.08/37.51  | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | | BETA: splitting (5490) gives:
% 221.08/37.51  | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | | |   (5499)  all_57_9 = e0 & op(e3, e0) = e0
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (5001), (5499), (function-axioms) are
% 221.08/37.51  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2434.
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | | |   (5500)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 =
% 221.08/37.51  | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | BETA: splitting (5500) gives:
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | |   (5501)  all_57_10 = e0 & op(e2, e0) = e0
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | ALPHA: (5501) implies:
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | |   (5502)  op(e2, e0) = e0
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (3964), (5502), (function-axioms) are
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2470.
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | |   (5503)  all_57_11 = e0 & op(e1, e0) = e0
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | ALPHA: (5503) implies:
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | |   (5504)  op(e1, e0) = e0
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (9), (36), (39), (91), (107), (158),
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | |            (161), (190), (208), (209), (210), (244), (295),
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | |            (368), (372), (373), (378), (3971), (5006),
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | |            (5497), (5498), (5504), (function-axioms) are
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1226.
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.51  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.51  | | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | | End of split
% 221.08/37.51  | | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | | End of split
% 221.08/37.51  | | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | End of split
% 221.08/37.51  | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | Case 2:
% 221.08/37.51  | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | |   (5505)  all_57_11 = e0 & op(e1, e0) = e0
% 221.08/37.51  | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | | REF_CLOSE: (161), (5031), (5505), (function-axioms) are
% 221.08/37.51  | | | | | | | | | | | | | | |            inconsistent by sub-proof #2341.
% 221.08/37.51  | | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | | End of split
% 221.08/37.51  | | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | | End of split
% 221.08/37.51  | | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | End of split
% 221.08/37.51  | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | Case 2:
% 221.08/37.51  | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | |   (5506)  all_57_1 = e0 & op(e3, e2) = e0
% 221.08/37.51  | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | ALPHA: (5506) implies:
% 221.08/37.51  | | | | | | | | | | | |   (5507)  op(e3, e2) = e0
% 221.08/37.51  | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | | REF_CLOSE: (171), (3960), (5507), (function-axioms) are
% 221.08/37.51  | | | | | | | | | | | |            inconsistent by sub-proof #1941.
% 221.08/37.51  | | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | End of split
% 221.08/37.51  | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | Case 2:
% 221.08/37.51  | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | |   (5508)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 221.08/37.51  | | | | | | | | | | |             & op(e3, e0) = e0)
% 221.08/37.51  | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | | REF_CLOSE: (169), (170), (5000), (5001), (5508),
% 221.08/37.51  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.08/37.51  | | | | | | | | | | |            #1544.
% 221.08/37.51  | | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | | End of split
% 221.08/37.51  | | | | | | | | | | 
% 221.08/37.51  | | | | | | | | | End of split
% 221.08/37.51  | | | | | | | | | 
% 221.08/37.51  | | | | | | | | End of split
% 221.08/37.51  | | | | | | | | 
% 221.08/37.51  | | | | | | | Case 2:
% 221.08/37.51  | | | | | | | | 
% 221.08/37.51  | | | | | | | |   (5509)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 &
% 221.08/37.51  | | | | | | | |             op(e0, e2) = e0)
% 221.08/37.51  | | | | | | | | 
% 221.08/37.51  | | | | | | | | REF_CLOSE: (159), (163), (3961), (3962), (5509),
% 221.08/37.51  | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.08/37.51  | | | | | | | |            #2024.
% 221.08/37.51  | | | | | | | | 
% 221.08/37.51  | | | | | | | End of split
% 221.08/37.51  | | | | | | | 
% 221.08/37.51  | | | | | | End of split
% 221.08/37.51  | | | | | | 
% 221.08/37.51  | | | | | Case 2:
% 221.08/37.51  | | | | | | 
% 221.08/37.51  | | | | | |   (5510)  all_12_2 = e3
% 221.08/37.52  | | | | | |   (5511)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0,
% 221.08/37.52  | | | | | |               e3) = all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~
% 221.08/37.52  | | | | | |             (all_12_1 = e1) & op(e0, e3) = all_12_1 & $i(all_12_1))
% 221.08/37.52  | | | | | | 
% 221.08/37.52  | | | | | | COMBINE_EQS: (325), (5510) imply:
% 221.08/37.52  | | | | | |   (5512)  all_4_2 = e3
% 221.08/37.52  | | | | | | 
% 221.08/37.52  | | | | | | SIMP: (5512) implies:
% 221.08/37.52  | | | | | |   (5513)  all_4_2 = e3
% 221.08/37.52  | | | | | | 
% 221.08/37.52  | | | | | | COMBINE_EQS: (318), (5513) imply:
% 221.08/37.52  | | | | | |   (5514)  all_22_2 = e3
% 221.08/37.52  | | | | | | 
% 221.08/37.52  | | | | | | REDUCE: (351), (5513) imply:
% 221.08/37.52  | | | | | |   (5515)   ~ (all_53_3 = e3)
% 221.08/37.52  | | | | | | 
% 221.08/37.52  | | | | | | REDUCE: (362), (5513) imply:
% 221.08/37.52  | | | | | |   (5516)   ~ (all_53_7 = e3)
% 221.08/37.52  | | | | | | 
% 221.08/37.52  | | | | | | REDUCE: (369), (5513) imply:
% 221.08/37.52  | | | | | |   (5517)   ~ (all_53_11 = e3)
% 221.08/37.52  | | | | | | 
% 221.08/37.52  | | | | | | REDUCE: (370), (5513) imply:
% 221.08/37.52  | | | | | |   (5518)   ~ (all_53_12 = e3)
% 221.08/37.52  | | | | | | 
% 221.08/37.52  | | | | | | REDUCE: (371), (5513) imply:
% 221.08/37.52  | | | | | |   (5519)   ~ (all_53_13 = e3)
% 221.08/37.52  | | | | | | 
% 221.08/37.52  | | | | | | REDUCE: (372), (5513) imply:
% 221.08/37.52  | | | | | |   (5520)   ~ (all_53_14 = e3)
% 221.08/37.52  | | | | | | 
% 221.08/37.52  | | | | | | BETA: splitting (213) gives:
% 221.08/37.52  | | | | | | 
% 221.08/37.52  | | | | | | Case 1:
% 221.08/37.52  | | | | | | | 
% 221.08/37.52  | | | | | | |   (5521)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 &
% 221.08/37.52  | | | | | | |             op(e2, e0) = e3)
% 221.08/37.52  | | | | | | | 
% 221.08/37.52  | | | | | | | REF_CLOSE: (165), (169), (5518), (5519), (5521), (function-axioms)
% 221.08/37.52  | | | | | | |            are inconsistent by sub-proof #2300.
% 221.08/37.52  | | | | | | | 
% 221.08/37.52  | | | | | | Case 2:
% 221.08/37.52  | | | | | | | 
% 221.08/37.52  | | | | | | |   (5522)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 &
% 221.08/37.52  | | | | | | |             op(e0, e0) = e3)
% 221.08/37.52  | | | | | | | 
% 221.08/37.52  | | | | | | | BETA: splitting (5522) gives:
% 221.08/37.52  | | | | | | | 
% 221.08/37.52  | | | | | | | Case 1:
% 221.08/37.52  | | | | | | | | 
% 221.08/37.52  | | | | | | | |   (5523)  all_57_11 = e3 & op(e1, e0) = e3
% 221.08/37.52  | | | | | | | | 
% 221.08/37.52  | | | | | | | | ALPHA: (5523) implies:
% 221.08/37.52  | | | | | | | |   (5524)  op(e1, e0) = e3
% 221.08/37.52  | | | | | | | | 
% 221.08/37.52  | | | | | | | | REF_CLOSE: (161), (5520), (5524), (function-axioms) are
% 221.08/37.52  | | | | | | | |            inconsistent by sub-proof #2330.
% 221.08/37.52  | | | | | | | | 
% 221.08/37.52  | | | | | | | Case 2:
% 221.08/37.52  | | | | | | | | 
% 221.08/37.52  | | | | | | | |   (5525)  all_57_15 = e3 & op(e0, e0) = e3
% 221.08/37.52  | | | | | | | | 
% 221.08/37.52  | | | | | | | | ALPHA: (5525) implies:
% 221.08/37.52  | | | | | | | |   (5526)  all_57_15 = e3
% 221.08/37.52  | | | | | | | |   (5527)  op(e0, e0) = e3
% 221.08/37.52  | | | | | | | | 
% 221.08/37.52  | | | | | | | | BETA: splitting (52) gives:
% 221.08/37.52  | | | | | | | | 
% 221.08/37.52  | | | | | | | | Case 1:
% 221.08/37.52  | | | | | | | | | 
% 221.08/37.52  | | | | | | | | |   (5528)   ~ (all_14_2 = e0)
% 221.08/37.52  | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | REDUCE: (328), (5528) imply:
% 221.08/37.52  | | | | | | | | |   (5529)   ~ (all_8_2 = e0)
% 221.08/37.52  | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | BETA: splitting (55) gives:
% 221.08/37.52  | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | Case 1:
% 221.08/37.52  | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | |   (5530)   ~ (all_16_2 = e1)
% 221.08/37.52  | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | REDUCE: (324), (5530) imply:
% 221.08/37.52  | | | | | | | | | |   (5531)   ~ (all_8_2 = e1)
% 221.08/37.52  | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | BETA: splitting (200) gives:
% 221.08/37.52  | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | Case 1:
% 221.08/37.52  | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | |   (5532)  all_55_5 = e3
% 221.08/37.52  | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | COMBINE_EQS: (266), (5532) imply:
% 221.08/37.52  | | | | | | | | | | |   (5533)  all_8_2 = e3
% 221.08/37.52  | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | REDUCE: (375), (5533) imply:
% 221.08/37.52  | | | | | | | | | | |   (5534)  $false
% 221.08/37.52  | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | CLOSE: (5534) is inconsistent.
% 221.08/37.52  | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | Case 2:
% 221.08/37.52  | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | |   (5535)   ~ (all_55_5 = e3)
% 221.08/37.52  | | | | | | | | | | |   (5536)  all_55_5 = e2 | all_55_5 = e1 | all_55_5 = e0
% 221.08/37.52  | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | BETA: splitting (5536) gives:
% 221.08/37.52  | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | Case 1:
% 221.08/37.52  | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | |   (5537)  all_55_5 = e2
% 221.08/37.52  | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | COMBINE_EQS: (266), (5537) imply:
% 221.08/37.52  | | | | | | | | | | | |   (5538)  all_8_2 = e2
% 221.08/37.52  | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | REDUCE: (349), (5538) imply:
% 221.08/37.52  | | | | | | | | | | | |   (5539)   ~ (all_53_1 = e2)
% 221.08/37.52  | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | REDUCE: (352), (5538) imply:
% 221.08/37.52  | | | | | | | | | | | |   (5540)   ~ (all_53_4 = e2)
% 221.08/37.52  | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | REDUCE: (354), (5538) imply:
% 221.08/37.52  | | | | | | | | | | | |   (5541)   ~ (all_53_6 = e2)
% 221.08/37.52  | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | REDUCE: (356), (5538) imply:
% 221.08/37.52  | | | | | | | | | | | |   (5542)   ~ (all_53_7 = e2)
% 221.08/37.52  | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | REDUCE: (358), (5538) imply:
% 221.08/37.52  | | | | | | | | | | | |   (5543)   ~ (all_53_9 = e2)
% 221.08/37.52  | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | REDUCE: (360), (5538) imply:
% 221.08/37.52  | | | | | | | | | | | |   (5544)   ~ (all_53_13 = e2)
% 221.08/37.52  | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | REDUCE: (375), (5538) imply:
% 221.08/37.52  | | | | | | | | | | | |   (5545)   ~ (e3 = e2)
% 221.08/37.52  | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | REDUCE: (42), (5538) imply:
% 221.08/37.52  | | | | | | | | | | | |   (5546)  op(e2, e2) = e2
% 221.08/37.52  | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | BETA: splitting (224) gives:
% 221.08/37.52  | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | Case 1:
% 221.08/37.52  | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | |   (5547)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 221.08/37.52  | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 221.08/37.52  | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | BETA: splitting (5547) gives:
% 221.08/37.52  | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | Case 1:
% 221.08/37.52  | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | |   (5548)  all_57_2 = e2 & op(e2, e3) = e2
% 221.08/37.52  | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | ALPHA: (5548) implies:
% 221.08/37.52  | | | | | | | | | | | | | |   (5549)  all_57_2 = e2
% 221.08/37.52  | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (207), (211), (212),
% 221.08/37.52  | | | | | | | | | | | | | |            (222), (223), (225), (5526), (5527), (5546),
% 221.08/37.52  | | | | | | | | | | | | | |            (5549), (function-axioms) are inconsistent by
% 221.08/37.52  | | | | | | | | | | | | | |            sub-proof #1169.
% 221.08/37.52  | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | Case 2:
% 221.08/37.52  | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | |   (5550)  all_57_3 = e2 & op(e2, e2) = e2
% 221.08/37.52  | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | ALPHA: (5550) implies:
% 221.08/37.52  | | | | | | | | | | | | | |   (5551)  all_57_3 = e2
% 221.08/37.52  | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (45), (58),
% 221.08/37.52  | | | | | | | | | | | | | |            (61), (64), (67), (82), (88), (103), (107), (111),
% 221.08/37.52  | | | | | | | | | | | | | |            (113), (114), (119), (121), (124), (126), (127),
% 221.08/37.52  | | | | | | | | | | | | | |            (129), (134), (135), (136), (137), (140), (141),
% 221.08/37.52  | | | | | | | | | | | | | |            (142), (144), (145), (149), (150), (158), (159),
% 221.08/37.52  | | | | | | | | | | | | | |            (160), (161), (163), (164), (165), (166), (168),
% 221.08/37.52  | | | | | | | | | | | | | |            (169), (170), (171), (191), (192), (194), (195),
% 221.08/37.52  | | | | | | | | | | | | | |            (196), (197), (198), (199), (201), (202), (203),
% 221.08/37.52  | | | | | | | | | | | | | |            (204), (205), (207), (208), (209), (211), (212),
% 221.08/37.52  | | | | | | | | | | | | | |            (214), (215), (216), (217), (218), (219), (220),
% 221.08/37.52  | | | | | | | | | | | | | |            (221), (222), (223), (224), (225), (226), (227),
% 221.08/37.52  | | | | | | | | | | | | | |            (228), (229), (230), (231), (232), (233), (234),
% 221.08/37.52  | | | | | | | | | | | | | |            (235), (236), (237), (245), (246), (248), (249),
% 221.08/37.52  | | | | | | | | | | | | | |            (256), (257), (258), (259), (267), (268), (269),
% 221.08/37.52  | | | | | | | | | | | | | |            (270), (277), (279), (299), (311), (315), (327),
% 221.08/37.52  | | | | | | | | | | | | | |            (336), (338), (340), (342), (344), (346), (348),
% 221.08/37.52  | | | | | | | | | | | | | |            (350), (361), (363), (364), (366), (368), (374),
% 221.08/37.52  | | | | | | | | | | | | | |            (376), (5511), (5514), (5516), (5517), (5518),
% 221.08/37.52  | | | | | | | | | | | | | |            (5519), (5520), (5526), (5527), (5539), (5540),
% 221.08/37.52  | | | | | | | | | | | | | |            (5541), (5542), (5543), (5544), (5546), (5551),
% 221.08/37.52  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.08/37.52  | | | | | | | | | | | | | |            #818.
% 221.08/37.52  | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | End of split
% 221.08/37.52  | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | Case 2:
% 221.08/37.52  | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | |   (5552)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 221.08/37.52  | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 221.08/37.52  | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | BETA: splitting (5552) gives:
% 221.08/37.52  | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | Case 1:
% 221.08/37.52  | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | |   (5553)  all_57_5 = e2 & op(e2, e1) = e2
% 221.08/37.52  | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | ALPHA: (5553) implies:
% 221.08/37.52  | | | | | | | | | | | | | |   (5554)  all_57_5 = e2
% 221.08/37.52  | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 221.08/37.52  | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | Case 1:
% 221.08/37.52  | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | |   (5555)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 221.08/37.52  | | | | | | | | | | | | | | |             & op(e2, e1) = e3)
% 221.08/37.52  | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | BETA: splitting (5555) gives:
% 221.08/37.52  | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | Case 1:
% 221.08/37.52  | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | |   (5556)  all_57_4 = e3 & op(e3, e1) = e3
% 221.08/37.52  | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | ALPHA: (5556) implies:
% 221.08/37.52  | | | | | | | | | | | | | | | |   (5557)  all_57_4 = e3
% 221.08/37.52  | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 221.08/37.52  | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.52  | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | |   (5558)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 221.08/37.52  | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 221.08/37.52  | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | BETA: splitting (5558) gives:
% 221.08/37.52  | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.52  | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | |   (5559)  all_57_2 = e3 & op(e2, e3) = e3
% 221.08/37.52  | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | ALPHA: (5559) implies:
% 221.08/37.52  | | | | | | | | | | | | | | | | | |   (5560)  all_57_2 = e3
% 221.08/37.52  | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 221.08/37.52  | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | |   (5561)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 221.08/37.52  | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (5546), (5560), (5561),
% 221.08/37.52  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.08/37.52  | | | | | | | | | | | | | | | | | | |            #817.
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | |   (5562)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 221.08/37.52  | | | | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0)
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | BETA: splitting (5562) gives:
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | |   (5563)  all_57_5 = e0 & op(e2, e1) = e0
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | ALPHA: (5563) implies:
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | |   (5564)  all_57_5 = e0
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5554), (5564) are inconsistent by sub-proof
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | |            #2363.
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | |   (5565)  all_57_10 = e0 & op(e2, e0) = e0
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | ALPHA: (5565) implies:
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | |   (5566)  all_57_10 = e0
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | |   (5567)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5567) gives:
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | |   (5568)  all_57_1 = e2 & op(e3, e2) = e2
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5568) implies:
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | |   (5569)  all_57_1 = e2
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | |   (5570)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5570) gives:
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | |   (5571)  all_57_1 = e3 & op(e3, e2) = e3
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5571) implies:
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | |   (5572)  all_57_1 = e3
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5569), (5572) imply:
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | |   (5573)  e3 = e2
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (207), (211), (212),
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | |            (222), (223), (225), (5526), (5527), (5546),
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | |            (5560), (5573), (function-axioms) are inconsistent
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #816.
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | |   (5574)  all_57_3 = e3 & op(e2, e2) = e3
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5574) implies:
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | |   (5575)  op(e2, e2) = e3
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5546), (5575), (function-axioms) are
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2298.
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | |   (5576)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5576) gives:
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | |   (5577)  all_57_7 = e3 & op(e1, e2) = e3
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5577) implies:
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | |   (5578)  all_57_7 = e3
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | |   (5579)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5546), (5569), (5579), (function-axioms) are
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1133.
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | |   (5580)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5580) gives:
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5581)  all_57_7 = e1 & op(e1, e2) = e1
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5581) implies:
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5582)  all_57_7 = e1
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5578), (5582) are inconsistent by sub-proof
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | |            #2115.
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5583)  all_57_13 = e1 & op(e0, e2) = e1
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5583) implies:
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5584)  all_57_13 = e1
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5585)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e1)
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5585) gives:
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5586)  all_57_0 = e1 & op(e3, e3) = e1
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5586) implies:
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5587)  all_57_0 = e1
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5588)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5588) gives:
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5589)  all_57_0 = e0 & op(e3, e3) = e0
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5589) implies:
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5590)  all_57_0 = e0
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5587), (5590) imply:
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5591)  e1 = e0
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5584), (5591) imply:
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5592)  all_57_13 = e0
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (227), (5546), (5569), (5578),
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5592), (function-axioms) are inconsistent by
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #871.
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5593)  all_57_1 = e0 & op(e3, e2) = e0
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5569), (5593) are inconsistent by sub-proof
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1723.
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5594)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5594) gives:
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5595)  all_57_4 = e0 & op(e3, e1) = e0
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5557), (5595) are inconsistent by sub-proof
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2491.
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5596)  all_57_9 = e0 & op(e3, e0) = e0
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5596) implies:
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5597)  all_57_9 = e0
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5598)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5598) gives:
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5599)  all_57_1 = e0 & op(e3, e2) = e0
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5569), (5599) are inconsistent by sub-proof
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1723.
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5600)  all_57_3 = e0 & op(e2, e2) = e0
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5600) implies:
% 221.08/37.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5601)  all_57_3 = e0
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5602)  op(e2, e2) = e0
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5558) gives:
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (223), (5554), (5560), (5566),
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5602), (function-axioms) are inconsistent by
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #815.
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5603)  all_57_3 = e3 & op(e2, e2) = e3
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5603) implies:
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5604)  all_57_3 = e3
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5601), (5604) are inconsistent by sub-proof
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2358.
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5605)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5605) gives:
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5606)  all_57_5 = e3 & op(e2, e1) = e3
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5606) implies:
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5607)  all_57_5 = e3
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (223), (224), (5566),
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5601), (5607) are inconsistent by sub-proof
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1518.
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5608)  all_57_10 = e3 & op(e2, e0) = e3
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5608) implies:
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5609)  all_57_10 = e3
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (207), (211), (212),
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5526), (5597), (5609) are inconsistent by
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1982.
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5610)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0)
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5610) gives:
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5611)  all_57_7 = e0 & op(e1, e2) = e0
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5611) implies:
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5612)  all_57_7 = e0
% 221.08/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5578), (5612) are inconsistent by sub-proof
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2269.
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5613)  all_57_13 = e0 & op(e0, e2) = e0
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5613) implies:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5614)  all_57_13 = e0
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (227), (5546), (5569), (5578),
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5614), (function-axioms) are inconsistent by
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #871.
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5615)  all_57_1 = e1 & op(e3, e2) = e1
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5569), (5615) are inconsistent by sub-proof
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2210.
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5616)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e1)
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5616) gives:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5617)  all_57_4 = e1 & op(e3, e1) = e1
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5617) implies:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5618)  all_57_4 = e1
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5557), (5618) are inconsistent by sub-proof
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2426.
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5619)  all_57_9 = e1 & op(e3, e0) = e1
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5619) implies:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5620)  all_57_9 = e1
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5621)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5621) gives:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5622)  all_57_0 = e0 & op(e3, e3) = e0
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5622) implies:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5623)  op(e3, e3) = e0
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5624)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5624) gives:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5625)  all_57_1 = e0 & op(e3, e2) = e0
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5625) implies:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5626)  all_57_1 = e0
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (9), (169), (235), (237), (5518),
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5620), (5623), (5626), (function-axioms) are
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2400.
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5627)  all_57_3 = e0 & op(e2, e2) = e0
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5627) implies:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5628)  op(e2, e2) = e0
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (223), (5554), (5560), (5566),
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5628), (function-axioms) are inconsistent by
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #815.
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5629)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0)
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5629) gives:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5630)  all_57_7 = e0 & op(e1, e2) = e0
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5630) implies:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5631)  all_57_7 = e0
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5578), (5631) imply:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5632)  e3 = e0
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5632) implies:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5633)  e3 = e0
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5557), (5633) imply:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5634)  all_57_4 = e0
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (169), (237), (5518), (5569), (5623),
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5634), (function-axioms) are inconsistent by
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1405.
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5635)  all_57_13 = e0 & op(e0, e2) = e0
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5635) implies:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5636)  all_57_13 = e0
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (227), (5546), (5569), (5578),
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5636), (function-axioms) are inconsistent by
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #871.
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5637)  all_57_1 = e0 & op(e3, e2) = e0
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5569), (5637) are inconsistent by sub-proof
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1723.
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5638)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5638) gives:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5639)  all_57_4 = e0 & op(e3, e1) = e0
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5639) implies:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5640)  all_57_4 = e0
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5557), (5640) are inconsistent by sub-proof
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2372.
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5641)  all_57_9 = e0 & op(e3, e0) = e0
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5641) implies:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5642)  all_57_9 = e0
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5620), (5642) imply:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5643)  e1 = e0
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5643) implies:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5644)  e1 = e0
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5584), (5644) imply:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5645)  all_57_13 = e0
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (227), (5546), (5569), (5578),
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5645), (function-axioms) are inconsistent by
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #871.
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | |   (5646)  all_57_13 = e3 & op(e0, e2) = e3
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5646) implies:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | |   (5647)  all_57_13 = e3
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (207), (208), (209),
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | |            (5526), (5527), (5647), (function-axioms) are
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1792.
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | |   (5648)  all_57_3 = e2 & op(e2, e2) = e2
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5648) implies:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | |   (5649)  all_57_3 = e2
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (45), (58),
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | |            (61), (64), (67), (82), (88), (103), (107), (111),
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | |            (113), (114), (119), (121), (124), (126), (127),
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | |            (129), (134), (135), (136), (137), (140), (141),
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | |            (142), (144), (145), (149), (150), (158), (159),
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | |            (160), (161), (163), (164), (165), (166), (168),
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | |            (169), (170), (171), (191), (192), (194), (195),
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | |            (196), (197), (198), (199), (201), (202), (203),
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | |            (204), (205), (207), (208), (209), (211), (212),
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | |            (214), (215), (216), (217), (218), (219), (220),
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | |            (221), (222), (223), (224), (225), (226), (227),
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | |            (228), (229), (230), (231), (232), (233), (234),
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | |            (235), (236), (237), (245), (246), (248), (249),
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | |            (256), (257), (258), (259), (267), (268), (269),
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | |            (270), (277), (279), (299), (311), (315), (327),
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | |            (336), (338), (340), (342), (344), (346), (348),
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | |            (350), (361), (363), (364), (366), (368), (374),
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | |            (376), (5511), (5514), (5516), (5517), (5518),
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | |            (5519), (5520), (5526), (5527), (5539), (5540),
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | |            (5541), (5542), (5543), (5544), (5546), (5649),
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | |            #818.
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | End of split
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | |   (5650)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5650) gives:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | |   (5651)  all_57_7 = e2 & op(e1, e2) = e2
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5651) implies:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | |   (5652)  all_57_7 = e2
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | |   (5653)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5653) gives:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | |   (5654)  all_57_6 = e3 & op(e1, e3) = e3
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5654) implies:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | |   (5655)  all_57_6 = e3
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | |   (5656)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5656) gives:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5657)  all_57_1 = e3 & op(e3, e2) = e3
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5657) implies:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5658)  all_57_1 = e3
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5659)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e1)
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5659) gives:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5660)  all_57_0 = e1 & op(e3, e3) = e1
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5660) implies:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5661)  all_57_0 = e1
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (231), (235), (5557),
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5658), (5661) are inconsistent by sub-proof
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1808.
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5662)  all_57_1 = e1 & op(e3, e2) = e1
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5662) implies:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5663)  all_57_1 = e1
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5658), (5663) imply:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5664)  e3 = e1
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5655), (5664) imply:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5665)  all_57_6 = e1
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (217), (226), (227), (228), (374), (5526),
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5546), (5658), (5665), (function-axioms) are
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1071.
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5666)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e1)
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5666) gives:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5667)  all_57_4 = e1 & op(e3, e1) = e1
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5667) implies:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5668)  all_57_4 = e1
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5557), (5668) imply:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5669)  e3 = e1
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5669) implies:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5670)  e3 = e1
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5655), (5670) imply:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5671)  all_57_6 = e1
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (217), (226), (227), (228), (374), (5526),
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5546), (5658), (5671), (function-axioms) are
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1071.
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5672)  all_57_9 = e1 & op(e3, e0) = e1
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5672) implies:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5673)  all_57_9 = e1
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5674)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5674) gives:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5675)  all_57_0 = e0 & op(e3, e3) = e0
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5675) implies:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5676)  op(e3, e3) = e0
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (235),
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5557), (5658), (5676), (function-axioms) are
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1220.
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5677)  all_57_1 = e0 & op(e3, e2) = e0
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5677) implies:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5678)  all_57_1 = e0
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5658), (5678) imply:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5679)  e3 = e0
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5655), (5679) imply:
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5680)  all_57_6 = e0
% 221.68/37.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (217), (374), (5526), (5652), (5680),
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1775.
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5681)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5681) gives:
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5682)  all_57_4 = e0 & op(e3, e1) = e0
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5682) implies:
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5683)  all_57_4 = e0
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5557), (5683) imply:
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5684)  e3 = e0
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5684) implies:
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5685)  e3 = e0
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5655), (5685) imply:
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5686)  all_57_6 = e0
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (217), (374), (5526), (5652), (5686),
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1775.
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5687)  all_57_9 = e0 & op(e3, e0) = e0
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5687) implies:
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5688)  all_57_9 = e0
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5673), (5688) are inconsistent by sub-proof
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2479.
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5689)  all_57_3 = e3 & op(e2, e2) = e3
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5689) implies:
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5690)  op(e2, e2) = e3
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5546), (5690), (function-axioms) are
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2298.
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | |   (5691)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5691) gives:
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5692)  all_57_7 = e3 & op(e1, e2) = e3
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5692) implies:
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5693)  all_57_7 = e3
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5652), (5693) imply:
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5694)  e3 = e2
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5560), (5694) imply:
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5695)  all_57_2 = e2
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (207), (211), (212),
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | |            (222), (223), (225), (5526), (5527), (5546),
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | |            (5695), (function-axioms) are inconsistent by
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1169.
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5696)  all_57_13 = e3 & op(e0, e2) = e3
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5696) implies:
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5697)  all_57_13 = e3
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (207), (208), (209),
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | |            (5526), (5527), (5697), (function-axioms) are
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1792.
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | |   (5698)  all_57_7 = e3 & op(e1, e2) = e3
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5698) implies:
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | |   (5699)  all_57_7 = e3
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5652), (5699) imply:
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | |   (5700)  e3 = e2
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (207), (211), (212),
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | |            (222), (223), (225), (5526), (5527), (5546),
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | |            (5560), (5700), (function-axioms) are inconsistent
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #816.
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | |   (5701)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (39), (211), (212),
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | |            (374), (5526), (5566), (5701), (function-axioms)
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #978.
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | |   (5702)  all_57_13 = e2 & op(e0, e2) = e2
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5702) implies:
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | |   (5703)  op(e0, e2) = e2
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (5542), (5703), (function-axioms) are
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2335.
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | End of split
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | End of split
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | End of split
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | End of split
% 221.68/37.54  | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | Case 2:
% 221.68/37.54  | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | |   (5704)  all_57_3 = e3 & op(e2, e2) = e3
% 221.68/37.54  | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | ALPHA: (5704) implies:
% 221.68/37.54  | | | | | | | | | | | | | | | | | |   (5705)  op(e2, e2) = e3
% 221.68/37.54  | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5546), (5705), (function-axioms) are
% 221.68/37.54  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2298.
% 221.68/37.54  | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | End of split
% 221.68/37.54  | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | Case 2:
% 221.68/37.54  | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | |   (5706)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 221.68/37.54  | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 221.68/37.54  | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (207), (211), (212),
% 221.68/37.54  | | | | | | | | | | | | | | | | |            (5526), (5527), (5554), (5706), (function-axioms)
% 221.68/37.54  | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1745.
% 221.68/37.54  | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | End of split
% 221.68/37.54  | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | Case 2:
% 221.68/37.54  | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | |   (5707)  all_57_5 = e3 & op(e2, e1) = e3
% 221.68/37.54  | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | ALPHA: (5707) implies:
% 221.68/37.54  | | | | | | | | | | | | | | | |   (5708)  all_57_5 = e3
% 221.68/37.54  | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5554), (5708) are inconsistent by sub-proof
% 221.68/37.54  | | | | | | | | | | | | | | | |            #2189.
% 221.68/37.54  | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | End of split
% 221.68/37.54  | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | Case 2:
% 221.68/37.54  | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | |   (5709)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 221.68/37.54  | | | | | | | | | | | | | | |             e3 & op(e0, e1) = e3)
% 221.68/37.54  | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (208),
% 221.68/37.54  | | | | | | | | | | | | | | |            (209), (374), (5526), (5709), (function-axioms)
% 221.68/37.54  | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1794.
% 221.68/37.54  | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | End of split
% 221.68/37.54  | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | Case 2:
% 221.68/37.54  | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | |   (5710)  all_57_10 = e2 & op(e2, e0) = e2
% 221.68/37.54  | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | REF_CLOSE: (165), (5544), (5710), (function-axioms) are
% 221.68/37.54  | | | | | | | | | | | | | |            inconsistent by sub-proof #2432.
% 221.68/37.54  | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | End of split
% 221.68/37.54  | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | End of split
% 221.68/37.54  | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | Case 2:
% 221.68/37.54  | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | |   (5711)  all_55_5 = e1 | all_55_5 = e0
% 221.68/37.54  | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | REF_CLOSE: (266), (5529), (5531), (5711) are inconsistent by
% 221.68/37.54  | | | | | | | | | | | |            sub-proof #1857.
% 221.68/37.54  | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | End of split
% 221.68/37.54  | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | End of split
% 221.68/37.54  | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | Case 2:
% 221.68/37.54  | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | |   (5712)  all_16_2 = e1
% 221.68/37.54  | | | | | | | | | |   (5713)  ( ~ (all_16_0 = e0) & op(all_16_1, e2) = all_16_0
% 221.68/37.54  | | | | | | | | | |             & op(e2, e1) = all_16_1 & $i(all_16_0) &
% 221.68/37.54  | | | | | | | | | |             $i(all_16_1)) | ( ~ (all_16_1 = e3) & op(e2, e1)
% 221.68/37.54  | | | | | | | | | |             = all_16_1 & $i(all_16_1))
% 221.68/37.54  | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | COMBINE_EQS: (324), (5712) imply:
% 221.68/37.54  | | | | | | | | | |   (5714)  all_8_2 = e1
% 221.68/37.54  | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | SIMP: (5714) implies:
% 221.68/37.54  | | | | | | | | | |   (5715)  all_8_2 = e1
% 221.68/37.54  | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | COMBINE_EQS: (305), (5715) imply:
% 221.68/37.54  | | | | | | | | | |   (5716)  all_26_2 = e1
% 221.68/37.54  | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | REDUCE: (349), (5715) imply:
% 221.68/37.54  | | | | | | | | | |   (5717)   ~ (all_53_1 = e1)
% 221.68/37.54  | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | REDUCE: (352), (5715) imply:
% 221.68/37.54  | | | | | | | | | |   (5718)   ~ (all_53_4 = e1)
% 221.68/37.54  | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | REDUCE: (354), (5715) imply:
% 221.68/37.54  | | | | | | | | | |   (5719)   ~ (all_53_6 = e1)
% 221.68/37.54  | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | REDUCE: (358), (5715) imply:
% 221.68/37.54  | | | | | | | | | |   (5720)   ~ (all_53_9 = e1)
% 221.68/37.54  | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | REDUCE: (360), (5715) imply:
% 221.68/37.54  | | | | | | | | | |   (5721)   ~ (all_53_13 = e1)
% 221.68/37.54  | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | REDUCE: (375), (5715) imply:
% 221.68/37.54  | | | | | | | | | |   (5722)   ~ (e3 = e1)
% 221.68/37.54  | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | REDUCE: (42), (5715) imply:
% 221.68/37.54  | | | | | | | | | |   (5723)  op(e2, e2) = e1
% 221.68/37.54  | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | BETA: splitting (223) gives:
% 221.68/37.54  | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | Case 1:
% 221.68/37.54  | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | |   (5724)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 221.68/37.54  | | | | | | | | | | |             & op(e2, e2) = e1)
% 221.68/37.54  | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | BETA: splitting (5724) gives:
% 221.68/37.54  | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | Case 1:
% 221.68/37.54  | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | |   (5725)  all_57_2 = e1 & op(e2, e3) = e1
% 221.68/37.54  | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | ALPHA: (5725) implies:
% 221.68/37.54  | | | | | | | | | | | |   (5726)  all_57_2 = e1
% 221.68/37.54  | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (207), (211), (212),
% 221.68/37.54  | | | | | | | | | | | |            (222), (224), (225), (5526), (5527), (5723),
% 221.68/37.54  | | | | | | | | | | | |            (5726), (function-axioms) are inconsistent by
% 221.68/37.54  | | | | | | | | | | | |            sub-proof #814.
% 221.68/37.54  | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | Case 2:
% 221.68/37.54  | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | |   (5727)  all_57_3 = e1 & op(e2, e2) = e1
% 221.68/37.54  | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | ALPHA: (5727) implies:
% 221.68/37.54  | | | | | | | | | | | |   (5728)  all_57_3 = e1
% 221.68/37.54  | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | BETA: splitting (58) gives:
% 221.68/37.54  | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | Case 1:
% 221.68/37.54  | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | |   (5729)   ~ (all_18_2 = e0)
% 221.68/37.54  | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | REDUCE: (327), (5729) imply:
% 221.68/37.54  | | | | | | | | | | | | |   (5730)   ~ (all_10_2 = e0)
% 221.68/37.54  | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | BETA: splitting (61) gives:
% 221.68/37.54  | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | Case 1:
% 221.68/37.54  | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | |   (5731)   ~ (all_20_2 = e2)
% 221.68/37.54  | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | REDUCE: (299), (5731) imply:
% 221.68/37.54  | | | | | | | | | | | | | |   (5732)   ~ (all_10_2 = e2)
% 221.68/37.54  | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | BETA: splitting (205) gives:
% 221.68/37.54  | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | Case 1:
% 221.68/37.54  | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | |   (5733)  all_55_0 = e3
% 221.68/37.54  | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | COMBINE_EQS: (277), (5733) imply:
% 221.68/37.54  | | | | | | | | | | | | | | |   (5734)  all_10_2 = e3
% 221.68/37.54  | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | REDUCE: (45), (5734) imply:
% 221.68/37.54  | | | | | | | | | | | | | | |   (5735)  op(e3, e3) = e3
% 221.68/37.54  | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (70), (107),
% 221.68/37.54  | | | | | | | | | | | | | | |            (137), (163), (166), (171), (204), (207), (208),
% 221.68/37.54  | | | | | | | | | | | | | | |            (209), (211), (212), (217), (221), (222), (223),
% 221.68/37.54  | | | | | | | | | | | | | | |            (224), (225), (226), (227), (228), (229), (230),
% 221.68/37.54  | | | | | | | | | | | | | | |            (231), (232), (233), (234), (235), (236), (270),
% 221.68/37.54  | | | | | | | | | | | | | | |            (374), (5526), (5527), (5713), (5716), (5718),
% 221.68/37.54  | | | | | | | | | | | | | | |            (5720), (5723), (5728), (5735), (function-axioms)
% 221.68/37.54  | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1732.
% 221.68/37.54  | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | Case 2:
% 221.68/37.54  | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | |   (5736)  all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 221.68/37.54  | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | REF_CLOSE: (277), (376), (5730), (5732), (5736) are
% 221.68/37.54  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1953.
% 221.68/37.54  | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | End of split
% 221.68/37.54  | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | Case 2:
% 221.68/37.54  | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | |   (5737)  all_20_2 = e2
% 221.68/37.54  | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | COMBINE_EQS: (299), (5737) imply:
% 221.68/37.54  | | | | | | | | | | | | | |   (5738)  all_10_2 = e2
% 221.68/37.54  | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | SIMP: (5738) implies:
% 221.68/37.54  | | | | | | | | | | | | | |   (5739)  all_10_2 = e2
% 221.68/37.54  | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | REDUCE: (340), (5739) imply:
% 221.68/37.54  | | | | | | | | | | | | | |   (5740)   ~ (all_53_2 = e2)
% 221.68/37.54  | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | REDUCE: (348), (5739) imply:
% 221.68/37.54  | | | | | | | | | | | | | |   (5741)   ~ (all_53_12 = e2)
% 221.68/37.54  | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | REDUCE: (45), (5739) imply:
% 221.68/37.54  | | | | | | | | | | | | | |   (5742)  op(e3, e3) = e2
% 221.68/37.54  | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 221.68/37.54  | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | Case 1:
% 221.68/37.54  | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | |   (5743)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 221.68/37.54  | | | | | | | | | | | | | | |             & op(e3, e2) = e2)
% 221.68/37.54  | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | BETA: splitting (5743) gives:
% 221.68/37.54  | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | Case 1:
% 221.68/37.54  | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | |   (5744)  all_57_0 = e2 & op(e3, e3) = e2
% 221.68/37.54  | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | ALPHA: (5744) implies:
% 221.68/37.54  | | | | | | | | | | | | | | | |   (5745)  all_57_0 = e2
% 221.68/37.54  | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | BETA: splitting (64) gives:
% 221.68/37.54  | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | Case 1:
% 221.68/37.54  | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | |   (5746)   ~ (all_22_2 = e3)
% 221.68/37.54  | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | REDUCE: (5514), (5746) imply:
% 221.68/37.54  | | | | | | | | | | | | | | | | |   (5747)  $false
% 221.68/37.54  | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | CLOSE: (5747) is inconsistent.
% 221.68/37.54  | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | Case 2:
% 221.68/37.54  | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | |   (5748)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0
% 221.68/37.54  | | | | | | | | | | | | | | | | |             & op(e0, e3) = all_22_1 & $i(all_22_0) &
% 221.68/37.54  | | | | | | | | | | | | | | | | |             $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0, e3)
% 221.68/37.54  | | | | | | | | | | | | | | | | |             = all_22_1 & $i(all_22_1))
% 221.68/37.54  | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 221.68/37.54  | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | Case 1:
% 221.68/37.54  | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | |   (5749)   ~ (all_24_2 = e0)
% 221.68/37.54  | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | REDUCE: (315), (5749) imply:
% 221.68/37.54  | | | | | | | | | | | | | | | | | |   (5750)   ~ (all_6_2 = e0)
% 221.68/37.54  | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | BETA: splitting (88) gives:
% 221.68/37.54  | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | Case 1:
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | |   (5751)   ~ (all_38_2 = e2)
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | REDUCE: (249), (5751) imply:
% 221.68/37.54  | | | | | | | | | | | | | | | | | | |   (5752)   ~ (all_6_2 = e2)
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | Case 1:
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | |   (5753)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | |             all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | |             op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | |               all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | |             $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | |             $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | |               all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | |             & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | |               all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | |             & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | |             $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | BETA: splitting (5753) gives:
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | |   (5754)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | |           all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | |           op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | |             all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | |           $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | |           $i(all_52_7)
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | ALPHA: (5754) implies:
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | |   (5755)  op(e3, e0) = all_52_7
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | |   (5756)  op(all_52_7, all_52_7) = e0
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | |   (5757)  all_55_10 = e3
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (374), (5757) are inconsistent by sub-proof
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | |            #2500.
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | |   (5758)   ~ (all_55_10 = e3)
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | |   (5759)  all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5759) gives:
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | |   (5760)  all_55_10 = e2
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (5752), (5760) are inconsistent by
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2499.
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | |   (5761)   ~ (all_55_10 = e2)
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | |   (5762)  all_55_10 = e1 | all_55_10 = e0
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5762) gives:
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | |   (5763)  all_55_10 = e1
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (336), (5763) imply:
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | |   (5764)  all_6_2 = e1
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5764) implies:
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | |   (5765)  all_6_2 = e1
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5752), (5765) imply:
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | |   (5766)   ~ (e2 = e1)
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (5765) imply:
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | |   (5767)  op(e1, e1) = e1
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | |   (5768)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e1)
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (226), (228), (229),
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | |            (5723), (5742), (5768), (function-axioms) are
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1677.
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | |   (5769)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e1)
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5769) gives:
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5770)  all_57_4 = e1 & op(e3, e1) = e1
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5770) implies:
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5771)  all_57_4 = e1
% 221.68/37.54  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (118),
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (126), (140), (141), (145), (146), (147),
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | |            (149), (150), (159), (164), (165), (169), (191),
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | |            (193), (197), (199), (201), (207), (208), (209),
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | |            (211), (212), (214), (215), (216), (217), (218),
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | |            (220), (221), (222), (223), (224), (225), (226),
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | |            (227), (228), (229), (230), (231), (232), (233),
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | |            (234), (235), (236), (237), (245), (247), (257),
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | |            (259), (267), (374), (5511), (5515), (5517),
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | |            (5518), (5519), (5526), (5527), (5717), (5720),
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | |            (5723), (5728), (5740), (5742), (5745), (5748),
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | |            (5767), (5771), (function-axioms) are inconsistent
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #715.
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5772)  all_57_9 = e1 & op(e3, e0) = e1
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5772) implies:
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5773)  all_57_9 = e1
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5774)  op(e3, e0) = e1
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (169), (207),
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | |            (208), (209), (211), (212), (214), (215), (216),
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | |            (217), (220), (221), (222), (223), (224), (225),
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | |            (226), (227), (228), (229), (230), (231), (232),
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (234), (235), (236), (237), (374), (5511),
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | |            (5518), (5526), (5527), (5723), (5728), (5742),
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | |            (5745), (5748), (5755), (5756), (5767), (5773),
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | |            (5774), (function-axioms) are inconsistent by
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #687.
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | |   (5775)  all_55_10 = e0
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (5750), (5775) are inconsistent by
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2118.
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | End of split
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | |   (5776)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | |           all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | |           op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | |             all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | |           & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | |           $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | |           $i(all_52_15)
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | ALPHA: (5776) implies:
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | |   (5777)  op(e2, e2) = all_52_11
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | |   (5778)  op(all_52_11, all_52_11) = e2
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | |   (5779)  all_55_10 = e3
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (374), (5779) are inconsistent by sub-proof
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | |            #2500.
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | |   (5780)   ~ (all_55_10 = e3)
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | |   (5781)  all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5781) gives:
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | |   (5782)  all_55_10 = e2
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (5752), (5782) are inconsistent by
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2499.
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | |   (5783)   ~ (all_55_10 = e2)
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | |   (5784)  all_55_10 = e1 | all_55_10 = e0
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5784) gives:
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | |   (5785)  all_55_10 = e1
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (336), (5785) imply:
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | |   (5786)  all_6_2 = e1
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5786) implies:
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | |   (5787)  all_6_2 = e1
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5752), (5787) imply:
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | |   (5788)   ~ (e2 = e1)
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (5787) imply:
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | |   (5789)  op(e1, e1) = e1
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (118),
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | |            (119), (126), (140), (141), (145), (146), (147),
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | |            (149), (150), (159), (164), (165), (169), (191),
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | |            (193), (197), (199), (201), (207), (208), (209),
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | |            (211), (212), (214), (215), (216), (217), (218),
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | |            (220), (221), (222), (223), (224), (225), (226),
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | |            (227), (228), (229), (230), (231), (232), (233),
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | |            (234), (235), (236), (237), (245), (247), (257),
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | |            (259), (267), (374), (5511), (5515), (5517),
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | |            (5518), (5519), (5526), (5527), (5717), (5720),
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | |            (5723), (5728), (5740), (5741), (5742), (5745),
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | |            (5748), (5777), (5778), (5789), (function-axioms)
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #672.
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | |   (5790)  all_55_10 = e0
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (5750), (5790) are inconsistent by
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2118.
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | End of split
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | End of split
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | Case 2:
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | |   (5791)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | |             & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | |             & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | |               all_52_21) = e1 & op(all_52_23, all_52_23) =
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | |             all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | |             = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | |             $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | |             & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | |             e0 & op(all_52_25, all_52_25) = e3 &
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | |             op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | |               all_52_29) = e1 & op(all_52_31, all_52_31) =
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | |             all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | |             = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | |             $i(all_52_29) & $i(all_52_31))
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | BETA: splitting (5791) gives:
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | |   (5792)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | |           all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | |           op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | |             all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | |           & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | |           & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | |           & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | |           $i(all_52_23)
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | ALPHA: (5792) implies:
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | |   (5793)  op(e1, e0) = all_52_23
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | |   (5794)  op(all_52_23, all_52_23) = e0
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | |   (5795)  all_55_10 = e3
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (374), (5795) are inconsistent by sub-proof
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | |            #2500.
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | |   (5796)   ~ (all_55_10 = e3)
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | |   (5797)  all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5797) gives:
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | |   (5798)  all_55_10 = e2
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (5752), (5798) are inconsistent by
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2499.
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | |   (5799)   ~ (all_55_10 = e2)
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | |   (5800)  all_55_10 = e1 | all_55_10 = e0
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5800) gives:
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | |   (5801)  all_55_10 = e1
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (336), (5801) imply:
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | |   (5802)  all_6_2 = e1
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5802) implies:
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | |   (5803)  all_6_2 = e1
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (368), (5803) imply:
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | |   (5804)   ~ (all_53_14 = e1)
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5752), (5803) imply:
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | |   (5805)   ~ (e2 = e1)
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (5803) imply:
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | |   (5806)  op(e1, e1) = e1
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | |   (5807)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e1)
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (226), (228), (229),
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | |            (5723), (5742), (5807), (function-axioms) are
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1677.
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | |   (5808)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e1)
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5808) gives:
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5809)  all_57_4 = e1 & op(e3, e1) = e1
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5809) implies:
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5810)  all_57_4 = e1
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (118),
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (126), (140), (141), (145), (146), (147),
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | |            (149), (150), (159), (164), (165), (169), (191),
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | |            (193), (197), (199), (201), (207), (208), (209),
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | |            (211), (212), (214), (215), (216), (217), (218),
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | |            (220), (221), (222), (223), (224), (225), (226),
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | |            (227), (228), (229), (230), (231), (232), (233),
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | |            (234), (235), (236), (237), (245), (247), (257),
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | |            (259), (267), (374), (5511), (5515), (5517),
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | |            (5518), (5519), (5526), (5527), (5717), (5720),
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | |            (5723), (5728), (5740), (5742), (5745), (5748),
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | |            (5806), (5810), (function-axioms) are inconsistent
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #715.
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5811)  all_57_9 = e1 & op(e3, e0) = e1
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5811) implies:
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5812)  all_57_9 = e1
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5813)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5813) gives:
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5814)  all_57_12 = e1 & op(e0, e3) = e1
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5814) implies:
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5815)  op(e0, e3) = e1
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (161), (194), (248), (5511), (5520),
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5527), (5748), (5793), (5794), (5804), (5815),
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #859.
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5816)  all_57_13 = e1 & op(e0, e2) = e1
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5816) implies:
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5817)  all_57_13 = e1
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5818)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e1)
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (169), (207), (208),
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (209), (223), (224), (225), (226), (228), (229),
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (233), (237), (5518), (5526), (5527),
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5723), (5728), (5742), (5817), (5818),
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #704.
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5819)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e3) = e1)
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5819) gives:
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5820)  all_57_6 = e1 & op(e1, e3) = e1
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5820) implies:
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5821)  all_57_6 = e1
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (169), (207),
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (211), (212), (217), (226), (227), (228), (231),
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (237), (374), (5518), (5526), (5723),
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5728), (5742), (5817), (5821), (function-axioms)
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #797.
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5822)  all_57_12 = e1 & op(e0, e3) = e1
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5822) implies:
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5823)  op(e0, e3) = e1
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (161), (194), (248), (5511), (5520),
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5527), (5748), (5793), (5794), (5804), (5823),
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #859.
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5824)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5824) gives:
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5825)  all_57_14 = e1 & op(e0, e1) = e1
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5825) implies:
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5826)  all_57_14 = e1
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5827)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e1)
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (169), (207),
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (208), (209), (212), (220), (221), (223), (224),
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (225), (231), (237), (374), (5518), (5526),
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5527), (5723), (5728), (5742), (5806), (5812),
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5826), (5827), (function-axioms) are inconsistent
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #698.
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5828)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e3) = e1)
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5828) gives:
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5829)  all_57_6 = e1 & op(e1, e3) = e1
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (169), (207),
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (208), (209), (211), (212), (214), (217), (220),
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (221), (222), (223), (224), (225), (226), (227),
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (228), (229), (230), (231), (232), (233), (234),
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (235), (236), (237), (374), (5518), (5526),
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5527), (5723), (5728), (5742), (5745), (5806),
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5812), (5826), (5829), (function-axioms) are
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #693.
% 221.68/37.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.68/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5830)  all_57_12 = e1 & op(e0, e3) = e1
% 221.68/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5830) implies:
% 221.68/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5831)  op(e0, e3) = e1
% 221.68/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (161), (194), (248), (5511), (5520),
% 221.68/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5527), (5748), (5793), (5794), (5804), (5831),
% 221.68/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.68/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #859.
% 221.68/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.68/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.68/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.68/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5832)  all_57_15 = e1 & op(e0, e0) = e1
% 221.68/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.68/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5832) implies:
% 221.68/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5833)  op(e0, e0) = e1
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5527), (5833), (function-axioms) are
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2183.
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | |   (5834)  all_55_10 = e0
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (5750), (5834) are inconsistent by
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2118.
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | End of split
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | |   (5835)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | |           all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | |           op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | |             all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | |           & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | |           & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | |           & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | |           $i(all_52_31)
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | ALPHA: (5835) implies:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | |   (5836)  op(e0, e0) = all_52_31
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | |   (5837)  op(all_52_31, all_52_31) = e0
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | |   (5838)  all_55_10 = e3
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (374), (5838) are inconsistent by sub-proof
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | |            #2500.
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | |   (5839)   ~ (all_55_10 = e3)
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | |   (5840)  all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5840) gives:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | |   (5841)  all_55_10 = e2
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (5752), (5841) are inconsistent by
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2499.
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | |   (5842)   ~ (all_55_10 = e2)
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | |   (5843)  all_55_10 = e1 | all_55_10 = e0
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5843) gives:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | |   (5844)  all_55_10 = e1
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (336), (5844) imply:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | |   (5845)  all_6_2 = e1
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5845) implies:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | |   (5846)  all_6_2 = e1
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5752), (5846) imply:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | |   (5847)   ~ (e2 = e1)
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (5846) imply:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | |   (5848)  op(e1, e1) = e1
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (118),
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | |            (119), (126), (140), (141), (145), (146), (147),
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | |            (149), (150), (159), (164), (165), (169), (191),
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | |            (193), (197), (199), (201), (207), (208), (209),
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | |            (211), (212), (214), (215), (216), (217), (218),
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | |            (220), (221), (222), (223), (224), (225), (226),
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | |            (227), (228), (229), (230), (231), (232), (233),
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | |            (234), (235), (236), (237), (245), (247), (257),
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | |            (259), (267), (374), (5511), (5515), (5517),
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | |            (5518), (5519), (5526), (5527), (5717), (5720),
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | |            (5723), (5728), (5740), (5742), (5745), (5748),
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | |            (5836), (5837), (5848), (function-axioms) are
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #670.
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | |   (5849)  all_55_10 = e0
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (5750), (5849) are inconsistent by
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2118.
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | End of split
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | End of split
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | End of split
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | Case 2:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | |   (5850)  all_38_2 = e2
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (5850) imply:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | |   (5851)  all_6_2 = e2
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | REDUCE: (374), (5851) imply:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | |   (5852)   ~ (e3 = e2)
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | REDUCE: (39), (5851) imply:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | |   (5853)  op(e1, e1) = e2
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (118),
% 221.79/37.56  | | | | | | | | | | | | | | | | | | |            (119), (126), (140), (141), (145), (146), (147),
% 221.79/37.56  | | | | | | | | | | | | | | | | | | |            (149), (150), (159), (164), (165), (169), (191),
% 221.79/37.56  | | | | | | | | | | | | | | | | | | |            (193), (197), (199), (201), (207), (208), (209),
% 221.79/37.56  | | | | | | | | | | | | | | | | | | |            (211), (212), (214), (215), (216), (217), (218),
% 221.79/37.56  | | | | | | | | | | | | | | | | | | |            (219), (220), (221), (222), (223), (224), (225),
% 221.79/37.56  | | | | | | | | | | | | | | | | | | |            (226), (227), (228), (229), (230), (231), (232),
% 221.79/37.56  | | | | | | | | | | | | | | | | | | |            (233), (234), (235), (236), (237), (245), (247),
% 221.79/37.56  | | | | | | | | | | | | | | | | | | |            (257), (259), (267), (374), (5511), (5515),
% 221.79/37.56  | | | | | | | | | | | | | | | | | | |            (5517), (5518), (5519), (5526), (5527), (5717),
% 221.79/37.56  | | | | | | | | | | | | | | | | | | |            (5720), (5723), (5728), (5740), (5742), (5745),
% 221.79/37.56  | | | | | | | | | | | | | | | | | | |            (5748), (5853), (function-axioms) are inconsistent
% 221.79/37.56  | | | | | | | | | | | | | | | | | | |            by sub-proof #655.
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | End of split
% 221.79/37.56  | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | Case 2:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | |   (5854)  all_24_2 = e0
% 221.79/37.56  | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (315), (5854) imply:
% 221.79/37.56  | | | | | | | | | | | | | | | | | |   (5855)  all_6_2 = e0
% 221.79/37.56  | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | SIMP: (5855) implies:
% 221.79/37.56  | | | | | | | | | | | | | | | | | |   (5856)  all_6_2 = e0
% 221.79/37.56  | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | REDUCE: (374), (5856) imply:
% 221.79/37.56  | | | | | | | | | | | | | | | | | |   (5857)   ~ (e3 = e0)
% 221.79/37.56  | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | REDUCE: (39), (5856) imply:
% 221.79/37.56  | | | | | | | | | | | | | | | | | |   (5858)  op(e1, e1) = e0
% 221.79/37.56  | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | Case 1:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | |   (5859)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 221.79/37.56  | | | | | | | | | | | | | | | | | | |             all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 221.79/37.56  | | | | | | | | | | | | | | | | | | |             op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 221.79/37.56  | | | | | | | | | | | | | | | | | | |               all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 221.79/37.56  | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 221.79/37.56  | | | | | | | | | | | | | | | | | | |             op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 221.79/37.56  | | | | | | | | | | | | | | | | | | |             $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 221.79/37.56  | | | | | | | | | | | | | | | | | | |             $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 221.79/37.56  | | | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 221.79/37.56  | | | | | | | | | | | | | | | | | | |               all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 221.79/37.56  | | | | | | | | | | | | | | | | | | |             & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 221.79/37.56  | | | | | | | | | | | | | | | | | | |               all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 221.79/37.56  | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 221.79/37.56  | | | | | | | | | | | | | | | | | | |             & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 221.79/37.56  | | | | | | | | | | | | | | | | | | |             $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | BETA: splitting (5859) gives:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | Case 1:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | |   (5860)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | |           all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | |           op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | |             all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | |           $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | |           $i(all_52_7)
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | ALPHA: (5860) implies:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | |   (5861)  op(e3, e0) = all_52_7
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | |   (5862)  op(e3, e3) = all_52_1
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | |   (5863)  op(all_52_7, all_52_7) = e0
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | |   (5864)  op(all_52_1, all_52_1) = e3
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | |   (5865)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e0)
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5865) gives:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | |   (5866)  all_57_6 = e0 & op(e1, e3) = e0
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5866) implies:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | |   (5867)  all_57_6 = e0
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | |   (5868)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e3)
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5868) gives:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | |   (5869)  all_57_0 = e3 & op(e3, e3) = e3
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5869) implies:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | |   (5870)  op(e3, e3) = e3
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5742), (5870), (function-axioms) are
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2490.
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | |   (5871)  all_57_2 = e3 & op(e2, e3) = e3
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5871) implies:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | |   (5872)  all_57_2 = e3
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | |   (5873)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5873) gives:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5874)  all_57_6 = e3 & op(e1, e3) = e3
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5874) implies:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5875)  all_57_6 = e3
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (230), (232), (234),
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | |            (5745), (5872), (5875), (function-axioms) are
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1286.
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5876)  all_57_7 = e3 & op(e1, e2) = e3
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5876) implies:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5877)  all_57_7 = e3
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5878)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (5867), (5877), (5878) are inconsistent
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #654.
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5879)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5879) gives:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5880)  all_57_8 = e1 & op(e1, e1) = e1
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5880) implies:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5881)  op(e1, e1) = e1
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5858), (5881), (function-axioms) are
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2427.
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5882)  all_57_11 = e1 & op(e1, e0) = e1
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5882) implies:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5883)  all_57_11 = e1
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5884)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5884) gives:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5885)  all_57_9 = e2 & op(e3, e0) = e2
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5885) implies:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5886)  all_57_9 = e2
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (169), (207),
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (208), (209), (221), (223), (224), (226), (228),
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (233), (237), (374), (5518), (5526),
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5527), (5723), (5728), (5742), (5877), (5883),
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5886), (function-axioms) are inconsistent by
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #653.
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5887)  all_57_10 = e2 & op(e2, e0) = e2
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5887) implies:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5888)  all_57_10 = e2
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5889)  op(e2, e0) = e2
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (118),
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (126), (140), (141), (145), (146), (147),
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (149), (150), (159), (164), (165), (191), (193),
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (197), (199), (201), (207), (208), (209), (211),
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (217), (221), (222), (228), (231), (233),
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (245), (247), (257), (259), (267), (374), (5515),
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5517), (5519), (5526), (5527), (5717), (5720),
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5723), (5740), (5742), (5862), (5864), (5867),
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5872), (5888), (5889), (function-axioms) are
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #648.
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5890)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (217), (223), (224), (225), (230), (232),
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (374), (5511), (5526), (5527), (5723), (5728),
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5742), (5748), (5867), (5872), (5877), (5890),
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #646.
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | |   (5891)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (374), (5526), (5891), (function-axioms)
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1786.
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | |   (5892)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e3) = e3)
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5892) gives:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | |   (5893)  all_57_6 = e3 & op(e1, e3) = e3
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5893) implies:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | |   (5894)  all_57_6 = e3
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5867), (5894) are inconsistent by sub-proof
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | |            #1822.
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | |   (5895)  all_57_12 = e3 & op(e0, e3) = e3
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5895) implies:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | |   (5896)  all_57_12 = e3
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | |   (5897)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5897) gives:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5898)  all_57_6 = e3 & op(e1, e3) = e3
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5898) implies:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5899)  all_57_6 = e3
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5867), (5899) are inconsistent by sub-proof
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | |            #1822.
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5900)  all_57_7 = e3 & op(e1, e2) = e3
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5900) implies:
% 221.79/37.56  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5901)  all_57_7 = e3
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5902)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (5728), (5742), (5867), (5896), (5901),
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5902), (function-axioms) are inconsistent by
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #645.
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5903)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5903) gives:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5904)  all_57_8 = e1 & op(e1, e1) = e1
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5904) implies:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5905)  op(e1, e1) = e1
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5858), (5905), (function-axioms) are
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2427.
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5906)  all_57_11 = e1 & op(e1, e0) = e1
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5906) implies:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5907)  all_57_11 = e1
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5908)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5908) gives:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5909)  all_57_9 = e2 & op(e3, e0) = e2
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5909) implies:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5910)  all_57_9 = e2
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (169), (207),
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (208), (209), (221), (223), (224), (226), (228),
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (233), (237), (374), (5518), (5526),
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5527), (5723), (5728), (5742), (5901), (5907),
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5910), (function-axioms) are inconsistent by
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #653.
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5911)  all_57_10 = e2 & op(e2, e0) = e2
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5911) implies:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5912)  all_57_10 = e2
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5913)  op(e2, e0) = e2
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5914)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e0)
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (118),
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (126), (140), (141), (145), (146), (147),
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (149), (150), (159), (164), (165), (169), (191),
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (193), (197), (199), (201), (207), (208), (209),
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (211), (212), (217), (221), (226), (227), (228),
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (233), (237), (245), (247), (257), (259),
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (267), (374), (5515), (5517), (5518), (5519),
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5526), (5527), (5717), (5720), (5723), (5740),
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5742), (5867), (5901), (5913), (5914),
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #644.
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5915)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5915) gives:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5916)  all_57_8 = e0 & op(e1, e1) = e0
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5916) implies:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5917)  all_57_8 = e0
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5918)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5918) gives:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5919)  all_57_2 = e3 & op(e2, e3) = e3
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5919) implies:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5920)  all_57_2 = e3
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (118),
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (126), (140), (141), (145), (146), (147),
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (149), (150), (159), (164), (165), (191), (193),
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (197), (199), (201), (207), (208), (209), (211),
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (217), (221), (222), (228), (231), (233),
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (245), (247), (257), (259), (267), (374), (5515),
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5517), (5519), (5526), (5527), (5717), (5720),
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5723), (5740), (5742), (5862), (5864), (5867),
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5912), (5913), (5920), (function-axioms) are
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #648.
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5921)  all_57_3 = e3 & op(e2, e2) = e3
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5921) implies:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5922)  op(e2, e2) = e3
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5723), (5922), (function-axioms) are
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1912.
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5923)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (118),
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (126), (140), (141), (145), (146), (147),
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (149), (150), (159), (164), (165), (169), (191),
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (193), (197), (199), (201), (207), (208), (209),
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (211), (212), (216), (217), (221), (222), (223),
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (225), (226), (227), (228), (229), (230),
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (232), (233), (234), (236), (237), (245),
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (247), (257), (259), (267), (374), (5511), (5515),
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5517), (5518), (5519), (5526), (5527), (5717),
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5720), (5723), (5728), (5740), (5742), (5745),
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5748), (5896), (5901), (5912), (5913), (5917),
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5923), (function-axioms) are inconsistent by
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #641.
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5924)  all_57_14 = e0 & op(e0, e1) = e0
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5924) implies:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5925)  all_57_14 = e0
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (208), (209), (5526),
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5896), (5925) are inconsistent by sub-proof
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1763.
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5926)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5926) gives:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5927)  all_57_11 = e2 & op(e1, e0) = e2
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5907), (5927) are inconsistent by sub-proof
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2048.
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5928)  all_57_15 = e2 & op(e0, e0) = e2
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (217), (374), (5526), (5867), (5901),
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5928), (function-axioms) are inconsistent by
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1034.
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | |   (5929)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (374), (5526), (5929), (function-axioms)
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1786.
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | |   (5930)  all_57_7 = e0 & op(e1, e2) = e0
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5930) implies:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | |   (5931)  all_57_7 = e0
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | |   (5932)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5932) gives:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | |   (5933)  all_57_1 = e3 & op(e3, e2) = e3
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5933) implies:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | |   (5934)  all_57_1 = e3
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | |   (5935)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5935) gives:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5936)  all_57_6 = e3 & op(e1, e3) = e3
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5936) implies:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5937)  all_57_6 = e3
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5938)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (217), (374), (5526), (5931), (5938),
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1155.
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5939)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5939) gives:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5940)  all_57_8 = e1 & op(e1, e1) = e1
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5940) implies:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5941)  op(e1, e1) = e1
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5858), (5941), (function-axioms) are
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2427.
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5942)  all_57_11 = e1 & op(e1, e0) = e1
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5942) implies:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5943)  all_57_11 = e1
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5944)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5944) gives:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5945)  all_57_9 = e2 & op(e3, e0) = e2
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (208),
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (209), (221), (223), (224), (226), (228), (229),
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (233), (374), (5526), (5527), (5723),
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5728), (5742), (5934), (5943), (5945),
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #640.
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5946)  all_57_10 = e2 & op(e2, e0) = e2
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5946) implies:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5947)  all_57_10 = e2
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5948)  op(e2, e0) = e2
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5949)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (230), (232), (234),
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5723), (5745), (5937), (5949), (function-axioms)
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #639.
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5950)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5950) gives:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5951)  all_57_5 = e3 & op(e2, e1) = e3
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5951) implies:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5952)  all_57_5 = e3
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5953)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e1)
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (226), (228), (229),
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5723), (5742), (5953), (function-axioms) are
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1677.
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5954)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e1)
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5954) gives:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5955)  all_57_4 = e1 & op(e3, e1) = e1
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (8), (9), (39), (107), (118), (119),
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (126), (140), (141), (145), (146), (147), (149),
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (150), (159), (164), (165), (169), (191), (193),
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (197), (199), (201), (228), (237), (245), (247),
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (257), (259), (267), (374), (5515), (5517),
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5518), (5519), (5527), (5717), (5720), (5723),
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5740), (5742), (5931), (5948), (5955),
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #638.
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5956)  all_57_9 = e1 & op(e3, e0) = e1
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5956) implies:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5957)  all_57_9 = e1
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5958)  op(e3, e0) = e1
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5959)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e1)
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (169), (226), (228),
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (229), (231), (237), (5518), (5723), (5742),
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5934), (5952), (5957), (5959), (function-axioms)
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #636.
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.79/37.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5960)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e1)
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5960) gives:
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5961)  all_57_8 = e1 & op(e1, e1) = e1
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5961) implies:
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5962)  op(e1, e1) = e1
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (169), (207),
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (208), (209), (211), (212), (214), (215), (216),
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (217), (220), (221), (222), (223), (224), (225),
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (226), (227), (228), (229), (230), (231), (232),
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (234), (235), (236), (237), (374), (5511),
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5518), (5526), (5527), (5723), (5728), (5742),
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5745), (5748), (5861), (5863), (5957), (5958),
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5962), (function-axioms) are inconsistent by
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #687.
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5963)  all_57_14 = e1 & op(e0, e1) = e1
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (118),
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (126), (140), (141), (145), (146), (147),
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (149), (150), (159), (164), (165), (169), (191),
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (193), (197), (199), (201), (207), (208), (209),
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (211), (212), (217), (221), (222), (223), (224),
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (225), (226), (227), (228), (229), (230), (231),
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (232), (233), (234), (235), (236), (237), (245),
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (247), (257), (259), (267), (374), (5515), (5517),
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5518), (5519), (5526), (5527), (5717), (5720),
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5723), (5728), (5740), (5742), (5745), (5934),
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5937), (5947), (5948), (5957), (5963),
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #632.
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5964)  all_57_10 = e3 & op(e2, e0) = e3
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5964) implies:
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5965)  all_57_10 = e3
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (207), (211), (212),
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5526), (5527), (5965), (function-axioms) are
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1746.
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5966)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5966) gives:
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5967)  all_57_11 = e2 & op(e1, e0) = e2
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5943), (5967) are inconsistent by sub-proof
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2048.
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5968)  all_57_15 = e2 & op(e0, e0) = e2
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (169), (231), (233),
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (237), (5518), (5526), (5742), (5934), (5968),
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #633.
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5969)  all_57_7 = e3 & op(e1, e2) = e3
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5969) implies:
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5970)  all_57_7 = e3
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5931), (5970) are inconsistent by sub-proof
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | |            #2269.
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.79/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | |   (5971)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (374), (5526), (5971), (function-axioms)
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1786.
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | |   (5972)  all_57_3 = e3 & op(e2, e2) = e3
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5972) implies:
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | |   (5973)  op(e2, e2) = e3
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5723), (5973), (function-axioms) are
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1912.
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | |   (5974)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (207), (208), (209),
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | |            (5526), (5527), (5931), (5974), (function-axioms)
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #993.
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | |   (5975)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5975) gives:
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_52_1,
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (5742), (5862) gives:
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | |   (5976)  all_52_1 = e2
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5864), (5976) imply:
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | |   (5977)  op(e2, e2) = e3
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5723), (5977), (function-axioms) are
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1912.
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | |   (5978)  all_57_11 = e0 & op(e1, e0) = e0
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5978) implies:
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | |   (5979)  all_57_11 = e0
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | |   (5980)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5980) gives:
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | |   (5981)  all_57_6 = e1 & op(e1, e3) = e1
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5981) implies:
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | |   (5982)  all_57_6 = e1
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | |   (5983)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5983) gives:
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5984)  all_57_6 = e3 & op(e1, e3) = e3
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5984) implies:
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5985)  all_57_6 = e3
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5982), (5985) are inconsistent by sub-proof
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | |            #2017.
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5986)  all_57_7 = e3 & op(e1, e2) = e3
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5986) implies:
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5987)  all_57_7 = e3
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5988)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e3)
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5988) gives:
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5989)  all_57_0 = e3 & op(e3, e3) = e3
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5989) implies:
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5990)  op(e3, e3) = e3
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5742), (5990), (function-axioms) are
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2490.
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5991)  all_57_2 = e3 & op(e2, e3) = e3
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5991) implies:
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5992)  all_57_2 = e3
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (118),
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (126), (140), (141), (145), (146), (147),
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (149), (150), (159), (164), (165), (169), (191),
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (193), (197), (199), (201), (207), (208), (209),
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (211), (212), (217), (221), (222), (223), (224),
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (225), (226), (227), (228), (229), (230), (231),
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (232), (233), (235), (236), (237), (245), (247),
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (257), (259), (267), (374), (5515), (5517),
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5518), (5519), (5526), (5527), (5717), (5720),
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5723), (5728), (5740), (5742), (5745), (5979),
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5982), (5987), (5992), (function-axioms) are
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #626.
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5993)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e3) = e3)
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5993) gives:
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5994)  all_57_6 = e3 & op(e1, e3) = e3
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5994) implies:
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5995)  all_57_6 = e3
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5982), (5995) imply:
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5996)  e3 = e1
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5996) implies:
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5997)  e3 = e1
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5987), (5997) imply:
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5998)  all_57_7 = e1
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (118),
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (126), (140), (141), (145), (146), (147),
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (149), (150), (159), (164), (165), (169), (191),
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (193), (197), (199), (201), (207), (208), (209),
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (211), (212), (214), (215), (216), (217), (219),
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (221), (222), (223), (224), (225), (226), (227),
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (228), (229), (230), (231), (232), (233), (234),
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (235), (236), (237), (245), (247), (257), (259),
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (267), (374), (5511), (5515), (5517), (5518),
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5519), (5526), (5527), (5717), (5720), (5723),
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5728), (5740), (5742), (5745), (5748), (5861),
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5862), (5863), (5864), (5979), (5995), (5998),
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #614.
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5999)  all_57_12 = e3 & op(e0, e3) = e3
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5999) implies:
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6000)  all_57_12 = e3
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6001)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6001) gives:
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6002)  all_57_9 = e1 & op(e3, e0) = e1
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6002) implies:
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6003)  all_57_9 = e1
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6004)  op(e3, e0) = e1
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6005)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6005) gives:
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6006)  all_57_9 = e2 & op(e3, e0) = e2
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6003), (6006) are inconsistent by sub-proof
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2481.
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6007)  all_57_10 = e2 & op(e2, e0) = e2
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6007) implies:
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6008)  all_57_10 = e2
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6009)  op(e2, e0) = e2
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6010)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e1)
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (118),
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (126), (140), (141), (145), (146), (147),
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (149), (150), (159), (164), (165), (169), (191),
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (193), (197), (199), (201), (207), (208), (209),
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (211), (212), (217), (221), (226), (228), (231),
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (237), (245), (247), (257), (259), (267),
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (374), (5515), (5517), (5518), (5519), (5526),
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5527), (5717), (5720), (5723), (5740), (5742),
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5982), (5987), (6003), (6009), (6010),
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #612.
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6011)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e1)
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6011) gives:
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6012)  all_57_8 = e1 & op(e1, e1) = e1
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6012) implies:
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6013)  op(e1, e1) = e1
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (169), (207),
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (208), (209), (211), (212), (214), (215), (216),
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (217), (220), (221), (222), (223), (224), (225),
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (226), (227), (228), (229), (230), (231), (232),
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (234), (235), (236), (237), (374), (5511),
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5518), (5526), (5527), (5723), (5728), (5742),
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5745), (5748), (5861), (5863), (6003), (6004),
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6013), (function-axioms) are inconsistent by
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #687.
% 221.91/37.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6014)  all_57_14 = e1 & op(e0, e1) = e1
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (118),
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (126), (140), (141), (145), (146), (147),
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (149), (150), (159), (164), (165), (191), (193),
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (197), (199), (201), (207), (208), (209), (211),
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (217), (221), (222), (223), (225), (228),
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (233), (245), (247), (257), (259), (267),
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (374), (5515), (5517), (5519), (5526), (5527),
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5717), (5720), (5723), (5740), (5742), (5982),
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6000), (6008), (6009), (6014), (function-axioms)
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #611.
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6015)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (217), (374), (5526), (5527), (5979),
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5982), (5987), (6015), (function-axioms) are
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #610.
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6016)  all_57_10 = e1 & op(e2, e0) = e1
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (169), (207),
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (208), (209), (211), (212), (217), (221), (222),
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (223), (224), (226), (227), (228), (229), (230),
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (232), (233), (235), (236), (237), (374),
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5518), (5526), (5527), (5723), (5728), (5742),
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5979), (5982), (5987), (6016), (function-axioms)
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #609.
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6017)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (5527), (5728), (5742), (5979), (5982),
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6000), (6017), (function-axioms) are inconsistent
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #608.
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | |   (6018)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (374), (5526), (6018), (function-axioms)
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1786.
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | |   (6019)  all_57_7 = e1 & op(e1, e2) = e1
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6019) implies:
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | |   (6020)  all_57_7 = e1
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | |   (6021)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6021) gives:
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6022)  all_57_6 = e3 & op(e1, e3) = e3
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6022) implies:
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6023)  all_57_6 = e3
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (118),
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (126), (140), (141), (145), (146), (147),
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | |            (149), (150), (159), (164), (165), (169), (191),
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | |            (193), (197), (199), (201), (207), (208), (209),
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | |            (211), (212), (214), (215), (216), (217), (219),
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | |            (221), (222), (223), (224), (225), (226), (227),
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | |            (228), (229), (230), (231), (232), (233), (234),
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | |            (235), (236), (237), (245), (247), (257), (259),
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | |            (267), (374), (5511), (5515), (5517), (5518),
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | |            (5519), (5526), (5527), (5717), (5720), (5723),
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | |            (5728), (5740), (5742), (5745), (5748), (5861),
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | |            (5862), (5863), (5864), (5979), (6020), (6023),
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | |            #614.
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6024)  all_57_7 = e3 & op(e1, e2) = e3
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6024) implies:
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6025)  all_57_7 = e3
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (6020), (6025) are inconsistent by sub-proof
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | |            #2115.
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | |   (6026)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (374), (5526), (6026), (function-axioms)
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1786.
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | |   (6027)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5858), (5979), (6027), (function-axioms) are
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #910.
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | |   (6028)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | |           all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | |           op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | |             all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | |           & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | |           $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | |           $i(all_52_15)
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | ALPHA: (6028) implies:
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | |   (6029)  op(e2, e2) = all_52_11
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | |   (6030)  op(all_52_11, all_52_11) = e2
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | |   (6031)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e0)
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6031) gives:
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | |   (6032)  all_57_6 = e0 & op(e1, e3) = e0
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6032) implies:
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | |   (6033)  all_57_6 = e0
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | |   (6034)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e3)
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6034) gives:
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | |   (6035)  all_57_0 = e3 & op(e3, e3) = e3
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6035) implies:
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | |   (6036)  op(e3, e3) = e3
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5742), (6036), (function-axioms) are
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2490.
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | |   (6037)  all_57_2 = e3 & op(e2, e3) = e3
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6037) implies:
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | |   (6038)  all_57_2 = e3
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (118),
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | |            (119), (126), (140), (141), (145), (146), (147),
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | |            (149), (150), (159), (164), (165), (169), (191),
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | |            (193), (197), (199), (201), (207), (208), (209),
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | |            (211), (212), (214), (215), (216), (217), (218),
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | |            (220), (221), (222), (223), (224), (225), (226),
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | |            (227), (228), (229), (230), (231), (232), (233),
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | |            (234), (235), (236), (237), (245), (247), (257),
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | |            (259), (267), (374), (5511), (5515), (5517),
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | |            (5518), (5519), (5526), (5527), (5717), (5720),
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | |            (5723), (5728), (5740), (5741), (5742), (5745),
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | |            (5748), (6029), (6030), (6033), (6038),
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | |            #606.
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | |   (6039)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e3) = e3)
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6039) gives:
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | |   (6040)  all_57_6 = e3 & op(e1, e3) = e3
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6040) implies:
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | |   (6041)  all_57_6 = e3
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (6033), (6041) are inconsistent by sub-proof
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | |            #1822.
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | |   (6042)  all_57_12 = e3 & op(e0, e3) = e3
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6042) implies:
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | |   (6043)  all_57_12 = e3
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | |   (6044)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6044) gives:
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6045)  all_57_6 = e3 & op(e1, e3) = e3
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6045) implies:
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6046)  all_57_6 = e3
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (6033), (6046) are inconsistent by sub-proof
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | |            #1822.
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6047)  all_57_7 = e3 & op(e1, e2) = e3
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6047) implies:
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6048)  all_57_7 = e3
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6049)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (5728), (5742), (6033), (6043), (6048),
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6049), (function-axioms) are inconsistent by
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #645.
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6050)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6050) gives:
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6051)  all_57_8 = e1 & op(e1, e1) = e1
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6051) implies:
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6052)  op(e1, e1) = e1
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (118),
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (126), (140), (141), (145), (146), (147),
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (149), (150), (159), (164), (165), (169), (191),
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (193), (197), (199), (201), (207), (208), (209),
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (211), (212), (214), (215), (216), (217), (218),
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (220), (221), (222), (223), (224), (225), (226),
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (227), (228), (229), (230), (231), (232), (233),
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (234), (235), (236), (237), (245), (247), (257),
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (259), (267), (374), (5511), (5515), (5517),
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5518), (5519), (5526), (5527), (5717), (5720),
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5723), (5728), (5740), (5741), (5742), (5745),
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5748), (6029), (6030), (6052), (function-axioms)
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #672.
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6053)  all_57_11 = e1 & op(e1, e0) = e1
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6053) implies:
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6054)  all_57_11 = e1
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6055)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6055) gives:
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6056)  all_57_9 = e2 & op(e3, e0) = e2
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6056) implies:
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6057)  all_57_9 = e2
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (169), (207),
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (208), (209), (221), (223), (224), (226), (228),
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (233), (237), (374), (5518), (5526),
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5527), (5723), (5728), (5742), (6048), (6054),
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6057), (function-axioms) are inconsistent by
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #653.
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6058)  all_57_10 = e2 & op(e2, e0) = e2
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6058) implies:
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6059)  all_57_10 = e2
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6060)  op(e2, e0) = e2
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6061)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e0)
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (118),
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (126), (140), (141), (145), (146), (147),
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (149), (150), (159), (164), (165), (169), (191),
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (193), (197), (199), (201), (207), (208), (209),
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (211), (212), (217), (221), (226), (227), (228),
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (233), (237), (245), (247), (257), (259),
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (267), (374), (5515), (5517), (5518), (5519),
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5526), (5527), (5717), (5720), (5723), (5740),
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5742), (6033), (6048), (6060), (6061),
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #644.
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6062)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6062) gives:
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6063)  all_57_8 = e0 & op(e1, e1) = e0
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6063) implies:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6064)  all_57_8 = e0
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6065)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6065) gives:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6066)  all_57_2 = e3 & op(e2, e3) = e3
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6066) implies:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6067)  all_57_2 = e3
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (118),
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (126), (140), (141), (145), (146), (147),
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (149), (150), (159), (164), (165), (191), (193),
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (197), (199), (201), (207), (208), (209), (211),
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (217), (221), (222), (228), (231), (233),
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (245), (247), (257), (259), (267), (374), (5515),
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5517), (5519), (5526), (5527), (5717), (5720),
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5723), (5740), (5742), (6029), (6030), (6033),
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6059), (6060), (6067), (function-axioms) are
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #607.
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6068)  all_57_3 = e3 & op(e2, e2) = e3
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6068) implies:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6069)  op(e2, e2) = e3
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5723), (6069), (function-axioms) are
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1912.
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6070)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6070) gives:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6071)  all_57_5 = e3 & op(e2, e1) = e3
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6071) implies:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6072)  all_57_5 = e3
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (118),
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (126), (140), (141), (145), (146), (147),
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (149), (150), (159), (164), (165), (169), (191),
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (193), (197), (199), (201), (207), (208), (209),
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (211), (212), (216), (217), (221), (222), (223),
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (225), (226), (227), (228), (229), (230),
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (232), (233), (234), (236), (237), (245),
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (247), (257), (259), (267), (374), (5511), (5515),
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5517), (5518), (5519), (5526), (5527), (5717),
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5720), (5723), (5728), (5740), (5742), (5745),
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5748), (6043), (6048), (6059), (6060), (6064),
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6072), (function-axioms) are inconsistent by
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #642.
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6073)  all_57_10 = e3 & op(e2, e0) = e3
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6073) implies:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6074)  all_57_10 = e3
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (207), (211), (212),
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5526), (5527), (6074), (function-axioms) are
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1746.
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6075)  all_57_14 = e0 & op(e0, e1) = e0
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6075) implies:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6076)  all_57_14 = e0
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (208), (209), (5526),
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6043), (6076) are inconsistent by sub-proof
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1763.
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6077)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6077) gives:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6078)  all_57_11 = e2 & op(e1, e0) = e2
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6054), (6078) are inconsistent by sub-proof
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2048.
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6079)  all_57_15 = e2 & op(e0, e0) = e2
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (217), (374), (5526), (6033), (6048),
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6079), (function-axioms) are inconsistent by
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1034.
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | |   (6080)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (374), (5526), (6080), (function-axioms)
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1786.
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | |   (6081)  all_57_7 = e0 & op(e1, e2) = e0
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6081) implies:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | |   (6082)  all_57_7 = e0
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | |   (6083)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6083) gives:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | |   (6084)  all_57_1 = e3 & op(e3, e2) = e3
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6084) implies:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | |   (6085)  all_57_1 = e3
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | |   (6086)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6086) gives:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6087)  all_57_6 = e3 & op(e1, e3) = e3
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6087) implies:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6088)  all_57_6 = e3
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6089)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (217), (374), (5526), (6082), (6089),
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1155.
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6090)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6090) gives:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6091)  all_57_8 = e1 & op(e1, e1) = e1
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6091) implies:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6092)  op(e1, e1) = e1
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (118),
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (126), (140), (141), (145), (146), (147),
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (149), (150), (159), (164), (165), (169), (191),
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (193), (197), (199), (201), (207), (208), (209),
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (211), (212), (214), (215), (216), (217), (218),
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (220), (221), (222), (223), (224), (225), (226),
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (227), (228), (229), (230), (231), (232), (233),
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (234), (235), (236), (237), (245), (247), (257),
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (259), (267), (374), (5511), (5515), (5517),
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5518), (5519), (5526), (5527), (5717), (5720),
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5723), (5728), (5740), (5741), (5742), (5745),
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5748), (6029), (6030), (6092), (function-axioms)
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #672.
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6093)  all_57_11 = e1 & op(e1, e0) = e1
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6093) implies:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6094)  all_57_11 = e1
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6095)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6095) gives:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6096)  all_57_9 = e2 & op(e3, e0) = e2
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (208),
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (209), (221), (223), (224), (226), (228), (229),
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (233), (374), (5526), (5527), (5723),
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5728), (5742), (6085), (6094), (6096),
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #640.
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6097)  all_57_10 = e2 & op(e2, e0) = e2
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6097) implies:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6098)  all_57_10 = e2
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6099)  op(e2, e0) = e2
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6100)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6100) gives:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6101)  all_57_2 = e0 & op(e2, e3) = e0
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6101) implies:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6102)  all_57_2 = e0
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6103)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e1)
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (226), (228), (229),
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5723), (5742), (6103), (function-axioms) are
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1677.
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6104)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e1)
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6104) gives:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6105)  all_57_4 = e1 & op(e3, e1) = e1
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (8), (9), (39), (107), (118), (119),
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (126), (140), (141), (145), (146), (147), (149),
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (150), (159), (164), (165), (169), (191), (193),
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (197), (199), (201), (228), (237), (245), (247),
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (257), (259), (267), (374), (5515), (5517),
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5518), (5519), (5527), (5717), (5720), (5723),
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5740), (5742), (6082), (6099), (6105),
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #638.
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6106)  all_57_9 = e1 & op(e3, e0) = e1
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6106) implies:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6107)  all_57_9 = e1
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6108)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e1)
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5728), (5742), (6102), (6108), (function-axioms)
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #801.
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6109)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e3) = e1)
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6109) gives:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6110)  all_57_6 = e1 & op(e1, e3) = e1
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6110) implies:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6111)  all_57_6 = e1
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (118),
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (126), (140), (141), (145), (146), (147),
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (149), (150), (159), (164), (165), (169), (191),
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (193), (197), (199), (201), (207), (208), (209),
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (211), (212), (214), (215), (216), (217), (218),
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (220), (221), (222), (223), (224), (225), (226),
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (227), (228), (229), (230), (231), (232), (233),
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (234), (235), (236), (237), (245), (247), (257),
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (259), (267), (374), (5511), (5515), (5517),
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5518), (5519), (5526), (5527), (5717), (5720),
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5723), (5728), (5740), (5742), (5745), (5748),
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6029), (6030), (6094), (6098), (6099), (6107),
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6111), (function-axioms) are inconsistent by
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #677.
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6112)  all_57_12 = e1 & op(e0, e3) = e1
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6112) implies:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6113)  op(e0, e3) = e1
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (207), (212), (223),
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (225), (5511), (5526), (5527), (5728),
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5748), (6094), (6102), (6107), (6113),
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #709.
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6114)  all_57_3 = e0 & op(e2, e2) = e0
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6114) implies:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6115)  all_57_3 = e0
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6116)  op(e2, e2) = e0
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6083) gives:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (169), (207),
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (208), (209), (211), (212), (217), (223), (224),
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (225), (227), (228), (229), (230), (231), (232),
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (234), (236), (237), (374), (5518), (5526),
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5527), (5742), (5745), (6082), (6085), (6115),
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6116), (function-axioms) are inconsistent by
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #605.
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6117)  all_57_3 = e3 & op(e2, e2) = e3
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6117) implies:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6118)  all_57_3 = e3
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (6115), (6118) are inconsistent by sub-proof
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2358.
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6119)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6119) gives:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6120)  all_57_7 = e3 & op(e1, e2) = e3
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6120) implies:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6121)  all_57_7 = e3
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (6082), (6121) are inconsistent by sub-proof
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2269.
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6122)  all_57_13 = e3 & op(e0, e2) = e3
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6122) implies:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6123)  all_57_13 = e3
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6086) gives:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6124)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e0)
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5742), (6115), (6124), (function-axioms) are
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1654.
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6125)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = e0)
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6125) gives:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6126)  all_57_6 = e0 & op(e1, e3) = e0
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (6088), (6126) are inconsistent by sub-proof
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2465.
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6127)  all_57_12 = e0 & op(e0, e3) = e0
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6127) implies:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6128)  all_57_12 = e0
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6129)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6129) gives:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6130)  all_57_12 = e2 & op(e0, e3) = e2
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6130) implies:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6131)  all_57_12 = e2
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (232), (234), (5745),
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6088), (6128), (6131) are inconsistent by
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #763.
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6132)  all_57_13 = e2 & op(e0, e2) = e2
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6132) implies:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6133)  all_57_13 = e2
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6123), (6133) imply:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6134)  e3 = e2
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (169), (207),
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (211), (212), (217), (223), (224), (225), (227),
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (228), (230), (231), (232), (233), (235), (236),
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (237), (374), (5518), (5526), (5742), (6088),
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6115), (6134), (function-axioms) are inconsistent
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #604.
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6135)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6135) gives:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6136)  all_57_14 = e2 & op(e0, e1) = e2
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6136) implies:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6137)  all_57_14 = e2
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (208), (5526), (6123), (6128),
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6137) are inconsistent by sub-proof #2215.
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6138)  all_57_15 = e2 & op(e0, e0) = e2
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6138) implies:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6139)  all_57_15 = e2
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5526), (6139) imply:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6140)  e3 = e2
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (169), (207),
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (211), (212), (217), (223), (224), (225), (227),
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (228), (230), (231), (232), (233), (235), (236),
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (237), (374), (5518), (5526), (5742), (6088),
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6115), (6140), (function-axioms) are inconsistent
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #604.
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6141)  all_57_7 = e3 & op(e1, e2) = e3
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6141) implies:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6142)  all_57_7 = e3
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (6082), (6142) are inconsistent by sub-proof
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2269.
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6143)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (374), (5526), (6143), (function-axioms)
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1786.
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6144)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0)
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6144) gives:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6145)  all_57_5 = e0 & op(e2, e1) = e0
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6145) implies:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6146)  all_57_5 = e0
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6147)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e3)
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6147) gives:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6148)  all_57_4 = e3 & op(e3, e1) = e3
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6148) implies:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6149)  all_57_4 = e3
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6150)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6150) gives:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6151)  all_57_2 = e3 & op(e2, e3) = e3
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6151) implies:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6152)  all_57_2 = e3
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (208),
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (209), (211), (212), (217), (221), (230), (231),
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (232), (234), (235), (374), (5526), (6082),
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6085), (6088), (6146), (6152), (function-axioms)
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #950.
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6153)  all_57_3 = e3 & op(e2, e2) = e3
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6153) implies:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6154)  op(e2, e2) = e3
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5723), (6154), (function-axioms) are
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1912.
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6155)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6155) gives:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6156)  all_57_5 = e3 & op(e2, e1) = e3
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6156) implies:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6157)  all_57_5 = e3
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6146), (6157) imply:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6158)  e3 = e0
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6088), (6158) imply:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6159)  all_57_6 = e0
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (118),
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (126), (140), (141), (145), (146), (147),
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (149), (150), (159), (164), (165), (191), (193),
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (197), (199), (201), (207), (211), (212), (217),
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (228), (231), (233), (245), (247), (257), (259),
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (267), (374), (5515), (5517), (5519), (5526),
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5527), (5717), (5720), (5723), (5740), (5742),
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6099), (6149), (6159), (function-axioms) are
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #651.
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6160)  all_57_10 = e3 & op(e2, e0) = e3
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6160) implies:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6161)  all_57_10 = e3
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (207), (212), (231),
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (235), (5526), (6085), (6149), (6161) are
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1436.
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6162)  all_57_5 = e3 & op(e2, e1) = e3
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6162) implies:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6163)  all_57_5 = e3
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6146), (6163) imply:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6164)  e3 = e0
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6164) implies:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6165)  e3 = e0
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6088), (6165) imply:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6166)  all_57_6 = e0
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (118),
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (126), (140), (141), (145), (146), (147),
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (149), (150), (159), (164), (165), (191), (193),
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (197), (199), (201), (207), (208), (209), (211),
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (217), (221), (228), (231), (233), (245),
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (247), (257), (259), (267), (374), (5515), (5517),
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5519), (5526), (5527), (5717), (5720), (5723),
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5740), (5742), (6099), (6146), (6166),
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #650.
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6167)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e1) = e3)
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (208),
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (209), (374), (5526), (6167), (function-axioms)
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1794.
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6168)  all_57_10 = e0 & op(e2, e0) = e0
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6168) implies:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6169)  all_57_10 = e0
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6098), (6169) are inconsistent by sub-proof
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2138.
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6170)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6170) gives:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6171)  all_57_11 = e2 & op(e1, e0) = e2
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6094), (6171) are inconsistent by sub-proof
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2048.
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6172)  all_57_15 = e2 & op(e0, e0) = e2
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (169), (231), (233),
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (237), (5518), (5526), (5742), (6085), (6172),
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #633.
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6173)  all_57_7 = e3 & op(e1, e2) = e3
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6173) implies:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6174)  all_57_7 = e3
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (6082), (6174) are inconsistent by sub-proof
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | |            #2269.
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | |   (6175)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (374), (5526), (6175), (function-axioms)
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1786.
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | |   (6176)  all_57_3 = e3 & op(e2, e2) = e3
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6176) implies:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | |   (6177)  op(e2, e2) = e3
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5723), (6177), (function-axioms) are
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1912.
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | |   (6178)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (207), (208), (209),
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | |            (5526), (5527), (6082), (6178), (function-axioms)
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #993.
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | |   (6179)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6179) gives:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | |              all_52_11, e2, e2, simplifying with (5723), (6029)
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | |              gives:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | |   (6180)  all_52_11 = e1
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6030), (6180) imply:
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | |   (6181)  op(e1, e1) = e2
% 221.91/37.61  | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (118),
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | |            (119), (126), (140), (141), (145), (146), (147),
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | |            (149), (150), (159), (164), (165), (169), (191),
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | |            (193), (197), (199), (201), (207), (208), (209),
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | |            (211), (212), (214), (215), (216), (217), (218),
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | |            (219), (220), (221), (222), (223), (224), (225),
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | |            (226), (227), (228), (229), (230), (231), (232),
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | |            (233), (234), (235), (236), (237), (245), (247),
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | |            (257), (259), (267), (374), (5511), (5515),
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | |            (5517), (5518), (5519), (5526), (5527), (5717),
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | |            (5720), (5723), (5728), (5740), (5742), (5745),
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | |            (5748), (6181), (function-axioms) are inconsistent
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #655.
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | |   (6182)  all_57_11 = e0 & op(e1, e0) = e0
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6182) implies:
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | |   (6183)  all_57_11 = e0
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | |   (6184)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6184) gives:
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | |   (6185)  all_57_6 = e1 & op(e1, e3) = e1
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6185) implies:
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | |   (6186)  all_57_6 = e1
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | |   (6187)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6187) gives:
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6188)  all_57_6 = e3 & op(e1, e3) = e3
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6188) implies:
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6189)  all_57_6 = e3
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (6186), (6189) are inconsistent by sub-proof
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | |            #2017.
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6190)  all_57_7 = e3 & op(e1, e2) = e3
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6190) implies:
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6191)  all_57_7 = e3
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6192)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e3)
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6192) gives:
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6193)  all_57_0 = e3 & op(e3, e3) = e3
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6193) implies:
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6194)  op(e3, e3) = e3
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5742), (6194), (function-axioms) are
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2490.
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6195)  all_57_2 = e3 & op(e2, e3) = e3
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6195) implies:
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6196)  all_57_2 = e3
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6197)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6197) gives:
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6198)  all_57_9 = e1 & op(e3, e0) = e1
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6198) implies:
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6199)  all_57_9 = e1
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (118),
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (126), (140), (141), (145), (146), (147),
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (149), (150), (159), (164), (165), (169), (191),
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (193), (197), (199), (201), (207), (208), (209),
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (211), (212), (217), (221), (222), (223), (224),
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (225), (227), (228), (230), (231), (232), (233),
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (237), (245), (247), (257), (259), (267), (374),
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5515), (5517), (5518), (5519), (5526), (5527),
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5717), (5720), (5723), (5728), (5740), (5742),
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5745), (6183), (6186), (6191), (6196), (6199),
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #628.
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6200)  all_57_10 = e1 & op(e2, e0) = e1
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6200) implies:
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6201)  all_57_10 = e1
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6202)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (169), (207),
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (208), (209), (211), (212), (217), (221), (222),
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (223), (224), (226), (227), (228), (229), (230),
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (232), (233), (235), (236), (237), (374),
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5518), (5526), (5527), (5723), (5728), (5742),
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6201), (6202), (function-axioms) are inconsistent
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #627.
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6203)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (217), (223), (224), (225), (230), (232),
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (374), (5526), (5527), (5723), (5728), (5742),
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6183), (6191), (6196), (6203), (function-axioms)
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #629.
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6204)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6204) gives:
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6205)  all_57_11 = e1 & op(e1, e0) = e1
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6205) implies:
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6206)  all_57_11 = e1
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6183), (6206) imply:
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6207)  e1 = e0
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6186), (6207) imply:
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6208)  all_57_6 = e0
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (118),
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (126), (140), (141), (145), (146), (147),
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (149), (150), (159), (164), (165), (169), (191),
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (193), (197), (199), (201), (207), (208), (209),
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (211), (212), (214), (215), (216), (217), (218),
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (220), (221), (222), (223), (224), (225), (226),
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (227), (228), (229), (230), (231), (232), (233),
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (234), (235), (236), (237), (245), (247), (257),
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (259), (267), (374), (5511), (5515), (5517),
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5518), (5519), (5526), (5527), (5717), (5720),
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5723), (5728), (5740), (5741), (5742), (5745),
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5748), (6029), (6030), (6196), (6208),
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #606.
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6209)  all_57_15 = e1 & op(e0, e0) = e1
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6209) implies:
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6210)  op(e0, e0) = e1
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5527), (6210), (function-axioms) are
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2183.
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 221.91/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6211)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e3) = e3)
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6211) gives:
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6212)  all_57_6 = e3 & op(e1, e3) = e3
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6212) implies:
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6213)  all_57_6 = e3
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6186), (6213) imply:
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6214)  e3 = e1
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6214) implies:
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6215)  e3 = e1
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6191), (6215) imply:
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6216)  all_57_7 = e1
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (118),
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (126), (140), (141), (145), (146), (147),
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (149), (150), (159), (164), (165), (169), (191),
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (193), (197), (199), (201), (207), (208), (209),
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (211), (212), (217), (221), (222), (223), (224),
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (225), (226), (227), (228), (229), (230), (231),
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (232), (233), (235), (236), (237), (245), (247),
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (257), (259), (267), (374), (5515), (5517),
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5518), (5519), (5526), (5527), (5717), (5720),
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5723), (5728), (5740), (5742), (6029), (6030),
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6183), (6213), (6216), (function-axioms) are
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #603.
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6217)  all_57_12 = e3 & op(e0, e3) = e3
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6217) implies:
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6218)  all_57_12 = e3
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6219)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6219) gives:
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6220)  all_57_9 = e1 & op(e3, e0) = e1
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6220) implies:
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6221)  all_57_9 = e1
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6222)  op(e3, e0) = e1
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6223)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6223) gives:
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6224)  all_57_9 = e2 & op(e3, e0) = e2
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6221), (6224) are inconsistent by sub-proof
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2481.
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6225)  all_57_10 = e2 & op(e2, e0) = e2
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6225) implies:
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6226)  all_57_10 = e2
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6227)  op(e2, e0) = e2
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6228)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e1)
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6228) gives:
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6229)  all_57_4 = e1 & op(e3, e1) = e1
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6229) implies:
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6230)  all_57_4 = e1
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6231)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e3)
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6231) gives:
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6232)  all_57_0 = e3 & op(e3, e3) = e3
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6232) implies:
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6233)  op(e3, e3) = e3
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5742), (6233), (function-axioms) are
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2490.
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6234)  all_57_1 = e3 & op(e3, e2) = e3
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6234) implies:
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6235)  all_57_1 = e3
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6236)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (5742), (6235), (6236),
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1676.
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6237)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6237) gives:
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6238)  all_57_4 = e0 & op(e3, e1) = e0
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6238) implies:
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6239)  all_57_4 = e0
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6230), (6239) imply:
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6240)  e1 = e0
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6186), (6240) imply:
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6241)  all_57_6 = e0
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (217), (226), (227), (228), (374), (5526),
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5723), (6235), (6241), (function-axioms) are
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1773.
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6242)  all_57_9 = e0 & op(e3, e0) = e0
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6242) implies:
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6243)  all_57_9 = e0
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6221), (6243) imply:
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6244)  e1 = e0
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6186), (6244) imply:
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6245)  all_57_6 = e0
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (217), (226), (227), (228), (374), (5526),
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5723), (6235), (6245), (function-axioms) are
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1773.
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6246)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e3)
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (169), (5518), (6230), (6246),
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2281.
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6247)  all_57_5 = e1 & op(e2, e1) = e1
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6247) implies:
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6248)  all_57_5 = e1
% 222.09/37.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (118),
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (126), (140), (141), (145), (146), (147),
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (149), (150), (159), (164), (165), (169), (191),
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (193), (197), (199), (201), (207), (208), (209),
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (211), (212), (217), (221), (226), (228), (231),
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (237), (245), (247), (257), (259), (267),
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (374), (5515), (5517), (5518), (5519), (5526),
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5527), (5717), (5720), (5723), (5740), (5742),
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6186), (6191), (6227), (6248), (function-axioms)
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #613.
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6249)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e1)
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6249) gives:
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6250)  all_57_8 = e1 & op(e1, e1) = e1
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6250) implies:
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6251)  op(e1, e1) = e1
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (118),
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (126), (140), (141), (145), (146), (147),
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (149), (150), (159), (164), (165), (169), (191),
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (193), (197), (199), (201), (207), (208), (209),
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (211), (212), (214), (215), (216), (217), (218),
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (220), (221), (222), (223), (224), (225), (226),
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (227), (228), (229), (230), (231), (232), (233),
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (234), (235), (236), (237), (245), (247), (257),
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (259), (267), (374), (5511), (5515), (5517),
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5518), (5519), (5526), (5527), (5717), (5720),
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5723), (5728), (5740), (5741), (5742), (5745),
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5748), (6029), (6030), (6221), (6222), (6251),
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #674.
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6252)  all_57_14 = e1 & op(e0, e1) = e1
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (118),
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (126), (140), (141), (145), (146), (147),
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (149), (150), (159), (164), (165), (191), (193),
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (197), (199), (201), (207), (208), (209), (211),
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (217), (221), (222), (223), (225), (228),
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (233), (245), (247), (257), (259), (267),
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (374), (5515), (5517), (5519), (5526), (5527),
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5717), (5720), (5723), (5740), (5742), (6186),
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6218), (6226), (6227), (6252), (function-axioms)
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #611.
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6253)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (217), (374), (5526), (5527), (6183),
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6186), (6191), (6253), (function-axioms) are
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #610.
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6254)  all_57_10 = e1 & op(e2, e0) = e1
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6254) implies:
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6255)  all_57_10 = e1
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6256)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (169), (207),
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (208), (209), (211), (212), (217), (221), (222),
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (223), (224), (226), (227), (228), (229), (230),
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (232), (233), (235), (236), (237), (374),
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5518), (5526), (5527), (5723), (5728), (5742),
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6255), (6256), (function-axioms) are inconsistent
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #627.
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6257)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (217), (374), (5526), (5527), (6183),
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6186), (6191), (6257), (function-axioms) are
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #610.
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6258)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (5527), (5728), (5742), (6183), (6186),
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6218), (6258), (function-axioms) are inconsistent
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #608.
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (6259)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (374), (5526), (6259), (function-axioms)
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1786.
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | |   (6260)  all_57_7 = e1 & op(e1, e2) = e1
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6260) implies:
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | |   (6261)  all_57_7 = e1
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (6262)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6262) gives:
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6263)  all_57_6 = e3 & op(e1, e3) = e3
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6263) implies:
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6264)  all_57_6 = e3
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (118),
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (126), (140), (141), (145), (146), (147),
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | |            (149), (150), (159), (164), (165), (169), (191),
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | |            (193), (197), (199), (201), (207), (208), (209),
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | |            (211), (212), (217), (221), (222), (223), (224),
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | |            (225), (226), (227), (228), (229), (230), (231),
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | |            (232), (233), (235), (236), (237), (245), (247),
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | |            (257), (259), (267), (374), (5515), (5517),
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | |            (5518), (5519), (5526), (5527), (5717), (5720),
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | |            (5723), (5728), (5740), (5742), (6029), (6030),
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | |            (6183), (6261), (6264), (function-axioms) are
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #603.
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6265)  all_57_7 = e3 & op(e1, e2) = e3
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6265) implies:
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6266)  all_57_7 = e3
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (6261), (6266) are inconsistent by sub-proof
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | |            #2115.
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (6267)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (374), (5526), (6267), (function-axioms)
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1786.
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | |   (6268)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6268) gives:
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | |   (6269)  all_57_8 = e1 & op(e1, e1) = e1
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6269) implies:
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | |   (6270)  op(e1, e1) = e1
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (118),
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | |            (119), (126), (140), (141), (145), (146), (147),
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | |            (149), (150), (159), (164), (165), (169), (191),
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | |            (193), (197), (199), (201), (207), (208), (209),
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | |            (211), (212), (214), (215), (216), (217), (218),
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | |            (220), (221), (222), (223), (224), (225), (226),
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | |            (227), (228), (229), (230), (231), (232), (233),
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | |            (234), (235), (236), (237), (245), (247), (257),
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | |            (259), (267), (374), (5511), (5515), (5517),
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | |            (5518), (5519), (5526), (5527), (5717), (5720),
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | |            (5723), (5728), (5740), (5741), (5742), (5745),
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | |            (5748), (6029), (6030), (6270), (function-axioms)
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #672.
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | |   (6271)  all_57_11 = e1 & op(e1, e0) = e1
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6271) implies:
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | |   (6272)  all_57_11 = e1
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6183), (6272) are inconsistent by sub-proof
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | |            #1862.
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | End of split
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | End of split
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | End of split
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | Case 2:
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | |   (6273)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 222.09/37.63  | | | | | | | | | | | | | | | | | | |             & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 222.09/37.63  | | | | | | | | | | | | | | | | | | |             & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 222.09/37.63  | | | | | | | | | | | | | | | | | | |               all_52_21) = e1 & op(all_52_23, all_52_23) =
% 222.09/37.63  | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 222.09/37.63  | | | | | | | | | | | | | | | | | | |             all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 222.09/37.63  | | | | | | | | | | | | | | | | | | |             = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 222.09/37.63  | | | | | | | | | | | | | | | | | | |             $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 222.09/37.63  | | | | | | | | | | | | | | | | | | |             & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 222.09/37.63  | | | | | | | | | | | | | | | | | | |             e0 & op(all_52_25, all_52_25) = e3 &
% 222.09/37.63  | | | | | | | | | | | | | | | | | | |             op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 222.09/37.63  | | | | | | | | | | | | | | | | | | |               all_52_29) = e1 & op(all_52_31, all_52_31) =
% 222.09/37.63  | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 222.09/37.63  | | | | | | | | | | | | | | | | | | |             all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 222.09/37.63  | | | | | | | | | | | | | | | | | | |             = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 222.09/37.63  | | | | | | | | | | | | | | | | | | |             $i(all_52_29) & $i(all_52_31))
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | BETA: splitting (6273) gives:
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | Case 1:
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | |   (6274)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | |           all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | |           op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | |             all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | |           & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | |           & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | |           & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | |           $i(all_52_23)
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | ALPHA: (6274) implies:
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | |   (6275)  op(e1, e1) = all_52_21
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | |   (6276)  op(all_52_21, all_52_21) = e1
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | |   (6277)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e0)
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6277) gives:
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | |   (6278)  all_57_6 = e0 & op(e1, e3) = e0
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6278) implies:
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | |   (6279)  all_57_6 = e0
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | |   (6280)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e3)
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6280) gives:
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | |   (6281)  all_57_0 = e3 & op(e3, e3) = e3
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6281) implies:
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | |   (6282)  op(e3, e3) = e3
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5742), (6282), (function-axioms) are
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2490.
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | |   (6283)  all_57_2 = e3 & op(e2, e3) = e3
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6283) implies:
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | |   (6284)  all_57_2 = e3
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (6285)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6285) gives:
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6286)  all_57_6 = e3 & op(e1, e3) = e3
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6286) implies:
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6287)  all_57_6 = e3
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (230), (232), (234),
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | |            (5745), (6284), (6287), (function-axioms) are
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1286.
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6288)  all_57_7 = e3 & op(e1, e2) = e3
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6288) implies:
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6289)  all_57_7 = e3
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6290)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (6279), (6289), (6290) are inconsistent
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #654.
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6291)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6291) gives:
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.09/37.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6292)  all_57_8 = e1 & op(e1, e1) = e1
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6292) implies:
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6293)  op(e1, e1) = e1
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5858), (6293), (function-axioms) are
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2427.
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6294)  all_57_11 = e1 & op(e1, e0) = e1
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6294) implies:
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6295)  all_57_11 = e1
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6296)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6296) gives:
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6297)  all_57_9 = e2 & op(e3, e0) = e2
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6297) implies:
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6298)  all_57_9 = e2
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (169), (207),
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (208), (209), (221), (223), (224), (226), (228),
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (233), (237), (374), (5518), (5526),
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5527), (5723), (5728), (5742), (6289), (6295),
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6298), (function-axioms) are inconsistent by
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #653.
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6299)  all_57_10 = e2 & op(e2, e0) = e2
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6299) implies:
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6300)  all_57_10 = e2
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6301)  op(e2, e0) = e2
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6302)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6302) gives:
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6303)  all_57_2 = e0 & op(e2, e3) = e0
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6303) implies:
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6304)  all_57_2 = e0
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6284), (6304) imply:
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6305)  e3 = e0
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6289), (6305) imply:
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6306)  all_57_7 = e0
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (118),
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (126), (140), (141), (145), (146), (147),
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (149), (150), (159), (164), (165), (169), (191),
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (193), (197), (199), (201), (207), (208), (209),
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (211), (212), (215), (217), (219), (221), (222),
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (223), (224), (225), (226), (227), (228), (229),
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (231), (232), (233), (234), (235), (236),
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (237), (245), (247), (257), (259), (267), (374),
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5515), (5517), (5518), (5519), (5526), (5527),
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5717), (5720), (5723), (5728), (5740), (5742),
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5745), (5858), (6306), (function-axioms) are
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #602.
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6307)  all_57_3 = e0 & op(e2, e2) = e0
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6307) implies:
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6308)  op(e2, e2) = e0
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5723), (6308), (function-axioms) are
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2352.
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6309)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0)
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (118),
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (126), (140), (141), (145), (146), (147),
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (149), (150), (159), (164), (165), (191), (193),
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (197), (199), (201), (207), (208), (209), (211),
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (217), (221), (228), (231), (233), (245),
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (247), (257), (259), (267), (374), (5515), (5517),
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5519), (5526), (5527), (5717), (5720), (5723),
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5740), (5742), (6279), (6300), (6301), (6309),
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #649.
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6310)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (217), (223), (224), (225), (230), (232),
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (374), (5511), (5526), (5527), (5723), (5728),
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5742), (5748), (6279), (6284), (6289), (6310),
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #646.
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | |   (6311)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (374), (5526), (6311), (function-axioms)
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1786.
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | |   (6312)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e3) = e3)
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6312) gives:
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | |   (6313)  all_57_6 = e3 & op(e1, e3) = e3
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6313) implies:
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | |   (6314)  all_57_6 = e3
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (6279), (6314) are inconsistent by sub-proof
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | |            #1822.
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | |   (6315)  all_57_12 = e3 & op(e0, e3) = e3
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6315) implies:
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | |   (6316)  all_57_12 = e3
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | |   (6317)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6317) gives:
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6318)  all_57_6 = e3 & op(e1, e3) = e3
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6318) implies:
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6319)  all_57_6 = e3
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (6279), (6319) are inconsistent by sub-proof
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | |            #1822.
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6320)  all_57_7 = e3 & op(e1, e2) = e3
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6320) implies:
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6321)  all_57_7 = e3
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6322)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (5728), (5742), (6279), (6316), (6321),
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6322), (function-axioms) are inconsistent by
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #645.
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6323)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6323) gives:
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6324)  all_57_8 = e1 & op(e1, e1) = e1
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.09/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6324) implies:
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6325)  op(e1, e1) = e1
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5858), (6325), (function-axioms) are
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2427.
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6326)  all_57_11 = e1 & op(e1, e0) = e1
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6326) implies:
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6327)  all_57_11 = e1
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6328)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6328) gives:
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6329)  all_57_9 = e2 & op(e3, e0) = e2
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6329) implies:
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6330)  all_57_9 = e2
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (169), (207),
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (208), (209), (221), (223), (224), (226), (228),
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (233), (237), (374), (5518), (5526),
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5527), (5723), (5728), (5742), (6321), (6327),
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6330), (function-axioms) are inconsistent by
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #653.
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6331)  all_57_10 = e2 & op(e2, e0) = e2
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6331) implies:
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6332)  all_57_10 = e2
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6333)  op(e2, e0) = e2
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6334)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e0)
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (118),
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (126), (140), (141), (145), (146), (147),
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (149), (150), (159), (164), (165), (169), (191),
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (193), (197), (199), (201), (207), (208), (209),
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (211), (212), (217), (221), (226), (227), (228),
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (233), (237), (245), (247), (257), (259),
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (267), (374), (5515), (5517), (5518), (5519),
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5526), (5527), (5717), (5720), (5723), (5740),
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5742), (6279), (6321), (6333), (6334),
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #644.
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6335)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6335) gives:
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6336)  all_57_8 = e0 & op(e1, e1) = e0
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6336) implies:
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6337)  all_57_8 = e0
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6338)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6338) gives:
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6339)  all_57_2 = e0 & op(e2, e3) = e0
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6339) implies:
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6340)  all_57_2 = e0
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6341)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6341) gives:
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6342)  all_57_2 = e3 & op(e2, e3) = e3
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6342) implies:
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6343)  all_57_2 = e3
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6340), (6343) imply:
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6344)  e3 = e0
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6344) implies:
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6345)  e3 = e0
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6321), (6345) imply:
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6346)  all_57_7 = e0
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (118),
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (126), (140), (141), (145), (146), (147),
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (149), (150), (159), (164), (165), (169), (191),
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (193), (197), (199), (201), (207), (208), (209),
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (211), (212), (215), (217), (219), (221), (222),
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (223), (224), (225), (226), (227), (228), (229),
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (231), (232), (233), (234), (235), (236),
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (237), (245), (247), (257), (259), (267), (374),
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5515), (5517), (5518), (5519), (5526), (5527),
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5717), (5720), (5723), (5728), (5740), (5742),
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5745), (5858), (6346), (function-axioms) are
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #602.
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6347)  all_57_3 = e3 & op(e2, e2) = e3
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6347) implies:
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6348)  op(e2, e2) = e3
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5723), (6348), (function-axioms) are
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1912.
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6349)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (118),
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (126), (140), (141), (145), (146), (147),
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (149), (150), (159), (164), (165), (169), (191),
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (193), (197), (199), (201), (207), (208), (209),
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (211), (212), (216), (217), (221), (222), (223),
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (225), (226), (227), (228), (229), (230),
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (232), (233), (234), (236), (237), (245),
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (247), (257), (259), (267), (374), (5511), (5515),
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5517), (5518), (5519), (5526), (5527), (5717),
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5720), (5723), (5728), (5740), (5742), (5745),
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5748), (6316), (6321), (6332), (6333), (6337),
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6349), (function-axioms) are inconsistent by
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #641.
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6350)  all_57_3 = e0 & op(e2, e2) = e0
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6350) implies:
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6351)  op(e2, e2) = e0
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5723), (6351), (function-axioms) are
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2352.
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6352)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0)
% 222.17/37.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (118),
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (126), (140), (141), (145), (146), (147),
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (149), (150), (159), (164), (165), (191), (193),
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (197), (199), (201), (207), (208), (209), (211),
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (217), (221), (228), (231), (233), (245),
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (247), (257), (259), (267), (374), (5515), (5517),
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5519), (5526), (5527), (5717), (5720), (5723),
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5740), (5742), (6279), (6332), (6333), (6352),
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #649.
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6353)  all_57_14 = e0 & op(e0, e1) = e0
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6353) implies:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6354)  all_57_14 = e0
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (208), (209), (5526),
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6316), (6354) are inconsistent by sub-proof
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1763.
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6355)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6355) gives:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6356)  all_57_11 = e2 & op(e1, e0) = e2
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6327), (6356) are inconsistent by sub-proof
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2048.
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6357)  all_57_15 = e2 & op(e0, e0) = e2
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (217), (374), (5526), (6279), (6321),
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6357), (function-axioms) are inconsistent by
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1034.
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | |   (6358)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (374), (5526), (6358), (function-axioms)
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1786.
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | |   (6359)  all_57_7 = e0 & op(e1, e2) = e0
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6359) implies:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | |   (6360)  all_57_7 = e0
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (118),
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | |            (119), (126), (140), (141), (145), (146), (147),
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | |            (149), (150), (159), (164), (165), (169), (191),
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | |            (193), (197), (199), (201), (207), (208), (209),
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | |            (211), (212), (215), (217), (219), (221), (222),
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | |            (223), (224), (225), (226), (227), (228), (229),
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | |            (230), (231), (232), (233), (234), (235), (236),
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | |            (237), (245), (247), (257), (259), (267), (374),
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | |            (5515), (5517), (5518), (5519), (5526), (5527),
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | |            (5717), (5720), (5723), (5728), (5740), (5742),
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | |            (5745), (5858), (6360), (function-axioms) are
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #602.
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | |   (6361)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6361) gives:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | |   (6362)  all_57_8 = e0 & op(e1, e1) = e0
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5527), (6275), (6276), (6362),
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | |            #601.
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | |   (6363)  all_57_11 = e0 & op(e1, e0) = e0
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6363) implies:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | |   (6364)  all_57_11 = e0
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | |   (6365)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6365) gives:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | |   (6366)  all_57_6 = e1 & op(e1, e3) = e1
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6366) implies:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | |   (6367)  all_57_6 = e1
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | |   (6368)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6368) gives:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6369)  all_57_6 = e3 & op(e1, e3) = e3
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6369) implies:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6370)  all_57_6 = e3
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (6367), (6370) are inconsistent by sub-proof
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | |            #2017.
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6371)  all_57_7 = e3 & op(e1, e2) = e3
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6371) implies:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6372)  all_57_7 = e3
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (118),
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (126), (140), (141), (145), (146), (147),
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | |            (149), (150), (159), (164), (165), (169), (191),
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | |            (193), (197), (199), (201), (207), (208), (209),
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | |            (211), (212), (217), (219), (221), (222), (223),
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (225), (226), (227), (228), (229), (230),
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (232), (233), (235), (236), (237), (245),
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | |            (247), (257), (259), (267), (374), (5515), (5517),
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | |            (5518), (5519), (5526), (5527), (5717), (5720),
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | |            (5723), (5728), (5740), (5742), (5745), (5858),
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | |            (6364), (6367), (6372), (function-axioms) are
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #599.
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | |   (6373)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (374), (5526), (6373), (function-axioms)
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1786.
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | |   (6374)  all_57_7 = e1 & op(e1, e2) = e1
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6374) implies:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | |   (6375)  all_57_7 = e1
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | |   (6376)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6376) gives:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6377)  all_57_6 = e3 & op(e1, e3) = e3
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6377) implies:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6378)  all_57_6 = e3
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6379)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6379) gives:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6380)  all_57_1 = e3 & op(e3, e2) = e3
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6380) implies:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6381)  all_57_1 = e3
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6382)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (217), (226), (227), (228), (374), (5526),
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5723), (5742), (6378), (6381), (6382),
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #625.
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6383)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6383) gives:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6384)  all_57_4 = e0 & op(e3, e1) = e0
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6384) implies:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6385)  all_57_4 = e0
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6386)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6386) gives:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6387)  all_57_9 = e2 & op(e3, e0) = e2
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (169), (207),
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (208), (209), (211), (212), (217), (221), (222),
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (223), (224), (226), (227), (228), (229), (230),
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (232), (233), (235), (236), (237), (374),
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5518), (5526), (5527), (5723), (5728), (5742),
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6364), (6385), (6387), (function-axioms) are
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #624.
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6388)  all_57_10 = e2 & op(e2, e0) = e2
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6388) implies:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6389)  all_57_10 = e2
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6390)  op(e2, e0) = e2
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6391)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6391) gives:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6392)  all_57_2 = e0 & op(e2, e3) = e0
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6392) implies:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6393)  all_57_2 = e0
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6394)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6394) gives:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6395)  all_57_9 = e1 & op(e3, e0) = e1
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6395) implies:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6396)  all_57_9 = e1
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6397)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e3)
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6397) gives:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6398)  all_57_4 = e3 & op(e3, e1) = e3
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (118),
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (126), (140), (141), (145), (146), (147),
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (149), (150), (159), (164), (165), (191), (193),
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (197), (199), (201), (207), (211), (212), (217),
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (228), (231), (233), (245), (247), (257), (259),
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (267), (374), (5515), (5517), (5519), (5526),
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5527), (5717), (5720), (5723), (5740), (5742),
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6378), (6385), (6390), (6398), (function-axioms)
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #623.
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6399)  all_57_5 = e3 & op(e2, e1) = e3
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6399) implies:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6400)  all_57_5 = e3
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6401)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (118),
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (126), (140), (141), (145), (146), (147),
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (149), (150), (159), (164), (165), (191), (193),
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (197), (199), (201), (207), (208), (209), (211),
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (217), (221), (223), (224), (228), (231),
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (245), (247), (257), (259), (267), (374),
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5515), (5517), (5519), (5526), (5527), (5717),
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5720), (5723), (5740), (5742), (6378), (6381),
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6385), (6390), (6393), (6400), (6401),
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #598.
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6402)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0)
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6402) gives:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6403)  all_57_7 = e0 & op(e1, e2) = e0
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (223), (224), (5728),
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6375), (6393), (6400), (6403) are inconsistent by
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #622.
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6404)  all_57_13 = e0 & op(e0, e2) = e0
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6404) implies:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6405)  all_57_13 = e0
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6406)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 222.17/37.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (118),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (126), (140), (141), (145), (146), (147),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (149), (150), (159), (164), (165), (169), (191),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (193), (197), (199), (201), (207), (208), (209),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (211), (212), (217), (221), (222), (223), (224),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (225), (226), (227), (228), (229), (230), (231),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (232), (233), (234), (235), (236), (237), (245),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (247), (257), (259), (267), (374), (5515), (5517),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5518), (5519), (5526), (5527), (5717), (5720),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5723), (5728), (5740), (5742), (5745), (6378),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6381), (6389), (6390), (6396), (6406),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #634.
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6407)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6407) gives:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6408)  all_57_14 = e2 & op(e0, e1) = e2
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6408) implies:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6409)  all_57_14 = e2
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6410)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6410) gives:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6411)  all_57_12 = e1 & op(e0, e3) = e1
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6411) implies:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6412)  op(e0, e3) = e1
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6413)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e1)
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6413) gives:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6414)  all_57_4 = e1 & op(e3, e1) = e1
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6414) implies:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6415)  all_57_4 = e1
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (231), (5742), (6381), (6396),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6415), (function-axioms) are inconsistent by
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1675.
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6416)  all_57_5 = e1 & op(e2, e1) = e1
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (208),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (209), (212), (221), (225), (226), (228), (229),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (231), (232), (233), (234), (235), (374),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5526), (5723), (5745), (6378), (6381), (6405),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6416), (function-axioms) are inconsistent by
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #620.
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6417)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e1)
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6417) gives:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6418)  all_57_8 = e1 & op(e1, e1) = e1
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6418) implies:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6419)  op(e1, e1) = e1
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (169), (207),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (208), (209), (211), (212), (216), (217), (226),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (227), (228), (229), (231), (233), (237), (374),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5511), (5518), (5526), (5527), (5723), (5742),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5748), (6375), (6412), (6419), (function-axioms)
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #711.
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6420)  all_57_14 = e1 & op(e0, e1) = e1
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (118),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (126), (140), (141), (145), (146), (147),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (149), (150), (159), (164), (165), (169), (191),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (193), (197), (199), (201), (207), (208), (209),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (211), (212), (217), (221), (222), (223), (224),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (225), (226), (227), (228), (229), (230), (231),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (232), (233), (234), (235), (236), (237), (245),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (247), (257), (259), (267), (374), (5515), (5517),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5518), (5519), (5526), (5527), (5717), (5720),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5723), (5728), (5740), (5742), (5745), (6378),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6381), (6389), (6390), (6396), (6420),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #632.
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6421)  all_57_13 = e1 & op(e0, e2) = e1
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6421) implies:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6422)  all_57_13 = e1
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (169), (207),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (208), (209), (211), (212), (217), (223), (224),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (225), (226), (227), (228), (229), (230), (231),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (232), (233), (236), (237), (374), (5518), (5526),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5527), (5723), (5728), (5742), (5745), (6381),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6409), (6422), (function-axioms) are inconsistent
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #769.
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6423)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6423) gives:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6424)  all_57_14 = e1 & op(e0, e1) = e1
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (118),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (126), (140), (141), (145), (146), (147),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (149), (150), (159), (164), (165), (169), (191),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (193), (197), (199), (201), (207), (208), (209),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (211), (212), (217), (221), (222), (223), (224),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (225), (226), (227), (228), (229), (230), (231),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (232), (233), (234), (235), (236), (237), (245),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (247), (257), (259), (267), (374), (5515), (5517),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5518), (5519), (5526), (5527), (5717), (5720),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5723), (5728), (5740), (5742), (5745), (6378),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6381), (6389), (6390), (6396), (6424),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #632.
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6425)  all_57_15 = e1 & op(e0, e0) = e1
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6425) implies:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6426)  op(e0, e0) = e1
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5527), (6426), (function-axioms) are
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2183.
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6427)  all_57_15 = e2 & op(e0, e0) = e2
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (169), (231), (233),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (237), (5518), (5526), (5742), (6381), (6427),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #633.
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6428)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e1) = e3)
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (208),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (209), (374), (5526), (6428), (function-axioms)
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1794.
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6429)  all_57_10 = e1 & op(e2, e0) = e1
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6389), (6429) are inconsistent by sub-proof
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2360.
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6430)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5527), (5728), (6364), (6393), (6430),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #618.
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6431)  all_57_3 = e0 & op(e2, e2) = e0
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6431) implies:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6432)  op(e2, e2) = e0
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5723), (6432), (function-axioms) are
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2352.
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6433)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0)
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (118),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (126), (140), (141), (145), (146), (147),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (149), (150), (159), (164), (165), (191), (193),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (197), (199), (201), (207), (208), (209), (211),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (217), (221), (228), (231), (233), (245),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (247), (257), (259), (267), (374), (5515), (5517),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5519), (5526), (5527), (5717), (5720), (5723),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5740), (5742), (6364), (6378), (6385), (6390),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6433), (function-axioms) are inconsistent by
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #616.
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6434)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6434) gives:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6435)  all_57_11 = e2 & op(e1, e0) = e2
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6364), (6435) are inconsistent by sub-proof
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1988.
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6436)  all_57_15 = e2 & op(e0, e0) = e2
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (169), (231), (233),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (237), (5518), (5526), (5742), (6381), (6436),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #707.
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6437)  all_57_9 = e0 & op(e3, e0) = e0
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6437) implies:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6438)  all_57_9 = e0
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (211), (212), (5526),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6364), (6438) are inconsistent by sub-proof
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1144.
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6439)  all_57_3 = e3 & op(e2, e2) = e3
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6439) implies:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6440)  op(e2, e2) = e3
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5723), (6440), (function-axioms) are
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1912.
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6441)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6441) gives:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6442)  all_57_7 = e3 & op(e1, e2) = e3
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6442) implies:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6443)  all_57_7 = e3
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6375), (6443) imply:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6444)  e3 = e1
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6444) implies:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6445)  e3 = e1
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6378), (6445) imply:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6446)  all_57_6 = e1
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (118),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (126), (140), (141), (145), (146), (147),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (149), (150), (159), (164), (165), (169), (191),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (193), (197), (199), (201), (207), (208), (209),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (211), (212), (217), (219), (221), (222), (223),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (225), (226), (227), (228), (229), (230),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (232), (233), (235), (236), (237), (245),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (247), (257), (259), (267), (374), (5515), (5517),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5518), (5519), (5526), (5527), (5717), (5720),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5723), (5728), (5740), (5742), (5745), (5858),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6364), (6443), (6446), (function-axioms) are
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #599.
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6447)  all_57_13 = e3 & op(e0, e2) = e3
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6447) implies:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6448)  all_57_13 = e3
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (207), (208), (209),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5526), (5527), (6448), (function-axioms) are
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1792.
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6449)  all_57_7 = e3 & op(e1, e2) = e3
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6449) implies:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6450)  all_57_7 = e3
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (6375), (6450) are inconsistent by sub-proof
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | |            #2115.
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | |   (6451)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (374), (5526), (6451), (function-axioms)
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1786.
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | |   (6452)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5858), (6364), (6452), (function-axioms) are
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #910.
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | |   (6453)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | |           all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | |           op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | |             all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | |           & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | |           & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | |           & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | |           $i(all_52_31)
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | ALPHA: (6453) implies:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | |   (6454)  op(e0, e0) = all_52_31
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | |   (6455)  op(e0, e2) = all_52_27
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | |   (6456)  op(all_52_31, all_52_31) = e0
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | |   (6457)  op(all_52_27, all_52_27) = e2
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | |   (6458)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e0)
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6458) gives:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | |   (6459)  all_57_6 = e0 & op(e1, e3) = e0
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6459) implies:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | |   (6460)  all_57_6 = e0
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | |   (6461)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e3)
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6461) gives:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | |   (6462)  all_57_0 = e3 & op(e3, e3) = e3
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6462) implies:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | |   (6463)  op(e3, e3) = e3
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5742), (6463), (function-axioms) are
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2490.
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | |   (6464)  all_57_2 = e3 & op(e2, e3) = e3
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6464) implies:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | |   (6465)  all_57_2 = e3
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.66  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | |   (6466)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6466) gives:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6467)  all_57_6 = e3 & op(e1, e3) = e3
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6467) implies:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6468)  all_57_6 = e3
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (230), (232), (234),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | |            (5745), (6465), (6468), (function-axioms) are
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1286.
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6469)  all_57_7 = e3 & op(e1, e2) = e3
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6469) implies:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6470)  all_57_7 = e3
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6471)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (6460), (6470), (6471) are inconsistent
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #654.
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6472)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6472) gives:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6473)  all_57_8 = e1 & op(e1, e1) = e1
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6473) implies:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6474)  op(e1, e1) = e1
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (118),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (126), (140), (141), (145), (146), (147),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (149), (150), (159), (164), (165), (169), (191),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (193), (197), (199), (201), (207), (208), (209),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (211), (212), (214), (215), (216), (217), (218),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (220), (221), (222), (223), (224), (225), (226),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (227), (228), (229), (230), (231), (232), (233),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (234), (235), (236), (237), (245), (247), (257),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (259), (267), (374), (5511), (5515), (5517),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5518), (5519), (5526), (5527), (5717), (5720),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5723), (5728), (5740), (5742), (5745), (5748),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6454), (6456), (6474), (function-axioms) are
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #670.
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6475)  all_57_11 = e1 & op(e1, e0) = e1
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6475) implies:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6476)  all_57_11 = e1
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6477)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6477) gives:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6478)  all_57_9 = e2 & op(e3, e0) = e2
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6478) implies:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6479)  all_57_9 = e2
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (169), (207),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (208), (209), (221), (223), (224), (226), (228),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (233), (237), (374), (5518), (5526),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5527), (5723), (5728), (5742), (6470), (6476),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6479), (function-axioms) are inconsistent by
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #653.
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6480)  all_57_10 = e2 & op(e2, e0) = e2
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6480) implies:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6481)  all_57_10 = e2
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6482)  op(e2, e0) = e2
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (118),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (126), (140), (141), (145), (146), (147),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (149), (150), (159), (164), (165), (169), (191),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (193), (197), (199), (201), (207), (208), (209),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (211), (212), (214), (215), (216), (217), (218),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (219), (220), (221), (222), (223), (224), (225),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (226), (227), (228), (229), (230), (231), (232),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (234), (235), (236), (237), (245), (247),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (257), (259), (267), (374), (5511), (5515),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5517), (5518), (5519), (5526), (5527), (5717),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5720), (5723), (5728), (5740), (5742), (5745),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5748), (6454), (6456), (6460), (6465), (6470),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6481), (6482), (function-axioms) are inconsistent
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #596.
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6483)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (217), (223), (224), (225), (230), (232),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (374), (5511), (5526), (5527), (5723), (5728),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5742), (5748), (6460), (6465), (6470), (6483),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #646.
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | |   (6484)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (374), (5526), (6484), (function-axioms)
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1786.
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | |   (6485)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e3) = e3)
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6485) gives:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | |   (6486)  all_57_6 = e3 & op(e1, e3) = e3
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6486) implies:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | |   (6487)  all_57_6 = e3
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (6460), (6487) are inconsistent by sub-proof
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | |            #1822.
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | |   (6488)  all_57_12 = e3 & op(e0, e3) = e3
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6488) implies:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | |   (6489)  all_57_12 = e3
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | |   (6490)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6490) gives:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6491)  all_57_6 = e3 & op(e1, e3) = e3
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6491) implies:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6492)  all_57_6 = e3
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (6460), (6492) are inconsistent by sub-proof
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | |            #1822.
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6493)  all_57_7 = e3 & op(e1, e2) = e3
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6493) implies:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6494)  all_57_7 = e3
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6495)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (5728), (5742), (6460), (6489), (6494),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6495), (function-axioms) are inconsistent by
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #645.
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6496)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6496) gives:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6497)  all_57_8 = e1 & op(e1, e1) = e1
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6497) implies:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6498)  op(e1, e1) = e1
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (118),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (126), (140), (141), (145), (146), (147),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (149), (150), (159), (164), (165), (169), (191),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (193), (197), (199), (201), (207), (208), (209),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (211), (212), (214), (215), (216), (217), (218),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (220), (221), (222), (223), (224), (225), (226),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (227), (228), (229), (230), (231), (232), (233),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (234), (235), (236), (237), (245), (247), (257),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (259), (267), (374), (5511), (5515), (5517),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5518), (5519), (5526), (5527), (5717), (5720),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5723), (5728), (5740), (5742), (5745), (5748),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6454), (6456), (6498), (function-axioms) are
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #670.
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6499)  all_57_11 = e1 & op(e1, e0) = e1
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6499) implies:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6500)  all_57_11 = e1
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6501)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6501) gives:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6502)  all_57_9 = e2 & op(e3, e0) = e2
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6502) implies:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6503)  all_57_9 = e2
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (169), (207),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (208), (209), (221), (223), (224), (226), (228),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (233), (237), (374), (5518), (5526),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5527), (5723), (5728), (5742), (6494), (6500),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6503), (function-axioms) are inconsistent by
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #653.
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6504)  all_57_10 = e2 & op(e2, e0) = e2
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6504) implies:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6505)  all_57_10 = e2
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6506)  op(e2, e0) = e2
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6507)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e0)
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (118),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (126), (140), (141), (145), (146), (147),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (149), (150), (159), (164), (165), (169), (191),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (193), (197), (199), (201), (207), (208), (209),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (211), (212), (217), (221), (226), (227), (228),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (233), (237), (245), (247), (257), (259),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (267), (374), (5515), (5517), (5518), (5519),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5526), (5527), (5717), (5720), (5723), (5740),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5742), (6460), (6494), (6506), (6507),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #644.
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6508)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6508) gives:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6509)  all_57_8 = e0 & op(e1, e1) = e0
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6509) implies:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6510)  all_57_8 = e0
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6511)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6511) gives:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6512)  all_57_2 = e3 & op(e2, e3) = e3
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6512) implies:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6513)  all_57_2 = e3
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (118),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (126), (140), (141), (145), (146), (147),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (149), (150), (159), (164), (165), (169), (191),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (193), (197), (199), (201), (207), (208), (209),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (211), (212), (214), (215), (216), (217), (218),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (219), (220), (221), (222), (223), (224), (225),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (226), (227), (228), (229), (230), (231), (232),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (234), (235), (236), (237), (245), (247),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (257), (259), (267), (374), (5511), (5515),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5517), (5518), (5519), (5526), (5527), (5717),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5720), (5723), (5728), (5740), (5742), (5745),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5748), (6454), (6456), (6460), (6494), (6505),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6506), (6513), (function-axioms) are inconsistent
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #596.
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6514)  all_57_3 = e3 & op(e2, e2) = e3
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6514) implies:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6515)  op(e2, e2) = e3
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5723), (6515), (function-axioms) are
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1912.
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6516)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (118),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (126), (140), (141), (145), (146), (147),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (149), (150), (159), (164), (165), (169), (191),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (193), (197), (199), (201), (207), (208), (209),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (211), (212), (216), (217), (221), (222), (223),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (225), (226), (227), (228), (229), (230),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (232), (233), (234), (236), (237), (245),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (247), (257), (259), (267), (374), (5511), (5515),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5517), (5518), (5519), (5526), (5527), (5717),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5720), (5723), (5728), (5740), (5742), (5745),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5748), (6489), (6494), (6505), (6506), (6510),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6516), (function-axioms) are inconsistent by
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #641.
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6517)  all_57_14 = e0 & op(e0, e1) = e0
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6517) implies:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6518)  all_57_14 = e0
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (208), (209), (5526),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6489), (6518) are inconsistent by sub-proof
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1763.
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6519)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6519) gives:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6520)  all_57_11 = e2 & op(e1, e0) = e2
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6500), (6520) are inconsistent by sub-proof
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2048.
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6521)  all_57_15 = e2 & op(e0, e0) = e2
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (217), (374), (5526), (6460), (6494),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6521), (function-axioms) are inconsistent by
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1034.
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | |   (6522)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (374), (5526), (6522), (function-axioms)
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1786.
% 222.17/37.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | |   (6523)  all_57_7 = e0 & op(e1, e2) = e0
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6523) implies:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | |   (6524)  all_57_7 = e0
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (118),
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | |            (119), (126), (140), (141), (145), (146), (147),
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | |            (149), (150), (159), (164), (165), (169), (191),
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | |            (193), (197), (199), (201), (207), (208), (209),
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | |            (211), (212), (214), (215), (216), (217), (218),
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | |            (219), (220), (221), (222), (223), (224), (225),
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | |            (226), (227), (228), (229), (230), (231), (232),
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | |            (233), (234), (235), (236), (237), (245), (247),
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | |            (257), (259), (267), (374), (5511), (5515),
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | |            (5517), (5518), (5519), (5526), (5527), (5717),
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | |            (5720), (5723), (5728), (5740), (5742), (5745),
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | |            (5748), (6454), (6456), (6524), (function-axioms)
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #597.
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | |   (6525)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6525) gives:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3,
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | |              all_52_31, e0, e0, simplifying with (5527), (6454)
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | |              gives:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | |   (6526)  all_52_31 = e3
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6456), (6526) imply:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | |   (6527)  op(e3, e3) = e0
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5742), (6527), (function-axioms) are
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2403.
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | |   (6528)  all_57_11 = e0 & op(e1, e0) = e0
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6528) implies:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | |   (6529)  all_57_11 = e0
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | |   (6530)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6530) gives:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | |   (6531)  all_57_6 = e1 & op(e1, e3) = e1
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6531) implies:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | |   (6532)  all_57_6 = e1
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | |   (6533)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6533) gives:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6534)  all_57_6 = e3 & op(e1, e3) = e3
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6534) implies:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6535)  all_57_6 = e3
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (6532), (6535) are inconsistent by sub-proof
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | |            #2017.
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6536)  all_57_7 = e3 & op(e1, e2) = e3
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6536) implies:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6537)  all_57_7 = e3
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (118),
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (126), (140), (141), (145), (146), (147),
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | |            (149), (150), (159), (164), (165), (169), (191),
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | |            (193), (197), (199), (201), (207), (208), (209),
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | |            (211), (212), (214), (215), (216), (217), (218),
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | |            (219), (220), (221), (222), (223), (224), (225),
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | |            (226), (227), (228), (229), (230), (231), (232),
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (234), (235), (236), (237), (245), (247),
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | |            (257), (259), (267), (374), (5511), (5515),
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | |            (5517), (5518), (5519), (5526), (5527), (5717),
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | |            (5720), (5723), (5728), (5740), (5742), (5745),
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | |            (5748), (6454), (6456), (6529), (6532), (6537),
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | |            #595.
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | |   (6538)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (374), (5526), (6538), (function-axioms)
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1786.
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | |   (6539)  all_57_7 = e1 & op(e1, e2) = e1
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6539) implies:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | |   (6540)  all_57_7 = e1
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | |   (6541)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6541) gives:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6542)  all_57_6 = e3 & op(e1, e3) = e3
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6542) implies:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6543)  all_57_6 = e3
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6544)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6544) gives:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6545)  all_57_1 = e3 & op(e3, e2) = e3
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6545) implies:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6546)  all_57_1 = e3
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6547)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (217), (226), (227), (228), (374), (5526),
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5723), (5742), (6543), (6546), (6547),
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #625.
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6548)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6548) gives:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6549)  all_57_4 = e0 & op(e3, e1) = e0
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6549) implies:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6550)  all_57_4 = e0
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6551)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6551) gives:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6552)  all_57_9 = e2 & op(e3, e0) = e2
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (169), (207),
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (208), (209), (211), (212), (217), (221), (222),
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (223), (224), (226), (227), (228), (229), (230),
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (232), (233), (235), (236), (237), (374),
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5518), (5526), (5527), (5723), (5728), (5742),
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6529), (6550), (6552), (function-axioms) are
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #624.
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6553)  all_57_10 = e2 & op(e2, e0) = e2
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6553) implies:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6554)  op(e2, e0) = e2
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6555)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6555) gives:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6556)  all_57_2 = e0 & op(e2, e3) = e0
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6556) implies:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6557)  all_57_2 = e0
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6558)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e3)
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6558) gives:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6559)  all_57_4 = e3 & op(e3, e1) = e3
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (118),
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (126), (140), (141), (145), (146), (147),
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (149), (150), (159), (164), (165), (191), (193),
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (197), (199), (201), (207), (211), (212), (217),
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (228), (231), (233), (245), (247), (257), (259),
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (267), (374), (5515), (5517), (5519), (5526),
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5527), (5717), (5720), (5723), (5740), (5742),
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6543), (6550), (6554), (6559), (function-axioms)
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #623.
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6560)  all_57_5 = e3 & op(e2, e1) = e3
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6560) implies:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6561)  all_57_5 = e3
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6562)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (118),
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (126), (140), (141), (145), (146), (147),
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (149), (150), (159), (164), (165), (191), (193),
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (197), (199), (201), (207), (208), (209), (211),
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (217), (221), (223), (224), (228), (231),
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (245), (247), (257), (259), (267), (374),
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5515), (5517), (5519), (5526), (5527), (5717),
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5720), (5723), (5740), (5742), (6543), (6546),
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6550), (6554), (6557), (6561), (6562),
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #598.
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6563)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0)
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6563) gives:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6564)  all_57_7 = e0 & op(e1, e2) = e0
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (223), (224), (5728),
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6540), (6557), (6561), (6564) are inconsistent by
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #622.
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6565)  all_57_13 = e0 & op(e0, e2) = e0
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6565) implies:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6566)  op(e0, e2) = e0
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5527), (6454), (6455), (6457), (6566),
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #858.
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6567)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e1) = e3)
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (208),
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (209), (374), (5526), (6567), (function-axioms)
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1794.
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6568)  all_57_3 = e0 & op(e2, e2) = e0
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6568) implies:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6569)  op(e2, e2) = e0
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5723), (6569), (function-axioms) are
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2352.
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6570)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0)
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (118),
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (126), (140), (141), (145), (146), (147),
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (149), (150), (159), (164), (165), (191), (193),
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (197), (199), (201), (207), (208), (209), (211),
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (217), (221), (228), (231), (233), (245),
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (247), (257), (259), (267), (374), (5515), (5517),
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5519), (5526), (5527), (5717), (5720), (5723),
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5740), (5742), (6529), (6543), (6550), (6554),
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6570), (function-axioms) are inconsistent by
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #616.
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6571)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6571) gives:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6572)  all_57_11 = e2 & op(e1, e0) = e2
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6529), (6572) are inconsistent by sub-proof
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1988.
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6573)  all_57_15 = e2 & op(e0, e0) = e2
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (169), (231), (233),
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (237), (5518), (5526), (5742), (6546), (6573),
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #707.
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6574)  all_57_9 = e0 & op(e3, e0) = e0
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6574) implies:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6575)  all_57_9 = e0
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (211), (212), (5526),
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6529), (6575) are inconsistent by sub-proof
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1144.
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6576)  all_57_3 = e3 & op(e2, e2) = e3
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6576) implies:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6577)  op(e2, e2) = e3
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5723), (6577), (function-axioms) are
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1912.
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6578)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6578) gives:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6579)  all_57_7 = e3 & op(e1, e2) = e3
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6579) implies:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6580)  all_57_7 = e3
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6540), (6580) imply:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6581)  e3 = e1
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6581) implies:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6582)  e3 = e1
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6543), (6582) imply:
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6583)  all_57_6 = e1
% 222.17/37.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (118),
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (126), (140), (141), (145), (146), (147),
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (149), (150), (159), (164), (165), (169), (191),
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (193), (197), (199), (201), (207), (208), (209),
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (211), (212), (214), (215), (216), (217), (218),
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (219), (220), (221), (222), (223), (224), (225),
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (226), (227), (228), (229), (230), (231), (232),
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (234), (235), (236), (237), (245), (247),
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (257), (259), (267), (374), (5511), (5515),
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5517), (5518), (5519), (5526), (5527), (5717),
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5720), (5723), (5728), (5740), (5742), (5745),
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5748), (6454), (6456), (6529), (6580), (6583),
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #595.
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6584)  all_57_13 = e3 & op(e0, e2) = e3
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6584) implies:
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6585)  all_57_13 = e3
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (207), (208), (209),
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5526), (5527), (6585), (function-axioms) are
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1792.
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6586)  all_57_7 = e3 & op(e1, e2) = e3
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6586) implies:
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6587)  all_57_7 = e3
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (6540), (6587) are inconsistent by sub-proof
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | | | |            #2115.
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | | |   (6588)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (374), (5526), (6588), (function-axioms)
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1786.
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | |   (6589)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6589) gives:
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | |   (6590)  all_57_8 = e1 & op(e1, e1) = e1
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6590) implies:
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | |   (6591)  op(e1, e1) = e1
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (118),
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | |            (119), (126), (140), (141), (145), (146), (147),
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | |            (149), (150), (159), (164), (165), (169), (191),
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | |            (193), (197), (199), (201), (207), (208), (209),
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | |            (211), (212), (214), (215), (216), (217), (218),
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | |            (220), (221), (222), (223), (224), (225), (226),
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | |            (227), (228), (229), (230), (231), (232), (233),
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | |            (234), (235), (236), (237), (245), (247), (257),
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | |            (259), (267), (374), (5511), (5515), (5517),
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | |            (5518), (5519), (5526), (5527), (5717), (5720),
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | |            (5723), (5728), (5740), (5742), (5745), (5748),
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | |            (6454), (6456), (6591), (function-axioms) are
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #670.
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | |   (6592)  all_57_11 = e1 & op(e1, e0) = e1
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6592) implies:
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | |   (6593)  all_57_11 = e1
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6529), (6593) are inconsistent by sub-proof
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | |            #1862.
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.71  | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | End of split
% 222.17/37.71  | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | End of split
% 222.17/37.71  | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | Case 2:
% 222.17/37.71  | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | |   (6594)  all_57_1 = e2 & op(e3, e2) = e2
% 222.17/37.71  | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | ALPHA: (6594) implies:
% 222.17/37.71  | | | | | | | | | | | | | | | |   (6595)  all_57_1 = e2
% 222.17/37.71  | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (169), (231), (233),
% 222.17/37.71  | | | | | | | | | | | | | | | |            (237), (5518), (5742), (6595), (function-axioms)
% 222.17/37.71  | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1650.
% 222.17/37.71  | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | End of split
% 222.17/37.71  | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | Case 2:
% 222.17/37.71  | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | |   (6596)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 222.17/37.71  | | | | | | | | | | | | | | |             & op(e3, e0) = e2)
% 222.17/37.71  | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | BETA: splitting (6596) gives:
% 222.17/37.71  | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | Case 1:
% 222.17/37.71  | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | |   (6597)  all_57_4 = e2 & op(e3, e1) = e2
% 222.17/37.71  | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | ALPHA: (6597) implies:
% 222.17/37.71  | | | | | | | | | | | | | | | |   (6598)  all_57_4 = e2
% 222.17/37.71  | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 222.17/37.71  | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.71  | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | |   (6599)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 222.17/37.71  | | | | | | | | | | | | | | | | |             & op(e3, e2) = e1)
% 222.17/37.71  | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (226), (228), (229),
% 222.17/37.71  | | | | | | | | | | | | | | | | |            (5723), (5742), (6599), (function-axioms) are
% 222.17/37.71  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1677.
% 222.17/37.71  | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.71  | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | |   (6600)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 222.17/37.71  | | | | | | | | | | | | | | | | |             & op(e3, e0) = e1)
% 222.17/37.71  | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (169), (231), (237),
% 222.17/37.71  | | | | | | | | | | | | | | | | |            (5518), (5742), (6598), (6600), (function-axioms)
% 222.17/37.71  | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #594.
% 222.17/37.71  | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | End of split
% 222.17/37.71  | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | Case 2:
% 222.17/37.71  | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | |   (6601)  all_57_9 = e2 & op(e3, e0) = e2
% 222.17/37.71  | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | ALPHA: (6601) implies:
% 222.17/37.71  | | | | | | | | | | | | | | | |   (6602)  all_57_9 = e2
% 222.17/37.71  | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 222.17/37.71  | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.71  | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | |   (6603)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 222.17/37.71  | | | | | | | | | | | | | | | | |             & op(e3, e2) = e1)
% 222.17/37.71  | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (226), (228), (229),
% 222.17/37.71  | | | | | | | | | | | | | | | | |            (5723), (5742), (6603), (function-axioms) are
% 222.17/37.71  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1677.
% 222.17/37.71  | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.71  | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | |   (6604)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 222.17/37.71  | | | | | | | | | | | | | | | | |             & op(e3, e0) = e1)
% 222.17/37.71  | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | BETA: splitting (6604) gives:
% 222.17/37.71  | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.71  | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | |   (6605)  all_57_4 = e1 & op(e3, e1) = e1
% 222.17/37.71  | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | | ALPHA: (6605) implies:
% 222.17/37.71  | | | | | | | | | | | | | | | | | |   (6606)  all_57_4 = e1
% 222.17/37.71  | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 222.17/37.71  | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | | |   (6607)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 222.17/37.71  | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e3)
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | BETA: splitting (6607) gives:
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | |   (6608)  all_57_0 = e3 & op(e3, e3) = e3
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | ALPHA: (6608) implies:
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | |   (6609)  op(e3, e3) = e3
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5742), (6609), (function-axioms) are
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2490.
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | |   (6610)  all_57_1 = e3 & op(e3, e2) = e3
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | ALPHA: (6610) implies:
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | |   (6611)  all_57_1 = e3
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (231), (5742), (6602), (6606),
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | |            (6611), (function-axioms) are inconsistent by
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | |            sub-proof #842.
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | | |   (6612)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 222.17/37.71  | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e3)
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (169), (5518), (6606), (6612),
% 222.17/37.71  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.17/37.71  | | | | | | | | | | | | | | | | | | |            #2281.
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.71  | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.71  | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | |   (6613)  all_57_9 = e1 & op(e3, e0) = e1
% 222.17/37.71  | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6602), (6613) are inconsistent by sub-proof
% 222.17/37.71  | | | | | | | | | | | | | | | | | |            #2451.
% 222.17/37.71  | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | End of split
% 222.17/37.71  | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | End of split
% 222.17/37.71  | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | End of split
% 222.17/37.71  | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | End of split
% 222.17/37.71  | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | End of split
% 222.17/37.71  | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | Case 2:
% 222.17/37.71  | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | |   (6614)  all_18_2 = e0
% 222.17/37.71  | | | | | | | | | | | | |   (6615)  ( ~ (all_18_0 = e1) & op(all_18_1, e3) = all_18_0
% 222.17/37.71  | | | | | | | | | | | | |             & op(e3, e0) = all_18_1 & $i(all_18_0) &
% 222.17/37.71  | | | | | | | | | | | | |             $i(all_18_1)) | ( ~ (all_18_1 = e2) & op(e3, e0)
% 222.17/37.71  | | | | | | | | | | | | |             = all_18_1 & $i(all_18_1))
% 222.17/37.71  | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | COMBINE_EQS: (327), (6614) imply:
% 222.17/37.71  | | | | | | | | | | | | |   (6616)  all_10_2 = e0
% 222.17/37.71  | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | SIMP: (6616) implies:
% 222.17/37.71  | | | | | | | | | | | | |   (6617)  all_10_2 = e0
% 222.17/37.71  | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | COMBINE_EQS: (279), (6617) imply:
% 222.17/37.71  | | | | | | | | | | | | |   (6618)  all_48_2 = e0
% 222.17/37.71  | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | REDUCE: (338), (6617) imply:
% 222.17/37.71  | | | | | | | | | | | | |   (6619)   ~ (all_53_1 = e0)
% 222.17/37.71  | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | REDUCE: (340), (6617) imply:
% 222.17/37.71  | | | | | | | | | | | | |   (6620)   ~ (all_53_2 = e0)
% 222.17/37.71  | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | REDUCE: (342), (6617) imply:
% 222.17/37.71  | | | | | | | | | | | | |   (6621)   ~ (all_53_3 = e0)
% 222.17/37.71  | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | REDUCE: (344), (6617) imply:
% 222.17/37.71  | | | | | | | | | | | | |   (6622)   ~ (all_53_4 = e0)
% 222.17/37.71  | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | REDUCE: (346), (6617) imply:
% 222.17/37.71  | | | | | | | | | | | | |   (6623)   ~ (all_53_8 = e0)
% 222.17/37.71  | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | REDUCE: (348), (6617) imply:
% 222.17/37.71  | | | | | | | | | | | | |   (6624)   ~ (all_53_12 = e0)
% 222.17/37.71  | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | REDUCE: (376), (6617) imply:
% 222.17/37.71  | | | | | | | | | | | | |   (6625)   ~ (e1 = e0)
% 222.17/37.71  | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | REDUCE: (45), (6617) imply:
% 222.17/37.71  | | | | | | | | | | | | |   (6626)  op(e3, e3) = e0
% 222.17/37.71  | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | BETA: splitting (230) gives:
% 222.17/37.71  | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | Case 1:
% 222.17/37.71  | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | |   (6627)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 222.17/37.71  | | | | | | | | | | | | | |             & op(e2, e3) = e0)
% 222.17/37.71  | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | BETA: splitting (6627) gives:
% 222.17/37.71  | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | Case 1:
% 222.17/37.71  | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | |   (6628)  all_57_0 = e0 & op(e3, e3) = e0
% 222.17/37.71  | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | ALPHA: (6628) implies:
% 222.17/37.71  | | | | | | | | | | | | | | |   (6629)  all_57_0 = e0
% 222.17/37.71  | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | BETA: splitting (64) gives:
% 222.17/37.71  | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | Case 1:
% 222.17/37.71  | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | |   (6630)   ~ (all_22_2 = e3)
% 222.17/37.71  | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | REDUCE: (5514), (6630) imply:
% 222.17/37.71  | | | | | | | | | | | | | | | |   (6631)  $false
% 222.17/37.71  | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | CLOSE: (6631) is inconsistent.
% 222.17/37.71  | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | Case 2:
% 222.17/37.71  | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | |   (6632)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0
% 222.17/37.71  | | | | | | | | | | | | | | | |             & op(e0, e3) = all_22_1 & $i(all_22_0) &
% 222.17/37.71  | | | | | | | | | | | | | | | |             $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0, e3)
% 222.17/37.71  | | | | | | | | | | | | | | | |             = all_22_1 & $i(all_22_1))
% 222.17/37.71  | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 222.17/37.71  | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.71  | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | |   (6633)   ~ (all_24_2 = e0)
% 222.17/37.71  | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | REDUCE: (315), (6633) imply:
% 222.17/37.71  | | | | | | | | | | | | | | | | |   (6634)   ~ (all_6_2 = e0)
% 222.17/37.71  | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | BETA: splitting (88) gives:
% 222.17/37.71  | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.71  | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | |   (6635)   ~ (all_38_2 = e2)
% 222.17/37.71  | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | | REDUCE: (249), (6635) imply:
% 222.17/37.71  | | | | | | | | | | | | | | | | | |   (6636)   ~ (all_6_2 = e2)
% 222.17/37.71  | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 222.17/37.71  | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | | |   (6637)  all_55_10 = e3
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (374), (6637) are inconsistent by sub-proof
% 222.17/37.71  | | | | | | | | | | | | | | | | | | |            #2500.
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | | |   (6638)   ~ (all_55_10 = e3)
% 222.17/37.71  | | | | | | | | | | | | | | | | | | |   (6639)  all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | BETA: splitting (6639) gives:
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | |   (6640)  all_55_10 = e2
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (6636), (6640) are inconsistent by
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | |            sub-proof #2499.
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | |   (6641)   ~ (all_55_10 = e2)
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | |   (6642)  all_55_10 = e1 | all_55_10 = e0
% 222.17/37.71  | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.72  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (9), (39), (103), (107), (145), (160),
% 222.17/37.72  | | | | | | | | | | | | | | | | | | | |            (164), (169), (197), (207), (208), (209), (211),
% 222.17/37.72  | | | | | | | | | | | | | | | | | | | |            (212), (214), (215), (216), (217), (218), (219),
% 222.17/37.72  | | | | | | | | | | | | | | | | | | | |            (220), (221), (222), (223), (224), (225), (226),
% 222.17/37.72  | | | | | | | | | | | | | | | | | | | |            (227), (228), (229), (230), (231), (232), (233),
% 222.17/37.72  | | | | | | | | | | | | | | | | | | | |            (234), (235), (236), (237), (257), (336), (374),
% 222.17/37.72  | | | | | | | | | | | | | | | | | | | |            (5511), (5518), (5526), (5527), (5723), (5728),
% 222.17/37.72  | | | | | | | | | | | | | | | | | | | |            (6615), (6618), (6620), (6621), (6624), (6626),
% 222.17/37.72  | | | | | | | | | | | | | | | | | | | |            (6629), (6632), (6634), (6636), (6642),
% 222.17/37.72  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.17/37.72  | | | | | | | | | | | | | | | | | | | |            #963.
% 222.17/37.72  | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.72  | | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.72  | | | | | | | | | | | | | | | | | | | 
% 222.17/37.72  | | | | | | | | | | | | | | | | | | End of split
% 222.17/37.72  | | | | | | | | | | | | | | | | | | 
% 222.17/37.72  | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.72  | | | | | | | | | | | | | | | | | | 
% 222.17/37.72  | | | | | | | | | | | | | | | | | |   (6643)  all_38_2 = e2
% 222.17/37.72  | | | | | | | | | | | | | | | | | | 
% 222.17/37.72  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (6643) imply:
% 222.17/37.72  | | | | | | | | | | | | | | | | | |   (6644)  all_6_2 = e2
% 222.17/37.72  | | | | | | | | | | | | | | | | | | 
% 222.17/37.72  | | | | | | | | | | | | | | | | | | REDUCE: (350), (6644) imply:
% 222.17/37.72  | | | | | | | | | | | | | | | | | |   (6645)   ~ (all_53_2 = e2)
% 222.17/37.72  | | | | | | | | | | | | | | | | | | 
% 222.17/37.72  | | | | | | | | | | | | | | | | | | REDUCE: (361), (6644) imply:
% 222.17/37.72  | | | | | | | | | | | | | | | | | |   (6646)   ~ (all_53_6 = e2)
% 222.17/37.72  | | | | | | | | | | | | | | | | | | 
% 222.17/37.72  | | | | | | | | | | | | | | | | | | REDUCE: (363), (6644) imply:
% 222.17/37.72  | | | | | | | | | | | | | | | | | |   (6647)   ~ (all_53_8 = e2)
% 222.17/37.72  | | | | | | | | | | | | | | | | | | 
% 222.17/37.72  | | | | | | | | | | | | | | | | | | REDUCE: (364), (6644) imply:
% 222.17/37.72  | | | | | | | | | | | | | | | | | |   (6648)   ~ (all_53_9 = e2)
% 222.17/37.72  | | | | | | | | | | | | | | | | | | 
% 222.17/37.72  | | | | | | | | | | | | | | | | | | REDUCE: (366), (6644) imply:
% 222.17/37.72  | | | | | | | | | | | | | | | | | |   (6649)   ~ (all_53_11 = e2)
% 222.17/37.72  | | | | | | | | | | | | | | | | | | 
% 222.17/37.72  | | | | | | | | | | | | | | | | | | REDUCE: (368), (6644) imply:
% 222.17/37.72  | | | | | | | | | | | | | | | | | |   (6650)   ~ (all_53_14 = e2)
% 222.17/37.72  | | | | | | | | | | | | | | | | | | 
% 222.17/37.72  | | | | | | | | | | | | | | | | | | REDUCE: (374), (6644) imply:
% 222.17/37.72  | | | | | | | | | | | | | | | | | |   (6651)   ~ (e3 = e2)
% 222.17/37.72  | | | | | | | | | | | | | | | | | | 
% 222.17/37.72  | | | | | | | | | | | | | | | | | | REDUCE: (39), (6644) imply:
% 222.17/37.72  | | | | | | | | | | | | | | | | | |   (6652)  op(e1, e1) = e2
% 222.17/37.72  | | | | | | | | | | | | | | | | | | 
% 222.17/37.72  | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 222.17/37.72  | | | | | | | | | | | | | | | | | | 
% 222.17/37.72  | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.72  | | | | | | | | | | | | | | | | | | | 
% 222.17/37.72  | | | | | | | | | | | | | | | | | | |   (6653)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 222.17/37.72  | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e2)
% 222.17/37.72  | | | | | | | | | | | | | | | | | | | 
% 222.17/37.72  | | | | | | | | | | | | | | | | | | | BETA: splitting (6653) gives:
% 222.17/37.72  | | | | | | | | | | | | | | | | | | | 
% 222.17/37.72  | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.72  | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.72  | | | | | | | | | | | | | | | | | | | |   (6654)  all_57_6 = e2 & op(e1, e3) = e2
% 222.17/37.72  | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.72  | | | | | | | | | | | | | | | | | | | | ALPHA: (6654) implies:
% 222.17/37.72  | | | | | | | | | | | | | | | | | | | |   (6655)  all_57_6 = e2
% 222.17/37.72  | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.72  | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 222.17/37.72  | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.72  | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.72  | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.72  | | | | | | | | | | | | | | | | | | | | |   (6656)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 222.17/37.72  | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 222.17/37.72  | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.72  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6656) gives:
% 222.17/37.72  | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.72  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.17/37.72  | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.72  | | | | | | | | | | | | | | | | | | | | | |   (6657)  all_57_6 = e1 & op(e1, e3) = e1
% 222.17/37.72  | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.72  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6657) implies:
% 222.17/37.72  | | | | | | | | | | | | | | | | | | | | | |   (6658)  all_57_6 = e1
% 222.17/37.72  | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.72  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6655), (6658) are inconsistent by sub-proof
% 222.17/37.72  | | | | | | | | | | | | | | | | | | | | | |            #2233.
% 222.17/37.72  | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.72  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.17/37.72  | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.72  | | | | | | | | | | | | | | | | | | | | | |   (6659)  all_57_7 = e1 & op(e1, e2) = e1
% 222.17/37.72  | | | | | | | | | | | | | | | | | | | | | | 
% 222.17/37.72  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6659) implies:
% 222.17/37.72  | | | | | | | | | | | | | | | | | | | | | |   (6660)  all_57_7 = e1
% 222.17/37.72  | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | |            (212), (217), (374), (5526), (6655), (6660),
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | |            #1245.
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | |   (6661)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6661) gives:
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | |   (6662)  all_57_8 = e1 & op(e1, e1) = e1
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6662) implies:
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | |   (6663)  op(e1, e1) = e1
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6652), (6663), (function-axioms) are
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2423.
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | |   (6664)  all_57_11 = e1 & op(e1, e0) = e1
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6664) implies:
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | |   (6665)  all_57_11 = e1
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | |   (6666)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e1)
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6666) gives:
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | |   (6667)  all_57_0 = e1 & op(e3, e3) = e1
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6629), (6667) are inconsistent by sub-proof
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | |            #2454.
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | |   (6668)  all_57_2 = e1 & op(e2, e3) = e1
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6668) implies:
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | |   (6669)  all_57_2 = e1
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (111),
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | |            (118), (119), (121), (122), (124), (127), (129),
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | |            (134), (135), (137), (142), (144), (145), (146),
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | |            (147), (149), (150), (158), (159), (160), (161),
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | |            (164), (165), (169), (171), (191), (193), (194),
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | |            (196), (197), (198), (199), (201), (202), (203),
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | |            (204), (207), (208), (209), (211), (212), (214),
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | |            (215), (216), (217), (218), (219), (220), (221),
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | |            (222), (223), (224), (225), (226), (227), (228),
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | |            (229), (230), (231), (232), (233), (234), (235),
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | |            (236), (237), (245), (247), (248), (256), (257),
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | |            (258), (259), (267), (268), (269), (270), (374),
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | |            (5511), (5515), (5517), (5518), (5519), (5520),
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | |            (5526), (5527), (5717), (5718), (5719), (5720),
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | |            (5721), (5723), (5728), (6619), (6620), (6621),
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | |            (6622), (6623), (6624), (6626), (6629), (6632),
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | |            (6645), (6646), (6647), (6648), (6649), (6650),
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | |            (6652), (6655), (6669), (function-axioms) are
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #572.
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | |   (6670)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e3) = e1)
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6670) gives:
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | |   (6671)  all_57_6 = e1 & op(e1, e3) = e1
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6671) implies:
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | |   (6672)  all_57_6 = e1
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6655), (6672) are inconsistent by sub-proof
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | |            #2233.
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | |   (6673)  all_57_12 = e1 & op(e0, e3) = e1
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6673) implies:
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | |   (6674)  all_57_12 = e1
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | |   (6675)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e3)
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6675) gives:
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6676)  all_57_0 = e3 & op(e3, e3) = e3
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6676) implies:
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6677)  op(e3, e3) = e3
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (6626), (6677), (function-axioms) are
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2494.
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6678)  all_57_2 = e3 & op(e2, e3) = e3
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6678) implies:
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6679)  all_57_2 = e3
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6680)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6680) gives:
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6681)  all_57_6 = e3 & op(e1, e3) = e3
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6681) implies:
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6682)  all_57_6 = e3
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (234), (6626), (6674), (6679),
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6682), (function-axioms) are inconsistent by
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1288.
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6683)  all_57_7 = e3 & op(e1, e2) = e3
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6683) implies:
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6684)  all_57_7 = e3
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6685)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6685) gives:
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6686)  all_57_1 = e0 & op(e3, e2) = e0
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6686) implies:
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6687)  all_57_1 = e0
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6688)  all_57_15 = e0 & op(e0, e0) = e0
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6688) implies:
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6689)  op(e0, e0) = e0
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5527), (6689), (function-axioms) are
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2304.
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6690)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6690) implies:
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6691)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0)
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6692)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6692) gives:
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6693)  all_57_1 = e2 & op(e3, e2) = e2
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6693) implies:
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6694)  all_57_1 = e2
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6687), (6694) imply:
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6695)  e2 = e0
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6695) implies:
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6696)  e2 = e0
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6655), (6696) imply:
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6697)  all_57_6 = e0
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (217), (234), (236), (374), (5526), (6626),
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6674), (6697), (function-axioms) are inconsistent
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1028.
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6698)  all_57_3 = e2 & op(e2, e2) = e2
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6698) implies:
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6699)  op(e2, e2) = e2
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5723), (6699), (function-axioms) are
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2306.
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6700)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6700) gives:
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6701)  all_57_7 = e2 & op(e1, e2) = e2
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6701) implies:
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6702)  all_57_7 = e2
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (111),
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (118), (119), (121), (122), (124), (127), (129),
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (134), (135), (137), (142), (144), (145), (146),
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (147), (149), (150), (158), (159), (160), (161),
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (165), (169), (171), (191), (193), (194),
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (196), (197), (198), (199), (201), (202), (203),
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (204), (207), (208), (209), (211), (212), (214),
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (215), (216), (217), (218), (219), (220), (221),
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (222), (223), (224), (225), (226), (227), (228),
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (229), (230), (231), (232), (233), (234), (235),
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (236), (237), (245), (247), (248), (256), (257),
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (258), (259), (267), (268), (269), (270), (374),
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5511), (5515), (5517), (5518), (5519), (5520),
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5526), (5527), (5717), (5718), (5719), (5720),
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5721), (5723), (5728), (6619), (6620), (6621),
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6622), (6623), (6624), (6626), (6629), (6632),
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6645), (6646), (6647), (6648), (6649), (6650),
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6652), (6702), (function-axioms) are inconsistent
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #577.
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6703)  all_57_13 = e2 & op(e0, e2) = e2
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6703) implies:
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6704)  all_57_13 = e2
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (111),
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (118), (119), (121), (122), (124), (127), (129),
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (134), (135), (137), (142), (144), (145), (146),
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (147), (149), (150), (158), (159), (160), (161),
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (165), (169), (171), (191), (193), (194),
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (196), (197), (198), (199), (201), (202), (203),
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (204), (207), (208), (209), (211), (212), (214),
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (215), (216), (217), (218), (219), (220), (221),
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (222), (223), (224), (225), (226), (227), (228),
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (229), (230), (231), (232), (233), (234), (235),
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (236), (237), (245), (247), (248), (256), (257),
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (258), (259), (267), (268), (269), (270), (374),
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5511), (5515), (5517), (5518), (5519), (5520),
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5526), (5527), (5717), (5718), (5719), (5720),
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5721), (5723), (5728), (6619), (6620), (6621),
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6622), (6623), (6624), (6626), (6629), (6632),
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6645), (6646), (6647), (6648), (6649), (6650),
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6652), (6655), (6674), (6679), (6684), (6687),
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6691), (6704), (function-axioms) are inconsistent
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #568.
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6705)  all_57_3 = e0 & op(e2, e2) = e0
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6705) implies:
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6706)  op(e2, e2) = e0
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5723), (6706), (function-axioms) are
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2352.
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6707)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0)
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6707) gives:
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6708)  all_57_7 = e0 & op(e1, e2) = e0
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.72  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6708) implies:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6709)  all_57_7 = e0
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (160), (169),
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (207), (208), (209), (211), (212), (214), (215),
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (216), (217), (218), (219), (220), (221), (223),
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (225), (226), (227), (228), (229), (230),
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (232), (233), (234), (235), (236), (237),
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (374), (5518), (5526), (5527), (5723), (5728),
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6621), (6624), (6626), (6674), (6679), (6709),
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1014.
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6710)  all_57_13 = e0 & op(e0, e2) = e0
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6710) implies:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6711)  all_57_13 = e0
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6712)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6712) gives:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6713)  all_57_2 = e2 & op(e2, e3) = e2
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6713) implies:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6714)  all_57_2 = e2
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (236), (6626), (6655), (6674),
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6714), (function-axioms) are inconsistent by
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1212.
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6715)  all_57_3 = e2 & op(e2, e2) = e2
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6715) implies:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6716)  op(e2, e2) = e2
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5723), (6716), (function-axioms) are
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2306.
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6717)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6717) gives:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6718)  all_57_5 = e2 & op(e2, e1) = e2
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6718) implies:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6719)  all_57_5 = e2
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6720)  all_57_15 = e0 & op(e0, e0) = e0
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6720) implies:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6721)  op(e0, e0) = e0
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5527), (6721), (function-axioms) are
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2304.
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6722)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6722) implies:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6723)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0)
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6724)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6724) gives:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6725)  all_57_1 = e2 & op(e3, e2) = e2
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6725) implies:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6726)  all_57_1 = e2
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6727)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e3)
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6727) gives:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6728)  all_57_0 = e3 & op(e3, e3) = e3
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6728) implies:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6729)  op(e3, e3) = e3
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (6626), (6729), (function-axioms) are
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2494.
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6730)  all_57_1 = e3 & op(e3, e2) = e3
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6730) implies:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6731)  all_57_1 = e3
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6726), (6731) imply:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6732)  e3 = e2
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6732) implies:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6733)  e3 = e2
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6679), (6733) imply:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6734)  all_57_2 = e2
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (236), (6626), (6655), (6674),
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6734), (function-axioms) are inconsistent by
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1212.
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6735)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e3)
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6735) gives:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6736)  all_57_4 = e3 & op(e3, e1) = e3
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6736) implies:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6737)  all_57_4 = e3
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6738)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e1)
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6738) gives:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6739)  all_57_4 = e1 & op(e3, e1) = e1
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6739) implies:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6740)  all_57_4 = e1
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6737), (6740) imply:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6741)  e3 = e1
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6741) implies:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6742)  e3 = e1
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6679), (6742) imply:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6743)  all_57_2 = e1
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (111),
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (118), (119), (121), (122), (124), (127), (129),
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (134), (135), (137), (142), (144), (145), (146),
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (147), (149), (150), (158), (159), (160), (161),
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (165), (169), (171), (191), (193), (194),
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (196), (197), (198), (199), (201), (202), (203),
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (204), (207), (208), (209), (211), (212), (214),
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (215), (216), (217), (218), (219), (220), (221),
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (222), (223), (224), (225), (226), (227), (228),
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (229), (230), (231), (232), (233), (234), (235),
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (236), (237), (245), (247), (248), (256), (257),
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (258), (259), (267), (268), (269), (270), (374),
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5511), (5515), (5517), (5518), (5519), (5520),
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5526), (5527), (5717), (5718), (5719), (5720),
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5721), (5723), (5728), (6619), (6620), (6621),
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6622), (6623), (6624), (6626), (6629), (6632),
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6645), (6646), (6647), (6648), (6649), (6650),
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6652), (6655), (6743), (function-axioms) are
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #572.
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6744)  all_57_5 = e1 & op(e2, e1) = e1
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6744) implies:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6745)  all_57_5 = e1
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6719), (6745) imply:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6746)  e2 = e1
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (226), (228), (5723),
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6684), (6726), (6746), (function-axioms) are
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #593.
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6747)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e1)
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6747) gives:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6748)  all_57_8 = e1 & op(e1, e1) = e1
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6748) implies:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6749)  op(e1, e1) = e1
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6652), (6749), (function-axioms) are
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2423.
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6750)  all_57_14 = e1 & op(e0, e1) = e1
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6750) implies:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6751)  all_57_14 = e1
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6752)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6752) gives:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6753)  all_57_12 = e2 & op(e0, e3) = e2
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6753) implies:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6754)  all_57_12 = e2
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (232), (6629), (6655), (6679),
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6754) are inconsistent by sub-proof #1927.
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6755)  all_57_13 = e2 & op(e0, e2) = e2
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6755) implies:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6756)  all_57_13 = e2
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6711), (6756) imply:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6757)  e2 = e0
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6726), (6757) imply:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6758)  all_57_1 = e0
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (111),
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (118), (119), (121), (122), (124), (127), (129),
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (134), (135), (137), (142), (144), (145), (146),
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (147), (149), (150), (158), (159), (160), (161),
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (165), (169), (171), (191), (193), (194),
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (196), (197), (198), (199), (201), (202), (203),
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (204), (207), (208), (209), (211), (212), (214),
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (215), (216), (217), (218), (219), (220), (221),
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (222), (223), (224), (225), (226), (227), (228),
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (229), (230), (231), (232), (233), (234), (235),
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (236), (237), (245), (247), (248), (256), (257),
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (258), (259), (267), (268), (269), (270), (374),
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5511), (5515), (5517), (5518), (5519), (5520),
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5526), (5527), (5717), (5718), (5719), (5720),
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5721), (5723), (5728), (6619), (6620), (6621),
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6622), (6623), (6624), (6626), (6629), (6632),
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6645), (6646), (6647), (6648), (6649), (6650),
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6652), (6655), (6674), (6679), (6684), (6723),
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6756), (6758), (function-axioms) are inconsistent
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #568.
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6759)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6759) gives:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6760)  all_57_14 = e2 & op(e0, e1) = e2
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6760) implies:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6761)  all_57_14 = e2
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (226), (228), (5723),
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6684), (6726), (6751), (6761), (function-axioms)
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #660.
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6762)  all_57_15 = e2 & op(e0, e0) = e2
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6762) implies:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6763)  all_57_15 = e2
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5526), (6763) imply:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6764)  e3 = e2
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6764) implies:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6765)  e3 = e2
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6679), (6765) imply:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6766)  all_57_2 = e2
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (236), (6626), (6655), (6674),
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6766), (function-axioms) are inconsistent by
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1212.
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6767)  all_57_9 = e3 & op(e3, e0) = e3
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6767) implies:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6768)  op(e3, e0) = e3
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (5518), (6768), (function-axioms) are
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2458.
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6769)  all_57_3 = e2 & op(e2, e2) = e2
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6769) implies:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6770)  op(e2, e2) = e2
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5723), (6770), (function-axioms) are
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2306.
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6771)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6771) gives:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6772)  all_57_7 = e2 & op(e1, e2) = e2
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6772) implies:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6773)  all_57_7 = e2
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (111),
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (118), (119), (121), (122), (124), (127), (129),
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (134), (135), (137), (142), (144), (145), (146),
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (147), (149), (150), (158), (159), (160), (161),
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (165), (169), (171), (191), (193), (194),
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (196), (197), (198), (199), (201), (202), (203),
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (204), (207), (208), (209), (211), (212), (214),
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (215), (216), (217), (218), (219), (220), (221),
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (222), (223), (224), (225), (226), (227), (228),
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (229), (230), (231), (232), (233), (234), (235),
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (236), (237), (245), (247), (248), (256), (257),
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (258), (259), (267), (268), (269), (270), (374),
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5511), (5515), (5517), (5518), (5519), (5520),
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5526), (5527), (5717), (5718), (5719), (5720),
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5721), (5723), (5728), (6619), (6620), (6621),
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6622), (6623), (6624), (6626), (6629), (6632),
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6645), (6646), (6647), (6648), (6649), (6650),
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6652), (6773), (function-axioms) are inconsistent
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #577.
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6774)  all_57_13 = e2 & op(e0, e2) = e2
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6774) implies:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6775)  all_57_13 = e2
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6711), (6775) imply:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6776)  e2 = e0
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6776) implies:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6777)  e2 = e0
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6655), (6777) imply:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6778)  all_57_6 = e0
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (217), (234), (236), (374), (5526), (6626),
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6674), (6778), (function-axioms) are inconsistent
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1028.
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6779)  all_57_10 = e2 & op(e2, e0) = e2
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6779) implies:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6780)  all_57_10 = e2
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6781)  all_57_15 = e0 & op(e0, e0) = e0
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6781) implies:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6782)  op(e0, e0) = e0
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5527), (6782), (function-axioms) are
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2304.
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6783)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6783) implies:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6784)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0)
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6784) gives:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6785)  all_57_9 = e0 & op(e3, e0) = e0
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (6624), (6785), (function-axioms) are
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2434.
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6786)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 =
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6786) gives:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6787)  all_57_10 = e0 & op(e2, e0) = e0
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6787) implies:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6788)  all_57_10 = e0
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6780), (6788) imply:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6789)  e2 = e0
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6655), (6789) imply:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6790)  all_57_6 = e0
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (217), (234), (236), (374), (5526), (6626),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6674), (6790), (function-axioms) are inconsistent
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1028.
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6791)  all_57_11 = e0 & op(e1, e0) = e0
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6665), (6791) are inconsistent by sub-proof
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1257.
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6792)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (374), (5526), (6792), (function-axioms)
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1786.
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | |   (6793)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e3) = e3)
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (6655), (6674), (6793) are inconsistent
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #990.
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | |   (6794)  all_57_7 = e2 & op(e1, e2) = e2
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | ALPHA: (6794) implies:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | |   (6795)  all_57_7 = e2
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (111),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | |            (118), (119), (121), (122), (124), (127), (129),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | |            (134), (135), (137), (142), (144), (145), (146),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | |            (147), (149), (150), (158), (159), (160), (161),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | |            (164), (165), (169), (171), (191), (193), (194),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | |            (196), (197), (198), (199), (201), (202), (203),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | |            (204), (207), (208), (209), (211), (212), (214),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | |            (215), (216), (217), (218), (219), (220), (221),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | |            (222), (223), (224), (225), (226), (227), (228),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | |            (229), (230), (231), (232), (233), (234), (235),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | |            (236), (237), (245), (247), (248), (256), (257),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | |            (258), (259), (267), (268), (269), (270), (374),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | |            (5511), (5515), (5517), (5518), (5519), (5520),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | |            (5526), (5527), (5717), (5718), (5719), (5720),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | |            (5721), (5723), (5728), (6619), (6620), (6621),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | |            (6622), (6623), (6624), (6626), (6629), (6632),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | |            (6645), (6646), (6647), (6648), (6649), (6650),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | |            (6652), (6795), (function-axioms) are inconsistent
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | |            by sub-proof #577.
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | |   (6796)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 222.54/37.74  | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e0) = e2)
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | BETA: splitting (6796) gives:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | |   (6797)  all_57_8 = e2 & op(e1, e1) = e2
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (39), (107), (111), (118),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | |            (119), (121), (122), (124), (127), (129), (134),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | |            (135), (137), (142), (144), (145), (146), (147),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | |            (149), (150), (158), (159), (160), (161), (164),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | |            (165), (169), (171), (191), (193), (194), (196),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | |            (197), (198), (199), (201), (202), (203), (204),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | |            (207), (208), (209), (211), (212), (214), (215),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | |            (216), (217), (218), (219), (220), (221), (222),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | |            (223), (224), (225), (226), (227), (228), (229),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | |            (230), (231), (232), (233), (234), (235), (236),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | |            (237), (245), (247), (248), (256), (257), (258),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | |            (259), (267), (268), (269), (270), (374), (5511),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | |            (5515), (5517), (5518), (5519), (5520), (5526),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | |            (5527), (5717), (5718), (5719), (5720), (5721),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | |            (5723), (5728), (6619), (6620), (6621), (6622),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | |            (6623), (6624), (6626), (6629), (6632), (6645),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | |            (6646), (6647), (6648), (6649), (6650), (6797),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | |            #581.
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | |   (6798)  all_57_11 = e2 & op(e1, e0) = e2
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | ALPHA: (6798) implies:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | |   (6799)  all_57_11 = e2
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | |   (6800)  op(e1, e0) = e2
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | |   (6801)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e0)
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6801) gives:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | |   (6802)  all_57_6 = e0 & op(e1, e3) = e0
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6802) implies:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | |   (6803)  all_57_6 = e0
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (160), (169),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | |            (207), (208), (211), (212), (217), (226), (227),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | |            (228), (229), (231), (232), (234), (236), (237),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | |            (374), (5518), (5526), (5527), (5723), (5728),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | |            (6621), (6624), (6626), (6803), (function-axioms)
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #983.
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | |   (6804)  all_57_7 = e0 & op(e1, e2) = e0
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6804) implies:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | |   (6805)  all_57_7 = e0
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | |            (212), (215), (217), (374), (5526), (6652),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | |            (6799), (6805), (function-axioms) are inconsistent
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1154.
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | |   (6806)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6806) gives:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | |   (6807)  all_57_8 = e0 & op(e1, e1) = e0
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6807) implies:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | |   (6808)  all_57_8 = e0
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | |   (6809)  op(e1, e1) = e0
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | |   (6810)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6810) gives:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | |   (6811)  all_57_9 = e1 & op(e3, e0) = e1
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6811) implies:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | |   (6812)  all_57_9 = e1
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | |   (6813)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6813) gives:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6814)  all_57_6 = e1 & op(e1, e3) = e1
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6814) implies:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6815)  all_57_6 = e1
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6816)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6816) gives:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6817)  all_57_6 = e3 & op(e1, e3) = e3
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6817) implies:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6818)  all_57_6 = e3
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (6815), (6818) are inconsistent by sub-proof
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2017.
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6819)  all_57_7 = e3 & op(e1, e2) = e3
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6819) implies:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6820)  all_57_7 = e3
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (111),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (118), (119), (121), (122), (124), (127), (129),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (134), (135), (137), (142), (144), (145), (146),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (147), (149), (150), (158), (159), (160), (161),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (165), (169), (171), (191), (193), (194),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (196), (197), (198), (199), (201), (202), (203),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (204), (207), (208), (209), (211), (212), (214),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (215), (216), (217), (218), (219), (220), (221),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (222), (223), (224), (225), (226), (227), (228),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (229), (230), (231), (232), (233), (234), (235),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (236), (237), (245), (247), (248), (256), (257),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (258), (259), (267), (268), (269), (270), (374),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5511), (5515), (5517), (5518), (5519), (5520),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5526), (5527), (5717), (5718), (5719), (5720),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5721), (5723), (5728), (6619), (6620), (6621),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6622), (6623), (6624), (6626), (6629), (6632),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6645), (6646), (6647), (6648), (6649), (6650),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6652), (6799), (6800), (6808), (6809), (6811),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6812), (6815), (6820), (function-axioms) are
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #565.
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6821)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (374), (5526), (6821), (function-axioms)
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1786.
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6822)  all_57_7 = e1 & op(e1, e2) = e1
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6822) implies:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6823)  all_57_7 = e1
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6824)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6824) gives:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6825)  all_57_6 = e3 & op(e1, e3) = e3
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6825) implies:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6826)  all_57_6 = e3
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6827)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e2)
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6827) gives:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6828)  all_57_0 = e2 & op(e3, e3) = e2
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6828) implies:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6829)  op(e3, e3) = e2
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6626), (6829), (function-axioms) are
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2403.
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6830)  all_57_1 = e2 & op(e3, e2) = e2
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6830) implies:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6831)  all_57_1 = e2
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (111),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (118), (119), (121), (122), (124), (127), (129),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (134), (135), (137), (142), (144), (145), (146),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (147), (149), (150), (158), (159), (160), (161),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (165), (169), (171), (191), (193), (194),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (196), (197), (198), (199), (201), (202), (203),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (204), (207), (208), (209), (211), (212), (214),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (215), (216), (217), (218), (219), (220), (221),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (222), (223), (224), (225), (226), (227), (228),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (229), (230), (231), (232), (233), (234), (235),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (236), (237), (245), (247), (248), (256), (257),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (258), (259), (267), (268), (269), (270), (374),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5511), (5515), (5517), (5518), (5519), (5520),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5526), (5527), (5717), (5718), (5719), (5720),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5721), (5723), (5728), (6619), (6620), (6621),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6622), (6623), (6624), (6626), (6629), (6632),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6645), (6646), (6647), (6648), (6649), (6650),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6652), (6799), (6800), (6808), (6809), (6811),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6812), (6823), (6826), (6831), (function-axioms)
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #563.
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6832)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e2)
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6832) gives:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6833)  all_57_4 = e2 & op(e3, e1) = e2
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6833) implies:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6834)  all_57_4 = e2
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6835)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6835) gives:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6836)  all_57_1 = e3 & op(e3, e2) = e3
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6836) implies:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6837)  all_57_1 = e3
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6838)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e3)
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6838) gives:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6839)  all_57_4 = e3 & op(e3, e1) = e3
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6839) implies:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6840)  all_57_4 = e3
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (235),
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6626), (6837), (6840), (function-axioms) are
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1220.
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6841)  all_57_5 = e3 & op(e2, e1) = e3
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6841) implies:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6842)  all_57_5 = e3
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6843)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 222.54/37.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (223), (224), (232),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (234), (5723), (5728), (6626), (6629), (6826),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6842), (6843), (function-axioms) are inconsistent
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1009.
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6844)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0)
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6844) gives:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6845)  all_57_5 = e0 & op(e2, e1) = e0
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (217), (226), (227), (228), (374), (5526),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5723), (6826), (6837), (6842), (6845),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1772.
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6846)  all_57_10 = e0 & op(e2, e0) = e0
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6846) implies:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6847)  all_57_10 = e0
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6848)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6848) gives:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6849)  all_57_1 = e2 & op(e3, e2) = e2
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6849) implies:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6850)  all_57_1 = e2
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (111),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (118), (119), (121), (122), (124), (127), (129),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (134), (135), (137), (142), (144), (145), (146),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (147), (149), (150), (158), (159), (160), (161),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (165), (169), (171), (191), (193), (194),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (196), (197), (198), (199), (201), (202), (203),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (204), (207), (208), (209), (211), (212), (214),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (215), (216), (217), (218), (219), (220), (221),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (222), (223), (224), (225), (226), (227), (228),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (229), (230), (231), (232), (233), (234), (235),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (236), (237), (245), (247), (248), (256), (257),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (258), (259), (267), (268), (269), (270), (374),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5511), (5515), (5517), (5518), (5519), (5520),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5526), (5527), (5717), (5718), (5719), (5720),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5721), (5723), (5728), (6619), (6620), (6621),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6622), (6623), (6624), (6626), (6629), (6632),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6645), (6646), (6647), (6648), (6649), (6650),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6652), (6799), (6800), (6808), (6809), (6811),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6812), (6823), (6826), (6850), (function-axioms)
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #563.
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6851)  all_57_3 = e2 & op(e2, e2) = e2
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6851) implies:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6852)  op(e2, e2) = e2
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5723), (6852), (function-axioms) are
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2306.
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6853)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6853) gives:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6854)  all_57_7 = e2 & op(e1, e2) = e2
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6854) implies:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6855)  all_57_7 = e2
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (111),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (118), (119), (121), (122), (124), (127), (129),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (134), (135), (137), (142), (144), (145), (146),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (147), (149), (150), (158), (159), (160), (161),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (165), (169), (171), (191), (193), (194),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (196), (197), (198), (199), (201), (202), (203),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (204), (207), (208), (209), (211), (212), (214),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (215), (216), (217), (218), (219), (220), (221),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (222), (223), (224), (225), (226), (227), (228),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (229), (230), (231), (232), (233), (234), (235),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (236), (237), (245), (247), (248), (256), (257),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (258), (259), (267), (268), (269), (270), (374),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5511), (5515), (5517), (5518), (5519), (5520),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5526), (5527), (5717), (5718), (5719), (5720),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5721), (5723), (5728), (6619), (6620), (6621),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6622), (6623), (6624), (6626), (6629), (6632),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6645), (6646), (6647), (6648), (6649), (6650),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6652), (6826), (6837), (6855), (function-axioms)
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #579.
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6856)  all_57_13 = e2 & op(e0, e2) = e2
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6856) implies:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6857)  all_57_13 = e2
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6858)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e1)
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6858) gives:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6859)  all_57_4 = e1 & op(e3, e1) = e1
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6834), (6859) are inconsistent by sub-proof
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2452.
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6860)  all_57_5 = e1 & op(e2, e1) = e1
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (226), (228), (229),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5723), (6837), (6842), (6860), (function-axioms)
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #580.
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6861)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e1)
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6861) gives:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6862)  all_57_8 = e1 & op(e1, e1) = e1
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6862) implies:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6863)  op(e1, e1) = e1
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6652), (6863), (function-axioms) are
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2423.
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6864)  all_57_14 = e1 & op(e0, e1) = e1
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6864) implies:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6865)  all_57_14 = e1
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6866)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6866) gives:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6867)  all_57_1 = e0 & op(e3, e2) = e0
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (217), (226), (227), (228), (374), (5526),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5723), (6826), (6837), (6867), (function-axioms)
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #725.
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6868)  all_57_3 = e0 & op(e2, e2) = e0
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6868) implies:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6869)  all_57_3 = e0
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (223), (224), (6842),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6847), (6869) are inconsistent by sub-proof
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1518.
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6870)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0)
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6870) gives:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6871)  all_57_7 = e0 & op(e1, e2) = e0
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6871) implies:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6872)  all_57_7 = e0
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (215), (217), (374), (5526), (6652),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6799), (6872), (function-axioms) are inconsistent
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1154.
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6873)  all_57_13 = e0 & op(e0, e2) = e0
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6873) implies:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6874)  all_57_13 = e0
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6857), (6874) imply:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6875)  e2 = e0
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6875) implies:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6876)  e2 = e0
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6834), (6876) imply:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6877)  all_57_4 = e0
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (169), (219), (226),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (228), (229), (233), (235), (237), (5518), (5723),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6626), (6629), (6652), (6842), (6865), (6877),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #928.
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6878)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e1) = e3)
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (208),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (209), (374), (5526), (6878), (function-axioms)
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1794.
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6879)  all_57_3 = e3 & op(e2, e2) = e3
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6879) implies:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6880)  op(e2, e2) = e3
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5723), (6880), (function-axioms) are
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1912.
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6881)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (107), (111),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (118), (119), (121), (122), (124), (127), (129),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (134), (135), (137), (142), (144), (145), (146),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (147), (149), (150), (158), (159), (160), (161),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (165), (169), (171), (191), (193), (194),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (196), (197), (198), (199), (201), (202), (203),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (204), (207), (208), (209), (211), (212), (214),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (215), (216), (217), (218), (219), (220), (221),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (222), (223), (224), (225), (226), (227), (228),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (229), (230), (231), (232), (233), (234), (235),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (236), (237), (245), (247), (248), (256), (257),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (258), (259), (267), (268), (269), (270), (374),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5511), (5515), (5517), (5518), (5519), (5520),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5526), (5527), (5717), (5718), (5719), (5720),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5721), (5723), (5728), (6619), (6620), (6621),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6622), (6623), (6624), (6626), (6629), (6632),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6645), (6646), (6647), (6648), (6649), (6650),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6652), (6799), (6800), (6808), (6809), (6811),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6812), (6823), (6826), (6881), (function-axioms)
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #564.
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6882)  all_57_9 = e2 & op(e3, e0) = e2
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6882) implies:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6883)  all_57_9 = e2
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6812), (6883) are inconsistent by sub-proof
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2444.
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6884)  all_57_7 = e3 & op(e1, e2) = e3
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6884) implies:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6885)  all_57_7 = e3
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (6823), (6885) are inconsistent by sub-proof
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2115.
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6886)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (374), (5526), (6886), (function-axioms)
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1786.
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | |   (6887)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6652), (6799), (6887), (function-axioms) are
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1725.
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | |   (6888)  all_57_10 = e1 & op(e2, e0) = e1
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6888) implies:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | |   (6889)  all_57_10 = e1
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | |   (6890)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6890) gives:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6891)  all_57_6 = e1 & op(e1, e3) = e1
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6891) implies:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6892)  all_57_6 = e1
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6893)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6893) gives:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6894)  all_57_2 = e2 & op(e2, e3) = e2
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6894) implies:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6895)  all_57_2 = e2
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6896)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (160), (169),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (207), (208), (209), (211), (212), (214), (215),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (216), (217), (218), (219), (220), (221), (223),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (225), (226), (227), (228), (229), (230),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (232), (233), (234), (235), (236), (237),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (374), (5518), (5526), (5527), (5723), (5728),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6621), (6624), (6626), (6896), (function-axioms)
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #916.
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6897)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0)
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6897) gives:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6898)  all_57_5 = e0 & op(e2, e1) = e0
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6898) implies:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6899)  all_57_5 = e0
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (207), (211), (212),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (225), (5526), (5723), (6799), (6895), (6899),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #683.
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6900)  all_57_10 = e0 & op(e2, e0) = e0
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6900) implies:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6901)  all_57_10 = e0
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6889), (6901) imply:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6902)  e1 = e0
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6892), (6902) imply:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6903)  all_57_6 = e0
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (160), (169),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (207), (208), (211), (212), (217), (226), (227),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (228), (229), (231), (232), (234), (236), (237),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (374), (5518), (5526), (5527), (5723), (5728),
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6621), (6624), (6626), (6903), (function-axioms)
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #983.
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6904)  all_57_3 = e2 & op(e2, e2) = e2
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6904) implies:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6905)  op(e2, e2) = e2
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5723), (6905), (function-axioms) are
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2306.
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6906)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 222.54/37.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (160), (169),
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (207), (208), (209), (211), (212), (214), (215),
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (216), (217), (218), (219), (220), (221), (222),
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (223), (224), (225), (226), (227), (228), (229),
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (231), (232), (233), (234), (235), (236),
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (237), (374), (5518), (5526), (5527), (5723),
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5728), (6621), (6624), (6626), (6889), (6892),
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6906), (function-axioms) are inconsistent by
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #914.
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6907)  all_57_7 = e1 & op(e1, e2) = e1
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6907) implies:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6908)  all_57_7 = e1
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6909)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6909) gives:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6910)  all_57_2 = e2 & op(e2, e3) = e2
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6910) implies:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6911)  all_57_2 = e2
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6912)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (160), (169),
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (207), (208), (209), (211), (212), (214), (215),
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (216), (217), (218), (219), (220), (221), (223),
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (225), (226), (227), (228), (229), (230),
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (232), (233), (234), (235), (236), (237),
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (374), (5518), (5526), (5527), (5723), (5728),
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6621), (6624), (6626), (6912), (function-axioms)
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #916.
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6913)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0)
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6913) gives:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6914)  all_57_5 = e0 & op(e2, e1) = e0
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6914) implies:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6915)  all_57_5 = e0
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (207), (211), (212),
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (225), (5526), (5723), (6799), (6911), (6915),
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #683.
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6916)  all_57_10 = e0 & op(e2, e0) = e0
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6916) implies:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6917)  all_57_10 = e0
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6889), (6917) imply:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6918)  e1 = e0
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6908), (6918) imply:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6919)  all_57_7 = e0
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (215), (217), (374), (5526), (6652),
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6799), (6919), (function-axioms) are inconsistent
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1154.
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6920)  all_57_3 = e2 & op(e2, e2) = e2
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6920) implies:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6921)  op(e2, e2) = e2
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5723), (6921), (function-axioms) are
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2306.
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6922)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6922) gives:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6923)  all_57_5 = e2 & op(e2, e1) = e2
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6923) implies:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6924)  all_57_5 = e2
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6925)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (160), (169),
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (207), (208), (209), (211), (212), (214), (215),
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (216), (217), (218), (219), (220), (221), (223),
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (225), (226), (227), (228), (229), (230),
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (232), (233), (234), (235), (236), (237),
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (374), (5518), (5526), (5527), (5723), (5728),
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6621), (6624), (6626), (6925), (function-axioms)
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #916.
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6926)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0)
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6926) gives:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6927)  all_57_5 = e0 & op(e2, e1) = e0
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6924), (6927) are inconsistent by sub-proof
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2428.
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6928)  all_57_10 = e0 & op(e2, e0) = e0
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6928) implies:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6929)  all_57_10 = e0
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6889), (6929) imply:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6930)  e1 = e0
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6930) implies:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6931)  e1 = e0
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6908), (6931) imply:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6932)  all_57_7 = e0
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (215), (217), (374), (5526), (6652),
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6799), (6932), (function-axioms) are inconsistent
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1154.
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6933)  all_57_10 = e2 & op(e2, e0) = e2
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6933) implies:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6934)  all_57_10 = e2
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6889), (6934) are inconsistent by sub-proof
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2144.
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | |   (6935)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6652), (6799), (6935), (function-axioms) are
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1725.
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | |   (6936)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (5527), (6799), (6936),
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | |            #1109.
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | |   (6937)  all_57_11 = e0 & op(e1, e0) = e0
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6937) implies:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | |   (6938)  all_57_11 = e0
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6799), (6938) are inconsistent by sub-proof
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | |            #1949.
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.76  | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | End of split
% 222.54/37.76  | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.76  | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | |   (6939)  all_24_2 = e0
% 222.54/37.76  | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | COMBINE_EQS: (315), (6939) imply:
% 222.54/37.76  | | | | | | | | | | | | | | | | |   (6940)  all_6_2 = e0
% 222.54/37.76  | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | SIMP: (6940) implies:
% 222.54/37.76  | | | | | | | | | | | | | | | | |   (6941)  all_6_2 = e0
% 222.54/37.76  | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | REDUCE: (374), (6941) imply:
% 222.54/37.76  | | | | | | | | | | | | | | | | |   (6942)   ~ (e3 = e0)
% 222.54/37.76  | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | REDUCE: (39), (6941) imply:
% 222.54/37.76  | | | | | | | | | | | | | | | | |   (6943)  op(e1, e1) = e0
% 222.54/37.76  | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 222.54/37.76  | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | |   (6944)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 222.54/37.76  | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 222.54/37.76  | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | BETA: splitting (6944) gives:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | |   (6945)  all_57_1 = e0 & op(e3, e2) = e0
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | ALPHA: (6945) implies:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | |   (6946)  all_57_1 = e0
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (169), (207), (208),
% 222.54/37.76  | | | | | | | | | | | | | | | | | | |            (209), (226), (227), (228), (229), (233), (235),
% 222.54/37.76  | | | | | | | | | | | | | | | | | | |            (237), (5518), (5526), (5527), (5723), (5728),
% 222.54/37.76  | | | | | | | | | | | | | | | | | | |            (6626), (6629), (6946), (function-axioms) are
% 222.54/37.76  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #824.
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | |   (6947)  all_57_3 = e0 & op(e2, e2) = e0
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | ALPHA: (6947) implies:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | |   (6948)  op(e2, e2) = e0
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5723), (6948), (function-axioms) are
% 222.54/37.76  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2352.
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.76  | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | |   (6949)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 222.54/37.76  | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0)
% 222.54/37.76  | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | BETA: splitting (6949) gives:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | |   (6950)  all_57_7 = e0 & op(e1, e2) = e0
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | ALPHA: (6950) implies:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | |   (6951)  all_57_7 = e0
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (160), (169),
% 222.54/37.76  | | | | | | | | | | | | | | | | | | |            (207), (208), (209), (211), (212), (214), (215),
% 222.54/37.76  | | | | | | | | | | | | | | | | | | |            (216), (217), (218), (219), (220), (221), (222),
% 222.54/37.76  | | | | | | | | | | | | | | | | | | |            (223), (224), (225), (226), (227), (228), (229),
% 222.54/37.76  | | | | | | | | | | | | | | | | | | |            (230), (231), (232), (233), (234), (235), (236),
% 222.54/37.76  | | | | | | | | | | | | | | | | | | |            (237), (374), (5518), (5526), (5527), (5723),
% 222.54/37.76  | | | | | | | | | | | | | | | | | | |            (5728), (6621), (6624), (6626), (6629), (6943),
% 222.54/37.76  | | | | | | | | | | | | | | | | | | |            (6951), (function-axioms) are inconsistent by
% 222.54/37.76  | | | | | | | | | | | | | | | | | | |            sub-proof #933.
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | |   (6952)  all_57_13 = e0 & op(e0, e2) = e0
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | ALPHA: (6952) implies:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | |   (6953)  all_57_13 = e0
% 222.54/37.76  | | | | | | | | | | | | | | | | | | |   (6954)  op(e0, e2) = e0
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | |   (6955)  all_57_15 = e0 & op(e0, e0) = e0
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | ALPHA: (6955) implies:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | |   (6956)  op(e0, e0) = e0
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5527), (6956), (function-axioms) are
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2304.
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | |   (6957)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | |                 e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | ALPHA: (6957) implies:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | |   (6958)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | |               e1) = e0)
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | |   (6959)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | |               e0) = e0)
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | BETA: splitting (6959) gives:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | |   (6960)  all_57_9 = e0 & op(e3, e0) = e0
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (6624), (6960), (function-axioms) are
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2434.
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | |   (6961)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 =
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6961) gives:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | |   (6962)  all_57_10 = e0 & op(e2, e0) = e0
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6962) implies:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | |   (6963)  all_57_10 = e0
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | |   (6964)  op(e2, e0) = e0
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | |   (6965)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e0)
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6965) gives:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | |   (6966)  all_57_6 = e0 & op(e1, e3) = e0
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6966) implies:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | |   (6967)  all_57_6 = e0
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (160), (169),
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | |            (207), (208), (211), (212), (217), (226), (227),
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | |            (228), (229), (231), (232), (234), (236), (237),
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | |            (374), (5518), (5526), (5527), (5723), (5728),
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | |            (6621), (6624), (6626), (6967), (function-axioms)
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #983.
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | |   (6968)  all_57_7 = e0 & op(e1, e2) = e0
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6968) implies:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | |   (6969)  all_57_7 = e0
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (208), (209), (228),
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | |            (229), (5526), (5527), (5723), (6953), (6958),
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | |            (6969), (function-axioms) are inconsistent by
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1765.
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | |   (6970)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6970) gives:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | |   (6971)  all_57_8 = e0 & op(e1, e1) = e0
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6971) implies:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | |   (6972)  all_57_8 = e0
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_7, e0,
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (159), (6954) gives:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | |   (6973)  all_53_7 = e0
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_13,
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | |              e0, e0, e2, simplifying with (165), (6964) gives:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | |   (6974)  all_53_13 = e0
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (129), (6973) imply:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | |   (6975)   ~ (all_53_6 = e0)
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (126), (6973) imply:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | |   (6976)   ~ (all_53_11 = e0)
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6976) implies:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | |   (6977)   ~ (all_53_11 = e0)
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (6974) imply:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | |   (6978)   ~ (all_53_9 = e0)
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (111), (6974) imply:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | |   (6979)   ~ (all_53_14 = e0)
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6979) implies:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | |   (6980)   ~ (all_53_14 = e0)
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | |   (6981)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | |             op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | |               all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | |               all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | |               all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6981) gives:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6982)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | |           all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_7)
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6982) implies:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6983)  op(e3, e0) = all_52_7
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6984)  op(e3, e1) = all_52_5
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6985)  op(e3, e2) = all_52_3
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6986)  op(e3, e3) = all_52_1
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6987)  op(all_52_7, all_52_7) = e0
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6988)  op(all_52_3, all_52_3) = e2
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6989)  op(all_52_1, all_52_1) = e3
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_12,
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_7, e0, e3, simplifying with (169), (6983)
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6990)  all_53_12 = all_52_7
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_8,
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_5, e1, e3, simplifying with (170), (6984)
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6991)  all_53_8 = all_52_5
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_4,
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_3, e2, e3, simplifying with (171), (6985)
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6992)  all_53_4 = all_52_3
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_52_1,
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (6626), (6986) gives:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6993)  all_52_1 = e0
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (6991) imply:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6994)  all_55_2 = all_52_5
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (6992) imply:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6995)  all_55_1 = all_52_3
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (6991), (6992) imply:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6996)   ~ (all_52_3 = all_52_5)
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (124), (6991) imply:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6997)   ~ (all_53_9 = all_52_5)
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6997) implies:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6998)   ~ (all_53_9 = all_52_5)
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (122), (6991) imply:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6999)   ~ (all_53_11 = all_52_5)
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6999) implies:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7000)   ~ (all_53_11 = all_52_5)
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6623), (6991) imply:
% 222.54/37.76  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7001)   ~ (all_52_5 = e0)
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7002)  all_55_12 = e3
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (247), (5515), (7002) are inconsistent by
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2001.
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7003)  all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7004)  all_55_4 = e3
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (7004) imply:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7005)  all_53_1 = e3
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7005) implies:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7006)  all_53_1 = e3
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (147), (7006) imply:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7007)   ~ (all_53_9 = e3)
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7007) implies:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7008)   ~ (all_53_9 = e3)
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7009)  all_55_6 = e3
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (7008), (7009) are inconsistent by
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2498.
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7010)  all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7010) gives:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7011)  all_55_6 = e2
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (7011) imply:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7012)  all_53_9 = e2
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7012) implies:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7013)  all_53_9 = e2
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (119), (7013) imply:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7014)   ~ (all_53_11 = e2)
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7014) implies:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7015)   ~ (all_53_11 = e2)
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6998), (7013) imply:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7016)   ~ (all_52_5 = e2)
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7016) implies:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7017)   ~ (all_52_5 = e2)
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7018)  all_55_14 = e3
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (7018) imply:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7019)  all_53_11 = e3
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5517), (7019) imply:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7020)  $false
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (7020) is inconsistent.
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7021)  all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7021) gives:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7022)  all_55_14 = e2
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (7022) imply:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7023)  all_53_11 = e2
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7015), (7023) imply:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7024)  $false
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (7024) is inconsistent.
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7025)  all_55_14 = e1 | all_55_14 = e0
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7025) gives:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7026)  all_55_14 = e1
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (7026) imply:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7027)  all_53_11 = e1
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7000), (7027) imply:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7028)   ~ (all_52_5 = e1)
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7028) implies:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7029)   ~ (all_52_5 = e1)
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7030)  all_55_2 = e3
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6994), (7030) imply:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7031)  all_52_5 = e3
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7031) implies:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7032)  all_52_5 = e3
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6996), (7032) imply:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7033)   ~ (all_52_3 = e3)
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7034)  all_55_1 = e3
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6995), (7033), (7034) are inconsistent by
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #562.
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7035)  all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (171), (270), (5718), (5723), (6622), (6985),
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6988), (7035), (function-axioms) are inconsistent
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #582.
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7036)  all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6994), (7001), (7017), (7029), (7036) are
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #558.
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7037)  all_55_14 = e0
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (7037) imply:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7038)  all_53_11 = e0
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6977), (7038) imply:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7039)  $false
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (7039) is inconsistent.
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7040)  all_55_6 = e1 | all_55_6 = e0
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (5720), (6978), (7040) are inconsistent by
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2161.
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7041)   ~ (all_55_4 = e3)
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7042)  all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (267), (7041) imply:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7043)   ~ (all_53_1 = e3)
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7044)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e3)
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7044) gives:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7045)  all_57_0 = e3 & op(e3, e3) = e3
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7045) implies:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7046)  op(e3, e3) = e3
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (6626), (7046), (function-axioms) are
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2494.
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7047)  all_57_2 = e3 & op(e2, e3) = e3
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7047) implies:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7048)  all_57_2 = e3
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7042) gives:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7049)  all_55_4 = e2
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (7049) imply:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7050)  all_53_1 = e2
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7050) implies:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7051)  all_53_1 = e2
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (7051) imply:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7052)   ~ (all_53_3 = e2)
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7052) implies:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7053)   ~ (all_53_3 = e2)
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7043), (7051) imply:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7054)   ~ (e3 = e2)
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7003) gives:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7055)  all_55_12 = e2
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (247), (7053), (7055) are inconsistent by
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1337.
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7056)   ~ (all_55_12 = e2)
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7057)  all_55_12 = e1 | all_55_12 = e0
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (160), (169),
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (207), (208), (209), (211), (212), (214), (215),
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (216), (217), (218), (219), (220), (221), (222),
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (223), (224), (226), (227), (228), (229), (230),
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (232), (233), (234), (235), (236), (237),
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (247), (374), (5511), (5518), (5526), (5527),
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5723), (5728), (6621), (6624), (6626), (6629),
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6632), (6963), (7048), (7053), (7057),
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #557.
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7058)  all_55_4 = e1 | all_55_4 = e0
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (5717), (6619), (7058) are inconsistent by
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #773.
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7059)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e3) = e3)
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7059) gives:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7060)  all_57_6 = e3 & op(e1, e3) = e3
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7060) implies:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7061)  all_57_6 = e3
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7062)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7062) gives:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7063)  all_57_6 = e1 & op(e1, e3) = e1
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7063) implies:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7064)  all_57_6 = e1
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7061), (7064) are inconsistent by sub-proof
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2017.
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7065)  all_57_7 = e1 & op(e1, e2) = e1
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7065) implies:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7066)  all_57_7 = e1
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7067)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e1)
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7067) gives:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7068)  all_57_0 = e1 & op(e3, e3) = e1
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7068) implies:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7069)  all_57_0 = e1
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6629), (7069) imply:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7070)  e1 = e0
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7070) implies:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7071)  e1 = e0
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7066), (7071) imply:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7072)  all_57_7 = e0
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (208), (209), (228),
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (229), (5526), (5527), (5723), (6953), (6958),
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7072), (function-axioms) are inconsistent by
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1765.
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7073)  all_57_2 = e1 & op(e2, e3) = e1
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7073) implies:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7074)  all_57_2 = e1
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7075)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7075) gives:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7076)  all_57_1 = e3 & op(e3, e2) = e3
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7076) implies:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7077)  all_57_1 = e3
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (160), (169),
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (207), (208), (211), (212), (217), (222), (223),
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (225), (226), (227), (228), (229), (231),
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (232), (234), (236), (237), (374), (5518), (5526),
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5527), (5723), (5728), (6621), (6624), (6626),
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6629), (7061), (7074), (7077), (function-axioms)
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #980.
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7078)  all_57_3 = e3 & op(e2, e2) = e3
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7078) implies:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7079)  op(e2, e2) = e3
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5723), (7079), (function-axioms) are
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1912.
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7080)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (208), (209),
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5526), (5527), (6958), (7066), (7080),
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #911.
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7081)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e3) = e1)
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7081) gives:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7082)  all_57_6 = e1 & op(e1, e3) = e1
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7082) implies:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7083)  all_57_6 = e1
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7061), (7083) are inconsistent by sub-proof
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2017.
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7084)  all_57_12 = e1 & op(e0, e3) = e1
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7084) implies:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7085)  op(e0, e3) = e1
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (216), (217), (374), (5511), (5526),
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6632), (6972), (7066), (7085), (function-axioms)
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #643.
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7086)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7086) gives:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7087)  all_57_8 = e1 & op(e1, e1) = e1
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7087) implies:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7088)  op(e1, e1) = e1
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6943), (7088), (function-axioms) are
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2427.
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7089)  all_57_11 = e1 & op(e1, e0) = e1
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7089) implies:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7090)  all_57_11 = e1
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7091)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e1)
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7091) gives:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7092)  all_57_0 = e1 & op(e3, e3) = e1
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7092) implies:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7093)  all_57_0 = e1
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6629), (7093) imply:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7094)  e1 = e0
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (211), (212), (5526),
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5527), (6963), (7090), (7094), (function-axioms)
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #932.
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7095)  all_57_2 = e1 & op(e2, e3) = e1
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7095) implies:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7096)  all_57_2 = e1
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7042) gives:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7097)  all_55_4 = e2
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (7097) imply:
% 222.54/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7098)  all_53_1 = e2
% 222.79/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7098) implies:
% 222.79/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7099)  all_53_1 = e2
% 222.79/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (7099) imply:
% 222.79/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7100)   ~ (all_53_3 = e2)
% 222.79/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7100) implies:
% 222.79/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7101)   ~ (all_53_3 = e2)
% 222.79/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7043), (7099) imply:
% 222.79/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7102)   ~ (e3 = e2)
% 222.79/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7003) gives:
% 222.79/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7103)  all_55_12 = e2
% 222.79/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (247), (7101), (7103) are inconsistent by
% 222.79/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1337.
% 222.79/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7104)   ~ (all_55_12 = e2)
% 222.79/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7105)  all_55_12 = e1 | all_55_12 = e0
% 222.79/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 222.79/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7106)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 222.79/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e3)
% 222.79/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7106) gives:
% 222.79/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7107)  all_57_0 = e3 & op(e3, e3) = e3
% 222.79/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7107) implies:
% 222.79/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7108)  all_57_0 = e3
% 222.79/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (230), (232), (234),
% 222.79/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7061), (7108) are inconsistent by sub-proof
% 222.79/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2010.
% 222.79/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7109)  all_57_1 = e3 & op(e3, e2) = e3
% 222.79/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7109) implies:
% 222.79/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7110)  all_57_1 = e3
% 222.79/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (160), (169),
% 222.79/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (207), (208), (211), (212), (217), (222), (223),
% 222.79/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (225), (226), (227), (228), (229), (231),
% 222.79/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (232), (234), (236), (237), (374), (5518), (5526),
% 222.79/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5527), (5723), (5728), (6621), (6624), (6626),
% 222.79/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6629), (7061), (7096), (7110), (function-axioms)
% 222.79/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #980.
% 222.79/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7111)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 222.79/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e3)
% 222.79/37.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (160), (169),
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (207), (208), (209), (211), (212), (214), (215),
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (216), (217), (218), (219), (220), (221), (222),
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (223), (224), (225), (226), (227), (228), (229),
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (231), (232), (233), (234), (235), (236),
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (237), (247), (374), (5511), (5518), (5526),
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5527), (5723), (5728), (6621), (6624), (6626),
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6629), (6632), (6963), (7061), (7090), (7101),
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7105), (7111), (function-axioms) are inconsistent
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #556.
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7112)  all_55_4 = e1 | all_55_4 = e0
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (5717), (6619), (7112) are inconsistent by
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #773.
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7113)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e3) = e1)
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7113) gives:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7114)  all_57_6 = e1 & op(e1, e3) = e1
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7114) implies:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7115)  all_57_6 = e1
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7061), (7115) are inconsistent by sub-proof
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2017.
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7116)  all_57_12 = e1 & op(e0, e3) = e1
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7116) implies:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7117)  op(e0, e3) = e1
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7042) gives:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7118)  all_55_4 = e2
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (7118) imply:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7119)  all_53_1 = e2
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7119) implies:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7120)  all_53_1 = e2
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (150), (7120) imply:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7121)   ~ (all_53_2 = e2)
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7121) implies:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7122)   ~ (all_53_2 = e2)
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (7120) imply:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7123)   ~ (all_53_3 = e2)
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7123) implies:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7124)   ~ (all_53_3 = e2)
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7043), (7120) imply:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7125)   ~ (e3 = e2)
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7003) gives:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7126)  all_55_12 = e2
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (247), (7124), (7126) are inconsistent by
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1337.
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7127)   ~ (all_55_12 = e2)
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7128)  all_55_12 = e1 | all_55_12 = e0
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7129)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e3)
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7129) gives:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7130)  all_57_0 = e3 & op(e3, e3) = e3
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7130) implies:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7131)  all_57_0 = e3
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (230), (232), (234),
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7061), (7131) are inconsistent by sub-proof
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2010.
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7132)  all_57_1 = e3 & op(e3, e2) = e3
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7132) implies:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7133)  all_57_1 = e3
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7134)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (5723), (7133), (7134),
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1768.
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7135)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7135) gives:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7136)  all_57_7 = e2 & op(e1, e2) = e2
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7136) implies:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7137)  all_57_7 = e2
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7138)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7138) gives:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7139)  all_57_9 = e2 & op(e3, e0) = e2
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7139) implies:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7140)  op(e3, e0) = e2
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7128) gives:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7141)  all_55_12 = e1
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (7141) imply:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7142)  all_53_3 = e1
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (7142) imply:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7143)   ~ (all_53_2 = e1)
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7144)  all_55_8 = e3
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (7144) imply:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7145)  all_53_2 = e3
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7145) implies:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7146)  all_53_2 = e3
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (7146) imply:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7147)   ~ (all_53_6 = e3)
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7147) implies:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7148)   ~ (all_53_6 = e3)
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (142), (7146) imply:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7149)   ~ (all_53_14 = e3)
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7150)  all_55_9 = e3
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (7148), (7150) are inconsistent by
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2159.
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7151)  all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7151) gives:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7152)  all_55_9 = e2
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (7152) imply:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7153)  all_53_6 = e2
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (127), (7153) imply:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7154)   ~ (all_53_14 = e2)
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7154) implies:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7155)   ~ (all_53_14 = e2)
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (194), (248), (5520), (5723), (6980), (6983),
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6987), (7140), (7155), (function-axioms) are
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #588.
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7156)  all_55_9 = e1 | all_55_9 = e0
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (5719), (6975), (7156) are inconsistent by
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1835.
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7157)  all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (6620), (7122), (7143), (7157) are
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #886.
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7158)  all_55_12 = e0
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (7158) imply:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7159)  all_53_3 = e0
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6621), (7159) imply:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7160)  $false
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (7160) is inconsistent.
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7161)  all_57_10 = e2 & op(e2, e0) = e2
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7161) implies:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7162)  all_57_10 = e2
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6963), (7162) imply:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7163)  e2 = e0
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7137), (7163) imply:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7164)  all_57_7 = e0
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (228), (5723), (6953), (7133),
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7164), (function-axioms) are inconsistent by
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1767.
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7165)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5511), (5526), (6632), (7117), (7165),
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1019.
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7166)  all_57_13 = e2 & op(e0, e2) = e2
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7166) implies:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7167)  all_57_13 = e2
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6953), (7167) are inconsistent by sub-proof
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1911.
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7168)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e3)
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (160), (169),
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (207), (208), (209), (211), (212), (214), (215),
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (216), (217), (218), (219), (220), (221), (222),
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (223), (224), (225), (226), (227), (228), (229),
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (231), (232), (233), (234), (235), (236),
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (237), (247), (374), (5511), (5518), (5526),
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5527), (5723), (5728), (6621), (6624), (6626),
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6629), (6632), (6963), (7061), (7090), (7124),
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7128), (7168), (function-axioms) are inconsistent
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #556.
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7169)  all_55_4 = e1 | all_55_4 = e0
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (5717), (6619), (7169) are inconsistent by
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #773.
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7170)  all_57_12 = e3 & op(e0, e3) = e3
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7170) implies:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7171)  all_57_12 = e3
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (160), (169),
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (207), (208), (209), (211), (212), (214), (215),
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (216), (217), (218), (219), (220), (221), (222),
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (223), (224), (225), (226), (227), (228), (229),
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (231), (232), (233), (234), (235), (236),
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (237), (374), (5518), (5526), (5527), (5723),
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5728), (6621), (6624), (6626), (6629), (6953),
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7171), (function-axioms) are inconsistent by
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #912.
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7172)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | |           all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | |           & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_15)
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5527), (6964), (7172), (function-axioms) are
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #848.
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | |   (7173)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | |             & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | |               all_52_21) = e1 & op(all_52_23, all_52_23) =
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | |             = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | |             & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(all_52_25, all_52_25) = e3 &
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | |             op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | |               all_52_29) = e1 & op(all_52_31, all_52_31) =
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | |             = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_29) & $i(all_52_31))
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7173) gives:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7174)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | |           all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | |           & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | |           & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | |           & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_23)
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5527), (6943), (7174), (function-axioms) are
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #847.
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7175)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | |           all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | |           & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | |           & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | |           & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_31)
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7175) implies:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7176)  op(e0, e0) = all_52_31
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7177)  op(e0, e2) = all_52_27
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7178)  op(all_52_27, all_52_27) = e2
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5527), (6954), (7176), (7177), (7178),
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | |            #858.
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | |   (7179)  all_57_11 = e0 & op(e1, e0) = e0
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7179) implies:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | |   (7180)  all_57_11 = e0
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (211), (212), (5526),
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | |            (5527), (6963), (7180), (function-axioms) are
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1087.
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | |   (7181)  all_57_11 = e0 & op(e1, e0) = e0
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7181) implies:
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | |   (7182)  all_57_11 = e0
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (160), (169),
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | |            (207), (208), (209), (211), (212), (214), (215),
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | |            (216), (217), (218), (219), (220), (221), (222),
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | |            (223), (224), (225), (226), (227), (228), (229),
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | |            (230), (231), (232), (233), (234), (235), (236),
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | |            (237), (374), (5518), (5526), (5527), (5723),
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | |            (5728), (6621), (6624), (6626), (6629), (6943),
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | |            (6953), (6958), (6959), (7182), (function-axioms)
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #909.
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.78  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.78  | | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | | End of split
% 222.79/37.78  | | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | | End of split
% 222.79/37.78  | | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | End of split
% 222.79/37.78  | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | Case 2:
% 222.79/37.78  | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | |   (7183)  all_57_2 = e0 & op(e2, e3) = e0
% 222.79/37.78  | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | ALPHA: (7183) implies:
% 222.79/37.78  | | | | | | | | | | | | | | |   (7184)  all_57_2 = e0
% 222.79/37.78  | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (160), (169),
% 222.79/37.78  | | | | | | | | | | | | | | |            (207), (208), (209), (211), (212), (214), (215),
% 222.79/37.78  | | | | | | | | | | | | | | |            (216), (217), (218), (219), (220), (221), (223),
% 222.79/37.78  | | | | | | | | | | | | | | |            (224), (225), (226), (227), (228), (229), (230),
% 222.79/37.78  | | | | | | | | | | | | | | |            (231), (232), (233), (234), (235), (236), (237),
% 222.79/37.78  | | | | | | | | | | | | | | |            (374), (5518), (5526), (5527), (5723), (5728),
% 222.79/37.78  | | | | | | | | | | | | | | |            (6621), (6624), (6626), (7184), (function-axioms)
% 222.79/37.78  | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1016.
% 222.79/37.78  | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | End of split
% 222.79/37.78  | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | Case 2:
% 222.79/37.78  | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | |   (7185)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 222.79/37.78  | | | | | | | | | | | | | |             e0 & op(e0, e3) = e0)
% 222.79/37.78  | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | BETA: splitting (7185) gives:
% 222.79/37.78  | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | Case 1:
% 222.79/37.78  | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | |   (7186)  all_57_6 = e0 & op(e1, e3) = e0
% 222.79/37.78  | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | ALPHA: (7186) implies:
% 222.79/37.78  | | | | | | | | | | | | | | |   (7187)  all_57_6 = e0
% 222.79/37.78  | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (160), (169),
% 222.79/37.78  | | | | | | | | | | | | | | |            (207), (208), (211), (212), (217), (226), (227),
% 222.79/37.78  | | | | | | | | | | | | | | |            (228), (229), (231), (232), (234), (236), (237),
% 222.79/37.78  | | | | | | | | | | | | | | |            (374), (5518), (5526), (5527), (5723), (5728),
% 222.79/37.78  | | | | | | | | | | | | | | |            (6621), (6624), (6626), (7187), (function-axioms)
% 222.79/37.78  | | | | | | | | | | | | | | |            are inconsistent by sub-proof #983.
% 222.79/37.78  | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | Case 2:
% 222.79/37.78  | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | |   (7188)  all_57_12 = e0 & op(e0, e3) = e0
% 222.79/37.78  | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | ALPHA: (7188) implies:
% 222.79/37.78  | | | | | | | | | | | | | | |   (7189)  op(e0, e3) = e0
% 222.79/37.78  | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | | REF_CLOSE: (160), (6621), (7189), (function-axioms) are
% 222.79/37.78  | | | | | | | | | | | | | | |            inconsistent by sub-proof #2366.
% 222.79/37.78  | | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | End of split
% 222.79/37.78  | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | End of split
% 222.79/37.78  | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | End of split
% 222.79/37.78  | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | End of split
% 222.79/37.78  | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | Case 2:
% 222.79/37.78  | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | |   (7190)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 222.79/37.78  | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 222.79/37.78  | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | BETA: splitting (7190) gives:
% 222.79/37.78  | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | Case 1:
% 222.79/37.78  | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | |   (7191)  all_57_5 = e1 & op(e2, e1) = e1
% 222.79/37.78  | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | ALPHA: (7191) implies:
% 222.79/37.78  | | | | | | | | | | | |   (7192)  all_57_5 = e1
% 222.79/37.78  | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | BETA: splitting (225) gives:
% 222.79/37.78  | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | Case 1:
% 222.79/37.78  | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | |   (7193)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 222.79/37.78  | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 222.79/37.78  | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | BETA: splitting (7193) gives:
% 222.79/37.78  | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | Case 1:
% 222.79/37.78  | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | |   (7194)  all_57_2 = e3 & op(e2, e3) = e3
% 222.79/37.78  | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | ALPHA: (7194) implies:
% 222.79/37.78  | | | | | | | | | | | | | |   (7195)  all_57_2 = e3
% 222.79/37.78  | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (222), (224), (5723),
% 222.79/37.78  | | | | | | | | | | | | | |            (7192), (7195), (function-axioms) are inconsistent
% 222.79/37.78  | | | | | | | | | | | | | |            by sub-proof #555.
% 222.79/37.78  | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | Case 2:
% 222.79/37.78  | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | |   (7196)  all_57_3 = e3 & op(e2, e2) = e3
% 222.79/37.78  | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | ALPHA: (7196) implies:
% 222.79/37.78  | | | | | | | | | | | | | |   (7197)  op(e2, e2) = e3
% 222.79/37.78  | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | | REF_CLOSE: (8), (5723), (7197), (function-axioms) are
% 222.79/37.78  | | | | | | | | | | | | | |            inconsistent by sub-proof #1912.
% 222.79/37.78  | | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | | End of split
% 222.79/37.78  | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | Case 2:
% 222.79/37.78  | | | | | | | | | | | | | 
% 222.79/37.78  | | | | | | | | | | | | |   (7198)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 222.79/37.78  | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 222.79/37.78  | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | BETA: splitting (7198) gives:
% 222.79/37.79  | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | Case 1:
% 222.79/37.79  | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | |   (7199)  all_57_5 = e3 & op(e2, e1) = e3
% 222.79/37.79  | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | ALPHA: (7199) implies:
% 222.79/37.79  | | | | | | | | | | | | | |   (7200)  all_57_5 = e3
% 222.79/37.79  | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | REF_CLOSE: (8), (7192), (7200) are inconsistent by sub-proof
% 222.79/37.79  | | | | | | | | | | | | | |            #2382.
% 222.79/37.79  | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | Case 2:
% 222.79/37.79  | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | |   (7201)  all_57_10 = e3 & op(e2, e0) = e3
% 222.79/37.79  | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | ALPHA: (7201) implies:
% 222.79/37.79  | | | | | | | | | | | | | |   (7202)  all_57_10 = e3
% 222.79/37.79  | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (207), (211), (212),
% 222.79/37.79  | | | | | | | | | | | | | |            (5526), (5527), (7202), (function-axioms) are
% 222.79/37.79  | | | | | | | | | | | | | |            inconsistent by sub-proof #1746.
% 222.79/37.79  | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | End of split
% 222.79/37.79  | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | End of split
% 222.79/37.79  | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | Case 2:
% 222.79/37.79  | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | |   (7203)  all_57_10 = e1 & op(e2, e0) = e1
% 222.79/37.79  | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | ALPHA: (7203) implies:
% 222.79/37.79  | | | | | | | | | | | |   (7204)  op(e2, e0) = e1
% 222.79/37.79  | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_13,
% 222.79/37.79  | | | | | | | | | | | |              e1, e0, e2, simplifying with (165), (7204) gives:
% 222.79/37.79  | | | | | | | | | | | |   (7205)  all_53_13 = e1
% 222.79/37.79  | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | REDUCE: (5721), (7205) imply:
% 222.79/37.79  | | | | | | | | | | | |   (7206)  $false
% 222.79/37.79  | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | CLOSE: (7206) is inconsistent.
% 222.79/37.79  | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | End of split
% 222.79/37.79  | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | End of split
% 222.79/37.79  | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | End of split
% 222.79/37.79  | | | | | | | | | 
% 222.79/37.79  | | | | | | | | Case 2:
% 222.79/37.79  | | | | | | | | | 
% 222.79/37.79  | | | | | | | | |   (7207)  all_14_2 = e0
% 222.79/37.79  | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | COMBINE_EQS: (328), (7207) imply:
% 222.79/37.79  | | | | | | | | |   (7208)  all_8_2 = e0
% 222.79/37.79  | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | REDUCE: (349), (7208) imply:
% 222.79/37.79  | | | | | | | | |   (7209)   ~ (all_53_1 = e0)
% 222.79/37.79  | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | REDUCE: (352), (7208) imply:
% 222.79/37.79  | | | | | | | | |   (7210)   ~ (all_53_4 = e0)
% 222.79/37.79  | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | REDUCE: (356), (7208) imply:
% 222.79/37.79  | | | | | | | | |   (7211)   ~ (all_53_7 = e0)
% 222.79/37.79  | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | REDUCE: (358), (7208) imply:
% 222.79/37.79  | | | | | | | | |   (7212)   ~ (all_53_9 = e0)
% 222.79/37.79  | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | REDUCE: (360), (7208) imply:
% 222.79/37.79  | | | | | | | | |   (7213)   ~ (all_53_13 = e0)
% 222.79/37.79  | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | REDUCE: (375), (7208) imply:
% 222.79/37.79  | | | | | | | | |   (7214)   ~ (e3 = e0)
% 222.79/37.79  | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | REDUCE: (42), (7208) imply:
% 222.79/37.79  | | | | | | | | |   (7215)  op(e2, e2) = e0
% 222.79/37.79  | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | BETA: splitting (226) gives:
% 222.79/37.79  | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | Case 1:
% 222.79/37.79  | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | |   (7216)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 222.79/37.79  | | | | | | | | | |             & op(e2, e2) = e0)
% 222.79/37.79  | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | BETA: splitting (7216) gives:
% 222.79/37.79  | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | Case 1:
% 222.79/37.79  | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | |   (7217)  all_57_1 = e0 & op(e3, e2) = e0
% 222.79/37.79  | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | ALPHA: (7217) implies:
% 222.79/37.79  | | | | | | | | | | |   (7218)  all_57_1 = e0
% 222.79/37.79  | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | BETA: splitting (229) gives:
% 222.79/37.79  | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | Case 1:
% 222.79/37.79  | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | |   (7219)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 222.79/37.79  | | | | | | | | | | | |             & op(e2, e2) = e3)
% 222.79/37.79  | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | BETA: splitting (7219) gives:
% 222.79/37.79  | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | Case 1:
% 222.79/37.79  | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | |   (7220)  all_57_1 = e3 & op(e3, e2) = e3
% 222.79/37.79  | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | REF_CLOSE: (7), (7218), (7220) are inconsistent by sub-proof
% 222.79/37.79  | | | | | | | | | | | | |            #2405.
% 222.79/37.79  | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | Case 2:
% 222.79/37.79  | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | |   (7221)  all_57_3 = e3 & op(e2, e2) = e3
% 222.79/37.79  | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | ALPHA: (7221) implies:
% 222.79/37.79  | | | | | | | | | | | | |   (7222)  all_57_3 = e3
% 222.79/37.79  | | | | | | | | | | | | |   (7223)  op(e2, e2) = e3
% 222.79/37.79  | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | BETA: splitting (222) gives:
% 222.79/37.79  | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | Case 1:
% 222.79/37.79  | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | |   (7224)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 222.79/37.79  | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 222.79/37.79  | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | BETA: splitting (7224) gives:
% 222.79/37.79  | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | Case 1:
% 222.79/37.79  | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | |   (7225)  all_57_2 = e0 & op(e2, e3) = e0
% 222.79/37.79  | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | ALPHA: (7225) implies:
% 222.79/37.79  | | | | | | | | | | | | | | |   (7226)  all_57_2 = e0
% 222.79/37.79  | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 222.79/37.79  | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | Case 1:
% 222.79/37.79  | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | |   (7227)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 222.79/37.79  | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 222.79/37.79  | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | BETA: splitting (7227) gives:
% 222.79/37.79  | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.79  | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | |   (7228)  all_57_2 = e3 & op(e2, e3) = e3
% 222.79/37.79  | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | ALPHA: (7228) implies:
% 222.79/37.79  | | | | | | | | | | | | | | | | |   (7229)  all_57_2 = e3
% 222.79/37.79  | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | COMBINE_EQS: (7226), (7229) imply:
% 222.79/37.79  | | | | | | | | | | | | | | | | |   (7230)  e3 = e0
% 222.79/37.79  | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | SIMP: (7230) implies:
% 222.79/37.79  | | | | | | | | | | | | | | | | |   (7231)  e3 = e0
% 222.79/37.79  | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | COMBINE_EQS: (7222), (7231) imply:
% 222.79/37.79  | | | | | | | | | | | | | | | | |   (7232)  all_57_3 = e0
% 222.79/37.79  | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 222.79/37.79  | | | | | | | | | | | | | | | | |            (7226), (7232) are inconsistent by sub-proof
% 222.79/37.79  | | | | | | | | | | | | | | | | |            #2246.
% 222.79/37.79  | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.79  | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, e3, e2,
% 222.79/37.79  | | | | | | | | | | | | | | | | |              e2, simplifying with (7215), (7223) gives:
% 222.79/37.79  | | | | | | | | | | | | | | | | |   (7233)  e3 = e0
% 222.79/37.79  | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | COMBINE_EQS: (7222), (7233) imply:
% 222.79/37.79  | | | | | | | | | | | | | | | | |   (7234)  all_57_3 = e0
% 222.79/37.79  | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 222.79/37.79  | | | | | | | | | | | | | | | | |            (7226), (7234) are inconsistent by sub-proof
% 222.79/37.79  | | | | | | | | | | | | | | | | |            #2246.
% 222.79/37.79  | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | End of split
% 222.79/37.79  | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | Case 2:
% 222.79/37.79  | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | |   (7235)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 222.79/37.79  | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 222.79/37.79  | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | BETA: splitting (7235) gives:
% 222.79/37.79  | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.79  | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | |   (7236)  all_57_5 = e3 & op(e2, e1) = e3
% 222.79/37.79  | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | ALPHA: (7236) implies:
% 222.79/37.79  | | | | | | | | | | | | | | | | |   (7237)  all_57_5 = e3
% 222.79/37.79  | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 222.79/37.79  | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.79  | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | |   (7238)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 222.79/37.79  | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 222.79/37.79  | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | BETA: splitting (7238) gives:
% 222.79/37.79  | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | |   (7239)  all_57_2 = e2 & op(e2, e3) = e2
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7226), (7239) are inconsistent by sub-proof
% 222.79/37.79  | | | | | | | | | | | | | | | | | | |            #2257.
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | |   (7240)  all_57_3 = e2 & op(e2, e2) = e2
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | ALPHA: (7240) implies:
% 222.79/37.79  | | | | | | | | | | | | | | | | | | |   (7241)  all_57_3 = e2
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7222), (7241) are inconsistent by sub-proof
% 222.79/37.79  | | | | | | | | | | | | | | | | | | |            #1166.
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.79  | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.79  | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | |   (7242)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 222.79/37.79  | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 222.79/37.79  | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | BETA: splitting (7242) gives:
% 222.79/37.79  | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | |   (7243)  all_57_5 = e2 & op(e2, e1) = e2
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7237), (7243) are inconsistent by sub-proof
% 222.79/37.79  | | | | | | | | | | | | | | | | | | |            #2425.
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | |   (7244)  all_57_10 = e2 & op(e2, e0) = e2
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | ALPHA: (7244) implies:
% 222.79/37.79  | | | | | | | | | | | | | | | | | | |   (7245)  all_57_10 = e2
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | |   (7246)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | BETA: splitting (7246) gives:
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | |   (7247)  all_57_2 = e1 & op(e2, e3) = e1
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | | ALPHA: (7247) implies:
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | |   (7248)  all_57_2 = e1
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7226), (7248) are inconsistent by sub-proof
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | |            #2473.
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | |   (7249)  all_57_3 = e1 & op(e2, e2) = e1
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | | ALPHA: (7249) implies:
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | |   (7250)  op(e2, e2) = e1
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7215), (7250), (function-axioms) are
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2352.
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | |   (7251)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | BETA: splitting (7251) gives:
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | |   (7252)  all_57_5 = e1 & op(e2, e1) = e1
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7237), (7252) are inconsistent by sub-proof
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | |            #2376.
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | |   (7253)  all_57_10 = e1 & op(e2, e0) = e1
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | | ALPHA: (7253) implies:
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | |   (7254)  all_57_10 = e1
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7245), (7254) are inconsistent by sub-proof
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | |            #2144.
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.79  | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | End of split
% 222.79/37.79  | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.79  | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | |   (7255)  all_57_10 = e3 & op(e2, e0) = e3
% 222.79/37.79  | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | ALPHA: (7255) implies:
% 222.79/37.79  | | | | | | | | | | | | | | | | |   (7256)  all_57_10 = e3
% 222.79/37.79  | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 222.79/37.79  | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.79  | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | |   (7257)  all_57_15 = e0 & op(e0, e0) = e0
% 222.79/37.79  | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | ALPHA: (7257) implies:
% 222.79/37.79  | | | | | | | | | | | | | | | | | |   (7258)  op(e0, e0) = e0
% 222.79/37.79  | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5527), (7258), (function-axioms) are
% 222.79/37.79  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2304.
% 222.79/37.79  | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.79  | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | |   (7259)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 222.79/37.79  | | | | | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 222.79/37.79  | | | | | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 222.79/37.79  | | | | | | | | | | | | | | | | | |                 e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 222.79/37.79  | | | | | | | | | | | | | | | | | |               e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 222.79/37.79  | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | ALPHA: (7259) implies:
% 222.79/37.79  | | | | | | | | | | | | | | | | | |   (7260)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 222.79/37.79  | | | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 222.79/37.79  | | | | | | | | | | | | | | | | | |               e0) = e0)
% 222.79/37.79  | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | BETA: splitting (7260) gives:
% 222.79/37.79  | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | |   (7261)  all_57_9 = e0 & op(e3, e0) = e0
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | ALPHA: (7261) implies:
% 222.79/37.79  | | | | | | | | | | | | | | | | | | |   (7262)  all_57_9 = e0
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (207), (211), (212),
% 222.79/37.79  | | | | | | | | | | | | | | | | | | |            (5526), (7256), (7262) are inconsistent by
% 222.79/37.79  | | | | | | | | | | | | | | | | | | |            sub-proof #1982.
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | |   (7263)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 =
% 222.79/37.79  | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | BETA: splitting (7263) gives:
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | |   (7264)  all_57_10 = e0 & op(e2, e0) = e0
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | ALPHA: (7264) implies:
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | |   (7265)  op(e2, e0) = e0
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (7213), (7265), (function-axioms) are
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2470.
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | |   (7266)  all_57_11 = e0 & op(e1, e0) = e0
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | ALPHA: (7266) implies:
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | |   (7267)  all_57_11 = e0
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (211), (212), (5526),
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | |            (5527), (7256), (7267), (function-axioms) are
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1748.
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.79  | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | End of split
% 222.79/37.79  | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | End of split
% 222.79/37.79  | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | End of split
% 222.79/37.79  | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | Case 2:
% 222.79/37.79  | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | |   (7268)  all_57_3 = e0 & op(e2, e2) = e0
% 222.79/37.79  | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | ALPHA: (7268) implies:
% 222.79/37.79  | | | | | | | | | | | | | | |   (7269)  all_57_3 = e0
% 222.79/37.79  | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (45), (58),
% 222.79/37.79  | | | | | | | | | | | | | | |            (61), (64), (67), (73), (88), (94), (107), (111),
% 222.79/37.79  | | | | | | | | | | | | | | |            (113), (114), (118), (119), (121), (122), (124),
% 222.79/37.79  | | | | | | | | | | | | | | |            (126), (127), (134), (135), (136), (137), (140),
% 222.79/37.79  | | | | | | | | | | | | | | |            (141), (142), (144), (145), (146), (147), (149),
% 222.79/37.79  | | | | | | | | | | | | | | |            (150), (158), (159), (160), (161), (163), (164),
% 222.79/37.79  | | | | | | | | | | | | | | |            (165), (166), (169), (170), (171), (191), (192),
% 222.79/37.79  | | | | | | | | | | | | | | |            (193), (194), (195), (196), (197), (198), (199),
% 222.79/37.79  | | | | | | | | | | | | | | |            (201), (202), (203), (204), (205), (207), (208),
% 222.79/37.79  | | | | | | | | | | | | | | |            (209), (211), (212), (214), (215), (216), (217),
% 222.79/37.79  | | | | | | | | | | | | | | |            (218), (219), (220), (221), (223), (224), (225),
% 222.79/37.79  | | | | | | | | | | | | | | |            (227), (228), (229), (230), (231), (232), (233),
% 222.79/37.79  | | | | | | | | | | | | | | |            (234), (235), (236), (237), (245), (246), (247),
% 222.79/37.79  | | | | | | | | | | | | | | |            (248), (249), (256), (257), (258), (259), (267),
% 222.79/37.79  | | | | | | | | | | | | | | |            (268), (269), (270), (277), (299), (315), (327),
% 222.79/37.79  | | | | | | | | | | | | | | |            (329), (332), (336), (338), (340), (342), (344),
% 222.79/37.79  | | | | | | | | | | | | | | |            (348), (350), (361), (363), (364), (366), (368),
% 222.79/37.79  | | | | | | | | | | | | | | |            (374), (376), (5511), (5514), (5515), (5516),
% 222.79/37.79  | | | | | | | | | | | | | | |            (5517), (5518), (5519), (5520), (5526), (5527),
% 222.79/37.79  | | | | | | | | | | | | | | |            (7209), (7210), (7211), (7212), (7213), (7215),
% 222.79/37.79  | | | | | | | | | | | | | | |            (7269), (function-axioms) are inconsistent by
% 222.79/37.79  | | | | | | | | | | | | | | |            sub-proof #370.
% 222.79/37.79  | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | End of split
% 222.79/37.79  | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | Case 2:
% 222.79/37.79  | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | |   (7270)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 222.79/37.79  | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0)
% 222.79/37.79  | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | BETA: splitting (7270) gives:
% 222.79/37.79  | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | Case 1:
% 222.79/37.79  | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | |   (7271)  all_57_5 = e0 & op(e2, e1) = e0
% 222.79/37.79  | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | ALPHA: (7271) implies:
% 222.79/37.79  | | | | | | | | | | | | | | |   (7272)  all_57_5 = e0
% 222.79/37.79  | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 222.79/37.79  | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | Case 1:
% 222.79/37.79  | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | |   (7273)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 222.79/37.79  | | | | | | | | | | | | | | | |             & op(e2, e1) = e3)
% 222.79/37.79  | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | BETA: splitting (7273) gives:
% 222.79/37.79  | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.79  | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | |   (7274)  all_57_4 = e3 & op(e3, e1) = e3
% 222.79/37.79  | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | ALPHA: (7274) implies:
% 222.79/37.79  | | | | | | | | | | | | | | | | |   (7275)  all_57_4 = e3
% 222.79/37.79  | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 222.79/37.79  | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.79  | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | |   (7276)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 222.79/37.79  | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e1)
% 222.79/37.79  | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | BETA: splitting (7276) gives:
% 222.79/37.79  | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | |   (7277)  all_57_0 = e1 & op(e3, e3) = e1
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | ALPHA: (7277) implies:
% 222.79/37.79  | | | | | | | | | | | | | | | | | | |   (7278)  all_57_0 = e1
% 222.79/37.79  | | | | | | | | | | | | | | | | | | |   (7279)  op(e3, e3) = e1
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | |   (7280)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e2)
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | BETA: splitting (7280) gives:
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | |   (7281)  all_57_0 = e2 & op(e3, e3) = e2
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | | ALPHA: (7281) implies:
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | |   (7282)  op(e3, e3) = e2
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7279), (7282), (function-axioms) are
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1950.
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | |   (7283)  all_57_1 = e2 & op(e3, e2) = e2
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7218), (7283) are inconsistent by sub-proof
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | |            #2483.
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | |   (7284)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e2)
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | BETA: splitting (7284) gives:
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | |   (7285)  all_57_4 = e2 & op(e3, e1) = e2
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7275), (7285) are inconsistent by sub-proof
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | |            #2487.
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | |   (7286)  all_57_9 = e2 & op(e3, e0) = e2
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | | ALPHA: (7286) implies:
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | |   (7287)  all_57_9 = e2
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (159), (165),
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | |            (207), (208), (209), (211), (212), (217), (224),
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | |            (227), (228), (229), (230), (374), (5526), (5527),
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | |            (7211), (7213), (7215), (7218), (7222), (7223),
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | |            (7272), (7278), (7286), (7287), (function-axioms)
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #368.
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | |   (7288)  all_57_1 = e1 & op(e3, e2) = e1
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7218), (7288) are inconsistent by sub-proof
% 222.79/37.79  | | | | | | | | | | | | | | | | | | |            #2446.
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.79  | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.79  | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | |   (7289)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 222.79/37.79  | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e1)
% 222.79/37.79  | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | BETA: splitting (7289) gives:
% 222.79/37.79  | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | |   (7290)  all_57_4 = e1 & op(e3, e1) = e1
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | ALPHA: (7290) implies:
% 222.79/37.79  | | | | | | | | | | | | | | | | | | |   (7291)  all_57_4 = e1
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7275), (7291) are inconsistent by sub-proof
% 222.79/37.79  | | | | | | | | | | | | | | | | | | |            #2426.
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | |   (7292)  all_57_9 = e1 & op(e3, e0) = e1
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | ALPHA: (7292) implies:
% 222.79/37.79  | | | | | | | | | | | | | | | | | | |   (7293)  all_57_9 = e1
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | |   (7294)  all_57_15 = e0 & op(e0, e0) = e0
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | ALPHA: (7294) implies:
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | |   (7295)  op(e0, e0) = e0
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5527), (7295), (function-axioms) are
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2304.
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | |   (7296)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | |                 e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | ALPHA: (7296) implies:
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | |   (7297)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | |               e1) = e0)
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | |   (7298)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | |               e0) = e0)
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | |   (7299)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e2)
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7299) gives:
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | | |   (7300)  all_57_0 = e2 & op(e3, e3) = e2
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7300) implies:
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | | |   (7301)  all_57_0 = e2
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | | |   (7302)  op(e3, e3) = e2
% 222.79/37.79  | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7298) gives:
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | |   (7303)  all_57_9 = e0 & op(e3, e0) = e0
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7303) implies:
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | |   (7304)  all_57_9 = e0
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7293), (7304) are inconsistent by sub-proof
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | |            #2479.
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | |   (7305)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 =
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7305) gives:
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | |   (7306)  all_57_10 = e0 & op(e2, e0) = e0
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7306) implies:
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | |   (7307)  op(e2, e0) = e0
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (7213), (7307), (function-axioms) are
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2470.
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | |   (7308)  all_57_11 = e0 & op(e1, e0) = e0
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7308) implies:
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | |   (7309)  all_57_11 = e0
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | |   (7310)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7310) gives:
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7311)  all_57_9 = e2 & op(e3, e0) = e2
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7311) implies:
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7312)  all_57_9 = e2
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7293), (7312) imply:
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7313)  e2 = e1
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7301), (7313) imply:
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7314)  all_57_0 = e1
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (159), (165),
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | |            (207), (208), (209), (211), (212), (217), (224),
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | |            (227), (228), (229), (230), (374), (5526), (5527),
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | |            (7211), (7213), (7215), (7218), (7222), (7223),
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | |            (7272), (7311), (7312), (7314), (function-axioms)
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #368.
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7315)  all_57_10 = e2 & op(e2, e0) = e2
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7315) implies:
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7316)  all_57_10 = e2
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7317)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7317) gives:
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7318)  all_57_2 = e1 & op(e2, e3) = e1
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7318) implies:
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7319)  all_57_2 = e1
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7320)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e3)
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7320) gives:
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7321)  all_57_0 = e3 & op(e3, e3) = e3
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7321) implies:
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7322)  op(e3, e3) = e3
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7302), (7322), (function-axioms) are
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2490.
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7323)  all_57_2 = e3 & op(e2, e3) = e3
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7319), (7323) are inconsistent by sub-proof
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #701.
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7324)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e3) = e3)
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7324) gives:
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7325)  all_57_6 = e3 & op(e1, e3) = e3
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7325) implies:
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7326)  all_57_6 = e3
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7327)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e0)
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (211), (212), (5526),
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7293), (7302), (7309), (7319), (7327),
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #367.
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7328)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = e0)
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7328) gives:
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7329)  all_57_6 = e0 & op(e1, e3) = e0
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (159), (208),
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (209), (211), (212), (217), (227), (228), (229),
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (374), (5526), (5527), (7211), (7215), (7218),
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7222), (7297), (7298), (7329), (function-axioms)
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #369.
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7330)  all_57_12 = e0 & op(e0, e3) = e0
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7330) implies:
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7331)  all_57_12 = e0
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, e3, e2,
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, simplifying with (7215), (7223) gives:
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7332)  e3 = e0
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7222), (7332) imply:
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7333)  all_57_3 = e0
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (67), (88),
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (94), (107), (121), (124), (134), (135), (137),
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (163), (166), (169), (170), (171), (195), (202),
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (203), (204), (207), (208), (209), (211), (212),
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (214), (215), (216), (217), (218), (219), (220),
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (221), (223), (224), (225), (227), (228), (229),
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (231), (232), (233), (234), (235), (236),
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (237), (249), (268), (269), (270), (315), (332),
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (336), (363), (364), (374), (5518), (5526),
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5527), (7210), (7212), (7272), (7293), (7301),
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7302), (7326), (7331), (7333), (function-axioms)
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #460.
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7334)  all_57_12 = e3 & op(e0, e3) = e3
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7334) implies:
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7335)  all_57_12 = e3
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7336)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e0)
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (211), (212), (5526),
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7293), (7302), (7309), (7319), (7336),
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #367.
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7337)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = e0)
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7337) gives:
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7338)  all_57_6 = e0 & op(e1, e3) = e0
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (159), (208),
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (209), (211), (212), (217), (227), (228), (229),
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (374), (5526), (5527), (7211), (7215), (7218),
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7222), (7297), (7298), (7338), (function-axioms)
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #369.
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7339)  all_57_12 = e0 & op(e0, e3) = e0
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7339) implies:
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7340)  all_57_12 = e0
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7335), (7340) imply:
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7341)  e3 = e0
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7222), (7341) imply:
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7342)  all_57_3 = e0
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (207), (212), (223),
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (225), (5526), (7272), (7293), (7316), (7342) are
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #967.
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7343)  all_57_3 = e1 & op(e2, e2) = e1
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7343) implies:
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7344)  op(e2, e2) = e1
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7215), (7344), (function-axioms) are
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2352.
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7345)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7345) gives:
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7346)  all_57_5 = e1 & op(e2, e1) = e1
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7346) implies:
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7347)  all_57_5 = e1
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7272), (7347) imply:
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7348)  e1 = e0
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7293), (7348) imply:
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7349)  all_57_9 = e0
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (211), (212), (5526),
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7309), (7349) are inconsistent by sub-proof
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1144.
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7350)  all_57_10 = e1 & op(e2, e0) = e1
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7350) implies:
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7351)  all_57_10 = e1
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7316), (7351) are inconsistent by sub-proof
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2144.
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | |   (7352)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7352) gives:
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7353)  all_57_11 = e2 & op(e1, e0) = e2
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7309), (7353) are inconsistent by sub-proof
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | |            #1988.
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7354)  all_57_15 = e2 & op(e0, e0) = e2
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5526), (7354) are inconsistent by sub-proof
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | |            #2323.
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | |   (7355)  all_57_1 = e2 & op(e3, e2) = e2
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7218), (7355) are inconsistent by sub-proof
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | |            #2483.
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | |   (7356)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e2)
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (7275), (7293), (7356) are inconsistent
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2480.
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.80  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.80  | | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | End of split
% 222.79/37.80  | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.80  | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | |   (7357)  all_57_5 = e3 & op(e2, e1) = e3
% 222.79/37.80  | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | ALPHA: (7357) implies:
% 222.79/37.80  | | | | | | | | | | | | | | | | |   (7358)  all_57_5 = e3
% 222.79/37.80  | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | COMBINE_EQS: (7272), (7358) imply:
% 222.79/37.80  | | | | | | | | | | | | | | | | |   (7359)  e3 = e0
% 222.79/37.80  | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | COMBINE_EQS: (7222), (7359) imply:
% 222.79/37.80  | | | | | | | | | | | | | | | | |   (7360)  all_57_3 = e0
% 222.79/37.80  | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (45), (58),
% 222.79/37.80  | | | | | | | | | | | | | | | | |            (61), (64), (67), (73), (88), (94), (107), (111),
% 222.79/37.80  | | | | | | | | | | | | | | | | |            (113), (114), (118), (119), (121), (122), (124),
% 222.79/37.80  | | | | | | | | | | | | | | | | |            (126), (127), (134), (135), (136), (137), (140),
% 222.79/37.80  | | | | | | | | | | | | | | | | |            (141), (142), (144), (145), (146), (147), (149),
% 222.79/37.80  | | | | | | | | | | | | | | | | |            (150), (158), (159), (160), (161), (163), (164),
% 222.79/37.80  | | | | | | | | | | | | | | | | |            (165), (166), (169), (170), (171), (191), (192),
% 222.79/37.80  | | | | | | | | | | | | | | | | |            (193), (194), (195), (196), (197), (198), (199),
% 222.79/37.80  | | | | | | | | | | | | | | | | |            (201), (202), (203), (204), (205), (207), (208),
% 222.79/37.80  | | | | | | | | | | | | | | | | |            (209), (211), (212), (214), (215), (216), (217),
% 222.79/37.80  | | | | | | | | | | | | | | | | |            (218), (219), (220), (221), (223), (224), (225),
% 222.79/37.80  | | | | | | | | | | | | | | | | |            (227), (228), (229), (230), (231), (232), (233),
% 222.79/37.80  | | | | | | | | | | | | | | | | |            (234), (235), (236), (237), (245), (246), (247),
% 222.79/37.80  | | | | | | | | | | | | | | | | |            (248), (249), (256), (257), (258), (259), (267),
% 222.79/37.80  | | | | | | | | | | | | | | | | |            (268), (269), (270), (277), (299), (315), (327),
% 222.79/37.80  | | | | | | | | | | | | | | | | |            (329), (332), (336), (338), (340), (342), (344),
% 222.79/37.80  | | | | | | | | | | | | | | | | |            (348), (350), (361), (363), (364), (366), (368),
% 222.79/37.80  | | | | | | | | | | | | | | | | |            (374), (376), (5511), (5514), (5515), (5516),
% 222.79/37.80  | | | | | | | | | | | | | | | | |            (5517), (5518), (5519), (5520), (5526), (5527),
% 222.79/37.80  | | | | | | | | | | | | | | | | |            (7209), (7210), (7211), (7212), (7213), (7215),
% 222.79/37.80  | | | | | | | | | | | | | | | | |            (7360), (function-axioms) are inconsistent by
% 222.79/37.80  | | | | | | | | | | | | | | | | |            sub-proof #370.
% 222.79/37.80  | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | End of split
% 222.79/37.80  | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | Case 2:
% 222.79/37.80  | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | |   (7361)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 222.79/37.80  | | | | | | | | | | | | | | | |             e3 & op(e0, e1) = e3)
% 222.79/37.80  | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (208),
% 222.79/37.80  | | | | | | | | | | | | | | | |            (209), (374), (5526), (7361), (function-axioms)
% 222.79/37.80  | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1794.
% 222.79/37.80  | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | End of split
% 222.79/37.80  | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | Case 2:
% 222.79/37.80  | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | |   (7362)  all_57_10 = e0 & op(e2, e0) = e0
% 222.79/37.80  | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | ALPHA: (7362) implies:
% 222.79/37.80  | | | | | | | | | | | | | | |   (7363)  op(e2, e0) = e0
% 222.79/37.80  | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | REF_CLOSE: (165), (7213), (7363), (function-axioms) are
% 222.79/37.80  | | | | | | | | | | | | | | |            inconsistent by sub-proof #2470.
% 222.79/37.80  | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | End of split
% 222.79/37.80  | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | End of split
% 222.79/37.80  | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | End of split
% 222.79/37.80  | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | Case 2:
% 222.79/37.80  | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | |   (7364)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 222.79/37.80  | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 222.79/37.80  | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | BETA: splitting (7364) gives:
% 222.79/37.80  | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | Case 1:
% 222.79/37.80  | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | |   (7365)  all_57_7 = e3 & op(e1, e2) = e3
% 222.79/37.80  | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | ALPHA: (7365) implies:
% 222.79/37.80  | | | | | | | | | | | | |   (7366)  all_57_7 = e3
% 222.79/37.80  | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (227), (228), (7215),
% 222.79/37.80  | | | | | | | | | | | | |            (7218), (7366), (function-axioms) are inconsistent
% 222.79/37.80  | | | | | | | | | | | | |            by sub-proof #1282.
% 222.79/37.80  | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | Case 2:
% 222.79/37.80  | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | |   (7367)  all_57_13 = e3 & op(e0, e2) = e3
% 222.79/37.80  | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | ALPHA: (7367) implies:
% 222.79/37.80  | | | | | | | | | | | | |   (7368)  all_57_13 = e3
% 222.79/37.80  | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (159), (207), (208),
% 222.79/37.80  | | | | | | | | | | | | |            (209), (5526), (5527), (7211), (7368),
% 222.79/37.80  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.79/37.80  | | | | | | | | | | | | |            #366.
% 222.79/37.80  | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | End of split
% 222.79/37.80  | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | End of split
% 222.79/37.80  | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | Case 2:
% 222.79/37.80  | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | |   (7369)  all_57_3 = e0 & op(e2, e2) = e0
% 222.79/37.80  | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | ALPHA: (7369) implies:
% 222.79/37.80  | | | | | | | | | | |   (7370)  all_57_3 = e0
% 222.79/37.80  | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (45), (58),
% 222.79/37.80  | | | | | | | | | | |            (61), (64), (67), (73), (88), (94), (107), (111),
% 222.79/37.80  | | | | | | | | | | |            (113), (114), (118), (119), (121), (122), (124),
% 222.79/37.80  | | | | | | | | | | |            (126), (127), (134), (135), (136), (137), (140),
% 222.79/37.80  | | | | | | | | | | |            (141), (142), (144), (145), (146), (147), (149),
% 222.79/37.80  | | | | | | | | | | |            (150), (158), (159), (160), (161), (163), (164),
% 222.79/37.80  | | | | | | | | | | |            (165), (166), (169), (170), (171), (191), (192),
% 222.79/37.80  | | | | | | | | | | |            (193), (194), (195), (196), (197), (198), (199),
% 222.79/37.80  | | | | | | | | | | |            (201), (202), (203), (204), (205), (207), (208),
% 222.79/37.80  | | | | | | | | | | |            (209), (211), (212), (214), (215), (216), (217),
% 222.79/37.80  | | | | | | | | | | |            (218), (219), (220), (221), (223), (224), (225),
% 222.79/37.80  | | | | | | | | | | |            (227), (228), (229), (230), (231), (232), (233),
% 222.79/37.80  | | | | | | | | | | |            (234), (235), (236), (237), (245), (246), (247),
% 222.79/37.80  | | | | | | | | | | |            (248), (249), (256), (257), (258), (259), (267),
% 222.79/37.80  | | | | | | | | | | |            (268), (269), (270), (277), (299), (315), (327),
% 222.79/37.80  | | | | | | | | | | |            (329), (332), (336), (338), (340), (342), (344),
% 222.79/37.80  | | | | | | | | | | |            (348), (350), (361), (363), (364), (366), (368),
% 222.79/37.80  | | | | | | | | | | |            (374), (376), (5511), (5514), (5515), (5516),
% 222.79/37.80  | | | | | | | | | | |            (5517), (5518), (5519), (5520), (5526), (5527),
% 222.79/37.80  | | | | | | | | | | |            (7209), (7210), (7211), (7212), (7213), (7215),
% 222.79/37.80  | | | | | | | | | | |            (7370), (function-axioms) are inconsistent by
% 222.79/37.80  | | | | | | | | | | |            sub-proof #370.
% 222.79/37.80  | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | End of split
% 222.79/37.80  | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | Case 2:
% 222.79/37.80  | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | |   (7371)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 222.79/37.80  | | | | | | | | | |             e0 & op(e0, e2) = e0)
% 222.79/37.80  | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | BETA: splitting (7371) gives:
% 222.79/37.80  | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | Case 1:
% 222.79/37.80  | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | |   (7372)  all_57_7 = e0 & op(e1, e2) = e0
% 222.79/37.80  | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | ALPHA: (7372) implies:
% 222.79/37.80  | | | | | | | | | | |   (7373)  all_57_7 = e0
% 222.79/37.80  | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | BETA: splitting (217) gives:
% 222.79/37.80  | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | Case 1:
% 222.79/37.80  | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | |   (7374)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 222.79/37.80  | | | | | | | | | | | |             & op(e1, e2) = e3)
% 222.79/37.80  | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | BETA: splitting (7374) gives:
% 222.79/37.80  | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | Case 1:
% 222.79/37.80  | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | |   (7375)  all_57_6 = e3 & op(e1, e3) = e3
% 222.79/37.80  | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | ALPHA: (7375) implies:
% 222.79/37.80  | | | | | | | | | | | | |   (7376)  all_57_6 = e3
% 222.79/37.80  | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | BETA: splitting (229) gives:
% 222.79/37.80  | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | Case 1:
% 222.79/37.80  | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | |   (7377)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 222.79/37.80  | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 222.79/37.80  | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | BETA: splitting (7377) gives:
% 222.79/37.80  | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | Case 1:
% 222.79/37.80  | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | |   (7378)  all_57_1 = e3 & op(e3, e2) = e3
% 222.79/37.80  | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | ALPHA: (7378) implies:
% 222.79/37.80  | | | | | | | | | | | | | | |   (7379)  all_57_1 = e3
% 222.79/37.80  | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 222.79/37.80  | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | Case 1:
% 222.79/37.80  | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | |   (7380)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 222.79/37.80  | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 222.79/37.80  | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | BETA: splitting (7380) gives:
% 222.79/37.80  | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.80  | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | |   (7381)  all_57_1 = e1 & op(e3, e2) = e1
% 222.79/37.80  | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 222.79/37.80  | | | | | | | | | | | | | | | | |            (212), (217), (374), (5526), (7373), (7376),
% 222.79/37.80  | | | | | | | | | | | | | | | | |            (7379), (7381), (function-axioms) are inconsistent
% 222.79/37.80  | | | | | | | | | | | | | | | | |            by sub-proof #929.
% 222.79/37.80  | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.80  | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | |   (7382)  all_57_3 = e1 & op(e2, e2) = e1
% 222.79/37.80  | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | ALPHA: (7382) implies:
% 222.79/37.80  | | | | | | | | | | | | | | | | |   (7383)  op(e2, e2) = e1
% 222.79/37.80  | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7215), (7383), (function-axioms) are
% 222.79/37.80  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2352.
% 222.79/37.80  | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | End of split
% 222.79/37.80  | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | Case 2:
% 222.79/37.80  | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | |   (7384)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 222.79/37.80  | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 222.79/37.80  | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | BETA: splitting (7384) gives:
% 222.79/37.80  | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.80  | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | |   (7385)  all_57_7 = e1 & op(e1, e2) = e1
% 222.79/37.80  | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7373), (7385) are inconsistent by sub-proof
% 222.79/37.80  | | | | | | | | | | | | | | | | |            #2200.
% 222.79/37.80  | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.80  | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | |   (7386)  all_57_13 = e1 & op(e0, e2) = e1
% 222.79/37.80  | | | | | | | | | | | | | | | | | 
% 222.79/37.80  | | | | | | | | | | | | | | | | | ALPHA: (7386) implies:
% 222.79/37.80  | | | | | | | | | | | | | | | | |   (7387)  all_57_13 = e1
% 222.79/37.81  | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 222.79/37.81  | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | |   (7388)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 222.79/37.81  | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 222.79/37.81  | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | BETA: splitting (7388) gives:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | |   (7389)  all_57_1 = e2 & op(e3, e2) = e2
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7379), (7389) are inconsistent by sub-proof
% 222.79/37.81  | | | | | | | | | | | | | | | | | | |            #1809.
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | |   (7390)  all_57_3 = e2 & op(e2, e2) = e2
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | ALPHA: (7390) implies:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | |   (7391)  all_57_3 = e2
% 222.79/37.81  | | | | | | | | | | | | | | | | | | |   (7392)  op(e2, e2) = e2
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | |   (7393)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | BETA: splitting (7393) gives:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | |   (7394)  all_57_2 = e0 & op(e2, e3) = e0
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | ALPHA: (7394) implies:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | |   (7395)  all_57_2 = e0
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | |   (7396)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7396) gives:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | |   (7397)  all_57_2 = e3 & op(e2, e3) = e3
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7397) implies:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | |   (7398)  all_57_2 = e3
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7395), (7398) are inconsistent by sub-proof
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | |            #2258.
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | |   (7399)  all_57_3 = e3 & op(e2, e2) = e3
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7391), (7399) are inconsistent by sub-proof
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | |            #845.
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | |   (7400)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7400) gives:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | |   (7401)  all_57_5 = e3 & op(e2, e1) = e3
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7401) implies:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | |   (7402)  all_57_5 = e3
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | |   (7403)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e1)
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7403) gives:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | |   (7404)  all_57_0 = e1 & op(e3, e3) = e1
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7404) implies:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | |   (7405)  op(e3, e3) = e1
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7406)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2)
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (223), (224), (7391),
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | |            (7395), (7402), (7405), (7406), (function-axioms)
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #819.
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7407)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e3) = e2)
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7407) gives:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7408)  all_57_6 = e2 & op(e1, e3) = e2
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7408) implies:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7409)  all_57_6 = e2
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7376), (7409) are inconsistent by sub-proof
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2463.
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7410)  all_57_12 = e2 & op(e0, e3) = e2
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7410) implies:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7411)  all_57_12 = e2
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7412)  all_57_15 = e0 & op(e0, e0) = e0
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7412) implies:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7413)  op(e0, e0) = e0
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5527), (7413), (function-axioms) are
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2304.
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7414)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7414) implies:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7415)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0)
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7415) gives:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7416)  all_57_12 = e0 & op(e0, e3) = e0
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7416) implies:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7417)  all_57_12 = e0
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7411), (7417) imply:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7418)  e2 = e0
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7391), (7418) imply:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7419)  all_57_3 = e0
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (223), (224), (7395),
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7402), (7419) are inconsistent by sub-proof
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2253.
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7420)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7420) gives:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7421)  all_57_13 = e0 & op(e0, e2) = e0
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7421) implies:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7422)  op(e0, e2) = e0
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (7211), (7422), (function-axioms) are
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2332.
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7423)  all_57_14 = e0 & op(e0, e1) = e0
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7423) implies:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7424)  all_57_14 = e0
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (208), (223), (224),
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5527), (7215), (7391), (7392), (7395), (7402),
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7411), (7424), (function-axioms) are inconsistent
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #365.
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | |   (7425)  all_57_2 = e1 & op(e2, e3) = e1
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7425) implies:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | |   (7426)  all_57_2 = e1
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7395), (7426) are inconsistent by sub-proof
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | |            #2473.
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | |   (7427)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e3) = e1)
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7427) gives:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | |   (7428)  all_57_6 = e1 & op(e1, e3) = e1
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7428) implies:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | |   (7429)  all_57_6 = e1
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (217), (374), (5526), (7373), (7429),
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | |            #1735.
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | |   (7430)  all_57_12 = e1 & op(e0, e3) = e1
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7430) implies:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | |   (7431)  all_57_12 = e1
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7432)  all_57_15 = e0 & op(e0, e0) = e0
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7432) implies:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7433)  op(e0, e0) = e0
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5527), (7433), (function-axioms) are
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2304.
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7434)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7434) implies:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7435)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0)
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7435) gives:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7436)  all_57_12 = e0 & op(e0, e3) = e0
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7436) implies:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7437)  all_57_12 = e0
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7431), (7437) are inconsistent by sub-proof
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2014.
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7438)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7438) gives:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7439)  all_57_13 = e0 & op(e0, e2) = e0
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7439) implies:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7440)  op(e0, e2) = e0
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (7211), (7440), (function-axioms) are
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2332.
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7441)  all_57_14 = e0 & op(e0, e1) = e0
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7441) implies:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7442)  all_57_14 = e0
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7443)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7443) gives:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7444)  all_57_12 = e2 & op(e0, e3) = e2
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7444) implies:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7445)  all_57_12 = e2
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (208), (223), (224),
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5527), (7215), (7391), (7392), (7395), (7402),
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7442), (7445), (function-axioms) are inconsistent
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #365.
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7446)  all_57_13 = e2 & op(e0, e2) = e2
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7446) implies:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7447)  all_57_13 = e2
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7387), (7447) are inconsistent by sub-proof
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2327.
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7448)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7448) gives:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7449)  all_57_14 = e2 & op(e0, e1) = e2
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7449) implies:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7450)  all_57_14 = e2
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7442), (7450) imply:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7451)  e2 = e0
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7451) implies:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7452)  e2 = e0
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7391), (7452) imply:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7453)  all_57_3 = e0
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (223), (224), (7395),
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7402), (7453) are inconsistent by sub-proof
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2253.
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7454)  all_57_15 = e2 & op(e0, e0) = e2
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7454) implies:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7455)  all_57_15 = e2
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5526), (7455) are inconsistent by sub-proof
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2058.
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | |   (7456)  all_57_10 = e3 & op(e2, e0) = e3
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7456) implies:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | |   (7457)  all_57_10 = e3
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | |   (7458)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e1)
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7458) gives:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | |   (7459)  all_57_0 = e1 & op(e3, e3) = e1
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7459) implies:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | |   (7460)  all_57_0 = e1
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7461)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7461) gives:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7462)  all_57_2 = e1 & op(e2, e3) = e1
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7395), (7462) are inconsistent by sub-proof
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2018.
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7463)  all_57_3 = e1 & op(e2, e2) = e1
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7463) implies:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7464)  op(e2, e2) = e1
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7215), (7464), (function-axioms) are
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2352.
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7465)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7465) gives:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7466)  all_57_5 = e1 & op(e2, e1) = e1
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7466) implies:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7467)  all_57_5 = e1
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7468)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e3)
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7468) gives:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7469)  all_57_4 = e3 & op(e3, e1) = e3
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7469) implies:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7470)  all_57_4 = e3
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (231), (235), (7379),
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7460), (7470) are inconsistent by sub-proof
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1808.
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7471)  all_57_5 = e3 & op(e2, e1) = e3
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7471) implies:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7472)  all_57_5 = e3
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7467), (7472) imply:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7473)  e3 = e1
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7473) implies:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7474)  e3 = e1
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7376), (7474) imply:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7475)  all_57_6 = e1
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (217), (374), (5526), (7373), (7475),
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1735.
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7476)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e1) = e3)
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (208),
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (209), (374), (5526), (7476), (function-axioms)
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1794.
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7477)  all_57_10 = e1 & op(e2, e0) = e1
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7477) implies:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7478)  all_57_10 = e1
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7457), (7478) imply:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7479)  e3 = e1
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7479) implies:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7480)  e3 = e1
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7376), (7480) imply:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7481)  all_57_6 = e1
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (217), (374), (5526), (7373), (7481),
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1735.
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | |   (7482)  all_57_2 = e1 & op(e2, e3) = e1
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7482) implies:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | |   (7483)  all_57_2 = e1
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7395), (7483) are inconsistent by sub-proof
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | |            #2473.
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | |   (7484)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e3) = e1)
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7484) gives:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | |   (7485)  all_57_6 = e1 & op(e1, e3) = e1
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7485) implies:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | |   (7486)  all_57_6 = e1
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (217), (374), (5526), (7373), (7486),
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | |            #1735.
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | |   (7487)  all_57_12 = e1 & op(e0, e3) = e1
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7487) implies:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | |   (7488)  all_57_12 = e1
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7489)  all_57_15 = e0 & op(e0, e0) = e0
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7489) implies:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7490)  op(e0, e0) = e0
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5527), (7490), (function-axioms) are
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2304.
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7491)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7491) implies:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7492)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0)
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7492) gives:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7493)  all_57_12 = e0 & op(e0, e3) = e0
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7493) implies:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7494)  all_57_12 = e0
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7488), (7494) are inconsistent by sub-proof
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2014.
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7495)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7495) gives:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7496)  all_57_13 = e0 & op(e0, e2) = e0
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7496) implies:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7497)  op(e0, e2) = e0
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (7211), (7497), (function-axioms) are
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2332.
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7498)  all_57_14 = e0 & op(e0, e1) = e0
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7498) implies:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7499)  all_57_14 = e0
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7500)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2)
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7500) gives:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7501)  all_57_0 = e2 & op(e3, e3) = e2
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7501) implies:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7502)  all_57_0 = e2
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7503)  op(e3, e3) = e2
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7504)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7387), (7488), (7504) are inconsistent by
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #991.
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7505)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7505) gives:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7506)  all_57_14 = e2 & op(e0, e1) = e2
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7506) implies:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7507)  all_57_14 = e2
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7499), (7507) imply:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7508)  e2 = e0
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7508) implies:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7509)  e2 = e0
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7391), (7509) imply:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7510)  all_57_3 = e0
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (169), (207),
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (208), (209), (211), (212), (217), (223), (224),
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (225), (227), (228), (229), (230), (231), (232),
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (234), (236), (237), (374), (5518), (5526),
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5527), (7215), (7373), (7379), (7502), (7503),
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7510), (function-axioms) are inconsistent by
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #605.
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7511)  all_57_15 = e2 & op(e0, e0) = e2
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7511) implies:
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7512)  all_57_15 = e2
% 222.79/37.81  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5526), (7512) are inconsistent by sub-proof
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2058.
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7513)  all_57_2 = e2 & op(e2, e3) = e2
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7513) implies:
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7514)  all_57_2 = e2
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7395), (7514) imply:
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7515)  e2 = e0
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7515) implies:
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7516)  e2 = e0
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7391), (7516) imply:
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7517)  all_57_3 = e0
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (223), (224), (7395),
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7457), (7517) are inconsistent by sub-proof
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2247.
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7518)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e3) = e2)
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7518) gives:
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7519)  all_57_6 = e2 & op(e1, e3) = e2
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7376), (7519) are inconsistent by sub-proof
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2012.
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7520)  all_57_12 = e2 & op(e0, e3) = e2
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7488), (7520) are inconsistent by sub-proof
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1922.
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | |   (7521)  all_57_3 = e0 & op(e2, e2) = e0
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | ALPHA: (7521) implies:
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | |   (7522)  all_57_3 = e0
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (45), (58),
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | |            (61), (64), (67), (73), (88), (94), (107), (111),
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | |            (113), (114), (118), (119), (121), (122), (124),
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | |            (126), (127), (134), (135), (136), (137), (140),
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | |            (141), (142), (144), (145), (146), (147), (149),
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | |            (150), (158), (159), (160), (161), (163), (164),
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | |            (165), (166), (169), (170), (171), (191), (192),
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | |            (193), (194), (195), (196), (197), (198), (199),
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | |            (201), (202), (203), (204), (205), (207), (208),
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | |            (209), (211), (212), (214), (215), (216), (217),
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | |            (218), (219), (220), (221), (223), (224), (225),
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | |            (227), (228), (229), (230), (231), (232), (233),
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | |            (234), (235), (236), (237), (245), (246), (247),
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | |            (248), (249), (256), (257), (258), (259), (267),
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | |            (268), (269), (270), (277), (299), (315), (327),
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | |            (329), (332), (336), (338), (340), (342), (344),
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | |            (348), (350), (361), (363), (364), (366), (368),
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | |            (374), (376), (5511), (5514), (5515), (5516),
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | |            (5517), (5518), (5519), (5520), (5526), (5527),
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | |            (7209), (7210), (7211), (7212), (7213), (7215),
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | |            (7522), (function-axioms) are inconsistent by
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | |            sub-proof #370.
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | |   (7523)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0)
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | BETA: splitting (7523) gives:
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | |   (7524)  all_57_5 = e0 & op(e2, e1) = e0
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | ALPHA: (7524) implies:
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | |   (7525)  all_57_5 = e0
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (208),
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | |            (209), (211), (212), (217), (221), (225), (230),
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | |            (231), (232), (233), (234), (235), (374), (5526),
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | |            (7373), (7376), (7379), (7391), (7525),
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | |            #948.
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | |   (7526)  all_57_10 = e0 & op(e2, e0) = e0
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | ALPHA: (7526) implies:
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | |   (7527)  op(e2, e0) = e0
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (7213), (7527), (function-axioms) are
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2470.
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.82  | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.82  | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | |   (7528)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 222.79/37.82  | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 222.79/37.82  | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | BETA: splitting (7528) gives:
% 222.79/37.82  | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | |   (7529)  all_57_7 = e2 & op(e1, e2) = e2
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7373), (7529) are inconsistent by sub-proof
% 222.79/37.82  | | | | | | | | | | | | | | | | | | |            #364.
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | |   (7530)  all_57_13 = e2 & op(e0, e2) = e2
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | ALPHA: (7530) implies:
% 222.79/37.82  | | | | | | | | | | | | | | | | | | |   (7531)  all_57_13 = e2
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7387), (7531) are inconsistent by sub-proof
% 222.79/37.82  | | | | | | | | | | | | | | | | | | |            #2327.
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.82  | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | End of split
% 222.79/37.82  | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | End of split
% 222.79/37.82  | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | End of split
% 222.79/37.82  | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | Case 2:
% 222.79/37.82  | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | |   (7532)  all_57_3 = e3 & op(e2, e2) = e3
% 222.79/37.82  | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | ALPHA: (7532) implies:
% 222.79/37.82  | | | | | | | | | | | | | | |   (7533)  all_57_3 = e3
% 222.79/37.82  | | | | | | | | | | | | | | |   (7534)  op(e2, e2) = e3
% 222.79/37.82  | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, e3, e2,
% 222.79/37.82  | | | | | | | | | | | | | | |              e2, simplifying with (7215), (7534) gives:
% 222.79/37.82  | | | | | | | | | | | | | | |   (7535)  e3 = e0
% 222.79/37.82  | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | COMBINE_EQS: (7533), (7535) imply:
% 222.79/37.82  | | | | | | | | | | | | | | |   (7536)  all_57_3 = e0
% 222.79/37.82  | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (45), (58),
% 222.79/37.82  | | | | | | | | | | | | | | |            (61), (64), (67), (73), (88), (94), (107), (111),
% 222.79/37.82  | | | | | | | | | | | | | | |            (113), (114), (118), (119), (121), (122), (124),
% 222.79/37.82  | | | | | | | | | | | | | | |            (126), (127), (134), (135), (136), (137), (140),
% 222.79/37.82  | | | | | | | | | | | | | | |            (141), (142), (144), (145), (146), (147), (149),
% 222.79/37.82  | | | | | | | | | | | | | | |            (150), (158), (159), (160), (161), (163), (164),
% 222.79/37.82  | | | | | | | | | | | | | | |            (165), (166), (169), (170), (171), (191), (192),
% 222.79/37.82  | | | | | | | | | | | | | | |            (193), (194), (195), (196), (197), (198), (199),
% 222.79/37.82  | | | | | | | | | | | | | | |            (201), (202), (203), (204), (205), (207), (208),
% 222.79/37.82  | | | | | | | | | | | | | | |            (209), (211), (212), (214), (215), (216), (217),
% 222.79/37.82  | | | | | | | | | | | | | | |            (218), (219), (220), (221), (223), (224), (225),
% 222.79/37.82  | | | | | | | | | | | | | | |            (227), (228), (229), (230), (231), (232), (233),
% 222.79/37.82  | | | | | | | | | | | | | | |            (234), (235), (236), (237), (245), (246), (247),
% 222.79/37.82  | | | | | | | | | | | | | | |            (248), (249), (256), (257), (258), (259), (267),
% 222.79/37.82  | | | | | | | | | | | | | | |            (268), (269), (270), (277), (299), (315), (327),
% 222.79/37.82  | | | | | | | | | | | | | | |            (329), (332), (336), (338), (340), (342), (344),
% 222.79/37.82  | | | | | | | | | | | | | | |            (348), (350), (361), (363), (364), (366), (368),
% 222.79/37.82  | | | | | | | | | | | | | | |            (374), (376), (5511), (5514), (5515), (5516),
% 222.79/37.82  | | | | | | | | | | | | | | |            (5517), (5518), (5519), (5520), (5526), (5527),
% 222.79/37.82  | | | | | | | | | | | | | | |            (7209), (7210), (7211), (7212), (7213), (7215),
% 222.79/37.82  | | | | | | | | | | | | | | |            (7536), (function-axioms) are inconsistent by
% 222.79/37.82  | | | | | | | | | | | | | | |            sub-proof #370.
% 222.79/37.82  | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | End of split
% 222.79/37.82  | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | Case 2:
% 222.79/37.82  | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | |   (7537)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 222.79/37.82  | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 222.79/37.82  | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | BETA: splitting (7537) gives:
% 222.79/37.82  | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | Case 1:
% 222.79/37.82  | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | |   (7538)  all_57_7 = e3 & op(e1, e2) = e3
% 222.79/37.82  | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | ALPHA: (7538) implies:
% 222.79/37.82  | | | | | | | | | | | | | | |   (7539)  all_57_7 = e3
% 222.79/37.82  | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | REF_CLOSE: (7), (7373), (7539) are inconsistent by sub-proof
% 222.79/37.82  | | | | | | | | | | | | | | |            #2269.
% 222.79/37.82  | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | Case 2:
% 222.79/37.82  | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | |   (7540)  all_57_13 = e3 & op(e0, e2) = e3
% 222.79/37.82  | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | ALPHA: (7540) implies:
% 222.79/37.82  | | | | | | | | | | | | | | |   (7541)  all_57_13 = e3
% 222.79/37.82  | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 222.79/37.82  | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | Case 1:
% 222.79/37.82  | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | |   (7542)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 222.79/37.82  | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 222.79/37.82  | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | BETA: splitting (7542) gives:
% 222.79/37.82  | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.82  | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | |   (7543)  all_57_1 = e1 & op(e3, e2) = e1
% 222.79/37.82  | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | ALPHA: (7543) implies:
% 222.79/37.82  | | | | | | | | | | | | | | | | |   (7544)  all_57_1 = e1
% 222.79/37.82  | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 222.79/37.82  | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.82  | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | |   (7545)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 222.79/37.82  | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 222.79/37.82  | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | BETA: splitting (7545) gives:
% 222.79/37.82  | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | |   (7546)  all_57_1 = e2 & op(e3, e2) = e2
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7544), (7546) are inconsistent by sub-proof
% 222.79/37.82  | | | | | | | | | | | | | | | | | | |            #2489.
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | |   (7547)  all_57_3 = e2 & op(e2, e2) = e2
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | ALPHA: (7547) implies:
% 222.79/37.82  | | | | | | | | | | | | | | | | | | |   (7548)  all_57_3 = e2
% 222.79/37.82  | | | | | | | | | | | | | | | | | | |   (7549)  op(e2, e2) = e2
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, e2, e2,
% 222.79/37.82  | | | | | | | | | | | | | | | | | | |              e2, simplifying with (7215), (7549) gives:
% 222.79/37.82  | | | | | | | | | | | | | | | | | | |   (7550)  e2 = e0
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7548), (7550) imply:
% 222.79/37.82  | | | | | | | | | | | | | | | | | | |   (7551)  all_57_3 = e0
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (45), (58),
% 222.79/37.82  | | | | | | | | | | | | | | | | | | |            (61), (64), (67), (73), (88), (94), (107), (111),
% 222.79/37.82  | | | | | | | | | | | | | | | | | | |            (113), (114), (118), (119), (121), (122), (124),
% 222.79/37.82  | | | | | | | | | | | | | | | | | | |            (126), (127), (134), (135), (136), (137), (140),
% 222.79/37.82  | | | | | | | | | | | | | | | | | | |            (141), (142), (144), (145), (146), (147), (149),
% 222.79/37.82  | | | | | | | | | | | | | | | | | | |            (150), (158), (159), (160), (161), (163), (164),
% 222.79/37.82  | | | | | | | | | | | | | | | | | | |            (165), (166), (169), (170), (171), (191), (192),
% 222.79/37.82  | | | | | | | | | | | | | | | | | | |            (193), (194), (195), (196), (197), (198), (199),
% 222.79/37.82  | | | | | | | | | | | | | | | | | | |            (201), (202), (203), (204), (205), (207), (208),
% 222.79/37.82  | | | | | | | | | | | | | | | | | | |            (209), (211), (212), (214), (215), (216), (217),
% 222.79/37.82  | | | | | | | | | | | | | | | | | | |            (218), (219), (220), (221), (223), (224), (225),
% 222.79/37.82  | | | | | | | | | | | | | | | | | | |            (227), (228), (229), (230), (231), (232), (233),
% 222.79/37.82  | | | | | | | | | | | | | | | | | | |            (234), (235), (236), (237), (245), (246), (247),
% 222.79/37.82  | | | | | | | | | | | | | | | | | | |            (248), (249), (256), (257), (258), (259), (267),
% 222.79/37.82  | | | | | | | | | | | | | | | | | | |            (268), (269), (270), (277), (299), (315), (327),
% 222.79/37.82  | | | | | | | | | | | | | | | | | | |            (329), (332), (336), (338), (340), (342), (344),
% 222.79/37.82  | | | | | | | | | | | | | | | | | | |            (348), (350), (361), (363), (364), (366), (368),
% 222.79/37.82  | | | | | | | | | | | | | | | | | | |            (374), (376), (5511), (5514), (5515), (5516),
% 222.79/37.82  | | | | | | | | | | | | | | | | | | |            (5517), (5518), (5519), (5520), (5526), (5527),
% 222.79/37.82  | | | | | | | | | | | | | | | | | | |            (7209), (7210), (7211), (7212), (7213), (7215),
% 222.79/37.82  | | | | | | | | | | | | | | | | | | |            (7551), (function-axioms) are inconsistent by
% 222.79/37.82  | | | | | | | | | | | | | | | | | | |            sub-proof #370.
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.82  | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.82  | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | |   (7552)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 222.79/37.82  | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 222.79/37.82  | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | BETA: splitting (7552) gives:
% 222.79/37.82  | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | |   (7553)  all_57_7 = e2 & op(e1, e2) = e2
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7373), (7553) are inconsistent by sub-proof
% 222.79/37.82  | | | | | | | | | | | | | | | | | | |            #364.
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | |   (7554)  all_57_13 = e2 & op(e0, e2) = e2
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7541), (7554) are inconsistent by sub-proof
% 222.79/37.82  | | | | | | | | | | | | | | | | | | |            #2146.
% 222.79/37.82  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.82  | | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | End of split
% 222.79/37.82  | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.82  | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | |   (7555)  all_57_3 = e1 & op(e2, e2) = e1
% 222.79/37.82  | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | ALPHA: (7555) implies:
% 222.79/37.82  | | | | | | | | | | | | | | | | |   (7556)  op(e2, e2) = e1
% 222.79/37.82  | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7215), (7556), (function-axioms) are
% 222.79/37.82  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2352.
% 222.79/37.82  | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | End of split
% 222.79/37.82  | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | Case 2:
% 222.79/37.82  | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | |   (7557)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 222.79/37.82  | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 222.79/37.82  | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | BETA: splitting (7557) gives:
% 222.79/37.82  | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.82  | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | |   (7558)  all_57_7 = e1 & op(e1, e2) = e1
% 222.79/37.82  | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | ALPHA: (7558) implies:
% 222.79/37.82  | | | | | | | | | | | | | | | | |   (7559)  all_57_7 = e1
% 222.79/37.82  | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7373), (7559) are inconsistent by sub-proof
% 222.79/37.82  | | | | | | | | | | | | | | | | |            #2211.
% 222.79/37.82  | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.82  | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | |   (7560)  all_57_13 = e1 & op(e0, e2) = e1
% 222.79/37.82  | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | ALPHA: (7560) implies:
% 222.79/37.82  | | | | | | | | | | | | | | | | |   (7561)  all_57_13 = e1
% 222.79/37.82  | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | COMBINE_EQS: (7541), (7561) imply:
% 222.79/37.82  | | | | | | | | | | | | | | | | |   (7562)  e3 = e1
% 222.79/37.82  | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | SIMP: (7562) implies:
% 222.79/37.82  | | | | | | | | | | | | | | | | |   (7563)  e3 = e1
% 222.79/37.82  | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | COMBINE_EQS: (7376), (7563) imply:
% 222.79/37.82  | | | | | | | | | | | | | | | | |   (7564)  all_57_6 = e1
% 222.79/37.82  | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 222.79/37.82  | | | | | | | | | | | | | | | | |            (212), (217), (374), (5526), (7373), (7564),
% 222.79/37.82  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.79/37.82  | | | | | | | | | | | | | | | | |            #1735.
% 222.79/37.82  | | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | | End of split
% 222.79/37.82  | | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | | End of split
% 222.79/37.82  | | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | End of split
% 222.79/37.82  | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | End of split
% 222.79/37.82  | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | Case 2:
% 222.79/37.82  | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | |   (7565)  all_57_7 = e3 & op(e1, e2) = e3
% 222.79/37.82  | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | ALPHA: (7565) implies:
% 222.79/37.82  | | | | | | | | | | | | |   (7566)  all_57_7 = e3
% 222.79/37.82  | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | REF_CLOSE: (7), (7373), (7566) are inconsistent by sub-proof
% 222.79/37.82  | | | | | | | | | | | | |            #2269.
% 222.79/37.82  | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | End of split
% 222.79/37.82  | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | Case 2:
% 222.79/37.82  | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | |   (7567)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 222.79/37.82  | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 222.79/37.82  | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 222.79/37.82  | | | | | | | | | | | |            (212), (374), (5526), (7567), (function-axioms)
% 222.79/37.82  | | | | | | | | | | | |            are inconsistent by sub-proof #1786.
% 222.79/37.82  | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | End of split
% 222.79/37.82  | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | Case 2:
% 222.79/37.82  | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | |   (7568)  all_57_13 = e0 & op(e0, e2) = e0
% 222.79/37.82  | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | ALPHA: (7568) implies:
% 222.79/37.82  | | | | | | | | | | |   (7569)  op(e0, e2) = e0
% 222.79/37.82  | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | REF_CLOSE: (159), (7211), (7569), (function-axioms) are
% 222.79/37.82  | | | | | | | | | | |            inconsistent by sub-proof #2332.
% 222.79/37.82  | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | End of split
% 222.79/37.82  | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | End of split
% 222.79/37.82  | | | | | | | | | 
% 222.79/37.82  | | | | | | | | End of split
% 222.79/37.82  | | | | | | | | 
% 222.79/37.82  | | | | | | | End of split
% 222.79/37.82  | | | | | | | 
% 222.79/37.82  | | | | | | End of split
% 222.79/37.82  | | | | | | 
% 222.79/37.82  | | | | | End of split
% 222.79/37.82  | | | | | 
% 222.79/37.82  | | | | Case 2:
% 222.79/37.82  | | | | | 
% 222.79/37.82  | | | | |   (7570)  all_10_2 = e1
% 222.79/37.82  | | | | |   (7571)  ( ~ (all_10_0 = e2) & op(all_10_1, e3) = all_10_0 & op(e3,
% 222.79/37.82  | | | | |               e1) = all_10_1 & $i(all_10_0) & $i(all_10_1)) | ( ~
% 222.79/37.82  | | | | |             (all_10_1 = e0) & op(e3, e1) = all_10_1 & $i(all_10_1))
% 222.79/37.82  | | | | | 
% 222.79/37.82  | | | | | COMBINE_EQS: (331), (7570) imply:
% 222.79/37.82  | | | | |   (7572)  all_36_2 = e1
% 222.79/37.82  | | | | | 
% 222.79/37.82  | | | | | REDUCE: (338), (7570) imply:
% 222.79/37.82  | | | | |   (7573)   ~ (all_53_1 = e1)
% 222.79/37.82  | | | | | 
% 222.79/37.82  | | | | | REDUCE: (340), (7570) imply:
% 222.79/37.82  | | | | |   (7574)   ~ (all_53_2 = e1)
% 222.79/37.82  | | | | | 
% 222.79/37.82  | | | | | REDUCE: (342), (7570) imply:
% 222.79/37.82  | | | | |   (7575)   ~ (all_53_3 = e1)
% 222.79/37.82  | | | | | 
% 222.79/37.82  | | | | | REDUCE: (344), (7570) imply:
% 222.79/37.82  | | | | |   (7576)   ~ (all_53_4 = e1)
% 222.79/37.82  | | | | | 
% 222.79/37.82  | | | | | REDUCE: (346), (7570) imply:
% 222.79/37.82  | | | | |   (7577)   ~ (all_53_8 = e1)
% 222.79/37.82  | | | | | 
% 222.79/37.82  | | | | | REDUCE: (348), (7570) imply:
% 222.79/37.82  | | | | |   (7578)   ~ (all_53_12 = e1)
% 222.79/37.82  | | | | | 
% 222.79/37.82  | | | | | BETA: splitting (232) gives:
% 222.79/37.82  | | | | | 
% 222.79/37.82  | | | | | Case 1:
% 222.79/37.82  | | | | | | 
% 222.79/37.82  | | | | | |   (7579)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 &
% 222.79/37.82  | | | | | |             op(e2, e3) = e1)
% 222.79/37.82  | | | | | | 
% 222.79/37.82  | | | | | | BETA: splitting (7579) gives:
% 222.79/37.82  | | | | | | 
% 222.79/37.82  | | | | | | Case 1:
% 222.79/37.82  | | | | | | | 
% 222.79/37.82  | | | | | | |   (7580)  all_57_0 = e1 & op(e3, e3) = e1
% 222.79/37.82  | | | | | | | 
% 222.79/37.82  | | | | | | | ALPHA: (7580) implies:
% 222.79/37.82  | | | | | | |   (7581)  all_57_0 = e1
% 222.79/37.82  | | | | | | |   (7582)  op(e3, e3) = e1
% 222.79/37.82  | | | | | | | 
% 222.79/37.82  | | | | | | | BETA: splitting (49) gives:
% 222.79/37.82  | | | | | | | 
% 222.79/37.82  | | | | | | | Case 1:
% 222.79/37.82  | | | | | | | | 
% 222.79/37.82  | | | | | | | |   (7583)   ~ (all_12_2 = e3)
% 222.79/37.82  | | | | | | | | 
% 222.79/37.82  | | | | | | | | REDUCE: (325), (7583) imply:
% 222.79/37.82  | | | | | | | |   (7584)   ~ (all_4_2 = e3)
% 222.79/37.82  | | | | | | | | 
% 222.79/37.82  | | | | | | | | BETA: splitting (52) gives:
% 222.79/37.82  | | | | | | | | 
% 222.79/37.82  | | | | | | | | Case 1:
% 222.79/37.82  | | | | | | | | | 
% 222.79/37.82  | | | | | | | | |   (7585)   ~ (all_14_2 = e0)
% 222.79/37.82  | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | REDUCE: (328), (7585) imply:
% 222.79/37.82  | | | | | | | | |   (7586)   ~ (all_8_2 = e0)
% 222.79/37.82  | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | BETA: splitting (55) gives:
% 222.79/37.82  | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | Case 1:
% 222.79/37.82  | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | |   (7587)   ~ (all_16_2 = e1)
% 222.79/37.82  | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | REDUCE: (324), (7587) imply:
% 222.79/37.82  | | | | | | | | | |   (7588)   ~ (all_8_2 = e1)
% 222.79/37.82  | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | BETA: splitting (200) gives:
% 222.79/37.82  | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | Case 1:
% 222.79/37.82  | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | |   (7589)  all_55_5 = e3
% 222.79/37.82  | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | COMBINE_EQS: (266), (7589) imply:
% 222.79/37.82  | | | | | | | | | | |   (7590)  all_8_2 = e3
% 222.79/37.82  | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | REDUCE: (375), (7590) imply:
% 222.79/37.82  | | | | | | | | | | |   (7591)  $false
% 222.79/37.82  | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | CLOSE: (7591) is inconsistent.
% 222.79/37.82  | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | Case 2:
% 222.79/37.82  | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | |   (7592)   ~ (all_55_5 = e3)
% 222.79/37.82  | | | | | | | | | | |   (7593)  all_55_5 = e2 | all_55_5 = e1 | all_55_5 = e0
% 222.79/37.82  | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | BETA: splitting (7593) gives:
% 222.79/37.82  | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | Case 1:
% 222.79/37.82  | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | |   (7594)  all_55_5 = e2
% 222.79/37.82  | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | COMBINE_EQS: (266), (7594) imply:
% 222.79/37.82  | | | | | | | | | | | |   (7595)  all_8_2 = e2
% 222.79/37.82  | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | REDUCE: (349), (7595) imply:
% 222.79/37.82  | | | | | | | | | | | |   (7596)   ~ (all_53_1 = e2)
% 222.79/37.82  | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | REDUCE: (352), (7595) imply:
% 222.79/37.82  | | | | | | | | | | | |   (7597)   ~ (all_53_4 = e2)
% 222.79/37.82  | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | REDUCE: (354), (7595) imply:
% 222.79/37.82  | | | | | | | | | | | |   (7598)   ~ (all_53_6 = e2)
% 222.79/37.82  | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | REDUCE: (356), (7595) imply:
% 222.79/37.82  | | | | | | | | | | | |   (7599)   ~ (all_53_7 = e2)
% 222.79/37.82  | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | REDUCE: (358), (7595) imply:
% 222.79/37.82  | | | | | | | | | | | |   (7600)   ~ (all_53_9 = e2)
% 222.79/37.82  | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | REDUCE: (360), (7595) imply:
% 222.79/37.82  | | | | | | | | | | | |   (7601)   ~ (all_53_13 = e2)
% 222.79/37.82  | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | REDUCE: (375), (7595) imply:
% 222.79/37.82  | | | | | | | | | | | |   (7602)   ~ (e3 = e2)
% 222.79/37.82  | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | BETA: splitting (224) gives:
% 222.79/37.82  | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | Case 1:
% 222.79/37.82  | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | |   (7603)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 222.79/37.82  | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 222.79/37.82  | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | BETA: splitting (7603) gives:
% 222.79/37.82  | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | Case 1:
% 222.79/37.82  | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | |   (7604)  all_57_2 = e2 & op(e2, e3) = e2
% 222.79/37.82  | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | | REF_CLOSE: (168), (7596), (7604), (function-axioms) are
% 222.79/37.82  | | | | | | | | | | | | | |            inconsistent by sub-proof #2504.
% 222.79/37.82  | | | | | | | | | | | | | | 
% 222.79/37.82  | | | | | | | | | | | | | Case 2:
% 222.79/37.82  | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | |   (7605)  all_57_3 = e2 & op(e2, e2) = e2
% 222.79/37.83  | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | ALPHA: (7605) implies:
% 222.79/37.83  | | | | | | | | | | | | | |   (7606)  all_57_3 = e2
% 222.79/37.83  | | | | | | | | | | | | | |   (7607)  op(e2, e2) = e2
% 222.79/37.83  | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 222.79/37.83  | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | Case 1:
% 222.79/37.83  | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | |   (7608)   ~ (all_24_2 = e0)
% 222.79/37.83  | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | REDUCE: (315), (7608) imply:
% 222.79/37.83  | | | | | | | | | | | | | | |   (7609)   ~ (all_6_2 = e0)
% 222.79/37.83  | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | BETA: splitting (76) gives:
% 222.79/37.83  | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | Case 1:
% 222.79/37.83  | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | |   (7610)   ~ (all_30_2 = e1)
% 222.79/37.83  | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | REDUCE: (330), (7610) imply:
% 222.79/37.83  | | | | | | | | | | | | | | | |   (7611)   ~ (all_4_2 = e1)
% 222.79/37.83  | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 222.79/37.83  | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.83  | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | |   (7612)  all_55_15 = e3
% 222.79/37.83  | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (7612) imply:
% 222.79/37.83  | | | | | | | | | | | | | | | | |   (7613)  all_4_2 = e3
% 222.79/37.83  | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | REDUCE: (7584), (7613) imply:
% 222.79/37.83  | | | | | | | | | | | | | | | | |   (7614)  $false
% 222.79/37.83  | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | CLOSE: (7614) is inconsistent.
% 222.79/37.83  | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.83  | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | |   (7615)   ~ (all_55_15 = e3)
% 222.79/37.83  | | | | | | | | | | | | | | | | |   (7616)  all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 222.79/37.83  | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | BETA: splitting (7616) gives:
% 222.79/37.83  | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | |   (7617)  all_55_15 = e2
% 222.79/37.83  | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (7617) imply:
% 222.79/37.83  | | | | | | | | | | | | | | | | | |   (7618)  all_4_2 = e2
% 222.79/37.83  | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | REDUCE: (373), (7618) imply:
% 222.79/37.83  | | | | | | | | | | | | | | | | | |   (7619)  $false
% 222.79/37.83  | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | CLOSE: (7619) is inconsistent.
% 222.79/37.83  | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | |   (7620)   ~ (all_55_15 = e2)
% 222.79/37.83  | | | | | | | | | | | | | | | | | |   (7621)  all_55_15 = e1 | all_55_15 = e0
% 222.79/37.83  | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | BETA: splitting (7621) gives:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | |   (7622)  all_55_15 = e1
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (7622) imply:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | |   (7623)  all_4_2 = e1
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | REDUCE: (7611), (7623) imply:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | |   (7624)  $false
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | CLOSE: (7624) is inconsistent.
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | |   (7625)  all_55_15 = e0
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (7625) imply:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | |   (7626)  all_4_2 = e0
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | REDUCE: (351), (7626) imply:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | |   (7627)   ~ (all_53_3 = e0)
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | REDUCE: (370), (7626) imply:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | |   (7628)   ~ (all_53_12 = e0)
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | REDUCE: (371), (7626) imply:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | |   (7629)   ~ (all_53_13 = e0)
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | REDUCE: (372), (7626) imply:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | |   (7630)   ~ (all_53_14 = e0)
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | REDUCE: (7584), (7626) imply:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | |   (7631)   ~ (e3 = e0)
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | REDUCE: (7611), (7626) imply:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | |   (7632)   ~ (e1 = e0)
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | REDUCE: (36), (7626) imply:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | |   (7633)  op(e0, e0) = e0
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | BETA: splitting (88) gives:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | |   (7634)   ~ (all_38_2 = e2)
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | REDUCE: (249), (7634) imply:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | |   (7635)   ~ (all_6_2 = e2)
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | |   (7636)  all_55_10 = e3
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (374), (7636) are inconsistent by sub-proof
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | |            #2500.
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | |   (7637)   ~ (all_55_10 = e3)
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | |   (7638)  all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7638) gives:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | |   (7639)  all_55_10 = e2
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (7635), (7639) are inconsistent by
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2499.
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | |   (7640)   ~ (all_55_10 = e2)
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | |   (7641)  all_55_10 = e1 | all_55_10 = e0
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7641) gives:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | |   (7642)  all_55_10 = e1
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (336), (7642) imply:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | |   (7643)  all_6_2 = e1
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7643) implies:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | |   (7644)  all_6_2 = e1
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (361), (7644) imply:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | |   (7645)   ~ (all_53_6 = e1)
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (364), (7644) imply:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | |   (7646)   ~ (all_53_9 = e1)
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7635), (7644) imply:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | |   (7647)   ~ (e2 = e1)
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (7644) imply:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | |   (7648)  op(e1, e1) = e1
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | |   (7649)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (171), (7576), (7607), (7649),
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | |            #362.
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | |   (7650)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7650) gives:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | |   (7651)  all_57_7 = e1 & op(e1, e2) = e1
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (7645), (7651), (function-axioms) are
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2265.
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | |   (7652)  all_57_13 = e1 & op(e0, e2) = e1
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7652) implies:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | |   (7653)  op(e0, e2) = e1
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7654)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (168), (7573), (7607), (7654),
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | |            #361.
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7655)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7655) gives:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7656)  all_57_5 = e1 & op(e2, e1) = e1
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (7646), (7656), (function-axioms) are
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2305.
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7657)  all_57_10 = e1 & op(e2, e0) = e1
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7657) implies:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7658)  op(e2, e0) = e1
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_7, e1,
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (159), (7653) gives:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7659)  all_53_7 = e1
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_13,
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e0, e2, simplifying with (165), (7658) gives:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7660)  all_53_13 = e1
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7661)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (39), (374), (7582), (7648), (7658), (7661),
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #359.
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7662)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_52_21) = e1 & op(all_52_23, all_52_23) =
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(all_52_25, all_52_25) = e3 &
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_52_29) = e1 & op(all_52_31, all_52_31) =
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_29) & $i(all_52_31))
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7662) gives:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7663)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_23)
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7663) implies:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7664)  op(e1, e2) = all_52_19
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7665)  op(all_52_19, all_52_19) = e2
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_6,
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_19, e2, e1, simplifying with (163), (7664)
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7666)  all_53_6 = all_52_19
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (7666) imply:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7667)  all_55_9 = all_52_19
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (137), (7666) imply:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7668)   ~ (all_53_4 = all_52_19)
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7598), (7666) imply:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7669)   ~ (all_52_19 = e2)
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7645), (7666) imply:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7670)   ~ (all_52_19 = e1)
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7671)  all_55_1 = e3
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (7671) imply:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7672)  all_53_4 = e3
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7672) implies:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7673)  all_53_4 = e3
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7668), (7673) imply:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7674)   ~ (all_52_19 = e3)
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7674) implies:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7675)   ~ (all_52_19 = e3)
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7676)  all_55_9 = e3
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7667), (7675), (7676) are inconsistent by
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1603.
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7677)  all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (256), (7598), (7633), (7645), (7664),
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7665), (7677), (function-axioms) are inconsistent
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2157.
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7678)  all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (196), (270), (7576), (7582), (7597), (7665),
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7667), (7668), (7669), (7670), (7678),
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #357.
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7679)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_31)
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7648), (7653), (7679), (function-axioms) are
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #356.
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | |   (7680)  all_55_10 = e0
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (7609), (7680) are inconsistent by
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2118.
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | |   (7681)  all_38_2 = e2
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (7681) imply:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | |   (7682)  all_6_2 = e2
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (7682) imply:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | |   (7683)  op(e1, e1) = e2
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | |   (7684)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2)
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (168), (7582), (7596), (7684),
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | |            #355.
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | |   (7685)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e3) = e2)
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7685) gives:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | |   (7686)  all_57_6 = e2 & op(e1, e3) = e2
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7686) implies:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | |   (7687)  all_57_6 = e2
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | |   (7688)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e0)
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7688) gives:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | |   (7689)  all_57_0 = e0 & op(e3, e3) = e0
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7581), (7689) are inconsistent by sub-proof
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | |            #1812.
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | |   (7690)  all_57_2 = e0 & op(e2, e3) = e0
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7690) implies:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | |   (7691)  all_57_2 = e0
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | |   (7692)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7692) gives:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7693)  all_57_9 = e2 & op(e3, e0) = e2
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7693) implies:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7694)  all_57_9 = e2
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7695)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7695) gives:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7696)  all_57_12 = e2 & op(e0, e3) = e2
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7696) implies:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7697)  all_57_12 = e2
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7698)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e0)
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7698) gives:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7699)  all_57_6 = e0 & op(e1, e3) = e0
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7606), (7687), (7691), (7699) are inconsistent by
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #354.
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7700)  all_57_7 = e0 & op(e1, e2) = e0
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7700) implies:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7701)  all_57_7 = e0
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (169), (211),
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (213), (217), (230), (232), (236), (374), (7578),
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7633), (7687), (7691), (7694), (7697), (7701),
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #351.
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7702)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7702) gives:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7703)  all_57_8 = e0 & op(e1, e1) = e0
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (7609), (7703), (function-axioms) are
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2412.
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7704)  all_57_11 = e0 & op(e1, e0) = e0
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (7630), (7704), (function-axioms) are
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2341.
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7705)  all_57_13 = e2 & op(e0, e2) = e2
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7705) implies:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7706)  op(e0, e2) = e2
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (7599), (7706), (function-axioms) are
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2335.
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7707)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7707) gives:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7708)  all_57_14 = e2 & op(e0, e1) = e2
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7708) implies:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7709)  all_57_14 = e2
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7710)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7710) gives:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7711)  all_57_12 = e1 & op(e0, e3) = e1
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (7575), (7711), (function-axioms) are
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1947.
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7712)  all_57_13 = e1 & op(e0, e2) = e1
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7712) implies:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7713)  all_57_13 = e1
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7714)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e3)
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (7582), (7691), (7714),
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1064.
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7715)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e3) = e3)
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7715) gives:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7716)  all_57_6 = e3 & op(e1, e3) = e3
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7716) implies:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7717)  all_57_6 = e3
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7687), (7717) are inconsistent by sub-proof
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2463.
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7718)  all_57_12 = e3 & op(e0, e3) = e3
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7718) implies:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7719)  all_57_12 = e3
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7720)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e0)
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7720) gives:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7721)  all_57_6 = e0 & op(e1, e3) = e0
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7606), (7687), (7691), (7721) are inconsistent by
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #354.
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7722)  all_57_7 = e0 & op(e1, e2) = e0
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7722) implies:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7723)  all_57_7 = e0
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7724)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7724) gives:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7725)  all_57_1 = e3 & op(e3, e2) = e3
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7725) implies:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7726)  all_57_1 = e3
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7727)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7727) gives:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7728)  all_57_6 = e3 & op(e1, e3) = e3
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7728) implies:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7729)  all_57_6 = e3
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7687), (7729) imply:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7730)  e3 = e2
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7730) implies:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7731)  e3 = e2
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7719), (7731) imply:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7732)  all_57_12 = e2
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (169), (211),
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (213), (217), (230), (232), (236), (374), (7578),
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7633), (7687), (7691), (7694), (7723), (7732),
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #351.
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7733)  all_57_7 = e3 & op(e1, e2) = e3
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7733) implies:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7734)  all_57_7 = e3
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (226), (227), (228),
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7713), (7726), (7734) are inconsistent by
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1214.
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7735)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7735) gives:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7736)  all_57_8 = e3 & op(e1, e1) = e3
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7736) implies:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7737)  op(e1, e1) = e3
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (374), (7737), (function-axioms) are
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2468.
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7738)  all_57_11 = e3 & op(e1, e0) = e3
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7738) implies:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7739)  all_57_11 = e3
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.83  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7740)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7740) gives:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7741)  all_57_6 = e1 & op(e1, e3) = e1
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7741) implies:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7742)  all_57_6 = e1
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (234), (7582), (7691), (7719),
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7742), (function-axioms) are inconsistent by
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #350.
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7743)  all_57_7 = e1 & op(e1, e2) = e1
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7743) implies:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7744)  all_57_7 = e1
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (39), (214), (7609), (7687),
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7739), (7744), (function-axioms) are inconsistent
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #349.
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7745)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (7683), (7739), (7745),
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2217.
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7746)  all_57_3 = e3 & op(e2, e2) = e3
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7746) implies:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7747)  op(e2, e2) = e3
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7607), (7747), (function-axioms) are
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2298.
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7748)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7748) gives:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7749)  all_57_7 = e3 & op(e1, e2) = e3
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7749) implies:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7750)  all_57_7 = e3
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7723), (7750) are inconsistent by sub-proof
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2269.
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7751)  all_57_13 = e3 & op(e0, e2) = e3
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7751) implies:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7752)  all_57_13 = e3
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7713), (7752) are inconsistent by sub-proof
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2268.
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7753)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7753) gives:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7754)  all_57_8 = e0 & op(e1, e1) = e0
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (7609), (7754), (function-axioms) are
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2412.
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7755)  all_57_11 = e0 & op(e1, e0) = e0
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (7630), (7755), (function-axioms) are
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2341.
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7756)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7633), (7709), (7756),
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1179.
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7757)  all_57_15 = e2 & op(e0, e0) = e2
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7757) implies:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7758)  op(e0, e0) = e2
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (373), (7758), (function-axioms) are
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2334.
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7759)  all_57_10 = e2 & op(e2, e0) = e2
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (7601), (7759), (function-axioms) are
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2432.
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | |   (7760)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (39), (161),
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | |            (214), (215), (217), (373), (374), (7609), (7630),
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | |            (7683), (7760), (function-axioms) are inconsistent
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #346.
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | |   (7761)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = e0)
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (160), (7627), (7687), (7761),
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | |            #1670.
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | |   (7762)  all_57_12 = e2 & op(e0, e3) = e2
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7762) implies:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | |   (7763)  op(e0, e3) = e2
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | |   (7764)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7764) gives:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | |   (7765)  all_57_9 = e2 & op(e3, e0) = e2
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7765) implies:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | |   (7766)  op(e3, e0) = e2
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_3, e2,
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, simplifying with (160), (7763) gives:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | |   (7767)  all_53_3 = e2
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_12,
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, e3, simplifying with (169), (7766) gives:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | |   (7768)  all_53_12 = e2
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | |   (7769)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | |             op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | |               all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | |               all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | |               all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7769) gives:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7770)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | |           all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_7)
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7607), (7766), (7770), (function-axioms) are
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2296.
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7771)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | |           all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | |           & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_15)
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7771) implies:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7772)  op(e2, e3) = all_52_9
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7773)  op(all_52_9, all_52_9) = e3
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_1,
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_9, e3, e2, simplifying with (168), (7772)
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7774)  all_53_1 = all_52_9
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (7774) imply:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7775)  all_55_4 = all_52_9
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7596), (7774) imply:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7776)   ~ (all_52_9 = e2)
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7573), (7774) imply:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7777)   ~ (all_52_9 = e1)
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7778)  all_55_4 = e3
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7775), (7778) imply:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7779)  all_52_9 = e3
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7779) implies:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7780)  all_52_9 = e3
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7773), (7780) imply:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7781)  op(e3, e3) = e3
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7582), (7781), (function-axioms) are
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2495.
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7782)   ~ (all_55_4 = e3)
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7783)  all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7775), (7782) imply:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7784)   ~ (all_52_9 = e3)
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7633), (7773), (7775), (7776), (7777), (7783),
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7784), (function-axioms) are inconsistent by
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #343.
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | |   (7785)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | |             & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | |               all_52_21) = e1 & op(all_52_23, all_52_23) =
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | |             = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | |             & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(all_52_25, all_52_25) = e3 &
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | |             op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | |               all_52_29) = e1 & op(all_52_31, all_52_31) =
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | |             = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_29) & $i(all_52_31))
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (7607), (7683), (7763), (7785),
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | |            #2259.
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | |   (7786)  all_57_10 = e2 & op(e2, e0) = e2
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (7601), (7786), (function-axioms) are
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2432.
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | |   (7787)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (39), (161),
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | |            (214), (215), (217), (373), (374), (7609), (7630),
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | |            (7683), (7787), (function-axioms) are inconsistent
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #346.
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.84  | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | End of split
% 222.79/37.84  | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | End of split
% 222.79/37.84  | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | Case 2:
% 222.79/37.84  | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | |   (7788)  all_30_2 = e1
% 222.79/37.84  | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | COMBINE_EQS: (330), (7788) imply:
% 222.79/37.84  | | | | | | | | | | | | | | | |   (7789)  all_4_2 = e1
% 222.79/37.84  | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | SIMP: (7789) implies:
% 222.79/37.84  | | | | | | | | | | | | | | | |   (7790)  all_4_2 = e1
% 222.79/37.84  | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | REDUCE: (362), (7790) imply:
% 222.79/37.84  | | | | | | | | | | | | | | | |   (7791)   ~ (all_53_7 = e1)
% 222.79/37.84  | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | REDUCE: (371), (7790) imply:
% 222.79/37.84  | | | | | | | | | | | | | | | |   (7792)   ~ (all_53_13 = e1)
% 222.79/37.84  | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | REDUCE: (7584), (7790) imply:
% 222.79/37.84  | | | | | | | | | | | | | | | |   (7793)   ~ (e3 = e1)
% 222.79/37.84  | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | REDUCE: (373), (7790) imply:
% 222.79/37.84  | | | | | | | | | | | | | | | |   (7794)   ~ (e2 = e1)
% 222.79/37.84  | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | REDUCE: (36), (7790) imply:
% 222.79/37.84  | | | | | | | | | | | | | | | |   (7795)  op(e0, e0) = e1
% 222.79/37.84  | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 222.79/37.84  | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.84  | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | |   (7796)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 222.79/37.84  | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 222.79/37.84  | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (171), (7576), (7607), (7796),
% 222.79/37.84  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.79/37.84  | | | | | | | | | | | | | | | | |            #362.
% 222.79/37.84  | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.84  | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | |   (7797)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 222.79/37.84  | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 222.79/37.84  | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | BETA: splitting (7797) gives:
% 222.79/37.84  | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | |   (7798)  all_57_7 = e1 & op(e1, e2) = e1
% 222.79/37.84  | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | ALPHA: (7798) implies:
% 222.79/37.84  | | | | | | | | | | | | | | | | | |   (7799)  all_57_7 = e1
% 222.79/37.84  | | | | | | | | | | | | | | | | | |   (7800)  op(e1, e2) = e1
% 222.79/37.84  | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | |   (7801)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 222.79/37.84  | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (168), (7573), (7607), (7801),
% 222.79/37.84  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.79/37.84  | | | | | | | | | | | | | | | | | | |            #361.
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | |   (7802)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 222.79/37.84  | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | BETA: splitting (7802) gives:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | |   (7803)  all_57_5 = e1 & op(e2, e1) = e1
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | ALPHA: (7803) implies:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | |   (7804)  all_57_5 = e1
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | |   (7805)  op(e2, e1) = e1
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_6, e1,
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | |              e2, e1, simplifying with (163), (7800) gives:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | |   (7806)  all_53_6 = e1
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_9, e1,
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (166), (7805) gives:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | |   (7807)  all_53_9 = e1
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | REDUCE: (364), (7807) imply:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | |   (7808)   ~ (all_6_2 = e1)
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | SIMP: (7808) implies:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | |   (7809)   ~ (all_6_2 = e1)
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | |   (7810)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | |             all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | |             op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | |               all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | |             $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | |             $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | |               all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | |             & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | |               all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | |             & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | |             $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7810) gives:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | |   (7811)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | |           all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | |           op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | |             all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_7)
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7811) implies:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | |   (7812)  op(e3, e0) = all_52_7
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | |   (7813)  op(e3, e3) = all_52_1
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | |   (7814)  op(all_52_7, all_52_7) = e0
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | |   (7815)  op(all_52_1, all_52_1) = e3
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | |   (7816)  all_55_10 = e3
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (374), (7816) are inconsistent by sub-proof
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | |            #2500.
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | |   (7817)   ~ (all_55_10 = e3)
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | |   (7818)  all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7818) gives:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | |   (7819)  all_55_10 = e2
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (336), (7819) imply:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | |   (7820)  all_6_2 = e2
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7820) implies:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | |   (7821)  all_6_2 = e2
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (7821) imply:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | |   (7822)  op(e1, e1) = e2
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | |   (7823)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2)
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7823) gives:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7824)  all_57_0 = e2 & op(e3, e3) = e2
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7824) implies:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7825)  op(e3, e3) = e2
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7607), (7813), (7815), (7825),
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | |            #1951.
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7826)  all_57_2 = e2 & op(e2, e3) = e2
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (7596), (7826), (function-axioms) are
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2504.
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | |   (7827)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e3) = e2)
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7827) gives:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7828)  all_57_6 = e2 & op(e1, e3) = e2
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7828) implies:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7829)  all_57_6 = e2
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (39), (214), (217),
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | |            (374), (7609), (7799), (7829), (function-axioms)
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #342.
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7830)  all_57_12 = e2 & op(e0, e3) = e2
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7830) implies:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7831)  all_57_12 = e2
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7832)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e2)
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (171), (7597), (7607), (7813), (7815),
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7832), (function-axioms) are inconsistent by
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #341.
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7833)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e2)
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7833) gives:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7834)  all_57_4 = e2 & op(e3, e1) = e2
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7834) implies:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7835)  all_57_4 = e2
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (39), (218), (221),
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (374), (7609), (7804), (7835), (function-axioms)
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #339.
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7836)  all_57_9 = e2 & op(e3, e0) = e2
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7836) implies:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7837)  op(e3, e0) = e2
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7838)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7838) gives:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_12,
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, e3, simplifying with (169), (7837) gives:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7839)  all_53_12 = e2
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (169), (7607), (7812), (7814), (7839),
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #338.
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7840)  all_57_13 = e2 & op(e0, e2) = e2
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7840) implies:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7841)  op(e0, e2) = e2
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (7599), (7841), (function-axioms) are
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2335.
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7842)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7842) gives:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7843)  all_57_14 = e2 & op(e0, e1) = e2
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7843) implies:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7844)  all_57_14 = e2
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7845)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e3)
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7845) gives:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7846)  all_57_4 = e3 & op(e3, e1) = e3
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7846) implies:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7847)  all_57_4 = e3
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7848)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7848) gives:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7849)  all_57_12 = e3 & op(e0, e3) = e3
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (218), (219),
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (220), (221), (374), (7831), (7844), (7847),
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7849), (function-axioms) are inconsistent by
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1873.
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7850)  all_57_13 = e3 & op(e0, e2) = e3
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7850) implies:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7851)  all_57_13 = e3
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7852)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e0)
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7852) gives:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7853)  all_57_4 = e0 & op(e3, e1) = e0
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7853) implies:
% 222.79/37.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7854)  all_57_4 = e0
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7847), (7854) imply:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7855)  e3 = e0
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7851), (7855) imply:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7856)  all_57_13 = e0
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (210), (218),
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (219), (220), (221), (374), (7795), (7831),
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7844), (7847), (7856), (function-axioms) are
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1871.
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7857)  all_57_5 = e0 & op(e2, e1) = e0
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7804), (7857) are inconsistent by sub-proof
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #942.
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7858)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (39), (7609), (7844), (7858),
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2411.
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7859)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7859) gives:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7860)  all_57_14 = e3 & op(e0, e1) = e3
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7860) implies:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7861)  all_57_14 = e3
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7844), (7861) imply:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7862)  e3 = e2
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7862) implies:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7863)  e3 = e2
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7847), (7863) imply:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7864)  all_57_4 = e2
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (218), (219),
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (220), (221), (374), (7844), (7864),
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2370.
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7865)  all_57_15 = e3 & op(e0, e0) = e3
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7865) implies:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7866)  all_57_15 = e3
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7867)  op(e0, e0) = e3
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (160), (207),
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (208), (211), (212), (214), (215), (217), (222),
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (223), (224), (225), (234), (374), (7575), (7582),
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7606), (7607), (7609), (7822), (7844), (7866),
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7867), (function-axioms) are inconsistent by
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #333.
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7868)  all_57_5 = e3 & op(e2, e1) = e3
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7868) implies:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7869)  all_57_5 = e3
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (159), (207),
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (209), (210), (218), (219), (7599), (7609),
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7795), (7822), (7844), (7869), (function-axioms)
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2174.
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7870)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e1) = e3)
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (39), (374), (7844), (7870),
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1890.
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7871)  all_57_15 = e2 & op(e0, e0) = e2
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7871) implies:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7872)  op(e0, e0) = e2
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7795), (7872), (function-axioms) are
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2177.
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | |   (7873)  all_55_10 = e1 | all_55_10 = e0
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (7609), (7809), (7873) are inconsistent by
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1685.
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | |   (7874)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | |           all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | |           op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | |             all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | |           & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_15)
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7874) implies:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | |   (7875)  op(e2, e1) = all_52_13
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | |   (7876)  op(all_52_13, all_52_13) = e1
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | |   (7877)  all_55_10 = e3
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (374), (7877) are inconsistent by sub-proof
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | |            #2500.
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | |   (7878)   ~ (all_55_10 = e3)
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | |   (7879)  all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7879) gives:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | |   (7880)  all_55_10 = e2
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (336), (7880) imply:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | |   (7881)  all_6_2 = e2
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7881) implies:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | |   (7882)  all_6_2 = e2
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (7882) imply:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | |   (7883)  op(e1, e1) = e2
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | |   (7884)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7884) gives:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7885)  all_57_9 = e2 & op(e3, e0) = e2
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7885) implies:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7886)  op(e3, e0) = e2
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_13, e1, e2, simplifying with (7805), (7875)
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7887)  all_52_13 = e1
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_12,
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, e3, simplifying with (169), (7886) gives:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7888)  all_53_12 = e2
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7876), (7887) imply:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7889)  op(e1, e1) = e1
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7883), (7889), (function-axioms) are
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2423.
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7890)  all_57_10 = e2 & op(e2, e0) = e2
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (7601), (7890), (function-axioms) are
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2432.
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | |   (7891)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7891) gives:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7892)  all_57_11 = e2 & op(e1, e0) = e2
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7892) implies:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7893)  all_57_11 = e2
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (39), (214), (217),
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | |            (374), (7609), (7799), (7893), (function-axioms)
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #348.
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7894)  all_57_15 = e2 & op(e0, e0) = e2
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7894) implies:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7895)  op(e0, e0) = e2
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7795), (7895), (function-axioms) are
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2177.
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | |   (7896)  all_55_10 = e1 | all_55_10 = e0
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (7609), (7809), (7896) are inconsistent by
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1685.
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | |   (7897)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | |             & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | |             & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | |               all_52_21) = e1 & op(all_52_23, all_52_23) =
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | |             all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | |             = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | |             $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | |             & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | |             e0 & op(all_52_25, all_52_25) = e3 &
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | |             op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | |               all_52_29) = e1 & op(all_52_31, all_52_31) =
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | |             all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | |             = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | |             $i(all_52_29) & $i(all_52_31))
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7897) gives:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | |   (7898)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | |           all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | |           op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | |             all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | |           & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | |           & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | |           & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_23)
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7898) implies:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | |   (7899)  op(e1, e0) = all_52_23
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | |   (7900)  op(e1, e1) = all_52_21
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | |   (7901)  op(e1, e2) = all_52_19
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | |   (7902)  op(e1, e3) = all_52_17
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | |   (7903)  op(all_52_23, all_52_23) = e0
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | |   (7904)  op(all_52_21, all_52_21) = e1
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | |   (7905)  op(all_52_19, all_52_19) = e2
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | |   (7906)  op(all_52_17, all_52_17) = e3
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | |   (7907)  all_55_10 = e3
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (374), (7907) are inconsistent by sub-proof
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | |            #2500.
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | |   (7908)   ~ (all_55_10 = e3)
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | |   (7909)  all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7909) gives:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | |   (7910)  all_55_10 = e2
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (336), (7910) imply:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | |   (7911)  all_6_2 = e2
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7911) implies:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | |   (7912)  all_6_2 = e2
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (7912) imply:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | |   (7913)  op(e1, e1) = e2
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | |   (7914)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2)
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (168), (7582), (7596), (7914),
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | |            #355.
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | |   (7915)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e3) = e2)
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7915) gives:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7916)  all_57_6 = e2 & op(e1, e3) = e2
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7916) implies:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7917)  all_57_6 = e2
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7918)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (7799), (7917), (7918) are inconsistent
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1246.
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7919)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7919) gives:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7920)  all_57_8 = e3 & op(e1, e1) = e3
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7920) implies:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7921)  op(e1, e1) = e3
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (374), (7921), (function-axioms) are
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2468.
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7922)  all_57_11 = e3 & op(e1, e0) = e3
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7922) implies:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7923)  all_57_11 = e3
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7924)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e0)
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7924) gives:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7925)  all_57_6 = e0 & op(e1, e3) = e0
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7917), (7925) are inconsistent by sub-proof
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2386.
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7926)  all_57_7 = e0 & op(e1, e2) = e0
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7926) implies:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7927)  all_57_7 = e0
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7799), (7927) imply:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7928)  e1 = e0
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7928) implies:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7929)  e1 = e0
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7581), (7929) imply:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7930)  all_57_0 = e0
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (39), (160), (168), (195), (232), (336),
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (374), (7573), (7575), (7902), (7906), (7930),
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1545.
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7931)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7931) gives:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7932)  all_57_8 = e0 & op(e1, e1) = e0
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7932) implies:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7933)  op(e1, e1) = e0
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (163), (7800), (7900), (7901), (7905),
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7933), (function-axioms) are inconsistent by
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #332.
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7934)  all_57_11 = e0 & op(e1, e0) = e0
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7934) implies:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7935)  all_57_11 = e0
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7923), (7935) are inconsistent by sub-proof
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1595.
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7936)  all_57_12 = e2 & op(e0, e3) = e2
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7936) implies:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7937)  all_57_12 = e2
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7938)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e2)
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (171), (7582), (7597), (7938),
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #331.
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7939)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e2)
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7939) gives:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7940)  all_57_4 = e2 & op(e3, e1) = e2
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7940) implies:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7941)  all_57_4 = e2
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7942)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7942) gives:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7943)  all_57_9 = e2 & op(e3, e0) = e2
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7943) implies:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7944)  all_57_9 = e2
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7945)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e3)
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7945) gives:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7946)  all_57_0 = e3 & op(e3, e3) = e3
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7946) implies:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7947)  op(e3, e3) = e3
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7582), (7947), (function-axioms) are
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2495.
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7948)  all_57_1 = e3 & op(e3, e2) = e3
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7948) implies:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7949)  all_57_1 = e3
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7950)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e3)
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7950) gives:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7951)  all_57_4 = e3 & op(e3, e1) = e3
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7951) implies:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7952)  all_57_4 = e3
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (231), (235), (7581),
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7949), (7952) are inconsistent by sub-proof
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1808.
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7953)  all_57_5 = e3 & op(e2, e1) = e3
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7804), (7953) are inconsistent by sub-proof
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #386.
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7954)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e1) = e3)
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7954) gives:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7955)  all_57_8 = e3 & op(e1, e1) = e3
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7955) implies:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7956)  op(e1, e1) = e3
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (374), (7956), (function-axioms) are
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2468.
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7957)  all_57_14 = e3 & op(e0, e1) = e3
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7957) implies:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7958)  all_57_14 = e3
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7959)  all_57_15 = e0 & op(e0, e0) = e0
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7959) implies:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7960)  op(e0, e0) = e0
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7795), (7960), (function-axioms) are
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2290.
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.79/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7961)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7961) implies:
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7962)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0)
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7962) gives:
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7963)  all_57_12 = e0 & op(e0, e3) = e0
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7937), (7963) are inconsistent by sub-proof
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2185.
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7964)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7964) gives:
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7965)  all_57_13 = e0 & op(e0, e2) = e0
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7965) implies:
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7966)  all_57_13 = e0
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7967)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7967) gives:
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7968)  all_57_0 = e0 & op(e3, e3) = e0
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7968) implies:
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7969)  all_57_0 = e0
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (233), (7941), (7944), (7949),
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7969) are inconsistent by sub-proof #2450.
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7970)  all_57_1 = e0 & op(e3, e2) = e0
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7949), (7970) are inconsistent by sub-proof
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1811.
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7971)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7971) gives:
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7972)  all_57_4 = e0 & op(e3, e1) = e0
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7972) implies:
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7973)  all_57_4 = e0
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7941), (7973) imply:
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7974)  e2 = e0
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7606), (7974) imply:
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7975)  all_57_3 = e0
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (227), (228), (7949),
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7966), (7975) are inconsistent by sub-proof
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1758.
% 222.94/37.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7976)  all_57_9 = e0 & op(e3, e0) = e0
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7976) implies:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7977)  all_57_9 = e0
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7944), (7977) imply:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7978)  e2 = e0
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7606), (7978) imply:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7979)  all_57_3 = e0
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (227), (228), (7949),
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7966), (7979) are inconsistent by sub-proof
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1758.
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7980)  all_57_14 = e0 & op(e0, e1) = e0
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7980) implies:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7981)  all_57_14 = e0
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7958), (7981) are inconsistent by sub-proof
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2420.
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7982)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e3)
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7982) gives:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7983)  all_57_4 = e3 & op(e3, e1) = e3
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7941), (7983) are inconsistent by sub-proof
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #877.
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7984)  all_57_9 = e3 & op(e3, e0) = e3
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (165), (212), (7601), (7607),
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7795), (7899), (7903), (7984), (function-axioms)
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1901.
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7985)  all_57_10 = e2 & op(e2, e0) = e2
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (7601), (7985), (function-axioms) are
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2432.
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7986)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7607), (7795), (7899), (7903), (7986),
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1902.
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7987)  all_57_9 = e2 & op(e3, e0) = e2
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7987) implies:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7988)  op(e3, e0) = e2
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (7578), (7607), (7900), (7904), (7913),
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7988), (function-axioms) are inconsistent by
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1874.
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | |   (7989)  all_55_10 = e1 | all_55_10 = e0
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (7609), (7809), (7989) are inconsistent by
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1685.
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | |   (7990)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | |           all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | |           op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | |             all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | |           & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | |           & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | |           & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_31)
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7990) implies:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | |   (7991)  op(e0, e0) = all_52_31
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | |   (7992)  op(all_52_31, all_52_31) = e0
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (7609), (7795), (7991), (7992),
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | |            #2086.
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | End of split
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | End of split
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | Case 2:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | |   (7993)  all_57_10 = e1 & op(e2, e0) = e1
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (7792), (7993), (function-axioms) are
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2084.
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | End of split
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | End of split
% 222.94/37.86  | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | Case 2:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | |   (7994)  all_57_13 = e1 & op(e0, e2) = e1
% 222.94/37.86  | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (7791), (7994), (function-axioms) are
% 222.94/37.86  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #330.
% 222.94/37.86  | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | End of split
% 222.94/37.86  | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | End of split
% 222.94/37.86  | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | End of split
% 222.94/37.86  | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | Case 2:
% 222.94/37.86  | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | |   (7995)  all_24_2 = e0
% 222.94/37.86  | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | COMBINE_EQS: (315), (7995) imply:
% 222.94/37.86  | | | | | | | | | | | | | | |   (7996)  all_6_2 = e0
% 222.94/37.86  | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | COMBINE_EQS: (311), (7996) imply:
% 222.94/37.86  | | | | | | | | | | | | | | |   (7997)  all_34_2 = e0
% 222.94/37.86  | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | REDUCE: (350), (7996) imply:
% 222.94/37.86  | | | | | | | | | | | | | | |   (7998)   ~ (all_53_2 = e0)
% 222.94/37.86  | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | REDUCE: (361), (7996) imply:
% 222.94/37.86  | | | | | | | | | | | | | | |   (7999)   ~ (all_53_6 = e0)
% 222.94/37.86  | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | REDUCE: (363), (7996) imply:
% 222.94/37.86  | | | | | | | | | | | | | | |   (8000)   ~ (all_53_8 = e0)
% 222.94/37.86  | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | REDUCE: (364), (7996) imply:
% 222.94/37.86  | | | | | | | | | | | | | | |   (8001)   ~ (all_53_9 = e0)
% 222.94/37.86  | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | REDUCE: (366), (7996) imply:
% 222.94/37.86  | | | | | | | | | | | | | | |   (8002)   ~ (all_53_11 = e0)
% 222.94/37.86  | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | REDUCE: (368), (7996) imply:
% 222.94/37.86  | | | | | | | | | | | | | | |   (8003)   ~ (all_53_14 = e0)
% 222.94/37.86  | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | REDUCE: (374), (7996) imply:
% 222.94/37.86  | | | | | | | | | | | | | | |   (8004)   ~ (e3 = e0)
% 222.94/37.86  | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 222.94/37.86  | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | Case 1:
% 222.94/37.86  | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | |   (8005)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 222.94/37.86  | | | | | | | | | | | | | | | |             & op(e1, e2) = e0)
% 222.94/37.86  | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | REF_CLOSE: (163), (164), (7998), (7999), (8005),
% 222.94/37.86  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.94/37.86  | | | | | | | | | | | | | | | |            #2038.
% 222.94/37.86  | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | Case 2:
% 222.94/37.86  | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | |   (8006)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 222.94/37.86  | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 222.94/37.86  | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | BETA: splitting (8006) gives:
% 222.94/37.86  | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | Case 1:
% 222.94/37.86  | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | |   (8007)  all_57_8 = e0 & op(e1, e1) = e0
% 222.94/37.86  | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | ALPHA: (8007) implies:
% 222.94/37.86  | | | | | | | | | | | | | | | | |   (8008)  all_57_8 = e0
% 222.94/37.86  | | | | | | | | | | | | | | | | |   (8009)  op(e1, e1) = e0
% 222.94/37.86  | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | BETA: splitting (76) gives:
% 222.94/37.86  | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | Case 1:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | |   (8010)   ~ (all_30_2 = e1)
% 222.94/37.86  | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | REDUCE: (330), (8010) imply:
% 222.94/37.86  | | | | | | | | | | | | | | | | | |   (8011)   ~ (all_4_2 = e1)
% 222.94/37.86  | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | Case 1:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | |   (8012)  all_55_15 = e3
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (7584), (8012) are inconsistent by
% 222.94/37.86  | | | | | | | | | | | | | | | | | | |            sub-proof #2503.
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | Case 2:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | |   (8013)   ~ (all_55_15 = e3)
% 222.94/37.86  | | | | | | | | | | | | | | | | | | |   (8014)  all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | BETA: splitting (8014) gives:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | Case 1:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | |   (8015)  all_55_15 = e2
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (373), (8015) are inconsistent by sub-proof
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | |            #2502.
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | Case 2:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | |   (8016)   ~ (all_55_15 = e2)
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | |   (8017)  all_55_15 = e1 | all_55_15 = e0
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | BETA: splitting (8017) gives:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | |   (8018)  all_55_15 = e1
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (8011), (8018) are inconsistent by
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | |            sub-proof #2501.
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | |   (8019)  all_55_15 = e0
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (8019) imply:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | |   (8020)  all_4_2 = e0
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | SIMP: (8020) implies:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | |   (8021)  all_4_2 = e0
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | REDUCE: (351), (8021) imply:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | |   (8022)   ~ (all_53_3 = e0)
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | REDUCE: (362), (8021) imply:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | |   (8023)   ~ (all_53_7 = e0)
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | REDUCE: (373), (8021) imply:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | |   (8024)   ~ (e2 = e0)
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | REDUCE: (8011), (8021) imply:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | |   (8025)   ~ (e1 = e0)
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (8021) imply:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | |   (8026)  op(e0, e0) = e0
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | |   (8027)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e0)
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8027) gives:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | |   (8028)  all_57_0 = e0 & op(e3, e3) = e0
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7581), (8028) are inconsistent by sub-proof
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | |            #1812.
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | |   (8029)  all_57_2 = e0 & op(e2, e3) = e0
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8029) implies:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | |   (8030)  all_57_2 = e0
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | |   (8031)  op(e2, e3) = e0
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | |   (8032)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8032) gives:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | |   (8033)  all_57_1 = e0 & op(e3, e2) = e0
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8033) implies:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | |   (8034)  op(e3, e2) = e0
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_1, e0,
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (168), (8031) gives:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | |   (8035)  all_53_1 = e0
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_4, e0,
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (171), (8034) gives:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | |   (8036)  all_53_4 = e0
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (147), (8035) imply:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | |   (8037)   ~ (all_53_9 = e0)
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (8035) imply:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | |   (8038)   ~ (all_53_13 = e0)
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8038) implies:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | |   (8039)   ~ (all_53_13 = e0)
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (8036) imply:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | |   (8040)   ~ (all_53_12 = e0)
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8040) implies:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | |   (8041)   ~ (all_53_12 = e0)
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8042)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | |               all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | |               all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | |               all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8026), (8031), (8034), (8042),
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | |            #2037.
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8043)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | |               all_52_21) = e1 & op(all_52_23, all_52_23) =
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(all_52_25, all_52_25) = e3 &
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | |               all_52_29) = e1 & op(all_52_31, all_52_31) =
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_29) & $i(all_52_31))
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8043) gives:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8044)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | |           & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | |           & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | |           & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_23)
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8044) implies:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8045)  op(e1, e1) = all_52_21
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8046)  op(all_52_21, all_52_21) = e1
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (165), (169), (171), (207), (7576), (8003),
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8009), (8033), (8039), (8041), (8045), (8046),
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1842.
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8047)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | |           & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | |           & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | |           & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_31)
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8047) implies:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8048)  op(e0, e1) = all_52_29
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8049)  op(all_52_29, all_52_29) = e1
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_11,
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_29, e1, e0, simplifying with (158), (8048)
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8050)  all_53_11 = all_52_29
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (8050) imply:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8051)  all_55_14 = all_52_29
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (122), (8050) imply:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8052)   ~ (all_53_8 = all_52_29)
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (119), (8050) imply:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8053)   ~ (all_53_9 = all_52_29)
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8002), (8050) imply:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8054)   ~ (all_52_29 = e0)
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (82) gives:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8055)   ~ (all_34_2 = e0)
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7997), (8055) imply:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8056)  $false
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8056) is inconsistent.
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8057)  ( ~ (all_34_0 = e3) & op(all_34_1, e1) = all_34_0
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = all_34_1 & $i(all_34_0) &
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_34_1)) | ( ~ (all_34_1 = e2) & op(e1, e0)
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_34_1 & $i(all_34_1))
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8058)  all_55_2 = e3
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (8058) imply:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8059)  all_53_8 = e3
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8059) implies:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8060)  all_53_8 = e3
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (124), (8060) imply:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8061)   ~ (all_53_9 = e3)
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8061) implies:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8062)   ~ (all_53_9 = e3)
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8052), (8060) imply:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8063)   ~ (all_52_29 = e3)
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8063) implies:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8064)   ~ (all_52_29 = e3)
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8065)  all_55_6 = e3
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (8062), (8065) are inconsistent by
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2498.
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8066)  all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8066) gives:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8067)  all_55_6 = e2
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (7600), (8067) are inconsistent by
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2398.
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8068)  all_55_6 = e1 | all_55_6 = e0
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8068) gives:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8069)  all_55_6 = e1
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (8069) imply:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8070)  all_53_9 = e1
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8070) implies:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8071)  all_53_9 = e1
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8053), (8071) imply:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8072)   ~ (all_52_29 = e1)
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8072) implies:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8073)   ~ (all_52_29 = e1)
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (191), (7607), (8049), (8051), (8054), (8064),
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8073), (function-axioms) are inconsistent by
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2025.
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8074)  all_55_6 = e0
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (8001), (8074) are inconsistent by
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2162.
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8075)  all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8075) gives:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8076)  all_55_2 = e2
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (8076) imply:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8077)  all_53_8 = e2
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8077) implies:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8078)  all_53_8 = e2
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (124), (8078) imply:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8079)   ~ (all_53_9 = e2)
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (8078) imply:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8080)   ~ (all_53_12 = e2)
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8080) implies:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8081)   ~ (all_53_12 = e2)
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8082)  all_55_3 = e3
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (8082) imply:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8083)  all_53_12 = e3
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (114), (8083) imply:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8084)   ~ (all_53_13 = e3)
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8084) implies:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8085)   ~ (all_53_13 = e3)
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8086)  all_55_7 = e3
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (8085), (8086) are inconsistent by
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2109.
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8087)  all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8087) gives:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8088)  all_55_7 = e2
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (7601), (8088) are inconsistent by
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2171.
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8089)   ~ (all_55_7 = e2)
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8090)  all_55_7 = e1 | all_55_7 = e0
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8091)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (169), (7601), (8081), (8091),
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1952.
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8092)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8092) gives:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8093)  all_57_11 = e2 & op(e1, e0) = e2
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8093) implies:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8094)  op(e1, e0) = e2
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8090) gives:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8095)  all_55_7 = e1
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (8095) imply:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8096)  all_53_13 = e1
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8096) implies:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8097)  all_53_13 = e1
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (8097) imply:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8098)   ~ (all_53_9 = e1)
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8099)  all_55_6 = e3
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (8099) imply:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8100)  all_53_9 = e3
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8100) implies:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8101)  all_53_9 = e3
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (166), (8101) imply:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8102)  op(e2, e1) = e3
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8057), (8094), (8102), (function-axioms) are
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1173.
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.94/37.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8103)  all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (7600), (8001), (8098), (8103) are
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2160.
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8104)  all_55_7 = e0
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (8039), (8104) are inconsistent by
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2130.
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8105)  all_57_15 = e2 & op(e0, e0) = e2
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8105) implies:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8106)  op(e0, e0) = e2
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (373), (8106), (function-axioms) are
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2334.
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8107)  all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (7578), (8041), (8081), (8107) are
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1546.
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8108)  all_55_2 = e1 | all_55_2 = e0
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8108) gives:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8109)  all_55_2 = e1
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (7577), (8109) are inconsistent by
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2032.
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8110)  all_55_2 = e0
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (8110) imply:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8111)  all_53_8 = e0
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8111) implies:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8112)  all_53_8 = e0
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (8112) imply:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8113)   ~ (all_53_4 = e0)
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (171), (8034), (8113), (function-axioms) are
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1941.
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | |   (8114)  all_57_3 = e0 & op(e2, e2) = e0
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8114) implies:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | |   (8115)  all_57_3 = e0
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | |            (8030), (8115) are inconsistent by sub-proof
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | |            #2246.
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | |   (8116)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0)
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (163), (7999), (8023), (8116),
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | |            #2024.
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | |   (8117)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = e0)
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (164), (7998), (8022), (8117),
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | |            #1859.
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | End of split
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | End of split
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | End of split
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | End of split
% 222.94/37.87  | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | Case 2:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | |   (8118)  all_30_2 = e1
% 222.94/37.87  | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (330), (8118) imply:
% 222.94/37.87  | | | | | | | | | | | | | | | | | |   (8119)  all_4_2 = e1
% 222.94/37.87  | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | SIMP: (8119) implies:
% 222.94/37.87  | | | | | | | | | | | | | | | | | |   (8120)  all_4_2 = e1
% 222.94/37.87  | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | REDUCE: (362), (8120) imply:
% 222.94/37.87  | | | | | | | | | | | | | | | | | |   (8121)   ~ (all_53_7 = e1)
% 222.94/37.87  | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | REDUCE: (371), (8120) imply:
% 222.94/37.87  | | | | | | | | | | | | | | | | | |   (8122)   ~ (all_53_13 = e1)
% 222.94/37.87  | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | REDUCE: (373), (8120) imply:
% 222.94/37.87  | | | | | | | | | | | | | | | | | |   (8123)   ~ (e2 = e1)
% 222.94/37.87  | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | REDUCE: (36), (8120) imply:
% 222.94/37.87  | | | | | | | | | | | | | | | | | |   (8124)  op(e0, e0) = e1
% 222.94/37.87  | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | Case 1:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | |   (8125)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 222.94/37.87  | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (171), (7576), (7607), (8125),
% 222.94/37.87  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.94/37.87  | | | | | | | | | | | | | | | | | | |            #362.
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | Case 2:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | |   (8126)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 222.94/37.87  | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | BETA: splitting (8126) gives:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | Case 1:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | |   (8127)  all_57_7 = e1 & op(e1, e2) = e1
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | ALPHA: (8127) implies:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | |   (8128)  all_57_7 = e1
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | |   (8129)  op(e1, e2) = e1
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | |   (8130)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (168), (7573), (7607), (8130),
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | |            #361.
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | |   (8131)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8131) gives:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | |   (8132)  all_57_5 = e1 & op(e2, e1) = e1
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8132) implies:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | |   (8133)  all_57_5 = e1
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | |   (8134)  op(e2, e1) = e1
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_6, e1,
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | |              e2, e1, simplifying with (163), (8129) gives:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | |   (8135)  all_53_6 = e1
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_9, e1,
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (166), (8134) gives:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | |   (8136)  all_53_9 = e1
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (129), (8135) imply:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | |   (8137)   ~ (all_53_7 = e1)
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (119), (8136) imply:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | |   (8138)   ~ (all_53_11 = e1)
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | SIMP: (8138) implies:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | |   (8139)   ~ (all_53_11 = e1)
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (8136) imply:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | |   (8140)   ~ (all_53_13 = e1)
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | |   (8141)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | |             all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | |             op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | |               all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | |               all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | |             & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | |               all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (39), (374), (7582), (8009), (8134), (8141),
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | |            #329.
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | |   (8142)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | |             & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | |             & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | |               all_52_21) = e1 & op(all_52_23, all_52_23) =
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | |             all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | |             = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | |             & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(all_52_25, all_52_25) = e3 &
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | |             op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | |               all_52_29) = e1 & op(all_52_31, all_52_31) =
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | |             all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | |             = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_29) & $i(all_52_31))
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8142) gives:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | |   (8143)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | |           all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | |           op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | |             all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | |           & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | |           & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | |           & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_23)
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8143) implies:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | |   (8144)  op(e1, e1) = all_52_21
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | |   (8145)  op(e1, e2) = all_52_19
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | |   (8146)  op(all_52_19, all_52_19) = e2
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (163), (8009), (8129), (8144), (8145),
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | |            (8146), (function-axioms) are inconsistent by
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #332.
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | |   (8147)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | |           all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | |           op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | |             all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | |           & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | |           & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | |           & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_31)
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8147) implies:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | |   (8148)  op(e0, e0) = all_52_31
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | |   (8149)  op(e0, e1) = all_52_29
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | |   (8150)  op(e0, e2) = all_52_27
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | |   (8151)  op(e0, e3) = all_52_25
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | |   (8152)  op(all_52_29, all_52_29) = e1
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | |   (8153)  op(all_52_27, all_52_27) = e2
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | |   (8154)  op(all_52_25, all_52_25) = e3
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | |              all_52_31, e0, e0, simplifying with (8124), (8148)
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | |   (8155)  all_52_31 = e1
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_11,
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | |              all_52_29, e1, e0, simplifying with (158), (8149)
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | |   (8156)  all_53_11 = all_52_29
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_7,
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | |              all_52_27, e2, e0, simplifying with (159), (8150)
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | |   (8157)  all_53_7 = all_52_27
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_3,
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | |              all_52_25, e3, e0, simplifying with (160), (8151)
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | |   (8158)  all_53_3 = all_52_25
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (8156) imply:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | |   (8159)  all_55_14 = all_52_29
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (8157) imply:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | |   (8160)  all_55_13 = all_52_27
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (8158) imply:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | |   (8161)  all_55_12 = all_52_25
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (8158) imply:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | |   (8162)   ~ (all_53_1 = all_52_25)
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (8156), (8158) imply:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | |   (8163)   ~ (all_52_25 = all_52_29)
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7575), (8158) imply:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | |   (8164)   ~ (all_52_25 = e1)
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (122), (8156) imply:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | |   (8165)   ~ (all_53_8 = all_52_29)
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8139), (8156) imply:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | |   (8166)   ~ (all_52_29 = e1)
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8002), (8156) imply:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | |   (8167)   ~ (all_52_29 = e0)
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | |   (8168)  all_55_1 = e3
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (8168) imply:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | |   (8169)  all_53_4 = e3
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8169) implies:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | |   (8170)  all_53_4 = e3
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (8170) imply:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | |   (8171)   ~ (all_53_8 = e3)
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8171) implies:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | |   (8172)   ~ (all_53_8 = e3)
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (8170) imply:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | |   (8173)   ~ (all_53_12 = e3)
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8173) implies:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | |   (8174)   ~ (all_53_12 = e3)
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8175)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e3)
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8175) gives:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8176)  all_57_4 = e3 & op(e3, e1) = e3
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8176) implies:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8177)  all_57_4 = e3
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8178)  all_55_2 = e3
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (8172), (8178) are inconsistent by
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2028.
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8179)   ~ (all_55_2 = e3)
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8180)  all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8180) gives:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8181)  all_55_2 = e2
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (8181) imply:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8182)  all_53_8 = e2
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8182) implies:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8183)  all_53_8 = e2
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (8183) imply:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8184)   ~ (all_53_12 = e2)
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8184) implies:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8185)   ~ (all_53_12 = e2)
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8165), (8183) imply:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8186)   ~ (all_52_29 = e2)
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8186) implies:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8187)   ~ (all_52_29 = e2)
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8188)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e2)
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8188) gives:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8189)  all_57_0 = e2 & op(e3, e3) = e2
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8189) implies:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8190)  op(e3, e3) = e2
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (191), (8152), (8159), (8166), (8167),
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8187), (8190), (function-axioms) are inconsistent
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1565.
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8191)  all_57_1 = e2 & op(e3, e2) = e2
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (171), (7597), (8191), (function-axioms) are
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2456.
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8192)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e2)
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (169), (8177), (8185), (8192),
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1208.
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8193)  all_55_2 = e1 | all_55_2 = e0
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (7577), (8000), (8193) are inconsistent by
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2030.
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8194)  all_57_5 = e3 & op(e2, e1) = e3
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (8133), (8194) are inconsistent by sub-proof
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #386.
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8195)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e1) = e3)
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8195) gives:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8196)  all_57_8 = e3 & op(e1, e1) = e3
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8196) implies:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8197)  op(e1, e1) = e3
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (374), (8197), (function-axioms) are
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2468.
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8198)  all_57_14 = e3 & op(e0, e1) = e3
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8198) implies:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8199)  all_57_14 = e3
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8200)  op(e0, e1) = e3
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8201)  all_55_2 = e3
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (8172), (8201) are inconsistent by
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2028.
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8202)   ~ (all_55_2 = e3)
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8203)  all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8204)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8204) gives:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8205)  all_57_12 = e2 & op(e0, e3) = e2
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8205) implies:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8206)  all_57_12 = e2
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8207)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8207) gives:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8208)  all_57_0 = e0 & op(e3, e3) = e0
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8208) implies:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8209)  op(e3, e3) = e0
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8149), (8152), (8200), (8209),
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1934.
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8210)  all_57_1 = e0 & op(e3, e2) = e0
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8210) implies:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8211)  op(e3, e2) = e0
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (136), (171), (192), (246), (7582), (7599),
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8121), (8153), (8160), (8211), (function-axioms)
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #326.
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8212)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8212) gives:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8213)  all_57_4 = e0 & op(e3, e1) = e0
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8213) implies:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8214)  op(e3, e1) = e0
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (8000), (8214), (function-axioms) are
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2267.
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8215)  all_57_9 = e0 & op(e3, e0) = e0
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8215) implies:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8216)  all_57_9 = e0
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8217)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e0)
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8217) gives:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8218)  all_57_0 = e0 & op(e3, e3) = e0
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8218) implies:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8219)  op(e3, e3) = e0
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8149), (8152), (8200), (8219),
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1934.
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8220)  all_57_2 = e0 & op(e2, e3) = e0
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8220) implies:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8221)  all_57_2 = e0
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8222)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e2)
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (171), (7582), (7597), (8222),
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #331.
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.94/37.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8223)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e2)
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8223) gives:
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8224)  all_57_4 = e2 & op(e3, e1) = e2
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8224) implies:
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8225)  all_57_4 = e2
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8226)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e3)
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8226) gives:
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8227)  all_57_0 = e3 & op(e3, e3) = e3
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8227) implies:
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8228)  op(e3, e3) = e3
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (191), (203), (269), (7577), (8000), (8152),
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8159), (8165), (8166), (8167), (8172), (8228),
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2029.
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8229)  all_57_2 = e3 & op(e2, e3) = e3
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8229) implies:
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8230)  all_57_2 = e3
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8221), (8230) are inconsistent by sub-proof
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2258.
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8231)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e3) = e3)
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8231) gives:
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8232)  all_57_6 = e3 & op(e1, e3) = e3
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8232) implies:
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8233)  all_57_6 = e3
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8234)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (7607), (8221), (8234),
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #831.
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8235)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8235) gives:
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8236)  all_57_5 = e3 & op(e2, e1) = e3
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8236) implies:
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8237)  all_57_5 = e3
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8133), (8237) imply:
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8238)  e3 = e1
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8238) implies:
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8239)  e3 = e1
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8233), (8239) imply:
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8240)  all_57_6 = e1
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (8), (9), (39), (216), (217), (374),
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8008), (8128), (8240), (function-axioms) are
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #325.
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8241)  all_57_10 = e3 & op(e2, e0) = e3
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8241) implies:
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8242)  op(e2, e0) = e3
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8203) gives:
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.94/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8243)  all_55_2 = e2
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (8243) imply:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8244)  all_53_8 = e2
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8244) implies:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8245)  all_53_8 = e2
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (8245) imply:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8246)   ~ (all_53_12 = e2)
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8246) implies:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8247)   ~ (all_53_12 = e2)
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8248)  all_55_14 = e3
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8159), (8248) imply:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8249)  all_52_29 = e3
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8163), (8249) imply:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8250)   ~ (all_52_25 = e3)
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8251)  all_55_3 = e3
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (8174), (8251) are inconsistent by
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2169.
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8252)  all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8252) gives:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8253)  all_55_3 = e2
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (8247), (8253) are inconsistent by
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1612.
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8254)  all_55_3 = e1 | all_55_3 = e0
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8254) gives:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8255)  all_55_3 = e1
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (7578), (8255) are inconsistent by
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #324.
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8256)  all_55_3 = e0
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (8256) imply:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8257)  all_53_12 = e0
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8257) implies:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8258)  all_53_12 = e0
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (114), (8258) imply:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8259)   ~ (all_53_13 = e0)
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8259) implies:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8260)   ~ (all_53_13 = e0)
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8261)  all_55_7 = e3
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (8261) imply:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8262)  all_53_13 = e3
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8262) implies:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8263)  all_53_13 = e3
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (8263) imply:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8264)   ~ (all_53_1 = e3)
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8265)  all_55_4 = e3
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (8264), (8265) are inconsistent by
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2170.
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8266)  all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8266) gives:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8267)  all_55_4 = e2
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (7596), (8267) are inconsistent by
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2168.
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8268)  all_55_4 = e1 | all_55_4 = e0
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8268) gives:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8269)  all_55_4 = e1
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (7573), (8269) are inconsistent by
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2166.
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8270)  all_55_4 = e0
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (8270) imply:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8271)  all_53_1 = e0
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8271) implies:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8272)  all_53_1 = e0
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8162), (8272) imply:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8273)   ~ (all_52_25 = e0)
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8273) implies:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8274)   ~ (all_52_25 = e0)
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (193), (7607), (8154), (8161), (8164), (8250),
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8274), (function-axioms) are inconsistent by
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #322.
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8275)  all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (7601), (8122), (8260), (8275) are
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #321.
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8276)  all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7607), (8152), (8159), (8166), (8167), (8276),
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2026.
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8277)  all_55_2 = e1 | all_55_2 = e0
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8277) gives:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8278)  all_55_2 = e1
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (8278) imply:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8279)  all_53_8 = e1
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8279) implies:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8280)  all_53_8 = e1
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (124), (8280) imply:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8281)   ~ (all_53_9 = e1)
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8281) implies:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8282)   ~ (all_53_9 = e1)
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8283)  all_55_6 = e3
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (8283) imply:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8284)  all_53_9 = e3
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8284) implies:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8285)  all_53_9 = e3
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (8285) imply:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8286)   ~ (all_53_13 = e3)
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8286) implies:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8287)   ~ (all_53_13 = e3)
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (8242), (8287), (function-axioms) are
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2301.
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8288)  all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8288) gives:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8289)  all_55_6 = e2
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (7600), (8289) are inconsistent by
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2398.
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8290)  all_55_6 = e1 | all_55_6 = e0
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (8001), (8282), (8290) are inconsistent by
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2161.
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8291)  all_55_2 = e0
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (8000), (8291) are inconsistent by
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2031.
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8292)  all_57_12 = e3 & op(e0, e3) = e3
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8292) implies:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8293)  all_57_12 = e3
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8206), (8293) imply:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8294)  e3 = e2
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8294) implies:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8295)  e3 = e2
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8199), (8295) imply:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8296)  all_57_14 = e2
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (218), (219),
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (220), (221), (374), (8225), (8296),
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2370.
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8297)  all_57_9 = e2 & op(e3, e0) = e2
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8297) implies:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8298)  all_57_9 = e2
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8216), (8298) imply:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8299)  e2 = e0
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7606), (8299) imply:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8300)  all_57_3 = e0
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8221), (8300) are inconsistent by sub-proof
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2246.
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8301)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = e0)
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8301) gives:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8302)  all_57_6 = e0 & op(e1, e3) = e0
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8302) implies:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8303)  op(e1, e3) = e0
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (7998), (8303), (function-axioms) are
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2154.
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8304)  all_57_12 = e0 & op(e0, e3) = e0
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8304) implies:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8305)  op(e0, e3) = e0
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (211), (212),
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (213), (8122), (8124), (8148), (8151), (8154),
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8216), (8305), (function-axioms) are inconsistent
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1303.
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8306)  all_57_13 = e2 & op(e0, e2) = e2
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8306) implies:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8307)  op(e0, e2) = e2
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (7599), (8307), (function-axioms) are
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2335.
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8308)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (8124), (8199), (8308),
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2087.
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | |   (8309)  all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8309) gives:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8310)  all_55_1 = e2
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (7597), (8310) are inconsistent by
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2284.
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8311)  all_55_1 = e1 | all_55_1 = e0
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8311) gives:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8312)  all_55_1 = e1
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (8312) imply:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8313)  all_53_4 = e1
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7576), (8313) imply:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8314)  $false
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8314) is inconsistent.
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8315)  all_55_1 = e0
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (8315) imply:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8316)  all_53_4 = e0
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (171), (8316) imply:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8317)  op(e3, e2) = e0
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (136), (171), (192), (246), (7582), (7599),
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8121), (8153), (8160), (8317), (function-axioms)
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #326.
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | |   (8318)  all_57_10 = e1 & op(e2, e0) = e1
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (8122), (8318), (function-axioms) are
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2084.
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | |   (8319)  all_57_13 = e1 & op(e0, e2) = e1
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (8121), (8319), (function-axioms) are
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #330.
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.88  | | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.88  | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | End of split
% 222.99/37.88  | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.88  | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | |   (8320)  all_57_11 = e0 & op(e1, e0) = e0
% 222.99/37.88  | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (8003), (8320), (function-axioms) are
% 222.99/37.88  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2341.
% 222.99/37.88  | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | End of split
% 222.99/37.88  | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | End of split
% 222.99/37.88  | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | End of split
% 222.99/37.88  | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | End of split
% 222.99/37.88  | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | Case 2:
% 222.99/37.88  | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | |   (8321)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 222.99/37.88  | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 222.99/37.88  | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | BETA: splitting (8321) gives:
% 222.99/37.88  | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | Case 1:
% 222.99/37.88  | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | |   (8322)  all_57_5 = e2 & op(e2, e1) = e2
% 222.99/37.88  | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | REF_CLOSE: (166), (7600), (8322), (function-axioms) are
% 222.99/37.88  | | | | | | | | | | | | | |            inconsistent by sub-proof #1858.
% 222.99/37.88  | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | Case 2:
% 222.99/37.88  | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | |   (8323)  all_57_10 = e2 & op(e2, e0) = e2
% 222.99/37.88  | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | REF_CLOSE: (165), (7601), (8323), (function-axioms) are
% 222.99/37.88  | | | | | | | | | | | | | |            inconsistent by sub-proof #2432.
% 222.99/37.88  | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | End of split
% 222.99/37.88  | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | End of split
% 222.99/37.88  | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | Case 2:
% 222.99/37.88  | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | |   (8324)  all_55_5 = e1 | all_55_5 = e0
% 222.99/37.88  | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | REF_CLOSE: (266), (7586), (7588), (8324) are inconsistent by
% 222.99/37.88  | | | | | | | | | | | |            sub-proof #1857.
% 222.99/37.88  | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | End of split
% 222.99/37.88  | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | End of split
% 222.99/37.88  | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | Case 2:
% 222.99/37.88  | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | |   (8325)  all_16_2 = e1
% 222.99/37.88  | | | | | | | | | |   (8326)  ( ~ (all_16_0 = e0) & op(all_16_1, e2) = all_16_0
% 222.99/37.88  | | | | | | | | | |             & op(e2, e1) = all_16_1 & $i(all_16_0) &
% 222.99/37.88  | | | | | | | | | |             $i(all_16_1)) | ( ~ (all_16_1 = e3) & op(e2, e1)
% 222.99/37.88  | | | | | | | | | |             = all_16_1 & $i(all_16_1))
% 222.99/37.88  | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | COMBINE_EQS: (324), (8325) imply:
% 222.99/37.88  | | | | | | | | | |   (8327)  all_8_2 = e1
% 222.99/37.88  | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | COMBINE_EQS: (305), (8327) imply:
% 222.99/37.88  | | | | | | | | | |   (8328)  all_26_2 = e1
% 222.99/37.88  | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | REDUCE: (354), (8327) imply:
% 222.99/37.88  | | | | | | | | | |   (8329)   ~ (all_53_6 = e1)
% 222.99/37.88  | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | REDUCE: (356), (8327) imply:
% 222.99/37.88  | | | | | | | | | |   (8330)   ~ (all_53_7 = e1)
% 222.99/37.88  | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | REDUCE: (358), (8327) imply:
% 222.99/37.88  | | | | | | | | | |   (8331)   ~ (all_53_9 = e1)
% 222.99/37.88  | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | REDUCE: (360), (8327) imply:
% 222.99/37.88  | | | | | | | | | |   (8332)   ~ (all_53_13 = e1)
% 222.99/37.88  | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | REDUCE: (375), (8327) imply:
% 222.99/37.88  | | | | | | | | | |   (8333)   ~ (e3 = e1)
% 222.99/37.88  | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | REDUCE: (42), (8327) imply:
% 222.99/37.88  | | | | | | | | | |   (8334)  op(e2, e2) = e1
% 222.99/37.88  | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | BETA: splitting (70) gives:
% 222.99/37.88  | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | Case 1:
% 222.99/37.88  | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | |   (8335)   ~ (all_26_2 = e1)
% 222.99/37.88  | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | REDUCE: (8328), (8335) imply:
% 222.99/37.88  | | | | | | | | | | |   (8336)  $false
% 222.99/37.88  | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | CLOSE: (8336) is inconsistent.
% 222.99/37.88  | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | Case 2:
% 222.99/37.88  | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | |   (8337)  ( ~ (all_26_0 = e3) & op(all_26_1, e2) = all_26_0
% 222.99/37.88  | | | | | | | | | | |             & op(e2, e1) = all_26_1 & $i(all_26_0) &
% 222.99/37.88  | | | | | | | | | | |             $i(all_26_1)) | ( ~ (all_26_1 = e0) & op(e2, e1)
% 222.99/37.88  | | | | | | | | | | |             = all_26_1 & $i(all_26_1))
% 222.99/37.88  | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | BETA: splitting (67) gives:
% 222.99/37.88  | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | Case 1:
% 222.99/37.88  | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | |   (8338)   ~ (all_24_2 = e0)
% 222.99/37.88  | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | REDUCE: (315), (8338) imply:
% 222.99/37.88  | | | | | | | | | | | |   (8339)   ~ (all_6_2 = e0)
% 222.99/37.88  | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | BETA: splitting (76) gives:
% 222.99/37.88  | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | Case 1:
% 222.99/37.88  | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | |   (8340)   ~ (all_30_2 = e1)
% 222.99/37.88  | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | REDUCE: (330), (8340) imply:
% 222.99/37.88  | | | | | | | | | | | | |   (8341)   ~ (all_4_2 = e1)
% 222.99/37.88  | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | BETA: splitting (211) gives:
% 222.99/37.88  | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | Case 1:
% 222.99/37.88  | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | |   (8342)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 222.99/37.88  | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 222.99/37.88  | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | BETA: splitting (8342) gives:
% 222.99/37.88  | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | Case 1:
% 222.99/37.88  | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | |   (8343)  all_57_9 = e1 & op(e3, e0) = e1
% 222.99/37.88  | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | REF_CLOSE: (169), (7578), (8343), (function-axioms) are
% 222.99/37.88  | | | | | | | | | | | | | | |            inconsistent by sub-proof #2131.
% 222.99/37.88  | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | Case 2:
% 222.99/37.88  | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | |   (8344)  all_57_10 = e1 & op(e2, e0) = e1
% 222.99/37.88  | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | REF_CLOSE: (165), (8332), (8344), (function-axioms) are
% 222.99/37.88  | | | | | | | | | | | | | | |            inconsistent by sub-proof #2084.
% 222.99/37.88  | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | End of split
% 222.99/37.88  | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | Case 2:
% 222.99/37.88  | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | |   (8345)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 222.99/37.88  | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 222.99/37.88  | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | BETA: splitting (8345) gives:
% 222.99/37.88  | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | Case 1:
% 222.99/37.88  | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | |   (8346)  all_57_11 = e1 & op(e1, e0) = e1
% 222.99/37.88  | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | ALPHA: (8346) implies:
% 222.99/37.88  | | | | | | | | | | | | | | |   (8347)  op(e1, e0) = e1
% 222.99/37.88  | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 222.99/37.88  | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | Case 1:
% 222.99/37.88  | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | |   (8348)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 222.99/37.88  | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 222.99/37.88  | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | BETA: splitting (8348) gives:
% 222.99/37.88  | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.88  | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | |   (8349)  all_57_12 = e1 & op(e0, e3) = e1
% 222.99/37.88  | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (7575), (8349), (function-axioms) are
% 222.99/37.88  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1947.
% 222.99/37.88  | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.88  | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | |   (8350)  all_57_13 = e1 & op(e0, e2) = e1
% 222.99/37.88  | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (8330), (8350), (function-axioms) are
% 222.99/37.88  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #330.
% 222.99/37.88  | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | End of split
% 222.99/37.88  | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | Case 2:
% 222.99/37.88  | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | |   (8351)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 222.99/37.88  | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 222.99/37.88  | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | BETA: splitting (8351) gives:
% 222.99/37.88  | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.88  | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | |   (8352)  all_57_14 = e1 & op(e0, e1) = e1
% 222.99/37.88  | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | ALPHA: (8352) implies:
% 222.99/37.88  | | | | | | | | | | | | | | | | |   (8353)  all_57_14 = e1
% 222.99/37.88  | | | | | | | | | | | | | | | | |   (8354)  op(e0, e1) = e1
% 222.99/37.88  | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 222.99/37.88  | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.88  | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | |   (8355)  all_55_15 = e3
% 222.99/37.88  | | | | | | | | | | | | | | | | | | 
% 222.99/37.88  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (8355) imply:
% 222.99/37.88  | | | | | | | | | | | | | | | | | |   (8356)  all_4_2 = e3
% 222.99/37.88  | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | REDUCE: (7584), (8356) imply:
% 222.99/37.89  | | | | | | | | | | | | | | | | | |   (8357)  $false
% 222.99/37.89  | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | CLOSE: (8357) is inconsistent.
% 222.99/37.89  | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | |   (8358)   ~ (all_55_15 = e3)
% 222.99/37.89  | | | | | | | | | | | | | | | | | |   (8359)  all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 222.99/37.89  | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | BETA: splitting (8359) gives:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | |   (8360)  all_55_15 = e2
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (8360) imply:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | |   (8361)  all_4_2 = e2
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | REDUCE: (373), (8361) imply:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | |   (8362)  $false
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | CLOSE: (8362) is inconsistent.
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | |   (8363)   ~ (all_55_15 = e2)
% 222.99/37.89  | | | | | | | | | | | | | | | | | | |   (8364)  all_55_15 = e1 | all_55_15 = e0
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | BETA: splitting (8364) gives:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | |   (8365)  all_55_15 = e1
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (8365) imply:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | |   (8366)  all_4_2 = e1
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | REDUCE: (8341), (8366) imply:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | |   (8367)  $false
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | CLOSE: (8367) is inconsistent.
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | |   (8368)  all_55_15 = e0
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (8368) imply:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | |   (8369)  all_4_2 = e0
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | REDUCE: (362), (8369) imply:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | |   (8370)   ~ (all_53_7 = e0)
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | REDUCE: (370), (8369) imply:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | |   (8371)   ~ (all_53_12 = e0)
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | REDUCE: (371), (8369) imply:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | |   (8372)   ~ (all_53_13 = e0)
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | REDUCE: (372), (8369) imply:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | |   (8373)   ~ (all_53_14 = e0)
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | REDUCE: (7584), (8369) imply:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | |   (8374)   ~ (e3 = e0)
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | REDUCE: (373), (8369) imply:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | |   (8375)   ~ (e2 = e0)
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | |   (8376)  all_57_15 = e0 & op(e0, e0) = e0
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | ALPHA: (8376) implies:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | |   (8377)  all_57_15 = e0
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | |   (8378)  op(e0, e0) = e0
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_11,
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | |              e1, e1, e0, simplifying with (158), (8354) gives:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | |   (8379)  all_53_11 = e1
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_14,
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | |              e1, e0, e1, simplifying with (161), (8347) gives:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | |   (8380)  all_53_14 = e1
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | REDUCE: (368), (8380) imply:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | |   (8381)   ~ (all_6_2 = e1)
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | SIMP: (8381) implies:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | |   (8382)   ~ (all_6_2 = e1)
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | |   (8383)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | |             all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | |             op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | |               all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | |               all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | |             & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | |               all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8383) gives:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | |   (8384)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | |           all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | |           op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | |             all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_7)
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8384) implies:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | |   (8385)  op(e3, e1) = all_52_5
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | |   (8386)  op(e3, e2) = all_52_3
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | |   (8387)  op(all_52_5, all_52_5) = e1
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | |   (8388)  op(all_52_3, all_52_3) = e2
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (169), (208),
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | |            (209), (210), (231), (7575), (7581), (8353),
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | |            (8371), (8377), (8378), (8385), (8386), (8387),
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | |            (8388), (function-axioms) are inconsistent by
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #319.
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | |   (8389)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | |           all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | |           op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | |             all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | |           & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_15)
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8389) implies:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | |   (8390)  op(e2, e0) = all_52_15
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | |   (8391)  op(e2, e1) = all_52_13
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | |   (8392)  op(e2, e2) = all_52_11
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | |   (8393)  op(all_52_15, all_52_15) = e0
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | |   (8394)  op(all_52_13, all_52_13) = e1
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | |   (8395)  all_55_10 = e3
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (374), (8395) are inconsistent by sub-proof
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | |            #2500.
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | |   (8396)  all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8396) gives:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | |   (8397)  all_55_10 = e2
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (336), (8397) imply:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | |   (8398)  all_6_2 = e2
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8398) implies:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | |   (8399)  all_6_2 = e2
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (364), (8399) imply:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | |   (8400)   ~ (all_53_9 = e2)
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_13,
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_15, e0, e2, simplifying with (165), (8390)
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | |   (8401)  all_53_13 = all_52_15
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_9,
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_13, e1, e2, simplifying with (166), (8391)
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | |   (8402)  all_53_9 = all_52_13
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_11, e2, e2, simplifying with (8334), (8392)
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | |   (8403)  all_52_11 = e1
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (8401) imply:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | |   (8404)  all_55_7 = all_52_15
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (8402) imply:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | |   (8405)  all_55_6 = all_52_13
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (8401), (8402) imply:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | |   (8406)   ~ (all_52_13 = all_52_15)
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8400), (8402) imply:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | |   (8407)   ~ (all_52_13 = e2)
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8331), (8402) imply:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | |   (8408)   ~ (all_52_13 = e1)
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (114), (8401) imply:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | |   (8409)   ~ (all_53_12 = all_52_15)
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8332), (8401) imply:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | |   (8410)   ~ (all_52_15 = e1)
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8372), (8401) imply:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | |   (8411)   ~ (all_52_15 = e0)
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8412)  all_55_3 = e3
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (8412) imply:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8413)  all_53_12 = e3
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8413) implies:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8414)  all_53_12 = e3
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8409), (8414) imply:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8415)   ~ (all_52_15 = e3)
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8415) implies:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8416)   ~ (all_52_15 = e3)
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8417)  all_55_7 = e3
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8404), (8416), (8417) are inconsistent by
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2063.
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8418)  all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8418) gives:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8419)  all_55_7 = e2
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8404), (8419) imply:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8420)  all_52_15 = e2
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8393), (8420) imply:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8421)  op(e2, e2) = e0
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8334), (8421), (function-axioms) are
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2352.
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8422)  all_55_7 = e1 | all_55_7 = e0
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8422) gives:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8423)  all_55_7 = e1
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8404), (8410), (8423) are inconsistent by
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2277.
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8424)  all_55_7 = e0
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8404), (8411), (8424) are inconsistent by
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2276.
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8425)  all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8425) gives:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8426)  all_55_3 = e2
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (8426) imply:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8427)  all_53_12 = e2
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8427) implies:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8428)  all_53_12 = e2
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8409), (8428) imply:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8429)   ~ (all_52_15 = e2)
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8429) implies:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8430)   ~ (all_52_15 = e2)
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8431)  all_55_7 = e3
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8404), (8431) imply:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8432)  all_52_15 = e3
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8432) implies:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8433)  all_52_15 = e3
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8406), (8433) imply:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8434)   ~ (all_52_13 = e3)
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8435)  all_55_6 = e3
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8405), (8434), (8435) are inconsistent by
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #318.
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8436)  all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8378), (8394), (8405), (8407), (8408), (8436),
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2289.
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8437)  all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8404), (8410), (8411), (8430), (8437) are
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2275.
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8438)  all_55_3 = e1 | all_55_3 = e0
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (7578), (8371), (8438) are inconsistent by
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2132.
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | |   (8439)  all_55_10 = e1 | all_55_10 = e0
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (8339), (8382), (8439) are inconsistent by
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1685.
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | |   (8440)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | |             & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | |             & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | |               all_52_21) = e1 & op(all_52_23, all_52_23) =
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | |             all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | |             = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | |             & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | |             e0 & op(all_52_25, all_52_25) = e3 &
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | |             op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | |               all_52_29) = e1 & op(all_52_31, all_52_31) =
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | |             all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | |             = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_29) & $i(all_52_31))
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8440) gives:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | |   (8441)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | |           all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | |           op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | |             all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | |           & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | |           & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | |           & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_23)
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8441) implies:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | |   (8442)  op(e1, e0) = all_52_23
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | |   (8443)  op(e1, e1) = all_52_21
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | |   (8444)  op(e1, e2) = all_52_19
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | |   (8445)  op(e1, e3) = all_52_17
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | |   (8446)  op(all_52_23, all_52_23) = e0
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | |   (8447)  op(all_52_21, all_52_21) = e1
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | |   (8448)  op(all_52_19, all_52_19) = e2
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | |   (8449)  op(all_52_17, all_52_17) = e3
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | |   (8450)  all_55_10 = e3
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (374), (8450) are inconsistent by sub-proof
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | |            #2500.
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | |   (8451)   ~ (all_55_10 = e3)
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | |   (8452)  all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8452) gives:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | |   (8453)  all_55_10 = e2
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (336), (8453) imply:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | |   (8454)  all_6_2 = e2
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8454) implies:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | |   (8455)  all_6_2 = e2
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (364), (8455) imply:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | |   (8456)   ~ (all_53_9 = e2)
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (374), (8455) imply:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | |   (8457)   ~ (e3 = e2)
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (8455) imply:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | |   (8458)  op(e1, e1) = e2
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8459)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e2)
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8459) gives:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8460)  all_57_4 = e2 & op(e3, e1) = e2
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8460) implies:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8461)  all_57_4 = e2
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8462)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8462) gives:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8463)  all_57_0 = e0 & op(e3, e3) = e0
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8463) implies:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8464)  all_57_0 = e0
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (39), (160), (168), (195), (232), (336),
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (374), (7573), (7575), (8445), (8449), (8464),
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1545.
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8465)  all_57_1 = e0 & op(e3, e2) = e0
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8465) implies:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8466)  all_57_1 = e0
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8467)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (8334), (8466), (8467),
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1738.
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8468)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8468) gives:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8469)  all_57_7 = e2 & op(e1, e2) = e2
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8469) implies:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8470)  all_57_7 = e2
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (161), (163),
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (214), (215), (217), (374), (8329), (8339),
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8373), (8458), (8470), (function-axioms) are
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1817.
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8471)  all_57_13 = e2 & op(e0, e2) = e2
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8471) implies:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8472)  all_57_13 = e2
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8473)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e0)
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8473) gives:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8474)  all_57_4 = e0 & op(e3, e1) = e0
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8461), (8474) are inconsistent by sub-proof
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2045.
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8475)  all_57_5 = e0 & op(e2, e1) = e0
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8475) implies:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8476)  all_57_5 = e0
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8477)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (8334), (8466), (8477),
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1737.
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8478)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8478) gives:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8479)  all_57_7 = e3 & op(e1, e2) = e3
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8479) implies:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8480)  all_57_7 = e3
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8481)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e3)
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8481) gives:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8482)  all_57_4 = e3 & op(e3, e1) = e3
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8482) implies:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8483)  all_57_4 = e3
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8461), (8483) imply:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8484)  e3 = e2
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8484) implies:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8485)  e3 = e2
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8480), (8485) imply:
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8486)  all_57_7 = e2
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (226), (227), (228),
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (229), (8334), (8472), (8486), (function-axioms)
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1696.
% 222.99/37.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8487)  all_57_5 = e3 & op(e2, e1) = e3
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8487) implies:
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8488)  all_57_5 = e3
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8476), (8488) are inconsistent by sub-proof
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2471.
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8489)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e1) = e3)
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8489) gives:
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8490)  all_57_8 = e3 & op(e1, e1) = e3
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8490) implies:
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8491)  op(e1, e1) = e3
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (374), (8491), (function-axioms) are
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2468.
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8492)  all_57_14 = e3 & op(e0, e1) = e3
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (8353), (8492) are inconsistent by sub-proof
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1966.
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8493)  all_57_13 = e3 & op(e0, e2) = e3
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (8472), (8493) are inconsistent by sub-proof
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1358.
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8494)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8494) gives:
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8495)  all_57_8 = e0 & op(e1, e1) = e0
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8495) implies:
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8496)  op(e1, e1) = e0
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (165), (169), (171), (207), (7576), (8371),
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8372), (8373), (8443), (8447), (8465), (8496),
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1842.
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8497)  all_57_14 = e0 & op(e0, e1) = e0
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8497) implies:
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8498)  all_57_14 = e0
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (208), (209),
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (210), (7575), (8377), (8378), (8498),
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #320.
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8499)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8499) gives:
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8500)  all_57_4 = e0 & op(e3, e1) = e0
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8500) implies:
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8501)  all_57_4 = e0
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8461), (8501) are inconsistent by sub-proof
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2441.
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8502)  all_57_9 = e0 & op(e3, e0) = e0
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (8371), (8502), (function-axioms) are
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2434.
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8503)  all_57_5 = e2 & op(e2, e1) = e2
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (8456), (8503), (function-axioms) are
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1858.
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8504)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e1) = e2)
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8504) gives:
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8505)  all_57_8 = e2 & op(e1, e1) = e2
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_23, e0, e1, simplifying with (8347), (8442)
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8506)  all_52_23 = e1
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_21, e1, e1, simplifying with (8443), (8458)
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8507)  all_52_21 = e2
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_6,
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_19, e2, e1, simplifying with (163), (8444)
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8508)  all_53_6 = all_52_19
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8446), (8506) imply:
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8509)  op(e1, e1) = e0
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (159), (161), (165), (169), (171), (190),
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (207), (226), (244), (362), (370), (371), (372),
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (373), (7576), (7584), (8334), (8341), (8443),
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8444), (8447), (8448), (8509), (function-axioms)
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1838.
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8510)  all_57_14 = e2 & op(e0, e1) = e2
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8510) implies:
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8511)  all_57_14 = e2
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8353), (8511) are inconsistent by sub-proof
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2178.
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | |   (8512)  all_55_10 = e1 | all_55_10 = e0
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (8339), (8382), (8512) are inconsistent by
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1685.
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | |   (8513)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | |           all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | |           op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | |             all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | |           & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | |           & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | |           & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_31)
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8513) implies:
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | |   (8514)  op(e0, e1) = all_52_29
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | |   (8515)  op(e0, e2) = all_52_27
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | |   (8516)  op(all_52_29, all_52_29) = e1
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | |   (8517)  op(all_52_27, all_52_27) = e2
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | |   (8518)  all_55_10 = e3
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (374), (8518) are inconsistent by sub-proof
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | |            #2500.
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | |   (8519)   ~ (all_55_10 = e3)
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | |   (8520)  all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8520) gives:
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | |   (8521)  all_55_10 = e2
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (336), (8521) imply:
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | |   (8522)  all_6_2 = e2
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8522) implies:
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | |   (8523)  all_6_2 = e2
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (364), (8523) imply:
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | |   (8524)   ~ (all_53_9 = e2)
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (374), (8523) imply:
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | |   (8525)   ~ (e3 = e2)
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8526)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e2)
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8526) gives:
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8527)  all_57_4 = e2 & op(e3, e1) = e2
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8527) implies:
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8528)  all_57_4 = e2
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8529)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e0)
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8529) gives:
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8530)  all_57_4 = e0 & op(e3, e1) = e0
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8528), (8530) are inconsistent by sub-proof
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2045.
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8531)  all_57_5 = e0 & op(e2, e1) = e0
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8531) implies:
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8532)  op(e2, e1) = e0
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (192), (246), (8326), (8330), (8334),
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8337), (8370), (8515), (8517), (8532),
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1709.
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8533)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8533) gives:
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8534)  all_57_8 = e0 & op(e1, e1) = e0
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (8339), (8534), (function-axioms) are
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2412.
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8535)  all_57_14 = e0 & op(e0, e1) = e0
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8535) implies:
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8536)  all_57_14 = e0
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (208), (209),
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (210), (7575), (8377), (8378), (8536),
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #320.
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8537)  all_57_5 = e2 & op(e2, e1) = e2
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (8524), (8537), (function-axioms) are
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1858.
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8538)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e1) = e2)
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8538) gives:
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8539)  all_57_8 = e2 & op(e1, e1) = e2
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8539) implies:
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8540)  op(e1, e1) = e2
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_29, e1, e0, simplifying with (8354), (8514)
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8541)  all_52_29 = e1
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8516), (8541) imply:
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8542)  op(e1, e1) = e1
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8540), (8542), (function-axioms) are
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2423.
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8543)  all_57_14 = e2 & op(e0, e1) = e2
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8543) implies:
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8544)  all_57_14 = e2
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8353), (8544) are inconsistent by sub-proof
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2178.
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | |   (8545)  all_55_10 = e1 | all_55_10 = e0
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (8339), (8382), (8545) are inconsistent by
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1685.
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | |   (8546)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | |                 e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (165), (169), (8371), (8372), (8373),
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | |            (8546), (function-axioms) are inconsistent by
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | |            sub-proof #2112.
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.90  | | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.90  | | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | End of split
% 222.99/37.90  | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.90  | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | |   (8547)  all_57_15 = e1 & op(e0, e0) = e1
% 222.99/37.90  | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | ALPHA: (8547) implies:
% 222.99/37.90  | | | | | | | | | | | | | | | | |   (8548)  op(e0, e0) = e1
% 222.99/37.90  | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (190), (244), (373), (7584), (8341), (8548),
% 222.99/37.90  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.99/37.90  | | | | | | | | | | | | | | | | |            #317.
% 222.99/37.90  | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | End of split
% 222.99/37.90  | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | End of split
% 222.99/37.90  | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | Case 2:
% 222.99/37.90  | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | |   (8549)  all_57_15 = e1 & op(e0, e0) = e1
% 222.99/37.90  | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | ALPHA: (8549) implies:
% 222.99/37.90  | | | | | | | | | | | | | | |   (8550)  op(e0, e0) = e1
% 222.99/37.90  | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | REF_CLOSE: (36), (190), (244), (373), (7584), (8341), (8550),
% 222.99/37.90  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.99/37.90  | | | | | | | | | | | | | | |            #317.
% 222.99/37.90  | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | End of split
% 222.99/37.90  | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | End of split
% 222.99/37.90  | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | Case 2:
% 222.99/37.90  | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | |   (8551)  all_30_2 = e1
% 222.99/37.90  | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | COMBINE_EQS: (330), (8551) imply:
% 222.99/37.90  | | | | | | | | | | | | |   (8552)  all_4_2 = e1
% 222.99/37.90  | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | SIMP: (8552) implies:
% 222.99/37.90  | | | | | | | | | | | | |   (8553)  all_4_2 = e1
% 222.99/37.90  | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | REDUCE: (372), (8553) imply:
% 222.99/37.90  | | | | | | | | | | | | |   (8554)   ~ (all_53_14 = e1)
% 222.99/37.90  | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | REDUCE: (373), (8553) imply:
% 222.99/37.90  | | | | | | | | | | | | |   (8555)   ~ (e2 = e1)
% 222.99/37.90  | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | REDUCE: (36), (8553) imply:
% 222.99/37.90  | | | | | | | | | | | | |   (8556)  op(e0, e0) = e1
% 222.99/37.90  | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | BETA: splitting (215) gives:
% 222.99/37.90  | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | Case 1:
% 222.99/37.90  | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | |   (8557)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 222.99/37.90  | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 222.99/37.90  | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | BETA: splitting (8557) gives:
% 222.99/37.90  | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | Case 1:
% 222.99/37.90  | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | |   (8558)  all_57_6 = e1 & op(e1, e3) = e1
% 222.99/37.90  | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | REF_CLOSE: (164), (7574), (8558), (function-axioms) are
% 222.99/37.90  | | | | | | | | | | | | | | |            inconsistent by sub-proof #316.
% 222.99/37.90  | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | Case 2:
% 222.99/37.90  | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | |   (8559)  all_57_7 = e1 & op(e1, e2) = e1
% 222.99/37.90  | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | REF_CLOSE: (163), (8329), (8559), (function-axioms) are
% 222.99/37.90  | | | | | | | | | | | | | | |            inconsistent by sub-proof #2265.
% 222.99/37.90  | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | End of split
% 222.99/37.90  | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | Case 2:
% 222.99/37.90  | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | |   (8560)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 222.99/37.90  | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 222.99/37.90  | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | BETA: splitting (8560) gives:
% 222.99/37.90  | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | Case 1:
% 222.99/37.90  | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | |   (8561)  all_57_8 = e1 & op(e1, e1) = e1
% 222.99/37.90  | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | ALPHA: (8561) implies:
% 222.99/37.90  | | | | | | | | | | | | | | |   (8562)  op(e1, e1) = e1
% 222.99/37.90  | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2, e1,
% 222.99/37.90  | | | | | | | | | | | | | | |              e1, e1, simplifying with (39), (8562) gives:
% 222.99/37.90  | | | | | | | | | | | | | | |   (8563)  all_6_2 = e1
% 222.99/37.90  | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | REDUCE: (366), (8563) imply:
% 222.99/37.90  | | | | | | | | | | | | | | |   (8564)   ~ (all_53_11 = e1)
% 222.99/37.90  | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 222.99/37.90  | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | Case 1:
% 222.99/37.90  | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | |   (8565)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 222.99/37.90  | | | | | | | | | | | | | | | |             all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 222.99/37.90  | | | | | | | | | | | | | | | |             op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 222.99/37.90  | | | | | | | | | | | | | | | |               all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 222.99/37.90  | | | | | | | | | | | | | | | |             op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 222.99/37.90  | | | | | | | | | | | | | | | |             op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 222.99/37.90  | | | | | | | | | | | | | | | |             $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 222.99/37.90  | | | | | | | | | | | | | | | |             $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 222.99/37.90  | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 222.99/37.90  | | | | | | | | | | | | | | | |               all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 222.99/37.90  | | | | | | | | | | | | | | | |             & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 222.99/37.90  | | | | | | | | | | | | | | | |               all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 222.99/37.90  | | | | | | | | | | | | | | | |             op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 222.99/37.90  | | | | | | | | | | | | | | | |             & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 222.99/37.90  | | | | | | | | | | | | | | | |             $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 222.99/37.90  | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | BETA: splitting (8565) gives:
% 222.99/37.90  | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.90  | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | |   (8566)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 222.99/37.90  | | | | | | | | | | | | | | | | |           all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 222.99/37.90  | | | | | | | | | | | | | | | | |           op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 222.99/37.90  | | | | | | | | | | | | | | | | |             all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 222.99/37.90  | | | | | | | | | | | | | | | | |           op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 222.99/37.90  | | | | | | | | | | | | | | | | |           op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 222.99/37.90  | | | | | | | | | | | | | | | | |           $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 222.99/37.90  | | | | | | | | | | | | | | | | |           $i(all_52_7)
% 222.99/37.90  | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (374), (7582), (8566), (function-axioms) are
% 222.99/37.90  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #360.
% 222.99/37.90  | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.90  | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | |   (8567)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 222.99/37.90  | | | | | | | | | | | | | | | | |           all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 222.99/37.90  | | | | | | | | | | | | | | | | |           op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 222.99/37.90  | | | | | | | | | | | | | | | | |             all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 222.99/37.90  | | | | | | | | | | | | | | | | |           & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 222.99/37.90  | | | | | | | | | | | | | | | | |           op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 222.99/37.90  | | | | | | | | | | | | | | | | |           $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 222.99/37.90  | | | | | | | | | | | | | | | | |           $i(all_52_15)
% 222.99/37.90  | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8334), (8562), (8567), (function-axioms) are
% 222.99/37.90  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1855.
% 222.99/37.90  | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | End of split
% 222.99/37.90  | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | Case 2:
% 222.99/37.90  | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | |   (8568)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 222.99/37.90  | | | | | | | | | | | | | | | |             & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 222.99/37.90  | | | | | | | | | | | | | | | |             & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 222.99/37.90  | | | | | | | | | | | | | | | |               all_52_21) = e1 & op(all_52_23, all_52_23) =
% 222.99/37.90  | | | | | | | | | | | | | | | |             e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 222.99/37.90  | | | | | | | | | | | | | | | |             all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 222.99/37.90  | | | | | | | | | | | | | | | |             = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 222.99/37.90  | | | | | | | | | | | | | | | |             $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 222.99/37.90  | | | | | | | | | | | | | | | |             & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 222.99/37.90  | | | | | | | | | | | | | | | |             e0 & op(all_52_25, all_52_25) = e3 &
% 222.99/37.90  | | | | | | | | | | | | | | | |             op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 222.99/37.90  | | | | | | | | | | | | | | | |               all_52_29) = e1 & op(all_52_31, all_52_31) =
% 222.99/37.90  | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 222.99/37.90  | | | | | | | | | | | | | | | |             all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 222.99/37.90  | | | | | | | | | | | | | | | |             = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 222.99/37.90  | | | | | | | | | | | | | | | |             $i(all_52_29) & $i(all_52_31))
% 222.99/37.90  | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | BETA: splitting (8568) gives:
% 222.99/37.90  | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.90  | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | |   (8569)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 222.99/37.90  | | | | | | | | | | | | | | | | |           all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 222.99/37.90  | | | | | | | | | | | | | | | | |           op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 222.99/37.90  | | | | | | | | | | | | | | | | |             all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 222.99/37.90  | | | | | | | | | | | | | | | | |           & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 222.99/37.90  | | | | | | | | | | | | | | | | |           & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 222.99/37.90  | | | | | | | | | | | | | | | | |           & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 222.99/37.90  | | | | | | | | | | | | | | | | |           $i(all_52_23)
% 222.99/37.90  | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | ALPHA: (8569) implies:
% 222.99/37.90  | | | | | | | | | | | | | | | | |   (8570)  op(e1, e0) = all_52_23
% 222.99/37.90  | | | | | | | | | | | | | | | | |   (8571)  op(e1, e2) = all_52_19
% 222.99/37.90  | | | | | | | | | | | | | | | | |   (8572)  op(e1, e3) = all_52_17
% 222.99/37.90  | | | | | | | | | | | | | | | | |   (8573)  op(all_52_23, all_52_23) = e0
% 222.99/37.90  | | | | | | | | | | | | | | | | |   (8574)  op(all_52_19, all_52_19) = e2
% 222.99/37.90  | | | | | | | | | | | | | | | | |   (8575)  op(all_52_17, all_52_17) = e3
% 222.99/37.90  | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_14,
% 222.99/37.90  | | | | | | | | | | | | | | | | |              all_52_23, e0, e1, simplifying with (161), (8570)
% 222.99/37.90  | | | | | | | | | | | | | | | | |              gives:
% 222.99/37.90  | | | | | | | | | | | | | | | | |   (8576)  all_53_14 = all_52_23
% 222.99/37.90  | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_6,
% 222.99/37.90  | | | | | | | | | | | | | | | | |              all_52_19, e2, e1, simplifying with (163), (8571)
% 222.99/37.90  | | | | | | | | | | | | | | | | |              gives:
% 222.99/37.90  | | | | | | | | | | | | | | | | |   (8577)  all_53_6 = all_52_19
% 222.99/37.90  | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_2,
% 222.99/37.90  | | | | | | | | | | | | | | | | |              all_52_17, e3, e1, simplifying with (164), (8572)
% 222.99/37.90  | | | | | | | | | | | | | | | | |              gives:
% 222.99/37.90  | | | | | | | | | | | | | | | | |   (8578)  all_53_2 = all_52_17
% 222.99/37.90  | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (8576) imply:
% 222.99/37.90  | | | | | | | | | | | | | | | | |   (8579)  all_55_11 = all_52_23
% 222.99/37.90  | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (8577) imply:
% 222.99/37.90  | | | | | | | | | | | | | | | | |   (8580)  all_55_9 = all_52_19
% 222.99/37.90  | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (8578) imply:
% 222.99/37.90  | | | | | | | | | | | | | | | | |   (8581)  all_55_8 = all_52_17
% 222.99/37.90  | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | REDUCE: (150), (8578) imply:
% 222.99/37.90  | | | | | | | | | | | | | | | | |   (8582)   ~ (all_53_1 = all_52_17)
% 222.99/37.90  | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | REDUCE: (145), (8578) imply:
% 222.99/37.90  | | | | | | | | | | | | | | | | |   (8583)   ~ (all_53_3 = all_52_17)
% 222.99/37.90  | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | SIMP: (8583) implies:
% 222.99/37.90  | | | | | | | | | | | | | | | | |   (8584)   ~ (all_53_3 = all_52_17)
% 222.99/37.90  | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | REDUCE: (7574), (8578) imply:
% 222.99/37.90  | | | | | | | | | | | | | | | | |   (8585)   ~ (all_52_17 = e1)
% 222.99/37.90  | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | REDUCE: (137), (8577) imply:
% 222.99/37.90  | | | | | | | | | | | | | | | | |   (8586)   ~ (all_53_4 = all_52_19)
% 222.99/37.90  | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | REDUCE: (129), (8577) imply:
% 222.99/37.90  | | | | | | | | | | | | | | | | |   (8587)   ~ (all_53_7 = all_52_19)
% 222.99/37.90  | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | SIMP: (8587) implies:
% 222.99/37.90  | | | | | | | | | | | | | | | | |   (8588)   ~ (all_53_7 = all_52_19)
% 222.99/37.90  | | | | | | | | | | | | | | | | | 
% 222.99/37.90  | | | | | | | | | | | | | | | | | REDUCE: (8329), (8577) imply:
% 222.99/37.90  | | | | | | | | | | | | | | | | |   (8589)   ~ (all_52_19 = e1)
% 222.99/37.91  | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | REDUCE: (113), (8576) imply:
% 222.99/37.91  | | | | | | | | | | | | | | | | |   (8590)   ~ (all_53_12 = all_52_23)
% 222.99/37.91  | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | REDUCE: (111), (8576) imply:
% 222.99/37.91  | | | | | | | | | | | | | | | | |   (8591)   ~ (all_53_13 = all_52_23)
% 222.99/37.91  | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | REDUCE: (8554), (8576) imply:
% 222.99/37.91  | | | | | | | | | | | | | | | | |   (8592)   ~ (all_52_23 = e1)
% 222.99/37.91  | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | BETA: splitting (85) gives:
% 222.99/37.91  | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | |   (8593)   ~ (all_36_2 = e1)
% 222.99/37.91  | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | REDUCE: (7572), (8593) imply:
% 222.99/37.91  | | | | | | | | | | | | | | | | | |   (8594)  $false
% 222.99/37.91  | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | CLOSE: (8594) is inconsistent.
% 222.99/37.91  | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | |   (8595)  ( ~ (all_36_0 = e0) & op(all_36_1, e3) = all_36_0
% 222.99/37.91  | | | | | | | | | | | | | | | | | |             & op(e3, e1) = all_36_1 & $i(all_36_0) &
% 222.99/37.91  | | | | | | | | | | | | | | | | | |             $i(all_36_1)) | ( ~ (all_36_1 = e2) & op(e3, e1)
% 222.99/37.91  | | | | | | | | | | | | | | | | | |             = all_36_1 & $i(all_36_1))
% 222.99/37.91  | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | |   (8596)  all_55_3 = e3
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (8596) imply:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | |   (8597)  all_53_12 = e3
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | SIMP: (8597) implies:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | |   (8598)  all_53_12 = e3
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | REDUCE: (134), (8598) imply:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | |   (8599)   ~ (all_53_4 = e3)
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | REDUCE: (121), (8598) imply:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | |   (8600)   ~ (all_53_8 = e3)
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | REDUCE: (169), (8598) imply:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | |   (8601)  op(e3, e0) = e3
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | |   (8602)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e2)
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | BETA: splitting (8602) gives:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | |   (8603)  all_57_0 = e2 & op(e3, e3) = e2
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | ALPHA: (8603) implies:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | |   (8604)  op(e3, e3) = e2
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7582), (8604), (function-axioms) are
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1950.
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | |   (8605)  all_57_1 = e2 & op(e3, e2) = e2
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | ALPHA: (8605) implies:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | |   (8606)  all_57_1 = e2
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | |   (8607)  op(e3, e2) = e2
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | |   (8608)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (39), (160), (168), (195), (232), (336),
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | |            (374), (7573), (7575), (8572), (8575), (8606),
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | |            (8608), (function-axioms) are inconsistent by
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #315.
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | |   (8609)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8609) gives:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | |   (8610)  all_57_4 = e0 & op(e3, e1) = e0
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8610) implies:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | |   (8611)  op(e3, e1) = e0
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_8, e0,
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (170), (8611) gives:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | |   (8612)  all_53_8 = e0
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_4, e2,
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (171), (8607) gives:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | |   (8613)  all_53_4 = e2
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (136), (8613) imply:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | |   (8614)   ~ (all_53_7 = e2)
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8614) implies:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | |   (8615)   ~ (all_53_7 = e2)
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8586), (8613) imply:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | |   (8616)   ~ (all_52_19 = e2)
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8616) implies:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | |   (8617)   ~ (all_52_19 = e2)
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8599), (8613) imply:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | |   (8618)   ~ (e3 = e2)
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8600), (8612) imply:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | |   (8619)   ~ (e3 = e0)
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7577), (8612) imply:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | |   (8620)   ~ (e1 = e0)
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8595) gives:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | |   (8621)   ~ (all_36_0 = e0) & op(all_36_1, e3) = all_36_0 &
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = all_36_1 & $i(all_36_0) &
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_36_1)
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8621) implies:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | |   (8622)  op(e3, e1) = all_36_1
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | |   (8623)  op(all_36_1, e3) = all_36_0
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7571) gives:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | |   (8624)   ~ (all_10_0 = e2) & op(all_10_1, e3) = all_10_0 &
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = all_10_1 & $i(all_10_0) &
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_10_1)
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8624) implies:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | |   (8625)   ~ (all_10_0 = e2)
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | |   (8626)  op(e3, e1) = all_10_1
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | |   (8627)  op(all_10_1, e3) = all_10_0
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_36_1,
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (8611), (8622) gives:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | |   (8628)  all_36_1 = e0
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_1,
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | |              all_36_1, e1, e3, simplifying with (8622), (8626)
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | |   (8629)  all_36_1 = all_10_1
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8628), (8629) imply:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | |   (8630)  all_10_1 = e0
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8630) implies:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | |   (8631)  all_10_1 = e0
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8623), (8628) imply:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | |   (8632)  op(e0, e3) = all_36_0
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8627), (8631) imply:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | |   (8633)  op(e0, e3) = all_10_0
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_3,
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | |              all_10_0, e3, e0, simplifying with (160), (8633)
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | |   (8634)  all_53_3 = all_10_0
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_3,
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | |              all_36_0, e3, e0, simplifying with (160), (8632)
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | |   (8635)  all_53_3 = all_36_0
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8634), (8635) imply:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | |   (8636)  all_36_0 = all_10_0
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8636) implies:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | |   (8637)  all_36_0 = all_10_0
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (8634) imply:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | |   (8638)  all_55_12 = all_10_0
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (8634) imply:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | |   (8639)   ~ (all_53_1 = all_10_0)
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (141), (8634) imply:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | |   (8640)   ~ (all_53_7 = all_10_0)
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8640) implies:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | |   (8641)   ~ (all_53_7 = all_10_0)
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (8634) imply:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | |   (8642)   ~ (all_53_11 = all_10_0)
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8642) implies:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | |   (8643)   ~ (all_53_11 = all_10_0)
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7575), (8634) imply:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | |   (8644)   ~ (all_10_0 = e1)
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8645)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (8615), (8625), (8633), (8645),
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | |            #314.
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8646)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8646) gives:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8647)  all_57_14 = e2 & op(e0, e1) = e2
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8647) implies:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8648)  all_57_14 = e2
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (39), (126), (147), (158),
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (160), (166), (168), (192), (193), (195), (196),
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (197), (201), (221), (231), (232), (246), (247),
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (267), (336), (374), (7573), (7575), (7582),
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8330), (8564), (8572), (8574), (8575), (8580),
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8581), (8582), (8584), (8585), (8588), (8589),
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8601), (8606), (8617), (8638), (8639), (8641),
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8643), (8644), (8647), (8648), (function-axioms)
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #310.
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8649)  all_57_15 = e2 & op(e0, e0) = e2
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8649) implies:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8650)  op(e0, e0) = e2
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8556), (8650), (function-axioms) are
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2177.
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | |   (8651)   ~ (all_10_1 = e0) & op(e3, e1) = all_10_1 &
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_10_1)
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8651) implies:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | |   (8652)   ~ (all_10_1 = e0)
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | |   (8653)  op(e3, e1) = all_10_1
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8611), (8622), (8652), (8653), (function-axioms)
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #309.
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | |   (8654)   ~ (all_36_1 = e2) & op(e3, e1) = all_36_1 &
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_36_1)
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8654) implies:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | |   (8655)   ~ (all_36_1 = e2)
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | |   (8656)  op(e3, e1) = all_36_1
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7571) gives:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | |   (8657)   ~ (all_10_0 = e2) & op(all_10_1, e3) = all_10_0 &
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = all_10_1 & $i(all_10_0) &
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_10_1)
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8657) implies:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | |   (8658)   ~ (all_10_0 = e2)
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | |   (8659)  op(e3, e1) = all_10_1
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | |   (8660)  op(all_10_1, e3) = all_10_0
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_36_1,
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (8611), (8656) gives:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | |   (8661)  all_36_1 = e0
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_1,
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | |              all_36_1, e1, e3, simplifying with (8656), (8659)
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | |   (8662)  all_36_1 = all_10_1
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8661), (8662) imply:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | |   (8663)  all_10_1 = e0
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8663) implies:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | |   (8664)  all_10_1 = e0
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8655), (8661) imply:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | |   (8665)   ~ (e2 = e0)
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8660), (8664) imply:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | |   (8666)  op(e0, e3) = all_10_0
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_3,
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | |              all_10_0, e3, e0, simplifying with (160), (8666)
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | |   (8667)  all_53_3 = all_10_0
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (8667) imply:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | |   (8668)  all_55_12 = all_10_0
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (8667) imply:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | |   (8669)   ~ (all_53_1 = all_10_0)
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (141), (8667) imply:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | |   (8670)   ~ (all_53_7 = all_10_0)
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8670) implies:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | |   (8671)   ~ (all_53_7 = all_10_0)
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (8667) imply:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | |   (8672)   ~ (all_53_11 = all_10_0)
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8672) implies:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | |   (8673)   ~ (all_53_11 = all_10_0)
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7575), (8667) imply:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | |   (8674)   ~ (all_10_0 = e1)
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8675)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (8615), (8658), (8666), (8675),
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | |            #314.
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8676)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8676) gives:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8677)  all_57_14 = e2 & op(e0, e1) = e2
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8677) implies:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8678)  all_57_14 = e2
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (39), (126), (147), (158),
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (160), (166), (168), (192), (193), (195), (196),
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (197), (201), (221), (231), (232), (246), (247),
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (267), (336), (374), (7573), (7575), (7582),
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8330), (8564), (8572), (8574), (8575), (8580),
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8581), (8582), (8584), (8585), (8588), (8589),
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8601), (8606), (8617), (8668), (8669), (8671),
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8673), (8674), (8677), (8678), (function-axioms)
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #310.
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8679)  all_57_15 = e2 & op(e0, e0) = e2
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8679) implies:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8680)  op(e0, e0) = e2
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8556), (8680), (function-axioms) are
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2177.
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | |   (8681)   ~ (all_10_1 = e0) & op(e3, e1) = all_10_1 &
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_10_1)
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8681) implies:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | |   (8682)   ~ (all_10_1 = e0)
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | |   (8683)  op(e3, e1) = all_10_1
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8611), (8656), (8682), (8683), (function-axioms)
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #309.
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | |   (8684)  all_57_9 = e0 & op(e3, e0) = e0
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8684) implies:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | |   (8685)  op(e3, e0) = e0
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8601), (8685), (function-axioms) are
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #313.
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | |   (8686)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e2)
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | BETA: splitting (8686) gives:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | |   (8687)  all_57_4 = e2 & op(e3, e1) = e2
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | ALPHA: (8687) implies:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | |   (8688)  all_57_4 = e2
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | |   (8689)  op(e3, e1) = e2
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | |   (8690)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8690) gives:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | |   (8691)  all_57_0 = e0 & op(e3, e3) = e0
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8691) implies:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | |   (8692)  all_57_0 = e0
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (39), (160), (168), (195), (232), (336),
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | |            (374), (7573), (7575), (8572), (8575), (8692),
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | |            #1545.
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | |   (8693)  all_57_1 = e0 & op(e3, e2) = e0
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8693) implies:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | |   (8694)  op(e3, e2) = e0
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_8, e2,
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (170), (8689) gives:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | |   (8695)  all_53_8 = e2
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_4, e0,
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (171), (8694) gives:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | |   (8696)  all_53_4 = e0
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (136), (8696) imply:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | |   (8697)   ~ (all_53_7 = e0)
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8697) implies:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | |   (8698)   ~ (all_53_7 = e0)
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8586), (8696) imply:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | |   (8699)   ~ (all_52_19 = e0)
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8699) implies:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | |   (8700)   ~ (all_52_19 = e0)
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7576), (8696) imply:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | |   (8701)   ~ (e1 = e0)
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (124), (8695) imply:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | |   (8702)   ~ (all_53_9 = e2)
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8702) implies:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | |   (8703)   ~ (all_53_9 = e2)
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8600), (8695) imply:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | |   (8704)   ~ (e3 = e2)
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7571) gives:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | |   (8705)   ~ (all_10_0 = e2) & op(all_10_1, e3) = all_10_0 &
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = all_10_1 & $i(all_10_0) &
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_10_1)
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.91  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8705) implies:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | |   (8706)   ~ (all_10_0 = e2)
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | |   (8707)  op(e3, e1) = all_10_1
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | |   (8708)  op(all_10_1, e3) = all_10_0
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8595) gives:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (8709)   ~ (all_36_0 = e0) & op(all_36_1, e3) = all_36_0 &
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = all_36_1 & $i(all_36_0) &
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_36_1)
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8709) implies:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (8710)   ~ (all_36_0 = e0)
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (8711)  op(e3, e1) = all_36_1
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (8712)  op(all_36_1, e3) = all_36_0
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_36_1,
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (8689), (8711) gives:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (8713)  all_36_1 = e2
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_1,
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | |              all_36_1, e1, e3, simplifying with (8707), (8711)
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (8714)  all_36_1 = all_10_1
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8713), (8714) imply:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (8715)  all_10_1 = e2
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8715) implies:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (8716)  all_10_1 = e2
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8712), (8713) imply:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (8717)  op(e2, e3) = all_36_0
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8708), (8716) imply:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (8718)  op(e2, e3) = all_10_0
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_1,
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | |              all_10_0, e3, e2, simplifying with (168), (8718)
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (8719)  all_53_1 = all_10_0
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_1,
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | |              all_36_0, e3, e2, simplifying with (168), (8717)
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (8720)  all_53_1 = all_36_0
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8719), (8720) imply:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (8721)  all_36_0 = all_10_0
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8721) implies:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (8722)  all_36_0 = all_10_0
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (8719) imply:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (8723)  all_55_4 = all_10_0
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (147), (8719) imply:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (8724)   ~ (all_53_9 = all_10_0)
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8724) implies:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (8725)   ~ (all_53_9 = all_10_0)
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7573), (8719) imply:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (8726)   ~ (all_10_0 = e1)
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8710), (8722) imply:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (8727)   ~ (all_10_0 = e0)
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8728)  all_55_4 = e3
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8723), (8728) imply:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8729)  all_10_0 = e3
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8725), (8729) imply:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8730)   ~ (all_53_9 = e3)
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8731)  all_55_6 = e3
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (8731) imply:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8732)  all_53_9 = e3
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8730), (8732) imply:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8733)  $false
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8733) is inconsistent.
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8734)  all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8734) gives:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8735)  all_55_6 = e2
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (8703), (8735) are inconsistent by
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2398.
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8736)  all_55_6 = e1 | all_55_6 = e0
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8736) gives:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8737)  all_55_6 = e1
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (8331), (8737) are inconsistent by
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2163.
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8738)  all_55_6 = e0
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (8738) imply:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8739)  all_53_9 = e0
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8739) implies:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8740)  all_53_9 = e0
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (119), (8740) imply:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8741)   ~ (all_53_11 = e0)
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8741) implies:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8742)   ~ (all_53_11 = e0)
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8743)  all_55_14 = e3
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (8743) imply:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8744)  all_53_11 = e3
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8744) implies:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8745)  all_53_11 = e3
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (126), (8745) imply:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8746)   ~ (all_53_7 = e3)
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8747)  all_55_13 = e3
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (8746), (8747) are inconsistent by
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2080.
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8748)  all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (136), (196), (204), (246), (270), (7576), (7582),
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8330), (8574), (8580), (8586), (8588), (8589),
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8599), (8698), (8748), (function-axioms) are
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #308.
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8749)  all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (126), (192), (196), (245), (246), (8330), (8334),
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8564), (8574), (8580), (8588), (8589), (8698),
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8700), (8742), (8749), (function-axioms) are
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1600.
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8750)  all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8750) gives:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8751)  all_55_4 = e2
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8723), (8751) imply:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8752)  all_10_0 = e2
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8706), (8752) imply:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8753)  $false
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8753) is inconsistent.
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8754)  all_55_4 = e1 | all_55_4 = e0
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8754) gives:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8755)  all_55_4 = e1
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8723), (8755) imply:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8756)  all_10_0 = e1
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8726), (8756) imply:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8757)  $false
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8757) is inconsistent.
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8758)  all_55_4 = e0
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8723), (8758) imply:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8759)  all_10_0 = e0
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8727), (8759) imply:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8760)  $false
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8760) is inconsistent.
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (8761)   ~ (all_36_1 = e2) & op(e3, e1) = all_36_1 &
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_36_1)
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8761) implies:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (8762)   ~ (all_36_1 = e2)
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (8763)  op(e3, e1) = all_36_1
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_36_1,
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (8689), (8763) gives:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (8764)  all_36_1 = e2
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8762), (8764) imply:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (8765)  $false
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8765) is inconsistent.
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | |   (8766)   ~ (all_10_1 = e0) & op(e3, e1) = all_10_1 &
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_10_1)
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8766) implies:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | |   (8767)   ~ (all_10_1 = e0)
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | |   (8768)  op(e3, e1) = all_10_1
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8595) gives:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (8769)   ~ (all_36_0 = e0) & op(all_36_1, e3) = all_36_0 &
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = all_36_1 & $i(all_36_0) &
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_36_1)
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8769) implies:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (8770)  op(e3, e1) = all_36_1
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_36_1,
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (8689), (8770) gives:
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (8771)  all_36_1 = e2
% 222.99/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_1,
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | |              all_36_1, e1, e3, simplifying with (8768), (8770)
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (8772)  all_36_1 = all_10_1
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8771), (8772) imply:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (8773)  all_10_1 = e2
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8773) implies:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (8774)  all_10_1 = e2
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8775)  all_55_9 = e3
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8580), (8775) imply:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8776)  all_52_19 = e3
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8776) implies:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8777)  all_52_19 = e3
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8574), (8777) imply:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8778)  op(e3, e3) = e2
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8779)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e1)
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (226), (228), (229),
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8334), (8778), (8779), (function-axioms) are
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1677.
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8780)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e1)
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8780) gives:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8781)  all_57_4 = e1 & op(e3, e1) = e1
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8688), (8781) are inconsistent by sub-proof
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2452.
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8782)  all_57_9 = e1 & op(e3, e0) = e1
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8782) implies:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8783)  all_57_9 = e1
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (237),
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8688), (8778), (8783), (function-axioms) are
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1604.
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8784)  all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8334), (8574), (8580), (8589), (8700), (8784),
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | |            #1602.
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (8785)   ~ (all_36_1 = e2) & op(e3, e1) = all_36_1 &
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_36_1)
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8689), (8785), (function-axioms) are inconsistent
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #307.
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | |   (8786)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8786) gives:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | |   (8787)  all_57_4 = e0 & op(e3, e1) = e0
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8787) implies:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | |   (8788)  all_57_4 = e0
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8688), (8788) are inconsistent by sub-proof
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | |            #2441.
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | |   (8789)  all_57_9 = e0 & op(e3, e0) = e0
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8789) implies:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | |   (8790)  op(e3, e0) = e0
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8601), (8790), (function-axioms) are
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #313.
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | End of split
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | |   (8791)  all_57_9 = e2 & op(e3, e0) = e2
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (8601), (8791), (function-axioms) are
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #306.
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | End of split
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | End of split
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | Case 2:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | |   (8792)   ~ (all_55_3 = e3)
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | REDUCE: (268), (8792) imply:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | |   (8793)   ~ (all_53_12 = e3)
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | Case 1:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | |   (8794)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | BETA: splitting (8794) gives:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | |   (8795)  all_57_9 = e3 & op(e3, e0) = e3
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | ALPHA: (8795) implies:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | |   (8796)  op(e3, e0) = e3
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (8793), (8796), (function-axioms) are
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2458.
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | |   (8797)  all_57_10 = e3 & op(e2, e0) = e3
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | ALPHA: (8797) implies:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | |   (8798)  all_57_10 = e3
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | |   (8799)  op(e2, e0) = e3
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_13,
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | |              e3, e0, e2, simplifying with (165), (8799) gives:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | |   (8800)  all_53_13 = e3
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | REDUCE: (8591), (8800) imply:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | |   (8801)   ~ (all_52_23 = e3)
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | SIMP: (8801) implies:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | |   (8802)   ~ (all_52_23 = e3)
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | |   (8803)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8803) gives:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | |   (8804)  all_57_2 = e2 & op(e2, e3) = e2
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8804) implies:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | |   (8805)  all_57_2 = e2
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | |   (8806)  op(e2, e3) = e2
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | |   (8807)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (8334), (8805), (8807),
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | |            #661.
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | |   (8808)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0)
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8808) gives:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (8809)  all_57_5 = e0 & op(e2, e1) = e0
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8809) implies:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (8810)  op(e2, e1) = e0
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_9, e0,
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (166), (8810) gives:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (8811)  all_53_9 = e0
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_1, e2,
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (168), (8806) gives:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (8812)  all_53_1 = e2
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (8812) imply:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (8813)   ~ (all_53_3 = e2)
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8813) implies:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (8814)   ~ (all_53_3 = e2)
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8582), (8812) imply:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (8815)   ~ (all_52_17 = e2)
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8815) implies:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (8816)   ~ (all_52_17 = e2)
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (124), (8811) imply:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (8817)   ~ (all_53_8 = e0)
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (119), (8811) imply:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (8818)   ~ (all_53_11 = e0)
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8818) implies:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (8819)   ~ (all_53_11 = e0)
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8337) gives:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8820)   ~ (all_26_0 = e3) & op(all_26_1, e2) = all_26_0 &
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_26_1 & $i(all_26_0) &
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_26_1)
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8820) implies:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8821)   ~ (all_26_0 = e3)
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8822)  op(e2, e1) = all_26_1
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8823)  op(all_26_1, e2) = all_26_0
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_26_1,
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (8810), (8822) gives:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8824)  all_26_1 = e0
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8823), (8824) imply:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8825)  op(e0, e2) = all_26_0
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_7,
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | |              all_26_0, e2, e0, simplifying with (159), (8825)
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8826)  all_53_7 = all_26_0
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (8826) imply:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8827)  all_55_13 = all_26_0
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (136), (8826) imply:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8828)   ~ (all_53_4 = all_26_0)
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (126), (8826) imply:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8829)   ~ (all_53_11 = all_26_0)
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8829) implies:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8830)   ~ (all_53_11 = all_26_0)
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8588), (8826) imply:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8831)   ~ (all_52_19 = all_26_0)
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8831) implies:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8832)   ~ (all_52_19 = all_26_0)
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8330), (8826) imply:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8833)   ~ (all_26_0 = e1)
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8834)  all_55_2 = e3
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (8834) imply:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8835)  all_53_8 = e3
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8835) implies:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8836)  all_53_8 = e3
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (8836) imply:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8837)   ~ (all_53_4 = e3)
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (122), (8836) imply:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8838)   ~ (all_53_11 = e3)
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8838) implies:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8839)   ~ (all_53_11 = e3)
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8840)  all_55_14 = e3
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (8839), (8840) are inconsistent by
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2294.
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8841)  all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8841) gives:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8842)  all_55_14 = e2
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (8842) imply:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8843)  all_53_11 = e2
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8843) implies:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8844)  all_53_11 = e2
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8830), (8844) imply:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8845)   ~ (all_26_0 = e2)
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8845) implies:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8846)   ~ (all_26_0 = e2)
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8847)  all_55_13 = e3
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8827), (8847) imply:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8848)  all_26_0 = e3
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8821), (8848) imply:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8849)  $false
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8849) is inconsistent.
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8850)  all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8850) gives:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8851)  all_55_13 = e2
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8827), (8851) imply:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8852)  all_26_0 = e2
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8852) implies:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8853)  all_26_0 = e2
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8846), (8853) imply:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8854)  $false
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8854) is inconsistent.
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8855)  all_55_13 = e1 | all_55_13 = e0
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8855) gives:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8856)  all_55_13 = e1
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8827), (8856) imply:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8857)  all_26_0 = e1
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8857) implies:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8858)  all_26_0 = e1
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8833), (8858) imply:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8859)  $false
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8859) is inconsistent.
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8860)  all_55_13 = e0
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8827), (8860) imply:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8861)  all_26_0 = e0
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8861) implies:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8862)  all_26_0 = e0
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8828), (8862) imply:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8863)   ~ (all_53_4 = e0)
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8832), (8862) imply:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8864)   ~ (all_52_19 = e0)
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8865)  all_55_1 = e3
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (8837), (8865) are inconsistent by
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2295.
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8866)  all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8866) gives:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8867)  all_55_1 = e2
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (8867) imply:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8868)  all_53_4 = e2
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8868) implies:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8869)  all_53_4 = e2
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8586), (8869) imply:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8870)   ~ (all_52_19 = e2)
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8870) implies:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8871)   ~ (all_52_19 = e2)
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (196), (7582), (8574), (8580), (8589),
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8864), (8871), (function-axioms) are inconsistent
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #358.
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8872)  all_55_1 = e1 | all_55_1 = e0
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (7576), (8863), (8872) are inconsistent by
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1730.
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8873)  all_55_14 = e1 | all_55_14 = e0
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (8564), (8819), (8873) are inconsistent by
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1720.
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8874)  all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8874) gives:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8875)  all_55_2 = e2
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (8875) imply:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8876)  all_53_8 = e2
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8876) implies:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8877)  all_53_8 = e2
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (122), (8877) imply:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8878)   ~ (all_53_11 = e2)
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8878) implies:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8879)   ~ (all_53_11 = e2)
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8880)  all_55_14 = e3
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (8880) imply:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8881)  all_53_11 = e3
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (8881) imply:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8882)   ~ (all_53_3 = e3)
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8883)  all_55_12 = e3
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (247), (8882), (8883) are inconsistent by
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2001.
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8884)  all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8884) gives:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8885)  all_55_12 = e2
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (247), (8814), (8885) are inconsistent by
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1337.
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8886)  all_55_12 = e1 | all_55_12 = e0
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (197), (247), (7575), (7582), (8575), (8581),
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8584), (8585), (8816), (8886), (function-axioms)
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #311.
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8887)  all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (8564), (8819), (8879), (8887) are
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1719.
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8888)  all_55_2 = e1 | all_55_2 = e0
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (7577), (8817), (8888) are inconsistent by
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2030.
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8889)   ~ (all_26_1 = e0) & op(e2, e1) = all_26_1 &
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_26_1)
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8326), (8810), (8889), (function-axioms) are
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1710.
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | |   (8890)  all_57_10 = e0 & op(e2, e0) = e0
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8890) implies:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | |   (8891)  all_57_10 = e0
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8798), (8891) are inconsistent by sub-proof
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | |            #1989.
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | |   (8892)  all_57_3 = e2 & op(e2, e2) = e2
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8892) implies:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | |   (8893)  op(e2, e2) = e2
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8334), (8893), (function-axioms) are
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2306.
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | |   (8894)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8894) gives:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | |   (8895)  all_57_5 = e2 & op(e2, e1) = e2
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8895) implies:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | |   (8896)  all_57_5 = e2
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | |   (8897)  op(e2, e1) = e2
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | |   (8898)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8898) gives:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | |   (8899)  all_57_2 = e0 & op(e2, e3) = e0
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8899) implies:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | |   (8900)  op(e2, e3) = e0
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_9, e2,
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (166), (8897) gives:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | |   (8901)  all_53_9 = e2
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_1, e0,
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (168), (8900) gives:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | |   (8902)  all_53_1 = e0
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8582), (8902) imply:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | |   (8903)   ~ (all_52_17 = e0)
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8903) implies:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | |   (8904)   ~ (all_52_17 = e0)
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (124), (8901) imply:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | |   (8905)   ~ (all_53_8 = e2)
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (119), (8901) imply:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | |   (8906)   ~ (all_53_11 = e2)
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8906) implies:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | |   (8907)   ~ (all_53_11 = e2)
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8908)  all_55_2 = e3
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (8908) imply:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8909)  all_53_8 = e3
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8909) implies:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8910)  all_53_8 = e3
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (8910) imply:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8911)   ~ (all_53_4 = e3)
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (122), (8910) imply:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8912)   ~ (all_53_11 = e3)
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8912) implies:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8913)   ~ (all_53_11 = e3)
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8914)  all_55_14 = e3
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (8914) imply:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8915)  all_53_11 = e3
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8913), (8915) imply:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8916)  $false
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8916) is inconsistent.
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8917)  all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8917) gives:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8918)  all_55_14 = e2
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (8918) imply:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8919)  all_53_11 = e2
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8907), (8919) imply:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8920)  $false
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8920) is inconsistent.
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8921)  all_55_14 = e1 | all_55_14 = e0
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8921) gives:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8922)  all_55_14 = e1
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (8564), (8922) are inconsistent by
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2165.
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8923)  all_55_14 = e0
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (8923) imply:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8924)  all_53_11 = e0
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8924) implies:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8925)  all_53_11 = e0
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (8925) imply:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8926)   ~ (all_53_3 = e0)
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (126), (8925) imply:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8927)   ~ (all_53_7 = e0)
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8928)  all_55_13 = e3
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (8928) imply:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8929)  all_53_7 = e3
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (141), (8929) imply:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8930)   ~ (all_53_3 = e3)
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8931)  all_55_12 = e3
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (247), (8930), (8931) are inconsistent by
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2001.
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8932)  all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8932) gives:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8933)  all_55_12 = e2
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (8933) imply:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8934)  all_53_3 = e2
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8584), (8934) imply:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8935)   ~ (all_52_17 = e2)
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8935) implies:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8936)   ~ (all_52_17 = e2)
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (197), (7582), (8575), (8581), (8585), (8904),
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8936), (function-axioms) are inconsistent by
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #312.
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8937)  all_55_12 = e1 | all_55_12 = e0
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (247), (7575), (8926), (8937) are inconsistent by
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1992.
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8938)  all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (136), (196), (204), (246), (270), (7576), (7582),
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8330), (8574), (8580), (8586), (8588), (8589),
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8911), (8927), (8938), (function-axioms) are
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #308.
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8939)  all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8939) gives:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8940)  all_55_2 = e2
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (8905), (8940) are inconsistent by
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2027.
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8941)  all_55_2 = e1 | all_55_2 = e0
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8941) gives:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8942)  all_55_2 = e1
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (7577), (8942) are inconsistent by
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2032.
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8943)  all_55_2 = e0
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (8943) imply:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8944)  all_53_8 = e0
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8944) implies:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8945)  all_53_8 = e0
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (8945) imply:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8946)   ~ (all_53_12 = e0)
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8946) implies:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8947)   ~ (all_53_12 = e0)
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (194), (202), (268), (7578), (8556), (8573),
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8579), (8590), (8592), (8793), (8802), (8947),
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1913.
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | |   (8948)  all_57_3 = e0 & op(e2, e2) = e0
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8948) implies:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | |   (8949)  op(e2, e2) = e0
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8334), (8949), (function-axioms) are
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2352.
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | |   (8950)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0)
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8950) gives:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | |   (8951)  all_57_5 = e0 & op(e2, e1) = e0
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8951) implies:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | |   (8952)  all_57_5 = e0
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8896), (8952) are inconsistent by sub-proof
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | |            #2363.
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | |   (8953)  all_57_10 = e0 & op(e2, e0) = e0
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8953) implies:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | |   (8954)  all_57_10 = e0
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8798), (8954) are inconsistent by sub-proof
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | |            #1989.
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | |   (8955)  all_57_10 = e2 & op(e2, e0) = e2
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (8798), (8955) are inconsistent by sub-proof
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | |            #2250.
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | End of split
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | End of split
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | Case 2:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | |   (8956)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | BETA: splitting (8956) gives:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | |   (8957)  all_57_11 = e3 & op(e1, e0) = e3
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | ALPHA: (8957) implies:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | |   (8958)  op(e1, e0) = e3
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_23,
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | |              e3, e0, e1, simplifying with (8570), (8958) gives:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | |   (8959)  all_52_23 = e3
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | REDUCE: (8573), (8959) imply:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | |   (8960)  op(e3, e3) = e0
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, e0, e3,
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | |              e3, simplifying with (7582), (8960) gives:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | |   (8961)  e1 = e0
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7581), (8961) imply:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | |   (8962)  all_57_0 = e0
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (39), (160), (168), (195), (232), (336),
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | |            (374), (7573), (7575), (8572), (8575), (8962),
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | |            #1545.
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | |   (8963)  all_57_15 = e3 & op(e0, e0) = e3
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | ALPHA: (8963) implies:
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | |   (8964)  op(e0, e0) = e3
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (8556), (8964), (function-axioms) are
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2183.
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | End of split
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | End of split
% 223.06/37.93  | | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | | End of split
% 223.06/37.93  | | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | End of split
% 223.06/37.93  | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | Case 2:
% 223.06/37.93  | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | |   (8965)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 223.06/37.93  | | | | | | | | | | | | | | | | |           all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 223.06/37.93  | | | | | | | | | | | | | | | | |           op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 223.06/37.93  | | | | | | | | | | | | | | | | |             all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 223.06/37.93  | | | | | | | | | | | | | | | | |           & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 223.06/37.93  | | | | | | | | | | | | | | | | |           & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 223.06/37.93  | | | | | | | | | | | | | | | | |           & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 223.06/37.93  | | | | | | | | | | | | | | | | |           $i(all_52_31)
% 223.06/37.93  | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | ALPHA: (8965) implies:
% 223.06/37.93  | | | | | | | | | | | | | | | | |   (8966)  op(e0, e0) = all_52_31
% 223.06/37.93  | | | | | | | | | | | | | | | | |   (8967)  op(all_52_31, all_52_31) = e0
% 223.06/37.93  | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (8339), (8556), (8966), (8967),
% 223.06/37.93  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.06/37.93  | | | | | | | | | | | | | | | | |            #2086.
% 223.06/37.93  | | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | End of split
% 223.06/37.93  | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | End of split
% 223.06/37.93  | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | Case 2:
% 223.06/37.93  | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | |   (8968)  all_57_11 = e1 & op(e1, e0) = e1
% 223.06/37.93  | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | REF_CLOSE: (161), (8554), (8968), (function-axioms) are
% 223.06/37.93  | | | | | | | | | | | | | | |            inconsistent by sub-proof #305.
% 223.06/37.93  | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | End of split
% 223.06/37.93  | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | End of split
% 223.06/37.93  | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | End of split
% 223.06/37.93  | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | Case 2:
% 223.06/37.93  | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | |   (8969)  all_24_2 = e0
% 223.06/37.93  | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | COMBINE_EQS: (315), (8969) imply:
% 223.06/37.93  | | | | | | | | | | | |   (8970)  all_6_2 = e0
% 223.06/37.93  | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | REDUCE: (350), (8970) imply:
% 223.06/37.93  | | | | | | | | | | | |   (8971)   ~ (all_53_2 = e0)
% 223.06/37.93  | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | REDUCE: (361), (8970) imply:
% 223.06/37.93  | | | | | | | | | | | |   (8972)   ~ (all_53_6 = e0)
% 223.06/37.93  | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | REDUCE: (363), (8970) imply:
% 223.06/37.93  | | | | | | | | | | | |   (8973)   ~ (all_53_8 = e0)
% 223.06/37.93  | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | REDUCE: (368), (8970) imply:
% 223.06/37.93  | | | | | | | | | | | |   (8974)   ~ (all_53_14 = e0)
% 223.06/37.93  | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | BETA: splitting (214) gives:
% 223.06/37.93  | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | Case 1:
% 223.06/37.93  | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | |   (8975)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 223.06/37.93  | | | | | | | | | | | | |             & op(e1, e2) = e0)
% 223.06/37.93  | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | REF_CLOSE: (163), (164), (8971), (8972), (8975),
% 223.06/37.93  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.06/37.93  | | | | | | | | | | | | |            #2038.
% 223.06/37.93  | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | Case 2:
% 223.06/37.93  | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | |   (8976)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 223.06/37.93  | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 223.06/37.93  | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | BETA: splitting (8976) gives:
% 223.06/37.93  | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | Case 1:
% 223.06/37.93  | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | |   (8977)  all_57_8 = e0 & op(e1, e1) = e0
% 223.06/37.93  | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | ALPHA: (8977) implies:
% 223.06/37.93  | | | | | | | | | | | | | |   (8978)  all_57_8 = e0
% 223.06/37.93  | | | | | | | | | | | | | |   (8979)  op(e1, e1) = e0
% 223.06/37.93  | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 223.06/37.93  | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | Case 1:
% 223.06/37.93  | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | |   (8980)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 223.06/37.93  | | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 223.06/37.93  | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | BETA: splitting (8980) gives:
% 223.06/37.93  | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | Case 1:
% 223.06/37.93  | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | |   (8981)  all_57_6 = e1 & op(e1, e3) = e1
% 223.06/37.93  | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | REF_CLOSE: (164), (7574), (8981), (function-axioms) are
% 223.06/37.93  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #316.
% 223.06/37.93  | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | Case 2:
% 223.06/37.93  | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | |   (8982)  all_57_7 = e1 & op(e1, e2) = e1
% 223.06/37.93  | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | REF_CLOSE: (163), (8329), (8982), (function-axioms) are
% 223.06/37.93  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2265.
% 223.06/37.93  | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | End of split
% 223.06/37.93  | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | Case 2:
% 223.06/37.93  | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | |   (8983)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 223.06/37.93  | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 223.06/37.93  | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | BETA: splitting (8983) gives:
% 223.06/37.93  | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | Case 1:
% 223.06/37.93  | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | |   (8984)  all_57_8 = e1 & op(e1, e1) = e1
% 223.06/37.93  | | | | | | | | | | | | | | | | 
% 223.06/37.93  | | | | | | | | | | | | | | | | ALPHA: (8984) implies:
% 223.06/37.94  | | | | | | | | | | | | | | | |   (8985)  op(e1, e1) = e1
% 223.06/37.94  | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8979), (8985), (function-axioms) are
% 223.06/37.94  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2427.
% 223.06/37.94  | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | Case 2:
% 223.06/37.94  | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | |   (8986)  all_57_11 = e1 & op(e1, e0) = e1
% 223.06/37.94  | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | ALPHA: (8986) implies:
% 223.06/37.94  | | | | | | | | | | | | | | | |   (8987)  all_57_11 = e1
% 223.06/37.94  | | | | | | | | | | | | | | | |   (8988)  op(e1, e0) = e1
% 223.06/37.94  | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 223.06/37.94  | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | Case 1:
% 223.06/37.94  | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | |   (8989)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 223.06/37.94  | | | | | | | | | | | | | | | | |             & op(e2, e1) = e1)
% 223.06/37.94  | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | BETA: splitting (8989) gives:
% 223.06/37.94  | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | Case 1:
% 223.06/37.94  | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | |   (8990)  all_57_4 = e1 & op(e3, e1) = e1
% 223.06/37.94  | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | ALPHA: (8990) implies:
% 223.06/37.94  | | | | | | | | | | | | | | | | | |   (8991)  op(e3, e1) = e1
% 223.06/37.94  | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_8, e1,
% 223.06/37.94  | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (170), (8991) gives:
% 223.06/37.94  | | | | | | | | | | | | | | | | | |   (8992)  all_53_8 = e1
% 223.06/37.94  | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | REDUCE: (7577), (8992) imply:
% 223.06/37.94  | | | | | | | | | | | | | | | | | |   (8993)  $false
% 223.06/37.94  | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | CLOSE: (8993) is inconsistent.
% 223.06/37.94  | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | Case 2:
% 223.06/37.94  | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | |   (8994)  all_57_5 = e1 & op(e2, e1) = e1
% 223.06/37.94  | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (8331), (8994), (function-axioms) are
% 223.06/37.94  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2305.
% 223.06/37.94  | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | End of split
% 223.06/37.94  | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | Case 2:
% 223.06/37.94  | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | |   (8995)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 223.06/37.94  | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e1)
% 223.06/37.94  | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | BETA: splitting (8995) gives:
% 223.06/37.94  | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | Case 1:
% 223.06/37.94  | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | |   (8996)  all_57_8 = e1 & op(e1, e1) = e1
% 223.06/37.94  | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | ALPHA: (8996) implies:
% 223.06/37.94  | | | | | | | | | | | | | | | | | |   (8997)  op(e1, e1) = e1
% 223.06/37.94  | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8979), (8997), (function-axioms) are
% 223.06/37.94  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2427.
% 223.06/37.94  | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | Case 2:
% 223.06/37.94  | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | |   (8998)  all_57_14 = e1 & op(e0, e1) = e1
% 223.06/37.94  | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | ALPHA: (8998) implies:
% 223.06/37.94  | | | | | | | | | | | | | | | | | |   (8999)  op(e0, e1) = e1
% 223.06/37.94  | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_11,
% 223.06/37.94  | | | | | | | | | | | | | | | | | |              e1, e1, e0, simplifying with (158), (8999) gives:
% 223.06/37.94  | | | | | | | | | | | | | | | | | |   (9000)  all_53_11 = e1
% 223.06/37.94  | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_14,
% 223.06/37.94  | | | | | | | | | | | | | | | | | |              e1, e0, e1, simplifying with (161), (8988) gives:
% 223.06/37.94  | | | | | | | | | | | | | | | | | |   (9001)  all_53_14 = e1
% 223.06/37.94  | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | REDUCE: (372), (9001) imply:
% 223.06/37.94  | | | | | | | | | | | | | | | | | |   (9002)   ~ (all_4_2 = e1)
% 223.06/37.94  | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | SIMP: (9002) implies:
% 223.06/37.94  | | | | | | | | | | | | | | | | | |   (9003)   ~ (all_4_2 = e1)
% 223.06/37.94  | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 223.06/37.94  | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | Case 1:
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | |   (9004)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 223.06/37.94  | | | | | | | | | | | | | | | | | | |             all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 223.06/37.94  | | | | | | | | | | | | | | | | | | |             op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 223.06/37.94  | | | | | | | | | | | | | | | | | | |               all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 223.06/37.94  | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 223.06/37.94  | | | | | | | | | | | | | | | | | | |             op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 223.06/37.94  | | | | | | | | | | | | | | | | | | |             $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 223.06/37.94  | | | | | | | | | | | | | | | | | | |             $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 223.06/37.94  | | | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 223.06/37.94  | | | | | | | | | | | | | | | | | | |               all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 223.06/37.94  | | | | | | | | | | | | | | | | | | |             & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 223.06/37.94  | | | | | | | | | | | | | | | | | | |               all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 223.06/37.94  | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 223.06/37.94  | | | | | | | | | | | | | | | | | | |             & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 223.06/37.94  | | | | | | | | | | | | | | | | | | |             $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | BETA: splitting (9004) gives:
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | Case 1:
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | |   (9005)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | |           all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | |           op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | |             all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | |           $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | |           $i(all_52_7)
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | ALPHA: (9005) implies:
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | |   (9006)  op(e3, e2) = all_52_3
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | |   (9007)  op(all_52_3, all_52_3) = e2
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | |   (9008)  all_55_15 = e3
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (7584), (9008) are inconsistent by
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | |            sub-proof #2503.
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | |   (9009)  all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9009) gives:
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | |   (9010)  all_55_15 = e2
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (373), (9010) are inconsistent by sub-proof
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | |            #2502.
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | |   (9011)   ~ (all_55_15 = e2)
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | |   (9012)  all_55_15 = e1 | all_55_15 = e0
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9012) gives:
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | |   (9013)  all_55_15 = e1
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (9003), (9013) are inconsistent by
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2501.
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | |   (9014)  all_55_15 = e0
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (9014) imply:
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | |   (9015)  all_4_2 = e0
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9015) implies:
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | |   (9016)  all_4_2 = e0
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (370), (9016) imply:
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | |   (9017)   ~ (all_53_12 = e0)
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (373), (9016) imply:
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | |   (9018)   ~ (e2 = e0)
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9003), (9016) imply:
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | |   (9019)   ~ (e1 = e0)
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (9016) imply:
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | |   (9020)  op(e0, e0) = e0
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | | |   (9021)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9021) gives:
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | | | |   (9022)  all_57_0 = e0 & op(e3, e3) = e0
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9022) implies:
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | | | |   (9023)  all_57_0 = e0
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (39), (160), (168),
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | | | |            (216), (217), (232), (374), (7573), (7575),
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | | | |            (8978), (8987), (9023), (function-axioms) are
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1678.
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | | | |   (9024)  all_57_1 = e0 & op(e3, e2) = e0
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9024) implies:
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | | | |   (9025)  op(e3, e2) = e0
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9006), (9007), (9020), (9025),
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | | | |            #2399.
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | | |   (9026)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (170), (8973), (9017), (9026),
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | | |            #1544.
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | End of split
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | End of split
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | Case 2:
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | |   (9027)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | |           all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | |           op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | |             all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | |           & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | |           $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | |           $i(all_52_15)
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | ALPHA: (9027) implies:
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | |   (9028)  op(e2, e2) = all_52_11
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | |   (9029)  op(all_52_11, all_52_11) = e2
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8334), (8979), (9028), (9029),
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | |            #1843.
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | End of split
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | Case 2:
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | |   (9030)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 223.06/37.94  | | | | | | | | | | | | | | | | | | |             & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 223.06/37.94  | | | | | | | | | | | | | | | | | | |             & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 223.06/37.94  | | | | | | | | | | | | | | | | | | |               all_52_21) = e1 & op(all_52_23, all_52_23) =
% 223.06/37.94  | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 223.06/37.94  | | | | | | | | | | | | | | | | | | |             all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 223.06/37.94  | | | | | | | | | | | | | | | | | | |             = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 223.06/37.94  | | | | | | | | | | | | | | | | | | |             $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 223.06/37.94  | | | | | | | | | | | | | | | | | | |             & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 223.06/37.94  | | | | | | | | | | | | | | | | | | |             e0 & op(all_52_25, all_52_25) = e3 &
% 223.06/37.94  | | | | | | | | | | | | | | | | | | |             op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 223.06/37.94  | | | | | | | | | | | | | | | | | | |               all_52_29) = e1 & op(all_52_31, all_52_31) =
% 223.06/37.94  | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 223.06/37.94  | | | | | | | | | | | | | | | | | | |             all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 223.06/37.94  | | | | | | | | | | | | | | | | | | |             = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 223.06/37.94  | | | | | | | | | | | | | | | | | | |             $i(all_52_29) & $i(all_52_31))
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | BETA: splitting (9030) gives:
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | Case 1:
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | |   (9031)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | |           all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | |           op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | |             all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | |           & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | |           & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | |           & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | |           $i(all_52_23)
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | 
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | | ALPHA: (9031) implies:
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | |   (9032)  op(e1, e1) = all_52_21
% 223.06/37.94  | | | | | | | | | | | | | | | | | | | |   (9033)  op(e1, e2) = all_52_19
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | |   (9034)  op(all_52_21, all_52_21) = e1
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | |   (9035)  op(all_52_19, all_52_19) = e2
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (159), (161), (165), (169), (171), (190),
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | |            (207), (226), (244), (362), (370), (371), (372),
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | |            (373), (7576), (7584), (8334), (8979), (9003),
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | |            (9032), (9033), (9034), (9035), (function-axioms)
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1838.
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | |   (9036)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | |           all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | |           op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | |             all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | |           & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | |           & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | |           & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | |           $i(all_52_31)
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | ALPHA: (9036) implies:
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | |   (9037)  op(e0, e1) = all_52_29
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | |   (9038)  op(all_52_29, all_52_29) = e1
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | |   (9039)  all_55_15 = e3
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (7584), (9039) are inconsistent by
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | |            sub-proof #2503.
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | |   (9040)  all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9040) gives:
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | |   (9041)  all_55_15 = e2
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (373), (9041) are inconsistent by sub-proof
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | |            #2502.
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | |   (9042)   ~ (all_55_15 = e2)
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | |   (9043)  all_55_15 = e1 | all_55_15 = e0
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9043) gives:
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | |   (9044)  all_55_15 = e1
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (9003), (9044) are inconsistent by
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2501.
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | |   (9045)  all_55_15 = e0
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (9045) imply:
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | |   (9046)  all_4_2 = e0
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9046) implies:
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | |   (9047)  all_4_2 = e0
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (370), (9047) imply:
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | |   (9048)   ~ (all_53_12 = e0)
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (373), (9047) imply:
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | |   (9049)   ~ (e2 = e0)
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9003), (9047) imply:
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | |   (9050)   ~ (e1 = e0)
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | |   (9051)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9051) gives:
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | | |   (9052)  all_57_0 = e0 & op(e3, e3) = e0
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9052) implies:
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | | |   (9053)  all_57_0 = e0
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (39), (160), (168),
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | | |            (216), (217), (232), (374), (7573), (7575),
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | | |            (8978), (8987), (9053), (function-axioms) are
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1678.
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | | |   (9054)  all_57_1 = e0 & op(e3, e2) = e0
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9054) implies:
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | | |   (9055)  op(e3, e2) = e0
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_29, e1, e0, simplifying with (8999), (9037)
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | | |   (9056)  all_52_29 = e1
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_4, e0,
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (171), (9055) gives:
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | | |   (9057)  all_53_4 = e0
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9038), (9056) imply:
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | | |   (9058)  op(e1, e1) = e1
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8979), (9058), (function-axioms) are
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2427.
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | |   (9059)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (170), (8973), (9048), (9059),
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | |            #1544.
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.94  | | | | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.94  | | | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | | End of split
% 223.10/37.94  | | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | End of split
% 223.10/37.94  | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | End of split
% 223.10/37.94  | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | End of split
% 223.10/37.94  | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | Case 2:
% 223.10/37.94  | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | |   (9060)  all_57_11 = e0 & op(e1, e0) = e0
% 223.10/37.94  | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | REF_CLOSE: (161), (8974), (9060), (function-axioms) are
% 223.10/37.94  | | | | | | | | | | | | | |            inconsistent by sub-proof #2341.
% 223.10/37.94  | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | End of split
% 223.10/37.94  | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | End of split
% 223.10/37.94  | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | End of split
% 223.10/37.94  | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | End of split
% 223.10/37.94  | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | End of split
% 223.10/37.94  | | | | | | | | | 
% 223.10/37.94  | | | | | | | | Case 2:
% 223.10/37.94  | | | | | | | | | 
% 223.10/37.94  | | | | | | | | |   (9061)  all_14_2 = e0
% 223.10/37.94  | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | COMBINE_EQS: (328), (9061) imply:
% 223.10/37.94  | | | | | | | | |   (9062)  all_8_2 = e0
% 223.10/37.94  | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | SIMP: (9062) implies:
% 223.10/37.94  | | | | | | | | |   (9063)  all_8_2 = e0
% 223.10/37.94  | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | REDUCE: (349), (9063) imply:
% 223.10/37.94  | | | | | | | | |   (9064)   ~ (all_53_1 = e0)
% 223.10/37.94  | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | REDUCE: (352), (9063) imply:
% 223.10/37.94  | | | | | | | | |   (9065)   ~ (all_53_4 = e0)
% 223.10/37.94  | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | REDUCE: (354), (9063) imply:
% 223.10/37.94  | | | | | | | | |   (9066)   ~ (all_53_6 = e0)
% 223.10/37.94  | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | REDUCE: (358), (9063) imply:
% 223.10/37.94  | | | | | | | | |   (9067)   ~ (all_53_9 = e0)
% 223.10/37.94  | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | REDUCE: (360), (9063) imply:
% 223.10/37.94  | | | | | | | | |   (9068)   ~ (all_53_13 = e0)
% 223.10/37.94  | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | BETA: splitting (222) gives:
% 223.10/37.94  | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | Case 1:
% 223.10/37.94  | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | |   (9069)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 223.10/37.94  | | | | | | | | | |             & op(e2, e2) = e0)
% 223.10/37.94  | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | BETA: splitting (9069) gives:
% 223.10/37.94  | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | Case 1:
% 223.10/37.94  | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | |   (9070)  all_57_2 = e0 & op(e2, e3) = e0
% 223.10/37.94  | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | ALPHA: (9070) implies:
% 223.10/37.94  | | | | | | | | | | |   (9071)  op(e2, e3) = e0
% 223.10/37.94  | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | REF_CLOSE: (168), (9064), (9071), (function-axioms) are
% 223.10/37.94  | | | | | | | | | | |            inconsistent by sub-proof #1943.
% 223.10/37.94  | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | Case 2:
% 223.10/37.94  | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | |   (9072)  all_57_3 = e0 & op(e2, e2) = e0
% 223.10/37.94  | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | ALPHA: (9072) implies:
% 223.10/37.94  | | | | | | | | | | |   (9073)  all_57_3 = e0
% 223.10/37.94  | | | | | | | | | | |   (9074)  op(e2, e2) = e0
% 223.10/37.94  | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | BETA: splitting (67) gives:
% 223.10/37.94  | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | Case 1:
% 223.10/37.94  | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | |   (9075)   ~ (all_24_2 = e0)
% 223.10/37.94  | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | REDUCE: (315), (9075) imply:
% 223.10/37.94  | | | | | | | | | | | |   (9076)   ~ (all_6_2 = e0)
% 223.10/37.94  | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | BETA: splitting (76) gives:
% 223.10/37.94  | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | Case 1:
% 223.10/37.94  | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | |   (9077)   ~ (all_30_2 = e1)
% 223.10/37.94  | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | REDUCE: (330), (9077) imply:
% 223.10/37.94  | | | | | | | | | | | | |   (9078)   ~ (all_4_2 = e1)
% 223.10/37.94  | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | BETA: splitting (190) gives:
% 223.10/37.94  | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | Case 1:
% 223.10/37.94  | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | |   (9079)  all_55_15 = e3
% 223.10/37.94  | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | REF_CLOSE: (244), (7584), (9079) are inconsistent by
% 223.10/37.94  | | | | | | | | | | | | | |            sub-proof #2503.
% 223.10/37.94  | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | Case 2:
% 223.10/37.94  | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | |   (9080)   ~ (all_55_15 = e3)
% 223.10/37.94  | | | | | | | | | | | | | |   (9081)  all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 223.10/37.94  | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | BETA: splitting (9081) gives:
% 223.10/37.94  | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | Case 1:
% 223.10/37.94  | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | |   (9082)  all_55_15 = e2
% 223.10/37.94  | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | REF_CLOSE: (244), (373), (9082) are inconsistent by sub-proof
% 223.10/37.94  | | | | | | | | | | | | | | |            #2502.
% 223.10/37.94  | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | Case 2:
% 223.10/37.94  | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | |   (9083)   ~ (all_55_15 = e2)
% 223.10/37.94  | | | | | | | | | | | | | | |   (9084)  all_55_15 = e1 | all_55_15 = e0
% 223.10/37.94  | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | BETA: splitting (9084) gives:
% 223.10/37.94  | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | Case 1:
% 223.10/37.94  | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | |   (9085)  all_55_15 = e1
% 223.10/37.94  | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | REF_CLOSE: (244), (9078), (9085) are inconsistent by
% 223.10/37.94  | | | | | | | | | | | | | | | |            sub-proof #2501.
% 223.10/37.94  | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | Case 2:
% 223.10/37.94  | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | |   (9086)  all_55_15 = e0
% 223.10/37.94  | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (9086) imply:
% 223.10/37.94  | | | | | | | | | | | | | | | |   (9087)  all_4_2 = e0
% 223.10/37.94  | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | SIMP: (9087) implies:
% 223.10/37.94  | | | | | | | | | | | | | | | |   (9088)  all_4_2 = e0
% 223.10/37.94  | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | REDUCE: (370), (9088) imply:
% 223.10/37.94  | | | | | | | | | | | | | | | |   (9089)   ~ (all_53_12 = e0)
% 223.10/37.94  | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | REDUCE: (372), (9088) imply:
% 223.10/37.94  | | | | | | | | | | | | | | | |   (9090)   ~ (all_53_14 = e0)
% 223.10/37.94  | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | REDUCE: (7584), (9088) imply:
% 223.10/37.94  | | | | | | | | | | | | | | | |   (9091)   ~ (e3 = e0)
% 223.10/37.94  | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | REDUCE: (373), (9088) imply:
% 223.10/37.94  | | | | | | | | | | | | | | | |   (9092)   ~ (e2 = e0)
% 223.10/37.94  | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | REDUCE: (9078), (9088) imply:
% 223.10/37.94  | | | | | | | | | | | | | | | |   (9093)   ~ (e1 = e0)
% 223.10/37.94  | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 223.10/37.94  | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.94  | | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | |   (9094)  all_57_15 = e0 & op(e0, e0) = e0
% 223.10/37.94  | | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | | ALPHA: (9094) implies:
% 223.10/37.94  | | | | | | | | | | | | | | | | |   (9095)  all_57_15 = e0
% 223.10/37.94  | | | | | | | | | | | | | | | | |   (9096)  op(e0, e0) = e0
% 223.10/37.94  | | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (85), (107),
% 223.10/37.94  | | | | | | | | | | | | | | | | |            (145), (160), (161), (163), (164), (166), (170),
% 223.10/37.94  | | | | | | | | | | | | | | | | |            (193), (208), (209), (210), (214), (218), (247),
% 223.10/37.94  | | | | | | | | | | | | | | | | |            (7571), (7572), (7575), (7577), (7582), (9066),
% 223.10/37.94  | | | | | | | | | | | | | | | | |            (9067), (9074), (9076), (9090), (9095), (9096),
% 223.10/37.94  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/37.94  | | | | | | | | | | | | | | | | |            #300.
% 223.10/37.94  | | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.94  | | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | |   (9097)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 223.10/37.94  | | | | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 223.10/37.94  | | | | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 223.10/37.94  | | | | | | | | | | | | | | | | |                 e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 223.10/37.94  | | | | | | | | | | | | | | | | |               e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 223.10/37.94  | | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (165), (169), (9068), (9089), (9090),
% 223.10/37.94  | | | | | | | | | | | | | | | | |            (9097), (function-axioms) are inconsistent by
% 223.10/37.94  | | | | | | | | | | | | | | | | |            sub-proof #2112.
% 223.10/37.94  | | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | | End of split
% 223.10/37.94  | | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | | End of split
% 223.10/37.94  | | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | | End of split
% 223.10/37.94  | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | End of split
% 223.10/37.94  | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | Case 2:
% 223.10/37.94  | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | |   (9098)  all_30_2 = e1
% 223.10/37.94  | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | COMBINE_EQS: (330), (9098) imply:
% 223.10/37.94  | | | | | | | | | | | | |   (9099)  all_4_2 = e1
% 223.10/37.94  | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | SIMP: (9099) implies:
% 223.10/37.94  | | | | | | | | | | | | |   (9100)  all_4_2 = e1
% 223.10/37.94  | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | REDUCE: (371), (9100) imply:
% 223.10/37.94  | | | | | | | | | | | | |   (9101)   ~ (all_53_13 = e1)
% 223.10/37.94  | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | REDUCE: (373), (9100) imply:
% 223.10/37.94  | | | | | | | | | | | | |   (9102)   ~ (e2 = e1)
% 223.10/37.94  | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | REDUCE: (36), (9100) imply:
% 223.10/37.94  | | | | | | | | | | | | |   (9103)  op(e0, e0) = e1
% 223.10/37.94  | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | BETA: splitting (107) gives:
% 223.10/37.94  | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | Case 1:
% 223.10/37.94  | | | | | | | | | | | | | | 
% 223.10/37.94  | | | | | | | | | | | | | |   (9104)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 223.10/37.94  | | | | | | | | | | | | | |             all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 223.10/37.94  | | | | | | | | | | | | | |             op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 223.10/37.94  | | | | | | | | | | | | | |               all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 223.10/37.94  | | | | | | | | | | | | | |             op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 223.10/37.94  | | | | | | | | | | | | | |             op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 223.10/37.94  | | | | | | | | | | | | | |             $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 223.10/37.94  | | | | | | | | | | | | | |             $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 223.10/37.94  | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 223.10/37.94  | | | | | | | | | | | | | |               all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 223.10/37.94  | | | | | | | | | | | | | |             & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 223.10/37.94  | | | | | | | | | | | | | |               all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 223.10/37.94  | | | | | | | | | | | | | |             op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 223.10/37.94  | | | | | | | | | | | | | |             & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 223.10/37.94  | | | | | | | | | | | | | |             $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 223.10/37.95  | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | BETA: splitting (9104) gives:
% 223.10/37.95  | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | Case 1:
% 223.10/37.95  | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | |   (9105)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 223.10/37.95  | | | | | | | | | | | | | | |           all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 223.10/37.95  | | | | | | | | | | | | | | |           op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 223.10/37.95  | | | | | | | | | | | | | | |             all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 223.10/37.95  | | | | | | | | | | | | | | |           op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 223.10/37.95  | | | | | | | | | | | | | | |           op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 223.10/37.95  | | | | | | | | | | | | | | |           $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 223.10/37.95  | | | | | | | | | | | | | | |           $i(all_52_7)
% 223.10/37.95  | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | REF_CLOSE: (39), (374), (7582), (9105), (function-axioms) are
% 223.10/37.95  | | | | | | | | | | | | | | |            inconsistent by sub-proof #360.
% 223.10/37.95  | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | Case 2:
% 223.10/37.95  | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | |   (9106)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 223.10/37.95  | | | | | | | | | | | | | | |           all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 223.10/37.95  | | | | | | | | | | | | | | |           op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 223.10/37.95  | | | | | | | | | | | | | | |             all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 223.10/37.95  | | | | | | | | | | | | | | |           & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 223.10/37.95  | | | | | | | | | | | | | | |           op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 223.10/37.95  | | | | | | | | | | | | | | |           $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 223.10/37.95  | | | | | | | | | | | | | | |           $i(all_52_15)
% 223.10/37.95  | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | REF_CLOSE: (6), (9074), (9103), (9106), (function-axioms) are
% 223.10/37.95  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1372.
% 223.10/37.95  | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | End of split
% 223.10/37.95  | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | Case 2:
% 223.10/37.95  | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | |   (9107)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 223.10/37.95  | | | | | | | | | | | | | |             & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 223.10/37.95  | | | | | | | | | | | | | |             & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 223.10/37.95  | | | | | | | | | | | | | |               all_52_21) = e1 & op(all_52_23, all_52_23) =
% 223.10/37.95  | | | | | | | | | | | | | |             e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 223.10/37.95  | | | | | | | | | | | | | |             all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 223.10/37.95  | | | | | | | | | | | | | |             = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 223.10/37.95  | | | | | | | | | | | | | |             $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 223.10/37.95  | | | | | | | | | | | | | |             & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 223.10/37.95  | | | | | | | | | | | | | |             e0 & op(all_52_25, all_52_25) = e3 &
% 223.10/37.95  | | | | | | | | | | | | | |             op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 223.10/37.95  | | | | | | | | | | | | | |               all_52_29) = e1 & op(all_52_31, all_52_31) =
% 223.10/37.95  | | | | | | | | | | | | | |             e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 223.10/37.95  | | | | | | | | | | | | | |             all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 223.10/37.95  | | | | | | | | | | | | | |             = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 223.10/37.95  | | | | | | | | | | | | | |             $i(all_52_29) & $i(all_52_31))
% 223.10/37.95  | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | BETA: splitting (9107) gives:
% 223.10/37.95  | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | Case 1:
% 223.10/37.95  | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | |   (9108)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 223.10/37.95  | | | | | | | | | | | | | | |           all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 223.10/37.95  | | | | | | | | | | | | | | |           op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 223.10/37.95  | | | | | | | | | | | | | | |             all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 223.10/37.95  | | | | | | | | | | | | | | |           & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 223.10/37.95  | | | | | | | | | | | | | | |           & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 223.10/37.95  | | | | | | | | | | | | | | |           & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 223.10/37.95  | | | | | | | | | | | | | | |           $i(all_52_23)
% 223.10/37.95  | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | ALPHA: (9108) implies:
% 223.10/37.95  | | | | | | | | | | | | | | |   (9109)  op(e1, e1) = all_52_21
% 223.10/37.95  | | | | | | | | | | | | | | |   (9110)  op(all_52_21, all_52_21) = e1
% 223.10/37.95  | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 223.10/37.95  | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | Case 1:
% 223.10/37.95  | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | |   (9111)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 223.10/37.95  | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 223.10/37.95  | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (168), (7573), (9074), (9111),
% 223.10/37.95  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/37.95  | | | | | | | | | | | | | | | |            #299.
% 223.10/37.95  | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | Case 2:
% 223.10/37.95  | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | |   (9112)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 223.10/37.95  | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 223.10/37.95  | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | BETA: splitting (9112) gives:
% 223.10/37.95  | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.95  | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | |   (9113)  all_57_5 = e1 & op(e2, e1) = e1
% 223.10/37.95  | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | ALPHA: (9113) implies:
% 223.10/37.95  | | | | | | | | | | | | | | | | |   (9114)  op(e2, e1) = e1
% 223.10/37.95  | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 223.10/37.95  | | | | | | | | | | | | | | | | |              all_52_21, e1, e1, simplifying with (39), (9109)
% 223.10/37.95  | | | | | | | | | | | | | | | | |              gives:
% 223.10/37.95  | | | | | | | | | | | | | | | | |   (9115)  all_52_21 = all_6_2
% 223.10/37.95  | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_9, e1,
% 223.10/37.95  | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (166), (9114) gives:
% 223.10/37.95  | | | | | | | | | | | | | | | | |   (9116)  all_53_9 = e1
% 223.10/37.95  | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | REDUCE: (364), (9116) imply:
% 223.10/37.95  | | | | | | | | | | | | | | | | |   (9117)   ~ (all_6_2 = e1)
% 223.10/37.95  | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | SIMP: (9117) implies:
% 223.10/37.95  | | | | | | | | | | | | | | | | |   (9118)   ~ (all_6_2 = e1)
% 223.10/37.95  | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | REDUCE: (9110), (9115) imply:
% 223.10/37.95  | | | | | | | | | | | | | | | | |   (9119)  op(all_6_2, all_6_2) = e1
% 223.10/37.95  | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 223.10/37.95  | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.95  | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | |   (9120)  all_55_10 = e3
% 223.10/37.95  | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (374), (9120) are inconsistent by sub-proof
% 223.10/37.95  | | | | | | | | | | | | | | | | | |            #2500.
% 223.10/37.95  | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.95  | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | |   (9121)  all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 223.10/37.95  | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | BETA: splitting (9121) gives:
% 223.10/37.95  | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | |   (9122)  all_55_10 = e2
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (336), (9122) imply:
% 223.10/37.95  | | | | | | | | | | | | | | | | | | |   (9123)  all_6_2 = e2
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | SIMP: (9123) implies:
% 223.10/37.95  | | | | | | | | | | | | | | | | | | |   (9124)  all_6_2 = e2
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | REDUCE: (9119), (9124) imply:
% 223.10/37.95  | | | | | | | | | | | | | | | | | | |   (9125)  op(e2, e2) = e1
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9074), (9125), (function-axioms) are
% 223.10/37.95  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2352.
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | |   (9126)  all_55_10 = e1 | all_55_10 = e0
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (9076), (9118), (9126) are inconsistent by
% 223.10/37.95  | | | | | | | | | | | | | | | | | | |            sub-proof #1685.
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.95  | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | End of split
% 223.10/37.95  | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.95  | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | |   (9127)  all_57_10 = e1 & op(e2, e0) = e1
% 223.10/37.95  | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (9101), (9127), (function-axioms) are
% 223.10/37.95  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2084.
% 223.10/37.95  | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | End of split
% 223.10/37.95  | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | End of split
% 223.10/37.95  | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | Case 2:
% 223.10/37.95  | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | |   (9128)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 223.10/37.95  | | | | | | | | | | | | | | |           all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 223.10/37.95  | | | | | | | | | | | | | | |           op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 223.10/37.95  | | | | | | | | | | | | | | |             all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 223.10/37.95  | | | | | | | | | | | | | | |           & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 223.10/37.95  | | | | | | | | | | | | | | |           & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 223.10/37.95  | | | | | | | | | | | | | | |           & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 223.10/37.95  | | | | | | | | | | | | | | |           $i(all_52_31)
% 223.10/37.95  | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | ALPHA: (9128) implies:
% 223.10/37.95  | | | | | | | | | | | | | | |   (9129)  op(e0, e0) = all_52_31
% 223.10/37.95  | | | | | | | | | | | | | | |   (9130)  op(all_52_31, all_52_31) = e0
% 223.10/37.95  | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | REF_CLOSE: (39), (9076), (9103), (9129), (9130),
% 223.10/37.95  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/37.95  | | | | | | | | | | | | | | |            #2086.
% 223.10/37.95  | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | End of split
% 223.10/37.95  | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | End of split
% 223.10/37.95  | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | End of split
% 223.10/37.95  | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | Case 2:
% 223.10/37.95  | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | |   (9131)  all_24_2 = e0
% 223.10/37.95  | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | COMBINE_EQS: (315), (9131) imply:
% 223.10/37.95  | | | | | | | | | | | |   (9132)  all_6_2 = e0
% 223.10/37.95  | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | SIMP: (9132) implies:
% 223.10/37.95  | | | | | | | | | | | |   (9133)  all_6_2 = e0
% 223.10/37.95  | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | REDUCE: (350), (9133) imply:
% 223.10/37.95  | | | | | | | | | | | |   (9134)   ~ (all_53_2 = e0)
% 223.10/37.95  | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | REDUCE: (363), (9133) imply:
% 223.10/37.95  | | | | | | | | | | | |   (9135)   ~ (all_53_8 = e0)
% 223.10/37.95  | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | REDUCE: (374), (9133) imply:
% 223.10/37.95  | | | | | | | | | | | |   (9136)   ~ (e3 = e0)
% 223.10/37.95  | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | REDUCE: (39), (9133) imply:
% 223.10/37.95  | | | | | | | | | | | |   (9137)  op(e1, e1) = e0
% 223.10/37.95  | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | BETA: splitting (231) gives:
% 223.10/37.95  | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | Case 1:
% 223.10/37.95  | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | |   (9138)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 223.10/37.95  | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 223.10/37.95  | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | REF_CLOSE: (4), (171), (7581), (9065), (9138),
% 223.10/37.95  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/37.95  | | | | | | | | | | | | |            #298.
% 223.10/37.95  | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | Case 2:
% 223.10/37.95  | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | |   (9139)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 223.10/37.95  | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 223.10/37.95  | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | BETA: splitting (9139) gives:
% 223.10/37.95  | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | Case 1:
% 223.10/37.95  | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | |   (9140)  all_57_4 = e0 & op(e3, e1) = e0
% 223.10/37.95  | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | ALPHA: (9140) implies:
% 223.10/37.95  | | | | | | | | | | | | | |   (9141)  op(e3, e1) = e0
% 223.10/37.95  | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | REF_CLOSE: (170), (9135), (9141), (function-axioms) are
% 223.10/37.95  | | | | | | | | | | | | | |            inconsistent by sub-proof #2267.
% 223.10/37.95  | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | Case 2:
% 223.10/37.95  | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | |   (9142)  all_57_9 = e0 & op(e3, e0) = e0
% 223.10/37.95  | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | ALPHA: (9142) implies:
% 223.10/37.95  | | | | | | | | | | | | | |   (9143)  all_57_9 = e0
% 223.10/37.95  | | | | | | | | | | | | | |   (9144)  op(e3, e0) = e0
% 223.10/37.95  | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 223.10/37.95  | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | Case 1:
% 223.10/37.95  | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | |   (9145)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 223.10/37.95  | | | | | | | | | | | | | | |             & op(e2, e3) = e0)
% 223.10/37.95  | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 223.10/37.95  | | | | | | | | | | | | | | |            (7581), (9073), (9145) are inconsistent by
% 223.10/37.95  | | | | | | | | | | | | | | |            sub-proof #297.
% 223.10/37.95  | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | Case 2:
% 223.10/37.95  | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | |   (9146)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 223.10/37.95  | | | | | | | | | | | | | | |             e0 & op(e0, e3) = e0)
% 223.10/37.95  | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | BETA: splitting (9146) gives:
% 223.10/37.95  | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | Case 1:
% 223.10/37.95  | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | |   (9147)  all_57_6 = e0 & op(e1, e3) = e0
% 223.10/37.95  | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | ALPHA: (9147) implies:
% 223.10/37.95  | | | | | | | | | | | | | | | |   (9148)  op(e1, e3) = e0
% 223.10/37.95  | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | REF_CLOSE: (164), (9134), (9148), (function-axioms) are
% 223.10/37.95  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2154.
% 223.10/37.95  | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | Case 2:
% 223.10/37.95  | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | |   (9149)  all_57_12 = e0 & op(e0, e3) = e0
% 223.10/37.95  | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | ALPHA: (9149) implies:
% 223.10/37.95  | | | | | | | | | | | | | | | |   (9150)  op(e0, e3) = e0
% 223.10/37.95  | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_3, e0,
% 223.10/37.95  | | | | | | | | | | | | | | | |              e3, e0, simplifying with (160), (9150) gives:
% 223.10/37.95  | | | | | | | | | | | | | | | |   (9151)  all_53_3 = e0
% 223.10/37.95  | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_12,
% 223.10/37.95  | | | | | | | | | | | | | | | |              e0, e0, e3, simplifying with (169), (9144) gives:
% 223.10/37.95  | | | | | | | | | | | | | | | |   (9152)  all_53_12 = e0
% 223.10/37.95  | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | REDUCE: (370), (9152) imply:
% 223.10/37.95  | | | | | | | | | | | | | | | |   (9153)   ~ (all_4_2 = e0)
% 223.10/37.95  | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | SIMP: (9153) implies:
% 223.10/37.95  | | | | | | | | | | | | | | | |   (9154)   ~ (all_4_2 = e0)
% 223.10/37.95  | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 223.10/37.95  | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.95  | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | |   (9155)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 223.10/37.95  | | | | | | | | | | | | | | | | |             all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 223.10/37.95  | | | | | | | | | | | | | | | | |             op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 223.10/37.95  | | | | | | | | | | | | | | | | |               all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 223.10/37.95  | | | | | | | | | | | | | | | | |             op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 223.10/37.95  | | | | | | | | | | | | | | | | |             op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 223.10/37.95  | | | | | | | | | | | | | | | | |             $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 223.10/37.95  | | | | | | | | | | | | | | | | |             $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 223.10/37.95  | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 223.10/37.95  | | | | | | | | | | | | | | | | |               all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 223.10/37.95  | | | | | | | | | | | | | | | | |             & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 223.10/37.95  | | | | | | | | | | | | | | | | |               all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 223.10/37.95  | | | | | | | | | | | | | | | | |             op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 223.10/37.95  | | | | | | | | | | | | | | | | |             & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 223.10/37.95  | | | | | | | | | | | | | | | | |             $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 223.10/37.95  | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | BETA: splitting (9155) gives:
% 223.10/37.95  | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.95  | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | |   (9156)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 223.10/37.95  | | | | | | | | | | | | | | | | | |           all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 223.10/37.95  | | | | | | | | | | | | | | | | | |           op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 223.10/37.95  | | | | | | | | | | | | | | | | | |             all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 223.10/37.95  | | | | | | | | | | | | | | | | | |           op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 223.10/37.95  | | | | | | | | | | | | | | | | | |           op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 223.10/37.95  | | | | | | | | | | | | | | | | | |           $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 223.10/37.95  | | | | | | | | | | | | | | | | | |           $i(all_52_7)
% 223.10/37.95  | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | ALPHA: (9156) implies:
% 223.10/37.95  | | | | | | | | | | | | | | | | | |   (9157)  op(e3, e0) = all_52_7
% 223.10/37.95  | | | | | | | | | | | | | | | | | |   (9158)  op(all_52_7, all_52_7) = e0
% 223.10/37.95  | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 223.10/37.95  | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | |   (9159)  all_55_15 = e3
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (7584), (9159) are inconsistent by
% 223.10/37.95  | | | | | | | | | | | | | | | | | | |            sub-proof #2503.
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | |   (9160)  all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | BETA: splitting (9160) gives:
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | |   (9161)  all_55_15 = e2
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (373), (9161) are inconsistent by sub-proof
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | |            #2502.
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | |   (9162)  all_55_15 = e1 | all_55_15 = e0
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (244), (9144), (9154), (9157), (9158),
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | |            (9162), (function-axioms) are inconsistent by
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | |            sub-proof #1325.
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.95  | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.95  | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | |   (9163)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 223.10/37.95  | | | | | | | | | | | | | | | | | |           all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 223.10/37.95  | | | | | | | | | | | | | | | | | |           op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 223.10/37.95  | | | | | | | | | | | | | | | | | |             all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 223.10/37.95  | | | | | | | | | | | | | | | | | |           & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 223.10/37.95  | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 223.10/37.95  | | | | | | | | | | | | | | | | | |           $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 223.10/37.95  | | | | | | | | | | | | | | | | | |           $i(all_52_15)
% 223.10/37.95  | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | ALPHA: (9163) implies:
% 223.10/37.95  | | | | | | | | | | | | | | | | | |   (9164)  op(e2, e2) = all_52_11
% 223.10/37.95  | | | | | | | | | | | | | | | | | |   (9165)  op(all_52_11, all_52_11) = e2
% 223.10/37.95  | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 223.10/37.95  | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | |   (9166)  all_55_15 = e3
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (7584), (9166) are inconsistent by
% 223.10/37.95  | | | | | | | | | | | | | | | | | | |            sub-proof #2503.
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | |   (9167)   ~ (all_55_15 = e3)
% 223.10/37.95  | | | | | | | | | | | | | | | | | | |   (9168)  all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | BETA: splitting (9168) gives:
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | |   (9169)  all_55_15 = e2
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (373), (9169) are inconsistent by sub-proof
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | |            #2502.
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | |   (9170)  all_55_15 = e1 | all_55_15 = e0
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (9), (36), (165), (211), (212), (213),
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | |            (244), (371), (373), (7584), (9074), (9143),
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | |            (9154), (9164), (9165), (9170), (function-axioms)
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1323.
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.95  | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | End of split
% 223.10/37.95  | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.95  | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | |   (9171)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 223.10/37.95  | | | | | | | | | | | | | | | | |             & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 223.10/37.95  | | | | | | | | | | | | | | | | |             & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 223.10/37.95  | | | | | | | | | | | | | | | | |               all_52_21) = e1 & op(all_52_23, all_52_23) =
% 223.10/37.95  | | | | | | | | | | | | | | | | |             e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 223.10/37.95  | | | | | | | | | | | | | | | | |             all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 223.10/37.95  | | | | | | | | | | | | | | | | |             = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 223.10/37.95  | | | | | | | | | | | | | | | | |             $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 223.10/37.95  | | | | | | | | | | | | | | | | |             & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 223.10/37.95  | | | | | | | | | | | | | | | | |             e0 & op(all_52_25, all_52_25) = e3 &
% 223.10/37.95  | | | | | | | | | | | | | | | | |             op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 223.10/37.95  | | | | | | | | | | | | | | | | |               all_52_29) = e1 & op(all_52_31, all_52_31) =
% 223.10/37.95  | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 223.10/37.95  | | | | | | | | | | | | | | | | |             all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 223.10/37.95  | | | | | | | | | | | | | | | | |             = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 223.10/37.95  | | | | | | | | | | | | | | | | |             $i(all_52_29) & $i(all_52_31))
% 223.10/37.95  | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | BETA: splitting (9171) gives:
% 223.10/37.95  | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.95  | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | |   (9172)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 223.10/37.95  | | | | | | | | | | | | | | | | | |           all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 223.10/37.95  | | | | | | | | | | | | | | | | | |           op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 223.10/37.95  | | | | | | | | | | | | | | | | | |             all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 223.10/37.95  | | | | | | | | | | | | | | | | | |           & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 223.10/37.95  | | | | | | | | | | | | | | | | | |           & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 223.10/37.95  | | | | | | | | | | | | | | | | | |           & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 223.10/37.95  | | | | | | | | | | | | | | | | | |           $i(all_52_23)
% 223.10/37.95  | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | ALPHA: (9172) implies:
% 223.10/37.95  | | | | | | | | | | | | | | | | | |   (9173)  op(e1, e1) = all_52_21
% 223.10/37.95  | | | | | | | | | | | | | | | | | |   (9174)  op(e1, e2) = all_52_19
% 223.10/37.95  | | | | | | | | | | | | | | | | | |   (9175)  op(all_52_19, all_52_19) = e2
% 223.10/37.95  | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 223.10/37.95  | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | |   (9176)  all_55_15 = e3
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (7584), (9176) are inconsistent by
% 223.10/37.95  | | | | | | | | | | | | | | | | | | |            sub-proof #2503.
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | |   (9177)   ~ (all_55_15 = e3)
% 223.10/37.95  | | | | | | | | | | | | | | | | | | |   (9178)  all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | BETA: splitting (9178) gives:
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | |   (9179)  all_55_15 = e2
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (373), (9179) are inconsistent by sub-proof
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | |            #2502.
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | |   (9180)   ~ (all_55_15 = e2)
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | |   (9181)  all_55_15 = e1 | all_55_15 = e0
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | BETA: splitting (9181) gives:
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | |   (9182)  all_55_15 = e1
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (9182) imply:
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | |   (9183)  all_4_2 = e1
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | | SIMP: (9183) implies:
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | |   (9184)  all_4_2 = e1
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | | REDUCE: (362), (9184) imply:
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | |   (9185)   ~ (all_53_7 = e1)
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | | REDUCE: (7584), (9184) imply:
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | |   (9186)   ~ (e3 = e1)
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | | REDUCE: (373), (9184) imply:
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | |   (9187)   ~ (e2 = e1)
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | | |   (9188)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (235), (237),
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | | |            (7582), (9074), (9143), (9188), (function-axioms)
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #294.
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | | |   (9189)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9189) gives:
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | | | |   (9190)  all_57_7 = e1 & op(e1, e2) = e1
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9190) implies:
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | | | |   (9191)  op(e1, e2) = e1
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (163), (9137), (9173), (9174), (9175),
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | | | |            (9191), (function-axioms) are inconsistent by
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #332.
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | | | |   (9192)  all_57_13 = e1 & op(e0, e2) = e1
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (9185), (9192), (function-axioms) are
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #330.
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | |   (9193)  all_55_15 = e0
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (9154), (9193) are inconsistent by
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | |            sub-proof #1884.
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.95  | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.95  | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | |   (9194)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 223.10/37.95  | | | | | | | | | | | | | | | | | |           all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 223.10/37.95  | | | | | | | | | | | | | | | | | |           op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 223.10/37.95  | | | | | | | | | | | | | | | | | |             all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 223.10/37.95  | | | | | | | | | | | | | | | | | |           & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 223.10/37.95  | | | | | | | | | | | | | | | | | |           & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 223.10/37.95  | | | | | | | | | | | | | | | | | |           & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 223.10/37.95  | | | | | | | | | | | | | | | | | |           $i(all_52_31)
% 223.10/37.95  | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | ALPHA: (9194) implies:
% 223.10/37.95  | | | | | | | | | | | | | | | | | |   (9195)  op(e0, e0) = all_52_31
% 223.10/37.95  | | | | | | | | | | | | | | | | | |   (9196)  op(e0, e3) = all_52_25
% 223.10/37.95  | | | | | | | | | | | | | | | | | |   (9197)  op(all_52_25, all_52_25) = e3
% 223.10/37.95  | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 223.10/37.95  | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | |   (9198)  all_55_15 = e3
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (7584), (9198) are inconsistent by
% 223.10/37.95  | | | | | | | | | | | | | | | | | | |            sub-proof #2503.
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | |   (9199)   ~ (all_55_15 = e3)
% 223.10/37.95  | | | | | | | | | | | | | | | | | | |   (9200)  all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | BETA: splitting (9200) gives:
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | |   (9201)  all_55_15 = e2
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (373), (9201) are inconsistent by sub-proof
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | |            #2502.
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | |   (9202)  all_55_15 = e1 | all_55_15 = e0
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (9), (36), (165), (211), (212), (213),
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | |            (244), (371), (373), (7584), (9143), (9150),
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | |            (9154), (9195), (9196), (9197), (9202),
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | |            #1302.
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.95  | | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.95  | | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | | End of split
% 223.10/37.95  | | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | | End of split
% 223.10/37.95  | | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | | End of split
% 223.10/37.95  | | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | | End of split
% 223.10/37.95  | | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | | End of split
% 223.10/37.95  | | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | | End of split
% 223.10/37.95  | | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | | End of split
% 223.10/37.95  | | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | End of split
% 223.10/37.95  | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | Case 2:
% 223.10/37.95  | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | |   (9203)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 223.10/37.95  | | | | | | | | | |             e0 & op(e2, e0) = e0)
% 223.10/37.95  | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | | REF_CLOSE: (165), (166), (9067), (9068), (9203),
% 223.10/37.95  | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/37.95  | | | | | | | | | |            #2022.
% 223.10/37.95  | | | | | | | | | | 
% 223.10/37.95  | | | | | | | | | End of split
% 223.10/37.95  | | | | | | | | | 
% 223.10/37.95  | | | | | | | | End of split
% 223.10/37.95  | | | | | | | | 
% 223.10/37.95  | | | | | | | Case 2:
% 223.10/37.95  | | | | | | | | 
% 223.10/37.95  | | | | | | | |   (9204)  all_12_2 = e3
% 223.10/37.95  | | | | | | | |   (9205)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 &
% 223.10/37.95  | | | | | | | |             op(e0, e3) = all_12_1 & $i(all_12_0) & $i(all_12_1))
% 223.10/37.95  | | | | | | | |           | ( ~ (all_12_1 = e1) & op(e0, e3) = all_12_1 &
% 223.10/37.95  | | | | | | | |             $i(all_12_1))
% 223.10/37.95  | | | | | | | | 
% 223.10/37.96  | | | | | | | | COMBINE_EQS: (325), (9204) imply:
% 223.10/37.96  | | | | | | | |   (9206)  all_4_2 = e3
% 223.10/37.96  | | | | | | | | 
% 223.10/37.96  | | | | | | | | COMBINE_EQS: (318), (9206) imply:
% 223.10/37.96  | | | | | | | |   (9207)  all_22_2 = e3
% 223.10/37.96  | | | | | | | | 
% 223.10/37.96  | | | | | | | | REDUCE: (362), (9206) imply:
% 223.10/37.96  | | | | | | | |   (9208)   ~ (all_53_7 = e3)
% 223.10/37.96  | | | | | | | | 
% 223.10/37.96  | | | | | | | | REDUCE: (370), (9206) imply:
% 223.10/37.96  | | | | | | | |   (9209)   ~ (all_53_12 = e3)
% 223.10/37.96  | | | | | | | | 
% 223.10/37.96  | | | | | | | | REDUCE: (371), (9206) imply:
% 223.10/37.96  | | | | | | | |   (9210)   ~ (all_53_13 = e3)
% 223.10/37.96  | | | | | | | | 
% 223.10/37.96  | | | | | | | | REDUCE: (372), (9206) imply:
% 223.10/37.96  | | | | | | | |   (9211)   ~ (all_53_14 = e3)
% 223.10/37.96  | | | | | | | | 
% 223.10/37.96  | | | | | | | | BETA: splitting (213) gives:
% 223.10/37.96  | | | | | | | | 
% 223.10/37.96  | | | | | | | | Case 1:
% 223.10/37.96  | | | | | | | | | 
% 223.10/37.96  | | | | | | | | |   (9212)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3
% 223.10/37.96  | | | | | | | | |             & op(e2, e0) = e3)
% 223.10/37.96  | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | REF_CLOSE: (165), (169), (9209), (9210), (9212),
% 223.10/37.96  | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/37.96  | | | | | | | | |            #2300.
% 223.10/37.96  | | | | | | | | | 
% 223.10/37.96  | | | | | | | | Case 2:
% 223.10/37.96  | | | | | | | | | 
% 223.10/37.96  | | | | | | | | |   (9213)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3
% 223.10/37.96  | | | | | | | | |             & op(e0, e0) = e3)
% 223.10/37.96  | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | BETA: splitting (9213) gives:
% 223.10/37.96  | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | Case 1:
% 223.10/37.96  | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | |   (9214)  all_57_11 = e3 & op(e1, e0) = e3
% 223.10/37.96  | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | ALPHA: (9214) implies:
% 223.10/37.96  | | | | | | | | | |   (9215)  op(e1, e0) = e3
% 223.10/37.96  | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | REF_CLOSE: (161), (9211), (9215), (function-axioms) are
% 223.10/37.96  | | | | | | | | | |            inconsistent by sub-proof #2330.
% 223.10/37.96  | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | Case 2:
% 223.10/37.96  | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | |   (9216)  all_57_15 = e3 & op(e0, e0) = e3
% 223.10/37.96  | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | ALPHA: (9216) implies:
% 223.10/37.96  | | | | | | | | | |   (9217)  all_57_15 = e3
% 223.10/37.96  | | | | | | | | | |   (9218)  op(e0, e0) = e3
% 223.10/37.96  | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | BETA: splitting (52) gives:
% 223.10/37.96  | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | Case 1:
% 223.10/37.96  | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | |   (9219)   ~ (all_14_2 = e0)
% 223.10/37.96  | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | REDUCE: (328), (9219) imply:
% 223.10/37.96  | | | | | | | | | | |   (9220)   ~ (all_8_2 = e0)
% 223.10/37.96  | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | BETA: splitting (55) gives:
% 223.10/37.96  | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | Case 1:
% 223.10/37.96  | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | |   (9221)   ~ (all_16_2 = e1)
% 223.10/37.96  | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | REDUCE: (324), (9221) imply:
% 223.10/37.96  | | | | | | | | | | | |   (9222)   ~ (all_8_2 = e1)
% 223.10/37.96  | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | BETA: splitting (200) gives:
% 223.10/37.96  | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | Case 1:
% 223.10/37.96  | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | |   (9223)  all_55_5 = e3
% 223.10/37.96  | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | REF_CLOSE: (266), (375), (9223) are inconsistent by sub-proof
% 223.10/37.96  | | | | | | | | | | | | |            #293.
% 223.10/37.96  | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | Case 2:
% 223.10/37.96  | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | |   (9224)   ~ (all_55_5 = e3)
% 223.10/37.96  | | | | | | | | | | | | |   (9225)  all_55_5 = e2 | all_55_5 = e1 | all_55_5 = e0
% 223.10/37.96  | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | BETA: splitting (9225) gives:
% 223.10/37.96  | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | Case 1:
% 223.10/37.96  | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | |   (9226)  all_55_5 = e2
% 223.10/37.96  | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | COMBINE_EQS: (266), (9226) imply:
% 223.10/37.96  | | | | | | | | | | | | | |   (9227)  all_8_2 = e2
% 223.10/37.96  | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | SIMP: (9227) implies:
% 223.10/37.96  | | | | | | | | | | | | | |   (9228)  all_8_2 = e2
% 223.10/37.96  | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | REDUCE: (352), (9228) imply:
% 223.10/37.96  | | | | | | | | | | | | | |   (9229)   ~ (all_53_4 = e2)
% 223.10/37.96  | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | REDUCE: (354), (9228) imply:
% 223.10/37.96  | | | | | | | | | | | | | |   (9230)   ~ (all_53_6 = e2)
% 223.10/37.96  | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | REDUCE: (356), (9228) imply:
% 223.10/37.96  | | | | | | | | | | | | | |   (9231)   ~ (all_53_7 = e2)
% 223.10/37.96  | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | REDUCE: (358), (9228) imply:
% 223.10/37.96  | | | | | | | | | | | | | |   (9232)   ~ (all_53_9 = e2)
% 223.10/37.96  | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | REDUCE: (360), (9228) imply:
% 223.10/37.96  | | | | | | | | | | | | | |   (9233)   ~ (all_53_13 = e2)
% 223.10/37.96  | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | REDUCE: (375), (9228) imply:
% 223.10/37.96  | | | | | | | | | | | | | |   (9234)   ~ (e3 = e2)
% 223.10/37.96  | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | REDUCE: (42), (9228) imply:
% 223.10/37.96  | | | | | | | | | | | | | |   (9235)  op(e2, e2) = e2
% 223.10/37.96  | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 223.10/37.96  | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | Case 1:
% 223.10/37.96  | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | |   (9236)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 223.10/37.96  | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 223.10/37.96  | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | BETA: splitting (9236) gives:
% 223.10/37.96  | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | Case 1:
% 223.10/37.96  | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | |   (9237)  all_57_1 = e2 & op(e3, e2) = e2
% 223.10/37.96  | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | REF_CLOSE: (171), (9229), (9237), (function-axioms) are
% 223.10/37.96  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2456.
% 223.10/37.96  | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | Case 2:
% 223.10/37.96  | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | |   (9238)  all_57_3 = e2 & op(e2, e2) = e2
% 223.10/37.96  | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | ALPHA: (9238) implies:
% 223.10/37.96  | | | | | | | | | | | | | | | |   (9239)  all_57_3 = e2
% 223.10/37.96  | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | BETA: splitting (64) gives:
% 223.10/37.96  | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.96  | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | |   (9240)   ~ (all_22_2 = e3)
% 223.10/37.96  | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | REDUCE: (9207), (9240) imply:
% 223.10/37.96  | | | | | | | | | | | | | | | | |   (9241)  $false
% 223.10/37.96  | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | CLOSE: (9241) is inconsistent.
% 223.10/37.96  | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.96  | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | |   (9242)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0
% 223.10/37.96  | | | | | | | | | | | | | | | | |             & op(e0, e3) = all_22_1 & $i(all_22_0) &
% 223.10/37.96  | | | | | | | | | | | | | | | | |             $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0, e3)
% 223.10/37.96  | | | | | | | | | | | | | | | | |             = all_22_1 & $i(all_22_1))
% 223.10/37.96  | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 223.10/37.96  | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | |   (9243)   ~ (all_24_2 = e0)
% 223.10/37.96  | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | REDUCE: (315), (9243) imply:
% 223.10/37.96  | | | | | | | | | | | | | | | | | |   (9244)   ~ (all_6_2 = e0)
% 223.10/37.96  | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | BETA: splitting (88) gives:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | |   (9245)   ~ (all_38_2 = e2)
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | REDUCE: (249), (9245) imply:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | |   (9246)   ~ (all_6_2 = e2)
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | |   (9247)  all_55_10 = e3
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (374), (9247) are inconsistent by sub-proof
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | |            #2500.
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | |   (9248)   ~ (all_55_10 = e3)
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | |   (9249)  all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | BETA: splitting (9249) gives:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | |   (9250)  all_55_10 = e2
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (9246), (9250) are inconsistent by
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | |            sub-proof #2499.
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | |   (9251)   ~ (all_55_10 = e2)
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | |   (9252)  all_55_10 = e1 | all_55_10 = e0
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9252) gives:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | |   (9253)  all_55_10 = e1
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (336), (9253) imply:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | |   (9254)  all_6_2 = e1
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | SIMP: (9254) implies:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | |   (9255)  all_6_2 = e1
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (374), (9255) imply:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | |   (9256)   ~ (e3 = e1)
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9246), (9255) imply:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | |   (9257)   ~ (e2 = e1)
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (9255) imply:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | |   (9258)  op(e1, e1) = e1
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | |   (9259)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9259) gives:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | |   (9260)  all_57_9 = e1 & op(e3, e0) = e1
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (7578), (9260), (function-axioms) are
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2131.
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | |   (9261)  all_57_10 = e1 & op(e2, e0) = e1
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9261) implies:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | |   (9262)  all_57_10 = e1
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | |   (9263)  op(e2, e0) = e1
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | |   (9264)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9264) gives:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9265)  all_57_1 = e1 & op(e3, e2) = e1
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9265) implies:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9266)  all_57_1 = e1
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9267)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (207), (208),
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (209), (226), (228), (229), (7575), (9217),
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9218), (9235), (9266), (9267), (function-axioms)
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #290.
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9268)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9268) gives:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9269)  all_57_14 = e1 & op(e0, e1) = e1
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9269) implies:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9270)  all_57_14 = e1
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9271)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9271) gives:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9272)  all_57_12 = e2 & op(e0, e3) = e2
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9272) implies:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9273)  all_57_12 = e2
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9274)  all_57_15 = e0 & op(e0, e0) = e0
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9274) implies:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9275)  op(e0, e0) = e0
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (161), (169), (213), (9209), (9211),
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9262), (9275), (function-axioms) are inconsistent
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2302.
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9276)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9276) implies:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9277)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0)
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9278)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (9235), (9266), (9278),
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #292.
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9279)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9279) gives:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9280)  all_57_7 = e3 & op(e1, e2) = e3
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9280) implies:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9281)  all_57_7 = e3
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9282)  op(e1, e2) = e3
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9283)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e3)
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9283) gives:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9284)  all_57_0 = e3 & op(e3, e3) = e3
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9284) implies:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9285)  op(e3, e3) = e3
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (64), (67),
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (82), (88), (107), (119), (121), (124), (127),
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (134), (158), (159), (161), (163), (165), (166),
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (169), (170), (171), (195), (199), (207), (208),
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (209), (211), (212), (214), (215), (216), (217),
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (218), (219), (220), (221), (222), (223), (224),
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (225), (226), (227), (228), (230), (231), (232),
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (234), (235), (236), (237), (249), (259),
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (311), (315), (336), (363), (364), (368), (374),
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9205), (9207), (9209), (9217), (9218), (9229),
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9231), (9232), (9233), (9235), (9239), (9281),
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9282), (9285), (function-axioms) are inconsistent
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1074.
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9286)  all_57_1 = e3 & op(e3, e2) = e3
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9286) implies:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9287)  all_57_1 = e3
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (226), (227), (228),
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9235), (9281), (9287), (function-axioms) are
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1167.
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9288)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e3)
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9288) gives:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9289)  all_57_4 = e3 & op(e3, e1) = e3
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9289) implies:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9290)  all_57_4 = e3
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9291)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (9235), (9266), (9291),
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1164.
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9292)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0)
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9292) gives:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9293)  all_57_7 = e0 & op(e1, e2) = e0
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9293) implies:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9294)  all_57_7 = e0
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (208), (209), (229),
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9217), (9218), (9239), (9266), (9277), (9294),
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #940.
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9295)  all_57_13 = e0 & op(e0, e2) = e0
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9295) implies:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9296)  all_57_13 = e0
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9297)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e2)
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9297) gives:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9298)  all_57_0 = e2 & op(e3, e3) = e2
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9298) implies:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9299)  op(e3, e3) = e2
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7582), (9299), (function-axioms) are
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1950.
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9300)  all_57_1 = e2 & op(e3, e2) = e2
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9300) implies:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9301)  all_57_1 = e2
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (227), (9235), (9281), (9296),
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9301), (function-axioms) are inconsistent by
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #871.
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9302)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e2)
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9302) gives:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9303)  all_57_4 = e2 & op(e3, e1) = e2
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9303) implies:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9304)  all_57_4 = e2
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9290), (9304) imply:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9305)  e3 = e2
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9281), (9305) imply:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9306)  all_57_7 = e2
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (208),
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (209), (211), (212), (217), (226), (227), (228),
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (229), (374), (9217), (9218), (9235), (9266),
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9306), (function-axioms) are inconsistent by
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #289.
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9307)  all_57_9 = e2 & op(e3, e0) = e2
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9307) implies:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9308)  all_57_9 = e2
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9309)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e2)
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (166), (169), (231),
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (237), (9209), (9232), (9308), (9309),
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #287.
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9310)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e1) = e2)
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9310) gives:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9311)  all_57_8 = e2 & op(e1, e1) = e2
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9311) implies:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9312)  op(e1, e1) = e2
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9258), (9312), (function-axioms) are
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2423.
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9313)  all_57_14 = e2 & op(e0, e1) = e2
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9313) implies:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9314)  all_57_14 = e2
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9315)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9315) gives:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9316)  all_57_12 = e1 & op(e0, e3) = e1
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (7575), (9316), (function-axioms) are
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1947.
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9317)  all_57_13 = e1 & op(e0, e2) = e1
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9317) implies:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9318)  all_57_13 = e1
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9319)  all_57_15 = e0 & op(e0, e0) = e0
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9319) implies:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9320)  op(e0, e0) = e0
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9218), (9320), (function-axioms) are
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2304.
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (9273), (9277), (9314), (9318) are
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #334.
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9218), (9268), (9314),
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1139.
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9321)  all_57_9 = e3 & op(e3, e0) = e3
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9321) implies:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9322)  op(e3, e0) = e3
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (9209), (9322), (function-axioms) are
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2458.
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9323)  all_57_13 = e3 & op(e0, e2) = e3
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9323) implies:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9324)  all_57_13 = e3
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (208), (209),
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9217), (9218), (9277), (9324), (function-axioms)
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2054.
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9325)  all_57_13 = e2 & op(e0, e2) = e2
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9325) implies:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9326)  op(e0, e2) = e2
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (9231), (9326), (function-axioms) are
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2335.
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9327)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (373), (9270), (9327),
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #286.
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9328)  all_57_15 = e1 & op(e0, e0) = e1
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9328) implies:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9329)  op(e0, e0) = e1
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9218), (9329), (function-axioms) are
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2183.
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9330)  all_57_3 = e1 & op(e2, e2) = e1
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.96  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9330) implies:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9331)  op(e2, e2) = e1
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9235), (9331), (function-axioms) are
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2306.
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | |   (9332)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9332) gives:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9333)  all_57_7 = e1 & op(e1, e2) = e1
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9333) implies:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9334)  all_57_7 = e1
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (214), (216), (217), (374), (9217), (9258),
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | |            (9334), (function-axioms) are inconsistent by
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1069.
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9335)  all_57_13 = e1 & op(e0, e2) = e1
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9335) implies:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9336)  all_57_13 = e1
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9337)  op(e0, e2) = e1
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_7, e1,
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (159), (9337) gives:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9338)  all_53_7 = e1
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_13,
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e0, e2, simplifying with (165), (9263) gives:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9339)  all_53_13 = e1
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (129), (9338) imply:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9340)   ~ (all_53_6 = e1)
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9341)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (39), (374), (7582), (9258), (9263), (9341),
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #359.
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9342)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_52_21) = e1 & op(all_52_23, all_52_23) =
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(all_52_25, all_52_25) = e3 &
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_52_29) = e1 & op(all_52_31, all_52_31) =
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_52_29) & $i(all_52_31))
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9342) gives:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9343)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_23)
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9343) implies:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9344)  op(e1, e0) = all_52_23
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9345)  op(e1, e1) = all_52_21
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9346)  op(e1, e2) = all_52_19
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9347)  op(e1, e3) = all_52_17
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9348)  op(all_52_23, all_52_23) = e0
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9349)  op(all_52_21, all_52_21) = e1
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9350)  op(all_52_19, all_52_19) = e2
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9351)  op(all_52_17, all_52_17) = e3
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_14,
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_23, e0, e1, simplifying with (161), (9344)
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9352)  all_53_14 = all_52_23
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_6,
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_19, e2, e1, simplifying with (163), (9346)
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9353)  all_53_6 = all_52_19
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_2,
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_17, e3, e1, simplifying with (164), (9347)
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9354)  all_53_2 = all_52_17
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (9353) imply:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9355)  all_55_9 = all_52_19
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (137), (9353) imply:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9356)   ~ (all_53_4 = all_52_19)
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9230), (9353) imply:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9357)   ~ (all_52_19 = e2)
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9340), (9353) imply:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9358)   ~ (all_52_19 = e1)
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9359)  all_55_1 = e3
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (9359) imply:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9360)  all_53_4 = e3
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9360) implies:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9361)  all_53_4 = e3
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9356), (9361) imply:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9362)   ~ (all_52_19 = e3)
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9362) implies:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9363)   ~ (all_52_19 = e3)
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9364)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9364) gives:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9365)  all_57_1 = e3 & op(e3, e2) = e3
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9365) implies:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9366)  all_57_1 = e3
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9367)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9367) gives:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9368)  all_57_6 = e3 & op(e1, e3) = e3
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9368) implies:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9369)  all_57_6 = e3
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9370)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e2)
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9370) gives:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9371)  all_57_6 = e2 & op(e1, e3) = e2
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9371) implies:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9372)  all_57_6 = e2
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (217), (226), (227), (228), (374), (9217),
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9336), (9366), (9372), (function-axioms) are
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #961.
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9373)  all_57_7 = e2 & op(e1, e2) = e2
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9373) implies:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9374)  all_57_7 = e2
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (208),
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (209), (211), (212), (217), (226), (229), (374),
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9217), (9218), (9235), (9336), (9369), (9374),
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #285.
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9375)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e0) = e2)
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9375) gives:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9376)  all_57_8 = e2 & op(e1, e1) = e2
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9376) implies:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9377)  op(e1, e1) = e2
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (214), (215), (217), (222), (223), (224),
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (225), (234), (374), (7582), (9205), (9217),
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9218), (9235), (9239), (9242), (9244), (9345),
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9349), (9377), (function-axioms) are inconsistent
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #284.
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9378)  all_57_11 = e2 & op(e1, e0) = e2
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9378) implies:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9379)  op(e1, e0) = e2
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9235), (9344), (9348), (9379),
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2369.
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9380)  all_57_7 = e3 & op(e1, e2) = e3
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9380) implies:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9381)  all_57_7 = e3
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (226), (227), (228),
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9336), (9366), (9381) are inconsistent by
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1214.
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9382)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (374), (9217), (9382), (function-axioms)
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1786.
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9383)  all_57_3 = e3 & op(e2, e2) = e3
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9383) implies:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9384)  op(e2, e2) = e3
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (9235), (9384), (function-axioms) are
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2298.
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9385)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9385) gives:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9386)  all_57_7 = e3 & op(e1, e2) = e3
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9386) implies:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9387)  all_57_7 = e3
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9388)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9388) gives:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9389)  all_57_1 = e0 & op(e3, e2) = e0
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9389) implies:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9390)  op(e3, e2) = e0
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9391)  all_55_9 = e3
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9355), (9363), (9391) are inconsistent by
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1603.
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9392)  all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (137), (171), (256), (9230), (9340), (9390),
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9392), (function-axioms) are inconsistent by
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1831.
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9393)  all_57_3 = e0 & op(e2, e2) = e0
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9393) implies:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9394)  op(e2, e2) = e0
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9235), (9394), (function-axioms) are
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2472.
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9395)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0)
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9395) gives:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9396)  all_57_7 = e0 & op(e1, e2) = e0
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9387), (9396) are inconsistent by sub-proof
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2042.
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9397)  all_57_13 = e0 & op(e0, e2) = e0
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9397) implies:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9398)  all_57_13 = e0
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9336), (9398) imply:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9399)  e1 = e0
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9399) implies:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9400)  e1 = e0
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7581), (9400) imply:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9401)  all_57_0 = e0
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (39), (160), (168), (195), (232), (336),
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (374), (7573), (7575), (9347), (9351), (9401),
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1545.
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9402)  all_57_13 = e3 & op(e0, e2) = e3
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9402) implies:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9403)  all_57_13 = e3
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (207), (208), (209),
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9217), (9218), (9403), (function-axioms) are
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1792.
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9404)  all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (196), (270), (7576), (7582), (9229), (9350),
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9355), (9356), (9357), (9358), (9404),
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #357.
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9405)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_52_31)
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9405) implies:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9406)  op(e0, e0) = all_52_31
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9407)  op(all_52_31, all_52_31) = e0
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7582), (9218), (9406), (9407),
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #283.
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | |   (9408)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9408) gives:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | |   (9409)  all_57_11 = e1 & op(e1, e0) = e1
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9409) implies:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | |   (9410)  all_57_11 = e1
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | |   (9411)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9411) gives:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9412)  all_57_1 = e1 & op(e3, e2) = e1
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9412) implies:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9413)  all_57_1 = e1
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9414)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9414) gives:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9415)  all_57_2 = e1 & op(e2, e3) = e1
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (7573), (9415), (function-axioms) are
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2156.
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9416)  all_57_3 = e1 & op(e2, e2) = e1
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9416) implies:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9417)  op(e2, e2) = e1
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (226), (228), (229),
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9413), (9417), (function-axioms) are inconsistent
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1908.
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9418)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9418) gives:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9419)  all_57_5 = e1 & op(e2, e1) = e1
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9419) implies:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9420)  all_57_5 = e1
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (208),
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (209), (218), (220), (221), (374), (9217), (9258),
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9420), (function-axioms) are inconsistent by
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #941.
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9421)  all_57_10 = e1 & op(e2, e0) = e1
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9421) implies:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9422)  all_57_10 = e1
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9423)  all_57_15 = e0 & op(e0, e0) = e0
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9423) implies:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9424)  op(e0, e0) = e0
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (161), (169), (213), (9209), (9211),
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9422), (9424), (function-axioms) are inconsistent
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2302.
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9425)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9425) implies:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9426)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0)
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9427)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (9235), (9413), (9427),
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #292.
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9428)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9428) gives:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9429)  all_57_7 = e3 & op(e1, e2) = e3
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9429) implies:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9430)  all_57_7 = e3
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9431)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e0)
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9431) gives:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9432)  all_57_6 = e0 & op(e1, e3) = e0
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9432) implies:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9433)  all_57_6 = e0
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (216), (9258), (9410), (9430),
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9433), (function-axioms) are inconsistent by
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1844.
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9434)  all_57_7 = e0 & op(e1, e2) = e0
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9434) implies:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9435)  all_57_7 = e0
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (208), (209), (229),
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9217), (9218), (9239), (9413), (9426), (9435),
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #940.
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9436)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (211), (212), (9217),
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9218), (9258), (9410), (9422), (9436),
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #282.
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9437)  all_57_13 = e3 & op(e0, e2) = e3
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9437) implies:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9438)  all_57_13 = e3
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (208), (209),
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9217), (9218), (9426), (9438), (function-axioms)
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2054.
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9439)  all_57_3 = e1 & op(e2, e2) = e1
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9439) implies:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9440)  op(e2, e2) = e1
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9235), (9440), (function-axioms) are
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2306.
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.97  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | |   (9441)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9441) gives:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9442)  all_57_7 = e1 & op(e1, e2) = e1
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9442) implies:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9443)  all_57_7 = e1
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (214), (216), (217), (374), (9217), (9258),
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | |            (9443), (function-axioms) are inconsistent by
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1069.
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9444)  all_57_13 = e1 & op(e0, e2) = e1
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9444) implies:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9445)  all_57_13 = e1
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9446)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (168), (7573), (9235), (9446),
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #361.
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9447)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9447) gives:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9448)  all_57_5 = e1 & op(e2, e1) = e1
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9448) implies:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9449)  all_57_5 = e1
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (208),
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (209), (218), (220), (221), (374), (9217), (9258),
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9449), (function-axioms) are inconsistent by
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #941.
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9450)  all_57_10 = e1 & op(e2, e0) = e1
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9450) implies:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9451)  all_57_10 = e1
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9452)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9452) gives:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9453)  all_57_9 = e2 & op(e3, e0) = e2
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9453) implies:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9454)  all_57_9 = e2
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9455)  all_57_15 = e0 & op(e0, e0) = e0
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9455) implies:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9456)  op(e0, e0) = e0
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (161), (169), (213), (9209), (9211),
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9451), (9456), (function-axioms) are inconsistent
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2302.
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9457)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9457) implies:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9458)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0)
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9459)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e2)
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9459) gives:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9460)  all_57_6 = e2 & op(e1, e3) = e2
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9460) implies:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9461)  all_57_6 = e2
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9462)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9462) gives:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9463)  all_57_6 = e3 & op(e1, e3) = e3
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9463) implies:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9464)  all_57_6 = e3
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (9461), (9464) are inconsistent by sub-proof
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2463.
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9465)  all_57_7 = e3 & op(e1, e2) = e3
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9465) implies:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9466)  all_57_7 = e3
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9467)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e1)
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9467) gives:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9468)  all_57_4 = e1 & op(e3, e1) = e1
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9468) implies:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9469)  all_57_4 = e1
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (218), (220),
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (221), (374), (9244), (9258), (9469),
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2407.
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9470)  all_57_5 = e1 & op(e2, e1) = e1
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9470) implies:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9471)  all_57_5 = e1
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (208),
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (209), (218), (220), (221), (374), (9217), (9258),
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9471), (function-axioms) are inconsistent by
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #941.
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9472)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e1)
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9472) gives:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9473)  all_57_8 = e1 & op(e1, e1) = e1
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9473) implies:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9474)  all_57_8 = e1
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9475)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e0)
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9475) gives:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9476)  all_57_6 = e0 & op(e1, e3) = e0
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9476) implies:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9477)  all_57_6 = e0
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (216), (9258), (9410), (9466),
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9477), (function-axioms) are inconsistent by
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1844.
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9478)  all_57_7 = e0 & op(e1, e2) = e0
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9478) implies:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9479)  all_57_7 = e0
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (39), (216), (217),
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (374), (9258), (9410), (9479), (function-axioms)
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1931.
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9480)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9480) gives:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9481)  all_57_8 = e0 & op(e1, e1) = e0
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9481) implies:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9482)  op(e1, e1) = e0
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9258), (9482), (function-axioms) are
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2427.
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9483)  all_57_11 = e0 & op(e1, e0) = e0
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9483) implies:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9484)  all_57_11 = e0
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9410), (9484) imply:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9485)  e1 = e0
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9485) implies:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9486)  e1 = e0
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9474), (9486) imply:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9487)  all_57_8 = e0
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7581), (9486) imply:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9488)  all_57_0 = e0
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (39), (160), (168),
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (216), (217), (232), (374), (7573), (7575),
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9410), (9487), (9488), (function-axioms) are
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1678.
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9489)  all_57_14 = e1 & op(e0, e1) = e1
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9489) implies:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9490)  all_57_14 = e1
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9491)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9491) gives:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9492)  all_57_12 = e2 & op(e0, e3) = e2
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9492) implies:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9493)  all_57_12 = e2
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9494)  all_57_15 = e0 & op(e0, e0) = e0
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9494) implies:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9495)  op(e0, e0) = e0
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (161), (169), (213), (9209), (9211),
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9451), (9495), (function-axioms) are inconsistent
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2302.
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9457) implies:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9496)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0)
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9496) gives:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9497)  all_57_12 = e0 & op(e0, e3) = e0
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9493), (9497) are inconsistent by sub-proof
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2185.
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9498)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9498) gives:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9499)  all_57_13 = e0 & op(e0, e2) = e0
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9499) implies:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9500)  all_57_13 = e0
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9445), (9500) imply:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9501)  e1 = e0
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9501) implies:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9502)  e1 = e0
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (211), (9218), (9410), (9451),
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9454), (9502), (function-axioms) are inconsistent
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #281.
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9503)  all_57_14 = e0 & op(e0, e1) = e0
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9503) implies:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9504)  all_57_14 = e0
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9490), (9504) imply:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9505)  e1 = e0
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (211), (9218), (9410), (9451),
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9454), (9505), (function-axioms) are inconsistent
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #281.
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9506)  all_57_13 = e2 & op(e0, e2) = e2
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9506) implies:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9507)  op(e0, e2) = e2
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (9231), (9507), (function-axioms) are
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2335.
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9508)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9508) gives:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9509)  all_57_14 = e2 & op(e0, e1) = e2
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9490), (9509) are inconsistent by sub-proof
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1968.
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9510)  all_57_15 = e2 & op(e0, e0) = e2
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9510) implies:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9511)  op(e0, e0) = e2
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (373), (9511), (function-axioms) are
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2334.
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9512)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (211), (212),
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (374), (9217), (9458), (9512), (function-axioms)
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1080.
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9513)  all_57_7 = e2 & op(e1, e2) = e2
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9513) implies:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9514)  all_57_7 = e2
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9515)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e0)
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (214), (217), (374), (9217), (9258),
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9454), (9514), (9515), (function-axioms) are
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #958.
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9516)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (211), (212), (9217),
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9218), (9258), (9410), (9451), (9516),
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #282.
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9517)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e0) = e2)
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9258), (9410), (9517), (function-axioms) are
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #956.
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9518)  all_57_10 = e2 & op(e2, e0) = e2
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (9233), (9518), (function-axioms) are
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2432.
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9519)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9519) gives:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9520)  all_57_11 = e2 & op(e1, e0) = e2
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9520) implies:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9521)  all_57_11 = e2
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9410), (9521) are inconsistent by sub-proof
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2113.
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9522)  all_57_15 = e2 & op(e0, e0) = e2
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9522) implies:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9523)  op(e0, e0) = e2
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (373), (9523), (function-axioms) are
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2334.
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | |   (9524)  all_57_15 = e1 & op(e0, e0) = e1
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9524) implies:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | |   (9525)  op(e0, e0) = e1
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9218), (9525), (function-axioms) are
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2183.
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | |   (9526)  all_55_10 = e0
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (9244), (9526) are inconsistent by
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2118.
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | |   (9527)  all_38_2 = e2
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (9527) imply:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | |   (9528)  all_6_2 = e2
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | REDUCE: (39), (9528) imply:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | |   (9529)  op(e1, e1) = e2
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | |   (9530)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | |             all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | |             op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | |               all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | |             $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | |             $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | |               all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | |             & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | |               all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | |             & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | |             $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | BETA: splitting (9530) gives:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | |   (9531)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | |           all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | |           op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | |             all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | |           $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | |           $i(all_52_7)
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | ALPHA: (9531) implies:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | |   (9532)  op(e3, e0) = all_52_7
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | |   (9533)  op(e3, e3) = all_52_1
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | |   (9534)  op(all_52_7, all_52_7) = e0
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | |   (9535)  op(all_52_1, all_52_1) = e3
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | |   (9536)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9536) gives:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | |   (9537)  all_57_9 = e2 & op(e3, e0) = e2
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9537) implies:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | |   (9538)  op(e3, e0) = e2
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_12,
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, e3, simplifying with (169), (9538) gives:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | |   (9539)  all_53_12 = e2
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (169), (9235), (9532), (9534), (9539),
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | |            #338.
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | |   (9540)  all_57_10 = e2 & op(e2, e0) = e2
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (9233), (9540), (function-axioms) are
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2432.
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | |   (9541)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9541) gives:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | |   (9542)  all_57_11 = e2 & op(e1, e0) = e2
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9542) implies:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | |   (9543)  all_57_11 = e2
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | |   (9544)  op(e1, e0) = e2
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | |   (9545)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9545) gives:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | |   (9546)  all_57_9 = e1 & op(e3, e0) = e1
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (7578), (9546), (function-axioms) are
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2131.
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | |   (9547)  all_57_10 = e1 & op(e2, e0) = e1
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9547) implies:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | |   (9548)  all_57_10 = e1
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9549)  all_57_15 = e0 & op(e0, e0) = e0
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9549) implies:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9550)  op(e0, e0) = e0
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (161), (169), (213), (9209), (9211),
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | |            (9548), (9550), (function-axioms) are inconsistent
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2302.
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9551)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9551) implies:
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9552)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0)
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9553)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0)
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.98  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9553) gives:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9554)  all_57_9 = e0 & op(e3, e0) = e0
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9554) implies:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9555)  all_57_9 = e0
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9556)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e2)
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9556) gives:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9557)  all_57_4 = e2 & op(e3, e1) = e2
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9557) implies:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9558)  all_57_4 = e2
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9559)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9559) gives:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9560)  all_57_6 = e1 & op(e1, e3) = e1
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9560) implies:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9561)  all_57_6 = e1
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9562)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e3)
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9562) gives:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9563)  all_57_0 = e3 & op(e3, e3) = e3
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9563) implies:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9564)  op(e3, e3) = e3
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (64), (67),
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (82), (88), (107), (119), (121), (124), (127),
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (134), (158), (159), (161), (163), (165), (166),
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (169), (170), (171), (195), (199), (207), (208),
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (209), (211), (212), (214), (215), (216), (217),
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (218), (219), (220), (221), (222), (223), (224),
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (225), (226), (227), (228), (229), (230), (231),
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (232), (233), (234), (235), (236), (237), (249),
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (259), (311), (315), (336), (363), (364), (368),
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (374), (9205), (9207), (9209), (9217), (9218),
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9229), (9231), (9232), (9233), (9235), (9239),
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9564), (function-axioms) are inconsistent by
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1073.
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9565)  all_57_1 = e3 & op(e3, e2) = e3
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9565) implies:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9566)  all_57_1 = e3
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (217), (226), (227), (228), (374), (9217),
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9235), (9561), (9566), (function-axioms) are
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1071.
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9567)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e3)
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (169), (9209), (9558), (9567),
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2448.
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9568)  all_57_7 = e1 & op(e1, e2) = e1
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9568) implies:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9569)  all_57_7 = e1
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9570)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e0)
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9570) gives:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9571)  all_57_6 = e0 & op(e1, e3) = e0
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9571) implies:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9572)  all_57_6 = e0
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (39), (217), (374), (9543), (9569),
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9572), (function-axioms) are inconsistent by
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2114.
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9573)  all_57_7 = e0 & op(e1, e2) = e0
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9573) implies:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9574)  all_57_7 = e0
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (215), (217), (374), (9217), (9529),
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9543), (9574), (function-axioms) are inconsistent
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1154.
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9575)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9575) gives:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9576)  all_57_8 = e0 & op(e1, e1) = e0
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (9244), (9576), (function-axioms) are
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2412.
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9577)  all_57_11 = e0 & op(e1, e0) = e0
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9577) implies:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9578)  all_57_11 = e0
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (211), (212), (9217),
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9555), (9578) are inconsistent by sub-proof
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1144.
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9579)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9529), (9543), (9579), (function-axioms) are
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1725.
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9580)  all_57_5 = e2 & op(e2, e1) = e2
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (9232), (9580), (function-axioms) are
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1858.
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9581)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e1) = e2)
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9581) gives:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9582)  all_57_8 = e2 & op(e1, e1) = e2
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9582) implies:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9583)  all_57_8 = e2
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9584)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e2)
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (171), (9229), (9235), (9533), (9535),
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9584), (function-axioms) are inconsistent by
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #341.
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9585)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e2)
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9585) gives:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9586)  all_57_4 = e2 & op(e3, e1) = e2
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9586) implies:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9587)  all_57_4 = e2
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9588)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e3)
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9588) gives:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9589)  all_57_4 = e3 & op(e3, e1) = e3
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9589) implies:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9590)  all_57_4 = e3
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (9587), (9590) are inconsistent by sub-proof
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2482.
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9591)  all_57_5 = e3 & op(e2, e1) = e3
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9591) implies:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9592)  all_57_5 = e3
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9593)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e0)
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9593) gives:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9594)  all_57_4 = e0 & op(e3, e1) = e0
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9594) implies:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9595)  all_57_4 = e0
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9587), (9595) imply:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9596)  e2 = e0
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9596) implies:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9597)  e2 = e0
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9543), (9597) imply:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9598)  all_57_11 = e0
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (211), (212), (9217),
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9555), (9598) are inconsistent by sub-proof
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1144.
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9599)  all_57_5 = e0 & op(e2, e1) = e0
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9592), (9599) are inconsistent by sub-proof
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2414.
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9600)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9600) gives:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9601)  all_57_8 = e0 & op(e1, e1) = e0
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (9244), (9601), (function-axioms) are
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2412.
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9602)  all_57_14 = e0 & op(e0, e1) = e0
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9602) implies:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9603)  all_57_14 = e0
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (219), (9583), (9587), (9592),
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9603) are inconsistent by sub-proof #1456.
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9604)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e1) = e3)
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (208), (209),
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (374), (9217), (9552), (9604), (function-axioms)
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1044.
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9605)  all_57_9 = e2 & op(e3, e0) = e2
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9605) implies:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9606)  all_57_9 = e2
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9555), (9606) imply:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9607)  e2 = e0
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9607) implies:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9608)  e2 = e0
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9543), (9608) imply:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9609)  all_57_11 = e0
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (211), (212), (9217),
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9555), (9609) are inconsistent by sub-proof
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1144.
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9610)  all_57_14 = e2 & op(e0, e1) = e2
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9610) implies:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9611)  all_57_14 = e2
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9612)  op(e0, e1) = e2
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9613)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9613) gives:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9614)  all_57_12 = e1 & op(e0, e3) = e1
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9614) implies:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9615)  op(e0, e3) = e1
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9205), (9242), (9544), (9615), (function-axioms)
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1147.
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9616)  all_57_13 = e1 & op(e0, e2) = e1
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9616) implies:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9617)  all_57_13 = e1
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9618)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e2)
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9618) gives:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9619)  all_57_0 = e2 & op(e3, e3) = e2
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9619) implies:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9620)  op(e3, e3) = e2
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (39), (67), (82), (107), (119), (158), (161),
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (166), (195), (199), (259), (311), (315), (336),
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (364), (368), (374), (9211), (9218), (9235),
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9544), (9612), (9620), (function-axioms) are
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1114.
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9621)  all_57_1 = e2 & op(e3, e2) = e2
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (171), (9229), (9621), (function-axioms) are
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2456.
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9622)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e2)
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9622) gives:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9623)  all_57_4 = e2 & op(e3, e1) = e2
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9623) implies:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9624)  all_57_4 = e2
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (218), (219),
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (220), (221), (374), (9611), (9624),
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2370.
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9625)  all_57_9 = e2 & op(e3, e0) = e2
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9625) implies:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9626)  all_57_9 = e2
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9627)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e1)
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9627) gives:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9628)  all_57_4 = e1 & op(e3, e1) = e1
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9628) implies:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9629)  all_57_4 = e1
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (39), (218), (221),
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (374), (9244), (9611), (9629), (function-axioms)
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2408.
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9630)  all_57_5 = e1 & op(e2, e1) = e1
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9630) implies:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9631)  all_57_5 = e1
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9632)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e0)
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9632) gives:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9633)  all_57_4 = e0 & op(e3, e1) = e0
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9633) implies:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9634)  all_57_4 = e0
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (208),
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (209), (221), (374), (9217), (9631), (9634),
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #943.
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9635)  all_57_5 = e0 & op(e2, e1) = e0
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9635) implies:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9636)  all_57_5 = e0
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9631), (9636) imply:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9637)  e1 = e0
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9617), (9637) imply:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9638)  all_57_13 = e0
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (208), (9205), (9218), (9242),
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9544), (9611), (9638), (function-axioms) are
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1100.
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9639)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9639) gives:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9640)  all_57_8 = e0 & op(e1, e1) = e0
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (9244), (9640), (function-axioms) are
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2412.
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9641)  all_57_14 = e0 & op(e0, e1) = e0
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9641) implies:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9642)  all_57_14 = e0
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9611), (9642) imply:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9643)  e2 = e0
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9543), (9643) imply:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9644)  all_57_11 = e0
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (211), (212), (9217),
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9555), (9644) are inconsistent by sub-proof
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1144.
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9645)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e1)
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9529), (9611), (9645), (function-axioms) are
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2198.
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9646)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9218), (9611), (9646),
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1139.
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9647)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 =
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9647) gives:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9648)  all_57_10 = e0 & op(e2, e0) = e0
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9548), (9648) are inconsistent by sub-proof
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1332.
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9649)  all_57_11 = e0 & op(e1, e0) = e0
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9543), (9649) are inconsistent by sub-proof
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2041.
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | |   (9650)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9218), (9543), (9650),
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | |            #1109.
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | |   (9651)  all_57_15 = e2 & op(e0, e0) = e2
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9651) implies:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | |   (9652)  op(e0, e0) = e2
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (373), (9652), (function-axioms) are
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2334.
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | |   (9653)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | |           all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | |           op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | |             all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | |           & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | |           $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | |           $i(all_52_15)
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | ALPHA: (9653) implies:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | |   (9654)  op(e2, e0) = all_52_15
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | |   (9655)  op(all_52_15, all_52_15) = e0
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | |   (9656)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (160), (165), (198), (258), (9205), (9210),
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | |            (9218), (9231), (9233), (9242), (9654), (9655),
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | |            (9656), (function-axioms) are inconsistent by
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #278.
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | |   (9657)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9657) gives:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | |   (9658)  all_57_14 = e2 & op(e0, e1) = e2
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9658) implies:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | |   (9659)  all_57_14 = e2
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (160), (207),
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | |            (208), (211), (212), (214), (215), (217), (222),
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | |            (223), (224), (225), (234), (374), (7575), (7582),
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | |            (9217), (9218), (9235), (9239), (9244), (9529),
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | |            (9659), (function-axioms) are inconsistent by
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #333.
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | |   (9660)  all_57_15 = e2 & op(e0, e0) = e2
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9660) implies:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | |   (9661)  op(e0, e0) = e2
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (373), (9661), (function-axioms) are
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2334.
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | 
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/37.99  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | |   (9662)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | |             & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | |             & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | |               all_52_21) = e1 & op(all_52_23, all_52_23) =
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | |             all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | |             = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | |             $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | |             & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | |             e0 & op(all_52_25, all_52_25) = e3 &
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | |             op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | |               all_52_29) = e1 & op(all_52_31, all_52_31) =
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | |             all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | |             = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | |             $i(all_52_29) & $i(all_52_31))
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | BETA: splitting (9662) gives:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | |   (9663)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | |           all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | |           op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | |             all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | |           & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | |           & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | |           & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | |           $i(all_52_23)
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | ALPHA: (9663) implies:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | |   (9664)  op(e1, e1) = all_52_21
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | |   (9665)  op(all_52_21, all_52_21) = e1
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | |            (212), (214), (215), (217), (222), (223), (224),
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | |            (225), (234), (374), (7582), (9205), (9217),
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | |            (9218), (9235), (9239), (9242), (9244), (9529),
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | |            (9664), (9665), (function-axioms) are inconsistent
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | |            by sub-proof #284.
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | |   (9666)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | |           all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | |           op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | |             all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | |           & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | |           & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | |           & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | |           $i(all_52_31)
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | ALPHA: (9666) implies:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | |   (9667)  op(e0, e0) = all_52_31
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | |   (9668)  op(all_52_31, all_52_31) = e0
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7582), (9218), (9667), (9668),
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | |            #283.
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.00  | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | |   (9669)  all_24_2 = e0
% 223.10/38.00  | | | | | | | | | | | | | | | | | |   (9670)  ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0
% 223.10/38.00  | | | | | | | | | | | | | | | | | |             & op(e1, e0) = all_24_1 & $i(all_24_0) &
% 223.10/38.00  | | | | | | | | | | | | | | | | | |             $i(all_24_1)) | ( ~ (all_24_1 = e3) & op(e1, e0)
% 223.10/38.00  | | | | | | | | | | | | | | | | | |             = all_24_1 & $i(all_24_1))
% 223.10/38.00  | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (315), (9669) imply:
% 223.10/38.00  | | | | | | | | | | | | | | | | | |   (9671)  all_6_2 = e0
% 223.10/38.00  | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | SIMP: (9671) implies:
% 223.10/38.00  | | | | | | | | | | | | | | | | | |   (9672)  all_6_2 = e0
% 223.10/38.00  | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (311), (9672) imply:
% 223.10/38.00  | | | | | | | | | | | | | | | | | |   (9673)  all_34_2 = e0
% 223.10/38.00  | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | REDUCE: (350), (9672) imply:
% 223.10/38.00  | | | | | | | | | | | | | | | | | |   (9674)   ~ (all_53_2 = e0)
% 223.10/38.00  | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | REDUCE: (361), (9672) imply:
% 223.10/38.00  | | | | | | | | | | | | | | | | | |   (9675)   ~ (all_53_6 = e0)
% 223.10/38.00  | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | REDUCE: (364), (9672) imply:
% 223.10/38.00  | | | | | | | | | | | | | | | | | |   (9676)   ~ (all_53_9 = e0)
% 223.10/38.00  | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | REDUCE: (368), (9672) imply:
% 223.10/38.00  | | | | | | | | | | | | | | | | | |   (9677)   ~ (all_53_14 = e0)
% 223.10/38.00  | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | REDUCE: (374), (9672) imply:
% 223.10/38.00  | | | | | | | | | | | | | | | | | |   (9678)   ~ (e3 = e0)
% 223.10/38.00  | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | |   (9679)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 223.10/38.00  | | | | | | | | | | | | | | | | | | |             all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 223.10/38.00  | | | | | | | | | | | | | | | | | | |             op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 223.10/38.00  | | | | | | | | | | | | | | | | | | |               all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 223.10/38.00  | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 223.10/38.00  | | | | | | | | | | | | | | | | | | |             op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 223.10/38.00  | | | | | | | | | | | | | | | | | | |             $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 223.10/38.00  | | | | | | | | | | | | | | | | | | |             $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 223.10/38.00  | | | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 223.10/38.00  | | | | | | | | | | | | | | | | | | |               all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 223.10/38.00  | | | | | | | | | | | | | | | | | | |             & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 223.10/38.00  | | | | | | | | | | | | | | | | | | |               all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 223.10/38.00  | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 223.10/38.00  | | | | | | | | | | | | | | | | | | |             & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 223.10/38.00  | | | | | | | | | | | | | | | | | | |             $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | BETA: splitting (9679) gives:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | |   (9680)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | |           all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | |           op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | |             all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | |           op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | |           $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | |           $i(all_52_7)
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (374), (7582), (9680), (function-axioms) are
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #360.
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | |   (9681)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | |           all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | |           op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | |             all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | |           & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | |           $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | |           $i(all_52_15)
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | ALPHA: (9681) implies:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | |   (9682)  op(e2, e0) = all_52_15
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | |   (9683)  op(e2, e1) = all_52_13
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | |   (9684)  op(e2, e2) = all_52_11
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | |   (9685)  op(all_52_15, all_52_15) = e0
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | |   (9686)  op(all_52_13, all_52_13) = e1
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | |   (9687)  op(all_52_11, all_52_11) = e2
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | |   (9688)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e0)
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (164), (9674), (9675), (9688),
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | |            #2038.
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | |   (9689)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9689) gives:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | |   (9690)  all_57_8 = e0 & op(e1, e1) = e0
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9690) implies:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | |   (9691)  all_57_8 = e0
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | |   (9692)  op(e1, e1) = e0
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_13,
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | |              all_52_15, e0, e2, simplifying with (165), (9682)
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | |              gives:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | |   (9693)  all_53_13 = all_52_15
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_9,
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | |              all_52_13, e1, e2, simplifying with (166), (9683)
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | |              gives:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | |   (9694)  all_53_9 = all_52_13
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | |              all_52_11, e2, e2, simplifying with (9235), (9684)
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | |              gives:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | |   (9695)  all_52_11 = e2
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (9693) imply:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | |   (9696)  all_55_7 = all_52_15
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (9694) imply:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | |   (9697)  all_55_6 = all_52_13
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9232), (9694) imply:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | |   (9698)   ~ (all_52_13 = e2)
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9676), (9694) imply:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | |   (9699)   ~ (all_52_13 = e0)
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (111), (9693) imply:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | |   (9700)   ~ (all_53_14 = all_52_15)
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | SIMP: (9700) implies:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | |   (9701)   ~ (all_53_14 = all_52_15)
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9210), (9693) imply:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | |   (9702)   ~ (all_52_15 = e3)
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9233), (9693) imply:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | |   (9703)   ~ (all_52_15 = e2)
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | |   (9704)  all_55_13 = e3
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (9208), (9704) are inconsistent by
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2080.
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | |   (9705)  all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | |   (9706)  all_55_9 = e3
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (9706) imply:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | |   (9707)  all_53_6 = e3
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9707) implies:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | |   (9708)  all_53_6 = e3
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (9708) imply:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | |   (9709)   ~ (all_53_2 = e3)
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (127), (9708) imply:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | |   (9710)   ~ (all_53_14 = e3)
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | |   (9711)  all_55_8 = e3
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (9709), (9711) are inconsistent by
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2496.
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | |   (9712)  all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9712) gives:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9713)  all_55_8 = e2
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (9713) imply:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9714)  all_53_2 = e2
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9714) implies:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9715)  all_53_2 = e2
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (142), (9715) imply:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9716)   ~ (all_53_14 = e2)
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9716) implies:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9717)   ~ (all_53_14 = e2)
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9718)  all_55_11 = e3
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (9718) imply:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9719)  all_53_14 = e3
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9211), (9719) imply:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9720)  $false
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (9720) is inconsistent.
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9721)  all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9721) gives:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9722)  all_55_11 = e2
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (9722) imply:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9723)  all_53_14 = e2
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9717), (9723) imply:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9724)  $false
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (9724) is inconsistent.
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9725)  all_55_11 = e1 | all_55_11 = e0
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9725) gives:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9726)  all_55_11 = e1
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (9726) imply:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9727)  all_53_14 = e1
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9701), (9727) imply:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9728)   ~ (all_52_15 = e1)
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9728) implies:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9729)   ~ (all_52_15 = e1)
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9730)  all_55_7 = e3
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9696), (9702), (9730) are inconsistent by
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2063.
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9731)   ~ (all_55_7 = e3)
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9732)  all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9218), (9685), (9696), (9702), (9703), (9729),
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9732), (function-axioms) are inconsistent by
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #276.
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9733)  all_55_11 = e0
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (9733) imply:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9734)  all_53_14 = e0
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9677), (9734) imply:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9735)  $false
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (9735) is inconsistent.
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9736)  all_55_8 = e1 | all_55_8 = e0
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (7574), (9674), (9736) are inconsistent by
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1974.
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | |   (9737)   ~ (all_55_9 = e3)
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | |   (9738)  all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (256), (9737) imply:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | |   (9739)   ~ (all_53_6 = e3)
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | |   (9740)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9740) gives:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9741)  all_57_6 = e3 & op(e1, e3) = e3
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9741) implies:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9742)  all_57_6 = e3
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9743)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2)
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (207), (211), (212),
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (222), (223), (224), (225), (7582), (9217),
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9218), (9235), (9239), (9743), (function-axioms)
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #337.
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9744)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e3) = e2)
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9744) gives:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9745)  all_57_6 = e2 & op(e1, e3) = e2
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (9742), (9745) are inconsistent by sub-proof
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2012.
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9746)  all_57_12 = e2 & op(e0, e3) = e2
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (165), (198), (258), (9205), (9210),
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9218), (9233), (9242), (9682), (9685), (9746),
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #279.
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9747)  all_57_7 = e3 & op(e1, e2) = e3
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9747) implies:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9748)  all_57_7 = e3
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9749)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9749) gives:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9750)  all_57_6 = e1 & op(e1, e3) = e1
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9750) implies:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9751)  all_57_6 = e1
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9752)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2)
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (207), (211), (212),
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (222), (223), (224), (225), (7582), (9217),
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9218), (9235), (9239), (9752), (function-axioms)
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #337.
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9753)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e3) = e2)
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9753) gives:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9754)  all_57_6 = e2 & op(e1, e3) = e2
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9751), (9754) are inconsistent by sub-proof
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1317.
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9755)  all_57_12 = e2 & op(e0, e3) = e2
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (165), (198), (258), (9205), (9210),
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9218), (9233), (9242), (9682), (9685), (9755),
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #279.
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9756)  all_57_7 = e1 & op(e1, e2) = e1
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9756) implies:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9757)  all_57_7 = e1
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9748), (9757) are inconsistent by sub-proof
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2115.
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9758)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9758) gives:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9759)  all_57_8 = e1 & op(e1, e1) = e1
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9759) implies:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9760)  op(e1, e1) = e1
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9692), (9760), (function-axioms) are
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2427.
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9761)  all_57_11 = e1 & op(e1, e0) = e1
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9761) implies:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9762)  all_57_11 = e1
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9738) gives:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9763)  all_55_9 = e2
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (9230), (9763) are inconsistent by
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2274.
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9764)   ~ (all_55_9 = e2)
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9765)  all_55_9 = e1 | all_55_9 = e0
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9766)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e2)
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9766) gives:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9767)  all_57_6 = e2 & op(e1, e3) = e2
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9767) implies:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9768)  all_57_6 = e2
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9769)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9769) gives:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9770)  all_57_1 = e1 & op(e3, e2) = e1
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9770) implies:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9771)  all_57_1 = e1
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9772)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (207), (208),
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (209), (226), (228), (229), (7575), (9217),
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9218), (9235), (9771), (9772), (function-axioms)
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #290.
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9773)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9773) gives:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9774)  all_57_14 = e1 & op(e0, e1) = e1
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9774) implies:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9775)  all_57_14 = e1
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9776)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (160), (165), (198), (258), (9205), (9210),
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9218), (9231), (9233), (9242), (9682), (9685),
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9776), (function-axioms) are inconsistent by
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #278.
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9777)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (373), (9775), (9777),
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #286.
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9778)  all_57_15 = e1 & op(e0, e0) = e1
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9778) implies:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9779)  op(e0, e0) = e1
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9218), (9779), (function-axioms) are
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2183.
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9780)  all_57_3 = e1 & op(e2, e2) = e1
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9780) implies:
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9781)  op(e2, e2) = e1
% 223.10/38.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9684), (9687), (9692), (9781),
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1843.
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9782)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9782) gives:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9783)  all_57_7 = e1 & op(e1, e2) = e1
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9783) implies:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9784)  all_57_7 = e1
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (217), (374), (9217), (9768), (9784),
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1245.
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9785)  all_57_13 = e1 & op(e0, e2) = e1
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9785) implies:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9786)  all_57_13 = e1
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9765) gives:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9787)  all_55_9 = e1
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (9787) imply:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9788)  all_53_6 = e1
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9788) implies:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9789)  all_53_6 = e1
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (129), (9789) imply:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9790)   ~ (all_53_7 = e1)
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9790) implies:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9791)   ~ (all_53_7 = e1)
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9739), (9789) imply:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9792)   ~ (e3 = e1)
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9230), (9789) imply:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9793)   ~ (e2 = e1)
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9794)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9794) gives:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9795)  all_57_1 = e0 & op(e3, e2) = e0
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9795) implies:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9796)  op(e3, e2) = e0
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (136), (171), (246), (9231), (9705), (9791),
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9796), (function-axioms) are inconsistent by
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #327.
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9797)  all_57_3 = e0 & op(e2, e2) = e0
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9797) implies:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9798)  op(e2, e2) = e0
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (9218), (9684), (9687), (9798),
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1229.
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9799)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0)
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9799) gives:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9800)  all_57_7 = e0 & op(e1, e2) = e0
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (9675), (9800), (function-axioms) are
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2039.
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9801)  all_57_13 = e0 & op(e0, e2) = e0
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9801) implies:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9802)  all_57_13 = e0
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9786), (9802) imply:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9803)  e1 = e0
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7581), (9803) imply:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9804)  all_57_0 = e0
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (39), (160), (168),
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (216), (217), (232), (374), (7573), (7575),
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9691), (9762), (9804), (function-axioms) are
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1678.
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9805)  all_55_9 = e0
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (9675), (9805) are inconsistent by
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2272.
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9806)  all_57_7 = e2 & op(e1, e2) = e2
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9806) implies:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9807)  all_57_7 = e2
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (208),
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (209), (211), (212), (217), (226), (227), (228),
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (229), (374), (9217), (9218), (9235), (9807),
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #275.
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9808)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e0) = e2)
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9808) gives:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9809)  all_57_8 = e2 & op(e1, e1) = e2
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9809) implies:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9810)  all_57_8 = e2
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9691), (9810) are inconsistent by sub-proof
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1957.
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9811)  all_57_11 = e2 & op(e1, e0) = e2
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9811) implies:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9812)  op(e1, e0) = e2
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (82), (199), (9670), (9673), (9683), (9686),
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9692), (9697), (9698), (9699), (9812),
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1945.
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (9813)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (374), (9217), (9813), (function-axioms)
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1786.
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | |   (9814)  all_57_11 = e0 & op(e1, e0) = e0
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (9677), (9814), (function-axioms) are
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2341.
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | |   (9815)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 223.10/38.01  | | | | | | | | | | | | | | | | | | |             & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 223.10/38.01  | | | | | | | | | | | | | | | | | | |             & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 223.10/38.01  | | | | | | | | | | | | | | | | | | |               all_52_21) = e1 & op(all_52_23, all_52_23) =
% 223.10/38.01  | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 223.10/38.01  | | | | | | | | | | | | | | | | | | |             all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 223.10/38.01  | | | | | | | | | | | | | | | | | | |             = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 223.10/38.01  | | | | | | | | | | | | | | | | | | |             $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 223.10/38.01  | | | | | | | | | | | | | | | | | | |             & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 223.10/38.01  | | | | | | | | | | | | | | | | | | |             e0 & op(all_52_25, all_52_25) = e3 &
% 223.10/38.01  | | | | | | | | | | | | | | | | | | |             op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 223.10/38.01  | | | | | | | | | | | | | | | | | | |               all_52_29) = e1 & op(all_52_31, all_52_31) =
% 223.10/38.01  | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 223.10/38.01  | | | | | | | | | | | | | | | | | | |             all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 223.10/38.01  | | | | | | | | | | | | | | | | | | |             = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 223.10/38.01  | | | | | | | | | | | | | | | | | | |             $i(all_52_29) & $i(all_52_31))
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | BETA: splitting (9815) gives:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | |   (9816)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | |           all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | |           op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | |             all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | |           & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | |           & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | |           & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | |           $i(all_52_23)
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | ALPHA: (9816) implies:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | |   (9817)  op(e1, e1) = all_52_21
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | |   (9818)  op(all_52_21, all_52_21) = e1
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | |   (9819)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e0)
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (164), (9674), (9675), (9819),
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | |            #2038.
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | |   (9820)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9820) gives:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | |   (9821)  all_57_8 = e0 & op(e1, e1) = e0
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9218), (9817), (9818), (9821),
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | |            #601.
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | |   (9822)  all_57_11 = e0 & op(e1, e0) = e0
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (9677), (9822), (function-axioms) are
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2341.
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | |   (9823)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | |           all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | |           op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | |             all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | |           & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | |           & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | |           & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | |           $i(all_52_31)
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | ALPHA: (9823) implies:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | |   (9824)  op(e0, e0) = all_52_31
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | |   (9825)  op(all_52_31, all_52_31) = e0
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7582), (9218), (9824), (9825),
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | |            #283.
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.01  | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | End of split
% 223.10/38.01  | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | End of split
% 223.10/38.01  | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | End of split
% 223.10/38.01  | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | Case 2:
% 223.10/38.01  | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | |   (9826)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 223.10/38.01  | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 223.10/38.01  | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | BETA: splitting (9826) gives:
% 223.10/38.01  | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | Case 1:
% 223.10/38.01  | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | |   (9827)  all_57_7 = e2 & op(e1, e2) = e2
% 223.10/38.01  | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | ALPHA: (9827) implies:
% 223.10/38.01  | | | | | | | | | | | | | | | |   (9828)  all_57_7 = e2
% 223.10/38.01  | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (208),
% 223.10/38.01  | | | | | | | | | | | | | | | |            (209), (211), (212), (217), (226), (227), (228),
% 223.10/38.01  | | | | | | | | | | | | | | | |            (229), (374), (9217), (9218), (9235), (9828),
% 223.10/38.01  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.01  | | | | | | | | | | | | | | | |            #275.
% 223.10/38.01  | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | Case 2:
% 223.10/38.01  | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | |   (9829)  all_57_13 = e2 & op(e0, e2) = e2
% 223.10/38.01  | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | ALPHA: (9829) implies:
% 223.10/38.01  | | | | | | | | | | | | | | | |   (9830)  op(e0, e2) = e2
% 223.10/38.01  | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | REF_CLOSE: (159), (9231), (9830), (function-axioms) are
% 223.10/38.01  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2335.
% 223.10/38.01  | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | End of split
% 223.10/38.01  | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | End of split
% 223.10/38.01  | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | Case 2:
% 223.10/38.01  | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | |   (9831)  all_55_5 = e1 | all_55_5 = e0
% 223.10/38.01  | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | REF_CLOSE: (266), (9220), (9222), (9831) are inconsistent by
% 223.10/38.01  | | | | | | | | | | | | | |            sub-proof #1857.
% 223.10/38.01  | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | End of split
% 223.10/38.01  | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | End of split
% 223.10/38.01  | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | Case 2:
% 223.10/38.01  | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | |   (9832)  all_16_2 = e1
% 223.10/38.01  | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | COMBINE_EQS: (324), (9832) imply:
% 223.10/38.01  | | | | | | | | | | | |   (9833)  all_8_2 = e1
% 223.10/38.01  | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | SIMP: (9833) implies:
% 223.10/38.01  | | | | | | | | | | | |   (9834)  all_8_2 = e1
% 223.10/38.01  | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | REDUCE: (356), (9834) imply:
% 223.10/38.01  | | | | | | | | | | | |   (9835)   ~ (all_53_7 = e1)
% 223.10/38.01  | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | REDUCE: (360), (9834) imply:
% 223.10/38.01  | | | | | | | | | | | |   (9836)   ~ (all_53_13 = e1)
% 223.10/38.01  | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | REDUCE: (375), (9834) imply:
% 223.10/38.01  | | | | | | | | | | | |   (9837)   ~ (e3 = e1)
% 223.10/38.01  | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | REDUCE: (42), (9834) imply:
% 223.10/38.01  | | | | | | | | | | | |   (9838)  op(e2, e2) = e1
% 223.10/38.01  | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | BETA: splitting (211) gives:
% 223.10/38.01  | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | Case 1:
% 223.10/38.01  | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | |   (9839)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 223.10/38.01  | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 223.10/38.01  | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | BETA: splitting (9839) gives:
% 223.10/38.01  | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | Case 1:
% 223.10/38.01  | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | |   (9840)  all_57_9 = e1 & op(e3, e0) = e1
% 223.10/38.01  | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | REF_CLOSE: (169), (7578), (9840), (function-axioms) are
% 223.10/38.01  | | | | | | | | | | | | | |            inconsistent by sub-proof #2131.
% 223.10/38.01  | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | Case 2:
% 223.10/38.01  | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | |   (9841)  all_57_10 = e1 & op(e2, e0) = e1
% 223.10/38.01  | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | REF_CLOSE: (165), (9836), (9841), (function-axioms) are
% 223.10/38.01  | | | | | | | | | | | | | |            inconsistent by sub-proof #2084.
% 223.10/38.01  | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | End of split
% 223.10/38.01  | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | Case 2:
% 223.10/38.01  | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | |   (9842)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 223.10/38.01  | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 223.10/38.01  | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | BETA: splitting (9842) gives:
% 223.10/38.01  | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | Case 1:
% 223.10/38.01  | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | |   (9843)  all_57_11 = e1 & op(e1, e0) = e1
% 223.10/38.01  | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | ALPHA: (9843) implies:
% 223.10/38.01  | | | | | | | | | | | | | |   (9844)  op(e1, e0) = e1
% 223.10/38.01  | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 223.10/38.01  | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | Case 1:
% 223.10/38.01  | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | |   (9845)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 223.10/38.01  | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 223.10/38.01  | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | BETA: splitting (9845) gives:
% 223.10/38.01  | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | Case 1:
% 223.10/38.01  | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | |   (9846)  all_57_12 = e1 & op(e0, e3) = e1
% 223.10/38.01  | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | REF_CLOSE: (160), (7575), (9846), (function-axioms) are
% 223.10/38.01  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1947.
% 223.10/38.01  | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | Case 2:
% 223.10/38.01  | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | |   (9847)  all_57_13 = e1 & op(e0, e2) = e1
% 223.10/38.01  | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | REF_CLOSE: (159), (9835), (9847), (function-axioms) are
% 223.10/38.01  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #330.
% 223.10/38.01  | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | End of split
% 223.10/38.01  | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | Case 2:
% 223.10/38.01  | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | |   (9848)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 223.10/38.01  | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 223.10/38.01  | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | BETA: splitting (9848) gives:
% 223.10/38.01  | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | Case 1:
% 223.10/38.01  | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | |   (9849)  all_57_14 = e1 & op(e0, e1) = e1
% 223.10/38.01  | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | ALPHA: (9849) implies:
% 223.10/38.01  | | | | | | | | | | | | | | | |   (9850)  op(e0, e1) = e1
% 223.10/38.01  | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_11,
% 223.10/38.01  | | | | | | | | | | | | | | | |              e1, e1, e0, simplifying with (158), (9850) gives:
% 223.10/38.01  | | | | | | | | | | | | | | | |   (9851)  all_53_11 = e1
% 223.10/38.01  | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_14,
% 223.10/38.01  | | | | | | | | | | | | | | | |              e1, e0, e1, simplifying with (161), (9844) gives:
% 223.10/38.01  | | | | | | | | | | | | | | | |   (9852)  all_53_14 = e1
% 223.10/38.01  | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | REDUCE: (119), (9851) imply:
% 223.10/38.01  | | | | | | | | | | | | | | | |   (9853)   ~ (all_53_9 = e1)
% 223.10/38.01  | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 223.10/38.01  | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.01  | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | |   (9854)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 223.10/38.01  | | | | | | | | | | | | | | | | |             all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 223.10/38.01  | | | | | | | | | | | | | | | | |             op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 223.10/38.01  | | | | | | | | | | | | | | | | |               all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 223.10/38.01  | | | | | | | | | | | | | | | | |             op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 223.10/38.01  | | | | | | | | | | | | | | | | |             op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 223.10/38.01  | | | | | | | | | | | | | | | | |             $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 223.10/38.01  | | | | | | | | | | | | | | | | |             $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 223.10/38.01  | | | | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 223.10/38.01  | | | | | | | | | | | | | | | | |               all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 223.10/38.01  | | | | | | | | | | | | | | | | |             & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 223.10/38.01  | | | | | | | | | | | | | | | | |               all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 223.10/38.01  | | | | | | | | | | | | | | | | |             op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 223.10/38.01  | | | | | | | | | | | | | | | | |             & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 223.10/38.01  | | | | | | | | | | | | | | | | |             $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 223.10/38.01  | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | BETA: splitting (9854) gives:
% 223.10/38.01  | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | |   (9855)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 223.10/38.01  | | | | | | | | | | | | | | | | | |           all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 223.10/38.01  | | | | | | | | | | | | | | | | | |           op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 223.10/38.01  | | | | | | | | | | | | | | | | | |             all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 223.10/38.01  | | | | | | | | | | | | | | | | | |           op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 223.10/38.01  | | | | | | | | | | | | | | | | | |           op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 223.10/38.01  | | | | | | | | | | | | | | | | | |           $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 223.10/38.01  | | | | | | | | | | | | | | | | | |           $i(all_52_7)
% 223.10/38.01  | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (374), (7582), (9855), (function-axioms) are
% 223.10/38.01  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #360.
% 223.10/38.01  | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | |   (9856)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 223.10/38.01  | | | | | | | | | | | | | | | | | |           all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 223.10/38.01  | | | | | | | | | | | | | | | | | |           op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 223.10/38.01  | | | | | | | | | | | | | | | | | |             all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 223.10/38.01  | | | | | | | | | | | | | | | | | |           & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 223.10/38.01  | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 223.10/38.01  | | | | | | | | | | | | | | | | | |           $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 223.10/38.01  | | | | | | | | | | | | | | | | | |           $i(all_52_15)
% 223.10/38.01  | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | ALPHA: (9856) implies:
% 223.10/38.01  | | | | | | | | | | | | | | | | | |   (9857)  op(e2, e0) = all_52_15
% 223.10/38.01  | | | | | | | | | | | | | | | | | |   (9858)  op(e2, e1) = all_52_13
% 223.10/38.01  | | | | | | | | | | | | | | | | | |   (9859)  op(e2, e2) = all_52_11
% 223.10/38.01  | | | | | | | | | | | | | | | | | |   (9860)  op(all_52_15, all_52_15) = e0
% 223.10/38.01  | | | | | | | | | | | | | | | | | |   (9861)  op(all_52_13, all_52_13) = e1
% 223.10/38.01  | | | | | | | | | | | | | | | | | |   (9862)  op(all_52_11, all_52_11) = e2
% 223.10/38.01  | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_13,
% 223.10/38.01  | | | | | | | | | | | | | | | | | |              all_52_15, e0, e2, simplifying with (165), (9857)
% 223.10/38.01  | | | | | | | | | | | | | | | | | |              gives:
% 223.10/38.01  | | | | | | | | | | | | | | | | | |   (9863)  all_53_13 = all_52_15
% 223.10/38.01  | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_9,
% 223.10/38.01  | | | | | | | | | | | | | | | | | |              all_52_13, e1, e2, simplifying with (166), (9858)
% 223.10/38.01  | | | | | | | | | | | | | | | | | |              gives:
% 223.10/38.01  | | | | | | | | | | | | | | | | | |   (9864)  all_53_9 = all_52_13
% 223.10/38.01  | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 223.10/38.01  | | | | | | | | | | | | | | | | | |              all_52_11, e2, e2, simplifying with (9838), (9859)
% 223.10/38.01  | | | | | | | | | | | | | | | | | |              gives:
% 223.10/38.01  | | | | | | | | | | | | | | | | | |   (9865)  all_52_11 = e1
% 223.10/38.01  | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (9863) imply:
% 223.10/38.01  | | | | | | | | | | | | | | | | | |   (9866)  all_55_7 = all_52_15
% 223.10/38.01  | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (9864) imply:
% 223.10/38.01  | | | | | | | | | | | | | | | | | |   (9867)  all_55_6 = all_52_13
% 223.10/38.01  | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | REDUCE: (124), (9864) imply:
% 223.10/38.01  | | | | | | | | | | | | | | | | | |   (9868)   ~ (all_53_8 = all_52_13)
% 223.10/38.01  | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | REDUCE: (364), (9864) imply:
% 223.10/38.01  | | | | | | | | | | | | | | | | | |   (9869)   ~ (all_52_13 = all_6_2)
% 223.10/38.01  | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | REDUCE: (9853), (9864) imply:
% 223.10/38.01  | | | | | | | | | | | | | | | | | |   (9870)   ~ (all_52_13 = e1)
% 223.10/38.01  | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | REDUCE: (114), (9863) imply:
% 223.10/38.01  | | | | | | | | | | | | | | | | | |   (9871)   ~ (all_53_12 = all_52_15)
% 223.10/38.01  | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | REDUCE: (9210), (9863) imply:
% 223.10/38.01  | | | | | | | | | | | | | | | | | |   (9872)   ~ (all_52_15 = e3)
% 223.10/38.01  | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | REDUCE: (9836), (9863) imply:
% 223.10/38.01  | | | | | | | | | | | | | | | | | |   (9873)   ~ (all_52_15 = e1)
% 223.10/38.01  | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | REDUCE: (9862), (9865) imply:
% 223.10/38.01  | | | | | | | | | | | | | | | | | |   (9874)  op(e1, e1) = e2
% 223.10/38.01  | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2, e2,
% 223.10/38.01  | | | | | | | | | | | | | | | | | |              e1, e1, simplifying with (39), (9874) gives:
% 223.10/38.01  | | | | | | | | | | | | | | | | | |   (9875)  all_6_2 = e2
% 223.10/38.01  | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | REDUCE: (363), (9875) imply:
% 223.10/38.01  | | | | | | | | | | | | | | | | | |   (9876)   ~ (all_53_8 = e2)
% 223.10/38.01  | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | REDUCE: (9869), (9875) imply:
% 223.10/38.01  | | | | | | | | | | | | | | | | | |   (9877)   ~ (all_52_13 = e2)
% 223.10/38.01  | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | |   (9878)  all_55_3 = e3
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (9209), (9878) are inconsistent by
% 223.10/38.01  | | | | | | | | | | | | | | | | | | |            sub-proof #2169.
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | |   (9879)  all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | |   (9880)  all_55_7 = e3
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9866), (9872), (9880) are inconsistent by
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | |            sub-proof #2063.
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | |   (9881)   ~ (all_55_7 = e3)
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | |   (9882)  all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | |   (9883)  all_55_2 = e3
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (9883) imply:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | |   (9884)  all_53_8 = e3
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | SIMP: (9884) implies:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | |   (9885)  all_53_8 = e3
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | REDUCE: (9868), (9885) imply:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | |   (9886)   ~ (all_52_13 = e3)
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | SIMP: (9886) implies:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | |   (9887)   ~ (all_52_13 = e3)
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | |   (9888)  all_55_6 = e3
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9867), (9887), (9888) are inconsistent by
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #318.
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | |   (9889)  all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9218), (9861), (9867), (9870), (9877),
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | |            (9889), (function-axioms) are inconsistent by
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1116.
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | |   (9890)  all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9890) gives:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | |   (9891)  all_55_2 = e2
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (9876), (9891) are inconsistent by
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2027.
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.01  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | |   (9892)  all_55_2 = e1 | all_55_2 = e0
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9892) gives:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | |   (9893)  all_55_2 = e1
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (7577), (9893) are inconsistent by
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2032.
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | |   (9894)  all_55_2 = e0
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (9894) imply:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | |   (9895)  all_53_8 = e0
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9895) implies:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | |   (9896)  all_53_8 = e0
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (9896) imply:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | |   (9897)   ~ (all_53_12 = e0)
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9897) implies:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | |   (9898)   ~ (all_53_12 = e0)
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9879) gives:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | |   (9899)  all_55_3 = e2
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (9899) imply:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | |   (9900)  all_53_12 = e2
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9900) implies:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | |   (9901)  all_53_12 = e2
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9871), (9901) imply:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | |   (9902)   ~ (all_52_15 = e2)
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9902) implies:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | |   (9903)   ~ (all_52_15 = e2)
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9218), (9860), (9866), (9872), (9873), (9882),
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | |            (9903), (function-axioms) are inconsistent by
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #276.
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | |   (9904)  all_55_3 = e1 | all_55_3 = e0
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (7578), (9898), (9904) are inconsistent by
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2132.
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.02  | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | End of split
% 223.10/38.02  | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.02  | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | |   (9905)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 223.10/38.02  | | | | | | | | | | | | | | | | |             & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 223.10/38.02  | | | | | | | | | | | | | | | | |             & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 223.10/38.02  | | | | | | | | | | | | | | | | |               all_52_21) = e1 & op(all_52_23, all_52_23) =
% 223.10/38.02  | | | | | | | | | | | | | | | | |             e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 223.10/38.02  | | | | | | | | | | | | | | | | |             all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 223.10/38.02  | | | | | | | | | | | | | | | | |             = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 223.10/38.02  | | | | | | | | | | | | | | | | |             $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 223.10/38.02  | | | | | | | | | | | | | | | | |             & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 223.10/38.02  | | | | | | | | | | | | | | | | |             e0 & op(all_52_25, all_52_25) = e3 &
% 223.10/38.02  | | | | | | | | | | | | | | | | |             op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 223.10/38.02  | | | | | | | | | | | | | | | | |               all_52_29) = e1 & op(all_52_31, all_52_31) =
% 223.10/38.02  | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 223.10/38.02  | | | | | | | | | | | | | | | | |             all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 223.10/38.02  | | | | | | | | | | | | | | | | |             = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 223.10/38.02  | | | | | | | | | | | | | | | | |             $i(all_52_29) & $i(all_52_31))
% 223.10/38.02  | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | BETA: splitting (9905) gives:
% 223.10/38.02  | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | |   (9906)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 223.10/38.02  | | | | | | | | | | | | | | | | | |           all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 223.10/38.02  | | | | | | | | | | | | | | | | | |           op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 223.10/38.02  | | | | | | | | | | | | | | | | | |             all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 223.10/38.02  | | | | | | | | | | | | | | | | | |           & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 223.10/38.02  | | | | | | | | | | | | | | | | | |           & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 223.10/38.02  | | | | | | | | | | | | | | | | | |           & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 223.10/38.02  | | | | | | | | | | | | | | | | | |           $i(all_52_23)
% 223.10/38.02  | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | ALPHA: (9906) implies:
% 223.10/38.02  | | | | | | | | | | | | | | | | | |   (9907)  op(e1, e0) = all_52_23
% 223.10/38.02  | | | | | | | | | | | | | | | | | |   (9908)  op(e1, e1) = all_52_21
% 223.10/38.02  | | | | | | | | | | | | | | | | | |   (9909)  op(all_52_23, all_52_23) = e0
% 223.10/38.02  | | | | | | | | | | | | | | | | | |   (9910)  op(all_52_21, all_52_21) = e1
% 223.10/38.02  | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 223.10/38.02  | | | | | | | | | | | | | | | | | |              all_52_23, e0, e1, simplifying with (9844), (9907)
% 223.10/38.02  | | | | | | | | | | | | | | | | | |              gives:
% 223.10/38.02  | | | | | | | | | | | | | | | | | |   (9911)  all_52_23 = e1
% 223.10/38.02  | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 223.10/38.02  | | | | | | | | | | | | | | | | | |              all_52_21, e1, e1, simplifying with (39), (9908)
% 223.10/38.02  | | | | | | | | | | | | | | | | | |              gives:
% 223.10/38.02  | | | | | | | | | | | | | | | | | |   (9912)  all_52_21 = all_6_2
% 223.10/38.02  | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | REDUCE: (9910), (9912) imply:
% 223.10/38.02  | | | | | | | | | | | | | | | | | |   (9913)  op(all_6_2, all_6_2) = e1
% 223.10/38.02  | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | REDUCE: (9909), (9911) imply:
% 223.10/38.02  | | | | | | | | | | | | | | | | | |   (9914)  op(e1, e1) = e0
% 223.10/38.02  | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2, e0,
% 223.10/38.02  | | | | | | | | | | | | | | | | | |              e1, e1, simplifying with (39), (9914) gives:
% 223.10/38.02  | | | | | | | | | | | | | | | | | |   (9915)  all_6_2 = e0
% 223.10/38.02  | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | REDUCE: (9913), (9915) imply:
% 223.10/38.02  | | | | | | | | | | | | | | | | | |   (9916)  op(e0, e0) = e1
% 223.10/38.02  | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9218), (9916), (function-axioms) are
% 223.10/38.02  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2183.
% 223.10/38.02  | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | |   (9917)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 223.10/38.02  | | | | | | | | | | | | | | | | | |           all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 223.10/38.02  | | | | | | | | | | | | | | | | | |           op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 223.10/38.02  | | | | | | | | | | | | | | | | | |             all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 223.10/38.02  | | | | | | | | | | | | | | | | | |           & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 223.10/38.02  | | | | | | | | | | | | | | | | | |           & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 223.10/38.02  | | | | | | | | | | | | | | | | | |           & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 223.10/38.02  | | | | | | | | | | | | | | | | | |           $i(all_52_31)
% 223.10/38.02  | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | ALPHA: (9917) implies:
% 223.10/38.02  | | | | | | | | | | | | | | | | | |   (9918)  op(e0, e0) = all_52_31
% 223.10/38.02  | | | | | | | | | | | | | | | | | |   (9919)  op(all_52_31, all_52_31) = e0
% 223.10/38.02  | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7582), (9218), (9918), (9919),
% 223.10/38.02  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.02  | | | | | | | | | | | | | | | | | |            #283.
% 223.10/38.02  | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | End of split
% 223.10/38.02  | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | End of split
% 223.10/38.02  | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | Case 2:
% 223.10/38.02  | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | |   (9920)  all_57_15 = e1 & op(e0, e0) = e1
% 223.10/38.02  | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | ALPHA: (9920) implies:
% 223.10/38.02  | | | | | | | | | | | | | | | |   (9921)  op(e0, e0) = e1
% 223.10/38.02  | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9218), (9921), (function-axioms) are
% 223.10/38.02  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2183.
% 223.10/38.02  | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | End of split
% 223.10/38.02  | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | End of split
% 223.10/38.02  | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | Case 2:
% 223.10/38.02  | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | |   (9922)  all_57_15 = e1 & op(e0, e0) = e1
% 223.10/38.02  | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | ALPHA: (9922) implies:
% 223.10/38.02  | | | | | | | | | | | | | |   (9923)  op(e0, e0) = e1
% 223.10/38.02  | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | REF_CLOSE: (8), (9218), (9923), (function-axioms) are
% 223.10/38.02  | | | | | | | | | | | | | |            inconsistent by sub-proof #2183.
% 223.10/38.02  | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | End of split
% 223.10/38.02  | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | End of split
% 223.10/38.02  | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | End of split
% 223.10/38.02  | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | Case 2:
% 223.10/38.02  | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | |   (9924)  all_14_2 = e0
% 223.10/38.02  | | | | | | | | | | |   (9925)  ( ~ (all_14_0 = e1) & op(all_14_1, e2) = all_14_0
% 223.10/38.02  | | | | | | | | | | |             & op(e2, e0) = all_14_1 & $i(all_14_0) &
% 223.10/38.02  | | | | | | | | | | |             $i(all_14_1)) | ( ~ (all_14_1 = e3) & op(e2, e0)
% 223.10/38.02  | | | | | | | | | | |             = all_14_1 & $i(all_14_1))
% 223.10/38.02  | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | COMBINE_EQS: (328), (9924) imply:
% 223.10/38.02  | | | | | | | | | | |   (9926)  all_8_2 = e0
% 223.10/38.02  | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | SIMP: (9926) implies:
% 223.10/38.02  | | | | | | | | | | |   (9927)  all_8_2 = e0
% 223.10/38.02  | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | COMBINE_EQS: (290), (9927) imply:
% 223.10/38.02  | | | | | | | | | | |   (9928)  all_50_2 = e0
% 223.10/38.02  | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | REDUCE: (349), (9927) imply:
% 223.10/38.02  | | | | | | | | | | |   (9929)   ~ (all_53_1 = e0)
% 223.10/38.02  | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | REDUCE: (352), (9927) imply:
% 223.10/38.02  | | | | | | | | | | |   (9930)   ~ (all_53_4 = e0)
% 223.10/38.02  | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | REDUCE: (354), (9927) imply:
% 223.10/38.02  | | | | | | | | | | |   (9931)   ~ (all_53_6 = e0)
% 223.10/38.02  | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | REDUCE: (356), (9927) imply:
% 223.10/38.02  | | | | | | | | | | |   (9932)   ~ (all_53_7 = e0)
% 223.10/38.02  | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | REDUCE: (358), (9927) imply:
% 223.10/38.02  | | | | | | | | | | |   (9933)   ~ (all_53_9 = e0)
% 223.10/38.02  | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | REDUCE: (360), (9927) imply:
% 223.10/38.02  | | | | | | | | | | |   (9934)   ~ (all_53_13 = e0)
% 223.10/38.02  | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | REDUCE: (375), (9927) imply:
% 223.10/38.02  | | | | | | | | | | |   (9935)   ~ (e3 = e0)
% 223.10/38.02  | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | BETA: splitting (222) gives:
% 223.10/38.02  | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | Case 1:
% 223.10/38.02  | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | |   (9936)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 223.10/38.02  | | | | | | | | | | | |             & op(e2, e2) = e0)
% 223.10/38.02  | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | BETA: splitting (9936) gives:
% 223.10/38.02  | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | Case 1:
% 223.10/38.02  | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | |   (9937)  all_57_2 = e0 & op(e2, e3) = e0
% 223.10/38.02  | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | ALPHA: (9937) implies:
% 223.10/38.02  | | | | | | | | | | | | |   (9938)  op(e2, e3) = e0
% 223.10/38.02  | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | REF_CLOSE: (168), (9929), (9938), (function-axioms) are
% 223.10/38.02  | | | | | | | | | | | | |            inconsistent by sub-proof #1943.
% 223.10/38.02  | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | Case 2:
% 223.10/38.02  | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | |   (9939)  all_57_3 = e0 & op(e2, e2) = e0
% 223.10/38.02  | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | ALPHA: (9939) implies:
% 223.10/38.02  | | | | | | | | | | | | |   (9940)  all_57_3 = e0
% 223.10/38.02  | | | | | | | | | | | | |   (9941)  op(e2, e2) = e0
% 223.10/38.02  | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | BETA: splitting (107) gives:
% 223.10/38.02  | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | Case 1:
% 223.10/38.02  | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | |   (9942)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 223.10/38.02  | | | | | | | | | | | | | |             all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 223.10/38.02  | | | | | | | | | | | | | |             op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 223.10/38.02  | | | | | | | | | | | | | |               all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 223.10/38.02  | | | | | | | | | | | | | |             op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 223.10/38.02  | | | | | | | | | | | | | |             op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 223.10/38.02  | | | | | | | | | | | | | |             $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 223.10/38.02  | | | | | | | | | | | | | |             $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 223.10/38.02  | | | | | | | | | | | | | |             & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 223.10/38.02  | | | | | | | | | | | | | |               all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 223.10/38.02  | | | | | | | | | | | | | |             & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 223.10/38.02  | | | | | | | | | | | | | |               all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 223.10/38.02  | | | | | | | | | | | | | |             op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 223.10/38.02  | | | | | | | | | | | | | |             & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 223.10/38.02  | | | | | | | | | | | | | |             $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 223.10/38.02  | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | BETA: splitting (9942) gives:
% 223.10/38.02  | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | Case 1:
% 223.10/38.02  | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | |   (9943)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 223.10/38.02  | | | | | | | | | | | | | | |           all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 223.10/38.02  | | | | | | | | | | | | | | |           op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 223.10/38.02  | | | | | | | | | | | | | | |             all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 223.10/38.02  | | | | | | | | | | | | | | |           op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 223.10/38.02  | | | | | | | | | | | | | | |           op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 223.10/38.02  | | | | | | | | | | | | | | |           $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 223.10/38.02  | | | | | | | | | | | | | | |           $i(all_52_7)
% 223.10/38.02  | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | REF_CLOSE: (39), (374), (7582), (9943), (function-axioms) are
% 223.10/38.02  | | | | | | | | | | | | | | |            inconsistent by sub-proof #360.
% 223.10/38.02  | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | Case 2:
% 223.10/38.02  | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | |   (9944)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 223.10/38.02  | | | | | | | | | | | | | | |           all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 223.10/38.02  | | | | | | | | | | | | | | |           op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 223.10/38.02  | | | | | | | | | | | | | | |             all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 223.10/38.02  | | | | | | | | | | | | | | |           & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 223.10/38.02  | | | | | | | | | | | | | | |           op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 223.10/38.02  | | | | | | | | | | | | | | |           $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 223.10/38.02  | | | | | | | | | | | | | | |           $i(all_52_15)
% 223.10/38.02  | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | ALPHA: (9944) implies:
% 223.10/38.02  | | | | | | | | | | | | | | |   (9945)  op(e2, e2) = all_52_11
% 223.10/38.02  | | | | | | | | | | | | | | |   (9946)  op(all_52_11, all_52_11) = e2
% 223.10/38.02  | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | REF_CLOSE: (9), (9218), (9941), (9945), (9946),
% 223.10/38.02  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.02  | | | | | | | | | | | | | | |            #1229.
% 223.10/38.02  | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | End of split
% 223.10/38.02  | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | Case 2:
% 223.10/38.02  | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | |   (9947)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 223.10/38.02  | | | | | | | | | | | | | |             & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 223.10/38.02  | | | | | | | | | | | | | |             & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 223.10/38.02  | | | | | | | | | | | | | |               all_52_21) = e1 & op(all_52_23, all_52_23) =
% 223.10/38.02  | | | | | | | | | | | | | |             e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 223.10/38.02  | | | | | | | | | | | | | |             all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 223.10/38.02  | | | | | | | | | | | | | |             = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 223.10/38.02  | | | | | | | | | | | | | |             $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 223.10/38.02  | | | | | | | | | | | | | |             & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 223.10/38.02  | | | | | | | | | | | | | |             e0 & op(all_52_25, all_52_25) = e3 &
% 223.10/38.02  | | | | | | | | | | | | | |             op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 223.10/38.02  | | | | | | | | | | | | | |               all_52_29) = e1 & op(all_52_31, all_52_31) =
% 223.10/38.02  | | | | | | | | | | | | | |             e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 223.10/38.02  | | | | | | | | | | | | | |             all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 223.10/38.02  | | | | | | | | | | | | | |             = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 223.10/38.02  | | | | | | | | | | | | | |             $i(all_52_29) & $i(all_52_31))
% 223.10/38.02  | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | BETA: splitting (9947) gives:
% 223.10/38.02  | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | Case 1:
% 223.10/38.02  | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | |   (9948)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 223.10/38.02  | | | | | | | | | | | | | | |           all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 223.10/38.02  | | | | | | | | | | | | | | |           op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 223.10/38.02  | | | | | | | | | | | | | | |             all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 223.10/38.02  | | | | | | | | | | | | | | |           & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 223.10/38.02  | | | | | | | | | | | | | | |           & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 223.10/38.02  | | | | | | | | | | | | | | |           & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 223.10/38.02  | | | | | | | | | | | | | | |           $i(all_52_23)
% 223.10/38.02  | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | ALPHA: (9948) implies:
% 223.10/38.02  | | | | | | | | | | | | | | |   (9949)  op(e1, e1) = all_52_21
% 223.10/38.02  | | | | | | | | | | | | | | |   (9950)  op(e1, e2) = all_52_19
% 223.10/38.02  | | | | | | | | | | | | | | |   (9951)  op(e1, e3) = all_52_17
% 223.10/38.02  | | | | | | | | | | | | | | |   (9952)  op(all_52_21, all_52_21) = e1
% 223.10/38.02  | | | | | | | | | | | | | | |   (9953)  op(all_52_19, all_52_19) = e2
% 223.10/38.02  | | | | | | | | | | | | | | |   (9954)  op(all_52_17, all_52_17) = e3
% 223.10/38.02  | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 223.10/38.02  | | | | | | | | | | | | | | |              all_52_21, e1, e1, simplifying with (39), (9949)
% 223.10/38.02  | | | | | | | | | | | | | | |              gives:
% 223.10/38.02  | | | | | | | | | | | | | | |   (9955)  all_52_21 = all_6_2
% 223.10/38.02  | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_6,
% 223.10/38.02  | | | | | | | | | | | | | | |              all_52_19, e2, e1, simplifying with (163), (9950)
% 223.10/38.02  | | | | | | | | | | | | | | |              gives:
% 223.10/38.02  | | | | | | | | | | | | | | |   (9956)  all_53_6 = all_52_19
% 223.10/38.02  | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_2,
% 223.10/38.02  | | | | | | | | | | | | | | |              all_52_17, e3, e1, simplifying with (164), (9951)
% 223.10/38.02  | | | | | | | | | | | | | | |              gives:
% 223.10/38.02  | | | | | | | | | | | | | | |   (9957)  all_53_2 = all_52_17
% 223.10/38.02  | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | COMBINE_EQS: (256), (9956) imply:
% 223.10/38.02  | | | | | | | | | | | | | | |   (9958)  all_55_9 = all_52_19
% 223.10/38.02  | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | REDUCE: (129), (9956) imply:
% 223.10/38.02  | | | | | | | | | | | | | | |   (9959)   ~ (all_53_7 = all_52_19)
% 223.10/38.02  | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | SIMP: (9959) implies:
% 223.10/38.02  | | | | | | | | | | | | | | |   (9960)   ~ (all_53_7 = all_52_19)
% 223.10/38.02  | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | REDUCE: (9931), (9956) imply:
% 223.10/38.02  | | | | | | | | | | | | | | |   (9961)   ~ (all_52_19 = e0)
% 223.10/38.02  | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | REDUCE: (9952), (9955) imply:
% 223.10/38.02  | | | | | | | | | | | | | | |   (9962)  op(all_6_2, all_6_2) = e1
% 223.10/38.02  | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 223.10/38.02  | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | Case 1:
% 223.10/38.02  | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | |   (9963)   ~ (all_24_2 = e0)
% 223.10/38.02  | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | REDUCE: (315), (9963) imply:
% 223.10/38.02  | | | | | | | | | | | | | | | |   (9964)   ~ (all_6_2 = e0)
% 223.10/38.02  | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | BETA: splitting (88) gives:
% 223.10/38.02  | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.02  | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | |   (9965)   ~ (all_38_2 = e2)
% 223.10/38.02  | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | REDUCE: (249), (9965) imply:
% 223.10/38.02  | | | | | | | | | | | | | | | | |   (9966)   ~ (all_6_2 = e2)
% 223.10/38.02  | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 223.10/38.02  | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | |   (9967)  all_55_10 = e3
% 223.10/38.02  | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (374), (9967) are inconsistent by sub-proof
% 223.10/38.02  | | | | | | | | | | | | | | | | | |            #2500.
% 223.10/38.02  | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | |   (9968)   ~ (all_55_10 = e3)
% 223.10/38.02  | | | | | | | | | | | | | | | | | |   (9969)  all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 223.10/38.02  | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | BETA: splitting (9969) gives:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | |   (9970)  all_55_10 = e2
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (9966), (9970) are inconsistent by
% 223.10/38.02  | | | | | | | | | | | | | | | | | | |            sub-proof #2499.
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | |   (9971)   ~ (all_55_10 = e2)
% 223.10/38.02  | | | | | | | | | | | | | | | | | | |   (9972)  all_55_10 = e1 | all_55_10 = e0
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | BETA: splitting (9972) gives:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | |   (9973)  all_55_10 = e1
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (336), (9973) imply:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | |   (9974)  all_6_2 = e1
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | SIMP: (9974) implies:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | |   (9975)  all_6_2 = e1
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | REDUCE: (374), (9975) imply:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | |   (9976)   ~ (e3 = e1)
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | REDUCE: (9966), (9975) imply:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | |   (9977)   ~ (e2 = e1)
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (9975) imply:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | |   (9978)  op(e1, e1) = e1
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | |   (9979)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9979) gives:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | |   (9980)  all_57_9 = e1 & op(e3, e0) = e1
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (7578), (9980), (function-axioms) are
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2131.
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | |   (9981)  all_57_10 = e1 & op(e2, e0) = e1
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9981) implies:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | |   (9982)  op(e2, e0) = e1
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | |   (9983)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9983) gives:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | |   (9984)  all_57_1 = e1 & op(e3, e2) = e1
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9984) implies:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | |   (9985)  all_57_1 = e1
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | |   (9986)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9986) gives:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9987)  all_57_1 = e3 & op(e3, e2) = e3
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9985), (9987) are inconsistent by sub-proof
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | |            #2196.
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9988)  all_57_3 = e3 & op(e2, e2) = e3
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9940), (9988) are inconsistent by sub-proof
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | |            #1309.
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | |   (9989)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9989) gives:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9990)  all_57_7 = e3 & op(e1, e2) = e3
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9990) implies:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9991)  all_57_7 = e3
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9992)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9941), (9985), (9992),
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2208.
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9993)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9993) gives:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9994)  all_57_7 = e2 & op(e1, e2) = e2
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (9991), (9994) are inconsistent by sub-proof
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2092.
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9995)  all_57_13 = e2 & op(e0, e2) = e2
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9995) implies:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9996)  all_57_13 = e2
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9997)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e3)
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9997) gives:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9998)  all_57_0 = e3 & op(e3, e3) = e3
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9998) implies:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9999)  op(e3, e3) = e3
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (67), (88),
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (94), (107), (121), (124), (134), (135), (137),
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (163), (166), (169), (170), (171), (195), (202),
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (203), (204), (207), (208), (209), (211), (212),
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (214), (215), (216), (217), (218), (219), (220),
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (221), (223), (224), (225), (227), (228), (229),
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (231), (232), (233), (234), (235), (236),
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (237), (249), (268), (269), (270), (315), (332),
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (336), (363), (364), (374), (9209), (9217),
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9218), (9930), (9933), (9940), (9999),
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1415.
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10000)  all_57_1 = e3 & op(e3, e2) = e3
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10000) implies:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10001)  all_57_1 = e3
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (227), (9940), (9991), (9996),
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10001) are inconsistent by sub-proof #1779.
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10002)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e3)
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10002) gives:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10003)  all_57_4 = e3 & op(e3, e1) = e3
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10003) implies:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10004)  all_57_4 = e3
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10005)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e0)
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10005) gives:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10006)  all_57_4 = e0 & op(e3, e1) = e0
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10006) implies:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10007)  all_57_4 = e0
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10004), (10007) imply:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10008)  e3 = e0
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9991), (10008) imply:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10009)  all_57_7 = e0
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (227), (228), (229),
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9940), (9941), (9985), (10009), (function-axioms)
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1378.
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10010)  all_57_5 = e0 & op(e2, e1) = e0
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (9933), (10010), (function-axioms) are
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2023.
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10011)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10011) gives:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10012)  all_57_8 = e0 & op(e1, e1) = e0
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10012) implies:
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10013)  op(e1, e1) = e0
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9978), (10013), (function-axioms) are
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2427.
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10014)  all_57_14 = e0 & op(e0, e1) = e0
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10014) implies:
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10015)  all_57_14 = e0
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10016)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10016) gives:
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10017)  all_57_12 = e1 & op(e0, e3) = e1
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (7575), (10017), (function-axioms) are
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1947.
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10018)  all_57_13 = e1 & op(e0, e2) = e1
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10018) implies:
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10019)  all_57_13 = e1
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (228), (229), (9940),
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9941), (9985), (10019), (function-axioms) are
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1193.
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10020)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10020) gives:
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10021)  all_57_14 = e1 & op(e0, e1) = e1
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10021) implies:
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10022)  all_57_14 = e1
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10015), (10022) imply:
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10023)  e1 = e0
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10023) implies:
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10024)  e1 = e0
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7581), (10024) imply:
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10025)  all_57_0 = e0
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (39), (160), (168), (195), (232), (336),
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (374), (7573), (7575), (9951), (9954), (10025),
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1545.
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10026)  all_57_15 = e1 & op(e0, e0) = e1
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10026) implies:
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10027)  op(e0, e0) = e1
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9218), (10027), (function-axioms) are
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2183.
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10028)  all_57_9 = e3 & op(e3, e0) = e3
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10028) implies:
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10029)  op(e3, e0) = e3
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (9209), (10029), (function-axioms) are
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2458.
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10030)  all_57_13 = e3 & op(e0, e2) = e3
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10030) implies:
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10031)  all_57_13 = e3
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (159), (207), (208),
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | |            (209), (9217), (9218), (9932), (10031),
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | |            #366.
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | |   (10032)  all_57_3 = e1 & op(e2, e2) = e1
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10032) implies:
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | |   (10033)  op(e2, e2) = e1
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9941), (10033), (function-axioms) are
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2352.
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | |   (10034)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10034) gives:
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | |   (10035)  all_57_7 = e1 & op(e1, e2) = e1
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10035) implies:
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | |   (10036)  all_57_7 = e1
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | |            (212), (214), (216), (217), (374), (9217), (9978),
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | |            (10036), (function-axioms) are inconsistent by
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1069.
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | |   (10037)  all_57_13 = e1 & op(e0, e2) = e1
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10037) implies:
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | |   (10038)  op(e0, e2) = e1
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_7, e1,
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (159), (10038) gives:
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | |   (10039)  all_53_7 = e1
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_13,
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | |              e1, e0, e2, simplifying with (165), (9982) gives:
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | |   (10040)  all_53_13 = e1
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9960), (10039) imply:
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | |   (10041)   ~ (all_52_19 = e1)
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10041) implies:
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | |   (10042)   ~ (all_52_19 = e1)
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (106) gives:
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | |   (10043)   ~ (all_50_2 = e0)
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9928), (10043) imply:
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | |   (10044)  $false
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (10044) is inconsistent.
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | |   (10045)  ( ~ (all_50_0 = e3) & op(all_50_1, e2) = all_50_0
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e0) = all_50_1 & $i(all_50_0) &
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_50_1)) | ( ~ (all_50_1 = e1) & op(e2, e0)
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | |              = all_50_1 & $i(all_50_1))
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (196), (9925), (9941), (9950), (9953), (9958),
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | |            (9961), (9982), (10042), (10045),
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | |            #271.
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | |   (10046)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10046) gives:
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | |   (10047)  all_57_11 = e1 & op(e1, e0) = e1
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10047) implies:
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | |   (10048)  all_57_11 = e1
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | |   (10049)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e0)
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10049) gives:
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | |   (10050)  all_57_6 = e0 & op(e1, e3) = e0
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10050) implies:
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | |   (10051)  all_57_6 = e0
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | |   (10052)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e3)
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10052) gives:
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10053)  all_57_6 = e3 & op(e1, e3) = e3
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10053) implies:
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10054)  all_57_6 = e3
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10051), (10054) are inconsistent by
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1822.
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10055)  all_57_7 = e3 & op(e1, e2) = e3
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10055) implies:
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10056)  all_57_7 = e3
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (216), (9978), (10048), (10051),
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | |            (10056), (function-axioms) are inconsistent by
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1844.
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | |   (10057)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e1, e0) = e3)
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (374), (9217), (10057), (function-axioms)
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1786.
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | |   (10058)  all_57_7 = e0 & op(e1, e2) = e0
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10058) implies:
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | |   (10059)  all_57_7 = e0
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (39), (216), (217),
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | |            (374), (9978), (10048), (10059), (function-axioms)
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1931.
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | |   (10060)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10060) gives:
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | |   (10061)  all_57_8 = e0 & op(e1, e1) = e0
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10061) implies:
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | |   (10062)  op(e1, e1) = e0
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9978), (10062), (function-axioms) are
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2427.
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | |   (10063)  all_57_11 = e0 & op(e1, e0) = e0
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10063) implies:
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | |   (10064)  all_57_11 = e0
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10048), (10064) imply:
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | |   (10065)  e1 = e0
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7581), (10065) imply:
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | |   (10066)  all_57_0 = e0
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (39), (160), (168), (195), (232), (336),
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | |            (374), (7573), (7575), (9951), (9954), (10066),
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | |            #1545.
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | |   (10067)  all_57_15 = e1 & op(e0, e0) = e1
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10067) implies:
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | |   (10068)  op(e0, e0) = e1
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9218), (10068), (function-axioms) are
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2183.
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | |   (10069)  all_55_10 = e0
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (9964), (10069) are inconsistent by
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | |            sub-proof #2118.
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.03  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.03  | | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | End of split
% 223.10/38.03  | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.03  | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | |   (10070)  all_38_2 = e2
% 223.10/38.03  | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (10070) imply:
% 223.10/38.03  | | | | | | | | | | | | | | | | |   (10071)  all_6_2 = e2
% 223.10/38.03  | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | REDUCE: (9962), (10071) imply:
% 223.10/38.03  | | | | | | | | | | | | | | | | |   (10072)  op(e2, e2) = e1
% 223.10/38.03  | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9941), (10072), (function-axioms) are
% 223.10/38.03  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2352.
% 223.10/38.03  | | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | End of split
% 223.10/38.03  | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | Case 2:
% 223.10/38.03  | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | |   (10073)  all_24_2 = e0
% 223.10/38.03  | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | | REF_CLOSE: (8), (315), (9218), (9962), (10073),
% 223.10/38.03  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.03  | | | | | | | | | | | | | | | |            #444.
% 223.10/38.03  | | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | End of split
% 223.10/38.03  | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | Case 2:
% 223.10/38.03  | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | |   (10074)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 223.10/38.03  | | | | | | | | | | | | | | |            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 223.10/38.03  | | | | | | | | | | | | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 223.10/38.03  | | | | | | | | | | | | | | |              all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 223.10/38.03  | | | | | | | | | | | | | | |            & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 223.10/38.03  | | | | | | | | | | | | | | |            & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 223.10/38.03  | | | | | | | | | | | | | | |            & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 223.10/38.03  | | | | | | | | | | | | | | |            $i(all_52_31)
% 223.10/38.03  | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | ALPHA: (10074) implies:
% 223.10/38.03  | | | | | | | | | | | | | | |   (10075)  op(e0, e0) = all_52_31
% 223.10/38.03  | | | | | | | | | | | | | | |   (10076)  op(all_52_31, all_52_31) = e0
% 223.10/38.03  | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | REF_CLOSE: (4), (7582), (9218), (10075), (10076),
% 223.10/38.03  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.03  | | | | | | | | | | | | | | |            #283.
% 223.10/38.03  | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | End of split
% 223.10/38.03  | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | End of split
% 223.10/38.03  | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | End of split
% 223.10/38.03  | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | Case 2:
% 223.10/38.03  | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | |   (10077)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 223.10/38.03  | | | | | | | | | | | |              e0 & op(e2, e0) = e0)
% 223.10/38.03  | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | REF_CLOSE: (165), (166), (9933), (9934), (10077),
% 223.10/38.03  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.03  | | | | | | | | | | | |            #2022.
% 223.10/38.03  | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | End of split
% 223.10/38.03  | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | End of split
% 223.10/38.03  | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | End of split
% 223.10/38.03  | | | | | | | | | 
% 223.10/38.03  | | | | | | | | End of split
% 223.10/38.03  | | | | | | | | 
% 223.10/38.03  | | | | | | | End of split
% 223.10/38.03  | | | | | | | 
% 223.10/38.03  | | | | | | Case 2:
% 223.10/38.03  | | | | | | | 
% 223.10/38.03  | | | | | | |   (10078)  all_57_2 = e1 & op(e2, e3) = e1
% 223.10/38.03  | | | | | | | 
% 223.10/38.03  | | | | | | | REF_CLOSE: (168), (7573), (10078), (function-axioms) are
% 223.10/38.03  | | | | | | |            inconsistent by sub-proof #2156.
% 223.10/38.03  | | | | | | | 
% 223.10/38.03  | | | | | | End of split
% 223.10/38.03  | | | | | | 
% 223.10/38.03  | | | | | Case 2:
% 223.10/38.03  | | | | | | 
% 223.10/38.03  | | | | | |   (10079)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 &
% 223.10/38.03  | | | | | |              op(e0, e3) = e1)
% 223.10/38.03  | | | | | | 
% 223.10/38.03  | | | | | | BETA: splitting (10079) gives:
% 223.10/38.03  | | | | | | 
% 223.10/38.03  | | | | | | Case 1:
% 223.10/38.03  | | | | | | | 
% 223.10/38.03  | | | | | | |   (10080)  all_57_6 = e1 & op(e1, e3) = e1
% 223.10/38.03  | | | | | | | 
% 223.10/38.03  | | | | | | | REF_CLOSE: (164), (7574), (10080), (function-axioms) are
% 223.10/38.03  | | | | | | |            inconsistent by sub-proof #316.
% 223.10/38.03  | | | | | | | 
% 223.10/38.03  | | | | | | Case 2:
% 223.10/38.03  | | | | | | | 
% 223.10/38.03  | | | | | | |   (10081)  all_57_12 = e1 & op(e0, e3) = e1
% 223.10/38.03  | | | | | | | 
% 223.10/38.03  | | | | | | | REF_CLOSE: (160), (7575), (10081), (function-axioms) are
% 223.10/38.03  | | | | | | |            inconsistent by sub-proof #1947.
% 223.10/38.03  | | | | | | | 
% 223.10/38.03  | | | | | | End of split
% 223.10/38.03  | | | | | | 
% 223.10/38.03  | | | | | End of split
% 223.10/38.03  | | | | | 
% 223.10/38.03  | | | | End of split
% 223.10/38.03  | | | | 
% 223.10/38.03  | | | Case 2:
% 223.10/38.03  | | | | 
% 223.10/38.03  | | | |   (10082)  all_8_2 = e3
% 223.10/38.03  | | | |   (10083)  ( ~ (all_8_0 = e0) & op(all_8_1, e2) = all_8_0 & op(e2, e3) =
% 223.10/38.03  | | | |              all_8_1 & $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e1) &
% 223.10/38.03  | | | |              op(e2, e3) = all_8_1 & $i(all_8_1))
% 223.10/38.03  | | | | 
% 223.10/38.03  | | | | COMBINE_EQS: (297), (10082) imply:
% 223.10/38.03  | | | |   (10084)  all_44_2 = e3
% 223.10/38.03  | | | | 
% 223.10/38.03  | | | | REDUCE: (349), (10082) imply:
% 223.10/38.03  | | | |   (10085)   ~ (all_53_1 = e3)
% 223.10/38.03  | | | | 
% 223.10/38.03  | | | | REDUCE: (352), (10082) imply:
% 223.10/38.03  | | | |   (10086)   ~ (all_53_4 = e3)
% 223.10/38.03  | | | | 
% 223.10/38.03  | | | | REDUCE: (354), (10082) imply:
% 223.10/38.03  | | | |   (10087)   ~ (all_53_6 = e3)
% 223.10/38.03  | | | | 
% 223.10/38.03  | | | | REDUCE: (356), (10082) imply:
% 223.10/38.03  | | | |   (10088)   ~ (all_53_7 = e3)
% 223.10/38.03  | | | | 
% 223.10/38.03  | | | | REDUCE: (358), (10082) imply:
% 223.10/38.03  | | | |   (10089)   ~ (all_53_9 = e3)
% 223.10/38.03  | | | | 
% 223.10/38.03  | | | | REDUCE: (360), (10082) imply:
% 223.10/38.03  | | | |   (10090)   ~ (all_53_13 = e3)
% 223.10/38.03  | | | | 
% 223.10/38.03  | | | | BETA: splitting (225) gives:
% 223.10/38.03  | | | | 
% 223.10/38.03  | | | | Case 1:
% 223.10/38.03  | | | | | 
% 223.10/38.03  | | | | |   (10091)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2,
% 223.10/38.03  | | | | |                e2) = e3)
% 223.10/38.03  | | | | | 
% 223.10/38.03  | | | | | BETA: splitting (10091) gives:
% 223.10/38.03  | | | | | 
% 223.10/38.03  | | | | | Case 1:
% 223.10/38.03  | | | | | | 
% 223.10/38.03  | | | | | |   (10092)  all_57_2 = e3 & op(e2, e3) = e3
% 223.10/38.03  | | | | | | 
% 223.10/38.03  | | | | | | REF_CLOSE: (168), (10085), (10092), (function-axioms) are
% 223.10/38.03  | | | | | |            inconsistent by sub-proof #2299.
% 223.10/38.03  | | | | | | 
% 223.10/38.03  | | | | | Case 2:
% 223.10/38.03  | | | | | | 
% 223.10/38.03  | | | | | |   (10093)  all_57_3 = e3 & op(e2, e2) = e3
% 223.10/38.03  | | | | | | 
% 223.10/38.03  | | | | | | ALPHA: (10093) implies:
% 223.10/38.03  | | | | | |   (10094)  all_57_3 = e3
% 223.10/38.03  | | | | | |   (10095)  op(e2, e2) = e3
% 223.10/38.03  | | | | | | 
% 223.10/38.03  | | | | | | BETA: splitting (46) gives:
% 223.10/38.03  | | | | | | 
% 223.10/38.03  | | | | | | Case 1:
% 223.10/38.03  | | | | | | | 
% 223.10/38.03  | | | | | | |   (10096)   ~ (all_10_2 = e1)
% 223.10/38.03  | | | | | | | 
% 223.10/38.03  | | | | | | | BETA: splitting (49) gives:
% 223.10/38.03  | | | | | | | 
% 223.10/38.03  | | | | | | | Case 1:
% 223.10/38.03  | | | | | | | | 
% 223.10/38.03  | | | | | | | |   (10097)   ~ (all_12_2 = e3)
% 223.10/38.03  | | | | | | | | 
% 223.10/38.03  | | | | | | | | REDUCE: (325), (10097) imply:
% 223.10/38.03  | | | | | | | |   (10098)   ~ (all_4_2 = e3)
% 223.10/38.03  | | | | | | | | 
% 223.10/38.03  | | | | | | | | BETA: splitting (58) gives:
% 223.10/38.03  | | | | | | | | 
% 223.10/38.03  | | | | | | | | Case 1:
% 223.10/38.03  | | | | | | | | | 
% 223.10/38.03  | | | | | | | | |   (10099)   ~ (all_18_2 = e0)
% 223.10/38.03  | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | REDUCE: (327), (10099) imply:
% 223.10/38.03  | | | | | | | | |   (10100)   ~ (all_10_2 = e0)
% 223.10/38.03  | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | BETA: splitting (61) gives:
% 223.10/38.03  | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | Case 1:
% 223.10/38.03  | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | |   (10101)   ~ (all_20_2 = e2)
% 223.10/38.03  | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | REDUCE: (299), (10101) imply:
% 223.10/38.03  | | | | | | | | | |   (10102)   ~ (all_10_2 = e2)
% 223.10/38.03  | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | BETA: splitting (205) gives:
% 223.10/38.03  | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | Case 1:
% 223.10/38.03  | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | |   (10103)  all_55_0 = e3
% 223.10/38.03  | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | COMBINE_EQS: (277), (10103) imply:
% 223.10/38.03  | | | | | | | | | | |   (10104)  all_10_2 = e3
% 223.10/38.03  | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | REDUCE: (348), (10104) imply:
% 223.10/38.03  | | | | | | | | | | |   (10105)   ~ (all_53_12 = e3)
% 223.10/38.03  | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | REDUCE: (45), (10104) imply:
% 223.10/38.03  | | | | | | | | | | |   (10106)  op(e3, e3) = e3
% 223.10/38.03  | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | BETA: splitting (221) gives:
% 223.10/38.03  | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | Case 1:
% 223.10/38.03  | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | |   (10107)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 223.10/38.03  | | | | | | | | | | | |              & op(e2, e1) = e3)
% 223.10/38.03  | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | BETA: splitting (10107) gives:
% 223.10/38.03  | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | Case 1:
% 223.10/38.03  | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | |   (10108)  all_57_4 = e3 & op(e3, e1) = e3
% 223.10/38.03  | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | ALPHA: (10108) implies:
% 223.10/38.03  | | | | | | | | | | | | |   (10109)  all_57_4 = e3
% 223.10/38.03  | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (235),
% 223.10/38.03  | | | | | | | | | | | | |            (10106), (10109), (function-axioms) are
% 223.10/38.03  | | | | | | | | | | | | |            inconsistent by sub-proof #2474.
% 223.10/38.03  | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | Case 2:
% 223.10/38.03  | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | |   (10110)  all_57_5 = e3 & op(e2, e1) = e3
% 223.10/38.03  | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | REF_CLOSE: (166), (10089), (10110), (function-axioms) are
% 223.10/38.03  | | | | | | | | | | | | |            inconsistent by sub-proof #270.
% 223.10/38.03  | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | End of split
% 223.10/38.03  | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | Case 2:
% 223.10/38.03  | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | |   (10111)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 223.10/38.03  | | | | | | | | | | | |              e3 & op(e0, e1) = e3)
% 223.10/38.03  | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | BETA: splitting (10111) gives:
% 223.10/38.03  | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | Case 1:
% 223.10/38.03  | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | |   (10112)  all_57_8 = e3 & op(e1, e1) = e3
% 223.10/38.03  | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | ALPHA: (10112) implies:
% 223.10/38.03  | | | | | | | | | | | | |   (10113)  op(e1, e1) = e3
% 223.10/38.03  | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | REF_CLOSE: (39), (374), (10113), (function-axioms) are
% 223.10/38.03  | | | | | | | | | | | | |            inconsistent by sub-proof #2468.
% 223.10/38.03  | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | Case 2:
% 223.10/38.03  | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | |   (10114)  all_57_14 = e3 & op(e0, e1) = e3
% 223.10/38.03  | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | ALPHA: (10114) implies:
% 223.10/38.03  | | | | | | | | | | | | |   (10115)  all_57_14 = e3
% 223.10/38.03  | | | | | | | | | | | | |   (10116)  op(e0, e1) = e3
% 223.10/38.03  | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | BETA: splitting (217) gives:
% 223.10/38.03  | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | Case 1:
% 223.10/38.03  | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | |   (10117)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 223.10/38.03  | | | | | | | | | | | | | |              & op(e1, e2) = e3)
% 223.10/38.03  | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | BETA: splitting (10117) gives:
% 223.10/38.03  | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | Case 1:
% 223.10/38.03  | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | |   (10118)  all_57_6 = e3 & op(e1, e3) = e3
% 223.10/38.03  | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | ALPHA: (10118) implies:
% 223.10/38.03  | | | | | | | | | | | | | | |   (10119)  all_57_6 = e3
% 223.10/38.03  | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (169), (171), (230),
% 223.10/38.03  | | | | | | | | | | | | | | |            (231), (232), (233), (234), (235), (237), (10086),
% 223.10/38.03  | | | | | | | | | | | | | | |            (10105), (10106), (10119), (function-axioms) are
% 223.10/38.03  | | | | | | | | | | | | | | |            inconsistent by sub-proof #268.
% 223.10/38.03  | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | Case 2:
% 223.10/38.03  | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | |   (10120)  all_57_7 = e3 & op(e1, e2) = e3
% 223.10/38.03  | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | REF_CLOSE: (163), (10087), (10120), (function-axioms) are
% 223.10/38.03  | | | | | | | | | | | | | | |            inconsistent by sub-proof #267.
% 223.10/38.03  | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | End of split
% 223.10/38.03  | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | Case 2:
% 223.10/38.03  | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | |   (10121)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 223.10/38.03  | | | | | | | | | | | | | |              e3 & op(e1, e0) = e3)
% 223.10/38.03  | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | BETA: splitting (10121) gives:
% 223.10/38.03  | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | Case 1:
% 223.10/38.03  | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | |   (10122)  all_57_8 = e3 & op(e1, e1) = e3
% 223.10/38.03  | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | ALPHA: (10122) implies:
% 223.10/38.03  | | | | | | | | | | | | | | |   (10123)  op(e1, e1) = e3
% 223.10/38.03  | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | REF_CLOSE: (39), (374), (10123), (function-axioms) are
% 223.10/38.03  | | | | | | | | | | | | | | |            inconsistent by sub-proof #2468.
% 223.10/38.03  | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | Case 2:
% 223.10/38.03  | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | |   (10124)  all_57_11 = e3 & op(e1, e0) = e3
% 223.10/38.03  | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | ALPHA: (10124) implies:
% 223.10/38.03  | | | | | | | | | | | | | | |   (10125)  all_57_11 = e3
% 223.10/38.03  | | | | | | | | | | | | | | |   (10126)  op(e1, e0) = e3
% 223.10/38.03  | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_11,
% 223.10/38.03  | | | | | | | | | | | | | | |              e3, e1, e0, simplifying with (158), (10116) gives:
% 223.10/38.03  | | | | | | | | | | | | | | |   (10127)  all_53_11 = e3
% 223.10/38.03  | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_14,
% 223.10/38.03  | | | | | | | | | | | | | | |              e3, e0, e1, simplifying with (161), (10126) gives:
% 223.10/38.03  | | | | | | | | | | | | | | |   (10128)  all_53_14 = e3
% 223.10/38.03  | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | REDUCE: (122), (10127) imply:
% 223.10/38.03  | | | | | | | | | | | | | | |   (10129)   ~ (all_53_8 = e3)
% 223.10/38.03  | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | REDUCE: (368), (10128) imply:
% 223.10/38.03  | | | | | | | | | | | | | | |   (10130)   ~ (all_6_2 = e3)
% 223.10/38.03  | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | REDUCE: (372), (10128) imply:
% 223.10/38.03  | | | | | | | | | | | | | | |   (10131)   ~ (all_4_2 = e3)
% 223.10/38.03  | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 223.10/38.03  | | | | | | | | | | | | | | | 
% 223.10/38.03  | | | | | | | | | | | | | | | Case 1:
% 223.10/38.03  | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | |   (10132)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 223.10/38.04  | | | | | | | | | | | | | | | |              all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 223.10/38.04  | | | | | | | | | | | | | | | |              op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 223.10/38.04  | | | | | | | | | | | | | | | |                all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 223.10/38.04  | | | | | | | | | | | | | | | |              op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 223.10/38.04  | | | | | | | | | | | | | | | |              op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 223.10/38.04  | | | | | | | | | | | | | | | |              $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 223.10/38.04  | | | | | | | | | | | | | | | |              $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 223.10/38.04  | | | | | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 223.10/38.04  | | | | | | | | | | | | | | | |                all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 223.10/38.04  | | | | | | | | | | | | | | | |              & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 223.10/38.04  | | | | | | | | | | | | | | | |                all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 223.10/38.04  | | | | | | | | | | | | | | | |              op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 223.10/38.04  | | | | | | | | | | | | | | | |              & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 223.10/38.04  | | | | | | | | | | | | | | | |              $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 223.10/38.04  | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | BETA: splitting (10132) gives:
% 223.10/38.04  | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.04  | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | |   (10133)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 223.10/38.04  | | | | | | | | | | | | | | | | |            all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 223.10/38.04  | | | | | | | | | | | | | | | | |            op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 223.10/38.04  | | | | | | | | | | | | | | | | |              all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 223.10/38.04  | | | | | | | | | | | | | | | | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 223.10/38.04  | | | | | | | | | | | | | | | | |            op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 223.10/38.04  | | | | | | | | | | | | | | | | |            $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 223.10/38.04  | | | | | | | | | | | | | | | | |            $i(all_52_7)
% 223.10/38.04  | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | ALPHA: (10133) implies:
% 223.10/38.04  | | | | | | | | | | | | | | | | |   (10134)  op(e3, e0) = all_52_7
% 223.10/38.04  | | | | | | | | | | | | | | | | |   (10135)  op(e3, e1) = all_52_5
% 223.10/38.04  | | | | | | | | | | | | | | | | |   (10136)  op(e3, e2) = all_52_3
% 223.10/38.04  | | | | | | | | | | | | | | | | |   (10137)  op(e3, e3) = all_52_1
% 223.10/38.04  | | | | | | | | | | | | | | | | |   (10138)  op(all_52_7, all_52_7) = e0
% 223.10/38.04  | | | | | | | | | | | | | | | | |   (10139)  op(all_52_5, all_52_5) = e1
% 223.10/38.04  | | | | | | | | | | | | | | | | |   (10140)  op(all_52_3, all_52_3) = e2
% 223.10/38.04  | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_12,
% 223.10/38.04  | | | | | | | | | | | | | | | | |              all_52_7, e0, e3, simplifying with (169), (10134)
% 223.10/38.04  | | | | | | | | | | | | | | | | |              gives:
% 223.10/38.04  | | | | | | | | | | | | | | | | |   (10141)  all_53_12 = all_52_7
% 223.10/38.04  | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_8,
% 223.10/38.04  | | | | | | | | | | | | | | | | |              all_52_5, e1, e3, simplifying with (170), (10135)
% 223.10/38.04  | | | | | | | | | | | | | | | | |              gives:
% 223.10/38.04  | | | | | | | | | | | | | | | | |   (10142)  all_53_8 = all_52_5
% 223.10/38.04  | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_4,
% 223.10/38.04  | | | | | | | | | | | | | | | | |              all_52_3, e2, e3, simplifying with (171), (10136)
% 223.10/38.04  | | | | | | | | | | | | | | | | |              gives:
% 223.10/38.04  | | | | | | | | | | | | | | | | |   (10143)  all_53_4 = all_52_3
% 223.10/38.04  | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_52_1,
% 223.10/38.04  | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (10106), (10137) gives:
% 223.10/38.04  | | | | | | | | | | | | | | | | |   (10144)  all_52_1 = e3
% 223.10/38.04  | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (10141) imply:
% 223.10/38.04  | | | | | | | | | | | | | | | | |   (10145)  all_55_3 = all_52_7
% 223.10/38.04  | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (10142) imply:
% 223.10/38.04  | | | | | | | | | | | | | | | | |   (10146)  all_55_2 = all_52_5
% 223.10/38.04  | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | REDUCE: (363), (10142) imply:
% 223.10/38.04  | | | | | | | | | | | | | | | | |   (10147)   ~ (all_52_5 = all_6_2)
% 223.10/38.04  | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | REDUCE: (10129), (10142) imply:
% 223.10/38.04  | | | | | | | | | | | | | | | | |   (10148)   ~ (all_52_5 = e3)
% 223.10/38.04  | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | REDUCE: (370), (10141) imply:
% 223.10/38.04  | | | | | | | | | | | | | | | | |   (10149)   ~ (all_52_7 = all_4_2)
% 223.10/38.04  | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | REDUCE: (10105), (10141) imply:
% 223.10/38.04  | | | | | | | | | | | | | | | | |   (10150)   ~ (all_52_7 = e3)
% 223.10/38.04  | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 223.10/38.04  | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | |   (10151)   ~ (all_24_2 = e0)
% 223.10/38.04  | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | REDUCE: (315), (10151) imply:
% 223.10/38.04  | | | | | | | | | | | | | | | | | |   (10152)   ~ (all_6_2 = e0)
% 223.10/38.04  | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | BETA: splitting (76) gives:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | |   (10153)   ~ (all_30_2 = e1)
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | REDUCE: (330), (10153) imply:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | |   (10154)   ~ (all_4_2 = e1)
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | |   (10155)  all_55_15 = e3
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (10155) imply:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | |   (10156)  all_4_2 = e3
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | REDUCE: (10098), (10156) imply:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | |   (10157)  $false
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | CLOSE: (10157) is inconsistent.
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | |   (10158)   ~ (all_55_15 = e3)
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | |   (10159)  all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | BETA: splitting (10159) gives:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | |   (10160)  all_55_15 = e2
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (10160) imply:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | |   (10161)  all_4_2 = e2
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | REDUCE: (373), (10161) imply:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | |   (10162)  $false
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | CLOSE: (10162) is inconsistent.
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | |   (10163)   ~ (all_55_15 = e2)
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | |   (10164)  all_55_15 = e1 | all_55_15 = e0
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10164) gives:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | |   (10165)  all_55_15 = e1
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (10165) imply:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | |   (10166)  all_4_2 = e1
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10154), (10166) imply:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | |   (10167)  $false
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (10167) is inconsistent.
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | |   (10168)  all_55_15 = e0
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (10168) imply:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | |   (10169)  all_4_2 = e0
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (351), (10169) imply:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | |   (10170)   ~ (all_53_3 = e0)
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (362), (10169) imply:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | |   (10171)   ~ (all_53_7 = e0)
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (371), (10169) imply:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | |   (10172)   ~ (all_53_13 = e0)
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10098), (10169) imply:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | |   (10173)   ~ (e3 = e0)
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (373), (10169) imply:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | |   (10174)   ~ (e2 = e0)
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10154), (10169) imply:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | |   (10175)   ~ (e1 = e0)
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (10169) imply:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | |   (10176)  op(e0, e0) = e0
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (88) gives:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | |   (10177)   ~ (all_38_2 = e2)
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (249), (10177) imply:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | |   (10178)   ~ (all_6_2 = e2)
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | |   (10179)  all_55_10 = e3
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (374), (10179) are inconsistent by
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2500.
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | |   (10180)   ~ (all_55_10 = e3)
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | |   (10181)  all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10181) gives:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | |   (10182)  all_55_10 = e2
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (10178), (10182) are inconsistent by
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2499.
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | |   (10183)   ~ (all_55_10 = e2)
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | |   (10184)  all_55_10 = e1 | all_55_10 = e0
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10184) gives:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10185)  all_55_10 = e1
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (336), (10185) imply:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10186)  all_6_2 = e1
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10186) implies:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10187)  all_6_2 = e1
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (350), (10187) imply:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10188)   ~ (all_53_2 = e1)
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (374), (10187) imply:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10189)   ~ (e3 = e1)
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10178), (10187) imply:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10190)   ~ (e2 = e1)
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (10187) imply:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10191)  op(e1, e1) = e1
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10192)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e1)
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10192) gives:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10193)  all_57_0 = e1 & op(e3, e3) = e1
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10193) implies:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10194)  op(e3, e3) = e1
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10106), (10194), (function-axioms) are
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2495.
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10195)  all_57_2 = e1 & op(e2, e3) = e1
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10195) implies:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10196)  all_57_2 = e1
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10197)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10197) gives:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10198)  all_57_2 = e0 & op(e2, e3) = e0
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (10196), (10198) are inconsistent by
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2467.
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10199)  all_57_3 = e0 & op(e2, e2) = e0
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10199) implies:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10200)  all_57_3 = e0
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10094), (10200) are inconsistent by
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2358.
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10201)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0)
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10201) gives:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10202)  all_57_5 = e0 & op(e2, e1) = e0
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10202) implies:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10203)  all_57_5 = e0
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10204)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e2)
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10204) gives:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10205)  all_57_4 = e2 & op(e3, e1) = e2
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10205) implies:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10206)  all_57_4 = e2
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10207)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e0)
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (10106), (10136), (10140), (10176),
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10207), (function-axioms) are inconsistent by
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #266.
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10208)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e0)
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10208) gives:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10209)  all_57_4 = e0 & op(e3, e1) = e0
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10209) implies:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10210)  op(e3, e1) = e0
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (10135), (10139), (10176), (10210),
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2167.
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10211)  all_57_9 = e0 & op(e3, e0) = e0
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10211) implies:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10212)  all_57_9 = e0
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10213)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10213) gives:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10214)  all_57_2 = e2 & op(e2, e3) = e2
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (218), (220),
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (221), (374), (10152), (10191), (10196), (10206),
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10214), (function-axioms) are inconsistent by
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #265.
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10215)  all_57_3 = e2 & op(e2, e2) = e2
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10215) implies:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10216)  op(e2, e2) = e2
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (165), (168), (225), (10085), (10090),
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10203), (10216), (function-axioms) are
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2129.
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10217)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10217) gives:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10218)  all_57_5 = e2 & op(e2, e1) = e2
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10218) implies:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10219)  all_57_5 = e2
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10203), (10219) imply:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10220)  e2 = e0
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10220) implies:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10221)  e2 = e0
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10206), (10221) imply:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10222)  all_57_4 = e0
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (233), (235), (10106),
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10212), (10222), (function-axioms) are
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2436.
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10223)  all_57_10 = e2 & op(e2, e0) = e2
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10223) implies:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10224)  all_57_10 = e2
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (211), (231), (10106),
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10125), (10135), (10136), (10139), (10140),
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10176), (10224), (function-axioms) are
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #263.
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10225)  all_57_5 = e2 & op(e2, e1) = e2
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10225) implies:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10226)  all_57_5 = e2
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10203), (10226) are inconsistent by
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2363.
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10227)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e1) = e2)
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10227) gives:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10228)  all_57_8 = e2 & op(e1, e1) = e2
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10228) implies:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10229)  op(e1, e1) = e2
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10191), (10229), (function-axioms) are
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2423.
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10230)  all_57_14 = e2 & op(e0, e1) = e2
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10230) implies:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10231)  all_57_14 = e2
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10115), (10231) are inconsistent by
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2410.
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10232)  all_57_10 = e0 & op(e2, e0) = e0
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10232) implies:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10233)  op(e2, e0) = e0
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (10172), (10233), (function-axioms) are
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2470.
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10234)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e3) = e1)
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10234) gives:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10235)  all_57_6 = e1 & op(e1, e3) = e1
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (10188), (10235), (function-axioms) are
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #316.
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10236)  all_57_12 = e1 & op(e0, e3) = e1
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10236) implies:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10237)  all_57_12 = e1
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10238)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10238) gives:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10239)  all_57_12 = e2 & op(e0, e3) = e2
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10237), (10239) are inconsistent by
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1922.
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10240)  all_57_13 = e2 & op(e0, e2) = e2
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10240) implies:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10241)  all_57_13 = e2
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10242)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e0)
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (10106), (10136), (10140), (10176),
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10242), (function-axioms) are inconsistent by
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #266.
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10243)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e0)
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10243) gives:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10244)  all_57_4 = e0 & op(e3, e1) = e0
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10244) implies:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10245)  op(e3, e1) = e0
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (10135), (10139), (10176), (10245),
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2167.
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10246)  all_57_9 = e0 & op(e3, e0) = e0
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10246) implies:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10247)  all_57_9 = e0
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10248)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10248) gives:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10249)  all_57_9 = e2 & op(e3, e0) = e2
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10247), (10249) are inconsistent by
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2486.
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10250)  all_57_10 = e2 & op(e2, e0) = e2
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10250) implies:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10251)  all_57_10 = e2
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (211), (231), (10106),
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10125), (10135), (10136), (10139), (10140),
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10176), (10251), (function-axioms) are
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #263.
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10252)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10252) gives:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10253)  all_57_11 = e2 & op(e1, e0) = e2
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10253) implies:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10254)  all_57_11 = e2
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10125), (10254) imply:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10255)  e3 = e2
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10115), (10255) imply:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10256)  all_57_14 = e2
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (207), (210), (10237),
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10241), (10256), (function-axioms) are
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1582.
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10257)  all_57_15 = e2 & op(e0, e0) = e2
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10257) implies:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10258)  op(e0, e0) = e2
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (373), (10258), (function-axioms) are
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2334.
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10259)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10259) gives:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10260)  all_57_14 = e2 & op(e0, e1) = e2
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10260) implies:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10261)  all_57_14 = e2
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10115), (10261) are inconsistent by
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2410.
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10262)  all_57_15 = e2 & op(e0, e0) = e2
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10262) implies:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10263)  op(e0, e0) = e2
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (373), (10263), (function-axioms) are
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2334.
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10264)  all_55_10 = e0
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (10152), (10264) are inconsistent by
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2118.
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | |   (10265)  all_38_2 = e2
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (10265) imply:
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | |   (10266)  all_6_2 = e2
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (364), (10266) imply:
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | |   (10267)   ~ (all_53_9 = e2)
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (374), (10266) imply:
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | |   (10268)   ~ (e3 = e2)
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (10266) imply:
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | |   (10269)  op(e1, e1) = e2
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | |   (10270)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e1)
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10270) gives:
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | |   (10271)  all_57_6 = e1 & op(e1, e3) = e1
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10271) implies:
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | |   (10272)  all_57_6 = e1
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10273)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e0)
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10273) gives:
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10274)  all_57_0 = e0 & op(e3, e3) = e0
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10274) implies:
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10275)  op(e3, e3) = e0
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10106), (10275), (function-axioms) are
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2494.
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10276)  all_57_2 = e0 & op(e2, e3) = e0
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10276) implies:
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10277)  all_57_2 = e0
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10278)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10278) gives:
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10279)  all_57_2 = e2 & op(e2, e3) = e2
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10277), (10279) are inconsistent by
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2257.
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10280)  all_57_3 = e2 & op(e2, e2) = e2
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10280) implies:
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10281)  op(e2, e2) = e2
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10095), (10281), (function-axioms) are
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2298.
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10282)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10282) gives:
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10283)  all_57_5 = e2 & op(e2, e1) = e2
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (10267), (10283), (function-axioms) are
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1858.
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10284)  all_57_10 = e2 & op(e2, e0) = e2
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10284) implies:
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10285)  all_57_10 = e2
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (211), (231), (10106),
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10125), (10135), (10136), (10139), (10140),
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10176), (10285), (function-axioms) are
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #263.
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10286)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = e0)
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10286) gives:
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10287)  all_57_6 = e0 & op(e1, e3) = e0
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10287) implies:
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10288)  all_57_6 = e0
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (10272), (10288) are inconsistent by
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2227.
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10289)  all_57_12 = e0 & op(e0, e3) = e0
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10289) implies:
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10290)  op(e0, e3) = e0
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (10170), (10290), (function-axioms) are
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2366.
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | |   (10291)  all_57_7 = e1 & op(e1, e2) = e1
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10291) implies:
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | |   (10292)  all_57_7 = e1
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10293)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10293) gives:
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10294)  all_57_1 = e0 & op(e3, e2) = e0
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10294) implies:
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10295)  op(e3, e2) = e0
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10136), (10140), (10176), (10295),
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2399.
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10296)  all_57_3 = e0 & op(e2, e2) = e0
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10094), (10296) are inconsistent by
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #262.
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10297)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0)
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (159), (10171), (10292), (10297),
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | |            #261.
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | |   (10298)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e0) = e1)
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (10125), (10269), (10298),
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | |            #260.
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | |   (10299)  all_30_2 = e1
% 223.10/38.05  | | | | | | | | | | | | | | | | | | |   (10300)  ( ~ (all_30_0 = e2) & op(all_30_1, e0) = all_30_0
% 223.10/38.05  | | | | | | | | | | | | | | | | | | |              & op(e0, e1) = all_30_1 & $i(all_30_0) &
% 223.10/38.05  | | | | | | | | | | | | | | | | | | |              $i(all_30_1)) | ( ~ (all_30_1 = e3) & op(e0, e1)
% 223.10/38.05  | | | | | | | | | | | | | | | | | | |              = all_30_1 & $i(all_30_1))
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (330), (10299) imply:
% 223.10/38.05  | | | | | | | | | | | | | | | | | | |   (10301)  all_4_2 = e1
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | SIMP: (10301) implies:
% 223.10/38.05  | | | | | | | | | | | | | | | | | | |   (10302)  all_4_2 = e1
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (295), (10302) imply:
% 223.10/38.05  | | | | | | | | | | | | | | | | | | |   (10303)  all_40_2 = e1
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | REDUCE: (10149), (10302) imply:
% 223.10/38.05  | | | | | | | | | | | | | | | | | | |   (10304)   ~ (all_52_7 = e1)
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | REDUCE: (36), (10302) imply:
% 223.10/38.05  | | | | | | | | | | | | | | | | | | |   (10305)  op(e0, e0) = e1
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | BETA: splitting (91) gives:
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | |   (10306)   ~ (all_40_2 = e1)
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | REDUCE: (10303), (10306) imply:
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | |   (10307)  $false
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | CLOSE: (10307) is inconsistent.
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | |   (10308)  ( ~ (all_40_0 = e3) & op(all_40_1, e0) = all_40_0
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | |              & op(e0, e1) = all_40_1 & $i(all_40_0) &
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | |              $i(all_40_1)) | ( ~ (all_40_1 = e2) & op(e0, e1)
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | |              = all_40_1 & $i(all_40_1))
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | BETA: splitting (10308) gives:
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | |   (10309)   ~ (all_40_0 = e3) & op(all_40_1, e0) = all_40_0 &
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | |            op(e0, e1) = all_40_1 & $i(all_40_0) &
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | |            $i(all_40_1)
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | ALPHA: (10309) implies:
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | |   (10310)  op(e0, e1) = all_40_1
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (202), (10116), (10134), (10138), (10145),
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | |            (10150), (10300), (10304), (10305), (10310),
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | |            #258.
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | |   (10311)   ~ (all_40_1 = e2) & op(e0, e1) = all_40_1 &
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | |            $i(all_40_1)
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | ALPHA: (10311) implies:
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | |   (10312)  op(e0, e1) = all_40_1
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (202), (10116), (10134), (10138), (10145),
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | |            (10150), (10300), (10304), (10305), (10312),
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | |            #258.
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.05  | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.05  | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | |   (10313)  all_24_2 = e0
% 223.10/38.05  | | | | | | | | | | | | | | | | | |   (10314)  ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0
% 223.10/38.05  | | | | | | | | | | | | | | | | | |              & op(e1, e0) = all_24_1 & $i(all_24_0) &
% 223.10/38.05  | | | | | | | | | | | | | | | | | |              $i(all_24_1)) | ( ~ (all_24_1 = e3) & op(e1, e0)
% 223.10/38.05  | | | | | | | | | | | | | | | | | |              = all_24_1 & $i(all_24_1))
% 223.10/38.05  | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (315), (10313) imply:
% 223.10/38.05  | | | | | | | | | | | | | | | | | |   (10315)  all_6_2 = e0
% 223.10/38.05  | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (311), (10315) imply:
% 223.10/38.05  | | | | | | | | | | | | | | | | | |   (10316)  all_34_2 = e0
% 223.10/38.05  | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | REDUCE: (10147), (10315) imply:
% 223.10/38.05  | | | | | | | | | | | | | | | | | |   (10317)   ~ (all_52_5 = e0)
% 223.10/38.05  | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | REDUCE: (39), (10315) imply:
% 223.10/38.05  | | | | | | | | | | | | | | | | | |   (10318)  op(e1, e1) = e0
% 223.10/38.05  | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | BETA: splitting (82) gives:
% 223.10/38.05  | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | |   (10319)   ~ (all_34_2 = e0)
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | REDUCE: (10316), (10319) imply:
% 223.10/38.05  | | | | | | | | | | | | | | | | | | |   (10320)  $false
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | CLOSE: (10320) is inconsistent.
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | |   (10321)  ( ~ (all_34_0 = e3) & op(all_34_1, e1) = all_34_0
% 223.10/38.05  | | | | | | | | | | | | | | | | | | |              & op(e1, e0) = all_34_1 & $i(all_34_0) &
% 223.10/38.05  | | | | | | | | | | | | | | | | | | |              $i(all_34_1)) | ( ~ (all_34_1 = e2) & op(e1, e0)
% 223.10/38.05  | | | | | | | | | | | | | | | | | | |              = all_34_1 & $i(all_34_1))
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (203), (10126), (10135), (10139), (10146),
% 223.10/38.05  | | | | | | | | | | | | | | | | | | |            (10148), (10314), (10317), (10318), (10321),
% 223.10/38.05  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.05  | | | | | | | | | | | | | | | | | | |            #256.
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.05  | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | End of split
% 223.10/38.05  | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.05  | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | |   (10322)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 223.10/38.05  | | | | | | | | | | | | | | | | |            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 223.10/38.05  | | | | | | | | | | | | | | | | |            op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 223.10/38.05  | | | | | | | | | | | | | | | | |              all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 223.10/38.05  | | | | | | | | | | | | | | | | |            & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 223.10/38.05  | | | | | | | | | | | | | | | | |            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 223.10/38.05  | | | | | | | | | | | | | | | | |            $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 223.10/38.05  | | | | | | | | | | | | | | | | |            $i(all_52_15)
% 223.10/38.05  | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10095), (10106), (10322), (function-axioms)
% 223.10/38.05  | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #255.
% 223.10/38.05  | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | End of split
% 223.10/38.05  | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | Case 2:
% 223.10/38.05  | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | |   (10323)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 223.10/38.05  | | | | | | | | | | | | | | | |              & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 223.10/38.05  | | | | | | | | | | | | | | | |              & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 223.10/38.05  | | | | | | | | | | | | | | | |                all_52_21) = e1 & op(all_52_23, all_52_23) =
% 223.10/38.05  | | | | | | | | | | | | | | | |              e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 223.10/38.05  | | | | | | | | | | | | | | | |              all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 223.10/38.05  | | | | | | | | | | | | | | | |              = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 223.10/38.05  | | | | | | | | | | | | | | | |              $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 223.10/38.05  | | | | | | | | | | | | | | | |              & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 223.10/38.05  | | | | | | | | | | | | | | | |              e0 & op(all_52_25, all_52_25) = e3 &
% 223.10/38.05  | | | | | | | | | | | | | | | |              op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 223.10/38.05  | | | | | | | | | | | | | | | |                all_52_29) = e1 & op(all_52_31, all_52_31) =
% 223.10/38.05  | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 223.10/38.05  | | | | | | | | | | | | | | | |              all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 223.10/38.05  | | | | | | | | | | | | | | | |              = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 223.10/38.05  | | | | | | | | | | | | | | | |              $i(all_52_29) & $i(all_52_31))
% 223.10/38.05  | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | BETA: splitting (10323) gives:
% 223.10/38.05  | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.05  | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | |   (10324)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 223.10/38.05  | | | | | | | | | | | | | | | | |            all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 223.10/38.05  | | | | | | | | | | | | | | | | |            op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 223.10/38.05  | | | | | | | | | | | | | | | | |              all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 223.10/38.05  | | | | | | | | | | | | | | | | |            & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 223.10/38.05  | | | | | | | | | | | | | | | | |            & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 223.10/38.05  | | | | | | | | | | | | | | | | |            & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 223.10/38.05  | | | | | | | | | | | | | | | | |            $i(all_52_23)
% 223.10/38.05  | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10106), (10126), (10324), (function-axioms)
% 223.10/38.05  | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #254.
% 223.10/38.05  | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.05  | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | |   (10325)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 223.10/38.05  | | | | | | | | | | | | | | | | |            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 223.10/38.05  | | | | | | | | | | | | | | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 223.10/38.05  | | | | | | | | | | | | | | | | |              all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 223.10/38.05  | | | | | | | | | | | | | | | | |            & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 223.10/38.05  | | | | | | | | | | | | | | | | |            & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 223.10/38.05  | | | | | | | | | | | | | | | | |            & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 223.10/38.05  | | | | | | | | | | | | | | | | |            $i(all_52_31)
% 223.10/38.05  | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | ALPHA: (10325) implies:
% 223.10/38.05  | | | | | | | | | | | | | | | | |   (10326)  op(e0, e1) = all_52_29
% 223.10/38.05  | | | | | | | | | | | | | | | | |   (10327)  op(all_52_29, all_52_29) = e1
% 223.10/38.05  | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3,
% 223.10/38.05  | | | | | | | | | | | | | | | | |              all_52_29, e1, e0, simplifying with (10116),
% 223.10/38.05  | | | | | | | | | | | | | | | | |              (10326) gives:
% 223.10/38.05  | | | | | | | | | | | | | | | | |   (10328)  all_52_29 = e3
% 223.10/38.05  | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | REDUCE: (10327), (10328) imply:
% 223.10/38.05  | | | | | | | | | | | | | | | | |   (10329)  op(e3, e3) = e1
% 223.10/38.05  | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10106), (10329), (function-axioms) are
% 223.10/38.05  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2495.
% 223.10/38.05  | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | End of split
% 223.10/38.05  | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | End of split
% 223.10/38.05  | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | End of split
% 223.10/38.05  | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | End of split
% 223.10/38.05  | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | End of split
% 223.10/38.05  | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | End of split
% 223.10/38.05  | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | Case 2:
% 223.10/38.05  | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | |   (10330)  all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 223.10/38.05  | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | REF_CLOSE: (277), (10096), (10100), (10102), (10330) are
% 223.10/38.05  | | | | | | | | | | |            inconsistent by sub-proof #1953.
% 223.10/38.05  | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | End of split
% 223.10/38.05  | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | Case 2:
% 223.10/38.05  | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | |   (10331)  all_20_2 = e2
% 223.10/38.05  | | | | | | | | | |   (10332)  ( ~ (all_20_0 = e1) & op(all_20_1, e3) = all_20_0
% 223.10/38.05  | | | | | | | | | |              & op(e3, e2) = all_20_1 & $i(all_20_0) &
% 223.10/38.05  | | | | | | | | | |              $i(all_20_1)) | ( ~ (all_20_1 = e0) & op(e3, e2)
% 223.10/38.05  | | | | | | | | | |              = all_20_1 & $i(all_20_1))
% 223.10/38.05  | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | COMBINE_EQS: (299), (10331) imply:
% 223.10/38.05  | | | | | | | | | |   (10333)  all_10_2 = e2
% 223.10/38.05  | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | COMBINE_EQS: (329), (10333) imply:
% 223.10/38.05  | | | | | | | | | |   (10334)  all_28_2 = e2
% 223.10/38.05  | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | REDUCE: (338), (10333) imply:
% 223.10/38.05  | | | | | | | | | |   (10335)   ~ (all_53_1 = e2)
% 223.10/38.05  | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | REDUCE: (340), (10333) imply:
% 223.10/38.05  | | | | | | | | | |   (10336)   ~ (all_53_2 = e2)
% 223.10/38.05  | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | REDUCE: (342), (10333) imply:
% 223.10/38.05  | | | | | | | | | |   (10337)   ~ (all_53_3 = e2)
% 223.10/38.05  | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | REDUCE: (344), (10333) imply:
% 223.10/38.05  | | | | | | | | | |   (10338)   ~ (all_53_4 = e2)
% 223.10/38.05  | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | REDUCE: (346), (10333) imply:
% 223.10/38.05  | | | | | | | | | |   (10339)   ~ (all_53_8 = e2)
% 223.10/38.05  | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | REDUCE: (348), (10333) imply:
% 223.10/38.05  | | | | | | | | | |   (10340)   ~ (all_53_12 = e2)
% 223.10/38.05  | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | REDUCE: (45), (10333) imply:
% 223.10/38.05  | | | | | | | | | |   (10341)  op(e3, e3) = e2
% 223.10/38.05  | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | BETA: splitting (67) gives:
% 223.10/38.05  | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | Case 1:
% 223.10/38.05  | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | |   (10342)   ~ (all_24_2 = e0)
% 223.10/38.05  | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | REDUCE: (315), (10342) imply:
% 223.10/38.05  | | | | | | | | | | |   (10343)   ~ (all_6_2 = e0)
% 223.10/38.05  | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | BETA: splitting (73) gives:
% 223.10/38.05  | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | Case 1:
% 223.10/38.05  | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | |   (10344)   ~ (all_28_2 = e2)
% 223.10/38.05  | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | REDUCE: (10334), (10344) imply:
% 223.10/38.05  | | | | | | | | | | | |   (10345)  $false
% 223.10/38.05  | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | CLOSE: (10345) is inconsistent.
% 223.10/38.05  | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | Case 2:
% 223.10/38.05  | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | |   (10346)  ( ~ (all_28_0 = e0) & op(all_28_1, e3) = all_28_0
% 223.10/38.05  | | | | | | | | | | | |              & op(e3, e2) = all_28_1 & $i(all_28_0) &
% 223.10/38.05  | | | | | | | | | | | |              $i(all_28_1)) | ( ~ (all_28_1 = e1) & op(e3, e2)
% 223.10/38.05  | | | | | | | | | | | |              = all_28_1 & $i(all_28_1))
% 223.10/38.05  | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | BETA: splitting (76) gives:
% 223.10/38.05  | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | Case 1:
% 223.10/38.05  | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | |   (10347)   ~ (all_30_2 = e1)
% 223.10/38.05  | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | REDUCE: (330), (10347) imply:
% 223.10/38.05  | | | | | | | | | | | | |   (10348)   ~ (all_4_2 = e1)
% 223.10/38.05  | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | BETA: splitting (190) gives:
% 223.10/38.05  | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | Case 1:
% 223.10/38.05  | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | |   (10349)  all_55_15 = e3
% 223.10/38.05  | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | COMBINE_EQS: (244), (10349) imply:
% 223.10/38.05  | | | | | | | | | | | | | |   (10350)  all_4_2 = e3
% 223.10/38.05  | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | REDUCE: (10098), (10350) imply:
% 223.10/38.05  | | | | | | | | | | | | | |   (10351)  $false
% 223.10/38.05  | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | CLOSE: (10351) is inconsistent.
% 223.10/38.05  | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | Case 2:
% 223.10/38.05  | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | |   (10352)   ~ (all_55_15 = e3)
% 223.10/38.05  | | | | | | | | | | | | | |   (10353)  all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 223.10/38.05  | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | BETA: splitting (10353) gives:
% 223.10/38.05  | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | Case 1:
% 223.10/38.05  | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | |   (10354)  all_55_15 = e2
% 223.10/38.05  | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | COMBINE_EQS: (244), (10354) imply:
% 223.10/38.05  | | | | | | | | | | | | | | |   (10355)  all_4_2 = e2
% 223.10/38.05  | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | REDUCE: (373), (10355) imply:
% 223.10/38.05  | | | | | | | | | | | | | | |   (10356)  $false
% 223.10/38.05  | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | CLOSE: (10356) is inconsistent.
% 223.10/38.05  | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | Case 2:
% 223.10/38.05  | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | |   (10357)   ~ (all_55_15 = e2)
% 223.10/38.05  | | | | | | | | | | | | | | |   (10358)  all_55_15 = e1 | all_55_15 = e0
% 223.10/38.05  | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | BETA: splitting (10358) gives:
% 223.10/38.05  | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | Case 1:
% 223.10/38.05  | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | |   (10359)  all_55_15 = e1
% 223.10/38.05  | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (10359) imply:
% 223.10/38.05  | | | | | | | | | | | | | | | |   (10360)  all_4_2 = e1
% 223.10/38.05  | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | REDUCE: (10348), (10360) imply:
% 223.10/38.05  | | | | | | | | | | | | | | | |   (10361)  $false
% 223.10/38.05  | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | CLOSE: (10361) is inconsistent.
% 223.10/38.05  | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | Case 2:
% 223.10/38.05  | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | |   (10362)  all_55_15 = e0
% 223.10/38.05  | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (10362) imply:
% 223.10/38.05  | | | | | | | | | | | | | | | |   (10363)  all_4_2 = e0
% 223.10/38.05  | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | REDUCE: (351), (10363) imply:
% 223.10/38.05  | | | | | | | | | | | | | | | |   (10364)   ~ (all_53_3 = e0)
% 223.10/38.05  | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | REDUCE: (362), (10363) imply:
% 223.10/38.05  | | | | | | | | | | | | | | | |   (10365)   ~ (all_53_7 = e0)
% 223.10/38.05  | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | REDUCE: (369), (10363) imply:
% 223.10/38.05  | | | | | | | | | | | | | | | |   (10366)   ~ (all_53_11 = e0)
% 223.10/38.05  | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | REDUCE: (370), (10363) imply:
% 223.10/38.05  | | | | | | | | | | | | | | | |   (10367)   ~ (all_53_12 = e0)
% 223.10/38.05  | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | REDUCE: (371), (10363) imply:
% 223.10/38.05  | | | | | | | | | | | | | | | |   (10368)   ~ (all_53_13 = e0)
% 223.10/38.05  | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | REDUCE: (372), (10363) imply:
% 223.10/38.05  | | | | | | | | | | | | | | | |   (10369)   ~ (all_53_14 = e0)
% 223.10/38.05  | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | REDUCE: (10098), (10363) imply:
% 223.10/38.05  | | | | | | | | | | | | | | | |   (10370)   ~ (e3 = e0)
% 223.10/38.05  | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | REDUCE: (373), (10363) imply:
% 223.10/38.05  | | | | | | | | | | | | | | | |   (10371)   ~ (e2 = e0)
% 223.10/38.05  | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | REDUCE: (10348), (10363) imply:
% 223.10/38.05  | | | | | | | | | | | | | | | |   (10372)   ~ (e1 = e0)
% 223.10/38.05  | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 223.10/38.05  | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.05  | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | |   (10373)  all_57_15 = e0 & op(e0, e0) = e0
% 223.10/38.05  | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | ALPHA: (10373) implies:
% 223.10/38.05  | | | | | | | | | | | | | | | | |   (10374)  all_57_15 = e0
% 223.10/38.05  | | | | | | | | | | | | | | | | |   (10375)  op(e0, e0) = e0
% 223.10/38.05  | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | BETA: splitting (88) gives:
% 223.10/38.05  | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.05  | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | |   (10376)   ~ (all_38_2 = e2)
% 223.10/38.05  | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | REDUCE: (249), (10376) imply:
% 223.10/38.05  | | | | | | | | | | | | | | | | | |   (10377)   ~ (all_6_2 = e2)
% 223.10/38.05  | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 223.10/38.05  | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | |   (10378)  all_55_10 = e3
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (374), (10378) are inconsistent by
% 223.10/38.05  | | | | | | | | | | | | | | | | | | |            sub-proof #2500.
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.05  | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.05  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | |   (10379)   ~ (all_55_10 = e3)
% 223.10/38.06  | | | | | | | | | | | | | | | | | | |   (10380)  all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | BETA: splitting (10380) gives:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | |   (10381)  all_55_10 = e2
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (10377), (10381) are inconsistent by
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | |            sub-proof #2499.
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | |   (10382)  all_55_10 = e1 | all_55_10 = e0
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | BETA: splitting (10382) gives:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | |   (10383)  all_55_10 = e1
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (336), (10383) imply:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | |   (10384)  all_6_2 = e1
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | SIMP: (10384) implies:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | |   (10385)  all_6_2 = e1
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | REDUCE: (361), (10385) imply:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | |   (10386)   ~ (all_53_6 = e1)
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | REDUCE: (363), (10385) imply:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | |   (10387)   ~ (all_53_8 = e1)
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | REDUCE: (368), (10385) imply:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | |   (10388)   ~ (all_53_14 = e1)
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (97) gives:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | |   (10389)   ~ (all_44_2 = e3)
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10084), (10389) imply:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | |   (10390)  $false
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (10390) is inconsistent.
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | |   (10391)  ( ~ (all_44_0 = e1) & op(all_44_1, e2) = all_44_0
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = all_44_1 & $i(all_44_0) &
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | |              $i(all_44_1)) | ( ~ (all_44_1 = e0) & op(e2, e3)
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | |              = all_44_1 & $i(all_44_1))
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | |   (10392)  all_55_3 = e3
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (10392) imply:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | |   (10393)  all_53_12 = e3
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10393) implies:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | |   (10394)  all_53_12 = e3
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (10394) imply:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | |   (10395)   ~ (all_53_8 = e3)
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (10394) imply:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | |   (10396)   ~ (all_53_14 = e3)
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10396) implies:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | |   (10397)   ~ (all_53_14 = e3)
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | |   (10398)  all_55_2 = e3
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (10395), (10398) are inconsistent by
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2028.
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | |   (10399)  all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10399) gives:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | |   (10400)  all_55_2 = e2
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (10339), (10400) are inconsistent by
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2027.
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | |   (10401)  all_55_2 = e1 | all_55_2 = e0
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10402)  all_55_11 = e3
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (10397), (10402) are inconsistent by
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2497.
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10403)  all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10401) gives:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10404)  all_55_2 = e1
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (10387), (10404) are inconsistent by
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2032.
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10405)  all_55_2 = e0
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (10405) imply:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10406)  all_53_8 = e0
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10406) implies:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10407)  all_53_8 = e0
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (124), (10407) imply:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10408)   ~ (all_53_9 = e0)
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10408) implies:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10409)   ~ (all_53_9 = e0)
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (170), (10407) imply:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10410)  op(e3, e1) = e0
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10403) gives:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10411)  all_55_11 = e2
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (10411) imply:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10412)  all_53_14 = e2
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10412) implies:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10413)  all_53_14 = e2
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (127), (10413) imply:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10414)   ~ (all_53_6 = e2)
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10415)  all_55_9 = e3
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (10087), (10415) are inconsistent by
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2159.
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10416)   ~ (all_55_9 = e3)
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10417)  all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10417) gives:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10418)  all_55_9 = e2
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (10414), (10418) are inconsistent by
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2274.
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10419)   ~ (all_55_9 = e2)
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10420)  all_55_9 = e1 | all_55_9 = e0
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10420) gives:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10421)  all_55_9 = e1
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (10386), (10421) are inconsistent by
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2273.
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10422)  all_55_9 = e0
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (10422) imply:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10423)  all_53_6 = e0
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10423) implies:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10424)  all_53_6 = e0
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (10424) imply:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10425)   ~ (all_53_2 = e0)
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (163), (10424) imply:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10426)  op(e1, e2) = e0
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (97), (107), (159), (160), (164),
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (165), (166), (168), (192), (222), (230), (244),
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (246), (362), (371), (10083), (10084), (10088),
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10094), (10095), (10098), (10341), (10348),
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10358), (10364), (10375), (10409), (10410),
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10425), (10426), (function-axioms) are
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #250.
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10427)  all_55_11 = e1 | all_55_11 = e0
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (10369), (10388), (10427) are inconsistent
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2307.
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | |   (10428)   ~ (all_55_3 = e3)
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | |   (10429)  all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (268), (10428) imply:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | |   (10430)   ~ (all_53_12 = e3)
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10429) gives:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | |   (10431)  all_55_3 = e2
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (10340), (10431) are inconsistent by
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1612.
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | |   (10432)   ~ (all_55_3 = e2)
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | |   (10433)  all_55_3 = e1 | all_55_3 = e0
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10433) gives:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | |   (10434)  all_55_3 = e1
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (10434) imply:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | |   (10435)  all_53_12 = e1
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10435) implies:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | |   (10436)  all_53_12 = e1
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (114), (10436) imply:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | |   (10437)   ~ (all_53_13 = e1)
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10437) implies:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | |   (10438)   ~ (all_53_13 = e1)
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10430), (10436) imply:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | |   (10439)   ~ (e3 = e1)
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10440)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (169), (10090), (10430), (10440),
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | |            #2300.
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10441)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10441) gives:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10442)  all_57_11 = e3 & op(e1, e0) = e3
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10442) implies:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10443)  all_57_11 = e3
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10444)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10444) gives:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10445)  all_57_9 = e2 & op(e3, e0) = e2
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10445) implies:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10446)  op(e3, e0) = e2
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (10340), (10446), (function-axioms) are
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2331.
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10447)  all_57_10 = e2 & op(e2, e0) = e2
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10447) implies:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10448)  op(e2, e0) = e2
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10449)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e3)
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (171), (10086), (10341), (10449),
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #249.
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10450)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e3)
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10450) gives:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10451)  all_57_4 = e3 & op(e3, e1) = e3
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10451) implies:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10452)  all_57_4 = e3
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10453)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e0)
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10453) gives:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10454)  all_57_0 = e0 & op(e3, e3) = e0
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10454) implies:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10455)  op(e3, e3) = e0
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10341), (10455), (function-axioms) are
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2403.
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10456)  all_57_1 = e0 & op(e3, e2) = e0
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10456) implies:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10457)  op(e3, e2) = e0
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10458)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10458) gives:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10459)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_7)
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10459) implies:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10460)  op(e3, e2) = all_52_3
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10461)  op(all_52_3, all_52_3) = e2
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10375), (10457), (10460), (10461),
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2399.
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10462)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_15)
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10462) implies:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10463)  op(e2, e0) = all_52_15
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10464)  op(e2, e2) = all_52_11
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10465)  op(all_52_15, all_52_15) = e0
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10095), (10448), (10463), (10464), (10465),
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #248.
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10466)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_52_21) = e1 & op(all_52_23, all_52_23) =
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(all_52_25, all_52_25) = e3 &
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_52_29) = e1 & op(all_52_31, all_52_31) =
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_29) & $i(all_52_31))
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10466) gives:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10467)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_23)
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10467) implies:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10468)  op(e1, e1) = all_52_21
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10469)  op(e1, e2) = all_52_19
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10470)  op(all_52_21, all_52_21) = e1
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10471)  op(all_52_19, all_52_19) = e2
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10472)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10472) gives:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10473)  all_57_2 = e1 & op(e2, e3) = e1
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10473) implies:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10474)  op(e2, e3) = e1
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (196), (256), (10083), (10087), (10095),
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10386), (10391), (10469), (10471), (10474),
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #244.
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10475)  all_57_3 = e1 & op(e2, e2) = e1
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10475) implies:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10476)  op(e2, e2) = e1
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10095), (10476), (function-axioms) are
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1912.
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10477)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10477) gives:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10478)  all_57_5 = e1 & op(e2, e1) = e1
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10478) implies:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10479)  op(e2, e1) = e1
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (166), (195), (336), (364), (374), (10089),
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10095), (10343), (10468), (10470), (10479),
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #243.
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10480)  all_57_10 = e1 & op(e2, e0) = e1
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (10438), (10480), (function-axioms) are
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2084.
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10481)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_31)
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10481) implies:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10482)  op(e0, e3) = all_52_25
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10483)  op(all_52_25, all_52_25) = e3
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (171), (193), (247), (10332), (10337),
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10341), (10346), (10364), (10457), (10482),
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10483), (function-axioms) are inconsistent by
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1567.
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10484)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e0)
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10484) gives:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10485)  all_57_4 = e0 & op(e3, e1) = e0
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10485) implies:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10486)  all_57_4 = e0
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10452), (10486) are inconsistent by
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2372.
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10487)  all_57_9 = e0 & op(e3, e0) = e0
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (10367), (10487), (function-axioms) are
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2434.
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10488)  all_57_9 = e3 & op(e3, e0) = e3
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10488) implies:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10489)  op(e3, e0) = e3
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (10430), (10489), (function-axioms) are
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2458.
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10490)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10490) gives:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10491)  all_57_11 = e2 & op(e1, e0) = e2
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10443), (10491) are inconsistent by
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2141.
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10492)  all_57_15 = e2 & op(e0, e0) = e2
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10492) implies:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10493)  op(e0, e0) = e2
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (373), (10493), (function-axioms) are
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2334.
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10494)  all_57_15 = e3 & op(e0, e0) = e3
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10494) implies:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10495)  op(e0, e0) = e3
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10375), (10495), (function-axioms) are
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2304.
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | |   (10496)  all_55_3 = e0
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (10367), (10496) are inconsistent by
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #885.
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | |   (10497)  all_55_10 = e0
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (10343), (10497) are inconsistent by
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | |            sub-proof #2118.
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.07  | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | |   (10498)  all_38_2 = e2
% 223.10/38.07  | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (10498) imply:
% 223.10/38.07  | | | | | | | | | | | | | | | | | |   (10499)  all_6_2 = e2
% 223.10/38.07  | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | REDUCE: (364), (10499) imply:
% 223.10/38.07  | | | | | | | | | | | | | | | | | |   (10500)   ~ (all_53_9 = e2)
% 223.10/38.07  | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | REDUCE: (374), (10499) imply:
% 223.10/38.07  | | | | | | | | | | | | | | | | | |   (10501)   ~ (e3 = e2)
% 223.10/38.07  | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | REDUCE: (39), (10499) imply:
% 223.10/38.07  | | | | | | | | | | | | | | | | | |   (10502)  op(e1, e1) = e2
% 223.10/38.07  | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | |   (10503)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 223.10/38.07  | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (168), (10095), (10335), (10503),
% 223.10/38.07  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.07  | | | | | | | | | | | | | | | | | | |            #242.
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | |   (10504)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 223.10/38.07  | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | BETA: splitting (10504) gives:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | |   (10505)  all_57_5 = e2 & op(e2, e1) = e2
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (10500), (10505), (function-axioms) are
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1858.
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | |   (10506)  all_57_10 = e2 & op(e2, e0) = e2
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | ALPHA: (10506) implies:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | |   (10507)  all_57_10 = e2
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | |   (10508)  op(e2, e0) = e2
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | |   (10509)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10509) gives:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | |   (10510)  all_57_12 = e2 & op(e0, e3) = e2
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10510) implies:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | |   (10511)  op(e0, e3) = e2
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (10337), (10511), (function-axioms) are
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1980.
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | |   (10512)  all_57_13 = e2 & op(e0, e2) = e2
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10512) implies:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | |   (10513)  all_57_13 = e2
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | |   (10514)  op(e0, e2) = e2
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_7, e2,
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (159), (10514) gives:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | |   (10515)  all_53_7 = e2
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_13,
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | |              e2, e0, e2, simplifying with (165), (10508) gives:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | |   (10516)  all_53_13 = e2
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (126), (10515) imply:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | |   (10517)   ~ (all_53_11 = e2)
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | SIMP: (10517) implies:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | |   (10518)   ~ (all_53_11 = e2)
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | |   (10519)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | |              all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | |              op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | |                all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | |                all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | |              & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | |                all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10519) gives:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | |   (10520)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | |            all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | |              all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_7)
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10520) implies:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | |   (10521)  op(e3, e1) = all_52_5
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | |   (10522)  op(e3, e2) = all_52_3
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | |   (10523)  op(e3, e3) = all_52_1
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | |   (10524)  op(all_52_5, all_52_5) = e1
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | |   (10525)  op(all_52_3, all_52_3) = e2
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | |   (10526)  op(all_52_1, all_52_1) = e3
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_8,
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | |              all_52_5, e1, e3, simplifying with (170), (10521)
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | |   (10527)  all_53_8 = all_52_5
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_4,
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | |              all_52_3, e2, e3, simplifying with (171), (10522)
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | |   (10528)  all_53_4 = all_52_3
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_52_1,
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (10341), (10523) gives:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | |   (10529)  all_52_1 = e2
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | |   (10530)  all_55_4 = e3
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (10085), (10530) are inconsistent by
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2170.
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | |   (10531)   ~ (all_55_4 = e3)
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | |   (10532)  all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10533)  all_55_14 = e3
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (10533) imply:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10534)  all_53_11 = e3
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (10534) imply:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10535)   ~ (all_53_3 = e3)
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10536)  all_55_12 = e3
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (10536) imply:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10537)  all_53_3 = e3
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10535), (10537) imply:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10538)  $false
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (10538) is inconsistent.
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10539)   ~ (all_55_12 = e3)
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10540)  all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10540) gives:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10541)  all_55_12 = e2
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (247), (10337), (10541) are inconsistent by
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1337.
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10542)   ~ (all_55_12 = e2)
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10543)  all_55_12 = e1 | all_55_12 = e0
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10544)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e3)
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (168), (10085), (10341), (10544),
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #241.
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10545)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e3) = e3)
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10545) gives:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10546)  all_57_6 = e3 & op(e1, e3) = e3
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10546) implies:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10547)  all_57_6 = e3
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10543) gives:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10548)  all_55_12 = e1
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (10548) imply:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10549)  all_53_3 = e1
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10549) implies:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10550)  all_53_3 = e1
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (10550) imply:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10551)   ~ (all_53_1 = e1)
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (10550) imply:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10552)   ~ (all_53_2 = e1)
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10535), (10550) imply:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10553)   ~ (e3 = e1)
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10337), (10550) imply:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10554)   ~ (e2 = e1)
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10555)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e1)
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (168), (10341), (10551), (10555),
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1598.
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10556)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e3) = e1)
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10556) gives:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10557)  all_57_6 = e1 & op(e1, e3) = e1
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (10552), (10557), (function-axioms) are
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #316.
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10558)  all_57_12 = e1 & op(e0, e3) = e1
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10558) implies:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10559)  all_57_12 = e1
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10560)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (168), (10095), (10551), (10560),
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #240.
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10561)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10561) gives:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10562)  all_57_5 = e1 & op(e2, e1) = e1
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10562) implies:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10563)  all_57_5 = e1
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10532) gives:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10564)  all_55_4 = e2
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (10564) imply:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10565)  all_53_1 = e2
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10335), (10565) imply:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10566)  $false
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (10566) is inconsistent.
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10567)   ~ (all_55_4 = e2)
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10568)  all_55_4 = e1 | all_55_4 = e0
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10569)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10569) gives:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10570)  all_57_2 = e0 & op(e2, e3) = e0
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10570) implies:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10571)  all_57_2 = e0
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10572)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e0)
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10572) gives:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10573)  all_57_6 = e0 & op(e1, e3) = e0
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10573) implies:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10574)  all_57_6 = e0
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10547), (10574) imply:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10575)  e3 = e0
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10094), (10575) imply:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10576)  all_57_3 = e0
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10571), (10576) are inconsistent by sub-proof
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2246.
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10577)  all_57_7 = e0 & op(e1, e2) = e0
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10577) implies:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10578)  op(e1, e2) = e0
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10568) gives:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10579)  all_55_4 = e1
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (10579) imply:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10580)  all_53_1 = e1
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10551), (10580) imply:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10581)  $false
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (10581) is inconsistent.
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10582)  all_55_4 = e0
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (10582) imply:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10583)  all_53_1 = e0
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (150), (10583) imply:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10584)   ~ (all_53_2 = e0)
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10584) implies:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10585)   ~ (all_53_2 = e0)
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (147), (10583) imply:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10586)   ~ (all_53_9 = e0)
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10586) implies:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10587)   ~ (all_53_9 = e0)
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10588)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e0)
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10588) gives:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10589)  all_57_0 = e0 & op(e3, e3) = e0
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10589) implies:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10590)  op(e3, e3) = e0
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (168), (234), (10335), (10547),
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10559), (10590), (function-axioms) are
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1921.
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10591)  all_57_1 = e0 & op(e3, e2) = e0
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10591) implies:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10592)  op(e3, e2) = e0
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10375), (10522), (10525), (10592),
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2399.
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10593)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e0)
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10593) gives:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10594)  all_57_4 = e0 & op(e3, e1) = e0
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10594) implies:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10595)  op(e3, e1) = e0
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (97), (107), (159), (160), (164),
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (165), (166), (168), (192), (222), (230), (244),
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (246), (362), (371), (10083), (10084), (10088),
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10094), (10095), (10098), (10341), (10348),
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10358), (10364), (10375), (10578), (10585),
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10587), (10595), (function-axioms) are
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #250.
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10596)  all_57_9 = e0 & op(e3, e0) = e0
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (10367), (10596), (function-axioms) are
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2434.
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10597)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10597) gives:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10598)  all_57_8 = e0 & op(e1, e1) = e0
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (10343), (10598), (function-axioms) are
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2412.
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10599)  all_57_11 = e0 & op(e1, e0) = e0
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (10369), (10599), (function-axioms) are
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2341.
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10600)  all_57_3 = e0 & op(e2, e2) = e0
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10600) implies:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10601)  op(e2, e2) = e0
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10341), (10523), (10526), (10601),
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1653.
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10602)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0)
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (165), (10368), (10563), (10602),
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #239.
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10603)  all_57_10 = e1 & op(e2, e0) = e1
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10603) implies:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10604)  all_57_10 = e1
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10507), (10604) are inconsistent by
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2144.
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10605)  all_55_12 = e0
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (247), (10364), (10605) are inconsistent by
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1993.
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10606)  all_57_12 = e3 & op(e0, e3) = e3
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10606) implies:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10607)  all_57_12 = e3
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10543) gives:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10608)  all_55_12 = e1
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (10608) imply:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10609)  all_53_3 = e1
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10609) implies:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10610)  all_53_3 = e1
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (10610) imply:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10611)   ~ (all_53_1 = e1)
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (10610) imply:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10612)   ~ (all_53_2 = e1)
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10535), (10610) imply:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10613)   ~ (e3 = e1)
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10337), (10610) imply:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10614)   ~ (e2 = e1)
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (164), (168), (232), (10341), (10607),
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10611), (10612), (function-axioms) are
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #238.
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10615)  all_55_12 = e0
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (247), (10364), (10615) are inconsistent by
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1993.
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10616)   ~ (all_55_14 = e3)
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10617)  all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (245), (10616) imply:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10618)   ~ (all_53_11 = e3)
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10617) gives:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10619)  all_55_14 = e2
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (10619) imply:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10620)  all_53_11 = e2
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10518), (10620) imply:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10621)  $false
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (10621) is inconsistent.
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10622)   ~ (all_55_14 = e2)
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10623)  all_55_14 = e1 | all_55_14 = e0
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10623) gives:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10624)  all_55_14 = e1
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (10624) imply:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10625)  all_53_11 = e1
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (10625) imply:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10626)   ~ (all_53_3 = e1)
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (119), (10625) imply:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10627)   ~ (all_53_9 = e1)
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10618), (10625) imply:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10628)   ~ (e3 = e1)
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10518), (10625) imply:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10629)   ~ (e2 = e1)
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10630)  all_55_6 = e3
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (10089), (10630) are inconsistent by
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2498.
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10631)   ~ (all_55_6 = e3)
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10632)  all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10633)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e3)
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10633) gives:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10634)  all_57_4 = e3 & op(e3, e1) = e3
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10634) implies:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10635)  op(e3, e1) = e3
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10636)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e0)
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10636) gives:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10637)  all_57_0 = e0 & op(e3, e3) = e0
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10637) implies:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10638)  op(e3, e3) = e0
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (10521), (10523), (10524), (10635), (10638),
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #237.
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10639)  all_57_1 = e0 & op(e3, e2) = e0
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10639) implies:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10640)  op(e3, e2) = e0
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10375), (10522), (10525), (10640),
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2399.
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10641)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e0)
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10641) gives:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10642)  all_57_4 = e0 & op(e3, e1) = e0
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10642) implies:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10643)  op(e3, e1) = e0
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (124), (170), (259), (10500), (10627), (10632),
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10643), (function-axioms) are inconsistent by
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1721.
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10644)  all_57_9 = e0 & op(e3, e0) = e0
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (10367), (10644), (function-axioms) are
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2434.
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10645)  all_57_5 = e3 & op(e2, e1) = e3
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (10089), (10645), (function-axioms) are
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #270.
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10646)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e1) = e3)
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10646) gives:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10647)  all_57_8 = e3 & op(e1, e1) = e3
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10647) implies:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10648)  op(e1, e1) = e3
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (374), (10648), (function-axioms) are
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2468.
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10649)  all_57_14 = e3 & op(e0, e1) = e3
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10649) implies:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10650)  all_57_14 = e3
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10651)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10651) gives:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10652)  all_57_12 = e1 & op(e0, e3) = e1
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (10626), (10652), (function-axioms) are
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1947.
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10653)  all_57_13 = e1 & op(e0, e2) = e1
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10513), (10653) are inconsistent by
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2205.
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10654)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10654) gives:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10655)  all_57_14 = e1 & op(e0, e1) = e1
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10650), (10655) are inconsistent by
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2319.
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10656)  all_57_15 = e1 & op(e0, e0) = e1
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10656) implies:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10657)  op(e0, e0) = e1
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (10375), (10657), (function-axioms) are
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2290.
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10658)  all_55_14 = e0
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (10658) imply:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10659)  all_53_11 = e0
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10366), (10659) imply:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10660)  $false
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (10660) is inconsistent.
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | |   (10661)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | |            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | |              all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_15)
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10661) implies:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | |   (10662)  op(e2, e0) = all_52_15
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | |   (10663)  op(e2, e2) = all_52_11
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | |   (10664)  op(all_52_15, all_52_15) = e0
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10095), (10508), (10662), (10663), (10664),
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | |            #248.
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | |   (10665)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | |              & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | |              & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | |                all_52_21) = e1 & op(all_52_23, all_52_23) =
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | |              all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | |              = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | |              & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(all_52_25, all_52_25) = e3 &
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | |              op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | |                all_52_29) = e1 & op(all_52_31, all_52_31) =
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | |              all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | |              = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_29) & $i(all_52_31))
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10665) gives:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | |   (10666)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | |            all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | |              all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | |            & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_23)
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10095), (10502), (10666), (function-axioms)
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #236.
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | |   (10667)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | |            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | |              all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | |            & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_31)
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10667) implies:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | |   (10668)  op(e0, e2) = all_52_27
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | |   (10669)  op(all_52_27, all_52_27) = e2
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | |              all_52_27, e2, e0, simplifying with (10514),
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | |              (10668) gives:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | |   (10670)  all_52_27 = e2
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10669), (10670) imply:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | |   (10671)  op(e2, e2) = e2
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10095), (10671), (function-axioms) are
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2298.
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | |   (10672)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10672) gives:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | |   (10673)  all_57_14 = e2 & op(e0, e1) = e2
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10673) implies:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | |   (10674)  all_57_14 = e2
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | |   (10675)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e3)
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10675) gives:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | |   (10676)  all_57_4 = e3 & op(e3, e1) = e3
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10676) implies:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | |   (10677)  all_57_4 = e3
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | |   (10678)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233),
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | |            (10095), (10341), (10677), (10678),
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | |            #235.
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | |   (10679)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10679) gives:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10680)  all_57_7 = e2 & op(e1, e2) = e2
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10680) implies:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10681)  all_57_7 = e2
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10682)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10682) gives:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10683)  all_57_1 = e0 & op(e3, e2) = e0
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10683) implies:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10684)  all_57_1 = e0
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10685)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e1)
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (9), (169), (171), (235), (10338),
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10340), (10677), (10684), (10685),
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #233.
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10686)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e1)
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10686) gives:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10687)  all_57_4 = e1 & op(e3, e1) = e1
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10687) implies:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10688)  all_57_4 = e1
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (39), (218), (221),
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (374), (10343), (10674), (10688),
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2408.
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10689)  all_57_9 = e1 & op(e3, e0) = e1
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10689) implies:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10690)  all_57_9 = e1
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10691)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e1)
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10691) gives:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10692)  all_57_6 = e1 & op(e1, e3) = e1
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10692) implies:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10693)  all_57_6 = e1
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10694)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e0)
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10694) gives:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10695)  all_57_6 = e0 & op(e1, e3) = e0
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10695) implies:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10696)  all_57_6 = e0
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (10693), (10696) are inconsistent by
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2227.
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10697)  all_57_7 = e0 & op(e1, e2) = e0
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10681), (10697) are inconsistent by
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2148.
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10698)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10698) gives:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10699)  all_57_8 = e0 & op(e1, e1) = e0
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (10343), (10699), (function-axioms) are
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2412.
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10700)  all_57_11 = e0 & op(e1, e0) = e0
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (39), (217), (374), (10681),
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10693), (10700), (function-axioms) are
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1586.
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10701)  all_57_7 = e1 & op(e1, e2) = e1
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10681), (10701) are inconsistent by
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2190.
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10702)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e0) = e1)
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10702) gives:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10703)  all_57_8 = e1 & op(e1, e1) = e1
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10703) implies:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10704)  op(e1, e1) = e1
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10502), (10704), (function-axioms) are
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2423.
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10705)  all_57_11 = e1 & op(e1, e0) = e1
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10705) implies:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10706)  all_57_11 = e1
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10707)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10707) gives:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10708)  all_57_9 = e3 & op(e3, e0) = e3
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10708) implies:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10709)  all_57_9 = e3
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10690), (10709) are inconsistent by
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1673.
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10710)  all_57_10 = e3 & op(e2, e0) = e3
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10710) implies:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10711)  all_57_10 = e3
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10712)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (169), (10340), (10711), (10712),
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1219.
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10713)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (10374), (10706), (10713) are
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1666.
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10714)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (10375), (10706), (10714),
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #232.
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10715)  all_57_3 = e0 & op(e2, e2) = e0
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10094), (10715) are inconsistent by
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #262.
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10716)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0)
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10716) gives:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10717)  all_57_7 = e0 & op(e1, e2) = e0
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10681), (10717) are inconsistent by
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2148.
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10718)  all_57_13 = e0 & op(e0, e2) = e0
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10718) implies:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10719)  op(e0, e2) = e0
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (10365), (10719), (function-axioms) are
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2332.
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10720)  all_57_13 = e2 & op(e0, e2) = e2
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10720) implies:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10721)  all_57_13 = e2
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (207), (208), (210),
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | |            (10375), (10674), (10721), (function-axioms) are
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1581.
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | |   (10722)  all_57_5 = e3 & op(e2, e1) = e3
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (10089), (10722), (function-axioms) are
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #270.
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | |   (10723)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e1) = e3)
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (39), (374), (10674), (10723),
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | |            #1890.
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | |   (10724)  all_57_15 = e2 & op(e0, e0) = e2
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10724) implies:
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | |   (10725)  op(e0, e0) = e2
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (373), (10725), (function-axioms) are
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2334.
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.08  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.08  | | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | End of split
% 223.10/38.08  | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.08  | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | |   (10726)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 223.10/38.08  | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 223.10/38.08  | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 223.10/38.08  | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 223.10/38.08  | | | | | | | | | | | | | | | | |                e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 223.10/38.08  | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (165), (169), (10367), (10368), (10369),
% 223.10/38.08  | | | | | | | | | | | | | | | | |            (10726), (function-axioms) are inconsistent by
% 223.10/38.08  | | | | | | | | | | | | | | | | |            sub-proof #2112.
% 223.10/38.08  | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | End of split
% 223.10/38.08  | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | End of split
% 223.10/38.08  | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | End of split
% 223.10/38.08  | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | End of split
% 223.10/38.08  | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | Case 2:
% 223.10/38.08  | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | |   (10727)  all_30_2 = e1
% 223.10/38.08  | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | COMBINE_EQS: (330), (10727) imply:
% 223.10/38.08  | | | | | | | | | | | | |   (10728)  all_4_2 = e1
% 223.10/38.08  | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | SIMP: (10728) implies:
% 223.10/38.08  | | | | | | | | | | | | |   (10729)  all_4_2 = e1
% 223.10/38.08  | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | REDUCE: (351), (10729) imply:
% 223.10/38.08  | | | | | | | | | | | | |   (10730)   ~ (all_53_3 = e1)
% 223.10/38.08  | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | REDUCE: (362), (10729) imply:
% 223.10/38.08  | | | | | | | | | | | | |   (10731)   ~ (all_53_7 = e1)
% 223.10/38.08  | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | REDUCE: (370), (10729) imply:
% 223.10/38.08  | | | | | | | | | | | | |   (10732)   ~ (all_53_12 = e1)
% 223.10/38.08  | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | REDUCE: (10098), (10729) imply:
% 223.10/38.08  | | | | | | | | | | | | |   (10733)   ~ (e3 = e1)
% 223.10/38.08  | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | REDUCE: (373), (10729) imply:
% 223.10/38.08  | | | | | | | | | | | | |   (10734)   ~ (e2 = e1)
% 223.10/38.08  | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | REDUCE: (36), (10729) imply:
% 223.10/38.08  | | | | | | | | | | | | |   (10735)  op(e0, e0) = e1
% 223.10/38.08  | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | BETA: splitting (88) gives:
% 223.10/38.08  | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | Case 1:
% 223.10/38.08  | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | |   (10736)   ~ (all_38_2 = e2)
% 223.10/38.08  | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | REDUCE: (249), (10736) imply:
% 223.10/38.08  | | | | | | | | | | | | | |   (10737)   ~ (all_6_2 = e2)
% 223.10/38.08  | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 223.10/38.08  | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | Case 1:
% 223.10/38.08  | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | |   (10738)  all_55_10 = e3
% 223.10/38.08  | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | REF_CLOSE: (336), (374), (10738) are inconsistent by
% 223.10/38.08  | | | | | | | | | | | | | | |            sub-proof #2500.
% 223.10/38.08  | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | Case 2:
% 223.10/38.08  | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | |   (10739)   ~ (all_55_10 = e3)
% 223.10/38.08  | | | | | | | | | | | | | | |   (10740)  all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 223.10/38.08  | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | BETA: splitting (10740) gives:
% 223.10/38.08  | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | Case 1:
% 223.10/38.08  | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | |   (10741)  all_55_10 = e2
% 223.10/38.08  | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | REF_CLOSE: (336), (10737), (10741) are inconsistent by
% 223.10/38.08  | | | | | | | | | | | | | | | |            sub-proof #2499.
% 223.10/38.08  | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | Case 2:
% 223.10/38.08  | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | |   (10742)   ~ (all_55_10 = e2)
% 223.10/38.08  | | | | | | | | | | | | | | | |   (10743)  all_55_10 = e1 | all_55_10 = e0
% 223.10/38.08  | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | BETA: splitting (10743) gives:
% 223.10/38.08  | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.08  | | | | | | | | | | | | | | | | | 
% 223.10/38.08  | | | | | | | | | | | | | | | | |   (10744)  all_55_10 = e1
% 223.10/38.09  | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | COMBINE_EQS: (336), (10744) imply:
% 223.10/38.09  | | | | | | | | | | | | | | | | |   (10745)  all_6_2 = e1
% 223.10/38.09  | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | SIMP: (10745) implies:
% 223.10/38.09  | | | | | | | | | | | | | | | | |   (10746)  all_6_2 = e1
% 223.10/38.09  | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | REDUCE: (350), (10746) imply:
% 223.10/38.09  | | | | | | | | | | | | | | | | |   (10747)   ~ (all_53_2 = e1)
% 223.10/38.09  | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | REDUCE: (361), (10746) imply:
% 223.10/38.09  | | | | | | | | | | | | | | | | |   (10748)   ~ (all_53_6 = e1)
% 223.10/38.09  | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | REDUCE: (39), (10746) imply:
% 223.10/38.09  | | | | | | | | | | | | | | | | |   (10749)  op(e1, e1) = e1
% 223.10/38.09  | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 223.10/38.09  | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | |   (10750)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 223.10/38.09  | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e1)
% 223.10/38.09  | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | BETA: splitting (10750) gives:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | |   (10751)  all_57_0 = e1 & op(e3, e3) = e1
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | ALPHA: (10751) implies:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | |   (10752)  op(e3, e3) = e1
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10341), (10752), (function-axioms) are
% 223.10/38.09  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1950.
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | |   (10753)  all_57_2 = e1 & op(e2, e3) = e1
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | ALPHA: (10753) implies:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | |   (10754)  op(e2, e3) = e1
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | |   (10755)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | BETA: splitting (10755) gives:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | |   (10756)  all_57_1 = e1 & op(e3, e2) = e1
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | ALPHA: (10756) implies:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | |   (10757)  op(e3, e2) = e1
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_1, e1,
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (168), (10754) gives:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | |   (10758)  all_53_1 = e1
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_4, e1,
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (171), (10757) gives:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | |   (10759)  all_53_4 = e1
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | REDUCE: (137), (10759) imply:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | |   (10760)   ~ (all_53_6 = e1)
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (97) gives:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | |   (10761)   ~ (all_44_2 = e3)
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10084), (10761) imply:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | |   (10762)  $false
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (10762) is inconsistent.
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | |   (10763)  ( ~ (all_44_0 = e1) & op(all_44_1, e2) = all_44_0
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = all_44_1 & $i(all_44_0) &
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | |              $i(all_44_1)) | ( ~ (all_44_1 = e0) & op(e2, e3)
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | |              = all_44_1 & $i(all_44_1))
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | |   (10764)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | |              all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | |              op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | |                all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | |                all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | |              & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | |                all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10764) gives:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | |   (10765)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | |            all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | |              all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_7)
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10765) implies:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | |   (10766)  op(e3, e2) = all_52_3
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | |   (10767)  op(all_52_3, all_52_3) = e2
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10763) gives:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | |   (10768)   ~ (all_44_0 = e1) & op(all_44_1, e2) = all_44_0 &
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = all_44_1 & $i(all_44_0) &
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_44_1)
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10768) implies:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | |   (10769)  op(e2, e3) = all_44_1
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10083), (10749), (10754), (10757), (10766),
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | |            (10767), (10769), (function-axioms) are
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #231.
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | |   (10770)   ~ (all_44_1 = e0) & op(e2, e3) = all_44_1 &
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_44_1)
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10770) implies:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | |   (10771)  op(e2, e3) = all_44_1
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10083), (10749), (10754), (10757), (10766),
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | |            (10767), (10771), (function-axioms) are
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #231.
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | |   (10772)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | |            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | |              all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_15)
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10772) implies:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | |   (10773)  op(e2, e3) = all_52_9
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | |   (10774)  op(all_52_9, all_52_9) = e3
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10083) gives:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | |   (10775)   ~ (all_8_0 = e0) & op(all_8_1, e2) = all_8_0 &
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e3) = all_8_1 & $i(all_8_0) & $i(all_8_1)
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10775) implies:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | |   (10776)  op(e2, e3) = all_8_1
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10346) gives:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_52_9,
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (10754), (10773) gives:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10777)  all_52_9 = e1
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_1,
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_9, e3, e2, simplifying with (10773),
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | | |              (10776) gives:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10778)  all_52_9 = all_8_1
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10777), (10778) imply:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10779)  all_8_1 = e1
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10774), (10777) imply:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10780)  op(e1, e1) = e3
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (374), (10780), (function-axioms) are
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2468.
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10781)   ~ (all_28_1 = e1) & op(e3, e2) = all_28_1 &
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_28_1)
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10757), (10781), (function-axioms) are
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1249.
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | |   (10782)   ~ (all_8_1 = e1) & op(e2, e3) = all_8_1 &
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_8_1)
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10782) implies:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | |   (10783)   ~ (all_8_1 = e1)
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | |   (10784)  op(e2, e3) = all_8_1
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_52_9,
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (10754), (10773) gives:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | |   (10785)  all_52_9 = e1
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_1,
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_9, e3, e2, simplifying with (10773),
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | |              (10784) gives:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | |   (10786)  all_52_9 = all_8_1
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10785), (10786) imply:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | |   (10787)  all_8_1 = e1
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10783), (10787) imply:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | |   (10788)  $false
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (10788) is inconsistent.
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | |   (10789)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | |              & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | |              & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | |                all_52_21) = e1 & op(all_52_23, all_52_23) =
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | |              all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | |              = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | |              & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(all_52_25, all_52_25) = e3 &
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | |              op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | |                all_52_29) = e1 & op(all_52_31, all_52_31) =
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | |              all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | |              = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_29) & $i(all_52_31))
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10789) gives:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | |   (10790)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | |            all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | |              all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | |            & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_23)
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10790) implies:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | |   (10791)  op(e1, e2) = all_52_19
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | |   (10792)  op(all_52_19, all_52_19) = e2
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (196), (256), (10083), (10087), (10095),
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | |            (10748), (10754), (10763), (10791), (10792),
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | |            #244.
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | |   (10793)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | |            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | |              all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | |            & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_31)
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10793) implies:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | |   (10794)  op(e0, e0) = all_52_31
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | |   (10795)  op(all_52_31, all_52_31) = e0
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (10343), (10735), (10794), (10795),
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | |            #2086.
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | |   (10796)  all_57_3 = e1 & op(e2, e2) = e1
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | ALPHA: (10796) implies:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | |   (10797)  op(e2, e2) = e1
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10095), (10797), (function-axioms) are
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1912.
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | |   (10798)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | BETA: splitting (10798) gives:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | |   (10799)  all_57_7 = e1 & op(e1, e2) = e1
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (10748), (10799), (function-axioms) are
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2265.
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | |   (10800)  all_57_13 = e1 & op(e0, e2) = e1
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (10731), (10800), (function-axioms) are
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #330.
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.09  | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | |   (10801)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 223.10/38.09  | | | | | | | | | | | | | | | | | |              e1 & op(e0, e3) = e1)
% 223.10/38.09  | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | BETA: splitting (10801) gives:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | |   (10802)  all_57_6 = e1 & op(e1, e3) = e1
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (10747), (10802), (function-axioms) are
% 223.10/38.09  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #316.
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | |   (10803)  all_57_12 = e1 & op(e0, e3) = e1
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (10730), (10803), (function-axioms) are
% 223.10/38.09  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1947.
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.09  | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | End of split
% 223.10/38.09  | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.09  | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | |   (10804)  all_55_10 = e0
% 223.10/38.09  | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (10343), (10804) are inconsistent by
% 223.10/38.09  | | | | | | | | | | | | | | | | |            sub-proof #2118.
% 223.10/38.09  | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | End of split
% 223.10/38.09  | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | End of split
% 223.10/38.09  | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | End of split
% 223.10/38.09  | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | Case 2:
% 223.10/38.09  | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | |   (10805)  all_38_2 = e2
% 223.10/38.09  | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | COMBINE_EQS: (249), (10805) imply:
% 223.10/38.09  | | | | | | | | | | | | | |   (10806)  all_6_2 = e2
% 223.10/38.09  | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | REDUCE: (374), (10806) imply:
% 223.10/38.09  | | | | | | | | | | | | | |   (10807)   ~ (e3 = e2)
% 223.10/38.09  | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | REDUCE: (39), (10806) imply:
% 223.10/38.09  | | | | | | | | | | | | | |   (10808)  op(e1, e1) = e2
% 223.10/38.09  | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 223.10/38.09  | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | Case 1:
% 223.10/38.09  | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | |   (10809)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 223.10/38.09  | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 223.10/38.09  | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | BETA: splitting (10809) gives:
% 223.10/38.09  | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | Case 1:
% 223.10/38.09  | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | |   (10810)  all_57_9 = e2 & op(e3, e0) = e2
% 223.10/38.09  | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | ALPHA: (10810) implies:
% 223.10/38.09  | | | | | | | | | | | | | | | |   (10811)  op(e3, e0) = e2
% 223.10/38.09  | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | REF_CLOSE: (169), (10340), (10811), (function-axioms) are
% 223.10/38.09  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2331.
% 223.10/38.09  | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | Case 2:
% 223.10/38.09  | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | |   (10812)  all_57_10 = e2 & op(e2, e0) = e2
% 223.10/38.09  | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | ALPHA: (10812) implies:
% 223.10/38.09  | | | | | | | | | | | | | | | |   (10813)  op(e2, e0) = e2
% 223.10/38.09  | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_13,
% 223.10/38.09  | | | | | | | | | | | | | | | |              e2, e0, e2, simplifying with (165), (10813) gives:
% 223.10/38.09  | | | | | | | | | | | | | | | |   (10814)  all_53_13 = e2
% 223.10/38.09  | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 223.10/38.09  | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.09  | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | |   (10815)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 223.10/38.09  | | | | | | | | | | | | | | | | |              all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 223.10/38.09  | | | | | | | | | | | | | | | | |              op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 223.10/38.09  | | | | | | | | | | | | | | | | |                all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 223.10/38.09  | | | | | | | | | | | | | | | | |              op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 223.10/38.09  | | | | | | | | | | | | | | | | |              op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 223.10/38.09  | | | | | | | | | | | | | | | | |              $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 223.10/38.09  | | | | | | | | | | | | | | | | |              $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 223.10/38.09  | | | | | | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 223.10/38.09  | | | | | | | | | | | | | | | | |                all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 223.10/38.09  | | | | | | | | | | | | | | | | |              & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 223.10/38.09  | | | | | | | | | | | | | | | | |                all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 223.10/38.09  | | | | | | | | | | | | | | | | |              op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 223.10/38.09  | | | | | | | | | | | | | | | | |              & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 223.10/38.09  | | | | | | | | | | | | | | | | |              $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 223.10/38.09  | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | BETA: splitting (10815) gives:
% 223.10/38.09  | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | |   (10816)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 223.10/38.09  | | | | | | | | | | | | | | | | | |            all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 223.10/38.09  | | | | | | | | | | | | | | | | | |            op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 223.10/38.09  | | | | | | | | | | | | | | | | | |              all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 223.10/38.09  | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 223.10/38.09  | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 223.10/38.09  | | | | | | | | | | | | | | | | | |            $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 223.10/38.09  | | | | | | | | | | | | | | | | | |            $i(all_52_7)
% 223.10/38.09  | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | ALPHA: (10816) implies:
% 223.10/38.09  | | | | | | | | | | | | | | | | | |   (10817)  op(e3, e0) = all_52_7
% 223.10/38.09  | | | | | | | | | | | | | | | | | |   (10818)  op(e3, e3) = all_52_1
% 223.10/38.09  | | | | | | | | | | | | | | | | | |   (10819)  op(all_52_7, all_52_7) = e0
% 223.10/38.09  | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_12,
% 223.10/38.09  | | | | | | | | | | | | | | | | | |              all_52_7, e0, e3, simplifying with (169), (10817)
% 223.10/38.09  | | | | | | | | | | | | | | | | | |              gives:
% 223.10/38.09  | | | | | | | | | | | | | | | | | |   (10820)  all_53_12 = all_52_7
% 223.10/38.09  | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_52_1,
% 223.10/38.09  | | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (10341), (10818) gives:
% 223.10/38.09  | | | | | | | | | | | | | | | | | |   (10821)  all_52_1 = e2
% 223.10/38.09  | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (10820) imply:
% 223.10/38.09  | | | | | | | | | | | | | | | | | |   (10822)  all_55_3 = all_52_7
% 223.10/38.09  | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | REDUCE: (10340), (10820) imply:
% 223.10/38.09  | | | | | | | | | | | | | | | | | |   (10823)   ~ (all_52_7 = e2)
% 223.10/38.09  | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | REDUCE: (10732), (10820) imply:
% 223.10/38.09  | | | | | | | | | | | | | | | | | |   (10824)   ~ (all_52_7 = e1)
% 223.10/38.09  | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | |   (10825)  all_55_3 = e3
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10822), (10825) imply:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | |   (10826)  all_52_7 = e3
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | SIMP: (10826) implies:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | |   (10827)  all_52_7 = e3
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | REDUCE: (10819), (10827) imply:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | |   (10828)  op(e3, e3) = e0
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10341), (10828), (function-axioms) are
% 223.10/38.09  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2403.
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | |   (10829)  all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10735), (10817), (10819), (10822), (10823),
% 223.10/38.09  | | | | | | | | | | | | | | | | | | |            (10824), (10829), (function-axioms) are
% 223.10/38.09  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #230.
% 223.10/38.09  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.09  | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | |   (10830)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 223.10/38.09  | | | | | | | | | | | | | | | | | |            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 223.10/38.09  | | | | | | | | | | | | | | | | | |            op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 223.10/38.09  | | | | | | | | | | | | | | | | | |              all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 223.10/38.09  | | | | | | | | | | | | | | | | | |            & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 223.10/38.09  | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 223.10/38.09  | | | | | | | | | | | | | | | | | |            $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 223.10/38.09  | | | | | | | | | | | | | | | | | |            $i(all_52_15)
% 223.10/38.09  | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | ALPHA: (10830) implies:
% 223.10/38.09  | | | | | | | | | | | | | | | | | |   (10831)  op(e2, e0) = all_52_15
% 223.10/38.09  | | | | | | | | | | | | | | | | | |   (10832)  op(e2, e2) = all_52_11
% 223.10/38.09  | | | | | | | | | | | | | | | | | |   (10833)  op(all_52_15, all_52_15) = e0
% 223.10/38.09  | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10095), (10813), (10831), (10832), (10833),
% 223.10/38.09  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.09  | | | | | | | | | | | | | | | | | |            #248.
% 223.10/38.09  | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | End of split
% 223.10/38.09  | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.09  | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | |   (10834)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 223.10/38.09  | | | | | | | | | | | | | | | | |              & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 223.10/38.09  | | | | | | | | | | | | | | | | |              & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 223.10/38.09  | | | | | | | | | | | | | | | | |                all_52_21) = e1 & op(all_52_23, all_52_23) =
% 223.10/38.09  | | | | | | | | | | | | | | | | |              e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 223.10/38.09  | | | | | | | | | | | | | | | | |              all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 223.10/38.09  | | | | | | | | | | | | | | | | |              = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 223.10/38.09  | | | | | | | | | | | | | | | | |              $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 223.10/38.09  | | | | | | | | | | | | | | | | |              & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 223.10/38.09  | | | | | | | | | | | | | | | | |              e0 & op(all_52_25, all_52_25) = e3 &
% 223.10/38.09  | | | | | | | | | | | | | | | | |              op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 223.10/38.09  | | | | | | | | | | | | | | | | |                all_52_29) = e1 & op(all_52_31, all_52_31) =
% 223.10/38.09  | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 223.10/38.09  | | | | | | | | | | | | | | | | |              all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 223.10/38.09  | | | | | | | | | | | | | | | | |              = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 223.10/38.09  | | | | | | | | | | | | | | | | |              $i(all_52_29) & $i(all_52_31))
% 223.10/38.09  | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | BETA: splitting (10834) gives:
% 223.10/38.09  | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | |   (10835)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 223.10/38.09  | | | | | | | | | | | | | | | | | |            all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 223.10/38.09  | | | | | | | | | | | | | | | | | |            op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 223.10/38.09  | | | | | | | | | | | | | | | | | |              all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 223.10/38.09  | | | | | | | | | | | | | | | | | |            & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 223.10/38.09  | | | | | | | | | | | | | | | | | |            & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 223.10/38.09  | | | | | | | | | | | | | | | | | |            & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 223.10/38.09  | | | | | | | | | | | | | | | | | |            $i(all_52_23)
% 223.10/38.09  | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10095), (10808), (10835), (function-axioms)
% 223.10/38.09  | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #236.
% 223.10/38.09  | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.09  | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | |   (10836)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 223.10/38.09  | | | | | | | | | | | | | | | | | |            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 223.10/38.09  | | | | | | | | | | | | | | | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 223.10/38.09  | | | | | | | | | | | | | | | | | |              all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 223.10/38.09  | | | | | | | | | | | | | | | | | |            & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 223.10/38.09  | | | | | | | | | | | | | | | | | |            & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 223.10/38.09  | | | | | | | | | | | | | | | | | |            & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 223.10/38.09  | | | | | | | | | | | | | | | | | |            $i(all_52_31)
% 223.10/38.09  | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | ALPHA: (10836) implies:
% 223.10/38.09  | | | | | | | | | | | | | | | | | |   (10837)  op(e0, e0) = all_52_31
% 223.10/38.09  | | | | | | | | | | | | | | | | | |   (10838)  op(all_52_31, all_52_31) = e0
% 223.10/38.09  | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (10343), (10735), (10837), (10838),
% 223.10/38.09  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.09  | | | | | | | | | | | | | | | | | |            #2086.
% 223.10/38.09  | | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | | End of split
% 223.10/38.09  | | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | End of split
% 223.10/38.09  | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | End of split
% 223.10/38.09  | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | Case 2:
% 223.10/38.09  | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | |   (10839)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 223.10/38.09  | | | | | | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 223.10/38.09  | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | BETA: splitting (10839) gives:
% 223.10/38.09  | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | Case 1:
% 223.10/38.09  | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | |   (10840)  all_57_11 = e2 & op(e1, e0) = e2
% 223.10/38.09  | | | | | | | | | | | | | | | | 
% 223.10/38.09  | | | | | | | | | | | | | | | | ALPHA: (10840) implies:
% 223.10/38.10  | | | | | | | | | | | | | | | |   (10841)  all_57_11 = e2
% 223.10/38.10  | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 223.10/38.10  | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.10  | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | |   (10842)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 223.10/38.10  | | | | | | | | | | | | | | | | |              & op(e1, e2) = e3)
% 223.10/38.10  | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | BETA: splitting (10842) gives:
% 223.10/38.10  | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.10  | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | |   (10843)  all_57_6 = e3 & op(e1, e3) = e3
% 223.10/38.10  | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | ALPHA: (10843) implies:
% 223.10/38.10  | | | | | | | | | | | | | | | | | |   (10844)  all_57_6 = e3
% 223.10/38.10  | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (214), (215),
% 223.10/38.10  | | | | | | | | | | | | | | | | | |            (217), (374), (10343), (10808), (10841), (10844),
% 223.10/38.10  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.10  | | | | | | | | | | | | | | | | | |            #229.
% 223.10/38.10  | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.10  | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | |   (10845)  all_57_7 = e3 & op(e1, e2) = e3
% 223.10/38.10  | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (10087), (10845), (function-axioms) are
% 223.10/38.10  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #267.
% 223.10/38.10  | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | End of split
% 223.10/38.10  | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.10  | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | |   (10846)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 223.10/38.10  | | | | | | | | | | | | | | | | |              e3 & op(e1, e0) = e3)
% 223.10/38.10  | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (39), (374), (10841), (10846),
% 223.10/38.10  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.10  | | | | | | | | | | | | | | | | |            #2040.
% 223.10/38.10  | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | End of split
% 223.10/38.10  | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | Case 2:
% 223.10/38.10  | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | |   (10847)  all_57_15 = e2 & op(e0, e0) = e2
% 223.10/38.10  | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | ALPHA: (10847) implies:
% 223.10/38.10  | | | | | | | | | | | | | | | |   (10848)  op(e0, e0) = e2
% 223.10/38.10  | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10735), (10848), (function-axioms) are
% 223.10/38.10  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2177.
% 223.10/38.10  | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | End of split
% 223.10/38.10  | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | End of split
% 223.10/38.10  | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | End of split
% 223.10/38.10  | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | End of split
% 223.10/38.10  | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | End of split
% 223.10/38.10  | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | Case 2:
% 223.10/38.10  | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | |   (10849)  all_24_2 = e0
% 223.10/38.10  | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | COMBINE_EQS: (315), (10849) imply:
% 223.10/38.10  | | | | | | | | | | |   (10850)  all_6_2 = e0
% 223.10/38.10  | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | SIMP: (10850) implies:
% 223.10/38.10  | | | | | | | | | | |   (10851)  all_6_2 = e0
% 223.10/38.10  | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | COMBINE_EQS: (311), (10851) imply:
% 223.10/38.10  | | | | | | | | | | |   (10852)  all_34_2 = e0
% 223.10/38.10  | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | REDUCE: (350), (10851) imply:
% 223.10/38.10  | | | | | | | | | | |   (10853)   ~ (all_53_2 = e0)
% 223.10/38.10  | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | REDUCE: (361), (10851) imply:
% 223.10/38.10  | | | | | | | | | | |   (10854)   ~ (all_53_6 = e0)
% 223.10/38.10  | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | REDUCE: (363), (10851) imply:
% 223.10/38.10  | | | | | | | | | | |   (10855)   ~ (all_53_8 = e0)
% 223.10/38.10  | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | REDUCE: (364), (10851) imply:
% 223.10/38.10  | | | | | | | | | | |   (10856)   ~ (all_53_9 = e0)
% 223.10/38.10  | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | REDUCE: (366), (10851) imply:
% 223.10/38.10  | | | | | | | | | | |   (10857)   ~ (all_53_11 = e0)
% 223.10/38.10  | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | REDUCE: (368), (10851) imply:
% 223.10/38.10  | | | | | | | | | | |   (10858)   ~ (all_53_14 = e0)
% 223.10/38.10  | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | REDUCE: (374), (10851) imply:
% 223.10/38.10  | | | | | | | | | | |   (10859)   ~ (e3 = e0)
% 223.10/38.10  | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | BETA: splitting (214) gives:
% 223.10/38.10  | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | Case 1:
% 223.10/38.10  | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | |   (10860)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 223.10/38.10  | | | | | | | | | | | |              & op(e1, e2) = e0)
% 223.10/38.10  | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | REF_CLOSE: (163), (164), (10853), (10854), (10860),
% 223.10/38.10  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.10  | | | | | | | | | | | |            #2038.
% 223.10/38.10  | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | Case 2:
% 223.10/38.10  | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | |   (10861)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 223.10/38.10  | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 223.10/38.10  | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | BETA: splitting (10861) gives:
% 223.10/38.10  | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | Case 1:
% 223.10/38.10  | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | |   (10862)  all_57_8 = e0 & op(e1, e1) = e0
% 223.10/38.10  | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | ALPHA: (10862) implies:
% 223.10/38.10  | | | | | | | | | | | | |   (10863)  all_57_8 = e0
% 223.10/38.10  | | | | | | | | | | | | |   (10864)  op(e1, e1) = e0
% 223.10/38.10  | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | BETA: splitting (73) gives:
% 223.10/38.10  | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | Case 1:
% 223.10/38.10  | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | |   (10865)   ~ (all_28_2 = e2)
% 223.10/38.10  | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | REDUCE: (10334), (10865) imply:
% 223.10/38.10  | | | | | | | | | | | | | |   (10866)  $false
% 223.10/38.10  | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | CLOSE: (10866) is inconsistent.
% 223.10/38.10  | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | Case 2:
% 223.10/38.10  | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | |   (10867)  ( ~ (all_28_0 = e0) & op(all_28_1, e3) = all_28_0
% 223.10/38.10  | | | | | | | | | | | | | |              & op(e3, e2) = all_28_1 & $i(all_28_0) &
% 223.10/38.10  | | | | | | | | | | | | | |              $i(all_28_1)) | ( ~ (all_28_1 = e1) & op(e3, e2)
% 223.10/38.10  | | | | | | | | | | | | | |              = all_28_1 & $i(all_28_1))
% 223.10/38.10  | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | BETA: splitting (76) gives:
% 223.10/38.10  | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | Case 1:
% 223.10/38.10  | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | |   (10868)   ~ (all_30_2 = e1)
% 223.10/38.10  | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | REDUCE: (330), (10868) imply:
% 223.10/38.10  | | | | | | | | | | | | | | |   (10869)   ~ (all_4_2 = e1)
% 223.10/38.10  | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 223.10/38.10  | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | Case 1:
% 223.10/38.10  | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | |   (10870)  all_55_15 = e3
% 223.10/38.10  | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | REF_CLOSE: (244), (10098), (10870) are inconsistent by
% 223.10/38.10  | | | | | | | | | | | | | | | |            sub-proof #2503.
% 223.10/38.10  | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | Case 2:
% 223.10/38.10  | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | |   (10871)   ~ (all_55_15 = e3)
% 223.10/38.10  | | | | | | | | | | | | | | | |   (10872)  all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 223.10/38.10  | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | BETA: splitting (10872) gives:
% 223.10/38.10  | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.10  | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | |   (10873)  all_55_15 = e2
% 223.10/38.10  | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (373), (10873) are inconsistent by
% 223.10/38.10  | | | | | | | | | | | | | | | | |            sub-proof #2502.
% 223.10/38.10  | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.10  | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | |   (10874)   ~ (all_55_15 = e2)
% 223.10/38.10  | | | | | | | | | | | | | | | | |   (10875)  all_55_15 = e1 | all_55_15 = e0
% 223.10/38.10  | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | BETA: splitting (10875) gives:
% 223.10/38.10  | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.10  | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | |   (10876)  all_55_15 = e1
% 223.10/38.10  | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (10869), (10876) are inconsistent by
% 223.10/38.10  | | | | | | | | | | | | | | | | | |            sub-proof #2501.
% 223.10/38.10  | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.10  | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | |   (10877)  all_55_15 = e0
% 223.10/38.10  | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (10877) imply:
% 223.10/38.10  | | | | | | | | | | | | | | | | | |   (10878)  all_4_2 = e0
% 223.10/38.10  | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | SIMP: (10878) implies:
% 223.10/38.10  | | | | | | | | | | | | | | | | | |   (10879)  all_4_2 = e0
% 223.10/38.10  | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | REDUCE: (351), (10879) imply:
% 223.10/38.10  | | | | | | | | | | | | | | | | | |   (10880)   ~ (all_53_3 = e0)
% 223.10/38.10  | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | REDUCE: (362), (10879) imply:
% 223.10/38.10  | | | | | | | | | | | | | | | | | |   (10881)   ~ (all_53_7 = e0)
% 223.10/38.10  | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | REDUCE: (373), (10879) imply:
% 223.10/38.10  | | | | | | | | | | | | | | | | | |   (10882)   ~ (e2 = e0)
% 223.10/38.10  | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | REDUCE: (10869), (10879) imply:
% 223.10/38.10  | | | | | | | | | | | | | | | | | |   (10883)   ~ (e1 = e0)
% 223.10/38.10  | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | REDUCE: (36), (10879) imply:
% 223.10/38.10  | | | | | | | | | | | | | | | | | |   (10884)  op(e0, e0) = e0
% 223.10/38.10  | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 223.10/38.10  | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | |   (10885)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 223.10/38.10  | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e0)
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | BETA: splitting (10885) gives:
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | |   (10886)  all_57_0 = e0 & op(e3, e3) = e0
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | ALPHA: (10886) implies:
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | |   (10887)  op(e3, e3) = e0
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10341), (10887), (function-axioms) are
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2403.
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | |   (10888)  all_57_2 = e0 & op(e2, e3) = e0
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | ALPHA: (10888) implies:
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | |   (10889)  all_57_2 = e0
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | |   (10890)  op(e2, e3) = e0
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | |   (10891)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10891) gives:
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | |   (10892)  all_57_1 = e0 & op(e3, e2) = e0
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10892) implies:
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | |   (10893)  op(e3, e2) = e0
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | |   (10894)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | |              all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | |              op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | |                all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | |                all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | |              & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | |                all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10894) gives:
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | |   (10895)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | |            all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | |              all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_7)
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10895) implies:
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | |   (10896)  op(e3, e2) = all_52_3
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | |   (10897)  op(all_52_3, all_52_3) = e2
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (36), (159), (163), (165), (166),
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | |            (222), (223), (224), (225), (226), (244), (362),
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | |            (371), (373), (10094), (10098), (10854), (10856),
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | |            (10869), (10875), (10896), (10897),
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | |            #228.
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | |   (10898)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | |            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | |              all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_15)
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10898) implies:
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | |   (10899)  op(e2, e3) = all_52_9
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | |   (10900)  op(all_52_9, all_52_9) = e3
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (160), (164), (168), (190), (230), (244),
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | |            (351), (373), (10098), (10341), (10853), (10869),
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | |            (10899), (10900), (function-axioms) are
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1570.
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | |   (10901)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | |              & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | |              & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | |                all_52_21) = e1 & op(all_52_23, all_52_23) =
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | |              all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | |              = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | |              & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(all_52_25, all_52_25) = e3 &
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | |              op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | |                all_52_29) = e1 & op(all_52_31, all_52_31) =
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | |              all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | |              = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_29) & $i(all_52_31))
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10901) gives:
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | |   (10902)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | |            all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | |              all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | |            & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_23)
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10902) implies:
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | |   (10903)  op(e1, e1) = all_52_21
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | |   (10904)  op(all_52_21, all_52_21) = e1
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (10083), (10864), (10884), (10890), (10903),
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | |            (10904), (function-axioms) are inconsistent by
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #227.
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | |   (10905)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | |            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | |              all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | |            & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_31)
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10905) implies:
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | |   (10906)  op(e0, e3) = all_52_25
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | |   (10907)  op(all_52_25, all_52_25) = e3
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (171), (193), (247), (10332), (10337),
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | |            (10341), (10867), (10880), (10893), (10906),
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | |            (10907), (function-axioms) are inconsistent by
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1567.
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | |   (10908)  all_57_3 = e0 & op(e2, e2) = e0
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10908) implies:
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | |   (10909)  all_57_3 = e0
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | |            (10889), (10909) are inconsistent by sub-proof
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | |            #2246.
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | |   (10910)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0)
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (163), (10854), (10881), (10910),
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | |            #2024.
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | |   (10911)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 223.10/38.10  | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = e0)
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (164), (10853), (10880), (10911),
% 223.10/38.10  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.10  | | | | | | | | | | | | | | | | | | |            #1859.
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.10  | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | End of split
% 223.10/38.10  | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | End of split
% 223.10/38.10  | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | End of split
% 223.10/38.10  | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | Case 2:
% 223.10/38.10  | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | |   (10912)  all_30_2 = e1
% 223.10/38.10  | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | COMBINE_EQS: (330), (10912) imply:
% 223.10/38.10  | | | | | | | | | | | | | | |   (10913)  all_4_2 = e1
% 223.10/38.10  | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | SIMP: (10913) implies:
% 223.10/38.10  | | | | | | | | | | | | | | |   (10914)  all_4_2 = e1
% 223.10/38.10  | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | REDUCE: (351), (10914) imply:
% 223.10/38.10  | | | | | | | | | | | | | | |   (10915)   ~ (all_53_3 = e1)
% 223.10/38.10  | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | REDUCE: (362), (10914) imply:
% 223.10/38.10  | | | | | | | | | | | | | | |   (10916)   ~ (all_53_7 = e1)
% 223.10/38.10  | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | REDUCE: (369), (10914) imply:
% 223.10/38.10  | | | | | | | | | | | | | | |   (10917)   ~ (all_53_11 = e1)
% 223.10/38.10  | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | REDUCE: (370), (10914) imply:
% 223.10/38.10  | | | | | | | | | | | | | | |   (10918)   ~ (all_53_12 = e1)
% 223.10/38.10  | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | REDUCE: (372), (10914) imply:
% 223.10/38.10  | | | | | | | | | | | | | | |   (10919)   ~ (all_53_14 = e1)
% 223.10/38.10  | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | REDUCE: (10098), (10914) imply:
% 223.10/38.10  | | | | | | | | | | | | | | |   (10920)   ~ (e3 = e1)
% 223.10/38.10  | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | REDUCE: (373), (10914) imply:
% 223.10/38.10  | | | | | | | | | | | | | | |   (10921)   ~ (e2 = e1)
% 223.10/38.10  | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | REDUCE: (36), (10914) imply:
% 223.10/38.10  | | | | | | | | | | | | | | |   (10922)  op(e0, e0) = e1
% 223.10/38.10  | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | BETA: splitting (82) gives:
% 223.10/38.10  | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | Case 1:
% 223.10/38.10  | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | |   (10923)   ~ (all_34_2 = e0)
% 223.10/38.10  | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | REDUCE: (10852), (10923) imply:
% 223.10/38.10  | | | | | | | | | | | | | | | |   (10924)  $false
% 223.10/38.10  | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | CLOSE: (10924) is inconsistent.
% 223.10/38.10  | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | Case 2:
% 223.10/38.10  | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | |   (10925)  ( ~ (all_34_0 = e3) & op(all_34_1, e1) = all_34_0
% 223.10/38.10  | | | | | | | | | | | | | | | |              & op(e1, e0) = all_34_1 & $i(all_34_0) &
% 223.10/38.10  | | | | | | | | | | | | | | | |              $i(all_34_1)) | ( ~ (all_34_1 = e2) & op(e1, e0)
% 223.10/38.10  | | | | | | | | | | | | | | | |              = all_34_1 & $i(all_34_1))
% 223.10/38.10  | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 223.10/38.10  | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.10  | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | |   (10926)  all_55_14 = e3
% 223.10/38.10  | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (10926) imply:
% 223.10/38.10  | | | | | | | | | | | | | | | | |   (10927)  all_53_11 = e3
% 223.10/38.10  | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | REDUCE: (140), (10927) imply:
% 223.10/38.10  | | | | | | | | | | | | | | | | |   (10928)   ~ (all_53_3 = e3)
% 223.10/38.10  | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 223.10/38.10  | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.10  | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | |   (10929)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 223.10/38.10  | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e2)
% 223.10/38.10  | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | BETA: splitting (10929) gives:
% 223.10/38.10  | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | |   (10930)  all_57_4 = e2 & op(e3, e1) = e2
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (237),
% 223.10/38.10  | | | | | | | | | | | | | | | | | | |            (10341), (10930), (function-axioms) are
% 223.10/38.10  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #226.
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | |   (10931)  all_57_5 = e2 & op(e2, e1) = e2
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | ALPHA: (10931) implies:
% 223.10/38.10  | | | | | | | | | | | | | | | | | | |   (10932)  all_57_5 = e2
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | |   (10933)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e3)
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | BETA: splitting (10933) gives:
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | |   (10934)  all_57_4 = e3 & op(e3, e1) = e3
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | ALPHA: (10934) implies:
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | |   (10935)  all_57_4 = e3
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | |   (10936)  all_55_12 = e3
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (10936) imply:
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | |   (10937)  all_53_3 = e3
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10928), (10937) imply:
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | |   (10938)  $false
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (10938) is inconsistent.
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | |   (10939)   ~ (all_55_12 = e3)
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | |   (10940)  all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10940) gives:
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | |   (10941)  all_55_12 = e2
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (10941) imply:
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | |   (10942)  all_53_3 = e2
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10337), (10942) imply:
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | |   (10943)  $false
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (10943) is inconsistent.
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | |   (10944)   ~ (all_55_12 = e2)
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | |   (10945)  all_55_12 = e1 | all_55_12 = e0
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | |   (10946)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e3)
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (168), (10085), (10341), (10946),
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | |            #241.
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | |   (10947)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e3) = e3)
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10947) gives:
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | | |   (10948)  all_57_6 = e3 & op(e1, e3) = e3
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10948) implies:
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | | |   (10949)  all_57_6 = e3
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (39), (158), (161),
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | | |            (215), (216), (217), (219), (374), (10863),
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | | |            (10864), (10917), (10919), (10932), (10935),
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | | |            (10949), (function-axioms) are inconsistent by
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #222.
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | | |   (10950)  all_57_12 = e3 & op(e0, e3) = e3
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (145), (149), (164), (168), (193),
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (247), (10337), (10341), (10915), (10928),
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | | |            (10945), (10950), (function-axioms) are
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #219.
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | |   (10951)  all_57_5 = e3 & op(e2, e1) = e3
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (10089), (10951), (function-axioms) are
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #270.
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | |   (10952)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e1) = e3)
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | BETA: splitting (10952) gives:
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | |   (10953)  all_57_8 = e3 & op(e1, e1) = e3
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.10  | | | | | | | | | | | | | | | | | | | | | ALPHA: (10953) implies:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | |   (10954)  op(e1, e1) = e3
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (374), (10954), (function-axioms) are
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2468.
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | |   (10955)  all_57_14 = e3 & op(e0, e1) = e3
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | ALPHA: (10955) implies:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | |   (10956)  all_57_14 = e3
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | |   (10957)  all_55_12 = e3
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (10957) imply:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | |   (10958)  all_53_3 = e3
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10928), (10958) imply:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | |   (10959)  $false
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (10959) is inconsistent.
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | |   (10960)   ~ (all_55_12 = e3)
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | |   (10961)  all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10961) gives:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | |   (10962)  all_55_12 = e2
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (10962) imply:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | |   (10963)  all_53_3 = e2
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10337), (10963) imply:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | |   (10964)  $false
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (10964) is inconsistent.
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | |   (10965)   ~ (all_55_12 = e2)
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | |   (10966)  all_55_12 = e1 | all_55_12 = e0
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | |   (10967)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e3)
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (168), (10085), (10341), (10967),
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | |            #241.
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | |   (10968)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e3) = e3)
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10968) gives:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | |   (10969)  all_57_6 = e3 & op(e1, e3) = e3
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10969) implies:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | |   (10970)  all_57_6 = e3
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10971)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e3)
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (171), (230), (232),
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            (234), (10086), (10970), (10971),
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            #269.
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10972)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e3)
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10972) gives:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10973)  all_57_4 = e3 & op(e3, e1) = e3
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10973) implies:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10974)  all_57_4 = e3
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (39), (158), (161),
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (215), (216), (217), (219), (374), (10863),
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10864), (10917), (10919), (10932), (10970),
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10974), (function-axioms) are inconsistent by
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #222.
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10975)  all_57_9 = e3 & op(e3, e0) = e3
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10975) implies:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10976)  op(e3, e0) = e3
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10977)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e1)
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10977) gives:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10978)  all_57_6 = e1 & op(e1, e3) = e1
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10970), (10978) are inconsistent by
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2117.
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10979)  all_57_7 = e1 & op(e1, e2) = e1
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10979) implies:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10980)  all_57_7 = e1
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10981)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e1)
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10981) gives:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10982)  all_57_4 = e1 & op(e3, e1) = e1
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10982) implies:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10983)  all_57_4 = e1
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10984)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e2)
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10984) gives:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10985)  all_57_6 = e2 & op(e1, e3) = e2
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10985) implies:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10986)  all_57_6 = e2
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10970), (10986) imply:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10987)  e3 = e2
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10956), (10987) imply:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10988)  all_57_14 = e2
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (39), (221), (374), (10932), (10983),
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10988), (function-axioms) are inconsistent by
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1889.
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10989)  all_57_7 = e2 & op(e1, e2) = e2
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10989) implies:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10990)  all_57_7 = e2
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10980), (10990) are inconsistent by
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1761.
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10991)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e1, e0) = e2)
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10991) gives:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10992)  all_57_8 = e2 & op(e1, e1) = e2
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10863), (10992) are inconsistent by
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2005.
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10993)  all_57_11 = e2 & op(e1, e0) = e2
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10993) implies:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10994)  all_57_11 = e2
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10995)  op(e1, e0) = e2
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10996)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10996) gives:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10997)  all_57_12 = e2 & op(e0, e3) = e2
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10997) implies:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10998)  op(e0, e3) = e2
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (10337), (10998), (function-axioms) are
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1980.
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10999)  all_57_13 = e2 & op(e0, e2) = e2
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10999) implies:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11000)  all_57_13 = e2
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11001)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11001) gives:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11002)  all_57_1 = e0 & op(e3, e2) = e0
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11002) implies:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11003)  all_57_1 = e0
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11004)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e0)
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (149), (168), (247), (10341), (10915),
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10966), (11004), (function-axioms) are
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #220.
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11005)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = e0)
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11005) gives:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11006)  all_57_6 = e0 & op(e1, e3) = e0
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11006) implies:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11007)  all_57_6 = e0
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (39), (217), (374), (10980),
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10994), (11007), (function-axioms) are
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2114.
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11008)  all_57_12 = e0 & op(e0, e3) = e0
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11008) implies:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11009)  all_57_12 = e0
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11010)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11010) gives:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11011)  all_57_2 = e0 & op(e2, e3) = e0
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (168), (247), (10915), (10966), (11011),
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #221.
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11012)  all_57_3 = e0 & op(e2, e2) = e0
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11012) implies:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11013)  all_57_3 = e0
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11014)  op(e2, e2) = e0
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (227), (228), (229),
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11000), (11003), (11013), (11014),
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1281.
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11015)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0)
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11015) gives:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11016)  all_57_5 = e0 & op(e2, e1) = e0
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (10856), (11016), (function-axioms) are
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2023.
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11017)  all_57_10 = e0 & op(e2, e0) = e0
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11017) implies:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11018)  all_57_10 = e0
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11019)  op(e2, e0) = e0
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10966) gives:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11020)  all_55_12 = e1
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (247), (10915), (11020) are inconsistent by
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1994.
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11021)  all_55_12 = e0
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (11021) imply:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11022)  all_53_3 = e0
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (11022) implies:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11023)  all_53_3 = e0
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (11023) imply:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11024)   ~ (all_53_1 = e0)
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10915), (11023) imply:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11025)   ~ (e1 = e0)
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (160), (11023) imply:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11026)  op(e0, e3) = e0
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11027)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11027) gives:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11028)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_7)
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11028) implies:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11029)  op(e3, e0) = all_52_7
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11030)  op(e3, e3) = all_52_1
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11031)  op(all_52_7, all_52_7) = e0
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11032)  op(all_52_1, all_52_1) = e3
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10925) gives:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_52_7,
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e3, simplifying with (10976), (11029) gives:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11033)  all_52_7 = e3
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11031), (11033) imply:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11034)  op(e3, e3) = e0
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (161), (169), (211), (10918), (10919),
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11018), (11030), (11032), (11034),
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #217.
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11035)   ~ (all_34_1 = e2) & op(e1, e0) = all_34_1 &
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_34_1)
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11035) implies:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11036)   ~ (all_34_1 = e2)
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11037)  op(e1, e0) = all_34_1
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10995), (11036), (11037), (function-axioms) are
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1190.
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11038)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_15)
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11038) implies:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11039)  op(e2, e0) = all_52_15
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11040)  op(all_52_15, all_52_15) = e0
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (161), (169), (211), (10918), (10919),
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11018), (11019), (11039), (11040),
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #216.
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11041)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_52_21) = e1 & op(all_52_23, all_52_23) =
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(all_52_25, all_52_25) = e3 &
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_52_29) = e1 & op(all_52_31, all_52_31) =
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_29) & $i(all_52_31))
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11041) gives:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11042)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_23)
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11042) implies:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11043)  op(e1, e3) = all_52_17
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11044)  op(all_52_17, all_52_17) = e3
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (150), (164), (190), (197), (201), (244),
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (257), (267), (374), (10098), (10335), (10336),
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10341), (10853), (11024), (11043), (11044),
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1864.
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11045)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_31)
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11045) implies:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11046)  op(e0, e0) = all_52_31
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11047)  op(e0, e3) = all_52_25
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11048)  op(all_52_25, all_52_25) = e3
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (160), (208), (209),
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (210), (10337), (10922), (11009), (11026),
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11046), (11047), (11048), (function-axioms) are
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1962.
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11049)  all_57_3 = e0 & op(e2, e2) = e0
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11049) implies:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11050)  all_57_3 = e0
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10094), (11050) imply:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11051)  e3 = e0
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10970), (11051) imply:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11052)  all_57_6 = e0
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (39), (217), (374), (10980),
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10994), (11052), (function-axioms) are
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2114.
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11053)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0)
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11053) gives:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11054)  all_57_7 = e0 & op(e1, e2) = e0
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11054) implies:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11055)  all_57_7 = e0
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (39), (215), (217),
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (374), (10864), (10994), (11055),
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1314.
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11056)  all_57_13 = e0 & op(e0, e2) = e0
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (11000), (11056) are inconsistent by
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1743.
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11057)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11057) gives:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11058)  all_57_14 = e2 & op(e0, e1) = e2
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11058) implies:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11059)  all_57_14 = e2
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (39), (221), (374), (10932), (10983),
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11059), (function-axioms) are inconsistent by
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1889.
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11060)  all_57_15 = e2 & op(e0, e0) = e2
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11060) implies:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11061)  op(e0, e0) = e2
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10922), (11061), (function-axioms) are
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2177.
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11062)  all_57_5 = e1 & op(e2, e1) = e1
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11062) implies:
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11063)  all_57_5 = e1
% 223.10/38.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10932), (11063) are inconsistent by
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1885.
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11064)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e1) = e1)
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (158), (10864), (10917), (11064),
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #224.
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11065)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e0) = e1)
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (161), (10864), (10919), (11065),
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #223.
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | |   (11066)  all_57_12 = e3 & op(e0, e3) = e3
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (145), (149), (164), (168), (193),
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (247), (10337), (10341), (10915), (10928),
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | |            (10966), (11066), (function-axioms) are
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #219.
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.12  | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | |   (11067)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 223.10/38.12  | | | | | | | | | | | | | | | | | |              e2 & op(e0, e1) = e2)
% 223.10/38.12  | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | BETA: splitting (11067) gives:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | |   (11068)  all_57_8 = e2 & op(e1, e1) = e2
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10863), (11068) are inconsistent by
% 223.10/38.12  | | | | | | | | | | | | | | | | | | |            sub-proof #2005.
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | |   (11069)  all_57_14 = e2 & op(e0, e1) = e2
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | ALPHA: (11069) implies:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | |   (11070)  all_57_14 = e2
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | |   (11071)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e3)
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | BETA: splitting (11071) gives:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | |   (11072)  all_57_4 = e3 & op(e3, e1) = e3
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | ALPHA: (11072) implies:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | |   (11073)  all_57_4 = e3
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | |   (11074)  all_55_12 = e3
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (11074) imply:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | |   (11075)  all_53_3 = e3
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10928), (11075) imply:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | |   (11076)  $false
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (11076) is inconsistent.
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | |   (11077)   ~ (all_55_12 = e3)
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | |   (11078)  all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11078) gives:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | |   (11079)  all_55_12 = e2
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (11079) imply:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | |   (11080)  all_53_3 = e2
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10337), (11080) imply:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | |   (11081)  $false
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (11081) is inconsistent.
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | |   (11082)   ~ (all_55_12 = e2)
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | |   (11083)  all_55_12 = e1 | all_55_12 = e0
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | |   (11084)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e3)
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (168), (10085), (10341), (11084),
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | |            #241.
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | |   (11085)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e3) = e3)
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11085) gives:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | |   (11086)  all_57_6 = e3 & op(e1, e3) = e3
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11086) implies:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | |   (11087)  all_57_6 = e3
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11088)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11088) gives:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11089)  all_57_12 = e3 & op(e0, e3) = e3
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (145), (149), (164), (168), (193),
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (247), (10337), (10341), (10915), (10928),
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11083), (11089), (function-axioms) are
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #219.
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11090)  all_57_13 = e3 & op(e0, e2) = e3
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11090) implies:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11091)  all_57_13 = e3
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11092)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e1)
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11092) gives:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11093)  all_57_6 = e1 & op(e1, e3) = e1
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (11087), (11093) are inconsistent by
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2117.
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11094)  all_57_7 = e1 & op(e1, e2) = e1
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11094) implies:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11095)  all_57_7 = e1
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11096)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233),
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10095), (10341), (11073), (11096),
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #235.
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11097)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11097) gives:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11098)  all_57_7 = e2 & op(e1, e2) = e2
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11098) implies:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11099)  all_57_7 = e2
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (11095), (11099) imply:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11100)  e2 = e1
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (11100) implies:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11101)  e2 = e1
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (11070), (11101) imply:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11102)  all_57_14 = e1
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (160), (209), (10337), (10922), (11091),
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11102), (function-axioms) are inconsistent by
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1967.
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11103)  all_57_13 = e2 & op(e0, e2) = e2
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11103) implies:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11104)  all_57_13 = e2
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (11091), (11104) imply:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11105)  e3 = e2
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (11073), (11105) imply:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11106)  all_57_4 = e2
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (218), (219),
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (220), (221), (374), (11070), (11106),
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2370.
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11107)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e0) = e1)
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (161), (10864), (10919), (11107),
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #223.
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11108)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (218), (219),
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | |            (220), (221), (374), (10922), (11070), (11073),
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | |            (11108), (function-axioms) are inconsistent by
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1872.
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | |   (11109)  all_57_12 = e3 & op(e0, e3) = e3
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (145), (149), (164), (168), (193),
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (247), (10337), (10341), (10915), (10928),
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | |            (11083), (11109), (function-axioms) are
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #219.
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | |   (11110)  all_57_5 = e3 & op(e2, e1) = e3
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (10089), (11110), (function-axioms) are
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #270.
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | |   (11111)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e1) = e3)
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (39), (374), (11070), (11111),
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | |            #2409.
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.12  | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | End of split
% 223.10/38.12  | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.12  | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | |   (11112)   ~ (all_55_14 = e3)
% 223.10/38.12  | | | | | | | | | | | | | | | | |   (11113)  all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 223.10/38.12  | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | REDUCE: (245), (11112) imply:
% 223.10/38.12  | | | | | | | | | | | | | | | | |   (11114)   ~ (all_53_11 = e3)
% 223.10/38.12  | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 223.10/38.12  | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | |   (11115)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 223.10/38.12  | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e3)
% 223.10/38.12  | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | BETA: splitting (11115) gives:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | |   (11116)  all_57_4 = e3 & op(e3, e1) = e3
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | ALPHA: (11116) implies:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | |   (11117)  all_57_4 = e3
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | |   (11118)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e1)
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | BETA: splitting (11118) gives:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | |   (11119)  all_57_4 = e1 & op(e3, e1) = e1
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | ALPHA: (11119) implies:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | |   (11120)  all_57_4 = e1
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (11117), (11120) are inconsistent by
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | |            sub-proof #2426.
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | |   (11121)  all_57_5 = e1 & op(e2, e1) = e1
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | ALPHA: (11121) implies:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | |   (11122)  all_57_5 = e1
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | |   (11123)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e1)
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11123) gives:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | |   (11124)  all_57_0 = e1 & op(e3, e3) = e1
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11124) implies:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | |   (11125)  op(e3, e3) = e1
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (169), (171), (235), (10338), (10340),
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | |            (11117), (11125), (function-axioms) are
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #234.
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | |   (11126)  all_57_1 = e1 & op(e3, e2) = e1
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11126) implies:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | |   (11127)  all_57_1 = e1
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | |   (11128)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (168), (10095), (10335), (11128),
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | |            #242.
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | |   (11129)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11129) gives:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | |   (11130)  all_57_5 = e2 & op(e2, e1) = e2
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11130) implies:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | |   (11131)  all_57_5 = e2
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11122), (11131) are inconsistent by
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1885.
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | |   (11132)  all_57_10 = e2 & op(e2, e0) = e2
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11132) implies:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | |   (11133)  all_57_10 = e2
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | |   (11134)  op(e2, e0) = e2
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11135)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11135) gives:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11136)  all_57_2 = e0 & op(e2, e3) = e0
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11136) implies:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11137)  all_57_2 = e0
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11138)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e2)
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11138) gives:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11139)  all_57_4 = e2 & op(e3, e1) = e2
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (237),
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10341), (11139), (function-axioms) are
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #226.
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11140)  all_57_5 = e2 & op(e2, e1) = e2
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11122), (11140) are inconsistent by
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2251.
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11141)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e1) = e2)
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11141) gives:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11142)  all_57_8 = e2 & op(e1, e1) = e2
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10863), (11142) are inconsistent by
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2005.
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11143)  all_57_14 = e2 & op(e0, e1) = e2
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11143) implies:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11144)  all_57_14 = e2
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11145)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e0)
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11145) gives:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11146)  all_57_0 = e0 & op(e3, e3) = e0
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11146) implies:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11147)  op(e3, e3) = e0
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10341), (11147), (function-axioms) are
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2403.
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11148)  all_57_1 = e0 & op(e3, e2) = e0
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11148) implies:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11149)  all_57_1 = e0
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (11127), (11149) imply:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11150)  e1 = e0
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (11122), (11150) imply:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11151)  all_57_5 = e0
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (219), (10864), (11117), (11144),
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11151), (function-axioms) are inconsistent by
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #215.
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11152)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e0)
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11152) gives:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11153)  all_57_4 = e0 & op(e3, e1) = e0
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11153) implies:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11154)  op(e3, e1) = e0
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (10855), (11154), (function-axioms) are
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2267.
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11155)  all_57_9 = e0 & op(e3, e0) = e0
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11155) implies:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11156)  all_57_9 = e0
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11157)  op(e3, e0) = e0
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11158)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e1)
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11158) gives:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11159)  all_57_0 = e1 & op(e3, e3) = e1
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11159) implies:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11160)  op(e3, e3) = e1
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (235), (11117), (11127), (11156),
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11160), (function-axioms) are inconsistent by
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #296.
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11161)  all_57_2 = e1 & op(e2, e3) = e1
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11161) implies:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11162)  all_57_2 = e1
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (11137), (11162) imply:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11163)  e1 = e0
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (11163) implies:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11164)  e1 = e0
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (11122), (11164) imply:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11165)  all_57_5 = e0
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (219), (10864), (11117), (11144),
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11165), (function-axioms) are inconsistent by
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #215.
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11166)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e3) = e1)
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11166) gives:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11167)  all_57_6 = e1 & op(e1, e3) = e1
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11167) implies:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11168)  op(e1, e3) = e1
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11113) gives:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11169)  all_55_14 = e2
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (11169) imply:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11170)  all_53_11 = e2
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (11170) implies:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11171)  all_53_11 = e2
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (126), (11171) imply:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11172)   ~ (all_53_7 = e2)
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11114), (11171) imply:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11173)   ~ (e3 = e2)
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11174)  all_55_13 = e3
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (10088), (11174) are inconsistent by
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2080.
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11175)   ~ (all_55_13 = e3)
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11176)  all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11176) gives:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11177)  all_55_13 = e2
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (11172), (11177) are inconsistent by
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2287.
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11178)   ~ (all_55_13 = e2)
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11179)  all_55_13 = e1 | all_55_13 = e0
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11179) gives:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11180)  all_55_13 = e1
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (10916), (11180) are inconsistent by
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2002.
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11181)  all_55_13 = e0
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (11181) imply:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11182)  all_53_7 = e0
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (11182) implies:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11183)  all_53_7 = e0
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (141), (11183) imply:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11184)   ~ (all_53_3 = e0)
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11172), (11183) imply:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11185)   ~ (e2 = e0)
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10916), (11183) imply:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11186)   ~ (e1 = e0)
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (159), (11183) imply:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11187)  op(e0, e2) = e0
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11188)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11188) gives:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11189)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_7)
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11189) implies:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11190)  op(e3, e0) = all_52_7
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11191)  op(all_52_7, all_52_7) = e0
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (10922), (11157), (11190), (11191),
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2000.
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11192)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_15)
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11192) implies:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11193)  op(e2, e0) = all_52_15
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11194)  op(e2, e2) = all_52_11
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11195)  op(all_52_15, all_52_15) = e0
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10095), (11134), (11193), (11194), (11195),
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #248.
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11196)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_52_21) = e1 & op(all_52_23, all_52_23) =
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(all_52_25, all_52_25) = e3 &
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_52_29) = e1 & op(all_52_31, all_52_31) =
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_29) & $i(all_52_31))
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11196) gives:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11197)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_23)
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11197) implies:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11198)  op(e1, e3) = all_52_17
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11199)  op(all_52_17, all_52_17) = e3
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (195), (336), (374), (11168), (11198),
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11199), (function-axioms) are inconsistent by
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1998.
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11200)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_31)
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11200) implies:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11201)  op(e0, e0) = all_52_31
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11202)  op(e0, e2) = all_52_27
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11203)  op(all_52_27, all_52_27) = e2
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (159), (160), (207),
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (208), (209), (210), (10915), (10922), (11172),
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11184), (11187), (11201), (11202), (11203),
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1876.
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11204)  all_55_14 = e1 | all_55_14 = e0
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (10857), (10917), (11204) are inconsistent
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1720.
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11205)  all_57_12 = e1 & op(e0, e3) = e1
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (10915), (11205), (function-axioms) are
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1947.
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11206)  all_57_3 = e0 & op(e2, e2) = e0
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11206) implies:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11207)  all_57_3 = e0
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10094), (11207) are inconsistent by
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2358.
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11208)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0)
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11208) gives:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11209)  all_57_5 = e0 & op(e2, e1) = e0
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (10856), (11209), (function-axioms) are
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2023.
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11210)  all_57_10 = e0 & op(e2, e0) = e0
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11210) implies:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11211)  all_57_10 = e0
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (11133), (11211) are inconsistent by
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2138.
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | |   (11212)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e1)
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11212) gives:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | |   (11213)  all_57_4 = e1 & op(e3, e1) = e1
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11213) implies:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | |   (11214)  all_57_4 = e1
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (11117), (11214) are inconsistent by
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2426.
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | |   (11215)  all_57_9 = e1 & op(e3, e0) = e1
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (10918), (11215), (function-axioms) are
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2131.
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | |   (11216)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e1) = e1)
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (158), (10864), (10917), (11216),
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | |            #224.
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | |   (11217)  all_57_5 = e3 & op(e2, e1) = e3
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (10089), (11217), (function-axioms) are
% 223.10/38.13  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #270.
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.13  | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | |   (11218)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 223.10/38.13  | | | | | | | | | | | | | | | | | |              e3 & op(e0, e1) = e3)
% 223.10/38.13  | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | BETA: splitting (11218) gives:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | |   (11219)  all_57_8 = e3 & op(e1, e1) = e3
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | ALPHA: (11219) implies:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | |   (11220)  op(e1, e1) = e3
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (374), (11220), (function-axioms) are
% 223.10/38.13  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2468.
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | |   (11221)  all_57_14 = e3 & op(e0, e1) = e3
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | ALPHA: (11221) implies:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | |   (11222)  all_57_14 = e3
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | |   (11223)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | BETA: splitting (11223) gives:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | |   (11224)  all_57_12 = e2 & op(e0, e3) = e2
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | ALPHA: (11224) implies:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | |   (11225)  op(e0, e3) = e2
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (10337), (11225), (function-axioms) are
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1980.
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | |   (11226)  all_57_13 = e2 & op(e0, e2) = e2
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | ALPHA: (11226) implies:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | |   (11227)  op(e0, e2) = e2
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11113) gives:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | |   (11228)  all_55_14 = e2
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (11228) imply:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | |   (11229)  all_53_11 = e2
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (126), (11229) imply:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | |   (11230)   ~ (all_53_7 = e2)
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (11227), (11230), (function-axioms) are
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2335.
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | |   (11231)  all_55_14 = e1 | all_55_14 = e0
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (10857), (10917), (11231) are inconsistent
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1720.
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | |   (11232)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (10922), (11222), (11232),
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | |            #1393.
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.13  | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | End of split
% 223.10/38.13  | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | End of split
% 223.10/38.13  | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | End of split
% 223.10/38.13  | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | End of split
% 223.10/38.13  | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | End of split
% 223.10/38.13  | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | Case 2:
% 223.10/38.13  | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | |   (11233)  all_57_11 = e0 & op(e1, e0) = e0
% 223.10/38.13  | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | REF_CLOSE: (161), (10858), (11233), (function-axioms) are
% 223.10/38.13  | | | | | | | | | | | | |            inconsistent by sub-proof #2341.
% 223.10/38.13  | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | End of split
% 223.10/38.13  | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | End of split
% 223.10/38.13  | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | End of split
% 223.10/38.13  | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | End of split
% 223.10/38.13  | | | | | | | | | 
% 223.10/38.13  | | | | | | | | Case 2:
% 223.10/38.13  | | | | | | | | | 
% 223.10/38.13  | | | | | | | | |   (11234)  all_18_2 = e0
% 223.10/38.13  | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | COMBINE_EQS: (327), (11234) imply:
% 223.10/38.13  | | | | | | | | |   (11235)  all_10_2 = e0
% 223.10/38.13  | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | SIMP: (11235) implies:
% 223.10/38.13  | | | | | | | | |   (11236)  all_10_2 = e0
% 223.10/38.13  | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | REDUCE: (338), (11236) imply:
% 223.10/38.13  | | | | | | | | |   (11237)   ~ (all_53_1 = e0)
% 223.10/38.13  | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | REDUCE: (342), (11236) imply:
% 223.10/38.13  | | | | | | | | |   (11238)   ~ (all_53_3 = e0)
% 223.10/38.13  | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | REDUCE: (344), (11236) imply:
% 223.10/38.13  | | | | | | | | |   (11239)   ~ (all_53_4 = e0)
% 223.10/38.13  | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | REDUCE: (346), (11236) imply:
% 223.10/38.13  | | | | | | | | |   (11240)   ~ (all_53_8 = e0)
% 223.10/38.13  | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | REDUCE: (348), (11236) imply:
% 223.10/38.13  | | | | | | | | |   (11241)   ~ (all_53_12 = e0)
% 223.10/38.13  | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | BETA: splitting (231) gives:
% 223.10/38.13  | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | Case 1:
% 223.10/38.13  | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | |   (11242)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 223.10/38.13  | | | | | | | | | |              & op(e3, e2) = e0)
% 223.10/38.13  | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | BETA: splitting (11242) gives:
% 223.10/38.13  | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | Case 1:
% 223.10/38.13  | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | |   (11243)  all_57_0 = e0 & op(e3, e3) = e0
% 223.10/38.13  | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | ALPHA: (11243) implies:
% 223.10/38.13  | | | | | | | | | | |   (11244)  all_57_0 = e0
% 223.10/38.13  | | | | | | | | | | |   (11245)  op(e3, e3) = e0
% 223.10/38.13  | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | BETA: splitting (67) gives:
% 223.10/38.13  | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | Case 1:
% 223.10/38.13  | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | |   (11246)   ~ (all_24_2 = e0)
% 223.10/38.13  | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | REDUCE: (315), (11246) imply:
% 223.10/38.13  | | | | | | | | | | | |   (11247)   ~ (all_6_2 = e0)
% 223.10/38.13  | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | BETA: splitting (76) gives:
% 223.10/38.13  | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | Case 1:
% 223.10/38.13  | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | |   (11248)   ~ (all_30_2 = e1)
% 223.10/38.13  | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | REDUCE: (330), (11248) imply:
% 223.10/38.13  | | | | | | | | | | | | |   (11249)   ~ (all_4_2 = e1)
% 223.10/38.13  | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | BETA: splitting (190) gives:
% 223.10/38.13  | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | Case 1:
% 223.10/38.13  | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | |   (11250)  all_55_15 = e3
% 223.10/38.13  | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | REF_CLOSE: (244), (10098), (11250) are inconsistent by
% 223.10/38.13  | | | | | | | | | | | | | |            sub-proof #2503.
% 223.10/38.13  | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | Case 2:
% 223.10/38.13  | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | |   (11251)   ~ (all_55_15 = e3)
% 223.10/38.13  | | | | | | | | | | | | | |   (11252)  all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 223.10/38.13  | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | BETA: splitting (11252) gives:
% 223.10/38.13  | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | Case 1:
% 223.10/38.13  | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | |   (11253)  all_55_15 = e2
% 223.10/38.13  | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | REF_CLOSE: (244), (373), (11253) are inconsistent by
% 223.10/38.13  | | | | | | | | | | | | | | |            sub-proof #2502.
% 223.10/38.13  | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | Case 2:
% 223.10/38.13  | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | |   (11254)   ~ (all_55_15 = e2)
% 223.10/38.13  | | | | | | | | | | | | | | |   (11255)  all_55_15 = e1 | all_55_15 = e0
% 223.10/38.13  | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | BETA: splitting (11255) gives:
% 223.10/38.13  | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | Case 1:
% 223.10/38.13  | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | |   (11256)  all_55_15 = e1
% 223.10/38.13  | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | REF_CLOSE: (244), (11249), (11256) are inconsistent by
% 223.10/38.13  | | | | | | | | | | | | | | | |            sub-proof #2501.
% 223.10/38.13  | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | Case 2:
% 223.10/38.13  | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | |   (11257)  all_55_15 = e0
% 223.10/38.13  | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (11257) imply:
% 223.10/38.13  | | | | | | | | | | | | | | | |   (11258)  all_4_2 = e0
% 223.10/38.13  | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | SIMP: (11258) implies:
% 223.10/38.13  | | | | | | | | | | | | | | | |   (11259)  all_4_2 = e0
% 223.10/38.13  | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | REDUCE: (362), (11259) imply:
% 223.10/38.13  | | | | | | | | | | | | | | | |   (11260)   ~ (all_53_7 = e0)
% 223.10/38.13  | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | REDUCE: (371), (11259) imply:
% 223.10/38.13  | | | | | | | | | | | | | | | |   (11261)   ~ (all_53_13 = e0)
% 223.10/38.13  | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | REDUCE: (10098), (11259) imply:
% 223.10/38.13  | | | | | | | | | | | | | | | |   (11262)   ~ (e3 = e0)
% 223.10/38.13  | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | REDUCE: (373), (11259) imply:
% 223.10/38.13  | | | | | | | | | | | | | | | |   (11263)   ~ (e2 = e0)
% 223.10/38.13  | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | REDUCE: (11249), (11259) imply:
% 223.10/38.13  | | | | | | | | | | | | | | | |   (11264)   ~ (e1 = e0)
% 223.10/38.13  | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | REDUCE: (36), (11259) imply:
% 223.10/38.13  | | | | | | | | | | | | | | | |   (11265)  op(e0, e0) = e0
% 223.10/38.13  | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 223.10/38.13  | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.13  | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | |   (11266)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 223.10/38.13  | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 223.10/38.13  | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (168), (10094), (11237), (11266),
% 223.10/38.13  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.13  | | | | | | | | | | | | | | | | |            #214.
% 223.10/38.13  | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.13  | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | |   (11267)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 223.10/38.13  | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0)
% 223.10/38.13  | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | BETA: splitting (11267) gives:
% 223.10/38.13  | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | |   (11268)  all_57_5 = e0 & op(e2, e1) = e0
% 223.10/38.13  | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | ALPHA: (11268) implies:
% 223.10/38.13  | | | | | | | | | | | | | | | | | |   (11269)  op(e2, e1) = e0
% 223.10/38.13  | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | |   (11270)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 223.10/38.13  | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (171), (10094), (11239), (11270),
% 223.10/38.13  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.13  | | | | | | | | | | | | | | | | | | |            #213.
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | |   (11271)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 223.10/38.13  | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0)
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | BETA: splitting (11271) gives:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | |   (11272)  all_57_7 = e0 & op(e1, e2) = e0
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | ALPHA: (11272) implies:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | |   (11273)  op(e1, e2) = e0
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_6, e0,
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | |              e2, e1, simplifying with (163), (11273) gives:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | |   (11274)  all_53_6 = e0
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_9, e0,
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (166), (11269) gives:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | |   (11275)  all_53_9 = e0
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | REDUCE: (119), (11275) imply:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | |   (11276)   ~ (all_53_11 = e0)
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | SIMP: (11276) implies:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | |   (11277)   ~ (all_53_11 = e0)
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | REDUCE: (364), (11275) imply:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | |   (11278)   ~ (all_6_2 = e0)
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | |   (11279)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | |              all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | |              op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | |                all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | |              $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | |              $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | |                all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | |              & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | |                all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | |              & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | |              $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (11245), (11265), (11269), (11279),
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | |            #1938.
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | |   (11280)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | |              & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | |              & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | |                all_52_21) = e1 & op(all_52_23, all_52_23) =
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | |              all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | |              = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | |              $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | |              & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | |              e0 & op(all_52_25, all_52_25) = e3 &
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | |              op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | |                all_52_29) = e1 & op(all_52_31, all_52_31) =
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | |              all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | |              = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | |              $i(all_52_29) & $i(all_52_31))
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11280) gives:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | |   (11281)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | |            all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | |            op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | |              all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | |            & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_23)
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11281) implies:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | |   (11282)  op(e1, e2) = all_52_19
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | |   (11283)  op(all_52_19, all_52_19) = e2
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (11265), (11273), (11282), (11283),
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | |            #2158.
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | |   (11284)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | |            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | |              all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | |            & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | |            & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | |            & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_31)
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11284) implies:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | |   (11285)  op(e0, e1) = all_52_29
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | |   (11286)  op(all_52_29, all_52_29) = e1
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_11,
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | |              all_52_29, e1, e0, simplifying with (158), (11285)
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | |              gives:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | |   (11287)  all_53_11 = all_52_29
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (11287) imply:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | |   (11288)  all_55_14 = all_52_29
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (122), (11287) imply:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | |   (11289)   ~ (all_53_8 = all_52_29)
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (366), (11287) imply:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | |   (11290)   ~ (all_52_29 = all_6_2)
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11277), (11287) imply:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | |   (11291)   ~ (all_52_29 = e0)
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (88) gives:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | |   (11292)   ~ (all_38_2 = e2)
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (249), (11292) imply:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | |   (11293)   ~ (all_6_2 = e2)
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | |   (11294)  all_55_10 = e3
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.13  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (374), (11294) are inconsistent by
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2500.
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | |   (11295)  all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11295) gives:
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | |   (11296)  all_55_10 = e2
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (11293), (11296) are inconsistent by
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2499.
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | |   (11297)  all_55_10 = e1 | all_55_10 = e0
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11297) gives:
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11298)  all_55_10 = e1
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (336), (11298) imply:
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11299)  all_6_2 = e1
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (11299) implies:
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11300)  all_6_2 = e1
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (363), (11300) imply:
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11301)   ~ (all_53_8 = e1)
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11290), (11300) imply:
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11302)   ~ (all_52_29 = e1)
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11303)  all_55_2 = e3
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (191), (269), (10095), (11286), (11288), (11289),
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11291), (11301), (11302), (11303),
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #212.
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11304)  all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11304) gives:
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11305)  all_55_2 = e2
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (11305) imply:
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11306)  all_53_8 = e2
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (11306) implies:
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11307)  all_53_8 = e2
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11289), (11307) imply:
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11308)   ~ (all_52_29 = e2)
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (191), (11245), (11285), (11286), (11288),
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11291), (11302), (11308), (function-axioms) are
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1191.
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11309)  all_55_2 = e1 | all_55_2 = e0
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (11240), (11301), (11309) are inconsistent
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2030.
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11310)  all_55_10 = e0
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (11247), (11310) are inconsistent by
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2118.
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | |   (11311)  all_38_2 = e2
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | |   (11312)  ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = all_38_1 & $i(all_38_0) &
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_38_1)) | ( ~ (all_38_1 = e3) & op(e1, e2)
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | |              = all_38_1 & $i(all_38_1))
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (11311) imply:
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | |   (11313)  all_6_2 = e2
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (11313) implies:
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | |   (11314)  all_6_2 = e2
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (332), (11314) imply:
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | |   (11315)  all_42_2 = e2
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11290), (11314) imply:
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | |   (11316)   ~ (all_52_29 = e2)
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (11314) imply:
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | |   (11317)  op(e1, e1) = e2
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (94) gives:
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | |   (11318)   ~ (all_42_2 = e2)
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11315), (11318) imply:
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | |   (11319)  $false
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (11319) is inconsistent.
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | |   (11320)  ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = all_42_1 & $i(all_42_0) &
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_42_1)) | ( ~ (all_42_1 = e0) & op(e1, e2)
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | |              = all_42_1 & $i(all_42_1))
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11312) gives:
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | |   (11321)   ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = all_38_1 & $i(all_38_0) &
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_38_1)
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11321) implies:
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | |   (11322)  op(e1, e2) = all_38_1
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (191), (11273), (11285), (11286), (11288),
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | |            (11291), (11316), (11317), (11320), (11322),
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | |            #210.
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | |   (11323)   ~ (all_38_1 = e3) & op(e1, e2) = all_38_1 &
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_38_1)
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11323) implies:
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | |   (11324)  op(e1, e2) = all_38_1
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (191), (11273), (11285), (11286), (11288),
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | |            (11291), (11316), (11317), (11320), (11324),
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | |            #210.
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | |   (11325)  all_57_13 = e0 & op(e0, e2) = e0
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | ALPHA: (11325) implies:
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | |   (11326)  op(e0, e2) = e0
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (11260), (11326), (function-axioms) are
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2332.
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.14  | | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | End of split
% 223.10/38.14  | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | Case 2:
% 223.10/38.14  | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | |   (11327)  all_57_10 = e0 & op(e2, e0) = e0
% 223.10/38.14  | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | ALPHA: (11327) implies:
% 223.10/38.14  | | | | | | | | | | | | | | | | | |   (11328)  op(e2, e0) = e0
% 223.10/38.14  | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (11261), (11328), (function-axioms) are
% 223.10/38.14  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2470.
% 223.10/38.14  | | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | | End of split
% 223.10/38.14  | | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | | End of split
% 223.10/38.14  | | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | | End of split
% 223.10/38.14  | | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | | End of split
% 223.10/38.14  | | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | End of split
% 223.10/38.14  | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | Case 2:
% 223.10/38.14  | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | |   (11329)  all_30_2 = e1
% 223.10/38.14  | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | COMBINE_EQS: (330), (11329) imply:
% 223.10/38.14  | | | | | | | | | | | | |   (11330)  all_4_2 = e1
% 223.10/38.14  | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | SIMP: (11330) implies:
% 223.10/38.14  | | | | | | | | | | | | |   (11331)  all_4_2 = e1
% 223.10/38.14  | | | | | | | | | | | | | 
% 223.10/38.14  | | | | | | | | | | | | | COMBINE_EQS: (295), (11331) imply:
% 223.54/38.14  | | | | | | | | | | | | |   (11332)  all_40_2 = e1
% 223.54/38.14  | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | REDUCE: (370), (11331) imply:
% 223.54/38.14  | | | | | | | | | | | | |   (11333)   ~ (all_53_12 = e1)
% 223.54/38.14  | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | REDUCE: (371), (11331) imply:
% 223.54/38.14  | | | | | | | | | | | | |   (11334)   ~ (all_53_13 = e1)
% 223.54/38.14  | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | REDUCE: (10098), (11331) imply:
% 223.54/38.14  | | | | | | | | | | | | |   (11335)   ~ (e3 = e1)
% 223.54/38.14  | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | REDUCE: (36), (11331) imply:
% 223.54/38.14  | | | | | | | | | | | | |   (11336)  op(e0, e0) = e1
% 223.54/38.14  | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | BETA: splitting (107) gives:
% 223.54/38.14  | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | Case 1:
% 223.54/38.14  | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | |   (11337)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 223.54/38.14  | | | | | | | | | | | | | |              all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 223.54/38.14  | | | | | | | | | | | | | |              op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 223.54/38.14  | | | | | | | | | | | | | |                all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 223.54/38.14  | | | | | | | | | | | | | |              op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 223.54/38.14  | | | | | | | | | | | | | |              op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 223.54/38.14  | | | | | | | | | | | | | |              $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 223.54/38.14  | | | | | | | | | | | | | |              $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 223.54/38.14  | | | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 223.54/38.14  | | | | | | | | | | | | | |                all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 223.54/38.14  | | | | | | | | | | | | | |              & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 223.54/38.14  | | | | | | | | | | | | | |                all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 223.54/38.14  | | | | | | | | | | | | | |              op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 223.54/38.14  | | | | | | | | | | | | | |              & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 223.54/38.14  | | | | | | | | | | | | | |              $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 223.54/38.14  | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | BETA: splitting (11337) gives:
% 223.54/38.14  | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | Case 1:
% 223.54/38.14  | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | |   (11338)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 223.54/38.14  | | | | | | | | | | | | | | |            all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 223.54/38.14  | | | | | | | | | | | | | | |            op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 223.54/38.14  | | | | | | | | | | | | | | |              all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 223.54/38.14  | | | | | | | | | | | | | | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 223.54/38.14  | | | | | | | | | | | | | | |            op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 223.54/38.14  | | | | | | | | | | | | | | |            $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 223.54/38.14  | | | | | | | | | | | | | | |            $i(all_52_7)
% 223.54/38.14  | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | ALPHA: (11338) implies:
% 223.54/38.14  | | | | | | | | | | | | | | |   (11339)  op(e3, e3) = all_52_1
% 223.54/38.14  | | | | | | | | | | | | | | |   (11340)  op(all_52_1, all_52_1) = e3
% 223.54/38.14  | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_52_1,
% 223.54/38.14  | | | | | | | | | | | | | | |              e3, e3, simplifying with (11245), (11339) gives:
% 223.54/38.14  | | | | | | | | | | | | | | |   (11341)  all_52_1 = e0
% 223.54/38.14  | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | REDUCE: (11340), (11341) imply:
% 223.54/38.14  | | | | | | | | | | | | | | |   (11342)  op(e0, e0) = e3
% 223.54/38.14  | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | REF_CLOSE: (8), (11336), (11342), (function-axioms) are
% 223.54/38.14  | | | | | | | | | | | | | | |            inconsistent by sub-proof #2183.
% 223.54/38.14  | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | Case 2:
% 223.54/38.14  | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | |   (11343)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 223.54/38.14  | | | | | | | | | | | | | | |            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 223.54/38.14  | | | | | | | | | | | | | | |            op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 223.54/38.14  | | | | | | | | | | | | | | |              all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 223.54/38.14  | | | | | | | | | | | | | | |            & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 223.54/38.14  | | | | | | | | | | | | | | |            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 223.54/38.14  | | | | | | | | | | | | | | |            $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 223.54/38.14  | | | | | | | | | | | | | | |            $i(all_52_15)
% 223.54/38.14  | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | REF_CLOSE: (5), (10095), (11245), (11343), (function-axioms)
% 223.54/38.14  | | | | | | | | | | | | | | |            are inconsistent by sub-proof #209.
% 223.54/38.14  | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | End of split
% 223.54/38.14  | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | Case 2:
% 223.54/38.14  | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | |   (11344)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 223.54/38.14  | | | | | | | | | | | | | |              & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 223.54/38.14  | | | | | | | | | | | | | |              & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 223.54/38.14  | | | | | | | | | | | | | |                all_52_21) = e1 & op(all_52_23, all_52_23) =
% 223.54/38.14  | | | | | | | | | | | | | |              e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 223.54/38.14  | | | | | | | | | | | | | |              all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 223.54/38.14  | | | | | | | | | | | | | |              = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 223.54/38.14  | | | | | | | | | | | | | |              $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 223.54/38.14  | | | | | | | | | | | | | |              & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 223.54/38.14  | | | | | | | | | | | | | |              e0 & op(all_52_25, all_52_25) = e3 &
% 223.54/38.14  | | | | | | | | | | | | | |              op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 223.54/38.14  | | | | | | | | | | | | | |                all_52_29) = e1 & op(all_52_31, all_52_31) =
% 223.54/38.14  | | | | | | | | | | | | | |              e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 223.54/38.14  | | | | | | | | | | | | | |              all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 223.54/38.14  | | | | | | | | | | | | | |              = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 223.54/38.14  | | | | | | | | | | | | | |              $i(all_52_29) & $i(all_52_31))
% 223.54/38.14  | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | BETA: splitting (11344) gives:
% 223.54/38.14  | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | Case 1:
% 223.54/38.14  | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | |   (11345)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 223.54/38.14  | | | | | | | | | | | | | | |            all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 223.54/38.14  | | | | | | | | | | | | | | |            op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 223.54/38.14  | | | | | | | | | | | | | | |              all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 223.54/38.14  | | | | | | | | | | | | | | |            & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 223.54/38.14  | | | | | | | | | | | | | | |            & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 223.54/38.14  | | | | | | | | | | | | | | |            & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 223.54/38.14  | | | | | | | | | | | | | | |            $i(all_52_23)
% 223.54/38.14  | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | ALPHA: (11345) implies:
% 223.54/38.14  | | | | | | | | | | | | | | |   (11346)  op(e1, e0) = all_52_23
% 223.54/38.14  | | | | | | | | | | | | | | |   (11347)  op(e1, e1) = all_52_21
% 223.54/38.14  | | | | | | | | | | | | | | |   (11348)  op(e1, e2) = all_52_19
% 223.54/38.14  | | | | | | | | | | | | | | |   (11349)  op(all_52_23, all_52_23) = e0
% 223.54/38.14  | | | | | | | | | | | | | | |   (11350)  op(all_52_21, all_52_21) = e1
% 223.54/38.14  | | | | | | | | | | | | | | |   (11351)  op(all_52_19, all_52_19) = e2
% 223.54/38.14  | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_14,
% 223.54/38.14  | | | | | | | | | | | | | | |              all_52_23, e0, e1, simplifying with (161), (11346)
% 223.54/38.14  | | | | | | | | | | | | | | |              gives:
% 223.54/38.14  | | | | | | | | | | | | | | |   (11352)  all_53_14 = all_52_23
% 223.54/38.14  | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 223.54/38.14  | | | | | | | | | | | | | | |              all_52_21, e1, e1, simplifying with (39), (11347)
% 223.54/38.14  | | | | | | | | | | | | | | |              gives:
% 223.54/38.14  | | | | | | | | | | | | | | |   (11353)  all_52_21 = all_6_2
% 223.54/38.14  | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_6,
% 223.54/38.14  | | | | | | | | | | | | | | |              all_52_19, e2, e1, simplifying with (163), (11348)
% 223.54/38.14  | | | | | | | | | | | | | | |              gives:
% 223.54/38.14  | | | | | | | | | | | | | | |   (11354)  all_53_6 = all_52_19
% 223.54/38.14  | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | COMBINE_EQS: (256), (11354) imply:
% 223.54/38.14  | | | | | | | | | | | | | | |   (11355)  all_55_9 = all_52_19
% 223.54/38.14  | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | REDUCE: (137), (11354) imply:
% 223.54/38.14  | | | | | | | | | | | | | | |   (11356)   ~ (all_53_4 = all_52_19)
% 223.54/38.14  | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | REDUCE: (10087), (11354) imply:
% 223.54/38.14  | | | | | | | | | | | | | | |   (11357)   ~ (all_52_19 = e3)
% 223.54/38.14  | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | REDUCE: (11350), (11353) imply:
% 223.54/38.14  | | | | | | | | | | | | | | |   (11358)  op(all_6_2, all_6_2) = e1
% 223.54/38.14  | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | BETA: splitting (91) gives:
% 223.54/38.14  | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | Case 1:
% 223.54/38.14  | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | |   (11359)   ~ (all_40_2 = e1)
% 223.54/38.14  | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | REDUCE: (11332), (11359) imply:
% 223.54/38.14  | | | | | | | | | | | | | | | |   (11360)  $false
% 223.54/38.14  | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | CLOSE: (11360) is inconsistent.
% 223.54/38.14  | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | Case 2:
% 223.54/38.14  | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | |   (11361)  ( ~ (all_40_0 = e3) & op(all_40_1, e0) = all_40_0
% 223.54/38.14  | | | | | | | | | | | | | | | |              & op(e0, e1) = all_40_1 & $i(all_40_0) &
% 223.54/38.14  | | | | | | | | | | | | | | | |              $i(all_40_1)) | ( ~ (all_40_1 = e2) & op(e0, e1)
% 223.54/38.14  | | | | | | | | | | | | | | | |              = all_40_1 & $i(all_40_1))
% 223.54/38.14  | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | BETA: splitting (88) gives:
% 223.54/38.14  | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.14  | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | |   (11362)   ~ (all_38_2 = e2)
% 223.54/38.14  | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | REDUCE: (249), (11362) imply:
% 223.54/38.14  | | | | | | | | | | | | | | | | |   (11363)   ~ (all_6_2 = e2)
% 223.54/38.14  | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 223.54/38.14  | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.14  | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | |   (11364)  all_55_10 = e3
% 223.54/38.14  | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (374), (11364) are inconsistent by
% 223.54/38.14  | | | | | | | | | | | | | | | | | |            sub-proof #2500.
% 223.54/38.14  | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.14  | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | |   (11365)   ~ (all_55_10 = e3)
% 223.54/38.14  | | | | | | | | | | | | | | | | | |   (11366)  all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 223.54/38.14  | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | BETA: splitting (11366) gives:
% 223.54/38.14  | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | |   (11367)  all_55_10 = e2
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (11363), (11367) are inconsistent by
% 223.54/38.14  | | | | | | | | | | | | | | | | | | |            sub-proof #2499.
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | |   (11368)   ~ (all_55_10 = e2)
% 223.54/38.14  | | | | | | | | | | | | | | | | | | |   (11369)  all_55_10 = e1 | all_55_10 = e0
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | BETA: splitting (11369) gives:
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | |   (11370)  all_55_10 = e1
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (336), (11370) imply:
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | |   (11371)  all_6_2 = e1
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | SIMP: (11371) implies:
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | |   (11372)  all_6_2 = e1
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | REDUCE: (364), (11372) imply:
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | |   (11373)   ~ (all_53_9 = e1)
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | REDUCE: (11363), (11372) imply:
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | |   (11374)   ~ (e2 = e1)
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (11372) imply:
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | |   (11375)  op(e1, e1) = e1
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | |   (11376)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11376) gives:
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | |   (11377)  all_57_2 = e1 & op(e2, e3) = e1
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11377) implies:
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | |   (11378)  all_57_2 = e1
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | |   (11379)  op(e2, e3) = e1
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | |   (11380)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11380) gives:
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | |   (11381)  all_57_1 = e1 & op(e3, e2) = e1
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11381) implies:
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | |   (11382)  op(e3, e2) = e1
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_1, e1,
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (168), (11379) gives:
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | |   (11383)  all_53_1 = e1
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_4, e1,
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (171), (11382) gives:
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | |   (11384)  all_53_4 = e1
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11356), (11384) imply:
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | |   (11385)   ~ (all_52_19 = e1)
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (11385) implies:
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | |   (11386)   ~ (all_52_19 = e1)
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (97) gives:
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | |   (11387)   ~ (all_44_2 = e3)
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10084), (11387) imply:
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | |   (11388)  $false
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (11388) is inconsistent.
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | |   (11389)  ( ~ (all_44_0 = e1) & op(all_44_1, e2) = all_44_0
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = all_44_1 & $i(all_44_0) &
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_44_1)) | ( ~ (all_44_1 = e0) & op(e2, e3)
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | |              = all_44_1 & $i(all_44_1))
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (196), (10083), (10095), (11348), (11351),
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | |            (11355), (11357), (11379), (11386), (11389),
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | |            #208.
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | |   (11390)  all_57_3 = e1 & op(e2, e2) = e1
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11390) implies:
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | |   (11391)  op(e2, e2) = e1
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10095), (11391), (function-axioms) are
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1912.
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | |   (11392)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11392) gives:
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | |   (11393)  all_57_7 = e1 & op(e1, e2) = e1
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11393) implies:
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | |   (11394)  all_57_7 = e1
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | |   (11395)  op(e1, e2) = e1
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | |   (11396)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (171), (10094), (11239), (11396),
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | |            #213.
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | |   (11397)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0)
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11397) gives:
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11398)  all_57_7 = e0 & op(e1, e2) = e0
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (11394), (11398) are inconsistent by
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #509.
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11399)  all_57_13 = e0 & op(e0, e2) = e0
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11399) implies:
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11400)  all_57_13 = e0
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11401)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e1)
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11401) gives:
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11402)  all_57_0 = e1 & op(e3, e3) = e1
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (11244), (11402) are inconsistent by
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2454.
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11403)  all_57_1 = e1 & op(e3, e2) = e1
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11403) implies:
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11404)  all_57_1 = e1
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11405)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 223.54/38.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e0)
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11405) gives:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11406)  all_57_6 = e0 & op(e1, e3) = e0
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11406) implies:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11407)  all_57_6 = e0
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (234), (236), (11245),
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11378), (11407), (function-axioms) are
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2390.
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11408)  all_57_7 = e0 & op(e1, e2) = e0
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (11394), (11408) are inconsistent by
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #509.
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11409)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11409) gives:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11410)  all_57_8 = e0 & op(e1, e1) = e0
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11410) implies:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11411)  op(e1, e1) = e0
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (163), (11347), (11348), (11351), (11395),
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11411), (function-axioms) are inconsistent by
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #332.
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11412)  all_57_11 = e0 & op(e1, e0) = e0
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11412) implies:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11413)  all_57_11 = e0
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11414)  op(e1, e0) = e0
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11415)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11415) gives:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11416)  all_57_9 = e3 & op(e3, e0) = e3
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11416) implies:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11417)  op(e3, e0) = e3
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11418)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e2)
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (11245), (11404), (11418),
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #207.
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11419)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e2)
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11419) gives:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11420)  all_57_4 = e2 & op(e3, e1) = e2
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11420) implies:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11421)  all_57_4 = e2
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11422)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e3)
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11422) gives:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11423)  all_57_6 = e3 & op(e1, e3) = e3
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11423) implies:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11424)  all_57_6 = e3
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11425)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2)
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11425) gives:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11426)  all_57_0 = e2 & op(e3, e3) = e2
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11426) implies:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11427)  op(e3, e3) = e2
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (171), (231), (233),
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (237), (11239), (11421), (11427),
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1320.
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11428)  all_57_2 = e2 & op(e2, e3) = e2
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (218), (220),
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (221), (374), (11247), (11375), (11378), (11421),
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11428), (function-axioms) are inconsistent by
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #265.
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11429)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e3) = e2)
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11429) gives:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11430)  all_57_6 = e2 & op(e1, e3) = e2
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11430) implies:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11431)  all_57_6 = e2
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (39), (214), (217),
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (374), (11247), (11394), (11431),
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #342.
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11432)  all_57_12 = e2 & op(e0, e3) = e2
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11432) implies:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11433)  all_57_12 = e2
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11434)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e0)
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11434) gives:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11435)  all_57_4 = e0 & op(e3, e1) = e0
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11435) implies:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11436)  op(e3, e1) = e0
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (11240), (11436), (function-axioms) are
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2267.
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11437)  all_57_5 = e0 & op(e2, e1) = e0
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11437) implies:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11438)  all_57_5 = e0
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11439)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11439) gives:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11440)  all_57_1 = e2 & op(e3, e2) = e2
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11440) implies:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11441)  all_57_1 = e2
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (11404), (11441) imply:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11442)  e2 = e1
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (11442) implies:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11443)  e2 = e1
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (11421), (11443) imply:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11444)  all_57_4 = e1
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (218), (220),
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (221), (374), (11247), (11375), (11444),
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2407.
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11445)  all_57_3 = e2 & op(e2, e2) = e2
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11445) implies:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11446)  op(e2, e2) = e2
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (165), (168), (225), (10085), (10090),
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11438), (11446), (function-axioms) are
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2129.
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11447)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11447) gives:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11448)  all_57_7 = e2 & op(e1, e2) = e2
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11448) implies:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11449)  all_57_7 = e2
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (11394), (11449) imply:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11450)  e2 = e1
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (11450) implies:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11451)  e2 = e1
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (11421), (11451) imply:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11452)  all_57_4 = e1
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (218), (220),
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (221), (374), (11247), (11375), (11452),
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2407.
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11453)  all_57_13 = e2 & op(e0, e2) = e2
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11453) implies:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11454)  all_57_13 = e2
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (11400), (11454) imply:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11455)  e2 = e0
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (11433), (11455) imply:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11456)  all_57_12 = e0
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (234), (11244), (11378), (11424),
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11456) are inconsistent by sub-proof #1426.
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11457)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11457) gives:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11458)  all_57_8 = e0 & op(e1, e1) = e0
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11458) implies:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11459)  op(e1, e1) = e0
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (163), (11347), (11348), (11351), (11395),
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11459), (function-axioms) are inconsistent by
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #332.
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11460)  all_57_14 = e0 & op(e0, e1) = e0
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11460) implies:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11461)  op(e0, e1) = e0
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (11336), (11346), (11349), (11361), (11414),
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11461), (function-axioms) are inconsistent by
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1227.
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11462)  all_57_7 = e3 & op(e1, e2) = e3
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (10087), (11462), (function-axioms) are
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #267.
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11463)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e1, e0) = e3)
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11463) gives:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11464)  all_57_8 = e3 & op(e1, e1) = e3
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11464) implies:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11465)  op(e1, e1) = e3
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (374), (11465), (function-axioms) are
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2468.
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11466)  all_57_11 = e3 & op(e1, e0) = e3
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11466) implies:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11467)  all_57_11 = e3
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11468)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11468) gives:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11469)  all_57_9 = e2 & op(e3, e0) = e2
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11417), (11469), (function-axioms) are
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #306.
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11470)  all_57_10 = e2 & op(e2, e0) = e2
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11470) implies:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11471)  all_57_10 = e2
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11472)  all_57_15 = e0 & op(e0, e0) = e0
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11472) implies:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11473)  op(e0, e0) = e0
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (11336), (11473), (function-axioms) are
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2290.
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11474)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11474) implies:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11475)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0)
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11475) gives:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11476)  all_57_9 = e0 & op(e3, e0) = e0
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11476) implies:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11477)  op(e3, e0) = e0
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (11417), (11477), (function-axioms) are
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #313.
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11478)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 =
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11478) gives:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11479)  all_57_10 = e0 & op(e2, e0) = e0
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (11471), (11479) are inconsistent by
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1751.
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (11413), (11467) are inconsistent by
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1595.
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11480)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (11336), (11467), (11480),
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1956.
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11481)  all_57_9 = e2 & op(e3, e0) = e2
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11417), (11481), (function-axioms) are
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #306.
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11482)  all_57_10 = e3 & op(e2, e0) = e3
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11482) implies:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11483)  op(e2, e0) = e3
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (10090), (11483), (function-axioms) are
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2301.
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11484)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11484) gives:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11485)  all_57_11 = e3 & op(e1, e0) = e3
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11485) implies:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11486)  all_57_11 = e3
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (11413), (11486) are inconsistent by
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1595.
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11487)  all_57_15 = e3 & op(e0, e0) = e3
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11487) implies:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11488)  all_57_15 = e3
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (214), (216), (217), (374), (11375),
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11394), (11488), (function-axioms) are
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1069.
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11489)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e1)
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (169), (218),
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (220), (221), (374), (11247), (11333), (11375),
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11489), (function-axioms) are inconsistent by
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2085.
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | |   (11490)  all_57_13 = e1 & op(e0, e2) = e1
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11490) implies:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | |   (11491)  all_57_13 = e1
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (207), (209),
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | |            (210), (11238), (11336), (11491),
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | |            #1918.
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | |   (11492)  all_57_3 = e1 & op(e2, e2) = e1
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11492) implies:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | |   (11493)  op(e2, e2) = e1
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10095), (11493), (function-axioms) are
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1912.
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | |   (11494)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11494) gives:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | |   (11495)  all_57_5 = e1 & op(e2, e1) = e1
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (11373), (11495), (function-axioms) are
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2305.
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | |   (11496)  all_57_10 = e1 & op(e2, e0) = e1
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (11334), (11496), (function-axioms) are
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2084.
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | |   (11497)  all_55_10 = e0
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (11247), (11497) are inconsistent by
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | |            sub-proof #2118.
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.15  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.15  | | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | End of split
% 223.54/38.15  | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.15  | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | |   (11498)  all_38_2 = e2
% 223.54/38.15  | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (249), (10095), (11358), (11498),
% 223.54/38.15  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.54/38.15  | | | | | | | | | | | | | | | | |            #206.
% 223.54/38.15  | | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | | End of split
% 223.54/38.15  | | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | End of split
% 223.54/38.15  | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | Case 2:
% 223.54/38.15  | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | |   (11499)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 223.54/38.15  | | | | | | | | | | | | | | |            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 223.54/38.15  | | | | | | | | | | | | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 223.54/38.15  | | | | | | | | | | | | | | |              all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 223.54/38.15  | | | | | | | | | | | | | | |            & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 223.54/38.15  | | | | | | | | | | | | | | |            & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 223.54/38.15  | | | | | | | | | | | | | | |            & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 223.54/38.15  | | | | | | | | | | | | | | |            $i(all_52_31)
% 223.54/38.15  | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | ALPHA: (11499) implies:
% 223.54/38.15  | | | | | | | | | | | | | | |   (11500)  op(e0, e0) = all_52_31
% 223.54/38.15  | | | | | | | | | | | | | | |   (11501)  op(all_52_31, all_52_31) = e0
% 223.54/38.15  | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | | REF_CLOSE: (39), (11247), (11336), (11500), (11501),
% 223.54/38.15  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.54/38.15  | | | | | | | | | | | | | | |            #2086.
% 223.54/38.15  | | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | End of split
% 223.54/38.15  | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | End of split
% 223.54/38.15  | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | End of split
% 223.54/38.15  | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | Case 2:
% 223.54/38.15  | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | |   (11502)  all_24_2 = e0
% 223.54/38.15  | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | COMBINE_EQS: (315), (11502) imply:
% 223.54/38.15  | | | | | | | | | | | |   (11503)  all_6_2 = e0
% 223.54/38.15  | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | SIMP: (11503) implies:
% 223.54/38.15  | | | | | | | | | | | |   (11504)  all_6_2 = e0
% 223.54/38.15  | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | REDUCE: (361), (11504) imply:
% 223.54/38.15  | | | | | | | | | | | |   (11505)   ~ (all_53_6 = e0)
% 223.54/38.15  | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | REDUCE: (364), (11504) imply:
% 223.54/38.15  | | | | | | | | | | | |   (11506)   ~ (all_53_9 = e0)
% 223.54/38.15  | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | REDUCE: (374), (11504) imply:
% 223.54/38.15  | | | | | | | | | | | |   (11507)   ~ (e3 = e0)
% 223.54/38.15  | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | REDUCE: (39), (11504) imply:
% 223.54/38.15  | | | | | | | | | | | |   (11508)  op(e1, e1) = e0
% 223.54/38.15  | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | BETA: splitting (226) gives:
% 223.54/38.15  | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | Case 1:
% 223.54/38.15  | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | |   (11509)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 223.54/38.15  | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 223.54/38.15  | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | REF_CLOSE: (7), (171), (10094), (11239), (11509),
% 223.54/38.15  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.54/38.15  | | | | | | | | | | | | |            #213.
% 223.54/38.15  | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | Case 2:
% 223.54/38.15  | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | |   (11510)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 223.54/38.15  | | | | | | | | | | | | |              e0 & op(e0, e2) = e0)
% 223.54/38.15  | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | BETA: splitting (11510) gives:
% 223.54/38.15  | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | Case 1:
% 223.54/38.15  | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | |   (11511)  all_57_7 = e0 & op(e1, e2) = e0
% 223.54/38.15  | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | REF_CLOSE: (163), (11505), (11511), (function-axioms) are
% 223.54/38.15  | | | | | | | | | | | | | |            inconsistent by sub-proof #2039.
% 223.54/38.15  | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | Case 2:
% 223.54/38.15  | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | |   (11512)  all_57_13 = e0 & op(e0, e2) = e0
% 223.54/38.15  | | | | | | | | | | | | | | 
% 223.54/38.15  | | | | | | | | | | | | | | ALPHA: (11512) implies:
% 223.54/38.15  | | | | | | | | | | | | | |   (11513)  op(e0, e2) = e0
% 223.54/38.15  | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 223.54/38.16  | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | Case 1:
% 223.54/38.16  | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | |   (11514)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 223.54/38.16  | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 223.54/38.16  | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | REF_CLOSE: (7), (168), (10094), (11237), (11514),
% 223.54/38.16  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.54/38.16  | | | | | | | | | | | | | | |            #214.
% 223.54/38.16  | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | Case 2:
% 223.54/38.16  | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | |   (11515)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 223.54/38.16  | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0)
% 223.54/38.16  | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | BETA: splitting (11515) gives:
% 223.54/38.16  | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | Case 1:
% 223.54/38.16  | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | |   (11516)  all_57_5 = e0 & op(e2, e1) = e0
% 223.54/38.16  | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | REF_CLOSE: (166), (11506), (11516), (function-axioms) are
% 223.54/38.16  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2023.
% 223.54/38.16  | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | Case 2:
% 223.54/38.16  | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | |   (11517)  all_57_10 = e0 & op(e2, e0) = e0
% 223.54/38.16  | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | ALPHA: (11517) implies:
% 223.54/38.16  | | | | | | | | | | | | | | | |   (11518)  all_57_10 = e0
% 223.54/38.16  | | | | | | | | | | | | | | | |   (11519)  op(e2, e0) = e0
% 223.54/38.16  | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_7, e0,
% 223.54/38.16  | | | | | | | | | | | | | | | |              e2, e0, simplifying with (159), (11513) gives:
% 223.54/38.16  | | | | | | | | | | | | | | | |   (11520)  all_53_7 = e0
% 223.54/38.16  | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_13,
% 223.54/38.16  | | | | | | | | | | | | | | | |              e0, e0, e2, simplifying with (165), (11519) gives:
% 223.54/38.16  | | | | | | | | | | | | | | | |   (11521)  all_53_13 = e0
% 223.54/38.16  | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | REDUCE: (371), (11521) imply:
% 223.54/38.16  | | | | | | | | | | | | | | | |   (11522)   ~ (all_4_2 = e0)
% 223.54/38.16  | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | SIMP: (11522) implies:
% 223.54/38.16  | | | | | | | | | | | | | | | |   (11523)   ~ (all_4_2 = e0)
% 223.54/38.16  | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 223.54/38.16  | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.16  | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | |   (11524)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 223.54/38.16  | | | | | | | | | | | | | | | | |              all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 223.54/38.16  | | | | | | | | | | | | | | | | |              op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 223.54/38.16  | | | | | | | | | | | | | | | | |                all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 223.54/38.16  | | | | | | | | | | | | | | | | |              op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 223.54/38.16  | | | | | | | | | | | | | | | | |              op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 223.54/38.16  | | | | | | | | | | | | | | | | |              $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 223.54/38.16  | | | | | | | | | | | | | | | | |              $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 223.54/38.16  | | | | | | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 223.54/38.16  | | | | | | | | | | | | | | | | |                all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 223.54/38.16  | | | | | | | | | | | | | | | | |              & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 223.54/38.16  | | | | | | | | | | | | | | | | |                all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 223.54/38.16  | | | | | | | | | | | | | | | | |              op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 223.54/38.16  | | | | | | | | | | | | | | | | |              & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 223.54/38.16  | | | | | | | | | | | | | | | | |              $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 223.54/38.16  | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | BETA: splitting (11524) gives:
% 223.54/38.16  | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | |   (11525)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 223.54/38.16  | | | | | | | | | | | | | | | | | |            all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 223.54/38.16  | | | | | | | | | | | | | | | | | |            op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 223.54/38.16  | | | | | | | | | | | | | | | | | |              all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 223.54/38.16  | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 223.54/38.16  | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 223.54/38.16  | | | | | | | | | | | | | | | | | |            $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 223.54/38.16  | | | | | | | | | | | | | | | | | |            $i(all_52_7)
% 223.54/38.16  | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | ALPHA: (11525) implies:
% 223.54/38.16  | | | | | | | | | | | | | | | | | |   (11526)  op(e3, e3) = all_52_1
% 223.54/38.16  | | | | | | | | | | | | | | | | | |   (11527)  op(all_52_1, all_52_1) = e3
% 223.54/38.16  | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | |   (11528)  all_55_15 = e3
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (10098), (11528) are inconsistent by
% 223.54/38.16  | | | | | | | | | | | | | | | | | | |            sub-proof #2503.
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | |   (11529)   ~ (all_55_15 = e3)
% 223.54/38.16  | | | | | | | | | | | | | | | | | | |   (11530)  all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | BETA: splitting (11530) gives:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | |   (11531)  all_55_15 = e2
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (373), (11531) are inconsistent by
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | |            sub-proof #2502.
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | |   (11532)  all_55_15 = e1 | all_55_15 = e0
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | BETA: splitting (11532) gives:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | |   (11533)  all_55_15 = e1
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (11533) imply:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | |   (11534)  all_4_2 = e1
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | SIMP: (11534) implies:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | |   (11535)  all_4_2 = e1
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | REDUCE: (370), (11535) imply:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | |   (11536)   ~ (all_53_12 = e1)
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | REDUCE: (372), (11535) imply:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | |   (11537)   ~ (all_53_14 = e1)
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | REDUCE: (10098), (11535) imply:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | |   (11538)   ~ (e3 = e1)
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (161), (169), (211), (11245), (11518),
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | |            (11526), (11527), (11536), (11537),
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | |            #217.
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | |   (11539)  all_55_15 = e0
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (11523), (11539) are inconsistent by
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | |            sub-proof #1884.
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.16  | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | |   (11540)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 223.54/38.16  | | | | | | | | | | | | | | | | | |            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 223.54/38.16  | | | | | | | | | | | | | | | | | |            op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 223.54/38.16  | | | | | | | | | | | | | | | | | |              all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 223.54/38.16  | | | | | | | | | | | | | | | | | |            & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 223.54/38.16  | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 223.54/38.16  | | | | | | | | | | | | | | | | | |            $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 223.54/38.16  | | | | | | | | | | | | | | | | | |            $i(all_52_15)
% 223.54/38.16  | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | ALPHA: (11540) implies:
% 223.54/38.16  | | | | | | | | | | | | | | | | | |   (11541)  op(e2, e0) = all_52_15
% 223.54/38.16  | | | | | | | | | | | | | | | | | |   (11542)  op(all_52_15, all_52_15) = e0
% 223.54/38.16  | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | |   (11543)  all_55_15 = e3
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (10098), (11543) are inconsistent by
% 223.54/38.16  | | | | | | | | | | | | | | | | | | |            sub-proof #2503.
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | |   (11544)  all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | BETA: splitting (11544) gives:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | |   (11545)  all_55_15 = e2
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (373), (11545) are inconsistent by
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | |            sub-proof #2502.
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | |   (11546)  all_55_15 = e1 | all_55_15 = e0
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | BETA: splitting (11546) gives:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | |   (11547)  all_55_15 = e1
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (11547) imply:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | |   (11548)  all_4_2 = e1
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | SIMP: (11548) implies:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | |   (11549)  all_4_2 = e1
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | REDUCE: (370), (11549) imply:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | |   (11550)   ~ (all_53_12 = e1)
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | REDUCE: (372), (11549) imply:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | |   (11551)   ~ (all_53_14 = e1)
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (161), (169), (211), (11518), (11519),
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | |            (11541), (11542), (11550), (11551),
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | |            #216.
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | |   (11552)  all_55_15 = e0
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (11523), (11552) are inconsistent by
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | |            sub-proof #1884.
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.16  | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | End of split
% 223.54/38.16  | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.16  | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | |   (11553)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 223.54/38.16  | | | | | | | | | | | | | | | | |              & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 223.54/38.16  | | | | | | | | | | | | | | | | |              & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 223.54/38.16  | | | | | | | | | | | | | | | | |                all_52_21) = e1 & op(all_52_23, all_52_23) =
% 223.54/38.16  | | | | | | | | | | | | | | | | |              e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 223.54/38.16  | | | | | | | | | | | | | | | | |              all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 223.54/38.16  | | | | | | | | | | | | | | | | |              = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 223.54/38.16  | | | | | | | | | | | | | | | | |              $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 223.54/38.16  | | | | | | | | | | | | | | | | |              & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 223.54/38.16  | | | | | | | | | | | | | | | | |              e0 & op(all_52_25, all_52_25) = e3 &
% 223.54/38.16  | | | | | | | | | | | | | | | | |              op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 223.54/38.16  | | | | | | | | | | | | | | | | |                all_52_29) = e1 & op(all_52_31, all_52_31) =
% 223.54/38.16  | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 223.54/38.16  | | | | | | | | | | | | | | | | |              all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 223.54/38.16  | | | | | | | | | | | | | | | | |              = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 223.54/38.16  | | | | | | | | | | | | | | | | |              $i(all_52_29) & $i(all_52_31))
% 223.54/38.16  | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | BETA: splitting (11553) gives:
% 223.54/38.16  | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | |   (11554)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 223.54/38.16  | | | | | | | | | | | | | | | | | |            all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 223.54/38.16  | | | | | | | | | | | | | | | | | |            op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 223.54/38.16  | | | | | | | | | | | | | | | | | |              all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 223.54/38.16  | | | | | | | | | | | | | | | | | |            & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 223.54/38.16  | | | | | | | | | | | | | | | | | |            & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 223.54/38.16  | | | | | | | | | | | | | | | | | |            & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 223.54/38.16  | | | | | | | | | | | | | | | | | |            $i(all_52_23)
% 223.54/38.16  | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | ALPHA: (11554) implies:
% 223.54/38.16  | | | | | | | | | | | | | | | | | |   (11555)  op(e1, e1) = all_52_21
% 223.54/38.16  | | | | | | | | | | | | | | | | | |   (11556)  op(e1, e2) = all_52_19
% 223.54/38.16  | | | | | | | | | | | | | | | | | |   (11557)  op(e1, e3) = all_52_17
% 223.54/38.16  | | | | | | | | | | | | | | | | | |   (11558)  op(all_52_19, all_52_19) = e2
% 223.54/38.16  | | | | | | | | | | | | | | | | | |   (11559)  op(all_52_17, all_52_17) = e3
% 223.54/38.16  | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | |   (11560)  all_55_15 = e3
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (10098), (11560) are inconsistent by
% 223.54/38.16  | | | | | | | | | | | | | | | | | | |            sub-proof #2503.
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | |   (11561)  all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | BETA: splitting (11561) gives:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | |   (11562)  all_55_15 = e2
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (373), (11562) are inconsistent by
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | |            sub-proof #2502.
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | |   (11563)  all_55_15 = e1 | all_55_15 = e0
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | BETA: splitting (11563) gives:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | |   (11564)  all_55_15 = e1
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (11564) imply:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | |   (11565)  all_4_2 = e1
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | SIMP: (11565) implies:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | |   (11566)  all_4_2 = e1
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | REDUCE: (372), (11566) imply:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | |   (11567)   ~ (all_53_14 = e1)
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | |   (11568)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e1)
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11568) gives:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | | |   (11569)  all_57_6 = e1 & op(e1, e3) = e1
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11569) implies:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | | |   (11570)  op(e1, e3) = e1
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (195), (336), (374), (11557), (11559),
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | | |            (11570), (function-axioms) are inconsistent by
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1998.
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | | |   (11571)  all_57_7 = e1 & op(e1, e2) = e1
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11571) implies:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | | |   (11572)  op(e1, e2) = e1
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (163), (11508), (11555), (11556), (11558),
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | | |            (11572), (function-axioms) are inconsistent by
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #332.
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | |   (11573)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e0) = e1)
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (161), (11508), (11567), (11573),
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | |            #223.
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | |   (11574)  all_55_15 = e0
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (11523), (11574) are inconsistent by
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | |            sub-proof #1884.
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.16  | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | |   (11575)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 223.54/38.16  | | | | | | | | | | | | | | | | | |            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 223.54/38.16  | | | | | | | | | | | | | | | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 223.54/38.16  | | | | | | | | | | | | | | | | | |              all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 223.54/38.16  | | | | | | | | | | | | | | | | | |            & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 223.54/38.16  | | | | | | | | | | | | | | | | | |            & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 223.54/38.16  | | | | | | | | | | | | | | | | | |            & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 223.54/38.16  | | | | | | | | | | | | | | | | | |            $i(all_52_31)
% 223.54/38.16  | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | ALPHA: (11575) implies:
% 223.54/38.16  | | | | | | | | | | | | | | | | | |   (11576)  op(e0, e0) = all_52_31
% 223.54/38.16  | | | | | | | | | | | | | | | | | |   (11577)  op(e0, e2) = all_52_27
% 223.54/38.16  | | | | | | | | | | | | | | | | | |   (11578)  op(all_52_27, all_52_27) = e2
% 223.54/38.16  | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | |   (11579)  all_55_15 = e3
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (10098), (11579) are inconsistent by
% 223.54/38.16  | | | | | | | | | | | | | | | | | | |            sub-proof #2503.
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | |   (11580)  all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | BETA: splitting (11580) gives:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | |   (11581)  all_55_15 = e2
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (373), (11581) are inconsistent by
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | |            sub-proof #2502.
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | |   (11582)   ~ (all_55_15 = e2)
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | |   (11583)  all_55_15 = e1 | all_55_15 = e0
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | BETA: splitting (11583) gives:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | |   (11584)  all_55_15 = e1
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (11584) imply:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | |   (11585)  all_4_2 = e1
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | SIMP: (11585) implies:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | |   (11586)  all_4_2 = e1
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | REDUCE: (370), (11586) imply:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | |   (11587)   ~ (all_53_12 = e1)
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | REDUCE: (372), (11586) imply:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | |   (11588)   ~ (all_53_14 = e1)
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | REDUCE: (373), (11586) imply:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | |   (11589)   ~ (e2 = e1)
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | |   (11590)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (169), (11518), (11587), (11590),
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | |            #218.
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | |   (11591)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11591) gives:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | | |   (11592)  all_57_11 = e1 & op(e1, e0) = e1
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (11588), (11592), (function-axioms) are
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #305.
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | | |   (11593)  all_57_15 = e1 & op(e0, e0) = e1
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11513), (11576), (11577), (11578), (11593),
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | | |            #1877.
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | |   (11594)  all_55_15 = e0
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (11523), (11594) are inconsistent by
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | |            sub-proof #1884.
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.16  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.16  | | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | | End of split
% 223.54/38.16  | | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | | End of split
% 223.54/38.16  | | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | | End of split
% 223.54/38.16  | | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | | End of split
% 223.54/38.16  | | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | | End of split
% 223.54/38.16  | | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | End of split
% 223.54/38.16  | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | End of split
% 223.54/38.16  | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | Case 2:
% 223.54/38.16  | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | |   (11595)  all_57_1 = e0 & op(e3, e2) = e0
% 223.54/38.16  | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | ALPHA: (11595) implies:
% 223.54/38.16  | | | | | | | | | | |   (11596)  op(e3, e2) = e0
% 223.54/38.16  | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | REF_CLOSE: (171), (11239), (11596), (function-axioms) are
% 223.54/38.16  | | | | | | | | | | |            inconsistent by sub-proof #1941.
% 223.54/38.16  | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | End of split
% 223.54/38.16  | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | Case 2:
% 223.54/38.16  | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | |   (11597)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 223.54/38.16  | | | | | | | | | |              & op(e3, e0) = e0)
% 223.54/38.16  | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | REF_CLOSE: (169), (170), (11240), (11241), (11597),
% 223.54/38.16  | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.54/38.16  | | | | | | | | | |            #1544.
% 223.54/38.16  | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | End of split
% 223.54/38.16  | | | | | | | | | 
% 223.54/38.16  | | | | | | | | End of split
% 223.54/38.16  | | | | | | | | 
% 223.54/38.16  | | | | | | | Case 2:
% 223.54/38.16  | | | | | | | | 
% 223.54/38.16  | | | | | | | |   (11598)  all_12_2 = e3
% 223.54/38.16  | | | | | | | |   (11599)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 &
% 223.54/38.16  | | | | | | | |              op(e0, e3) = all_12_1 & $i(all_12_0) &
% 223.54/38.16  | | | | | | | |              $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0, e3) =
% 223.54/38.16  | | | | | | | |              all_12_1 & $i(all_12_1))
% 223.54/38.16  | | | | | | | | 
% 223.54/38.16  | | | | | | | | COMBINE_EQS: (325), (11598) imply:
% 223.54/38.16  | | | | | | | |   (11600)  all_4_2 = e3
% 223.54/38.16  | | | | | | | | 
% 223.54/38.16  | | | | | | | | COMBINE_EQS: (318), (11600) imply:
% 223.54/38.16  | | | | | | | |   (11601)  all_22_2 = e3
% 223.54/38.16  | | | | | | | | 
% 223.54/38.16  | | | | | | | | REDUCE: (370), (11600) imply:
% 223.54/38.16  | | | | | | | |   (11602)   ~ (all_53_12 = e3)
% 223.54/38.16  | | | | | | | | 
% 223.54/38.16  | | | | | | | | REDUCE: (372), (11600) imply:
% 223.54/38.16  | | | | | | | |   (11603)   ~ (all_53_14 = e3)
% 223.54/38.16  | | | | | | | | 
% 223.54/38.16  | | | | | | | | BETA: splitting (221) gives:
% 223.54/38.16  | | | | | | | | 
% 223.54/38.16  | | | | | | | | Case 1:
% 223.54/38.16  | | | | | | | | | 
% 223.54/38.16  | | | | | | | | |   (11604)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 223.54/38.16  | | | | | | | | |              & op(e2, e1) = e3)
% 223.54/38.16  | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | BETA: splitting (11604) gives:
% 223.54/38.16  | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | Case 1:
% 223.54/38.16  | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | |   (11605)  all_57_4 = e3 & op(e3, e1) = e3
% 223.54/38.16  | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | ALPHA: (11605) implies:
% 223.54/38.16  | | | | | | | | | |   (11606)  all_57_4 = e3
% 223.54/38.16  | | | | | | | | | |   (11607)  op(e3, e1) = e3
% 223.54/38.16  | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | BETA: splitting (217) gives:
% 223.54/38.16  | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | Case 1:
% 223.54/38.16  | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | |   (11608)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 223.54/38.16  | | | | | | | | | | |              & op(e1, e2) = e3)
% 223.54/38.16  | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | BETA: splitting (11608) gives:
% 223.54/38.16  | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | Case 1:
% 223.54/38.16  | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | |   (11609)  all_57_6 = e3 & op(e1, e3) = e3
% 223.54/38.16  | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | ALPHA: (11609) implies:
% 223.54/38.16  | | | | | | | | | | | |   (11610)  all_57_6 = e3
% 223.54/38.16  | | | | | | | | | | | |   (11611)  op(e1, e3) = e3
% 223.54/38.16  | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (39), (45),
% 223.54/38.16  | | | | | | | | | | | |            (58), (64), (67), (88), (107), (121), (122),
% 223.54/38.16  | | | | | | | | | | | |            (135), (141), (142), (145), (150), (158), (159),
% 223.54/38.16  | | | | | | | | | | | |            (160), (161), (163), (164), (165), (166), (168),
% 223.54/38.16  | | | | | | | | | | | |            (169), (170), (171), (195), (205), (207), (208),
% 223.54/38.16  | | | | | | | | | | | |            (209), (210), (211), (212), (213), (214), (215),
% 223.54/38.16  | | | | | | | | | | | |            (216), (217), (218), (219), (220), (221), (222),
% 223.54/38.16  | | | | | | | | | | | |            (223), (224), (225), (226), (227), (228), (229),
% 223.54/38.16  | | | | | | | | | | | |            (230), (231), (232), (233), (234), (235), (236),
% 223.54/38.16  | | | | | | | | | | | |            (237), (249), (277), (315), (327), (336), (338),
% 223.54/38.16  | | | | | | | | | | | |            (342), (344), (346), (348), (361), (363), (364),
% 223.54/38.16  | | | | | | | | | | | |            (366), (368), (373), (10088), (10090), (10094),
% 223.54/38.16  | | | | | | | | | | | |            (10095), (10096), (11599), (11601), (11602),
% 223.54/38.16  | | | | | | | | | | | |            (11603), (11606), (11607), (11610), (11611),
% 223.54/38.16  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.54/38.16  | | | | | | | | | | | |            #187.
% 223.54/38.16  | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | Case 2:
% 223.54/38.16  | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | |   (11612)  all_57_7 = e3 & op(e1, e2) = e3
% 223.54/38.16  | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | | REF_CLOSE: (163), (10087), (11612), (function-axioms) are
% 223.54/38.16  | | | | | | | | | | | |            inconsistent by sub-proof #267.
% 223.54/38.16  | | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | End of split
% 223.54/38.16  | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | Case 2:
% 223.54/38.16  | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | |   (11613)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 223.54/38.16  | | | | | | | | | | |              e3 & op(e1, e0) = e3)
% 223.54/38.16  | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | | REF_CLOSE: (39), (161), (374), (11603), (11613),
% 223.54/38.16  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.54/38.16  | | | | | | | | | | |            #2310.
% 223.54/38.16  | | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | End of split
% 223.54/38.16  | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | Case 2:
% 223.54/38.16  | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | |   (11614)  all_57_5 = e3 & op(e2, e1) = e3
% 223.54/38.16  | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | | REF_CLOSE: (166), (10089), (11614), (function-axioms) are
% 223.54/38.16  | | | | | | | | | |            inconsistent by sub-proof #270.
% 223.54/38.16  | | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | End of split
% 223.54/38.16  | | | | | | | | | 
% 223.54/38.16  | | | | | | | | Case 2:
% 223.54/38.16  | | | | | | | | | 
% 223.54/38.16  | | | | | | | | |   (11615)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3
% 223.54/38.16  | | | | | | | | |              & op(e0, e1) = e3)
% 223.54/38.16  | | | | | | | | | 
% 223.54/38.16  | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (161), (165),
% 223.54/38.16  | | | | | | | | |            (169), (207), (208), (209), (213), (374), (10090),
% 223.54/38.16  | | | | | | | | |            (11602), (11603), (11615), (function-axioms) are
% 223.54/38.16  | | | | | | | | |            inconsistent by sub-proof #186.
% 223.54/38.16  | | | | | | | | | 
% 223.54/38.16  | | | | | | | | End of split
% 223.54/38.16  | | | | | | | | 
% 223.54/38.16  | | | | | | | End of split
% 223.54/38.16  | | | | | | | 
% 223.54/38.16  | | | | | | Case 2:
% 223.54/38.16  | | | | | | | 
% 223.54/38.16  | | | | | | |   (11616)  all_10_2 = e1
% 223.54/38.16  | | | | | | | 
% 223.54/38.16  | | | | | | | REDUCE: (338), (11616) imply:
% 223.54/38.16  | | | | | | |   (11617)   ~ (all_53_1 = e1)
% 223.54/38.16  | | | | | | | 
% 223.54/38.16  | | | | | | | REDUCE: (340), (11616) imply:
% 223.54/38.16  | | | | | | |   (11618)   ~ (all_53_2 = e1)
% 223.54/38.16  | | | | | | | 
% 223.54/38.16  | | | | | | | REDUCE: (342), (11616) imply:
% 223.54/38.16  | | | | | | |   (11619)   ~ (all_53_3 = e1)
% 223.54/38.16  | | | | | | | 
% 223.54/38.16  | | | | | | | REDUCE: (344), (11616) imply:
% 223.54/38.16  | | | | | | |   (11620)   ~ (all_53_4 = e1)
% 223.54/38.16  | | | | | | | 
% 223.54/38.16  | | | | | | | REDUCE: (346), (11616) imply:
% 223.54/38.16  | | | | | | |   (11621)   ~ (all_53_8 = e1)
% 223.54/38.16  | | | | | | | 
% 223.54/38.16  | | | | | | | BETA: splitting (232) gives:
% 223.54/38.16  | | | | | | | 
% 223.54/38.16  | | | | | | | Case 1:
% 223.54/38.16  | | | | | | | | 
% 223.54/38.17  | | | | | | | |   (11622)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 &
% 223.54/38.17  | | | | | | | |              op(e2, e3) = e1)
% 223.54/38.17  | | | | | | | | 
% 223.54/38.17  | | | | | | | | BETA: splitting (11622) gives:
% 223.54/38.17  | | | | | | | | 
% 223.54/38.17  | | | | | | | | Case 1:
% 223.54/38.17  | | | | | | | | | 
% 223.54/38.17  | | | | | | | | |   (11623)  all_57_0 = e1 & op(e3, e3) = e1
% 223.54/38.17  | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | ALPHA: (11623) implies:
% 223.54/38.17  | | | | | | | | |   (11624)  all_57_0 = e1
% 223.54/38.17  | | | | | | | | |   (11625)  op(e3, e3) = e1
% 223.54/38.17  | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | BETA: splitting (49) gives:
% 223.54/38.17  | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | Case 1:
% 223.54/38.17  | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | |   (11626)   ~ (all_12_2 = e3)
% 223.54/38.17  | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | REDUCE: (325), (11626) imply:
% 223.54/38.17  | | | | | | | | | |   (11627)   ~ (all_4_2 = e3)
% 223.54/38.17  | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | BETA: splitting (67) gives:
% 223.54/38.17  | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | Case 1:
% 223.54/38.17  | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | |   (11628)   ~ (all_24_2 = e0)
% 223.54/38.17  | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | REDUCE: (315), (11628) imply:
% 223.54/38.17  | | | | | | | | | | |   (11629)   ~ (all_6_2 = e0)
% 223.54/38.17  | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | BETA: splitting (76) gives:
% 223.54/38.17  | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | Case 1:
% 223.54/38.17  | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | |   (11630)   ~ (all_30_2 = e1)
% 223.54/38.17  | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | REDUCE: (330), (11630) imply:
% 223.54/38.17  | | | | | | | | | | | |   (11631)   ~ (all_4_2 = e1)
% 223.54/38.17  | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | BETA: splitting (190) gives:
% 223.54/38.17  | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | Case 1:
% 223.54/38.17  | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | |   (11632)  all_55_15 = e3
% 223.54/38.17  | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | REF_CLOSE: (244), (11627), (11632) are inconsistent by
% 223.54/38.17  | | | | | | | | | | | | |            sub-proof #2503.
% 223.54/38.17  | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | Case 2:
% 223.54/38.17  | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | |   (11633)   ~ (all_55_15 = e3)
% 223.54/38.17  | | | | | | | | | | | | |   (11634)  all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 223.54/38.17  | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | BETA: splitting (11634) gives:
% 223.54/38.17  | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | Case 1:
% 223.54/38.17  | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | |   (11635)  all_55_15 = e2
% 223.54/38.17  | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | REF_CLOSE: (244), (373), (11635) are inconsistent by
% 223.54/38.17  | | | | | | | | | | | | | |            sub-proof #2502.
% 223.54/38.17  | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | Case 2:
% 223.54/38.17  | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | |   (11636)   ~ (all_55_15 = e2)
% 223.54/38.17  | | | | | | | | | | | | | |   (11637)  all_55_15 = e1 | all_55_15 = e0
% 223.54/38.17  | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | BETA: splitting (11637) gives:
% 223.54/38.17  | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | Case 1:
% 223.54/38.17  | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | |   (11638)  all_55_15 = e1
% 223.54/38.17  | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | REF_CLOSE: (244), (11631), (11638) are inconsistent by
% 223.54/38.17  | | | | | | | | | | | | | | |            sub-proof #2501.
% 223.54/38.17  | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | Case 2:
% 223.54/38.17  | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | |   (11639)  all_55_15 = e0
% 223.54/38.17  | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | COMBINE_EQS: (244), (11639) imply:
% 223.54/38.17  | | | | | | | | | | | | | | |   (11640)  all_4_2 = e0
% 223.54/38.17  | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | SIMP: (11640) implies:
% 223.54/38.17  | | | | | | | | | | | | | | |   (11641)  all_4_2 = e0
% 223.54/38.17  | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | REDUCE: (351), (11641) imply:
% 223.54/38.17  | | | | | | | | | | | | | | |   (11642)   ~ (all_53_3 = e0)
% 223.54/38.17  | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | REDUCE: (362), (11641) imply:
% 223.54/38.17  | | | | | | | | | | | | | | |   (11643)   ~ (all_53_7 = e0)
% 223.54/38.17  | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | REDUCE: (370), (11641) imply:
% 223.54/38.17  | | | | | | | | | | | | | | |   (11644)   ~ (all_53_12 = e0)
% 223.54/38.17  | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | REDUCE: (371), (11641) imply:
% 223.54/38.17  | | | | | | | | | | | | | | |   (11645)   ~ (all_53_13 = e0)
% 223.54/38.17  | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | REDUCE: (372), (11641) imply:
% 223.54/38.17  | | | | | | | | | | | | | | |   (11646)   ~ (all_53_14 = e0)
% 223.54/38.17  | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | REDUCE: (11627), (11641) imply:
% 223.54/38.17  | | | | | | | | | | | | | | |   (11647)   ~ (e3 = e0)
% 223.54/38.17  | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | REDUCE: (11631), (11641) imply:
% 223.54/38.17  | | | | | | | | | | | | | | |   (11648)   ~ (e1 = e0)
% 223.54/38.17  | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | REDUCE: (36), (11641) imply:
% 223.54/38.17  | | | | | | | | | | | | | | |   (11649)  op(e0, e0) = e0
% 223.54/38.17  | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | BETA: splitting (88) gives:
% 223.54/38.17  | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | Case 1:
% 223.54/38.17  | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | |   (11650)   ~ (all_38_2 = e2)
% 223.54/38.17  | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | REDUCE: (249), (11650) imply:
% 223.54/38.17  | | | | | | | | | | | | | | | |   (11651)   ~ (all_6_2 = e2)
% 223.54/38.17  | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 223.54/38.17  | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.17  | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | |   (11652)  all_55_10 = e3
% 223.54/38.17  | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (374), (11652) are inconsistent by
% 223.54/38.17  | | | | | | | | | | | | | | | | |            sub-proof #2500.
% 223.54/38.17  | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.17  | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | |   (11653)   ~ (all_55_10 = e3)
% 223.54/38.17  | | | | | | | | | | | | | | | | |   (11654)  all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 223.54/38.17  | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | BETA: splitting (11654) gives:
% 223.54/38.17  | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | |   (11655)  all_55_10 = e2
% 223.54/38.17  | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (11651), (11655) are inconsistent by
% 223.54/38.17  | | | | | | | | | | | | | | | | | |            sub-proof #2499.
% 223.54/38.17  | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | |   (11656)   ~ (all_55_10 = e2)
% 223.54/38.17  | | | | | | | | | | | | | | | | | |   (11657)  all_55_10 = e1 | all_55_10 = e0
% 223.54/38.17  | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | BETA: splitting (11657) gives:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | |   (11658)  all_55_10 = e1
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (336), (11658) imply:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | |   (11659)  all_6_2 = e1
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | SIMP: (11659) implies:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | |   (11660)  all_6_2 = e1
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | REDUCE: (361), (11660) imply:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | |   (11661)   ~ (all_53_6 = e1)
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | REDUCE: (364), (11660) imply:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | |   (11662)   ~ (all_53_9 = e1)
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | REDUCE: (374), (11660) imply:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | |   (11663)   ~ (e3 = e1)
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | REDUCE: (11651), (11660) imply:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | |   (11664)   ~ (e2 = e1)
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | REDUCE: (39), (11660) imply:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | |   (11665)  op(e1, e1) = e1
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | |   (11666)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (168), (10095), (11617), (11666),
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | |            #240.
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | |   (11667)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | BETA: splitting (11667) gives:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | |   (11668)  all_57_5 = e1 & op(e2, e1) = e1
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (11662), (11668), (function-axioms) are
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2305.
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | |   (11669)  all_57_10 = e1 & op(e2, e0) = e1
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | ALPHA: (11669) implies:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | |   (11670)  op(e2, e0) = e1
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | |   (11671)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (171), (10095), (11620), (11671),
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | |            #185.
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | |   (11672)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11672) gives:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | |   (11673)  all_57_7 = e1 & op(e1, e2) = e1
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (11661), (11673), (function-axioms) are
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2265.
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | |   (11674)  all_57_13 = e1 & op(e0, e2) = e1
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11674) implies:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | |   (11675)  op(e0, e2) = e1
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_7, e1,
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (159), (11675) gives:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | |   (11676)  all_53_7 = e1
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_13,
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | |              e1, e0, e2, simplifying with (165), (11670) gives:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | |   (11677)  all_53_13 = e1
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (114), (11677) imply:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | |   (11678)   ~ (all_53_12 = e1)
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (111), (11677) imply:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | |   (11679)   ~ (all_53_14 = e1)
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (11679) implies:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | |   (11680)   ~ (all_53_14 = e1)
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | |   (11681)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | |              all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | |              op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | |                all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | |                all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | |              & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | |                all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (39), (374), (11625), (11665), (11670),
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | |            (11681), (function-axioms) are inconsistent by
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #359.
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | |   (11682)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | |              & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | |              & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | |                all_52_21) = e1 & op(all_52_23, all_52_23) =
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | |              all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | |              = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | |              & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(all_52_25, all_52_25) = e3 &
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | |              op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | |                all_52_29) = e1 & op(all_52_31, all_52_31) =
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | |              all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | |              = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_29) & $i(all_52_31))
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11682) gives:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | |   (11683)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | |            & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_23)
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11683) implies:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | |   (11684)  op(e1, e0) = all_52_23
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | |   (11685)  op(e1, e2) = all_52_19
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | |   (11686)  op(all_52_19, all_52_19) = e2
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_14,
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_23, e0, e1, simplifying with (161), (11684)
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | |   (11687)  all_53_14 = all_52_23
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_6,
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_19, e2, e1, simplifying with (163), (11685)
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | |   (11688)  all_53_6 = all_52_19
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (11687) imply:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | |   (11689)  all_55_11 = all_52_23
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (11688) imply:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | |   (11690)  all_55_9 = all_52_19
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (137), (11688) imply:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | |   (11691)   ~ (all_53_4 = all_52_19)
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (127), (11687), (11688) imply:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | |   (11692)   ~ (all_52_19 = all_52_23)
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10087), (11688) imply:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | |   (11693)   ~ (all_52_19 = e3)
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11661), (11688) imply:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | |   (11694)   ~ (all_52_19 = e1)
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (11687) imply:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | |   (11695)   ~ (all_53_12 = all_52_23)
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11680), (11687) imply:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | |   (11696)   ~ (all_52_23 = e1)
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11646), (11687) imply:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | |   (11697)   ~ (all_52_23 = e0)
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11698)  all_55_1 = e3
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (10086), (11698) are inconsistent by
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2295.
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11699)  all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11700)  all_55_11 = e3
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (11689), (11700) imply:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11701)  all_52_23 = e3
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (11701) implies:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11702)  all_52_23 = e3
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11695), (11702) imply:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11703)   ~ (all_53_12 = e3)
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11704)  all_55_3 = e3
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (11703), (11704) are inconsistent by
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2169.
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11705)  all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11705) gives:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11706)  all_55_3 = e2
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (11706) imply:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11707)  all_53_12 = e2
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (11707) implies:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11708)  all_53_12 = e2
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (11708) imply:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11709)   ~ (all_53_4 = e2)
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11699) gives:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11710)  all_55_1 = e2
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (11709), (11710) are inconsistent by
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2284.
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11711)  all_55_1 = e1 | all_55_1 = e0
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11711) gives:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11712)  all_55_1 = e1
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (11620), (11712) are inconsistent by
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2283.
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11713)  all_55_1 = e0
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (11713) imply:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11714)  all_53_4 = e0
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (11714) implies:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11715)  all_53_4 = e0
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11691), (11715) imply:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11716)   ~ (all_52_19 = e0)
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (11716) implies:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11717)   ~ (all_52_19 = e0)
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11718)  all_55_9 = e3
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11690), (11693), (11718) are inconsistent by
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1603.
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11719)   ~ (all_55_9 = e3)
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11720)  all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11720) gives:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11721)  all_55_9 = e2
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (11690), (11721) imply:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11722)  all_52_19 = e2
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (11722) implies:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11723)  all_52_19 = e2
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11693), (11723) imply:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11724)   ~ (e3 = e2)
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11686), (11723) imply:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11725)  op(e2, e2) = e2
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10095), (11725), (function-axioms) are
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2298.
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11726)  all_55_9 = e1 | all_55_9 = e0
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11690), (11694), (11717), (11726) are
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1883.
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11727)  all_55_3 = e1 | all_55_3 = e0
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (11644), (11678), (11727) are inconsistent
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2132.
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11728)  all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11728) gives:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11729)  all_55_11 = e2
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (11689), (11729) imply:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11730)  all_52_23 = e2
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (11730) implies:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11731)  all_52_23 = e2
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11692), (11731) imply:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11732)   ~ (all_52_19 = e2)
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11733)  all_55_9 = e3
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (11690), (11733) imply:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11734)  all_52_19 = e3
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11693), (11734) imply:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11735)  $false
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (11735) is inconsistent.
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11736)  all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11736) gives:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11737)  all_55_9 = e2
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (11690), (11737) imply:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11738)  all_52_19 = e2
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11732), (11738) imply:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11739)  $false
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (11739) is inconsistent.
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11740)   ~ (all_55_9 = e2)
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11741)  all_55_9 = e1 | all_55_9 = e0
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11741) gives:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11742)  all_55_9 = e1
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (11690), (11742) imply:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11743)  all_52_19 = e1
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11694), (11743) imply:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11744)  $false
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (11744) is inconsistent.
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11745)  all_55_9 = e0
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (11690), (11745) imply:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11746)  all_52_19 = e0
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11732), (11746) imply:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11747)   ~ (e2 = e0)
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11685), (11746) imply:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11748)  op(e1, e2) = e0
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (11649), (11685), (11686), (11748),
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2158.
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11749)  all_55_11 = e1 | all_55_11 = e0
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11689), (11696), (11697), (11749) are
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2107.
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | |   (11750)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | |            & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_31)
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11665), (11675), (11750), (function-axioms)
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #356.
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | |   (11751)  all_55_10 = e0
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (11629), (11751) are inconsistent by
% 223.54/38.17  | | | | | | | | | | | | | | | | | | |            sub-proof #2118.
% 223.54/38.17  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.17  | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | End of split
% 223.54/38.17  | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | End of split
% 223.54/38.17  | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | Case 2:
% 223.54/38.17  | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | |   (11752)  all_38_2 = e2
% 223.54/38.17  | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (11752) imply:
% 223.54/38.17  | | | | | | | | | | | | | | | |   (11753)  all_6_2 = e2
% 223.54/38.17  | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | REDUCE: (374), (11753) imply:
% 223.54/38.17  | | | | | | | | | | | | | | | |   (11754)   ~ (e3 = e2)
% 223.54/38.17  | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | REDUCE: (39), (11753) imply:
% 223.54/38.17  | | | | | | | | | | | | | | | |   (11755)  op(e1, e1) = e2
% 223.54/38.17  | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 223.54/38.17  | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.17  | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | |   (11756)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 223.54/38.17  | | | | | | | | | | | | | | | | |              all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 223.54/38.17  | | | | | | | | | | | | | | | | |              op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 223.54/38.17  | | | | | | | | | | | | | | | | |                all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 223.54/38.17  | | | | | | | | | | | | | | | | |              op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 223.54/38.17  | | | | | | | | | | | | | | | | |              op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 223.54/38.17  | | | | | | | | | | | | | | | | |              $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 223.54/38.17  | | | | | | | | | | | | | | | | |              $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 223.54/38.17  | | | | | | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 223.54/38.17  | | | | | | | | | | | | | | | | |                all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 223.54/38.17  | | | | | | | | | | | | | | | | |              & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 223.54/38.17  | | | | | | | | | | | | | | | | |                all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 223.54/38.17  | | | | | | | | | | | | | | | | |              op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 223.54/38.17  | | | | | | | | | | | | | | | | |              & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 223.54/38.17  | | | | | | | | | | | | | | | | |              $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 223.54/38.17  | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | BETA: splitting (11756) gives:
% 223.54/38.17  | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | |   (11757)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 223.54/38.17  | | | | | | | | | | | | | | | | | |            all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 223.54/38.17  | | | | | | | | | | | | | | | | | |            op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 223.54/38.17  | | | | | | | | | | | | | | | | | |              all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 223.54/38.17  | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 223.54/38.17  | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 223.54/38.17  | | | | | | | | | | | | | | | | | |            $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 223.54/38.17  | | | | | | | | | | | | | | | | | |            $i(all_52_7)
% 223.54/38.17  | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (374), (11625), (11757), (function-axioms)
% 223.54/38.17  | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #360.
% 223.54/38.17  | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.17  | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | |   (11758)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 223.54/38.17  | | | | | | | | | | | | | | | | | |            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 223.54/38.17  | | | | | | | | | | | | | | | | | |            op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 223.54/38.17  | | | | | | | | | | | | | | | | | |              all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 223.54/38.17  | | | | | | | | | | | | | | | | | |            & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 223.54/38.17  | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 223.54/38.17  | | | | | | | | | | | | | | | | | |            $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 223.54/38.17  | | | | | | | | | | | | | | | | | |            $i(all_52_15)
% 223.54/38.17  | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10095), (11625), (11758), (function-axioms)
% 223.54/38.17  | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #184.
% 223.54/38.17  | | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | | End of split
% 223.54/38.17  | | | | | | | | | | | | | | | | | 
% 223.54/38.17  | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.17  | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | |   (11759)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 223.54/38.18  | | | | | | | | | | | | | | | | |              & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 223.54/38.18  | | | | | | | | | | | | | | | | |              & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 223.54/38.18  | | | | | | | | | | | | | | | | |                all_52_21) = e1 & op(all_52_23, all_52_23) =
% 223.54/38.18  | | | | | | | | | | | | | | | | |              e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 223.54/38.18  | | | | | | | | | | | | | | | | |              all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 223.54/38.18  | | | | | | | | | | | | | | | | |              = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 223.54/38.18  | | | | | | | | | | | | | | | | |              $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 223.54/38.18  | | | | | | | | | | | | | | | | |              & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 223.54/38.18  | | | | | | | | | | | | | | | | |              e0 & op(all_52_25, all_52_25) = e3 &
% 223.54/38.18  | | | | | | | | | | | | | | | | |              op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 223.54/38.18  | | | | | | | | | | | | | | | | |                all_52_29) = e1 & op(all_52_31, all_52_31) =
% 223.54/38.18  | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 223.54/38.18  | | | | | | | | | | | | | | | | |              all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 223.54/38.18  | | | | | | | | | | | | | | | | |              = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 223.54/38.18  | | | | | | | | | | | | | | | | |              $i(all_52_29) & $i(all_52_31))
% 223.54/38.18  | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | BETA: splitting (11759) gives:
% 223.54/38.18  | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.18  | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | |   (11760)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 223.54/38.18  | | | | | | | | | | | | | | | | | |            all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 223.54/38.18  | | | | | | | | | | | | | | | | | |            op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 223.54/38.18  | | | | | | | | | | | | | | | | | |              all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 223.54/38.18  | | | | | | | | | | | | | | | | | |            & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 223.54/38.18  | | | | | | | | | | | | | | | | | |            & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 223.54/38.18  | | | | | | | | | | | | | | | | | |            & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 223.54/38.18  | | | | | | | | | | | | | | | | | |            $i(all_52_23)
% 223.54/38.18  | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | ALPHA: (11760) implies:
% 223.54/38.18  | | | | | | | | | | | | | | | | | |   (11761)  op(e1, e1) = all_52_21
% 223.54/38.18  | | | | | | | | | | | | | | | | | |   (11762)  op(e1, e3) = all_52_17
% 223.54/38.18  | | | | | | | | | | | | | | | | | |   (11763)  op(all_52_21, all_52_21) = e1
% 223.54/38.18  | | | | | | | | | | | | | | | | | |   (11764)  op(all_52_17, all_52_17) = e3
% 223.54/38.18  | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 223.54/38.18  | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | |   (11765)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 223.54/38.18  | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e2)
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | BETA: splitting (11765) gives:
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | |   (11766)  all_57_6 = e2 & op(e1, e3) = e2
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | ALPHA: (11766) implies:
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | |   (11767)  all_57_6 = e2
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | |   (11768)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e1)
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11768) gives:
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | |   (11769)  all_57_6 = e1 & op(e1, e3) = e1
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11769) implies:
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | |   (11770)  op(e1, e3) = e1
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (195), (336), (374), (11762), (11764),
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | |            (11770), (function-axioms) are inconsistent by
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1998.
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | |   (11771)  all_57_7 = e1 & op(e1, e2) = e1
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11771) implies:
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | |   (11772)  all_57_7 = e1
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (39), (214), (217),
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | |            (374), (11629), (11767), (11772),
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | |            #342.
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | |   (11773)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e0) = e1)
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (39), (161),
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | |            (165), (166), (168), (195), (212), (213), (214),
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | |            (215), (217), (223), (336), (364), (373), (374),
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | |            (10089), (10090), (10095), (11617), (11629),
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | |            (11646), (11649), (11755), (11761), (11763),
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | |            (11773), (function-axioms) are inconsistent by
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | |            sub-proof #183.
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | |   (11774)  all_57_7 = e2 & op(e1, e2) = e2
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | ALPHA: (11774) implies:
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | |   (11775)  all_57_7 = e2
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | |   (11776)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e1)
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11776) gives:
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | |   (11777)  all_57_6 = e1 & op(e1, e3) = e1
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11777) implies:
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | |   (11778)  op(e1, e3) = e1
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (195), (336), (374), (11762), (11764),
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | |            (11778), (function-axioms) are inconsistent by
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1998.
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | |   (11779)  all_57_7 = e1 & op(e1, e2) = e1
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11775), (11779) are inconsistent by
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2190.
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | |   (11780)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e0) = e1)
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (39), (161),
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | |            (165), (166), (168), (195), (212), (213), (214),
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | |            (215), (217), (223), (336), (364), (373), (374),
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | |            (10089), (10090), (10095), (11617), (11629),
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | |            (11646), (11649), (11755), (11761), (11763),
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | |            (11780), (function-axioms) are inconsistent by
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | |            sub-proof #183.
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | |   (11781)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 223.54/38.18  | | | | | | | | | | | | | | | | | | |              e2 & op(e1, e0) = e2)
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | BETA: splitting (11781) gives:
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | |   (11782)  all_57_8 = e2 & op(e1, e1) = e2
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | |              all_52_21, e1, e1, simplifying with (11755),
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | |              (11761) gives:
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | |   (11783)  all_52_21 = e2
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | REDUCE: (11763), (11783) imply:
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | |   (11784)  op(e2, e2) = e1
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10095), (11784), (function-axioms) are
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1912.
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | |   (11785)  all_57_11 = e2 & op(e1, e0) = e2
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (161), (214),
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | |            (215), (217), (374), (11629), (11646), (11755),
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | |            (11785), (function-axioms) are inconsistent by
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | |            sub-proof #347.
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.18  | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.18  | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | |   (11786)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 223.54/38.18  | | | | | | | | | | | | | | | | | |            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 223.54/38.18  | | | | | | | | | | | | | | | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 223.54/38.18  | | | | | | | | | | | | | | | | | |              all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 223.54/38.18  | | | | | | | | | | | | | | | | | |            & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 223.54/38.18  | | | | | | | | | | | | | | | | | |            & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 223.54/38.18  | | | | | | | | | | | | | | | | | |            & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 223.54/38.18  | | | | | | | | | | | | | | | | | |            $i(all_52_31)
% 223.54/38.18  | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | ALPHA: (11786) implies:
% 223.54/38.18  | | | | | | | | | | | | | | | | | |   (11787)  op(e0, e2) = all_52_27
% 223.54/38.18  | | | | | | | | | | | | | | | | | |   (11788)  op(e0, e3) = all_52_25
% 223.54/38.18  | | | | | | | | | | | | | | | | | |   (11789)  op(all_52_27, all_52_27) = e2
% 223.54/38.18  | | | | | | | | | | | | | | | | | |   (11790)  op(all_52_25, all_52_25) = e3
% 223.54/38.18  | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_7,
% 223.54/38.18  | | | | | | | | | | | | | | | | | |              all_52_27, e2, e0, simplifying with (159), (11787)
% 223.54/38.18  | | | | | | | | | | | | | | | | | |              gives:
% 223.54/38.18  | | | | | | | | | | | | | | | | | |   (11791)  all_53_7 = all_52_27
% 223.54/38.18  | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_3,
% 223.54/38.18  | | | | | | | | | | | | | | | | | |              all_52_25, e3, e0, simplifying with (160), (11788)
% 223.54/38.18  | | | | | | | | | | | | | | | | | |              gives:
% 223.54/38.18  | | | | | | | | | | | | | | | | | |   (11792)  all_53_3 = all_52_25
% 223.54/38.18  | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (11791) imply:
% 223.54/38.18  | | | | | | | | | | | | | | | | | |   (11793)  all_55_13 = all_52_27
% 223.54/38.18  | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (11792) imply:
% 223.54/38.18  | | | | | | | | | | | | | | | | | |   (11794)  all_55_12 = all_52_25
% 223.54/38.18  | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | REDUCE: (149), (11792) imply:
% 223.54/38.18  | | | | | | | | | | | | | | | | | |   (11795)   ~ (all_53_1 = all_52_25)
% 223.54/38.18  | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | REDUCE: (11619), (11792) imply:
% 223.54/38.18  | | | | | | | | | | | | | | | | | |   (11796)   ~ (all_52_25 = e1)
% 223.54/38.18  | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | REDUCE: (11642), (11792) imply:
% 223.54/38.18  | | | | | | | | | | | | | | | | | |   (11797)   ~ (all_52_25 = e0)
% 223.54/38.18  | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | REDUCE: (10088), (11791) imply:
% 223.54/38.18  | | | | | | | | | | | | | | | | | |   (11798)   ~ (all_52_27 = e3)
% 223.54/38.18  | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | REDUCE: (11643), (11791) imply:
% 223.54/38.18  | | | | | | | | | | | | | | | | | |   (11799)   ~ (all_52_27 = e0)
% 223.54/38.18  | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | BETA: splitting (97) gives:
% 223.54/38.18  | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | |   (11800)   ~ (all_44_2 = e3)
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | REDUCE: (10084), (11800) imply:
% 223.54/38.18  | | | | | | | | | | | | | | | | | | |   (11801)  $false
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | CLOSE: (11801) is inconsistent.
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | |   (11802)  ( ~ (all_44_0 = e1) & op(all_44_1, e2) = all_44_0
% 223.54/38.18  | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = all_44_1 & $i(all_44_0) &
% 223.54/38.18  | | | | | | | | | | | | | | | | | | |              $i(all_44_1)) | ( ~ (all_44_1 = e0) & op(e2, e3)
% 223.54/38.18  | | | | | | | | | | | | | | | | | | |              = all_44_1 & $i(all_44_1))
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | |   (11803)  all_55_12 = e3
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (11794), (11803) imply:
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | |   (11804)  all_52_25 = e3
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | SIMP: (11804) implies:
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | |   (11805)  all_52_25 = e3
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | REDUCE: (11790), (11805) imply:
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | |   (11806)  op(e3, e3) = e3
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (11625), (11806), (function-axioms) are
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2495.
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | |   (11807)  all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | BETA: splitting (11807) gives:
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | |   (11808)  all_55_12 = e2
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (11794), (11808) imply:
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | |   (11809)  all_52_25 = e2
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | SIMP: (11809) implies:
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | |   (11810)  all_52_25 = e2
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | REDUCE: (11795), (11810) imply:
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | |   (11811)   ~ (all_53_1 = e2)
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | |   (11812)  all_55_4 = e3
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (11812) imply:
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | |   (11813)  all_53_1 = e3
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10085), (11813) imply:
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | |   (11814)  $false
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (11814) is inconsistent.
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | |   (11815)  all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11815) gives:
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | |   (11816)  all_55_4 = e2
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (11816) imply:
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | |   (11817)  all_53_1 = e2
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11811), (11817) imply:
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | |   (11818)  $false
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (11818) is inconsistent.
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | |   (11819)  all_55_4 = e1 | all_55_4 = e0
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11819) gives:
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | | |   (11820)  all_55_4 = e1
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (11617), (11820) are inconsistent by
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2166.
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | | |   (11821)  all_55_4 = e0
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (11821) imply:
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | | |   (11822)  all_53_1 = e0
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (11822) implies:
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | | |   (11823)  all_53_1 = e0
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (168), (11823) imply:
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | | |   (11824)  op(e2, e3) = e0
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (192), (10083), (10095), (11787), (11789),
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | | |            (11793), (11798), (11799), (11802), (11824),
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | | |            #252.
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | |   (11825)  all_55_12 = e1 | all_55_12 = e0
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11794), (11796), (11797), (11825) are
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #323.
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.18  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.18  | | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | | End of split
% 223.54/38.18  | | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | End of split
% 223.54/38.18  | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | End of split
% 223.54/38.18  | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | End of split
% 223.54/38.18  | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | End of split
% 223.54/38.18  | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | End of split
% 223.54/38.18  | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | Case 2:
% 223.54/38.18  | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | |   (11826)  all_30_2 = e1
% 223.54/38.18  | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | COMBINE_EQS: (330), (11826) imply:
% 223.54/38.18  | | | | | | | | | | | |   (11827)  all_4_2 = e1
% 223.54/38.18  | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | SIMP: (11827) implies:
% 223.54/38.18  | | | | | | | | | | | |   (11828)  all_4_2 = e1
% 223.54/38.18  | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | REDUCE: (371), (11828) imply:
% 223.54/38.18  | | | | | | | | | | | |   (11829)   ~ (all_53_13 = e1)
% 223.54/38.18  | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | REDUCE: (11627), (11828) imply:
% 223.54/38.18  | | | | | | | | | | | |   (11830)   ~ (e3 = e1)
% 223.54/38.18  | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | REDUCE: (373), (11828) imply:
% 223.54/38.18  | | | | | | | | | | | |   (11831)   ~ (e2 = e1)
% 223.54/38.18  | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | REDUCE: (36), (11828) imply:
% 223.54/38.18  | | | | | | | | | | | |   (11832)  op(e0, e0) = e1
% 223.54/38.18  | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | BETA: splitting (223) gives:
% 223.54/38.18  | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | Case 1:
% 223.54/38.18  | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | |   (11833)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 223.54/38.18  | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 223.54/38.18  | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | REF_CLOSE: (8), (168), (10095), (11617), (11833),
% 223.54/38.18  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.54/38.18  | | | | | | | | | | | | |            #240.
% 223.54/38.18  | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | Case 2:
% 223.54/38.18  | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | |   (11834)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 223.54/38.18  | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 223.54/38.18  | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | BETA: splitting (11834) gives:
% 223.54/38.18  | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | Case 1:
% 223.54/38.18  | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | |   (11835)  all_57_5 = e1 & op(e2, e1) = e1
% 223.54/38.18  | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | ALPHA: (11835) implies:
% 223.54/38.18  | | | | | | | | | | | | | |   (11836)  op(e2, e1) = e1
% 223.54/38.18  | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 223.54/38.18  | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | Case 1:
% 223.54/38.18  | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | |   (11837)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 223.54/38.18  | | | | | | | | | | | | | | |              all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 223.54/38.18  | | | | | | | | | | | | | | |              op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 223.54/38.18  | | | | | | | | | | | | | | |                all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 223.54/38.18  | | | | | | | | | | | | | | |              op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 223.54/38.18  | | | | | | | | | | | | | | |              op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 223.54/38.18  | | | | | | | | | | | | | | |              $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 223.54/38.18  | | | | | | | | | | | | | | |              $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 223.54/38.18  | | | | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 223.54/38.18  | | | | | | | | | | | | | | |                all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 223.54/38.18  | | | | | | | | | | | | | | |              & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 223.54/38.18  | | | | | | | | | | | | | | |                all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 223.54/38.18  | | | | | | | | | | | | | | |              op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 223.54/38.18  | | | | | | | | | | | | | | |              & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 223.54/38.18  | | | | | | | | | | | | | | |              $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 223.54/38.18  | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | BETA: splitting (11837) gives:
% 223.54/38.18  | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | Case 1:
% 223.54/38.18  | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | |   (11838)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 223.54/38.18  | | | | | | | | | | | | | | | |            all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 223.54/38.18  | | | | | | | | | | | | | | | |            op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 223.54/38.18  | | | | | | | | | | | | | | | |              all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 223.54/38.18  | | | | | | | | | | | | | | | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 223.54/38.18  | | | | | | | | | | | | | | | |            op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 223.54/38.18  | | | | | | | | | | | | | | | |            $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 223.54/38.18  | | | | | | | | | | | | | | | |            $i(all_52_7)
% 223.54/38.18  | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | REF_CLOSE: (39), (374), (11625), (11838), (function-axioms)
% 223.54/38.18  | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #360.
% 223.54/38.18  | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | Case 2:
% 223.54/38.18  | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | |   (11839)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 223.54/38.18  | | | | | | | | | | | | | | | |            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 223.54/38.18  | | | | | | | | | | | | | | | |            op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 223.54/38.18  | | | | | | | | | | | | | | | |              all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 223.54/38.18  | | | | | | | | | | | | | | | |            & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 223.54/38.18  | | | | | | | | | | | | | | | |            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 223.54/38.18  | | | | | | | | | | | | | | | |            $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 223.54/38.18  | | | | | | | | | | | | | | | |            $i(all_52_15)
% 223.54/38.18  | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10095), (11625), (11839), (function-axioms)
% 223.54/38.18  | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #184.
% 223.54/38.18  | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | End of split
% 223.54/38.18  | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | Case 2:
% 223.54/38.18  | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | |   (11840)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 223.54/38.18  | | | | | | | | | | | | | | |              & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 223.54/38.18  | | | | | | | | | | | | | | |              & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 223.54/38.18  | | | | | | | | | | | | | | |                all_52_21) = e1 & op(all_52_23, all_52_23) =
% 223.54/38.18  | | | | | | | | | | | | | | |              e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 223.54/38.18  | | | | | | | | | | | | | | |              all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 223.54/38.18  | | | | | | | | | | | | | | |              = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 223.54/38.18  | | | | | | | | | | | | | | |              $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 223.54/38.18  | | | | | | | | | | | | | | |              & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 223.54/38.18  | | | | | | | | | | | | | | |              e0 & op(all_52_25, all_52_25) = e3 &
% 223.54/38.18  | | | | | | | | | | | | | | |              op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 223.54/38.18  | | | | | | | | | | | | | | |                all_52_29) = e1 & op(all_52_31, all_52_31) =
% 223.54/38.18  | | | | | | | | | | | | | | |              e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 223.54/38.18  | | | | | | | | | | | | | | |              all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 223.54/38.18  | | | | | | | | | | | | | | |              = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 223.54/38.18  | | | | | | | | | | | | | | |              $i(all_52_29) & $i(all_52_31))
% 223.54/38.18  | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | BETA: splitting (11840) gives:
% 223.54/38.18  | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | Case 1:
% 223.54/38.18  | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | |   (11841)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 223.54/38.18  | | | | | | | | | | | | | | | |            all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 223.54/38.18  | | | | | | | | | | | | | | | |            op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 223.54/38.18  | | | | | | | | | | | | | | | |              all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 223.54/38.18  | | | | | | | | | | | | | | | |            & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 223.54/38.18  | | | | | | | | | | | | | | | |            & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 223.54/38.18  | | | | | | | | | | | | | | | |            & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 223.54/38.18  | | | | | | | | | | | | | | | |            $i(all_52_23)
% 223.54/38.18  | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | ALPHA: (11841) implies:
% 223.54/38.18  | | | | | | | | | | | | | | | |   (11842)  op(e1, e1) = all_52_21
% 223.54/38.18  | | | | | | | | | | | | | | | |   (11843)  op(all_52_21, all_52_21) = e1
% 223.54/38.18  | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | REF_CLOSE: (39), (166), (195), (336), (364), (374), (10089),
% 223.54/38.18  | | | | | | | | | | | | | | | |            (10095), (11629), (11836), (11842), (11843),
% 223.54/38.18  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.54/38.18  | | | | | | | | | | | | | | | |            #243.
% 223.54/38.18  | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | Case 2:
% 223.54/38.18  | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | |   (11844)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 223.54/38.18  | | | | | | | | | | | | | | | |            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 223.54/38.18  | | | | | | | | | | | | | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 223.54/38.18  | | | | | | | | | | | | | | | |              all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 223.54/38.18  | | | | | | | | | | | | | | | |            & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 223.54/38.18  | | | | | | | | | | | | | | | |            & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 223.54/38.18  | | | | | | | | | | | | | | | |            & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 223.54/38.18  | | | | | | | | | | | | | | | |            $i(all_52_31)
% 223.54/38.18  | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | ALPHA: (11844) implies:
% 223.54/38.18  | | | | | | | | | | | | | | | |   (11845)  op(e0, e0) = all_52_31
% 223.54/38.18  | | | | | | | | | | | | | | | |   (11846)  op(all_52_31, all_52_31) = e0
% 223.54/38.18  | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | REF_CLOSE: (39), (11629), (11832), (11845), (11846),
% 223.54/38.18  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.54/38.18  | | | | | | | | | | | | | | | |            #2086.
% 223.54/38.18  | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | End of split
% 223.54/38.18  | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | End of split
% 223.54/38.18  | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | Case 2:
% 223.54/38.18  | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | |   (11847)  all_57_10 = e1 & op(e2, e0) = e1
% 223.54/38.18  | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | REF_CLOSE: (165), (11829), (11847), (function-axioms) are
% 223.54/38.18  | | | | | | | | | | | | | |            inconsistent by sub-proof #2084.
% 223.54/38.18  | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | End of split
% 223.54/38.18  | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | End of split
% 223.54/38.18  | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | End of split
% 223.54/38.18  | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | Case 2:
% 223.54/38.18  | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | |   (11848)  all_24_2 = e0
% 223.54/38.18  | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | COMBINE_EQS: (315), (11848) imply:
% 223.54/38.18  | | | | | | | | | | |   (11849)  all_6_2 = e0
% 223.54/38.18  | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | SIMP: (11849) implies:
% 223.54/38.18  | | | | | | | | | | |   (11850)  all_6_2 = e0
% 223.54/38.18  | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | REDUCE: (361), (11850) imply:
% 223.54/38.18  | | | | | | | | | | |   (11851)   ~ (all_53_6 = e0)
% 223.54/38.18  | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | REDUCE: (363), (11850) imply:
% 223.54/38.18  | | | | | | | | | | |   (11852)   ~ (all_53_8 = e0)
% 223.54/38.18  | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | REDUCE: (364), (11850) imply:
% 223.54/38.18  | | | | | | | | | | |   (11853)   ~ (all_53_9 = e0)
% 223.54/38.18  | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | REDUCE: (366), (11850) imply:
% 223.54/38.18  | | | | | | | | | | |   (11854)   ~ (all_53_11 = e0)
% 223.54/38.18  | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | REDUCE: (39), (11850) imply:
% 223.54/38.18  | | | | | | | | | | |   (11855)  op(e1, e1) = e0
% 223.54/38.18  | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | BETA: splitting (76) gives:
% 223.54/38.18  | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | Case 1:
% 223.54/38.18  | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | |   (11856)   ~ (all_30_2 = e1)
% 223.54/38.18  | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | REDUCE: (330), (11856) imply:
% 223.54/38.18  | | | | | | | | | | | |   (11857)   ~ (all_4_2 = e1)
% 223.54/38.18  | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | BETA: splitting (107) gives:
% 223.54/38.18  | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | Case 1:
% 223.54/38.18  | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | |   (11858)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 223.54/38.18  | | | | | | | | | | | | |              all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 223.54/38.18  | | | | | | | | | | | | |              op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 223.54/38.18  | | | | | | | | | | | | |                all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 223.54/38.18  | | | | | | | | | | | | |              op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 223.54/38.18  | | | | | | | | | | | | |              op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 223.54/38.18  | | | | | | | | | | | | |              $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 223.54/38.18  | | | | | | | | | | | | |              $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 223.54/38.18  | | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 223.54/38.18  | | | | | | | | | | | | |                all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 223.54/38.18  | | | | | | | | | | | | |              & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 223.54/38.18  | | | | | | | | | | | | |                all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 223.54/38.18  | | | | | | | | | | | | |              op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 223.54/38.18  | | | | | | | | | | | | |              & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 223.54/38.18  | | | | | | | | | | | | |              $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 223.54/38.18  | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | BETA: splitting (11858) gives:
% 223.54/38.18  | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | Case 1:
% 223.54/38.18  | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | |   (11859)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 223.54/38.18  | | | | | | | | | | | | | |            all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 223.54/38.18  | | | | | | | | | | | | | |            op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 223.54/38.18  | | | | | | | | | | | | | |              all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 223.54/38.18  | | | | | | | | | | | | | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 223.54/38.18  | | | | | | | | | | | | | |            op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 223.54/38.18  | | | | | | | | | | | | | |            $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 223.54/38.18  | | | | | | | | | | | | | |            $i(all_52_7)
% 223.54/38.18  | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | ALPHA: (11859) implies:
% 223.54/38.18  | | | | | | | | | | | | | |   (11860)  op(e3, e2) = all_52_3
% 223.54/38.18  | | | | | | | | | | | | | |   (11861)  op(all_52_3, all_52_3) = e2
% 223.54/38.18  | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 223.54/38.18  | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | Case 1:
% 223.54/38.18  | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | |   (11862)  all_55_15 = e3
% 223.54/38.18  | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | REF_CLOSE: (244), (11627), (11862) are inconsistent by
% 223.54/38.18  | | | | | | | | | | | | | | |            sub-proof #2503.
% 223.54/38.18  | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | Case 2:
% 223.54/38.18  | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | |   (11863)   ~ (all_55_15 = e3)
% 223.54/38.18  | | | | | | | | | | | | | | |   (11864)  all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 223.54/38.18  | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | BETA: splitting (11864) gives:
% 223.54/38.18  | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | Case 1:
% 223.54/38.18  | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | |   (11865)  all_55_15 = e2
% 223.54/38.18  | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | REF_CLOSE: (244), (373), (11865) are inconsistent by
% 223.54/38.18  | | | | | | | | | | | | | | | |            sub-proof #2502.
% 223.54/38.18  | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | Case 2:
% 223.54/38.18  | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | |   (11866)   ~ (all_55_15 = e2)
% 223.54/38.18  | | | | | | | | | | | | | | | |   (11867)  all_55_15 = e1 | all_55_15 = e0
% 223.54/38.18  | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (36), (159), (163), (165), (166),
% 223.54/38.18  | | | | | | | | | | | | | | | |            (222), (223), (224), (225), (226), (244), (362),
% 223.54/38.18  | | | | | | | | | | | | | | | |            (371), (373), (10094), (11627), (11851), (11853),
% 223.54/38.18  | | | | | | | | | | | | | | | |            (11857), (11860), (11861), (11867),
% 223.54/38.18  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.54/38.18  | | | | | | | | | | | | | | | |            #228.
% 223.54/38.18  | | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | | End of split
% 223.54/38.18  | | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | | End of split
% 223.54/38.18  | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | Case 2:
% 223.54/38.18  | | | | | | | | | | | | | | 
% 223.54/38.18  | | | | | | | | | | | | | |   (11868)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 223.54/38.18  | | | | | | | | | | | | | |            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 223.54/38.18  | | | | | | | | | | | | | |            op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 223.54/38.18  | | | | | | | | | | | | | |              all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 223.54/38.18  | | | | | | | | | | | | | |            & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 223.54/38.18  | | | | | | | | | | | | | |            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 223.54/38.18  | | | | | | | | | | | | | |            $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 223.54/38.18  | | | | | | | | | | | | | |            $i(all_52_15)
% 223.54/38.18  | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | ALPHA: (11868) implies:
% 223.54/38.19  | | | | | | | | | | | | | |   (11869)  op(e2, e2) = all_52_11
% 223.54/38.19  | | | | | | | | | | | | | |   (11870)  op(e2, e3) = all_52_9
% 223.54/38.19  | | | | | | | | | | | | | |   (11871)  op(all_52_11, all_52_11) = e2
% 223.54/38.19  | | | | | | | | | | | | | |   (11872)  op(all_52_9, all_52_9) = e3
% 223.54/38.19  | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 223.54/38.19  | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | Case 1:
% 223.54/38.19  | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | |   (11873)  all_55_15 = e3
% 223.54/38.19  | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | REF_CLOSE: (244), (11627), (11873) are inconsistent by
% 223.54/38.19  | | | | | | | | | | | | | | |            sub-proof #2503.
% 223.54/38.19  | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | Case 2:
% 223.54/38.19  | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | |   (11874)   ~ (all_55_15 = e3)
% 223.54/38.19  | | | | | | | | | | | | | | |   (11875)  all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 223.54/38.19  | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | BETA: splitting (11875) gives:
% 223.54/38.19  | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | Case 1:
% 223.54/38.19  | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | |   (11876)  all_55_15 = e2
% 223.54/38.19  | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | REF_CLOSE: (244), (373), (11876) are inconsistent by
% 223.54/38.19  | | | | | | | | | | | | | | | |            sub-proof #2502.
% 223.54/38.19  | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | Case 2:
% 223.54/38.19  | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | |   (11877)   ~ (all_55_15 = e2)
% 223.54/38.19  | | | | | | | | | | | | | | | |   (11878)  all_55_15 = e1 | all_55_15 = e0
% 223.54/38.19  | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | BETA: splitting (11878) gives:
% 223.54/38.19  | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.19  | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | |   (11879)  all_55_15 = e1
% 223.54/38.19  | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (11857), (11879) are inconsistent by
% 223.54/38.19  | | | | | | | | | | | | | | | | |            sub-proof #2501.
% 223.54/38.19  | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.19  | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | |   (11880)  all_55_15 = e0
% 223.54/38.19  | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (11880) imply:
% 223.54/38.19  | | | | | | | | | | | | | | | | |   (11881)  all_4_2 = e0
% 223.54/38.19  | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | SIMP: (11881) implies:
% 223.54/38.19  | | | | | | | | | | | | | | | | |   (11882)  all_4_2 = e0
% 223.54/38.19  | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | REDUCE: (362), (11882) imply:
% 223.54/38.19  | | | | | | | | | | | | | | | | |   (11883)   ~ (all_53_7 = e0)
% 223.54/38.19  | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | REDUCE: (371), (11882) imply:
% 223.54/38.19  | | | | | | | | | | | | | | | | |   (11884)   ~ (all_53_13 = e0)
% 223.54/38.19  | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | REDUCE: (11627), (11882) imply:
% 223.54/38.19  | | | | | | | | | | | | | | | | |   (11885)   ~ (e3 = e0)
% 223.54/38.19  | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | REDUCE: (373), (11882) imply:
% 223.54/38.19  | | | | | | | | | | | | | | | | |   (11886)   ~ (e2 = e0)
% 223.54/38.19  | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | REDUCE: (11857), (11882) imply:
% 223.54/38.19  | | | | | | | | | | | | | | | | |   (11887)   ~ (e1 = e0)
% 223.54/38.19  | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | REDUCE: (36), (11882) imply:
% 223.54/38.19  | | | | | | | | | | | | | | | | |   (11888)  op(e0, e0) = e0
% 223.54/38.19  | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 223.54/38.19  | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.19  | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | |   (11889)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 223.54/38.19  | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 223.54/38.19  | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | BETA: splitting (11889) gives:
% 223.54/38.19  | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | |   (11890)  all_57_2 = e0 & op(e2, e3) = e0
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | ALPHA: (11890) implies:
% 223.54/38.19  | | | | | | | | | | | | | | | | | | |   (11891)  all_57_2 = e0
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | |   (11892)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | BETA: splitting (11892) gives:
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | |   (11893)  all_57_1 = e0 & op(e3, e2) = e0
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | | ALPHA: (11890) implies:
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | |   (11894)  op(e2, e3) = e0
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | | ALPHA: (11893) implies:
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | |   (11895)  op(e3, e2) = e0
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3,
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | |              all_52_11, e2, e2, simplifying with (10095),
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | |              (11869) gives:
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | |   (11896)  all_52_11 = e3
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_1, e0,
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (168), (11894) gives:
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | |   (11897)  all_53_1 = e0
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_1,
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | |              all_52_9, e3, e2, simplifying with (168), (11870)
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | |              gives:
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | |   (11898)  all_53_1 = all_52_9
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_4, e0,
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (171), (11895) gives:
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | |   (11899)  all_53_4 = e0
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (11897), (11898) imply:
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | |   (11900)  all_52_9 = e0
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | | REDUCE: (150), (11897) imply:
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | |   (11901)   ~ (all_53_2 = e0)
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | | SIMP: (11901) implies:
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | |   (11902)   ~ (all_53_2 = e0)
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (11897) imply:
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | |   (11903)   ~ (all_53_3 = e0)
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | | SIMP: (11903) implies:
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | |   (11904)   ~ (all_53_3 = e0)
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | | REDUCE: (11871), (11896) imply:
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | |   (11905)  op(e3, e3) = e2
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (160), (164), (168), (230), (11870),
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | |            (11872), (11888), (11902), (11904), (11905),
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | |            #1571.
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | |   (11906)  all_57_3 = e0 & op(e2, e2) = e0
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | | ALPHA: (11906) implies:
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | |   (11907)  all_57_3 = e0
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | |            (11891), (11907) are inconsistent by sub-proof
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | |            #2246.
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | |   (11908)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0)
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (163), (11851), (11883), (11908),
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | |            #2024.
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | |   (11909)  all_57_3 = e0 & op(e2, e2) = e0
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | ALPHA: (11909) implies:
% 223.54/38.19  | | | | | | | | | | | | | | | | | | |   (11910)  op(e2, e2) = e0
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (11869), (11871), (11888), (11910),
% 223.54/38.19  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.54/38.19  | | | | | | | | | | | | | | | | | | |            #2270.
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.19  | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.19  | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | |   (11911)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 223.54/38.19  | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0)
% 223.54/38.19  | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (166), (11853), (11884), (11911),
% 223.54/38.19  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.54/38.19  | | | | | | | | | | | | | | | | | |            #2022.
% 223.54/38.19  | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | End of split
% 223.54/38.19  | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | End of split
% 223.54/38.19  | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | End of split
% 223.54/38.19  | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | End of split
% 223.54/38.19  | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | End of split
% 223.54/38.19  | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | Case 2:
% 223.54/38.19  | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | |   (11912)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 223.54/38.19  | | | | | | | | | | | | |              & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 223.54/38.19  | | | | | | | | | | | | |              & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 223.54/38.19  | | | | | | | | | | | | |                all_52_21) = e1 & op(all_52_23, all_52_23) =
% 223.54/38.19  | | | | | | | | | | | | |              e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 223.54/38.19  | | | | | | | | | | | | |              all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 223.54/38.19  | | | | | | | | | | | | |              = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 223.54/38.19  | | | | | | | | | | | | |              $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 223.54/38.19  | | | | | | | | | | | | |              & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 223.54/38.19  | | | | | | | | | | | | |              e0 & op(all_52_25, all_52_25) = e3 &
% 223.54/38.19  | | | | | | | | | | | | |              op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 223.54/38.19  | | | | | | | | | | | | |                all_52_29) = e1 & op(all_52_31, all_52_31) =
% 223.54/38.19  | | | | | | | | | | | | |              e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 223.54/38.19  | | | | | | | | | | | | |              all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 223.54/38.19  | | | | | | | | | | | | |              = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 223.54/38.19  | | | | | | | | | | | | |              $i(all_52_29) & $i(all_52_31))
% 223.54/38.19  | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | BETA: splitting (11912) gives:
% 223.54/38.19  | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | Case 1:
% 223.54/38.19  | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | |   (11913)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 223.54/38.19  | | | | | | | | | | | | | |            all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 223.54/38.19  | | | | | | | | | | | | | |            op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 223.54/38.19  | | | | | | | | | | | | | |              all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 223.54/38.19  | | | | | | | | | | | | | |            & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 223.54/38.19  | | | | | | | | | | | | | |            & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 223.54/38.19  | | | | | | | | | | | | | |            & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 223.54/38.19  | | | | | | | | | | | | | |            $i(all_52_23)
% 223.54/38.19  | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | ALPHA: (11913) implies:
% 223.54/38.19  | | | | | | | | | | | | | |   (11914)  op(e1, e1) = all_52_21
% 223.54/38.19  | | | | | | | | | | | | | |   (11915)  op(e1, e2) = all_52_19
% 223.54/38.19  | | | | | | | | | | | | | |   (11916)  op(all_52_21, all_52_21) = e1
% 223.54/38.19  | | | | | | | | | | | | | |   (11917)  op(all_52_19, all_52_19) = e2
% 223.54/38.19  | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 223.54/38.19  | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | Case 1:
% 223.54/38.19  | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | |   (11918)  all_55_15 = e3
% 223.54/38.19  | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | REF_CLOSE: (244), (11627), (11918) are inconsistent by
% 223.54/38.19  | | | | | | | | | | | | | | |            sub-proof #2503.
% 223.54/38.19  | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | Case 2:
% 223.54/38.19  | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | |   (11919)   ~ (all_55_15 = e3)
% 223.54/38.19  | | | | | | | | | | | | | | |   (11920)  all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 223.54/38.19  | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | BETA: splitting (11920) gives:
% 223.54/38.19  | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | Case 1:
% 223.54/38.19  | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | |   (11921)  all_55_15 = e2
% 223.54/38.19  | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | REF_CLOSE: (244), (373), (11921) are inconsistent by
% 223.54/38.19  | | | | | | | | | | | | | | | |            sub-proof #2502.
% 223.54/38.19  | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | Case 2:
% 223.54/38.19  | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | |   (11922)   ~ (all_55_15 = e2)
% 223.54/38.19  | | | | | | | | | | | | | | | |   (11923)  all_55_15 = e1 | all_55_15 = e0
% 223.54/38.19  | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | BETA: splitting (11923) gives:
% 223.54/38.19  | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.19  | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | |   (11924)  all_55_15 = e1
% 223.54/38.19  | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (11857), (11924) are inconsistent by
% 223.54/38.19  | | | | | | | | | | | | | | | | |            sub-proof #2501.
% 223.54/38.19  | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.19  | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | |   (11925)  all_55_15 = e0
% 223.54/38.19  | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (11925) imply:
% 223.54/38.19  | | | | | | | | | | | | | | | | |   (11926)  all_4_2 = e0
% 223.54/38.19  | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | SIMP: (11926) implies:
% 223.54/38.19  | | | | | | | | | | | | | | | | |   (11927)  all_4_2 = e0
% 223.54/38.19  | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | REDUCE: (362), (11927) imply:
% 223.54/38.19  | | | | | | | | | | | | | | | | |   (11928)   ~ (all_53_7 = e0)
% 223.54/38.19  | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | REDUCE: (370), (11927) imply:
% 223.54/38.19  | | | | | | | | | | | | | | | | |   (11929)   ~ (all_53_12 = e0)
% 223.54/38.19  | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | REDUCE: (371), (11927) imply:
% 223.54/38.19  | | | | | | | | | | | | | | | | |   (11930)   ~ (all_53_13 = e0)
% 223.54/38.19  | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | REDUCE: (372), (11927) imply:
% 223.54/38.19  | | | | | | | | | | | | | | | | |   (11931)   ~ (all_53_14 = e0)
% 223.54/38.19  | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | REDUCE: (11627), (11927) imply:
% 223.54/38.19  | | | | | | | | | | | | | | | | |   (11932)   ~ (e3 = e0)
% 223.54/38.19  | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | REDUCE: (373), (11927) imply:
% 223.54/38.19  | | | | | | | | | | | | | | | | |   (11933)   ~ (e2 = e0)
% 223.54/38.19  | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | REDUCE: (11857), (11927) imply:
% 223.54/38.19  | | | | | | | | | | | | | | | | |   (11934)   ~ (e1 = e0)
% 223.54/38.19  | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | REDUCE: (36), (11927) imply:
% 223.54/38.19  | | | | | | | | | | | | | | | | |   (11935)  op(e0, e0) = e0
% 223.54/38.19  | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 223.54/38.19  | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.19  | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | |   (11936)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 223.54/38.19  | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 223.54/38.19  | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | BETA: splitting (11936) gives:
% 223.54/38.19  | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | |   (11937)  all_57_2 = e0 & op(e2, e3) = e0
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | ALPHA: (11937) implies:
% 223.54/38.19  | | | | | | | | | | | | | | | | | | |   (11938)  all_57_2 = e0
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | |   (11939)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | BETA: splitting (11939) gives:
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | |   (11940)  all_57_1 = e0 & op(e3, e2) = e0
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (165), (169), (171), (207), (11620),
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | |            (11855), (11914), (11916), (11929), (11930),
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | |            (11931), (11940), (function-axioms) are
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1842.
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | |   (11941)  all_57_3 = e0 & op(e2, e2) = e0
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | | ALPHA: (11941) implies:
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | |   (11942)  all_57_3 = e0
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | |            (11938), (11942) are inconsistent by sub-proof
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | |            #2246.
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | |   (11943)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0)
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (159), (11915), (11917), (11928), (11935),
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | |            (11943), (function-axioms) are inconsistent by
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | |            sub-proof #1841.
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | |   (11944)  all_57_3 = e0 & op(e2, e2) = e0
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10094), (11944) are inconsistent by
% 223.54/38.19  | | | | | | | | | | | | | | | | | | |            sub-proof #262.
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | End of split
% 223.54/38.19  | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.19  | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | |   (11945)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 223.54/38.19  | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0)
% 223.54/38.19  | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (166), (11853), (11930), (11945),
% 223.54/38.19  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.54/38.19  | | | | | | | | | | | | | | | | | |            #2022.
% 223.54/38.19  | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | End of split
% 223.54/38.19  | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | End of split
% 223.54/38.19  | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | End of split
% 223.54/38.19  | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | End of split
% 223.54/38.19  | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | Case 2:
% 223.54/38.19  | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | |   (11946)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 223.54/38.19  | | | | | | | | | | | | | |            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 223.54/38.19  | | | | | | | | | | | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 223.54/38.19  | | | | | | | | | | | | | |              all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 223.54/38.19  | | | | | | | | | | | | | |            & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 223.54/38.19  | | | | | | | | | | | | | |            & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 223.54/38.19  | | | | | | | | | | | | | |            & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 223.54/38.19  | | | | | | | | | | | | | |            $i(all_52_31)
% 223.54/38.19  | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | ALPHA: (11946) implies:
% 223.54/38.19  | | | | | | | | | | | | | |   (11947)  op(e0, e2) = all_52_27
% 223.54/38.19  | | | | | | | | | | | | | |   (11948)  op(all_52_27, all_52_27) = e2
% 223.54/38.19  | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 223.54/38.19  | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | Case 1:
% 223.54/38.19  | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | |   (11949)  all_55_15 = e3
% 223.54/38.19  | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | REF_CLOSE: (244), (11627), (11949) are inconsistent by
% 223.54/38.19  | | | | | | | | | | | | | | |            sub-proof #2503.
% 223.54/38.19  | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | Case 2:
% 223.54/38.19  | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | |   (11950)   ~ (all_55_15 = e3)
% 223.54/38.19  | | | | | | | | | | | | | | |   (11951)  all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 223.54/38.19  | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | BETA: splitting (11951) gives:
% 223.54/38.19  | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | Case 1:
% 223.54/38.19  | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | |   (11952)  all_55_15 = e2
% 223.54/38.19  | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | REF_CLOSE: (244), (373), (11952) are inconsistent by
% 223.54/38.19  | | | | | | | | | | | | | | | |            sub-proof #2502.
% 223.54/38.19  | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | Case 2:
% 223.54/38.19  | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | |   (11953)  all_55_15 = e1 | all_55_15 = e0
% 223.54/38.19  | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | REF_CLOSE: (97), (159), (165), (166), (168), (192), (222),
% 223.54/38.19  | | | | | | | | | | | | | | | |            (244), (246), (362), (371), (10083), (10084),
% 223.54/38.19  | | | | | | | | | | | | | | | |            (10088), (10094), (10095), (11627), (11853),
% 223.54/38.19  | | | | | | | | | | | | | | | |            (11857), (11947), (11948), (11953),
% 223.54/38.19  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.54/38.19  | | | | | | | | | | | | | | | |            #251.
% 223.54/38.19  | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | End of split
% 223.54/38.19  | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | End of split
% 223.54/38.19  | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | End of split
% 223.54/38.19  | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | End of split
% 223.54/38.19  | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | Case 2:
% 223.54/38.19  | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | |   (11954)  all_30_2 = e1
% 223.54/38.19  | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | COMBINE_EQS: (330), (11954) imply:
% 223.54/38.19  | | | | | | | | | | | |   (11955)  all_4_2 = e1
% 223.54/38.19  | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | SIMP: (11955) implies:
% 223.54/38.19  | | | | | | | | | | | |   (11956)  all_4_2 = e1
% 223.54/38.19  | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | REDUCE: (371), (11956) imply:
% 223.54/38.19  | | | | | | | | | | | |   (11957)   ~ (all_53_13 = e1)
% 223.54/38.19  | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | REDUCE: (372), (11956) imply:
% 223.54/38.19  | | | | | | | | | | | |   (11958)   ~ (all_53_14 = e1)
% 223.54/38.19  | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | REDUCE: (11627), (11956) imply:
% 223.54/38.19  | | | | | | | | | | | |   (11959)   ~ (e3 = e1)
% 223.54/38.19  | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | BETA: splitting (223) gives:
% 223.54/38.19  | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | Case 1:
% 223.54/38.19  | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | |   (11960)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 223.54/38.19  | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 223.54/38.19  | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | REF_CLOSE: (8), (168), (10095), (11617), (11960),
% 223.54/38.19  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.54/38.19  | | | | | | | | | | | | |            #240.
% 223.54/38.19  | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | Case 2:
% 223.54/38.19  | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | |   (11961)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 223.54/38.19  | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 223.54/38.19  | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | BETA: splitting (11961) gives:
% 223.54/38.19  | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | Case 1:
% 223.54/38.19  | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | |   (11962)  all_57_5 = e1 & op(e2, e1) = e1
% 223.54/38.19  | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | ALPHA: (11962) implies:
% 223.54/38.19  | | | | | | | | | | | | | |   (11963)  op(e2, e1) = e1
% 223.54/38.19  | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 223.54/38.19  | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | Case 1:
% 223.54/38.19  | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | |   (11964)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 223.54/38.19  | | | | | | | | | | | | | | |              & op(e1, e2) = e1)
% 223.54/38.19  | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | BETA: splitting (11964) gives:
% 223.54/38.19  | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | Case 1:
% 223.54/38.19  | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | |   (11965)  all_57_6 = e1 & op(e1, e3) = e1
% 223.54/38.19  | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | REF_CLOSE: (164), (11618), (11965), (function-axioms) are
% 223.54/38.19  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #316.
% 223.54/38.19  | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | Case 2:
% 223.54/38.19  | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | |   (11966)  all_57_7 = e1 & op(e1, e2) = e1
% 223.54/38.19  | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | ALPHA: (11966) implies:
% 223.54/38.19  | | | | | | | | | | | | | | | |   (11967)  op(e1, e2) = e1
% 223.54/38.19  | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_6, e1,
% 223.54/38.19  | | | | | | | | | | | | | | | |              e2, e1, simplifying with (163), (11967) gives:
% 223.54/38.19  | | | | | | | | | | | | | | | |   (11968)  all_53_6 = e1
% 223.54/38.19  | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_9, e1,
% 223.54/38.19  | | | | | | | | | | | | | | | |              e1, e2, simplifying with (166), (11963) gives:
% 223.54/38.19  | | | | | | | | | | | | | | | |   (11969)  all_53_9 = e1
% 223.54/38.19  | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | REDUCE: (129), (11968) imply:
% 223.54/38.19  | | | | | | | | | | | | | | | |   (11970)   ~ (all_53_7 = e1)
% 223.54/38.19  | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | SIMP: (11970) implies:
% 223.54/38.19  | | | | | | | | | | | | | | | |   (11971)   ~ (all_53_7 = e1)
% 223.54/38.19  | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | REDUCE: (119), (11969) imply:
% 223.54/38.19  | | | | | | | | | | | | | | | |   (11972)   ~ (all_53_11 = e1)
% 223.54/38.19  | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | SIMP: (11972) implies:
% 223.54/38.19  | | | | | | | | | | | | | | | |   (11973)   ~ (all_53_11 = e1)
% 223.54/38.19  | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 223.54/38.19  | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.19  | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | |   (11974)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 223.54/38.19  | | | | | | | | | | | | | | | | |              all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 223.54/38.19  | | | | | | | | | | | | | | | | |              op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 223.54/38.19  | | | | | | | | | | | | | | | | |                all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 223.54/38.19  | | | | | | | | | | | | | | | | |              op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 223.54/38.19  | | | | | | | | | | | | | | | | |              op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 223.54/38.19  | | | | | | | | | | | | | | | | |              $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 223.54/38.19  | | | | | | | | | | | | | | | | |              $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 223.54/38.19  | | | | | | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 223.54/38.19  | | | | | | | | | | | | | | | | |                all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 223.54/38.19  | | | | | | | | | | | | | | | | |              & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 223.54/38.19  | | | | | | | | | | | | | | | | |                all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 223.54/38.19  | | | | | | | | | | | | | | | | |              op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 223.54/38.19  | | | | | | | | | | | | | | | | |              & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 223.54/38.19  | | | | | | | | | | | | | | | | |              $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 223.54/38.19  | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (39), (374), (11625), (11855), (11963),
% 223.54/38.19  | | | | | | | | | | | | | | | | |            (11974), (function-axioms) are inconsistent by
% 223.54/38.19  | | | | | | | | | | | | | | | | |            sub-proof #329.
% 223.54/38.19  | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.19  | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | |   (11975)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 223.54/38.19  | | | | | | | | | | | | | | | | |              & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 223.54/38.19  | | | | | | | | | | | | | | | | |              & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 223.54/38.19  | | | | | | | | | | | | | | | | |                all_52_21) = e1 & op(all_52_23, all_52_23) =
% 223.54/38.19  | | | | | | | | | | | | | | | | |              e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 223.54/38.19  | | | | | | | | | | | | | | | | |              all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 223.54/38.19  | | | | | | | | | | | | | | | | |              = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 223.54/38.19  | | | | | | | | | | | | | | | | |              $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 223.54/38.19  | | | | | | | | | | | | | | | | |              & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 223.54/38.19  | | | | | | | | | | | | | | | | |              e0 & op(all_52_25, all_52_25) = e3 &
% 223.54/38.19  | | | | | | | | | | | | | | | | |              op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 223.54/38.19  | | | | | | | | | | | | | | | | |                all_52_29) = e1 & op(all_52_31, all_52_31) =
% 223.54/38.19  | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 223.54/38.19  | | | | | | | | | | | | | | | | |              all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 223.54/38.19  | | | | | | | | | | | | | | | | |              = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 223.54/38.19  | | | | | | | | | | | | | | | | |              $i(all_52_29) & $i(all_52_31))
% 223.54/38.19  | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | BETA: splitting (11975) gives:
% 223.54/38.19  | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.19  | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | |   (11976)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 223.54/38.19  | | | | | | | | | | | | | | | | | |            all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 223.54/38.19  | | | | | | | | | | | | | | | | | |            op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 223.54/38.19  | | | | | | | | | | | | | | | | | |              all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 223.54/38.19  | | | | | | | | | | | | | | | | | |            & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 223.54/38.19  | | | | | | | | | | | | | | | | | |            & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 223.54/38.19  | | | | | | | | | | | | | | | | | |            & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 223.54/38.19  | | | | | | | | | | | | | | | | | |            $i(all_52_23)
% 223.54/38.19  | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | ALPHA: (11976) implies:
% 223.54/38.19  | | | | | | | | | | | | | | | | | |   (11977)  op(e1, e1) = all_52_21
% 223.54/38.19  | | | | | | | | | | | | | | | | | |   (11978)  op(e1, e2) = all_52_19
% 223.54/38.19  | | | | | | | | | | | | | | | | | |   (11979)  op(all_52_19, all_52_19) = e2
% 223.54/38.19  | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (163), (11855), (11967), (11977), (11978),
% 223.54/38.19  | | | | | | | | | | | | | | | | | |            (11979), (function-axioms) are inconsistent by
% 223.54/38.19  | | | | | | | | | | | | | | | | | |            sub-proof #332.
% 223.54/38.19  | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.19  | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | |   (11980)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 223.54/38.19  | | | | | | | | | | | | | | | | | |            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 223.54/38.19  | | | | | | | | | | | | | | | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 223.54/38.19  | | | | | | | | | | | | | | | | | |              all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 223.54/38.19  | | | | | | | | | | | | | | | | | |            & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 223.54/38.19  | | | | | | | | | | | | | | | | | |            & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 223.54/38.19  | | | | | | | | | | | | | | | | | |            & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 223.54/38.19  | | | | | | | | | | | | | | | | | |            $i(all_52_31)
% 223.54/38.19  | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | ALPHA: (11980) implies:
% 223.54/38.19  | | | | | | | | | | | | | | | | | |   (11981)  op(e0, e1) = all_52_29
% 223.54/38.19  | | | | | | | | | | | | | | | | | |   (11982)  op(e0, e2) = all_52_27
% 223.54/38.19  | | | | | | | | | | | | | | | | | |   (11983)  op(all_52_29, all_52_29) = e1
% 223.54/38.19  | | | | | | | | | | | | | | | | | |   (11984)  op(all_52_27, all_52_27) = e2
% 223.54/38.19  | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_11,
% 223.54/38.19  | | | | | | | | | | | | | | | | | |              all_52_29, e1, e0, simplifying with (158), (11981)
% 223.54/38.19  | | | | | | | | | | | | | | | | | |              gives:
% 223.54/38.19  | | | | | | | | | | | | | | | | | |   (11985)  all_53_11 = all_52_29
% 223.54/38.19  | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_7,
% 223.54/38.19  | | | | | | | | | | | | | | | | | |              all_52_27, e2, e0, simplifying with (159), (11982)
% 223.54/38.19  | | | | | | | | | | | | | | | | | |              gives:
% 223.54/38.19  | | | | | | | | | | | | | | | | | |   (11986)  all_53_7 = all_52_27
% 223.54/38.19  | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (11985) imply:
% 223.54/38.19  | | | | | | | | | | | | | | | | | |   (11987)  all_55_14 = all_52_29
% 223.54/38.19  | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (11986) imply:
% 223.54/38.19  | | | | | | | | | | | | | | | | | |   (11988)  all_55_13 = all_52_27
% 223.54/38.19  | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | REDUCE: (136), (11986) imply:
% 223.54/38.19  | | | | | | | | | | | | | | | | | |   (11989)   ~ (all_53_4 = all_52_27)
% 223.54/38.19  | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | REDUCE: (10088), (11986) imply:
% 223.54/38.19  | | | | | | | | | | | | | | | | | |   (11990)   ~ (all_52_27 = e3)
% 223.54/38.19  | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | REDUCE: (11971), (11986) imply:
% 223.54/38.19  | | | | | | | | | | | | | | | | | |   (11991)   ~ (all_52_27 = e1)
% 223.54/38.19  | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | REDUCE: (122), (11985) imply:
% 223.54/38.19  | | | | | | | | | | | | | | | | | |   (11992)   ~ (all_53_8 = all_52_29)
% 223.54/38.19  | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | REDUCE: (11973), (11985) imply:
% 223.54/38.19  | | | | | | | | | | | | | | | | | |   (11993)   ~ (all_52_29 = e1)
% 223.54/38.19  | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | REDUCE: (11854), (11985) imply:
% 223.54/38.19  | | | | | | | | | | | | | | | | | |   (11994)   ~ (all_52_29 = e0)
% 223.54/38.19  | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 223.54/38.19  | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | |   (11995)  all_55_1 = e3
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (10086), (11995) are inconsistent by
% 223.54/38.19  | | | | | | | | | | | | | | | | | | |            sub-proof #2295.
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | |   (11996)  all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | |   (11997)  all_55_2 = e3
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (191), (269), (10095), (11621), (11983), (11987),
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | |            (11992), (11993), (11994), (11997),
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | |            #212.
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | |   (11998)  all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | BETA: splitting (11998) gives:
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | |   (11999)  all_55_2 = e2
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (11999) imply:
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | |   (12000)  all_53_8 = e2
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | | SIMP: (12000) implies:
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | |   (12001)  all_53_8 = e2
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (12001) imply:
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | |   (12002)   ~ (all_53_4 = e2)
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11996) gives:
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.19  | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.20  | | | | | | | | | | | | | | | | | | | | | |   (12003)  all_55_1 = e2
% 223.54/38.20  | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.20  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (12002), (12003) are inconsistent by
% 223.54/38.20  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2284.
% 223.54/38.20  | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.20  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.20  | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.20  | | | | | | | | | | | | | | | | | | | | | |   (12004)  all_55_1 = e1 | all_55_1 = e0
% 223.54/38.20  | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.20  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12004) gives:
% 223.54/38.20  | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.20  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.20  | | | | | | | | | | | | | | | | | | | | | | |   (12005)  all_55_1 = e1
% 223.54/38.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.20  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (11620), (12005) are inconsistent by
% 223.54/38.20  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2283.
% 223.54/38.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.20  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.20  | | | | | | | | | | | | | | | | | | | | | | |   (12006)  all_55_1 = e0
% 223.54/38.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.20  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (12006) imply:
% 223.54/38.20  | | | | | | | | | | | | | | | | | | | | | | |   (12007)  all_53_4 = e0
% 223.54/38.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.20  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (12007) implies:
% 223.54/38.20  | | | | | | | | | | | | | | | | | | | | | | |   (12008)  all_53_4 = e0
% 223.54/38.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.20  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11989), (12008) imply:
% 223.54/38.20  | | | | | | | | | | | | | | | | | | | | | | |   (12009)   ~ (all_52_27 = e0)
% 223.54/38.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.20  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (12009) implies:
% 223.54/38.20  | | | | | | | | | | | | | | | | | | | | | | |   (12010)   ~ (all_52_27 = e0)
% 223.54/38.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.20  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 223.54/38.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.20  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.54/38.20  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.20  | | | | | | | | | | | | | | | | | | | | | | | |   (12011)  all_55_13 = e3
% 223.54/38.20  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.20  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11988), (11990), (12011) are inconsistent by
% 223.54/38.20  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1648.
% 223.54/38.20  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.54/38.20  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.54/38.20  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | | |   (12012)   ~ (all_55_13 = e3)
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | | |   (12013)  all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12013) gives:
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | | | |   (12014)  all_55_13 = e2
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (11988), (12014) imply:
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | | | |   (12015)  all_52_27 = e2
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (12015) implies:
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | | | |   (12016)  all_52_27 = e2
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11990), (12016) imply:
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | | | |   (12017)   ~ (e3 = e2)
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11984), (12016) imply:
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | | | |   (12018)  op(e2, e2) = e2
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10095), (12018), (function-axioms) are
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2298.
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | | | |   (12019)  all_55_13 = e1 | all_55_13 = e0
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11988), (11991), (12010), (12019) are
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1615.
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | |   (12020)  all_55_2 = e1 | all_55_2 = e0
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (11621), (11852), (12020) are inconsistent
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2030.
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.20  | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | End of split
% 223.74/38.20  | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | End of split
% 223.74/38.20  | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | End of split
% 223.74/38.20  | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | Case 2:
% 223.74/38.20  | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | |   (12021)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 223.74/38.20  | | | | | | | | | | | | | | |              e1 & op(e1, e0) = e1)
% 223.74/38.20  | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | REF_CLOSE: (4), (161), (11855), (11958), (12021),
% 223.74/38.20  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.74/38.20  | | | | | | | | | | | | | | |            #223.
% 223.74/38.20  | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | End of split
% 223.74/38.20  | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | Case 2:
% 223.74/38.20  | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | |   (12022)  all_57_10 = e1 & op(e2, e0) = e1
% 223.74/38.20  | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | REF_CLOSE: (165), (11957), (12022), (function-axioms) are
% 223.74/38.20  | | | | | | | | | | | | | |            inconsistent by sub-proof #2084.
% 223.74/38.20  | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | End of split
% 223.74/38.20  | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | End of split
% 223.74/38.20  | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | End of split
% 223.74/38.20  | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | End of split
% 223.74/38.20  | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | Case 2:
% 223.74/38.20  | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | |   (12023)  all_12_2 = e3
% 223.74/38.20  | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | COMBINE_EQS: (325), (12023) imply:
% 223.74/38.20  | | | | | | | | | |   (12024)  all_4_2 = e3
% 223.74/38.20  | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | SIMP: (12024) implies:
% 223.74/38.20  | | | | | | | | | |   (12025)  all_4_2 = e3
% 223.74/38.20  | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | REDUCE: (370), (12025) imply:
% 223.74/38.20  | | | | | | | | | |   (12026)   ~ (all_53_12 = e3)
% 223.74/38.20  | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | REDUCE: (372), (12025) imply:
% 223.74/38.20  | | | | | | | | | |   (12027)   ~ (all_53_14 = e3)
% 223.74/38.20  | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | REDUCE: (36), (12025) imply:
% 223.74/38.20  | | | | | | | | | |   (12028)  op(e0, e0) = e3
% 223.74/38.20  | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | BETA: splitting (221) gives:
% 223.74/38.20  | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | Case 1:
% 223.74/38.20  | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | |   (12029)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 223.74/38.20  | | | | | | | | | | |              & op(e2, e1) = e3)
% 223.74/38.20  | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | BETA: splitting (12029) gives:
% 223.74/38.20  | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | Case 1:
% 223.74/38.20  | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | |   (12030)  all_57_4 = e3 & op(e3, e1) = e3
% 223.74/38.20  | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | ALPHA: (12030) implies:
% 223.74/38.20  | | | | | | | | | | | |   (12031)  all_57_4 = e3
% 223.74/38.20  | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | BETA: splitting (107) gives:
% 223.74/38.20  | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | Case 1:
% 223.74/38.20  | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | |   (12032)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 223.74/38.20  | | | | | | | | | | | | |              all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 223.74/38.20  | | | | | | | | | | | | |              op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 223.74/38.20  | | | | | | | | | | | | |                all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 223.74/38.20  | | | | | | | | | | | | |              op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 223.74/38.20  | | | | | | | | | | | | |              op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 223.74/38.20  | | | | | | | | | | | | |              $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 223.74/38.20  | | | | | | | | | | | | |              $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 223.74/38.20  | | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 223.74/38.20  | | | | | | | | | | | | |                all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 223.74/38.20  | | | | | | | | | | | | |              & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 223.74/38.20  | | | | | | | | | | | | |                all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 223.74/38.20  | | | | | | | | | | | | |              op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 223.74/38.20  | | | | | | | | | | | | |              & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 223.74/38.20  | | | | | | | | | | | | |              $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 223.74/38.20  | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | BETA: splitting (12032) gives:
% 223.74/38.20  | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | Case 1:
% 223.74/38.20  | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | |   (12033)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 223.74/38.20  | | | | | | | | | | | | | |            all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 223.74/38.20  | | | | | | | | | | | | | |            op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 223.74/38.20  | | | | | | | | | | | | | |              all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 223.74/38.20  | | | | | | | | | | | | | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 223.74/38.20  | | | | | | | | | | | | | |            op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 223.74/38.20  | | | | | | | | | | | | | |            $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 223.74/38.20  | | | | | | | | | | | | | |            $i(all_52_7)
% 223.74/38.20  | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | ALPHA: (12033) implies:
% 223.74/38.20  | | | | | | | | | | | | | |   (12034)  op(e3, e3) = all_52_1
% 223.74/38.20  | | | | | | | | | | | | | |   (12035)  op(all_52_1, all_52_1) = e3
% 223.74/38.20  | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | ALPHA: (12030) implies:
% 223.74/38.20  | | | | | | | | | | | | | |   (12036)  op(e3, e1) = e3
% 223.74/38.20  | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_8, e3,
% 223.74/38.20  | | | | | | | | | | | | | |              e1, e3, simplifying with (170), (12036) gives:
% 223.74/38.20  | | | | | | | | | | | | | |   (12037)  all_53_8 = e3
% 223.74/38.20  | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_52_1,
% 223.74/38.20  | | | | | | | | | | | | | |              e3, e3, simplifying with (11625), (12034) gives:
% 223.74/38.20  | | | | | | | | | | | | | |   (12038)  all_52_1 = e1
% 223.74/38.20  | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | REDUCE: (363), (12037) imply:
% 223.74/38.20  | | | | | | | | | | | | | |   (12039)   ~ (all_6_2 = e3)
% 223.74/38.20  | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | REDUCE: (12035), (12038) imply:
% 223.74/38.20  | | | | | | | | | | | | | |   (12040)  op(e1, e1) = e3
% 223.74/38.20  | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | REF_CLOSE: (39), (374), (12040), (function-axioms) are
% 223.74/38.20  | | | | | | | | | | | | | |            inconsistent by sub-proof #2468.
% 223.74/38.20  | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | Case 2:
% 223.74/38.20  | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | |   (12041)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 223.74/38.20  | | | | | | | | | | | | | |            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 223.74/38.20  | | | | | | | | | | | | | |            op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 223.74/38.20  | | | | | | | | | | | | | |              all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 223.74/38.20  | | | | | | | | | | | | | |            & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 223.74/38.20  | | | | | | | | | | | | | |            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 223.74/38.20  | | | | | | | | | | | | | |            $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 223.74/38.20  | | | | | | | | | | | | | |            $i(all_52_15)
% 223.74/38.20  | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | REF_CLOSE: (6), (10095), (11625), (12041), (function-axioms)
% 223.74/38.20  | | | | | | | | | | | | | |            are inconsistent by sub-proof #184.
% 223.74/38.20  | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | End of split
% 223.74/38.20  | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | Case 2:
% 223.74/38.20  | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | |   (12042)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 223.74/38.20  | | | | | | | | | | | | |              & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 223.74/38.20  | | | | | | | | | | | | |              & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 223.74/38.20  | | | | | | | | | | | | |                all_52_21) = e1 & op(all_52_23, all_52_23) =
% 223.74/38.20  | | | | | | | | | | | | |              e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 223.74/38.20  | | | | | | | | | | | | |              all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 223.74/38.20  | | | | | | | | | | | | |              = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 223.74/38.20  | | | | | | | | | | | | |              $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 223.74/38.20  | | | | | | | | | | | | |              & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 223.74/38.20  | | | | | | | | | | | | |              e0 & op(all_52_25, all_52_25) = e3 &
% 223.74/38.20  | | | | | | | | | | | | |              op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 223.74/38.20  | | | | | | | | | | | | |                all_52_29) = e1 & op(all_52_31, all_52_31) =
% 223.74/38.20  | | | | | | | | | | | | |              e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 223.74/38.20  | | | | | | | | | | | | |              all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 223.74/38.20  | | | | | | | | | | | | |              = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 223.74/38.20  | | | | | | | | | | | | |              $i(all_52_29) & $i(all_52_31))
% 223.74/38.20  | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | BETA: splitting (12042) gives:
% 223.74/38.20  | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | Case 1:
% 223.74/38.20  | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | |   (12043)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 223.74/38.20  | | | | | | | | | | | | | |            all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 223.74/38.20  | | | | | | | | | | | | | |            op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 223.74/38.20  | | | | | | | | | | | | | |              all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 223.74/38.20  | | | | | | | | | | | | | |            & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 223.74/38.20  | | | | | | | | | | | | | |            & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 223.74/38.20  | | | | | | | | | | | | | |            & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 223.74/38.20  | | | | | | | | | | | | | |            $i(all_52_23)
% 223.74/38.20  | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | ALPHA: (12043) implies:
% 223.74/38.20  | | | | | | | | | | | | | |   (12044)  op(e1, e3) = all_52_17
% 223.74/38.20  | | | | | | | | | | | | | |   (12045)  op(all_52_17, all_52_17) = e3
% 223.74/38.20  | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 223.74/38.20  | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | Case 1:
% 223.74/38.20  | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | |   (12046)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 223.74/38.20  | | | | | | | | | | | | | | |              & op(e1, e2) = e3)
% 223.74/38.20  | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | BETA: splitting (12046) gives:
% 223.74/38.20  | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | Case 1:
% 223.74/38.20  | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | |   (12047)  all_57_6 = e3 & op(e1, e3) = e3
% 223.74/38.20  | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (121), (135), (164),
% 223.74/38.20  | | | | | | | | | | | | | | | |            (169), (170), (171), (230), (231), (232), (233),
% 223.74/38.20  | | | | | | | | | | | | | | | |            (234), (235), (237), (11621), (11624), (12026),
% 223.74/38.20  | | | | | | | | | | | | | | | |            (12031), (12044), (12045), (12047),
% 223.74/38.20  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.74/38.20  | | | | | | | | | | | | | | | |            #182.
% 223.74/38.20  | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | Case 2:
% 223.74/38.20  | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | |   (12048)  all_57_7 = e3 & op(e1, e2) = e3
% 223.74/38.20  | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | ALPHA: (12048) implies:
% 223.74/38.20  | | | | | | | | | | | | | | | |   (12049)  all_57_7 = e3
% 223.74/38.20  | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 223.74/38.20  | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.20  | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | |   (12050)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 223.74/38.20  | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 223.74/38.20  | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (171), (10095), (11620), (12050),
% 223.74/38.20  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.74/38.20  | | | | | | | | | | | | | | | | |            #185.
% 223.74/38.20  | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.20  | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | |   (12051)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 223.74/38.20  | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 223.74/38.20  | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | BETA: splitting (12051) gives:
% 223.74/38.20  | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.20  | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | |   (12052)  all_57_7 = e1 & op(e1, e2) = e1
% 223.74/38.20  | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (12049), (12052) are inconsistent by
% 223.74/38.20  | | | | | | | | | | | | | | | | | |            sub-proof #2104.
% 223.74/38.20  | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.20  | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | |   (12053)  all_57_13 = e1 & op(e0, e2) = e1
% 223.74/38.20  | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | | ALPHA: (12053) implies:
% 223.74/38.20  | | | | | | | | | | | | | | | | | |   (12054)  all_57_13 = e1
% 223.74/38.20  | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 223.74/38.20  | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | | |   (12055)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 223.74/38.20  | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e3)
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (168), (10085), (11625), (12055),
% 223.74/38.20  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.74/38.20  | | | | | | | | | | | | | | | | | | |            #181.
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | | |   (12056)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 223.74/38.20  | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e3) = e3)
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | BETA: splitting (12056) gives:
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | |   (12057)  all_57_6 = e3 & op(e1, e3) = e3
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (121), (135), (164),
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | |            (169), (170), (171), (230), (231), (232), (233),
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | |            (234), (235), (237), (11621), (11624), (12026),
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | |            (12031), (12044), (12045), (12057),
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | |            #182.
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | |   (12058)  all_57_12 = e3 & op(e0, e3) = e3
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | ALPHA: (12058) implies:
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | |   (12059)  all_57_12 = e3
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | |   (12060)  all_57_15 = e0 & op(e0, e0) = e0
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | ALPHA: (12060) implies:
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | |   (12061)  op(e0, e0) = e0
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12028), (12061), (function-axioms) are
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2304.
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | |   (12062)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | ALPHA: (12062) implies:
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | |   (12063)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | |                e1) = e0)
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12063) gives:
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | |   (12064)  all_57_12 = e0 & op(e0, e3) = e0
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12064) implies:
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | |   (12065)  all_57_12 = e0
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12059), (12065) are inconsistent by
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2153.
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | |   (12066)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12066) gives:
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | |   (12067)  all_57_13 = e0 & op(e0, e2) = e0
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12067) implies:
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | |   (12068)  all_57_13 = e0
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (12054), (12068) are inconsistent by
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1760.
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | |   (12069)  all_57_14 = e0 & op(e0, e1) = e0
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12069) implies:
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | |   (12070)  all_57_14 = e0
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (36), (209), (373), (12054),
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | |            (12059), (12070), (function-axioms) are
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #179.
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.20  | | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.20  | | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | End of split
% 223.74/38.20  | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | End of split
% 223.74/38.20  | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | End of split
% 223.74/38.20  | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | Case 2:
% 223.74/38.20  | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | |   (12071)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 223.74/38.20  | | | | | | | | | | | | | | |              e3 & op(e1, e0) = e3)
% 223.74/38.20  | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | REF_CLOSE: (39), (161), (374), (12027), (12071),
% 223.74/38.20  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.74/38.20  | | | | | | | | | | | | | | |            #2310.
% 223.74/38.20  | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | End of split
% 223.74/38.20  | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | Case 2:
% 223.74/38.20  | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | |   (12072)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 223.74/38.20  | | | | | | | | | | | | | |            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 223.74/38.20  | | | | | | | | | | | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 223.74/38.20  | | | | | | | | | | | | | |              all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 223.74/38.20  | | | | | | | | | | | | | |            & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 223.74/38.20  | | | | | | | | | | | | | |            & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 223.74/38.20  | | | | | | | | | | | | | |            & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 223.74/38.20  | | | | | | | | | | | | | |            $i(all_52_31)
% 223.74/38.20  | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | ALPHA: (12072) implies:
% 223.74/38.20  | | | | | | | | | | | | | |   (12073)  op(e0, e0) = all_52_31
% 223.74/38.20  | | | | | | | | | | | | | |   (12074)  op(all_52_31, all_52_31) = e0
% 223.74/38.20  | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | REF_CLOSE: (4), (11625), (12028), (12073), (12074),
% 223.74/38.20  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.74/38.20  | | | | | | | | | | | | | |            #283.
% 223.74/38.20  | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | End of split
% 223.74/38.20  | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | End of split
% 223.74/38.20  | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | Case 2:
% 223.74/38.20  | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | |   (12075)  all_57_5 = e3 & op(e2, e1) = e3
% 223.74/38.20  | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | REF_CLOSE: (166), (10089), (12075), (function-axioms) are
% 223.74/38.20  | | | | | | | | | | | |            inconsistent by sub-proof #270.
% 223.74/38.20  | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | End of split
% 223.74/38.20  | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | Case 2:
% 223.74/38.20  | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | |   (12076)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 223.74/38.20  | | | | | | | | | | |              e3 & op(e0, e1) = e3)
% 223.74/38.20  | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (161), (165),
% 223.74/38.20  | | | | | | | | | | |            (169), (207), (208), (209), (213), (374), (10090),
% 223.74/38.20  | | | | | | | | | | |            (12026), (12027), (12076), (function-axioms) are
% 223.74/38.20  | | | | | | | | | | |            inconsistent by sub-proof #186.
% 223.74/38.20  | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | End of split
% 223.74/38.20  | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | End of split
% 223.74/38.20  | | | | | | | | | 
% 223.74/38.20  | | | | | | | | Case 2:
% 223.74/38.20  | | | | | | | | | 
% 223.74/38.20  | | | | | | | | |   (12077)  all_57_2 = e1 & op(e2, e3) = e1
% 223.74/38.20  | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | REF_CLOSE: (168), (11617), (12077), (function-axioms) are
% 223.74/38.20  | | | | | | | | |            inconsistent by sub-proof #2156.
% 223.74/38.20  | | | | | | | | | 
% 223.74/38.20  | | | | | | | | End of split
% 223.74/38.20  | | | | | | | | 
% 223.74/38.20  | | | | | | | Case 2:
% 223.74/38.20  | | | | | | | | 
% 223.74/38.20  | | | | | | | |   (12078)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 &
% 223.74/38.20  | | | | | | | |              op(e0, e3) = e1)
% 223.74/38.20  | | | | | | | | 
% 223.74/38.20  | | | | | | | | BETA: splitting (12078) gives:
% 223.74/38.20  | | | | | | | | 
% 223.74/38.20  | | | | | | | | Case 1:
% 223.74/38.20  | | | | | | | | | 
% 223.74/38.20  | | | | | | | | |   (12079)  all_57_6 = e1 & op(e1, e3) = e1
% 223.74/38.20  | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | REF_CLOSE: (164), (11618), (12079), (function-axioms) are
% 223.74/38.20  | | | | | | | | |            inconsistent by sub-proof #316.
% 223.74/38.20  | | | | | | | | | 
% 223.74/38.20  | | | | | | | | Case 2:
% 223.74/38.20  | | | | | | | | | 
% 223.74/38.20  | | | | | | | | |   (12080)  all_57_12 = e1 & op(e0, e3) = e1
% 223.74/38.20  | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | REF_CLOSE: (160), (11619), (12080), (function-axioms) are
% 223.74/38.20  | | | | | | | | |            inconsistent by sub-proof #1947.
% 223.74/38.20  | | | | | | | | | 
% 223.74/38.20  | | | | | | | | End of split
% 223.74/38.20  | | | | | | | | 
% 223.74/38.20  | | | | | | | End of split
% 223.74/38.20  | | | | | | | 
% 223.74/38.20  | | | | | | End of split
% 223.74/38.20  | | | | | | 
% 223.74/38.20  | | | | | End of split
% 223.74/38.20  | | | | | 
% 223.74/38.20  | | | | Case 2:
% 223.74/38.20  | | | | | 
% 223.74/38.20  | | | | |   (12081)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 &
% 223.74/38.20  | | | | |              op(e2, e0) = e3)
% 223.74/38.20  | | | | | 
% 223.74/38.20  | | | | | REF_CLOSE: (165), (166), (10089), (10090), (12081), (function-axioms)
% 223.74/38.20  | | | | |            are inconsistent by sub-proof #178.
% 223.74/38.20  | | | | | 
% 223.74/38.20  | | | | End of split
% 223.74/38.20  | | | | 
% 223.74/38.20  | | | End of split
% 223.74/38.20  | | | 
% 223.74/38.20  | | Case 2:
% 223.74/38.20  | | | 
% 223.74/38.20  | | |   (12082)  all_6_2 = e3
% 223.74/38.20  | | |   (12083)  ( ~ (all_6_0 = e0) & op(all_6_1, e1) = all_6_0 & op(e1, e3) =
% 223.74/38.20  | | |              all_6_1 & $i(all_6_0) & $i(all_6_1)) | ( ~ (all_6_1 = e2) &
% 223.74/38.20  | | |              op(e1, e3) = all_6_1 & $i(all_6_1))
% 223.74/38.20  | | | 
% 223.74/38.20  | | | COMBINE_EQS: (333), (12082) imply:
% 223.74/38.20  | | |   (12084)  all_46_2 = e3
% 223.74/38.20  | | | 
% 223.74/38.20  | | | REDUCE: (350), (12082) imply:
% 223.74/38.20  | | |   (12085)   ~ (all_53_2 = e3)
% 223.74/38.20  | | | 
% 223.74/38.20  | | | REDUCE: (361), (12082) imply:
% 223.74/38.20  | | |   (12086)   ~ (all_53_6 = e3)
% 223.74/38.20  | | | 
% 223.74/38.20  | | | REDUCE: (363), (12082) imply:
% 223.74/38.20  | | |   (12087)   ~ (all_53_8 = e3)
% 223.74/38.20  | | | 
% 223.74/38.20  | | | REDUCE: (364), (12082) imply:
% 223.74/38.20  | | |   (12088)   ~ (all_53_9 = e3)
% 223.74/38.20  | | | 
% 223.74/38.20  | | | REDUCE: (366), (12082) imply:
% 223.74/38.20  | | |   (12089)   ~ (all_53_11 = e3)
% 223.74/38.20  | | | 
% 223.74/38.20  | | | REDUCE: (368), (12082) imply:
% 223.74/38.20  | | |   (12090)   ~ (all_53_14 = e3)
% 223.74/38.20  | | | 
% 223.74/38.20  | | | BETA: splitting (221) gives:
% 223.74/38.20  | | | 
% 223.74/38.20  | | | Case 1:
% 223.74/38.20  | | | | 
% 223.74/38.20  | | | |   (12091)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2,
% 223.74/38.20  | | | |                e1) = e3)
% 223.74/38.20  | | | | 
% 223.74/38.20  | | | | BETA: splitting (12091) gives:
% 223.74/38.20  | | | | 
% 223.74/38.20  | | | | Case 1:
% 223.74/38.20  | | | | | 
% 223.74/38.20  | | | | |   (12092)  all_57_4 = e3 & op(e3, e1) = e3
% 223.74/38.20  | | | | | 
% 223.74/38.20  | | | | | REF_CLOSE: (170), (12087), (12092), (function-axioms) are inconsistent
% 223.74/38.20  | | | | |            by sub-proof #177.
% 223.74/38.20  | | | | | 
% 223.74/38.20  | | | | Case 2:
% 223.74/38.20  | | | | | 
% 223.74/38.20  | | | | |   (12093)  all_57_5 = e3 & op(e2, e1) = e3
% 223.74/38.20  | | | | | 
% 223.74/38.20  | | | | | REF_CLOSE: (166), (12088), (12093), (function-axioms) are inconsistent
% 223.74/38.20  | | | | |            by sub-proof #270.
% 223.74/38.20  | | | | | 
% 223.74/38.20  | | | | End of split
% 223.74/38.20  | | | | 
% 223.74/38.20  | | | Case 2:
% 223.74/38.20  | | | | 
% 223.74/38.20  | | | |   (12094)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0,
% 223.74/38.20  | | | |                e1) = e3)
% 223.74/38.20  | | | | 
% 223.74/38.20  | | | | BETA: splitting (12094) gives:
% 223.74/38.20  | | | | 
% 223.74/38.20  | | | | Case 1:
% 223.74/38.20  | | | | | 
% 223.74/38.20  | | | | |   (12095)  all_57_8 = e3 & op(e1, e1) = e3
% 223.74/38.20  | | | | | 
% 223.74/38.20  | | | | | ALPHA: (12095) implies:
% 223.74/38.20  | | | | |   (12096)  all_57_8 = e3
% 223.74/38.20  | | | | |   (12097)  op(e1, e1) = e3
% 223.74/38.20  | | | | | 
% 223.74/38.20  | | | | | BETA: splitting (43) gives:
% 223.74/38.20  | | | | | 
% 223.74/38.20  | | | | | Case 1:
% 223.74/38.20  | | | | | | 
% 223.74/38.20  | | | | | |   (12098)   ~ (all_8_2 = e3)
% 223.74/38.20  | | | | | | 
% 223.74/38.20  | | | | | | BETA: splitting (46) gives:
% 223.74/38.20  | | | | | | 
% 223.74/38.20  | | | | | | Case 1:
% 223.74/38.20  | | | | | | | 
% 223.74/38.20  | | | | | | |   (12099)   ~ (all_10_2 = e1)
% 223.74/38.20  | | | | | | | 
% 223.74/38.20  | | | | | | | BETA: splitting (49) gives:
% 223.74/38.20  | | | | | | | 
% 223.74/38.20  | | | | | | | Case 1:
% 223.74/38.20  | | | | | | | | 
% 223.74/38.20  | | | | | | | |   (12100)   ~ (all_12_2 = e3)
% 223.74/38.20  | | | | | | | | 
% 223.74/38.20  | | | | | | | | REDUCE: (325), (12100) imply:
% 223.74/38.20  | | | | | | | |   (12101)   ~ (all_4_2 = e3)
% 223.74/38.20  | | | | | | | | 
% 223.74/38.20  | | | | | | | | BETA: splitting (52) gives:
% 223.74/38.20  | | | | | | | | 
% 223.74/38.20  | | | | | | | | Case 1:
% 223.74/38.20  | | | | | | | | | 
% 223.74/38.20  | | | | | | | | |   (12102)   ~ (all_14_2 = e0)
% 223.74/38.20  | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | REDUCE: (328), (12102) imply:
% 223.74/38.20  | | | | | | | | |   (12103)   ~ (all_8_2 = e0)
% 223.74/38.20  | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | BETA: splitting (55) gives:
% 223.74/38.20  | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | Case 1:
% 223.74/38.20  | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | |   (12104)   ~ (all_16_2 = e1)
% 223.74/38.20  | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | REDUCE: (324), (12104) imply:
% 223.74/38.20  | | | | | | | | | |   (12105)   ~ (all_8_2 = e1)
% 223.74/38.20  | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | BETA: splitting (200) gives:
% 223.74/38.20  | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | Case 1:
% 223.74/38.20  | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | |   (12106)  all_55_5 = e3
% 223.74/38.20  | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | REF_CLOSE: (266), (12098), (12106) are inconsistent by
% 223.74/38.20  | | | | | | | | | | |            sub-proof #293.
% 223.74/38.20  | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | Case 2:
% 223.74/38.20  | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | |   (12107)   ~ (all_55_5 = e3)
% 223.74/38.20  | | | | | | | | | | |   (12108)  all_55_5 = e2 | all_55_5 = e1 | all_55_5 = e0
% 223.74/38.20  | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | BETA: splitting (12108) gives:
% 223.74/38.20  | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | Case 1:
% 223.74/38.20  | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | |   (12109)  all_55_5 = e2
% 223.74/38.20  | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | COMBINE_EQS: (266), (12109) imply:
% 223.74/38.20  | | | | | | | | | | | |   (12110)  all_8_2 = e2
% 223.74/38.20  | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | SIMP: (12110) implies:
% 223.74/38.20  | | | | | | | | | | | |   (12111)  all_8_2 = e2
% 223.74/38.20  | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | REDUCE: (349), (12111) imply:
% 223.74/38.20  | | | | | | | | | | | |   (12112)   ~ (all_53_1 = e2)
% 223.74/38.20  | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | REDUCE: (352), (12111) imply:
% 223.74/38.20  | | | | | | | | | | | |   (12113)   ~ (all_53_4 = e2)
% 223.74/38.20  | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | REDUCE: (354), (12111) imply:
% 223.74/38.20  | | | | | | | | | | | |   (12114)   ~ (all_53_6 = e2)
% 223.74/38.20  | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | REDUCE: (356), (12111) imply:
% 223.74/38.20  | | | | | | | | | | | |   (12115)   ~ (all_53_7 = e2)
% 223.74/38.20  | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | REDUCE: (358), (12111) imply:
% 223.74/38.20  | | | | | | | | | | | |   (12116)   ~ (all_53_9 = e2)
% 223.74/38.20  | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | REDUCE: (360), (12111) imply:
% 223.74/38.20  | | | | | | | | | | | |   (12117)   ~ (all_53_13 = e2)
% 223.74/38.20  | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | REDUCE: (12098), (12111) imply:
% 223.74/38.20  | | | | | | | | | | | |   (12118)   ~ (e3 = e2)
% 223.74/38.20  | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | BETA: splitting (228) gives:
% 223.74/38.20  | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | Case 1:
% 223.74/38.20  | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | |   (12119)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 223.74/38.20  | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 223.74/38.20  | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | BETA: splitting (12119) gives:
% 223.74/38.20  | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | Case 1:
% 223.74/38.20  | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | |   (12120)  all_57_1 = e2 & op(e3, e2) = e2
% 223.74/38.20  | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | REF_CLOSE: (171), (12113), (12120), (function-axioms) are
% 223.74/38.20  | | | | | | | | | | | | | |            inconsistent by sub-proof #2456.
% 223.74/38.20  | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | Case 2:
% 223.74/38.20  | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | |   (12121)  all_57_3 = e2 & op(e2, e2) = e2
% 223.74/38.20  | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | ALPHA: (12121) implies:
% 223.74/38.20  | | | | | | | | | | | | | |   (12122)  all_57_3 = e2
% 223.74/38.20  | | | | | | | | | | | | | |   (12123)  op(e2, e2) = e2
% 223.74/38.20  | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | BETA: splitting (58) gives:
% 223.74/38.20  | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | Case 1:
% 223.74/38.20  | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | |   (12124)   ~ (all_18_2 = e0)
% 223.74/38.20  | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | REDUCE: (327), (12124) imply:
% 223.74/38.20  | | | | | | | | | | | | | | |   (12125)   ~ (all_10_2 = e0)
% 223.74/38.20  | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | BETA: splitting (61) gives:
% 223.74/38.20  | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | Case 1:
% 223.74/38.20  | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | |   (12126)   ~ (all_20_2 = e2)
% 223.74/38.20  | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | REDUCE: (299), (12126) imply:
% 223.74/38.20  | | | | | | | | | | | | | | | |   (12127)   ~ (all_10_2 = e2)
% 223.74/38.20  | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | BETA: splitting (205) gives:
% 223.74/38.20  | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.20  | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | |   (12128)  all_55_0 = e3
% 223.74/38.20  | | | | | | | | | | | | | | | | | 
% 223.74/38.20  | | | | | | | | | | | | | | | | | COMBINE_EQS: (277), (12128) imply:
% 223.74/38.21  | | | | | | | | | | | | | | | | |   (12129)  all_10_2 = e3
% 223.74/38.21  | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | SIMP: (12129) implies:
% 223.74/38.21  | | | | | | | | | | | | | | | | |   (12130)  all_10_2 = e3
% 223.74/38.21  | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | REDUCE: (338), (12130) imply:
% 223.74/38.21  | | | | | | | | | | | | | | | | |   (12131)   ~ (all_53_1 = e3)
% 223.74/38.21  | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | REDUCE: (344), (12130) imply:
% 223.74/38.21  | | | | | | | | | | | | | | | | |   (12132)   ~ (all_53_4 = e3)
% 223.74/38.21  | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | REDUCE: (45), (12130) imply:
% 223.74/38.21  | | | | | | | | | | | | | | | | |   (12133)  op(e3, e3) = e3
% 223.74/38.21  | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 223.74/38.21  | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | |   (12134)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 223.74/38.21  | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e3)
% 223.74/38.21  | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (168), (12123), (12131), (12134),
% 223.74/38.21  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.74/38.21  | | | | | | | | | | | | | | | | | |            #2297.
% 223.74/38.21  | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | |   (12135)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 223.74/38.21  | | | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 223.74/38.21  | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | BETA: splitting (12135) gives:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | |   (12136)  all_57_5 = e3 & op(e2, e1) = e3
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (12088), (12136), (function-axioms) are
% 223.74/38.21  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #270.
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | |   (12137)  all_57_10 = e3 & op(e2, e0) = e3
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | ALPHA: (12137) implies:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | |   (12138)  all_57_10 = e3
% 223.74/38.21  | | | | | | | | | | | | | | | | | | |   (12139)  op(e2, e0) = e3
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | |   (12140)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e3)
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (171), (12123), (12132), (12140),
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | |            #2285.
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | |   (12141)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | BETA: splitting (12141) gives:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | |   (12142)  all_57_7 = e3 & op(e1, e2) = e3
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (12086), (12142), (function-axioms) are
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #267.
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | |   (12143)  all_57_13 = e3 & op(e0, e2) = e3
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | ALPHA: (12143) implies:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | |   (12144)  all_57_13 = e3
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | |   (12145)  op(e0, e2) = e3
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_7, e3,
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (159), (12145) gives:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | |   (12146)  all_53_7 = e3
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_13,
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | |              e3, e0, e2, simplifying with (165), (12139) gives:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | |   (12147)  all_53_13 = e3
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | REDUCE: (114), (12147) imply:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | |   (12148)   ~ (all_53_12 = e3)
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | REDUCE: (111), (12147) imply:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | |   (12149)   ~ (all_53_14 = e3)
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | REDUCE: (371), (12147) imply:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | |   (12150)   ~ (all_4_2 = e3)
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | |   (12151)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | |              all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | |              op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | |                all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | |                all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | |              & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | |                all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12151) gives:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | |   (12152)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | |            all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | |              all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_7)
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12152) implies:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | |   (12153)  op(e3, e0) = all_52_7
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | |   (12154)  op(e3, e1) = all_52_5
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | |   (12155)  op(e3, e2) = all_52_3
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | |   (12156)  op(e3, e3) = all_52_1
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | |   (12157)  op(all_52_7, all_52_7) = e0
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | |   (12158)  op(all_52_5, all_52_5) = e1
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | |   (12159)  op(all_52_3, all_52_3) = e2
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | |   (12160)  op(all_52_1, all_52_1) = e3
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_12,
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | |              all_52_7, e0, e3, simplifying with (169), (12153)
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | |   (12161)  all_53_12 = all_52_7
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_8,
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | |              all_52_5, e1, e3, simplifying with (170), (12154)
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | |   (12162)  all_53_8 = all_52_5
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_4,
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | |              all_52_3, e2, e3, simplifying with (171), (12155)
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | |   (12163)  all_53_4 = all_52_3
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_52_1,
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (12133), (12156) gives:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | |   (12164)  all_52_1 = e3
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12113), (12163) imply:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | |   (12165)   ~ (all_52_3 = e2)
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (76) gives:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | |   (12166)   ~ (all_30_2 = e1)
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (330), (12166) imply:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | |   (12167)   ~ (all_4_2 = e1)
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | |   (12168)  all_55_15 = e3
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (12168) imply:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | |   (12169)  all_4_2 = e3
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12101), (12169) imply:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | |   (12170)  $false
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (12170) is inconsistent.
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | |   (12171)   ~ (all_55_15 = e3)
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | |   (12172)  all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12172) gives:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12173)  all_55_15 = e2
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (12173) imply:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12174)  all_4_2 = e2
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (373), (12174) imply:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12175)  $false
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (12175) is inconsistent.
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12176)   ~ (all_55_15 = e2)
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12177)  all_55_15 = e1 | all_55_15 = e0
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12177) gives:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12178)  all_55_15 = e1
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (12178) imply:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12179)  all_4_2 = e1
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12167), (12179) imply:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12180)  $false
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (12180) is inconsistent.
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12181)  all_55_15 = e0
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (12181) imply:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12182)  all_4_2 = e0
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (351), (12182) imply:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12183)   ~ (all_53_3 = e0)
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12101), (12182) imply:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12184)   ~ (e3 = e0)
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (373), (12182) imply:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12185)   ~ (e2 = e0)
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12167), (12182) imply:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12186)   ~ (e1 = e0)
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (12182) imply:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12187)  op(e0, e0) = e0
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12188)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e2)
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12188) gives:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12189)  all_57_6 = e2 & op(e1, e3) = e2
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12189) implies:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12190)  all_57_6 = e2
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12191)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e0)
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12191) gives:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12192)  all_57_0 = e0 & op(e3, e3) = e0
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12192) implies:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12193)  op(e3, e3) = e0
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12133), (12193), (function-axioms) are
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2494.
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12194)  all_57_2 = e0 & op(e2, e3) = e0
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12194) implies:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12195)  all_57_2 = e0
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12196)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (12123), (12195), (12196),
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1152.
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12197)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12197) gives:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12198)  all_57_5 = e1 & op(e2, e1) = e1
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12198) implies:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12199)  all_57_5 = e1
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12200)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12200) gives:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12201)  all_57_9 = e2 & op(e3, e0) = e2
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12201) implies:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12202)  all_57_9 = e2
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12203)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e0)
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (12133), (12155), (12159), (12187),
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12203), (function-axioms) are inconsistent by
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #266.
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12204)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e0)
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12204) gives:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12205)  all_57_4 = e0 & op(e3, e1) = e0
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12205) implies:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12206)  op(e3, e1) = e0
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (12154), (12158), (12187), (12206),
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2167.
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12207)  all_57_9 = e0 & op(e3, e0) = e0
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12207) implies:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12208)  all_57_9 = e0
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (12202), (12208) imply:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12209)  e2 = e0
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (12122), (12209) imply:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12210)  all_57_3 = e0
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (224), (12138), (12195), (12199),
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12210) are inconsistent by sub-proof #2249.
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12211)  all_57_10 = e2 & op(e2, e0) = e2
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (12117), (12211), (function-axioms) are
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2432.
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12212)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (36), (161), (169),
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (211), (213), (231), (373), (12090), (12133),
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12148), (12154), (12155), (12158), (12159),
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12187), (12212), (function-axioms) are
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #174.
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12213)  all_57_10 = e1 & op(e2, e0) = e1
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12213) implies:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12214)  all_57_10 = e1
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (161), (169), (213), (12090), (12148),
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12187), (12214), (function-axioms) are
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2302.
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12215)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = e0)
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12215) gives:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12216)  all_57_6 = e0 & op(e1, e3) = e0
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12216) implies:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12217)  all_57_6 = e0
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (12190), (12217) are inconsistent by
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1846.
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12218)  all_57_12 = e0 & op(e0, e3) = e0
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12218) implies:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12219)  op(e0, e3) = e0
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (12183), (12219), (function-axioms) are
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2366.
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12220)  all_57_7 = e2 & op(e1, e2) = e2
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (12114), (12220), (function-axioms) are
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #173.
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12221)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e1, e0) = e2)
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12221) gives:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12222)  all_57_8 = e2 & op(e1, e1) = e2
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (12096), (12222) are inconsistent by
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #172.
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12223)  all_57_11 = e2 & op(e1, e0) = e2
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12223) implies:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12224)  all_57_11 = e2
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (161), (169), (211),
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (213), (231), (12090), (12133), (12148), (12154),
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12155), (12158), (12159), (12187), (12224),
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #175.
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | |   (12225)  all_30_2 = e1
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (330), (12225) imply:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | |   (12226)  all_4_2 = e1
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (351), (12226) imply:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | |   (12227)   ~ (all_53_3 = e1)
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (372), (12226) imply:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | |   (12228)   ~ (all_53_14 = e1)
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12101), (12226) imply:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | |   (12229)   ~ (e3 = e1)
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (373), (12226) imply:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | |   (12230)   ~ (e2 = e1)
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (12226) imply:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | |   (12231)  op(e0, e0) = e1
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | |   (12232)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e2)
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (171), (12113), (12123), (12156), (12160),
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | |            (12232), (function-axioms) are inconsistent by
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #341.
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | |   (12233)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e2)
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12233) gives:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12234)  all_57_4 = e2 & op(e3, e1) = e2
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12234) implies:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12235)  all_57_4 = e2
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12236)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (169), (231),
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (237), (12117), (12148), (12235), (12236),
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #171.
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12237)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12237) gives:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12238)  all_57_11 = e2 & op(e1, e0) = e2
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12238) implies:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12239)  all_57_11 = e2
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12240)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e1)
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12240) gives:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12241)  all_57_4 = e1 & op(e3, e1) = e1
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12241) implies:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12242)  all_57_4 = e1
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (12235), (12242) are inconsistent by
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2430.
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12243)  all_57_5 = e1 & op(e2, e1) = e1
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12243) implies:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12244)  all_57_5 = e1
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12245)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e0)
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12245) gives:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12246)  all_57_4 = e0 & op(e3, e1) = e0
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12246) implies:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12247)  all_57_4 = e0
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (12235), (12247) are inconsistent by
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2441.
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12248)  all_57_5 = e0 & op(e2, e1) = e0
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (12244), (12248) are inconsistent by
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #942.
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12249)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12249) gives:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12250)  all_57_8 = e0 & op(e1, e1) = e0
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12096), (12250) are inconsistent by
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #170.
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12251)  all_57_14 = e0 & op(e0, e1) = e0
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12251) implies:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12252)  all_57_14 = e0
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12253)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12253) gives:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12254)  all_57_2 = e0 & op(e2, e3) = e0
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12254) implies:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12255)  all_57_2 = e0
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12256)  all_57_15 = e0 & op(e0, e0) = e0
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12256) implies:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12257)  all_57_15 = e0
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12258)  op(e0, e0) = e0
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (208), (209),
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (210), (12227), (12252), (12257), (12258),
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #320.
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12259)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12259) implies:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12260)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0)
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12260) gives:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12261)  all_57_9 = e0 & op(e3, e0) = e0
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12261) implies:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12262)  op(e3, e0) = e0
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (12153), (12157), (12231), (12262),
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2000.
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12263)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 =
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12263) gives:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12264)  all_57_10 = e0 & op(e2, e0) = e0
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12138), (12264) are inconsistent by
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1981.
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12265)  all_57_11 = e0 & op(e1, e0) = e0
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12265) implies:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12266)  all_57_11 = e0
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (12239), (12266) imply:
% 223.74/38.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12267)  e2 = e0
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (12122), (12267) imply:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12268)  all_57_3 = e0
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (223), (224), (12138),
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12255), (12268) are inconsistent by sub-proof
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2247.
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12269)  all_57_3 = e0 & op(e2, e2) = e0
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12269) implies:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12270)  op(e2, e2) = e0
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (12123), (12270), (function-axioms) are
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2472.
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12271)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0)
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12271) gives:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12272)  all_57_5 = e0 & op(e2, e1) = e0
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (12244), (12272) are inconsistent by
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #942.
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12273)  all_57_10 = e0 & op(e2, e0) = e0
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12138), (12273) are inconsistent by
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1981.
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12274)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e1) = e1)
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12274) gives:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12275)  all_57_8 = e1 & op(e1, e1) = e1
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (12096), (12275) are inconsistent by
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #169.
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12276)  all_57_14 = e1 & op(e0, e1) = e1
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12276) implies:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12277)  all_57_14 = e1
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (159), (207), (209),
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (210), (12115), (12231), (12277),
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2175.
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12278)  all_57_15 = e2 & op(e0, e0) = e2
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12278) implies:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12279)  op(e0, e0) = e2
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (12231), (12279), (function-axioms) are
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2177.
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12280)  all_57_9 = e2 & op(e3, e0) = e2
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12280) implies:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12281)  all_57_9 = e2
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12282)  op(e3, e0) = e2
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12283)  all_57_15 = e0 & op(e0, e0) = e0
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12283) implies:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12284)  op(e0, e0) = e0
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (12231), (12284), (function-axioms) are
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2290.
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12285)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12285) implies:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12286)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0)
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12287)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0)
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12287) gives:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12288)  all_57_9 = e0 & op(e3, e0) = e0
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12288) implies:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12289)  op(e3, e0) = e0
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (12153), (12157), (12231), (12289),
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2000.
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12290)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 =
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12290) gives:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12291)  all_57_10 = e0 & op(e2, e0) = e0
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12291) implies:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12292)  all_57_10 = e0
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12138), (12292) are inconsistent by
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1989.
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12293)  all_57_11 = e0 & op(e1, e0) = e0
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12293) implies:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12294)  all_57_11 = e0
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12295)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e2)
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12295) gives:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12296)  all_57_6 = e2 & op(e1, e3) = e2
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12296) implies:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12297)  all_57_6 = e2
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12298)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e1)
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12298) gives:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12299)  all_57_0 = e1 & op(e3, e3) = e1
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12299) implies:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12300)  op(e3, e3) = e1
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (12133), (12300), (function-axioms) are
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2495.
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12301)  all_57_2 = e1 & op(e2, e3) = e1
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12301) implies:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12302)  all_57_2 = e1
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12303)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (12123), (12302), (12303),
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2457.
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12304)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0)
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12304) gives:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12305)  all_57_5 = e0 & op(e2, e1) = e0
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12305) implies:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12306)  all_57_5 = e0
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12307)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e0)
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (12133), (12302), (12307),
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2466.
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12308)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = e0)
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12308) gives:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12309)  all_57_6 = e0 & op(e1, e3) = e0
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (12297), (12309) are inconsistent by
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2386.
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12310)  all_57_12 = e0 & op(e0, e3) = e0
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12310) implies:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12311)  all_57_12 = e0
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12312)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e2)
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (166), (169), (231),
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (237), (12116), (12148), (12281), (12312),
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #287.
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12313)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e1) = e2)
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12313) gives:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12314)  all_57_8 = e2 & op(e1, e1) = e2
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (12096), (12314) are inconsistent by
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #172.
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12315)  all_57_14 = e2 & op(e0, e1) = e2
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12315) implies:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12316)  all_57_14 = e2
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12317)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e1)
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12317) gives:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12318)  all_57_6 = e1 & op(e1, e3) = e1
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12318) implies:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12319)  all_57_6 = e1
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (12297), (12319) imply:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12320)  e2 = e1
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (12316), (12320) imply:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12321)  all_57_14 = e1
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12322)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (12144), (12311), (12322) are
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2061.
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12323)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (12231), (12321), (12323), (function-axioms)
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2176.
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12324)  all_57_7 = e1 & op(e1, e2) = e1
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12324) implies:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12325)  all_57_7 = e1
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12326)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12326) gives:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12327)  all_57_1 = e0 & op(e3, e2) = e0
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12327) implies:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12328)  op(e3, e2) = e0
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12286) gives:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e2,
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e3, simplifying with (12153), (12282) gives:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12329)  all_52_7 = e2
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e0,
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (12155), (12328) gives:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12330)  all_52_3 = e0
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12165), (12330) imply:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12331)   ~ (e2 = e0)
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12157), (12329) imply:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12332)  op(e2, e2) = e0
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (12123), (12332), (function-axioms) are
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2472.
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12333)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12333) gives:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12334)  all_57_13 = e0 & op(e0, e2) = e0
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12334) implies:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12335)  all_57_13 = e0
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12144), (12335) are inconsistent by
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2184.
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12336)  all_57_14 = e0 & op(e0, e1) = e0
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (159), (209), (230),
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (232), (12115), (12133), (12231), (12297),
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12336), (function-axioms) are inconsistent by
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1960.
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12337)  all_57_3 = e0 & op(e2, e2) = e0
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12337) implies:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12338)  all_57_3 = e0
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12339)  op(e2, e2) = e0
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12138), (12306), (12338), (12339),
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2348.
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12340)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0)
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12340) gives:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12341)  all_57_7 = e0 & op(e1, e2) = e0
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12341) implies:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12342)  all_57_7 = e0
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (12325), (12342) are inconsistent by
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2211.
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12343)  all_57_13 = e0 & op(e0, e2) = e0
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12343) implies:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12344)  all_57_13 = e0
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12144), (12344) are inconsistent by
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2184.
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12345)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e0) = e1)
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12345) gives:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12346)  all_57_8 = e1 & op(e1, e1) = e1
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (12096), (12346) are inconsistent by
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #168.
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12347)  all_57_11 = e1 & op(e1, e0) = e1
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (12228), (12347), (function-axioms) are
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #305.
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12348)  all_57_10 = e0 & op(e2, e0) = e0
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12348) implies:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12349)  all_57_10 = e0
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12138), (12349) are inconsistent by
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1989.
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12350)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e3) = e1)
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12350) gives:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12351)  all_57_6 = e1 & op(e1, e3) = e1
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12351) implies:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12352)  all_57_6 = e1
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (12297), (12352) are inconsistent by
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2233.
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12353)  all_57_12 = e1 & op(e0, e3) = e1
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (12227), (12353), (function-axioms) are
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1947.
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12354)  all_57_7 = e2 & op(e1, e2) = e2
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (12114), (12354), (function-axioms) are
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #173.
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12355)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e1, e0) = e2)
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12355) gives:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12356)  all_57_8 = e2 & op(e1, e1) = e2
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (12096), (12356) are inconsistent by
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #172.
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12357)  all_57_11 = e2 & op(e1, e0) = e2
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (12294), (12357) are inconsistent by
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1988.
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | |   (12358)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | |            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | |              all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_15)
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12358) implies:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | |   (12359)  op(e2, e0) = all_52_15
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | |   (12360)  op(all_52_15, all_52_15) = e0
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3,
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | |              all_52_15, e0, e2, simplifying with (12139),
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | |              (12359) gives:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | |   (12361)  all_52_15 = e3
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12360), (12361) imply:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | |   (12362)  op(e3, e3) = e0
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12133), (12362), (function-axioms) are
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2494.
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | |   (12363)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | |              & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | |              & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | |                all_52_21) = e1 & op(all_52_23, all_52_23) =
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | |              all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | |              = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | |              & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | |              e0 & op(all_52_25, all_52_25) = e3 &
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | |              op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | |                all_52_29) = e1 & op(all_52_31, all_52_31) =
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | |              all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | |              = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_29) & $i(all_52_31))
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (45), (12097), (12099), (12133), (12145),
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | |            (12363), (function-axioms) are inconsistent by
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #166.
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.22  | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | End of split
% 223.74/38.22  | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.22  | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | |   (12364)  all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 223.74/38.22  | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | REF_CLOSE: (277), (12099), (12125), (12127), (12364) are
% 223.74/38.22  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1953.
% 223.74/38.22  | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | End of split
% 223.74/38.22  | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | Case 2:
% 223.74/38.22  | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | |   (12365)  all_20_2 = e2
% 223.74/38.22  | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | COMBINE_EQS: (299), (12365) imply:
% 223.74/38.22  | | | | | | | | | | | | | | | |   (12366)  all_10_2 = e2
% 223.74/38.22  | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | SIMP: (12366) implies:
% 223.74/38.22  | | | | | | | | | | | | | | | |   (12367)  all_10_2 = e2
% 223.74/38.22  | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | REDUCE: (348), (12367) imply:
% 223.74/38.22  | | | | | | | | | | | | | | | |   (12368)   ~ (all_53_12 = e2)
% 223.74/38.22  | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | REDUCE: (45), (12367) imply:
% 223.74/38.22  | | | | | | | | | | | | | | | |   (12369)  op(e3, e3) = e2
% 223.74/38.22  | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 223.74/38.22  | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.22  | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | |   (12370)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 223.74/38.22  | | | | | | | | | | | | | | | | |              & op(e2, e1) = e2)
% 223.74/38.22  | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | BETA: splitting (12370) gives:
% 223.74/38.22  | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | |   (12371)  all_57_4 = e2 & op(e3, e1) = e2
% 223.74/38.22  | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (237),
% 223.74/38.22  | | | | | | | | | | | | | | | | | |            (12369), (12371), (function-axioms) are
% 223.74/38.22  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #226.
% 223.74/38.22  | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | |   (12372)  all_57_5 = e2 & op(e2, e1) = e2
% 223.74/38.22  | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (12116), (12372), (function-axioms) are
% 223.74/38.22  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1858.
% 223.74/38.22  | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | End of split
% 223.74/38.22  | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.22  | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | |   (12373)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 223.74/38.22  | | | | | | | | | | | | | | | | |              e2 & op(e0, e1) = e2)
% 223.74/38.22  | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | BETA: splitting (12373) gives:
% 223.74/38.22  | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | |   (12374)  all_57_8 = e2 & op(e1, e1) = e2
% 223.74/38.22  | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (12096), (12374) are inconsistent by
% 223.74/38.22  | | | | | | | | | | | | | | | | | |            sub-proof #165.
% 223.74/38.22  | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | |   (12375)  all_57_14 = e2 & op(e0, e1) = e2
% 223.74/38.22  | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | ALPHA: (12375) implies:
% 223.74/38.22  | | | | | | | | | | | | | | | | | |   (12376)  op(e0, e1) = e2
% 223.74/38.22  | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | |   (12377)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 223.74/38.22  | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (169), (12117), (12368), (12377),
% 223.74/38.22  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.74/38.22  | | | | | | | | | | | | | | | | | | |            #1952.
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | |   (12378)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 223.74/38.22  | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | BETA: splitting (12378) gives:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | |   (12379)  all_57_11 = e2 & op(e1, e0) = e2
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | ALPHA: (12379) implies:
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | |   (12380)  op(e1, e0) = e2
% 223.74/38.22  | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_11,
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | |              e2, e1, e0, simplifying with (158), (12376) gives:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | |   (12381)  all_53_11 = e2
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_14,
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | |              e2, e0, e1, simplifying with (161), (12380) gives:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | |   (12382)  all_53_14 = e2
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (12381) imply:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | |   (12383)   ~ (all_53_3 = e2)
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | REDUCE: (372), (12382) imply:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | |   (12384)   ~ (all_4_2 = e2)
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | |   (12385)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | |              all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | |              op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | |                all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | |              $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | |              $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | |                all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | |              & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | |                all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | |              & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | |              $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12385) gives:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | |   (12386)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | |            all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | |            op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | |              all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_7)
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12386) implies:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | |   (12387)  op(e3, e3) = all_52_1
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | |   (12388)  op(all_52_1, all_52_1) = e3
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (12123), (12369), (12387), (12388),
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | |            #1951.
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | |   (12389)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | |            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | |            op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | |              all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_15)
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12389) implies:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | |   (12390)  op(e2, e0) = all_52_15
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | |   (12391)  op(e2, e3) = all_52_9
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | |   (12392)  op(all_52_15, all_52_15) = e0
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | |   (12393)  op(all_52_9, all_52_9) = e3
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_13,
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | |              all_52_15, e0, e2, simplifying with (165), (12390)
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | |              gives:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | |   (12394)  all_53_13 = all_52_15
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_1,
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | |              all_52_9, e3, e2, simplifying with (168), (12391)
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | |              gives:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | |   (12395)  all_53_1 = all_52_9
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (12394) imply:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | |   (12396)  all_55_7 = all_52_15
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (12395) imply:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | |   (12397)  all_55_4 = all_52_9
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (12395) imply:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | |   (12398)   ~ (all_53_3 = all_52_9)
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | SIMP: (12398) implies:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | |   (12399)   ~ (all_53_3 = all_52_9)
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12112), (12395) imply:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | |   (12400)   ~ (all_52_9 = e2)
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (371), (12394) imply:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | |   (12401)   ~ (all_52_15 = all_4_2)
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12117), (12394) imply:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | |   (12402)   ~ (all_52_15 = e2)
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (76) gives:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | |   (12403)   ~ (all_30_2 = e1)
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (330), (12403) imply:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | |   (12404)   ~ (all_4_2 = e1)
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | |   (12405)  all_55_15 = e3
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (12405) imply:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | |   (12406)  all_4_2 = e3
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12101), (12406) imply:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | |   (12407)  $false
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (12407) is inconsistent.
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | |   (12408)  all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12408) gives:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | |   (12409)  all_55_15 = e2
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (12409) imply:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | |   (12410)  all_4_2 = e2
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (373), (12410) imply:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | |   (12411)  $false
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (12411) is inconsistent.
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | |   (12412)  all_55_15 = e1 | all_55_15 = e0
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12412) gives:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12413)  all_55_15 = e1
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (12413) imply:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12414)  all_4_2 = e1
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12404), (12414) imply:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12415)  $false
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (12415) is inconsistent.
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12416)  all_55_15 = e0
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (12416) imply:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12417)  all_4_2 = e0
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (351), (12417) imply:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12418)   ~ (all_53_3 = e0)
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (362), (12417) imply:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12419)   ~ (all_53_7 = e0)
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (12417) imply:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12420)  op(e0, e0) = e0
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12421)  all_55_13 = e3
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (12421) imply:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12422)  all_53_7 = e3
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (141), (12422) imply:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12423)   ~ (all_53_3 = e3)
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12424)  all_55_12 = e3
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (247), (12423), (12424) are inconsistent by
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2001.
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12425)  all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12425) gives:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12426)  all_55_12 = e2
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (247), (12383), (12426) are inconsistent by
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1337.
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12427)  all_55_12 = e1 | all_55_12 = e0
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12427) gives:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12428)  all_55_12 = e1
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (12428) imply:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12429)  all_53_3 = e1
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12399), (12429) imply:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12430)   ~ (all_52_9 = e1)
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (12430) implies:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12431)   ~ (all_52_9 = e1)
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12432)  all_55_4 = e3
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (12397), (12432) imply:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12433)  all_52_9 = e3
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (12433) implies:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12434)  all_52_9 = e3
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12393), (12434) imply:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12435)  op(e3, e3) = e3
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (12369), (12435), (function-axioms) are
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2490.
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12436)   ~ (all_55_4 = e3)
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12437)  all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12397), (12436) imply:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12438)   ~ (all_52_9 = e3)
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12393), (12397), (12400), (12420), (12431),
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12437), (12438), (function-axioms) are
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #343.
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12439)  all_55_12 = e0
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (12439) imply:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12440)  all_53_3 = e0
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12418), (12440) imply:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12441)  $false
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (12441) is inconsistent.
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12442)  all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12442) gives:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12443)  all_55_13 = e2
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (12443) imply:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12444)  all_53_7 = e2
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12115), (12444) imply:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12445)  $false
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (12445) is inconsistent.
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12446)  all_55_13 = e1 | all_55_13 = e0
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12446) gives:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12447)  all_55_13 = e1
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (12447) imply:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12448)  all_53_7 = e1
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (129), (12448) imply:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12449)   ~ (all_53_6 = e1)
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12450)  all_55_9 = e3
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (12086), (12450) are inconsistent by
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2159.
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12451)   ~ (all_55_9 = e3)
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12452)  all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12452) gives:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12453)  all_55_9 = e2
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (12453) imply:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12454)  all_53_6 = e2
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12114), (12454) imply:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12455)  $false
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (12455) is inconsistent.
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12456)   ~ (all_55_9 = e2)
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12457)  all_55_9 = e1 | all_55_9 = e0
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12457) gives:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12458)  all_55_9 = e1
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (12458) imply:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12459)  all_53_6 = e1
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12449), (12459) imply:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12460)  $false
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (12460) is inconsistent.
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12461)  all_55_9 = e0
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (12461) imply:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12462)  all_53_6 = e0
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (12462) imply:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12463)   ~ (all_53_2 = e0)
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12086), (12462) imply:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12464)   ~ (e3 = e0)
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12114), (12462) imply:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12465)   ~ (e2 = e0)
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (160), (164), (168), (230), (12369),
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12391), (12393), (12418), (12420), (12463),
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1571.
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12466)  all_55_13 = e0
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (12466) imply:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12467)  all_53_7 = e0
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12419), (12467) imply:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12468)  $false
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (12468) is inconsistent.
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | |   (12469)  all_30_2 = e1
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | |   (12470)  ( ~ (all_30_0 = e2) & op(all_30_1, e0) = all_30_0
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | |              & op(e0, e1) = all_30_1 & $i(all_30_0) &
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_30_1)) | ( ~ (all_30_1 = e3) & op(e0, e1)
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | |              = all_30_1 & $i(all_30_1))
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (330), (12469) imply:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | |   (12471)  all_4_2 = e1
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (295), (12471) imply:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | |   (12472)  all_40_2 = e1
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12401), (12471) imply:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | |   (12473)   ~ (all_52_15 = e1)
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (12471) imply:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | |   (12474)  op(e0, e0) = e1
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (91) gives:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | |   (12475)   ~ (all_40_2 = e1)
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12472), (12475) imply:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | |   (12476)  $false
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (12476) is inconsistent.
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | |   (12477)  ( ~ (all_40_0 = e3) & op(all_40_1, e0) = all_40_0
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e0, e1) = all_40_1 & $i(all_40_0) &
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_40_1)) | ( ~ (all_40_1 = e2) & op(e0, e1)
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | |              = all_40_1 & $i(all_40_1))
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12470) gives:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | |   (12478)   ~ (all_30_0 = e2) & op(all_30_1, e0) = all_30_0 &
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e1) = all_30_1 & $i(all_30_0) &
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_30_1)
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12478) implies:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | |   (12479)  op(e0, e1) = all_30_1
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (198), (12376), (12390), (12392), (12396),
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | |            (12402), (12470), (12473), (12474), (12477),
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | |            (12479), (function-axioms) are inconsistent by
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #163.
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | |   (12480)   ~ (all_30_1 = e3) & op(e0, e1) = all_30_1 &
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_30_1)
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12480) implies:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | |   (12481)  op(e0, e1) = all_30_1
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (198), (12376), (12390), (12392), (12396),
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | |            (12402), (12470), (12473), (12474), (12477),
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | |            (12481), (function-axioms) are inconsistent by
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #163.
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | |   (12482)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | |              & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | |              & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | |                all_52_21) = e1 & op(all_52_23, all_52_23) =
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | |              all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | |              = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | |              $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | |              & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | |              e0 & op(all_52_25, all_52_25) = e3 &
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | |              op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | |                all_52_29) = e1 & op(all_52_31, all_52_31) =
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | |              all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | |              = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | |              $i(all_52_29) & $i(all_52_31))
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (12123), (12376), (12380), (12482),
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | |            #1944.
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | |   (12483)  all_57_15 = e2 & op(e0, e0) = e2
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | ALPHA: (12483) implies:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | |   (12484)  op(e0, e0) = e2
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (373), (12484), (function-axioms) are
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2334.
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.23  | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | End of split
% 223.74/38.23  | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | End of split
% 223.74/38.23  | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | End of split
% 223.74/38.23  | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | Case 2:
% 223.74/38.23  | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | |   (12485)  all_18_2 = e0
% 223.74/38.23  | | | | | | | | | | | | | | |   (12486)  ( ~ (all_18_0 = e1) & op(all_18_1, e3) = all_18_0
% 223.74/38.23  | | | | | | | | | | | | | | |              & op(e3, e0) = all_18_1 & $i(all_18_0) &
% 223.74/38.23  | | | | | | | | | | | | | | |              $i(all_18_1)) | ( ~ (all_18_1 = e2) & op(e3, e0)
% 223.74/38.23  | | | | | | | | | | | | | | |              = all_18_1 & $i(all_18_1))
% 223.74/38.23  | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | COMBINE_EQS: (327), (12485) imply:
% 223.74/38.23  | | | | | | | | | | | | | | |   (12487)  all_10_2 = e0
% 223.74/38.23  | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | COMBINE_EQS: (279), (12487) imply:
% 223.74/38.23  | | | | | | | | | | | | | | |   (12488)  all_48_2 = e0
% 223.74/38.23  | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | REDUCE: (338), (12487) imply:
% 223.74/38.23  | | | | | | | | | | | | | | |   (12489)   ~ (all_53_1 = e0)
% 223.74/38.23  | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | REDUCE: (342), (12487) imply:
% 223.74/38.23  | | | | | | | | | | | | | | |   (12490)   ~ (all_53_3 = e0)
% 223.74/38.23  | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | REDUCE: (344), (12487) imply:
% 223.74/38.23  | | | | | | | | | | | | | | |   (12491)   ~ (all_53_4 = e0)
% 223.74/38.23  | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | REDUCE: (346), (12487) imply:
% 223.74/38.23  | | | | | | | | | | | | | | |   (12492)   ~ (all_53_8 = e0)
% 223.74/38.23  | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | REDUCE: (348), (12487) imply:
% 223.74/38.23  | | | | | | | | | | | | | | |   (12493)   ~ (all_53_12 = e0)
% 223.74/38.23  | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | REDUCE: (12099), (12487) imply:
% 223.74/38.23  | | | | | | | | | | | | | | |   (12494)   ~ (e1 = e0)
% 223.74/38.23  | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | REDUCE: (45), (12487) imply:
% 223.74/38.23  | | | | | | | | | | | | | | |   (12495)  op(e3, e3) = e0
% 223.74/38.23  | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | BETA: splitting (76) gives:
% 223.74/38.23  | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | Case 1:
% 223.74/38.23  | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | |   (12496)   ~ (all_30_2 = e1)
% 223.74/38.23  | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | REDUCE: (330), (12496) imply:
% 223.74/38.23  | | | | | | | | | | | | | | | |   (12497)   ~ (all_4_2 = e1)
% 223.74/38.23  | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 223.74/38.23  | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.23  | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | |   (12498)  all_55_15 = e3
% 223.74/38.23  | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (12101), (12498) are inconsistent by
% 223.74/38.23  | | | | | | | | | | | | | | | | |            sub-proof #2503.
% 223.74/38.23  | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.23  | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | |   (12499)   ~ (all_55_15 = e3)
% 223.74/38.23  | | | | | | | | | | | | | | | | |   (12500)  all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 223.74/38.23  | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | BETA: splitting (12500) gives:
% 223.74/38.23  | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | |   (12501)  all_55_15 = e2
% 223.74/38.23  | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (373), (12501) are inconsistent by
% 223.74/38.23  | | | | | | | | | | | | | | | | | |            sub-proof #2502.
% 223.74/38.23  | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | |   (12502)   ~ (all_55_15 = e2)
% 223.74/38.23  | | | | | | | | | | | | | | | | | |   (12503)  all_55_15 = e1 | all_55_15 = e0
% 223.74/38.23  | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | BETA: splitting (12503) gives:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | |   (12504)  all_55_15 = e1
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (12497), (12504) are inconsistent by
% 223.74/38.23  | | | | | | | | | | | | | | | | | | |            sub-proof #2501.
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | |   (12505)  all_55_15 = e0
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (12505) imply:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | |   (12506)  all_4_2 = e0
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | SIMP: (12506) implies:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | |   (12507)  all_4_2 = e0
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | REDUCE: (362), (12507) imply:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | |   (12508)   ~ (all_53_7 = e0)
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | REDUCE: (371), (12507) imply:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | |   (12509)   ~ (all_53_13 = e0)
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | REDUCE: (372), (12507) imply:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | |   (12510)   ~ (all_53_14 = e0)
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | REDUCE: (12101), (12507) imply:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | |   (12511)   ~ (e3 = e0)
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | REDUCE: (373), (12507) imply:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | |   (12512)   ~ (e2 = e0)
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | REDUCE: (36), (12507) imply:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | |   (12513)  op(e0, e0) = e0
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | |   (12514)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e0)
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | BETA: splitting (12514) gives:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | |   (12515)  all_57_4 = e0 & op(e3, e1) = e0
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | ALPHA: (12515) implies:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | |   (12516)  op(e3, e1) = e0
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (12492), (12516), (function-axioms) are
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2267.
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | |   (12517)  all_57_5 = e0 & op(e2, e1) = e0
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | ALPHA: (12517) implies:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | |   (12518)  op(e2, e1) = e0
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | |   (12519)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (171), (12123), (12491), (12519),
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | |            #1940.
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | |   (12520)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0)
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12520) gives:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | |   (12521)  all_57_7 = e0 & op(e1, e2) = e0
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12521) implies:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | |   (12522)  op(e1, e2) = e0
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_6, e0,
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | |              e2, e1, simplifying with (163), (12522) gives:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | |   (12523)  all_53_6 = e0
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_9, e0,
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (166), (12518) gives:
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | |   (12524)  all_53_9 = e0
% 223.74/38.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (12523) imply:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | |   (12525)   ~ (all_53_2 = e0)
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (127), (12523) imply:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | |   (12526)   ~ (all_53_14 = e0)
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (12524) imply:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | |   (12527)   ~ (all_53_13 = e0)
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | |   (12528)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | |              all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | |              op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | |                all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | |                all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | |              & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | |                all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (12495), (12513), (12518), (12528),
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | |            #1938.
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | |   (12529)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | |              & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | |              & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | |                all_52_21) = e1 & op(all_52_23, all_52_23) =
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | |              all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | |              = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | |              & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(all_52_25, all_52_25) = e3 &
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | |              op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | |                all_52_29) = e1 & op(all_52_31, all_52_31) =
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | |              all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | |              = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_29) & $i(all_52_31))
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12529) gives:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | |   (12530)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | |            & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_23)
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12530) implies:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | |   (12531)  op(e1, e2) = all_52_19
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | |   (12532)  op(all_52_19, all_52_19) = e2
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (12513), (12522), (12531), (12532),
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | |            #2158.
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | |   (12533)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | |            & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_31)
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12533) implies:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | |   (12534)  op(e0, e3) = all_52_25
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | |   (12535)  op(all_52_25, all_52_25) = e3
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_3,
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_25, e3, e0, simplifying with (160), (12534)
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | |   (12536)  all_53_3 = all_52_25
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (12536) imply:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | |   (12537)  all_55_12 = all_52_25
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (12536) imply:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | |   (12538)   ~ (all_53_1 = all_52_25)
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (12536) imply:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | |   (12539)   ~ (all_53_2 = all_52_25)
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12490), (12536) imply:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | |   (12540)   ~ (all_52_25 = e0)
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12541)  all_55_4 = e3
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (12541) imply:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12542)  all_53_1 = e3
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (12542) implies:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12543)  all_53_1 = e3
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (150), (12543) imply:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12544)   ~ (all_53_2 = e3)
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (12543) imply:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12545)   ~ (all_53_13 = e3)
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (12545) implies:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12546)   ~ (all_53_13 = e3)
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12538), (12543) imply:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12547)   ~ (all_52_25 = e3)
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (12547) implies:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12548)   ~ (all_52_25 = e3)
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12549)  all_55_7 = e3
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (12546), (12549) are inconsistent by
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2109.
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12550)  all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12550) gives:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12551)  all_55_7 = e2
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (12117), (12551) are inconsistent by
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2171.
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12552)  all_55_7 = e1 | all_55_7 = e0
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12552) gives:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12553)  all_55_7 = e1
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (12553) imply:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12554)  all_53_13 = e1
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (12554) implies:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12555)  all_53_13 = e1
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (111), (12555) imply:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12556)   ~ (all_53_14 = e1)
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (12556) implies:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12557)   ~ (all_53_14 = e1)
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12558)  all_55_11 = e3
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (12090), (12558) are inconsistent by
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2497.
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12559)  all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12559) gives:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12560)  all_55_11 = e2
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (12560) imply:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12561)  all_53_14 = e2
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (12561) implies:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12562)  all_53_14 = e2
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (142), (12562) imply:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12563)   ~ (all_53_2 = e2)
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12564)  all_55_8 = e3
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (12085), (12564) are inconsistent by
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2496.
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12565)  all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12565) gives:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12566)  all_55_8 = e2
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (12566) imply:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12567)  all_53_2 = e2
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12563), (12567) imply:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12568)  $false
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (12568) is inconsistent.
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12569)  all_55_8 = e1 | all_55_8 = e0
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12569) gives:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12570)  all_55_8 = e1
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (12570) imply:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12571)  all_53_2 = e1
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (12571) implies:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12572)  all_53_2 = e1
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12539), (12572) imply:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12573)   ~ (all_52_25 = e1)
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (12573) implies:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12574)   ~ (all_52_25 = e1)
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (193), (12123), (12535), (12537), (12540),
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12548), (12574), (function-axioms) are
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #322.
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12575)  all_55_8 = e0
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (12525), (12575) are inconsistent by
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1997.
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12576)  all_55_11 = e1 | all_55_11 = e0
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (12510), (12557), (12576) are inconsistent
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2307.
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12577)  all_55_7 = e0
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (12509), (12577) are inconsistent by
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2130.
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12578)  all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12578) gives:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12579)  all_55_4 = e2
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (12112), (12579) are inconsistent by
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2168.
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12580)  all_55_4 = e1 | all_55_4 = e0
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12580) gives:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12581)  all_55_4 = e1
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (12581) imply:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12582)  all_53_1 = e1
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (12582) implies:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12583)  all_53_1 = e1
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (150), (12583) imply:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12584)   ~ (all_53_2 = e1)
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (12584) implies:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12585)   ~ (all_53_2 = e1)
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12538), (12583) imply:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12586)   ~ (all_52_25 = e1)
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (12586) implies:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12587)   ~ (all_52_25 = e1)
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12588)  all_55_8 = e3
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (12085), (12588) are inconsistent by
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2496.
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12589)  all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12589) gives:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12590)  all_55_8 = e2
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (12590) imply:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12591)  all_53_2 = e2
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (12591) implies:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12592)  all_53_2 = e2
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12539), (12592) imply:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12593)   ~ (all_52_25 = e2)
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (12593) implies:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12594)   ~ (all_52_25 = e2)
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12595)  all_55_12 = e3
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (12537), (12595) imply:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12596)  all_52_25 = e3
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (12596) implies:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12597)  all_52_25 = e3
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12535), (12597) imply:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12598)  op(e3, e3) = e3
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12495), (12598), (function-axioms) are
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2494.
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12599)  all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12537), (12540), (12587), (12594), (12599) are
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1563.
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12600)  all_55_8 = e1 | all_55_8 = e0
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (12525), (12585), (12600) are inconsistent
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1974.
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12601)  all_55_4 = e0
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (12489), (12601) are inconsistent by
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1865.
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | |   (12602)  all_57_13 = e0 & op(e0, e2) = e0
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12602) implies:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | |   (12603)  op(e0, e2) = e0
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (12508), (12603), (function-axioms) are
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2332.
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | |   (12604)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | BETA: splitting (12604) gives:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | |   (12605)  all_57_8 = e0 & op(e1, e1) = e0
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12096), (12605) are inconsistent by
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | |            sub-proof #162.
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | |   (12606)  all_57_14 = e0 & op(e0, e1) = e0
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | ALPHA: (12606) implies:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | |   (12607)  all_57_14 = e0
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | |   (12608)  all_57_15 = e0 & op(e0, e0) = e0
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12608) implies:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | |   (12609)  all_57_15 = e0
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (159), (208),
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | |            (209), (210), (373), (12115), (12513), (12607),
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | |            (12609), (function-axioms) are inconsistent by
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2120.
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | |   (12610)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (165), (169), (12493), (12509), (12510),
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | |            (12610), (function-axioms) are inconsistent by
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2112.
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.24  | | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.24  | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | End of split
% 223.74/38.24  | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | End of split
% 223.74/38.24  | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | Case 2:
% 223.74/38.24  | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | |   (12611)  all_30_2 = e1
% 223.74/38.24  | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | COMBINE_EQS: (330), (12611) imply:
% 223.74/38.24  | | | | | | | | | | | | | | | |   (12612)  all_4_2 = e1
% 223.74/38.24  | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | SIMP: (12612) implies:
% 223.74/38.24  | | | | | | | | | | | | | | | |   (12613)  all_4_2 = e1
% 223.74/38.24  | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | REDUCE: (351), (12613) imply:
% 223.74/38.24  | | | | | | | | | | | | | | | |   (12614)   ~ (all_53_3 = e1)
% 223.74/38.24  | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | REDUCE: (12101), (12613) imply:
% 223.74/38.24  | | | | | | | | | | | | | | | |   (12615)   ~ (e3 = e1)
% 223.74/38.24  | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | REDUCE: (373), (12613) imply:
% 223.74/38.24  | | | | | | | | | | | | | | | |   (12616)   ~ (e2 = e1)
% 223.74/38.24  | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | REDUCE: (36), (12613) imply:
% 223.74/38.24  | | | | | | | | | | | | | | | |   (12617)  op(e0, e0) = e1
% 223.74/38.24  | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 223.74/38.24  | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.24  | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | |   (12618)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 223.74/38.24  | | | | | | | | | | | | | | | | |              all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 223.74/38.24  | | | | | | | | | | | | | | | | |              op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 223.74/38.24  | | | | | | | | | | | | | | | | |                all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 223.74/38.24  | | | | | | | | | | | | | | | | |              op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 223.74/38.24  | | | | | | | | | | | | | | | | |              op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 223.74/38.24  | | | | | | | | | | | | | | | | |              $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 223.74/38.24  | | | | | | | | | | | | | | | | |              $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 223.74/38.24  | | | | | | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 223.74/38.24  | | | | | | | | | | | | | | | | |                all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 223.74/38.24  | | | | | | | | | | | | | | | | |              & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 223.74/38.24  | | | | | | | | | | | | | | | | |                all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 223.74/38.24  | | | | | | | | | | | | | | | | |              op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 223.74/38.24  | | | | | | | | | | | | | | | | |              & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 223.74/38.24  | | | | | | | | | | | | | | | | |              $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 223.74/38.24  | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | BETA: splitting (12618) gives:
% 223.74/38.24  | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | |   (12619)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 223.74/38.24  | | | | | | | | | | | | | | | | | |            all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 223.74/38.24  | | | | | | | | | | | | | | | | | |            op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 223.74/38.24  | | | | | | | | | | | | | | | | | |              all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 223.74/38.24  | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 223.74/38.24  | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 223.74/38.24  | | | | | | | | | | | | | | | | | |            $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 223.74/38.24  | | | | | | | | | | | | | | | | | |            $i(all_52_7)
% 223.74/38.24  | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | ALPHA: (12619) implies:
% 223.74/38.24  | | | | | | | | | | | | | | | | | |   (12620)  op(e3, e3) = all_52_1
% 223.74/38.24  | | | | | | | | | | | | | | | | | |   (12621)  op(all_52_1, all_52_1) = e3
% 223.74/38.24  | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (159), (160), (207),
% 223.74/38.24  | | | | | | | | | | | | | | | | | |            (208), (209), (210), (12115), (12490), (12495),
% 223.74/38.24  | | | | | | | | | | | | | | | | | |            (12614), (12617), (12620), (12621),
% 223.74/38.24  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.74/38.24  | | | | | | | | | | | | | | | | | |            #1915.
% 223.74/38.24  | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | |   (12622)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 223.74/38.24  | | | | | | | | | | | | | | | | | |            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 223.74/38.24  | | | | | | | | | | | | | | | | | |            op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 223.74/38.24  | | | | | | | | | | | | | | | | | |              all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 223.74/38.24  | | | | | | | | | | | | | | | | | |            & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 223.74/38.24  | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 223.74/38.24  | | | | | | | | | | | | | | | | | |            $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 223.74/38.24  | | | | | | | | | | | | | | | | | |            $i(all_52_15)
% 223.74/38.24  | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | ALPHA: (12622) implies:
% 223.74/38.24  | | | | | | | | | | | | | | | | | |   (12623)  op(e2, e0) = all_52_15
% 223.74/38.24  | | | | | | | | | | | | | | | | | |   (12624)  op(e2, e3) = all_52_9
% 223.74/38.24  | | | | | | | | | | | | | | | | | |   (12625)  op(all_52_15, all_52_15) = e0
% 223.74/38.24  | | | | | | | | | | | | | | | | | |   (12626)  op(all_52_9, all_52_9) = e3
% 223.74/38.24  | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (103), (159), (160),
% 223.74/38.24  | | | | | | | | | | | | | | | | | |            (165), (168), (169), (201), (207), (208), (209),
% 223.74/38.24  | | | | | | | | | | | | | | | | | |            (210), (212), (267), (12112), (12115), (12117),
% 223.74/38.24  | | | | | | | | | | | | | | | | | |            (12486), (12488), (12489), (12490), (12493),
% 223.74/38.24  | | | | | | | | | | | | | | | | | |            (12495), (12614), (12617), (12623), (12624),
% 223.74/38.24  | | | | | | | | | | | | | | | | | |            (12625), (12626), (function-axioms) are
% 223.74/38.24  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1894.
% 223.74/38.24  | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | End of split
% 223.74/38.24  | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.24  | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | |   (12627)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 223.74/38.24  | | | | | | | | | | | | | | | | |              & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 223.74/38.24  | | | | | | | | | | | | | | | | |              & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 223.74/38.24  | | | | | | | | | | | | | | | | |                all_52_21) = e1 & op(all_52_23, all_52_23) =
% 223.74/38.24  | | | | | | | | | | | | | | | | |              e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 223.74/38.24  | | | | | | | | | | | | | | | | |              all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 223.74/38.24  | | | | | | | | | | | | | | | | |              = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 223.74/38.24  | | | | | | | | | | | | | | | | |              $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 223.74/38.24  | | | | | | | | | | | | | | | | |              & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 223.74/38.24  | | | | | | | | | | | | | | | | |              e0 & op(all_52_25, all_52_25) = e3 &
% 223.74/38.24  | | | | | | | | | | | | | | | | |              op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 223.74/38.24  | | | | | | | | | | | | | | | | |                all_52_29) = e1 & op(all_52_31, all_52_31) =
% 223.74/38.24  | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 223.74/38.24  | | | | | | | | | | | | | | | | |              all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 223.74/38.24  | | | | | | | | | | | | | | | | |              = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 223.74/38.24  | | | | | | | | | | | | | | | | |              $i(all_52_29) & $i(all_52_31))
% 223.74/38.24  | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | BETA: splitting (12627) gives:
% 223.74/38.24  | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | |   (12628)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 223.74/38.24  | | | | | | | | | | | | | | | | | |            all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 223.74/38.24  | | | | | | | | | | | | | | | | | |            op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 223.74/38.24  | | | | | | | | | | | | | | | | | |              all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 223.74/38.24  | | | | | | | | | | | | | | | | | |            & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 223.74/38.24  | | | | | | | | | | | | | | | | | |            & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 223.74/38.24  | | | | | | | | | | | | | | | | | |            & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 223.74/38.24  | | | | | | | | | | | | | | | | | |            $i(all_52_23)
% 223.74/38.24  | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | ALPHA: (12628) implies:
% 223.74/38.24  | | | | | | | | | | | | | | | | | |   (12629)  op(e1, e1) = all_52_21
% 223.74/38.24  | | | | | | | | | | | | | | | | | |   (12630)  op(all_52_21, all_52_21) = e1
% 223.74/38.24  | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (12097), (12099), (12629), (12630),
% 223.74/38.24  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.74/38.24  | | | | | | | | | | | | | | | | | |            #167.
% 223.74/38.24  | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.24  | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | |   (12631)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 223.74/38.24  | | | | | | | | | | | | | | | | | |            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 223.74/38.24  | | | | | | | | | | | | | | | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 223.74/38.24  | | | | | | | | | | | | | | | | | |              all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 223.74/38.24  | | | | | | | | | | | | | | | | | |            & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 223.74/38.24  | | | | | | | | | | | | | | | | | |            & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 223.74/38.24  | | | | | | | | | | | | | | | | | |            & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 223.74/38.24  | | | | | | | | | | | | | | | | | |            $i(all_52_31)
% 223.74/38.24  | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | ALPHA: (12631) implies:
% 223.74/38.24  | | | | | | | | | | | | | | | | | |   (12632)  op(e0, e0) = all_52_31
% 223.74/38.24  | | | | | | | | | | | | | | | | | |   (12633)  op(all_52_31, all_52_31) = e0
% 223.74/38.24  | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12097), (12617), (12632), (12633),
% 223.74/38.24  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.74/38.24  | | | | | | | | | | | | | | | | | |            #161.
% 223.74/38.24  | | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | | End of split
% 223.74/38.24  | | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | | End of split
% 223.74/38.24  | | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | | End of split
% 223.74/38.24  | | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | | End of split
% 223.74/38.24  | | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | End of split
% 223.74/38.24  | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | Case 2:
% 223.74/38.24  | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | |   (12634)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 223.74/38.24  | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 223.74/38.24  | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | | REF_CLOSE: (159), (163), (12114), (12115), (12634),
% 223.74/38.24  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.74/38.24  | | | | | | | | | | | | |            #160.
% 223.74/38.24  | | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | End of split
% 223.74/38.24  | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | Case 2:
% 223.74/38.24  | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | |   (12635)  all_55_5 = e1 | all_55_5 = e0
% 223.74/38.24  | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | | REF_CLOSE: (266), (12103), (12105), (12635) are inconsistent
% 223.74/38.24  | | | | | | | | | | | |            by sub-proof #1857.
% 223.74/38.24  | | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | | End of split
% 223.74/38.24  | | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | End of split
% 223.74/38.24  | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | Case 2:
% 223.74/38.24  | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | |   (12636)  all_16_2 = e1
% 223.74/38.24  | | | | | | | | | |   (12637)  ( ~ (all_16_0 = e0) & op(all_16_1, e2) = all_16_0
% 223.74/38.24  | | | | | | | | | |              & op(e2, e1) = all_16_1 & $i(all_16_0) &
% 223.74/38.24  | | | | | | | | | |              $i(all_16_1)) | ( ~ (all_16_1 = e3) & op(e2, e1)
% 223.74/38.24  | | | | | | | | | |              = all_16_1 & $i(all_16_1))
% 223.74/38.24  | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | COMBINE_EQS: (324), (12636) imply:
% 223.74/38.24  | | | | | | | | | |   (12638)  all_8_2 = e1
% 223.74/38.24  | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | COMBINE_EQS: (305), (12638) imply:
% 223.74/38.24  | | | | | | | | | |   (12639)  all_26_2 = e1
% 223.74/38.24  | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | REDUCE: (349), (12638) imply:
% 223.74/38.24  | | | | | | | | | |   (12640)   ~ (all_53_1 = e1)
% 223.74/38.24  | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | REDUCE: (356), (12638) imply:
% 223.74/38.24  | | | | | | | | | |   (12641)   ~ (all_53_7 = e1)
% 223.74/38.24  | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | REDUCE: (358), (12638) imply:
% 223.74/38.24  | | | | | | | | | |   (12642)   ~ (all_53_9 = e1)
% 223.74/38.24  | | | | | | | | | | 
% 223.74/38.24  | | | | | | | | | | REDUCE: (360), (12638) imply:
% 223.74/38.24  | | | | | | | | | |   (12643)   ~ (all_53_13 = e1)
% 223.74/38.25  | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | REDUCE: (12098), (12638) imply:
% 223.74/38.25  | | | | | | | | | |   (12644)   ~ (e3 = e1)
% 223.74/38.25  | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | REDUCE: (42), (12638) imply:
% 223.74/38.25  | | | | | | | | | |   (12645)  op(e2, e2) = e1
% 223.74/38.25  | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | BETA: splitting (58) gives:
% 223.74/38.25  | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | Case 1:
% 223.74/38.25  | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | |   (12646)   ~ (all_18_2 = e0)
% 223.74/38.25  | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | REDUCE: (327), (12646) imply:
% 223.74/38.25  | | | | | | | | | | |   (12647)   ~ (all_10_2 = e0)
% 223.74/38.25  | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | BETA: splitting (61) gives:
% 223.74/38.25  | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | Case 1:
% 223.74/38.25  | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | |   (12648)   ~ (all_20_2 = e2)
% 223.74/38.25  | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | REDUCE: (299), (12648) imply:
% 223.74/38.25  | | | | | | | | | | | |   (12649)   ~ (all_10_2 = e2)
% 223.74/38.25  | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | BETA: splitting (205) gives:
% 223.74/38.25  | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | Case 1:
% 223.74/38.25  | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | |   (12650)  all_55_0 = e3
% 223.74/38.25  | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | COMBINE_EQS: (277), (12650) imply:
% 223.74/38.25  | | | | | | | | | | | | |   (12651)  all_10_2 = e3
% 223.74/38.25  | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | SIMP: (12651) implies:
% 223.74/38.25  | | | | | | | | | | | | |   (12652)  all_10_2 = e3
% 223.74/38.25  | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | REDUCE: (338), (12652) imply:
% 223.74/38.25  | | | | | | | | | | | | |   (12653)   ~ (all_53_1 = e3)
% 223.74/38.25  | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | REDUCE: (344), (12652) imply:
% 223.74/38.25  | | | | | | | | | | | | |   (12654)   ~ (all_53_4 = e3)
% 223.74/38.25  | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | REDUCE: (45), (12652) imply:
% 223.74/38.25  | | | | | | | | | | | | |   (12655)  op(e3, e3) = e3
% 223.74/38.25  | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | BETA: splitting (225) gives:
% 223.74/38.25  | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | Case 1:
% 223.74/38.25  | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | |   (12656)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 223.74/38.25  | | | | | | | | | | | | | |              & op(e2, e2) = e3)
% 223.74/38.25  | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | REF_CLOSE: (8), (168), (12645), (12653), (12656),
% 223.74/38.25  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.74/38.25  | | | | | | | | | | | | | |            #159.
% 223.74/38.25  | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | Case 2:
% 223.74/38.25  | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | |   (12657)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 223.74/38.25  | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 223.74/38.25  | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | BETA: splitting (12657) gives:
% 223.74/38.25  | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | Case 1:
% 223.74/38.25  | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | |   (12658)  all_57_5 = e3 & op(e2, e1) = e3
% 223.74/38.25  | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | REF_CLOSE: (166), (12088), (12658), (function-axioms) are
% 223.74/38.25  | | | | | | | | | | | | | | |            inconsistent by sub-proof #270.
% 223.74/38.25  | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | Case 2:
% 223.74/38.25  | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | |   (12659)  all_57_10 = e3 & op(e2, e0) = e3
% 223.74/38.25  | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | ALPHA: (12659) implies:
% 223.74/38.25  | | | | | | | | | | | | | | |   (12660)  all_57_10 = e3
% 223.74/38.25  | | | | | | | | | | | | | | |   (12661)  op(e2, e0) = e3
% 223.74/38.25  | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 223.74/38.25  | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | Case 1:
% 223.74/38.25  | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | |   (12662)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 223.74/38.25  | | | | | | | | | | | | | | | |              & op(e2, e2) = e3)
% 223.74/38.25  | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | REF_CLOSE: (8), (171), (12645), (12654), (12662),
% 223.74/38.25  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.74/38.25  | | | | | | | | | | | | | | | |            #1851.
% 223.74/38.25  | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | Case 2:
% 223.74/38.25  | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | |   (12663)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 223.74/38.25  | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 223.74/38.25  | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | BETA: splitting (12663) gives:
% 223.74/38.25  | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.25  | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | |   (12664)  all_57_7 = e3 & op(e1, e2) = e3
% 223.74/38.25  | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (12086), (12664), (function-axioms) are
% 223.74/38.25  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #267.
% 223.74/38.25  | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.25  | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | |   (12665)  all_57_13 = e3 & op(e0, e2) = e3
% 223.74/38.25  | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | ALPHA: (12665) implies:
% 223.74/38.25  | | | | | | | | | | | | | | | | |   (12666)  all_57_13 = e3
% 223.74/38.25  | | | | | | | | | | | | | | | | |   (12667)  op(e0, e2) = e3
% 223.74/38.25  | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_7, e3,
% 223.74/38.25  | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (159), (12667) gives:
% 223.74/38.25  | | | | | | | | | | | | | | | | |   (12668)  all_53_7 = e3
% 223.74/38.25  | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_13,
% 223.74/38.25  | | | | | | | | | | | | | | | | |              e3, e0, e2, simplifying with (165), (12661) gives:
% 223.74/38.25  | | | | | | | | | | | | | | | | |   (12669)  all_53_13 = e3
% 223.74/38.25  | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | REDUCE: (114), (12669) imply:
% 223.74/38.25  | | | | | | | | | | | | | | | | |   (12670)   ~ (all_53_12 = e3)
% 223.74/38.25  | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | REDUCE: (111), (12669) imply:
% 223.74/38.25  | | | | | | | | | | | | | | | | |   (12671)   ~ (all_53_14 = e3)
% 223.74/38.25  | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | REDUCE: (371), (12669) imply:
% 223.74/38.25  | | | | | | | | | | | | | | | | |   (12672)   ~ (all_4_2 = e3)
% 223.74/38.25  | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 223.74/38.25  | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | |   (12673)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 223.74/38.25  | | | | | | | | | | | | | | | | | |              all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 223.74/38.25  | | | | | | | | | | | | | | | | | |              op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 223.74/38.25  | | | | | | | | | | | | | | | | | |                all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 223.74/38.25  | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 223.74/38.25  | | | | | | | | | | | | | | | | | |              op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 223.74/38.25  | | | | | | | | | | | | | | | | | |              $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 223.74/38.25  | | | | | | | | | | | | | | | | | |              $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 223.74/38.25  | | | | | | | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 223.74/38.25  | | | | | | | | | | | | | | | | | |                all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 223.74/38.25  | | | | | | | | | | | | | | | | | |              & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 223.74/38.25  | | | | | | | | | | | | | | | | | |                all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 223.74/38.25  | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 223.74/38.25  | | | | | | | | | | | | | | | | | |              & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 223.74/38.25  | | | | | | | | | | | | | | | | | |              $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 223.74/38.25  | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | BETA: splitting (12673) gives:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | |   (12674)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 223.74/38.25  | | | | | | | | | | | | | | | | | | |            all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 223.74/38.25  | | | | | | | | | | | | | | | | | | |            op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 223.74/38.25  | | | | | | | | | | | | | | | | | | |              all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 223.74/38.25  | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 223.74/38.25  | | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 223.74/38.25  | | | | | | | | | | | | | | | | | | |            $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 223.74/38.25  | | | | | | | | | | | | | | | | | | |            $i(all_52_7)
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | ALPHA: (12674) implies:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | |   (12675)  op(e3, e0) = all_52_7
% 223.74/38.25  | | | | | | | | | | | | | | | | | | |   (12676)  op(e3, e1) = all_52_5
% 223.74/38.25  | | | | | | | | | | | | | | | | | | |   (12677)  op(e3, e2) = all_52_3
% 223.74/38.25  | | | | | | | | | | | | | | | | | | |   (12678)  op(e3, e3) = all_52_1
% 223.74/38.25  | | | | | | | | | | | | | | | | | | |   (12679)  op(all_52_7, all_52_7) = e0
% 223.74/38.25  | | | | | | | | | | | | | | | | | | |   (12680)  op(all_52_5, all_52_5) = e1
% 223.74/38.25  | | | | | | | | | | | | | | | | | | |   (12681)  op(all_52_3, all_52_3) = e2
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_12,
% 223.74/38.25  | | | | | | | | | | | | | | | | | | |              all_52_7, e0, e3, simplifying with (169), (12675)
% 223.74/38.25  | | | | | | | | | | | | | | | | | | |              gives:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | |   (12682)  all_53_12 = all_52_7
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_8,
% 223.74/38.25  | | | | | | | | | | | | | | | | | | |              all_52_5, e1, e3, simplifying with (170), (12676)
% 223.74/38.25  | | | | | | | | | | | | | | | | | | |              gives:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | |   (12683)  all_53_8 = all_52_5
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_4,
% 223.74/38.25  | | | | | | | | | | | | | | | | | | |              all_52_3, e2, e3, simplifying with (171), (12677)
% 223.74/38.25  | | | | | | | | | | | | | | | | | | |              gives:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | |   (12684)  all_53_4 = all_52_3
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_52_1,
% 223.74/38.25  | | | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (12655), (12678) gives:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | |   (12685)  all_52_1 = e3
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | REDUCE: (12087), (12683) imply:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | |   (12686)   ~ (all_52_5 = e3)
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | BETA: splitting (76) gives:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | |   (12687)   ~ (all_30_2 = e1)
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | REDUCE: (330), (12687) imply:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | |   (12688)   ~ (all_4_2 = e1)
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | |   (12689)  all_55_15 = e3
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (12689) imply:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | |   (12690)  all_4_2 = e3
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | REDUCE: (12101), (12690) imply:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | |   (12691)  $false
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | CLOSE: (12691) is inconsistent.
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | |   (12692)   ~ (all_55_15 = e3)
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | |   (12693)  all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12693) gives:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | |   (12694)  all_55_15 = e2
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (12694) imply:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | |   (12695)  all_4_2 = e2
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (373), (12695) imply:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | |   (12696)  $false
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (12696) is inconsistent.
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | |   (12697)   ~ (all_55_15 = e2)
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | |   (12698)  all_55_15 = e1 | all_55_15 = e0
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12698) gives:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | |   (12699)  all_55_15 = e1
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (12699) imply:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | |   (12700)  all_4_2 = e1
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12688), (12700) imply:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | |   (12701)  $false
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (12701) is inconsistent.
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | |   (12702)  all_55_15 = e0
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (12702) imply:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | |   (12703)  all_4_2 = e0
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (372), (12703) imply:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | |   (12704)   ~ (all_53_14 = e0)
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12101), (12703) imply:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | |   (12705)   ~ (e3 = e0)
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (373), (12703) imply:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | |   (12706)   ~ (e2 = e0)
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12688), (12703) imply:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | |   (12707)   ~ (e1 = e0)
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (12703) imply:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | |   (12708)  op(e0, e0) = e0
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | |   (12709)  all_57_15 = e0 & op(e0, e0) = e0
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12709) implies:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | |   (12710)  all_57_15 = e0
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | |   (12711)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e1)
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12711) gives:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12712)  all_57_0 = e1 & op(e3, e3) = e1
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12712) implies:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12713)  op(e3, e3) = e1
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (12655), (12713), (function-axioms) are
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2495.
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12714)  all_57_1 = e1 & op(e3, e2) = e1
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12714) implies:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12715)  all_57_1 = e1
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (226), (228), (12645),
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | |            (12666), (12715), (function-axioms) are
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2145.
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | |   (12716)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e1)
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12716) gives:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12717)  all_57_4 = e1 & op(e3, e1) = e1
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12717) implies:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12718)  all_57_4 = e1
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12719)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e0)
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12719) gives:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12720)  all_57_4 = e0 & op(e3, e1) = e0
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12720) implies:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12721)  op(e3, e1) = e0
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (12676), (12680), (12708), (12721),
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2167.
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12722)  all_57_5 = e0 & op(e2, e1) = e0
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12722) implies:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12723)  all_57_5 = e0
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12724)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e2)
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12724) gives:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12725)  all_57_4 = e2 & op(e3, e1) = e2
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (12718), (12725) are inconsistent by
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1125.
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12726)  all_57_5 = e2 & op(e2, e1) = e2
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12726) implies:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12727)  all_57_5 = e2
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (12723), (12727) are inconsistent by
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2363.
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12728)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e1) = e2)
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12728) gives:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12729)  all_57_8 = e2 & op(e1, e1) = e2
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (12096), (12729) are inconsistent by
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #172.
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12730)  all_57_14 = e2 & op(e0, e1) = e2
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12730) implies:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12731)  all_57_14 = e2
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12732)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e0)
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (12655), (12677), (12681), (12708),
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12732), (function-axioms) are inconsistent by
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #266.
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12733)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e0)
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12733) gives:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12734)  all_57_4 = e0 & op(e3, e1) = e0
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12734) implies:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12735)  op(e3, e1) = e0
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (12676), (12680), (12708), (12735),
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2167.
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12736)  all_57_9 = e0 & op(e3, e0) = e0
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12736) implies:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12737)  all_57_9 = e0
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12738)  op(e3, e0) = e0
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12739)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12739) gives:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12740)  all_57_12 = e1 & op(e0, e3) = e1
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12740) implies:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12741)  all_57_12 = e1
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12742)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12742) gives:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12743)  all_57_2 = e2 & op(e2, e3) = e2
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12743) implies:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12744)  all_57_2 = e2
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12745)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12745) gives:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12746)  all_57_9 = e2 & op(e3, e0) = e2
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12746) implies:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12747)  all_57_9 = e2
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (12737), (12747) imply:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12748)  e2 = e0
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (12748) implies:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12749)  e2 = e0
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (12744), (12749) imply:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12750)  all_57_2 = e0
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (224), (225), (12645),
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12723), (12750), (function-axioms) are
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1848.
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12751)  all_57_10 = e2 & op(e2, e0) = e2
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12751) implies:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12752)  all_57_10 = e2
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (12660), (12752) imply:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12753)  e3 = e2
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (12666), (12753) imply:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12754)  all_57_13 = e2
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (207), (210), (12731),
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12741), (12754), (function-axioms) are
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1582.
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12755)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (36), (161), (169),
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (211), (213), (231), (373), (12090), (12655),
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12670), (12676), (12677), (12680), (12681),
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12708), (12755), (function-axioms) are
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #174.
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12756)  all_57_3 = e2 & op(e2, e2) = e2
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12756) implies:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12757)  op(e2, e2) = e2
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (12645), (12757), (function-axioms) are
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2306.
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12758)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12758) gives:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12759)  all_57_5 = e2 & op(e2, e1) = e2
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12759) implies:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12760)  all_57_5 = e2
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (12723), (12760) imply:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12761)  e2 = e0
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (12761) implies:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12762)  e2 = e0
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (12731), (12762) imply:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12763)  all_57_14 = e0
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (208), (209),
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (210), (373), (12666), (12708), (12710), (12763),
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #157.
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12764)  all_57_10 = e2 & op(e2, e0) = e2
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12764) implies:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12765)  all_57_10 = e2
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (12660), (12765) imply:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12766)  e3 = e2
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (12766) implies:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12767)  e3 = e2
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (12666), (12767) imply:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12768)  all_57_13 = e2
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (207), (210), (12731),
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12741), (12768), (function-axioms) are
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1582.
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12769)  all_57_13 = e1 & op(e0, e2) = e1
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (12641), (12769), (function-axioms) are
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #330.
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12770)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12770) gives:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12771)  all_57_14 = e1 & op(e0, e1) = e1
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (12731), (12771) are inconsistent by
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2375.
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12772)  all_57_15 = e1 & op(e0, e0) = e1
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12772) implies:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12773)  op(e0, e0) = e1
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (12675), (12679), (12738), (12773),
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2000.
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12774)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12774) gives:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12775)  all_57_8 = e0 & op(e1, e1) = e0
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12096), (12775) are inconsistent by
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #170.
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12776)  all_57_14 = e0 & op(e0, e1) = e0
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12776) implies:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12777)  all_57_14 = e0
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (208), (209),
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (210), (373), (12666), (12708), (12710), (12777),
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #157.
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12778)  all_57_9 = e1 & op(e3, e0) = e1
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (231), (12655), (12676), (12677),
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | |            (12680), (12681), (12708), (12778),
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | |            #264.
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.25  | | | | | | | | | | | | | | | | | | | | | | | |   (12779)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12779) implies:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | |   (12780)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0)
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12780) gives:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | |   (12781)  all_57_9 = e0 & op(e3, e0) = e0
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12781) implies:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | |   (12782)  all_57_9 = e0
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12783)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (12660), (12782), (12783) are
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1991.
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12784)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (36), (161), (169),
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | |            (211), (213), (231), (373), (12090), (12655),
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | |            (12670), (12676), (12677), (12680), (12681),
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | |            (12708), (12784), (function-axioms) are
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #174.
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | |   (12785)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 =
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12785) gives:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12786)  all_57_10 = e0 & op(e2, e0) = e0
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12660), (12786) are inconsistent by
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1981.
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12787)  all_57_11 = e0 & op(e1, e0) = e0
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (12704), (12787), (function-axioms) are
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2341.
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | |   (12788)  all_30_2 = e1
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (330), (12788) imply:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | |   (12789)  all_4_2 = e1
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | REDUCE: (369), (12789) imply:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | |   (12790)   ~ (all_53_11 = e1)
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | |   (12791)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e1)
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12791) gives:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | |   (12792)  all_57_4 = e1 & op(e3, e1) = e1
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12792) implies:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | |   (12793)  op(e3, e1) = e1
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_5, e1,
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (12676), (12793) gives:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | |   (12794)  all_52_5 = e1
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12680), (12794) imply:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | |   (12795)  op(e1, e1) = e1
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (12097), (12795), (function-axioms) are
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #156.
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | |   (12796)  all_57_5 = e1 & op(e2, e1) = e1
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (12642), (12796), (function-axioms) are
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2305.
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | |   (12797)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e1) = e1)
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12797) gives:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | |   (12798)  all_57_8 = e1 & op(e1, e1) = e1
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12798) implies:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | |   (12799)  op(e1, e1) = e1
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (12097), (12799), (function-axioms) are
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #156.
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | |   (12800)  all_57_14 = e1 & op(e0, e1) = e1
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (12790), (12800), (function-axioms) are
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #225.
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | |   (12801)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 223.74/38.26  | | | | | | | | | | | | | | | | | | |            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 223.74/38.26  | | | | | | | | | | | | | | | | | | |            op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 223.74/38.26  | | | | | | | | | | | | | | | | | | |              all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 223.74/38.26  | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 223.74/38.26  | | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 223.74/38.26  | | | | | | | | | | | | | | | | | | |            $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 223.74/38.26  | | | | | | | | | | | | | | | | | | |            $i(all_52_15)
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | ALPHA: (12801) implies:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | |   (12802)  op(e2, e2) = all_52_11
% 223.74/38.26  | | | | | | | | | | | | | | | | | | |   (12803)  op(all_52_11, all_52_11) = e2
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (12097), (12645), (12802), (12803),
% 223.74/38.26  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.74/38.26  | | | | | | | | | | | | | | | | | | |            #155.
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.26  | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | |   (12804)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 223.74/38.26  | | | | | | | | | | | | | | | | | |              & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 223.74/38.26  | | | | | | | | | | | | | | | | | |              & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 223.74/38.26  | | | | | | | | | | | | | | | | | |                all_52_21) = e1 & op(all_52_23, all_52_23) =
% 223.74/38.26  | | | | | | | | | | | | | | | | | |              e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 223.74/38.26  | | | | | | | | | | | | | | | | | |              all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 223.74/38.26  | | | | | | | | | | | | | | | | | |              = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 223.74/38.26  | | | | | | | | | | | | | | | | | |              $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 223.74/38.26  | | | | | | | | | | | | | | | | | |              & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 223.74/38.26  | | | | | | | | | | | | | | | | | |              e0 & op(all_52_25, all_52_25) = e3 &
% 223.74/38.26  | | | | | | | | | | | | | | | | | |              op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 223.74/38.26  | | | | | | | | | | | | | | | | | |                all_52_29) = e1 & op(all_52_31, all_52_31) =
% 223.74/38.26  | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 223.74/38.26  | | | | | | | | | | | | | | | | | |              all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 223.74/38.26  | | | | | | | | | | | | | | | | | |              = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 223.74/38.26  | | | | | | | | | | | | | | | | | |              $i(all_52_29) & $i(all_52_31))
% 223.74/38.26  | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (45), (12097), (12099), (12655), (12667),
% 223.74/38.26  | | | | | | | | | | | | | | | | | |            (12804), (function-axioms) are inconsistent by
% 223.74/38.26  | | | | | | | | | | | | | | | | | |            sub-proof #166.
% 223.74/38.26  | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | End of split
% 223.74/38.26  | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | End of split
% 223.74/38.26  | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | End of split
% 223.74/38.26  | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | End of split
% 223.74/38.26  | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | End of split
% 223.74/38.26  | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | Case 2:
% 223.74/38.26  | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | |   (12805)  all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 223.74/38.26  | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | REF_CLOSE: (277), (12099), (12647), (12649), (12805) are
% 223.74/38.26  | | | | | | | | | | | | |            inconsistent by sub-proof #1953.
% 223.74/38.26  | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | End of split
% 223.74/38.26  | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | Case 2:
% 223.74/38.26  | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | |   (12806)  all_20_2 = e2
% 223.74/38.26  | | | | | | | | | | | |   (12807)  ( ~ (all_20_0 = e1) & op(all_20_1, e3) = all_20_0
% 223.74/38.26  | | | | | | | | | | | |              & op(e3, e2) = all_20_1 & $i(all_20_0) &
% 223.74/38.26  | | | | | | | | | | | |              $i(all_20_1)) | ( ~ (all_20_1 = e0) & op(e3, e2)
% 223.74/38.26  | | | | | | | | | | | |              = all_20_1 & $i(all_20_1))
% 223.74/38.26  | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | COMBINE_EQS: (299), (12806) imply:
% 223.74/38.26  | | | | | | | | | | | |   (12808)  all_10_2 = e2
% 223.74/38.26  | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | SIMP: (12808) implies:
% 223.74/38.26  | | | | | | | | | | | |   (12809)  all_10_2 = e2
% 223.74/38.26  | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | COMBINE_EQS: (329), (12809) imply:
% 223.74/38.26  | | | | | | | | | | | |   (12810)  all_28_2 = e2
% 223.74/38.26  | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | REDUCE: (338), (12809) imply:
% 223.74/38.26  | | | | | | | | | | | |   (12811)   ~ (all_53_1 = e2)
% 223.74/38.26  | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | REDUCE: (340), (12809) imply:
% 223.74/38.26  | | | | | | | | | | | |   (12812)   ~ (all_53_2 = e2)
% 223.74/38.26  | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | REDUCE: (342), (12809) imply:
% 223.74/38.26  | | | | | | | | | | | |   (12813)   ~ (all_53_3 = e2)
% 223.74/38.26  | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | REDUCE: (45), (12809) imply:
% 223.74/38.26  | | | | | | | | | | | |   (12814)  op(e3, e3) = e2
% 223.74/38.26  | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | BETA: splitting (107) gives:
% 223.74/38.26  | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | Case 1:
% 223.74/38.26  | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | |   (12815)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 223.74/38.26  | | | | | | | | | | | | |              all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 223.74/38.26  | | | | | | | | | | | | |              op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 223.74/38.26  | | | | | | | | | | | | |                all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 223.74/38.26  | | | | | | | | | | | | |              op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 223.74/38.26  | | | | | | | | | | | | |              op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 223.74/38.26  | | | | | | | | | | | | |              $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 223.74/38.26  | | | | | | | | | | | | |              $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 223.74/38.26  | | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 223.74/38.26  | | | | | | | | | | | | |                all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 223.74/38.26  | | | | | | | | | | | | |              & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 223.74/38.26  | | | | | | | | | | | | |                all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 223.74/38.26  | | | | | | | | | | | | |              op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 223.74/38.26  | | | | | | | | | | | | |              & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 223.74/38.26  | | | | | | | | | | | | |              $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 223.74/38.26  | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | BETA: splitting (12815) gives:
% 223.74/38.26  | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | Case 1:
% 223.74/38.26  | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | |   (12816)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 223.74/38.26  | | | | | | | | | | | | | |            all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 223.74/38.26  | | | | | | | | | | | | | |            op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 223.74/38.26  | | | | | | | | | | | | | |              all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 223.74/38.26  | | | | | | | | | | | | | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 223.74/38.26  | | | | | | | | | | | | | |            op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 223.74/38.26  | | | | | | | | | | | | | |            $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 223.74/38.26  | | | | | | | | | | | | | |            $i(all_52_7)
% 223.74/38.26  | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | ALPHA: (12816) implies:
% 223.74/38.26  | | | | | | | | | | | | | |   (12817)  op(e3, e3) = all_52_1
% 223.74/38.26  | | | | | | | | | | | | | |   (12818)  op(all_52_1, all_52_1) = e3
% 223.74/38.26  | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 223.74/38.26  | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | Case 1:
% 223.74/38.26  | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | |   (12819)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 223.74/38.26  | | | | | | | | | | | | | | |              & op(e2, e3) = e2)
% 223.74/38.26  | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | BETA: splitting (12819) gives:
% 223.74/38.26  | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | Case 1:
% 223.74/38.26  | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | |   (12820)  all_57_0 = e2 & op(e3, e3) = e2
% 223.74/38.26  | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_52_1,
% 223.74/38.26  | | | | | | | | | | | | | | | |              e3, e3, simplifying with (12814), (12817) gives:
% 223.74/38.26  | | | | | | | | | | | | | | | |   (12821)  all_52_1 = e2
% 223.74/38.26  | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | REDUCE: (12818), (12821) imply:
% 223.74/38.26  | | | | | | | | | | | | | | | |   (12822)  op(e2, e2) = e3
% 223.74/38.26  | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | REF_CLOSE: (8), (12645), (12822), (function-axioms) are
% 223.74/38.26  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1912.
% 223.74/38.26  | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | Case 2:
% 223.74/38.26  | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | |   (12823)  all_57_2 = e2 & op(e2, e3) = e2
% 223.74/38.26  | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | REF_CLOSE: (168), (12811), (12823), (function-axioms) are
% 223.74/38.26  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2504.
% 223.74/38.26  | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | End of split
% 223.74/38.26  | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | Case 2:
% 223.74/38.26  | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | |   (12824)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 223.74/38.26  | | | | | | | | | | | | | | |              e2 & op(e0, e3) = e2)
% 223.74/38.26  | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (164), (168),
% 223.74/38.26  | | | | | | | | | | | | | | |            (230), (232), (236), (12085), (12640), (12813),
% 223.74/38.26  | | | | | | | | | | | | | | |            (12814), (12824), (function-axioms) are
% 223.74/38.26  | | | | | | | | | | | | | | |            inconsistent by sub-proof #152.
% 223.74/38.26  | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | End of split
% 223.74/38.26  | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | Case 2:
% 223.74/38.26  | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | |   (12825)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 223.74/38.26  | | | | | | | | | | | | | |            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 223.74/38.26  | | | | | | | | | | | | | |            op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 223.74/38.26  | | | | | | | | | | | | | |              all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 223.74/38.26  | | | | | | | | | | | | | |            & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 223.74/38.26  | | | | | | | | | | | | | |            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 223.74/38.26  | | | | | | | | | | | | | |            $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 223.74/38.26  | | | | | | | | | | | | | |            $i(all_52_15)
% 223.74/38.26  | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | ALPHA: (12825) implies:
% 223.74/38.26  | | | | | | | | | | | | | |   (12826)  op(e2, e2) = all_52_11
% 223.74/38.26  | | | | | | | | | | | | | |   (12827)  op(all_52_11, all_52_11) = e2
% 223.74/38.26  | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | REF_CLOSE: (9), (12097), (12645), (12826), (12827),
% 223.74/38.26  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.74/38.26  | | | | | | | | | | | | | |            #155.
% 223.74/38.26  | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | End of split
% 223.74/38.26  | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | Case 2:
% 223.74/38.26  | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | |   (12828)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 223.74/38.26  | | | | | | | | | | | | |              & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 223.74/38.26  | | | | | | | | | | | | |              & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 223.74/38.26  | | | | | | | | | | | | |                all_52_21) = e1 & op(all_52_23, all_52_23) =
% 223.74/38.26  | | | | | | | | | | | | |              e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 223.74/38.26  | | | | | | | | | | | | |              all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 223.74/38.26  | | | | | | | | | | | | |              = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 223.74/38.26  | | | | | | | | | | | | |              $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 223.74/38.26  | | | | | | | | | | | | |              & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 223.74/38.26  | | | | | | | | | | | | |              e0 & op(all_52_25, all_52_25) = e3 &
% 223.74/38.26  | | | | | | | | | | | | |              op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 223.74/38.26  | | | | | | | | | | | | |                all_52_29) = e1 & op(all_52_31, all_52_31) =
% 223.74/38.26  | | | | | | | | | | | | |              e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 223.74/38.26  | | | | | | | | | | | | |              all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 223.74/38.26  | | | | | | | | | | | | |              = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 223.74/38.26  | | | | | | | | | | | | |              $i(all_52_29) & $i(all_52_31))
% 223.74/38.26  | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | BETA: splitting (12828) gives:
% 223.74/38.26  | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | Case 1:
% 223.74/38.26  | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | |   (12829)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 223.74/38.26  | | | | | | | | | | | | | |            all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 223.74/38.26  | | | | | | | | | | | | | |            op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 223.74/38.26  | | | | | | | | | | | | | |              all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 223.74/38.26  | | | | | | | | | | | | | |            & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 223.74/38.26  | | | | | | | | | | | | | |            & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 223.74/38.26  | | | | | | | | | | | | | |            & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 223.74/38.26  | | | | | | | | | | | | | |            $i(all_52_23)
% 223.74/38.26  | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | ALPHA: (12829) implies:
% 223.74/38.26  | | | | | | | | | | | | | |   (12830)  op(e1, e1) = all_52_21
% 223.74/38.26  | | | | | | | | | | | | | |   (12831)  op(all_52_21, all_52_21) = e1
% 223.74/38.26  | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | REF_CLOSE: (45), (12097), (12099), (12830), (12831),
% 223.74/38.26  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.74/38.26  | | | | | | | | | | | | | |            #167.
% 223.74/38.26  | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | Case 2:
% 223.74/38.26  | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | |   (12832)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 223.74/38.26  | | | | | | | | | | | | | |            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 223.74/38.26  | | | | | | | | | | | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 223.74/38.26  | | | | | | | | | | | | | |              all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 223.74/38.26  | | | | | | | | | | | | | |            & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 223.74/38.26  | | | | | | | | | | | | | |            & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 223.74/38.26  | | | | | | | | | | | | | |            & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 223.74/38.26  | | | | | | | | | | | | | |            $i(all_52_31)
% 223.74/38.26  | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | ALPHA: (12832) implies:
% 223.74/38.26  | | | | | | | | | | | | | |   (12833)  op(e0, e0) = all_52_31
% 223.74/38.26  | | | | | | | | | | | | | |   (12834)  op(e0, e3) = all_52_25
% 223.74/38.26  | | | | | | | | | | | | | |   (12835)  op(all_52_31, all_52_31) = e0
% 223.74/38.26  | | | | | | | | | | | | | |   (12836)  op(all_52_25, all_52_25) = e3
% 223.74/38.26  | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 223.74/38.26  | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | Case 1:
% 223.74/38.26  | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | |   (12837)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 223.74/38.26  | | | | | | | | | | | | | | |              & op(e2, e3) = e2)
% 223.74/38.26  | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | BETA: splitting (12837) gives:
% 223.74/38.26  | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | Case 1:
% 223.74/38.26  | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | |   (12838)  all_57_0 = e2 & op(e3, e3) = e2
% 223.74/38.26  | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2,
% 223.74/38.26  | | | | | | | | | | | | | | | |              all_52_31, e0, e0, simplifying with (36), (12833)
% 223.74/38.26  | | | | | | | | | | | | | | | |              gives:
% 223.74/38.26  | | | | | | | | | | | | | | | |   (12839)  all_52_31 = all_4_2
% 223.74/38.26  | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_3,
% 223.74/38.26  | | | | | | | | | | | | | | | |              all_52_25, e3, e0, simplifying with (160), (12834)
% 223.74/38.26  | | | | | | | | | | | | | | | |              gives:
% 223.74/38.26  | | | | | | | | | | | | | | | |   (12840)  all_53_3 = all_52_25
% 223.74/38.26  | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (12840) imply:
% 223.74/38.26  | | | | | | | | | | | | | | | |   (12841)  all_55_12 = all_52_25
% 223.74/38.26  | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | REDUCE: (149), (12840) imply:
% 223.74/38.26  | | | | | | | | | | | | | | | |   (12842)   ~ (all_53_1 = all_52_25)
% 223.74/38.26  | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | REDUCE: (145), (12840) imply:
% 223.74/38.26  | | | | | | | | | | | | | | | |   (12843)   ~ (all_53_2 = all_52_25)
% 223.74/38.26  | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | REDUCE: (351), (12840) imply:
% 223.74/38.26  | | | | | | | | | | | | | | | |   (12844)   ~ (all_52_25 = all_4_2)
% 223.74/38.26  | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | REDUCE: (12813), (12840) imply:
% 223.74/38.26  | | | | | | | | | | | | | | | |   (12845)   ~ (all_52_25 = e2)
% 223.74/38.26  | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | BETA: splitting (73) gives:
% 223.74/38.26  | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.26  | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | |   (12846)   ~ (all_28_2 = e2)
% 223.74/38.26  | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | REDUCE: (12810), (12846) imply:
% 223.74/38.26  | | | | | | | | | | | | | | | | |   (12847)  $false
% 223.74/38.26  | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | CLOSE: (12847) is inconsistent.
% 223.74/38.26  | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.26  | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | |   (12848)  ( ~ (all_28_0 = e0) & op(all_28_1, e3) = all_28_0
% 223.74/38.26  | | | | | | | | | | | | | | | | |              & op(e3, e2) = all_28_1 & $i(all_28_0) &
% 223.74/38.26  | | | | | | | | | | | | | | | | |              $i(all_28_1)) | ( ~ (all_28_1 = e1) & op(e3, e2)
% 223.74/38.26  | | | | | | | | | | | | | | | | |              = all_28_1 & $i(all_28_1))
% 223.74/38.26  | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | BETA: splitting (76) gives:
% 223.74/38.26  | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | |   (12849)   ~ (all_30_2 = e1)
% 223.74/38.26  | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | REDUCE: (330), (12849) imply:
% 223.74/38.26  | | | | | | | | | | | | | | | | | |   (12850)   ~ (all_4_2 = e1)
% 223.74/38.26  | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | |   (12851)  all_55_15 = e3
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (12851) imply:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | |   (12852)  all_4_2 = e3
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | REDUCE: (12101), (12852) imply:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | |   (12853)  $false
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | CLOSE: (12853) is inconsistent.
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | |   (12854)  all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | BETA: splitting (12854) gives:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | |   (12855)  all_55_15 = e2
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (12855) imply:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | |   (12856)  all_4_2 = e2
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | REDUCE: (373), (12856) imply:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | |   (12857)  $false
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | CLOSE: (12857) is inconsistent.
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | |   (12858)   ~ (all_55_15 = e2)
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | |   (12859)  all_55_15 = e1 | all_55_15 = e0
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | BETA: splitting (12859) gives:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | |   (12860)  all_55_15 = e1
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (12860) imply:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | |   (12861)  all_4_2 = e1
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | REDUCE: (12850), (12861) imply:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | |   (12862)  $false
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | CLOSE: (12862) is inconsistent.
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | |   (12863)  all_55_15 = e0
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (12863) imply:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | |   (12864)  all_4_2 = e0
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | REDUCE: (371), (12864) imply:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | |   (12865)   ~ (all_53_13 = e0)
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | REDUCE: (12844), (12864) imply:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | |   (12866)   ~ (all_52_25 = e0)
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | |   (12867)  all_55_6 = e3
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (12088), (12867) are inconsistent by
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2498.
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | |   (12868)  all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | |   (12869)  all_55_8 = e3
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (12869) imply:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | |   (12870)  all_53_2 = e3
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12085), (12870) imply:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | |   (12871)  $false
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (12871) is inconsistent.
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | |   (12872)  all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | |   (12873)  all_55_7 = e3
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (12873) imply:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | |   (12874)  all_53_13 = e3
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (12874) implies:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | |   (12875)  all_53_13 = e3
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (12875) imply:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | |   (12876)   ~ (all_53_1 = e3)
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | |   (12877)  all_55_4 = e3
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (12877) imply:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | |   (12878)  all_53_1 = e3
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12876), (12878) imply:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | |   (12879)  $false
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (12879) is inconsistent.
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | |   (12880)  all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12880) gives:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12881)  all_55_4 = e2
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (12881) imply:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12882)  all_53_1 = e2
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12811), (12882) imply:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12883)  $false
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (12883) is inconsistent.
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12884)  all_55_4 = e1 | all_55_4 = e0
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12884) gives:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12885)  all_55_4 = e1
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (12885) imply:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12886)  all_53_1 = e1
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12640), (12886) imply:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12887)  $false
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (12887) is inconsistent.
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12888)  all_55_4 = e0
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (12888) imply:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12889)  all_53_1 = e0
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (150), (12889) imply:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12890)   ~ (all_53_2 = e0)
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (12890) implies:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12891)   ~ (all_53_2 = e0)
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12842), (12889) imply:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12892)   ~ (all_52_25 = e0)
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12872) gives:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12893)  all_55_8 = e2
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (12812), (12893) are inconsistent by
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2406.
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12894)  all_55_8 = e1 | all_55_8 = e0
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12894) gives:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12895)  all_55_8 = e1
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (12895) imply:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12896)  all_53_2 = e1
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (12896) implies:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12897)  all_53_2 = e1
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12843), (12897) imply:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12898)   ~ (all_52_25 = e1)
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (12898) implies:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12899)   ~ (all_52_25 = e1)
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (193), (12814), (12836), (12841), (12845),
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12866), (12899), (function-axioms) are
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1562.
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12900)  all_55_8 = e0
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (12891), (12900) are inconsistent by
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1997.
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | |   (12901)  all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12901) gives:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | |   (12902)  all_55_7 = e2
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (12902) imply:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | |   (12903)  all_53_13 = e2
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (12903) implies:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | |   (12904)  all_53_13 = e2
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (12904) imply:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | |   (12905)   ~ (all_53_9 = e2)
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12868) gives:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12906)  all_55_6 = e2
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (12905), (12906) are inconsistent by
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2398.
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.26  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12907)  all_55_6 = e1 | all_55_6 = e0
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12907) gives:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12908)  all_55_6 = e1
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (12642), (12908) are inconsistent by
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2163.
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12909)  all_55_6 = e0
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (12909) imply:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12910)  all_53_9 = e0
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (12910) implies:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12911)  all_53_9 = e0
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (147), (12911) imply:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12912)   ~ (all_53_1 = e0)
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12913)  all_55_4 = e3
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (12913) imply:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12914)  all_53_1 = e3
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (12914) implies:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12915)  all_53_1 = e3
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12842), (12915) imply:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12916)   ~ (all_52_25 = e3)
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (12916) implies:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12917)   ~ (all_52_25 = e3)
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12918)  all_55_12 = e3
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12841), (12917), (12918) are inconsistent by
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1683.
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12919)  all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12919) gives:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12920)  all_55_12 = e2
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12841), (12845), (12920) are inconsistent by
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1682.
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12921)  all_55_12 = e1 | all_55_12 = e0
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12921) gives:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12922)  all_55_12 = e1
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (12841), (12922) imply:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12923)  all_52_25 = e1
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (12923) implies:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12924)  all_52_25 = e1
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12843), (12924) imply:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12925)   ~ (all_53_2 = e1)
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12872) gives:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12926)  all_55_8 = e2
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (12812), (12926) are inconsistent by
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2406.
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12927)  all_55_8 = e1 | all_55_8 = e0
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12927) gives:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12928)  all_55_8 = e1
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (12925), (12928) are inconsistent by
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2367.
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12929)  all_55_8 = e0
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (12929) imply:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12930)  all_53_2 = e0
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (12930) implies:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12931)  all_53_2 = e0
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (12931) imply:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12932)   ~ (all_53_6 = e0)
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (12932) implies:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12933)   ~ (all_53_6 = e0)
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (160), (163), (171), (193), (226), (244),
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (247), (351), (362), (373), (12645), (12807),
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12813), (12814), (12834), (12836), (12848),
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12850), (12854), (12933), (function-axioms) are
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1566.
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12934)  all_55_12 = e0
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12841), (12866), (12934) are inconsistent by
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1564.
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12935)  all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (12640), (12811), (12912), (12935) are
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #772.
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | |   (12936)  all_55_7 = e1 | all_55_7 = e0
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (12643), (12865), (12936) are inconsistent
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1322.
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.27  | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | |   (12937)  all_30_2 = e1
% 223.74/38.27  | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (330), (12937) imply:
% 223.74/38.27  | | | | | | | | | | | | | | | | | |   (12938)  all_4_2 = e1
% 223.74/38.27  | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | REDUCE: (36), (12938) imply:
% 223.74/38.27  | | | | | | | | | | | | | | | | | |   (12939)  op(e0, e0) = e1
% 223.74/38.27  | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12097), (12833), (12835), (12939),
% 223.74/38.27  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.74/38.27  | | | | | | | | | | | | | | | | | |            #161.
% 223.74/38.27  | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | End of split
% 223.74/38.27  | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | End of split
% 223.74/38.27  | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | Case 2:
% 223.74/38.27  | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | |   (12940)  all_57_2 = e2 & op(e2, e3) = e2
% 223.74/38.27  | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | REF_CLOSE: (168), (12811), (12940), (function-axioms) are
% 223.74/38.27  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2504.
% 223.74/38.27  | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | End of split
% 223.74/38.27  | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | Case 2:
% 223.74/38.27  | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | |   (12941)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 223.74/38.27  | | | | | | | | | | | | | | |              e2 & op(e0, e3) = e2)
% 223.74/38.27  | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (164), (168),
% 223.74/38.27  | | | | | | | | | | | | | | |            (230), (232), (236), (12085), (12640), (12813),
% 223.74/38.27  | | | | | | | | | | | | | | |            (12814), (12941), (function-axioms) are
% 223.74/38.27  | | | | | | | | | | | | | | |            inconsistent by sub-proof #152.
% 223.74/38.27  | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | End of split
% 223.74/38.27  | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | End of split
% 223.74/38.27  | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | End of split
% 223.74/38.27  | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | End of split
% 223.74/38.27  | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | Case 2:
% 223.74/38.27  | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | |   (12942)  all_18_2 = e0
% 223.74/38.27  | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | COMBINE_EQS: (327), (12942) imply:
% 223.74/38.27  | | | | | | | | | | |   (12943)  all_10_2 = e0
% 223.74/38.27  | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | SIMP: (12943) implies:
% 223.74/38.27  | | | | | | | | | | |   (12944)  all_10_2 = e0
% 223.74/38.27  | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | REDUCE: (338), (12944) imply:
% 223.74/38.27  | | | | | | | | | | |   (12945)   ~ (all_53_1 = e0)
% 223.74/38.27  | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | REDUCE: (340), (12944) imply:
% 223.74/38.27  | | | | | | | | | | |   (12946)   ~ (all_53_2 = e0)
% 223.74/38.27  | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | REDUCE: (342), (12944) imply:
% 223.74/38.27  | | | | | | | | | | |   (12947)   ~ (all_53_3 = e0)
% 223.74/38.27  | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | REDUCE: (344), (12944) imply:
% 223.74/38.27  | | | | | | | | | | |   (12948)   ~ (all_53_4 = e0)
% 223.74/38.27  | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | REDUCE: (346), (12944) imply:
% 223.74/38.27  | | | | | | | | | | |   (12949)   ~ (all_53_8 = e0)
% 223.74/38.27  | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | REDUCE: (45), (12944) imply:
% 223.74/38.27  | | | | | | | | | | |   (12950)  op(e3, e3) = e0
% 223.74/38.27  | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | BETA: splitting (107) gives:
% 223.74/38.27  | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | Case 1:
% 223.74/38.27  | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | |   (12951)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 223.74/38.27  | | | | | | | | | | | |              all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 223.74/38.27  | | | | | | | | | | | |              op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 223.74/38.27  | | | | | | | | | | | |                all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 223.74/38.27  | | | | | | | | | | | |              op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 223.74/38.27  | | | | | | | | | | | |              op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 223.74/38.27  | | | | | | | | | | | |              $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 223.74/38.27  | | | | | | | | | | | |              $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 223.74/38.27  | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 223.74/38.27  | | | | | | | | | | | |                all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 223.74/38.27  | | | | | | | | | | | |              & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 223.74/38.27  | | | | | | | | | | | |                all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 223.74/38.27  | | | | | | | | | | | |              op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 223.74/38.27  | | | | | | | | | | | |              & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 223.74/38.27  | | | | | | | | | | | |              $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 223.74/38.27  | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | BETA: splitting (12951) gives:
% 223.74/38.27  | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | Case 1:
% 223.74/38.27  | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | |   (12952)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 223.74/38.27  | | | | | | | | | | | | |            all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 223.74/38.27  | | | | | | | | | | | | |            op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 223.74/38.27  | | | | | | | | | | | | |              all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 223.74/38.27  | | | | | | | | | | | | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 223.74/38.27  | | | | | | | | | | | | |            op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 223.74/38.27  | | | | | | | | | | | | |            $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 223.74/38.27  | | | | | | | | | | | | |            $i(all_52_7)
% 223.74/38.27  | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | ALPHA: (12952) implies:
% 223.74/38.27  | | | | | | | | | | | | |   (12953)  op(e3, e3) = all_52_1
% 223.74/38.27  | | | | | | | | | | | | |   (12954)  op(all_52_1, all_52_1) = e3
% 223.74/38.27  | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | BETA: splitting (230) gives:
% 223.74/38.27  | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | Case 1:
% 223.74/38.27  | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | |   (12955)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 223.74/38.27  | | | | | | | | | | | | | |              & op(e2, e3) = e0)
% 223.74/38.27  | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | BETA: splitting (12955) gives:
% 223.74/38.27  | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | Case 1:
% 223.74/38.27  | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | |   (12956)  all_57_0 = e0 & op(e3, e3) = e0
% 223.74/38.27  | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_52_1,
% 223.74/38.27  | | | | | | | | | | | | | | |              e3, e3, simplifying with (12950), (12953) gives:
% 223.74/38.27  | | | | | | | | | | | | | | |   (12957)  all_52_1 = e0
% 223.74/38.27  | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | REDUCE: (12954), (12957) imply:
% 223.74/38.27  | | | | | | | | | | | | | | |   (12958)  op(e0, e0) = e3
% 223.74/38.27  | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | REF_CLOSE: (36), (12101), (12958), (function-axioms) are
% 223.74/38.27  | | | | | | | | | | | | | | |            inconsistent by sub-proof #151.
% 223.74/38.27  | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | Case 2:
% 223.74/38.27  | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | |   (12959)  all_57_2 = e0 & op(e2, e3) = e0
% 223.74/38.27  | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | ALPHA: (12959) implies:
% 223.74/38.27  | | | | | | | | | | | | | | |   (12960)  op(e2, e3) = e0
% 223.74/38.27  | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | REF_CLOSE: (168), (12945), (12960), (function-axioms) are
% 223.74/38.27  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1943.
% 223.74/38.27  | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | End of split
% 223.74/38.27  | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | Case 2:
% 223.74/38.27  | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | |   (12961)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 223.74/38.27  | | | | | | | | | | | | | |              e0 & op(e0, e3) = e0)
% 223.74/38.27  | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | REF_CLOSE: (160), (164), (12946), (12947), (12961),
% 223.74/38.27  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.74/38.27  | | | | | | | | | | | | | |            #1859.
% 223.74/38.27  | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | End of split
% 223.74/38.27  | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | Case 2:
% 223.74/38.27  | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | |   (12962)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 223.74/38.27  | | | | | | | | | | | | |            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 223.74/38.27  | | | | | | | | | | | | |            op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 223.74/38.27  | | | | | | | | | | | | |              all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 223.74/38.27  | | | | | | | | | | | | |            & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 223.74/38.27  | | | | | | | | | | | | |            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 223.74/38.27  | | | | | | | | | | | | |            $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 223.74/38.27  | | | | | | | | | | | | |            $i(all_52_15)
% 223.74/38.27  | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | ALPHA: (12962) implies:
% 223.74/38.27  | | | | | | | | | | | | |   (12963)  op(e2, e2) = all_52_11
% 223.74/38.27  | | | | | | | | | | | | |   (12964)  op(all_52_11, all_52_11) = e2
% 223.74/38.27  | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | REF_CLOSE: (9), (12097), (12645), (12963), (12964),
% 223.74/38.27  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.74/38.27  | | | | | | | | | | | | |            #155.
% 223.74/38.27  | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | End of split
% 223.74/38.27  | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | Case 2:
% 223.74/38.27  | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | |   (12965)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 223.74/38.27  | | | | | | | | | | | |              & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 223.74/38.27  | | | | | | | | | | | |              & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 223.74/38.27  | | | | | | | | | | | |                all_52_21) = e1 & op(all_52_23, all_52_23) =
% 223.74/38.27  | | | | | | | | | | | |              e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 223.74/38.27  | | | | | | | | | | | |              all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 223.74/38.27  | | | | | | | | | | | |              = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 223.74/38.27  | | | | | | | | | | | |              $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 223.74/38.27  | | | | | | | | | | | |              & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 223.74/38.27  | | | | | | | | | | | |              e0 & op(all_52_25, all_52_25) = e3 &
% 223.74/38.27  | | | | | | | | | | | |              op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 223.74/38.27  | | | | | | | | | | | |                all_52_29) = e1 & op(all_52_31, all_52_31) =
% 223.74/38.27  | | | | | | | | | | | |              e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 223.74/38.27  | | | | | | | | | | | |              all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 223.74/38.27  | | | | | | | | | | | |              = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 223.74/38.27  | | | | | | | | | | | |              $i(all_52_29) & $i(all_52_31))
% 223.74/38.27  | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | BETA: splitting (12965) gives:
% 223.74/38.27  | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | Case 1:
% 223.74/38.27  | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | |   (12966)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 223.74/38.27  | | | | | | | | | | | | |            all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 223.74/38.27  | | | | | | | | | | | | |            op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 223.74/38.27  | | | | | | | | | | | | |              all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 223.74/38.27  | | | | | | | | | | | | |            & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 223.74/38.27  | | | | | | | | | | | | |            & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 223.74/38.27  | | | | | | | | | | | | |            & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 223.74/38.27  | | | | | | | | | | | | |            $i(all_52_23)
% 223.74/38.27  | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | ALPHA: (12966) implies:
% 223.74/38.27  | | | | | | | | | | | | |   (12967)  op(e1, e1) = all_52_21
% 223.74/38.27  | | | | | | | | | | | | |   (12968)  op(all_52_21, all_52_21) = e1
% 223.74/38.27  | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | REF_CLOSE: (45), (12097), (12099), (12967), (12968),
% 223.74/38.27  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.74/38.27  | | | | | | | | | | | | |            #167.
% 223.74/38.27  | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | Case 2:
% 223.74/38.27  | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | |   (12969)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 223.74/38.27  | | | | | | | | | | | | |            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 223.74/38.27  | | | | | | | | | | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 223.74/38.27  | | | | | | | | | | | | |              all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 223.74/38.27  | | | | | | | | | | | | |            & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 223.74/38.27  | | | | | | | | | | | | |            & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 223.74/38.27  | | | | | | | | | | | | |            & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 223.74/38.27  | | | | | | | | | | | | |            $i(all_52_31)
% 223.74/38.27  | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | ALPHA: (12969) implies:
% 223.74/38.27  | | | | | | | | | | | | |   (12970)  op(e0, e0) = all_52_31
% 223.74/38.27  | | | | | | | | | | | | |   (12971)  op(e0, e2) = all_52_27
% 223.74/38.27  | | | | | | | | | | | | |   (12972)  op(all_52_31, all_52_31) = e0
% 223.74/38.27  | | | | | | | | | | | | |   (12973)  op(all_52_27, all_52_27) = e2
% 223.74/38.27  | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2,
% 223.74/38.27  | | | | | | | | | | | | |              all_52_31, e0, e0, simplifying with (36), (12970)
% 223.74/38.27  | | | | | | | | | | | | |              gives:
% 223.74/38.27  | | | | | | | | | | | | |   (12974)  all_52_31 = all_4_2
% 223.74/38.27  | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_7,
% 223.74/38.27  | | | | | | | | | | | | |              all_52_27, e2, e0, simplifying with (159), (12971)
% 223.74/38.27  | | | | | | | | | | | | |              gives:
% 223.74/38.27  | | | | | | | | | | | | |   (12975)  all_53_7 = all_52_27
% 223.74/38.27  | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | COMBINE_EQS: (246), (12975) imply:
% 223.74/38.27  | | | | | | | | | | | | |   (12976)  all_55_13 = all_52_27
% 223.74/38.27  | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | REDUCE: (362), (12975) imply:
% 223.74/38.27  | | | | | | | | | | | | |   (12977)   ~ (all_52_27 = all_4_2)
% 223.74/38.27  | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | REDUCE: (12641), (12975) imply:
% 223.74/38.27  | | | | | | | | | | | | |   (12978)   ~ (all_52_27 = e1)
% 223.74/38.27  | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | BETA: splitting (70) gives:
% 223.74/38.27  | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | Case 1:
% 223.74/38.27  | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | |   (12979)   ~ (all_26_2 = e1)
% 223.74/38.27  | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | REDUCE: (12639), (12979) imply:
% 223.74/38.27  | | | | | | | | | | | | | |   (12980)  $false
% 223.74/38.27  | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | CLOSE: (12980) is inconsistent.
% 223.74/38.27  | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | Case 2:
% 223.74/38.27  | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | |   (12981)  ( ~ (all_26_0 = e3) & op(all_26_1, e2) = all_26_0
% 223.74/38.27  | | | | | | | | | | | | | |              & op(e2, e1) = all_26_1 & $i(all_26_0) &
% 223.74/38.27  | | | | | | | | | | | | | |              $i(all_26_1)) | ( ~ (all_26_1 = e0) & op(e2, e1)
% 223.74/38.27  | | | | | | | | | | | | | |              = all_26_1 & $i(all_26_1))
% 223.74/38.27  | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | BETA: splitting (76) gives:
% 223.74/38.27  | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | Case 1:
% 223.74/38.27  | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | |   (12982)   ~ (all_30_2 = e1)
% 223.74/38.27  | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | REDUCE: (330), (12982) imply:
% 223.74/38.27  | | | | | | | | | | | | | | |   (12983)   ~ (all_4_2 = e1)
% 223.74/38.27  | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 223.74/38.27  | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | Case 1:
% 223.74/38.27  | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | |   (12984)  all_55_15 = e3
% 223.74/38.27  | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | REF_CLOSE: (244), (12101), (12984) are inconsistent by
% 223.74/38.27  | | | | | | | | | | | | | | | |            sub-proof #2503.
% 223.74/38.27  | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | Case 2:
% 223.74/38.27  | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | |   (12985)   ~ (all_55_15 = e3)
% 223.74/38.27  | | | | | | | | | | | | | | | |   (12986)  all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 223.74/38.27  | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | BETA: splitting (12986) gives:
% 223.74/38.27  | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.27  | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | |   (12987)  all_55_15 = e2
% 223.74/38.27  | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (373), (12987) are inconsistent by
% 223.74/38.27  | | | | | | | | | | | | | | | | |            sub-proof #2502.
% 223.74/38.27  | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.27  | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | |   (12988)   ~ (all_55_15 = e2)
% 223.74/38.27  | | | | | | | | | | | | | | | | |   (12989)  all_55_15 = e1 | all_55_15 = e0
% 223.74/38.27  | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | BETA: splitting (12989) gives:
% 223.74/38.27  | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | |   (12990)  all_55_15 = e1
% 223.74/38.27  | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (12983), (12990) are inconsistent by
% 223.74/38.27  | | | | | | | | | | | | | | | | | |            sub-proof #2501.
% 223.74/38.27  | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | |   (12991)  all_55_15 = e0
% 223.74/38.27  | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (12991) imply:
% 223.74/38.27  | | | | | | | | | | | | | | | | | |   (12992)  all_4_2 = e0
% 223.74/38.27  | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | SIMP: (12992) implies:
% 223.74/38.27  | | | | | | | | | | | | | | | | | |   (12993)  all_4_2 = e0
% 223.74/38.27  | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | REDUCE: (370), (12993) imply:
% 223.74/38.27  | | | | | | | | | | | | | | | | | |   (12994)   ~ (all_53_12 = e0)
% 223.74/38.27  | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | REDUCE: (371), (12993) imply:
% 223.74/38.27  | | | | | | | | | | | | | | | | | |   (12995)   ~ (all_53_13 = e0)
% 223.74/38.27  | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | REDUCE: (372), (12993) imply:
% 223.74/38.27  | | | | | | | | | | | | | | | | | |   (12996)   ~ (all_53_14 = e0)
% 223.74/38.27  | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | REDUCE: (12977), (12993) imply:
% 223.74/38.27  | | | | | | | | | | | | | | | | | |   (12997)   ~ (all_52_27 = e0)
% 223.74/38.27  | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | REDUCE: (12101), (12993) imply:
% 223.74/38.27  | | | | | | | | | | | | | | | | | |   (12998)   ~ (e3 = e0)
% 223.74/38.27  | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | REDUCE: (373), (12993) imply:
% 223.74/38.27  | | | | | | | | | | | | | | | | | |   (12999)   ~ (e2 = e0)
% 223.74/38.27  | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | REDUCE: (12983), (12993) imply:
% 223.74/38.27  | | | | | | | | | | | | | | | | | |   (13000)   ~ (e1 = e0)
% 223.74/38.27  | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | |   (13001)  all_57_15 = e0 & op(e0, e0) = e0
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | ALPHA: (13001) implies:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | |   (13002)  all_57_15 = e0
% 223.74/38.27  | | | | | | | | | | | | | | | | | | |   (13003)  op(e0, e0) = e0
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | |   (13004)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | BETA: splitting (13004) gives:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | |   (13005)  all_57_1 = e0 & op(e3, e2) = e0
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | ALPHA: (13005) implies:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | |   (13006)  op(e3, e2) = e0
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (171), (12948), (13006), (function-axioms) are
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1941.
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | |   (13007)  all_57_3 = e0 & op(e2, e2) = e0
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | ALPHA: (13007) implies:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | |   (13008)  op(e2, e2) = e0
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (192), (12950), (12973), (12976), (12978),
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | |            (12997), (13008), (function-axioms) are
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1177.
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | |   (13009)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0)
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | BETA: splitting (13009) gives:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | |   (13010)  all_57_7 = e0 & op(e1, e2) = e0
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | ALPHA: (13010) implies:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | |   (13011)  all_57_7 = e0
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | |   (13012)  op(e1, e2) = e0
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | |   (13013)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e0)
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13013) gives:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | |   (13014)  all_57_4 = e0 & op(e3, e1) = e0
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13014) implies:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | |   (13015)  op(e3, e1) = e0
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (12949), (13015), (function-axioms) are
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2267.
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | |   (13016)  all_57_5 = e0 & op(e2, e1) = e0
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13016) implies:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | |   (13017)  op(e2, e1) = e0
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (107), (129), (159), (163), (166),
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | |            (192), (246), (12637), (12641), (12642), (12645),
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | |            (12950), (12981), (13003), (13012), (13017),
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | |            #1553.
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | |   (13018)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13018) gives:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | |   (13019)  all_57_8 = e0 & op(e1, e1) = e0
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12096), (13019) are inconsistent by
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #170.
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | |   (13020)  all_57_14 = e0 & op(e0, e1) = e0
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13020) implies:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | |   (13021)  all_57_14 = e0
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | |   (13022)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13022) gives:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | |   (13023)  all_57_12 = e1 & op(e0, e3) = e1
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13023) implies:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | |   (13024)  all_57_12 = e1
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | |   (13025)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13025) gives:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13026)  all_57_2 = e0 & op(e2, e3) = e0
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13026) implies:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13027)  all_57_2 = e0
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (208), (209), (210),
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (226), (228), (229), (234), (236), (12645),
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12950), (13002), (13011), (13021), (13024),
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13027), (function-axioms) are inconsistent by
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1554.
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13028)  all_57_3 = e0 & op(e2, e2) = e0
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13028) implies:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13029)  op(e2, e2) = e0
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (192), (12950), (12973), (12976), (12978),
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12997), (13029), (function-axioms) are
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1177.
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | |   (13030)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0)
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (107), (129), (159), (163), (165),
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | |            (166), (192), (246), (12637), (12641), (12642),
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | |            (12645), (12950), (12981), (12995), (13003),
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | |            (13012), (13030), (function-axioms) are
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1552.
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | |   (13031)  all_57_13 = e1 & op(e0, e2) = e1
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13031) implies:
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | |   (13032)  all_57_13 = e1
% 223.74/38.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.28  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (209), (210), (13002),
% 223.74/38.28  | | | | | | | | | | | | | | | | | | | | | | | | |            (13003), (13021), (13032), (function-axioms) are
% 223.74/38.28  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2123.
% 223.74/38.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.28  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.28  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.28  | | | | | | | | | | | | | | | | | | | | | | | |   (13033)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 223.74/38.28  | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 223.74/38.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.28  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (13003), (13021), (13033), (function-axioms)
% 223.74/38.28  | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2121.
% 223.74/38.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.28  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.28  | | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.28  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.28  | | | | | | | | | | | | | | | | | | | | | End of split
% 223.74/38.28  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.28  | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.28  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.28  | | | | | | | | | | | | | | | | | | | | |   (13034)  all_57_13 = e0 & op(e0, e2) = e0
% 223.74/38.28  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.28  | | | | | | | | | | | | | | | | | | | | | ALPHA: (13034) implies:
% 223.74/38.28  | | | | | | | | | | | | | | | | | | | | |   (13035)  all_57_13 = e0
% 223.74/38.28  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.28  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 223.74/38.28  | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.28  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.28  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.28  | | | | | | | | | | | | | | | | | | | | | |   (13036)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 223.74/38.28  | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e0)
% 223.74/38.28  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.28  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13036) gives:
% 223.74/38.28  | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.28  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 223.74/38.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.28  | | | | | | | | | | | | | | | | | | | | | | |   (13037)  all_57_4 = e0 & op(e3, e1) = e0
% 223.74/38.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.28  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13037) implies:
% 223.74/38.28  | | | | | | | | | | | | | | | | | | | | | | |   (13038)  op(e3, e1) = e0
% 223.74/38.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.28  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (12949), (13038), (function-axioms) are
% 223.74/38.28  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2267.
% 223.74/38.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.28  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 223.74/38.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.28  | | | | | | | | | | | | | | | | | | | | | | |   (13039)  all_57_5 = e0 & op(e2, e1) = e0
% 223.74/38.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 223.74/38.28  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13039) implies:
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | |   (13040)  op(e2, e1) = e0
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | |   (13041)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e0)
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13041) gives:
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | |   (13042)  all_57_6 = e0 & op(e1, e3) = e0
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13042) implies:
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | |   (13043)  op(e1, e3) = e0
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (12946), (13043), (function-axioms) are
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2154.
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | |   (13044)  all_57_7 = e0 & op(e1, e2) = e0
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13044) implies:
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | |   (13045)  op(e1, e2) = e0
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (107), (129), (159), (163), (166),
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | |            (192), (246), (12637), (12641), (12642), (12645),
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | |            (12950), (12981), (13003), (13040), (13045),
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | |            #1553.
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | |   (13046)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13046) gives:
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | |   (13047)  all_57_8 = e0 & op(e1, e1) = e0
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12096), (13047) are inconsistent by
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #170.
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | |   (13048)  all_57_11 = e0 & op(e1, e0) = e0
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (12996), (13048), (function-axioms) are
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2341.
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | |   (13049)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13049) gives:
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | |   (13050)  all_57_8 = e0 & op(e1, e1) = e0
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12096), (13050) are inconsistent by
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #170.
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | |   (13051)  all_57_14 = e0 & op(e0, e1) = e0
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13051) implies:
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | |   (13052)  all_57_14 = e0
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | |   (13053)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13053) gives:
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | |   (13054)  all_57_12 = e2 & op(e0, e3) = e2
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (208), (209), (210),
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | |            (13002), (13003), (13052), (13054),
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | |            #158.
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | |   (13055)  all_57_13 = e2 & op(e0, e2) = e2
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13055) implies:
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | |   (13056)  all_57_13 = e2
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (13035), (13056) are inconsistent by
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1911.
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | |   (13057)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (36), (373), (13052), (13057),
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | |            #2127.
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | End of split
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | End of split
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | End of split
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | Case 2:
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | |   (13058)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 224.03/38.28  | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 224.03/38.28  | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 224.03/38.28  | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 224.03/38.28  | | | | | | | | | | | | | | | | | | |                e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (165), (169), (12994), (12995), (12996),
% 224.03/38.28  | | | | | | | | | | | | | | | | | | |            (13058), (function-axioms) are inconsistent by
% 224.03/38.28  | | | | | | | | | | | | | | | | | | |            sub-proof #2112.
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | End of split
% 224.03/38.28  | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | End of split
% 224.03/38.28  | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | End of split
% 224.03/38.28  | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | End of split
% 224.03/38.28  | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | Case 2:
% 224.03/38.28  | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | |   (13059)  all_30_2 = e1
% 224.03/38.28  | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | REF_CLOSE: (7), (36), (330), (12097), (12970), (12972),
% 224.03/38.28  | | | | | | | | | | | | | | |            (13059), (function-axioms) are inconsistent by
% 224.03/38.28  | | | | | | | | | | | | | | |            sub-proof #150.
% 224.03/38.28  | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | End of split
% 224.03/38.28  | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | End of split
% 224.03/38.28  | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | End of split
% 224.03/38.28  | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | End of split
% 224.03/38.28  | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | End of split
% 224.03/38.28  | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | End of split
% 224.03/38.28  | | | | | | | | | 
% 224.03/38.28  | | | | | | | | Case 2:
% 224.03/38.28  | | | | | | | | | 
% 224.03/38.28  | | | | | | | | |   (13060)  all_14_2 = e0
% 224.03/38.28  | | | | | | | | |   (13061)  ( ~ (all_14_0 = e1) & op(all_14_1, e2) = all_14_0 &
% 224.03/38.28  | | | | | | | | |              op(e2, e0) = all_14_1 & $i(all_14_0) &
% 224.03/38.28  | | | | | | | | |              $i(all_14_1)) | ( ~ (all_14_1 = e3) & op(e2, e0)
% 224.03/38.28  | | | | | | | | |              = all_14_1 & $i(all_14_1))
% 224.03/38.28  | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | COMBINE_EQS: (328), (13060) imply:
% 224.03/38.28  | | | | | | | | |   (13062)  all_8_2 = e0
% 224.03/38.28  | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | SIMP: (13062) implies:
% 224.03/38.28  | | | | | | | | |   (13063)  all_8_2 = e0
% 224.03/38.28  | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | COMBINE_EQS: (290), (13063) imply:
% 224.03/38.28  | | | | | | | | |   (13064)  all_50_2 = e0
% 224.03/38.28  | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | REDUCE: (352), (13063) imply:
% 224.03/38.28  | | | | | | | | |   (13065)   ~ (all_53_4 = e0)
% 224.03/38.28  | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | REDUCE: (354), (13063) imply:
% 224.03/38.28  | | | | | | | | |   (13066)   ~ (all_53_6 = e0)
% 224.03/38.28  | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | REDUCE: (356), (13063) imply:
% 224.03/38.28  | | | | | | | | |   (13067)   ~ (all_53_7 = e0)
% 224.03/38.28  | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | REDUCE: (358), (13063) imply:
% 224.03/38.28  | | | | | | | | |   (13068)   ~ (all_53_9 = e0)
% 224.03/38.28  | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | REDUCE: (360), (13063) imply:
% 224.03/38.28  | | | | | | | | |   (13069)   ~ (all_53_13 = e0)
% 224.03/38.28  | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | REDUCE: (12098), (13063) imply:
% 224.03/38.28  | | | | | | | | |   (13070)   ~ (e3 = e0)
% 224.03/38.28  | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | BETA: splitting (226) gives:
% 224.03/38.28  | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | Case 1:
% 224.03/38.28  | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | |   (13071)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 224.03/38.28  | | | | | | | | | |              & op(e2, e2) = e0)
% 224.03/38.28  | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | BETA: splitting (13071) gives:
% 224.03/38.28  | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | Case 1:
% 224.03/38.28  | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | |   (13072)  all_57_1 = e0 & op(e3, e2) = e0
% 224.03/38.28  | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | ALPHA: (13072) implies:
% 224.03/38.28  | | | | | | | | | | |   (13073)  op(e3, e2) = e0
% 224.03/38.28  | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | REF_CLOSE: (171), (13065), (13073), (function-axioms) are
% 224.03/38.28  | | | | | | | | | | |            inconsistent by sub-proof #1941.
% 224.03/38.28  | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | Case 2:
% 224.03/38.28  | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | |   (13074)  all_57_3 = e0 & op(e2, e2) = e0
% 224.03/38.28  | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | ALPHA: (13074) implies:
% 224.03/38.28  | | | | | | | | | | |   (13075)  all_57_3 = e0
% 224.03/38.28  | | | | | | | | | | |   (13076)  op(e2, e2) = e0
% 224.03/38.28  | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | BETA: splitting (58) gives:
% 224.03/38.28  | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | Case 1:
% 224.03/38.28  | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | |   (13077)   ~ (all_18_2 = e0)
% 224.03/38.28  | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | REDUCE: (327), (13077) imply:
% 224.03/38.28  | | | | | | | | | | | |   (13078)   ~ (all_10_2 = e0)
% 224.03/38.28  | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | BETA: splitting (61) gives:
% 224.03/38.28  | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | Case 1:
% 224.03/38.28  | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | |   (13079)   ~ (all_20_2 = e2)
% 224.03/38.28  | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | REDUCE: (299), (13079) imply:
% 224.03/38.28  | | | | | | | | | | | | |   (13080)   ~ (all_10_2 = e2)
% 224.03/38.28  | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | BETA: splitting (205) gives:
% 224.03/38.28  | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | Case 1:
% 224.03/38.28  | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | |   (13081)  all_55_0 = e3
% 224.03/38.28  | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | COMBINE_EQS: (277), (13081) imply:
% 224.03/38.28  | | | | | | | | | | | | | |   (13082)  all_10_2 = e3
% 224.03/38.28  | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | SIMP: (13082) implies:
% 224.03/38.28  | | | | | | | | | | | | | |   (13083)  all_10_2 = e3
% 224.03/38.28  | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | REDUCE: (344), (13083) imply:
% 224.03/38.28  | | | | | | | | | | | | | |   (13084)   ~ (all_53_4 = e3)
% 224.03/38.28  | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | REDUCE: (348), (13083) imply:
% 224.03/38.28  | | | | | | | | | | | | | |   (13085)   ~ (all_53_12 = e3)
% 224.03/38.28  | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | REDUCE: (45), (13083) imply:
% 224.03/38.28  | | | | | | | | | | | | | |   (13086)  op(e3, e3) = e3
% 224.03/38.28  | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 224.03/38.28  | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | Case 1:
% 224.03/38.28  | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | |   (13087)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 224.03/38.28  | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 224.03/38.28  | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (45), (106), (107), (136), (159), (163),
% 224.03/38.28  | | | | | | | | | | | | | | |            (165), (169), (171), (204), (229), (270), (12086),
% 224.03/38.28  | | | | | | | | | | | | | | |            (12097), (12099), (13061), (13064), (13065),
% 224.03/38.28  | | | | | | | | | | | | | | |            (13069), (13075), (13076), (13084), (13085),
% 224.03/38.28  | | | | | | | | | | | | | | |            (13086), (13087), (function-axioms) are
% 224.03/38.28  | | | | | | | | | | | | | | |            inconsistent by sub-proof #147.
% 224.03/38.28  | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | Case 2:
% 224.03/38.28  | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | |   (13088)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 224.03/38.28  | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 224.03/38.28  | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | REF_CLOSE: (36), (161), (12090), (12101), (13088),
% 224.03/38.28  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.03/38.28  | | | | | | | | | | | | | | |            #146.
% 224.03/38.28  | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | End of split
% 224.03/38.28  | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | Case 2:
% 224.03/38.28  | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | |   (13089)  all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 224.03/38.28  | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | REF_CLOSE: (277), (12099), (13078), (13080), (13089) are
% 224.03/38.28  | | | | | | | | | | | | | |            inconsistent by sub-proof #1953.
% 224.03/38.28  | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | End of split
% 224.03/38.28  | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | Case 2:
% 224.03/38.28  | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | |   (13090)  all_20_2 = e2
% 224.03/38.28  | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | COMBINE_EQS: (299), (13090) imply:
% 224.03/38.28  | | | | | | | | | | | | |   (13091)  all_10_2 = e2
% 224.03/38.28  | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | SIMP: (13091) implies:
% 224.03/38.28  | | | | | | | | | | | | |   (13092)  all_10_2 = e2
% 224.03/38.28  | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | REDUCE: (348), (13092) imply:
% 224.03/38.28  | | | | | | | | | | | | |   (13093)   ~ (all_53_12 = e2)
% 224.03/38.28  | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | REDUCE: (45), (13092) imply:
% 224.03/38.28  | | | | | | | | | | | | |   (13094)  op(e3, e3) = e2
% 224.03/38.28  | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | BETA: splitting (107) gives:
% 224.03/38.28  | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | Case 1:
% 224.03/38.28  | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | |   (13095)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 224.03/38.28  | | | | | | | | | | | | | |              all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 224.03/38.28  | | | | | | | | | | | | | |              op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 224.03/38.28  | | | | | | | | | | | | | |                all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 224.03/38.28  | | | | | | | | | | | | | |              op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 224.03/38.28  | | | | | | | | | | | | | |              op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 224.03/38.28  | | | | | | | | | | | | | |              $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 224.03/38.28  | | | | | | | | | | | | | |              $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 224.03/38.28  | | | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 224.03/38.28  | | | | | | | | | | | | | |                all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 224.03/38.28  | | | | | | | | | | | | | |              & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 224.03/38.28  | | | | | | | | | | | | | |                all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 224.03/38.28  | | | | | | | | | | | | | |              op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 224.03/38.28  | | | | | | | | | | | | | |              & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 224.03/38.28  | | | | | | | | | | | | | |              $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 224.03/38.28  | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | BETA: splitting (13095) gives:
% 224.03/38.28  | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | Case 1:
% 224.03/38.28  | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | |   (13096)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 224.03/38.28  | | | | | | | | | | | | | | |            all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 224.03/38.28  | | | | | | | | | | | | | | |            op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 224.03/38.28  | | | | | | | | | | | | | | |              all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 224.03/38.28  | | | | | | | | | | | | | | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 224.03/38.28  | | | | | | | | | | | | | | |            op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 224.03/38.28  | | | | | | | | | | | | | | |            $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 224.03/38.28  | | | | | | | | | | | | | | |            $i(all_52_7)
% 224.03/38.28  | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | ALPHA: (13096) implies:
% 224.03/38.28  | | | | | | | | | | | | | | |   (13097)  op(e3, e3) = all_52_1
% 224.03/38.28  | | | | | | | | | | | | | | |   (13098)  op(all_52_1, all_52_1) = e3
% 224.03/38.28  | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | REF_CLOSE: (7), (13076), (13094), (13097), (13098),
% 224.03/38.28  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.03/38.28  | | | | | | | | | | | | | | |            #1653.
% 224.03/38.28  | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | Case 2:
% 224.03/38.28  | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | |   (13099)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 224.03/38.28  | | | | | | | | | | | | | | |            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 224.03/38.28  | | | | | | | | | | | | | | |            op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 224.03/38.28  | | | | | | | | | | | | | | |              all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 224.03/38.28  | | | | | | | | | | | | | | |            & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 224.03/38.28  | | | | | | | | | | | | | | |            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 224.03/38.28  | | | | | | | | | | | | | | |            $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 224.03/38.28  | | | | | | | | | | | | | | |            $i(all_52_15)
% 224.03/38.28  | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | ALPHA: (13099) implies:
% 224.03/38.28  | | | | | | | | | | | | | | |   (13100)  op(e2, e2) = all_52_11
% 224.03/38.28  | | | | | | | | | | | | | | |   (13101)  op(all_52_11, all_52_11) = e2
% 224.03/38.28  | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 224.03/38.28  | | | | | | | | | | | | | | |              all_52_11, e2, e2, simplifying with (13076),
% 224.03/38.28  | | | | | | | | | | | | | | |              (13100) gives:
% 224.03/38.28  | | | | | | | | | | | | | | |   (13102)  all_52_11 = e0
% 224.03/38.28  | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | REDUCE: (13101), (13102) imply:
% 224.03/38.28  | | | | | | | | | | | | | | |   (13103)  op(e0, e0) = e2
% 224.03/38.28  | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | REF_CLOSE: (36), (373), (13103), (function-axioms) are
% 224.03/38.28  | | | | | | | | | | | | | | |            inconsistent by sub-proof #2334.
% 224.03/38.28  | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | End of split
% 224.03/38.28  | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | Case 2:
% 224.03/38.28  | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | |   (13104)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 224.03/38.28  | | | | | | | | | | | | | |              & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 224.03/38.28  | | | | | | | | | | | | | |              & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 224.03/38.28  | | | | | | | | | | | | | |                all_52_21) = e1 & op(all_52_23, all_52_23) =
% 224.03/38.28  | | | | | | | | | | | | | |              e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 224.03/38.28  | | | | | | | | | | | | | |              all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 224.03/38.28  | | | | | | | | | | | | | |              = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 224.03/38.28  | | | | | | | | | | | | | |              $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 224.03/38.28  | | | | | | | | | | | | | |              & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 224.03/38.28  | | | | | | | | | | | | | |              e0 & op(all_52_25, all_52_25) = e3 &
% 224.03/38.28  | | | | | | | | | | | | | |              op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 224.03/38.28  | | | | | | | | | | | | | |                all_52_29) = e1 & op(all_52_31, all_52_31) =
% 224.03/38.28  | | | | | | | | | | | | | |              e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 224.03/38.28  | | | | | | | | | | | | | |              all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 224.03/38.28  | | | | | | | | | | | | | |              = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 224.03/38.28  | | | | | | | | | | | | | |              $i(all_52_29) & $i(all_52_31))
% 224.03/38.28  | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | BETA: splitting (13104) gives:
% 224.03/38.28  | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | Case 1:
% 224.03/38.28  | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | |   (13105)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 224.03/38.28  | | | | | | | | | | | | | | |            all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 224.03/38.28  | | | | | | | | | | | | | | |            op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 224.03/38.28  | | | | | | | | | | | | | | |              all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 224.03/38.28  | | | | | | | | | | | | | | |            & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 224.03/38.28  | | | | | | | | | | | | | | |            & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 224.03/38.28  | | | | | | | | | | | | | | |            & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 224.03/38.28  | | | | | | | | | | | | | | |            $i(all_52_23)
% 224.03/38.28  | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | ALPHA: (13105) implies:
% 224.03/38.28  | | | | | | | | | | | | | | |   (13106)  op(e1, e1) = all_52_21
% 224.03/38.28  | | | | | | | | | | | | | | |   (13107)  op(all_52_21, all_52_21) = e1
% 224.03/38.28  | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | REF_CLOSE: (45), (12097), (12099), (13106), (13107),
% 224.03/38.28  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.03/38.28  | | | | | | | | | | | | | | |            #167.
% 224.03/38.28  | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | Case 2:
% 224.03/38.28  | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | |   (13108)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 224.03/38.28  | | | | | | | | | | | | | | |            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 224.03/38.28  | | | | | | | | | | | | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 224.03/38.28  | | | | | | | | | | | | | | |              all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 224.03/38.28  | | | | | | | | | | | | | | |            & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 224.03/38.28  | | | | | | | | | | | | | | |            & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 224.03/38.28  | | | | | | | | | | | | | | |            & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 224.03/38.28  | | | | | | | | | | | | | | |            $i(all_52_31)
% 224.03/38.28  | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | ALPHA: (13108) implies:
% 224.03/38.28  | | | | | | | | | | | | | | |   (13109)  op(e0, e0) = all_52_31
% 224.03/38.28  | | | | | | | | | | | | | | |   (13110)  op(e0, e1) = all_52_29
% 224.03/38.28  | | | | | | | | | | | | | | |   (13111)  op(all_52_31, all_52_31) = e0
% 224.03/38.28  | | | | | | | | | | | | | | |   (13112)  op(all_52_29, all_52_29) = e1
% 224.03/38.28  | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 224.03/38.28  | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | Case 1:
% 224.03/38.28  | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | |   (13113)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 224.03/38.28  | | | | | | | | | | | | | | | |              & op(e3, e2) = e2)
% 224.03/38.28  | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | BETA: splitting (13113) gives:
% 224.03/38.28  | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | Case 1:
% 224.03/38.28  | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | |   (13114)  all_57_0 = e2 & op(e3, e3) = e2
% 224.03/38.28  | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2,
% 224.03/38.28  | | | | | | | | | | | | | | | | |              all_52_31, e0, e0, simplifying with (36), (13109)
% 224.03/38.28  | | | | | | | | | | | | | | | | |              gives:
% 224.03/38.28  | | | | | | | | | | | | | | | | |   (13115)  all_52_31 = all_4_2
% 224.03/38.28  | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_11,
% 224.03/38.28  | | | | | | | | | | | | | | | | |              all_52_29, e1, e0, simplifying with (158), (13110)
% 224.03/38.28  | | | | | | | | | | | | | | | | |              gives:
% 224.03/38.28  | | | | | | | | | | | | | | | | |   (13116)  all_53_11 = all_52_29
% 224.03/38.28  | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (13116) imply:
% 224.03/38.28  | | | | | | | | | | | | | | | | |   (13117)  all_55_14 = all_52_29
% 224.03/38.28  | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | REDUCE: (122), (13116) imply:
% 224.03/38.28  | | | | | | | | | | | | | | | | |   (13118)   ~ (all_53_8 = all_52_29)
% 224.03/38.28  | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | REDUCE: (12089), (13116) imply:
% 224.03/38.28  | | | | | | | | | | | | | | | | |   (13119)   ~ (all_52_29 = e3)
% 224.03/38.28  | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | BETA: splitting (76) gives:
% 224.03/38.28  | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | Case 1:
% 224.03/38.28  | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | |   (13120)   ~ (all_30_2 = e1)
% 224.03/38.28  | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | REDUCE: (330), (13120) imply:
% 224.03/38.28  | | | | | | | | | | | | | | | | | |   (13121)   ~ (all_4_2 = e1)
% 224.03/38.28  | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 224.03/38.28  | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | Case 1:
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | |   (13122)  all_55_15 = e3
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (12101), (13122) are inconsistent by
% 224.03/38.28  | | | | | | | | | | | | | | | | | | |            sub-proof #2503.
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | Case 2:
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | |   (13123)   ~ (all_55_15 = e3)
% 224.03/38.28  | | | | | | | | | | | | | | | | | | |   (13124)  all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | BETA: splitting (13124) gives:
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | Case 1:
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | |   (13125)  all_55_15 = e2
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (373), (13125) are inconsistent by
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | |            sub-proof #2502.
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | Case 2:
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | |   (13126)   ~ (all_55_15 = e2)
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | |   (13127)  all_55_15 = e1 | all_55_15 = e0
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | BETA: splitting (13127) gives:
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | |   (13128)  all_55_15 = e1
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (13121), (13128) are inconsistent by
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | |            sub-proof #2501.
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | |   (13129)  all_55_15 = e0
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (13129) imply:
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | |   (13130)  all_4_2 = e0
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | SIMP: (13130) implies:
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | |   (13131)  all_4_2 = e0
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | REDUCE: (370), (13131) imply:
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | |   (13132)   ~ (all_53_12 = e0)
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | REDUCE: (372), (13131) imply:
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | |   (13133)   ~ (all_53_14 = e0)
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | REDUCE: (373), (13131) imply:
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | |   (13134)   ~ (e2 = e0)
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | REDUCE: (13121), (13131) imply:
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | |   (13135)   ~ (e1 = e0)
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | |   (13136)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e0)
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | |            (13075), (13094), (13136), (function-axioms) are
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1654.
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | |   (13137)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = e0)
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13137) gives:
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | |   (13138)  all_57_6 = e0 & op(e1, e3) = e0
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13138) implies:
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | |   (13139)  op(e1, e3) = e0
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | |   (13140)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e0)
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (171), (13065), (13094), (13140),
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | |            #1321.
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | |   (13141)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e0)
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13141) gives:
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | |   (13142)  all_57_4 = e0 & op(e3, e1) = e0
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (100), (164), (170), (191), (12083), (12084),
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | |            (12097), (13110), (13112), (13117), (13118),
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | |            (13119), (13139), (13142), (function-axioms) are
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #143.
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | |   (13143)  all_57_9 = e0 & op(e3, e0) = e0
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (13132), (13143), (function-axioms) are
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2434.
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | |   (13144)  all_57_12 = e0 & op(e0, e3) = e0
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13144) implies:
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | |   (13145)  all_57_12 = e0
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | |   (13146)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e3)
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13146) gives:
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | |   (13147)  all_57_0 = e3 & op(e3, e3) = e3
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13147) implies:
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | |   (13148)  op(e3, e3) = e3
% 224.03/38.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (13094), (13148), (function-axioms) are
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2490.
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | |   (13149)  all_57_2 = e3 & op(e2, e3) = e3
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13149) implies:
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | |   (13150)  all_57_2 = e3
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | |   (13151)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e1)
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (13094), (13150), (13151),
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | |            #753.
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | |   (13152)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e3) = e1)
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13152) gives:
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13153)  all_57_6 = e1 & op(e1, e3) = e1
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13153) implies:
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13154)  all_57_6 = e1
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13155)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e0)
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13155) gives:
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13156)  all_57_6 = e0 & op(e1, e3) = e0
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (13154), (13156) are inconsistent by
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2347.
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13157)  all_57_7 = e0 & op(e1, e2) = e0
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13157) implies:
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13158)  all_57_7 = e0
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (227), (228), (229),
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (233), (237), (13075), (13076), (13094),
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13158), (function-axioms) are inconsistent by
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1296.
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13159)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13159) gives:
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13160)  all_57_8 = e0 & op(e1, e1) = e0
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12096), (13075), (13150), (13160) are
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #142.
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13161)  all_57_11 = e0 & op(e1, e0) = e0
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (13133), (13161), (function-axioms) are
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2341.
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13162)  all_57_12 = e1 & op(e0, e3) = e1
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13162) implies:
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13163)  all_57_12 = e1
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (13145), (13163) are inconsistent by
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2014.
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | |   (13164)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e3) = e3)
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13164) gives:
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | |   (13165)  all_57_6 = e3 & op(e1, e3) = e3
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (12085), (13165), (function-axioms) are
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #153.
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | |   (13166)  all_57_12 = e3 & op(e0, e3) = e3
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13166) implies:
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | |   (13167)  all_57_12 = e3
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (13145), (13167) are inconsistent by
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2153.
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | End of split
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | End of split
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | End of split
% 224.03/38.29  | | | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | | End of split
% 224.03/38.29  | | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | Case 2:
% 224.03/38.29  | | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | |   (13168)  all_30_2 = e1
% 224.03/38.29  | | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (36), (330), (12097), (13109), (13111),
% 224.03/38.29  | | | | | | | | | | | | | | | | | |            (13168), (function-axioms) are inconsistent by
% 224.03/38.29  | | | | | | | | | | | | | | | | | |            sub-proof #150.
% 224.03/38.29  | | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | End of split
% 224.03/38.29  | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | Case 2:
% 224.03/38.29  | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | |   (13169)  all_57_1 = e2 & op(e3, e2) = e2
% 224.03/38.29  | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | ALPHA: (13169) implies:
% 224.03/38.29  | | | | | | | | | | | | | | | | |   (13170)  all_57_1 = e2
% 224.03/38.29  | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (237),
% 224.03/38.29  | | | | | | | | | | | | | | | | |            (13094), (13170), (function-axioms) are
% 224.03/38.29  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1655.
% 224.03/38.29  | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | End of split
% 224.03/38.29  | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | Case 2:
% 224.03/38.29  | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | |   (13171)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 224.03/38.29  | | | | | | | | | | | | | | | |              & op(e3, e0) = e2)
% 224.03/38.29  | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | BETA: splitting (13171) gives:
% 224.03/38.29  | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | Case 1:
% 224.03/38.29  | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | |   (13172)  all_57_4 = e2 & op(e3, e1) = e2
% 224.03/38.29  | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | ALPHA: (13172) implies:
% 224.03/38.29  | | | | | | | | | | | | | | | | |   (13173)  all_57_4 = e2
% 224.03/38.29  | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (171), (231), (233),
% 224.03/38.29  | | | | | | | | | | | | | | | | |            (237), (13065), (13094), (13173),
% 224.03/38.29  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.03/38.29  | | | | | | | | | | | | | | | | |            #1320.
% 224.03/38.29  | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | Case 2:
% 224.03/38.29  | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | |   (13174)  all_57_9 = e2 & op(e3, e0) = e2
% 224.03/38.29  | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | ALPHA: (13174) implies:
% 224.03/38.29  | | | | | | | | | | | | | | | | |   (13175)  op(e3, e0) = e2
% 224.03/38.29  | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (13093), (13175), (function-axioms) are
% 224.03/38.29  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2331.
% 224.03/38.29  | | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | End of split
% 224.03/38.29  | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | End of split
% 224.03/38.29  | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | End of split
% 224.03/38.29  | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | End of split
% 224.03/38.29  | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | End of split
% 224.03/38.29  | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | Case 2:
% 224.03/38.29  | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | |   (13176)  all_18_2 = e0
% 224.03/38.29  | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | COMBINE_EQS: (327), (13176) imply:
% 224.03/38.29  | | | | | | | | | | | |   (13177)  all_10_2 = e0
% 224.03/38.29  | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | SIMP: (13177) implies:
% 224.03/38.29  | | | | | | | | | | | |   (13178)  all_10_2 = e0
% 224.03/38.29  | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | REDUCE: (340), (13178) imply:
% 224.03/38.29  | | | | | | | | | | | |   (13179)   ~ (all_53_2 = e0)
% 224.03/38.29  | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | REDUCE: (346), (13178) imply:
% 224.03/38.29  | | | | | | | | | | | |   (13180)   ~ (all_53_8 = e0)
% 224.03/38.29  | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | REDUCE: (45), (13178) imply:
% 224.03/38.29  | | | | | | | | | | | |   (13181)  op(e3, e3) = e0
% 224.03/38.29  | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | BETA: splitting (214) gives:
% 224.03/38.29  | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | Case 1:
% 224.03/38.29  | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | |   (13182)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 224.03/38.29  | | | | | | | | | | | | |              & op(e1, e2) = e0)
% 224.03/38.29  | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | REF_CLOSE: (163), (164), (13066), (13179), (13182),
% 224.03/38.29  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.03/38.29  | | | | | | | | | | | | |            #2038.
% 224.03/38.29  | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | Case 2:
% 224.03/38.29  | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | |   (13183)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 224.03/38.29  | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 224.03/38.29  | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | BETA: splitting (13183) gives:
% 224.03/38.29  | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | Case 1:
% 224.03/38.29  | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | |   (13184)  all_57_8 = e0 & op(e1, e1) = e0
% 224.03/38.29  | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | REF_CLOSE: (7), (12096), (13184) are inconsistent by
% 224.03/38.29  | | | | | | | | | | | | | |            sub-proof #170.
% 224.03/38.29  | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | Case 2:
% 224.03/38.29  | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | |   (13185)  all_57_11 = e0 & op(e1, e0) = e0
% 224.03/38.29  | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | ALPHA: (13185) implies:
% 224.03/38.29  | | | | | | | | | | | | | |   (13186)  op(e1, e0) = e0
% 224.03/38.29  | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 224.03/38.29  | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | Case 1:
% 224.03/38.29  | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | |   (13187)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 224.03/38.29  | | | | | | | | | | | | | | |              & op(e2, e1) = e0)
% 224.03/38.29  | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | REF_CLOSE: (166), (170), (13068), (13180), (13187),
% 224.03/38.29  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.03/38.29  | | | | | | | | | | | | | | |            #141.
% 224.03/38.29  | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | Case 2:
% 224.03/38.29  | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | |   (13188)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 224.03/38.29  | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 224.03/38.29  | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | BETA: splitting (13188) gives:
% 224.03/38.29  | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | Case 1:
% 224.03/38.29  | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | |   (13189)  all_57_8 = e0 & op(e1, e1) = e0
% 224.03/38.29  | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12096), (13189) are inconsistent by
% 224.03/38.29  | | | | | | | | | | | | | | | |            sub-proof #162.
% 224.03/38.29  | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | Case 2:
% 224.03/38.29  | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | |   (13190)  all_57_14 = e0 & op(e0, e1) = e0
% 224.03/38.29  | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | ALPHA: (13190) implies:
% 224.03/38.29  | | | | | | | | | | | | | | | |   (13191)  all_57_14 = e0
% 224.03/38.29  | | | | | | | | | | | | | | | |   (13192)  op(e0, e1) = e0
% 224.03/38.29  | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (9), (36), (39), (91), (107), (158),
% 224.03/38.29  | | | | | | | | | | | | | | | |            (161), (190), (208), (209), (210), (244), (295),
% 224.03/38.29  | | | | | | | | | | | | | | | |            (368), (372), (373), (12101), (13076), (13181),
% 224.03/38.29  | | | | | | | | | | | | | | | |            (13186), (13191), (13192), (function-axioms) are
% 224.03/38.29  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1226.
% 224.03/38.29  | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | End of split
% 224.03/38.29  | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | End of split
% 224.03/38.29  | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | End of split
% 224.03/38.29  | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | End of split
% 224.03/38.29  | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | End of split
% 224.03/38.29  | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | End of split
% 224.03/38.29  | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | Case 2:
% 224.03/38.29  | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | |   (13193)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 224.03/38.29  | | | | | | | | | |              e0 & op(e0, e2) = e0)
% 224.03/38.29  | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | REF_CLOSE: (159), (163), (13066), (13067), (13193),
% 224.03/38.29  | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.03/38.29  | | | | | | | | | |            #2024.
% 224.03/38.29  | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | End of split
% 224.03/38.29  | | | | | | | | | 
% 224.03/38.29  | | | | | | | | End of split
% 224.03/38.29  | | | | | | | | 
% 224.03/38.29  | | | | | | | Case 2:
% 224.03/38.29  | | | | | | | | 
% 224.03/38.29  | | | | | | | |   (13194)  all_12_2 = e3
% 224.03/38.29  | | | | | | | |   (13195)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 &
% 224.03/38.29  | | | | | | | |              op(e0, e3) = all_12_1 & $i(all_12_0) &
% 224.03/38.29  | | | | | | | |              $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0, e3) =
% 224.03/38.29  | | | | | | | |              all_12_1 & $i(all_12_1))
% 224.03/38.29  | | | | | | | | 
% 224.03/38.29  | | | | | | | | COMBINE_EQS: (325), (13194) imply:
% 224.03/38.29  | | | | | | | |   (13196)  all_4_2 = e3
% 224.03/38.29  | | | | | | | | 
% 224.03/38.29  | | | | | | | | COMBINE_EQS: (318), (13196) imply:
% 224.03/38.29  | | | | | | | |   (13197)  all_22_2 = e3
% 224.03/38.29  | | | | | | | | 
% 224.03/38.29  | | | | | | | | REDUCE: (370), (13196) imply:
% 224.03/38.29  | | | | | | | |   (13198)   ~ (all_53_12 = e3)
% 224.03/38.29  | | | | | | | | 
% 224.03/38.29  | | | | | | | | REDUCE: (371), (13196) imply:
% 224.03/38.29  | | | | | | | |   (13199)   ~ (all_53_13 = e3)
% 224.03/38.29  | | | | | | | | 
% 224.03/38.29  | | | | | | | | BETA: splitting (213) gives:
% 224.03/38.29  | | | | | | | | 
% 224.03/38.29  | | | | | | | | Case 1:
% 224.03/38.29  | | | | | | | | | 
% 224.03/38.29  | | | | | | | | |   (13200)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3
% 224.03/38.29  | | | | | | | | |              & op(e2, e0) = e3)
% 224.03/38.29  | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | REF_CLOSE: (165), (169), (13198), (13199), (13200),
% 224.03/38.29  | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.03/38.29  | | | | | | | | |            #2300.
% 224.03/38.29  | | | | | | | | | 
% 224.03/38.29  | | | | | | | | Case 2:
% 224.03/38.29  | | | | | | | | | 
% 224.03/38.29  | | | | | | | | |   (13201)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 224.03/38.29  | | | | | | | | |              e3 & op(e0, e0) = e3)
% 224.03/38.29  | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | BETA: splitting (13201) gives:
% 224.03/38.29  | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | Case 1:
% 224.03/38.29  | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | |   (13202)  all_57_11 = e3 & op(e1, e0) = e3
% 224.03/38.29  | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | ALPHA: (13202) implies:
% 224.03/38.29  | | | | | | | | | |   (13203)  op(e1, e0) = e3
% 224.03/38.29  | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | REF_CLOSE: (161), (12090), (13203), (function-axioms) are
% 224.03/38.29  | | | | | | | | | |            inconsistent by sub-proof #2330.
% 224.03/38.29  | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | Case 2:
% 224.03/38.29  | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | |   (13204)  all_57_15 = e3 & op(e0, e0) = e3
% 224.03/38.29  | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | ALPHA: (13204) implies:
% 224.03/38.29  | | | | | | | | | |   (13205)  all_57_15 = e3
% 224.03/38.29  | | | | | | | | | |   (13206)  op(e0, e0) = e3
% 224.03/38.29  | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | BETA: splitting (225) gives:
% 224.03/38.29  | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | Case 1:
% 224.03/38.29  | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | |   (13207)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 224.03/38.29  | | | | | | | | | | |              & op(e2, e2) = e3)
% 224.03/38.29  | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | BETA: splitting (13207) gives:
% 224.03/38.29  | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | Case 1:
% 224.03/38.29  | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | |   (13208)  all_57_2 = e3 & op(e2, e3) = e3
% 224.03/38.29  | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | ALPHA: (13208) implies:
% 224.03/38.29  | | | | | | | | | | | |   (13209)  all_57_2 = e3
% 224.03/38.29  | | | | | | | | | | | |   (13210)  op(e2, e3) = e3
% 224.03/38.29  | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | BETA: splitting (229) gives:
% 224.03/38.29  | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | Case 1:
% 224.03/38.29  | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | |   (13211)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 224.03/38.29  | | | | | | | | | | | | |              & op(e2, e2) = e3)
% 224.03/38.29  | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | BETA: splitting (13211) gives:
% 224.03/38.29  | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | Case 1:
% 224.03/38.29  | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | |   (13212)  all_57_1 = e3 & op(e3, e2) = e3
% 224.03/38.29  | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | ALPHA: (13212) implies:
% 224.03/38.29  | | | | | | | | | | | | | |   (13213)  all_57_1 = e3
% 224.03/38.29  | | | | | | | | | | | | | |   (13214)  op(e3, e2) = e3
% 224.03/38.29  | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_1, e3,
% 224.03/38.29  | | | | | | | | | | | | | |              e3, e2, simplifying with (168), (13210) gives:
% 224.03/38.29  | | | | | | | | | | | | | |   (13215)  all_53_1 = e3
% 224.03/38.29  | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_4, e3,
% 224.03/38.29  | | | | | | | | | | | | | |              e2, e3, simplifying with (171), (13214) gives:
% 224.03/38.29  | | | | | | | | | | | | | |   (13216)  all_53_4 = e3
% 224.03/38.29  | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | REDUCE: (149), (13215) imply:
% 224.03/38.29  | | | | | | | | | | | | | |   (13217)   ~ (all_53_3 = e3)
% 224.03/38.29  | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | SIMP: (13217) implies:
% 224.03/38.29  | | | | | | | | | | | | | |   (13218)   ~ (all_53_3 = e3)
% 224.03/38.29  | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | REDUCE: (136), (13216) imply:
% 224.03/38.29  | | | | | | | | | | | | | |   (13219)   ~ (all_53_7 = e3)
% 224.03/38.29  | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | SIMP: (13219) implies:
% 224.03/38.29  | | | | | | | | | | | | | |   (13220)   ~ (all_53_7 = e3)
% 224.03/38.29  | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | REDUCE: (134), (13216) imply:
% 224.03/38.29  | | | | | | | | | | | | | |   (13221)   ~ (all_53_12 = e3)
% 224.03/38.29  | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | REDUCE: (344), (13216) imply:
% 224.03/38.29  | | | | | | | | | | | | | |   (13222)   ~ (all_10_2 = e3)
% 224.03/38.29  | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | SIMP: (13222) implies:
% 224.03/38.29  | | | | | | | | | | | | | |   (13223)   ~ (all_10_2 = e3)
% 224.03/38.29  | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | REDUCE: (352), (13216) imply:
% 224.03/38.29  | | | | | | | | | | | | | |   (13224)   ~ (all_8_2 = e3)
% 224.03/38.29  | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 224.03/38.29  | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | Case 1:
% 224.03/38.29  | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | |   (13225)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 224.03/38.29  | | | | | | | | | | | | | | |              all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 224.03/38.29  | | | | | | | | | | | | | | |              op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 224.03/38.29  | | | | | | | | | | | | | | |                all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 224.03/38.29  | | | | | | | | | | | | | | |              op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 224.03/38.29  | | | | | | | | | | | | | | |              op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 224.03/38.29  | | | | | | | | | | | | | | |              $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 224.03/38.29  | | | | | | | | | | | | | | |              $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 224.03/38.29  | | | | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 224.03/38.29  | | | | | | | | | | | | | | |                all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 224.03/38.29  | | | | | | | | | | | | | | |              & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 224.03/38.29  | | | | | | | | | | | | | | |                all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 224.03/38.29  | | | | | | | | | | | | | | |              op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 224.03/38.29  | | | | | | | | | | | | | | |              & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 224.03/38.29  | | | | | | | | | | | | | | |              $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 224.03/38.29  | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | BETA: splitting (13225) gives:
% 224.03/38.29  | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | Case 1:
% 224.03/38.29  | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | |   (13226)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 224.03/38.29  | | | | | | | | | | | | | | | |            all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 224.03/38.29  | | | | | | | | | | | | | | | |            op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 224.03/38.29  | | | | | | | | | | | | | | | |              all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 224.03/38.29  | | | | | | | | | | | | | | | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 224.03/38.29  | | | | | | | | | | | | | | | |            op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 224.03/38.29  | | | | | | | | | | | | | | | |            $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 224.03/38.29  | | | | | | | | | | | | | | | |            $i(all_52_7)
% 224.03/38.29  | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | ALPHA: (13226) implies:
% 224.03/38.29  | | | | | | | | | | | | | | | |   (13227)  op(e3, e2) = all_52_3
% 224.03/38.29  | | | | | | | | | | | | | | | |   (13228)  op(e3, e3) = all_52_1
% 224.03/38.29  | | | | | | | | | | | | | | | |   (13229)  op(all_52_3, all_52_3) = e2
% 224.03/38.29  | | | | | | | | | | | | | | | |   (13230)  op(all_52_1, all_52_1) = e3
% 224.03/38.29  | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_52_3,
% 224.03/38.29  | | | | | | | | | | | | | | | |              e2, e3, simplifying with (13214), (13227) gives:
% 224.03/38.29  | | | | | | | | | | | | | | | |   (13231)  all_52_3 = e3
% 224.03/38.29  | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2,
% 224.03/38.29  | | | | | | | | | | | | | | | |              all_52_1, e3, e3, simplifying with (45), (13228)
% 224.03/38.29  | | | | | | | | | | | | | | | |              gives:
% 224.03/38.29  | | | | | | | | | | | | | | | |   (13232)  all_52_1 = all_10_2
% 224.03/38.29  | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | REDUCE: (13230), (13232) imply:
% 224.03/38.29  | | | | | | | | | | | | | | | |   (13233)  op(all_10_2, all_10_2) = e3
% 224.03/38.29  | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | REDUCE: (13229), (13231) imply:
% 224.03/38.29  | | | | | | | | | | | | | | | |   (13234)  op(e3, e3) = e2
% 224.03/38.29  | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, e2,
% 224.03/38.29  | | | | | | | | | | | | | | | |              e3, e3, simplifying with (45), (13234) gives:
% 224.03/38.29  | | | | | | | | | | | | | | | |   (13235)  all_10_2 = e2
% 224.03/38.29  | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | REDUCE: (13233), (13235) imply:
% 224.03/38.29  | | | | | | | | | | | | | | | |   (13236)  op(e2, e2) = e3
% 224.03/38.29  | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | REF_CLOSE: (42), (12098), (13236), (function-axioms) are
% 224.03/38.29  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #140.
% 224.03/38.29  | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | Case 2:
% 224.03/38.29  | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | |   (13237)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 224.03/38.29  | | | | | | | | | | | | | | | |            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 224.03/38.29  | | | | | | | | | | | | | | | |            op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 224.03/38.29  | | | | | | | | | | | | | | | |              all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 224.03/38.29  | | | | | | | | | | | | | | | |            & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 224.03/38.29  | | | | | | | | | | | | | | | |            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 224.03/38.29  | | | | | | | | | | | | | | | |            $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 224.03/38.29  | | | | | | | | | | | | | | | |            $i(all_52_15)
% 224.03/38.29  | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | ALPHA: (13237) implies:
% 224.03/38.29  | | | | | | | | | | | | | | | |   (13238)  op(e2, e3) = all_52_9
% 224.03/38.29  | | | | | | | | | | | | | | | |   (13239)  op(all_52_9, all_52_9) = e3
% 224.03/38.29  | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_52_9,
% 224.03/38.29  | | | | | | | | | | | | | | | |              e3, e2, simplifying with (13210), (13238) gives:
% 224.03/38.29  | | | | | | | | | | | | | | | |   (13240)  all_52_9 = e3
% 224.03/38.29  | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | REDUCE: (13239), (13240) imply:
% 224.03/38.29  | | | | | | | | | | | | | | | |   (13241)  op(e3, e3) = e3
% 224.03/38.29  | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, e3,
% 224.03/38.29  | | | | | | | | | | | | | | | |              e3, e3, simplifying with (45), (13241) gives:
% 224.03/38.29  | | | | | | | | | | | | | | | |   (13242)  all_10_2 = e3
% 224.03/38.29  | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | REDUCE: (13223), (13242) imply:
% 224.03/38.29  | | | | | | | | | | | | | | | |   (13243)  $false
% 224.03/38.29  | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | CLOSE: (13243) is inconsistent.
% 224.03/38.29  | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | End of split
% 224.03/38.29  | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | Case 2:
% 224.03/38.29  | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | |   (13244)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 224.03/38.29  | | | | | | | | | | | | | | |              & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 224.03/38.29  | | | | | | | | | | | | | | |              & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 224.03/38.29  | | | | | | | | | | | | | | |                all_52_21) = e1 & op(all_52_23, all_52_23) =
% 224.03/38.29  | | | | | | | | | | | | | | |              e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 224.03/38.29  | | | | | | | | | | | | | | |              all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 224.03/38.29  | | | | | | | | | | | | | | |              = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 224.03/38.29  | | | | | | | | | | | | | | |              $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 224.03/38.29  | | | | | | | | | | | | | | |              & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 224.03/38.29  | | | | | | | | | | | | | | |              e0 & op(all_52_25, all_52_25) = e3 &
% 224.03/38.29  | | | | | | | | | | | | | | |              op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 224.03/38.29  | | | | | | | | | | | | | | |                all_52_29) = e1 & op(all_52_31, all_52_31) =
% 224.03/38.29  | | | | | | | | | | | | | | |              e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 224.03/38.29  | | | | | | | | | | | | | | |              all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 224.03/38.29  | | | | | | | | | | | | | | |              = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 224.03/38.29  | | | | | | | | | | | | | | |              $i(all_52_29) & $i(all_52_31))
% 224.03/38.29  | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | BETA: splitting (13244) gives:
% 224.03/38.29  | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | Case 1:
% 224.03/38.29  | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | |   (13245)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 224.03/38.29  | | | | | | | | | | | | | | | |            all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 224.03/38.29  | | | | | | | | | | | | | | | |            op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 224.03/38.29  | | | | | | | | | | | | | | | |              all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 224.03/38.29  | | | | | | | | | | | | | | | |            & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 224.03/38.29  | | | | | | | | | | | | | | | |            & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 224.03/38.29  | | | | | | | | | | | | | | | |            & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 224.03/38.29  | | | | | | | | | | | | | | | |            $i(all_52_23)
% 224.03/38.29  | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | ALPHA: (13245) implies:
% 224.03/38.29  | | | | | | | | | | | | | | | |   (13246)  op(e1, e1) = all_52_21
% 224.03/38.29  | | | | | | | | | | | | | | | |   (13247)  op(all_52_21, all_52_21) = e1
% 224.03/38.29  | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | REF_CLOSE: (45), (12097), (12099), (13246), (13247),
% 224.03/38.29  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.03/38.29  | | | | | | | | | | | | | | | |            #167.
% 224.03/38.29  | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | Case 2:
% 224.03/38.29  | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | |   (13248)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 224.03/38.29  | | | | | | | | | | | | | | | |            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 224.03/38.29  | | | | | | | | | | | | | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 224.03/38.29  | | | | | | | | | | | | | | | |              all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 224.03/38.29  | | | | | | | | | | | | | | | |            & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 224.03/38.29  | | | | | | | | | | | | | | | |            & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 224.03/38.29  | | | | | | | | | | | | | | | |            & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 224.03/38.29  | | | | | | | | | | | | | | | |            $i(all_52_31)
% 224.03/38.29  | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | ALPHA: (13248) implies:
% 224.03/38.29  | | | | | | | | | | | | | | | |   (13249)  op(e0, e0) = all_52_31
% 224.03/38.29  | | | | | | | | | | | | | | | |   (13250)  op(e0, e1) = all_52_29
% 224.03/38.29  | | | | | | | | | | | | | | | |   (13251)  op(e0, e2) = all_52_27
% 224.03/38.29  | | | | | | | | | | | | | | | |   (13252)  op(e0, e3) = all_52_25
% 224.03/38.29  | | | | | | | | | | | | | | | |   (13253)  op(all_52_31, all_52_31) = e0
% 224.03/38.29  | | | | | | | | | | | | | | | |   (13254)  op(all_52_29, all_52_29) = e1
% 224.03/38.29  | | | | | | | | | | | | | | | |   (13255)  op(all_52_27, all_52_27) = e2
% 224.03/38.29  | | | | | | | | | | | | | | | |   (13256)  op(all_52_25, all_52_25) = e3
% 224.03/38.29  | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3,
% 224.03/38.29  | | | | | | | | | | | | | | | |              all_52_31, e0, e0, simplifying with (13206),
% 224.03/38.29  | | | | | | | | | | | | | | | |              (13249) gives:
% 224.03/38.29  | | | | | | | | | | | | | | | |   (13257)  all_52_31 = e3
% 224.03/38.29  | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_11,
% 224.03/38.29  | | | | | | | | | | | | | | | |              all_52_29, e1, e0, simplifying with (158), (13250)
% 224.03/38.29  | | | | | | | | | | | | | | | |              gives:
% 224.03/38.29  | | | | | | | | | | | | | | | |   (13258)  all_53_11 = all_52_29
% 224.03/38.29  | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_7,
% 224.03/38.29  | | | | | | | | | | | | | | | |              all_52_27, e2, e0, simplifying with (159), (13251)
% 224.03/38.29  | | | | | | | | | | | | | | | |              gives:
% 224.03/38.29  | | | | | | | | | | | | | | | |   (13259)  all_53_7 = all_52_27
% 224.03/38.29  | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_3,
% 224.03/38.29  | | | | | | | | | | | | | | | |              all_52_25, e3, e0, simplifying with (160), (13252)
% 224.03/38.29  | | | | | | | | | | | | | | | |              gives:
% 224.03/38.29  | | | | | | | | | | | | | | | |   (13260)  all_53_3 = all_52_25
% 224.03/38.29  | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | REDUCE: (13218), (13260) imply:
% 224.03/38.29  | | | | | | | | | | | | | | | |   (13261)   ~ (all_52_25 = e3)
% 224.03/38.29  | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | REDUCE: (126), (13258), (13259) imply:
% 224.03/38.29  | | | | | | | | | | | | | | | |   (13262)   ~ (all_52_27 = all_52_29)
% 224.03/38.29  | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | REDUCE: (356), (13259) imply:
% 224.03/38.29  | | | | | | | | | | | | | | | |   (13263)   ~ (all_52_27 = all_8_2)
% 224.03/38.29  | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | REDUCE: (13220), (13259) imply:
% 224.03/38.29  | | | | | | | | | | | | | | | |   (13264)   ~ (all_52_27 = e3)
% 224.03/38.29  | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | REDUCE: (12089), (13258) imply:
% 224.03/38.29  | | | | | | | | | | | | | | | |   (13265)   ~ (all_52_29 = e3)
% 224.03/38.29  | | | | | | | | | | | | | | | | 
% 224.03/38.29  | | | | | | | | | | | | | | | | REDUCE: (13253), (13257) imply:
% 224.03/38.29  | | | | | | | | | | | | | | | |   (13266)  op(e3, e3) = e0
% 224.03/38.29  | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, e0,
% 224.03/38.30  | | | | | | | | | | | | | | | |              e3, e3, simplifying with (45), (13266) gives:
% 224.03/38.30  | | | | | | | | | | | | | | | |   (13267)  all_10_2 = e0
% 224.03/38.30  | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | REDUCE: (340), (13267) imply:
% 224.03/38.30  | | | | | | | | | | | | | | | |   (13268)   ~ (all_53_2 = e0)
% 224.03/38.30  | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | REDUCE: (346), (13267) imply:
% 224.03/38.30  | | | | | | | | | | | | | | | |   (13269)   ~ (all_53_8 = e0)
% 224.03/38.30  | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | REDUCE: (348), (13267) imply:
% 224.03/38.30  | | | | | | | | | | | | | | | |   (13270)   ~ (all_53_12 = e0)
% 224.03/38.30  | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | REDUCE: (13223), (13267) imply:
% 224.03/38.30  | | | | | | | | | | | | | | | |   (13271)   ~ (e3 = e0)
% 224.03/38.30  | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | REDUCE: (12099), (13267) imply:
% 224.03/38.30  | | | | | | | | | | | | | | | |   (13272)   ~ (e1 = e0)
% 224.03/38.30  | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 224.03/38.30  | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | Case 1:
% 224.03/38.30  | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | |   (13273)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 224.03/38.30  | | | | | | | | | | | | | | | | |              & op(e2, e3) = e0)
% 224.03/38.30  | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | BETA: splitting (13273) gives:
% 224.03/38.30  | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | Case 1:
% 224.03/38.30  | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | |   (13274)  all_57_0 = e0 & op(e3, e3) = e0
% 224.03/38.30  | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | ALPHA: (13274) implies:
% 224.03/38.30  | | | | | | | | | | | | | | | | | |   (13275)  all_57_0 = e0
% 224.03/38.30  | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | BETA: splitting (52) gives:
% 224.03/38.30  | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | Case 1:
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | |   (13276)   ~ (all_14_2 = e0)
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | REDUCE: (328), (13276) imply:
% 224.03/38.30  | | | | | | | | | | | | | | | | | | |   (13277)   ~ (all_8_2 = e0)
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | BETA: splitting (55) gives:
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | Case 1:
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | |   (13278)   ~ (all_16_2 = e1)
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | REDUCE: (324), (13278) imply:
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | |   (13279)   ~ (all_8_2 = e1)
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | |   (13280)  all_55_5 = e3
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (266), (13280) imply:
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | |   (13281)  all_8_2 = e3
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | REDUCE: (12098), (13281) imply:
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | |   (13282)  $false
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | CLOSE: (13282) is inconsistent.
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | |   (13283)   ~ (all_55_5 = e3)
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | |   (13284)  all_55_5 = e2 | all_55_5 = e1 | all_55_5 = e0
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13284) gives:
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | |   (13285)  all_55_5 = e2
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (266), (13285) imply:
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | |   (13286)  all_8_2 = e2
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (358), (13286) imply:
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | |   (13287)   ~ (all_53_9 = e2)
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (360), (13286) imply:
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | |   (13288)   ~ (all_53_13 = e2)
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12098), (13286) imply:
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | |   (13289)   ~ (e3 = e2)
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (42), (13286) imply:
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | |   (13290)  op(e2, e2) = e2
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | |   (13291)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13291) gives:
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | |   (13292)  all_57_2 = e2 & op(e2, e3) = e2
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13292) implies:
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | |   (13293)  all_57_2 = e2
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (207), (211), (212),
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | |            (222), (223), (225), (13205), (13206), (13290),
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | |            (13293), (function-axioms) are inconsistent by
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1169.
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | |   (13294)  all_57_3 = e2 & op(e2, e2) = e2
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13294) implies:
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | |   (13295)  all_57_3 = e2
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (64) gives:
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (13296)   ~ (all_22_2 = e3)
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (13197), (13296) imply:
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (13297)  $false
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (13297) is inconsistent.
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (13298)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e0, e3) = all_22_1 & $i(all_22_0) &
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0, e3)
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | |              = all_22_1 & $i(all_22_1))
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | |   (13299)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e2)
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13299) gives:
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13300)  all_57_4 = e2 & op(e3, e1) = e2
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13300) implies:
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13301)  all_57_4 = e2
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13302)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e1)
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13302) gives:
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13303)  all_57_0 = e1 & op(e3, e3) = e1
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13303) implies:
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13304)  op(e3, e3) = e1
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (13206), (13249), (13253), (13304),
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #283.
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13305)  all_57_1 = e1 & op(e3, e2) = e1
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (13213), (13305) are inconsistent by
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2453.
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13306)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e1)
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13306) gives:
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13307)  all_57_4 = e1 & op(e3, e1) = e1
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13307) implies:
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13308)  all_57_4 = e1
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (13301), (13308) are inconsistent by
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2430.
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13309)  all_57_9 = e1 & op(e3, e0) = e1
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13309) implies:
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13310)  all_57_9 = e1
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13311)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (169), (231),
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (237), (13198), (13288), (13301), (13311),
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #171.
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13312)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13312) gives:
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13313)  all_57_11 = e2 & op(e1, e0) = e2
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13313) implies:
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13314)  all_57_11 = e2
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13315)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e0)
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13315) gives:
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13316)  all_57_6 = e0 & op(e1, e3) = e0
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13316) implies:
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13317)  op(e1, e3) = e0
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (13268), (13317), (function-axioms) are
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2154.
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13318)  all_57_7 = e0 & op(e1, e2) = e0
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13318) implies:
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13319)  all_57_7 = e0
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (207), (209),
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (227), (232), (234), (373), (13195), (13206),
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13209), (13213), (13249), (13251), (13252),
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13253), (13255), (13256), (13266), (13290),
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13298), (13319), (function-axioms) are
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #137.
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13320)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13320) gives:
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13321)  all_57_8 = e0 & op(e1, e1) = e0
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13321) implies:
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13322)  all_57_8 = e0
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (12096), (13322) imply:
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13323)  e3 = e0
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (13323) implies:
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13324)  e3 = e0
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.03/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13213), (13324) imply:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13325)  all_57_1 = e0
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (9), (169), (235), (237), (13198),
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13266), (13310), (13325), (function-axioms) are
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2400.
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13326)  all_57_11 = e0 & op(e1, e0) = e0
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13326) implies:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13327)  all_57_11 = e0
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13314), (13327) imply:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13328)  e2 = e0
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13301), (13328) imply:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13329)  all_57_4 = e0
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (9), (169), (235), (237), (13198),
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13266), (13310), (13329), (function-axioms) are
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1403.
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13330)  all_57_15 = e2 & op(e0, e0) = e2
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13330) implies:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13331)  op(e0, e0) = e2
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (373), (13331), (function-axioms) are
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2334.
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13332)  all_57_5 = e2 & op(e2, e1) = e2
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (13287), (13332), (function-axioms) are
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1858.
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | |   (13333)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e1) = e2)
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13333) gives:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13334)  all_57_8 = e2 & op(e1, e1) = e2
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13334) implies:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13335)  all_57_8 = e2
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (12096), (13335) imply:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13336)  e3 = e2
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (13336) implies:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13337)  e3 = e2
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13213), (13337) imply:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13338)  all_57_1 = e2
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (169), (207), (208),
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (209), (211), (212), (226), (227), (228), (229),
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (233), (235), (237), (13198), (13205),
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13206), (13266), (13270), (13275), (13290),
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13295), (13338), (function-axioms) are
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #839.
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13339)  all_57_14 = e2 & op(e0, e1) = e2
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13339) implies:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13340)  all_57_14 = e2
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13341)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e0)
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13341) gives:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13342)  all_57_4 = e0 & op(e3, e1) = e0
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13342) implies:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13343)  op(e3, e1) = e0
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (13269), (13343), (function-axioms) are
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2267.
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13344)  all_57_5 = e0 & op(e2, e1) = e0
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13344) implies:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13345)  all_57_5 = e0
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13346)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13346) gives:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13347)  all_57_2 = e1 & op(e2, e3) = e1
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13347) implies:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13348)  all_57_2 = e1
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (13209), (13348) are inconsistent by
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2397.
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13349)  all_57_3 = e1 & op(e2, e2) = e1
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13349) implies:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13350)  op(e2, e2) = e1
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (13290), (13350), (function-axioms) are
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2306.
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13351)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13351) gives:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13352)  all_57_5 = e1 & op(e2, e1) = e1
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (13345), (13352) are inconsistent by
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2361.
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13353)  all_57_10 = e1 & op(e2, e0) = e1
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13353) implies:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13354)  all_57_10 = e1
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13355)  all_57_15 = e0 & op(e0, e0) = e0
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13355) implies:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13356)  op(e0, e0) = e0
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (161), (169), (213), (12090), (13198),
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13354), (13356), (function-axioms) are
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2302.
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13357)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13357) implies:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13358)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0)
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (232), (234), (13206),
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13209), (13249), (13251), (13253), (13255),
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13266), (13340), (13358), (function-axioms) are
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #138.
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13359)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13359) gives:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13360)  all_57_8 = e0 & op(e1, e1) = e0
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13360) implies:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13361)  all_57_8 = e0
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (12096), (13361) imply:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13362)  e3 = e0
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (169), (207), (208),
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (209), (211), (212), (227), (228), (229), (231),
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (235), (237), (13198), (13205), (13206),
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13213), (13266), (13270), (13275), (13295),
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13362), (function-axioms) are inconsistent by
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #881.
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13363)  all_57_14 = e0 & op(e0, e1) = e0
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13363) implies:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13364)  all_57_14 = e0
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (13340), (13364) are inconsistent by
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2422.
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | |   (13365)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13365) gives:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | |   (13366)  all_57_5 = e2 & op(e2, e1) = e2
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (13287), (13366), (function-axioms) are
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1858.
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | |   (13367)  all_57_10 = e2 & op(e2, e0) = e2
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (13288), (13367), (function-axioms) are
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2432.
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | |   (13368)  all_55_5 = e1 | all_55_5 = e0
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (266), (13277), (13279), (13368) are inconsistent
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1857.
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | End of split
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | End of split
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | Case 2:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | |   (13369)  all_16_2 = e1
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (324), (13369) imply:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | |   (13370)  all_8_2 = e1
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | SIMP: (13370) implies:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | |   (13371)  all_8_2 = e1
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | REDUCE: (358), (13371) imply:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | |   (13372)   ~ (all_53_9 = e1)
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | REDUCE: (360), (13371) imply:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | |   (13373)   ~ (all_53_13 = e1)
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | REDUCE: (13263), (13371) imply:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | |   (13374)   ~ (all_52_27 = e1)
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | REDUCE: (12098), (13371) imply:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | |   (13375)   ~ (e3 = e1)
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | REDUCE: (42), (13371) imply:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | |   (13376)  op(e2, e2) = e1
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | |   (13377)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13377) gives:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | |   (13378)  all_57_2 = e1 & op(e2, e3) = e1
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13378) implies:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | |   (13379)  all_57_2 = e1
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (207), (211), (212),
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | |            (222), (224), (225), (13205), (13206), (13376),
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | |            (13379), (function-axioms) are inconsistent by
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #814.
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | |   (13380)  all_57_3 = e1 & op(e2, e2) = e1
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13380) implies:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | |   (13381)  all_57_3 = e1
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (64) gives:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | |   (13382)   ~ (all_22_2 = e3)
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (13197), (13382) imply:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | |   (13383)  $false
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (13383) is inconsistent.
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | |   (13384)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | |              & op(e0, e3) = all_22_1 & $i(all_22_0) &
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0, e3)
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | |              = all_22_1 & $i(all_22_1))
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | |   (13385)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e1)
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13385) gives:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (13386)  all_57_0 = e1 & op(e3, e3) = e1
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13386) implies:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (13387)  op(e3, e3) = e1
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (13206), (13249), (13253), (13387),
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | |            #283.
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (13388)  all_57_1 = e1 & op(e3, e2) = e1
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13388) implies:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (13389)  all_57_1 = e1
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (166), (223),
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | |            (226), (228), (229), (13209), (13372), (13373),
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | |            (13389), (function-axioms) are inconsistent by
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1907.
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | |   (13390)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e1)
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13390) gives:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (13391)  all_57_4 = e1 & op(e3, e1) = e1
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13391) implies:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (13392)  all_57_4 = e1
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.30  | | | | | | | | | | | | | | | | | | | | | | | | | |   (13393)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e2)
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (13214), (13266), (13393),
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | |            #1195.
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | |   (13394)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e2)
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13394) gives:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13395)  all_57_4 = e2 & op(e3, e1) = e2
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13395) implies:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13396)  all_57_4 = e2
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (207), (219), (222),
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (232), (234), (12097), (13206), (13209),
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13249), (13251), (13253), (13255), (13266),
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13376), (13396), (function-axioms) are
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #136.
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13397)  all_57_9 = e2 & op(e3, e0) = e2
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13397) implies:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13398)  all_57_9 = e2
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13399)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13399) gives:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13400)  all_57_9 = e1 & op(e3, e0) = e1
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13400) implies:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13401)  all_57_9 = e1
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (207), (219), (222),
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (232), (234), (235), (12097), (13206),
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13209), (13214), (13249), (13251), (13253),
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13255), (13266), (13376), (13401),
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #135.
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13402)  all_57_10 = e1 & op(e2, e0) = e1
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (13373), (13402), (function-axioms) are
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2084.
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13403)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13403) gives:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13404)  all_57_11 = e1 & op(e1, e0) = e1
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13404) implies:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13405)  all_57_11 = e1
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13406)  all_57_15 = e0 & op(e0, e0) = e0
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13406) implies:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13407)  op(e0, e0) = e0
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (13206), (13407), (function-axioms) are
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2304.
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13408)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13408) implies:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13409)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0)
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13410)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0)
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13410) gives:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13411)  all_57_9 = e0 & op(e3, e0) = e0
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (13270), (13411), (function-axioms) are
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2434.
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13412)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 =
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13412) gives:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13413)  all_57_10 = e0 & op(e2, e0) = e0
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13413) implies:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13414)  all_57_10 = e0
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13415)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (13209), (13376), (13415),
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1799.
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13416)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13416) gives:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13417)  all_57_5 = e2 & op(e2, e1) = e2
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13417) implies:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13418)  all_57_5 = e2
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13419)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e0)
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13419) gives:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13420)  all_57_6 = e0 & op(e1, e3) = e0
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13420) implies:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13421)  op(e1, e3) = e0
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (13268), (13421), (function-axioms) are
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2154.
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13422)  all_57_7 = e0 & op(e1, e2) = e0
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13422) implies:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13423)  all_57_7 = e0
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13424)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13424) gives:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13425)  all_57_1 = e2 & op(e3, e2) = e2
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13425) implies:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13426)  op(e3, e2) = e2
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (13214), (13426), (function-axioms) are
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1549.
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13427)  all_57_3 = e2 & op(e2, e2) = e2
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13427) implies:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13428)  op(e2, e2) = e2
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (207), (209),
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (227), (232), (234), (373), (13195), (13206),
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13209), (13213), (13249), (13251), (13252),
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13253), (13255), (13256), (13266), (13384),
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13423), (13428), (function-axioms) are
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #137.
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13429)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13429) gives:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13430)  all_57_7 = e2 & op(e1, e2) = e2
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (13423), (13430) are inconsistent by
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #364.
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13431)  all_57_13 = e2 & op(e0, e2) = e2
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13431) implies:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13432)  all_57_13 = e2
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13433)  op(e0, e2) = e2
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13434)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e2)
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13434) gives:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13435)  all_57_6 = e2 & op(e1, e3) = e2
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13435) implies:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13436)  all_57_6 = e2
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13437)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e0)
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13437) gives:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13438)  all_57_4 = e0 & op(e3, e1) = e0
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13438) implies:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13439)  all_57_4 = e0
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (169), (226), (228),
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (229), (233), (235), (237), (13198), (13266),
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13275), (13376), (13439), (function-axioms) are
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1012.
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13440)  all_57_5 = e0 & op(e2, e1) = e0
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (208), (209), (228),
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (229), (13205), (13206), (13376), (13409),
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13418), (13423), (13432), (13440),
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #134.
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13441)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13441) gives:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13442)  all_57_8 = e0 & op(e1, e1) = e0
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13442) implies:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13443)  all_57_8 = e0
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (12096), (13443) imply:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13444)  e3 = e0
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13213), (13444) imply:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13445)  all_57_1 = e0
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (169), (207), (208),
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (209), (226), (227), (228), (229), (233), (235),
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (237), (13198), (13205), (13206), (13266),
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13275), (13376), (13381), (13445),
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #824.
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13446)  all_57_14 = e0 & op(e0, e1) = e0
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13446) implies:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13447)  all_57_14 = e0
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13448)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e1)
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13448) gives:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13449)  all_57_0 = e1 & op(e3, e3) = e1
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13449) implies:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13450)  all_57_0 = e1
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13451)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e0)
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13451) gives:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (13274), (13450) are inconsistent by
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1812.
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13452)  all_57_1 = e0 & op(e3, e2) = e0
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (13213), (13452) are inconsistent by
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1811.
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13453)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e0)
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (170), (13269), (13398), (13453),
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1972.
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13454)  all_57_2 = e1 & op(e2, e3) = e1
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13454) implies:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13455)  all_57_2 = e1
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (208), (209), (236),
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13205), (13266), (13436), (13447), (13455),
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #894.
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13456)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e3) = e1)
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13456) gives:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13457)  all_57_6 = e1 & op(e1, e3) = e1
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13457) implies:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13458)  all_57_6 = e1
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13436), (13458) imply:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13459)  e2 = e1
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (222), (224), (13209),
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13376), (13418), (13459), (function-axioms) are
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #133.
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13460)  all_57_12 = e1 & op(e0, e3) = e1
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13460) implies:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13461)  all_57_12 = e1
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13462)  op(e0, e3) = e1
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13463)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13463) gives:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13464)  all_57_2 = e0 & op(e2, e3) = e0
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13464) implies:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13465)  all_57_2 = e0
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (208), (209), (234),
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (236), (13205), (13266), (13447), (13461),
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13465), (function-axioms) are inconsistent by
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1555.
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13466)  all_57_3 = e0 & op(e2, e2) = e0
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13466) implies:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13467)  all_57_3 = e0
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13468)  op(e2, e2) = e0
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (227), (229), (13423),
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13432), (13467), (13468), (function-axioms) are
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2202.
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13469)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0)
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13469) gives:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13470)  all_57_5 = e0 & op(e2, e1) = e0
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (208), (209), (228),
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (229), (13205), (13206), (13376), (13409),
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13418), (13423), (13432), (13470),
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #134.
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13446) implies:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13471)  op(e0, e1) = e0
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_29,
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e1, e0, simplifying with (13250), (13471)
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13472)  all_52_29 = e0
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_27,
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e2, e0, simplifying with (13251), (13433)
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13473)  all_52_27 = e2
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_25,
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e3, e0, simplifying with (13252), (13462)
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13474)  all_52_25 = e1
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (13264), (13473) imply:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13475)   ~ (e3 = e2)
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (13254), (13472) imply:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13476)  op(e0, e0) = e1
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (209), (210), (13447),
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13461), (13476), (function-axioms) are
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2070.
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13477)  all_57_7 = e2 & op(e1, e2) = e2
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13477) implies:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13478)  all_57_7 = e2
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (226), (227), (228),
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (229), (13376), (13432), (13478),
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1696.
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13479)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e1, e0) = e2)
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13479) gives:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13480)  all_57_8 = e2 & op(e1, e1) = e2
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (12096), (13480) are inconsistent by
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #165.
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13481)  all_57_11 = e2 & op(e1, e0) = e2
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13481) implies:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13482)  all_57_11 = e2
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13405), (13482) imply:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13483)  e2 = e1
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (222), (224), (13209),
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13376), (13418), (13483), (function-axioms) are
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #133.
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13484)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13484) gives:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13485)  all_57_8 = e0 & op(e1, e1) = e0
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13485) implies:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13486)  all_57_8 = e0
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (12096), (13486) imply:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13487)  e3 = e0
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (13487) implies:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13488)  e3 = e0
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13213), (13488) imply:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13489)  all_57_1 = e0
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (169), (207), (208),
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (209), (226), (227), (228), (229), (233), (235),
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (237), (13198), (13205), (13206), (13266),
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13275), (13376), (13381), (13489),
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #824.
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13490)  all_57_11 = e0 & op(e1, e0) = e0
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13490) implies:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13491)  all_57_11 = e0
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (211), (212), (13205),
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13206), (13414), (13491), (function-axioms) are
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1087.
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13492)  all_57_10 = e2 & op(e2, e0) = e2
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13492) implies:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13493)  all_57_10 = e2
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (13414), (13493) are inconsistent by
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2138.
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13494)  all_57_11 = e0 & op(e1, e0) = e0
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13494) implies:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13495)  all_57_11 = e0
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13405), (13495) imply:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13496)  e1 = e0
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13392), (13496) imply:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13497)  all_57_4 = e0
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (169), (226), (228),
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (229), (233), (235), (237), (13198), (13266),
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13275), (13376), (13497), (function-axioms) are
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1012.
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13498)  all_57_15 = e1 & op(e0, e0) = e1
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13498) implies:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13499)  op(e0, e0) = e1
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (13206), (13499), (function-axioms) are
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2183.
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (13500)  all_57_9 = e1 & op(e3, e0) = e1
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13500) implies:
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (13501)  all_57_9 = e1
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (207), (219), (222),
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (232), (234), (235), (12097), (13206),
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | |            (13209), (13214), (13249), (13251), (13253),
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | |            (13255), (13266), (13376), (13501),
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | |            #135.
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.12/38.31  | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | End of split
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | |   (13502)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13502) gives:
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | |   (13503)  all_57_5 = e1 & op(e2, e1) = e1
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13503) implies:
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | |   (13504)  all_57_5 = e1
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (222), (224), (13209),
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | |            (13376), (13504), (function-axioms) are
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #555.
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | |   (13505)  all_57_10 = e1 & op(e2, e0) = e1
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (13373), (13505), (function-axioms) are
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2084.
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | End of split
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | End of split
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | End of split
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | Case 2:
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | |   (13506)  all_14_2 = e0
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (328), (13506) imply:
% 224.12/38.32  | | | | | | | | | | | | | | | | | | |   (13507)  all_8_2 = e0
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | SIMP: (13507) implies:
% 224.12/38.32  | | | | | | | | | | | | | | | | | | |   (13508)  all_8_2 = e0
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | REDUCE: (354), (13508) imply:
% 224.12/38.32  | | | | | | | | | | | | | | | | | | |   (13509)   ~ (all_53_6 = e0)
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | REDUCE: (358), (13508) imply:
% 224.12/38.32  | | | | | | | | | | | | | | | | | | |   (13510)   ~ (all_53_9 = e0)
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | REDUCE: (360), (13508) imply:
% 224.12/38.32  | | | | | | | | | | | | | | | | | | |   (13511)   ~ (all_53_13 = e0)
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | Case 1:
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | |   (13512)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e0)
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (170), (13269), (13510), (13512),
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | |            #141.
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | Case 2:
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | |   (13513)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | BETA: splitting (13513) gives:
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | |   (13514)  all_57_8 = e0 & op(e1, e1) = e0
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12096), (13514) are inconsistent by
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | |            sub-proof #170.
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | |   (13515)  all_57_14 = e0 & op(e0, e1) = e0
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | ALPHA: (13515) implies:
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | |   (13516)  op(e0, e1) = e0
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | |   (13517)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13517) gives:
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | |   (13518)  all_57_2 = e0 & op(e2, e3) = e0
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (13209), (13518) are inconsistent by
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1805.
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | |   (13519)  all_57_3 = e0 & op(e2, e2) = e0
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13519) implies:
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | |   (13520)  all_57_3 = e0
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | | |   (13521)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e0)
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (164), (13268), (13509), (13521),
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | | |            #2038.
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | | |   (13522)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13522) gives:
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | | | |   (13523)  all_57_8 = e0 & op(e1, e1) = e0
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | | | |            (12096), (13209), (13520), (13523) are
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #142.
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_29,
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e1, e0, simplifying with (13250), (13516)
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | | | |   (13524)  all_52_29 = e0
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (13254), (13524) imply:
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | | | |   (13525)  op(e0, e0) = e1
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (13206), (13525), (function-axioms) are
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2183.
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | |   (13526)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0)
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (166), (13510), (13511), (13526),
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | |            #2022.
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | End of split
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | End of split
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | End of split
% 224.12/38.32  | | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | End of split
% 224.12/38.32  | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | Case 2:
% 224.12/38.32  | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | |   (13527)  all_57_2 = e0 & op(e2, e3) = e0
% 224.12/38.32  | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (13209), (13527) are inconsistent by
% 224.12/38.32  | | | | | | | | | | | | | | | | | |            sub-proof #1805.
% 224.12/38.32  | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | End of split
% 224.12/38.32  | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | Case 2:
% 224.12/38.32  | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | |   (13528)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 224.12/38.32  | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = e0)
% 224.12/38.32  | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | BETA: splitting (13528) gives:
% 224.12/38.32  | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | Case 1:
% 224.12/38.32  | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | |   (13529)  all_57_6 = e0 & op(e1, e3) = e0
% 224.12/38.32  | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | ALPHA: (13529) implies:
% 224.12/38.32  | | | | | | | | | | | | | | | | | |   (13530)  op(e1, e3) = e0
% 224.12/38.32  | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (13268), (13530), (function-axioms) are
% 224.12/38.32  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2154.
% 224.12/38.32  | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | Case 2:
% 224.12/38.32  | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | |   (13531)  all_57_12 = e0 & op(e0, e3) = e0
% 224.12/38.32  | | | | | | | | | | | | | | | | | | 
% 224.12/38.32  | | | | | | | | | | | | | | | | | | ALPHA: (13531) implies:
% 224.12/38.32  | | | | | | | | | | | | | | | | | |   (13532)  all_57_12 = e0
% 224.12/38.32  | | | | | | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (232), (234), (13206),
% 224.22/38.32  | | | | | | | | | | | | | | | | | |            (13209), (13249), (13253), (13266), (13532),
% 224.22/38.32  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.22/38.32  | | | | | | | | | | | | | | | | | |            #139.
% 224.22/38.32  | | | | | | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | | | | | End of split
% 224.22/38.32  | | | | | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | | | | End of split
% 224.22/38.32  | | | | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | | | End of split
% 224.22/38.32  | | | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | | End of split
% 224.22/38.32  | | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | Case 2:
% 224.22/38.32  | | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | |   (13533)  all_57_3 = e3 & op(e2, e2) = e3
% 224.22/38.32  | | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | | ALPHA: (13533) implies:
% 224.22/38.32  | | | | | | | | | | | | | |   (13534)  op(e2, e2) = e3
% 224.22/38.32  | | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_2, e3,
% 224.22/38.32  | | | | | | | | | | | | | |              e2, e2, simplifying with (42), (13534) gives:
% 224.22/38.32  | | | | | | | | | | | | | |   (13535)  all_8_2 = e3
% 224.22/38.32  | | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | | REDUCE: (12098), (13535) imply:
% 224.22/38.32  | | | | | | | | | | | | | |   (13536)  $false
% 224.22/38.32  | | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | | CLOSE: (13536) is inconsistent.
% 224.22/38.32  | | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | End of split
% 224.22/38.32  | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | Case 2:
% 224.22/38.32  | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | |   (13537)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 224.22/38.32  | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 224.22/38.32  | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | BETA: splitting (13537) gives:
% 224.22/38.32  | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | Case 1:
% 224.22/38.32  | | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | |   (13538)  all_57_7 = e3 & op(e1, e2) = e3
% 224.22/38.32  | | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | | REF_CLOSE: (163), (12086), (13538), (function-axioms) are
% 224.22/38.32  | | | | | | | | | | | | | |            inconsistent by sub-proof #267.
% 224.22/38.32  | | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | Case 2:
% 224.22/38.32  | | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | |   (13539)  all_57_13 = e3 & op(e0, e2) = e3
% 224.22/38.32  | | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | | ALPHA: (13539) implies:
% 224.22/38.32  | | | | | | | | | | | | | |   (13540)  all_57_13 = e3
% 224.22/38.32  | | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (207), (208), (209),
% 224.22/38.32  | | | | | | | | | | | | | |            (13205), (13206), (13540), (function-axioms) are
% 224.22/38.32  | | | | | | | | | | | | | |            inconsistent by sub-proof #1792.
% 224.22/38.32  | | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | End of split
% 224.22/38.32  | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | End of split
% 224.22/38.32  | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | Case 2:
% 224.22/38.32  | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | |   (13541)  all_57_3 = e3 & op(e2, e2) = e3
% 224.22/38.32  | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | ALPHA: (13541) implies:
% 224.22/38.32  | | | | | | | | | | | |   (13542)  op(e2, e2) = e3
% 224.22/38.32  | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | REF_CLOSE: (42), (12098), (13542), (function-axioms) are
% 224.22/38.32  | | | | | | | | | | | |            inconsistent by sub-proof #140.
% 224.22/38.32  | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | End of split
% 224.22/38.32  | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | Case 2:
% 224.22/38.32  | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | |   (13543)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 224.22/38.32  | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 224.22/38.32  | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | BETA: splitting (13543) gives:
% 224.22/38.32  | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | Case 1:
% 224.22/38.32  | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | |   (13544)  all_57_5 = e3 & op(e2, e1) = e3
% 224.22/38.32  | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | REF_CLOSE: (166), (12088), (13544), (function-axioms) are
% 224.22/38.32  | | | | | | | | | | | |            inconsistent by sub-proof #270.
% 224.22/38.32  | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | Case 2:
% 224.22/38.32  | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | |   (13545)  all_57_10 = e3 & op(e2, e0) = e3
% 224.22/38.32  | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | ALPHA: (13545) implies:
% 224.22/38.32  | | | | | | | | | | | |   (13546)  all_57_10 = e3
% 224.22/38.32  | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (207), (211), (212),
% 224.22/38.32  | | | | | | | | | | | |            (13205), (13206), (13546), (function-axioms) are
% 224.22/38.32  | | | | | | | | | | | |            inconsistent by sub-proof #1746.
% 224.22/38.32  | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | End of split
% 224.22/38.32  | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | End of split
% 224.22/38.32  | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | End of split
% 224.22/38.32  | | | | | | | | | 
% 224.22/38.32  | | | | | | | | End of split
% 224.22/38.32  | | | | | | | | 
% 224.22/38.32  | | | | | | | End of split
% 224.22/38.32  | | | | | | | 
% 224.22/38.32  | | | | | | Case 2:
% 224.22/38.32  | | | | | | | 
% 224.22/38.32  | | | | | | |   (13547)  all_10_2 = e1
% 224.22/38.32  | | | | | | |   (13548)  ( ~ (all_10_0 = e2) & op(all_10_1, e3) = all_10_0 &
% 224.22/38.32  | | | | | | |              op(e3, e1) = all_10_1 & $i(all_10_0) & $i(all_10_1))
% 224.22/38.32  | | | | | | |            | ( ~ (all_10_1 = e0) & op(e3, e1) = all_10_1 &
% 224.22/38.32  | | | | | | |              $i(all_10_1))
% 224.22/38.32  | | | | | | | 
% 224.22/38.32  | | | | | | | COMBINE_EQS: (331), (13547) imply:
% 224.22/38.32  | | | | | | |   (13549)  all_36_2 = e1
% 224.22/38.32  | | | | | | | 
% 224.22/38.32  | | | | | | | REDUCE: (338), (13547) imply:
% 224.22/38.32  | | | | | | |   (13550)   ~ (all_53_1 = e1)
% 224.22/38.32  | | | | | | | 
% 224.22/38.32  | | | | | | | REDUCE: (340), (13547) imply:
% 224.22/38.32  | | | | | | |   (13551)   ~ (all_53_2 = e1)
% 224.22/38.32  | | | | | | | 
% 224.22/38.32  | | | | | | | REDUCE: (342), (13547) imply:
% 224.22/38.32  | | | | | | |   (13552)   ~ (all_53_3 = e1)
% 224.22/38.32  | | | | | | | 
% 224.22/38.32  | | | | | | | REDUCE: (344), (13547) imply:
% 224.22/38.32  | | | | | | |   (13553)   ~ (all_53_4 = e1)
% 224.22/38.32  | | | | | | | 
% 224.22/38.32  | | | | | | | REDUCE: (346), (13547) imply:
% 224.22/38.32  | | | | | | |   (13554)   ~ (all_53_8 = e1)
% 224.22/38.32  | | | | | | | 
% 224.22/38.32  | | | | | | | BETA: splitting (232) gives:
% 224.22/38.32  | | | | | | | 
% 224.22/38.32  | | | | | | | Case 1:
% 224.22/38.32  | | | | | | | | 
% 224.22/38.32  | | | | | | | |   (13555)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 &
% 224.22/38.32  | | | | | | | |              op(e2, e3) = e1)
% 224.22/38.32  | | | | | | | | 
% 224.22/38.32  | | | | | | | | BETA: splitting (13555) gives:
% 224.22/38.32  | | | | | | | | 
% 224.22/38.32  | | | | | | | | Case 1:
% 224.22/38.32  | | | | | | | | | 
% 224.22/38.32  | | | | | | | | |   (13556)  all_57_0 = e1 & op(e3, e3) = e1
% 224.22/38.32  | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | ALPHA: (13556) implies:
% 224.22/38.32  | | | | | | | | |   (13557)  all_57_0 = e1
% 224.22/38.32  | | | | | | | | |   (13558)  op(e3, e3) = e1
% 224.22/38.32  | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | BETA: splitting (49) gives:
% 224.22/38.32  | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | Case 1:
% 224.22/38.32  | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | |   (13559)   ~ (all_12_2 = e3)
% 224.22/38.32  | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | REDUCE: (325), (13559) imply:
% 224.22/38.32  | | | | | | | | | |   (13560)   ~ (all_4_2 = e3)
% 224.22/38.32  | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | BETA: splitting (52) gives:
% 224.22/38.32  | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | Case 1:
% 224.22/38.32  | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | |   (13561)   ~ (all_14_2 = e0)
% 224.22/38.32  | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | REDUCE: (328), (13561) imply:
% 224.22/38.32  | | | | | | | | | | |   (13562)   ~ (all_8_2 = e0)
% 224.22/38.32  | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | BETA: splitting (55) gives:
% 224.22/38.32  | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | Case 1:
% 224.22/38.32  | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | |   (13563)   ~ (all_16_2 = e1)
% 224.22/38.32  | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | REDUCE: (324), (13563) imply:
% 224.22/38.32  | | | | | | | | | | | |   (13564)   ~ (all_8_2 = e1)
% 224.22/38.32  | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | BETA: splitting (200) gives:
% 224.22/38.32  | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | Case 1:
% 224.22/38.32  | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | |   (13565)  all_55_5 = e3
% 224.22/38.32  | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | REF_CLOSE: (266), (12098), (13565) are inconsistent by
% 224.22/38.32  | | | | | | | | | | | | |            sub-proof #293.
% 224.22/38.32  | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | Case 2:
% 224.22/38.32  | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | |   (13566)   ~ (all_55_5 = e3)
% 224.22/38.32  | | | | | | | | | | | | |   (13567)  all_55_5 = e2 | all_55_5 = e1 | all_55_5 = e0
% 224.22/38.32  | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | BETA: splitting (13567) gives:
% 224.22/38.32  | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | Case 1:
% 224.22/38.32  | | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | |   (13568)  all_55_5 = e2
% 224.22/38.32  | | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | | COMBINE_EQS: (266), (13568) imply:
% 224.22/38.32  | | | | | | | | | | | | | |   (13569)  all_8_2 = e2
% 224.22/38.32  | | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | | SIMP: (13569) implies:
% 224.22/38.32  | | | | | | | | | | | | | |   (13570)  all_8_2 = e2
% 224.22/38.32  | | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | | REDUCE: (349), (13570) imply:
% 224.22/38.32  | | | | | | | | | | | | | |   (13571)   ~ (all_53_1 = e2)
% 224.22/38.32  | | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | | REDUCE: (352), (13570) imply:
% 224.22/38.32  | | | | | | | | | | | | | |   (13572)   ~ (all_53_4 = e2)
% 224.22/38.32  | | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | | REDUCE: (354), (13570) imply:
% 224.22/38.32  | | | | | | | | | | | | | |   (13573)   ~ (all_53_6 = e2)
% 224.22/38.32  | | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | | REDUCE: (356), (13570) imply:
% 224.22/38.32  | | | | | | | | | | | | | |   (13574)   ~ (all_53_7 = e2)
% 224.22/38.32  | | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | | REDUCE: (358), (13570) imply:
% 224.22/38.32  | | | | | | | | | | | | | |   (13575)   ~ (all_53_9 = e2)
% 224.22/38.32  | | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | | REDUCE: (360), (13570) imply:
% 224.22/38.32  | | | | | | | | | | | | | |   (13576)   ~ (all_53_13 = e2)
% 224.22/38.32  | | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | | REDUCE: (12098), (13570) imply:
% 224.22/38.32  | | | | | | | | | | | | | |   (13577)   ~ (e3 = e2)
% 224.22/38.32  | | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | | REDUCE: (42), (13570) imply:
% 224.22/38.32  | | | | | | | | | | | | | |   (13578)  op(e2, e2) = e2
% 224.22/38.32  | | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | | BETA: splitting (76) gives:
% 224.22/38.32  | | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | | Case 1:
% 224.22/38.32  | | | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | | |   (13579)   ~ (all_30_2 = e1)
% 224.22/38.32  | | | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | | | REDUCE: (330), (13579) imply:
% 224.22/38.32  | | | | | | | | | | | | | | |   (13580)   ~ (all_4_2 = e1)
% 224.22/38.32  | | | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 224.22/38.32  | | | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | | | Case 1:
% 224.22/38.32  | | | | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | | | |   (13581)  all_55_15 = e3
% 224.22/38.32  | | | | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | | | | REF_CLOSE: (244), (13560), (13581) are inconsistent by
% 224.22/38.32  | | | | | | | | | | | | | | | |            sub-proof #2503.
% 224.22/38.32  | | | | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | | | Case 2:
% 224.22/38.32  | | | | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | | | |   (13582)   ~ (all_55_15 = e3)
% 224.22/38.32  | | | | | | | | | | | | | | | |   (13583)  all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 224.22/38.32  | | | | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | | | | BETA: splitting (13583) gives:
% 224.22/38.32  | | | | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.32  | | | | | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | | | | |   (13584)  all_55_15 = e2
% 224.22/38.32  | | | | | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (373), (13584) are inconsistent by
% 224.22/38.32  | | | | | | | | | | | | | | | | |            sub-proof #2502.
% 224.22/38.32  | | | | | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.32  | | | | | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | | | | |   (13585)   ~ (all_55_15 = e2)
% 224.22/38.32  | | | | | | | | | | | | | | | | |   (13586)  all_55_15 = e1 | all_55_15 = e0
% 224.22/38.32  | | | | | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | | | | | BETA: splitting (13586) gives:
% 224.22/38.32  | | | | | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.32  | | | | | | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | | | | | |   (13587)  all_55_15 = e1
% 224.22/38.32  | | | | | | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (13580), (13587) are inconsistent by
% 224.22/38.32  | | | | | | | | | | | | | | | | | |            sub-proof #2501.
% 224.22/38.32  | | | | | | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.32  | | | | | | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | | | | | |   (13588)  all_55_15 = e0
% 224.22/38.32  | | | | | | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (13588) imply:
% 224.22/38.32  | | | | | | | | | | | | | | | | | |   (13589)  all_4_2 = e0
% 224.22/38.32  | | | | | | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | | | | | | SIMP: (13589) implies:
% 224.22/38.32  | | | | | | | | | | | | | | | | | |   (13590)  all_4_2 = e0
% 224.22/38.32  | | | | | | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | | | | | | REDUCE: (351), (13590) imply:
% 224.22/38.32  | | | | | | | | | | | | | | | | | |   (13591)   ~ (all_53_3 = e0)
% 224.22/38.32  | | | | | | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | | | | | | REDUCE: (362), (13590) imply:
% 224.22/38.32  | | | | | | | | | | | | | | | | | |   (13592)   ~ (all_53_7 = e0)
% 224.22/38.32  | | | | | | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | | | | | | REDUCE: (369), (13590) imply:
% 224.22/38.32  | | | | | | | | | | | | | | | | | |   (13593)   ~ (all_53_11 = e0)
% 224.22/38.32  | | | | | | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | | | | | | REDUCE: (370), (13590) imply:
% 224.22/38.32  | | | | | | | | | | | | | | | | | |   (13594)   ~ (all_53_12 = e0)
% 224.22/38.32  | | | | | | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | | | | | | REDUCE: (371), (13590) imply:
% 224.22/38.32  | | | | | | | | | | | | | | | | | |   (13595)   ~ (all_53_13 = e0)
% 224.22/38.32  | | | | | | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | | | | | | REDUCE: (372), (13590) imply:
% 224.22/38.32  | | | | | | | | | | | | | | | | | |   (13596)   ~ (all_53_14 = e0)
% 224.22/38.32  | | | | | | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | | | | | | REDUCE: (13560), (13590) imply:
% 224.22/38.32  | | | | | | | | | | | | | | | | | |   (13597)   ~ (e3 = e0)
% 224.22/38.32  | | | | | | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | | | | | | REDUCE: (13580), (13590) imply:
% 224.22/38.32  | | | | | | | | | | | | | | | | | |   (13598)   ~ (e1 = e0)
% 224.22/38.32  | | | | | | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 224.22/38.32  | | | | | | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.32  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | | | | | | |   (13599)  all_57_15 = e0 & op(e0, e0) = e0
% 224.22/38.32  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.32  | | | | | | | | | | | | | | | | | | | ALPHA: (13599) implies:
% 224.22/38.32  | | | | | | | | | | | | | | | | | | |   (13600)  all_57_15 = e0
% 224.22/38.33  | | | | | | | | | | | | | | | | | | |   (13601)  op(e0, e0) = e0
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | BETA: splitting (85) gives:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | |   (13602)   ~ (all_36_2 = e1)
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | REDUCE: (13549), (13602) imply:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | |   (13603)  $false
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | CLOSE: (13603) is inconsistent.
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | |   (13604)  ( ~ (all_36_0 = e0) & op(all_36_1, e3) = all_36_0
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | |              & op(e3, e1) = all_36_1 & $i(all_36_0) &
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | |              $i(all_36_1)) | ( ~ (all_36_1 = e2) & op(e3, e1)
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | |              = all_36_1 & $i(all_36_1))
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | |   (13605)  all_55_4 = e3
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (13605) imply:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | |   (13606)  all_53_1 = e3
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | SIMP: (13606) implies:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | |   (13607)  all_53_1 = e3
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | REDUCE: (150), (13607) imply:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | |   (13608)   ~ (all_53_2 = e3)
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (13607) imply:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | |   (13609)   ~ (all_53_3 = e3)
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | SIMP: (13609) implies:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | |   (13610)   ~ (all_53_3 = e3)
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | REDUCE: (147), (13607) imply:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | |   (13611)   ~ (all_53_9 = e3)
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (13607) imply:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | |   (13612)   ~ (all_53_13 = e3)
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | SIMP: (13612) implies:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | |   (13613)   ~ (all_53_13 = e3)
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | |   (13614)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e3)
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13614) gives:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | |   (13615)  all_57_2 = e3 & op(e2, e3) = e3
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13615) implies:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | |   (13616)  all_57_2 = e3
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | |   (13617)  all_55_12 = e3
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (13617) imply:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | |   (13618)  all_53_3 = e3
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (13610), (13618) imply:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | |   (13619)  $false
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (13619) is inconsistent.
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | |   (13620)   ~ (all_55_12 = e3)
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | |   (13621)  all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13621) gives:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | |   (13622)  all_55_12 = e2
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (13622) imply:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | |   (13623)  all_53_3 = e2
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (13623) imply:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | |   (13624)   ~ (all_53_2 = e2)
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (141), (13623) imply:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | |   (13625)   ~ (all_53_7 = e2)
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (13623) imply:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | |   (13626)   ~ (all_53_11 = e2)
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (13626) implies:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | |   (13627)   ~ (all_53_11 = e2)
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | |   (13628)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13628) gives:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13629)  all_57_12 = e3 & op(e0, e3) = e3
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13629) implies:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13630)  op(e0, e3) = e3
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (13610), (13630), (function-axioms) are
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #132.
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13631)  all_57_13 = e3 & op(e0, e2) = e3
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13631) implies:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13632)  all_57_13 = e3
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13633)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (171), (13553), (13578), (13633),
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #362.
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13634)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13634) gives:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13635)  all_57_7 = e1 & op(e1, e2) = e1
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13635) implies:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13636)  all_57_7 = e1
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13637)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2)
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (168), (13558), (13571), (13637),
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #355.
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13638)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e3) = e2)
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13638) gives:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13639)  all_57_6 = e2 & op(e1, e3) = e2
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13639) implies:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13640)  all_57_6 = e2
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (145), (160), (197), (230), (257),
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12085), (13551), (13557), (13616), (13624),
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13640), (function-axioms) are inconsistent by
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #131.
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13641)  all_57_12 = e2 & op(e0, e3) = e2
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13641) implies:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13642)  all_57_12 = e2
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13643)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13643) gives:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13644)  all_57_1 = e0 & op(e3, e2) = e0
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13644) implies:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13645)  all_57_1 = e0
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13646)  op(e3, e2) = e0
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13647)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e2)
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13647) gives:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13648)  all_57_6 = e2 & op(e1, e3) = e2
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13648) implies:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13649)  all_57_6 = e2
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13650)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e0)
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13650) gives:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13651)  all_57_0 = e0 & op(e3, e3) = e0
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13651) implies:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13652)  all_57_0 = e0
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (232), (13616), (13642), (13649),
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13652) are inconsistent by sub-proof #1927.
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13653)  all_57_2 = e0 & op(e2, e3) = e0
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (13616), (13653) are inconsistent by
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1805.
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13654)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = e0)
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13654) gives:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13655)  all_57_6 = e0 & op(e1, e3) = e0
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (13649), (13655) are inconsistent by
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2386.
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13656)  all_57_12 = e0 & op(e0, e3) = e0
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (145), (160), (197), (257), (12085), (13551),
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13624), (13656), (function-axioms) are
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1369.
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13657)  all_57_7 = e2 & op(e1, e2) = e2
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13657) implies:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13658)  all_57_7 = e2
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (227), (13578), (13632), (13645),
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13658), (function-axioms) are inconsistent by
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1958.
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13659)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e1, e0) = e2)
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13659) gives:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13660)  all_57_8 = e2 & op(e1, e1) = e2
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (12096), (13660) are inconsistent by
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #165.
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13661)  all_57_11 = e2 & op(e1, e0) = e2
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13661) implies:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13662)  all_57_11 = e2
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13663)  op(e1, e0) = e2
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13664)  all_55_14 = e3
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (13664) imply:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13665)  all_53_11 = e3
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12089), (13665) imply:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13666)  $false
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (13666) is inconsistent.
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13667)  all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13667) gives:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13668)  all_55_14 = e2
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (13668) imply:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13669)  all_53_11 = e2
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (13627), (13669) imply:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13670)  $false
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (13670) is inconsistent.
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13671)  all_55_14 = e1 | all_55_14 = e0
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13671) gives:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13672)  all_55_14 = e1
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (13672) imply:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13673)  all_53_11 = e1
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (13673) implies:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13674)  all_53_11 = e1
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (126), (13674) imply:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13675)   ~ (all_53_7 = e1)
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (119), (13674) imply:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13676)   ~ (all_53_9 = e1)
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (158), (13674) imply:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13677)  op(e0, e1) = e1
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13678)  all_55_6 = e3
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (12088), (13678) are inconsistent by
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2498.
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13679)  all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13679) gives:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13680)  all_55_6 = e2
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (13575), (13680) are inconsistent by
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2398.
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13681)  all_55_6 = e1 | all_55_6 = e0
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13682)  all_55_13 = e3
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (13682) imply:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13683)  all_53_7 = e3
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (13683) implies:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13684)  all_53_7 = e3
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (136), (13684) imply:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13685)   ~ (all_53_4 = e3)
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13686)  all_55_1 = e3
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (13686) imply:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13687)  all_53_4 = e3
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (13685), (13687) imply:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13688)  $false
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (13688) is inconsistent.
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13689)   ~ (all_55_1 = e3)
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13690)  all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13691)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (13578), (13616), (13691),
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #817.
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13692)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0)
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13692) gives:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13693)  all_57_5 = e0 & op(e2, e1) = e0
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13693) implies:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13694)  op(e2, e1) = e0
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13695)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13695) gives:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13696)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_7)
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13696) implies:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13697)  op(e3, e2) = all_52_3
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13698)  op(all_52_3, all_52_3) = e2
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (13601), (13646), (13697), (13698),
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2399.
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13699)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_15)
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13699) implies:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13700)  op(e2, e0) = all_52_15
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13701)  op(e2, e1) = all_52_13
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13702)  op(all_52_15, all_52_15) = e0
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13703)  op(all_52_13, all_52_13) = e1
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13690) gives:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13704)  all_55_1 = e2
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (13704) imply:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13705)  all_53_4 = e2
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (13572), (13705) imply:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13706)  $false
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (13706) is inconsistent.
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13707)   ~ (all_55_1 = e2)
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13708)  all_55_1 = e1 | all_55_1 = e0
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13708) gives:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13709)  all_55_1 = e1
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (13709) imply:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13710)  all_53_4 = e1
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (13553), (13710) imply:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13711)  $false
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (13711) is inconsistent.
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13712)  all_55_1 = e0
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (13712) imply:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13713)  all_53_4 = e0
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (137), (13713) imply:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13714)   ~ (all_53_6 = e0)
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (13714) implies:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13715)   ~ (all_53_6 = e0)
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (13572), (13713) imply:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13716)   ~ (e2 = e0)
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13717)  all_55_9 = e3
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (12086), (13717) are inconsistent by
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2159.
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13718)   ~ (all_55_9 = e3)
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13719)  all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13719) gives:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13720)  all_55_9 = e2
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (13573), (13720) are inconsistent by
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2274.
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13721)   ~ (all_55_9 = e2)
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13722)  all_55_9 = e1 | all_55_9 = e0
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13722) gives:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13723)  all_55_9 = e1
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (13723) imply:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13724)  all_53_6 = e1
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (13724) implies:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13725)  all_53_6 = e1
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12086), (13725) imply:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13726)   ~ (e3 = e1)
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (13573), (13725) imply:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13727)   ~ (e2 = e1)
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_13, e1, e2, simplifying with (13694),
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (13701) gives:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13728)  all_52_13 = e0
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (13703), (13728) imply:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13729)  op(e0, e0) = e1
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (159), (160), (169),
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (207), (208), (209), (210), (13552), (13574),
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13591), (13594), (13662), (13700), (13702),
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13729), (function-axioms) are inconsistent by
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1895.
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13730)  all_55_9 = e0
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (13715), (13730) are inconsistent by
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2272.
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13731)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_52_21) = e1 & op(all_52_23, all_52_23) =
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(all_52_25, all_52_25) = e3 &
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_52_29) = e1 & op(all_52_31, all_52_31) =
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_29) & $i(all_52_31))
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13731) gives:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13732)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_23)
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13732) implies:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13733)  op(e1, e0) = all_52_23
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13734)  op(all_52_23, all_52_23) = e0
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (13578), (13663), (13733), (13734),
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2369.
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13735)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_31)
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13735) implies:
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13736)  op(e0, e1) = all_52_29
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13737)  op(all_52_29, all_52_29) = e1
% 224.22/38.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (244), (373), (12097), (13583), (13677),
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13736), (13737), (function-axioms) are
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #130.
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13738)  all_57_10 = e0 & op(e2, e0) = e0
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (118), (165), (259), (13676), (13681), (13738),
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2090.
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13739)  all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (13574), (13592), (13675), (13739) are
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1601.
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13740)  all_55_14 = e0
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (13593), (13740) are inconsistent by
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2288.
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13741)  all_57_3 = e0 & op(e2, e2) = e0
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13741) implies:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13742)  op(e2, e2) = e0
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (13578), (13742), (function-axioms) are
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2472.
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13743)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0)
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (159), (13592), (13636), (13743),
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #261.
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13744)  all_57_13 = e1 & op(e0, e2) = e1
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (13632), (13744) are inconsistent by
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2264.
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | |   (13745)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13745) gives:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13746)  all_57_14 = e3 & op(e0, e1) = e3
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (12089), (13746), (function-axioms) are
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #129.
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13747)  all_57_15 = e3 & op(e0, e0) = e3
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13747) implies:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13748)  op(e0, e0) = e3
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (13601), (13748), (function-axioms) are
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2304.
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | |   (13749)  all_55_12 = e1 | all_55_12 = e0
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (247), (13552), (13591), (13749) are inconsistent
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1992.
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | |   (13750)  all_57_3 = e3 & op(e2, e2) = e3
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13750) implies:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | |   (13751)  op(e2, e2) = e3
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (13578), (13751), (function-axioms) are
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2298.
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | |   (13752)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (166), (12088), (13613), (13752),
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | |            #178.
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | |   (13753)   ~ (all_55_4 = e3)
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | |   (13754)  all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | REDUCE: (267), (13753) imply:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | |   (13755)   ~ (all_53_1 = e3)
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | |   (13756)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e3)
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (168), (13578), (13755), (13756),
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | |            #2297.
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | |   (13757)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13757) gives:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | |   (13758)  all_57_5 = e3 & op(e2, e1) = e3
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (12088), (13758), (function-axioms) are
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #270.
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | |   (13759)  all_57_10 = e3 & op(e2, e0) = e3
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13759) implies:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | |   (13760)  all_57_10 = e3
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | |   (13761)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (168), (13550), (13578), (13761),
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | |            #361.
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | |   (13762)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13762) gives:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | |   (13763)  all_57_5 = e1 & op(e2, e1) = e1
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13763) implies:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | |   (13764)  op(e2, e1) = e1
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13754) gives:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | |   (13765)  all_55_4 = e2
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (13571), (13765) are inconsistent by
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2168.
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | |   (13766)  all_55_4 = e1 | all_55_4 = e0
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13766) gives:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13767)  all_55_4 = e1
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (13550), (13767) are inconsistent by
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2166.
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13768)  all_55_4 = e0
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (13768) imply:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13769)  all_53_1 = e0
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (13769) implies:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13770)  all_53_1 = e0
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (150), (13770) imply:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13771)   ~ (all_53_2 = e0)
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (13771) implies:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13772)   ~ (all_53_2 = e0)
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (13770) imply:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13773)   ~ (all_53_3 = e0)
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (147), (13770) imply:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13774)   ~ (all_53_9 = e0)
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (13774) implies:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13775)   ~ (all_53_9 = e0)
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13776)  all_55_8 = e3
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (12085), (13776) are inconsistent by
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2496.
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13777)   ~ (all_55_8 = e3)
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13778)  all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13779)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e0)
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13779) gives:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13780)  all_57_6 = e0 & op(e1, e3) = e0
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13780) implies:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13781)  op(e1, e3) = e0
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (13772), (13781), (function-axioms) are
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2154.
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13782)  all_57_7 = e0 & op(e1, e2) = e0
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13782) implies:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13783)  all_57_7 = e0
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13784)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e1)
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13784) gives:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13785)  all_57_6 = e1 & op(e1, e3) = e1
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (13551), (13785), (function-axioms) are
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #316.
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13786)  all_57_7 = e1 & op(e1, e2) = e1
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13786) implies:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13787)  all_57_7 = e1
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (13783), (13787) are inconsistent by
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2211.
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13788)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e0) = e1)
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13788) gives:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13789)  all_57_8 = e1 & op(e1, e1) = e1
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13789) implies:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13790)  op(e1, e1) = e1
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (12097), (13790), (function-axioms) are
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #156.
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13791)  all_57_11 = e1 & op(e1, e0) = e1
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13791) implies:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13792)  op(e1, e0) = e1
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13778) gives:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13793)  all_55_8 = e2
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (13793) imply:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13794)  all_53_2 = e2
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (13794) implies:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13795)  all_53_2 = e2
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (13795) imply:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13796)   ~ (all_53_3 = e2)
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (13796) implies:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13797)   ~ (all_53_3 = e2)
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13798)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (171), (13553), (13578), (13798),
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #362.
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13799)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13799) gives:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13800)  all_57_7 = e1 & op(e1, e2) = e1
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13800) implies:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13801)  all_57_7 = e1
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (13783), (13801) are inconsistent by
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2211.
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13802)  all_57_13 = e1 & op(e0, e2) = e1
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13802) implies:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13803)  all_57_13 = e1
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13804)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13804) gives:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13805)  all_57_12 = e3 & op(e0, e3) = e3
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13805) implies:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13806)  op(e0, e3) = e3
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13807)  all_55_12 = e3
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (13807) imply:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13808)  all_53_3 = e3
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (13808) implies:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13809)  all_53_3 = e3
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (141), (13809) imply:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13810)   ~ (all_53_7 = e3)
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (13810) implies:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13811)   ~ (all_53_7 = e3)
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13812)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13812) gives:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13813)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_7)
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13813) implies:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13814)  op(e3, e1) = all_52_5
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13815)  op(all_52_5, all_52_5) = e1
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13816)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e0)
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13816) gives:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13817)  all_57_4 = e0 & op(e3, e1) = e0
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13817) implies:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13818)  op(e3, e1) = e0
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (13601), (13814), (13815), (13818),
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2167.
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13819)  all_57_5 = e0 & op(e2, e1) = e0
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (13775), (13819), (function-axioms) are
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2023.
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13820)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (209), (210), (12096),
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13600), (13601), (13803), (13820),
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #128.
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13821)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_15)
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (192), (246), (12097), (13574), (13592), (13764),
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13811), (13821), (function-axioms) are
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #126.
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13822)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_52_21) = e1 & op(all_52_23, all_52_23) =
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(all_52_25, all_52_25) = e3 &
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_52_29) = e1 & op(all_52_31, all_52_31) =
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_29) & $i(all_52_31))
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13822) gives:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13823)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_23)
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13823) implies:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13824)  op(e1, e0) = all_52_23
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13825)  op(all_52_23, all_52_23) = e0
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12097), (13792), (13824), (13825),
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #125.
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13826)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_31)
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13826) implies:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13827)  op(e0, e3) = all_52_25
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13828)  op(all_52_25, all_52_25) = e3
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13829)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e0)
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13829) gives:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13830)  all_57_4 = e0 & op(e3, e1) = e0
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13830) implies:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13831)  op(e3, e1) = e0
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (193), (247), (13548), (13552), (13558),
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13591), (13604), (13827), (13828), (13831),
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #302.
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13832)  all_57_5 = e0 & op(e2, e1) = e0
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (13775), (13832), (function-axioms) are
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2023.
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13833)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (209), (210), (12096),
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13600), (13601), (13803), (13833),
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #128.
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13834)   ~ (all_55_12 = e3)
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (247), (13834) imply:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13835)   ~ (all_53_3 = e3)
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (13806), (13835), (function-axioms) are
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #132.
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13836)  all_57_13 = e3 & op(e0, e2) = e3
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (13836) implies:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13837)  all_57_13 = e3
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (13803), (13837) are inconsistent by
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2268.
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13838)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (207), (211),
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (12089), (13760), (13838),
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #124.
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13839)  all_55_8 = e1 | all_55_8 = e0
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (13551), (13772), (13839) are inconsistent
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1974.
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13840)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13840) gives:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13841)  all_57_8 = e0 & op(e1, e1) = e0
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12096), (13841) are inconsistent by
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #170.
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13842)  all_57_11 = e0 & op(e1, e0) = e0
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (13596), (13842), (function-axioms) are
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2341.
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | |   (13843)  all_57_10 = e1 & op(e2, e0) = e1
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (13760), (13843) are inconsistent by
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2349.
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.34  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | |   (13844)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 224.22/38.35  | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 224.22/38.35  | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 224.22/38.35  | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 224.22/38.35  | | | | | | | | | | | | | | | | | | |                e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (165), (169), (13594), (13595), (13596),
% 224.22/38.35  | | | | | | | | | | | | | | | | | | |            (13844), (function-axioms) are inconsistent by
% 224.22/38.35  | | | | | | | | | | | | | | | | | | |            sub-proof #2112.
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.35  | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | End of split
% 224.22/38.35  | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | End of split
% 224.22/38.35  | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | End of split
% 224.22/38.35  | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | Case 2:
% 224.22/38.35  | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | |   (13845)  all_30_2 = e1
% 224.22/38.35  | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | COMBINE_EQS: (330), (13845) imply:
% 224.22/38.35  | | | | | | | | | | | | | | |   (13846)  all_4_2 = e1
% 224.22/38.35  | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | SIMP: (13846) implies:
% 224.22/38.35  | | | | | | | | | | | | | | |   (13847)  all_4_2 = e1
% 224.22/38.35  | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | REDUCE: (370), (13847) imply:
% 224.22/38.35  | | | | | | | | | | | | | | |   (13848)   ~ (all_53_12 = e1)
% 224.22/38.35  | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | REDUCE: (371), (13847) imply:
% 224.22/38.35  | | | | | | | | | | | | | | |   (13849)   ~ (all_53_13 = e1)
% 224.22/38.35  | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | REDUCE: (372), (13847) imply:
% 224.22/38.35  | | | | | | | | | | | | | | |   (13850)   ~ (all_53_14 = e1)
% 224.22/38.35  | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | REDUCE: (13560), (13847) imply:
% 224.22/38.35  | | | | | | | | | | | | | | |   (13851)   ~ (e3 = e1)
% 224.22/38.35  | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | REDUCE: (373), (13847) imply:
% 224.22/38.35  | | | | | | | | | | | | | | |   (13852)   ~ (e2 = e1)
% 224.22/38.35  | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | REDUCE: (36), (13847) imply:
% 224.22/38.35  | | | | | | | | | | | | | | |   (13853)  op(e0, e0) = e1
% 224.22/38.35  | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 224.22/38.35  | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | Case 1:
% 224.22/38.35  | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | |   (13854)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 224.22/38.35  | | | | | | | | | | | | | | | |              & op(e1, e2) = e1)
% 224.22/38.35  | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | BETA: splitting (13854) gives:
% 224.22/38.35  | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.35  | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | |   (13855)  all_57_6 = e1 & op(e1, e3) = e1
% 224.22/38.35  | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (13551), (13855), (function-axioms) are
% 224.22/38.35  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #316.
% 224.22/38.35  | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.35  | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | |   (13856)  all_57_7 = e1 & op(e1, e2) = e1
% 224.22/38.35  | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | ALPHA: (13856) implies:
% 224.22/38.35  | | | | | | | | | | | | | | | | |   (13857)  op(e1, e2) = e1
% 224.22/38.35  | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 224.22/38.35  | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | |   (13858)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 224.22/38.35  | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 224.22/38.35  | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (168), (13550), (13578), (13858),
% 224.22/38.35  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.22/38.35  | | | | | | | | | | | | | | | | | |            #361.
% 224.22/38.35  | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | |   (13859)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 224.22/38.35  | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 224.22/38.35  | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | BETA: splitting (13859) gives:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | |   (13860)  all_57_5 = e1 & op(e2, e1) = e1
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | ALPHA: (13860) implies:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | |   (13861)  op(e2, e1) = e1
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_6, e1,
% 224.22/38.35  | | | | | | | | | | | | | | | | | | |              e2, e1, simplifying with (163), (13857) gives:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | |   (13862)  all_53_6 = e1
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_9, e1,
% 224.22/38.35  | | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (166), (13861) gives:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | |   (13863)  all_53_9 = e1
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | REDUCE: (127), (13862) imply:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | |   (13864)   ~ (all_53_14 = e1)
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | REDUCE: (118), (13863) imply:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | |   (13865)   ~ (all_53_13 = e1)
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | |   (13866)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | |              all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | |              op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | |                all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | |              $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | |              $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | |                all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | |              & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | |                all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | |              & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | |              $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | BETA: splitting (13866) gives:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | |   (13867)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | |            all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | |            op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | |              all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | |            $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | |            $i(all_52_7)
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | ALPHA: (13867) implies:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | |   (13868)  op(e3, e0) = all_52_7
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | |   (13869)  op(e3, e3) = all_52_1
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | |   (13870)  op(all_52_7, all_52_7) = e0
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_12,
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | |              all_52_7, e0, e3, simplifying with (169), (13868)
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | |              gives:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | |   (13871)  all_53_12 = all_52_7
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_52_1,
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (13558), (13869) gives:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | |   (13872)  all_52_1 = e1
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (13871) imply:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | |   (13873)  all_55_3 = all_52_7
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | REDUCE: (114), (13871) imply:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | |   (13874)   ~ (all_53_13 = all_52_7)
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | SIMP: (13874) implies:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | |   (13875)   ~ (all_53_13 = all_52_7)
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (13871) imply:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | |   (13876)   ~ (all_53_14 = all_52_7)
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | SIMP: (13876) implies:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | |   (13877)   ~ (all_53_14 = all_52_7)
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | REDUCE: (13848), (13871) imply:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | |   (13878)   ~ (all_52_7 = e1)
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | |   (13879)  all_55_4 = e3
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (13879) imply:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | |   (13880)  all_53_1 = e3
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | SIMP: (13880) implies:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | |   (13881)  all_53_1 = e3
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (13881) imply:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | |   (13882)   ~ (all_53_13 = e3)
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | SIMP: (13882) implies:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | |   (13883)   ~ (all_53_13 = e3)
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | |   (13884)  all_55_7 = e3
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (13883), (13884) are inconsistent by
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2109.
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | |   (13885)  all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13885) gives:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | |   (13886)  all_55_7 = e2
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (13576), (13886) are inconsistent by
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2171.
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | |   (13887)  all_55_7 = e1 | all_55_7 = e0
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13887) gives:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (13888)  all_55_7 = e1
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (13849), (13888) are inconsistent by
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1970.
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (13889)  all_55_7 = e0
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (13889) imply:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (13890)  all_53_13 = e0
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (13890) implies:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (13891)  all_53_13 = e0
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (111), (13891) imply:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (13892)   ~ (all_53_14 = e0)
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (13892) implies:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (13893)   ~ (all_53_14 = e0)
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (13849), (13891) imply:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (13894)   ~ (e1 = e0)
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | |   (13895)  all_55_11 = e3
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (13895) imply:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | |   (13896)  all_53_14 = e3
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12090), (13896) imply:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | |   (13897)  $false
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (13897) is inconsistent.
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | |   (13898)  all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13898) gives:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13899)  all_55_11 = e2
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (13899) imply:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13900)  all_53_14 = e2
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (13877), (13900) imply:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13901)   ~ (all_52_7 = e2)
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (13901) implies:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13902)   ~ (all_52_7 = e2)
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13903)  all_55_3 = e3
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (13558), (13868), (13869), (13870), (13873),
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13903), (function-axioms) are inconsistent by
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #122.
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13904)  all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13853), (13868), (13870), (13873), (13878),
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13902), (13904), (function-axioms) are
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #230.
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13905)  all_55_11 = e1 | all_55_11 = e0
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (13850), (13893), (13905) are inconsistent
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2307.
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | |   (13906)  all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13906) gives:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | |   (13907)  all_55_4 = e2
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (13571), (13907) are inconsistent by
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2168.
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | |   (13908)  all_55_4 = e1 | all_55_4 = e0
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13908) gives:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | |   (13909)  all_55_4 = e1
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (13550), (13909) are inconsistent by
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2166.
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | |   (13910)  all_55_4 = e0
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (13910) imply:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | |   (13911)  all_53_1 = e0
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (13911) implies:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | |   (13912)  all_53_1 = e0
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (150), (13912) imply:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | |   (13913)   ~ (all_53_2 = e0)
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (13913) implies:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | |   (13914)   ~ (all_53_2 = e0)
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (13912) imply:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | |   (13915)   ~ (all_53_13 = e0)
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (13915) implies:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | |   (13916)   ~ (all_53_13 = e0)
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (13917)  all_55_8 = e3
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (13917) imply:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (13918)  all_53_2 = e3
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12085), (13918) imply:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (13919)  $false
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (13919) is inconsistent.
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (13920)  all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13920) gives:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | |   (13921)  all_55_8 = e2
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (13921) imply:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | |   (13922)  all_53_2 = e2
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (142), (13922) imply:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | |   (13923)   ~ (all_53_14 = e2)
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (13923) implies:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | |   (13924)   ~ (all_53_14 = e2)
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13925)  all_55_11 = e3
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (12090), (13925) are inconsistent by
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2497.
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13926)  all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13927)  all_55_7 = e3
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (13927) imply:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13928)  all_53_13 = e3
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (13928) implies:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13929)  all_53_13 = e3
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (13875), (13929) imply:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13930)   ~ (all_52_7 = e3)
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (13930) implies:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13931)   ~ (all_52_7 = e3)
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13926) gives:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13932)  all_55_11 = e2
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (13924), (13932) are inconsistent by
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2282.
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13933)  all_55_11 = e1 | all_55_11 = e0
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13933) gives:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13934)  all_55_11 = e1
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (13850), (13934) are inconsistent by
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2309.
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13935)  all_55_11 = e0
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (13935) imply:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13936)  all_53_14 = e0
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (13936) implies:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13937)  all_53_14 = e0
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (13877), (13937) imply:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13938)   ~ (all_52_7 = e0)
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (13938) implies:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13939)   ~ (all_52_7 = e0)
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13940)  all_55_3 = e3
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13873), (13931), (13940) are inconsistent by
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1451.
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13941)  all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13941) gives:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13942)  all_55_3 = e2
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13578), (13870), (13873), (13939), (13942),
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #850.
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13943)  all_55_3 = e1 | all_55_3 = e0
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13873), (13878), (13939), (13943) are
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #121.
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (13944)  all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (13576), (13849), (13916), (13944) are
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #321.
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | |   (13945)  all_55_8 = e1 | all_55_8 = e0
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (13551), (13914), (13945) are inconsistent
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1974.
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | |   (13946)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | |            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | |            op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | |              all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | |            $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | |            $i(all_52_15)
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (12097), (13861), (13946), (function-axioms)
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #120.
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | |   (13947)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | |              & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | |              & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | |                all_52_21) = e1 & op(all_52_23, all_52_23) =
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | |              all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | |              = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | |              $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | |              & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | |              e0 & op(all_52_25, all_52_25) = e3 &
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | |              op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | |                all_52_29) = e1 & op(all_52_31, all_52_31) =
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | |              all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | |              = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | |              $i(all_52_29) & $i(all_52_31))
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (12097), (13853), (13857), (13947),
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | |            #118.
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | |   (13948)  all_57_10 = e1 & op(e2, e0) = e1
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (13849), (13948), (function-axioms) are
% 224.22/38.35  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2084.
% 224.22/38.35  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.35  | | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | | End of split
% 224.22/38.35  | | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | End of split
% 224.22/38.35  | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | Case 2:
% 224.22/38.35  | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | |   (13949)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 224.22/38.35  | | | | | | | | | | | | | | | |              e1 & op(e1, e0) = e1)
% 224.22/38.35  | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | REF_CLOSE: (8), (161), (12097), (13850), (13949),
% 224.22/38.35  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.22/38.35  | | | | | | | | | | | | | | | |            #117.
% 224.22/38.35  | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | End of split
% 224.22/38.35  | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | End of split
% 224.22/38.35  | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | Case 2:
% 224.22/38.35  | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | |   (13950)  all_55_5 = e1 | all_55_5 = e0
% 224.22/38.35  | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | REF_CLOSE: (266), (13562), (13564), (13950) are inconsistent
% 224.22/38.35  | | | | | | | | | | | | | |            by sub-proof #1857.
% 224.22/38.35  | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | End of split
% 224.22/38.35  | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | End of split
% 224.22/38.35  | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | Case 2:
% 224.22/38.35  | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | |   (13951)  all_16_2 = e1
% 224.22/38.35  | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | COMBINE_EQS: (324), (13951) imply:
% 224.22/38.35  | | | | | | | | | | | |   (13952)  all_8_2 = e1
% 224.22/38.35  | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | SIMP: (13952) implies:
% 224.22/38.35  | | | | | | | | | | | |   (13953)  all_8_2 = e1
% 224.22/38.35  | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | REDUCE: (354), (13953) imply:
% 224.22/38.35  | | | | | | | | | | | |   (13954)   ~ (all_53_6 = e1)
% 224.22/38.35  | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | REDUCE: (358), (13953) imply:
% 224.22/38.35  | | | | | | | | | | | |   (13955)   ~ (all_53_9 = e1)
% 224.22/38.35  | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | REDUCE: (12098), (13953) imply:
% 224.22/38.35  | | | | | | | | | | | |   (13956)   ~ (e3 = e1)
% 224.22/38.35  | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | REDUCE: (42), (13953) imply:
% 224.22/38.35  | | | | | | | | | | | |   (13957)  op(e2, e2) = e1
% 224.22/38.35  | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | BETA: splitting (215) gives:
% 224.22/38.35  | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | Case 1:
% 224.22/38.35  | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | |   (13958)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 224.22/38.35  | | | | | | | | | | | | |              & op(e1, e2) = e1)
% 224.22/38.35  | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | BETA: splitting (13958) gives:
% 224.22/38.35  | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | Case 1:
% 224.22/38.35  | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | |   (13959)  all_57_6 = e1 & op(e1, e3) = e1
% 224.22/38.35  | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | REF_CLOSE: (164), (13551), (13959), (function-axioms) are
% 224.22/38.35  | | | | | | | | | | | | | |            inconsistent by sub-proof #316.
% 224.22/38.35  | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | Case 2:
% 224.22/38.35  | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | |   (13960)  all_57_7 = e1 & op(e1, e2) = e1
% 224.22/38.35  | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | REF_CLOSE: (163), (13954), (13960), (function-axioms) are
% 224.22/38.35  | | | | | | | | | | | | | |            inconsistent by sub-proof #2265.
% 224.22/38.35  | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | End of split
% 224.22/38.35  | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | Case 2:
% 224.22/38.35  | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | |   (13961)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 224.22/38.35  | | | | | | | | | | | | |              e1 & op(e1, e0) = e1)
% 224.22/38.35  | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | BETA: splitting (13961) gives:
% 224.22/38.35  | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | Case 1:
% 224.22/38.35  | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | |   (13962)  all_57_8 = e1 & op(e1, e1) = e1
% 224.22/38.35  | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | ALPHA: (13962) implies:
% 224.22/38.35  | | | | | | | | | | | | | |   (13963)  op(e1, e1) = e1
% 224.22/38.35  | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | REF_CLOSE: (8), (12097), (13963), (function-axioms) are
% 224.22/38.35  | | | | | | | | | | | | | |            inconsistent by sub-proof #156.
% 224.22/38.35  | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | Case 2:
% 224.22/38.35  | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | |   (13964)  all_57_11 = e1 & op(e1, e0) = e1
% 224.22/38.35  | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | ALPHA: (13964) implies:
% 224.22/38.35  | | | | | | | | | | | | | |   (13965)  op(e1, e0) = e1
% 224.22/38.35  | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 224.22/38.35  | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | Case 1:
% 224.22/38.35  | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | |   (13966)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 224.22/38.35  | | | | | | | | | | | | | | |              & op(e2, e1) = e1)
% 224.22/38.35  | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | BETA: splitting (13966) gives:
% 224.22/38.35  | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | Case 1:
% 224.22/38.35  | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | |   (13967)  all_57_4 = e1 & op(e3, e1) = e1
% 224.22/38.35  | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | REF_CLOSE: (170), (13554), (13967), (function-axioms) are
% 224.22/38.35  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #116.
% 224.22/38.35  | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | Case 2:
% 224.22/38.35  | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | |   (13968)  all_57_5 = e1 & op(e2, e1) = e1
% 224.22/38.35  | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | REF_CLOSE: (166), (13955), (13968), (function-axioms) are
% 224.22/38.35  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2305.
% 224.22/38.35  | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | End of split
% 224.22/38.35  | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | Case 2:
% 224.22/38.35  | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | |   (13969)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 224.22/38.35  | | | | | | | | | | | | | | |              e1 & op(e0, e1) = e1)
% 224.22/38.35  | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | BETA: splitting (13969) gives:
% 224.22/38.35  | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | Case 1:
% 224.22/38.35  | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | |   (13970)  all_57_8 = e1 & op(e1, e1) = e1
% 224.22/38.35  | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | ALPHA: (13970) implies:
% 224.22/38.35  | | | | | | | | | | | | | | | |   (13971)  op(e1, e1) = e1
% 224.22/38.35  | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | REF_CLOSE: (8), (12097), (13971), (function-axioms) are
% 224.22/38.35  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #156.
% 224.22/38.35  | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | Case 2:
% 224.22/38.35  | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | |   (13972)  all_57_14 = e1 & op(e0, e1) = e1
% 224.22/38.35  | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | ALPHA: (13972) implies:
% 224.22/38.35  | | | | | | | | | | | | | | | |   (13973)  all_57_14 = e1
% 224.22/38.35  | | | | | | | | | | | | | | | |   (13974)  op(e0, e1) = e1
% 224.22/38.35  | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_11,
% 224.22/38.35  | | | | | | | | | | | | | | | |              e1, e1, e0, simplifying with (158), (13974) gives:
% 224.22/38.35  | | | | | | | | | | | | | | | |   (13975)  all_53_11 = e1
% 224.22/38.35  | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_14,
% 224.22/38.35  | | | | | | | | | | | | | | | |              e1, e0, e1, simplifying with (161), (13965) gives:
% 224.22/38.35  | | | | | | | | | | | | | | | |   (13976)  all_53_14 = e1
% 224.22/38.35  | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | REDUCE: (372), (13976) imply:
% 224.22/38.35  | | | | | | | | | | | | | | | |   (13977)   ~ (all_4_2 = e1)
% 224.22/38.35  | | | | | | | | | | | | | | | | 
% 224.22/38.35  | | | | | | | | | | | | | | | | SIMP: (13977) implies:
% 224.22/38.35  | | | | | | | | | | | | | | | |   (13978)   ~ (all_4_2 = e1)
% 224.22/38.36  | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 224.22/38.36  | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.36  | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | |   (13979)  all_55_15 = e3
% 224.22/38.36  | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (13560), (13979) are inconsistent by
% 224.22/38.36  | | | | | | | | | | | | | | | | |            sub-proof #2503.
% 224.22/38.36  | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.36  | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | |   (13980)   ~ (all_55_15 = e3)
% 224.22/38.36  | | | | | | | | | | | | | | | | |   (13981)  all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 224.22/38.36  | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 224.22/38.36  | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.36  | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | |   (13982)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 224.22/38.36  | | | | | | | | | | | | | | | | | |              all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 224.22/38.36  | | | | | | | | | | | | | | | | | |              op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 224.22/38.36  | | | | | | | | | | | | | | | | | |                all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 224.22/38.36  | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 224.22/38.36  | | | | | | | | | | | | | | | | | |              op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 224.22/38.36  | | | | | | | | | | | | | | | | | |              $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 224.22/38.36  | | | | | | | | | | | | | | | | | |              $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 224.22/38.36  | | | | | | | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 224.22/38.36  | | | | | | | | | | | | | | | | | |                all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 224.22/38.36  | | | | | | | | | | | | | | | | | |              & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 224.22/38.36  | | | | | | | | | | | | | | | | | |                all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 224.22/38.36  | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 224.22/38.36  | | | | | | | | | | | | | | | | | |              & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 224.22/38.36  | | | | | | | | | | | | | | | | | |              $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 224.22/38.36  | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | BETA: splitting (13982) gives:
% 224.22/38.36  | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | |   (13983)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 224.22/38.36  | | | | | | | | | | | | | | | | | | |            all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 224.22/38.36  | | | | | | | | | | | | | | | | | | |            op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 224.22/38.36  | | | | | | | | | | | | | | | | | | |              all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 224.22/38.36  | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 224.22/38.36  | | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 224.22/38.36  | | | | | | | | | | | | | | | | | | |            $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 224.22/38.36  | | | | | | | | | | | | | | | | | | |            $i(all_52_7)
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | ALPHA: (13983) implies:
% 224.22/38.36  | | | | | | | | | | | | | | | | | | |   (13984)  op(e3, e1) = all_52_5
% 224.22/38.36  | | | | | | | | | | | | | | | | | | |   (13985)  op(e3, e2) = all_52_3
% 224.22/38.36  | | | | | | | | | | | | | | | | | | |   (13986)  op(all_52_5, all_52_5) = e1
% 224.22/38.36  | | | | | | | | | | | | | | | | | | |   (13987)  op(all_52_3, all_52_3) = e2
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | BETA: splitting (13981) gives:
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | |   (13988)  all_55_15 = e2
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (373), (13988) are inconsistent by
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | |            sub-proof #2502.
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | |   (13989)   ~ (all_55_15 = e2)
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | |   (13990)  all_55_15 = e1 | all_55_15 = e0
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | BETA: splitting (13990) gives:
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | |   (13991)  all_55_15 = e1
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (13978), (13991) are inconsistent by
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | |            sub-proof #2501.
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | |   (13992)  all_55_15 = e0
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (13992) imply:
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | |   (13993)  all_4_2 = e0
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | SIMP: (13993) implies:
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | |   (13994)  all_4_2 = e0
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | REDUCE: (351), (13994) imply:
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | |   (13995)   ~ (all_53_3 = e0)
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | REDUCE: (362), (13994) imply:
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | |   (13996)   ~ (all_53_7 = e0)
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | REDUCE: (370), (13994) imply:
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | |   (13997)   ~ (all_53_12 = e0)
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | REDUCE: (13560), (13994) imply:
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | |   (13998)   ~ (e3 = e0)
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | REDUCE: (373), (13994) imply:
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | |   (13999)   ~ (e2 = e0)
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | REDUCE: (13978), (13994) imply:
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | |   (14000)   ~ (e1 = e0)
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | |   (14001)  all_57_15 = e0 & op(e0, e0) = e0
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14001) implies:
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | |   (14002)  all_57_15 = e0
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | |   (14003)  op(e0, e0) = e0
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (169), (208),
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | |            (209), (210), (231), (13552), (13557), (13973),
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | |            (13984), (13985), (13986), (13987), (13997),
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | |            (14002), (14003), (function-axioms) are
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #319.
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | |   (14004)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14004) implies:
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | |   (14005)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | |                e1) = e0)
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (159), (160), (13973), (13995), (13996),
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | |            (14005), (function-axioms) are inconsistent by
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #115.
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | |   (14006)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 224.22/38.36  | | | | | | | | | | | | | | | | | | |            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 224.22/38.36  | | | | | | | | | | | | | | | | | | |            op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 224.22/38.36  | | | | | | | | | | | | | | | | | | |              all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 224.22/38.36  | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 224.22/38.36  | | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 224.22/38.36  | | | | | | | | | | | | | | | | | | |            $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 224.22/38.36  | | | | | | | | | | | | | | | | | | |            $i(all_52_15)
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | ALPHA: (14006) implies:
% 224.22/38.36  | | | | | | | | | | | | | | | | | | |   (14007)  op(e2, e2) = all_52_11
% 224.22/38.36  | | | | | | | | | | | | | | | | | | |   (14008)  op(all_52_11, all_52_11) = e2
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (12097), (13957), (14007), (14008),
% 224.22/38.36  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.22/38.36  | | | | | | | | | | | | | | | | | | |            #155.
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.36  | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.36  | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | |   (14009)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 224.22/38.36  | | | | | | | | | | | | | | | | | |              & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 224.22/38.36  | | | | | | | | | | | | | | | | | |              & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 224.22/38.36  | | | | | | | | | | | | | | | | | |                all_52_21) = e1 & op(all_52_23, all_52_23) =
% 224.22/38.36  | | | | | | | | | | | | | | | | | |              e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 224.22/38.36  | | | | | | | | | | | | | | | | | |              all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 224.22/38.36  | | | | | | | | | | | | | | | | | |              = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 224.22/38.36  | | | | | | | | | | | | | | | | | |              $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 224.22/38.36  | | | | | | | | | | | | | | | | | |              & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 224.22/38.36  | | | | | | | | | | | | | | | | | |              e0 & op(all_52_25, all_52_25) = e3 &
% 224.22/38.36  | | | | | | | | | | | | | | | | | |              op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 224.22/38.36  | | | | | | | | | | | | | | | | | |                all_52_29) = e1 & op(all_52_31, all_52_31) =
% 224.22/38.36  | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 224.22/38.36  | | | | | | | | | | | | | | | | | |              all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 224.22/38.36  | | | | | | | | | | | | | | | | | |              = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 224.22/38.36  | | | | | | | | | | | | | | | | | |              $i(all_52_29) & $i(all_52_31))
% 224.22/38.36  | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | BETA: splitting (14009) gives:
% 224.22/38.36  | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | |   (14010)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 224.22/38.36  | | | | | | | | | | | | | | | | | | |            all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 224.22/38.36  | | | | | | | | | | | | | | | | | | |            op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 224.22/38.36  | | | | | | | | | | | | | | | | | | |              all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 224.22/38.36  | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 224.22/38.36  | | | | | | | | | | | | | | | | | | |            & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 224.22/38.36  | | | | | | | | | | | | | | | | | | |            & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 224.22/38.36  | | | | | | | | | | | | | | | | | | |            $i(all_52_23)
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | ALPHA: (14010) implies:
% 224.22/38.36  | | | | | | | | | | | | | | | | | | |   (14011)  op(e1, e0) = all_52_23
% 224.22/38.36  | | | | | | | | | | | | | | | | | | |   (14012)  op(all_52_23, all_52_23) = e0
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12097), (13965), (14011), (14012),
% 224.22/38.36  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.22/38.36  | | | | | | | | | | | | | | | | | | |            #125.
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | |   (14013)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 224.22/38.36  | | | | | | | | | | | | | | | | | | |            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 224.22/38.36  | | | | | | | | | | | | | | | | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 224.22/38.36  | | | | | | | | | | | | | | | | | | |              all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 224.22/38.36  | | | | | | | | | | | | | | | | | | |            & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 224.22/38.36  | | | | | | | | | | | | | | | | | | |            & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 224.22/38.36  | | | | | | | | | | | | | | | | | | |            & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 224.22/38.36  | | | | | | | | | | | | | | | | | | |            $i(all_52_31)
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | ALPHA: (14013) implies:
% 224.22/38.36  | | | | | | | | | | | | | | | | | | |   (14014)  op(e0, e1) = all_52_29
% 224.22/38.36  | | | | | | | | | | | | | | | | | | |   (14015)  op(all_52_29, all_52_29) = e1
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (244), (373), (12097), (13974), (13981),
% 224.22/38.36  | | | | | | | | | | | | | | | | | | |            (14014), (14015), (function-axioms) are
% 224.22/38.36  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #130.
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.36  | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | End of split
% 224.22/38.36  | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | End of split
% 224.22/38.36  | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | End of split
% 224.22/38.36  | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | End of split
% 224.22/38.36  | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | End of split
% 224.22/38.36  | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | End of split
% 224.22/38.36  | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | End of split
% 224.22/38.36  | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | Case 2:
% 224.22/38.36  | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | |   (14016)  all_14_2 = e0
% 224.22/38.36  | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | COMBINE_EQS: (328), (14016) imply:
% 224.22/38.36  | | | | | | | | | | |   (14017)  all_8_2 = e0
% 224.22/38.36  | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | SIMP: (14017) implies:
% 224.22/38.36  | | | | | | | | | | |   (14018)  all_8_2 = e0
% 224.22/38.36  | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | REDUCE: (349), (14018) imply:
% 224.22/38.36  | | | | | | | | | | |   (14019)   ~ (all_53_1 = e0)
% 224.22/38.36  | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | REDUCE: (352), (14018) imply:
% 224.22/38.36  | | | | | | | | | | |   (14020)   ~ (all_53_4 = e0)
% 224.22/38.36  | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | REDUCE: (354), (14018) imply:
% 224.22/38.36  | | | | | | | | | | |   (14021)   ~ (all_53_6 = e0)
% 224.22/38.36  | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | REDUCE: (356), (14018) imply:
% 224.22/38.36  | | | | | | | | | | |   (14022)   ~ (all_53_7 = e0)
% 224.22/38.36  | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | REDUCE: (358), (14018) imply:
% 224.22/38.36  | | | | | | | | | | |   (14023)   ~ (all_53_9 = e0)
% 224.22/38.36  | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | REDUCE: (12098), (14018) imply:
% 224.22/38.36  | | | | | | | | | | |   (14024)   ~ (e3 = e0)
% 224.22/38.36  | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | BETA: splitting (226) gives:
% 224.22/38.36  | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | Case 1:
% 224.22/38.36  | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | |   (14025)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 224.22/38.36  | | | | | | | | | | | |              & op(e2, e2) = e0)
% 224.22/38.36  | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | BETA: splitting (14025) gives:
% 224.22/38.36  | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | Case 1:
% 224.22/38.36  | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | |   (14026)  all_57_1 = e0 & op(e3, e2) = e0
% 224.22/38.36  | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | ALPHA: (14026) implies:
% 224.22/38.36  | | | | | | | | | | | | |   (14027)  op(e3, e2) = e0
% 224.22/38.36  | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | REF_CLOSE: (171), (14020), (14027), (function-axioms) are
% 224.22/38.36  | | | | | | | | | | | | |            inconsistent by sub-proof #1941.
% 224.22/38.36  | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | Case 2:
% 224.22/38.36  | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | |   (14028)  all_57_3 = e0 & op(e2, e2) = e0
% 224.22/38.36  | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | ALPHA: (14028) implies:
% 224.22/38.36  | | | | | | | | | | | | |   (14029)  all_57_3 = e0
% 224.22/38.36  | | | | | | | | | | | | |   (14030)  op(e2, e2) = e0
% 224.22/38.36  | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | BETA: splitting (76) gives:
% 224.22/38.36  | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | Case 1:
% 224.22/38.36  | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | |   (14031)   ~ (all_30_2 = e1)
% 224.22/38.36  | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | REDUCE: (330), (14031) imply:
% 224.22/38.36  | | | | | | | | | | | | | |   (14032)   ~ (all_4_2 = e1)
% 224.22/38.36  | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 224.22/38.36  | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | Case 1:
% 224.22/38.36  | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | |   (14033)  all_55_15 = e3
% 224.22/38.36  | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | COMBINE_EQS: (244), (14033) imply:
% 224.22/38.36  | | | | | | | | | | | | | | |   (14034)  all_4_2 = e3
% 224.22/38.36  | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | REDUCE: (13560), (14034) imply:
% 224.22/38.36  | | | | | | | | | | | | | | |   (14035)  $false
% 224.22/38.36  | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | CLOSE: (14035) is inconsistent.
% 224.22/38.36  | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | Case 2:
% 224.22/38.36  | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | |   (14036)   ~ (all_55_15 = e3)
% 224.22/38.36  | | | | | | | | | | | | | | |   (14037)  all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 224.22/38.36  | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | BETA: splitting (14037) gives:
% 224.22/38.36  | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | Case 1:
% 224.22/38.36  | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | |   (14038)  all_55_15 = e2
% 224.22/38.36  | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (14038) imply:
% 224.22/38.36  | | | | | | | | | | | | | | | |   (14039)  all_4_2 = e2
% 224.22/38.36  | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | REDUCE: (373), (14039) imply:
% 224.22/38.36  | | | | | | | | | | | | | | | |   (14040)  $false
% 224.22/38.36  | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | CLOSE: (14040) is inconsistent.
% 224.22/38.36  | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | Case 2:
% 224.22/38.36  | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | |   (14041)   ~ (all_55_15 = e2)
% 224.22/38.36  | | | | | | | | | | | | | | | |   (14042)  all_55_15 = e1 | all_55_15 = e0
% 224.22/38.36  | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | BETA: splitting (14042) gives:
% 224.22/38.36  | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.36  | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | |   (14043)  all_55_15 = e1
% 224.22/38.36  | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (14043) imply:
% 224.22/38.36  | | | | | | | | | | | | | | | | |   (14044)  all_4_2 = e1
% 224.22/38.36  | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | REDUCE: (14032), (14044) imply:
% 224.22/38.36  | | | | | | | | | | | | | | | | |   (14045)  $false
% 224.22/38.36  | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | CLOSE: (14045) is inconsistent.
% 224.22/38.36  | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.36  | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | |   (14046)  all_55_15 = e0
% 224.22/38.36  | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (14046) imply:
% 224.22/38.36  | | | | | | | | | | | | | | | | |   (14047)  all_4_2 = e0
% 224.22/38.36  | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | REDUCE: (370), (14047) imply:
% 224.22/38.36  | | | | | | | | | | | | | | | | |   (14048)   ~ (all_53_12 = e0)
% 224.22/38.36  | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | REDUCE: (371), (14047) imply:
% 224.22/38.36  | | | | | | | | | | | | | | | | |   (14049)   ~ (all_53_13 = e0)
% 224.22/38.36  | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | REDUCE: (372), (14047) imply:
% 224.22/38.36  | | | | | | | | | | | | | | | | |   (14050)   ~ (all_53_14 = e0)
% 224.22/38.36  | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | REDUCE: (373), (14047) imply:
% 224.22/38.36  | | | | | | | | | | | | | | | | |   (14051)   ~ (e2 = e0)
% 224.22/38.36  | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | REDUCE: (14032), (14047) imply:
% 224.22/38.36  | | | | | | | | | | | | | | | | |   (14052)   ~ (e1 = e0)
% 224.22/38.36  | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 224.22/38.36  | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.36  | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | |   (14053)  all_57_15 = e0 & op(e0, e0) = e0
% 224.22/38.36  | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | ALPHA: (14053) implies:
% 224.22/38.36  | | | | | | | | | | | | | | | | | |   (14054)  all_57_15 = e0
% 224.22/38.36  | | | | | | | | | | | | | | | | | |   (14055)  op(e0, e0) = e0
% 224.22/38.36  | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 224.22/38.36  | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | |   (14056)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 224.22/38.36  | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e0)
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | BETA: splitting (14056) gives:
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | |   (14057)  all_57_6 = e0 & op(e1, e3) = e0
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | ALPHA: (14057) implies:
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | |   (14058)  op(e1, e3) = e0
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (85), (107), (145),
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | |            (160), (164), (166), (170), (193), (208), (209),
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | |            (210), (218), (247), (12096), (13548), (13549),
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | |            (13552), (13554), (13558), (14023), (14030),
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | |            (14054), (14055), (14058), (function-axioms) are
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #114.
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | |   (14059)  all_57_7 = e0 & op(e1, e2) = e0
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (14021), (14059), (function-axioms) are
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2039.
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | |   (14060)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 224.22/38.36  | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | BETA: splitting (14060) gives:
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | |   (14061)  all_57_8 = e0 & op(e1, e1) = e0
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12096), (14061) are inconsistent by
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | |            sub-proof #170.
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | |   (14062)  all_57_11 = e0 & op(e1, e0) = e0
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (14050), (14062), (function-axioms) are
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2341.
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.36  | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.36  | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | |   (14063)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 224.22/38.36  | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 224.22/38.36  | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 224.22/38.36  | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 224.22/38.36  | | | | | | | | | | | | | | | | | |                e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 224.22/38.36  | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (165), (169), (14048), (14049), (14050),
% 224.22/38.36  | | | | | | | | | | | | | | | | | |            (14063), (function-axioms) are inconsistent by
% 224.22/38.36  | | | | | | | | | | | | | | | | | |            sub-proof #2112.
% 224.22/38.36  | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | End of split
% 224.22/38.36  | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | End of split
% 224.22/38.36  | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | End of split
% 224.22/38.36  | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | End of split
% 224.22/38.36  | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | Case 2:
% 224.22/38.36  | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | |   (14064)  all_30_2 = e1
% 224.22/38.36  | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | COMBINE_EQS: (330), (14064) imply:
% 224.22/38.36  | | | | | | | | | | | | | |   (14065)  all_4_2 = e1
% 224.22/38.36  | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | SIMP: (14065) implies:
% 224.22/38.36  | | | | | | | | | | | | | |   (14066)  all_4_2 = e1
% 224.22/38.36  | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | REDUCE: (371), (14066) imply:
% 224.22/38.36  | | | | | | | | | | | | | |   (14067)   ~ (all_53_13 = e1)
% 224.22/38.36  | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | REDUCE: (372), (14066) imply:
% 224.22/38.36  | | | | | | | | | | | | | |   (14068)   ~ (all_53_14 = e1)
% 224.22/38.36  | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | REDUCE: (13560), (14066) imply:
% 224.22/38.36  | | | | | | | | | | | | | |   (14069)   ~ (e3 = e1)
% 224.22/38.36  | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | REDUCE: (373), (14066) imply:
% 224.22/38.36  | | | | | | | | | | | | | |   (14070)   ~ (e2 = e1)
% 224.22/38.36  | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | REDUCE: (36), (14066) imply:
% 224.22/38.36  | | | | | | | | | | | | | |   (14071)  op(e0, e0) = e1
% 224.22/38.36  | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 224.22/38.36  | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | Case 1:
% 224.22/38.36  | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | |   (14072)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 224.22/38.36  | | | | | | | | | | | | | | |              & op(e1, e2) = e1)
% 224.22/38.36  | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | BETA: splitting (14072) gives:
% 224.22/38.36  | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | Case 1:
% 224.22/38.36  | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | |   (14073)  all_57_6 = e1 & op(e1, e3) = e1
% 224.22/38.36  | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | REF_CLOSE: (164), (13551), (14073), (function-axioms) are
% 224.22/38.36  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #316.
% 224.22/38.36  | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | Case 2:
% 224.22/38.36  | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | |   (14074)  all_57_7 = e1 & op(e1, e2) = e1
% 224.22/38.36  | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | ALPHA: (14074) implies:
% 224.22/38.36  | | | | | | | | | | | | | | | |   (14075)  all_57_7 = e1
% 224.22/38.36  | | | | | | | | | | | | | | | |   (14076)  op(e1, e2) = e1
% 224.22/38.36  | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 224.22/38.36  | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.36  | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | |   (14077)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 224.22/38.36  | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 224.22/38.36  | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (168), (13550), (14030), (14077),
% 224.22/38.36  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.22/38.36  | | | | | | | | | | | | | | | | |            #299.
% 224.22/38.36  | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.36  | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | |   (14078)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 224.22/38.36  | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 224.22/38.36  | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | BETA: splitting (14078) gives:
% 224.22/38.36  | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.36  | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | |   (14079)  all_57_5 = e1 & op(e2, e1) = e1
% 224.22/38.36  | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | ALPHA: (14079) implies:
% 224.22/38.36  | | | | | | | | | | | | | | | | | |   (14080)  all_57_5 = e1
% 224.22/38.36  | | | | | | | | | | | | | | | | | |   (14081)  op(e2, e1) = e1
% 224.22/38.36  | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_6, e1,
% 224.22/38.36  | | | | | | | | | | | | | | | | | |              e2, e1, simplifying with (163), (14076) gives:
% 224.22/38.36  | | | | | | | | | | | | | | | | | |   (14082)  all_53_6 = e1
% 224.22/38.36  | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_9, e1,
% 224.22/38.36  | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (166), (14081) gives:
% 224.22/38.36  | | | | | | | | | | | | | | | | | |   (14083)  all_53_9 = e1
% 224.22/38.36  | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 224.22/38.36  | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | |   (14084)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 224.22/38.36  | | | | | | | | | | | | | | | | | | |              all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 224.22/38.36  | | | | | | | | | | | | | | | | | | |              op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 224.22/38.36  | | | | | | | | | | | | | | | | | | |                all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 224.22/38.36  | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 224.22/38.36  | | | | | | | | | | | | | | | | | | |              op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 224.22/38.36  | | | | | | | | | | | | | | | | | | |              $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 224.22/38.36  | | | | | | | | | | | | | | | | | | |              $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 224.22/38.36  | | | | | | | | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 224.22/38.36  | | | | | | | | | | | | | | | | | | |                all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 224.22/38.36  | | | | | | | | | | | | | | | | | | |              & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 224.22/38.36  | | | | | | | | | | | | | | | | | | |                all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 224.22/38.36  | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 224.22/38.36  | | | | | | | | | | | | | | | | | | |              & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 224.22/38.36  | | | | | | | | | | | | | | | | | | |              $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | BETA: splitting (14084) gives:
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | |   (14085)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | |            all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | |            op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | |              all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | |            $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | |            $i(all_52_7)
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | ALPHA: (14085) implies:
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | |   (14086)  op(e3, e0) = all_52_7
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | |   (14087)  op(e3, e3) = all_52_1
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | |   (14088)  op(all_52_7, all_52_7) = e0
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_12,
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | |              all_52_7, e0, e3, simplifying with (169), (14086)
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | |              gives:
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | |   (14089)  all_53_12 = all_52_7
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_52_1,
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (13558), (14087) gives:
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | |   (14090)  all_52_1 = e1
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | |   (14091)  all_55_4 = e3
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (14091) imply:
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | |   (14092)  all_53_1 = e3
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | SIMP: (14092) implies:
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | |   (14093)  all_53_1 = e3
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (14093) imply:
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | |   (14094)   ~ (all_53_3 = e3)
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | SIMP: (14094) implies:
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | |   (14095)   ~ (all_53_3 = e3)
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (14093) imply:
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | |   (14096)   ~ (all_53_13 = e3)
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | SIMP: (14096) implies:
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | |   (14097)   ~ (all_53_13 = e3)
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | |   (14098)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14098) gives:
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | | |   (14099)  all_57_12 = e3 & op(e0, e3) = e3
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14099) implies:
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | | |   (14100)  op(e0, e3) = e3
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (14095), (14100), (function-axioms) are
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #132.
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | | |   (14101)  all_57_13 = e3 & op(e0, e2) = e3
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14101) implies:
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | | |   (14102)  all_57_13 = e3
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (159), (161), (165),
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | | |            (207), (208), (209), (213), (12090), (13558),
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | | |            (14022), (14086), (14087), (14088), (14097),
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | | |            (14102), (function-axioms) are inconsistent by
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #112.
% 224.22/38.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | |   (14103)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14103) gives:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | |   (14104)  all_57_14 = e3 & op(e0, e1) = e3
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (12089), (14104), (function-axioms) are
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #129.
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | |   (14105)  all_57_15 = e3 & op(e0, e0) = e3
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14105) implies:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | |   (14106)  op(e0, e0) = e3
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (14071), (14106), (function-axioms) are
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2183.
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | |   (14107)   ~ (all_55_4 = e3)
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | |   (14108)  all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | REDUCE: (267), (14107) imply:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | |   (14109)   ~ (all_53_1 = e3)
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14108) gives:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | |   (14110)  all_55_4 = e2
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (14110) imply:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | |   (14111)  all_53_1 = e2
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | SIMP: (14111) implies:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | |   (14112)  all_53_1 = e2
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (150), (14112) imply:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | |   (14113)   ~ (all_53_2 = e2)
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | SIMP: (14113) implies:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | |   (14114)   ~ (all_53_2 = e2)
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (14112) imply:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | |   (14115)   ~ (all_53_13 = e2)
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | SIMP: (14115) implies:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | |   (14116)   ~ (all_53_13 = e2)
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14109), (14112) imply:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | |   (14117)   ~ (e3 = e2)
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | |   (14118)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e2)
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14118) gives:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | |   (14119)  all_57_6 = e2 & op(e1, e3) = e2
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14119) implies:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | |   (14120)  all_57_6 = e2
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | |   (14121)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14121) gives:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | |   (14122)  all_57_2 = e2 & op(e2, e3) = e2
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14122) implies:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | |   (14123)  all_57_2 = e2
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14124)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e3)
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14124) gives:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14125)  all_57_2 = e3 & op(e2, e3) = e3
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14125) implies:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14126)  all_57_2 = e3
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (145), (160), (197), (230), (257),
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12085), (13551), (13557), (14114), (14120),
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14126), (function-axioms) are inconsistent by
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #131.
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14127)  all_57_3 = e3 & op(e2, e2) = e3
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14127) implies:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14128)  op(e2, e2) = e3
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (12098), (14128), (function-axioms) are
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #140.
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14129)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14129) gives:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14130)  all_57_5 = e3 & op(e2, e1) = e3
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (12088), (14130), (function-axioms) are
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #270.
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14131)  all_57_10 = e3 & op(e2, e0) = e3
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14131) implies:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14132)  all_57_10 = e3
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14133)  all_55_8 = e3
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (12085), (14133) are inconsistent by
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2496.
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14134)  all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14134) gives:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14135)  all_55_8 = e2
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (14114), (14135) are inconsistent by
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2406.
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14136)  all_55_8 = e1 | all_55_8 = e0
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14137)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e0)
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14137) gives:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14138)  all_57_0 = e0 & op(e3, e3) = e0
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14138) implies:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14139)  all_57_0 = e0
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13557), (14139) imply:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14140)  e1 = e0
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14080), (14140) imply:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14141)  all_57_5 = e0
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14029), (14030), (14132), (14141),
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2348.
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14142)  all_57_2 = e0 & op(e2, e3) = e0
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14142) implies:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14143)  all_57_2 = e0
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (223), (224), (14029),
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14132), (14143) are inconsistent by sub-proof
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2247.
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14144)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = e0)
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14144) gives:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14145)  all_57_6 = e0 & op(e1, e3) = e0
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14145) implies:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14146)  all_57_6 = e0
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14120), (14146) imply:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14147)  e2 = e0
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14123), (14147) imply:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14148)  all_57_2 = e0
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (223), (224), (14029),
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14132), (14148) are inconsistent by sub-proof
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2247.
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14149)  all_57_12 = e0 & op(e0, e3) = e0
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14149) implies:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14150)  op(e0, e3) = e0
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (145), (160), (257), (13551), (14136), (14150),
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2365.
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | |   (14151)  all_57_3 = e2 & op(e2, e2) = e2
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14151) implies:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | |   (14152)  op(e2, e2) = e2
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (14030), (14152), (function-axioms) are
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2472.
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | |   (14153)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14153) gives:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | |   (14154)  all_57_5 = e2 & op(e2, e1) = e2
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (14080), (14154) are inconsistent by
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2251.
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | |   (14155)  all_57_10 = e2 & op(e2, e0) = e2
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (14116), (14155), (function-axioms) are
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2432.
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | |   (14156)  all_57_7 = e2 & op(e1, e2) = e2
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14156) implies:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | |   (14157)  all_57_7 = e2
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (14075), (14157) are inconsistent by
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1761.
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | |   (14158)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e1, e0) = e2)
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14158) gives:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | |   (14159)  all_57_8 = e2 & op(e1, e1) = e2
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (12096), (14159) are inconsistent by
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #172.
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | |   (14160)  all_57_11 = e2 & op(e1, e0) = e2
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14160) implies:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | |   (14161)  all_57_11 = e2
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | |   (14162)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14162) gives:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | |   (14163)  all_57_2 = e2 & op(e2, e3) = e2
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14163) implies:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | |   (14164)  all_57_2 = e2
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14165)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e3)
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (168), (12098), (14109), (14165),
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #111.
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14166)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14166) gives:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14167)  all_57_5 = e3 & op(e2, e1) = e3
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (12088), (14167), (function-axioms) are
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #270.
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14168)  all_57_10 = e3 & op(e2, e0) = e3
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14168) implies:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14169)  all_57_10 = e3
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14170)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e0)
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14170) gives:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14171)  all_57_6 = e0 & op(e1, e3) = e0
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14171) implies:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14172)  op(e1, e3) = e0
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14173)  all_57_15 = e0 & op(e0, e0) = e0
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14173) implies:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14174)  all_57_15 = e0
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14175)  op(e0, e0) = e0
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (85), (107), (145),
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (160), (164), (166), (170), (193), (208), (209),
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (210), (218), (247), (12096), (13548), (13549),
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (13552), (13554), (13558), (14023), (14030),
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14172), (14174), (14175), (function-axioms) are
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #114.
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14176)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14176) implies:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14177)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0)
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14177) gives:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14178)  all_57_9 = e0 & op(e3, e0) = e0
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14178) implies:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14179)  op(e3, e0) = e0
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (14071), (14086), (14088), (14179),
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2000.
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14180)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 =
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14180) gives:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14181)  all_57_10 = e0 & op(e2, e0) = e0
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (14169), (14181) are inconsistent by
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1981.
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14182)  all_57_11 = e0 & op(e1, e0) = e0
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (14161), (14182) are inconsistent by
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2041.
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14183)  all_57_7 = e0 & op(e1, e2) = e0
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (14021), (14183), (function-axioms) are
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2039.
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14184)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14184) gives:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14185)  all_57_8 = e0 & op(e1, e1) = e0
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12096), (14185) are inconsistent by
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #162.
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14186)  all_57_11 = e0 & op(e1, e0) = e0
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14186) implies:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14187)  all_57_11 = e0
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14161), (14187) imply:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14188)  e2 = e0
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14164), (14188) imply:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14189)  all_57_2 = e0
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (223), (224), (14029),
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14169), (14189) are inconsistent by sub-proof
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2247.
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | |   (14190)  all_57_3 = e2 & op(e2, e2) = e2
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14190) implies:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | |   (14191)  op(e2, e2) = e2
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (14030), (14191), (function-axioms) are
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2472.
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | |   (14192)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14192) gives:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | |   (14193)  all_57_5 = e2 & op(e2, e1) = e2
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (14080), (14193) are inconsistent by
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2251.
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | |   (14194)  all_57_10 = e2 & op(e2, e0) = e2
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (14116), (14194), (function-axioms) are
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2432.
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | |   (14195)  all_55_4 = e1 | all_55_4 = e0
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (13550), (14019), (14195) are inconsistent
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #773.
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | |   (14196)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | |            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | |            op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | |              all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | |            $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | |            $i(all_52_15)
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (12097), (14081), (14196), (function-axioms)
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #120.
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | |   (14197)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 224.22/38.37  | | | | | | | | | | | | | | | | | | |              & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 224.22/38.37  | | | | | | | | | | | | | | | | | | |              & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 224.22/38.37  | | | | | | | | | | | | | | | | | | |                all_52_21) = e1 & op(all_52_23, all_52_23) =
% 224.22/38.37  | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 224.22/38.37  | | | | | | | | | | | | | | | | | | |              all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 224.22/38.37  | | | | | | | | | | | | | | | | | | |              = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 224.22/38.37  | | | | | | | | | | | | | | | | | | |              $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 224.22/38.37  | | | | | | | | | | | | | | | | | | |              & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 224.22/38.37  | | | | | | | | | | | | | | | | | | |              e0 & op(all_52_25, all_52_25) = e3 &
% 224.22/38.37  | | | | | | | | | | | | | | | | | | |              op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 224.22/38.37  | | | | | | | | | | | | | | | | | | |                all_52_29) = e1 & op(all_52_31, all_52_31) =
% 224.22/38.37  | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 224.22/38.37  | | | | | | | | | | | | | | | | | | |              all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 224.22/38.37  | | | | | | | | | | | | | | | | | | |              = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 224.22/38.37  | | | | | | | | | | | | | | | | | | |              $i(all_52_29) & $i(all_52_31))
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (12097), (14071), (14076), (14197),
% 224.22/38.37  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.22/38.37  | | | | | | | | | | | | | | | | | | |            #118.
% 224.22/38.37  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.37  | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.37  | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | |   (14198)  all_57_10 = e1 & op(e2, e0) = e1
% 224.22/38.37  | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (14067), (14198), (function-axioms) are
% 224.22/38.37  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2084.
% 224.22/38.37  | | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | | End of split
% 224.22/38.37  | | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | | End of split
% 224.22/38.37  | | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | End of split
% 224.22/38.37  | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | Case 2:
% 224.22/38.37  | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | |   (14199)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 224.22/38.37  | | | | | | | | | | | | | | |              e1 & op(e1, e0) = e1)
% 224.22/38.37  | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | | REF_CLOSE: (8), (161), (12097), (14068), (14199),
% 224.22/38.37  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.22/38.37  | | | | | | | | | | | | | | |            #117.
% 224.22/38.37  | | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | End of split
% 224.22/38.37  | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | End of split
% 224.22/38.37  | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | End of split
% 224.22/38.37  | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | Case 2:
% 224.22/38.37  | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | |   (14200)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 224.22/38.37  | | | | | | | | | | | |              e0 & op(e0, e2) = e0)
% 224.22/38.37  | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | REF_CLOSE: (159), (163), (14021), (14022), (14200),
% 224.22/38.37  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.22/38.37  | | | | | | | | | | | |            #2024.
% 224.22/38.37  | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | End of split
% 224.22/38.37  | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | End of split
% 224.22/38.37  | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | Case 2:
% 224.22/38.37  | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | |   (14201)  all_12_2 = e3
% 224.22/38.37  | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | COMBINE_EQS: (325), (14201) imply:
% 224.22/38.37  | | | | | | | | | |   (14202)  all_4_2 = e3
% 224.22/38.37  | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | SIMP: (14202) implies:
% 224.22/38.37  | | | | | | | | | |   (14203)  all_4_2 = e3
% 224.22/38.37  | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | REDUCE: (370), (14203) imply:
% 224.22/38.37  | | | | | | | | | |   (14204)   ~ (all_53_12 = e3)
% 224.22/38.37  | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | REDUCE: (371), (14203) imply:
% 224.22/38.37  | | | | | | | | | |   (14205)   ~ (all_53_13 = e3)
% 224.22/38.37  | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | REDUCE: (36), (14203) imply:
% 224.22/38.37  | | | | | | | | | |   (14206)  op(e0, e0) = e3
% 224.22/38.37  | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | BETA: splitting (225) gives:
% 224.22/38.37  | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | Case 1:
% 224.22/38.37  | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | |   (14207)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 224.22/38.37  | | | | | | | | | | |              & op(e2, e2) = e3)
% 224.22/38.37  | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | BETA: splitting (14207) gives:
% 224.22/38.37  | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | Case 1:
% 224.22/38.37  | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | |   (14208)  all_57_2 = e3 & op(e2, e3) = e3
% 224.22/38.37  | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | ALPHA: (14208) implies:
% 224.22/38.37  | | | | | | | | | | | |   (14209)  op(e2, e3) = e3
% 224.22/38.37  | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | BETA: splitting (237) gives:
% 224.22/38.37  | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | Case 1:
% 224.22/38.37  | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | |   (14210)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 224.22/38.37  | | | | | | | | | | | | |              & op(e3, e2) = e3)
% 224.22/38.37  | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | BETA: splitting (14210) gives:
% 224.22/38.37  | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | Case 1:
% 224.22/38.37  | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | |   (14211)  all_57_0 = e3 & op(e3, e3) = e3
% 224.22/38.37  | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | ALPHA: (14211) implies:
% 224.22/38.37  | | | | | | | | | | | | | |   (14212)  op(e3, e3) = e3
% 224.22/38.37  | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | REF_CLOSE: (8), (13558), (14212), (function-axioms) are
% 224.22/38.37  | | | | | | | | | | | | | |            inconsistent by sub-proof #2495.
% 224.22/38.37  | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | Case 2:
% 224.22/38.37  | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | |   (14213)  all_57_1 = e3 & op(e3, e2) = e3
% 224.22/38.37  | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | ALPHA: (14213) implies:
% 224.22/38.37  | | | | | | | | | | | | | |   (14214)  op(e3, e2) = e3
% 224.22/38.37  | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_1, e3,
% 224.22/38.37  | | | | | | | | | | | | | |              e3, e2, simplifying with (168), (14209) gives:
% 224.22/38.37  | | | | | | | | | | | | | |   (14215)  all_53_1 = e3
% 224.22/38.37  | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_4, e3,
% 224.22/38.37  | | | | | | | | | | | | | |              e2, e3, simplifying with (171), (14214) gives:
% 224.22/38.37  | | | | | | | | | | | | | |   (14216)  all_53_4 = e3
% 224.22/38.37  | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 224.22/38.37  | | | | | | | | | | | | | | 
% 224.22/38.37  | | | | | | | | | | | | | | Case 1:
% 224.22/38.37  | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | |   (14217)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 224.22/38.38  | | | | | | | | | | | | | | |              all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 224.22/38.38  | | | | | | | | | | | | | | |              op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 224.22/38.38  | | | | | | | | | | | | | | |                all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 224.22/38.38  | | | | | | | | | | | | | | |              op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 224.22/38.38  | | | | | | | | | | | | | | |              op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 224.22/38.38  | | | | | | | | | | | | | | |              $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 224.22/38.38  | | | | | | | | | | | | | | |              $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 224.22/38.38  | | | | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 224.22/38.38  | | | | | | | | | | | | | | |                all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 224.22/38.38  | | | | | | | | | | | | | | |              & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 224.22/38.38  | | | | | | | | | | | | | | |                all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 224.22/38.38  | | | | | | | | | | | | | | |              op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 224.22/38.38  | | | | | | | | | | | | | | |              & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 224.22/38.38  | | | | | | | | | | | | | | |              $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 224.22/38.38  | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | BETA: splitting (14217) gives:
% 224.22/38.38  | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | Case 1:
% 224.22/38.38  | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | |   (14218)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 224.22/38.38  | | | | | | | | | | | | | | | |            all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 224.22/38.38  | | | | | | | | | | | | | | | |            op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 224.22/38.38  | | | | | | | | | | | | | | | |              all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 224.22/38.38  | | | | | | | | | | | | | | | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 224.22/38.38  | | | | | | | | | | | | | | | |            op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 224.22/38.38  | | | | | | | | | | | | | | | |            $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 224.22/38.38  | | | | | | | | | | | | | | | |            $i(all_52_7)
% 224.22/38.38  | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | ALPHA: (14218) implies:
% 224.22/38.38  | | | | | | | | | | | | | | | |   (14219)  op(e3, e2) = all_52_3
% 224.22/38.38  | | | | | | | | | | | | | | | |   (14220)  op(e3, e3) = all_52_1
% 224.22/38.38  | | | | | | | | | | | | | | | |   (14221)  op(all_52_3, all_52_3) = e2
% 224.22/38.38  | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_52_3,
% 224.22/38.38  | | | | | | | | | | | | | | | |              e2, e3, simplifying with (14214), (14219) gives:
% 224.22/38.38  | | | | | | | | | | | | | | | |   (14222)  all_52_3 = e3
% 224.22/38.38  | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_52_1,
% 224.22/38.38  | | | | | | | | | | | | | | | |              e3, e3, simplifying with (13558), (14220) gives:
% 224.22/38.38  | | | | | | | | | | | | | | | |   (14223)  all_52_1 = e1
% 224.22/38.38  | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | REDUCE: (14221), (14222) imply:
% 224.22/38.38  | | | | | | | | | | | | | | | |   (14224)  op(e3, e3) = e2
% 224.22/38.38  | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (13558), (14224), (function-axioms) are
% 224.22/38.38  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1950.
% 224.22/38.38  | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | Case 2:
% 224.22/38.38  | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | |   (14225)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 224.22/38.38  | | | | | | | | | | | | | | | |            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 224.22/38.38  | | | | | | | | | | | | | | | |            op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 224.22/38.38  | | | | | | | | | | | | | | | |              all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 224.22/38.38  | | | | | | | | | | | | | | | |            & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 224.22/38.38  | | | | | | | | | | | | | | | |            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 224.22/38.38  | | | | | | | | | | | | | | | |            $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 224.22/38.38  | | | | | | | | | | | | | | | |            $i(all_52_15)
% 224.22/38.38  | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | ALPHA: (14225) implies:
% 224.22/38.38  | | | | | | | | | | | | | | | |   (14226)  op(e2, e3) = all_52_9
% 224.22/38.38  | | | | | | | | | | | | | | | |   (14227)  op(all_52_9, all_52_9) = e3
% 224.22/38.38  | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_52_9,
% 224.22/38.38  | | | | | | | | | | | | | | | |              e3, e2, simplifying with (14209), (14226) gives:
% 224.22/38.38  | | | | | | | | | | | | | | | |   (14228)  all_52_9 = e3
% 224.22/38.38  | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | REDUCE: (14227), (14228) imply:
% 224.22/38.38  | | | | | | | | | | | | | | | |   (14229)  op(e3, e3) = e3
% 224.22/38.38  | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | REF_CLOSE: (8), (13558), (14229), (function-axioms) are
% 224.22/38.38  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2495.
% 224.22/38.38  | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | End of split
% 224.22/38.38  | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | Case 2:
% 224.22/38.38  | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | |   (14230)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 224.22/38.38  | | | | | | | | | | | | | | |              & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 224.22/38.38  | | | | | | | | | | | | | | |              & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 224.22/38.38  | | | | | | | | | | | | | | |                all_52_21) = e1 & op(all_52_23, all_52_23) =
% 224.22/38.38  | | | | | | | | | | | | | | |              e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 224.22/38.38  | | | | | | | | | | | | | | |              all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 224.22/38.38  | | | | | | | | | | | | | | |              = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 224.22/38.38  | | | | | | | | | | | | | | |              $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 224.22/38.38  | | | | | | | | | | | | | | |              & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 224.22/38.38  | | | | | | | | | | | | | | |              e0 & op(all_52_25, all_52_25) = e3 &
% 224.22/38.38  | | | | | | | | | | | | | | |              op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 224.22/38.38  | | | | | | | | | | | | | | |                all_52_29) = e1 & op(all_52_31, all_52_31) =
% 224.22/38.38  | | | | | | | | | | | | | | |              e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 224.22/38.38  | | | | | | | | | | | | | | |              all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 224.22/38.38  | | | | | | | | | | | | | | |              = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 224.22/38.38  | | | | | | | | | | | | | | |              $i(all_52_29) & $i(all_52_31))
% 224.22/38.38  | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | BETA: splitting (14230) gives:
% 224.22/38.38  | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | Case 1:
% 224.22/38.38  | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | |   (14231)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 224.22/38.38  | | | | | | | | | | | | | | | |            all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 224.22/38.38  | | | | | | | | | | | | | | | |            op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 224.22/38.38  | | | | | | | | | | | | | | | |              all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 224.22/38.38  | | | | | | | | | | | | | | | |            & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 224.22/38.38  | | | | | | | | | | | | | | | |            & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 224.22/38.38  | | | | | | | | | | | | | | | |            & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 224.22/38.38  | | | | | | | | | | | | | | | |            $i(all_52_23)
% 224.22/38.38  | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | ALPHA: (14231) implies:
% 224.22/38.38  | | | | | | | | | | | | | | | |   (14232)  op(e1, e0) = all_52_23
% 224.22/38.38  | | | | | | | | | | | | | | | |   (14233)  op(e1, e1) = all_52_21
% 224.22/38.38  | | | | | | | | | | | | | | | |   (14234)  op(e1, e2) = all_52_19
% 224.22/38.38  | | | | | | | | | | | | | | | |   (14235)  op(all_52_23, all_52_23) = e0
% 224.22/38.38  | | | | | | | | | | | | | | | |   (14236)  op(all_52_19, all_52_19) = e2
% 224.22/38.38  | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_14,
% 224.22/38.38  | | | | | | | | | | | | | | | |              all_52_23, e0, e1, simplifying with (161), (14232)
% 224.22/38.38  | | | | | | | | | | | | | | | |              gives:
% 224.22/38.38  | | | | | | | | | | | | | | | |   (14237)  all_53_14 = all_52_23
% 224.22/38.38  | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3,
% 224.22/38.38  | | | | | | | | | | | | | | | |              all_52_21, e1, e1, simplifying with (12097),
% 224.22/38.38  | | | | | | | | | | | | | | | |              (14233) gives:
% 224.22/38.38  | | | | | | | | | | | | | | | |   (14238)  all_52_21 = e3
% 224.22/38.38  | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_6,
% 224.22/38.38  | | | | | | | | | | | | | | | |              all_52_19, e2, e1, simplifying with (163), (14234)
% 224.22/38.38  | | | | | | | | | | | | | | | |              gives:
% 224.22/38.38  | | | | | | | | | | | | | | | |   (14239)  all_53_6 = all_52_19
% 224.22/38.38  | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (164), (215), (12097), (13551),
% 224.22/38.38  | | | | | | | | | | | | | | | |            (14232), (14234), (14235), (14236),
% 224.22/38.38  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.22/38.38  | | | | | | | | | | | | | | | |            #110.
% 224.22/38.38  | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | Case 2:
% 224.22/38.38  | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | |   (14240)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 224.22/38.38  | | | | | | | | | | | | | | | |            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 224.22/38.38  | | | | | | | | | | | | | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 224.22/38.38  | | | | | | | | | | | | | | | |              all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 224.22/38.38  | | | | | | | | | | | | | | | |            & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 224.22/38.38  | | | | | | | | | | | | | | | |            & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 224.22/38.38  | | | | | | | | | | | | | | | |            & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 224.22/38.38  | | | | | | | | | | | | | | | |            $i(all_52_31)
% 224.22/38.38  | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | ALPHA: (14240) implies:
% 224.22/38.38  | | | | | | | | | | | | | | | |   (14241)  op(e0, e0) = all_52_31
% 224.22/38.38  | | | | | | | | | | | | | | | |   (14242)  op(all_52_31, all_52_31) = e0
% 224.22/38.38  | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (13558), (14206), (14241), (14242),
% 224.22/38.38  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.22/38.38  | | | | | | | | | | | | | | | |            #283.
% 224.22/38.38  | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | End of split
% 224.22/38.38  | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | End of split
% 224.22/38.38  | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | End of split
% 224.22/38.38  | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | Case 2:
% 224.22/38.38  | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | |   (14243)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 224.22/38.38  | | | | | | | | | | | | |              & op(e3, e0) = e3)
% 224.22/38.38  | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | REF_CLOSE: (169), (170), (12087), (14204), (14243),
% 224.22/38.38  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.22/38.38  | | | | | | | | | | | | |            #109.
% 224.22/38.38  | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | End of split
% 224.22/38.38  | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | Case 2:
% 224.22/38.38  | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | |   (14244)  all_57_3 = e3 & op(e2, e2) = e3
% 224.22/38.38  | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | ALPHA: (14244) implies:
% 224.22/38.38  | | | | | | | | | | | |   (14245)  op(e2, e2) = e3
% 224.22/38.38  | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | REF_CLOSE: (42), (12098), (14245), (function-axioms) are
% 224.22/38.38  | | | | | | | | | | | |            inconsistent by sub-proof #140.
% 224.22/38.38  | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | End of split
% 224.22/38.38  | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | Case 2:
% 224.22/38.38  | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | |   (14246)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 224.22/38.38  | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 224.22/38.38  | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | REF_CLOSE: (165), (166), (12088), (14205), (14246),
% 224.22/38.38  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.22/38.38  | | | | | | | | | | |            #178.
% 224.22/38.38  | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | End of split
% 224.22/38.38  | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | End of split
% 224.22/38.38  | | | | | | | | | 
% 224.22/38.38  | | | | | | | | Case 2:
% 224.22/38.38  | | | | | | | | | 
% 224.22/38.38  | | | | | | | | |   (14247)  all_57_2 = e1 & op(e2, e3) = e1
% 224.22/38.38  | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | REF_CLOSE: (168), (13550), (14247), (function-axioms) are
% 224.22/38.38  | | | | | | | | |            inconsistent by sub-proof #2156.
% 224.22/38.38  | | | | | | | | | 
% 224.22/38.38  | | | | | | | | End of split
% 224.22/38.38  | | | | | | | | 
% 224.22/38.38  | | | | | | | Case 2:
% 224.22/38.38  | | | | | | | | 
% 224.22/38.38  | | | | | | | |   (14248)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 &
% 224.22/38.38  | | | | | | | |              op(e0, e3) = e1)
% 224.22/38.38  | | | | | | | | 
% 224.22/38.38  | | | | | | | | BETA: splitting (14248) gives:
% 224.22/38.38  | | | | | | | | 
% 224.22/38.38  | | | | | | | | Case 1:
% 224.22/38.38  | | | | | | | | | 
% 224.22/38.38  | | | | | | | | |   (14249)  all_57_6 = e1 & op(e1, e3) = e1
% 224.22/38.38  | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | REF_CLOSE: (164), (13551), (14249), (function-axioms) are
% 224.22/38.38  | | | | | | | | |            inconsistent by sub-proof #316.
% 224.22/38.38  | | | | | | | | | 
% 224.22/38.38  | | | | | | | | Case 2:
% 224.22/38.38  | | | | | | | | | 
% 224.22/38.38  | | | | | | | | |   (14250)  all_57_12 = e1 & op(e0, e3) = e1
% 224.22/38.38  | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | REF_CLOSE: (160), (13552), (14250), (function-axioms) are
% 224.22/38.38  | | | | | | | | |            inconsistent by sub-proof #1947.
% 224.22/38.38  | | | | | | | | | 
% 224.22/38.38  | | | | | | | | End of split
% 224.22/38.38  | | | | | | | | 
% 224.22/38.38  | | | | | | | End of split
% 224.22/38.38  | | | | | | | 
% 224.22/38.38  | | | | | | End of split
% 224.22/38.38  | | | | | | 
% 224.22/38.38  | | | | | Case 2:
% 224.22/38.38  | | | | | | 
% 224.22/38.38  | | | | | |   (14251)  all_8_2 = e3
% 224.22/38.38  | | | | | |   (14252)  ( ~ (all_8_0 = e0) & op(all_8_1, e2) = all_8_0 & op(e2,
% 224.22/38.38  | | | | | |                e3) = all_8_1 & $i(all_8_0) & $i(all_8_1)) | ( ~
% 224.22/38.38  | | | | | |              (all_8_1 = e1) & op(e2, e3) = all_8_1 & $i(all_8_1))
% 224.22/38.38  | | | | | | 
% 224.22/38.38  | | | | | | REDUCE: (349), (14251) imply:
% 224.22/38.38  | | | | | |   (14253)   ~ (all_53_1 = e3)
% 224.22/38.38  | | | | | | 
% 224.22/38.38  | | | | | | REDUCE: (352), (14251) imply:
% 224.22/38.38  | | | | | |   (14254)   ~ (all_53_4 = e3)
% 224.22/38.38  | | | | | | 
% 224.22/38.38  | | | | | | REDUCE: (356), (14251) imply:
% 224.22/38.38  | | | | | |   (14255)   ~ (all_53_7 = e3)
% 224.22/38.38  | | | | | | 
% 224.22/38.38  | | | | | | REDUCE: (360), (14251) imply:
% 224.22/38.38  | | | | | |   (14256)   ~ (all_53_13 = e3)
% 224.22/38.38  | | | | | | 
% 224.22/38.38  | | | | | | BETA: splitting (225) gives:
% 224.22/38.38  | | | | | | 
% 224.22/38.38  | | | | | | Case 1:
% 224.22/38.38  | | | | | | | 
% 224.22/38.38  | | | | | | |   (14257)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 &
% 224.22/38.38  | | | | | | |              op(e2, e2) = e3)
% 224.22/38.38  | | | | | | | 
% 224.22/38.38  | | | | | | | BETA: splitting (14257) gives:
% 224.22/38.38  | | | | | | | 
% 224.22/38.38  | | | | | | | Case 1:
% 224.22/38.38  | | | | | | | | 
% 224.22/38.38  | | | | | | | |   (14258)  all_57_2 = e3 & op(e2, e3) = e3
% 224.22/38.38  | | | | | | | | 
% 224.22/38.38  | | | | | | | | REF_CLOSE: (168), (14253), (14258), (function-axioms) are
% 224.22/38.38  | | | | | | | |            inconsistent by sub-proof #2299.
% 224.22/38.38  | | | | | | | | 
% 224.22/38.38  | | | | | | | Case 2:
% 224.22/38.38  | | | | | | | | 
% 224.22/38.38  | | | | | | | |   (14259)  all_57_3 = e3 & op(e2, e2) = e3
% 224.22/38.38  | | | | | | | | 
% 224.22/38.38  | | | | | | | | ALPHA: (14259) implies:
% 224.22/38.38  | | | | | | | |   (14260)  all_57_3 = e3
% 224.22/38.38  | | | | | | | |   (14261)  op(e2, e2) = e3
% 224.22/38.38  | | | | | | | | 
% 224.22/38.38  | | | | | | | | BETA: splitting (46) gives:
% 224.22/38.38  | | | | | | | | 
% 224.22/38.38  | | | | | | | | Case 1:
% 224.22/38.38  | | | | | | | | | 
% 224.22/38.38  | | | | | | | | |   (14262)   ~ (all_10_2 = e1)
% 224.22/38.38  | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | BETA: splitting (49) gives:
% 224.22/38.38  | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | Case 1:
% 224.22/38.38  | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | |   (14263)   ~ (all_12_2 = e3)
% 224.22/38.38  | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | REDUCE: (325), (14263) imply:
% 224.22/38.38  | | | | | | | | | |   (14264)   ~ (all_4_2 = e3)
% 224.22/38.38  | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | BETA: splitting (213) gives:
% 224.22/38.38  | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | Case 1:
% 224.22/38.38  | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | |   (14265)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 224.22/38.38  | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 224.22/38.38  | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | BETA: splitting (14265) gives:
% 224.22/38.38  | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | Case 1:
% 224.22/38.38  | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | |   (14266)  all_57_9 = e3 & op(e3, e0) = e3
% 224.22/38.38  | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | ALPHA: (14266) implies:
% 224.22/38.38  | | | | | | | | | | | |   (14267)  all_57_9 = e3
% 224.22/38.38  | | | | | | | | | | | |   (14268)  op(e3, e0) = e3
% 224.22/38.38  | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | BETA: splitting (210) gives:
% 224.22/38.38  | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | Case 1:
% 224.22/38.38  | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | |   (14269)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 224.22/38.38  | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 224.22/38.38  | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | BETA: splitting (14269) gives:
% 224.22/38.38  | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | Case 1:
% 224.22/38.38  | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | |   (14270)  all_57_12 = e3 & op(e0, e3) = e3
% 224.22/38.38  | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | ALPHA: (14270) implies:
% 224.22/38.38  | | | | | | | | | | | | | |   (14271)  all_57_12 = e3
% 224.22/38.38  | | | | | | | | | | | | | |   (14272)  op(e0, e3) = e3
% 224.22/38.38  | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_3, e3,
% 224.22/38.38  | | | | | | | | | | | | | |              e3, e0, simplifying with (160), (14272) gives:
% 224.22/38.38  | | | | | | | | | | | | | |   (14273)  all_53_3 = e3
% 224.22/38.38  | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_12,
% 224.22/38.38  | | | | | | | | | | | | | |              e3, e0, e3, simplifying with (169), (14268) gives:
% 224.22/38.38  | | | | | | | | | | | | | |   (14274)  all_53_12 = e3
% 224.22/38.38  | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | REDUCE: (114), (14274) imply:
% 224.22/38.38  | | | | | | | | | | | | | |   (14275)   ~ (all_53_13 = e3)
% 224.22/38.38  | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | REDUCE: (348), (14274) imply:
% 224.22/38.38  | | | | | | | | | | | | | |   (14276)   ~ (all_10_2 = e3)
% 224.22/38.38  | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | SIMP: (14276) implies:
% 224.22/38.38  | | | | | | | | | | | | | |   (14277)   ~ (all_10_2 = e3)
% 224.22/38.38  | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | REDUCE: (370), (14274) imply:
% 224.22/38.38  | | | | | | | | | | | | | |   (14278)   ~ (all_4_2 = e3)
% 224.22/38.38  | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 224.22/38.38  | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | Case 1:
% 224.22/38.38  | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | |   (14279)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 224.22/38.38  | | | | | | | | | | | | | | |              all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 224.22/38.38  | | | | | | | | | | | | | | |              op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 224.22/38.38  | | | | | | | | | | | | | | |                all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 224.22/38.38  | | | | | | | | | | | | | | |              op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 224.22/38.38  | | | | | | | | | | | | | | |              op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 224.22/38.38  | | | | | | | | | | | | | | |              $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 224.22/38.38  | | | | | | | | | | | | | | |              $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 224.22/38.38  | | | | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 224.22/38.38  | | | | | | | | | | | | | | |                all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 224.22/38.38  | | | | | | | | | | | | | | |              & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 224.22/38.38  | | | | | | | | | | | | | | |                all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 224.22/38.38  | | | | | | | | | | | | | | |              op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 224.22/38.38  | | | | | | | | | | | | | | |              & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 224.22/38.38  | | | | | | | | | | | | | | |              $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 224.22/38.38  | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | BETA: splitting (14279) gives:
% 224.22/38.38  | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | Case 1:
% 224.22/38.38  | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | |   (14280)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 224.22/38.38  | | | | | | | | | | | | | | | |            all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 224.22/38.38  | | | | | | | | | | | | | | | |            op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 224.22/38.38  | | | | | | | | | | | | | | | |              all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 224.22/38.38  | | | | | | | | | | | | | | | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 224.22/38.38  | | | | | | | | | | | | | | | |            op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 224.22/38.38  | | | | | | | | | | | | | | | |            $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 224.22/38.38  | | | | | | | | | | | | | | | |            $i(all_52_7)
% 224.22/38.38  | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | ALPHA: (14280) implies:
% 224.22/38.38  | | | | | | | | | | | | | | | |   (14281)  op(e3, e0) = all_52_7
% 224.22/38.38  | | | | | | | | | | | | | | | |   (14282)  op(e3, e3) = all_52_1
% 224.22/38.38  | | | | | | | | | | | | | | | |   (14283)  op(all_52_7, all_52_7) = e0
% 224.22/38.38  | | | | | | | | | | | | | | | |   (14284)  op(all_52_1, all_52_1) = e3
% 224.22/38.38  | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_52_7,
% 224.22/38.38  | | | | | | | | | | | | | | | |              e0, e3, simplifying with (14268), (14281) gives:
% 224.22/38.38  | | | | | | | | | | | | | | | |   (14285)  all_52_7 = e3
% 224.22/38.38  | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2,
% 224.22/38.38  | | | | | | | | | | | | | | | |              all_52_1, e3, e3, simplifying with (45), (14282)
% 224.22/38.38  | | | | | | | | | | | | | | | |              gives:
% 224.22/38.38  | | | | | | | | | | | | | | | |   (14286)  all_52_1 = all_10_2
% 224.22/38.38  | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | REDUCE: (14284), (14286) imply:
% 224.22/38.38  | | | | | | | | | | | | | | | |   (14287)  op(all_10_2, all_10_2) = e3
% 224.22/38.38  | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | REDUCE: (14283), (14285) imply:
% 224.22/38.38  | | | | | | | | | | | | | | | |   (14288)  op(e3, e3) = e0
% 224.22/38.38  | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, e0,
% 224.22/38.38  | | | | | | | | | | | | | | | |              e3, e3, simplifying with (45), (14288) gives:
% 224.22/38.38  | | | | | | | | | | | | | | | |   (14289)  all_10_2 = e0
% 224.22/38.38  | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | REDUCE: (14287), (14289) imply:
% 224.22/38.38  | | | | | | | | | | | | | | | |   (14290)  op(e0, e0) = e3
% 224.22/38.38  | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | REF_CLOSE: (36), (14264), (14290), (function-axioms) are
% 224.22/38.38  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #151.
% 224.22/38.38  | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | Case 2:
% 224.22/38.38  | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | |   (14291)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 224.22/38.38  | | | | | | | | | | | | | | | |            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 224.22/38.38  | | | | | | | | | | | | | | | |            op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 224.22/38.38  | | | | | | | | | | | | | | | |              all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 224.22/38.38  | | | | | | | | | | | | | | | |            & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 224.22/38.38  | | | | | | | | | | | | | | | |            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 224.22/38.38  | | | | | | | | | | | | | | | |            $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 224.22/38.38  | | | | | | | | | | | | | | | |            $i(all_52_15)
% 224.22/38.38  | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | ALPHA: (14291) implies:
% 224.22/38.38  | | | | | | | | | | | | | | | |   (14292)  op(e2, e0) = all_52_15
% 224.22/38.38  | | | | | | | | | | | | | | | |   (14293)  op(e2, e1) = all_52_13
% 224.22/38.38  | | | | | | | | | | | | | | | |   (14294)  op(e2, e2) = all_52_11
% 224.22/38.38  | | | | | | | | | | | | | | | |   (14295)  op(e2, e3) = all_52_9
% 224.22/38.38  | | | | | | | | | | | | | | | |   (14296)  op(all_52_15, all_52_15) = e0
% 224.22/38.38  | | | | | | | | | | | | | | | |   (14297)  op(all_52_13, all_52_13) = e1
% 224.22/38.38  | | | | | | | | | | | | | | | |   (14298)  op(all_52_11, all_52_11) = e2
% 224.22/38.38  | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_13,
% 224.22/38.38  | | | | | | | | | | | | | | | |              all_52_15, e0, e2, simplifying with (165), (14292)
% 224.22/38.38  | | | | | | | | | | | | | | | |              gives:
% 224.22/38.38  | | | | | | | | | | | | | | | |   (14299)  all_53_13 = all_52_15
% 224.22/38.38  | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_9,
% 224.22/38.38  | | | | | | | | | | | | | | | |              all_52_13, e1, e2, simplifying with (166), (14293)
% 224.22/38.38  | | | | | | | | | | | | | | | |              gives:
% 224.22/38.38  | | | | | | | | | | | | | | | |   (14300)  all_53_9 = all_52_13
% 224.22/38.38  | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3,
% 224.22/38.38  | | | | | | | | | | | | | | | |              all_52_11, e2, e2, simplifying with (14261),
% 224.22/38.38  | | | | | | | | | | | | | | | |              (14294) gives:
% 224.22/38.38  | | | | | | | | | | | | | | | |   (14301)  all_52_11 = e3
% 224.22/38.38  | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_1,
% 224.22/38.38  | | | | | | | | | | | | | | | |              all_52_9, e3, e2, simplifying with (168), (14295)
% 224.22/38.38  | | | | | | | | | | | | | | | |              gives:
% 224.22/38.38  | | | | | | | | | | | | | | | |   (14302)  all_53_1 = all_52_9
% 224.22/38.38  | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (14299) imply:
% 224.22/38.38  | | | | | | | | | | | | | | | |   (14303)  all_55_7 = all_52_15
% 224.22/38.38  | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | REDUCE: (338), (14302) imply:
% 224.22/38.38  | | | | | | | | | | | | | | | |   (14304)   ~ (all_52_9 = all_10_2)
% 224.22/38.38  | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | REDUCE: (14253), (14302) imply:
% 224.22/38.38  | | | | | | | | | | | | | | | |   (14305)   ~ (all_52_9 = e3)
% 224.22/38.38  | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | REDUCE: (118), (14299), (14300) imply:
% 224.22/38.38  | | | | | | | | | | | | | | | |   (14306)   ~ (all_52_13 = all_52_15)
% 224.22/38.38  | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | REDUCE: (12088), (14300) imply:
% 224.22/38.38  | | | | | | | | | | | | | | | |   (14307)   ~ (all_52_13 = e3)
% 224.22/38.38  | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | REDUCE: (371), (14299) imply:
% 224.22/38.38  | | | | | | | | | | | | | | | |   (14308)   ~ (all_52_15 = all_4_2)
% 224.22/38.38  | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | REDUCE: (14256), (14299) imply:
% 224.22/38.38  | | | | | | | | | | | | | | | |   (14309)   ~ (all_52_15 = e3)
% 224.22/38.38  | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | REDUCE: (14298), (14301) imply:
% 224.22/38.38  | | | | | | | | | | | | | | | |   (14310)  op(e3, e3) = e2
% 224.22/38.38  | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, e2,
% 224.22/38.38  | | | | | | | | | | | | | | | |              e3, e3, simplifying with (45), (14310) gives:
% 224.22/38.38  | | | | | | | | | | | | | | | |   (14311)  all_10_2 = e2
% 224.22/38.38  | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | REDUCE: (14304), (14311) imply:
% 224.22/38.38  | | | | | | | | | | | | | | | |   (14312)   ~ (all_52_9 = e2)
% 224.22/38.38  | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | REDUCE: (14277), (14311) imply:
% 224.22/38.38  | | | | | | | | | | | | | | | |   (14313)   ~ (e3 = e2)
% 224.22/38.38  | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | BETA: splitting (76) gives:
% 224.22/38.38  | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.38  | | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | |   (14314)   ~ (all_30_2 = e1)
% 224.22/38.38  | | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | | REDUCE: (330), (14314) imply:
% 224.22/38.38  | | | | | | | | | | | | | | | | |   (14315)   ~ (all_4_2 = e1)
% 224.22/38.38  | | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 224.22/38.38  | | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.38  | | | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | | |   (14316)  all_55_15 = e3
% 224.22/38.38  | | | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (14264), (14316) are inconsistent by
% 224.22/38.38  | | | | | | | | | | | | | | | | | |            sub-proof #2503.
% 224.22/38.38  | | | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.38  | | | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | | |   (14317)   ~ (all_55_15 = e3)
% 224.22/38.38  | | | | | | | | | | | | | | | | | |   (14318)  all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 224.22/38.38  | | | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | | | BETA: splitting (14318) gives:
% 224.22/38.38  | | | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | | | |   (14319)  all_55_15 = e2
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (373), (14319) are inconsistent by
% 224.22/38.38  | | | | | | | | | | | | | | | | | | |            sub-proof #2502.
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | | | |   (14320)   ~ (all_55_15 = e2)
% 224.22/38.38  | | | | | | | | | | | | | | | | | | |   (14321)  all_55_15 = e1 | all_55_15 = e0
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | BETA: splitting (14321) gives:
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | |   (14322)  all_55_15 = e1
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (244), (14315), (14322) are inconsistent by
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | |            sub-proof #2501.
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | |   (14323)  all_55_15 = e0
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (14323) imply:
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | |   (14324)  all_4_2 = e0
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | SIMP: (14324) implies:
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | |   (14325)  all_4_2 = e0
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | REDUCE: (362), (14325) imply:
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | |   (14326)   ~ (all_53_7 = e0)
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | REDUCE: (372), (14325) imply:
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | |   (14327)   ~ (all_53_14 = e0)
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | REDUCE: (14308), (14325) imply:
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | |   (14328)   ~ (all_52_15 = e0)
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | REDUCE: (14264), (14325) imply:
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | |   (14329)   ~ (e3 = e0)
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | REDUCE: (373), (14325) imply:
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | |   (14330)   ~ (e2 = e0)
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | REDUCE: (14315), (14325) imply:
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | |   (14331)   ~ (e1 = e0)
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (14325) imply:
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | |   (14332)  op(e0, e0) = e0
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | |   (14333)  all_57_15 = e0 & op(e0, e0) = e0
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | | ALPHA: (14333) implies:
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | |   (14334)  all_57_15 = e0
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | | |   (14335)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (14261), (14268), (14292), (14294),
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | | |            (14296), (14335), (function-axioms) are
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #108.
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | | |   (14336)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14336) gives:
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | | | |   (14337)  all_57_11 = e2 & op(e1, e0) = e2
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14337) implies:
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | | | |   (14338)  all_57_11 = e2
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | | | | |   (14339)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14339) gives:
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | | | | | |   (14340)  all_57_9 = e1 & op(e3, e0) = e1
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (14267), (14340) are inconsistent by
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1669.
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | | | | | |   (14341)  all_57_10 = e1 & op(e2, e0) = e1
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14341) implies:
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | | | | | |   (14342)  all_57_10 = e1
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | | | | | |   (14343)  op(e2, e0) = e1
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | | | | | | |   (14344)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 224.22/38.38  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (232), (14260), (14261), (14271), (14310),
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | |            (14344), (function-axioms) are inconsistent by
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #106.
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | |   (14345)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14345) gives:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14346)  all_57_5 = e2 & op(e2, e1) = e2
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14346) implies:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14347)  all_57_5 = e2
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14348)  op(e2, e1) = e2
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14349)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14349) gives:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14350)  all_57_2 = e0 & op(e2, e3) = e0
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14350) implies:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14351)  all_57_2 = e0
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14352)  op(e2, e3) = e0
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14353)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e1)
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (14310), (14351), (14353),
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #105.
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14354)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e3) = e1)
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14354) gives:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14355)  all_57_6 = e1 & op(e1, e3) = e1
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14355) implies:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14356)  all_57_6 = e1
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14357)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e0)
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14357) gives:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14358)  all_57_6 = e0 & op(e1, e3) = e0
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (14356), (14358) are inconsistent by
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2347.
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14359)  all_57_7 = e0 & op(e1, e2) = e0
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14359) implies:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14360)  all_57_7 = e0
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14361)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (237),
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14261), (14310), (14361), (function-axioms) are
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #104.
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14362)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14362) gives:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14363)  all_57_7 = e2 & op(e1, e2) = e2
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (14360), (14363) are inconsistent by
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #364.
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14364)  all_57_13 = e2 & op(e0, e2) = e2
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14364) implies:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14365)  all_57_13 = e2
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14366)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14366) gives:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14367)  all_57_12 = e1 & op(e0, e3) = e1
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14367) implies:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14368)  all_57_12 = e1
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (236), (14310), (14351), (14356),
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14368), (function-axioms) are inconsistent by
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #103.
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14369)  all_57_13 = e1 & op(e0, e2) = e1
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14369) implies:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14370)  all_57_13 = e1
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (14365), (14370) are inconsistent by
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2327.
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14371)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14371) gives:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14372)  all_57_14 = e1 & op(e0, e1) = e1
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14372) implies:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14373)  all_57_14 = e1
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14374)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e0)
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14374) gives:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14375)  all_57_4 = e0 & op(e3, e1) = e0
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14375) implies:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14376)  all_57_4 = e0
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14377)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e1)
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14377) gives:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14378)  all_57_0 = e1 & op(e3, e3) = e1
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14378) implies:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14379)  op(e3, e3) = e1
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (234), (14271), (14351), (14356),
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14379), (function-axioms) are inconsistent by
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #350.
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14380)  all_57_1 = e1 & op(e3, e2) = e1
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14380) implies:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14381)  all_57_1 = e1
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14382)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e0)
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14382) gives:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14383)  all_57_0 = e0 & op(e3, e3) = e0
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14383) implies:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14384)  op(e3, e3) = e0
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14385)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e2)
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (14381), (14384), (14385),
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #207.
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14386)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e2)
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14386) gives:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14387)  all_57_4 = e2 & op(e3, e1) = e2
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14387) implies:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14388)  all_57_4 = e2
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (14376), (14388) are inconsistent by
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2441.
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14389)  all_57_9 = e2 & op(e3, e0) = e2
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (14268), (14389), (function-axioms) are
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #306.
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14390)  all_57_1 = e0 & op(e3, e2) = e0
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (14381), (14390) are inconsistent by
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2493.
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14391)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e0)
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14391) gives:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_15,
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e0, e2, simplifying with (14292), (14343)
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14392)  all_52_15 = e1
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e1, e2, simplifying with (14293), (14348)
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14393)  all_52_13 = e2
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e0,
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (14295), (14352) gives:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14394)  all_52_9 = e0
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14309), (14392) imply:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14395)   ~ (e3 = e1)
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14297), (14393) imply:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14396)  op(e2, e2) = e1
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (226), (228), (229),
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14381), (14396), (function-axioms) are
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1908.
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14397)  all_57_9 = e0 & op(e3, e0) = e0
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14397) implies:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14398)  op(e3, e0) = e0
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (14268), (14398), (function-axioms) are
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #313.
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14399)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e1)
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14399) gives:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14400)  all_57_4 = e1 & op(e3, e1) = e1
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14400) implies:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14401)  all_57_4 = e1
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (14376), (14401) are inconsistent by
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2438.
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14402)  all_57_9 = e1 & op(e3, e0) = e1
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14402) implies:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14403)  all_57_9 = e1
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14267), (14403) imply:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14404)  e3 = e1
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14271), (14404) imply:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14405)  all_57_12 = e1
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (236), (14310), (14351), (14356),
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14405), (function-axioms) are inconsistent by
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #103.
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14406)  all_57_5 = e0 & op(e2, e1) = e0
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (14347), (14406) are inconsistent by
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2428.
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14407)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14407) gives:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14408)  all_57_8 = e0 & op(e1, e1) = e0
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (12096), (14260), (14271), (14310),
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14356), (14408), (function-axioms) are
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #102.
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14409)  all_57_14 = e0 & op(e0, e1) = e0
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14409) implies:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14410)  all_57_14 = e0
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (14373), (14410) are inconsistent by
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2122.
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14411)  all_57_15 = e1 & op(e0, e0) = e1
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14411) implies:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14412)  op(e0, e0) = e1
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (14332), (14412), (function-axioms) are
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2290.
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14413)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14413) gives:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14414)  all_57_8 = e0 & op(e1, e1) = e0
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (12096), (14260), (14271), (14310),
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14356), (14414), (function-axioms) are
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #102.
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14415)  all_57_11 = e0 & op(e1, e0) = e0
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (14327), (14415), (function-axioms) are
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2341.
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14416)  all_57_12 = e1 & op(e0, e3) = e1
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (14271), (14416) are inconsistent by
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2230.
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14417)  all_57_3 = e0 & op(e2, e2) = e0
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14417) implies:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14418)  op(e2, e2) = e0
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (14294), (14298), (14332), (14418),
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2270.
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14419)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0)
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14419) gives:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14420)  all_57_5 = e0 & op(e2, e1) = e0
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14420) implies:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14421)  all_57_5 = e0
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (14347), (14421) are inconsistent by
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2363.
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14422)  all_57_10 = e0 & op(e2, e0) = e0
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14422) implies:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14423)  all_57_10 = e0
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (14342), (14423) are inconsistent by
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1531.
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14424)  all_57_10 = e2 & op(e2, e0) = e2
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14424) implies:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14425)  all_57_10 = e2
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (211), (14267), (14334), (14338),
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14425) are inconsistent by sub-proof #1668.
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | |   (14426)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (14332), (14338), (14426),
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | |            #176.
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | |   (14427)  all_57_15 = e2 & op(e0, e0) = e2
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14427) implies:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | |   (14428)  op(e0, e0) = e2
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (373), (14428), (function-axioms) are
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2334.
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | |   (14429)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | ALPHA: (14429) implies:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | |   (14430)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | |                e1) = e0)
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14430) gives:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | |   (14431)  all_57_12 = e0 & op(e0, e3) = e0
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (14271), (14431) are inconsistent by
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2237.
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | |   (14432)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14432) gives:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | |   (14433)  all_57_13 = e0 & op(e0, e2) = e0
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14433) implies:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | |   (14434)  op(e0, e2) = e0
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (14326), (14434), (function-axioms) are
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2332.
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | |   (14435)  all_57_14 = e0 & op(e0, e1) = e0
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14435) implies:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | |   (14436)  all_57_14 = e0
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (207), (208),
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | |            (209), (210), (219), (220), (231), (233), (237),
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | |            (373), (12096), (14267), (14271), (14310),
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | |            (14332), (14436), (function-axioms) are
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #100.
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.39  | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | End of split
% 224.22/38.39  | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.39  | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | |   (14437)  all_30_2 = e1
% 224.22/38.39  | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | COMBINE_EQS: (330), (14437) imply:
% 224.22/38.39  | | | | | | | | | | | | | | | | |   (14438)  all_4_2 = e1
% 224.22/38.39  | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | SIMP: (14438) implies:
% 224.22/38.39  | | | | | | | | | | | | | | | | |   (14439)  all_4_2 = e1
% 224.22/38.39  | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | REDUCE: (362), (14439) imply:
% 224.22/38.39  | | | | | | | | | | | | | | | | |   (14440)   ~ (all_53_7 = e1)
% 224.22/38.39  | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | REDUCE: (369), (14439) imply:
% 224.22/38.39  | | | | | | | | | | | | | | | | |   (14441)   ~ (all_53_11 = e1)
% 224.22/38.39  | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | REDUCE: (372), (14439) imply:
% 224.22/38.39  | | | | | | | | | | | | | | | | |   (14442)   ~ (all_53_14 = e1)
% 224.22/38.39  | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | REDUCE: (14308), (14439) imply:
% 224.22/38.39  | | | | | | | | | | | | | | | | |   (14443)   ~ (all_52_15 = e1)
% 224.22/38.39  | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | REDUCE: (14264), (14439) imply:
% 224.22/38.39  | | | | | | | | | | | | | | | | |   (14444)   ~ (e3 = e1)
% 224.22/38.39  | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | REDUCE: (373), (14439) imply:
% 224.22/38.39  | | | | | | | | | | | | | | | | |   (14445)   ~ (e2 = e1)
% 224.22/38.39  | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | REDUCE: (36), (14439) imply:
% 224.22/38.39  | | | | | | | | | | | | | | | | |   (14446)  op(e0, e0) = e1
% 224.22/38.39  | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 224.22/38.39  | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | |   (14447)  all_55_7 = e3
% 224.22/38.39  | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14303), (14447) imply:
% 224.22/38.39  | | | | | | | | | | | | | | | | | |   (14448)  all_52_15 = e3
% 224.22/38.39  | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | REDUCE: (14309), (14448) imply:
% 224.22/38.39  | | | | | | | | | | | | | | | | | |   (14449)  $false
% 224.22/38.39  | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | CLOSE: (14449) is inconsistent.
% 224.22/38.39  | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | |   (14450)   ~ (all_55_7 = e3)
% 224.22/38.39  | | | | | | | | | | | | | | | | | |   (14451)  all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 224.22/38.39  | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | |   (14452)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 224.22/38.39  | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e2)
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | BETA: splitting (14452) gives:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | |   (14453)  all_57_4 = e2 & op(e3, e1) = e2
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (237),
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | |            (14310), (14453), (function-axioms) are
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #226.
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | |   (14454)  all_57_5 = e2 & op(e2, e1) = e2
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | ALPHA: (14454) implies:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | |   (14455)  all_57_5 = e2
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | |   (14456)  op(e2, e1) = e2
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | |   (14457)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e1)
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14457) gives:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | |   (14458)  all_57_4 = e1 & op(e3, e1) = e1
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14458) implies:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | |   (14459)  all_57_4 = e1
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | |   (14460)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e0)
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14460) gives:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | |   (14461)  all_57_0 = e0 & op(e3, e3) = e0
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14461) implies:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | |   (14462)  op(e3, e3) = e0
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (14310), (14462), (function-axioms) are
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2403.
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | |   (14463)  all_57_1 = e0 & op(e3, e2) = e0
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14463) implies:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | |   (14464)  all_57_1 = e0
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | |   (14465)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e1)
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14465) gives:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | |   (14466)  all_57_0 = e1 & op(e3, e3) = e1
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14466) implies:
% 224.22/38.39  | | | | | | | | | | | | | | | | | | | | | | | | | |   (14467)  op(e3, e3) = e1
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (14310), (14467), (function-axioms) are
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1950.
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | |   (14468)  all_57_2 = e1 & op(e2, e3) = e1
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14468) implies:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | |   (14469)  all_57_2 = e1
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | |   (14470)  op(e2, e3) = e1
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14460) gives:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14471)  all_57_0 = e0 & op(e3, e3) = e0
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14471) implies:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14472)  op(e3, e3) = e0
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (14310), (14472), (function-axioms) are
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2403.
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14473)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (237),
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14261), (14310), (14473), (function-axioms) are
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #104.
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14474)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14474) gives:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14475)  all_57_7 = e2 & op(e1, e2) = e2
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (161), (212), (214),
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (215), (223), (224), (225), (230), (12096),
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14260), (14261), (14268), (14271), (14292),
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14294), (14296), (14310), (14442), (14446),
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14475), (function-axioms) are inconsistent by
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #98.
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14476)  all_57_13 = e2 & op(e0, e2) = e2
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14476) implies:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14477)  all_57_13 = e2
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14478)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14478) gives:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14479)  all_57_2 = e0 & op(e2, e3) = e0
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (14469), (14479) are inconsistent by
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2467.
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14480)  all_57_3 = e0 & op(e2, e2) = e0
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14480) implies:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14481)  all_57_3 = e0
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14482)  op(e2, e2) = e0
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (227), (228), (229),
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14464), (14477), (14481), (14482),
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1281.
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14483)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0)
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14483) gives:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14484)  all_57_5 = e0 & op(e2, e1) = e0
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14484) implies:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14485)  all_57_5 = e0
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14455), (14485) imply:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14486)  e2 = e0
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14477), (14486) imply:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14487)  all_57_13 = e0
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (161), (212), (214),
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (215), (223), (224), (225), (228), (230), (231),
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (237), (12096), (14260), (14261), (14268),
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14271), (14292), (14294), (14296), (14310),
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14442), (14446), (14487), (function-axioms) are
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #97.
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14488)  all_57_10 = e0 & op(e2, e0) = e0
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14488) implies:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14489)  op(e2, e0) = e0
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14490)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (14261), (14268), (14292), (14294),
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14296), (14490), (function-axioms) are
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #108.
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14491)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14491) gives:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14492)  all_57_11 = e2 & op(e1, e0) = e2
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14492) implies:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14493)  all_57_11 = e2
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14494)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e0)
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14494) gives:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14495)  all_57_4 = e0 & op(e3, e1) = e0
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (14459), (14495) are inconsistent by
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2429.
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14496)  all_57_5 = e0 & op(e2, e1) = e0
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14496) implies:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14497)  all_57_5 = e0
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14455), (14497) imply:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14498)  e2 = e0
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14493), (14498) imply:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14499)  all_57_11 = e0
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (9), (212), (14261), (14268),
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14292), (14294), (14296), (14446), (14499),
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #99.
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14500)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14500) gives:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14501)  all_57_8 = e0 & op(e1, e1) = e0
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12096), (14501) are inconsistent by
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #170.
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14502)  all_57_14 = e0 & op(e0, e1) = e0
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14502) implies:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14503)  all_57_14 = e0
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_15,
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e0, e2, simplifying with (14292), (14489)
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14504)  all_52_15 = e0
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e1, e2, simplifying with (14293), (14456)
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14505)  all_52_13 = e2
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e1,
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (14295), (14470) gives:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14506)  all_52_9 = e1
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14309), (14504) imply:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14507)   ~ (e3 = e0)
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14443), (14504) imply:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14508)   ~ (e1 = e0)
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14296), (14504) imply:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14509)  op(e0, e0) = e0
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (207), (208),
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (209), (210), (219), (220), (231), (233), (237),
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (373), (12096), (14267), (14271), (14310),
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14503), (14509), (function-axioms) are
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #100.
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14510)  all_57_15 = e2 & op(e0, e0) = e2
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14510) implies:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14511)  op(e0, e0) = e2
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (14446), (14511), (function-axioms) are
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2177.
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14512)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e0)
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14512) gives:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14513)  all_57_4 = e0 & op(e3, e1) = e0
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (14459), (14513) are inconsistent by
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2429.
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14514)  all_57_9 = e0 & op(e3, e0) = e0
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14514) implies:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14515)  op(e3, e0) = e0
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (14268), (14515), (function-axioms) are
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #313.
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | |   (14516)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e3) = e1)
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14516) gives:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | |   (14517)  all_57_6 = e1 & op(e1, e3) = e1
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14517) implies:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | |   (14518)  all_57_6 = e1
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14519)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14519) gives:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14520)  all_57_1 = e1 & op(e3, e2) = e1
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (14464), (14520) are inconsistent by
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2446.
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14521)  all_57_3 = e1 & op(e2, e2) = e1
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14521) implies:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14522)  op(e2, e2) = e1
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (14296), (14303), (14443), (14446), (14451),
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14522), (function-axioms) are inconsistent by
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1688.
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14523)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14523) gives:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14524)  all_57_7 = e1 & op(e1, e2) = e1
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14524) implies:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14525)  all_57_7 = e1
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14526)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e0)
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14526) gives:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14527)  all_57_6 = e0 & op(e1, e3) = e0
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14527) implies:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14528)  all_57_6 = e0
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (14518), (14528) are inconsistent by
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2227.
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14529)  all_57_7 = e0 & op(e1, e2) = e0
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (14525), (14529) are inconsistent by
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #509.
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14530)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14530) gives:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14531)  all_57_8 = e0 & op(e1, e1) = e0
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14531) implies:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14532)  all_57_8 = e0
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (12096), (14532) imply:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14533)  e3 = e0
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14260), (14533) imply:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14534)  all_57_3 = e0
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (14271), (14310), (14518), (14534),
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1632.
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14535)  all_57_11 = e0 & op(e1, e0) = e0
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14535) implies:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14536)  all_57_11 = e0
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (9), (212), (14261), (14268),
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14292), (14294), (14296), (14446), (14536),
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #99.
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14537)  all_57_13 = e1 & op(e0, e2) = e1
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (14440), (14537), (function-axioms) are
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #330.
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | |   (14538)  all_57_12 = e1 & op(e0, e3) = e1
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14538) implies:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | |   (14539)  all_57_12 = e1
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14271), (14539) imply:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | |   (14540)  e3 = e1
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (14540) implies:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | |   (14541)  e3 = e1
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14267), (14541) imply:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | |   (14542)  all_57_9 = e1
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (231), (237), (14310),
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | |            (14459), (14542), (function-axioms) are
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1672.
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | |   (14543)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e0)
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14543) gives:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | |   (14544)  all_57_4 = e0 & op(e3, e1) = e0
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14544) implies:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | |   (14545)  all_57_4 = e0
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (14459), (14545) are inconsistent by
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2438.
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | |   (14546)  all_57_9 = e0 & op(e3, e0) = e0
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14546) implies:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | |   (14547)  op(e3, e0) = e0
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (14268), (14547), (function-axioms) are
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #313.
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | |   (14548)  all_57_5 = e1 & op(e2, e1) = e1
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14548) implies:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | |   (14549)  all_57_5 = e1
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (14455), (14549) are inconsistent by
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1885.
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | |   (14550)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e1) = e1)
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14550) gives:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | |   (14551)  all_57_8 = e1 & op(e1, e1) = e1
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (12096), (14551) are inconsistent by
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #169.
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | |   (14552)  all_57_14 = e1 & op(e0, e1) = e1
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (14441), (14552), (function-axioms) are
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #225.
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | |   (14553)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 224.22/38.40  | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e1) = e2)
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | BETA: splitting (14553) gives:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | |   (14554)  all_57_8 = e2 & op(e1, e1) = e2
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (12096), (14554) are inconsistent by
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | |            sub-proof #172.
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | |   (14555)  all_57_14 = e2 & op(e0, e1) = e2
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | ALPHA: (14555) implies:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | |   (14556)  all_57_14 = e2
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | |   (14557)  all_57_15 = e0 & op(e0, e0) = e0
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | ALPHA: (14557) implies:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | |   (14558)  op(e0, e0) = e0
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (14446), (14558), (function-axioms) are
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2290.
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | |   (14559)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | ALPHA: (14559) implies:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | |   (14560)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | |                e1) = e0)
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14560) gives:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | |   (14561)  all_57_12 = e0 & op(e0, e3) = e0
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14561) implies:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | |   (14562)  all_57_12 = e0
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (14271), (14562) are inconsistent by
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2153.
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | |   (14563)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14563) gives:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | |   (14564)  all_57_13 = e0 & op(e0, e2) = e0
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14564) implies:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | |   (14565)  all_57_13 = e0
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (161), (212), (214),
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | |            (215), (223), (224), (225), (228), (230), (231),
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | |            (233), (237), (12096), (14260), (14261), (14268),
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | |            (14271), (14292), (14294), (14296), (14310),
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | |            (14442), (14446), (14565), (function-axioms) are
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #97.
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | |   (14566)  all_57_14 = e0 & op(e0, e1) = e0
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14566) implies:
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | |   (14567)  all_57_14 = e0
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (14556), (14567) are inconsistent by
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2422.
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.40  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.40  | | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | | End of split
% 224.22/38.40  | | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | End of split
% 224.22/38.40  | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | End of split
% 224.22/38.40  | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | Case 2:
% 224.22/38.40  | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | |   (14568)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 224.22/38.40  | | | | | | | | | | | | | | |              & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 224.22/38.40  | | | | | | | | | | | | | | |              & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 224.22/38.40  | | | | | | | | | | | | | | |                all_52_21) = e1 & op(all_52_23, all_52_23) =
% 224.22/38.40  | | | | | | | | | | | | | | |              e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 224.22/38.40  | | | | | | | | | | | | | | |              all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 224.22/38.40  | | | | | | | | | | | | | | |              = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 224.22/38.40  | | | | | | | | | | | | | | |              $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 224.22/38.40  | | | | | | | | | | | | | | |              & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 224.22/38.40  | | | | | | | | | | | | | | |              e0 & op(all_52_25, all_52_25) = e3 &
% 224.22/38.40  | | | | | | | | | | | | | | |              op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 224.22/38.40  | | | | | | | | | | | | | | |                all_52_29) = e1 & op(all_52_31, all_52_31) =
% 224.22/38.40  | | | | | | | | | | | | | | |              e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 224.22/38.40  | | | | | | | | | | | | | | |              all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 224.22/38.40  | | | | | | | | | | | | | | |              = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 224.22/38.40  | | | | | | | | | | | | | | |              $i(all_52_29) & $i(all_52_31))
% 224.22/38.40  | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | BETA: splitting (14568) gives:
% 224.22/38.40  | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | Case 1:
% 224.22/38.40  | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | |   (14569)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 224.22/38.40  | | | | | | | | | | | | | | | |            all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 224.22/38.40  | | | | | | | | | | | | | | | |            op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 224.22/38.40  | | | | | | | | | | | | | | | |              all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 224.22/38.40  | | | | | | | | | | | | | | | |            & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 224.22/38.40  | | | | | | | | | | | | | | | |            & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 224.22/38.40  | | | | | | | | | | | | | | | |            & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 224.22/38.40  | | | | | | | | | | | | | | | |            $i(all_52_23)
% 224.22/38.40  | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | ALPHA: (14569) implies:
% 224.22/38.40  | | | | | | | | | | | | | | | |   (14570)  op(e1, e1) = all_52_21
% 224.22/38.40  | | | | | | | | | | | | | | | |   (14571)  op(all_52_21, all_52_21) = e1
% 224.22/38.40  | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | REF_CLOSE: (45), (12097), (14262), (14570), (14571),
% 224.22/38.40  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.22/38.40  | | | | | | | | | | | | | | | |            #167.
% 224.22/38.40  | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | Case 2:
% 224.22/38.40  | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | |   (14572)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 224.22/38.40  | | | | | | | | | | | | | | | |            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 224.22/38.40  | | | | | | | | | | | | | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 224.22/38.40  | | | | | | | | | | | | | | | |              all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 224.22/38.40  | | | | | | | | | | | | | | | |            & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 224.22/38.40  | | | | | | | | | | | | | | | |            & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 224.22/38.40  | | | | | | | | | | | | | | | |            & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 224.22/38.40  | | | | | | | | | | | | | | | |            $i(all_52_31)
% 224.22/38.40  | | | | | | | | | | | | | | | | 
% 224.22/38.40  | | | | | | | | | | | | | | | | ALPHA: (14572) implies:
% 224.22/38.40  | | | | | | | | | | | | | | | |   (14573)  op(e0, e3) = all_52_25
% 224.22/38.41  | | | | | | | | | | | | | | | |   (14574)  op(all_52_25, all_52_25) = e3
% 224.22/38.41  | | | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | | | | REF_CLOSE: (45), (14272), (14277), (14573), (14574),
% 224.22/38.41  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.22/38.41  | | | | | | | | | | | | | | | |            #96.
% 224.22/38.41  | | | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | | | End of split
% 224.22/38.41  | | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | | End of split
% 224.22/38.41  | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | Case 2:
% 224.22/38.41  | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | |   (14575)  all_57_13 = e3 & op(e0, e2) = e3
% 224.22/38.41  | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | | ALPHA: (14575) implies:
% 224.22/38.41  | | | | | | | | | | | | | |   (14576)  op(e0, e2) = e3
% 224.22/38.41  | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_7, e3,
% 224.22/38.41  | | | | | | | | | | | | | |              e2, e0, simplifying with (159), (14576) gives:
% 224.22/38.41  | | | | | | | | | | | | | |   (14577)  all_53_7 = e3
% 224.22/38.41  | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | | REDUCE: (14255), (14577) imply:
% 224.22/38.41  | | | | | | | | | | | | | |   (14578)  $false
% 224.22/38.41  | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | | CLOSE: (14578) is inconsistent.
% 224.22/38.41  | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | End of split
% 224.22/38.41  | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | Case 2:
% 224.22/38.41  | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | |   (14579)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 224.22/38.41  | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 224.22/38.41  | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | BETA: splitting (14579) gives:
% 224.22/38.41  | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | Case 1:
% 224.22/38.41  | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | |   (14580)  all_57_14 = e3 & op(e0, e1) = e3
% 224.22/38.41  | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | | REF_CLOSE: (158), (12089), (14580), (function-axioms) are
% 224.22/38.41  | | | | | | | | | | | | | |            inconsistent by sub-proof #129.
% 224.22/38.41  | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | Case 2:
% 224.22/38.41  | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | |   (14581)  all_57_15 = e3 & op(e0, e0) = e3
% 224.22/38.41  | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | | ALPHA: (14581) implies:
% 224.22/38.41  | | | | | | | | | | | | | |   (14582)  op(e0, e0) = e3
% 224.22/38.41  | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | | REF_CLOSE: (36), (14264), (14582), (function-axioms) are
% 224.22/38.41  | | | | | | | | | | | | | |            inconsistent by sub-proof #151.
% 224.22/38.41  | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | End of split
% 224.22/38.41  | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | End of split
% 224.22/38.41  | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | Case 2:
% 224.22/38.41  | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | |   (14583)  all_57_10 = e3 & op(e2, e0) = e3
% 224.22/38.41  | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | ALPHA: (14583) implies:
% 224.22/38.41  | | | | | | | | | | | |   (14584)  op(e2, e0) = e3
% 224.22/38.41  | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | REF_CLOSE: (165), (14256), (14584), (function-axioms) are
% 224.22/38.41  | | | | | | | | | | | |            inconsistent by sub-proof #2301.
% 224.22/38.41  | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | End of split
% 224.22/38.41  | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | Case 2:
% 224.22/38.41  | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | |   (14585)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 224.22/38.41  | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 224.22/38.41  | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | REF_CLOSE: (36), (161), (12090), (14264), (14585),
% 224.22/38.41  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.22/38.41  | | | | | | | | | | |            #146.
% 224.22/38.41  | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | End of split
% 224.22/38.41  | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | Case 2:
% 224.22/38.41  | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | |   (14586)  all_12_2 = e3
% 224.22/38.41  | | | | | | | | | |   (14587)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0
% 224.22/38.41  | | | | | | | | | |              & op(e0, e3) = all_12_1 & $i(all_12_0) &
% 224.22/38.41  | | | | | | | | | |              $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0, e3)
% 224.22/38.41  | | | | | | | | | |              = all_12_1 & $i(all_12_1))
% 224.22/38.41  | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | COMBINE_EQS: (325), (14586) imply:
% 224.22/38.41  | | | | | | | | | |   (14588)  all_4_2 = e3
% 224.22/38.41  | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | SIMP: (14588) implies:
% 224.22/38.41  | | | | | | | | | |   (14589)  all_4_2 = e3
% 224.22/38.41  | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | COMBINE_EQS: (318), (14589) imply:
% 224.22/38.41  | | | | | | | | | |   (14590)  all_22_2 = e3
% 224.22/38.41  | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | REDUCE: (351), (14589) imply:
% 224.22/38.41  | | | | | | | | | |   (14591)   ~ (all_53_3 = e3)
% 224.22/38.41  | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | REDUCE: (370), (14589) imply:
% 224.22/38.41  | | | | | | | | | |   (14592)   ~ (all_53_12 = e3)
% 224.22/38.41  | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | REDUCE: (36), (14589) imply:
% 224.22/38.41  | | | | | | | | | |   (14593)  op(e0, e0) = e3
% 224.22/38.41  | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | BETA: splitting (236) gives:
% 224.22/38.41  | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | Case 1:
% 224.22/38.41  | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | |   (14594)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 224.22/38.41  | | | | | | | | | | |              & op(e2, e3) = e3)
% 224.22/38.41  | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | BETA: splitting (14594) gives:
% 224.22/38.41  | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | Case 1:
% 224.22/38.41  | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | |   (14595)  all_57_0 = e3 & op(e3, e3) = e3
% 224.22/38.41  | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | ALPHA: (14595) implies:
% 224.22/38.41  | | | | | | | | | | | |   (14596)  op(e3, e3) = e3
% 224.22/38.41  | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, e3,
% 224.22/38.41  | | | | | | | | | | | |              e3, e3, simplifying with (45), (14596) gives:
% 224.22/38.41  | | | | | | | | | | | |   (14597)  all_10_2 = e3
% 224.22/38.41  | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | BETA: splitting (107) gives:
% 224.22/38.41  | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | Case 1:
% 224.22/38.41  | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | |   (14598)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 224.22/38.41  | | | | | | | | | | | | |              all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 224.22/38.41  | | | | | | | | | | | | |              op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 224.22/38.41  | | | | | | | | | | | | |                all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 224.22/38.41  | | | | | | | | | | | | |              op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 224.22/38.41  | | | | | | | | | | | | |              op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 224.22/38.41  | | | | | | | | | | | | |              $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 224.22/38.41  | | | | | | | | | | | | |              $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 224.22/38.41  | | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 224.22/38.41  | | | | | | | | | | | | |                all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 224.22/38.41  | | | | | | | | | | | | |              & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 224.22/38.41  | | | | | | | | | | | | |                all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 224.22/38.41  | | | | | | | | | | | | |              op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 224.22/38.41  | | | | | | | | | | | | |              & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 224.22/38.41  | | | | | | | | | | | | |              $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 224.22/38.41  | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (169), (170), (171), (235),
% 224.22/38.41  | | | | | | | | | | | | |            (14254), (14261), (14596), (14598),
% 224.22/38.41  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.22/38.41  | | | | | | | | | | | | |            #94.
% 224.22/38.41  | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | Case 2:
% 224.22/38.41  | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | |   (14599)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 224.22/38.41  | | | | | | | | | | | | |              & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 224.22/38.41  | | | | | | | | | | | | |              & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 224.22/38.41  | | | | | | | | | | | | |                all_52_21) = e1 & op(all_52_23, all_52_23) =
% 224.22/38.41  | | | | | | | | | | | | |              e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 224.22/38.41  | | | | | | | | | | | | |              all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 224.22/38.41  | | | | | | | | | | | | |              = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 224.22/38.41  | | | | | | | | | | | | |              $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 224.22/38.41  | | | | | | | | | | | | |              & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 224.22/38.41  | | | | | | | | | | | | |              e0 & op(all_52_25, all_52_25) = e3 &
% 224.22/38.41  | | | | | | | | | | | | |              op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 224.22/38.41  | | | | | | | | | | | | |                all_52_29) = e1 & op(all_52_31, all_52_31) =
% 224.22/38.41  | | | | | | | | | | | | |              e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 224.22/38.41  | | | | | | | | | | | | |              all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 224.22/38.41  | | | | | | | | | | | | |              = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 224.22/38.41  | | | | | | | | | | | | |              $i(all_52_29) & $i(all_52_31))
% 224.22/38.41  | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | BETA: splitting (14599) gives:
% 224.22/38.41  | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | Case 1:
% 224.22/38.41  | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | |   (14600)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 224.22/38.41  | | | | | | | | | | | | | |            all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 224.22/38.41  | | | | | | | | | | | | | |            op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 224.22/38.41  | | | | | | | | | | | | | |              all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 224.22/38.41  | | | | | | | | | | | | | |            & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 224.22/38.41  | | | | | | | | | | | | | |            & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 224.22/38.41  | | | | | | | | | | | | | |            & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 224.22/38.41  | | | | | | | | | | | | | |            $i(all_52_23)
% 224.22/38.41  | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | | ALPHA: (14600) implies:
% 224.22/38.41  | | | | | | | | | | | | | |   (14601)  op(e1, e1) = all_52_21
% 224.22/38.41  | | | | | | | | | | | | | |   (14602)  op(all_52_21, all_52_21) = e1
% 224.22/38.41  | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | | REF_CLOSE: (45), (12097), (14262), (14601), (14602),
% 224.22/38.41  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.22/38.41  | | | | | | | | | | | | | |            #167.
% 224.22/38.41  | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | Case 2:
% 224.22/38.41  | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | |   (14603)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 224.22/38.41  | | | | | | | | | | | | | |            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 224.22/38.41  | | | | | | | | | | | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 224.22/38.41  | | | | | | | | | | | | | |              all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 224.22/38.41  | | | | | | | | | | | | | |            & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 224.22/38.41  | | | | | | | | | | | | | |            & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 224.22/38.41  | | | | | | | | | | | | | |            & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 224.22/38.41  | | | | | | | | | | | | | |            $i(all_52_31)
% 224.22/38.41  | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | | REF_CLOSE: (7), (14593), (14596), (14603), (function-axioms)
% 224.22/38.41  | | | | | | | | | | | | | |            are inconsistent by sub-proof #1442.
% 224.22/38.41  | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | End of split
% 224.22/38.41  | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | End of split
% 224.22/38.41  | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | Case 2:
% 224.22/38.41  | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | |   (14604)  all_57_2 = e3 & op(e2, e3) = e3
% 224.22/38.41  | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | REF_CLOSE: (168), (14253), (14604), (function-axioms) are
% 224.22/38.41  | | | | | | | | | | | |            inconsistent by sub-proof #2299.
% 224.22/38.41  | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | End of split
% 224.22/38.41  | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | Case 2:
% 224.22/38.41  | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | |   (14605)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 224.22/38.41  | | | | | | | | | | |              e3 & op(e0, e3) = e3)
% 224.22/38.41  | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | BETA: splitting (14605) gives:
% 224.22/38.41  | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | Case 1:
% 224.22/38.41  | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | |   (14606)  all_57_6 = e3 & op(e1, e3) = e3
% 224.22/38.41  | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | ALPHA: (14606) implies:
% 224.22/38.41  | | | | | | | | | | | |   (14607)  all_57_6 = e3
% 224.22/38.41  | | | | | | | | | | | |   (14608)  op(e1, e3) = e3
% 224.22/38.41  | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | BETA: splitting (237) gives:
% 224.22/38.41  | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | Case 1:
% 224.22/38.41  | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | |   (14609)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 224.22/38.41  | | | | | | | | | | | | |              & op(e3, e2) = e3)
% 224.22/38.41  | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (171), (230), (232),
% 224.22/38.41  | | | | | | | | | | | | |            (234), (14254), (14607), (14609),
% 224.22/38.41  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.22/38.41  | | | | | | | | | | | | |            #269.
% 224.22/38.41  | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | Case 2:
% 224.22/38.41  | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | |   (14610)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 224.22/38.41  | | | | | | | | | | | | |              & op(e3, e0) = e3)
% 224.22/38.41  | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | BETA: splitting (14610) gives:
% 224.22/38.41  | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | Case 1:
% 224.22/38.41  | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | |   (14611)  all_57_4 = e3 & op(e3, e1) = e3
% 224.22/38.41  | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | | ALPHA: (14611) implies:
% 224.22/38.41  | | | | | | | | | | | | | |   (14612)  all_57_4 = e3
% 224.22/38.41  | | | | | | | | | | | | | |   (14613)  op(e3, e1) = e3
% 224.22/38.41  | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (39), (45),
% 224.22/38.41  | | | | | | | | | | | | | |            (58), (64), (67), (88), (107), (121), (122),
% 224.22/38.41  | | | | | | | | | | | | | |            (135), (141), (142), (145), (150), (158), (159),
% 224.22/38.41  | | | | | | | | | | | | | |            (160), (161), (163), (164), (165), (166), (168),
% 224.22/38.41  | | | | | | | | | | | | | |            (169), (170), (171), (195), (205), (207), (208),
% 224.22/38.41  | | | | | | | | | | | | | |            (209), (210), (211), (212), (213), (214), (215),
% 224.22/38.41  | | | | | | | | | | | | | |            (216), (217), (218), (219), (220), (221), (222),
% 224.22/38.41  | | | | | | | | | | | | | |            (223), (224), (225), (226), (227), (228), (229),
% 224.22/38.41  | | | | | | | | | | | | | |            (230), (231), (232), (233), (234), (235), (236),
% 224.22/38.41  | | | | | | | | | | | | | |            (237), (249), (277), (315), (327), (336), (338),
% 224.22/38.41  | | | | | | | | | | | | | |            (342), (344), (346), (348), (361), (363), (364),
% 224.22/38.41  | | | | | | | | | | | | | |            (366), (368), (373), (12090), (14255), (14256),
% 224.22/38.41  | | | | | | | | | | | | | |            (14260), (14261), (14262), (14587), (14590),
% 224.22/38.41  | | | | | | | | | | | | | |            (14592), (14607), (14608), (14612), (14613),
% 224.22/38.41  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.22/38.41  | | | | | | | | | | | | | |            #187.
% 224.22/38.41  | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | Case 2:
% 224.22/38.41  | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | |   (14614)  all_57_9 = e3 & op(e3, e0) = e3
% 224.22/38.41  | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | | ALPHA: (14614) implies:
% 224.22/38.41  | | | | | | | | | | | | | |   (14615)  op(e3, e0) = e3
% 224.22/38.41  | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | | REF_CLOSE: (169), (14592), (14615), (function-axioms) are
% 224.22/38.41  | | | | | | | | | | | | | |            inconsistent by sub-proof #2458.
% 224.22/38.41  | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | End of split
% 224.22/38.41  | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | End of split
% 224.22/38.41  | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | Case 2:
% 224.22/38.41  | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | |   (14616)  all_57_12 = e3 & op(e0, e3) = e3
% 224.22/38.41  | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | ALPHA: (14616) implies:
% 224.22/38.41  | | | | | | | | | | | |   (14617)  op(e0, e3) = e3
% 224.22/38.41  | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | REF_CLOSE: (160), (14591), (14617), (function-axioms) are
% 224.22/38.41  | | | | | | | | | | | |            inconsistent by sub-proof #132.
% 224.22/38.41  | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | End of split
% 224.22/38.41  | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | End of split
% 224.22/38.41  | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | End of split
% 224.22/38.41  | | | | | | | | | 
% 224.22/38.41  | | | | | | | | Case 2:
% 224.22/38.41  | | | | | | | | | 
% 224.22/38.41  | | | | | | | | |   (14618)  all_10_2 = e1
% 224.22/38.41  | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | REDUCE: (338), (14618) imply:
% 224.22/38.41  | | | | | | | | |   (14619)   ~ (all_53_1 = e1)
% 224.22/38.41  | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | REDUCE: (340), (14618) imply:
% 224.22/38.41  | | | | | | | | |   (14620)   ~ (all_53_2 = e1)
% 224.22/38.41  | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | REDUCE: (342), (14618) imply:
% 224.22/38.41  | | | | | | | | |   (14621)   ~ (all_53_3 = e1)
% 224.22/38.41  | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | REDUCE: (344), (14618) imply:
% 224.22/38.41  | | | | | | | | |   (14622)   ~ (all_53_4 = e1)
% 224.22/38.41  | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | REDUCE: (346), (14618) imply:
% 224.22/38.41  | | | | | | | | |   (14623)   ~ (all_53_8 = e1)
% 224.22/38.41  | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | REDUCE: (348), (14618) imply:
% 224.22/38.41  | | | | | | | | |   (14624)   ~ (all_53_12 = e1)
% 224.22/38.41  | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | REDUCE: (45), (14618) imply:
% 224.22/38.41  | | | | | | | | |   (14625)  op(e3, e3) = e1
% 224.22/38.41  | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | BETA: splitting (236) gives:
% 224.22/38.41  | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | Case 1:
% 224.22/38.41  | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | |   (14626)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 224.22/38.41  | | | | | | | | | |              & op(e2, e3) = e3)
% 224.22/38.41  | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | REF_CLOSE: (8), (168), (14253), (14625), (14626),
% 224.22/38.41  | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.22/38.41  | | | | | | | | | |            #181.
% 224.22/38.41  | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | Case 2:
% 224.22/38.41  | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | |   (14627)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 224.22/38.41  | | | | | | | | | |              e3 & op(e0, e3) = e3)
% 224.22/38.41  | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | BETA: splitting (14627) gives:
% 224.22/38.41  | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | Case 1:
% 224.22/38.41  | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | |   (14628)  all_57_6 = e3 & op(e1, e3) = e3
% 224.22/38.41  | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | REF_CLOSE: (164), (12085), (14628), (function-axioms) are
% 224.22/38.41  | | | | | | | | | | |            inconsistent by sub-proof #153.
% 224.22/38.41  | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | Case 2:
% 224.22/38.41  | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | |   (14629)  all_57_12 = e3 & op(e0, e3) = e3
% 224.22/38.41  | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | ALPHA: (14629) implies:
% 224.22/38.41  | | | | | | | | | | |   (14630)  all_57_12 = e3
% 224.22/38.41  | | | | | | | | | | |   (14631)  op(e0, e3) = e3
% 224.22/38.41  | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | BETA: splitting (237) gives:
% 224.22/38.41  | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | Case 1:
% 224.22/38.41  | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | |   (14632)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 224.22/38.41  | | | | | | | | | | | |              & op(e3, e2) = e3)
% 224.22/38.41  | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | BETA: splitting (14632) gives:
% 224.22/38.41  | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | Case 1:
% 224.22/38.41  | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | |   (14633)  all_57_0 = e3 & op(e3, e3) = e3
% 224.22/38.41  | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | ALPHA: (14633) implies:
% 224.22/38.41  | | | | | | | | | | | | |   (14634)  op(e3, e3) = e3
% 224.22/38.41  | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | REF_CLOSE: (8), (14625), (14634), (function-axioms) are
% 224.22/38.41  | | | | | | | | | | | | |            inconsistent by sub-proof #2495.
% 224.22/38.41  | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | Case 2:
% 224.22/38.41  | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | |   (14635)  all_57_1 = e3 & op(e3, e2) = e3
% 224.22/38.41  | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | REF_CLOSE: (171), (14254), (14635), (function-axioms) are
% 224.22/38.41  | | | | | | | | | | | | |            inconsistent by sub-proof #2286.
% 224.22/38.41  | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | End of split
% 224.22/38.41  | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | Case 2:
% 224.22/38.41  | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | |   (14636)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 224.22/38.41  | | | | | | | | | | | |              & op(e3, e0) = e3)
% 224.22/38.41  | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | BETA: splitting (14636) gives:
% 224.22/38.41  | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | Case 1:
% 224.22/38.41  | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | |   (14637)  all_57_4 = e3 & op(e3, e1) = e3
% 224.22/38.41  | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | REF_CLOSE: (170), (12087), (14637), (function-axioms) are
% 224.22/38.41  | | | | | | | | | | | | |            inconsistent by sub-proof #177.
% 224.22/38.41  | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | Case 2:
% 224.22/38.41  | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | |   (14638)  all_57_9 = e3 & op(e3, e0) = e3
% 224.22/38.41  | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | ALPHA: (14638) implies:
% 224.22/38.41  | | | | | | | | | | | | |   (14639)  op(e3, e0) = e3
% 224.22/38.41  | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_3, e3,
% 224.22/38.41  | | | | | | | | | | | | |              e3, e0, simplifying with (160), (14631) gives:
% 224.22/38.41  | | | | | | | | | | | | |   (14640)  all_53_3 = e3
% 224.22/38.41  | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_12,
% 224.22/38.41  | | | | | | | | | | | | |              e3, e0, e3, simplifying with (169), (14639) gives:
% 224.22/38.41  | | | | | | | | | | | | |   (14641)  all_53_12 = e3
% 224.22/38.41  | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | REDUCE: (370), (14641) imply:
% 224.22/38.41  | | | | | | | | | | | | |   (14642)   ~ (all_4_2 = e3)
% 224.22/38.41  | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | SIMP: (14642) implies:
% 224.22/38.41  | | | | | | | | | | | | |   (14643)   ~ (all_4_2 = e3)
% 224.22/38.41  | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | BETA: splitting (107) gives:
% 224.22/38.41  | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | Case 1:
% 224.22/38.41  | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | |   (14644)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 224.22/38.41  | | | | | | | | | | | | | |              all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 224.22/38.41  | | | | | | | | | | | | | |              op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 224.22/38.41  | | | | | | | | | | | | | |                all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 224.22/38.41  | | | | | | | | | | | | | |              op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 224.22/38.41  | | | | | | | | | | | | | |              op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 224.22/38.41  | | | | | | | | | | | | | |              $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 224.22/38.41  | | | | | | | | | | | | | |              $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 224.22/38.41  | | | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 224.22/38.41  | | | | | | | | | | | | | |                all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 224.22/38.41  | | | | | | | | | | | | | |              & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 224.22/38.41  | | | | | | | | | | | | | |                all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 224.22/38.41  | | | | | | | | | | | | | |              op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 224.22/38.41  | | | | | | | | | | | | | |              & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 224.22/38.41  | | | | | | | | | | | | | |              $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 224.22/38.41  | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | | BETA: splitting (14644) gives:
% 224.22/38.41  | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | | Case 1:
% 224.22/38.41  | | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | | |   (14645)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 224.22/38.41  | | | | | | | | | | | | | | |            all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 224.22/38.41  | | | | | | | | | | | | | | |            op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 224.22/38.41  | | | | | | | | | | | | | | |              all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 224.22/38.41  | | | | | | | | | | | | | | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 224.22/38.41  | | | | | | | | | | | | | | |            op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 224.22/38.41  | | | | | | | | | | | | | | |            $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 224.22/38.41  | | | | | | | | | | | | | | |            $i(all_52_7)
% 224.22/38.41  | | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | | | ALPHA: (14645) implies:
% 224.22/38.41  | | | | | | | | | | | | | | |   (14646)  op(e3, e0) = all_52_7
% 224.22/38.41  | | | | | | | | | | | | | | |   (14647)  op(e3, e3) = all_52_1
% 224.22/38.41  | | | | | | | | | | | | | | |   (14648)  op(all_52_7, all_52_7) = e0
% 224.22/38.41  | | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | | | REF_CLOSE: (4), (14625), (14639), (14646), (14647), (14648),
% 224.22/38.41  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.22/38.41  | | | | | | | | | | | | | | |            #123.
% 224.22/38.41  | | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | | Case 2:
% 224.22/38.41  | | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | | |   (14649)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 224.22/38.41  | | | | | | | | | | | | | | |            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 224.22/38.41  | | | | | | | | | | | | | | |            op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 224.22/38.41  | | | | | | | | | | | | | | |              all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 224.22/38.41  | | | | | | | | | | | | | | |            & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 224.22/38.41  | | | | | | | | | | | | | | |            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 224.22/38.41  | | | | | | | | | | | | | | |            $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 224.22/38.41  | | | | | | | | | | | | | | |            $i(all_52_15)
% 224.22/38.41  | | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | | | ALPHA: (14649) implies:
% 224.22/38.41  | | | | | | | | | | | | | | |   (14650)  op(e2, e2) = all_52_11
% 224.22/38.41  | | | | | | | | | | | | | | |   (14651)  op(all_52_11, all_52_11) = e2
% 224.22/38.41  | | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3,
% 224.22/38.41  | | | | | | | | | | | | | | |              all_52_11, e2, e2, simplifying with (14261),
% 224.22/38.41  | | | | | | | | | | | | | | |              (14650) gives:
% 224.22/38.41  | | | | | | | | | | | | | | |   (14652)  all_52_11 = e3
% 224.22/38.41  | | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | | | REDUCE: (14651), (14652) imply:
% 224.22/38.41  | | | | | | | | | | | | | | |   (14653)  op(e3, e3) = e2
% 224.22/38.41  | | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (164), (168), (232), (14619), (14620),
% 224.22/38.41  | | | | | | | | | | | | | | |            (14630), (14653), (function-axioms) are
% 224.22/38.41  | | | | | | | | | | | | | | |            inconsistent by sub-proof #238.
% 224.22/38.41  | | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | | End of split
% 224.22/38.41  | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | Case 2:
% 224.22/38.41  | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | |   (14654)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 224.22/38.41  | | | | | | | | | | | | | |              & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 224.22/38.41  | | | | | | | | | | | | | |              & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 224.22/38.41  | | | | | | | | | | | | | |                all_52_21) = e1 & op(all_52_23, all_52_23) =
% 224.22/38.41  | | | | | | | | | | | | | |              e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 224.22/38.41  | | | | | | | | | | | | | |              all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 224.22/38.41  | | | | | | | | | | | | | |              = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 224.22/38.41  | | | | | | | | | | | | | |              $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 224.22/38.41  | | | | | | | | | | | | | |              & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 224.22/38.41  | | | | | | | | | | | | | |              e0 & op(all_52_25, all_52_25) = e3 &
% 224.22/38.41  | | | | | | | | | | | | | |              op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 224.22/38.41  | | | | | | | | | | | | | |                all_52_29) = e1 & op(all_52_31, all_52_31) =
% 224.22/38.41  | | | | | | | | | | | | | |              e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 224.22/38.41  | | | | | | | | | | | | | |              all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 224.22/38.41  | | | | | | | | | | | | | |              = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 224.22/38.41  | | | | | | | | | | | | | |              $i(all_52_29) & $i(all_52_31))
% 224.22/38.41  | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | | BETA: splitting (14654) gives:
% 224.22/38.41  | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | | Case 1:
% 224.22/38.41  | | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | | |   (14655)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 224.22/38.41  | | | | | | | | | | | | | | |            all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 224.22/38.41  | | | | | | | | | | | | | | |            op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 224.22/38.41  | | | | | | | | | | | | | | |              all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 224.22/38.41  | | | | | | | | | | | | | | |            & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 224.22/38.41  | | | | | | | | | | | | | | |            & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 224.22/38.41  | | | | | | | | | | | | | | |            & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 224.22/38.41  | | | | | | | | | | | | | | |            $i(all_52_23)
% 224.22/38.41  | | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | | | ALPHA: (14655) implies:
% 224.22/38.41  | | | | | | | | | | | | | | |   (14656)  op(e1, e1) = all_52_21
% 224.22/38.41  | | | | | | | | | | | | | | |   (14657)  op(e1, e2) = all_52_19
% 224.22/38.41  | | | | | | | | | | | | | | |   (14658)  op(e1, e3) = all_52_17
% 224.22/38.41  | | | | | | | | | | | | | | |   (14659)  op(all_52_21, all_52_21) = e1
% 224.22/38.41  | | | | | | | | | | | | | | |   (14660)  op(all_52_19, all_52_19) = e2
% 224.22/38.41  | | | | | | | | | | | | | | |   (14661)  op(all_52_17, all_52_17) = e3
% 224.22/38.41  | | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3,
% 224.22/38.41  | | | | | | | | | | | | | | |              all_52_21, e1, e1, simplifying with (12097),
% 224.22/38.41  | | | | | | | | | | | | | | |              (14656) gives:
% 224.22/38.41  | | | | | | | | | | | | | | |   (14662)  all_52_21 = e3
% 224.22/38.41  | | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_6,
% 224.22/38.41  | | | | | | | | | | | | | | |              all_52_19, e2, e1, simplifying with (163), (14657)
% 224.22/38.41  | | | | | | | | | | | | | | |              gives:
% 224.22/38.41  | | | | | | | | | | | | | | |   (14663)  all_53_6 = all_52_19
% 224.22/38.41  | | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_2,
% 224.22/38.41  | | | | | | | | | | | | | | |              all_52_17, e3, e1, simplifying with (164), (14658)
% 224.22/38.41  | | | | | | | | | | | | | | |              gives:
% 224.22/38.41  | | | | | | | | | | | | | | |   (14664)  all_53_2 = all_52_17
% 224.22/38.41  | | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | | | REDUCE: (12085), (14664) imply:
% 224.22/38.41  | | | | | | | | | | | | | | |   (14665)   ~ (all_52_17 = e3)
% 224.22/38.41  | | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | | | BETA: splitting (76) gives:
% 224.22/38.41  | | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | | | Case 1:
% 224.22/38.41  | | | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | | | |   (14666)   ~ (all_30_2 = e1)
% 224.22/38.41  | | | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | | | | REDUCE: (330), (14666) imply:
% 224.22/38.41  | | | | | | | | | | | | | | | |   (14667)   ~ (all_4_2 = e1)
% 224.22/38.41  | | | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 224.22/38.41  | | | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.41  | | | | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | | | | |   (14668)  all_55_15 = e3
% 224.22/38.41  | | | | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (14668) imply:
% 224.22/38.41  | | | | | | | | | | | | | | | | |   (14669)  all_4_2 = e3
% 224.22/38.41  | | | | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | | | | | REDUCE: (14643), (14669) imply:
% 224.22/38.41  | | | | | | | | | | | | | | | | |   (14670)  $false
% 224.22/38.41  | | | | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | | | | | CLOSE: (14670) is inconsistent.
% 224.22/38.41  | | | | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.41  | | | | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | | | | |   (14671)   ~ (all_55_15 = e3)
% 224.22/38.41  | | | | | | | | | | | | | | | | |   (14672)  all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 224.22/38.41  | | | | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | | | | | BETA: splitting (14672) gives:
% 224.22/38.41  | | | | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.41  | | | | | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | | | | | |   (14673)  all_55_15 = e2
% 224.22/38.41  | | | | | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (14673) imply:
% 224.22/38.41  | | | | | | | | | | | | | | | | | |   (14674)  all_4_2 = e2
% 224.22/38.41  | | | | | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | | | | | | REDUCE: (373), (14674) imply:
% 224.22/38.41  | | | | | | | | | | | | | | | | | |   (14675)  $false
% 224.22/38.41  | | | | | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | | | | | | CLOSE: (14675) is inconsistent.
% 224.22/38.41  | | | | | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.41  | | | | | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | | | | | |   (14676)   ~ (all_55_15 = e2)
% 224.22/38.41  | | | | | | | | | | | | | | | | | |   (14677)  all_55_15 = e1 | all_55_15 = e0
% 224.22/38.41  | | | | | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | | | | | | BETA: splitting (14677) gives:
% 224.22/38.41  | | | | | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.41  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.41  | | | | | | | | | | | | | | | | | | |   (14678)  all_55_15 = e1
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (14678) imply:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | |   (14679)  all_4_2 = e1
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | REDUCE: (14667), (14679) imply:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | |   (14680)  $false
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | CLOSE: (14680) is inconsistent.
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | |   (14681)  all_55_15 = e0
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (14681) imply:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | |   (14682)  all_4_2 = e0
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | REDUCE: (362), (14682) imply:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | |   (14683)   ~ (all_53_7 = e0)
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | REDUCE: (371), (14682) imply:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | |   (14684)   ~ (all_53_13 = e0)
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | REDUCE: (14643), (14682) imply:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | |   (14685)   ~ (e3 = e0)
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | REDUCE: (373), (14682) imply:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | |   (14686)   ~ (e2 = e0)
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | REDUCE: (14667), (14682) imply:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | |   (14687)   ~ (e1 = e0)
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | REDUCE: (36), (14682) imply:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | |   (14688)  op(e0, e0) = e0
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | |   (14689)  all_57_15 = e0 & op(e0, e0) = e0
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | ALPHA: (14689) implies:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | |   (14690)  all_57_15 = e0
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | |   (14691)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14691) gives:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | |   (14692)  all_57_12 = e2 & op(e0, e3) = e2
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14692) implies:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | |   (14693)  all_57_12 = e2
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (14630), (14693) are inconsistent by
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2392.
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | |   (14694)  all_57_13 = e2 & op(e0, e2) = e2
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14694) implies:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | |   (14695)  all_57_13 = e2
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | |   (14696)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14696) gives:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | |   (14697)  all_57_12 = e1 & op(e0, e3) = e1
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (14621), (14697), (function-axioms) are
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1947.
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | |   (14698)  all_57_13 = e1 & op(e0, e2) = e1
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14698) implies:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | |   (14699)  all_57_13 = e1
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (14695), (14699) are inconsistent by
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2327.
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | |   (14700)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14700) gives:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | |   (14701)  all_57_14 = e1 & op(e0, e1) = e1
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14701) implies:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | |   (14702)  all_57_14 = e1
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | |   (14703)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (171), (14261), (14622), (14703),
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | |            #185.
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | |   (14704)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14704) gives:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | |   (14705)  all_57_7 = e1 & op(e1, e2) = e1
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14705) implies:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | |   (14706)  all_57_7 = e1
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | |   (14707)  op(e1, e2) = e1
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14708)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e0)
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14708) gives:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14709)  all_57_6 = e0 & op(e1, e3) = e0
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14709) implies:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14710)  all_57_6 = e0
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14711)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2)
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14711) gives:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14712)  all_57_0 = e2 & op(e3, e3) = e2
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14712) implies:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14713)  op(e3, e3) = e2
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (164), (168), (232), (14619), (14620),
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14630), (14713), (function-axioms) are
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #238.
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14714)  all_57_2 = e2 & op(e2, e3) = e2
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14714) implies:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14715)  all_57_2 = e2
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14716)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e2)
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (14706), (14710), (14716) are
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #93.
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14717)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e1, e0) = e2)
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14717) gives:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14718)  all_57_8 = e2 & op(e1, e1) = e2
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (12096), (14718) are inconsistent by
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #172.
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14719)  all_57_11 = e2 & op(e1, e0) = e2
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14719) implies:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14720)  all_57_11 = e2
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14721)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14721) gives:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14722)  all_57_9 = e1 & op(e3, e0) = e1
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (14624), (14722), (function-axioms) are
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2131.
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14723)  all_57_10 = e1 & op(e2, e0) = e1
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14723) implies:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14724)  all_57_10 = e1
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14725)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14725) gives:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14726)  all_57_1 = e0 & op(e3, e2) = e0
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14726) implies:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14727)  all_57_1 = e0
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14728)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e2)
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14728) gives:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14729)  all_57_0 = e2 & op(e3, e3) = e2
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14729) implies:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14730)  op(e3, e3) = e2
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (232), (14260), (14630), (14715), (14730),
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #107.
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14731)  all_57_1 = e2 & op(e3, e2) = e2
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14731) implies:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14732)  all_57_1 = e2
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14727), (14732) imply:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14733)  e2 = e0
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (14733) implies:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14734)  e2 = e0
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14720), (14734) imply:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14735)  all_57_11 = e0
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (160), (169),
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (208), (209), (210), (211), (212), (373), (14621),
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14624), (14639), (14688), (14690), (14702),
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14735), (function-axioms) are inconsistent by
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #92.
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14736)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e2)
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14736) gives:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14709) implies:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14737)  op(e1, e3) = e0
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_17,
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e3, e1, simplifying with (14658), (14737)
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14738)  all_52_17 = e0
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14661), (14738) imply:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14739)  op(e0, e0) = e3
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (14688), (14739), (function-axioms) are
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2304.
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14740)  all_57_9 = e2 & op(e3, e0) = e2
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14740) implies:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14741)  all_57_9 = e2
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (213), (14688), (14720), (14724),
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14741), (function-axioms) are inconsistent by
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #352.
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14742)  all_57_3 = e0 & op(e2, e2) = e0
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (14260), (14742) are inconsistent by
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #262.
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14743)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0)
% 224.22/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (159), (14657), (14660), (14683), (14688),
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14743), (function-axioms) are inconsistent by
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1841.
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14744)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14744) gives:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14745)  all_57_11 = e1 & op(e1, e0) = e1
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (14720), (14745) are inconsistent by
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1726.
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14746)  all_57_15 = e1 & op(e0, e0) = e1
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14746) implies:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14747)  op(e0, e0) = e1
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (14688), (14747), (function-axioms) are
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2290.
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14748)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e3) = e2)
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (14630), (14710), (14748) are
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2391.
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14749)  all_57_7 = e0 & op(e1, e2) = e0
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14749) implies:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14750)  op(e1, e2) = e0
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (14657), (14660), (14688), (14750),
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2158.
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14751)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14751) gives:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14752)  all_57_8 = e0 & op(e1, e1) = e0
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14752) implies:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14753)  op(e1, e1) = e0
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (163), (14656), (14657), (14660), (14707),
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14753), (function-axioms) are inconsistent by
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #332.
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14754)  all_57_11 = e0 & op(e1, e0) = e0
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14754) implies:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14755)  all_57_11 = e0
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (160), (169),
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (208), (209), (210), (211), (212), (373), (14621),
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14624), (14639), (14688), (14690), (14702),
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14755), (function-axioms) are inconsistent by
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #92.
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | |   (14756)  all_57_13 = e1 & op(e0, e2) = e1
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14756) implies:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | |   (14757)  all_57_13 = e1
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (14695), (14757) are inconsistent by
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2327.
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | |   (14758)  all_57_15 = e1 & op(e0, e0) = e1
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14758) implies:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | |   (14759)  op(e0, e0) = e1
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (14688), (14759), (function-axioms) are
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2290.
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | |   (14760)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14760) gives:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | |   (14761)  all_57_14 = e2 & op(e0, e1) = e2
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14761) implies:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | |   (14762)  all_57_14 = e2
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | |   (14763)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e1)
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14763) gives:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | |   (14764)  all_57_4 = e1 & op(e3, e1) = e1
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (14623), (14764), (function-axioms) are
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #116.
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | |   (14765)  all_57_5 = e1 & op(e2, e1) = e1
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14765) implies:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | |   (14766)  all_57_5 = e1
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | |   (14767)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14767) gives:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | |   (14768)  all_57_2 = e0 & op(e2, e3) = e0
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14768) implies:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | |   (14769)  all_57_2 = e0
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | |   (14770)  op(e2, e3) = e0
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14771)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e0)
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14771) gives:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14772)  all_57_4 = e0 & op(e3, e1) = e0
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14772) implies:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14773)  all_57_4 = e0
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14774)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e2)
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14774) gives:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14775)  all_57_0 = e2 & op(e3, e3) = e2
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14775) implies:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14776)  op(e3, e3) = e2
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (164), (168), (232), (14619), (14620),
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14630), (14776), (function-axioms) are
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #238.
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14777)  all_57_1 = e2 & op(e3, e2) = e2
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14777) implies:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14778)  all_57_1 = e2
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14779)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2)
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14779) gives:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14780)  all_57_0 = e2 & op(e3, e3) = e2
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14780) implies:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14781)  op(e3, e3) = e2
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (237),
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14773), (14778), (14781), (function-axioms) are
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1658.
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14782)  all_57_2 = e2 & op(e2, e3) = e2
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14782) implies:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14783)  all_57_2 = e2
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14769), (14783) imply:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14784)  e2 = e0
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14762), (14784) imply:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14785)  all_57_14 = e0
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (208), (209),
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (210), (14621), (14688), (14690), (14785),
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #320.
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14786)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e3) = e2)
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14786) gives:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14787)  all_57_6 = e2 & op(e1, e3) = e2
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14787) implies:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14788)  all_57_6 = e2
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14789)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14789) gives:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14790)  all_57_12 = e1 & op(e0, e3) = e1
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (14621), (14790), (function-axioms) are
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1947.
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14791)  all_57_13 = e1 & op(e0, e2) = e1
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14791) implies:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14792)  all_57_13 = e1
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14793)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14793) gives:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14794)  all_57_1 = e0 & op(e3, e2) = e0
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14794) implies:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14795)  all_57_1 = e0
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14778), (14795) imply:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14796)  e2 = e0
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14762), (14796) imply:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14797)  all_57_14 = e0
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (209), (210), (14688),
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14690), (14792), (14797), (function-axioms) are
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2123.
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14798)  all_57_3 = e0 & op(e2, e2) = e0
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14798) implies:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14799)  all_57_3 = e0
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14769), (14799) are inconsistent by sub-proof
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2246.
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14800)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0)
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (159), (14657), (14660), (14683), (14688),
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14800), (function-axioms) are inconsistent by
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1841.
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14801)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14801) gives:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14802)  all_57_14 = e1 & op(e0, e1) = e1
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14802) implies:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14803)  all_57_14 = e1
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14762), (14803) imply:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14804)  e2 = e1
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (14804) implies:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14805)  e2 = e1
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14788), (14805) imply:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14806)  all_57_6 = e1
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (234), (14625), (14630), (14769),
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14806), (function-axioms) are inconsistent by
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #350.
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14807)  all_57_15 = e1 & op(e0, e0) = e1
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14807) implies:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14808)  op(e0, e0) = e1
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (14688), (14808), (function-axioms) are
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2290.
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14809)  all_57_12 = e2 & op(e0, e3) = e2
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (14630), (14809) are inconsistent by
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2232.
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14810)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e2)
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14810) gives:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14811)  all_57_4 = e2 & op(e3, e1) = e2
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14811) implies:
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14812)  all_57_4 = e2
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14773), (14812) imply:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14813)  e2 = e0
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (14813) implies:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14814)  e2 = e0
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14762), (14814) imply:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14815)  all_57_14 = e0
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (208), (209),
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (210), (14621), (14688), (14690), (14815),
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #320.
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14816)  all_57_9 = e2 & op(e3, e0) = e2
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (14639), (14816), (function-axioms) are
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #306.
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14817)  all_57_5 = e0 & op(e2, e1) = e0
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (14766), (14817) are inconsistent by
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #942.
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14818)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14818) gives:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14819)  all_57_8 = e0 & op(e1, e1) = e0
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14819) implies:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14820)  op(e1, e1) = e0
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (14252), (14656), (14659), (14688), (14770),
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14820), (function-axioms) are inconsistent by
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #227.
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14821)  all_57_14 = e0 & op(e0, e1) = e0
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14821) implies:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14822)  all_57_14 = e0
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (208), (209),
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (210), (14621), (14688), (14690), (14822),
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #320.
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | |   (14823)  all_57_3 = e0 & op(e2, e2) = e0
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (14260), (14823) are inconsistent by
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #262.
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | |   (14824)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0)
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14824) gives:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | |   (14825)  all_57_5 = e0 & op(e2, e1) = e0
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14825) implies:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | |   (14826)  all_57_5 = e0
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (14766), (14826) are inconsistent by
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2350.
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | |   (14827)  all_57_10 = e0 & op(e2, e0) = e0
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14827) implies:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | |   (14828)  op(e2, e0) = e0
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (14684), (14828), (function-axioms) are
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2470.
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | |   (14829)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e1) = e1)
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14829) gives:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | |   (14830)  all_57_8 = e1 & op(e1, e1) = e1
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (12096), (14830) are inconsistent by
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #168.
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | |   (14831)  all_57_14 = e1 & op(e0, e1) = e1
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14831) implies:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | |   (14832)  all_57_14 = e1
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (14762), (14832) are inconsistent by
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2178.
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | |   (14833)  all_57_15 = e2 & op(e0, e0) = e2
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14833) implies:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | |   (14834)  op(e0, e0) = e2
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (373), (14834), (function-axioms) are
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2334.
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | |   (14835)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | ALPHA: (14835) implies:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | |   (14836)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | |                e1) = e0)
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | |   (14837)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | |                e0) = e0)
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | BETA: splitting (14836) gives:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | |   (14838)  all_57_12 = e0 & op(e0, e3) = e0
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (14630), (14838) are inconsistent by
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | |            sub-proof #2237.
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | |   (14839)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14839) gives:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | |   (14840)  all_57_13 = e0 & op(e0, e2) = e0
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14840) implies:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | |   (14841)  op(e0, e2) = e0
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (14683), (14841), (function-axioms) are
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2332.
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | |   (14842)  all_57_14 = e0 & op(e0, e1) = e0
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14842) implies:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | |   (14843)  all_57_14 = e0
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | |   (14844)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14844) gives:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | |   (14845)  all_57_12 = e2 & op(e0, e3) = e2
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (14630), (14845) are inconsistent by
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2232.
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | |   (14846)  all_57_13 = e2 & op(e0, e2) = e2
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14846) implies:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | |   (14847)  all_57_13 = e2
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | |   (14848)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (171), (14261), (14622), (14848),
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | |            #185.
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | |   (14849)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14849) gives:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | |   (14850)  all_57_7 = e1 & op(e1, e2) = e1
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14850) implies:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | |   (14851)  all_57_7 = e1
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14852)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e1)
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14852) gives:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14853)  all_57_4 = e1 & op(e3, e1) = e1
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (14623), (14853), (function-axioms) are
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #116.
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14854)  all_57_5 = e1 & op(e2, e1) = e1
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14854) implies:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14855)  all_57_5 = e1
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14856)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14856) gives:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14857)  all_57_2 = e0 & op(e2, e3) = e0
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14857) implies:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14858)  all_57_2 = e0
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14837) gives:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14859)  all_57_9 = e0 & op(e3, e0) = e0
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14859) implies:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14860)  op(e3, e0) = e0
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (14639), (14860), (function-axioms) are
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #313.
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14861)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 =
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14861) gives:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14862)  all_57_10 = e0 & op(e2, e0) = e0
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14862) implies:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14863)  op(e2, e0) = e0
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (14684), (14863), (function-axioms) are
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2470.
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14864)  all_57_11 = e0 & op(e1, e0) = e0
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14864) implies:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14865)  all_57_11 = e0
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14866)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e2)
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14866) gives:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14867)  all_57_6 = e2 & op(e1, e3) = e2
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14867) implies:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14868)  all_57_6 = e2
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14869)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14869) gives:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14870)  all_57_9 = e2 & op(e3, e0) = e2
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (14639), (14870), (function-axioms) are
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #306.
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14871)  all_57_10 = e2 & op(e2, e0) = e2
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14871) implies:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14872)  all_57_10 = e2
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14873)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14873) gives:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14874)  all_57_9 = e1 & op(e3, e0) = e1
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (14624), (14874), (function-axioms) are
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2131.
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14875)  all_57_10 = e1 & op(e2, e0) = e1
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14875) implies:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14876)  all_57_10 = e1
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14872), (14876) imply:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14877)  e2 = e1
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (14877) implies:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14878)  e2 = e1
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14868), (14878) imply:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14879)  all_57_6 = e1
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (234), (14625), (14630), (14858),
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14879), (function-axioms) are inconsistent by
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #350.
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14880)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14880) gives:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14881)  all_57_11 = e1 & op(e1, e0) = e1
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (14865), (14881) are inconsistent by
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1750.
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14882)  all_57_15 = e1 & op(e0, e0) = e1
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14882) implies:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14883)  op(e0, e0) = e1
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (14688), (14883), (function-axioms) are
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2290.
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14884)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14884) gives:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14885)  all_57_11 = e2 & op(e1, e0) = e2
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14885) implies:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14886)  all_57_11 = e2
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (14865), (14886) are inconsistent by
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1949.
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14887)  all_57_15 = e2 & op(e0, e0) = e2
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14887) implies:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14888)  op(e0, e0) = e2
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (373), (14888), (function-axioms) are
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2334.
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14889)  all_57_7 = e2 & op(e1, e2) = e2
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14889) implies:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14890)  all_57_7 = e2
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14851), (14890) imply:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14891)  e2 = e1
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (14891) implies:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14892)  e2 = e1
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14847), (14892) imply:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14893)  all_57_13 = e1
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (36), (209), (373), (14630),
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14843), (14893), (function-axioms) are
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #179.
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14894)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e1, e0) = e2)
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14894) gives:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14895)  all_57_8 = e2 & op(e1, e1) = e2
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (12096), (14895) are inconsistent by
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #165.
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14896)  all_57_11 = e2 & op(e1, e0) = e2
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14896) implies:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14897)  all_57_11 = e2
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (14865), (14897) are inconsistent by
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1949.
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14898)  all_57_3 = e0 & op(e2, e2) = e0
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (14260), (14898) are inconsistent by
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #262.
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14899)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0)
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (165), (14684), (14855), (14899),
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #239.
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (14900)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e1) = e1)
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (12096), (14843), (14900) are
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #101.
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | |   (14901)  all_57_13 = e1 & op(e0, e2) = e1
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14901) implies:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | |   (14902)  all_57_13 = e1
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (36), (209), (373), (14630),
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | |            (14843), (14902), (function-axioms) are
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #179.
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | |   (14903)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (36), (373), (14843), (14903),
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | |            #2127.
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.43  | | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.43  | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | End of split
% 224.61/38.43  | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | End of split
% 224.61/38.43  | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | Case 2:
% 224.61/38.43  | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | |   (14904)  all_30_2 = e1
% 224.61/38.43  | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | COMBINE_EQS: (330), (14904) imply:
% 224.61/38.43  | | | | | | | | | | | | | | | |   (14905)  all_4_2 = e1
% 224.61/38.43  | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | SIMP: (14905) implies:
% 224.61/38.43  | | | | | | | | | | | | | | | |   (14906)  all_4_2 = e1
% 224.61/38.43  | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | REDUCE: (362), (14906) imply:
% 224.61/38.43  | | | | | | | | | | | | | | | |   (14907)   ~ (all_53_7 = e1)
% 224.61/38.43  | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | REDUCE: (14643), (14906) imply:
% 224.61/38.43  | | | | | | | | | | | | | | | |   (14908)   ~ (e3 = e1)
% 224.61/38.43  | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 224.61/38.43  | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.43  | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | |   (14909)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 224.61/38.43  | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 224.61/38.43  | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (171), (14261), (14622), (14909),
% 224.61/38.43  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.61/38.43  | | | | | | | | | | | | | | | | |            #185.
% 224.61/38.43  | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.43  | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | |   (14910)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 224.61/38.43  | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 224.61/38.43  | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | BETA: splitting (14910) gives:
% 224.61/38.43  | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | |   (14911)  all_57_7 = e1 & op(e1, e2) = e1
% 224.61/38.43  | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | ALPHA: (14911) implies:
% 224.61/38.43  | | | | | | | | | | | | | | | | | |   (14912)  op(e1, e2) = e1
% 224.61/38.43  | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (12097), (14657), (14660), (14912),
% 224.61/38.43  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.61/38.43  | | | | | | | | | | | | | | | | | |            #119.
% 224.61/38.43  | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.43  | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | |   (14913)  all_57_13 = e1 & op(e0, e2) = e1
% 224.61/38.43  | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (14907), (14913), (function-axioms) are
% 224.61/38.43  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #330.
% 224.61/38.43  | | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | | End of split
% 224.61/38.43  | | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | | End of split
% 224.61/38.43  | | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | End of split
% 224.61/38.43  | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | Case 2:
% 224.61/38.43  | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | |   (14914)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 224.61/38.43  | | | | | | | | | | | | | | |            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 224.61/38.43  | | | | | | | | | | | | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 224.61/38.43  | | | | | | | | | | | | | | |              all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 224.61/38.43  | | | | | | | | | | | | | | |            & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 224.61/38.43  | | | | | | | | | | | | | | |            & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 224.61/38.43  | | | | | | | | | | | | | | |            & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 224.61/38.43  | | | | | | | | | | | | | | |            $i(all_52_31)
% 224.61/38.43  | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | ALPHA: (14914) implies:
% 224.61/38.43  | | | | | | | | | | | | | | |   (14915)  op(e0, e3) = all_52_25
% 224.61/38.43  | | | | | | | | | | | | | | |   (14916)  op(all_52_25, all_52_25) = e3
% 224.61/38.43  | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3,
% 224.61/38.43  | | | | | | | | | | | | | | |              all_52_25, e3, e0, simplifying with (14631),
% 224.61/38.43  | | | | | | | | | | | | | | |              (14915) gives:
% 224.61/38.43  | | | | | | | | | | | | | | |   (14917)  all_52_25 = e3
% 224.61/38.43  | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | REDUCE: (14916), (14917) imply:
% 224.61/38.43  | | | | | | | | | | | | | | |   (14918)  op(e3, e3) = e3
% 224.61/38.43  | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | | REF_CLOSE: (8), (14625), (14918), (function-axioms) are
% 224.61/38.43  | | | | | | | | | | | | | | |            inconsistent by sub-proof #2495.
% 224.61/38.43  | | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | | End of split
% 224.61/38.43  | | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | | End of split
% 224.61/38.43  | | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | | End of split
% 224.61/38.43  | | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | | End of split
% 224.61/38.43  | | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | | End of split
% 224.61/38.43  | | | | | | | | | | 
% 224.61/38.43  | | | | | | | | | End of split
% 224.61/38.43  | | | | | | | | | 
% 224.61/38.43  | | | | | | | | End of split
% 224.61/38.43  | | | | | | | | 
% 224.61/38.43  | | | | | | | End of split
% 224.61/38.43  | | | | | | | 
% 224.61/38.43  | | | | | | Case 2:
% 224.61/38.43  | | | | | | | 
% 224.61/38.43  | | | | | | |   (14919)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 &
% 224.61/38.43  | | | | | | |              op(e2, e0) = e3)
% 224.61/38.43  | | | | | | | 
% 224.61/38.43  | | | | | | | REF_CLOSE: (165), (166), (12088), (14256), (14919),
% 224.61/38.43  | | | | | | |            (function-axioms) are inconsistent by sub-proof #178.
% 224.61/38.43  | | | | | | | 
% 224.61/38.43  | | | | | | End of split
% 224.61/38.43  | | | | | | 
% 224.61/38.43  | | | | | End of split
% 224.61/38.43  | | | | | 
% 224.61/38.43  | | | | Case 2:
% 224.61/38.43  | | | | | 
% 224.61/38.43  | | | | |   (14920)  all_57_14 = e3 & op(e0, e1) = e3
% 224.61/38.43  | | | | | 
% 224.61/38.43  | | | | | REF_CLOSE: (158), (12089), (14920), (function-axioms) are inconsistent
% 224.61/38.43  | | | | |            by sub-proof #129.
% 224.61/38.43  | | | | | 
% 224.61/38.43  | | | | End of split
% 224.61/38.43  | | | | 
% 224.61/38.43  | | | End of split
% 224.61/38.43  | | | 
% 224.61/38.43  | | End of split
% 224.61/38.43  | | 
% 224.61/38.43  | Case 2:
% 224.61/38.43  | | 
% 224.61/38.43  | |   (14921)  all_4_2 = e2
% 224.61/38.43  | |   (14922)  ( ~ (all_4_0 = e3) & op(all_4_1, e0) = all_4_0 & op(e0, e2) =
% 224.61/38.43  | |              all_4_1 & $i(all_4_0) & $i(all_4_1)) | ( ~ (all_4_1 = e1) &
% 224.61/38.43  | |              op(e0, e2) = all_4_1 & $i(all_4_1))
% 224.61/38.43  | | 
% 224.61/38.43  | | COMBINE_EQS: (309), (14921) imply:
% 224.61/38.43  | |   (14923)  all_32_2 = e2
% 224.61/38.43  | | 
% 224.61/38.43  | | REDUCE: (351), (14921) imply:
% 224.61/38.43  | |   (14924)   ~ (all_53_3 = e2)
% 224.61/38.43  | | 
% 224.61/38.43  | | REDUCE: (362), (14921) imply:
% 224.61/38.43  | |   (14925)   ~ (all_53_7 = e2)
% 224.61/38.43  | | 
% 224.61/38.43  | | REDUCE: (369), (14921) imply:
% 224.61/38.43  | |   (14926)   ~ (all_53_11 = e2)
% 224.61/38.43  | | 
% 224.61/38.43  | | REDUCE: (370), (14921) imply:
% 224.61/38.43  | |   (14927)   ~ (all_53_12 = e2)
% 224.61/38.43  | | 
% 224.61/38.43  | | REDUCE: (371), (14921) imply:
% 224.61/38.43  | |   (14928)   ~ (all_53_13 = e2)
% 224.61/38.43  | | 
% 224.61/38.43  | | REDUCE: (372), (14921) imply:
% 224.61/38.43  | |   (14929)   ~ (all_53_14 = e2)
% 224.61/38.43  | | 
% 224.61/38.43  | | BETA: splitting (212) gives:
% 224.61/38.43  | | 
% 224.61/38.43  | | Case 1:
% 224.61/38.43  | | | 
% 224.61/38.43  | | |   (14930)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2,
% 224.61/38.43  | | |                e0) = e2)
% 224.61/38.43  | | | 
% 224.61/38.43  | | | REF_CLOSE: (165), (169), (14927), (14928), (14930), (function-axioms) are
% 224.61/38.43  | | |            inconsistent by sub-proof #1952.
% 224.61/38.43  | | | 
% 224.61/38.43  | | Case 2:
% 224.61/38.43  | | | 
% 224.61/38.43  | | |   (14931)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0,
% 224.61/38.43  | | |                e0) = e2)
% 224.61/38.43  | | | 
% 224.61/38.43  | | | BETA: splitting (14931) gives:
% 224.61/38.43  | | | 
% 224.61/38.43  | | | Case 1:
% 224.61/38.43  | | | | 
% 224.61/38.43  | | | |   (14932)  all_57_11 = e2 & op(e1, e0) = e2
% 224.61/38.43  | | | | 
% 224.61/38.43  | | | | REF_CLOSE: (161), (14929), (14932), (function-axioms) are inconsistent
% 224.61/38.43  | | | |            by sub-proof #91.
% 224.61/38.43  | | | | 
% 224.61/38.43  | | | Case 2:
% 224.61/38.43  | | | | 
% 224.61/38.44  | | | |   (14933)  all_57_15 = e2 & op(e0, e0) = e2
% 224.61/38.44  | | | | 
% 224.61/38.44  | | | | ALPHA: (14933) implies:
% 224.61/38.44  | | | |   (14934)  all_57_15 = e2
% 224.61/38.44  | | | |   (14935)  op(e0, e0) = e2
% 224.61/38.44  | | | | 
% 224.61/38.44  | | | | BETA: splitting (40) gives:
% 224.61/38.44  | | | | 
% 224.61/38.44  | | | | Case 1:
% 224.61/38.44  | | | | | 
% 224.61/38.44  | | | | |   (14936)   ~ (all_6_2 = e3)
% 224.61/38.44  | | | | | 
% 224.61/38.44  | | | | | BETA: splitting (43) gives:
% 224.61/38.44  | | | | | 
% 224.61/38.44  | | | | | Case 1:
% 224.61/38.44  | | | | | | 
% 224.61/38.44  | | | | | |   (14937)   ~ (all_8_2 = e3)
% 224.61/38.44  | | | | | | 
% 224.61/38.44  | | | | | | BETA: splitting (46) gives:
% 224.61/38.44  | | | | | | 
% 224.61/38.44  | | | | | | Case 1:
% 224.61/38.44  | | | | | | | 
% 224.61/38.44  | | | | | | |   (14938)   ~ (all_10_2 = e1)
% 224.61/38.44  | | | | | | | 
% 224.61/38.44  | | | | | | | BETA: splitting (52) gives:
% 224.61/38.44  | | | | | | | 
% 224.61/38.44  | | | | | | | Case 1:
% 224.61/38.44  | | | | | | | | 
% 224.61/38.44  | | | | | | | |   (14939)   ~ (all_14_2 = e0)
% 224.61/38.44  | | | | | | | | 
% 224.61/38.44  | | | | | | | | REDUCE: (328), (14939) imply:
% 224.61/38.44  | | | | | | | |   (14940)   ~ (all_8_2 = e0)
% 224.61/38.44  | | | | | | | | 
% 224.61/38.44  | | | | | | | | BETA: splitting (55) gives:
% 224.61/38.44  | | | | | | | | 
% 224.61/38.44  | | | | | | | | Case 1:
% 224.61/38.44  | | | | | | | | | 
% 224.61/38.44  | | | | | | | | |   (14941)   ~ (all_16_2 = e1)
% 224.61/38.44  | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | REDUCE: (324), (14941) imply:
% 224.61/38.44  | | | | | | | | |   (14942)   ~ (all_8_2 = e1)
% 224.61/38.44  | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | BETA: splitting (200) gives:
% 224.61/38.44  | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | Case 1:
% 224.61/38.44  | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | |   (14943)  all_55_5 = e3
% 224.61/38.44  | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | COMBINE_EQS: (266), (14943) imply:
% 224.61/38.44  | | | | | | | | | |   (14944)  all_8_2 = e3
% 224.61/38.44  | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | REDUCE: (14937), (14944) imply:
% 224.61/38.44  | | | | | | | | | |   (14945)  $false
% 224.61/38.44  | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | CLOSE: (14945) is inconsistent.
% 224.61/38.44  | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | Case 2:
% 224.61/38.44  | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | |   (14946)   ~ (all_55_5 = e3)
% 224.61/38.44  | | | | | | | | | |   (14947)  all_55_5 = e2 | all_55_5 = e1 | all_55_5 = e0
% 224.61/38.44  | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | BETA: splitting (14947) gives:
% 224.61/38.44  | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | Case 1:
% 224.61/38.44  | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | |   (14948)  all_55_5 = e2
% 224.61/38.44  | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | COMBINE_EQS: (266), (14948) imply:
% 224.61/38.44  | | | | | | | | | | |   (14949)  all_8_2 = e2
% 224.61/38.44  | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | REDUCE: (349), (14949) imply:
% 224.61/38.44  | | | | | | | | | | |   (14950)   ~ (all_53_1 = e2)
% 224.61/38.44  | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | REDUCE: (352), (14949) imply:
% 224.61/38.44  | | | | | | | | | | |   (14951)   ~ (all_53_4 = e2)
% 224.61/38.44  | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | REDUCE: (358), (14949) imply:
% 224.61/38.44  | | | | | | | | | | |   (14952)   ~ (all_53_9 = e2)
% 224.61/38.44  | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | REDUCE: (14937), (14949) imply:
% 224.61/38.44  | | | | | | | | | | |   (14953)   ~ (e3 = e2)
% 224.61/38.44  | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | BETA: splitting (224) gives:
% 224.61/38.44  | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | Case 1:
% 224.61/38.44  | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | |   (14954)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 224.61/38.44  | | | | | | | | | | | |              & op(e2, e2) = e2)
% 224.61/38.44  | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | BETA: splitting (14954) gives:
% 224.61/38.44  | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | Case 1:
% 224.61/38.44  | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | |   (14955)  all_57_2 = e2 & op(e2, e3) = e2
% 224.61/38.44  | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | REF_CLOSE: (168), (14950), (14955), (function-axioms) are
% 224.61/38.44  | | | | | | | | | | | | |            inconsistent by sub-proof #2504.
% 224.61/38.44  | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | Case 2:
% 224.61/38.44  | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | |   (14956)  all_57_3 = e2 & op(e2, e2) = e2
% 224.61/38.44  | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | ALPHA: (14956) implies:
% 224.61/38.44  | | | | | | | | | | | | |   (14957)  all_57_3 = e2
% 224.61/38.44  | | | | | | | | | | | | |   (14958)  op(e2, e2) = e2
% 224.61/38.44  | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | BETA: splitting (58) gives:
% 224.61/38.44  | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | Case 1:
% 224.61/38.44  | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | |   (14959)   ~ (all_18_2 = e0)
% 224.61/38.44  | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | REDUCE: (327), (14959) imply:
% 224.61/38.44  | | | | | | | | | | | | | |   (14960)   ~ (all_10_2 = e0)
% 224.61/38.44  | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | BETA: splitting (61) gives:
% 224.61/38.44  | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | Case 1:
% 224.61/38.44  | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | |   (14961)   ~ (all_20_2 = e2)
% 224.61/38.44  | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | REDUCE: (299), (14961) imply:
% 224.61/38.44  | | | | | | | | | | | | | | |   (14962)   ~ (all_10_2 = e2)
% 224.61/38.44  | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 224.61/38.44  | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | Case 1:
% 224.61/38.44  | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | |   (14963)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 224.61/38.44  | | | | | | | | | | | | | | | |              & op(e2, e3) = e2)
% 224.61/38.44  | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | BETA: splitting (14963) gives:
% 224.61/38.44  | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.44  | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | |   (14964)  all_57_0 = e2 & op(e3, e3) = e2
% 224.61/38.44  | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | ALPHA: (14964) implies:
% 224.61/38.44  | | | | | | | | | | | | | | | | |   (14965)  op(e3, e3) = e2
% 224.61/38.44  | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | BETA: splitting (205) gives:
% 224.61/38.44  | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | |   (14966)  all_55_0 = e3
% 224.61/38.44  | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (277), (14966) imply:
% 224.61/38.44  | | | | | | | | | | | | | | | | | |   (14967)  all_10_2 = e3
% 224.61/38.44  | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | REDUCE: (45), (14967) imply:
% 224.61/38.44  | | | | | | | | | | | | | | | | | |   (14968)  op(e3, e3) = e3
% 224.61/38.44  | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (14965), (14968), (function-axioms) are
% 224.61/38.44  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2490.
% 224.61/38.44  | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | |   (14969)  all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 224.61/38.44  | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | REF_CLOSE: (277), (14938), (14960), (14962), (14969) are
% 224.61/38.44  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1953.
% 224.61/38.44  | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | End of split
% 224.61/38.44  | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.44  | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | |   (14970)  all_57_2 = e2 & op(e2, e3) = e2
% 224.61/38.44  | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (14950), (14970), (function-axioms) are
% 224.61/38.44  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2504.
% 224.61/38.44  | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | End of split
% 224.61/38.44  | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | Case 2:
% 224.61/38.44  | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | |   (14971)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 224.61/38.44  | | | | | | | | | | | | | | | |              e2 & op(e0, e3) = e2)
% 224.61/38.44  | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | BETA: splitting (14971) gives:
% 224.61/38.44  | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.44  | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | |   (14972)  all_57_6 = e2 & op(e1, e3) = e2
% 224.61/38.44  | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | ALPHA: (14972) implies:
% 224.61/38.44  | | | | | | | | | | | | | | | | |   (14973)  all_57_6 = e2
% 224.61/38.44  | | | | | | | | | | | | | | | | |   (14974)  op(e1, e3) = e2
% 224.61/38.44  | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | BETA: splitting (205) gives:
% 224.61/38.44  | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | |   (14975)  all_55_0 = e3
% 224.61/38.44  | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (277), (14975) imply:
% 224.61/38.44  | | | | | | | | | | | | | | | | | |   (14976)  all_10_2 = e3
% 224.61/38.44  | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | REDUCE: (344), (14976) imply:
% 224.61/38.44  | | | | | | | | | | | | | | | | | |   (14977)   ~ (all_53_4 = e3)
% 224.61/38.44  | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | REDUCE: (346), (14976) imply:
% 224.61/38.44  | | | | | | | | | | | | | | | | | |   (14978)   ~ (all_53_8 = e3)
% 224.61/38.44  | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | REDUCE: (348), (14976) imply:
% 224.61/38.44  | | | | | | | | | | | | | | | | | |   (14979)   ~ (all_53_12 = e3)
% 224.61/38.44  | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | REDUCE: (45), (14976) imply:
% 224.61/38.44  | | | | | | | | | | | | | | | | | |   (14980)  op(e3, e3) = e3
% 224.61/38.44  | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | |   (14981)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 224.61/38.44  | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e2)
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (171), (14951), (14980), (14981),
% 224.61/38.44  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.61/38.44  | | | | | | | | | | | | | | | | | | |            #2455.
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | |   (14982)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 224.61/38.44  | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e2)
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | BETA: splitting (14982) gives:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | |   (14983)  all_57_4 = e2 & op(e3, e1) = e2
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | ALPHA: (14983) implies:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | |   (14984)  all_57_4 = e2
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | |   (14985)  op(e3, e1) = e2
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | |   (14986)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e3)
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14986) gives:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | |   (14987)  all_57_0 = e3 & op(e3, e3) = e3
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14987) implies:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | |   (14988)  all_57_0 = e3
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_2, e2,
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | |              e3, e1, simplifying with (164), (14974) gives:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | |   (14989)  all_53_2 = e2
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_8, e2,
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (170), (14985) gives:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | |   (14990)  all_53_8 = e2
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (14989) imply:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | |   (14991)   ~ (all_53_6 = e2)
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | SIMP: (14991) implies:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | |   (14992)   ~ (all_53_6 = e2)
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (142), (14989) imply:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | |   (14993)   ~ (all_53_14 = e2)
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (14990) imply:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | |   (14994)   ~ (all_53_12 = e2)
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (363), (14990) imply:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | |   (14995)   ~ (all_6_2 = e2)
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | SIMP: (14995) implies:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | |   (14996)   ~ (all_6_2 = e2)
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | |   (14997)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | |              all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | |              op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | |                all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | |                all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | |              & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | |                all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14997) gives:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | |   (14998)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | |            all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | |              all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_7)
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (14958), (14985), (14998), (function-axioms)
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #90.
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | |   (14999)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | |            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | |              all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_15)
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (14999) implies:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | |   (15000)  op(e2, e0) = all_52_15
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | |   (15001)  op(e2, e2) = all_52_11
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | |   (15002)  op(all_52_15, all_52_15) = e0
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_13,
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | |              all_52_15, e0, e2, simplifying with (165), (15000)
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | |   (15003)  all_53_13 = all_52_15
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | |              all_52_11, e2, e2, simplifying with (14958),
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | |              (15001) gives:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | |   (15004)  all_52_11 = e2
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (15003) imply:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | |   (15005)  all_55_7 = all_52_15
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (114), (15003) imply:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | |   (15006)   ~ (all_53_12 = all_52_15)
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (111), (15003) imply:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | |   (15007)   ~ (all_53_14 = all_52_15)
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (15007) implies:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | |   (15008)   ~ (all_53_14 = all_52_15)
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14928), (15003) imply:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | |   (15009)   ~ (all_52_15 = e2)
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | |   (15010)   ~ (all_24_2 = e0)
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (315), (15010) imply:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | |   (15011)   ~ (all_6_2 = e0)
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | |   (15012)  all_55_10 = e3
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (14936), (15012) are inconsistent by
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2500.
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | |   (15013)   ~ (all_55_10 = e3)
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | |   (15014)  all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15014) gives:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15015)  all_55_10 = e2
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (14996), (15015) are inconsistent by
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2499.
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15016)   ~ (all_55_10 = e2)
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15017)  all_55_10 = e1 | all_55_10 = e0
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15017) gives:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15018)  all_55_10 = e1
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (336), (15018) imply:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15019)  all_6_2 = e1
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (15019) implies:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15020)  all_6_2 = e1
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (361), (15020) imply:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15021)   ~ (all_53_6 = e1)
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (368), (15020) imply:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15022)   ~ (all_53_14 = e1)
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14936), (15020) imply:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15023)   ~ (e3 = e1)
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14996), (15020) imply:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15024)   ~ (e2 = e1)
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (15020) imply:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15025)  op(e1, e1) = e1
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15026)  all_55_3 = e3
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (14979), (15026) are inconsistent by
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2169.
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15027)   ~ (all_55_3 = e3)
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15028)  all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15029)  all_55_1 = e3
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (14977), (15029) are inconsistent by
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2295.
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15030)  all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15031)  all_55_11 = e3
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (15031) imply:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15032)  all_53_14 = e3
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (15032) implies:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15033)  all_53_14 = e3
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (127), (15033) imply:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15034)   ~ (all_53_6 = e3)
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15008), (15033) imply:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15035)   ~ (all_52_15 = e3)
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (15035) implies:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15036)   ~ (all_52_15 = e3)
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15037)  all_55_9 = e3
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (15037) imply:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15038)  all_53_6 = e3
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15034), (15038) imply:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15039)  $false
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (15039) is inconsistent.
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15040)  all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15040) gives:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15041)  all_55_9 = e2
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (15041) imply:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15042)  all_53_6 = e2
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14992), (15042) imply:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15043)  $false
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (15043) is inconsistent.
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15044)  all_55_9 = e1 | all_55_9 = e0
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15044) gives:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15045)  all_55_9 = e1
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (15045) imply:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15046)  all_53_6 = e1
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15021), (15046) imply:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15047)  $false
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (15047) is inconsistent.
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15048)  all_55_9 = e0
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (15048) imply:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15049)  all_53_6 = e0
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (137), (15049) imply:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15050)   ~ (all_53_4 = e0)
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15030) gives:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15051)  all_55_1 = e2
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (14951), (15051) are inconsistent by
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2284.
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15052)  all_55_1 = e1 | all_55_1 = e0
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15052) gives:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15053)  all_55_1 = e1
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (15053) imply:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15054)  all_53_4 = e1
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (15054) implies:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15055)  all_53_4 = e1
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (15055) imply:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15056)   ~ (all_53_12 = e1)
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (15056) implies:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15057)   ~ (all_53_12 = e1)
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15028) gives:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15058)  all_55_3 = e2
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (14927), (15058) are inconsistent by
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1612.
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15059)  all_55_3 = e1 | all_55_3 = e0
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15059) gives:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15060)  all_55_3 = e1
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (15057), (15060) are inconsistent by
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #324.
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15061)  all_55_3 = e0
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (15061) imply:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15062)  all_53_12 = e0
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (15062) implies:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15063)  all_53_12 = e0
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15006), (15063) imply:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15064)   ~ (all_52_15 = e0)
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (15064) implies:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15065)   ~ (all_52_15 = e0)
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15066)  all_55_7 = e3
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15005), (15036), (15066) are inconsistent by
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2063.
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15067)  all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15002), (15005), (15009), (15025), (15065),
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15067), (function-axioms) are inconsistent by
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #89.
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15068)  all_55_1 = e0
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (15050), (15068) are inconsistent by
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2076.
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15069)   ~ (all_55_11 = e3)
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15070)  all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (248), (15069) imply:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15071)   ~ (all_53_14 = e3)
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15072)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15072) gives:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15073)  all_57_9 = e3 & op(e3, e0) = e3
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15073) implies:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15074)  op(e3, e0) = e3
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (14979), (15074), (function-axioms) are
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2458.
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15075)  all_57_10 = e3 & op(e2, e0) = e3
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15075) implies:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15076)  all_57_10 = e3
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15070) gives:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15077)  all_55_11 = e2
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (14929), (15077) are inconsistent by
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2282.
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15078)   ~ (all_55_11 = e2)
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15079)  all_55_11 = e1 | all_55_11 = e0
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15080)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15080) gives:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15081)  all_57_9 = e1 & op(e3, e0) = e1
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15081) implies:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15082)  all_57_9 = e1
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15079) gives:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15083)  all_55_11 = e1
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (15083) imply:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15084)  all_53_14 = e1
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15022), (15084) imply:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15085)  $false
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (15085) is inconsistent.
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15086)  all_55_11 = e0
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (15086) imply:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15087)  all_53_14 = e0
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (15087) imply:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15088)   ~ (all_53_12 = e0)
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15008), (15087) imply:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15089)   ~ (all_52_15 = e0)
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (15089) implies:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15090)   ~ (all_52_15 = e0)
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15071), (15087) imply:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15091)   ~ (e3 = e0)
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14929), (15087) imply:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15092)   ~ (e2 = e0)
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15093)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e0)
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15093) gives:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15094)  all_57_0 = e0 & op(e3, e3) = e0
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15094) implies:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15095)  op(e3, e3) = e0
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (14980), (15095), (function-axioms) are
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2494.
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15096)  all_57_1 = e0 & op(e3, e2) = e0
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15096) implies:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15097)  all_57_1 = e0
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15028) gives:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15098)  all_55_3 = e2
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (14927), (15098) are inconsistent by
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1612.
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15099)   ~ (all_55_3 = e2)
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15100)  all_55_3 = e1 | all_55_3 = e0
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15100) gives:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15101)  all_55_3 = e1
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (15101) imply:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15102)  all_53_12 = e1
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (15102) implies:
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15103)  all_53_12 = e1
% 224.61/38.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15006), (15103) imply:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15104)   ~ (all_52_15 = e1)
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (15104) implies:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15105)   ~ (all_52_15 = e1)
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15106)  all_55_7 = e3
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (15005), (15106) imply:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15107)  all_52_15 = e3
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15002), (15107) imply:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15108)  op(e3, e3) = e0
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (9), (169), (235), (237), (14979),
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15082), (15097), (15108), (function-axioms) are
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2400.
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15109)  all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15005), (15009), (15090), (15105), (15109) are
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2275.
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15110)  all_55_3 = e0
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (15088), (15110) are inconsistent by
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #885.
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15111)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e0)
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15111) gives:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15112)  all_57_4 = e0 & op(e3, e1) = e0
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (14984), (15112) are inconsistent by
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2045.
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15113)  all_57_9 = e0 & op(e3, e0) = e0
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (15088), (15113), (function-axioms) are
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2434.
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15114)  all_57_10 = e1 & op(e2, e0) = e1
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15114) implies:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15115)  all_57_10 = e1
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (15076), (15115) are inconsistent by
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2248.
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15116)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (161), (14935), (15022), (15116),
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #88.
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15117)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (161), (14934), (15071), (15117),
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #87.
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15118)  all_55_10 = e0
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (15011), (15118) are inconsistent by
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2118.
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | |   (15119)  all_24_2 = e0
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (315), (15119) imply:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | |   (15120)  all_6_2 = e0
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (361), (15120) imply:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | |   (15121)   ~ (all_53_6 = e0)
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (368), (15120) imply:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | |   (15122)   ~ (all_53_14 = e0)
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14936), (15120) imply:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | |   (15123)   ~ (e3 = e0)
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14996), (15120) imply:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | |   (15124)   ~ (e2 = e0)
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (15120) imply:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | |   (15125)  op(e1, e1) = e0
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | |   (15126)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e0)
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15126) gives:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15127)  all_57_4 = e0 & op(e3, e1) = e0
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15127) implies:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15128)  all_57_4 = e0
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (14984), (15128) are inconsistent by
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2441.
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15129)  all_57_5 = e0 & op(e2, e1) = e0
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15129) implies:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15130)  all_57_5 = e0
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15131)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e3)
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15131) gives:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15132)  all_57_4 = e3 & op(e3, e1) = e3
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15132) implies:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15133)  all_57_4 = e3
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (235),
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14980), (15133), (function-axioms) are
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2474.
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15134)  all_57_5 = e3 & op(e2, e1) = e3
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15134) implies:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15135)  all_57_5 = e3
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (15130), (15135) are inconsistent by
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2471.
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15136)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e1) = e3)
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15136) gives:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15137)  all_57_8 = e3 & op(e1, e1) = e3
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15137) implies:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15138)  op(e1, e1) = e3
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (14936), (15138), (function-axioms) are
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2468.
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15139)  all_57_14 = e3 & op(e0, e1) = e3
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15139) implies:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15140)  all_57_14 = e3
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15141)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e1)
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15141) gives:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15142)  all_57_4 = e1 & op(e3, e1) = e1
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15142) implies:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15143)  all_57_4 = e1
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (14984), (15143) are inconsistent by
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2430.
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15144)  all_57_5 = e1 & op(e2, e1) = e1
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15144) implies:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15145)  all_57_5 = e1
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (15130), (15145) are inconsistent by
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2350.
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15146)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e1) = e1)
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15146) gives:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15147)  all_57_8 = e1 & op(e1, e1) = e1
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15147) implies:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15148)  op(e1, e1) = e1
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (15125), (15148), (function-axioms) are
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2427.
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15149)  all_57_14 = e1 & op(e0, e1) = e1
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15149) implies:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15150)  all_57_14 = e1
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (15140), (15150) are inconsistent by
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2326.
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | |   (15151)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15151) gives:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15152)  all_57_8 = e0 & op(e1, e1) = e0
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15152) implies:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15153)  all_57_8 = e0
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15154)  all_55_11 = e3
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (15154) imply:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15155)  all_53_14 = e3
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (15155) implies:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15156)  all_53_14 = e3
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (127), (15156) imply:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15157)   ~ (all_53_6 = e3)
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15158)  all_55_9 = e3
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (15157), (15158) are inconsistent by
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2159.
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15159)   ~ (all_55_9 = e3)
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15160)  all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15160) gives:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15161)  all_55_9 = e2
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (14992), (15161) are inconsistent by
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2274.
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15162)   ~ (all_55_9 = e2)
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15163)  all_55_9 = e1 | all_55_9 = e0
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15164)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e1)
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15164) gives:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15165)  all_57_6 = e1 & op(e1, e3) = e1
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (14973), (15165) are inconsistent by
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2389.
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15166)  all_57_7 = e1 & op(e1, e2) = e1
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15166) implies:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15167)  all_57_7 = e1
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15163) gives:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15168)  all_55_9 = e1
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (15168) imply:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15169)  all_53_6 = e1
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (137), (15169) imply:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15170)   ~ (all_53_4 = e1)
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15157), (15169) imply:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15171)   ~ (e3 = e1)
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14992), (15169) imply:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15172)   ~ (e2 = e1)
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15173)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e1)
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15173) gives:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15174)  all_57_0 = e1 & op(e3, e3) = e1
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15174) implies:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15175)  op(e3, e3) = e1
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (14980), (15175), (function-axioms) are
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2495.
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15176)  all_57_1 = e1 & op(e3, e2) = e1
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15176) implies:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15177)  op(e3, e2) = e1
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (171), (15170), (15177), (function-axioms) are
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #363.
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15178)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e1)
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15178) gives:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15179)  all_57_4 = e1 & op(e3, e1) = e1
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15179) implies:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15180)  all_57_4 = e1
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14984), (15180) imply:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15181)  e2 = e1
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (15181) implies:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15182)  e2 = e1
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14973), (15182) imply:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15183)  all_57_6 = e1
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (8), (9), (39), (216), (217), (14936),
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15153), (15167), (15183), (function-axioms) are
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #325.
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15184)  all_57_9 = e1 & op(e3, e0) = e1
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15184) implies:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15185)  all_57_9 = e1
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (161), (207), (14934), (14935), (15000),
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15002), (15009), (15122), (15185),
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #83.
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15186)  all_55_9 = e0
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (15186) imply:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15187)  all_53_6 = e0
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15121), (15187) imply:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15188)  $false
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (15188) is inconsistent.
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15189)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e0) = e1)
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15189) gives:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15190)  all_57_8 = e1 & op(e1, e1) = e1
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15190) implies:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15191)  op(e1, e1) = e1
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (15125), (15191), (function-axioms) are
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2427.
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15192)  all_57_11 = e1 & op(e1, e0) = e1
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15192) implies:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15193)  all_57_11 = e1
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15194)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e3)
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (163), (230), (232),
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (234), (14988), (15157), (15194),
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #82.
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15195)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e1, e0) = e3)
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (39), (14936), (15193), (15195),
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1819.
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15196)   ~ (all_55_11 = e3)
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15197)  all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (248), (15196) imply:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15198)   ~ (all_53_14 = e3)
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15199)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e3)
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15199) gives:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15200)  all_57_6 = e3 & op(e1, e3) = e3
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15200) implies:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15201)  all_57_6 = e3
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (230), (232), (234),
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14988), (15201) are inconsistent by sub-proof
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2010.
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15202)  all_57_7 = e3 & op(e1, e2) = e3
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15202) implies:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15203)  all_57_7 = e3
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15204)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15204) gives:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15205)  all_57_9 = e3 & op(e3, e0) = e3
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15205) implies:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15206)  op(e3, e0) = e3
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (14979), (15206), (function-axioms) are
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2458.
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15207)  all_57_10 = e3 & op(e2, e0) = e3
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15207) implies:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15208)  op(e2, e0) = e3
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15197) gives:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15209)  all_55_11 = e2
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (15209) imply:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15210)  all_53_14 = e2
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14929), (15210) imply:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15211)  $false
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (15211) is inconsistent.
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15212)  all_55_11 = e1 | all_55_11 = e0
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15212) gives:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15213)  all_55_11 = e1
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (15213) imply:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15214)  all_53_14 = e1
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (15214) imply:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15215)   ~ (all_53_12 = e1)
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (202), (268), (14927), (14979), (14980), (15000),
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15002), (15208), (15215), (function-axioms) are
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1999.
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15216)  all_55_11 = e0
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (15216) imply:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15217)  all_53_14 = e0
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15122), (15217) imply:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15218)  $false
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (15218) is inconsistent.
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15219)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15219) gives:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15220)  all_57_11 = e3 & op(e1, e0) = e3
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15220) implies:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15221)  op(e1, e0) = e3
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (15198), (15221), (function-axioms) are
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2330.
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15222)  all_57_15 = e3 & op(e0, e0) = e3
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15222) implies:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15223)  all_57_15 = e3
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15224)  op(e0, e0) = e3
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14934), (15223) imply:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15225)  e3 = e2
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (15203), (15225) imply:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15226)  all_57_7 = e2
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (208),
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (209), (211), (212), (217), (226), (227), (228),
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (229), (14936), (14958), (15223), (15224),
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15226), (function-axioms) are inconsistent by
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #275.
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15227)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e1, e0) = e3)
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (161), (14936), (15198), (15227),
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2310.
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15228)  all_57_14 = e0 & op(e0, e1) = e0
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15228) implies:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15229)  all_57_14 = e0
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15230)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e3)
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15230) gives:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15231)  all_57_4 = e3 & op(e3, e1) = e3
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15231) implies:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15232)  all_57_4 = e3
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (235),
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14980), (15232), (function-axioms) are
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2474.
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15233)  all_57_5 = e3 & op(e2, e1) = e3
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15233) implies:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15234)  all_57_5 = e3
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15235)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e1)
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15235) gives:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15236)  all_57_4 = e1 & op(e3, e1) = e1
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15236) implies:
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15237)  all_57_4 = e1
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (14984), (15237) are inconsistent by
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2430.
% 224.61/38.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15238)  all_57_5 = e1 & op(e2, e1) = e1
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (15234), (15238) are inconsistent by
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2376.
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15239)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e1) = e1)
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (15125), (15229), (15239), (function-axioms)
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #81.
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15240)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e1) = e3)
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (39), (14936), (15229), (15240),
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2419.
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | |   (15241)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | |              & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | |              & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | |                all_52_21) = e1 & op(all_52_23, all_52_23) =
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | |              all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | |              = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | |              & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(all_52_25, all_52_25) = e3 &
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | |              op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | |                all_52_29) = e1 & op(all_52_31, all_52_31) =
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | |              all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | |              = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_29) & $i(all_52_31))
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15241) gives:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | |   (15242)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | |            all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | |              all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | |            & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_23)
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (14958), (14974), (15242), (function-axioms)
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #80.
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | |   (15243)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | |            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | |              all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | |            & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_31)
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (14935), (14958), (15243), (function-axioms)
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #79.
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | |   (15244)  all_57_1 = e3 & op(e3, e2) = e3
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (171), (14977), (15244), (function-axioms) are
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2286.
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | |   (15245)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e3)
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (169), (231), (233),
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | |            (235), (14979), (14980), (15245),
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | |            #1955.
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | |   (15246)  all_57_9 = e2 & op(e3, e0) = e2
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | ALPHA: (15246) implies:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | |   (15247)  op(e3, e0) = e2
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (14927), (15247), (function-axioms) are
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2331.
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.46  | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | |   (15248)  all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 224.61/38.46  | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | REF_CLOSE: (277), (14938), (14960), (14962), (15248) are
% 224.61/38.46  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1953.
% 224.61/38.46  | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | End of split
% 224.61/38.46  | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.46  | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | |   (15249)  all_57_12 = e2 & op(e0, e3) = e2
% 224.61/38.46  | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | ALPHA: (15249) implies:
% 224.61/38.46  | | | | | | | | | | | | | | | | |   (15250)  op(e0, e3) = e2
% 224.61/38.46  | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (14924), (15250), (function-axioms) are
% 224.61/38.46  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1980.
% 224.61/38.46  | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | End of split
% 224.61/38.46  | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | End of split
% 224.61/38.46  | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | Case 2:
% 224.61/38.46  | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | |   (15251)  all_20_2 = e2
% 224.61/38.46  | | | | | | | | | | | | | | |   (15252)  ( ~ (all_20_0 = e1) & op(all_20_1, e3) = all_20_0
% 224.61/38.46  | | | | | | | | | | | | | | |              & op(e3, e2) = all_20_1 & $i(all_20_0) &
% 224.61/38.46  | | | | | | | | | | | | | | |              $i(all_20_1)) | ( ~ (all_20_1 = e0) & op(e3, e2)
% 224.61/38.46  | | | | | | | | | | | | | | |              = all_20_1 & $i(all_20_1))
% 224.61/38.46  | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | COMBINE_EQS: (299), (15251) imply:
% 224.61/38.46  | | | | | | | | | | | | | | |   (15253)  all_10_2 = e2
% 224.61/38.46  | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | COMBINE_EQS: (329), (15253) imply:
% 224.61/38.46  | | | | | | | | | | | | | | |   (15254)  all_28_2 = e2
% 224.61/38.46  | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | REDUCE: (45), (15253) imply:
% 224.61/38.46  | | | | | | | | | | | | | | |   (15255)  op(e3, e3) = e2
% 224.61/38.46  | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 224.61/38.46  | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | Case 1:
% 224.61/38.46  | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | |   (15256)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 224.61/38.46  | | | | | | | | | | | | | | | |              & op(e2, e1) = e2)
% 224.61/38.46  | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | BETA: splitting (15256) gives:
% 224.61/38.46  | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.46  | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | |   (15257)  all_57_4 = e2 & op(e3, e1) = e2
% 224.61/38.46  | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (237),
% 224.61/38.46  | | | | | | | | | | | | | | | | |            (15255), (15257), (function-axioms) are
% 224.61/38.46  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #226.
% 224.61/38.46  | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.46  | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | |   (15258)  all_57_5 = e2 & op(e2, e1) = e2
% 224.61/38.46  | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (14952), (15258), (function-axioms) are
% 224.61/38.46  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1858.
% 224.61/38.46  | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | End of split
% 224.61/38.46  | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | Case 2:
% 224.61/38.46  | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | |   (15259)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 224.61/38.46  | | | | | | | | | | | | | | | |              e2 & op(e0, e1) = e2)
% 224.61/38.46  | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | BETA: splitting (15259) gives:
% 224.61/38.46  | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.46  | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | |   (15260)  all_57_8 = e2 & op(e1, e1) = e2
% 224.61/38.46  | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | ALPHA: (15260) implies:
% 224.61/38.46  | | | | | | | | | | | | | | | | |   (15261)  all_57_8 = e2
% 224.61/38.46  | | | | | | | | | | | | | | | | |   (15262)  op(e1, e1) = e2
% 224.61/38.46  | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2, e2,
% 224.61/38.46  | | | | | | | | | | | | | | | | |              e1, e1, simplifying with (39), (15262) gives:
% 224.61/38.46  | | | | | | | | | | | | | | | | |   (15263)  all_6_2 = e2
% 224.61/38.46  | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (15263) imply:
% 224.61/38.46  | | | | | | | | | | | | | | | | |   (15264)  all_38_2 = e2
% 224.61/38.46  | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | COMBINE_EQS: (332), (15263) imply:
% 224.61/38.46  | | | | | | | | | | | | | | | | |   (15265)  all_42_2 = e2
% 224.61/38.46  | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | REDUCE: (350), (15263) imply:
% 224.61/38.46  | | | | | | | | | | | | | | | | |   (15266)   ~ (all_53_2 = e2)
% 224.61/38.46  | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | REDUCE: (361), (15263) imply:
% 224.61/38.46  | | | | | | | | | | | | | | | | |   (15267)   ~ (all_53_6 = e2)
% 224.61/38.46  | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | REDUCE: (363), (15263) imply:
% 224.61/38.46  | | | | | | | | | | | | | | | | |   (15268)   ~ (all_53_8 = e2)
% 224.61/38.46  | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 224.61/38.46  | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | |   (15269)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 224.61/38.46  | | | | | | | | | | | | | | | | | |              all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 224.61/38.46  | | | | | | | | | | | | | | | | | |              op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 224.61/38.46  | | | | | | | | | | | | | | | | | |                all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 224.61/38.46  | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 224.61/38.46  | | | | | | | | | | | | | | | | | |              op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 224.61/38.46  | | | | | | | | | | | | | | | | | |              $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 224.61/38.46  | | | | | | | | | | | | | | | | | |              $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 224.61/38.46  | | | | | | | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 224.61/38.46  | | | | | | | | | | | | | | | | | |                all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 224.61/38.46  | | | | | | | | | | | | | | | | | |              & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 224.61/38.46  | | | | | | | | | | | | | | | | | |                all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 224.61/38.46  | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 224.61/38.46  | | | | | | | | | | | | | | | | | |              & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 224.61/38.46  | | | | | | | | | | | | | | | | | |              $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 224.61/38.46  | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | BETA: splitting (15269) gives:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | |   (15270)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 224.61/38.46  | | | | | | | | | | | | | | | | | | |            all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 224.61/38.46  | | | | | | | | | | | | | | | | | | |            op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 224.61/38.46  | | | | | | | | | | | | | | | | | | |              all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 224.61/38.46  | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 224.61/38.46  | | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 224.61/38.46  | | | | | | | | | | | | | | | | | | |            $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 224.61/38.46  | | | | | | | | | | | | | | | | | | |            $i(all_52_7)
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | ALPHA: (15270) implies:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | |   (15271)  op(e3, e3) = all_52_1
% 224.61/38.46  | | | | | | | | | | | | | | | | | | |   (15272)  op(all_52_1, all_52_1) = e3
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (14958), (15255), (15271), (15272),
% 224.61/38.46  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.61/38.46  | | | | | | | | | | | | | | | | | | |            #1951.
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | |   (15273)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 224.61/38.46  | | | | | | | | | | | | | | | | | | |            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 224.61/38.46  | | | | | | | | | | | | | | | | | | |            op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 224.61/38.46  | | | | | | | | | | | | | | | | | | |              all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 224.61/38.46  | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 224.61/38.46  | | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 224.61/38.46  | | | | | | | | | | | | | | | | | | |            $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 224.61/38.46  | | | | | | | | | | | | | | | | | | |            $i(all_52_15)
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | ALPHA: (15273) implies:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | |   (15274)  op(e2, e0) = all_52_15
% 224.61/38.46  | | | | | | | | | | | | | | | | | | |   (15275)  op(e2, e1) = all_52_13
% 224.61/38.46  | | | | | | | | | | | | | | | | | | |   (15276)  op(e2, e2) = all_52_11
% 224.61/38.46  | | | | | | | | | | | | | | | | | | |   (15277)  op(e2, e3) = all_52_9
% 224.61/38.46  | | | | | | | | | | | | | | | | | | |   (15278)  op(all_52_15, all_52_15) = e0
% 224.61/38.46  | | | | | | | | | | | | | | | | | | |   (15279)  op(all_52_13, all_52_13) = e1
% 224.61/38.46  | | | | | | | | | | | | | | | | | | |   (15280)  op(all_52_9, all_52_9) = e3
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_13,
% 224.61/38.46  | | | | | | | | | | | | | | | | | | |              all_52_15, e0, e2, simplifying with (165), (15274)
% 224.61/38.46  | | | | | | | | | | | | | | | | | | |              gives:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | |   (15281)  all_53_13 = all_52_15
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_9,
% 224.61/38.46  | | | | | | | | | | | | | | | | | | |              all_52_13, e1, e2, simplifying with (166), (15275)
% 224.61/38.46  | | | | | | | | | | | | | | | | | | |              gives:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | |   (15282)  all_53_9 = all_52_13
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 224.61/38.46  | | | | | | | | | | | | | | | | | | |              all_52_11, e2, e2, simplifying with (14958),
% 224.61/38.46  | | | | | | | | | | | | | | | | | | |              (15276) gives:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | |   (15283)  all_52_11 = e2
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_1,
% 224.61/38.46  | | | | | | | | | | | | | | | | | | |              all_52_9, e3, e2, simplifying with (168), (15277)
% 224.61/38.46  | | | | | | | | | | | | | | | | | | |              gives:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | |   (15284)  all_53_1 = all_52_9
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (15281) imply:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | |   (15285)  all_55_7 = all_52_15
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (15282) imply:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | |   (15286)  all_55_6 = all_52_13
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (15284) imply:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | |   (15287)  all_55_4 = all_52_9
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | REDUCE: (150), (15284) imply:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | |   (15288)   ~ (all_53_2 = all_52_9)
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | SIMP: (15288) implies:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | |   (15289)   ~ (all_53_2 = all_52_9)
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | REDUCE: (149), (15284) imply:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | |   (15290)   ~ (all_53_3 = all_52_9)
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | SIMP: (15290) implies:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | |   (15291)   ~ (all_53_3 = all_52_9)
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | REDUCE: (147), (15282), (15284) imply:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | |   (15292)   ~ (all_52_9 = all_52_13)
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | REDUCE: (14950), (15284) imply:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | |   (15293)   ~ (all_52_9 = e2)
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | REDUCE: (124), (15282) imply:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | |   (15294)   ~ (all_53_8 = all_52_13)
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | REDUCE: (119), (15282) imply:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | |   (15295)   ~ (all_53_11 = all_52_13)
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | SIMP: (15295) implies:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | |   (15296)   ~ (all_53_11 = all_52_13)
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | REDUCE: (14952), (15282) imply:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | |   (15297)   ~ (all_52_13 = e2)
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | REDUCE: (114), (15281) imply:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | |   (15298)   ~ (all_53_12 = all_52_15)
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | REDUCE: (111), (15281) imply:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | |   (15299)   ~ (all_53_14 = all_52_15)
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | SIMP: (15299) implies:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | |   (15300)   ~ (all_53_14 = all_52_15)
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | REDUCE: (14928), (15281) imply:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | |   (15301)   ~ (all_52_15 = e2)
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | BETA: splitting (73) gives:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | |   (15302)   ~ (all_28_2 = e2)
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | REDUCE: (15254), (15302) imply:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | |   (15303)  $false
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | CLOSE: (15303) is inconsistent.
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | |   (15304)  ( ~ (all_28_0 = e0) & op(all_28_1, e3) = all_28_0
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = all_28_1 & $i(all_28_0) &
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | |              $i(all_28_1)) | ( ~ (all_28_1 = e1) & op(e3, e2)
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | |              = all_28_1 & $i(all_28_1))
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | BETA: splitting (79) gives:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | |   (15305)   ~ (all_32_2 = e2)
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | REDUCE: (14923), (15305) imply:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | |   (15306)  $false
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | CLOSE: (15306) is inconsistent.
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | |   (15307)  ( ~ (all_32_0 = e1) & op(all_32_1, e0) = all_32_0
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | |              & op(e0, e2) = all_32_1 & $i(all_32_0) &
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | |              $i(all_32_1)) | ( ~ (all_32_1 = e3) & op(e0, e2)
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | |              = all_32_1 & $i(all_32_1))
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (88) gives:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | |   (15308)   ~ (all_38_2 = e2)
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15264), (15308) imply:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | |   (15309)  $false
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (15309) is inconsistent.
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | |   (15310)  ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = all_38_1 & $i(all_38_0) &
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | |              $i(all_38_1)) | ( ~ (all_38_1 = e3) & op(e1, e2)
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | |              = all_38_1 & $i(all_38_1))
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (94) gives:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | |   (15311)   ~ (all_42_2 = e2)
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15265), (15311) imply:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | |   (15312)  $false
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (15312) is inconsistent.
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | |   (15313)  ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = all_42_1 & $i(all_42_0) &
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_42_1)) | ( ~ (all_42_1 = e0) & op(e1, e2)
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | |              = all_42_1 & $i(all_42_1))
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | |   (15314)  all_55_14 = e3
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (15314) imply:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | |   (15315)  all_53_11 = e3
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (15315) imply:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | |   (15316)   ~ (all_53_3 = e3)
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (126), (15315) imply:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | |   (15317)   ~ (all_53_7 = e3)
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15296), (15315) imply:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | |   (15318)   ~ (all_52_13 = e3)
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (15318) implies:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | |   (15319)   ~ (all_52_13 = e3)
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | |   (15320)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (160), (15316), (15317), (15320),
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | |            #77.
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | |   (15321)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15321) gives:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | |   (15322)  all_57_14 = e3 & op(e0, e1) = e3
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15322) implies:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | |   (15323)  all_57_14 = e3
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15324)  all_55_6 = e3
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15286), (15319), (15324) are inconsistent by
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #318.
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15325)  all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15326)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15326) gives:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15327)  all_57_12 = e1 & op(e0, e3) = e1
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15327) implies:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15328)  all_57_12 = e1
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15329)  op(e0, e3) = e1
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15330)  all_57_15 = e0 & op(e0, e0) = e0
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15330) implies:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15331)  op(e0, e0) = e0
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (14935), (15331), (function-axioms) are
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #86.
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15332)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15332) implies:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15333)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0)
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15333) gives:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15334)  all_57_12 = e0 & op(e0, e3) = e0
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (15328), (15334) are inconsistent by
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1279.
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15335)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15335) gives:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_3, e1,
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, simplifying with (160), (15329) gives:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15336)  all_53_3 = e1
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15291), (15336) imply:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15337)   ~ (all_52_9 = e1)
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (201), (15255), (15262), (15279), (15280),
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15286), (15287), (15292), (15293), (15297),
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15325), (15337), (function-axioms) are
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #75.
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15338)  all_57_14 = e0 & op(e0, e1) = e0
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15338) implies:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15339)  all_57_14 = e0
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (15323), (15339) are inconsistent by
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2420.
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15340)  all_57_13 = e1 & op(e0, e2) = e1
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15340) implies:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15341)  all_57_13 = e1
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15342)  op(e0, e2) = e1
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15343)  all_57_15 = e0 & op(e0, e0) = e0
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15343) implies:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15344)  op(e0, e0) = e0
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (14935), (15344), (function-axioms) are
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #86.
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15345)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15345) implies:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15346)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0)
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15346) gives:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15347)  all_57_12 = e0 & op(e0, e3) = e0
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15347) implies:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15348)  op(e0, e3) = e0
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_7, e1,
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (159), (15342) gives:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15349)  all_53_7 = e1
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_3, e0,
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, simplifying with (160), (15348) gives:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15350)  all_53_3 = e0
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (15350) imply:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15351)   ~ (all_53_2 = e0)
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (136), (15349) imply:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15352)   ~ (all_53_4 = e1)
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (129), (15349) imply:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15353)   ~ (all_53_6 = e1)
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14922) gives:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15354)   ~ (all_4_0 = e3) & op(all_4_1, e0) = all_4_0 &
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = all_4_1 & $i(all_4_0) & $i(all_4_1)
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15354) implies:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15355)   ~ (all_4_0 = e3)
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15356)  op(e0, e2) = all_4_1
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15357)  op(all_4_1, e0) = all_4_0
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15307) gives:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15358)   ~ (all_32_0 = e1) & op(all_32_1, e0) = all_32_0 &
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = all_32_1 & $i(all_32_0) &
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_32_1)
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15358) implies:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15359)   ~ (all_32_0 = e1)
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15360)  op(e0, e2) = all_32_1
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15361)  op(all_32_1, e0) = all_32_0
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_32_1,
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (15342), (15360) gives:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15362)  all_32_1 = e1
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_1,
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_32_1, e2, e0, simplifying with (15356),
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (15360) gives:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15363)  all_32_1 = all_4_1
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (15362), (15363) imply:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15364)  all_4_1 = e1
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (15364) implies:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15365)  all_4_1 = e1
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15361), (15362) imply:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15366)  op(e1, e0) = all_32_0
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15357), (15365) imply:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15367)  op(e1, e0) = all_4_0
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_14,
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_4_0, e0, e1, simplifying with (161), (15367)
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15368)  all_53_14 = all_4_0
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_14,
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_32_0, e0, e1, simplifying with (161), (15366)
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15369)  all_53_14 = all_32_0
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (15368), (15369) imply:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15370)  all_32_0 = all_4_0
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (15370) implies:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15371)  all_32_0 = all_4_0
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (15368) imply:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15372)  all_55_11 = all_4_0
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (142), (15368) imply:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15373)   ~ (all_53_2 = all_4_0)
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (127), (15368) imply:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15374)   ~ (all_53_6 = all_4_0)
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14929), (15368) imply:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15375)   ~ (all_4_0 = e2)
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15359), (15371) imply:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15376)   ~ (all_4_0 = e1)
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15377)  all_55_11 = e3
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15355), (15372), (15377) are inconsistent by
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #74.
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15378)  all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15378) gives:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15379)  all_55_11 = e2
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (15372), (15379) imply:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15380)  all_4_0 = e2
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15375), (15380) imply:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15381)  $false
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (15381) is inconsistent.
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15382)  all_55_11 = e1 | all_55_11 = e0
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15382) gives:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15383)  all_55_11 = e1
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15372), (15376), (15383) are inconsistent by
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #73.
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15384)  all_55_11 = e0
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (15372), (15384) imply:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15385)  all_4_0 = e0
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (15385) implies:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15386)  all_4_0 = e0
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15374), (15386) imply:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15387)   ~ (all_53_6 = e0)
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (144), (196), (197), (201), (256), (257), (15255),
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15262), (15266), (15267), (15279), (15280),
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15286), (15287), (15289), (15292), (15293),
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15297), (15325), (15351), (15353), (15387),
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #72.
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15388)   ~ (all_32_1 = e3) & op(e0, e2) = all_32_1 &
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_32_1)
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15388) implies:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15389)  op(e0, e2) = all_32_1
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_32_1,
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (15342), (15389) gives:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15390)  all_32_1 = e1
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_1,
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_32_1, e2, e0, simplifying with (15356),
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (15389) gives:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15391)  all_32_1 = all_4_1
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (15390), (15391) imply:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15392)  all_4_1 = e1
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (15392) implies:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15393)  all_4_1 = e1
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15357), (15393) imply:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15394)  op(e1, e0) = all_4_0
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_14,
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_4_0, e0, e1, simplifying with (161), (15394)
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15395)  all_53_14 = all_4_0
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (15395) imply:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15396)  all_55_11 = all_4_0
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (127), (15395) imply:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15397)   ~ (all_53_6 = all_4_0)
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (15395) imply:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15398)   ~ (all_53_12 = all_4_0)
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15300), (15395) imply:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15399)   ~ (all_52_15 = all_4_0)
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (15399) implies:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15400)   ~ (all_52_15 = all_4_0)
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14929), (15395) imply:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15401)   ~ (all_4_0 = e2)
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15402)  all_55_1 = e3
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (15402) imply:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15403)  all_53_4 = e3
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (15403) implies:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15404)  all_53_4 = e3
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (137), (15404) imply:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15405)   ~ (all_53_6 = e3)
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (15405) implies:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15406)   ~ (all_53_6 = e3)
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (15404) imply:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15407)   ~ (all_53_12 = e3)
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (15407) implies:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15408)   ~ (all_53_12 = e3)
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15409)  all_55_9 = e3
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (15409) imply:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15410)  all_53_6 = e3
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15406), (15410) imply:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15411)  $false
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (15411) is inconsistent.
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15412)  all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15412) gives:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15413)  all_55_9 = e2
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (15413) imply:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15414)  all_53_6 = e2
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15267), (15414) imply:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15415)  $false
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (15415) is inconsistent.
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15416)  all_55_9 = e1 | all_55_9 = e0
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15416) gives:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15417)  all_55_9 = e1
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (15417) imply:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15418)  all_53_6 = e1
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15353), (15418) imply:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15419)  $false
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (15419) is inconsistent.
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15420)  all_55_9 = e0
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (15420) imply:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15421)  all_53_6 = e0
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15397), (15421) imply:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15422)   ~ (all_4_0 = e0)
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (15422) implies:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15423)   ~ (all_4_0 = e0)
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15424)  all_55_11 = e3
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (15396), (15424) imply:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15425)  all_4_0 = e3
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15355), (15425) imply:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15426)  $false
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (15426) is inconsistent.
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15427)  all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15427) gives:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15428)  all_55_11 = e2
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (15396), (15428) imply:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15429)  all_4_0 = e2
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15401), (15429) imply:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15430)  $false
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (15430) is inconsistent.
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15431)  all_55_11 = e1 | all_55_11 = e0
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15431) gives:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15432)  all_55_11 = e1
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (15396), (15432) imply:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15433)  all_4_0 = e1
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15398), (15433) imply:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15434)   ~ (all_53_12 = e1)
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15400), (15433) imply:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15435)   ~ (all_52_15 = e1)
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15436)  all_55_3 = e3
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (15408), (15436) are inconsistent by
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2169.
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15437)  all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15437) gives:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15438)  all_55_3 = e2
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (14927), (15438) are inconsistent by
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1612.
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15439)   ~ (all_55_3 = e2)
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15440)  all_55_3 = e1 | all_55_3 = e0
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15440) gives:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15441)  all_55_3 = e1
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (15434), (15441) are inconsistent by
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #324.
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15442)  all_55_3 = e0
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (15442) imply:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15443)  all_53_12 = e0
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (15443) implies:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15444)  all_53_12 = e0
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15298), (15444) imply:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15445)   ~ (all_52_15 = e0)
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (15445) implies:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15446)   ~ (all_52_15 = e0)
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14927), (15444) imply:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15447)   ~ (e2 = e0)
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (198), (15255), (15278), (15285), (15301),
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15435), (15446), (function-axioms) are
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #71.
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15448)  all_55_11 = e0
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (15396), (15448) imply:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15449)  all_4_0 = e0
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15423), (15449) imply:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15450)  $false
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (15450) is inconsistent.
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15451)  all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15451) gives:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15452)  all_55_1 = e2
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (15452) imply:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15453)  all_53_4 = e2
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14951), (15453) imply:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15454)  $false
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (15454) is inconsistent.
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15455)  all_55_1 = e1 | all_55_1 = e0
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15455) gives:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15456)  all_55_1 = e1
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (15456) imply:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15457)  all_53_4 = e1
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15352), (15457) imply:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15458)  $false
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (15458) is inconsistent.
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15459)  all_55_1 = e0
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (15459) imply:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15460)  all_53_4 = e0
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (137), (15460) imply:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15461)   ~ (all_53_6 = e0)
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (15461) implies:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15462)   ~ (all_53_6 = e0)
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (144), (196), (197), (201), (256), (257), (15255),
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15262), (15266), (15267), (15279), (15280),
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15286), (15287), (15289), (15292), (15293),
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15297), (15325), (15351), (15353), (15462),
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #72.
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15463)   ~ (all_4_1 = e1) & op(e0, e2) = all_4_1 &
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_4_1)
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15307), (15342), (15463), (function-axioms) are
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #69.
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15464)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15464) gives:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15465)  all_57_13 = e0 & op(e0, e2) = e0
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (15341), (15465) are inconsistent by
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1920.
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15466)  all_57_14 = e0 & op(e0, e1) = e0
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15466) implies:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15467)  all_57_14 = e0
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (15323), (15467) are inconsistent by
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2420.
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15468)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15468) gives:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15469)  all_57_14 = e1 & op(e0, e1) = e1
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (15323), (15469) are inconsistent by
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2319.
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15470)  all_57_15 = e1 & op(e0, e0) = e1
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15470) implies:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15471)  op(e0, e0) = e1
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (14935), (15471), (function-axioms) are
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2177.
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | |   (15472)  all_57_15 = e3 & op(e0, e0) = e3
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15472) implies:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | |   (15473)  all_57_15 = e3
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (14934), (15473) are inconsistent by
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2058.
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | |   (15474)   ~ (all_55_14 = e3)
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | |   (15475)  all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (245), (15474) imply:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | |   (15476)   ~ (all_53_11 = e3)
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | |   (15477)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15477) gives:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | |   (15478)  all_57_12 = e3 & op(e0, e3) = e3
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15478) implies:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | |   (15479)  all_57_12 = e3
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | |   (15480)  op(e0, e3) = e3
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_3, e3,
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, simplifying with (160), (15480) gives:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | |   (15481)  all_53_3 = e3
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (15481) imply:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | |   (15482)   ~ (all_53_2 = e3)
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (141), (15481) imply:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | |   (15483)   ~ (all_53_7 = e3)
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (15483) implies:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | |   (15484)   ~ (all_53_7 = e3)
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (15481) imply:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | |   (15485)   ~ (all_53_11 = e3)
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15486)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e3)
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15486) gives:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15487)  all_57_6 = e3 & op(e1, e3) = e3
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (15482), (15487), (function-axioms) are
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #153.
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15488)  all_57_7 = e3 & op(e1, e2) = e3
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15488) implies:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15489)  all_57_7 = e3
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15490)  op(e1, e2) = e3
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_6, e3,
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e1, simplifying with (163), (15490) gives:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15491)  all_53_6 = e3
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (127), (15491) imply:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15492)   ~ (all_53_14 = e3)
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (15492) implies:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15493)   ~ (all_53_14 = e3)
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15313) gives:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15494)   ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = all_42_1 & $i(all_42_0) &
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_42_1)
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15494) implies:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15495)   ~ (all_42_0 = e3)
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15496)  op(e1, e2) = all_42_1
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15497)  op(all_42_1, e1) = all_42_0
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15310) gives:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15498)   ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = all_38_1 & $i(all_38_0) &
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_38_1)
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15498) implies:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15499)   ~ (all_38_0 = e0)
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15500)  op(e1, e2) = all_38_1
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15501)  op(all_38_1, e1) = all_38_0
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_42_1,
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e1, simplifying with (15490), (15496) gives:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15502)  all_42_1 = e3
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_38_1,
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_42_1, e2, e1, simplifying with (15496),
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (15500) gives:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15503)  all_42_1 = all_38_1
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (15502), (15503) imply:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15504)  all_38_1 = e3
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (15504) implies:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15505)  all_38_1 = e3
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15497), (15502) imply:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15506)  op(e3, e1) = all_42_0
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15501), (15505) imply:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15507)  op(e3, e1) = all_38_0
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_8,
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_38_0, e1, e3, simplifying with (170), (15507)
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15508)  all_53_8 = all_38_0
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_8,
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_42_0, e1, e3, simplifying with (170), (15506)
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15509)  all_53_8 = all_42_0
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (15508), (15509) imply:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15510)  all_42_0 = all_38_0
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (15510) implies:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15511)  all_42_0 = all_38_0
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (15508) imply:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15512)  all_55_2 = all_38_0
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (122), (15508) imply:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15513)   ~ (all_53_11 = all_38_0)
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (15513) implies:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15514)   ~ (all_53_11 = all_38_0)
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15294), (15508) imply:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15515)   ~ (all_52_13 = all_38_0)
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (15515) implies:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15516)   ~ (all_52_13 = all_38_0)
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15268), (15508) imply:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15517)   ~ (all_38_0 = e2)
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15495), (15511) imply:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15518)   ~ (all_38_0 = e3)
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15519)  all_55_2 = e3
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (15512), (15519) imply:
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15520)  all_38_0 = e3
% 224.61/38.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15518), (15520) imply:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15521)  $false
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (15521) is inconsistent.
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15522)  all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (199), (245), (14926), (15255), (15279), (15286),
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15296), (15297), (15475), (15499), (15512),
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15514), (15516), (15517), (15522),
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #67.
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15523)   ~ (all_38_1 = e3) & op(e1, e2) = all_38_1 &
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_38_1)
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15490), (15523), (function-axioms) are
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1444.
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15524)   ~ (all_42_1 = e0) & op(e1, e2) = all_42_1 &
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_42_1)
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15524) implies:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15525)   ~ (all_42_1 = e0)
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15526)  op(e1, e2) = all_42_1
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15310) gives:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15527)   ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = all_38_1 & $i(all_38_0) &
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_38_1)
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15527) implies:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15528)   ~ (all_38_0 = e0)
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15529)  op(e1, e2) = all_38_1
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15530)  op(all_38_1, e1) = all_38_0
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_42_1,
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e1, simplifying with (15490), (15526) gives:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15531)  all_42_1 = e3
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_38_1,
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_42_1, e2, e1, simplifying with (15526),
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (15529) gives:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15532)  all_42_1 = all_38_1
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (15531), (15532) imply:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15533)  all_38_1 = e3
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (15533) implies:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15534)  all_38_1 = e3
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15530), (15534) imply:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15535)  op(e3, e1) = all_38_0
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_8,
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_38_0, e1, e3, simplifying with (170), (15535)
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15536)  all_53_8 = all_38_0
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (15536) imply:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15537)  all_55_2 = all_38_0
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (122), (15536) imply:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15538)   ~ (all_53_11 = all_38_0)
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (15538) implies:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15539)   ~ (all_53_11 = all_38_0)
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (15536) imply:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15540)   ~ (all_53_12 = all_38_0)
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (15540) implies:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15541)   ~ (all_53_12 = all_38_0)
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15294), (15536) imply:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15542)   ~ (all_52_13 = all_38_0)
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (15542) implies:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15543)   ~ (all_52_13 = all_38_0)
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15268), (15536) imply:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15544)   ~ (all_38_0 = e2)
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15545)  all_55_2 = e3
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (15537), (15545) imply:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15546)  all_38_0 = e3
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (15546) implies:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15547)  all_38_0 = e3
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15541), (15547) imply:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15548)   ~ (all_53_12 = e3)
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15549)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e3)
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15549) gives:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15550)  all_57_4 = e3 & op(e3, e1) = e3
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15550) implies:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15551)  all_57_4 = e3
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15552)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15552) gives:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15553)  all_57_9 = e3 & op(e3, e0) = e3
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15553) implies:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15554)  op(e3, e0) = e3
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (15548), (15554), (function-axioms) are
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2458.
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15555)  all_57_10 = e3 & op(e2, e0) = e3
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15555) implies:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15556)  all_57_10 = e3
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15557)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e3)
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15557) gives:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15558)  all_57_2 = e3 & op(e2, e3) = e3
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15558) implies:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15559)  all_57_2 = e3
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15560)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e1)
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15560) gives:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15561)  all_57_0 = e1 & op(e3, e3) = e1
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15561) implies:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15562)  op(e3, e3) = e1
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (169), (171), (235), (14927), (14951),
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15551), (15562), (function-axioms) are
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #234.
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15563)  all_57_2 = e1 & op(e2, e3) = e1
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (15559), (15563) are inconsistent by
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1928.
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15564)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e3) = e1)
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15564) gives:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15565)  all_57_6 = e1 & op(e1, e3) = e1
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15565) implies:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15566)  all_57_6 = e1
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15567)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e0)
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15567) gives:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15568)  all_57_6 = e0 & op(e1, e3) = e0
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (15566), (15568) are inconsistent by
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2347.
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15569)  all_57_7 = e0 & op(e1, e2) = e0
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15569) implies:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15570)  op(e1, e2) = e0
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15310) gives:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15525), (15526), (15529), (15570),
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #211.
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15571)   ~ (all_38_1 = e3) & op(e1, e2) = all_38_1 &
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_38_1)
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15525), (15526), (15529), (15570),
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #211.
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15572)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15572) gives:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15573)  all_57_8 = e0 & op(e1, e1) = e0
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15573) implies:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15574)  all_57_8 = e0
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (15261), (15574) imply:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15575)  e2 = e0
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (15575) implies:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15576)  e2 = e0
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14957), (15576) imply:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15577)  all_57_3 = e0
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (223), (224), (15556),
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15559), (15577) are inconsistent by sub-proof
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1433.
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15578)  all_57_11 = e0 & op(e1, e0) = e0
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15578) implies:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15579)  all_57_11 = e0
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15580)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15580) gives:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15581)  all_57_9 = e1 & op(e3, e0) = e1
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15581) implies:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15582)  all_57_9 = e1
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15583)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e0)
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15583) gives:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15584)  all_57_0 = e0 & op(e3, e3) = e0
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15584) implies:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15585)  op(e3, e3) = e0
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (15255), (15585), (function-axioms) are
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2403.
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15586)  all_57_1 = e0 & op(e3, e2) = e0
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15586) implies:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15587)  all_57_1 = e0
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15588)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e0)
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15588) gives:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15589)  all_57_0 = e0 & op(e3, e3) = e0
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15589) implies:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15590)  op(e3, e3) = e0
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (9), (169), (235), (237), (15548),
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15582), (15587), (15590), (function-axioms) are
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2400.
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15591)  all_57_2 = e0 & op(e2, e3) = e0
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (15559), (15591) are inconsistent by
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1805.
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15592)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = e0)
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15592) gives:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15593)  all_57_6 = e0 & op(e1, e3) = e0
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (15566), (15593) are inconsistent by
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2347.
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15594)  all_57_12 = e0 & op(e0, e3) = e0
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (15479), (15594) are inconsistent by
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2237.
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15595)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e0)
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15595) gives:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15596)  all_57_4 = e0 & op(e3, e1) = e0
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (15551), (15596) are inconsistent by
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2491.
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15597)  all_57_9 = e0 & op(e3, e0) = e0
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (15582), (15597) are inconsistent by
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1990.
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15598)  all_57_10 = e1 & op(e2, e0) = e1
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (15556), (15598) are inconsistent by
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2349.
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15599)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15599) gives:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15600)  all_57_11 = e1 & op(e1, e0) = e1
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15600) implies:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15601)  all_57_11 = e1
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (15579), (15601) are inconsistent by
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1862.
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15602)  all_57_15 = e1 & op(e0, e0) = e1
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15602) implies:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15603)  op(e0, e0) = e1
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (14935), (15603), (function-axioms) are
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2177.
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15604)  all_57_12 = e1 & op(e0, e3) = e1
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (15479), (15604) are inconsistent by
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2230.
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15605)  all_57_3 = e3 & op(e2, e2) = e3
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15605) implies:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15606)  op(e2, e2) = e3
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (14958), (15606), (function-axioms) are
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2298.
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15607)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15607) gives:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15608)  all_57_5 = e3 & op(e2, e1) = e3
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15608) implies:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15609)  all_57_5 = e3
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (169), (215), (216),
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (218), (219), (220), (222), (223), (224), (225),
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (226), (227), (228), (230), (234), (237), (14957),
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14958), (15255), (15262), (15479), (15489),
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15548), (15556), (15609), (function-axioms) are
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #65.
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15555) implies:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15610)  op(e2, e0) = e3
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_15,
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, e2, simplifying with (15274), (15610)
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15611)  all_52_15 = e3
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15278), (15611) imply:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15612)  op(e3, e3) = e0
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (15255), (15612), (function-axioms) are
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2403.
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15613)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (39), (67), (82), (107), (119), (158),
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (159), (160), (161), (165), (166), (169), (195),
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (199), (209), (212), (259), (311), (315), (336),
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (364), (368), (14924), (14925), (14927), (14928),
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14936), (14958), (15255), (15493), (15613),
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #64.
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15614)  all_57_5 = e3 & op(e2, e1) = e3
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15614) implies:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15615)  all_57_5 = e3
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15616)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15616) gives:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15617)  all_57_9 = e3 & op(e3, e0) = e3
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15617) implies:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15618)  op(e3, e0) = e3
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (15548), (15618), (function-axioms) are
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2458.
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15619)  all_57_10 = e3 & op(e2, e0) = e3
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15619) implies:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15620)  all_57_10 = e3
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (169), (215), (216),
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (218), (219), (220), (222), (223), (224), (225),
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (226), (227), (228), (230), (234), (237), (14957),
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14958), (15255), (15262), (15479), (15489),
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15548), (15615), (15620), (function-axioms) are
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #65.
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15621)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (39), (67), (82), (107), (119), (158),
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (159), (160), (161), (165), (166), (169), (195),
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (199), (209), (212), (259), (311), (315), (336),
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (364), (368), (14924), (14925), (14927), (14928),
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14936), (14958), (15255), (15493), (15621),
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #64.
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15622)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e1) = e3)
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (158), (14936), (15476), (15622),
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #63.
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15623)  all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (199), (245), (14926), (15255), (15279), (15286),
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15296), (15297), (15475), (15528), (15537),
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15539), (15543), (15544), (15623),
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #67.
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15624)   ~ (all_38_1 = e3) & op(e1, e2) = all_38_1 &
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_38_1)
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15490), (15624), (function-axioms) are
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1444.
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15625)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e1, e0) = e3)
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15625) gives:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15626)  all_57_8 = e3 & op(e1, e1) = e3
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15626) implies:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15627)  op(e1, e1) = e3
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (14936), (15627), (function-axioms) are
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2468.
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15628)  all_57_11 = e3 & op(e1, e0) = e3
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15628) implies:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15629)  all_57_11 = e3
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15630)  op(e1, e0) = e3
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_14,
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, e1, simplifying with (161), (15630) gives:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15631)  all_53_14 = e3
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (127), (15631) imply:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15632)   ~ (all_53_6 = e3)
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15633)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e3)
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15633) gives:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15634)  all_57_1 = e3 & op(e3, e2) = e3
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15634) implies:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15635)  all_57_1 = e3
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15636)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e3)
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15636) gives:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15637)  all_57_2 = e3 & op(e2, e3) = e3
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15637) implies:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15638)  all_57_2 = e3
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15639)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e0)
% 224.61/38.48  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15639) gives:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15640)  all_57_0 = e0 & op(e3, e3) = e0
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15640) implies:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15641)  op(e3, e3) = e0
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (15255), (15641), (function-axioms) are
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2403.
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15642)  all_57_2 = e0 & op(e2, e3) = e0
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15642) implies:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15643)  all_57_2 = e0
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (15638), (15643) are inconsistent by
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2258.
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15644)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = e0)
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15644) gives:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15645)  all_57_6 = e0 & op(e1, e3) = e0
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15645) implies:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15646)  all_57_6 = e0
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15647)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e1)
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (15255), (15638), (15647),
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #749.
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15648)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e3) = e1)
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (15479), (15646), (15648) are
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2226.
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15649)  all_57_12 = e0 & op(e0, e3) = e0
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15649) implies:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15650)  all_57_12 = e0
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (15479), (15650) are inconsistent by
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2153.
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15651)  all_57_3 = e3 & op(e2, e2) = e3
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15651) implies:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15652)  op(e2, e2) = e3
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (14958), (15652), (function-axioms) are
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2298.
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15653)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15653) gives:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15654)  all_57_5 = e3 & op(e2, e1) = e3
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15654) implies:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15655)  op(e2, e1) = e3
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e1, e2, simplifying with (15275), (15655)
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15656)  all_52_13 = e3
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15279), (15656) imply:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15657)  op(e3, e3) = e1
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (15255), (15657), (function-axioms) are
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1950.
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15658)  all_57_10 = e3 & op(e2, e0) = e3
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15658) implies:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15659)  all_57_10 = e3
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15660)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15660) gives:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15661)  all_57_9 = e1 & op(e3, e0) = e1
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15661) implies:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15662)  all_57_9 = e1
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15663)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e0)
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (15255), (15635), (15663),
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1676.
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15664)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e0)
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15664) gives:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15665)  all_57_4 = e0 & op(e3, e1) = e0
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15665) implies:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15666)  all_57_4 = e0
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15667)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e3)
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15667) gives:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15668)  all_57_4 = e3 & op(e3, e1) = e3
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15668) implies:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15669)  all_57_4 = e3
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (15666), (15669) are inconsistent by
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2372.
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15670)  all_57_5 = e3 & op(e2, e1) = e3
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15670) implies:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15671)  all_57_5 = e3
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15672)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15672) gives:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15673)  all_57_2 = e0 & op(e2, e3) = e0
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15673) implies:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15674)  all_57_2 = e0
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15675)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e1)
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (15255), (15674), (15675),
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #105.
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15676)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e3) = e1)
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15676) gives:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15677)  all_57_6 = e1 & op(e1, e3) = e1
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15677) implies:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15678)  all_57_6 = e1
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15679)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e1)
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15679) gives:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15680)  all_57_4 = e1 & op(e3, e1) = e1
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15680) implies:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15681)  all_57_4 = e1
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (231), (237), (15255),
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15662), (15681), (function-axioms) are
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1672.
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15682)  all_57_5 = e1 & op(e2, e1) = e1
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15682) implies:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15683)  all_57_5 = e1
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (15671), (15683) imply:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15684)  e3 = e1
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (15479), (15684) imply:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15685)  all_57_12 = e1
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (236), (15255), (15674), (15678),
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15685), (function-axioms) are inconsistent by
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #103.
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15686)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e1) = e1)
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15686) gives:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15687)  all_57_8 = e1 & op(e1, e1) = e1
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15687) implies:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15688)  op(e1, e1) = e1
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (15262), (15688), (function-axioms) are
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2423.
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15689)  all_57_14 = e1 & op(e0, e1) = e1
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15689) implies:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15690)  all_57_14 = e1
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15691)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15691) gives:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15692)  all_57_2 = e1 & op(e2, e3) = e1
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15692) implies:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15693)  all_57_2 = e1
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (15674), (15693) imply:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15694)  e1 = e0
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (15694) implies:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15695)  e1 = e0
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (15690), (15695) imply:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15696)  all_57_14 = e0
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (219), (220), (15666),
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15671), (15696), (function-axioms) are
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2378.
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15697)  all_57_3 = e1 & op(e2, e2) = e1
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15697) implies:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15698)  op(e2, e2) = e1
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (14958), (15698), (function-axioms) are
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2306.
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15699)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15699) gives:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15700)  all_57_5 = e1 & op(e2, e1) = e1
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15700) implies:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15701)  all_57_5 = e1
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (39), (221), (14936), (15666), (15690),
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15701), (function-axioms) are inconsistent by
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #62.
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15702)  all_57_10 = e1 & op(e2, e0) = e1
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15702) implies:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15703)  all_57_10 = e1
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (15659), (15703) imply:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15704)  e3 = e1
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (15671), (15704) imply:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15705)  all_57_5 = e1
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (39), (221), (14936), (15666), (15690),
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15705), (function-axioms) are inconsistent by
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #62.
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15706)  all_57_12 = e1 & op(e0, e3) = e1
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (15479), (15706) are inconsistent by
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2230.
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15707)  all_57_3 = e0 & op(e2, e2) = e0
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15707) implies:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15708)  all_57_3 = e0
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (223), (224), (15659),
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15671), (15708) are inconsistent by sub-proof
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1693.
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15709)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0)
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15709) gives:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15710)  all_57_5 = e0 & op(e2, e1) = e0
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (15671), (15710) are inconsistent by
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2414.
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15711)  all_57_10 = e0 & op(e2, e0) = e0
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (207), (14934), (14935), (15274), (15278),
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15301), (15711), (function-axioms) are
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #84.
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15712)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e1) = e3)
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (158), (14936), (15476), (15712),
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #63.
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15713)  all_57_9 = e0 & op(e3, e0) = e0
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (15662), (15713) are inconsistent by
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1990.
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15714)  all_57_10 = e1 & op(e2, e0) = e1
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (15659), (15714) are inconsistent by
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2349.
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15715)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15715) gives:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15716)  all_57_11 = e1 & op(e1, e0) = e1
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15716) implies:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15717)  all_57_11 = e1
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (15629), (15717) are inconsistent by
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2218.
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15718)  all_57_15 = e1 & op(e0, e0) = e1
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15718) implies:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15719)  op(e0, e0) = e1
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (14935), (15719), (function-axioms) are
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2177.
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15720)  all_57_3 = e3 & op(e2, e2) = e3
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15720) implies:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15721)  op(e2, e2) = e3
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (14958), (15721), (function-axioms) are
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2298.
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15722)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15722) gives:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15723)  all_57_7 = e3 & op(e1, e2) = e3
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (15632), (15723), (function-axioms) are
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #267.
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15724)  all_57_13 = e3 & op(e0, e2) = e3
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (15484), (15724), (function-axioms) are
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #78.
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | |   (15725)  all_57_13 = e3 & op(e0, e2) = e3
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15725) implies:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | |   (15726)  op(e0, e2) = e3
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_7, e3,
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (159), (15726) gives:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | |   (15727)  all_53_7 = e3
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (141), (15727) imply:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | |   (15728)   ~ (all_53_3 = e3)
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (136), (15727) imply:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | |   (15729)   ~ (all_53_4 = e3)
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (129), (15727) imply:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | |   (15730)   ~ (all_53_6 = e3)
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (126), (15727) imply:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | |   (15731)   ~ (all_53_11 = e3)
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14922) gives:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15732)   ~ (all_4_0 = e3) & op(all_4_1, e0) = all_4_0 &
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = all_4_1 & $i(all_4_0) & $i(all_4_1)
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15732) implies:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15733)   ~ (all_4_0 = e3)
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15734)  op(e0, e2) = all_4_1
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15735)  op(all_4_1, e0) = all_4_0
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15307) gives:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15736)   ~ (all_32_0 = e1) & op(all_32_1, e0) = all_32_0 &
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = all_32_1 & $i(all_32_0) &
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_32_1)
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15736) implies:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15737)   ~ (all_32_0 = e1)
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15738)  op(e0, e2) = all_32_1
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15739)  op(all_32_1, e0) = all_32_0
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_32_1,
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (15726), (15738) gives:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15740)  all_32_1 = e3
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_1,
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_32_1, e2, e0, simplifying with (15734),
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (15738) gives:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15741)  all_32_1 = all_4_1
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (15740), (15741) imply:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15742)  all_4_1 = e3
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (15742) implies:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15743)  all_4_1 = e3
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15739), (15740) imply:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15744)  op(e3, e0) = all_32_0
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15735), (15743) imply:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15745)  op(e3, e0) = all_4_0
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_12,
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_4_0, e0, e3, simplifying with (169), (15745)
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15746)  all_53_12 = all_4_0
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_12,
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_32_0, e0, e3, simplifying with (169), (15744)
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15747)  all_53_12 = all_32_0
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (15746), (15747) imply:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15748)  all_32_0 = all_4_0
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (15748) implies:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15749)  all_32_0 = all_4_0
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (15746) imply:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15750)  all_55_3 = all_4_0
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (15746) imply:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15751)   ~ (all_53_4 = all_4_0)
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (15746) imply:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15752)   ~ (all_53_8 = all_4_0)
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (15746) imply:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15753)   ~ (all_53_14 = all_4_0)
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (15753) implies:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15754)   ~ (all_53_14 = all_4_0)
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15298), (15746) imply:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15755)   ~ (all_52_15 = all_4_0)
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (15755) implies:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15756)   ~ (all_52_15 = all_4_0)
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14927), (15746) imply:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15757)   ~ (all_4_0 = e2)
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15737), (15749) imply:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15758)   ~ (all_4_0 = e1)
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15759)  all_55_3 = e3
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (15750), (15759) imply:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15760)  all_4_0 = e3
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15733), (15760) imply:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15761)  $false
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (15761) is inconsistent.
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15762)   ~ (all_55_3 = e3)
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15763)  all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15763) gives:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15764)  all_55_3 = e2
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (15750), (15764) imply:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15765)  all_4_0 = e2
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15757), (15765) imply:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15766)  $false
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (15766) is inconsistent.
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15767)   ~ (all_55_3 = e2)
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15768)  all_55_3 = e1 | all_55_3 = e0
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15768) gives:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15769)  all_55_3 = e1
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (15750), (15769) imply:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15770)  all_4_0 = e1
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15758), (15770) imply:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15771)  $false
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (15771) is inconsistent.
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15772)  all_55_3 = e0
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (15750), (15772) imply:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15773)  all_4_0 = e0
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15751), (15773) imply:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15774)   ~ (all_53_4 = e0)
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15752), (15773) imply:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15775)   ~ (all_53_8 = e0)
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15754), (15773) imply:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15776)   ~ (all_53_14 = e0)
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15756), (15773) imply:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15777)   ~ (all_52_15 = e0)
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15733), (15773) imply:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15778)   ~ (e3 = e0)
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15757), (15773) imply:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15779)   ~ (e2 = e0)
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15758), (15773) imply:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15780)   ~ (e1 = e0)
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15745), (15773) imply:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15781)  op(e3, e0) = e0
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15782)  all_55_1 = e3
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (15782) imply:
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15783)  all_53_4 = e3
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15729), (15783) imply:
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15784)  $false
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (15784) is inconsistent.
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15785)   ~ (all_55_1 = e3)
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15786)  all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15787)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e3)
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (171), (15255), (15729), (15787),
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #249.
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15788)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e3)
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15788) gives:
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15789)  all_57_4 = e3 & op(e3, e1) = e3
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15789) implies:
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15790)  all_57_4 = e3
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15791)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e1)
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15791) gives:
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15792)  all_57_0 = e1 & op(e3, e3) = e1
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15792) implies:
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15793)  op(e3, e3) = e1
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (169), (171), (235), (14927), (14951),
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15790), (15793), (function-axioms) are
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #234.
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15794)  all_57_1 = e1 & op(e3, e2) = e1
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15794) implies:
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15795)  all_57_1 = e1
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15796)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e0)
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (171), (15255), (15774), (15796),
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1321.
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15797)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e0)
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15797) gives:
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15798)  all_57_4 = e0 & op(e3, e1) = e0
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15798) implies:
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15799)  op(e3, e1) = e0
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (15775), (15799), (function-axioms) are
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2267.
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15800)  all_57_9 = e0 & op(e3, e0) = e0
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15800) implies:
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15801)  all_57_9 = e0
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15786) gives:
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15802)  all_55_1 = e2
% 224.61/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (15802) imply:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15803)  all_53_4 = e2
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14951), (15803) imply:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15804)  $false
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (15804) is inconsistent.
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15805)  all_55_1 = e1 | all_55_1 = e0
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15805) gives:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15806)  all_55_1 = e1
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (15806) imply:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15807)  all_53_4 = e1
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (137), (15807) imply:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15808)   ~ (all_53_6 = e1)
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (15808) implies:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15809)   ~ (all_53_6 = e1)
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (171), (15807) imply:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15810)  op(e3, e2) = e1
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15811)  all_55_9 = e3
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (15730), (15811) are inconsistent by
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2159.
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15812)  all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (127), (142), (144), (145), (164), (193), (194),
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (197), (198), (201), (235), (247), (248), (256),
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (257), (14924), (14929), (15252), (15255),
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15266), (15267), (15278), (15280), (15285),
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15287), (15289), (15291), (15293), (15300),
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15301), (15304), (15728), (15777), (15790),
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15795), (15801), (15809), (15810), (15812),
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #59.
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15813)  all_55_1 = e0
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (15813) imply:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15814)  all_53_4 = e0
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15774), (15814) imply:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15815)  $false
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (15815) is inconsistent.
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15816)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e1)
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15816) gives:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15817)  all_57_4 = e1 & op(e3, e1) = e1
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (15790), (15817) are inconsistent by
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2484.
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15818)  all_57_9 = e1 & op(e3, e0) = e1
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15818) implies:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15819)  all_57_9 = e1
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (161), (207), (14934), (14935), (15274),
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15278), (15301), (15776), (15819),
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #83.
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15820)  all_57_9 = e3 & op(e3, e0) = e3
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15820) implies:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15821)  op(e3, e0) = e3
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (15781), (15821), (function-axioms) are
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #313.
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15822)   ~ (all_32_1 = e3) & op(e0, e2) = all_32_1 &
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_32_1)
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15822) implies:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15823)   ~ (all_32_1 = e3)
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15824)  op(e0, e2) = all_32_1
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15726), (15734), (15823), (15824),
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #58.
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15825)   ~ (all_4_1 = e1) & op(e0, e2) = all_4_1 &
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_4_1)
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15825) implies:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15826)   ~ (all_4_1 = e1)
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15827)  op(e0, e2) = all_4_1
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15307) gives:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15828)   ~ (all_32_0 = e1) & op(all_32_1, e0) = all_32_0 &
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = all_32_1 & $i(all_32_0) &
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_32_1)
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15828) implies:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15829)   ~ (all_32_0 = e1)
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15830)  op(e0, e2) = all_32_1
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15831)  op(all_32_1, e0) = all_32_0
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_32_1,
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (15726), (15830) gives:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15832)  all_32_1 = e3
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_1,
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_32_1, e2, e0, simplifying with (15827),
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (15830) gives:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15833)  all_32_1 = all_4_1
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (15832), (15833) imply:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15834)  all_4_1 = e3
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (15834) implies:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15835)  all_4_1 = e3
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15831), (15832) imply:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15836)  op(e3, e0) = all_32_0
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_12,
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_32_0, e0, e3, simplifying with (169), (15836)
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15837)  all_53_12 = all_32_0
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (15837) imply:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15838)  all_55_3 = all_32_0
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (15837) imply:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15839)   ~ (all_53_4 = all_32_0)
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (15837) imply:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15840)   ~ (all_53_8 = all_32_0)
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (15837) imply:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15841)   ~ (all_53_14 = all_32_0)
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (15841) implies:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15842)   ~ (all_53_14 = all_32_0)
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15298), (15837) imply:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15843)   ~ (all_52_15 = all_32_0)
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (15843) implies:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15844)   ~ (all_52_15 = all_32_0)
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14927), (15837) imply:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15845)   ~ (all_32_0 = e2)
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15846)  all_55_1 = e3
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (15729), (15846) are inconsistent by
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2295.
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15847)   ~ (all_55_1 = e3)
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15848)  all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15849)  all_55_9 = e3
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (15730), (15849) are inconsistent by
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2159.
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15850)   ~ (all_55_9 = e3)
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15851)  all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15852)  all_55_3 = e3
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (15838), (15852) imply:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15853)  all_32_0 = e3
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (15853) implies:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15854)  all_32_0 = e3
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15840), (15854) imply:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15855)   ~ (all_53_8 = e3)
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15842), (15854) imply:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15856)   ~ (all_53_14 = e3)
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15857)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e3)
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15857) gives:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15858)  all_57_4 = e3 & op(e3, e1) = e3
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (15855), (15858), (function-axioms) are
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #177.
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15859)  all_57_5 = e3 & op(e2, e1) = e3
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15859) implies:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15860)  op(e2, e1) = e3
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15861)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e3)
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15861) gives:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15862)  all_57_6 = e3 & op(e1, e3) = e3
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15862) implies:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15863)  all_57_6 = e3
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15864)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e3)
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (171), (230), (232),
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (234), (15729), (15863), (15864),
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #269.
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15865)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e3)
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15865) gives:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15866)  all_57_4 = e3 & op(e3, e1) = e3
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (15855), (15866), (function-axioms) are
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #177.
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e1, e2, simplifying with (15275), (15860)
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15867)  all_52_13 = e3
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15279), (15867) imply:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15868)  op(e3, e3) = e1
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (15255), (15868), (function-axioms) are
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1950.
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15869)  all_57_7 = e3 & op(e1, e2) = e3
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (15730), (15869), (function-axioms) are
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #267.
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15870)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e1, e0) = e3)
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (161), (14936), (15856), (15870),
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2310.
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15871)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e1) = e3)
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (158), (14936), (15476), (15871),
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #63.
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15872)   ~ (all_55_3 = e3)
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15873)  all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15838), (15872) imply:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15874)   ~ (all_32_0 = e3)
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15875)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e3)
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (171), (15255), (15729), (15875),
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #249.
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15876)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e3)
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15876) gives:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15877)  all_57_4 = e3 & op(e3, e1) = e3
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15877) implies:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15878)  all_57_4 = e3
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15879)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e1)
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15879) gives:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15880)  all_57_0 = e1 & op(e3, e3) = e1
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15880) implies:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15881)  op(e3, e3) = e1
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (169), (171), (235), (14927), (14951),
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15878), (15881), (function-axioms) are
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #234.
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15882)  all_57_1 = e1 & op(e3, e2) = e1
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15882) implies:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15883)  all_57_1 = e1
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15873) gives:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15884)  all_55_3 = e2
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15838), (15845), (15884) are inconsistent by
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #57.
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15885)   ~ (all_55_3 = e2)
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15886)  all_55_3 = e1 | all_55_3 = e0
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15886) gives:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15887)  all_55_3 = e1
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15829), (15838), (15887) are inconsistent by
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #56.
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15888)  all_55_3 = e0
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (15838), (15888) imply:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15889)  all_32_0 = e0
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (15889) implies:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15890)  all_32_0 = e0
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15839), (15890) imply:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15891)   ~ (all_53_4 = e0)
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15842), (15890) imply:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15892)   ~ (all_53_14 = e0)
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15844), (15890) imply:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15893)   ~ (all_52_15 = e0)
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15845), (15890) imply:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15894)   ~ (e2 = e0)
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15848) gives:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15895)  all_55_1 = e2
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (15895) imply:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15896)  all_53_4 = e2
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14951), (15896) imply:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15897)  $false
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (15897) is inconsistent.
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15898)  all_55_1 = e1 | all_55_1 = e0
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15899)  all_57_15 = e0 & op(e0, e0) = e0
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15899) implies:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15900)  op(e0, e0) = e0
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (14935), (15900), (function-axioms) are
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #86.
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15901)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15901) implies:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15902)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0)
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15902) gives:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15903)  all_57_9 = e0 & op(e3, e0) = e0
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15903) implies:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15904)  all_57_9 = e0
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15898) gives:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15905)  all_55_1 = e1
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (15905) imply:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15906)  all_53_4 = e1
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (137), (15906) imply:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15907)   ~ (all_53_6 = e1)
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (15907) implies:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15908)   ~ (all_53_6 = e1)
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (171), (15906) imply:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15909)  op(e3, e2) = e1
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (127), (142), (144), (145), (164), (193), (194),
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (197), (198), (201), (235), (247), (248), (256),
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (257), (14924), (14929), (15252), (15255),
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15266), (15267), (15278), (15280), (15285),
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15287), (15289), (15291), (15293), (15300),
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15301), (15304), (15728), (15851), (15878),
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15883), (15893), (15904), (15908), (15909),
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #59.
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15910)  all_55_1 = e0
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (15910) imply:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15911)  all_53_4 = e0
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15891), (15911) imply:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15912)  $false
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (15912) is inconsistent.
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15913)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 =
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15913) gives:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15914)  all_57_10 = e0 & op(e2, e0) = e0
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (207), (14934), (14935), (15274), (15278),
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15301), (15914), (function-axioms) are
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #84.
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15915)  all_57_11 = e0 & op(e1, e0) = e0
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (15892), (15915), (function-axioms) are
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2341.
% 224.92/38.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15916)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e1)
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15916) gives:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15917)  all_57_4 = e1 & op(e3, e1) = e1
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15917) implies:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15918)  all_57_4 = e1
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (15878), (15918) are inconsistent by
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2426.
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15919)  all_57_9 = e1 & op(e3, e0) = e1
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15919) implies:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15920)  all_57_9 = e1
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15873) gives:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15921)  all_55_3 = e2
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15838), (15845), (15921) are inconsistent by
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #57.
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15922)   ~ (all_55_3 = e2)
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15923)  all_55_3 = e1 | all_55_3 = e0
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15923) gives:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15924)  all_55_3 = e1
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15829), (15838), (15924) are inconsistent by
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #56.
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15925)  all_55_3 = e0
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (15838), (15925) imply:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15926)  all_32_0 = e0
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (15926) implies:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15927)  all_32_0 = e0
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15842), (15927) imply:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15928)   ~ (all_53_14 = e0)
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15845), (15927) imply:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15929)   ~ (e2 = e0)
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15829), (15927) imply:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15930)   ~ (e1 = e0)
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (161), (207), (14934), (14935), (15274),
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (15278), (15301), (15920), (15928),
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #83.
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15931)  all_57_9 = e3 & op(e3, e0) = e3
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15931) implies:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15932)  op(e3, e0) = e3
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15873) gives:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15933)  all_55_3 = e2
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15838), (15845), (15933) are inconsistent by
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #57.
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15934)  all_55_3 = e1 | all_55_3 = e0
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15934) gives:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15935)  all_55_3 = e1
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15829), (15838), (15935) are inconsistent by
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #56.
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15936)  all_55_3 = e0
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (15838), (15936) imply:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15937)  all_32_0 = e0
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (15937) implies:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15938)  all_32_0 = e0
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15874), (15938) imply:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15939)   ~ (e3 = e0)
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15836), (15938) imply:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15940)  op(e3, e0) = e0
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (15932), (15940), (function-axioms) are
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #313.
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15941)   ~ (all_32_1 = e3) & op(e0, e2) = all_32_1 &
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_32_1)
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (15941) implies:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15942)   ~ (all_32_1 = e3)
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15943)  op(e0, e2) = all_32_1
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15726), (15827), (15942), (15943),
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #58.
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | |   (15944)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (158), (14934), (15476), (15944),
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | |            #55.
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.51  | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | |   (15945)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 224.92/38.51  | | | | | | | | | | | | | | | | | |              & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 224.92/38.51  | | | | | | | | | | | | | | | | | |              & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 224.92/38.51  | | | | | | | | | | | | | | | | | |                all_52_21) = e1 & op(all_52_23, all_52_23) =
% 224.92/38.51  | | | | | | | | | | | | | | | | | |              e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 224.92/38.51  | | | | | | | | | | | | | | | | | |              all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 224.92/38.51  | | | | | | | | | | | | | | | | | |              = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 224.92/38.51  | | | | | | | | | | | | | | | | | |              $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 224.92/38.51  | | | | | | | | | | | | | | | | | |              & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 224.92/38.51  | | | | | | | | | | | | | | | | | |              e0 & op(all_52_25, all_52_25) = e3 &
% 224.92/38.51  | | | | | | | | | | | | | | | | | |              op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 224.92/38.51  | | | | | | | | | | | | | | | | | |                all_52_29) = e1 & op(all_52_31, all_52_31) =
% 224.92/38.51  | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 224.92/38.51  | | | | | | | | | | | | | | | | | |              all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 224.92/38.51  | | | | | | | | | | | | | | | | | |              = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 224.92/38.51  | | | | | | | | | | | | | | | | | |              $i(all_52_29) & $i(all_52_31))
% 224.92/38.51  | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | BETA: splitting (15945) gives:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | |   (15946)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 224.92/38.51  | | | | | | | | | | | | | | | | | | |            all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 224.92/38.51  | | | | | | | | | | | | | | | | | | |            op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 224.92/38.51  | | | | | | | | | | | | | | | | | | |              all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 224.92/38.51  | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 224.92/38.51  | | | | | | | | | | | | | | | | | | |            & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 224.92/38.51  | | | | | | | | | | | | | | | | | | |            & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 224.92/38.51  | | | | | | | | | | | | | | | | | | |            $i(all_52_23)
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (14958), (15262), (15946), (function-axioms)
% 224.92/38.51  | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2260.
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | |   (15947)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 224.92/38.51  | | | | | | | | | | | | | | | | | | |            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 224.92/38.51  | | | | | | | | | | | | | | | | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 224.92/38.51  | | | | | | | | | | | | | | | | | | |              all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 224.92/38.51  | | | | | | | | | | | | | | | | | | |            & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 224.92/38.51  | | | | | | | | | | | | | | | | | | |            & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 224.92/38.51  | | | | | | | | | | | | | | | | | | |            & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 224.92/38.51  | | | | | | | | | | | | | | | | | | |            $i(all_52_31)
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (14935), (14958), (15947), (function-axioms)
% 224.92/38.51  | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #79.
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.51  | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | End of split
% 224.92/38.51  | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.51  | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | |   (15948)  all_57_14 = e2 & op(e0, e1) = e2
% 224.92/38.51  | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (14926), (15948), (function-axioms) are
% 224.92/38.51  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #54.
% 224.92/38.51  | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | End of split
% 224.92/38.51  | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | End of split
% 224.92/38.51  | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | End of split
% 224.92/38.51  | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | Case 2:
% 224.92/38.51  | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | |   (15949)  all_18_2 = e0
% 224.92/38.51  | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | COMBINE_EQS: (327), (15949) imply:
% 224.92/38.51  | | | | | | | | | | | | | |   (15950)  all_10_2 = e0
% 224.92/38.51  | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | REDUCE: (338), (15950) imply:
% 224.92/38.51  | | | | | | | | | | | | | |   (15951)   ~ (all_53_1 = e0)
% 224.92/38.51  | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | REDUCE: (346), (15950) imply:
% 224.92/38.51  | | | | | | | | | | | | | |   (15952)   ~ (all_53_8 = e0)
% 224.92/38.51  | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | REDUCE: (348), (15950) imply:
% 224.92/38.51  | | | | | | | | | | | | | |   (15953)   ~ (all_53_12 = e0)
% 224.92/38.51  | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | REDUCE: (45), (15950) imply:
% 224.92/38.51  | | | | | | | | | | | | | |   (15954)  op(e3, e3) = e0
% 224.92/38.51  | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 224.92/38.51  | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | Case 1:
% 224.92/38.51  | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | |   (15955)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 224.92/38.51  | | | | | | | | | | | | | | |              & op(e2, e3) = e2)
% 224.92/38.51  | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | REF_CLOSE: (5), (168), (14950), (15954), (15955),
% 224.92/38.51  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.92/38.51  | | | | | | | | | | | | | | |            #1929.
% 224.92/38.51  | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | Case 2:
% 224.92/38.51  | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | |   (15956)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 224.92/38.51  | | | | | | | | | | | | | | |              e2 & op(e0, e3) = e2)
% 224.92/38.51  | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | BETA: splitting (15956) gives:
% 224.92/38.51  | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | Case 1:
% 224.92/38.51  | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | |   (15957)  all_57_6 = e2 & op(e1, e3) = e2
% 224.92/38.51  | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | ALPHA: (15957) implies:
% 224.92/38.51  | | | | | | | | | | | | | | | |   (15958)  op(e1, e3) = e2
% 224.92/38.51  | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 224.92/38.51  | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.51  | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | |   (15959)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 224.92/38.51  | | | | | | | | | | | | | | | | |              & op(e3, e2) = e2)
% 224.92/38.51  | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (171), (14951), (15954), (15959),
% 224.92/38.51  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.92/38.51  | | | | | | | | | | | | | | | | |            #1935.
% 224.92/38.51  | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.51  | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | |   (15960)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 224.92/38.51  | | | | | | | | | | | | | | | | |              & op(e3, e0) = e2)
% 224.92/38.51  | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | BETA: splitting (15960) gives:
% 224.92/38.51  | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | |   (15961)  all_57_4 = e2 & op(e3, e1) = e2
% 224.92/38.51  | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | ALPHA: (15961) implies:
% 224.92/38.51  | | | | | | | | | | | | | | | | | |   (15962)  op(e3, e1) = e2
% 224.92/38.51  | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_2, e2,
% 224.92/38.51  | | | | | | | | | | | | | | | | | |              e3, e1, simplifying with (164), (15958) gives:
% 224.92/38.51  | | | | | | | | | | | | | | | | | |   (15963)  all_53_2 = e2
% 224.92/38.51  | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_8, e2,
% 224.92/38.51  | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (170), (15962) gives:
% 224.92/38.51  | | | | | | | | | | | | | | | | | |   (15964)  all_53_8 = e2
% 224.92/38.51  | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | REDUCE: (363), (15964) imply:
% 224.92/38.51  | | | | | | | | | | | | | | | | | |   (15965)   ~ (all_6_2 = e2)
% 224.92/38.51  | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | SIMP: (15965) implies:
% 224.92/38.51  | | | | | | | | | | | | | | | | | |   (15966)   ~ (all_6_2 = e2)
% 224.92/38.51  | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | |   (15967)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 224.92/38.51  | | | | | | | | | | | | | | | | | | |              all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 224.92/38.51  | | | | | | | | | | | | | | | | | | |              op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 224.92/38.51  | | | | | | | | | | | | | | | | | | |                all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 224.92/38.51  | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 224.92/38.51  | | | | | | | | | | | | | | | | | | |              op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 224.92/38.51  | | | | | | | | | | | | | | | | | | |              $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 224.92/38.51  | | | | | | | | | | | | | | | | | | |              $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 224.92/38.51  | | | | | | | | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 224.92/38.51  | | | | | | | | | | | | | | | | | | |                all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 224.92/38.51  | | | | | | | | | | | | | | | | | | |              & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 224.92/38.51  | | | | | | | | | | | | | | | | | | |                all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 224.92/38.51  | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 224.92/38.51  | | | | | | | | | | | | | | | | | | |              & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 224.92/38.51  | | | | | | | | | | | | | | | | | | |              $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | BETA: splitting (15967) gives:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | |   (15968)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | |            all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | |            op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | |              all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | |            $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | |            $i(all_52_7)
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | ALPHA: (15968) implies:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | |   (15969)  op(e3, e3) = all_52_1
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | |   (15970)  op(all_52_1, all_52_1) = e3
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (14935), (15954), (15969), (15970),
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | |            #53.
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | |   (15971)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | |            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | |            op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | |              all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | |            $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | |            $i(all_52_15)
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | ALPHA: (15971) implies:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | |   (15972)  op(e2, e0) = all_52_15
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | |   (15973)  op(e2, e3) = all_52_9
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | |   (15974)  op(all_52_15, all_52_15) = e0
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | |   (15975)  op(all_52_9, all_52_9) = e3
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_13,
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | |              all_52_15, e0, e2, simplifying with (165), (15972)
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | |              gives:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | |   (15976)  all_53_13 = all_52_15
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_1,
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | |              all_52_9, e3, e2, simplifying with (168), (15973)
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | |              gives:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | |   (15977)  all_53_1 = all_52_9
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (15977) imply:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | |   (15978)  all_55_4 = all_52_9
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | REDUCE: (14950), (15977) imply:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | |   (15979)   ~ (all_52_9 = e2)
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | REDUCE: (15951), (15977) imply:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | |   (15980)   ~ (all_52_9 = e0)
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | REDUCE: (14928), (15976) imply:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | |   (15981)   ~ (all_52_15 = e2)
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | |   (15982)   ~ (all_24_2 = e0)
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | REDUCE: (315), (15982) imply:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | |   (15983)   ~ (all_6_2 = e0)
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | |   (15984)  all_55_10 = e3
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (14936), (15984) are inconsistent by
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2500.
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | |   (15985)  all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15985) gives:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | |   (15986)  all_55_10 = e2
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (15966), (15986) are inconsistent by
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2499.
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | |   (15987)  all_55_10 = e1 | all_55_10 = e0
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15987) gives:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | |   (15988)  all_55_10 = e1
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (336), (15988) imply:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | |   (15989)  all_6_2 = e1
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (15989) implies:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | |   (15990)  all_6_2 = e1
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (15990) imply:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | |   (15991)  op(e1, e1) = e1
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | |   (15992)  all_55_4 = e3
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15954), (15975), (15978), (15980), (15992),
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | |            #52.
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | |   (15993)   ~ (all_55_4 = e3)
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | |   (15994)  all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15978), (15993) imply:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | |   (15995)   ~ (all_52_9 = e3)
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15994) gives:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | |   (15996)  all_55_4 = e2
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15978), (15979), (15996) are inconsistent by
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #345.
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | |   (15997)  all_55_4 = e1 | all_55_4 = e0
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15997) gives:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15998)  all_55_4 = e1
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (15978), (15998) imply:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (15999)  all_52_9 = e1
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (15999) implies:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16000)  all_52_9 = e1
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15995), (16000) imply:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16001)   ~ (e3 = e1)
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (15975), (16000) imply:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16002)  op(e1, e1) = e3
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (15991), (16002), (function-axioms) are
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #156.
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16003)  all_55_4 = e0
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15978), (15980), (16003) are inconsistent by
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #60.
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | |   (16004)  all_55_10 = e0
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (15983), (16004) are inconsistent by
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2118.
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | |   (16005)  all_24_2 = e0
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (315), (16005) imply:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | |   (16006)  all_6_2 = e0
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | SIMP: (16006) implies:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | |   (16007)  all_6_2 = e0
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | REDUCE: (368), (16007) imply:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | |   (16008)   ~ (all_53_14 = e0)
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | REDUCE: (15966), (16007) imply:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | |   (16009)   ~ (e2 = e0)
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | |   (16010)  all_57_15 = e0 & op(e0, e0) = e0
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16010) implies:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | |   (16011)  op(e0, e0) = e0
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (14935), (16011), (function-axioms) are
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #86.
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | |   (16012)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16012) implies:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | |   (16013)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | |                e0) = e0)
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16013) gives:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | |   (16014)  all_57_9 = e0 & op(e3, e0) = e0
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (15953), (16014), (function-axioms) are
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2434.
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | |   (16015)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 =
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16015) gives:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | |   (16016)  all_57_10 = e0 & op(e2, e0) = e0
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (207), (14934), (14935), (15972), (15974),
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | |            (15981), (16016), (function-axioms) are
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #84.
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | |   (16017)  all_57_11 = e0 & op(e1, e0) = e0
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (16008), (16017), (function-axioms) are
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2341.
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | |   (16018)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 224.92/38.51  | | | | | | | | | | | | | | | | | | |              & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 224.92/38.51  | | | | | | | | | | | | | | | | | | |              & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 224.92/38.51  | | | | | | | | | | | | | | | | | | |                all_52_21) = e1 & op(all_52_23, all_52_23) =
% 224.92/38.51  | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 224.92/38.51  | | | | | | | | | | | | | | | | | | |              all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 224.92/38.51  | | | | | | | | | | | | | | | | | | |              = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 224.92/38.51  | | | | | | | | | | | | | | | | | | |              $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 224.92/38.51  | | | | | | | | | | | | | | | | | | |              & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 224.92/38.51  | | | | | | | | | | | | | | | | | | |              e0 & op(all_52_25, all_52_25) = e3 &
% 224.92/38.51  | | | | | | | | | | | | | | | | | | |              op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 224.92/38.51  | | | | | | | | | | | | | | | | | | |                all_52_29) = e1 & op(all_52_31, all_52_31) =
% 224.92/38.51  | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 224.92/38.51  | | | | | | | | | | | | | | | | | | |              all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 224.92/38.51  | | | | | | | | | | | | | | | | | | |              = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 224.92/38.51  | | | | | | | | | | | | | | | | | | |              $i(all_52_29) & $i(all_52_31))
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | BETA: splitting (16018) gives:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | |   (16019)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | |            all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | |            op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | |              all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | |            & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | |            & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | |            $i(all_52_23)
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (14958), (15958), (16019), (function-axioms)
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #80.
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | |   (16020)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | |            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | |              all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | |            & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | |            & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | |            & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | |            $i(all_52_31)
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (14935), (14958), (16020), (function-axioms)
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #79.
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.51  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.51  | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.51  | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | |   (16021)  all_57_9 = e2 & op(e3, e0) = e2
% 224.92/38.51  | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | ALPHA: (16021) implies:
% 224.92/38.51  | | | | | | | | | | | | | | | | | |   (16022)  op(e3, e0) = e2
% 224.92/38.51  | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (14927), (16022), (function-axioms) are
% 224.92/38.51  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2331.
% 224.92/38.51  | | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | | End of split
% 224.92/38.51  | | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | End of split
% 224.92/38.51  | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | Case 2:
% 224.92/38.51  | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | |   (16023)  all_57_12 = e2 & op(e0, e3) = e2
% 224.92/38.51  | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | ALPHA: (16023) implies:
% 224.92/38.51  | | | | | | | | | | | | | | | |   (16024)  op(e0, e3) = e2
% 224.92/38.51  | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | | REF_CLOSE: (160), (14924), (16024), (function-axioms) are
% 224.92/38.51  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1980.
% 224.92/38.51  | | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | | End of split
% 224.92/38.51  | | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | | End of split
% 224.92/38.51  | | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | End of split
% 224.92/38.51  | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | End of split
% 224.92/38.51  | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | Case 2:
% 224.92/38.51  | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | |   (16025)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 224.92/38.51  | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 224.92/38.51  | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | BETA: splitting (16025) gives:
% 224.92/38.51  | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | Case 1:
% 224.92/38.51  | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | |   (16026)  all_57_5 = e2 & op(e2, e1) = e2
% 224.92/38.51  | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | REF_CLOSE: (166), (14952), (16026), (function-axioms) are
% 224.92/38.51  | | | | | | | | | | | | |            inconsistent by sub-proof #1858.
% 224.92/38.51  | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | Case 2:
% 224.92/38.51  | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | |   (16027)  all_57_10 = e2 & op(e2, e0) = e2
% 224.92/38.51  | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | | REF_CLOSE: (165), (14928), (16027), (function-axioms) are
% 224.92/38.51  | | | | | | | | | | | | |            inconsistent by sub-proof #2432.
% 224.92/38.51  | | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | | End of split
% 224.92/38.51  | | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | | End of split
% 224.92/38.51  | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | Case 2:
% 224.92/38.51  | | | | | | | | | | | 
% 224.92/38.51  | | | | | | | | | | |   (16028)  all_55_5 = e1 | all_55_5 = e0
% 224.92/38.52  | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | REF_CLOSE: (266), (14940), (14942), (16028) are inconsistent
% 224.92/38.52  | | | | | | | | | | |            by sub-proof #1857.
% 224.92/38.52  | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | End of split
% 224.92/38.52  | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | End of split
% 224.92/38.52  | | | | | | | | | 
% 224.92/38.52  | | | | | | | | Case 2:
% 224.92/38.52  | | | | | | | | | 
% 224.92/38.52  | | | | | | | | |   (16029)  all_16_2 = e1
% 224.92/38.52  | | | | | | | | |   (16030)  ( ~ (all_16_0 = e0) & op(all_16_1, e2) = all_16_0 &
% 224.92/38.52  | | | | | | | | |              op(e2, e1) = all_16_1 & $i(all_16_0) &
% 224.92/38.52  | | | | | | | | |              $i(all_16_1)) | ( ~ (all_16_1 = e3) & op(e2, e1)
% 224.92/38.52  | | | | | | | | |              = all_16_1 & $i(all_16_1))
% 224.92/38.52  | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | COMBINE_EQS: (324), (16029) imply:
% 224.92/38.52  | | | | | | | | |   (16031)  all_8_2 = e1
% 224.92/38.52  | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | SIMP: (16031) implies:
% 224.92/38.52  | | | | | | | | |   (16032)  all_8_2 = e1
% 224.92/38.52  | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | COMBINE_EQS: (305), (16032) imply:
% 224.92/38.52  | | | | | | | | |   (16033)  all_26_2 = e1
% 224.92/38.52  | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | REDUCE: (349), (16032) imply:
% 224.92/38.52  | | | | | | | | |   (16034)   ~ (all_53_1 = e1)
% 224.92/38.52  | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | REDUCE: (352), (16032) imply:
% 224.92/38.52  | | | | | | | | |   (16035)   ~ (all_53_4 = e1)
% 224.92/38.52  | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | REDUCE: (354), (16032) imply:
% 224.92/38.52  | | | | | | | | |   (16036)   ~ (all_53_6 = e1)
% 224.92/38.52  | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | REDUCE: (356), (16032) imply:
% 224.92/38.52  | | | | | | | | |   (16037)   ~ (all_53_7 = e1)
% 224.92/38.52  | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | REDUCE: (358), (16032) imply:
% 224.92/38.52  | | | | | | | | |   (16038)   ~ (all_53_9 = e1)
% 224.92/38.52  | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | REDUCE: (360), (16032) imply:
% 224.92/38.52  | | | | | | | | |   (16039)   ~ (all_53_13 = e1)
% 224.92/38.52  | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | REDUCE: (14937), (16032) imply:
% 224.92/38.52  | | | | | | | | |   (16040)   ~ (e3 = e1)
% 224.92/38.52  | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | BETA: splitting (223) gives:
% 224.92/38.52  | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | Case 1:
% 224.92/38.52  | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | |   (16041)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 224.92/38.52  | | | | | | | | | |              & op(e2, e2) = e1)
% 224.92/38.52  | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | BETA: splitting (16041) gives:
% 224.92/38.52  | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | Case 1:
% 224.92/38.52  | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | |   (16042)  all_57_2 = e1 & op(e2, e3) = e1
% 224.92/38.52  | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | REF_CLOSE: (168), (16034), (16042), (function-axioms) are
% 224.92/38.52  | | | | | | | | | | |            inconsistent by sub-proof #2156.
% 224.92/38.52  | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | Case 2:
% 224.92/38.52  | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | |   (16043)  all_57_3 = e1 & op(e2, e2) = e1
% 224.92/38.52  | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | ALPHA: (16043) implies:
% 224.92/38.52  | | | | | | | | | | |   (16044)  all_57_3 = e1
% 224.92/38.52  | | | | | | | | | | |   (16045)  op(e2, e2) = e1
% 224.92/38.52  | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | BETA: splitting (58) gives:
% 224.92/38.52  | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | Case 1:
% 224.92/38.52  | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | |   (16046)   ~ (all_18_2 = e0)
% 224.92/38.52  | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | REDUCE: (327), (16046) imply:
% 224.92/38.52  | | | | | | | | | | | |   (16047)   ~ (all_10_2 = e0)
% 224.92/38.52  | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | BETA: splitting (61) gives:
% 224.92/38.52  | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | Case 1:
% 224.92/38.52  | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | |   (16048)   ~ (all_20_2 = e2)
% 224.92/38.52  | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | REDUCE: (299), (16048) imply:
% 224.92/38.52  | | | | | | | | | | | | |   (16049)   ~ (all_10_2 = e2)
% 224.92/38.52  | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | BETA: splitting (205) gives:
% 224.92/38.52  | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | Case 1:
% 224.92/38.52  | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | |   (16050)  all_55_0 = e3
% 224.92/38.52  | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | COMBINE_EQS: (277), (16050) imply:
% 224.92/38.52  | | | | | | | | | | | | | |   (16051)  all_10_2 = e3
% 224.92/38.52  | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | REDUCE: (338), (16051) imply:
% 224.92/38.52  | | | | | | | | | | | | | |   (16052)   ~ (all_53_1 = e3)
% 224.92/38.52  | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | REDUCE: (342), (16051) imply:
% 224.92/38.52  | | | | | | | | | | | | | |   (16053)   ~ (all_53_3 = e3)
% 224.92/38.52  | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | REDUCE: (344), (16051) imply:
% 224.92/38.52  | | | | | | | | | | | | | |   (16054)   ~ (all_53_4 = e3)
% 224.92/38.52  | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | REDUCE: (346), (16051) imply:
% 224.92/38.52  | | | | | | | | | | | | | |   (16055)   ~ (all_53_8 = e3)
% 224.92/38.52  | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | REDUCE: (348), (16051) imply:
% 224.92/38.52  | | | | | | | | | | | | | |   (16056)   ~ (all_53_12 = e3)
% 224.92/38.52  | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | REDUCE: (45), (16051) imply:
% 224.92/38.52  | | | | | | | | | | | | | |   (16057)  op(e3, e3) = e3
% 224.92/38.52  | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 224.92/38.52  | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | Case 1:
% 224.92/38.52  | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | |   (16058)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 224.92/38.52  | | | | | | | | | | | | | | |              & op(e2, e3) = e3)
% 224.92/38.52  | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | BETA: splitting (16058) gives:
% 224.92/38.52  | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | Case 1:
% 224.92/38.52  | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | |   (16059)  all_57_0 = e3 & op(e3, e3) = e3
% 224.92/38.52  | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | ALPHA: (16059) implies:
% 224.92/38.52  | | | | | | | | | | | | | | | |   (16060)  all_57_0 = e3
% 224.92/38.52  | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 224.92/38.52  | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.52  | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | |   (16061)   ~ (all_24_2 = e0)
% 224.92/38.52  | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | REDUCE: (315), (16061) imply:
% 224.92/38.52  | | | | | | | | | | | | | | | | |   (16062)   ~ (all_6_2 = e0)
% 224.92/38.52  | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | BETA: splitting (88) gives:
% 224.92/38.52  | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | |   (16063)   ~ (all_38_2 = e2)
% 224.92/38.52  | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | REDUCE: (249), (16063) imply:
% 224.92/38.52  | | | | | | | | | | | | | | | | | |   (16064)   ~ (all_6_2 = e2)
% 224.92/38.52  | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | |   (16065)  all_55_10 = e3
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (14936), (16065) are inconsistent by
% 224.92/38.52  | | | | | | | | | | | | | | | | | | |            sub-proof #2500.
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | |   (16066)  all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | BETA: splitting (16066) gives:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | |   (16067)  all_55_10 = e2
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (16064), (16067) are inconsistent by
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | |            sub-proof #2499.
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | |   (16068)   ~ (all_55_10 = e2)
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | |   (16069)  all_55_10 = e1 | all_55_10 = e0
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | BETA: splitting (16069) gives:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | |   (16070)  all_55_10 = e1
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (336), (16070) imply:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | |   (16071)  all_6_2 = e1
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | SIMP: (16071) implies:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | |   (16072)  all_6_2 = e1
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | REDUCE: (368), (16072) imply:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | |   (16073)   ~ (all_53_14 = e1)
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | REDUCE: (16064), (16072) imply:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | |   (16074)   ~ (e2 = e1)
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (16072) imply:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | |   (16075)  op(e1, e1) = e1
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | |   (16076)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16076) gives:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | |   (16077)  all_57_9 = e1 & op(e3, e0) = e1
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16077) implies:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | |   (16078)  all_57_9 = e1
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | |   (16079)  op(e3, e0) = e1
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (107), (111), (113), (114), (118),
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | |            (146), (161), (166), (168), (169), (194), (198),
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | |            (207), (225), (248), (258), (14927), (14928),
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | |            (14929), (14934), (14935), (16045), (16057),
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | |            (16075), (16078), (16079), (function-axioms) are
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #49.
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | |   (16080)  all_57_10 = e1 & op(e2, e0) = e1
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (16039), (16080), (function-axioms) are
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2084.
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | |   (16081)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (161), (14935), (16073), (16081),
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | |            #88.
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | |   (16082)  all_55_10 = e0
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (16062), (16082) are inconsistent by
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | |            sub-proof #2118.
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.52  | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | |   (16083)  all_38_2 = e2
% 224.92/38.52  | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (16083) imply:
% 224.92/38.52  | | | | | | | | | | | | | | | | | |   (16084)  all_6_2 = e2
% 224.92/38.52  | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | REDUCE: (361), (16084) imply:
% 224.92/38.52  | | | | | | | | | | | | | | | | | |   (16085)   ~ (all_53_6 = e2)
% 224.92/38.52  | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | REDUCE: (364), (16084) imply:
% 224.92/38.52  | | | | | | | | | | | | | | | | | |   (16086)   ~ (all_53_9 = e2)
% 224.92/38.52  | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | REDUCE: (39), (16084) imply:
% 224.92/38.52  | | | | | | | | | | | | | | | | | |   (16087)  op(e1, e1) = e2
% 224.92/38.52  | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | |   (16088)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 224.92/38.52  | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | BETA: splitting (16088) gives:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | |   (16089)  all_57_2 = e2 & op(e2, e3) = e2
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | ALPHA: (16089) implies:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | |   (16090)  op(e2, e3) = e2
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | |   (16091)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16091) gives:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | |   (16092)  all_57_1 = e2 & op(e3, e2) = e2
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16092) implies:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | |   (16093)  op(e3, e2) = e2
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_1, e2,
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (168), (16090) gives:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | |   (16094)  all_53_1 = e2
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_4, e2,
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (171), (16093) gives:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | |   (16095)  all_53_4 = e2
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (147), (16094) imply:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | |   (16096)   ~ (all_53_9 = e2)
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (137), (16095) imply:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | |   (16097)   ~ (all_53_6 = e2)
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (136), (16095) imply:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | |   (16098)   ~ (all_53_7 = e2)
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (16095) imply:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | |   (16099)   ~ (all_53_8 = e2)
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | SIMP: (16099) implies:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | |   (16100)   ~ (all_53_8 = e2)
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | |   (16101)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | |              all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | |              op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | |                all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | |                all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | |              & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | |                all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16101) gives:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | |   (16102)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | |            all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | |              all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_7)
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16102) implies:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | |   (16103)  op(e3, e2) = all_52_3
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | |   (16104)  op(all_52_3, all_52_3) = e2
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_52_3,
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (16093), (16103) gives:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | |   (16105)  all_52_3 = e2
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (16104), (16105) imply:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | |   (16106)  op(e2, e2) = e2
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (16045), (16106), (function-axioms) are
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2306.
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | |   (16107)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | |            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | |              all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_15)
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (16045), (16090), (16107), (function-axioms)
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #48.
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | |   (16108)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | |              & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | |              & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | |                all_52_21) = e1 & op(all_52_23, all_52_23) =
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | |              all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | |              = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | |              & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(all_52_25, all_52_25) = e3 &
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | |              op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | |                all_52_29) = e1 & op(all_52_31, all_52_31) =
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | |              all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | |              = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_29) & $i(all_52_31))
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16108) gives:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | |   (16109)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | |            all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | |              all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | |            & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_23)
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16109) implies:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | |   (16110)  op(e1, e1) = all_52_21
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | |   (16111)  op(e1, e2) = all_52_19
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | |   (16112)  op(e1, e3) = all_52_17
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | |   (16113)  op(all_52_21, all_52_21) = e1
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | |   (16114)  op(all_52_19, all_52_19) = e2
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | |   (16115)  op(all_52_17, all_52_17) = e3
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | |              all_52_21, e1, e1, simplifying with (16087),
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | |              (16110) gives:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | |   (16116)  all_52_21 = e2
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_6,
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | |              all_52_19, e2, e1, simplifying with (163), (16111)
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | |   (16117)  all_53_6 = all_52_19
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_2,
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | |              all_52_17, e3, e1, simplifying with (164), (16112)
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | |   (16118)  all_53_2 = all_52_17
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (16117) imply:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | |   (16119)  all_55_9 = all_52_19
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (129), (16117) imply:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | |   (16120)   ~ (all_53_7 = all_52_19)
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (16120) implies:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | |   (16121)   ~ (all_53_7 = all_52_19)
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (16085), (16117) imply:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | |   (16122)   ~ (all_52_19 = e2)
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (16036), (16117) imply:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | |   (16123)   ~ (all_52_19 = e1)
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | |   (16124)  all_55_6 = e3
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (16124) imply:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | |   (16125)  all_53_9 = e3
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (16125) implies:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | |   (16126)  all_53_9 = e3
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (16126) imply:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | |   (16127)   ~ (all_53_13 = e3)
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (16127) implies:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | |   (16128)   ~ (all_53_13 = e3)
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (166), (16126) imply:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | |   (16129)  op(e2, e1) = e3
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | |   (16130)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (169), (16056), (16128), (16130),
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | |            #2300.
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | |   (16131)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16131) gives:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16132)  all_57_11 = e3 & op(e1, e0) = e3
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16132) implies:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16133)  all_57_11 = e3
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (39), (163), (195), (215), (336),
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14936), (16036), (16087), (16112), (16115),
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16133), (function-axioms) are inconsistent by
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1731.
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16134)  all_57_15 = e3 & op(e0, e0) = e3
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16134) implies:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16135)  all_57_15 = e3
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16136)  op(e0, e0) = e3
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (70), (107),
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (137), (163), (166), (171), (204), (207), (211),
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (217), (230), (232), (234), (270), (14936),
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16030), (16033), (16035), (16038), (16045),
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16057), (16060), (16129), (16135), (16136),
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1785.
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | |   (16137)  all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16137) gives:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | |   (16138)  all_55_6 = e2
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (16086), (16138) are inconsistent by
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2398.
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | |   (16139)  all_55_6 = e1 | all_55_6 = e0
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16139) gives:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16140)  all_55_6 = e1
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (16038), (16140) are inconsistent by
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2163.
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16141)  all_55_6 = e0
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (16141) imply:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16142)  all_53_9 = e0
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (16142) implies:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16143)  all_53_9 = e0
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (124), (16143) imply:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16144)   ~ (all_53_8 = e0)
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (119), (16143) imply:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16145)   ~ (all_53_11 = e0)
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (16145) implies:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16146)   ~ (all_53_11 = e0)
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16147)  all_55_2 = e3
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (16055), (16147) are inconsistent by
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2028.
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16148)  all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16148) gives:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16149)  all_55_2 = e2
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (16100), (16149) are inconsistent by
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2027.
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16150)  all_55_2 = e1 | all_55_2 = e0
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16150) gives:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16151)  all_55_2 = e1
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (16151) imply:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16152)  all_53_8 = e1
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (16152) implies:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16153)  all_53_8 = e1
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (122), (16153) imply:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16154)   ~ (all_53_11 = e1)
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (16154) implies:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16155)   ~ (all_53_11 = e1)
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16156)  all_55_14 = e3
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (16156) imply:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16157)  all_53_11 = e3
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (126), (16157) imply:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16158)   ~ (all_53_7 = e3)
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16159)  all_55_13 = e3
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (16159) imply:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16160)  all_53_7 = e3
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (16158), (16160) imply:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16161)  $false
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (16161) is inconsistent.
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16162)  all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16162) gives:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16163)  all_55_13 = e2
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (14925), (16163) are inconsistent by
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2287.
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16164)  all_55_13 = e1 | all_55_13 = e0
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16164) gives:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16165)  all_55_13 = e1
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (16037), (16165) are inconsistent by
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2002.
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16166)  all_55_13 = e0
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (16166) imply:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16167)  all_53_7 = e0
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (16167) implies:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16168)  all_53_7 = e0
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (16121), (16168) imply:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16169)   ~ (all_52_19 = e0)
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (16169) implies:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16170)   ~ (all_52_19 = e0)
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (196), (16057), (16114), (16119), (16122),
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16123), (16170), (function-axioms) are
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1370.
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16171)  all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (14926), (16146), (16155), (16171) are
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1719.
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16172)  all_55_2 = e0
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (16144), (16172) are inconsistent by
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2031.
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | |   (16173)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | |            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | |              all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | |            & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_31)
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (14935), (16045), (16173), (function-axioms)
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #50.
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | |   (16174)  all_57_3 = e2 & op(e2, e2) = e2
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16174) implies:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | |   (16175)  op(e2, e2) = e2
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (16045), (16175), (function-axioms) are
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2306.
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | |   (16176)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (163), (14925), (16085), (16176),
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | |            #160.
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | |   (16177)  all_57_3 = e2 & op(e2, e2) = e2
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | ALPHA: (16177) implies:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | |   (16178)  op(e2, e2) = e2
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (16045), (16178), (function-axioms) are
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2306.
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | |   (16179)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 224.92/38.53  | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | BETA: splitting (16179) gives:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | |   (16180)  all_57_5 = e2 & op(e2, e1) = e2
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (16086), (16180), (function-axioms) are
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1858.
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | |   (16181)  all_57_10 = e2 & op(e2, e0) = e2
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (14928), (16181), (function-axioms) are
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2432.
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.53  | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | End of split
% 224.92/38.53  | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.53  | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | |   (16182)  all_24_2 = e0
% 224.92/38.53  | | | | | | | | | | | | | | | | |   (16183)  ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0
% 224.92/38.53  | | | | | | | | | | | | | | | | |              & op(e1, e0) = all_24_1 & $i(all_24_0) &
% 224.92/38.53  | | | | | | | | | | | | | | | | |              $i(all_24_1)) | ( ~ (all_24_1 = e3) & op(e1, e0)
% 224.92/38.53  | | | | | | | | | | | | | | | | |              = all_24_1 & $i(all_24_1))
% 224.92/38.53  | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | COMBINE_EQS: (315), (16182) imply:
% 224.92/38.53  | | | | | | | | | | | | | | | | |   (16184)  all_6_2 = e0
% 224.92/38.53  | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | SIMP: (16184) implies:
% 224.92/38.53  | | | | | | | | | | | | | | | | |   (16185)  all_6_2 = e0
% 224.92/38.53  | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | COMBINE_EQS: (311), (16185) imply:
% 224.92/38.53  | | | | | | | | | | | | | | | | |   (16186)  all_34_2 = e0
% 224.92/38.53  | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | REDUCE: (363), (16185) imply:
% 224.92/38.53  | | | | | | | | | | | | | | | | |   (16187)   ~ (all_53_8 = e0)
% 224.92/38.53  | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | REDUCE: (14936), (16185) imply:
% 224.92/38.53  | | | | | | | | | | | | | | | | |   (16188)   ~ (e3 = e0)
% 224.92/38.53  | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | REDUCE: (39), (16185) imply:
% 224.92/38.53  | | | | | | | | | | | | | | | | |   (16189)  op(e1, e1) = e0
% 224.92/38.53  | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 224.92/38.53  | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | |   (16190)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 224.92/38.53  | | | | | | | | | | | | | | | | | |              all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 224.92/38.53  | | | | | | | | | | | | | | | | | |              op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 224.92/38.53  | | | | | | | | | | | | | | | | | |                all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 224.92/38.53  | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 224.92/38.53  | | | | | | | | | | | | | | | | | |              op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 224.92/38.53  | | | | | | | | | | | | | | | | | |              $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 224.92/38.53  | | | | | | | | | | | | | | | | | |              $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 224.92/38.53  | | | | | | | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 224.92/38.53  | | | | | | | | | | | | | | | | | |                all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 224.92/38.53  | | | | | | | | | | | | | | | | | |              & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 224.92/38.53  | | | | | | | | | | | | | | | | | |                all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 224.92/38.53  | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 224.92/38.53  | | | | | | | | | | | | | | | | | |              & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 224.92/38.53  | | | | | | | | | | | | | | | | | |              $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 224.92/38.53  | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | BETA: splitting (16190) gives:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | |   (16191)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 224.92/38.53  | | | | | | | | | | | | | | | | | | |            all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 224.92/38.53  | | | | | | | | | | | | | | | | | | |            op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 224.92/38.53  | | | | | | | | | | | | | | | | | | |              all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 224.92/38.53  | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 224.92/38.53  | | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 224.92/38.53  | | | | | | | | | | | | | | | | | | |            $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 224.92/38.53  | | | | | | | | | | | | | | | | | | |            $i(all_52_7)
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | ALPHA: (16191) implies:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | |   (16192)  op(e3, e0) = all_52_7
% 224.92/38.53  | | | | | | | | | | | | | | | | | | |   (16193)  op(e3, e1) = all_52_5
% 224.92/38.53  | | | | | | | | | | | | | | | | | | |   (16194)  op(e3, e3) = all_52_1
% 224.92/38.53  | | | | | | | | | | | | | | | | | | |   (16195)  op(all_52_7, all_52_7) = e0
% 224.92/38.53  | | | | | | | | | | | | | | | | | | |   (16196)  op(all_52_5, all_52_5) = e1
% 224.92/38.53  | | | | | | | | | | | | | | | | | | |   (16197)  op(all_52_1, all_52_1) = e3
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_12,
% 224.92/38.53  | | | | | | | | | | | | | | | | | | |              all_52_7, e0, e3, simplifying with (169), (16192)
% 224.92/38.53  | | | | | | | | | | | | | | | | | | |              gives:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | |   (16198)  all_53_12 = all_52_7
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_8,
% 224.92/38.53  | | | | | | | | | | | | | | | | | | |              all_52_5, e1, e3, simplifying with (170), (16193)
% 224.92/38.53  | | | | | | | | | | | | | | | | | | |              gives:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | |   (16199)  all_53_8 = all_52_5
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (16199) imply:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | |   (16200)  all_55_2 = all_52_5
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | REDUCE: (16055), (16199) imply:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | |   (16201)   ~ (all_52_5 = e3)
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | REDUCE: (16187), (16199) imply:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | |   (16202)   ~ (all_52_5 = e0)
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | BETA: splitting (82) gives:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | |   (16203)   ~ (all_34_2 = e0)
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | REDUCE: (16186), (16203) imply:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | |   (16204)  $false
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | CLOSE: (16204) is inconsistent.
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | |   (16205)  ( ~ (all_34_0 = e3) & op(all_34_1, e1) = all_34_0
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | |              & op(e1, e0) = all_34_1 & $i(all_34_0) &
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | |              $i(all_34_1)) | ( ~ (all_34_1 = e2) & op(e1, e0)
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | |              = all_34_1 & $i(all_34_1))
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | |   (16206)  all_55_13 = e3
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (16206) imply:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | |   (16207)  all_53_7 = e3
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | SIMP: (16207) implies:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | |   (16208)  all_53_7 = e3
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | REDUCE: (129), (16208) imply:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | |   (16209)   ~ (all_53_6 = e3)
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | |   (16210)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e3)
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (163), (230), (232),
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | |            (234), (16060), (16209), (16210),
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | |            #82.
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | |   (16211)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e1, e0) = e3)
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16211) gives:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | |   (16212)  all_57_8 = e3 & op(e1, e1) = e3
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16212) implies:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | |   (16213)  op(e1, e1) = e3
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (14936), (16213), (function-axioms) are
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2468.
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | |   (16214)  all_57_11 = e3 & op(e1, e0) = e3
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16214) implies:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | |   (16215)  op(e1, e0) = e3
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (203), (16183), (16189), (16193), (16196),
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | |            (16200), (16201), (16202), (16205), (16215),
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | |            #256.
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | |   (16216)  all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16216) gives:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | |   (16217)  all_55_13 = e2
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (14925), (16217) are inconsistent by
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2287.
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | |   (16218)  all_55_13 = e1 | all_55_13 = e0
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | |   (16219)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e0)
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16219) gives:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | |   (16220)  all_57_0 = e0 & op(e3, e3) = e0
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16220) implies:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | |   (16221)  op(e3, e3) = e0
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (14935), (16194), (16197), (16221),
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | |            #53.
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | |   (16222)  all_57_1 = e0 & op(e3, e2) = e0
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16222) implies:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | |   (16223)  op(e3, e2) = e0
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (136), (171), (246), (16037), (16218), (16223),
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | |            #328.
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | |   (16224)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e0)
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16224) gives:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | |   (16225)  all_57_4 = e0 & op(e3, e1) = e0
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16225) implies:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | |   (16226)  op(e3, e1) = e0
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (16187), (16226), (function-axioms) are
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2267.
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | |   (16227)  all_57_9 = e0 & op(e3, e0) = e0
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16227) implies:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | |   (16228)  op(e3, e0) = e0
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (14935), (16192), (16195), (16228),
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | |            #47.
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | |   (16229)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 224.92/38.53  | | | | | | | | | | | | | | | | | | |            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 224.92/38.53  | | | | | | | | | | | | | | | | | | |            op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 224.92/38.53  | | | | | | | | | | | | | | | | | | |              all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 224.92/38.53  | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 224.92/38.53  | | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 224.92/38.53  | | | | | | | | | | | | | | | | | | |            $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 224.92/38.53  | | | | | | | | | | | | | | | | | | |            $i(all_52_15)
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | ALPHA: (16229) implies:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | |   (16230)  op(e2, e2) = all_52_11
% 224.92/38.53  | | | | | | | | | | | | | | | | | | |   (16231)  op(all_52_11, all_52_11) = e2
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (16045), (16189), (16230), (16231),
% 224.92/38.53  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.92/38.53  | | | | | | | | | | | | | | | | | | |            #1843.
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.53  | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | |   (16232)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 224.92/38.53  | | | | | | | | | | | | | | | | | |              & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 224.92/38.53  | | | | | | | | | | | | | | | | | |              & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 224.92/38.53  | | | | | | | | | | | | | | | | | |                all_52_21) = e1 & op(all_52_23, all_52_23) =
% 224.92/38.53  | | | | | | | | | | | | | | | | | |              e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 224.92/38.53  | | | | | | | | | | | | | | | | | |              all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 224.92/38.53  | | | | | | | | | | | | | | | | | |              = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 224.92/38.53  | | | | | | | | | | | | | | | | | |              $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 224.92/38.53  | | | | | | | | | | | | | | | | | |              & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 224.92/38.53  | | | | | | | | | | | | | | | | | |              e0 & op(all_52_25, all_52_25) = e3 &
% 224.92/38.53  | | | | | | | | | | | | | | | | | |              op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 224.92/38.53  | | | | | | | | | | | | | | | | | |                all_52_29) = e1 & op(all_52_31, all_52_31) =
% 224.92/38.53  | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 224.92/38.53  | | | | | | | | | | | | | | | | | |              all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 224.92/38.53  | | | | | | | | | | | | | | | | | |              = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 224.92/38.53  | | | | | | | | | | | | | | | | | |              $i(all_52_29) & $i(all_52_31))
% 224.92/38.53  | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | BETA: splitting (16232) gives:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | |   (16233)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 224.92/38.53  | | | | | | | | | | | | | | | | | | |            all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 224.92/38.53  | | | | | | | | | | | | | | | | | | |            op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 224.92/38.53  | | | | | | | | | | | | | | | | | | |              all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 224.92/38.53  | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 224.92/38.53  | | | | | | | | | | | | | | | | | | |            & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 224.92/38.53  | | | | | | | | | | | | | | | | | | |            & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 224.92/38.53  | | | | | | | | | | | | | | | | | | |            $i(all_52_23)
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (14935), (16189), (16233), (function-axioms)
% 224.92/38.53  | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #46.
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | |   (16234)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 224.92/38.53  | | | | | | | | | | | | | | | | | | |            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 224.92/38.53  | | | | | | | | | | | | | | | | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 224.92/38.53  | | | | | | | | | | | | | | | | | | |              all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 224.92/38.53  | | | | | | | | | | | | | | | | | | |            & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 224.92/38.53  | | | | | | | | | | | | | | | | | | |            & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 224.92/38.53  | | | | | | | | | | | | | | | | | | |            & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 224.92/38.53  | | | | | | | | | | | | | | | | | | |            $i(all_52_31)
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (14935), (16045), (16234), (function-axioms)
% 224.92/38.53  | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #50.
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.53  | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | End of split
% 224.92/38.53  | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | End of split
% 224.92/38.53  | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | Case 2:
% 224.92/38.53  | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | |   (16235)  all_57_2 = e3 & op(e2, e3) = e3
% 224.92/38.53  | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | REF_CLOSE: (168), (16052), (16235), (function-axioms) are
% 224.92/38.53  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2299.
% 224.92/38.53  | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | End of split
% 224.92/38.53  | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | Case 2:
% 224.92/38.53  | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | |   (16236)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 224.92/38.53  | | | | | | | | | | | | | | |              e3 & op(e0, e3) = e3)
% 224.92/38.53  | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | BETA: splitting (16236) gives:
% 224.92/38.53  | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | Case 1:
% 224.92/38.53  | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | |   (16237)  all_57_6 = e3 & op(e1, e3) = e3
% 224.92/38.53  | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | ALPHA: (16237) implies:
% 224.92/38.53  | | | | | | | | | | | | | | | |   (16238)  all_57_6 = e3
% 224.92/38.53  | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (169), (171), (230),
% 224.92/38.53  | | | | | | | | | | | | | | | |            (231), (232), (233), (234), (235), (237), (16054),
% 224.92/38.53  | | | | | | | | | | | | | | | |            (16056), (16057), (16238), (function-axioms) are
% 224.92/38.53  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #268.
% 224.92/38.53  | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | Case 2:
% 224.92/38.53  | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | |   (16239)  all_57_12 = e3 & op(e0, e3) = e3
% 224.92/38.53  | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | ALPHA: (16239) implies:
% 224.92/38.53  | | | | | | | | | | | | | | | |   (16240)  op(e0, e3) = e3
% 224.92/38.53  | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | REF_CLOSE: (160), (16053), (16240), (function-axioms) are
% 224.92/38.53  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #132.
% 224.92/38.53  | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | End of split
% 224.92/38.53  | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | End of split
% 224.92/38.53  | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | Case 2:
% 224.92/38.53  | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | |   (16241)  all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 224.92/38.53  | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | REF_CLOSE: (277), (14938), (16047), (16049), (16241) are
% 224.92/38.53  | | | | | | | | | | | | | |            inconsistent by sub-proof #1953.
% 224.92/38.53  | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | End of split
% 224.92/38.53  | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | Case 2:
% 224.92/38.53  | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | |   (16242)  all_20_2 = e2
% 224.92/38.53  | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | COMBINE_EQS: (299), (16242) imply:
% 224.92/38.53  | | | | | | | | | | | | |   (16243)  all_10_2 = e2
% 224.92/38.53  | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | SIMP: (16243) implies:
% 224.92/38.53  | | | | | | | | | | | | |   (16244)  all_10_2 = e2
% 224.92/38.53  | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | REDUCE: (338), (16244) imply:
% 224.92/38.53  | | | | | | | | | | | | |   (16245)   ~ (all_53_1 = e2)
% 224.92/38.53  | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | REDUCE: (45), (16244) imply:
% 224.92/38.53  | | | | | | | | | | | | |   (16246)  op(e3, e3) = e2
% 224.92/38.53  | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | BETA: splitting (228) gives:
% 224.92/38.53  | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | Case 1:
% 224.92/38.53  | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | |   (16247)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 224.92/38.53  | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 224.92/38.53  | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (237),
% 224.92/38.53  | | | | | | | | | | | | | |            (16045), (16246), (16247), (function-axioms) are
% 224.92/38.53  | | | | | | | | | | | | | |            inconsistent by sub-proof #1591.
% 224.92/38.53  | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | Case 2:
% 224.92/38.53  | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | |   (16248)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 224.92/38.53  | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 224.92/38.53  | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | BETA: splitting (16248) gives:
% 224.92/38.53  | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | Case 1:
% 224.92/38.53  | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | |   (16249)  all_57_7 = e2 & op(e1, e2) = e2
% 224.92/38.53  | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | ALPHA: (16249) implies:
% 224.92/38.53  | | | | | | | | | | | | | | |   (16250)  all_57_7 = e2
% 224.92/38.53  | | | | | | | | | | | | | | |   (16251)  op(e1, e2) = e2
% 224.92/38.53  | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 224.92/38.53  | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | Case 1:
% 224.92/38.53  | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | |   (16252)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 224.92/38.53  | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 224.92/38.53  | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | BETA: splitting (16252) gives:
% 224.92/38.53  | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.53  | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | |   (16253)  all_57_2 = e2 & op(e2, e3) = e2
% 224.92/38.53  | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (16245), (16253), (function-axioms) are
% 224.92/38.53  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2504.
% 224.92/38.53  | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.53  | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | |   (16254)  all_57_3 = e2 & op(e2, e2) = e2
% 224.92/38.53  | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | ALPHA: (16254) implies:
% 224.92/38.53  | | | | | | | | | | | | | | | | |   (16255)  op(e2, e2) = e2
% 224.92/38.53  | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (16045), (16255), (function-axioms) are
% 224.92/38.53  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2306.
% 224.92/38.53  | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | End of split
% 224.92/38.53  | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | Case 2:
% 224.92/38.53  | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | |   (16256)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 224.92/38.53  | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 224.92/38.53  | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | BETA: splitting (16256) gives:
% 224.92/38.53  | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.53  | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | |   (16257)  all_57_5 = e2 & op(e2, e1) = e2
% 224.92/38.53  | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | ALPHA: (16257) implies:
% 224.92/38.53  | | | | | | | | | | | | | | | | |   (16258)  op(e2, e1) = e2
% 224.92/38.53  | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 224.92/38.53  | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | |   (16259)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 224.92/38.53  | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2)
% 224.92/38.53  | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | BETA: splitting (16259) gives:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | |   (16260)  all_57_0 = e2 & op(e3, e3) = e2
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_6, e2,
% 224.92/38.53  | | | | | | | | | | | | | | | | | | |              e2, e1, simplifying with (163), (16251) gives:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | |   (16261)  all_53_6 = e2
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_9, e2,
% 224.92/38.53  | | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (166), (16258) gives:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | |   (16262)  all_53_9 = e2
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | REDUCE: (364), (16262) imply:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | |   (16263)   ~ (all_6_2 = e2)
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | SIMP: (16263) implies:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | |   (16264)   ~ (all_6_2 = e2)
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (39), (107), (14935), (16045),
% 224.92/38.53  | | | | | | | | | | | | | | | | | | |            (16246), (16251), (16264), (function-axioms) are
% 224.92/38.53  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #44.
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | |   (16265)  all_57_2 = e2 & op(e2, e3) = e2
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (16245), (16265), (function-axioms) are
% 224.92/38.53  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2504.
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.53  | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | |   (16266)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 224.92/38.53  | | | | | | | | | | | | | | | | | |              e2 & op(e0, e3) = e2)
% 224.92/38.53  | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | BETA: splitting (16266) gives:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | |   (16267)  all_57_6 = e2 & op(e1, e3) = e2
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | ALPHA: (16267) implies:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | |   (16268)  all_57_6 = e2
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | |   (16269)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e1)
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (168), (16034), (16246), (16269),
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | |            #1598.
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | |   (16270)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e3) = e1)
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | BETA: splitting (16270) gives:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | |   (16271)  all_57_6 = e1 & op(e1, e3) = e1
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (16268), (16271) are inconsistent by
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | |            sub-proof #2389.
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | |   (16272)  all_57_12 = e1 & op(e0, e3) = e1
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | ALPHA: (16272) implies:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | |   (16273)  all_57_12 = e1
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | |   (16274)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e3)
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16274) gives:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | |   (16275)  all_57_6 = e3 & op(e1, e3) = e3
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16275) implies:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | |   (16276)  all_57_6 = e3
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (16268), (16276) are inconsistent by
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2463.
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | |   (16277)  all_57_7 = e3 & op(e1, e2) = e3
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16277) implies:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | |   (16278)  all_57_7 = e3
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (16250), (16278) are inconsistent by
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2102.
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | |   (16279)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e1, e0) = e3)
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16279) gives:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | |   (16280)  all_57_8 = e3 & op(e1, e1) = e3
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16280) implies:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | |   (16281)  op(e1, e1) = e3
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (14936), (16281), (function-axioms) are
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2468.
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | |   (16282)  all_57_11 = e3 & op(e1, e0) = e3
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16282) implies:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | |   (16283)  all_57_11 = e3
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | |   (16284)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16284) gives:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | | |   (16285)  all_57_9 = e1 & op(e3, e0) = e1
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16285) implies:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | | |   (16286)  all_57_9 = e1
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | | |   (16287)  op(e3, e0) = e1
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | | | |   (16288)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e1)
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16288) gives:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16289)  all_57_6 = e1 & op(e1, e3) = e1
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16289) implies:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16290)  all_57_6 = e1
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (16268), (16290) are inconsistent by
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2233.
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16291)  all_57_7 = e1 & op(e1, e2) = e1
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (16036), (16291), (function-axioms) are
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2265.
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | |   (16292)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e0) = e1)
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16292) gives:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16293)  all_57_8 = e1 & op(e1, e1) = e1
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16293) implies:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16294)  op(e1, e1) = e1
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16295)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e3)
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16295) gives:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16296)  all_57_0 = e3 & op(e3, e3) = e3
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16296) implies:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16297)  op(e3, e3) = e3
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (107), (111), (113), (114), (118),
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (146), (161), (166), (168), (169), (194), (198),
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (207), (225), (248), (258), (14927), (14928),
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14929), (14934), (14935), (16045), (16286),
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16287), (16294), (16297), (function-axioms) are
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #49.
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16298)  all_57_2 = e3 & op(e2, e3) = e3
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (230), (232), (16246),
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16268), (16298), (function-axioms) are
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #154.
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16299)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e3) = e3)
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (16268), (16273), (16299) are
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1213.
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16300)  all_57_11 = e1 & op(e1, e0) = e1
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16300) implies:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16301)  all_57_11 = e1
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (16283), (16301) are inconsistent by
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2218.
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | |   (16302)  all_57_10 = e1 & op(e2, e0) = e1
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (16039), (16302), (function-axioms) are
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2084.
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | |   (16303)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16303) gives:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | |   (16304)  all_57_11 = e1 & op(e1, e0) = e1
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (16283), (16304) are inconsistent by
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2143.
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | |   (16305)  all_57_15 = e1 & op(e0, e0) = e1
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16305) implies:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | |   (16306)  op(e0, e0) = e1
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (14935), (16306), (function-axioms) are
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2177.
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | |   (16307)  all_57_12 = e2 & op(e0, e3) = e2
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | ALPHA: (16307) implies:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | |   (16308)  op(e0, e3) = e2
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (14924), (16308), (function-axioms) are
% 224.92/38.54  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1980.
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.54  | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | End of split
% 224.92/38.54  | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.54  | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | |   (16309)  all_57_10 = e2 & op(e2, e0) = e2
% 224.92/38.54  | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (14928), (16309), (function-axioms) are
% 224.92/38.54  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2432.
% 224.92/38.54  | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | End of split
% 224.92/38.54  | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | End of split
% 224.92/38.54  | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | Case 2:
% 224.92/38.54  | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | |   (16310)  all_57_13 = e2 & op(e0, e2) = e2
% 224.92/38.54  | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | ALPHA: (16310) implies:
% 224.92/38.54  | | | | | | | | | | | | | | |   (16311)  op(e0, e2) = e2
% 224.92/38.54  | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | REF_CLOSE: (159), (14925), (16311), (function-axioms) are
% 224.92/38.54  | | | | | | | | | | | | | | |            inconsistent by sub-proof #2335.
% 224.92/38.54  | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | End of split
% 224.92/38.54  | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | End of split
% 224.92/38.54  | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | End of split
% 224.92/38.54  | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | Case 2:
% 224.92/38.54  | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | |   (16312)  all_18_2 = e0
% 224.92/38.54  | | | | | | | | | | | |   (16313)  ( ~ (all_18_0 = e1) & op(all_18_1, e3) = all_18_0
% 224.92/38.54  | | | | | | | | | | | |              & op(e3, e0) = all_18_1 & $i(all_18_0) &
% 224.92/38.54  | | | | | | | | | | | |              $i(all_18_1)) | ( ~ (all_18_1 = e2) & op(e3, e0)
% 224.92/38.54  | | | | | | | | | | | |              = all_18_1 & $i(all_18_1))
% 224.92/38.54  | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | COMBINE_EQS: (327), (16312) imply:
% 224.92/38.54  | | | | | | | | | | | |   (16314)  all_10_2 = e0
% 224.92/38.54  | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | SIMP: (16314) implies:
% 224.92/38.54  | | | | | | | | | | | |   (16315)  all_10_2 = e0
% 224.92/38.54  | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | COMBINE_EQS: (279), (16315) imply:
% 224.92/38.54  | | | | | | | | | | | |   (16316)  all_48_2 = e0
% 224.92/38.54  | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | REDUCE: (338), (16315) imply:
% 224.92/38.54  | | | | | | | | | | | |   (16317)   ~ (all_53_1 = e0)
% 224.92/38.54  | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | REDUCE: (340), (16315) imply:
% 224.92/38.54  | | | | | | | | | | | |   (16318)   ~ (all_53_2 = e0)
% 224.92/38.54  | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | REDUCE: (342), (16315) imply:
% 224.92/38.54  | | | | | | | | | | | |   (16319)   ~ (all_53_3 = e0)
% 224.92/38.54  | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | REDUCE: (344), (16315) imply:
% 224.92/38.54  | | | | | | | | | | | |   (16320)   ~ (all_53_4 = e0)
% 224.92/38.54  | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | REDUCE: (346), (16315) imply:
% 224.92/38.54  | | | | | | | | | | | |   (16321)   ~ (all_53_8 = e0)
% 224.92/38.54  | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | REDUCE: (348), (16315) imply:
% 224.92/38.54  | | | | | | | | | | | |   (16322)   ~ (all_53_12 = e0)
% 224.92/38.54  | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | REDUCE: (14938), (16315) imply:
% 224.92/38.54  | | | | | | | | | | | |   (16323)   ~ (e1 = e0)
% 224.92/38.54  | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | BETA: splitting (231) gives:
% 224.92/38.54  | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | Case 1:
% 224.92/38.54  | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | |   (16324)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 224.92/38.54  | | | | | | | | | | | | |              & op(e3, e2) = e0)
% 224.92/38.54  | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | BETA: splitting (16324) gives:
% 224.92/38.54  | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | Case 1:
% 224.92/38.54  | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | |   (16325)  all_57_0 = e0 & op(e3, e3) = e0
% 224.92/38.54  | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | ALPHA: (16325) implies:
% 224.92/38.54  | | | | | | | | | | | | | |   (16326)  all_57_0 = e0
% 224.92/38.54  | | | | | | | | | | | | | |   (16327)  op(e3, e3) = e0
% 224.92/38.54  | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 224.92/38.54  | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | Case 1:
% 224.92/38.54  | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | |   (16328)   ~ (all_24_2 = e0)
% 224.92/38.54  | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | REDUCE: (315), (16328) imply:
% 224.92/38.54  | | | | | | | | | | | | | | |   (16329)   ~ (all_6_2 = e0)
% 224.92/38.54  | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | BETA: splitting (88) gives:
% 224.92/38.54  | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | Case 1:
% 224.92/38.54  | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | |   (16330)   ~ (all_38_2 = e2)
% 224.92/38.54  | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | REDUCE: (249), (16330) imply:
% 224.92/38.54  | | | | | | | | | | | | | | | |   (16331)   ~ (all_6_2 = e2)
% 224.92/38.54  | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 224.92/38.54  | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.54  | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | |   (16332)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 224.92/38.54  | | | | | | | | | | | | | | | | |              all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 224.92/38.54  | | | | | | | | | | | | | | | | |              op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 224.92/38.54  | | | | | | | | | | | | | | | | |                all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 224.92/38.54  | | | | | | | | | | | | | | | | |              op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 224.92/38.54  | | | | | | | | | | | | | | | | |              op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 224.92/38.54  | | | | | | | | | | | | | | | | |              $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 224.92/38.54  | | | | | | | | | | | | | | | | |              $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 224.92/38.54  | | | | | | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 224.92/38.54  | | | | | | | | | | | | | | | | |                all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 224.92/38.54  | | | | | | | | | | | | | | | | |              & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 224.92/38.54  | | | | | | | | | | | | | | | | |                all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 224.92/38.54  | | | | | | | | | | | | | | | | |              op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 224.92/38.54  | | | | | | | | | | | | | | | | |              & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 224.92/38.54  | | | | | | | | | | | | | | | | |              $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 224.92/38.54  | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | BETA: splitting (16332) gives:
% 224.92/38.54  | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | |   (16333)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 224.92/38.54  | | | | | | | | | | | | | | | | | |            all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 224.92/38.54  | | | | | | | | | | | | | | | | | |            op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 224.92/38.54  | | | | | | | | | | | | | | | | | |              all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 224.92/38.54  | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 224.92/38.54  | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 224.92/38.54  | | | | | | | | | | | | | | | | | |            $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 224.92/38.54  | | | | | | | | | | | | | | | | | |            $i(all_52_7)
% 224.92/38.54  | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | ALPHA: (16333) implies:
% 224.92/38.54  | | | | | | | | | | | | | | | | | |   (16334)  op(e3, e3) = all_52_1
% 224.92/38.54  | | | | | | | | | | | | | | | | | |   (16335)  op(all_52_1, all_52_1) = e3
% 224.92/38.54  | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (14935), (16327), (16334), (16335),
% 224.92/38.54  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.92/38.54  | | | | | | | | | | | | | | | | | |            #53.
% 224.92/38.54  | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | |   (16336)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 224.92/38.54  | | | | | | | | | | | | | | | | | |            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 224.92/38.54  | | | | | | | | | | | | | | | | | |            op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 224.92/38.54  | | | | | | | | | | | | | | | | | |              all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 224.92/38.54  | | | | | | | | | | | | | | | | | |            & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 224.92/38.54  | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 224.92/38.54  | | | | | | | | | | | | | | | | | |            $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 224.92/38.54  | | | | | | | | | | | | | | | | | |            $i(all_52_15)
% 224.92/38.54  | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (16045), (16331), (16336), (function-axioms)
% 224.92/38.54  | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #45.
% 224.92/38.54  | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | End of split
% 224.92/38.54  | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.54  | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | |   (16337)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 224.92/38.54  | | | | | | | | | | | | | | | | |              & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 224.92/38.54  | | | | | | | | | | | | | | | | |              & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 224.92/38.54  | | | | | | | | | | | | | | | | |                all_52_21) = e1 & op(all_52_23, all_52_23) =
% 224.92/38.54  | | | | | | | | | | | | | | | | |              e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 224.92/38.54  | | | | | | | | | | | | | | | | |              all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 224.92/38.54  | | | | | | | | | | | | | | | | |              = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 224.92/38.54  | | | | | | | | | | | | | | | | |              $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 224.92/38.54  | | | | | | | | | | | | | | | | |              & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 224.92/38.54  | | | | | | | | | | | | | | | | |              e0 & op(all_52_25, all_52_25) = e3 &
% 224.92/38.54  | | | | | | | | | | | | | | | | |              op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 224.92/38.54  | | | | | | | | | | | | | | | | |                all_52_29) = e1 & op(all_52_31, all_52_31) =
% 224.92/38.54  | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 224.92/38.54  | | | | | | | | | | | | | | | | |              all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 224.92/38.54  | | | | | | | | | | | | | | | | |              = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 224.92/38.54  | | | | | | | | | | | | | | | | |              $i(all_52_29) & $i(all_52_31))
% 224.92/38.54  | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | BETA: splitting (16337) gives:
% 224.92/38.54  | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | |   (16338)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 224.92/38.54  | | | | | | | | | | | | | | | | | |            all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 224.92/38.54  | | | | | | | | | | | | | | | | | |            op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 224.92/38.54  | | | | | | | | | | | | | | | | | |              all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 224.92/38.54  | | | | | | | | | | | | | | | | | |            & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 224.92/38.54  | | | | | | | | | | | | | | | | | |            & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 224.92/38.54  | | | | | | | | | | | | | | | | | |            & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 224.92/38.54  | | | | | | | | | | | | | | | | | |            $i(all_52_23)
% 224.92/38.54  | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | ALPHA: (16338) implies:
% 224.92/38.54  | | | | | | | | | | | | | | | | | |   (16339)  op(e1, e3) = all_52_17
% 224.92/38.54  | | | | | | | | | | | | | | | | | |   (16340)  op(all_52_17, all_52_17) = e3
% 224.92/38.54  | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | |   (16341)  all_55_10 = e3
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (14936), (16341) are inconsistent by
% 224.92/38.54  | | | | | | | | | | | | | | | | | | |            sub-proof #2500.
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | |   (16342)   ~ (all_55_10 = e3)
% 224.92/38.54  | | | | | | | | | | | | | | | | | | |   (16343)  all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | BETA: splitting (16343) gives:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | |   (16344)  all_55_10 = e2
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (16331), (16344) are inconsistent by
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | |            sub-proof #2499.
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | |   (16345)   ~ (all_55_10 = e2)
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | |   (16346)  all_55_10 = e1 | all_55_10 = e0
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | BETA: splitting (16346) gives:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | |   (16347)  all_55_10 = e1
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (336), (16347) imply:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | |   (16348)  all_6_2 = e1
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | SIMP: (16348) implies:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | |   (16349)  all_6_2 = e1
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | REDUCE: (350), (16349) imply:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | |   (16350)   ~ (all_53_2 = e1)
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | REDUCE: (16331), (16349) imply:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | |   (16351)   ~ (e2 = e1)
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (16349) imply:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | |   (16352)  op(e1, e1) = e1
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | |   (16353)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e1)
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (226), (228), (229),
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | |            (16045), (16326), (16353), (function-axioms) are
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1551.
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | |   (16354)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e1)
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16354) gives:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | |   (16355)  all_57_4 = e1 & op(e3, e1) = e1
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16355) implies:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | |   (16356)  all_57_4 = e1
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (218), (220),
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | |            (221), (14936), (16329), (16352), (16356),
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | |            #2407.
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | |   (16357)  all_57_9 = e1 & op(e3, e0) = e1
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16357) implies:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | |   (16358)  op(e3, e0) = e1
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_2,
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | |              all_52_17, e3, e1, simplifying with (164), (16339)
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | |   (16359)  all_53_2 = all_52_17
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_12,
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | |              e1, e0, e3, simplifying with (169), (16358) gives:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | |   (16360)  all_53_12 = e1
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (103) gives:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | |   (16361)   ~ (all_48_2 = e0)
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (16316), (16361) imply:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | |   (16362)  $false
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (16362) is inconsistent.
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | |   (16363)  ( ~ (all_48_0 = e2) & op(all_48_1, e3) = all_48_0
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = all_48_1 & $i(all_48_0) &
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_48_1)) | ( ~ (all_48_1 = e1) & op(e3, e0)
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | |              = all_48_1 & $i(all_48_1))
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (197), (257), (16313), (16318), (16327),
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | |            (16339), (16340), (16350), (16358), (16363),
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | |            #999.
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | |   (16364)  all_55_10 = e0
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (16329), (16364) are inconsistent by
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | |            sub-proof #2118.
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.54  | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | |   (16365)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 224.92/38.54  | | | | | | | | | | | | | | | | | |            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 224.92/38.54  | | | | | | | | | | | | | | | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 224.92/38.54  | | | | | | | | | | | | | | | | | |              all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 224.92/38.54  | | | | | | | | | | | | | | | | | |            & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 224.92/38.54  | | | | | | | | | | | | | | | | | |            & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 224.92/38.54  | | | | | | | | | | | | | | | | | |            & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 224.92/38.54  | | | | | | | | | | | | | | | | | |            $i(all_52_31)
% 224.92/38.54  | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | ALPHA: (16365) implies:
% 224.92/38.54  | | | | | | | | | | | | | | | | | |   (16366)  op(e0, e0) = all_52_31
% 224.92/38.54  | | | | | | | | | | | | | | | | | |   (16367)  op(all_52_31, all_52_31) = e0
% 224.92/38.54  | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | |   (16368)  all_55_10 = e3
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (14936), (16368) are inconsistent by
% 224.92/38.54  | | | | | | | | | | | | | | | | | | |            sub-proof #2500.
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | |   (16369)   ~ (all_55_10 = e3)
% 224.92/38.54  | | | | | | | | | | | | | | | | | | |   (16370)  all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | BETA: splitting (16370) gives:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | |   (16371)  all_55_10 = e2
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (16331), (16371) are inconsistent by
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | |            sub-proof #2499.
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | |   (16372)   ~ (all_55_10 = e2)
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | |   (16373)  all_55_10 = e1 | all_55_10 = e0
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | BETA: splitting (16373) gives:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | |   (16374)  all_55_10 = e1
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (336), (16374) imply:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | |   (16375)  all_6_2 = e1
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | SIMP: (16375) implies:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | |   (16376)  all_6_2 = e1
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | REDUCE: (366), (16376) imply:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | |   (16377)   ~ (all_53_11 = e1)
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | REDUCE: (16331), (16376) imply:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | |   (16378)   ~ (e2 = e1)
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (16376) imply:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | |   (16379)  op(e1, e1) = e1
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | |   (16380)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e1)
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (226), (228), (229),
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | |            (16045), (16326), (16380), (function-axioms) are
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1551.
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | |   (16381)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e1)
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16381) gives:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | |   (16382)  all_57_4 = e1 & op(e3, e1) = e1
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16382) implies:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | |   (16383)  all_57_4 = e1
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (218), (220),
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | |            (221), (14936), (16329), (16379), (16383),
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | |            #2407.
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | |   (16384)  all_57_9 = e1 & op(e3, e0) = e1
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | |   (16385)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e1)
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16385) gives:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | |   (16386)  all_57_4 = e1 & op(e3, e1) = e1
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16386) implies:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | |   (16387)  all_57_4 = e1
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (218), (220),
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | |            (221), (14936), (16329), (16379), (16387),
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | |            #2407.
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | |   (16388)  all_57_5 = e1 & op(e2, e1) = e1
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (16038), (16388), (function-axioms) are
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2305.
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | |   (16389)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e1) = e1)
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16389) gives:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16384) implies:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | |   (16390)  op(e3, e0) = e1
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_31, e0, e0, simplifying with (14935),
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | |              (16366) gives:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | |   (16391)  all_52_31 = e2
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_12,
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e0, e3, simplifying with (169), (16390) gives:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | |   (16392)  all_53_12 = e1
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (16367), (16391) imply:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | |   (16393)  op(e2, e2) = e0
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (16045), (16393), (function-axioms) are
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2352.
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | |   (16394)  all_57_14 = e1 & op(e0, e1) = e1
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (16377), (16394), (function-axioms) are
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #225.
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | |   (16395)  all_55_10 = e0
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (16329), (16395) are inconsistent by
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | |            sub-proof #2118.
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.54  | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | End of split
% 224.92/38.54  | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | End of split
% 224.92/38.54  | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | Case 2:
% 224.92/38.54  | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | |   (16396)  all_38_2 = e2
% 224.92/38.54  | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (16396) imply:
% 224.92/38.54  | | | | | | | | | | | | | | | |   (16397)  all_6_2 = e2
% 224.92/38.54  | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | REDUCE: (361), (16397) imply:
% 224.92/38.54  | | | | | | | | | | | | | | | |   (16398)   ~ (all_53_6 = e2)
% 224.92/38.54  | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | REDUCE: (364), (16397) imply:
% 224.92/38.54  | | | | | | | | | | | | | | | |   (16399)   ~ (all_53_9 = e2)
% 224.92/38.54  | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | REDUCE: (14936), (16397) imply:
% 224.92/38.54  | | | | | | | | | | | | | | | |   (16400)   ~ (e3 = e2)
% 224.92/38.54  | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | REDUCE: (39), (16397) imply:
% 224.92/38.54  | | | | | | | | | | | | | | | |   (16401)  op(e1, e1) = e2
% 224.92/38.54  | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 224.92/38.54  | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.54  | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | |   (16402)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 224.92/38.54  | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 224.92/38.54  | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | BETA: splitting (16402) gives:
% 224.92/38.54  | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | |   (16403)  all_57_2 = e2 & op(e2, e3) = e2
% 224.92/38.54  | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | ALPHA: (16403) implies:
% 224.92/38.54  | | | | | | | | | | | | | | | | | |   (16404)  all_57_2 = e2
% 224.92/38.54  | | | | | | | | | | | | | | | | | |   (16405)  op(e2, e3) = e2
% 224.92/38.54  | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | |   (16406)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 224.92/38.54  | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e2)
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | BETA: splitting (16406) gives:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | |   (16407)  all_57_0 = e2 & op(e3, e3) = e2
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | ALPHA: (16407) implies:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | |   (16408)  op(e3, e3) = e2
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | |   (16409)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e0)
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (16404), (16408), (16409), (function-axioms)
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1577.
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | |   (16410)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = e0)
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16410) gives:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.54  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | |   (16411)  all_57_6 = e0 & op(e1, e3) = e0
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16411) implies:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | |   (16412)  all_57_6 = e0
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | |   (16413)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e1)
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (168), (16034), (16408), (16413),
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | |            #1598.
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | |   (16414)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e3) = e1)
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16414) gives:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | | |   (16415)  all_57_6 = e1 & op(e1, e3) = e1
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16415) implies:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | | |   (16416)  all_57_6 = e1
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (16412), (16416) imply:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | | |   (16417)  e1 = e0
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (16417) implies:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | | |   (16418)  e1 = e0
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (16044), (16418) imply:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | | |   (16419)  all_57_3 = e0
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | | |            (230), (232), (236), (16404), (16408), (16412),
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | | |            (16419), (function-axioms) are inconsistent by
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1628.
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | | |   (16420)  all_57_12 = e1 & op(e0, e3) = e1
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16420) implies:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | | |   (16421)  all_57_12 = e1
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (236), (16404), (16408), (16412),
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | | |            (16421), (function-axioms) are inconsistent by
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1630.
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | |   (16422)  all_57_12 = e0 & op(e0, e3) = e0
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16422) implies:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | |   (16423)  op(e0, e3) = e0
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (16319), (16423), (function-axioms) are
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2366.
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | |   (16424)  all_57_1 = e2 & op(e3, e2) = e2
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | ALPHA: (16424) implies:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | |   (16425)  op(e3, e2) = e2
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_1, e2,
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (168), (16405) gives:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | |   (16426)  all_53_1 = e2
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_4, e2,
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (171), (16425) gives:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | |   (16427)  all_53_4 = e2
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | REDUCE: (150), (16426) imply:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | |   (16428)   ~ (all_53_2 = e2)
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | SIMP: (16428) implies:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | |   (16429)   ~ (all_53_2 = e2)
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (16426) imply:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | |   (16430)   ~ (all_53_3 = e2)
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | |   (16431)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | |              all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | |              op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | |                all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | |              $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | |              $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | |                all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | |              & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | |                all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | |              & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | |              $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16431) gives:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | |   (16432)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | |            all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | |            op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | |              all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_7)
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16432) implies:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | |   (16433)  op(e3, e3) = all_52_1
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | |   (16434)  op(all_52_1, all_52_1) = e3
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (14935), (16327), (16433), (16434),
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | |            #53.
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | |   (16435)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | |            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | |            op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | |              all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_15)
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (16045), (16405), (16435), (function-axioms)
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #48.
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | |   (16436)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | |              & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | |              & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | |                all_52_21) = e1 & op(all_52_23, all_52_23) =
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | |              all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | |              = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | |              $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | |              & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | |              e0 & op(all_52_25, all_52_25) = e3 &
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | |              op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | |                all_52_29) = e1 & op(all_52_31, all_52_31) =
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | |              all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | |              = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | |              $i(all_52_29) & $i(all_52_31))
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16436) gives:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | |   (16437)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | |            all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | |            op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | |              all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | |            & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_23)
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16437) implies:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | |   (16438)  op(e1, e0) = all_52_23
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | |   (16439)  op(e1, e1) = all_52_21
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | |   (16440)  op(e1, e3) = all_52_17
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | |   (16441)  op(all_52_23, all_52_23) = e0
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | |   (16442)  op(all_52_21, all_52_21) = e1
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | |   (16443)  op(all_52_17, all_52_17) = e3
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_14,
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | |              all_52_23, e0, e1, simplifying with (161), (16438)
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | |              gives:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | |   (16444)  all_53_14 = all_52_23
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | |              all_52_21, e1, e1, simplifying with (16401),
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | |              (16439) gives:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | |   (16445)  all_52_21 = e2
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_2,
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | |              all_52_17, e3, e1, simplifying with (164), (16440)
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | |              gives:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | |   (16446)  all_53_2 = all_52_17
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (16446) imply:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | |   (16447)  all_55_8 = all_52_17
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (16446) imply:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | |   (16448)   ~ (all_53_3 = all_52_17)
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | SIMP: (16448) implies:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | |   (16449)   ~ (all_53_3 = all_52_17)
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (16429), (16446) imply:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | |   (16450)   ~ (all_52_17 = e2)
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (16318), (16446) imply:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | |   (16451)   ~ (all_52_17 = e0)
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | |   (16452)  all_55_13 = e3
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (16452) imply:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | |   (16453)  all_53_7 = e3
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (16453) implies:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | |   (16454)  all_53_7 = e3
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (141), (16454) imply:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | |   (16455)   ~ (all_53_3 = e3)
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (193), (197), (247), (14924), (16319), (16327),
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | |            (16443), (16447), (16449), (16450), (16451),
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | |            (16455), (function-axioms) are inconsistent by
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #43.
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | |   (16456)   ~ (all_55_13 = e3)
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (246), (16456) imply:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | |   (16457)   ~ (all_53_7 = e3)
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (9), (39), (159), (164), (214),
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | |            (229), (14935), (16045), (16318), (16329),
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | |            (16425), (16438), (16441), (16457),
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | |            #42.
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | |   (16458)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | |            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | |              all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | |            & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | |            & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | |            & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_31)
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (14935), (16045), (16458), (function-axioms)
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #50.
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | |   (16459)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 224.92/38.55  | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e2)
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | BETA: splitting (16459) gives:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | |   (16460)  all_57_4 = e2 & op(e3, e1) = e2
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | ALPHA: (16460) implies:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | |   (16461)  all_57_4 = e2
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (159), (163), (226),
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | |            (228), (229), (231), (233), (237), (14925),
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | |            (16045), (16326), (16398), (16461),
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | |            #39.
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | |   (16462)  all_57_9 = e2 & op(e3, e0) = e2
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | ALPHA: (16462) implies:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | |   (16463)  op(e3, e0) = e2
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (14927), (16463), (function-axioms) are
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2331.
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.55  | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | |   (16464)  all_57_3 = e2 & op(e2, e2) = e2
% 224.92/38.55  | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | ALPHA: (16464) implies:
% 224.92/38.55  | | | | | | | | | | | | | | | | | |   (16465)  op(e2, e2) = e2
% 224.92/38.55  | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (16045), (16465), (function-axioms) are
% 224.92/38.55  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2306.
% 224.92/38.55  | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | End of split
% 224.92/38.55  | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.55  | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | |   (16466)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 224.92/38.55  | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 224.92/38.55  | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | BETA: splitting (16466) gives:
% 224.92/38.55  | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | |   (16467)  all_57_5 = e2 & op(e2, e1) = e2
% 224.92/38.55  | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (16399), (16467), (function-axioms) are
% 224.92/38.55  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1858.
% 224.92/38.55  | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | |   (16468)  all_57_10 = e2 & op(e2, e0) = e2
% 224.92/38.55  | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (14928), (16468), (function-axioms) are
% 224.92/38.55  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2432.
% 224.92/38.55  | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | End of split
% 224.92/38.55  | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | End of split
% 224.92/38.55  | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | End of split
% 224.92/38.55  | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | Case 2:
% 224.92/38.55  | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | |   (16469)  all_24_2 = e0
% 224.92/38.55  | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | COMBINE_EQS: (315), (16469) imply:
% 224.92/38.55  | | | | | | | | | | | | | | |   (16470)  all_6_2 = e0
% 224.92/38.55  | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | REDUCE: (361), (16470) imply:
% 224.92/38.55  | | | | | | | | | | | | | | |   (16471)   ~ (all_53_6 = e0)
% 224.92/38.55  | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | REDUCE: (364), (16470) imply:
% 224.92/38.55  | | | | | | | | | | | | | | |   (16472)   ~ (all_53_9 = e0)
% 224.92/38.55  | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | REDUCE: (368), (16470) imply:
% 224.92/38.55  | | | | | | | | | | | | | | |   (16473)   ~ (all_53_14 = e0)
% 224.92/38.55  | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | REDUCE: (39), (16470) imply:
% 224.92/38.55  | | | | | | | | | | | | | | |   (16474)  op(e1, e1) = e0
% 224.92/38.55  | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 224.92/38.55  | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | Case 1:
% 224.92/38.55  | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | |   (16475)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 224.92/38.55  | | | | | | | | | | | | | | | |              all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 224.92/38.55  | | | | | | | | | | | | | | | |              op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 224.92/38.55  | | | | | | | | | | | | | | | |                all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 224.92/38.55  | | | | | | | | | | | | | | | |              op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 224.92/38.55  | | | | | | | | | | | | | | | |              op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 224.92/38.55  | | | | | | | | | | | | | | | |              $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 224.92/38.55  | | | | | | | | | | | | | | | |              $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 224.92/38.55  | | | | | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 224.92/38.55  | | | | | | | | | | | | | | | |                all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 224.92/38.55  | | | | | | | | | | | | | | | |              & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 224.92/38.55  | | | | | | | | | | | | | | | |                all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 224.92/38.55  | | | | | | | | | | | | | | | |              op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 224.92/38.55  | | | | | | | | | | | | | | | |              & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 224.92/38.55  | | | | | | | | | | | | | | | |              $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 224.92/38.55  | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | BETA: splitting (16475) gives:
% 224.92/38.55  | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.55  | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | |   (16476)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 224.92/38.55  | | | | | | | | | | | | | | | | |            all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 224.92/38.55  | | | | | | | | | | | | | | | | |            op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 224.92/38.55  | | | | | | | | | | | | | | | | |              all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 224.92/38.55  | | | | | | | | | | | | | | | | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 224.92/38.55  | | | | | | | | | | | | | | | | |            op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 224.92/38.55  | | | | | | | | | | | | | | | | |            $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 224.92/38.55  | | | | | | | | | | | | | | | | |            $i(all_52_7)
% 224.92/38.55  | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | ALPHA: (16476) implies:
% 224.92/38.55  | | | | | | | | | | | | | | | | |   (16477)  op(e3, e3) = all_52_1
% 224.92/38.55  | | | | | | | | | | | | | | | | |   (16478)  op(all_52_1, all_52_1) = e3
% 224.92/38.55  | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (14935), (16327), (16477), (16478),
% 224.92/38.55  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.92/38.55  | | | | | | | | | | | | | | | | |            #53.
% 224.92/38.55  | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.55  | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | |   (16479)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 224.92/38.55  | | | | | | | | | | | | | | | | |            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 224.92/38.55  | | | | | | | | | | | | | | | | |            op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 224.92/38.55  | | | | | | | | | | | | | | | | |              all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 224.92/38.55  | | | | | | | | | | | | | | | | |            & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 224.92/38.55  | | | | | | | | | | | | | | | | |            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 224.92/38.55  | | | | | | | | | | | | | | | | |            $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 224.92/38.55  | | | | | | | | | | | | | | | | |            $i(all_52_15)
% 224.92/38.55  | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | ALPHA: (16479) implies:
% 224.92/38.55  | | | | | | | | | | | | | | | | |   (16480)  op(e2, e2) = all_52_11
% 224.92/38.55  | | | | | | | | | | | | | | | | |   (16481)  op(all_52_11, all_52_11) = e2
% 224.92/38.55  | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (16045), (16474), (16480), (16481),
% 224.92/38.55  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.92/38.55  | | | | | | | | | | | | | | | | |            #1843.
% 224.92/38.55  | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | End of split
% 224.92/38.55  | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | Case 2:
% 224.92/38.55  | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | |   (16482)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 224.92/38.55  | | | | | | | | | | | | | | | |              & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 224.92/38.55  | | | | | | | | | | | | | | | |              & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 224.92/38.55  | | | | | | | | | | | | | | | |                all_52_21) = e1 & op(all_52_23, all_52_23) =
% 224.92/38.55  | | | | | | | | | | | | | | | |              e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 224.92/38.55  | | | | | | | | | | | | | | | |              all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 224.92/38.55  | | | | | | | | | | | | | | | |              = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 224.92/38.55  | | | | | | | | | | | | | | | |              $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 224.92/38.55  | | | | | | | | | | | | | | | |              & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 224.92/38.55  | | | | | | | | | | | | | | | |              e0 & op(all_52_25, all_52_25) = e3 &
% 224.92/38.55  | | | | | | | | | | | | | | | |              op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 224.92/38.55  | | | | | | | | | | | | | | | |                all_52_29) = e1 & op(all_52_31, all_52_31) =
% 224.92/38.55  | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 224.92/38.55  | | | | | | | | | | | | | | | |              all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 224.92/38.55  | | | | | | | | | | | | | | | |              = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 224.92/38.55  | | | | | | | | | | | | | | | |              $i(all_52_29) & $i(all_52_31))
% 224.92/38.55  | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | BETA: splitting (16482) gives:
% 224.92/38.55  | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.55  | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | |   (16483)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 224.92/38.55  | | | | | | | | | | | | | | | | |            all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 224.92/38.55  | | | | | | | | | | | | | | | | |            op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 224.92/38.55  | | | | | | | | | | | | | | | | |              all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 224.92/38.55  | | | | | | | | | | | | | | | | |            & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 224.92/38.55  | | | | | | | | | | | | | | | | |            & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 224.92/38.55  | | | | | | | | | | | | | | | | |            & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 224.92/38.55  | | | | | | | | | | | | | | | | |            $i(all_52_23)
% 224.92/38.55  | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (161), (163), (164), (214), (14935), (16318),
% 224.92/38.55  | | | | | | | | | | | | | | | | |            (16471), (16473), (16483), (function-axioms) are
% 224.92/38.55  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #38.
% 224.92/38.55  | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.55  | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | |   (16484)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 224.92/38.55  | | | | | | | | | | | | | | | | |            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 224.92/38.55  | | | | | | | | | | | | | | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 224.92/38.55  | | | | | | | | | | | | | | | | |              all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 224.92/38.55  | | | | | | | | | | | | | | | | |            & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 224.92/38.55  | | | | | | | | | | | | | | | | |            & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 224.92/38.55  | | | | | | | | | | | | | | | | |            & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 224.92/38.55  | | | | | | | | | | | | | | | | |            $i(all_52_31)
% 224.92/38.55  | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | ALPHA: (16484) implies:
% 224.92/38.55  | | | | | | | | | | | | | | | | |   (16485)  op(e0, e0) = all_52_31
% 224.92/38.55  | | | | | | | | | | | | | | | | |   (16486)  op(all_52_31, all_52_31) = e0
% 224.92/38.55  | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 224.92/38.55  | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | |   (16487)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 224.92/38.55  | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 224.92/38.55  | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | BETA: splitting (16487) gives:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | |   (16488)  all_57_2 = e0 & op(e2, e3) = e0
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | ALPHA: (16488) implies:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | |   (16489)  op(e2, e3) = e0
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (16317), (16489), (function-axioms) are
% 224.92/38.55  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1943.
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | |   (16490)  all_57_3 = e0 & op(e2, e2) = e0
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | ALPHA: (16490) implies:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | |   (16491)  op(e2, e2) = e0
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (16045), (16491), (function-axioms) are
% 224.92/38.55  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2352.
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.55  | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | |   (16492)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 224.92/38.55  | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0)
% 224.92/38.55  | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | BETA: splitting (16492) gives:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | |   (16493)  all_57_5 = e0 & op(e2, e1) = e0
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (16472), (16493), (function-axioms) are
% 224.92/38.55  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2023.
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | |   (16494)  all_57_10 = e0 & op(e2, e0) = e0
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | ALPHA: (16494) implies:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | |   (16495)  op(e2, e0) = e0
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | |   (16496)  all_57_15 = e0 & op(e0, e0) = e0
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (14934), (16496) are inconsistent by
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | |            sub-proof #85.
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | |              all_52_31, e0, e0, simplifying with (14935),
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | |              (16485) gives:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | |   (16497)  all_52_31 = e2
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_13,
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | |              e0, e0, e2, simplifying with (165), (16495) gives:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | |   (16498)  all_53_13 = e0
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | REDUCE: (16486), (16497) imply:
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | |   (16499)  op(e2, e2) = e0
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (16045), (16499), (function-axioms) are
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2352.
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.55  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.55  | | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | | End of split
% 224.92/38.55  | | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | | End of split
% 224.92/38.55  | | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | | End of split
% 224.92/38.55  | | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | End of split
% 224.92/38.55  | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | Case 2:
% 224.92/38.55  | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | |   (16500)  all_57_1 = e0 & op(e3, e2) = e0
% 224.92/38.55  | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | ALPHA: (16500) implies:
% 224.92/38.55  | | | | | | | | | | | | | |   (16501)  op(e3, e2) = e0
% 224.92/38.55  | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | | REF_CLOSE: (171), (16320), (16501), (function-axioms) are
% 224.92/38.55  | | | | | | | | | | | | | |            inconsistent by sub-proof #1941.
% 224.92/38.55  | | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | End of split
% 224.92/38.55  | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | Case 2:
% 224.92/38.55  | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | |   (16502)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 224.92/38.55  | | | | | | | | | | | | |              & op(e3, e0) = e0)
% 224.92/38.55  | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | | REF_CLOSE: (169), (170), (16321), (16322), (16502),
% 224.92/38.55  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.92/38.55  | | | | | | | | | | | | |            #1544.
% 224.92/38.55  | | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | | End of split
% 224.92/38.55  | | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | End of split
% 224.92/38.55  | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | End of split
% 224.92/38.55  | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | Case 2:
% 224.92/38.55  | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | |   (16503)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 224.92/38.55  | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 224.92/38.55  | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | BETA: splitting (16503) gives:
% 224.92/38.55  | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | Case 1:
% 224.92/38.55  | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | |   (16504)  all_57_5 = e1 & op(e2, e1) = e1
% 224.92/38.55  | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | REF_CLOSE: (166), (16038), (16504), (function-axioms) are
% 224.92/38.55  | | | | | | | | | | |            inconsistent by sub-proof #2305.
% 224.92/38.55  | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | Case 2:
% 224.92/38.55  | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | |   (16505)  all_57_10 = e1 & op(e2, e0) = e1
% 224.92/38.55  | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | | REF_CLOSE: (165), (16039), (16505), (function-axioms) are
% 224.92/38.55  | | | | | | | | | | |            inconsistent by sub-proof #2084.
% 224.92/38.55  | | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | End of split
% 224.92/38.55  | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | End of split
% 224.92/38.55  | | | | | | | | | 
% 224.92/38.55  | | | | | | | | End of split
% 224.92/38.55  | | | | | | | | 
% 224.92/38.55  | | | | | | | Case 2:
% 224.92/38.55  | | | | | | | | 
% 224.92/38.55  | | | | | | | |   (16506)  all_14_2 = e0
% 224.92/38.55  | | | | | | | |   (16507)  ( ~ (all_14_0 = e1) & op(all_14_1, e2) = all_14_0 &
% 224.92/38.55  | | | | | | | |              op(e2, e0) = all_14_1 & $i(all_14_0) &
% 224.92/38.55  | | | | | | | |              $i(all_14_1)) | ( ~ (all_14_1 = e3) & op(e2, e0) =
% 224.92/38.55  | | | | | | | |              all_14_1 & $i(all_14_1))
% 224.92/38.55  | | | | | | | | 
% 224.92/38.55  | | | | | | | | COMBINE_EQS: (328), (16506) imply:
% 224.92/38.55  | | | | | | | |   (16508)  all_8_2 = e0
% 224.92/38.55  | | | | | | | | 
% 224.92/38.55  | | | | | | | | COMBINE_EQS: (290), (16508) imply:
% 224.92/38.55  | | | | | | | |   (16509)  all_50_2 = e0
% 224.92/38.55  | | | | | | | | 
% 224.92/38.55  | | | | | | | | REDUCE: (352), (16508) imply:
% 224.92/38.55  | | | | | | | |   (16510)   ~ (all_53_4 = e0)
% 224.92/38.55  | | | | | | | | 
% 224.92/38.55  | | | | | | | | REDUCE: (354), (16508) imply:
% 224.92/38.55  | | | | | | | |   (16511)   ~ (all_53_6 = e0)
% 224.92/38.55  | | | | | | | | 
% 224.92/38.55  | | | | | | | | REDUCE: (356), (16508) imply:
% 224.92/38.55  | | | | | | | |   (16512)   ~ (all_53_7 = e0)
% 224.92/38.55  | | | | | | | | 
% 224.92/38.55  | | | | | | | | REDUCE: (358), (16508) imply:
% 224.92/38.55  | | | | | | | |   (16513)   ~ (all_53_9 = e0)
% 224.92/38.55  | | | | | | | | 
% 224.92/38.55  | | | | | | | | REDUCE: (360), (16508) imply:
% 224.92/38.55  | | | | | | | |   (16514)   ~ (all_53_13 = e0)
% 224.92/38.55  | | | | | | | | 
% 224.92/38.55  | | | | | | | | REDUCE: (14937), (16508) imply:
% 224.92/38.55  | | | | | | | |   (16515)   ~ (e3 = e0)
% 224.92/38.55  | | | | | | | | 
% 224.92/38.55  | | | | | | | | BETA: splitting (226) gives:
% 224.92/38.55  | | | | | | | | 
% 224.92/38.55  | | | | | | | | Case 1:
% 224.92/38.55  | | | | | | | | | 
% 224.92/38.55  | | | | | | | | |   (16516)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 224.92/38.55  | | | | | | | | |              & op(e2, e2) = e0)
% 224.92/38.55  | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | BETA: splitting (16516) gives:
% 224.92/38.55  | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | Case 1:
% 224.92/38.55  | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | |   (16517)  all_57_1 = e0 & op(e3, e2) = e0
% 224.92/38.55  | | | | | | | | | | 
% 224.92/38.55  | | | | | | | | | | ALPHA: (16517) implies:
% 224.92/38.56  | | | | | | | | | |   (16518)  op(e3, e2) = e0
% 224.92/38.56  | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | REF_CLOSE: (171), (16510), (16518), (function-axioms) are
% 224.92/38.56  | | | | | | | | | |            inconsistent by sub-proof #1941.
% 224.92/38.56  | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | Case 2:
% 224.92/38.56  | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | |   (16519)  all_57_3 = e0 & op(e2, e2) = e0
% 224.92/38.56  | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | ALPHA: (16519) implies:
% 224.92/38.56  | | | | | | | | | |   (16520)  all_57_3 = e0
% 224.92/38.56  | | | | | | | | | |   (16521)  op(e2, e2) = e0
% 224.92/38.56  | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | BETA: splitting (58) gives:
% 224.92/38.56  | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | Case 1:
% 224.92/38.56  | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | |   (16522)   ~ (all_18_2 = e0)
% 224.92/38.56  | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | REDUCE: (327), (16522) imply:
% 224.92/38.56  | | | | | | | | | | |   (16523)   ~ (all_10_2 = e0)
% 224.92/38.56  | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | BETA: splitting (61) gives:
% 224.92/38.56  | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | Case 1:
% 224.92/38.56  | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | |   (16524)   ~ (all_20_2 = e2)
% 224.92/38.56  | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | REDUCE: (299), (16524) imply:
% 224.92/38.56  | | | | | | | | | | | |   (16525)   ~ (all_10_2 = e2)
% 224.92/38.56  | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | BETA: splitting (205) gives:
% 224.92/38.56  | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | Case 1:
% 224.92/38.56  | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | |   (16526)  all_55_0 = e3
% 224.92/38.56  | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | COMBINE_EQS: (277), (16526) imply:
% 224.92/38.56  | | | | | | | | | | | | |   (16527)  all_10_2 = e3
% 224.92/38.56  | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | REDUCE: (338), (16527) imply:
% 224.92/38.56  | | | | | | | | | | | | |   (16528)   ~ (all_53_1 = e3)
% 224.92/38.56  | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | REDUCE: (344), (16527) imply:
% 224.92/38.56  | | | | | | | | | | | | |   (16529)   ~ (all_53_4 = e3)
% 224.92/38.56  | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | REDUCE: (346), (16527) imply:
% 224.92/38.56  | | | | | | | | | | | | |   (16530)   ~ (all_53_8 = e3)
% 224.92/38.56  | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | REDUCE: (348), (16527) imply:
% 224.92/38.56  | | | | | | | | | | | | |   (16531)   ~ (all_53_12 = e3)
% 224.92/38.56  | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | REDUCE: (45), (16527) imply:
% 224.92/38.56  | | | | | | | | | | | | |   (16532)  op(e3, e3) = e3
% 224.92/38.56  | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | BETA: splitting (237) gives:
% 224.92/38.56  | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | Case 1:
% 224.92/38.56  | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | |   (16533)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 224.92/38.56  | | | | | | | | | | | | | |              & op(e3, e2) = e3)
% 224.92/38.56  | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | BETA: splitting (16533) gives:
% 224.92/38.56  | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | Case 1:
% 224.92/38.56  | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | |   (16534)  all_57_0 = e3 & op(e3, e3) = e3
% 224.92/38.56  | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | ALPHA: (16534) implies:
% 224.92/38.56  | | | | | | | | | | | | | | |   (16535)  all_57_0 = e3
% 224.92/38.56  | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 224.92/38.56  | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | Case 1:
% 224.92/38.56  | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | |   (16536)   ~ (all_24_2 = e0)
% 224.92/38.56  | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | REDUCE: (315), (16536) imply:
% 224.92/38.56  | | | | | | | | | | | | | | | |   (16537)   ~ (all_6_2 = e0)
% 224.92/38.56  | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | BETA: splitting (88) gives:
% 224.92/38.56  | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.56  | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | |   (16538)   ~ (all_38_2 = e2)
% 224.92/38.56  | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | REDUCE: (249), (16538) imply:
% 224.92/38.56  | | | | | | | | | | | | | | | | |   (16539)   ~ (all_6_2 = e2)
% 224.92/38.56  | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 224.92/38.56  | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | |   (16540)  all_55_10 = e3
% 224.92/38.56  | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (14936), (16540) are inconsistent by
% 224.92/38.56  | | | | | | | | | | | | | | | | | |            sub-proof #2500.
% 224.92/38.56  | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | |   (16541)   ~ (all_55_10 = e3)
% 224.92/38.56  | | | | | | | | | | | | | | | | | |   (16542)  all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 224.92/38.56  | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | BETA: splitting (16542) gives:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | |   (16543)  all_55_10 = e2
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (16539), (16543) are inconsistent by
% 224.92/38.56  | | | | | | | | | | | | | | | | | | |            sub-proof #2499.
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | |   (16544)   ~ (all_55_10 = e2)
% 224.92/38.56  | | | | | | | | | | | | | | | | | | |   (16545)  all_55_10 = e1 | all_55_10 = e0
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | BETA: splitting (16545) gives:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | |   (16546)  all_55_10 = e1
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (336), (16546) imply:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | |   (16547)  all_6_2 = e1
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | SIMP: (16547) implies:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | |   (16548)  all_6_2 = e1
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | REDUCE: (361), (16548) imply:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | |   (16549)   ~ (all_53_6 = e1)
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | REDUCE: (363), (16548) imply:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | |   (16550)   ~ (all_53_8 = e1)
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | REDUCE: (364), (16548) imply:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | |   (16551)   ~ (all_53_9 = e1)
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | REDUCE: (366), (16548) imply:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | |   (16552)   ~ (all_53_11 = e1)
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | REDUCE: (14936), (16548) imply:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | |   (16553)   ~ (e3 = e1)
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | REDUCE: (16539), (16548) imply:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | |   (16554)   ~ (e2 = e1)
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (16548) imply:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | |   (16555)  op(e1, e1) = e1
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | BETA: splitting (106) gives:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | |   (16556)   ~ (all_50_2 = e0)
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | REDUCE: (16509), (16556) imply:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | |   (16557)  $false
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | CLOSE: (16557) is inconsistent.
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | |   (16558)  ( ~ (all_50_0 = e3) & op(all_50_1, e2) = all_50_0
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | |              & op(e2, e0) = all_50_1 & $i(all_50_0) &
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | |              $i(all_50_1)) | ( ~ (all_50_1 = e1) & op(e2, e0)
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | |              = all_50_1 & $i(all_50_1))
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | |   (16559)  all_55_13 = e3
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (16559) imply:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | |   (16560)  all_53_7 = e3
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | SIMP: (16560) implies:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | |   (16561)  all_53_7 = e3
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (126), (16561) imply:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | |   (16562)   ~ (all_53_11 = e3)
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | SIMP: (16562) implies:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | |   (16563)   ~ (all_53_11 = e3)
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | |   (16564)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16564) gives:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | |   (16565)  all_57_12 = e3 & op(e0, e3) = e3
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16565) implies:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | |   (16566)  all_57_12 = e3
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | |            (230), (232), (234), (16520), (16532), (16566),
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | |            #2223.
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | |   (16567)  all_57_13 = e3 & op(e0, e2) = e3
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16567) implies:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | |   (16568)  all_57_13 = e3
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | |   (16569)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e3)
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16569) gives:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | |   (16570)  all_57_6 = e3 & op(e1, e3) = e3
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16570) implies:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | |   (16571)  all_57_6 = e3
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (230), (232), (234),
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | |            (16535), (16571) are inconsistent by sub-proof
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | |            #2010.
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | |   (16572)  all_57_7 = e3 & op(e1, e2) = e3
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16572) implies:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | |   (16573)  all_57_7 = e3
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (227), (228), (16520),
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | |            (16521), (16568), (16573), (function-axioms) are
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2007.
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | |   (16574)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e1, e0) = e3)
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16574) gives:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | |   (16575)  all_57_8 = e3 & op(e1, e1) = e3
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16575) implies:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | |   (16576)  op(e1, e1) = e3
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (16555), (16576), (function-axioms) are
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #156.
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | |   (16577)  all_57_11 = e3 & op(e1, e0) = e3
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16577) implies:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | |   (16578)  all_57_11 = e3
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | |   (16579)  op(e1, e0) = e3
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16580)  all_57_15 = e0 & op(e0, e0) = e0
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16580) implies:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16581)  all_57_15 = e0
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (14934), (16581) are inconsistent by
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2126.
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16582)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16582) implies:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16583)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0)
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16584)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0)
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16585)  all_55_14 = e3
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (16563), (16585) are inconsistent by
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2294.
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16586)   ~ (all_55_14 = e3)
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16587)  all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16587) gives:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16588)  all_55_14 = e2
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (14926), (16588) are inconsistent by
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2293.
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16589)   ~ (all_55_14 = e2)
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16590)  all_55_14 = e1 | all_55_14 = e0
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16591)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e3)
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16591) gives:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16592)  all_57_4 = e3 & op(e3, e1) = e3
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16592) implies:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16593)  all_57_4 = e3
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (235),
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16532), (16593), (function-axioms) are
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2474.
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16594)  all_57_5 = e3 & op(e2, e1) = e3
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16594) implies:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16595)  all_57_5 = e3
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16596)  op(e2, e1) = e3
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16597)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16597) gives:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16598)  all_57_1 = e1 & op(e3, e2) = e1
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16598) implies:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16599)  all_57_1 = e1
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16600)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (16521), (16599), (16600),
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2208.
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16601)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16601) gives:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16602)  all_57_7 = e2 & op(e1, e2) = e2
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16602) implies:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16603)  all_57_7 = e2
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16590) gives:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16604)  all_55_14 = e1
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (16552), (16604) are inconsistent by
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2165.
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16605)  all_55_14 = e0
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (16605) imply:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16606)  all_53_11 = e0
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (16606) implies:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16607)  all_53_11 = e0
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (16607) imply:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16608)   ~ (all_53_3 = e0)
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (122), (16607) imply:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16609)   ~ (all_53_8 = e0)
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14926), (16607) imply:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16610)   ~ (e2 = e0)
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (16552), (16607) imply:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16611)   ~ (e1 = e0)
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16612)  all_55_2 = e3
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (16530), (16612) are inconsistent by
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2028.
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16613)  all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16583) gives:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16614)  all_57_12 = e0 & op(e0, e3) = e0
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16614) implies:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16615)  op(e0, e3) = e0
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (16608), (16615), (function-axioms) are
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2366.
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16616)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16616) gives:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16617)  all_57_13 = e0 & op(e0, e2) = e0
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16617) implies:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16618)  op(e0, e2) = e0
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (16512), (16618), (function-axioms) are
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2332.
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16619)  all_57_14 = e0 & op(e0, e1) = e0
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16619) implies:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16620)  all_57_14 = e0
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16621)  op(e0, e1) = e0
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16622)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e0)
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16622) gives:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16623)  all_57_0 = e0 & op(e3, e3) = e0
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16623) implies:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16624)  op(e3, e3) = e0
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (169), (170), (218),
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (219), (220), (237), (16531), (16555), (16595),
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16599), (16609), (16624), (function-axioms) are
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #37.
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16625)  all_57_2 = e0 & op(e2, e3) = e0
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16625) implies:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16626)  all_57_2 = e0
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (223), (224), (16520),
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16595), (16626) are inconsistent by sub-proof
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2253.
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16627)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = e0)
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16627) gives:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16628)  all_57_6 = e0 & op(e1, e3) = e0
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16628) implies:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16629)  all_57_6 = e0
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16630)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16630) gives:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16631)  all_57_2 = e2 & op(e2, e3) = e2
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16631) implies:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16632)  all_57_2 = e2
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16584) gives:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16633)  all_57_9 = e0 & op(e3, e0) = e0
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16633) implies:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16634)  op(e3, e0) = e0
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16613) gives:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16635)  all_55_2 = e2
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (16635) imply:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16636)  all_53_8 = e2
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (16636) implies:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16637)  all_53_8 = e2
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (124), (16637) imply:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16638)   ~ (all_53_9 = e2)
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (16638) implies:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16639)   ~ (all_53_9 = e2)
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (16637) imply:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16640)   ~ (all_53_12 = e2)
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16641)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16641) gives:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16642)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_7)
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16642) implies:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16643)  op(e3, e0) = all_52_7
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16644)  op(all_52_7, all_52_7) = e0
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (14935), (16634), (16643), (16644),
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #47.
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16645)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_15)
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16645) implies:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16646)  op(e2, e0) = all_52_15
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16647)  op(all_52_15, all_52_15) = e0
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16648)  all_55_6 = e3
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (16648) imply:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16649)  all_53_9 = e3
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (16649) implies:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16650)  all_53_9 = e3
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (16650) imply:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16651)   ~ (all_53_13 = e3)
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (16651) implies:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16652)   ~ (all_53_13 = e3)
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16653)  all_55_7 = e3
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (16652), (16653) are inconsistent by
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2109.
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16654)  all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16654) gives:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16655)  all_55_7 = e2
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (14928), (16655) are inconsistent by
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2171.
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16656)  all_55_7 = e1 | all_55_7 = e0
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16656) gives:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16657)  all_55_7 = e1
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (16657) imply:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16658)  all_53_13 = e1
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (16658) implies:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16659)  all_53_13 = e1
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (114), (16659) imply:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16660)   ~ (all_53_12 = e1)
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (165), (16659) imply:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16661)  op(e2, e0) = e1
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16662)  all_55_3 = e3
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (16662) imply:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16663)  all_53_12 = e3
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (16531), (16663) imply:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16664)  $false
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (16664) is inconsistent.
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16665)  all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16507) gives:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16666)   ~ (all_14_0 = e1) & op(all_14_1, e2) = all_14_0 &
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = all_14_1 & $i(all_14_0) &
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_14_1)
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16666) implies:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16667)  op(e2, e0) = all_14_1
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (14927), (16507), (16555), (16558),
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16646), (16647), (16660), (16661), (16665),
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16667), (function-axioms) are inconsistent by
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #36.
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16668)   ~ (all_14_1 = e3) & op(e2, e0) = all_14_1 &
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_14_1)
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16668) implies:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16669)  op(e2, e0) = all_14_1
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (14927), (16507), (16555), (16558),
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16646), (16647), (16660), (16661), (16665),
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16669), (function-axioms) are inconsistent by
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #36.
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16670)  all_55_7 = e0
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (16514), (16670) are inconsistent by
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2130.
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16671)  all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (16513), (16551), (16639), (16671) are
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2160.
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16672)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_52_21) = e1 & op(all_52_23, all_52_23) =
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(all_52_25, all_52_25) = e3 &
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_52_29) = e1 & op(all_52_31, all_52_31) =
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_29) & $i(all_52_31))
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16672) gives:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16673)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_23)
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16673) implies:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16674)  op(e1, e0) = all_52_23
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16675)  op(e1, e1) = all_52_21
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16676)  op(all_52_23, all_52_23) = e0
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16677)  all_55_6 = e3
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (16677) imply:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16678)  all_53_9 = e3
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (16678) implies:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16679)  all_53_9 = e3
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (16679) imply:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16680)   ~ (all_53_13 = e3)
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (16680) implies:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16681)   ~ (all_53_13 = e3)
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16682)  all_55_7 = e3
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (16681), (16682) are inconsistent by
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2109.
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16683)   ~ (all_55_7 = e3)
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16684)  all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16684) gives:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16685)  all_55_7 = e2
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (14928), (16685) are inconsistent by
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2171.
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16686)   ~ (all_55_7 = e2)
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16687)  all_55_7 = e1 | all_55_7 = e0
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16687) gives:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16688)  all_55_7 = e1
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (16688) imply:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16689)  all_53_13 = e1
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (16689) implies:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16690)  all_53_13 = e1
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (114), (16690) imply:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16691)   ~ (all_53_12 = e1)
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16692)  all_55_3 = e3
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (16692) imply:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16693)  all_53_12 = e3
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (16531), (16693) imply:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16694)  $false
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (16694) is inconsistent.
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16695)   ~ (all_55_3 = e3)
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16696)  all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16696) gives:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16697)  all_55_3 = e2
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (16697) imply:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16698)  all_53_12 = e2
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14927), (16698) imply:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16699)  $false
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (16699) is inconsistent.
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16700)   ~ (all_55_3 = e2)
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16701)  all_55_3 = e1 | all_55_3 = e0
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16701) gives:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16702)  all_55_3 = e1
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (16702) imply:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16703)  all_53_12 = e1
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (16691), (16703) imply:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16704)  $false
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (16704) is inconsistent.
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16705)  all_55_3 = e0
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (16705) imply:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16706)  all_53_12 = e0
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3,
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_23, e0, e1, simplifying with (16579),
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (16674) gives:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16707)  all_52_23 = e3
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_21, e1, e1, simplifying with (16555),
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (16675) gives:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16708)  all_52_21 = e1
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (16676), (16707) imply:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16709)  op(e3, e3) = e0
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (169), (170), (218),
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (219), (220), (237), (16531), (16555), (16595),
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16599), (16609), (16709), (function-axioms) are
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #37.
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16710)  all_55_7 = e0
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (16514), (16710) are inconsistent by
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2130.
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16711)  all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (16513), (16551), (16639), (16711) are
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2160.
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16712)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_31)
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16712) implies:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16713)  op(e0, e0) = all_52_31
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16714)  op(e0, e1) = all_52_29
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16715)  op(all_52_31, all_52_31) = e0
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16716)  op(all_52_29, all_52_29) = e1
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16717)  all_55_6 = e3
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (16717) imply:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16718)  all_53_9 = e3
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (16718) implies:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16719)  all_53_9 = e3
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (16719) imply:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16720)   ~ (all_53_13 = e3)
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (16720) implies:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16721)   ~ (all_53_13 = e3)
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16722)  all_55_7 = e3
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (16721), (16722) are inconsistent by
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2109.
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16723)  all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16723) gives:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16724)  all_55_7 = e2
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (14928), (16724) are inconsistent by
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2171.
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16725)  all_55_7 = e1 | all_55_7 = e0
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16725) gives:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16726)  all_55_7 = e1
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (16726) imply:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16727)  all_53_13 = e1
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (16727) implies:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16728)  all_53_13 = e1
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (114), (16728) imply:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16729)   ~ (all_53_12 = e1)
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16730)  all_55_3 = e3
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (16730) imply:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16731)  all_53_12 = e3
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (16531), (16731) imply:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16732)  $false
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (16732) is inconsistent.
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16733)  all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (268), (14927), (16537), (16621), (16713),
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16714), (16715), (16716), (16729), (16733),
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #34.
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16734)  all_55_7 = e0
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (16514), (16734) are inconsistent by
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2130.
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16735)  all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (16513), (16551), (16639), (16735) are
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2160.
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16736)  all_55_2 = e1 | all_55_2 = e0
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (16550), (16609), (16736) are inconsistent
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2030.
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16737)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 =
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16737) gives:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16738)  all_57_10 = e0 & op(e2, e0) = e0
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16738) implies:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16739)  all_57_10 = e0
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (223), (16520), (16595), (16632),
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16739) are inconsistent by sub-proof #1530.
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16740)  all_57_11 = e0 & op(e1, e0) = e0
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16740) implies:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16741)  all_57_11 = e0
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (67), (88),
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (94), (107), (121), (124), (134), (135), (137),
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (163), (166), (169), (170), (171), (195), (202),
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (203), (204), (207), (208), (209), (211), (212),
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (213), (214), (215), (216), (217), (218), (219),
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (220), (223), (224), (227), (228), (229), (230),
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (232), (233), (234), (235), (249), (268),
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (269), (270), (315), (332), (336), (363), (364),
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14936), (16510), (16513), (16520), (16521),
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16531), (16532), (16535), (16568), (16595),
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16596), (16741), (function-axioms) are
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1408.
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16742)  all_57_3 = e2 & op(e2, e2) = e2
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16742) implies:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16743)  op(e2, e2) = e2
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (16521), (16743), (function-axioms) are
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2472.
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16744)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16744) gives:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16745)  all_57_5 = e2 & op(e2, e1) = e2
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16745) implies:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16746)  all_57_5 = e2
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (16595), (16746) imply:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16747)  e3 = e2
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (16578), (16747) imply:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16748)  all_57_11 = e2
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (39), (217), (14936), (16603), (16629),
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16748), (function-axioms) are inconsistent by
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1638.
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16749)  all_57_10 = e2 & op(e2, e0) = e2
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (14928), (16749), (function-axioms) are
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2432.
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16750)  all_57_12 = e0 & op(e0, e3) = e0
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16750) implies:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16751)  all_57_12 = e0
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (67), (88),
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (94), (107), (121), (124), (134), (135), (137),
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (163), (166), (169), (170), (171), (195), (202),
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (203), (204), (207), (208), (209), (210), (211),
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (214), (215), (216), (217), (218), (219),
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (220), (221), (223), (224), (225), (227), (228),
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (229), (230), (231), (232), (233), (234), (235),
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (236), (237), (249), (268), (269), (270), (315),
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (332), (336), (363), (364), (14935), (14936),
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16510), (16513), (16520), (16531), (16532),
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16620), (16751), (function-axioms) are
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #33.
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16752)  all_57_13 = e2 & op(e0, e2) = e2
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16752) implies:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16753)  op(e0, e2) = e2
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (14925), (16753), (function-axioms) are
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2335.
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16754)  all_57_3 = e1 & op(e2, e2) = e1
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16754) implies:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16755)  op(e2, e2) = e1
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (16521), (16755), (function-axioms) are
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2352.
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16756)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (163), (16549), (16568), (16756),
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2262.
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16757)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e1) = e3)
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16757) gives:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16758)  all_57_8 = e3 & op(e1, e1) = e3
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16758) implies:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16759)  op(e1, e1) = e3
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (16555), (16759), (function-axioms) are
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #156.
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16760)  all_57_14 = e3 & op(e0, e1) = e3
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (16563), (16760), (function-axioms) are
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #129.
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | |   (16761)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16761) gives:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | |   (16762)  all_57_14 = e3 & op(e0, e1) = e3
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (16563), (16762), (function-axioms) are
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #129.
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | |   (16763)  all_57_15 = e3 & op(e0, e0) = e3
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16763) implies:
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | |   (16764)  all_57_15 = e3
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | |   (16765)  op(e0, e0) = e3
% 224.92/38.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (67), (88),
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | |            (94), (107), (121), (124), (134), (135), (137),
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | |            (163), (166), (169), (170), (171), (195), (202),
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | |            (203), (204), (207), (208), (209), (211), (212),
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | |            (214), (215), (216), (217), (218), (219), (220),
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | |            (221), (223), (224), (225), (227), (228), (229),
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | |            (230), (231), (232), (233), (234), (235), (236),
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | |            (237), (249), (268), (269), (270), (315), (332),
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | |            (336), (363), (364), (14936), (16510), (16513),
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | |            (16520), (16531), (16532), (16764), (16765),
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | |            #1415.
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | |   (16766)   ~ (all_55_13 = e3)
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (246), (16766) imply:
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | |   (16767)   ~ (all_53_7 = e3)
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | |   (16768)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16768) gives:
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | |   (16769)  all_57_12 = e3 & op(e0, e3) = e3
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16769) implies:
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | |   (16770)  all_57_12 = e3
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | |            (230), (232), (234), (16520), (16532), (16770),
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | |            #2223.
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | |   (16771)  all_57_13 = e3 & op(e0, e2) = e3
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (16767), (16771), (function-axioms) are
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #78.
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | |   (16772)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16772) gives:
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | |   (16773)  all_57_14 = e3 & op(e0, e1) = e3
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16773) implies:
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | |   (16774)  all_57_14 = e3
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | | |   (16775)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e3)
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (171), (14937), (16529), (16775),
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | | |            #32.
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | | |   (16776)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16776) gives:
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | |   (16777)  all_57_7 = e3 & op(e1, e2) = e3
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16777) implies:
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | |   (16778)  all_57_7 = e3
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | |   (16779)  op(e1, e2) = e3
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16780)  all_57_15 = e0 & op(e0, e0) = e0
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16780) implies:
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16781)  all_57_15 = e0
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (14934), (16781) are inconsistent by
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2126.
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.57  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16782)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16782) implies:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16783)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0)
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16784)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0)
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16785)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16785) gives:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16786)  all_57_1 = e2 & op(e3, e2) = e2
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16786) implies:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16787)  all_57_1 = e2
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16788)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e0)
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16788) gives:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16789)  all_57_4 = e0 & op(e3, e1) = e0
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16789) implies:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16790)  all_57_4 = e0
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16791)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (16521), (16787), (16791),
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2209.
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16792)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16792) gives:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16793)  all_57_7 = e1 & op(e1, e2) = e1
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (16549), (16793), (function-axioms) are
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2265.
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16794)  all_57_13 = e1 & op(e0, e2) = e1
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16794) implies:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16795)  all_57_13 = e1
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16796)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e2)
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16796) gives:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16797)  all_57_4 = e2 & op(e3, e1) = e2
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16797) implies:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16798)  all_57_4 = e2
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (16790), (16798) imply:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16799)  e2 = e0
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (227), (228), (16520),
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16778), (16787), (16799) are inconsistent by
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1392.
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16800)  all_57_5 = e2 & op(e2, e1) = e2
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16800) implies:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16801)  all_57_5 = e2
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16802)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e2)
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16802) gives:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16803)  all_57_6 = e2 & op(e1, e3) = e2
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16803) implies:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16804)  all_57_6 = e2
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16805)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e0)
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16805) gives:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16806)  all_57_6 = e0 & op(e1, e3) = e0
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16806) implies:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16807)  all_57_6 = e0
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (16804), (16807) imply:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16808)  e2 = e0
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (16787), (16808) imply:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16809)  all_57_1 = e0
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (227), (228), (16520),
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16778), (16809) are inconsistent by sub-proof
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2098.
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16810)  all_57_7 = e0 & op(e1, e2) = e0
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (16511), (16810), (function-axioms) are
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2039.
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16811)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16811) gives:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16812)  all_57_8 = e0 & op(e1, e1) = e0
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16812) implies:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16813)  op(e1, e1) = e0
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (16555), (16813), (function-axioms) are
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2427.
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16814)  all_57_11 = e0 & op(e1, e0) = e0
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16814) implies:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16815)  all_57_11 = e0
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16816)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e3)
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16816) gives:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16817)  all_57_2 = e3 & op(e2, e3) = e3
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16817) implies:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16818)  all_57_2 = e3
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (169), (207),
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (208), (209), (213), (221), (222), (223), (224),
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (225), (226), (228), (231), (233), (235), (14936),
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16520), (16531), (16532), (16778), (16815),
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16818), (function-axioms) are inconsistent by
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1329.
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16819)  all_57_3 = e3 & op(e2, e2) = e3
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16819) implies:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16820)  op(e2, e2) = e3
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (14937), (16820), (function-axioms) are
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #140.
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16821)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16821) gives:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16822)  all_57_5 = e3 & op(e2, e1) = e3
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16822) implies:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16823)  all_57_5 = e3
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (16801), (16823) imply:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16824)  e3 = e2
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (16824) implies:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16825)  e3 = e2
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (16774), (16825) imply:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16826)  all_57_14 = e2
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (39), (221), (14936), (16790), (16801),
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16826), (function-axioms) are inconsistent by
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2188.
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16827)  all_57_10 = e3 & op(e2, e0) = e3
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16827) implies:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16828)  op(e2, e0) = e3
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16829)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16829) gives:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16830)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_7)
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16830) implies:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16831)  op(e3, e2) = all_52_3
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16832)  op(all_52_3, all_52_3) = e2
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (171), (204), (270), (16507), (16510), (16521),
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16529), (16558), (16828), (16831), (16832),
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #149.
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16833)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_15)
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16833) implies:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16834)  op(e2, e0) = all_52_15
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16835)  op(all_52_15, all_52_15) = e0
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (16507), (16532), (16558), (16828), (16834),
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16835), (function-axioms) are inconsistent by
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #148.
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16836)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_52_21) = e1 & op(all_52_23, all_52_23) =
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(all_52_25, all_52_25) = e3 &
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_52_29) = e1 & op(all_52_31, all_52_31) =
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_29) & $i(all_52_31))
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16836) gives:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16837)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_23)
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16837) implies:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16838)  op(e1, e2) = all_52_19
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16839)  op(all_52_19, all_52_19) = e2
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16558) gives:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3,
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_19, e2, e1, simplifying with (16779),
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (16838) gives:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16840)  all_52_19 = e3
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (16839), (16840) imply:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16841)  op(e3, e3) = e2
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (169), (223), (224),
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (225), (227), (228), (230), (231), (232), (233),
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (235), (236), (237), (16520), (16531), (16778),
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16804), (16841), (function-axioms) are
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #729.
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16842)   ~ (all_50_1 = e1) & op(e2, e0) = all_50_1 &
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_50_1)
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16842) implies:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16843)   ~ (all_50_1 = e1)
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16844)  op(e2, e0) = all_50_1
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3,
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_19, e2, e1, simplifying with (16779),
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (16838) gives:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16845)  all_52_19 = e3
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_50_1,
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e2, simplifying with (16828), (16844) gives:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16846)  all_50_1 = e3
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (16839), (16845) imply:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16847)  op(e3, e3) = e2
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (169), (223), (224),
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (225), (227), (228), (230), (231), (232), (233),
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (235), (236), (237), (16520), (16531), (16778),
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16804), (16847), (function-axioms) are
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #729.
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16848)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_31)
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16848) implies:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16849)  op(e0, e0) = all_52_31
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16850)  op(e0, e3) = all_52_25
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16851)  op(all_52_25, all_52_25) = e3
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (159), (14935), (16512), (16774),
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16783), (16849), (16850), (16851),
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #29.
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16852)  all_57_7 = e2 & op(e1, e2) = e2
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16852) implies:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16853)  all_57_7 = e2
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (16778), (16853) imply:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16854)  e3 = e2
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (16774), (16854) imply:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16855)  all_57_14 = e2
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (39), (221), (14936), (16790), (16801),
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16855), (function-axioms) are inconsistent by
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2188.
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16856)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e1, e0) = e2)
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16856) gives:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16857)  all_57_8 = e2 & op(e1, e1) = e2
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16857) implies:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16858)  op(e1, e1) = e2
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (16555), (16858), (function-axioms) are
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2423.
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16859)  all_57_11 = e2 & op(e1, e0) = e2
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16859) implies:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16860)  all_57_11 = e2
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16861)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e1)
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16861) gives:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16862)  all_57_0 = e1 & op(e3, e3) = e1
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16862) implies:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16863)  op(e3, e3) = e1
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (16532), (16863), (function-axioms) are
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2495.
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16864)  all_57_1 = e1 & op(e3, e2) = e1
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16864) implies:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16865)  all_57_1 = e1
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (226), (228), (229),
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16778), (16795), (16865), (function-axioms) are
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #291.
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16866)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e1)
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16866) gives:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16867)  all_57_4 = e1 & op(e3, e1) = e1
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16867) implies:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16868)  all_57_4 = e1
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (218), (220),
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (221), (14936), (16555), (16801), (16868),
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2416.
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16869)  all_57_9 = e1 & op(e3, e0) = e1
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16869) implies:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16870)  all_57_9 = e1
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16784) gives:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16871)  all_57_9 = e0 & op(e3, e0) = e0
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16871) implies:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16872)  all_57_9 = e0
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (16870), (16872) imply:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16873)  e1 = e0
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (16795), (16873) imply:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16874)  all_57_13 = e0
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (227), (228), (231),
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (235), (16520), (16532), (16778), (16787),
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16874), (function-axioms) are inconsistent by
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2093.
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16875)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 =
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16875) gives:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16876)  all_57_10 = e0 & op(e2, e0) = e0
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16876) implies:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16877)  op(e2, e0) = e0
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (16514), (16877), (function-axioms) are
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2470.
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16878)  all_57_11 = e0 & op(e1, e0) = e0
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16878) implies:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16879)  all_57_11 = e0
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (16860), (16879) imply:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16880)  e2 = e0
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (16787), (16880) imply:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16881)  all_57_1 = e0
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (227), (228), (16520),
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16778), (16881) are inconsistent by sub-proof
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2098.
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16882)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e1) = e2)
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (16555), (16774), (16882),
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2089.
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16883)  all_57_5 = e0 & op(e2, e1) = e0
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (16513), (16883), (function-axioms) are
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2023.
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16884)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (16555), (16774), (16884),
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1234.
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16885)  all_57_3 = e2 & op(e2, e2) = e2
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16885) implies:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16886)  op(e2, e2) = e2
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (16521), (16886), (function-axioms) are
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2472.
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16887)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (159), (14925), (16778), (16887),
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #28.
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | |   (16888)  all_57_13 = e3 & op(e0, e2) = e3
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (16767), (16888), (function-axioms) are
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #78.
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | |   (16889)  all_57_15 = e3 & op(e0, e0) = e3
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16889) implies:
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | |   (16890)  all_57_15 = e3
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | |   (16891)  op(e0, e0) = e3
% 225.23/38.58  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (67), (88),
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | |            (94), (107), (121), (124), (134), (135), (137),
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | |            (163), (166), (169), (170), (171), (195), (202),
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | |            (203), (204), (207), (208), (209), (211), (212),
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | |            (214), (215), (216), (217), (218), (219), (220),
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | |            (221), (223), (224), (225), (227), (228), (229),
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | |            (230), (231), (232), (233), (234), (235), (236),
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | |            (237), (249), (268), (269), (270), (315), (332),
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | |            (336), (363), (364), (14936), (16510), (16513),
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | |            (16520), (16531), (16532), (16890), (16891),
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | |            #1415.
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | |   (16892)  all_55_10 = e0
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (16537), (16892) are inconsistent by
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | |            sub-proof #2118.
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.59  | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | End of split
% 225.23/38.59  | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.59  | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | |   (16893)  all_38_2 = e2
% 225.23/38.59  | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (16893) imply:
% 225.23/38.59  | | | | | | | | | | | | | | | | |   (16894)  all_6_2 = e2
% 225.23/38.59  | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | REDUCE: (361), (16894) imply:
% 225.23/38.59  | | | | | | | | | | | | | | | | |   (16895)   ~ (all_53_6 = e2)
% 225.23/38.59  | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | REDUCE: (364), (16894) imply:
% 225.23/38.59  | | | | | | | | | | | | | | | | |   (16896)   ~ (all_53_9 = e2)
% 225.23/38.59  | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | REDUCE: (39), (16894) imply:
% 225.23/38.59  | | | | | | | | | | | | | | | | |   (16897)  op(e1, e1) = e2
% 225.23/38.59  | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 225.23/38.59  | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | |   (16898)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 225.23/38.59  | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 225.23/38.59  | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | BETA: splitting (16898) gives:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | |   (16899)  all_57_2 = e2 & op(e2, e3) = e2
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | ALPHA: (16899) implies:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | |   (16900)  all_57_2 = e2
% 225.23/38.59  | | | | | | | | | | | | | | | | | | |   (16901)  op(e2, e3) = e2
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | |   (16902)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | BETA: splitting (16902) gives:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | |   (16903)  all_57_1 = e2 & op(e3, e2) = e2
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | ALPHA: (16903) implies:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | |   (16904)  all_57_1 = e2
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | |   (16905)  op(e3, e2) = e2
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_1, e2,
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (168), (16901) gives:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | |   (16906)  all_53_1 = e2
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_4, e2,
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (171), (16905) gives:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | |   (16907)  all_53_4 = e2
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (16906) imply:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | |   (16908)   ~ (all_53_13 = e2)
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | REDUCE: (137), (16907) imply:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | |   (16909)   ~ (all_53_6 = e2)
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | REDUCE: (136), (16907) imply:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | |   (16910)   ~ (all_53_7 = e2)
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (16907) imply:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | |   (16911)   ~ (all_53_12 = e2)
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | REDUCE: (16529), (16907) imply:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | |   (16912)   ~ (e3 = e2)
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | |   (16913)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | |              all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | |              op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | |                all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | |                all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | |              & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | |                all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (42), (14937), (16521), (16901), (16905),
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | |            (16913), (function-axioms) are inconsistent by
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #27.
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | |   (16914)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | |              & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | |              & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | |                all_52_21) = e1 & op(all_52_23, all_52_23) =
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | |              all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | |              = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | |              & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | |              e0 & op(all_52_25, all_52_25) = e3 &
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | |              op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | |                all_52_29) = e1 & op(all_52_31, all_52_31) =
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | |              all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | |              = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_29) & $i(all_52_31))
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16914) gives:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | |   (16915)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | |            all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | |              all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | |            & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_23)
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (16521), (16897), (16915), (function-axioms)
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #26.
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | |   (16916)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | |            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | |              all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | |            & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | |            & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | |            & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_31)
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16916) implies:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | |   (16917)  op(e0, e0) = all_52_31
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | |   (16918)  op(e0, e2) = all_52_27
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | |   (16919)  op(e0, e3) = all_52_25
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | |   (16920)  op(all_52_31, all_52_31) = e0
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | |   (16921)  op(all_52_27, all_52_27) = e2
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | |   (16922)  op(all_52_25, all_52_25) = e3
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | |              all_52_31, e0, e0, simplifying with (14935),
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | |              (16917) gives:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | |   (16923)  all_52_31 = e2
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_7,
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | |              all_52_27, e2, e0, simplifying with (159), (16918)
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | |   (16924)  all_53_7 = all_52_27
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_3,
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | |              all_52_25, e3, e0, simplifying with (160), (16919)
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | |   (16925)  all_53_3 = all_52_25
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (16924) imply:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | |   (16926)  all_55_13 = all_52_27
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (129), (16924) imply:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | |   (16927)   ~ (all_53_6 = all_52_27)
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14925), (16924) imply:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | |   (16928)   ~ (all_52_27 = e2)
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (16512), (16924) imply:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | |   (16929)   ~ (all_52_27 = e0)
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | |   (16930)  all_55_6 = e3
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (16930) imply:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | |   (16931)  all_53_9 = e3
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (16931) implies:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | |   (16932)  all_53_9 = e3
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (16932) imply:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | |   (16933)   ~ (all_53_13 = e3)
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (16933) implies:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | |   (16934)   ~ (all_53_13 = e3)
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | |   (16935)  all_55_7 = e3
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (16934), (16935) are inconsistent by
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2109.
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | |   (16936)   ~ (all_55_7 = e3)
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | |   (16937)  all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16937) gives:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | |   (16938)  all_55_7 = e2
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (14928), (16938) are inconsistent by
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2171.
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | |   (16939)   ~ (all_55_7 = e2)
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | |   (16940)  all_55_7 = e1 | all_55_7 = e0
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16940) gives:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16941)  all_55_7 = e1
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (16941) imply:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16942)  all_53_13 = e1
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (16942) implies:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16943)  all_53_13 = e1
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (114), (16943) imply:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16944)   ~ (all_53_12 = e1)
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (111), (16943) imply:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16945)   ~ (all_53_14 = e1)
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (16945) implies:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16946)   ~ (all_53_14 = e1)
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (16934), (16943) imply:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16947)   ~ (e3 = e1)
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14928), (16943) imply:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16948)   ~ (e2 = e1)
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16949)  all_55_3 = e3
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (16531), (16949) are inconsistent by
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2169.
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16950)   ~ (all_55_3 = e3)
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16951)  all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16951) gives:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16952)  all_55_3 = e2
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (14927), (16952) are inconsistent by
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1612.
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16953)  all_55_3 = e1 | all_55_3 = e0
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16953) gives:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16954)  all_55_3 = e1
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (16944), (16954) are inconsistent by
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #324.
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16955)  all_55_3 = e0
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (16955) imply:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16956)  all_53_12 = e0
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (16956) implies:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16957)  all_53_12 = e0
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (16957) imply:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16958)   ~ (all_53_14 = e0)
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (16958) implies:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16959)   ~ (all_53_14 = e0)
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16960)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e1)
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (16532), (16904), (16960),
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2096.
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16961)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e1)
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16961) gives:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16962)  all_57_4 = e1 & op(e3, e1) = e1
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16962) implies:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16963)  all_57_4 = e1
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16964)  all_55_11 = e3
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (16964) imply:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16965)  all_53_14 = e3
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (16965) implies:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16966)  all_53_14 = e3
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (127), (16966) imply:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16967)   ~ (all_53_6 = e3)
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16968)  all_55_9 = e3
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (16967), (16968) are inconsistent by
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2159.
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16969)  all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16969) gives:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16970)  all_55_9 = e2
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (16895), (16970) are inconsistent by
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2274.
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16971)  all_55_9 = e1 | all_55_9 = e0
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16971) gives:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16972)  all_55_9 = e1
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (16972) imply:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16973)  all_53_6 = e1
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (16973) implies:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16974)  all_53_6 = e1
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (16927), (16974) imply:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16975)   ~ (all_52_27 = e1)
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (16975) implies:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16976)   ~ (all_52_27 = e1)
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16977)  all_55_13 = e3
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (16926), (16977) imply:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16978)  all_52_27 = e3
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (16978) implies:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16979)  all_52_27 = e3
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (16921), (16979) imply:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16980)  op(e3, e3) = e2
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (169), (237), (16531), (16904), (16963),
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16980), (function-axioms) are inconsistent by
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1308.
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16981)  all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16521), (16921), (16926), (16929), (16976),
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16981), (function-axioms) are inconsistent by
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1614.
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16982)  all_55_9 = e0
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (16511), (16982) are inconsistent by
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2272.
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16983)  all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (14929), (16946), (16959), (16983) are
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2133.
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16984)  all_57_9 = e1 & op(e3, e0) = e1
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (16944), (16984), (function-axioms) are
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2131.
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16985)  all_55_7 = e0
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (16514), (16985) are inconsistent by
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2130.
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | |   (16986)   ~ (all_55_6 = e3)
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (259), (16986) imply:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | |   (16987)   ~ (all_53_9 = e3)
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | |   (16988)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e3)
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (168), (14937), (16528), (16988),
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | |            #111.
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | |   (16989)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16989) gives:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | |   (16990)  all_57_5 = e3 & op(e2, e1) = e3
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (16987), (16990), (function-axioms) are
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #270.
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | |   (16991)  all_57_10 = e3 & op(e2, e0) = e3
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16991) implies:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | |   (16992)  all_57_10 = e3
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16993)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e3)
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16993) gives:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16994)  all_57_4 = e3 & op(e3, e1) = e3
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16994) implies:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16995)  all_57_4 = e3
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (235),
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16532), (16995), (function-axioms) are
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2474.
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16996)  all_57_5 = e3 & op(e2, e1) = e3
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16996) implies:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16997)  all_57_5 = e3
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (223), (16520), (16900), (16992),
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16997) are inconsistent by sub-proof #1694.
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16998)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e1) = e3)
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16998) gives:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (16999)  all_57_8 = e3 & op(e1, e1) = e3
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (16999) implies:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17000)  op(e1, e1) = e3
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (14936), (17000), (function-axioms) are
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2468.
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17001)  all_57_14 = e3 & op(e0, e1) = e3
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17001) implies:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17002)  all_57_14 = e3
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17003)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e0)
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17003) gives:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17004)  all_57_4 = e0 & op(e3, e1) = e0
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17004) implies:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17005)  all_57_4 = e0
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17006)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e1)
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17006) gives:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17007)  all_57_4 = e1 & op(e3, e1) = e1
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17007) implies:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17008)  all_57_4 = e1
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (17005), (17008) are inconsistent by
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2438.
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17009)  all_57_5 = e1 & op(e2, e1) = e1
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17009) implies:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17010)  all_57_5 = e1
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17011)  all_57_15 = e0 & op(e0, e0) = e0
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17011) implies:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17012)  all_57_15 = e0
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14934), (17012) imply:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17013)  e2 = e0
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (17013) implies:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17014)  e2 = e0
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (16900), (17014) imply:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17015)  all_57_2 = e0
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (224), (16520), (16992), (17010),
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17015) are inconsistent by sub-proof #2249.
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17016)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17016) implies:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17017)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0)
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (159), (14935), (16512), (16917),
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16919), (16922), (17002), (17017),
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #29.
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17018)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e1) = e1)
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17018) gives:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17019)  all_57_8 = e1 & op(e1, e1) = e1
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17019) implies:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17020)  op(e1, e1) = e1
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (16897), (17020), (function-axioms) are
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2423.
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17021)  all_57_14 = e1 & op(e0, e1) = e1
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17021) implies:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17022)  all_57_14 = e1
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (221), (223),
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (231), (233), (235), (14936), (16520),
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16532), (16992), (17022), (function-axioms) are
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1692.
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17023)  all_57_5 = e0 & op(e2, e1) = e0
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17023) implies:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17024)  all_57_5 = e0
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16520), (16521), (16992), (17024),
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2348.
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17025)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (39), (16537), (17002), (17025),
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1717.
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | |   (17026)  all_57_3 = e2 & op(e2, e2) = e2
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | ALPHA: (17026) implies:
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | |   (17027)  op(e2, e2) = e2
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.59  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (16521), (17027), (function-axioms) are
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2472.
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | |   (17028)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (163), (14925), (16895), (17028),
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | |            #160.
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | |   (17029)  all_57_3 = e2 & op(e2, e2) = e2
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | ALPHA: (17029) implies:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | |   (17030)  op(e2, e2) = e2
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (16521), (17030), (function-axioms) are
% 225.23/38.60  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2472.
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.60  | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | |   (17031)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 225.23/38.60  | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 225.23/38.60  | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | BETA: splitting (17031) gives:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | |   (17032)  all_57_5 = e2 & op(e2, e1) = e2
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (16896), (17032), (function-axioms) are
% 225.23/38.60  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1858.
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | |   (17033)  all_57_10 = e2 & op(e2, e0) = e2
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (14928), (17033), (function-axioms) are
% 225.23/38.60  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2432.
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.60  | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | End of split
% 225.23/38.60  | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | End of split
% 225.23/38.60  | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | Case 2:
% 225.23/38.60  | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | |   (17034)  all_24_2 = e0
% 225.23/38.60  | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | COMBINE_EQS: (315), (17034) imply:
% 225.23/38.60  | | | | | | | | | | | | | | | |   (17035)  all_6_2 = e0
% 225.23/38.60  | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | SIMP: (17035) implies:
% 225.23/38.60  | | | | | | | | | | | | | | | |   (17036)  all_6_2 = e0
% 225.23/38.60  | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | REDUCE: (350), (17036) imply:
% 225.23/38.60  | | | | | | | | | | | | | | | |   (17037)   ~ (all_53_2 = e0)
% 225.23/38.60  | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | REDUCE: (363), (17036) imply:
% 225.23/38.60  | | | | | | | | | | | | | | | |   (17038)   ~ (all_53_8 = e0)
% 225.23/38.60  | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 225.23/38.60  | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.60  | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | |   (17039)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 225.23/38.60  | | | | | | | | | | | | | | | | |              & op(e2, e3) = e0)
% 225.23/38.60  | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 225.23/38.60  | | | | | | | | | | | | | | | | |            (16520), (16532), (17039), (function-axioms) are
% 225.23/38.60  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2229.
% 225.23/38.60  | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.60  | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | |   (17040)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 225.23/38.60  | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = e0)
% 225.23/38.60  | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | BETA: splitting (17040) gives:
% 225.23/38.60  | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | |   (17041)  all_57_6 = e0 & op(e1, e3) = e0
% 225.23/38.60  | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | ALPHA: (17041) implies:
% 225.23/38.60  | | | | | | | | | | | | | | | | | |   (17042)  op(e1, e3) = e0
% 225.23/38.60  | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (17037), (17042), (function-axioms) are
% 225.23/38.60  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2154.
% 225.23/38.60  | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | |   (17043)  all_57_12 = e0 & op(e0, e3) = e0
% 225.23/38.60  | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | ALPHA: (17043) implies:
% 225.23/38.60  | | | | | | | | | | | | | | | | | |   (17044)  all_57_12 = e0
% 225.23/38.60  | | | | | | | | | | | | | | | | | |   (17045)  op(e0, e3) = e0
% 225.23/38.60  | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | |   (17046)  all_57_15 = e0 & op(e0, e0) = e0
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (14934), (17046) are inconsistent by
% 225.23/38.60  | | | | | | | | | | | | | | | | | | |            sub-proof #85.
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | |   (17047)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 225.23/38.60  | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 225.23/38.60  | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 225.23/38.60  | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 225.23/38.60  | | | | | | | | | | | | | | | | | | |                e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | ALPHA: (17047) implies:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | |   (17048)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 225.23/38.60  | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 225.23/38.60  | | | | | | | | | | | | | | | | | | |                e0) = e0)
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | |   (17049)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e0)
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (170), (16513), (17038), (17049),
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | |            #141.
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | |   (17050)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | BETA: splitting (17050) gives:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | |   (17051)  all_57_8 = e0 & op(e1, e1) = e0
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | ALPHA: (17051) implies:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | |   (17052)  all_57_8 = e0
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | |   (17053)  op(e1, e1) = e0
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17048) gives:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | |   (17054)  all_57_9 = e0 & op(e3, e0) = e0
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17054) implies:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | |   (17055)  all_57_9 = e0
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | |   (17056)  op(e3, e0) = e0
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_3, e0,
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | |              e3, e0, simplifying with (160), (17045) gives:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | |   (17057)  all_53_3 = e0
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_12,
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | |              e0, e0, e3, simplifying with (169), (17056) gives:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | |   (17058)  all_53_12 = e0
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (141), (17057) imply:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | |   (17059)   ~ (all_53_7 = e0)
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (17057) imply:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | |   (17060)   ~ (all_53_11 = e0)
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | SIMP: (17060) implies:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | |   (17061)   ~ (all_53_11 = e0)
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14927), (17058) imply:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | |   (17062)   ~ (e2 = e0)
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | |   (17063)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | |              all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | |              op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | |                all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | |                all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | |              & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | |                all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17063) gives:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | |   (17064)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | |            all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | |              all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_7)
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17064) implies:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | |   (17065)  op(e3, e0) = all_52_7
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | |   (17066)  op(all_52_7, all_52_7) = e0
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (14935), (17056), (17065), (17066),
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | |            #47.
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | |   (17067)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | |            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | |              all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_15)
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17067) implies:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | |   (17068)  op(e2, e0) = all_52_15
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | |   (17069)  op(e2, e1) = all_52_13
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | |   (17070)  op(e2, e2) = all_52_11
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | |   (17071)  op(all_52_15, all_52_15) = e0
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | |   (17072)  op(all_52_13, all_52_13) = e1
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | |   (17073)  op(all_52_11, all_52_11) = e2
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_13,
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | |              all_52_15, e0, e2, simplifying with (165), (17068)
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | |   (17074)  all_53_13 = all_52_15
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_9,
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | |              all_52_13, e1, e2, simplifying with (166), (17069)
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | |   (17075)  all_53_9 = all_52_13
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | |              all_52_11, e2, e2, simplifying with (16521),
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | |              (17070) gives:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | |   (17076)  all_52_11 = e0
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (17075) imply:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | |   (17077)  all_55_6 = all_52_13
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (124), (17075) imply:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | |   (17078)   ~ (all_53_8 = all_52_13)
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (119), (17075) imply:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | |   (17079)   ~ (all_53_11 = all_52_13)
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (17079) implies:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | |   (17080)   ~ (all_53_11 = all_52_13)
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (16513), (17075) imply:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | |   (17081)   ~ (all_52_13 = e0)
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (106) gives:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | |   (17082)   ~ (all_50_2 = e0)
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (16509), (17082) imply:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | |   (17083)  $false
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (17083) is inconsistent.
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | |   (17084)  ( ~ (all_50_0 = e3) & op(all_50_1, e2) = all_50_0
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e0) = all_50_1 & $i(all_50_0) &
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_50_1)) | ( ~ (all_50_1 = e1) & op(e2, e0)
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | |              = all_50_1 & $i(all_50_1))
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17085)  all_55_13 = e3
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (17085) imply:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17086)  all_53_7 = e3
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (17086) implies:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17087)  all_53_7 = e3
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (126), (17087) imply:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17088)   ~ (all_53_11 = e3)
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (17088) implies:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17089)   ~ (all_53_11 = e3)
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17090)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e3)
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (171), (14937), (16529), (17090),
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #32.
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17091)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17091) gives:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17092)  all_57_7 = e3 & op(e1, e2) = e3
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17092) implies:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17093)  all_57_7 = e3
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (42), (67),
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (88), (94), (107), (121), (124), (134), (135),
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (137), (159), (163), (166), (168), (169), (170),
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (171), (195), (202), (203), (204), (207), (208),
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (209), (210), (211), (212), (213), (214), (215),
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (216), (217), (218), (219), (220), (221), (223),
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (225), (227), (228), (229), (230), (231),
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (232), (233), (234), (235), (236), (237), (249),
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (268), (269), (270), (315), (332), (336), (363),
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (364), (14925), (14936), (14937), (16507),
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16510), (16513), (16520), (16521), (16528),
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16531), (16532), (16535), (17044), (17052),
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17055), (17056), (17068), (17071), (17084),
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17093), (function-axioms) are inconsistent by
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #25.
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17094)  all_57_13 = e3 & op(e0, e2) = e3
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17094) implies:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17095)  all_57_13 = e3
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17096)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (17044), (17095), (17096) are
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2216.
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17097)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17097) gives:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17098)  all_57_14 = e1 & op(e0, e1) = e1
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17098) implies:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17099)  all_57_14 = e1
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17100)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e3)
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17100) gives:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17101)  all_57_4 = e3 & op(e3, e1) = e3
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17101) implies:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17102)  all_57_4 = e3
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (235),
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16532), (17102), (function-axioms) are
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2474.
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17103)  all_57_5 = e3 & op(e2, e1) = e3
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17103) implies:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17104)  all_57_5 = e3
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17105)  all_55_14 = e3
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (17089), (17105) are inconsistent by
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2294.
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17106)  all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17107)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e2)
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17107) gives:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17108)  all_57_4 = e2 & op(e3, e1) = e2
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17108) implies:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17109)  all_57_4 = e2
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17106) gives:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17110)  all_55_14 = e2
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (17110) imply:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17111)  all_53_11 = e2
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14926), (17111) imply:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17112)  $false
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (17112) is inconsistent.
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17113)  all_55_14 = e1 | all_55_14 = e0
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17114)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e1)
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17114) gives:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17115)  all_57_0 = e1 & op(e3, e3) = e1
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17115) implies:
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17116)  op(e3, e3) = e1
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.60  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (16532), (17116), (function-axioms) are
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2495.
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17117)  all_57_1 = e1 & op(e3, e2) = e1
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17117) implies:
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17118)  all_57_1 = e1
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17113) gives:
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17119)  all_55_14 = e1
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (17119) imply:
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17120)  all_53_11 = e1
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (17120) implies:
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17121)  all_53_11 = e1
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (122), (17121) imply:
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17122)   ~ (all_53_8 = e1)
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17080), (17121) imply:
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17123)   ~ (all_52_13 = e1)
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (17123) implies:
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17124)   ~ (all_52_13 = e1)
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17125)  all_55_2 = e3
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (16530), (17125) are inconsistent by
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2028.
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17126)  all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17126) gives:
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17127)  all_55_2 = e2
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (17127) imply:
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17128)  all_53_8 = e2
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (17128) implies:
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17129)  all_53_8 = e2
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17078), (17129) imply:
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17130)   ~ (all_52_13 = e2)
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (17130) implies:
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17131)   ~ (all_52_13 = e2)
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17132)  all_55_6 = e3
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (17077), (17132) imply:
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17133)  all_52_13 = e3
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (17133) implies:
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17134)  all_52_13 = e3
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17072), (17134) imply:
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17135)  op(e3, e3) = e1
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (235), (237), (17055),
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17118), (17135), (function-axioms) are
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #295.
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17136)  all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17077), (17081), (17124), (17131), (17136) are
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #68.
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17137)  all_55_2 = e1 | all_55_2 = e0
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (17038), (17122), (17137) are inconsistent
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2030.
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17138)  all_55_14 = e0
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (17061), (17138) are inconsistent by
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2288.
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17139)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e1)
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17139) gives:
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17140)  all_57_4 = e1 & op(e3, e1) = e1
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (17109), (17140) are inconsistent by
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2452.
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17141)  all_57_9 = e1 & op(e3, e0) = e1
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17141) implies:
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17142)  all_57_9 = e1
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (17055), (17142) imply:
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17143)  e1 = e0
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (17099), (17143) imply:
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17144)  all_57_14 = e0
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (67), (88),
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (94), (107), (121), (124), (134), (135), (137),
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (163), (166), (169), (170), (171), (195), (202),
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (203), (204), (207), (208), (209), (210), (211),
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (214), (215), (216), (217), (218), (219),
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (220), (221), (223), (224), (225), (227), (228),
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (229), (230), (231), (232), (233), (234), (235),
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (236), (237), (249), (268), (269), (270), (315),
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (332), (336), (363), (364), (14935), (14936),
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16510), (16513), (16520), (16531), (16532),
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17044), (17144), (function-axioms) are
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #33.
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17145)  all_57_5 = e2 & op(e2, e1) = e2
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17145) implies:
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17146)  all_57_5 = e2
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (17104), (17146) are inconsistent by
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2189.
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17147)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e1) = e2)
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (17052), (17099), (17147) are
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1188.
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17148)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e1) = e3)
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (158), (14936), (17089), (17148),
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #63.
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17149)  all_57_15 = e1 & op(e0, e0) = e1
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17149) implies:
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17150)  op(e0, e0) = e1
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (160), (208), (209),
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (210), (14924), (16521), (17044), (17070),
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17073), (17150), (function-axioms) are
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1228.
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17151)   ~ (all_55_13 = e3)
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (246), (17151) imply:
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17152)   ~ (all_53_7 = e3)
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17153)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e3)
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (171), (14937), (16529), (17153),
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #32.
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17154)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17154) gives:
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17155)  all_57_7 = e3 & op(e1, e2) = e3
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17155) implies:
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17156)  all_57_7 = e3
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (42), (67),
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (88), (94), (107), (121), (124), (134), (135),
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (137), (159), (163), (166), (168), (169), (170),
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (171), (195), (202), (203), (204), (207), (208),
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (209), (210), (211), (212), (213), (214), (215),
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (216), (217), (218), (219), (220), (221), (223),
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (225), (227), (228), (229), (230), (231),
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (232), (233), (234), (235), (236), (237), (249),
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (268), (269), (270), (315), (332), (336), (363),
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (364), (14925), (14936), (14937), (16507),
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16510), (16513), (16520), (16521), (16528),
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16531), (16532), (16535), (17044), (17052),
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17055), (17056), (17068), (17071), (17084),
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17156), (function-axioms) are inconsistent by
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #25.
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17157)  all_57_13 = e3 & op(e0, e2) = e3
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (17152), (17157), (function-axioms) are
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #78.
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | |   (17158)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | |              & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | |              & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | |                all_52_21) = e1 & op(all_52_23, all_52_23) =
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | |              all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | |              = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | |              & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(all_52_25, all_52_25) = e3 &
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | |              op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | |                all_52_29) = e1 & op(all_52_31, all_52_31) =
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | |              all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | |              = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_29) & $i(all_52_31))
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17158) gives:
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | |   (17159)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | |            all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | |              all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | |            & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_23)
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (14935), (17053), (17159), (function-axioms)
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #46.
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | |   (17160)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | |            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | |              all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | |            & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_31)
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17160) implies:
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | |   (17161)  op(e0, e0) = all_52_31
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | |   (17162)  op(e0, e3) = all_52_25
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | |   (17163)  op(all_52_25, all_52_25) = e3
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (14935), (17045), (17161), (17162), (17163),
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | |            #31.
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | |   (17164)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 =
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17164) gives:
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | |   (17165)  all_57_10 = e0 & op(e2, e0) = e0
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17165) implies:
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | |   (17166)  op(e2, e0) = e0
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (16514), (17166), (function-axioms) are
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2470.
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | |   (17167)  all_57_11 = e0 & op(e1, e0) = e0
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17167) implies:
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | |   (17168)  all_57_11 = e0
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (45), (67),
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | |            (88), (94), (107), (121), (124), (134), (135),
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | |            (137), (163), (164), (166), (169), (170), (171),
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | |            (195), (202), (203), (204), (205), (207), (208),
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | |            (209), (210), (211), (212), (213), (214), (215),
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | |            (216), (217), (218), (219), (220), (221), (223),
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | |            (224), (225), (227), (228), (229), (230), (231),
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | |            (232), (233), (234), (235), (236), (237), (249),
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | |            (268), (269), (270), (277), (315), (332), (336),
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | |            (348), (363), (364), (14936), (14938), (16510),
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | |            (16513), (16520), (16521), (16523), (16525),
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | |            (16531), (16532), (16535), (17037), (17038),
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | |            (17053), (17168), (function-axioms) are
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1294.
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | |   (17169)  all_57_14 = e0 & op(e0, e1) = e0
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | ALPHA: (17169) implies:
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | |   (17170)  all_57_14 = e0
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (67), (88),
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | |            (94), (107), (121), (124), (134), (135), (137),
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | |            (163), (166), (169), (170), (171), (195), (202),
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | |            (203), (204), (207), (208), (209), (210), (211),
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | |            (212), (214), (215), (216), (217), (218), (219),
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | |            (220), (221), (223), (224), (225), (227), (228),
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | |            (229), (230), (231), (232), (233), (234), (235),
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | |            (236), (237), (249), (268), (269), (270), (315),
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | |            (332), (336), (363), (364), (14935), (14936),
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | |            (16510), (16513), (16520), (16531), (16532),
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | |            (17044), (17170), (function-axioms) are
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #33.
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.61  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.61  | | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | | End of split
% 225.23/38.61  | | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | | End of split
% 225.23/38.61  | | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | End of split
% 225.23/38.61  | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | Case 2:
% 225.23/38.61  | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | |   (17171)  all_57_1 = e3 & op(e3, e2) = e3
% 225.23/38.61  | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | | REF_CLOSE: (171), (16529), (17171), (function-axioms) are
% 225.23/38.61  | | | | | | | | | | | | | | |            inconsistent by sub-proof #2286.
% 225.23/38.61  | | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | End of split
% 225.23/38.61  | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | Case 2:
% 225.23/38.61  | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | |   (17172)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 225.23/38.61  | | | | | | | | | | | | | |              & op(e3, e0) = e3)
% 225.23/38.61  | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (169), (231), (233),
% 225.23/38.61  | | | | | | | | | | | | | |            (235), (16531), (16532), (17172),
% 225.23/38.61  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.23/38.61  | | | | | | | | | | | | | |            #1955.
% 225.23/38.61  | | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | End of split
% 225.23/38.61  | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | Case 2:
% 225.23/38.61  | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | |   (17173)  all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 225.23/38.61  | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | | REF_CLOSE: (277), (14938), (16523), (16525), (17173) are
% 225.23/38.61  | | | | | | | | | | | | |            inconsistent by sub-proof #1953.
% 225.23/38.61  | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | End of split
% 225.23/38.61  | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | Case 2:
% 225.23/38.61  | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | |   (17174)  all_20_2 = e2
% 225.23/38.61  | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | COMBINE_EQS: (299), (17174) imply:
% 225.23/38.61  | | | | | | | | | | | |   (17175)  all_10_2 = e2
% 225.23/38.61  | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | SIMP: (17175) implies:
% 225.23/38.61  | | | | | | | | | | | |   (17176)  all_10_2 = e2
% 225.23/38.61  | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | REDUCE: (338), (17176) imply:
% 225.23/38.61  | | | | | | | | | | | |   (17177)   ~ (all_53_1 = e2)
% 225.23/38.61  | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | REDUCE: (45), (17176) imply:
% 225.23/38.61  | | | | | | | | | | | |   (17178)  op(e3, e3) = e2
% 225.23/38.61  | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | BETA: splitting (228) gives:
% 225.23/38.61  | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | Case 1:
% 225.23/38.61  | | | | | | | | | | | | | 
% 225.23/38.61  | | | | | | | | | | | | |   (17179)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 225.23/38.61  | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 225.23/38.62  | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (237),
% 225.23/38.62  | | | | | | | | | | | | |            (16521), (17178), (17179), (function-axioms) are
% 225.23/38.62  | | | | | | | | | | | | |            inconsistent by sub-proof #1297.
% 225.23/38.62  | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | Case 2:
% 225.23/38.62  | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | |   (17180)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 225.23/38.62  | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 225.23/38.62  | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | BETA: splitting (17180) gives:
% 225.23/38.62  | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | Case 1:
% 225.23/38.62  | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | |   (17181)  all_57_7 = e2 & op(e1, e2) = e2
% 225.23/38.62  | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | ALPHA: (17181) implies:
% 225.23/38.62  | | | | | | | | | | | | | |   (17182)  op(e1, e2) = e2
% 225.23/38.62  | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 225.23/38.62  | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | Case 1:
% 225.23/38.62  | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | |   (17183)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 225.23/38.62  | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 225.23/38.62  | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | BETA: splitting (17183) gives:
% 225.23/38.62  | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | Case 1:
% 225.23/38.62  | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | |   (17184)  all_57_2 = e2 & op(e2, e3) = e2
% 225.23/38.62  | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | REF_CLOSE: (168), (17177), (17184), (function-axioms) are
% 225.23/38.62  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2504.
% 225.23/38.62  | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | Case 2:
% 225.23/38.62  | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | |   (17185)  all_57_3 = e2 & op(e2, e2) = e2
% 225.23/38.62  | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | ALPHA: (17185) implies:
% 225.23/38.62  | | | | | | | | | | | | | | | |   (17186)  op(e2, e2) = e2
% 225.23/38.62  | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | REF_CLOSE: (5), (16521), (17186), (function-axioms) are
% 225.23/38.62  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2472.
% 225.23/38.62  | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | End of split
% 225.23/38.62  | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | Case 2:
% 225.23/38.62  | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | |   (17187)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 225.23/38.62  | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 225.23/38.62  | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | BETA: splitting (17187) gives:
% 225.23/38.62  | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | Case 1:
% 225.23/38.62  | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | |   (17188)  all_57_5 = e2 & op(e2, e1) = e2
% 225.23/38.62  | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | ALPHA: (17188) implies:
% 225.23/38.62  | | | | | | | | | | | | | | | |   (17189)  op(e2, e1) = e2
% 225.23/38.62  | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_6, e2,
% 225.23/38.62  | | | | | | | | | | | | | | | |              e2, e1, simplifying with (163), (17182) gives:
% 225.23/38.62  | | | | | | | | | | | | | | | |   (17190)  all_53_6 = e2
% 225.23/38.62  | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_9, e2,
% 225.23/38.62  | | | | | | | | | | | | | | | |              e1, e2, simplifying with (166), (17189) gives:
% 225.23/38.62  | | | | | | | | | | | | | | | |   (17191)  all_53_9 = e2
% 225.23/38.62  | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | REDUCE: (137), (17190) imply:
% 225.23/38.62  | | | | | | | | | | | | | | | |   (17192)   ~ (all_53_4 = e2)
% 225.23/38.62  | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | REDUCE: (124), (17191) imply:
% 225.23/38.62  | | | | | | | | | | | | | | | |   (17193)   ~ (all_53_8 = e2)
% 225.23/38.62  | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | REDUCE: (119), (17191) imply:
% 225.23/38.62  | | | | | | | | | | | | | | | |   (17194)   ~ (all_53_11 = e2)
% 225.23/38.62  | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | REDUCE: (364), (17191) imply:
% 225.23/38.62  | | | | | | | | | | | | | | | |   (17195)   ~ (all_6_2 = e2)
% 225.23/38.62  | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | SIMP: (17195) implies:
% 225.23/38.62  | | | | | | | | | | | | | | | |   (17196)   ~ (all_6_2 = e2)
% 225.23/38.62  | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 225.23/38.62  | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.62  | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | |   (17197)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 225.23/38.62  | | | | | | | | | | | | | | | | |              all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 225.23/38.62  | | | | | | | | | | | | | | | | |              op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 225.23/38.62  | | | | | | | | | | | | | | | | |                all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 225.23/38.62  | | | | | | | | | | | | | | | | |              op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 225.23/38.62  | | | | | | | | | | | | | | | | |              op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 225.23/38.62  | | | | | | | | | | | | | | | | |              $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 225.23/38.62  | | | | | | | | | | | | | | | | |              $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 225.23/38.62  | | | | | | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 225.23/38.62  | | | | | | | | | | | | | | | | |                all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 225.23/38.62  | | | | | | | | | | | | | | | | |              & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 225.23/38.62  | | | | | | | | | | | | | | | | |                all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 225.23/38.62  | | | | | | | | | | | | | | | | |              op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 225.23/38.62  | | | | | | | | | | | | | | | | |              & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 225.23/38.62  | | | | | | | | | | | | | | | | |              $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 225.23/38.62  | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | BETA: splitting (17197) gives:
% 225.23/38.62  | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | |   (17198)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 225.23/38.62  | | | | | | | | | | | | | | | | | |            all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 225.23/38.62  | | | | | | | | | | | | | | | | | |            op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 225.23/38.62  | | | | | | | | | | | | | | | | | |              all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 225.23/38.62  | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 225.23/38.62  | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 225.23/38.62  | | | | | | | | | | | | | | | | | |            $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 225.23/38.62  | | | | | | | | | | | | | | | | | |            $i(all_52_7)
% 225.23/38.62  | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | ALPHA: (17198) implies:
% 225.23/38.62  | | | | | | | | | | | | | | | | | |   (17199)  op(e3, e3) = all_52_1
% 225.23/38.62  | | | | | | | | | | | | | | | | | |   (17200)  op(all_52_1, all_52_1) = e3
% 225.23/38.62  | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (16521), (17178), (17199), (17200),
% 225.23/38.62  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.23/38.62  | | | | | | | | | | | | | | | | | |            #1653.
% 225.23/38.62  | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | |   (17201)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 225.23/38.62  | | | | | | | | | | | | | | | | | |            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 225.23/38.62  | | | | | | | | | | | | | | | | | |            op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 225.23/38.62  | | | | | | | | | | | | | | | | | |              all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 225.23/38.62  | | | | | | | | | | | | | | | | | |            & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 225.23/38.62  | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 225.23/38.62  | | | | | | | | | | | | | | | | | |            $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 225.23/38.62  | | | | | | | | | | | | | | | | | |            $i(all_52_15)
% 225.23/38.62  | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | ALPHA: (17201) implies:
% 225.23/38.62  | | | | | | | | | | | | | | | | | |   (17202)  op(e2, e1) = all_52_13
% 225.23/38.62  | | | | | | | | | | | | | | | | | |   (17203)  op(e2, e2) = all_52_11
% 225.23/38.62  | | | | | | | | | | | | | | | | | |   (17204)  op(all_52_13, all_52_13) = e1
% 225.23/38.62  | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 225.23/38.62  | | | | | | | | | | | | | | | | | |              all_52_13, e1, e2, simplifying with (17189),
% 225.23/38.62  | | | | | | | | | | | | | | | | | |              (17202) gives:
% 225.23/38.62  | | | | | | | | | | | | | | | | | |   (17205)  all_52_13 = e2
% 225.23/38.62  | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 225.23/38.62  | | | | | | | | | | | | | | | | | |              all_52_11, e2, e2, simplifying with (16521),
% 225.23/38.62  | | | | | | | | | | | | | | | | | |              (17203) gives:
% 225.23/38.62  | | | | | | | | | | | | | | | | | |   (17206)  all_52_11 = e0
% 225.23/38.62  | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | REDUCE: (17204), (17205) imply:
% 225.23/38.62  | | | | | | | | | | | | | | | | | |   (17207)  op(e2, e2) = e1
% 225.23/38.62  | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (16521), (17207), (function-axioms) are
% 225.23/38.62  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2352.
% 225.23/38.62  | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | End of split
% 225.23/38.62  | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.62  | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | |   (17208)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 225.23/38.62  | | | | | | | | | | | | | | | | |              & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 225.23/38.62  | | | | | | | | | | | | | | | | |              & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 225.23/38.62  | | | | | | | | | | | | | | | | |                all_52_21) = e1 & op(all_52_23, all_52_23) =
% 225.23/38.62  | | | | | | | | | | | | | | | | |              e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 225.23/38.62  | | | | | | | | | | | | | | | | |              all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 225.23/38.62  | | | | | | | | | | | | | | | | |              = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 225.23/38.62  | | | | | | | | | | | | | | | | |              $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 225.23/38.62  | | | | | | | | | | | | | | | | |              & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 225.23/38.62  | | | | | | | | | | | | | | | | |              e0 & op(all_52_25, all_52_25) = e3 &
% 225.23/38.62  | | | | | | | | | | | | | | | | |              op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 225.23/38.62  | | | | | | | | | | | | | | | | |                all_52_29) = e1 & op(all_52_31, all_52_31) =
% 225.23/38.62  | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 225.23/38.62  | | | | | | | | | | | | | | | | |              all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 225.23/38.62  | | | | | | | | | | | | | | | | |              = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 225.23/38.62  | | | | | | | | | | | | | | | | |              $i(all_52_29) & $i(all_52_31))
% 225.23/38.62  | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | BETA: splitting (17208) gives:
% 225.23/38.62  | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | |   (17209)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 225.23/38.62  | | | | | | | | | | | | | | | | | |            all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 225.23/38.62  | | | | | | | | | | | | | | | | | |            op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 225.23/38.62  | | | | | | | | | | | | | | | | | |              all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 225.23/38.62  | | | | | | | | | | | | | | | | | |            & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 225.23/38.62  | | | | | | | | | | | | | | | | | |            & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 225.23/38.62  | | | | | | | | | | | | | | | | | |            & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 225.23/38.62  | | | | | | | | | | | | | | | | | |            $i(all_52_23)
% 225.23/38.62  | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | ALPHA: (17209) implies:
% 225.23/38.62  | | | | | | | | | | | | | | | | | |   (17210)  op(e1, e2) = all_52_19
% 225.23/38.62  | | | | | | | | | | | | | | | | | |   (17211)  op(all_52_19, all_52_19) = e2
% 225.23/38.62  | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 225.23/38.62  | | | | | | | | | | | | | | | | | |              all_52_19, e2, e1, simplifying with (17182),
% 225.23/38.62  | | | | | | | | | | | | | | | | | |              (17210) gives:
% 225.23/38.62  | | | | | | | | | | | | | | | | | |   (17212)  all_52_19 = e2
% 225.23/38.62  | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | REDUCE: (17211), (17212) imply:
% 225.23/38.62  | | | | | | | | | | | | | | | | | |   (17213)  op(e2, e2) = e2
% 225.23/38.62  | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (16521), (17213), (function-axioms) are
% 225.23/38.62  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2472.
% 225.23/38.62  | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | |   (17214)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 225.23/38.62  | | | | | | | | | | | | | | | | | |            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 225.23/38.62  | | | | | | | | | | | | | | | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 225.23/38.62  | | | | | | | | | | | | | | | | | |              all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 225.23/38.62  | | | | | | | | | | | | | | | | | |            & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 225.23/38.62  | | | | | | | | | | | | | | | | | |            & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 225.23/38.62  | | | | | | | | | | | | | | | | | |            & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 225.23/38.62  | | | | | | | | | | | | | | | | | |            $i(all_52_31)
% 225.23/38.62  | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | ALPHA: (17214) implies:
% 225.23/38.62  | | | | | | | | | | | | | | | | | |   (17215)  op(e0, e0) = all_52_31
% 225.23/38.62  | | | | | | | | | | | | | | | | | |   (17216)  op(e0, e1) = all_52_29
% 225.23/38.62  | | | | | | | | | | | | | | | | | |   (17217)  op(e0, e2) = all_52_27
% 225.23/38.62  | | | | | | | | | | | | | | | | | |   (17218)  op(e0, e3) = all_52_25
% 225.23/38.62  | | | | | | | | | | | | | | | | | |   (17219)  op(all_52_31, all_52_31) = e0
% 225.23/38.62  | | | | | | | | | | | | | | | | | |   (17220)  op(all_52_29, all_52_29) = e1
% 225.23/38.62  | | | | | | | | | | | | | | | | | |   (17221)  op(all_52_27, all_52_27) = e2
% 225.23/38.62  | | | | | | | | | | | | | | | | | |   (17222)  op(all_52_25, all_52_25) = e3
% 225.23/38.62  | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 225.23/38.62  | | | | | | | | | | | | | | | | | |              all_52_31, e0, e0, simplifying with (14935),
% 225.23/38.62  | | | | | | | | | | | | | | | | | |              (17215) gives:
% 225.23/38.62  | | | | | | | | | | | | | | | | | |   (17223)  all_52_31 = e2
% 225.23/38.62  | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_11,
% 225.23/38.62  | | | | | | | | | | | | | | | | | |              all_52_29, e1, e0, simplifying with (158), (17216)
% 225.23/38.62  | | | | | | | | | | | | | | | | | |              gives:
% 225.23/38.62  | | | | | | | | | | | | | | | | | |   (17224)  all_53_11 = all_52_29
% 225.23/38.62  | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_7,
% 225.23/38.62  | | | | | | | | | | | | | | | | | |              all_52_27, e2, e0, simplifying with (159), (17217)
% 225.23/38.62  | | | | | | | | | | | | | | | | | |              gives:
% 225.23/38.62  | | | | | | | | | | | | | | | | | |   (17225)  all_53_7 = all_52_27
% 225.23/38.62  | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_3,
% 225.23/38.62  | | | | | | | | | | | | | | | | | |              all_52_25, e3, e0, simplifying with (160), (17218)
% 225.23/38.62  | | | | | | | | | | | | | | | | | |              gives:
% 225.23/38.62  | | | | | | | | | | | | | | | | | |   (17226)  all_53_3 = all_52_25
% 225.23/38.62  | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (17224) imply:
% 225.23/38.62  | | | | | | | | | | | | | | | | | |   (17227)  all_55_14 = all_52_29
% 225.23/38.62  | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (17225) imply:
% 225.23/38.62  | | | | | | | | | | | | | | | | | |   (17228)  all_55_13 = all_52_27
% 225.23/38.62  | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | REDUCE: (136), (17225) imply:
% 225.23/38.62  | | | | | | | | | | | | | | | | | |   (17229)   ~ (all_53_4 = all_52_27)
% 225.23/38.62  | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | REDUCE: (126), (17224), (17225) imply:
% 225.23/38.62  | | | | | | | | | | | | | | | | | |   (17230)   ~ (all_52_27 = all_52_29)
% 225.23/38.62  | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | REDUCE: (16512), (17225) imply:
% 225.23/38.62  | | | | | | | | | | | | | | | | | |   (17231)   ~ (all_52_27 = e0)
% 225.23/38.62  | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | REDUCE: (122), (17224) imply:
% 225.23/38.62  | | | | | | | | | | | | | | | | | |   (17232)   ~ (all_53_8 = all_52_29)
% 225.23/38.62  | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | REDUCE: (366), (17224) imply:
% 225.23/38.62  | | | | | | | | | | | | | | | | | |   (17233)   ~ (all_52_29 = all_6_2)
% 225.23/38.62  | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | REDUCE: (14926), (17224) imply:
% 225.23/38.62  | | | | | | | | | | | | | | | | | |   (17234)   ~ (all_52_29 = e2)
% 225.23/38.62  | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | |   (17235)   ~ (all_24_2 = e0)
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | REDUCE: (315), (17235) imply:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | |   (17236)   ~ (all_6_2 = e0)
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | |   (17237)  all_55_10 = e3
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (14936), (17237) are inconsistent by
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | |            sub-proof #2500.
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | |   (17238)  all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | BETA: splitting (17238) gives:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | |   (17239)  all_55_10 = e2
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (17196), (17239) are inconsistent by
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | |            sub-proof #2499.
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | |   (17240)   ~ (all_55_10 = e2)
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | |   (17241)  all_55_10 = e1 | all_55_10 = e0
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17241) gives:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | |   (17242)  all_55_10 = e1
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (336), (17242) imply:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | |   (17243)  all_6_2 = e1
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | SIMP: (17243) implies:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | |   (17244)  all_6_2 = e1
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (363), (17244) imply:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | |   (17245)   ~ (all_53_8 = e1)
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17233), (17244) imply:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | |   (17246)   ~ (all_52_29 = e1)
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17196), (17244) imply:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | |   (17247)   ~ (e2 = e1)
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | |   (17248)  all_55_1 = e3
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (17248) imply:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | |   (17249)  all_53_4 = e3
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (17249) implies:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | |   (17250)  all_53_4 = e3
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (17250) imply:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | |   (17251)   ~ (all_53_8 = e3)
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (17251) implies:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | |   (17252)   ~ (all_53_8 = e3)
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | |   (17253)  all_55_2 = e3
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (17252), (17253) are inconsistent by
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2028.
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | |   (17254)  all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17254) gives:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | |   (17255)  all_55_2 = e2
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (17193), (17255) are inconsistent by
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2027.
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | |   (17256)  all_55_2 = e1 | all_55_2 = e0
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17256) gives:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17257)  all_55_2 = e1
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (17245), (17257) are inconsistent by
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2032.
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17258)  all_55_2 = e0
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (17258) imply:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17259)  all_53_8 = e0
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (17259) implies:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17260)  all_53_8 = e0
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17232), (17260) imply:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17261)   ~ (all_52_29 = e0)
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (17261) implies:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17262)   ~ (all_52_29 = e0)
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (191), (17178), (17220), (17227), (17234),
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | |            (17246), (17262), (function-axioms) are
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1565.
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | |   (17263)  all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17263) gives:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | |   (17264)  all_55_1 = e2
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (17192), (17264) are inconsistent by
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2284.
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | |   (17265)  all_55_1 = e1 | all_55_1 = e0
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17265) gives:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | |   (17266)  all_55_1 = e1
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (17266) imply:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | |   (17267)  all_53_4 = e1
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (17267) implies:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | |   (17268)  all_53_4 = e1
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17229), (17268) imply:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | |   (17269)   ~ (all_52_27 = e1)
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (17269) implies:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | |   (17270)   ~ (all_52_27 = e1)
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17271)  all_55_13 = e3
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (17228), (17271) imply:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17272)  all_52_27 = e3
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17230), (17272) imply:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17273)   ~ (all_52_29 = e3)
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (17273) implies:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17274)   ~ (all_52_29 = e3)
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17275)  all_55_14 = e3
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (17227), (17275) imply:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17276)  all_52_29 = e3
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17274), (17276) imply:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17277)  $false
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (17277) is inconsistent.
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17278)  all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17278) gives:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17279)  all_55_14 = e2
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (17227), (17279) imply:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17280)  all_52_29 = e2
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17234), (17280) imply:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17281)  $false
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (17281) is inconsistent.
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17282)  all_55_14 = e1 | all_55_14 = e0
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17282) gives:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17283)  all_55_14 = e1
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (17227), (17283) imply:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17284)  all_52_29 = e1
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17246), (17284) imply:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17285)  $false
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (17285) is inconsistent.
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17286)  all_55_14 = e0
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (17227), (17286) imply:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17287)  all_52_29 = e0
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17220), (17287) imply:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17288)  op(e0, e0) = e1
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (17215), (17219), (17236), (17288),
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2086.
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17289)  all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16521), (17221), (17228), (17231), (17270),
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | |            (17289), (function-axioms) are inconsistent by
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1614.
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | |   (17290)  all_55_1 = e0
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (16510), (17290) are inconsistent by
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2076.
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | |   (17291)  all_55_10 = e0
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (17236), (17291) are inconsistent by
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2118.
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | |   (17292)  all_24_2 = e0
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (315), (17292) imply:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | |   (17293)  all_6_2 = e0
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | SIMP: (17293) implies:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | |   (17294)  all_6_2 = e0
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | REDUCE: (350), (17294) imply:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | |   (17295)   ~ (all_53_2 = e0)
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | REDUCE: (17196), (17294) imply:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | |   (17296)   ~ (e2 = e0)
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | |   (17297)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e0)
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | |            (16520), (17178), (17297), (function-axioms) are
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1654.
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | |   (17298)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = e0)
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | BETA: splitting (17298) gives:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | |   (17299)  all_57_6 = e0 & op(e1, e3) = e0
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | ALPHA: (17299) implies:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | |   (17300)  op(e1, e3) = e0
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (17295), (17300), (function-axioms) are
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2154.
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | |   (17301)  all_57_12 = e0 & op(e0, e3) = e0
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | ALPHA: (17301) implies:
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | |   (17302)  op(e0, e3) = e0
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (14935), (17215), (17218), (17222), (17302),
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | |            #31.
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.62  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.62  | | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | | End of split
% 225.23/38.62  | | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | End of split
% 225.23/38.62  | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | Case 2:
% 225.23/38.62  | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | |   (17303)  all_57_10 = e2 & op(e2, e0) = e2
% 225.23/38.62  | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | | REF_CLOSE: (165), (14928), (17303), (function-axioms) are
% 225.23/38.62  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2432.
% 225.23/38.62  | | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | End of split
% 225.23/38.62  | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | End of split
% 225.23/38.62  | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | Case 2:
% 225.23/38.62  | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | |   (17304)  all_57_13 = e2 & op(e0, e2) = e2
% 225.23/38.62  | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | ALPHA: (17304) implies:
% 225.23/38.62  | | | | | | | | | | | | | |   (17305)  op(e0, e2) = e2
% 225.23/38.62  | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | REF_CLOSE: (159), (14925), (17305), (function-axioms) are
% 225.23/38.62  | | | | | | | | | | | | | |            inconsistent by sub-proof #2335.
% 225.23/38.62  | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | End of split
% 225.23/38.62  | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | End of split
% 225.23/38.62  | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | End of split
% 225.23/38.62  | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | Case 2:
% 225.23/38.62  | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | |   (17306)  all_18_2 = e0
% 225.23/38.62  | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | COMBINE_EQS: (327), (17306) imply:
% 225.23/38.62  | | | | | | | | | | |   (17307)  all_10_2 = e0
% 225.23/38.62  | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | SIMP: (17307) implies:
% 225.23/38.62  | | | | | | | | | | |   (17308)  all_10_2 = e0
% 225.23/38.62  | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | REDUCE: (342), (17308) imply:
% 225.23/38.62  | | | | | | | | | | |   (17309)   ~ (all_53_3 = e0)
% 225.23/38.62  | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | REDUCE: (348), (17308) imply:
% 225.23/38.62  | | | | | | | | | | |   (17310)   ~ (all_53_12 = e0)
% 225.23/38.62  | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | REDUCE: (14938), (17308) imply:
% 225.23/38.62  | | | | | | | | | | |   (17311)   ~ (e1 = e0)
% 225.23/38.62  | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | REDUCE: (45), (17308) imply:
% 225.23/38.62  | | | | | | | | | | |   (17312)  op(e3, e3) = e0
% 225.23/38.62  | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | BETA: splitting (207) gives:
% 225.23/38.62  | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | Case 1:
% 225.23/38.62  | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | |   (17313)  all_57_15 = e0 & op(e0, e0) = e0
% 225.23/38.62  | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | REF_CLOSE: (5), (14934), (17313) are inconsistent by
% 225.23/38.62  | | | | | | | | | | | |            sub-proof #85.
% 225.23/38.62  | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | Case 2:
% 225.23/38.62  | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | |   (17314)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 225.23/38.62  | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 225.23/38.62  | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 225.23/38.62  | | | | | | | | | | | |                  e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 225.23/38.62  | | | | | | | | | | | |                e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 225.23/38.62  | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | ALPHA: (17314) implies:
% 225.23/38.62  | | | | | | | | | | | |   (17315)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 225.23/38.62  | | | | | | | | | | | |              e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 225.23/38.62  | | | | | | | | | | | |                e1) = e0)
% 225.23/38.62  | | | | | | | | | | | |   (17316)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 225.23/38.62  | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 225.23/38.62  | | | | | | | | | | | |                e0) = e0)
% 225.23/38.62  | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | BETA: splitting (17315) gives:
% 225.23/38.62  | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | Case 1:
% 225.23/38.62  | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | |   (17317)  all_57_12 = e0 & op(e0, e3) = e0
% 225.23/38.62  | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | ALPHA: (17317) implies:
% 225.23/38.62  | | | | | | | | | | | | |   (17318)  op(e0, e3) = e0
% 225.23/38.62  | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | REF_CLOSE: (160), (17309), (17318), (function-axioms) are
% 225.23/38.62  | | | | | | | | | | | | |            inconsistent by sub-proof #2366.
% 225.23/38.62  | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | Case 2:
% 225.23/38.62  | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | |   (17319)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 225.23/38.62  | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 225.23/38.62  | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | BETA: splitting (17319) gives:
% 225.23/38.62  | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | Case 1:
% 225.23/38.62  | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | |   (17320)  all_57_13 = e0 & op(e0, e2) = e0
% 225.23/38.62  | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | ALPHA: (17320) implies:
% 225.23/38.62  | | | | | | | | | | | | | |   (17321)  op(e0, e2) = e0
% 225.23/38.62  | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | REF_CLOSE: (159), (16512), (17321), (function-axioms) are
% 225.23/38.62  | | | | | | | | | | | | | |            inconsistent by sub-proof #2332.
% 225.23/38.62  | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | Case 2:
% 225.23/38.62  | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | |   (17322)  all_57_14 = e0 & op(e0, e1) = e0
% 225.23/38.62  | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | ALPHA: (17322) implies:
% 225.23/38.62  | | | | | | | | | | | | | |   (17323)  all_57_14 = e0
% 225.23/38.62  | | | | | | | | | | | | | |   (17324)  op(e0, e1) = e0
% 225.23/38.62  | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | BETA: splitting (17316) gives:
% 225.23/38.62  | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | Case 1:
% 225.23/38.62  | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | |   (17325)  all_57_9 = e0 & op(e3, e0) = e0
% 225.23/38.62  | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | REF_CLOSE: (169), (17310), (17325), (function-axioms) are
% 225.23/38.62  | | | | | | | | | | | | | | |            inconsistent by sub-proof #2434.
% 225.23/38.62  | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | Case 2:
% 225.23/38.62  | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | |   (17326)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 =
% 225.23/38.62  | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 225.23/38.62  | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | BETA: splitting (17326) gives:
% 225.23/38.62  | | | | | | | | | | | | | | | 
% 225.23/38.62  | | | | | | | | | | | | | | | Case 1:
% 225.23/38.62  | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | |   (17327)  all_57_10 = e0 & op(e2, e0) = e0
% 225.23/38.63  | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | ALPHA: (17327) implies:
% 225.23/38.63  | | | | | | | | | | | | | | | |   (17328)  op(e2, e0) = e0
% 225.23/38.63  | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | REF_CLOSE: (165), (16514), (17328), (function-axioms) are
% 225.23/38.63  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2470.
% 225.23/38.63  | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | Case 2:
% 225.23/38.63  | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | |   (17329)  all_57_11 = e0 & op(e1, e0) = e0
% 225.23/38.63  | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | ALPHA: (17329) implies:
% 225.23/38.63  | | | | | | | | | | | | | | | |   (17330)  all_57_11 = e0
% 225.23/38.63  | | | | | | | | | | | | | | | |   (17331)  op(e1, e0) = e0
% 225.23/38.63  | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (39), (42), (88), (107),
% 225.23/38.63  | | | | | | | | | | | | | | | |            (111), (118), (119), (126), (140), (158), (159),
% 225.23/38.63  | | | | | | | | | | | | | | | |            (160), (161), (163), (165), (166), (168), (195),
% 225.23/38.63  | | | | | | | | | | | | | | | |            (198), (199), (208), (209), (210), (211), (214),
% 225.23/38.63  | | | | | | | | | | | | | | | |            (215), (217), (218), (219), (221), (222), (224),
% 225.23/38.63  | | | | | | | | | | | | | | | |            (225), (228), (231), (233), (234), (237), (249),
% 225.23/38.63  | | | | | | | | | | | | | | | |            (258), (259), (336), (361), (364), (368), (14924),
% 225.23/38.63  | | | | | | | | | | | | | | | |            (14925), (14928), (14929), (14935), (14936),
% 225.23/38.63  | | | | | | | | | | | | | | | |            (14937), (16521), (17312), (17315), (17323),
% 225.23/38.63  | | | | | | | | | | | | | | | |            (17324), (17330), (17331), (function-axioms) are
% 225.23/38.63  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #22.
% 225.23/38.63  | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | End of split
% 225.23/38.63  | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | End of split
% 225.23/38.63  | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | End of split
% 225.23/38.63  | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | End of split
% 225.23/38.63  | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | End of split
% 225.23/38.63  | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | End of split
% 225.23/38.63  | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | End of split
% 225.23/38.63  | | | | | | | | | 
% 225.23/38.63  | | | | | | | | Case 2:
% 225.23/38.63  | | | | | | | | | 
% 225.23/38.63  | | | | | | | | |   (17332)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0
% 225.23/38.63  | | | | | | | | |              & op(e0, e2) = e0)
% 225.23/38.63  | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | REF_CLOSE: (159), (163), (16511), (16512), (17332),
% 225.23/38.63  | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.23/38.63  | | | | | | | | |            #2024.
% 225.23/38.63  | | | | | | | | | 
% 225.23/38.63  | | | | | | | | End of split
% 225.23/38.63  | | | | | | | | 
% 225.23/38.63  | | | | | | | End of split
% 225.23/38.63  | | | | | | | 
% 225.23/38.63  | | | | | | Case 2:
% 225.23/38.63  | | | | | | | 
% 225.23/38.63  | | | | | | |   (17333)  all_10_2 = e1
% 225.23/38.63  | | | | | | |   (17334)  ( ~ (all_10_0 = e2) & op(all_10_1, e3) = all_10_0 &
% 225.23/38.63  | | | | | | |              op(e3, e1) = all_10_1 & $i(all_10_0) & $i(all_10_1))
% 225.23/38.63  | | | | | | |            | ( ~ (all_10_1 = e0) & op(e3, e1) = all_10_1 &
% 225.23/38.63  | | | | | | |              $i(all_10_1))
% 225.23/38.63  | | | | | | | 
% 225.23/38.63  | | | | | | | COMBINE_EQS: (331), (17333) imply:
% 225.23/38.63  | | | | | | |   (17335)  all_36_2 = e1
% 225.23/38.63  | | | | | | | 
% 225.23/38.63  | | | | | | | REDUCE: (338), (17333) imply:
% 225.23/38.63  | | | | | | |   (17336)   ~ (all_53_1 = e1)
% 225.23/38.63  | | | | | | | 
% 225.23/38.63  | | | | | | | REDUCE: (340), (17333) imply:
% 225.23/38.63  | | | | | | |   (17337)   ~ (all_53_2 = e1)
% 225.23/38.63  | | | | | | | 
% 225.23/38.63  | | | | | | | REDUCE: (342), (17333) imply:
% 225.23/38.63  | | | | | | |   (17338)   ~ (all_53_3 = e1)
% 225.23/38.63  | | | | | | | 
% 225.23/38.63  | | | | | | | REDUCE: (344), (17333) imply:
% 225.23/38.63  | | | | | | |   (17339)   ~ (all_53_4 = e1)
% 225.23/38.63  | | | | | | | 
% 225.23/38.63  | | | | | | | REDUCE: (346), (17333) imply:
% 225.23/38.63  | | | | | | |   (17340)   ~ (all_53_8 = e1)
% 225.23/38.63  | | | | | | | 
% 225.23/38.63  | | | | | | | REDUCE: (348), (17333) imply:
% 225.23/38.63  | | | | | | |   (17341)   ~ (all_53_12 = e1)
% 225.23/38.63  | | | | | | | 
% 225.23/38.63  | | | | | | | BETA: splitting (232) gives:
% 225.23/38.63  | | | | | | | 
% 225.23/38.63  | | | | | | | Case 1:
% 225.23/38.63  | | | | | | | | 
% 225.23/38.63  | | | | | | | |   (17342)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 &
% 225.23/38.63  | | | | | | | |              op(e2, e3) = e1)
% 225.23/38.63  | | | | | | | | 
% 225.23/38.63  | | | | | | | | BETA: splitting (17342) gives:
% 225.23/38.63  | | | | | | | | 
% 225.23/38.63  | | | | | | | | Case 1:
% 225.23/38.63  | | | | | | | | | 
% 225.23/38.63  | | | | | | | | |   (17343)  all_57_0 = e1 & op(e3, e3) = e1
% 225.23/38.63  | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | ALPHA: (17343) implies:
% 225.23/38.63  | | | | | | | | |   (17344)  all_57_0 = e1
% 225.23/38.63  | | | | | | | | |   (17345)  op(e3, e3) = e1
% 225.23/38.63  | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | BETA: splitting (52) gives:
% 225.23/38.63  | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | Case 1:
% 225.23/38.63  | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | |   (17346)   ~ (all_14_2 = e0)
% 225.23/38.63  | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | REDUCE: (328), (17346) imply:
% 225.23/38.63  | | | | | | | | | |   (17347)   ~ (all_8_2 = e0)
% 225.23/38.63  | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | BETA: splitting (55) gives:
% 225.23/38.63  | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | Case 1:
% 225.23/38.63  | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | |   (17348)   ~ (all_16_2 = e1)
% 225.23/38.63  | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | REDUCE: (324), (17348) imply:
% 225.23/38.63  | | | | | | | | | | |   (17349)   ~ (all_8_2 = e1)
% 225.23/38.63  | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | REF_CLOSE: (42), (85), (107), (150), (160), (164), (168),
% 225.23/38.63  | | | | | | | | | | |            (169), (170), (171), (200), (201), (234), (235),
% 225.23/38.63  | | | | | | | | | | |            (266), (267), (349), (352), (14924), (14927),
% 225.23/38.63  | | | | | | | | | | |            (14935), (14937), (17334), (17335), (17336),
% 225.23/38.63  | | | | | | | | | | |            (17340), (17345), (17347), (17349),
% 225.23/38.63  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.23/38.63  | | | | | | | | | | |            #20.
% 225.23/38.63  | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | Case 2:
% 225.23/38.63  | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | |   (17350)  all_16_2 = e1
% 225.23/38.63  | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | COMBINE_EQS: (324), (17350) imply:
% 225.23/38.63  | | | | | | | | | | |   (17351)  all_8_2 = e1
% 225.23/38.63  | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | SIMP: (17351) implies:
% 225.23/38.63  | | | | | | | | | | |   (17352)  all_8_2 = e1
% 225.23/38.63  | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | REDUCE: (354), (17352) imply:
% 225.23/38.63  | | | | | | | | | | |   (17353)   ~ (all_53_6 = e1)
% 225.23/38.63  | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | REDUCE: (356), (17352) imply:
% 225.23/38.63  | | | | | | | | | | |   (17354)   ~ (all_53_7 = e1)
% 225.23/38.63  | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | REDUCE: (360), (17352) imply:
% 225.23/38.63  | | | | | | | | | | |   (17355)   ~ (all_53_13 = e1)
% 225.23/38.63  | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | REDUCE: (14937), (17352) imply:
% 225.23/38.63  | | | | | | | | | | |   (17356)   ~ (e3 = e1)
% 225.23/38.63  | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | REDUCE: (42), (17352) imply:
% 225.23/38.63  | | | | | | | | | | |   (17357)  op(e2, e2) = e1
% 225.23/38.63  | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | BETA: splitting (211) gives:
% 225.23/38.63  | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | Case 1:
% 225.23/38.63  | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | |   (17358)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 225.23/38.63  | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 225.23/38.63  | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | BETA: splitting (17358) gives:
% 225.23/38.63  | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | Case 1:
% 225.23/38.63  | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | |   (17359)  all_57_9 = e1 & op(e3, e0) = e1
% 225.23/38.63  | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | REF_CLOSE: (169), (17341), (17359), (function-axioms) are
% 225.23/38.63  | | | | | | | | | | | | |            inconsistent by sub-proof #2131.
% 225.23/38.63  | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | Case 2:
% 225.23/38.63  | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | |   (17360)  all_57_10 = e1 & op(e2, e0) = e1
% 225.23/38.63  | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | REF_CLOSE: (165), (17355), (17360), (function-axioms) are
% 225.23/38.63  | | | | | | | | | | | | |            inconsistent by sub-proof #2084.
% 225.23/38.63  | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | End of split
% 225.23/38.63  | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | Case 2:
% 225.23/38.63  | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | |   (17361)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 225.23/38.63  | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 225.23/38.63  | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | BETA: splitting (17361) gives:
% 225.23/38.63  | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | Case 1:
% 225.23/38.63  | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | |   (17362)  all_57_11 = e1 & op(e1, e0) = e1
% 225.23/38.63  | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | ALPHA: (17362) implies:
% 225.23/38.63  | | | | | | | | | | | | |   (17363)  all_57_11 = e1
% 225.23/38.63  | | | | | | | | | | | | |   (17364)  op(e1, e0) = e1
% 225.23/38.63  | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | BETA: splitting (208) gives:
% 225.23/38.63  | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | Case 1:
% 225.23/38.63  | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | |   (17365)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 225.23/38.63  | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 225.23/38.63  | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | BETA: splitting (17365) gives:
% 225.23/38.63  | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | Case 1:
% 225.23/38.63  | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | |   (17366)  all_57_12 = e1 & op(e0, e3) = e1
% 225.23/38.63  | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | REF_CLOSE: (160), (17338), (17366), (function-axioms) are
% 225.23/38.63  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1947.
% 225.23/38.63  | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | Case 2:
% 225.23/38.63  | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | |   (17367)  all_57_13 = e1 & op(e0, e2) = e1
% 225.23/38.63  | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | REF_CLOSE: (159), (17354), (17367), (function-axioms) are
% 225.23/38.63  | | | | | | | | | | | | | | |            inconsistent by sub-proof #330.
% 225.23/38.63  | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | End of split
% 225.23/38.63  | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | Case 2:
% 225.23/38.63  | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | |   (17368)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 225.23/38.63  | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 225.23/38.63  | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | BETA: splitting (17368) gives:
% 225.23/38.63  | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | Case 1:
% 225.23/38.63  | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | |   (17369)  all_57_14 = e1 & op(e0, e1) = e1
% 225.23/38.63  | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | ALPHA: (17369) implies:
% 225.23/38.63  | | | | | | | | | | | | | | |   (17370)  all_57_14 = e1
% 225.23/38.63  | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 225.23/38.63  | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | Case 1:
% 225.23/38.63  | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | |   (17371)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 225.23/38.63  | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 225.23/38.63  | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | BETA: splitting (17371) gives:
% 225.23/38.63  | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.63  | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | |   (17372)  all_57_1 = e1 & op(e3, e2) = e1
% 225.23/38.63  | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | ALPHA: (17372) implies:
% 225.23/38.63  | | | | | | | | | | | | | | | | |   (17373)  all_57_1 = e1
% 225.23/38.63  | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (226), (228), (229),
% 225.23/38.63  | | | | | | | | | | | | | | | | |            (17357), (17373), (function-axioms) are
% 225.23/38.63  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1908.
% 225.23/38.63  | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.63  | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | |   (17374)  all_57_3 = e1 & op(e2, e2) = e1
% 225.23/38.63  | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | ALPHA: (17374) implies:
% 225.23/38.63  | | | | | | | | | | | | | | | | |   (17375)  all_57_3 = e1
% 225.23/38.63  | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_14,
% 225.23/38.63  | | | | | | | | | | | | | | | | |              e1, e0, e1, simplifying with (161), (17364) gives:
% 225.23/38.63  | | | | | | | | | | | | | | | | |   (17376)  all_53_14 = e1
% 225.23/38.63  | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | REDUCE: (368), (17376) imply:
% 225.23/38.63  | | | | | | | | | | | | | | | | |   (17377)   ~ (all_6_2 = e1)
% 225.23/38.63  | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | SIMP: (17377) implies:
% 225.23/38.63  | | | | | | | | | | | | | | | | |   (17378)   ~ (all_6_2 = e1)
% 225.23/38.63  | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | REDUCE: (14929), (17376) imply:
% 225.23/38.63  | | | | | | | | | | | | | | | | |   (17379)   ~ (e2 = e1)
% 225.23/38.63  | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 225.23/38.63  | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | |   (17380)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 225.23/38.63  | | | | | | | | | | | | | | | | | |              all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 225.23/38.63  | | | | | | | | | | | | | | | | | |              op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 225.23/38.63  | | | | | | | | | | | | | | | | | |                all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 225.23/38.63  | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 225.23/38.63  | | | | | | | | | | | | | | | | | |              op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 225.23/38.63  | | | | | | | | | | | | | | | | | |              $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 225.23/38.63  | | | | | | | | | | | | | | | | | |              $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 225.23/38.63  | | | | | | | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 225.23/38.63  | | | | | | | | | | | | | | | | | |                all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 225.23/38.63  | | | | | | | | | | | | | | | | | |              & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 225.23/38.63  | | | | | | | | | | | | | | | | | |                all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 225.23/38.63  | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 225.23/38.63  | | | | | | | | | | | | | | | | | |              & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 225.23/38.63  | | | | | | | | | | | | | | | | | |              $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 225.23/38.63  | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | BETA: splitting (17380) gives:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | |   (17381)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 225.23/38.63  | | | | | | | | | | | | | | | | | | |            all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 225.23/38.63  | | | | | | | | | | | | | | | | | | |            op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 225.23/38.63  | | | | | | | | | | | | | | | | | | |              all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 225.23/38.63  | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 225.23/38.63  | | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 225.23/38.63  | | | | | | | | | | | | | | | | | | |            $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 225.23/38.63  | | | | | | | | | | | | | | | | | | |            $i(all_52_7)
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (14936), (17345), (17381), (function-axioms)
% 225.23/38.63  | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #360.
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | |   (17382)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 225.23/38.63  | | | | | | | | | | | | | | | | | | |            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 225.23/38.63  | | | | | | | | | | | | | | | | | | |            op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 225.23/38.63  | | | | | | | | | | | | | | | | | | |              all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 225.23/38.63  | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 225.23/38.63  | | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 225.23/38.63  | | | | | | | | | | | | | | | | | | |            $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 225.23/38.63  | | | | | | | | | | | | | | | | | | |            $i(all_52_15)
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | ALPHA: (17382) implies:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | |   (17383)  op(e2, e0) = all_52_15
% 225.23/38.63  | | | | | | | | | | | | | | | | | | |   (17384)  op(e2, e2) = all_52_11
% 225.23/38.63  | | | | | | | | | | | | | | | | | | |   (17385)  op(e2, e3) = all_52_9
% 225.23/38.63  | | | | | | | | | | | | | | | | | | |   (17386)  op(all_52_15, all_52_15) = e0
% 225.23/38.63  | | | | | | | | | | | | | | | | | | |   (17387)  op(all_52_11, all_52_11) = e2
% 225.23/38.63  | | | | | | | | | | | | | | | | | | |   (17388)  op(all_52_9, all_52_9) = e3
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_13,
% 225.23/38.63  | | | | | | | | | | | | | | | | | | |              all_52_15, e0, e2, simplifying with (165), (17383)
% 225.23/38.63  | | | | | | | | | | | | | | | | | | |              gives:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | |   (17389)  all_53_13 = all_52_15
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 225.23/38.63  | | | | | | | | | | | | | | | | | | |              all_52_11, e2, e2, simplifying with (17357),
% 225.23/38.63  | | | | | | | | | | | | | | | | | | |              (17384) gives:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | |   (17390)  all_52_11 = e1
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_1,
% 225.23/38.63  | | | | | | | | | | | | | | | | | | |              all_52_9, e3, e2, simplifying with (168), (17385)
% 225.23/38.63  | | | | | | | | | | | | | | | | | | |              gives:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | |   (17391)  all_53_1 = all_52_9
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | REDUCE: (14928), (17389) imply:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | |   (17392)   ~ (all_52_15 = e2)
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | REDUCE: (17387), (17390) imply:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | |   (17393)  op(e1, e1) = e2
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2, e2,
% 225.23/38.63  | | | | | | | | | | | | | | | | | | |              e1, e1, simplifying with (39), (17393) gives:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | |   (17394)  all_6_2 = e2
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | REDUCE: (361), (17394) imply:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | |   (17395)   ~ (all_53_6 = e2)
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | REDUCE: (14936), (17394) imply:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | |   (17396)   ~ (e3 = e2)
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | |   (17397)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2)
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | BETA: splitting (17397) gives:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | |   (17398)  all_57_0 = e2 & op(e3, e3) = e2
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | ALPHA: (17398) implies:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | |   (17399)  op(e3, e3) = e2
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (17345), (17399), (function-axioms) are
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1950.
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | |   (17400)  all_57_2 = e2 & op(e2, e3) = e2
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | ALPHA: (17400) implies:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | |   (17401)  op(e2, e3) = e2
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | |   (17402)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17402) gives:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | |   (17403)  all_57_1 = e2 & op(e3, e2) = e2
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17403) implies:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | |   (17404)  all_57_1 = e2
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | |   (17405)  op(e3, e2) = e2
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | |   (17406)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e2)
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17406) gives:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (17407)  all_57_0 = e2 & op(e3, e3) = e2
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17407) implies:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (17408)  op(e3, e3) = e2
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (237),
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | |            (17404), (17408), (function-axioms) are
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1655.
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e2,
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (17385), (17401) gives:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (17409)  all_52_9 = e2
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17388), (17409) imply:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (17410)  op(e2, e2) = e3
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (17357), (17410), (function-axioms) are
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1912.
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | |   (17411)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e2)
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17411) gives:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (17412)  all_57_4 = e2 & op(e3, e1) = e2
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17412) implies:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (17413)  all_57_4 = e2
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17414)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e0)
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17414) gives:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17415)  all_57_0 = e0 & op(e3, e3) = e0
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17415) implies:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17416)  all_57_0 = e0
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (159), (163), (226),
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (228), (229), (231), (233), (237), (14925),
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17357), (17395), (17413), (17416),
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #39.
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17417)  all_57_1 = e0 & op(e3, e2) = e0
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (17404), (17417) are inconsistent by
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1723.
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17418)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e0)
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17418) gives:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17419)  all_57_4 = e0 & op(e3, e1) = e0
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (17413), (17419) are inconsistent by
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2045.
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17420)  all_57_9 = e0 & op(e3, e0) = e0
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17420) implies:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17421)  op(e3, e0) = e0
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17422)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e3)
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (226), (228), (229),
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (233), (17357), (17404), (17405), (17413),
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17422), (function-axioms) are inconsistent by
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #40.
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17423)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e3)
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17423) gives:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17424)  all_57_4 = e3 & op(e3, e1) = e3
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17424) implies:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17425)  all_57_4 = e3
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (17413), (17425) are inconsistent by
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2482.
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17426)  all_57_9 = e3 & op(e3, e0) = e3
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17426) implies:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17427)  op(e3, e0) = e3
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (17421), (17427), (function-axioms) are
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #313.
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (17428)  all_57_9 = e2 & op(e3, e0) = e2
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17428) implies:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (17429)  op(e3, e0) = e2
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (14927), (17429), (function-axioms) are
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2331.
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | |   (17430)  all_57_3 = e2 & op(e2, e2) = e2
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17430) implies:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | |   (17431)  op(e2, e2) = e2
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (17357), (17431), (function-axioms) are
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2306.
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | |   (17432)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (163), (14925), (17395), (17432),
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | |            #160.
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | |   (17433)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e3) = e2)
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | BETA: splitting (17433) gives:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | |   (17434)  all_57_6 = e2 & op(e1, e3) = e2
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | ALPHA: (17434) implies:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | |   (17435)  all_57_6 = e2
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | |   (17436)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17436) gives:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | |   (17437)  all_57_1 = e2 & op(e3, e2) = e2
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17437) implies:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | |   (17438)  all_57_1 = e2
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | |   (17439)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e3)
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17439) gives:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (17440)  all_57_6 = e3 & op(e1, e3) = e3
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17440) implies:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (17441)  all_57_6 = e3
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (17435), (17441) are inconsistent by
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2463.
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (17442)  all_57_7 = e3 & op(e1, e2) = e3
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17442) implies:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (17443)  all_57_7 = e3
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17444)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17444) gives:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17445)  all_57_2 = e2 & op(e2, e3) = e2
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17445) implies:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17446)  all_57_2 = e2
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17447)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e0)
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (17435), (17443), (17447) are
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1165.
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17448)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17448) gives:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17449)  all_57_8 = e0 & op(e1, e1) = e0
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17449) implies:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17450)  op(e1, e1) = e0
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (17357), (17384), (17387), (17450),
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1843.
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17451)  all_57_11 = e0 & op(e1, e0) = e0
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17451) implies:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17452)  all_57_11 = e0
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (17363), (17452) imply:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17453)  e1 = e0
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (17344), (17453) imply:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17454)  all_57_0 = e0
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17342) gives:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (17343), (17454) are inconsistent by
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2454.
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17455)  all_57_2 = e1 & op(e2, e3) = e1
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (17336), (17455), (function-axioms) are
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2156.
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17456)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e3) = e1)
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17456) gives:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17457)  all_57_6 = e1 & op(e1, e3) = e1
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (17435), (17457) are inconsistent by
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2389.
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17458)  all_57_12 = e1 & op(e0, e3) = e1
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17458) implies:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17459)  all_57_12 = e1
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17460)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e0)
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17460) gives:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17461)  all_57_0 = e0 & op(e3, e3) = e0
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17461) implies:
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17462)  op(e3, e3) = e0
% 225.23/38.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (236), (17435), (17446), (17459),
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17462), (function-axioms) are inconsistent by
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1212.
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17463)  all_57_2 = e0 & op(e2, e3) = e0
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (17446), (17463) are inconsistent by
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1700.
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17464)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = e0)
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17464) gives:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17465)  all_57_6 = e0 & op(e1, e3) = e0
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (17435), (17465) are inconsistent by
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2386.
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17466)  all_57_12 = e0 & op(e0, e3) = e0
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (17459), (17466) are inconsistent by
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1279.
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17467)  all_57_3 = e2 & op(e2, e2) = e2
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17467) implies:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17468)  op(e2, e2) = e2
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (17357), (17468), (function-axioms) are
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2306.
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17469)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17469) gives:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17470)  all_57_5 = e2 & op(e2, e1) = e2
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17470) implies:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17471)  all_57_5 = e2
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17472)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e3)
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17472) gives:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17473)  all_57_4 = e3 & op(e3, e1) = e3
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17473) implies:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17474)  all_57_4 = e3
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17475)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e0)
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17475) gives:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17476)  all_57_0 = e0 & op(e3, e3) = e0
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (17344), (17476) are inconsistent by
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1812.
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17477)  all_57_1 = e0 & op(e3, e2) = e0
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (17438), (17477) are inconsistent by
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1723.
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17478)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e0)
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17478) gives:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17479)  all_57_4 = e0 & op(e3, e1) = e0
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (17474), (17479) are inconsistent by
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2491.
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17480)  all_57_9 = e0 & op(e3, e0) = e0
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17480) implies:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17481)  op(e3, e0) = e0
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17482)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17482) gives:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17483)  all_57_9 = e3 & op(e3, e0) = e3
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17483) implies:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17484)  op(e3, e0) = e3
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (17481), (17484), (function-axioms) are
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #313.
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17485)  all_57_10 = e3 & op(e2, e0) = e3
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17485) implies:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17486)  all_57_10 = e3
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17487)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17487) gives:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17488)  all_57_2 = e0 & op(e2, e3) = e0
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17488) implies:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17489)  all_57_2 = e0
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17490)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e0)
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17490) gives:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17491)  all_57_6 = e0 & op(e1, e3) = e0
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17491) implies:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17492)  all_57_6 = e0
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (17435), (17492) imply:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17493)  e2 = e0
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (17493) implies:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17494)  e2 = e0
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (17471), (17494) imply:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17495)  all_57_5 = e0
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (224), (225), (17357),
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17489), (17495), (function-axioms) are
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1848.
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17496)  all_57_7 = e0 & op(e1, e2) = e0
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (17443), (17496) are inconsistent by
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2042.
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17497)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17497) gives:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17498)  all_57_8 = e0 & op(e1, e1) = e0
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17498) implies:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17499)  op(e1, e1) = e0
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (17357), (17384), (17387), (17499),
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1843.
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17500)  all_57_11 = e0 & op(e1, e0) = e0
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17500) implies:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17501)  all_57_11 = e0
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (17363), (17501) imply:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17502)  e1 = e0
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (17375), (17502) imply:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17503)  all_57_3 = e0
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (223), (224), (17486),
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17489), (17503) are inconsistent by sub-proof
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2247.
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17504)  all_57_3 = e0 & op(e2, e2) = e0
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17504) implies:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17505)  op(e2, e2) = e0
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (17357), (17505), (function-axioms) are
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2352.
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17506)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0)
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17506) gives:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17507)  all_57_5 = e0 & op(e2, e1) = e0
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17507) implies:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17508)  all_57_5 = e0
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (17471), (17508) imply:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17509)  e2 = e0
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14934), (17509) imply:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17510)  all_57_15 = e0
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (169), (212), (14927), (17363),
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17486), (17510), (function-axioms) are
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #19.
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17511)  all_57_10 = e0 & op(e2, e0) = e0
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (207), (14934), (14935), (17383), (17386),
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17392), (17511), (function-axioms) are
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #84.
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17512)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17512) gives:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17513)  all_57_11 = e3 & op(e1, e0) = e3
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17513) implies:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17514)  all_57_11 = e3
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (17363), (17514) are inconsistent by
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2218.
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17515)  all_57_15 = e3 & op(e0, e0) = e3
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17515) implies:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17516)  all_57_15 = e3
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17517)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e0)
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17517) gives:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17518)  all_57_6 = e0 & op(e1, e3) = e0
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17518) implies:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17519)  all_57_6 = e0
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (17435), (17519) are inconsistent by
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1846.
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17520)  all_57_7 = e0 & op(e1, e2) = e0
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17520) implies:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17521)  all_57_7 = e0
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (17435), (17439), (17521) are
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #353.
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17522)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e1, e0) = e3)
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (14936), (17516), (17522),
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1786.
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17523)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17523) gives:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17524)  all_57_8 = e0 & op(e1, e1) = e0
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17524) implies:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17525)  op(e1, e1) = e0
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (17357), (17384), (17387), (17525),
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1843.
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17526)  all_57_11 = e0 & op(e1, e0) = e0
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17526) implies:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17527)  all_57_11 = e0
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (207), (211),
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (215), (217), (14936), (17393), (17435),
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17516), (17527), (function-axioms) are
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1122.
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17528)  all_57_5 = e3 & op(e2, e1) = e3
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17528) implies:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17529)  all_57_5 = e3
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (17471), (17529) are inconsistent by
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2189.
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17530)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e1) = e3)
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17530) gives:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17531)  all_57_8 = e3 & op(e1, e1) = e3
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17531) implies:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17532)  op(e1, e1) = e3
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (17357), (17384), (17387), (17532),
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #155.
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17533)  all_57_14 = e3 & op(e0, e1) = e3
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17533) implies:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17534)  all_57_14 = e3
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (17370), (17534) are inconsistent by
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2326.
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17535)  all_57_10 = e2 & op(e2, e0) = e2
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (14928), (17535), (function-axioms) are
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2432.
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | |   (17536)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e1, e0) = e3)
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17536) gives:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | |   (17537)  all_57_8 = e3 & op(e1, e1) = e3
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17537) implies:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | |   (17538)  op(e1, e1) = e3
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (17357), (17384), (17387), (17538),
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | |            #155.
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | |   (17539)  all_57_11 = e3 & op(e1, e0) = e3
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17539) implies:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | |   (17540)  all_57_11 = e3
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (17363), (17540) are inconsistent by
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2218.
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | |   (17541)  all_57_3 = e2 & op(e2, e2) = e2
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17541) implies:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | |   (17542)  op(e2, e2) = e2
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (17357), (17542), (function-axioms) are
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2306.
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | |   (17543)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (163), (14925), (17395), (17543),
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | |            #160.
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | |   (17544)  all_57_12 = e2 & op(e0, e3) = e2
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | ALPHA: (17544) implies:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | |   (17545)  op(e0, e3) = e2
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (14924), (17545), (function-axioms) are
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1980.
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.64  | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | |   (17546)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 225.23/38.64  | | | | | | | | | | | | | | | | | |              & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 225.23/38.64  | | | | | | | | | | | | | | | | | |              & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 225.23/38.64  | | | | | | | | | | | | | | | | | |                all_52_21) = e1 & op(all_52_23, all_52_23) =
% 225.23/38.64  | | | | | | | | | | | | | | | | | |              e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 225.23/38.64  | | | | | | | | | | | | | | | | | |              all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 225.23/38.64  | | | | | | | | | | | | | | | | | |              = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 225.23/38.64  | | | | | | | | | | | | | | | | | |              $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 225.23/38.64  | | | | | | | | | | | | | | | | | |              & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 225.23/38.64  | | | | | | | | | | | | | | | | | |              e0 & op(all_52_25, all_52_25) = e3 &
% 225.23/38.64  | | | | | | | | | | | | | | | | | |              op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 225.23/38.64  | | | | | | | | | | | | | | | | | |                all_52_29) = e1 & op(all_52_31, all_52_31) =
% 225.23/38.64  | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 225.23/38.64  | | | | | | | | | | | | | | | | | |              all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 225.23/38.64  | | | | | | | | | | | | | | | | | |              = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 225.23/38.64  | | | | | | | | | | | | | | | | | |              $i(all_52_29) & $i(all_52_31))
% 225.23/38.64  | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | BETA: splitting (17546) gives:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | |   (17547)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 225.23/38.64  | | | | | | | | | | | | | | | | | | |            all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 225.23/38.64  | | | | | | | | | | | | | | | | | | |            op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 225.23/38.64  | | | | | | | | | | | | | | | | | | |              all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 225.23/38.64  | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 225.23/38.64  | | | | | | | | | | | | | | | | | | |            & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 225.23/38.64  | | | | | | | | | | | | | | | | | | |            & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 225.23/38.64  | | | | | | | | | | | | | | | | | | |            $i(all_52_23)
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | ALPHA: (17547) implies:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | |   (17548)  op(e1, e0) = all_52_23
% 225.23/38.64  | | | | | | | | | | | | | | | | | | |   (17549)  op(e1, e1) = all_52_21
% 225.23/38.64  | | | | | | | | | | | | | | | | | | |   (17550)  op(all_52_23, all_52_23) = e0
% 225.23/38.64  | | | | | | | | | | | | | | | | | | |   (17551)  op(all_52_21, all_52_21) = e1
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 225.23/38.64  | | | | | | | | | | | | | | | | | | |              all_52_23, e0, e1, simplifying with (17364),
% 225.23/38.64  | | | | | | | | | | | | | | | | | | |              (17548) gives:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | |   (17552)  all_52_23 = e1
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 225.23/38.64  | | | | | | | | | | | | | | | | | | |              all_52_21, e1, e1, simplifying with (39), (17549)
% 225.23/38.64  | | | | | | | | | | | | | | | | | | |              gives:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | |   (17553)  all_52_21 = all_6_2
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | REDUCE: (17551), (17553) imply:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | |   (17554)  op(all_6_2, all_6_2) = e1
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | REDUCE: (17550), (17552) imply:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | |   (17555)  op(e1, e1) = e0
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2, e0,
% 225.23/38.64  | | | | | | | | | | | | | | | | | | |              e1, e1, simplifying with (39), (17555) gives:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | |   (17556)  all_6_2 = e0
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | REDUCE: (14936), (17556) imply:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | |   (17557)   ~ (e3 = e0)
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | REDUCE: (17378), (17556) imply:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | |   (17558)   ~ (e1 = e0)
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | REDUCE: (17554), (17556) imply:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | |   (17559)  op(e0, e0) = e1
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (159), (207), (209),
% 225.23/38.64  | | | | | | | | | | | | | | | | | | |            (210), (14925), (17370), (17559),
% 225.23/38.64  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.23/38.64  | | | | | | | | | | | | | | | | | | |            #2175.
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | |   (17560)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 225.23/38.64  | | | | | | | | | | | | | | | | | | |            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 225.23/38.64  | | | | | | | | | | | | | | | | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 225.23/38.64  | | | | | | | | | | | | | | | | | | |              all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 225.23/38.64  | | | | | | | | | | | | | | | | | | |            & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 225.23/38.64  | | | | | | | | | | | | | | | | | | |            & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 225.23/38.64  | | | | | | | | | | | | | | | | | | |            & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 225.23/38.64  | | | | | | | | | | | | | | | | | | |            $i(all_52_31)
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (14935), (17357), (17560), (function-axioms)
% 225.23/38.64  | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #50.
% 225.23/38.64  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.64  | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | End of split
% 225.23/38.64  | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | End of split
% 225.23/38.64  | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | Case 2:
% 225.23/38.64  | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | |   (17561)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 225.23/38.64  | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 225.23/38.64  | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | BETA: splitting (17561) gives:
% 225.23/38.64  | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.64  | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | |   (17562)  all_57_7 = e1 & op(e1, e2) = e1
% 225.23/38.64  | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (17353), (17562), (function-axioms) are
% 225.23/38.64  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2265.
% 225.23/38.64  | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.64  | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | |   (17563)  all_57_13 = e1 & op(e0, e2) = e1
% 225.23/38.64  | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (17354), (17563), (function-axioms) are
% 225.23/38.64  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #330.
% 225.23/38.64  | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | End of split
% 225.23/38.64  | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | End of split
% 225.23/38.64  | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | Case 2:
% 225.23/38.64  | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | |   (17564)  all_57_15 = e1 & op(e0, e0) = e1
% 225.23/38.64  | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | ALPHA: (17564) implies:
% 225.23/38.64  | | | | | | | | | | | | | | |   (17565)  op(e0, e0) = e1
% 225.23/38.64  | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | REF_CLOSE: (6), (14935), (17565), (function-axioms) are
% 225.23/38.64  | | | | | | | | | | | | | | |            inconsistent by sub-proof #2177.
% 225.23/38.64  | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | End of split
% 225.23/38.64  | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | End of split
% 225.23/38.64  | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | Case 2:
% 225.23/38.64  | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | |   (17566)  all_57_15 = e1 & op(e0, e0) = e1
% 225.23/38.64  | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | ALPHA: (17566) implies:
% 225.23/38.64  | | | | | | | | | | | | |   (17567)  op(e0, e0) = e1
% 225.23/38.64  | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | REF_CLOSE: (6), (14935), (17567), (function-axioms) are
% 225.23/38.64  | | | | | | | | | | | | |            inconsistent by sub-proof #2177.
% 225.23/38.64  | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | End of split
% 225.23/38.64  | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | End of split
% 225.23/38.64  | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | End of split
% 225.23/38.64  | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | Case 2:
% 225.23/38.64  | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | |   (17568)  all_14_2 = e0
% 225.23/38.64  | | | | | | | | | |   (17569)  ( ~ (all_14_0 = e1) & op(all_14_1, e2) = all_14_0
% 225.23/38.64  | | | | | | | | | |              & op(e2, e0) = all_14_1 & $i(all_14_0) &
% 225.23/38.64  | | | | | | | | | |              $i(all_14_1)) | ( ~ (all_14_1 = e3) & op(e2, e0)
% 225.23/38.64  | | | | | | | | | |              = all_14_1 & $i(all_14_1))
% 225.23/38.64  | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | COMBINE_EQS: (328), (17568) imply:
% 225.23/38.64  | | | | | | | | | |   (17570)  all_8_2 = e0
% 225.23/38.64  | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | SIMP: (17570) implies:
% 225.23/38.64  | | | | | | | | | |   (17571)  all_8_2 = e0
% 225.23/38.64  | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | COMBINE_EQS: (290), (17571) imply:
% 225.23/38.64  | | | | | | | | | |   (17572)  all_50_2 = e0
% 225.23/38.64  | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | REDUCE: (349), (17571) imply:
% 225.23/38.64  | | | | | | | | | |   (17573)   ~ (all_53_1 = e0)
% 225.23/38.64  | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | REDUCE: (352), (17571) imply:
% 225.23/38.64  | | | | | | | | | |   (17574)   ~ (all_53_4 = e0)
% 225.23/38.64  | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | REDUCE: (354), (17571) imply:
% 225.23/38.64  | | | | | | | | | |   (17575)   ~ (all_53_6 = e0)
% 225.23/38.64  | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | REDUCE: (356), (17571) imply:
% 225.23/38.64  | | | | | | | | | |   (17576)   ~ (all_53_7 = e0)
% 225.23/38.64  | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | REDUCE: (358), (17571) imply:
% 225.23/38.64  | | | | | | | | | |   (17577)   ~ (all_53_9 = e0)
% 225.23/38.64  | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | REDUCE: (360), (17571) imply:
% 225.23/38.64  | | | | | | | | | |   (17578)   ~ (all_53_13 = e0)
% 225.23/38.64  | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | REDUCE: (14937), (17571) imply:
% 225.23/38.64  | | | | | | | | | |   (17579)   ~ (e3 = e0)
% 225.23/38.64  | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | BETA: splitting (222) gives:
% 225.23/38.64  | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | Case 1:
% 225.23/38.64  | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | |   (17580)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 225.23/38.64  | | | | | | | | | | |              & op(e2, e2) = e0)
% 225.23/38.64  | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | BETA: splitting (17580) gives:
% 225.23/38.64  | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | Case 1:
% 225.23/38.64  | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | |   (17581)  all_57_2 = e0 & op(e2, e3) = e0
% 225.23/38.64  | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | ALPHA: (17581) implies:
% 225.23/38.64  | | | | | | | | | | | |   (17582)  op(e2, e3) = e0
% 225.23/38.64  | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | REF_CLOSE: (168), (17573), (17582), (function-axioms) are
% 225.23/38.64  | | | | | | | | | | | |            inconsistent by sub-proof #1943.
% 225.23/38.64  | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | Case 2:
% 225.23/38.64  | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | |   (17583)  all_57_3 = e0 & op(e2, e2) = e0
% 225.23/38.64  | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | ALPHA: (17583) implies:
% 225.23/38.64  | | | | | | | | | | | |   (17584)  all_57_3 = e0
% 225.23/38.64  | | | | | | | | | | | |   (17585)  op(e2, e2) = e0
% 225.23/38.64  | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | BETA: splitting (67) gives:
% 225.23/38.64  | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | Case 1:
% 225.23/38.64  | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | |   (17586)   ~ (all_24_2 = e0)
% 225.23/38.64  | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | REDUCE: (315), (17586) imply:
% 225.23/38.64  | | | | | | | | | | | | |   (17587)   ~ (all_6_2 = e0)
% 225.23/38.64  | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | BETA: splitting (79) gives:
% 225.23/38.64  | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | Case 1:
% 225.23/38.64  | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | |   (17588)   ~ (all_32_2 = e2)
% 225.23/38.64  | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | REDUCE: (14923), (17588) imply:
% 225.23/38.64  | | | | | | | | | | | | | |   (17589)  $false
% 225.23/38.64  | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | CLOSE: (17589) is inconsistent.
% 225.23/38.64  | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | Case 2:
% 225.23/38.64  | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | |   (17590)  ( ~ (all_32_0 = e1) & op(all_32_1, e0) = all_32_0
% 225.23/38.64  | | | | | | | | | | | | | |              & op(e0, e2) = all_32_1 & $i(all_32_0) &
% 225.23/38.64  | | | | | | | | | | | | | |              $i(all_32_1)) | ( ~ (all_32_1 = e3) & op(e0, e2)
% 225.23/38.64  | | | | | | | | | | | | | |              = all_32_1 & $i(all_32_1))
% 225.23/38.64  | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | BETA: splitting (88) gives:
% 225.23/38.64  | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | Case 1:
% 225.23/38.64  | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | |   (17591)   ~ (all_38_2 = e2)
% 225.23/38.64  | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | REDUCE: (249), (17591) imply:
% 225.23/38.64  | | | | | | | | | | | | | | |   (17592)   ~ (all_6_2 = e2)
% 225.23/38.64  | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 225.23/38.64  | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | Case 1:
% 225.23/38.64  | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | |   (17593)  all_55_10 = e3
% 225.23/38.64  | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | REF_CLOSE: (336), (14936), (17593) are inconsistent by
% 225.23/38.64  | | | | | | | | | | | | | | | |            sub-proof #2500.
% 225.23/38.64  | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | Case 2:
% 225.23/38.64  | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | |   (17594)   ~ (all_55_10 = e3)
% 225.23/38.64  | | | | | | | | | | | | | | | |   (17595)  all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 225.23/38.64  | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | BETA: splitting (17595) gives:
% 225.23/38.64  | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.64  | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | |   (17596)  all_55_10 = e2
% 225.23/38.64  | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (17592), (17596) are inconsistent by
% 225.23/38.64  | | | | | | | | | | | | | | | | |            sub-proof #2499.
% 225.23/38.64  | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.64  | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | |   (17597)   ~ (all_55_10 = e2)
% 225.23/38.64  | | | | | | | | | | | | | | | | |   (17598)  all_55_10 = e1 | all_55_10 = e0
% 225.23/38.64  | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | BETA: splitting (17598) gives:
% 225.23/38.64  | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.64  | | | | | | | | | | | | | | | | | | 
% 225.23/38.64  | | | | | | | | | | | | | | | | | |   (17599)  all_55_10 = e1
% 225.23/38.65  | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (336), (17599) imply:
% 225.23/38.65  | | | | | | | | | | | | | | | | | |   (17600)  all_6_2 = e1
% 225.23/38.65  | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | SIMP: (17600) implies:
% 225.23/38.65  | | | | | | | | | | | | | | | | | |   (17601)  all_6_2 = e1
% 225.23/38.65  | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | REDUCE: (366), (17601) imply:
% 225.23/38.65  | | | | | | | | | | | | | | | | | |   (17602)   ~ (all_53_11 = e1)
% 225.23/38.65  | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | REDUCE: (368), (17601) imply:
% 225.23/38.65  | | | | | | | | | | | | | | | | | |   (17603)   ~ (all_53_14 = e1)
% 225.23/38.65  | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | REDUCE: (14936), (17601) imply:
% 225.23/38.65  | | | | | | | | | | | | | | | | | |   (17604)   ~ (e3 = e1)
% 225.23/38.65  | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | REDUCE: (17592), (17601) imply:
% 225.23/38.65  | | | | | | | | | | | | | | | | | |   (17605)   ~ (e2 = e1)
% 225.23/38.65  | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | REDUCE: (39), (17601) imply:
% 225.23/38.65  | | | | | | | | | | | | | | | | | |   (17606)  op(e1, e1) = e1
% 225.23/38.65  | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | |   (17607)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 225.23/38.65  | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | BETA: splitting (17607) gives:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | |   (17608)  all_57_12 = e1 & op(e0, e3) = e1
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (17338), (17608), (function-axioms) are
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1947.
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | |   (17609)  all_57_13 = e1 & op(e0, e2) = e1
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | ALPHA: (17609) implies:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | |   (17610)  op(e0, e2) = e1
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | |   (17611)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17611) gives:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | |   (17612)  all_57_9 = e1 & op(e3, e0) = e1
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (17341), (17612), (function-axioms) are
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2131.
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | |   (17613)  all_57_10 = e1 & op(e2, e0) = e1
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17613) implies:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | |   (17614)  op(e2, e0) = e1
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_7, e1,
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (159), (17610) gives:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | |   (17615)  all_53_7 = e1
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_13,
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | |              e1, e0, e2, simplifying with (165), (17614) gives:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | |   (17616)  all_53_13 = e1
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (129), (17615) imply:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | |   (17617)   ~ (all_53_6 = e1)
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (106) gives:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | |   (17618)   ~ (all_50_2 = e0)
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17572), (17618) imply:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | |   (17619)  $false
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (17619) is inconsistent.
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | |   (17620)  ( ~ (all_50_0 = e3) & op(all_50_1, e2) = all_50_0
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e0) = all_50_1 & $i(all_50_0) &
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_50_1)) | ( ~ (all_50_1 = e1) & op(e2, e0)
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | |              = all_50_1 & $i(all_50_1))
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | |   (17621)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | |              all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | |              op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | |                all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | |                all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | |              & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | |                all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17621) gives:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | |   (17622)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_7)
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17622) implies:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | |   (17623)  op(e3, e3) = all_52_1
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | |   (17624)  op(all_52_1, all_52_1) = e3
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (14922), (17345), (17590), (17606), (17610),
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | |            (17623), (17624), (function-axioms) are
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #18.
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | |   (17625)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_15)
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17625) implies:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | |   (17626)  op(e2, e0) = all_52_15
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | |   (17627)  op(all_52_15, all_52_15) = e0
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17569) gives:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17628)   ~ (all_14_0 = e1) & op(all_14_1, e2) = all_14_0 &
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = all_14_1 & $i(all_14_0) &
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_14_1)
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17628) implies:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17629)  op(e2, e0) = all_14_1
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (17606), (17614), (17626), (17627), (17629),
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | |            #17.
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17630)   ~ (all_14_1 = e3) & op(e2, e0) = all_14_1 &
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_14_1)
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17630) implies:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17631)  op(e2, e0) = all_14_1
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (17606), (17614), (17626), (17627), (17631),
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | |            #17.
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | |   (17632)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | |              & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | |              & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | |                all_52_21) = e1 & op(all_52_23, all_52_23) =
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | |              all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | |              = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | |              & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(all_52_25, all_52_25) = e3 &
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | |              op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | |                all_52_29) = e1 & op(all_52_31, all_52_31) =
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | |              all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | |              = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_29) & $i(all_52_31))
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17632) gives:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | |   (17633)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | |            & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_23)
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17633) implies:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | |   (17634)  op(e1, e2) = all_52_19
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | |   (17635)  op(all_52_19, all_52_19) = e2
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17620) gives:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17636)   ~ (all_50_0 = e3) & op(all_50_1, e2) = all_50_0 &
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = all_50_1 & $i(all_50_0) &
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_50_1)
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17636) implies:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17637)  op(e2, e0) = all_50_1
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17569) gives:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17638)   ~ (all_14_0 = e1) & op(all_14_1, e2) = all_14_0 &
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = all_14_1 & $i(all_14_0) &
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_14_1)
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17638) implies:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17639)  op(e2, e0) = all_14_1
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (196), (256), (17569), (17575), (17585),
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17614), (17617), (17620), (17634), (17635),
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17637), (17639), (function-axioms) are
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #16.
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17640)   ~ (all_14_1 = e3) & op(e2, e0) = all_14_1 &
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_14_1)
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17640) implies:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17641)  op(e2, e0) = all_14_1
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (196), (256), (17569), (17575), (17585),
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17614), (17617), (17620), (17634), (17635),
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17637), (17641), (function-axioms) are
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #16.
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17642)   ~ (all_50_1 = e1) & op(e2, e0) = all_50_1 &
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_50_1)
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17569), (17614), (17642), (function-axioms) are
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #272.
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | |   (17643)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | |            & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_31)
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17643) implies:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | |   (17644)  op(e0, e2) = all_52_27
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | |   (17645)  op(all_52_27, all_52_27) = e2
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17620) gives:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_27, e2, e0, simplifying with (17610),
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | |              (17644) gives:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17646)  all_52_27 = e1
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17645), (17646) imply:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17647)  op(e1, e1) = e2
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (17606), (17647), (function-axioms) are
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2423.
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17648)   ~ (all_50_1 = e1) & op(e2, e0) = all_50_1 &
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_50_1)
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17569), (17614), (17648), (function-axioms) are
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #272.
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | |   (17649)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (161), (14935), (17603), (17649),
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | |            #88.
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | |   (17650)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 225.23/38.65  | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (158), (14935), (17602), (17650),
% 225.23/38.65  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.23/38.65  | | | | | | | | | | | | | | | | | | |            #15.
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.65  | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | |   (17651)  all_55_10 = e0
% 225.23/38.65  | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (17587), (17651) are inconsistent by
% 225.23/38.65  | | | | | | | | | | | | | | | | | |            sub-proof #2118.
% 225.23/38.65  | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | End of split
% 225.23/38.65  | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | End of split
% 225.23/38.65  | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | End of split
% 225.23/38.65  | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | Case 2:
% 225.23/38.65  | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | |   (17652)  all_38_2 = e2
% 225.23/38.65  | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | COMBINE_EQS: (249), (17652) imply:
% 225.23/38.65  | | | | | | | | | | | | | | |   (17653)  all_6_2 = e2
% 225.23/38.65  | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | REDUCE: (14936), (17653) imply:
% 225.23/38.65  | | | | | | | | | | | | | | |   (17654)   ~ (e3 = e2)
% 225.23/38.65  | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | REDUCE: (39), (17653) imply:
% 225.23/38.65  | | | | | | | | | | | | | | |   (17655)  op(e1, e1) = e2
% 225.23/38.65  | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 225.23/38.65  | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | Case 1:
% 225.23/38.65  | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | |   (17656)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 225.23/38.65  | | | | | | | | | | | | | | | |              & op(e2, e3) = e2)
% 225.23/38.65  | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | BETA: splitting (17656) gives:
% 225.23/38.65  | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.65  | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | |   (17657)  all_57_0 = e2 & op(e3, e3) = e2
% 225.23/38.65  | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | ALPHA: (17657) implies:
% 225.23/38.65  | | | | | | | | | | | | | | | | |   (17658)  op(e3, e3) = e2
% 225.23/38.65  | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (17345), (17658), (function-axioms) are
% 225.23/38.65  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1950.
% 225.23/38.65  | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.65  | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | |   (17659)  all_57_2 = e2 & op(e2, e3) = e2
% 225.23/38.65  | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | ALPHA: (17659) implies:
% 225.23/38.65  | | | | | | | | | | | | | | | | |   (17660)  all_57_2 = e2
% 225.23/38.65  | | | | | | | | | | | | | | | | |   (17661)  op(e2, e3) = e2
% 225.23/38.65  | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 225.23/38.65  | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | |   (17662)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 225.23/38.65  | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e2)
% 225.23/38.65  | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | BETA: splitting (17662) gives:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | |   (17663)  all_57_0 = e2 & op(e3, e3) = e2
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | ALPHA: (17663) implies:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | |   (17664)  op(e3, e3) = e2
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (17345), (17664), (function-axioms) are
% 225.23/38.65  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1950.
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | |   (17665)  all_57_1 = e2 & op(e3, e2) = e2
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | ALPHA: (17665) implies:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | |   (17666)  op(e3, e2) = e2
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_1, e2,
% 225.23/38.65  | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (168), (17661) gives:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | |   (17667)  all_53_1 = e2
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_4, e2,
% 225.23/38.65  | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (171), (17666) gives:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | |   (17668)  all_53_4 = e2
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | REDUCE: (149), (17667) imply:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | |   (17669)   ~ (all_53_3 = e2)
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | REDUCE: (146), (17667) imply:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | |   (17670)   ~ (all_53_13 = e2)
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | REDUCE: (136), (17668) imply:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | |   (17671)   ~ (all_53_7 = e2)
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | REDUCE: (135), (17668) imply:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | |   (17672)   ~ (all_53_8 = e2)
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | SIMP: (17672) implies:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | |   (17673)   ~ (all_53_8 = e2)
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | REDUCE: (134), (17668) imply:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | |   (17674)   ~ (all_53_12 = e2)
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | |   (17675)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | |              all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | |              op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | |                all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | |              $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | |              $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | |                all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | |              & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | |                all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | |              & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | |              $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (42), (14937), (17585), (17661), (17666),
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | |            (17675), (function-axioms) are inconsistent by
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | |            sub-proof #27.
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | |   (17676)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | |              & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | |              & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | |                all_52_21) = e1 & op(all_52_23, all_52_23) =
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | |              all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | |              = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | |              $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | |              & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | |              e0 & op(all_52_25, all_52_25) = e3 &
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | |              op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | |                all_52_29) = e1 & op(all_52_31, all_52_31) =
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | |              all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | |              = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | |              $i(all_52_29) & $i(all_52_31))
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | BETA: splitting (17676) gives:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | |   (17677)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | |            all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | |            op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | |              all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | |            & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | |            & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | |            $i(all_52_23)
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (17585), (17655), (17677), (function-axioms)
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #26.
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | |   (17678)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | |            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | |              all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | |            & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | |            & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | |            & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | |            $i(all_52_31)
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | ALPHA: (17678) implies:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | |   (17679)  op(e0, e0) = all_52_31
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | |   (17680)  op(e0, e1) = all_52_29
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | |   (17681)  op(e0, e3) = all_52_25
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | |   (17682)  op(all_52_31, all_52_31) = e0
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | |   (17683)  op(all_52_29, all_52_29) = e1
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | |   (17684)  op(all_52_25, all_52_25) = e3
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | |              all_52_31, e0, e0, simplifying with (14935),
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | |              (17679) gives:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | |   (17685)  all_52_31 = e2
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_11,
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | |              all_52_29, e1, e0, simplifying with (158), (17680)
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | |              gives:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | |   (17686)  all_53_11 = all_52_29
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_3,
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | |              all_52_25, e3, e0, simplifying with (160), (17681)
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | |              gives:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | |   (17687)  all_53_3 = all_52_25
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | |   (17688)  all_55_2 = e3
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (17688) imply:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | |   (17689)  all_53_8 = e3
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | SIMP: (17689) implies:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | |   (17690)  all_53_8 = e3
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (124), (17690) imply:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | |   (17691)   ~ (all_53_9 = e3)
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | SIMP: (17691) implies:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | |   (17692)   ~ (all_53_9 = e3)
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (17690) imply:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | |   (17693)   ~ (all_53_12 = e3)
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | SIMP: (17693) implies:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | |   (17694)   ~ (all_53_12 = e3)
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | |   (17695)  all_55_3 = e3
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (17695) imply:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | |   (17696)  all_53_12 = e3
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17694), (17696) imply:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | |   (17697)  $false
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (17697) is inconsistent.
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | |   (17698)   ~ (all_55_3 = e3)
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | |   (17699)  all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17699) gives:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | |   (17700)  all_55_3 = e2
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (14927), (17700) are inconsistent by
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1612.
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | |   (17701)   ~ (all_55_3 = e2)
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | |   (17702)  all_55_3 = e1 | all_55_3 = e0
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17702) gives:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | |   (17703)  all_55_3 = e1
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (17341), (17703) are inconsistent by
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #324.
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | |   (17704)  all_55_3 = e0
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (17704) imply:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | |   (17705)  all_53_12 = e0
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (17705) implies:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | |   (17706)  all_53_12 = e0
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (17706) imply:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | |   (17707)   ~ (all_53_14 = e0)
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (17707) implies:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | |   (17708)   ~ (all_53_14 = e0)
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14927), (17706) imply:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | |   (17709)   ~ (e2 = e0)
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17341), (17706) imply:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | |   (17710)   ~ (e1 = e0)
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17711)  all_57_15 = e0 & op(e0, e0) = e0
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17711) implies:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17712)  all_57_15 = e0
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17713)  op(e0, e0) = e0
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (85), (107),
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | |            (145), (160), (161), (163), (164), (166), (170),
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | |            (193), (208), (209), (210), (214), (218), (247),
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | |            (17334), (17335), (17338), (17340), (17345),
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | |            (17575), (17577), (17585), (17587), (17708),
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | |            (17712), (17713), (function-axioms) are
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #300.
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17714)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17714) implies:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17715)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0)
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17716)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e3)
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (42), (14937), (17660), (17716),
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #14.
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17717)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17717) gives:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17718)  all_57_5 = e3 & op(e2, e1) = e3
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (17692), (17718), (function-axioms) are
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #270.
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17719)  all_57_10 = e3 & op(e2, e0) = e3
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17719) implies:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17720)  all_57_10 = e3
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17721)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e0)
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17721) gives:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17722)  all_57_4 = e0 & op(e3, e1) = e0
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17722) implies:
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17723)  all_57_4 = e0
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (159), (219),
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (220), (221), (14935), (14936), (17576), (17679),
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17681), (17684), (17715), (17723),
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #13.
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17724)  all_57_5 = e0 & op(e2, e1) = e0
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17724) implies:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17725)  all_57_5 = e0
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17584), (17585), (17720), (17725),
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2348.
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17726)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17726) gives:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17727)  all_57_8 = e0 & op(e1, e1) = e0
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (17587), (17727), (function-axioms) are
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2412.
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17728)  all_57_14 = e0 & op(e0, e1) = e0
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17728) implies:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17729)  op(e0, e1) = e0
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (268), (17341), (17587), (17679), (17680),
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17682), (17683), (17702), (17729),
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #35.
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | |   (17730)   ~ (all_55_2 = e3)
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | |   (17731)  all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (269), (17730) imply:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | |   (17732)   ~ (all_53_8 = e3)
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17731) gives:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | |   (17733)  all_55_2 = e2
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (17733) imply:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | |   (17734)  all_53_8 = e2
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17673), (17734) imply:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | |   (17735)  $false
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (17735) is inconsistent.
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | |   (17736)   ~ (all_55_2 = e2)
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | |   (17737)  all_55_2 = e1 | all_55_2 = e0
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17737) gives:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | |   (17738)  all_55_2 = e1
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (17738) imply:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | |   (17739)  all_53_8 = e1
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17340), (17739) imply:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | |   (17740)  $false
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (17740) is inconsistent.
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | |   (17741)  all_55_2 = e0
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (17741) imply:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | |   (17742)  all_53_8 = e0
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (124), (17742) imply:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | |   (17743)   ~ (all_53_9 = e0)
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (17742) imply:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | |   (17744)   ~ (all_53_12 = e0)
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (17744) implies:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | |   (17745)   ~ (all_53_12 = e0)
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17673), (17742) imply:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | |   (17746)   ~ (e2 = e0)
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17340), (17742) imply:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | |   (17747)   ~ (e1 = e0)
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | |   (17748)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e0)
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17748) gives:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17749)  all_57_4 = e0 & op(e3, e1) = e0
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17749) implies:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17750)  all_57_4 = e0
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17751)  all_57_15 = e0 & op(e0, e0) = e0
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17751) implies:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17752)  op(e0, e0) = e0
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (14935), (17752), (function-axioms) are
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #86.
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17753)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17753) implies:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17754)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0)
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (159), (219),
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (220), (221), (14935), (14936), (17576), (17679),
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17681), (17684), (17750), (17754),
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #13.
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17755)  all_57_5 = e0 & op(e2, e1) = e0
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (17577), (17755), (function-axioms) are
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2023.
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | |   (17756)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17756) gives:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17757)  all_57_8 = e0 & op(e1, e1) = e0
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (17587), (17757), (function-axioms) are
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2412.
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17758)  all_57_14 = e0 & op(e0, e1) = e0
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17758) implies:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17759)  all_57_14 = e0
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17760)  op(e0, e1) = e0
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17761)  all_55_3 = e3
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (17761) imply:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17762)  all_53_12 = e3
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (17762) implies:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17763)  all_53_12 = e3
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (114), (17763) imply:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17764)   ~ (all_53_13 = e3)
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (17764) implies:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17765)   ~ (all_53_13 = e3)
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17766)  all_57_15 = e0 & op(e0, e0) = e0
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17766) implies:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17767)  all_57_15 = e0
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17768)  op(e0, e0) = e0
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (208), (209),
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (210), (17338), (17759), (17767), (17768),
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #320.
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17769)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17769) implies:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17770)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0)
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17771)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0)
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17772)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17772) gives:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17773)  all_57_12 = e1 & op(e0, e3) = e1
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (17338), (17773), (function-axioms) are
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1947.
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17774)  all_57_13 = e1 & op(e0, e2) = e1
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17774) implies:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17775)  all_57_13 = e1
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17776)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e3)
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17776) gives:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17777)  all_57_1 = e3 & op(e3, e2) = e3
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17777) implies:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17778)  op(e3, e2) = e3
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (17666), (17778), (function-axioms) are
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1549.
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17779)  all_57_3 = e3 & op(e2, e2) = e3
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17779) implies:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17780)  op(e2, e2) = e3
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (14937), (17780), (function-axioms) are
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #140.
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17781)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17781) gives:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17782)  all_57_7 = e3 & op(e1, e2) = e3
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17782) implies:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17783)  all_57_7 = e3
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17784)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e3)
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (42), (14937), (17660), (17784),
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #14.
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17785)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17785) gives:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17786)  all_57_5 = e3 & op(e2, e1) = e3
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17786) implies:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17787)  all_57_5 = e3
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17771) gives:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17788)  all_57_9 = e0 & op(e3, e0) = e0
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (17745), (17788), (function-axioms) are
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2434.
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17789)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 =
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17789) gives:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17790)  all_57_10 = e0 & op(e2, e0) = e0
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17790) implies:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17791)  all_57_10 = e0
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (223), (224), (17584),
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17787), (17791) are inconsistent by sub-proof
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1518.
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17792)  all_57_11 = e0 & op(e1, e0) = e0
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17792) implies:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17793)  all_57_11 = e0
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17794)  op(e1, e0) = e0
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17795)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e0)
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17795) gives:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17796)  all_57_0 = e0 & op(e3, e3) = e0
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17796) implies:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17797)  op(e3, e3) = e0
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (39), (42), (88), (107),
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (111), (118), (119), (126), (140), (158), (159),
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (160), (161), (163), (165), (166), (168), (195),
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (198), (199), (208), (209), (210), (211), (214),
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (215), (217), (218), (219), (221), (222), (224),
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (225), (228), (231), (233), (234), (237), (249),
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (258), (259), (336), (361), (364), (368), (14924),
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14925), (14928), (14929), (14935), (14936),
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (14937), (17585), (17759), (17760), (17770),
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17793), (17794), (17797), (function-axioms) are
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #22.
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17798)  all_57_1 = e0 & op(e3, e2) = e0
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17798) implies:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17799)  all_57_1 = e0
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (227), (228), (17584),
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17783), (17799) are inconsistent by sub-proof
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2098.
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17800)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e0)
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17800) gives:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17801)  all_57_4 = e0 & op(e3, e1) = e0
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17801) implies:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17802)  all_57_4 = e0
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (219), (17655), (17759), (17787),
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17802), (function-axioms) are inconsistent by
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2379.
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17803)  all_57_9 = e0 & op(e3, e0) = e0
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (17745), (17803), (function-axioms) are
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2434.
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17804)  all_57_10 = e3 & op(e2, e0) = e3
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17804) implies:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17805)  op(e2, e0) = e3
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (17765), (17805), (function-axioms) are
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2301.
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17806)  all_57_13 = e3 & op(e0, e2) = e3
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (17775), (17806) are inconsistent by
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1977.
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17807)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17807) gives:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17808)  all_57_14 = e1 & op(e0, e1) = e1
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (17759), (17808) are inconsistent by
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2381.
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17809)  all_57_15 = e1 & op(e0, e0) = e1
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17809) implies:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17810)  op(e0, e0) = e1
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (17587), (17679), (17682), (17810),
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2086.
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17811)  all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (268), (14927), (17341), (17587), (17679),
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17680), (17682), (17683), (17760), (17811),
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #34.
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.66  | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | |   (17812)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 225.23/38.66  | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e2)
% 225.23/38.66  | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | BETA: splitting (17812) gives:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | |   (17813)  all_57_4 = e2 & op(e3, e1) = e2
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | ALPHA: (17813) implies:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | |   (17814)  all_57_4 = e2
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | |   (17815)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e0)
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | BETA: splitting (17815) gives:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | |   (17816)  all_57_4 = e0 & op(e3, e1) = e0
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | ALPHA: (17816) implies:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | |   (17817)  all_57_4 = e0
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (17814), (17817) imply:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | |   (17818)  e2 = e0
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (17660), (17818) imply:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | |   (17819)  all_57_2 = e0
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | |            (17584), (17819) are inconsistent by sub-proof
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | |            #2246.
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | |   (17820)  all_57_5 = e0 & op(e2, e1) = e0
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (17577), (17820), (function-axioms) are
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2023.
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | |   (17821)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | BETA: splitting (17821) gives:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | |   (17822)  all_57_8 = e0 & op(e1, e1) = e0
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (17587), (17822), (function-axioms) are
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2412.
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | |   (17823)  all_57_14 = e0 & op(e0, e1) = e0
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | ALPHA: (17823) implies:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | |   (17824)  all_57_14 = e0
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | |   (17825)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e1)
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17825) gives:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | |   (17826)  all_57_4 = e1 & op(e3, e1) = e1
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (17340), (17826), (function-axioms) are
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #116.
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | |   (17827)  all_57_5 = e1 & op(e2, e1) = e1
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17827) implies:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | |   (17828)  all_57_5 = e1
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (39), (218), (221),
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | |            (14936), (17587), (17814), (17828),
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | |            #339.
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | |   (17829)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e1) = e1)
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17829) gives:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | |   (17830)  all_57_8 = e1 & op(e1, e1) = e1
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17830) implies:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | |   (17831)  op(e1, e1) = e1
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (17655), (17831), (function-axioms) are
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2423.
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | |   (17832)  all_57_14 = e1 & op(e0, e1) = e1
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (17832) implies:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | |   (17833)  all_57_14 = e1
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (17824), (17833) are inconsistent by
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2122.
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | |   (17834)  all_57_9 = e2 & op(e3, e0) = e2
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | ALPHA: (17834) implies:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | |   (17835)  op(e3, e0) = e2
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (14927), (17835), (function-axioms) are
% 225.23/38.66  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2331.
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.66  | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | End of split
% 225.23/38.66  | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | End of split
% 225.23/38.66  | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | Case 2:
% 225.23/38.66  | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | |   (17836)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 225.23/38.66  | | | | | | | | | | | | | | | |              e2 & op(e0, e3) = e2)
% 225.23/38.66  | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | BETA: splitting (17836) gives:
% 225.23/38.66  | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.66  | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | |   (17837)  all_57_6 = e2 & op(e1, e3) = e2
% 225.23/38.66  | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | ALPHA: (17837) implies:
% 225.23/38.66  | | | | | | | | | | | | | | | | |   (17838)  all_57_6 = e2
% 225.23/38.66  | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 225.23/38.66  | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | |   (17839)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 225.23/38.66  | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e0)
% 225.23/38.66  | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | BETA: splitting (17839) gives:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | |   (17840)  all_57_6 = e0 & op(e1, e3) = e0
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | ALPHA: (17840) implies:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | |   (17841)  all_57_6 = e0
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (17838), (17841) are inconsistent by
% 225.23/38.66  | | | | | | | | | | | | | | | | | | |            sub-proof #1846.
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | |   (17842)  all_57_7 = e0 & op(e1, e2) = e0
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (17575), (17842), (function-axioms) are
% 225.23/38.66  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2039.
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.66  | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | |   (17843)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 225.23/38.66  | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 225.23/38.66  | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | BETA: splitting (17843) gives:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | |   (17844)  all_57_8 = e0 & op(e1, e1) = e0
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (17587), (17844), (function-axioms) are
% 225.23/38.66  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2412.
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | |   (17845)  all_57_11 = e0 & op(e1, e0) = e0
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | ALPHA: (17845) implies:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | |   (17846)  all_57_11 = e0
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | |   (17847)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e1)
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | BETA: splitting (17847) gives:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | |   (17848)  all_57_6 = e1 & op(e1, e3) = e1
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (17337), (17848), (function-axioms) are
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #316.
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | |   (17849)  all_57_7 = e1 & op(e1, e2) = e1
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | ALPHA: (17849) implies:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | |   (17850)  all_57_7 = e1
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (39), (214), (217),
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | |            (14936), (17587), (17838), (17850),
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | |            #342.
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | |   (17851)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e0) = e1)
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (17655), (17846), (17851),
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | |            #1861.
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.66  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.66  | | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | End of split
% 225.23/38.66  | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.66  | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | |   (17852)  all_57_12 = e2 & op(e0, e3) = e2
% 225.23/38.66  | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | ALPHA: (17852) implies:
% 225.23/38.66  | | | | | | | | | | | | | | | | |   (17853)  op(e0, e3) = e2
% 225.23/38.66  | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (14924), (17853), (function-axioms) are
% 225.23/38.66  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1980.
% 225.23/38.66  | | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | | End of split
% 225.23/38.66  | | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | | End of split
% 225.23/38.66  | | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | | End of split
% 225.23/38.66  | | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | End of split
% 225.23/38.66  | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | Case 2:
% 225.23/38.66  | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | |   (17854)  all_24_2 = e0
% 225.23/38.66  | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | COMBINE_EQS: (315), (17854) imply:
% 225.23/38.66  | | | | | | | | | | | | |   (17855)  all_6_2 = e0
% 225.23/38.66  | | | | | | | | | | | | | 
% 225.23/38.66  | | | | | | | | | | | | | REDUCE: (350), (17855) imply:
% 225.23/38.67  | | | | | | | | | | | | |   (17856)   ~ (all_53_2 = e0)
% 225.23/38.67  | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | REDUCE: (363), (17855) imply:
% 225.23/38.67  | | | | | | | | | | | | |   (17857)   ~ (all_53_8 = e0)
% 225.23/38.67  | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | BETA: splitting (231) gives:
% 225.23/38.67  | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | Case 1:
% 225.23/38.67  | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | |   (17858)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 225.23/38.67  | | | | | | | | | | | | | |              & op(e3, e2) = e0)
% 225.23/38.67  | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | REF_CLOSE: (4), (171), (17344), (17574), (17858),
% 225.23/38.67  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.23/38.67  | | | | | | | | | | | | | |            #298.
% 225.23/38.67  | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | Case 2:
% 225.23/38.67  | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | |   (17859)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 225.23/38.67  | | | | | | | | | | | | | |              & op(e3, e0) = e0)
% 225.23/38.67  | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | BETA: splitting (17859) gives:
% 225.23/38.67  | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | Case 1:
% 225.23/38.67  | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | |   (17860)  all_57_4 = e0 & op(e3, e1) = e0
% 225.23/38.67  | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | ALPHA: (17860) implies:
% 225.23/38.67  | | | | | | | | | | | | | | |   (17861)  op(e3, e1) = e0
% 225.23/38.67  | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | REF_CLOSE: (170), (17857), (17861), (function-axioms) are
% 225.23/38.67  | | | | | | | | | | | | | | |            inconsistent by sub-proof #2267.
% 225.23/38.67  | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | Case 2:
% 225.23/38.67  | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | |   (17862)  all_57_9 = e0 & op(e3, e0) = e0
% 225.23/38.67  | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | ALPHA: (17862) implies:
% 225.23/38.67  | | | | | | | | | | | | | | |   (17863)  op(e3, e0) = e0
% 225.23/38.67  | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 225.23/38.67  | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | Case 1:
% 225.23/38.67  | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | |   (17864)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 225.23/38.67  | | | | | | | | | | | | | | | |              & op(e2, e3) = e0)
% 225.23/38.67  | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 225.23/38.67  | | | | | | | | | | | | | | | |            (17344), (17584), (17864) are inconsistent by
% 225.23/38.67  | | | | | | | | | | | | | | | |            sub-proof #297.
% 225.23/38.67  | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | Case 2:
% 225.23/38.67  | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | |   (17865)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 225.23/38.67  | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = e0)
% 225.23/38.67  | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | BETA: splitting (17865) gives:
% 225.23/38.67  | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.67  | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | |   (17866)  all_57_6 = e0 & op(e1, e3) = e0
% 225.23/38.67  | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | ALPHA: (17866) implies:
% 225.23/38.67  | | | | | | | | | | | | | | | | |   (17867)  op(e1, e3) = e0
% 225.23/38.67  | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (17856), (17867), (function-axioms) are
% 225.23/38.67  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2154.
% 225.23/38.67  | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.67  | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | |   (17868)  all_57_12 = e0 & op(e0, e3) = e0
% 225.23/38.67  | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | ALPHA: (17868) implies:
% 225.23/38.67  | | | | | | | | | | | | | | | | |   (17869)  op(e0, e3) = e0
% 225.23/38.67  | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_3, e0,
% 225.23/38.67  | | | | | | | | | | | | | | | | |              e3, e0, simplifying with (160), (17869) gives:
% 225.23/38.67  | | | | | | | | | | | | | | | | |   (17870)  all_53_3 = e0
% 225.23/38.67  | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_12,
% 225.23/38.67  | | | | | | | | | | | | | | | | |              e0, e0, e3, simplifying with (169), (17863) gives:
% 225.23/38.67  | | | | | | | | | | | | | | | | |   (17871)  all_53_12 = e0
% 225.23/38.67  | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | REDUCE: (141), (17870) imply:
% 225.23/38.67  | | | | | | | | | | | | | | | | |   (17872)   ~ (all_53_7 = e0)
% 225.23/38.67  | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | REDUCE: (140), (17870) imply:
% 225.23/38.67  | | | | | | | | | | | | | | | | |   (17873)   ~ (all_53_11 = e0)
% 225.23/38.67  | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | SIMP: (17873) implies:
% 225.23/38.67  | | | | | | | | | | | | | | | | |   (17874)   ~ (all_53_11 = e0)
% 225.23/38.67  | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | REDUCE: (113), (17871) imply:
% 225.23/38.67  | | | | | | | | | | | | | | | | |   (17875)   ~ (all_53_14 = e0)
% 225.23/38.67  | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | SIMP: (17875) implies:
% 225.23/38.67  | | | | | | | | | | | | | | | | |   (17876)   ~ (all_53_14 = e0)
% 225.23/38.67  | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | REDUCE: (14927), (17871) imply:
% 225.23/38.67  | | | | | | | | | | | | | | | | |   (17877)   ~ (e2 = e0)
% 225.23/38.67  | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 225.23/38.67  | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | |   (17878)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 225.23/38.67  | | | | | | | | | | | | | | | | | |              all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 225.23/38.67  | | | | | | | | | | | | | | | | | |              op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 225.23/38.67  | | | | | | | | | | | | | | | | | |                all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 225.23/38.67  | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 225.23/38.67  | | | | | | | | | | | | | | | | | |              op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 225.23/38.67  | | | | | | | | | | | | | | | | | |              $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 225.23/38.67  | | | | | | | | | | | | | | | | | |              $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 225.23/38.67  | | | | | | | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 225.23/38.67  | | | | | | | | | | | | | | | | | |                all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 225.23/38.67  | | | | | | | | | | | | | | | | | |              & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 225.23/38.67  | | | | | | | | | | | | | | | | | |                all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 225.23/38.67  | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 225.23/38.67  | | | | | | | | | | | | | | | | | |              & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 225.23/38.67  | | | | | | | | | | | | | | | | | |              $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 225.23/38.67  | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | BETA: splitting (17878) gives:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | |   (17879)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 225.23/38.67  | | | | | | | | | | | | | | | | | | |            all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 225.23/38.67  | | | | | | | | | | | | | | | | | | |            op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 225.23/38.67  | | | | | | | | | | | | | | | | | | |              all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 225.23/38.67  | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 225.23/38.67  | | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 225.23/38.67  | | | | | | | | | | | | | | | | | | |            $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 225.23/38.67  | | | | | | | | | | | | | | | | | | |            $i(all_52_7)
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | ALPHA: (17879) implies:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | |   (17880)  op(e3, e0) = all_52_7
% 225.23/38.67  | | | | | | | | | | | | | | | | | | |   (17881)  op(all_52_7, all_52_7) = e0
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (14935), (17863), (17880), (17881),
% 225.23/38.67  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.23/38.67  | | | | | | | | | | | | | | | | | | |            #47.
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | |   (17882)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 225.23/38.67  | | | | | | | | | | | | | | | | | | |            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 225.23/38.67  | | | | | | | | | | | | | | | | | | |            op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 225.23/38.67  | | | | | | | | | | | | | | | | | | |              all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 225.23/38.67  | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 225.23/38.67  | | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 225.23/38.67  | | | | | | | | | | | | | | | | | | |            $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 225.23/38.67  | | | | | | | | | | | | | | | | | | |            $i(all_52_15)
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | ALPHA: (17882) implies:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | |   (17883)  op(e2, e1) = all_52_13
% 225.23/38.67  | | | | | | | | | | | | | | | | | | |   (17884)  op(e2, e2) = all_52_11
% 225.23/38.67  | | | | | | | | | | | | | | | | | | |   (17885)  op(e2, e3) = all_52_9
% 225.23/38.67  | | | | | | | | | | | | | | | | | | |   (17886)  op(all_52_13, all_52_13) = e1
% 225.23/38.67  | | | | | | | | | | | | | | | | | | |   (17887)  op(all_52_9, all_52_9) = e3
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_9,
% 225.23/38.67  | | | | | | | | | | | | | | | | | | |              all_52_13, e1, e2, simplifying with (166), (17883)
% 225.23/38.67  | | | | | | | | | | | | | | | | | | |              gives:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | |   (17888)  all_53_9 = all_52_13
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 225.23/38.67  | | | | | | | | | | | | | | | | | | |              all_52_11, e2, e2, simplifying with (17585),
% 225.23/38.67  | | | | | | | | | | | | | | | | | | |              (17884) gives:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | |   (17889)  all_52_11 = e0
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_1,
% 225.23/38.67  | | | | | | | | | | | | | | | | | | |              all_52_9, e3, e2, simplifying with (168), (17885)
% 225.23/38.67  | | | | | | | | | | | | | | | | | | |              gives:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | |   (17890)  all_53_1 = all_52_9
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (17888) imply:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | |   (17891)  all_55_6 = all_52_13
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (17890) imply:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | |   (17892)  all_55_4 = all_52_9
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | REDUCE: (150), (17890) imply:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | |   (17893)   ~ (all_53_2 = all_52_9)
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | SIMP: (17893) implies:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | |   (17894)   ~ (all_53_2 = all_52_9)
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | REDUCE: (17336), (17890) imply:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | |   (17895)   ~ (all_52_9 = e1)
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | REDUCE: (17573), (17890) imply:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | |   (17896)   ~ (all_52_9 = e0)
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | REDUCE: (124), (17888) imply:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | |   (17897)   ~ (all_53_8 = all_52_13)
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | REDUCE: (119), (17888) imply:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | |   (17898)   ~ (all_53_11 = all_52_13)
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | SIMP: (17898) implies:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | |   (17899)   ~ (all_53_11 = all_52_13)
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | REDUCE: (17577), (17888) imply:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | |   (17900)   ~ (all_52_13 = e0)
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | |   (17901)  all_55_1 = e3
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (17901) imply:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | |   (17902)  all_53_4 = e3
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | SIMP: (17902) implies:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | |   (17903)  all_53_4 = e3
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | REDUCE: (137), (17903) imply:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | |   (17904)   ~ (all_53_6 = e3)
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | SIMP: (17904) implies:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | |   (17905)   ~ (all_53_6 = e3)
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | REDUCE: (136), (17903) imply:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | |   (17906)   ~ (all_53_7 = e3)
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | SIMP: (17906) implies:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | |   (17907)   ~ (all_53_7 = e3)
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | |   (17908)  all_55_13 = e3
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (17908) imply:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | |   (17909)  all_53_7 = e3
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | REDUCE: (17907), (17909) imply:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | |   (17910)  $false
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | CLOSE: (17910) is inconsistent.
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | |   (17911)  all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17911) gives:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | |   (17912)  all_55_13 = e2
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (17912) imply:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | |   (17913)  all_53_7 = e2
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14925), (17913) imply:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | |   (17914)  $false
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (17914) is inconsistent.
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | |   (17915)  all_55_13 = e1 | all_55_13 = e0
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17915) gives:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | |   (17916)  all_55_13 = e1
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (17916) imply:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | |   (17917)  all_53_7 = e1
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (129), (17917) imply:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | |   (17918)   ~ (all_53_6 = e1)
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | |   (17919)  all_55_9 = e3
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (17905), (17919) are inconsistent by
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2159.
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | |   (17920)  all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17920) gives:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | |   (17921)  all_55_9 = e2
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (17921) imply:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | |   (17922)  all_53_6 = e2
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (17922) implies:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | |   (17923)  all_53_6 = e2
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (17923) imply:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | |   (17924)   ~ (all_53_2 = e2)
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17925)  all_55_8 = e3
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (17925) imply:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17926)  all_53_2 = e3
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (17926) implies:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17927)  all_53_2 = e3
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17894), (17927) imply:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17928)   ~ (all_52_9 = e3)
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (17928) implies:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17929)   ~ (all_52_9 = e3)
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17930)  all_55_4 = e3
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (17892), (17930) imply:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17931)  all_52_9 = e3
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (17931) implies:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17932)  all_52_9 = e3
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17929), (17932) imply:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17933)  $false
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (17933) is inconsistent.
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17934)  all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (14937), (17887), (17892), (17895), (17896),
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17934), (function-axioms) are inconsistent by
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #12.
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | |   (17935)  all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17935) gives:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17936)  all_55_8 = e2
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (17924), (17936) are inconsistent by
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2406.
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (17937)  all_55_8 = e1 | all_55_8 = e0
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (145), (160), (257), (17337), (17869), (17937),
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2365.
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | |   (17938)  all_55_9 = e1 | all_55_9 = e0
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (17575), (17918), (17938) are inconsistent
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1835.
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | |   (17939)  all_55_13 = e0
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (17939) imply:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | |   (17940)  all_53_7 = e0
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17576), (17940) imply:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | |   (17941)  $false
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (17941) is inconsistent.
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | |   (17942)  all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | BETA: splitting (17942) gives:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | |   (17943)  all_55_1 = e2
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (17943) imply:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | |   (17944)  all_53_4 = e2
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | SIMP: (17944) implies:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | |   (17945)  all_53_4 = e2
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (17945) imply:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | |   (17946)   ~ (all_53_8 = e2)
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | SIMP: (17946) implies:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | |   (17947)   ~ (all_53_8 = e2)
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | |   (17948)  all_55_2 = e3
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (17948) imply:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | |   (17949)  all_53_8 = e3
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | SIMP: (17949) implies:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | |   (17950)  all_53_8 = e3
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (122), (17950) imply:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | |   (17951)   ~ (all_53_11 = e3)
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | SIMP: (17951) implies:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | |   (17952)   ~ (all_53_11 = e3)
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17897), (17950) imply:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | |   (17953)   ~ (all_52_13 = e3)
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | SIMP: (17953) implies:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | |   (17954)   ~ (all_52_13 = e3)
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | |   (17955)  all_55_14 = e3
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (17952), (17955) are inconsistent by
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2294.
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | |   (17956)  all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17956) gives:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | |   (17957)  all_55_14 = e2
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (17957) imply:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | |   (17958)  all_53_11 = e2
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14926), (17958) imply:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | |   (17959)  $false
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (17959) is inconsistent.
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | |   (17960)  all_55_14 = e1 | all_55_14 = e0
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17960) gives:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | |   (17961)  all_55_14 = e1
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (17961) imply:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | |   (17962)  all_53_11 = e1
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17899), (17962) imply:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | |   (17963)   ~ (all_52_13 = e1)
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (17963) implies:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | |   (17964)   ~ (all_52_13 = e1)
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (199), (17585), (17886), (17891), (17900),
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | |            (17954), (17964), (function-axioms) are
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #24.
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | |   (17965)  all_55_14 = e0
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (17965) imply:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | |   (17966)  all_53_11 = e0
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17874), (17966) imply:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | |   (17967)  $false
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (17967) is inconsistent.
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | |   (17968)  all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (17340), (17857), (17947), (17968) are
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1937.
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | |   (17969)  all_55_1 = e1 | all_55_1 = e0
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (17339), (17574), (17969) are inconsistent
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1730.
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.67  | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | |   (17970)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 225.23/38.67  | | | | | | | | | | | | | | | | | |              & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 225.23/38.67  | | | | | | | | | | | | | | | | | |              & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 225.23/38.67  | | | | | | | | | | | | | | | | | |                all_52_21) = e1 & op(all_52_23, all_52_23) =
% 225.23/38.67  | | | | | | | | | | | | | | | | | |              e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 225.23/38.67  | | | | | | | | | | | | | | | | | |              all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 225.23/38.67  | | | | | | | | | | | | | | | | | |              = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 225.23/38.67  | | | | | | | | | | | | | | | | | |              $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 225.23/38.67  | | | | | | | | | | | | | | | | | |              & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 225.23/38.67  | | | | | | | | | | | | | | | | | |              e0 & op(all_52_25, all_52_25) = e3 &
% 225.23/38.67  | | | | | | | | | | | | | | | | | |              op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 225.23/38.67  | | | | | | | | | | | | | | | | | |                all_52_29) = e1 & op(all_52_31, all_52_31) =
% 225.23/38.67  | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 225.23/38.67  | | | | | | | | | | | | | | | | | |              all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 225.23/38.67  | | | | | | | | | | | | | | | | | |              = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 225.23/38.67  | | | | | | | | | | | | | | | | | |              $i(all_52_29) & $i(all_52_31))
% 225.23/38.67  | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | BETA: splitting (17970) gives:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | Case 1:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | |   (17971)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 225.23/38.67  | | | | | | | | | | | | | | | | | | |            all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 225.23/38.67  | | | | | | | | | | | | | | | | | | |            op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 225.23/38.67  | | | | | | | | | | | | | | | | | | |              all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 225.23/38.67  | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 225.23/38.67  | | | | | | | | | | | | | | | | | | |            & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 225.23/38.67  | | | | | | | | | | | | | | | | | | |            & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 225.23/38.67  | | | | | | | | | | | | | | | | | | |            $i(all_52_23)
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (161), (163), (164), (214), (14935), (17575),
% 225.23/38.67  | | | | | | | | | | | | | | | | | | |            (17856), (17876), (17971), (function-axioms) are
% 225.23/38.67  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #38.
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | Case 2:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | |   (17972)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 225.23/38.67  | | | | | | | | | | | | | | | | | | |            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 225.23/38.67  | | | | | | | | | | | | | | | | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 225.23/38.67  | | | | | | | | | | | | | | | | | | |              all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 225.23/38.67  | | | | | | | | | | | | | | | | | | |            & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 225.23/38.67  | | | | | | | | | | | | | | | | | | |            & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 225.23/38.67  | | | | | | | | | | | | | | | | | | |            & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 225.23/38.67  | | | | | | | | | | | | | | | | | | |            $i(all_52_31)
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | ALPHA: (17972) implies:
% 225.23/38.67  | | | | | | | | | | | | | | | | | | |   (17973)  op(e0, e0) = all_52_31
% 225.23/38.67  | | | | | | | | | | | | | | | | | | |   (17974)  op(e0, e3) = all_52_25
% 225.23/38.67  | | | | | | | | | | | | | | | | | | |   (17975)  op(all_52_25, all_52_25) = e3
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (14935), (17869), (17973), (17974), (17975),
% 225.23/38.67  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.23/38.67  | | | | | | | | | | | | | | | | | | |            #31.
% 225.23/38.67  | | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | | End of split
% 225.23/38.67  | | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | | End of split
% 225.23/38.67  | | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | | End of split
% 225.23/38.67  | | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | | End of split
% 225.23/38.67  | | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | | End of split
% 225.23/38.67  | | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | | End of split
% 225.23/38.67  | | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | | End of split
% 225.23/38.67  | | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | End of split
% 225.23/38.67  | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | Case 2:
% 225.23/38.67  | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | |   (17976)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 225.23/38.67  | | | | | | | | | | |              e0 & op(e2, e0) = e0)
% 225.23/38.67  | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | | REF_CLOSE: (165), (166), (17577), (17578), (17976),
% 225.23/38.67  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.23/38.67  | | | | | | | | | | |            #2022.
% 225.23/38.67  | | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | | End of split
% 225.23/38.67  | | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | End of split
% 225.23/38.67  | | | | | | | | | 
% 225.23/38.67  | | | | | | | | Case 2:
% 225.23/38.67  | | | | | | | | | 
% 225.23/38.67  | | | | | | | | |   (17977)  all_57_2 = e1 & op(e2, e3) = e1
% 225.23/38.67  | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | REF_CLOSE: (168), (17336), (17977), (function-axioms) are
% 225.23/38.67  | | | | | | | | |            inconsistent by sub-proof #2156.
% 225.23/38.67  | | | | | | | | | 
% 225.23/38.67  | | | | | | | | End of split
% 225.23/38.67  | | | | | | | | 
% 225.23/38.67  | | | | | | | Case 2:
% 225.23/38.67  | | | | | | | | 
% 225.23/38.67  | | | | | | | |   (17978)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 &
% 225.23/38.67  | | | | | | | |              op(e0, e3) = e1)
% 225.23/38.67  | | | | | | | | 
% 225.23/38.67  | | | | | | | | BETA: splitting (17978) gives:
% 225.23/38.67  | | | | | | | | 
% 225.23/38.67  | | | | | | | | Case 1:
% 225.23/38.67  | | | | | | | | | 
% 225.23/38.67  | | | | | | | | |   (17979)  all_57_6 = e1 & op(e1, e3) = e1
% 225.23/38.67  | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | REF_CLOSE: (164), (17337), (17979), (function-axioms) are
% 225.23/38.67  | | | | | | | | |            inconsistent by sub-proof #316.
% 225.23/38.67  | | | | | | | | | 
% 225.23/38.67  | | | | | | | | Case 2:
% 225.23/38.67  | | | | | | | | | 
% 225.23/38.67  | | | | | | | | |   (17980)  all_57_12 = e1 & op(e0, e3) = e1
% 225.23/38.67  | | | | | | | | | 
% 225.23/38.67  | | | | | | | | | REF_CLOSE: (160), (17338), (17980), (function-axioms) are
% 225.23/38.67  | | | | | | | | |            inconsistent by sub-proof #1947.
% 225.23/38.67  | | | | | | | | | 
% 225.23/38.67  | | | | | | | | End of split
% 225.23/38.67  | | | | | | | | 
% 225.23/38.67  | | | | | | | End of split
% 225.23/38.67  | | | | | | | 
% 225.23/38.67  | | | | | | End of split
% 225.23/38.67  | | | | | | 
% 225.23/38.67  | | | | | Case 2:
% 225.23/38.67  | | | | | | 
% 225.23/38.67  | | | | | |   (17981)  all_8_2 = e3
% 225.23/38.67  | | | | | |   (17982)  ( ~ (all_8_0 = e0) & op(all_8_1, e2) = all_8_0 & op(e2,
% 225.23/38.67  | | | | | |                e3) = all_8_1 & $i(all_8_0) & $i(all_8_1)) | ( ~
% 225.23/38.67  | | | | | |              (all_8_1 = e1) & op(e2, e3) = all_8_1 & $i(all_8_1))
% 225.23/38.67  | | | | | | 
% 225.23/38.67  | | | | | | COMBINE_EQS: (297), (17981) imply:
% 225.23/38.67  | | | | | |   (17983)  all_44_2 = e3
% 225.23/38.67  | | | | | | 
% 225.23/38.67  | | | | | | REDUCE: (349), (17981) imply:
% 225.23/38.67  | | | | | |   (17984)   ~ (all_53_1 = e3)
% 225.23/38.67  | | | | | | 
% 225.23/38.67  | | | | | | REDUCE: (352), (17981) imply:
% 225.23/38.67  | | | | | |   (17985)   ~ (all_53_4 = e3)
% 225.23/38.67  | | | | | | 
% 225.23/38.67  | | | | | | REDUCE: (354), (17981) imply:
% 225.23/38.67  | | | | | |   (17986)   ~ (all_53_6 = e3)
% 225.23/38.67  | | | | | | 
% 225.23/38.67  | | | | | | REDUCE: (356), (17981) imply:
% 225.23/38.67  | | | | | |   (17987)   ~ (all_53_7 = e3)
% 225.23/38.67  | | | | | | 
% 225.23/38.67  | | | | | | REDUCE: (358), (17981) imply:
% 225.23/38.67  | | | | | |   (17988)   ~ (all_53_9 = e3)
% 225.23/38.67  | | | | | | 
% 225.23/38.67  | | | | | | REDUCE: (360), (17981) imply:
% 225.23/38.67  | | | | | |   (17989)   ~ (all_53_13 = e3)
% 225.23/38.67  | | | | | | 
% 225.23/38.67  | | | | | | BETA: splitting (225) gives:
% 225.23/38.67  | | | | | | 
% 225.23/38.67  | | | | | | Case 1:
% 225.23/38.67  | | | | | | | 
% 225.23/38.67  | | | | | | |   (17990)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 &
% 225.23/38.67  | | | | | | |              op(e2, e2) = e3)
% 225.23/38.67  | | | | | | | 
% 225.23/38.67  | | | | | | | BETA: splitting (17990) gives:
% 225.23/38.67  | | | | | | | 
% 225.23/38.67  | | | | | | | Case 1:
% 225.23/38.67  | | | | | | | | 
% 225.23/38.67  | | | | | | | |   (17991)  all_57_2 = e3 & op(e2, e3) = e3
% 225.23/38.67  | | | | | | | | 
% 225.23/38.67  | | | | | | | | REF_CLOSE: (168), (17984), (17991), (function-axioms) are
% 225.23/38.67  | | | | | | | |            inconsistent by sub-proof #2299.
% 225.23/38.67  | | | | | | | | 
% 225.23/38.67  | | | | | | | Case 2:
% 225.23/38.67  | | | | | | | | 
% 225.23/38.67  | | | | | | | |   (17992)  all_57_3 = e3 & op(e2, e2) = e3
% 225.23/38.67  | | | | | | | | 
% 225.23/38.67  | | | | | | | | ALPHA: (17992) implies:
% 225.23/38.67  | | | | | | | |   (17993)  all_57_3 = e3
% 225.23/38.67  | | | | | | | |   (17994)  op(e2, e2) = e3
% 225.23/38.67  | | | | | | | | 
% 225.23/38.67  | | | | | | | | BETA: splitting (46) gives:
% 225.23/38.67  | | | | | | | | 
% 225.23/38.67  | | | | | | | | Case 1:
% 225.23/38.67  | | | | | | | | | 
% 225.58/38.67  | | | | | | | | |   (17995)   ~ (all_10_2 = e1)
% 225.58/38.67  | | | | | | | | | 
% 225.58/38.67  | | | | | | | | | BETA: splitting (58) gives:
% 225.58/38.67  | | | | | | | | | 
% 225.58/38.67  | | | | | | | | | Case 1:
% 225.58/38.67  | | | | | | | | | | 
% 225.58/38.67  | | | | | | | | | |   (17996)   ~ (all_18_2 = e0)
% 225.58/38.67  | | | | | | | | | | 
% 225.58/38.67  | | | | | | | | | | REDUCE: (327), (17996) imply:
% 225.58/38.67  | | | | | | | | | |   (17997)   ~ (all_10_2 = e0)
% 225.58/38.67  | | | | | | | | | | 
% 225.58/38.67  | | | | | | | | | | BETA: splitting (61) gives:
% 225.58/38.67  | | | | | | | | | | 
% 225.58/38.67  | | | | | | | | | | Case 1:
% 225.58/38.67  | | | | | | | | | | | 
% 225.58/38.67  | | | | | | | | | | |   (17998)   ~ (all_20_2 = e2)
% 225.58/38.67  | | | | | | | | | | | 
% 225.58/38.67  | | | | | | | | | | | REDUCE: (299), (17998) imply:
% 225.58/38.67  | | | | | | | | | | |   (17999)   ~ (all_10_2 = e2)
% 225.58/38.67  | | | | | | | | | | | 
% 225.58/38.67  | | | | | | | | | | | BETA: splitting (205) gives:
% 225.58/38.67  | | | | | | | | | | | 
% 225.58/38.67  | | | | | | | | | | | Case 1:
% 225.58/38.67  | | | | | | | | | | | | 
% 225.58/38.67  | | | | | | | | | | | |   (18000)  all_55_0 = e3
% 225.58/38.67  | | | | | | | | | | | | 
% 225.58/38.67  | | | | | | | | | | | | COMBINE_EQS: (277), (18000) imply:
% 225.58/38.67  | | | | | | | | | | | |   (18001)  all_10_2 = e3
% 225.58/38.67  | | | | | | | | | | | | 
% 225.58/38.67  | | | | | | | | | | | | REDUCE: (342), (18001) imply:
% 225.58/38.67  | | | | | | | | | | | |   (18002)   ~ (all_53_3 = e3)
% 225.58/38.67  | | | | | | | | | | | | 
% 225.58/38.67  | | | | | | | | | | | | REDUCE: (348), (18001) imply:
% 225.58/38.67  | | | | | | | | | | | |   (18003)   ~ (all_53_12 = e3)
% 225.58/38.67  | | | | | | | | | | | | 
% 225.58/38.67  | | | | | | | | | | | | REDUCE: (45), (18001) imply:
% 225.58/38.67  | | | | | | | | | | | |   (18004)  op(e3, e3) = e3
% 225.58/38.67  | | | | | | | | | | | | 
% 225.58/38.67  | | | | | | | | | | | | BETA: splitting (210) gives:
% 225.58/38.67  | | | | | | | | | | | | 
% 225.58/38.67  | | | | | | | | | | | | Case 1:
% 225.58/38.67  | | | | | | | | | | | | | 
% 225.58/38.67  | | | | | | | | | | | | |   (18005)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 225.58/38.67  | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 225.58/38.67  | | | | | | | | | | | | | 
% 225.58/38.67  | | | | | | | | | | | | | REF_CLOSE: (159), (160), (17987), (18002), (18005),
% 225.58/38.67  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.58/38.67  | | | | | | | | | | | | |            #77.
% 225.58/38.67  | | | | | | | | | | | | | 
% 225.58/38.67  | | | | | | | | | | | | Case 2:
% 225.58/38.67  | | | | | | | | | | | | | 
% 225.58/38.67  | | | | | | | | | | | | |   (18006)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 225.58/38.67  | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 225.58/38.67  | | | | | | | | | | | | | 
% 225.58/38.67  | | | | | | | | | | | | | BETA: splitting (18006) gives:
% 225.58/38.67  | | | | | | | | | | | | | 
% 225.58/38.67  | | | | | | | | | | | | | Case 1:
% 225.58/38.67  | | | | | | | | | | | | | | 
% 225.58/38.67  | | | | | | | | | | | | | |   (18007)  all_57_14 = e3 & op(e0, e1) = e3
% 225.58/38.67  | | | | | | | | | | | | | | 
% 225.58/38.67  | | | | | | | | | | | | | | ALPHA: (18007) implies:
% 225.58/38.67  | | | | | | | | | | | | | |   (18008)  all_57_14 = e3
% 225.58/38.67  | | | | | | | | | | | | | | 
% 225.58/38.67  | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 225.58/38.67  | | | | | | | | | | | | | | 
% 225.58/38.67  | | | | | | | | | | | | | | Case 1:
% 225.58/38.67  | | | | | | | | | | | | | | | 
% 225.58/38.67  | | | | | | | | | | | | | | |   (18009)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 225.58/38.67  | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 225.58/38.67  | | | | | | | | | | | | | | | 
% 225.58/38.67  | | | | | | | | | | | | | | | REF_CLOSE: (165), (169), (17989), (18003), (18009),
% 225.58/38.67  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.58/38.67  | | | | | | | | | | | | | | |            #2300.
% 225.58/38.67  | | | | | | | | | | | | | | | 
% 225.58/38.67  | | | | | | | | | | | | | | Case 2:
% 225.58/38.67  | | | | | | | | | | | | | | | 
% 225.58/38.67  | | | | | | | | | | | | | | |   (18010)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 225.58/38.67  | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 225.58/38.67  | | | | | | | | | | | | | | | 
% 225.58/38.67  | | | | | | | | | | | | | | | BETA: splitting (18010) gives:
% 225.58/38.67  | | | | | | | | | | | | | | | 
% 225.58/38.67  | | | | | | | | | | | | | | | Case 1:
% 225.58/38.67  | | | | | | | | | | | | | | | | 
% 225.58/38.67  | | | | | | | | | | | | | | | |   (18011)  all_57_11 = e3 & op(e1, e0) = e3
% 225.58/38.67  | | | | | | | | | | | | | | | | 
% 225.58/38.67  | | | | | | | | | | | | | | | | ALPHA: (18011) implies:
% 225.58/38.67  | | | | | | | | | | | | | | | |   (18012)  op(e1, e0) = e3
% 225.58/38.67  | | | | | | | | | | | | | | | | 
% 225.58/38.67  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_14,
% 225.58/38.67  | | | | | | | | | | | | | | | |              e3, e0, e1, simplifying with (161), (18012) gives:
% 225.58/38.67  | | | | | | | | | | | | | | | |   (18013)  all_53_14 = e3
% 225.58/38.67  | | | | | | | | | | | | | | | | 
% 225.58/38.67  | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 225.58/38.67  | | | | | | | | | | | | | | | | 
% 225.58/38.67  | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.67  | | | | | | | | | | | | | | | | | 
% 225.58/38.67  | | | | | | | | | | | | | | | | |   (18014)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 225.58/38.67  | | | | | | | | | | | | | | | | |              all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 225.58/38.67  | | | | | | | | | | | | | | | | |              op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 225.58/38.67  | | | | | | | | | | | | | | | | |                all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 225.58/38.67  | | | | | | | | | | | | | | | | |              op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 225.58/38.67  | | | | | | | | | | | | | | | | |              op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 225.58/38.67  | | | | | | | | | | | | | | | | |              $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 225.58/38.67  | | | | | | | | | | | | | | | | |              $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 225.58/38.67  | | | | | | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 225.58/38.67  | | | | | | | | | | | | | | | | |                all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 225.58/38.67  | | | | | | | | | | | | | | | | |              & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 225.58/38.67  | | | | | | | | | | | | | | | | |                all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 225.58/38.67  | | | | | | | | | | | | | | | | |              op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 225.58/38.67  | | | | | | | | | | | | | | | | |              & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 225.58/38.67  | | | | | | | | | | | | | | | | |              $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 225.58/38.67  | | | | | | | | | | | | | | | | | 
% 225.58/38.67  | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (169), (170), (171), (235),
% 225.58/38.67  | | | | | | | | | | | | | | | | |            (17985), (17994), (18004), (18014),
% 225.58/38.67  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.58/38.67  | | | | | | | | | | | | | | | | |            #94.
% 225.58/38.67  | | | | | | | | | | | | | | | | | 
% 225.58/38.67  | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.67  | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | |   (18015)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 225.58/38.68  | | | | | | | | | | | | | | | | |              & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 225.58/38.68  | | | | | | | | | | | | | | | | |              & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 225.58/38.68  | | | | | | | | | | | | | | | | |                all_52_21) = e1 & op(all_52_23, all_52_23) =
% 225.58/38.68  | | | | | | | | | | | | | | | | |              e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 225.58/38.68  | | | | | | | | | | | | | | | | |              all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 225.58/38.68  | | | | | | | | | | | | | | | | |              = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 225.58/38.68  | | | | | | | | | | | | | | | | |              $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 225.58/38.68  | | | | | | | | | | | | | | | | |              & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 225.58/38.68  | | | | | | | | | | | | | | | | |              e0 & op(all_52_25, all_52_25) = e3 &
% 225.58/38.68  | | | | | | | | | | | | | | | | |              op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 225.58/38.68  | | | | | | | | | | | | | | | | |                all_52_29) = e1 & op(all_52_31, all_52_31) =
% 225.58/38.68  | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 225.58/38.68  | | | | | | | | | | | | | | | | |              all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 225.58/38.68  | | | | | | | | | | | | | | | | |              = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 225.58/38.68  | | | | | | | | | | | | | | | | |              $i(all_52_29) & $i(all_52_31))
% 225.58/38.68  | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | BETA: splitting (18015) gives:
% 225.58/38.68  | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | |   (18016)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 225.58/38.68  | | | | | | | | | | | | | | | | | |            all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 225.58/38.68  | | | | | | | | | | | | | | | | | |            op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 225.58/38.68  | | | | | | | | | | | | | | | | | |              all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 225.58/38.68  | | | | | | | | | | | | | | | | | |            & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 225.58/38.68  | | | | | | | | | | | | | | | | | |            & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 225.58/38.68  | | | | | | | | | | | | | | | | | |            & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 225.58/38.68  | | | | | | | | | | | | | | | | | |            $i(all_52_23)
% 225.58/38.68  | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (18004), (18012), (18016), (function-axioms)
% 225.58/38.68  | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #254.
% 225.58/38.68  | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | |   (18017)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 225.58/38.68  | | | | | | | | | | | | | | | | | |            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 225.58/38.68  | | | | | | | | | | | | | | | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 225.58/38.68  | | | | | | | | | | | | | | | | | |              all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 225.58/38.68  | | | | | | | | | | | | | | | | | |            & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 225.58/38.68  | | | | | | | | | | | | | | | | | |            & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 225.58/38.68  | | | | | | | | | | | | | | | | | |            & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 225.58/38.68  | | | | | | | | | | | | | | | | | |            $i(all_52_31)
% 225.58/38.68  | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | ALPHA: (18017) implies:
% 225.58/38.68  | | | | | | | | | | | | | | | | | |   (18018)  op(e0, e0) = all_52_31
% 225.58/38.68  | | | | | | | | | | | | | | | | | |   (18019)  op(all_52_31, all_52_31) = e0
% 225.58/38.68  | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (14935), (17994), (18018), (18019),
% 225.58/38.68  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.58/38.68  | | | | | | | | | | | | | | | | | |            #11.
% 225.58/38.68  | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | End of split
% 225.58/38.68  | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | End of split
% 225.58/38.68  | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | Case 2:
% 225.58/38.68  | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | |   (18020)  all_57_15 = e3 & op(e0, e0) = e3
% 225.58/38.68  | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | ALPHA: (18020) implies:
% 225.58/38.68  | | | | | | | | | | | | | | | |   (18021)  all_57_15 = e3
% 225.58/38.68  | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (207), (208), (209),
% 225.58/38.68  | | | | | | | | | | | | | | | |            (18008), (18021) are inconsistent by sub-proof
% 225.58/38.68  | | | | | | | | | | | | | | | |            #2312.
% 225.58/38.68  | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | End of split
% 225.58/38.68  | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | End of split
% 225.58/38.68  | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | Case 2:
% 225.58/38.68  | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | |   (18022)  all_57_15 = e3 & op(e0, e0) = e3
% 225.58/38.68  | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | ALPHA: (18022) implies:
% 225.58/38.68  | | | | | | | | | | | | | |   (18023)  all_57_15 = e3
% 225.58/38.68  | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | REF_CLOSE: (9), (14934), (18023) are inconsistent by
% 225.58/38.68  | | | | | | | | | | | | | |            sub-proof #2058.
% 225.58/38.68  | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | End of split
% 225.58/38.68  | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | End of split
% 225.58/38.68  | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | Case 2:
% 225.58/38.68  | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | |   (18024)  all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 225.58/38.68  | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | REF_CLOSE: (277), (17995), (17997), (17999), (18024) are
% 225.58/38.68  | | | | | | | | | | | |            inconsistent by sub-proof #1953.
% 225.58/38.68  | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | End of split
% 225.58/38.68  | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | Case 2:
% 225.58/38.68  | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | |   (18025)  all_20_2 = e2
% 225.58/38.68  | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | COMBINE_EQS: (299), (18025) imply:
% 225.58/38.68  | | | | | | | | | | |   (18026)  all_10_2 = e2
% 225.58/38.68  | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | SIMP: (18026) implies:
% 225.58/38.68  | | | | | | | | | | |   (18027)  all_10_2 = e2
% 225.58/38.68  | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | REDUCE: (338), (18027) imply:
% 225.58/38.68  | | | | | | | | | | |   (18028)   ~ (all_53_1 = e2)
% 225.58/38.68  | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | REDUCE: (45), (18027) imply:
% 225.58/38.68  | | | | | | | | | | |   (18029)  op(e3, e3) = e2
% 225.58/38.68  | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | BETA: splitting (228) gives:
% 225.58/38.68  | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | Case 1:
% 225.58/38.68  | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | |   (18030)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 225.58/38.68  | | | | | | | | | | | |              & op(e2, e2) = e2)
% 225.58/38.68  | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (237),
% 225.58/38.68  | | | | | | | | | | | |            (17994), (18029), (18030), (function-axioms) are
% 225.58/38.68  | | | | | | | | | | | |            inconsistent by sub-proof #104.
% 225.58/38.68  | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | Case 2:
% 225.58/38.68  | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | |   (18031)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 225.58/38.68  | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 225.58/38.68  | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | BETA: splitting (18031) gives:
% 225.58/38.68  | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | Case 1:
% 225.58/38.68  | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | |   (18032)  all_57_7 = e2 & op(e1, e2) = e2
% 225.58/38.68  | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | ALPHA: (18032) implies:
% 225.58/38.68  | | | | | | | | | | | | |   (18033)  all_57_7 = e2
% 225.58/38.68  | | | | | | | | | | | | |   (18034)  op(e1, e2) = e2
% 225.58/38.68  | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | BETA: splitting (224) gives:
% 225.58/38.68  | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | Case 1:
% 225.58/38.68  | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | |   (18035)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 225.58/38.68  | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 225.58/38.68  | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | REF_CLOSE: (9), (168), (17994), (18028), (18035),
% 225.58/38.68  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.58/38.68  | | | | | | | | | | | | | |            #242.
% 225.58/38.68  | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | Case 2:
% 225.58/38.68  | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | |   (18036)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 225.58/38.68  | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 225.58/38.68  | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | BETA: splitting (18036) gives:
% 225.58/38.68  | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | Case 1:
% 225.58/38.68  | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | |   (18037)  all_57_5 = e2 & op(e2, e1) = e2
% 225.58/38.68  | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | ALPHA: (18037) implies:
% 225.58/38.68  | | | | | | | | | | | | | | |   (18038)  all_57_5 = e2
% 225.58/38.68  | | | | | | | | | | | | | | |   (18039)  op(e2, e1) = e2
% 225.58/38.68  | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_6, e2,
% 225.58/38.68  | | | | | | | | | | | | | | |              e2, e1, simplifying with (163), (18034) gives:
% 225.58/38.68  | | | | | | | | | | | | | | |   (18040)  all_53_6 = e2
% 225.58/38.68  | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_9, e2,
% 225.58/38.68  | | | | | | | | | | | | | | |              e1, e2, simplifying with (166), (18039) gives:
% 225.58/38.68  | | | | | | | | | | | | | | |   (18041)  all_53_9 = e2
% 225.58/38.68  | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | REDUCE: (144), (18040) imply:
% 225.58/38.68  | | | | | | | | | | | | | | |   (18042)   ~ (all_53_2 = e2)
% 225.58/38.68  | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | REDUCE: (127), (18040) imply:
% 225.58/38.68  | | | | | | | | | | | | | | |   (18043)   ~ (all_53_14 = e2)
% 225.58/38.68  | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | REDUCE: (124), (18041) imply:
% 225.58/38.68  | | | | | | | | | | | | | | |   (18044)   ~ (all_53_8 = e2)
% 225.58/38.68  | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | REDUCE: (119), (18041) imply:
% 225.58/38.68  | | | | | | | | | | | | | | |   (18045)   ~ (all_53_11 = e2)
% 225.58/38.68  | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | REDUCE: (118), (18041) imply:
% 225.58/38.68  | | | | | | | | | | | | | | |   (18046)   ~ (all_53_13 = e2)
% 225.58/38.68  | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | REDUCE: (364), (18041) imply:
% 225.58/38.68  | | | | | | | | | | | | | | |   (18047)   ~ (all_6_2 = e2)
% 225.58/38.68  | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | SIMP: (18047) implies:
% 225.58/38.68  | | | | | | | | | | | | | | |   (18048)   ~ (all_6_2 = e2)
% 225.58/38.68  | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | REDUCE: (17988), (18041) imply:
% 225.58/38.68  | | | | | | | | | | | | | | |   (18049)   ~ (e3 = e2)
% 225.58/38.68  | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 225.58/38.68  | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | Case 1:
% 225.58/38.68  | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | |   (18050)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 225.58/38.68  | | | | | | | | | | | | | | | |              all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 225.58/38.68  | | | | | | | | | | | | | | | |              op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 225.58/38.68  | | | | | | | | | | | | | | | |                all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 225.58/38.68  | | | | | | | | | | | | | | | |              op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 225.58/38.68  | | | | | | | | | | | | | | | |              op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 225.58/38.68  | | | | | | | | | | | | | | | |              $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 225.58/38.68  | | | | | | | | | | | | | | | |              $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 225.58/38.68  | | | | | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 225.58/38.68  | | | | | | | | | | | | | | | |                all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 225.58/38.68  | | | | | | | | | | | | | | | |              & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 225.58/38.68  | | | | | | | | | | | | | | | |                all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 225.58/38.68  | | | | | | | | | | | | | | | |              op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 225.58/38.68  | | | | | | | | | | | | | | | |              & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 225.58/38.68  | | | | | | | | | | | | | | | |              $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 225.58/38.68  | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | BETA: splitting (18050) gives:
% 225.58/38.68  | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.68  | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | |   (18051)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 225.58/38.68  | | | | | | | | | | | | | | | | |            all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 225.58/38.68  | | | | | | | | | | | | | | | | |            op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 225.58/38.68  | | | | | | | | | | | | | | | | |              all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 225.58/38.68  | | | | | | | | | | | | | | | | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 225.58/38.68  | | | | | | | | | | | | | | | | |            op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 225.58/38.68  | | | | | | | | | | | | | | | | |            $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 225.58/38.68  | | | | | | | | | | | | | | | | |            $i(all_52_7)
% 225.58/38.68  | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | ALPHA: (18051) implies:
% 225.58/38.68  | | | | | | | | | | | | | | | | |   (18052)  op(e3, e0) = all_52_7
% 225.58/38.68  | | | | | | | | | | | | | | | | |   (18053)  op(e3, e1) = all_52_5
% 225.58/38.68  | | | | | | | | | | | | | | | | |   (18054)  op(e3, e2) = all_52_3
% 225.58/38.68  | | | | | | | | | | | | | | | | |   (18055)  op(e3, e3) = all_52_1
% 225.58/38.68  | | | | | | | | | | | | | | | | |   (18056)  op(all_52_7, all_52_7) = e0
% 225.58/38.68  | | | | | | | | | | | | | | | | |   (18057)  op(all_52_5, all_52_5) = e1
% 225.58/38.68  | | | | | | | | | | | | | | | | |   (18058)  op(all_52_3, all_52_3) = e2
% 225.58/38.68  | | | | | | | | | | | | | | | | |   (18059)  op(all_52_1, all_52_1) = e3
% 225.58/38.68  | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_12,
% 225.58/38.68  | | | | | | | | | | | | | | | | |              all_52_7, e0, e3, simplifying with (169), (18052)
% 225.58/38.68  | | | | | | | | | | | | | | | | |              gives:
% 225.58/38.68  | | | | | | | | | | | | | | | | |   (18060)  all_53_12 = all_52_7
% 225.58/38.68  | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_8,
% 225.58/38.68  | | | | | | | | | | | | | | | | |              all_52_5, e1, e3, simplifying with (170), (18053)
% 225.58/38.68  | | | | | | | | | | | | | | | | |              gives:
% 225.58/38.68  | | | | | | | | | | | | | | | | |   (18061)  all_53_8 = all_52_5
% 225.58/38.68  | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_4,
% 225.58/38.68  | | | | | | | | | | | | | | | | |              all_52_3, e2, e3, simplifying with (171), (18054)
% 225.58/38.68  | | | | | | | | | | | | | | | | |              gives:
% 225.58/38.68  | | | | | | | | | | | | | | | | |   (18062)  all_53_4 = all_52_3
% 225.58/38.68  | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_52_1,
% 225.58/38.68  | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (18029), (18055) gives:
% 225.58/38.68  | | | | | | | | | | | | | | | | |   (18063)  all_52_1 = e2
% 225.58/38.68  | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (18060) imply:
% 225.58/38.68  | | | | | | | | | | | | | | | | |   (18064)  all_55_3 = all_52_7
% 225.58/38.68  | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (18061) imply:
% 225.58/38.68  | | | | | | | | | | | | | | | | |   (18065)  all_55_2 = all_52_5
% 225.58/38.68  | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | REDUCE: (17985), (18062) imply:
% 225.58/38.68  | | | | | | | | | | | | | | | | |   (18066)   ~ (all_52_3 = e3)
% 225.58/38.68  | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | REDUCE: (122), (18061) imply:
% 225.58/38.68  | | | | | | | | | | | | | | | | |   (18067)   ~ (all_53_11 = all_52_5)
% 225.58/38.68  | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | SIMP: (18067) implies:
% 225.58/38.68  | | | | | | | | | | | | | | | | |   (18068)   ~ (all_53_11 = all_52_5)
% 225.58/38.68  | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | REDUCE: (363), (18061) imply:
% 225.58/38.68  | | | | | | | | | | | | | | | | |   (18069)   ~ (all_52_5 = all_6_2)
% 225.58/38.68  | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | REDUCE: (18044), (18061) imply:
% 225.58/38.68  | | | | | | | | | | | | | | | | |   (18070)   ~ (all_52_5 = e2)
% 225.58/38.68  | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | REDUCE: (114), (18060) imply:
% 225.58/38.68  | | | | | | | | | | | | | | | | |   (18071)   ~ (all_53_13 = all_52_7)
% 225.58/38.68  | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | SIMP: (18071) implies:
% 225.58/38.68  | | | | | | | | | | | | | | | | |   (18072)   ~ (all_53_13 = all_52_7)
% 225.58/38.68  | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | REDUCE: (113), (18060) imply:
% 225.58/38.68  | | | | | | | | | | | | | | | | |   (18073)   ~ (all_53_14 = all_52_7)
% 225.58/38.68  | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | SIMP: (18073) implies:
% 225.58/38.68  | | | | | | | | | | | | | | | | |   (18074)   ~ (all_53_14 = all_52_7)
% 225.58/38.68  | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | REDUCE: (14927), (18060) imply:
% 225.58/38.68  | | | | | | | | | | | | | | | | |   (18075)   ~ (all_52_7 = e2)
% 225.58/38.68  | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 225.58/38.68  | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | |   (18076)   ~ (all_24_2 = e0)
% 225.58/38.68  | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | REDUCE: (315), (18076) imply:
% 225.58/38.68  | | | | | | | | | | | | | | | | | |   (18077)   ~ (all_6_2 = e0)
% 225.58/38.68  | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | |   (18078)  all_55_10 = e3
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (14936), (18078) are inconsistent by
% 225.58/38.68  | | | | | | | | | | | | | | | | | | |            sub-proof #2500.
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | |   (18079)   ~ (all_55_10 = e3)
% 225.58/38.68  | | | | | | | | | | | | | | | | | | |   (18080)  all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | BETA: splitting (18080) gives:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | |   (18081)  all_55_10 = e2
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (18048), (18081) are inconsistent by
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | |            sub-proof #2499.
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | |   (18082)   ~ (all_55_10 = e2)
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | |   (18083)  all_55_10 = e1 | all_55_10 = e0
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | BETA: splitting (18083) gives:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | |   (18084)  all_55_10 = e1
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (336), (18084) imply:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | |   (18085)  all_6_2 = e1
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | SIMP: (18085) implies:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | |   (18086)  all_6_2 = e1
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | REDUCE: (350), (18086) imply:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | |   (18087)   ~ (all_53_2 = e1)
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | REDUCE: (366), (18086) imply:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | |   (18088)   ~ (all_53_11 = e1)
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | REDUCE: (368), (18086) imply:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | |   (18089)   ~ (all_53_14 = e1)
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | REDUCE: (18069), (18086) imply:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | |   (18090)   ~ (all_52_5 = e1)
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | REDUCE: (18048), (18086) imply:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | |   (18091)   ~ (e2 = e1)
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (18086) imply:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | |   (18092)  op(e1, e1) = e1
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (79) gives:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | |   (18093)   ~ (all_32_2 = e2)
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14923), (18093) imply:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | |   (18094)  $false
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (18094) is inconsistent.
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | |   (18095)  ( ~ (all_32_0 = e1) & op(all_32_1, e0) = all_32_0
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | |              & op(e0, e2) = all_32_1 & $i(all_32_0) &
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | |              $i(all_32_1)) | ( ~ (all_32_1 = e3) & op(e0, e2)
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | |              = all_32_1 & $i(all_32_1))
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | |   (18096)  all_55_7 = e3
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (18096) imply:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | |   (18097)  all_53_13 = e3
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17989), (18097) imply:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | |   (18098)  $false
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (18098) is inconsistent.
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | |   (18099)  all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | |   (18100)  all_55_11 = e3
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (18100) imply:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | |   (18101)  all_53_14 = e3
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (18101) implies:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | |   (18102)  all_53_14 = e3
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (142), (18102) imply:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | |   (18103)   ~ (all_53_2 = e3)
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | |   (18104)  all_55_8 = e3
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (18103), (18104) are inconsistent by
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2496.
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | |   (18105)   ~ (all_55_8 = e3)
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | |   (18106)  all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | |   (18107)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e3)
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (171), (235), (17985), (17994),
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | |            (18052), (18053), (18054), (18056), (18057),
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | |            (18058), (18066), (18107), (function-axioms) are
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #10.
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | |   (18108)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e3)
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18108) gives:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18109)  all_57_4 = e3 & op(e3, e1) = e3
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18109) implies:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18110)  all_57_4 = e3
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18111)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e3)
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (168), (235), (17984), (17994),
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18052), (18053), (18054), (18056), (18057),
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18058), (18066), (18111), (function-axioms) are
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #9.
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18112)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e3) = e3)
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18112) gives:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18113)  all_57_6 = e3 & op(e1, e3) = e3
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (18103), (18113), (function-axioms) are
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #153.
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18114)  all_57_12 = e3 & op(e0, e3) = e3
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18114) implies:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18115)  all_57_12 = e3
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18116)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18116) gives:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18117)  all_57_12 = e1 & op(e0, e3) = e1
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18117) implies:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18118)  all_57_12 = e1
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (18115), (18118) imply:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18119)  e3 = e1
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (18110), (18119) imply:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18120)  all_57_4 = e1
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (218), (220),
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (221), (14936), (18038), (18092), (18120),
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2416.
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18121)  all_57_13 = e1 & op(e0, e2) = e1
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18121) implies:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18122)  op(e0, e2) = e1
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18106) gives:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18123)  all_55_8 = e2
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (18123) imply:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18124)  all_53_2 = e2
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (18042), (18124) imply:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18125)  $false
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (18125) is inconsistent.
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18126)  all_55_8 = e1 | all_55_8 = e0
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18126) gives:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18127)  all_55_8 = e1
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (18127) imply:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18128)  all_53_2 = e1
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (18087), (18128) imply:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18129)  $false
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (18129) is inconsistent.
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18130)  all_55_8 = e0
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (18130) imply:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18131)  all_53_2 = e0
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (150), (18131) imply:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18132)   ~ (all_53_1 = e0)
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (164), (18131) imply:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18133)  op(e1, e3) = e0
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18134)  all_55_4 = e3
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (17984), (18134) are inconsistent by
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2170.
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18135)  all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18135) gives:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18136)  all_55_4 = e2
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (18028), (18136) are inconsistent by
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2168.
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18137)  all_55_4 = e1 | all_55_4 = e0
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18137) gives:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18138)  all_55_4 = e1
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (18138) imply:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18139)  all_53_1 = e1
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (18139) implies:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18140)  all_53_1 = e1
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (18140) imply:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18141)   ~ (all_53_3 = e1)
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (18141) implies:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18142)   ~ (all_53_3 = e1)
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18143)  all_55_12 = e3
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (18143) imply:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18144)  all_53_3 = e3
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (18144) implies:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18145)  all_53_3 = e3
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (18145) imply:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18146)   ~ (all_53_11 = e3)
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (18146) implies:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18147)   ~ (all_53_11 = e3)
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18148)  all_55_14 = e3
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (18147), (18148) are inconsistent by
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2294.
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18149)  all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18149) gives:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18150)  all_55_14 = e2
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (14926), (18150) are inconsistent by
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2293.
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18151)  all_55_14 = e1 | all_55_14 = e0
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18151) gives:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18152)  all_55_14 = e1
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (18088), (18152) are inconsistent by
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2165.
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18153)  all_55_14 = e0
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (18153) imply:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18154)  all_53_11 = e0
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (18154) implies:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18155)  all_53_11 = e0
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (18068), (18155) imply:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18156)   ~ (all_52_5 = e0)
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (18156) implies:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18157)   ~ (all_52_5 = e0)
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18158)  all_55_2 = e3
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (18065), (18158) imply:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18159)  all_52_5 = e3
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (18159) implies:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18160)  all_52_5 = e3
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (18057), (18160) imply:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18161)  op(e3, e3) = e1
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (14922), (18055), (18059), (18092), (18095),
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18122), (18161), (function-axioms) are
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #18.
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18162)  all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18065), (18070), (18090), (18157), (18162) are
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #558.
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18163)  all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (145), (164), (247), (14924), (18133), (18142),
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18163), (function-axioms) are inconsistent by
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1336.
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18164)  all_55_4 = e0
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (18132), (18164) are inconsistent by
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1865.
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18165)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (158), (14935), (18088), (18165),
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #15.
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18166)  all_57_9 = e3 & op(e3, e0) = e3
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18166) implies:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18167)  all_57_9 = e3
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18168)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18168) gives:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18169)  all_57_9 = e1 & op(e3, e0) = e1
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18169) implies:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18170)  all_57_9 = e1
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (18167), (18170) are inconsistent by
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1673.
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18171)  all_57_10 = e1 & op(e2, e0) = e1
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18171) implies:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18172)  all_57_10 = e1
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18106) gives:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18173)  all_55_8 = e2
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (18173) imply:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18174)  all_53_2 = e2
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (18042), (18174) imply:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18175)  $false
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (18175) is inconsistent.
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18176)  all_55_8 = e1 | all_55_8 = e0
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18177)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18177) gives:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18178)  all_57_2 = e0 & op(e2, e3) = e0
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18178) implies:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18179)  op(e2, e3) = e0
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18176) gives:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18180)  all_55_8 = e1
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (18087), (18180) are inconsistent by
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2367.
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18181)  all_55_8 = e0
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.68  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (18181) imply:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18182)  all_53_2 = e0
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (18182) implies:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18183)  all_53_2 = e0
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (150), (18183) imply:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18184)   ~ (all_53_1 = e0)
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (18179), (18184), (function-axioms) are
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1943.
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18185)  all_57_3 = e0 & op(e2, e2) = e0
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18185) implies:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18186)  op(e2, e2) = e0
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (18029), (18055), (18059), (18186),
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1653.
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18187)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0)
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18187) gives:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18188)  all_57_5 = e0 & op(e2, e1) = e0
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (18038), (18188) are inconsistent by
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2428.
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18189)  all_57_10 = e0 & op(e2, e0) = e0
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (18172), (18189) are inconsistent by
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1332.
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18190)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (161), (14935), (18089), (18190),
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #88.
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | |   (18191)  all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18191) gives:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | |   (18192)  all_55_11 = e2
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (14929), (18192) are inconsistent by
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2282.
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | |   (18193)  all_55_11 = e1 | all_55_11 = e0
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18193) gives:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | |   (18194)  all_55_11 = e1
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (18089), (18194) are inconsistent by
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2309.
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | |   (18195)  all_55_11 = e0
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (18195) imply:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | |   (18196)  all_53_14 = e0
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (18196) implies:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | |   (18197)  all_53_14 = e0
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (111), (18197) imply:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | |   (18198)   ~ (all_53_13 = e0)
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (18074), (18197) imply:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | |   (18199)   ~ (all_52_7 = e0)
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (18199) implies:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | |   (18200)   ~ (all_52_7 = e0)
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18099) gives:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18201)  all_55_7 = e2
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (14928), (18201) are inconsistent by
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2171.
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18202)  all_55_7 = e1 | all_55_7 = e0
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18202) gives:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18203)  all_55_7 = e1
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (18203) imply:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18204)  all_53_13 = e1
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (18204) implies:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18205)  all_53_13 = e1
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (18072), (18205) imply:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18206)   ~ (all_52_7 = e1)
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (18206) implies:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18207)   ~ (all_52_7 = e1)
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (202), (14935), (18055), (18056), (18059),
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18064), (18075), (18200), (18207),
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #8.
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18208)  all_55_7 = e0
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (18198), (18208) are inconsistent by
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2130.
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | End of split
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | |   (18209)  all_55_10 = e0
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (18077), (18209) are inconsistent by
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | |            sub-proof #2118.
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | End of split
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | End of split
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | End of split
% 225.58/38.69  | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | |   (18210)  all_24_2 = e0
% 225.58/38.69  | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (315), (18210) imply:
% 225.58/38.69  | | | | | | | | | | | | | | | | | |   (18211)  all_6_2 = e0
% 225.58/38.69  | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | SIMP: (18211) implies:
% 225.58/38.69  | | | | | | | | | | | | | | | | | |   (18212)  all_6_2 = e0
% 225.58/38.69  | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | REDUCE: (350), (18212) imply:
% 225.58/38.69  | | | | | | | | | | | | | | | | | |   (18213)   ~ (all_53_2 = e0)
% 225.58/38.69  | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | REDUCE: (368), (18212) imply:
% 225.58/38.69  | | | | | | | | | | | | | | | | | |   (18214)   ~ (all_53_14 = e0)
% 225.58/38.69  | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | REDUCE: (18048), (18212) imply:
% 225.58/38.69  | | | | | | | | | | | | | | | | | |   (18215)   ~ (e2 = e0)
% 225.58/38.69  | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | |   (18216)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 225.58/38.69  | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e0)
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | BETA: splitting (18216) gives:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | |   (18217)  all_57_6 = e0 & op(e1, e3) = e0
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | ALPHA: (18217) implies:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | |   (18218)  op(e1, e3) = e0
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (18213), (18218), (function-axioms) are
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2154.
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | |   (18219)  all_57_7 = e0 & op(e1, e2) = e0
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (18033), (18219) are inconsistent by
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | |            sub-proof #2148.
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | End of split
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | |   (18220)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 225.58/38.69  | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | BETA: splitting (18220) gives:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | |   (18221)  all_57_8 = e0 & op(e1, e1) = e0
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | ALPHA: (18221) implies:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | |   (18222)  all_57_8 = e0
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | |   (18223)  op(e1, e1) = e0
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | |   (18224)  all_55_7 = e3
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (18224) imply:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | |   (18225)  all_53_13 = e3
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | REDUCE: (17989), (18225) imply:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | |   (18226)  $false
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | CLOSE: (18226) is inconsistent.
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | |   (18227)  all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | |   (18228)  all_55_11 = e3
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (18228) imply:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | |   (18229)  all_53_14 = e3
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | SIMP: (18229) implies:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | |   (18230)  all_53_14 = e3
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (142), (18230) imply:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | |   (18231)   ~ (all_53_2 = e3)
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | |   (18232)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e3)
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (171), (235), (17985), (17994),
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | |            (18052), (18053), (18054), (18056), (18057),
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | |            (18058), (18066), (18232), (function-axioms) are
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #10.
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | |   (18233)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e3)
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18233) gives:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | |   (18234)  all_57_4 = e3 & op(e3, e1) = e3
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18234) implies:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | |   (18235)  all_57_4 = e3
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | |   (18236)  op(e3, e1) = e3
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | |   (18237)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e3)
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18237) gives:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | |   (18238)  all_57_6 = e3 & op(e1, e3) = e3
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (18231), (18238), (function-axioms) are
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #153.
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | |   (18239)  all_57_7 = e3 & op(e1, e2) = e3
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (17986), (18239), (function-axioms) are
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #267.
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | |   (18240)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e1, e0) = e3)
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18240) gives:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | |   (18241)  all_57_8 = e3 & op(e1, e1) = e3
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18241) implies:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | |   (18242)  op(e1, e1) = e3
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (14936), (18242), (function-axioms) are
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2468.
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | |   (18243)  all_57_11 = e3 & op(e1, e0) = e3
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18243) implies:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | |   (18244)  all_57_11 = e3
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18245)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e1)
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (18038), (18235), (18245) are
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #200.
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18246)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e1) = e1)
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18246) gives:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18247)  all_57_8 = e1 & op(e1, e1) = e1
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18247) implies:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18248)  op(e1, e1) = e1
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (18223), (18248), (function-axioms) are
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2427.
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18249)  all_57_14 = e1 & op(e0, e1) = e1
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18249) implies:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18250)  all_57_14 = e1
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18251)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e3)
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (168), (235), (17984), (17994),
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18052), (18053), (18054), (18056), (18057),
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18058), (18066), (18251), (function-axioms) are
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #9.
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18252)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e3) = e3)
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18252) gives:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18253)  all_57_6 = e3 & op(e1, e3) = e3
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (18231), (18253), (function-axioms) are
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #153.
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18254)  all_57_12 = e3 & op(e0, e3) = e3
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18254) implies:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18255)  all_57_12 = e3
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18256)  all_57_15 = e0 & op(e0, e0) = e0
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18256) implies:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18257)  op(e0, e0) = e0
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (14935), (18257), (function-axioms) are
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #86.
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18258)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18258) implies:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18259)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0)
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18260)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e1)
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18260) gives:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18261)  all_57_6 = e1 & op(e1, e3) = e1
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18261) implies:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18262)  all_57_6 = e1
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18259) gives:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18263)  all_57_12 = e0 & op(e0, e3) = e0
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18263) implies:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18264)  all_57_12 = e0
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (18255), (18264) imply:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18265)  e3 = e0
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (17993), (18265) imply:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18266)  all_57_3 = e0
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (18029), (18255), (18262), (18266),
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1632.
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18267)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18267) gives:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18268)  all_57_13 = e0 & op(e0, e2) = e0
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18268) implies:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18269)  all_57_13 = e0
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18270)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18270) gives:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18271)  all_57_1 = e1 & op(e3, e2) = e1
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18271) implies:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18272)  all_57_1 = e1
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18273)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e0)
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18273) gives:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18274)  all_57_0 = e0 & op(e3, e3) = e0
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18274) implies:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18275)  op(e3, e3) = e0
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (18053), (18055), (18057), (18236), (18275),
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #237.
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18276)  all_57_1 = e0 & op(e3, e2) = e0
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (18272), (18276) are inconsistent by
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2493.
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18277)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e0)
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18277) gives:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18278)  all_57_4 = e0 & op(e3, e1) = e0
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (161), (163),
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (166), (171), (207), (211), (214), (216), (217),
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (219), (221), (235), (237), (14935), (14936),
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17985), (17986), (17988), (17994), (18033),
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18038), (18052), (18053), (18054), (18056),
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18057), (18058), (18066), (18214), (18278),
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #7.
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18279)  all_57_9 = e0 & op(e3, e0) = e0
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18279) implies:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18280)  op(e3, e0) = e0
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (14935), (18052), (18056), (18280),
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #47.
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18281)  all_57_3 = e1 & op(e2, e2) = e1
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18281) implies:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18282)  op(e2, e2) = e1
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (39), (107), (14935), (18029),
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18034), (18048), (18282), (function-axioms) are
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #44.
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18283)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18283) gives:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18284)  all_57_7 = e1 & op(e1, e2) = e1
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18284) implies:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18285)  all_57_7 = e1
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (8), (9), (39), (216), (217), (14936),
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18222), (18262), (18285), (function-axioms) are
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #325.
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18286)  all_57_13 = e1 & op(e0, e2) = e1
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18286) implies:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18287)  all_57_13 = e1
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (18269), (18287) are inconsistent by
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1760.
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18288)  all_57_14 = e0 & op(e0, e1) = e0
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18288) implies:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18289)  all_57_14 = e0
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (18250), (18289) are inconsistent by
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2122.
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18290)  all_57_7 = e1 & op(e1, e2) = e1
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18290) implies:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18291)  all_57_7 = e1
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (18033), (18291) imply:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18292)  e2 = e1
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (18038), (18292) imply:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18293)  all_57_5 = e1
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (220), (18222), (18235), (18250),
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18293) are inconsistent by sub-proof #1187.
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18294)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e0) = e1)
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (18223), (18244), (18294),
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #6.
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | |   (18295)  all_57_9 = e3 & op(e3, e0) = e3
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18295) implies:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | |   (18296)  all_57_9 = e3
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | |   (18297)  op(e3, e0) = e3
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | |   (18298)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e3)
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18298) gives:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | |   (18299)  all_57_6 = e3 & op(e1, e3) = e3
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (18231), (18299), (function-axioms) are
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #153.
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | |   (18300)  all_57_7 = e3 & op(e1, e2) = e3
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (17986), (18300), (function-axioms) are
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #267.
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | |   (18301)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e1, e0) = e3)
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18301) gives:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | |   (18302)  all_57_8 = e3 & op(e1, e1) = e3
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18302) implies:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | |   (18303)  op(e1, e1) = e3
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (14936), (18303), (function-axioms) are
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2468.
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | |   (18304)  all_57_11 = e3 & op(e1, e0) = e3
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18304) implies:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | |   (18305)  all_57_11 = e3
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18306)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e0)
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18306) gives:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18307)  all_57_0 = e0 & op(e3, e3) = e0
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18307) implies:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18308)  op(e3, e3) = e0
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (14935), (18055), (18059), (18308),
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #53.
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18309)  all_57_1 = e0 & op(e3, e2) = e0
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18309) implies:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18310)  all_57_1 = e0
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18311)  op(e3, e2) = e0
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18312)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18312) gives:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18313)  all_57_1 = e1 & op(e3, e2) = e1
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (18310), (18313) are inconsistent by
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2446.
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18314)  all_57_3 = e1 & op(e2, e2) = e1
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18314) implies:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18315)  op(e2, e2) = e1
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (39), (107), (14935), (18029),
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18034), (18048), (18315), (function-axioms) are
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #44.
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18316)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18316) gives:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18317)  all_57_7 = e1 & op(e1, e2) = e1
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (18033), (18317) are inconsistent by
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2190.
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18318)  all_57_13 = e1 & op(e0, e2) = e1
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18318) implies:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18319)  all_57_13 = e1
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18320)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e3)
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (168), (235), (17984), (17994),
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18052), (18053), (18054), (18056), (18057),
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18058), (18066), (18320), (function-axioms) are
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #9.
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18321)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e3) = e3)
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18321) gives:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18322)  all_57_6 = e3 & op(e1, e3) = e3
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (18231), (18322), (function-axioms) are
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #153.
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18323)  all_57_12 = e3 & op(e0, e3) = e3
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18323) implies:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18324)  all_57_12 = e3
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18325)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e0)
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18325) gives:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18326)  all_57_0 = e0 & op(e3, e3) = e0
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18326) implies:
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18327)  op(e3, e3) = e0
% 225.58/38.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (14935), (18055), (18059), (18327),
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #53.
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18328)  all_57_2 = e0 & op(e2, e3) = e0
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18328) implies:
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18329)  all_57_2 = e0
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18330)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e1)
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18330) gives:
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18331)  all_57_6 = e1 & op(e1, e3) = e1
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18331) implies:
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18332)  all_57_6 = e1
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18333)  all_57_15 = e0 & op(e0, e0) = e0
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18333) implies:
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18334)  op(e0, e0) = e0
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (18054), (18058), (18311), (18334),
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2399.
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18335)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18335) implies:
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18336)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0)
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18336) gives:
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18337)  all_57_12 = e0 & op(e0, e3) = e0
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18337) implies:
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18338)  all_57_12 = e0
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (18324), (18338) imply:
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18339)  e3 = e0
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (17993), (18339) imply:
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18340)  all_57_3 = e0
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18329), (18340) are inconsistent by sub-proof
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2246.
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18341)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18341) gives:
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18342)  all_57_13 = e0 & op(e0, e2) = e0
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18342) implies:
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18343)  all_57_13 = e0
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (18319), (18343) are inconsistent by
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1760.
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18344)  all_57_14 = e0 & op(e0, e1) = e0
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18344) implies:
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18345)  all_57_14 = e0
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18346)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e3)
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18346) gives:
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18347)  all_57_4 = e3 & op(e3, e1) = e3
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18347) implies:
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18348)  all_57_4 = e3
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18349)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e1)
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18349) gives:
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18350)  all_57_4 = e1 & op(e3, e1) = e1
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.58/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18350) implies:
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18351)  all_57_4 = e1
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (18348), (18351) imply:
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18352)  e3 = e1
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (18296), (18352) imply:
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18353)  all_57_9 = e1
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (231), (237), (18029),
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18351), (18353), (function-axioms) are
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1672.
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18354)  all_57_5 = e1 & op(e2, e1) = e1
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18354) implies:
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18355)  all_57_5 = e1
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (18038), (18355) imply:
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18356)  e2 = e1
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (18033), (18356) imply:
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18357)  all_57_7 = e1
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (8), (9), (39), (216), (217), (14936),
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18222), (18332), (18357), (function-axioms) are
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #325.
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18358)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e1) = e1)
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (18223), (18345), (18358), (function-axioms)
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #81.
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18359)  all_57_5 = e3 & op(e2, e1) = e3
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (17988), (18359), (function-axioms) are
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #270.
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18360)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e1) = e3)
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18360) gives:
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18361)  all_57_8 = e3 & op(e1, e1) = e3
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18361) implies:
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18362)  op(e1, e1) = e3
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (14936), (18362), (function-axioms) are
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2468.
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18363)  all_57_14 = e3 & op(e0, e1) = e3
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18363) implies:
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18364)  all_57_14 = e3
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (18345), (18364) imply:
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18365)  e3 = e0
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (17993), (18365) imply:
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18366)  all_57_3 = e0
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18329), (18366) are inconsistent by sub-proof
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2246.
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18367)  all_57_7 = e1 & op(e1, e2) = e1
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (18033), (18367) are inconsistent by
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2190.
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18368)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e0) = e1)
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (18223), (18305), (18368),
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #6.
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18369)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = e0)
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18369) gives:
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18370)  all_57_6 = e0 & op(e1, e3) = e0
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18370) implies:
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18371)  op(e1, e3) = e0
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (18213), (18371), (function-axioms) are
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2154.
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18372)  all_57_12 = e0 & op(e0, e3) = e0
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (18324), (18372) are inconsistent by
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2237.
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18373)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e0)
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18373) gives:
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18374)  all_57_4 = e0 & op(e3, e1) = e0
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (161), (163),
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (166), (171), (207), (211), (214), (216), (217),
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (219), (221), (235), (237), (14935), (14936),
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17985), (17986), (17988), (17994), (18033),
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18038), (18052), (18053), (18054), (18056),
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18057), (18058), (18066), (18214), (18374),
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #7.
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18375)  all_57_9 = e0 & op(e3, e0) = e0
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18375) implies:
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18376)  op(e3, e0) = e0
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (18297), (18376), (function-axioms) are
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #313.
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | |   (18377)  all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18377) gives:
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | |   (18378)  all_55_11 = e2
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (14929), (18378) are inconsistent by
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2282.
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | |   (18379)  all_55_11 = e1 | all_55_11 = e0
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18379) gives:
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | |   (18380)  all_55_11 = e1
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (18380) imply:
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | |   (18381)  all_53_14 = e1
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (18381) implies:
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | |   (18382)  all_53_14 = e1
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (111), (18382) imply:
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | |   (18383)   ~ (all_53_13 = e1)
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (18074), (18382) imply:
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | |   (18384)   ~ (all_52_7 = e1)
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (18384) implies:
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | |   (18385)   ~ (all_52_7 = e1)
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18227) gives:
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | |   (18386)  all_55_7 = e2
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (14928), (18386) are inconsistent by
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2171.
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | |   (18387)  all_55_7 = e1 | all_55_7 = e0
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18387) gives:
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | |   (18388)  all_55_7 = e1
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (18383), (18388) are inconsistent by
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1970.
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | |   (18389)  all_55_7 = e0
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (18389) imply:
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | |   (18390)  all_53_13 = e0
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (18390) implies:
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | |   (18391)  all_53_13 = e0
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (18072), (18391) imply:
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | |   (18392)   ~ (all_52_7 = e0)
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (18392) implies:
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | |   (18393)   ~ (all_52_7 = e0)
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (202), (14935), (18055), (18056), (18059),
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | |            (18064), (18075), (18385), (18393),
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | |            #8.
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | |   (18394)  all_55_11 = e0
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (18214), (18394) are inconsistent by
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2308.
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | |   (18395)  all_57_11 = e0 & op(e1, e0) = e0
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (18214), (18395), (function-axioms) are
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2341.
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.70  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.70  | | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | End of split
% 225.63/38.70  | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.70  | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | |   (18396)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 225.63/38.70  | | | | | | | | | | | | | | | | |            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 225.63/38.70  | | | | | | | | | | | | | | | | |            op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 225.63/38.70  | | | | | | | | | | | | | | | | |              all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 225.63/38.70  | | | | | | | | | | | | | | | | |            & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 225.63/38.70  | | | | | | | | | | | | | | | | |            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 225.63/38.70  | | | | | | | | | | | | | | | | |            $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 225.63/38.70  | | | | | | | | | | | | | | | | |            $i(all_52_15)
% 225.63/38.70  | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | ALPHA: (18396) implies:
% 225.63/38.70  | | | | | | | | | | | | | | | | |   (18397)  op(e2, e1) = all_52_13
% 225.63/38.70  | | | | | | | | | | | | | | | | |   (18398)  op(e2, e2) = all_52_11
% 225.63/38.70  | | | | | | | | | | | | | | | | |   (18399)  op(all_52_13, all_52_13) = e1
% 225.63/38.70  | | | | | | | | | | | | | | | | |   (18400)  op(all_52_11, all_52_11) = e2
% 225.63/38.70  | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 225.63/38.70  | | | | | | | | | | | | | | | | |              all_52_13, e1, e2, simplifying with (18039),
% 225.63/38.70  | | | | | | | | | | | | | | | | |              (18397) gives:
% 225.63/38.70  | | | | | | | | | | | | | | | | |   (18401)  all_52_13 = e2
% 225.63/38.70  | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3,
% 225.63/38.70  | | | | | | | | | | | | | | | | |              all_52_11, e2, e2, simplifying with (17994),
% 225.63/38.70  | | | | | | | | | | | | | | | | |              (18398) gives:
% 225.63/38.70  | | | | | | | | | | | | | | | | |   (18402)  all_52_11 = e3
% 225.63/38.70  | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | REDUCE: (18399), (18401) imply:
% 225.63/38.70  | | | | | | | | | | | | | | | | |   (18403)  op(e2, e2) = e1
% 225.63/38.70  | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (39), (107), (14935), (18029),
% 225.63/38.70  | | | | | | | | | | | | | | | | |            (18034), (18048), (18403), (function-axioms) are
% 225.63/38.70  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #44.
% 225.63/38.70  | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | End of split
% 225.63/38.70  | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | Case 2:
% 225.63/38.70  | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | |   (18404)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 225.63/38.70  | | | | | | | | | | | | | | | |              & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 225.63/38.70  | | | | | | | | | | | | | | | |              & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 225.63/38.70  | | | | | | | | | | | | | | | |                all_52_21) = e1 & op(all_52_23, all_52_23) =
% 225.63/38.70  | | | | | | | | | | | | | | | |              e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 225.63/38.70  | | | | | | | | | | | | | | | |              all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 225.63/38.70  | | | | | | | | | | | | | | | |              = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 225.63/38.70  | | | | | | | | | | | | | | | |              $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 225.63/38.70  | | | | | | | | | | | | | | | |              & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 225.63/38.70  | | | | | | | | | | | | | | | |              e0 & op(all_52_25, all_52_25) = e3 &
% 225.63/38.70  | | | | | | | | | | | | | | | |              op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 225.63/38.70  | | | | | | | | | | | | | | | |                all_52_29) = e1 & op(all_52_31, all_52_31) =
% 225.63/38.70  | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 225.63/38.70  | | | | | | | | | | | | | | | |              all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 225.63/38.70  | | | | | | | | | | | | | | | |              = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 225.63/38.70  | | | | | | | | | | | | | | | |              $i(all_52_29) & $i(all_52_31))
% 225.63/38.70  | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | BETA: splitting (18404) gives:
% 225.63/38.70  | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.70  | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | |   (18405)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 225.63/38.70  | | | | | | | | | | | | | | | | |            all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 225.63/38.70  | | | | | | | | | | | | | | | | |            op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 225.63/38.70  | | | | | | | | | | | | | | | | |              all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 225.63/38.70  | | | | | | | | | | | | | | | | |            & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 225.63/38.70  | | | | | | | | | | | | | | | | |            & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 225.63/38.70  | | | | | | | | | | | | | | | | |            & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 225.63/38.70  | | | | | | | | | | | | | | | | |            $i(all_52_23)
% 225.63/38.70  | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | ALPHA: (18405) implies:
% 225.63/38.70  | | | | | | | | | | | | | | | | |   (18406)  op(e1, e2) = all_52_19
% 225.63/38.70  | | | | | | | | | | | | | | | | |   (18407)  op(all_52_19, all_52_19) = e2
% 225.63/38.70  | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 225.63/38.70  | | | | | | | | | | | | | | | | |              all_52_19, e2, e1, simplifying with (18034),
% 225.63/38.70  | | | | | | | | | | | | | | | | |              (18406) gives:
% 225.63/38.70  | | | | | | | | | | | | | | | | |   (18408)  all_52_19 = e2
% 225.63/38.70  | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | REDUCE: (18407), (18408) imply:
% 225.63/38.70  | | | | | | | | | | | | | | | | |   (18409)  op(e2, e2) = e2
% 225.63/38.70  | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (17994), (18409), (function-axioms) are
% 225.63/38.70  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2298.
% 225.63/38.70  | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.70  | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | |   (18410)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 225.63/38.70  | | | | | | | | | | | | | | | | |            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 225.63/38.70  | | | | | | | | | | | | | | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 225.63/38.70  | | | | | | | | | | | | | | | | |              all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 225.63/38.70  | | | | | | | | | | | | | | | | |            & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 225.63/38.70  | | | | | | | | | | | | | | | | |            & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 225.63/38.70  | | | | | | | | | | | | | | | | |            & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 225.63/38.70  | | | | | | | | | | | | | | | | |            $i(all_52_31)
% 225.63/38.70  | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | ALPHA: (18410) implies:
% 225.63/38.70  | | | | | | | | | | | | | | | | |   (18411)  op(e0, e0) = all_52_31
% 225.63/38.70  | | | | | | | | | | | | | | | | |   (18412)  op(all_52_31, all_52_31) = e0
% 225.63/38.70  | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (14935), (17994), (18411), (18412),
% 225.63/38.70  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.70  | | | | | | | | | | | | | | | | |            #11.
% 225.63/38.70  | | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | | End of split
% 225.63/38.70  | | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | End of split
% 225.63/38.70  | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | Case 2:
% 225.63/38.70  | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | |   (18413)  all_57_10 = e2 & op(e2, e0) = e2
% 225.63/38.70  | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | | REF_CLOSE: (165), (14928), (18413), (function-axioms) are
% 225.63/38.70  | | | | | | | | | | | | | | |            inconsistent by sub-proof #2432.
% 225.63/38.70  | | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | | End of split
% 225.63/38.70  | | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | End of split
% 225.63/38.70  | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | Case 2:
% 225.63/38.70  | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | |   (18414)  all_57_13 = e2 & op(e0, e2) = e2
% 225.63/38.70  | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | ALPHA: (18414) implies:
% 225.63/38.70  | | | | | | | | | | | | |   (18415)  op(e0, e2) = e2
% 225.63/38.70  | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | | REF_CLOSE: (159), (14925), (18415), (function-axioms) are
% 225.63/38.70  | | | | | | | | | | | | |            inconsistent by sub-proof #2335.
% 225.63/38.70  | | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | End of split
% 225.63/38.70  | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | End of split
% 225.63/38.70  | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | End of split
% 225.63/38.70  | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | Case 2:
% 225.63/38.70  | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | |   (18416)  all_18_2 = e0
% 225.63/38.70  | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | COMBINE_EQS: (327), (18416) imply:
% 225.63/38.70  | | | | | | | | | |   (18417)  all_10_2 = e0
% 225.63/38.70  | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | SIMP: (18417) implies:
% 225.63/38.70  | | | | | | | | | |   (18418)  all_10_2 = e0
% 225.63/38.70  | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | REDUCE: (338), (18418) imply:
% 225.63/38.70  | | | | | | | | | |   (18419)   ~ (all_53_1 = e0)
% 225.63/38.70  | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | REDUCE: (340), (18418) imply:
% 225.63/38.70  | | | | | | | | | |   (18420)   ~ (all_53_2 = e0)
% 225.63/38.70  | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | REDUCE: (342), (18418) imply:
% 225.63/38.70  | | | | | | | | | |   (18421)   ~ (all_53_3 = e0)
% 225.63/38.70  | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | REDUCE: (344), (18418) imply:
% 225.63/38.70  | | | | | | | | | |   (18422)   ~ (all_53_4 = e0)
% 225.63/38.70  | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | REDUCE: (348), (18418) imply:
% 225.63/38.70  | | | | | | | | | |   (18423)   ~ (all_53_12 = e0)
% 225.63/38.70  | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | REDUCE: (45), (18418) imply:
% 225.63/38.70  | | | | | | | | | |   (18424)  op(e3, e3) = e0
% 225.63/38.70  | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | BETA: splitting (107) gives:
% 225.63/38.70  | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | Case 1:
% 225.63/38.70  | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | |   (18425)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 225.63/38.70  | | | | | | | | | | |              all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 225.63/38.70  | | | | | | | | | | |              op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 225.63/38.70  | | | | | | | | | | |                all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 225.63/38.70  | | | | | | | | | | |              op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 225.63/38.70  | | | | | | | | | | |              op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 225.63/38.70  | | | | | | | | | | |              $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 225.63/38.70  | | | | | | | | | | |              $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 225.63/38.70  | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 225.63/38.70  | | | | | | | | | | |                all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 225.63/38.70  | | | | | | | | | | |              & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 225.63/38.70  | | | | | | | | | | |                all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 225.63/38.70  | | | | | | | | | | |              op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 225.63/38.70  | | | | | | | | | | |              & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 225.63/38.70  | | | | | | | | | | |              $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 225.63/38.70  | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | BETA: splitting (18425) gives:
% 225.63/38.70  | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | Case 1:
% 225.63/38.70  | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | |   (18426)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 225.63/38.70  | | | | | | | | | | | |            all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 225.63/38.70  | | | | | | | | | | | |            op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 225.63/38.70  | | | | | | | | | | | |              all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 225.63/38.70  | | | | | | | | | | | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 225.63/38.70  | | | | | | | | | | | |            op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 225.63/38.70  | | | | | | | | | | | |            $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 225.63/38.70  | | | | | | | | | | | |            $i(all_52_7)
% 225.63/38.70  | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | ALPHA: (18426) implies:
% 225.63/38.70  | | | | | | | | | | | |   (18427)  op(e3, e3) = all_52_1
% 225.63/38.70  | | | | | | | | | | | |   (18428)  op(all_52_1, all_52_1) = e3
% 225.63/38.70  | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | REF_CLOSE: (9), (14935), (18424), (18427), (18428),
% 225.63/38.70  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.70  | | | | | | | | | | | |            #53.
% 225.63/38.70  | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | Case 2:
% 225.63/38.70  | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | |   (18429)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 225.63/38.70  | | | | | | | | | | | |            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 225.63/38.70  | | | | | | | | | | | |            op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 225.63/38.70  | | | | | | | | | | | |              all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 225.63/38.70  | | | | | | | | | | | |            & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 225.63/38.70  | | | | | | | | | | | |            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 225.63/38.70  | | | | | | | | | | | |            $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 225.63/38.70  | | | | | | | | | | | |            $i(all_52_15)
% 225.63/38.70  | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | REF_CLOSE: (5), (17994), (18424), (18429), (function-axioms)
% 225.63/38.70  | | | | | | | | | | | |            are inconsistent by sub-proof #209.
% 225.63/38.70  | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | End of split
% 225.63/38.70  | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | Case 2:
% 225.63/38.70  | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | |   (18430)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 225.63/38.70  | | | | | | | | | | |              & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 225.63/38.70  | | | | | | | | | | |              & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 225.63/38.70  | | | | | | | | | | |                all_52_21) = e1 & op(all_52_23, all_52_23) =
% 225.63/38.70  | | | | | | | | | | |              e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 225.63/38.70  | | | | | | | | | | |              all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 225.63/38.70  | | | | | | | | | | |              = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 225.63/38.70  | | | | | | | | | | |              $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 225.63/38.70  | | | | | | | | | | |              & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 225.63/38.70  | | | | | | | | | | |              e0 & op(all_52_25, all_52_25) = e3 &
% 225.63/38.70  | | | | | | | | | | |              op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 225.63/38.70  | | | | | | | | | | |                all_52_29) = e1 & op(all_52_31, all_52_31) =
% 225.63/38.70  | | | | | | | | | | |              e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 225.63/38.70  | | | | | | | | | | |              all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 225.63/38.70  | | | | | | | | | | |              = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 225.63/38.70  | | | | | | | | | | |              $i(all_52_29) & $i(all_52_31))
% 225.63/38.70  | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | BETA: splitting (18430) gives:
% 225.63/38.70  | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | Case 1:
% 225.63/38.70  | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | |   (18431)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 225.63/38.70  | | | | | | | | | | | |            all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 225.63/38.70  | | | | | | | | | | | |            op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 225.63/38.70  | | | | | | | | | | | |              all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 225.63/38.70  | | | | | | | | | | | |            & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 225.63/38.70  | | | | | | | | | | | |            & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 225.63/38.70  | | | | | | | | | | | |            & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 225.63/38.70  | | | | | | | | | | | |            $i(all_52_23)
% 225.63/38.70  | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | ALPHA: (18431) implies:
% 225.63/38.70  | | | | | | | | | | | |   (18432)  op(e1, e0) = all_52_23
% 225.63/38.70  | | | | | | | | | | | |   (18433)  op(e1, e1) = all_52_21
% 225.63/38.70  | | | | | | | | | | | |   (18434)  op(e1, e2) = all_52_19
% 225.63/38.70  | | | | | | | | | | | |   (18435)  op(e1, e3) = all_52_17
% 225.63/38.70  | | | | | | | | | | | |   (18436)  op(all_52_23, all_52_23) = e0
% 225.63/38.70  | | | | | | | | | | | |   (18437)  op(all_52_21, all_52_21) = e1
% 225.63/38.70  | | | | | | | | | | | |   (18438)  op(all_52_19, all_52_19) = e2
% 225.63/38.70  | | | | | | | | | | | |   (18439)  op(all_52_17, all_52_17) = e3
% 225.63/38.70  | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_14,
% 225.63/38.70  | | | | | | | | | | | |              all_52_23, e0, e1, simplifying with (161), (18432)
% 225.63/38.70  | | | | | | | | | | | |              gives:
% 225.63/38.70  | | | | | | | | | | | |   (18440)  all_53_14 = all_52_23
% 225.63/38.70  | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 225.63/38.70  | | | | | | | | | | | |              all_52_21, e1, e1, simplifying with (39), (18433)
% 225.63/38.70  | | | | | | | | | | | |              gives:
% 225.63/38.70  | | | | | | | | | | | |   (18441)  all_52_21 = all_6_2
% 225.63/38.70  | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_6,
% 225.63/38.70  | | | | | | | | | | | |              all_52_19, e2, e1, simplifying with (163), (18434)
% 225.63/38.70  | | | | | | | | | | | |              gives:
% 225.63/38.70  | | | | | | | | | | | |   (18442)  all_53_6 = all_52_19
% 225.63/38.70  | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_2,
% 225.63/38.70  | | | | | | | | | | | |              all_52_17, e3, e1, simplifying with (164), (18435)
% 225.63/38.70  | | | | | | | | | | | |              gives:
% 225.63/38.70  | | | | | | | | | | | |   (18443)  all_53_2 = all_52_17
% 225.63/38.70  | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | COMBINE_EQS: (256), (18442) imply:
% 225.63/38.70  | | | | | | | | | | | |   (18444)  all_55_9 = all_52_19
% 225.63/38.70  | | | | | | | | | | | | 
% 225.63/38.70  | | | | | | | | | | | | COMBINE_EQS: (257), (18443) imply:
% 225.63/38.70  | | | | | | | | | | | |   (18445)  all_55_8 = all_52_17
% 225.63/38.70  | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | REDUCE: (150), (18443) imply:
% 225.63/38.71  | | | | | | | | | | | |   (18446)   ~ (all_53_1 = all_52_17)
% 225.63/38.71  | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | REDUCE: (145), (18443) imply:
% 225.63/38.71  | | | | | | | | | | | |   (18447)   ~ (all_53_3 = all_52_17)
% 225.63/38.71  | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | SIMP: (18447) implies:
% 225.63/38.71  | | | | | | | | | | | |   (18448)   ~ (all_53_3 = all_52_17)
% 225.63/38.71  | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | REDUCE: (18420), (18443) imply:
% 225.63/38.71  | | | | | | | | | | | |   (18449)   ~ (all_52_17 = e0)
% 225.63/38.71  | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | REDUCE: (361), (18442) imply:
% 225.63/38.71  | | | | | | | | | | | |   (18450)   ~ (all_52_19 = all_6_2)
% 225.63/38.71  | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | REDUCE: (17986), (18442) imply:
% 225.63/38.71  | | | | | | | | | | | |   (18451)   ~ (all_52_19 = e3)
% 225.63/38.71  | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | REDUCE: (18437), (18441) imply:
% 225.63/38.71  | | | | | | | | | | | |   (18452)  op(all_6_2, all_6_2) = e1
% 225.63/38.71  | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | BETA: splitting (67) gives:
% 225.63/38.71  | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | Case 1:
% 225.63/38.71  | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | |   (18453)   ~ (all_24_2 = e0)
% 225.63/38.71  | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | REDUCE: (315), (18453) imply:
% 225.63/38.71  | | | | | | | | | | | | |   (18454)   ~ (all_6_2 = e0)
% 225.63/38.71  | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | BETA: splitting (88) gives:
% 225.63/38.71  | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | Case 1:
% 225.63/38.71  | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | |   (18455)   ~ (all_38_2 = e2)
% 225.63/38.71  | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | REDUCE: (249), (18455) imply:
% 225.63/38.71  | | | | | | | | | | | | | |   (18456)   ~ (all_6_2 = e2)
% 225.63/38.71  | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 225.63/38.71  | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | Case 1:
% 225.63/38.71  | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | |   (18457)  all_55_10 = e3
% 225.63/38.71  | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | REF_CLOSE: (336), (14936), (18457) are inconsistent by
% 225.63/38.71  | | | | | | | | | | | | | | |            sub-proof #2500.
% 225.63/38.71  | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | Case 2:
% 225.63/38.71  | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | |   (18458)   ~ (all_55_10 = e3)
% 225.63/38.71  | | | | | | | | | | | | | | |   (18459)  all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 225.63/38.71  | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | BETA: splitting (18459) gives:
% 225.63/38.71  | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | Case 1:
% 225.63/38.71  | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | |   (18460)  all_55_10 = e2
% 225.63/38.71  | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | REF_CLOSE: (336), (18456), (18460) are inconsistent by
% 225.63/38.71  | | | | | | | | | | | | | | | |            sub-proof #2499.
% 225.63/38.71  | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | Case 2:
% 225.63/38.71  | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | |   (18461)   ~ (all_55_10 = e2)
% 225.63/38.71  | | | | | | | | | | | | | | | |   (18462)  all_55_10 = e1 | all_55_10 = e0
% 225.63/38.71  | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | BETA: splitting (18462) gives:
% 225.63/38.71  | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.71  | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | |   (18463)  all_55_10 = e1
% 225.63/38.71  | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | COMBINE_EQS: (336), (18463) imply:
% 225.63/38.71  | | | | | | | | | | | | | | | | |   (18464)  all_6_2 = e1
% 225.63/38.71  | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | SIMP: (18464) implies:
% 225.63/38.71  | | | | | | | | | | | | | | | | |   (18465)  all_6_2 = e1
% 225.63/38.71  | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | REDUCE: (366), (18465) imply:
% 225.63/38.71  | | | | | | | | | | | | | | | | |   (18466)   ~ (all_53_11 = e1)
% 225.63/38.71  | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | REDUCE: (18450), (18465) imply:
% 225.63/38.71  | | | | | | | | | | | | | | | | |   (18467)   ~ (all_52_19 = e1)
% 225.63/38.71  | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | REDUCE: (14936), (18465) imply:
% 225.63/38.71  | | | | | | | | | | | | | | | | |   (18468)   ~ (e3 = e1)
% 225.63/38.71  | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | REDUCE: (18456), (18465) imply:
% 225.63/38.71  | | | | | | | | | | | | | | | | |   (18469)   ~ (e2 = e1)
% 225.63/38.71  | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | REDUCE: (39), (18465) imply:
% 225.63/38.71  | | | | | | | | | | | | | | | | |   (18470)  op(e1, e1) = e1
% 225.63/38.71  | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | BETA: splitting (97) gives:
% 225.63/38.71  | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | |   (18471)   ~ (all_44_2 = e3)
% 225.63/38.71  | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | REDUCE: (17983), (18471) imply:
% 225.63/38.71  | | | | | | | | | | | | | | | | | |   (18472)  $false
% 225.63/38.71  | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | CLOSE: (18472) is inconsistent.
% 225.63/38.71  | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | |   (18473)  ( ~ (all_44_0 = e1) & op(all_44_1, e2) = all_44_0
% 225.63/38.71  | | | | | | | | | | | | | | | | | |              & op(e2, e3) = all_44_1 & $i(all_44_0) &
% 225.63/38.71  | | | | | | | | | | | | | | | | | |              $i(all_44_1)) | ( ~ (all_44_1 = e0) & op(e2, e3)
% 225.63/38.71  | | | | | | | | | | | | | | | | | |              = all_44_1 & $i(all_44_1))
% 225.63/38.71  | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | |   (18474)  all_55_14 = e3
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (18474) imply:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | |   (18475)  all_53_11 = e3
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | REDUCE: (140), (18475) imply:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | |   (18476)   ~ (all_53_3 = e3)
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | |   (18477)  all_55_12 = e3
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (18477) imply:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | |   (18478)  all_53_3 = e3
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | REDUCE: (18476), (18478) imply:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | |   (18479)  $false
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | CLOSE: (18479) is inconsistent.
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | |   (18480)   ~ (all_55_12 = e3)
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | |   (18481)  all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | BETA: splitting (18481) gives:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | |   (18482)  all_55_12 = e2
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (18482) imply:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | |   (18483)  all_53_3 = e2
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | REDUCE: (14924), (18483) imply:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | |   (18484)  $false
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | CLOSE: (18484) is inconsistent.
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | |   (18485)   ~ (all_55_12 = e2)
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | |   (18486)  all_55_12 = e1 | all_55_12 = e0
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18486) gives:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | |   (18487)  all_55_12 = e1
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (18487) imply:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | |   (18488)  all_53_3 = e1
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (18488) imply:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | |   (18489)   ~ (all_53_1 = e1)
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | |   (18490)  all_55_4 = e3
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (17984), (18490) are inconsistent by
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2170.
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | |   (18491)  all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18491) gives:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | |   (18492)  all_55_4 = e2
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (18492) imply:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | |   (18493)  all_53_1 = e2
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (18493) implies:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | |   (18494)  all_53_1 = e2
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (18446), (18494) imply:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | |   (18495)   ~ (all_52_17 = e2)
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (18495) implies:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | |   (18496)   ~ (all_52_17 = e2)
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (193), (197), (247), (14924), (18421), (18424),
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | |            (18439), (18445), (18448), (18449), (18476),
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | |            (18496), (function-axioms) are inconsistent by
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #43.
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | |   (18497)  all_55_4 = e1 | all_55_4 = e0
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (18419), (18489), (18497) are inconsistent
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #773.
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | |   (18498)  all_55_12 = e0
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (18498) imply:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | |   (18499)  all_53_3 = e0
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (18421), (18499) imply:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | |   (18500)  $false
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (18500) is inconsistent.
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | |   (18501)   ~ (all_55_14 = e3)
% 225.63/38.71  | | | | | | | | | | | | | | | | | | |   (18502)  all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | REDUCE: (245), (18501) imply:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | |   (18503)   ~ (all_53_11 = e3)
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | |   (18504)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | BETA: splitting (18504) gives:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | |   (18505)  all_57_12 = e3 & op(e0, e3) = e3
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | ALPHA: (18505) implies:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | |   (18506)  all_57_12 = e3
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | |   (18507)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18507) gives:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | |   (18508)  all_57_12 = e1 & op(e0, e3) = e1
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (18506), (18508) are inconsistent by
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2230.
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | |   (18509)  all_57_13 = e1 & op(e0, e2) = e1
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18509) implies:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | |   (18510)  all_57_13 = e1
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | |   (18511)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e3)
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18511) gives:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | |   (18512)  all_57_4 = e3 & op(e3, e1) = e3
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18512) implies:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | |   (18513)  all_57_4 = e3
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18502) gives:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | |   (18514)  all_55_14 = e2
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (18514) imply:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | |   (18515)  all_53_11 = e2
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14926), (18515) imply:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | |   (18516)  $false
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (18516) is inconsistent.
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | |   (18517)   ~ (all_55_14 = e2)
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | |   (18518)  all_55_14 = e1 | all_55_14 = e0
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18519)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e2)
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18519) gives:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18520)  all_57_4 = e2 & op(e3, e1) = e2
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18520) implies:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18521)  all_57_4 = e2
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (18513), (18521) are inconsistent by
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2482.
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18522)  all_57_5 = e2 & op(e2, e1) = e2
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18522) implies:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18523)  all_57_5 = e2
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18524)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e0)
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18524) gives:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18525)  all_57_4 = e0 & op(e3, e1) = e0
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18525) implies:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18526)  op(e3, e1) = e0
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (122), (170), (245), (18466), (18518), (18526),
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2164.
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18527)  all_57_5 = e0 & op(e2, e1) = e0
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (18523), (18527) are inconsistent by
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2428.
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18528)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18528) gives:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18529)  all_57_8 = e0 & op(e1, e1) = e0
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18529) implies:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18530)  op(e1, e1) = e0
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (18470), (18530), (function-axioms) are
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2427.
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18531)  all_57_14 = e0 & op(e0, e1) = e0
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18531) implies:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18532)  all_57_14 = e0
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18533)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e2)
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18533) gives:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18534)  all_57_0 = e2 & op(e3, e3) = e2
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18534) implies:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18535)  op(e3, e3) = e2
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (169), (171),
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (219), (220), (221), (231), (14936), (18422),
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18423), (18532), (18535), (function-axioms) are
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1293.
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18536)  all_57_1 = e2 & op(e3, e2) = e2
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18536) implies:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18537)  op(e3, e2) = e2
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18538)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18538) gives:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18539)  all_57_2 = e0 & op(e2, e3) = e0
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18539) implies:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18540)  op(e2, e3) = e0
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (18419), (18540), (function-axioms) are
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1943.
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18541)  all_57_3 = e0 & op(e2, e2) = e0
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18541) implies:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18542)  all_57_3 = e0
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (17993), (18542) imply:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18543)  e3 = e0
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (18543) implies:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18544)  e3 = e0
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (18513), (18544) imply:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18545)  all_57_4 = e0
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (219), (220),
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (221), (14936), (18532), (18545),
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2371.
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18546)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0)
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18546) gives:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18547)  all_57_5 = e0 & op(e2, e1) = e0
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18547) implies:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18548)  all_57_5 = e0
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (18523), (18548) imply:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18549)  e2 = e0
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14934), (18549) imply:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18550)  all_57_15 = e0
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (209), (18506), (18510), (18532),
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18550) are inconsistent by sub-proof #2124.
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18551)  all_57_10 = e0 & op(e2, e0) = e0
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18551) implies:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18552)  all_57_10 = e0
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18553)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18553) gives:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18554)  all_57_2 = e1 & op(e2, e3) = e1
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18554) implies:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18555)  op(e2, e3) = e1
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (196), (17982), (17994), (18434), (18438),
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18444), (18451), (18467), (18473), (18555),
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #208.
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18556)  all_57_3 = e1 & op(e2, e2) = e1
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18556) implies:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18557)  op(e2, e2) = e1
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (9), (39), (159), (164), (214),
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (229), (14935), (17987), (18420), (18432),
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18436), (18454), (18537), (18557),
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #42.
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18558)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (9), (220), (18470), (18513),
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18532), (18552), (18558), (function-axioms) are
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #191.
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18559)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e2)
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (169), (14927), (18513), (18559),
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1208.
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18560)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e1) = e2)
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18560) gives:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18561)  all_57_8 = e2 & op(e1, e1) = e2
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18561) implies:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18562)  op(e1, e1) = e2
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (18470), (18562), (function-axioms) are
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2423.
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18563)  all_57_14 = e2 & op(e0, e1) = e2
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (14926), (18563), (function-axioms) are
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #54.
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | |   (18564)  all_57_5 = e3 & op(e2, e1) = e3
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (17988), (18564), (function-axioms) are
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #270.
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | |   (18565)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e1) = e3)
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18565) gives:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | |   (18566)  all_57_8 = e3 & op(e1, e1) = e3
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18566) implies:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | |   (18567)  op(e1, e1) = e3
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (17995), (18433), (18437), (18567),
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | |            #167.
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | |   (18568)  all_57_14 = e3 & op(e0, e1) = e3
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (18503), (18568), (function-axioms) are
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #129.
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | |   (18569)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (158), (14935), (18466), (18569),
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | |            #15.
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | |   (18570)  all_57_13 = e3 & op(e0, e2) = e3
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (17987), (18570), (function-axioms) are
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #78.
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | |   (18571)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (158), (14934), (18503), (18571),
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | |            #55.
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.71  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.71  | | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | End of split
% 225.63/38.71  | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.71  | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | |   (18572)  all_55_10 = e0
% 225.63/38.71  | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (18454), (18572) are inconsistent by
% 225.63/38.71  | | | | | | | | | | | | | | | | |            sub-proof #2118.
% 225.63/38.71  | | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | | End of split
% 225.63/38.71  | | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | | End of split
% 225.63/38.71  | | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | End of split
% 225.63/38.71  | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | Case 2:
% 225.63/38.71  | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | |   (18573)  all_38_2 = e2
% 225.63/38.71  | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | | REF_CLOSE: (8), (249), (17994), (18452), (18573),
% 225.63/38.71  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.71  | | | | | | | | | | | | | |            #206.
% 225.63/38.71  | | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | End of split
% 225.63/38.71  | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | Case 2:
% 225.63/38.71  | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | |   (18574)  all_24_2 = e0
% 225.63/38.71  | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | COMBINE_EQS: (315), (18574) imply:
% 225.63/38.71  | | | | | | | | | | | | |   (18575)  all_6_2 = e0
% 225.63/38.71  | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | REDUCE: (18452), (18575) imply:
% 225.63/38.71  | | | | | | | | | | | | |   (18576)  op(e0, e0) = e1
% 225.63/38.71  | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | REF_CLOSE: (6), (14935), (18576), (function-axioms) are
% 225.63/38.71  | | | | | | | | | | | | |            inconsistent by sub-proof #2177.
% 225.63/38.71  | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | End of split
% 225.63/38.71  | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | Case 2:
% 225.63/38.71  | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | |   (18577)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 225.63/38.71  | | | | | | | | | | | |            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 225.63/38.71  | | | | | | | | | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 225.63/38.71  | | | | | | | | | | | |              all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 225.63/38.71  | | | | | | | | | | | |            & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 225.63/38.71  | | | | | | | | | | | |            & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 225.63/38.71  | | | | | | | | | | | |            & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 225.63/38.71  | | | | | | | | | | | |            $i(all_52_31)
% 225.63/38.71  | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | ALPHA: (18577) implies:
% 225.63/38.71  | | | | | | | | | | | |   (18578)  op(e0, e0) = all_52_31
% 225.63/38.71  | | | | | | | | | | | |   (18579)  op(all_52_31, all_52_31) = e0
% 225.63/38.71  | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | REF_CLOSE: (7), (14935), (17994), (18578), (18579),
% 225.63/38.71  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.71  | | | | | | | | | | | |            #11.
% 225.63/38.71  | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | End of split
% 225.63/38.71  | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | End of split
% 225.63/38.71  | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | End of split
% 225.63/38.71  | | | | | | | | | 
% 225.63/38.71  | | | | | | | | Case 2:
% 225.63/38.71  | | | | | | | | | 
% 225.63/38.71  | | | | | | | | |   (18580)  all_10_2 = e1
% 225.63/38.71  | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | REDUCE: (338), (18580) imply:
% 225.63/38.71  | | | | | | | | |   (18581)   ~ (all_53_1 = e1)
% 225.63/38.71  | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | REDUCE: (342), (18580) imply:
% 225.63/38.71  | | | | | | | | |   (18582)   ~ (all_53_3 = e1)
% 225.63/38.71  | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | REDUCE: (344), (18580) imply:
% 225.63/38.71  | | | | | | | | |   (18583)   ~ (all_53_4 = e1)
% 225.63/38.71  | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | REDUCE: (346), (18580) imply:
% 225.63/38.71  | | | | | | | | |   (18584)   ~ (all_53_8 = e1)
% 225.63/38.71  | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | REDUCE: (348), (18580) imply:
% 225.63/38.71  | | | | | | | | |   (18585)   ~ (all_53_12 = e1)
% 225.63/38.71  | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | BETA: splitting (107) gives:
% 225.63/38.71  | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | Case 1:
% 225.63/38.71  | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | |   (18586)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 225.63/38.71  | | | | | | | | | |              all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 225.63/38.71  | | | | | | | | | |              op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 225.63/38.71  | | | | | | | | | |                all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 225.63/38.71  | | | | | | | | | |              op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 225.63/38.71  | | | | | | | | | |              op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 225.63/38.71  | | | | | | | | | |              $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 225.63/38.71  | | | | | | | | | |              $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 225.63/38.71  | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 225.63/38.71  | | | | | | | | | |                all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 225.63/38.71  | | | | | | | | | |              & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 225.63/38.71  | | | | | | | | | |                all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 225.63/38.71  | | | | | | | | | |              op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 225.63/38.71  | | | | | | | | | |              & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 225.63/38.71  | | | | | | | | | |              $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 225.63/38.71  | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | BETA: splitting (18586) gives:
% 225.63/38.71  | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | Case 1:
% 225.63/38.71  | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | |   (18587)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 225.63/38.71  | | | | | | | | | | |            all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 225.63/38.71  | | | | | | | | | | |            op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 225.63/38.71  | | | | | | | | | | |              all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 225.63/38.71  | | | | | | | | | | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 225.63/38.71  | | | | | | | | | | |            op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 225.63/38.71  | | | | | | | | | | |            $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 225.63/38.71  | | | | | | | | | | |            $i(all_52_7)
% 225.63/38.71  | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | ALPHA: (18587) implies:
% 225.63/38.71  | | | | | | | | | | |   (18588)  op(e3, e3) = all_52_1
% 225.63/38.71  | | | | | | | | | | |   (18589)  op(all_52_1, all_52_1) = e3
% 225.63/38.71  | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | BETA: splitting (233) gives:
% 225.63/38.71  | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | Case 1:
% 225.63/38.71  | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | |   (18590)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 225.63/38.71  | | | | | | | | | | | |              & op(e3, e2) = e1)
% 225.63/38.71  | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | BETA: splitting (18590) gives:
% 225.63/38.71  | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | Case 1:
% 225.63/38.71  | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | |   (18591)  all_57_0 = e1 & op(e3, e3) = e1
% 225.63/38.71  | | | | | | | | | | | | | 
% 225.63/38.71  | | | | | | | | | | | | | ALPHA: (18591) implies:
% 225.63/38.71  | | | | | | | | | | | | |   (18592)  op(e3, e3) = e1
% 225.63/38.71  | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_52_1,
% 225.63/38.72  | | | | | | | | | | | | |              e3, e3, simplifying with (18588), (18592) gives:
% 225.63/38.72  | | | | | | | | | | | | |   (18593)  all_52_1 = e1
% 225.63/38.72  | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | REDUCE: (18589), (18593) imply:
% 225.63/38.72  | | | | | | | | | | | | |   (18594)  op(e1, e1) = e3
% 225.63/38.72  | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | REF_CLOSE: (39), (14936), (18594), (function-axioms) are
% 225.63/38.72  | | | | | | | | | | | | |            inconsistent by sub-proof #2468.
% 225.63/38.72  | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | Case 2:
% 225.63/38.72  | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | |   (18595)  all_57_1 = e1 & op(e3, e2) = e1
% 225.63/38.72  | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | ALPHA: (18595) implies:
% 225.63/38.72  | | | | | | | | | | | | |   (18596)  op(e3, e2) = e1
% 225.63/38.72  | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | REF_CLOSE: (171), (18583), (18596), (function-axioms) are
% 225.63/38.72  | | | | | | | | | | | | |            inconsistent by sub-proof #363.
% 225.63/38.72  | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | End of split
% 225.63/38.72  | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | Case 2:
% 225.63/38.72  | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | |   (18597)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 225.63/38.72  | | | | | | | | | | | |              & op(e3, e0) = e1)
% 225.63/38.72  | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | BETA: splitting (18597) gives:
% 225.63/38.72  | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | Case 1:
% 225.63/38.72  | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | |   (18598)  all_57_4 = e1 & op(e3, e1) = e1
% 225.63/38.72  | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | REF_CLOSE: (170), (18584), (18598), (function-axioms) are
% 225.63/38.72  | | | | | | | | | | | | |            inconsistent by sub-proof #116.
% 225.63/38.72  | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | Case 2:
% 225.63/38.72  | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | |   (18599)  all_57_9 = e1 & op(e3, e0) = e1
% 225.63/38.72  | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | REF_CLOSE: (169), (18585), (18599), (function-axioms) are
% 225.63/38.72  | | | | | | | | | | | | |            inconsistent by sub-proof #2131.
% 225.63/38.72  | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | End of split
% 225.63/38.72  | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | End of split
% 225.63/38.72  | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | Case 2:
% 225.63/38.72  | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | |   (18600)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 225.63/38.72  | | | | | | | | | | |            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 225.63/38.72  | | | | | | | | | | |            op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 225.63/38.72  | | | | | | | | | | |              all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 225.63/38.72  | | | | | | | | | | |            & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 225.63/38.72  | | | | | | | | | | |            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 225.63/38.72  | | | | | | | | | | |            $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 225.63/38.72  | | | | | | | | | | |            $i(all_52_15)
% 225.63/38.72  | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | ALPHA: (18600) implies:
% 225.63/38.72  | | | | | | | | | | |   (18601)  op(e2, e2) = all_52_11
% 225.63/38.72  | | | | | | | | | | |   (18602)  op(all_52_11, all_52_11) = e2
% 225.63/38.72  | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | BETA: splitting (233) gives:
% 225.63/38.72  | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | Case 1:
% 225.63/38.72  | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | |   (18603)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 225.63/38.72  | | | | | | | | | | | |              & op(e3, e2) = e1)
% 225.63/38.72  | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | BETA: splitting (18603) gives:
% 225.63/38.72  | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | Case 1:
% 225.63/38.72  | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | |   (18604)  all_57_0 = e1 & op(e3, e3) = e1
% 225.63/38.72  | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | ALPHA: (18604) implies:
% 225.63/38.72  | | | | | | | | | | | | |   (18605)  op(e3, e3) = e1
% 225.63/38.72  | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3,
% 225.63/38.72  | | | | | | | | | | | | |              all_52_11, e2, e2, simplifying with (17994),
% 225.63/38.72  | | | | | | | | | | | | |              (18601) gives:
% 225.63/38.72  | | | | | | | | | | | | |   (18606)  all_52_11 = e3
% 225.63/38.72  | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | REDUCE: (18602), (18606) imply:
% 225.63/38.72  | | | | | | | | | | | | |   (18607)  op(e3, e3) = e2
% 225.63/38.72  | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | REF_CLOSE: (6), (18605), (18607), (function-axioms) are
% 225.63/38.72  | | | | | | | | | | | | |            inconsistent by sub-proof #1950.
% 225.63/38.72  | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | Case 2:
% 225.63/38.72  | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | |   (18608)  all_57_1 = e1 & op(e3, e2) = e1
% 225.63/38.72  | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | ALPHA: (18608) implies:
% 225.63/38.72  | | | | | | | | | | | | |   (18609)  op(e3, e2) = e1
% 225.63/38.72  | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | REF_CLOSE: (171), (18583), (18609), (function-axioms) are
% 225.63/38.72  | | | | | | | | | | | | |            inconsistent by sub-proof #363.
% 225.63/38.72  | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | End of split
% 225.63/38.72  | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | Case 2:
% 225.63/38.72  | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | |   (18610)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 225.63/38.72  | | | | | | | | | | | |              & op(e3, e0) = e1)
% 225.63/38.72  | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | BETA: splitting (18610) gives:
% 225.63/38.72  | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | Case 1:
% 225.63/38.72  | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | |   (18611)  all_57_4 = e1 & op(e3, e1) = e1
% 225.63/38.72  | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | REF_CLOSE: (170), (18584), (18611), (function-axioms) are
% 225.63/38.72  | | | | | | | | | | | | |            inconsistent by sub-proof #116.
% 225.63/38.72  | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | Case 2:
% 225.63/38.72  | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | |   (18612)  all_57_9 = e1 & op(e3, e0) = e1
% 225.63/38.72  | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | REF_CLOSE: (169), (18585), (18612), (function-axioms) are
% 225.63/38.72  | | | | | | | | | | | | |            inconsistent by sub-proof #2131.
% 225.63/38.72  | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | End of split
% 225.63/38.72  | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | End of split
% 225.63/38.72  | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | End of split
% 225.63/38.72  | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | Case 2:
% 225.63/38.72  | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | |   (18613)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 225.63/38.72  | | | | | | | | | |              & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 225.63/38.72  | | | | | | | | | |              & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 225.63/38.72  | | | | | | | | | |                all_52_21) = e1 & op(all_52_23, all_52_23) =
% 225.63/38.72  | | | | | | | | | |              e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 225.63/38.72  | | | | | | | | | |              all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 225.63/38.72  | | | | | | | | | |              = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 225.63/38.72  | | | | | | | | | |              $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 225.63/38.72  | | | | | | | | | |              & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 225.63/38.72  | | | | | | | | | |              e0 & op(all_52_25, all_52_25) = e3 &
% 225.63/38.72  | | | | | | | | | |              op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 225.63/38.72  | | | | | | | | | |                all_52_29) = e1 & op(all_52_31, all_52_31) =
% 225.63/38.72  | | | | | | | | | |              e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 225.63/38.72  | | | | | | | | | |              all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 225.63/38.72  | | | | | | | | | |              = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 225.63/38.72  | | | | | | | | | |              $i(all_52_29) & $i(all_52_31))
% 225.63/38.72  | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | BETA: splitting (18613) gives:
% 225.63/38.72  | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | Case 1:
% 225.63/38.72  | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | |   (18614)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 225.63/38.72  | | | | | | | | | | |            all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 225.63/38.72  | | | | | | | | | | |            op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 225.63/38.72  | | | | | | | | | | |              all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 225.63/38.72  | | | | | | | | | | |            & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 225.63/38.72  | | | | | | | | | | |            & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 225.63/38.72  | | | | | | | | | | |            & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 225.63/38.72  | | | | | | | | | | |            $i(all_52_23)
% 225.63/38.72  | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | ALPHA: (18614) implies:
% 225.63/38.72  | | | | | | | | | | |   (18615)  op(e1, e0) = all_52_23
% 225.63/38.72  | | | | | | | | | | |   (18616)  op(e1, e1) = all_52_21
% 225.63/38.72  | | | | | | | | | | |   (18617)  op(all_52_23, all_52_23) = e0
% 225.63/38.72  | | | | | | | | | | |   (18618)  op(all_52_21, all_52_21) = e1
% 225.63/38.72  | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_14,
% 225.63/38.72  | | | | | | | | | | |              all_52_23, e0, e1, simplifying with (161), (18615)
% 225.63/38.72  | | | | | | | | | | |              gives:
% 225.63/38.72  | | | | | | | | | | |   (18619)  all_53_14 = all_52_23
% 225.63/38.72  | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2,
% 225.63/38.72  | | | | | | | | | | |              all_52_21, e1, e1, simplifying with (39), (18616)
% 225.63/38.72  | | | | | | | | | | |              gives:
% 225.63/38.72  | | | | | | | | | | |   (18620)  all_52_21 = all_6_2
% 225.63/38.72  | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | COMBINE_EQS: (248), (18619) imply:
% 225.63/38.72  | | | | | | | | | | |   (18621)  all_55_11 = all_52_23
% 225.63/38.72  | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | REDUCE: (111), (18619) imply:
% 225.63/38.72  | | | | | | | | | | |   (18622)   ~ (all_53_13 = all_52_23)
% 225.63/38.72  | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | REDUCE: (14929), (18619) imply:
% 225.63/38.72  | | | | | | | | | | |   (18623)   ~ (all_52_23 = e2)
% 225.63/38.72  | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | REDUCE: (18618), (18620) imply:
% 225.63/38.72  | | | | | | | | | | |   (18624)  op(all_6_2, all_6_2) = e1
% 225.63/38.72  | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | BETA: splitting (67) gives:
% 225.63/38.72  | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | Case 1:
% 225.63/38.72  | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | |   (18625)   ~ (all_24_2 = e0)
% 225.63/38.72  | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | REDUCE: (315), (18625) imply:
% 225.63/38.72  | | | | | | | | | | | |   (18626)   ~ (all_6_2 = e0)
% 225.63/38.72  | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | BETA: splitting (79) gives:
% 225.63/38.72  | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | Case 1:
% 225.63/38.72  | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | |   (18627)   ~ (all_32_2 = e2)
% 225.63/38.72  | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | REDUCE: (14923), (18627) imply:
% 225.63/38.72  | | | | | | | | | | | | |   (18628)  $false
% 225.63/38.72  | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | CLOSE: (18628) is inconsistent.
% 225.63/38.72  | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | Case 2:
% 225.63/38.72  | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | |   (18629)  ( ~ (all_32_0 = e1) & op(all_32_1, e0) = all_32_0
% 225.63/38.72  | | | | | | | | | | | | |              & op(e0, e2) = all_32_1 & $i(all_32_0) &
% 225.63/38.72  | | | | | | | | | | | | |              $i(all_32_1)) | ( ~ (all_32_1 = e3) & op(e0, e2)
% 225.63/38.72  | | | | | | | | | | | | |              = all_32_1 & $i(all_32_1))
% 225.63/38.72  | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | BETA: splitting (88) gives:
% 225.63/38.72  | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | Case 1:
% 225.63/38.72  | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | |   (18630)   ~ (all_38_2 = e2)
% 225.63/38.72  | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | REDUCE: (249), (18630) imply:
% 225.63/38.72  | | | | | | | | | | | | | |   (18631)   ~ (all_6_2 = e2)
% 225.63/38.72  | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 225.63/38.72  | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | Case 1:
% 225.63/38.72  | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | |   (18632)  all_55_10 = e3
% 225.63/38.72  | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | REF_CLOSE: (336), (14936), (18632) are inconsistent by
% 225.63/38.72  | | | | | | | | | | | | | | |            sub-proof #2500.
% 225.63/38.72  | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | Case 2:
% 225.63/38.72  | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | |   (18633)   ~ (all_55_10 = e3)
% 225.63/38.72  | | | | | | | | | | | | | | |   (18634)  all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 225.63/38.72  | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | BETA: splitting (18634) gives:
% 225.63/38.72  | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | Case 1:
% 225.63/38.72  | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | |   (18635)  all_55_10 = e2
% 225.63/38.72  | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | REF_CLOSE: (336), (18631), (18635) are inconsistent by
% 225.63/38.72  | | | | | | | | | | | | | | | |            sub-proof #2499.
% 225.63/38.72  | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | Case 2:
% 225.63/38.72  | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | |   (18636)   ~ (all_55_10 = e2)
% 225.63/38.72  | | | | | | | | | | | | | | | |   (18637)  all_55_10 = e1 | all_55_10 = e0
% 225.63/38.72  | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | BETA: splitting (18637) gives:
% 225.63/38.72  | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.72  | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | |   (18638)  all_55_10 = e1
% 225.63/38.72  | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | COMBINE_EQS: (336), (18638) imply:
% 225.63/38.72  | | | | | | | | | | | | | | | | |   (18639)  all_6_2 = e1
% 225.63/38.72  | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | SIMP: (18639) implies:
% 225.63/38.72  | | | | | | | | | | | | | | | | |   (18640)  all_6_2 = e1
% 225.63/38.72  | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | REDUCE: (364), (18640) imply:
% 225.63/38.72  | | | | | | | | | | | | | | | | |   (18641)   ~ (all_53_9 = e1)
% 225.63/38.72  | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | REDUCE: (366), (18640) imply:
% 225.63/38.72  | | | | | | | | | | | | | | | | |   (18642)   ~ (all_53_11 = e1)
% 225.63/38.72  | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | REDUCE: (14936), (18640) imply:
% 225.63/38.72  | | | | | | | | | | | | | | | | |   (18643)   ~ (e3 = e1)
% 225.63/38.72  | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | REDUCE: (18631), (18640) imply:
% 225.63/38.72  | | | | | | | | | | | | | | | | |   (18644)   ~ (e2 = e1)
% 225.63/38.72  | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 225.63/38.72  | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.72  | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | |   (18645)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 225.63/38.72  | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 225.63/38.72  | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | | BETA: splitting (18645) gives:
% 225.63/38.72  | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | | |   (18646)  all_57_12 = e1 & op(e0, e3) = e1
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (18582), (18646), (function-axioms) are
% 225.63/38.72  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1947.
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | | |   (18647)  all_57_13 = e1 & op(e0, e2) = e1
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | ALPHA: (18647) implies:
% 225.63/38.72  | | | | | | | | | | | | | | | | | | |   (18648)  op(e0, e2) = e1
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | |   (18649)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (168), (17994), (18581), (18649),
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | |            #240.
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | |   (18650)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | BETA: splitting (18650) gives:
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | |   (18651)  all_57_5 = e1 & op(e2, e1) = e1
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (18641), (18651), (function-axioms) are
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2305.
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | |   (18652)  all_57_10 = e1 & op(e2, e0) = e1
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | ALPHA: (18652) implies:
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | |   (18653)  op(e2, e0) = e1
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_7, e1,
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (159), (18648) gives:
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | |   (18654)  all_53_7 = e1
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_13,
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | |              e1, e0, e2, simplifying with (165), (18653) gives:
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | |   (18655)  all_53_13 = e1
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | REDUCE: (18622), (18655) imply:
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | |   (18656)   ~ (all_52_23 = e1)
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | SIMP: (18656) implies:
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | |   (18657)   ~ (all_52_23 = e1)
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14922) gives:
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | |   (18658)   ~ (all_4_0 = e3) & op(all_4_1, e0) = all_4_0 &
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = all_4_1 & $i(all_4_0) & $i(all_4_1)
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18658) implies:
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | |   (18659)   ~ (all_4_0 = e3)
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | |   (18660)  op(e0, e2) = all_4_1
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | |   (18661)  op(all_4_1, e0) = all_4_0
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18629) gives:
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | |   (18662)   ~ (all_32_0 = e1) & op(all_32_1, e0) = all_32_0 &
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = all_32_1 & $i(all_32_0) &
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | |            $i(all_32_1)
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18662) implies:
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | |   (18663)   ~ (all_32_0 = e1)
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | |   (18664)  op(e0, e2) = all_32_1
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | |   (18665)  op(all_32_1, e0) = all_32_0
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_32_1,
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (18648), (18664) gives:
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | |   (18666)  all_32_1 = e1
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_1,
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | |              all_32_1, e2, e0, simplifying with (18660),
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | |              (18664) gives:
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | |   (18667)  all_32_1 = all_4_1
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (18666), (18667) imply:
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | |   (18668)  all_4_1 = e1
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (18665), (18666) imply:
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | |   (18669)  op(e1, e0) = all_32_0
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (18661), (18668) imply:
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | |   (18670)  op(e1, e0) = all_4_0
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_23,
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | |              all_4_0, e0, e1, simplifying with (18615), (18670)
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | |   (18671)  all_52_23 = all_4_0
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_23,
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | |              all_32_0, e0, e1, simplifying with (18615),
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | |              (18669) gives:
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | |   (18672)  all_52_23 = all_32_0
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (18671), (18672) imply:
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | |   (18673)  all_32_0 = all_4_0
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (18673) implies:
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | |   (18674)  all_32_0 = all_4_0
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (18621), (18671) imply:
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | |   (18675)  all_55_11 = all_4_0
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (18623), (18671) imply:
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | |   (18676)   ~ (all_4_0 = e2)
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (18663), (18674) imply:
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | |   (18677)   ~ (all_4_0 = e1)
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (194), (14935), (18615), (18617), (18659),
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | |            (18670), (18675), (18676), (18677),
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | |            #5.
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | |   (18678)   ~ (all_32_1 = e3) & op(e0, e2) = all_32_1 &
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | |            $i(all_32_1)
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18678) implies:
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | |   (18679)  op(e0, e2) = all_32_1
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_32_1,
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (18648), (18679) gives:
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | |   (18680)  all_32_1 = e1
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_1,
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | |              all_32_1, e2, e0, simplifying with (18660),
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | |              (18679) gives:
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | |   (18681)  all_32_1 = all_4_1
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (18680), (18681) imply:
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | |   (18682)  all_4_1 = e1
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (18661), (18682) imply:
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | |   (18683)  op(e1, e0) = all_4_0
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_23,
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | |              all_4_0, e0, e1, simplifying with (18615), (18683)
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | |   (18684)  all_52_23 = all_4_0
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (18621), (18684) imply:
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | |   (18685)  all_55_11 = all_4_0
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (18623), (18684) imply:
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | |   (18686)   ~ (all_4_0 = e2)
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (18657), (18684) imply:
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | |   (18687)   ~ (all_4_0 = e1)
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (194), (14935), (18615), (18617), (18659),
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | |            (18683), (18685), (18686), (18687),
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | |            #5.
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | |   (18688)   ~ (all_4_1 = e1) & op(e0, e2) = all_4_1 &
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | |            $i(all_4_1)
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18629), (18648), (18688), (function-axioms) are
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #69.
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.72  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.72  | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.72  | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | |   (18689)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 225.63/38.72  | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 225.63/38.72  | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (158), (14935), (18642), (18689),
% 225.63/38.72  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.72  | | | | | | | | | | | | | | | | | |            #15.
% 225.63/38.72  | | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | End of split
% 225.63/38.72  | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.72  | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | |   (18690)  all_55_10 = e0
% 225.63/38.72  | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | REF_CLOSE: (336), (18626), (18690) are inconsistent by
% 225.63/38.72  | | | | | | | | | | | | | | | | |            sub-proof #2118.
% 225.63/38.72  | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | End of split
% 225.63/38.72  | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | End of split
% 225.63/38.72  | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | End of split
% 225.63/38.72  | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | Case 2:
% 225.63/38.72  | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | |   (18691)  all_38_2 = e2
% 225.63/38.72  | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | COMBINE_EQS: (249), (18691) imply:
% 225.63/38.72  | | | | | | | | | | | | | |   (18692)  all_6_2 = e2
% 225.63/38.72  | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | REDUCE: (18624), (18692) imply:
% 225.63/38.72  | | | | | | | | | | | | | |   (18693)  op(e2, e2) = e1
% 225.63/38.72  | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | REF_CLOSE: (8), (17994), (18693), (function-axioms) are
% 225.63/38.72  | | | | | | | | | | | | | |            inconsistent by sub-proof #1912.
% 225.63/38.72  | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | End of split
% 225.63/38.72  | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | End of split
% 225.63/38.72  | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | Case 2:
% 225.63/38.72  | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | |   (18694)  all_24_2 = e0
% 225.63/38.72  | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | COMBINE_EQS: (315), (18694) imply:
% 225.63/38.72  | | | | | | | | | | | |   (18695)  all_6_2 = e0
% 225.63/38.72  | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | REDUCE: (18624), (18695) imply:
% 225.63/38.72  | | | | | | | | | | | |   (18696)  op(e0, e0) = e1
% 225.63/38.72  | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | REF_CLOSE: (6), (14935), (18696), (function-axioms) are
% 225.63/38.72  | | | | | | | | | | | |            inconsistent by sub-proof #2177.
% 225.63/38.72  | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | End of split
% 225.63/38.72  | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | Case 2:
% 225.63/38.72  | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | |   (18697)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 225.63/38.72  | | | | | | | | | | |            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 225.63/38.72  | | | | | | | | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 225.63/38.72  | | | | | | | | | | |              all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 225.63/38.72  | | | | | | | | | | |            & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 225.63/38.72  | | | | | | | | | | |            & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 225.63/38.72  | | | | | | | | | | |            & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 225.63/38.72  | | | | | | | | | | |            $i(all_52_31)
% 225.63/38.72  | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | ALPHA: (18697) implies:
% 225.63/38.72  | | | | | | | | | | |   (18698)  op(e0, e0) = all_52_31
% 225.63/38.72  | | | | | | | | | | |   (18699)  op(all_52_31, all_52_31) = e0
% 225.63/38.72  | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | REF_CLOSE: (7), (14935), (17994), (18698), (18699),
% 225.63/38.72  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.72  | | | | | | | | | | |            #11.
% 225.63/38.72  | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | End of split
% 225.63/38.72  | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | End of split
% 225.63/38.72  | | | | | | | | | 
% 225.63/38.72  | | | | | | | | End of split
% 225.63/38.72  | | | | | | | | 
% 225.63/38.72  | | | | | | | End of split
% 225.63/38.72  | | | | | | | 
% 225.63/38.72  | | | | | | Case 2:
% 225.63/38.72  | | | | | | | 
% 225.63/38.72  | | | | | | |   (18700)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 &
% 225.63/38.72  | | | | | | |              op(e2, e0) = e3)
% 225.63/38.72  | | | | | | | 
% 225.63/38.72  | | | | | | | REF_CLOSE: (165), (166), (17988), (17989), (18700),
% 225.63/38.72  | | | | | | |            (function-axioms) are inconsistent by sub-proof #178.
% 225.63/38.72  | | | | | | | 
% 225.63/38.72  | | | | | | End of split
% 225.63/38.72  | | | | | | 
% 225.63/38.72  | | | | | End of split
% 225.63/38.72  | | | | | 
% 225.63/38.72  | | | | Case 2:
% 225.63/38.72  | | | | | 
% 225.63/38.72  | | | | |   (18701)  all_6_2 = e3
% 225.63/38.72  | | | | |   (18702)  ( ~ (all_6_0 = e0) & op(all_6_1, e1) = all_6_0 & op(e1, e3)
% 225.63/38.72  | | | | |              = all_6_1 & $i(all_6_0) & $i(all_6_1)) | ( ~ (all_6_1 =
% 225.63/38.72  | | | | |                e2) & op(e1, e3) = all_6_1 & $i(all_6_1))
% 225.63/38.72  | | | | | 
% 225.63/38.72  | | | | | COMBINE_EQS: (333), (18701) imply:
% 225.63/38.72  | | | | |   (18703)  all_46_2 = e3
% 225.63/38.72  | | | | | 
% 225.63/38.72  | | | | | REDUCE: (350), (18701) imply:
% 225.63/38.72  | | | | |   (18704)   ~ (all_53_2 = e3)
% 225.63/38.72  | | | | | 
% 225.63/38.72  | | | | | REDUCE: (361), (18701) imply:
% 225.63/38.72  | | | | |   (18705)   ~ (all_53_6 = e3)
% 225.63/38.72  | | | | | 
% 225.63/38.72  | | | | | REDUCE: (363), (18701) imply:
% 225.63/38.72  | | | | |   (18706)   ~ (all_53_8 = e3)
% 225.63/38.72  | | | | | 
% 225.63/38.72  | | | | | REDUCE: (364), (18701) imply:
% 225.63/38.72  | | | | |   (18707)   ~ (all_53_9 = e3)
% 225.63/38.72  | | | | | 
% 225.63/38.72  | | | | | REDUCE: (366), (18701) imply:
% 225.63/38.72  | | | | |   (18708)   ~ (all_53_11 = e3)
% 225.63/38.72  | | | | | 
% 225.63/38.72  | | | | | REDUCE: (368), (18701) imply:
% 225.63/38.72  | | | | |   (18709)   ~ (all_53_14 = e3)
% 225.63/38.72  | | | | | 
% 225.63/38.72  | | | | | BETA: splitting (217) gives:
% 225.63/38.72  | | | | | 
% 225.63/38.72  | | | | | Case 1:
% 225.63/38.72  | | | | | | 
% 225.63/38.72  | | | | | |   (18710)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 &
% 225.63/38.72  | | | | | |              op(e1, e2) = e3)
% 225.63/38.72  | | | | | | 
% 225.63/38.72  | | | | | | BETA: splitting (18710) gives:
% 225.63/38.72  | | | | | | 
% 225.63/38.72  | | | | | | Case 1:
% 225.63/38.72  | | | | | | | 
% 225.63/38.72  | | | | | | |   (18711)  all_57_6 = e3 & op(e1, e3) = e3
% 225.63/38.72  | | | | | | | 
% 225.63/38.72  | | | | | | | REF_CLOSE: (164), (18704), (18711), (function-axioms) are
% 225.63/38.72  | | | | | | |            inconsistent by sub-proof #153.
% 225.63/38.72  | | | | | | | 
% 225.63/38.72  | | | | | | Case 2:
% 225.63/38.72  | | | | | | | 
% 225.63/38.72  | | | | | | |   (18712)  all_57_7 = e3 & op(e1, e2) = e3
% 225.63/38.72  | | | | | | | 
% 225.63/38.72  | | | | | | | REF_CLOSE: (163), (18705), (18712), (function-axioms) are
% 225.63/38.72  | | | | | | |            inconsistent by sub-proof #267.
% 225.63/38.72  | | | | | | | 
% 225.63/38.72  | | | | | | End of split
% 225.63/38.72  | | | | | | 
% 225.63/38.72  | | | | | Case 2:
% 225.63/38.72  | | | | | | 
% 225.63/38.72  | | | | | |   (18713)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 &
% 225.63/38.72  | | | | | |              op(e1, e0) = e3)
% 225.63/38.72  | | | | | | 
% 225.63/38.72  | | | | | | BETA: splitting (18713) gives:
% 225.63/38.72  | | | | | | 
% 225.63/38.72  | | | | | | Case 1:
% 225.63/38.72  | | | | | | | 
% 225.63/38.72  | | | | | | |   (18714)  all_57_8 = e3 & op(e1, e1) = e3
% 225.63/38.72  | | | | | | | 
% 225.63/38.72  | | | | | | | ALPHA: (18714) implies:
% 225.63/38.72  | | | | | | |   (18715)  all_57_8 = e3
% 225.63/38.72  | | | | | | |   (18716)  op(e1, e1) = e3
% 225.63/38.72  | | | | | | | 
% 225.63/38.72  | | | | | | | BETA: splitting (43) gives:
% 225.63/38.72  | | | | | | | 
% 225.63/38.72  | | | | | | | Case 1:
% 225.63/38.72  | | | | | | | | 
% 225.63/38.72  | | | | | | | |   (18717)   ~ (all_8_2 = e3)
% 225.63/38.72  | | | | | | | | 
% 225.63/38.72  | | | | | | | | BETA: splitting (46) gives:
% 225.63/38.72  | | | | | | | | 
% 225.63/38.72  | | | | | | | | Case 1:
% 225.63/38.72  | | | | | | | | | 
% 225.63/38.72  | | | | | | | | |   (18718)   ~ (all_10_2 = e1)
% 225.63/38.72  | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | BETA: splitting (52) gives:
% 225.63/38.72  | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | Case 1:
% 225.63/38.72  | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | |   (18719)   ~ (all_14_2 = e0)
% 225.63/38.72  | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | REDUCE: (328), (18719) imply:
% 225.63/38.72  | | | | | | | | | |   (18720)   ~ (all_8_2 = e0)
% 225.63/38.72  | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | BETA: splitting (55) gives:
% 225.63/38.72  | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | Case 1:
% 225.63/38.72  | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | |   (18721)   ~ (all_16_2 = e1)
% 225.63/38.72  | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | REDUCE: (324), (18721) imply:
% 225.63/38.72  | | | | | | | | | | |   (18722)   ~ (all_8_2 = e1)
% 225.63/38.72  | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | BETA: splitting (200) gives:
% 225.63/38.72  | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | Case 1:
% 225.63/38.72  | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | |   (18723)  all_55_5 = e3
% 225.63/38.72  | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | COMBINE_EQS: (266), (18723) imply:
% 225.63/38.72  | | | | | | | | | | | |   (18724)  all_8_2 = e3
% 225.63/38.72  | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | REDUCE: (18717), (18724) imply:
% 225.63/38.72  | | | | | | | | | | | |   (18725)  $false
% 225.63/38.72  | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | CLOSE: (18725) is inconsistent.
% 225.63/38.72  | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | Case 2:
% 225.63/38.72  | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | |   (18726)   ~ (all_55_5 = e3)
% 225.63/38.72  | | | | | | | | | | | |   (18727)  all_55_5 = e2 | all_55_5 = e1 | all_55_5 = e0
% 225.63/38.72  | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | BETA: splitting (18727) gives:
% 225.63/38.72  | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | Case 1:
% 225.63/38.72  | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | |   (18728)  all_55_5 = e2
% 225.63/38.72  | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | COMBINE_EQS: (266), (18728) imply:
% 225.63/38.72  | | | | | | | | | | | | |   (18729)  all_8_2 = e2
% 225.63/38.72  | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | REDUCE: (354), (18729) imply:
% 225.63/38.72  | | | | | | | | | | | | |   (18730)   ~ (all_53_6 = e2)
% 225.63/38.72  | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | REDUCE: (358), (18729) imply:
% 225.63/38.72  | | | | | | | | | | | | |   (18731)   ~ (all_53_9 = e2)
% 225.63/38.72  | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | REDUCE: (18717), (18729) imply:
% 225.63/38.72  | | | | | | | | | | | | |   (18732)   ~ (e3 = e2)
% 225.63/38.72  | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | REDUCE: (42), (18729) imply:
% 225.63/38.72  | | | | | | | | | | | | |   (18733)  op(e2, e2) = e2
% 225.63/38.72  | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | BETA: splitting (220) gives:
% 225.63/38.72  | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | Case 1:
% 225.63/38.72  | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | |   (18734)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 225.63/38.72  | | | | | | | | | | | | | |              & op(e2, e1) = e2)
% 225.63/38.72  | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | BETA: splitting (18734) gives:
% 225.63/38.72  | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | Case 1:
% 225.63/38.72  | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | |   (18735)  all_57_4 = e2 & op(e3, e1) = e2
% 225.63/38.72  | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | ALPHA: (18735) implies:
% 225.63/38.72  | | | | | | | | | | | | | | |   (18736)  op(e3, e1) = e2
% 225.63/38.72  | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 225.63/38.72  | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | Case 1:
% 225.63/38.72  | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | |   (18737)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 225.63/38.72  | | | | | | | | | | | | | | | |              & op(e1, e2) = e2)
% 225.63/38.72  | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | BETA: splitting (18737) gives:
% 225.63/38.72  | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.72  | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | |   (18738)  all_57_6 = e2 & op(e1, e3) = e2
% 225.63/38.72  | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | ALPHA: (18738) implies:
% 225.63/38.72  | | | | | | | | | | | | | | | | |   (18739)  op(e1, e3) = e2
% 225.63/38.72  | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_2, e2,
% 225.63/38.72  | | | | | | | | | | | | | | | | |              e3, e1, simplifying with (164), (18739) gives:
% 225.63/38.72  | | | | | | | | | | | | | | | | |   (18740)  all_53_2 = e2
% 225.63/38.72  | | | | | | | | | | | | | | | | | 
% 225.63/38.72  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_8, e2,
% 225.63/38.72  | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (170), (18736) gives:
% 225.63/38.72  | | | | | | | | | | | | | | | | |   (18741)  all_53_8 = e2
% 225.63/38.72  | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | REDUCE: (124), (18741) imply:
% 225.63/38.73  | | | | | | | | | | | | | | | | |   (18742)   ~ (all_53_9 = e2)
% 225.63/38.73  | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | BETA: splitting (18702) gives:
% 225.63/38.73  | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | |   (18743)   ~ (all_6_0 = e0) & op(all_6_1, e1) = all_6_0 &
% 225.63/38.73  | | | | | | | | | | | | | | | | | |            op(e1, e3) = all_6_1 & $i(all_6_0) & $i(all_6_1)
% 225.63/38.73  | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | ALPHA: (18743) implies:
% 225.63/38.73  | | | | | | | | | | | | | | | | | |   (18744)   ~ (all_6_0 = e0)
% 225.63/38.73  | | | | | | | | | | | | | | | | | |   (18745)  op(e1, e3) = all_6_1
% 225.63/38.73  | | | | | | | | | | | | | | | | | |   (18746)  op(all_6_1, e1) = all_6_0
% 225.63/38.73  | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | |   (18747)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 225.63/38.73  | | | | | | | | | | | | | | | | | | |              all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 225.63/38.73  | | | | | | | | | | | | | | | | | | |              op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 225.63/38.73  | | | | | | | | | | | | | | | | | | |                all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 225.63/38.73  | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 225.63/38.73  | | | | | | | | | | | | | | | | | | |              op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 225.63/38.73  | | | | | | | | | | | | | | | | | | |              $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 225.63/38.73  | | | | | | | | | | | | | | | | | | |              $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 225.63/38.73  | | | | | | | | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 225.63/38.73  | | | | | | | | | | | | | | | | | | |                all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 225.63/38.73  | | | | | | | | | | | | | | | | | | |              & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 225.63/38.73  | | | | | | | | | | | | | | | | | | |                all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 225.63/38.73  | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 225.63/38.73  | | | | | | | | | | | | | | | | | | |              & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 225.63/38.73  | | | | | | | | | | | | | | | | | | |              $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | BETA: splitting (18747) gives:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |   (18748)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |            all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |            op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |              all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |            $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |            $i(all_52_7)
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (18733), (18736), (18748), (function-axioms)
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #90.
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |   (18749)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |            op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |              all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |            $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |            $i(all_52_15)
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | ALPHA: (18749) implies:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |   (18750)  op(e2, e1) = all_52_13
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |   (18751)  op(all_52_13, all_52_13) = e1
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_6_1,
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |              e3, e1, simplifying with (18739), (18745) gives:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |   (18752)  all_6_1 = e2
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_9,
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |              all_52_13, e1, e2, simplifying with (166), (18750)
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |              gives:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |   (18753)  all_53_9 = all_52_13
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (18753) imply:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |   (18754)  all_55_6 = all_52_13
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | REDUCE: (18707), (18753) imply:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |   (18755)   ~ (all_52_13 = e3)
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | REDUCE: (18731), (18753) imply:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |   (18756)   ~ (all_52_13 = e2)
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | REDUCE: (18746), (18752) imply:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |   (18757)  op(e2, e1) = all_6_0
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |              all_6_0, e1, e2, simplifying with (18750), (18757)
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |              gives:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |   (18758)  all_52_13 = all_6_0
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (18754), (18758) imply:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |   (18759)  all_55_6 = all_6_0
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | REDUCE: (18755), (18758) imply:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |   (18760)   ~ (all_6_0 = e3)
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | REDUCE: (18756), (18758) imply:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |   (18761)   ~ (all_6_0 = e2)
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | REDUCE: (18751), (18758) imply:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |   (18762)  op(all_6_0, all_6_0) = e1
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | |   (18763)  all_55_6 = e3
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (18759), (18763) imply:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | |   (18764)  all_6_0 = e3
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | SIMP: (18764) implies:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | |   (18765)  all_6_0 = e3
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | REDUCE: (18760), (18765) imply:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | |   (18766)  $false
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | CLOSE: (18766) is inconsistent.
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | |   (18767)   ~ (all_55_6 = e3)
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | |   (18768)  all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18768) gives:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | |   (18769)  all_55_6 = e2
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (18759), (18769) imply:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | |   (18770)  all_6_0 = e2
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | SIMP: (18770) implies:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | |   (18771)  all_6_0 = e2
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (18761), (18771) imply:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | |   (18772)  $false
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (18772) is inconsistent.
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | |   (18773)  all_55_6 = e1 | all_55_6 = e0
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18773) gives:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | |   (18774)  all_55_6 = e1
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (18759), (18774) imply:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | |   (18775)  all_6_0 = e1
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (18775) implies:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | |   (18776)  all_6_0 = e1
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (18760), (18776) imply:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | |   (18777)   ~ (e3 = e1)
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (18762), (18776) imply:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | |   (18778)  op(e1, e1) = e1
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (18716), (18778), (function-axioms) are
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #156.
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | |   (18779)  all_55_6 = e0
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (18759), (18779) imply:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | |   (18780)  all_6_0 = e0
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (18780) implies:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | |   (18781)  all_6_0 = e0
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (18744), (18781) imply:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | |   (18782)  $false
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (18782) is inconsistent.
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | |   (18783)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 225.63/38.73  | | | | | | | | | | | | | | | | | | |              & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 225.63/38.73  | | | | | | | | | | | | | | | | | | |              & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 225.63/38.73  | | | | | | | | | | | | | | | | | | |                all_52_21) = e1 & op(all_52_23, all_52_23) =
% 225.63/38.73  | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 225.63/38.73  | | | | | | | | | | | | | | | | | | |              all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 225.63/38.73  | | | | | | | | | | | | | | | | | | |              = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 225.63/38.73  | | | | | | | | | | | | | | | | | | |              $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 225.63/38.73  | | | | | | | | | | | | | | | | | | |              & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 225.63/38.73  | | | | | | | | | | | | | | | | | | |              e0 & op(all_52_25, all_52_25) = e3 &
% 225.63/38.73  | | | | | | | | | | | | | | | | | | |              op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 225.63/38.73  | | | | | | | | | | | | | | | | | | |                all_52_29) = e1 & op(all_52_31, all_52_31) =
% 225.63/38.73  | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 225.63/38.73  | | | | | | | | | | | | | | | | | | |              all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 225.63/38.73  | | | | | | | | | | | | | | | | | | |              = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 225.63/38.73  | | | | | | | | | | | | | | | | | | |              $i(all_52_29) & $i(all_52_31))
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | BETA: splitting (18783) gives:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |   (18784)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |            all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |            op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |              all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |            & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |            & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |            $i(all_52_23)
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | ALPHA: (18784) implies:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |   (18785)  op(e1, e1) = all_52_21
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |   (18786)  op(all_52_21, all_52_21) = e1
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (18716), (18718), (18785), (18786),
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |            #167.
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |   (18787)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |              all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |            & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |            & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |            & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |            $i(all_52_31)
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (14935), (18733), (18787), (function-axioms)
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #79.
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.73  | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | |   (18788)   ~ (all_6_1 = e2) & op(e1, e3) = all_6_1 &
% 225.63/38.73  | | | | | | | | | | | | | | | | | |            $i(all_6_1)
% 225.63/38.73  | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | ALPHA: (18788) implies:
% 225.63/38.73  | | | | | | | | | | | | | | | | | |   (18789)   ~ (all_6_1 = e2)
% 225.63/38.73  | | | | | | | | | | | | | | | | | |   (18790)  op(e1, e3) = all_6_1
% 225.63/38.73  | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | BETA: splitting (100) gives:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | |   (18791)   ~ (all_46_2 = e3)
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | REDUCE: (18703), (18791) imply:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | |   (18792)  $false
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | CLOSE: (18792) is inconsistent.
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | |   (18793)  ( ~ (all_46_0 = e2) & op(all_46_1, e1) = all_46_0
% 225.63/38.73  | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = all_46_1 & $i(all_46_0) &
% 225.63/38.73  | | | | | | | | | | | | | | | | | | |              $i(all_46_1)) | ( ~ (all_46_1 = e0) & op(e1, e3)
% 225.63/38.73  | | | | | | | | | | | | | | | | | | |              = all_46_1 & $i(all_46_1))
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | BETA: splitting (18793) gives:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |   (18794)   ~ (all_46_0 = e2) & op(all_46_1, e1) = all_46_0 &
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = all_46_1 & $i(all_46_0) &
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |            $i(all_46_1)
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | ALPHA: (18794) implies:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |   (18795)  op(e1, e3) = all_46_1
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18739), (18789), (18790), (18795),
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |            #4.
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |   (18796)   ~ (all_46_1 = e0) & op(e1, e3) = all_46_1 &
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |            $i(all_46_1)
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | ALPHA: (18796) implies:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |   (18797)  op(e1, e3) = all_46_1
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18739), (18789), (18790), (18797),
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |            #4.
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.73  | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | End of split
% 225.63/38.73  | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.73  | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | |   (18798)  all_57_7 = e2 & op(e1, e2) = e2
% 225.63/38.73  | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (18730), (18798), (function-axioms) are
% 225.63/38.73  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #173.
% 225.63/38.73  | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | End of split
% 225.63/38.73  | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | Case 2:
% 225.63/38.73  | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | |   (18799)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 225.63/38.73  | | | | | | | | | | | | | | | |              e2 & op(e1, e0) = e2)
% 225.63/38.73  | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | BETA: splitting (18799) gives:
% 225.63/38.73  | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.73  | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | |   (18800)  all_57_8 = e2 & op(e1, e1) = e2
% 225.63/38.73  | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (18715), (18800) are inconsistent by
% 225.63/38.73  | | | | | | | | | | | | | | | | |            sub-proof #165.
% 225.63/38.73  | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.73  | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | |   (18801)  all_57_11 = e2 & op(e1, e0) = e2
% 225.63/38.73  | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (14929), (18801), (function-axioms) are
% 225.63/38.73  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #91.
% 225.63/38.73  | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | End of split
% 225.63/38.73  | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | End of split
% 225.63/38.73  | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | Case 2:
% 225.63/38.73  | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | |   (18802)  all_57_5 = e2 & op(e2, e1) = e2
% 225.63/38.73  | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | REF_CLOSE: (166), (18731), (18802), (function-axioms) are
% 225.63/38.73  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1858.
% 225.63/38.73  | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | End of split
% 225.63/38.73  | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | Case 2:
% 225.63/38.73  | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | |   (18803)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 225.63/38.73  | | | | | | | | | | | | | |              e2 & op(e0, e1) = e2)
% 225.63/38.73  | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | BETA: splitting (18803) gives:
% 225.63/38.73  | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | Case 1:
% 225.63/38.73  | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | |   (18804)  all_57_8 = e2 & op(e1, e1) = e2
% 225.63/38.73  | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | REF_CLOSE: (9), (18715), (18804) are inconsistent by
% 225.63/38.73  | | | | | | | | | | | | | | |            sub-proof #165.
% 225.63/38.73  | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | Case 2:
% 225.63/38.73  | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | |   (18805)  all_57_14 = e2 & op(e0, e1) = e2
% 225.63/38.73  | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | REF_CLOSE: (158), (14926), (18805), (function-axioms) are
% 225.63/38.73  | | | | | | | | | | | | | | |            inconsistent by sub-proof #54.
% 225.63/38.73  | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | End of split
% 225.63/38.73  | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | End of split
% 225.63/38.73  | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | Case 2:
% 225.63/38.73  | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | |   (18806)  all_55_5 = e1 | all_55_5 = e0
% 225.63/38.73  | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | REF_CLOSE: (266), (18720), (18722), (18806) are inconsistent
% 225.63/38.73  | | | | | | | | | | | | |            by sub-proof #1857.
% 225.63/38.73  | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | End of split
% 225.63/38.73  | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | End of split
% 225.63/38.73  | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | Case 2:
% 225.63/38.73  | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | |   (18807)  all_16_2 = e1
% 225.63/38.73  | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | COMBINE_EQS: (324), (18807) imply:
% 225.63/38.73  | | | | | | | | | | |   (18808)  all_8_2 = e1
% 225.63/38.73  | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | SIMP: (18808) implies:
% 225.63/38.73  | | | | | | | | | | |   (18809)  all_8_2 = e1
% 225.63/38.73  | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | REDUCE: (358), (18809) imply:
% 225.63/38.73  | | | | | | | | | | |   (18810)   ~ (all_53_9 = e1)
% 225.63/38.73  | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | REDUCE: (360), (18809) imply:
% 225.63/38.73  | | | | | | | | | | |   (18811)   ~ (all_53_13 = e1)
% 225.63/38.73  | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | REDUCE: (18717), (18809) imply:
% 225.63/38.73  | | | | | | | | | | |   (18812)   ~ (e3 = e1)
% 225.63/38.73  | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | REDUCE: (42), (18809) imply:
% 225.63/38.73  | | | | | | | | | | |   (18813)  op(e2, e2) = e1
% 225.63/38.73  | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | BETA: splitting (107) gives:
% 225.63/38.73  | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | Case 1:
% 225.63/38.73  | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | |   (18814)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 225.63/38.73  | | | | | | | | | | | |              all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 225.63/38.73  | | | | | | | | | | | |              op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 225.63/38.73  | | | | | | | | | | | |                all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 225.63/38.73  | | | | | | | | | | | |              op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 225.63/38.73  | | | | | | | | | | | |              op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 225.63/38.73  | | | | | | | | | | | |              $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 225.63/38.73  | | | | | | | | | | | |              $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 225.63/38.73  | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 225.63/38.73  | | | | | | | | | | | |                all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 225.63/38.73  | | | | | | | | | | | |              & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 225.63/38.73  | | | | | | | | | | | |                all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 225.63/38.73  | | | | | | | | | | | |              op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 225.63/38.73  | | | | | | | | | | | |              & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 225.63/38.73  | | | | | | | | | | | |              $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 225.63/38.73  | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | BETA: splitting (18814) gives:
% 225.63/38.73  | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | Case 1:
% 225.63/38.73  | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | |   (18815)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 225.63/38.73  | | | | | | | | | | | | |            all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 225.63/38.73  | | | | | | | | | | | | |            op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 225.63/38.73  | | | | | | | | | | | | |              all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 225.63/38.73  | | | | | | | | | | | | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 225.63/38.73  | | | | | | | | | | | | |            op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 225.63/38.73  | | | | | | | | | | | | |            $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 225.63/38.73  | | | | | | | | | | | | |            $i(all_52_7)
% 225.63/38.73  | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | ALPHA: (18815) implies:
% 225.63/38.73  | | | | | | | | | | | | |   (18816)  op(e3, e0) = all_52_7
% 225.63/38.73  | | | | | | | | | | | | |   (18817)  op(e3, e1) = all_52_5
% 225.63/38.73  | | | | | | | | | | | | |   (18818)  op(e3, e2) = all_52_3
% 225.63/38.73  | | | | | | | | | | | | |   (18819)  op(e3, e3) = all_52_1
% 225.63/38.73  | | | | | | | | | | | | |   (18820)  op(all_52_7, all_52_7) = e0
% 225.63/38.73  | | | | | | | | | | | | |   (18821)  op(all_52_5, all_52_5) = e1
% 225.63/38.73  | | | | | | | | | | | | |   (18822)  op(all_52_3, all_52_3) = e2
% 225.63/38.73  | | | | | | | | | | | | |   (18823)  op(all_52_1, all_52_1) = e3
% 225.63/38.73  | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_12,
% 225.63/38.73  | | | | | | | | | | | | |              all_52_7, e0, e3, simplifying with (169), (18816)
% 225.63/38.73  | | | | | | | | | | | | |              gives:
% 225.63/38.73  | | | | | | | | | | | | |   (18824)  all_53_12 = all_52_7
% 225.63/38.73  | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_8,
% 225.63/38.73  | | | | | | | | | | | | |              all_52_5, e1, e3, simplifying with (170), (18817)
% 225.63/38.73  | | | | | | | | | | | | |              gives:
% 225.63/38.73  | | | | | | | | | | | | |   (18825)  all_53_8 = all_52_5
% 225.63/38.73  | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_4,
% 225.63/38.73  | | | | | | | | | | | | |              all_52_3, e2, e3, simplifying with (171), (18818)
% 225.63/38.73  | | | | | | | | | | | | |              gives:
% 225.63/38.73  | | | | | | | | | | | | |   (18826)  all_53_4 = all_52_3
% 225.63/38.73  | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2,
% 225.63/38.73  | | | | | | | | | | | | |              all_52_1, e3, e3, simplifying with (45), (18819)
% 225.63/38.73  | | | | | | | | | | | | |              gives:
% 225.63/38.73  | | | | | | | | | | | | |   (18827)  all_52_1 = all_10_2
% 225.63/38.73  | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | COMBINE_EQS: (268), (18824) imply:
% 225.63/38.73  | | | | | | | | | | | | |   (18828)  all_55_3 = all_52_7
% 225.63/38.73  | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | REDUCE: (344), (18826) imply:
% 225.63/38.73  | | | | | | | | | | | | |   (18829)   ~ (all_52_3 = all_10_2)
% 225.63/38.73  | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | REDUCE: (114), (18824) imply:
% 225.63/38.73  | | | | | | | | | | | | |   (18830)   ~ (all_53_13 = all_52_7)
% 225.63/38.73  | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | SIMP: (18830) implies:
% 225.63/38.73  | | | | | | | | | | | | |   (18831)   ~ (all_53_13 = all_52_7)
% 225.63/38.73  | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | REDUCE: (14927), (18824) imply:
% 225.63/38.73  | | | | | | | | | | | | |   (18832)   ~ (all_52_7 = e2)
% 225.63/38.73  | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | REDUCE: (18823), (18827) imply:
% 225.63/38.73  | | | | | | | | | | | | |   (18833)  op(all_10_2, all_10_2) = e3
% 225.63/38.73  | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | BETA: splitting (58) gives:
% 225.63/38.73  | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | Case 1:
% 225.63/38.73  | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | |   (18834)   ~ (all_18_2 = e0)
% 225.63/38.73  | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | REDUCE: (327), (18834) imply:
% 225.63/38.73  | | | | | | | | | | | | | |   (18835)   ~ (all_10_2 = e0)
% 225.63/38.73  | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | BETA: splitting (61) gives:
% 225.63/38.73  | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | Case 1:
% 225.63/38.73  | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | |   (18836)   ~ (all_20_2 = e2)
% 225.63/38.73  | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | REDUCE: (299), (18836) imply:
% 225.63/38.73  | | | | | | | | | | | | | | |   (18837)   ~ (all_10_2 = e2)
% 225.63/38.73  | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | BETA: splitting (205) gives:
% 225.63/38.73  | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | Case 1:
% 225.63/38.73  | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | |   (18838)  all_55_0 = e3
% 225.63/38.73  | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | COMBINE_EQS: (277), (18838) imply:
% 225.63/38.73  | | | | | | | | | | | | | | | |   (18839)  all_10_2 = e3
% 225.63/38.73  | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | REDUCE: (338), (18839) imply:
% 225.63/38.73  | | | | | | | | | | | | | | | |   (18840)   ~ (all_53_1 = e3)
% 225.63/38.73  | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | REDUCE: (342), (18839) imply:
% 225.63/38.73  | | | | | | | | | | | | | | | |   (18841)   ~ (all_53_3 = e3)
% 225.63/38.73  | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | REDUCE: (18829), (18839) imply:
% 225.63/38.73  | | | | | | | | | | | | | | | |   (18842)   ~ (all_52_3 = e3)
% 225.63/38.73  | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | REDUCE: (45), (18839) imply:
% 225.63/38.73  | | | | | | | | | | | | | | | |   (18843)  op(e3, e3) = e3
% 225.63/38.73  | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 225.63/38.73  | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.73  | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | |   (18844)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 225.63/38.73  | | | | | | | | | | | | | | | | |              & op(e2, e2) = e3)
% 225.63/38.73  | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | BETA: splitting (18844) gives:
% 225.63/38.73  | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | |   (18845)  all_57_2 = e3 & op(e2, e3) = e3
% 225.63/38.73  | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (18840), (18845), (function-axioms) are
% 225.63/38.73  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2299.
% 225.63/38.73  | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | |   (18846)  all_57_3 = e3 & op(e2, e2) = e3
% 225.63/38.73  | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | ALPHA: (18846) implies:
% 225.63/38.73  | | | | | | | | | | | | | | | | | |   (18847)  op(e2, e2) = e3
% 225.63/38.73  | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (235), (18816), (18817), (18818),
% 225.63/38.73  | | | | | | | | | | | | | | | | | |            (18820), (18821), (18822), (18842), (18843),
% 225.63/38.73  | | | | | | | | | | | | | | | | | |            (18847), (function-axioms) are inconsistent by
% 225.63/38.73  | | | | | | | | | | | | | | | | | |            sub-proof #95.
% 225.63/38.73  | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | End of split
% 225.63/38.73  | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.73  | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | |   (18848)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 225.63/38.73  | | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 225.63/38.73  | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | BETA: splitting (18848) gives:
% 225.63/38.73  | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | |   (18849)  all_57_5 = e3 & op(e2, e1) = e3
% 225.63/38.73  | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (18707), (18849), (function-axioms) are
% 225.63/38.73  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #270.
% 225.63/38.73  | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | |   (18850)  all_57_10 = e3 & op(e2, e0) = e3
% 225.63/38.73  | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | ALPHA: (18850) implies:
% 225.63/38.73  | | | | | | | | | | | | | | | | | |   (18851)  all_57_10 = e3
% 225.63/38.73  | | | | | | | | | | | | | | | | | |   (18852)  op(e2, e0) = e3
% 225.63/38.73  | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | |   (18853)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 225.63/38.73  | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e3)
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | BETA: splitting (18853) gives:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |   (18854)  all_57_1 = e3 & op(e3, e2) = e3
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | ALPHA: (18854) implies:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |   (18855)  all_57_1 = e3
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | |   (18856)  op(e3, e2) = e3
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | |   (18857)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e2)
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18857) gives:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | |   (18858)  all_57_0 = e2 & op(e3, e3) = e2
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18858) implies:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | |   (18859)  op(e3, e3) = e2
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (18843), (18859), (function-axioms) are
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2490.
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | |   (18860)  all_57_1 = e2 & op(e3, e2) = e2
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18860) implies:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | |   (18861)  op(e3, e2) = e2
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (18856), (18861), (function-axioms) are
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1549.
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | |   (18862)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e2)
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18862) gives:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | |   (18863)  all_57_4 = e2 & op(e3, e1) = e2
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18863) implies:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | |   (18864)  all_57_4 = e2
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | |   (18865)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e1)
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18865) gives:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | |   (18866)  all_57_4 = e1 & op(e3, e1) = e1
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (18864), (18866) are inconsistent by
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2452.
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | |   (18867)  all_57_5 = e1 & op(e2, e1) = e1
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (18810), (18867), (function-axioms) are
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2305.
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | |   (18868)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e1) = e1)
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18868) gives:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | |   (18869)  all_57_8 = e1 & op(e1, e1) = e1
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18869) implies:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | |   (18870)  op(e1, e1) = e1
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (18716), (18870), (function-axioms) are
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #156.
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | |   (18871)  all_57_14 = e1 & op(e0, e1) = e1
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18871) implies:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | |   (18872)  all_57_14 = e1
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | |   (18873)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18873) gives:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | |   (18874)  all_57_1 = e2 & op(e3, e2) = e2
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18874) implies:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | |   (18875)  all_57_1 = e2
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (226), (228), (229),
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (233), (18813), (18843), (18864), (18875),
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | |            #41.
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | |   (18876)  all_57_3 = e2 & op(e2, e2) = e2
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18876) implies:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | |   (18877)  op(e2, e2) = e2
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (18813), (18877), (function-axioms) are
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2306.
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | |   (18878)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18878) gives:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | |   (18879)  all_57_7 = e2 & op(e1, e2) = e2
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18879) implies:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | |   (18880)  all_57_7 = e2
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18881)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18881) gives:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18882)  all_57_12 = e3 & op(e0, e3) = e3
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18882) implies:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18883)  op(e0, e3) = e3
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (18841), (18883), (function-axioms) are
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #132.
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18884)  all_57_13 = e3 & op(e0, e2) = e3
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18884) implies:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18885)  all_57_13 = e3
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18886)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e0)
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18886) gives:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.73  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18887)  all_57_4 = e0 & op(e3, e1) = e0
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (18864), (18887) are inconsistent by
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2045.
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18888)  all_57_5 = e0 & op(e2, e1) = e0
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18888) implies:
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18889)  all_57_5 = e0
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18890)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18890) gives:
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18891)  all_57_1 = e0 & op(e3, e2) = e0
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (18855), (18891) are inconsistent by
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1811.
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18892)  all_57_3 = e0 & op(e2, e2) = e0
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18892) implies:
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18893)  all_57_3 = e0
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18894)  op(e2, e2) = e0
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (223), (224),
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (225), (18811), (18889), (18893), (18894),
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1689.
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18895)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0)
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18895) gives:
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18896)  all_57_7 = e0 & op(e1, e2) = e0
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18896) implies:
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18897)  all_57_7 = e0
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (18880), (18897) are inconsistent by
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2207.
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18898)  all_57_13 = e0 & op(e0, e2) = e0
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18898) implies:
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18899)  all_57_13 = e0
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (18885), (18899) are inconsistent by
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2184.
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18900)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18900) gives:
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18901)  all_57_8 = e0 & op(e1, e1) = e0
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (18715), (18901) are inconsistent by
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #170.
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18902)  all_57_14 = e0 & op(e0, e1) = e0
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (18872), (18902) are inconsistent by
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2181.
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (18903)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (207), (211),
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (18708), (18851), (18903),
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #124.
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | |   (18904)  all_57_13 = e2 & op(e0, e2) = e2
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18904) implies:
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | |   (18905)  op(e0, e2) = e2
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (14925), (18905), (function-axioms) are
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2335.
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | |   (18906)  all_57_9 = e2 & op(e3, e0) = e2
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18906) implies:
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | |   (18907)  op(e3, e0) = e2
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (14927), (18907), (function-axioms) are
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2331.
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | |   (18908)  all_57_3 = e3 & op(e2, e2) = e3
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | ALPHA: (18908) implies:
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | |   (18909)  op(e2, e2) = e3
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (235), (18816), (18817), (18818),
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | |            (18820), (18821), (18822), (18842), (18843),
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | |            (18909), (function-axioms) are inconsistent by
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | |            sub-proof #95.
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | |   (18910)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 225.63/38.74  | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | BETA: splitting (18910) gives:
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | |   (18911)  all_57_7 = e3 & op(e1, e2) = e3
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (18705), (18911), (function-axioms) are
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #267.
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | |   (18912)  all_57_13 = e3 & op(e0, e2) = e3
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | ALPHA: (18912) implies:
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | |   (18913)  op(e0, e2) = e3
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_7, e3,
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (159), (18913) gives:
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | |   (18914)  all_53_7 = e3
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_13,
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | |              e3, e0, e2, simplifying with (165), (18852) gives:
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | |   (18915)  all_53_13 = e3
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | REDUCE: (18831), (18915) imply:
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | |   (18916)   ~ (all_52_7 = e3)
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | SIMP: (18916) implies:
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | |   (18917)   ~ (all_52_7 = e3)
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | BETA: splitting (79) gives:
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | |   (18918)   ~ (all_32_2 = e2)
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | REDUCE: (14923), (18918) imply:
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | |   (18919)  $false
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | CLOSE: (18919) is inconsistent.
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | |   (18920)  ( ~ (all_32_0 = e1) & op(all_32_1, e0) = all_32_0
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | |              & op(e0, e2) = all_32_1 & $i(all_32_0) &
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | |              $i(all_32_1)) | ( ~ (all_32_1 = e3) & op(e0, e2)
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | |              = all_32_1 & $i(all_32_1))
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14922) gives:
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | |   (18921)   ~ (all_4_0 = e3) & op(all_4_1, e0) = all_4_0 &
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = all_4_1 & $i(all_4_0) & $i(all_4_1)
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18921) implies:
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | |   (18922)  op(e0, e2) = all_4_1
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (202), (14922), (14935), (18816), (18820),
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | |            (18828), (18832), (18913), (18917), (18920),
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | |            (18922), (function-axioms) are inconsistent by
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #3.
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | |   (18923)   ~ (all_4_1 = e1) & op(e0, e2) = all_4_1 &
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | |            $i(all_4_1)
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (18923) implies:
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | |   (18924)  op(e0, e2) = all_4_1
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (202), (14922), (14935), (18816), (18820),
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | |            (18828), (18832), (18913), (18917), (18920),
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | |            (18924), (function-axioms) are inconsistent by
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #3.
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.74  | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | End of split
% 225.63/38.74  | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | End of split
% 225.63/38.74  | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | Case 2:
% 225.63/38.74  | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | |   (18925)  all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 225.63/38.74  | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | REF_CLOSE: (277), (18718), (18835), (18837), (18925) are
% 225.63/38.74  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1953.
% 225.63/38.74  | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | End of split
% 225.63/38.74  | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | Case 2:
% 225.63/38.74  | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | |   (18926)  all_20_2 = e2
% 225.63/38.74  | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | COMBINE_EQS: (299), (18926) imply:
% 225.63/38.74  | | | | | | | | | | | | | | |   (18927)  all_10_2 = e2
% 225.63/38.74  | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | SIMP: (18927) implies:
% 225.63/38.74  | | | | | | | | | | | | | | |   (18928)  all_10_2 = e2
% 225.63/38.74  | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | REDUCE: (18833), (18928) imply:
% 225.63/38.74  | | | | | | | | | | | | | | |   (18929)  op(e2, e2) = e3
% 225.63/38.74  | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | REF_CLOSE: (8), (18813), (18929), (function-axioms) are
% 225.63/38.74  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1912.
% 225.63/38.74  | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | End of split
% 225.63/38.74  | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | Case 2:
% 225.63/38.74  | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | |   (18930)  all_18_2 = e0
% 225.63/38.74  | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | COMBINE_EQS: (327), (18930) imply:
% 225.63/38.74  | | | | | | | | | | | | | |   (18931)  all_10_2 = e0
% 225.63/38.74  | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | REDUCE: (45), (18931) imply:
% 225.63/38.74  | | | | | | | | | | | | | |   (18932)  op(e3, e3) = e0
% 225.63/38.74  | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | REF_CLOSE: (9), (14935), (18819), (18823), (18932),
% 225.63/38.74  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.74  | | | | | | | | | | | | | |            #53.
% 225.63/38.74  | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | End of split
% 225.63/38.74  | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | Case 2:
% 225.63/38.74  | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | |   (18933)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 225.63/38.74  | | | | | | | | | | | | |            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 225.63/38.74  | | | | | | | | | | | | |            op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 225.63/38.74  | | | | | | | | | | | | |              all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 225.63/38.74  | | | | | | | | | | | | |            & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 225.63/38.74  | | | | | | | | | | | | |            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 225.63/38.74  | | | | | | | | | | | | |            $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 225.63/38.74  | | | | | | | | | | | | |            $i(all_52_15)
% 225.63/38.74  | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | ALPHA: (18933) implies:
% 225.63/38.74  | | | | | | | | | | | | |   (18934)  op(e2, e2) = all_52_11
% 225.63/38.74  | | | | | | | | | | | | |   (18935)  op(all_52_11, all_52_11) = e2
% 225.63/38.74  | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | REF_CLOSE: (9), (18716), (18813), (18934), (18935),
% 225.63/38.74  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.74  | | | | | | | | | | | | |            #155.
% 225.63/38.74  | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | End of split
% 225.63/38.74  | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | Case 2:
% 225.63/38.74  | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | |   (18936)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 225.63/38.74  | | | | | | | | | | | |              & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 225.63/38.74  | | | | | | | | | | | |              & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 225.63/38.74  | | | | | | | | | | | |                all_52_21) = e1 & op(all_52_23, all_52_23) =
% 225.63/38.74  | | | | | | | | | | | |              e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 225.63/38.74  | | | | | | | | | | | |              all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 225.63/38.74  | | | | | | | | | | | |              = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 225.63/38.74  | | | | | | | | | | | |              $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 225.63/38.74  | | | | | | | | | | | |              & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 225.63/38.74  | | | | | | | | | | | |              e0 & op(all_52_25, all_52_25) = e3 &
% 225.63/38.74  | | | | | | | | | | | |              op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 225.63/38.74  | | | | | | | | | | | |                all_52_29) = e1 & op(all_52_31, all_52_31) =
% 225.63/38.74  | | | | | | | | | | | |              e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 225.63/38.74  | | | | | | | | | | | |              all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 225.63/38.74  | | | | | | | | | | | |              = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 225.63/38.74  | | | | | | | | | | | |              $i(all_52_29) & $i(all_52_31))
% 225.63/38.74  | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | BETA: splitting (18936) gives:
% 225.63/38.74  | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | Case 1:
% 225.63/38.74  | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | |   (18937)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 225.63/38.74  | | | | | | | | | | | | |            all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 225.63/38.74  | | | | | | | | | | | | |            op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 225.63/38.74  | | | | | | | | | | | | |              all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 225.63/38.74  | | | | | | | | | | | | |            & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 225.63/38.74  | | | | | | | | | | | | |            & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 225.63/38.74  | | | | | | | | | | | | |            & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 225.63/38.74  | | | | | | | | | | | | |            $i(all_52_23)
% 225.63/38.74  | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | ALPHA: (18937) implies:
% 225.63/38.74  | | | | | | | | | | | | |   (18938)  op(e1, e1) = all_52_21
% 225.63/38.74  | | | | | | | | | | | | |   (18939)  op(all_52_21, all_52_21) = e1
% 225.63/38.74  | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | REF_CLOSE: (45), (18716), (18718), (18938), (18939),
% 225.63/38.74  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.74  | | | | | | | | | | | | |            #167.
% 225.63/38.74  | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | Case 2:
% 225.63/38.74  | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | |   (18940)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 225.63/38.74  | | | | | | | | | | | | |            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 225.63/38.74  | | | | | | | | | | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 225.63/38.74  | | | | | | | | | | | | |              all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 225.63/38.74  | | | | | | | | | | | | |            & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 225.63/38.74  | | | | | | | | | | | | |            & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 225.63/38.74  | | | | | | | | | | | | |            & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 225.63/38.74  | | | | | | | | | | | | |            $i(all_52_31)
% 225.63/38.74  | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | REF_CLOSE: (4), (14935), (18813), (18940), (function-axioms)
% 225.63/38.74  | | | | | | | | | | | | |            are inconsistent by sub-proof #50.
% 225.63/38.74  | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | End of split
% 225.63/38.74  | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | End of split
% 225.63/38.74  | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | End of split
% 225.63/38.74  | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | Case 2:
% 225.63/38.74  | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | |   (18941)  all_14_2 = e0
% 225.63/38.74  | | | | | | | | | |   (18942)  ( ~ (all_14_0 = e1) & op(all_14_1, e2) = all_14_0
% 225.63/38.74  | | | | | | | | | |              & op(e2, e0) = all_14_1 & $i(all_14_0) &
% 225.63/38.74  | | | | | | | | | |              $i(all_14_1)) | ( ~ (all_14_1 = e3) & op(e2, e0)
% 225.63/38.74  | | | | | | | | | |              = all_14_1 & $i(all_14_1))
% 225.63/38.74  | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | COMBINE_EQS: (328), (18941) imply:
% 225.63/38.74  | | | | | | | | | |   (18943)  all_8_2 = e0
% 225.63/38.74  | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | SIMP: (18943) implies:
% 225.63/38.74  | | | | | | | | | |   (18944)  all_8_2 = e0
% 225.63/38.74  | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | COMBINE_EQS: (290), (18944) imply:
% 225.63/38.74  | | | | | | | | | |   (18945)  all_50_2 = e0
% 225.63/38.74  | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | REDUCE: (352), (18944) imply:
% 225.63/38.74  | | | | | | | | | |   (18946)   ~ (all_53_4 = e0)
% 225.63/38.74  | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | REDUCE: (354), (18944) imply:
% 225.63/38.74  | | | | | | | | | |   (18947)   ~ (all_53_6 = e0)
% 225.63/38.74  | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | REDUCE: (356), (18944) imply:
% 225.63/38.74  | | | | | | | | | |   (18948)   ~ (all_53_7 = e0)
% 225.63/38.74  | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | REDUCE: (358), (18944) imply:
% 225.63/38.74  | | | | | | | | | |   (18949)   ~ (all_53_9 = e0)
% 225.63/38.74  | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | REDUCE: (360), (18944) imply:
% 225.63/38.74  | | | | | | | | | |   (18950)   ~ (all_53_13 = e0)
% 225.63/38.74  | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | REDUCE: (18717), (18944) imply:
% 225.63/38.74  | | | | | | | | | |   (18951)   ~ (e3 = e0)
% 225.63/38.74  | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | BETA: splitting (226) gives:
% 225.63/38.74  | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | Case 1:
% 225.63/38.74  | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | |   (18952)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 225.63/38.74  | | | | | | | | | | |              & op(e2, e2) = e0)
% 225.63/38.74  | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | BETA: splitting (18952) gives:
% 225.63/38.74  | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | Case 1:
% 225.63/38.74  | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | |   (18953)  all_57_1 = e0 & op(e3, e2) = e0
% 225.63/38.74  | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | ALPHA: (18953) implies:
% 225.63/38.74  | | | | | | | | | | | |   (18954)  op(e3, e2) = e0
% 225.63/38.74  | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | REF_CLOSE: (171), (18946), (18954), (function-axioms) are
% 225.63/38.74  | | | | | | | | | | | |            inconsistent by sub-proof #1941.
% 225.63/38.74  | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | Case 2:
% 225.63/38.74  | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | |   (18955)  all_57_3 = e0 & op(e2, e2) = e0
% 225.63/38.74  | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | ALPHA: (18955) implies:
% 225.63/38.74  | | | | | | | | | | | |   (18956)  all_57_3 = e0
% 225.63/38.74  | | | | | | | | | | | |   (18957)  op(e2, e2) = e0
% 225.63/38.74  | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | BETA: splitting (58) gives:
% 225.63/38.74  | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | Case 1:
% 225.63/38.74  | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | |   (18958)   ~ (all_18_2 = e0)
% 225.63/38.74  | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | REDUCE: (327), (18958) imply:
% 225.63/38.74  | | | | | | | | | | | | |   (18959)   ~ (all_10_2 = e0)
% 225.63/38.74  | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | BETA: splitting (61) gives:
% 225.63/38.74  | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | Case 1:
% 225.63/38.74  | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | |   (18960)   ~ (all_20_2 = e2)
% 225.63/38.74  | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | REDUCE: (299), (18960) imply:
% 225.63/38.74  | | | | | | | | | | | | | |   (18961)   ~ (all_10_2 = e2)
% 225.63/38.74  | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | BETA: splitting (205) gives:
% 225.63/38.74  | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | Case 1:
% 225.63/38.74  | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | |   (18962)  all_55_0 = e3
% 225.63/38.74  | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | COMBINE_EQS: (277), (18962) imply:
% 225.63/38.74  | | | | | | | | | | | | | | |   (18963)  all_10_2 = e3
% 225.63/38.74  | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | REDUCE: (344), (18963) imply:
% 225.63/38.74  | | | | | | | | | | | | | | |   (18964)   ~ (all_53_4 = e3)
% 225.63/38.74  | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | REDUCE: (348), (18963) imply:
% 225.63/38.74  | | | | | | | | | | | | | | |   (18965)   ~ (all_53_12 = e3)
% 225.63/38.74  | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | REDUCE: (45), (18963) imply:
% 225.63/38.74  | | | | | | | | | | | | | | |   (18966)  op(e3, e3) = e3
% 225.63/38.74  | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 225.63/38.74  | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | Case 1:
% 225.63/38.74  | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | |   (18967)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 225.63/38.74  | | | | | | | | | | | | | | | |              & op(e2, e2) = e3)
% 225.63/38.74  | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | REF_CLOSE: (42), (171), (18717), (18964), (18967),
% 225.63/38.74  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.74  | | | | | | | | | | | | | | | |            #32.
% 225.63/38.74  | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | Case 2:
% 225.63/38.74  | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | |   (18968)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 225.63/38.74  | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 225.63/38.74  | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | BETA: splitting (18968) gives:
% 225.63/38.74  | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.74  | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | |   (18969)  all_57_7 = e3 & op(e1, e2) = e3
% 225.63/38.74  | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (18705), (18969), (function-axioms) are
% 225.63/38.74  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #267.
% 225.63/38.74  | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.74  | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | |   (18970)  all_57_13 = e3 & op(e0, e2) = e3
% 225.63/38.74  | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | ALPHA: (18970) implies:
% 225.63/38.74  | | | | | | | | | | | | | | | | |   (18971)  all_57_13 = e3
% 225.63/38.74  | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 225.63/38.74  | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.74  | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | |   (18972)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 225.63/38.74  | | | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 225.63/38.74  | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (45), (106), (107), (136), (159), (163),
% 225.63/38.74  | | | | | | | | | | | | | | | | | |            (165), (169), (171), (204), (229), (270), (18705),
% 225.63/38.74  | | | | | | | | | | | | | | | | | |            (18716), (18718), (18942), (18945), (18946),
% 225.63/38.74  | | | | | | | | | | | | | | | | | |            (18950), (18956), (18957), (18964), (18965),
% 225.63/38.74  | | | | | | | | | | | | | | | | | |            (18966), (18972), (function-axioms) are
% 225.63/38.74  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #147.
% 225.63/38.74  | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.74  | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | |   (18973)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 225.63/38.74  | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 225.63/38.74  | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (159), (161), (207),
% 225.63/38.74  | | | | | | | | | | | | | | | | | |            (208), (209), (18709), (18948), (18971), (18973),
% 225.63/38.74  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.74  | | | | | | | | | | | | | | | | | |            #113.
% 225.63/38.74  | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | End of split
% 225.63/38.74  | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | End of split
% 225.63/38.74  | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | End of split
% 225.63/38.74  | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | Case 2:
% 225.63/38.74  | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | |   (18974)  all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 225.63/38.74  | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | REF_CLOSE: (277), (18718), (18959), (18961), (18974) are
% 225.63/38.74  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1953.
% 225.63/38.74  | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | End of split
% 225.63/38.74  | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | Case 2:
% 225.63/38.74  | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | |   (18975)  all_20_2 = e2
% 225.63/38.74  | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | COMBINE_EQS: (299), (18975) imply:
% 225.63/38.74  | | | | | | | | | | | | | |   (18976)  all_10_2 = e2
% 225.63/38.74  | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | SIMP: (18976) implies:
% 225.63/38.74  | | | | | | | | | | | | | |   (18977)  all_10_2 = e2
% 225.63/38.74  | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | REDUCE: (45), (18977) imply:
% 225.63/38.74  | | | | | | | | | | | | | |   (18978)  op(e3, e3) = e2
% 225.63/38.74  | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 225.63/38.74  | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | Case 1:
% 225.63/38.74  | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | |   (18979)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 225.63/38.74  | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 225.63/38.74  | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (237),
% 225.63/38.74  | | | | | | | | | | | | | | |            (18957), (18978), (18979), (function-axioms) are
% 225.63/38.74  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1297.
% 225.63/38.74  | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | Case 2:
% 225.63/38.74  | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | |   (18980)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 225.63/38.74  | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 225.63/38.74  | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | BETA: splitting (18980) gives:
% 225.63/38.74  | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | Case 1:
% 225.63/38.74  | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | |   (18981)  all_57_7 = e2 & op(e1, e2) = e2
% 225.63/38.74  | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | ALPHA: (18981) implies:
% 225.63/38.74  | | | | | | | | | | | | | | | |   (18982)  all_57_7 = e2
% 225.63/38.74  | | | | | | | | | | | | | | | |   (18983)  op(e1, e2) = e2
% 225.63/38.74  | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 225.63/38.74  | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.74  | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | |   (18984)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 225.63/38.74  | | | | | | | | | | | | | | | | |              & op(e2, e1) = e2)
% 225.63/38.74  | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | BETA: splitting (18984) gives:
% 225.63/38.74  | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.74  | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | |   (18985)  all_57_4 = e2 & op(e3, e1) = e2
% 225.63/38.74  | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | ALPHA: (18985) implies:
% 225.63/38.74  | | | | | | | | | | | | | | | | | |   (18986)  all_57_4 = e2
% 225.63/38.74  | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (171), (231), (233),
% 225.63/38.74  | | | | | | | | | | | | | | | | | |            (237), (18946), (18978), (18986),
% 225.63/38.74  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.74  | | | | | | | | | | | | | | | | | |            #1320.
% 225.63/38.74  | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.74  | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | |   (18987)  all_57_5 = e2 & op(e2, e1) = e2
% 225.63/38.74  | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | ALPHA: (18987) implies:
% 225.63/38.74  | | | | | | | | | | | | | | | | | |   (18988)  all_57_5 = e2
% 225.63/38.74  | | | | | | | | | | | | | | | | | |   (18989)  op(e2, e1) = e2
% 225.63/38.74  | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_6, e2,
% 225.63/38.74  | | | | | | | | | | | | | | | | | |              e2, e1, simplifying with (163), (18983) gives:
% 225.63/38.74  | | | | | | | | | | | | | | | | | |   (18990)  all_53_6 = e2
% 225.63/38.74  | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_9, e2,
% 225.63/38.74  | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (166), (18989) gives:
% 225.63/38.74  | | | | | | | | | | | | | | | | | |   (18991)  all_53_9 = e2
% 225.63/38.74  | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | REDUCE: (137), (18990) imply:
% 225.63/38.74  | | | | | | | | | | | | | | | | | |   (18992)   ~ (all_53_4 = e2)
% 225.63/38.74  | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | REDUCE: (129), (18990) imply:
% 225.63/38.74  | | | | | | | | | | | | | | | | | |   (18993)   ~ (all_53_7 = e2)
% 225.63/38.74  | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | REDUCE: (119), (18991) imply:
% 225.63/38.74  | | | | | | | | | | | | | | | | | |   (18994)   ~ (all_53_11 = e2)
% 225.63/38.74  | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | REDUCE: (18707), (18991) imply:
% 225.63/38.74  | | | | | | | | | | | | | | | | | |   (18995)   ~ (e3 = e2)
% 225.63/38.74  | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 225.63/38.74  | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | |   (18996)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 225.63/38.74  | | | | | | | | | | | | | | | | | | |              all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 225.63/38.74  | | | | | | | | | | | | | | | | | | |              op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 225.63/38.74  | | | | | | | | | | | | | | | | | | |                all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 225.63/38.74  | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 225.63/38.74  | | | | | | | | | | | | | | | | | | |              op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 225.63/38.74  | | | | | | | | | | | | | | | | | | |              $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 225.63/38.74  | | | | | | | | | | | | | | | | | | |              $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 225.63/38.74  | | | | | | | | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 225.63/38.74  | | | | | | | | | | | | | | | | | | |                all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 225.63/38.74  | | | | | | | | | | | | | | | | | | |              & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 225.63/38.74  | | | | | | | | | | | | | | | | | | |                all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 225.63/38.74  | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 225.63/38.74  | | | | | | | | | | | | | | | | | | |              & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 225.63/38.74  | | | | | | | | | | | | | | | | | | |              $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | BETA: splitting (18996) gives:
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | |   (18997)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | |            all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | |            op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | |              all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | |            $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | |            $i(all_52_7)
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | ALPHA: (18997) implies:
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | |   (18998)  op(e3, e3) = all_52_1
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | |   (18999)  op(all_52_1, all_52_1) = e3
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (18957), (18978), (18998), (18999),
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | |            #1653.
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | |   (19000)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | |            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | |            op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | |              all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | |            $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | |            $i(all_52_15)
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | ALPHA: (19000) implies:
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | |   (19001)  op(e2, e1) = all_52_13
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | |   (19002)  op(e2, e2) = all_52_11
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | |   (19003)  op(all_52_13, all_52_13) = e1
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | |   (19004)  op(all_52_11, all_52_11) = e2
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | |              all_52_13, e1, e2, simplifying with (18989),
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | |              (19001) gives:
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | |   (19005)  all_52_13 = e2
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | REDUCE: (19003), (19005) imply:
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | |   (19006)  op(e2, e2) = e1
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (18716), (19002), (19004), (19006),
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | |            #155.
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.74  | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.74  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | |   (19007)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 225.63/38.75  | | | | | | | | | | | | | | | | | | |              & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 225.63/38.75  | | | | | | | | | | | | | | | | | | |              & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 225.63/38.75  | | | | | | | | | | | | | | | | | | |                all_52_21) = e1 & op(all_52_23, all_52_23) =
% 225.63/38.75  | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 225.63/38.75  | | | | | | | | | | | | | | | | | | |              all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 225.63/38.75  | | | | | | | | | | | | | | | | | | |              = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 225.63/38.75  | | | | | | | | | | | | | | | | | | |              $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 225.63/38.75  | | | | | | | | | | | | | | | | | | |              & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 225.63/38.75  | | | | | | | | | | | | | | | | | | |              e0 & op(all_52_25, all_52_25) = e3 &
% 225.63/38.75  | | | | | | | | | | | | | | | | | | |              op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 225.63/38.75  | | | | | | | | | | | | | | | | | | |                all_52_29) = e1 & op(all_52_31, all_52_31) =
% 225.63/38.75  | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 225.63/38.75  | | | | | | | | | | | | | | | | | | |              all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 225.63/38.75  | | | | | | | | | | | | | | | | | | |              = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 225.63/38.75  | | | | | | | | | | | | | | | | | | |              $i(all_52_29) & $i(all_52_31))
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | BETA: splitting (19007) gives:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | |   (19008)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | |            all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | |            op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | |              all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | |            & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | |            & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | |            $i(all_52_23)
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | ALPHA: (19008) implies:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | |   (19009)  op(e1, e1) = all_52_21
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | |   (19010)  op(all_52_21, all_52_21) = e1
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (18716), (18718), (19009), (19010),
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | |            #167.
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | |   (19011)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | |            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | |              all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | |            & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | |            & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | |            & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | |            $i(all_52_31)
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | ALPHA: (19011) implies:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | |   (19012)  op(e0, e0) = all_52_31
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | |   (19013)  op(e0, e1) = all_52_29
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | |   (19014)  op(e0, e2) = all_52_27
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | |   (19015)  op(e0, e3) = all_52_25
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | |   (19016)  op(all_52_31, all_52_31) = e0
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | |   (19017)  op(all_52_29, all_52_29) = e1
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | |   (19018)  op(all_52_27, all_52_27) = e2
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | |   (19019)  op(all_52_25, all_52_25) = e3
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | |              all_52_31, e0, e0, simplifying with (14935),
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | |              (19012) gives:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | |   (19020)  all_52_31 = e2
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_11,
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | |              all_52_29, e1, e0, simplifying with (158), (19013)
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | |              gives:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | |   (19021)  all_53_11 = all_52_29
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_7,
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | |              all_52_27, e2, e0, simplifying with (159), (19014)
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | |              gives:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | |   (19022)  all_53_7 = all_52_27
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_3,
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | |              all_52_25, e3, e0, simplifying with (160), (19015)
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | |              gives:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | |   (19023)  all_53_3 = all_52_25
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (19021) imply:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | |   (19024)  all_55_14 = all_52_29
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (19022) imply:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | |   (19025)  all_55_13 = all_52_27
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | REDUCE: (136), (19022) imply:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | |   (19026)   ~ (all_53_4 = all_52_27)
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | REDUCE: (126), (19021), (19022) imply:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | |   (19027)   ~ (all_52_27 = all_52_29)
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | REDUCE: (14925), (19022) imply:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | |   (19028)   ~ (all_52_27 = e2)
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | REDUCE: (18948), (19022) imply:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | |   (19029)   ~ (all_52_27 = e0)
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | REDUCE: (122), (19021) imply:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | |   (19030)   ~ (all_53_8 = all_52_29)
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | REDUCE: (18708), (19021) imply:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | |   (19031)   ~ (all_52_29 = e3)
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | REDUCE: (14926), (19021) imply:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | |   (19032)   ~ (all_52_29 = e2)
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | |   (19033)  all_55_14 = e3
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (19024), (19033) imply:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | |   (19034)  all_52_29 = e3
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | REDUCE: (19031), (19034) imply:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | |   (19035)  $false
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | CLOSE: (19035) is inconsistent.
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | |   (19036)   ~ (all_55_14 = e3)
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | |   (19037)  all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | |   (19038)  all_55_13 = e3
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (19025), (19038) imply:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | |   (19039)  all_52_27 = e3
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | SIMP: (19039) implies:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | |   (19040)  all_52_27 = e3
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (19026), (19040) imply:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | |   (19041)   ~ (all_53_4 = e3)
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (19027), (19040) imply:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | |   (19042)   ~ (all_52_29 = e3)
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | |   (19043)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e3)
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (171), (18978), (19041), (19043),
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | |            #249.
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | |   (19044)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e3)
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19044) gives:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | |   (19045)  all_57_4 = e3 & op(e3, e1) = e3
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (18706), (19045), (function-axioms) are
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #177.
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | |   (19046)  all_57_9 = e3 & op(e3, e0) = e3
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19046) implies:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | |   (19047)  op(e3, e0) = e3
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | |   (19048)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e0)
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | |            (18956), (18978), (19048), (function-axioms) are
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1654.
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | |   (19049)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = e0)
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19049) gives:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | |   (19050)  all_57_6 = e0 & op(e1, e3) = e0
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19050) implies:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | |   (19051)  op(e1, e3) = e0
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19052)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e0)
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (171), (18946), (18978), (19052),
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1321.
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19053)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e0)
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19053) gives:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19054)  all_57_4 = e0 & op(e3, e1) = e0
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (100), (164), (170), (191), (18702), (18703),
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18716), (19013), (19017), (19024), (19030),
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19031), (19051), (19054), (function-axioms) are
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #143.
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19055)  all_57_9 = e0 & op(e3, e0) = e0
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19055) implies:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19056)  op(e3, e0) = e0
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (19047), (19056), (function-axioms) are
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #313.
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | |   (19057)  all_57_12 = e0 & op(e0, e3) = e0
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19057) implies:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | |   (19058)  op(e0, e3) = e0
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (14935), (19012), (19015), (19019), (19058),
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | |            #31.
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | |   (19059)   ~ (all_55_13 = e3)
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | |   (19060)  all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (19025), (19059) imply:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | |   (19061)   ~ (all_52_27 = e3)
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | |   (19062)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e3)
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19062) gives:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | |   (19063)  all_57_1 = e3 & op(e3, e2) = e3
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19063) implies:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | |   (19064)  all_57_1 = e3
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19060) gives:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | |   (19065)  all_55_13 = e2
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19025), (19028), (19065) are inconsistent by
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1647.
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | |   (19066)   ~ (all_55_13 = e2)
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | |   (19067)  all_55_13 = e1 | all_55_13 = e0
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | |   (19068)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (171), (18957), (19025), (19026), (19029),
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | |            (19067), (19068), (function-axioms) are
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2.
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | |   (19069)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19069) gives:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19070)  all_57_7 = e1 & op(e1, e2) = e1
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19070) implies:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19071)  all_57_7 = e1
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (18982), (19071) are inconsistent by
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1761.
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19072)  all_57_13 = e1 & op(e0, e2) = e1
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19072) implies:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19073)  all_57_13 = e1
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19074)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19074) gives:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19075)  all_57_12 = e3 & op(e0, e3) = e3
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19075) implies:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19076)  all_57_12 = e3
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19067) gives:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19077)  all_55_13 = e1
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (19025), (19077) imply:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19078)  all_52_27 = e1
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (19078) implies:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19079)  all_52_27 = e1
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (19026), (19079) imply:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19080)   ~ (all_53_4 = e1)
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (19027), (19079) imply:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19081)   ~ (all_52_29 = e1)
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (19081) implies:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19082)   ~ (all_52_29 = e1)
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (19028), (19079) imply:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19083)   ~ (e2 = e1)
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19084)  all_55_1 = e3
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (19084) imply:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19085)  all_53_4 = e3
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (19085) implies:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19086)  all_53_4 = e3
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (19086) imply:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19087)   ~ (all_53_12 = e3)
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (19087) implies:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19088)   ~ (all_53_12 = e3)
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19089)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19089) gives:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19090)  all_57_9 = e3 & op(e3, e0) = e3
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19090) implies:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19091)  op(e3, e0) = e3
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (19088), (19091), (function-axioms) are
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2458.
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19092)  all_57_10 = e3 & op(e2, e0) = e3
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19092) implies:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19093)  all_57_10 = e3
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19094)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19094) gives:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19095)  all_57_2 = e1 & op(e2, e3) = e1
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19095) implies:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19096)  all_57_2 = e1
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19097)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e1)
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19097) gives:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19098)  all_57_4 = e1 & op(e3, e1) = e1
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19098) implies:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19099)  all_57_4 = e1
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19100)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e0)
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19100) gives:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19101)  all_57_4 = e0 & op(e3, e1) = e0
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19101) implies:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19102)  all_57_4 = e0
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (19099), (19102) imply:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19103)  e1 = e0
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (19096), (19103) imply:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19104)  all_57_2 = e0
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (223), (224), (18956),
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19093), (19104) are inconsistent by sub-proof
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2247.
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19105)  all_57_5 = e0 & op(e2, e1) = e0
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19105) implies:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19106)  all_57_5 = e0
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18956), (18957), (19096), (19106),
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2353.
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19107)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19107) gives:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19108)  all_57_8 = e0 & op(e1, e1) = e0
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (18715), (19108) are inconsistent by
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #170.
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19109)  all_57_14 = e0 & op(e0, e1) = e0
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19109) implies:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19110)  all_57_14 = e0
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19037) gives:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19111)  all_55_14 = e2
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (19024), (19111) imply:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19112)  all_52_29 = e2
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (19032), (19112) imply:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19113)  $false
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (19113) is inconsistent.
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19114)   ~ (all_55_14 = e2)
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19115)  all_55_14 = e1 | all_55_14 = e0
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19115) gives:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19116)  all_55_14 = e1
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (19024), (19116) imply:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19117)  all_52_29 = e1
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (19082), (19117) imply:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19118)  $false
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (19118) is inconsistent.
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19119)  all_55_14 = e0
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (19024), (19119) imply:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19120)  all_52_29 = e0
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (19032), (19120) imply:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19121)   ~ (e2 = e0)
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (19017), (19120) imply:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19122)  op(e0, e0) = e1
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (209), (19073), (19076), (19110),
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19122), (function-axioms) are inconsistent by
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2069.
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19123)  all_57_5 = e1 & op(e2, e1) = e1
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19123) implies:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19124)  all_57_5 = e1
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (222), (224), (225),
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19093), (19096), (19124), (function-axioms) are
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #66.
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19125)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e1) = e1)
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19125) gives:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19126)  all_57_8 = e1 & op(e1, e1) = e1
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19126) implies:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19127)  op(e1, e1) = e1
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (18716), (19127), (function-axioms) are
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #156.
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19128)  all_57_14 = e1 & op(e0, e1) = e1
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19128) implies:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19129)  all_57_14 = e1
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19130)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e0)
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (223), (224), (18956),
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18978), (19093), (19130), (function-axioms) are
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #552.
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19131)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = e0)
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19131) gives:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19132)  all_57_6 = e0 & op(e1, e3) = e0
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19132) implies:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19133)  op(e1, e3) = e0
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19134)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e0)
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19134) gives:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19135)  all_57_4 = e0 & op(e3, e1) = e0
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (100), (164), (170), (191), (18702), (18703),
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18716), (19013), (19017), (19024), (19030),
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19031), (19133), (19135), (function-axioms) are
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #143.
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19136)  all_57_5 = e0 & op(e2, e1) = e0
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19136) implies:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19137)  all_57_5 = e0
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18956), (18957), (19096), (19137),
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2353.
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19138)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19138) gives:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19139)  all_57_8 = e0 & op(e1, e1) = e0
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (18715), (19139) are inconsistent by
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #170.
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19140)  all_57_14 = e0 & op(e0, e1) = e0
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19140) implies:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19141)  all_57_14 = e0
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (19129), (19141) imply:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19142)  e1 = e0
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (19096), (19142) imply:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19143)  all_57_2 = e0
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (223), (224), (18956),
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19093), (19143) are inconsistent by sub-proof
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2247.
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19144)  all_57_12 = e0 & op(e0, e3) = e0
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19144) implies:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19145)  op(e0, e3) = e0
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (14935), (19012), (19015), (19019), (19145),
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #31.
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19146)  all_57_3 = e1 & op(e2, e2) = e1
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19146) implies:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19147)  op(e2, e2) = e1
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (18957), (19147), (function-axioms) are
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2352.
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19148)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19148) gives:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19149)  all_57_5 = e1 & op(e2, e1) = e1
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (18988), (19149) are inconsistent by
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1886.
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19150)  all_57_10 = e1 & op(e2, e0) = e1
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19150) implies:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19151)  all_57_10 = e1
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (19093), (19151) imply:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19152)  e3 = e1
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (19152) implies:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19153)  e3 = e1
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (19064), (19153) imply:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19154)  all_57_1 = e1
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (228), (229), (18956),
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18957), (19073), (19154), (function-axioms) are
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1193.
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19155)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19155) gives:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19156)  all_57_11 = e3 & op(e1, e0) = e3
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19156) implies:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19157)  op(e1, e0) = e3
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (18709), (19157), (function-axioms) are
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2330.
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19158)  all_57_15 = e3 & op(e0, e0) = e3
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19158) implies:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19159)  all_57_15 = e3
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (207), (208), (209),
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (227), (228), (18956), (19064), (19076), (19159)
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1037.
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19160)  all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 225.63/38.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (192), (270), (18946), (18957), (18992), (19018),
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19025), (19026), (19029), (19061), (19160),
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1541.
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19161)  all_55_13 = e0
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19025), (19029), (19161) are inconsistent by
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1639.
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19162)  all_57_13 = e3 & op(e0, e2) = e3
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19162) implies:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19163)  all_57_13 = e3
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (171), (227), (18957), (18982),
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19025), (19026), (19029), (19067), (19163),
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1.
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19164)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19164) gives:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19165)  all_57_14 = e3 & op(e0, e1) = e3
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (18708), (19165), (function-axioms) are
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #129.
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19166)  all_57_15 = e3 & op(e0, e0) = e3
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19166) implies:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19167)  all_57_15 = e3
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14934), (19167) imply:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19168)  e3 = e2
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (19168) implies:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19169)  e3 = e2
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (19064), (19169) imply:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19170)  all_57_1 = e2
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (233), (237),
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18978), (19170), (function-axioms) are
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1655.
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | |   (19171)  all_57_3 = e3 & op(e2, e2) = e3
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19171) implies:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | |   (19172)  op(e2, e2) = e3
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (14935), (19012), (19016), (19172),
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | |            #11.
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | |   (19173)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19173) gives:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | |   (19174)  all_57_7 = e3 & op(e1, e2) = e3
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (18705), (19174), (function-axioms) are
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #267.
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | |   (19175)  all_57_13 = e3 & op(e0, e2) = e3
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19175) implies:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | |   (19176)  all_57_13 = e3
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19060) gives:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | |   (19177)  all_55_13 = e2
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19025), (19028), (19177) are inconsistent by
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1647.
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | |   (19178)  all_55_13 = e1 | all_55_13 = e0
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (171), (227), (18957), (18982),
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | |            (19025), (19026), (19029), (19176), (19178),
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | |            #1.
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.76  | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | End of split
% 225.63/38.76  | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.76  | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | |   (19179)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 225.63/38.76  | | | | | | | | | | | | | | | | |              e2 & op(e0, e1) = e2)
% 225.63/38.76  | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | BETA: splitting (19179) gives:
% 225.63/38.76  | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | |   (19180)  all_57_8 = e2 & op(e1, e1) = e2
% 225.63/38.76  | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (18715), (19180) are inconsistent by
% 225.63/38.76  | | | | | | | | | | | | | | | | | |            sub-proof #165.
% 225.63/38.76  | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | |   (19181)  all_57_14 = e2 & op(e0, e1) = e2
% 225.63/38.76  | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (14926), (19181), (function-axioms) are
% 225.63/38.76  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #54.
% 225.63/38.76  | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | End of split
% 225.63/38.76  | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | End of split
% 225.63/38.76  | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | Case 2:
% 225.63/38.76  | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | |   (19182)  all_57_13 = e2 & op(e0, e2) = e2
% 225.63/38.76  | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | ALPHA: (19182) implies:
% 225.63/38.76  | | | | | | | | | | | | | | | |   (19183)  op(e0, e2) = e2
% 225.63/38.76  | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | REF_CLOSE: (159), (14925), (19183), (function-axioms) are
% 225.63/38.76  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2335.
% 225.63/38.76  | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | End of split
% 225.63/38.76  | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | End of split
% 225.63/38.76  | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | End of split
% 225.63/38.76  | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | Case 2:
% 225.63/38.76  | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | |   (19184)  all_18_2 = e0
% 225.63/38.76  | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | COMBINE_EQS: (327), (19184) imply:
% 225.63/38.76  | | | | | | | | | | | | |   (19185)  all_10_2 = e0
% 225.63/38.76  | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | REDUCE: (338), (19185) imply:
% 225.63/38.76  | | | | | | | | | | | | |   (19186)   ~ (all_53_1 = e0)
% 225.63/38.76  | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | REDUCE: (340), (19185) imply:
% 225.63/38.76  | | | | | | | | | | | | |   (19187)   ~ (all_53_2 = e0)
% 225.63/38.76  | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | REDUCE: (346), (19185) imply:
% 225.63/38.76  | | | | | | | | | | | | |   (19188)   ~ (all_53_8 = e0)
% 225.63/38.76  | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | REDUCE: (45), (19185) imply:
% 225.63/38.76  | | | | | | | | | | | | |   (19189)  op(e3, e3) = e0
% 225.63/38.76  | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | BETA: splitting (218) gives:
% 225.63/38.76  | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | Case 1:
% 225.63/38.76  | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | |   (19190)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 225.63/38.76  | | | | | | | | | | | | | |              & op(e2, e1) = e0)
% 225.63/38.76  | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | REF_CLOSE: (166), (170), (18949), (19188), (19190),
% 225.63/38.76  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.76  | | | | | | | | | | | | | |            #141.
% 225.63/38.76  | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | Case 2:
% 225.63/38.76  | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | |   (19191)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 225.63/38.76  | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 225.63/38.76  | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | BETA: splitting (19191) gives:
% 225.63/38.76  | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | Case 1:
% 225.63/38.76  | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | |   (19192)  all_57_8 = e0 & op(e1, e1) = e0
% 225.63/38.76  | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | REF_CLOSE: (7), (18715), (19192) are inconsistent by
% 225.63/38.76  | | | | | | | | | | | | | | |            sub-proof #170.
% 225.63/38.76  | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | Case 2:
% 225.63/38.76  | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | |   (19193)  all_57_14 = e0 & op(e0, e1) = e0
% 225.63/38.76  | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | ALPHA: (19193) implies:
% 225.63/38.76  | | | | | | | | | | | | | | |   (19194)  op(e0, e1) = e0
% 225.63/38.76  | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 225.63/38.76  | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | Case 1:
% 225.63/38.76  | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | |   (19195)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 225.63/38.76  | | | | | | | | | | | | | | | |              & op(e1, e2) = e0)
% 225.63/38.76  | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | REF_CLOSE: (163), (164), (18947), (19187), (19195),
% 225.63/38.76  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.76  | | | | | | | | | | | | | | | |            #2038.
% 225.63/38.76  | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | Case 2:
% 225.63/38.76  | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | |   (19196)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 225.63/38.76  | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 225.63/38.76  | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | BETA: splitting (19196) gives:
% 225.63/38.76  | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.76  | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | |   (19197)  all_57_8 = e0 & op(e1, e1) = e0
% 225.63/38.76  | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (18715), (19197) are inconsistent by
% 225.63/38.76  | | | | | | | | | | | | | | | | |            sub-proof #170.
% 225.63/38.76  | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.76  | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | |   (19198)  all_57_11 = e0 & op(e1, e0) = e0
% 225.63/38.76  | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | ALPHA: (19198) implies:
% 225.63/38.76  | | | | | | | | | | | | | | | | |   (19199)  op(e1, e0) = e0
% 225.63/38.76  | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 225.63/38.76  | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | |   (19200)  all_57_15 = e0 & op(e0, e0) = e0
% 225.63/38.76  | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | ALPHA: (19200) implies:
% 225.63/38.76  | | | | | | | | | | | | | | | | | |   (19201)  op(e0, e0) = e0
% 225.63/38.76  | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (14935), (19201), (function-axioms) are
% 225.63/38.76  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #86.
% 225.63/38.76  | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | |   (19202)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 225.63/38.76  | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 225.63/38.76  | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 225.63/38.76  | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 225.63/38.76  | | | | | | | | | | | | | | | | | |                e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 225.63/38.76  | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | ALPHA: (19202) implies:
% 225.63/38.76  | | | | | | | | | | | | | | | | | |   (19203)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 225.63/38.76  | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 225.63/38.76  | | | | | | | | | | | | | | | | | |                e1) = e0)
% 225.63/38.76  | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_11,
% 225.63/38.76  | | | | | | | | | | | | | | | | | |              e0, e1, e0, simplifying with (158), (19194) gives:
% 225.63/38.76  | | | | | | | | | | | | | | | | | |   (19204)  all_53_11 = e0
% 225.63/38.76  | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_14,
% 225.63/38.76  | | | | | | | | | | | | | | | | | |              e0, e0, e1, simplifying with (161), (19199) gives:
% 225.63/38.76  | | | | | | | | | | | | | | | | | |   (19205)  all_53_14 = e0
% 225.63/38.76  | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | REDUCE: (140), (19204) imply:
% 225.63/38.76  | | | | | | | | | | | | | | | | | |   (19206)   ~ (all_53_3 = e0)
% 225.63/38.76  | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | REDUCE: (113), (19205) imply:
% 225.63/38.76  | | | | | | | | | | | | | | | | | |   (19207)   ~ (all_53_12 = e0)
% 225.63/38.76  | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | REDUCE: (14929), (19205) imply:
% 225.63/38.76  | | | | | | | | | | | | | | | | | |   (19208)   ~ (e2 = e0)
% 225.63/38.76  | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | |   (19209)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 225.63/38.76  | | | | | | | | | | | | | | | | | | |              all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 225.63/38.76  | | | | | | | | | | | | | | | | | | |              op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 225.63/38.76  | | | | | | | | | | | | | | | | | | |                all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 225.63/38.76  | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 225.63/38.76  | | | | | | | | | | | | | | | | | | |              op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 225.63/38.76  | | | | | | | | | | | | | | | | | | |              $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 225.63/38.76  | | | | | | | | | | | | | | | | | | |              $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 225.63/38.76  | | | | | | | | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 225.63/38.76  | | | | | | | | | | | | | | | | | | |                all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 225.63/38.76  | | | | | | | | | | | | | | | | | | |              & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 225.63/38.76  | | | | | | | | | | | | | | | | | | |                all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 225.63/38.76  | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 225.63/38.76  | | | | | | | | | | | | | | | | | | |              & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 225.63/38.76  | | | | | | | | | | | | | | | | | | |              $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | BETA: splitting (19209) gives:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | |   (19210)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | |            all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | |            op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | |              all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | |            $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | |            $i(all_52_7)
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | ALPHA: (19210) implies:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | |   (19211)  op(e3, e3) = all_52_1
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | |   (19212)  op(all_52_1, all_52_1) = e3
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (14935), (19189), (19211), (19212),
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | |            #53.
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | |   (19213)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | |            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | |            op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | |              all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | |            $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | |            $i(all_52_15)
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | ALPHA: (19213) implies:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | |   (19214)  op(e2, e1) = all_52_13
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | |   (19215)  op(e2, e3) = all_52_9
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | |   (19216)  op(all_52_13, all_52_13) = e1
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | |   (19217)  op(all_52_9, all_52_9) = e3
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_9,
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | |              all_52_13, e1, e2, simplifying with (166), (19214)
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | |              gives:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | |   (19218)  all_53_9 = all_52_13
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_1,
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | |              all_52_9, e3, e2, simplifying with (168), (19215)
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | |              gives:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | |   (19219)  all_53_1 = all_52_9
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (19219) imply:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | |   (19220)  all_55_4 = all_52_9
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (19219) imply:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | |   (19221)   ~ (all_53_3 = all_52_9)
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | SIMP: (19221) implies:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | |   (19222)   ~ (all_53_3 = all_52_9)
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | REDUCE: (19186), (19219) imply:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | |   (19223)   ~ (all_52_9 = e0)
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | |   (19224)  all_55_9 = e3
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (18705), (19224) are inconsistent by
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | |            sub-proof #2159.
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | |   (19225)  all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | |   (19226)  all_55_13 = e3
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (19226) imply:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | |   (19227)  all_53_7 = e3
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (141), (19227) imply:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | |   (19228)   ~ (all_53_3 = e3)
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | |   (19229)  all_55_12 = e3
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (247), (19228), (19229) are inconsistent by
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2001.
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | |   (19230)  all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19230) gives:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | |   (19231)  all_55_12 = e2
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (19231) imply:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | |   (19232)  all_53_3 = e2
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14924), (19232) imply:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | |   (19233)  $false
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (19233) is inconsistent.
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | |   (19234)  all_55_12 = e1 | all_55_12 = e0
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19234) gives:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | |   (19235)  all_55_12 = e1
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (19235) imply:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | |   (19236)  all_53_3 = e1
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (19222), (19236) imply:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | |   (19237)   ~ (all_52_9 = e1)
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (19237) implies:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | |   (19238)   ~ (all_52_9 = e1)
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | |   (19239)  all_55_4 = e3
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19189), (19217), (19220), (19223), (19239),
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | |            #52.
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | |   (19240)  all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (18717), (19217), (19220), (19223), (19238),
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | |            (19240), (function-axioms) are inconsistent by
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #12.
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | |   (19241)  all_55_12 = e0
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (19241) imply:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | |   (19242)  all_53_3 = e0
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (19206), (19242) imply:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | |   (19243)  $false
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (19243) is inconsistent.
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | |   (19244)   ~ (all_55_13 = e3)
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | |   (19245)  all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (246), (19244) imply:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | |   (19246)   ~ (all_53_7 = e3)
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19245) gives:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | |   (19247)  all_55_13 = e2
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (19247) imply:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | |   (19248)  all_53_7 = e2
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14925), (19248) imply:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | |   (19249)  $false
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (19249) is inconsistent.
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | |   (19250)  all_55_13 = e1 | all_55_13 = e0
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19250) gives:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | |   (19251)  all_55_13 = e1
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (19251) imply:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | |   (19252)  all_53_7 = e1
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (136), (19252) imply:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | |   (19253)   ~ (all_53_4 = e1)
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (129), (19252) imply:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | |   (19254)   ~ (all_53_6 = e1)
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19225) gives:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | |   (19255)  all_55_9 = e2
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (19255) imply:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | |   (19256)  all_53_6 = e2
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (19256) implies:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | |   (19257)  all_53_6 = e2
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (137), (19257) imply:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | |   (19258)   ~ (all_53_4 = e2)
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | |   (19259)  all_55_1 = e3
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (19259) imply:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | |   (19260)  all_53_4 = e3
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (19260) implies:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | |   (19261)  all_53_4 = e3
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (19261) imply:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | |   (19262)   ~ (all_53_12 = e3)
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (19262) implies:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | |   (19263)   ~ (all_53_12 = e3)
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19264)  all_55_3 = e3
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (19263), (19264) are inconsistent by
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2169.
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19265)   ~ (all_55_3 = e3)
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19266)  all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19266) gives:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19267)  all_55_3 = e2
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (14927), (19267) are inconsistent by
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1612.
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19268)  all_55_3 = e1 | all_55_3 = e0
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19268) gives:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19269)  all_55_3 = e1
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (19269) imply:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19270)  all_53_12 = e1
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (19270) implies:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19271)  all_53_12 = e1
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (19271) imply:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19272)   ~ (all_53_8 = e1)
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (19263), (19271) imply:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19273)   ~ (e3 = e1)
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19274)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e1)
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19274) gives:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19275)  all_57_4 = e1 & op(e3, e1) = e1
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (19272), (19275), (function-axioms) are
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #116.
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19276)  all_57_5 = e1 & op(e2, e1) = e1
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19276) implies:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19277)  op(e2, e1) = e1
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (18716), (18948), (19214), (19216),
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19246), (19250), (19277), (function-axioms) are
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #127.
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19278)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e1) = e1)
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19278) gives:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19279)  all_57_8 = e1 & op(e1, e1) = e1
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19279) implies:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19280)  op(e1, e1) = e1
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (18716), (19280), (function-axioms) are
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #156.
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19281)  all_57_14 = e1 & op(e0, e1) = e1
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19281) implies:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19282)  all_57_14 = e1
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (159), (160), (18948), (19203), (19206),
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19282), (function-axioms) are inconsistent by
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #115.
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19283)  all_55_3 = e0
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (19207), (19283) are inconsistent by
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #885.
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | |   (19284)  all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (18946), (19253), (19258), (19284) are
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #592.
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | |   (19285)  all_55_9 = e1 | all_55_9 = e0
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (18947), (19254), (19285) are inconsistent
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1835.
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | |   (19286)  all_55_13 = e0
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (19286) imply:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | |   (19287)  all_53_7 = e0
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (18948), (19287) imply:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | |   (19288)  $false
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (19288) is inconsistent.
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | |   (19289)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 225.63/38.76  | | | | | | | | | | | | | | | | | | |              & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 225.63/38.76  | | | | | | | | | | | | | | | | | | |              & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 225.63/38.76  | | | | | | | | | | | | | | | | | | |                all_52_21) = e1 & op(all_52_23, all_52_23) =
% 225.63/38.76  | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 225.63/38.76  | | | | | | | | | | | | | | | | | | |              all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 225.63/38.76  | | | | | | | | | | | | | | | | | | |              = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 225.63/38.76  | | | | | | | | | | | | | | | | | | |              $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 225.63/38.76  | | | | | | | | | | | | | | | | | | |              & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 225.63/38.76  | | | | | | | | | | | | | | | | | | |              e0 & op(all_52_25, all_52_25) = e3 &
% 225.63/38.76  | | | | | | | | | | | | | | | | | | |              op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 225.63/38.76  | | | | | | | | | | | | | | | | | | |                all_52_29) = e1 & op(all_52_31, all_52_31) =
% 225.63/38.76  | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 225.63/38.76  | | | | | | | | | | | | | | | | | | |              all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 225.63/38.76  | | | | | | | | | | | | | | | | | | |              = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 225.63/38.76  | | | | | | | | | | | | | | | | | | |              $i(all_52_29) & $i(all_52_31))
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | BETA: splitting (19289) gives:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | |   (19290)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | |            all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | |            op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | |              all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | |            & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | |            & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | |            $i(all_52_23)
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | ALPHA: (19290) implies:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | |   (19291)  op(e1, e0) = all_52_23
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | |   (19292)  op(all_52_23, all_52_23) = e0
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (14935), (19199), (19291), (19292),
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | |            #51.
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | |   (19293)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | |            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | |              all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | |            & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | |            & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | |            & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | |            $i(all_52_31)
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | ALPHA: (19293) implies:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | |   (19294)  op(e0, e0) = all_52_31
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | |   (19295)  op(e0, e1) = all_52_29
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | |   (19296)  op(all_52_31, all_52_31) = e0
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | |   (19297)  op(all_52_29, all_52_29) = e1
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | |              all_52_29, e1, e0, simplifying with (19194),
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | |              (19295) gives:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | |   (19298)  all_52_29 = e0
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | REDUCE: (19297), (19298) imply:
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | |   (19299)  op(e0, e0) = e1
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (18716), (19294), (19296), (19299),
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | |            #161.
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.76  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.76  | | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | | End of split
% 225.63/38.76  | | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | | End of split
% 225.63/38.76  | | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | | End of split
% 225.63/38.76  | | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | | End of split
% 225.63/38.76  | | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | | End of split
% 225.63/38.76  | | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | | End of split
% 225.63/38.76  | | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | End of split
% 225.63/38.76  | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | Case 2:
% 225.63/38.76  | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | |   (19300)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 225.63/38.76  | | | | | | | | | | |              e0 & op(e0, e2) = e0)
% 225.63/38.76  | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | | REF_CLOSE: (159), (163), (18947), (18948), (19300),
% 225.63/38.76  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.76  | | | | | | | | | | |            #2024.
% 225.63/38.76  | | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | | End of split
% 225.63/38.76  | | | | | | | | | | 
% 225.63/38.76  | | | | | | | | | End of split
% 225.63/38.76  | | | | | | | | | 
% 225.63/38.76  | | | | | | | | Case 2:
% 225.63/38.76  | | | | | | | | | 
% 225.63/38.77  | | | | | | | | |   (19301)  all_10_2 = e1
% 225.63/38.77  | | | | | | | | |   (19302)  ( ~ (all_10_0 = e2) & op(all_10_1, e3) = all_10_0 &
% 225.63/38.77  | | | | | | | | |              op(e3, e1) = all_10_1 & $i(all_10_0) &
% 225.63/38.77  | | | | | | | | |              $i(all_10_1)) | ( ~ (all_10_1 = e0) & op(e3, e1)
% 225.63/38.77  | | | | | | | | |              = all_10_1 & $i(all_10_1))
% 225.63/38.77  | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | COMBINE_EQS: (331), (19301) imply:
% 225.63/38.77  | | | | | | | | |   (19303)  all_36_2 = e1
% 225.63/38.77  | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | REDUCE: (338), (19301) imply:
% 225.63/38.77  | | | | | | | | |   (19304)   ~ (all_53_1 = e1)
% 225.63/38.77  | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | REDUCE: (340), (19301) imply:
% 225.63/38.77  | | | | | | | | |   (19305)   ~ (all_53_2 = e1)
% 225.63/38.77  | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | REDUCE: (344), (19301) imply:
% 225.63/38.77  | | | | | | | | |   (19306)   ~ (all_53_4 = e1)
% 225.63/38.77  | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | REDUCE: (346), (19301) imply:
% 225.63/38.77  | | | | | | | | |   (19307)   ~ (all_53_8 = e1)
% 225.63/38.77  | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | REDUCE: (348), (19301) imply:
% 225.63/38.77  | | | | | | | | |   (19308)   ~ (all_53_12 = e1)
% 225.63/38.77  | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | BETA: splitting (233) gives:
% 225.63/38.77  | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | Case 1:
% 225.63/38.77  | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | |   (19309)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 225.63/38.77  | | | | | | | | | |              & op(e3, e2) = e1)
% 225.63/38.77  | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | BETA: splitting (19309) gives:
% 225.63/38.77  | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | Case 1:
% 225.63/38.77  | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | |   (19310)  all_57_0 = e1 & op(e3, e3) = e1
% 225.63/38.77  | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | ALPHA: (19310) implies:
% 225.63/38.77  | | | | | | | | | | |   (19311)  all_57_0 = e1
% 225.63/38.77  | | | | | | | | | | |   (19312)  op(e3, e3) = e1
% 225.63/38.77  | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | BETA: splitting (52) gives:
% 225.63/38.77  | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | Case 1:
% 225.63/38.77  | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | |   (19313)   ~ (all_14_2 = e0)
% 225.63/38.77  | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | REDUCE: (328), (19313) imply:
% 225.63/38.77  | | | | | | | | | | | |   (19314)   ~ (all_8_2 = e0)
% 225.63/38.77  | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | BETA: splitting (55) gives:
% 225.63/38.77  | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | Case 1:
% 225.63/38.77  | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | |   (19315)   ~ (all_16_2 = e1)
% 225.63/38.77  | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | REDUCE: (324), (19315) imply:
% 225.63/38.77  | | | | | | | | | | | | |   (19316)   ~ (all_8_2 = e1)
% 225.63/38.77  | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | REF_CLOSE: (42), (85), (107), (150), (160), (164), (168),
% 225.63/38.77  | | | | | | | | | | | | |            (169), (170), (171), (200), (201), (234), (235),
% 225.63/38.77  | | | | | | | | | | | | |            (266), (267), (349), (352), (14924), (14927),
% 225.63/38.77  | | | | | | | | | | | | |            (14935), (18717), (19302), (19303), (19304),
% 225.63/38.77  | | | | | | | | | | | | |            (19307), (19312), (19314), (19316),
% 225.63/38.77  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.77  | | | | | | | | | | | | |            #20.
% 225.63/38.77  | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | Case 2:
% 225.63/38.77  | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | |   (19317)  all_16_2 = e1
% 225.63/38.77  | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | COMBINE_EQS: (324), (19317) imply:
% 225.63/38.77  | | | | | | | | | | | | |   (19318)  all_8_2 = e1
% 225.63/38.77  | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | SIMP: (19318) implies:
% 225.63/38.77  | | | | | | | | | | | | |   (19319)  all_8_2 = e1
% 225.63/38.77  | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | REDUCE: (354), (19319) imply:
% 225.63/38.77  | | | | | | | | | | | | |   (19320)   ~ (all_53_6 = e1)
% 225.63/38.77  | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | REDUCE: (18717), (19319) imply:
% 225.63/38.77  | | | | | | | | | | | | |   (19321)   ~ (e3 = e1)
% 225.63/38.77  | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | REDUCE: (42), (19319) imply:
% 225.63/38.77  | | | | | | | | | | | | |   (19322)  op(e2, e2) = e1
% 225.63/38.77  | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | BETA: splitting (215) gives:
% 225.63/38.77  | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | Case 1:
% 225.63/38.77  | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | |   (19323)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 225.63/38.77  | | | | | | | | | | | | | |              & op(e1, e2) = e1)
% 225.63/38.77  | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | BETA: splitting (19323) gives:
% 225.63/38.77  | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | Case 1:
% 225.63/38.77  | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | |   (19324)  all_57_6 = e1 & op(e1, e3) = e1
% 225.63/38.77  | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | REF_CLOSE: (164), (19305), (19324), (function-axioms) are
% 225.63/38.77  | | | | | | | | | | | | | | |            inconsistent by sub-proof #316.
% 225.63/38.77  | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | Case 2:
% 225.63/38.77  | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | |   (19325)  all_57_7 = e1 & op(e1, e2) = e1
% 225.63/38.77  | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | REF_CLOSE: (163), (19320), (19325), (function-axioms) are
% 225.63/38.77  | | | | | | | | | | | | | | |            inconsistent by sub-proof #2265.
% 225.63/38.77  | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | End of split
% 225.63/38.77  | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | Case 2:
% 225.63/38.77  | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | |   (19326)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 225.63/38.77  | | | | | | | | | | | | | |              e1 & op(e1, e0) = e1)
% 225.63/38.77  | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | BETA: splitting (19326) gives:
% 225.63/38.77  | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | Case 1:
% 225.63/38.77  | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | |   (19327)  all_57_8 = e1 & op(e1, e1) = e1
% 225.63/38.77  | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | ALPHA: (19327) implies:
% 225.63/38.77  | | | | | | | | | | | | | | |   (19328)  op(e1, e1) = e1
% 225.63/38.77  | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | REF_CLOSE: (8), (18716), (19328), (function-axioms) are
% 225.63/38.77  | | | | | | | | | | | | | | |            inconsistent by sub-proof #156.
% 225.63/38.77  | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | Case 2:
% 225.63/38.77  | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | |   (19329)  all_57_11 = e1 & op(e1, e0) = e1
% 225.63/38.77  | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | ALPHA: (19329) implies:
% 225.63/38.77  | | | | | | | | | | | | | | |   (19330)  all_57_11 = e1
% 225.63/38.77  | | | | | | | | | | | | | | |   (19331)  op(e1, e0) = e1
% 225.63/38.77  | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_14,
% 225.63/38.77  | | | | | | | | | | | | | | |              e1, e0, e1, simplifying with (161), (19331) gives:
% 225.63/38.77  | | | | | | | | | | | | | | |   (19332)  all_53_14 = e1
% 225.63/38.77  | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | REDUCE: (14929), (19332) imply:
% 225.63/38.77  | | | | | | | | | | | | | | |   (19333)   ~ (e2 = e1)
% 225.63/38.77  | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 225.63/38.77  | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | Case 1:
% 225.63/38.77  | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | |   (19334)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 225.63/38.77  | | | | | | | | | | | | | | | |              all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 225.63/38.77  | | | | | | | | | | | | | | | |              op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 225.63/38.77  | | | | | | | | | | | | | | | |                all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 225.63/38.77  | | | | | | | | | | | | | | | |              op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 225.63/38.77  | | | | | | | | | | | | | | | |              op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 225.63/38.77  | | | | | | | | | | | | | | | |              $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 225.63/38.77  | | | | | | | | | | | | | | | |              $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 225.63/38.77  | | | | | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 225.63/38.77  | | | | | | | | | | | | | | | |                all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 225.63/38.77  | | | | | | | | | | | | | | | |              & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 225.63/38.77  | | | | | | | | | | | | | | | |                all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 225.63/38.77  | | | | | | | | | | | | | | | |              op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 225.63/38.77  | | | | | | | | | | | | | | | |              & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 225.63/38.77  | | | | | | | | | | | | | | | |              $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 225.63/38.77  | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | BETA: splitting (19334) gives:
% 225.63/38.77  | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.77  | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | |   (19335)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 225.63/38.77  | | | | | | | | | | | | | | | | |            all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 225.63/38.77  | | | | | | | | | | | | | | | | |            op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 225.63/38.77  | | | | | | | | | | | | | | | | |              all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 225.63/38.77  | | | | | | | | | | | | | | | | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 225.63/38.77  | | | | | | | | | | | | | | | | |            op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 225.63/38.77  | | | | | | | | | | | | | | | | |            $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 225.63/38.77  | | | | | | | | | | | | | | | | |            $i(all_52_7)
% 225.63/38.77  | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | ALPHA: (19335) implies:
% 225.63/38.77  | | | | | | | | | | | | | | | | |   (19336)  op(e3, e0) = all_52_7
% 225.63/38.77  | | | | | | | | | | | | | | | | |   (19337)  op(e3, e3) = all_52_1
% 225.63/38.77  | | | | | | | | | | | | | | | | |   (19338)  op(all_52_7, all_52_7) = e0
% 225.63/38.77  | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_12,
% 225.63/38.77  | | | | | | | | | | | | | | | | |              all_52_7, e0, e3, simplifying with (169), (19336)
% 225.63/38.77  | | | | | | | | | | | | | | | | |              gives:
% 225.63/38.77  | | | | | | | | | | | | | | | | |   (19339)  all_53_12 = all_52_7
% 225.63/38.77  | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_52_1,
% 225.63/38.77  | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (19312), (19337) gives:
% 225.63/38.77  | | | | | | | | | | | | | | | | |   (19340)  all_52_1 = e1
% 225.63/38.77  | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (19339) imply:
% 225.63/38.77  | | | | | | | | | | | | | | | | |   (19341)  all_55_3 = all_52_7
% 225.63/38.77  | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | REDUCE: (14927), (19339) imply:
% 225.63/38.77  | | | | | | | | | | | | | | | | |   (19342)   ~ (all_52_7 = e2)
% 225.63/38.77  | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | REDUCE: (19308), (19339) imply:
% 225.63/38.77  | | | | | | | | | | | | | | | | |   (19343)   ~ (all_52_7 = e1)
% 225.63/38.77  | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 225.63/38.77  | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | |   (19344)  all_55_3 = e3
% 225.63/38.77  | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (19312), (19336), (19337), (19338), (19341),
% 225.63/38.77  | | | | | | | | | | | | | | | | | |            (19344), (function-axioms) are inconsistent by
% 225.63/38.77  | | | | | | | | | | | | | | | | | |            sub-proof #122.
% 225.63/38.77  | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | |   (19345)   ~ (all_55_3 = e3)
% 225.63/38.77  | | | | | | | | | | | | | | | | | |   (19346)  all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 225.63/38.77  | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | REDUCE: (19341), (19345) imply:
% 225.63/38.77  | | | | | | | | | | | | | | | | | |   (19347)   ~ (all_52_7 = e3)
% 225.63/38.77  | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | BETA: splitting (19346) gives:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | |   (19348)  all_55_3 = e2
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19341), (19342), (19348) are inconsistent by
% 225.63/38.77  | | | | | | | | | | | | | | | | | | |            sub-proof #1450.
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | |   (19349)  all_55_3 = e1 | all_55_3 = e0
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | |   (19350)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | BETA: splitting (19350) gives:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | |   (19351)  all_57_9 = e3 & op(e3, e0) = e3
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | ALPHA: (19351) implies:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | |   (19352)  op(e3, e0) = e3
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (19312), (19336), (19337), (19338), (19352),
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | |            #123.
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | |   (19353)  all_57_10 = e3 & op(e2, e0) = e3
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | ALPHA: (19353) implies:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | |   (19354)  all_57_10 = e3
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | |   (19355)  all_57_15 = e0 & op(e0, e0) = e0
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19355) implies:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | |   (19356)  all_57_15 = e0
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (169), (212), (14927), (19330),
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | |            (19354), (19356), (function-axioms) are
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #19.
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | |   (19357)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19357) implies:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | |   (19358)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | |                e0) = e0)
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19358) gives:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | |   (19359)  all_57_9 = e0 & op(e3, e0) = e0
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19359) implies:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | |   (19360)  op(e3, e0) = e0
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (14935), (19336), (19338), (19360),
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | |            #47.
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | |   (19361)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 =
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19361) gives:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | |   (19362)  all_57_10 = e0 & op(e2, e0) = e0
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19362) implies:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | |   (19363)  all_57_10 = e0
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (19354), (19363) are inconsistent by
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1989.
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | |   (19364)  all_57_11 = e0 & op(e1, e0) = e0
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19364) implies:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | |   (19365)  all_57_11 = e0
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (19330), (19365) are inconsistent by
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1862.
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | |   (19366)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | BETA: splitting (19366) gives:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | |   (19367)  all_57_11 = e3 & op(e1, e0) = e3
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | ALPHA: (19367) implies:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | |   (19368)  op(e1, e0) = e3
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (18709), (19368), (function-axioms) are
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2330.
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | |   (19369)  all_57_15 = e3 & op(e0, e0) = e3
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | ALPHA: (19369) implies:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | |   (19370)  op(e0, e0) = e3
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19338), (19341), (19343), (19347), (19349),
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | |            (19370), (function-axioms) are inconsistent by
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | |            sub-proof #1448.
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.77  | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | End of split
% 225.63/38.77  | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.77  | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | |   (19371)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 225.63/38.77  | | | | | | | | | | | | | | | | |            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 225.63/38.77  | | | | | | | | | | | | | | | | |            op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 225.63/38.77  | | | | | | | | | | | | | | | | |              all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 225.63/38.77  | | | | | | | | | | | | | | | | |            & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 225.63/38.77  | | | | | | | | | | | | | | | | |            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 225.63/38.77  | | | | | | | | | | | | | | | | |            $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 225.63/38.77  | | | | | | | | | | | | | | | | |            $i(all_52_15)
% 225.63/38.77  | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | ALPHA: (19371) implies:
% 225.63/38.77  | | | | | | | | | | | | | | | | |   (19372)  op(e2, e2) = all_52_11
% 225.63/38.77  | | | | | | | | | | | | | | | | |   (19373)  op(all_52_11, all_52_11) = e2
% 225.63/38.77  | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (18716), (19322), (19372), (19373),
% 225.63/38.77  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.77  | | | | | | | | | | | | | | | | |            #155.
% 225.63/38.77  | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | End of split
% 225.63/38.77  | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | Case 2:
% 225.63/38.77  | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | |   (19374)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 225.63/38.77  | | | | | | | | | | | | | | | |              & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 225.63/38.77  | | | | | | | | | | | | | | | |              & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 225.63/38.77  | | | | | | | | | | | | | | | |                all_52_21) = e1 & op(all_52_23, all_52_23) =
% 225.63/38.77  | | | | | | | | | | | | | | | |              e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 225.63/38.77  | | | | | | | | | | | | | | | |              all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 225.63/38.77  | | | | | | | | | | | | | | | |              = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 225.63/38.77  | | | | | | | | | | | | | | | |              $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 225.63/38.77  | | | | | | | | | | | | | | | |              & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 225.63/38.77  | | | | | | | | | | | | | | | |              e0 & op(all_52_25, all_52_25) = e3 &
% 225.63/38.77  | | | | | | | | | | | | | | | |              op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 225.63/38.77  | | | | | | | | | | | | | | | |                all_52_29) = e1 & op(all_52_31, all_52_31) =
% 225.63/38.77  | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 225.63/38.77  | | | | | | | | | | | | | | | |              all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 225.63/38.77  | | | | | | | | | | | | | | | |              = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 225.63/38.77  | | | | | | | | | | | | | | | |              $i(all_52_29) & $i(all_52_31))
% 225.63/38.77  | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | BETA: splitting (19374) gives:
% 225.63/38.77  | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.77  | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | |   (19375)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 225.63/38.77  | | | | | | | | | | | | | | | | |            all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 225.63/38.77  | | | | | | | | | | | | | | | | |            op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 225.63/38.77  | | | | | | | | | | | | | | | | |              all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 225.63/38.77  | | | | | | | | | | | | | | | | |            & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 225.63/38.77  | | | | | | | | | | | | | | | | |            & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 225.63/38.77  | | | | | | | | | | | | | | | | |            & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 225.63/38.77  | | | | | | | | | | | | | | | | |            $i(all_52_23)
% 225.63/38.77  | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | ALPHA: (19375) implies:
% 225.63/38.77  | | | | | | | | | | | | | | | | |   (19376)  op(e1, e0) = all_52_23
% 225.63/38.77  | | | | | | | | | | | | | | | | |   (19377)  op(all_52_23, all_52_23) = e0
% 225.63/38.77  | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (18716), (19331), (19376), (19377),
% 225.63/38.77  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.77  | | | | | | | | | | | | | | | | |            #125.
% 225.63/38.77  | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.77  | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | |   (19378)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 225.63/38.77  | | | | | | | | | | | | | | | | |            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 225.63/38.77  | | | | | | | | | | | | | | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 225.63/38.77  | | | | | | | | | | | | | | | | |              all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 225.63/38.77  | | | | | | | | | | | | | | | | |            & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 225.63/38.77  | | | | | | | | | | | | | | | | |            & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 225.63/38.77  | | | | | | | | | | | | | | | | |            & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 225.63/38.77  | | | | | | | | | | | | | | | | |            $i(all_52_31)
% 225.63/38.77  | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (14935), (19322), (19378), (function-axioms)
% 225.63/38.77  | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #50.
% 225.63/38.77  | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | End of split
% 225.63/38.77  | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | End of split
% 225.63/38.77  | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | End of split
% 225.63/38.77  | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | End of split
% 225.63/38.77  | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | End of split
% 225.63/38.77  | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | Case 2:
% 225.63/38.77  | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | |   (19379)  all_14_2 = e0
% 225.63/38.77  | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | COMBINE_EQS: (328), (19379) imply:
% 225.63/38.77  | | | | | | | | | | | |   (19380)  all_8_2 = e0
% 225.63/38.77  | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | REDUCE: (349), (19380) imply:
% 225.63/38.77  | | | | | | | | | | | |   (19381)   ~ (all_53_1 = e0)
% 225.63/38.77  | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | REDUCE: (352), (19380) imply:
% 225.63/38.77  | | | | | | | | | | | |   (19382)   ~ (all_53_4 = e0)
% 225.63/38.77  | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | REDUCE: (354), (19380) imply:
% 225.63/38.77  | | | | | | | | | | | |   (19383)   ~ (all_53_6 = e0)
% 225.63/38.77  | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | REDUCE: (356), (19380) imply:
% 225.63/38.77  | | | | | | | | | | | |   (19384)   ~ (all_53_7 = e0)
% 225.63/38.77  | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | REDUCE: (358), (19380) imply:
% 225.63/38.77  | | | | | | | | | | | |   (19385)   ~ (all_53_9 = e0)
% 225.63/38.77  | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | REDUCE: (360), (19380) imply:
% 225.63/38.77  | | | | | | | | | | | |   (19386)   ~ (all_53_13 = e0)
% 225.63/38.77  | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | REDUCE: (18717), (19380) imply:
% 225.63/38.77  | | | | | | | | | | | |   (19387)   ~ (e3 = e0)
% 225.63/38.77  | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | BETA: splitting (226) gives:
% 225.63/38.77  | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | Case 1:
% 225.63/38.77  | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | |   (19388)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 225.63/38.77  | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 225.63/38.77  | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | BETA: splitting (19388) gives:
% 225.63/38.77  | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | Case 1:
% 225.63/38.77  | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | |   (19389)  all_57_1 = e0 & op(e3, e2) = e0
% 225.63/38.77  | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | ALPHA: (19389) implies:
% 225.63/38.77  | | | | | | | | | | | | | |   (19390)  op(e3, e2) = e0
% 225.63/38.77  | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | REF_CLOSE: (171), (19382), (19390), (function-axioms) are
% 225.63/38.77  | | | | | | | | | | | | | |            inconsistent by sub-proof #1941.
% 225.63/38.77  | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | Case 2:
% 225.63/38.77  | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | |   (19391)  all_57_3 = e0 & op(e2, e2) = e0
% 225.63/38.77  | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | ALPHA: (19391) implies:
% 225.63/38.77  | | | | | | | | | | | | | |   (19392)  all_57_3 = e0
% 225.63/38.77  | | | | | | | | | | | | | |   (19393)  op(e2, e2) = e0
% 225.63/38.77  | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 225.63/38.77  | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | Case 1:
% 225.63/38.77  | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | |   (19394)  all_55_14 = e3
% 225.63/38.77  | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | COMBINE_EQS: (245), (19394) imply:
% 225.63/38.77  | | | | | | | | | | | | | | |   (19395)  all_53_11 = e3
% 225.63/38.77  | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | REDUCE: (18708), (19395) imply:
% 225.63/38.77  | | | | | | | | | | | | | | |   (19396)  $false
% 225.63/38.77  | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | CLOSE: (19396) is inconsistent.
% 225.63/38.77  | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | Case 2:
% 225.63/38.77  | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | |   (19397)  all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 225.63/38.77  | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 225.63/38.77  | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | Case 1:
% 225.63/38.77  | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | |   (19398)  all_55_3 = e3
% 225.63/38.77  | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (19398) imply:
% 225.63/38.77  | | | | | | | | | | | | | | | |   (19399)  all_53_12 = e3
% 225.63/38.77  | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | SIMP: (19399) implies:
% 225.63/38.77  | | | | | | | | | | | | | | | |   (19400)  all_53_12 = e3
% 225.63/38.77  | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | REDUCE: (134), (19400) imply:
% 225.63/38.77  | | | | | | | | | | | | | | | |   (19401)   ~ (all_53_4 = e3)
% 225.63/38.77  | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | REDUCE: (114), (19400) imply:
% 225.63/38.77  | | | | | | | | | | | | | | | |   (19402)   ~ (all_53_13 = e3)
% 225.63/38.77  | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | SIMP: (19402) implies:
% 225.63/38.77  | | | | | | | | | | | | | | | |   (19403)   ~ (all_53_13 = e3)
% 225.63/38.77  | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | REDUCE: (113), (19400) imply:
% 225.63/38.77  | | | | | | | | | | | | | | | |   (19404)   ~ (all_53_14 = e3)
% 225.63/38.77  | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | REDUCE: (169), (19400) imply:
% 225.63/38.77  | | | | | | | | | | | | | | | |   (19405)  op(e3, e0) = e3
% 225.63/38.77  | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 225.63/38.77  | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.77  | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | |   (19406)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 225.63/38.77  | | | | | | | | | | | | | | | | |              & op(e2, e2) = e3)
% 225.63/38.77  | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (171), (18717), (19401), (19406),
% 225.63/38.77  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.77  | | | | | | | | | | | | | | | | |            #32.
% 225.63/38.77  | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.77  | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | |   (19407)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 225.63/38.77  | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 225.63/38.77  | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | BETA: splitting (19407) gives:
% 225.63/38.77  | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | |   (19408)  all_57_7 = e3 & op(e1, e2) = e3
% 225.63/38.77  | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (18705), (19408), (function-axioms) are
% 225.63/38.77  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #267.
% 225.63/38.77  | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | |   (19409)  all_57_13 = e3 & op(e0, e2) = e3
% 225.63/38.77  | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | ALPHA: (19409) implies:
% 225.63/38.77  | | | | | | | | | | | | | | | | | |   (19410)  all_57_13 = e3
% 225.63/38.77  | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | |   (19411)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 225.63/38.77  | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e3)
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | BETA: splitting (19411) gives:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | |   (19412)  all_57_2 = e3 & op(e2, e3) = e3
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | ALPHA: (19412) implies:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | |   (19413)  all_57_2 = e3
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | |   (19414)  all_57_15 = e0 & op(e0, e0) = e0
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | ALPHA: (19414) implies:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | |   (19415)  op(e0, e0) = e0
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (14935), (19415), (function-axioms) are
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #86.
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | |   (19416)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | ALPHA: (19416) implies:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | |   (19417)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | |                e0) = e0)
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19417) gives:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | |   (19418)  all_57_9 = e0 & op(e3, e0) = e0
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19418) implies:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | |   (19419)  op(e3, e0) = e0
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (19405), (19419), (function-axioms) are
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #313.
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | |   (19420)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 =
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19420) gives:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | |   (19421)  all_57_10 = e0 & op(e2, e0) = e0
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19421) implies:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | |   (19422)  op(e2, e0) = e0
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (19386), (19422), (function-axioms) are
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2470.
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | |   (19423)  all_57_11 = e0 & op(e1, e0) = e0
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19423) implies:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | |   (19424)  op(e1, e0) = e0
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | |   (19425)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2)
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19425) gives:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | |   (19426)  all_57_0 = e2 & op(e3, e3) = e2
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19426) implies:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | |   (19427)  op(e3, e3) = e2
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (19312), (19427), (function-axioms) are
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1950.
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | |   (19428)  all_57_2 = e2 & op(e2, e3) = e2
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (19413), (19428) are inconsistent by
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1925.
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | |   (19429)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e3) = e2)
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19429) gives:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | |   (19430)  all_57_6 = e2 & op(e1, e3) = e2
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19430) implies:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | |   (19431)  all_57_6 = e2
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | |   (19432)  all_55_1 = e3
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (19401), (19432) are inconsistent by
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2295.
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | |   (19433)   ~ (all_55_1 = e3)
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | |   (19434)  all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19434) gives:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19435)  all_55_1 = e2
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (19435) imply:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19436)  all_53_4 = e2
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (19436) implies:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19437)  all_53_4 = e2
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (19437) imply:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19438)   ~ (all_53_8 = e2)
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (19438) implies:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19439)   ~ (all_53_8 = e2)
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (19401), (19437) imply:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19440)   ~ (e3 = e2)
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19441)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19441) gives:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19442)  all_57_1 = e1 & op(e3, e2) = e1
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19442) implies:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19443)  op(e3, e2) = e1
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (171), (19306), (19443), (function-axioms) are
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #363.
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19444)  all_57_3 = e1 & op(e2, e2) = e1
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19444) implies:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19445)  op(e2, e2) = e1
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (19393), (19445), (function-axioms) are
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2352.
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19446)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19446) gives:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19447)  all_57_7 = e1 & op(e1, e2) = e1
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19447) implies:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19448)  all_57_7 = e1
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19449)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e0)
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19449) gives:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19450)  all_57_0 = e0 & op(e3, e3) = e0
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19450) implies:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19451)  all_57_0 = e0
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (19311), (19451) imply:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19452)  e1 = e0
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (19448), (19452) imply:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19453)  all_57_7 = e0
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (227), (228), (229),
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19392), (19393), (19410), (19453),
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2199.
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19454)  all_57_2 = e0 & op(e2, e3) = e0
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19454) implies:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19455)  all_57_2 = e0
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19392), (19455) are inconsistent by sub-proof
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2246.
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19456)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = e0)
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19456) gives:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19457)  all_57_6 = e0 & op(e1, e3) = e0
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (19431), (19457) are inconsistent by
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2386.
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19458)  all_57_12 = e0 & op(e0, e3) = e0
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19458) implies:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19459)  op(e0, e3) = e0
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19460)  all_55_2 = e3
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (18706), (19460) are inconsistent by
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2028.
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19461)  all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19461) gives:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19462)  all_55_2 = e2
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (19439), (19462) are inconsistent by
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2027.
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19463)  all_55_2 = e1 | all_55_2 = e0
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19464)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19464) gives:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19465)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_7)
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19465) implies:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19466)  op(e3, e0) = all_52_7
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19467)  op(e3, e3) = all_52_1
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19468)  op(all_52_7, all_52_7) = e0
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (159), (161), (165),
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (207), (208), (209), (213), (18709), (19312),
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19384), (19403), (19410), (19466), (19467),
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19468), (function-axioms) are inconsistent by
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #112.
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19469)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_15)
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19469) implies:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19470)  op(e2, e1) = all_52_13
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19471)  op(e2, e2) = all_52_11
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19472)  op(all_52_13, all_52_13) = e1
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19473)  op(all_52_11, all_52_11) = e2
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19463) gives:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19474)  all_55_2 = e1
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (19307), (19474) are inconsistent by
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2032.
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19475)  all_55_2 = e0
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (19475) imply:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19476)  all_53_8 = e0
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (19476) implies:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19477)  all_53_8 = e0
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (124), (19477) imply:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19478)   ~ (all_53_9 = e0)
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (122), (19477) imply:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19479)   ~ (all_53_11 = e0)
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (19479) implies:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19480)   ~ (all_53_11 = e0)
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19397) gives:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19481)  all_55_14 = e2
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (14926), (19481) are inconsistent by
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2293.
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19482)  all_55_14 = e1 | all_55_14 = e0
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19482) gives:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19483)  all_55_14 = e1
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (19483) imply:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19484)  all_53_11 = e1
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (19484) implies:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19485)  all_53_11 = e1
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (119), (19485) imply:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19486)   ~ (all_53_9 = e1)
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19487)  all_55_6 = e3
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (18707), (19487) are inconsistent by
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2498.
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19488)   ~ (all_55_6 = e3)
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19489)  all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19489) gives:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19490)  all_55_6 = e2
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (19490) imply:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19491)  all_53_9 = e2
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (19491) implies:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19492)  all_53_9 = e2
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (166), (19492) imply:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19493)  op(e2, e1) = e2
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_13, e1, e2, simplifying with (19470),
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (19493) gives:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19494)  all_52_13 = e2
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (19472), (19494) imply:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19495)  op(e2, e2) = e1
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (18716), (19471), (19473), (19495),
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #155.
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19496)  all_55_6 = e1 | all_55_6 = e0
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (19385), (19486), (19496) are inconsistent
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2161.
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19497)  all_55_14 = e0
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (19480), (19497) are inconsistent by
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2288.
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19498)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_52_21) = e1 & op(all_52_23, all_52_23) =
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(all_52_25, all_52_25) = e3 &
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_52_29) = e1 & op(all_52_31, all_52_31) =
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_29) & $i(all_52_31))
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19498) gives:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19499)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_23)
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19499) implies:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19500)  op(e1, e0) = all_52_23
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19501)  op(all_52_23, all_52_23) = e0
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (14935), (19424), (19500), (19501),
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #51.
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19502)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_31)
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19502) implies:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19503)  op(e0, e0) = all_52_31
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19504)  op(e0, e3) = all_52_25
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19505)  op(all_52_25, all_52_25) = e3
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (14935), (19459), (19503), (19504), (19505),
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #31.
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19506)  all_57_13 = e1 & op(e0, e2) = e1
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (19410), (19506) are inconsistent by
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2264.
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19507)  all_55_1 = e1 | all_55_1 = e0
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (19306), (19382), (19507) are inconsistent
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1730.
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | |   (19508)  all_57_12 = e2 & op(e0, e3) = e2
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19508) implies:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | |   (19509)  op(e0, e3) = e2
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (14924), (19509), (function-axioms) are
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1980.
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | |   (19510)  all_57_3 = e3 & op(e2, e2) = e3
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | ALPHA: (19510) implies:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | |   (19511)  op(e2, e2) = e3
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (18717), (19511), (function-axioms) are
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #140.
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | |   (19512)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 225.63/38.78  | | | | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (166), (18707), (19403), (19512),
% 225.63/38.78  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.78  | | | | | | | | | | | | | | | | | | |            #178.
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.78  | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | End of split
% 225.63/38.78  | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | End of split
% 225.63/38.78  | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | Case 2:
% 225.63/38.78  | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | |   (19513)   ~ (all_55_3 = e3)
% 225.63/38.78  | | | | | | | | | | | | | | | |   (19514)  all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 225.63/38.78  | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | REDUCE: (268), (19513) imply:
% 225.63/38.78  | | | | | | | | | | | | | | | |   (19515)   ~ (all_53_12 = e3)
% 225.63/38.78  | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | BETA: splitting (19514) gives:
% 225.63/38.78  | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.78  | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | |   (19516)  all_55_3 = e2
% 225.63/38.78  | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (14927), (19516) are inconsistent by
% 225.63/38.78  | | | | | | | | | | | | | | | | |            sub-proof #1612.
% 225.63/38.78  | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.78  | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | |   (19517)   ~ (all_55_3 = e2)
% 225.63/38.78  | | | | | | | | | | | | | | | | |   (19518)  all_55_3 = e1 | all_55_3 = e0
% 225.63/38.78  | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 225.63/38.78  | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | |   (19519)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 225.63/38.78  | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e3)
% 225.63/38.78  | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | BETA: splitting (19519) gives:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | |   (19520)  all_57_0 = e3 & op(e3, e3) = e3
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | ALPHA: (19520) implies:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | |   (19521)  op(e3, e3) = e3
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (19312), (19521), (function-axioms) are
% 225.63/38.78  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2495.
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | |   (19522)  all_57_1 = e3 & op(e3, e2) = e3
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | ALPHA: (19522) implies:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | |   (19523)  op(e3, e2) = e3
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | |   (19524)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | BETA: splitting (19524) gives:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | |   (19525)  all_57_9 = e3 & op(e3, e0) = e3
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | ALPHA: (19525) implies:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | |   (19526)  op(e3, e0) = e3
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (19515), (19526), (function-axioms) are
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2458.
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | |   (19527)  all_57_10 = e3 & op(e2, e0) = e3
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | ALPHA: (19527) implies:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | |   (19528)  all_57_10 = e3
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | |   (19529)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19529) gives:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | |   (19530)  all_57_9 = e1 & op(e3, e0) = e1
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (19308), (19530), (function-axioms) are
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2131.
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | |   (19531)  all_57_10 = e1 & op(e2, e0) = e1
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19531) implies:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | |   (19532)  all_57_10 = e1
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (19528), (19532) are inconsistent by
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2248.
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | |   (19533)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19533) gives:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | |   (19534)  all_57_11 = e1 & op(e1, e0) = e1
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19534) implies:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | |   (19535)  all_57_11 = e1
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | |   (19536)  op(e1, e0) = e1
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | |   (19537)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e0)
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19537) gives:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | |   (19538)  all_57_6 = e0 & op(e1, e3) = e0
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19538) implies:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | |   (19539)  all_57_6 = e0
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | |   (19540)  all_57_15 = e0 & op(e0, e0) = e0
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19540) implies:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | |   (19541)  all_57_15 = e0
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (169), (212), (14927), (19528),
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | |            (19535), (19541), (function-axioms) are
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #19.
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | |   (19542)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19542) implies:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | |   (19543)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e0)
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19543) gives:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19544)  all_57_9 = e0 & op(e3, e0) = e0
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19544) implies:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19545)  all_57_9 = e0
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19518) gives:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19546)  all_55_3 = e1
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (19308), (19546) are inconsistent by
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #324.
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19547)  all_55_3 = e0
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (19547) imply:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19548)  all_53_12 = e0
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (19548) implies:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19549)  all_53_12 = e0
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (19549) imply:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19550)   ~ (all_53_8 = e0)
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (114), (19549) imply:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19551)   ~ (all_53_13 = e0)
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14927), (19549) imply:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19552)   ~ (e2 = e0)
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (19308), (19549) imply:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19553)   ~ (e1 = e0)
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (169), (19549) imply:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19554)  op(e3, e0) = e0
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19555)  all_55_2 = e3
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (18706), (19555) are inconsistent by
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2028.
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19556)  all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19557)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (235), (237),
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19312), (19393), (19545), (19557),
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #294.
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19558)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19558) gives:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19559)  all_57_7 = e1 & op(e1, e2) = e1
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19559) implies:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19560)  all_57_7 = e1
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19561)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e2)
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (19539), (19560), (19561) are
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #93.
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19562)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e1, e0) = e2)
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19562) gives:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19563)  all_57_8 = e2 & op(e1, e1) = e2
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (18715), (19563) are inconsistent by
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #165.
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19564)  all_57_11 = e2 & op(e1, e0) = e2
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19564) implies:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19565)  all_57_11 = e2
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (19535), (19565) are inconsistent by
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2113.
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19566)  all_57_13 = e1 & op(e0, e2) = e1
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19566) implies:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19567)  all_57_13 = e1
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19556) gives:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19568)  all_55_2 = e2
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (19568) imply:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19569)  all_53_8 = e2
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (19569) implies:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19570)  all_53_8 = e2
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (19570) imply:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19571)   ~ (all_53_4 = e2)
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (124), (19570) imply:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19572)   ~ (all_53_9 = e2)
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (19572) implies:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19573)   ~ (all_53_9 = e2)
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19574)  all_55_1 = e3
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (19574) imply:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19575)  all_53_4 = e3
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (137), (19575) imply:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19576)   ~ (all_53_6 = e3)
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (136), (19575) imply:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19577)   ~ (all_53_7 = e3)
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (19577) implies:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19578)   ~ (all_53_7 = e3)
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19579)  all_55_13 = e3
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (19578), (19579) are inconsistent by
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2080.
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19580)   ~ (all_55_13 = e3)
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19581)  all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19581) gives:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19582)  all_55_13 = e2
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (14925), (19582) are inconsistent by
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2287.
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19583)   ~ (all_55_13 = e2)
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19584)  all_55_13 = e1 | all_55_13 = e0
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19585)  all_55_6 = e3
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (18707), (19585) are inconsistent by
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2498.
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19586)  all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19586) gives:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19587)  all_55_6 = e2
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (19573), (19587) are inconsistent by
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2398.
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19588)  all_55_6 = e1 | all_55_6 = e0
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19588) gives:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19589)  all_55_6 = e1
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (19589) imply:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19590)  all_53_9 = e1
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (19590) implies:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19591)  all_53_9 = e1
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (19591) imply:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19592)   ~ (all_53_13 = e1)
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (19592) implies:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19593)   ~ (all_53_13 = e1)
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (166), (19591) imply:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19594)  op(e2, e1) = e1
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19595)  all_55_7 = e3
% 225.63/38.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (19595) imply:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19596)  all_53_13 = e3
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (19596) implies:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19597)  all_53_13 = e3
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (19597) imply:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19598)   ~ (all_53_1 = e3)
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19599)  all_55_4 = e3
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (19598), (19599) are inconsistent by
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2170.
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19600)   ~ (all_55_4 = e3)
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19601)  all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19601) gives:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19602)  all_55_4 = e2
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (19602) imply:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19603)  all_53_1 = e2
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (19603) implies:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19604)  all_53_1 = e2
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (150), (19604) imply:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19605)   ~ (all_53_2 = e2)
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (19605) implies:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19606)   ~ (all_53_2 = e2)
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (19598), (19604) imply:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19607)   ~ (e3 = e2)
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19584) gives:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19608)  all_55_13 = e1
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (19608) imply:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19609)  all_53_7 = e1
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (19609) implies:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19610)  all_53_7 = e1
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (129), (19610) imply:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19611)   ~ (all_53_6 = e1)
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (19578), (19610) imply:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19612)   ~ (e3 = e1)
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14925), (19610) imply:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19613)   ~ (e2 = e1)
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19614)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19614) gives:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19615)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_7)
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19615) implies:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19616)  op(e3, e0) = all_52_7
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19617)  op(all_52_7, all_52_7) = e0
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (14935), (19554), (19616), (19617),
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #47.
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19618)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_15)
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (192), (246), (14925), (18716), (19384), (19578),
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19594), (19618), (function-axioms) are
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #126.
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19619)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_52_21) = e1 & op(all_52_23, all_52_23) =
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(all_52_25, all_52_25) = e3 &
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_52_29) = e1 & op(all_52_31, all_52_31) =
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_52_29) & $i(all_52_31))
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19619) gives:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19620)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_23)
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19620) implies:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19621)  op(e1, e0) = all_52_23
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19622)  op(all_52_23, all_52_23) = e0
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (18716), (19536), (19621), (19622),
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #125.
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19623)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_31)
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19623) implies:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19624)  op(e0, e1) = all_52_29
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19625)  op(all_52_29, all_52_29) = e1
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19626)  all_55_9 = e3
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (19626) imply:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19627)  all_53_6 = e3
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (18705), (19627) imply:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19628)  $false
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (19628) is inconsistent.
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19629)   ~ (all_55_9 = e3)
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19630)  all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19631)  all_55_8 = e3
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (18704), (19631) are inconsistent by
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2496.
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19632)   ~ (all_55_8 = e3)
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19633)  all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19634)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e0)
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19634) gives:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19635)  all_57_4 = e0 & op(e3, e1) = e0
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19635) implies:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19636)  op(e3, e1) = e0
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (19550), (19636), (function-axioms) are
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2267.
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19637)  all_57_5 = e0 & op(e2, e1) = e0
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19637) implies:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19638)  all_57_5 = e0
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (223), (224),
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (225), (19392), (19393), (19593), (19638),
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1689.
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19639)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19639) gives:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19640)  all_57_8 = e0 & op(e1, e1) = e0
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (18715), (19640) are inconsistent by
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #170.
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19641)  all_57_14 = e0 & op(e0, e1) = e0
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19641) implies:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19642)  op(e0, e1) = e0
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19633) gives:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19643)  all_55_8 = e2
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (19606), (19643) are inconsistent by
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2406.
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19644)  all_55_8 = e1 | all_55_8 = e0
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19644) gives:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19645)  all_55_8 = e1
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (19305), (19645) are inconsistent by
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2367.
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19646)  all_55_8 = e0
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (19646) imply:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19647)  all_53_2 = e0
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (19647) implies:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19648)  all_53_2 = e0
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (19648) imply:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19649)   ~ (all_53_3 = e0)
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (19649) implies:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19650)   ~ (all_53_3 = e0)
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (19648) imply:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19651)   ~ (all_53_6 = e0)
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19630) gives:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19652)  all_55_9 = e2
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (19652) imply:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19653)  all_53_6 = e2
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (19653) implies:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19654)  all_53_6 = e2
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_29, e1, e0, simplifying with (19624),
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (19642) gives:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19655)  all_52_29 = e0
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (19625), (19655) imply:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19656)  op(e0, e0) = e1
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (160), (207), (209),
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (210), (19567), (19650), (19656),
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1918.
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19657)  all_55_9 = e1 | all_55_9 = e0
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (256), (19383), (19611), (19657) are inconsistent
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1835.
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19658)  all_55_13 = e0
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (19384), (19658) are inconsistent by
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2261.
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19659)  all_55_4 = e1 | all_55_4 = e0
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (267), (19304), (19381), (19659) are inconsistent
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #773.
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19660)  all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (14928), (19386), (19593), (19660) are
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #321.
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19661)  all_55_6 = e0
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (19385), (19661) are inconsistent by
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2162.
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19662)  all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (19306), (19382), (19571), (19662) are
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #592.
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19663)  all_55_2 = e1 | all_55_2 = e0
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (19307), (19550), (19663) are inconsistent
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2030.
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19664)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 =
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19664) gives:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19665)  all_57_10 = e0 & op(e2, e0) = e0
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19665) implies:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19666)  op(e2, e0) = e0
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (19386), (19666), (function-axioms) are
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2470.
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19667)  all_57_11 = e0 & op(e1, e0) = e0
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19667) implies:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19668)  all_57_11 = e0
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (19535), (19668) are inconsistent by
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1862.
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | |   (19669)  all_57_7 = e0 & op(e1, e2) = e0
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19669) implies:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | |   (19670)  all_57_7 = e0
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | |   (19671)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (19393), (19523), (19671),
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | |            #1184.
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | |   (19672)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19672) gives:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19673)  all_57_7 = e2 & op(e1, e2) = e2
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (19670), (19673) are inconsistent by
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #364.
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19674)  all_57_13 = e2 & op(e0, e2) = e2
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19674) implies:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (19675)  all_57_13 = e2
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (227), (229), (19392),
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19393), (19670), (19675), (function-axioms) are
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2202.
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | |   (19676)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19676) gives:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | |   (19677)  all_57_8 = e0 & op(e1, e1) = e0
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (18715), (19677) are inconsistent by
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #170.
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | |   (19678)  all_57_11 = e0 & op(e1, e0) = e0
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19678) implies:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | |   (19679)  all_57_11 = e0
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (19535), (19679) are inconsistent by
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1862.
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | |   (19680)  all_57_15 = e1 & op(e0, e0) = e1
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (19680) implies:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | |   (19681)  op(e0, e0) = e1
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (14935), (19681), (function-axioms) are
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2177.
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | |   (19682)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (161), (14934), (18709), (19682),
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | |            #87.
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.79  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.79  | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.79  | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | |   (19683)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 225.63/38.79  | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e3)
% 225.63/38.79  | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (170), (18706), (19515), (19683),
% 225.63/38.79  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.79  | | | | | | | | | | | | | | | | | |            #109.
% 225.63/38.79  | | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | End of split
% 225.63/38.79  | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | End of split
% 225.63/38.79  | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | End of split
% 225.63/38.79  | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | End of split
% 225.63/38.79  | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | End of split
% 225.63/38.79  | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | Case 2:
% 225.63/38.79  | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | |   (19684)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 225.63/38.79  | | | | | | | | | | | | |              e0 & op(e0, e2) = e0)
% 225.63/38.79  | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | REF_CLOSE: (159), (163), (19383), (19384), (19684),
% 225.63/38.79  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.79  | | | | | | | | | | | | |            #2024.
% 225.63/38.79  | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | End of split
% 225.63/38.79  | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | End of split
% 225.63/38.79  | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | Case 2:
% 225.63/38.79  | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | |   (19685)  all_57_1 = e1 & op(e3, e2) = e1
% 225.63/38.79  | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | ALPHA: (19685) implies:
% 225.63/38.79  | | | | | | | | | | |   (19686)  op(e3, e2) = e1
% 225.63/38.79  | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | REF_CLOSE: (171), (19306), (19686), (function-axioms) are
% 225.63/38.79  | | | | | | | | | | |            inconsistent by sub-proof #363.
% 225.63/38.79  | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | End of split
% 225.63/38.79  | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | Case 2:
% 225.63/38.79  | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | |   (19687)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 225.63/38.79  | | | | | | | | | |              & op(e3, e0) = e1)
% 225.63/38.79  | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | BETA: splitting (19687) gives:
% 225.63/38.79  | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | Case 1:
% 225.63/38.79  | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | |   (19688)  all_57_4 = e1 & op(e3, e1) = e1
% 225.63/38.79  | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | REF_CLOSE: (170), (19307), (19688), (function-axioms) are
% 225.63/38.79  | | | | | | | | | | |            inconsistent by sub-proof #116.
% 225.63/38.79  | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | Case 2:
% 225.63/38.79  | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | |   (19689)  all_57_9 = e1 & op(e3, e0) = e1
% 225.63/38.79  | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | REF_CLOSE: (169), (19308), (19689), (function-axioms) are
% 225.63/38.79  | | | | | | | | | | |            inconsistent by sub-proof #2131.
% 225.63/38.79  | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | End of split
% 225.63/38.79  | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | End of split
% 225.63/38.79  | | | | | | | | | 
% 225.63/38.79  | | | | | | | | End of split
% 225.63/38.79  | | | | | | | | 
% 225.63/38.79  | | | | | | | Case 2:
% 225.63/38.79  | | | | | | | | 
% 225.63/38.79  | | | | | | | |   (19690)  all_8_2 = e3
% 225.63/38.79  | | | | | | | | 
% 225.63/38.79  | | | | | | | | REDUCE: (352), (19690) imply:
% 225.63/38.79  | | | | | | | |   (19691)   ~ (all_53_4 = e3)
% 225.63/38.79  | | | | | | | | 
% 225.63/38.79  | | | | | | | | REDUCE: (356), (19690) imply:
% 225.63/38.79  | | | | | | | |   (19692)   ~ (all_53_7 = e3)
% 225.63/38.79  | | | | | | | | 
% 225.63/38.79  | | | | | | | | REDUCE: (360), (19690) imply:
% 225.63/38.79  | | | | | | | |   (19693)   ~ (all_53_13 = e3)
% 225.63/38.79  | | | | | | | | 
% 225.63/38.79  | | | | | | | | BETA: splitting (229) gives:
% 225.63/38.79  | | | | | | | | 
% 225.63/38.79  | | | | | | | | Case 1:
% 225.63/38.79  | | | | | | | | | 
% 225.63/38.79  | | | | | | | | |   (19694)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 225.63/38.79  | | | | | | | | |              & op(e2, e2) = e3)
% 225.63/38.79  | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | BETA: splitting (19694) gives:
% 225.63/38.79  | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | Case 1:
% 225.63/38.79  | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | |   (19695)  all_57_1 = e3 & op(e3, e2) = e3
% 225.63/38.79  | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | REF_CLOSE: (171), (19691), (19695), (function-axioms) are
% 225.63/38.79  | | | | | | | | | |            inconsistent by sub-proof #2286.
% 225.63/38.79  | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | Case 2:
% 225.63/38.79  | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | |   (19696)  all_57_3 = e3 & op(e2, e2) = e3
% 225.63/38.79  | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | ALPHA: (19696) implies:
% 225.63/38.79  | | | | | | | | | |   (19697)  all_57_3 = e3
% 225.63/38.79  | | | | | | | | | |   (19698)  op(e2, e2) = e3
% 225.63/38.79  | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | BETA: splitting (210) gives:
% 225.63/38.79  | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | Case 1:
% 225.63/38.79  | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | |   (19699)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 225.63/38.79  | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 225.63/38.79  | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | BETA: splitting (19699) gives:
% 225.63/38.79  | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | Case 1:
% 225.63/38.79  | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | |   (19700)  all_57_12 = e3 & op(e0, e3) = e3
% 225.63/38.79  | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | ALPHA: (19700) implies:
% 225.63/38.79  | | | | | | | | | | | |   (19701)  all_57_12 = e3
% 225.63/38.79  | | | | | | | | | | | |   (19702)  op(e0, e3) = e3
% 225.63/38.79  | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | BETA: splitting (213) gives:
% 225.63/38.79  | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | Case 1:
% 225.63/38.79  | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | |   (19703)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 225.63/38.79  | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 225.63/38.79  | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | BETA: splitting (19703) gives:
% 225.63/38.79  | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | Case 1:
% 225.63/38.79  | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | |   (19704)  all_57_9 = e3 & op(e3, e0) = e3
% 225.63/38.79  | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | ALPHA: (19704) implies:
% 225.63/38.79  | | | | | | | | | | | | | |   (19705)  op(e3, e0) = e3
% 225.63/38.79  | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_3, e3,
% 225.63/38.79  | | | | | | | | | | | | | |              e3, e0, simplifying with (160), (19702) gives:
% 225.63/38.79  | | | | | | | | | | | | | |   (19706)  all_53_3 = e3
% 225.63/38.79  | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_12,
% 225.63/38.79  | | | | | | | | | | | | | |              e3, e0, e3, simplifying with (169), (19705) gives:
% 225.63/38.79  | | | | | | | | | | | | | |   (19707)  all_53_12 = e3
% 225.63/38.79  | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | REDUCE: (348), (19707) imply:
% 225.63/38.79  | | | | | | | | | | | | | |   (19708)   ~ (all_10_2 = e3)
% 225.63/38.79  | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | SIMP: (19708) implies:
% 225.63/38.79  | | | | | | | | | | | | | |   (19709)   ~ (all_10_2 = e3)
% 225.63/38.79  | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | BETA: splitting (46) gives:
% 225.63/38.79  | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | Case 1:
% 225.63/38.79  | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | |   (19710)   ~ (all_10_2 = e1)
% 225.63/38.79  | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 225.63/38.79  | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | Case 1:
% 225.63/38.79  | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | |   (19711)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 225.63/38.79  | | | | | | | | | | | | | | | |              all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 225.63/38.79  | | | | | | | | | | | | | | | |              op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 225.63/38.79  | | | | | | | | | | | | | | | |                all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 225.63/38.79  | | | | | | | | | | | | | | | |              op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 225.63/38.79  | | | | | | | | | | | | | | | |              op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 225.63/38.79  | | | | | | | | | | | | | | | |              $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 225.63/38.79  | | | | | | | | | | | | | | | |              $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 225.63/38.79  | | | | | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 225.63/38.79  | | | | | | | | | | | | | | | |                all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 225.63/38.79  | | | | | | | | | | | | | | | |              & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 225.63/38.79  | | | | | | | | | | | | | | | |                all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 225.63/38.79  | | | | | | | | | | | | | | | |              op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 225.63/38.79  | | | | | | | | | | | | | | | |              & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 225.63/38.79  | | | | | | | | | | | | | | | |              $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 225.63/38.79  | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | BETA: splitting (19711) gives:
% 225.63/38.79  | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.79  | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | |   (19712)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 225.63/38.79  | | | | | | | | | | | | | | | | |            all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 225.63/38.79  | | | | | | | | | | | | | | | | |            op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 225.63/38.79  | | | | | | | | | | | | | | | | |              all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 225.63/38.79  | | | | | | | | | | | | | | | | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 225.63/38.79  | | | | | | | | | | | | | | | | |            op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 225.63/38.79  | | | | | | | | | | | | | | | | |            $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 225.63/38.79  | | | | | | | | | | | | | | | | |            $i(all_52_7)
% 225.63/38.79  | | | | | | | | | | | | | | | | | 
% 225.63/38.79  | | | | | | | | | | | | | | | | | ALPHA: (19712) implies:
% 225.63/38.80  | | | | | | | | | | | | | | | | |   (19713)  op(e3, e0) = all_52_7
% 225.63/38.80  | | | | | | | | | | | | | | | | |   (19714)  op(e3, e3) = all_52_1
% 225.63/38.80  | | | | | | | | | | | | | | | | |   (19715)  op(all_52_7, all_52_7) = e0
% 225.63/38.80  | | | | | | | | | | | | | | | | |   (19716)  op(all_52_1, all_52_1) = e3
% 225.63/38.80  | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_52_7,
% 225.63/38.80  | | | | | | | | | | | | | | | | |              e0, e3, simplifying with (19705), (19713) gives:
% 225.63/38.80  | | | | | | | | | | | | | | | | |   (19717)  all_52_7 = e3
% 225.63/38.80  | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | | REDUCE: (19715), (19717) imply:
% 225.63/38.80  | | | | | | | | | | | | | | | | |   (19718)  op(e3, e3) = e0
% 225.63/38.80  | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (14935), (19714), (19716), (19718),
% 225.63/38.80  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.80  | | | | | | | | | | | | | | | | |            #53.
% 225.63/38.80  | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.80  | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | |   (19719)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 225.63/38.80  | | | | | | | | | | | | | | | | |            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 225.63/38.80  | | | | | | | | | | | | | | | | |            op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 225.63/38.80  | | | | | | | | | | | | | | | | |              all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 225.63/38.80  | | | | | | | | | | | | | | | | |            & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 225.63/38.80  | | | | | | | | | | | | | | | | |            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 225.63/38.80  | | | | | | | | | | | | | | | | |            $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 225.63/38.80  | | | | | | | | | | | | | | | | |            $i(all_52_15)
% 225.63/38.80  | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | | ALPHA: (19719) implies:
% 225.63/38.80  | | | | | | | | | | | | | | | | |   (19720)  op(e2, e0) = all_52_15
% 225.63/38.80  | | | | | | | | | | | | | | | | |   (19721)  op(e2, e1) = all_52_13
% 225.63/38.80  | | | | | | | | | | | | | | | | |   (19722)  op(e2, e2) = all_52_11
% 225.63/38.80  | | | | | | | | | | | | | | | | |   (19723)  op(all_52_15, all_52_15) = e0
% 225.63/38.80  | | | | | | | | | | | | | | | | |   (19724)  op(all_52_13, all_52_13) = e1
% 225.63/38.80  | | | | | | | | | | | | | | | | |   (19725)  op(all_52_11, all_52_11) = e2
% 225.63/38.80  | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_13,
% 225.63/38.80  | | | | | | | | | | | | | | | | |              all_52_15, e0, e2, simplifying with (165), (19720)
% 225.63/38.80  | | | | | | | | | | | | | | | | |              gives:
% 225.63/38.80  | | | | | | | | | | | | | | | | |   (19726)  all_53_13 = all_52_15
% 225.63/38.80  | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_53_9,
% 225.63/38.80  | | | | | | | | | | | | | | | | |              all_52_13, e1, e2, simplifying with (166), (19721)
% 225.63/38.80  | | | | | | | | | | | | | | | | |              gives:
% 225.63/38.80  | | | | | | | | | | | | | | | | |   (19727)  all_53_9 = all_52_13
% 225.63/38.80  | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3,
% 225.63/38.80  | | | | | | | | | | | | | | | | |              all_52_11, e2, e2, simplifying with (19698),
% 225.63/38.80  | | | | | | | | | | | | | | | | |              (19722) gives:
% 225.63/38.80  | | | | | | | | | | | | | | | | |   (19728)  all_52_11 = e3
% 225.63/38.80  | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | | REDUCE: (18707), (19727) imply:
% 225.63/38.80  | | | | | | | | | | | | | | | | |   (19729)   ~ (all_52_13 = e3)
% 225.63/38.80  | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | | REDUCE: (19725), (19728) imply:
% 225.63/38.80  | | | | | | | | | | | | | | | | |   (19730)  op(e3, e3) = e2
% 225.63/38.80  | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, e2,
% 225.63/38.80  | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (45), (19730) gives:
% 225.63/38.80  | | | | | | | | | | | | | | | | |   (19731)  all_10_2 = e2
% 225.63/38.80  | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | | REDUCE: (19709), (19731) imply:
% 225.63/38.80  | | | | | | | | | | | | | | | | |   (19732)   ~ (e3 = e2)
% 225.63/38.80  | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 225.63/38.80  | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.80  | | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | | |   (19733)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 225.63/38.80  | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 225.63/38.80  | | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (223), (224), (225),
% 225.63/38.80  | | | | | | | | | | | | | | | | | |            (230), (232), (19697), (19698), (19701), (19730),
% 225.63/38.80  | | | | | | | | | | | | | | | | | |            (19733), (function-axioms) are inconsistent by
% 225.63/38.80  | | | | | | | | | | | | | | | | | |            sub-proof #106.
% 225.63/38.80  | | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.80  | | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | | |   (19734)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 225.63/38.80  | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 225.63/38.80  | | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | | | BETA: splitting (19734) gives:
% 225.63/38.80  | | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.80  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | | | |   (19735)  all_57_5 = e2 & op(e2, e1) = e2
% 225.63/38.80  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | | | | ALPHA: (19735) implies:
% 225.63/38.80  | | | | | | | | | | | | | | | | | | |   (19736)  op(e2, e1) = e2
% 225.63/38.80  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 225.63/38.80  | | | | | | | | | | | | | | | | | | |              e2, e1, e2, simplifying with (19721), (19736)
% 225.63/38.80  | | | | | | | | | | | | | | | | | | |              gives:
% 225.63/38.80  | | | | | | | | | | | | | | | | | | |   (19737)  all_52_13 = e2
% 225.63/38.80  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | | | | REDUCE: (19724), (19737) imply:
% 225.63/38.80  | | | | | | | | | | | | | | | | | | |   (19738)  op(e2, e2) = e1
% 225.63/38.80  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (18716), (19722), (19725), (19738),
% 225.63/38.80  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.80  | | | | | | | | | | | | | | | | | | |            #155.
% 225.63/38.80  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.80  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | | | |   (19739)  all_57_10 = e2 & op(e2, e0) = e2
% 225.63/38.80  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | | | | ALPHA: (19739) implies:
% 225.63/38.80  | | | | | | | | | | | | | | | | | | |   (19740)  op(e2, e0) = e2
% 225.63/38.80  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (19698), (19720), (19722), (19723), (19740),
% 225.63/38.80  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.80  | | | | | | | | | | | | | | | | | | |            #248.
% 225.63/38.80  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.80  | | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | | End of split
% 225.63/38.80  | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | End of split
% 225.63/38.80  | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | Case 2:
% 225.63/38.80  | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | |   (19741)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 225.63/38.80  | | | | | | | | | | | | | | | |              & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 225.63/38.80  | | | | | | | | | | | | | | | |              & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 225.63/38.80  | | | | | | | | | | | | | | | |                all_52_21) = e1 & op(all_52_23, all_52_23) =
% 225.63/38.80  | | | | | | | | | | | | | | | |              e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 225.63/38.80  | | | | | | | | | | | | | | | |              all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 225.63/38.80  | | | | | | | | | | | | | | | |              = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 225.63/38.80  | | | | | | | | | | | | | | | |              $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 225.63/38.80  | | | | | | | | | | | | | | | |              & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 225.63/38.80  | | | | | | | | | | | | | | | |              e0 & op(all_52_25, all_52_25) = e3 &
% 225.63/38.80  | | | | | | | | | | | | | | | |              op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 225.63/38.80  | | | | | | | | | | | | | | | |                all_52_29) = e1 & op(all_52_31, all_52_31) =
% 225.63/38.80  | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 225.63/38.80  | | | | | | | | | | | | | | | |              all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 225.63/38.80  | | | | | | | | | | | | | | | |              = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 225.63/38.80  | | | | | | | | | | | | | | | |              $i(all_52_29) & $i(all_52_31))
% 225.63/38.80  | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | BETA: splitting (19741) gives:
% 225.63/38.80  | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.80  | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | |   (19742)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 225.63/38.80  | | | | | | | | | | | | | | | | |            all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 225.63/38.80  | | | | | | | | | | | | | | | | |            op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 225.63/38.80  | | | | | | | | | | | | | | | | |              all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 225.63/38.80  | | | | | | | | | | | | | | | | |            & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 225.63/38.80  | | | | | | | | | | | | | | | | |            & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 225.63/38.80  | | | | | | | | | | | | | | | | |            & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 225.63/38.80  | | | | | | | | | | | | | | | | |            $i(all_52_23)
% 225.63/38.80  | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | | ALPHA: (19742) implies:
% 225.63/38.80  | | | | | | | | | | | | | | | | |   (19743)  op(e1, e1) = all_52_21
% 225.63/38.80  | | | | | | | | | | | | | | | | |   (19744)  op(all_52_21, all_52_21) = e1
% 225.63/38.80  | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (18716), (19710), (19743), (19744),
% 225.63/38.80  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.80  | | | | | | | | | | | | | | | | |            #167.
% 225.63/38.80  | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.80  | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | |   (19745)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 225.63/38.80  | | | | | | | | | | | | | | | | |            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 225.63/38.80  | | | | | | | | | | | | | | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 225.63/38.80  | | | | | | | | | | | | | | | | |              all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 225.63/38.80  | | | | | | | | | | | | | | | | |            & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 225.63/38.80  | | | | | | | | | | | | | | | | |            & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 225.63/38.80  | | | | | | | | | | | | | | | | |            & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 225.63/38.80  | | | | | | | | | | | | | | | | |            $i(all_52_31)
% 225.63/38.80  | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | | ALPHA: (19745) implies:
% 225.63/38.80  | | | | | | | | | | | | | | | | |   (19746)  op(e0, e3) = all_52_25
% 225.63/38.80  | | | | | | | | | | | | | | | | |   (19747)  op(all_52_25, all_52_25) = e3
% 225.63/38.80  | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (19702), (19709), (19746), (19747),
% 225.63/38.80  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.80  | | | | | | | | | | | | | | | | |            #96.
% 225.63/38.80  | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | End of split
% 225.63/38.80  | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | End of split
% 225.63/38.80  | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | Case 2:
% 225.63/38.80  | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | |   (19748)  all_10_2 = e1
% 225.63/38.80  | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | REDUCE: (338), (19748) imply:
% 225.63/38.80  | | | | | | | | | | | | | | |   (19749)   ~ (all_53_1 = e1)
% 225.63/38.80  | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | REDUCE: (340), (19748) imply:
% 225.63/38.80  | | | | | | | | | | | | | | |   (19750)   ~ (all_53_2 = e1)
% 225.63/38.80  | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | REDUCE: (19709), (19748) imply:
% 225.63/38.80  | | | | | | | | | | | | | | |   (19751)   ~ (e3 = e1)
% 225.63/38.80  | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | REDUCE: (45), (19748) imply:
% 225.63/38.80  | | | | | | | | | | | | | | |   (19752)  op(e3, e3) = e1
% 225.63/38.80  | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 225.63/38.80  | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | Case 1:
% 225.63/38.80  | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | |   (19753)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 225.63/38.80  | | | | | | | | | | | | | | | |              all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 225.63/38.80  | | | | | | | | | | | | | | | |              op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 225.63/38.80  | | | | | | | | | | | | | | | |                all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 225.63/38.80  | | | | | | | | | | | | | | | |              op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 225.63/38.80  | | | | | | | | | | | | | | | |              op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 225.63/38.80  | | | | | | | | | | | | | | | |              $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 225.63/38.80  | | | | | | | | | | | | | | | |              $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 225.63/38.80  | | | | | | | | | | | | | | | |              & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 225.63/38.80  | | | | | | | | | | | | | | | |                all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 225.63/38.80  | | | | | | | | | | | | | | | |              & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 225.63/38.80  | | | | | | | | | | | | | | | |                all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 225.63/38.80  | | | | | | | | | | | | | | | |              op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 225.63/38.80  | | | | | | | | | | | | | | | |              & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 225.63/38.80  | | | | | | | | | | | | | | | |              $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 225.63/38.80  | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | BETA: splitting (19753) gives:
% 225.63/38.80  | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.80  | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | |   (19754)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 225.63/38.80  | | | | | | | | | | | | | | | | |            all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 225.63/38.80  | | | | | | | | | | | | | | | | |            op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 225.63/38.80  | | | | | | | | | | | | | | | | |              all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 225.63/38.80  | | | | | | | | | | | | | | | | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 225.63/38.80  | | | | | | | | | | | | | | | | |            op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 225.63/38.80  | | | | | | | | | | | | | | | | |            $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 225.63/38.80  | | | | | | | | | | | | | | | | |            $i(all_52_7)
% 225.63/38.80  | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | | ALPHA: (19754) implies:
% 225.63/38.80  | | | | | | | | | | | | | | | | |   (19755)  op(e3, e0) = all_52_7
% 225.63/38.80  | | | | | | | | | | | | | | | | |   (19756)  op(e3, e3) = all_52_1
% 225.63/38.80  | | | | | | | | | | | | | | | | |   (19757)  op(all_52_7, all_52_7) = e0
% 225.63/38.80  | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (19705), (19752), (19755), (19756), (19757),
% 225.63/38.80  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.80  | | | | | | | | | | | | | | | | |            #123.
% 225.63/38.80  | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.80  | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | |   (19758)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 225.63/38.80  | | | | | | | | | | | | | | | | |            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 225.63/38.80  | | | | | | | | | | | | | | | | |            op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 225.63/38.80  | | | | | | | | | | | | | | | | |              all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 225.63/38.80  | | | | | | | | | | | | | | | | |            & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 225.63/38.80  | | | | | | | | | | | | | | | | |            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 225.63/38.80  | | | | | | | | | | | | | | | | |            $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 225.63/38.80  | | | | | | | | | | | | | | | | |            $i(all_52_15)
% 225.63/38.80  | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | | ALPHA: (19758) implies:
% 225.63/38.80  | | | | | | | | | | | | | | | | |   (19759)  op(e2, e2) = all_52_11
% 225.63/38.80  | | | | | | | | | | | | | | | | |   (19760)  op(all_52_11, all_52_11) = e2
% 225.63/38.80  | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 225.63/38.80  | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.80  | | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | | |   (19761)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 225.63/38.80  | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e1)
% 225.63/38.80  | | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | | | BETA: splitting (19761) gives:
% 225.63/38.80  | | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.80  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3,
% 225.63/38.80  | | | | | | | | | | | | | | | | | | |              all_52_11, e2, e2, simplifying with (19698),
% 225.63/38.80  | | | | | | | | | | | | | | | | | | |              (19759) gives:
% 225.63/38.80  | | | | | | | | | | | | | | | | | | |   (19762)  all_52_11 = e3
% 225.63/38.80  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | | | | REDUCE: (19760), (19762) imply:
% 225.63/38.80  | | | | | | | | | | | | | | | | | | |   (19763)  op(e3, e3) = e2
% 225.63/38.80  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (164), (168), (232), (19701), (19749),
% 225.63/38.80  | | | | | | | | | | | | | | | | | | |            (19750), (19763), (function-axioms) are
% 225.63/38.80  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #238.
% 225.63/38.80  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.80  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | | | |   (19764)  all_57_2 = e1 & op(e2, e3) = e1
% 225.63/38.80  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (19749), (19764), (function-axioms) are
% 225.63/38.80  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2156.
% 225.63/38.80  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.80  | | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.80  | | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | | |   (19765)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 225.63/38.80  | | | | | | | | | | | | | | | | | |              e1 & op(e0, e3) = e1)
% 225.63/38.80  | | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | | | BETA: splitting (19765) gives:
% 225.63/38.80  | | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.80  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | | | |   (19766)  all_57_6 = e1 & op(e1, e3) = e1
% 225.63/38.80  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (19750), (19766), (function-axioms) are
% 225.63/38.80  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #316.
% 225.63/38.80  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.80  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | | | |   (19767)  all_57_12 = e1 & op(e0, e3) = e1
% 225.63/38.80  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (19701), (19767) are inconsistent by
% 225.63/38.80  | | | | | | | | | | | | | | | | | | |            sub-proof #2230.
% 225.63/38.80  | | | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | | | End of split
% 225.63/38.80  | | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | | End of split
% 225.63/38.80  | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | End of split
% 225.63/38.80  | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | Case 2:
% 225.63/38.80  | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | |   (19768)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 225.63/38.80  | | | | | | | | | | | | | | | |              & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 225.63/38.80  | | | | | | | | | | | | | | | |              & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 225.63/38.80  | | | | | | | | | | | | | | | |                all_52_21) = e1 & op(all_52_23, all_52_23) =
% 225.63/38.80  | | | | | | | | | | | | | | | |              e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 225.63/38.80  | | | | | | | | | | | | | | | |              all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 225.63/38.80  | | | | | | | | | | | | | | | |              = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 225.63/38.80  | | | | | | | | | | | | | | | |              $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 225.63/38.80  | | | | | | | | | | | | | | | |              & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 225.63/38.80  | | | | | | | | | | | | | | | |              e0 & op(all_52_25, all_52_25) = e3 &
% 225.63/38.80  | | | | | | | | | | | | | | | |              op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 225.63/38.80  | | | | | | | | | | | | | | | |                all_52_29) = e1 & op(all_52_31, all_52_31) =
% 225.63/38.80  | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 225.63/38.80  | | | | | | | | | | | | | | | |              all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 225.63/38.80  | | | | | | | | | | | | | | | |              = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 225.63/38.80  | | | | | | | | | | | | | | | |              $i(all_52_29) & $i(all_52_31))
% 225.63/38.80  | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | BETA: splitting (19768) gives:
% 225.63/38.80  | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | Case 1:
% 225.63/38.80  | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | |   (19769)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 225.63/38.80  | | | | | | | | | | | | | | | | |            all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 225.63/38.80  | | | | | | | | | | | | | | | | |            op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 225.63/38.80  | | | | | | | | | | | | | | | | |              all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 225.63/38.80  | | | | | | | | | | | | | | | | |            & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 225.63/38.80  | | | | | | | | | | | | | | | | |            & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 225.63/38.80  | | | | | | | | | | | | | | | | |            & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 225.63/38.80  | | | | | | | | | | | | | | | | |            $i(all_52_23)
% 225.63/38.80  | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | | ALPHA: (19769) implies:
% 225.63/38.80  | | | | | | | | | | | | | | | | |   (19770)  op(e1, e0) = all_52_23
% 225.63/38.80  | | | | | | | | | | | | | | | | |   (19771)  op(e1, e2) = all_52_19
% 225.63/38.80  | | | | | | | | | | | | | | | | |   (19772)  op(all_52_23, all_52_23) = e0
% 225.63/38.80  | | | | | | | | | | | | | | | | |   (19773)  op(all_52_19, all_52_19) = e2
% 225.63/38.80  | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (164), (215), (18716), (19750),
% 225.63/38.80  | | | | | | | | | | | | | | | | |            (19770), (19771), (19772), (19773),
% 225.63/38.80  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.80  | | | | | | | | | | | | | | | | |            #110.
% 225.63/38.80  | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | Case 2:
% 225.63/38.80  | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | |   (19774)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 225.63/38.80  | | | | | | | | | | | | | | | | |            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 225.63/38.80  | | | | | | | | | | | | | | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 225.63/38.80  | | | | | | | | | | | | | | | | |              all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 225.63/38.80  | | | | | | | | | | | | | | | | |            & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 225.63/38.80  | | | | | | | | | | | | | | | | |            & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 225.63/38.80  | | | | | | | | | | | | | | | | |            & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 225.63/38.80  | | | | | | | | | | | | | | | | |            $i(all_52_31)
% 225.63/38.80  | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | | ALPHA: (19774) implies:
% 225.63/38.80  | | | | | | | | | | | | | | | | |   (19775)  op(e0, e3) = all_52_25
% 225.63/38.80  | | | | | | | | | | | | | | | | |   (19776)  op(all_52_25, all_52_25) = e3
% 225.63/38.80  | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (19702), (19709), (19775), (19776),
% 225.63/38.80  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.80  | | | | | | | | | | | | | | | | |            #96.
% 225.63/38.80  | | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | | End of split
% 225.63/38.80  | | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | | End of split
% 225.63/38.80  | | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | End of split
% 225.63/38.80  | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | Case 2:
% 225.63/38.80  | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | |   (19777)  all_57_10 = e3 & op(e2, e0) = e3
% 225.63/38.80  | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | ALPHA: (19777) implies:
% 225.63/38.80  | | | | | | | | | | | | | |   (19778)  op(e2, e0) = e3
% 225.63/38.80  | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | REF_CLOSE: (165), (19693), (19778), (function-axioms) are
% 225.63/38.80  | | | | | | | | | | | | | |            inconsistent by sub-proof #2301.
% 225.63/38.80  | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | End of split
% 225.63/38.80  | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | Case 2:
% 225.63/38.80  | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | |   (19779)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 225.63/38.80  | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 225.63/38.80  | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | BETA: splitting (19779) gives:
% 225.63/38.80  | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | Case 1:
% 225.63/38.80  | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | |   (19780)  all_57_11 = e3 & op(e1, e0) = e3
% 225.63/38.80  | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | ALPHA: (19780) implies:
% 225.63/38.80  | | | | | | | | | | | | | |   (19781)  op(e1, e0) = e3
% 225.63/38.80  | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | REF_CLOSE: (161), (18709), (19781), (function-axioms) are
% 225.63/38.80  | | | | | | | | | | | | | |            inconsistent by sub-proof #2330.
% 225.63/38.80  | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | Case 2:
% 225.63/38.80  | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | |   (19782)  all_57_15 = e3 & op(e0, e0) = e3
% 225.63/38.80  | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | ALPHA: (19782) implies:
% 225.63/38.80  | | | | | | | | | | | | | |   (19783)  all_57_15 = e3
% 225.63/38.80  | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | | REF_CLOSE: (9), (14934), (19783) are inconsistent by
% 225.63/38.80  | | | | | | | | | | | | | |            sub-proof #2058.
% 225.63/38.80  | | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | | End of split
% 225.63/38.80  | | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | End of split
% 225.63/38.80  | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | Case 2:
% 225.63/38.80  | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | |   (19784)  all_57_13 = e3 & op(e0, e2) = e3
% 225.63/38.80  | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | | REF_CLOSE: (159), (19692), (19784), (function-axioms) are
% 225.63/38.80  | | | | | | | | | | | |            inconsistent by sub-proof #78.
% 225.63/38.80  | | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | End of split
% 225.63/38.80  | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | Case 2:
% 225.63/38.80  | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | |   (19785)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 225.63/38.80  | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 225.63/38.80  | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | | REF_CLOSE: (9), (158), (14934), (18708), (19785),
% 225.63/38.80  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 225.63/38.80  | | | | | | | | | | |            #55.
% 225.63/38.80  | | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | End of split
% 225.63/38.80  | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | End of split
% 225.63/38.80  | | | | | | | | | 
% 225.63/38.80  | | | | | | | | Case 2:
% 225.63/38.80  | | | | | | | | | 
% 225.63/38.80  | | | | | | | | |   (19786)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3
% 225.63/38.80  | | | | | | | | |              & op(e0, e2) = e3)
% 225.63/38.80  | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | BETA: splitting (19786) gives:
% 225.63/38.80  | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | Case 1:
% 225.63/38.80  | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | |   (19787)  all_57_7 = e3 & op(e1, e2) = e3
% 225.63/38.80  | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | REF_CLOSE: (163), (18705), (19787), (function-axioms) are
% 225.63/38.80  | | | | | | | | | |            inconsistent by sub-proof #267.
% 225.63/38.80  | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | Case 2:
% 225.63/38.80  | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | |   (19788)  all_57_13 = e3 & op(e0, e2) = e3
% 225.63/38.80  | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | | REF_CLOSE: (159), (19692), (19788), (function-axioms) are
% 225.63/38.80  | | | | | | | | | |            inconsistent by sub-proof #78.
% 225.63/38.80  | | | | | | | | | | 
% 225.63/38.80  | | | | | | | | | End of split
% 225.63/38.80  | | | | | | | | | 
% 225.63/38.80  | | | | | | | | End of split
% 225.63/38.80  | | | | | | | | 
% 225.63/38.80  | | | | | | | End of split
% 225.63/38.80  | | | | | | | 
% 225.63/38.80  | | | | | | Case 2:
% 225.63/38.80  | | | | | | | 
% 225.63/38.80  | | | | | | |   (19789)  all_57_11 = e3 & op(e1, e0) = e3
% 225.63/38.80  | | | | | | | 
% 225.63/38.80  | | | | | | | ALPHA: (19789) implies:
% 225.63/38.80  | | | | | | |   (19790)  op(e1, e0) = e3
% 225.63/38.80  | | | | | | | 
% 225.63/38.80  | | | | | | | REF_CLOSE: (161), (18709), (19790), (function-axioms) are
% 225.63/38.80  | | | | | | |            inconsistent by sub-proof #2330.
% 225.63/38.80  | | | | | | | 
% 225.63/38.80  | | | | | | End of split
% 225.63/38.80  | | | | | | 
% 225.63/38.80  | | | | | End of split
% 225.63/38.80  | | | | | 
% 225.63/38.80  | | | | End of split
% 225.63/38.80  | | | | 
% 225.63/38.80  | | | End of split
% 225.63/38.80  | | | 
% 225.63/38.80  | | End of split
% 225.63/38.80  | | 
% 225.63/38.80  | End of split
% 225.63/38.80  | 
% 225.63/38.80  End of proof
% 225.63/38.80  
% 225.63/38.80  Sub-proof #1 shows that the following formulas are inconsistent:
% 225.63/38.80  ----------------------------------------------------------------
% 225.63/38.80    (1)   ~ (e3 = e1)
% 225.63/38.80    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 225.63/38.80           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 225.63/38.80    (3)  all_57_7 = e2
% 225.63/38.80    (4)  op(e2, e2) = e0
% 225.63/38.80    (5)  all_55_13 = e1 | all_55_13 = e0
% 225.63/38.80    (6)  op(e3, e2) = all_53_4
% 225.63/38.80    (7)  all_55_13 = all_52_27
% 225.63/38.80    (8)   ~ (e1 = e0)
% 225.63/38.80    (9)  all_57_13 = e3
% 225.63/38.80    (10)   ~ (all_52_27 = e0)
% 225.63/38.80    (11)   ~ (all_53_4 = all_52_27)
% 225.63/38.80    (12)   ~ (e2 = e1)
% 225.63/38.80    (13)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 225.63/38.80          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 225.63/38.80  
% 225.63/38.80  Begin of proof
% 225.63/38.80  | 
% 225.63/38.80  | BETA: splitting (13) gives:
% 225.63/38.80  | 
% 225.63/38.80  | Case 1:
% 225.63/38.80  | | 
% 225.63/38.80  | |   (14)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) =
% 225.63/38.80  | |           e1)
% 225.63/38.80  | | 
% 225.63/38.80  | | REF_CLOSE: (2), (4), (5), (6), (7), (8), (10), (11), (14) are inconsistent
% 225.63/38.80  | |            by sub-proof #2.
% 225.63/38.80  | | 
% 225.63/38.80  | Case 2:
% 225.63/38.80  | | 
% 225.63/38.80  | |   (15)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 225.63/38.80  | |           e1)
% 225.63/38.80  | | 
% 225.63/38.80  | | BETA: splitting (15) gives:
% 225.63/38.80  | | 
% 225.63/38.80  | | Case 1:
% 225.63/38.80  | | | 
% 225.63/38.80  | | |   (16)  all_57_7 = e1 & op(e1, e2) = e1
% 225.63/38.80  | | | 
% 225.63/38.80  | | | REF_CLOSE: (3), (12), (16) are inconsistent by sub-proof #2190.
% 225.63/38.80  | | | 
% 225.63/38.80  | | Case 2:
% 225.63/38.80  | | | 
% 225.63/38.80  | | |   (17)  all_57_13 = e1 & op(e0, e2) = e1
% 225.63/38.80  | | | 
% 225.63/38.80  | | | ALPHA: (17) implies:
% 225.63/38.80  | | |   (18)  all_57_13 = e1
% 225.63/38.80  | | | 
% 225.63/38.80  | | | REF_CLOSE: (1), (9), (18) are inconsistent by sub-proof #2268.
% 225.63/38.80  | | | 
% 225.63/38.80  | | End of split
% 225.63/38.80  | | 
% 225.63/38.80  | End of split
% 225.63/38.80  | 
% 225.63/38.80  End of proof
% 225.63/38.80  
% 225.63/38.80  Sub-proof #2 shows that the following formulas are inconsistent:
% 225.63/38.80  ----------------------------------------------------------------
% 225.63/38.80    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 225.63/38.80           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 225.63/38.81    (2)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1)
% 225.63/38.81    (3)  op(e2, e2) = e0
% 225.63/38.81    (4)  all_55_13 = e1 | all_55_13 = e0
% 225.63/38.81    (5)  op(e3, e2) = all_53_4
% 225.63/38.81    (6)  all_55_13 = all_52_27
% 225.63/38.81    (7)   ~ (e1 = e0)
% 225.63/38.81    (8)   ~ (all_52_27 = e0)
% 225.63/38.81    (9)   ~ (all_53_4 = all_52_27)
% 225.63/38.81  
% 225.63/38.81  Begin of proof
% 225.63/38.81  | 
% 225.63/38.81  | BETA: splitting (2) gives:
% 225.63/38.81  | 
% 225.63/38.81  | Case 1:
% 225.63/38.81  | | 
% 225.63/38.81  | |   (10)  all_57_1 = e1 & op(e3, e2) = e1
% 225.63/38.81  | | 
% 225.63/38.81  | | ALPHA: (10) implies:
% 225.63/38.81  | |   (11)  op(e3, e2) = e1
% 225.63/38.81  | | 
% 225.63/38.81  | | BETA: splitting (4) gives:
% 225.63/38.81  | | 
% 225.63/38.81  | | Case 1:
% 225.63/38.81  | | | 
% 225.63/38.81  | | |   (12)  all_55_13 = e1
% 225.63/38.81  | | | 
% 225.63/38.81  | | | COMBINE_EQS: (6), (12) imply:
% 225.63/38.81  | | |   (13)  all_52_27 = e1
% 225.63/38.81  | | | 
% 225.63/38.81  | | | SIMP: (13) implies:
% 225.63/38.81  | | |   (14)  all_52_27 = e1
% 225.63/38.81  | | | 
% 225.63/38.81  | | | REDUCE: (9), (14) imply:
% 225.63/38.81  | | |   (15)   ~ (all_53_4 = e1)
% 225.63/38.81  | | | 
% 225.63/38.81  | | | REF_CLOSE: (1), (5), (11), (15) are inconsistent by sub-proof #363.
% 225.63/38.81  | | | 
% 225.63/38.81  | | Case 2:
% 225.63/38.81  | | | 
% 225.63/38.81  | | |   (16)  all_55_13 = e0
% 225.63/38.81  | | | 
% 225.63/38.81  | | | REF_CLOSE: (6), (8), (16) are inconsistent by sub-proof #1639.
% 225.63/38.81  | | | 
% 225.63/38.81  | | End of split
% 225.63/38.81  | | 
% 225.63/38.81  | Case 2:
% 225.63/38.81  | | 
% 225.63/38.81  | |   (17)  all_57_3 = e1 & op(e2, e2) = e1
% 225.63/38.81  | | 
% 225.63/38.81  | | ALPHA: (17) implies:
% 225.63/38.81  | |   (18)  op(e2, e2) = e1
% 225.63/38.81  | | 
% 225.63/38.81  | | REF_CLOSE: (1), (3), (7), (18) are inconsistent by sub-proof #2352.
% 225.63/38.81  | | 
% 225.63/38.81  | End of split
% 225.63/38.81  | 
% 225.63/38.81  End of proof
% 225.63/38.81  
% 225.63/38.81  Sub-proof #3 shows that the following formulas are inconsistent:
% 225.63/38.81  ----------------------------------------------------------------
% 225.63/38.81    (1)   ~ (all_52_7 = e3)
% 225.63/38.81    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 225.63/38.81           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 225.63/38.81    (3)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 225.63/38.81    (4)  op(all_52_7, all_52_7) = e0
% 225.63/38.81    (5)  all_55_3 = all_52_7
% 225.63/38.81    (6)  op(e0, e2) = all_4_1
% 225.63/38.81    (7)  ( ~ (all_4_0 = e3) & op(all_4_1, e0) = all_4_0 & op(e0, e2) = all_4_1 &
% 225.63/38.81           $i(all_4_0) & $i(all_4_1)) | ( ~ (all_4_1 = e1) & op(e0, e2) = all_4_1
% 225.63/38.81           & $i(all_4_1))
% 225.63/38.81    (8)  op(e0, e2) = e3
% 225.63/38.81    (9)  ( ~ (all_32_0 = e1) & op(all_32_1, e0) = all_32_0 & op(e0, e2) = all_32_1
% 225.63/38.81           & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 = e3) & op(e0, e2) =
% 225.63/38.81           all_32_1 & $i(all_32_1))
% 225.63/38.81    (10)  op(e0, e0) = e2
% 225.63/38.81    (11)  op(e3, e0) = all_52_7
% 225.63/38.81    (12)   ~ (all_52_7 = e2)
% 225.63/38.81  
% 225.63/38.81  Begin of proof
% 225.63/38.81  | 
% 225.63/38.81  | GROUND_INST: instantiating (2) with e3, all_4_1, e2, e0, simplifying with (6),
% 225.63/38.81  |              (8) gives:
% 225.63/38.81  |   (13)  all_4_1 = e3
% 225.63/38.81  | 
% 225.63/38.81  | BETA: splitting (9) gives:
% 225.63/38.81  | 
% 225.63/38.81  | Case 1:
% 225.63/38.81  | | 
% 225.63/38.81  | |   (14)   ~ (all_32_0 = e1) & op(all_32_1, e0) = all_32_0 & op(e0, e2) =
% 225.63/38.81  | |         all_32_1 & $i(all_32_0) & $i(all_32_1)
% 225.63/38.81  | | 
% 225.63/38.81  | | ALPHA: (14) implies:
% 225.63/38.81  | |   (15)   ~ (all_32_0 = e1)
% 225.63/38.81  | |   (16)  op(e0, e2) = all_32_1
% 225.63/38.81  | |   (17)  op(all_32_1, e0) = all_32_0
% 225.63/38.81  | | 
% 225.63/38.81  | | GROUND_INST: instantiating (2) with e3, all_32_1, e2, e0, simplifying with
% 225.63/38.81  | |              (8), (16) gives:
% 225.63/38.81  | |   (18)  all_32_1 = e3
% 225.63/38.81  | | 
% 225.63/38.81  | | REDUCE: (17), (18) imply:
% 225.63/38.81  | |   (19)  op(e3, e0) = all_32_0
% 225.63/38.81  | | 
% 225.63/38.81  | | GROUND_INST: instantiating (2) with all_52_7, all_32_0, e0, e3, simplifying
% 225.63/38.81  | |              with (11), (19) gives:
% 225.63/38.81  | |   (20)  all_52_7 = all_32_0
% 225.63/38.81  | | 
% 225.63/38.81  | | COMBINE_EQS: (5), (20) imply:
% 225.63/38.81  | |   (21)  all_55_3 = all_32_0
% 225.63/38.81  | | 
% 225.63/38.81  | | REDUCE: (1), (20) imply:
% 225.63/38.81  | |   (22)   ~ (all_32_0 = e3)
% 225.63/38.81  | | 
% 225.63/38.81  | | REDUCE: (12), (20) imply:
% 225.63/38.81  | |   (23)   ~ (all_32_0 = e2)
% 225.63/38.81  | | 
% 225.63/38.81  | | BETA: splitting (3) gives:
% 225.63/38.81  | | 
% 225.63/38.81  | | Case 1:
% 225.63/38.81  | | | 
% 225.63/38.81  | | |   (24)  all_55_3 = e3
% 225.63/38.81  | | | 
% 225.63/38.81  | | | COMBINE_EQS: (21), (24) imply:
% 225.63/38.81  | | |   (25)  all_32_0 = e3
% 225.63/38.81  | | | 
% 225.63/38.81  | | | SIMP: (25) implies:
% 225.63/38.81  | | |   (26)  all_32_0 = e3
% 225.63/38.81  | | | 
% 225.63/38.81  | | | REDUCE: (22), (26) imply:
% 225.63/38.81  | | |   (27)  $false
% 225.63/38.81  | | | 
% 225.63/38.81  | | | CLOSE: (27) is inconsistent.
% 225.63/38.81  | | | 
% 225.63/38.81  | | Case 2:
% 225.63/38.81  | | | 
% 225.63/38.81  | | |   (28)  all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 225.63/38.81  | | | 
% 225.63/38.81  | | | BETA: splitting (28) gives:
% 225.63/38.81  | | | 
% 225.63/38.81  | | | Case 1:
% 225.63/38.81  | | | | 
% 225.63/38.81  | | | |   (29)  all_55_3 = e2
% 225.63/38.81  | | | | 
% 225.63/38.81  | | | | REF_CLOSE: (21), (23), (29) are inconsistent by sub-proof #57.
% 225.63/38.81  | | | | 
% 225.63/38.81  | | | Case 2:
% 225.63/38.81  | | | | 
% 225.63/38.81  | | | |   (30)   ~ (all_55_3 = e2)
% 225.63/38.81  | | | |   (31)  all_55_3 = e1 | all_55_3 = e0
% 225.63/38.81  | | | | 
% 225.63/38.81  | | | | BETA: splitting (31) gives:
% 225.63/38.81  | | | | 
% 225.63/38.81  | | | | Case 1:
% 225.63/38.81  | | | | | 
% 225.63/38.81  | | | | |   (32)  all_55_3 = e1
% 225.63/38.81  | | | | | 
% 225.63/38.81  | | | | | REF_CLOSE: (15), (21), (32) are inconsistent by sub-proof #56.
% 225.63/38.81  | | | | | 
% 225.63/38.81  | | | | Case 2:
% 225.63/38.81  | | | | | 
% 225.63/38.81  | | | | |   (33)  all_55_3 = e0
% 225.63/38.81  | | | | | 
% 225.63/38.81  | | | | | COMBINE_EQS: (21), (33) imply:
% 225.63/38.81  | | | | |   (34)  all_32_0 = e0
% 225.63/38.81  | | | | | 
% 225.63/38.81  | | | | | SIMP: (34) implies:
% 225.63/38.81  | | | | |   (35)  all_32_0 = e0
% 225.63/38.81  | | | | | 
% 225.63/38.81  | | | | | REDUCE: (23), (35) imply:
% 225.63/38.81  | | | | |   (36)   ~ (e2 = e0)
% 225.63/38.81  | | | | | 
% 225.63/38.81  | | | | | SIMP: (36) implies:
% 225.63/38.81  | | | | |   (37)   ~ (e2 = e0)
% 225.63/38.81  | | | | | 
% 225.63/38.81  | | | | | REDUCE: (19), (35) imply:
% 225.63/38.81  | | | | |   (38)  op(e3, e0) = e0
% 225.63/38.81  | | | | | 
% 225.63/38.81  | | | | | REF_CLOSE: (2), (4), (10), (11), (37), (38) are inconsistent by
% 225.63/38.81  | | | | |            sub-proof #47.
% 225.63/38.81  | | | | | 
% 225.63/38.81  | | | | End of split
% 225.63/38.81  | | | | 
% 225.63/38.81  | | | End of split
% 225.63/38.81  | | | 
% 225.63/38.81  | | End of split
% 225.63/38.81  | | 
% 225.63/38.81  | Case 2:
% 225.63/38.81  | | 
% 225.63/38.81  | |   (39)   ~ (all_32_1 = e3) & op(e0, e2) = all_32_1 & $i(all_32_1)
% 225.63/38.81  | | 
% 225.63/38.81  | | ALPHA: (39) implies:
% 225.63/38.81  | |   (40)   ~ (all_32_1 = e3)
% 225.63/38.81  | |   (41)  op(e0, e2) = all_32_1
% 225.63/38.81  | | 
% 225.63/38.81  | | BETA: splitting (7) gives:
% 225.63/38.81  | | 
% 225.63/38.81  | | Case 1:
% 225.63/38.81  | | | 
% 225.63/38.81  | | |   (42)   ~ (all_4_0 = e3) & op(all_4_1, e0) = all_4_0 & op(e0, e2) =
% 225.63/38.81  | | |         all_4_1 & $i(all_4_0) & $i(all_4_1)
% 225.63/38.81  | | | 
% 225.63/38.81  | | | REF_CLOSE: (2), (6), (8), (40), (41) are inconsistent by sub-proof #58.
% 225.63/38.81  | | | 
% 225.63/38.81  | | Case 2:
% 225.63/38.81  | | | 
% 225.63/38.81  | | |   (43)   ~ (all_4_1 = e1) & op(e0, e2) = all_4_1 & $i(all_4_1)
% 225.63/38.81  | | | 
% 225.63/38.81  | | | REF_CLOSE: (2), (6), (8), (40), (41) are inconsistent by sub-proof #58.
% 225.63/38.81  | | | 
% 225.63/38.81  | | End of split
% 225.63/38.81  | | 
% 225.63/38.81  | End of split
% 225.63/38.81  | 
% 225.63/38.81  End of proof
% 225.63/38.81  
% 225.63/38.81  Sub-proof #4 shows that the following formulas are inconsistent:
% 225.63/38.81  ----------------------------------------------------------------
% 225.63/38.81    (1)  op(e1, e3) = all_46_1
% 225.63/38.81    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 225.63/38.81           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 225.63/38.81    (3)  op(e1, e3) = e2
% 225.63/38.81    (4)   ~ (all_6_1 = e2)
% 225.63/38.81    (5)  op(e1, e3) = all_6_1
% 225.63/38.81  
% 225.63/38.81  Begin of proof
% 225.63/38.81  | 
% 225.63/38.81  | GROUND_INST: instantiating (2) with all_6_1, all_46_1, e3, e1, simplifying
% 225.63/38.81  |              with (1), (5) gives:
% 225.63/38.81  |   (6)  all_46_1 = all_6_1
% 225.63/38.81  | 
% 225.63/38.81  | GROUND_INST: instantiating (2) with e2, all_46_1, e3, e1, simplifying with
% 225.63/38.81  |              (1), (3) gives:
% 225.63/38.81  |   (7)  all_46_1 = e2
% 225.63/38.81  | 
% 225.63/38.81  | COMBINE_EQS: (6), (7) imply:
% 225.63/38.81  |   (8)  all_6_1 = e2
% 225.63/38.81  | 
% 225.63/38.81  | REDUCE: (4), (8) imply:
% 225.63/38.81  |   (9)  $false
% 225.63/38.81  | 
% 225.63/38.81  | CLOSE: (9) is inconsistent.
% 225.63/38.81  | 
% 225.63/38.81  End of proof
% 225.63/38.81  
% 225.63/38.81  Sub-proof #5 shows that the following formulas are inconsistent:
% 225.63/38.81  ----------------------------------------------------------------
% 225.63/38.81    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 225.63/38.81           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 225.63/38.81    (2)   ~ (all_4_0 = e2)
% 225.63/38.81    (3)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 225.63/38.81    (4)  op(e1, e0) = all_4_0
% 225.63/38.81    (5)  op(e1, e0) = all_52_23
% 225.63/38.81    (6)  op(all_52_23, all_52_23) = e0
% 225.63/38.81    (7)  all_55_11 = all_4_0
% 225.63/38.81    (8)   ~ (all_4_0 = e1)
% 225.63/38.81    (9)  op(e0, e0) = e2
% 225.63/38.81    (10)   ~ (all_4_0 = e3)
% 225.63/38.81  
% 225.63/38.81  Begin of proof
% 225.63/38.81  | 
% 225.63/38.81  | BETA: splitting (3) gives:
% 225.63/38.81  | 
% 225.63/38.81  | Case 1:
% 225.63/38.81  | | 
% 225.63/38.81  | |   (11)  all_55_11 = e3
% 225.63/38.81  | | 
% 225.63/38.81  | | REF_CLOSE: (7), (10), (11) are inconsistent by sub-proof #74.
% 225.63/38.81  | | 
% 225.63/38.81  | Case 2:
% 225.63/38.81  | | 
% 225.63/38.81  | |   (12)  all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 225.63/38.81  | | 
% 225.63/38.81  | | BETA: splitting (12) gives:
% 225.63/38.81  | | 
% 225.63/38.81  | | Case 1:
% 225.63/38.81  | | | 
% 225.63/38.81  | | |   (13)  all_55_11 = e2
% 225.63/38.81  | | | 
% 225.63/38.81  | | | COMBINE_EQS: (7), (13) imply:
% 225.63/38.81  | | |   (14)  all_4_0 = e2
% 225.63/38.81  | | | 
% 225.63/38.81  | | | SIMP: (14) implies:
% 225.63/38.81  | | |   (15)  all_4_0 = e2
% 225.63/38.81  | | | 
% 225.63/38.81  | | | REDUCE: (2), (15) imply:
% 225.63/38.81  | | |   (16)  $false
% 225.63/38.81  | | | 
% 225.63/38.81  | | | CLOSE: (16) is inconsistent.
% 225.63/38.81  | | | 
% 225.63/38.81  | | Case 2:
% 225.63/38.81  | | | 
% 225.63/38.81  | | |   (17)   ~ (all_55_11 = e2)
% 225.63/38.81  | | |   (18)  all_55_11 = e1 | all_55_11 = e0
% 225.63/38.81  | | | 
% 225.63/38.81  | | | BETA: splitting (18) gives:
% 225.63/38.81  | | | 
% 225.63/38.81  | | | Case 1:
% 225.63/38.81  | | | | 
% 225.63/38.81  | | | |   (19)  all_55_11 = e1
% 225.63/38.81  | | | | 
% 225.63/38.81  | | | | REF_CLOSE: (7), (8), (19) are inconsistent by sub-proof #73.
% 225.63/38.81  | | | | 
% 225.63/38.81  | | | Case 2:
% 225.63/38.81  | | | | 
% 225.63/38.81  | | | |   (20)  all_55_11 = e0
% 225.63/38.81  | | | | 
% 225.63/38.81  | | | | COMBINE_EQS: (7), (20) imply:
% 225.63/38.81  | | | |   (21)  all_4_0 = e0
% 225.63/38.81  | | | | 
% 225.63/38.81  | | | | SIMP: (21) implies:
% 225.63/38.81  | | | |   (22)  all_4_0 = e0
% 225.63/38.81  | | | | 
% 225.63/38.81  | | | | REDUCE: (2), (22) imply:
% 225.63/38.81  | | | |   (23)   ~ (e2 = e0)
% 225.63/38.81  | | | | 
% 225.63/38.81  | | | | SIMP: (23) implies:
% 225.63/38.81  | | | |   (24)   ~ (e2 = e0)
% 225.63/38.81  | | | | 
% 225.63/38.81  | | | | REDUCE: (4), (22) imply:
% 225.63/38.81  | | | |   (25)  op(e1, e0) = e0
% 225.63/38.81  | | | | 
% 225.63/38.81  | | | | REF_CLOSE: (1), (5), (6), (9), (24), (25) are inconsistent by sub-proof
% 225.63/38.81  | | | |            #51.
% 225.63/38.81  | | | | 
% 225.63/38.81  | | | End of split
% 225.63/38.81  | | | 
% 225.63/38.81  | | End of split
% 225.63/38.81  | | 
% 225.63/38.81  | End of split
% 225.63/38.81  | 
% 225.63/38.81  End of proof
% 225.63/38.81  
% 225.63/38.81  Sub-proof #6 shows that the following formulas are inconsistent:
% 225.63/38.81  ----------------------------------------------------------------
% 225.63/38.81    (1)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 225.63/38.81    (2)   ~ (e3 = e1)
% 225.63/38.81    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 225.63/38.81           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 225.63/38.81    (4)   ~ (e1 = e0)
% 225.63/38.81    (5)  op(e1, e1) = e0
% 225.63/38.81    (6)  all_57_11 = e3
% 225.63/38.81  
% 225.63/38.81  Begin of proof
% 225.63/38.81  | 
% 225.63/38.81  | BETA: splitting (1) gives:
% 225.63/38.81  | 
% 225.63/38.81  | Case 1:
% 225.63/38.81  | | 
% 225.63/38.81  | |   (7)  all_57_8 = e1 & op(e1, e1) = e1
% 225.63/38.81  | | 
% 225.63/38.81  | | ALPHA: (7) implies:
% 225.63/38.81  | |   (8)  op(e1, e1) = e1
% 225.63/38.81  | | 
% 225.63/38.81  | | REF_CLOSE: (3), (4), (5), (8) are inconsistent by sub-proof #2427.
% 225.63/38.81  | | 
% 225.63/38.81  | Case 2:
% 225.63/38.81  | | 
% 225.63/38.81  | |   (9)  all_57_11 = e1 & op(e1, e0) = e1
% 225.63/38.81  | | 
% 225.63/38.81  | | REF_CLOSE: (2), (6), (9) are inconsistent by sub-proof #2143.
% 225.63/38.81  | | 
% 225.63/38.81  | End of split
% 225.63/38.81  | 
% 225.63/38.81  End of proof
% 225.63/38.81  
% 225.63/38.81  Sub-proof #7 shows that the following formulas are inconsistent:
% 225.63/38.81  ----------------------------------------------------------------
% 225.63/38.81    (1)  op(e3, e1) = all_52_5
% 225.63/38.81    (2)   ~ (e3 = e1)
% 225.63/38.81    (3)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 225.63/38.81         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 225.63/38.81    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 225.63/38.81           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 225.63/38.81    (5)  op(all_52_5, all_52_5) = e1
% 225.63/38.81    (6)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 225.63/38.81         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 225.63/38.81    (7)   ~ (all_6_2 = e3)
% 225.63/38.81    (8)  op(e1, e1) = all_6_2
% 225.63/38.81    (9)  op(all_52_7, all_52_7) = e0
% 225.63/38.81    (10)  op(e3, e2) = all_52_3
% 225.63/38.81    (11)  all_57_7 = e2
% 225.63/38.81    (12)  op(all_52_3, all_52_3) = e2
% 225.63/38.81    (13)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 225.63/38.81          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 225.63/38.81    (14)   ~ (e3 = e2)
% 225.63/38.81    (15)  op(e1, e0) = all_53_14
% 225.63/38.81    (16)   ~ (e3 = e0)
% 225.63/38.81    (17)  all_57_4 = e0 & op(e3, e1) = e0
% 225.63/38.81    (18)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 225.63/38.81          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 225.63/38.81    (19)   ~ (all_52_3 = e3)
% 225.63/38.81    (20)  op(e3, e2) = all_53_4
% 225.63/38.81    (21)   ~ (e2 = e0)
% 225.63/38.81    (22)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 225.63/38.81          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 225.63/38.81    (23)   ~ (all_53_9 = e3)
% 225.63/38.81    (24)   ~ (e1 = e0)
% 225.63/38.81    (25)  all_57_5 = e2
% 225.63/38.81    (26)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 225.63/38.81          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 225.63/38.81    (27)   ~ (all_53_14 = e0)
% 225.63/38.81    (28)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 225.63/38.81              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 225.63/38.81                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 225.63/38.81                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 225.63/38.81    (29)  op(e2, e2) = e3
% 225.63/38.81    (30)   ~ (all_53_6 = e3)
% 225.63/38.81    (31)   ~ (e2 = e1)
% 225.63/38.81    (32)  op(e0, e0) = e2
% 225.63/38.81    (33)  op(e2, e1) = all_53_9
% 225.63/38.81    (34)  op(e1, e2) = all_53_6
% 225.63/38.81    (35)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 225.63/38.81          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 225.63/38.81    (36)  op(e3, e0) = all_52_7
% 225.63/38.81    (37)   ~ (all_53_4 = e3)
% 225.63/38.81    (38)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 225.63/38.81          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 225.63/38.81  
% 225.63/38.81  Begin of proof
% 225.63/38.81  | 
% 225.63/38.81  | ALPHA: (17) implies:
% 225.63/38.81  |   (39)  all_57_4 = e0
% 225.63/38.81  |   (40)  op(e3, e1) = e0
% 225.63/38.81  | 
% 225.63/38.81  | BETA: splitting (22) gives:
% 225.63/38.81  | 
% 225.63/38.81  | Case 1:
% 225.63/38.81  | | 
% 225.63/38.81  | |   (41)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) =
% 225.63/38.81  | |           e3)
% 225.63/38.81  | | 
% 225.63/38.81  | | REF_CLOSE: (1), (2), (4), (5), (9), (10), (12), (13), (14), (16), (19),
% 225.63/38.81  | |            (20), (29), (36), (37), (41) are inconsistent by sub-proof #10.
% 225.63/38.81  | | 
% 225.63/38.81  | Case 2:
% 225.63/38.81  | | 
% 225.63/38.81  | |   (42)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) =
% 225.63/38.81  | |           e3)
% 225.63/38.81  | | 
% 225.63/38.81  | | BETA: splitting (42) gives:
% 225.63/38.81  | | 
% 225.63/38.81  | | Case 1:
% 225.63/38.81  | | | 
% 225.63/38.81  | | |   (43)  all_57_4 = e3 & op(e3, e1) = e3
% 225.63/38.81  | | | 
% 225.63/38.81  | | | ALPHA: (43) implies:
% 225.63/38.81  | | |   (44)  all_57_4 = e3
% 225.63/38.81  | | | 
% 225.63/38.81  | | | REF_CLOSE: (16), (39), (44) are inconsistent by sub-proof #2372.
% 225.63/38.81  | | | 
% 225.63/38.81  | | Case 2:
% 225.63/38.81  | | | 
% 225.63/38.81  | | |   (45)  all_57_9 = e3 & op(e3, e0) = e3
% 225.63/38.81  | | | 
% 225.63/38.81  | | | ALPHA: (45) implies:
% 225.63/38.81  | | |   (46)  all_57_9 = e3
% 225.63/38.81  | | |   (47)  op(e3, e0) = e3
% 225.63/38.81  | | | 
% 225.63/38.81  | | | BETA: splitting (28) gives:
% 225.63/38.81  | | | 
% 225.63/38.81  | | | Case 1:
% 225.63/38.81  | | | | 
% 225.63/38.81  | | | |   (48)  all_57_15 = e0 & op(e0, e0) = e0
% 225.63/38.81  | | | | 
% 225.63/38.81  | | | | ALPHA: (48) implies:
% 225.63/38.81  | | | |   (49)  op(e0, e0) = e0
% 225.63/38.81  | | | | 
% 225.63/38.81  | | | | REF_CLOSE: (1), (4), (5), (24), (40), (49) are inconsistent by sub-proof
% 225.63/38.81  | | | |            #2167.
% 225.63/38.81  | | | | 
% 225.63/38.81  | | | Case 2:
% 225.63/38.81  | | | | 
% 225.63/38.81  | | | |   (50)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2,
% 225.63/38.81  | | | |               e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) &
% 225.63/38.81  | | | |         ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0,
% 225.63/38.81  | | | |               e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 225.63/38.81  | | | | 
% 225.63/38.81  | | | | ALPHA: (50) implies:
% 225.63/38.81  | | | |   (51)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0)
% 225.63/38.81  | | | |           = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 225.63/38.81  | | | | 
% 225.63/38.81  | | | | BETA: splitting (51) gives:
% 225.63/38.81  | | | | 
% 225.63/38.81  | | | | Case 1:
% 225.63/38.81  | | | | | 
% 225.63/38.81  | | | | |   (52)  all_57_9 = e0 & op(e3, e0) = e0
% 225.63/38.81  | | | | | 
% 225.63/38.81  | | | | | ALPHA: (52) implies:
% 225.63/38.81  | | | | |   (53)  op(e3, e0) = e0
% 225.63/38.81  | | | | | 
% 225.63/38.81  | | | | | REF_CLOSE: (4), (16), (47), (53) are inconsistent by sub-proof #313.
% 225.63/38.81  | | | | | 
% 225.63/38.81  | | | | Case 2:
% 225.63/38.81  | | | | | 
% 225.63/38.81  | | | | |   (54)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 225.63/38.81  | | | | |             e0) = e0)
% 225.63/38.81  | | | | | 
% 225.63/38.81  | | | | | BETA: splitting (54) gives:
% 225.63/38.81  | | | | | 
% 225.63/38.81  | | | | | Case 1:
% 225.63/38.81  | | | | | | 
% 225.63/38.81  | | | | | |   (55)  all_57_10 = e0 & op(e2, e0) = e0
% 225.63/38.81  | | | | | | 
% 225.63/38.81  | | | | | | ALPHA: (55) implies:
% 225.63/38.81  | | | | | |   (56)  all_57_10 = e0
% 225.63/38.81  | | | | | | 
% 225.63/38.81  | | | | | | BETA: splitting (35) gives:
% 225.63/38.81  | | | | | | 
% 225.63/38.81  | | | | | | Case 1:
% 225.63/38.81  | | | | | | | 
% 225.63/38.81  | | | | | | |   (57)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 &
% 225.63/38.81  | | | | | | |           op(e2, e0) = e1)
% 225.63/38.81  | | | | | | | 
% 225.63/38.81  | | | | | | | BETA: splitting (57) gives:
% 225.63/38.81  | | | | | | | 
% 225.63/38.81  | | | | | | | Case 1:
% 225.63/38.81  | | | | | | | | 
% 225.63/38.81  | | | | | | | |   (58)  all_57_9 = e1 & op(e3, e0) = e1
% 225.63/38.81  | | | | | | | | 
% 225.63/38.81  | | | | | | | | ALPHA: (58) implies:
% 225.63/38.82  | | | | | | | |   (59)  all_57_9 = e1
% 225.63/38.82  | | | | | | | | 
% 225.63/38.82  | | | | | | | | REF_CLOSE: (2), (46), (59) are inconsistent by sub-proof #1673.
% 225.63/38.82  | | | | | | | | 
% 225.63/38.82  | | | | | | | Case 2:
% 225.63/38.82  | | | | | | | | 
% 225.63/38.82  | | | | | | | |   (60)  all_57_10 = e1 & op(e2, e0) = e1
% 225.63/38.82  | | | | | | | | 
% 225.63/38.82  | | | | | | | | ALPHA: (60) implies:
% 225.63/38.82  | | | | | | | |   (61)  all_57_10 = e1
% 225.63/38.82  | | | | | | | | 
% 225.63/38.82  | | | | | | | | REF_CLOSE: (24), (56), (61) are inconsistent by sub-proof #1531.
% 225.63/38.82  | | | | | | | | 
% 225.63/38.82  | | | | | | | End of split
% 225.63/38.82  | | | | | | | 
% 225.63/38.82  | | | | | | Case 2:
% 225.63/38.82  | | | | | | | 
% 225.63/38.82  | | | | | | |   (62)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 &
% 225.63/38.82  | | | | | | |           op(e0, e0) = e1)
% 225.63/38.82  | | | | | | | 
% 225.63/38.82  | | | | | | | BETA: splitting (62) gives:
% 225.63/38.82  | | | | | | | 
% 225.63/38.82  | | | | | | | Case 1:
% 225.63/38.82  | | | | | | | | 
% 225.63/38.82  | | | | | | | |   (63)  all_57_11 = e1 & op(e1, e0) = e1
% 225.63/38.82  | | | | | | | | 
% 225.63/38.82  | | | | | | | | ALPHA: (63) implies:
% 225.63/38.82  | | | | | | | |   (64)  all_57_11 = e1
% 225.63/38.82  | | | | | | | | 
% 225.63/38.82  | | | | | | | | BETA: splitting (26) gives:
% 225.63/38.82  | | | | | | | | 
% 225.63/38.82  | | | | | | | | Case 1:
% 225.63/38.82  | | | | | | | | | 
% 225.63/38.82  | | | | | | | | |   (65)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 &
% 225.63/38.82  | | | | | | | | |           op(e2, e1) = e3)
% 225.63/38.82  | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | BETA: splitting (65) gives:
% 225.63/38.82  | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | Case 1:
% 225.63/38.82  | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | |   (66)  all_57_4 = e3 & op(e3, e1) = e3
% 225.63/38.82  | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | ALPHA: (66) implies:
% 225.63/38.82  | | | | | | | | | |   (67)  all_57_4 = e3
% 225.63/38.82  | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | REF_CLOSE: (16), (39), (67) are inconsistent by sub-proof
% 225.63/38.82  | | | | | | | | | |            #2372.
% 225.63/38.82  | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | Case 2:
% 225.63/38.82  | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | |   (68)  all_57_5 = e3 & op(e2, e1) = e3
% 225.63/38.82  | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | REF_CLOSE: (4), (23), (33), (68) are inconsistent by
% 225.63/38.82  | | | | | | | | | |            sub-proof #270.
% 225.63/38.82  | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | End of split
% 225.63/38.82  | | | | | | | | | 
% 225.63/38.82  | | | | | | | | Case 2:
% 225.63/38.82  | | | | | | | | | 
% 225.63/38.82  | | | | | | | | |   (69)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 &
% 225.63/38.82  | | | | | | | | |           op(e0, e1) = e3)
% 225.63/38.82  | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | BETA: splitting (69) gives:
% 225.63/38.82  | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | Case 1:
% 225.63/38.82  | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | |   (70)  all_57_8 = e3 & op(e1, e1) = e3
% 225.63/38.82  | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | ALPHA: (70) implies:
% 225.63/38.82  | | | | | | | | | |   (71)  op(e1, e1) = e3
% 225.63/38.82  | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | REF_CLOSE: (4), (7), (8), (71) are inconsistent by sub-proof
% 225.63/38.82  | | | | | | | | | |            #2468.
% 225.63/38.82  | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | Case 2:
% 225.63/38.82  | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | |   (72)  all_57_14 = e3 & op(e0, e1) = e3
% 225.63/38.82  | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | ALPHA: (72) implies:
% 225.63/38.82  | | | | | | | | | |   (73)  all_57_14 = e3
% 225.63/38.82  | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | BETA: splitting (3) gives:
% 225.63/38.82  | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | Case 1:
% 225.63/38.82  | | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | |   (74)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 225.63/38.82  | | | | | | | | | | |           & op(e1, e2) = e0)
% 225.63/38.82  | | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | | BETA: splitting (74) gives:
% 225.63/38.82  | | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | | Case 1:
% 225.63/38.82  | | | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | | |   (75)  all_57_6 = e0 & op(e1, e3) = e0
% 225.63/38.82  | | | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | | | ALPHA: (75) implies:
% 225.63/38.82  | | | | | | | | | | | |   (76)  all_57_6 = e0
% 225.63/38.82  | | | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | | | REF_CLOSE: (2), (4), (6), (7), (8), (11), (14), (16), (64),
% 225.63/38.82  | | | | | | | | | | | |            (76) are inconsistent by sub-proof #1818.
% 225.63/38.82  | | | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | | Case 2:
% 225.63/38.82  | | | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | | |   (77)  all_57_7 = e0 & op(e1, e2) = e0
% 225.63/38.82  | | | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | | | REF_CLOSE: (11), (21), (77) are inconsistent by sub-proof
% 225.63/38.82  | | | | | | | | | | | |            #2148.
% 225.63/38.82  | | | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | | End of split
% 225.63/38.82  | | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | Case 2:
% 225.63/38.82  | | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | |   (78)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 225.63/38.82  | | | | | | | | | | |           e0 & op(e1, e0) = e0)
% 225.63/38.82  | | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | | BETA: splitting (78) gives:
% 225.63/38.82  | | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | | Case 1:
% 225.63/38.82  | | | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | | |   (79)  all_57_8 = e0 & op(e1, e1) = e0
% 225.63/38.82  | | | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | | | ALPHA: (79) implies:
% 225.63/38.82  | | | | | | | | | | | |   (80)  all_57_8 = e0
% 225.63/38.82  | | | | | | | | | | | |   (81)  op(e1, e1) = e0
% 225.63/38.82  | | | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | | | BETA: splitting (6) gives:
% 225.63/38.82  | | | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | | | Case 1:
% 225.63/38.82  | | | | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | | | |   (82)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 225.63/38.82  | | | | | | | | | | | | |           & op(e1, e2) = e3)
% 225.63/38.82  | | | | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | | | | BETA: splitting (82) gives:
% 225.63/38.82  | | | | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | | | | Case 1:
% 225.63/38.82  | | | | | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | | | | |   (83)  all_57_6 = e3 & op(e1, e3) = e3
% 225.63/38.82  | | | | | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | | | | | ALPHA: (83) implies:
% 225.63/38.82  | | | | | | | | | | | | | |   (84)  all_57_6 = e3
% 225.63/38.82  | | | | | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | | | | | BETA: splitting (18) gives:
% 225.63/38.82  | | | | | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | | | | | Case 1:
% 225.63/38.82  | | | | | | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | | | | | |   (85)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 225.63/38.82  | | | | | | | | | | | | | | |           & op(e2, e1) = e1)
% 225.63/38.82  | | | | | | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | | | | | | BETA: splitting (85) gives:
% 225.63/38.82  | | | | | | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | | | | | | Case 1:
% 225.63/38.82  | | | | | | | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | | | | | | |   (86)  all_57_4 = e1 & op(e3, e1) = e1
% 225.63/38.82  | | | | | | | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | | | | | | | REF_CLOSE: (24), (39), (86) are inconsistent by sub-proof
% 225.63/38.82  | | | | | | | | | | | | | | | |            #1411.
% 225.63/38.82  | | | | | | | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | | | | | | Case 2:
% 225.63/38.82  | | | | | | | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | | | | | | |   (87)  all_57_5 = e1 & op(e2, e1) = e1
% 225.63/38.82  | | | | | | | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | | | | | | | ALPHA: (87) implies:
% 225.63/38.82  | | | | | | | | | | | | | | | |   (88)  all_57_5 = e1
% 225.63/38.82  | | | | | | | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | | | | | | | REF_CLOSE: (25), (31), (88) are inconsistent by sub-proof
% 225.63/38.82  | | | | | | | | | | | | | | | |            #1885.
% 225.63/38.82  | | | | | | | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | | | | | | End of split
% 225.63/38.82  | | | | | | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | | | | | Case 2:
% 225.63/38.82  | | | | | | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | | | | | |   (89)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 225.63/38.82  | | | | | | | | | | | | | | |           e1 & op(e0, e1) = e1)
% 225.63/38.82  | | | | | | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | | | | | | BETA: splitting (89) gives:
% 225.63/38.82  | | | | | | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | | | | | | Case 1:
% 225.63/38.82  | | | | | | | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | | | | | | |   (90)  all_57_8 = e1 & op(e1, e1) = e1
% 225.63/38.82  | | | | | | | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | | | | | | | ALPHA: (90) implies:
% 225.63/38.82  | | | | | | | | | | | | | | | |   (91)  op(e1, e1) = e1
% 225.63/38.82  | | | | | | | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (24), (81), (91) are inconsistent by
% 225.63/38.82  | | | | | | | | | | | | | | | |            sub-proof #2427.
% 225.63/38.82  | | | | | | | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | | | | | | Case 2:
% 225.63/38.82  | | | | | | | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | | | | | | |   (92)  all_57_14 = e1 & op(e0, e1) = e1
% 225.63/38.82  | | | | | | | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | | | | | | | ALPHA: (92) implies:
% 225.63/38.82  | | | | | | | | | | | | | | | |   (93)  all_57_14 = e1
% 225.63/38.82  | | | | | | | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | | | | | | | COMBINE_EQS: (73), (93) imply:
% 225.63/38.82  | | | | | | | | | | | | | | | |   (94)  e3 = e1
% 225.63/38.82  | | | | | | | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | | | | | | | SIMP: (94) implies:
% 225.63/38.82  | | | | | | | | | | | | | | | |   (95)  e3 = e1
% 225.63/38.82  | | | | | | | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | | | | | | | COMBINE_EQS: (84), (95) imply:
% 225.63/38.82  | | | | | | | | | | | | | | | |   (96)  all_57_6 = e1
% 225.63/38.82  | | | | | | | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (6), (7), (8), (14), (21), (31), (38),
% 225.63/38.82  | | | | | | | | | | | | | | | |            (64), (80), (96) are inconsistent by sub-proof
% 225.63/38.82  | | | | | | | | | | | | | | | |            #2003.
% 225.63/38.82  | | | | | | | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | | | | | | End of split
% 225.63/38.82  | | | | | | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | | | | | End of split
% 225.63/38.82  | | | | | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | | | | Case 2:
% 225.63/38.82  | | | | | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | | | | |   (97)  all_57_7 = e3 & op(e1, e2) = e3
% 225.63/38.82  | | | | | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | | | | | REF_CLOSE: (4), (30), (34), (97) are inconsistent by
% 225.63/38.82  | | | | | | | | | | | | | |            sub-proof #267.
% 225.63/38.82  | | | | | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | | | | End of split
% 225.63/38.82  | | | | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | | | Case 2:
% 225.63/38.82  | | | | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | | | |   (98)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 225.63/38.82  | | | | | | | | | | | | |           e3 & op(e1, e0) = e3)
% 225.63/38.82  | | | | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | | | | REF_CLOSE: (2), (4), (7), (8), (64), (98) are inconsistent by
% 225.63/38.82  | | | | | | | | | | | | |            sub-proof #2004.
% 225.63/38.82  | | | | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | | | End of split
% 225.63/38.82  | | | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | | Case 2:
% 225.63/38.82  | | | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | | |   (99)  all_57_11 = e0 & op(e1, e0) = e0
% 225.63/38.82  | | | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | | | REF_CLOSE: (4), (15), (27), (99) are inconsistent by
% 225.63/38.82  | | | | | | | | | | | |            sub-proof #2341.
% 225.63/38.82  | | | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | | End of split
% 225.63/38.82  | | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | | End of split
% 225.63/38.82  | | | | | | | | | | 
% 225.63/38.82  | | | | | | | | | End of split
% 225.63/38.82  | | | | | | | | | 
% 225.63/38.82  | | | | | | | | End of split
% 225.63/38.82  | | | | | | | | 
% 225.63/38.82  | | | | | | | Case 2:
% 225.63/38.82  | | | | | | | | 
% 225.63/38.82  | | | | | | | |   (100)  all_57_15 = e1 & op(e0, e0) = e1
% 225.63/38.82  | | | | | | | | 
% 225.63/38.82  | | | | | | | | ALPHA: (100) implies:
% 225.63/38.82  | | | | | | | |   (101)  op(e0, e0) = e1
% 225.63/38.82  | | | | | | | | 
% 225.63/38.82  | | | | | | | | REF_CLOSE: (4), (31), (32), (101) are inconsistent by sub-proof
% 225.63/38.82  | | | | | | | |            #2177.
% 225.63/38.82  | | | | | | | | 
% 225.63/38.82  | | | | | | | End of split
% 225.63/38.82  | | | | | | | 
% 225.63/38.82  | | | | | | End of split
% 225.63/38.82  | | | | | | 
% 225.63/38.82  | | | | | Case 2:
% 225.63/38.82  | | | | | | 
% 225.63/38.82  | | | | | |   (102)  all_57_11 = e0 & op(e1, e0) = e0
% 225.63/38.82  | | | | | | 
% 225.63/38.82  | | | | | | REF_CLOSE: (4), (15), (27), (102) are inconsistent by sub-proof
% 225.63/38.82  | | | | | |            #2341.
% 225.63/38.82  | | | | | | 
% 225.63/38.82  | | | | | End of split
% 225.63/38.82  | | | | | 
% 225.63/38.82  | | | | End of split
% 225.63/38.82  | | | | 
% 225.63/38.82  | | | End of split
% 225.63/38.82  | | | 
% 225.63/38.82  | | End of split
% 225.63/38.82  | | 
% 225.63/38.82  | End of split
% 225.63/38.82  | 
% 225.63/38.82  End of proof
% 225.63/38.82  
% 225.63/38.82  Sub-proof #8 shows that the following formulas are inconsistent:
% 225.63/38.82  ----------------------------------------------------------------
% 225.63/38.82    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 225.63/38.82           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 225.63/38.82    (2)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 225.63/38.82    (3)  op(all_52_7, all_52_7) = e0
% 225.63/38.82    (4)  all_55_3 = all_52_7
% 225.63/38.82    (5)   ~ (all_52_7 = e1)
% 225.63/38.82    (6)  op(e3, e3) = all_52_1
% 225.63/38.82    (7)  op(all_52_1, all_52_1) = e3
% 225.63/38.82    (8)   ~ (all_52_7 = e0)
% 225.63/38.82    (9)  op(e0, e0) = e2
% 225.63/38.82    (10)   ~ (all_52_7 = e2)
% 225.63/38.82  
% 225.63/38.82  Begin of proof
% 225.63/38.82  | 
% 225.63/38.82  | BETA: splitting (2) gives:
% 225.63/38.82  | 
% 225.63/38.82  | Case 1:
% 225.63/38.82  | | 
% 225.63/38.82  | |   (11)  all_55_3 = e3
% 225.63/38.82  | | 
% 225.63/38.82  | | COMBINE_EQS: (4), (11) imply:
% 225.63/38.82  | |   (12)  all_52_7 = e3
% 225.63/38.82  | | 
% 225.63/38.82  | | SIMP: (12) implies:
% 225.63/38.82  | |   (13)  all_52_7 = e3
% 225.63/38.82  | | 
% 225.63/38.82  | | REDUCE: (10), (13) imply:
% 225.63/38.82  | |   (14)   ~ (e3 = e2)
% 225.63/38.82  | | 
% 225.63/38.82  | | REDUCE: (3), (13) imply:
% 225.63/38.82  | |   (15)  op(e3, e3) = e0
% 225.63/38.82  | | 
% 225.63/38.82  | | REF_CLOSE: (1), (6), (7), (9), (14), (15) are inconsistent by sub-proof #53.
% 225.63/38.82  | | 
% 225.63/38.82  | Case 2:
% 225.63/38.82  | | 
% 225.63/38.82  | |   (16)  all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 225.63/38.82  | | 
% 225.63/38.82  | | BETA: splitting (16) gives:
% 225.63/38.82  | | 
% 225.63/38.82  | | Case 1:
% 225.63/38.82  | | | 
% 225.63/38.82  | | |   (17)  all_55_3 = e2
% 225.63/38.82  | | | 
% 225.63/38.82  | | | REF_CLOSE: (4), (10), (17) are inconsistent by sub-proof #1450.
% 225.63/38.82  | | | 
% 225.63/38.82  | | Case 2:
% 225.63/38.82  | | | 
% 225.63/38.82  | | |   (18)  all_55_3 = e1 | all_55_3 = e0
% 225.63/38.82  | | | 
% 225.63/38.82  | | | REF_CLOSE: (4), (5), (8), (18) are inconsistent by sub-proof #121.
% 225.63/38.82  | | | 
% 225.63/38.82  | | End of split
% 225.63/38.82  | | 
% 225.63/38.82  | End of split
% 225.63/38.82  | 
% 225.63/38.82  End of proof
% 225.63/38.82  
% 225.63/38.82  Sub-proof #9 shows that the following formulas are inconsistent:
% 225.63/38.82  ----------------------------------------------------------------
% 225.63/38.82    (1)  op(e2, e3) = all_53_1
% 225.63/38.82    (2)  op(e3, e1) = all_52_5
% 225.63/38.82    (3)   ~ (e3 = e1)
% 225.63/38.82    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 225.63/38.82           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 225.63/38.82    (5)  op(all_52_5, all_52_5) = e1
% 225.63/38.82    (6)  op(all_52_7, all_52_7) = e0
% 225.63/38.82    (7)  op(e3, e2) = all_52_3
% 225.63/38.82    (8)  op(all_52_3, all_52_3) = e2
% 225.63/38.82    (9)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 225.63/38.82         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 225.63/38.82    (10)   ~ (e3 = e2)
% 225.63/38.82    (11)   ~ (e3 = e0)
% 225.63/38.82    (12)   ~ (all_52_3 = e3)
% 225.63/38.82    (13)  op(e2, e2) = e3
% 225.63/38.82    (14)   ~ (all_53_1 = e3)
% 225.63/38.82    (15)  op(e3, e0) = all_52_7
% 225.63/38.82    (16)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3)
% 225.63/38.82  
% 225.63/38.82  Begin of proof
% 225.63/38.82  | 
% 225.63/38.82  | BETA: splitting (16) gives:
% 225.63/38.82  | 
% 225.63/38.82  | Case 1:
% 225.63/38.82  | | 
% 225.63/38.82  | |   (17)  all_57_0 = e3 & op(e3, e3) = e3
% 225.63/38.82  | | 
% 225.63/38.82  | | ALPHA: (17) implies:
% 225.63/38.82  | |   (18)  op(e3, e3) = e3
% 225.63/38.82  | | 
% 225.63/38.82  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 225.63/38.82  | |            (15), (18) are inconsistent by sub-proof #95.
% 225.63/38.82  | | 
% 225.63/38.82  | Case 2:
% 225.63/38.82  | | 
% 225.63/38.82  | |   (19)  all_57_2 = e3 & op(e2, e3) = e3
% 225.63/38.82  | | 
% 225.63/38.82  | | REF_CLOSE: (1), (4), (14), (19) are inconsistent by sub-proof #2299.
% 225.63/38.82  | | 
% 225.63/38.82  | End of split
% 225.63/38.82  | 
% 225.63/38.82  End of proof
% 225.63/38.82  
% 225.63/38.82  Sub-proof #10 shows that the following formulas are inconsistent:
% 225.63/38.82  ----------------------------------------------------------------
% 225.63/38.82    (1)  op(e3, e1) = all_52_5
% 225.63/38.82    (2)   ~ (e3 = e1)
% 225.63/38.82    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 225.63/38.82           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 225.63/38.82    (4)  op(all_52_5, all_52_5) = e1
% 225.63/38.82    (5)  op(all_52_7, all_52_7) = e0
% 225.63/38.82    (6)  op(e3, e2) = all_52_3
% 225.63/38.82    (7)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3)
% 225.63/38.82    (8)  op(all_52_3, all_52_3) = e2
% 225.63/38.82    (9)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 225.63/38.82         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 225.63/38.82    (10)   ~ (e3 = e2)
% 225.63/38.82    (11)   ~ (e3 = e0)
% 225.63/38.82    (12)   ~ (all_52_3 = e3)
% 225.63/38.82    (13)  op(e3, e2) = all_53_4
% 225.63/38.82    (14)  op(e2, e2) = e3
% 225.63/38.82    (15)  op(e3, e0) = all_52_7
% 225.63/38.82    (16)   ~ (all_53_4 = e3)
% 225.63/38.82  
% 225.63/38.82  Begin of proof
% 225.63/38.82  | 
% 225.63/38.82  | BETA: splitting (7) gives:
% 225.63/38.82  | 
% 225.63/38.82  | Case 1:
% 225.63/38.82  | | 
% 225.63/38.82  | |   (17)  all_57_0 = e3 & op(e3, e3) = e3
% 225.63/38.82  | | 
% 225.63/38.82  | | ALPHA: (17) implies:
% 225.63/38.82  | |   (18)  op(e3, e3) = e3
% 225.63/38.82  | | 
% 225.63/38.82  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (14),
% 225.63/38.82  | |            (15), (18) are inconsistent by sub-proof #95.
% 225.63/38.82  | | 
% 225.63/38.82  | Case 2:
% 225.63/38.82  | | 
% 225.63/38.82  | |   (19)  all_57_1 = e3 & op(e3, e2) = e3
% 225.63/38.82  | | 
% 225.63/38.82  | | REF_CLOSE: (3), (13), (16), (19) are inconsistent by sub-proof #2286.
% 225.63/38.82  | | 
% 225.63/38.82  | End of split
% 225.63/38.82  | 
% 225.63/38.82  End of proof
% 225.63/38.82  
% 225.63/38.82  Sub-proof #11 shows that the following formulas are inconsistent:
% 225.63/38.82  ----------------------------------------------------------------
% 225.63/38.82    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 225.63/38.82           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 225.63/38.82    (2)   ~ (e3 = e0)
% 225.63/38.82    (3)  op(e0, e0) = all_52_31
% 225.63/38.82    (4)  op(e2, e2) = e3
% 225.63/38.82    (5)  op(e0, e0) = e2
% 225.63/38.82    (6)  op(all_52_31, all_52_31) = e0
% 225.63/38.82  
% 225.63/38.82  Begin of proof
% 225.63/38.82  | 
% 225.63/38.82  | GROUND_INST: instantiating (1) with e2, all_52_31, e0, e0, simplifying with
% 225.63/38.82  |              (3), (5) gives:
% 225.63/38.82  |   (7)  all_52_31 = e2
% 225.63/38.82  | 
% 225.63/38.82  | REDUCE: (6), (7) imply:
% 225.63/38.82  |   (8)  op(e2, e2) = e0
% 225.63/38.83  | 
% 225.63/38.83  | GROUND_INST: instantiating (1) with e3, e0, e2, e2, simplifying with (4), (8)
% 225.63/38.83  |              gives:
% 225.63/38.83  |   (9)  e3 = e0
% 225.63/38.83  | 
% 225.63/38.83  | REDUCE: (2), (9) imply:
% 225.63/38.83  |   (10)  $false
% 225.63/38.83  | 
% 225.63/38.83  | CLOSE: (10) is inconsistent.
% 225.63/38.83  | 
% 225.63/38.83  End of proof
% 225.63/38.83  
% 225.63/38.83  Sub-proof #12 shows that the following formulas are inconsistent:
% 225.63/38.83  ----------------------------------------------------------------
% 225.63/38.83    (1)  all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 225.63/38.83    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 225.63/38.83           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 225.63/38.83    (3)  all_55_4 = all_52_9
% 225.63/38.83    (4)   ~ (all_52_9 = e0)
% 225.63/38.83    (5)   ~ (all_8_2 = e3)
% 225.63/38.83    (6)   ~ (all_52_9 = e1)
% 225.63/38.83    (7)  op(e2, e2) = all_8_2
% 225.63/38.83    (8)  op(all_52_9, all_52_9) = e3
% 225.63/38.83  
% 225.63/38.83  Begin of proof
% 225.63/38.83  | 
% 225.63/38.83  | BETA: splitting (1) gives:
% 225.63/38.83  | 
% 225.63/38.83  | Case 1:
% 225.63/38.83  | | 
% 225.63/38.83  | |   (9)  all_55_4 = e2
% 225.63/38.83  | | 
% 225.63/38.83  | | COMBINE_EQS: (3), (9) imply:
% 225.63/38.83  | |   (10)  all_52_9 = e2
% 225.63/38.83  | | 
% 225.63/38.83  | | SIMP: (10) implies:
% 225.63/38.83  | |   (11)  all_52_9 = e2
% 225.63/38.83  | | 
% 225.63/38.83  | | REDUCE: (8), (11) imply:
% 225.63/38.83  | |   (12)  op(e2, e2) = e3
% 225.63/38.83  | | 
% 225.63/38.83  | | REF_CLOSE: (2), (5), (7), (12) are inconsistent by sub-proof #140.
% 225.63/38.83  | | 
% 225.63/38.83  | Case 2:
% 225.63/38.83  | | 
% 225.63/38.83  | |   (13)  all_55_4 = e1 | all_55_4 = e0
% 225.63/38.83  | | 
% 225.63/38.83  | | BETA: splitting (13) gives:
% 225.63/38.83  | | 
% 225.63/38.83  | | Case 1:
% 225.63/38.83  | | | 
% 225.63/38.83  | | |   (14)  all_55_4 = e1
% 225.63/38.83  | | | 
% 225.63/38.83  | | | REF_CLOSE: (3), (6), (14) are inconsistent by sub-proof #344.
% 225.63/38.83  | | | 
% 225.63/38.83  | | Case 2:
% 225.63/38.83  | | | 
% 225.63/38.83  | | |   (15)  all_55_4 = e0
% 225.63/38.83  | | | 
% 225.63/38.83  | | | REF_CLOSE: (3), (4), (15) are inconsistent by sub-proof #60.
% 225.63/38.83  | | | 
% 225.63/38.83  | | End of split
% 225.63/38.83  | | 
% 225.63/38.83  | End of split
% 225.63/38.83  | 
% 225.63/38.83  End of proof
% 225.63/38.83  
% 225.63/38.83  Sub-proof #13 shows that the following formulas are inconsistent:
% 225.63/38.83  ----------------------------------------------------------------
% 225.63/38.83    (1)   ~ (e3 = e1)
% 225.63/38.83    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 225.63/38.83           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 225.63/38.83    (3)   ~ (all_6_2 = e3)
% 225.63/38.83    (4)  op(e1, e1) = all_6_2
% 225.63/38.83    (5)  all_57_4 = e0
% 225.63/38.83    (6)  op(e0, e3) = all_52_25
% 225.63/38.83    (7)   ~ (e3 = e2)
% 225.63/38.83    (8)   ~ (e3 = e0)
% 225.63/38.83    (9)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 225.63/38.83         (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 225.63/38.83    (10)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 225.63/38.83          | (all_57_14 = e0 & op(e0, e1) = e0)
% 225.63/38.83    (11)   ~ (all_53_7 = e0)
% 225.63/38.83    (12)  op(e0, e0) = all_52_31
% 225.63/38.83    (13)  op(all_52_25, all_52_25) = e3
% 225.63/38.83    (14)   ~ (e2 = e0)
% 225.63/38.83    (15)   ~ (e1 = e0)
% 225.63/38.83    (16)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 225.63/38.83          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 225.63/38.83    (17)  op(e0, e2) = all_53_7
% 225.63/38.83    (18)   ~ (e2 = e1)
% 225.63/38.83    (19)  op(e0, e0) = e2
% 225.63/38.83    (20)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 225.63/38.83          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 225.63/38.83  
% 225.63/38.83  Begin of proof
% 225.63/38.83  | 
% 225.63/38.83  | BETA: splitting (10) gives:
% 225.63/38.83  | 
% 225.63/38.83  | Case 1:
% 225.63/38.83  | | 
% 225.63/38.83  | |   (21)  all_57_12 = e0 & op(e0, e3) = e0
% 225.63/38.83  | | 
% 225.63/38.83  | | ALPHA: (21) implies:
% 225.63/38.83  | |   (22)  op(e0, e3) = e0
% 225.63/38.83  | | 
% 225.63/38.83  | | REF_CLOSE: (2), (6), (7), (12), (13), (19), (22) are inconsistent by
% 225.63/38.83  | |            sub-proof #31.
% 225.63/38.83  | | 
% 225.63/38.83  | Case 2:
% 225.63/38.83  | | 
% 225.63/38.83  | |   (23)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 225.63/38.83  | |           e0)
% 225.63/38.83  | | 
% 225.63/38.83  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (11), (14), (15), (16),
% 225.63/38.83  | |            (17), (18), (20), (23) are inconsistent by sub-proof #1399.
% 225.63/38.83  | | 
% 225.63/38.83  | End of split
% 225.63/38.83  | 
% 225.63/38.83  End of proof
% 225.63/38.83  
% 225.63/38.83  Sub-proof #14 shows that the following formulas are inconsistent:
% 225.63/38.83  ----------------------------------------------------------------
% 225.63/38.83    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 225.63/38.83           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 225.63/38.83    (2)  all_57_2 = e2
% 225.63/38.83    (3)   ~ (all_8_2 = e3)
% 225.63/38.83    (4)   ~ (e3 = e2)
% 225.63/38.83    (5)  op(e2, e2) = all_8_2
% 225.63/38.83    (6)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3)
% 225.63/38.83  
% 225.63/38.83  Begin of proof
% 225.63/38.83  | 
% 225.63/38.83  | BETA: splitting (6) gives:
% 225.63/38.83  | 
% 225.63/38.83  | Case 1:
% 225.63/38.83  | | 
% 225.63/38.83  | |   (7)  all_57_2 = e3 & op(e2, e3) = e3
% 225.63/38.83  | | 
% 225.63/38.83  | | ALPHA: (7) implies:
% 225.63/38.83  | |   (8)  all_57_2 = e3
% 225.63/38.83  | | 
% 225.63/38.83  | | COMBINE_EQS: (2), (8) imply:
% 225.63/38.83  | |   (9)  e3 = e2
% 225.63/38.83  | | 
% 225.63/38.83  | | REDUCE: (4), (9) imply:
% 225.63/38.83  | |   (10)  $false
% 225.63/38.83  | | 
% 225.63/38.83  | | CLOSE: (10) is inconsistent.
% 225.63/38.83  | | 
% 225.63/38.83  | Case 2:
% 225.63/38.83  | | 
% 225.63/38.83  | |   (11)  all_57_3 = e3 & op(e2, e2) = e3
% 225.63/38.83  | | 
% 225.63/38.83  | | ALPHA: (11) implies:
% 225.63/38.83  | |   (12)  op(e2, e2) = e3
% 225.63/38.83  | | 
% 225.63/38.83  | | REF_CLOSE: (1), (3), (5), (12) are inconsistent by sub-proof #140.
% 225.63/38.83  | | 
% 225.63/38.83  | End of split
% 225.63/38.83  | 
% 225.63/38.83  End of proof
% 225.63/38.83  
% 225.63/38.83  Sub-proof #15 shows that the following formulas are inconsistent:
% 225.63/38.83  ----------------------------------------------------------------
% 225.63/38.83    (1)  op(e0, e1) = all_53_11
% 225.63/38.83    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 225.63/38.83           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 225.63/38.83    (3)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 225.63/38.83    (4)   ~ (all_53_11 = e1)
% 225.63/38.83    (5)   ~ (e2 = e1)
% 225.63/38.83    (6)  op(e0, e0) = e2
% 225.63/38.83  
% 225.63/38.83  Begin of proof
% 225.63/38.83  | 
% 225.63/38.83  | BETA: splitting (3) gives:
% 225.63/38.83  | 
% 225.63/38.83  | Case 1:
% 225.63/38.83  | | 
% 225.63/38.83  | |   (7)  all_57_14 = e1 & op(e0, e1) = e1
% 225.63/38.83  | | 
% 225.63/38.83  | | REF_CLOSE: (1), (2), (4), (7) are inconsistent by sub-proof #225.
% 225.63/38.83  | | 
% 225.63/38.83  | Case 2:
% 225.63/38.83  | | 
% 225.63/38.83  | |   (8)  all_57_15 = e1 & op(e0, e0) = e1
% 225.63/38.83  | | 
% 225.63/38.83  | | ALPHA: (8) implies:
% 225.63/38.83  | |   (9)  op(e0, e0) = e1
% 225.63/38.83  | | 
% 225.63/38.83  | | REF_CLOSE: (2), (5), (6), (9) are inconsistent by sub-proof #2177.
% 225.63/38.83  | | 
% 225.63/38.83  | End of split
% 225.63/38.83  | 
% 225.63/38.83  End of proof
% 225.63/38.83  
% 225.63/38.83  Sub-proof #16 shows that the following formulas are inconsistent:
% 225.63/38.83  ----------------------------------------------------------------
% 225.63/38.83    (1)  ( ~ (all_50_0 = e3) & op(all_50_1, e2) = all_50_0 & op(e2, e0) = all_50_1
% 225.63/38.83           & $i(all_50_0) & $i(all_50_1)) | ( ~ (all_50_1 = e1) & op(e2, e0) =
% 225.63/38.83           all_50_1 & $i(all_50_1))
% 225.63/38.83    (2)   ~ (all_53_6 = e0)
% 225.63/38.83    (3)  ( ~ (all_14_0 = e1) & op(all_14_1, e2) = all_14_0 & op(e2, e0) = all_14_1
% 225.63/38.83           & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e3) & op(e2, e0) =
% 225.63/38.83           all_14_1 & $i(all_14_1))
% 225.63/38.83    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 225.63/38.83           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 225.63/38.83    (5)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 225.63/38.83    (6)  all_55_9 = all_53_6
% 225.63/38.83    (7)  op(e2, e2) = e0
% 225.63/38.83    (8)  op(e2, e0) = e1
% 225.63/38.83    (9)   ~ (all_53_6 = e1)
% 225.63/38.83    (10)  op(e2, e0) = all_14_1
% 225.63/38.83    (11)  op(e1, e2) = all_52_19
% 225.63/38.83    (12)  op(all_52_19, all_52_19) = e2
% 225.63/38.83    (13)  op(e1, e2) = all_53_6
% 225.63/38.83    (14)  op(e2, e0) = all_50_1
% 225.63/38.83  
% 225.63/38.83  Begin of proof
% 225.63/38.83  | 
% 225.63/38.83  | GROUND_INST: instantiating (4) with all_53_6, all_52_19, e2, e1, simplifying
% 225.63/38.83  |              with (11), (13) gives:
% 225.63/38.83  |   (15)  all_53_6 = all_52_19
% 225.63/38.83  | 
% 225.63/38.83  | GROUND_INST: instantiating (4) with e1, all_50_1, e0, e2, simplifying with
% 225.63/38.83  |              (8), (14) gives:
% 225.63/38.83  |   (16)  all_50_1 = e1
% 225.63/38.83  | 
% 225.63/38.83  | GROUND_INST: instantiating (4) with all_14_1, all_50_1, e0, e2, simplifying
% 225.63/38.83  |              with (10), (14) gives:
% 225.63/38.83  |   (17)  all_50_1 = all_14_1
% 225.63/38.83  | 
% 225.63/38.83  | COMBINE_EQS: (16), (17) imply:
% 225.63/38.83  |   (18)  all_14_1 = e1
% 225.63/38.83  | 
% 225.63/38.83  | COMBINE_EQS: (6), (15) imply:
% 225.63/38.83  |   (19)  all_55_9 = all_52_19
% 225.63/38.83  | 
% 225.63/38.83  | REDUCE: (9), (15) imply:
% 225.63/38.83  |   (20)   ~ (all_52_19 = e1)
% 225.63/38.83  | 
% 225.63/38.83  | REDUCE: (2), (15) imply:
% 225.63/38.83  |   (21)   ~ (all_52_19 = e0)
% 225.63/38.83  | 
% 225.63/38.83  | REF_CLOSE: (1), (3), (4), (5), (7), (8), (11), (12), (19), (20), (21) are
% 225.63/38.83  |            inconsistent by sub-proof #271.
% 225.63/38.83  | 
% 225.63/38.83  End of proof
% 225.63/38.83  
% 225.63/38.83  Sub-proof #17 shows that the following formulas are inconsistent:
% 225.63/38.83  ----------------------------------------------------------------
% 225.63/38.83    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 225.63/38.83           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 225.63/38.83    (2)  op(e2, e0) = all_52_15
% 225.63/38.83    (3)  op(e2, e0) = e1
% 225.63/38.83    (4)  op(e1, e1) = e1
% 225.63/38.83    (5)   ~ (e1 = e0)
% 225.63/38.83    (6)  op(e2, e0) = all_14_1
% 225.63/38.83    (7)  op(all_52_15, all_52_15) = e0
% 225.63/38.83  
% 225.63/38.83  Begin of proof
% 225.63/38.83  | 
% 225.63/38.83  | GROUND_INST: instantiating (1) with e1, all_52_15, e0, e2, simplifying with
% 225.63/38.83  |              (2), (3) gives:
% 225.63/38.83  |   (8)  all_52_15 = e1
% 225.63/38.83  | 
% 225.63/38.83  | GROUND_INST: instantiating (1) with all_14_1, all_52_15, e0, e2, simplifying
% 225.63/38.83  |              with (2), (6) gives:
% 225.63/38.83  |   (9)  all_52_15 = all_14_1
% 225.63/38.83  | 
% 225.63/38.83  | COMBINE_EQS: (8), (9) imply:
% 225.63/38.83  |   (10)  all_14_1 = e1
% 225.63/38.83  | 
% 225.63/38.83  | REDUCE: (7), (8) imply:
% 225.63/38.83  |   (11)  op(e1, e1) = e0
% 225.63/38.83  | 
% 225.63/38.83  | REF_CLOSE: (1), (4), (5), (11) are inconsistent by sub-proof #2427.
% 225.63/38.83  | 
% 225.63/38.83  End of proof
% 225.63/38.83  
% 225.63/38.83  Sub-proof #18 shows that the following formulas are inconsistent:
% 225.63/38.83  ----------------------------------------------------------------
% 225.63/38.83    (1)  op(e3, e3) = e1
% 225.63/38.83    (2)   ~ (e3 = e1)
% 225.63/38.83    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 225.63/38.83           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 225.63/38.83    (4)  op(e0, e2) = e1
% 225.63/38.83    (5)  ( ~ (all_4_0 = e3) & op(all_4_1, e0) = all_4_0 & op(e0, e2) = all_4_1 &
% 225.63/38.83           $i(all_4_0) & $i(all_4_1)) | ( ~ (all_4_1 = e1) & op(e0, e2) = all_4_1
% 225.63/38.83           & $i(all_4_1))
% 225.63/38.83    (6)  op(e3, e3) = all_52_1
% 225.63/38.83    (7)  op(e1, e1) = e1
% 225.63/38.83    (8)  op(all_52_1, all_52_1) = e3
% 225.63/38.83    (9)  ( ~ (all_32_0 = e1) & op(all_32_1, e0) = all_32_0 & op(e0, e2) = all_32_1
% 225.63/38.83           & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 = e3) & op(e0, e2) =
% 225.63/38.83           all_32_1 & $i(all_32_1))
% 225.63/38.83  
% 225.63/38.83  Begin of proof
% 225.63/38.83  | 
% 225.63/38.83  | BETA: splitting (9) gives:
% 225.63/38.83  | 
% 225.63/38.83  | Case 1:
% 225.63/38.83  | | 
% 225.63/38.83  | | 
% 225.63/38.83  | | GROUND_INST: instantiating (3) with e1, all_52_1, e3, e3, simplifying with
% 225.63/38.83  | |              (1), (6) gives:
% 225.63/38.83  | |   (10)  all_52_1 = e1
% 225.63/38.83  | | 
% 225.63/38.83  | | REDUCE: (8), (10) imply:
% 225.63/38.83  | |   (11)  op(e1, e1) = e3
% 225.63/38.83  | | 
% 225.63/38.83  | | REF_CLOSE: (2), (3), (7), (11) are inconsistent by sub-proof #156.
% 225.63/38.83  | | 
% 225.63/38.83  | Case 2:
% 225.63/38.83  | | 
% 225.63/38.83  | |   (12)   ~ (all_32_1 = e3) & op(e0, e2) = all_32_1 & $i(all_32_1)
% 225.63/38.83  | | 
% 225.63/38.83  | | ALPHA: (12) implies:
% 225.63/38.83  | |   (13)   ~ (all_32_1 = e3)
% 225.63/38.83  | |   (14)  op(e0, e2) = all_32_1
% 225.63/38.83  | | 
% 225.63/38.83  | | BETA: splitting (5) gives:
% 225.63/38.83  | | 
% 225.63/38.83  | | Case 1:
% 225.63/38.83  | | | 
% 225.63/38.83  | | | 
% 225.63/38.83  | | | GROUND_INST: instantiating (3) with e1, all_32_1, e2, e0, simplifying with
% 225.63/38.83  | | |              (4), (14) gives:
% 225.63/38.83  | | |   (15)  all_32_1 = e1
% 225.63/38.83  | | | 
% 225.63/38.83  | | | GROUND_INST: instantiating (3) with e1, all_52_1, e3, e3, simplifying with
% 225.63/38.83  | | |              (1), (6) gives:
% 225.63/38.83  | | |   (16)  all_52_1 = e1
% 225.63/38.83  | | | 
% 225.63/38.83  | | | REDUCE: (13), (15) imply:
% 225.63/38.83  | | |   (17)   ~ (e3 = e1)
% 225.63/38.83  | | | 
% 225.63/38.83  | | | REDUCE: (8), (16) imply:
% 225.63/38.83  | | |   (18)  op(e1, e1) = e3
% 225.63/38.83  | | | 
% 225.63/38.83  | | | REF_CLOSE: (2), (3), (7), (18) are inconsistent by sub-proof #156.
% 225.63/38.83  | | | 
% 225.63/38.83  | | Case 2:
% 225.63/38.83  | | | 
% 225.63/38.83  | | |   (19)   ~ (all_4_1 = e1) & op(e0, e2) = all_4_1 & $i(all_4_1)
% 225.63/38.83  | | | 
% 225.63/38.83  | | | REF_CLOSE: (3), (4), (9), (19) are inconsistent by sub-proof #69.
% 225.63/38.83  | | | 
% 225.63/38.83  | | End of split
% 225.63/38.83  | | 
% 225.63/38.83  | End of split
% 225.63/38.83  | 
% 225.63/38.83  End of proof
% 225.63/38.83  
% 225.63/38.83  Sub-proof #19 shows that the following formulas are inconsistent:
% 225.63/38.83  ----------------------------------------------------------------
% 225.63/38.83    (1)  all_57_15 = e0
% 225.63/38.83    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 225.63/38.83           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 225.63/38.83    (3)   ~ (e3 = e2)
% 225.63/38.83    (4)   ~ (e2 = e0)
% 225.63/38.83    (5)  all_57_10 = e3
% 225.63/38.83    (6)  all_57_11 = e1
% 225.63/38.83    (7)   ~ (e2 = e1)
% 225.63/38.83    (8)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 225.63/38.83         (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 225.63/38.83    (9)   ~ (all_53_12 = e2)
% 225.63/38.83    (10)  op(e3, e0) = all_53_12
% 225.63/38.83  
% 225.63/38.83  Begin of proof
% 225.63/38.83  | 
% 225.63/38.83  | BETA: splitting (8) gives:
% 225.63/38.83  | 
% 225.63/38.83  | Case 1:
% 225.63/38.83  | | 
% 225.63/38.83  | |   (11)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 225.63/38.83  | |           e2)
% 225.63/38.83  | | 
% 225.63/38.83  | | REF_CLOSE: (2), (3), (5), (9), (10), (11) are inconsistent by sub-proof
% 225.63/38.83  | |            #1219.
% 225.63/38.83  | | 
% 225.63/38.83  | Case 2:
% 225.63/38.83  | | 
% 225.63/38.83  | |   (12)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 225.63/38.83  | |           e2)
% 225.63/38.83  | | 
% 225.63/38.83  | | REF_CLOSE: (1), (4), (6), (7), (12) are inconsistent by sub-proof #1666.
% 225.63/38.83  | | 
% 225.63/38.83  | End of split
% 225.63/38.83  | 
% 225.63/38.83  End of proof
% 225.63/38.83  
% 225.63/38.83  Sub-proof #20 shows that the following formulas are inconsistent:
% 225.63/38.83  ----------------------------------------------------------------
% 225.63/38.83    (1)  op(e3, e3) = e1
% 225.63/38.83    (2)  op(e2, e3) = all_53_1
% 225.63/38.83    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 225.63/38.83           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 225.63/38.83    (4)   ~ (all_36_2 = e1) | ( ~ (all_36_0 = e0) & op(all_36_1, e3) = all_36_0 &
% 225.63/38.83           op(e3, e1) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 =
% 225.63/38.83             e2) & op(e3, e1) = all_36_1 & $i(all_36_1))
% 225.63/38.83    (5)  all_55_5 = all_8_2
% 225.63/38.83    (6)   ~ (all_53_8 = e1)
% 225.63/38.83    (7)   ~ (all_53_1 = all_8_2)
% 225.63/38.83    (8)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 225.63/38.83         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 225.63/38.83    (9)  all_55_4 = all_53_1
% 225.63/38.83    (10)   ~ (all_8_2 = e1)
% 225.63/38.83    (11)   ~ (all_8_2 = e3)
% 225.63/38.83    (12)  all_55_5 = e3 | all_55_5 = e2 | all_55_5 = e1 | all_55_5 = e0
% 225.63/38.83    (13)  op(e0, e3) = all_53_3
% 225.63/38.83    (14)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 225.63/38.83    (15)   ~ (all_53_3 = e2)
% 225.63/38.83    (16)   ~ (all_53_1 = e1)
% 225.63/38.83    (17)  ( ~ (all_10_0 = e2) & op(all_10_1, e3) = all_10_0 & op(e3, e1) =
% 225.63/38.83            all_10_1 & $i(all_10_0) & $i(all_10_1)) | ( ~ (all_10_1 = e0) & op(e3,
% 225.63/38.83              e1) = all_10_1 & $i(all_10_1))
% 225.63/38.83    (18)  op(e3, e2) = all_53_4
% 225.63/38.83    (19)   ~ (all_53_1 = all_53_2)
% 225.63/38.83    (20)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 225.63/38.83            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 225.63/38.83            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 225.63/38.83            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 225.63/38.83              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 225.63/38.83            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 225.63/38.83            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 225.63/38.83              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 225.63/38.83              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 225.63/38.83            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 225.63/38.83            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 225.63/38.83            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 225.63/38.83              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 225.63/38.83              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 225.63/38.83            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 225.63/38.83              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 225.63/38.83            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 225.63/38.83            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 225.63/38.83              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 225.63/38.83              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 225.63/38.83            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 225.63/38.83            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 225.63/38.83    (21)  op(e2, e2) = all_8_2
% 225.63/38.83    (22)  all_36_2 = e1
% 225.63/38.83    (23)  op(e1, e3) = all_53_2
% 225.63/38.83    (24)   ~ (all_8_2 = e0)
% 225.63/38.83    (25)  op(e0, e0) = e2
% 225.63/38.83    (26)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 225.63/38.83          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 225.63/38.83    (27)   ~ (all_53_12 = e2)
% 225.63/38.83    (28)   ~ (all_53_4 = all_8_2)
% 225.63/38.83    (29)  op(e3, e1) = all_53_8
% 225.63/38.83    (30)  op(e3, e0) = all_53_12
% 225.63/38.83  
% 225.63/38.83  Begin of proof
% 225.63/38.83  | 
% 225.63/38.83  | BETA: splitting (12) gives:
% 225.63/38.83  | 
% 225.63/38.83  | Case 1:
% 225.63/38.83  | | 
% 225.63/38.83  | |   (31)  all_55_5 = e3
% 225.63/38.83  | | 
% 225.63/38.83  | | REF_CLOSE: (5), (11), (31) are inconsistent by sub-proof #293.
% 225.63/38.83  | | 
% 225.63/38.83  | Case 2:
% 225.63/38.83  | | 
% 225.63/38.83  | |   (32)   ~ (all_55_5 = e3)
% 225.63/38.83  | |   (33)  all_55_5 = e2 | all_55_5 = e1 | all_55_5 = e0
% 225.63/38.83  | | 
% 225.63/38.83  | | BETA: splitting (33) gives:
% 225.63/38.83  | | 
% 225.63/38.83  | | Case 1:
% 225.63/38.83  | | | 
% 225.63/38.83  | | |   (34)  all_55_5 = e2
% 225.63/38.83  | | | 
% 225.63/38.83  | | | COMBINE_EQS: (5), (34) imply:
% 225.63/38.83  | | |   (35)  all_8_2 = e2
% 225.63/38.83  | | | 
% 225.63/38.83  | | | SIMP: (35) implies:
% 225.63/38.83  | | |   (36)  all_8_2 = e2
% 225.63/38.83  | | | 
% 225.63/38.83  | | | REDUCE: (7), (36) imply:
% 225.63/38.83  | | |   (37)   ~ (all_53_1 = e2)
% 225.63/38.83  | | | 
% 225.63/38.83  | | | REDUCE: (28), (36) imply:
% 225.63/38.83  | | |   (38)   ~ (all_53_4 = e2)
% 225.63/38.83  | | | 
% 225.63/38.83  | | | REDUCE: (11), (36) imply:
% 225.63/38.83  | | |   (39)   ~ (e3 = e2)
% 225.63/38.83  | | | 
% 225.63/38.83  | | | SIMP: (39) implies:
% 225.63/38.83  | | |   (40)   ~ (e3 = e2)
% 225.63/38.83  | | | 
% 225.63/38.83  | | | REDUCE: (10), (36) imply:
% 225.63/38.83  | | |   (41)   ~ (e2 = e1)
% 225.63/38.83  | | | 
% 225.63/38.83  | | | REDUCE: (24), (36) imply:
% 225.63/38.83  | | |   (42)   ~ (e2 = e0)
% 225.63/38.83  | | | 
% 225.63/38.83  | | | REDUCE: (21), (36) imply:
% 225.63/38.83  | | |   (43)  op(e2, e2) = e2
% 225.63/38.83  | | | 
% 225.63/38.83  | | | BETA: splitting (26) gives:
% 225.63/38.83  | | | 
% 225.63/38.83  | | | Case 1:
% 225.63/38.83  | | | | 
% 225.63/38.83  | | | |   (44)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3)
% 225.63/38.83  | | | |           = e2)
% 225.63/38.83  | | | | 
% 225.63/38.83  | | | | REF_CLOSE: (1), (2), (3), (37), (41), (44) are inconsistent by sub-proof
% 225.63/38.83  | | | |            #355.
% 225.63/38.83  | | | | 
% 225.63/38.83  | | | Case 2:
% 225.63/38.83  | | | | 
% 225.63/38.83  | | | |   (45)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3)
% 225.63/38.83  | | | |           = e2)
% 225.63/38.83  | | | | 
% 225.63/38.83  | | | | BETA: splitting (45) gives:
% 225.63/38.83  | | | | 
% 225.63/38.83  | | | | Case 1:
% 225.63/38.83  | | | | | 
% 225.63/38.83  | | | | |   (46)  all_57_6 = e2 & op(e1, e3) = e2
% 225.63/38.83  | | | | | 
% 225.63/38.83  | | | | | ALPHA: (46) implies:
% 225.63/38.83  | | | | |   (47)  op(e1, e3) = e2
% 225.63/38.83  | | | | | 
% 225.63/38.83  | | | | | BETA: splitting (8) gives:
% 225.63/38.83  | | | | | 
% 225.63/38.83  | | | | | Case 1:
% 225.63/38.83  | | | | | | 
% 225.63/38.83  | | | | | |   (48)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3,
% 225.63/38.83  | | | | | |             e2) = e2)
% 225.63/38.83  | | | | | | 
% 225.63/38.83  | | | | | | REF_CLOSE: (1), (3), (18), (38), (41), (48) are inconsistent by
% 225.63/38.83  | | | | | |            sub-proof #331.
% 225.63/38.83  | | | | | | 
% 225.63/38.83  | | | | | Case 2:
% 225.63/38.83  | | | | | | 
% 225.63/38.83  | | | | | |   (49)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3,
% 225.63/38.83  | | | | | |             e0) = e2)
% 225.63/38.83  | | | | | | 
% 225.63/38.83  | | | | | | BETA: splitting (49) gives:
% 225.63/38.83  | | | | | | 
% 225.63/38.83  | | | | | | Case 1:
% 225.63/38.83  | | | | | | | 
% 225.63/38.83  | | | | | | |   (50)  all_57_4 = e2 & op(e3, e1) = e2
% 225.63/38.83  | | | | | | | 
% 225.63/38.83  | | | | | | | ALPHA: (50) implies:
% 225.63/38.83  | | | | | | |   (51)  op(e3, e1) = e2
% 225.63/38.83  | | | | | | | 
% 225.63/38.83  | | | | | | | GROUND_INST: instantiating (3) with all_53_2, e2, e3, e1,
% 225.63/38.83  | | | | | | |              simplifying with (23), (47) gives:
% 225.63/38.83  | | | | | | |   (52)  all_53_2 = e2
% 225.63/38.83  | | | | | | | 
% 225.63/38.83  | | | | | | | GROUND_INST: instantiating (3) with all_53_8, e2, e1, e3,
% 225.63/38.83  | | | | | | |              simplifying with (29), (51) gives:
% 225.63/38.83  | | | | | | |   (53)  all_53_8 = e2
% 225.63/38.83  | | | | | | | 
% 225.63/38.83  | | | | | | | BETA: splitting (4) gives:
% 225.63/38.83  | | | | | | | 
% 225.63/38.83  | | | | | | | Case 1:
% 225.63/38.83  | | | | | | | | 
% 225.63/38.83  | | | | | | | |   (54)   ~ (all_36_2 = e1)
% 225.63/38.83  | | | | | | | | 
% 225.63/38.83  | | | | | | | | REDUCE: (22), (54) imply:
% 225.63/38.83  | | | | | | | |   (55)  $false
% 225.63/38.83  | | | | | | | | 
% 225.63/38.83  | | | | | | | | CLOSE: (55) is inconsistent.
% 225.63/38.83  | | | | | | | | 
% 225.63/38.83  | | | | | | | Case 2:
% 225.63/38.83  | | | | | | | | 
% 225.63/38.83  | | | | | | | |   (56)  ( ~ (all_36_0 = e0) & op(all_36_1, e3) = all_36_0 &
% 225.63/38.83  | | | | | | | |           op(e3, e1) = all_36_1 & $i(all_36_0) & $i(all_36_1)) |
% 225.63/38.83  | | | | | | | |         ( ~ (all_36_1 = e2) & op(e3, e1) = all_36_1 &
% 225.63/38.83  | | | | | | | |           $i(all_36_1))
% 225.63/38.83  | | | | | | | | 
% 225.63/38.83  | | | | | | | | BETA: splitting (20) gives:
% 225.63/38.83  | | | | | | | | 
% 225.63/38.83  | | | | | | | | Case 1:
% 225.63/38.83  | | | | | | | | | 
% 225.63/38.83  | | | | | | | | |   (57)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 225.63/38.83  | | | | | | | | |           all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 225.63/38.83  | | | | | | | | |           op(all_52_3, all_52_3) = e2 & op(all_52_5, all_52_5)
% 225.63/38.83  | | | | | | | | |           = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3) =
% 225.63/38.83  | | | | | | | | |           all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) =
% 225.63/38.83  | | | | | | | | |           all_52_5 & op(e3, e0) = all_52_7 & $i(all_52_1) &
% 225.63/38.83  | | | | | | | | |           $i(all_52_3) & $i(all_52_5) & $i(all_52_7)) |
% 225.63/38.83  | | | | | | | | |         (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 225.63/38.83  | | | | | | | | |           all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 225.63/38.83  | | | | | | | | |           op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 225.63/38.83  | | | | | | | | |             all_52_13) = e1 & op(all_52_15, all_52_15) = e0 &
% 225.63/38.83  | | | | | | | | |           op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 225.63/38.83  | | | | | | | | |           op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 225.63/38.83  | | | | | | | | |           $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 225.63/38.83  | | | | | | | | |           $i(all_52_15))
% 225.63/38.83  | | | | | | | | | 
% 225.63/38.83  | | | | | | | | | BETA: splitting (57) gives:
% 225.63/38.83  | | | | | | | | | 
% 225.63/38.83  | | | | | | | | | Case 1:
% 225.63/38.83  | | | | | | | | | | 
% 225.63/38.83  | | | | | | | | | |   (58)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 225.63/38.83  | | | | | | | | | |         all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 225.63/38.83  | | | | | | | | | |         op(all_52_3, all_52_3) = e2 & op(all_52_5, all_52_5)
% 225.63/38.83  | | | | | | | | | |         = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3) =
% 225.63/38.83  | | | | | | | | | |         all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) =
% 225.63/38.83  | | | | | | | | | |         all_52_5 & op(e3, e0) = all_52_7 & $i(all_52_1) &
% 225.63/38.83  | | | | | | | | | |         $i(all_52_3) & $i(all_52_5) & $i(all_52_7)
% 225.63/38.83  | | | | | | | | | | 
% 225.63/38.83  | | | | | | | | | | REF_CLOSE: (3), (41), (43), (51), (58) are inconsistent by
% 225.63/38.83  | | | | | | | | | |            sub-proof #90.
% 225.63/38.83  | | | | | | | | | | 
% 225.63/38.83  | | | | | | | | | Case 2:
% 225.63/38.83  | | | | | | | | | | 
% 225.63/38.83  | | | | | | | | | |   (59)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 225.63/38.83  | | | | | | | | | |         all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 225.63/38.83  | | | | | | | | | |         op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 225.63/38.83  | | | | | | | | | |           all_52_13) = e1 & op(all_52_15, all_52_15) = e0 &
% 225.63/38.83  | | | | | | | | | |         op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 225.63/38.83  | | | | | | | | | |         op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 225.63/38.83  | | | | | | | | | |         $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 225.63/38.83  | | | | | | | | | |         $i(all_52_15)
% 225.63/38.83  | | | | | | | | | | 
% 225.63/38.83  | | | | | | | | | | ALPHA: (59) implies:
% 225.63/38.83  | | | | | | | | | |   (60)  op(e2, e3) = all_52_9
% 225.63/38.83  | | | | | | | | | |   (61)  op(all_52_9, all_52_9) = e3
% 225.63/38.83  | | | | | | | | | | 
% 225.63/38.83  | | | | | | | | | | BETA: splitting (17) gives:
% 225.63/38.83  | | | | | | | | | | 
% 225.63/38.83  | | | | | | | | | | Case 1:
% 225.63/38.83  | | | | | | | | | | | 
% 225.63/38.83  | | | | | | | | | | |   (62)   ~ (all_10_0 = e2) & op(all_10_1, e3) = all_10_0 &
% 225.63/38.83  | | | | | | | | | | |         op(e3, e1) = all_10_1 & $i(all_10_0) &
% 225.63/38.83  | | | | | | | | | | |         $i(all_10_1)
% 225.63/38.83  | | | | | | | | | | | 
% 225.63/38.83  | | | | | | | | | | | ALPHA: (62) implies:
% 225.63/38.83  | | | | | | | | | | |   (63)  op(e3, e1) = all_10_1
% 225.63/38.83  | | | | | | | | | | | 
% 225.63/38.83  | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (9), (14), (16), (37), (51), (56),
% 225.63/38.83  | | | | | | | | | | |            (60), (61), (63) are inconsistent by sub-proof
% 225.63/38.83  | | | | | | | | | | |            #21.
% 225.63/38.83  | | | | | | | | | | | 
% 225.63/38.83  | | | | | | | | | | Case 2:
% 225.63/38.83  | | | | | | | | | | | 
% 225.63/38.83  | | | | | | | | | | |   (64)   ~ (all_10_1 = e0) & op(e3, e1) = all_10_1 &
% 225.63/38.83  | | | | | | | | | | |         $i(all_10_1)
% 225.63/38.83  | | | | | | | | | | | 
% 225.63/38.83  | | | | | | | | | | | ALPHA: (64) implies:
% 225.63/38.83  | | | | | | | | | | |   (65)  op(e3, e1) = all_10_1
% 225.63/38.83  | | | | | | | | | | | 
% 225.63/38.84  | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (9), (14), (16), (37), (51), (56),
% 225.63/38.84  | | | | | | | | | | |            (60), (61), (65) are inconsistent by sub-proof
% 225.63/38.84  | | | | | | | | | | |            #21.
% 225.63/38.84  | | | | | | | | | | | 
% 225.63/38.84  | | | | | | | | | | End of split
% 225.63/38.84  | | | | | | | | | | 
% 225.63/38.84  | | | | | | | | | End of split
% 225.63/38.84  | | | | | | | | | 
% 225.63/38.84  | | | | | | | | Case 2:
% 225.63/38.84  | | | | | | | | | 
% 225.63/38.84  | | | | | | | | |   (66)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 225.63/38.84  | | | | | | | | |           all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 225.63/38.84  | | | | | | | | |           op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 225.63/38.84  | | | | | | | | |             all_52_21) = e1 & op(all_52_23, all_52_23) = e0 &
% 225.63/38.84  | | | | | | | | |           op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19 &
% 225.63/38.84  | | | | | | | | |           op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23 &
% 225.63/38.84  | | | | | | | | |           $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 225.63/38.84  | | | | | | | | |           $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 &
% 225.63/38.84  | | | | | | | | |           all_52_28 = e1 & all_52_30 = e0 & op(all_52_25,
% 225.63/38.84  | | | | | | | | |             all_52_25) = e3 & op(all_52_27, all_52_27) = e2 &
% 225.63/38.84  | | | | | | | | |           op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 225.63/38.84  | | | | | | | | |             all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0,
% 225.63/38.84  | | | | | | | | |             e2) = all_52_27 & op(e0, e1) = all_52_29 & op(e0,
% 225.63/38.84  | | | | | | | | |             e0) = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 225.63/38.84  | | | | | | | | |           $i(all_52_29) & $i(all_52_31))
% 225.63/38.84  | | | | | | | | | 
% 225.63/38.84  | | | | | | | | | BETA: splitting (66) gives:
% 225.63/38.84  | | | | | | | | | 
% 225.63/38.84  | | | | | | | | | Case 1:
% 225.63/38.84  | | | | | | | | | | 
% 225.63/38.84  | | | | | | | | | |   (67)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 225.63/38.84  | | | | | | | | | |         all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 225.63/38.84  | | | | | | | | | |         op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 225.63/38.84  | | | | | | | | | |           all_52_21) = e1 & op(all_52_23, all_52_23) = e0 &
% 225.63/38.84  | | | | | | | | | |         op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19 &
% 225.63/38.84  | | | | | | | | | |         op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23 &
% 225.63/38.84  | | | | | | | | | |         $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 225.63/38.84  | | | | | | | | | |         $i(all_52_23)
% 225.63/38.84  | | | | | | | | | | 
% 225.63/38.84  | | | | | | | | | | REF_CLOSE: (3), (40), (43), (47), (67) are inconsistent by
% 225.63/38.84  | | | | | | | | | |            sub-proof #80.
% 225.63/38.84  | | | | | | | | | | 
% 225.63/38.84  | | | | | | | | | Case 2:
% 225.63/38.84  | | | | | | | | | | 
% 225.63/38.84  | | | | | | | | | |   (68)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 225.63/38.84  | | | | | | | | | |         all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 225.63/38.84  | | | | | | | | | |         op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 225.63/38.84  | | | | | | | | | |           all_52_29) = e1 & op(all_52_31, all_52_31) = e0 &
% 225.63/38.84  | | | | | | | | | |         op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 225.63/38.84  | | | | | | | | | |         op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 &
% 225.63/38.84  | | | | | | | | | |         $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 225.63/38.84  | | | | | | | | | |         $i(all_52_31)
% 225.63/38.84  | | | | | | | | | | 
% 225.63/38.84  | | | | | | | | | | ALPHA: (68) implies:
% 225.63/38.84  | | | | | | | | | |   (69)  op(e0, e0) = all_52_31
% 225.63/38.84  | | | | | | | | | |   (70)  op(all_52_31, all_52_31) = e0
% 225.63/38.84  | | | | | | | | | | 
% 225.63/38.84  | | | | | | | | | | BETA: splitting (17) gives:
% 225.63/38.84  | | | | | | | | | | 
% 225.63/38.84  | | | | | | | | | | Case 1:
% 225.63/38.84  | | | | | | | | | | | 
% 225.63/38.84  | | | | | | | | | | | 
% 225.63/38.84  | | | | | | | | | | | GROUND_INST: instantiating (3) with e2, all_52_31, e0, e0,
% 225.63/38.84  | | | | | | | | | | |              simplifying with (25), (69) gives:
% 225.63/38.84  | | | | | | | | | | |   (71)  all_52_31 = e2
% 225.63/38.84  | | | | | | | | | | | 
% 225.63/38.84  | | | | | | | | | | | REDUCE: (70), (71) imply:
% 225.63/38.84  | | | | | | | | | | |   (72)  op(e2, e2) = e0
% 225.63/38.84  | | | | | | | | | | | 
% 225.63/38.84  | | | | | | | | | | | REF_CLOSE: (3), (42), (43), (72) are inconsistent by
% 225.63/38.84  | | | | | | | | | | |            sub-proof #2472.
% 225.63/38.84  | | | | | | | | | | | 
% 225.63/38.84  | | | | | | | | | | Case 2:
% 225.63/38.84  | | | | | | | | | | | 
% 225.63/38.84  | | | | | | | | | | |   (73)   ~ (all_10_1 = e0) & op(e3, e1) = all_10_1 &
% 225.63/38.84  | | | | | | | | | | |         $i(all_10_1)
% 225.63/38.84  | | | | | | | | | | | 
% 225.63/38.84  | | | | | | | | | | | ALPHA: (73) implies:
% 225.63/38.84  | | | | | | | | | | |   (74)   ~ (all_10_1 = e0)
% 225.63/38.84  | | | | | | | | | | |   (75)  op(e3, e1) = all_10_1
% 225.63/38.84  | | | | | | | | | | | 
% 225.63/38.84  | | | | | | | | | | | GROUND_INST: instantiating (3) with e2, all_52_31, e0, e0,
% 225.63/38.84  | | | | | | | | | | |              simplifying with (25), (69) gives:
% 225.63/38.84  | | | | | | | | | | |   (76)  all_52_31 = e2
% 225.63/38.84  | | | | | | | | | | | 
% 225.63/38.84  | | | | | | | | | | | GROUND_INST: instantiating (3) with e2, all_10_1, e1, e3,
% 225.63/38.84  | | | | | | | | | | |              simplifying with (51), (75) gives:
% 225.63/38.84  | | | | | | | | | | |   (77)  all_10_1 = e2
% 225.63/38.84  | | | | | | | | | | | 
% 225.63/38.84  | | | | | | | | | | | REDUCE: (70), (76) imply:
% 225.63/38.84  | | | | | | | | | | |   (78)  op(e2, e2) = e0
% 225.63/38.84  | | | | | | | | | | | 
% 225.63/38.84  | | | | | | | | | | | REF_CLOSE: (3), (42), (43), (78) are inconsistent by
% 225.63/38.84  | | | | | | | | | | |            sub-proof #2472.
% 225.63/38.84  | | | | | | | | | | | 
% 225.63/38.84  | | | | | | | | | | End of split
% 225.63/38.84  | | | | | | | | | | 
% 225.63/38.84  | | | | | | | | | End of split
% 225.63/38.84  | | | | | | | | | 
% 225.63/38.84  | | | | | | | | End of split
% 225.63/38.84  | | | | | | | | 
% 225.63/38.84  | | | | | | | End of split
% 225.63/38.84  | | | | | | | 
% 225.63/38.84  | | | | | | Case 2:
% 225.63/38.84  | | | | | | | 
% 225.63/38.84  | | | | | | |   (79)  all_57_9 = e2 & op(e3, e0) = e2
% 225.63/38.84  | | | | | | | 
% 225.63/38.84  | | | | | | | ALPHA: (79) implies:
% 225.63/38.84  | | | | | | |   (80)  op(e3, e0) = e2
% 225.63/38.84  | | | | | | | 
% 225.63/38.84  | | | | | | | REF_CLOSE: (3), (27), (30), (80) are inconsistent by sub-proof
% 225.63/38.84  | | | | | | |            #2331.
% 225.63/38.84  | | | | | | | 
% 225.63/38.84  | | | | | | End of split
% 225.63/38.84  | | | | | | 
% 225.63/38.84  | | | | | End of split
% 225.63/38.84  | | | | | 
% 225.63/38.84  | | | | Case 2:
% 225.63/38.84  | | | | | 
% 225.63/38.84  | | | | |   (81)  all_57_12 = e2 & op(e0, e3) = e2
% 225.63/38.84  | | | | | 
% 225.63/38.84  | | | | | ALPHA: (81) implies:
% 225.63/38.84  | | | | |   (82)  op(e0, e3) = e2
% 225.63/38.84  | | | | | 
% 225.63/38.84  | | | | | REF_CLOSE: (3), (13), (15), (82) are inconsistent by sub-proof #1980.
% 225.63/38.84  | | | | | 
% 225.63/38.84  | | | | End of split
% 225.63/38.84  | | | | 
% 225.63/38.84  | | | End of split
% 225.63/38.84  | | | 
% 225.63/38.84  | | Case 2:
% 225.63/38.84  | | | 
% 225.63/38.84  | | |   (83)  all_55_5 = e1 | all_55_5 = e0
% 225.63/38.84  | | | 
% 225.63/38.84  | | | REF_CLOSE: (5), (10), (24), (83) are inconsistent by sub-proof #1857.
% 225.63/38.84  | | | 
% 225.63/38.84  | | End of split
% 225.63/38.84  | | 
% 225.63/38.84  | End of split
% 225.63/38.84  | 
% 225.63/38.84  End of proof
% 225.63/38.84  
% 225.63/38.84  Sub-proof #21 shows that the following formulas are inconsistent:
% 225.63/38.84  ----------------------------------------------------------------
% 225.63/38.84    (1)  ( ~ (all_36_0 = e0) & op(all_36_1, e3) = all_36_0 & op(e3, e1) = all_36_1
% 225.63/38.84           & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e2) & op(e3, e1) =
% 225.63/38.84           all_36_1 & $i(all_36_1))
% 225.63/38.84    (2)  op(e3, e3) = e1
% 225.63/38.84    (3)  op(e2, e3) = all_53_1
% 225.63/38.84    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 225.63/38.84           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 225.63/38.84    (5)  op(e3, e1) = all_10_1
% 225.63/38.84    (6)  op(e2, e3) = all_52_9
% 225.63/38.84    (7)  op(e3, e1) = e2
% 225.63/38.84    (8)  all_55_4 = all_53_1
% 225.63/38.84    (9)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 225.63/38.84    (10)   ~ (all_53_1 = e1)
% 225.63/38.84    (11)  op(all_52_9, all_52_9) = e3
% 225.63/38.84    (12)   ~ (all_53_1 = e2)
% 225.63/38.84  
% 225.63/38.84  Begin of proof
% 225.63/38.84  | 
% 225.63/38.84  | GROUND_INST: instantiating (4) with all_53_1, all_52_9, e3, e2, simplifying
% 225.63/38.84  |              with (3), (6) gives:
% 225.63/38.84  |   (13)  all_53_1 = all_52_9
% 225.63/38.84  | 
% 225.63/38.84  | GROUND_INST: instantiating (4) with e2, all_10_1, e1, e3, simplifying with
% 225.63/38.84  |              (5), (7) gives:
% 225.63/38.84  |   (14)  all_10_1 = e2
% 225.63/38.84  | 
% 225.63/38.84  | COMBINE_EQS: (8), (13) imply:
% 225.63/38.84  |   (15)  all_55_4 = all_52_9
% 225.63/38.84  | 
% 225.63/38.84  | REDUCE: (12), (13) imply:
% 225.63/38.84  |   (16)   ~ (all_52_9 = e2)
% 225.63/38.84  | 
% 225.63/38.84  | REDUCE: (10), (13) imply:
% 225.63/38.84  |   (17)   ~ (all_52_9 = e1)
% 225.63/38.84  | 
% 225.63/38.84  | BETA: splitting (1) gives:
% 225.63/38.84  | 
% 225.63/38.84  | Case 1:
% 225.63/38.84  | | 
% 225.63/38.84  | |   (18)   ~ (all_36_0 = e0) & op(all_36_1, e3) = all_36_0 & op(e3, e1) =
% 225.63/38.84  | |         all_36_1 & $i(all_36_0) & $i(all_36_1)
% 225.63/38.84  | | 
% 225.63/38.84  | | ALPHA: (18) implies:
% 225.63/38.84  | |   (19)   ~ (all_36_0 = e0)
% 225.63/38.84  | |   (20)  op(e3, e1) = all_36_1
% 225.63/38.84  | |   (21)  op(all_36_1, e3) = all_36_0
% 225.63/38.84  | | 
% 225.63/38.84  | | GROUND_INST: instantiating (4) with e2, all_36_1, e1, e3, simplifying with
% 225.63/38.84  | |              (7), (20) gives:
% 225.63/38.84  | |   (22)  all_36_1 = e2
% 225.63/38.84  | | 
% 225.63/38.84  | | REDUCE: (21), (22) imply:
% 225.63/38.84  | |   (23)  op(e2, e3) = all_36_0
% 225.63/38.84  | | 
% 225.63/38.84  | | GROUND_INST: instantiating (4) with all_52_9, all_36_0, e3, e2, simplifying
% 225.63/38.84  | |              with (6), (23) gives:
% 225.63/38.84  | |   (24)  all_52_9 = all_36_0
% 225.63/38.84  | | 
% 225.63/38.84  | | COMBINE_EQS: (15), (24) imply:
% 225.63/38.84  | |   (25)  all_55_4 = all_36_0
% 225.63/38.84  | | 
% 225.63/38.84  | | REDUCE: (16), (24) imply:
% 225.63/38.84  | |   (26)   ~ (all_36_0 = e2)
% 225.63/38.84  | | 
% 225.63/38.84  | | REDUCE: (17), (24) imply:
% 225.63/38.84  | |   (27)   ~ (all_36_0 = e1)
% 225.63/38.84  | | 
% 225.63/38.84  | | REDUCE: (11), (24) imply:
% 225.63/38.84  | |   (28)  op(all_36_0, all_36_0) = e3
% 225.63/38.84  | | 
% 225.63/38.84  | | BETA: splitting (9) gives:
% 225.63/38.84  | | 
% 225.63/38.84  | | Case 1:
% 225.63/38.84  | | | 
% 225.63/38.84  | | |   (29)  all_55_4 = e3
% 225.63/38.84  | | | 
% 225.63/38.84  | | | COMBINE_EQS: (25), (29) imply:
% 225.63/38.84  | | |   (30)  all_36_0 = e3
% 225.63/38.84  | | | 
% 225.63/38.84  | | | REDUCE: (27), (30) imply:
% 225.63/38.84  | | |   (31)   ~ (e3 = e1)
% 225.63/38.84  | | | 
% 225.63/38.84  | | | REDUCE: (28), (30) imply:
% 225.63/38.84  | | |   (32)  op(e3, e3) = e3
% 225.63/38.84  | | | 
% 225.63/38.84  | | | REF_CLOSE: (2), (4), (31), (32) are inconsistent by sub-proof #2495.
% 225.63/38.84  | | | 
% 225.63/38.84  | | Case 2:
% 225.63/38.84  | | | 
% 225.63/38.84  | | |   (33)  all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 225.63/38.84  | | | 
% 225.63/38.84  | | | BETA: splitting (33) gives:
% 225.63/38.84  | | | 
% 225.63/38.84  | | | Case 1:
% 225.63/38.84  | | | | 
% 225.63/38.84  | | | |   (34)  all_55_4 = e2
% 225.63/38.84  | | | | 
% 225.63/38.84  | | | | COMBINE_EQS: (25), (34) imply:
% 225.63/38.84  | | | |   (35)  all_36_0 = e2
% 225.63/38.84  | | | | 
% 225.63/38.84  | | | | REDUCE: (26), (35) imply:
% 225.63/38.84  | | | |   (36)  $false
% 225.63/38.84  | | | | 
% 225.63/38.84  | | | | CLOSE: (36) is inconsistent.
% 225.63/38.84  | | | | 
% 225.63/38.84  | | | Case 2:
% 225.63/38.84  | | | | 
% 225.63/38.84  | | | |   (37)  all_55_4 = e1 | all_55_4 = e0
% 225.63/38.84  | | | | 
% 225.63/38.84  | | | | BETA: splitting (37) gives:
% 225.63/38.84  | | | | 
% 225.63/38.84  | | | | Case 1:
% 225.63/38.84  | | | | | 
% 225.63/38.84  | | | | |   (38)  all_55_4 = e1
% 225.63/38.84  | | | | | 
% 225.63/38.84  | | | | | COMBINE_EQS: (25), (38) imply:
% 225.63/38.84  | | | | |   (39)  all_36_0 = e1
% 225.63/38.84  | | | | | 
% 225.63/38.84  | | | | | REDUCE: (27), (39) imply:
% 225.63/38.84  | | | | |   (40)  $false
% 225.63/38.84  | | | | | 
% 225.63/38.84  | | | | | CLOSE: (40) is inconsistent.
% 225.63/38.84  | | | | | 
% 225.63/38.84  | | | | Case 2:
% 225.63/38.84  | | | | | 
% 225.63/38.84  | | | | |   (41)  all_55_4 = e0
% 225.63/38.84  | | | | | 
% 225.63/38.84  | | | | | COMBINE_EQS: (25), (41) imply:
% 225.63/38.84  | | | | |   (42)  all_36_0 = e0
% 225.63/38.84  | | | | | 
% 225.63/38.84  | | | | | REDUCE: (19), (42) imply:
% 225.63/38.84  | | | | |   (43)  $false
% 225.63/38.84  | | | | | 
% 225.63/38.84  | | | | | CLOSE: (43) is inconsistent.
% 225.63/38.84  | | | | | 
% 225.63/38.84  | | | | End of split
% 225.63/38.84  | | | | 
% 225.63/38.84  | | | End of split
% 225.63/38.84  | | | 
% 225.63/38.84  | | End of split
% 225.63/38.84  | | 
% 225.63/38.84  | Case 2:
% 225.63/38.84  | | 
% 225.63/38.84  | |   (44)   ~ (all_36_1 = e2) & op(e3, e1) = all_36_1 & $i(all_36_1)
% 225.63/38.84  | | 
% 225.63/38.84  | | REF_CLOSE: (4), (7), (44) are inconsistent by sub-proof #307.
% 225.63/38.84  | | 
% 225.63/38.84  | End of split
% 225.63/38.84  | 
% 225.63/38.84  End of proof
% 225.63/38.84  
% 225.63/38.84  Sub-proof #22 shows that the following formulas are inconsistent:
% 225.63/38.84  ----------------------------------------------------------------
% 225.63/38.84    (1)  op(e0, e1) = all_53_11
% 225.63/38.84    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 225.63/38.84    (3)  op(e2, e3) = all_53_1
% 225.63/38.84    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 225.63/38.84         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 225.63/38.84    (5)   ~ (e3 = e1)
% 225.63/38.84    (6)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 225.63/38.84         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 225.63/38.84    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 225.63/38.84           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 225.63/38.84    (8)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 225.63/38.84         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 225.63/38.84    (9)   ~ (all_6_2 = e3)
% 225.63/38.84    (10)  op(e1, e1) = all_6_2
% 225.63/38.84    (11)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 225.63/38.84          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 225.63/38.84    (12)   ~ (all_53_13 = e2)
% 225.63/38.84    (13)   ~ (all_53_7 = e2)
% 225.63/38.84    (14)  op(e0, e1) = e0
% 225.63/38.84    (15)  op(e2, e2) = e0
% 225.63/38.84    (16)   ~ (all_53_9 = all_53_11)
% 225.63/38.84    (17)   ~ (all_53_9 = all_6_2)
% 225.63/38.84    (18)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 225.63/38.84          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 225.63/38.84    (19)   ~ (all_53_14 = all_6_2)
% 225.63/38.84    (20)   ~ (all_8_2 = e3)
% 225.63/38.84    (21)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 225.63/38.84          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 225.63/38.84    (22)   ~ (e3 = e2)
% 225.63/38.84    (23)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 225.63/38.84    (24)  op(e1, e0) = all_53_14
% 225.63/38.84    (25)  all_55_7 = e3 | all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 225.63/38.84    (26)   ~ (e3 = e0)
% 225.63/38.84    (27)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 225.63/38.84          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 225.63/38.84    (28)  op(e0, e3) = all_53_3
% 225.63/38.84    (29)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 225.63/38.84          | (all_57_14 = e0 & op(e0, e1) = e0)
% 225.63/38.84    (30)   ~ (all_53_9 = all_53_13)
% 225.63/38.84    (31)   ~ (all_53_3 = e2)
% 225.63/38.84    (32)  op(e3, e3) = e0
% 225.63/38.84    (33)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 225.63/38.84          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 225.63/38.84            e1)
% 225.63/38.84    (34)  all_57_11 = e0
% 225.63/38.84    (35)  all_55_6 = all_53_9
% 225.63/38.84    (36)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 225.63/38.84            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 225.63/38.84            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 225.63/38.84            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 225.63/38.84              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 225.63/38.84            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 225.63/38.84            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 225.63/38.84              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 225.63/38.84              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 225.63/38.84            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 225.63/38.84            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 225.63/38.84            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 225.63/38.84              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 225.63/38.84              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 225.63/38.84            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 225.63/38.84              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 225.63/38.84            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 225.63/38.84            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 225.63/38.84              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 225.63/38.84              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 225.63/38.84            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 225.63/38.84            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 225.63/38.84    (37)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 225.63/38.84          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 225.63/38.84    (38)   ~ (e1 = e0)
% 225.63/38.84    (39)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 225.63/38.84            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 225.63/38.84              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 225.63/38.84    (40)   ~ (all_53_3 = all_53_11)
% 225.63/38.84    (41)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 225.63/38.84          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 225.63/38.84    (42)   ~ (all_53_7 = all_53_11)
% 225.63/38.84    (43)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 225.63/38.84          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 225.63/38.84            e3)
% 225.63/38.84    (44)  op(e2, e2) = all_8_2
% 225.63/38.84    (45)  op(e0, e2) = all_53_7
% 225.63/38.84    (46)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 225.63/38.84          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 225.63/38.84            e2)
% 225.63/38.84    (47)  all_55_10 = all_6_2
% 225.63/38.84    (48)   ~ (all_53_6 = all_6_2)
% 225.63/38.84    (49)  op(e2, e0) = all_53_13
% 225.63/38.84    (50)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 225.63/38.84          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 225.63/38.84    (51)  all_38_2 = all_6_2
% 225.63/38.84    (52)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 225.63/38.84          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 225.63/38.84    (53)   ~ (all_53_13 = all_53_14)
% 225.63/38.84    (54)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 225.63/38.84          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 225.63/38.84    (55)   ~ (e2 = e1)
% 225.63/38.84    (56)  op(e0, e0) = e2
% 225.63/38.84    (57)  op(e2, e1) = all_53_9
% 225.63/38.84    (58)  op(e1, e2) = all_53_6
% 225.63/38.84    (59)  op(e1, e0) = e0
% 225.63/38.84    (60)   ~ (all_53_14 = e2)
% 225.63/38.84    (61)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 225.63/38.84          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 225.63/38.84    (62)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 225.63/38.84          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 225.63/38.84    (63)  all_57_14 = e0
% 225.63/38.84    (64)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 225.63/38.84          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 226.12/38.84    (65)  all_55_7 = all_53_13
% 226.12/38.84  
% 226.12/38.84  Begin of proof
% 226.12/38.84  | 
% 226.12/38.84  | GROUND_INST: instantiating (7) with all_53_11, e0, e1, e0, simplifying with
% 226.12/38.84  |              (1), (14) gives:
% 226.12/38.84  |   (66)  all_53_11 = e0
% 226.12/38.84  | 
% 226.12/38.84  | GROUND_INST: instantiating (7) with all_53_14, e0, e0, e1, simplifying with
% 226.12/38.84  |              (24), (59) gives:
% 226.12/38.84  |   (67)  all_53_14 = e0
% 226.12/38.84  | 
% 226.12/38.84  | REDUCE: (40), (66) imply:
% 226.12/38.84  |   (68)   ~ (all_53_3 = e0)
% 226.12/38.84  | 
% 226.12/38.84  | REDUCE: (42), (66) imply:
% 226.12/38.84  |   (69)   ~ (all_53_7 = e0)
% 226.12/38.84  | 
% 226.12/38.84  | REDUCE: (16), (66) imply:
% 226.12/38.84  |   (70)   ~ (all_53_9 = e0)
% 226.12/38.84  | 
% 226.12/38.84  | REDUCE: (53), (67) imply:
% 226.12/38.84  |   (71)   ~ (all_53_13 = e0)
% 226.12/38.84  | 
% 226.12/38.84  | REDUCE: (19), (67) imply:
% 226.12/38.84  |   (72)   ~ (all_6_2 = e0)
% 226.12/38.84  | 
% 226.12/38.84  | SIMP: (72) implies:
% 226.12/38.84  |   (73)   ~ (all_6_2 = e0)
% 226.12/38.84  | 
% 226.12/38.84  | REDUCE: (60), (67) imply:
% 226.12/38.84  |   (74)   ~ (e2 = e0)
% 226.12/38.84  | 
% 226.12/38.84  | SIMP: (74) implies:
% 226.12/38.84  |   (75)   ~ (e2 = e0)
% 226.12/38.84  | 
% 226.12/38.84  | BETA: splitting (36) gives:
% 226.12/38.84  | 
% 226.12/38.84  | Case 1:
% 226.12/38.84  | | 
% 226.12/38.84  | |   (76)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 226.12/38.84  | |           op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 226.12/38.84  | |           op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3,
% 226.12/38.84  | |             e3) = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 &
% 226.12/38.84  | |           op(e3, e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5)
% 226.12/38.84  | |           & $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1
% 226.12/38.84  | |           & all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 226.12/38.84  | |             all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 226.12/38.84  | |             all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11
% 226.12/38.84  | |           & op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 226.12/38.84  | |           $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 226.12/38.84  | | 
% 226.12/38.84  | | BETA: splitting (76) gives:
% 226.12/38.84  | | 
% 226.12/38.84  | | Case 1:
% 226.12/38.84  | | | 
% 226.12/38.84  | | |   (77)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 226.12/38.84  | | |         op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 226.12/38.84  | | |         op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3,
% 226.12/38.84  | | |           e3) = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 &
% 226.12/38.84  | | |         op(e3, e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5)
% 226.12/38.84  | | |         & $i(all_52_7)
% 226.12/38.84  | | | 
% 226.12/38.84  | | | ALPHA: (77) implies:
% 226.12/38.84  | | |   (78)  op(e3, e3) = all_52_1
% 226.12/38.84  | | |   (79)  op(all_52_1, all_52_1) = e3
% 226.12/38.84  | | | 
% 226.12/38.84  | | | REF_CLOSE: (7), (22), (32), (56), (78), (79) are inconsistent by sub-proof
% 226.12/38.84  | | |            #53.
% 226.12/38.84  | | | 
% 226.12/38.84  | | Case 2:
% 226.12/38.84  | | | 
% 226.12/38.84  | | |   (80)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0 &
% 226.12/38.84  | | |         op(all_52_9, all_52_9) = e3 & op(all_52_11, all_52_11) = e2 &
% 226.12/38.84  | | |         op(all_52_13, all_52_13) = e1 & op(all_52_15, all_52_15) = e0 &
% 226.12/38.84  | | |         op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 & op(e2, e1) =
% 226.12/38.84  | | |         all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) & $i(all_52_11)
% 226.12/38.84  | | |         & $i(all_52_13) & $i(all_52_15)
% 226.12/38.84  | | | 
% 226.12/38.84  | | | ALPHA: (80) implies:
% 226.12/38.84  | | |   (81)  op(e2, e0) = all_52_15
% 226.12/38.84  | | |   (82)  op(e2, e1) = all_52_13
% 226.12/38.84  | | |   (83)  op(e2, e2) = all_52_11
% 226.12/38.84  | | |   (84)  op(e2, e3) = all_52_9
% 226.12/38.85  | | |   (85)  op(all_52_15, all_52_15) = e0
% 226.12/38.85  | | |   (86)  op(all_52_13, all_52_13) = e1
% 226.12/38.85  | | |   (87)  op(all_52_11, all_52_11) = e2
% 226.12/38.85  | | |   (88)  op(all_52_9, all_52_9) = e3
% 226.12/38.85  | | | 
% 226.12/38.85  | | | GROUND_INST: instantiating (7) with all_53_13, all_52_15, e0, e2,
% 226.12/38.85  | | |              simplifying with (49), (81) gives:
% 226.12/38.85  | | |   (89)  all_53_13 = all_52_15
% 226.12/38.85  | | | 
% 226.12/38.85  | | | GROUND_INST: instantiating (7) with all_53_9, all_52_13, e1, e2,
% 226.12/38.85  | | |              simplifying with (57), (82) gives:
% 226.12/38.85  | | |   (90)  all_53_9 = all_52_13
% 226.12/38.85  | | | 
% 226.12/38.85  | | | GROUND_INST: instantiating (7) with e0, all_52_11, e2, e2, simplifying
% 226.12/38.85  | | |              with (15), (83) gives:
% 226.12/38.85  | | |   (91)  all_52_11 = e0
% 226.12/38.85  | | | 
% 226.12/38.85  | | | GROUND_INST: instantiating (7) with all_53_1, all_52_9, e3, e2,
% 226.12/38.85  | | |              simplifying with (3), (84) gives:
% 226.12/38.85  | | |   (92)  all_53_1 = all_52_9
% 226.12/38.85  | | | 
% 226.12/38.85  | | | COMBINE_EQS: (65), (89) imply:
% 226.12/38.85  | | |   (93)  all_55_7 = all_52_15
% 226.12/38.85  | | | 
% 226.12/38.85  | | | COMBINE_EQS: (35), (90) imply:
% 226.12/38.85  | | |   (94)  all_55_6 = all_52_13
% 226.12/38.85  | | | 
% 226.12/38.85  | | | REDUCE: (30), (89), (90) imply:
% 226.12/38.85  | | |   (95)   ~ (all_52_13 = all_52_15)
% 226.12/38.85  | | | 
% 226.12/38.85  | | | REDUCE: (17), (90) imply:
% 226.12/38.85  | | |   (96)   ~ (all_52_13 = all_6_2)
% 226.12/38.85  | | | 
% 226.12/38.85  | | | REDUCE: (70), (90) imply:
% 226.12/38.85  | | |   (97)   ~ (all_52_13 = e0)
% 226.12/38.85  | | | 
% 226.12/38.85  | | | REDUCE: (12), (89) imply:
% 226.12/38.85  | | |   (98)   ~ (all_52_15 = e2)
% 226.12/38.85  | | | 
% 226.12/38.85  | | | REDUCE: (71), (89) imply:
% 226.12/38.85  | | |   (99)   ~ (all_52_15 = e0)
% 226.12/38.85  | | | 
% 226.12/38.85  | | | BETA: splitting (39) gives:
% 226.12/38.85  | | | 
% 226.12/38.85  | | | Case 1:
% 226.12/38.85  | | | | 
% 226.12/38.85  | | | |   (100)   ~ (all_38_2 = e2)
% 226.12/38.85  | | | | 
% 226.12/38.85  | | | | REDUCE: (51), (100) imply:
% 226.12/38.85  | | | |   (101)   ~ (all_6_2 = e2)
% 226.12/38.85  | | | | 
% 226.12/38.85  | | | | BETA: splitting (2) gives:
% 226.12/38.85  | | | | 
% 226.12/38.85  | | | | Case 1:
% 226.12/38.85  | | | | | 
% 226.12/38.85  | | | | |   (102)  all_55_10 = e3
% 226.12/38.85  | | | | | 
% 226.12/38.85  | | | | | REF_CLOSE: (9), (47), (102) are inconsistent by sub-proof #2500.
% 226.12/38.85  | | | | | 
% 226.12/38.85  | | | | Case 2:
% 226.12/38.85  | | | | | 
% 226.12/38.85  | | | | |   (103)  all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 226.12/38.85  | | | | | 
% 226.12/38.85  | | | | | BETA: splitting (103) gives:
% 226.12/38.85  | | | | | 
% 226.12/38.85  | | | | | Case 1:
% 226.12/38.85  | | | | | | 
% 226.12/38.85  | | | | | |   (104)  all_55_10 = e2
% 226.12/38.85  | | | | | | 
% 226.12/38.85  | | | | | | REF_CLOSE: (47), (101), (104) are inconsistent by sub-proof #2499.
% 226.12/38.85  | | | | | | 
% 226.12/38.85  | | | | | Case 2:
% 226.12/38.85  | | | | | | 
% 226.12/38.85  | | | | | |   (105)  all_55_10 = e1 | all_55_10 = e0
% 226.12/38.85  | | | | | | 
% 226.12/38.85  | | | | | | BETA: splitting (105) gives:
% 226.12/38.85  | | | | | | 
% 226.12/38.85  | | | | | | Case 1:
% 226.12/38.85  | | | | | | | 
% 226.12/38.85  | | | | | | |   (106)  all_55_10 = e1
% 226.12/38.85  | | | | | | | 
% 226.12/38.85  | | | | | | | COMBINE_EQS: (47), (106) imply:
% 226.12/38.85  | | | | | | |   (107)  all_6_2 = e1
% 226.12/38.85  | | | | | | | 
% 226.12/38.85  | | | | | | | SIMP: (107) implies:
% 226.12/38.85  | | | | | | |   (108)  all_6_2 = e1
% 226.12/38.85  | | | | | | | 
% 226.12/38.85  | | | | | | | REDUCE: (96), (108) imply:
% 226.12/38.85  | | | | | | |   (109)   ~ (all_52_13 = e1)
% 226.12/38.85  | | | | | | | 
% 226.12/38.85  | | | | | | | REDUCE: (10), (108) imply:
% 226.12/38.85  | | | | | | |   (110)  op(e1, e1) = e1
% 226.12/38.85  | | | | | | | 
% 226.12/38.85  | | | | | | | BETA: splitting (25) gives:
% 226.12/38.85  | | | | | | | 
% 226.12/38.85  | | | | | | | Case 1:
% 226.12/38.85  | | | | | | | | 
% 226.12/38.85  | | | | | | | |   (111)  all_55_7 = e3
% 226.12/38.85  | | | | | | | | 
% 226.12/38.85  | | | | | | | | COMBINE_EQS: (93), (111) imply:
% 226.12/38.85  | | | | | | | |   (112)  all_52_15 = e3
% 226.12/38.85  | | | | | | | | 
% 226.12/38.85  | | | | | | | | SIMP: (112) implies:
% 226.12/38.85  | | | | | | | |   (113)  all_52_15 = e3
% 226.12/38.85  | | | | | | | | 
% 226.12/38.85  | | | | | | | | REDUCE: (95), (113) imply:
% 226.12/38.85  | | | | | | | |   (114)   ~ (all_52_13 = e3)
% 226.12/38.85  | | | | | | | | 
% 226.12/38.85  | | | | | | | | REF_CLOSE: (7), (15), (23), (38), (86), (94), (97), (109), (114)
% 226.12/38.85  | | | | | | | |            are inconsistent by sub-proof #24.
% 226.12/38.85  | | | | | | | | 
% 226.12/38.85  | | | | | | | Case 2:
% 226.12/38.85  | | | | | | | | 
% 226.12/38.85  | | | | | | | |   (115)  all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 226.12/38.85  | | | | | | | | 
% 226.12/38.85  | | | | | | | | REF_CLOSE: (7), (85), (93), (98), (99), (110), (115) are
% 226.12/38.85  | | | | | | | |            inconsistent by sub-proof #89.
% 226.12/38.85  | | | | | | | | 
% 226.12/38.85  | | | | | | | End of split
% 226.12/38.85  | | | | | | | 
% 226.12/38.85  | | | | | | Case 2:
% 226.12/38.85  | | | | | | | 
% 226.12/38.85  | | | | | | |   (116)  all_55_10 = e0
% 226.12/38.85  | | | | | | | 
% 226.12/38.85  | | | | | | | REF_CLOSE: (47), (73), (116) are inconsistent by sub-proof #2118.
% 226.12/38.85  | | | | | | | 
% 226.12/38.85  | | | | | | End of split
% 226.12/38.85  | | | | | | 
% 226.12/38.85  | | | | | End of split
% 226.12/38.85  | | | | | 
% 226.12/38.85  | | | | End of split
% 226.12/38.85  | | | | 
% 226.12/38.85  | | | Case 2:
% 226.12/38.85  | | | | 
% 226.12/38.85  | | | |   (117)  all_38_2 = e2
% 226.12/38.85  | | | | 
% 226.12/38.85  | | | | COMBINE_EQS: (51), (117) imply:
% 226.12/38.85  | | | |   (118)  all_6_2 = e2
% 226.12/38.85  | | | | 
% 226.12/38.85  | | | | SIMP: (118) implies:
% 226.12/38.85  | | | |   (119)  all_6_2 = e2
% 226.12/38.85  | | | | 
% 226.12/38.85  | | | | REDUCE: (48), (119) imply:
% 226.12/38.85  | | | |   (120)   ~ (all_53_6 = e2)
% 226.12/38.85  | | | | 
% 226.12/38.85  | | | | REDUCE: (9), (119) imply:
% 226.12/38.85  | | | |   (121)   ~ (e3 = e2)
% 226.12/38.85  | | | | 
% 226.12/38.85  | | | | REDUCE: (10), (119) imply:
% 226.12/38.85  | | | |   (122)  op(e1, e1) = e2
% 226.12/38.85  | | | | 
% 226.12/38.85  | | | | BETA: splitting (4) gives:
% 226.12/38.85  | | | | 
% 226.12/38.85  | | | | Case 1:
% 226.12/38.85  | | | | | 
% 226.12/38.85  | | | | |   (123)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2,
% 226.12/38.85  | | | | |              e2) = e2)
% 226.12/38.85  | | | | | 
% 226.12/38.85  | | | | | BETA: splitting (123) gives:
% 226.12/38.85  | | | | | 
% 226.12/38.85  | | | | | Case 1:
% 226.12/38.85  | | | | | | 
% 226.12/38.85  | | | | | |   (124)  all_57_1 = e2 & op(e3, e2) = e2
% 226.12/38.85  | | | | | | 
% 226.12/38.85  | | | | | | ALPHA: (124) implies:
% 226.12/38.85  | | | | | |   (125)  all_57_1 = e2
% 226.12/38.85  | | | | | |   (126)  op(e3, e2) = e2
% 226.12/38.85  | | | | | | 
% 226.12/38.85  | | | | | | BETA: splitting (52) gives:
% 226.12/38.85  | | | | | | 
% 226.12/38.85  | | | | | | Case 1:
% 226.12/38.85  | | | | | | | 
% 226.12/38.85  | | | | | | |   (127)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 &
% 226.12/38.85  | | | | | | |            op(e2, e2) = e2)
% 226.12/38.85  | | | | | | | 
% 226.12/38.85  | | | | | | | BETA: splitting (127) gives:
% 226.12/38.85  | | | | | | | 
% 226.12/38.85  | | | | | | | Case 1:
% 226.12/38.85  | | | | | | | | 
% 226.12/38.85  | | | | | | | |   (128)  all_57_2 = e2 & op(e2, e3) = e2
% 226.12/38.85  | | | | | | | | 
% 226.12/38.85  | | | | | | | | ALPHA: (128) implies:
% 226.12/38.85  | | | | | | | |   (129)  op(e2, e3) = e2
% 226.12/38.85  | | | | | | | | 
% 226.12/38.85  | | | | | | | | GROUND_INST: instantiating (7) with all_52_9, e2, e3, e2,
% 226.12/38.85  | | | | | | | |              simplifying with (84), (129) gives:
% 226.12/38.85  | | | | | | | |   (130)  all_52_9 = e2
% 226.12/38.85  | | | | | | | | 
% 226.12/38.85  | | | | | | | | REDUCE: (88), (130) imply:
% 226.12/38.85  | | | | | | | |   (131)  op(e2, e2) = e3
% 226.12/38.85  | | | | | | | | 
% 226.12/38.85  | | | | | | | | REF_CLOSE: (7), (20), (44), (131) are inconsistent by sub-proof
% 226.12/38.85  | | | | | | | |            #140.
% 226.12/38.85  | | | | | | | | 
% 226.12/38.85  | | | | | | | Case 2:
% 226.12/38.85  | | | | | | | | 
% 226.12/38.85  | | | | | | | |   (132)  all_57_3 = e2 & op(e2, e2) = e2
% 226.12/38.85  | | | | | | | | 
% 226.12/38.85  | | | | | | | | ALPHA: (132) implies:
% 226.12/38.85  | | | | | | | |   (133)  op(e2, e2) = e2
% 226.12/38.85  | | | | | | | | 
% 226.12/38.85  | | | | | | | | REF_CLOSE: (7), (15), (75), (133) are inconsistent by sub-proof
% 226.12/38.85  | | | | | | | |            #2472.
% 226.12/38.85  | | | | | | | | 
% 226.12/38.85  | | | | | | | End of split
% 226.12/38.85  | | | | | | | 
% 226.12/38.85  | | | | | | Case 2:
% 226.12/38.85  | | | | | | | 
% 226.12/38.85  | | | | | | |   (134)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 &
% 226.12/38.85  | | | | | | |            op(e2, e0) = e2)
% 226.12/38.85  | | | | | | | 
% 226.12/38.85  | | | | | | | BETA: splitting (134) gives:
% 226.12/38.85  | | | | | | | 
% 226.12/38.85  | | | | | | | Case 1:
% 226.12/38.85  | | | | | | | | 
% 226.12/38.85  | | | | | | | |   (135)  all_57_5 = e2 & op(e2, e1) = e2
% 226.12/38.85  | | | | | | | | 
% 226.12/38.85  | | | | | | | | ALPHA: (135) implies:
% 226.12/38.85  | | | | | | | |   (136)  all_57_5 = e2
% 226.12/38.85  | | | | | | | | 
% 226.12/38.85  | | | | | | | | BETA: splitting (61) gives:
% 226.12/38.85  | | | | | | | | 
% 226.12/38.85  | | | | | | | | Case 1:
% 226.12/38.85  | | | | | | | | | 
% 226.12/38.85  | | | | | | | | |   (137)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 &
% 226.12/38.85  | | | | | | | | |            op(e2, e3) = e2)
% 226.12/38.85  | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | BETA: splitting (137) gives:
% 226.12/38.85  | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | Case 1:
% 226.12/38.85  | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | |   (138)  all_57_0 = e2 & op(e3, e3) = e2
% 226.12/38.85  | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | ALPHA: (138) implies:
% 226.12/38.85  | | | | | | | | | |   (139)  op(e3, e3) = e2
% 226.12/38.85  | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | REF_CLOSE: (5), (7), (11), (18), (22), (26), (37), (38),
% 226.12/38.85  | | | | | | | | | |            (55), (75), (125), (139) are inconsistent by
% 226.12/38.85  | | | | | | | | | |            sub-proof #1655.
% 226.12/38.85  | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | Case 2:
% 226.12/38.85  | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | |   (140)  all_57_2 = e2 & op(e2, e3) = e2
% 226.12/38.85  | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | ALPHA: (140) implies:
% 226.12/38.85  | | | | | | | | | |   (141)  all_57_2 = e2
% 226.12/38.85  | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | BETA: splitting (50) gives:
% 226.12/38.85  | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | Case 1:
% 226.12/38.85  | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | |   (142)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 226.12/38.85  | | | | | | | | | | |            & op(e2, e2) = e3)
% 226.12/38.85  | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | BETA: splitting (142) gives:
% 226.12/38.85  | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | Case 1:
% 226.12/38.85  | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | |   (143)  all_57_2 = e3 & op(e2, e3) = e3
% 226.12/38.85  | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | ALPHA: (143) implies:
% 226.12/38.85  | | | | | | | | | | | |   (144)  all_57_2 = e3
% 226.12/38.85  | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | REF_CLOSE: (22), (141), (144) are inconsistent by sub-proof
% 226.12/38.85  | | | | | | | | | | | |            #1800.
% 226.12/38.85  | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | Case 2:
% 226.12/38.85  | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | |   (145)  all_57_3 = e3 & op(e2, e2) = e3
% 226.12/38.85  | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | ALPHA: (145) implies:
% 226.12/38.85  | | | | | | | | | | | |   (146)  op(e2, e2) = e3
% 226.12/38.85  | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | REF_CLOSE: (7), (20), (44), (146) are inconsistent by
% 226.12/38.85  | | | | | | | | | | | |            sub-proof #140.
% 226.12/38.85  | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | End of split
% 226.12/38.85  | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | Case 2:
% 226.12/38.85  | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | |   (147)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 226.12/38.85  | | | | | | | | | | |            e3 & op(e2, e0) = e3)
% 226.12/38.85  | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | BETA: splitting (147) gives:
% 226.12/38.85  | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | Case 1:
% 226.12/38.85  | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | |   (148)  all_57_5 = e3 & op(e2, e1) = e3
% 226.12/38.85  | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | ALPHA: (148) implies:
% 226.12/38.85  | | | | | | | | | | | |   (149)  all_57_5 = e3
% 226.12/38.85  | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | REF_CLOSE: (22), (136), (149) are inconsistent by sub-proof
% 226.12/38.85  | | | | | | | | | | | |            #2189.
% 226.12/38.85  | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | Case 2:
% 226.12/38.85  | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | |   (150)  all_57_10 = e3 & op(e2, e0) = e3
% 226.12/38.85  | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | ALPHA: (150) implies:
% 226.12/38.85  | | | | | | | | | | | |   (151)  all_57_10 = e3
% 226.12/38.85  | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | BETA: splitting (62) gives:
% 226.12/38.85  | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | Case 1:
% 226.12/38.85  | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | |   (152)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 226.12/38.85  | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 226.12/38.85  | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | BETA: splitting (152) gives:
% 226.12/38.85  | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | Case 1:
% 226.12/38.85  | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | |   (153)  all_57_9 = e1 & op(e3, e0) = e1
% 226.12/38.85  | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | ALPHA: (153) implies:
% 226.12/38.85  | | | | | | | | | | | | | |   (154)  all_57_9 = e1
% 226.12/38.85  | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | BETA: splitting (37) gives:
% 226.12/38.85  | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | Case 1:
% 226.12/38.85  | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | |   (155)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 226.12/38.85  | | | | | | | | | | | | | | |            & op(e3, e2) = e3)
% 226.12/38.85  | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | BETA: splitting (155) gives:
% 226.12/38.85  | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | Case 1:
% 226.12/38.85  | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | |   (156)  all_57_0 = e3 & op(e3, e3) = e3
% 226.12/38.85  | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | | ALPHA: (156) implies:
% 226.12/38.85  | | | | | | | | | | | | | | | |   (157)  op(e3, e3) = e3
% 226.12/38.85  | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | | REF_CLOSE: (7), (26), (32), (157) are inconsistent by
% 226.12/38.85  | | | | | | | | | | | | | | | |            sub-proof #2494.
% 226.12/38.85  | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | Case 2:
% 226.12/38.85  | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | |   (158)  all_57_1 = e3 & op(e3, e2) = e3
% 226.12/38.85  | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | | ALPHA: (158) implies:
% 226.12/38.85  | | | | | | | | | | | | | | | |   (159)  op(e3, e2) = e3
% 226.12/38.85  | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | | REF_CLOSE: (7), (22), (126), (159) are inconsistent by
% 226.12/38.85  | | | | | | | | | | | | | | | |            sub-proof #1549.
% 226.12/38.85  | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | End of split
% 226.12/38.85  | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | Case 2:
% 226.12/38.85  | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | |   (160)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 226.12/38.85  | | | | | | | | | | | | | | |            & op(e3, e0) = e3)
% 226.12/38.85  | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | BETA: splitting (160) gives:
% 226.12/38.85  | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | Case 1:
% 226.12/38.85  | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | |   (161)  all_57_4 = e3 & op(e3, e1) = e3
% 226.12/38.85  | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | | ALPHA: (161) implies:
% 226.12/38.85  | | | | | | | | | | | | | | | |   (162)  all_57_4 = e3
% 226.12/38.85  | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | | BETA: splitting (27) gives:
% 226.12/38.85  | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | | Case 1:
% 226.12/38.85  | | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | | |   (163)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 226.12/38.85  | | | | | | | | | | | | | | | | |            & op(e2, e1) = e1)
% 226.12/38.85  | | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | | | BETA: splitting (163) gives:
% 226.12/38.85  | | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | | | Case 1:
% 226.12/38.85  | | | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | | | |   (164)  all_57_4 = e1 & op(e3, e1) = e1
% 226.12/38.85  | | | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (162), (164) are inconsistent by sub-proof
% 226.12/38.85  | | | | | | | | | | | | | | | | | |            #2484.
% 226.12/38.85  | | | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | | | Case 2:
% 226.12/38.85  | | | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | | | |   (165)  all_57_5 = e1 & op(e2, e1) = e1
% 226.12/38.85  | | | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | | | | ALPHA: (165) implies:
% 226.12/38.85  | | | | | | | | | | | | | | | | | |   (166)  all_57_5 = e1
% 226.12/38.85  | | | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (136), (166) imply:
% 226.12/38.85  | | | | | | | | | | | | | | | | | |   (167)  e2 = e1
% 226.12/38.85  | | | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (141), (167) imply:
% 226.12/38.85  | | | | | | | | | | | | | | | | | |   (168)  all_57_2 = e1
% 226.12/38.85  | | | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (22), (26), (38), (50), (52), (54),
% 226.12/38.85  | | | | | | | | | | | | | | | | | |            (55), (75), (151), (166), (168) are inconsistent
% 226.12/38.85  | | | | | | | | | | | | | | | | | |            by sub-proof #66.
% 226.12/38.85  | | | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | | | End of split
% 226.12/38.85  | | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | | Case 2:
% 226.12/38.85  | | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | | |   (169)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 226.12/38.85  | | | | | | | | | | | | | | | | |            e1 & op(e0, e1) = e1)
% 226.12/38.85  | | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (28), (29), (38), (45), (55), (68), (69),
% 226.12/38.85  | | | | | | | | | | | | | | | | |            (122), (169) are inconsistent by sub-proof #23.
% 226.12/38.85  | | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | | End of split
% 226.12/38.85  | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | Case 2:
% 226.12/38.85  | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | |   (170)  all_57_9 = e3 & op(e3, e0) = e3
% 226.12/38.85  | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | | ALPHA: (170) implies:
% 226.12/38.85  | | | | | | | | | | | | | | | |   (171)  all_57_9 = e3
% 226.12/38.85  | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | | REF_CLOSE: (5), (154), (171) are inconsistent by sub-proof
% 226.12/38.85  | | | | | | | | | | | | | | | |            #1673.
% 226.12/38.85  | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | End of split
% 226.12/38.85  | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | End of split
% 226.12/38.85  | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | Case 2:
% 226.12/38.85  | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | |   (172)  all_57_10 = e1 & op(e2, e0) = e1
% 226.12/38.85  | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | REF_CLOSE: (5), (151), (172) are inconsistent by sub-proof
% 226.12/38.85  | | | | | | | | | | | | | |            #2349.
% 226.12/38.85  | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | End of split
% 226.12/38.85  | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | Case 2:
% 226.12/38.85  | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | |   (173)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 226.12/38.85  | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 226.12/38.85  | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | BETA: splitting (173) gives:
% 226.12/38.85  | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | Case 1:
% 226.12/38.85  | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | |   (174)  all_57_11 = e1 & op(e1, e0) = e1
% 226.12/38.85  | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | REF_CLOSE: (34), (38), (174) are inconsistent by sub-proof
% 226.12/38.85  | | | | | | | | | | | | | |            #1750.
% 226.12/38.85  | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | Case 2:
% 226.12/38.85  | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | |   (175)  all_57_15 = e1 & op(e0, e0) = e1
% 226.12/38.85  | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | ALPHA: (175) implies:
% 226.12/38.85  | | | | | | | | | | | | | |   (176)  op(e0, e0) = e1
% 226.12/38.85  | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (15), (22), (26), (33), (38), (43),
% 226.12/38.85  | | | | | | | | | | | | | |            (46), (55), (63), (75), (83), (87), (176) are
% 226.12/38.85  | | | | | | | | | | | | | |            inconsistent by sub-proof #2065.
% 226.12/38.85  | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | End of split
% 226.12/38.85  | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | End of split
% 226.12/38.85  | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | End of split
% 226.12/38.85  | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | End of split
% 226.12/38.85  | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | End of split
% 226.12/38.85  | | | | | | | | | 
% 226.12/38.85  | | | | | | | | Case 2:
% 226.12/38.85  | | | | | | | | | 
% 226.12/38.85  | | | | | | | | |   (177)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 &
% 226.12/38.85  | | | | | | | | |            op(e0, e3) = e2)
% 226.12/38.85  | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | BETA: splitting (177) gives:
% 226.12/38.85  | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | Case 1:
% 226.12/38.85  | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | |   (178)  all_57_6 = e2 & op(e1, e3) = e2
% 226.12/38.85  | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | ALPHA: (178) implies:
% 226.12/38.85  | | | | | | | | | |   (179)  all_57_6 = e2
% 226.12/38.85  | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | BETA: splitting (41) gives:
% 226.12/38.85  | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | Case 1:
% 226.12/38.85  | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | |   (180)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 226.12/38.85  | | | | | | | | | | |            & op(e2, e1) = e3)
% 226.12/38.85  | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | BETA: splitting (180) gives:
% 226.12/38.85  | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | Case 1:
% 226.12/38.85  | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | |   (181)  all_57_4 = e3 & op(e3, e1) = e3
% 226.12/38.85  | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | ALPHA: (181) implies:
% 226.12/38.85  | | | | | | | | | | | |   (182)  all_57_4 = e3
% 226.12/38.85  | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | BETA: splitting (8) gives:
% 226.12/38.85  | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | Case 1:
% 226.12/38.85  | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | |   (183)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 226.12/38.85  | | | | | | | | | | | | |            & op(e1, e2) = e3)
% 226.12/38.85  | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | BETA: splitting (183) gives:
% 226.12/38.85  | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | Case 1:
% 226.12/38.85  | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | |   (184)  all_57_6 = e3 & op(e1, e3) = e3
% 226.12/38.85  | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | ALPHA: (184) implies:
% 226.12/38.85  | | | | | | | | | | | | | |   (185)  all_57_6 = e3
% 226.12/38.85  | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | COMBINE_EQS: (179), (185) imply:
% 226.12/38.85  | | | | | | | | | | | | | |   (186)  e3 = e2
% 226.12/38.85  | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | SIMP: (186) implies:
% 226.12/38.85  | | | | | | | | | | | | | |   (187)  e3 = e2
% 226.12/38.85  | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | COMBINE_EQS: (182), (187) imply:
% 226.12/38.85  | | | | | | | | | | | | | |   (188)  all_57_4 = e2
% 226.12/38.85  | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | BETA: splitting (41) gives:
% 226.12/38.85  | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | Case 1:
% 226.12/38.85  | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | BETA: splitting (180) gives:
% 226.12/38.85  | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | Case 1:
% 226.12/38.85  | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | | REF_CLOSE: (22), (182), (188) are inconsistent by sub-proof
% 226.12/38.85  | | | | | | | | | | | | | | | |            #2482.
% 226.12/38.85  | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | Case 2:
% 226.12/38.85  | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | |   (189)  all_57_5 = e3 & op(e2, e1) = e3
% 226.12/38.85  | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | | ALPHA: (189) implies:
% 226.12/38.85  | | | | | | | | | | | | | | | |   (190)  all_57_5 = e3
% 226.12/38.85  | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | | REF_CLOSE: (22), (136), (190) are inconsistent by sub-proof
% 226.12/38.85  | | | | | | | | | | | | | | | |            #2189.
% 226.12/38.85  | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | End of split
% 226.12/38.85  | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | Case 2:
% 226.12/38.85  | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | |   (191)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 226.12/38.85  | | | | | | | | | | | | | | |            e3 & op(e0, e1) = e3)
% 226.12/38.85  | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 226.12/38.85  | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | Case 1:
% 226.12/38.85  | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | |   (192)  all_57_8 = e3 & op(e1, e1) = e3
% 226.12/38.85  | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | | ALPHA: (192) implies:
% 226.12/38.85  | | | | | | | | | | | | | | | |   (193)  op(e1, e1) = e3
% 226.12/38.85  | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (10), (193) are inconsistent by
% 226.12/38.85  | | | | | | | | | | | | | | | |            sub-proof #2468.
% 226.12/38.85  | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | Case 2:
% 226.12/38.85  | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | |   (194)  all_57_14 = e3 & op(e0, e1) = e3
% 226.12/38.85  | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | | ALPHA: (194) implies:
% 226.12/38.85  | | | | | | | | | | | | | | | |   (195)  all_57_14 = e3
% 226.12/38.85  | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | | BETA: splitting (27) gives:
% 226.12/38.85  | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | | Case 1:
% 226.12/38.85  | | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | | |   (196)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 226.12/38.85  | | | | | | | | | | | | | | | | |            & op(e2, e1) = e1)
% 226.12/38.85  | | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 226.12/38.85  | | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | | | Case 1:
% 226.12/38.85  | | | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | | | |   (197)  all_57_4 = e1 & op(e3, e1) = e1
% 226.12/38.85  | | | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (188), (197) are inconsistent by sub-proof
% 226.12/38.85  | | | | | | | | | | | | | | | | | |            #2452.
% 226.12/38.85  | | | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | | | Case 2:
% 226.12/38.85  | | | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | | | |   (198)  all_57_5 = e1 & op(e2, e1) = e1
% 226.12/38.85  | | | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | | | | ALPHA: (198) implies:
% 226.12/38.85  | | | | | | | | | | | | | | | | | |   (199)  all_57_5 = e1
% 226.12/38.85  | | | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10), (21), (26), (38), (73), (75), (188),
% 226.12/38.85  | | | | | | | | | | | | | | | | | |            (195), (199) are inconsistent by sub-proof #340.
% 226.12/38.85  | | | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | | | End of split
% 226.12/38.85  | | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | | Case 2:
% 226.12/38.85  | | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | | |   (200)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 226.12/38.85  | | | | | | | | | | | | | | | | |            e1 & op(e0, e1) = e1)
% 226.12/38.85  | | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (55), (122), (195), (200) are
% 226.12/38.85  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1815.
% 226.12/38.85  | | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | | End of split
% 226.12/38.85  | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | End of split
% 226.12/38.85  | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | End of split
% 226.12/38.85  | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | Case 2:
% 226.12/38.85  | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | |   (201)  all_57_7 = e3 & op(e1, e2) = e3
% 226.12/38.85  | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | ALPHA: (201) implies:
% 226.12/38.85  | | | | | | | | | | | | | |   (202)  all_57_7 = e3
% 226.12/38.85  | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | BETA: splitting (27) gives:
% 226.12/38.85  | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | Case 1:
% 226.12/38.85  | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | |   (203)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 226.12/38.85  | | | | | | | | | | | | | | |            & op(e2, e1) = e1)
% 226.12/38.85  | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 226.12/38.85  | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | Case 1:
% 226.12/38.85  | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | |   (204)  all_57_4 = e1 & op(e3, e1) = e1
% 226.12/38.85  | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | | ALPHA: (204) implies:
% 226.12/38.85  | | | | | | | | | | | | | | | |   (205)  all_57_4 = e1
% 226.12/38.85  | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | | COMBINE_EQS: (182), (205) imply:
% 226.12/38.85  | | | | | | | | | | | | | | | |   (206)  e3 = e1
% 226.12/38.85  | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | | COMBINE_EQS: (202), (206) imply:
% 226.12/38.85  | | | | | | | | | | | | | | | |   (207)  all_57_7 = e1
% 226.12/38.85  | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (10), (22), (26), (38),
% 226.12/38.85  | | | | | | | | | | | | | | | |            (73), (75), (179), (207) are inconsistent by
% 226.12/38.85  | | | | | | | | | | | | | | | |            sub-proof #342.
% 226.12/38.85  | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | Case 2:
% 226.12/38.85  | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | |   (208)  all_57_5 = e1 & op(e2, e1) = e1
% 226.12/38.85  | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | | REF_CLOSE: (55), (136), (208) are inconsistent by sub-proof
% 226.12/38.85  | | | | | | | | | | | | | | | |            #1886.
% 226.12/38.85  | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | End of split
% 226.12/38.85  | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | Case 2:
% 226.12/38.85  | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | |   (209)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 226.12/38.85  | | | | | | | | | | | | | | |            e1 & op(e0, e1) = e1)
% 226.12/38.85  | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | REF_CLOSE: (7), (28), (29), (38), (45), (55), (68), (69),
% 226.12/38.85  | | | | | | | | | | | | | | |            (122), (209) are inconsistent by sub-proof #23.
% 226.12/38.85  | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | End of split
% 226.12/38.85  | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | End of split
% 226.12/38.85  | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | Case 2:
% 226.12/38.85  | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | |   (210)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 226.12/38.85  | | | | | | | | | | | | |            e3 & op(e1, e0) = e3)
% 226.12/38.85  | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | BETA: splitting (210) gives:
% 226.12/38.85  | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | Case 1:
% 226.12/38.85  | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | |   (211)  all_57_8 = e3 & op(e1, e1) = e3
% 226.12/38.85  | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | ALPHA: (211) implies:
% 226.12/38.85  | | | | | | | | | | | | | |   (212)  op(e1, e1) = e3
% 226.12/38.85  | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (10), (212) are inconsistent by
% 226.12/38.85  | | | | | | | | | | | | | |            sub-proof #2468.
% 226.12/38.85  | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | Case 2:
% 226.12/38.85  | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | |   (213)  all_57_11 = e3 & op(e1, e0) = e3
% 226.12/38.85  | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | ALPHA: (213) implies:
% 226.12/38.85  | | | | | | | | | | | | | |   (214)  all_57_11 = e3
% 226.12/38.85  | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | BETA: splitting (64) gives:
% 226.12/38.85  | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | Case 1:
% 226.12/38.85  | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | |   (215)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 226.12/38.85  | | | | | | | | | | | | | | |            & op(e1, e2) = e1)
% 226.12/38.85  | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 226.12/38.85  | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | Case 1:
% 226.12/38.85  | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | |   (216)  all_57_6 = e1 & op(e1, e3) = e1
% 226.12/38.85  | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | | REF_CLOSE: (55), (179), (216) are inconsistent by sub-proof
% 226.12/38.85  | | | | | | | | | | | | | | | |            #2389.
% 226.12/38.85  | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | Case 2:
% 226.12/38.85  | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | |   (217)  all_57_7 = e1 & op(e1, e2) = e1
% 226.12/38.85  | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | | ALPHA: (217) implies:
% 226.12/38.85  | | | | | | | | | | | | | | | |   (218)  all_57_7 = e1
% 226.12/38.85  | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (10), (26), (38), (73), (75), (179),
% 226.12/38.85  | | | | | | | | | | | | | | | |            (214), (218) are inconsistent by sub-proof #349.
% 226.12/38.85  | | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | End of split
% 226.12/38.85  | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | Case 2:
% 226.12/38.85  | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | |   (219)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 226.12/38.85  | | | | | | | | | | | | | | |            e1 & op(e1, e0) = e1)
% 226.12/38.85  | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (55), (122), (214), (219) are
% 226.12/38.85  | | | | | | | | | | | | | | |            inconsistent by sub-proof #260.
% 226.12/38.85  | | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | | End of split
% 226.12/38.85  | | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | End of split
% 226.12/38.85  | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | End of split
% 226.12/38.85  | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | Case 2:
% 226.12/38.85  | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | |   (220)  all_57_5 = e3 & op(e2, e1) = e3
% 226.12/38.85  | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | ALPHA: (220) implies:
% 226.12/38.85  | | | | | | | | | | | |   (221)  all_57_5 = e3
% 226.12/38.85  | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | REF_CLOSE: (22), (136), (221) are inconsistent by sub-proof
% 226.12/38.85  | | | | | | | | | | | |            #2189.
% 226.12/38.85  | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | End of split
% 226.12/38.85  | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | Case 2:
% 226.12/38.85  | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | |   (222)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 226.12/38.85  | | | | | | | | | | |            e3 & op(e0, e1) = e3)
% 226.12/38.85  | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | BETA: splitting (222) gives:
% 226.12/38.85  | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | Case 1:
% 226.12/38.85  | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | |   (223)  all_57_8 = e3 & op(e1, e1) = e3
% 226.12/38.85  | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | ALPHA: (223) implies:
% 226.12/38.85  | | | | | | | | | | | |   (224)  op(e1, e1) = e3
% 226.12/38.85  | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | REF_CLOSE: (7), (9), (10), (224) are inconsistent by
% 226.12/38.85  | | | | | | | | | | | |            sub-proof #2468.
% 226.12/38.85  | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | Case 2:
% 226.12/38.85  | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | |   (225)  all_57_14 = e3 & op(e0, e1) = e3
% 226.12/38.85  | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | ALPHA: (225) implies:
% 226.12/38.85  | | | | | | | | | | | |   (226)  all_57_14 = e3
% 226.12/38.85  | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | BETA: splitting (29) gives:
% 226.12/38.85  | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | Case 1:
% 226.12/38.85  | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | |   (227)  all_57_12 = e0 & op(e0, e3) = e0
% 226.12/38.85  | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | ALPHA: (227) implies:
% 226.12/38.85  | | | | | | | | | | | | |   (228)  op(e0, e3) = e0
% 226.12/38.85  | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | REF_CLOSE: (7), (28), (68), (228) are inconsistent by
% 226.12/38.85  | | | | | | | | | | | | |            sub-proof #2366.
% 226.12/38.85  | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | Case 2:
% 226.12/38.85  | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | |   (229)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 226.12/38.85  | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 226.12/38.85  | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | | REF_CLOSE: (7), (26), (45), (69), (226), (229) are
% 226.12/38.85  | | | | | | | | | | | | |            inconsistent by sub-proof #30.
% 226.12/38.85  | | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | | End of split
% 226.12/38.85  | | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | | End of split
% 226.12/38.85  | | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | End of split
% 226.12/38.85  | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | Case 2:
% 226.12/38.85  | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | |   (230)  all_57_12 = e2 & op(e0, e3) = e2
% 226.12/38.85  | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | ALPHA: (230) implies:
% 226.12/38.85  | | | | | | | | | |   (231)  op(e0, e3) = e2
% 226.12/38.85  | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | | REF_CLOSE: (7), (28), (31), (231) are inconsistent by
% 226.12/38.85  | | | | | | | | | |            sub-proof #1980.
% 226.12/38.85  | | | | | | | | | | 
% 226.12/38.85  | | | | | | | | | End of split
% 226.12/38.85  | | | | | | | | | 
% 226.12/38.85  | | | | | | | | End of split
% 226.12/38.85  | | | | | | | | 
% 226.12/38.85  | | | | | | | Case 2:
% 226.12/38.85  | | | | | | | | 
% 226.12/38.85  | | | | | | | |   (232)  all_57_10 = e2 & op(e2, e0) = e2
% 226.12/38.85  | | | | | | | | 
% 226.12/38.85  | | | | | | | | REF_CLOSE: (7), (12), (49), (232) are inconsistent by sub-proof
% 226.12/38.85  | | | | | | | |            #2432.
% 226.12/38.85  | | | | | | | | 
% 226.12/38.85  | | | | | | | End of split
% 226.12/38.85  | | | | | | | 
% 226.12/38.85  | | | | | | End of split
% 226.12/38.85  | | | | | | 
% 226.12/38.85  | | | | | Case 2:
% 226.12/38.85  | | | | | | 
% 226.12/38.85  | | | | | |   (233)  all_57_3 = e2 & op(e2, e2) = e2
% 226.12/38.85  | | | | | | 
% 226.12/38.85  | | | | | | ALPHA: (233) implies:
% 226.12/38.85  | | | | | |   (234)  op(e2, e2) = e2
% 226.12/38.85  | | | | | | 
% 226.12/38.85  | | | | | | REF_CLOSE: (7), (15), (75), (234) are inconsistent by sub-proof
% 226.12/38.85  | | | | | |            #2472.
% 226.12/38.85  | | | | | | 
% 226.12/38.85  | | | | | End of split
% 226.12/38.85  | | | | | 
% 226.12/38.85  | | | | Case 2:
% 226.12/38.85  | | | | | 
% 226.12/38.85  | | | | |   (235)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0,
% 226.12/38.85  | | | | |              e2) = e2)
% 226.12/38.85  | | | | | 
% 226.12/38.85  | | | | | REF_CLOSE: (7), (13), (45), (58), (120), (235) are inconsistent by
% 226.12/38.85  | | | | |            sub-proof #160.
% 226.12/38.85  | | | | | 
% 226.12/38.85  | | | | End of split
% 226.12/38.85  | | | | 
% 226.12/38.86  | | | End of split
% 226.12/38.86  | | | 
% 226.12/38.86  | | End of split
% 226.12/38.86  | | 
% 226.12/38.86  | Case 2:
% 226.12/38.86  | | 
% 226.12/38.86  | |   (236)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 226.12/38.86  | |            & op(all_52_17, all_52_17) = e3 & op(all_52_19, all_52_19) = e2 &
% 226.12/38.86  | |            op(all_52_21, all_52_21) = e1 & op(all_52_23, all_52_23) = e0 &
% 226.12/38.86  | |            op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) =
% 226.12/38.86  | |            all_52_21 & op(e1, e0) = all_52_23 & $i(all_52_17) &
% 226.12/38.86  | |            $i(all_52_19) & $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 226.12/38.86  | |            & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0 &
% 226.12/38.86  | |            op(all_52_25, all_52_25) = e3 & op(all_52_27, all_52_27) = e2 &
% 226.12/38.86  | |            op(all_52_29, all_52_29) = e1 & op(all_52_31, all_52_31) = e0 &
% 226.12/38.86  | |            op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 & op(e0, e1) =
% 226.12/38.86  | |            all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 226.12/38.86  | |            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 226.12/38.86  | | 
% 226.12/38.86  | | BETA: splitting (236) gives:
% 226.12/38.86  | | 
% 226.12/38.86  | | Case 1:
% 226.12/38.86  | | | 
% 226.12/38.86  | | |   (237)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 226.12/38.86  | | |          & op(all_52_17, all_52_17) = e3 & op(all_52_19, all_52_19) = e2 &
% 226.12/38.86  | | |          op(all_52_21, all_52_21) = e1 & op(all_52_23, all_52_23) = e0 &
% 226.12/38.86  | | |          op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) =
% 226.12/38.86  | | |          all_52_21 & op(e1, e0) = all_52_23 & $i(all_52_17) &
% 226.12/38.86  | | |          $i(all_52_19) & $i(all_52_21) & $i(all_52_23)
% 226.12/38.86  | | | 
% 226.12/38.86  | | | ALPHA: (237) implies:
% 226.12/38.86  | | |   (238)  op(e1, e0) = all_52_23
% 226.12/38.86  | | |   (239)  op(all_52_23, all_52_23) = e0
% 226.12/38.86  | | | 
% 226.12/38.86  | | | REF_CLOSE: (7), (56), (59), (75), (238), (239) are inconsistent by
% 226.12/38.86  | | |            sub-proof #51.
% 226.12/38.86  | | | 
% 226.12/38.86  | | Case 2:
% 226.12/38.86  | | | 
% 226.12/38.86  | | |   (240)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 226.12/38.86  | | |          & op(all_52_25, all_52_25) = e3 & op(all_52_27, all_52_27) = e2 &
% 226.12/38.86  | | |          op(all_52_29, all_52_29) = e1 & op(all_52_31, all_52_31) = e0 &
% 226.12/38.86  | | |          op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 & op(e0, e1) =
% 226.12/38.86  | | |          all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 226.12/38.86  | | |          $i(all_52_27) & $i(all_52_29) & $i(all_52_31)
% 226.12/38.86  | | | 
% 226.12/38.86  | | | ALPHA: (240) implies:
% 226.12/38.86  | | |   (241)  op(e0, e0) = all_52_31
% 226.12/38.86  | | |   (242)  op(e0, e1) = all_52_29
% 226.12/38.86  | | |   (243)  op(all_52_31, all_52_31) = e0
% 226.12/38.86  | | |   (244)  op(all_52_29, all_52_29) = e1
% 226.12/38.86  | | | 
% 226.12/38.86  | | | GROUND_INST: instantiating (7) with e0, all_52_29, e1, e0, simplifying
% 226.12/38.86  | | |              with (14), (242) gives:
% 226.12/38.86  | | |   (245)  all_52_29 = e0
% 226.12/38.86  | | | 
% 226.12/38.86  | | | REDUCE: (244), (245) imply:
% 226.12/38.86  | | |   (246)  op(e0, e0) = e1
% 226.12/38.86  | | | 
% 226.12/38.86  | | | REF_CLOSE: (7), (10), (73), (241), (243), (246) are inconsistent by
% 226.12/38.86  | | |            sub-proof #2086.
% 226.12/38.86  | | | 
% 226.12/38.86  | | End of split
% 226.12/38.86  | | 
% 226.12/38.86  | End of split
% 226.12/38.86  | 
% 226.12/38.86  End of proof
% 226.12/38.86  
% 226.12/38.86  Sub-proof #23 shows that the following formulas are inconsistent:
% 226.12/38.86  ----------------------------------------------------------------
% 226.12/38.86    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.12/38.86           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.12/38.86    (2)  op(e0, e3) = all_53_3
% 226.12/38.86    (3)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 226.12/38.86         (all_57_14 = e0 & op(e0, e1) = e0)
% 226.12/38.86    (4)   ~ (all_53_7 = e0)
% 226.12/38.86    (5)   ~ (e1 = e0)
% 226.12/38.86    (6)  op(e0, e2) = all_53_7
% 226.12/38.86    (7)   ~ (all_53_3 = e0)
% 226.12/38.86    (8)  op(e1, e1) = e2
% 226.12/38.86    (9)   ~ (e2 = e1)
% 226.12/38.86    (10)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 226.12/38.86  
% 226.12/38.86  Begin of proof
% 226.12/38.86  | 
% 226.12/38.86  | BETA: splitting (10) gives:
% 226.12/38.86  | 
% 226.12/38.86  | Case 1:
% 226.12/38.86  | | 
% 226.12/38.86  | |   (11)  all_57_8 = e1 & op(e1, e1) = e1
% 226.12/38.86  | | 
% 226.12/38.86  | | ALPHA: (11) implies:
% 226.12/38.86  | |   (12)  op(e1, e1) = e1
% 226.12/38.86  | | 
% 226.12/38.86  | | REF_CLOSE: (1), (8), (9), (12) are inconsistent by sub-proof #2423.
% 226.12/38.86  | | 
% 226.12/38.86  | Case 2:
% 226.12/38.86  | | 
% 226.12/38.86  | |   (13)  all_57_14 = e1 & op(e0, e1) = e1
% 226.12/38.86  | | 
% 226.12/38.86  | | ALPHA: (13) implies:
% 226.12/38.86  | |   (14)  all_57_14 = e1
% 226.12/38.86  | | 
% 226.12/38.86  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (14) are inconsistent by
% 226.12/38.86  | |            sub-proof #115.
% 226.12/38.86  | | 
% 226.12/38.86  | End of split
% 226.12/38.86  | 
% 226.12/38.86  End of proof
% 226.12/38.86  
% 226.12/38.86  Sub-proof #24 shows that the following formulas are inconsistent:
% 226.12/38.86  ----------------------------------------------------------------
% 226.12/38.86    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.12/38.86           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.12/38.86    (2)   ~ (all_52_13 = e0)
% 226.12/38.86    (3)  all_55_6 = all_52_13
% 226.12/38.86    (4)  op(e2, e2) = e0
% 226.12/38.86    (5)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 226.12/38.86    (6)  op(all_52_13, all_52_13) = e1
% 226.12/38.86    (7)   ~ (all_52_13 = e3)
% 226.12/38.86    (8)   ~ (all_52_13 = e1)
% 226.12/38.86    (9)   ~ (e1 = e0)
% 226.12/38.86  
% 226.12/38.86  Begin of proof
% 226.12/38.86  | 
% 226.12/38.86  | BETA: splitting (5) gives:
% 226.12/38.86  | 
% 226.12/38.86  | Case 1:
% 226.12/38.86  | | 
% 226.12/38.86  | |   (10)  all_55_6 = e3
% 226.12/38.86  | | 
% 226.12/38.86  | | REF_CLOSE: (3), (7), (10) are inconsistent by sub-proof #318.
% 226.12/38.86  | | 
% 226.12/38.86  | Case 2:
% 226.12/38.86  | | 
% 226.12/38.86  | |   (11)  all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 226.12/38.86  | | 
% 226.12/38.86  | | BETA: splitting (11) gives:
% 226.12/38.86  | | 
% 226.12/38.86  | | Case 1:
% 226.12/38.86  | | | 
% 226.12/38.86  | | |   (12)  all_55_6 = e2
% 226.12/38.86  | | | 
% 226.12/38.86  | | | COMBINE_EQS: (3), (12) imply:
% 226.12/38.86  | | |   (13)  all_52_13 = e2
% 226.12/38.86  | | | 
% 226.12/38.86  | | | SIMP: (13) implies:
% 226.12/38.86  | | |   (14)  all_52_13 = e2
% 226.12/38.86  | | | 
% 226.12/38.86  | | | REDUCE: (6), (14) imply:
% 226.12/38.86  | | |   (15)  op(e2, e2) = e1
% 226.12/38.86  | | | 
% 226.12/38.86  | | | REF_CLOSE: (1), (4), (9), (15) are inconsistent by sub-proof #2352.
% 226.12/38.86  | | | 
% 226.12/38.86  | | Case 2:
% 226.12/38.86  | | | 
% 226.12/38.86  | | |   (16)  all_55_6 = e1 | all_55_6 = e0
% 226.12/38.86  | | | 
% 226.12/38.86  | | | BETA: splitting (16) gives:
% 226.12/38.86  | | | 
% 226.12/38.86  | | | Case 1:
% 226.12/38.86  | | | | 
% 226.12/38.86  | | | |   (17)  all_55_6 = e1
% 226.12/38.86  | | | | 
% 226.12/38.86  | | | | REF_CLOSE: (3), (8), (17) are inconsistent by sub-proof #2291.
% 226.12/38.86  | | | | 
% 226.12/38.86  | | | Case 2:
% 226.12/38.86  | | | | 
% 226.12/38.86  | | | |   (18)  all_55_6 = e0
% 226.12/38.86  | | | | 
% 226.12/38.86  | | | | REF_CLOSE: (2), (3), (18) are inconsistent by sub-proof #76.
% 226.12/38.86  | | | | 
% 226.12/38.86  | | | End of split
% 226.12/38.86  | | | 
% 226.12/38.86  | | End of split
% 226.12/38.86  | | 
% 226.12/38.86  | End of split
% 226.12/38.86  | 
% 226.12/38.86  End of proof
% 226.12/38.86  
% 226.12/38.86  Sub-proof #25 shows that the following formulas are inconsistent:
% 226.12/38.86  ----------------------------------------------------------------
% 226.12/38.86    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 226.12/38.86    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 226.12/38.86    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 226.12/38.86         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 226.12/38.86    (4)  ( ~ (all_50_0 = e3) & op(all_50_1, e2) = all_50_0 & op(e2, e0) = all_50_1
% 226.12/38.86           & $i(all_50_0) & $i(all_50_1)) | ( ~ (all_50_1 = e1) & op(e2, e0) =
% 226.12/38.86           all_50_1 & $i(all_50_1))
% 226.12/38.86    (5)  op(e2, e3) = all_53_1
% 226.12/38.86    (6)  all_57_12 = e0
% 226.12/38.86    (7)  ( ~ (all_14_0 = e1) & op(all_14_1, e2) = all_14_0 & op(e2, e0) = all_14_1
% 226.12/38.86           & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e3) & op(e2, e0) =
% 226.12/38.86           all_14_1 & $i(all_14_1))
% 226.12/38.86    (8)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 226.12/38.86         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 226.12/38.86    (9)   ~ (all_53_8 = all_53_12)
% 226.12/38.86    (10)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 226.12/38.86          (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 226.12/38.86    (11)   ~ (e3 = e1)
% 226.12/38.86    (12)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 226.12/38.86          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 226.12/38.86    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.12/38.86            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.12/38.86    (14)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 226.12/38.86          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 226.12/38.86    (15)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 226.12/38.86            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 226.12/38.86              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 226.12/38.86    (16)   ~ (all_6_2 = e3)
% 226.12/38.86    (17)  op(e1, e1) = all_6_2
% 226.12/38.86    (18)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 226.12/38.86    (19)   ~ (all_53_9 = e0)
% 226.12/38.86    (20)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 226.12/38.86          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 226.12/38.86    (21)   ~ (all_53_4 = all_53_12)
% 226.12/38.86    (22)   ~ (all_53_7 = e2)
% 226.12/38.86    (23)   ~ (all_53_8 = all_53_9)
% 226.12/38.86    (24)  op(e2, e0) = all_52_15
% 226.12/38.86    (25)  all_42_2 = all_6_2
% 226.12/38.86    (26)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 226.12/38.86          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 226.12/38.86    (27)  op(e2, e2) = e0
% 226.12/38.86    (28)   ~ (all_53_9 = all_6_2)
% 226.12/38.86    (29)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 226.12/38.86          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 226.12/38.86    (30)  all_57_3 = e0
% 226.12/38.86    (31)   ~ (all_8_2 = e3)
% 226.12/38.86    (32)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 226.12/38.86          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 226.12/38.86    (33)   ~ (e3 = e2)
% 226.12/38.86    (34)  all_55_1 = all_53_4
% 226.12/38.86    (35)   ~ (e3 = e0)
% 226.12/38.86    (36)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 226.12/38.86          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 226.12/38.86    (37)  op(e3, e3) = e3
% 226.12/38.86    (38)  op(e3, e0) = e0
% 226.12/38.86    (39)   ~ (all_53_8 = all_6_2)
% 226.12/38.86    (40)  all_55_2 = all_53_8
% 226.12/38.86    (41)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 226.12/38.86    (42)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 226.12/38.86          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 226.12/38.86            e1)
% 226.12/38.86    (43)  all_57_9 = e0
% 226.12/38.86    (44)   ~ (all_53_4 = all_53_8)
% 226.12/38.86    (45)  op(e3, e2) = all_53_4
% 226.12/38.86    (46)   ~ (e2 = e0)
% 226.12/38.86    (47)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 226.12/38.86            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 226.12/38.86            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 226.12/38.86            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 226.12/38.86              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 226.12/38.86            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 226.12/38.86            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 226.12/38.86              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 226.12/38.86              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 226.12/38.86            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 226.12/38.86            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 226.12/38.86            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 226.12/38.86              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 226.12/38.86              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 226.12/38.86            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 226.12/38.86              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 226.12/38.86            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 226.12/38.86            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 226.12/38.86              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 226.12/38.86              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 226.12/38.86            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 226.12/38.86            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 226.12/38.86    (48)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 226.12/38.86          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 226.12/38.86    (49)   ~ (e1 = e0)
% 226.12/38.86    (50)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 226.12/38.86            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 226.12/38.86              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 226.12/38.86    (51)   ~ (all_53_4 = e0)
% 226.12/38.86    (52)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 226.12/38.86          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 226.12/38.86    (53)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 226.12/38.86          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 226.12/38.86    (54)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 226.12/38.86          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 226.12/38.86            e3)
% 226.12/38.86    (55)  op(e2, e2) = all_8_2
% 226.12/38.86    (56)   ~ (all_53_4 = all_53_6)
% 226.12/38.86    (57)  op(e0, e2) = all_53_7
% 226.12/38.86    (58)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 226.12/38.86          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 226.12/38.86            e2)
% 226.12/38.86    (59)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 226.12/38.86              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 226.12/38.86                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 226.12/38.86                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 226.12/38.86    (60)  all_55_10 = all_6_2
% 226.12/38.86    (61)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 226.12/38.86          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 226.12/38.86    (62)  all_38_2 = all_6_2
% 226.12/38.86    (63)  all_55_3 = all_53_12
% 226.12/38.86    (64)   ~ (all_53_12 = e3)
% 226.12/38.86    (65)  all_57_0 = e3
% 226.12/38.86    (66)  all_57_7 = e3
% 226.12/38.86    (67)  all_57_8 = e0
% 226.12/38.86    (68)  op(all_52_15, all_52_15) = e0
% 226.12/38.86    (69)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 226.12/38.86            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 226.12/38.86              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 226.12/38.86    (70)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 226.12/38.86          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 226.12/38.86    (71)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 226.12/38.86          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 226.12/38.86    (72)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 226.12/38.86          (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 226.12/38.86    (73)   ~ (all_53_1 = e3)
% 226.12/38.86    (74)   ~ (e2 = e1)
% 226.12/38.86    (75)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 226.12/38.86          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 226.12/38.86    (76)  op(e2, e1) = all_53_9
% 226.12/38.86    (77)  op(e1, e2) = all_53_6
% 226.12/38.86    (78)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 226.12/38.86          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 226.12/38.86    (79)  all_24_2 = all_6_2
% 226.12/38.86    (80)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 226.12/38.86          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 226.12/38.86    (81)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 226.12/38.86          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 226.12/38.86    (82)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 226.12/38.86          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 226.12/38.86    (83)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 226.12/38.86          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 226.12/38.86    (84)  op(e3, e1) = all_53_8
% 226.12/38.86    (85)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 226.12/38.86          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 226.12/38.86    (86)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 226.12/38.86          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 226.12/38.86    (87)  op(e3, e0) = all_53_12
% 226.12/38.86  
% 226.12/38.86  Begin of proof
% 226.12/38.86  | 
% 226.12/38.86  | BETA: splitting (10) gives:
% 226.12/38.86  | 
% 226.12/38.86  | Case 1:
% 226.12/38.86  | | 
% 226.12/38.86  | |   (88)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 226.12/38.86  | |           e2)
% 226.12/38.86  | | 
% 226.12/38.86  | | BETA: splitting (88) gives:
% 226.12/38.86  | | 
% 226.12/38.86  | | Case 1:
% 226.12/38.86  | | | 
% 226.12/38.86  | | |   (89)  all_57_1 = e2 & op(e3, e2) = e2
% 226.12/38.86  | | | 
% 226.12/38.86  | | | ALPHA: (89) implies:
% 226.12/38.86  | | |   (90)  all_57_1 = e2
% 226.12/38.86  | | | 
% 226.12/38.86  | | | BETA: splitting (86) gives:
% 226.12/38.86  | | | 
% 226.12/38.86  | | | Case 1:
% 226.12/38.86  | | | | 
% 226.12/38.86  | | | |   (91)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2)
% 226.12/38.86  | | | |           = e2)
% 226.12/38.86  | | | | 
% 226.12/38.86  | | | | BETA: splitting (91) gives:
% 226.12/38.86  | | | | 
% 226.12/38.86  | | | | Case 1:
% 226.12/38.86  | | | | | 
% 226.12/38.86  | | | | |   (92)  all_57_6 = e2 & op(e1, e3) = e2
% 226.12/38.86  | | | | | 
% 226.12/38.86  | | | | | ALPHA: (92) implies:
% 226.12/38.86  | | | | |   (93)  all_57_6 = e2
% 226.12/38.86  | | | | | 
% 226.12/38.86  | | | | | BETA: splitting (8) gives:
% 226.12/38.86  | | | | | 
% 226.12/38.86  | | | | | Case 1:
% 226.12/38.86  | | | | | | 
% 226.12/38.86  | | | | | |   (94)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2,
% 226.12/38.86  | | | | | |             e3) = e1)
% 226.12/38.86  | | | | | | 
% 226.12/38.86  | | | | | | BETA: splitting (94) gives:
% 226.12/38.86  | | | | | | 
% 226.12/38.86  | | | | | | Case 1:
% 226.12/38.86  | | | | | | | 
% 226.12/38.86  | | | | | | |   (95)  all_57_0 = e1 & op(e3, e3) = e1
% 226.12/38.86  | | | | | | | 
% 226.12/38.86  | | | | | | | ALPHA: (95) implies:
% 226.12/38.86  | | | | | | |   (96)  op(e3, e3) = e1
% 226.12/38.86  | | | | | | | 
% 226.12/38.86  | | | | | | | REF_CLOSE: (11), (13), (37), (96) are inconsistent by sub-proof
% 226.12/38.86  | | | | | | |            #2495.
% 226.12/38.86  | | | | | | | 
% 226.12/38.86  | | | | | | Case 2:
% 226.12/38.86  | | | | | | | 
% 226.12/38.86  | | | | | | |   (97)  all_57_2 = e1 & op(e2, e3) = e1
% 226.12/38.86  | | | | | | | 
% 226.12/38.86  | | | | | | | ALPHA: (97) implies:
% 226.12/38.86  | | | | | | |   (98)  all_57_2 = e1
% 226.12/38.86  | | | | | | | 
% 226.12/38.86  | | | | | | | BETA: splitting (54) gives:
% 226.12/38.86  | | | | | | | 
% 226.12/38.86  | | | | | | | Case 1:
% 226.12/38.86  | | | | | | | | 
% 226.12/38.86  | | | | | | | |   (99)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 &
% 226.12/38.86  | | | | | | | |           op(e0, e2) = e3)
% 226.12/38.86  | | | | | | | | 
% 226.12/38.86  | | | | | | | | BETA: splitting (99) gives:
% 226.12/38.86  | | | | | | | | 
% 226.12/38.86  | | | | | | | | Case 1:
% 226.12/38.86  | | | | | | | | | 
% 226.12/38.86  | | | | | | | | |   (100)  all_57_12 = e3 & op(e0, e3) = e3
% 226.12/38.86  | | | | | | | | | 
% 226.12/38.86  | | | | | | | | | ALPHA: (100) implies:
% 226.12/38.86  | | | | | | | | |   (101)  all_57_12 = e3
% 226.12/38.86  | | | | | | | | | 
% 226.12/38.86  | | | | | | | | | REF_CLOSE: (13), (35), (37), (46), (49), (81), (93), (98),
% 226.12/38.86  | | | | | | | | |            (101) are inconsistent by sub-proof #2236.
% 226.12/38.86  | | | | | | | | | 
% 226.12/38.86  | | | | | | | | Case 2:
% 226.12/38.86  | | | | | | | | | 
% 226.12/38.86  | | | | | | | | |   (102)  all_57_13 = e3 & op(e0, e2) = e3
% 226.12/38.86  | | | | | | | | | 
% 226.12/38.86  | | | | | | | | | ALPHA: (102) implies:
% 226.12/38.86  | | | | | | | | |   (103)  all_57_13 = e3
% 226.12/38.86  | | | | | | | | | 
% 226.12/38.86  | | | | | | | | | REF_CLOSE: (11), (30), (49), (66), (74), (85), (90), (103) are
% 226.12/38.86  | | | | | | | | |            inconsistent by sub-proof #2008.
% 226.12/38.86  | | | | | | | | | 
% 226.12/38.86  | | | | | | | | End of split
% 226.12/38.86  | | | | | | | | 
% 226.12/38.86  | | | | | | | Case 2:
% 226.12/38.86  | | | | | | | | 
% 226.12/38.86  | | | | | | | |   (104)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 &
% 226.12/38.86  | | | | | | | |            op(e0, e0) = e3)
% 226.12/38.86  | | | | | | | | 
% 226.12/38.86  | | | | | | | | BETA: splitting (104) gives:
% 226.12/38.86  | | | | | | | | 
% 226.12/38.86  | | | | | | | | Case 1:
% 226.12/38.86  | | | | | | | | | 
% 226.12/38.86  | | | | | | | | |   (105)  all_57_14 = e3 & op(e0, e1) = e3
% 226.12/38.86  | | | | | | | | | 
% 226.12/38.86  | | | | | | | | | ALPHA: (105) implies:
% 226.12/38.86  | | | | | | | | |   (106)  all_57_14 = e3
% 226.12/38.86  | | | | | | | | | 
% 226.12/38.86  | | | | | | | | | BETA: splitting (20) gives:
% 226.12/38.86  | | | | | | | | | 
% 226.12/38.86  | | | | | | | | | Case 1:
% 226.12/38.86  | | | | | | | | | | 
% 226.12/38.86  | | | | | | | | | |   (107)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 226.12/38.86  | | | | | | | | | |            & op(e3, e2) = e1)
% 226.12/38.86  | | | | | | | | | | 
% 226.12/38.86  | | | | | | | | | | BETA: splitting (107) gives:
% 226.12/38.86  | | | | | | | | | | 
% 226.12/38.86  | | | | | | | | | | Case 1:
% 226.12/38.86  | | | | | | | | | | | 
% 226.12/38.86  | | | | | | | | | | |   (108)  all_57_0 = e1 & op(e3, e3) = e1
% 226.12/38.86  | | | | | | | | | | | 
% 226.12/38.86  | | | | | | | | | | | ALPHA: (108) implies:
% 226.12/38.86  | | | | | | | | | | |   (109)  op(e3, e3) = e1
% 226.12/38.86  | | | | | | | | | | | 
% 226.12/38.86  | | | | | | | | | | | BETA: splitting (71) gives:
% 226.12/38.86  | | | | | | | | | | | 
% 226.12/38.86  | | | | | | | | | | | Case 1:
% 226.12/38.86  | | | | | | | | | | | | 
% 226.12/38.86  | | | | | | | | | | | |   (110)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 226.12/38.86  | | | | | | | | | | | |            & op(e2, e3) = e3)
% 226.12/38.86  | | | | | | | | | | | | 
% 226.12/38.86  | | | | | | | | | | | | BETA: splitting (110) gives:
% 226.12/38.86  | | | | | | | | | | | | 
% 226.12/38.86  | | | | | | | | | | | | Case 1:
% 226.12/38.86  | | | | | | | | | | | | | 
% 226.12/38.86  | | | | | | | | | | | | |   (111)  all_57_0 = e3 & op(e3, e3) = e3
% 226.12/38.86  | | | | | | | | | | | | | 
% 226.12/38.86  | | | | | | | | | | | | | REF_CLOSE: (11), (13), (37), (109) are inconsistent by
% 226.12/38.86  | | | | | | | | | | | | |            sub-proof #2495.
% 226.12/38.86  | | | | | | | | | | | | | 
% 226.12/38.86  | | | | | | | | | | | | Case 2:
% 226.12/38.86  | | | | | | | | | | | | | 
% 226.12/38.86  | | | | | | | | | | | | |   (112)  all_57_2 = e3 & op(e2, e3) = e3
% 226.12/38.86  | | | | | | | | | | | | | 
% 226.12/38.86  | | | | | | | | | | | | | REF_CLOSE: (11), (98), (112) are inconsistent by sub-proof
% 226.12/38.86  | | | | | | | | | | | | |            #701.
% 226.12/38.86  | | | | | | | | | | | | | 
% 226.12/38.86  | | | | | | | | | | | | End of split
% 226.12/38.86  | | | | | | | | | | | | 
% 226.12/38.86  | | | | | | | | | | | Case 2:
% 226.12/38.86  | | | | | | | | | | | | 
% 226.12/38.86  | | | | | | | | | | | |   (113)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 226.12/38.86  | | | | | | | | | | | |            e3 & op(e0, e3) = e3)
% 226.12/38.86  | | | | | | | | | | | | 
% 226.12/38.86  | | | | | | | | | | | | REF_CLOSE: (6), (33), (35), (93), (113) are inconsistent by
% 226.12/38.86  | | | | | | | | | | | |            sub-proof #550.
% 226.12/38.86  | | | | | | | | | | | | 
% 226.12/38.86  | | | | | | | | | | | End of split
% 226.12/38.86  | | | | | | | | | | | 
% 226.12/38.86  | | | | | | | | | | Case 2:
% 226.12/38.86  | | | | | | | | | | | 
% 226.12/38.87  | | | | | | | | | | |   (114)  all_57_1 = e1 & op(e3, e2) = e1
% 226.12/38.87  | | | | | | | | | | | 
% 226.12/38.87  | | | | | | | | | | | REF_CLOSE: (74), (90), (114) are inconsistent by sub-proof
% 226.12/38.87  | | | | | | | | | | |            #2210.
% 226.12/38.87  | | | | | | | | | | | 
% 226.12/38.87  | | | | | | | | | | End of split
% 226.12/38.87  | | | | | | | | | | 
% 226.12/38.87  | | | | | | | | | Case 2:
% 226.12/38.87  | | | | | | | | | | 
% 226.12/38.87  | | | | | | | | | |   (115)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 226.12/38.87  | | | | | | | | | |            & op(e3, e0) = e1)
% 226.12/38.87  | | | | | | | | | | 
% 226.12/38.87  | | | | | | | | | | BETA: splitting (115) gives:
% 226.12/38.87  | | | | | | | | | | 
% 226.12/38.87  | | | | | | | | | | Case 1:
% 226.12/38.87  | | | | | | | | | | | 
% 226.12/38.87  | | | | | | | | | | |   (116)  all_57_4 = e1 & op(e3, e1) = e1
% 226.12/38.87  | | | | | | | | | | | 
% 226.12/38.87  | | | | | | | | | | | ALPHA: (116) implies:
% 226.12/38.87  | | | | | | | | | | |   (117)  all_57_4 = e1
% 226.12/38.87  | | | | | | | | | | | 
% 226.12/38.87  | | | | | | | | | | | BETA: splitting (80) gives:
% 226.12/38.87  | | | | | | | | | | | 
% 226.12/38.87  | | | | | | | | | | | Case 1:
% 226.12/38.87  | | | | | | | | | | | | 
% 226.12/38.87  | | | | | | | | | | | |   (118)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 226.12/38.87  | | | | | | | | | | | |            & op(e2, e1) = e2)
% 226.12/38.87  | | | | | | | | | | | | 
% 226.12/38.87  | | | | | | | | | | | | BETA: splitting (118) gives:
% 226.12/38.87  | | | | | | | | | | | | 
% 226.12/38.87  | | | | | | | | | | | | Case 1:
% 226.12/38.87  | | | | | | | | | | | | | 
% 226.12/38.87  | | | | | | | | | | | | |   (119)  all_57_4 = e2 & op(e3, e1) = e2
% 226.12/38.87  | | | | | | | | | | | | | 
% 226.12/38.87  | | | | | | | | | | | | | ALPHA: (119) implies:
% 226.12/38.87  | | | | | | | | | | | | |   (120)  all_57_4 = e2
% 226.12/38.87  | | | | | | | | | | | | | 
% 226.12/38.87  | | | | | | | | | | | | | REF_CLOSE: (74), (117), (120) are inconsistent by sub-proof
% 226.12/38.87  | | | | | | | | | | | | |            #2430.
% 226.12/38.87  | | | | | | | | | | | | | 
% 226.12/38.87  | | | | | | | | | | | | Case 2:
% 226.12/38.87  | | | | | | | | | | | | | 
% 226.12/38.87  | | | | | | | | | | | | |   (121)  all_57_5 = e2 & op(e2, e1) = e2
% 226.12/38.87  | | | | | | | | | | | | | 
% 226.12/38.87  | | | | | | | | | | | | | ALPHA: (121) implies:
% 226.12/38.87  | | | | | | | | | | | | |   (122)  all_57_5 = e2
% 226.12/38.87  | | | | | | | | | | | | | 
% 226.12/38.87  | | | | | | | | | | | | | BETA: splitting (61) gives:
% 226.12/38.87  | | | | | | | | | | | | | 
% 226.12/38.87  | | | | | | | | | | | | | Case 1:
% 226.12/38.87  | | | | | | | | | | | | | | 
% 226.12/38.87  | | | | | | | | | | | | | |   (123)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 226.12/38.87  | | | | | | | | | | | | | |            & op(e2, e2) = e3)
% 226.12/38.87  | | | | | | | | | | | | | | 
% 226.12/38.87  | | | | | | | | | | | | | | REF_CLOSE: (5), (13), (31), (55), (73), (123) are
% 226.12/38.87  | | | | | | | | | | | | | |            inconsistent by sub-proof #111.
% 226.12/38.87  | | | | | | | | | | | | | | 
% 226.12/38.87  | | | | | | | | | | | | | Case 2:
% 226.12/38.87  | | | | | | | | | | | | | | 
% 226.12/38.87  | | | | | | | | | | | | | |   (124)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 226.12/38.87  | | | | | | | | | | | | | |            e3 & op(e2, e0) = e3)
% 226.12/38.87  | | | | | | | | | | | | | | 
% 226.12/38.87  | | | | | | | | | | | | | | BETA: splitting (124) gives:
% 226.12/38.87  | | | | | | | | | | | | | | 
% 226.12/38.87  | | | | | | | | | | | | | | Case 1:
% 226.12/38.87  | | | | | | | | | | | | | | | 
% 226.12/38.87  | | | | | | | | | | | | | | |   (125)  all_57_5 = e3 & op(e2, e1) = e3
% 226.12/38.87  | | | | | | | | | | | | | | | 
% 226.12/38.87  | | | | | | | | | | | | | | | REF_CLOSE: (11), (13), (16), (17), (33), (52), (106), (117),
% 226.12/38.87  | | | | | | | | | | | | | | |            (122), (125) are inconsistent by sub-proof #1888.
% 226.12/38.87  | | | | | | | | | | | | | | | 
% 226.12/38.87  | | | | | | | | | | | | | | Case 2:
% 226.12/38.87  | | | | | | | | | | | | | | | 
% 226.12/38.87  | | | | | | | | | | | | | | |   (126)  all_57_10 = e3 & op(e2, e0) = e3
% 226.12/38.87  | | | | | | | | | | | | | | | 
% 226.12/38.87  | | | | | | | | | | | | | | | ALPHA: (126) implies:
% 226.12/38.87  | | | | | | | | | | | | | | |   (127)  op(e2, e0) = e3
% 226.12/38.87  | | | | | | | | | | | | | | | 
% 226.12/38.87  | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (13), (24), (35), (37), (68), (127) are
% 226.12/38.87  | | | | | | | | | | | | | | |            inconsistent by sub-proof #148.
% 226.12/38.87  | | | | | | | | | | | | | | | 
% 226.12/38.87  | | | | | | | | | | | | | | End of split
% 226.12/38.87  | | | | | | | | | | | | | | 
% 226.12/38.87  | | | | | | | | | | | | | End of split
% 226.12/38.87  | | | | | | | | | | | | | 
% 226.12/38.87  | | | | | | | | | | | | End of split
% 226.12/38.87  | | | | | | | | | | | | 
% 226.12/38.87  | | | | | | | | | | | Case 2:
% 226.12/38.87  | | | | | | | | | | | | 
% 226.12/38.87  | | | | | | | | | | | |   (128)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 226.12/38.87  | | | | | | | | | | | |            e2 & op(e0, e1) = e2)
% 226.12/38.87  | | | | | | | | | | | | 
% 226.12/38.87  | | | | | | | | | | | | BETA: splitting (128) gives:
% 226.12/38.87  | | | | | | | | | | | | 
% 226.12/38.87  | | | | | | | | | | | | Case 1:
% 226.12/38.87  | | | | | | | | | | | | | 
% 226.12/38.87  | | | | | | | | | | | | |   (129)  all_57_8 = e2 & op(e1, e1) = e2
% 226.12/38.87  | | | | | | | | | | | | | 
% 226.12/38.87  | | | | | | | | | | | | | ALPHA: (129) implies:
% 226.12/38.87  | | | | | | | | | | | | |   (130)  all_57_8 = e2
% 226.12/38.87  | | | | | | | | | | | | | 
% 226.12/38.87  | | | | | | | | | | | | | COMBINE_EQS: (67), (130) imply:
% 226.12/38.87  | | | | | | | | | | | | |   (131)  e2 = e0
% 226.12/38.87  | | | | | | | | | | | | | 
% 226.12/38.87  | | | | | | | | | | | | | REF_CLOSE: (10), (11), (30), (33), (46), (49), (66), (74),
% 226.12/38.87  | | | | | | | | | | | | |            (85), (90), (131) are inconsistent by sub-proof
% 226.12/38.87  | | | | | | | | | | | | |            #1392.
% 226.12/38.87  | | | | | | | | | | | | | 
% 226.12/38.87  | | | | | | | | | | | | Case 2:
% 226.12/38.87  | | | | | | | | | | | | | 
% 226.12/38.87  | | | | | | | | | | | | |   (132)  all_57_14 = e2 & op(e0, e1) = e2
% 226.12/38.87  | | | | | | | | | | | | | 
% 226.12/38.87  | | | | | | | | | | | | | ALPHA: (132) implies:
% 226.12/38.87  | | | | | | | | | | | | |   (133)  all_57_14 = e2
% 226.12/38.87  | | | | | | | | | | | | | 
% 226.12/38.87  | | | | | | | | | | | | | REF_CLOSE: (33), (106), (133) are inconsistent by sub-proof
% 226.12/38.87  | | | | | | | | | | | | |            #2410.
% 226.12/38.87  | | | | | | | | | | | | | 
% 226.12/38.87  | | | | | | | | | | | | End of split
% 226.12/38.87  | | | | | | | | | | | | 
% 226.12/38.87  | | | | | | | | | | | End of split
% 226.12/38.87  | | | | | | | | | | | 
% 226.12/38.87  | | | | | | | | | | Case 2:
% 226.12/38.87  | | | | | | | | | | | 
% 226.12/38.87  | | | | | | | | | | |   (134)  all_57_9 = e1 & op(e3, e0) = e1
% 226.12/38.87  | | | | | | | | | | | 
% 226.12/38.87  | | | | | | | | | | | ALPHA: (134) implies:
% 226.12/38.87  | | | | | | | | | | |   (135)  all_57_9 = e1
% 226.12/38.87  | | | | | | | | | | | 
% 226.12/38.87  | | | | | | | | | | | COMBINE_EQS: (43), (135) imply:
% 226.12/38.87  | | | | | | | | | | |   (136)  e1 = e0
% 226.12/38.87  | | | | | | | | | | | 
% 226.12/38.87  | | | | | | | | | | | REF_CLOSE: (3), (11), (30), (33), (35), (46), (49), (61),
% 226.12/38.87  | | | | | | | | | | |            (70), (74), (98), (136) are inconsistent by
% 226.12/38.87  | | | | | | | | | | |            sub-proof #1252.
% 226.12/38.87  | | | | | | | | | | | 
% 226.12/38.87  | | | | | | | | | | End of split
% 226.12/38.87  | | | | | | | | | | 
% 226.12/38.87  | | | | | | | | | End of split
% 226.12/38.87  | | | | | | | | | 
% 226.12/38.87  | | | | | | | | Case 2:
% 226.12/38.87  | | | | | | | | | 
% 226.12/38.87  | | | | | | | | |   (137)  all_57_15 = e3 & op(e0, e0) = e3
% 226.12/38.87  | | | | | | | | | 
% 226.12/38.87  | | | | | | | | | ALPHA: (137) implies:
% 226.12/38.87  | | | | | | | | |   (138)  all_57_15 = e3
% 226.12/38.87  | | | | | | | | |   (139)  op(e0, e0) = e3
% 226.12/38.87  | | | | | | | | | 
% 226.12/38.87  | | | | | | | | | REF_CLOSE: (1), (2), (3), (8), (9), (10), (11), (12), (13),
% 226.12/38.87  | | | | | | | | |            (14), (15), (16), (17), (18), (19), (20), (21),
% 226.12/38.87  | | | | | | | | |            (23), (25), (26), (28), (29), (30), (32), (33),
% 226.12/38.87  | | | | | | | | |            (34), (35), (36), (37), (39), (40), (41), (42),
% 226.12/38.87  | | | | | | | | |            (44), (45), (46), (47), (48), (49), (50), (51),
% 226.12/38.87  | | | | | | | | |            (52), (53), (56), (58), (59), (60), (61), (62),
% 226.12/38.87  | | | | | | | | |            (63), (64), (69), (70), (71), (74), (75), (76),
% 226.12/38.87  | | | | | | | | |            (77), (78), (79), (80), (81), (82), (83), (84),
% 226.12/38.87  | | | | | | | | |            (85), (86), (87), (138), (139) are inconsistent by
% 226.12/38.87  | | | | | | | | |            sub-proof #1415.
% 226.12/38.87  | | | | | | | | | 
% 226.12/38.87  | | | | | | | | End of split
% 226.12/38.87  | | | | | | | | 
% 226.12/38.87  | | | | | | | End of split
% 226.12/38.87  | | | | | | | 
% 226.12/38.87  | | | | | | End of split
% 226.12/38.87  | | | | | | 
% 226.12/38.87  | | | | | Case 2:
% 226.12/38.87  | | | | | | 
% 226.12/38.87  | | | | | |   (140)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 &
% 226.12/38.87  | | | | | |            op(e0, e3) = e1)
% 226.12/38.87  | | | | | | 
% 226.12/38.87  | | | | | | REF_CLOSE: (6), (49), (74), (93), (140) are inconsistent by
% 226.12/38.87  | | | | | |            sub-proof #1513.
% 226.12/38.87  | | | | | | 
% 226.12/38.87  | | | | | End of split
% 226.12/38.87  | | | | | 
% 226.12/38.87  | | | | Case 2:
% 226.12/38.87  | | | | | 
% 226.12/38.87  | | | | |   (141)  all_57_7 = e2 & op(e1, e2) = e2
% 226.12/38.87  | | | | | 
% 226.12/38.87  | | | | | REF_CLOSE: (33), (66), (141) are inconsistent by sub-proof #2092.
% 226.12/38.87  | | | | | 
% 226.12/38.87  | | | | End of split
% 226.12/38.87  | | | | 
% 226.12/38.87  | | | Case 2:
% 226.12/38.87  | | | | 
% 226.12/38.87  | | | |   (142)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1,
% 226.12/38.87  | | | |              e0) = e2)
% 226.12/38.87  | | | | 
% 226.12/38.87  | | | | BETA: splitting (142) gives:
% 226.12/38.87  | | | | 
% 226.12/38.87  | | | | Case 1:
% 226.12/38.87  | | | | | 
% 226.12/38.87  | | | | |   (143)  all_57_8 = e2 & op(e1, e1) = e2
% 226.12/38.87  | | | | | 
% 226.12/38.87  | | | | | ALPHA: (143) implies:
% 226.12/38.87  | | | | |   (144)  all_57_8 = e2
% 226.12/38.87  | | | | | 
% 226.12/38.87  | | | | | COMBINE_EQS: (67), (144) imply:
% 226.12/38.87  | | | | |   (145)  e2 = e0
% 226.12/38.87  | | | | | 
% 226.12/38.87  | | | | | COMBINE_EQS: (90), (145) imply:
% 226.12/38.87  | | | | |   (146)  all_57_1 = e0
% 226.12/38.87  | | | | | 
% 226.12/38.87  | | | | | REF_CLOSE: (10), (11), (30), (33), (46), (49), (66), (74), (85), (146)
% 226.12/38.87  | | | | |            are inconsistent by sub-proof #2098.
% 226.12/38.87  | | | | | 
% 226.12/38.87  | | | | Case 2:
% 226.12/38.87  | | | | | 
% 226.12/38.87  | | | | |   (147)  all_57_11 = e2 & op(e1, e0) = e2
% 226.12/38.87  | | | | | 
% 226.12/38.87  | | | | | ALPHA: (147) implies:
% 226.12/38.87  | | | | |   (148)  all_57_11 = e2
% 226.12/38.87  | | | | | 
% 226.12/38.87  | | | | | BETA: splitting (54) gives:
% 226.12/38.87  | | | | | 
% 226.12/38.87  | | | | | Case 1:
% 226.12/38.87  | | | | | | 
% 226.12/38.87  | | | | | |   (149)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 &
% 226.12/38.87  | | | | | |            op(e0, e2) = e3)
% 226.12/38.87  | | | | | | 
% 226.12/38.87  | | | | | | BETA: splitting (149) gives:
% 226.12/38.87  | | | | | | 
% 226.12/38.87  | | | | | | Case 1:
% 226.12/38.87  | | | | | | | 
% 226.12/38.87  | | | | | | |   (150)  all_57_12 = e3 & op(e0, e3) = e3
% 226.12/38.87  | | | | | | | 
% 226.12/38.87  | | | | | | | ALPHA: (150) implies:
% 226.12/38.87  | | | | | | |   (151)  all_57_12 = e3
% 226.12/38.87  | | | | | | | 
% 226.12/38.87  | | | | | | | REF_CLOSE: (3), (8), (11), (13), (30), (33), (35), (37), (46),
% 226.12/38.87  | | | | | | |            (49), (61), (70), (74), (78), (81), (151) are
% 226.12/38.87  | | | | | | |            inconsistent by sub-proof #2223.
% 226.12/38.87  | | | | | | | 
% 226.12/38.87  | | | | | | Case 2:
% 226.12/38.87  | | | | | | | 
% 226.12/38.87  | | | | | | |   (152)  all_57_13 = e3 & op(e0, e2) = e3
% 226.12/38.87  | | | | | | | 
% 226.12/38.87  | | | | | | | ALPHA: (152) implies:
% 226.12/38.87  | | | | | | |   (153)  all_57_13 = e3
% 226.12/38.87  | | | | | | | 
% 226.12/38.87  | | | | | | | REF_CLOSE: (6), (8), (11), (13), (14), (16), (17), (30), (33),
% 226.12/38.87  | | | | | | |            (46), (49), (65), (74), (78), (85), (90), (148), (153)
% 226.12/38.87  | | | | | | |            are inconsistent by sub-proof #1306.
% 226.12/38.87  | | | | | | | 
% 226.12/38.87  | | | | | | End of split
% 226.12/38.87  | | | | | | 
% 226.12/38.87  | | | | | Case 2:
% 226.12/38.87  | | | | | | 
% 226.12/38.87  | | | | | |   (154)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 &
% 226.12/38.87  | | | | | |            op(e0, e0) = e3)
% 226.12/38.87  | | | | | | 
% 226.12/38.87  | | | | | | BETA: splitting (154) gives:
% 226.12/38.87  | | | | | | 
% 226.12/38.87  | | | | | | Case 1:
% 226.12/38.87  | | | | | | | 
% 226.12/38.87  | | | | | | |   (155)  all_57_14 = e3 & op(e0, e1) = e3
% 226.12/38.87  | | | | | | | 
% 226.12/38.87  | | | | | | | ALPHA: (155) implies:
% 226.12/38.87  | | | | | | |   (156)  all_57_14 = e3
% 226.12/38.87  | | | | | | | 
% 226.12/38.87  | | | | | | | BETA: splitting (72) gives:
% 226.12/38.87  | | | | | | | 
% 226.12/38.87  | | | | | | | Case 1:
% 226.12/38.87  | | | | | | | | 
% 226.12/38.87  | | | | | | | |   (157)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 &
% 226.12/38.87  | | | | | | | |            op(e2, e0) = e3)
% 226.12/38.87  | | | | | | | | 
% 226.12/38.87  | | | | | | | | BETA: splitting (157) gives:
% 226.12/38.87  | | | | | | | | 
% 226.12/38.87  | | | | | | | | Case 1:
% 226.12/38.87  | | | | | | | | | 
% 226.12/38.87  | | | | | | | | |   (158)  all_57_9 = e3 & op(e3, e0) = e3
% 226.12/38.87  | | | | | | | | | 
% 226.12/38.87  | | | | | | | | | ALPHA: (158) implies:
% 226.12/38.87  | | | | | | | | |   (159)  op(e3, e0) = e3
% 226.12/38.87  | | | | | | | | | 
% 226.12/38.87  | | | | | | | | | REF_CLOSE: (13), (35), (38), (159) are inconsistent by
% 226.12/38.87  | | | | | | | | |            sub-proof #313.
% 226.12/38.87  | | | | | | | | | 
% 226.12/38.87  | | | | | | | | Case 2:
% 226.12/38.87  | | | | | | | | | 
% 226.12/38.87  | | | | | | | | |   (160)  all_57_10 = e3 & op(e2, e0) = e3
% 226.12/38.87  | | | | | | | | | 
% 226.12/38.87  | | | | | | | | | ALPHA: (160) implies:
% 226.12/38.87  | | | | | | | | |   (161)  op(e2, e0) = e3
% 226.12/38.87  | | | | | | | | | 
% 226.12/38.87  | | | | | | | | | REF_CLOSE: (4), (7), (13), (24), (35), (37), (68), (161) are
% 226.12/38.87  | | | | | | | | |            inconsistent by sub-proof #148.
% 226.12/38.87  | | | | | | | | | 
% 226.12/38.87  | | | | | | | | End of split
% 226.12/38.87  | | | | | | | | 
% 226.12/38.87  | | | | | | | Case 2:
% 226.12/38.87  | | | | | | | | 
% 226.12/38.87  | | | | | | | |   (162)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 &
% 226.12/38.87  | | | | | | | |            op(e0, e0) = e3)
% 226.12/38.87  | | | | | | | | 
% 226.12/38.87  | | | | | | | | BETA: splitting (162) gives:
% 226.12/38.87  | | | | | | | | 
% 226.12/38.87  | | | | | | | | Case 1:
% 226.12/38.87  | | | | | | | | | 
% 226.12/38.87  | | | | | | | | |   (163)  all_57_11 = e3 & op(e1, e0) = e3
% 226.12/38.87  | | | | | | | | | 
% 226.12/38.87  | | | | | | | | | ALPHA: (163) implies:
% 226.12/38.87  | | | | | | | | |   (164)  all_57_11 = e3
% 226.12/38.87  | | | | | | | | | 
% 226.12/38.87  | | | | | | | | | REF_CLOSE: (33), (148), (164) are inconsistent by sub-proof
% 226.12/38.87  | | | | | | | | |            #2119.
% 226.12/38.87  | | | | | | | | | 
% 226.12/38.87  | | | | | | | | Case 2:
% 226.12/38.87  | | | | | | | | | 
% 226.12/38.87  | | | | | | | | |   (165)  all_57_15 = e3 & op(e0, e0) = e3
% 226.12/38.87  | | | | | | | | | 
% 226.12/38.87  | | | | | | | | | ALPHA: (165) implies:
% 226.12/38.87  | | | | | | | | |   (166)  all_57_15 = e3
% 226.12/38.87  | | | | | | | | | 
% 226.12/38.87  | | | | | | | | | REF_CLOSE: (6), (11), (33), (42), (46), (49), (58), (74),
% 226.12/38.87  | | | | | | | | |            (156), (166) are inconsistent by sub-proof #2322.
% 226.12/38.87  | | | | | | | | | 
% 226.12/38.87  | | | | | | | | End of split
% 226.12/38.87  | | | | | | | | 
% 226.12/38.87  | | | | | | | End of split
% 226.12/38.87  | | | | | | | 
% 226.12/38.87  | | | | | | Case 2:
% 226.12/38.87  | | | | | | | 
% 226.12/38.87  | | | | | | |   (167)  all_57_15 = e3 & op(e0, e0) = e3
% 226.12/38.87  | | | | | | | 
% 226.12/38.87  | | | | | | | ALPHA: (167) implies:
% 226.12/38.87  | | | | | | |   (168)  all_57_15 = e3
% 226.12/38.87  | | | | | | |   (169)  op(e0, e0) = e3
% 226.12/38.87  | | | | | | | 
% 226.12/38.87  | | | | | | | REF_CLOSE: (1), (2), (3), (8), (9), (10), (11), (12), (13), (14),
% 226.12/38.87  | | | | | | |            (15), (16), (17), (18), (19), (20), (21), (23), (25),
% 226.12/38.87  | | | | | | |            (26), (28), (29), (30), (32), (33), (34), (35), (36),
% 226.12/38.87  | | | | | | |            (37), (39), (40), (41), (42), (44), (45), (46), (47),
% 226.12/38.87  | | | | | | |            (48), (49), (50), (51), (52), (53), (56), (58), (59),
% 226.12/38.87  | | | | | | |            (60), (61), (62), (63), (64), (69), (70), (71), (74),
% 226.12/38.87  | | | | | | |            (75), (76), (77), (78), (79), (80), (81), (82), (83),
% 226.12/38.87  | | | | | | |            (84), (85), (86), (87), (168), (169) are inconsistent
% 226.12/38.87  | | | | | | |            by sub-proof #1415.
% 226.12/38.87  | | | | | | | 
% 226.12/38.87  | | | | | | End of split
% 226.12/38.87  | | | | | | 
% 226.12/38.87  | | | | | End of split
% 226.12/38.87  | | | | | 
% 226.12/38.87  | | | | End of split
% 226.12/38.87  | | | | 
% 226.12/38.87  | | | End of split
% 226.12/38.87  | | | 
% 226.12/38.87  | | Case 2:
% 226.12/38.87  | | | 
% 226.12/38.87  | | |   (170)  all_57_3 = e2 & op(e2, e2) = e2
% 226.12/38.87  | | | 
% 226.12/38.87  | | | ALPHA: (170) implies:
% 226.12/38.87  | | |   (171)  op(e2, e2) = e2
% 226.12/38.87  | | | 
% 226.12/38.87  | | | REF_CLOSE: (13), (27), (46), (171) are inconsistent by sub-proof #2472.
% 226.12/38.87  | | | 
% 226.12/38.87  | | End of split
% 226.12/38.87  | | 
% 226.12/38.87  | Case 2:
% 226.12/38.87  | | 
% 226.12/38.87  | |   (172)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 226.12/38.87  | |            e2)
% 226.12/38.87  | | 
% 226.12/38.87  | | REF_CLOSE: (13), (22), (33), (57), (66), (172) are inconsistent by sub-proof
% 226.12/38.87  | |            #28.
% 226.12/38.87  | | 
% 226.12/38.87  | End of split
% 226.12/38.87  | 
% 226.12/38.87  End of proof
% 226.12/38.87  
% 226.12/38.87  Sub-proof #26 shows that the following formulas are inconsistent:
% 226.12/38.87  ----------------------------------------------------------------
% 226.12/38.87    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.12/38.87           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.12/38.87    (2)  op(e2, e2) = e0
% 226.12/38.87    (3)   ~ (e1 = e0)
% 226.12/38.87    (4)  op(e1, e1) = e2
% 226.12/38.87    (5)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 &
% 226.12/38.87         op(all_52_17, all_52_17) = e3 & op(all_52_19, all_52_19) = e2 &
% 226.12/38.87         op(all_52_21, all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1,
% 226.12/38.87           e3) = all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 &
% 226.12/38.87         op(e1, e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 226.12/38.87         $i(all_52_23)
% 226.12/38.87  
% 226.12/38.87  Begin of proof
% 226.12/38.87  | 
% 226.12/38.87  | ALPHA: (5) implies:
% 226.12/38.87  |   (6)  op(e1, e1) = all_52_21
% 226.12/38.87  |   (7)  op(all_52_21, all_52_21) = e1
% 226.12/38.87  | 
% 226.12/38.87  | GROUND_INST: instantiating (1) with e2, all_52_21, e1, e1, simplifying with
% 226.12/38.87  |              (4), (6) gives:
% 226.12/38.87  |   (8)  all_52_21 = e2
% 226.12/38.87  | 
% 226.12/38.87  | REDUCE: (7), (8) imply:
% 226.12/38.87  |   (9)  op(e2, e2) = e1
% 226.12/38.87  | 
% 226.12/38.87  | REF_CLOSE: (1), (2), (3), (9) are inconsistent by sub-proof #2352.
% 226.12/38.87  | 
% 226.12/38.87  End of proof
% 226.12/38.87  
% 226.12/38.87  Sub-proof #27 shows that the following formulas are inconsistent:
% 226.12/38.87  ----------------------------------------------------------------
% 226.12/38.87    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.12/38.87           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.12/38.87    (2)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 226.12/38.87           op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 226.12/38.87           op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 226.12/38.87           = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3, e0)
% 226.12/38.87           = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) & $i(all_52_7))
% 226.12/38.87         | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0 &
% 226.12/38.87           op(all_52_9, all_52_9) = e3 & op(all_52_11, all_52_11) = e2 &
% 226.12/38.87           op(all_52_13, all_52_13) = e1 & op(all_52_15, all_52_15) = e0 & op(e2,
% 226.12/38.87             e3) = all_52_9 & op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13 &
% 226.12/38.87           op(e2, e0) = all_52_15 & $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 226.12/38.87           $i(all_52_15))
% 226.12/38.87    (3)  op(e2, e2) = e0
% 226.12/38.87    (4)   ~ (all_8_2 = e3)
% 226.12/38.87    (5)   ~ (e2 = e0)
% 226.12/38.87    (6)  op(e2, e3) = e2
% 226.12/38.87    (7)  op(e2, e2) = all_8_2
% 226.12/38.87    (8)  op(e3, e2) = e2
% 226.12/38.87  
% 226.12/38.87  Begin of proof
% 226.12/38.87  | 
% 226.12/38.87  | BETA: splitting (2) gives:
% 226.12/38.87  | 
% 226.12/38.87  | Case 1:
% 226.12/38.87  | | 
% 226.12/38.87  | |   (9)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 226.12/38.87  | |        op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 226.12/38.87  | |        op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3,
% 226.12/38.87  | |          e3) = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 &
% 226.12/38.87  | |        op(e3, e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 226.12/38.87  | |        $i(all_52_7)
% 226.12/38.87  | | 
% 226.12/38.87  | | ALPHA: (9) implies:
% 226.12/38.87  | |   (10)  op(e3, e2) = all_52_3
% 226.12/38.87  | |   (11)  op(all_52_3, all_52_3) = e2
% 226.12/38.87  | | 
% 226.12/38.87  | | GROUND_INST: instantiating (1) with e2, all_52_3, e2, e3, simplifying with
% 226.12/38.87  | |              (8), (10) gives:
% 226.12/38.87  | |   (12)  all_52_3 = e2
% 226.12/38.87  | | 
% 226.12/38.87  | | REDUCE: (11), (12) imply:
% 226.12/38.87  | |   (13)  op(e2, e2) = e2
% 226.12/38.87  | | 
% 226.12/38.87  | | REF_CLOSE: (1), (3), (5), (13) are inconsistent by sub-proof #2472.
% 226.12/38.87  | | 
% 226.12/38.87  | Case 2:
% 226.12/38.87  | | 
% 226.12/38.87  | |   (14)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0 &
% 226.12/38.87  | |         op(all_52_9, all_52_9) = e3 & op(all_52_11, all_52_11) = e2 &
% 226.12/38.87  | |         op(all_52_13, all_52_13) = e1 & op(all_52_15, all_52_15) = e0 &
% 226.12/38.87  | |         op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 & op(e2, e1) =
% 226.12/38.87  | |         all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) & $i(all_52_11) &
% 226.12/38.87  | |         $i(all_52_13) & $i(all_52_15)
% 226.12/38.87  | | 
% 226.12/38.87  | | ALPHA: (14) implies:
% 226.12/38.87  | |   (15)  op(e2, e3) = all_52_9
% 226.12/38.87  | |   (16)  op(all_52_9, all_52_9) = e3
% 226.12/38.87  | | 
% 226.12/38.87  | | GROUND_INST: instantiating (1) with e2, all_52_9, e3, e2, simplifying with
% 226.12/38.87  | |              (6), (15) gives:
% 226.12/38.87  | |   (17)  all_52_9 = e2
% 226.12/38.87  | | 
% 226.12/38.87  | | REDUCE: (16), (17) imply:
% 226.12/38.87  | |   (18)  op(e2, e2) = e3
% 226.12/38.87  | | 
% 226.12/38.87  | | REF_CLOSE: (1), (4), (7), (18) are inconsistent by sub-proof #140.
% 226.12/38.87  | | 
% 226.12/38.87  | End of split
% 226.12/38.87  | 
% 226.12/38.87  End of proof
% 226.12/38.87  
% 226.12/38.87  Sub-proof #28 shows that the following formulas are inconsistent:
% 226.12/38.87  ----------------------------------------------------------------
% 226.12/38.87    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.12/38.87           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.12/38.87    (2)   ~ (all_53_7 = e2)
% 226.12/38.87    (3)   ~ (e3 = e2)
% 226.12/38.87    (4)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 226.12/38.87    (5)  op(e0, e2) = all_53_7
% 226.12/38.87    (6)  all_57_7 = e3
% 226.12/38.87  
% 226.12/38.87  Begin of proof
% 226.12/38.87  | 
% 226.12/38.87  | BETA: splitting (4) gives:
% 226.12/38.87  | 
% 226.12/38.87  | Case 1:
% 226.12/38.87  | | 
% 226.12/38.87  | |   (7)  all_57_7 = e2 & op(e1, e2) = e2
% 226.12/38.87  | | 
% 226.12/38.87  | | ALPHA: (7) implies:
% 226.12/38.87  | |   (8)  all_57_7 = e2
% 226.12/38.87  | | 
% 226.12/38.87  | | REF_CLOSE: (3), (6), (8) are inconsistent by sub-proof #2102.
% 226.12/38.87  | | 
% 226.12/38.87  | Case 2:
% 226.12/38.87  | | 
% 226.12/38.87  | |   (9)  all_57_13 = e2 & op(e0, e2) = e2
% 226.12/38.87  | | 
% 226.12/38.87  | | ALPHA: (9) implies:
% 226.12/38.87  | |   (10)  op(e0, e2) = e2
% 226.12/38.87  | | 
% 226.12/38.87  | | REF_CLOSE: (1), (2), (5), (10) are inconsistent by sub-proof #2335.
% 226.12/38.87  | | 
% 226.12/38.87  | End of split
% 226.12/38.87  | 
% 226.12/38.87  End of proof
% 226.12/38.87  
% 226.12/38.87  Sub-proof #29 shows that the following formulas are inconsistent:
% 226.12/38.87  ----------------------------------------------------------------
% 226.12/38.87    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.12/38.87           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.12/38.87    (2)  all_57_14 = e3
% 226.12/38.87    (3)  op(e0, e3) = all_52_25
% 226.12/38.87    (4)   ~ (e3 = e2)
% 226.12/38.87    (5)   ~ (e3 = e0)
% 226.12/38.87    (6)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 226.12/38.87         (all_57_14 = e0 & op(e0, e1) = e0)
% 226.12/38.87    (7)   ~ (all_53_7 = e0)
% 226.12/38.87    (8)  op(e0, e0) = all_52_31
% 226.12/38.87    (9)  op(all_52_25, all_52_25) = e3
% 226.12/38.87    (10)  op(e0, e2) = all_53_7
% 226.12/38.87    (11)  op(e0, e0) = e2
% 226.12/38.87  
% 226.12/38.87  Begin of proof
% 226.12/38.87  | 
% 226.12/38.87  | BETA: splitting (6) gives:
% 226.12/38.87  | 
% 226.12/38.87  | Case 1:
% 226.12/38.87  | | 
% 226.12/38.87  | |   (12)  all_57_12 = e0 & op(e0, e3) = e0
% 226.12/38.87  | | 
% 226.12/38.87  | | ALPHA: (12) implies:
% 226.12/38.87  | |   (13)  op(e0, e3) = e0
% 226.12/38.87  | | 
% 226.12/38.87  | | REF_CLOSE: (1), (3), (4), (8), (9), (11), (13) are inconsistent by sub-proof
% 226.12/38.87  | |            #31.
% 226.12/38.87  | | 
% 226.12/38.87  | Case 2:
% 226.12/38.87  | | 
% 226.12/38.87  | |   (14)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 226.12/38.87  | |           e0)
% 226.12/38.87  | | 
% 226.12/38.87  | | REF_CLOSE: (1), (2), (5), (7), (10), (14) are inconsistent by sub-proof #30.
% 226.12/38.87  | | 
% 226.12/38.87  | End of split
% 226.12/38.87  | 
% 226.12/38.87  End of proof
% 226.12/38.87  
% 226.12/38.87  Sub-proof #30 shows that the following formulas are inconsistent:
% 226.12/38.87  ----------------------------------------------------------------
% 226.12/38.87    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.12/38.87           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.12/38.87    (2)  all_57_14 = e3
% 226.12/38.87    (3)   ~ (e3 = e0)
% 226.12/38.87    (4)   ~ (all_53_7 = e0)
% 226.12/38.87    (5)  op(e0, e2) = all_53_7
% 226.12/38.87    (6)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 226.12/38.87  
% 226.12/38.87  Begin of proof
% 226.12/38.87  | 
% 226.12/38.87  | BETA: splitting (6) gives:
% 226.12/38.87  | 
% 226.12/38.87  | Case 1:
% 226.12/38.87  | | 
% 226.12/38.87  | |   (7)  all_57_13 = e0 & op(e0, e2) = e0
% 226.12/38.87  | | 
% 226.12/38.87  | | ALPHA: (7) implies:
% 226.12/38.87  | |   (8)  op(e0, e2) = e0
% 226.12/38.87  | | 
% 226.12/38.87  | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #2332.
% 226.12/38.87  | | 
% 226.12/38.87  | Case 2:
% 226.12/38.87  | | 
% 226.12/38.87  | |   (9)  all_57_14 = e0 & op(e0, e1) = e0
% 226.12/38.87  | | 
% 226.12/38.87  | | REF_CLOSE: (2), (3), (9) are inconsistent by sub-proof #2314.
% 226.12/38.87  | | 
% 226.12/38.87  | End of split
% 226.12/38.87  | 
% 226.12/38.87  End of proof
% 226.12/38.87  
% 226.12/38.87  Sub-proof #31 shows that the following formulas are inconsistent:
% 226.12/38.87  ----------------------------------------------------------------
% 226.12/38.87    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.12/38.87           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.12/38.87    (2)  op(e0, e3) = e0
% 226.12/38.87    (3)  op(e0, e3) = all_52_25
% 226.12/38.87    (4)   ~ (e3 = e2)
% 226.12/38.87    (5)  op(e0, e0) = all_52_31
% 226.12/38.87    (6)  op(all_52_25, all_52_25) = e3
% 226.12/38.87    (7)  op(e0, e0) = e2
% 226.12/38.87  
% 226.12/38.87  Begin of proof
% 226.12/38.87  | 
% 226.12/38.87  | GROUND_INST: instantiating (1) with e2, all_52_31, e0, e0, simplifying with
% 226.12/38.87  |              (5), (7) gives:
% 226.12/38.87  |   (8)  all_52_31 = e2
% 226.12/38.87  | 
% 226.12/38.87  | GROUND_INST: instantiating (1) with e0, all_52_25, e3, e0, simplifying with
% 226.12/38.87  |              (2), (3) gives:
% 226.12/38.87  |   (9)  all_52_25 = e0
% 226.12/38.87  | 
% 226.12/38.87  | REDUCE: (6), (9) imply:
% 226.12/38.87  |   (10)  op(e0, e0) = e3
% 226.12/38.87  | 
% 226.12/38.87  | GROUND_INST: instantiating (1) with e2, e3, e0, e0, simplifying with (7), (10)
% 226.12/38.87  |              gives:
% 226.12/38.87  |   (11)  e3 = e2
% 226.12/38.87  | 
% 226.12/38.87  | REDUCE: (4), (11) imply:
% 226.12/38.87  |   (12)  $false
% 226.12/38.87  | 
% 226.12/38.87  | CLOSE: (12) is inconsistent.
% 226.12/38.87  | 
% 226.12/38.87  End of proof
% 226.12/38.87  
% 226.12/38.87  Sub-proof #32 shows that the following formulas are inconsistent:
% 226.12/38.87  ----------------------------------------------------------------
% 226.12/38.87    (1)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3)
% 226.12/38.87    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.12/38.87           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.12/38.87    (3)   ~ (all_8_2 = e3)
% 226.12/38.87    (4)  op(e3, e2) = all_53_4
% 226.12/38.87    (5)  op(e2, e2) = all_8_2
% 226.12/38.87    (6)   ~ (all_53_4 = e3)
% 226.12/38.87  
% 226.12/38.87  Begin of proof
% 226.12/38.87  | 
% 226.12/38.87  | BETA: splitting (1) gives:
% 226.12/38.87  | 
% 226.12/38.87  | Case 1:
% 226.12/38.87  | | 
% 226.12/38.87  | |   (7)  all_57_1 = e3 & op(e3, e2) = e3
% 226.12/38.87  | | 
% 226.12/38.87  | | REF_CLOSE: (2), (4), (6), (7) are inconsistent by sub-proof #2286.
% 226.12/38.87  | | 
% 226.12/38.87  | Case 2:
% 226.12/38.87  | | 
% 226.12/38.87  | |   (8)  all_57_3 = e3 & op(e2, e2) = e3
% 226.12/38.87  | | 
% 226.12/38.88  | | ALPHA: (8) implies:
% 226.12/38.88  | |   (9)  op(e2, e2) = e3
% 226.12/38.88  | | 
% 226.12/38.88  | | REF_CLOSE: (2), (3), (5), (9) are inconsistent by sub-proof #140.
% 226.12/38.88  | | 
% 226.12/38.88  | End of split
% 226.12/38.88  | 
% 226.12/38.88  End of proof
% 226.12/38.88  
% 226.12/38.88  Sub-proof #33 shows that the following formulas are inconsistent:
% 226.12/38.88  ----------------------------------------------------------------
% 226.12/38.88    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 226.12/38.88    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 226.12/38.88    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 226.12/38.88         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 226.12/38.88    (4)  all_57_12 = e0
% 226.12/38.88    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 226.12/38.88         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 226.12/38.88    (6)   ~ (all_53_8 = all_53_12)
% 226.12/38.88    (7)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 226.12/38.88         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 226.12/38.88    (8)   ~ (e3 = e1)
% 226.12/38.88    (9)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 226.12/38.88         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 226.12/38.88    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.12/38.88            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.12/38.88    (11)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 226.12/38.88          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 226.12/38.88    (12)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 226.12/38.88            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 226.12/38.88              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 226.12/38.88    (13)   ~ (all_6_2 = e3)
% 226.12/38.88    (14)  op(e1, e1) = all_6_2
% 226.12/38.88    (15)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 226.12/38.88    (16)   ~ (all_53_9 = e0)
% 226.12/38.88    (17)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 226.12/38.88          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 226.12/38.88    (18)   ~ (all_53_4 = all_53_12)
% 226.12/38.88    (19)   ~ (all_53_8 = all_53_9)
% 226.12/38.88    (20)  all_42_2 = all_6_2
% 226.12/38.88    (21)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 226.12/38.88          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 226.12/38.88    (22)   ~ (all_53_9 = all_6_2)
% 226.12/38.88    (23)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 226.12/38.88          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 226.12/38.88    (24)  all_57_3 = e0
% 226.12/38.88    (25)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 226.12/38.88          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 226.12/38.88    (26)   ~ (e3 = e2)
% 226.12/38.88    (27)  all_55_1 = all_53_4
% 226.12/38.88    (28)   ~ (e3 = e0)
% 226.12/38.88    (29)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 226.12/38.88          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 226.12/38.88    (30)  op(e3, e3) = e3
% 226.12/38.88    (31)   ~ (all_53_8 = all_6_2)
% 226.12/38.88    (32)  all_55_2 = all_53_8
% 226.12/38.88    (33)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 226.12/38.88    (34)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 226.12/38.88          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 226.12/38.88            e1)
% 226.12/38.88    (35)   ~ (all_53_4 = all_53_8)
% 226.12/38.88    (36)  op(e3, e2) = all_53_4
% 226.12/38.88    (37)   ~ (e2 = e0)
% 226.12/38.88    (38)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 226.12/38.88            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 226.12/38.88            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 226.12/38.88            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 226.12/38.88              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 226.12/38.88            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 226.12/38.88            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 226.12/38.88              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 226.12/38.88              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 226.12/38.88            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 226.12/38.88            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 226.12/38.88            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 226.12/38.88              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 226.12/38.88              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 226.12/38.88            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 226.12/38.88              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 226.12/38.88            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 226.12/38.88            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 226.12/38.88              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 226.12/38.88              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 226.12/38.88            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 226.12/38.88            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 226.12/38.88    (39)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 226.12/38.88          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 226.12/38.88    (40)   ~ (e1 = e0)
% 226.12/38.88    (41)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 226.12/38.88            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 226.12/38.88              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 226.12/38.88    (42)   ~ (all_53_4 = e0)
% 226.12/38.88    (43)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 226.12/38.88          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 226.12/38.88    (44)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 226.12/38.88          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 226.12/38.88    (45)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 226.12/38.88          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 226.12/38.88            e3)
% 226.12/38.88    (46)   ~ (all_53_4 = all_53_6)
% 226.12/38.88    (47)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 226.12/38.88          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 226.12/38.88            e2)
% 226.12/38.88    (48)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 226.12/38.88              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 226.12/38.88                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 226.12/38.88                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 226.12/38.88    (49)  all_55_10 = all_6_2
% 226.12/38.88    (50)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 226.12/38.88          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 226.12/38.88    (51)  all_38_2 = all_6_2
% 226.12/38.88    (52)  all_55_3 = all_53_12
% 226.12/38.88    (53)   ~ (all_53_12 = e3)
% 226.12/38.88    (54)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 226.12/38.88            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 226.12/38.88              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 226.12/38.88    (55)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 226.12/38.88          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 226.12/38.88    (56)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 226.12/38.88          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 226.12/38.88    (57)   ~ (e2 = e1)
% 226.12/38.88    (58)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 226.12/38.88          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 226.12/38.88    (59)  op(e0, e0) = e2
% 226.12/38.88    (60)  op(e2, e1) = all_53_9
% 226.12/38.88    (61)  op(e1, e2) = all_53_6
% 226.12/38.88    (62)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 226.12/38.88          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 226.12/38.88    (63)  all_24_2 = all_6_2
% 226.12/38.88    (64)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 226.12/38.88          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 226.12/38.88    (65)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 226.12/38.88          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 226.12/38.88    (66)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 226.12/38.88          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 226.12/38.88    (67)  all_57_14 = e0
% 226.12/38.88    (68)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 226.12/38.88          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 226.12/38.88    (69)  op(e3, e1) = all_53_8
% 226.12/38.88    (70)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 226.12/38.88          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 226.12/38.88    (71)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 226.12/38.88          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 226.12/38.88    (72)  op(e3, e0) = all_53_12
% 226.12/38.88  
% 226.12/38.88  Begin of proof
% 226.12/38.88  | 
% 226.12/38.88  | BETA: splitting (34) gives:
% 226.12/38.88  | 
% 226.12/38.88  | Case 1:
% 226.12/38.88  | | 
% 226.12/38.88  | |   (73)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 226.12/38.88  | |           e1)
% 226.12/38.88  | | 
% 226.12/38.88  | | BETA: splitting (73) gives:
% 226.12/38.88  | | 
% 226.12/38.88  | | Case 1:
% 226.12/38.88  | | | 
% 226.12/38.88  | | |   (74)  all_57_12 = e1 & op(e0, e3) = e1
% 226.12/38.88  | | | 
% 226.12/38.88  | | | ALPHA: (74) implies:
% 226.12/38.88  | | |   (75)  all_57_12 = e1
% 226.12/38.88  | | | 
% 226.12/38.88  | | | REF_CLOSE: (4), (40), (75) are inconsistent by sub-proof #2014.
% 226.12/38.88  | | | 
% 226.12/38.88  | | Case 2:
% 226.12/38.88  | | | 
% 226.12/38.88  | | |   (76)  all_57_13 = e1 & op(e0, e2) = e1
% 226.12/38.88  | | | 
% 226.12/38.88  | | | ALPHA: (76) implies:
% 226.12/38.88  | | |   (77)  all_57_13 = e1
% 226.12/38.88  | | | 
% 226.12/38.88  | | | BETA: splitting (45) gives:
% 226.12/38.88  | | | 
% 226.12/38.88  | | | Case 1:
% 226.12/38.88  | | | | 
% 226.12/38.88  | | | |   (78)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0,
% 226.12/38.88  | | | |             e2) = e3)
% 226.12/38.88  | | | | 
% 226.12/38.88  | | | | BETA: splitting (78) gives:
% 226.12/38.88  | | | | 
% 226.12/38.88  | | | | Case 1:
% 226.12/38.88  | | | | | 
% 226.12/38.88  | | | | |   (79)  all_57_12 = e3 & op(e0, e3) = e3
% 226.12/38.88  | | | | | 
% 226.12/38.88  | | | | | ALPHA: (79) implies:
% 226.12/38.88  | | | | |   (80)  all_57_12 = e3
% 226.12/38.88  | | | | | 
% 226.12/38.88  | | | | | REF_CLOSE: (3), (5), (8), (10), (24), (26), (28), (30), (37), (40),
% 226.12/38.88  | | | | |            (50), (55), (57), (62), (65), (80) are inconsistent by
% 226.12/38.88  | | | | |            sub-proof #2223.
% 226.12/38.88  | | | | | 
% 226.12/38.88  | | | | Case 2:
% 226.12/38.88  | | | | | 
% 226.12/38.88  | | | | |   (81)  all_57_13 = e3 & op(e0, e2) = e3
% 226.12/38.88  | | | | | 
% 226.12/38.88  | | | | | ALPHA: (81) implies:
% 226.12/38.88  | | | | |   (82)  all_57_13 = e3
% 226.12/38.88  | | | | | 
% 226.12/38.88  | | | | | REF_CLOSE: (8), (77), (82) are inconsistent by sub-proof #2268.
% 226.12/38.88  | | | | | 
% 226.12/38.88  | | | | End of split
% 226.12/38.88  | | | | 
% 226.12/38.88  | | | Case 2:
% 226.12/38.88  | | | | 
% 226.12/38.88  | | | |   (83)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0,
% 226.12/38.88  | | | |             e0) = e3)
% 226.12/38.88  | | | | 
% 226.12/38.88  | | | | BETA: splitting (83) gives:
% 226.12/38.88  | | | | 
% 226.12/38.88  | | | | Case 1:
% 226.12/38.88  | | | | | 
% 226.12/38.88  | | | | |   (84)  all_57_14 = e3 & op(e0, e1) = e3
% 226.12/38.88  | | | | | 
% 226.12/38.88  | | | | | ALPHA: (84) implies:
% 226.12/38.88  | | | | |   (85)  all_57_14 = e3
% 226.12/38.88  | | | | | 
% 226.12/38.88  | | | | | REF_CLOSE: (28), (67), (85) are inconsistent by sub-proof #2420.
% 226.12/38.88  | | | | | 
% 226.12/38.88  | | | | Case 2:
% 226.12/38.88  | | | | | 
% 226.12/38.88  | | | | |   (86)  all_57_15 = e3 & op(e0, e0) = e3
% 226.12/38.88  | | | | | 
% 226.12/38.88  | | | | | ALPHA: (86) implies:
% 226.12/38.88  | | | | |   (87)  all_57_15 = e3
% 226.12/38.88  | | | | |   (88)  op(e0, e0) = e3
% 226.12/38.88  | | | | | 
% 226.12/38.88  | | | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12),
% 226.12/38.88  | | | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 226.12/38.88  | | | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 226.12/38.88  | | | | |            (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 226.12/38.88  | | | | |            (43), (44), (46), (47), (48), (49), (50), (51), (52), (53),
% 226.12/38.88  | | | | |            (54), (55), (56), (57), (58), (60), (61), (62), (63), (64),
% 226.12/38.88  | | | | |            (65), (66), (68), (69), (70), (71), (72), (87), (88) are
% 226.12/38.88  | | | | |            inconsistent by sub-proof #1415.
% 226.12/38.88  | | | | | 
% 226.12/38.88  | | | | End of split
% 226.12/38.88  | | | | 
% 226.12/38.88  | | | End of split
% 226.12/38.88  | | | 
% 226.12/38.88  | | End of split
% 226.12/38.88  | | 
% 226.12/38.88  | Case 2:
% 226.12/38.88  | | 
% 226.12/38.88  | |   (89)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 226.12/38.88  | |           e1)
% 226.12/38.88  | | 
% 226.12/38.88  | | BETA: splitting (89) gives:
% 226.12/38.88  | | 
% 226.12/38.88  | | Case 1:
% 226.12/38.88  | | | 
% 226.12/38.88  | | |   (90)  all_57_14 = e1 & op(e0, e1) = e1
% 226.12/38.88  | | | 
% 226.12/38.88  | | | ALPHA: (90) implies:
% 226.12/38.88  | | |   (91)  all_57_14 = e1
% 226.12/38.88  | | | 
% 226.12/38.88  | | | REF_CLOSE: (40), (67), (91) are inconsistent by sub-proof #2122.
% 226.12/38.88  | | | 
% 226.12/38.88  | | Case 2:
% 226.12/38.88  | | | 
% 226.12/38.88  | | |   (92)  all_57_15 = e1 & op(e0, e0) = e1
% 226.12/38.88  | | | 
% 226.12/38.88  | | | ALPHA: (92) implies:
% 226.12/38.88  | | |   (93)  op(e0, e0) = e1
% 226.12/38.88  | | | 
% 226.12/38.88  | | | REF_CLOSE: (10), (57), (59), (93) are inconsistent by sub-proof #2177.
% 226.12/38.88  | | | 
% 226.12/38.88  | | End of split
% 226.12/38.88  | | 
% 226.12/38.88  | End of split
% 226.12/38.88  | 
% 226.12/38.88  End of proof
% 226.12/38.88  
% 226.12/38.88  Sub-proof #34 shows that the following formulas are inconsistent:
% 226.12/38.88  ----------------------------------------------------------------
% 226.12/38.88    (1)  all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 226.12/38.88    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.12/38.88           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.12/38.88    (3)  op(e1, e1) = all_6_2
% 226.12/38.88    (4)  op(e0, e1) = e0
% 226.12/38.88    (5)  op(e0, e0) = all_52_31
% 226.12/38.88    (6)  op(e0, e1) = all_52_29
% 226.12/38.88    (7)   ~ (all_53_12 = e1)
% 226.12/38.88    (8)  op(all_52_29, all_52_29) = e1
% 226.12/38.88    (9)  all_55_3 = all_53_12
% 226.12/38.88    (10)   ~ (all_6_2 = e0)
% 226.12/38.88    (11)   ~ (all_53_12 = e2)
% 226.12/38.88    (12)  op(all_52_31, all_52_31) = e0
% 226.12/38.88  
% 226.12/38.88  Begin of proof
% 226.12/38.88  | 
% 226.12/38.88  | BETA: splitting (1) gives:
% 226.12/38.88  | 
% 226.12/38.88  | Case 1:
% 226.12/38.88  | | 
% 226.12/38.88  | |   (13)  all_55_3 = e2
% 226.12/38.88  | | 
% 226.12/38.88  | | COMBINE_EQS: (9), (13) imply:
% 226.12/38.88  | |   (14)  all_53_12 = e2
% 226.12/38.88  | | 
% 226.12/38.88  | | REDUCE: (11), (14) imply:
% 226.12/38.88  | |   (15)  $false
% 226.12/38.88  | | 
% 226.12/38.88  | | CLOSE: (15) is inconsistent.
% 226.12/38.88  | | 
% 226.12/38.88  | Case 2:
% 226.12/38.88  | | 
% 226.12/38.88  | |   (16)  all_55_3 = e1 | all_55_3 = e0
% 226.12/38.88  | | 
% 226.12/38.88  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (16) are
% 226.12/38.88  | |            inconsistent by sub-proof #35.
% 226.12/38.88  | | 
% 226.12/38.88  | End of split
% 226.12/38.88  | 
% 226.12/38.88  End of proof
% 226.12/38.88  
% 226.12/38.88  Sub-proof #35 shows that the following formulas are inconsistent:
% 226.12/38.88  ----------------------------------------------------------------
% 226.12/38.88    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.12/38.88           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.12/38.88    (2)  op(e1, e1) = all_6_2
% 226.12/38.88    (3)  op(e0, e1) = e0
% 226.12/38.88    (4)  op(e0, e0) = all_52_31
% 226.12/38.88    (5)  op(e0, e1) = all_52_29
% 226.12/38.88    (6)   ~ (all_53_12 = e1)
% 226.12/38.88    (7)  all_55_3 = e1 | all_55_3 = e0
% 226.12/38.88    (8)  op(all_52_29, all_52_29) = e1
% 226.12/38.88    (9)  all_55_3 = all_53_12
% 226.12/38.88    (10)   ~ (all_6_2 = e0)
% 226.12/38.88    (11)  op(all_52_31, all_52_31) = e0
% 226.12/38.88  
% 226.12/38.88  Begin of proof
% 226.12/38.88  | 
% 226.12/38.88  | BETA: splitting (7) gives:
% 226.12/38.88  | 
% 226.12/38.88  | Case 1:
% 226.12/38.88  | | 
% 226.12/38.88  | |   (12)  all_55_3 = e1
% 226.12/38.88  | | 
% 226.12/38.88  | | COMBINE_EQS: (9), (12) imply:
% 226.12/38.88  | |   (13)  all_53_12 = e1
% 226.12/38.88  | | 
% 226.12/38.88  | | REDUCE: (6), (13) imply:
% 226.12/38.88  | |   (14)  $false
% 226.12/38.88  | | 
% 226.12/38.88  | | CLOSE: (14) is inconsistent.
% 226.12/38.88  | | 
% 226.12/38.88  | Case 2:
% 226.12/38.88  | | 
% 226.12/38.88  | | 
% 226.12/38.88  | | GROUND_INST: instantiating (1) with e0, all_52_29, e1, e0, simplifying with
% 226.12/38.88  | |              (3), (5) gives:
% 226.12/38.88  | |   (15)  all_52_29 = e0
% 226.12/38.88  | | 
% 226.12/38.88  | | REDUCE: (8), (15) imply:
% 226.12/38.88  | |   (16)  op(e0, e0) = e1
% 226.12/38.88  | | 
% 226.12/38.88  | | REF_CLOSE: (1), (2), (4), (10), (11), (16) are inconsistent by sub-proof
% 226.12/38.88  | |            #2086.
% 226.12/38.88  | | 
% 226.12/38.88  | End of split
% 226.12/38.88  | 
% 226.12/38.88  End of proof
% 226.12/38.88  
% 226.12/38.88  Sub-proof #36 shows that the following formulas are inconsistent:
% 226.12/38.88  ----------------------------------------------------------------
% 226.12/38.88    (1)  ( ~ (all_50_0 = e3) & op(all_50_1, e2) = all_50_0 & op(e2, e0) = all_50_1
% 226.12/38.88           & $i(all_50_0) & $i(all_50_1)) | ( ~ (all_50_1 = e1) & op(e2, e0) =
% 226.12/38.88           all_50_1 & $i(all_50_1))
% 226.12/38.88    (2)  ( ~ (all_14_0 = e1) & op(all_14_1, e2) = all_14_0 & op(e2, e0) = all_14_1
% 226.12/38.88           & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e3) & op(e2, e0) =
% 226.12/38.88           all_14_1 & $i(all_14_1))
% 226.12/38.88    (3)  all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 226.12/38.88    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.12/38.88           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.12/38.88    (5)  op(e2, e0) = all_52_15
% 226.12/38.88    (6)  op(e2, e0) = e1
% 226.12/38.88    (7)  op(e1, e1) = e1
% 226.12/38.88    (8)   ~ (all_53_12 = e1)
% 226.12/38.88    (9)  op(e2, e0) = all_14_1
% 226.12/38.88    (10)  all_55_3 = all_53_12
% 226.12/38.88    (11)  op(all_52_15, all_52_15) = e0
% 226.12/38.88    (12)   ~ (all_53_12 = e2)
% 226.12/38.88  
% 226.12/38.88  Begin of proof
% 226.12/38.88  | 
% 226.12/38.88  | BETA: splitting (1) gives:
% 226.12/38.88  | 
% 226.12/38.88  | Case 1:
% 226.12/38.88  | | 
% 226.12/38.88  | |   (13)   ~ (all_50_0 = e3) & op(all_50_1, e2) = all_50_0 & op(e2, e0) =
% 226.12/38.88  | |         all_50_1 & $i(all_50_0) & $i(all_50_1)
% 226.12/38.88  | | 
% 226.12/38.88  | | ALPHA: (13) implies:
% 226.12/38.88  | |   (14)  op(e2, e0) = all_50_1
% 226.12/38.88  | | 
% 226.12/38.88  | | BETA: splitting (3) gives:
% 226.12/38.88  | | 
% 226.12/38.88  | | Case 1:
% 226.12/38.88  | | | 
% 226.12/38.88  | | |   (15)  all_55_3 = e2
% 226.12/38.88  | | | 
% 226.12/38.88  | | | COMBINE_EQS: (10), (15) imply:
% 226.12/38.88  | | |   (16)  all_53_12 = e2
% 226.12/38.88  | | | 
% 226.12/38.88  | | | REDUCE: (12), (16) imply:
% 226.12/38.88  | | |   (17)  $false
% 226.12/38.88  | | | 
% 226.12/38.88  | | | CLOSE: (17) is inconsistent.
% 226.12/38.88  | | | 
% 226.12/38.88  | | Case 2:
% 226.12/38.88  | | | 
% 226.12/38.88  | | |   (18)  all_55_3 = e1 | all_55_3 = e0
% 226.12/38.88  | | | 
% 226.12/38.88  | | | BETA: splitting (18) gives:
% 226.12/38.88  | | | 
% 226.12/38.88  | | | Case 1:
% 226.12/38.88  | | | | 
% 226.12/38.88  | | | |   (19)  all_55_3 = e1
% 226.12/38.88  | | | | 
% 226.12/38.88  | | | | COMBINE_EQS: (10), (19) imply:
% 226.12/38.88  | | | |   (20)  all_53_12 = e1
% 226.12/38.88  | | | | 
% 226.12/38.88  | | | | REDUCE: (8), (20) imply:
% 226.12/38.88  | | | |   (21)  $false
% 226.12/38.88  | | | | 
% 226.12/38.88  | | | | CLOSE: (21) is inconsistent.
% 226.12/38.88  | | | | 
% 226.12/38.88  | | | Case 2:
% 226.12/38.88  | | | | 
% 226.12/38.88  | | | |   (22)  all_55_3 = e0
% 226.12/38.88  | | | | 
% 226.12/38.88  | | | | COMBINE_EQS: (10), (22) imply:
% 226.12/38.88  | | | |   (23)  all_53_12 = e0
% 226.12/38.88  | | | | 
% 226.12/38.88  | | | | REDUCE: (8), (23) imply:
% 226.12/38.88  | | | |   (24)   ~ (e1 = e0)
% 226.12/38.88  | | | | 
% 226.12/38.88  | | | | SIMP: (24) implies:
% 226.12/38.88  | | | |   (25)   ~ (e1 = e0)
% 226.12/38.88  | | | | 
% 226.12/38.88  | | | | GROUND_INST: instantiating (4) with e1, all_50_1, e0, e2, simplifying
% 226.12/38.88  | | | |              with (6), (14) gives:
% 226.12/38.88  | | | |   (26)  all_50_1 = e1
% 226.12/38.88  | | | | 
% 226.12/38.88  | | | | GROUND_INST: instantiating (4) with all_50_1, all_52_15, e0, e2,
% 226.12/38.88  | | | |              simplifying with (5), (14) gives:
% 226.12/38.88  | | | |   (27)  all_52_15 = all_50_1
% 226.12/38.88  | | | | 
% 226.12/38.88  | | | | GROUND_INST: instantiating (4) with all_14_1, all_52_15, e0, e2,
% 226.12/38.88  | | | |              simplifying with (5), (9) gives:
% 226.12/38.88  | | | |   (28)  all_52_15 = all_14_1
% 226.12/38.88  | | | | 
% 226.12/38.88  | | | | COMBINE_EQS: (27), (28) imply:
% 226.12/38.88  | | | |   (29)  all_50_1 = all_14_1
% 226.12/38.88  | | | | 
% 226.12/38.88  | | | | SIMP: (29) implies:
% 226.12/38.88  | | | |   (30)  all_50_1 = all_14_1
% 226.12/38.88  | | | | 
% 226.12/38.88  | | | | COMBINE_EQS: (26), (30) imply:
% 226.12/38.88  | | | |   (31)  all_14_1 = e1
% 226.12/38.88  | | | | 
% 226.12/38.88  | | | | COMBINE_EQS: (28), (31) imply:
% 226.12/38.88  | | | |   (32)  all_52_15 = e1
% 226.12/38.88  | | | | 
% 226.12/38.88  | | | | REDUCE: (11), (32) imply:
% 226.12/38.88  | | | |   (33)  op(e1, e1) = e0
% 226.12/38.88  | | | | 
% 226.12/38.88  | | | | REF_CLOSE: (4), (7), (25), (33) are inconsistent by sub-proof #2427.
% 226.12/38.88  | | | | 
% 226.12/38.88  | | | End of split
% 226.12/38.88  | | | 
% 226.12/38.88  | | End of split
% 226.12/38.88  | | 
% 226.12/38.88  | Case 2:
% 226.12/38.88  | | 
% 226.12/38.88  | |   (34)   ~ (all_50_1 = e1) & op(e2, e0) = all_50_1 & $i(all_50_1)
% 226.12/38.88  | | 
% 226.12/38.88  | | REF_CLOSE: (2), (4), (6), (34) are inconsistent by sub-proof #272.
% 226.12/38.88  | | 
% 226.12/38.88  | End of split
% 226.12/38.88  | 
% 226.12/38.88  End of proof
% 226.12/38.88  
% 226.12/38.88  Sub-proof #37 shows that the following formulas are inconsistent:
% 226.12/38.88  ----------------------------------------------------------------
% 226.12/38.88    (1)   ~ (e3 = e1)
% 226.12/38.88    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.12/38.88           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.12/38.88    (3)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 226.12/38.88         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 226.12/38.88    (4)   ~ (e3 = e2)
% 226.12/38.88    (5)   ~ (e3 = e0)
% 226.12/38.88    (6)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 226.12/38.88         (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 226.12/38.88    (7)  all_57_1 = e1
% 226.12/38.88    (8)  op(e3, e3) = e0
% 226.12/38.88    (9)  all_57_5 = e3
% 226.12/38.88    (10)  op(e1, e1) = e1
% 226.12/38.88    (11)   ~ (e2 = e0)
% 226.12/38.89    (12)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 226.12/38.89          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 226.12/38.89    (13)   ~ (e1 = e0)
% 226.12/38.89    (14)   ~ (all_53_12 = e3)
% 226.12/38.89    (15)   ~ (all_53_8 = e0)
% 226.12/38.89    (16)   ~ (e2 = e1)
% 226.12/38.89    (17)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 226.12/38.89          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 226.12/38.89    (18)  op(e3, e1) = all_53_8
% 226.12/38.89    (19)  op(e3, e0) = all_53_12
% 226.12/38.89  
% 226.12/38.89  Begin of proof
% 226.12/38.89  | 
% 226.12/38.89  | BETA: splitting (12) gives:
% 226.12/38.89  | 
% 226.12/38.89  | Case 1:
% 226.12/38.89  | | 
% 226.12/38.89  | |   (20)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) =
% 226.12/38.89  | |           e3)
% 226.12/38.89  | | 
% 226.12/38.89  | | BETA: splitting (20) gives:
% 226.12/38.89  | | 
% 226.12/38.89  | | Case 1:
% 226.12/38.89  | | | 
% 226.12/38.89  | | |   (21)  all_57_0 = e3 & op(e3, e3) = e3
% 226.12/38.89  | | | 
% 226.12/38.89  | | | ALPHA: (21) implies:
% 226.12/38.89  | | |   (22)  op(e3, e3) = e3
% 226.12/38.89  | | | 
% 226.12/38.89  | | | REF_CLOSE: (2), (5), (8), (22) are inconsistent by sub-proof #2494.
% 226.12/38.89  | | | 
% 226.12/38.89  | | Case 2:
% 226.12/38.89  | | | 
% 226.12/38.89  | | |   (23)  all_57_1 = e3 & op(e3, e2) = e3
% 226.12/38.89  | | | 
% 226.12/38.89  | | | REF_CLOSE: (1), (7), (23) are inconsistent by sub-proof #2196.
% 226.12/38.89  | | | 
% 226.12/38.89  | | End of split
% 226.12/38.89  | | 
% 226.12/38.89  | Case 2:
% 226.12/38.89  | | 
% 226.12/38.89  | |   (24)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) =
% 226.12/38.89  | |           e3)
% 226.12/38.89  | | 
% 226.12/38.89  | | BETA: splitting (24) gives:
% 226.12/38.89  | | 
% 226.12/38.89  | | Case 1:
% 226.12/38.89  | | | 
% 226.12/38.89  | | |   (25)  all_57_4 = e3 & op(e3, e1) = e3
% 226.12/38.89  | | | 
% 226.12/38.89  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (9), (10), (11), (13), (15),
% 226.12/38.89  | | |            (16), (17), (18), (25) are inconsistent by sub-proof #1903.
% 226.12/38.89  | | | 
% 226.12/38.89  | | Case 2:
% 226.12/38.89  | | | 
% 226.12/38.89  | | |   (26)  all_57_9 = e3 & op(e3, e0) = e3
% 226.12/38.89  | | | 
% 226.12/38.89  | | | ALPHA: (26) implies:
% 226.12/38.89  | | |   (27)  op(e3, e0) = e3
% 226.12/38.89  | | | 
% 226.12/38.89  | | | REF_CLOSE: (2), (14), (19), (27) are inconsistent by sub-proof #2458.
% 226.12/38.89  | | | 
% 226.12/38.89  | | End of split
% 226.12/38.89  | | 
% 226.12/38.89  | End of split
% 226.12/38.89  | 
% 226.12/38.89  End of proof
% 226.12/38.89  
% 226.12/38.89  Sub-proof #38 shows that the following formulas are inconsistent:
% 226.12/38.89  ----------------------------------------------------------------
% 226.12/38.89    (1)   ~ (all_53_6 = e0)
% 226.12/38.89    (2)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 226.12/38.89         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 226.12/38.89    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.12/38.89           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.12/38.89    (4)  op(e1, e0) = all_53_14
% 226.12/38.89    (5)   ~ (all_53_2 = e0)
% 226.12/38.89    (6)   ~ (all_53_14 = e0)
% 226.12/38.89    (7)  op(e1, e3) = all_53_2
% 226.12/38.89    (8)   ~ (e2 = e1)
% 226.12/38.89    (9)  op(e0, e0) = e2
% 226.12/38.89    (10)  op(e1, e2) = all_53_6
% 226.12/38.89    (11)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 &
% 226.12/38.89          op(all_52_17, all_52_17) = e3 & op(all_52_19, all_52_19) = e2 &
% 226.12/38.89          op(all_52_21, all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1,
% 226.12/38.89            e3) = all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 &
% 226.12/38.89          op(e1, e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 226.12/38.89          $i(all_52_23)
% 226.12/38.89  
% 226.12/38.89  Begin of proof
% 226.12/38.89  | 
% 226.12/38.89  | ALPHA: (11) implies:
% 226.12/38.89  |   (12)  op(e1, e1) = all_52_21
% 226.12/38.89  |   (13)  op(all_52_21, all_52_21) = e1
% 226.12/38.89  | 
% 226.12/38.89  | BETA: splitting (2) gives:
% 226.12/38.89  | 
% 226.12/38.89  | Case 1:
% 226.12/38.89  | | 
% 226.12/38.89  | |   (14)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) =
% 226.12/38.89  | |           e0)
% 226.12/38.89  | | 
% 226.12/38.89  | | REF_CLOSE: (1), (3), (5), (7), (10), (14) are inconsistent by sub-proof
% 226.12/38.89  | |            #2038.
% 226.12/38.89  | | 
% 226.12/38.89  | Case 2:
% 226.12/38.89  | | 
% 226.12/38.89  | |   (15)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 226.12/38.89  | |           e0)
% 226.12/38.89  | | 
% 226.12/38.89  | | BETA: splitting (15) gives:
% 226.12/38.89  | | 
% 226.12/38.89  | | Case 1:
% 226.12/38.89  | | | 
% 226.12/38.89  | | |   (16)  all_57_8 = e0 & op(e1, e1) = e0
% 226.12/38.89  | | | 
% 226.12/38.89  | | | ALPHA: (16) implies:
% 226.12/38.89  | | |   (17)  op(e1, e1) = e0
% 226.12/38.89  | | | 
% 226.12/38.89  | | | GROUND_INST: instantiating (3) with e0, all_52_21, e1, e1, simplifying
% 226.12/38.89  | | |              with (12), (17) gives:
% 226.12/38.89  | | |   (18)  all_52_21 = e0
% 226.12/38.89  | | | 
% 226.12/38.89  | | | REDUCE: (13), (18) imply:
% 226.12/38.89  | | |   (19)  op(e0, e0) = e1
% 226.12/38.89  | | | 
% 226.12/38.89  | | | REF_CLOSE: (3), (8), (9), (19) are inconsistent by sub-proof #2177.
% 226.12/38.89  | | | 
% 226.12/38.89  | | Case 2:
% 226.12/38.89  | | | 
% 226.12/38.89  | | |   (20)  all_57_11 = e0 & op(e1, e0) = e0
% 226.12/38.89  | | | 
% 226.12/38.89  | | | REF_CLOSE: (3), (4), (6), (20) are inconsistent by sub-proof #2341.
% 226.12/38.89  | | | 
% 226.12/38.89  | | End of split
% 226.12/38.89  | | 
% 226.12/38.89  | End of split
% 226.12/38.89  | 
% 226.12/38.89  End of proof
% 226.12/38.89  
% 226.12/38.89  Sub-proof #39 shows that the following formulas are inconsistent:
% 226.12/38.89  ----------------------------------------------------------------
% 226.12/38.89    (1)   ~ (all_53_6 = e2)
% 226.12/38.89    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 226.12/38.89         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 226.12/38.89    (3)   ~ (e3 = e1)
% 226.12/38.89    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.12/38.89           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.12/38.89    (5)  all_57_4 = e2
% 226.12/38.89    (6)  op(e2, e2) = e1
% 226.12/38.89    (7)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 226.12/38.89         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 226.12/38.89    (8)   ~ (all_53_7 = e2)
% 226.12/38.89    (9)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 226.12/38.89         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 226.12/38.89    (10)   ~ (e3 = e2)
% 226.12/38.89    (11)   ~ (e3 = e0)
% 226.12/38.89    (12)  all_57_0 = e0
% 226.12/38.89    (13)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 226.12/38.89          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 226.12/38.89    (14)   ~ (e2 = e0)
% 226.12/38.89    (15)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 226.12/38.89          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 226.12/38.89    (16)   ~ (e1 = e0)
% 226.12/38.89    (17)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 226.12/38.89          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 226.12/38.89    (18)  op(e0, e2) = all_53_7
% 226.12/38.89    (19)   ~ (e2 = e1)
% 226.12/38.89    (20)  op(e1, e2) = all_53_6
% 226.12/38.89  
% 226.12/38.89  Begin of proof
% 226.12/38.89  | 
% 226.12/38.89  | BETA: splitting (7) gives:
% 226.12/38.89  | 
% 226.12/38.89  | Case 1:
% 226.12/38.89  | | 
% 226.12/38.89  | |   (21)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) =
% 226.12/38.89  | |           e1)
% 226.12/38.89  | | 
% 226.12/38.89  | | REF_CLOSE: (2), (3), (4), (6), (10), (11), (12), (13), (14), (16), (17),
% 226.12/38.89  | |            (19), (21) are inconsistent by sub-proof #1551.
% 226.12/38.89  | | 
% 226.12/38.89  | Case 2:
% 226.12/38.89  | | 
% 226.12/38.89  | |   (22)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) =
% 226.12/38.89  | |           e1)
% 226.12/38.89  | | 
% 226.12/38.89  | | BETA: splitting (22) gives:
% 226.12/38.89  | | 
% 226.12/38.89  | | Case 1:
% 226.12/38.89  | | | 
% 226.12/38.89  | | |   (23)  all_57_4 = e1 & op(e3, e1) = e1
% 226.12/38.89  | | | 
% 226.12/38.89  | | | REF_CLOSE: (5), (19), (23) are inconsistent by sub-proof #2452.
% 226.12/38.89  | | | 
% 226.12/38.89  | | Case 2:
% 226.12/38.89  | | | 
% 226.12/38.89  | | |   (24)  all_57_9 = e1 & op(e3, e0) = e1
% 226.12/38.89  | | | 
% 226.12/38.89  | | | ALPHA: (24) implies:
% 226.12/38.89  | | |   (25)  all_57_9 = e1
% 226.12/38.89  | | | 
% 226.12/38.89  | | | BETA: splitting (2) gives:
% 226.12/38.89  | | | 
% 226.12/38.89  | | | Case 1:
% 226.12/38.89  | | | | 
% 226.12/38.89  | | | |   (26)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2)
% 226.12/38.89  | | | |           = e2)
% 226.12/38.89  | | | | 
% 226.12/38.89  | | | | BETA: splitting (26) gives:
% 226.12/38.89  | | | | 
% 226.12/38.89  | | | | Case 1:
% 226.12/38.89  | | | | | 
% 226.12/38.89  | | | | |   (27)  all_57_1 = e2 & op(e3, e2) = e2
% 226.12/38.89  | | | | | 
% 226.12/38.89  | | | | | ALPHA: (27) implies:
% 226.12/38.89  | | | | |   (28)  all_57_1 = e2
% 226.12/38.89  | | | | |   (29)  op(e3, e2) = e2
% 226.12/38.89  | | | | | 
% 226.12/38.89  | | | | | BETA: splitting (15) gives:
% 226.12/38.89  | | | | | 
% 226.12/38.89  | | | | | Case 1:
% 226.12/38.89  | | | | | | 
% 226.12/38.89  | | | | | |   (30)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3,
% 226.12/38.89  | | | | | |             e2) = e3)
% 226.12/38.89  | | | | | | 
% 226.12/38.89  | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (9), (10), (11), (13),
% 226.12/38.89  | | | | | |            (14), (16), (17), (19), (28), (29), (30) are inconsistent
% 226.12/38.89  | | | | | |            by sub-proof #40.
% 226.12/38.89  | | | | | | 
% 226.12/38.89  | | | | | Case 2:
% 226.12/38.89  | | | | | | 
% 226.12/38.89  | | | | | |   (31)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3,
% 226.12/38.89  | | | | | |             e0) = e3)
% 226.12/38.89  | | | | | | 
% 226.12/38.89  | | | | | | REF_CLOSE: (3), (5), (10), (25), (31) are inconsistent by sub-proof
% 226.12/38.89  | | | | | |            #1609.
% 226.12/38.89  | | | | | | 
% 226.12/38.89  | | | | | End of split
% 226.12/38.89  | | | | | 
% 226.12/38.89  | | | | Case 2:
% 226.12/38.89  | | | | | 
% 226.12/38.89  | | | | |   (32)  all_57_3 = e2 & op(e2, e2) = e2
% 226.12/38.89  | | | | | 
% 226.12/38.89  | | | | | ALPHA: (32) implies:
% 226.12/38.89  | | | | |   (33)  op(e2, e2) = e2
% 226.12/38.89  | | | | | 
% 226.12/38.89  | | | | | REF_CLOSE: (4), (6), (19), (33) are inconsistent by sub-proof #2306.
% 226.12/38.89  | | | | | 
% 226.12/38.89  | | | | End of split
% 226.12/38.89  | | | | 
% 226.12/38.89  | | | Case 2:
% 226.12/38.89  | | | | 
% 226.12/38.89  | | | |   (34)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2)
% 226.12/38.89  | | | |           = e2)
% 226.12/38.89  | | | | 
% 226.12/38.89  | | | | REF_CLOSE: (1), (4), (8), (18), (20), (34) are inconsistent by sub-proof
% 226.12/38.89  | | | |            #160.
% 226.12/38.89  | | | | 
% 226.12/38.89  | | | End of split
% 226.12/38.89  | | | 
% 226.12/38.89  | | End of split
% 226.12/38.89  | | 
% 226.12/38.89  | End of split
% 226.12/38.89  | 
% 226.12/38.89  End of proof
% 226.12/38.89  
% 226.12/38.89  Sub-proof #40 shows that the following formulas are inconsistent:
% 226.12/38.89  ----------------------------------------------------------------
% 226.12/38.89    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 226.12/38.89         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 226.12/38.89    (2)   ~ (e3 = e1)
% 226.12/38.89    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.12/38.89           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.12/38.89    (4)  all_57_4 = e2
% 226.12/38.89    (5)  op(e2, e2) = e1
% 226.12/38.89    (6)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 226.12/38.89         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 226.12/38.89    (7)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3)
% 226.12/38.89    (8)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 226.12/38.89         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 226.12/38.89    (9)   ~ (e3 = e2)
% 226.12/38.89    (10)   ~ (e3 = e0)
% 226.12/38.89    (11)  all_57_1 = e2
% 226.12/38.89    (12)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 226.12/38.89          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 226.12/38.89    (13)   ~ (e2 = e0)
% 226.12/38.89    (14)   ~ (e1 = e0)
% 226.12/38.89    (15)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 226.12/38.89          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 226.12/38.89    (16)  op(e3, e2) = e2
% 226.12/38.89    (17)   ~ (e2 = e1)
% 226.12/38.89  
% 226.12/38.89  Begin of proof
% 226.12/38.89  | 
% 226.12/38.89  | BETA: splitting (7) gives:
% 226.12/38.89  | 
% 226.12/38.89  | Case 1:
% 226.12/38.89  | | 
% 226.12/38.89  | |   (18)  all_57_0 = e3 & op(e3, e3) = e3
% 226.12/38.89  | | 
% 226.12/38.89  | | ALPHA: (18) implies:
% 226.12/38.89  | |   (19)  op(e3, e3) = e3
% 226.12/38.89  | | 
% 226.12/38.89  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13),
% 226.12/38.89  | |            (14), (15), (17), (19) are inconsistent by sub-proof #41.
% 226.12/38.89  | | 
% 226.12/38.89  | Case 2:
% 226.12/38.89  | | 
% 226.12/38.89  | |   (20)  all_57_1 = e3 & op(e3, e2) = e3
% 226.12/38.89  | | 
% 226.12/38.89  | | ALPHA: (20) implies:
% 226.12/38.89  | |   (21)  op(e3, e2) = e3
% 226.12/38.89  | | 
% 226.12/38.89  | | REF_CLOSE: (3), (9), (16), (21) are inconsistent by sub-proof #1549.
% 226.12/38.89  | | 
% 226.12/38.89  | End of split
% 226.12/38.89  | 
% 226.12/38.89  End of proof
% 226.12/38.89  
% 226.12/38.89  Sub-proof #41 shows that the following formulas are inconsistent:
% 226.12/38.89  ----------------------------------------------------------------
% 226.12/38.89    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 226.12/38.89         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 226.12/38.89    (2)   ~ (e3 = e1)
% 226.12/38.89    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.12/38.89           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.12/38.89    (4)  all_57_4 = e2
% 226.12/38.89    (5)  op(e2, e2) = e1
% 226.12/38.89    (6)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 226.12/38.89         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 226.12/38.89    (7)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 226.12/38.89         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 226.12/38.89    (8)   ~ (e3 = e2)
% 226.12/38.89    (9)   ~ (e3 = e0)
% 226.12/38.89    (10)  all_57_1 = e2
% 226.12/38.89    (11)  op(e3, e3) = e3
% 226.12/38.89    (12)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 226.12/38.89          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 226.12/38.89    (13)   ~ (e2 = e0)
% 226.12/38.89    (14)   ~ (e1 = e0)
% 226.12/38.89    (15)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 226.12/38.89          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 226.12/38.89    (16)   ~ (e2 = e1)
% 226.12/38.89  
% 226.12/38.89  Begin of proof
% 226.12/38.89  | 
% 226.12/38.89  | BETA: splitting (6) gives:
% 226.12/38.89  | 
% 226.12/38.89  | Case 1:
% 226.12/38.89  | | 
% 226.12/38.89  | |   (17)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) =
% 226.12/38.89  | |           e1)
% 226.12/38.89  | | 
% 226.12/38.89  | | REF_CLOSE: (1), (2), (3), (5), (8), (9), (11), (12), (13), (14), (15), (16),
% 226.12/38.89  | |            (17) are inconsistent by sub-proof #1856.
% 226.12/38.89  | | 
% 226.12/38.89  | Case 2:
% 226.12/38.89  | | 
% 226.12/38.89  | |   (18)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) =
% 226.12/38.89  | |           e1)
% 226.12/38.89  | | 
% 226.12/38.89  | | BETA: splitting (18) gives:
% 226.12/38.89  | | 
% 226.12/38.89  | | Case 1:
% 226.12/38.89  | | | 
% 226.12/38.89  | | |   (19)  all_57_4 = e1 & op(e3, e1) = e1
% 226.12/38.89  | | | 
% 226.12/38.89  | | | ALPHA: (19) implies:
% 226.12/38.89  | | |   (20)  all_57_4 = e1
% 226.12/38.89  | | | 
% 226.12/38.89  | | | COMBINE_EQS: (4), (20) imply:
% 226.12/38.89  | | |   (21)  e2 = e1
% 226.12/38.89  | | | 
% 226.12/38.89  | | | COMBINE_EQS: (10), (21) imply:
% 226.12/38.89  | | |   (22)  all_57_1 = e1
% 226.12/38.89  | | | 
% 226.12/38.89  | | | REF_CLOSE: (1), (2), (3), (5), (8), (9), (12), (13), (14), (15), (16),
% 226.12/38.89  | | |            (22) are inconsistent by sub-proof #1908.
% 226.12/38.89  | | | 
% 226.12/38.89  | | Case 2:
% 226.12/38.89  | | | 
% 226.12/38.89  | | |   (23)  all_57_9 = e1 & op(e3, e0) = e1
% 226.12/38.89  | | | 
% 226.12/38.89  | | | ALPHA: (23) implies:
% 226.12/38.89  | | |   (24)  all_57_9 = e1
% 226.12/38.89  | | | 
% 226.12/38.89  | | | BETA: splitting (7) gives:
% 226.12/38.89  | | | 
% 226.12/38.89  | | | Case 1:
% 226.12/38.89  | | | | 
% 226.12/38.89  | | | |   (25)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2)
% 226.12/38.89  | | | |           = e0)
% 226.12/38.89  | | | | 
% 226.12/38.89  | | | | REF_CLOSE: (3), (9), (10), (11), (13), (25) are inconsistent by
% 226.12/38.89  | | | |            sub-proof #1722.
% 226.12/38.89  | | | | 
% 226.12/38.89  | | | Case 2:
% 226.12/38.89  | | | | 
% 226.12/38.89  | | | |   (26)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0)
% 226.12/38.89  | | | |           = e0)
% 226.12/38.89  | | | | 
% 226.12/38.89  | | | | BETA: splitting (26) gives:
% 226.12/38.89  | | | | 
% 226.12/38.89  | | | | Case 1:
% 226.12/38.89  | | | | | 
% 226.12/38.89  | | | | |   (27)  all_57_4 = e0 & op(e3, e1) = e0
% 226.12/38.89  | | | | | 
% 226.12/38.89  | | | | | REF_CLOSE: (4), (13), (27) are inconsistent by sub-proof #2045.
% 226.12/38.89  | | | | | 
% 226.12/38.89  | | | | Case 2:
% 226.12/38.89  | | | | | 
% 226.12/38.89  | | | | |   (28)  all_57_9 = e0 & op(e3, e0) = e0
% 226.12/38.89  | | | | | 
% 226.12/38.89  | | | | | REF_CLOSE: (14), (24), (28) are inconsistent by sub-proof #1990.
% 226.12/38.89  | | | | | 
% 226.12/38.89  | | | | End of split
% 226.12/38.89  | | | | 
% 226.12/38.89  | | | End of split
% 226.12/38.89  | | | 
% 226.12/38.89  | | End of split
% 226.12/38.89  | | 
% 226.12/38.89  | End of split
% 226.12/38.89  | 
% 226.12/38.89  End of proof
% 226.12/38.89  
% 226.12/38.89  Sub-proof #42 shows that the following formulas are inconsistent:
% 226.12/38.89  ----------------------------------------------------------------
% 226.12/38.89    (1)   ~ (all_53_7 = e3)
% 226.12/38.89    (2)   ~ (e3 = e1)
% 226.12/38.89    (3)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 226.12/38.89         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 226.12/38.89    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.12/38.89           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.12/38.89    (5)  op(e1, e1) = all_6_2
% 226.12/38.89    (6)  op(e2, e2) = e1
% 226.12/38.89    (7)   ~ (e3 = e2)
% 226.12/38.89    (8)   ~ (e3 = e0)
% 226.12/38.89    (9)   ~ (all_53_2 = e0)
% 226.12/38.89    (10)  op(e1, e0) = all_52_23
% 226.12/38.89    (11)   ~ (e2 = e0)
% 226.12/38.89    (12)  op(all_52_23, all_52_23) = e0
% 226.12/38.89    (13)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 226.12/38.89          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 226.12/38.89    (14)  op(e0, e2) = all_53_7
% 226.12/38.89    (15)  op(e3, e2) = e2
% 226.12/38.89    (16)  op(e1, e3) = all_53_2
% 226.12/38.89    (17)  op(e0, e0) = e2
% 226.12/38.89    (18)   ~ (all_6_2 = e0)
% 226.12/38.89  
% 226.12/38.89  Begin of proof
% 226.12/38.89  | 
% 226.12/38.89  | BETA: splitting (13) gives:
% 226.12/38.89  | 
% 226.12/38.89  | Case 1:
% 226.12/38.89  | | 
% 226.12/38.89  | |   (19)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 226.12/38.89  | |           e3)
% 226.12/38.89  | | 
% 226.12/38.89  | | BETA: splitting (19) gives:
% 226.12/38.89  | | 
% 226.12/38.89  | | Case 1:
% 226.12/38.89  | | | 
% 226.12/38.89  | | |   (20)  all_57_1 = e3 & op(e3, e2) = e3
% 226.12/38.89  | | | 
% 226.12/38.89  | | | ALPHA: (20) implies:
% 226.12/38.89  | | |   (21)  op(e3, e2) = e3
% 226.12/38.89  | | | 
% 226.12/38.89  | | | REF_CLOSE: (4), (7), (15), (21) are inconsistent by sub-proof #1549.
% 226.12/38.89  | | | 
% 226.12/38.89  | | Case 2:
% 226.12/38.89  | | | 
% 226.12/38.89  | | |   (22)  all_57_3 = e3 & op(e2, e2) = e3
% 226.12/38.89  | | | 
% 226.12/38.89  | | | ALPHA: (22) implies:
% 226.12/38.89  | | |   (23)  op(e2, e2) = e3
% 226.12/38.89  | | | 
% 226.12/38.89  | | | REF_CLOSE: (2), (4), (6), (23) are inconsistent by sub-proof #1912.
% 226.12/38.89  | | | 
% 226.12/38.89  | | End of split
% 226.12/38.89  | | 
% 226.12/38.89  | Case 2:
% 226.12/38.89  | | 
% 226.12/38.89  | |   (24)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 226.12/38.89  | |           e3)
% 226.12/38.89  | | 
% 226.12/38.89  | | BETA: splitting (24) gives:
% 226.12/38.89  | | 
% 226.12/38.89  | | Case 1:
% 226.12/38.89  | | | 
% 226.12/38.89  | | |   (25)  all_57_7 = e3 & op(e1, e2) = e3
% 226.12/38.89  | | | 
% 226.12/38.89  | | | ALPHA: (25) implies:
% 226.12/38.89  | | |   (26)  all_57_7 = e3
% 226.12/38.89  | | | 
% 226.12/38.89  | | | BETA: splitting (3) gives:
% 226.12/38.89  | | | 
% 226.12/38.89  | | | Case 1:
% 226.12/38.89  | | | | 
% 226.12/38.89  | | | |   (27)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2)
% 226.12/38.89  | | | |           = e0)
% 226.12/38.89  | | | | 
% 226.12/38.89  | | | | BETA: splitting (27) gives:
% 226.12/38.89  | | | | 
% 226.12/38.89  | | | | Case 1:
% 226.12/38.89  | | | | | 
% 226.12/38.89  | | | | |   (28)  all_57_6 = e0 & op(e1, e3) = e0
% 226.12/38.89  | | | | | 
% 226.12/38.89  | | | | | ALPHA: (28) implies:
% 226.12/38.89  | | | | |   (29)  op(e1, e3) = e0
% 226.12/38.89  | | | | | 
% 226.12/38.89  | | | | | REF_CLOSE: (4), (9), (16), (29) are inconsistent by sub-proof #2154.
% 226.12/38.89  | | | | | 
% 226.12/38.89  | | | | Case 2:
% 226.12/38.89  | | | | | 
% 226.12/38.89  | | | | |   (30)  all_57_7 = e0 & op(e1, e2) = e0
% 226.12/38.89  | | | | | 
% 226.12/38.89  | | | | | ALPHA: (30) implies:
% 226.12/38.89  | | | | |   (31)  all_57_7 = e0
% 226.12/38.89  | | | | | 
% 226.12/38.89  | | | | | REF_CLOSE: (8), (26), (31) are inconsistent by sub-proof #2269.
% 226.12/38.89  | | | | | 
% 226.12/38.89  | | | | End of split
% 226.12/38.89  | | | | 
% 226.12/38.89  | | | Case 2:
% 226.12/38.89  | | | | 
% 226.12/38.89  | | | |   (32)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0)
% 226.12/38.89  | | | |           = e0)
% 226.12/38.89  | | | | 
% 226.12/38.89  | | | | BETA: splitting (32) gives:
% 226.12/38.89  | | | | 
% 226.12/38.89  | | | | Case 1:
% 226.12/38.89  | | | | | 
% 226.12/38.89  | | | | |   (33)  all_57_8 = e0 & op(e1, e1) = e0
% 226.12/38.89  | | | | | 
% 226.12/38.89  | | | | | REF_CLOSE: (4), (5), (18), (33) are inconsistent by sub-proof #2412.
% 226.12/38.89  | | | | | 
% 226.12/38.89  | | | | Case 2:
% 226.12/38.89  | | | | | 
% 226.12/38.89  | | | | |   (34)  all_57_11 = e0 & op(e1, e0) = e0
% 226.12/38.89  | | | | | 
% 226.12/38.89  | | | | | ALPHA: (34) implies:
% 226.12/38.89  | | | | |   (35)  op(e1, e0) = e0
% 226.12/38.89  | | | | | 
% 226.12/38.89  | | | | | REF_CLOSE: (4), (10), (11), (12), (17), (35) are inconsistent by
% 226.12/38.89  | | | | |            sub-proof #51.
% 226.12/38.89  | | | | | 
% 226.12/38.89  | | | | End of split
% 226.12/38.89  | | | | 
% 226.12/38.89  | | | End of split
% 226.12/38.89  | | | 
% 226.12/38.89  | | Case 2:
% 226.12/38.89  | | | 
% 226.12/38.89  | | |   (36)  all_57_13 = e3 & op(e0, e2) = e3
% 226.12/38.89  | | | 
% 226.12/38.89  | | | REF_CLOSE: (1), (4), (14), (36) are inconsistent by sub-proof #78.
% 226.12/38.89  | | | 
% 226.12/38.89  | | End of split
% 226.12/38.89  | | 
% 226.12/38.89  | End of split
% 226.12/38.89  | 
% 226.12/38.89  End of proof
% 226.12/38.89  
% 226.12/38.89  Sub-proof #43 shows that the following formulas are inconsistent:
% 226.12/38.89  ----------------------------------------------------------------
% 226.12/38.89    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.12/38.89           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.12/38.89    (2)   ~ (all_53_3 = e3)
% 226.12/38.89    (3)   ~ (all_52_17 = e2)
% 226.12/38.89    (4)  op(all_52_17, all_52_17) = e3
% 226.12/38.89    (5)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 226.12/38.89    (6)   ~ (all_53_3 = e2)
% 226.12/38.89    (7)   ~ (all_53_3 = all_52_17)
% 226.12/38.89    (8)  op(e3, e3) = e0
% 226.12/38.89    (9)  all_55_12 = all_53_3
% 226.12/38.89    (10)   ~ (all_53_3 = e0)
% 226.12/38.89    (11)   ~ (all_52_17 = e0)
% 226.12/38.89    (12)  all_55_8 = all_52_17
% 226.12/38.89    (13)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 226.12/38.89  
% 226.12/38.89  Begin of proof
% 226.12/38.89  | 
% 226.12/38.89  | BETA: splitting (13) gives:
% 226.12/38.89  | 
% 226.12/38.89  | Case 1:
% 226.12/38.89  | | 
% 226.12/38.89  | |   (14)  all_55_12 = e3
% 226.12/38.89  | | 
% 226.12/38.89  | | COMBINE_EQS: (9), (14) imply:
% 226.12/38.89  | |   (15)  all_53_3 = e3
% 226.12/38.89  | | 
% 226.12/38.89  | | REDUCE: (2), (15) imply:
% 226.12/38.89  | |   (16)  $false
% 226.12/38.89  | | 
% 226.12/38.89  | | CLOSE: (16) is inconsistent.
% 226.12/38.90  | | 
% 226.12/38.90  | Case 2:
% 226.12/38.90  | | 
% 226.12/38.90  | |   (17)  all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 226.12/38.90  | | 
% 226.12/38.90  | | BETA: splitting (17) gives:
% 226.12/38.90  | | 
% 226.12/38.90  | | Case 1:
% 226.12/38.90  | | | 
% 226.12/38.90  | | |   (18)  all_55_12 = e2
% 226.12/38.90  | | | 
% 226.12/38.90  | | | COMBINE_EQS: (9), (18) imply:
% 226.12/38.90  | | |   (19)  all_53_3 = e2
% 226.12/38.90  | | | 
% 226.12/38.90  | | | REDUCE: (6), (19) imply:
% 226.12/38.90  | | |   (20)  $false
% 226.12/38.90  | | | 
% 226.12/38.90  | | | CLOSE: (20) is inconsistent.
% 226.12/38.90  | | | 
% 226.12/38.90  | | Case 2:
% 226.12/38.90  | | | 
% 226.12/38.90  | | |   (21)  all_55_12 = e1 | all_55_12 = e0
% 226.12/38.90  | | | 
% 226.12/38.90  | | | BETA: splitting (21) gives:
% 226.12/38.90  | | | 
% 226.12/38.90  | | | Case 1:
% 226.12/38.90  | | | | 
% 226.12/38.90  | | | |   (22)  all_55_12 = e1
% 226.12/38.90  | | | | 
% 226.12/38.90  | | | | COMBINE_EQS: (9), (22) imply:
% 226.12/38.90  | | | |   (23)  all_53_3 = e1
% 226.12/38.90  | | | | 
% 226.12/38.90  | | | | SIMP: (23) implies:
% 226.12/38.90  | | | |   (24)  all_53_3 = e1
% 226.12/38.90  | | | | 
% 226.12/38.90  | | | | REDUCE: (7), (24) imply:
% 226.12/38.90  | | | |   (25)   ~ (all_52_17 = e1)
% 226.12/38.90  | | | | 
% 226.12/38.90  | | | | SIMP: (25) implies:
% 226.12/38.90  | | | |   (26)   ~ (all_52_17 = e1)
% 226.12/38.90  | | | | 
% 226.12/38.90  | | | | BETA: splitting (5) gives:
% 226.12/38.90  | | | | 
% 226.12/38.90  | | | | Case 1:
% 226.12/38.90  | | | | | 
% 226.12/38.90  | | | | |   (27)  all_55_8 = e3
% 226.12/38.90  | | | | | 
% 226.12/38.90  | | | | | COMBINE_EQS: (12), (27) imply:
% 226.12/38.90  | | | | |   (28)  all_52_17 = e3
% 226.12/38.90  | | | | | 
% 226.12/38.90  | | | | | REDUCE: (11), (28) imply:
% 226.12/38.90  | | | | |   (29)   ~ (e3 = e0)
% 226.12/38.90  | | | | | 
% 226.12/38.90  | | | | | REDUCE: (4), (28) imply:
% 226.12/38.90  | | | | |   (30)  op(e3, e3) = e3
% 226.12/38.90  | | | | | 
% 226.12/38.90  | | | | | REF_CLOSE: (1), (8), (29), (30) are inconsistent by sub-proof #2494.
% 226.12/38.90  | | | | | 
% 226.12/38.90  | | | | Case 2:
% 226.12/38.90  | | | | | 
% 226.12/38.90  | | | | |   (31)  all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 226.12/38.90  | | | | | 
% 226.12/38.90  | | | | | REF_CLOSE: (3), (11), (12), (26), (31) are inconsistent by sub-proof
% 226.12/38.90  | | | | |            #1867.
% 226.12/38.90  | | | | | 
% 226.12/38.90  | | | | End of split
% 226.12/38.90  | | | | 
% 226.12/38.90  | | | Case 2:
% 226.12/38.90  | | | | 
% 226.12/38.90  | | | |   (32)  all_55_12 = e0
% 226.12/38.90  | | | | 
% 226.12/38.90  | | | | REF_CLOSE: (9), (10), (32) are inconsistent by sub-proof #1993.
% 226.12/38.90  | | | | 
% 226.12/38.90  | | | End of split
% 226.12/38.90  | | | 
% 226.12/38.90  | | End of split
% 226.12/38.90  | | 
% 226.12/38.90  | End of split
% 226.12/38.90  | 
% 226.12/38.90  End of proof
% 226.12/38.90  
% 226.12/38.90  Sub-proof #44 shows that the following formulas are inconsistent:
% 226.12/38.90  ----------------------------------------------------------------
% 226.12/38.90    (1)   ~ (e3 = e1)
% 226.12/38.90    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.12/38.90           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.12/38.90    (3)  op(e1, e1) = all_6_2
% 226.12/38.90    (4)  op(e2, e2) = e1
% 226.12/38.90    (5)   ~ (all_6_2 = e2)
% 226.12/38.90    (6)  op(e3, e3) = e2
% 226.12/38.90    (7)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 226.12/38.90           op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 226.12/38.90           op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 226.12/38.90           = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3, e0)
% 226.12/38.90           = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) & $i(all_52_7))
% 226.12/38.90         | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0 &
% 226.12/38.90           op(all_52_9, all_52_9) = e3 & op(all_52_11, all_52_11) = e2 &
% 226.12/38.90           op(all_52_13, all_52_13) = e1 & op(all_52_15, all_52_15) = e0 & op(e2,
% 226.12/38.90             e3) = all_52_9 & op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13 &
% 226.12/38.90           op(e2, e0) = all_52_15 & $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 226.12/38.90           $i(all_52_15)) | (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 226.12/38.90           all_52_22 = e0 & op(all_52_17, all_52_17) = e3 & op(all_52_19,
% 226.12/38.90             all_52_19) = e2 & op(all_52_21, all_52_21) = e1 & op(all_52_23,
% 226.12/38.90             all_52_23) = e0 & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19 &
% 226.12/38.90           op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23 & $i(all_52_17) &
% 226.12/38.90           $i(all_52_19) & $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3 &
% 226.12/38.90           all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0 & op(all_52_25,
% 226.12/38.90             all_52_25) = e3 & op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 226.12/38.90             all_52_29) = e1 & op(all_52_31, all_52_31) = e0 & op(e0, e3) =
% 226.12/38.90           all_52_25 & op(e0, e2) = all_52_27 & op(e0, e1) = all_52_29 & op(e0,
% 226.12/38.90             e0) = all_52_31 & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 226.12/38.90           $i(all_52_31))
% 226.12/38.90    (8)   ~ (e1 = e0)
% 226.12/38.90    (9)  op(e1, e2) = e2
% 226.12/38.90    (10)   ~ (e2 = e1)
% 226.12/38.90    (11)  op(e0, e0) = e2
% 226.12/38.90  
% 226.12/38.90  Begin of proof
% 226.12/38.90  | 
% 226.12/38.90  | BETA: splitting (7) gives:
% 226.12/38.90  | 
% 226.12/38.90  | Case 1:
% 226.12/38.90  | | 
% 226.12/38.90  | |   (12)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 226.12/38.90  | |           op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 226.12/38.90  | |           op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3,
% 226.12/38.90  | |             e3) = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 &
% 226.12/38.90  | |           op(e3, e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5)
% 226.12/38.90  | |           & $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1
% 226.12/38.90  | |           & all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 226.12/38.90  | |             all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 226.12/38.90  | |             all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11
% 226.12/38.90  | |           & op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 226.12/38.90  | |           $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 226.12/38.90  | | 
% 226.12/38.90  | | BETA: splitting (12) gives:
% 226.12/38.90  | | 
% 226.12/38.90  | | Case 1:
% 226.12/38.90  | | | 
% 226.12/38.90  | | |   (13)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 226.12/38.90  | | |         op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 226.12/38.90  | | |         op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3,
% 226.12/38.90  | | |           e3) = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 &
% 226.12/38.90  | | |         op(e3, e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5)
% 226.12/38.90  | | |         & $i(all_52_7)
% 226.12/38.90  | | | 
% 226.12/38.90  | | | REF_CLOSE: (1), (2), (4), (6), (13) are inconsistent by sub-proof #1597.
% 226.12/38.90  | | | 
% 226.12/38.90  | | Case 2:
% 226.12/38.90  | | | 
% 226.12/38.90  | | |   (14)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0 &
% 226.12/38.90  | | |         op(all_52_9, all_52_9) = e3 & op(all_52_11, all_52_11) = e2 &
% 226.12/38.90  | | |         op(all_52_13, all_52_13) = e1 & op(all_52_15, all_52_15) = e0 &
% 226.12/38.90  | | |         op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 & op(e2, e1) =
% 226.12/38.90  | | |         all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) & $i(all_52_11)
% 226.12/38.90  | | |         & $i(all_52_13) & $i(all_52_15)
% 226.12/38.90  | | | 
% 226.12/38.90  | | | REF_CLOSE: (2), (3), (4), (5), (14) are inconsistent by sub-proof #45.
% 226.12/38.90  | | | 
% 226.12/38.90  | | End of split
% 226.12/38.90  | | 
% 226.12/38.90  | Case 2:
% 226.12/38.90  | | 
% 226.12/38.90  | |   (15)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 &
% 226.12/38.90  | |           op(all_52_17, all_52_17) = e3 & op(all_52_19, all_52_19) = e2 &
% 226.12/38.90  | |           op(all_52_21, all_52_21) = e1 & op(all_52_23, all_52_23) = e0 &
% 226.12/38.90  | |           op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) =
% 226.12/38.90  | |           all_52_21 & op(e1, e0) = all_52_23 & $i(all_52_17) & $i(all_52_19)
% 226.12/38.90  | |           & $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3 & all_52_26 =
% 226.12/38.90  | |           e2 & all_52_28 = e1 & all_52_30 = e0 & op(all_52_25, all_52_25) =
% 226.12/38.90  | |           e3 & op(all_52_27, all_52_27) = e2 & op(all_52_29, all_52_29) = e1
% 226.12/38.90  | |           & op(all_52_31, all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0,
% 226.12/38.90  | |             e2) = all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0) =
% 226.12/38.90  | |           all_52_31 & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 226.12/38.90  | |           $i(all_52_31))
% 226.12/38.90  | | 
% 226.12/38.90  | | BETA: splitting (15) gives:
% 226.12/38.90  | | 
% 226.12/38.90  | | Case 1:
% 226.12/38.90  | | | 
% 226.12/38.90  | | |   (16)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 226.12/38.90  | | |         & op(all_52_17, all_52_17) = e3 & op(all_52_19, all_52_19) = e2 &
% 226.12/38.90  | | |         op(all_52_21, all_52_21) = e1 & op(all_52_23, all_52_23) = e0 &
% 226.12/38.90  | | |         op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) =
% 226.12/38.90  | | |         all_52_21 & op(e1, e0) = all_52_23 & $i(all_52_17) & $i(all_52_19)
% 226.12/38.90  | | |         & $i(all_52_21) & $i(all_52_23)
% 226.12/38.90  | | | 
% 226.12/38.90  | | | ALPHA: (16) implies:
% 226.12/38.90  | | |   (17)  op(e1, e2) = all_52_19
% 226.12/38.90  | | |   (18)  op(all_52_19, all_52_19) = e2
% 226.12/38.90  | | | 
% 226.12/38.90  | | | GROUND_INST: instantiating (2) with e2, all_52_19, e2, e1, simplifying
% 226.12/38.90  | | |              with (9), (17) gives:
% 226.12/38.90  | | |   (19)  all_52_19 = e2
% 226.12/38.90  | | | 
% 226.12/38.90  | | | REDUCE: (18), (19) imply:
% 226.12/38.90  | | |   (20)  op(e2, e2) = e2
% 226.12/38.90  | | | 
% 226.12/38.90  | | | REF_CLOSE: (2), (4), (10), (20) are inconsistent by sub-proof #2306.
% 226.12/38.90  | | | 
% 226.12/38.90  | | Case 2:
% 226.12/38.90  | | | 
% 226.12/38.90  | | |   (21)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 226.12/38.90  | | |         & op(all_52_25, all_52_25) = e3 & op(all_52_27, all_52_27) = e2 &
% 226.12/38.90  | | |         op(all_52_29, all_52_29) = e1 & op(all_52_31, all_52_31) = e0 &
% 226.12/38.90  | | |         op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 & op(e0, e1) =
% 226.12/38.90  | | |         all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) & $i(all_52_27)
% 226.12/38.90  | | |         & $i(all_52_29) & $i(all_52_31)
% 226.12/38.90  | | | 
% 226.12/38.90  | | | REF_CLOSE: (2), (4), (8), (11), (21) are inconsistent by sub-proof #50.
% 226.12/38.90  | | | 
% 226.12/38.90  | | End of split
% 226.12/38.90  | | 
% 226.12/38.90  | End of split
% 226.12/38.90  | 
% 226.12/38.90  End of proof
% 226.12/38.90  
% 226.12/38.90  Sub-proof #45 shows that the following formulas are inconsistent:
% 226.12/38.90  ----------------------------------------------------------------
% 226.12/38.90    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.12/38.90           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.12/38.90    (2)  op(e1, e1) = all_6_2
% 226.12/38.90    (3)  op(e2, e2) = e1
% 226.12/38.90    (4)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0 &
% 226.12/38.90         op(all_52_9, all_52_9) = e3 & op(all_52_11, all_52_11) = e2 &
% 226.12/38.90         op(all_52_13, all_52_13) = e1 & op(all_52_15, all_52_15) = e0 & op(e2,
% 226.12/38.90           e3) = all_52_9 & op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13 &
% 226.12/38.90         op(e2, e0) = all_52_15 & $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 226.12/38.90         $i(all_52_15)
% 226.12/38.90    (5)   ~ (all_6_2 = e2)
% 226.12/38.90  
% 226.12/38.90  Begin of proof
% 226.12/38.90  | 
% 226.12/38.90  | ALPHA: (4) implies:
% 226.12/38.90  |   (6)  op(e2, e2) = all_52_11
% 226.12/38.90  |   (7)  op(all_52_11, all_52_11) = e2
% 226.12/38.90  | 
% 226.12/38.90  | GROUND_INST: instantiating (1) with e1, all_52_11, e2, e2, simplifying with
% 226.12/38.90  |              (3), (6) gives:
% 226.12/38.90  |   (8)  all_52_11 = e1
% 226.12/38.90  | 
% 226.12/38.90  | REDUCE: (7), (8) imply:
% 226.12/38.90  |   (9)  op(e1, e1) = e2
% 226.12/38.90  | 
% 226.12/38.90  | GROUND_INST: instantiating (1) with all_6_2, e2, e1, e1, simplifying with (2),
% 226.12/38.90  |              (9) gives:
% 226.12/38.90  |   (10)  all_6_2 = e2
% 226.12/38.90  | 
% 226.12/38.90  | REDUCE: (5), (10) imply:
% 226.12/38.90  |   (11)  $false
% 226.12/38.90  | 
% 226.12/38.90  | CLOSE: (11) is inconsistent.
% 226.12/38.90  | 
% 226.12/38.90  End of proof
% 226.12/38.90  
% 226.12/38.90  Sub-proof #46 shows that the following formulas are inconsistent:
% 226.12/38.90  ----------------------------------------------------------------
% 226.12/38.90    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.12/38.90           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.12/38.90    (2)  op(e1, e1) = e0
% 226.12/38.90    (3)   ~ (e2 = e1)
% 226.12/38.90    (4)  op(e0, e0) = e2
% 226.12/38.90    (5)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 &
% 226.12/38.90         op(all_52_17, all_52_17) = e3 & op(all_52_19, all_52_19) = e2 &
% 226.12/38.90         op(all_52_21, all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1,
% 226.12/38.90           e3) = all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 &
% 226.12/38.90         op(e1, e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 226.12/38.90         $i(all_52_23)
% 226.12/38.90  
% 226.12/38.90  Begin of proof
% 226.12/38.90  | 
% 226.12/38.90  | ALPHA: (5) implies:
% 226.12/38.90  |   (6)  op(e1, e1) = all_52_21
% 226.12/38.90  |   (7)  op(all_52_21, all_52_21) = e1
% 226.12/38.90  | 
% 226.12/38.90  | GROUND_INST: instantiating (1) with e0, all_52_21, e1, e1, simplifying with
% 226.12/38.90  |              (2), (6) gives:
% 226.12/38.90  |   (8)  all_52_21 = e0
% 226.12/38.90  | 
% 226.12/38.90  | REDUCE: (7), (8) imply:
% 226.12/38.90  |   (9)  op(e0, e0) = e1
% 226.12/38.90  | 
% 226.12/38.90  | REF_CLOSE: (1), (3), (4), (9) are inconsistent by sub-proof #2177.
% 226.12/38.90  | 
% 226.12/38.90  End of proof
% 226.12/38.90  
% 226.12/38.90  Sub-proof #47 shows that the following formulas are inconsistent:
% 226.12/38.90  ----------------------------------------------------------------
% 226.12/38.90    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.12/38.90           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.12/38.90    (2)  op(all_52_7, all_52_7) = e0
% 226.12/38.90    (3)  op(e3, e0) = e0
% 226.12/38.90    (4)   ~ (e2 = e0)
% 226.12/38.90    (5)  op(e0, e0) = e2
% 226.12/38.90    (6)  op(e3, e0) = all_52_7
% 226.12/38.90  
% 226.12/38.90  Begin of proof
% 226.12/38.90  | 
% 226.12/38.90  | GROUND_INST: instantiating (1) with e0, all_52_7, e0, e3, simplifying with
% 226.12/38.90  |              (3), (6) gives:
% 226.12/38.90  |   (7)  all_52_7 = e0
% 226.12/38.90  | 
% 226.12/38.90  | REDUCE: (2), (7) imply:
% 226.12/38.90  |   (8)  op(e0, e0) = e0
% 226.12/38.90  | 
% 226.12/38.90  | GROUND_INST: instantiating (1) with e2, e0, e0, e0, simplifying with (5), (8)
% 226.12/38.90  |              gives:
% 226.12/38.90  |   (9)  e2 = e0
% 226.12/38.90  | 
% 226.12/38.90  | REDUCE: (4), (9) imply:
% 226.12/38.90  |   (10)  $false
% 226.12/38.90  | 
% 226.12/38.90  | CLOSE: (10) is inconsistent.
% 226.12/38.90  | 
% 226.12/38.90  End of proof
% 226.12/38.90  
% 226.12/38.90  Sub-proof #48 shows that the following formulas are inconsistent:
% 226.12/38.90  ----------------------------------------------------------------
% 226.12/38.90    (1)   ~ (e3 = e1)
% 226.12/38.90    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.12/38.90           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.12/38.90    (3)  op(e2, e2) = e1
% 226.12/38.90    (4)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0 &
% 226.12/38.90         op(all_52_9, all_52_9) = e3 & op(all_52_11, all_52_11) = e2 &
% 226.12/38.90         op(all_52_13, all_52_13) = e1 & op(all_52_15, all_52_15) = e0 & op(e2,
% 226.12/38.90           e3) = all_52_9 & op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13 &
% 226.12/38.90         op(e2, e0) = all_52_15 & $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 226.12/38.90         $i(all_52_15)
% 226.12/38.90    (5)  op(e2, e3) = e2
% 226.12/38.90  
% 226.12/38.90  Begin of proof
% 226.12/38.90  | 
% 226.12/38.90  | ALPHA: (4) implies:
% 226.12/38.90  |   (6)  op(e2, e2) = all_52_11
% 226.12/38.90  |   (7)  op(e2, e3) = all_52_9
% 226.12/38.90  |   (8)  op(all_52_9, all_52_9) = e3
% 226.12/38.90  | 
% 226.12/38.90  | GROUND_INST: instantiating (2) with e1, all_52_11, e2, e2, simplifying with
% 226.12/38.90  |              (3), (6) gives:
% 226.12/38.90  |   (9)  all_52_11 = e1
% 226.12/38.90  | 
% 226.12/38.90  | GROUND_INST: instantiating (2) with e2, all_52_9, e3, e2, simplifying with
% 226.12/38.90  |              (5), (7) gives:
% 226.12/38.90  |   (10)  all_52_9 = e2
% 226.12/38.90  | 
% 226.12/38.90  | REDUCE: (8), (10) imply:
% 226.12/38.90  |   (11)  op(e2, e2) = e3
% 226.12/38.90  | 
% 226.12/38.90  | REF_CLOSE: (1), (2), (3), (11) are inconsistent by sub-proof #1912.
% 226.12/38.90  | 
% 226.12/38.90  End of proof
% 226.12/38.90  
% 226.12/38.90  Sub-proof #49 shows that the following formulas are inconsistent:
% 226.12/38.90  ----------------------------------------------------------------
% 226.12/38.90    (1)  op(e2, e3) = all_53_1
% 226.12/38.90    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.12/38.90           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.12/38.90    (3)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 226.12/38.91    (4)  op(e2, e2) = e1
% 226.12/38.91    (5)   ~ (all_53_13 = e2)
% 226.12/38.91    (6)  all_57_9 = e1
% 226.12/38.91    (7)   ~ (all_53_12 = all_53_13)
% 226.12/38.91    (8)  op(e3, e0) = e1
% 226.12/38.91    (9)  op(e1, e0) = all_53_14
% 226.12/38.91    (10)  all_55_7 = e3 | all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 226.12/38.91    (11)   ~ (e3 = e0)
% 226.12/38.91    (12)  op(e3, e3) = e3
% 226.12/38.91    (13)   ~ (all_53_9 = all_53_13)
% 226.12/38.91    (14)  op(e1, e1) = e1
% 226.12/38.91    (15)   ~ (e2 = e0)
% 226.12/38.91    (16)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 226.12/38.91            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 226.12/38.91            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 226.12/38.91            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 226.12/38.91              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 226.12/38.91            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 226.12/38.91            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 226.12/38.91              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 226.12/38.91              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 226.12/38.91            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 226.12/38.91            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 226.12/38.91            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 226.12/38.91              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 226.12/38.91              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 226.12/38.91            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 226.12/38.91              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 226.12/38.91            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 226.12/38.91            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 226.12/38.91              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 226.12/38.91              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 226.12/38.91            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 226.12/38.91            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 226.12/38.91    (17)  all_57_15 = e2
% 226.12/38.91    (18)   ~ (e1 = e0)
% 226.12/38.91    (19)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 226.12/38.91              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 226.12/38.91                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 226.12/38.91                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 226.12/38.91    (20)   ~ (all_53_1 = all_53_13)
% 226.12/38.91    (21)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 226.12/38.91          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 226.12/38.91    (22)  all_55_11 = all_53_14
% 226.12/38.91    (23)   ~ (all_53_13 = all_53_14)
% 226.12/38.91    (24)  op(e0, e0) = e2
% 226.12/38.91    (25)  op(e2, e1) = all_53_9
% 226.12/38.91    (26)   ~ (all_53_14 = e2)
% 226.12/38.91    (27)   ~ (all_53_12 = e2)
% 226.12/38.91    (28)   ~ (all_53_12 = all_53_14)
% 226.12/38.91    (29)  all_55_7 = all_53_13
% 226.12/38.91    (30)  op(e3, e0) = all_53_12
% 226.12/38.91  
% 226.12/38.91  Begin of proof
% 226.12/38.91  | 
% 226.12/38.91  | GROUND_INST: instantiating (2) with all_53_12, e1, e0, e3, simplifying with
% 226.12/38.91  |              (8), (30) gives:
% 226.12/38.91  |   (31)  all_53_12 = e1
% 226.12/38.91  | 
% 226.12/38.91  | REDUCE: (7), (31) imply:
% 226.12/38.91  |   (32)   ~ (all_53_13 = e1)
% 226.12/38.91  | 
% 226.12/38.91  | SIMP: (32) implies:
% 226.12/38.91  |   (33)   ~ (all_53_13 = e1)
% 226.12/38.91  | 
% 226.12/38.91  | REDUCE: (28), (31) imply:
% 226.12/38.91  |   (34)   ~ (all_53_14 = e1)
% 226.12/38.91  | 
% 226.12/38.91  | SIMP: (34) implies:
% 226.12/38.91  |   (35)   ~ (all_53_14 = e1)
% 226.12/38.91  | 
% 226.12/38.91  | REDUCE: (27), (31) imply:
% 226.12/38.91  |   (36)   ~ (e2 = e1)
% 226.12/38.91  | 
% 226.12/38.91  | SIMP: (36) implies:
% 226.12/38.91  |   (37)   ~ (e2 = e1)
% 226.12/38.91  | 
% 226.12/38.91  | BETA: splitting (16) gives:
% 226.12/38.91  | 
% 226.12/38.91  | Case 1:
% 226.12/38.91  | | 
% 226.12/38.91  | |   (38)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 226.12/38.91  | |           op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 226.12/38.91  | |           op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3,
% 226.12/38.91  | |             e3) = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 &
% 226.12/38.91  | |           op(e3, e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5)
% 226.12/38.91  | |           & $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1
% 226.12/38.91  | |           & all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 226.12/38.91  | |             all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 226.12/38.91  | |             all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11
% 226.12/38.91  | |           & op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 226.12/38.91  | |           $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 226.12/38.91  | | 
% 226.12/38.91  | | REF_CLOSE: (2), (4), (8), (14), (18), (37), (38) are inconsistent by
% 226.12/38.91  | |            sub-proof #1854.
% 226.12/38.91  | | 
% 226.12/38.91  | Case 2:
% 226.12/38.91  | | 
% 226.12/38.91  | |   (39)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 &
% 226.12/38.91  | |           op(all_52_17, all_52_17) = e3 & op(all_52_19, all_52_19) = e2 &
% 226.12/38.91  | |           op(all_52_21, all_52_21) = e1 & op(all_52_23, all_52_23) = e0 &
% 226.12/38.91  | |           op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) =
% 226.12/38.91  | |           all_52_21 & op(e1, e0) = all_52_23 & $i(all_52_17) & $i(all_52_19)
% 226.12/38.91  | |           & $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3 & all_52_26 =
% 226.12/38.91  | |           e2 & all_52_28 = e1 & all_52_30 = e0 & op(all_52_25, all_52_25) =
% 226.12/38.91  | |           e3 & op(all_52_27, all_52_27) = e2 & op(all_52_29, all_52_29) = e1
% 226.12/38.91  | |           & op(all_52_31, all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0,
% 226.12/38.91  | |             e2) = all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0) =
% 226.12/38.91  | |           all_52_31 & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 226.12/38.91  | |           $i(all_52_31))
% 226.12/38.91  | | 
% 226.12/38.91  | | BETA: splitting (39) gives:
% 226.12/38.91  | | 
% 226.12/38.91  | | Case 1:
% 226.12/38.91  | | | 
% 226.12/38.91  | | |   (40)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 226.12/38.91  | | |         & op(all_52_17, all_52_17) = e3 & op(all_52_19, all_52_19) = e2 &
% 226.12/38.91  | | |         op(all_52_21, all_52_21) = e1 & op(all_52_23, all_52_23) = e0 &
% 226.12/38.91  | | |         op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) =
% 226.12/38.91  | | |         all_52_21 & op(e1, e0) = all_52_23 & $i(all_52_17) & $i(all_52_19)
% 226.12/38.91  | | |         & $i(all_52_21) & $i(all_52_23)
% 226.12/38.91  | | | 
% 226.12/38.91  | | | ALPHA: (40) implies:
% 226.12/38.91  | | |   (41)  op(e1, e0) = all_52_23
% 226.12/38.91  | | |   (42)  op(all_52_23, all_52_23) = e0
% 226.12/38.91  | | | 
% 226.12/38.91  | | | GROUND_INST: instantiating (2) with all_53_14, all_52_23, e0, e1,
% 226.12/38.91  | | |              simplifying with (9), (41) gives:
% 226.12/38.91  | | |   (43)  all_53_14 = all_52_23
% 226.12/38.91  | | | 
% 226.12/38.91  | | | COMBINE_EQS: (22), (43) imply:
% 226.12/38.91  | | |   (44)  all_55_11 = all_52_23
% 226.12/38.91  | | | 
% 226.12/38.91  | | | REDUCE: (23), (43) imply:
% 226.12/38.91  | | |   (45)   ~ (all_53_13 = all_52_23)
% 226.12/38.91  | | | 
% 226.12/38.91  | | | REDUCE: (26), (43) imply:
% 226.12/38.91  | | |   (46)   ~ (all_52_23 = e2)
% 226.12/38.91  | | | 
% 226.12/38.91  | | | REDUCE: (35), (43) imply:
% 226.12/38.91  | | |   (47)   ~ (all_52_23 = e1)
% 226.12/38.91  | | | 
% 226.12/38.91  | | | BETA: splitting (10) gives:
% 226.12/38.91  | | | 
% 226.12/38.91  | | | Case 1:
% 226.12/38.91  | | | | 
% 226.12/38.91  | | | |   (48)  all_55_7 = e3
% 226.12/38.91  | | | | 
% 226.12/38.91  | | | | COMBINE_EQS: (29), (48) imply:
% 226.12/38.91  | | | |   (49)  all_53_13 = e3
% 226.12/38.91  | | | | 
% 226.12/38.91  | | | | REDUCE: (20), (49) imply:
% 226.12/38.91  | | | |   (50)   ~ (all_53_1 = e3)
% 226.12/38.91  | | | | 
% 226.12/38.91  | | | | REDUCE: (13), (49) imply:
% 226.12/38.91  | | | |   (51)   ~ (all_53_9 = e3)
% 226.12/38.91  | | | | 
% 226.12/38.91  | | | | REDUCE: (33), (49) imply:
% 226.12/38.91  | | | |   (52)   ~ (e3 = e1)
% 226.12/38.91  | | | | 
% 226.12/38.91  | | | | BETA: splitting (21) gives:
% 226.12/38.91  | | | | 
% 226.12/38.91  | | | | Case 1:
% 226.12/38.91  | | | | | 
% 226.12/38.91  | | | | |   (53)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2,
% 226.12/38.91  | | | | |             e2) = e3)
% 226.12/38.91  | | | | | 
% 226.12/38.91  | | | | | REF_CLOSE: (1), (2), (4), (50), (52), (53) are inconsistent by
% 226.12/38.91  | | | | |            sub-proof #159.
% 226.12/38.91  | | | | | 
% 226.12/38.91  | | | | Case 2:
% 226.12/38.91  | | | | | 
% 226.12/38.91  | | | | |   (54)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2,
% 226.12/38.91  | | | | |             e0) = e3)
% 226.12/38.91  | | | | | 
% 226.12/38.91  | | | | | BETA: splitting (54) gives:
% 226.12/38.91  | | | | | 
% 226.12/38.91  | | | | | Case 1:
% 226.12/38.91  | | | | | | 
% 226.12/38.91  | | | | | |   (55)  all_57_5 = e3 & op(e2, e1) = e3
% 226.12/38.91  | | | | | | 
% 226.12/38.91  | | | | | | REF_CLOSE: (2), (25), (51), (55) are inconsistent by sub-proof #270.
% 226.12/38.91  | | | | | | 
% 226.12/38.91  | | | | | Case 2:
% 226.12/38.91  | | | | | | 
% 226.12/38.91  | | | | | |   (56)  all_57_10 = e3 & op(e2, e0) = e3
% 226.12/38.91  | | | | | | 
% 226.12/38.91  | | | | | | ALPHA: (56) implies:
% 226.12/38.91  | | | | | |   (57)  all_57_10 = e3
% 226.12/38.91  | | | | | | 
% 226.12/38.91  | | | | | | BETA: splitting (19) gives:
% 226.12/38.91  | | | | | | 
% 226.12/38.91  | | | | | | Case 1:
% 226.12/38.91  | | | | | | | 
% 226.12/38.91  | | | | | | |   (58)  all_57_15 = e0 & op(e0, e0) = e0
% 226.12/38.91  | | | | | | | 
% 226.12/38.91  | | | | | | | ALPHA: (58) implies:
% 226.12/38.91  | | | | | | |   (59)  all_57_15 = e0
% 226.12/38.91  | | | | | | | 
% 226.12/38.91  | | | | | | | REF_CLOSE: (15), (17), (59) are inconsistent by sub-proof #2126.
% 226.12/38.91  | | | | | | | 
% 226.12/38.91  | | | | | | Case 2:
% 226.12/38.91  | | | | | | | 
% 226.12/38.91  | | | | | | |   (60)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 &
% 226.12/38.91  | | | | | | |             op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0))
% 226.12/38.91  | | | | | | |         & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 226.12/38.91  | | | | | | |             op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 226.12/38.91  | | | | | | | 
% 226.12/38.91  | | | | | | | ALPHA: (60) implies:
% 226.12/38.91  | | | | | | |   (61)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 &
% 226.12/38.91  | | | | | | |           op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 226.12/38.91  | | | | | | | 
% 226.12/38.91  | | | | | | | BETA: splitting (61) gives:
% 226.12/38.91  | | | | | | | 
% 226.12/38.91  | | | | | | | Case 1:
% 226.12/38.91  | | | | | | | | 
% 226.12/38.91  | | | | | | | |   (62)  all_57_9 = e0 & op(e3, e0) = e0
% 226.12/38.91  | | | | | | | | 
% 226.12/38.91  | | | | | | | | REF_CLOSE: (6), (18), (62) are inconsistent by sub-proof #1990.
% 226.12/38.91  | | | | | | | | 
% 226.12/38.91  | | | | | | | Case 2:
% 226.12/38.91  | | | | | | | | 
% 226.12/38.91  | | | | | | | |   (63)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 226.12/38.91  | | | | | | | |           op(e1, e0) = e0)
% 226.12/38.91  | | | | | | | | 
% 226.12/38.91  | | | | | | | | BETA: splitting (63) gives:
% 226.12/38.91  | | | | | | | | 
% 226.12/38.91  | | | | | | | | Case 1:
% 226.12/38.91  | | | | | | | | | 
% 226.12/38.91  | | | | | | | | |   (64)  all_57_10 = e0 & op(e2, e0) = e0
% 226.12/38.91  | | | | | | | | | 
% 226.12/38.91  | | | | | | | | | ALPHA: (64) implies:
% 226.12/38.91  | | | | | | | | |   (65)  all_57_10 = e0
% 226.12/38.91  | | | | | | | | | 
% 226.12/38.91  | | | | | | | | | REF_CLOSE: (11), (57), (65) are inconsistent by sub-proof
% 226.12/38.91  | | | | | | | | |            #1989.
% 226.12/38.91  | | | | | | | | | 
% 226.12/38.91  | | | | | | | | Case 2:
% 226.12/38.91  | | | | | | | | | 
% 226.12/38.91  | | | | | | | | |   (66)  all_57_11 = e0 & op(e1, e0) = e0
% 226.12/38.91  | | | | | | | | | 
% 226.12/38.91  | | | | | | | | | ALPHA: (66) implies:
% 226.12/38.91  | | | | | | | | |   (67)  op(e1, e0) = e0
% 226.12/38.91  | | | | | | | | | 
% 226.12/38.91  | | | | | | | | | REF_CLOSE: (2), (15), (24), (41), (42), (67) are inconsistent
% 226.12/38.91  | | | | | | | | |            by sub-proof #51.
% 226.12/38.91  | | | | | | | | | 
% 226.12/38.91  | | | | | | | | End of split
% 226.12/38.91  | | | | | | | | 
% 226.12/38.91  | | | | | | | End of split
% 226.12/38.91  | | | | | | | 
% 226.12/38.91  | | | | | | End of split
% 226.12/38.91  | | | | | | 
% 226.12/38.91  | | | | | End of split
% 226.12/38.91  | | | | | 
% 226.12/38.91  | | | | End of split
% 226.12/38.91  | | | | 
% 226.12/38.91  | | | Case 2:
% 226.12/38.91  | | | | 
% 226.12/38.91  | | | |   (68)  all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 226.12/38.91  | | | | 
% 226.12/38.91  | | | | BETA: splitting (68) gives:
% 226.12/38.91  | | | | 
% 226.12/38.91  | | | | Case 1:
% 226.12/38.91  | | | | | 
% 226.12/38.91  | | | | |   (69)  all_55_7 = e2
% 226.12/38.91  | | | | | 
% 226.12/38.91  | | | | | REF_CLOSE: (5), (29), (69) are inconsistent by sub-proof #2171.
% 226.12/38.91  | | | | | 
% 226.12/38.91  | | | | Case 2:
% 226.12/38.91  | | | | | 
% 226.12/38.91  | | | | |   (70)  all_55_7 = e1 | all_55_7 = e0
% 226.12/38.91  | | | | | 
% 226.12/38.91  | | | | | BETA: splitting (70) gives:
% 226.12/38.91  | | | | | 
% 226.12/38.91  | | | | | Case 1:
% 226.12/38.91  | | | | | | 
% 226.12/38.91  | | | | | |   (71)  all_55_7 = e1
% 226.12/38.91  | | | | | | 
% 226.12/38.91  | | | | | | REF_CLOSE: (29), (33), (71) are inconsistent by sub-proof #1970.
% 226.12/38.91  | | | | | | 
% 226.12/38.91  | | | | | Case 2:
% 226.12/38.91  | | | | | | 
% 226.12/38.91  | | | | | |   (72)  all_55_7 = e0
% 226.12/38.91  | | | | | | 
% 226.12/38.91  | | | | | | COMBINE_EQS: (29), (72) imply:
% 226.12/38.91  | | | | | |   (73)  all_53_13 = e0
% 226.12/38.91  | | | | | | 
% 226.12/38.91  | | | | | | SIMP: (73) implies:
% 226.12/38.91  | | | | | |   (74)  all_53_13 = e0
% 226.12/38.91  | | | | | | 
% 226.12/38.91  | | | | | | REDUCE: (45), (74) imply:
% 226.12/38.91  | | | | | |   (75)   ~ (all_52_23 = e0)
% 226.12/38.91  | | | | | | 
% 226.12/38.91  | | | | | | SIMP: (75) implies:
% 226.12/38.91  | | | | | |   (76)   ~ (all_52_23 = e0)
% 226.12/38.91  | | | | | | 
% 226.12/38.91  | | | | | | REF_CLOSE: (2), (3), (12), (42), (44), (46), (47), (76) are
% 226.12/38.91  | | | | | |            inconsistent by sub-proof #2105.
% 226.12/38.91  | | | | | | 
% 226.12/38.91  | | | | | End of split
% 226.12/38.91  | | | | | 
% 226.12/38.91  | | | | End of split
% 226.12/38.91  | | | | 
% 226.12/38.91  | | | End of split
% 226.12/38.91  | | | 
% 226.12/38.91  | | Case 2:
% 226.12/38.91  | | | 
% 226.12/38.91  | | |   (77)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 226.12/38.91  | | |         & op(all_52_25, all_52_25) = e3 & op(all_52_27, all_52_27) = e2 &
% 226.12/38.91  | | |         op(all_52_29, all_52_29) = e1 & op(all_52_31, all_52_31) = e0 &
% 226.12/38.91  | | |         op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 & op(e0, e1) =
% 226.12/38.91  | | |         all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) & $i(all_52_27)
% 226.12/38.91  | | |         & $i(all_52_29) & $i(all_52_31)
% 226.12/38.91  | | | 
% 226.12/38.91  | | | REF_CLOSE: (2), (4), (18), (24), (77) are inconsistent by sub-proof #50.
% 226.12/38.91  | | | 
% 226.12/38.91  | | End of split
% 226.12/38.91  | | 
% 226.12/38.91  | End of split
% 226.12/38.91  | 
% 226.12/38.91  End of proof
% 226.12/38.91  
% 226.12/38.91  Sub-proof #50 shows that the following formulas are inconsistent:
% 226.12/38.91  ----------------------------------------------------------------
% 226.12/38.91    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.12/38.91           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.12/38.91    (2)  op(e2, e2) = e1
% 226.12/38.91    (3)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0 &
% 226.12/38.91         op(all_52_25, all_52_25) = e3 & op(all_52_27, all_52_27) = e2 &
% 226.12/38.91         op(all_52_29, all_52_29) = e1 & op(all_52_31, all_52_31) = e0 & op(e0,
% 226.12/38.91           e3) = all_52_25 & op(e0, e2) = all_52_27 & op(e0, e1) = all_52_29 &
% 226.12/38.91         op(e0, e0) = all_52_31 & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 226.12/38.91         $i(all_52_31)
% 226.12/38.91    (4)   ~ (e1 = e0)
% 226.12/38.91    (5)  op(e0, e0) = e2
% 226.12/38.91  
% 226.12/38.91  Begin of proof
% 226.12/38.91  | 
% 226.12/38.91  | ALPHA: (3) implies:
% 226.12/38.91  |   (6)  op(e0, e0) = all_52_31
% 226.12/38.91  |   (7)  op(all_52_31, all_52_31) = e0
% 226.12/38.91  | 
% 226.12/38.91  | GROUND_INST: instantiating (1) with e2, all_52_31, e0, e0, simplifying with
% 226.12/38.91  |              (5), (6) gives:
% 226.12/38.91  |   (8)  all_52_31 = e2
% 226.12/38.91  | 
% 226.12/38.91  | REDUCE: (7), (8) imply:
% 226.12/38.91  |   (9)  op(e2, e2) = e0
% 226.12/38.91  | 
% 226.12/38.91  | REF_CLOSE: (1), (2), (4), (9) are inconsistent by sub-proof #2352.
% 226.12/38.91  | 
% 226.12/38.91  End of proof
% 226.12/38.91  
% 226.12/38.91  Sub-proof #51 shows that the following formulas are inconsistent:
% 226.12/38.91  ----------------------------------------------------------------
% 226.12/38.91    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.12/38.91           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.12/38.91    (2)  op(e1, e0) = all_52_23
% 226.12/38.91    (3)   ~ (e2 = e0)
% 226.12/38.91    (4)  op(all_52_23, all_52_23) = e0
% 226.12/38.91    (5)  op(e0, e0) = e2
% 226.12/38.91    (6)  op(e1, e0) = e0
% 226.12/38.91  
% 226.12/38.91  Begin of proof
% 226.12/38.91  | 
% 226.12/38.91  | GROUND_INST: instantiating (1) with e0, all_52_23, e0, e1, simplifying with
% 226.12/38.91  |              (2), (6) gives:
% 226.12/38.91  |   (7)  all_52_23 = e0
% 226.12/38.91  | 
% 226.12/38.91  | REDUCE: (4), (7) imply:
% 226.12/38.91  |   (8)  op(e0, e0) = e0
% 226.12/38.91  | 
% 226.12/38.91  | GROUND_INST: instantiating (1) with e2, e0, e0, e0, simplifying with (5), (8)
% 226.12/38.91  |              gives:
% 226.12/38.91  |   (9)  e2 = e0
% 226.12/38.91  | 
% 226.12/38.91  | REDUCE: (3), (9) imply:
% 226.12/38.91  |   (10)  $false
% 226.12/38.91  | 
% 226.12/38.91  | CLOSE: (10) is inconsistent.
% 226.12/38.91  | 
% 226.12/38.91  End of proof
% 226.12/38.91  
% 226.12/38.91  Sub-proof #52 shows that the following formulas are inconsistent:
% 226.12/38.91  ----------------------------------------------------------------
% 226.12/38.91    (1)  all_55_4 = e3
% 226.12/38.91    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.12/38.91           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.12/38.91    (3)  all_55_4 = all_52_9
% 226.12/38.91    (4)   ~ (all_52_9 = e0)
% 226.12/38.91    (5)  op(e3, e3) = e0
% 226.12/38.91    (6)  op(all_52_9, all_52_9) = e3
% 226.12/38.91  
% 226.12/38.91  Begin of proof
% 226.12/38.91  | 
% 226.12/38.91  | COMBINE_EQS: (1), (3) imply:
% 226.12/38.91  |   (7)  all_52_9 = e3
% 226.12/38.91  | 
% 226.12/38.91  | SIMP: (7) implies:
% 226.12/38.91  |   (8)  all_52_9 = e3
% 226.12/38.91  | 
% 226.12/38.91  | REDUCE: (4), (8) imply:
% 226.12/38.91  |   (9)   ~ (e3 = e0)
% 226.12/38.91  | 
% 226.12/38.91  | REDUCE: (6), (8) imply:
% 226.12/38.91  |   (10)  op(e3, e3) = e3
% 226.12/38.91  | 
% 226.12/38.91  | REF_CLOSE: (2), (5), (9), (10) are inconsistent by sub-proof #2494.
% 226.12/38.91  | 
% 226.12/38.91  End of proof
% 226.12/38.91  
% 226.12/38.91  Sub-proof #53 shows that the following formulas are inconsistent:
% 226.12/38.91  ----------------------------------------------------------------
% 226.12/38.91    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.12/38.91           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.12/38.91    (2)   ~ (e3 = e2)
% 226.12/38.91    (3)  op(e3, e3) = e0
% 226.12/38.91    (4)  op(e3, e3) = all_52_1
% 226.12/38.91    (5)  op(all_52_1, all_52_1) = e3
% 226.12/38.91    (6)  op(e0, e0) = e2
% 226.12/38.91  
% 226.12/38.91  Begin of proof
% 226.12/38.91  | 
% 226.12/38.91  | GROUND_INST: instantiating (1) with e0, all_52_1, e3, e3, simplifying with
% 226.12/38.91  |              (3), (4) gives:
% 226.12/38.91  |   (7)  all_52_1 = e0
% 226.12/38.91  | 
% 226.12/38.91  | REDUCE: (5), (7) imply:
% 226.12/38.91  |   (8)  op(e0, e0) = e3
% 226.12/38.91  | 
% 226.12/38.91  | GROUND_INST: instantiating (1) with e2, e3, e0, e0, simplifying with (6), (8)
% 226.12/38.91  |              gives:
% 226.12/38.91  |   (9)  e3 = e2
% 226.12/38.91  | 
% 226.12/38.91  | REDUCE: (2), (9) imply:
% 226.12/38.91  |   (10)  $false
% 226.12/38.91  | 
% 226.12/38.91  | CLOSE: (10) is inconsistent.
% 226.12/38.91  | 
% 226.12/38.91  End of proof
% 226.12/38.91  
% 226.12/38.91  Sub-proof #54 shows that the following formulas are inconsistent:
% 226.12/38.91  ----------------------------------------------------------------
% 226.12/38.91    (1)  all_57_14 = e2 & op(e0, e1) = e2
% 226.12/38.91    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.12/38.91           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.12/38.91    (3)  op(e0, e1) = all_53_11
% 226.12/38.91    (4)   ~ (all_53_11 = e2)
% 226.12/38.91  
% 226.12/38.91  Begin of proof
% 226.12/38.91  | 
% 226.12/38.91  | ALPHA: (1) implies:
% 226.12/38.91  |   (5)  op(e0, e1) = e2
% 226.12/38.91  | 
% 226.12/38.91  | GROUND_INST: instantiating (2) with all_53_11, e2, e1, e0, simplifying with
% 226.12/38.91  |              (3), (5) gives:
% 226.12/38.91  |   (6)  all_53_11 = e2
% 226.12/38.91  | 
% 226.12/38.91  | REDUCE: (4), (6) imply:
% 226.12/38.91  |   (7)  $false
% 226.12/38.91  | 
% 226.12/38.91  | CLOSE: (7) is inconsistent.
% 226.12/38.91  | 
% 226.12/38.91  End of proof
% 226.12/38.91  
% 226.12/38.91  Sub-proof #55 shows that the following formulas are inconsistent:
% 226.12/38.91  ----------------------------------------------------------------
% 226.12/38.91    (1)  op(e0, e1) = all_53_11
% 226.12/38.91    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.12/38.91           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.12/38.91    (3)   ~ (e3 = e2)
% 226.12/38.91    (4)  all_57_15 = e2
% 226.12/38.91    (5)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 226.12/38.91    (6)   ~ (all_53_11 = e3)
% 226.12/38.91  
% 226.12/38.91  Begin of proof
% 226.12/38.91  | 
% 226.12/38.91  | BETA: splitting (5) gives:
% 226.12/38.91  | 
% 226.12/38.91  | Case 1:
% 226.12/38.91  | | 
% 226.12/38.91  | |   (7)  all_57_14 = e3 & op(e0, e1) = e3
% 226.12/38.91  | | 
% 226.12/38.91  | | REF_CLOSE: (1), (2), (6), (7) are inconsistent by sub-proof #129.
% 226.12/38.91  | | 
% 226.12/38.91  | Case 2:
% 226.12/38.91  | | 
% 226.12/38.91  | |   (8)  all_57_15 = e3 & op(e0, e0) = e3
% 226.12/38.91  | | 
% 226.12/38.91  | | ALPHA: (8) implies:
% 226.12/38.91  | |   (9)  all_57_15 = e3
% 226.12/38.91  | | 
% 226.12/38.91  | | REF_CLOSE: (3), (4), (9) are inconsistent by sub-proof #2058.
% 226.12/38.91  | | 
% 226.12/38.91  | End of split
% 226.12/38.91  | 
% 226.12/38.91  End of proof
% 226.12/38.91  
% 226.12/38.91  Sub-proof #56 shows that the following formulas are inconsistent:
% 226.12/38.91  ----------------------------------------------------------------
% 226.12/38.91    (1)  all_55_3 = all_32_0
% 226.12/38.91    (2)  all_55_3 = e1
% 226.12/38.91    (3)   ~ (all_32_0 = e1)
% 226.12/38.91  
% 226.12/38.91  Begin of proof
% 226.12/38.91  | 
% 226.12/38.91  | COMBINE_EQS: (1), (2) imply:
% 226.12/38.91  |   (4)  all_32_0 = e1
% 226.12/38.91  | 
% 226.12/38.91  | SIMP: (4) implies:
% 226.12/38.91  |   (5)  all_32_0 = e1
% 226.12/38.91  | 
% 226.12/38.91  | REDUCE: (3), (5) imply:
% 226.12/38.91  |   (6)  $false
% 226.12/38.91  | 
% 226.12/38.91  | CLOSE: (6) is inconsistent.
% 226.12/38.91  | 
% 226.12/38.91  End of proof
% 226.12/38.91  
% 226.12/38.91  Sub-proof #57 shows that the following formulas are inconsistent:
% 226.12/38.91  ----------------------------------------------------------------
% 226.12/38.91    (1)  all_55_3 = all_32_0
% 226.12/38.91    (2)  all_55_3 = e2
% 226.12/38.91    (3)   ~ (all_32_0 = e2)
% 226.12/38.91  
% 226.12/38.91  Begin of proof
% 226.12/38.91  | 
% 226.12/38.91  | COMBINE_EQS: (1), (2) imply:
% 226.12/38.91  |   (4)  all_32_0 = e2
% 226.12/38.91  | 
% 226.12/38.91  | SIMP: (4) implies:
% 226.12/38.91  |   (5)  all_32_0 = e2
% 226.12/38.91  | 
% 226.12/38.91  | REDUCE: (3), (5) imply:
% 226.12/38.91  |   (6)  $false
% 226.12/38.91  | 
% 226.12/38.91  | CLOSE: (6) is inconsistent.
% 226.12/38.91  | 
% 226.12/38.91  End of proof
% 226.12/38.91  
% 226.12/38.91  Sub-proof #58 shows that the following formulas are inconsistent:
% 226.12/38.91  ----------------------------------------------------------------
% 226.12/38.91    (1)  op(e0, e2) = all_32_1
% 226.12/38.91    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.12/38.91           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.12/38.91    (3)  op(e0, e2) = all_4_1
% 226.12/38.91    (4)  op(e0, e2) = e3
% 226.12/38.91    (5)   ~ (all_32_1 = e3)
% 226.12/38.91  
% 226.12/38.91  Begin of proof
% 226.12/38.91  | 
% 226.12/38.91  | GROUND_INST: instantiating (2) with all_4_1, all_32_1, e2, e0, simplifying
% 226.12/38.91  |              with (1), (3) gives:
% 226.12/38.91  |   (6)  all_32_1 = all_4_1
% 226.12/38.91  | 
% 226.12/38.91  | GROUND_INST: instantiating (2) with e3, all_32_1, e2, e0, simplifying with
% 226.12/38.91  |              (1), (4) gives:
% 226.12/38.91  |   (7)  all_32_1 = e3
% 226.12/38.91  | 
% 226.12/38.91  | COMBINE_EQS: (6), (7) imply:
% 226.12/38.91  |   (8)  all_4_1 = e3
% 226.12/38.91  | 
% 226.12/38.91  | REDUCE: (5), (7) imply:
% 226.12/38.91  |   (9)  $false
% 226.12/38.91  | 
% 226.12/38.91  | CLOSE: (9) is inconsistent.
% 226.12/38.91  | 
% 226.12/38.91  End of proof
% 226.12/38.91  
% 226.12/38.91  Sub-proof #59 shows that the following formulas are inconsistent:
% 226.12/38.91  ----------------------------------------------------------------
% 226.12/38.91    (1)   ~ (all_53_2 = e2)
% 226.12/38.91    (2)   ~ (all_53_6 = all_53_14)
% 226.12/38.91    (3)   ~ (all_53_6 = e2)
% 226.12/38.91    (4)   ~ (all_53_2 = all_52_9)
% 226.12/38.91    (5)   ~ (all_52_9 = e2)
% 226.12/38.91    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.12/38.91           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.12/38.91    (7)   ~ (all_53_3 = e3)
% 226.12/38.91    (8)  ( ~ (all_28_0 = e0) & op(all_28_1, e3) = all_28_0 & op(e3, e2) = all_28_1
% 226.12/38.91           & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 = e1) & op(e3, e2) =
% 226.12/38.91           all_28_1 & $i(all_28_1))
% 226.12/38.91    (9)  op(e3, e2) = e1
% 226.12/38.91    (10)  all_55_4 = all_52_9
% 226.12/38.92    (11)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 226.12/38.92    (12)  all_55_9 = all_53_6
% 226.12/38.92    (13)  all_55_7 = all_52_15
% 226.12/38.92    (14)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 226.12/38.92          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 226.12/38.92    (15)  all_57_4 = e3
% 226.12/38.92    (16)  all_55_7 = e3 | all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 226.12/38.92    (17)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 226.12/38.92    (18)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 226.12/38.92    (19)  all_57_1 = e1
% 226.12/38.92    (20)  all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 226.12/38.92    (21)  op(e3, e3) = e2
% 226.12/38.92    (22)   ~ (all_53_3 = e2)
% 226.12/38.92    (23)  all_57_9 = e0
% 226.12/38.92    (24)   ~ (all_53_6 = e1)
% 226.12/38.92    (25)  all_55_12 = all_53_3
% 226.12/38.92    (26)   ~ (all_53_2 = all_53_14)
% 226.12/38.92    (27)   ~ (all_53_2 = all_53_3)
% 226.12/38.92    (28)  all_55_8 = all_53_2
% 226.12/38.92    (29)  ( ~ (all_20_0 = e1) & op(all_20_1, e3) = all_20_0 & op(e3, e2) =
% 226.12/38.92            all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e0) & op(e3,
% 226.12/38.92              e2) = all_20_1 & $i(all_20_1))
% 226.12/38.92    (30)  op(all_52_9, all_52_9) = e3
% 226.12/38.92    (31)   ~ (all_53_14 = all_52_15)
% 226.12/38.92    (32)  all_55_11 = all_53_14
% 226.12/38.92    (33)  op(e1, e3) = all_53_2
% 226.12/38.92    (34)  op(all_52_15, all_52_15) = e0
% 226.12/38.92    (35)   ~ (all_53_14 = e2)
% 226.12/38.92    (36)   ~ (all_53_2 = all_53_6)
% 226.12/38.92    (37)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 226.12/38.92    (38)   ~ (all_52_15 = e0)
% 226.12/38.92    (39)   ~ (all_52_15 = e2)
% 226.12/38.92    (40)   ~ (all_53_3 = all_52_9)
% 226.12/38.92  
% 226.12/38.92  Begin of proof
% 226.12/38.92  | 
% 226.12/38.92  | BETA: splitting (20) gives:
% 226.12/38.92  | 
% 226.12/38.92  | Case 1:
% 226.12/38.92  | | 
% 226.12/38.92  | |   (41)  all_55_9 = e2
% 226.12/38.92  | | 
% 226.12/38.92  | | COMBINE_EQS: (12), (41) imply:
% 226.12/38.92  | |   (42)  all_53_6 = e2
% 226.12/38.92  | | 
% 226.12/38.92  | | REDUCE: (3), (42) imply:
% 226.12/38.92  | |   (43)  $false
% 226.12/38.92  | | 
% 226.12/38.92  | | CLOSE: (43) is inconsistent.
% 226.12/38.92  | | 
% 226.12/38.92  | Case 2:
% 226.12/38.92  | | 
% 226.12/38.92  | |   (44)   ~ (all_55_9 = e2)
% 226.12/38.92  | |   (45)  all_55_9 = e1 | all_55_9 = e0
% 226.12/38.92  | | 
% 226.12/38.92  | | BETA: splitting (45) gives:
% 226.12/38.92  | | 
% 226.12/38.92  | | Case 1:
% 226.12/38.92  | | | 
% 226.12/38.92  | | |   (46)  all_55_9 = e1
% 226.12/38.92  | | | 
% 226.12/38.92  | | | REF_CLOSE: (12), (24), (46) are inconsistent by sub-proof #2273.
% 226.12/38.92  | | | 
% 226.12/38.92  | | Case 2:
% 226.12/38.92  | | | 
% 226.12/38.92  | | |   (47)  all_55_9 = e0
% 226.12/38.92  | | | 
% 226.12/38.92  | | | COMBINE_EQS: (12), (47) imply:
% 226.12/38.92  | | |   (48)  all_53_6 = e0
% 226.12/38.92  | | | 
% 226.12/38.92  | | | SIMP: (48) implies:
% 226.12/38.92  | | |   (49)  all_53_6 = e0
% 226.12/38.92  | | | 
% 226.12/38.92  | | | REDUCE: (36), (49) imply:
% 226.12/38.92  | | |   (50)   ~ (all_53_2 = e0)
% 226.12/38.92  | | | 
% 226.12/38.92  | | | REDUCE: (2), (49) imply:
% 226.12/38.92  | | |   (51)   ~ (all_53_14 = e0)
% 226.12/38.92  | | | 
% 226.12/38.92  | | | SIMP: (51) implies:
% 226.12/38.92  | | |   (52)   ~ (all_53_14 = e0)
% 226.12/38.92  | | | 
% 226.12/38.92  | | | REDUCE: (3), (49) imply:
% 226.12/38.92  | | |   (53)   ~ (e2 = e0)
% 226.12/38.92  | | | 
% 226.12/38.92  | | | SIMP: (53) implies:
% 226.12/38.92  | | |   (54)   ~ (e2 = e0)
% 226.12/38.92  | | | 
% 226.12/38.92  | | | BETA: splitting (29) gives:
% 226.12/38.92  | | | 
% 226.12/38.92  | | | Case 1:
% 226.12/38.92  | | | | 
% 226.12/38.92  | | | |   (55)   ~ (all_20_0 = e1) & op(all_20_1, e3) = all_20_0 & op(e3, e2) =
% 226.12/38.92  | | | |         all_20_1 & $i(all_20_0) & $i(all_20_1)
% 226.12/38.92  | | | | 
% 226.12/38.92  | | | | ALPHA: (55) implies:
% 226.12/38.92  | | | |   (56)   ~ (all_20_0 = e1)
% 226.12/38.92  | | | |   (57)  op(e3, e2) = all_20_1
% 226.12/38.92  | | | |   (58)  op(all_20_1, e3) = all_20_0
% 226.12/38.92  | | | | 
% 226.12/38.92  | | | | BETA: splitting (8) gives:
% 226.12/38.92  | | | | 
% 226.12/38.92  | | | | Case 1:
% 226.12/38.92  | | | | | 
% 226.12/38.92  | | | | |   (59)   ~ (all_28_0 = e0) & op(all_28_1, e3) = all_28_0 & op(e3, e2)
% 226.12/38.92  | | | | |         = all_28_1 & $i(all_28_0) & $i(all_28_1)
% 226.12/38.92  | | | | | 
% 226.12/38.92  | | | | | ALPHA: (59) implies:
% 226.12/38.92  | | | | |   (60)   ~ (all_28_0 = e0)
% 226.12/38.92  | | | | |   (61)  op(e3, e2) = all_28_1
% 226.12/38.92  | | | | |   (62)  op(all_28_1, e3) = all_28_0
% 226.12/38.92  | | | | | 
% 226.12/38.92  | | | | | GROUND_INST: instantiating (6) with all_20_1, all_28_1, e2, e3,
% 226.12/38.92  | | | | |              simplifying with (57), (61) gives:
% 226.12/38.92  | | | | |   (63)  all_28_1 = all_20_1
% 226.12/38.92  | | | | | 
% 226.12/38.92  | | | | | GROUND_INST: instantiating (6) with e1, all_28_1, e2, e3, simplifying
% 226.12/38.92  | | | | |              with (9), (61) gives:
% 226.12/38.92  | | | | |   (64)  all_28_1 = e1
% 226.12/38.92  | | | | | 
% 226.12/38.92  | | | | | COMBINE_EQS: (63), (64) imply:
% 226.12/38.92  | | | | |   (65)  all_20_1 = e1
% 226.12/38.92  | | | | | 
% 226.12/38.92  | | | | | REDUCE: (62), (64) imply:
% 226.12/38.92  | | | | |   (66)  op(e1, e3) = all_28_0
% 226.12/38.92  | | | | | 
% 226.12/38.92  | | | | | REDUCE: (58), (65) imply:
% 226.12/38.92  | | | | |   (67)  op(e1, e3) = all_20_0
% 226.12/38.92  | | | | | 
% 226.12/38.92  | | | | | GROUND_INST: instantiating (6) with all_53_2, all_20_0, e3, e1,
% 226.12/38.92  | | | | |              simplifying with (33), (67) gives:
% 226.12/38.92  | | | | |   (68)  all_53_2 = all_20_0
% 226.12/38.92  | | | | | 
% 226.12/38.92  | | | | | GROUND_INST: instantiating (6) with all_53_2, all_28_0, e3, e1,
% 226.12/38.92  | | | | |              simplifying with (33), (66) gives:
% 226.12/38.92  | | | | |   (69)  all_53_2 = all_28_0
% 226.12/38.92  | | | | | 
% 226.12/38.92  | | | | | COMBINE_EQS: (68), (69) imply:
% 226.12/38.92  | | | | |   (70)  all_28_0 = all_20_0
% 226.12/38.92  | | | | | 
% 226.12/38.92  | | | | | COMBINE_EQS: (28), (68) imply:
% 226.12/38.92  | | | | |   (71)  all_55_8 = all_20_0
% 226.12/38.92  | | | | | 
% 226.12/38.92  | | | | | REDUCE: (26), (68) imply:
% 226.12/38.92  | | | | |   (72)   ~ (all_53_14 = all_20_0)
% 226.12/38.92  | | | | | 
% 226.12/38.92  | | | | | SIMP: (72) implies:
% 226.12/38.92  | | | | |   (73)   ~ (all_53_14 = all_20_0)
% 226.12/38.92  | | | | | 
% 226.12/38.92  | | | | | REDUCE: (1), (68) imply:
% 226.12/38.92  | | | | |   (74)   ~ (all_20_0 = e2)
% 226.12/38.92  | | | | | 
% 226.12/38.92  | | | | | REDUCE: (60), (70) imply:
% 226.12/38.92  | | | | |   (75)   ~ (all_20_0 = e0)
% 226.12/38.92  | | | | | 
% 226.12/38.92  | | | | | BETA: splitting (17) gives:
% 226.12/38.92  | | | | | 
% 226.12/38.92  | | | | | Case 1:
% 226.12/38.92  | | | | | | 
% 226.12/38.92  | | | | | |   (76)  all_55_8 = e3
% 226.12/38.92  | | | | | | 
% 226.12/38.92  | | | | | | COMBINE_EQS: (71), (76) imply:
% 226.12/38.92  | | | | | |   (77)  all_20_0 = e3
% 226.12/38.92  | | | | | | 
% 226.12/38.92  | | | | | | SIMP: (77) implies:
% 226.12/38.92  | | | | | |   (78)  all_20_0 = e3
% 226.12/38.92  | | | | | | 
% 226.12/38.92  | | | | | | REDUCE: (73), (78) imply:
% 226.12/38.92  | | | | | |   (79)   ~ (all_53_14 = e3)
% 226.12/38.92  | | | | | | 
% 226.12/38.92  | | | | | | REF_CLOSE: (6), (11), (13), (16), (21), (31), (32), (34), (35),
% 226.12/38.92  | | | | | |            (38), (39), (52), (54), (79) are inconsistent by
% 226.12/38.92  | | | | | |            sub-proof #61.
% 226.12/38.92  | | | | | | 
% 226.12/38.92  | | | | | Case 2:
% 226.12/38.92  | | | | | | 
% 226.12/38.92  | | | | | |   (80)  all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 226.12/38.92  | | | | | | 
% 226.12/38.92  | | | | | | BETA: splitting (80) gives:
% 226.12/38.92  | | | | | | 
% 226.12/38.92  | | | | | | Case 1:
% 226.12/38.92  | | | | | | | 
% 226.12/38.92  | | | | | | |   (81)  all_55_8 = e2
% 226.12/38.92  | | | | | | | 
% 226.12/38.92  | | | | | | | COMBINE_EQS: (71), (81) imply:
% 226.12/38.92  | | | | | | |   (82)  all_20_0 = e2
% 226.12/38.92  | | | | | | | 
% 226.12/38.92  | | | | | | | SIMP: (82) implies:
% 226.12/38.92  | | | | | | |   (83)  all_20_0 = e2
% 226.12/38.92  | | | | | | | 
% 226.12/38.92  | | | | | | | REDUCE: (74), (83) imply:
% 226.12/38.92  | | | | | | |   (84)  $false
% 226.12/38.92  | | | | | | | 
% 226.12/38.92  | | | | | | | CLOSE: (84) is inconsistent.
% 226.12/38.92  | | | | | | | 
% 226.12/38.92  | | | | | | Case 2:
% 226.12/38.92  | | | | | | | 
% 226.12/38.92  | | | | | | |   (85)  all_55_8 = e1 | all_55_8 = e0
% 226.12/38.92  | | | | | | | 
% 226.12/38.92  | | | | | | | BETA: splitting (85) gives:
% 226.12/38.92  | | | | | | | 
% 226.12/38.92  | | | | | | | Case 1:
% 226.12/38.92  | | | | | | | | 
% 226.12/38.92  | | | | | | | |   (86)  all_55_8 = e1
% 226.12/38.92  | | | | | | | | 
% 226.12/38.92  | | | | | | | | COMBINE_EQS: (71), (86) imply:
% 226.12/38.92  | | | | | | | |   (87)  all_20_0 = e1
% 226.12/38.92  | | | | | | | | 
% 226.12/38.92  | | | | | | | | SIMP: (87) implies:
% 226.12/38.92  | | | | | | | |   (88)  all_20_0 = e1
% 226.12/38.92  | | | | | | | | 
% 226.12/38.92  | | | | | | | | REDUCE: (56), (88) imply:
% 226.12/38.92  | | | | | | | |   (89)  $false
% 226.12/38.92  | | | | | | | | 
% 226.12/38.92  | | | | | | | | CLOSE: (89) is inconsistent.
% 226.12/38.92  | | | | | | | | 
% 226.12/38.92  | | | | | | | Case 2:
% 226.12/38.92  | | | | | | | | 
% 226.12/38.92  | | | | | | | |   (90)  all_55_8 = e0
% 226.12/38.92  | | | | | | | | 
% 226.12/38.92  | | | | | | | | COMBINE_EQS: (71), (90) imply:
% 226.12/38.92  | | | | | | | |   (91)  all_20_0 = e0
% 226.12/38.92  | | | | | | | | 
% 226.12/38.92  | | | | | | | | SIMP: (91) implies:
% 226.12/38.92  | | | | | | | |   (92)  all_20_0 = e0
% 226.12/38.92  | | | | | | | | 
% 226.12/38.92  | | | | | | | | REDUCE: (75), (92) imply:
% 226.12/38.92  | | | | | | | |   (93)  $false
% 226.12/38.92  | | | | | | | | 
% 226.12/38.92  | | | | | | | | CLOSE: (93) is inconsistent.
% 226.12/38.92  | | | | | | | | 
% 226.12/38.92  | | | | | | | End of split
% 226.12/38.92  | | | | | | | 
% 226.12/38.92  | | | | | | End of split
% 226.12/38.92  | | | | | | 
% 226.12/38.92  | | | | | End of split
% 226.12/38.92  | | | | | 
% 226.12/38.92  | | | | Case 2:
% 226.12/38.92  | | | | | 
% 226.12/38.92  | | | | |   (94)   ~ (all_28_1 = e1) & op(e3, e2) = all_28_1 & $i(all_28_1)
% 226.12/38.92  | | | | | 
% 226.12/38.92  | | | | | REF_CLOSE: (6), (9), (94) are inconsistent by sub-proof #1249.
% 226.12/38.92  | | | | | 
% 226.12/38.92  | | | | End of split
% 226.12/38.92  | | | | 
% 226.12/38.92  | | | Case 2:
% 226.12/38.92  | | | | 
% 226.12/38.92  | | | |   (95)   ~ (all_20_1 = e0) & op(e3, e2) = all_20_1 & $i(all_20_1)
% 226.12/38.92  | | | | 
% 226.12/38.92  | | | | ALPHA: (95) implies:
% 226.12/38.92  | | | |   (96)  op(e3, e2) = all_20_1
% 226.12/38.92  | | | | 
% 226.12/38.92  | | | | BETA: splitting (8) gives:
% 226.12/38.92  | | | | 
% 226.12/38.92  | | | | Case 1:
% 226.12/38.92  | | | | | 
% 226.12/38.92  | | | | |   (97)   ~ (all_28_0 = e0) & op(all_28_1, e3) = all_28_0 & op(e3, e2)
% 226.12/38.92  | | | | |         = all_28_1 & $i(all_28_0) & $i(all_28_1)
% 226.12/38.92  | | | | | 
% 226.12/38.92  | | | | | ALPHA: (97) implies:
% 226.12/38.92  | | | | |   (98)  op(e3, e2) = all_28_1
% 226.12/38.92  | | | | |   (99)  op(all_28_1, e3) = all_28_0
% 226.12/38.92  | | | | | 
% 226.12/38.92  | | | | | GROUND_INST: instantiating (6) with all_20_1, all_28_1, e2, e3,
% 226.12/38.92  | | | | |              simplifying with (96), (98) gives:
% 226.12/38.92  | | | | |   (100)  all_28_1 = all_20_1
% 226.12/38.92  | | | | | 
% 226.12/38.92  | | | | | GROUND_INST: instantiating (6) with e1, all_28_1, e2, e3, simplifying
% 226.12/38.92  | | | | |              with (9), (98) gives:
% 226.12/38.92  | | | | |   (101)  all_28_1 = e1
% 226.12/38.92  | | | | | 
% 226.12/38.92  | | | | | COMBINE_EQS: (100), (101) imply:
% 226.12/38.92  | | | | |   (102)  all_20_1 = e1
% 226.12/38.92  | | | | | 
% 226.12/38.92  | | | | | REDUCE: (99), (101) imply:
% 226.12/38.92  | | | | |   (103)  op(e1, e3) = all_28_0
% 226.12/38.92  | | | | | 
% 226.12/38.92  | | | | | GROUND_INST: instantiating (6) with all_53_2, all_28_0, e3, e1,
% 226.12/38.92  | | | | |              simplifying with (33), (103) gives:
% 226.12/38.92  | | | | |   (104)  all_53_2 = all_28_0
% 226.12/38.92  | | | | | 
% 226.12/38.92  | | | | | COMBINE_EQS: (28), (104) imply:
% 226.12/38.92  | | | | |   (105)  all_55_8 = all_28_0
% 226.12/38.92  | | | | | 
% 226.12/38.92  | | | | | REDUCE: (27), (104) imply:
% 226.12/38.92  | | | | |   (106)   ~ (all_53_3 = all_28_0)
% 226.12/38.92  | | | | | 
% 226.12/38.92  | | | | | SIMP: (106) implies:
% 226.12/38.92  | | | | |   (107)   ~ (all_53_3 = all_28_0)
% 226.12/38.92  | | | | | 
% 226.12/38.92  | | | | | REDUCE: (26), (104) imply:
% 226.12/38.92  | | | | |   (108)   ~ (all_53_14 = all_28_0)
% 226.12/38.92  | | | | | 
% 226.12/38.92  | | | | | SIMP: (108) implies:
% 226.12/38.92  | | | | |   (109)   ~ (all_53_14 = all_28_0)
% 226.12/38.92  | | | | | 
% 226.12/38.92  | | | | | REDUCE: (4), (104) imply:
% 226.12/38.92  | | | | |   (110)   ~ (all_52_9 = all_28_0)
% 226.12/38.92  | | | | | 
% 226.12/38.92  | | | | | SIMP: (110) implies:
% 226.12/38.92  | | | | |   (111)   ~ (all_52_9 = all_28_0)
% 226.12/38.92  | | | | | 
% 226.12/38.92  | | | | | REDUCE: (1), (104) imply:
% 226.12/38.92  | | | | |   (112)   ~ (all_28_0 = e2)
% 226.12/38.92  | | | | | 
% 226.12/38.92  | | | | | REDUCE: (50), (104) imply:
% 226.12/38.92  | | | | |   (113)   ~ (all_28_0 = e0)
% 226.12/38.92  | | | | | 
% 226.12/38.92  | | | | | BETA: splitting (17) gives:
% 226.12/38.92  | | | | | 
% 226.12/38.92  | | | | | Case 1:
% 226.12/38.92  | | | | | | 
% 226.12/38.92  | | | | | |   (114)  all_55_8 = e3
% 226.12/38.92  | | | | | | 
% 226.12/38.92  | | | | | | COMBINE_EQS: (105), (114) imply:
% 226.12/38.92  | | | | | |   (115)  all_28_0 = e3
% 226.12/38.92  | | | | | | 
% 226.12/38.92  | | | | | | SIMP: (115) implies:
% 226.12/38.92  | | | | | |   (116)  all_28_0 = e3
% 226.12/38.92  | | | | | | 
% 226.12/38.92  | | | | | | REDUCE: (109), (116) imply:
% 226.12/38.92  | | | | | |   (117)   ~ (all_53_14 = e3)
% 226.12/38.92  | | | | | | 
% 226.12/38.92  | | | | | | REF_CLOSE: (6), (11), (13), (16), (21), (31), (32), (34), (35),
% 226.12/38.92  | | | | | |            (38), (39), (52), (54), (117) are inconsistent by
% 226.12/38.92  | | | | | |            sub-proof #61.
% 226.12/38.92  | | | | | | 
% 226.12/38.92  | | | | | Case 2:
% 226.12/38.92  | | | | | | 
% 226.12/38.92  | | | | | |   (118)  all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 226.12/38.92  | | | | | | 
% 226.12/38.92  | | | | | | BETA: splitting (118) gives:
% 226.12/38.92  | | | | | | 
% 226.12/38.92  | | | | | | Case 1:
% 226.12/38.92  | | | | | | | 
% 226.12/38.92  | | | | | | |   (119)  all_55_8 = e2
% 226.12/38.92  | | | | | | | 
% 226.12/38.92  | | | | | | | COMBINE_EQS: (105), (119) imply:
% 226.12/38.92  | | | | | | |   (120)  all_28_0 = e2
% 226.12/38.92  | | | | | | | 
% 226.12/38.92  | | | | | | | SIMP: (120) implies:
% 226.12/38.92  | | | | | | |   (121)  all_28_0 = e2
% 226.12/38.92  | | | | | | | 
% 226.12/38.92  | | | | | | | REDUCE: (112), (121) imply:
% 226.12/38.92  | | | | | | |   (122)  $false
% 226.12/38.92  | | | | | | | 
% 226.12/38.92  | | | | | | | CLOSE: (122) is inconsistent.
% 226.12/38.92  | | | | | | | 
% 226.12/38.92  | | | | | | Case 2:
% 226.12/38.92  | | | | | | | 
% 226.12/38.92  | | | | | | |   (123)   ~ (all_55_8 = e2)
% 226.12/38.92  | | | | | | |   (124)  all_55_8 = e1 | all_55_8 = e0
% 226.12/38.92  | | | | | | | 
% 226.12/38.92  | | | | | | | BETA: splitting (124) gives:
% 226.12/38.92  | | | | | | | 
% 226.12/38.92  | | | | | | | Case 1:
% 226.12/38.92  | | | | | | | | 
% 226.12/38.92  | | | | | | | |   (125)  all_55_8 = e1
% 226.12/38.92  | | | | | | | | 
% 226.12/38.92  | | | | | | | | COMBINE_EQS: (105), (125) imply:
% 226.12/38.92  | | | | | | | |   (126)  all_28_0 = e1
% 226.12/38.92  | | | | | | | | 
% 226.12/38.92  | | | | | | | | REDUCE: (107), (126) imply:
% 226.12/38.92  | | | | | | | |   (127)   ~ (all_53_3 = e1)
% 226.12/38.92  | | | | | | | | 
% 226.12/38.92  | | | | | | | | REDUCE: (111), (126) imply:
% 226.12/38.92  | | | | | | | |   (128)   ~ (all_52_9 = e1)
% 226.12/38.92  | | | | | | | | 
% 226.12/38.92  | | | | | | | | REDUCE: (112), (126) imply:
% 226.12/38.92  | | | | | | | |   (129)   ~ (e2 = e1)
% 226.12/38.92  | | | | | | | | 
% 226.12/38.92  | | | | | | | | SIMP: (129) implies:
% 226.12/38.92  | | | | | | | |   (130)   ~ (e2 = e1)
% 226.12/38.92  | | | | | | | | 
% 226.12/38.92  | | | | | | | | BETA: splitting (37) gives:
% 226.12/38.92  | | | | | | | | 
% 226.12/38.92  | | | | | | | | Case 1:
% 226.12/38.92  | | | | | | | | | 
% 226.12/38.92  | | | | | | | | |   (131)  all_55_12 = e3
% 226.12/38.92  | | | | | | | | | 
% 226.12/38.92  | | | | | | | | | REF_CLOSE: (7), (25), (131) are inconsistent by sub-proof
% 226.12/38.92  | | | | | | | | |            #2001.
% 226.12/38.92  | | | | | | | | | 
% 226.12/38.92  | | | | | | | | Case 2:
% 226.12/38.92  | | | | | | | | | 
% 226.12/38.92  | | | | | | | | |   (132)  all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 226.12/38.92  | | | | | | | | | 
% 226.12/38.92  | | | | | | | | | BETA: splitting (132) gives:
% 226.12/38.92  | | | | | | | | | 
% 226.12/38.92  | | | | | | | | | Case 1:
% 226.12/38.92  | | | | | | | | | | 
% 226.12/38.92  | | | | | | | | | |   (133)  all_55_12 = e2
% 226.12/38.92  | | | | | | | | | | 
% 226.12/38.92  | | | | | | | | | | REF_CLOSE: (22), (25), (133) are inconsistent by sub-proof
% 226.12/38.92  | | | | | | | | | |            #1337.
% 226.12/38.92  | | | | | | | | | | 
% 226.12/38.92  | | | | | | | | | Case 2:
% 226.12/38.92  | | | | | | | | | | 
% 226.12/38.92  | | | | | | | | | |   (134)   ~ (all_55_12 = e2)
% 226.12/38.92  | | | | | | | | | |   (135)  all_55_12 = e1 | all_55_12 = e0
% 226.12/38.92  | | | | | | | | | | 
% 226.12/38.92  | | | | | | | | | | BETA: splitting (135) gives:
% 226.12/38.92  | | | | | | | | | | 
% 226.12/38.92  | | | | | | | | | | Case 1:
% 226.12/38.92  | | | | | | | | | | | 
% 226.12/38.92  | | | | | | | | | | |   (136)  all_55_12 = e1
% 226.12/38.92  | | | | | | | | | | | 
% 226.12/38.92  | | | | | | | | | | | REF_CLOSE: (25), (127), (136) are inconsistent by sub-proof
% 226.12/38.92  | | | | | | | | | | |            #1994.
% 226.12/38.92  | | | | | | | | | | | 
% 226.12/38.92  | | | | | | | | | | Case 2:
% 226.12/38.92  | | | | | | | | | | | 
% 226.12/38.92  | | | | | | | | | | |   (137)  all_55_12 = e0
% 226.12/38.92  | | | | | | | | | | | 
% 226.12/38.92  | | | | | | | | | | | COMBINE_EQS: (25), (137) imply:
% 226.12/38.92  | | | | | | | | | | |   (138)  all_53_3 = e0
% 226.12/38.92  | | | | | | | | | | | 
% 226.12/38.92  | | | | | | | | | | | SIMP: (138) implies:
% 226.12/38.92  | | | | | | | | | | |   (139)  all_53_3 = e0
% 226.12/38.92  | | | | | | | | | | | 
% 226.12/38.92  | | | | | | | | | | | REDUCE: (40), (139) imply:
% 226.12/38.92  | | | | | | | | | | |   (140)   ~ (all_52_9 = e0)
% 226.12/38.92  | | | | | | | | | | | 
% 226.12/38.92  | | | | | | | | | | | SIMP: (140) implies:
% 226.12/38.92  | | | | | | | | | | |   (141)   ~ (all_52_9 = e0)
% 226.12/38.92  | | | | | | | | | | | 
% 226.12/38.92  | | | | | | | | | | | BETA: splitting (18) gives:
% 226.12/38.92  | | | | | | | | | | | 
% 226.12/38.92  | | | | | | | | | | | Case 1:
% 226.12/38.92  | | | | | | | | | | | | 
% 226.12/38.92  | | | | | | | | | | | |   (142)  all_55_4 = e3
% 226.12/38.92  | | | | | | | | | | | | 
% 226.12/38.92  | | | | | | | | | | | | COMBINE_EQS: (10), (142) imply:
% 226.12/38.92  | | | | | | | | | | | |   (143)  all_52_9 = e3
% 226.12/38.92  | | | | | | | | | | | | 
% 226.12/38.92  | | | | | | | | | | | | SIMP: (143) implies:
% 226.12/38.92  | | | | | | | | | | | |   (144)  all_52_9 = e3
% 226.12/38.92  | | | | | | | | | | | | 
% 226.12/38.92  | | | | | | | | | | | | REDUCE: (5), (144) imply:
% 226.12/38.92  | | | | | | | | | | | |   (145)   ~ (e3 = e2)
% 226.12/38.92  | | | | | | | | | | | | 
% 226.12/38.92  | | | | | | | | | | | | REDUCE: (30), (144) imply:
% 226.12/38.92  | | | | | | | | | | | |   (146)  op(e3, e3) = e3
% 226.12/38.92  | | | | | | | | | | | | 
% 226.12/38.92  | | | | | | | | | | | | REF_CLOSE: (6), (14), (15), (19), (23), (54), (130), (145),
% 226.12/38.92  | | | | | | | | | | | |            (146) are inconsistent by sub-proof #2485.
% 226.12/38.92  | | | | | | | | | | | | 
% 226.12/38.92  | | | | | | | | | | | Case 2:
% 226.12/38.92  | | | | | | | | | | | | 
% 226.12/38.92  | | | | | | | | | | | |   (147)  all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 226.12/38.92  | | | | | | | | | | | | 
% 226.12/38.92  | | | | | | | | | | | | BETA: splitting (147) gives:
% 226.12/38.92  | | | | | | | | | | | | 
% 226.12/38.92  | | | | | | | | | | | | Case 1:
% 226.12/38.92  | | | | | | | | | | | | | 
% 226.12/38.92  | | | | | | | | | | | | |   (148)  all_55_4 = e2
% 226.12/38.92  | | | | | | | | | | | | | 
% 226.12/38.92  | | | | | | | | | | | | | REF_CLOSE: (5), (10), (148) are inconsistent by sub-proof
% 226.12/38.92  | | | | | | | | | | | | |            #345.
% 226.12/38.92  | | | | | | | | | | | | | 
% 226.12/38.92  | | | | | | | | | | | | Case 2:
% 226.12/38.92  | | | | | | | | | | | | | 
% 226.12/38.92  | | | | | | | | | | | | |   (149)  all_55_4 = e1 | all_55_4 = e0
% 226.12/38.92  | | | | | | | | | | | | | 
% 226.12/38.92  | | | | | | | | | | | | | BETA: splitting (149) gives:
% 226.12/38.92  | | | | | | | | | | | | | 
% 226.12/38.92  | | | | | | | | | | | | | Case 1:
% 226.12/38.92  | | | | | | | | | | | | | | 
% 226.12/38.92  | | | | | | | | | | | | | |   (150)  all_55_4 = e1
% 226.12/38.92  | | | | | | | | | | | | | | 
% 226.12/38.92  | | | | | | | | | | | | | | REF_CLOSE: (10), (128), (150) are inconsistent by sub-proof
% 226.12/38.92  | | | | | | | | | | | | | |            #344.
% 226.12/38.92  | | | | | | | | | | | | | | 
% 226.12/38.92  | | | | | | | | | | | | | Case 2:
% 226.12/38.92  | | | | | | | | | | | | | | 
% 226.12/38.92  | | | | | | | | | | | | | |   (151)  all_55_4 = e0
% 226.12/38.92  | | | | | | | | | | | | | | 
% 226.12/38.92  | | | | | | | | | | | | | | REF_CLOSE: (10), (141), (151) are inconsistent by sub-proof
% 226.12/38.92  | | | | | | | | | | | | | |            #60.
% 226.12/38.92  | | | | | | | | | | | | | | 
% 226.12/38.92  | | | | | | | | | | | | | End of split
% 226.12/38.92  | | | | | | | | | | | | | 
% 226.12/38.92  | | | | | | | | | | | | End of split
% 226.12/38.92  | | | | | | | | | | | | 
% 226.12/38.92  | | | | | | | | | | | End of split
% 226.12/38.92  | | | | | | | | | | | 
% 226.12/38.92  | | | | | | | | | | End of split
% 226.12/38.92  | | | | | | | | | | 
% 226.12/38.92  | | | | | | | | | End of split
% 226.12/38.92  | | | | | | | | | 
% 226.12/38.92  | | | | | | | | End of split
% 226.12/38.92  | | | | | | | | 
% 226.12/38.92  | | | | | | | Case 2:
% 226.12/38.92  | | | | | | | | 
% 226.12/38.92  | | | | | | | |   (152)  all_55_8 = e0
% 226.12/38.92  | | | | | | | | 
% 226.12/38.92  | | | | | | | | COMBINE_EQS: (105), (152) imply:
% 226.12/38.92  | | | | | | | |   (153)  all_28_0 = e0
% 226.12/38.92  | | | | | | | | 
% 226.12/38.92  | | | | | | | | REDUCE: (113), (153) imply:
% 226.12/38.92  | | | | | | | |   (154)  $false
% 226.12/38.92  | | | | | | | | 
% 226.12/38.92  | | | | | | | | CLOSE: (154) is inconsistent.
% 226.12/38.92  | | | | | | | | 
% 226.12/38.92  | | | | | | | End of split
% 226.12/38.92  | | | | | | | 
% 226.12/38.92  | | | | | | End of split
% 226.12/38.92  | | | | | | 
% 226.12/38.92  | | | | | End of split
% 226.12/38.92  | | | | | 
% 226.12/38.92  | | | | Case 2:
% 226.12/38.92  | | | | | 
% 226.12/38.92  | | | | |   (155)   ~ (all_28_1 = e1) & op(e3, e2) = all_28_1 & $i(all_28_1)
% 226.12/38.92  | | | | | 
% 226.12/38.92  | | | | | REF_CLOSE: (6), (9), (155) are inconsistent by sub-proof #1249.
% 226.12/38.92  | | | | | 
% 226.12/38.92  | | | | End of split
% 226.12/38.92  | | | | 
% 226.12/38.92  | | | End of split
% 226.12/38.92  | | | 
% 226.12/38.92  | | End of split
% 226.12/38.92  | | 
% 226.12/38.92  | End of split
% 226.12/38.92  | 
% 226.12/38.92  End of proof
% 226.12/38.92  
% 226.12/38.92  Sub-proof #60 shows that the following formulas are inconsistent:
% 226.12/38.92  ----------------------------------------------------------------
% 226.12/38.92    (1)  all_55_4 = all_52_9
% 226.12/38.92    (2)  all_55_4 = e0
% 226.12/38.92    (3)   ~ (all_52_9 = e0)
% 226.12/38.92  
% 226.12/38.92  Begin of proof
% 226.12/38.92  | 
% 226.12/38.92  | COMBINE_EQS: (1), (2) imply:
% 226.12/38.92  |   (4)  all_52_9 = e0
% 226.12/38.92  | 
% 226.12/38.92  | SIMP: (4) implies:
% 226.12/38.92  |   (5)  all_52_9 = e0
% 226.12/38.92  | 
% 226.12/38.92  | REDUCE: (3), (5) imply:
% 226.12/38.92  |   (6)  $false
% 226.12/38.92  | 
% 226.12/38.92  | CLOSE: (6) is inconsistent.
% 226.12/38.92  | 
% 226.12/38.92  End of proof
% 226.12/38.92  
% 226.12/38.92  Sub-proof #61 shows that the following formulas are inconsistent:
% 226.12/38.92  ----------------------------------------------------------------
% 226.12/38.92    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.12/38.92           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.12/38.92    (2)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 226.12/38.92    (3)  all_55_7 = all_52_15
% 226.12/38.92    (4)  all_55_7 = e3 | all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 226.12/38.92    (5)  op(e3, e3) = e2
% 226.12/38.92    (6)   ~ (all_53_14 = e3)
% 226.12/38.92    (7)   ~ (e2 = e0)
% 226.12/38.92    (8)   ~ (all_53_14 = e0)
% 226.12/38.92    (9)   ~ (all_53_14 = all_52_15)
% 226.12/38.92    (10)  all_55_11 = all_53_14
% 226.12/38.92    (11)  op(all_52_15, all_52_15) = e0
% 226.12/38.92    (12)   ~ (all_53_14 = e2)
% 226.12/38.92    (13)   ~ (all_52_15 = e0)
% 226.12/38.92    (14)   ~ (all_52_15 = e2)
% 226.12/38.92  
% 226.12/38.92  Begin of proof
% 226.12/38.92  | 
% 226.12/38.92  | BETA: splitting (2) gives:
% 226.12/38.92  | 
% 226.12/38.92  | Case 1:
% 226.12/38.92  | | 
% 226.12/38.92  | |   (15)  all_55_11 = e3
% 226.12/38.92  | | 
% 226.12/38.92  | | REF_CLOSE: (6), (10), (15) are inconsistent by sub-proof #2497.
% 226.12/38.92  | | 
% 226.12/38.92  | Case 2:
% 226.12/38.92  | | 
% 226.12/38.92  | |   (16)  all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 226.12/38.92  | | 
% 226.12/38.92  | | BETA: splitting (16) gives:
% 226.12/38.92  | | 
% 226.12/38.92  | | Case 1:
% 226.12/38.92  | | | 
% 226.12/38.92  | | |   (17)  all_55_11 = e2
% 226.12/38.92  | | | 
% 226.12/38.92  | | | REF_CLOSE: (10), (12), (17) are inconsistent by sub-proof #2282.
% 226.12/38.92  | | | 
% 226.12/38.92  | | Case 2:
% 226.12/38.92  | | | 
% 226.12/38.92  | | |   (18)  all_55_11 = e1 | all_55_11 = e0
% 226.12/38.92  | | | 
% 226.12/38.92  | | | BETA: splitting (18) gives:
% 226.12/38.92  | | | 
% 226.12/38.92  | | | Case 1:
% 226.12/38.92  | | | | 
% 226.12/38.92  | | | |   (19)  all_55_11 = e1
% 226.12/38.92  | | | | 
% 226.12/38.92  | | | | COMBINE_EQS: (10), (19) imply:
% 226.12/38.92  | | | |   (20)  all_53_14 = e1
% 226.12/38.92  | | | | 
% 226.12/38.92  | | | | SIMP: (20) implies:
% 226.12/38.92  | | | |   (21)  all_53_14 = e1
% 226.12/38.92  | | | | 
% 226.12/38.92  | | | | REDUCE: (9), (21) imply:
% 226.12/38.92  | | | |   (22)   ~ (all_52_15 = e1)
% 226.12/38.92  | | | | 
% 226.12/38.92  | | | | SIMP: (22) implies:
% 226.12/38.92  | | | |   (23)   ~ (all_52_15 = e1)
% 226.12/38.92  | | | | 
% 226.12/38.92  | | | | REF_CLOSE: (1), (3), (4), (5), (7), (11), (13), (14), (23) are
% 226.12/38.92  | | | |            inconsistent by sub-proof #71.
% 226.12/38.92  | | | | 
% 226.12/38.92  | | | Case 2:
% 226.12/38.92  | | | | 
% 226.12/38.92  | | | |   (24)  all_55_11 = e0
% 226.12/38.92  | | | | 
% 226.12/38.92  | | | | REF_CLOSE: (8), (10), (24) are inconsistent by sub-proof #2308.
% 226.12/38.92  | | | | 
% 226.12/38.92  | | | End of split
% 226.12/38.92  | | | 
% 226.12/38.92  | | End of split
% 226.12/38.92  | | 
% 226.12/38.92  | End of split
% 226.12/38.92  | 
% 226.12/38.92  End of proof
% 226.12/38.92  
% 226.12/38.92  Sub-proof #62 shows that the following formulas are inconsistent:
% 226.12/38.92  ----------------------------------------------------------------
% 226.12/38.92    (1)   ~ (e3 = e1)
% 226.12/38.92    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.12/38.92           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.12/38.92    (3)   ~ (all_6_2 = e3)
% 226.12/38.92    (4)  op(e1, e1) = all_6_2
% 226.12/38.92    (5)  all_57_4 = e0
% 226.12/38.92    (6)   ~ (e3 = e0)
% 226.12/38.92    (7)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 226.12/38.92         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 226.12/38.92    (8)  all_57_14 = e1
% 226.12/38.92    (9)  all_57_5 = e1
% 226.12/38.92  
% 226.12/38.92  Begin of proof
% 226.12/38.92  | 
% 226.12/38.92  | BETA: splitting (7) gives:
% 226.12/38.92  | 
% 226.12/38.92  | Case 1:
% 226.12/38.92  | | 
% 226.12/38.92  | |   (10)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) =
% 226.12/38.92  | |           e3)
% 226.12/38.92  | | 
% 226.12/38.92  | | BETA: splitting (10) gives:
% 226.12/38.92  | | 
% 226.12/38.92  | | Case 1:
% 226.12/38.92  | | | 
% 226.12/38.92  | | |   (11)  all_57_4 = e3 & op(e3, e1) = e3
% 226.12/38.92  | | | 
% 226.12/38.92  | | | REF_CLOSE: (5), (6), (11) are inconsistent by sub-proof #1618.
% 226.12/38.92  | | | 
% 226.12/38.92  | | Case 2:
% 226.12/38.92  | | | 
% 226.12/38.92  | | |   (12)  all_57_5 = e3 & op(e2, e1) = e3
% 226.12/38.92  | | | 
% 226.12/38.92  | | | ALPHA: (12) implies:
% 226.12/38.92  | | |   (13)  all_57_5 = e3
% 226.12/38.92  | | | 
% 226.12/38.92  | | | REF_CLOSE: (1), (9), (13) are inconsistent by sub-proof #2382.
% 226.12/38.92  | | | 
% 226.12/38.92  | | End of split
% 226.12/38.92  | | 
% 226.12/38.92  | Case 2:
% 226.12/38.92  | | 
% 226.12/38.92  | |   (14)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) =
% 226.12/38.92  | |           e3)
% 226.12/38.92  | | 
% 226.12/38.92  | | REF_CLOSE: (1), (2), (3), (4), (8), (14) are inconsistent by sub-proof
% 226.12/38.92  | |            #2263.
% 226.12/38.92  | | 
% 226.12/38.92  | End of split
% 226.12/38.92  | 
% 226.12/38.92  End of proof
% 226.12/38.92  
% 226.12/38.92  Sub-proof #63 shows that the following formulas are inconsistent:
% 226.12/38.92  ----------------------------------------------------------------
% 226.12/38.92    (1)  op(e0, e1) = all_53_11
% 226.12/38.92    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.12/38.92           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.12/38.92    (3)   ~ (all_6_2 = e3)
% 226.12/38.92    (4)  op(e1, e1) = all_6_2
% 226.12/38.92    (5)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 226.12/38.92    (6)   ~ (all_53_11 = e3)
% 226.12/38.92  
% 226.12/38.92  Begin of proof
% 226.12/38.92  | 
% 226.12/38.92  | BETA: splitting (5) gives:
% 226.12/38.92  | 
% 226.12/38.92  | Case 1:
% 226.12/38.92  | | 
% 226.12/38.92  | |   (7)  all_57_8 = e3 & op(e1, e1) = e3
% 226.12/38.92  | | 
% 226.12/38.92  | | ALPHA: (7) implies:
% 226.12/38.92  | |   (8)  op(e1, e1) = e3
% 226.12/38.92  | | 
% 226.12/38.92  | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #2468.
% 226.12/38.92  | | 
% 226.12/38.92  | Case 2:
% 226.12/38.92  | | 
% 226.12/38.92  | |   (9)  all_57_14 = e3 & op(e0, e1) = e3
% 226.12/38.92  | | 
% 226.12/38.92  | | REF_CLOSE: (1), (2), (6), (9) are inconsistent by sub-proof #129.
% 226.12/38.92  | | 
% 226.12/38.92  | End of split
% 226.12/38.92  | 
% 226.12/38.92  End of proof
% 226.12/38.92  
% 226.12/38.92  Sub-proof #64 shows that the following formulas are inconsistent:
% 226.12/38.92  ----------------------------------------------------------------
% 226.12/38.92    (1)  op(e0, e1) = all_53_11
% 226.12/38.92    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 226.12/38.92    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.12/38.92           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.12/38.93    (4)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 226.12/38.93           op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 226.12/38.93             e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 226.12/38.93    (5)   ~ (all_6_2 = e3)
% 226.12/38.93    (6)  op(e1, e1) = all_6_2
% 226.12/38.93    (7)  all_34_2 = all_6_2
% 226.12/38.93    (8)   ~ (all_53_13 = e2)
% 226.12/38.93    (9)   ~ (all_53_7 = e2)
% 226.12/38.93    (10)   ~ (all_53_9 = all_53_11)
% 226.12/38.93    (11)   ~ (all_53_9 = all_6_2)
% 226.12/38.93    (12)   ~ (all_53_14 = all_6_2)
% 226.12/38.93    (13)   ~ (e3 = e2)
% 226.12/38.93    (14)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 226.12/38.93    (15)  op(e1, e0) = all_53_14
% 226.12/38.93    (16)  op(e0, e3) = all_53_3
% 226.12/38.93    (17)  op(e3, e3) = e2
% 226.12/38.93    (18)   ~ (all_53_3 = e2)
% 226.12/38.93    (19)   ~ (all_53_14 = e3)
% 226.12/38.93    (20)  all_55_6 = all_53_9
% 226.12/38.93    (21)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 226.12/38.93    (22)   ~ (e2 = e0)
% 226.12/38.93    (23)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 226.12/38.93            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 226.12/38.93            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 226.12/38.93            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 226.12/38.93              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 226.12/38.93            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 226.12/38.93            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 226.12/38.93              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 226.12/38.93              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 226.12/38.93            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 226.12/38.93            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 226.12/38.93            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 226.12/38.93              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 226.12/38.93              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 226.12/38.93            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 226.12/38.93              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 226.12/38.93            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 226.12/38.93            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 226.12/38.93              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 226.12/38.93              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 226.12/38.93            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 226.12/38.93            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 226.12/38.93    (24)  op(e2, e2) = e2
% 226.12/38.93    (25)  op(e0, e2) = all_53_7
% 226.12/38.93    (26)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 226.12/38.93          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 226.12/38.93            e2)
% 226.12/38.93    (27)  all_55_10 = all_6_2
% 226.12/38.93    (28)  op(e2, e0) = all_53_13
% 226.12/38.93    (29)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 226.12/38.93          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 226.12/38.93    (30)  op(e2, e1) = all_53_9
% 226.12/38.93    (31)  all_24_2 = all_6_2
% 226.12/38.93    (32)   ~ (all_53_12 = e2)
% 226.12/38.93    (33)   ~ (all_34_2 = e0) | ( ~ (all_34_0 = e3) & op(all_34_1, e1) = all_34_0 &
% 226.12/38.93            op(e1, e0) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 226.12/38.93              e2) & op(e1, e0) = all_34_1 & $i(all_34_1))
% 226.12/38.93    (34)  op(e3, e0) = all_53_12
% 226.12/38.93  
% 226.12/38.93  Begin of proof
% 226.12/38.93  | 
% 226.12/38.93  | BETA: splitting (21) gives:
% 226.12/38.93  | 
% 226.12/38.93  | Case 1:
% 226.12/38.93  | | 
% 226.12/38.93  | |   (35)  all_57_11 = e3 & op(e1, e0) = e3
% 226.12/38.93  | | 
% 226.12/38.93  | | ALPHA: (35) implies:
% 226.12/38.93  | |   (36)  op(e1, e0) = e3
% 226.12/38.93  | | 
% 226.12/38.93  | | REF_CLOSE: (3), (15), (19), (36) are inconsistent by sub-proof #2330.
% 226.12/38.93  | | 
% 226.12/38.93  | Case 2:
% 226.12/38.93  | | 
% 226.12/38.93  | |   (37)  all_57_15 = e3 & op(e0, e0) = e3
% 226.12/38.93  | | 
% 226.12/38.93  | | ALPHA: (37) implies:
% 226.12/38.93  | |   (38)  all_57_15 = e3
% 226.12/38.93  | |   (39)  op(e0, e0) = e3
% 226.12/38.93  | | 
% 226.12/38.93  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 226.12/38.93  | |            (13), (14), (15), (16), (17), (18), (19), (20), (22), (23), (24),
% 226.12/38.93  | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (38),
% 226.12/38.93  | |            (39) are inconsistent by sub-proof #1072.
% 226.12/38.93  | | 
% 226.12/38.93  | End of split
% 226.12/38.93  | 
% 226.12/38.93  End of proof
% 226.12/38.93  
% 226.12/38.93  Sub-proof #65 shows that the following formulas are inconsistent:
% 226.12/38.93  ----------------------------------------------------------------
% 226.12/38.93    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 226.12/38.93         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 226.12/38.93    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 226.12/38.93         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 226.12/38.93    (3)   ~ (e3 = e1)
% 226.12/38.93    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.12/38.93           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.12/38.93    (5)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 226.12/38.93         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 226.12/38.93    (6)   ~ (e3 = e2)
% 226.12/38.93    (7)   ~ (e3 = e0)
% 226.12/38.93    (8)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 226.12/38.93         (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 226.12/38.93    (9)  op(e3, e3) = e2
% 226.12/38.93    (10)  all_57_5 = e3
% 226.12/38.93    (11)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 226.12/38.93          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 226.12/38.93    (12)   ~ (e2 = e0)
% 226.12/38.93    (13)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 226.12/38.93          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 226.12/38.93    (14)  op(e2, e2) = e2
% 226.12/38.93    (15)   ~ (e1 = e0)
% 226.12/38.93    (16)  all_57_12 = e3
% 226.12/38.93    (17)  all_57_10 = e3
% 226.12/38.93    (18)  op(e1, e1) = e2
% 226.12/38.93    (19)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 226.12/38.93          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 226.12/38.93    (20)   ~ (all_53_12 = e3)
% 226.12/38.93    (21)  all_57_7 = e3
% 226.12/38.93    (22)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 226.12/38.93          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 226.12/38.93    (23)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 226.12/38.93          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 226.12/38.93    (24)   ~ (e2 = e1)
% 226.12/38.93    (25)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 226.12/38.93          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 226.12/38.93    (26)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 226.12/38.93          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 226.12/38.93    (27)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 226.12/38.93          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 226.12/38.93    (28)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 226.12/38.93          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 226.12/38.93    (29)  all_57_3 = e2
% 226.12/38.93    (30)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 226.12/38.93          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 226.12/38.93    (31)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 226.12/38.93          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 226.12/38.93    (32)  op(e3, e0) = all_53_12
% 226.12/38.93  
% 226.12/38.93  Begin of proof
% 226.12/38.93  | 
% 226.12/38.93  | BETA: splitting (1) gives:
% 226.12/38.93  | 
% 226.12/38.93  | Case 1:
% 226.12/38.93  | | 
% 226.12/38.93  | |   (33)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) =
% 226.12/38.93  | |           e1)
% 226.12/38.93  | | 
% 226.12/38.93  | | BETA: splitting (33) gives:
% 226.12/38.93  | | 
% 226.12/38.93  | | Case 1:
% 226.12/38.93  | | | 
% 226.12/38.93  | | |   (34)  all_57_2 = e1 & op(e2, e3) = e1
% 226.12/38.93  | | | 
% 226.12/38.93  | | | ALPHA: (34) implies:
% 226.12/38.93  | | |   (35)  all_57_2 = e1
% 226.12/38.93  | | | 
% 226.12/38.93  | | | BETA: splitting (13) gives:
% 226.12/38.93  | | | 
% 226.12/38.93  | | | Case 1:
% 226.12/38.93  | | | | 
% 226.12/38.93  | | | |   (36)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2)
% 226.12/38.93  | | | |           = e3)
% 226.12/38.93  | | | | 
% 226.12/38.93  | | | | BETA: splitting (36) gives:
% 226.12/38.93  | | | | 
% 226.12/38.93  | | | | Case 1:
% 226.12/38.93  | | | | | 
% 226.12/38.93  | | | | |   (37)  all_57_0 = e3 & op(e3, e3) = e3
% 226.12/38.93  | | | | | 
% 226.12/38.93  | | | | | ALPHA: (37) implies:
% 226.12/38.93  | | | | |   (38)  op(e3, e3) = e3
% 226.12/38.93  | | | | | 
% 226.12/38.93  | | | | | REF_CLOSE: (1), (3), (4), (6), (7), (10), (12), (14), (15), (16),
% 226.12/38.93  | | | | |            (19), (22), (23), (24), (25), (27), (29), (35), (38) are
% 226.12/38.93  | | | | |            inconsistent by sub-proof #2235.
% 226.12/38.93  | | | | | 
% 226.12/38.93  | | | | Case 2:
% 226.12/38.93  | | | | | 
% 226.12/38.93  | | | | |   (39)  all_57_1 = e3 & op(e3, e2) = e3
% 226.12/38.93  | | | | | 
% 226.12/38.93  | | | | | ALPHA: (39) implies:
% 226.12/38.93  | | | | |   (40)  all_57_1 = e3
% 226.12/38.93  | | | | | 
% 226.12/38.93  | | | | | REF_CLOSE: (2), (3), (4), (6), (7), (11), (12), (14), (15), (21),
% 226.12/38.93  | | | | |            (24), (30), (40) are inconsistent by sub-proof #1167.
% 226.12/38.93  | | | | | 
% 226.12/38.93  | | | | End of split
% 226.12/38.93  | | | | 
% 226.12/38.93  | | | Case 2:
% 226.12/38.93  | | | | 
% 226.12/38.93  | | | |   (41)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0)
% 226.12/38.93  | | | |           = e3)
% 226.12/38.93  | | | | 
% 226.12/38.93  | | | | BETA: splitting (41) gives:
% 226.12/38.93  | | | | 
% 226.12/38.93  | | | | Case 1:
% 226.12/38.93  | | | | | 
% 226.12/38.93  | | | | |   (42)  all_57_4 = e3 & op(e3, e1) = e3
% 226.12/38.93  | | | | | 
% 226.12/38.93  | | | | | ALPHA: (42) implies:
% 226.12/38.93  | | | | |   (43)  all_57_4 = e3
% 226.12/38.93  | | | | | 
% 226.12/38.93  | | | | | BETA: splitting (27) gives:
% 226.12/38.93  | | | | | 
% 226.12/38.93  | | | | | Case 1:
% 226.12/38.93  | | | | | | 
% 226.12/38.93  | | | | | |   (44)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2,
% 226.12/38.93  | | | | | |             e3) = e0)
% 226.12/38.93  | | | | | | 
% 226.12/38.93  | | | | | | BETA: splitting (44) gives:
% 226.12/38.93  | | | | | | 
% 226.12/38.93  | | | | | | Case 1:
% 226.12/38.93  | | | | | | | 
% 226.12/38.93  | | | | | | |   (45)  all_57_0 = e0 & op(e3, e3) = e0
% 226.12/38.93  | | | | | | | 
% 226.12/38.93  | | | | | | | ALPHA: (45) implies:
% 226.12/38.93  | | | | | | |   (46)  op(e3, e3) = e0
% 226.12/38.93  | | | | | | | 
% 226.12/38.93  | | | | | | | REF_CLOSE: (4), (9), (12), (46) are inconsistent by sub-proof
% 226.12/38.93  | | | | | | |            #2403.
% 226.12/38.93  | | | | | | | 
% 226.12/38.93  | | | | | | Case 2:
% 226.12/38.93  | | | | | | | 
% 226.12/38.93  | | | | | | |   (47)  all_57_2 = e0 & op(e2, e3) = e0
% 226.12/38.93  | | | | | | | 
% 226.12/38.93  | | | | | | | REF_CLOSE: (15), (35), (47) are inconsistent by sub-proof #2467.
% 226.12/38.93  | | | | | | | 
% 226.12/38.93  | | | | | | End of split
% 226.12/38.93  | | | | | | 
% 226.12/38.93  | | | | | Case 2:
% 226.12/38.93  | | | | | | 
% 226.12/38.93  | | | | | |   (48)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0,
% 226.12/38.93  | | | | | |             e3) = e0)
% 226.12/38.93  | | | | | | 
% 226.12/38.93  | | | | | | BETA: splitting (48) gives:
% 226.12/38.93  | | | | | | 
% 226.12/38.93  | | | | | | Case 1:
% 226.12/38.93  | | | | | | | 
% 226.12/38.93  | | | | | | |   (49)  all_57_6 = e0 & op(e1, e3) = e0
% 226.12/38.93  | | | | | | | 
% 226.12/38.93  | | | | | | | ALPHA: (49) implies:
% 226.12/38.93  | | | | | | |   (50)  all_57_6 = e0
% 226.12/38.93  | | | | | | | 
% 226.12/38.93  | | | | | | | BETA: splitting (28) gives:
% 226.12/38.93  | | | | | | | 
% 226.12/38.93  | | | | | | | Case 1:
% 226.12/38.93  | | | | | | | | 
% 226.12/38.93  | | | | | | | |   (51)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 &
% 226.12/38.93  | | | | | | | |           op(e1, e2) = e1)
% 226.12/38.93  | | | | | | | | 
% 226.12/38.93  | | | | | | | | BETA: splitting (51) gives:
% 226.12/38.93  | | | | | | | | 
% 226.12/38.93  | | | | | | | | Case 1:
% 226.12/38.93  | | | | | | | | | 
% 226.12/38.93  | | | | | | | | |   (52)  all_57_6 = e1 & op(e1, e3) = e1
% 226.12/38.93  | | | | | | | | | 
% 226.12/38.93  | | | | | | | | | REF_CLOSE: (15), (50), (52) are inconsistent by sub-proof
% 226.12/38.93  | | | | | | | | |            #2044.
% 226.12/38.93  | | | | | | | | | 
% 226.12/38.93  | | | | | | | | Case 2:
% 226.12/38.93  | | | | | | | | | 
% 226.12/38.93  | | | | | | | | |   (53)  all_57_7 = e1 & op(e1, e2) = e1
% 226.12/38.93  | | | | | | | | | 
% 226.12/38.93  | | | | | | | | | ALPHA: (53) implies:
% 226.12/38.93  | | | | | | | | |   (54)  all_57_7 = e1
% 226.12/38.93  | | | | | | | | | 
% 226.12/38.93  | | | | | | | | | COMBINE_EQS: (21), (54) imply:
% 226.12/38.93  | | | | | | | | |   (55)  e3 = e1
% 226.12/38.93  | | | | | | | | | 
% 226.12/38.93  | | | | | | | | | SIMP: (55) implies:
% 226.12/38.93  | | | | | | | | |   (56)  e3 = e1
% 226.12/38.93  | | | | | | | | | 
% 226.12/38.93  | | | | | | | | | COMBINE_EQS: (10), (56) imply:
% 226.12/38.93  | | | | | | | | |   (57)  all_57_5 = e1
% 226.12/38.93  | | | | | | | | | 
% 226.12/38.93  | | | | | | | | | REF_CLOSE: (3), (4), (6), (7), (12), (15), (17), (19), (22),
% 226.12/38.93  | | | | | | | | |            (23), (24), (35), (57) are inconsistent by
% 226.12/38.93  | | | | | | | | |            sub-proof #66.
% 226.12/38.93  | | | | | | | | | 
% 226.12/38.93  | | | | | | | | End of split
% 226.12/38.93  | | | | | | | | 
% 226.12/38.93  | | | | | | | Case 2:
% 226.12/38.93  | | | | | | | | 
% 226.12/38.93  | | | | | | | |   (58)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 &
% 226.12/38.93  | | | | | | | |           op(e1, e0) = e1)
% 226.12/38.93  | | | | | | | | 
% 226.12/38.93  | | | | | | | | BETA: splitting (58) gives:
% 226.12/38.93  | | | | | | | | 
% 226.12/38.93  | | | | | | | | Case 1:
% 226.12/38.93  | | | | | | | | | 
% 226.12/38.93  | | | | | | | | |   (59)  all_57_8 = e1 & op(e1, e1) = e1
% 226.12/38.93  | | | | | | | | | 
% 226.12/38.93  | | | | | | | | | ALPHA: (59) implies:
% 226.12/38.93  | | | | | | | | |   (60)  op(e1, e1) = e1
% 226.12/38.93  | | | | | | | | | 
% 226.12/38.93  | | | | | | | | | REF_CLOSE: (4), (18), (24), (60) are inconsistent by sub-proof
% 226.12/38.93  | | | | | | | | |            #2423.
% 226.12/38.93  | | | | | | | | | 
% 226.12/38.93  | | | | | | | | Case 2:
% 226.12/38.93  | | | | | | | | | 
% 226.12/38.93  | | | | | | | | |   (61)  all_57_11 = e1 & op(e1, e0) = e1
% 226.12/38.93  | | | | | | | | | 
% 226.12/38.93  | | | | | | | | | ALPHA: (61) implies:
% 226.12/38.93  | | | | | | | | |   (62)  all_57_11 = e1
% 226.12/38.93  | | | | | | | | | 
% 226.12/38.93  | | | | | | | | | BETA: splitting (5) gives:
% 226.12/38.93  | | | | | | | | | 
% 226.12/38.93  | | | | | | | | | Case 1:
% 226.12/38.93  | | | | | | | | | | 
% 226.12/38.93  | | | | | | | | | |   (63)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 &
% 226.12/38.93  | | | | | | | | | |           op(e2, e1) = e0)
% 226.12/38.93  | | | | | | | | | | 
% 226.12/38.93  | | | | | | | | | | BETA: splitting (63) gives:
% 226.12/38.93  | | | | | | | | | | 
% 226.12/38.93  | | | | | | | | | | Case 1:
% 226.12/38.93  | | | | | | | | | | | 
% 226.12/38.93  | | | | | | | | | | |   (64)  all_57_4 = e0 & op(e3, e1) = e0
% 226.12/38.93  | | | | | | | | | | | 
% 226.12/38.93  | | | | | | | | | | | REF_CLOSE: (7), (43), (64) are inconsistent by sub-proof
% 226.12/38.93  | | | | | | | | | | |            #2491.
% 226.12/38.93  | | | | | | | | | | | 
% 226.12/38.93  | | | | | | | | | | Case 2:
% 226.12/38.93  | | | | | | | | | | | 
% 226.12/38.93  | | | | | | | | | | |   (65)  all_57_5 = e0 & op(e2, e1) = e0
% 226.12/38.93  | | | | | | | | | | | 
% 226.12/38.93  | | | | | | | | | | | REF_CLOSE: (7), (10), (65) are inconsistent by sub-proof
% 226.12/38.93  | | | | | | | | | | |            #2414.
% 226.12/38.93  | | | | | | | | | | | 
% 226.12/38.93  | | | | | | | | | | End of split
% 226.12/38.93  | | | | | | | | | | 
% 226.12/38.93  | | | | | | | | | Case 2:
% 226.12/38.93  | | | | | | | | | | 
% 226.12/38.93  | | | | | | | | | |   (66)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0
% 226.12/38.93  | | | | | | | | | |           & op(e0, e1) = e0)
% 226.12/38.93  | | | | | | | | | | 
% 226.12/38.93  | | | | | | | | | | BETA: splitting (66) gives:
% 226.12/38.93  | | | | | | | | | | 
% 226.12/38.93  | | | | | | | | | | Case 1:
% 226.12/38.93  | | | | | | | | | | | 
% 226.12/38.93  | | | | | | | | | | |   (67)  all_57_8 = e0 & op(e1, e1) = e0
% 226.12/38.93  | | | | | | | | | | | 
% 226.12/38.93  | | | | | | | | | | | ALPHA: (67) implies:
% 226.12/38.93  | | | | | | | | | | |   (68)  all_57_8 = e0
% 226.12/38.93  | | | | | | | | | | |   (69)  op(e1, e1) = e0
% 226.12/38.93  | | | | | | | | | | | 
% 226.12/38.93  | | | | | | | | | | | REF_CLOSE: (3), (4), (6), (8), (10), (12), (15), (24), (26),
% 226.12/38.93  | | | | | | | | | | |            (43), (68), (69) are inconsistent by sub-proof
% 226.12/38.93  | | | | | | | | | | |            #1181.
% 226.12/38.93  | | | | | | | | | | | 
% 226.12/38.93  | | | | | | | | | | Case 2:
% 226.12/38.93  | | | | | | | | | | | 
% 226.12/38.93  | | | | | | | | | | |   (70)  all_57_14 = e0 & op(e0, e1) = e0
% 226.12/38.93  | | | | | | | | | | | 
% 226.12/38.93  | | | | | | | | | | | ALPHA: (70) implies:
% 226.12/38.93  | | | | | | | | | | |   (71)  all_57_14 = e0
% 226.12/38.93  | | | | | | | | | | | 
% 226.12/38.93  | | | | | | | | | | | BETA: splitting (8) gives:
% 226.12/38.93  | | | | | | | | | | | 
% 226.12/38.93  | | | | | | | | | | | Case 1:
% 226.12/38.93  | | | | | | | | | | | | 
% 226.12/38.93  | | | | | | | | | | | |   (72)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 226.12/38.93  | | | | | | | | | | | |           & op(e2, e1) = e1)
% 226.12/38.93  | | | | | | | | | | | | 
% 226.12/38.93  | | | | | | | | | | | | BETA: splitting (72) gives:
% 226.12/38.93  | | | | | | | | | | | | 
% 226.12/38.93  | | | | | | | | | | | | Case 1:
% 226.12/38.93  | | | | | | | | | | | | | 
% 226.12/38.93  | | | | | | | | | | | | |   (73)  all_57_4 = e1 & op(e3, e1) = e1
% 226.12/38.93  | | | | | | | | | | | | | 
% 226.12/38.93  | | | | | | | | | | | | | ALPHA: (73) implies:
% 226.12/38.93  | | | | | | | | | | | | |   (74)  all_57_4 = e1
% 226.12/38.93  | | | | | | | | | | | | | 
% 226.12/38.93  | | | | | | | | | | | | | COMBINE_EQS: (43), (74) imply:
% 226.12/38.93  | | | | | | | | | | | | |   (75)  e3 = e1
% 226.12/38.93  | | | | | | | | | | | | | 
% 226.12/38.93  | | | | | | | | | | | | | COMBINE_EQS: (10), (75) imply:
% 226.12/38.93  | | | | | | | | | | | | |   (76)  all_57_5 = e1
% 226.12/38.93  | | | | | | | | | | | | | 
% 226.12/38.93  | | | | | | | | | | | | | REF_CLOSE: (3), (4), (6), (7), (12), (15), (17), (19), (22),
% 226.12/38.93  | | | | | | | | | | | | |            (23), (24), (35), (76) are inconsistent by
% 226.12/38.93  | | | | | | | | | | | | |            sub-proof #66.
% 226.12/38.93  | | | | | | | | | | | | | 
% 226.12/38.93  | | | | | | | | | | | | Case 2:
% 226.12/38.93  | | | | | | | | | | | | | 
% 226.12/38.93  | | | | | | | | | | | | |   (77)  all_57_5 = e1 & op(e2, e1) = e1
% 226.12/38.93  | | | | | | | | | | | | | 
% 226.12/38.93  | | | | | | | | | | | | | ALPHA: (77) implies:
% 226.12/38.93  | | | | | | | | | | | | |   (78)  all_57_5 = e1
% 226.12/38.93  | | | | | | | | | | | | | 
% 226.12/38.93  | | | | | | | | | | | | | REF_CLOSE: (3), (4), (6), (7), (12), (15), (17), (19), (22),
% 226.12/38.93  | | | | | | | | | | | | |            (23), (24), (35), (78) are inconsistent by
% 226.12/38.93  | | | | | | | | | | | | |            sub-proof #66.
% 226.12/38.93  | | | | | | | | | | | | | 
% 226.12/38.93  | | | | | | | | | | | | End of split
% 226.12/38.93  | | | | | | | | | | | | 
% 226.12/38.93  | | | | | | | | | | | Case 2:
% 226.12/38.93  | | | | | | | | | | | | 
% 226.12/38.93  | | | | | | | | | | | |   (79)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 226.12/38.93  | | | | | | | | | | | |           e1 & op(e0, e1) = e1)
% 226.12/38.93  | | | | | | | | | | | | 
% 226.12/38.93  | | | | | | | | | | | | BETA: splitting (79) gives:
% 226.12/38.93  | | | | | | | | | | | | 
% 226.12/38.93  | | | | | | | | | | | | Case 1:
% 226.12/38.93  | | | | | | | | | | | | | 
% 226.12/38.93  | | | | | | | | | | | | |   (80)  all_57_8 = e1 & op(e1, e1) = e1
% 226.12/38.93  | | | | | | | | | | | | | 
% 226.12/38.93  | | | | | | | | | | | | | ALPHA: (80) implies:
% 226.12/38.93  | | | | | | | | | | | | |   (81)  op(e1, e1) = e1
% 226.12/38.93  | | | | | | | | | | | | | 
% 226.12/38.93  | | | | | | | | | | | | | REF_CLOSE: (4), (6), (12), (21), (24), (31), (50), (62), (81)
% 226.12/38.93  | | | | | | | | | | | | |            are inconsistent by sub-proof #1844.
% 226.12/38.93  | | | | | | | | | | | | | 
% 226.12/38.93  | | | | | | | | | | | | Case 2:
% 226.12/38.93  | | | | | | | | | | | | | 
% 226.12/38.93  | | | | | | | | | | | | |   (82)  all_57_14 = e1 & op(e0, e1) = e1
% 226.12/38.93  | | | | | | | | | | | | | 
% 226.12/38.93  | | | | | | | | | | | | | REF_CLOSE: (15), (71), (82) are inconsistent by sub-proof
% 226.12/38.93  | | | | | | | | | | | | |            #2381.
% 226.12/38.93  | | | | | | | | | | | | | 
% 226.12/38.93  | | | | | | | | | | | | End of split
% 226.12/38.93  | | | | | | | | | | | | 
% 226.12/38.93  | | | | | | | | | | | End of split
% 226.12/38.93  | | | | | | | | | | | 
% 226.12/38.93  | | | | | | | | | | End of split
% 226.12/38.93  | | | | | | | | | | 
% 226.12/38.93  | | | | | | | | | End of split
% 226.12/38.93  | | | | | | | | | 
% 226.12/38.93  | | | | | | | | End of split
% 226.12/38.93  | | | | | | | | 
% 226.12/38.93  | | | | | | | End of split
% 226.12/38.93  | | | | | | | 
% 226.12/38.93  | | | | | | Case 2:
% 226.12/38.93  | | | | | | | 
% 226.12/38.93  | | | | | | |   (83)  all_57_12 = e0 & op(e0, e3) = e0
% 226.12/38.93  | | | | | | | 
% 226.12/38.93  | | | | | | | REF_CLOSE: (7), (16), (83) are inconsistent by sub-proof #2237.
% 226.12/38.93  | | | | | | | 
% 226.12/38.93  | | | | | | End of split
% 226.12/38.93  | | | | | | 
% 226.12/38.93  | | | | | End of split
% 226.12/38.93  | | | | | 
% 226.12/38.93  | | | | Case 2:
% 226.12/38.93  | | | | | 
% 226.12/38.93  | | | | |   (84)  all_57_9 = e3 & op(e3, e0) = e3
% 226.12/38.93  | | | | | 
% 226.12/38.93  | | | | | ALPHA: (84) implies:
% 226.12/38.93  | | | | |   (85)  op(e3, e0) = e3
% 226.12/38.93  | | | | | 
% 226.12/38.93  | | | | | REF_CLOSE: (4), (20), (32), (85) are inconsistent by sub-proof #2458.
% 226.12/38.93  | | | | | 
% 226.12/38.93  | | | | End of split
% 226.12/38.93  | | | | 
% 226.12/38.93  | | | End of split
% 226.12/38.93  | | | 
% 226.12/38.93  | | Case 2:
% 226.12/38.93  | | | 
% 226.12/38.93  | | |   (86)  all_57_3 = e1 & op(e2, e2) = e1
% 226.12/38.93  | | | 
% 226.12/38.93  | | | ALPHA: (86) implies:
% 226.12/38.93  | | |   (87)  op(e2, e2) = e1
% 226.12/38.93  | | | 
% 226.12/38.93  | | | REF_CLOSE: (4), (14), (24), (87) are inconsistent by sub-proof #2306.
% 226.12/38.93  | | | 
% 226.12/38.93  | | End of split
% 226.12/38.93  | | 
% 226.12/38.93  | Case 2:
% 226.12/38.93  | | 
% 226.12/38.93  | |   (88)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) =
% 226.12/38.93  | |           e1)
% 226.12/38.93  | | 
% 226.12/38.93  | | BETA: splitting (88) gives:
% 226.12/38.93  | | 
% 226.12/38.93  | | Case 1:
% 226.12/38.93  | | | 
% 226.12/38.93  | | |   (89)  all_57_5 = e1 & op(e2, e1) = e1
% 226.12/38.93  | | | 
% 226.12/38.93  | | | ALPHA: (89) implies:
% 226.12/38.93  | | |   (90)  all_57_5 = e1
% 226.12/38.93  | | | 
% 226.12/38.93  | | | REF_CLOSE: (3), (10), (90) are inconsistent by sub-proof #2382.
% 226.12/38.93  | | | 
% 226.12/38.93  | | Case 2:
% 226.12/38.93  | | | 
% 226.12/38.93  | | |   (91)  all_57_10 = e1 & op(e2, e0) = e1
% 226.12/38.93  | | | 
% 226.12/38.93  | | | ALPHA: (91) implies:
% 226.12/38.93  | | |   (92)  all_57_10 = e1
% 226.12/38.93  | | | 
% 226.12/38.93  | | | REF_CLOSE: (3), (17), (92) are inconsistent by sub-proof #2248.
% 226.12/38.93  | | | 
% 226.12/38.93  | | End of split
% 226.12/38.93  | | 
% 226.12/38.93  | End of split
% 226.12/38.93  | 
% 226.12/38.93  End of proof
% 226.12/38.93  
% 226.12/38.93  Sub-proof #66 shows that the following formulas are inconsistent:
% 226.12/38.93  ----------------------------------------------------------------
% 226.12/38.93    (1)   ~ (e3 = e1)
% 226.12/38.93    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.12/38.93           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.12/38.93    (3)   ~ (e3 = e2)
% 226.12/38.93    (4)   ~ (e3 = e0)
% 226.12/38.93    (5)   ~ (e2 = e0)
% 226.12/38.93    (6)   ~ (e1 = e0)
% 226.12/38.93    (7)  all_57_10 = e3
% 226.12/38.93    (8)  all_57_2 = e1
% 226.12/38.93    (9)  all_57_5 = e1
% 226.12/38.93    (10)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 226.12/38.93          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 226.12/38.93    (11)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 226.12/38.93          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 226.12/38.93    (12)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 226.12/38.93          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 226.12/38.93    (13)   ~ (e2 = e1)
% 226.12/38.93  
% 226.12/38.93  Begin of proof
% 226.12/38.93  | 
% 226.12/38.93  | BETA: splitting (12) gives:
% 226.12/38.93  | 
% 226.12/38.93  | Case 1:
% 226.12/38.93  | | 
% 226.12/38.93  | |   (14)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) =
% 226.12/38.93  | |           e0)
% 226.12/38.93  | | 
% 226.12/38.93  | | BETA: splitting (14) gives:
% 226.12/38.93  | | 
% 226.12/38.93  | | Case 1:
% 226.12/38.93  | | | 
% 226.12/38.93  | | |   (15)  all_57_2 = e0 & op(e2, e3) = e0
% 226.12/38.93  | | | 
% 226.12/38.93  | | | REF_CLOSE: (6), (8), (15) are inconsistent by sub-proof #2467.
% 226.12/38.93  | | | 
% 226.12/38.93  | | Case 2:
% 226.12/38.93  | | | 
% 226.12/38.93  | | |   (16)  all_57_3 = e0 & op(e2, e2) = e0
% 226.12/38.93  | | | 
% 226.12/38.93  | | | ALPHA: (16) implies:
% 226.12/38.93  | | |   (17)  all_57_3 = e0
% 226.12/38.93  | | |   (18)  op(e2, e2) = e0
% 226.12/38.93  | | | 
% 226.12/38.93  | | | REF_CLOSE: (1), (2), (3), (4), (5), (8), (9), (10), (11), (13), (17), (18)
% 226.12/38.93  | | |            are inconsistent by sub-proof #1536.
% 226.12/38.93  | | | 
% 226.12/38.93  | | End of split
% 226.12/38.93  | | 
% 226.12/38.93  | Case 2:
% 226.12/38.93  | | 
% 226.12/38.93  | |   (19)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 226.12/38.93  | |           e0)
% 226.12/38.93  | | 
% 226.12/38.93  | | BETA: splitting (19) gives:
% 226.12/38.93  | | 
% 226.12/38.93  | | Case 1:
% 226.12/38.93  | | | 
% 226.12/38.93  | | |   (20)  all_57_5 = e0 & op(e2, e1) = e0
% 226.12/38.93  | | | 
% 226.12/38.93  | | | REF_CLOSE: (6), (9), (20) are inconsistent by sub-proof #942.
% 226.12/38.93  | | | 
% 226.12/38.93  | | Case 2:
% 226.12/38.93  | | | 
% 226.12/38.93  | | |   (21)  all_57_10 = e0 & op(e2, e0) = e0
% 226.12/38.93  | | | 
% 226.12/38.93  | | | REF_CLOSE: (4), (7), (21) are inconsistent by sub-proof #1981.
% 226.12/38.93  | | | 
% 226.12/38.93  | | End of split
% 226.12/38.93  | | 
% 226.12/38.93  | End of split
% 226.12/38.93  | 
% 226.12/38.93  End of proof
% 226.12/38.93  
% 226.12/38.93  Sub-proof #67 shows that the following formulas are inconsistent:
% 226.12/38.93  ----------------------------------------------------------------
% 226.12/38.93    (1)   ~ (all_38_0 = e0)
% 226.12/38.93    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.12/38.93           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.12/38.93    (3)  all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 226.12/38.93    (4)   ~ (all_53_11 = all_52_13)
% 226.12/38.93    (5)   ~ (all_53_11 = all_38_0)
% 226.12/38.93    (6)  all_55_6 = all_52_13
% 226.12/38.93    (7)  all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 226.12/38.93    (8)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 226.12/38.94    (9)   ~ (all_52_13 = e2)
% 226.12/38.94    (10)  op(all_52_13, all_52_13) = e1
% 226.12/38.94    (11)  op(e3, e3) = e2
% 226.12/38.94    (12)   ~ (all_53_11 = e2)
% 226.12/38.94    (13)   ~ (all_52_13 = all_38_0)
% 226.12/38.94    (14)  all_55_2 = all_38_0
% 226.12/38.94    (15)  all_55_14 = all_53_11
% 226.12/38.94    (16)   ~ (all_38_0 = e2)
% 226.12/38.94  
% 226.12/38.94  Begin of proof
% 226.12/38.94  | 
% 226.12/38.94  | BETA: splitting (7) gives:
% 226.12/38.94  | 
% 226.12/38.94  | Case 1:
% 226.12/38.94  | | 
% 226.12/38.94  | |   (17)  all_55_2 = e2
% 226.12/38.94  | | 
% 226.12/38.94  | | REF_CLOSE: (14), (16), (17) are inconsistent by sub-proof #1452.
% 226.12/38.94  | | 
% 226.12/38.94  | Case 2:
% 226.12/38.94  | | 
% 226.12/38.94  | |   (18)   ~ (all_55_2 = e2)
% 226.12/38.94  | |   (19)  all_55_2 = e1 | all_55_2 = e0
% 226.12/38.94  | | 
% 226.12/38.94  | | BETA: splitting (19) gives:
% 226.12/38.94  | | 
% 226.12/38.94  | | Case 1:
% 226.12/38.94  | | | 
% 226.12/38.94  | | |   (20)  all_55_2 = e1
% 226.12/38.94  | | | 
% 226.12/38.94  | | | COMBINE_EQS: (14), (20) imply:
% 226.12/38.94  | | |   (21)  all_38_0 = e1
% 226.12/38.94  | | | 
% 226.12/38.94  | | | SIMP: (21) implies:
% 226.12/38.94  | | |   (22)  all_38_0 = e1
% 226.12/38.94  | | | 
% 226.12/38.94  | | | REDUCE: (5), (22) imply:
% 226.12/38.94  | | |   (23)   ~ (all_53_11 = e1)
% 226.12/38.94  | | | 
% 226.12/38.94  | | | REDUCE: (13), (22) imply:
% 226.12/38.94  | | |   (24)   ~ (all_52_13 = e1)
% 226.12/38.94  | | | 
% 226.12/38.94  | | | REDUCE: (16), (22) imply:
% 226.12/38.94  | | |   (25)   ~ (e2 = e1)
% 226.12/38.94  | | | 
% 226.12/38.94  | | | SIMP: (25) implies:
% 226.12/38.94  | | |   (26)   ~ (e2 = e1)
% 226.12/38.94  | | | 
% 226.12/38.94  | | | BETA: splitting (3) gives:
% 226.12/38.94  | | | 
% 226.12/38.94  | | | Case 1:
% 226.12/38.94  | | | | 
% 226.12/38.94  | | | |   (27)  all_55_14 = e2
% 226.12/38.94  | | | | 
% 226.12/38.94  | | | | REF_CLOSE: (12), (15), (27) are inconsistent by sub-proof #2293.
% 226.12/38.94  | | | | 
% 226.12/38.94  | | | Case 2:
% 226.12/38.94  | | | | 
% 226.12/38.94  | | | |   (28)  all_55_14 = e1 | all_55_14 = e0
% 226.12/38.94  | | | | 
% 226.12/38.94  | | | | BETA: splitting (28) gives:
% 226.12/38.94  | | | | 
% 226.12/38.94  | | | | Case 1:
% 226.12/38.94  | | | | | 
% 226.12/38.94  | | | | |   (29)  all_55_14 = e1
% 226.12/38.94  | | | | | 
% 226.12/38.94  | | | | | REF_CLOSE: (15), (23), (29) are inconsistent by sub-proof #2165.
% 226.12/38.94  | | | | | 
% 226.12/38.94  | | | | Case 2:
% 226.12/38.94  | | | | | 
% 226.12/38.94  | | | | |   (30)  all_55_14 = e0
% 226.12/38.94  | | | | | 
% 226.12/38.94  | | | | | COMBINE_EQS: (15), (30) imply:
% 226.12/38.94  | | | | |   (31)  all_53_11 = e0
% 226.12/38.94  | | | | | 
% 226.12/38.94  | | | | | SIMP: (31) implies:
% 226.12/38.94  | | | | |   (32)  all_53_11 = e0
% 226.12/38.94  | | | | | 
% 226.12/38.94  | | | | | REDUCE: (4), (32) imply:
% 226.12/38.94  | | | | |   (33)   ~ (all_52_13 = e0)
% 226.12/38.94  | | | | | 
% 226.12/38.94  | | | | | SIMP: (33) implies:
% 226.12/38.94  | | | | |   (34)   ~ (all_52_13 = e0)
% 226.12/38.94  | | | | | 
% 226.12/38.94  | | | | | BETA: splitting (8) gives:
% 226.12/38.94  | | | | | 
% 226.12/38.94  | | | | | Case 1:
% 226.12/38.94  | | | | | | 
% 226.12/38.94  | | | | | |   (35)  all_55_6 = e3
% 226.12/38.94  | | | | | | 
% 226.12/38.94  | | | | | | COMBINE_EQS: (6), (35) imply:
% 226.12/38.94  | | | | | |   (36)  all_52_13 = e3
% 226.12/38.94  | | | | | | 
% 226.12/38.94  | | | | | | SIMP: (36) implies:
% 226.12/38.94  | | | | | |   (37)  all_52_13 = e3
% 226.12/38.94  | | | | | | 
% 226.12/38.94  | | | | | | REDUCE: (10), (37) imply:
% 226.12/38.94  | | | | | |   (38)  op(e3, e3) = e1
% 226.12/38.94  | | | | | | 
% 226.12/38.94  | | | | | | REF_CLOSE: (2), (11), (26), (38) are inconsistent by sub-proof
% 226.12/38.94  | | | | | |            #1950.
% 226.12/38.94  | | | | | | 
% 226.12/38.94  | | | | | Case 2:
% 226.12/38.94  | | | | | | 
% 226.12/38.94  | | | | | |   (39)  all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 226.12/38.94  | | | | | | 
% 226.12/38.94  | | | | | | REF_CLOSE: (6), (9), (24), (34), (39) are inconsistent by sub-proof
% 226.12/38.94  | | | | | |            #68.
% 226.12/38.94  | | | | | | 
% 226.12/38.94  | | | | | End of split
% 226.12/38.94  | | | | | 
% 226.12/38.94  | | | | End of split
% 226.12/38.94  | | | | 
% 226.12/38.94  | | | End of split
% 226.12/38.94  | | | 
% 226.12/38.94  | | Case 2:
% 226.12/38.94  | | | 
% 226.12/38.94  | | |   (40)  all_55_2 = e0
% 226.12/38.94  | | | 
% 226.12/38.94  | | | REF_CLOSE: (1), (14), (40) are inconsistent by sub-proof #1446.
% 226.12/38.94  | | | 
% 226.12/38.94  | | End of split
% 226.12/38.94  | | 
% 226.12/38.94  | End of split
% 226.12/38.94  | 
% 226.12/38.94  End of proof
% 226.12/38.94  
% 226.12/38.94  Sub-proof #68 shows that the following formulas are inconsistent:
% 226.12/38.94  ----------------------------------------------------------------
% 226.12/38.94    (1)   ~ (all_52_13 = e0)
% 226.12/38.94    (2)  all_55_6 = all_52_13
% 226.12/38.94    (3)   ~ (all_52_13 = e2)
% 226.12/38.94    (4)   ~ (all_52_13 = e1)
% 226.12/38.94    (5)  all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 226.12/38.94  
% 226.12/38.94  Begin of proof
% 226.12/38.94  | 
% 226.12/38.94  | BETA: splitting (5) gives:
% 226.12/38.94  | 
% 226.12/38.94  | Case 1:
% 226.12/38.94  | | 
% 226.12/38.94  | |   (6)  all_55_6 = e2
% 226.12/38.94  | | 
% 226.12/38.94  | | REF_CLOSE: (2), (3), (6) are inconsistent by sub-proof #2292.
% 226.12/38.94  | | 
% 226.12/38.94  | Case 2:
% 226.12/38.94  | | 
% 226.12/38.94  | |   (7)  all_55_6 = e1 | all_55_6 = e0
% 226.12/38.94  | | 
% 226.12/38.94  | | BETA: splitting (7) gives:
% 226.12/38.94  | | 
% 226.12/38.94  | | Case 1:
% 226.12/38.94  | | | 
% 226.12/38.94  | | |   (8)  all_55_6 = e1
% 226.12/38.94  | | | 
% 226.12/38.94  | | | REF_CLOSE: (2), (4), (8) are inconsistent by sub-proof #2291.
% 226.12/38.94  | | | 
% 226.12/38.94  | | Case 2:
% 226.12/38.94  | | | 
% 226.12/38.94  | | |   (9)  all_55_6 = e0
% 226.12/38.94  | | | 
% 226.12/38.94  | | | REF_CLOSE: (1), (2), (9) are inconsistent by sub-proof #76.
% 226.12/38.94  | | | 
% 226.12/38.94  | | End of split
% 226.12/38.94  | | 
% 226.12/38.94  | End of split
% 226.12/38.94  | 
% 226.12/38.94  End of proof
% 226.12/38.94  
% 226.12/38.94  Sub-proof #69 shows that the following formulas are inconsistent:
% 226.12/38.94  ----------------------------------------------------------------
% 226.12/38.94    (1)   ~ (all_4_1 = e1) & op(e0, e2) = all_4_1 & $i(all_4_1)
% 226.12/38.94    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.12/38.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.12/38.94    (3)  op(e0, e2) = e1
% 226.12/38.94    (4)  ( ~ (all_32_0 = e1) & op(all_32_1, e0) = all_32_0 & op(e0, e2) = all_32_1
% 226.12/38.94           & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 = e3) & op(e0, e2) =
% 226.12/38.94           all_32_1 & $i(all_32_1))
% 226.12/38.94  
% 226.12/38.94  Begin of proof
% 226.12/38.94  | 
% 226.12/38.94  | ALPHA: (1) implies:
% 226.12/38.94  |   (5)   ~ (all_4_1 = e1)
% 226.12/38.94  |   (6)  op(e0, e2) = all_4_1
% 226.12/38.94  | 
% 226.12/38.94  | BETA: splitting (4) gives:
% 226.12/38.94  | 
% 226.12/38.94  | Case 1:
% 226.12/38.94  | | 
% 226.12/38.94  | |   (7)   ~ (all_32_0 = e1) & op(all_32_1, e0) = all_32_0 & op(e0, e2) =
% 226.12/38.94  | |        all_32_1 & $i(all_32_0) & $i(all_32_1)
% 226.12/38.94  | | 
% 226.12/38.94  | | ALPHA: (7) implies:
% 226.12/38.94  | |   (8)  op(e0, e2) = all_32_1
% 226.12/38.94  | | 
% 226.12/38.94  | | REF_CLOSE: (2), (3), (5), (6), (8) are inconsistent by sub-proof #70.
% 226.12/38.94  | | 
% 226.12/38.94  | Case 2:
% 226.12/38.94  | | 
% 226.12/38.94  | |   (9)   ~ (all_32_1 = e3) & op(e0, e2) = all_32_1 & $i(all_32_1)
% 226.12/38.94  | | 
% 226.12/38.94  | | ALPHA: (9) implies:
% 226.12/38.94  | |   (10)  op(e0, e2) = all_32_1
% 226.12/38.94  | | 
% 226.12/38.94  | | REF_CLOSE: (2), (3), (5), (6), (10) are inconsistent by sub-proof #70.
% 226.12/38.94  | | 
% 226.12/38.94  | End of split
% 226.12/38.94  | 
% 226.12/38.94  End of proof
% 226.12/38.94  
% 226.12/38.94  Sub-proof #70 shows that the following formulas are inconsistent:
% 226.12/38.94  ----------------------------------------------------------------
% 226.12/38.94    (1)  op(e0, e2) = all_32_1
% 226.12/38.94    (2)   ~ (all_4_1 = e1)
% 226.12/38.94    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.12/38.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.12/38.94    (4)  op(e0, e2) = e1
% 226.12/38.94    (5)  op(e0, e2) = all_4_1
% 226.12/38.94  
% 226.12/38.94  Begin of proof
% 226.12/38.94  | 
% 226.12/38.94  | GROUND_INST: instantiating (3) with all_4_1, all_32_1, e2, e0, simplifying
% 226.12/38.94  |              with (1), (5) gives:
% 226.12/38.94  |   (6)  all_32_1 = all_4_1
% 226.12/38.94  | 
% 226.12/38.94  | GROUND_INST: instantiating (3) with e1, all_32_1, e2, e0, simplifying with
% 226.12/38.94  |              (1), (4) gives:
% 226.12/38.94  |   (7)  all_32_1 = e1
% 226.12/38.94  | 
% 226.12/38.94  | COMBINE_EQS: (6), (7) imply:
% 226.12/38.94  |   (8)  all_4_1 = e1
% 226.12/38.94  | 
% 226.12/38.94  | REDUCE: (2), (8) imply:
% 226.12/38.94  |   (9)  $false
% 226.12/38.94  | 
% 226.12/38.94  | CLOSE: (9) is inconsistent.
% 226.12/38.94  | 
% 226.12/38.94  End of proof
% 226.12/38.94  
% 226.12/38.94  Sub-proof #71 shows that the following formulas are inconsistent:
% 226.12/38.94  ----------------------------------------------------------------
% 226.12/38.94    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.12/38.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.12/38.94    (2)  all_55_7 = all_52_15
% 226.12/38.94    (3)   ~ (all_52_15 = e1)
% 226.12/38.94    (4)  all_55_7 = e3 | all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 226.12/38.94    (5)  op(e3, e3) = e2
% 226.12/38.94    (6)   ~ (e2 = e0)
% 226.12/38.94    (7)  op(all_52_15, all_52_15) = e0
% 226.12/38.94    (8)   ~ (all_52_15 = e0)
% 226.12/38.94    (9)   ~ (all_52_15 = e2)
% 226.12/38.94  
% 226.12/38.94  Begin of proof
% 226.12/38.94  | 
% 226.12/38.94  | BETA: splitting (4) gives:
% 226.12/38.94  | 
% 226.12/38.94  | Case 1:
% 226.12/38.94  | | 
% 226.12/38.94  | |   (10)  all_55_7 = e3
% 226.12/38.94  | | 
% 226.12/38.94  | | COMBINE_EQS: (2), (10) imply:
% 226.12/38.94  | |   (11)  all_52_15 = e3
% 226.12/38.94  | | 
% 226.12/38.94  | | SIMP: (11) implies:
% 226.12/38.94  | |   (12)  all_52_15 = e3
% 226.12/38.94  | | 
% 226.12/38.94  | | REDUCE: (7), (12) imply:
% 226.12/38.94  | |   (13)  op(e3, e3) = e0
% 226.12/38.94  | | 
% 226.12/38.94  | | REF_CLOSE: (1), (5), (6), (13) are inconsistent by sub-proof #2403.
% 226.12/38.94  | | 
% 226.12/38.94  | Case 2:
% 226.12/38.94  | | 
% 226.12/38.94  | |   (14)  all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 226.12/38.94  | | 
% 226.12/38.94  | | REF_CLOSE: (2), (3), (8), (9), (14) are inconsistent by sub-proof #2275.
% 226.12/38.94  | | 
% 226.12/38.94  | End of split
% 226.12/38.94  | 
% 226.12/38.94  End of proof
% 226.12/38.94  
% 226.12/38.94  Sub-proof #72 shows that the following formulas are inconsistent:
% 226.12/38.94  ----------------------------------------------------------------
% 226.12/38.94    (1)   ~ (all_53_2 = e2)
% 226.12/38.94    (2)   ~ (all_53_6 = e2)
% 226.12/38.94    (3)   ~ (all_53_2 = all_52_9)
% 226.12/38.94    (4)   ~ (all_53_6 = e0)
% 226.12/38.94    (5)   ~ (all_52_9 = e2)
% 226.12/38.94    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.12/38.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.12/38.94    (7)  all_55_4 = all_52_9
% 226.12/38.94    (8)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 226.12/38.94    (9)  all_55_9 = all_53_6
% 226.12/38.94    (10)  all_55_6 = all_52_13
% 226.12/38.94    (11)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 226.12/38.94    (12)   ~ (all_53_2 = e0)
% 226.12/38.94    (13)   ~ (all_52_13 = e2)
% 226.12/38.94    (14)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 226.12/38.94    (15)  op(all_52_13, all_52_13) = e1
% 226.12/38.94    (16)  op(e3, e3) = e2
% 226.12/38.94    (17)   ~ (all_53_6 = e1)
% 226.12/38.94    (18)   ~ (all_52_9 = all_52_13)
% 226.12/38.94    (19)  all_55_8 = all_53_2
% 226.12/38.94    (20)  op(all_52_9, all_52_9) = e3
% 226.12/38.94    (21)  op(e1, e1) = e2
% 226.12/38.94    (22)  all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 226.12/38.94    (23)   ~ (all_53_2 = all_53_6)
% 226.12/38.94  
% 226.12/38.94  Begin of proof
% 226.12/38.94  | 
% 226.12/38.94  | BETA: splitting (8) gives:
% 226.12/38.94  | 
% 226.12/38.94  | Case 1:
% 226.12/38.94  | | 
% 226.12/38.94  | |   (24)  all_55_9 = e3
% 226.12/38.94  | | 
% 226.12/38.94  | | COMBINE_EQS: (9), (24) imply:
% 226.12/38.94  | |   (25)  all_53_6 = e3
% 226.12/38.94  | | 
% 226.12/38.94  | | SIMP: (25) implies:
% 226.12/38.94  | |   (26)  all_53_6 = e3
% 226.12/38.94  | | 
% 226.12/38.94  | | REDUCE: (23), (26) imply:
% 226.12/38.94  | |   (27)   ~ (all_53_2 = e3)
% 226.12/38.94  | | 
% 226.12/38.94  | | BETA: splitting (11) gives:
% 226.12/38.94  | | 
% 226.12/38.94  | | Case 1:
% 226.12/38.94  | | | 
% 226.12/38.94  | | |   (28)  all_55_8 = e3
% 226.12/38.94  | | | 
% 226.12/38.94  | | | REF_CLOSE: (19), (27), (28) are inconsistent by sub-proof #2496.
% 226.12/38.94  | | | 
% 226.12/38.94  | | Case 2:
% 226.12/38.94  | | | 
% 226.12/38.94  | | |   (29)  all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 226.12/38.94  | | | 
% 226.12/38.94  | | | BETA: splitting (29) gives:
% 226.12/38.94  | | | 
% 226.12/38.94  | | | Case 1:
% 226.12/38.94  | | | | 
% 226.12/38.94  | | | |   (30)  all_55_8 = e2
% 226.12/38.94  | | | | 
% 226.12/38.94  | | | | REF_CLOSE: (1), (19), (30) are inconsistent by sub-proof #2406.
% 226.12/38.94  | | | | 
% 226.12/38.94  | | | Case 2:
% 226.12/38.94  | | | | 
% 226.12/38.94  | | | |   (31)  all_55_8 = e1 | all_55_8 = e0
% 226.12/38.94  | | | | 
% 226.12/38.94  | | | | BETA: splitting (31) gives:
% 226.12/38.94  | | | | 
% 226.12/38.94  | | | | Case 1:
% 226.12/38.94  | | | | | 
% 226.12/38.94  | | | | |   (32)  all_55_8 = e1
% 226.12/38.94  | | | | | 
% 226.12/38.94  | | | | | COMBINE_EQS: (19), (32) imply:
% 226.12/38.94  | | | | |   (33)  all_53_2 = e1
% 226.12/38.94  | | | | | 
% 226.12/38.94  | | | | | SIMP: (33) implies:
% 226.12/38.94  | | | | |   (34)  all_53_2 = e1
% 226.12/38.94  | | | | | 
% 226.12/38.94  | | | | | REDUCE: (3), (34) imply:
% 226.12/38.94  | | | | |   (35)   ~ (all_52_9 = e1)
% 226.12/38.94  | | | | | 
% 226.12/38.94  | | | | | REF_CLOSE: (5), (6), (7), (10), (13), (14), (15), (16), (18), (20),
% 226.12/38.94  | | | | |            (21), (22), (35) are inconsistent by sub-proof #75.
% 226.12/38.94  | | | | | 
% 226.12/38.94  | | | | Case 2:
% 226.12/38.94  | | | | | 
% 226.12/38.94  | | | | |   (36)  all_55_8 = e0
% 226.12/38.94  | | | | | 
% 226.12/38.94  | | | | | REF_CLOSE: (12), (19), (36) are inconsistent by sub-proof #1997.
% 226.12/38.94  | | | | | 
% 226.12/38.94  | | | | End of split
% 226.12/38.94  | | | | 
% 226.12/38.94  | | | End of split
% 226.12/38.94  | | | 
% 226.12/38.94  | | End of split
% 226.12/38.94  | | 
% 226.12/38.94  | Case 2:
% 226.12/38.94  | | 
% 226.12/38.94  | |   (37)  all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 226.12/38.94  | | 
% 226.12/38.94  | | REF_CLOSE: (2), (4), (9), (17), (37) are inconsistent by sub-proof #2271.
% 226.12/38.94  | | 
% 226.12/38.94  | End of split
% 226.12/38.94  | 
% 226.12/38.94  End of proof
% 226.12/38.94  
% 226.12/38.94  Sub-proof #73 shows that the following formulas are inconsistent:
% 226.12/38.94  ----------------------------------------------------------------
% 226.12/38.94    (1)  all_55_11 = all_4_0
% 226.12/38.94    (2)  all_55_11 = e1
% 226.12/38.94    (3)   ~ (all_4_0 = e1)
% 226.12/38.94  
% 226.12/38.94  Begin of proof
% 226.12/38.94  | 
% 226.12/38.94  | COMBINE_EQS: (1), (2) imply:
% 226.12/38.94  |   (4)  all_4_0 = e1
% 226.12/38.94  | 
% 226.12/38.94  | SIMP: (4) implies:
% 226.12/38.94  |   (5)  all_4_0 = e1
% 226.12/38.94  | 
% 226.12/38.94  | REDUCE: (3), (5) imply:
% 226.12/38.94  |   (6)  $false
% 226.12/38.94  | 
% 226.12/38.94  | CLOSE: (6) is inconsistent.
% 226.12/38.94  | 
% 226.12/38.94  End of proof
% 226.12/38.94  
% 226.12/38.94  Sub-proof #74 shows that the following formulas are inconsistent:
% 226.12/38.94  ----------------------------------------------------------------
% 226.12/38.94    (1)  all_55_11 = all_4_0
% 226.12/38.94    (2)  all_55_11 = e3
% 226.12/38.94    (3)   ~ (all_4_0 = e3)
% 226.12/38.94  
% 226.12/38.94  Begin of proof
% 226.12/38.94  | 
% 226.12/38.94  | COMBINE_EQS: (1), (2) imply:
% 226.12/38.94  |   (4)  all_4_0 = e3
% 226.12/38.94  | 
% 226.12/38.94  | SIMP: (4) implies:
% 226.12/38.94  |   (5)  all_4_0 = e3
% 226.12/38.94  | 
% 226.12/38.94  | REDUCE: (3), (5) imply:
% 226.12/38.94  |   (6)  $false
% 226.12/38.94  | 
% 226.12/38.94  | CLOSE: (6) is inconsistent.
% 226.12/38.94  | 
% 226.12/38.94  End of proof
% 226.12/38.94  
% 226.12/38.94  Sub-proof #75 shows that the following formulas are inconsistent:
% 226.12/38.94  ----------------------------------------------------------------
% 226.12/38.94    (1)   ~ (all_52_9 = e2)
% 226.12/38.94    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.12/38.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.12/38.94    (3)  all_55_4 = all_52_9
% 226.12/38.94    (4)  all_55_6 = all_52_13
% 226.12/38.94    (5)   ~ (all_52_13 = e2)
% 226.12/38.94    (6)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 226.12/38.94    (7)  op(all_52_13, all_52_13) = e1
% 226.12/38.94    (8)  op(e3, e3) = e2
% 226.12/38.94    (9)   ~ (all_52_9 = all_52_13)
% 226.12/38.94    (10)  op(all_52_9, all_52_9) = e3
% 226.12/38.94    (11)  op(e1, e1) = e2
% 226.12/38.94    (12)  all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 226.12/38.94    (13)   ~ (all_52_9 = e1)
% 226.12/38.94  
% 226.12/38.94  Begin of proof
% 226.12/38.94  | 
% 226.12/38.94  | SIMP: (13) implies:
% 226.12/38.94  |   (14)   ~ (all_52_9 = e1)
% 226.12/38.94  | 
% 226.12/38.94  | BETA: splitting (6) gives:
% 226.12/38.94  | 
% 226.12/38.94  | Case 1:
% 226.12/38.94  | | 
% 226.12/38.94  | |   (15)  all_55_4 = e3
% 226.12/38.94  | | 
% 226.12/38.94  | | COMBINE_EQS: (3), (15) imply:
% 226.12/38.94  | |   (16)  all_52_9 = e3
% 226.12/38.94  | | 
% 226.12/38.94  | | REDUCE: (1), (16) imply:
% 226.12/38.94  | |   (17)   ~ (e3 = e2)
% 226.12/38.94  | | 
% 226.12/38.94  | | REDUCE: (10), (16) imply:
% 226.12/38.94  | |   (18)  op(e3, e3) = e3
% 226.12/38.94  | | 
% 226.12/38.94  | | REF_CLOSE: (2), (8), (17), (18) are inconsistent by sub-proof #2490.
% 226.12/38.94  | | 
% 226.12/38.94  | Case 2:
% 226.12/38.94  | | 
% 226.12/38.94  | |   (19)  all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 226.12/38.94  | | 
% 226.12/38.94  | | BETA: splitting (19) gives:
% 226.12/38.94  | | 
% 226.12/38.94  | | Case 1:
% 226.12/38.94  | | | 
% 226.12/38.94  | | |   (20)  all_55_4 = e2
% 226.12/38.94  | | | 
% 226.12/38.94  | | | REF_CLOSE: (1), (3), (20) are inconsistent by sub-proof #345.
% 226.12/38.94  | | | 
% 226.12/38.94  | | Case 2:
% 226.12/38.94  | | | 
% 226.12/38.94  | | |   (21)  all_55_4 = e1 | all_55_4 = e0
% 226.12/38.94  | | | 
% 226.12/38.94  | | | BETA: splitting (21) gives:
% 226.12/38.94  | | | 
% 226.12/38.94  | | | Case 1:
% 226.12/38.94  | | | | 
% 226.12/38.94  | | | |   (22)  all_55_4 = e1
% 226.12/38.94  | | | | 
% 226.12/38.94  | | | | COMBINE_EQS: (3), (22) imply:
% 226.12/38.94  | | | |   (23)  all_52_9 = e1
% 226.12/38.94  | | | | 
% 226.12/38.94  | | | | REDUCE: (14), (23) imply:
% 226.12/38.94  | | | |   (24)  $false
% 226.12/38.94  | | | | 
% 226.12/38.94  | | | | CLOSE: (24) is inconsistent.
% 226.12/38.94  | | | | 
% 226.12/38.94  | | | Case 2:
% 226.12/38.94  | | | | 
% 226.12/38.94  | | | |   (25)  all_55_4 = e0
% 226.12/38.94  | | | | 
% 226.12/38.94  | | | | COMBINE_EQS: (3), (25) imply:
% 226.12/38.94  | | | |   (26)  all_52_9 = e0
% 226.12/38.94  | | | | 
% 226.12/38.94  | | | | REDUCE: (9), (26) imply:
% 226.12/38.94  | | | |   (27)   ~ (all_52_13 = e0)
% 226.12/38.94  | | | | 
% 226.12/38.94  | | | | SIMP: (27) implies:
% 226.12/38.94  | | | |   (28)   ~ (all_52_13 = e0)
% 226.12/38.94  | | | | 
% 226.12/38.94  | | | | BETA: splitting (12) gives:
% 226.12/38.94  | | | | 
% 226.12/38.94  | | | | Case 1:
% 226.12/38.94  | | | | | 
% 226.12/38.94  | | | | |   (29)  all_55_6 = e2
% 226.12/38.94  | | | | | 
% 226.12/38.94  | | | | | COMBINE_EQS: (4), (29) imply:
% 226.12/38.94  | | | | |   (30)  all_52_13 = e2
% 226.12/38.94  | | | | | 
% 226.12/38.94  | | | | | REDUCE: (5), (30) imply:
% 226.12/38.94  | | | | |   (31)  $false
% 226.12/38.94  | | | | | 
% 226.12/38.94  | | | | | CLOSE: (31) is inconsistent.
% 226.12/38.94  | | | | | 
% 226.12/38.94  | | | | Case 2:
% 226.12/38.94  | | | | | 
% 226.12/38.94  | | | | |   (32)   ~ (all_55_6 = e2)
% 226.12/38.94  | | | | |   (33)  all_55_6 = e1 | all_55_6 = e0
% 226.12/38.94  | | | | | 
% 226.12/38.94  | | | | | BETA: splitting (33) gives:
% 226.12/38.94  | | | | | 
% 226.12/38.94  | | | | | Case 1:
% 226.12/38.94  | | | | | | 
% 226.12/38.94  | | | | | |   (34)  all_55_6 = e1
% 226.12/38.94  | | | | | | 
% 226.12/38.94  | | | | | | COMBINE_EQS: (4), (34) imply:
% 226.12/38.94  | | | | | |   (35)  all_52_13 = e1
% 226.12/38.94  | | | | | | 
% 226.12/38.94  | | | | | | SIMP: (35) implies:
% 226.12/38.94  | | | | | |   (36)  all_52_13 = e1
% 226.12/38.94  | | | | | | 
% 226.12/38.94  | | | | | | REDUCE: (5), (36) imply:
% 226.12/38.94  | | | | | |   (37)   ~ (e2 = e1)
% 226.12/38.94  | | | | | | 
% 226.12/38.94  | | | | | | SIMP: (37) implies:
% 226.12/38.94  | | | | | |   (38)   ~ (e2 = e1)
% 226.12/38.94  | | | | | | 
% 226.12/38.94  | | | | | | REDUCE: (7), (36) imply:
% 226.12/38.94  | | | | | |   (39)  op(e1, e1) = e1
% 226.12/38.94  | | | | | | 
% 226.12/38.94  | | | | | | REF_CLOSE: (2), (11), (38), (39) are inconsistent by sub-proof
% 226.12/38.94  | | | | | |            #2423.
% 226.12/38.94  | | | | | | 
% 226.12/38.94  | | | | | Case 2:
% 226.12/38.94  | | | | | | 
% 226.12/38.94  | | | | | |   (40)  all_55_6 = e0
% 226.12/38.94  | | | | | | 
% 226.12/38.94  | | | | | | REF_CLOSE: (4), (28), (40) are inconsistent by sub-proof #76.
% 226.12/38.94  | | | | | | 
% 226.12/38.94  | | | | | End of split
% 226.12/38.94  | | | | | 
% 226.12/38.94  | | | | End of split
% 226.12/38.94  | | | | 
% 226.12/38.94  | | | End of split
% 226.12/38.94  | | | 
% 226.12/38.94  | | End of split
% 226.12/38.94  | | 
% 226.12/38.94  | End of split
% 226.12/38.94  | 
% 226.12/38.94  End of proof
% 226.12/38.94  
% 226.12/38.94  Sub-proof #76 shows that the following formulas are inconsistent:
% 226.12/38.94  ----------------------------------------------------------------
% 226.12/38.94    (1)  all_55_6 = all_52_13
% 226.12/38.94    (2)  all_55_6 = e0
% 226.12/38.94    (3)   ~ (all_52_13 = e0)
% 226.12/38.94  
% 226.12/38.94  Begin of proof
% 226.12/38.94  | 
% 226.12/38.94  | COMBINE_EQS: (1), (2) imply:
% 226.12/38.94  |   (4)  all_52_13 = e0
% 226.12/38.94  | 
% 226.12/38.94  | SIMP: (4) implies:
% 226.12/38.94  |   (5)  all_52_13 = e0
% 226.12/38.94  | 
% 226.12/38.94  | REDUCE: (3), (5) imply:
% 226.12/38.94  |   (6)  $false
% 226.12/38.94  | 
% 226.12/38.94  | CLOSE: (6) is inconsistent.
% 226.12/38.94  | 
% 226.12/38.94  End of proof
% 226.12/38.94  
% 226.12/38.94  Sub-proof #77 shows that the following formulas are inconsistent:
% 226.12/38.94  ----------------------------------------------------------------
% 226.12/38.94    (1)   ~ (all_53_7 = e3)
% 226.12/38.94    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.12/38.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.12/38.94    (3)   ~ (all_53_3 = e3)
% 226.12/38.94    (4)  op(e0, e3) = all_53_3
% 226.12/38.94    (5)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 226.12/38.94    (6)  op(e0, e2) = all_53_7
% 226.12/38.94  
% 226.12/38.94  Begin of proof
% 226.12/38.94  | 
% 226.12/38.94  | BETA: splitting (5) gives:
% 226.12/38.94  | 
% 226.12/38.94  | Case 1:
% 226.12/38.94  | | 
% 226.12/38.94  | |   (7)  all_57_12 = e3 & op(e0, e3) = e3
% 226.12/38.94  | | 
% 226.12/38.94  | | ALPHA: (7) implies:
% 226.12/38.94  | |   (8)  op(e0, e3) = e3
% 226.12/38.94  | | 
% 226.12/38.94  | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #132.
% 226.12/38.94  | | 
% 226.12/38.94  | Case 2:
% 226.12/38.94  | | 
% 226.12/38.94  | |   (9)  all_57_13 = e3 & op(e0, e2) = e3
% 226.12/38.94  | | 
% 226.12/38.94  | | REF_CLOSE: (1), (2), (6), (9) are inconsistent by sub-proof #78.
% 226.12/38.94  | | 
% 226.12/38.94  | End of split
% 226.12/38.94  | 
% 226.12/38.94  End of proof
% 226.12/38.94  
% 226.12/38.94  Sub-proof #78 shows that the following formulas are inconsistent:
% 226.12/38.94  ----------------------------------------------------------------
% 226.12/38.94    (1)  all_57_13 = e3 & op(e0, e2) = e3
% 226.12/38.94    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.12/38.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.12/38.94    (3)  op(e0, e2) = all_53_7
% 226.12/38.94    (4)   ~ (all_53_7 = e3)
% 226.12/38.94  
% 226.12/38.94  Begin of proof
% 226.12/38.94  | 
% 226.12/38.94  | ALPHA: (1) implies:
% 226.12/38.94  |   (5)  op(e0, e2) = e3
% 226.12/38.94  | 
% 226.12/38.94  | GROUND_INST: instantiating (2) with all_53_7, e3, e2, e0, simplifying with
% 226.12/38.94  |              (3), (5) gives:
% 226.12/38.94  |   (6)  all_53_7 = e3
% 226.12/38.94  | 
% 226.12/38.94  | REDUCE: (4), (6) imply:
% 226.12/38.94  |   (7)  $false
% 226.12/38.94  | 
% 226.12/38.94  | CLOSE: (7) is inconsistent.
% 226.12/38.94  | 
% 226.12/38.94  End of proof
% 226.12/38.94  
% 226.12/38.94  Sub-proof #79 shows that the following formulas are inconsistent:
% 226.12/38.94  ----------------------------------------------------------------
% 226.12/38.94    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.12/38.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.12/38.94    (2)   ~ (e2 = e0)
% 226.12/38.94    (3)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0 &
% 226.12/38.94         op(all_52_25, all_52_25) = e3 & op(all_52_27, all_52_27) = e2 &
% 226.12/38.94         op(all_52_29, all_52_29) = e1 & op(all_52_31, all_52_31) = e0 & op(e0,
% 226.12/38.94           e3) = all_52_25 & op(e0, e2) = all_52_27 & op(e0, e1) = all_52_29 &
% 226.12/38.94         op(e0, e0) = all_52_31 & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 226.12/38.94         $i(all_52_31)
% 226.12/38.94    (4)  op(e2, e2) = e2
% 226.12/38.94    (5)  op(e0, e0) = e2
% 226.12/38.94  
% 226.12/38.94  Begin of proof
% 226.12/38.94  | 
% 226.12/38.94  | ALPHA: (3) implies:
% 226.12/38.94  |   (6)  op(e0, e0) = all_52_31
% 226.12/38.94  |   (7)  op(all_52_31, all_52_31) = e0
% 226.12/38.94  | 
% 226.12/38.94  | GROUND_INST: instantiating (1) with e2, all_52_31, e0, e0, simplifying with
% 226.12/38.94  |              (5), (6) gives:
% 226.12/38.94  |   (8)  all_52_31 = e2
% 226.12/38.94  | 
% 226.54/38.94  | REDUCE: (7), (8) imply:
% 226.54/38.94  |   (9)  op(e2, e2) = e0
% 226.54/38.94  | 
% 226.54/38.94  | REF_CLOSE: (1), (2), (4), (9) are inconsistent by sub-proof #2472.
% 226.54/38.94  | 
% 226.54/38.94  End of proof
% 226.54/38.94  
% 226.54/38.94  Sub-proof #80 shows that the following formulas are inconsistent:
% 226.54/38.94  ----------------------------------------------------------------
% 226.54/38.94    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.54/38.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.54/38.94    (2)  op(e1, e3) = e2
% 226.54/38.94    (3)   ~ (e3 = e2)
% 226.54/38.94    (4)  op(e2, e2) = e2
% 226.54/38.94    (5)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 &
% 226.54/38.94         op(all_52_17, all_52_17) = e3 & op(all_52_19, all_52_19) = e2 &
% 226.54/38.94         op(all_52_21, all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1,
% 226.54/38.94           e3) = all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 &
% 226.54/38.94         op(e1, e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 226.54/38.94         $i(all_52_23)
% 226.54/38.94  
% 226.54/38.94  Begin of proof
% 226.54/38.94  | 
% 226.54/38.94  | ALPHA: (5) implies:
% 226.54/38.94  |   (6)  op(e1, e3) = all_52_17
% 226.54/38.95  |   (7)  op(all_52_17, all_52_17) = e3
% 226.54/38.95  | 
% 226.54/38.95  | GROUND_INST: instantiating (1) with e2, all_52_17, e3, e1, simplifying with
% 226.54/38.95  |              (2), (6) gives:
% 226.54/38.95  |   (8)  all_52_17 = e2
% 226.54/38.95  | 
% 226.54/38.95  | REDUCE: (7), (8) imply:
% 226.54/38.95  |   (9)  op(e2, e2) = e3
% 226.54/38.95  | 
% 226.54/38.95  | REF_CLOSE: (1), (3), (4), (9) are inconsistent by sub-proof #2298.
% 226.54/38.95  | 
% 226.54/38.95  End of proof
% 226.54/38.95  
% 226.54/38.95  Sub-proof #81 shows that the following formulas are inconsistent:
% 226.54/38.95  ----------------------------------------------------------------
% 226.54/38.95    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.54/38.95           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.54/38.95    (2)   ~ (e1 = e0)
% 226.54/38.95    (3)  op(e1, e1) = e0
% 226.54/38.95    (4)  all_57_14 = e0
% 226.54/38.95    (5)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 226.54/38.95  
% 226.54/38.95  Begin of proof
% 226.54/38.95  | 
% 226.54/38.95  | BETA: splitting (5) gives:
% 226.54/38.95  | 
% 226.54/38.95  | Case 1:
% 226.54/38.95  | | 
% 226.54/38.95  | |   (6)  all_57_8 = e1 & op(e1, e1) = e1
% 226.54/38.95  | | 
% 226.54/38.95  | | ALPHA: (6) implies:
% 226.54/38.95  | |   (7)  op(e1, e1) = e1
% 226.54/38.95  | | 
% 226.54/38.95  | | REF_CLOSE: (1), (2), (3), (7) are inconsistent by sub-proof #2427.
% 226.54/38.95  | | 
% 226.54/38.95  | Case 2:
% 226.54/38.95  | | 
% 226.54/38.95  | |   (8)  all_57_14 = e1 & op(e0, e1) = e1
% 226.54/38.95  | | 
% 226.54/38.95  | | REF_CLOSE: (2), (4), (8) are inconsistent by sub-proof #2381.
% 226.54/38.95  | | 
% 226.54/38.95  | End of split
% 226.54/38.95  | 
% 226.54/38.95  End of proof
% 226.54/38.95  
% 226.54/38.95  Sub-proof #82 shows that the following formulas are inconsistent:
% 226.54/38.95  ----------------------------------------------------------------
% 226.54/38.95    (1)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 226.54/38.95         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 226.54/38.95    (2)   ~ (e3 = e1)
% 226.54/38.95    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.54/38.95           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.54/38.95    (4)   ~ (e3 = e2)
% 226.54/38.95    (5)   ~ (e3 = e0)
% 226.54/38.95    (6)   ~ (e2 = e0)
% 226.54/38.95    (7)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3)
% 226.54/38.95    (8)   ~ (e1 = e0)
% 226.54/38.95    (9)  all_57_0 = e3
% 226.54/38.95    (10)   ~ (all_53_6 = e3)
% 226.54/38.95    (11)   ~ (e2 = e1)
% 226.54/38.95    (12)  op(e1, e2) = all_53_6
% 226.54/38.95    (13)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 226.54/38.95          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 226.54/38.95    (14)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 226.54/38.95          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 226.54/38.95  
% 226.54/38.95  Begin of proof
% 226.54/38.95  | 
% 226.54/38.95  | BETA: splitting (7) gives:
% 226.54/38.95  | 
% 226.54/38.95  | Case 1:
% 226.54/38.95  | | 
% 226.54/38.95  | |   (15)  all_57_6 = e3 & op(e1, e3) = e3
% 226.54/38.95  | | 
% 226.54/38.95  | | ALPHA: (15) implies:
% 226.54/38.95  | |   (16)  all_57_6 = e3
% 226.54/38.95  | | 
% 226.54/38.95  | | REF_CLOSE: (1), (2), (4), (5), (6), (8), (9), (11), (13), (14), (16) are
% 226.54/38.95  | |            inconsistent by sub-proof #2010.
% 226.54/38.95  | | 
% 226.54/38.95  | Case 2:
% 226.54/38.95  | | 
% 226.54/38.95  | |   (17)  all_57_7 = e3 & op(e1, e2) = e3
% 226.54/38.95  | | 
% 226.54/38.95  | | REF_CLOSE: (3), (10), (12), (17) are inconsistent by sub-proof #267.
% 226.54/38.95  | | 
% 226.54/38.95  | End of split
% 226.54/38.95  | 
% 226.54/38.95  End of proof
% 226.54/38.95  
% 226.54/38.95  Sub-proof #83 shows that the following formulas are inconsistent:
% 226.54/38.95  ----------------------------------------------------------------
% 226.54/38.95    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.54/38.95           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.54/38.95    (2)  all_57_9 = e1
% 226.54/38.95    (3)  op(e2, e0) = all_52_15
% 226.54/38.95    (4)  op(e1, e0) = all_53_14
% 226.54/38.95    (5)   ~ (e2 = e0)
% 226.54/38.95    (6)  all_57_15 = e2
% 226.54/38.95    (7)   ~ (e1 = e0)
% 226.54/38.95    (8)   ~ (all_53_14 = e0)
% 226.54/38.95    (9)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 226.54/38.95             | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 226.54/38.95               e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 226.54/38.95               op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 226.54/38.95    (10)  op(all_52_15, all_52_15) = e0
% 226.54/38.95    (11)  op(e0, e0) = e2
% 226.54/38.95    (12)   ~ (all_52_15 = e2)
% 226.54/38.95  
% 226.54/38.95  Begin of proof
% 226.54/38.95  | 
% 226.54/38.95  | BETA: splitting (9) gives:
% 226.54/38.95  | 
% 226.54/38.95  | Case 1:
% 226.54/38.95  | | 
% 226.54/38.95  | |   (13)  all_57_15 = e0 & op(e0, e0) = e0
% 226.54/38.95  | | 
% 226.54/38.95  | | ALPHA: (13) implies:
% 226.54/38.95  | |   (14)  op(e0, e0) = e0
% 226.54/38.95  | | 
% 226.54/38.95  | | REF_CLOSE: (1), (5), (11), (14) are inconsistent by sub-proof #86.
% 226.54/38.95  | | 
% 226.54/38.95  | Case 2:
% 226.54/38.95  | | 
% 226.54/38.95  | |   (15)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 226.54/38.95  | |             e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0 &
% 226.54/38.95  | |             op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 226.54/38.95  | |           (all_57_14 = e0 & op(e0, e1) = e0))
% 226.54/38.95  | | 
% 226.54/38.95  | | ALPHA: (15) implies:
% 226.54/38.95  | |   (16)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 226.54/38.95  | |           e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 226.54/38.95  | | 
% 226.54/38.95  | | BETA: splitting (16) gives:
% 226.54/38.95  | | 
% 226.54/38.95  | | Case 1:
% 226.54/38.95  | | | 
% 226.54/38.95  | | |   (17)  all_57_9 = e0 & op(e3, e0) = e0
% 226.54/38.95  | | | 
% 226.54/38.95  | | | REF_CLOSE: (2), (7), (17) are inconsistent by sub-proof #1990.
% 226.54/38.95  | | | 
% 226.54/38.95  | | Case 2:
% 226.54/38.95  | | | 
% 226.54/38.95  | | |   (18)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 226.54/38.95  | | |           = e0)
% 226.54/38.95  | | | 
% 226.54/38.95  | | | BETA: splitting (18) gives:
% 226.54/38.95  | | | 
% 226.54/38.95  | | | Case 1:
% 226.54/38.95  | | | | 
% 226.54/38.95  | | | |   (19)  all_57_10 = e0 & op(e2, e0) = e0
% 226.54/38.95  | | | | 
% 226.54/38.95  | | | | REF_CLOSE: (1), (3), (5), (6), (9), (10), (11), (12), (19) are
% 226.54/38.95  | | | |            inconsistent by sub-proof #84.
% 226.54/38.95  | | | | 
% 226.54/38.95  | | | Case 2:
% 226.54/38.95  | | | | 
% 226.54/38.95  | | | |   (20)  all_57_11 = e0 & op(e1, e0) = e0
% 226.54/38.95  | | | | 
% 226.54/38.95  | | | | REF_CLOSE: (1), (4), (8), (20) are inconsistent by sub-proof #2341.
% 226.54/38.95  | | | | 
% 226.54/38.95  | | | End of split
% 226.54/38.95  | | | 
% 226.54/38.95  | | End of split
% 226.54/38.95  | | 
% 226.54/38.95  | End of split
% 226.54/38.95  | 
% 226.54/38.95  End of proof
% 226.54/38.95  
% 226.54/38.95  Sub-proof #84 shows that the following formulas are inconsistent:
% 226.54/38.95  ----------------------------------------------------------------
% 226.54/38.95    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.54/38.95           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.54/38.95    (2)  op(e2, e0) = all_52_15
% 226.54/38.95    (3)  all_57_10 = e0 & op(e2, e0) = e0
% 226.54/38.95    (4)   ~ (e2 = e0)
% 226.54/38.95    (5)  all_57_15 = e2
% 226.54/38.95    (6)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 226.54/38.95             | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 226.54/38.95               e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 226.54/38.95               op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 226.54/38.95    (7)  op(all_52_15, all_52_15) = e0
% 226.54/38.95    (8)  op(e0, e0) = e2
% 226.54/38.95    (9)   ~ (all_52_15 = e2)
% 226.54/38.95  
% 226.54/38.95  Begin of proof
% 226.54/38.95  | 
% 226.54/38.95  | ALPHA: (3) implies:
% 226.54/38.95  |   (10)  op(e2, e0) = e0
% 226.54/38.95  | 
% 226.54/38.95  | BETA: splitting (6) gives:
% 226.54/38.95  | 
% 226.54/38.95  | Case 1:
% 226.54/38.95  | | 
% 226.54/38.95  | |   (11)  all_57_15 = e0 & op(e0, e0) = e0
% 226.54/38.95  | | 
% 226.54/38.95  | | REF_CLOSE: (4), (5), (11) are inconsistent by sub-proof #85.
% 226.54/38.95  | | 
% 226.54/38.95  | Case 2:
% 226.54/38.95  | | 
% 226.54/38.95  | | 
% 226.54/38.95  | | GROUND_INST: instantiating (1) with all_52_15, e0, e0, e2, simplifying with
% 226.54/38.95  | |              (2), (10) gives:
% 226.54/38.95  | |   (12)  all_52_15 = e0
% 226.54/38.95  | | 
% 226.54/38.95  | | REDUCE: (9), (12) imply:
% 226.54/38.95  | |   (13)   ~ (e2 = e0)
% 226.54/38.95  | | 
% 226.54/38.95  | | REDUCE: (7), (12) imply:
% 226.54/38.95  | |   (14)  op(e0, e0) = e0
% 226.54/38.95  | | 
% 226.54/38.95  | | REF_CLOSE: (1), (4), (8), (14) are inconsistent by sub-proof #86.
% 226.54/38.95  | | 
% 226.54/38.95  | End of split
% 226.54/38.95  | 
% 226.54/38.95  End of proof
% 226.54/38.95  
% 226.54/38.95  Sub-proof #85 shows that the following formulas are inconsistent:
% 226.54/38.95  ----------------------------------------------------------------
% 226.54/38.95    (1)  all_57_15 = e0 & op(e0, e0) = e0
% 226.54/38.95    (2)  all_57_15 = e2
% 226.54/38.95    (3)   ~ (e2 = e0)
% 226.54/38.95  
% 226.54/38.95  Begin of proof
% 226.54/38.95  | 
% 226.54/38.95  | ALPHA: (1) implies:
% 226.54/38.95  |   (4)  all_57_15 = e0
% 226.54/38.95  | 
% 226.54/38.95  | COMBINE_EQS: (2), (4) imply:
% 226.54/38.95  |   (5)  e2 = e0
% 226.54/38.95  | 
% 226.54/38.95  | REDUCE: (3), (5) imply:
% 226.54/38.95  |   (6)  $false
% 226.54/38.95  | 
% 226.54/38.95  | CLOSE: (6) is inconsistent.
% 226.54/38.95  | 
% 226.54/38.95  End of proof
% 226.54/38.95  
% 226.54/38.95  Sub-proof #86 shows that the following formulas are inconsistent:
% 226.54/38.95  ----------------------------------------------------------------
% 226.54/38.95    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.54/38.95           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.54/38.95    (2)  op(e0, e0) = e2
% 226.54/38.95    (3)  op(e0, e0) = e0
% 226.54/38.95    (4)   ~ (e2 = e0)
% 226.54/38.95  
% 226.54/38.95  Begin of proof
% 226.54/38.95  | 
% 226.54/38.95  | GROUND_INST: instantiating (1) with e2, e0, e0, e0, simplifying with (2), (3)
% 226.54/38.95  |              gives:
% 226.54/38.95  |   (5)  e2 = e0
% 226.54/38.95  | 
% 226.54/38.95  | REDUCE: (4), (5) imply:
% 226.54/38.95  |   (6)  $false
% 226.54/38.95  | 
% 226.54/38.95  | CLOSE: (6) is inconsistent.
% 226.54/38.95  | 
% 226.54/38.95  End of proof
% 226.54/38.95  
% 226.54/38.95  Sub-proof #87 shows that the following formulas are inconsistent:
% 226.54/38.95  ----------------------------------------------------------------
% 226.54/38.95    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.54/38.95           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.54/38.95    (2)   ~ (e3 = e2)
% 226.54/38.95    (3)  op(e1, e0) = all_53_14
% 226.54/38.95    (4)   ~ (all_53_14 = e3)
% 226.54/38.95    (5)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 226.54/38.95    (6)  all_57_15 = e2
% 226.54/38.95  
% 226.54/38.95  Begin of proof
% 226.54/38.95  | 
% 226.54/38.95  | BETA: splitting (5) gives:
% 226.54/38.95  | 
% 226.54/38.95  | Case 1:
% 226.54/38.95  | | 
% 226.54/38.95  | |   (7)  all_57_11 = e3 & op(e1, e0) = e3
% 226.54/38.95  | | 
% 226.54/38.95  | | ALPHA: (7) implies:
% 226.54/38.95  | |   (8)  op(e1, e0) = e3
% 226.54/38.95  | | 
% 226.54/38.95  | | REF_CLOSE: (1), (3), (4), (8) are inconsistent by sub-proof #2330.
% 226.54/38.95  | | 
% 226.54/38.95  | Case 2:
% 226.54/38.95  | | 
% 226.54/38.95  | |   (9)  all_57_15 = e3 & op(e0, e0) = e3
% 226.54/38.95  | | 
% 226.54/38.95  | | ALPHA: (9) implies:
% 226.54/38.95  | |   (10)  all_57_15 = e3
% 226.54/38.95  | | 
% 226.54/38.95  | | COMBINE_EQS: (6), (10) imply:
% 226.54/38.95  | |   (11)  e3 = e2
% 226.54/38.95  | | 
% 226.54/38.95  | | REDUCE: (2), (11) imply:
% 226.54/38.95  | |   (12)  $false
% 226.54/38.95  | | 
% 226.54/38.95  | | CLOSE: (12) is inconsistent.
% 226.54/38.95  | | 
% 226.54/38.95  | End of split
% 226.54/38.95  | 
% 226.54/38.95  End of proof
% 226.54/38.95  
% 226.54/38.95  Sub-proof #88 shows that the following formulas are inconsistent:
% 226.54/38.95  ----------------------------------------------------------------
% 226.54/38.95    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.54/38.95           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.54/38.95    (2)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 226.54/38.95    (3)  op(e1, e0) = all_53_14
% 226.54/38.95    (4)   ~ (all_53_14 = e1)
% 226.54/38.95    (5)   ~ (e2 = e1)
% 226.54/38.95    (6)  op(e0, e0) = e2
% 226.54/38.95  
% 226.54/38.95  Begin of proof
% 226.54/38.95  | 
% 226.54/38.95  | BETA: splitting (2) gives:
% 226.54/38.95  | 
% 226.54/38.95  | Case 1:
% 226.54/38.95  | | 
% 226.54/38.95  | |   (7)  all_57_11 = e1 & op(e1, e0) = e1
% 226.54/38.95  | | 
% 226.54/38.95  | | REF_CLOSE: (1), (3), (4), (7) are inconsistent by sub-proof #305.
% 226.54/38.95  | | 
% 226.54/38.95  | Case 2:
% 226.54/38.95  | | 
% 226.54/38.95  | |   (8)  all_57_15 = e1 & op(e0, e0) = e1
% 226.54/38.95  | | 
% 226.54/38.95  | | ALPHA: (8) implies:
% 226.54/38.95  | |   (9)  op(e0, e0) = e1
% 226.54/38.95  | | 
% 226.54/38.95  | | REF_CLOSE: (1), (5), (6), (9) are inconsistent by sub-proof #2177.
% 226.54/38.95  | | 
% 226.54/38.95  | End of split
% 226.54/38.95  | 
% 226.54/38.95  End of proof
% 226.54/38.95  
% 226.54/38.95  Sub-proof #89 shows that the following formulas are inconsistent:
% 226.54/38.95  ----------------------------------------------------------------
% 226.54/38.95    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.54/38.95           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.54/38.95    (2)  all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 226.54/38.95    (3)  all_55_7 = all_52_15
% 226.54/38.95    (4)  op(e1, e1) = e1
% 226.54/38.95    (5)  op(all_52_15, all_52_15) = e0
% 226.54/38.95    (6)   ~ (all_52_15 = e0)
% 226.54/38.95    (7)   ~ (all_52_15 = e2)
% 226.54/38.95  
% 226.54/38.95  Begin of proof
% 226.54/38.95  | 
% 226.54/38.95  | BETA: splitting (2) gives:
% 226.54/38.95  | 
% 226.54/38.95  | Case 1:
% 226.54/38.95  | | 
% 226.54/38.95  | |   (8)  all_55_7 = e2
% 226.54/38.95  | | 
% 226.54/38.95  | | REF_CLOSE: (3), (7), (8) are inconsistent by sub-proof #2278.
% 226.54/38.95  | | 
% 226.54/38.95  | Case 2:
% 226.54/38.95  | | 
% 226.54/38.95  | |   (9)  all_55_7 = e1 | all_55_7 = e0
% 226.54/38.95  | | 
% 226.54/38.95  | | BETA: splitting (9) gives:
% 226.54/38.95  | | 
% 226.54/38.95  | | Case 1:
% 226.54/38.95  | | | 
% 226.54/38.95  | | |   (10)  all_55_7 = e1
% 226.54/38.95  | | | 
% 226.54/38.95  | | | COMBINE_EQS: (3), (10) imply:
% 226.54/38.95  | | |   (11)  all_52_15 = e1
% 226.54/38.95  | | | 
% 226.54/38.95  | | | SIMP: (11) implies:
% 226.54/38.95  | | |   (12)  all_52_15 = e1
% 226.54/38.95  | | | 
% 226.54/38.95  | | | REDUCE: (6), (12) imply:
% 226.54/38.95  | | |   (13)   ~ (e1 = e0)
% 226.54/38.95  | | | 
% 226.54/38.95  | | | REDUCE: (5), (12) imply:
% 226.54/38.95  | | |   (14)  op(e1, e1) = e0
% 226.54/38.95  | | | 
% 226.54/38.95  | | | REF_CLOSE: (1), (4), (13), (14) are inconsistent by sub-proof #2427.
% 226.54/38.95  | | | 
% 226.54/38.95  | | Case 2:
% 226.54/38.95  | | | 
% 226.54/38.95  | | |   (15)  all_55_7 = e0
% 226.54/38.95  | | | 
% 226.54/38.95  | | | REF_CLOSE: (3), (6), (15) are inconsistent by sub-proof #2276.
% 226.54/38.95  | | | 
% 226.54/38.95  | | End of split
% 226.54/38.95  | | 
% 226.54/38.95  | End of split
% 226.54/38.95  | 
% 226.54/38.95  End of proof
% 226.54/38.95  
% 226.54/38.95  Sub-proof #90 shows that the following formulas are inconsistent:
% 226.54/38.95  ----------------------------------------------------------------
% 226.54/38.95    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.54/38.95           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.54/38.95    (2)  op(e3, e1) = e2
% 226.54/38.95    (3)  op(e2, e2) = e2
% 226.54/38.95    (4)   ~ (e2 = e1)
% 226.54/38.95    (5)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 226.54/38.95         op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 226.54/38.95           all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3) = all_52_1 &
% 226.54/38.95         op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 226.54/38.95         $i(all_52_1) & $i(all_52_3) & $i(all_52_5) & $i(all_52_7)
% 226.54/38.95  
% 226.54/38.95  Begin of proof
% 226.54/38.95  | 
% 226.54/38.95  | ALPHA: (5) implies:
% 226.54/38.95  |   (6)  op(e3, e1) = all_52_5
% 226.54/38.95  |   (7)  op(all_52_5, all_52_5) = e1
% 226.54/38.95  | 
% 226.54/38.95  | GROUND_INST: instantiating (1) with e2, all_52_5, e1, e3, simplifying with
% 226.54/38.95  |              (2), (6) gives:
% 226.54/38.95  |   (8)  all_52_5 = e2
% 226.54/38.95  | 
% 226.54/38.95  | REDUCE: (7), (8) imply:
% 226.54/38.95  |   (9)  op(e2, e2) = e1
% 226.54/38.95  | 
% 226.54/38.95  | REF_CLOSE: (1), (3), (4), (9) are inconsistent by sub-proof #2306.
% 226.54/38.95  | 
% 226.54/38.95  End of proof
% 226.54/38.95  
% 226.54/38.95  Sub-proof #91 shows that the following formulas are inconsistent:
% 226.54/38.95  ----------------------------------------------------------------
% 226.54/38.95    (1)  all_57_11 = e2 & op(e1, e0) = e2
% 226.54/38.95    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.54/38.95           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.54/38.95    (3)  op(e1, e0) = all_53_14
% 226.54/38.95    (4)   ~ (all_53_14 = e2)
% 226.54/38.95  
% 226.54/38.95  Begin of proof
% 226.54/38.95  | 
% 226.54/38.95  | ALPHA: (1) implies:
% 226.54/38.95  |   (5)  op(e1, e0) = e2
% 226.54/38.95  | 
% 226.54/38.95  | GROUND_INST: instantiating (2) with all_53_14, e2, e0, e1, simplifying with
% 226.54/38.95  |              (3), (5) gives:
% 226.54/38.95  |   (6)  all_53_14 = e2
% 226.54/38.95  | 
% 226.54/38.95  | REDUCE: (4), (6) imply:
% 226.54/38.95  |   (7)  $false
% 226.54/38.95  | 
% 226.54/38.95  | CLOSE: (7) is inconsistent.
% 226.54/38.95  | 
% 226.54/38.95  End of proof
% 226.54/38.95  
% 226.54/38.95  Sub-proof #92 shows that the following formulas are inconsistent:
% 226.54/38.95  ----------------------------------------------------------------
% 226.54/38.95    (1)  op(e0, e0) = all_4_2
% 226.54/38.95    (2)  all_57_15 = e0
% 226.54/38.95    (3)   ~ (e3 = e1)
% 226.54/38.95    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.54/38.95           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.54/38.95    (5)   ~ (e3 = e2)
% 226.54/38.95    (6)   ~ (e3 = e0)
% 226.54/38.95    (7)   ~ (all_4_2 = e2)
% 226.54/38.95    (8)  op(e0, e3) = all_53_3
% 226.54/38.95    (9)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 226.54/38.95         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 226.54/38.95    (10)  op(e3, e0) = e3
% 226.54/38.95    (11)  all_57_11 = e0
% 226.54/38.95    (12)   ~ (e2 = e0)
% 226.54/38.95    (13)   ~ (e1 = e0)
% 226.54/38.95    (14)   ~ (all_53_12 = e1)
% 226.54/38.95    (15)  all_57_14 = e1
% 226.54/38.95    (16)  op(e0, e0) = e0
% 226.54/38.95    (17)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 226.54/38.95          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 226.54/38.95            e3)
% 226.54/38.95    (18)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 226.54/38.95          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 226.54/38.95            e2)
% 226.54/38.95    (19)   ~ (all_53_3 = e1)
% 226.54/38.95    (20)   ~ (e2 = e1)
% 226.54/38.95    (21)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 226.54/38.95          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 226.54/38.95    (22)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 226.54/38.95          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 226.54/38.95    (23)  op(e3, e0) = all_53_12
% 226.54/38.95  
% 226.54/38.95  Begin of proof
% 226.54/38.95  | 
% 226.54/38.95  | BETA: splitting (21) gives:
% 226.54/38.95  | 
% 226.54/38.95  | Case 1:
% 226.54/38.95  | | 
% 226.54/38.95  | |   (24)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 226.54/38.95  | |           e2)
% 226.54/38.95  | | 
% 226.54/38.95  | | BETA: splitting (24) gives:
% 226.54/38.95  | | 
% 226.54/38.95  | | Case 1:
% 226.54/38.95  | | | 
% 226.54/38.95  | | |   (25)  all_57_9 = e2 & op(e3, e0) = e2
% 226.54/38.95  | | | 
% 226.54/38.95  | | | REF_CLOSE: (4), (5), (10), (25) are inconsistent by sub-proof #306.
% 226.54/38.95  | | | 
% 226.54/38.95  | | Case 2:
% 226.54/38.95  | | | 
% 226.54/38.95  | | |   (26)  all_57_10 = e2 & op(e2, e0) = e2
% 226.54/38.95  | | | 
% 226.54/38.95  | | | ALPHA: (26) implies:
% 226.54/38.95  | | |   (27)  all_57_10 = e2
% 226.54/38.95  | | | 
% 226.54/38.95  | | | BETA: splitting (22) gives:
% 226.54/38.95  | | | 
% 226.54/38.95  | | | Case 1:
% 226.54/38.95  | | | | 
% 226.54/38.95  | | | |   (28)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0)
% 226.54/38.95  | | | |           = e1)
% 226.54/38.95  | | | | 
% 226.54/38.95  | | | | BETA: splitting (28) gives:
% 226.54/38.95  | | | | 
% 226.54/38.95  | | | | Case 1:
% 226.54/38.95  | | | | | 
% 226.54/38.95  | | | | |   (29)  all_57_9 = e1 & op(e3, e0) = e1
% 226.54/38.95  | | | | | 
% 226.54/38.95  | | | | | REF_CLOSE: (4), (14), (23), (29) are inconsistent by sub-proof #2131.
% 226.54/38.95  | | | | | 
% 226.54/38.95  | | | | Case 2:
% 226.54/38.95  | | | | | 
% 226.54/38.95  | | | | |   (30)  all_57_10 = e1 & op(e2, e0) = e1
% 226.54/38.95  | | | | | 
% 226.54/38.95  | | | | | REF_CLOSE: (20), (27), (30) are inconsistent by sub-proof #2360.
% 226.54/38.95  | | | | | 
% 226.54/38.95  | | | | End of split
% 226.54/38.95  | | | | 
% 226.54/38.95  | | | Case 2:
% 226.54/38.95  | | | | 
% 226.54/38.95  | | | |   (31)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0,
% 226.54/38.95  | | | |             e0) = e1)
% 226.54/38.95  | | | | 
% 226.54/38.95  | | | | BETA: splitting (31) gives:
% 226.54/38.95  | | | | 
% 226.54/38.95  | | | | Case 1:
% 226.54/38.95  | | | | | 
% 226.54/38.95  | | | | |   (32)  all_57_11 = e1 & op(e1, e0) = e1
% 226.54/38.95  | | | | | 
% 226.54/38.95  | | | | | ALPHA: (32) implies:
% 226.54/38.95  | | | | |   (33)  all_57_11 = e1
% 226.54/38.95  | | | | | 
% 226.54/38.95  | | | | | COMBINE_EQS: (11), (33) imply:
% 226.54/38.95  | | | | |   (34)  e1 = e0
% 226.54/38.95  | | | | | 
% 226.54/38.95  | | | | | SIMP: (34) implies:
% 226.54/38.95  | | | | |   (35)  e1 = e0
% 226.54/38.95  | | | | | 
% 226.54/38.95  | | | | | COMBINE_EQS: (15), (35) imply:
% 226.54/38.95  | | | | |   (36)  all_57_14 = e0
% 226.54/38.95  | | | | | 
% 226.54/38.95  | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (9), (12), (13), (16), (17),
% 226.54/38.95  | | | | |            (18), (19), (20), (36) are inconsistent by sub-proof #320.
% 226.54/38.95  | | | | | 
% 226.54/38.95  | | | | Case 2:
% 226.54/38.95  | | | | | 
% 226.54/38.95  | | | | |   (37)  all_57_15 = e1 & op(e0, e0) = e1
% 226.54/38.95  | | | | | 
% 226.54/38.95  | | | | | ALPHA: (37) implies:
% 226.54/38.95  | | | | |   (38)  op(e0, e0) = e1
% 226.54/38.95  | | | | | 
% 226.54/38.95  | | | | | REF_CLOSE: (4), (13), (16), (38) are inconsistent by sub-proof #2290.
% 226.54/38.95  | | | | | 
% 226.54/38.95  | | | | End of split
% 226.54/38.95  | | | | 
% 226.54/38.95  | | | End of split
% 226.54/38.95  | | | 
% 226.54/38.95  | | End of split
% 226.54/38.95  | | 
% 226.54/38.95  | Case 2:
% 226.54/38.95  | | 
% 226.54/38.95  | |   (39)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 226.54/38.95  | |           e2)
% 226.54/38.95  | | 
% 226.54/38.95  | | BETA: splitting (39) gives:
% 226.54/38.95  | | 
% 226.54/38.95  | | Case 1:
% 226.54/38.95  | | | 
% 226.54/38.95  | | |   (40)  all_57_11 = e2 & op(e1, e0) = e2
% 226.54/38.95  | | | 
% 226.54/38.95  | | | REF_CLOSE: (11), (12), (40) are inconsistent by sub-proof #1988.
% 226.54/38.95  | | | 
% 226.54/38.95  | | Case 2:
% 226.54/38.95  | | | 
% 226.54/38.95  | | |   (41)  all_57_15 = e2 & op(e0, e0) = e2
% 226.54/38.95  | | | 
% 226.54/38.95  | | | ALPHA: (41) implies:
% 226.54/38.95  | | |   (42)  op(e0, e0) = e2
% 226.54/38.95  | | | 
% 226.54/38.95  | | | REF_CLOSE: (1), (4), (7), (42) are inconsistent by sub-proof #2334.
% 226.54/38.95  | | | 
% 226.54/38.95  | | End of split
% 226.54/38.95  | | 
% 226.54/38.95  | End of split
% 226.54/38.96  | 
% 226.54/38.96  End of proof
% 226.54/38.96  
% 226.54/38.96  Sub-proof #93 shows that the following formulas are inconsistent:
% 226.54/38.96  ----------------------------------------------------------------
% 226.54/38.96    (1)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2)
% 226.54/38.96    (2)  all_57_7 = e1
% 226.54/38.96    (3)  all_57_6 = e0
% 226.54/38.96    (4)   ~ (e2 = e0)
% 226.54/38.96    (5)   ~ (e2 = e1)
% 226.54/38.96  
% 226.54/38.96  Begin of proof
% 226.54/38.96  | 
% 226.54/38.96  | BETA: splitting (1) gives:
% 226.54/38.96  | 
% 226.54/38.96  | Case 1:
% 226.54/38.96  | | 
% 226.54/38.96  | |   (6)  all_57_6 = e2 & op(e1, e3) = e2
% 226.54/38.96  | | 
% 226.54/38.96  | | ALPHA: (6) implies:
% 226.54/38.96  | |   (7)  all_57_6 = e2
% 226.54/38.96  | | 
% 226.54/38.96  | | REF_CLOSE: (3), (4), (7) are inconsistent by sub-proof #1846.
% 226.54/38.96  | | 
% 226.54/38.96  | Case 2:
% 226.54/38.96  | | 
% 226.54/38.96  | |   (8)  all_57_7 = e2 & op(e1, e2) = e2
% 226.54/38.96  | | 
% 226.54/38.96  | | ALPHA: (8) implies:
% 226.54/38.96  | |   (9)  all_57_7 = e2
% 226.54/38.96  | | 
% 226.54/38.96  | | REF_CLOSE: (2), (5), (9) are inconsistent by sub-proof #1761.
% 226.54/38.96  | | 
% 226.54/38.96  | End of split
% 226.54/38.96  | 
% 226.54/38.96  End of proof
% 226.54/38.96  
% 226.54/38.96  Sub-proof #94 shows that the following formulas are inconsistent:
% 226.54/38.96  ----------------------------------------------------------------
% 226.54/38.96    (1)   ~ (e3 = e1)
% 226.54/38.96    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.54/38.96           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.54/38.96    (3)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 226.54/38.96           op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 226.54/38.96           op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 226.54/38.96           = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3, e0)
% 226.54/38.96           = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) & $i(all_52_7))
% 226.54/38.96         | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0 &
% 226.54/38.96           op(all_52_9, all_52_9) = e3 & op(all_52_11, all_52_11) = e2 &
% 226.54/38.96           op(all_52_13, all_52_13) = e1 & op(all_52_15, all_52_15) = e0 & op(e2,
% 226.54/38.96             e3) = all_52_9 & op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13 &
% 226.54/38.96           op(e2, e0) = all_52_15 & $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 226.54/38.96           $i(all_52_15))
% 226.54/38.96    (4)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 226.54/38.96         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 226.54/38.96    (5)   ~ (e3 = e2)
% 226.54/38.96    (6)   ~ (e3 = e0)
% 226.54/38.96    (7)  op(e3, e3) = e3
% 226.54/38.96    (8)  op(e3, e2) = all_53_4
% 226.54/38.96    (9)  op(e2, e2) = e3
% 226.54/38.96    (10)  op(e3, e1) = all_53_8
% 226.54/38.96    (11)   ~ (all_53_4 = e3)
% 226.54/38.96    (12)  op(e3, e0) = all_53_12
% 226.54/38.96  
% 226.54/38.96  Begin of proof
% 226.54/38.96  | 
% 226.54/38.96  | BETA: splitting (3) gives:
% 226.54/38.96  | 
% 226.54/38.96  | Case 1:
% 226.54/38.96  | | 
% 226.54/38.96  | |   (13)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 226.54/38.96  | |         op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 226.54/38.96  | |         op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3,
% 226.54/38.96  | |           e3) = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 &
% 226.54/38.96  | |         op(e3, e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 226.54/38.96  | |         $i(all_52_7)
% 226.54/38.96  | | 
% 226.54/38.96  | | ALPHA: (13) implies:
% 226.54/38.96  | |   (14)  op(e3, e0) = all_52_7
% 226.54/38.96  | |   (15)  op(e3, e1) = all_52_5
% 226.54/38.96  | |   (16)  op(e3, e2) = all_52_3
% 226.54/38.96  | |   (17)  op(e3, e3) = all_52_1
% 226.54/38.96  | |   (18)  op(all_52_7, all_52_7) = e0
% 226.54/38.96  | |   (19)  op(all_52_5, all_52_5) = e1
% 226.54/38.96  | |   (20)  op(all_52_3, all_52_3) = e2
% 226.54/38.96  | | 
% 226.54/38.96  | | GROUND_INST: instantiating (2) with all_53_12, all_52_7, e0, e3, simplifying
% 226.54/38.96  | |              with (12), (14) gives:
% 226.54/38.96  | |   (21)  all_53_12 = all_52_7
% 226.54/38.96  | | 
% 226.54/38.96  | | GROUND_INST: instantiating (2) with all_53_8, all_52_5, e1, e3, simplifying
% 226.54/38.96  | |              with (10), (15) gives:
% 226.54/38.96  | |   (22)  all_53_8 = all_52_5
% 226.54/38.96  | | 
% 226.54/38.96  | | GROUND_INST: instantiating (2) with all_53_4, all_52_3, e2, e3, simplifying
% 226.54/38.96  | |              with (8), (16) gives:
% 226.54/38.96  | |   (23)  all_53_4 = all_52_3
% 226.54/38.96  | | 
% 226.54/38.96  | | GROUND_INST: instantiating (2) with e3, all_52_1, e3, e3, simplifying with
% 226.54/38.96  | |              (7), (17) gives:
% 226.54/38.96  | |   (24)  all_52_1 = e3
% 226.54/38.96  | | 
% 226.54/38.96  | | REDUCE: (11), (23) imply:
% 226.54/38.96  | |   (25)   ~ (all_52_3 = e3)
% 226.54/38.96  | | 
% 226.54/38.96  | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (9), (14), (15), (16), (18), (19),
% 226.54/38.96  | |            (20), (25) are inconsistent by sub-proof #95.
% 226.54/38.96  | | 
% 226.54/38.96  | Case 2:
% 226.54/38.96  | | 
% 226.54/38.96  | |   (26)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0 &
% 226.54/38.96  | |         op(all_52_9, all_52_9) = e3 & op(all_52_11, all_52_11) = e2 &
% 226.54/38.96  | |         op(all_52_13, all_52_13) = e1 & op(all_52_15, all_52_15) = e0 &
% 226.54/38.96  | |         op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 & op(e2, e1) =
% 226.54/38.96  | |         all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) & $i(all_52_11) &
% 226.54/38.96  | |         $i(all_52_13) & $i(all_52_15)
% 226.54/38.96  | | 
% 226.54/38.96  | | REF_CLOSE: (2), (5), (7), (9), (26) are inconsistent by sub-proof #255.
% 226.54/38.96  | | 
% 226.54/38.96  | End of split
% 226.54/38.96  | 
% 226.54/38.96  End of proof
% 226.54/38.96  
% 226.54/38.96  Sub-proof #95 shows that the following formulas are inconsistent:
% 226.54/38.96  ----------------------------------------------------------------
% 226.54/38.96    (1)  op(e3, e1) = all_52_5
% 226.54/38.96    (2)   ~ (e3 = e1)
% 226.54/38.96    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.54/38.96           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.54/38.96    (4)  op(all_52_5, all_52_5) = e1
% 226.54/38.96    (5)  op(all_52_7, all_52_7) = e0
% 226.54/38.96    (6)  op(e3, e2) = all_52_3
% 226.54/38.96    (7)  op(all_52_3, all_52_3) = e2
% 226.54/38.96    (8)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 226.54/38.96         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 226.54/38.96    (9)   ~ (e3 = e2)
% 226.54/38.96    (10)   ~ (e3 = e0)
% 226.54/38.96    (11)  op(e3, e3) = e3
% 226.54/38.96    (12)   ~ (all_52_3 = e3)
% 226.54/38.96    (13)  op(e2, e2) = e3
% 226.54/38.96    (14)  op(e3, e0) = all_52_7
% 226.54/38.96  
% 226.54/38.96  Begin of proof
% 226.54/38.96  | 
% 226.54/38.96  | BETA: splitting (8) gives:
% 226.54/38.96  | 
% 226.54/38.96  | Case 1:
% 226.54/38.96  | | 
% 226.54/38.96  | |   (15)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) =
% 226.54/38.96  | |           e2)
% 226.54/38.96  | | 
% 226.54/38.96  | | BETA: splitting (15) gives:
% 226.54/38.96  | | 
% 226.54/38.96  | | Case 1:
% 226.54/38.96  | | | 
% 226.54/38.96  | | |   (16)  all_57_0 = e2 & op(e3, e3) = e2
% 226.54/38.96  | | | 
% 226.54/38.96  | | | ALPHA: (16) implies:
% 226.54/38.96  | | |   (17)  op(e3, e3) = e2
% 226.54/38.96  | | | 
% 226.54/38.96  | | | REF_CLOSE: (3), (9), (11), (17) are inconsistent by sub-proof #2490.
% 226.54/38.96  | | | 
% 226.54/38.96  | | Case 2:
% 226.54/38.96  | | | 
% 226.54/38.96  | | |   (18)  all_57_1 = e2 & op(e3, e2) = e2
% 226.54/38.96  | | | 
% 226.54/38.96  | | | ALPHA: (18) implies:
% 226.54/38.96  | | |   (19)  op(e3, e2) = e2
% 226.54/38.96  | | | 
% 226.54/38.96  | | | GROUND_INST: instantiating (3) with all_52_3, e2, e2, e3, simplifying with
% 226.54/38.96  | | |              (6), (19) gives:
% 226.54/38.96  | | |   (20)  all_52_3 = e2
% 226.54/38.96  | | | 
% 226.54/38.96  | | | REDUCE: (12), (20) imply:
% 226.54/38.96  | | |   (21)   ~ (e3 = e2)
% 226.54/38.96  | | | 
% 226.54/38.96  | | | REDUCE: (7), (20) imply:
% 226.54/38.96  | | |   (22)  op(e2, e2) = e2
% 226.54/38.96  | | | 
% 226.54/38.96  | | | REF_CLOSE: (3), (9), (13), (22) are inconsistent by sub-proof #2298.
% 226.54/38.96  | | | 
% 226.54/38.96  | | End of split
% 226.54/38.96  | | 
% 226.54/38.96  | Case 2:
% 226.54/38.96  | | 
% 226.54/38.96  | |   (23)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) =
% 226.54/38.96  | |           e2)
% 226.54/38.96  | | 
% 226.54/38.96  | | BETA: splitting (23) gives:
% 226.54/38.96  | | 
% 226.54/38.96  | | Case 1:
% 226.54/38.96  | | | 
% 226.54/38.96  | | |   (24)  all_57_4 = e2 & op(e3, e1) = e2
% 226.54/38.96  | | | 
% 226.54/38.96  | | | ALPHA: (24) implies:
% 226.54/38.96  | | |   (25)  op(e3, e1) = e2
% 226.54/38.96  | | | 
% 226.54/38.96  | | | GROUND_INST: instantiating (3) with all_52_5, e2, e1, e3, simplifying with
% 226.54/38.96  | | |              (1), (25) gives:
% 226.54/38.96  | | |   (26)  all_52_5 = e2
% 226.54/38.96  | | | 
% 226.54/38.96  | | | REDUCE: (4), (26) imply:
% 226.54/38.96  | | |   (27)  op(e2, e2) = e1
% 226.54/38.96  | | | 
% 226.54/38.96  | | | REF_CLOSE: (2), (3), (13), (27) are inconsistent by sub-proof #1912.
% 226.54/38.96  | | | 
% 226.54/38.96  | | Case 2:
% 226.54/38.96  | | | 
% 226.54/38.96  | | |   (28)  all_57_9 = e2 & op(e3, e0) = e2
% 226.54/38.96  | | | 
% 226.54/38.96  | | | ALPHA: (28) implies:
% 226.54/38.96  | | |   (29)  op(e3, e0) = e2
% 226.54/38.96  | | | 
% 226.54/38.96  | | | GROUND_INST: instantiating (3) with all_52_7, e2, e0, e3, simplifying with
% 226.54/38.96  | | |              (14), (29) gives:
% 226.54/38.96  | | |   (30)  all_52_7 = e2
% 226.54/38.96  | | | 
% 226.54/38.96  | | | REDUCE: (5), (30) imply:
% 226.54/38.96  | | |   (31)  op(e2, e2) = e0
% 226.54/38.96  | | | 
% 226.54/38.96  | | | GROUND_INST: instantiating (3) with e3, e0, e2, e2, simplifying with (13),
% 226.54/38.96  | | |              (31) gives:
% 226.54/38.96  | | |   (32)  e3 = e0
% 226.54/38.96  | | | 
% 226.54/38.96  | | | REDUCE: (10), (32) imply:
% 226.54/38.96  | | |   (33)  $false
% 226.54/38.96  | | | 
% 226.54/38.96  | | | CLOSE: (33) is inconsistent.
% 226.54/38.96  | | | 
% 226.54/38.96  | | End of split
% 226.54/38.96  | | 
% 226.54/38.96  | End of split
% 226.54/38.96  | 
% 226.54/38.96  End of proof
% 226.54/38.96  
% 226.54/38.96  Sub-proof #96 shows that the following formulas are inconsistent:
% 226.54/38.96  ----------------------------------------------------------------
% 226.54/38.96    (1)  op(e3, e3) = all_10_2
% 226.54/38.96    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.54/38.96           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.54/38.96    (3)  op(e0, e3) = all_52_25
% 226.54/38.96    (4)  op(e0, e3) = e3
% 226.54/38.96    (5)  op(all_52_25, all_52_25) = e3
% 226.54/38.96    (6)   ~ (all_10_2 = e3)
% 226.54/38.96  
% 226.54/38.96  Begin of proof
% 226.54/38.96  | 
% 226.54/38.96  | GROUND_INST: instantiating (2) with e3, all_52_25, e3, e0, simplifying with
% 226.54/38.96  |              (3), (4) gives:
% 226.54/38.96  |   (7)  all_52_25 = e3
% 226.54/38.96  | 
% 226.54/38.96  | REDUCE: (5), (7) imply:
% 226.54/38.96  |   (8)  op(e3, e3) = e3
% 226.54/38.96  | 
% 226.54/38.96  | GROUND_INST: instantiating (2) with all_10_2, e3, e3, e3, simplifying with
% 226.54/38.96  |              (1), (8) gives:
% 226.54/38.96  |   (9)  all_10_2 = e3
% 226.54/38.96  | 
% 226.54/38.96  | REDUCE: (6), (9) imply:
% 226.54/38.96  |   (10)  $false
% 226.54/38.96  | 
% 226.54/38.96  | CLOSE: (10) is inconsistent.
% 226.54/38.96  | 
% 226.54/38.96  End of proof
% 226.54/38.96  
% 226.54/38.96  Sub-proof #97 shows that the following formulas are inconsistent:
% 226.54/38.96  ----------------------------------------------------------------
% 226.54/38.96    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 226.54/38.96         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 226.54/38.96    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 226.54/38.96         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 226.54/38.96    (3)   ~ (e3 = e1)
% 226.54/38.96    (4)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 226.54/38.96         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 226.54/38.96    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.54/38.96           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.54/38.96    (6)  all_57_3 = e3
% 226.54/38.96    (7)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 226.54/38.96         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 226.54/38.96    (8)  op(e2, e0) = all_52_15
% 226.54/38.96    (9)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 226.54/38.96         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 226.54/38.96    (10)   ~ (e3 = e2)
% 226.54/38.96    (11)  op(e1, e0) = all_53_14
% 226.54/38.96    (12)   ~ (e3 = e0)
% 226.54/38.96    (13)  op(e2, e2) = all_52_11
% 226.54/38.96    (14)  op(e3, e3) = e2
% 226.54/38.96    (15)  op(e3, e0) = e3
% 226.54/38.96    (16)   ~ (e2 = e0)
% 226.54/38.96    (17)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 226.54/38.96          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 226.54/38.96    (18)   ~ (e1 = e0)
% 226.54/38.96    (19)  all_57_12 = e3
% 226.54/38.96    (20)  all_57_8 = e3
% 226.54/38.96    (21)   ~ (all_53_14 = e1)
% 226.54/38.96    (22)  op(e0, e0) = e1
% 226.54/38.96    (23)  all_57_13 = e0
% 226.54/38.96    (24)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 226.54/38.96          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 226.54/38.96    (25)  op(all_52_15, all_52_15) = e0
% 226.54/38.96    (26)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 226.54/38.96          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 226.54/38.96    (27)  op(e2, e2) = e3
% 226.54/38.96    (28)   ~ (e2 = e1)
% 226.54/38.96    (29)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 226.54/38.96          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 226.54/38.96    (30)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 226.54/38.96          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 226.54/38.96    (31)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 226.54/38.96          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 226.54/38.96  
% 226.54/38.96  Begin of proof
% 226.54/38.96  | 
% 226.54/38.96  | BETA: splitting (2) gives:
% 226.54/38.96  | 
% 226.54/38.96  | Case 1:
% 226.54/38.96  | | 
% 226.54/38.96  | |   (32)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 226.54/38.96  | |           e2)
% 226.54/38.96  | | 
% 226.54/38.96  | | REF_CLOSE: (3), (5), (7), (9), (10), (12), (14), (16), (17), (18), (27),
% 226.54/38.96  | |            (28), (32) are inconsistent by sub-proof #104.
% 226.54/38.96  | | 
% 226.54/38.96  | Case 2:
% 226.54/38.96  | | 
% 226.54/38.96  | |   (33)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 226.54/38.96  | |           e2)
% 226.54/38.96  | | 
% 226.54/38.96  | | BETA: splitting (33) gives:
% 226.54/38.96  | | 
% 226.54/38.96  | | Case 1:
% 226.54/38.96  | | | 
% 226.54/38.96  | | |   (34)  all_57_7 = e2 & op(e1, e2) = e2
% 226.54/38.96  | | | 
% 226.54/38.96  | | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (10), (11), (12), (13), (14),
% 226.54/38.96  | | |            (15), (16), (18), (19), (20), (21), (22), (24), (25), (26),
% 226.54/38.96  | | |            (27), (28), (29), (30), (31), (34) are inconsistent by
% 226.54/38.96  | | |            sub-proof #98.
% 226.54/38.96  | | | 
% 226.54/38.96  | | Case 2:
% 226.54/38.96  | | | 
% 226.54/38.96  | | |   (35)  all_57_13 = e2 & op(e0, e2) = e2
% 226.54/38.96  | | | 
% 226.54/38.96  | | | REF_CLOSE: (16), (23), (35) are inconsistent by sub-proof #2316.
% 226.54/38.96  | | | 
% 226.54/38.96  | | End of split
% 226.54/38.96  | | 
% 226.54/38.96  | End of split
% 226.54/38.96  | 
% 226.54/38.96  End of proof
% 226.54/38.96  
% 226.54/38.96  Sub-proof #98 shows that the following formulas are inconsistent:
% 226.54/38.96  ----------------------------------------------------------------
% 226.54/38.96    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 226.54/38.96         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 226.54/38.96    (2)   ~ (e3 = e1)
% 226.54/38.96    (3)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 226.54/38.96         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 226.54/38.96    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.54/38.96           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.54/38.96    (5)  all_57_3 = e3
% 226.54/38.96    (6)  op(e2, e0) = all_52_15
% 226.54/38.96    (7)   ~ (e3 = e2)
% 226.54/38.96    (8)  op(e1, e0) = all_53_14
% 226.54/38.96    (9)   ~ (e3 = e0)
% 226.54/38.96    (10)  op(e2, e2) = all_52_11
% 226.54/38.96    (11)  op(e3, e3) = e2
% 226.54/38.96    (12)  op(e3, e0) = e3
% 226.54/38.96    (13)   ~ (e2 = e0)
% 226.54/38.96    (14)   ~ (e1 = e0)
% 226.54/38.96    (15)  all_57_12 = e3
% 226.54/38.96    (16)  all_57_8 = e3
% 226.54/38.96    (17)   ~ (all_53_14 = e1)
% 226.54/38.96    (18)  all_57_7 = e2 & op(e1, e2) = e2
% 226.54/38.96    (19)  op(e0, e0) = e1
% 226.54/38.96    (20)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 226.54/38.96          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 226.54/38.96    (21)  op(all_52_15, all_52_15) = e0
% 226.54/38.96    (22)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 226.54/38.96          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 226.54/38.96    (23)  op(e2, e2) = e3
% 226.54/38.96    (24)   ~ (e2 = e1)
% 226.54/38.96    (25)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 226.54/38.96          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 226.54/38.96    (26)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 226.54/38.96          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 226.54/38.96    (27)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 226.54/38.96          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 226.54/38.96  
% 226.54/38.96  Begin of proof
% 226.54/38.96  | 
% 226.54/38.96  | ALPHA: (18) implies:
% 226.54/38.96  |   (28)  all_57_7 = e2
% 226.54/38.96  | 
% 226.54/38.96  | BETA: splitting (27) gives:
% 226.54/38.96  | 
% 226.54/38.96  | Case 1:
% 226.54/38.96  | | 
% 226.54/38.96  | |   (29)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) =
% 226.54/38.96  | |           e1)
% 226.54/38.96  | | 
% 226.54/38.96  | | BETA: splitting (29) gives:
% 226.54/38.96  | | 
% 226.54/38.96  | | Case 1:
% 226.54/38.96  | | | 
% 226.54/38.96  | | |   (30)  all_57_6 = e1 & op(e1, e3) = e1
% 226.54/38.96  | | | 
% 226.54/38.96  | | | ALPHA: (30) implies:
% 226.54/38.96  | | |   (31)  all_57_6 = e1
% 226.54/38.96  | | | 
% 226.54/38.96  | | | BETA: splitting (3) gives:
% 226.54/38.96  | | | 
% 226.54/38.96  | | | Case 1:
% 226.54/38.96  | | | | 
% 226.54/38.96  | | | |   (32)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2)
% 226.54/38.96  | | | |           = e0)
% 226.54/38.96  | | | | 
% 226.54/38.96  | | | | BETA: splitting (32) gives:
% 226.54/38.96  | | | | 
% 226.54/38.96  | | | | Case 1:
% 226.54/38.96  | | | | | 
% 226.54/38.96  | | | | |   (33)  all_57_6 = e0 & op(e1, e3) = e0
% 226.54/38.96  | | | | | 
% 226.54/38.96  | | | | | REF_CLOSE: (14), (31), (33) are inconsistent by sub-proof #2347.
% 226.54/38.96  | | | | | 
% 226.54/38.96  | | | | Case 2:
% 226.54/38.96  | | | | | 
% 226.54/38.96  | | | | |   (34)  all_57_7 = e0 & op(e1, e2) = e0
% 226.54/38.96  | | | | | 
% 226.54/38.96  | | | | | REF_CLOSE: (13), (28), (34) are inconsistent by sub-proof #2148.
% 226.54/38.96  | | | | | 
% 226.54/38.96  | | | | End of split
% 226.54/38.96  | | | | 
% 226.54/38.96  | | | Case 2:
% 226.54/38.96  | | | | 
% 226.54/38.96  | | | |   (35)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0)
% 226.54/38.96  | | | |           = e0)
% 226.54/38.96  | | | | 
% 226.54/38.96  | | | | BETA: splitting (35) gives:
% 226.54/38.96  | | | | 
% 226.54/38.96  | | | | Case 1:
% 226.54/38.96  | | | | | 
% 226.54/38.96  | | | | |   (36)  all_57_8 = e0 & op(e1, e1) = e0
% 226.54/38.96  | | | | | 
% 226.54/38.96  | | | | | REF_CLOSE: (1), (2), (4), (5), (7), (9), (11), (13), (14), (15), (16),
% 226.54/38.96  | | | | |            (20), (22), (24), (26), (31), (36) are inconsistent by
% 226.54/38.96  | | | | |            sub-proof #102.
% 226.54/38.96  | | | | | 
% 226.54/38.96  | | | | Case 2:
% 226.54/38.96  | | | | | 
% 226.54/38.96  | | | | |   (37)  all_57_11 = e0 & op(e1, e0) = e0
% 226.54/38.96  | | | | | 
% 226.54/38.96  | | | | | ALPHA: (37) implies:
% 226.54/38.96  | | | | |   (38)  all_57_11 = e0
% 226.54/38.96  | | | | | 
% 226.54/38.96  | | | | | REF_CLOSE: (4), (6), (7), (9), (10), (12), (13), (19), (21), (23),
% 226.54/38.96  | | | | |            (24), (25), (38) are inconsistent by sub-proof #99.
% 226.54/38.96  | | | | | 
% 226.54/38.96  | | | | End of split
% 226.54/38.96  | | | | 
% 226.54/38.96  | | | End of split
% 226.54/38.96  | | | 
% 226.54/38.96  | | Case 2:
% 226.54/38.96  | | | 
% 226.54/38.96  | | |   (39)  all_57_7 = e1 & op(e1, e2) = e1
% 226.54/38.96  | | | 
% 226.54/38.96  | | | REF_CLOSE: (24), (28), (39) are inconsistent by sub-proof #2190.
% 226.54/38.96  | | | 
% 226.54/38.96  | | End of split
% 226.54/38.96  | | 
% 226.54/38.96  | Case 2:
% 226.54/38.96  | | 
% 226.54/38.96  | |   (40)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) =
% 226.54/38.96  | |           e1)
% 226.54/38.96  | | 
% 226.54/38.96  | | BETA: splitting (40) gives:
% 226.54/38.96  | | 
% 226.54/38.96  | | Case 1:
% 226.54/38.96  | | | 
% 226.54/38.96  | | |   (41)  all_57_8 = e1 & op(e1, e1) = e1
% 226.54/38.96  | | | 
% 226.54/38.96  | | | REF_CLOSE: (2), (16), (41) are inconsistent by sub-proof #169.
% 226.54/38.96  | | | 
% 226.54/38.96  | | Case 2:
% 226.54/38.96  | | | 
% 226.54/38.96  | | |   (42)  all_57_11 = e1 & op(e1, e0) = e1
% 226.54/38.96  | | | 
% 226.54/38.96  | | | REF_CLOSE: (4), (8), (17), (42) are inconsistent by sub-proof #305.
% 226.54/38.96  | | | 
% 226.54/38.96  | | End of split
% 226.54/38.96  | | 
% 226.54/38.96  | End of split
% 226.54/38.96  | 
% 226.54/38.96  End of proof
% 226.54/38.96  
% 226.54/38.96  Sub-proof #99 shows that the following formulas are inconsistent:
% 226.54/38.96  ----------------------------------------------------------------
% 226.54/38.96    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.54/38.96           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.54/38.96    (2)  op(e2, e0) = all_52_15
% 226.54/38.96    (3)   ~ (e3 = e2)
% 226.54/38.96    (4)   ~ (e3 = e0)
% 226.54/38.96    (5)  op(e2, e2) = all_52_11
% 226.54/38.96    (6)  op(e3, e0) = e3
% 226.54/38.96    (7)  all_57_11 = e0
% 226.54/38.96    (8)   ~ (e2 = e0)
% 226.54/38.96    (9)  op(e0, e0) = e1
% 226.54/38.96    (10)  op(all_52_15, all_52_15) = e0
% 226.54/38.97    (11)  op(e2, e2) = e3
% 226.54/38.97    (12)   ~ (e2 = e1)
% 226.54/38.97    (13)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 226.54/38.97          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 226.54/38.97  
% 226.54/38.97  Begin of proof
% 226.54/38.97  | 
% 226.54/38.97  | BETA: splitting (13) gives:
% 226.54/38.97  | 
% 226.54/38.97  | Case 1:
% 226.54/38.97  | | 
% 226.54/38.97  | |   (14)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 226.54/38.97  | |           e2)
% 226.54/38.97  | | 
% 226.54/38.97  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (10), (11), (14) are inconsistent
% 226.54/38.97  | |            by sub-proof #108.
% 226.54/38.97  | | 
% 226.54/38.97  | Case 2:
% 226.54/38.97  | | 
% 226.54/38.97  | |   (15)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 226.54/38.97  | |           e2)
% 226.54/38.97  | | 
% 226.54/38.97  | | BETA: splitting (15) gives:
% 226.54/38.97  | | 
% 226.54/38.97  | | Case 1:
% 226.54/38.97  | | | 
% 226.54/38.97  | | |   (16)  all_57_11 = e2 & op(e1, e0) = e2
% 226.54/38.97  | | | 
% 226.54/38.97  | | | ALPHA: (16) implies:
% 226.54/38.97  | | |   (17)  all_57_11 = e2
% 226.54/38.97  | | | 
% 226.54/38.97  | | | REF_CLOSE: (7), (8), (17) are inconsistent by sub-proof #1949.
% 226.54/38.97  | | | 
% 226.54/38.97  | | Case 2:
% 226.54/38.97  | | | 
% 226.54/38.97  | | |   (18)  all_57_15 = e2 & op(e0, e0) = e2
% 226.54/38.97  | | | 
% 226.54/38.97  | | | ALPHA: (18) implies:
% 226.54/38.97  | | |   (19)  op(e0, e0) = e2
% 226.54/38.97  | | | 
% 226.54/38.97  | | | REF_CLOSE: (1), (9), (12), (19) are inconsistent by sub-proof #2177.
% 226.54/38.97  | | | 
% 226.54/38.97  | | End of split
% 226.54/38.97  | | 
% 226.54/38.97  | End of split
% 226.54/38.97  | 
% 226.54/38.97  End of proof
% 226.54/38.97  
% 226.54/38.97  Sub-proof #100 shows that the following formulas are inconsistent:
% 226.54/38.97  ----------------------------------------------------------------
% 226.54/38.97    (1)  op(e0, e0) = all_4_2
% 226.54/38.97    (2)   ~ (e3 = e1)
% 226.54/38.97    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.54/38.97           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.54/38.97    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 226.54/38.97         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 226.54/38.97    (5)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 226.54/38.97         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 226.54/38.97    (6)   ~ (e3 = e2)
% 226.54/38.97    (7)   ~ (e3 = e0)
% 226.54/38.97    (8)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 226.54/38.97         (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 226.54/38.97    (9)   ~ (all_4_2 = e2)
% 226.54/38.97    (10)  op(e3, e3) = e2
% 226.54/38.97    (11)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 226.54/38.97          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 226.54/38.97            e1)
% 226.54/38.97    (12)   ~ (e2 = e0)
% 226.54/38.97    (13)  all_57_9 = e3
% 226.54/38.97    (14)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 226.54/38.97          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 226.54/38.97    (15)   ~ (e1 = e0)
% 226.54/38.97    (16)  all_57_12 = e3
% 226.54/38.97    (17)  all_57_8 = e3
% 226.54/38.97    (18)  op(e0, e0) = e0
% 226.54/38.97    (19)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 226.54/38.97          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 226.54/38.97            e3)
% 226.54/38.97    (20)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 226.54/38.97          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 226.54/38.97            e2)
% 226.54/38.97    (21)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 226.54/38.97              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 226.54/38.97                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 226.54/38.97                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 226.54/38.97    (22)   ~ (e2 = e1)
% 226.54/38.97    (23)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 226.54/38.97          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 226.54/38.97    (24)  all_57_14 = e0
% 226.54/38.97  
% 226.54/38.97  Begin of proof
% 226.54/38.97  | 
% 226.54/38.97  | BETA: splitting (20) gives:
% 226.54/38.97  | 
% 226.54/38.97  | Case 1:
% 226.54/38.97  | | 
% 226.54/38.97  | |   (25)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 226.54/38.97  | |           e2)
% 226.54/38.97  | | 
% 226.54/38.97  | | BETA: splitting (25) gives:
% 226.54/38.97  | | 
% 226.54/38.97  | | Case 1:
% 226.54/38.97  | | | 
% 226.54/38.97  | | |   (26)  all_57_12 = e2 & op(e0, e3) = e2
% 226.54/38.97  | | | 
% 226.54/38.97  | | | REF_CLOSE: (6), (16), (26) are inconsistent by sub-proof #2232.
% 226.54/38.97  | | | 
% 226.54/38.97  | | Case 2:
% 226.54/38.97  | | | 
% 226.54/38.97  | | |   (27)  all_57_13 = e2 & op(e0, e2) = e2
% 226.54/38.97  | | | 
% 226.54/38.97  | | | ALPHA: (27) implies:
% 226.54/38.97  | | |   (28)  all_57_13 = e2
% 226.54/38.97  | | | 
% 226.54/38.97  | | | BETA: splitting (23) gives:
% 226.54/38.97  | | | 
% 226.54/38.97  | | | Case 1:
% 226.54/38.97  | | | | 
% 226.54/38.97  | | | |   (29)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1)
% 226.54/38.97  | | | |           = e2)
% 226.54/38.97  | | | | 
% 226.54/38.97  | | | | BETA: splitting (29) gives:
% 226.54/38.97  | | | | 
% 226.54/38.97  | | | | Case 1:
% 226.54/38.97  | | | | | 
% 226.54/38.97  | | | | |   (30)  all_57_4 = e2 & op(e3, e1) = e2
% 226.54/38.97  | | | | | 
% 226.54/38.97  | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (10), (12), (14), (15), (22),
% 226.54/38.97  | | | | |            (30) are inconsistent by sub-proof #226.
% 226.54/38.97  | | | | | 
% 226.54/38.97  | | | | Case 2:
% 226.54/38.97  | | | | | 
% 226.54/38.97  | | | | |   (31)  all_57_5 = e2 & op(e2, e1) = e2
% 226.54/38.97  | | | | | 
% 226.54/38.97  | | | | | ALPHA: (31) implies:
% 226.54/38.97  | | | | |   (32)  all_57_5 = e2
% 226.54/38.97  | | | | | 
% 226.54/38.97  | | | | | BETA: splitting (8) gives:
% 226.54/38.97  | | | | | 
% 226.54/38.97  | | | | | Case 1:
% 226.54/38.97  | | | | | | 
% 226.54/38.97  | | | | | |   (33)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2,
% 226.54/38.97  | | | | | |             e1) = e1)
% 226.54/38.97  | | | | | | 
% 226.54/38.97  | | | | | | BETA: splitting (33) gives:
% 226.54/38.97  | | | | | | 
% 226.54/38.97  | | | | | | Case 1:
% 226.54/38.97  | | | | | | | 
% 226.54/38.97  | | | | | | |   (34)  all_57_4 = e1 & op(e3, e1) = e1
% 226.54/38.97  | | | | | | | 
% 226.54/38.97  | | | | | | | ALPHA: (34) implies:
% 226.54/38.97  | | | | | | |   (35)  all_57_4 = e1
% 226.54/38.97  | | | | | | | 
% 226.54/38.97  | | | | | | | BETA: splitting (11) gives:
% 226.54/38.97  | | | | | | | 
% 226.54/38.97  | | | | | | | Case 1:
% 226.54/38.97  | | | | | | | | 
% 226.54/38.97  | | | | | | | |   (36)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 &
% 226.54/38.97  | | | | | | | |           op(e0, e2) = e1)
% 226.54/38.97  | | | | | | | | 
% 226.54/38.97  | | | | | | | | BETA: splitting (36) gives:
% 226.54/38.97  | | | | | | | | 
% 226.54/38.97  | | | | | | | | Case 1:
% 226.54/38.97  | | | | | | | | | 
% 226.54/38.97  | | | | | | | | |   (37)  all_57_12 = e1 & op(e0, e3) = e1
% 226.54/38.97  | | | | | | | | | 
% 226.54/38.97  | | | | | | | | | ALPHA: (37) implies:
% 226.54/38.97  | | | | | | | | |   (38)  all_57_12 = e1
% 226.54/38.97  | | | | | | | | | 
% 226.54/38.97  | | | | | | | | | COMBINE_EQS: (16), (38) imply:
% 226.54/38.97  | | | | | | | | |   (39)  e3 = e1
% 226.54/38.97  | | | | | | | | | 
% 226.54/38.97  | | | | | | | | | COMBINE_EQS: (13), (39) imply:
% 226.54/38.97  | | | | | | | | |   (40)  all_57_9 = e1
% 226.54/38.97  | | | | | | | | | 
% 226.54/38.97  | | | | | | | | | REF_CLOSE: (2), (3), (5), (6), (7), (10), (12), (14), (15),
% 226.54/38.97  | | | | | | | | |            (35), (40) are inconsistent by sub-proof #1672.
% 226.54/38.97  | | | | | | | | | 
% 226.54/38.97  | | | | | | | | Case 2:
% 226.54/38.97  | | | | | | | | | 
% 226.54/38.97  | | | | | | | | |   (41)  all_57_13 = e1 & op(e0, e2) = e1
% 226.54/38.97  | | | | | | | | | 
% 226.54/38.97  | | | | | | | | | ALPHA: (41) implies:
% 226.54/38.97  | | | | | | | | |   (42)  all_57_13 = e1
% 226.54/38.97  | | | | | | | | | 
% 226.54/38.97  | | | | | | | | | REF_CLOSE: (1), (3), (6), (9), (12), (16), (20), (22), (24),
% 226.54/38.97  | | | | | | | | |            (42) are inconsistent by sub-proof #179.
% 226.54/38.97  | | | | | | | | | 
% 226.54/38.97  | | | | | | | | End of split
% 226.54/38.97  | | | | | | | | 
% 226.54/38.97  | | | | | | | Case 2:
% 226.54/38.97  | | | | | | | | 
% 226.54/38.97  | | | | | | | |   (43)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 &
% 226.54/38.97  | | | | | | | |           op(e0, e0) = e1)
% 226.54/38.97  | | | | | | | | 
% 226.54/38.97  | | | | | | | | REF_CLOSE: (3), (15), (18), (24), (43) are inconsistent by
% 226.54/38.97  | | | | | | | |            sub-proof #2121.
% 226.54/38.97  | | | | | | | | 
% 226.54/38.97  | | | | | | | End of split
% 226.54/38.97  | | | | | | | 
% 226.54/38.97  | | | | | | Case 2:
% 226.54/38.97  | | | | | | | 
% 226.54/38.97  | | | | | | |   (44)  all_57_5 = e1 & op(e2, e1) = e1
% 226.54/38.97  | | | | | | | 
% 226.54/38.97  | | | | | | | ALPHA: (44) implies:
% 226.54/38.97  | | | | | | |   (45)  all_57_5 = e1
% 226.54/38.97  | | | | | | | 
% 226.54/38.97  | | | | | | | COMBINE_EQS: (32), (45) imply:
% 226.54/38.97  | | | | | | |   (46)  e2 = e1
% 226.54/38.97  | | | | | | | 
% 226.54/38.97  | | | | | | | COMBINE_EQS: (28), (46) imply:
% 226.54/38.97  | | | | | | |   (47)  all_57_13 = e1
% 226.54/38.97  | | | | | | | 
% 226.54/38.97  | | | | | | | REF_CLOSE: (1), (3), (6), (9), (12), (16), (20), (22), (24), (47)
% 226.54/38.97  | | | | | | |            are inconsistent by sub-proof #179.
% 226.54/38.97  | | | | | | | 
% 226.54/38.97  | | | | | | End of split
% 226.54/38.97  | | | | | | 
% 226.54/38.97  | | | | | Case 2:
% 226.54/38.97  | | | | | | 
% 226.54/38.97  | | | | | |   (48)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0,
% 226.54/38.97  | | | | | |             e1) = e1)
% 226.54/38.97  | | | | | | 
% 226.54/38.97  | | | | | | REF_CLOSE: (2), (15), (17), (24), (48) are inconsistent by sub-proof
% 226.54/38.97  | | | | | |            #101.
% 226.54/38.97  | | | | | | 
% 226.54/38.97  | | | | | End of split
% 226.54/38.97  | | | | | 
% 226.54/38.97  | | | | End of split
% 226.54/38.97  | | | | 
% 226.54/38.97  | | | Case 2:
% 226.54/38.97  | | | | 
% 226.54/38.97  | | | |   (49)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1)
% 226.54/38.97  | | | |           = e2)
% 226.54/38.97  | | | | 
% 226.54/38.97  | | | | BETA: splitting (49) gives:
% 226.54/38.97  | | | | 
% 226.54/38.97  | | | | Case 1:
% 226.54/38.97  | | | | | 
% 226.54/38.97  | | | | |   (50)  all_57_8 = e2 & op(e1, e1) = e2
% 226.54/38.97  | | | | | 
% 226.54/38.97  | | | | | REF_CLOSE: (6), (17), (50) are inconsistent by sub-proof #165.
% 226.54/38.97  | | | | | 
% 226.54/38.97  | | | | Case 2:
% 226.54/38.97  | | | | | 
% 226.54/38.97  | | | | |   (51)  all_57_14 = e2 & op(e0, e1) = e2
% 226.54/38.97  | | | | | 
% 226.54/38.97  | | | | | ALPHA: (51) implies:
% 226.54/38.97  | | | | |   (52)  all_57_14 = e2
% 226.54/38.97  | | | | | 
% 226.54/38.97  | | | | | REF_CLOSE: (2), (3), (6), (7), (11), (12), (15), (18), (19), (21),
% 226.54/38.97  | | | | |            (22), (28), (52) are inconsistent by sub-proof #1581.
% 226.54/38.97  | | | | | 
% 226.54/38.97  | | | | End of split
% 226.54/38.97  | | | | 
% 226.54/38.97  | | | End of split
% 226.54/38.97  | | | 
% 226.54/38.97  | | End of split
% 226.54/38.97  | | 
% 226.54/38.97  | Case 2:
% 226.54/38.97  | | 
% 226.54/38.97  | |   (53)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 226.54/38.97  | |           e2)
% 226.54/38.97  | | 
% 226.54/38.97  | | REF_CLOSE: (1), (3), (9), (12), (24), (53) are inconsistent by sub-proof
% 226.54/38.97  | |            #180.
% 226.54/38.97  | | 
% 226.54/38.97  | End of split
% 226.54/38.97  | 
% 226.54/38.97  End of proof
% 226.54/38.97  
% 226.54/38.97  Sub-proof #101 shows that the following formulas are inconsistent:
% 226.54/38.97  ----------------------------------------------------------------
% 226.54/38.97    (1)   ~ (e3 = e1)
% 226.54/38.97    (2)   ~ (e1 = e0)
% 226.54/38.97    (3)  all_57_8 = e3
% 226.54/38.97    (4)  all_57_14 = e0
% 226.54/38.97    (5)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 226.54/38.97  
% 226.54/38.97  Begin of proof
% 226.54/38.97  | 
% 226.54/38.97  | BETA: splitting (5) gives:
% 226.54/38.97  | 
% 226.54/38.97  | Case 1:
% 226.54/38.97  | | 
% 226.54/38.97  | |   (6)  all_57_8 = e1 & op(e1, e1) = e1
% 226.54/38.97  | | 
% 226.54/38.97  | | REF_CLOSE: (1), (3), (6) are inconsistent by sub-proof #169.
% 226.54/38.97  | | 
% 226.54/38.97  | Case 2:
% 226.54/38.97  | | 
% 226.54/38.97  | |   (7)  all_57_14 = e1 & op(e0, e1) = e1
% 226.54/38.97  | | 
% 226.54/38.97  | | ALPHA: (7) implies:
% 226.54/38.97  | |   (8)  all_57_14 = e1
% 226.54/38.97  | | 
% 226.54/38.97  | | REF_CLOSE: (2), (4), (8) are inconsistent by sub-proof #2122.
% 226.54/38.97  | | 
% 226.54/38.97  | End of split
% 226.54/38.97  | 
% 226.54/38.97  End of proof
% 226.54/38.97  
% 226.54/38.97  Sub-proof #102 shows that the following formulas are inconsistent:
% 226.54/38.97  ----------------------------------------------------------------
% 226.54/38.97    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 226.54/38.97         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 226.54/38.97    (2)   ~ (e3 = e1)
% 226.54/38.97    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.54/38.97           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.54/38.97    (4)  all_57_3 = e3
% 226.54/38.97    (5)  all_57_8 = e0 & op(e1, e1) = e0
% 226.54/38.97    (6)  all_57_6 = e1
% 226.54/38.97    (7)   ~ (e3 = e2)
% 226.54/38.97    (8)   ~ (e3 = e0)
% 226.54/38.97    (9)  op(e3, e3) = e2
% 226.54/38.97    (10)   ~ (e2 = e0)
% 226.54/38.97    (11)   ~ (e1 = e0)
% 226.54/38.97    (12)  all_57_12 = e3
% 226.54/38.97    (13)  all_57_8 = e3
% 226.54/38.97    (14)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 226.54/38.97          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 226.54/38.97    (15)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 226.54/38.97          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 226.54/38.97    (16)   ~ (e2 = e1)
% 226.54/38.97    (17)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 226.54/38.97          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 226.54/38.97  
% 226.54/38.97  Begin of proof
% 226.54/38.97  | 
% 226.54/38.97  | ALPHA: (5) implies:
% 226.54/38.97  |   (18)  all_57_8 = e0
% 226.54/38.97  | 
% 226.54/38.97  | COMBINE_EQS: (13), (18) imply:
% 226.54/38.97  |   (19)  e3 = e0
% 226.54/38.97  | 
% 226.54/38.97  | SIMP: (19) implies:
% 226.54/38.97  |   (20)  e3 = e0
% 226.54/38.97  | 
% 226.54/38.97  | COMBINE_EQS: (4), (20) imply:
% 226.54/38.97  |   (21)  all_57_3 = e0
% 226.54/38.97  | 
% 226.54/38.97  | REF_CLOSE: (1), (2), (3), (6), (7), (8), (9), (10), (11), (12), (14), (15),
% 226.54/38.97  |            (16), (17), (21) are inconsistent by sub-proof #1632.
% 226.54/38.97  | 
% 226.54/38.97  End of proof
% 226.54/38.97  
% 226.54/38.97  Sub-proof #103 shows that the following formulas are inconsistent:
% 226.54/38.97  ----------------------------------------------------------------
% 226.54/38.97    (1)   ~ (e3 = e1)
% 226.54/38.97    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.54/38.97           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.54/38.97    (3)  all_57_6 = e1
% 226.54/38.97    (4)   ~ (e3 = e2)
% 226.54/38.97    (5)   ~ (e3 = e0)
% 226.54/38.97    (6)  op(e3, e3) = e2
% 226.54/38.97    (7)  all_57_12 = e1
% 226.54/38.97    (8)  all_57_2 = e0
% 226.54/38.97    (9)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 226.54/38.97         (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 226.54/38.97  
% 226.54/38.97  Begin of proof
% 226.54/38.97  | 
% 226.54/38.97  | BETA: splitting (9) gives:
% 226.54/38.97  | 
% 226.54/38.97  | Case 1:
% 226.54/38.97  | | 
% 226.54/38.97  | |   (10)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) =
% 226.54/38.97  | |           e3)
% 226.54/38.97  | | 
% 226.54/38.97  | | BETA: splitting (10) gives:
% 226.54/38.97  | | 
% 226.54/38.97  | | Case 1:
% 226.54/38.97  | | | 
% 226.54/38.97  | | |   (11)  all_57_0 = e3 & op(e3, e3) = e3
% 226.54/38.97  | | | 
% 226.54/38.97  | | | ALPHA: (11) implies:
% 226.54/38.97  | | |   (12)  op(e3, e3) = e3
% 226.54/38.97  | | | 
% 226.54/38.97  | | | REF_CLOSE: (2), (4), (6), (12) are inconsistent by sub-proof #2490.
% 226.54/38.97  | | | 
% 226.54/38.97  | | Case 2:
% 226.54/38.97  | | | 
% 226.54/38.97  | | |   (13)  all_57_2 = e3 & op(e2, e3) = e3
% 226.54/38.97  | | | 
% 226.54/38.97  | | | ALPHA: (13) implies:
% 226.54/38.97  | | |   (14)  all_57_2 = e3
% 226.54/38.97  | | | 
% 226.54/38.97  | | | REF_CLOSE: (5), (8), (14) are inconsistent by sub-proof #2258.
% 226.54/38.97  | | | 
% 226.54/38.97  | | End of split
% 226.54/38.97  | | 
% 226.54/38.97  | Case 2:
% 226.54/38.97  | | 
% 226.54/38.97  | |   (15)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) =
% 226.54/38.97  | |           e3)
% 226.54/38.97  | | 
% 226.54/38.97  | | REF_CLOSE: (1), (3), (7), (15) are inconsistent by sub-proof #1206.
% 226.54/38.97  | | 
% 226.54/38.97  | End of split
% 226.54/38.97  | 
% 226.54/38.97  End of proof
% 226.54/38.97  
% 226.54/38.97  Sub-proof #104 shows that the following formulas are inconsistent:
% 226.54/38.97  ----------------------------------------------------------------
% 226.54/38.97    (1)   ~ (e3 = e1)
% 226.54/38.97    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.54/38.97           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.54/38.97    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 226.54/38.97         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 226.54/38.97    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2)
% 226.54/38.97    (5)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 226.54/38.97         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 226.54/38.97    (6)   ~ (e3 = e2)
% 226.54/38.97    (7)   ~ (e3 = e0)
% 226.54/38.97    (8)  op(e3, e3) = e2
% 226.54/38.97    (9)   ~ (e2 = e0)
% 226.54/38.97    (10)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 226.54/38.97          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 226.54/38.97    (11)   ~ (e1 = e0)
% 226.54/38.97    (12)  op(e2, e2) = e3
% 226.54/38.97    (13)   ~ (e2 = e1)
% 226.54/38.97  
% 226.54/38.97  Begin of proof
% 226.54/38.97  | 
% 226.54/38.97  | BETA: splitting (4) gives:
% 226.54/38.97  | 
% 226.54/38.97  | Case 1:
% 226.54/38.97  | | 
% 226.54/38.97  | |   (14)  all_57_1 = e2 & op(e3, e2) = e2
% 226.54/38.97  | | 
% 226.54/38.97  | | ALPHA: (14) implies:
% 226.54/38.97  | |   (15)  all_57_1 = e2
% 226.54/38.97  | | 
% 226.54/38.97  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (13), (15)
% 226.54/38.97  | |            are inconsistent by sub-proof #1655.
% 226.54/38.97  | | 
% 226.54/38.97  | Case 2:
% 226.54/38.97  | | 
% 226.54/38.97  | |   (16)  all_57_3 = e2 & op(e2, e2) = e2
% 226.54/38.97  | | 
% 226.54/38.97  | | ALPHA: (16) implies:
% 226.54/38.97  | |   (17)  op(e2, e2) = e2
% 226.54/38.97  | | 
% 226.54/38.97  | | REF_CLOSE: (2), (6), (12), (17) are inconsistent by sub-proof #2298.
% 226.54/38.97  | | 
% 226.54/38.97  | End of split
% 226.54/38.97  | 
% 226.54/38.97  End of proof
% 226.54/38.97  
% 226.54/38.97  Sub-proof #105 shows that the following formulas are inconsistent:
% 226.54/38.97  ----------------------------------------------------------------
% 226.54/38.97    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.54/38.97           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.54/38.97    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1)
% 226.54/38.97    (3)  op(e3, e3) = e2
% 226.54/38.97    (4)   ~ (e1 = e0)
% 226.54/38.97    (5)  all_57_2 = e0
% 226.54/38.97    (6)   ~ (e2 = e1)
% 226.54/38.97  
% 226.54/38.97  Begin of proof
% 226.54/38.97  | 
% 226.54/38.97  | BETA: splitting (2) gives:
% 226.54/38.97  | 
% 226.54/38.97  | Case 1:
% 226.54/38.97  | | 
% 226.54/38.97  | |   (7)  all_57_0 = e1 & op(e3, e3) = e1
% 226.54/38.97  | | 
% 226.54/38.97  | | ALPHA: (7) implies:
% 226.54/38.97  | |   (8)  op(e3, e3) = e1
% 226.54/38.97  | | 
% 226.54/38.97  | | REF_CLOSE: (1), (3), (6), (8) are inconsistent by sub-proof #1950.
% 226.54/38.97  | | 
% 226.54/38.97  | Case 2:
% 226.54/38.97  | | 
% 226.54/38.97  | |   (9)  all_57_2 = e1 & op(e2, e3) = e1
% 226.54/38.97  | | 
% 226.54/38.97  | | ALPHA: (9) implies:
% 226.54/38.97  | |   (10)  all_57_2 = e1
% 226.54/38.97  | | 
% 226.54/38.97  | | REF_CLOSE: (4), (5), (10) are inconsistent by sub-proof #2473.
% 226.54/38.97  | | 
% 226.54/38.97  | End of split
% 226.54/38.97  | 
% 226.54/38.97  End of proof
% 226.54/38.97  
% 226.54/38.97  Sub-proof #106 shows that the following formulas are inconsistent:
% 226.54/38.97  ----------------------------------------------------------------
% 226.54/38.97    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 226.54/38.97         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 226.54/38.97    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 226.54/38.97         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 226.54/38.97    (3)   ~ (e3 = e1)
% 226.54/38.97    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.54/38.97           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.54/38.97    (5)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2)
% 226.54/38.97    (6)  all_57_3 = e3
% 226.54/38.97    (7)   ~ (e3 = e2)
% 226.54/38.97    (8)   ~ (e3 = e0)
% 226.54/38.97    (9)  op(e3, e3) = e2
% 226.54/38.97    (10)   ~ (e2 = e0)
% 226.54/38.97    (11)   ~ (e1 = e0)
% 226.54/38.97    (12)  all_57_12 = e3
% 226.54/38.97    (13)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 226.54/38.97          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 226.54/38.97    (14)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 226.54/38.97          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 226.54/38.97    (15)  op(e2, e2) = e3
% 226.54/38.97    (16)   ~ (e2 = e1)
% 226.54/38.97    (17)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 226.54/38.97          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 226.54/38.97  
% 226.54/38.97  Begin of proof
% 226.54/38.97  | 
% 226.54/38.97  | BETA: splitting (5) gives:
% 226.54/38.97  | 
% 226.54/38.97  | Case 1:
% 226.54/38.97  | | 
% 226.54/38.97  | |   (18)  all_57_2 = e2 & op(e2, e3) = e2
% 226.54/38.97  | | 
% 226.54/38.97  | | ALPHA: (18) implies:
% 226.54/38.97  | |   (19)  all_57_2 = e2
% 226.54/38.97  | | 
% 226.54/38.97  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13),
% 226.54/38.97  | |            (14), (16), (17), (19) are inconsistent by sub-proof #107.
% 226.54/38.97  | | 
% 226.54/38.97  | Case 2:
% 226.54/38.97  | | 
% 226.54/38.97  | |   (20)  all_57_3 = e2 & op(e2, e2) = e2
% 226.54/38.97  | | 
% 226.54/38.97  | | ALPHA: (20) implies:
% 226.54/38.97  | |   (21)  op(e2, e2) = e2
% 226.54/38.97  | | 
% 226.54/38.97  | | REF_CLOSE: (4), (7), (15), (21) are inconsistent by sub-proof #2298.
% 226.54/38.97  | | 
% 226.54/38.97  | End of split
% 226.54/38.97  | 
% 226.54/38.97  End of proof
% 226.54/38.97  
% 226.54/38.97  Sub-proof #107 shows that the following formulas are inconsistent:
% 226.54/38.97  ----------------------------------------------------------------
% 226.54/38.97    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 226.54/38.97         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 226.54/38.97    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 226.54/38.97         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 226.54/38.97    (3)   ~ (e3 = e1)
% 226.54/38.97    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.54/38.97           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.54/38.97    (5)  all_57_3 = e3
% 226.54/38.97    (6)  all_57_2 = e2
% 226.54/38.97    (7)   ~ (e3 = e2)
% 226.54/38.97    (8)   ~ (e3 = e0)
% 226.54/38.97    (9)  op(e3, e3) = e2
% 226.54/38.97    (10)   ~ (e2 = e0)
% 226.54/38.97    (11)   ~ (e1 = e0)
% 226.54/38.97    (12)  all_57_12 = e3
% 226.54/38.97    (13)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 226.54/38.98          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 226.54/38.98    (14)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 226.54/38.98          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 226.54/38.98    (15)   ~ (e2 = e1)
% 226.54/38.98    (16)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 226.54/38.98          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 226.54/38.98  
% 226.54/38.98  Begin of proof
% 226.54/38.98  | 
% 226.54/38.98  | BETA: splitting (2) gives:
% 226.54/38.98  | 
% 226.54/38.98  | Case 1:
% 226.54/38.98  | | 
% 226.54/38.98  | |   (17)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) =
% 226.54/38.98  | |           e1)
% 226.54/38.98  | | 
% 226.54/38.98  | | REF_CLOSE: (4), (6), (9), (15), (17) are inconsistent by sub-proof #1633.
% 226.54/38.98  | | 
% 226.54/38.98  | Case 2:
% 226.54/38.98  | | 
% 226.54/38.98  | |   (18)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) =
% 226.54/38.98  | |           e1)
% 226.54/38.98  | | 
% 226.54/38.98  | | BETA: splitting (18) gives:
% 226.54/38.98  | | 
% 226.54/38.98  | | Case 1:
% 226.54/38.98  | | | 
% 226.54/38.98  | | |   (19)  all_57_6 = e1 & op(e1, e3) = e1
% 226.54/38.98  | | | 
% 226.54/38.98  | | | ALPHA: (19) implies:
% 226.54/38.98  | | |   (20)  all_57_6 = e1
% 226.54/38.98  | | | 
% 226.54/38.98  | | | BETA: splitting (16) gives:
% 226.54/38.98  | | | 
% 226.54/38.98  | | | Case 1:
% 226.54/38.98  | | | | 
% 226.54/38.98  | | | |   (21)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3)
% 226.54/38.98  | | | |           = e0)
% 226.54/38.98  | | | | 
% 226.54/38.98  | | | | REF_CLOSE: (4), (6), (9), (10), (21) are inconsistent by sub-proof
% 226.54/38.98  | | | |            #1577.
% 226.54/38.98  | | | | 
% 226.54/38.98  | | | Case 2:
% 226.54/38.98  | | | | 
% 226.54/38.98  | | | |   (22)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3)
% 226.54/38.98  | | | |           = e0)
% 226.54/38.98  | | | | 
% 226.54/38.98  | | | | BETA: splitting (22) gives:
% 226.54/38.98  | | | | 
% 226.54/38.98  | | | | Case 1:
% 226.54/38.98  | | | | | 
% 226.54/38.98  | | | | |   (23)  all_57_6 = e0 & op(e1, e3) = e0
% 226.54/38.98  | | | | | 
% 226.54/38.98  | | | | | REF_CLOSE: (11), (20), (23) are inconsistent by sub-proof #2347.
% 226.54/38.98  | | | | | 
% 226.54/38.98  | | | | Case 2:
% 226.54/38.98  | | | | | 
% 226.54/38.98  | | | | |   (24)  all_57_12 = e0 & op(e0, e3) = e0
% 226.54/38.98  | | | | | 
% 226.54/38.98  | | | | | ALPHA: (24) implies:
% 226.54/38.98  | | | | |   (25)  all_57_12 = e0
% 226.54/38.98  | | | | | 
% 226.54/38.98  | | | | | COMBINE_EQS: (12), (25) imply:
% 226.54/38.98  | | | | |   (26)  e3 = e0
% 226.54/38.98  | | | | | 
% 226.54/38.98  | | | | | SIMP: (26) implies:
% 226.54/38.98  | | | | |   (27)  e3 = e0
% 226.54/38.98  | | | | | 
% 226.54/38.98  | | | | | COMBINE_EQS: (5), (27) imply:
% 226.54/38.98  | | | | |   (28)  all_57_3 = e0
% 226.54/38.98  | | | | | 
% 226.54/38.98  | | | | | REF_CLOSE: (1), (3), (4), (7), (8), (9), (10), (11), (12), (13), (14),
% 226.54/38.98  | | | | |            (15), (16), (20), (28) are inconsistent by sub-proof #1632.
% 226.54/38.98  | | | | | 
% 226.54/38.98  | | | | End of split
% 226.54/38.98  | | | | 
% 226.54/38.98  | | | End of split
% 226.54/38.98  | | | 
% 226.54/38.98  | | Case 2:
% 226.54/38.98  | | | 
% 226.54/38.98  | | |   (29)  all_57_12 = e1 & op(e0, e3) = e1
% 226.54/38.98  | | | 
% 226.54/38.98  | | | ALPHA: (29) implies:
% 226.54/38.98  | | |   (30)  all_57_12 = e1
% 226.54/38.98  | | | 
% 226.54/38.98  | | | REF_CLOSE: (3), (12), (30) are inconsistent by sub-proof #2151.
% 226.54/38.98  | | | 
% 226.54/38.98  | | End of split
% 226.54/38.98  | | 
% 226.54/38.98  | End of split
% 226.54/38.98  | 
% 226.54/38.98  End of proof
% 226.54/38.98  
% 226.54/38.98  Sub-proof #108 shows that the following formulas are inconsistent:
% 226.54/38.98  ----------------------------------------------------------------
% 226.54/38.98    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.54/38.98           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.54/38.98    (2)  op(e2, e0) = all_52_15
% 226.54/38.98    (3)   ~ (e3 = e2)
% 226.54/38.98    (4)   ~ (e3 = e0)
% 226.54/38.98    (5)  op(e2, e2) = all_52_11
% 226.54/38.98    (6)  op(e3, e0) = e3
% 226.54/38.98    (7)  op(all_52_15, all_52_15) = e0
% 226.54/38.98    (8)  op(e2, e2) = e3
% 226.54/38.98    (9)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 226.54/38.98  
% 226.54/38.98  Begin of proof
% 226.54/38.98  | 
% 226.54/38.98  | BETA: splitting (9) gives:
% 226.54/38.98  | 
% 226.54/38.98  | Case 1:
% 226.54/38.98  | | 
% 226.54/38.98  | |   (10)  all_57_9 = e2 & op(e3, e0) = e2
% 226.54/38.98  | | 
% 226.54/38.98  | | REF_CLOSE: (1), (3), (6), (10) are inconsistent by sub-proof #306.
% 226.54/38.98  | | 
% 226.54/38.98  | Case 2:
% 226.54/38.98  | | 
% 226.54/38.98  | |   (11)  all_57_10 = e2 & op(e2, e0) = e2
% 226.54/38.98  | | 
% 226.54/38.98  | | ALPHA: (11) implies:
% 226.54/38.98  | |   (12)  op(e2, e0) = e2
% 226.54/38.98  | | 
% 226.54/38.98  | | REF_CLOSE: (1), (2), (4), (5), (7), (8), (12) are inconsistent by sub-proof
% 226.54/38.98  | |            #248.
% 226.54/38.98  | | 
% 226.54/38.98  | End of split
% 226.54/38.98  | 
% 226.54/38.98  End of proof
% 226.54/38.98  
% 226.54/38.98  Sub-proof #109 shows that the following formulas are inconsistent:
% 226.54/38.98  ----------------------------------------------------------------
% 226.54/38.98    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.54/38.98           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.54/38.98    (2)   ~ (all_53_8 = e3)
% 226.54/38.98    (3)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 226.54/38.98    (4)   ~ (all_53_12 = e3)
% 226.54/38.98    (5)  op(e3, e1) = all_53_8
% 226.54/38.98    (6)  op(e3, e0) = all_53_12
% 226.54/38.98  
% 226.54/38.98  Begin of proof
% 226.54/38.98  | 
% 226.54/38.98  | BETA: splitting (3) gives:
% 226.54/38.98  | 
% 226.54/38.98  | Case 1:
% 226.54/38.98  | | 
% 226.54/38.98  | |   (7)  all_57_4 = e3 & op(e3, e1) = e3
% 226.54/38.98  | | 
% 226.54/38.98  | | REF_CLOSE: (1), (2), (5), (7) are inconsistent by sub-proof #177.
% 226.54/38.98  | | 
% 226.54/38.98  | Case 2:
% 226.54/38.98  | | 
% 226.54/38.98  | |   (8)  all_57_9 = e3 & op(e3, e0) = e3
% 226.54/38.98  | | 
% 226.54/38.98  | | ALPHA: (8) implies:
% 226.54/38.98  | |   (9)  op(e3, e0) = e3
% 226.54/38.98  | | 
% 226.54/38.98  | | REF_CLOSE: (1), (4), (6), (9) are inconsistent by sub-proof #2458.
% 226.54/38.98  | | 
% 226.54/38.98  | End of split
% 226.54/38.98  | 
% 226.54/38.98  End of proof
% 226.54/38.98  
% 226.54/38.98  Sub-proof #110 shows that the following formulas are inconsistent:
% 226.54/38.98  ----------------------------------------------------------------
% 226.54/38.98    (1)   ~ (all_53_2 = e1)
% 226.54/38.98    (2)   ~ (e3 = e1)
% 226.54/38.98    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.54/38.98           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.54/38.98    (4)   ~ (e3 = e2)
% 226.54/38.98    (5)   ~ (e3 = e0)
% 226.54/38.98    (6)  op(e1, e1) = e3
% 226.54/38.98    (7)  op(e1, e0) = all_52_23
% 226.54/38.98    (8)  op(all_52_23, all_52_23) = e0
% 226.54/38.98    (9)  op(e1, e2) = all_52_19
% 226.54/38.98    (10)  op(e1, e3) = all_53_2
% 226.54/38.98    (11)  op(all_52_19, all_52_19) = e2
% 226.54/38.98    (12)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 226.54/38.98          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 226.54/38.98  
% 226.54/38.98  Begin of proof
% 226.54/38.98  | 
% 226.54/38.98  | BETA: splitting (12) gives:
% 226.54/38.98  | 
% 226.54/38.98  | Case 1:
% 226.54/38.98  | | 
% 226.54/38.98  | |   (13)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) =
% 226.54/38.98  | |           e1)
% 226.54/38.98  | | 
% 226.54/38.98  | | BETA: splitting (13) gives:
% 226.54/38.98  | | 
% 226.54/38.98  | | Case 1:
% 226.54/38.98  | | | 
% 226.54/38.98  | | |   (14)  all_57_6 = e1 & op(e1, e3) = e1
% 226.54/38.98  | | | 
% 226.54/38.98  | | | REF_CLOSE: (1), (3), (10), (14) are inconsistent by sub-proof #316.
% 226.54/38.98  | | | 
% 226.54/38.98  | | Case 2:
% 226.54/38.98  | | | 
% 226.54/38.98  | | |   (15)  all_57_7 = e1 & op(e1, e2) = e1
% 226.54/38.98  | | | 
% 226.54/38.98  | | | ALPHA: (15) implies:
% 226.54/38.98  | | |   (16)  op(e1, e2) = e1
% 226.54/38.98  | | | 
% 226.54/38.98  | | | REF_CLOSE: (3), (4), (6), (9), (11), (16) are inconsistent by sub-proof
% 226.54/38.98  | | |            #119.
% 226.54/38.98  | | | 
% 226.54/38.98  | | End of split
% 226.54/38.98  | | 
% 226.54/38.98  | Case 2:
% 226.54/38.98  | | 
% 226.54/38.98  | |   (17)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) =
% 226.54/38.98  | |           e1)
% 226.54/38.98  | | 
% 226.54/38.98  | | BETA: splitting (17) gives:
% 226.54/38.98  | | 
% 226.54/38.98  | | Case 1:
% 226.54/38.98  | | | 
% 226.54/38.98  | | |   (18)  all_57_8 = e1 & op(e1, e1) = e1
% 226.54/38.98  | | | 
% 226.54/38.98  | | | ALPHA: (18) implies:
% 226.54/38.98  | | |   (19)  op(e1, e1) = e1
% 226.54/38.98  | | | 
% 226.54/38.98  | | | REF_CLOSE: (2), (3), (6), (19) are inconsistent by sub-proof #156.
% 226.54/38.98  | | | 
% 226.54/38.98  | | Case 2:
% 226.54/38.98  | | | 
% 226.54/38.98  | | |   (20)  all_57_11 = e1 & op(e1, e0) = e1
% 226.54/38.98  | | | 
% 226.54/38.98  | | | ALPHA: (20) implies:
% 226.54/38.98  | | |   (21)  op(e1, e0) = e1
% 226.54/38.98  | | | 
% 226.54/38.98  | | | REF_CLOSE: (3), (5), (6), (7), (8), (21) are inconsistent by sub-proof
% 226.54/38.98  | | |            #125.
% 226.54/38.98  | | | 
% 226.54/38.98  | | End of split
% 226.54/38.98  | | 
% 226.54/38.98  | End of split
% 226.54/38.98  | 
% 226.54/38.98  End of proof
% 226.54/38.98  
% 226.54/38.98  Sub-proof #111 shows that the following formulas are inconsistent:
% 226.54/38.98  ----------------------------------------------------------------
% 226.54/38.98    (1)  op(e2, e3) = all_53_1
% 226.54/38.98    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.54/38.98           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.54/38.98    (3)   ~ (all_8_2 = e3)
% 226.54/38.98    (4)  op(e2, e2) = all_8_2
% 226.54/38.98    (5)   ~ (all_53_1 = e3)
% 226.54/38.98    (6)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3)
% 226.54/38.98  
% 226.54/38.98  Begin of proof
% 226.54/38.98  | 
% 226.54/38.98  | BETA: splitting (6) gives:
% 226.54/38.98  | 
% 226.54/38.98  | Case 1:
% 226.54/38.98  | | 
% 226.54/38.98  | |   (7)  all_57_2 = e3 & op(e2, e3) = e3
% 226.54/38.98  | | 
% 226.54/38.98  | | REF_CLOSE: (1), (2), (5), (7) are inconsistent by sub-proof #2299.
% 226.54/38.98  | | 
% 226.54/38.98  | Case 2:
% 226.54/38.98  | | 
% 226.54/38.98  | |   (8)  all_57_3 = e3 & op(e2, e2) = e3
% 226.54/38.98  | | 
% 226.54/38.98  | | ALPHA: (8) implies:
% 226.54/38.98  | |   (9)  op(e2, e2) = e3
% 226.54/38.98  | | 
% 226.54/38.98  | | REF_CLOSE: (2), (3), (4), (9) are inconsistent by sub-proof #140.
% 226.54/38.98  | | 
% 226.54/38.98  | End of split
% 226.54/38.98  | 
% 226.54/38.98  End of proof
% 226.54/38.98  
% 226.54/38.98  Sub-proof #112 shows that the following formulas are inconsistent:
% 226.54/38.98  ----------------------------------------------------------------
% 226.54/38.98    (1)  op(e3, e3) = e1
% 226.54/38.98    (2)   ~ (e3 = e1)
% 226.54/38.98    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.54/38.98           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.54/38.98    (4)  op(all_52_7, all_52_7) = e0
% 226.54/38.98    (5)   ~ (all_53_13 = e3)
% 226.54/38.98    (6)   ~ (e3 = e2)
% 226.54/38.98    (7)  op(e1, e0) = all_53_14
% 226.54/38.98    (8)   ~ (e3 = e0)
% 226.54/38.98    (9)   ~ (all_53_7 = e0)
% 226.54/38.98    (10)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 226.54/38.98          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 226.54/38.98            e1)
% 226.54/38.98    (11)  op(e3, e3) = all_52_1
% 226.54/38.98    (12)   ~ (all_53_14 = e3)
% 226.54/38.98    (13)   ~ (e2 = e0)
% 226.54/38.98    (14)   ~ (e1 = e0)
% 226.54/38.98    (15)  all_57_13 = e3
% 226.54/38.98    (16)  op(e0, e2) = all_53_7
% 226.54/38.98    (17)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 226.54/38.98          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 226.54/38.98            e2)
% 226.54/38.98    (18)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 226.54/38.98              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 226.54/38.98                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 226.54/38.98                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 226.54/38.98    (19)  op(e2, e0) = all_53_13
% 226.54/38.98    (20)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 226.54/38.98          (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 226.54/38.98    (21)   ~ (e2 = e1)
% 226.54/38.98    (22)  op(e3, e0) = all_52_7
% 226.54/38.98  
% 226.54/38.98  Begin of proof
% 226.54/38.98  | 
% 226.54/38.98  | BETA: splitting (20) gives:
% 226.54/38.98  | 
% 226.54/38.98  | Case 1:
% 226.54/38.98  | | 
% 226.54/38.98  | |   (23)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 226.54/38.98  | |           e3)
% 226.54/38.98  | | 
% 226.54/38.98  | | BETA: splitting (23) gives:
% 226.54/38.98  | | 
% 226.54/38.98  | | Case 1:
% 226.54/38.98  | | | 
% 226.54/38.98  | | |   (24)  all_57_9 = e3 & op(e3, e0) = e3
% 226.54/38.98  | | | 
% 226.54/38.98  | | | ALPHA: (24) implies:
% 226.54/38.98  | | |   (25)  op(e3, e0) = e3
% 226.54/38.98  | | | 
% 226.54/38.98  | | | REF_CLOSE: (1), (3), (4), (11), (14), (22), (25) are inconsistent by
% 226.54/38.98  | | |            sub-proof #123.
% 226.54/38.98  | | | 
% 226.54/38.98  | | Case 2:
% 226.54/38.98  | | | 
% 226.54/38.98  | | |   (26)  all_57_10 = e3 & op(e2, e0) = e3
% 226.54/38.98  | | | 
% 226.54/38.98  | | | ALPHA: (26) implies:
% 226.54/38.98  | | |   (27)  op(e2, e0) = e3
% 226.54/38.98  | | | 
% 226.54/38.98  | | | REF_CLOSE: (3), (5), (19), (27) are inconsistent by sub-proof #2301.
% 226.54/38.98  | | | 
% 226.54/38.98  | | End of split
% 226.54/38.98  | | 
% 226.54/38.98  | Case 2:
% 226.54/38.98  | | 
% 226.54/38.98  | |   (28)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 226.54/38.98  | |           e3)
% 226.54/38.98  | | 
% 226.54/38.98  | | REF_CLOSE: (2), (3), (6), (7), (8), (9), (10), (12), (13), (14), (15), (16),
% 226.54/38.98  | |            (17), (18), (21), (28) are inconsistent by sub-proof #113.
% 226.54/38.98  | | 
% 226.54/38.98  | End of split
% 226.54/38.98  | 
% 226.54/38.98  End of proof
% 226.54/38.98  
% 226.54/38.98  Sub-proof #113 shows that the following formulas are inconsistent:
% 226.54/38.98  ----------------------------------------------------------------
% 226.54/38.98    (1)   ~ (e3 = e1)
% 226.54/38.98    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.54/38.98           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.54/38.98    (3)   ~ (e3 = e2)
% 226.54/38.98    (4)  op(e1, e0) = all_53_14
% 226.54/38.98    (5)   ~ (e3 = e0)
% 226.54/38.98    (6)   ~ (all_53_7 = e0)
% 226.54/38.98    (7)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 226.54/38.98         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 226.54/38.98    (8)   ~ (all_53_14 = e3)
% 226.54/38.98    (9)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 226.54/38.98    (10)   ~ (e2 = e0)
% 226.54/38.98    (11)   ~ (e1 = e0)
% 226.54/38.98    (12)  all_57_13 = e3
% 226.54/38.98    (13)  op(e0, e2) = all_53_7
% 226.54/38.98    (14)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 226.54/38.98          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 226.54/38.98            e2)
% 226.54/38.98    (15)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 226.54/38.98              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 226.54/38.98                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 226.54/38.98                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 226.54/38.98    (16)   ~ (e2 = e1)
% 226.54/38.98  
% 226.54/38.98  Begin of proof
% 226.54/38.98  | 
% 226.54/38.98  | BETA: splitting (9) gives:
% 226.54/38.98  | 
% 226.54/38.98  | Case 1:
% 226.54/38.98  | | 
% 226.54/38.98  | |   (17)  all_57_11 = e3 & op(e1, e0) = e3
% 226.54/38.98  | | 
% 226.54/38.98  | | ALPHA: (17) implies:
% 226.54/38.98  | |   (18)  op(e1, e0) = e3
% 226.54/38.98  | | 
% 226.54/38.98  | | REF_CLOSE: (2), (4), (8), (18) are inconsistent by sub-proof #2330.
% 226.54/38.98  | | 
% 226.54/38.98  | Case 2:
% 226.54/38.98  | | 
% 226.54/38.98  | |   (19)  all_57_15 = e3 & op(e0, e0) = e3
% 226.54/38.98  | | 
% 226.54/38.98  | | ALPHA: (19) implies:
% 226.54/38.98  | |   (20)  all_57_15 = e3
% 226.54/38.98  | |   (21)  op(e0, e0) = e3
% 226.54/38.98  | | 
% 226.54/38.98  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (10), (11), (12), (13), (14), (15),
% 226.54/38.98  | |            (16), (20), (21) are inconsistent by sub-proof #366.
% 226.54/38.98  | | 
% 226.54/38.98  | End of split
% 226.54/38.98  | 
% 226.54/38.98  End of proof
% 226.54/38.98  
% 226.54/38.98  Sub-proof #114 shows that the following formulas are inconsistent:
% 226.54/38.98  ----------------------------------------------------------------
% 226.54/38.98    (1)  op(e1, e3) = e0
% 226.54/38.98    (2)  op(e3, e3) = e1
% 226.54/38.98    (3)  all_57_15 = e0
% 226.54/38.98    (4)   ~ (e3 = e1)
% 226.54/38.98    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.54/38.98           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.54/38.98    (6)   ~ (all_36_2 = e1) | ( ~ (all_36_0 = e0) & op(all_36_1, e3) = all_36_0 &
% 226.54/38.98           op(e3, e1) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 =
% 226.54/38.98             e2) & op(e3, e1) = all_36_1 & $i(all_36_1))
% 226.54/38.98    (7)   ~ (all_53_9 = e0)
% 226.54/38.98    (8)   ~ (all_53_8 = e1)
% 226.54/38.98    (9)  op(e2, e2) = e0
% 226.54/38.98    (10)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 226.54/38.98          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 226.54/38.98    (11)   ~ (e3 = e2)
% 226.54/38.98    (12)   ~ (e3 = e0)
% 226.54/38.98    (13)  op(e0, e3) = all_53_3
% 226.54/38.98    (14)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 226.54/38.98          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 226.54/38.98            e1)
% 226.54/38.98    (15)  ( ~ (all_10_0 = e2) & op(all_10_1, e3) = all_10_0 & op(e3, e1) =
% 226.54/38.98            all_10_1 & $i(all_10_0) & $i(all_10_1)) | ( ~ (all_10_1 = e0) & op(e3,
% 226.54/38.98              e1) = all_10_1 & $i(all_10_1))
% 226.54/38.98    (16)   ~ (e2 = e0)
% 226.54/38.98    (17)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 226.54/38.98            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 226.54/38.98            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 226.54/38.98            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 226.54/38.98              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 226.54/38.98            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 226.54/38.98            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 226.54/38.98              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 226.54/38.98              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 226.54/38.98            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 226.54/38.98            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 226.54/38.98            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 226.54/38.98              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 226.54/38.98              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 226.54/38.98            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 226.54/38.98              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 226.54/38.98            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 226.54/38.98            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 226.54/38.98              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 226.54/38.98              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 226.54/38.98            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 226.54/38.98            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 226.54/38.98    (18)  all_55_12 = all_53_3
% 226.54/38.98    (19)   ~ (e1 = e0)
% 226.54/38.98    (20)  all_57_8 = e3
% 226.54/38.98    (21)   ~ (all_53_2 = all_53_3)
% 226.54/38.98    (22)  op(e0, e0) = e0
% 226.54/38.98    (23)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 226.54/38.98          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 226.54/38.98            e3)
% 226.54/38.98    (24)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 226.54/38.98          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 226.54/38.98            e2)
% 226.54/38.98    (25)   ~ (all_53_3 = e1)
% 226.54/38.98    (26)  all_36_2 = e1
% 226.54/38.98    (27)  op(e1, e3) = all_53_2
% 226.54/38.98    (28)   ~ (e2 = e1)
% 226.54/38.98    (29)  op(e2, e1) = all_53_9
% 226.54/38.98    (30)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 226.54/38.98    (31)  op(e3, e1) = all_53_8
% 226.54/38.98  
% 226.54/38.98  Begin of proof
% 226.54/38.98  | 
% 226.54/38.98  | BETA: splitting (10) gives:
% 226.54/38.98  | 
% 226.54/38.98  | Case 1:
% 226.54/38.98  | | 
% 226.54/38.98  | |   (32)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) =
% 226.54/38.98  | |           e0)
% 226.54/38.98  | | 
% 226.54/38.98  | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (9), (12), (13), (15), (16), (17),
% 226.54/38.98  | |            (18), (21), (22), (25), (26), (27), (29), (30), (31), (32) are
% 226.54/38.98  | |            inconsistent by sub-proof #301.
% 226.54/38.98  | | 
% 226.54/38.98  | Case 2:
% 226.54/38.98  | | 
% 226.54/38.98  | |   (33)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 226.54/38.98  | |           e0)
% 226.54/38.98  | | 
% 226.54/38.98  | | BETA: splitting (33) gives:
% 226.54/38.98  | | 
% 226.54/38.98  | | Case 1:
% 226.54/38.98  | | | 
% 226.54/38.99  | | |   (34)  all_57_8 = e0 & op(e1, e1) = e0
% 226.54/38.99  | | | 
% 226.54/38.99  | | | REF_CLOSE: (12), (20), (34) are inconsistent by sub-proof #170.
% 226.54/38.99  | | | 
% 226.54/38.99  | | Case 2:
% 226.54/38.99  | | | 
% 226.54/38.99  | | |   (35)  all_57_14 = e0 & op(e0, e1) = e0
% 226.54/38.99  | | | 
% 226.54/38.99  | | | ALPHA: (35) implies:
% 226.54/38.99  | | |   (36)  all_57_14 = e0
% 226.54/38.99  | | | 
% 226.54/38.99  | | | REF_CLOSE: (3), (4), (5), (11), (12), (13), (14), (16), (19), (22), (23),
% 226.54/38.99  | | |            (24), (25), (28), (36) are inconsistent by sub-proof #320.
% 226.54/38.99  | | | 
% 226.54/38.99  | | End of split
% 226.54/38.99  | | 
% 226.54/38.99  | End of split
% 226.54/38.99  | 
% 226.54/38.99  End of proof
% 226.54/38.99  
% 226.54/38.99  Sub-proof #115 shows that the following formulas are inconsistent:
% 226.54/38.99  ----------------------------------------------------------------
% 226.54/38.99    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.54/38.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.54/38.99    (2)  op(e0, e3) = all_53_3
% 226.54/38.99    (3)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 226.54/38.99         (all_57_14 = e0 & op(e0, e1) = e0)
% 226.54/38.99    (4)   ~ (all_53_7 = e0)
% 226.54/38.99    (5)   ~ (e1 = e0)
% 226.54/38.99    (6)  all_57_14 = e1
% 226.54/38.99    (7)  op(e0, e2) = all_53_7
% 226.54/38.99    (8)   ~ (all_53_3 = e0)
% 226.54/38.99  
% 226.54/38.99  Begin of proof
% 226.54/38.99  | 
% 226.54/38.99  | BETA: splitting (3) gives:
% 226.54/38.99  | 
% 226.54/38.99  | Case 1:
% 226.54/38.99  | | 
% 226.54/38.99  | |   (9)  all_57_12 = e0 & op(e0, e3) = e0
% 226.54/38.99  | | 
% 226.54/38.99  | | ALPHA: (9) implies:
% 226.54/38.99  | |   (10)  op(e0, e3) = e0
% 226.54/38.99  | | 
% 226.54/38.99  | | REF_CLOSE: (1), (2), (8), (10) are inconsistent by sub-proof #2366.
% 226.54/38.99  | | 
% 226.54/38.99  | Case 2:
% 226.54/38.99  | | 
% 226.54/38.99  | |   (11)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 226.54/38.99  | |           e0)
% 226.54/38.99  | | 
% 226.54/38.99  | | BETA: splitting (11) gives:
% 226.54/38.99  | | 
% 226.54/38.99  | | Case 1:
% 226.54/38.99  | | | 
% 226.54/38.99  | | |   (12)  all_57_13 = e0 & op(e0, e2) = e0
% 226.54/38.99  | | | 
% 226.54/38.99  | | | ALPHA: (12) implies:
% 226.54/38.99  | | |   (13)  op(e0, e2) = e0
% 226.54/38.99  | | | 
% 226.54/38.99  | | | REF_CLOSE: (1), (4), (7), (13) are inconsistent by sub-proof #2332.
% 226.54/38.99  | | | 
% 226.54/38.99  | | Case 2:
% 226.54/38.99  | | | 
% 226.54/38.99  | | |   (14)  all_57_14 = e0 & op(e0, e1) = e0
% 226.54/38.99  | | | 
% 226.54/38.99  | | | ALPHA: (14) implies:
% 226.54/38.99  | | |   (15)  all_57_14 = e0
% 226.54/38.99  | | | 
% 226.54/38.99  | | | REF_CLOSE: (5), (6), (15) are inconsistent by sub-proof #2122.
% 226.54/38.99  | | | 
% 226.54/38.99  | | End of split
% 226.54/38.99  | | 
% 226.54/38.99  | End of split
% 226.54/38.99  | 
% 226.54/38.99  End of proof
% 226.54/38.99  
% 226.54/38.99  Sub-proof #116 shows that the following formulas are inconsistent:
% 226.54/38.99  ----------------------------------------------------------------
% 226.54/38.99    (1)  all_57_4 = e1 & op(e3, e1) = e1
% 226.54/38.99    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.54/38.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.54/38.99    (3)  op(e3, e1) = all_53_8
% 226.54/38.99    (4)   ~ (all_53_8 = e1)
% 226.54/38.99  
% 226.54/38.99  Begin of proof
% 226.54/38.99  | 
% 226.54/38.99  | ALPHA: (1) implies:
% 226.54/38.99  |   (5)  op(e3, e1) = e1
% 226.54/38.99  | 
% 226.54/38.99  | GROUND_INST: instantiating (2) with all_53_8, e1, e1, e3, simplifying with
% 226.54/38.99  |              (3), (5) gives:
% 226.54/38.99  |   (6)  all_53_8 = e1
% 226.54/38.99  | 
% 226.54/38.99  | REDUCE: (4), (6) imply:
% 226.54/38.99  |   (7)  $false
% 226.54/38.99  | 
% 226.54/38.99  | CLOSE: (7) is inconsistent.
% 226.54/38.99  | 
% 226.54/38.99  End of proof
% 226.54/38.99  
% 226.54/38.99  Sub-proof #117 shows that the following formulas are inconsistent:
% 226.54/38.99  ----------------------------------------------------------------
% 226.54/38.99    (1)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 226.54/38.99    (2)   ~ (e3 = e1)
% 226.54/38.99    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.54/38.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.54/38.99    (4)  op(e1, e0) = all_53_14
% 226.54/38.99    (5)  op(e1, e1) = e3
% 226.54/38.99    (6)   ~ (all_53_14 = e1)
% 226.54/38.99  
% 226.54/38.99  Begin of proof
% 226.54/38.99  | 
% 226.54/38.99  | BETA: splitting (1) gives:
% 226.54/38.99  | 
% 226.54/38.99  | Case 1:
% 226.54/38.99  | | 
% 226.54/38.99  | |   (7)  all_57_8 = e1 & op(e1, e1) = e1
% 226.54/38.99  | | 
% 226.54/38.99  | | ALPHA: (7) implies:
% 226.54/38.99  | |   (8)  op(e1, e1) = e1
% 226.54/38.99  | | 
% 226.54/38.99  | | REF_CLOSE: (2), (3), (5), (8) are inconsistent by sub-proof #156.
% 226.54/38.99  | | 
% 226.54/38.99  | Case 2:
% 226.54/38.99  | | 
% 226.54/38.99  | |   (9)  all_57_11 = e1 & op(e1, e0) = e1
% 226.54/38.99  | | 
% 226.54/38.99  | | REF_CLOSE: (3), (4), (6), (9) are inconsistent by sub-proof #305.
% 226.54/38.99  | | 
% 226.54/38.99  | End of split
% 226.54/38.99  | 
% 226.54/38.99  End of proof
% 226.54/38.99  
% 226.54/38.99  Sub-proof #118 shows that the following formulas are inconsistent:
% 226.54/38.99  ----------------------------------------------------------------
% 226.54/38.99    (1)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 &
% 226.54/38.99           op(all_52_17, all_52_17) = e3 & op(all_52_19, all_52_19) = e2 &
% 226.54/38.99           op(all_52_21, all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1,
% 226.54/38.99             e3) = all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 &
% 226.54/38.99           op(e1, e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21)
% 226.54/38.99           & $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 226.54/38.99           all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 226.54/38.99             all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 226.54/38.99             all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 226.54/38.99           op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 226.54/38.99           $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 226.54/38.99    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.54/38.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.54/38.99    (3)   ~ (e3 = e2)
% 226.54/38.99    (4)   ~ (e3 = e0)
% 226.54/38.99    (5)  op(e1, e1) = e3
% 226.54/38.99    (6)  op(e1, e2) = e1
% 226.54/38.99    (7)  op(e0, e0) = e1
% 226.54/38.99  
% 226.54/38.99  Begin of proof
% 226.54/38.99  | 
% 226.54/38.99  | BETA: splitting (1) gives:
% 226.54/38.99  | 
% 226.54/38.99  | Case 1:
% 226.54/38.99  | | 
% 226.54/38.99  | |   (8)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 &
% 226.54/38.99  | |        op(all_52_17, all_52_17) = e3 & op(all_52_19, all_52_19) = e2 &
% 226.54/38.99  | |        op(all_52_21, all_52_21) = e1 & op(all_52_23, all_52_23) = e0 &
% 226.54/38.99  | |        op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) =
% 226.54/38.99  | |        all_52_21 & op(e1, e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 226.54/38.99  | |        $i(all_52_21) & $i(all_52_23)
% 226.54/38.99  | | 
% 226.54/38.99  | | ALPHA: (8) implies:
% 226.54/38.99  | |   (9)  op(e1, e2) = all_52_19
% 226.54/38.99  | |   (10)  op(all_52_19, all_52_19) = e2
% 226.54/38.99  | | 
% 226.54/38.99  | | REF_CLOSE: (2), (3), (5), (6), (9), (10) are inconsistent by sub-proof #119.
% 226.54/38.99  | | 
% 226.54/38.99  | Case 2:
% 226.54/38.99  | | 
% 226.54/38.99  | |   (11)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0 &
% 226.54/38.99  | |         op(all_52_25, all_52_25) = e3 & op(all_52_27, all_52_27) = e2 &
% 226.54/38.99  | |         op(all_52_29, all_52_29) = e1 & op(all_52_31, all_52_31) = e0 &
% 226.54/38.99  | |         op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 & op(e0, e1) =
% 226.54/38.99  | |         all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 226.54/38.99  | |         $i(all_52_29) & $i(all_52_31)
% 226.54/38.99  | | 
% 226.54/38.99  | | ALPHA: (11) implies:
% 226.54/38.99  | |   (12)  op(e0, e0) = all_52_31
% 226.54/38.99  | |   (13)  op(all_52_31, all_52_31) = e0
% 226.54/38.99  | | 
% 226.54/38.99  | | REF_CLOSE: (2), (4), (5), (7), (12), (13) are inconsistent by sub-proof
% 226.54/38.99  | |            #161.
% 226.54/38.99  | | 
% 226.54/38.99  | End of split
% 226.54/38.99  | 
% 226.54/38.99  End of proof
% 226.54/38.99  
% 226.54/38.99  Sub-proof #119 shows that the following formulas are inconsistent:
% 226.54/38.99  ----------------------------------------------------------------
% 226.54/38.99    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.54/38.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.54/38.99    (2)   ~ (e3 = e2)
% 226.54/38.99    (3)  op(e1, e1) = e3
% 226.54/38.99    (4)  op(e1, e2) = e1
% 226.54/38.99    (5)  op(e1, e2) = all_52_19
% 226.54/38.99    (6)  op(all_52_19, all_52_19) = e2
% 226.54/38.99  
% 226.54/38.99  Begin of proof
% 226.54/38.99  | 
% 226.54/38.99  | GROUND_INST: instantiating (1) with all_52_19, e1, e2, e1, simplifying with
% 226.54/38.99  |              (4), (5) gives:
% 226.54/38.99  |   (7)  all_52_19 = e1
% 226.54/38.99  | 
% 226.54/38.99  | REDUCE: (6), (7) imply:
% 226.54/38.99  |   (8)  op(e1, e1) = e2
% 226.54/38.99  | 
% 226.54/38.99  | GROUND_INST: instantiating (1) with e3, e2, e1, e1, simplifying with (3), (8)
% 226.54/38.99  |              gives:
% 226.54/38.99  |   (9)  e3 = e2
% 226.54/38.99  | 
% 226.54/38.99  | REDUCE: (2), (9) imply:
% 226.54/38.99  |   (10)  $false
% 226.54/38.99  | 
% 226.54/38.99  | CLOSE: (10) is inconsistent.
% 226.54/38.99  | 
% 226.54/38.99  End of proof
% 226.54/38.99  
% 226.54/38.99  Sub-proof #120 shows that the following formulas are inconsistent:
% 226.54/38.99  ----------------------------------------------------------------
% 226.54/38.99    (1)   ~ (e3 = e1)
% 226.54/38.99    (2)  op(e2, e1) = e1
% 226.54/38.99    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.54/38.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.54/38.99    (4)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0 &
% 226.54/38.99         op(all_52_9, all_52_9) = e3 & op(all_52_11, all_52_11) = e2 &
% 226.54/38.99         op(all_52_13, all_52_13) = e1 & op(all_52_15, all_52_15) = e0 & op(e2,
% 226.54/38.99           e3) = all_52_9 & op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13 &
% 226.54/38.99         op(e2, e0) = all_52_15 & $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 226.54/38.99         $i(all_52_15)
% 226.54/38.99    (5)  op(e1, e1) = e3
% 226.54/38.99  
% 226.54/38.99  Begin of proof
% 226.54/38.99  | 
% 226.54/38.99  | ALPHA: (4) implies:
% 226.54/38.99  |   (6)  op(e2, e1) = all_52_13
% 226.54/38.99  |   (7)  op(all_52_13, all_52_13) = e1
% 226.54/38.99  | 
% 226.54/38.99  | GROUND_INST: instantiating (3) with e1, all_52_13, e1, e2, simplifying with
% 226.54/38.99  |              (2), (6) gives:
% 226.54/38.99  |   (8)  all_52_13 = e1
% 226.54/38.99  | 
% 226.54/38.99  | REDUCE: (7), (8) imply:
% 226.54/38.99  |   (9)  op(e1, e1) = e1
% 226.54/38.99  | 
% 226.54/38.99  | REF_CLOSE: (1), (3), (5), (9) are inconsistent by sub-proof #156.
% 226.54/38.99  | 
% 226.54/38.99  End of proof
% 226.54/38.99  
% 226.54/38.99  Sub-proof #121 shows that the following formulas are inconsistent:
% 226.54/38.99  ----------------------------------------------------------------
% 226.54/38.99    (1)  all_55_3 = e1 | all_55_3 = e0
% 226.54/38.99    (2)  all_55_3 = all_52_7
% 226.54/38.99    (3)   ~ (all_52_7 = e1)
% 226.54/38.99    (4)   ~ (all_52_7 = e0)
% 226.54/38.99  
% 226.54/38.99  Begin of proof
% 226.54/38.99  | 
% 226.54/38.99  | BETA: splitting (1) gives:
% 226.54/38.99  | 
% 226.54/38.99  | Case 1:
% 226.54/38.99  | | 
% 226.54/38.99  | |   (5)  all_55_3 = e1
% 226.54/38.99  | | 
% 226.54/38.99  | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #1449.
% 226.54/38.99  | | 
% 226.54/38.99  | Case 2:
% 226.54/38.99  | | 
% 226.54/38.99  | |   (6)  all_55_3 = e0
% 226.54/38.99  | | 
% 226.54/38.99  | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #376.
% 226.54/38.99  | | 
% 226.54/38.99  | End of split
% 226.54/38.99  | 
% 226.54/38.99  End of proof
% 226.54/38.99  
% 226.54/38.99  Sub-proof #122 shows that the following formulas are inconsistent:
% 226.54/38.99  ----------------------------------------------------------------
% 226.54/38.99    (1)  all_55_3 = e3
% 226.54/38.99    (2)  op(e3, e3) = e1
% 226.54/38.99    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.54/38.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.54/38.99    (4)  op(all_52_7, all_52_7) = e0
% 226.54/38.99    (5)  all_55_3 = all_52_7
% 226.54/38.99    (6)  op(e3, e3) = all_52_1
% 226.54/38.99    (7)   ~ (e1 = e0)
% 226.54/38.99    (8)  op(e3, e0) = all_52_7
% 226.54/38.99  
% 226.54/38.99  Begin of proof
% 226.54/38.99  | 
% 226.54/38.99  | COMBINE_EQS: (1), (5) imply:
% 226.54/38.99  |   (9)  all_52_7 = e3
% 226.54/38.99  | 
% 226.54/38.99  | SIMP: (9) implies:
% 226.54/38.99  |   (10)  all_52_7 = e3
% 226.54/38.99  | 
% 226.54/38.99  | REDUCE: (8), (10) imply:
% 226.54/38.99  |   (11)  op(e3, e0) = e3
% 226.54/38.99  | 
% 226.54/38.99  | REF_CLOSE: (2), (3), (4), (6), (7), (8), (11) are inconsistent by sub-proof
% 226.54/38.99  |            #123.
% 226.54/38.99  | 
% 226.54/38.99  End of proof
% 226.54/38.99  
% 226.54/38.99  Sub-proof #123 shows that the following formulas are inconsistent:
% 226.54/38.99  ----------------------------------------------------------------
% 226.54/38.99    (1)  op(e3, e3) = e1
% 226.54/38.99    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.54/38.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.54/38.99    (3)  op(all_52_7, all_52_7) = e0
% 226.54/38.99    (4)  op(e3, e3) = all_52_1
% 226.54/38.99    (5)  op(e3, e0) = e3
% 226.54/38.99    (6)   ~ (e1 = e0)
% 226.54/38.99    (7)  op(e3, e0) = all_52_7
% 226.54/38.99  
% 226.54/38.99  Begin of proof
% 226.54/38.99  | 
% 226.54/38.99  | GROUND_INST: instantiating (2) with e3, all_52_7, e0, e3, simplifying with
% 226.54/38.99  |              (5), (7) gives:
% 226.54/38.99  |   (8)  all_52_7 = e3
% 226.54/38.99  | 
% 226.54/38.99  | GROUND_INST: instantiating (2) with e1, all_52_1, e3, e3, simplifying with
% 226.54/38.99  |              (1), (4) gives:
% 226.54/38.99  |   (9)  all_52_1 = e1
% 226.54/38.99  | 
% 226.54/38.99  | REDUCE: (3), (8) imply:
% 226.54/38.99  |   (10)  op(e3, e3) = e0
% 226.54/38.99  | 
% 226.54/38.99  | GROUND_INST: instantiating (2) with e1, e0, e3, e3, simplifying with (1), (10)
% 226.54/38.99  |              gives:
% 226.54/38.99  |   (11)  e1 = e0
% 226.54/38.99  | 
% 226.54/38.99  | REDUCE: (6), (11) imply:
% 226.54/38.99  |   (12)  $false
% 226.54/38.99  | 
% 226.54/38.99  | CLOSE: (12) is inconsistent.
% 226.54/38.99  | 
% 226.54/38.99  End of proof
% 226.54/38.99  
% 226.54/38.99  Sub-proof #124 shows that the following formulas are inconsistent:
% 226.54/38.99  ----------------------------------------------------------------
% 226.54/38.99    (1)  op(e0, e1) = all_53_11
% 226.54/38.99    (2)   ~ (e3 = e1)
% 226.54/38.99    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.54/38.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.54/38.99    (4)   ~ (e3 = e2)
% 226.54/38.99    (5)   ~ (e3 = e0)
% 226.54/38.99    (6)   ~ (e2 = e0)
% 226.54/38.99    (7)   ~ (e1 = e0)
% 226.54/38.99    (8)  all_57_10 = e3
% 226.54/38.99    (9)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 226.54/38.99             | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 226.54/38.99               e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 226.54/38.99               op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 226.54/38.99    (10)   ~ (e2 = e1)
% 226.54/38.99    (11)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 226.54/38.99          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 226.54/38.99    (12)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 226.54/38.99    (13)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 226.54/38.99          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 226.54/38.99    (14)   ~ (all_53_11 = e3)
% 226.54/38.99  
% 226.54/38.99  Begin of proof
% 226.54/38.99  | 
% 226.54/38.99  | BETA: splitting (12) gives:
% 226.54/38.99  | 
% 226.54/38.99  | Case 1:
% 226.54/38.99  | | 
% 226.54/38.99  | |   (15)  all_57_14 = e3 & op(e0, e1) = e3
% 226.54/38.99  | | 
% 226.54/38.99  | | REF_CLOSE: (1), (3), (14), (15) are inconsistent by sub-proof #129.
% 226.54/38.99  | | 
% 226.54/38.99  | Case 2:
% 226.54/38.99  | | 
% 226.54/38.99  | |   (16)  all_57_15 = e3 & op(e0, e0) = e3
% 226.54/38.99  | | 
% 226.54/38.99  | | ALPHA: (16) implies:
% 226.54/38.99  | |   (17)  all_57_15 = e3
% 226.54/38.99  | |   (18)  op(e0, e0) = e3
% 226.54/38.99  | | 
% 226.54/38.99  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13), (17),
% 226.54/38.99  | |            (18) are inconsistent by sub-proof #1746.
% 226.54/38.99  | | 
% 226.54/38.99  | End of split
% 226.54/38.99  | 
% 226.54/38.99  End of proof
% 226.54/38.99  
% 226.54/38.99  Sub-proof #125 shows that the following formulas are inconsistent:
% 226.54/38.99  ----------------------------------------------------------------
% 226.54/38.99    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.54/38.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.54/38.99    (2)   ~ (e3 = e0)
% 226.54/38.99    (3)  op(e1, e1) = e3
% 226.54/38.99    (4)  op(e1, e0) = all_52_23
% 226.54/38.99    (5)  op(all_52_23, all_52_23) = e0
% 226.54/38.99    (6)  op(e1, e0) = e1
% 226.54/38.99  
% 226.54/38.99  Begin of proof
% 226.54/38.99  | 
% 226.54/38.99  | GROUND_INST: instantiating (1) with all_52_23, e1, e0, e1, simplifying with
% 226.54/38.99  |              (4), (6) gives:
% 226.54/38.99  |   (7)  all_52_23 = e1
% 226.54/38.99  | 
% 226.54/38.99  | REDUCE: (5), (7) imply:
% 226.54/38.99  |   (8)  op(e1, e1) = e0
% 226.54/38.99  | 
% 226.54/38.99  | GROUND_INST: instantiating (1) with e3, e0, e1, e1, simplifying with (3), (8)
% 226.54/38.99  |              gives:
% 226.54/38.99  |   (9)  e3 = e0
% 226.54/38.99  | 
% 226.54/38.99  | REDUCE: (2), (9) imply:
% 226.54/38.99  |   (10)  $false
% 226.54/38.99  | 
% 226.54/38.99  | CLOSE: (10) is inconsistent.
% 226.54/38.99  | 
% 226.54/38.99  End of proof
% 226.54/38.99  
% 226.54/38.99  Sub-proof #126 shows that the following formulas are inconsistent:
% 226.54/38.99  ----------------------------------------------------------------
% 226.54/38.99    (1)  all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 226.54/38.99    (2)   ~ (all_53_7 = e3)
% 226.54/38.99    (3)  op(e2, e1) = e1
% 226.54/38.99    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.54/38.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.54/38.99    (5)   ~ (all_53_7 = e2)
% 226.54/38.99    (6)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0 &
% 226.54/38.99         op(all_52_9, all_52_9) = e3 & op(all_52_11, all_52_11) = e2 &
% 226.54/38.99         op(all_52_13, all_52_13) = e1 & op(all_52_15, all_52_15) = e0 & op(e2,
% 226.54/38.99           e3) = all_52_9 & op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13 &
% 226.54/38.99         op(e2, e0) = all_52_15 & $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 226.54/38.99         $i(all_52_15)
% 226.54/38.99    (7)  op(e1, e1) = e3
% 226.54/38.99    (8)   ~ (all_53_7 = e0)
% 226.54/38.99    (9)  all_55_13 = all_53_7
% 226.54/38.99  
% 226.54/38.99  Begin of proof
% 226.54/38.99  | 
% 226.54/38.99  | ALPHA: (6) implies:
% 226.54/38.99  |   (10)  op(e2, e1) = all_52_13
% 226.54/38.99  |   (11)  op(all_52_13, all_52_13) = e1
% 226.54/38.99  | 
% 226.54/38.99  | BETA: splitting (1) gives:
% 226.54/38.99  | 
% 226.54/38.99  | Case 1:
% 226.54/38.99  | | 
% 226.54/38.99  | |   (12)  all_55_13 = e3
% 226.54/38.99  | | 
% 226.54/38.99  | | REF_CLOSE: (2), (9), (12) are inconsistent by sub-proof #2080.
% 226.54/38.99  | | 
% 226.54/38.99  | Case 2:
% 226.54/38.99  | | 
% 226.54/38.99  | |   (13)   ~ (all_55_13 = e3)
% 226.54/38.99  | |   (14)  all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 226.54/38.99  | | 
% 226.54/38.99  | | BETA: splitting (14) gives:
% 226.54/38.99  | | 
% 226.54/38.99  | | Case 1:
% 226.54/38.99  | | | 
% 226.54/38.99  | | |   (15)  all_55_13 = e2
% 226.54/38.99  | | | 
% 226.54/38.99  | | | REF_CLOSE: (5), (9), (15) are inconsistent by sub-proof #2287.
% 226.54/38.99  | | | 
% 226.54/38.99  | | Case 2:
% 226.54/38.99  | | | 
% 226.54/38.99  | | |   (16)  all_55_13 = e1 | all_55_13 = e0
% 226.54/38.99  | | | 
% 226.54/38.99  | | | REF_CLOSE: (2), (3), (4), (7), (8), (9), (10), (11), (16) are inconsistent
% 226.54/38.99  | | |            by sub-proof #127.
% 226.54/38.99  | | | 
% 226.54/38.99  | | End of split
% 226.54/38.99  | | 
% 226.54/38.99  | End of split
% 226.54/38.99  | 
% 226.54/38.99  End of proof
% 226.54/38.99  
% 226.54/38.99  Sub-proof #127 shows that the following formulas are inconsistent:
% 226.54/38.99  ----------------------------------------------------------------
% 226.54/38.99    (1)   ~ (all_53_7 = e3)
% 226.54/38.99    (2)  op(e2, e1) = all_52_13
% 226.54/38.99    (3)  op(e2, e1) = e1
% 226.54/38.99    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.54/38.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.54/38.99    (5)  all_55_13 = e1 | all_55_13 = e0
% 226.54/38.99    (6)  op(e1, e1) = e3
% 226.54/38.99    (7)  op(all_52_13, all_52_13) = e1
% 226.54/38.99    (8)   ~ (all_53_7 = e0)
% 226.54/38.99    (9)  all_55_13 = all_53_7
% 226.54/38.99  
% 226.54/38.99  Begin of proof
% 226.54/38.99  | 
% 226.54/38.99  | BETA: splitting (5) gives:
% 226.54/38.99  | 
% 226.54/38.99  | Case 1:
% 226.54/38.99  | | 
% 226.54/38.99  | |   (10)  all_55_13 = e1
% 226.54/38.99  | | 
% 226.54/38.99  | | COMBINE_EQS: (9), (10) imply:
% 226.54/38.99  | |   (11)  all_53_7 = e1
% 226.54/38.99  | | 
% 226.54/38.99  | | SIMP: (11) implies:
% 226.54/38.99  | |   (12)  all_53_7 = e1
% 226.54/38.99  | | 
% 226.54/38.99  | | REDUCE: (1), (12) imply:
% 226.54/38.99  | |   (13)   ~ (e3 = e1)
% 226.54/38.99  | | 
% 226.54/38.99  | | SIMP: (13) implies:
% 226.54/38.99  | |   (14)   ~ (e3 = e1)
% 226.54/38.99  | | 
% 226.54/38.99  | | GROUND_INST: instantiating (4) with e1, all_52_13, e1, e2, simplifying with
% 226.54/38.99  | |              (2), (3) gives:
% 226.54/38.99  | |   (15)  all_52_13 = e1
% 226.54/38.99  | | 
% 226.54/38.99  | | REDUCE: (7), (15) imply:
% 226.54/38.99  | |   (16)  op(e1, e1) = e1
% 226.54/38.99  | | 
% 226.54/38.99  | | REF_CLOSE: (4), (6), (14), (16) are inconsistent by sub-proof #156.
% 226.54/38.99  | | 
% 226.54/38.99  | Case 2:
% 226.54/38.99  | | 
% 226.54/38.99  | |   (17)  all_55_13 = e0
% 226.54/38.99  | | 
% 226.54/38.99  | | REF_CLOSE: (8), (9), (17) are inconsistent by sub-proof #2261.
% 226.54/38.99  | | 
% 226.54/38.99  | End of split
% 226.54/38.99  | 
% 226.54/38.99  End of proof
% 226.54/38.99  
% 226.54/38.99  Sub-proof #128 shows that the following formulas are inconsistent:
% 226.54/38.99  ----------------------------------------------------------------
% 226.54/38.99    (1)  all_57_15 = e0
% 226.54/38.99    (2)  all_57_13 = e1
% 226.54/38.99    (3)   ~ (e3 = e1)
% 226.54/38.99    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.54/38.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.54/38.99    (5)   ~ (e3 = e2)
% 226.54/38.99    (6)   ~ (e3 = e0)
% 226.54/38.99    (7)   ~ (e2 = e0)
% 226.54/39.00    (8)  all_57_8 = e3
% 226.54/39.00    (9)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 226.54/39.00    (10)  op(e0, e0) = e0
% 226.54/39.00    (11)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 226.54/39.00          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 226.54/39.00            e3)
% 226.54/39.00    (12)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 226.54/39.00          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 226.54/39.00            e2)
% 226.54/39.00    (13)   ~ (e2 = e1)
% 226.54/39.00  
% 226.54/39.00  Begin of proof
% 226.54/39.00  | 
% 226.54/39.00  | BETA: splitting (9) gives:
% 226.54/39.00  | 
% 226.54/39.00  | Case 1:
% 226.54/39.00  | | 
% 226.54/39.00  | |   (14)  all_57_8 = e0 & op(e1, e1) = e0
% 226.54/39.00  | | 
% 226.54/39.00  | | REF_CLOSE: (6), (8), (14) are inconsistent by sub-proof #170.
% 226.54/39.00  | | 
% 226.54/39.00  | Case 2:
% 226.54/39.00  | | 
% 226.54/39.00  | |   (15)  all_57_14 = e0 & op(e0, e1) = e0
% 226.54/39.00  | | 
% 226.54/39.00  | | ALPHA: (15) implies:
% 226.54/39.00  | |   (16)  all_57_14 = e0
% 226.54/39.00  | | 
% 226.54/39.00  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (10), (11), (12), (13), (16)
% 226.54/39.00  | |            are inconsistent by sub-proof #2123.
% 226.54/39.00  | | 
% 226.54/39.00  | End of split
% 226.54/39.00  | 
% 226.54/39.00  End of proof
% 226.54/39.00  
% 226.54/39.00  Sub-proof #129 shows that the following formulas are inconsistent:
% 226.54/39.00  ----------------------------------------------------------------
% 226.54/39.00    (1)  all_57_14 = e3 & op(e0, e1) = e3
% 226.54/39.00    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.54/39.00           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.54/39.00    (3)  op(e0, e1) = all_53_11
% 226.54/39.00    (4)   ~ (all_53_11 = e3)
% 226.54/39.00  
% 226.54/39.00  Begin of proof
% 226.54/39.00  | 
% 226.54/39.00  | ALPHA: (1) implies:
% 226.54/39.00  |   (5)  op(e0, e1) = e3
% 226.54/39.00  | 
% 226.54/39.00  | GROUND_INST: instantiating (2) with all_53_11, e3, e1, e0, simplifying with
% 226.54/39.00  |              (3), (5) gives:
% 226.54/39.00  |   (6)  all_53_11 = e3
% 226.54/39.00  | 
% 226.54/39.00  | REDUCE: (4), (6) imply:
% 226.54/39.00  |   (7)  $false
% 226.54/39.00  | 
% 226.54/39.00  | CLOSE: (7) is inconsistent.
% 226.54/39.00  | 
% 226.54/39.00  End of proof
% 226.54/39.00  
% 226.54/39.00  Sub-proof #130 shows that the following formulas are inconsistent:
% 226.54/39.00  ----------------------------------------------------------------
% 226.54/39.00    (1)  all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 226.54/39.00    (2)   ~ (e3 = e1)
% 226.54/39.00    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.54/39.00           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.54/39.00    (4)  all_55_15 = all_4_2
% 226.54/39.00    (5)  op(e1, e1) = e3
% 226.54/39.00    (6)   ~ (all_4_2 = e2)
% 226.54/39.00    (7)  op(e0, e1) = all_52_29
% 226.54/39.00    (8)  op(all_52_29, all_52_29) = e1
% 226.54/39.00    (9)  op(e0, e1) = e1
% 226.54/39.00  
% 226.54/39.00  Begin of proof
% 226.54/39.00  | 
% 226.54/39.00  | BETA: splitting (1) gives:
% 226.54/39.00  | 
% 226.54/39.00  | Case 1:
% 226.54/39.00  | | 
% 226.54/39.00  | |   (10)  all_55_15 = e2
% 226.54/39.00  | | 
% 226.54/39.00  | | REF_CLOSE: (4), (6), (10) are inconsistent by sub-proof #2502.
% 226.54/39.00  | | 
% 226.54/39.00  | Case 2:
% 226.54/39.00  | | 
% 226.54/39.00  | | 
% 226.54/39.00  | | GROUND_INST: instantiating (3) with e1, all_52_29, e1, e0, simplifying with
% 226.54/39.00  | |              (7), (9) gives:
% 226.54/39.00  | |   (11)  all_52_29 = e1
% 226.54/39.00  | | 
% 226.54/39.00  | | REDUCE: (8), (11) imply:
% 226.54/39.00  | |   (12)  op(e1, e1) = e1
% 226.54/39.00  | | 
% 226.54/39.00  | | REF_CLOSE: (2), (3), (5), (12) are inconsistent by sub-proof #156.
% 226.54/39.00  | | 
% 226.54/39.00  | End of split
% 226.54/39.00  | 
% 226.54/39.00  End of proof
% 226.54/39.00  
% 226.54/39.00  Sub-proof #131 shows that the following formulas are inconsistent:
% 226.54/39.00  ----------------------------------------------------------------
% 226.54/39.00    (1)   ~ (all_53_2 = e2)
% 226.54/39.00    (2)   ~ (all_53_2 = e1)
% 226.54/39.00    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.54/39.00           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.54/39.00    (4)   ~ (all_53_2 = e3)
% 226.54/39.00    (5)   ~ (e3 = e0)
% 226.54/39.00    (6)  all_57_0 = e1
% 226.54/39.00    (7)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 226.54/39.00    (8)  op(e0, e3) = all_53_3
% 226.54/39.00    (9)  all_57_6 = e2
% 226.54/39.00    (10)   ~ (e2 = e0)
% 226.54/39.00    (11)  all_57_2 = e3
% 226.54/39.00    (12)   ~ (e1 = e0)
% 226.54/39.00    (13)   ~ (all_53_2 = all_53_3)
% 226.54/39.00    (14)  all_55_8 = all_53_2
% 226.54/39.00    (15)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 226.54/39.00          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 226.54/39.00  
% 226.54/39.00  Begin of proof
% 226.54/39.00  | 
% 226.54/39.00  | BETA: splitting (15) gives:
% 226.54/39.00  | 
% 226.54/39.00  | Case 1:
% 226.54/39.00  | | 
% 226.54/39.00  | |   (16)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) =
% 226.54/39.00  | |           e0)
% 226.54/39.00  | | 
% 226.54/39.00  | | BETA: splitting (16) gives:
% 226.54/39.00  | | 
% 226.54/39.00  | | Case 1:
% 226.54/39.00  | | | 
% 226.54/39.00  | | |   (17)  all_57_0 = e0 & op(e3, e3) = e0
% 226.54/39.00  | | | 
% 226.54/39.00  | | | REF_CLOSE: (6), (12), (17) are inconsistent by sub-proof #1812.
% 226.54/39.00  | | | 
% 226.54/39.00  | | Case 2:
% 226.54/39.00  | | | 
% 226.54/39.00  | | |   (18)  all_57_2 = e0 & op(e2, e3) = e0
% 226.54/39.00  | | | 
% 226.54/39.00  | | | REF_CLOSE: (5), (11), (18) are inconsistent by sub-proof #1805.
% 226.54/39.00  | | | 
% 226.54/39.00  | | End of split
% 226.54/39.00  | | 
% 226.54/39.00  | Case 2:
% 226.54/39.00  | | 
% 226.54/39.00  | |   (19)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) =
% 226.54/39.00  | |           e0)
% 226.54/39.00  | | 
% 226.54/39.00  | | BETA: splitting (19) gives:
% 226.54/39.00  | | 
% 226.54/39.00  | | Case 1:
% 226.54/39.00  | | | 
% 226.54/39.00  | | |   (20)  all_57_6 = e0 & op(e1, e3) = e0
% 226.54/39.00  | | | 
% 226.54/39.00  | | | REF_CLOSE: (9), (10), (20) are inconsistent by sub-proof #2386.
% 226.54/39.00  | | | 
% 226.54/39.00  | | Case 2:
% 226.54/39.00  | | | 
% 226.54/39.00  | | |   (21)  all_57_12 = e0 & op(e0, e3) = e0
% 226.54/39.00  | | | 
% 226.54/39.00  | | | REF_CLOSE: (1), (2), (3), (4), (7), (8), (13), (14), (21) are inconsistent
% 226.54/39.00  | | |            by sub-proof #1369.
% 226.54/39.00  | | | 
% 226.54/39.00  | | End of split
% 226.54/39.00  | | 
% 226.54/39.00  | End of split
% 226.54/39.00  | 
% 226.54/39.00  End of proof
% 226.54/39.00  
% 226.54/39.00  Sub-proof #132 shows that the following formulas are inconsistent:
% 226.54/39.00  ----------------------------------------------------------------
% 226.54/39.00    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.54/39.00           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.54/39.00    (2)  op(e0, e3) = all_53_3
% 226.54/39.00    (3)  op(e0, e3) = e3
% 226.54/39.00    (4)   ~ (all_53_3 = e3)
% 226.54/39.00  
% 226.54/39.00  Begin of proof
% 226.54/39.00  | 
% 226.54/39.00  | GROUND_INST: instantiating (1) with all_53_3, e3, e3, e0, simplifying with
% 226.54/39.00  |              (2), (3) gives:
% 226.54/39.00  |   (5)  all_53_3 = e3
% 226.54/39.00  | 
% 226.54/39.00  | REDUCE: (4), (5) imply:
% 226.54/39.00  |   (6)  $false
% 226.54/39.00  | 
% 226.54/39.00  | CLOSE: (6) is inconsistent.
% 226.54/39.00  | 
% 226.54/39.00  End of proof
% 226.54/39.00  
% 226.54/39.00  Sub-proof #133 shows that the following formulas are inconsistent:
% 226.54/39.00  ----------------------------------------------------------------
% 226.54/39.00    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.54/39.00           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.54/39.00    (2)  e2 = e1
% 226.54/39.00    (3)  op(e2, e2) = e1
% 226.54/39.00    (4)   ~ (e3 = e2)
% 226.54/39.00    (5)   ~ (e3 = e0)
% 226.54/39.00    (6)   ~ (e2 = e0)
% 226.54/39.00    (7)  all_57_2 = e3
% 226.54/39.00    (8)   ~ (e1 = e0)
% 226.54/39.00    (9)  all_57_5 = e2
% 226.54/39.00    (10)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 226.54/39.00          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 226.54/39.00    (11)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 226.54/39.00          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 226.54/39.00    (12)   ~ (e2 = e1)
% 226.54/39.00  
% 226.54/39.00  Begin of proof
% 226.54/39.00  | 
% 226.54/39.00  | SIMP: (2) implies:
% 226.54/39.00  |   (13)  e2 = e1
% 226.54/39.00  | 
% 226.54/39.00  | COMBINE_EQS: (9), (13) imply:
% 226.54/39.00  |   (14)  all_57_5 = e1
% 226.54/39.00  | 
% 226.54/39.00  | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (10), (11), (12), (14) are
% 226.54/39.00  |            inconsistent by sub-proof #555.
% 226.54/39.00  | 
% 226.54/39.00  End of proof
% 226.54/39.00  
% 226.54/39.00  Sub-proof #134 shows that the following formulas are inconsistent:
% 226.54/39.00  ----------------------------------------------------------------
% 226.54/39.00    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 226.54/39.00         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 226.54/39.00    (2)   ~ (e3 = e1)
% 226.54/39.00    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.54/39.00           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.54/39.00    (4)  op(e2, e2) = e1
% 226.54/39.00    (5)   ~ (e3 = e2)
% 226.54/39.00    (6)   ~ (e3 = e0)
% 226.54/39.00    (7)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 226.54/39.00         (all_57_14 = e0 & op(e0, e1) = e0)
% 226.54/39.00    (8)  all_57_15 = e3
% 226.54/39.00    (9)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 226.54/39.00         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 226.54/39.00    (10)   ~ (e2 = e0)
% 226.54/39.00    (11)  all_57_13 = e2
% 226.54/39.00    (12)   ~ (e1 = e0)
% 226.54/39.00    (13)  all_57_5 = e2
% 226.54/39.00    (14)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 226.54/39.00          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 226.54/39.00    (15)  op(e0, e0) = e3
% 226.54/39.00    (16)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 226.54/39.00          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 226.54/39.00            e2)
% 226.54/39.00    (17)  all_57_5 = e0 & op(e2, e1) = e0
% 226.54/39.00    (18)   ~ (e2 = e1)
% 226.54/39.00    (19)  all_57_7 = e0
% 226.54/39.00  
% 226.54/39.00  Begin of proof
% 226.54/39.00  | 
% 226.54/39.00  | ALPHA: (17) implies:
% 226.54/39.00  |   (20)  all_57_5 = e0
% 226.54/39.00  | 
% 226.54/39.00  | COMBINE_EQS: (13), (20) imply:
% 226.54/39.00  |   (21)  e2 = e0
% 226.54/39.00  | 
% 226.54/39.00  | COMBINE_EQS: (11), (21) imply:
% 226.54/39.00  |   (22)  all_57_13 = e0
% 226.54/39.00  | 
% 226.54/39.00  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (14),
% 226.54/39.00  |            (15), (16), (18), (19), (22) are inconsistent by sub-proof #1765.
% 226.54/39.00  | 
% 226.54/39.00  End of proof
% 226.54/39.00  
% 226.54/39.00  Sub-proof #135 shows that the following formulas are inconsistent:
% 226.54/39.00  ----------------------------------------------------------------
% 226.54/39.00    (1)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 226.54/39.00         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 226.54/39.00    (2)   ~ (e3 = e1)
% 226.54/39.00    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.54/39.00           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.54/39.00    (4)  op(e2, e2) = e1
% 226.54/39.00    (5)  all_57_9 = e1
% 226.54/39.00    (6)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 226.54/39.00         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 226.54/39.00    (7)   ~ (e3 = e2)
% 226.54/39.00    (8)   ~ (e3 = e0)
% 226.54/39.00    (9)  op(e1, e1) = e3
% 226.54/39.00    (10)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 226.54/39.00          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 226.54/39.00    (11)  op(e3, e3) = e0
% 226.54/39.00    (12)  op(e0, e0) = all_52_31
% 226.54/39.00    (13)   ~ (e2 = e0)
% 226.54/39.00    (14)  all_57_2 = e3
% 226.54/39.00    (15)   ~ (e1 = e0)
% 226.54/39.00    (16)  op(e0, e0) = e3
% 226.54/39.00    (17)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 226.54/39.00              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 226.54/39.00                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 226.54/39.00                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 226.54/39.00    (18)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 226.54/39.00          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 226.54/39.00    (19)  op(e0, e2) = all_52_27
% 226.54/39.00    (20)  op(e3, e2) = e3
% 226.54/39.00    (21)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 226.54/39.00          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 226.54/39.00    (22)   ~ (e2 = e1)
% 226.54/39.00    (23)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 226.54/39.00          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 226.54/39.00    (24)  op(all_52_31, all_52_31) = e0
% 226.54/39.00    (25)  op(all_52_27, all_52_27) = e2
% 226.54/39.00  
% 226.54/39.00  Begin of proof
% 226.54/39.00  | 
% 226.54/39.00  | BETA: splitting (6) gives:
% 226.54/39.00  | 
% 226.54/39.00  | Case 1:
% 226.54/39.00  | | 
% 226.54/39.00  | |   (26)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) =
% 226.54/39.00  | |           e2)
% 226.54/39.00  | | 
% 226.54/39.00  | | REF_CLOSE: (3), (7), (11), (13), (20), (26) are inconsistent by sub-proof
% 226.54/39.00  | |            #1195.
% 226.54/39.00  | | 
% 226.54/39.00  | Case 2:
% 226.54/39.00  | | 
% 226.54/39.00  | |   (27)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) =
% 226.54/39.00  | |           e2)
% 226.54/39.00  | | 
% 226.54/39.00  | | BETA: splitting (27) gives:
% 226.54/39.00  | | 
% 226.54/39.00  | | Case 1:
% 226.54/39.00  | | | 
% 226.54/39.00  | | |   (28)  all_57_4 = e2 & op(e3, e1) = e2
% 226.54/39.00  | | | 
% 226.54/39.00  | | | ALPHA: (28) implies:
% 226.54/39.00  | | |   (29)  all_57_4 = e2
% 226.54/39.00  | | | 
% 226.54/39.00  | | | REF_CLOSE: (1), (2), (3), (4), (7), (8), (9), (10), (11), (12), (13),
% 226.54/39.00  | | |            (14), (15), (16), (17), (18), (19), (21), (22), (23), (24),
% 226.54/39.00  | | |            (25), (29) are inconsistent by sub-proof #136.
% 226.54/39.00  | | | 
% 226.54/39.00  | | Case 2:
% 226.54/39.00  | | | 
% 226.54/39.00  | | |   (30)  all_57_9 = e2 & op(e3, e0) = e2
% 226.54/39.00  | | | 
% 226.54/39.00  | | | REF_CLOSE: (5), (22), (30) are inconsistent by sub-proof #2481.
% 226.54/39.00  | | | 
% 226.54/39.00  | | End of split
% 226.54/39.00  | | 
% 226.54/39.00  | End of split
% 226.54/39.00  | 
% 226.54/39.00  End of proof
% 226.54/39.00  
% 226.54/39.00  Sub-proof #136 shows that the following formulas are inconsistent:
% 226.54/39.00  ----------------------------------------------------------------
% 226.54/39.00    (1)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 226.54/39.00         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 226.54/39.00    (2)   ~ (e3 = e1)
% 226.54/39.00    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.54/39.00           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.54/39.00    (4)  all_57_4 = e2
% 226.54/39.00    (5)  op(e2, e2) = e1
% 226.54/39.00    (6)   ~ (e3 = e2)
% 226.54/39.00    (7)   ~ (e3 = e0)
% 226.54/39.00    (8)  op(e1, e1) = e3
% 226.54/39.00    (9)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 226.54/39.00         (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 226.54/39.00    (10)  op(e3, e3) = e0
% 226.54/39.00    (11)  op(e0, e0) = all_52_31
% 226.54/39.00    (12)   ~ (e2 = e0)
% 226.54/39.00    (13)  all_57_2 = e3
% 226.54/39.00    (14)   ~ (e1 = e0)
% 226.54/39.00    (15)  op(e0, e0) = e3
% 226.54/39.00    (16)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 226.54/39.00              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 226.54/39.00                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 226.54/39.00                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 226.54/39.00    (17)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 226.54/39.00          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 226.54/39.00    (18)  op(e0, e2) = all_52_27
% 226.54/39.00    (19)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 226.54/39.00          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 226.54/39.00    (20)   ~ (e2 = e1)
% 226.54/39.00    (21)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 226.54/39.00          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 226.54/39.00    (22)  op(all_52_31, all_52_31) = e0
% 226.54/39.00    (23)  op(all_52_27, all_52_27) = e2
% 226.54/39.00  
% 226.54/39.00  Begin of proof
% 226.54/39.00  | 
% 226.54/39.00  | BETA: splitting (9) gives:
% 226.54/39.00  | 
% 226.54/39.00  | Case 1:
% 226.54/39.00  | | 
% 226.54/39.00  | |   (24)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) =
% 226.54/39.00  | |           e1)
% 226.54/39.00  | | 
% 226.54/39.00  | | BETA: splitting (24) gives:
% 226.54/39.00  | | 
% 226.54/39.00  | | Case 1:
% 226.54/39.00  | | | 
% 226.54/39.00  | | |   (25)  all_57_4 = e1 & op(e3, e1) = e1
% 226.54/39.00  | | | 
% 226.54/39.00  | | | ALPHA: (25) implies:
% 226.54/39.00  | | |   (26)  all_57_4 = e1
% 226.54/39.00  | | | 
% 226.54/39.00  | | | REF_CLOSE: (4), (20), (26) are inconsistent by sub-proof #2430.
% 226.54/39.00  | | | 
% 226.54/39.00  | | Case 2:
% 226.54/39.00  | | | 
% 226.54/39.00  | | |   (27)  all_57_5 = e1 & op(e2, e1) = e1
% 226.54/39.00  | | | 
% 226.54/39.00  | | | ALPHA: (27) implies:
% 226.54/39.00  | | |   (28)  all_57_5 = e1
% 226.54/39.00  | | | 
% 226.54/39.00  | | | REF_CLOSE: (3), (5), (6), (7), (12), (13), (14), (17), (19), (20), (28)
% 226.54/39.00  | | |            are inconsistent by sub-proof #555.
% 226.54/39.00  | | | 
% 226.54/39.00  | | End of split
% 226.54/39.00  | | 
% 226.54/39.00  | Case 2:
% 226.54/39.00  | | 
% 226.54/39.00  | |   (29)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) =
% 226.54/39.00  | |           e1)
% 226.54/39.00  | | 
% 226.54/39.00  | | BETA: splitting (29) gives:
% 226.54/39.00  | | 
% 226.54/39.00  | | Case 1:
% 226.54/39.00  | | | 
% 226.54/39.00  | | |   (30)  all_57_8 = e1 & op(e1, e1) = e1
% 226.54/39.00  | | | 
% 226.54/39.00  | | | ALPHA: (30) implies:
% 226.54/39.00  | | |   (31)  op(e1, e1) = e1
% 226.54/39.00  | | | 
% 226.54/39.00  | | | REF_CLOSE: (2), (3), (8), (31) are inconsistent by sub-proof #156.
% 226.54/39.00  | | | 
% 226.54/39.00  | | Case 2:
% 226.54/39.00  | | | 
% 226.54/39.00  | | |   (32)  all_57_14 = e1 & op(e0, e1) = e1
% 226.54/39.00  | | | 
% 226.54/39.00  | | | ALPHA: (32) implies:
% 226.54/39.00  | | |   (33)  all_57_14 = e1
% 226.54/39.00  | | | 
% 226.54/39.00  | | | BETA: splitting (16) gives:
% 226.54/39.00  | | | 
% 226.54/39.00  | | | Case 1:
% 226.54/39.00  | | | | 
% 226.54/39.00  | | | |   (34)  all_57_15 = e0 & op(e0, e0) = e0
% 226.54/39.00  | | | | 
% 226.54/39.00  | | | | ALPHA: (34) implies:
% 226.54/39.00  | | | |   (35)  op(e0, e0) = e0
% 226.54/39.00  | | | | 
% 226.54/39.00  | | | | REF_CLOSE: (3), (7), (15), (35) are inconsistent by sub-proof #2304.
% 226.54/39.00  | | | | 
% 226.54/39.00  | | | Case 2:
% 226.54/39.00  | | | | 
% 226.54/39.00  | | | |   (36)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2,
% 226.54/39.00  | | | |               e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) &
% 226.54/39.00  | | | |         ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0,
% 226.54/39.00  | | | |               e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 226.54/39.00  | | | | 
% 226.54/39.00  | | | | ALPHA: (36) implies:
% 226.54/39.00  | | | |   (37)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0,
% 226.54/39.00  | | | |             e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 226.54/39.00  | | | | 
% 226.54/39.00  | | | | BETA: splitting (37) gives:
% 226.54/39.00  | | | | 
% 226.54/39.00  | | | | Case 1:
% 226.54/39.00  | | | | | 
% 226.54/39.00  | | | | |   (38)  all_57_12 = e0 & op(e0, e3) = e0
% 226.54/39.00  | | | | | 
% 226.54/39.00  | | | | | ALPHA: (38) implies:
% 226.54/39.00  | | | | |   (39)  all_57_12 = e0
% 226.54/39.00  | | | | | 
% 226.54/39.00  | | | | | REF_CLOSE: (1), (2), (3), (6), (10), (11), (12), (13), (14), (15),
% 226.54/39.00  | | | | |            (20), (21), (22), (39) are inconsistent by sub-proof #139.
% 226.54/39.00  | | | | | 
% 226.54/39.00  | | | | Case 2:
% 226.54/39.00  | | | | | 
% 226.54/39.00  | | | | |   (40)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 226.54/39.00  | | | | |             e1) = e0)
% 226.54/39.00  | | | | | 
% 226.54/39.00  | | | | | BETA: splitting (40) gives:
% 226.54/39.00  | | | | | 
% 226.54/39.00  | | | | | Case 1:
% 226.54/39.00  | | | | | | 
% 226.54/39.00  | | | | | |   (41)  all_57_13 = e0 & op(e0, e2) = e0
% 226.54/39.00  | | | | | | 
% 226.54/39.00  | | | | | | ALPHA: (41) implies:
% 226.54/39.00  | | | | | |   (42)  op(e0, e2) = e0
% 226.54/39.00  | | | | | | 
% 226.54/39.00  | | | | | | REF_CLOSE: (3), (6), (11), (15), (18), (23), (42) are inconsistent
% 226.54/39.00  | | | | | |            by sub-proof #858.
% 226.54/39.00  | | | | | | 
% 226.54/39.00  | | | | | Case 2:
% 226.54/39.00  | | | | | | 
% 226.54/39.00  | | | | | |   (43)  all_57_14 = e0 & op(e0, e1) = e0
% 226.54/39.00  | | | | | | 
% 226.54/39.00  | | | | | | REF_CLOSE: (14), (33), (43) are inconsistent by sub-proof #2181.
% 226.54/39.00  | | | | | | 
% 226.54/39.00  | | | | | End of split
% 226.54/39.00  | | | | | 
% 226.54/39.00  | | | | End of split
% 226.54/39.00  | | | | 
% 226.54/39.00  | | | End of split
% 226.54/39.00  | | | 
% 226.54/39.00  | | End of split
% 226.54/39.00  | | 
% 226.54/39.00  | End of split
% 226.54/39.01  | 
% 226.54/39.01  End of proof
% 226.54/39.01  
% 226.54/39.01  Sub-proof #137 shows that the following formulas are inconsistent:
% 226.54/39.01  ----------------------------------------------------------------
% 226.54/39.01    (1)  op(e0, e0) = all_4_2
% 226.54/39.01    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 226.54/39.01         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 226.54/39.01    (3)   ~ (e3 = e1)
% 226.54/39.01    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.54/39.01           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.54/39.01    (5)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) = all_22_1
% 226.54/39.01           & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0, e3) =
% 226.54/39.01           all_22_1 & $i(all_22_1))
% 226.54/39.01    (6)  op(e0, e3) = all_52_25
% 226.54/39.01    (7)   ~ (e3 = e2)
% 226.54/39.01    (8)   ~ (e3 = e0)
% 226.54/39.01    (9)   ~ (all_4_2 = e2)
% 226.54/39.01    (10)  op(e3, e3) = e0
% 226.54/39.01    (11)  op(e0, e0) = all_52_31
% 226.54/39.01    (12)  op(all_52_25, all_52_25) = e3
% 226.54/39.01    (13)   ~ (e2 = e0)
% 226.54/39.01    (14)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 226.54/39.01            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 226.54/39.01              e3) = all_12_1 & $i(all_12_1))
% 226.54/39.01    (15)  all_57_2 = e3
% 226.54/39.01    (16)  op(e2, e2) = e2
% 226.54/39.01    (17)   ~ (e1 = e0)
% 226.54/39.01    (18)  op(e0, e0) = e3
% 226.54/39.01    (19)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 226.54/39.01          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 226.54/39.01            e2)
% 226.54/39.01    (20)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 226.54/39.01              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 226.54/39.01                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 226.54/39.01                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 226.54/39.01    (21)  op(e0, e2) = all_52_27
% 226.54/39.01    (22)  all_57_1 = e3
% 226.54/39.01    (23)   ~ (e2 = e1)
% 226.54/39.01    (24)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 226.54/39.01          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 226.54/39.01    (25)  op(all_52_31, all_52_31) = e0
% 226.54/39.01    (26)  op(all_52_27, all_52_27) = e2
% 226.54/39.01    (27)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 226.54/39.01          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 226.54/39.01    (28)  all_57_7 = e0
% 226.54/39.01  
% 226.54/39.01  Begin of proof
% 226.54/39.01  | 
% 226.54/39.01  | BETA: splitting (27) gives:
% 226.54/39.01  | 
% 226.54/39.01  | Case 1:
% 226.54/39.01  | | 
% 226.54/39.01  | |   (29)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) =
% 226.54/39.01  | |           e1)
% 226.54/39.01  | | 
% 226.54/39.01  | | REF_CLOSE: (3), (4), (16), (22), (23), (29) are inconsistent by sub-proof
% 226.54/39.01  | |            #1168.
% 226.54/39.01  | | 
% 226.54/39.01  | Case 2:
% 226.54/39.01  | | 
% 226.54/39.01  | |   (30)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 226.54/39.01  | |           e1)
% 226.54/39.01  | | 
% 226.54/39.01  | | BETA: splitting (30) gives:
% 226.54/39.01  | | 
% 226.54/39.01  | | Case 1:
% 226.54/39.01  | | | 
% 226.54/39.01  | | |   (31)  all_57_7 = e1 & op(e1, e2) = e1
% 226.54/39.01  | | | 
% 226.54/39.01  | | | REF_CLOSE: (17), (28), (31) are inconsistent by sub-proof #2200.
% 226.54/39.01  | | | 
% 226.54/39.01  | | Case 2:
% 226.54/39.01  | | | 
% 226.54/39.01  | | |   (32)  all_57_13 = e1 & op(e0, e2) = e1
% 226.54/39.01  | | | 
% 226.54/39.01  | | | ALPHA: (32) implies:
% 226.54/39.01  | | |   (33)  all_57_13 = e1
% 226.54/39.01  | | | 
% 226.54/39.01  | | | BETA: splitting (20) gives:
% 226.54/39.01  | | | 
% 226.54/39.01  | | | Case 1:
% 226.54/39.01  | | | | 
% 226.54/39.01  | | | |   (34)  all_57_15 = e0 & op(e0, e0) = e0
% 226.54/39.01  | | | | 
% 226.54/39.01  | | | | ALPHA: (34) implies:
% 226.54/39.01  | | | |   (35)  op(e0, e0) = e0
% 226.54/39.01  | | | | 
% 226.54/39.01  | | | | REF_CLOSE: (4), (8), (18), (35) are inconsistent by sub-proof #2304.
% 226.54/39.01  | | | | 
% 226.54/39.01  | | | Case 2:
% 226.54/39.01  | | | | 
% 226.54/39.01  | | | |   (36)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2,
% 226.54/39.01  | | | |               e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) &
% 226.54/39.01  | | | |         ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0,
% 226.54/39.01  | | | |               e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 226.54/39.01  | | | | 
% 226.54/39.01  | | | | ALPHA: (36) implies:
% 226.54/39.01  | | | |   (37)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0,
% 226.54/39.01  | | | |             e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 226.54/39.01  | | | | 
% 226.54/39.01  | | | | BETA: splitting (19) gives:
% 226.54/39.01  | | | | 
% 226.54/39.01  | | | | Case 1:
% 226.54/39.01  | | | | | 
% 226.54/39.01  | | | | |   (38)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0,
% 226.54/39.01  | | | | |             e2) = e2)
% 226.54/39.01  | | | | | 
% 226.54/39.01  | | | | | BETA: splitting (38) gives:
% 226.54/39.01  | | | | | 
% 226.54/39.01  | | | | | Case 1:
% 226.54/39.01  | | | | | | 
% 226.54/39.01  | | | | | |   (39)  all_57_12 = e2 & op(e0, e3) = e2
% 226.54/39.01  | | | | | | 
% 226.54/39.01  | | | | | | ALPHA: (39) implies:
% 226.54/39.01  | | | | | |   (40)  op(e0, e3) = e2
% 226.54/39.01  | | | | | | 
% 226.54/39.01  | | | | | | REF_CLOSE: (4), (5), (6), (7), (12), (14), (16), (40) are
% 226.54/39.01  | | | | | |            inconsistent by sub-proof #833.
% 226.54/39.01  | | | | | | 
% 226.54/39.01  | | | | | Case 2:
% 226.54/39.01  | | | | | | 
% 226.54/39.01  | | | | | |   (41)  all_57_13 = e2 & op(e0, e2) = e2
% 226.54/39.01  | | | | | | 
% 226.54/39.01  | | | | | | ALPHA: (41) implies:
% 226.54/39.01  | | | | | |   (42)  all_57_13 = e2
% 226.54/39.01  | | | | | | 
% 226.54/39.01  | | | | | | REF_CLOSE: (23), (33), (42) are inconsistent by sub-proof #2327.
% 226.54/39.01  | | | | | | 
% 226.54/39.01  | | | | | End of split
% 226.54/39.01  | | | | | 
% 226.54/39.01  | | | | Case 2:
% 226.54/39.01  | | | | | 
% 226.54/39.01  | | | | |   (43)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0,
% 226.54/39.01  | | | | |             e0) = e2)
% 226.54/39.01  | | | | | 
% 226.54/39.01  | | | | | BETA: splitting (43) gives:
% 226.54/39.01  | | | | | 
% 226.54/39.01  | | | | | Case 1:
% 226.54/39.01  | | | | | | 
% 226.54/39.01  | | | | | |   (44)  all_57_14 = e2 & op(e0, e1) = e2
% 226.54/39.01  | | | | | | 
% 226.54/39.01  | | | | | | ALPHA: (44) implies:
% 226.54/39.01  | | | | | |   (45)  all_57_14 = e2
% 226.54/39.01  | | | | | | 
% 226.54/39.01  | | | | | | REF_CLOSE: (2), (3), (4), (7), (10), (11), (13), (15), (17), (18),
% 226.54/39.01  | | | | | |            (21), (23), (24), (25), (26), (37), (45) are inconsistent
% 226.54/39.01  | | | | | |            by sub-proof #138.
% 226.54/39.01  | | | | | | 
% 226.54/39.01  | | | | | Case 2:
% 226.54/39.01  | | | | | | 
% 226.54/39.01  | | | | | |   (46)  all_57_15 = e2 & op(e0, e0) = e2
% 226.54/39.01  | | | | | | 
% 226.54/39.01  | | | | | | ALPHA: (46) implies:
% 226.54/39.01  | | | | | |   (47)  op(e0, e0) = e2
% 226.54/39.01  | | | | | | 
% 226.54/39.01  | | | | | | REF_CLOSE: (1), (4), (9), (47) are inconsistent by sub-proof #2334.
% 226.54/39.01  | | | | | | 
% 226.54/39.01  | | | | | End of split
% 226.54/39.01  | | | | | 
% 226.54/39.01  | | | | End of split
% 226.54/39.01  | | | | 
% 226.54/39.01  | | | End of split
% 226.54/39.01  | | | 
% 226.54/39.01  | | End of split
% 226.54/39.01  | | 
% 226.54/39.01  | End of split
% 226.54/39.01  | 
% 226.54/39.01  End of proof
% 226.54/39.01  
% 226.54/39.01  Sub-proof #138 shows that the following formulas are inconsistent:
% 226.54/39.01  ----------------------------------------------------------------
% 226.54/39.01    (1)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 226.54/39.01         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 226.54/39.01    (2)   ~ (e3 = e1)
% 226.54/39.01    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.54/39.01           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.54/39.01    (4)   ~ (e3 = e2)
% 226.54/39.01    (5)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 226.54/39.01         (all_57_14 = e0 & op(e0, e1) = e0)
% 226.54/39.01    (6)  op(e3, e3) = e0
% 226.54/39.01    (7)  op(e0, e0) = all_52_31
% 226.54/39.01    (8)   ~ (e2 = e0)
% 226.54/39.01    (9)  all_57_2 = e3
% 226.54/39.01    (10)   ~ (e1 = e0)
% 226.54/39.01    (11)  all_57_14 = e2
% 226.54/39.01    (12)  op(e0, e0) = e3
% 226.54/39.01    (13)  op(e0, e2) = all_52_27
% 226.54/39.01    (14)   ~ (e2 = e1)
% 226.54/39.01    (15)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 226.54/39.01          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 226.54/39.01    (16)  op(all_52_31, all_52_31) = e0
% 226.54/39.01    (17)  op(all_52_27, all_52_27) = e2
% 226.54/39.01  
% 226.54/39.01  Begin of proof
% 226.54/39.01  | 
% 226.54/39.01  | BETA: splitting (5) gives:
% 226.54/39.01  | 
% 226.54/39.01  | Case 1:
% 226.54/39.01  | | 
% 226.54/39.01  | |   (18)  all_57_12 = e0 & op(e0, e3) = e0
% 226.54/39.01  | | 
% 226.54/39.01  | | ALPHA: (18) implies:
% 226.54/39.01  | |   (19)  all_57_12 = e0
% 226.54/39.01  | | 
% 226.54/39.01  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (12), (14), (15),
% 226.54/39.01  | |            (16), (19) are inconsistent by sub-proof #139.
% 226.54/39.01  | | 
% 226.54/39.01  | Case 2:
% 226.54/39.01  | | 
% 226.54/39.01  | |   (20)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 226.54/39.01  | |           e0)
% 226.54/39.01  | | 
% 226.54/39.01  | | BETA: splitting (20) gives:
% 226.54/39.01  | | 
% 226.54/39.01  | | Case 1:
% 226.54/39.01  | | | 
% 226.54/39.01  | | |   (21)  all_57_13 = e0 & op(e0, e2) = e0
% 226.54/39.01  | | | 
% 226.54/39.01  | | | ALPHA: (21) implies:
% 226.54/39.01  | | |   (22)  op(e0, e2) = e0
% 226.54/39.01  | | | 
% 226.54/39.01  | | | REF_CLOSE: (3), (4), (7), (12), (13), (17), (22) are inconsistent by
% 226.54/39.01  | | |            sub-proof #858.
% 226.54/39.01  | | | 
% 226.54/39.01  | | Case 2:
% 226.54/39.01  | | | 
% 226.54/39.01  | | |   (23)  all_57_14 = e0 & op(e0, e1) = e0
% 226.54/39.01  | | | 
% 226.54/39.01  | | | REF_CLOSE: (8), (11), (23) are inconsistent by sub-proof #2173.
% 226.54/39.01  | | | 
% 226.54/39.01  | | End of split
% 226.54/39.01  | | 
% 226.54/39.01  | End of split
% 226.54/39.01  | 
% 226.54/39.01  End of proof
% 226.54/39.01  
% 226.54/39.01  Sub-proof #139 shows that the following formulas are inconsistent:
% 226.54/39.01  ----------------------------------------------------------------
% 226.54/39.01    (1)  all_57_12 = e0
% 226.54/39.01    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 226.54/39.01         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 226.54/39.01    (3)   ~ (e3 = e1)
% 226.54/39.01    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.54/39.01           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.54/39.01    (5)   ~ (e3 = e2)
% 226.54/39.01    (6)  op(e3, e3) = e0
% 226.54/39.01    (7)  op(e0, e0) = all_52_31
% 226.54/39.01    (8)   ~ (e2 = e0)
% 226.54/39.01    (9)  all_57_2 = e3
% 226.54/39.01    (10)   ~ (e1 = e0)
% 226.54/39.01    (11)  op(e0, e0) = e3
% 226.54/39.01    (12)   ~ (e2 = e1)
% 226.54/39.01    (13)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 226.54/39.01          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 226.54/39.01    (14)  op(all_52_31, all_52_31) = e0
% 226.54/39.01  
% 226.54/39.01  Begin of proof
% 226.54/39.01  | 
% 226.54/39.01  | BETA: splitting (2) gives:
% 226.54/39.01  | 
% 226.54/39.01  | Case 1:
% 226.54/39.01  | | 
% 226.54/39.01  | |   (15)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) =
% 226.54/39.01  | |           e1)
% 226.54/39.01  | | 
% 226.54/39.01  | | BETA: splitting (15) gives:
% 226.54/39.01  | | 
% 226.54/39.01  | | Case 1:
% 226.54/39.01  | | | 
% 226.54/39.01  | | |   (16)  all_57_0 = e1 & op(e3, e3) = e1
% 226.54/39.01  | | | 
% 226.54/39.01  | | | ALPHA: (16) implies:
% 226.54/39.01  | | |   (17)  op(e3, e3) = e1
% 226.54/39.01  | | | 
% 226.54/39.01  | | | REF_CLOSE: (4), (7), (10), (11), (14), (17) are inconsistent by sub-proof
% 226.54/39.01  | | |            #283.
% 226.54/39.01  | | | 
% 226.54/39.01  | | Case 2:
% 226.54/39.01  | | | 
% 226.54/39.01  | | |   (18)  all_57_2 = e1 & op(e2, e3) = e1
% 226.54/39.01  | | | 
% 226.54/39.01  | | | REF_CLOSE: (3), (9), (18) are inconsistent by sub-proof #1928.
% 226.54/39.01  | | | 
% 226.54/39.01  | | End of split
% 226.54/39.01  | | 
% 226.54/39.01  | Case 2:
% 226.54/39.01  | | 
% 226.54/39.01  | |   (19)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) =
% 226.54/39.01  | |           e1)
% 226.54/39.01  | | 
% 226.54/39.01  | | BETA: splitting (19) gives:
% 226.54/39.01  | | 
% 226.54/39.01  | | Case 1:
% 226.54/39.01  | | | 
% 226.54/39.01  | | |   (20)  all_57_6 = e1 & op(e1, e3) = e1
% 226.54/39.01  | | | 
% 226.54/39.01  | | | ALPHA: (20) implies:
% 226.54/39.01  | | |   (21)  all_57_6 = e1
% 226.54/39.01  | | | 
% 226.54/39.01  | | | BETA: splitting (13) gives:
% 226.54/39.01  | | | 
% 226.54/39.01  | | | Case 1:
% 226.54/39.01  | | | | 
% 226.54/39.01  | | | |   (22)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3)
% 226.54/39.01  | | | |           = e2)
% 226.54/39.01  | | | | 
% 226.54/39.01  | | | | REF_CLOSE: (4), (5), (6), (8), (9), (22) are inconsistent by sub-proof
% 226.54/39.01  | | | |            #1924.
% 226.54/39.01  | | | | 
% 226.54/39.01  | | | Case 2:
% 226.54/39.01  | | | | 
% 226.54/39.01  | | | |   (23)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3)
% 226.54/39.01  | | | |           = e2)
% 226.54/39.01  | | | | 
% 226.54/39.01  | | | | BETA: splitting (23) gives:
% 226.54/39.01  | | | | 
% 226.54/39.01  | | | | Case 1:
% 226.54/39.01  | | | | | 
% 226.54/39.01  | | | | |   (24)  all_57_6 = e2 & op(e1, e3) = e2
% 226.54/39.01  | | | | | 
% 226.54/39.01  | | | | | REF_CLOSE: (12), (21), (24) are inconsistent by sub-proof #1317.
% 226.54/39.01  | | | | | 
% 226.54/39.01  | | | | Case 2:
% 226.54/39.01  | | | | | 
% 226.54/39.01  | | | | |   (25)  all_57_12 = e2 & op(e0, e3) = e2
% 226.54/39.01  | | | | | 
% 226.54/39.01  | | | | | ALPHA: (25) implies:
% 226.54/39.01  | | | | |   (26)  all_57_12 = e2
% 226.54/39.01  | | | | | 
% 226.54/39.01  | | | | | REF_CLOSE: (1), (8), (26) are inconsistent by sub-proof #2385.
% 226.54/39.01  | | | | | 
% 226.54/39.01  | | | | End of split
% 226.54/39.01  | | | | 
% 226.54/39.01  | | | End of split
% 226.54/39.01  | | | 
% 226.54/39.01  | | Case 2:
% 226.54/39.01  | | | 
% 226.54/39.01  | | |   (27)  all_57_12 = e1 & op(e0, e3) = e1
% 226.54/39.01  | | | 
% 226.54/39.01  | | | ALPHA: (27) implies:
% 226.54/39.01  | | |   (28)  all_57_12 = e1
% 226.54/39.01  | | | 
% 226.54/39.01  | | | REF_CLOSE: (1), (10), (28) are inconsistent by sub-proof #2014.
% 226.54/39.01  | | | 
% 226.54/39.01  | | End of split
% 226.54/39.01  | | 
% 226.54/39.01  | End of split
% 226.54/39.01  | 
% 226.54/39.01  End of proof
% 226.54/39.01  
% 226.54/39.01  Sub-proof #140 shows that the following formulas are inconsistent:
% 226.54/39.01  ----------------------------------------------------------------
% 226.54/39.01    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.54/39.01           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.54/39.01    (2)  op(e2, e2) = all_8_2
% 226.54/39.01    (3)  op(e2, e2) = e3
% 226.54/39.01    (4)   ~ (all_8_2 = e3)
% 226.54/39.01  
% 226.54/39.01  Begin of proof
% 226.54/39.01  | 
% 226.54/39.01  | GROUND_INST: instantiating (1) with all_8_2, e3, e2, e2, simplifying with (2),
% 226.54/39.01  |              (3) gives:
% 226.54/39.01  |   (5)  all_8_2 = e3
% 226.54/39.01  | 
% 226.54/39.01  | REDUCE: (4), (5) imply:
% 226.54/39.01  |   (6)  $false
% 226.54/39.01  | 
% 226.54/39.01  | CLOSE: (6) is inconsistent.
% 226.54/39.01  | 
% 226.54/39.01  End of proof
% 226.54/39.01  
% 226.54/39.01  Sub-proof #141 shows that the following formulas are inconsistent:
% 226.54/39.01  ----------------------------------------------------------------
% 226.54/39.01    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.54/39.01           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.54/39.01    (2)   ~ (all_53_9 = e0)
% 226.54/39.01    (3)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0)
% 226.54/39.01    (4)   ~ (all_53_8 = e0)
% 226.54/39.01    (5)  op(e2, e1) = all_53_9
% 226.54/39.01    (6)  op(e3, e1) = all_53_8
% 226.54/39.01  
% 226.54/39.01  Begin of proof
% 226.54/39.01  | 
% 226.54/39.01  | BETA: splitting (3) gives:
% 226.54/39.01  | 
% 226.54/39.01  | Case 1:
% 226.54/39.01  | | 
% 226.54/39.01  | |   (7)  all_57_4 = e0 & op(e3, e1) = e0
% 226.54/39.01  | | 
% 226.54/39.01  | | ALPHA: (7) implies:
% 226.54/39.01  | |   (8)  op(e3, e1) = e0
% 226.54/39.01  | | 
% 226.54/39.01  | | REF_CLOSE: (1), (4), (6), (8) are inconsistent by sub-proof #2267.
% 226.54/39.01  | | 
% 226.54/39.01  | Case 2:
% 226.54/39.01  | | 
% 226.54/39.01  | |   (9)  all_57_5 = e0 & op(e2, e1) = e0
% 226.54/39.01  | | 
% 226.54/39.01  | | REF_CLOSE: (1), (2), (5), (9) are inconsistent by sub-proof #2023.
% 226.54/39.01  | | 
% 226.54/39.01  | End of split
% 226.54/39.01  | 
% 226.54/39.01  End of proof
% 226.54/39.01  
% 226.54/39.01  Sub-proof #142 shows that the following formulas are inconsistent:
% 226.54/39.01  ----------------------------------------------------------------
% 226.54/39.01    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 226.54/39.01         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 226.54/39.01    (2)   ~ (e3 = e1)
% 226.54/39.01    (3)  all_57_8 = e0 & op(e1, e1) = e0
% 226.54/39.01    (4)  all_57_3 = e0
% 226.54/39.01    (5)   ~ (e3 = e2)
% 226.54/39.01    (6)   ~ (e3 = e0)
% 226.54/39.01    (7)   ~ (e2 = e0)
% 226.54/39.01    (8)  all_57_2 = e3
% 226.54/39.01    (9)   ~ (e1 = e0)
% 226.54/39.01    (10)  all_57_8 = e3
% 226.54/39.01    (11)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 226.54/39.01          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 226.54/39.01    (12)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 226.54/39.01          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 226.54/39.01    (13)   ~ (e2 = e1)
% 226.54/39.01  
% 226.54/39.01  Begin of proof
% 226.54/39.01  | 
% 226.54/39.01  | ALPHA: (3) implies:
% 226.54/39.01  |   (14)  all_57_8 = e0
% 226.54/39.01  | 
% 226.54/39.01  | COMBINE_EQS: (10), (14) imply:
% 226.54/39.01  |   (15)  e3 = e0
% 226.54/39.01  | 
% 226.54/39.01  | COMBINE_EQS: (8), (15) imply:
% 226.54/39.01  |   (16)  all_57_2 = e0
% 226.54/39.01  | 
% 226.54/39.01  | REF_CLOSE: (1), (2), (4), (5), (6), (7), (9), (11), (12), (13), (16) are
% 226.54/39.01  |            inconsistent by sub-proof #2246.
% 226.54/39.01  | 
% 226.54/39.01  End of proof
% 226.54/39.01  
% 226.54/39.01  Sub-proof #143 shows that the following formulas are inconsistent:
% 226.54/39.01  ----------------------------------------------------------------
% 226.54/39.01    (1)  op(e1, e3) = e0
% 226.54/39.01    (2)   ~ (all_53_8 = all_52_29)
% 226.54/39.01    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.54/39.01           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.54/39.01    (4)  all_46_2 = e3
% 226.54/39.01    (5)  all_57_4 = e0 & op(e3, e1) = e0
% 226.54/39.01    (6)  op(e1, e1) = e3
% 226.54/39.01    (7)  all_55_14 = all_52_29
% 226.54/39.01    (8)   ~ (all_52_29 = e3)
% 226.54/39.01    (9)   ~ (all_46_2 = e3) | ( ~ (all_46_0 = e2) & op(all_46_1, e1) = all_46_0 &
% 226.54/39.01           op(e1, e3) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 =
% 226.54/39.01             e0) & op(e1, e3) = all_46_1 & $i(all_46_1))
% 226.54/39.01    (10)  op(e0, e1) = all_52_29
% 226.54/39.01    (11)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 226.54/39.01    (12)  op(all_52_29, all_52_29) = e1
% 226.54/39.01    (13)  op(e1, e3) = all_53_2
% 226.54/39.01    (14)  op(e3, e1) = all_53_8
% 226.54/39.01    (15)  ( ~ (all_6_0 = e0) & op(all_6_1, e1) = all_6_0 & op(e1, e3) = all_6_1 &
% 226.54/39.01            $i(all_6_0) & $i(all_6_1)) | ( ~ (all_6_1 = e2) & op(e1, e3) = all_6_1
% 226.54/39.01            & $i(all_6_1))
% 226.54/39.01  
% 226.54/39.01  Begin of proof
% 226.54/39.01  | 
% 226.54/39.01  | ALPHA: (5) implies:
% 226.54/39.01  |   (16)  op(e3, e1) = e0
% 226.54/39.01  | 
% 226.54/39.01  | GROUND_INST: instantiating (3) with all_53_2, e0, e3, e1, simplifying with
% 226.54/39.01  |              (1), (13) gives:
% 226.54/39.01  |   (17)  all_53_2 = e0
% 226.54/39.01  | 
% 226.54/39.01  | GROUND_INST: instantiating (3) with all_53_8, e0, e1, e3, simplifying with
% 226.54/39.01  |              (14), (16) gives:
% 226.54/39.01  |   (18)  all_53_8 = e0
% 226.54/39.01  | 
% 226.54/39.01  | REDUCE: (2), (18) imply:
% 226.54/39.01  |   (19)   ~ (all_52_29 = e0)
% 226.54/39.01  | 
% 226.54/39.01  | SIMP: (19) implies:
% 226.54/39.01  |   (20)   ~ (all_52_29 = e0)
% 226.54/39.01  | 
% 226.54/39.01  | BETA: splitting (9) gives:
% 226.54/39.01  | 
% 226.54/39.01  | Case 1:
% 226.54/39.01  | | 
% 226.54/39.01  | |   (21)   ~ (all_46_2 = e3)
% 226.54/39.01  | | 
% 226.54/39.01  | | REDUCE: (4), (21) imply:
% 226.54/39.01  | |   (22)  $false
% 226.54/39.01  | | 
% 226.54/39.01  | | CLOSE: (22) is inconsistent.
% 226.54/39.01  | | 
% 226.54/39.01  | Case 2:
% 226.54/39.01  | | 
% 226.54/39.01  | |   (23)  ( ~ (all_46_0 = e2) & op(all_46_1, e1) = all_46_0 & op(e1, e3) =
% 226.54/39.01  | |           all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 = e0) &
% 226.54/39.01  | |           op(e1, e3) = all_46_1 & $i(all_46_1))
% 226.54/39.01  | | 
% 226.54/39.01  | | BETA: splitting (23) gives:
% 226.54/39.01  | | 
% 226.54/39.01  | | Case 1:
% 226.54/39.01  | | | 
% 226.54/39.01  | | |   (24)   ~ (all_46_0 = e2) & op(all_46_1, e1) = all_46_0 & op(e1, e3) =
% 226.54/39.01  | | |         all_46_1 & $i(all_46_0) & $i(all_46_1)
% 226.54/39.01  | | | 
% 226.54/39.01  | | | ALPHA: (24) implies:
% 226.54/39.01  | | |   (25)   ~ (all_46_0 = e2)
% 226.54/39.01  | | |   (26)  op(e1, e3) = all_46_1
% 226.54/39.01  | | |   (27)  op(all_46_1, e1) = all_46_0
% 226.54/39.01  | | | 
% 226.54/39.01  | | | BETA: splitting (15) gives:
% 226.54/39.01  | | | 
% 226.54/39.01  | | | Case 1:
% 226.54/39.01  | | | | 
% 226.54/39.01  | | | |   (28)   ~ (all_6_0 = e0) & op(all_6_1, e1) = all_6_0 & op(e1, e3) =
% 226.54/39.01  | | | |         all_6_1 & $i(all_6_0) & $i(all_6_1)
% 226.54/39.01  | | | | 
% 226.54/39.01  | | | | ALPHA: (28) implies:
% 226.54/39.01  | | | |   (29)  op(e1, e3) = all_6_1
% 226.54/39.01  | | | | 
% 226.54/39.01  | | | | REF_CLOSE: (1), (3), (6), (7), (8), (10), (11), (12), (20), (25), (26),
% 226.54/39.01  | | | |            (27), (29) are inconsistent by sub-proof #145.
% 226.54/39.01  | | | | 
% 226.54/39.01  | | | Case 2:
% 226.54/39.01  | | | | 
% 226.54/39.01  | | | |   (30)   ~ (all_6_1 = e2) & op(e1, e3) = all_6_1 & $i(all_6_1)
% 226.54/39.01  | | | | 
% 226.54/39.01  | | | | ALPHA: (30) implies:
% 226.54/39.01  | | | |   (31)  op(e1, e3) = all_6_1
% 226.54/39.01  | | | | 
% 226.54/39.01  | | | | REF_CLOSE: (1), (3), (6), (7), (8), (10), (11), (12), (20), (25), (26),
% 226.54/39.01  | | | |            (27), (31) are inconsistent by sub-proof #145.
% 226.54/39.01  | | | | 
% 226.54/39.01  | | | End of split
% 226.54/39.01  | | | 
% 226.54/39.01  | | Case 2:
% 226.54/39.01  | | | 
% 226.54/39.01  | | |   (32)   ~ (all_46_1 = e0) & op(e1, e3) = all_46_1 & $i(all_46_1)
% 226.54/39.01  | | | 
% 226.54/39.01  | | | ALPHA: (32) implies:
% 226.54/39.01  | | |   (33)   ~ (all_46_1 = e0)
% 226.54/39.01  | | |   (34)  op(e1, e3) = all_46_1
% 226.54/39.01  | | | 
% 226.54/39.01  | | | BETA: splitting (15) gives:
% 226.54/39.01  | | | 
% 226.54/39.01  | | | Case 1:
% 226.54/39.01  | | | | 
% 226.54/39.01  | | | |   (35)   ~ (all_6_0 = e0) & op(all_6_1, e1) = all_6_0 & op(e1, e3) =
% 226.54/39.01  | | | |         all_6_1 & $i(all_6_0) & $i(all_6_1)
% 226.54/39.01  | | | | 
% 226.54/39.01  | | | | ALPHA: (35) implies:
% 226.54/39.01  | | | |   (36)  op(e1, e3) = all_6_1
% 226.54/39.01  | | | | 
% 226.54/39.01  | | | | REF_CLOSE: (1), (3), (33), (34), (36) are inconsistent by sub-proof
% 226.54/39.01  | | | |            #144.
% 226.54/39.01  | | | | 
% 226.54/39.01  | | | Case 2:
% 226.54/39.01  | | | | 
% 226.54/39.01  | | | |   (37)   ~ (all_6_1 = e2) & op(e1, e3) = all_6_1 & $i(all_6_1)
% 226.54/39.01  | | | | 
% 226.54/39.01  | | | | ALPHA: (37) implies:
% 226.54/39.02  | | | |   (38)  op(e1, e3) = all_6_1
% 226.54/39.02  | | | | 
% 226.54/39.02  | | | | REF_CLOSE: (1), (3), (33), (34), (38) are inconsistent by sub-proof
% 226.54/39.02  | | | |            #144.
% 226.54/39.02  | | | | 
% 226.54/39.02  | | | End of split
% 226.54/39.02  | | | 
% 226.54/39.02  | | End of split
% 226.54/39.02  | | 
% 226.54/39.02  | End of split
% 226.54/39.02  | 
% 226.54/39.02  End of proof
% 226.54/39.02  
% 226.54/39.02  Sub-proof #144 shows that the following formulas are inconsistent:
% 226.54/39.02  ----------------------------------------------------------------
% 226.54/39.02    (1)  op(e1, e3) = e0
% 226.54/39.02    (2)  op(e1, e3) = all_46_1
% 226.54/39.02    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.54/39.02           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.54/39.02    (4)   ~ (all_46_1 = e0)
% 226.54/39.02    (5)  op(e1, e3) = all_6_1
% 226.54/39.02  
% 226.54/39.02  Begin of proof
% 226.54/39.02  | 
% 226.54/39.02  | GROUND_INST: instantiating (3) with e0, all_46_1, e3, e1, simplifying with
% 226.54/39.02  |              (1), (2) gives:
% 226.54/39.02  |   (6)  all_46_1 = e0
% 226.54/39.02  | 
% 226.54/39.02  | GROUND_INST: instantiating (3) with all_6_1, all_46_1, e3, e1, simplifying
% 226.54/39.02  |              with (2), (5) gives:
% 226.54/39.02  |   (7)  all_46_1 = all_6_1
% 226.54/39.02  | 
% 226.54/39.02  | COMBINE_EQS: (6), (7) imply:
% 226.54/39.02  |   (8)  all_6_1 = e0
% 226.54/39.02  | 
% 226.54/39.02  | REDUCE: (4), (6) imply:
% 226.54/39.02  |   (9)  $false
% 226.54/39.02  | 
% 226.54/39.02  | CLOSE: (9) is inconsistent.
% 226.54/39.02  | 
% 226.54/39.02  End of proof
% 226.54/39.02  
% 226.54/39.02  Sub-proof #145 shows that the following formulas are inconsistent:
% 226.54/39.02  ----------------------------------------------------------------
% 226.54/39.02    (1)  op(e1, e3) = e0
% 226.54/39.02    (2)   ~ (all_52_29 = e0)
% 226.54/39.02    (3)  op(e1, e3) = all_46_1
% 226.54/39.02    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.54/39.02           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.54/39.02    (5)   ~ (all_46_0 = e2)
% 226.54/39.02    (6)  op(e1, e1) = e3
% 226.54/39.02    (7)  all_55_14 = all_52_29
% 226.54/39.02    (8)   ~ (all_52_29 = e3)
% 226.54/39.02    (9)  op(all_46_1, e1) = all_46_0
% 226.54/39.02    (10)  op(e0, e1) = all_52_29
% 226.54/39.02    (11)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 226.54/39.02    (12)  op(all_52_29, all_52_29) = e1
% 226.54/39.02    (13)  op(e1, e3) = all_6_1
% 226.54/39.02  
% 226.54/39.02  Begin of proof
% 226.54/39.02  | 
% 226.54/39.02  | GROUND_INST: instantiating (4) with e0, all_46_1, e3, e1, simplifying with
% 226.54/39.02  |              (1), (3) gives:
% 226.54/39.02  |   (14)  all_46_1 = e0
% 226.54/39.02  | 
% 226.54/39.02  | GROUND_INST: instantiating (4) with all_6_1, all_46_1, e3, e1, simplifying
% 226.54/39.02  |              with (3), (13) gives:
% 226.54/39.02  |   (15)  all_46_1 = all_6_1
% 226.54/39.02  | 
% 226.54/39.02  | COMBINE_EQS: (14), (15) imply:
% 226.54/39.02  |   (16)  all_6_1 = e0
% 226.54/39.02  | 
% 226.54/39.02  | REDUCE: (9), (14) imply:
% 226.54/39.02  |   (17)  op(e0, e1) = all_46_0
% 226.54/39.02  | 
% 226.54/39.02  | GROUND_INST: instantiating (4) with all_52_29, all_46_0, e1, e0, simplifying
% 226.54/39.02  |              with (10), (17) gives:
% 226.54/39.02  |   (18)  all_52_29 = all_46_0
% 226.54/39.02  | 
% 226.54/39.02  | COMBINE_EQS: (7), (18) imply:
% 226.54/39.02  |   (19)  all_55_14 = all_46_0
% 226.54/39.02  | 
% 226.54/39.02  | REDUCE: (8), (18) imply:
% 226.54/39.02  |   (20)   ~ (all_46_0 = e3)
% 226.54/39.02  | 
% 226.54/39.02  | REDUCE: (2), (18) imply:
% 226.54/39.02  |   (21)   ~ (all_46_0 = e0)
% 226.54/39.02  | 
% 226.54/39.02  | REDUCE: (12), (18) imply:
% 226.54/39.02  |   (22)  op(all_46_0, all_46_0) = e1
% 226.54/39.02  | 
% 226.54/39.02  | BETA: splitting (11) gives:
% 226.54/39.02  | 
% 226.54/39.02  | Case 1:
% 226.54/39.02  | | 
% 226.54/39.02  | |   (23)  all_55_14 = e3
% 226.54/39.02  | | 
% 226.54/39.02  | | COMBINE_EQS: (19), (23) imply:
% 226.54/39.02  | |   (24)  all_46_0 = e3
% 226.54/39.02  | | 
% 226.54/39.02  | | SIMP: (24) implies:
% 226.54/39.02  | |   (25)  all_46_0 = e3
% 226.54/39.02  | | 
% 226.54/39.02  | | REDUCE: (20), (25) imply:
% 226.54/39.02  | |   (26)  $false
% 226.54/39.02  | | 
% 226.54/39.02  | | CLOSE: (26) is inconsistent.
% 226.54/39.02  | | 
% 226.54/39.02  | Case 2:
% 226.54/39.02  | | 
% 226.54/39.02  | |   (27)   ~ (all_55_14 = e3)
% 226.54/39.02  | |   (28)  all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 226.54/39.02  | | 
% 226.54/39.02  | | BETA: splitting (28) gives:
% 226.54/39.02  | | 
% 226.54/39.02  | | Case 1:
% 226.54/39.02  | | | 
% 226.54/39.02  | | |   (29)  all_55_14 = e2
% 226.54/39.02  | | | 
% 226.54/39.02  | | | COMBINE_EQS: (19), (29) imply:
% 226.54/39.02  | | |   (30)  all_46_0 = e2
% 226.54/39.02  | | | 
% 226.54/39.02  | | | SIMP: (30) implies:
% 226.54/39.02  | | |   (31)  all_46_0 = e2
% 226.54/39.02  | | | 
% 226.54/39.02  | | | REDUCE: (5), (31) imply:
% 226.54/39.02  | | |   (32)  $false
% 226.54/39.02  | | | 
% 226.54/39.02  | | | CLOSE: (32) is inconsistent.
% 226.54/39.02  | | | 
% 226.54/39.02  | | Case 2:
% 226.54/39.02  | | | 
% 226.54/39.02  | | |   (33)  all_55_14 = e1 | all_55_14 = e0
% 226.54/39.02  | | | 
% 226.54/39.02  | | | BETA: splitting (33) gives:
% 226.54/39.02  | | | 
% 226.54/39.02  | | | Case 1:
% 226.54/39.02  | | | | 
% 226.54/39.02  | | | |   (34)  all_55_14 = e1
% 226.54/39.02  | | | | 
% 226.54/39.02  | | | | COMBINE_EQS: (19), (34) imply:
% 226.54/39.02  | | | |   (35)  all_46_0 = e1
% 226.54/39.02  | | | | 
% 226.54/39.02  | | | | SIMP: (35) implies:
% 226.54/39.02  | | | |   (36)  all_46_0 = e1
% 226.54/39.02  | | | | 
% 226.54/39.02  | | | | REDUCE: (20), (36) imply:
% 226.54/39.02  | | | |   (37)   ~ (e3 = e1)
% 226.54/39.02  | | | | 
% 226.54/39.02  | | | | SIMP: (37) implies:
% 226.54/39.02  | | | |   (38)   ~ (e3 = e1)
% 226.54/39.02  | | | | 
% 226.54/39.02  | | | | REDUCE: (22), (36) imply:
% 226.54/39.02  | | | |   (39)  op(e1, e1) = e1
% 226.54/39.02  | | | | 
% 226.54/39.02  | | | | REF_CLOSE: (4), (6), (38), (39) are inconsistent by sub-proof #156.
% 226.54/39.02  | | | | 
% 226.54/39.02  | | | Case 2:
% 226.54/39.02  | | | | 
% 226.54/39.02  | | | |   (40)  all_55_14 = e0
% 226.54/39.02  | | | | 
% 226.54/39.02  | | | | COMBINE_EQS: (19), (40) imply:
% 226.54/39.02  | | | |   (41)  all_46_0 = e0
% 226.54/39.02  | | | | 
% 226.54/39.02  | | | | SIMP: (41) implies:
% 226.54/39.02  | | | |   (42)  all_46_0 = e0
% 226.54/39.02  | | | | 
% 226.54/39.02  | | | | REDUCE: (21), (42) imply:
% 226.54/39.02  | | | |   (43)  $false
% 226.54/39.02  | | | | 
% 226.54/39.02  | | | | CLOSE: (43) is inconsistent.
% 226.54/39.02  | | | | 
% 226.54/39.02  | | | End of split
% 226.54/39.02  | | | 
% 226.54/39.02  | | End of split
% 226.54/39.02  | | 
% 226.54/39.02  | End of split
% 226.54/39.02  | 
% 226.54/39.02  End of proof
% 226.54/39.02  
% 226.54/39.02  Sub-proof #146 shows that the following formulas are inconsistent:
% 226.54/39.02  ----------------------------------------------------------------
% 226.54/39.02    (1)  op(e0, e0) = all_4_2
% 226.54/39.02    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.54/39.02           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.54/39.02    (3)  op(e1, e0) = all_53_14
% 226.54/39.02    (4)   ~ (all_53_14 = e3)
% 226.54/39.02    (5)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 226.54/39.02    (6)   ~ (all_4_2 = e3)
% 226.54/39.02  
% 226.54/39.02  Begin of proof
% 226.54/39.02  | 
% 226.54/39.02  | BETA: splitting (5) gives:
% 226.54/39.02  | 
% 226.54/39.02  | Case 1:
% 226.54/39.02  | | 
% 226.54/39.02  | |   (7)  all_57_11 = e3 & op(e1, e0) = e3
% 226.54/39.02  | | 
% 226.54/39.02  | | ALPHA: (7) implies:
% 226.54/39.02  | |   (8)  op(e1, e0) = e3
% 226.54/39.02  | | 
% 226.54/39.02  | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #2330.
% 226.54/39.02  | | 
% 226.54/39.02  | Case 2:
% 226.54/39.02  | | 
% 226.54/39.02  | |   (9)  all_57_15 = e3 & op(e0, e0) = e3
% 226.54/39.02  | | 
% 226.54/39.02  | | ALPHA: (9) implies:
% 226.54/39.02  | |   (10)  op(e0, e0) = e3
% 226.54/39.02  | | 
% 226.54/39.02  | | REF_CLOSE: (1), (2), (6), (10) are inconsistent by sub-proof #151.
% 226.54/39.02  | | 
% 226.54/39.02  | End of split
% 226.54/39.02  | 
% 226.54/39.02  End of proof
% 226.54/39.02  
% 226.54/39.02  Sub-proof #147 shows that the following formulas are inconsistent:
% 226.54/39.02  ----------------------------------------------------------------
% 226.54/39.02    (1)  op(e3, e3) = all_10_2
% 226.54/39.02    (2)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 226.54/39.02    (3)  ( ~ (all_14_0 = e1) & op(all_14_1, e2) = all_14_0 & op(e2, e0) = all_14_1
% 226.54/39.02           & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e3) & op(e2, e0) =
% 226.54/39.02           all_14_1 & $i(all_14_1))
% 226.54/39.02    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.54/39.02           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.54/39.02    (5)  all_50_2 = e0
% 226.54/39.02    (6)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 226.54/39.02    (7)  op(e2, e2) = e0
% 226.54/39.02    (8)  all_57_3 = e0
% 226.54/39.02    (9)   ~ (e3 = e2)
% 226.54/39.02    (10)  all_55_1 = all_53_4
% 226.54/39.02    (11)   ~ (e3 = e0)
% 226.54/39.02    (12)  op(e1, e1) = e3
% 226.54/39.02    (13)  op(e3, e3) = e3
% 226.54/39.02    (14)   ~ (all_53_4 = all_53_7)
% 226.54/39.02    (15)  op(e3, e2) = all_53_4
% 226.54/39.02    (16)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 226.54/39.02            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 226.54/39.02            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 226.54/39.02            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 226.54/39.02              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 226.54/39.02            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 226.54/39.02            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 226.54/39.02              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 226.54/39.02              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 226.54/39.02            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 226.54/39.02            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 226.54/39.02            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 226.54/39.02              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 226.54/39.02              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 226.54/39.02            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 226.54/39.02              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 226.54/39.02            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 226.54/39.02            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 226.54/39.02              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 226.54/39.02              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 226.54/39.02            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 226.54/39.02            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 226.54/39.02    (17)   ~ (all_53_4 = e0)
% 226.54/39.02    (18)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 226.54/39.02          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 226.54/39.02    (19)   ~ (all_10_2 = e1)
% 226.54/39.02    (20)  op(e0, e2) = all_53_7
% 226.54/39.02    (21)   ~ (all_53_13 = e0)
% 226.54/39.02    (22)   ~ (all_50_2 = e0) | ( ~ (all_50_0 = e3) & op(all_50_1, e2) = all_50_0 &
% 226.54/39.02            op(e2, e0) = all_50_1 & $i(all_50_0) & $i(all_50_1)) | ( ~ (all_50_1 =
% 226.54/39.02              e1) & op(e2, e0) = all_50_1 & $i(all_50_1))
% 226.54/39.02    (23)  op(e2, e0) = all_53_13
% 226.54/39.02    (24)   ~ (all_53_12 = e3)
% 226.54/39.02    (25)   ~ (all_53_6 = e3)
% 226.54/39.02    (26)  op(e1, e2) = all_53_6
% 226.54/39.02    (27)   ~ (all_53_4 = e3)
% 226.54/39.02    (28)  op(e3, e0) = all_53_12
% 226.54/39.02  
% 226.54/39.02  Begin of proof
% 226.54/39.02  | 
% 226.54/39.02  | BETA: splitting (6) gives:
% 226.54/39.02  | 
% 226.54/39.02  | Case 1:
% 226.54/39.02  | | 
% 226.54/39.02  | |   (29)  all_57_9 = e3 & op(e3, e0) = e3
% 226.54/39.02  | | 
% 226.54/39.02  | | ALPHA: (29) implies:
% 226.54/39.02  | |   (30)  op(e3, e0) = e3
% 226.54/39.02  | | 
% 226.54/39.02  | | REF_CLOSE: (4), (24), (28), (30) are inconsistent by sub-proof #2458.
% 226.54/39.02  | | 
% 226.54/39.02  | Case 2:
% 226.54/39.02  | | 
% 226.54/39.02  | |   (31)  all_57_10 = e3 & op(e2, e0) = e3
% 226.54/39.02  | | 
% 226.54/39.02  | | ALPHA: (31) implies:
% 226.54/39.02  | |   (32)  op(e2, e0) = e3
% 226.54/39.02  | | 
% 226.54/39.02  | | BETA: splitting (18) gives:
% 226.54/39.02  | | 
% 226.54/39.02  | | Case 1:
% 226.54/39.02  | | | 
% 226.54/39.02  | | |   (33)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 226.54/39.02  | | |           e3)
% 226.54/39.02  | | | 
% 226.54/39.02  | | | BETA: splitting (33) gives:
% 226.54/39.02  | | | 
% 226.54/39.02  | | | Case 1:
% 226.54/39.02  | | | | 
% 226.54/39.02  | | | |   (34)  all_57_1 = e3 & op(e3, e2) = e3
% 226.54/39.02  | | | | 
% 226.54/39.02  | | | | REF_CLOSE: (4), (15), (27), (34) are inconsistent by sub-proof #2286.
% 226.54/39.02  | | | | 
% 226.54/39.02  | | | Case 2:
% 226.54/39.02  | | | | 
% 226.54/39.02  | | | |   (35)  all_57_3 = e3 & op(e2, e2) = e3
% 226.54/39.02  | | | | 
% 226.54/39.02  | | | | ALPHA: (35) implies:
% 226.54/39.02  | | | |   (36)  all_57_3 = e3
% 226.54/39.02  | | | | 
% 226.54/39.02  | | | | REF_CLOSE: (8), (11), (36) are inconsistent by sub-proof #2358.
% 226.54/39.02  | | | | 
% 226.54/39.02  | | | End of split
% 226.54/39.02  | | | 
% 226.54/39.02  | | Case 2:
% 226.54/39.02  | | | 
% 226.54/39.02  | | |   (37)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 226.54/39.02  | | |           e3)
% 226.54/39.02  | | | 
% 226.54/39.02  | | | BETA: splitting (37) gives:
% 226.54/39.02  | | | 
% 226.54/39.02  | | | Case 1:
% 226.54/39.02  | | | | 
% 226.54/39.02  | | | |   (38)  all_57_7 = e3 & op(e1, e2) = e3
% 226.54/39.02  | | | | 
% 226.54/39.02  | | | | REF_CLOSE: (4), (25), (26), (38) are inconsistent by sub-proof #267.
% 226.54/39.02  | | | | 
% 226.54/39.02  | | | Case 2:
% 226.54/39.02  | | | | 
% 226.54/39.02  | | | |   (39)  all_57_13 = e3 & op(e0, e2) = e3
% 226.54/39.02  | | | | 
% 226.54/39.02  | | | | ALPHA: (39) implies:
% 226.85/39.02  | | | |   (40)  op(e0, e2) = e3
% 226.85/39.02  | | | | 
% 226.85/39.02  | | | | GROUND_INST: instantiating (4) with all_53_7, e3, e2, e0, simplifying
% 226.85/39.02  | | | |              with (20), (40) gives:
% 226.85/39.02  | | | |   (41)  all_53_7 = e3
% 226.85/39.02  | | | | 
% 226.85/39.02  | | | | GROUND_INST: instantiating (4) with all_53_13, e3, e0, e2, simplifying
% 226.85/39.02  | | | |              with (23), (32) gives:
% 226.85/39.02  | | | |   (42)  all_53_13 = e3
% 226.85/39.02  | | | | 
% 226.85/39.02  | | | | BETA: splitting (22) gives:
% 226.85/39.02  | | | | 
% 226.85/39.02  | | | | Case 1:
% 226.85/39.02  | | | | | 
% 226.85/39.02  | | | | |   (43)   ~ (all_50_2 = e0)
% 226.85/39.02  | | | | | 
% 226.85/39.02  | | | | | REDUCE: (5), (43) imply:
% 226.85/39.02  | | | | |   (44)  $false
% 226.85/39.02  | | | | | 
% 226.85/39.02  | | | | | CLOSE: (44) is inconsistent.
% 226.85/39.02  | | | | | 
% 226.85/39.02  | | | | Case 2:
% 226.85/39.02  | | | | | 
% 226.85/39.02  | | | | |   (45)  ( ~ (all_50_0 = e3) & op(all_50_1, e2) = all_50_0 & op(e2, e0)
% 226.85/39.02  | | | | |           = all_50_1 & $i(all_50_0) & $i(all_50_1)) | ( ~ (all_50_1 =
% 226.85/39.02  | | | | |             e1) & op(e2, e0) = all_50_1 & $i(all_50_1))
% 226.85/39.02  | | | | | 
% 226.85/39.02  | | | | | BETA: splitting (16) gives:
% 226.85/39.02  | | | | | 
% 226.85/39.02  | | | | | Case 1:
% 226.85/39.02  | | | | | | 
% 226.85/39.02  | | | | | |   (46)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 =
% 226.85/39.02  | | | | | |           e0 & op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3)
% 226.85/39.02  | | | | | |           = e2 & op(all_52_5, all_52_5) = e1 & op(all_52_7,
% 226.85/39.02  | | | | | |             all_52_7) = e0 & op(e3, e3) = all_52_1 & op(e3, e2) =
% 226.85/39.02  | | | | | |           all_52_3 & op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 226.85/39.02  | | | | | |           $i(all_52_1) & $i(all_52_3) & $i(all_52_5) & $i(all_52_7))
% 226.85/39.02  | | | | | |         | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 226.85/39.02  | | | | | |           all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 226.85/39.02  | | | | | |           op(all_52_11, all_52_11) = e2 & op(all_52_13, all_52_13) =
% 226.85/39.02  | | | | | |           e1 & op(all_52_15, all_52_15) = e0 & op(e2, e3) = all_52_9
% 226.85/39.02  | | | | | |           & op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13 & op(e2,
% 226.85/39.02  | | | | | |             e0) = all_52_15 & $i(all_52_9) & $i(all_52_11) &
% 226.85/39.02  | | | | | |           $i(all_52_13) & $i(all_52_15))
% 226.85/39.02  | | | | | | 
% 226.85/39.02  | | | | | | BETA: splitting (46) gives:
% 226.85/39.02  | | | | | | 
% 226.85/39.02  | | | | | | Case 1:
% 226.85/39.02  | | | | | | | 
% 226.85/39.02  | | | | | | |   (47)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 =
% 226.85/39.02  | | | | | | |         e0 & op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3)
% 226.85/39.02  | | | | | | |         = e2 & op(all_52_5, all_52_5) = e1 & op(all_52_7,
% 226.85/39.02  | | | | | | |           all_52_7) = e0 & op(e3, e3) = all_52_1 & op(e3, e2) =
% 226.85/39.02  | | | | | | |         all_52_3 & op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 226.85/39.02  | | | | | | |         $i(all_52_1) & $i(all_52_3) & $i(all_52_5) & $i(all_52_7)
% 226.85/39.02  | | | | | | | 
% 226.85/39.02  | | | | | | | ALPHA: (47) implies:
% 226.85/39.02  | | | | | | |   (48)  op(e3, e2) = all_52_3
% 226.85/39.02  | | | | | | |   (49)  op(all_52_3, all_52_3) = e2
% 226.85/39.02  | | | | | | | 
% 226.85/39.02  | | | | | | | REF_CLOSE: (2), (3), (4), (7), (10), (15), (17), (27), (32), (45),
% 226.85/39.02  | | | | | | |            (48), (49) are inconsistent by sub-proof #149.
% 226.85/39.02  | | | | | | | 
% 226.85/39.02  | | | | | | Case 2:
% 226.85/39.02  | | | | | | | 
% 226.85/39.02  | | | | | | |   (50)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 226.85/39.02  | | | | | | |         all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 226.85/39.02  | | | | | | |         op(all_52_11, all_52_11) = e2 & op(all_52_13, all_52_13) =
% 226.85/39.02  | | | | | | |         e1 & op(all_52_15, all_52_15) = e0 & op(e2, e3) = all_52_9
% 226.85/39.02  | | | | | | |         & op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13 & op(e2,
% 226.85/39.02  | | | | | | |           e0) = all_52_15 & $i(all_52_9) & $i(all_52_11) &
% 226.85/39.02  | | | | | | |         $i(all_52_13) & $i(all_52_15)
% 226.85/39.02  | | | | | | | 
% 226.85/39.02  | | | | | | | ALPHA: (50) implies:
% 226.85/39.02  | | | | | | |   (51)  op(e2, e0) = all_52_15
% 226.85/39.02  | | | | | | |   (52)  op(all_52_15, all_52_15) = e0
% 226.85/39.02  | | | | | | | 
% 226.85/39.02  | | | | | | | REF_CLOSE: (3), (4), (11), (13), (32), (45), (51), (52) are
% 226.85/39.02  | | | | | | |            inconsistent by sub-proof #148.
% 226.85/39.02  | | | | | | | 
% 226.85/39.02  | | | | | | End of split
% 226.85/39.02  | | | | | | 
% 226.85/39.02  | | | | | Case 2:
% 226.85/39.02  | | | | | | 
% 226.85/39.02  | | | | | |   (53)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 226.85/39.02  | | | | | |           all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 226.85/39.02  | | | | | |           op(all_52_19, all_52_19) = e2 & op(all_52_21, all_52_21) =
% 226.85/39.02  | | | | | |           e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 226.85/39.02  | | | | | |           all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) =
% 226.85/39.02  | | | | | |           all_52_21 & op(e1, e0) = all_52_23 & $i(all_52_17) &
% 226.85/39.02  | | | | | |           $i(all_52_19) & $i(all_52_21) & $i(all_52_23)) |
% 226.85/39.02  | | | | | |         (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 226.85/39.02  | | | | | |           all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 226.85/39.02  | | | | | |           op(all_52_27, all_52_27) = e2 & op(all_52_29, all_52_29) =
% 226.85/39.02  | | | | | |           e1 & op(all_52_31, all_52_31) = e0 & op(e0, e3) =
% 226.85/39.02  | | | | | |           all_52_25 & op(e0, e2) = all_52_27 & op(e0, e1) =
% 226.85/39.02  | | | | | |           all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 226.85/39.02  | | | | | |           $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 226.85/39.02  | | | | | | 
% 226.85/39.02  | | | | | | REF_CLOSE: (1), (4), (9), (12), (13), (19), (40), (53) are
% 226.85/39.02  | | | | | |            inconsistent by sub-proof #166.
% 226.85/39.02  | | | | | | 
% 226.85/39.02  | | | | | End of split
% 226.85/39.02  | | | | | 
% 226.85/39.02  | | | | End of split
% 226.85/39.02  | | | | 
% 226.85/39.02  | | | End of split
% 226.85/39.02  | | | 
% 226.85/39.02  | | End of split
% 226.85/39.02  | | 
% 226.85/39.02  | End of split
% 226.85/39.02  | 
% 226.85/39.02  End of proof
% 226.85/39.02  
% 226.85/39.02  Sub-proof #148 shows that the following formulas are inconsistent:
% 226.85/39.02  ----------------------------------------------------------------
% 226.85/39.02    (1)  ( ~ (all_50_0 = e3) & op(all_50_1, e2) = all_50_0 & op(e2, e0) = all_50_1
% 226.85/39.02           & $i(all_50_0) & $i(all_50_1)) | ( ~ (all_50_1 = e1) & op(e2, e0) =
% 226.85/39.02           all_50_1 & $i(all_50_1))
% 226.85/39.02    (2)  ( ~ (all_14_0 = e1) & op(all_14_1, e2) = all_14_0 & op(e2, e0) = all_14_1
% 226.85/39.02           & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e3) & op(e2, e0) =
% 226.85/39.02           all_14_1 & $i(all_14_1))
% 226.85/39.02    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.85/39.02           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.85/39.02    (4)  op(e2, e0) = e3
% 226.85/39.02    (5)  op(e2, e0) = all_52_15
% 226.85/39.02    (6)   ~ (e3 = e0)
% 226.85/39.02    (7)  op(e3, e3) = e3
% 226.85/39.02    (8)  op(all_52_15, all_52_15) = e0
% 226.85/39.02  
% 226.85/39.02  Begin of proof
% 226.85/39.02  | 
% 226.85/39.02  | BETA: splitting (2) gives:
% 226.85/39.02  | 
% 226.85/39.02  | Case 1:
% 226.85/39.02  | | 
% 226.85/39.02  | |   (9)   ~ (all_14_0 = e1) & op(all_14_1, e2) = all_14_0 & op(e2, e0) =
% 226.85/39.02  | |        all_14_1 & $i(all_14_0) & $i(all_14_1)
% 226.85/39.02  | | 
% 226.85/39.02  | | ALPHA: (9) implies:
% 226.85/39.02  | |   (10)  op(e2, e0) = all_14_1
% 226.85/39.02  | | 
% 226.85/39.02  | | GROUND_INST: instantiating (3) with e3, all_52_15, e0, e2, simplifying with
% 226.85/39.02  | |              (4), (5) gives:
% 226.85/39.02  | |   (11)  all_52_15 = e3
% 226.85/39.02  | | 
% 226.85/39.02  | | GROUND_INST: instantiating (3) with all_14_1, all_52_15, e0, e2, simplifying
% 226.85/39.02  | |              with (5), (10) gives:
% 226.85/39.02  | |   (12)  all_52_15 = all_14_1
% 226.85/39.02  | | 
% 226.85/39.02  | | COMBINE_EQS: (11), (12) imply:
% 226.85/39.02  | |   (13)  all_14_1 = e3
% 226.85/39.02  | | 
% 226.85/39.02  | | REDUCE: (8), (11) imply:
% 226.85/39.02  | |   (14)  op(e3, e3) = e0
% 226.85/39.02  | | 
% 226.85/39.02  | | REF_CLOSE: (3), (6), (7), (14) are inconsistent by sub-proof #2494.
% 226.85/39.02  | | 
% 226.85/39.02  | Case 2:
% 226.85/39.02  | | 
% 226.85/39.02  | |   (15)   ~ (all_14_1 = e3) & op(e2, e0) = all_14_1 & $i(all_14_1)
% 226.85/39.02  | | 
% 226.85/39.02  | | REF_CLOSE: (1), (3), (4), (15) are inconsistent by sub-proof #1326.
% 226.85/39.02  | | 
% 226.85/39.02  | End of split
% 226.85/39.02  | 
% 226.85/39.02  End of proof
% 226.85/39.02  
% 226.85/39.02  Sub-proof #149 shows that the following formulas are inconsistent:
% 226.85/39.02  ----------------------------------------------------------------
% 226.85/39.02    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 226.85/39.02    (2)  ( ~ (all_50_0 = e3) & op(all_50_1, e2) = all_50_0 & op(e2, e0) = all_50_1
% 226.85/39.02           & $i(all_50_0) & $i(all_50_1)) | ( ~ (all_50_1 = e1) & op(e2, e0) =
% 226.85/39.02           all_50_1 & $i(all_50_1))
% 226.85/39.02    (3)  ( ~ (all_14_0 = e1) & op(all_14_1, e2) = all_14_0 & op(e2, e0) = all_14_1
% 226.85/39.02           & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e3) & op(e2, e0) =
% 226.85/39.02           all_14_1 & $i(all_14_1))
% 226.85/39.02    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.85/39.02           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.85/39.02    (5)  op(e2, e0) = e3
% 226.85/39.02    (6)  op(e3, e2) = all_52_3
% 226.85/39.02    (7)  op(all_52_3, all_52_3) = e2
% 226.85/39.02    (8)  op(e2, e2) = e0
% 226.85/39.02    (9)  all_55_1 = all_53_4
% 226.85/39.02    (10)  op(e3, e2) = all_53_4
% 226.85/39.02    (11)   ~ (all_53_4 = e0)
% 226.85/39.02    (12)   ~ (all_53_4 = e3)
% 226.85/39.02  
% 226.85/39.02  Begin of proof
% 226.85/39.02  | 
% 226.85/39.02  | BETA: splitting (3) gives:
% 226.85/39.02  | 
% 226.85/39.02  | Case 1:
% 226.85/39.02  | | 
% 226.85/39.02  | |   (13)   ~ (all_14_0 = e1) & op(all_14_1, e2) = all_14_0 & op(e2, e0) =
% 226.85/39.02  | |         all_14_1 & $i(all_14_0) & $i(all_14_1)
% 226.85/39.02  | | 
% 226.85/39.02  | | ALPHA: (13) implies:
% 226.85/39.02  | |   (14)   ~ (all_14_0 = e1)
% 226.85/39.02  | |   (15)  op(e2, e0) = all_14_1
% 226.85/39.02  | |   (16)  op(all_14_1, e2) = all_14_0
% 226.85/39.02  | | 
% 226.85/39.03  | | GROUND_INST: instantiating (4) with e3, all_14_1, e0, e2, simplifying with
% 226.85/39.03  | |              (5), (15) gives:
% 226.85/39.03  | |   (17)  all_14_1 = e3
% 226.85/39.03  | | 
% 226.85/39.03  | | GROUND_INST: instantiating (4) with all_53_4, all_52_3, e2, e3, simplifying
% 226.85/39.03  | |              with (6), (10) gives:
% 226.85/39.03  | |   (18)  all_53_4 = all_52_3
% 226.85/39.03  | | 
% 226.85/39.03  | | COMBINE_EQS: (9), (18) imply:
% 226.85/39.03  | |   (19)  all_55_1 = all_52_3
% 226.85/39.03  | | 
% 226.85/39.03  | | REDUCE: (12), (18) imply:
% 226.85/39.03  | |   (20)   ~ (all_52_3 = e3)
% 226.85/39.03  | | 
% 226.85/39.03  | | REDUCE: (11), (18) imply:
% 226.85/39.03  | |   (21)   ~ (all_52_3 = e0)
% 226.85/39.03  | | 
% 226.85/39.03  | | REDUCE: (16), (17) imply:
% 226.85/39.03  | |   (22)  op(e3, e2) = all_14_0
% 226.85/39.03  | | 
% 226.85/39.03  | | GROUND_INST: instantiating (4) with all_52_3, all_14_0, e2, e3, simplifying
% 226.85/39.03  | |              with (6), (22) gives:
% 226.85/39.03  | |   (23)  all_52_3 = all_14_0
% 226.85/39.03  | | 
% 226.85/39.03  | | COMBINE_EQS: (19), (23) imply:
% 226.85/39.03  | |   (24)  all_55_1 = all_14_0
% 226.85/39.03  | | 
% 226.85/39.03  | | REDUCE: (20), (23) imply:
% 226.85/39.03  | |   (25)   ~ (all_14_0 = e3)
% 226.85/39.03  | | 
% 226.85/39.03  | | REDUCE: (21), (23) imply:
% 226.85/39.03  | |   (26)   ~ (all_14_0 = e0)
% 226.85/39.03  | | 
% 226.85/39.03  | | REDUCE: (7), (23) imply:
% 226.85/39.03  | |   (27)  op(all_14_0, all_14_0) = e2
% 226.85/39.03  | | 
% 226.85/39.03  | | BETA: splitting (1) gives:
% 226.85/39.03  | | 
% 226.85/39.03  | | Case 1:
% 226.85/39.03  | | | 
% 226.85/39.03  | | |   (28)  all_55_1 = e3
% 226.85/39.03  | | | 
% 226.85/39.03  | | | REF_CLOSE: (24), (25), (28) are inconsistent by sub-proof #1225.
% 226.85/39.03  | | | 
% 226.85/39.03  | | Case 2:
% 226.85/39.03  | | | 
% 226.85/39.03  | | |   (29)  all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 226.85/39.03  | | | 
% 226.85/39.03  | | | BETA: splitting (29) gives:
% 226.85/39.03  | | | 
% 226.85/39.03  | | | Case 1:
% 226.85/39.03  | | | | 
% 226.85/39.03  | | | |   (30)  all_55_1 = e2
% 226.85/39.03  | | | | 
% 226.85/39.03  | | | | COMBINE_EQS: (24), (30) imply:
% 226.85/39.03  | | | |   (31)  all_14_0 = e2
% 226.85/39.03  | | | | 
% 226.85/39.03  | | | | SIMP: (31) implies:
% 226.85/39.03  | | | |   (32)  all_14_0 = e2
% 226.85/39.03  | | | | 
% 226.85/39.03  | | | | REDUCE: (26), (32) imply:
% 226.85/39.03  | | | |   (33)   ~ (e2 = e0)
% 226.85/39.03  | | | | 
% 226.85/39.03  | | | | REDUCE: (27), (32) imply:
% 226.85/39.03  | | | |   (34)  op(e2, e2) = e2
% 226.85/39.03  | | | | 
% 226.85/39.03  | | | | REF_CLOSE: (4), (8), (33), (34) are inconsistent by sub-proof #2472.
% 226.85/39.03  | | | | 
% 226.85/39.03  | | | Case 2:
% 226.85/39.03  | | | | 
% 226.85/39.03  | | | |   (35)  all_55_1 = e1 | all_55_1 = e0
% 226.85/39.03  | | | | 
% 226.85/39.03  | | | | REF_CLOSE: (14), (24), (26), (35) are inconsistent by sub-proof #1197.
% 226.85/39.03  | | | | 
% 226.85/39.03  | | | End of split
% 226.85/39.03  | | | 
% 226.85/39.03  | | End of split
% 226.85/39.03  | | 
% 226.85/39.03  | Case 2:
% 226.85/39.03  | | 
% 226.85/39.03  | |   (36)   ~ (all_14_1 = e3) & op(e2, e0) = all_14_1 & $i(all_14_1)
% 226.85/39.03  | | 
% 226.85/39.03  | | REF_CLOSE: (2), (4), (5), (36) are inconsistent by sub-proof #1326.
% 226.85/39.03  | | 
% 226.85/39.03  | End of split
% 226.85/39.03  | 
% 226.85/39.03  End of proof
% 226.85/39.03  
% 226.85/39.03  Sub-proof #150 shows that the following formulas are inconsistent:
% 226.85/39.03  ----------------------------------------------------------------
% 226.85/39.03    (1)  op(e0, e0) = all_4_2
% 226.85/39.03    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.85/39.03           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.85/39.03    (3)   ~ (e3 = e0)
% 226.85/39.03    (4)  op(e1, e1) = e3
% 226.85/39.03    (5)  op(e0, e0) = all_52_31
% 226.85/39.03    (6)  all_30_2 = all_4_2
% 226.85/39.03    (7)  all_30_2 = e1
% 226.85/39.03    (8)  op(all_52_31, all_52_31) = e0
% 226.85/39.03  
% 226.85/39.03  Begin of proof
% 226.85/39.03  | 
% 226.85/39.03  | COMBINE_EQS: (6), (7) imply:
% 226.85/39.03  |   (9)  all_4_2 = e1
% 226.85/39.03  | 
% 226.85/39.03  | SIMP: (9) implies:
% 226.85/39.03  |   (10)  all_4_2 = e1
% 226.85/39.03  | 
% 226.85/39.03  | REDUCE: (1), (10) imply:
% 226.85/39.03  |   (11)  op(e0, e0) = e1
% 226.85/39.03  | 
% 226.85/39.03  | REF_CLOSE: (2), (3), (4), (5), (8), (11) are inconsistent by sub-proof #161.
% 226.85/39.03  | 
% 226.85/39.03  End of proof
% 226.85/39.03  
% 226.85/39.03  Sub-proof #151 shows that the following formulas are inconsistent:
% 226.85/39.03  ----------------------------------------------------------------
% 226.85/39.03    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.85/39.03           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.85/39.03    (2)  op(e0, e0) = all_4_2
% 226.85/39.03    (3)  op(e0, e0) = e3
% 226.85/39.03    (4)   ~ (all_4_2 = e3)
% 226.85/39.03  
% 226.85/39.03  Begin of proof
% 226.85/39.03  | 
% 226.85/39.03  | GROUND_INST: instantiating (1) with all_4_2, e3, e0, e0, simplifying with (2),
% 226.85/39.03  |              (3) gives:
% 226.85/39.03  |   (5)  all_4_2 = e3
% 226.85/39.03  | 
% 226.85/39.03  | REDUCE: (4), (5) imply:
% 226.85/39.03  |   (6)  $false
% 226.85/39.03  | 
% 226.85/39.03  | CLOSE: (6) is inconsistent.
% 226.85/39.03  | 
% 226.85/39.03  End of proof
% 226.85/39.03  
% 226.85/39.03  Sub-proof #152 shows that the following formulas are inconsistent:
% 226.85/39.03  ----------------------------------------------------------------
% 226.85/39.03    (1)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 226.85/39.03    (2)  op(e2, e3) = all_53_1
% 226.85/39.03    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 226.85/39.03         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 226.85/39.03    (4)   ~ (e3 = e1)
% 226.85/39.03    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.85/39.03           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.85/39.03    (6)   ~ (all_53_2 = e3)
% 226.85/39.03    (7)   ~ (e3 = e2)
% 226.85/39.03    (8)   ~ (e3 = e0)
% 226.85/39.03    (9)  op(e0, e3) = all_53_3
% 226.85/39.03    (10)  op(e3, e3) = e2
% 226.85/39.03    (11)   ~ (all_53_3 = e2)
% 226.85/39.03    (12)   ~ (all_53_1 = e1)
% 226.85/39.03    (13)   ~ (e2 = e0)
% 226.85/39.03    (14)   ~ (e1 = e0)
% 226.85/39.03    (15)  op(e1, e3) = all_53_2
% 226.85/39.03    (16)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 226.85/39.03          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 226.85/39.03    (17)   ~ (e2 = e1)
% 226.85/39.03    (18)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 226.85/39.03          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 226.85/39.03  
% 226.85/39.03  Begin of proof
% 226.85/39.03  | 
% 226.85/39.03  | BETA: splitting (1) gives:
% 226.85/39.03  | 
% 226.85/39.03  | Case 1:
% 226.85/39.03  | | 
% 226.85/39.03  | |   (19)  all_57_6 = e2 & op(e1, e3) = e2
% 226.85/39.03  | | 
% 226.85/39.03  | | ALPHA: (19) implies:
% 226.85/39.03  | |   (20)  all_57_6 = e2
% 226.85/39.03  | | 
% 226.85/39.03  | | BETA: splitting (3) gives:
% 226.85/39.03  | | 
% 226.85/39.03  | | Case 1:
% 226.85/39.03  | | | 
% 226.85/39.03  | | |   (21)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) =
% 226.85/39.03  | | |           e1)
% 226.85/39.03  | | | 
% 226.85/39.03  | | | REF_CLOSE: (2), (5), (10), (12), (17), (21) are inconsistent by sub-proof
% 226.85/39.03  | | |            #1598.
% 226.85/39.03  | | | 
% 226.85/39.03  | | Case 2:
% 226.85/39.03  | | | 
% 226.85/39.03  | | |   (22)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) =
% 226.85/39.03  | | |           e1)
% 226.85/39.03  | | | 
% 226.85/39.03  | | | BETA: splitting (22) gives:
% 226.85/39.03  | | | 
% 226.85/39.03  | | | Case 1:
% 226.85/39.03  | | | | 
% 226.85/39.03  | | | |   (23)  all_57_6 = e1 & op(e1, e3) = e1
% 226.85/39.03  | | | | 
% 226.85/39.03  | | | | REF_CLOSE: (17), (20), (23) are inconsistent by sub-proof #2389.
% 226.85/39.03  | | | | 
% 226.85/39.03  | | | Case 2:
% 226.85/39.03  | | | | 
% 226.85/39.03  | | | |   (24)  all_57_12 = e1 & op(e0, e3) = e1
% 226.85/39.03  | | | | 
% 226.85/39.03  | | | | ALPHA: (24) implies:
% 226.85/39.03  | | | |   (25)  all_57_12 = e1
% 226.85/39.03  | | | | 
% 226.85/39.03  | | | | BETA: splitting (16) gives:
% 226.85/39.03  | | | | 
% 226.85/39.03  | | | | Case 1:
% 226.85/39.03  | | | | | 
% 226.85/39.03  | | | | |   (26)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2,
% 226.85/39.03  | | | | |             e3) = e3)
% 226.85/39.03  | | | | | 
% 226.85/39.03  | | | | | BETA: splitting (26) gives:
% 226.85/39.03  | | | | | 
% 226.85/39.03  | | | | | Case 1:
% 226.85/39.03  | | | | | | 
% 226.85/39.03  | | | | | |   (27)  all_57_0 = e3 & op(e3, e3) = e3
% 226.85/39.03  | | | | | | 
% 226.85/39.03  | | | | | | ALPHA: (27) implies:
% 226.85/39.03  | | | | | |   (28)  op(e3, e3) = e3
% 226.85/39.03  | | | | | | 
% 226.85/39.03  | | | | | | REF_CLOSE: (5), (7), (10), (28) are inconsistent by sub-proof #2490.
% 226.85/39.03  | | | | | | 
% 226.85/39.03  | | | | | Case 2:
% 226.85/39.03  | | | | | | 
% 226.85/39.03  | | | | | |   (29)  all_57_2 = e3 & op(e2, e3) = e3
% 226.85/39.03  | | | | | | 
% 226.85/39.03  | | | | | | REF_CLOSE: (3), (4), (5), (8), (10), (13), (14), (17), (18), (20),
% 226.85/39.03  | | | | | |            (29) are inconsistent by sub-proof #154.
% 226.85/39.03  | | | | | | 
% 226.85/39.03  | | | | | End of split
% 226.85/39.03  | | | | | 
% 226.85/39.03  | | | | Case 2:
% 226.85/39.03  | | | | | 
% 226.85/39.03  | | | | |   (30)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0,
% 226.85/39.03  | | | | |             e3) = e3)
% 226.85/39.03  | | | | | 
% 226.85/39.03  | | | | | BETA: splitting (30) gives:
% 226.85/39.03  | | | | | 
% 226.85/39.03  | | | | | Case 1:
% 226.85/39.03  | | | | | | 
% 226.85/39.03  | | | | | |   (31)  all_57_6 = e3 & op(e1, e3) = e3
% 226.85/39.03  | | | | | | 
% 226.85/39.03  | | | | | | REF_CLOSE: (5), (6), (15), (31) are inconsistent by sub-proof #153.
% 226.85/39.03  | | | | | | 
% 226.85/39.03  | | | | | Case 2:
% 226.85/39.03  | | | | | | 
% 226.85/39.03  | | | | | |   (32)  all_57_12 = e3 & op(e0, e3) = e3
% 226.85/39.03  | | | | | | 
% 226.85/39.03  | | | | | | ALPHA: (32) implies:
% 226.85/39.03  | | | | | |   (33)  all_57_12 = e3
% 226.85/39.03  | | | | | | 
% 226.85/39.03  | | | | | | REF_CLOSE: (4), (25), (33) are inconsistent by sub-proof #2151.
% 226.85/39.03  | | | | | | 
% 226.85/39.03  | | | | | End of split
% 226.85/39.03  | | | | | 
% 226.85/39.03  | | | | End of split
% 226.85/39.03  | | | | 
% 226.85/39.03  | | | End of split
% 226.85/39.03  | | | 
% 226.85/39.03  | | End of split
% 226.85/39.03  | | 
% 226.85/39.03  | Case 2:
% 226.85/39.03  | | 
% 226.85/39.03  | |   (34)  all_57_12 = e2 & op(e0, e3) = e2
% 226.85/39.03  | | 
% 226.85/39.03  | | ALPHA: (34) implies:
% 226.85/39.03  | |   (35)  op(e0, e3) = e2
% 226.85/39.03  | | 
% 226.85/39.03  | | REF_CLOSE: (5), (9), (11), (35) are inconsistent by sub-proof #1980.
% 226.85/39.03  | | 
% 226.85/39.03  | End of split
% 226.85/39.03  | 
% 226.85/39.03  End of proof
% 226.85/39.03  
% 226.85/39.03  Sub-proof #153 shows that the following formulas are inconsistent:
% 226.85/39.03  ----------------------------------------------------------------
% 226.85/39.03    (1)  all_57_6 = e3 & op(e1, e3) = e3
% 226.85/39.03    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.85/39.03           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.85/39.03    (3)  op(e1, e3) = all_53_2
% 226.85/39.03    (4)   ~ (all_53_2 = e3)
% 226.85/39.03  
% 226.85/39.03  Begin of proof
% 226.85/39.03  | 
% 226.85/39.03  | ALPHA: (1) implies:
% 226.85/39.03  |   (5)  op(e1, e3) = e3
% 226.85/39.03  | 
% 226.85/39.03  | GROUND_INST: instantiating (2) with all_53_2, e3, e3, e1, simplifying with
% 226.85/39.03  |              (3), (5) gives:
% 226.85/39.03  |   (6)  all_53_2 = e3
% 226.85/39.03  | 
% 226.85/39.03  | REDUCE: (4), (6) imply:
% 226.85/39.03  |   (7)  $false
% 226.85/39.03  | 
% 226.85/39.03  | CLOSE: (7) is inconsistent.
% 226.85/39.03  | 
% 226.85/39.03  End of proof
% 226.85/39.03  
% 226.85/39.03  Sub-proof #154 shows that the following formulas are inconsistent:
% 226.85/39.03  ----------------------------------------------------------------
% 226.85/39.03    (1)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 226.85/39.03         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 226.85/39.03    (2)   ~ (e3 = e1)
% 226.85/39.03    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.85/39.03           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.85/39.03    (4)  all_57_2 = e3 & op(e2, e3) = e3
% 226.85/39.03    (5)   ~ (e3 = e0)
% 226.85/39.03    (6)  op(e3, e3) = e2
% 226.85/39.03    (7)  all_57_6 = e2
% 226.85/39.03    (8)   ~ (e2 = e0)
% 226.85/39.03    (9)   ~ (e1 = e0)
% 226.85/39.03    (10)   ~ (e2 = e1)
% 226.85/39.03    (11)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 226.85/39.03          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 226.85/39.03  
% 226.85/39.03  Begin of proof
% 226.85/39.03  | 
% 226.85/39.03  | ALPHA: (4) implies:
% 226.85/39.03  |   (12)  all_57_2 = e3
% 226.85/39.03  | 
% 226.85/39.03  | BETA: splitting (11) gives:
% 226.85/39.03  | 
% 226.85/39.03  | Case 1:
% 226.85/39.03  | | 
% 226.85/39.03  | |   (13)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) =
% 226.85/39.03  | |           e0)
% 226.85/39.03  | | 
% 226.85/39.03  | | REF_CLOSE: (3), (5), (6), (8), (12), (13) are inconsistent by sub-proof
% 226.85/39.03  | |            #758.
% 226.85/39.03  | | 
% 226.85/39.03  | Case 2:
% 226.85/39.03  | | 
% 226.85/39.03  | |   (14)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) =
% 226.85/39.03  | |           e0)
% 226.85/39.03  | | 
% 226.85/39.03  | | BETA: splitting (14) gives:
% 226.85/39.03  | | 
% 226.85/39.03  | | Case 1:
% 226.85/39.03  | | | 
% 226.85/39.03  | | |   (15)  all_57_6 = e0 & op(e1, e3) = e0
% 226.85/39.03  | | | 
% 226.85/39.03  | | | REF_CLOSE: (7), (8), (15) are inconsistent by sub-proof #2386.
% 226.85/39.03  | | | 
% 226.85/39.03  | | Case 2:
% 226.85/39.03  | | | 
% 226.85/39.03  | | |   (16)  all_57_12 = e0 & op(e0, e3) = e0
% 226.85/39.03  | | | 
% 226.85/39.03  | | | ALPHA: (16) implies:
% 226.85/39.03  | | |   (17)  all_57_12 = e0
% 226.85/39.03  | | | 
% 226.85/39.03  | | | BETA: splitting (1) gives:
% 226.85/39.03  | | | 
% 226.85/39.03  | | | Case 1:
% 226.85/39.03  | | | | 
% 226.85/39.03  | | | |   (18)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3)
% 226.85/39.03  | | | |           = e1)
% 226.85/39.03  | | | | 
% 226.85/39.03  | | | | REF_CLOSE: (2), (3), (6), (10), (12), (18) are inconsistent by sub-proof
% 226.85/39.03  | | | |            #749.
% 226.85/39.03  | | | | 
% 226.85/39.03  | | | Case 2:
% 226.85/39.03  | | | | 
% 226.85/39.03  | | | |   (19)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3)
% 226.85/39.03  | | | |           = e1)
% 226.85/39.03  | | | | 
% 226.85/39.03  | | | | REF_CLOSE: (7), (9), (10), (17), (19) are inconsistent by sub-proof
% 226.85/39.03  | | | |            #1313.
% 226.85/39.03  | | | | 
% 226.85/39.03  | | | End of split
% 226.85/39.03  | | | 
% 226.85/39.03  | | End of split
% 226.85/39.03  | | 
% 226.85/39.03  | End of split
% 226.85/39.03  | 
% 226.85/39.03  End of proof
% 226.85/39.03  
% 226.85/39.03  Sub-proof #155 shows that the following formulas are inconsistent:
% 226.85/39.03  ----------------------------------------------------------------
% 226.85/39.03    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.85/39.03           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.85/39.03    (2)  op(e2, e2) = e1
% 226.85/39.03    (3)   ~ (e3 = e2)
% 226.85/39.03    (4)  op(e1, e1) = e3
% 226.85/39.03    (5)  op(e2, e2) = all_52_11
% 226.85/39.03    (6)  op(all_52_11, all_52_11) = e2
% 226.85/39.03  
% 226.85/39.03  Begin of proof
% 226.85/39.03  | 
% 226.85/39.03  | GROUND_INST: instantiating (1) with e1, all_52_11, e2, e2, simplifying with
% 226.85/39.03  |              (2), (5) gives:
% 226.85/39.03  |   (7)  all_52_11 = e1
% 226.85/39.03  | 
% 226.85/39.03  | REDUCE: (6), (7) imply:
% 226.85/39.03  |   (8)  op(e1, e1) = e2
% 226.85/39.03  | 
% 226.85/39.03  | GROUND_INST: instantiating (1) with e3, e2, e1, e1, simplifying with (4), (8)
% 226.85/39.03  |              gives:
% 226.85/39.03  |   (9)  e3 = e2
% 226.85/39.03  | 
% 226.85/39.03  | REDUCE: (3), (9) imply:
% 226.85/39.03  |   (10)  $false
% 226.85/39.03  | 
% 226.85/39.03  | CLOSE: (10) is inconsistent.
% 226.85/39.03  | 
% 226.85/39.03  End of proof
% 226.85/39.03  
% 226.85/39.03  Sub-proof #156 shows that the following formulas are inconsistent:
% 226.85/39.03  ----------------------------------------------------------------
% 226.85/39.03    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.85/39.03           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.85/39.03    (2)  op(e1, e1) = e3
% 226.85/39.03    (3)  op(e1, e1) = e1
% 226.85/39.03    (4)   ~ (e3 = e1)
% 226.85/39.03  
% 226.85/39.03  Begin of proof
% 226.85/39.03  | 
% 226.85/39.03  | GROUND_INST: instantiating (1) with e3, e1, e1, e1, simplifying with (2), (3)
% 226.85/39.03  |              gives:
% 226.85/39.03  |   (5)  e3 = e1
% 226.85/39.03  | 
% 226.85/39.03  | REDUCE: (4), (5) imply:
% 226.85/39.03  |   (6)  $false
% 226.85/39.03  | 
% 226.85/39.03  | CLOSE: (6) is inconsistent.
% 226.85/39.03  | 
% 226.85/39.03  End of proof
% 226.85/39.03  
% 226.85/39.03  Sub-proof #157 shows that the following formulas are inconsistent:
% 226.85/39.03  ----------------------------------------------------------------
% 226.85/39.03    (1)  op(e0, e0) = all_4_2
% 226.85/39.03    (2)  all_57_15 = e0
% 226.85/39.03    (3)   ~ (e3 = e1)
% 226.85/39.03    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.85/39.03           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.85/39.03    (5)   ~ (e3 = e2)
% 226.85/39.03    (6)   ~ (e3 = e0)
% 226.85/39.03    (7)   ~ (all_4_2 = e2)
% 226.85/39.03    (8)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 226.85/39.03         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 226.85/39.03    (9)   ~ (e2 = e0)
% 226.85/39.03    (10)   ~ (e1 = e0)
% 226.85/39.03    (11)  all_57_13 = e3
% 226.85/39.03    (12)  op(e0, e0) = e0
% 226.85/39.03    (13)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 226.85/39.03          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 226.85/39.03            e3)
% 226.85/39.03    (14)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 226.85/39.03          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 226.85/39.03            e2)
% 226.85/39.03    (15)   ~ (e2 = e1)
% 226.85/39.03    (16)  all_57_14 = e0
% 226.85/39.03  
% 226.85/39.03  Begin of proof
% 226.85/39.03  | 
% 226.85/39.03  | BETA: splitting (14) gives:
% 226.85/39.03  | 
% 226.85/39.03  | Case 1:
% 226.85/39.03  | | 
% 226.85/39.03  | |   (17)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 226.85/39.03  | |           e2)
% 226.85/39.03  | | 
% 226.85/39.03  | | BETA: splitting (17) gives:
% 226.85/39.03  | | 
% 226.85/39.03  | | Case 1:
% 226.85/39.03  | | | 
% 226.85/39.03  | | |   (18)  all_57_12 = e2 & op(e0, e3) = e2
% 226.85/39.03  | | | 
% 226.85/39.03  | | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (9), (10), (12), (13), (14),
% 226.85/39.03  | | |            (15), (16), (18) are inconsistent by sub-proof #158.
% 226.85/39.03  | | | 
% 226.85/39.03  | | Case 2:
% 226.85/39.03  | | | 
% 226.85/39.03  | | |   (19)  all_57_13 = e2 & op(e0, e2) = e2
% 226.85/39.03  | | | 
% 226.85/39.03  | | | ALPHA: (19) implies:
% 226.85/39.03  | | |   (20)  all_57_13 = e2
% 226.85/39.03  | | | 
% 226.85/39.03  | | | REF_CLOSE: (5), (11), (20) are inconsistent by sub-proof #2203.
% 226.85/39.03  | | | 
% 226.85/39.03  | | End of split
% 226.85/39.03  | | 
% 226.85/39.03  | Case 2:
% 226.85/39.03  | | 
% 226.85/39.03  | |   (21)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 226.85/39.03  | |           e2)
% 226.85/39.03  | | 
% 226.85/39.03  | | REF_CLOSE: (1), (4), (7), (9), (16), (21) are inconsistent by sub-proof
% 226.85/39.03  | |            #180.
% 226.85/39.03  | | 
% 226.85/39.03  | End of split
% 226.85/39.03  | 
% 226.85/39.03  End of proof
% 226.85/39.03  
% 226.85/39.03  Sub-proof #158 shows that the following formulas are inconsistent:
% 226.85/39.03  ----------------------------------------------------------------
% 226.85/39.03    (1)  all_57_15 = e0
% 226.85/39.03    (2)   ~ (e3 = e1)
% 226.85/39.03    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.85/39.03           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.85/39.03    (4)  all_57_12 = e2 & op(e0, e3) = e2
% 226.85/39.03    (5)   ~ (e3 = e2)
% 226.85/39.03    (6)   ~ (e3 = e0)
% 226.85/39.03    (7)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 226.85/39.03         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 226.85/39.03    (8)   ~ (e2 = e0)
% 226.85/39.03    (9)   ~ (e1 = e0)
% 226.85/39.03    (10)  op(e0, e0) = e0
% 226.85/39.03    (11)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 226.85/39.03          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 226.85/39.03            e3)
% 226.85/39.03    (12)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 226.85/39.03          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 226.85/39.03            e2)
% 226.85/39.03    (13)   ~ (e2 = e1)
% 226.85/39.03    (14)  all_57_14 = e0
% 226.85/39.03  
% 226.85/39.03  Begin of proof
% 226.85/39.03  | 
% 226.85/39.03  | ALPHA: (4) implies:
% 226.85/39.03  |   (15)  all_57_12 = e2
% 226.85/39.03  | 
% 226.85/39.03  | BETA: splitting (7) gives:
% 226.85/39.03  | 
% 226.85/39.03  | Case 1:
% 226.85/39.03  | | 
% 226.85/39.03  | |   (16)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 226.85/39.03  | |           e1)
% 226.85/39.03  | | 
% 226.85/39.03  | | BETA: splitting (16) gives:
% 226.85/39.03  | | 
% 226.85/39.03  | | Case 1:
% 226.85/39.03  | | | 
% 226.85/39.03  | | |   (17)  all_57_12 = e1 & op(e0, e3) = e1
% 226.85/39.03  | | | 
% 226.85/39.03  | | | ALPHA: (17) implies:
% 226.85/39.03  | | |   (18)  all_57_12 = e1
% 226.85/39.03  | | | 
% 226.85/39.03  | | | REF_CLOSE: (13), (15), (18) are inconsistent by sub-proof #2321.
% 226.85/39.03  | | | 
% 226.85/39.03  | | Case 2:
% 226.85/39.03  | | | 
% 226.85/39.03  | | |   (19)  all_57_13 = e1 & op(e0, e2) = e1
% 226.85/39.03  | | | 
% 226.85/39.03  | | | ALPHA: (19) implies:
% 226.85/39.03  | | |   (20)  all_57_13 = e1
% 226.85/39.03  | | | 
% 226.85/39.03  | | | REF_CLOSE: (1), (2), (3), (5), (6), (8), (10), (11), (12), (13), (14),
% 226.85/39.03  | | |            (20) are inconsistent by sub-proof #2123.
% 226.85/39.03  | | | 
% 226.85/39.03  | | End of split
% 226.85/39.03  | | 
% 226.85/39.03  | Case 2:
% 226.85/39.03  | | 
% 226.85/39.03  | |   (21)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 226.85/39.03  | |           e1)
% 226.85/39.03  | | 
% 226.85/39.03  | | REF_CLOSE: (3), (9), (10), (14), (21) are inconsistent by sub-proof #2121.
% 226.85/39.03  | | 
% 226.85/39.03  | End of split
% 226.85/39.03  | 
% 226.85/39.03  End of proof
% 226.85/39.03  
% 226.85/39.03  Sub-proof #159 shows that the following formulas are inconsistent:
% 226.85/39.03  ----------------------------------------------------------------
% 226.85/39.03    (1)  op(e2, e3) = all_53_1
% 226.85/39.03    (2)   ~ (e3 = e1)
% 226.85/39.03    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.85/39.03           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.85/39.03    (4)  op(e2, e2) = e1
% 226.85/39.03    (5)   ~ (all_53_1 = e3)
% 226.85/39.03    (6)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3)
% 226.85/39.03  
% 226.85/39.03  Begin of proof
% 226.85/39.03  | 
% 226.85/39.03  | BETA: splitting (6) gives:
% 226.85/39.03  | 
% 226.85/39.03  | Case 1:
% 226.85/39.03  | | 
% 226.85/39.03  | |   (7)  all_57_2 = e3 & op(e2, e3) = e3
% 226.85/39.03  | | 
% 226.85/39.03  | | REF_CLOSE: (1), (3), (5), (7) are inconsistent by sub-proof #2299.
% 226.85/39.03  | | 
% 226.85/39.03  | Case 2:
% 226.85/39.03  | | 
% 226.85/39.03  | |   (8)  all_57_3 = e3 & op(e2, e2) = e3
% 226.85/39.03  | | 
% 226.85/39.03  | | ALPHA: (8) implies:
% 226.85/39.03  | |   (9)  op(e2, e2) = e3
% 226.85/39.03  | | 
% 226.85/39.03  | | REF_CLOSE: (2), (3), (4), (9) are inconsistent by sub-proof #1912.
% 226.85/39.03  | | 
% 226.85/39.03  | End of split
% 226.85/39.03  | 
% 226.85/39.03  End of proof
% 226.85/39.03  
% 226.85/39.03  Sub-proof #160 shows that the following formulas are inconsistent:
% 226.85/39.03  ----------------------------------------------------------------
% 226.85/39.03    (1)   ~ (all_53_6 = e2)
% 226.85/39.03    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.85/39.03           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.85/39.03    (3)   ~ (all_53_7 = e2)
% 226.85/39.04    (4)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 226.85/39.04    (5)  op(e0, e2) = all_53_7
% 226.85/39.04    (6)  op(e1, e2) = all_53_6
% 226.85/39.04  
% 226.85/39.04  Begin of proof
% 226.85/39.04  | 
% 226.85/39.04  | BETA: splitting (4) gives:
% 226.85/39.04  | 
% 226.85/39.04  | Case 1:
% 226.85/39.04  | | 
% 226.85/39.04  | |   (7)  all_57_7 = e2 & op(e1, e2) = e2
% 226.85/39.04  | | 
% 226.85/39.04  | | REF_CLOSE: (1), (2), (6), (7) are inconsistent by sub-proof #173.
% 226.85/39.04  | | 
% 226.85/39.04  | Case 2:
% 226.85/39.04  | | 
% 226.85/39.04  | |   (8)  all_57_13 = e2 & op(e0, e2) = e2
% 226.85/39.04  | | 
% 226.85/39.04  | | ALPHA: (8) implies:
% 226.85/39.04  | |   (9)  op(e0, e2) = e2
% 226.85/39.04  | | 
% 226.85/39.04  | | REF_CLOSE: (2), (3), (5), (9) are inconsistent by sub-proof #2335.
% 226.85/39.04  | | 
% 226.85/39.04  | End of split
% 226.85/39.04  | 
% 226.85/39.04  End of proof
% 226.85/39.04  
% 226.85/39.04  Sub-proof #161 shows that the following formulas are inconsistent:
% 226.85/39.04  ----------------------------------------------------------------
% 226.85/39.04    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.85/39.04           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.85/39.04    (2)   ~ (e3 = e0)
% 226.85/39.04    (3)  op(e1, e1) = e3
% 226.85/39.04    (4)  op(e0, e0) = all_52_31
% 226.85/39.04    (5)  op(e0, e0) = e1
% 226.85/39.04    (6)  op(all_52_31, all_52_31) = e0
% 226.85/39.04  
% 226.85/39.04  Begin of proof
% 226.85/39.04  | 
% 226.85/39.04  | GROUND_INST: instantiating (1) with e1, all_52_31, e0, e0, simplifying with
% 226.85/39.04  |              (4), (5) gives:
% 226.85/39.04  |   (7)  all_52_31 = e1
% 226.85/39.04  | 
% 226.85/39.04  | REDUCE: (6), (7) imply:
% 226.85/39.04  |   (8)  op(e1, e1) = e0
% 226.85/39.04  | 
% 226.85/39.04  | GROUND_INST: instantiating (1) with e3, e0, e1, e1, simplifying with (3), (8)
% 226.85/39.04  |              gives:
% 226.85/39.04  |   (9)  e3 = e0
% 226.85/39.04  | 
% 226.85/39.04  | REDUCE: (2), (9) imply:
% 226.85/39.04  |   (10)  $false
% 226.85/39.04  | 
% 226.85/39.04  | CLOSE: (10) is inconsistent.
% 226.85/39.04  | 
% 226.85/39.04  End of proof
% 226.85/39.04  
% 226.85/39.04  Sub-proof #162 shows that the following formulas are inconsistent:
% 226.85/39.04  ----------------------------------------------------------------
% 226.85/39.04    (1)  all_57_8 = e0 & op(e1, e1) = e0
% 226.85/39.04    (2)  all_57_8 = e3
% 226.85/39.04    (3)   ~ (e3 = e0)
% 226.85/39.04  
% 226.85/39.04  Begin of proof
% 226.85/39.04  | 
% 226.85/39.04  | ALPHA: (1) implies:
% 226.85/39.04  |   (4)  all_57_8 = e0
% 226.85/39.04  | 
% 226.85/39.04  | COMBINE_EQS: (2), (4) imply:
% 226.85/39.04  |   (5)  e3 = e0
% 226.85/39.04  | 
% 226.85/39.04  | SIMP: (5) implies:
% 226.85/39.04  |   (6)  e3 = e0
% 226.85/39.04  | 
% 226.85/39.04  | REDUCE: (3), (6) imply:
% 226.85/39.04  |   (7)  $false
% 226.85/39.04  | 
% 226.85/39.04  | CLOSE: (7) is inconsistent.
% 226.85/39.04  | 
% 226.85/39.04  End of proof
% 226.85/39.04  
% 226.85/39.04  Sub-proof #163 shows that the following formulas are inconsistent:
% 226.85/39.04  ----------------------------------------------------------------
% 226.85/39.04    (1)  ( ~ (all_40_0 = e3) & op(all_40_1, e0) = all_40_0 & op(e0, e1) = all_40_1
% 226.85/39.04           & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 = e2) & op(e0, e1) =
% 226.85/39.04           all_40_1 & $i(all_40_1))
% 226.85/39.04    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.85/39.04           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.85/39.04    (3)  all_55_7 = all_52_15
% 226.85/39.04    (4)  op(e2, e0) = all_52_15
% 226.85/39.04    (5)  ( ~ (all_30_0 = e2) & op(all_30_1, e0) = all_30_0 & op(e0, e1) = all_30_1
% 226.85/39.04           & $i(all_30_0) & $i(all_30_1)) | ( ~ (all_30_1 = e3) & op(e0, e1) =
% 226.85/39.04           all_30_1 & $i(all_30_1))
% 226.85/39.04    (6)   ~ (all_52_15 = e1)
% 226.85/39.04    (7)  all_55_7 = e3 | all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 226.85/39.04    (8)  op(e0, e0) = e1
% 226.85/39.04    (9)  op(all_52_15, all_52_15) = e0
% 226.85/39.04    (10)  op(e0, e1) = all_30_1
% 226.85/39.04    (11)  op(e0, e1) = e2
% 226.85/39.04    (12)   ~ (all_52_15 = e2)
% 226.85/39.04  
% 226.85/39.04  Begin of proof
% 226.85/39.04  | 
% 226.85/39.04  | GROUND_INST: instantiating (2) with e2, all_30_1, e1, e0, simplifying with
% 226.85/39.04  |              (10), (11) gives:
% 226.85/39.04  |   (13)  all_30_1 = e2
% 226.85/39.04  | 
% 226.85/39.04  | BETA: splitting (1) gives:
% 226.85/39.04  | 
% 226.85/39.04  | Case 1:
% 226.85/39.04  | | 
% 226.85/39.04  | |   (14)   ~ (all_40_0 = e3) & op(all_40_1, e0) = all_40_0 & op(e0, e1) =
% 226.85/39.04  | |         all_40_1 & $i(all_40_0) & $i(all_40_1)
% 226.85/39.04  | | 
% 226.85/39.04  | | ALPHA: (14) implies:
% 226.85/39.04  | |   (15)   ~ (all_40_0 = e3)
% 226.85/39.04  | |   (16)  op(e0, e1) = all_40_1
% 226.85/39.04  | |   (17)  op(all_40_1, e0) = all_40_0
% 226.85/39.04  | | 
% 226.85/39.04  | | GROUND_INST: instantiating (2) with e2, all_40_1, e1, e0, simplifying with
% 226.85/39.04  | |              (11), (16) gives:
% 226.85/39.04  | |   (18)  all_40_1 = e2
% 226.85/39.04  | | 
% 226.85/39.04  | | REDUCE: (17), (18) imply:
% 226.85/39.04  | |   (19)  op(e2, e0) = all_40_0
% 226.85/39.04  | | 
% 226.85/39.04  | | GROUND_INST: instantiating (2) with all_52_15, all_40_0, e0, e2, simplifying
% 226.85/39.04  | |              with (4), (19) gives:
% 226.85/39.04  | |   (20)  all_52_15 = all_40_0
% 226.85/39.04  | | 
% 226.85/39.04  | | COMBINE_EQS: (3), (20) imply:
% 226.85/39.04  | |   (21)  all_55_7 = all_40_0
% 226.85/39.04  | | 
% 226.85/39.04  | | BETA: splitting (7) gives:
% 226.85/39.04  | | 
% 226.85/39.04  | | Case 1:
% 226.85/39.04  | | | 
% 226.85/39.04  | | |   (22)  all_55_7 = e3
% 226.85/39.04  | | | 
% 226.85/39.04  | | | COMBINE_EQS: (21), (22) imply:
% 226.85/39.04  | | |   (23)  all_40_0 = e3
% 226.85/39.04  | | | 
% 226.85/39.04  | | | SIMP: (23) implies:
% 226.85/39.04  | | |   (24)  all_40_0 = e3
% 226.85/39.04  | | | 
% 226.85/39.04  | | | REDUCE: (15), (24) imply:
% 226.85/39.04  | | |   (25)  $false
% 226.85/39.04  | | | 
% 226.85/39.04  | | | CLOSE: (25) is inconsistent.
% 226.85/39.04  | | | 
% 226.85/39.04  | | Case 2:
% 226.85/39.04  | | | 
% 226.85/39.04  | | |   (26)  all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 226.85/39.04  | | | 
% 226.85/39.04  | | | REF_CLOSE: (2), (3), (6), (8), (9), (12), (26) are inconsistent by
% 226.85/39.04  | | |            sub-proof #2078.
% 226.85/39.04  | | | 
% 226.85/39.04  | | End of split
% 226.85/39.04  | | 
% 226.85/39.04  | Case 2:
% 226.85/39.04  | | 
% 226.85/39.04  | |   (27)   ~ (all_40_1 = e2) & op(e0, e1) = all_40_1 & $i(all_40_1)
% 226.85/39.04  | | 
% 226.85/39.04  | | ALPHA: (27) implies:
% 226.85/39.04  | |   (28)   ~ (all_40_1 = e2)
% 226.85/39.04  | |   (29)  op(e0, e1) = all_40_1
% 226.85/39.04  | | 
% 226.85/39.04  | | BETA: splitting (5) gives:
% 226.85/39.04  | | 
% 226.85/39.04  | | Case 1:
% 226.85/39.04  | | | 
% 226.85/39.04  | | |   (30)   ~ (all_30_0 = e2) & op(all_30_1, e0) = all_30_0 & op(e0, e1) =
% 226.85/39.04  | | |         all_30_1 & $i(all_30_0) & $i(all_30_1)
% 226.85/39.04  | | | 
% 226.85/39.04  | | | REF_CLOSE: (2), (10), (11), (28), (29) are inconsistent by sub-proof #164.
% 226.85/39.04  | | | 
% 226.85/39.04  | | Case 2:
% 226.85/39.04  | | | 
% 226.85/39.04  | | |   (31)   ~ (all_30_1 = e3) & op(e0, e1) = all_30_1 & $i(all_30_1)
% 226.85/39.04  | | | 
% 226.85/39.04  | | | REF_CLOSE: (2), (10), (11), (28), (29) are inconsistent by sub-proof #164.
% 226.85/39.04  | | | 
% 226.85/39.04  | | End of split
% 226.85/39.04  | | 
% 226.85/39.04  | End of split
% 226.85/39.04  | 
% 226.85/39.04  End of proof
% 226.85/39.04  
% 226.85/39.04  Sub-proof #164 shows that the following formulas are inconsistent:
% 226.85/39.04  ----------------------------------------------------------------
% 226.85/39.04    (1)   ~ (all_40_1 = e2)
% 226.85/39.04    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.85/39.04           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.85/39.04    (3)  op(e0, e1) = all_40_1
% 226.85/39.04    (4)  op(e0, e1) = all_30_1
% 226.85/39.04    (5)  op(e0, e1) = e2
% 226.85/39.04  
% 226.85/39.04  Begin of proof
% 226.85/39.04  | 
% 226.85/39.04  | GROUND_INST: instantiating (2) with all_30_1, all_40_1, e1, e0, simplifying
% 226.85/39.04  |              with (3), (4) gives:
% 226.85/39.04  |   (6)  all_40_1 = all_30_1
% 226.85/39.04  | 
% 226.85/39.04  | GROUND_INST: instantiating (2) with e2, all_40_1, e1, e0, simplifying with
% 226.85/39.04  |              (3), (5) gives:
% 226.85/39.04  |   (7)  all_40_1 = e2
% 226.85/39.04  | 
% 226.85/39.04  | COMBINE_EQS: (6), (7) imply:
% 226.85/39.04  |   (8)  all_30_1 = e2
% 226.85/39.04  | 
% 226.85/39.04  | REDUCE: (1), (7) imply:
% 226.85/39.04  |   (9)  $false
% 226.85/39.04  | 
% 226.85/39.04  | CLOSE: (9) is inconsistent.
% 226.85/39.04  | 
% 226.85/39.04  End of proof
% 226.85/39.04  
% 226.85/39.04  Sub-proof #165 shows that the following formulas are inconsistent:
% 226.85/39.04  ----------------------------------------------------------------
% 226.85/39.04    (1)  all_57_8 = e2 & op(e1, e1) = e2
% 226.85/39.04    (2)  all_57_8 = e3
% 226.85/39.04    (3)   ~ (e3 = e2)
% 226.85/39.04  
% 226.85/39.04  Begin of proof
% 226.85/39.04  | 
% 226.85/39.04  | ALPHA: (1) implies:
% 226.85/39.04  |   (4)  all_57_8 = e2
% 226.85/39.04  | 
% 226.85/39.04  | COMBINE_EQS: (2), (4) imply:
% 226.85/39.04  |   (5)  e3 = e2
% 226.85/39.04  | 
% 226.85/39.04  | REDUCE: (3), (5) imply:
% 226.85/39.04  |   (6)  $false
% 226.85/39.04  | 
% 226.85/39.04  | CLOSE: (6) is inconsistent.
% 226.85/39.04  | 
% 226.85/39.04  End of proof
% 226.85/39.04  
% 226.85/39.04  Sub-proof #166 shows that the following formulas are inconsistent:
% 226.85/39.04  ----------------------------------------------------------------
% 226.85/39.04    (1)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 &
% 226.85/39.04           op(all_52_17, all_52_17) = e3 & op(all_52_19, all_52_19) = e2 &
% 226.85/39.04           op(all_52_21, all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1,
% 226.85/39.04             e3) = all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 &
% 226.85/39.04           op(e1, e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21)
% 226.85/39.04           & $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 226.85/39.04           all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 226.85/39.04             all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 226.85/39.04             all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 226.85/39.04           op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 226.85/39.04           $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 226.85/39.04    (2)  op(e3, e3) = all_10_2
% 226.85/39.04    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.85/39.04           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.85/39.04    (4)   ~ (e3 = e2)
% 226.85/39.04    (5)  op(e1, e1) = e3
% 226.85/39.04    (6)  op(e3, e3) = e3
% 226.85/39.04    (7)  op(e0, e2) = e3
% 226.85/39.04    (8)   ~ (all_10_2 = e1)
% 226.85/39.04  
% 226.85/39.04  Begin of proof
% 226.85/39.04  | 
% 226.85/39.04  | BETA: splitting (1) gives:
% 226.85/39.04  | 
% 226.85/39.04  | Case 1:
% 226.85/39.04  | | 
% 226.85/39.04  | |   (9)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 &
% 226.85/39.04  | |        op(all_52_17, all_52_17) = e3 & op(all_52_19, all_52_19) = e2 &
% 226.85/39.04  | |        op(all_52_21, all_52_21) = e1 & op(all_52_23, all_52_23) = e0 &
% 226.85/39.04  | |        op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) =
% 226.85/39.04  | |        all_52_21 & op(e1, e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 226.85/39.04  | |        $i(all_52_21) & $i(all_52_23)
% 226.85/39.04  | | 
% 226.85/39.04  | | ALPHA: (9) implies:
% 226.85/39.04  | |   (10)  op(e1, e1) = all_52_21
% 226.85/39.04  | |   (11)  op(all_52_21, all_52_21) = e1
% 226.85/39.04  | | 
% 226.85/39.04  | | REF_CLOSE: (2), (3), (5), (8), (10), (11) are inconsistent by sub-proof
% 226.85/39.04  | |            #167.
% 226.85/39.04  | | 
% 226.85/39.04  | Case 2:
% 226.85/39.04  | | 
% 226.85/39.04  | |   (12)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0 &
% 226.85/39.04  | |         op(all_52_25, all_52_25) = e3 & op(all_52_27, all_52_27) = e2 &
% 226.85/39.04  | |         op(all_52_29, all_52_29) = e1 & op(all_52_31, all_52_31) = e0 &
% 226.85/39.04  | |         op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 & op(e0, e1) =
% 226.85/39.04  | |         all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 226.85/39.04  | |         $i(all_52_29) & $i(all_52_31)
% 226.85/39.04  | | 
% 226.85/39.04  | | ALPHA: (12) implies:
% 226.85/39.04  | |   (13)  op(e0, e2) = all_52_27
% 226.85/39.04  | |   (14)  op(all_52_27, all_52_27) = e2
% 226.85/39.04  | | 
% 226.85/39.04  | | GROUND_INST: instantiating (3) with e3, all_52_27, e2, e0, simplifying with
% 226.85/39.04  | |              (7), (13) gives:
% 226.85/39.04  | |   (15)  all_52_27 = e3
% 226.85/39.04  | | 
% 226.85/39.04  | | REDUCE: (14), (15) imply:
% 226.85/39.04  | |   (16)  op(e3, e3) = e2
% 226.85/39.04  | | 
% 226.85/39.04  | | REF_CLOSE: (3), (4), (6), (16) are inconsistent by sub-proof #2490.
% 226.85/39.04  | | 
% 226.85/39.04  | End of split
% 226.85/39.04  | 
% 226.85/39.04  End of proof
% 226.85/39.04  
% 226.85/39.04  Sub-proof #167 shows that the following formulas are inconsistent:
% 226.85/39.04  ----------------------------------------------------------------
% 226.85/39.04    (1)  op(e3, e3) = all_10_2
% 226.85/39.04    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.85/39.04           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.85/39.04    (3)  op(e1, e1) = e3
% 226.85/39.04    (4)  op(e1, e1) = all_52_21
% 226.85/39.04    (5)   ~ (all_10_2 = e1)
% 226.85/39.04    (6)  op(all_52_21, all_52_21) = e1
% 226.85/39.04  
% 226.85/39.04  Begin of proof
% 226.85/39.04  | 
% 226.85/39.04  | GROUND_INST: instantiating (2) with e3, all_52_21, e1, e1, simplifying with
% 226.85/39.04  |              (3), (4) gives:
% 226.85/39.04  |   (7)  all_52_21 = e3
% 226.85/39.04  | 
% 226.85/39.04  | REDUCE: (6), (7) imply:
% 226.85/39.04  |   (8)  op(e3, e3) = e1
% 226.85/39.04  | 
% 226.85/39.04  | GROUND_INST: instantiating (2) with all_10_2, e1, e3, e3, simplifying with
% 226.85/39.04  |              (1), (8) gives:
% 226.85/39.04  |   (9)  all_10_2 = e1
% 226.85/39.04  | 
% 226.85/39.04  | REDUCE: (5), (9) imply:
% 226.85/39.04  |   (10)  $false
% 226.85/39.04  | 
% 226.85/39.04  | CLOSE: (10) is inconsistent.
% 226.85/39.04  | 
% 226.85/39.04  End of proof
% 226.85/39.04  
% 226.85/39.04  Sub-proof #168 shows that the following formulas are inconsistent:
% 226.85/39.04  ----------------------------------------------------------------
% 226.85/39.04    (1)  all_57_8 = e1 & op(e1, e1) = e1
% 226.85/39.04    (2)  all_57_8 = e3
% 226.85/39.04    (3)   ~ (e3 = e1)
% 226.85/39.04  
% 226.85/39.04  Begin of proof
% 226.85/39.04  | 
% 226.85/39.04  | ALPHA: (1) implies:
% 226.85/39.04  |   (4)  all_57_8 = e1
% 226.85/39.04  | 
% 226.85/39.04  | COMBINE_EQS: (2), (4) imply:
% 226.85/39.04  |   (5)  e3 = e1
% 226.85/39.04  | 
% 226.85/39.04  | SIMP: (5) implies:
% 226.85/39.04  |   (6)  e3 = e1
% 226.85/39.04  | 
% 226.85/39.04  | REDUCE: (3), (6) imply:
% 226.85/39.04  |   (7)  $false
% 226.85/39.04  | 
% 226.85/39.04  | CLOSE: (7) is inconsistent.
% 226.85/39.04  | 
% 226.85/39.04  End of proof
% 226.85/39.04  
% 226.85/39.04  Sub-proof #169 shows that the following formulas are inconsistent:
% 226.85/39.04  ----------------------------------------------------------------
% 226.85/39.04    (1)  all_57_8 = e1 & op(e1, e1) = e1
% 226.85/39.04    (2)  all_57_8 = e3
% 226.85/39.04    (3)   ~ (e3 = e1)
% 226.85/39.04  
% 226.85/39.04  Begin of proof
% 226.85/39.04  | 
% 226.85/39.04  | ALPHA: (1) implies:
% 226.85/39.04  |   (4)  all_57_8 = e1
% 226.85/39.04  | 
% 226.85/39.04  | COMBINE_EQS: (2), (4) imply:
% 226.85/39.04  |   (5)  e3 = e1
% 226.85/39.04  | 
% 226.85/39.04  | REDUCE: (3), (5) imply:
% 226.85/39.04  |   (6)  $false
% 226.85/39.04  | 
% 226.85/39.04  | CLOSE: (6) is inconsistent.
% 226.85/39.04  | 
% 226.85/39.04  End of proof
% 226.85/39.04  
% 226.85/39.04  Sub-proof #170 shows that the following formulas are inconsistent:
% 226.85/39.04  ----------------------------------------------------------------
% 226.85/39.04    (1)  all_57_8 = e0 & op(e1, e1) = e0
% 226.85/39.04    (2)  all_57_8 = e3
% 226.85/39.04    (3)   ~ (e3 = e0)
% 226.85/39.04  
% 226.85/39.04  Begin of proof
% 226.85/39.04  | 
% 226.85/39.04  | ALPHA: (1) implies:
% 226.85/39.04  |   (4)  all_57_8 = e0
% 226.85/39.04  | 
% 226.85/39.04  | COMBINE_EQS: (2), (4) imply:
% 226.85/39.04  |   (5)  e3 = e0
% 226.85/39.04  | 
% 226.85/39.04  | REDUCE: (3), (5) imply:
% 226.85/39.04  |   (6)  $false
% 226.85/39.04  | 
% 226.85/39.04  | CLOSE: (6) is inconsistent.
% 226.85/39.04  | 
% 226.85/39.04  End of proof
% 226.85/39.04  
% 226.85/39.04  Sub-proof #171 shows that the following formulas are inconsistent:
% 226.85/39.04  ----------------------------------------------------------------
% 226.85/39.04    (1)   ~ (e3 = e1)
% 226.85/39.04    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.85/39.04           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.85/39.04    (3)  all_57_4 = e2
% 226.85/39.04    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 226.85/39.04         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 226.85/39.04    (5)   ~ (all_53_13 = e2)
% 226.85/39.04    (6)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 226.85/39.04         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 226.85/39.04    (7)   ~ (e3 = e2)
% 226.85/39.04    (8)   ~ (e3 = e0)
% 226.85/39.04    (9)   ~ (e2 = e0)
% 226.85/39.04    (10)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 226.85/39.04          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 226.85/39.04    (11)   ~ (e1 = e0)
% 226.85/39.04    (12)  op(e2, e0) = all_53_13
% 226.85/39.04    (13)   ~ (all_53_12 = e3)
% 226.85/39.04    (14)   ~ (e2 = e1)
% 226.85/39.04    (15)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 226.85/39.04    (16)  op(e3, e0) = all_53_12
% 226.85/39.04  
% 226.85/39.04  Begin of proof
% 226.85/39.04  | 
% 226.85/39.04  | BETA: splitting (15) gives:
% 226.85/39.04  | 
% 226.85/39.04  | Case 1:
% 226.85/39.04  | | 
% 226.85/39.04  | |   (17)  all_57_9 = e2 & op(e3, e0) = e2
% 226.85/39.04  | | 
% 226.85/39.04  | | ALPHA: (17) implies:
% 226.85/39.04  | |   (18)  all_57_9 = e2
% 226.85/39.04  | | 
% 226.85/39.04  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (13), (14),
% 226.85/39.04  | |            (16), (18) are inconsistent by sub-proof #288.
% 226.85/39.04  | | 
% 226.85/39.04  | Case 2:
% 226.85/39.04  | | 
% 226.85/39.04  | |   (19)  all_57_10 = e2 & op(e2, e0) = e2
% 226.85/39.04  | | 
% 226.85/39.04  | | REF_CLOSE: (2), (5), (12), (19) are inconsistent by sub-proof #2432.
% 226.85/39.04  | | 
% 226.85/39.04  | End of split
% 226.85/39.04  | 
% 226.85/39.04  End of proof
% 226.85/39.04  
% 226.85/39.04  Sub-proof #172 shows that the following formulas are inconsistent:
% 226.85/39.04  ----------------------------------------------------------------
% 226.85/39.04    (1)  all_57_8 = e2 & op(e1, e1) = e2
% 226.85/39.04    (2)  all_57_8 = e3
% 226.85/39.04    (3)   ~ (e3 = e2)
% 226.85/39.04  
% 226.85/39.04  Begin of proof
% 226.85/39.04  | 
% 226.85/39.04  | ALPHA: (1) implies:
% 226.85/39.04  |   (4)  all_57_8 = e2
% 226.85/39.04  | 
% 226.85/39.04  | COMBINE_EQS: (2), (4) imply:
% 226.85/39.04  |   (5)  e3 = e2
% 226.85/39.04  | 
% 226.85/39.04  | SIMP: (5) implies:
% 226.85/39.04  |   (6)  e3 = e2
% 226.85/39.04  | 
% 226.85/39.04  | REDUCE: (3), (6) imply:
% 226.85/39.04  |   (7)  $false
% 226.85/39.04  | 
% 226.85/39.04  | CLOSE: (7) is inconsistent.
% 226.85/39.04  | 
% 226.85/39.04  End of proof
% 226.85/39.04  
% 226.85/39.04  Sub-proof #173 shows that the following formulas are inconsistent:
% 226.85/39.04  ----------------------------------------------------------------
% 226.85/39.04    (1)  all_57_7 = e2 & op(e1, e2) = e2
% 226.85/39.04    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.85/39.04           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.85/39.04    (3)  op(e1, e2) = all_53_6
% 226.85/39.04    (4)   ~ (all_53_6 = e2)
% 226.85/39.04  
% 226.85/39.04  Begin of proof
% 226.85/39.04  | 
% 226.85/39.04  | ALPHA: (1) implies:
% 226.85/39.04  |   (5)  op(e1, e2) = e2
% 226.85/39.04  | 
% 226.85/39.04  | GROUND_INST: instantiating (2) with all_53_6, e2, e2, e1, simplifying with
% 226.85/39.04  |              (3), (5) gives:
% 226.85/39.04  |   (6)  all_53_6 = e2
% 226.85/39.04  | 
% 226.85/39.04  | REDUCE: (4), (6) imply:
% 226.85/39.04  |   (7)  $false
% 226.85/39.04  | 
% 226.85/39.04  | CLOSE: (7) is inconsistent.
% 226.85/39.04  | 
% 226.85/39.04  End of proof
% 226.85/39.04  
% 226.85/39.04  Sub-proof #174 shows that the following formulas are inconsistent:
% 226.85/39.04  ----------------------------------------------------------------
% 226.85/39.04    (1)  op(e0, e0) = all_4_2
% 226.85/39.04    (2)  op(e3, e1) = all_52_5
% 226.85/39.04    (3)   ~ (e3 = e1)
% 226.85/39.04    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.85/39.04           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.85/39.04    (5)  op(all_52_5, all_52_5) = e1
% 226.85/39.04    (6)  op(e3, e2) = all_52_3
% 226.85/39.04    (7)  op(all_52_3, all_52_3) = e2
% 226.85/39.04    (8)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 226.85/39.04    (9)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 226.85/39.04         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 226.85/39.04    (10)  op(e1, e0) = all_53_14
% 226.85/39.04    (11)   ~ (e3 = e0)
% 226.85/39.04    (12)  op(e3, e3) = e3
% 226.85/39.04    (13)   ~ (all_4_2 = e2)
% 226.85/39.04    (14)   ~ (all_53_14 = e3)
% 226.85/39.04    (15)   ~ (e2 = e0)
% 226.85/39.04    (16)   ~ (e1 = e0)
% 226.85/39.04    (17)  op(e0, e0) = e0
% 226.85/39.04    (18)   ~ (all_53_12 = e3)
% 226.85/39.04    (19)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 226.85/39.04          (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 226.85/39.04    (20)   ~ (e2 = e1)
% 226.85/39.04    (21)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 226.85/39.04          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 226.85/39.04    (22)  op(e3, e0) = all_53_12
% 226.85/39.04  
% 226.85/39.04  Begin of proof
% 226.85/39.04  | 
% 226.85/39.04  | BETA: splitting (8) gives:
% 226.85/39.04  | 
% 226.85/39.04  | Case 1:
% 226.85/39.04  | | 
% 226.85/39.04  | |   (23)  all_57_11 = e2 & op(e1, e0) = e2
% 226.85/39.04  | | 
% 226.85/39.04  | | ALPHA: (23) implies:
% 226.85/39.04  | |   (24)  all_57_11 = e2
% 226.85/39.04  | | 
% 226.85/39.04  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (14), (15),
% 226.85/39.04  | |            (16), (17), (18), (19), (20), (21), (22), (24) are inconsistent
% 226.85/39.04  | |            by sub-proof #175.
% 226.85/39.04  | | 
% 226.85/39.04  | Case 2:
% 226.85/39.04  | | 
% 226.85/39.04  | |   (25)  all_57_15 = e2 & op(e0, e0) = e2
% 226.85/39.04  | | 
% 226.85/39.04  | | ALPHA: (25) implies:
% 226.85/39.04  | |   (26)  op(e0, e0) = e2
% 226.85/39.04  | | 
% 226.85/39.04  | | REF_CLOSE: (1), (4), (13), (26) are inconsistent by sub-proof #2334.
% 226.85/39.04  | | 
% 226.85/39.04  | End of split
% 226.85/39.04  | 
% 226.85/39.04  End of proof
% 226.85/39.04  
% 226.85/39.04  Sub-proof #175 shows that the following formulas are inconsistent:
% 226.85/39.04  ----------------------------------------------------------------
% 226.85/39.04    (1)  op(e3, e1) = all_52_5
% 226.85/39.04    (2)   ~ (e3 = e1)
% 226.85/39.04    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.85/39.04           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.85/39.04    (4)  op(all_52_5, all_52_5) = e1
% 226.85/39.04    (5)  op(e3, e2) = all_52_3
% 226.85/39.04    (6)  op(all_52_3, all_52_3) = e2
% 226.85/39.04    (7)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 226.85/39.04         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 226.85/39.04    (8)  op(e1, e0) = all_53_14
% 226.85/39.04    (9)   ~ (e3 = e0)
% 226.85/39.04    (10)  op(e3, e3) = e3
% 226.85/39.04    (11)  all_57_11 = e2
% 226.85/39.04    (12)   ~ (all_53_14 = e3)
% 226.85/39.04    (13)   ~ (e2 = e0)
% 226.85/39.04    (14)   ~ (e1 = e0)
% 226.85/39.04    (15)  op(e0, e0) = e0
% 226.85/39.04    (16)   ~ (all_53_12 = e3)
% 226.85/39.04    (17)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 226.85/39.04          (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 226.85/39.04    (18)   ~ (e2 = e1)
% 226.85/39.04    (19)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 226.85/39.04          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 226.85/39.04    (20)  op(e3, e0) = all_53_12
% 226.85/39.04  
% 226.85/39.04  Begin of proof
% 226.85/39.04  | 
% 226.85/39.04  | BETA: splitting (19) gives:
% 226.85/39.04  | 
% 226.85/39.04  | Case 1:
% 226.85/39.04  | | 
% 226.85/39.05  | |   (21)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) =
% 226.85/39.05  | |           e1)
% 226.85/39.05  | | 
% 226.85/39.05  | | BETA: splitting (21) gives:
% 226.85/39.05  | | 
% 226.85/39.05  | | Case 1:
% 226.85/39.05  | | | 
% 226.85/39.05  | | |   (22)  all_57_9 = e1 & op(e3, e0) = e1
% 226.85/39.05  | | | 
% 226.85/39.05  | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (9), (10), (13), (14), (15), (22)
% 226.85/39.05  | | |            are inconsistent by sub-proof #264.
% 226.85/39.05  | | | 
% 226.85/39.05  | | Case 2:
% 226.85/39.05  | | | 
% 226.85/39.05  | | |   (23)  all_57_10 = e1 & op(e2, e0) = e1
% 226.85/39.05  | | | 
% 226.85/39.05  | | | ALPHA: (23) implies:
% 226.85/39.05  | | |   (24)  all_57_10 = e1
% 226.85/39.05  | | | 
% 226.85/39.05  | | | REF_CLOSE: (2), (3), (8), (9), (12), (15), (16), (17), (20), (24) are
% 226.85/39.05  | | |            inconsistent by sub-proof #2302.
% 226.85/39.05  | | | 
% 226.85/39.05  | | End of split
% 226.85/39.05  | | 
% 226.85/39.05  | Case 2:
% 226.85/39.05  | | 
% 226.85/39.05  | |   (25)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 226.85/39.05  | |           e1)
% 226.85/39.05  | | 
% 226.85/39.05  | | REF_CLOSE: (3), (11), (14), (15), (18), (25) are inconsistent by sub-proof
% 226.85/39.05  | |            #176.
% 226.85/39.05  | | 
% 226.85/39.05  | End of split
% 226.85/39.05  | 
% 226.85/39.05  End of proof
% 226.85/39.05  
% 226.85/39.05  Sub-proof #176 shows that the following formulas are inconsistent:
% 226.85/39.05  ----------------------------------------------------------------
% 226.85/39.05    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.85/39.05           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.85/39.05    (2)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 226.85/39.05    (3)  all_57_11 = e2
% 226.85/39.05    (4)   ~ (e1 = e0)
% 226.85/39.05    (5)  op(e0, e0) = e0
% 226.85/39.05    (6)   ~ (e2 = e1)
% 226.85/39.05  
% 226.85/39.05  Begin of proof
% 226.85/39.05  | 
% 226.85/39.05  | BETA: splitting (2) gives:
% 226.85/39.05  | 
% 226.85/39.05  | Case 1:
% 226.85/39.05  | | 
% 226.85/39.05  | |   (7)  all_57_11 = e1 & op(e1, e0) = e1
% 226.85/39.05  | | 
% 226.85/39.05  | | ALPHA: (7) implies:
% 226.85/39.05  | |   (8)  all_57_11 = e1
% 226.85/39.05  | | 
% 226.85/39.05  | | REF_CLOSE: (3), (6), (8) are inconsistent by sub-proof #2113.
% 226.85/39.05  | | 
% 226.85/39.05  | Case 2:
% 226.85/39.05  | | 
% 226.85/39.05  | |   (9)  all_57_15 = e1 & op(e0, e0) = e1
% 226.85/39.05  | | 
% 226.85/39.05  | | ALPHA: (9) implies:
% 226.85/39.05  | |   (10)  op(e0, e0) = e1
% 226.85/39.05  | | 
% 226.85/39.05  | | REF_CLOSE: (1), (4), (5), (10) are inconsistent by sub-proof #2290.
% 226.85/39.05  | | 
% 226.85/39.05  | End of split
% 226.85/39.05  | 
% 226.85/39.05  End of proof
% 226.85/39.05  
% 226.85/39.05  Sub-proof #177 shows that the following formulas are inconsistent:
% 226.85/39.05  ----------------------------------------------------------------
% 226.85/39.05    (1)  all_57_4 = e3 & op(e3, e1) = e3
% 226.85/39.05    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.85/39.05           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.85/39.05    (3)  op(e3, e1) = all_53_8
% 226.85/39.05    (4)   ~ (all_53_8 = e3)
% 226.85/39.05  
% 226.85/39.05  Begin of proof
% 226.85/39.05  | 
% 226.85/39.05  | ALPHA: (1) implies:
% 226.85/39.05  |   (5)  op(e3, e1) = e3
% 226.85/39.05  | 
% 226.85/39.05  | GROUND_INST: instantiating (2) with all_53_8, e3, e1, e3, simplifying with
% 226.85/39.05  |              (3), (5) gives:
% 226.85/39.05  |   (6)  all_53_8 = e3
% 226.85/39.05  | 
% 226.85/39.05  | REDUCE: (4), (6) imply:
% 226.85/39.05  |   (7)  $false
% 226.85/39.05  | 
% 226.85/39.05  | CLOSE: (7) is inconsistent.
% 226.85/39.05  | 
% 226.85/39.05  End of proof
% 226.85/39.05  
% 226.85/39.05  Sub-proof #178 shows that the following formulas are inconsistent:
% 226.85/39.05  ----------------------------------------------------------------
% 226.85/39.05    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.85/39.05           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.85/39.05    (2)   ~ (all_53_13 = e3)
% 226.85/39.05    (3)   ~ (all_53_9 = e3)
% 226.85/39.05    (4)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 226.85/39.05    (5)  op(e2, e0) = all_53_13
% 226.85/39.05    (6)  op(e2, e1) = all_53_9
% 226.85/39.05  
% 226.85/39.05  Begin of proof
% 226.85/39.05  | 
% 226.85/39.05  | BETA: splitting (4) gives:
% 226.85/39.05  | 
% 226.85/39.05  | Case 1:
% 226.85/39.05  | | 
% 226.85/39.05  | |   (7)  all_57_5 = e3 & op(e2, e1) = e3
% 226.85/39.05  | | 
% 226.85/39.05  | | REF_CLOSE: (1), (3), (6), (7) are inconsistent by sub-proof #270.
% 226.85/39.05  | | 
% 226.85/39.05  | Case 2:
% 226.85/39.05  | | 
% 226.85/39.05  | |   (8)  all_57_10 = e3 & op(e2, e0) = e3
% 226.85/39.05  | | 
% 226.85/39.05  | | ALPHA: (8) implies:
% 226.85/39.05  | |   (9)  op(e2, e0) = e3
% 226.85/39.05  | | 
% 226.85/39.05  | | REF_CLOSE: (1), (2), (5), (9) are inconsistent by sub-proof #2301.
% 226.85/39.05  | | 
% 226.85/39.05  | End of split
% 226.85/39.05  | 
% 226.85/39.05  End of proof
% 226.85/39.05  
% 226.85/39.05  Sub-proof #179 shows that the following formulas are inconsistent:
% 226.85/39.05  ----------------------------------------------------------------
% 226.85/39.05    (1)  op(e0, e0) = all_4_2
% 226.85/39.05    (2)  all_57_13 = e1
% 226.85/39.05    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.85/39.05           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.85/39.05    (4)   ~ (e3 = e2)
% 226.85/39.05    (5)   ~ (all_4_2 = e2)
% 226.85/39.05    (6)   ~ (e2 = e0)
% 226.85/39.05    (7)  all_57_12 = e3
% 226.85/39.05    (8)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2) |
% 226.85/39.05         (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 226.85/39.05    (9)   ~ (e2 = e1)
% 226.85/39.05    (10)  all_57_14 = e0
% 226.85/39.05  
% 226.85/39.05  Begin of proof
% 226.85/39.05  | 
% 226.85/39.05  | BETA: splitting (8) gives:
% 226.85/39.05  | 
% 226.85/39.05  | Case 1:
% 226.85/39.05  | | 
% 226.85/39.05  | |   (11)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 226.85/39.05  | |           e2)
% 226.85/39.05  | | 
% 226.85/39.05  | | BETA: splitting (11) gives:
% 226.85/39.05  | | 
% 226.85/39.05  | | Case 1:
% 226.85/39.05  | | | 
% 226.85/39.05  | | |   (12)  all_57_12 = e2 & op(e0, e3) = e2
% 226.85/39.05  | | | 
% 226.85/39.05  | | | ALPHA: (12) implies:
% 226.85/39.05  | | |   (13)  all_57_12 = e2
% 226.85/39.05  | | | 
% 226.85/39.05  | | | REF_CLOSE: (4), (7), (13) are inconsistent by sub-proof #2392.
% 226.85/39.05  | | | 
% 226.85/39.05  | | Case 2:
% 226.85/39.05  | | | 
% 226.85/39.05  | | |   (14)  all_57_13 = e2 & op(e0, e2) = e2
% 226.85/39.05  | | | 
% 226.85/39.05  | | | REF_CLOSE: (2), (9), (14) are inconsistent by sub-proof #2101.
% 226.85/39.05  | | | 
% 226.85/39.05  | | End of split
% 226.85/39.05  | | 
% 226.85/39.05  | Case 2:
% 226.85/39.05  | | 
% 226.85/39.05  | |   (15)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 226.85/39.05  | |           e2)
% 226.85/39.05  | | 
% 226.85/39.05  | | REF_CLOSE: (1), (3), (5), (6), (10), (15) are inconsistent by sub-proof
% 226.85/39.05  | |            #180.
% 226.85/39.05  | | 
% 226.85/39.05  | End of split
% 226.85/39.05  | 
% 226.85/39.05  End of proof
% 226.85/39.05  
% 226.85/39.05  Sub-proof #180 shows that the following formulas are inconsistent:
% 226.85/39.05  ----------------------------------------------------------------
% 226.85/39.05    (1)  op(e0, e0) = all_4_2
% 226.85/39.05    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.85/39.05           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.85/39.05    (3)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 226.85/39.05    (4)   ~ (all_4_2 = e2)
% 226.85/39.05    (5)   ~ (e2 = e0)
% 226.85/39.05    (6)  all_57_14 = e0
% 226.85/39.05  
% 226.85/39.05  Begin of proof
% 226.85/39.05  | 
% 226.85/39.05  | BETA: splitting (3) gives:
% 226.85/39.05  | 
% 226.85/39.05  | Case 1:
% 226.85/39.05  | | 
% 226.85/39.05  | |   (7)  all_57_14 = e2 & op(e0, e1) = e2
% 226.85/39.05  | | 
% 226.85/39.05  | | REF_CLOSE: (5), (6), (7) are inconsistent by sub-proof #2074.
% 226.85/39.05  | | 
% 226.85/39.05  | Case 2:
% 226.85/39.05  | | 
% 226.85/39.05  | |   (8)  all_57_15 = e2 & op(e0, e0) = e2
% 226.85/39.05  | | 
% 226.85/39.05  | | ALPHA: (8) implies:
% 226.85/39.05  | |   (9)  op(e0, e0) = e2
% 226.85/39.05  | | 
% 226.85/39.05  | | REF_CLOSE: (1), (2), (4), (9) are inconsistent by sub-proof #2334.
% 226.85/39.05  | | 
% 226.85/39.05  | End of split
% 226.85/39.05  | 
% 226.85/39.05  End of proof
% 226.85/39.05  
% 226.85/39.05  Sub-proof #181 shows that the following formulas are inconsistent:
% 226.85/39.05  ----------------------------------------------------------------
% 226.85/39.05    (1)  op(e3, e3) = e1
% 226.85/39.05    (2)  op(e2, e3) = all_53_1
% 226.85/39.05    (3)   ~ (e3 = e1)
% 226.85/39.05    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.85/39.05           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.85/39.05    (5)   ~ (all_53_1 = e3)
% 226.85/39.05    (6)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3)
% 226.85/39.05  
% 226.85/39.05  Begin of proof
% 226.85/39.05  | 
% 226.85/39.05  | BETA: splitting (6) gives:
% 226.85/39.05  | 
% 226.85/39.05  | Case 1:
% 226.85/39.05  | | 
% 226.85/39.05  | |   (7)  all_57_0 = e3 & op(e3, e3) = e3
% 226.85/39.05  | | 
% 226.85/39.05  | | ALPHA: (7) implies:
% 226.85/39.05  | |   (8)  op(e3, e3) = e3
% 226.85/39.05  | | 
% 226.85/39.05  | | REF_CLOSE: (1), (3), (4), (8) are inconsistent by sub-proof #2495.
% 226.85/39.05  | | 
% 226.85/39.05  | Case 2:
% 226.85/39.05  | | 
% 226.85/39.05  | |   (9)  all_57_2 = e3 & op(e2, e3) = e3
% 226.85/39.05  | | 
% 226.85/39.05  | | REF_CLOSE: (2), (4), (5), (9) are inconsistent by sub-proof #2299.
% 226.85/39.05  | | 
% 226.85/39.05  | End of split
% 226.85/39.05  | 
% 226.85/39.05  End of proof
% 226.85/39.05  
% 226.85/39.05  Sub-proof #182 shows that the following formulas are inconsistent:
% 226.85/39.05  ----------------------------------------------------------------
% 226.85/39.05    (1)  op(e1, e3) = all_52_17
% 226.85/39.05    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 226.85/39.05         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 226.85/39.05    (3)   ~ (all_53_8 = all_53_12)
% 226.85/39.05    (4)   ~ (e3 = e1)
% 226.85/39.05    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.85/39.05           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.85/39.05    (6)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 226.85/39.05         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 226.85/39.05    (7)   ~ (all_53_8 = e1)
% 226.85/39.05    (8)  op(all_52_17, all_52_17) = e3
% 226.85/39.05    (9)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 226.85/39.05         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 226.85/39.05    (10)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 226.85/39.05          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 226.85/39.05    (11)  all_57_4 = e3
% 226.85/39.05    (12)   ~ (e3 = e2)
% 226.85/39.05    (13)   ~ (e3 = e0)
% 226.85/39.05    (14)  all_57_0 = e1
% 226.85/39.05    (15)   ~ (all_53_4 = all_53_8)
% 226.85/39.05    (16)  op(e3, e2) = all_53_4
% 226.85/39.05    (17)   ~ (e2 = e0)
% 226.85/39.05    (18)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 226.85/39.05          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 226.85/39.05    (19)   ~ (e1 = e0)
% 226.85/39.05    (20)   ~ (all_53_12 = e3)
% 226.85/39.05    (21)  op(e1, e3) = all_53_2
% 226.85/39.05    (22)   ~ (e2 = e1)
% 226.85/39.05    (23)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 226.85/39.05          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 226.85/39.05    (24)  all_57_6 = e3 & op(e1, e3) = e3
% 226.85/39.05    (25)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 226.85/39.05          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 226.85/39.05    (26)  op(e3, e1) = all_53_8
% 226.85/39.05    (27)  op(e3, e0) = all_53_12
% 226.85/39.05  
% 226.85/39.05  Begin of proof
% 226.85/39.05  | 
% 226.85/39.05  | ALPHA: (24) implies:
% 226.85/39.05  |   (28)  all_57_6 = e3
% 226.85/39.05  |   (29)  op(e1, e3) = e3
% 226.85/39.05  | 
% 226.85/39.05  | BETA: splitting (18) gives:
% 226.85/39.05  | 
% 226.85/39.05  | Case 1:
% 226.85/39.05  | | 
% 226.85/39.05  | |   (30)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) =
% 226.85/39.05  | |           e3)
% 226.85/39.05  | | 
% 226.85/39.05  | | BETA: splitting (30) gives:
% 226.85/39.05  | | 
% 226.85/39.05  | | Case 1:
% 226.85/39.05  | | | 
% 226.85/39.05  | | |   (31)  all_57_0 = e3 & op(e3, e3) = e3
% 226.85/39.05  | | | 
% 226.85/39.05  | | | ALPHA: (31) implies:
% 226.85/39.05  | | |   (32)  all_57_0 = e3
% 226.85/39.05  | | | 
% 226.85/39.05  | | | REF_CLOSE: (2), (4), (12), (13), (17), (19), (22), (23), (25), (28), (32)
% 226.85/39.05  | | |            are inconsistent by sub-proof #2010.
% 226.85/39.05  | | | 
% 226.85/39.05  | | Case 2:
% 226.85/39.05  | | | 
% 226.85/39.05  | | |   (33)  all_57_1 = e3 & op(e3, e2) = e3
% 226.85/39.05  | | | 
% 226.85/39.05  | | | ALPHA: (33) implies:
% 226.85/39.05  | | |   (34)  all_57_1 = e3
% 226.85/39.05  | | | 
% 226.85/39.05  | | | REF_CLOSE: (9), (10), (11), (12), (13), (14), (17), (19), (22), (34) are
% 226.85/39.05  | | |            inconsistent by sub-proof #1808.
% 226.85/39.05  | | | 
% 226.85/39.05  | | End of split
% 226.85/39.05  | | 
% 226.85/39.05  | Case 2:
% 226.85/39.05  | | 
% 226.85/39.05  | |   (35)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) =
% 226.85/39.05  | |           e3)
% 226.85/39.05  | | 
% 226.85/39.05  | | BETA: splitting (35) gives:
% 226.85/39.05  | | 
% 226.85/39.05  | | Case 1:
% 226.85/39.05  | | | 
% 226.85/39.05  | | |   (36)  all_57_4 = e3 & op(e3, e1) = e3
% 226.85/39.05  | | | 
% 226.85/39.05  | | | ALPHA: (36) implies:
% 226.85/39.05  | | |   (37)  op(e3, e1) = e3
% 226.85/39.05  | | | 
% 226.85/39.05  | | | GROUND_INST: instantiating (5) with all_53_2, e3, e3, e1, simplifying with
% 226.85/39.05  | | |              (21), (29) gives:
% 226.85/39.05  | | |   (38)  all_53_2 = e3
% 226.85/39.05  | | | 
% 226.85/39.05  | | | GROUND_INST: instantiating (5) with all_53_2, all_52_17, e3, e1,
% 226.85/39.05  | | |              simplifying with (1), (21) gives:
% 226.85/39.05  | | |   (39)  all_53_2 = all_52_17
% 226.85/39.05  | | | 
% 226.85/39.05  | | | GROUND_INST: instantiating (5) with all_53_8, e3, e1, e3, simplifying with
% 226.85/39.05  | | |              (26), (37) gives:
% 226.85/39.05  | | |   (40)  all_53_8 = e3
% 226.85/39.05  | | | 
% 226.85/39.05  | | | COMBINE_EQS: (38), (39) imply:
% 226.85/39.05  | | |   (41)  all_52_17 = e3
% 226.85/39.05  | | | 
% 226.85/39.05  | | | SIMP: (41) implies:
% 226.85/39.05  | | |   (42)  all_52_17 = e3
% 226.85/39.05  | | | 
% 226.85/39.05  | | | REDUCE: (15), (40) imply:
% 226.85/39.05  | | |   (43)   ~ (all_53_4 = e3)
% 226.85/39.05  | | | 
% 226.85/39.05  | | | REDUCE: (3), (40) imply:
% 226.85/39.05  | | |   (44)   ~ (all_53_12 = e3)
% 226.85/39.05  | | | 
% 226.85/39.05  | | | REDUCE: (8), (42) imply:
% 226.85/39.05  | | |   (45)  op(e3, e3) = e3
% 226.85/39.05  | | | 
% 226.85/39.05  | | | REF_CLOSE: (2), (4), (5), (6), (9), (10), (12), (13), (16), (17), (18),
% 226.85/39.05  | | |            (19), (20), (22), (23), (25), (27), (28), (43), (45) are
% 226.85/39.05  | | |            inconsistent by sub-proof #268.
% 226.85/39.05  | | | 
% 226.85/39.05  | | Case 2:
% 226.85/39.05  | | | 
% 226.85/39.05  | | |   (46)  all_57_9 = e3 & op(e3, e0) = e3
% 226.85/39.05  | | | 
% 226.85/39.05  | | | ALPHA: (46) implies:
% 226.85/39.05  | | |   (47)  op(e3, e0) = e3
% 226.85/39.05  | | | 
% 226.85/39.05  | | | REF_CLOSE: (5), (20), (27), (47) are inconsistent by sub-proof #2458.
% 226.85/39.05  | | | 
% 226.85/39.05  | | End of split
% 226.85/39.05  | | 
% 226.85/39.05  | End of split
% 226.85/39.05  | 
% 226.85/39.05  End of proof
% 226.85/39.05  
% 226.85/39.05  Sub-proof #183 shows that the following formulas are inconsistent:
% 226.85/39.05  ----------------------------------------------------------------
% 226.85/39.05    (1)  op(e0, e0) = all_4_2
% 226.85/39.05    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 226.85/39.05    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 226.85/39.05         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 226.85/39.05    (4)  op(e2, e3) = all_53_1
% 226.85/39.05    (5)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 226.85/39.05    (6)   ~ (e3 = e1)
% 226.85/39.05    (7)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 226.85/39.05         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 226.85/39.05    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.85/39.05           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.85/39.05    (9)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 226.85/39.05         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 226.85/39.05    (10)   ~ (all_6_2 = e3)
% 226.85/39.05    (11)  op(e1, e1) = all_6_2
% 226.85/39.05    (12)   ~ (all_53_13 = e3)
% 226.85/39.05    (13)   ~ (all_53_9 = all_6_2)
% 226.85/39.05    (14)   ~ (e3 = e2)
% 226.85/39.05    (15)  op(e1, e0) = all_53_14
% 226.85/39.05    (16)   ~ (e3 = e0)
% 226.85/39.05    (17)   ~ (all_4_2 = e2)
% 226.85/39.05    (18)   ~ (all_53_1 = e1)
% 226.85/39.05    (19)  op(e1, e1) = all_52_21
% 226.85/39.05    (20)   ~ (e2 = e0)
% 226.85/39.05    (21)   ~ (all_53_9 = e3)
% 226.85/39.05    (22)   ~ (e1 = e0)
% 226.85/39.05    (23)  op(e0, e0) = e0
% 226.85/39.05    (24)   ~ (all_53_14 = e0)
% 226.85/39.05    (25)  all_55_10 = all_6_2
% 226.85/39.05    (26)  op(e1, e1) = e2
% 226.85/39.05    (27)  op(e2, e0) = all_53_13
% 226.85/39.05    (28)  op(e2, e2) = e3
% 226.85/39.05    (29)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 226.85/39.05          (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 226.85/39.05    (30)   ~ (e2 = e1)
% 226.85/39.05    (31)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 226.85/39.05          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 226.85/39.05    (32)  op(e2, e1) = all_53_9
% 226.85/39.05    (33)   ~ (all_6_2 = e0)
% 226.85/39.05    (34)  op(all_52_21, all_52_21) = e1
% 226.85/39.05    (35)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 226.85/39.05          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 226.85/39.05  
% 226.85/39.05  Begin of proof
% 226.85/39.05  | 
% 226.85/39.05  | BETA: splitting (5) gives:
% 226.85/39.05  | 
% 226.85/39.05  | Case 1:
% 226.85/39.05  | | 
% 226.85/39.05  | |   (36)  all_57_8 = e1 & op(e1, e1) = e1
% 226.85/39.05  | | 
% 226.85/39.05  | | ALPHA: (36) implies:
% 226.85/39.05  | |   (37)  op(e1, e1) = e1
% 226.85/39.05  | | 
% 226.85/39.05  | | REF_CLOSE: (8), (26), (30), (37) are inconsistent by sub-proof #2423.
% 226.85/39.05  | | 
% 226.85/39.05  | Case 2:
% 226.85/39.05  | | 
% 226.85/39.05  | |   (38)  all_57_11 = e1 & op(e1, e0) = e1
% 226.85/39.05  | | 
% 226.85/39.05  | | ALPHA: (38) implies:
% 226.85/39.05  | |   (39)  all_57_11 = e1
% 226.85/39.05  | | 
% 226.85/39.05  | | BETA: splitting (29) gives:
% 226.85/39.05  | | 
% 226.85/39.05  | | Case 1:
% 226.85/39.05  | | | 
% 226.85/39.05  | | |   (40)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 226.85/39.05  | | |           e3)
% 226.85/39.05  | | | 
% 226.85/39.05  | | | BETA: splitting (40) gives:
% 226.85/39.05  | | | 
% 226.85/39.05  | | | Case 1:
% 226.85/39.05  | | | | 
% 226.85/39.05  | | | |   (41)  all_57_9 = e3 & op(e3, e0) = e3
% 226.85/39.05  | | | | 
% 226.85/39.05  | | | | ALPHA: (41) implies:
% 226.85/39.05  | | | |   (42)  op(e3, e0) = e3
% 226.85/39.05  | | | | 
% 226.85/39.05  | | | | BETA: splitting (31) gives:
% 226.85/39.05  | | | | 
% 226.85/39.05  | | | | Case 1:
% 226.85/39.05  | | | | | 
% 226.85/39.05  | | | | |   (43)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2,
% 226.85/39.05  | | | | |             e0) = e2)
% 226.85/39.05  | | | | | 
% 226.85/39.05  | | | | | BETA: splitting (43) gives:
% 226.85/39.05  | | | | | 
% 226.85/39.05  | | | | | Case 1:
% 226.85/39.05  | | | | | | 
% 226.85/39.05  | | | | | |   (44)  all_57_9 = e2 & op(e3, e0) = e2
% 226.85/39.05  | | | | | | 
% 226.85/39.05  | | | | | | REF_CLOSE: (8), (14), (42), (44) are inconsistent by sub-proof #306.
% 226.85/39.05  | | | | | | 
% 226.85/39.05  | | | | | Case 2:
% 226.85/39.05  | | | | | | 
% 226.85/39.05  | | | | | |   (45)  all_57_10 = e2 & op(e2, e0) = e2
% 226.85/39.05  | | | | | | 
% 226.85/39.05  | | | | | | ALPHA: (45) implies:
% 226.85/39.05  | | | | | |   (46)  all_57_10 = e2
% 226.85/39.05  | | | | | | 
% 226.85/39.05  | | | | | | BETA: splitting (3) gives:
% 226.85/39.05  | | | | | | 
% 226.85/39.05  | | | | | | Case 1:
% 226.85/39.05  | | | | | | | 
% 226.85/39.05  | | | | | | |   (47)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 &
% 226.85/39.05  | | | | | | |           op(e2, e2) = e1)
% 226.85/39.05  | | | | | | | 
% 226.85/39.05  | | | | | | | REF_CLOSE: (4), (6), (8), (18), (28), (47) are inconsistent by
% 226.85/39.05  | | | | | | |            sub-proof #240.
% 226.85/39.05  | | | | | | | 
% 226.85/39.05  | | | | | | Case 2:
% 226.85/39.05  | | | | | | | 
% 226.85/39.05  | | | | | | |   (48)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 &
% 226.85/39.05  | | | | | | |           op(e2, e0) = e1)
% 226.85/39.05  | | | | | | | 
% 226.85/39.05  | | | | | | | BETA: splitting (48) gives:
% 226.85/39.05  | | | | | | | 
% 226.85/39.05  | | | | | | | Case 1:
% 226.85/39.05  | | | | | | | | 
% 226.85/39.05  | | | | | | | |   (49)  all_57_5 = e1 & op(e2, e1) = e1
% 226.85/39.05  | | | | | | | | 
% 226.85/39.05  | | | | | | | | ALPHA: (49) implies:
% 226.85/39.05  | | | | | | | |   (50)  op(e2, e1) = e1
% 226.85/39.05  | | | | | | | | 
% 226.85/39.05  | | | | | | | | REF_CLOSE: (2), (8), (10), (11), (13), (19), (21), (25), (28),
% 226.85/39.05  | | | | | | | |            (32), (33), (34), (50) are inconsistent by sub-proof
% 226.85/39.05  | | | | | | | |            #243.
% 226.85/39.05  | | | | | | | | 
% 226.85/39.05  | | | | | | | Case 2:
% 226.85/39.05  | | | | | | | | 
% 226.85/39.05  | | | | | | | |   (51)  all_57_10 = e1 & op(e2, e0) = e1
% 226.85/39.05  | | | | | | | | 
% 226.85/39.05  | | | | | | | | ALPHA: (51) implies:
% 226.85/39.05  | | | | | | | |   (52)  all_57_10 = e1
% 226.85/39.05  | | | | | | | | 
% 226.85/39.05  | | | | | | | | REF_CLOSE: (30), (46), (52) are inconsistent by sub-proof #2144.
% 226.85/39.05  | | | | | | | | 
% 226.85/39.05  | | | | | | | End of split
% 226.85/39.05  | | | | | | | 
% 226.85/39.05  | | | | | | End of split
% 226.85/39.05  | | | | | | 
% 226.85/39.05  | | | | | End of split
% 226.85/39.05  | | | | | 
% 226.85/39.05  | | | | Case 2:
% 226.85/39.05  | | | | | 
% 226.85/39.05  | | | | |   (53)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0,
% 226.85/39.05  | | | | |             e0) = e2)
% 226.85/39.05  | | | | | 
% 226.85/39.05  | | | | | REF_CLOSE: (1), (6), (7), (8), (9), (10), (11), (14), (15), (16),
% 226.85/39.05  | | | | |            (17), (20), (22), (24), (26), (30), (33), (35), (53) are
% 226.85/39.05  | | | | |            inconsistent by sub-proof #346.
% 226.85/39.05  | | | | | 
% 226.85/39.05  | | | | End of split
% 226.85/39.05  | | | | 
% 226.85/39.05  | | | Case 2:
% 226.85/39.05  | | | | 
% 226.85/39.05  | | | |   (54)  all_57_10 = e3 & op(e2, e0) = e3
% 226.85/39.05  | | | | 
% 226.85/39.05  | | | | ALPHA: (54) implies:
% 226.85/39.05  | | | |   (55)  op(e2, e0) = e3
% 226.85/39.05  | | | | 
% 226.85/39.05  | | | | REF_CLOSE: (8), (12), (27), (55) are inconsistent by sub-proof #2301.
% 226.85/39.05  | | | | 
% 226.85/39.05  | | | End of split
% 226.85/39.05  | | | 
% 226.85/39.05  | | Case 2:
% 226.85/39.05  | | | 
% 226.85/39.05  | | |   (56)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0)
% 226.85/39.05  | | |           = e3)
% 226.85/39.05  | | | 
% 226.85/39.05  | | | REF_CLOSE: (6), (8), (16), (23), (39), (56) are inconsistent by sub-proof
% 226.85/39.05  | | |            #232.
% 226.85/39.05  | | | 
% 226.85/39.05  | | End of split
% 226.85/39.05  | | 
% 226.85/39.05  | End of split
% 226.85/39.05  | 
% 226.85/39.05  End of proof
% 226.85/39.05  
% 226.85/39.05  Sub-proof #184 shows that the following formulas are inconsistent:
% 226.85/39.05  ----------------------------------------------------------------
% 226.85/39.05    (1)  op(e3, e3) = e1
% 226.85/39.05    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.85/39.05           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.85/39.05    (3)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0 &
% 226.85/39.05         op(all_52_9, all_52_9) = e3 & op(all_52_11, all_52_11) = e2 &
% 226.85/39.05         op(all_52_13, all_52_13) = e1 & op(all_52_15, all_52_15) = e0 & op(e2,
% 226.85/39.05           e3) = all_52_9 & op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13 &
% 226.85/39.05         op(e2, e0) = all_52_15 & $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 226.85/39.05         $i(all_52_15)
% 226.85/39.05    (4)  op(e2, e2) = e3
% 226.85/39.05    (5)   ~ (e2 = e1)
% 226.85/39.05  
% 226.85/39.05  Begin of proof
% 226.85/39.05  | 
% 226.85/39.05  | ALPHA: (3) implies:
% 226.85/39.05  |   (6)  op(e2, e2) = all_52_11
% 226.85/39.05  |   (7)  op(all_52_11, all_52_11) = e2
% 226.85/39.05  | 
% 226.85/39.05  | GROUND_INST: instantiating (2) with e3, all_52_11, e2, e2, simplifying with
% 226.85/39.05  |              (4), (6) gives:
% 226.85/39.05  |   (8)  all_52_11 = e3
% 226.85/39.05  | 
% 226.85/39.05  | REDUCE: (7), (8) imply:
% 226.85/39.05  |   (9)  op(e3, e3) = e2
% 226.85/39.05  | 
% 226.85/39.05  | REF_CLOSE: (1), (2), (5), (9) are inconsistent by sub-proof #1950.
% 226.85/39.05  | 
% 226.85/39.05  End of proof
% 226.85/39.05  
% 226.85/39.05  Sub-proof #185 shows that the following formulas are inconsistent:
% 226.85/39.05  ----------------------------------------------------------------
% 226.85/39.05    (1)   ~ (e3 = e1)
% 226.85/39.05    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.85/39.05           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.85/39.05    (3)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1)
% 226.85/39.05    (4)   ~ (all_53_4 = e1)
% 226.85/39.05    (5)  op(e3, e2) = all_53_4
% 226.85/39.05    (6)  op(e2, e2) = e3
% 226.85/39.05  
% 226.85/39.05  Begin of proof
% 226.85/39.05  | 
% 226.85/39.05  | BETA: splitting (3) gives:
% 226.85/39.05  | 
% 226.85/39.05  | Case 1:
% 226.85/39.05  | | 
% 226.85/39.05  | |   (7)  all_57_1 = e1 & op(e3, e2) = e1
% 226.85/39.05  | | 
% 226.85/39.05  | | ALPHA: (7) implies:
% 226.85/39.06  | |   (8)  op(e3, e2) = e1
% 226.85/39.06  | | 
% 226.85/39.06  | | REF_CLOSE: (2), (4), (5), (8) are inconsistent by sub-proof #363.
% 226.85/39.06  | | 
% 226.85/39.06  | Case 2:
% 226.85/39.06  | | 
% 226.85/39.06  | |   (9)  all_57_3 = e1 & op(e2, e2) = e1
% 226.85/39.06  | | 
% 226.85/39.06  | | ALPHA: (9) implies:
% 226.85/39.06  | |   (10)  op(e2, e2) = e1
% 226.85/39.06  | | 
% 226.85/39.06  | | REF_CLOSE: (1), (2), (6), (10) are inconsistent by sub-proof #1912.
% 226.85/39.06  | | 
% 226.85/39.06  | End of split
% 226.85/39.06  | 
% 226.85/39.06  End of proof
% 226.85/39.06  
% 226.85/39.06  Sub-proof #186 shows that the following formulas are inconsistent:
% 226.85/39.06  ----------------------------------------------------------------
% 226.85/39.06    (1)   ~ (e3 = e1)
% 226.85/39.06    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.85/39.06           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.85/39.06    (3)   ~ (all_6_2 = e3)
% 226.85/39.06    (4)  op(e1, e1) = all_6_2
% 226.85/39.06    (5)   ~ (all_53_13 = e3)
% 226.85/39.06    (6)   ~ (e3 = e2)
% 226.85/39.06    (7)  op(e1, e0) = all_53_14
% 226.85/39.06    (8)   ~ (e3 = e0)
% 226.85/39.06    (9)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 226.85/39.06         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 226.85/39.06    (10)   ~ (all_53_14 = e3)
% 226.85/39.06    (11)   ~ (e2 = e0)
% 226.85/39.06    (12)   ~ (e1 = e0)
% 226.85/39.06    (13)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 226.85/39.06          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 226.85/39.06            e2)
% 226.85/39.06    (14)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 226.85/39.06              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 226.85/39.06                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 226.85/39.06                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 226.85/39.06    (15)  op(e2, e0) = all_53_13
% 226.85/39.06    (16)   ~ (all_53_12 = e3)
% 226.85/39.06    (17)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 226.85/39.06          (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 226.85/39.06    (18)   ~ (e2 = e1)
% 226.85/39.06    (19)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 226.85/39.06    (20)  op(e3, e0) = all_53_12
% 226.85/39.06  
% 226.85/39.06  Begin of proof
% 226.85/39.06  | 
% 226.85/39.06  | BETA: splitting (19) gives:
% 226.85/39.06  | 
% 226.85/39.06  | Case 1:
% 226.85/39.06  | | 
% 226.85/39.06  | |   (21)  all_57_8 = e3 & op(e1, e1) = e3
% 226.85/39.06  | | 
% 226.85/39.06  | | ALPHA: (21) implies:
% 226.85/39.06  | |   (22)  op(e1, e1) = e3
% 226.85/39.06  | | 
% 226.85/39.06  | | REF_CLOSE: (2), (3), (4), (22) are inconsistent by sub-proof #2468.
% 226.85/39.06  | | 
% 226.85/39.06  | Case 2:
% 226.85/39.06  | | 
% 226.85/39.06  | |   (23)  all_57_14 = e3 & op(e0, e1) = e3
% 226.85/39.06  | | 
% 226.85/39.06  | | ALPHA: (23) implies:
% 226.85/39.06  | |   (24)  all_57_14 = e3
% 226.85/39.06  | | 
% 226.85/39.06  | | BETA: splitting (17) gives:
% 226.85/39.06  | | 
% 226.85/39.06  | | Case 1:
% 226.85/39.06  | | | 
% 226.85/39.06  | | |   (25)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 226.85/39.06  | | |           e3)
% 226.85/39.06  | | | 
% 226.85/39.06  | | | REF_CLOSE: (2), (5), (15), (16), (20), (25) are inconsistent by sub-proof
% 226.85/39.06  | | |            #2300.
% 226.85/39.06  | | | 
% 226.85/39.06  | | Case 2:
% 226.85/39.06  | | | 
% 226.85/39.06  | | |   (26)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0)
% 226.85/39.06  | | |           = e3)
% 226.85/39.06  | | | 
% 226.85/39.06  | | | REF_CLOSE: (1), (2), (6), (7), (8), (9), (10), (11), (12), (13), (14),
% 226.85/39.06  | | |            (18), (24), (26) are inconsistent by sub-proof #2311.
% 226.85/39.06  | | | 
% 226.85/39.06  | | End of split
% 226.85/39.06  | | 
% 226.85/39.06  | End of split
% 226.85/39.06  | 
% 226.85/39.06  End of proof
% 226.85/39.06  
% 226.85/39.06  Sub-proof #187 shows that the following formulas are inconsistent:
% 226.85/39.06  ----------------------------------------------------------------
% 226.85/39.06    (1)  op(e3, e3) = all_10_2
% 226.85/39.06    (2)   ~ (all_53_7 = e3)
% 226.85/39.06    (3)  op(e0, e0) = all_4_2
% 226.85/39.06    (4)  op(e0, e1) = all_53_11
% 226.85/39.06    (5)   ~ (all_53_3 = all_10_2)
% 226.85/39.06    (6)   ~ (all_53_1 = all_10_2)
% 226.85/39.06    (7)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 226.85/39.06    (8)  op(e3, e1) = e3
% 226.85/39.06    (9)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 226.85/39.06         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 226.85/39.06    (10)  op(e2, e3) = all_53_1
% 226.85/39.06    (11)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 226.85/39.06          (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 226.85/39.06    (12)   ~ (all_53_8 = all_53_12)
% 226.85/39.06    (13)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 226.85/39.06          (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 226.85/39.06    (14)   ~ (all_53_8 = all_53_11)
% 226.85/39.06    (15)   ~ (e3 = e1)
% 226.85/39.06    (16)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 226.85/39.06          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 226.85/39.06    (17)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 226.85/39.06            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 226.85/39.06    (18)  all_55_0 = all_10_2
% 226.85/39.06    (19)  all_22_2 = e3
% 226.85/39.06    (20)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 226.85/39.06          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 226.85/39.06    (21)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 226.85/39.06            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 226.85/39.06              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 226.85/39.06    (22)   ~ (all_53_8 = all_10_2)
% 226.85/39.06    (23)   ~ (all_53_3 = all_53_7)
% 226.85/39.06    (24)  op(e1, e3) = e3
% 226.85/39.06    (25)  op(e1, e1) = all_6_2
% 226.85/39.06    (26)  all_57_3 = e3
% 226.85/39.06    (27)  all_55_0 = e3 | all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 226.85/39.06    (28)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 226.85/39.06          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 226.85/39.06    (29)   ~ (all_53_11 = all_6_2)
% 226.85/39.06    (30)   ~ (all_18_2 = e0) | ( ~ (all_18_0 = e1) & op(all_18_1, e3) = all_18_0 &
% 226.85/39.06            op(e3, e0) = all_18_1 & $i(all_18_0) & $i(all_18_1)) | ( ~ (all_18_1 =
% 226.85/39.06              e2) & op(e3, e0) = all_18_1 & $i(all_18_1))
% 226.85/39.06    (31)   ~ (all_53_13 = e3)
% 226.85/39.06    (32)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 226.85/39.06          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 226.85/39.06    (33)   ~ (all_53_9 = all_6_2)
% 226.85/39.06    (34)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 226.85/39.06          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 226.85/39.06    (35)   ~ (all_53_14 = all_6_2)
% 226.85/39.06    (36)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 226.85/39.06          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 226.85/39.06    (37)  all_57_4 = e3
% 226.85/39.06    (38)   ~ (e3 = e2)
% 226.85/39.06    (39)   ~ (all_53_4 = all_10_2)
% 226.85/39.06    (40)  op(e1, e0) = all_53_14
% 226.85/39.06    (41)   ~ (e3 = e0)
% 226.85/39.06    (42)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 226.85/39.06          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 226.85/39.06    (43)   ~ (all_53_8 = all_6_2)
% 226.85/39.06    (44)   ~ (all_4_2 = e2)
% 226.85/39.06    (45)  op(e0, e3) = all_53_3
% 226.85/39.06    (46)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 226.85/39.06          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 226.85/39.06            e1)
% 226.85/39.06    (47)   ~ (all_53_4 = all_53_8)
% 226.85/39.06    (48)   ~ (all_53_14 = e3)
% 226.85/39.06    (49)  op(e3, e2) = all_53_4
% 226.85/39.06    (50)   ~ (all_53_1 = all_53_2)
% 226.85/39.06    (51)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 226.85/39.06          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 226.85/39.06    (52)   ~ (e2 = e0)
% 226.85/39.06    (53)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 226.85/39.06            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 226.85/39.06            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 226.85/39.06            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 226.85/39.06              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 226.85/39.06            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 226.85/39.06            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 226.85/39.06              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 226.85/39.06              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 226.85/39.06            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 226.85/39.06            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 226.85/39.06            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 226.85/39.06              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 226.85/39.06              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 226.85/39.06            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 226.85/39.06              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 226.85/39.06            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 226.85/39.06            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 226.85/39.06              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 226.85/39.06              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 226.85/39.06            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 226.85/39.06            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 226.85/39.06    (54)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 226.85/39.06            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 226.85/39.06              e3) = all_12_1 & $i(all_12_1))
% 226.85/39.06    (55)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 226.85/39.06          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 226.85/39.06    (56)   ~ (all_53_2 = all_53_14)
% 226.85/39.06    (57)   ~ (e1 = e0)
% 226.85/39.06    (58)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 226.85/39.06            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 226.85/39.06              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 226.85/39.06    (59)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 226.85/39.06          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 226.85/39.06    (60)  all_57_6 = e3
% 226.85/39.06    (61)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 226.85/39.06          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 226.85/39.06    (62)   ~ (all_53_2 = all_53_3)
% 226.85/39.06    (63)   ~ (all_10_2 = e1)
% 226.85/39.06    (64)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 226.85/39.06          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 226.85/39.06            e3)
% 226.85/39.06    (65)  op(e0, e2) = all_53_7
% 226.85/39.06    (66)  all_18_2 = all_10_2
% 226.85/39.06    (67)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 226.85/39.06          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 226.85/39.06            e2)
% 226.85/39.06    (68)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 226.85/39.06              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 226.85/39.06                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 226.85/39.06                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 226.85/39.06    (69)  all_55_10 = all_6_2
% 226.85/39.06    (70)   ~ (all_53_6 = all_6_2)
% 226.85/39.06    (71)  op(e2, e0) = all_53_13
% 226.85/39.06    (72)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 226.85/39.06          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 226.85/39.06    (73)  all_38_2 = all_6_2
% 226.85/39.06    (74)   ~ (all_53_12 = e3)
% 226.85/39.06    (75)  op(e1, e3) = all_53_2
% 226.85/39.06    (76)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 226.85/39.06          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 226.85/39.06    (77)  op(e2, e2) = e3
% 226.85/39.06    (78)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 226.85/39.06          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 226.85/39.06    (79)   ~ (all_53_12 = all_10_2)
% 226.85/39.06    (80)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 226.85/39.06          (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 226.85/39.06    (81)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 226.85/39.06          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 226.85/39.06    (82)   ~ (e2 = e1)
% 226.85/39.06    (83)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 226.85/39.06          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 226.85/39.06    (84)  op(e2, e1) = all_53_9
% 226.85/39.06    (85)  op(e1, e2) = all_53_6
% 226.85/39.06    (86)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 226.85/39.06          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 226.85/39.06    (87)  all_24_2 = all_6_2
% 226.85/39.06    (88)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 226.85/39.06          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 226.85/39.06    (89)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 226.85/39.06          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 226.85/39.06    (90)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 226.85/39.06          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 226.85/39.06    (91)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 226.85/39.06          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 226.85/39.06    (92)   ~ (all_22_2 = e3) | ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 &
% 226.85/39.06            op(e0, e3) = all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 =
% 226.85/39.06              e2) & op(e0, e3) = all_22_1 & $i(all_22_1))
% 226.85/39.06    (93)  op(e3, e1) = all_53_8
% 226.85/39.06    (94)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 226.85/39.06          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 226.85/39.06    (95)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 226.85/39.06          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 226.85/39.06    (96)  op(e3, e0) = all_53_12
% 226.85/39.06  
% 226.85/39.06  Begin of proof
% 226.85/39.06  | 
% 226.85/39.06  | BETA: splitting (80) gives:
% 226.85/39.06  | 
% 226.85/39.06  | Case 1:
% 226.85/39.06  | | 
% 226.85/39.06  | |   (97)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 226.85/39.06  | |           e3)
% 226.85/39.06  | | 
% 226.85/39.06  | | REF_CLOSE: (17), (31), (71), (74), (96), (97) are inconsistent by sub-proof
% 226.85/39.06  | |            #2300.
% 226.85/39.06  | | 
% 226.85/39.06  | Case 2:
% 226.85/39.06  | | 
% 226.85/39.06  | |   (98)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 226.85/39.06  | |           e3)
% 226.85/39.06  | | 
% 226.85/39.06  | | BETA: splitting (98) gives:
% 226.85/39.06  | | 
% 226.85/39.06  | | Case 1:
% 226.85/39.06  | | | 
% 226.85/39.06  | | |   (99)  all_57_11 = e3 & op(e1, e0) = e3
% 226.85/39.06  | | | 
% 226.85/39.06  | | | ALPHA: (99) implies:
% 226.85/39.06  | | |   (100)  op(e1, e0) = e3
% 226.85/39.06  | | | 
% 226.85/39.06  | | | REF_CLOSE: (17), (40), (48), (100) are inconsistent by sub-proof #2330.
% 226.85/39.06  | | | 
% 226.85/39.06  | | Case 2:
% 226.85/39.06  | | | 
% 226.85/39.06  | | |   (101)  all_57_15 = e3 & op(e0, e0) = e3
% 226.85/39.06  | | | 
% 226.85/39.06  | | | ALPHA: (101) implies:
% 226.85/39.06  | | |   (102)  all_57_15 = e3
% 226.85/39.06  | | |   (103)  op(e0, e0) = e3
% 226.85/39.06  | | | 
% 226.85/39.06  | | | GROUND_INST: instantiating (17) with all_53_2, e3, e3, e1, simplifying
% 226.85/39.06  | | |              with (24), (75) gives:
% 226.85/39.06  | | |   (104)  all_53_2 = e3
% 226.85/39.06  | | | 
% 226.85/39.06  | | | GROUND_INST: instantiating (17) with all_53_8, e3, e1, e3, simplifying
% 226.85/39.06  | | |              with (8), (93) gives:
% 226.85/39.06  | | |   (105)  all_53_8 = e3
% 226.85/39.06  | | | 
% 226.85/39.06  | | | REDUCE: (50), (104) imply:
% 226.85/39.06  | | |   (106)   ~ (all_53_1 = e3)
% 226.85/39.06  | | | 
% 226.85/39.06  | | | REDUCE: (62), (104) imply:
% 226.85/39.06  | | |   (107)   ~ (all_53_3 = e3)
% 226.85/39.06  | | | 
% 226.85/39.06  | | | SIMP: (107) implies:
% 226.85/39.06  | | |   (108)   ~ (all_53_3 = e3)
% 226.85/39.06  | | | 
% 226.85/39.06  | | | REDUCE: (56), (104) imply:
% 226.85/39.06  | | |   (109)   ~ (all_53_14 = e3)
% 226.85/39.06  | | | 
% 226.85/39.06  | | | REDUCE: (47), (105) imply:
% 226.85/39.06  | | |   (110)   ~ (all_53_4 = e3)
% 226.85/39.06  | | | 
% 226.85/39.06  | | | REDUCE: (14), (105) imply:
% 226.85/39.06  | | |   (111)   ~ (all_53_11 = e3)
% 226.85/39.06  | | | 
% 226.85/39.06  | | | SIMP: (111) implies:
% 226.85/39.06  | | |   (112)   ~ (all_53_11 = e3)
% 226.85/39.06  | | | 
% 226.85/39.06  | | | REDUCE: (12), (105) imply:
% 226.85/39.06  | | |   (113)   ~ (all_53_12 = e3)
% 226.85/39.06  | | | 
% 226.85/39.06  | | | REDUCE: (22), (105) imply:
% 226.85/39.06  | | |   (114)   ~ (all_10_2 = e3)
% 226.85/39.06  | | | 
% 226.85/39.06  | | | SIMP: (114) implies:
% 226.85/39.06  | | |   (115)   ~ (all_10_2 = e3)
% 226.85/39.06  | | | 
% 226.85/39.06  | | | REDUCE: (43), (105) imply:
% 226.85/39.06  | | |   (116)   ~ (all_6_2 = e3)
% 226.85/39.06  | | | 
% 226.85/39.06  | | | SIMP: (116) implies:
% 226.85/39.06  | | |   (117)   ~ (all_6_2 = e3)
% 226.85/39.06  | | | 
% 226.85/39.06  | | | BETA: splitting (30) gives:
% 226.85/39.06  | | | 
% 226.85/39.06  | | | Case 1:
% 226.85/39.06  | | | | 
% 226.85/39.06  | | | |   (118)   ~ (all_18_2 = e0)
% 226.85/39.06  | | | | 
% 226.85/39.06  | | | | REDUCE: (66), (118) imply:
% 226.85/39.06  | | | |   (119)   ~ (all_10_2 = e0)
% 226.85/39.06  | | | | 
% 226.85/39.06  | | | | BETA: splitting (53) gives:
% 226.85/39.06  | | | | 
% 226.85/39.06  | | | | Case 1:
% 226.85/39.06  | | | | | 
% 226.85/39.06  | | | | |   (120)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 =
% 226.85/39.06  | | | | |            e0 & op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) =
% 226.85/39.06  | | | | |            e2 & op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) =
% 226.85/39.06  | | | | |            e0 & op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 & op(e3,
% 226.85/39.06  | | | | |              e1) = all_52_5 & op(e3, e0) = all_52_7 & $i(all_52_1) &
% 226.85/39.06  | | | | |            $i(all_52_3) & $i(all_52_5) & $i(all_52_7)) | (all_52_8 =
% 226.85/39.06  | | | | |            e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0 &
% 226.85/39.06  | | | | |            op(all_52_9, all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 226.85/39.06  | | | | |            & op(all_52_13, all_52_13) = e1 & op(all_52_15, all_52_15)
% 226.85/39.06  | | | | |            = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 226.85/39.06  | | | | |            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 226.85/39.06  | | | | |            $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 226.85/39.06  | | | | |            $i(all_52_15))
% 226.85/39.06  | | | | | 
% 226.85/39.06  | | | | | BETA: splitting (120) gives:
% 226.85/39.06  | | | | | 
% 226.85/39.06  | | | | | Case 1:
% 226.85/39.06  | | | | | | 
% 226.85/39.06  | | | | | |   (121)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 =
% 226.85/39.06  | | | | | |          e0 & op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) =
% 226.85/39.06  | | | | | |          e2 & op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) =
% 226.85/39.06  | | | | | |          e0 & op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 & op(e3,
% 226.85/39.06  | | | | | |            e1) = all_52_5 & op(e3, e0) = all_52_7 & $i(all_52_1) &
% 226.85/39.06  | | | | | |          $i(all_52_3) & $i(all_52_5) & $i(all_52_7)
% 226.85/39.06  | | | | | | 
% 226.85/39.06  | | | | | | ALPHA: (121) implies:
% 226.85/39.06  | | | | | |   (122)  op(e3, e1) = all_52_5
% 226.85/39.06  | | | | | |   (123)  op(all_52_5, all_52_5) = e1
% 226.85/39.06  | | | | | | 
% 226.85/39.06  | | | | | | BETA: splitting (27) gives:
% 226.85/39.06  | | | | | | 
% 226.85/39.06  | | | | | | Case 1:
% 226.85/39.06  | | | | | | | 
% 226.85/39.06  | | | | | | |   (124)  all_55_0 = e3
% 226.85/39.06  | | | | | | | 
% 226.85/39.06  | | | | | | | COMBINE_EQS: (18), (124) imply:
% 226.85/39.06  | | | | | | |   (125)  all_10_2 = e3
% 226.85/39.06  | | | | | | | 
% 226.85/39.06  | | | | | | | REDUCE: (115), (125) imply:
% 226.85/39.06  | | | | | | |   (126)  $false
% 226.85/39.06  | | | | | | | 
% 226.85/39.06  | | | | | | | CLOSE: (126) is inconsistent.
% 226.85/39.06  | | | | | | | 
% 226.85/39.06  | | | | | | Case 2:
% 226.85/39.06  | | | | | | | 
% 226.85/39.06  | | | | | | |   (127)   ~ (all_55_0 = e3)
% 226.85/39.06  | | | | | | |   (128)  all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 226.85/39.06  | | | | | | | 
% 226.85/39.06  | | | | | | | BETA: splitting (128) gives:
% 226.85/39.06  | | | | | | | 
% 226.85/39.06  | | | | | | | Case 1:
% 226.85/39.06  | | | | | | | | 
% 226.85/39.06  | | | | | | | |   (129)  all_55_0 = e2
% 226.85/39.06  | | | | | | | | 
% 226.85/39.06  | | | | | | | | COMBINE_EQS: (18), (129) imply:
% 226.85/39.06  | | | | | | | |   (130)  all_10_2 = e2
% 226.85/39.06  | | | | | | | | 
% 226.85/39.06  | | | | | | | | REDUCE: (39), (130) imply:
% 226.85/39.06  | | | | | | | |   (131)   ~ (all_53_4 = e2)
% 226.85/39.06  | | | | | | | | 
% 226.85/39.06  | | | | | | | | REDUCE: (79), (130) imply:
% 226.85/39.06  | | | | | | | |   (132)   ~ (all_53_12 = e2)
% 226.85/39.06  | | | | | | | | 
% 226.85/39.06  | | | | | | | | REDUCE: (115), (130) imply:
% 226.85/39.06  | | | | | | | |   (133)   ~ (e3 = e2)
% 226.85/39.06  | | | | | | | | 
% 226.85/39.06  | | | | | | | | GROUND_INST: instantiating (17) with e3, all_52_5, e1, e3,
% 226.85/39.06  | | | | | | | |              simplifying with (8), (122) gives:
% 226.85/39.06  | | | | | | | |   (134)  all_52_5 = e3
% 226.85/39.06  | | | | | | | | 
% 226.85/39.06  | | | | | | | | REDUCE: (123), (134) imply:
% 226.85/39.06  | | | | | | | |   (135)  op(e3, e3) = e1
% 226.85/39.06  | | | | | | | | 
% 226.85/39.06  | | | | | | | | REF_CLOSE: (17), (32), (37), (38), (49), (82), (96), (131),
% 226.85/39.06  | | | | | | | |            (132), (135) are inconsistent by sub-proof #234.
% 226.85/39.06  | | | | | | | | 
% 226.85/39.06  | | | | | | | Case 2:
% 226.85/39.06  | | | | | | | | 
% 226.85/39.06  | | | | | | | |   (136)  all_55_0 = e1 | all_55_0 = e0
% 226.85/39.06  | | | | | | | | 
% 226.85/39.06  | | | | | | | | REF_CLOSE: (18), (63), (119), (136) are inconsistent by
% 226.85/39.06  | | | | | | | |            sub-proof #1954.
% 226.85/39.06  | | | | | | | | 
% 226.85/39.06  | | | | | | | End of split
% 226.85/39.06  | | | | | | | 
% 226.85/39.06  | | | | | | End of split
% 226.85/39.06  | | | | | | 
% 226.85/39.06  | | | | | Case 2:
% 226.85/39.06  | | | | | | 
% 226.85/39.06  | | | | | |   (137)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14
% 226.85/39.06  | | | | | |          = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 226.85/39.06  | | | | | |            all_52_11) = e2 & op(all_52_13, all_52_13) = e1 &
% 226.85/39.06  | | | | | |          op(all_52_15, all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 226.85/39.06  | | | | | |          op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13 & op(e2,
% 226.85/39.06  | | | | | |            e0) = all_52_15 & $i(all_52_9) & $i(all_52_11) &
% 226.85/39.06  | | | | | |          $i(all_52_13) & $i(all_52_15)
% 226.85/39.06  | | | | | | 
% 226.85/39.06  | | | | | | ALPHA: (137) implies:
% 226.85/39.06  | | | | | |   (138)  op(e2, e0) = all_52_15
% 226.85/39.06  | | | | | |   (139)  op(e2, e2) = all_52_11
% 226.85/39.06  | | | | | |   (140)  op(e2, e3) = all_52_9
% 226.85/39.06  | | | | | |   (141)  op(all_52_15, all_52_15) = e0
% 226.85/39.06  | | | | | |   (142)  op(all_52_11, all_52_11) = e2
% 226.85/39.06  | | | | | |   (143)  op(all_52_9, all_52_9) = e3
% 226.85/39.06  | | | | | | 
% 226.85/39.06  | | | | | | BETA: splitting (27) gives:
% 226.85/39.07  | | | | | | 
% 226.85/39.07  | | | | | | Case 1:
% 226.85/39.07  | | | | | | | 
% 226.85/39.07  | | | | | | |   (144)  all_55_0 = e3
% 226.85/39.07  | | | | | | | 
% 226.85/39.07  | | | | | | | COMBINE_EQS: (18), (144) imply:
% 226.85/39.07  | | | | | | |   (145)  all_10_2 = e3
% 226.85/39.07  | | | | | | | 
% 226.85/39.07  | | | | | | | REDUCE: (115), (145) imply:
% 226.85/39.07  | | | | | | |   (146)  $false
% 226.85/39.07  | | | | | | | 
% 226.85/39.07  | | | | | | | CLOSE: (146) is inconsistent.
% 226.85/39.07  | | | | | | | 
% 226.85/39.07  | | | | | | Case 2:
% 226.85/39.07  | | | | | | | 
% 226.85/39.07  | | | | | | |   (147)   ~ (all_55_0 = e3)
% 226.85/39.07  | | | | | | |   (148)  all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 226.85/39.07  | | | | | | | 
% 226.85/39.07  | | | | | | | BETA: splitting (148) gives:
% 226.85/39.07  | | | | | | | 
% 226.85/39.07  | | | | | | | Case 1:
% 226.85/39.07  | | | | | | | | 
% 226.85/39.07  | | | | | | | |   (149)  all_55_0 = e2
% 226.85/39.07  | | | | | | | | 
% 226.85/39.07  | | | | | | | | COMBINE_EQS: (18), (149) imply:
% 226.85/39.07  | | | | | | | |   (150)  all_10_2 = e2
% 226.85/39.07  | | | | | | | | 
% 226.85/39.07  | | | | | | | | REDUCE: (6), (150) imply:
% 226.85/39.07  | | | | | | | |   (151)   ~ (all_53_1 = e2)
% 226.85/39.07  | | | | | | | | 
% 226.85/39.07  | | | | | | | | REDUCE: (5), (150) imply:
% 226.85/39.07  | | | | | | | |   (152)   ~ (all_53_3 = e2)
% 226.85/39.07  | | | | | | | | 
% 226.85/39.07  | | | | | | | | REDUCE: (39), (150) imply:
% 226.85/39.07  | | | | | | | |   (153)   ~ (all_53_4 = e2)
% 226.85/39.07  | | | | | | | | 
% 226.85/39.07  | | | | | | | | REDUCE: (79), (150) imply:
% 226.85/39.07  | | | | | | | |   (154)   ~ (all_53_12 = e2)
% 226.85/39.07  | | | | | | | | 
% 226.85/39.07  | | | | | | | | REDUCE: (115), (150) imply:
% 226.85/39.07  | | | | | | | |   (155)   ~ (e3 = e2)
% 226.85/39.07  | | | | | | | | 
% 226.85/39.07  | | | | | | | | REDUCE: (1), (150) imply:
% 226.85/39.07  | | | | | | | |   (156)  op(e3, e3) = e2
% 226.85/39.07  | | | | | | | | 
% 226.85/39.07  | | | | | | | | BETA: splitting (32) gives:
% 226.85/39.07  | | | | | | | | 
% 226.85/39.07  | | | | | | | | Case 1:
% 226.85/39.07  | | | | | | | | | 
% 226.85/39.07  | | | | | | | | |   (157)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 &
% 226.85/39.07  | | | | | | | | |            op(e3, e2) = e2)
% 226.85/39.07  | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | BETA: splitting (157) gives:
% 226.85/39.07  | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | Case 1:
% 226.85/39.07  | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | |   (158)  all_57_0 = e2 & op(e3, e3) = e2
% 226.85/39.07  | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | ALPHA: (158) implies:
% 226.85/39.07  | | | | | | | | | |   (159)  all_57_0 = e2
% 226.85/39.07  | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | GROUND_INST: instantiating (17) with all_53_13, all_52_15, e0,
% 226.85/39.07  | | | | | | | | | |              e2, simplifying with (71), (138) gives:
% 226.85/39.07  | | | | | | | | | |   (160)  all_53_13 = all_52_15
% 226.85/39.07  | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | GROUND_INST: instantiating (17) with e3, all_52_11, e2, e2,
% 226.85/39.07  | | | | | | | | | |              simplifying with (77), (139) gives:
% 226.85/39.07  | | | | | | | | | |   (161)  all_52_11 = e3
% 226.85/39.07  | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | GROUND_INST: instantiating (17) with all_53_1, all_52_9, e3,
% 226.85/39.07  | | | | | | | | | |              e2, simplifying with (10), (140) gives:
% 226.85/39.07  | | | | | | | | | |   (162)  all_53_1 = all_52_9
% 226.85/39.07  | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | REDUCE: (31), (160) imply:
% 226.85/39.07  | | | | | | | | | |   (163)   ~ (all_52_15 = e3)
% 226.85/39.07  | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | BETA: splitting (92) gives:
% 226.85/39.07  | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | Case 1:
% 226.85/39.07  | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | |   (164)   ~ (all_22_2 = e3)
% 226.85/39.07  | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | REDUCE: (19), (164) imply:
% 226.85/39.07  | | | | | | | | | | |   (165)  $false
% 226.85/39.07  | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | CLOSE: (165) is inconsistent.
% 226.85/39.07  | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | Case 2:
% 226.85/39.07  | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | |   (166)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0
% 226.85/39.07  | | | | | | | | | | |            & op(e0, e3) = all_22_1 & $i(all_22_0) &
% 226.85/39.07  | | | | | | | | | | |            $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0, e3)
% 226.85/39.07  | | | | | | | | | | |            = all_22_1 & $i(all_22_1))
% 226.85/39.07  | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | BETA: splitting (21) gives:
% 226.85/39.07  | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | Case 1:
% 226.85/39.07  | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | |   (167)   ~ (all_24_2 = e0)
% 226.85/39.07  | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | REDUCE: (87), (167) imply:
% 226.85/39.07  | | | | | | | | | | | |   (168)   ~ (all_6_2 = e0)
% 226.85/39.07  | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | BETA: splitting (58) gives:
% 226.85/39.07  | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | Case 1:
% 226.85/39.07  | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | |   (169)   ~ (all_38_2 = e2)
% 226.85/39.07  | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | REDUCE: (73), (169) imply:
% 226.85/39.07  | | | | | | | | | | | | |   (170)   ~ (all_6_2 = e2)
% 226.85/39.07  | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | BETA: splitting (7) gives:
% 226.85/39.07  | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | Case 1:
% 226.85/39.07  | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | |   (171)  all_55_10 = e3
% 226.85/39.07  | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | REF_CLOSE: (69), (117), (171) are inconsistent by sub-proof
% 226.85/39.07  | | | | | | | | | | | | | |            #2500.
% 226.85/39.07  | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | Case 2:
% 226.85/39.07  | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | |   (172)   ~ (all_55_10 = e3)
% 226.85/39.07  | | | | | | | | | | | | | |   (173)  all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 226.85/39.07  | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | BETA: splitting (173) gives:
% 226.85/39.07  | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | Case 1:
% 226.85/39.07  | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | |   (174)  all_55_10 = e2
% 226.85/39.07  | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | REF_CLOSE: (69), (170), (174) are inconsistent by sub-proof
% 226.85/39.07  | | | | | | | | | | | | | | |            #2499.
% 226.85/39.07  | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | Case 2:
% 226.85/39.07  | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | |   (175)   ~ (all_55_10 = e2)
% 226.85/39.07  | | | | | | | | | | | | | | |   (176)  all_55_10 = e1 | all_55_10 = e0
% 226.85/39.07  | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | BETA: splitting (176) gives:
% 226.85/39.07  | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | Case 1:
% 226.85/39.07  | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | |   (177)  all_55_10 = e1
% 226.85/39.07  | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | COMBINE_EQS: (69), (177) imply:
% 226.85/39.07  | | | | | | | | | | | | | | | |   (178)  all_6_2 = e1
% 226.85/39.07  | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | SIMP: (178) implies:
% 226.85/39.07  | | | | | | | | | | | | | | | |   (179)  all_6_2 = e1
% 226.85/39.07  | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | REDUCE: (29), (179) imply:
% 226.85/39.07  | | | | | | | | | | | | | | | |   (180)   ~ (all_53_11 = e1)
% 226.85/39.07  | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | REDUCE: (35), (179) imply:
% 226.85/39.07  | | | | | | | | | | | | | | | |   (181)   ~ (all_53_14 = e1)
% 226.85/39.07  | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | REDUCE: (117), (179) imply:
% 226.85/39.07  | | | | | | | | | | | | | | | |   (182)   ~ (e3 = e1)
% 226.85/39.07  | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | REDUCE: (170), (179) imply:
% 226.85/39.07  | | | | | | | | | | | | | | | |   (183)   ~ (e2 = e1)
% 226.85/39.07  | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | REDUCE: (25), (179) imply:
% 226.85/39.07  | | | | | | | | | | | | | | | |   (184)  op(e1, e1) = e1
% 226.85/39.07  | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | BETA: splitting (83) gives:
% 226.85/39.07  | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | Case 1:
% 226.85/39.07  | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | |   (185)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 226.85/39.07  | | | | | | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 226.85/39.07  | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 226.85/39.07  | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | Case 1:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | |   (186)  all_57_9 = e2 & op(e3, e0) = e2
% 226.85/39.07  | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | ALPHA: (186) implies:
% 226.85/39.07  | | | | | | | | | | | | | | | | | |   (187)  op(e3, e0) = e2
% 226.85/39.07  | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (96), (154), (187) are inconsistent by
% 226.85/39.07  | | | | | | | | | | | | | | | | | |            sub-proof #2331.
% 226.85/39.07  | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | Case 2:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | |   (188)  all_57_10 = e2 & op(e2, e0) = e2
% 226.85/39.07  | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | ALPHA: (188) implies:
% 226.85/39.07  | | | | | | | | | | | | | | | | | |   (189)  all_57_10 = e2
% 226.85/39.07  | | | | | | | | | | | | | | | | | |   (190)  op(e2, e0) = e2
% 226.85/39.07  | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | BETA: splitting (90) gives:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | Case 1:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | |   (191)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 226.85/39.07  | | | | | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | Case 1:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | |   (192)  all_57_9 = e1 & op(e3, e0) = e1
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | ALPHA: (192) implies:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | |   (193)  all_57_9 = e1
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | BETA: splitting (34) gives:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | Case 1:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | |   (194)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e0)
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | |   (195)  all_57_0 = e0 & op(e3, e3) = e0
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (195) implies:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | |   (196)  op(e3, e3) = e0
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (52), (156), (196) are inconsistent by
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2403.
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | |   (197)  all_57_1 = e0 & op(e3, e2) = e0
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (197) implies:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | |   (198)  all_57_1 = e0
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9) gives:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | |   (199)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | |   (200)  all_57_2 = e1 & op(e2, e3) = e1
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (200) implies:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | |   (201)  all_57_2 = e1
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (89) gives:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | |   (202)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e0)
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | |   (203)  all_57_0 = e0 & op(e3, e3) = e0
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (203) implies:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | |   (204)  op(e3, e3) = e0
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (32), (37), (38), (52), (82), (193), (198),
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | |            (204) are inconsistent by sub-proof #2402.
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | |   (205)  all_57_2 = e0 & op(e2, e3) = e0
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (205) implies:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | |   (206)  all_57_2 = e0
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (57), (201), (206) are inconsistent by sub-proof
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | |            #2473.
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | |   (207)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e3) = e0)
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | |   (208)  all_57_6 = e0 & op(e1, e3) = e0
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (208) implies:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | |   (209)  all_57_6 = e0
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (60), (209) imply:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | |   (210)  e3 = e0
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (210) implies:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | |   (211)  e3 = e0
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (26), (211) imply:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | |   (212)  all_57_3 = e0
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11), (13), (15), (17), (20), (25), (38),
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | |            (41), (46), (52), (57), (61), (67), (68), (72),
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | |            (76), (78), (82), (83), (86), (89), (90), (94),
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | |            (102), (103), (117), (156), (159), (198), (209),
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | |            (212) are inconsistent by sub-proof #690.
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | |   (213)  all_57_12 = e0 & op(e0, e3) = e0
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (213) implies:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | |   (214)  all_57_12 = e0
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (94) gives:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (215)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (216)  all_57_1 = e1 & op(e3, e2) = e1
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (57), (198), (216) are inconsistent by sub-proof
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2446.
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (217)  all_57_3 = e1 & op(e2, e2) = e1
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (217) implies:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (218)  op(e2, e2) = e1
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (17), (38), (41), (52), (57), (68), (72),
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (76), (81), (82), (83), (90), (102), (103), (201),
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (218) are inconsistent by sub-proof #814.
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (219)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (220)  all_57_7 = e1 & op(e1, e2) = e1
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (220) implies:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (221)  all_57_7 = e1
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (20), (25), (38), (41), (52),
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (57), (68), (82), (83), (90), (95), (102), (117),
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (184), (221) are inconsistent by sub-proof #1069.
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (222)  all_57_13 = e1 & op(e0, e2) = e1
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (222) implies:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (223)  all_57_13 = e1
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13) gives:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (224)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (17), (28), (34), (38), (41), (52), (55),
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (57), (74), (77), (82), (96), (156), (224) are
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #205.
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (225)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (226)  all_57_7 = e2 & op(e1, e2) = e2
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (226) implies:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (227)  all_57_7 = e2
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (228)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (229)  all_57_12 = e2 & op(e0, e3) = e2
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (229) implies:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (230)  op(e0, e3) = e2
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (45), (152), (230) are inconsistent by
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1980.
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (231)  all_57_13 = e2 & op(e0, e2) = e2
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (231) implies:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (232)  all_57_13 = e2
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (223), (232) imply:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (233)  e2 = e1
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (227), (233) imply:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (234)  all_57_7 = e1
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (20), (25), (38), (41), (52),
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (57), (68), (82), (83), (90), (95), (102), (117),
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (184), (234) are inconsistent by sub-proof #1069.
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (235)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (236)  all_57_14 = e2 & op(e0, e1) = e2
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (236) implies:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (237)  all_57_14 = e2
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (81) gives:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (238)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e0)
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (239)  all_57_2 = e0 & op(e2, e3) = e0
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (239) implies:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (240)  all_57_2 = e0
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (201), (240) imply:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (241)  e1 = e0
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (193), (241) imply:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (242)  all_57_9 = e0
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (20), (25), (38), (41), (52),
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (57), (68), (82), (83), (90), (102), (117), (184),
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (227), (242) are inconsistent by sub-proof #959.
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (243)  all_57_3 = e0 & op(e2, e2) = e0
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (243) implies:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (244)  all_57_3 = e0
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (15), (38), (41), (46), (52), (57), (61),
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (82), (94), (102), (198), (214), (237), (244) are
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #484.
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (245)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e2, e0) = e0)
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (246)  all_57_5 = e0 & op(e2, e1) = e0
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (246) implies:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (247)  all_57_5 = e0
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (36) gives:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (248)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e0)
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (248) gives:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (249)  all_57_4 = e0 & op(e3, e1) = e0
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (249) implies:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (250)  all_57_4 = e0
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (37), (250) imply:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (251)  e3 = e0
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (26), (251) imply:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (252)  all_57_3 = e0
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (15), (38), (41), (57), (72), (82), (189),
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (247), (252) are inconsistent by sub-proof #2355.
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (103), (138), (139), (141), (142), (163),
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (190) are inconsistent by sub-proof #204.
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (253)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (253) gives:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (254)  all_57_8 = e0 & op(e1, e1) = e0
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (254) implies:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (255)  op(e1, e1) = e0
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (17), (37), (42), (57), (82), (237), (247),
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (255) are inconsistent by sub-proof #215.
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (256)  all_57_14 = e0 & op(e0, e1) = e0
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (256) implies:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (257)  all_57_14 = e0
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (237), (257) imply:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (258)  e2 = e0
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (258) implies:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (259)  e2 = e0
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (159), (259) imply:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (260)  all_57_0 = e0
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (15), (38), (52), (57), (60), (82), (86),
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (214), (260) are inconsistent by sub-proof #1425.
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (261)  all_57_10 = e0 & op(e2, e0) = e0
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (261) implies:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (262)  all_57_10 = e0
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (189), (262) imply:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (263)  e2 = e0
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (159), (263) imply:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (264)  all_57_0 = e0
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (15), (38), (52), (57), (60), (82), (86),
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (214), (264) are inconsistent by sub-proof #1425.
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (265)  all_57_15 = e2 & op(e0, e0) = e2
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (265) implies:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (266)  op(e0, e0) = e2
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (17), (44), (266) are inconsistent by
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2334.
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (267)  all_57_13 = e2 & op(e0, e2) = e2
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (82), (223), (267) are inconsistent by sub-proof
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2101.
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | |   (268)  all_57_3 = e1 & op(e2, e2) = e1
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (268) implies:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | |   (269)  op(e2, e2) = e1
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (17), (77), (269) are inconsistent by
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1912.
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | |   (270)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (270) gives:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | |   (271)  all_57_5 = e1 & op(e2, e1) = e1
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (271) implies:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | |   (272)  all_57_5 = e1
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (17), (25), (36), (38), (41), (46), (52),
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | |            (57), (59), (67), (68), (82), (88), (102), (117),
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | |            (184), (272) are inconsistent by sub-proof #941.
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | |   (273)  all_57_10 = e1 & op(e2, e0) = e1
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (82), (189), (273) are inconsistent by sub-proof
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | |            #2360.
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | End of split
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | End of split
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | Case 2:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | |   (274)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e0)
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (274) gives:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | |   (275)  all_57_4 = e0 & op(e3, e1) = e0
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (275) implies:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | |   (276)  all_57_4 = e0
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (37), (41), (276) are inconsistent by sub-proof
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | |            #2372.
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | |   (277)  all_57_9 = e0 & op(e3, e0) = e0
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (277) implies:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | |   (278)  all_57_9 = e0
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (57), (193), (278) are inconsistent by sub-proof
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | |            #2479.
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | End of split
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | End of split
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | Case 2:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | |   (279)  all_57_10 = e1 & op(e2, e0) = e1
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | ALPHA: (279) implies:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | |   (280)  all_57_10 = e1
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (82), (189), (280) are inconsistent by sub-proof
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | |            #2144.
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | End of split
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | Case 2:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | |   (281)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 226.85/39.07  | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | BETA: splitting (281) gives:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | Case 1:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | |   (282)  all_57_11 = e1 & op(e1, e0) = e1
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (40), (181), (282) are inconsistent by
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | |            sub-proof #305.
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | Case 2:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | |   (283)  all_57_15 = e1 & op(e0, e0) = e1
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | ALPHA: (283) implies:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | |   (284)  op(e0, e0) = e1
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (17), (103), (284) are inconsistent by
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | |            sub-proof #2183.
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | End of split
% 226.85/39.07  | | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | | End of split
% 226.85/39.07  | | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | End of split
% 226.85/39.07  | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | Case 2:
% 226.85/39.07  | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | |   (285)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 226.85/39.07  | | | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 226.85/39.07  | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | BETA: splitting (285) gives:
% 226.85/39.07  | | | | | | | | | | | | | | | | | 
% 226.85/39.07  | | | | | | | | | | | | | | | | | Case 1:
% 226.85/39.07  | | | | | | | | | | | | | | | | | | 
% 227.06/39.07  | | | | | | | | | | | | | | | | | |   (286)  all_57_11 = e2 & op(e1, e0) = e2
% 227.06/39.07  | | | | | | | | | | | | | | | | | | 
% 227.06/39.07  | | | | | | | | | | | | | | | | | | ALPHA: (286) implies:
% 227.06/39.07  | | | | | | | | | | | | | | | | | |   (287)  all_57_11 = e2
% 227.06/39.07  | | | | | | | | | | | | | | | | | |   (288)  op(e1, e0) = e2
% 227.06/39.07  | | | | | | | | | | | | | | | | | | 
% 227.06/39.07  | | | | | | | | | | | | | | | | | | BETA: splitting (16) gives:
% 227.06/39.07  | | | | | | | | | | | | | | | | | | 
% 227.06/39.07  | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.07  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.07  | | | | | | | | | | | | | | | | | | |   (289)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 227.06/39.07  | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e0)
% 227.06/39.07  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.07  | | | | | | | | | | | | | | | | | | | BETA: splitting (289) gives:
% 227.06/39.07  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.07  | | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.07  | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.07  | | | | | | | | | | | | | | | | | | | |   (290)  all_57_6 = e0 & op(e1, e3) = e0
% 227.06/39.07  | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.07  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (60), (290) are inconsistent by sub-proof
% 227.06/39.07  | | | | | | | | | | | | | | | | | | | |            #2465.
% 227.06/39.07  | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.07  | | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.07  | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.07  | | | | | | | | | | | | | | | | | | | |   (291)  all_57_7 = e0 & op(e1, e2) = e0
% 227.06/39.07  | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.07  | | | | | | | | | | | | | | | | | | | | ALPHA: (291) implies:
% 227.06/39.07  | | | | | | | | | | | | | | | | | | | |   (292)  all_57_7 = e0
% 227.06/39.07  | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.07  | | | | | | | | | | | | | | | | | | | | BETA: splitting (13) gives:
% 227.06/39.07  | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.07  | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.07  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.07  | | | | | | | | | | | | | | | | | | | | |   (293)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 227.06/39.07  | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 227.06/39.07  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.07  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (17), (28), (34), (38), (41), (52), (55),
% 227.06/39.07  | | | | | | | | | | | | | | | | | | | | |            (57), (74), (77), (82), (96), (156), (293) are
% 227.06/39.07  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #205.
% 227.06/39.07  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.07  | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.07  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.07  | | | | | | | | | | | | | | | | | | | | |   (294)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 227.06/39.07  | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 227.06/39.07  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.07  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (294) gives:
% 227.06/39.07  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.07  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.07  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.07  | | | | | | | | | | | | | | | | | | | | | |   (295)  all_57_7 = e2 & op(e1, e2) = e2
% 227.06/39.07  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.07  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (52), (292), (295) are inconsistent by sub-proof
% 227.06/39.07  | | | | | | | | | | | | | | | | | | | | | |            #364.
% 227.06/39.07  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.07  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.07  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.07  | | | | | | | | | | | | | | | | | | | | | |   (296)  all_57_13 = e2 & op(e0, e2) = e2
% 227.06/39.07  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.07  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (296) implies:
% 227.06/39.07  | | | | | | | | | | | | | | | | | | | | | |   (297)  all_57_13 = e2
% 227.06/39.07  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.07  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (46) gives:
% 227.06/39.07  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.07  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.07  | | | | | | | | | | | | | | | | | | | | | | |   (298)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 227.06/39.07  | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 227.06/39.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.07  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (298) gives:
% 227.06/39.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.07  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.07  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.07  | | | | | | | | | | | | | | | | | | | | | | | |   (299)  all_57_12 = e1 & op(e0, e3) = e1
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (299) implies:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | |   (300)  op(e0, e3) = e1
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (54), (166), (288), (300) are inconsistent
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1147.
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | |   (301)  all_57_13 = e1 & op(e0, e2) = e1
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (301) implies:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | |   (302)  all_57_13 = e1
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (297), (302) imply:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | |   (303)  e2 = e1
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (287), (303) imply:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | |   (304)  all_57_11 = e1
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (17), (20), (25), (38), (41), (52), (82),
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | |            (95), (117), (184), (292), (304) are inconsistent
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1931.
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | |   (305)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (305) gives:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | |   (306)  all_57_14 = e1 & op(e0, e1) = e1
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (17), (180), (306) are inconsistent by
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #225.
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | |   (307)  all_57_15 = e1 & op(e0, e0) = e1
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (307) implies:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | |   (308)  op(e0, e0) = e1
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (17), (103), (308) are inconsistent by
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2183.
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | |   (309)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 227.06/39.08  | | | | | | | | | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (52), (57), (184), (287), (309) are
% 227.06/39.08  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1108.
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.08  | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | |   (310)  all_57_15 = e2 & op(e0, e0) = e2
% 227.06/39.08  | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | ALPHA: (310) implies:
% 227.06/39.08  | | | | | | | | | | | | | | | | | |   (311)  op(e0, e0) = e2
% 227.06/39.08  | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (17), (44), (311) are inconsistent by
% 227.06/39.08  | | | | | | | | | | | | | | | | | |            sub-proof #2334.
% 227.06/39.08  | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | End of split
% 227.06/39.08  | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | End of split
% 227.06/39.08  | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | Case 2:
% 227.06/39.08  | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | |   (312)  all_55_10 = e0
% 227.06/39.08  | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | REF_CLOSE: (69), (168), (312) are inconsistent by sub-proof
% 227.06/39.08  | | | | | | | | | | | | | | | |            #2118.
% 227.06/39.08  | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | End of split
% 227.06/39.08  | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | End of split
% 227.06/39.08  | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | End of split
% 227.06/39.08  | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | Case 2:
% 227.06/39.08  | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | |   (313)  all_38_2 = e2
% 227.06/39.08  | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | COMBINE_EQS: (73), (313) imply:
% 227.06/39.08  | | | | | | | | | | | | |   (314)  all_6_2 = e2
% 227.06/39.08  | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | REDUCE: (25), (314) imply:
% 227.06/39.08  | | | | | | | | | | | | |   (315)  op(e1, e1) = e2
% 227.06/39.08  | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | BETA: splitting (83) gives:
% 227.06/39.08  | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | Case 1:
% 227.06/39.08  | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | |   (316)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 227.06/39.08  | | | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 227.06/39.08  | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | BETA: splitting (316) gives:
% 227.06/39.08  | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | Case 1:
% 227.06/39.08  | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | |   (317)  all_57_9 = e2 & op(e3, e0) = e2
% 227.06/39.08  | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | ALPHA: (317) implies:
% 227.06/39.08  | | | | | | | | | | | | | | |   (318)  op(e3, e0) = e2
% 227.06/39.08  | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | REF_CLOSE: (17), (96), (154), (318) are inconsistent by
% 227.06/39.08  | | | | | | | | | | | | | | |            sub-proof #2331.
% 227.06/39.08  | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | Case 2:
% 227.06/39.08  | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | |   (319)  all_57_10 = e2 & op(e2, e0) = e2
% 227.06/39.08  | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | ALPHA: (319) implies:
% 227.06/39.08  | | | | | | | | | | | | | | |   (320)  all_57_10 = e2
% 227.06/39.08  | | | | | | | | | | | | | | |   (321)  op(e2, e0) = e2
% 227.06/39.08  | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 227.06/39.08  | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | Case 1:
% 227.06/39.08  | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | |   (322)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 227.06/39.08  | | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 227.06/39.08  | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | BETA: splitting (322) gives:
% 227.06/39.08  | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.08  | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | |   (323)  all_57_12 = e2 & op(e0, e3) = e2
% 227.06/39.08  | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | ALPHA: (323) implies:
% 227.06/39.08  | | | | | | | | | | | | | | | | |   (324)  op(e0, e3) = e2
% 227.06/39.08  | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (45), (152), (324) are inconsistent by
% 227.06/39.08  | | | | | | | | | | | | | | | | |            sub-proof #1980.
% 227.06/39.08  | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.08  | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | |   (325)  all_57_13 = e2 & op(e0, e2) = e2
% 227.06/39.08  | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (15), (16), (17), (20), (25), (38), (41),
% 227.06/39.08  | | | | | | | | | | | | | | | | |            (46), (51), (52), (57), (60), (61), (67), (68),
% 227.06/39.08  | | | | | | | | | | | | | | | | |            (82), (83), (90), (91), (94), (95), (102), (103),
% 227.06/39.08  | | | | | | | | | | | | | | | | |            (117), (138), (139), (141), (142), (163), (168),
% 227.06/39.08  | | | | | | | | | | | | | | | | |            (315), (320), (321), (325) are inconsistent by
% 227.06/39.08  | | | | | | | | | | | | | | | | |            sub-proof #202.
% 227.06/39.08  | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | End of split
% 227.06/39.08  | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | Case 2:
% 227.06/39.08  | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | |   (326)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 227.06/39.08  | | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 227.06/39.08  | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | BETA: splitting (326) gives:
% 227.06/39.08  | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.08  | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | |   (327)  all_57_14 = e2 & op(e0, e1) = e2
% 227.06/39.08  | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | ALPHA: (327) implies:
% 227.06/39.08  | | | | | | | | | | | | | | | | |   (328)  all_57_14 = e2
% 227.06/39.08  | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | BETA: splitting (36) gives:
% 227.06/39.08  | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | |   (329)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 227.06/39.08  | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e0)
% 227.06/39.08  | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | BETA: splitting (329) gives:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | |   (330)  all_57_4 = e0 & op(e3, e1) = e0
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | ALPHA: (330) implies:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | |   (331)  all_57_4 = e0
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (37), (41), (331) are inconsistent by sub-proof
% 227.06/39.08  | | | | | | | | | | | | | | | | | | |            #2372.
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | |   (332)  all_57_5 = e0 & op(e2, e1) = e0
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | ALPHA: (332) implies:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | |   (333)  all_57_5 = e0
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | BETA: splitting (13) gives:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | |   (334)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | BETA: splitting (334) gives:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | |   (335)  all_57_1 = e2 & op(e3, e2) = e2
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | ALPHA: (335) implies:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | |   (336)  all_57_1 = e2
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (17), (28), (34), (38), (41), (52), (55),
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | |            (57), (74), (82), (96), (156), (336) are
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1650.
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | |   (337)  all_57_3 = e2 & op(e2, e2) = e2
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | ALPHA: (337) implies:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | |   (338)  op(e2, e2) = e2
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (17), (31), (38), (41), (71), (72), (106),
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | |            (333), (338) are inconsistent by sub-proof #2129.
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | |   (339)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | BETA: splitting (339) gives:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | |   (340)  all_57_7 = e2 & op(e1, e2) = e2
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | ALPHA: (340) implies:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | |   (341)  all_57_7 = e2
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16) gives:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | |   (342)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e0)
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (342) gives:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | |   (343)  all_57_6 = e0 & op(e1, e3) = e0
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (343) implies:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | |   (344)  all_57_6 = e0
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (17), (20), (25), (38), (41), (52), (57),
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | |            (68), (82), (83), (90), (102), (117), (341), (344)
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1775.
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | |   (345)  all_57_7 = e0 & op(e1, e2) = e0
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (345) implies:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | |   (346)  all_57_7 = e0
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (52), (341), (346) are inconsistent by sub-proof
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | |            #2207.
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | |   (347)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (347) gives:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | |   (348)  all_57_8 = e0 & op(e1, e1) = e0
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (348) implies:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | |   (349)  op(e1, e1) = e0
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (17), (37), (42), (57), (82), (328), (333),
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | |            (349) are inconsistent by sub-proof #215.
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | |   (350)  all_57_11 = e0 & op(e1, e0) = e0
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (350) implies:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | |   (351)  all_57_11 = e0
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (91) gives:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | |   (352)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e1)
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (352) gives:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | | |   (353)  all_57_6 = e1 & op(e1, e3) = e1
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (353) implies:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | | |   (354)  all_57_6 = e1
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (17), (20), (25), (38), (41), (52), (57),
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | | |            (68), (82), (83), (90), (102), (103), (117),
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | | |            (341), (354) are inconsistent by sub-proof #1078.
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | | |   (355)  all_57_7 = e1 & op(e1, e2) = e1
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (355) implies:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | | |   (356)  all_57_7 = e1
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (82), (341), (356) are inconsistent by sub-proof
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | | |            #1761.
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | |   (357)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e1, e0) = e1)
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (57), (82), (315), (351), (357) are
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1861.
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | |   (358)  all_57_13 = e2 & op(e0, e2) = e2
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (15), (16), (17), (20), (25), (38), (41),
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | |            (46), (51), (52), (57), (60), (61), (67), (68),
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | |            (82), (83), (90), (91), (94), (95), (102), (103),
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | |            (117), (138), (139), (141), (142), (163), (168),
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | |            (315), (320), (321), (358) are inconsistent by
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | |            sub-proof #202.
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.08  | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | |   (359)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 227.06/39.08  | | | | | | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 227.06/39.08  | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (25), (52), (168), (328), (359) are
% 227.06/39.08  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2411.
% 227.06/39.08  | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | End of split
% 227.06/39.08  | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.08  | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | |   (360)  all_57_15 = e2 & op(e0, e0) = e2
% 227.06/39.08  | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | ALPHA: (360) implies:
% 227.06/39.08  | | | | | | | | | | | | | | | | |   (361)  op(e0, e0) = e2
% 227.06/39.08  | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (17), (44), (361) are inconsistent by
% 227.06/39.08  | | | | | | | | | | | | | | | | |            sub-proof #2334.
% 227.06/39.08  | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | End of split
% 227.06/39.08  | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | End of split
% 227.06/39.08  | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | End of split
% 227.06/39.08  | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | Case 2:
% 227.06/39.08  | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | |   (362)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 227.06/39.08  | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 227.06/39.08  | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | REF_CLOSE: (3), (15), (16), (17), (20), (25), (38), (41),
% 227.06/39.08  | | | | | | | | | | | | | |            (44), (52), (57), (60), (82), (91), (117), (168),
% 227.06/39.08  | | | | | | | | | | | | | |            (315), (362) are inconsistent by sub-proof #201.
% 227.06/39.08  | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | End of split
% 227.06/39.08  | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | End of split
% 227.06/39.08  | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | Case 2:
% 227.06/39.08  | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | |   (363)  all_24_2 = e0
% 227.06/39.08  | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | COMBINE_EQS: (87), (363) imply:
% 227.06/39.08  | | | | | | | | | | | |   (364)  all_6_2 = e0
% 227.06/39.08  | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | SIMP: (364) implies:
% 227.06/39.08  | | | | | | | | | | | |   (365)  all_6_2 = e0
% 227.06/39.08  | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | REDUCE: (70), (365) imply:
% 227.06/39.08  | | | | | | | | | | | |   (366)   ~ (all_53_6 = e0)
% 227.06/39.08  | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | REDUCE: (35), (365) imply:
% 227.06/39.08  | | | | | | | | | | | |   (367)   ~ (all_53_14 = e0)
% 227.06/39.08  | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | REDUCE: (117), (365) imply:
% 227.06/39.08  | | | | | | | | | | | |   (368)   ~ (e3 = e0)
% 227.06/39.08  | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | BETA: splitting (16) gives:
% 227.06/39.08  | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | Case 1:
% 227.06/39.08  | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | |   (369)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 227.06/39.08  | | | | | | | | | | | | |            & op(e1, e2) = e0)
% 227.06/39.08  | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | BETA: splitting (369) gives:
% 227.06/39.08  | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | Case 1:
% 227.06/39.08  | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | |   (370)  all_57_6 = e0 & op(e1, e3) = e0
% 227.06/39.08  | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | REF_CLOSE: (41), (60), (370) are inconsistent by sub-proof
% 227.06/39.08  | | | | | | | | | | | | | |            #2465.
% 227.06/39.08  | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | Case 2:
% 227.06/39.08  | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | |   (371)  all_57_7 = e0 & op(e1, e2) = e0
% 227.06/39.08  | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | REF_CLOSE: (17), (85), (366), (371) are inconsistent by
% 227.06/39.08  | | | | | | | | | | | | | |            sub-proof #2039.
% 227.06/39.08  | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | End of split
% 227.06/39.08  | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | Case 2:
% 227.06/39.08  | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | |   (372)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 227.06/39.08  | | | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 227.06/39.08  | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | BETA: splitting (372) gives:
% 227.06/39.08  | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | Case 1:
% 227.06/39.08  | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | |   (373)  all_57_8 = e0 & op(e1, e1) = e0
% 227.06/39.08  | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | ALPHA: (373) implies:
% 227.06/39.08  | | | | | | | | | | | | | |   (374)  all_57_8 = e0
% 227.06/39.08  | | | | | | | | | | | | | |   (375)  op(e1, e1) = e0
% 227.06/39.08  | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | BETA: splitting (76) gives:
% 227.06/39.08  | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | Case 1:
% 227.06/39.08  | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | |   (376)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 227.06/39.08  | | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 227.06/39.08  | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | REF_CLOSE: (10), (17), (38), (77), (151), (376) are
% 227.06/39.08  | | | | | | | | | | | | | | |            inconsistent by sub-proof #242.
% 227.06/39.08  | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | Case 2:
% 227.06/39.08  | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | |   (377)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 227.06/39.08  | | | | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 227.06/39.08  | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | BETA: splitting (377) gives:
% 227.06/39.08  | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | Case 1:
% 227.06/39.08  | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | |   (378)  all_57_5 = e2 & op(e2, e1) = e2
% 227.06/39.08  | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | ALPHA: (378) implies:
% 227.06/39.08  | | | | | | | | | | | | | | | |   (379)  all_57_5 = e2
% 227.06/39.08  | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | REF_CLOSE: (3), (11), (13), (15), (17), (20), (25), (32),
% 227.06/39.08  | | | | | | | | | | | | | | | |            (37), (38), (41), (42), (44), (45), (46), (49),
% 227.06/39.08  | | | | | | | | | | | | | | | |            (51), (52), (57), (60), (61), (64), (67), (68),
% 227.06/39.08  | | | | | | | | | | | | | | | |            (81), (82), (83), (85), (86), (88), (90), (91),
% 227.06/39.08  | | | | | | | | | | | | | | | |            (94), (96), (102), (103), (117), (138), (139),
% 227.06/39.08  | | | | | | | | | | | | | | | |            (141), (142), (152), (153), (154), (159), (163),
% 227.06/39.08  | | | | | | | | | | | | | | | |            (366), (374), (375), (379) are inconsistent by
% 227.06/39.08  | | | | | | | | | | | | | | | |            sub-proof #198.
% 227.06/39.08  | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | Case 2:
% 227.06/39.08  | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | |   (380)  all_57_10 = e2 & op(e2, e0) = e2
% 227.06/39.08  | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | ALPHA: (380) implies:
% 227.06/39.08  | | | | | | | | | | | | | | | |   (381)  all_57_10 = e2
% 227.06/39.08  | | | | | | | | | | | | | | | |   (382)  op(e2, e0) = e2
% 227.06/39.08  | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | BETA: splitting (81) gives:
% 227.06/39.08  | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.08  | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | |   (383)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 227.06/39.08  | | | | | | | | | | | | | | | | |            & op(e2, e2) = e0)
% 227.06/39.08  | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | BETA: splitting (383) gives:
% 227.06/39.08  | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | |   (384)  all_57_2 = e0 & op(e2, e3) = e0
% 227.06/39.08  | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | ALPHA: (384) implies:
% 227.06/39.08  | | | | | | | | | | | | | | | | | |   (385)  all_57_2 = e0
% 227.06/39.08  | | | | | | | | | | | | | | | | | |   (386)  op(e2, e3) = e0
% 227.06/39.08  | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (9), (11), (13), (15), (17), (20), (25),
% 227.06/39.08  | | | | | | | | | | | | | | | | | |            (28), (32), (34), (36), (37), (38), (40), (41),
% 227.06/39.08  | | | | | | | | | | | | | | | | | |            (42), (44), (45), (46), (49), (51), (52), (54),
% 227.06/39.08  | | | | | | | | | | | | | | | | | |            (55), (57), (59), (60), (61), (64), (67), (68),
% 227.06/39.08  | | | | | | | | | | | | | | | | | |            (72), (74), (76), (77), (78), (81), (82), (83),
% 227.06/39.08  | | | | | | | | | | | | | | | | | |            (85), (86), (88), (90), (91), (94), (95), (96),
% 227.06/39.08  | | | | | | | | | | | | | | | | | |            (102), (103), (117), (138), (139), (140), (141),
% 227.06/39.08  | | | | | | | | | | | | | | | | | |            (142), (143), (152), (153), (154), (156), (159),
% 227.06/39.08  | | | | | | | | | | | | | | | | | |            (163), (166), (366), (367), (374), (375), (381),
% 227.06/39.08  | | | | | | | | | | | | | | | | | |            (382), (385), (386) are inconsistent by sub-proof
% 227.06/39.08  | | | | | | | | | | | | | | | | | |            #196.
% 227.06/39.08  | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | |   (387)  all_57_3 = e0 & op(e2, e2) = e0
% 227.06/39.08  | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | ALPHA: (387) implies:
% 227.06/39.08  | | | | | | | | | | | | | | | | | |   (388)  op(e2, e2) = e0
% 227.06/39.08  | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (38), (103), (139), (142), (388) are
% 227.06/39.08  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1229.
% 227.06/39.08  | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | End of split
% 227.06/39.08  | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.08  | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | |   (389)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 227.06/39.08  | | | | | | | | | | | | | | | | |            e0 & op(e2, e0) = e0)
% 227.06/39.08  | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | BETA: splitting (389) gives:
% 227.06/39.08  | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | |   (390)  all_57_5 = e0 & op(e2, e1) = e0
% 227.06/39.08  | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | ALPHA: (390) implies:
% 227.06/39.08  | | | | | | | | | | | | | | | | | |   (391)  all_57_5 = e0
% 227.06/39.08  | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | BETA: splitting (89) gives:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | |   (392)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 227.06/39.08  | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e0)
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | BETA: splitting (392) gives:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | |   (393)  all_57_0 = e0 & op(e3, e3) = e0
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | ALPHA: (393) implies:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | |   (394)  op(e3, e3) = e0
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (52), (156), (394) are inconsistent by
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | |            sub-proof #2403.
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | |   (395)  all_57_2 = e0 & op(e2, e3) = e0
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | ALPHA: (395) implies:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | |   (396)  all_57_2 = e0
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | |   (397)  op(e2, e3) = e0
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (9), (11), (13), (15), (17), (20), (25),
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | |            (28), (32), (34), (36), (37), (38), (40), (41),
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | |            (42), (44), (45), (46), (49), (51), (52), (54),
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | |            (55), (57), (59), (60), (61), (64), (67), (68),
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | |            (72), (74), (76), (77), (78), (81), (82), (83),
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | |            (85), (86), (88), (90), (91), (94), (95), (96),
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | |            (102), (103), (117), (138), (139), (140), (141),
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | |            (142), (143), (152), (153), (154), (156), (159),
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | |            (163), (166), (366), (367), (374), (375), (381),
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | |            (382), (396), (397) are inconsistent by sub-proof
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | |            #196.
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | |   (398)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 227.06/39.08  | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e3) = e0)
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | BETA: splitting (398) gives:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | |   (399)  all_57_6 = e0 & op(e1, e3) = e0
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | ALPHA: (399) implies:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | |   (400)  all_57_6 = e0
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (60), (400) imply:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | |   (401)  e3 = e0
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | SIMP: (401) implies:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | |   (402)  e3 = e0
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (26), (402) imply:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | |   (403)  all_57_3 = e0
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (15), (38), (41), (57), (72), (82), (381),
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | |            (391), (403) are inconsistent by sub-proof #2355.
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | |   (404)  all_57_12 = e0 & op(e0, e3) = e0
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | ALPHA: (404) implies:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | |   (405)  all_57_12 = e0
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | BETA: splitting (88) gives:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | |   (406)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e2)
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (406) gives:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | |   (407)  all_57_4 = e2 & op(e3, e1) = e2
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (17), (28), (34), (38), (41), (52), (55),
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | |            (57), (74), (82), (96), (156), (407) are
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #195.
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | |   (408)  all_57_5 = e2 & op(e2, e1) = e2
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (408) implies:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | |   (409)  all_57_5 = e2
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (11), (13), (15), (17), (20), (25), (32),
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | |            (37), (38), (41), (42), (44), (45), (46), (49),
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | |            (51), (52), (57), (60), (61), (64), (67), (68),
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | |            (81), (82), (83), (85), (86), (88), (90), (91),
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | |            (94), (96), (102), (103), (117), (138), (139),
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | |            (141), (142), (152), (153), (154), (159), (163),
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | |            (366), (374), (375), (409) are inconsistent by
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #198.
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | |   (410)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e1) = e2)
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (410) gives:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | |   (411)  all_57_8 = e2 & op(e1, e1) = e2
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (411) implies:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | |   (412)  all_57_8 = e2
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (374), (412) imply:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | |   (413)  e2 = e0
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (159), (413) imply:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | |   (414)  all_57_0 = e0
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (15), (38), (52), (57), (60), (82), (86),
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | |            (405), (414) are inconsistent by sub-proof #1425.
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | |   (415)  all_57_14 = e2 & op(e0, e1) = e2
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (415) implies:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | |   (416)  all_57_14 = e2
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (17), (37), (42), (57), (82), (375), (391),
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | |            (416) are inconsistent by sub-proof #215.
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.08  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.08  | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.08  | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | |   (417)  all_57_10 = e0 & op(e2, e0) = e0
% 227.06/39.08  | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | ALPHA: (417) implies:
% 227.06/39.08  | | | | | | | | | | | | | | | | | |   (418)  all_57_10 = e0
% 227.06/39.08  | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | | REF_CLOSE: (52), (381), (418) are inconsistent by sub-proof
% 227.06/39.08  | | | | | | | | | | | | | | | | | |            #2138.
% 227.06/39.08  | | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | | End of split
% 227.06/39.08  | | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | | End of split
% 227.06/39.08  | | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | | End of split
% 227.06/39.08  | | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | End of split
% 227.06/39.08  | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | Case 2:
% 227.06/39.08  | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | |   (419)  all_57_11 = e0 & op(e1, e0) = e0
% 227.06/39.08  | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | | REF_CLOSE: (17), (40), (367), (419) are inconsistent by
% 227.06/39.08  | | | | | | | | | | | | | |            sub-proof #2341.
% 227.06/39.08  | | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | | End of split
% 227.06/39.08  | | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | | End of split
% 227.06/39.08  | | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | | End of split
% 227.06/39.08  | | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | End of split
% 227.06/39.08  | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | Case 2:
% 227.06/39.08  | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | |   (420)  all_57_1 = e2 & op(e3, e2) = e2
% 227.06/39.08  | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | ALPHA: (420) implies:
% 227.06/39.08  | | | | | | | | | |   (421)  all_57_1 = e2
% 227.06/39.08  | | | | | | | | | | 
% 227.06/39.08  | | | | | | | | | | REF_CLOSE: (15), (17), (28), (34), (38), (41), (52), (55),
% 227.06/39.09  | | | | | | | | | |            (57), (74), (82), (96), (156), (421) are
% 227.06/39.09  | | | | | | | | | |            inconsistent by sub-proof #1650.
% 227.06/39.09  | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | End of split
% 227.06/39.09  | | | | | | | | | 
% 227.06/39.09  | | | | | | | | Case 2:
% 227.06/39.09  | | | | | | | | | 
% 227.06/39.09  | | | | | | | | |   (422)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 &
% 227.06/39.09  | | | | | | | | |            op(e3, e0) = e2)
% 227.06/39.09  | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | REF_CLOSE: (15), (17), (28), (34), (38), (41), (52), (55),
% 227.06/39.09  | | | | | | | | |            (57), (74), (82), (96), (154), (156), (422) are
% 227.06/39.09  | | | | | | | | |            inconsistent by sub-proof #194.
% 227.06/39.09  | | | | | | | | | 
% 227.06/39.09  | | | | | | | | End of split
% 227.06/39.09  | | | | | | | | 
% 227.06/39.09  | | | | | | | Case 2:
% 227.06/39.09  | | | | | | | | 
% 227.06/39.09  | | | | | | | |   (423)  all_55_0 = e1 | all_55_0 = e0
% 227.06/39.09  | | | | | | | | 
% 227.06/39.09  | | | | | | | | REF_CLOSE: (18), (63), (119), (423) are inconsistent by
% 227.06/39.09  | | | | | | | |            sub-proof #1954.
% 227.06/39.09  | | | | | | | | 
% 227.06/39.09  | | | | | | | End of split
% 227.06/39.09  | | | | | | | 
% 227.06/39.09  | | | | | | End of split
% 227.06/39.09  | | | | | | 
% 227.06/39.09  | | | | | End of split
% 227.06/39.09  | | | | | 
% 227.06/39.09  | | | | Case 2:
% 227.06/39.09  | | | | | 
% 227.06/39.09  | | | | |   (424)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22
% 227.06/39.09  | | | | |            = e0 & op(all_52_17, all_52_17) = e3 & op(all_52_19,
% 227.06/39.09  | | | | |              all_52_19) = e2 & op(all_52_21, all_52_21) = e1 &
% 227.06/39.09  | | | | |            op(all_52_23, all_52_23) = e0 & op(e1, e3) = all_52_17 &
% 227.06/39.09  | | | | |            op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 227.06/39.09  | | | | |              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 227.06/39.09  | | | | |            $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3 &
% 227.06/39.09  | | | | |            all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0 &
% 227.06/39.09  | | | | |            op(all_52_25, all_52_25) = e3 & op(all_52_27, all_52_27) =
% 227.06/39.09  | | | | |            e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 227.06/39.09  | | | | |              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 227.06/39.09  | | | | |            all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 227.06/39.09  | | | | |            & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 227.06/39.09  | | | | |            $i(all_52_31))
% 227.06/39.09  | | | | | 
% 227.06/39.09  | | | | | BETA: splitting (424) gives:
% 227.06/39.09  | | | | | 
% 227.06/39.09  | | | | | Case 1:
% 227.06/39.09  | | | | | | 
% 227.06/39.09  | | | | | |   (425)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 227.06/39.09  | | | | | |          all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 227.06/39.09  | | | | | |          op(all_52_19, all_52_19) = e2 & op(all_52_21, all_52_21) =
% 227.06/39.09  | | | | | |          e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) = all_52_17
% 227.06/39.09  | | | | | |          & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 227.06/39.09  | | | | | |            e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 227.06/39.09  | | | | | |          $i(all_52_21) & $i(all_52_23)
% 227.06/39.09  | | | | | | 
% 227.06/39.09  | | | | | | ALPHA: (425) implies:
% 227.06/39.09  | | | | | |   (426)  op(e1, e3) = all_52_17
% 227.06/39.09  | | | | | |   (427)  op(all_52_17, all_52_17) = e3
% 227.06/39.09  | | | | | | 
% 227.06/39.09  | | | | | | BETA: splitting (27) gives:
% 227.06/39.09  | | | | | | 
% 227.06/39.09  | | | | | | Case 1:
% 227.06/39.09  | | | | | | | 
% 227.06/39.09  | | | | | | |   (428)  all_55_0 = e3
% 227.06/39.09  | | | | | | | 
% 227.06/39.09  | | | | | | | COMBINE_EQS: (18), (428) imply:
% 227.06/39.09  | | | | | | |   (429)  all_10_2 = e3
% 227.06/39.09  | | | | | | | 
% 227.06/39.09  | | | | | | | REDUCE: (115), (429) imply:
% 227.06/39.09  | | | | | | |   (430)  $false
% 227.06/39.09  | | | | | | | 
% 227.06/39.09  | | | | | | | CLOSE: (430) is inconsistent.
% 227.06/39.09  | | | | | | | 
% 227.06/39.09  | | | | | | Case 2:
% 227.06/39.09  | | | | | | | 
% 227.06/39.09  | | | | | | |   (431)   ~ (all_55_0 = e3)
% 227.06/39.09  | | | | | | |   (432)  all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 227.06/39.09  | | | | | | | 
% 227.06/39.09  | | | | | | | BETA: splitting (432) gives:
% 227.06/39.09  | | | | | | | 
% 227.06/39.09  | | | | | | | Case 1:
% 227.06/39.09  | | | | | | | | 
% 227.06/39.09  | | | | | | | |   (433)  all_55_0 = e2
% 227.06/39.09  | | | | | | | | 
% 227.06/39.09  | | | | | | | | COMBINE_EQS: (18), (433) imply:
% 227.06/39.09  | | | | | | | |   (434)  all_10_2 = e2
% 227.06/39.09  | | | | | | | | 
% 227.06/39.09  | | | | | | | | REDUCE: (79), (434) imply:
% 227.06/39.09  | | | | | | | |   (435)   ~ (all_53_12 = e2)
% 227.06/39.09  | | | | | | | | 
% 227.06/39.09  | | | | | | | | REDUCE: (115), (434) imply:
% 227.06/39.09  | | | | | | | |   (436)   ~ (e3 = e2)
% 227.06/39.09  | | | | | | | | 
% 227.06/39.09  | | | | | | | | REDUCE: (1), (434) imply:
% 227.06/39.09  | | | | | | | |   (437)  op(e3, e3) = e2
% 227.06/39.09  | | | | | | | | 
% 227.06/39.09  | | | | | | | | BETA: splitting (32) gives:
% 227.06/39.09  | | | | | | | | 
% 227.06/39.09  | | | | | | | | Case 1:
% 227.06/39.09  | | | | | | | | | 
% 227.06/39.09  | | | | | | | | |   (438)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 &
% 227.06/39.09  | | | | | | | | |            op(e3, e2) = e2)
% 227.06/39.09  | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | BETA: splitting (438) gives:
% 227.06/39.09  | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | Case 1:
% 227.06/39.09  | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | |   (439)  all_57_0 = e2 & op(e3, e3) = e2
% 227.06/39.09  | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | GROUND_INST: instantiating (17) with e3, all_52_17, e3, e1,
% 227.06/39.09  | | | | | | | | | |              simplifying with (24), (426) gives:
% 227.06/39.09  | | | | | | | | | |   (440)  all_52_17 = e3
% 227.06/39.09  | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | REDUCE: (427), (440) imply:
% 227.06/39.09  | | | | | | | | | |   (441)  op(e3, e3) = e3
% 227.06/39.09  | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | REF_CLOSE: (17), (38), (437), (441) are inconsistent by
% 227.06/39.09  | | | | | | | | | |            sub-proof #2490.
% 227.06/39.09  | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | Case 2:
% 227.06/39.09  | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | |   (442)  all_57_1 = e2 & op(e3, e2) = e2
% 227.06/39.09  | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | ALPHA: (442) implies:
% 227.06/39.09  | | | | | | | | | |   (443)  all_57_1 = e2
% 227.06/39.09  | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | REF_CLOSE: (15), (17), (28), (34), (38), (41), (52), (55),
% 227.06/39.09  | | | | | | | | | |            (57), (74), (82), (96), (437), (443) are
% 227.06/39.09  | | | | | | | | | |            inconsistent by sub-proof #1650.
% 227.06/39.09  | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | End of split
% 227.06/39.09  | | | | | | | | | 
% 227.06/39.09  | | | | | | | | Case 2:
% 227.06/39.09  | | | | | | | | | 
% 227.06/39.09  | | | | | | | | |   (444)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 &
% 227.06/39.09  | | | | | | | | |            op(e3, e0) = e2)
% 227.06/39.09  | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | REF_CLOSE: (15), (17), (28), (34), (38), (41), (52), (55),
% 227.06/39.09  | | | | | | | | |            (57), (74), (82), (96), (435), (437), (444) are
% 227.06/39.09  | | | | | | | | |            inconsistent by sub-proof #194.
% 227.06/39.09  | | | | | | | | | 
% 227.06/39.09  | | | | | | | | End of split
% 227.06/39.09  | | | | | | | | 
% 227.06/39.09  | | | | | | | Case 2:
% 227.06/39.09  | | | | | | | | 
% 227.06/39.09  | | | | | | | |   (445)  all_55_0 = e1 | all_55_0 = e0
% 227.06/39.09  | | | | | | | | 
% 227.06/39.09  | | | | | | | | REF_CLOSE: (18), (63), (119), (445) are inconsistent by
% 227.06/39.09  | | | | | | | |            sub-proof #1954.
% 227.06/39.09  | | | | | | | | 
% 227.06/39.09  | | | | | | | End of split
% 227.06/39.09  | | | | | | | 
% 227.06/39.09  | | | | | | End of split
% 227.06/39.09  | | | | | | 
% 227.06/39.09  | | | | | Case 2:
% 227.06/39.09  | | | | | | 
% 227.06/39.09  | | | | | |   (446)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 227.06/39.09  | | | | | |          all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 227.06/39.09  | | | | | |          op(all_52_27, all_52_27) = e2 & op(all_52_29, all_52_29) =
% 227.06/39.09  | | | | | |          e1 & op(all_52_31, all_52_31) = e0 & op(e0, e3) = all_52_25
% 227.06/39.09  | | | | | |          & op(e0, e2) = all_52_27 & op(e0, e1) = all_52_29 & op(e0,
% 227.06/39.09  | | | | | |            e0) = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 227.06/39.09  | | | | | |          $i(all_52_29) & $i(all_52_31)
% 227.06/39.09  | | | | | | 
% 227.06/39.09  | | | | | | ALPHA: (446) implies:
% 227.06/39.09  | | | | | |   (447)  op(e0, e0) = all_52_31
% 227.06/39.09  | | | | | |   (448)  op(all_52_31, all_52_31) = e0
% 227.06/39.09  | | | | | | 
% 227.06/39.09  | | | | | | BETA: splitting (27) gives:
% 227.06/39.09  | | | | | | 
% 227.06/39.09  | | | | | | Case 1:
% 227.06/39.09  | | | | | | | 
% 227.06/39.09  | | | | | | |   (449)  all_55_0 = e3
% 227.06/39.09  | | | | | | | 
% 227.06/39.09  | | | | | | | COMBINE_EQS: (18), (449) imply:
% 227.06/39.09  | | | | | | |   (450)  all_10_2 = e3
% 227.06/39.09  | | | | | | | 
% 227.06/39.09  | | | | | | | REDUCE: (115), (450) imply:
% 227.06/39.09  | | | | | | |   (451)  $false
% 227.06/39.09  | | | | | | | 
% 227.06/39.09  | | | | | | | CLOSE: (451) is inconsistent.
% 227.06/39.09  | | | | | | | 
% 227.06/39.09  | | | | | | Case 2:
% 227.06/39.09  | | | | | | | 
% 227.06/39.09  | | | | | | |   (452)   ~ (all_55_0 = e3)
% 227.06/39.09  | | | | | | |   (453)  all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 227.06/39.09  | | | | | | | 
% 227.06/39.09  | | | | | | | BETA: splitting (453) gives:
% 227.06/39.09  | | | | | | | 
% 227.06/39.09  | | | | | | | Case 1:
% 227.06/39.09  | | | | | | | | 
% 227.06/39.09  | | | | | | | |   (454)  all_55_0 = e2
% 227.06/39.09  | | | | | | | | 
% 227.06/39.09  | | | | | | | | COMBINE_EQS: (18), (454) imply:
% 227.06/39.09  | | | | | | | |   (455)  all_10_2 = e2
% 227.06/39.09  | | | | | | | | 
% 227.06/39.09  | | | | | | | | REDUCE: (79), (455) imply:
% 227.06/39.09  | | | | | | | |   (456)   ~ (all_53_12 = e2)
% 227.06/39.09  | | | | | | | | 
% 227.06/39.09  | | | | | | | | REDUCE: (115), (455) imply:
% 227.06/39.09  | | | | | | | |   (457)   ~ (e3 = e2)
% 227.06/39.09  | | | | | | | | 
% 227.06/39.09  | | | | | | | | REDUCE: (1), (455) imply:
% 227.06/39.09  | | | | | | | |   (458)  op(e3, e3) = e2
% 227.06/39.09  | | | | | | | | 
% 227.06/39.09  | | | | | | | | BETA: splitting (32) gives:
% 227.06/39.09  | | | | | | | | 
% 227.06/39.09  | | | | | | | | Case 1:
% 227.06/39.09  | | | | | | | | | 
% 227.06/39.09  | | | | | | | | |   (459)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 &
% 227.06/39.09  | | | | | | | | |            op(e3, e2) = e2)
% 227.06/39.09  | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | BETA: splitting (459) gives:
% 227.06/39.09  | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | Case 1:
% 227.06/39.09  | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | |   (460)  all_57_0 = e2 & op(e3, e3) = e2
% 227.06/39.09  | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | REF_CLOSE: (17), (52), (103), (447), (448), (460) are
% 227.06/39.09  | | | | | | | | | |            inconsistent by sub-proof #441.
% 227.06/39.09  | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | Case 2:
% 227.06/39.09  | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | |   (461)  all_57_1 = e2 & op(e3, e2) = e2
% 227.06/39.09  | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | ALPHA: (461) implies:
% 227.06/39.09  | | | | | | | | | |   (462)  all_57_1 = e2
% 227.06/39.09  | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | REF_CLOSE: (15), (17), (28), (34), (38), (41), (52), (55),
% 227.06/39.09  | | | | | | | | | |            (57), (74), (82), (96), (458), (462) are
% 227.06/39.09  | | | | | | | | | |            inconsistent by sub-proof #1650.
% 227.06/39.09  | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | End of split
% 227.06/39.09  | | | | | | | | | 
% 227.06/39.09  | | | | | | | | Case 2:
% 227.06/39.09  | | | | | | | | | 
% 227.06/39.09  | | | | | | | | |   (463)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 &
% 227.06/39.09  | | | | | | | | |            op(e3, e0) = e2)
% 227.06/39.09  | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | REF_CLOSE: (15), (17), (28), (34), (38), (41), (52), (55),
% 227.06/39.09  | | | | | | | | |            (57), (74), (82), (96), (456), (458), (463) are
% 227.06/39.09  | | | | | | | | |            inconsistent by sub-proof #194.
% 227.06/39.09  | | | | | | | | | 
% 227.06/39.09  | | | | | | | | End of split
% 227.06/39.09  | | | | | | | | 
% 227.06/39.09  | | | | | | | Case 2:
% 227.06/39.09  | | | | | | | | 
% 227.06/39.09  | | | | | | | |   (464)  all_55_0 = e1 | all_55_0 = e0
% 227.06/39.09  | | | | | | | | 
% 227.06/39.09  | | | | | | | | REF_CLOSE: (18), (63), (119), (464) are inconsistent by
% 227.06/39.09  | | | | | | | |            sub-proof #1954.
% 227.06/39.09  | | | | | | | | 
% 227.06/39.09  | | | | | | | End of split
% 227.06/39.09  | | | | | | | 
% 227.06/39.09  | | | | | | End of split
% 227.06/39.09  | | | | | | 
% 227.06/39.09  | | | | | End of split
% 227.06/39.09  | | | | | 
% 227.06/39.09  | | | | End of split
% 227.06/39.09  | | | | 
% 227.06/39.09  | | | Case 2:
% 227.06/39.09  | | | | 
% 227.06/39.09  | | | |   (465)  all_18_2 = e0
% 227.06/39.09  | | | | 
% 227.06/39.09  | | | | COMBINE_EQS: (66), (465) imply:
% 227.06/39.09  | | | |   (466)  all_10_2 = e0
% 227.06/39.09  | | | | 
% 227.06/39.09  | | | | SIMP: (466) implies:
% 227.06/39.09  | | | |   (467)  all_10_2 = e0
% 227.06/39.09  | | | | 
% 227.06/39.09  | | | | REDUCE: (6), (467) imply:
% 227.06/39.09  | | | |   (468)   ~ (all_53_1 = e0)
% 227.06/39.09  | | | | 
% 227.06/39.09  | | | | REDUCE: (5), (467) imply:
% 227.06/39.09  | | | |   (469)   ~ (all_53_3 = e0)
% 227.06/39.09  | | | | 
% 227.06/39.09  | | | | REDUCE: (39), (467) imply:
% 227.06/39.09  | | | |   (470)   ~ (all_53_4 = e0)
% 227.06/39.09  | | | | 
% 227.06/39.09  | | | | REDUCE: (79), (467) imply:
% 227.06/39.09  | | | |   (471)   ~ (all_53_12 = e0)
% 227.06/39.09  | | | | 
% 227.06/39.09  | | | | REDUCE: (115), (467) imply:
% 227.06/39.09  | | | |   (472)   ~ (e3 = e0)
% 227.06/39.09  | | | | 
% 227.06/39.09  | | | | REDUCE: (63), (467) imply:
% 227.06/39.09  | | | |   (473)   ~ (e1 = e0)
% 227.06/39.09  | | | | 
% 227.06/39.09  | | | | REDUCE: (1), (467) imply:
% 227.06/39.09  | | | |   (474)  op(e3, e3) = e0
% 227.06/39.09  | | | | 
% 227.06/39.09  | | | | BETA: splitting (53) gives:
% 227.06/39.09  | | | | 
% 227.06/39.09  | | | | Case 1:
% 227.06/39.09  | | | | | 
% 227.06/39.09  | | | | |   (475)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 =
% 227.06/39.09  | | | | |            e0 & op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) =
% 227.06/39.09  | | | | |            e2 & op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) =
% 227.06/39.09  | | | | |            e0 & op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 & op(e3,
% 227.06/39.09  | | | | |              e1) = all_52_5 & op(e3, e0) = all_52_7 & $i(all_52_1) &
% 227.06/39.09  | | | | |            $i(all_52_3) & $i(all_52_5) & $i(all_52_7)) | (all_52_8 =
% 227.06/39.09  | | | | |            e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0 &
% 227.06/39.09  | | | | |            op(all_52_9, all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 227.06/39.09  | | | | |            & op(all_52_13, all_52_13) = e1 & op(all_52_15, all_52_15)
% 227.06/39.09  | | | | |            = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 227.06/39.09  | | | | |            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 227.06/39.09  | | | | |            $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 227.06/39.09  | | | | |            $i(all_52_15))
% 227.06/39.09  | | | | | 
% 227.06/39.09  | | | | | BETA: splitting (475) gives:
% 227.06/39.09  | | | | | 
% 227.06/39.09  | | | | | Case 1:
% 227.06/39.09  | | | | | | 
% 227.06/39.09  | | | | | |   (476)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 =
% 227.06/39.09  | | | | | |          e0 & op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) =
% 227.06/39.09  | | | | | |          e2 & op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) =
% 227.06/39.09  | | | | | |          e0 & op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 & op(e3,
% 227.06/39.09  | | | | | |            e1) = all_52_5 & op(e3, e0) = all_52_7 & $i(all_52_1) &
% 227.06/39.09  | | | | | |          $i(all_52_3) & $i(all_52_5) & $i(all_52_7)
% 227.06/39.09  | | | | | | 
% 227.06/39.09  | | | | | | ALPHA: (476) implies:
% 227.06/39.09  | | | | | |   (477)  op(e3, e1) = all_52_5
% 227.06/39.09  | | | | | |   (478)  op(e3, e3) = all_52_1
% 227.06/39.09  | | | | | |   (479)  op(all_52_5, all_52_5) = e1
% 227.06/39.09  | | | | | | 
% 227.06/39.09  | | | | | | REF_CLOSE: (8), (17), (57), (474), (477), (478), (479) are
% 227.06/39.09  | | | | | |            inconsistent by sub-proof #237.
% 227.06/39.09  | | | | | | 
% 227.06/39.09  | | | | | Case 2:
% 227.06/39.09  | | | | | | 
% 227.06/39.09  | | | | | |   (480)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14
% 227.06/39.09  | | | | | |          = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 227.06/39.09  | | | | | |            all_52_11) = e2 & op(all_52_13, all_52_13) = e1 &
% 227.06/39.09  | | | | | |          op(all_52_15, all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 227.06/39.09  | | | | | |          op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13 & op(e2,
% 227.06/39.09  | | | | | |            e0) = all_52_15 & $i(all_52_9) & $i(all_52_11) &
% 227.06/39.09  | | | | | |          $i(all_52_13) & $i(all_52_15)
% 227.06/39.09  | | | | | | 
% 227.06/39.09  | | | | | | ALPHA: (480) implies:
% 227.06/39.09  | | | | | |   (481)  op(e2, e2) = all_52_11
% 227.06/39.09  | | | | | |   (482)  op(all_52_11, all_52_11) = e2
% 227.06/39.09  | | | | | | 
% 227.06/39.09  | | | | | | BETA: splitting (89) gives:
% 227.06/39.09  | | | | | | 
% 227.06/39.09  | | | | | | Case 1:
% 227.06/39.09  | | | | | | | 
% 227.06/39.09  | | | | | | |   (483)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 &
% 227.06/39.09  | | | | | | |            op(e2, e3) = e0)
% 227.06/39.09  | | | | | | | 
% 227.06/39.09  | | | | | | | BETA: splitting (483) gives:
% 227.06/39.09  | | | | | | | 
% 227.06/39.09  | | | | | | | Case 1:
% 227.06/39.09  | | | | | | | | 
% 227.06/39.09  | | | | | | | |   (484)  all_57_0 = e0 & op(e3, e3) = e0
% 227.06/39.09  | | | | | | | | 
% 227.06/39.09  | | | | | | | | GROUND_INST: instantiating (17) with e3, all_52_11, e2, e2,
% 227.06/39.09  | | | | | | | |              simplifying with (77), (481) gives:
% 227.06/39.09  | | | | | | | |   (485)  all_52_11 = e3
% 227.06/39.09  | | | | | | | | 
% 227.06/39.09  | | | | | | | | REDUCE: (482), (485) imply:
% 227.06/39.09  | | | | | | | |   (486)  op(e3, e3) = e2
% 227.06/39.09  | | | | | | | | 
% 227.06/39.09  | | | | | | | | REF_CLOSE: (17), (52), (474), (486) are inconsistent by
% 227.06/39.09  | | | | | | | |            sub-proof #2403.
% 227.06/39.09  | | | | | | | | 
% 227.06/39.09  | | | | | | | Case 2:
% 227.06/39.09  | | | | | | | | 
% 227.06/39.09  | | | | | | | |   (487)  all_57_2 = e0 & op(e2, e3) = e0
% 227.06/39.09  | | | | | | | | 
% 227.06/39.09  | | | | | | | | ALPHA: (487) implies:
% 227.06/39.09  | | | | | | | |   (488)  op(e2, e3) = e0
% 227.06/39.09  | | | | | | | | 
% 227.06/39.09  | | | | | | | | REF_CLOSE: (10), (17), (468), (488) are inconsistent by
% 227.06/39.09  | | | | | | | |            sub-proof #1943.
% 227.06/39.09  | | | | | | | | 
% 227.06/39.09  | | | | | | | End of split
% 227.06/39.09  | | | | | | | 
% 227.06/39.09  | | | | | | Case 2:
% 227.06/39.09  | | | | | | | 
% 227.06/39.09  | | | | | | |   (489)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 &
% 227.06/39.09  | | | | | | |            op(e0, e3) = e0)
% 227.06/39.09  | | | | | | | 
% 227.06/39.09  | | | | | | | REF_CLOSE: (17), (41), (45), (60), (469), (489) are inconsistent
% 227.06/39.09  | | | | | | |            by sub-proof #193.
% 227.06/39.09  | | | | | | | 
% 227.06/39.09  | | | | | | End of split
% 227.06/39.09  | | | | | | 
% 227.06/39.09  | | | | | End of split
% 227.06/39.09  | | | | | 
% 227.06/39.09  | | | | Case 2:
% 227.06/39.09  | | | | | 
% 227.06/39.09  | | | | |   (490)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22
% 227.06/39.09  | | | | |            = e0 & op(all_52_17, all_52_17) = e3 & op(all_52_19,
% 227.06/39.09  | | | | |              all_52_19) = e2 & op(all_52_21, all_52_21) = e1 &
% 227.06/39.09  | | | | |            op(all_52_23, all_52_23) = e0 & op(e1, e3) = all_52_17 &
% 227.06/39.09  | | | | |            op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 227.06/39.09  | | | | |              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 227.06/39.09  | | | | |            $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3 &
% 227.06/39.09  | | | | |            all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0 &
% 227.06/39.09  | | | | |            op(all_52_25, all_52_25) = e3 & op(all_52_27, all_52_27) =
% 227.06/39.09  | | | | |            e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 227.06/39.09  | | | | |              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 227.06/39.09  | | | | |            all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 227.06/39.09  | | | | |            & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 227.06/39.09  | | | | |            $i(all_52_31))
% 227.06/39.09  | | | | | 
% 227.06/39.09  | | | | | BETA: splitting (490) gives:
% 227.06/39.09  | | | | | 
% 227.06/39.09  | | | | | Case 1:
% 227.06/39.09  | | | | | | 
% 227.06/39.09  | | | | | |   (491)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 227.06/39.09  | | | | | |          all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 227.06/39.09  | | | | | |          op(all_52_19, all_52_19) = e2 & op(all_52_21, all_52_21) =
% 227.06/39.09  | | | | | |          e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) = all_52_17
% 227.06/39.09  | | | | | |          & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 227.06/39.09  | | | | | |            e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 227.06/39.09  | | | | | |          $i(all_52_21) & $i(all_52_23)
% 227.06/39.09  | | | | | | 
% 227.06/39.09  | | | | | | ALPHA: (491) implies:
% 227.06/39.09  | | | | | |   (492)  op(e1, e3) = all_52_17
% 227.06/39.09  | | | | | |   (493)  op(all_52_17, all_52_17) = e3
% 227.06/39.09  | | | | | | 
% 227.06/39.09  | | | | | | GROUND_INST: instantiating (17) with e3, all_52_17, e3, e1,
% 227.06/39.09  | | | | | |              simplifying with (24), (492) gives:
% 227.06/39.09  | | | | | |   (494)  all_52_17 = e3
% 227.06/39.09  | | | | | | 
% 227.06/39.09  | | | | | | REDUCE: (493), (494) imply:
% 227.06/39.09  | | | | | |   (495)  op(e3, e3) = e3
% 227.06/39.09  | | | | | | 
% 227.06/39.09  | | | | | | REF_CLOSE: (11), (15), (17), (28), (32), (34), (38), (41), (49),
% 227.06/39.09  | | | | | |            (52), (55), (57), (60), (74), (82), (86), (89), (96),
% 227.06/39.09  | | | | | |            (110), (495) are inconsistent by sub-proof #268.
% 227.06/39.09  | | | | | | 
% 227.06/39.09  | | | | | Case 2:
% 227.06/39.09  | | | | | | 
% 227.06/39.09  | | | | | |   (496)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 227.06/39.09  | | | | | |          all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 227.06/39.09  | | | | | |          op(all_52_27, all_52_27) = e2 & op(all_52_29, all_52_29) =
% 227.06/39.09  | | | | | |          e1 & op(all_52_31, all_52_31) = e0 & op(e0, e3) = all_52_25
% 227.06/39.09  | | | | | |          & op(e0, e2) = all_52_27 & op(e0, e1) = all_52_29 & op(e0,
% 227.06/39.09  | | | | | |            e0) = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 227.06/39.09  | | | | | |          $i(all_52_29) & $i(all_52_31)
% 227.06/39.09  | | | | | | 
% 227.06/39.09  | | | | | | ALPHA: (496) implies:
% 227.06/39.09  | | | | | |   (497)  op(e0, e0) = all_52_31
% 227.06/39.09  | | | | | |   (498)  op(e0, e1) = all_52_29
% 227.06/39.09  | | | | | |   (499)  op(e0, e2) = all_52_27
% 227.06/39.09  | | | | | |   (500)  op(e0, e3) = all_52_25
% 227.06/39.09  | | | | | |   (501)  op(all_52_31, all_52_31) = e0
% 227.06/39.09  | | | | | |   (502)  op(all_52_29, all_52_29) = e1
% 227.06/39.09  | | | | | |   (503)  op(all_52_27, all_52_27) = e2
% 227.06/39.09  | | | | | | 
% 227.06/39.09  | | | | | | BETA: splitting (89) gives:
% 227.06/39.09  | | | | | | 
% 227.06/39.09  | | | | | | Case 1:
% 227.06/39.09  | | | | | | | 
% 227.06/39.09  | | | | | | |   (504)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 &
% 227.06/39.09  | | | | | | |            op(e2, e3) = e0)
% 227.06/39.09  | | | | | | | 
% 227.06/39.09  | | | | | | | BETA: splitting (504) gives:
% 227.06/39.09  | | | | | | | 
% 227.06/39.09  | | | | | | | Case 1:
% 227.06/39.09  | | | | | | | | 
% 227.06/39.09  | | | | | | | |   (505)  all_57_0 = e0 & op(e3, e3) = e0
% 227.06/39.09  | | | | | | | | 
% 227.06/39.09  | | | | | | | | ALPHA: (505) implies:
% 227.06/39.09  | | | | | | | |   (506)  all_57_0 = e0
% 227.06/39.09  | | | | | | | | 
% 227.06/39.09  | | | | | | | | GROUND_INST: instantiating (17) with e3, all_52_31, e0, e0,
% 227.06/39.09  | | | | | | | |              simplifying with (103), (497) gives:
% 227.06/39.09  | | | | | | | |   (507)  all_52_31 = e3
% 227.06/39.09  | | | | | | | | 
% 227.06/39.09  | | | | | | | | GROUND_INST: instantiating (17) with all_53_11, all_52_29, e1,
% 227.06/39.09  | | | | | | | |              e0, simplifying with (4), (498) gives:
% 227.06/39.09  | | | | | | | |   (508)  all_53_11 = all_52_29
% 227.06/39.09  | | | | | | | | 
% 227.06/39.09  | | | | | | | | GROUND_INST: instantiating (17) with all_53_7, all_52_27, e2,
% 227.06/39.09  | | | | | | | |              e0, simplifying with (65), (499) gives:
% 227.06/39.09  | | | | | | | |   (509)  all_53_7 = all_52_27
% 227.06/39.09  | | | | | | | | 
% 227.06/39.09  | | | | | | | | GROUND_INST: instantiating (17) with all_53_3, all_52_25, e3,
% 227.06/39.09  | | | | | | | |              e0, simplifying with (45), (500) gives:
% 227.06/39.09  | | | | | | | |   (510)  all_53_3 = all_52_25
% 227.06/39.09  | | | | | | | | 
% 227.06/39.09  | | | | | | | | REDUCE: (23), (509), (510) imply:
% 227.06/39.09  | | | | | | | |   (511)   ~ (all_52_25 = all_52_27)
% 227.06/39.09  | | | | | | | | 
% 227.06/39.09  | | | | | | | | REDUCE: (108), (510) imply:
% 227.06/39.09  | | | | | | | |   (512)   ~ (all_52_25 = e3)
% 227.06/39.09  | | | | | | | | 
% 227.06/39.09  | | | | | | | | REDUCE: (469), (510) imply:
% 227.06/39.09  | | | | | | | |   (513)   ~ (all_52_25 = e0)
% 227.06/39.09  | | | | | | | | 
% 227.06/39.09  | | | | | | | | REDUCE: (2), (509) imply:
% 227.06/39.09  | | | | | | | |   (514)   ~ (all_52_27 = e3)
% 227.06/39.09  | | | | | | | | 
% 227.06/39.09  | | | | | | | | REDUCE: (29), (508) imply:
% 227.06/39.09  | | | | | | | |   (515)   ~ (all_52_29 = all_6_2)
% 227.06/39.09  | | | | | | | | 
% 227.06/39.09  | | | | | | | | REDUCE: (112), (508) imply:
% 227.06/39.09  | | | | | | | |   (516)   ~ (all_52_29 = e3)
% 227.06/39.09  | | | | | | | | 
% 227.06/39.09  | | | | | | | | BETA: splitting (92) gives:
% 227.06/39.09  | | | | | | | | 
% 227.06/39.09  | | | | | | | | Case 1:
% 227.06/39.09  | | | | | | | | | 
% 227.06/39.09  | | | | | | | | |   (517)   ~ (all_22_2 = e3)
% 227.06/39.09  | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | REDUCE: (19), (517) imply:
% 227.06/39.09  | | | | | | | | |   (518)  $false
% 227.06/39.09  | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | CLOSE: (518) is inconsistent.
% 227.06/39.09  | | | | | | | | | 
% 227.06/39.09  | | | | | | | | Case 2:
% 227.06/39.09  | | | | | | | | | 
% 227.06/39.09  | | | | | | | | |   (519)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 &
% 227.06/39.09  | | | | | | | | |            op(e0, e3) = all_22_1 & $i(all_22_0) &
% 227.06/39.09  | | | | | | | | |            $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0, e3) =
% 227.06/39.09  | | | | | | | | |            all_22_1 & $i(all_22_1))
% 227.06/39.09  | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | BETA: splitting (21) gives:
% 227.06/39.09  | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | Case 1:
% 227.06/39.09  | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | |   (520)   ~ (all_24_2 = e0)
% 227.06/39.09  | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | REDUCE: (87), (520) imply:
% 227.06/39.09  | | | | | | | | | |   (521)   ~ (all_6_2 = e0)
% 227.06/39.09  | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | BETA: splitting (58) gives:
% 227.06/39.09  | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | Case 1:
% 227.06/39.09  | | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | |   (522)   ~ (all_38_2 = e2)
% 227.06/39.09  | | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | | REDUCE: (73), (522) imply:
% 227.06/39.09  | | | | | | | | | | |   (523)   ~ (all_6_2 = e2)
% 227.06/39.09  | | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | | BETA: splitting (7) gives:
% 227.06/39.09  | | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | | Case 1:
% 227.06/39.09  | | | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | | |   (524)  all_55_10 = e3
% 227.06/39.09  | | | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | | | REF_CLOSE: (69), (117), (524) are inconsistent by sub-proof
% 227.06/39.09  | | | | | | | | | | | |            #2500.
% 227.06/39.09  | | | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | | Case 2:
% 227.06/39.09  | | | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | | |   (525)   ~ (all_55_10 = e3)
% 227.06/39.09  | | | | | | | | | | | |   (526)  all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 227.06/39.09  | | | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | | | BETA: splitting (526) gives:
% 227.06/39.09  | | | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | | | Case 1:
% 227.06/39.09  | | | | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | | | |   (527)  all_55_10 = e2
% 227.06/39.09  | | | | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | | | | REF_CLOSE: (69), (523), (527) are inconsistent by sub-proof
% 227.06/39.09  | | | | | | | | | | | | |            #2499.
% 227.06/39.09  | | | | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | | | Case 2:
% 227.06/39.09  | | | | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | | | |   (528)   ~ (all_55_10 = e2)
% 227.06/39.09  | | | | | | | | | | | | |   (529)  all_55_10 = e1 | all_55_10 = e0
% 227.06/39.09  | | | | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | | | | BETA: splitting (529) gives:
% 227.06/39.09  | | | | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | | | | Case 1:
% 227.06/39.09  | | | | | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | | | | |   (530)  all_55_10 = e1
% 227.06/39.09  | | | | | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | | | | | COMBINE_EQS: (69), (530) imply:
% 227.06/39.09  | | | | | | | | | | | | | |   (531)  all_6_2 = e1
% 227.06/39.09  | | | | | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | | | | | SIMP: (531) implies:
% 227.06/39.09  | | | | | | | | | | | | | |   (532)  all_6_2 = e1
% 227.06/39.09  | | | | | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | | | | | REDUCE: (35), (532) imply:
% 227.06/39.09  | | | | | | | | | | | | | |   (533)   ~ (all_53_14 = e1)
% 227.06/39.09  | | | | | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | | | | | REDUCE: (117), (532) imply:
% 227.06/39.09  | | | | | | | | | | | | | |   (534)   ~ (e3 = e1)
% 227.06/39.09  | | | | | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | | | | | REDUCE: (523), (532) imply:
% 227.06/39.09  | | | | | | | | | | | | | |   (535)   ~ (e2 = e1)
% 227.06/39.09  | | | | | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | | | | | REDUCE: (25), (532) imply:
% 227.06/39.09  | | | | | | | | | | | | | |   (536)  op(e1, e1) = e1
% 227.06/39.09  | | | | | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | | | | | BETA: splitting (46) gives:
% 227.06/39.09  | | | | | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | | | | | Case 1:
% 227.06/39.09  | | | | | | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | | | | | |   (537)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 227.06/39.09  | | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 227.06/39.09  | | | | | | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | | | | | | BETA: splitting (537) gives:
% 227.06/39.09  | | | | | | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | | | | | | Case 1:
% 227.06/39.09  | | | | | | | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | | | | | | |   (538)  all_57_12 = e1 & op(e0, e3) = e1
% 227.06/39.09  | | | | | | | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | | | | | | | ALPHA: (538) implies:
% 227.06/39.09  | | | | | | | | | | | | | | | |   (539)  all_57_12 = e1
% 227.06/39.09  | | | | | | | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | | | | | | | BETA: splitting (86) gives:
% 227.06/39.09  | | | | | | | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.09  | | | | | | | | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | | | | | | | |   (540)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 227.06/39.09  | | | | | | | | | | | | | | | | |            & op(e2, e3) = e2)
% 227.06/39.09  | | | | | | | | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | | | | | | | | BETA: splitting (540) gives:
% 227.06/39.09  | | | | | | | | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.09  | | | | | | | | | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | | | | | | | | |   (541)  all_57_0 = e2 & op(e3, e3) = e2
% 227.06/39.09  | | | | | | | | | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | | | | | | | | | ALPHA: (541) implies:
% 227.06/39.09  | | | | | | | | | | | | | | | | | |   (542)  op(e3, e3) = e2
% 227.06/39.09  | | | | | | | | | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (52), (474), (542) are inconsistent by
% 227.06/39.09  | | | | | | | | | | | | | | | | | |            sub-proof #2403.
% 227.06/39.09  | | | | | | | | | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.09  | | | | | | | | | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | | | | | | | | |   (543)  all_57_2 = e2 & op(e2, e3) = e2
% 227.06/39.09  | | | | | | | | | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | | | | | | | | | ALPHA: (543) implies:
% 227.06/39.09  | | | | | | | | | | | | | | | | | |   (544)  all_57_2 = e2
% 227.06/39.09  | | | | | | | | | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | | | | | | | | | BETA: splitting (9) gives:
% 227.06/39.09  | | | | | | | | | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.09  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | | | | | | | | | |   (545)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 227.06/39.09  | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 227.06/39.09  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | | | | | | | | | | BETA: splitting (545) gives:
% 227.06/39.09  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.09  | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | | | | | | | | | | |   (546)  all_57_2 = e1 & op(e2, e3) = e1
% 227.06/39.09  | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (82), (544), (546) are inconsistent by sub-proof
% 227.06/39.09  | | | | | | | | | | | | | | | | | | | |            #2244.
% 227.06/39.09  | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.09  | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | | | | | | | | | | |   (547)  all_57_3 = e1 & op(e2, e2) = e1
% 227.06/39.09  | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | | | | | | | | | | | ALPHA: (547) implies:
% 227.06/39.09  | | | | | | | | | | | | | | | | | | | |   (548)  op(e2, e2) = e1
% 227.06/39.09  | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (17), (77), (548) are inconsistent by
% 227.06/39.09  | | | | | | | | | | | | | | | | | | | |            sub-proof #1912.
% 227.06/39.09  | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.09  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.09  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | | | | | | | | | |   (549)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 227.06/39.09  | | | | | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 227.06/39.09  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | | | | | | | | | | BETA: splitting (549) gives:
% 227.06/39.09  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.09  | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | | | | | | | | | | |   (550)  all_57_5 = e1 & op(e2, e1) = e1
% 227.06/39.09  | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | | | | | | | | | | | ALPHA: (550) implies:
% 227.06/39.09  | | | | | | | | | | | | | | | | | | | |   (551)  all_57_5 = e1
% 227.06/39.09  | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (17), (25), (36), (38), (41), (46), (52),
% 227.06/39.09  | | | | | | | | | | | | | | | | | | | |            (57), (59), (67), (68), (82), (88), (102), (117),
% 227.06/39.09  | | | | | | | | | | | | | | | | | | | |            (536), (551) are inconsistent by sub-proof #941.
% 227.06/39.09  | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.09  | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | | | | | | | | | | |   (552)  all_57_10 = e1 & op(e2, e0) = e1
% 227.06/39.09  | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | | | | | | | | | | | ALPHA: (552) implies:
% 227.06/39.09  | | | | | | | | | | | | | | | | | | | |   (553)  all_57_10 = e1
% 227.06/39.09  | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | | | | | | | | | | | BETA: splitting (81) gives:
% 227.06/39.09  | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.09  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | | | | | | | | | | | |   (554)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 227.06/39.09  | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e0)
% 227.06/39.09  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (554) gives:
% 227.06/39.09  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.09  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.09  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | |   (555)  all_57_2 = e0 & op(e2, e3) = e0
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (555) implies:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | |   (556)  op(e2, e3) = e0
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (17), (468), (556) are inconsistent by
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1943.
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | |   (557)  all_57_3 = e0 & op(e2, e2) = e0
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (557) implies:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | |   (558)  all_57_3 = e0
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (26), (558) imply:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | |   (559)  e3 = e0
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | SIMP: (559) implies:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | |   (560)  e3 = e0
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (60), (560) imply:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | |   (561)  all_57_6 = e0
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (17), (20), (25), (38), (41), (52), (57),
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | |            (68), (78), (82), (83), (86), (90), (102), (117),
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | |            (474), (539), (561) are inconsistent by sub-proof
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | |            #1028.
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | |   (562)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | |            e0 & op(e2, e0) = e0)
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (562) gives:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | |   (563)  all_57_5 = e0 & op(e2, e1) = e0
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (563) implies:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | |   (564)  all_57_5 = e0
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (88) gives:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | |   (565)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e2)
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (565) gives:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | |   (566)  all_57_4 = e2 & op(e3, e1) = e2
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (25), (38), (41), (57), (59), (117), (474),
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | |            (498), (502), (564), (566) are inconsistent by
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1930.
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | |   (567)  all_57_5 = e2 & op(e2, e1) = e2
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (567) implies:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | |   (568)  all_57_5 = e2
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (52), (564), (568) are inconsistent by sub-proof
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | |            #2363.
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | |   (569)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e1) = e2)
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (569) gives:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | |   (570)  all_57_8 = e2 & op(e1, e1) = e2
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (570) implies:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | |   (571)  op(e1, e1) = e2
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (82), (536), (571) are inconsistent by
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2423.
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | |   (572)  all_57_14 = e2 & op(e0, e1) = e2
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (572) implies:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | |   (573)  all_57_14 = e2
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (68) gives:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | |   (574)  all_57_15 = e0 & op(e0, e0) = e0
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (574) implies:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | |   (575)  op(e0, e0) = e0
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (17), (40), (41), (48), (74), (80), (96),
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | |            (553), (575) are inconsistent by sub-proof #2302.
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | |   (576)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (576) implies:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | |   (577)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e0)
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (577) gives:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | |   (578)  all_57_12 = e0 & op(e0, e3) = e0
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (578) implies:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | |   (579)  all_57_12 = e0
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (15), (38), (52), (57), (60), (82), (86),
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | |            (506), (579) are inconsistent by sub-proof #1425.
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | |   (580)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (580) gives:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (581)  all_57_13 = e0 & op(e0, e2) = e0
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (581) implies:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (582)  op(e0, e2) = e0
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (38), (103), (497), (499), (503), (582) are
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #858.
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (583)  all_57_14 = e0 & op(e0, e1) = e0
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (583) implies:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (584)  all_57_14 = e0
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (17), (38), (41), (46), (52), (57), (67),
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (78), (82), (86), (102), (474), (539), (544),
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (573), (584) are inconsistent by sub-proof #936.
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | |   (585)  all_57_10 = e0 & op(e2, e0) = e0
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (585) implies:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | |   (586)  all_57_10 = e0
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (553), (586) imply:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | |   (587)  e1 = e0
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | SIMP: (587) implies:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | |   (588)  e1 = e0
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (539), (588) imply:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | |   (589)  all_57_12 = e0
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (15), (38), (52), (57), (60), (82), (86),
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | |            (506), (589) are inconsistent by sub-proof #1425.
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.10  | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | End of split
% 227.06/39.10  | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.10  | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | |   (590)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 227.06/39.10  | | | | | | | | | | | | | | | | |            e2 & op(e0, e3) = e2)
% 227.06/39.10  | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | BETA: splitting (590) gives:
% 227.06/39.10  | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | |   (591)  all_57_6 = e2 & op(e1, e3) = e2
% 227.06/39.10  | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (60), (591) are inconsistent by sub-proof
% 227.06/39.10  | | | | | | | | | | | | | | | | | |            #2012.
% 227.06/39.10  | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | |   (592)  all_57_12 = e2 & op(e0, e3) = e2
% 227.06/39.10  | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | REF_CLOSE: (82), (539), (592) are inconsistent by sub-proof
% 227.06/39.10  | | | | | | | | | | | | | | | | | |            #1922.
% 227.06/39.10  | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | End of split
% 227.06/39.10  | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | End of split
% 227.06/39.10  | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | Case 2:
% 227.06/39.10  | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | |   (593)  all_57_13 = e1 & op(e0, e2) = e1
% 227.06/39.10  | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | ALPHA: (593) implies:
% 227.06/39.10  | | | | | | | | | | | | | | | |   (594)  all_57_13 = e1
% 227.06/39.10  | | | | | | | | | | | | | | | |   (595)  op(e0, e2) = e1
% 227.06/39.10  | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | BETA: splitting (68) gives:
% 227.06/39.10  | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.10  | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | |   (596)  all_57_15 = e0 & op(e0, e0) = e0
% 227.06/39.10  | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | ALPHA: (596) implies:
% 227.06/39.10  | | | | | | | | | | | | | | | | |   (597)  op(e0, e0) = e0
% 227.06/39.10  | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (41), (103), (597) are inconsistent by
% 227.06/39.10  | | | | | | | | | | | | | | | | |            sub-proof #2304.
% 227.06/39.10  | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.10  | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | |   (598)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 227.06/39.10  | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 227.06/39.10  | | | | | | | | | | | | | | | | |              op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 227.06/39.10  | | | | | | | | | | | | | | | | |                e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 227.06/39.10  | | | | | | | | | | | | | | | | |              e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 227.06/39.10  | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | ALPHA: (598) implies:
% 227.06/39.10  | | | | | | | | | | | | | | | | |   (599)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 227.06/39.10  | | | | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 227.06/39.10  | | | | | | | | | | | | | | | | |              e1) = e0)
% 227.06/39.10  | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | BETA: splitting (599) gives:
% 227.06/39.10  | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | |   (600)  all_57_12 = e0 & op(e0, e3) = e0
% 227.06/39.10  | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | ALPHA: (600) implies:
% 227.06/39.10  | | | | | | | | | | | | | | | | | |   (601)  all_57_12 = e0
% 227.06/39.10  | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (15), (38), (52), (57), (60), (82), (86),
% 227.06/39.10  | | | | | | | | | | | | | | | | | |            (506), (601) are inconsistent by sub-proof #1425.
% 227.06/39.10  | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | |   (602)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 227.06/39.10  | | | | | | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 227.06/39.10  | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | BETA: splitting (602) gives:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | |   (603)  all_57_13 = e0 & op(e0, e2) = e0
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | ALPHA: (603) implies:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | |   (604)  op(e0, e2) = e0
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (38), (103), (497), (499), (503), (604) are
% 227.06/39.10  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #858.
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | |   (605)  all_57_14 = e0 & op(e0, e1) = e0
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | ALPHA: (605) implies:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | |   (606)  all_57_14 = e0
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | BETA: splitting (88) gives:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | |   (607)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e2)
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | BETA: splitting (607) gives:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | |   (608)  all_57_4 = e2 & op(e3, e1) = e2
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | ALPHA: (608) implies:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | |   (609)  all_57_4 = e2
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (37), (38), (609) are inconsistent by sub-proof
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | |            #2482.
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | |   (610)  all_57_5 = e2 & op(e2, e1) = e2
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | ALPHA: (610) implies:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | |   (611)  all_57_5 = e2
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (81) gives:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | |   (612)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e0)
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (612) gives:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | |   (613)  all_57_2 = e0 & op(e2, e3) = e0
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (613) implies:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | |   (614)  op(e2, e3) = e0
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (17), (468), (614) are inconsistent by
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1943.
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | |   (615)  all_57_3 = e0 & op(e2, e2) = e0
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (17), (25), (26), (37), (38), (41), (42),
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | |            (52), (57), (59), (82), (88), (117), (606), (615)
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #192.
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | |   (616)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e2, e0) = e0)
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (616) gives:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | |   (617)  all_57_5 = e0 & op(e2, e1) = e0
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (52), (611), (617) are inconsistent by sub-proof
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | |            #2428.
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | |   (618)  all_57_10 = e0 & op(e2, e0) = e0
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (618) implies:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | |   (619)  all_57_10 = e0
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9) gives:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | |   (620)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (620) gives:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | |   (621)  all_57_2 = e1 & op(e2, e3) = e1
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (621) implies:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | |   (622)  all_57_2 = e1
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (86) gives:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | |   (623)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e2)
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (623) gives:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (624)  all_57_0 = e2 & op(e3, e3) = e2
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (624) implies:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (625)  op(e3, e3) = e2
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (17), (25), (34), (38), (41), (42), (49),
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (52), (57), (59), (82), (88), (96), (117), (470),
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (471), (606), (625) are inconsistent by sub-proof
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1293.
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (626)  all_57_2 = e2 & op(e2, e3) = e2
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (626) implies:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (627)  all_57_2 = e2
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (622), (627) imply:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (628)  e2 = e1
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (628) implies:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (629)  e2 = e1
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (611), (629) imply:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (630)  all_57_5 = e1
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (37), (38), (52), (82), (88), (536), (606),
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (630) are inconsistent by sub-proof #1231.
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | |   (631)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e3) = e2)
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (631) gives:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (632)  all_57_6 = e2 & op(e1, e3) = e2
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (632) implies:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (633)  all_57_6 = e2
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (17), (38), (41), (46), (52), (57), (67),
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (78), (82), (102), (474), (606), (622), (633) are
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #894.
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (634)  all_57_12 = e2 & op(e0, e3) = e2
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (634) implies:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (635)  all_57_12 = e2
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (636)  op(e0, e3) = e2
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (90) gives:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (637)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (637) gives:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (638)  all_57_9 = e1 & op(e3, e0) = e1
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (638) implies:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (639)  all_57_9 = e1
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (32) gives:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (640)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e2)
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (640) gives:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (641)  all_57_0 = e2 & op(e3, e3) = e2
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (641) implies:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (642)  op(e3, e3) = e2
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (17), (25), (34), (38), (41), (42), (49),
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (52), (57), (59), (82), (88), (96), (117), (470),
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (471), (606), (642) are inconsistent by sub-proof
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1293.
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (643)  all_57_1 = e2 & op(e3, e2) = e2
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (643) implies:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (644)  all_57_1 = e2
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (51) gives:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (645)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e0)
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (645) gives:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (646)  all_57_1 = e0 & op(e3, e2) = e0
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (646) implies:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (647)  all_57_1 = e0
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (17), (28), (32), (37), (38), (41), (52),
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (55), (57), (74), (82), (83), (90), (96), (102),
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (103), (474), (506), (619), (647) are inconsistent
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #905.
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (648)  all_57_3 = e0 & op(e2, e2) = e0
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (648) implies:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (649)  all_57_3 = e0
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (26), (649) imply:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (650)  e3 = e0
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (37), (650) imply:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (651)  all_57_4 = e0
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (38), (41), (55), (74), (96), (474), (644),
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (651) are inconsistent by sub-proof #1405.
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (652)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0)
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (652) gives:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (605) implies:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (653)  op(e0, e1) = e0
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_52_29, e0, e1, e0,
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (498), (653) gives:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (654)  all_52_29 = e0
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_52_27, e1, e2, e0,
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (499), (595) gives:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (655)  all_52_27 = e1
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_52_25, e2, e3, e0,
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (500), (636) gives:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (656)  all_52_25 = e2
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (512), (656) imply:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (657)   ~ (e3 = e2)
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (502), (654) imply:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (658)  op(e0, e0) = e1
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (17), (38), (41), (52), (64), (67), (82),
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (594), (606), (658) are inconsistent by sub-proof
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2068.
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (659)  all_57_13 = e0 & op(e0, e2) = e0
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (659) implies:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (660)  op(e0, e2) = e0
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (38), (103), (497), (499), (503), (660) are
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #858.
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (661)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e2)
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (661) gives:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (662)  all_57_4 = e2 & op(e3, e1) = e2
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (662) implies:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (663)  all_57_4 = e2
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (37), (663) imply:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (664)  e3 = e2
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (60), (664) imply:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (665)  all_57_6 = e2
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (15), (17), (38), (41), (52), (57), (78),
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (82), (89), (506), (635), (665) are inconsistent
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1926.
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (666)  all_57_9 = e2 & op(e3, e0) = e2
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (666) implies:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (667)  all_57_9 = e2
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (639), (667) imply:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (668)  e2 = e1
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (668) implies:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (669)  e2 = e1
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (611), (669) imply:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (670)  all_57_5 = e1
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (37), (38), (52), (82), (88), (536), (606),
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (670) are inconsistent by sub-proof #1231.
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (671)  all_57_10 = e1 & op(e2, e0) = e1
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (671) implies:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (672)  all_57_10 = e1
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (57), (619), (672) are inconsistent by sub-proof
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1531.
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (673)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (673) gives:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (674)  all_57_11 = e1 & op(e1, e0) = e1
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (40), (533), (674) are inconsistent by
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #305.
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (675)  all_57_15 = e1 & op(e0, e0) = e1
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (675) implies:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (676)  op(e0, e0) = e1
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (17), (38), (41), (52), (64), (67), (82),
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (594), (606), (676) are inconsistent by sub-proof
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2068.
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | |   (677)  all_57_3 = e1 & op(e2, e2) = e1
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (677) implies:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | |   (678)  all_57_3 = e1
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | |   (679)  op(e2, e2) = e1
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11), (13), (15), (16), (17), (20), (25),
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | |            (28), (32), (34), (36), (38), (41), (42), (45),
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | |            (46), (51), (52), (55), (57), (59), (61), (67),
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | |            (68), (72), (74), (76), (78), (81), (82), (83),
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | |            (86), (88), (89), (90), (91), (94), (95), (96),
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | |            (102), (103), (117), (469), (471), (474), (506),
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | |            (594), (678), (679) are inconsistent by sub-proof
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | |            #976.
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.10  | | | | | | | | | | | | | | | | | | | | | | | |   (680)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (37), (38), (52), (57), (82), (88), (536),
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | |            (606), (619), (680) are inconsistent by sub-proof
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | |            #191.
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | |   (681)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e1) = e2)
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | BETA: splitting (681) gives:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | |   (682)  all_57_8 = e2 & op(e1, e1) = e2
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | ALPHA: (682) implies:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | |   (683)  op(e1, e1) = e2
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (82), (536), (683) are inconsistent by
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | |            sub-proof #2423.
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | |   (684)  all_57_14 = e2 & op(e0, e1) = e2
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (52), (606), (684) are inconsistent by sub-proof
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | |            #2074.
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.11  | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | End of split
% 227.06/39.11  | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | End of split
% 227.06/39.11  | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | End of split
% 227.06/39.11  | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | Case 2:
% 227.06/39.11  | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | |   (685)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 227.06/39.11  | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 227.06/39.11  | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | BETA: splitting (685) gives:
% 227.06/39.11  | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | Case 1:
% 227.06/39.11  | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | |   (686)  all_57_14 = e1 & op(e0, e1) = e1
% 227.06/39.11  | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | ALPHA: (686) implies:
% 227.06/39.11  | | | | | | | | | | | | | | | |   (687)  all_57_14 = e1
% 227.06/39.11  | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | BETA: splitting (68) gives:
% 227.06/39.11  | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.11  | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | |   (688)  all_57_15 = e0 & op(e0, e0) = e0
% 227.06/39.11  | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | ALPHA: (688) implies:
% 227.06/39.11  | | | | | | | | | | | | | | | | |   (689)  op(e0, e0) = e0
% 227.06/39.11  | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (41), (103), (689) are inconsistent by
% 227.06/39.11  | | | | | | | | | | | | | | | | |            sub-proof #2304.
% 227.06/39.11  | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.11  | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | |   (690)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 227.06/39.11  | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 227.06/39.11  | | | | | | | | | | | | | | | | |              op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 227.06/39.11  | | | | | | | | | | | | | | | | |                e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 227.06/39.11  | | | | | | | | | | | | | | | | |              e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 227.06/39.11  | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | ALPHA: (690) implies:
% 227.06/39.11  | | | | | | | | | | | | | | | | |   (691)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 227.06/39.11  | | | | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 227.06/39.11  | | | | | | | | | | | | | | | | |              e1) = e0)
% 227.06/39.11  | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | BETA: splitting (691) gives:
% 227.06/39.11  | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | |   (692)  all_57_12 = e0 & op(e0, e3) = e0
% 227.06/39.11  | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | ALPHA: (692) implies:
% 227.06/39.11  | | | | | | | | | | | | | | | | | |   (693)  all_57_12 = e0
% 227.06/39.11  | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (15), (38), (52), (57), (60), (82), (86),
% 227.06/39.11  | | | | | | | | | | | | | | | | | |            (506), (693) are inconsistent by sub-proof #1425.
% 227.06/39.11  | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | |   (694)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 227.06/39.11  | | | | | | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 227.06/39.11  | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (38), (57), (103), (497), (499), (503),
% 227.06/39.11  | | | | | | | | | | | | | | | | | |            (687), (694) are inconsistent by sub-proof #190.
% 227.06/39.11  | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | End of split
% 227.06/39.11  | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | End of split
% 227.06/39.11  | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | Case 2:
% 227.06/39.11  | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | |   (695)  all_57_15 = e1 & op(e0, e0) = e1
% 227.06/39.11  | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | ALPHA: (695) implies:
% 227.06/39.11  | | | | | | | | | | | | | | | |   (696)  op(e0, e0) = e1
% 227.06/39.11  | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | REF_CLOSE: (15), (17), (103), (696) are inconsistent by
% 227.06/39.11  | | | | | | | | | | | | | | | |            sub-proof #2183.
% 227.06/39.11  | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | End of split
% 227.06/39.11  | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | End of split
% 227.06/39.11  | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | Case 2:
% 227.06/39.11  | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | |   (697)  all_55_10 = e0
% 227.06/39.11  | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | REF_CLOSE: (69), (521), (697) are inconsistent by sub-proof
% 227.06/39.11  | | | | | | | | | | | | | |            #2118.
% 227.06/39.11  | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | End of split
% 227.06/39.11  | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | End of split
% 227.06/39.11  | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | End of split
% 227.06/39.11  | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | Case 2:
% 227.06/39.11  | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | |   (698)  all_38_2 = e2
% 227.06/39.11  | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | COMBINE_EQS: (73), (698) imply:
% 227.06/39.11  | | | | | | | | | | |   (699)  all_6_2 = e2
% 227.06/39.11  | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | SIMP: (699) implies:
% 227.06/39.11  | | | | | | | | | | |   (700)  all_6_2 = e2
% 227.06/39.11  | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | REDUCE: (515), (700) imply:
% 227.06/39.11  | | | | | | | | | | |   (701)   ~ (all_52_29 = e2)
% 227.06/39.11  | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | REDUCE: (117), (700) imply:
% 227.06/39.11  | | | | | | | | | | |   (702)   ~ (e3 = e2)
% 227.06/39.11  | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | REDUCE: (25), (700) imply:
% 227.06/39.11  | | | | | | | | | | |   (703)  op(e1, e1) = e2
% 227.06/39.11  | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | BETA: splitting (32) gives:
% 227.06/39.11  | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | Case 1:
% 227.06/39.11  | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | |   (704)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 227.06/39.11  | | | | | | | | | | | |            & op(e3, e2) = e2)
% 227.06/39.11  | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | BETA: splitting (704) gives:
% 227.06/39.11  | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | Case 1:
% 227.06/39.11  | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | |   (705)  all_57_0 = e2 & op(e3, e3) = e2
% 227.06/39.11  | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | ALPHA: (705) implies:
% 227.06/39.11  | | | | | | | | | | | | |   (706)  op(e3, e3) = e2
% 227.06/39.11  | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | REF_CLOSE: (17), (52), (474), (706) are inconsistent by
% 227.06/39.11  | | | | | | | | | | | | |            sub-proof #2403.
% 227.06/39.11  | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | Case 2:
% 227.06/39.11  | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | |   (707)  all_57_1 = e2 & op(e3, e2) = e2
% 227.06/39.11  | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | ALPHA: (707) implies:
% 227.06/39.11  | | | | | | | | | | | | |   (708)  all_57_1 = e2
% 227.06/39.11  | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | REF_CLOSE: (3), (9), (10), (15), (16), (17), (20), (25),
% 227.06/39.11  | | | | | | | | | | | | |            (26), (28), (32), (37), (38), (41), (42), (44),
% 227.06/39.11  | | | | | | | | | | | | |            (52), (55), (57), (60), (68), (74), (77), (81),
% 227.06/39.11  | | | | | | | | | | | | |            (82), (83), (86), (90), (91), (96), (102), (103),
% 227.06/39.11  | | | | | | | | | | | | |            (117), (468), (474), (497), (499), (501), (503),
% 227.06/39.11  | | | | | | | | | | | | |            (506), (521), (703), (708) are inconsistent by
% 227.06/39.11  | | | | | | | | | | | | |            sub-proof #189.
% 227.06/39.11  | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | End of split
% 227.06/39.11  | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | Case 2:
% 227.06/39.11  | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | |   (709)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 227.06/39.11  | | | | | | | | | | | |            & op(e3, e0) = e2)
% 227.06/39.11  | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | BETA: splitting (709) gives:
% 227.06/39.11  | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | Case 1:
% 227.06/39.11  | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | |   (710)  all_57_4 = e2 & op(e3, e1) = e2
% 227.06/39.11  | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | ALPHA: (710) implies:
% 227.06/39.11  | | | | | | | | | | | | |   (711)  all_57_4 = e2
% 227.06/39.11  | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | COMBINE_EQS: (37), (711) imply:
% 227.06/39.11  | | | | | | | | | | | | |   (712)  e3 = e2
% 227.06/39.11  | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | SIMP: (712) implies:
% 227.06/39.11  | | | | | | | | | | | | |   (713)  e3 = e2
% 227.06/39.11  | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | COMBINE_EQS: (60), (713) imply:
% 227.06/39.11  | | | | | | | | | | | | |   (714)  all_57_6 = e2
% 227.06/39.11  | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (20), (25), (38), (41), (52),
% 227.06/39.11  | | | | | | | | | | | | |            (57), (68), (82), (83), (90), (91), (102), (117),
% 227.06/39.11  | | | | | | | | | | | | |            (521), (703), (714) are inconsistent by sub-proof
% 227.06/39.11  | | | | | | | | | | | | |            #203.
% 227.06/39.11  | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | Case 2:
% 227.06/39.11  | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | |   (715)  all_57_9 = e2 & op(e3, e0) = e2
% 227.06/39.11  | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | ALPHA: (715) implies:
% 227.06/39.11  | | | | | | | | | | | | |   (716)  all_57_9 = e2
% 227.06/39.11  | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | BETA: splitting (28) gives:
% 227.06/39.11  | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | Case 1:
% 227.06/39.11  | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | |   (717)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 227.06/39.11  | | | | | | | | | | | | | |            & op(e3, e2) = e1)
% 227.06/39.11  | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | BETA: splitting (717) gives:
% 227.06/39.11  | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | Case 1:
% 227.06/39.11  | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | |   (718)  all_57_0 = e1 & op(e3, e3) = e1
% 227.06/39.11  | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | ALPHA: (718) implies:
% 227.06/39.11  | | | | | | | | | | | | | | |   (719)  op(e3, e3) = e1
% 227.06/39.11  | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | REF_CLOSE: (17), (57), (103), (497), (501), (719) are
% 227.06/39.11  | | | | | | | | | | | | | | |            inconsistent by sub-proof #283.
% 227.06/39.11  | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | Case 2:
% 227.06/39.11  | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | |   (720)  all_57_1 = e1 & op(e3, e2) = e1
% 227.06/39.11  | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | ALPHA: (720) implies:
% 227.06/39.11  | | | | | | | | | | | | | | |   (721)  all_57_1 = e1
% 227.06/39.11  | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | BETA: splitting (13) gives:
% 227.06/39.11  | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | Case 1:
% 227.06/39.11  | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | |   (722)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 227.06/39.11  | | | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 227.06/39.11  | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | BETA: splitting (722) gives:
% 227.06/39.11  | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.11  | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | |   (723)  all_57_1 = e2 & op(e3, e2) = e2
% 227.06/39.11  | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | ALPHA: (723) implies:
% 227.06/39.11  | | | | | | | | | | | | | | | | |   (724)  all_57_1 = e2
% 227.06/39.11  | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (9), (10), (15), (16), (17), (20), (25),
% 227.06/39.11  | | | | | | | | | | | | | | | | |            (26), (28), (32), (37), (38), (41), (42), (44),
% 227.06/39.11  | | | | | | | | | | | | | | | | |            (52), (55), (57), (60), (68), (74), (77), (81),
% 227.06/39.11  | | | | | | | | | | | | | | | | |            (82), (83), (86), (90), (91), (96), (102), (103),
% 227.06/39.11  | | | | | | | | | | | | | | | | |            (117), (468), (474), (497), (499), (501), (503),
% 227.06/39.11  | | | | | | | | | | | | | | | | |            (506), (521), (703), (724) are inconsistent by
% 227.06/39.11  | | | | | | | | | | | | | | | | |            sub-proof #189.
% 227.06/39.11  | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.11  | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | |   (725)  all_57_3 = e2 & op(e2, e2) = e2
% 227.06/39.11  | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | ALPHA: (725) implies:
% 227.06/39.11  | | | | | | | | | | | | | | | | |   (726)  op(e2, e2) = e2
% 227.06/39.11  | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (38), (77), (726) are inconsistent by
% 227.06/39.11  | | | | | | | | | | | | | | | | |            sub-proof #2298.
% 227.06/39.11  | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | End of split
% 227.06/39.11  | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | Case 2:
% 227.06/39.11  | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | |   (727)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 227.06/39.11  | | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 227.06/39.11  | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | BETA: splitting (727) gives:
% 227.06/39.11  | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.11  | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | |   (728)  all_57_7 = e2 & op(e1, e2) = e2
% 227.06/39.11  | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | ALPHA: (728) implies:
% 227.06/39.11  | | | | | | | | | | | | | | | | |   (729)  all_57_7 = e2
% 227.06/39.11  | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | BETA: splitting (51) gives:
% 227.06/39.11  | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | |   (730)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 227.06/39.11  | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e0)
% 227.06/39.11  | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | BETA: splitting (730) gives:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | |   (731)  all_57_1 = e0 & op(e3, e2) = e0
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | ALPHA: (731) implies:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | |   (732)  op(e3, e2) = e0
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (49), (470), (732) are inconsistent by
% 227.06/39.11  | | | | | | | | | | | | | | | | | | |            sub-proof #1941.
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | |   (733)  all_57_3 = e0 & op(e2, e2) = e0
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | ALPHA: (733) implies:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | |   (734)  all_57_3 = e0
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (26), (734) imply:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | |   (735)  e3 = e0
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (60), (735) imply:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | |   (736)  all_57_6 = e0
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (17), (20), (25), (38), (41), (52), (57),
% 227.06/39.11  | | | | | | | | | | | | | | | | | | |            (68), (82), (83), (90), (102), (117), (729), (736)
% 227.06/39.11  | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1775.
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.11  | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | |   (737)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 227.06/39.11  | | | | | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0)
% 227.06/39.11  | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | BETA: splitting (737) gives:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | |   (738)  all_57_7 = e0 & op(e1, e2) = e0
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (52), (729), (738) are inconsistent by sub-proof
% 227.06/39.11  | | | | | | | | | | | | | | | | | | |            #2148.
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | |   (739)  all_57_13 = e0 & op(e0, e2) = e0
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | ALPHA: (739) implies:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | |   (740)  op(e0, e2) = e0
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (38), (103), (497), (499), (503), (740) are
% 227.06/39.11  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #858.
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.11  | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | End of split
% 227.06/39.11  | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.11  | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | |   (741)  all_57_13 = e2 & op(e0, e2) = e2
% 227.06/39.11  | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | ALPHA: (741) implies:
% 227.06/39.11  | | | | | | | | | | | | | | | | |   (742)  all_57_13 = e2
% 227.06/39.11  | | | | | | | | | | | | | | | | |   (743)  op(e0, e2) = e2
% 227.06/39.11  | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | BETA: splitting (51) gives:
% 227.06/39.11  | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | |   (744)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 227.06/39.11  | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e0)
% 227.06/39.11  | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | BETA: splitting (744) gives:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | |   (745)  all_57_1 = e0 & op(e3, e2) = e0
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | ALPHA: (745) implies:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | |   (746)  op(e3, e2) = e0
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (49), (470), (746) are inconsistent by
% 227.06/39.11  | | | | | | | | | | | | | | | | | | |            sub-proof #1941.
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | |   (747)  all_57_3 = e0 & op(e2, e2) = e0
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | ALPHA: (747) implies:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | |   (748)  all_57_3 = e0
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (26), (748) imply:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | |   (749)  e3 = e0
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | SIMP: (749) implies:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | |   (750)  e3 = e0
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (60), (750) imply:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | |   (751)  all_57_6 = e0
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (15), (17), (20), (25), (38), (41), (52),
% 227.06/39.11  | | | | | | | | | | | | | | | | | | |            (57), (68), (78), (82), (83), (86), (90), (102),
% 227.06/39.11  | | | | | | | | | | | | | | | | | | |            (117), (474), (506), (751) are inconsistent by
% 227.06/39.11  | | | | | | | | | | | | | | | | | | |            sub-proof #869.
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.11  | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | |   (752)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 227.06/39.11  | | | | | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0)
% 227.06/39.11  | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | BETA: splitting (752) gives:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | |   (753)  all_57_7 = e0 & op(e1, e2) = e0
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | ALPHA: (753) implies:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | |   (754)  all_57_7 = e0
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | BETA: splitting (91) gives:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | |   (755)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e1)
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | BETA: splitting (755) gives:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | |   (756)  all_57_6 = e1 & op(e1, e3) = e1
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | ALPHA: (756) implies:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | |   (757)  all_57_6 = e1
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (17), (20), (25), (38), (41), (52), (57),
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | |            (68), (82), (83), (90), (102), (117), (754), (757)
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1735.
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | |   (758)  all_57_7 = e1 & op(e1, e2) = e1
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (57), (754), (758) are inconsistent by sub-proof
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | |            #2200.
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | |   (759)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | |            e1 & op(e1, e0) = e1)
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | BETA: splitting (759) gives:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | |   (760)  all_57_8 = e1 & op(e1, e1) = e1
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | ALPHA: (760) implies:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | |   (761)  op(e1, e1) = e1
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (82), (703), (761) are inconsistent by
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | |            sub-proof #2423.
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | |   (762)  all_57_11 = e1 & op(e1, e0) = e1
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | ALPHA: (762) implies:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | |   (763)  all_57_11 = e1
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (68) gives:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | |   (764)  all_57_15 = e0 & op(e0, e0) = e0
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (764) implies:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | |   (765)  op(e0, e0) = e0
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (41), (103), (765) are inconsistent by
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2304.
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | |   (766)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | |                e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (766) implies:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | |   (767)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | |              e1) = e0)
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | |   (768)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | |              e0) = e0)
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (767) gives:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | |   (769)  all_57_12 = e0 & op(e0, e3) = e0
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (769) implies:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | |   (770)  all_57_12 = e0
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (15), (38), (52), (57), (60), (82), (86),
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | |            (506), (770) are inconsistent by sub-proof #1425.
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | |   (771)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (771) gives:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | |   (772)  all_57_13 = e0 & op(e0, e2) = e0
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (772) implies:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | |   (773)  op(e0, e2) = e0
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (38), (103), (497), (499), (503), (773) are
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #858.
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | |   (774)  all_57_14 = e0 & op(e0, e1) = e0
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (774) implies:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | |   (775)  all_57_14 = e0
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (46) gives:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | |   (776)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (776) gives:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | |   (777)  all_57_12 = e1 & op(e0, e3) = e1
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (777) implies:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | |   (778)  all_57_12 = e1
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | |   (779)  op(e0, e3) = e1
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (768) gives:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (780)  all_57_9 = e0 & op(e3, e0) = e0
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (96), (471), (780) are inconsistent by
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2434.
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (781)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 =
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (781) gives:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (782)  all_57_10 = e0 & op(e2, e0) = e0
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (782) implies:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (783)  all_57_10 = e0
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (90) gives:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (784)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (784) gives:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (785)  all_57_9 = e1 & op(e3, e0) = e1
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (785) implies:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (786)  all_57_9 = e1
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (38), (52), (54), (82), (83), (102), (519),
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (779), (783), (786) are inconsistent by sub-proof
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1018.
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (787)  all_57_10 = e1 & op(e2, e0) = e1
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (787) implies:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (788)  all_57_10 = e1
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (783), (788) imply:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (789)  e1 = e0
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (789) implies:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (790)  e1 = e0
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (721), (790) imply:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (791)  all_57_1 = e0
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (17), (28), (32), (37), (38), (41), (52),
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (55), (57), (74), (82), (83), (90), (96), (102),
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (103), (474), (506), (763), (783), (791) are
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #906.
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (792)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (792) gives:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (774) implies:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (793)  op(e0, e1) = e0
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_52_29, e0, e1, e0,
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (498), (793) gives:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (794)  all_52_29 = e0
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_52_27, e2, e2, e0,
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (499), (743) gives:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (795)  all_52_27 = e2
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_52_25, e1, e3, e0,
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (500), (779) gives:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (796)  all_52_25 = e1
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (511), (795), (796) imply:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (797)   ~ (e2 = e1)
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (512), (796) imply:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (798)   ~ (e3 = e1)
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (701), (794) imply:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (799)   ~ (e2 = e0)
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (502), (794) imply:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (800)  op(e0, e0) = e1
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (17), (38), (41), (52), (64), (67), (82),
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (775), (778), (800) are inconsistent by sub-proof
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2070.
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (801)  all_57_15 = e1 & op(e0, e0) = e1
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (801) implies:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (802)  op(e0, e0) = e1
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (17), (38), (41), (52), (64), (67), (82),
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (775), (778), (802) are inconsistent by sub-proof
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2070.
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (803)  all_57_11 = e0 & op(e1, e0) = e0
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (803) implies:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (804)  all_57_11 = e0
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (763), (804) imply:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (805)  e1 = e0
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (17), (28), (32), (37), (38), (41), (52),
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (55), (57), (74), (82), (90), (96), (103), (474),
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (506), (716), (721), (763), (805) are inconsistent
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #188.
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | |   (806)  all_57_13 = e1 & op(e0, e2) = e1
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (82), (742), (806) are inconsistent by sub-proof
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            #2205.
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | |   (807)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (807) gives:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | |   (808)  all_57_14 = e1 & op(e0, e1) = e1
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (808) implies:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | |   (809)  all_57_14 = e1
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (775), (809) imply:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | |   (810)  e1 = e0
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (17), (28), (32), (37), (38), (41), (52),
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            (55), (57), (74), (82), (90), (96), (103), (474),
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            (506), (716), (721), (763), (810) are inconsistent
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #188.
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | |   (811)  all_57_15 = e1 & op(e0, e0) = e1
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (811) implies:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | |   (812)  op(e0, e0) = e1
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (17), (103), (812) are inconsistent by
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2183.
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | |   (813)  all_57_13 = e0 & op(e0, e2) = e0
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | ALPHA: (813) implies:
% 227.06/39.11  | | | | | | | | | | | | | | | | | | |   (814)  op(e0, e2) = e0
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (38), (103), (497), (499), (503), (814) are
% 227.06/39.11  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #858.
% 227.06/39.11  | | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | | End of split
% 227.06/39.11  | | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | | End of split
% 227.06/39.11  | | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | | End of split
% 227.06/39.11  | | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | | End of split
% 227.06/39.11  | | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | | End of split
% 227.06/39.11  | | | | | | | | | | | | | | 
% 227.06/39.11  | | | | | | | | | | | | | Case 2:
% 227.06/39.11  | | | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | | |   (815)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 227.06/39.12  | | | | | | | | | | | | | |            & op(e3, e0) = e1)
% 227.06/39.12  | | | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | | | REF_CLOSE: (15), (37), (82), (716), (815) are inconsistent by
% 227.06/39.12  | | | | | | | | | | | | | |            sub-proof #1194.
% 227.06/39.12  | | | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | | End of split
% 227.06/39.12  | | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | End of split
% 227.06/39.12  | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | End of split
% 227.06/39.12  | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | End of split
% 227.06/39.12  | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | Case 2:
% 227.06/39.12  | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | |   (816)  all_24_2 = e0
% 227.06/39.12  | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | COMBINE_EQS: (87), (816) imply:
% 227.06/39.12  | | | | | | | | | |   (817)  all_6_2 = e0
% 227.06/39.12  | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | SIMP: (817) implies:
% 227.06/39.12  | | | | | | | | | |   (818)  all_6_2 = e0
% 227.06/39.12  | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | REDUCE: (70), (818) imply:
% 227.06/39.12  | | | | | | | | | |   (819)   ~ (all_53_6 = e0)
% 227.06/39.12  | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | REDUCE: (33), (818) imply:
% 227.06/39.12  | | | | | | | | | |   (820)   ~ (all_53_9 = e0)
% 227.06/39.12  | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | BETA: splitting (81) gives:
% 227.06/39.12  | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | Case 1:
% 227.06/39.12  | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | |   (821)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 227.06/39.12  | | | | | | | | | | |            & op(e2, e2) = e0)
% 227.06/39.12  | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | BETA: splitting (821) gives:
% 227.06/39.12  | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | Case 1:
% 227.06/39.12  | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | |   (822)  all_57_2 = e0 & op(e2, e3) = e0
% 227.06/39.12  | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | ALPHA: (822) implies:
% 227.06/39.12  | | | | | | | | | | | |   (823)  op(e2, e3) = e0
% 227.06/39.12  | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | REF_CLOSE: (10), (17), (468), (823) are inconsistent by
% 227.06/39.12  | | | | | | | | | | | |            sub-proof #1943.
% 227.06/39.12  | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | Case 2:
% 227.06/39.12  | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | |   (824)  all_57_3 = e0 & op(e2, e2) = e0
% 227.06/39.12  | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | ALPHA: (824) implies:
% 227.06/39.12  | | | | | | | | | | | |   (825)  all_57_3 = e0
% 227.06/39.12  | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | COMBINE_EQS: (26), (825) imply:
% 227.06/39.12  | | | | | | | | | | | |   (826)  e3 = e0
% 227.06/39.12  | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | COMBINE_EQS: (60), (826) imply:
% 227.06/39.12  | | | | | | | | | | | |   (827)  all_57_6 = e0
% 227.06/39.12  | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | REF_CLOSE: (11), (15), (17), (20), (25), (38), (41), (52),
% 227.06/39.12  | | | | | | | | | | | |            (57), (68), (78), (82), (83), (86), (90), (102),
% 227.06/39.12  | | | | | | | | | | | |            (117), (474), (506), (827) are inconsistent by
% 227.06/39.12  | | | | | | | | | | | |            sub-proof #869.
% 227.06/39.12  | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | End of split
% 227.06/39.12  | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | Case 2:
% 227.06/39.12  | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | |   (828)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 227.06/39.12  | | | | | | | | | | |            e0 & op(e2, e0) = e0)
% 227.06/39.12  | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | BETA: splitting (828) gives:
% 227.06/39.12  | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | Case 1:
% 227.06/39.12  | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | |   (829)  all_57_5 = e0 & op(e2, e1) = e0
% 227.06/39.12  | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | REF_CLOSE: (17), (84), (820), (829) are inconsistent by
% 227.06/39.12  | | | | | | | | | | | |            sub-proof #2023.
% 227.06/39.12  | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | Case 2:
% 227.06/39.12  | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | |   (830)  all_57_10 = e0 & op(e2, e0) = e0
% 227.06/39.12  | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | ALPHA: (830) implies:
% 227.06/39.12  | | | | | | | | | | | |   (831)  all_57_10 = e0
% 227.06/39.12  | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | BETA: splitting (68) gives:
% 227.06/39.12  | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | Case 1:
% 227.06/39.12  | | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | |   (832)  all_57_15 = e0 & op(e0, e0) = e0
% 227.06/39.12  | | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | | ALPHA: (832) implies:
% 227.06/39.12  | | | | | | | | | | | | |   (833)  op(e0, e0) = e0
% 227.06/39.12  | | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | | REF_CLOSE: (17), (41), (103), (833) are inconsistent by
% 227.06/39.12  | | | | | | | | | | | | |            sub-proof #2304.
% 227.06/39.12  | | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | Case 2:
% 227.06/39.12  | | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | |   (834)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 227.06/39.12  | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 227.06/39.12  | | | | | | | | | | | | |              op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 227.06/39.12  | | | | | | | | | | | | |                e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 227.06/39.12  | | | | | | | | | | | | |              e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 227.06/39.12  | | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | | ALPHA: (834) implies:
% 227.06/39.12  | | | | | | | | | | | | |   (835)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 227.06/39.12  | | | | | | | | | | | | |            e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 227.06/39.12  | | | | | | | | | | | | |              e1) = e0)
% 227.06/39.12  | | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | | BETA: splitting (835) gives:
% 227.06/39.12  | | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | | Case 1:
% 227.06/39.12  | | | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | | |   (836)  all_57_12 = e0 & op(e0, e3) = e0
% 227.06/39.12  | | | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | | | ALPHA: (836) implies:
% 227.06/39.12  | | | | | | | | | | | | | |   (837)  all_57_12 = e0
% 227.06/39.12  | | | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | | | REF_CLOSE: (11), (15), (38), (52), (57), (60), (82), (86),
% 227.06/39.12  | | | | | | | | | | | | | |            (506), (837) are inconsistent by sub-proof #1425.
% 227.06/39.12  | | | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | | Case 2:
% 227.06/39.12  | | | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | | |   (838)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 227.06/39.12  | | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 227.06/39.12  | | | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | | | BETA: splitting (838) gives:
% 227.06/39.12  | | | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | | | Case 1:
% 227.06/39.12  | | | | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | | | |   (839)  all_57_13 = e0 & op(e0, e2) = e0
% 227.06/39.12  | | | | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | | | | ALPHA: (839) implies:
% 227.06/39.12  | | | | | | | | | | | | | | |   (840)  op(e0, e2) = e0
% 227.06/39.12  | | | | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | | | | REF_CLOSE: (17), (38), (103), (497), (499), (503), (840) are
% 227.06/39.12  | | | | | | | | | | | | | | |            inconsistent by sub-proof #858.
% 227.06/39.12  | | | | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | | | Case 2:
% 227.06/39.12  | | | | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | | | |   (841)  all_57_14 = e0 & op(e0, e1) = e0
% 227.06/39.12  | | | | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | | | | ALPHA: (841) implies:
% 227.06/39.12  | | | | | | | | | | | | | | |   (842)  all_57_14 = e0
% 227.06/39.12  | | | | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | | | | BETA: splitting (51) gives:
% 227.06/39.12  | | | | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | | | | Case 1:
% 227.06/39.12  | | | | | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | | | | |   (843)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 227.06/39.12  | | | | | | | | | | | | | | | |            & op(e2, e2) = e0)
% 227.06/39.12  | | | | | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | | | | | BETA: splitting (843) gives:
% 227.06/39.12  | | | | | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.12  | | | | | | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | | | | | |   (844)  all_57_1 = e0 & op(e3, e2) = e0
% 227.06/39.12  | | | | | | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | | | | | | ALPHA: (844) implies:
% 227.06/39.12  | | | | | | | | | | | | | | | | |   (845)  all_57_1 = e0
% 227.06/39.12  | | | | | | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (17), (28), (32), (37), (38), (41), (52),
% 227.06/39.12  | | | | | | | | | | | | | | | | |            (55), (57), (74), (82), (83), (90), (96), (102),
% 227.06/39.12  | | | | | | | | | | | | | | | | |            (103), (474), (506), (831), (845) are inconsistent
% 227.06/39.12  | | | | | | | | | | | | | | | | |            by sub-proof #905.
% 227.06/39.12  | | | | | | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.12  | | | | | | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | | | | | |   (846)  all_57_3 = e0 & op(e2, e2) = e0
% 227.06/39.12  | | | | | | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (17), (25), (26), (37), (38), (41), (42),
% 227.06/39.12  | | | | | | | | | | | | | | | | |            (52), (57), (59), (82), (88), (117), (842), (846)
% 227.06/39.12  | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #192.
% 227.06/39.12  | | | | | | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | | | | | End of split
% 227.06/39.12  | | | | | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | | | | Case 2:
% 227.06/39.12  | | | | | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | | | | |   (847)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 227.06/39.12  | | | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0)
% 227.06/39.12  | | | | | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | | | | | BETA: splitting (847) gives:
% 227.06/39.12  | | | | | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.12  | | | | | | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | | | | | |   (848)  all_57_7 = e0 & op(e1, e2) = e0
% 227.06/39.12  | | | | | | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (85), (819), (848) are inconsistent by
% 227.06/39.12  | | | | | | | | | | | | | | | | |            sub-proof #2039.
% 227.06/39.12  | | | | | | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.12  | | | | | | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | | | | | |   (849)  all_57_13 = e0 & op(e0, e2) = e0
% 227.06/39.12  | | | | | | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | | | | | | ALPHA: (849) implies:
% 227.06/39.12  | | | | | | | | | | | | | | | | |   (850)  op(e0, e2) = e0
% 227.06/39.12  | | | | | | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (38), (103), (497), (499), (503), (850) are
% 227.06/39.12  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #858.
% 227.06/39.12  | | | | | | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | | | | | End of split
% 227.06/39.12  | | | | | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | | | | End of split
% 227.06/39.12  | | | | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | | | End of split
% 227.06/39.12  | | | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | | End of split
% 227.06/39.12  | | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | End of split
% 227.06/39.12  | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | End of split
% 227.06/39.12  | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | End of split
% 227.06/39.12  | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | End of split
% 227.06/39.12  | | | | | | | | | 
% 227.06/39.12  | | | | | | | | End of split
% 227.06/39.12  | | | | | | | | 
% 227.06/39.12  | | | | | | | Case 2:
% 227.06/39.12  | | | | | | | | 
% 227.06/39.12  | | | | | | | |   (851)  all_57_2 = e0 & op(e2, e3) = e0
% 227.06/39.12  | | | | | | | | 
% 227.06/39.12  | | | | | | | | ALPHA: (851) implies:
% 227.06/39.12  | | | | | | | |   (852)  op(e2, e3) = e0
% 227.06/39.12  | | | | | | | | 
% 227.06/39.12  | | | | | | | | REF_CLOSE: (10), (17), (468), (852) are inconsistent by
% 227.06/39.12  | | | | | | | |            sub-proof #1943.
% 227.06/39.12  | | | | | | | | 
% 227.06/39.12  | | | | | | | End of split
% 227.06/39.12  | | | | | | | 
% 227.06/39.12  | | | | | | Case 2:
% 227.06/39.12  | | | | | | | 
% 227.06/39.12  | | | | | | |   (853)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 &
% 227.06/39.12  | | | | | | |            op(e0, e3) = e0)
% 227.06/39.12  | | | | | | | 
% 227.06/39.12  | | | | | | | REF_CLOSE: (17), (41), (45), (60), (469), (853) are inconsistent
% 227.06/39.12  | | | | | | |            by sub-proof #193.
% 227.06/39.12  | | | | | | | 
% 227.06/39.12  | | | | | | End of split
% 227.06/39.12  | | | | | | 
% 227.06/39.12  | | | | | End of split
% 227.06/39.12  | | | | | 
% 227.06/39.12  | | | | End of split
% 227.06/39.12  | | | | 
% 227.06/39.12  | | | End of split
% 227.06/39.12  | | | 
% 227.06/39.12  | | End of split
% 227.06/39.12  | | 
% 227.06/39.12  | End of split
% 227.06/39.12  | 
% 227.06/39.12  End of proof
% 227.06/39.12  
% 227.06/39.12  Sub-proof #188 shows that the following formulas are inconsistent:
% 227.06/39.12  ----------------------------------------------------------------
% 227.06/39.12    (1)  all_57_9 = e2
% 227.06/39.12    (2)   ~ (e3 = e1)
% 227.06/39.12    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.06/39.12           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.06/39.12    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 227.06/39.12         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 227.06/39.12    (5)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 227.06/39.12         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 227.06/39.12    (6)  all_57_4 = e3
% 227.06/39.12    (7)   ~ (e3 = e2)
% 227.06/39.12    (8)   ~ (e3 = e0)
% 227.06/39.12    (9)  all_57_0 = e0
% 227.06/39.12    (10)  all_57_1 = e1
% 227.06/39.12    (11)  op(e3, e3) = e0
% 227.06/39.12    (12)   ~ (e2 = e0)
% 227.06/39.12    (13)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 227.06/39.12          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 227.06/39.12    (14)   ~ (e1 = e0)
% 227.06/39.12    (15)  e1 = e0
% 227.06/39.12    (16)  op(e0, e0) = e3
% 227.06/39.12    (17)   ~ (all_53_12 = e3)
% 227.06/39.12    (18)  all_57_11 = e1
% 227.06/39.12    (19)   ~ (e2 = e1)
% 227.06/39.12    (20)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 227.06/39.12          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 227.06/39.12    (21)  op(e3, e0) = all_53_12
% 227.06/39.12  
% 227.06/39.12  Begin of proof
% 227.06/39.12  | 
% 227.06/39.12  | COMBINE_EQS: (15), (18) imply:
% 227.06/39.12  |   (22)  all_57_11 = e0
% 227.06/39.12  | 
% 227.06/39.12  | COMBINE_EQS: (10), (15) imply:
% 227.06/39.12  |   (23)  all_57_1 = e0
% 227.06/39.12  | 
% 227.06/39.12  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13),
% 227.06/39.12  |            (14), (16), (17), (19), (20), (21), (22), (23) are inconsistent by
% 227.06/39.12  |            sub-proof #902.
% 227.06/39.12  | 
% 227.06/39.12  End of proof
% 227.06/39.12  
% 227.06/39.12  Sub-proof #189 shows that the following formulas are inconsistent:
% 227.06/39.12  ----------------------------------------------------------------
% 227.06/39.12    (1)  op(e0, e0) = all_4_2
% 227.06/39.12    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 227.06/39.12         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 227.06/39.12    (3)  op(e2, e3) = all_53_1
% 227.06/39.12    (4)   ~ (e3 = e1)
% 227.06/39.12    (5)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 227.06/39.12         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 227.06/39.12    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.06/39.12           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.06/39.12    (7)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 227.06/39.12         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 227.06/39.12    (8)   ~ (all_6_2 = e3)
% 227.06/39.12    (9)  op(e1, e1) = all_6_2
% 227.06/39.12    (10)  all_57_3 = e3
% 227.06/39.12    (11)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 227.06/39.12          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 227.06/39.12    (12)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 227.06/39.12          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 227.06/39.12    (13)  all_57_4 = e3
% 227.06/39.12    (14)   ~ (e3 = e2)
% 227.06/39.12    (15)   ~ (e3 = e0)
% 227.06/39.12    (16)  all_57_1 = e2
% 227.06/39.12    (17)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 227.06/39.12          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 227.06/39.12    (18)   ~ (all_4_2 = e2)
% 227.06/39.12    (19)  all_57_0 = e0
% 227.06/39.12    (20)  all_57_15 = e3
% 227.06/39.12    (21)  op(e3, e3) = e0
% 227.06/39.12    (22)  op(e0, e0) = all_52_31
% 227.06/39.12    (23)   ~ (e2 = e0)
% 227.06/39.12    (24)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 227.06/39.12          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 227.06/39.12    (25)   ~ (all_53_1 = e0)
% 227.06/39.12    (26)   ~ (e1 = e0)
% 227.06/39.12    (27)  all_57_6 = e3
% 227.06/39.12    (28)  op(e0, e0) = e3
% 227.06/39.12    (29)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 227.06/39.12              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 227.06/39.12                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 227.06/39.12                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 227.06/39.12    (30)  op(e1, e1) = e2
% 227.06/39.12    (31)   ~ (all_53_12 = e3)
% 227.06/39.12    (32)  op(e0, e2) = all_52_27
% 227.06/39.12    (33)  op(e2, e2) = e3
% 227.06/39.12    (34)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 227.06/39.12          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 227.06/39.12    (35)   ~ (e2 = e1)
% 227.06/39.12    (36)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 227.06/39.12          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 227.06/39.12    (37)   ~ (all_6_2 = e0)
% 227.06/39.12    (38)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 227.06/39.12          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 227.06/39.12    (39)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 227.06/39.12          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 227.06/39.12    (40)  op(all_52_31, all_52_31) = e0
% 227.06/39.12    (41)  op(all_52_27, all_52_27) = e2
% 227.06/39.12    (42)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 227.06/39.12          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 227.06/39.12    (43)  op(e3, e0) = all_53_12
% 227.06/39.12  
% 227.06/39.12  Begin of proof
% 227.06/39.12  | 
% 227.06/39.12  | BETA: splitting (11) gives:
% 227.06/39.12  | 
% 227.06/39.12  | Case 1:
% 227.06/39.12  | | 
% 227.06/39.12  | |   (44)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) =
% 227.06/39.12  | |           e1)
% 227.06/39.12  | | 
% 227.06/39.12  | | BETA: splitting (44) gives:
% 227.06/39.12  | | 
% 227.06/39.12  | | Case 1:
% 227.06/39.12  | | | 
% 227.06/39.12  | | |   (45)  all_57_0 = e1 & op(e3, e3) = e1
% 227.06/39.12  | | | 
% 227.06/39.12  | | | ALPHA: (45) implies:
% 227.06/39.12  | | |   (46)  op(e3, e3) = e1
% 227.06/39.12  | | | 
% 227.06/39.12  | | | REF_CLOSE: (6), (22), (26), (28), (40), (46) are inconsistent by sub-proof
% 227.06/39.12  | | |            #283.
% 227.06/39.12  | | | 
% 227.06/39.12  | | Case 2:
% 227.06/39.12  | | | 
% 227.06/39.12  | | |   (47)  all_57_1 = e1 & op(e3, e2) = e1
% 227.06/39.12  | | | 
% 227.06/39.12  | | | REF_CLOSE: (16), (35), (47) are inconsistent by sub-proof #2210.
% 227.06/39.12  | | | 
% 227.06/39.12  | | End of split
% 227.06/39.12  | | 
% 227.06/39.12  | Case 2:
% 227.06/39.12  | | 
% 227.06/39.12  | |   (48)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) =
% 227.06/39.12  | |           e1)
% 227.06/39.12  | | 
% 227.06/39.12  | | BETA: splitting (48) gives:
% 227.06/39.12  | | 
% 227.06/39.12  | | Case 1:
% 227.06/39.12  | | | 
% 227.06/39.12  | | |   (49)  all_57_4 = e1 & op(e3, e1) = e1
% 227.06/39.12  | | | 
% 227.06/39.12  | | | REF_CLOSE: (4), (13), (49) are inconsistent by sub-proof #2484.
% 227.06/39.12  | | | 
% 227.06/39.12  | | Case 2:
% 227.06/39.12  | | | 
% 227.06/39.12  | | |   (50)  all_57_9 = e1 & op(e3, e0) = e1
% 227.06/39.12  | | | 
% 227.06/39.12  | | | ALPHA: (50) implies:
% 227.06/39.12  | | |   (51)  all_57_9 = e1
% 227.06/39.12  | | | 
% 227.06/39.12  | | | BETA: splitting (36) gives:
% 227.06/39.12  | | | 
% 227.06/39.12  | | | Case 1:
% 227.06/39.12  | | | | 
% 227.06/39.12  | | | |   (52)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0)
% 227.06/39.12  | | | |           = e2)
% 227.06/39.12  | | | | 
% 227.06/39.12  | | | | BETA: splitting (52) gives:
% 227.06/39.12  | | | | 
% 227.06/39.12  | | | | Case 1:
% 227.06/39.12  | | | | | 
% 227.06/39.12  | | | | |   (53)  all_57_9 = e2 & op(e3, e0) = e2
% 227.06/39.12  | | | | | 
% 227.06/39.12  | | | | | REF_CLOSE: (35), (51), (53) are inconsistent by sub-proof #2481.
% 227.06/39.12  | | | | | 
% 227.06/39.12  | | | | Case 2:
% 227.06/39.12  | | | | | 
% 227.06/39.12  | | | | |   (54)  all_57_10 = e2 & op(e2, e0) = e2
% 227.06/39.12  | | | | | 
% 227.06/39.12  | | | | | ALPHA: (54) implies:
% 227.06/39.12  | | | | |   (55)  all_57_10 = e2
% 227.06/39.12  | | | | | 
% 227.06/39.12  | | | | | BETA: splitting (34) gives:
% 227.06/39.12  | | | | | 
% 227.06/39.12  | | | | | Case 1:
% 227.06/39.12  | | | | | | 
% 227.06/39.12  | | | | | |   (56)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2,
% 227.06/39.12  | | | | | |             e2) = e0)
% 227.06/39.12  | | | | | | 
% 227.06/39.12  | | | | | | BETA: splitting (56) gives:
% 227.06/39.12  | | | | | | 
% 227.06/39.12  | | | | | | Case 1:
% 227.06/39.12  | | | | | | | 
% 227.06/39.12  | | | | | | |   (57)  all_57_2 = e0 & op(e2, e3) = e0
% 227.06/39.12  | | | | | | | 
% 227.06/39.12  | | | | | | | ALPHA: (57) implies:
% 227.06/39.12  | | | | | | |   (58)  op(e2, e3) = e0
% 227.06/39.12  | | | | | | | 
% 227.06/39.12  | | | | | | | REF_CLOSE: (3), (6), (25), (58) are inconsistent by sub-proof
% 227.06/39.12  | | | | | | |            #1943.
% 227.06/39.12  | | | | | | | 
% 227.06/39.12  | | | | | | Case 2:
% 227.06/39.12  | | | | | | | 
% 227.06/39.12  | | | | | | |   (59)  all_57_3 = e0 & op(e2, e2) = e0
% 227.06/39.12  | | | | | | | 
% 227.06/39.12  | | | | | | | ALPHA: (59) implies:
% 227.06/39.12  | | | | | | |   (60)  all_57_3 = e0
% 227.06/39.12  | | | | | | | 
% 227.06/39.12  | | | | | | | REF_CLOSE: (6), (10), (12), (13), (14), (15), (21), (23), (24),
% 227.06/39.12  | | | | | | |            (31), (35), (43), (51), (60) are inconsistent by
% 227.06/39.12  | | | | | | |            sub-proof #1204.
% 227.06/39.12  | | | | | | | 
% 227.06/39.12  | | | | | | End of split
% 227.06/39.12  | | | | | | 
% 227.06/39.12  | | | | | Case 2:
% 227.06/39.12  | | | | | | 
% 227.06/39.12  | | | | | |   (61)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2,
% 227.06/39.12  | | | | | |             e0) = e0)
% 227.06/39.12  | | | | | | 
% 227.06/39.12  | | | | | | BETA: splitting (61) gives:
% 227.06/39.12  | | | | | | 
% 227.06/39.12  | | | | | | Case 1:
% 227.06/39.12  | | | | | | | 
% 227.06/39.12  | | | | | | |   (62)  all_57_5 = e0 & op(e2, e1) = e0
% 227.06/39.12  | | | | | | | 
% 227.06/39.12  | | | | | | | ALPHA: (62) implies:
% 227.06/39.12  | | | | | | |   (63)  all_57_5 = e0
% 227.06/39.12  | | | | | | | 
% 227.06/39.12  | | | | | | | BETA: splitting (2) gives:
% 227.06/39.12  | | | | | | | 
% 227.06/39.12  | | | | | | | Case 1:
% 227.06/39.12  | | | | | | | | 
% 227.06/39.12  | | | | | | | |   (64)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 &
% 227.06/39.12  | | | | | | | |           op(e2, e2) = e1)
% 227.06/39.12  | | | | | | | | 
% 227.06/39.12  | | | | | | | | BETA: splitting (64) gives:
% 227.06/39.12  | | | | | | | | 
% 227.06/39.12  | | | | | | | | Case 1:
% 227.06/39.12  | | | | | | | | | 
% 227.06/39.12  | | | | | | | | |   (65)  all_57_2 = e1 & op(e2, e3) = e1
% 227.06/39.12  | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | ALPHA: (65) implies:
% 227.06/39.12  | | | | | | | | |   (66)  all_57_2 = e1
% 227.06/39.12  | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | BETA: splitting (17) gives:
% 227.06/39.12  | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | Case 1:
% 227.06/39.12  | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | |   (67)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 &
% 227.06/39.12  | | | | | | | | | |           op(e2, e1) = e1)
% 227.06/39.12  | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | BETA: splitting (67) gives:
% 227.06/39.12  | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | Case 1:
% 227.06/39.12  | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | |   (68)  all_57_4 = e1 & op(e3, e1) = e1
% 227.06/39.12  | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | REF_CLOSE: (4), (13), (68) are inconsistent by sub-proof
% 227.06/39.12  | | | | | | | | | | |            #2484.
% 227.06/39.12  | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | Case 2:
% 227.06/39.12  | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | |   (69)  all_57_5 = e1 & op(e2, e1) = e1
% 227.06/39.12  | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | REF_CLOSE: (26), (63), (69) are inconsistent by sub-proof
% 227.06/39.12  | | | | | | | | | | |            #2361.
% 227.06/39.12  | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | End of split
% 227.06/39.12  | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | Case 2:
% 227.06/39.12  | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | |   (70)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1
% 227.06/39.12  | | | | | | | | | |           & op(e0, e1) = e1)
% 227.06/39.12  | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | BETA: splitting (70) gives:
% 227.06/39.12  | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | Case 1:
% 227.06/39.12  | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | |   (71)  all_57_8 = e1 & op(e1, e1) = e1
% 227.06/39.12  | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | ALPHA: (71) implies:
% 227.06/39.12  | | | | | | | | | | |   (72)  op(e1, e1) = e1
% 227.06/39.12  | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | REF_CLOSE: (6), (30), (35), (72) are inconsistent by
% 227.06/39.12  | | | | | | | | | | |            sub-proof #2423.
% 227.06/39.12  | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | Case 2:
% 227.06/39.12  | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | |   (73)  all_57_14 = e1 & op(e0, e1) = e1
% 227.06/39.12  | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | ALPHA: (73) implies:
% 227.06/39.12  | | | | | | | | | | |   (74)  all_57_14 = e1
% 227.06/39.12  | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | BETA: splitting (29) gives:
% 227.06/39.12  | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | Case 1:
% 227.06/39.12  | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | |   (75)  all_57_15 = e0 & op(e0, e0) = e0
% 227.06/39.12  | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | ALPHA: (75) implies:
% 227.06/39.12  | | | | | | | | | | | |   (76)  op(e0, e0) = e0
% 227.06/39.12  | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | REF_CLOSE: (6), (15), (28), (76) are inconsistent by
% 227.06/39.12  | | | | | | | | | | | |            sub-proof #2304.
% 227.06/39.12  | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | Case 2:
% 227.06/39.12  | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | |   (77)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 227.06/39.12  | | | | | | | | | | | |             e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 227.06/39.12  | | | | | | | | | | | |             op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 227.06/39.12  | | | | | | | | | | | |               e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 227.06/39.12  | | | | | | | | | | | |             e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 227.06/39.12  | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | ALPHA: (77) implies:
% 227.06/39.12  | | | | | | | | | | | |   (78)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 227.06/39.12  | | | | | | | | | | | |           e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 227.06/39.12  | | | | | | | | | | | |             e1) = e0)
% 227.06/39.12  | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | BETA: splitting (78) gives:
% 227.06/39.12  | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | Case 1:
% 227.06/39.12  | | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | |   (79)  all_57_12 = e0 & op(e0, e3) = e0
% 227.06/39.12  | | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | | ALPHA: (79) implies:
% 227.06/39.12  | | | | | | | | | | | | |   (80)  all_57_12 = e0
% 227.06/39.12  | | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | | REF_CLOSE: (14), (19), (23), (27), (35), (38), (66), (80) are
% 227.06/39.12  | | | | | | | | | | | | |            inconsistent by sub-proof #1426.
% 227.06/39.12  | | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | Case 2:
% 227.06/39.12  | | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | |   (81)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 227.06/39.12  | | | | | | | | | | | | |           e0 & op(e0, e1) = e0)
% 227.06/39.12  | | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | | REF_CLOSE: (6), (14), (22), (26), (28), (32), (41), (74),
% 227.06/39.12  | | | | | | | | | | | | |            (81) are inconsistent by sub-proof #190.
% 227.06/39.12  | | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | | End of split
% 227.06/39.12  | | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | | End of split
% 227.06/39.12  | | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | | End of split
% 227.06/39.12  | | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | End of split
% 227.06/39.12  | | | | | | | | | 
% 227.06/39.12  | | | | | | | | Case 2:
% 227.06/39.12  | | | | | | | | | 
% 227.06/39.12  | | | | | | | | |   (82)  all_57_3 = e1 & op(e2, e2) = e1
% 227.06/39.12  | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | ALPHA: (82) implies:
% 227.06/39.12  | | | | | | | | |   (83)  op(e2, e2) = e1
% 227.06/39.12  | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | REF_CLOSE: (4), (6), (33), (83) are inconsistent by sub-proof
% 227.06/39.12  | | | | | | | | |            #1912.
% 227.06/39.12  | | | | | | | | | 
% 227.06/39.12  | | | | | | | | End of split
% 227.06/39.12  | | | | | | | | 
% 227.06/39.12  | | | | | | | Case 2:
% 227.06/39.12  | | | | | | | | 
% 227.06/39.12  | | | | | | | |   (84)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 &
% 227.06/39.12  | | | | | | | |           op(e2, e0) = e1)
% 227.06/39.12  | | | | | | | | 
% 227.06/39.12  | | | | | | | | BETA: splitting (84) gives:
% 227.06/39.12  | | | | | | | | 
% 227.06/39.12  | | | | | | | | Case 1:
% 227.06/39.12  | | | | | | | | | 
% 227.06/39.12  | | | | | | | | |   (85)  all_57_5 = e1 & op(e2, e1) = e1
% 227.06/39.12  | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | ALPHA: (85) implies:
% 227.06/39.12  | | | | | | | | |   (86)  all_57_5 = e1
% 227.06/39.12  | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | REF_CLOSE: (26), (63), (86) are inconsistent by sub-proof
% 227.06/39.12  | | | | | | | | |            #2350.
% 227.06/39.12  | | | | | | | | | 
% 227.06/39.12  | | | | | | | | Case 2:
% 227.06/39.12  | | | | | | | | | 
% 227.06/39.12  | | | | | | | | |   (87)  all_57_10 = e1 & op(e2, e0) = e1
% 227.06/39.12  | | | | | | | | | 
% 227.06/39.12  | | | | | | | | | REF_CLOSE: (35), (55), (87) are inconsistent by sub-proof
% 227.06/39.12  | | | | | | | | |            #2360.
% 227.06/39.12  | | | | | | | | | 
% 227.06/39.12  | | | | | | | | End of split
% 227.06/39.12  | | | | | | | | 
% 227.06/39.12  | | | | | | | End of split
% 227.06/39.12  | | | | | | | 
% 227.06/39.12  | | | | | | Case 2:
% 227.06/39.12  | | | | | | | 
% 227.06/39.12  | | | | | | |   (88)  all_57_10 = e0 & op(e2, e0) = e0
% 227.06/39.12  | | | | | | | 
% 227.06/39.12  | | | | | | | ALPHA: (88) implies:
% 227.06/39.12  | | | | | | |   (89)  all_57_10 = e0
% 227.06/39.12  | | | | | | | 
% 227.06/39.12  | | | | | | | COMBINE_EQS: (55), (89) imply:
% 227.06/39.12  | | | | | | |   (90)  e2 = e0
% 227.06/39.12  | | | | | | | 
% 227.06/39.12  | | | | | | | COMBINE_EQS: (16), (90) imply:
% 227.06/39.12  | | | | | | |   (91)  all_57_1 = e0
% 227.06/39.12  | | | | | | | 
% 227.06/39.12  | | | | | | | REF_CLOSE: (4), (6), (11), (12), (13), (14), (15), (19), (20),
% 227.06/39.12  | | | | | | |            (21), (23), (24), (26), (28), (31), (35), (36), (39),
% 227.06/39.12  | | | | | | |            (43), (89), (91) are inconsistent by sub-proof #905.
% 227.06/39.12  | | | | | | | 
% 227.06/39.12  | | | | | | End of split
% 227.06/39.12  | | | | | | 
% 227.06/39.12  | | | | | End of split
% 227.06/39.12  | | | | | 
% 227.06/39.12  | | | | End of split
% 227.06/39.12  | | | | 
% 227.06/39.12  | | | Case 2:
% 227.06/39.12  | | | | 
% 227.06/39.12  | | | |   (92)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0,
% 227.06/39.12  | | | |             e0) = e2)
% 227.06/39.12  | | | | 
% 227.06/39.12  | | | | REF_CLOSE: (1), (4), (5), (6), (7), (8), (9), (14), (15), (18), (23),
% 227.06/39.12  | | | |            (26), (27), (30), (35), (37), (42), (92) are inconsistent by
% 227.06/39.12  | | | |            sub-proof #201.
% 227.06/39.12  | | | | 
% 227.06/39.12  | | | End of split
% 227.06/39.12  | | | 
% 227.06/39.12  | | End of split
% 227.06/39.12  | | 
% 227.06/39.12  | End of split
% 227.06/39.12  | 
% 227.06/39.12  End of proof
% 227.06/39.12  
% 227.06/39.12  Sub-proof #190 shows that the following formulas are inconsistent:
% 227.06/39.12  ----------------------------------------------------------------
% 227.06/39.12    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.06/39.12           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.06/39.12    (2)   ~ (e3 = e2)
% 227.06/39.12    (3)  op(e0, e0) = all_52_31
% 227.06/39.12    (4)   ~ (e1 = e0)
% 227.06/39.12    (5)  all_57_14 = e1
% 227.06/39.12    (6)  op(e0, e0) = e3
% 227.06/39.12    (7)  op(e0, e2) = all_52_27
% 227.06/39.12    (8)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 227.06/39.12    (9)  op(all_52_27, all_52_27) = e2
% 227.06/39.12  
% 227.06/39.12  Begin of proof
% 227.06/39.12  | 
% 227.06/39.12  | BETA: splitting (8) gives:
% 227.06/39.12  | 
% 227.06/39.12  | Case 1:
% 227.06/39.12  | | 
% 227.06/39.12  | |   (10)  all_57_13 = e0 & op(e0, e2) = e0
% 227.06/39.12  | | 
% 227.06/39.12  | | ALPHA: (10) implies:
% 227.06/39.12  | |   (11)  op(e0, e2) = e0
% 227.06/39.12  | | 
% 227.06/39.12  | | REF_CLOSE: (1), (2), (3), (6), (7), (9), (11) are inconsistent by sub-proof
% 227.06/39.12  | |            #858.
% 227.06/39.12  | | 
% 227.06/39.12  | Case 2:
% 227.06/39.12  | | 
% 227.06/39.12  | |   (12)  all_57_14 = e0 & op(e0, e1) = e0
% 227.06/39.12  | | 
% 227.06/39.12  | | ALPHA: (12) implies:
% 227.06/39.12  | |   (13)  all_57_14 = e0
% 227.06/39.12  | | 
% 227.06/39.12  | | REF_CLOSE: (4), (5), (13) are inconsistent by sub-proof #2122.
% 227.06/39.12  | | 
% 227.06/39.12  | End of split
% 227.06/39.12  | 
% 227.06/39.12  End of proof
% 227.06/39.12  
% 227.06/39.12  Sub-proof #191 shows that the following formulas are inconsistent:
% 227.06/39.12  ----------------------------------------------------------------
% 227.06/39.12    (1)  all_57_10 = e0
% 227.06/39.13    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.06/39.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.06/39.13    (3)  all_57_4 = e3
% 227.06/39.13    (4)   ~ (e3 = e2)
% 227.06/39.13    (5)  op(e1, e1) = e1
% 227.06/39.13    (6)   ~ (e2 = e0)
% 227.06/39.13    (7)   ~ (e1 = e0)
% 227.06/39.13    (8)   ~ (e2 = e1)
% 227.06/39.13    (9)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 227.06/39.13         (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 227.06/39.13    (10)  all_57_14 = e0
% 227.06/39.13    (11)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 227.06/39.13  
% 227.06/39.13  Begin of proof
% 227.06/39.13  | 
% 227.06/39.13  | BETA: splitting (11) gives:
% 227.06/39.13  | 
% 227.06/39.13  | Case 1:
% 227.06/39.13  | | 
% 227.06/39.13  | |   (12)  all_57_5 = e1 & op(e2, e1) = e1
% 227.06/39.13  | | 
% 227.06/39.13  | | ALPHA: (12) implies:
% 227.06/39.13  | |   (13)  all_57_5 = e1
% 227.06/39.13  | | 
% 227.06/39.13  | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (9), (10), (13) are inconsistent by
% 227.06/39.13  | |            sub-proof #1231.
% 227.06/39.13  | | 
% 227.06/39.13  | Case 2:
% 227.06/39.13  | | 
% 227.06/39.13  | |   (14)  all_57_10 = e1 & op(e2, e0) = e1
% 227.06/39.13  | | 
% 227.06/39.13  | | REF_CLOSE: (1), (7), (14) are inconsistent by sub-proof #2242.
% 227.06/39.13  | | 
% 227.06/39.13  | End of split
% 227.06/39.13  | 
% 227.06/39.13  End of proof
% 227.06/39.13  
% 227.06/39.13  Sub-proof #192 shows that the following formulas are inconsistent:
% 227.06/39.13  ----------------------------------------------------------------
% 227.06/39.13    (1)   ~ (e3 = e1)
% 227.06/39.13    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.06/39.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.06/39.13    (3)   ~ (all_6_2 = e3)
% 227.06/39.13    (4)  op(e1, e1) = all_6_2
% 227.06/39.13    (5)  all_57_3 = e3
% 227.06/39.13    (6)  all_57_4 = e3
% 227.06/39.13    (7)   ~ (e3 = e2)
% 227.06/39.13    (8)   ~ (e3 = e0)
% 227.06/39.13    (9)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 227.06/39.13         (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 227.06/39.13    (10)  all_57_3 = e0 & op(e2, e2) = e0
% 227.06/39.13    (11)   ~ (e2 = e0)
% 227.06/39.13    (12)   ~ (e1 = e0)
% 227.06/39.13    (13)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 227.06/39.13          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 227.06/39.13    (14)   ~ (e2 = e1)
% 227.06/39.13    (15)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 227.06/39.13          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 227.06/39.13    (16)  all_57_14 = e0
% 227.06/39.13  
% 227.06/39.13  Begin of proof
% 227.06/39.13  | 
% 227.06/39.13  | ALPHA: (10) implies:
% 227.06/39.13  |   (17)  all_57_3 = e0
% 227.06/39.13  | 
% 227.06/39.13  | COMBINE_EQS: (5), (17) imply:
% 227.06/39.13  |   (18)  e3 = e0
% 227.06/39.13  | 
% 227.06/39.13  | COMBINE_EQS: (6), (18) imply:
% 227.06/39.13  |   (19)  all_57_4 = e0
% 227.06/39.13  | 
% 227.06/39.13  | REF_CLOSE: (1), (2), (3), (4), (7), (8), (9), (11), (12), (13), (14), (15),
% 227.06/39.13  |            (16), (19) are inconsistent by sub-proof #2371.
% 227.06/39.13  | 
% 227.06/39.13  End of proof
% 227.06/39.13  
% 227.06/39.13  Sub-proof #193 shows that the following formulas are inconsistent:
% 227.06/39.13  ----------------------------------------------------------------
% 227.06/39.13    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.06/39.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.06/39.13    (2)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 227.06/39.13    (3)   ~ (e3 = e0)
% 227.06/39.13    (4)  op(e0, e3) = all_53_3
% 227.06/39.13    (5)  all_57_6 = e3
% 227.06/39.13    (6)   ~ (all_53_3 = e0)
% 227.06/39.13  
% 227.06/39.13  Begin of proof
% 227.06/39.13  | 
% 227.06/39.13  | BETA: splitting (2) gives:
% 227.06/39.13  | 
% 227.06/39.13  | Case 1:
% 227.06/39.13  | | 
% 227.06/39.13  | |   (7)  all_57_6 = e0 & op(e1, e3) = e0
% 227.06/39.13  | | 
% 227.06/39.13  | | ALPHA: (7) implies:
% 227.06/39.13  | |   (8)  all_57_6 = e0
% 227.06/39.13  | | 
% 227.06/39.13  | | REF_CLOSE: (3), (5), (8) are inconsistent by sub-proof #1822.
% 227.06/39.13  | | 
% 227.06/39.13  | Case 2:
% 227.06/39.13  | | 
% 227.06/39.13  | |   (9)  all_57_12 = e0 & op(e0, e3) = e0
% 227.06/39.13  | | 
% 227.06/39.13  | | ALPHA: (9) implies:
% 227.06/39.13  | |   (10)  op(e0, e3) = e0
% 227.06/39.13  | | 
% 227.06/39.13  | | REF_CLOSE: (1), (4), (6), (10) are inconsistent by sub-proof #2366.
% 227.06/39.13  | | 
% 227.06/39.13  | End of split
% 227.06/39.13  | 
% 227.06/39.13  End of proof
% 227.06/39.13  
% 227.06/39.13  Sub-proof #194 shows that the following formulas are inconsistent:
% 227.06/39.13  ----------------------------------------------------------------
% 227.06/39.13    (1)   ~ (e3 = e1)
% 227.06/39.13    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.06/39.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.06/39.13    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 227.06/39.13         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 227.06/39.13    (4)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 227.06/39.13         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 227.06/39.13    (5)   ~ (e3 = e2)
% 227.06/39.13    (6)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 227.06/39.13    (7)   ~ (e3 = e0)
% 227.06/39.13    (8)  op(e3, e3) = e2
% 227.06/39.13    (9)   ~ (e2 = e0)
% 227.06/39.13    (10)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 227.06/39.13          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 227.06/39.13    (11)   ~ (e1 = e0)
% 227.06/39.13    (12)   ~ (all_53_12 = e3)
% 227.06/39.13    (13)   ~ (e2 = e1)
% 227.06/39.13    (14)   ~ (all_53_12 = e2)
% 227.06/39.13    (15)  op(e3, e0) = all_53_12
% 227.06/39.13  
% 227.06/39.13  Begin of proof
% 227.06/39.13  | 
% 227.06/39.13  | BETA: splitting (6) gives:
% 227.06/39.13  | 
% 227.06/39.13  | Case 1:
% 227.06/39.13  | | 
% 227.06/39.13  | |   (16)  all_57_4 = e2 & op(e3, e1) = e2
% 227.06/39.13  | | 
% 227.06/39.13  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 227.06/39.13  | |            (15), (16) are inconsistent by sub-proof #195.
% 227.06/39.13  | | 
% 227.06/39.13  | Case 2:
% 227.06/39.13  | | 
% 227.06/39.13  | |   (17)  all_57_9 = e2 & op(e3, e0) = e2
% 227.06/39.13  | | 
% 227.06/39.13  | | ALPHA: (17) implies:
% 227.06/39.13  | |   (18)  op(e3, e0) = e2
% 227.06/39.13  | | 
% 227.06/39.13  | | REF_CLOSE: (2), (14), (15), (18) are inconsistent by sub-proof #2331.
% 227.06/39.13  | | 
% 227.06/39.13  | End of split
% 227.06/39.13  | 
% 227.06/39.13  End of proof
% 227.06/39.13  
% 227.06/39.13  Sub-proof #195 shows that the following formulas are inconsistent:
% 227.06/39.13  ----------------------------------------------------------------
% 227.06/39.13    (1)   ~ (e3 = e1)
% 227.06/39.13    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.06/39.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.06/39.13    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 227.06/39.13         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 227.06/39.13    (4)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 227.06/39.13         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 227.06/39.13    (5)   ~ (e3 = e2)
% 227.06/39.13    (6)   ~ (e3 = e0)
% 227.06/39.13    (7)  op(e3, e3) = e2
% 227.06/39.13    (8)   ~ (e2 = e0)
% 227.06/39.13    (9)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 227.06/39.13         (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 227.06/39.13    (10)   ~ (e1 = e0)
% 227.06/39.13    (11)  all_57_4 = e2 & op(e3, e1) = e2
% 227.06/39.13    (12)   ~ (all_53_12 = e3)
% 227.06/39.13    (13)   ~ (e2 = e1)
% 227.06/39.13    (14)  op(e3, e0) = all_53_12
% 227.06/39.13  
% 227.06/39.13  Begin of proof
% 227.06/39.13  | 
% 227.06/39.13  | ALPHA: (11) implies:
% 227.06/39.13  |   (15)  all_57_4 = e2
% 227.06/39.13  | 
% 227.06/39.13  | BETA: splitting (9) gives:
% 227.06/39.13  | 
% 227.06/39.13  | Case 1:
% 227.06/39.13  | | 
% 227.06/39.13  | |   (16)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) =
% 227.06/39.13  | |           e3)
% 227.06/39.13  | | 
% 227.06/39.13  | | BETA: splitting (16) gives:
% 227.06/39.13  | | 
% 227.06/39.13  | | Case 1:
% 227.06/39.13  | | | 
% 227.06/39.13  | | |   (17)  all_57_0 = e3 & op(e3, e3) = e3
% 227.06/39.13  | | | 
% 227.06/39.13  | | | ALPHA: (17) implies:
% 227.06/39.13  | | |   (18)  op(e3, e3) = e3
% 227.06/39.13  | | | 
% 227.06/39.13  | | | REF_CLOSE: (2), (5), (7), (18) are inconsistent by sub-proof #2490.
% 227.06/39.13  | | | 
% 227.06/39.13  | | Case 2:
% 227.06/39.13  | | | 
% 227.06/39.13  | | |   (19)  all_57_1 = e3 & op(e3, e2) = e3
% 227.06/39.13  | | | 
% 227.06/39.13  | | | ALPHA: (19) implies:
% 227.06/39.13  | | |   (20)  all_57_1 = e3
% 227.06/39.13  | | | 
% 227.06/39.13  | | | BETA: splitting (3) gives:
% 227.06/39.13  | | | 
% 227.06/39.13  | | | Case 1:
% 227.06/39.13  | | | | 
% 227.06/39.13  | | | |   (21)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2)
% 227.06/39.13  | | | |           = e1)
% 227.06/39.13  | | | | 
% 227.06/39.13  | | | | REF_CLOSE: (1), (2), (7), (13), (20), (21) are inconsistent by sub-proof
% 227.06/39.13  | | | |            #1607.
% 227.06/39.13  | | | | 
% 227.06/39.13  | | | Case 2:
% 227.06/39.13  | | | | 
% 227.06/39.13  | | | |   (22)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0)
% 227.06/39.13  | | | |           = e1)
% 227.06/39.13  | | | | 
% 227.06/39.13  | | | | REF_CLOSE: (2), (4), (5), (6), (7), (8), (9), (10), (12), (13), (14),
% 227.06/39.13  | | | |            (15), (22) are inconsistent by sub-proof #594.
% 227.06/39.13  | | | | 
% 227.06/39.13  | | | End of split
% 227.06/39.13  | | | 
% 227.06/39.13  | | End of split
% 227.06/39.13  | | 
% 227.06/39.13  | Case 2:
% 227.06/39.13  | | 
% 227.06/39.13  | |   (23)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) =
% 227.06/39.13  | |           e3)
% 227.06/39.13  | | 
% 227.06/39.13  | | REF_CLOSE: (2), (5), (12), (14), (15), (23) are inconsistent by sub-proof
% 227.06/39.13  | |            #2448.
% 227.06/39.13  | | 
% 227.06/39.13  | End of split
% 227.06/39.13  | 
% 227.06/39.13  End of proof
% 227.06/39.13  
% 227.06/39.13  Sub-proof #196 shows that the following formulas are inconsistent:
% 227.06/39.13  ----------------------------------------------------------------
% 227.06/39.13    (1)  op(e0, e0) = all_4_2
% 227.06/39.13    (2)  all_57_0 = e2
% 227.06/39.13    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 227.06/39.13         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 227.06/39.13    (4)   ~ (all_53_6 = e0)
% 227.06/39.13    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 227.06/39.13         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 227.06/39.13    (6)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 227.06/39.13         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.06/39.13    (7)   ~ (e3 = e1)
% 227.06/39.13    (8)  op(e2, e3) = e0
% 227.06/39.13    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.06/39.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.06/39.13    (10)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 227.06/39.13          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 227.06/39.13    (11)   ~ (all_6_2 = e3)
% 227.06/39.13    (12)  op(e1, e1) = all_6_2
% 227.06/39.13    (13)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 227.06/39.13          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 227.06/39.13    (14)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 227.06/39.13            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 227.06/39.13              e3) = all_22_1 & $i(all_22_1))
% 227.06/39.13    (15)  op(e2, e3) = all_52_9
% 227.06/39.13    (16)  op(e2, e0) = all_52_15
% 227.06/39.13    (17)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 227.06/39.13          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 227.06/39.13    (18)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 227.06/39.13          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 227.06/39.13    (19)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 227.06/39.13          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 227.06/39.13    (20)  all_57_4 = e3
% 227.06/39.13    (21)   ~ (e3 = e2)
% 227.06/39.13    (22)  op(e1, e0) = all_53_14
% 227.06/39.13    (23)   ~ (e3 = e0)
% 227.06/39.13    (24)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 227.06/39.13          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 227.06/39.13    (25)   ~ (all_4_2 = e2)
% 227.06/39.13    (26)  op(e0, e3) = all_53_3
% 227.06/39.13    (27)  all_57_15 = e3
% 227.06/39.13    (28)  op(e2, e2) = all_52_11
% 227.06/39.13    (29)  op(e3, e3) = e2
% 227.06/39.13    (30)   ~ (all_53_3 = e2)
% 227.06/39.13    (31)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 227.06/39.13          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 227.06/39.13            e1)
% 227.06/39.13    (32)  all_57_10 = e2
% 227.06/39.13    (33)  op(e2, e0) = e2
% 227.06/39.13    (34)  op(e3, e2) = all_53_4
% 227.06/39.13    (35)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 227.06/39.13          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 227.06/39.13    (36)   ~ (e2 = e0)
% 227.06/39.13    (37)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 227.06/39.13            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 227.06/39.13              e3) = all_12_1 & $i(all_12_1))
% 227.06/39.13    (38)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 227.06/39.13          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 227.06/39.13    (39)   ~ (e1 = e0)
% 227.06/39.13    (40)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 227.06/39.13          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 227.06/39.13    (41)  all_57_6 = e3
% 227.06/39.13    (42)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 227.06/39.13          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 227.06/39.13    (43)   ~ (all_53_14 = e0)
% 227.06/39.13    (44)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 227.06/39.13          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 227.06/39.13            e3)
% 227.06/39.13    (45)  op(e0, e0) = e3
% 227.06/39.13    (46)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.06/39.13          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 227.06/39.13            e2)
% 227.06/39.13    (47)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 227.06/39.13              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 227.06/39.13                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 227.06/39.13                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 227.06/39.13    (48)  op(all_52_9, all_52_9) = e3
% 227.06/39.13    (49)  op(e1, e1) = e0
% 227.06/39.13    (50)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 227.06/39.13          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 227.06/39.13    (51)  all_57_2 = e0
% 227.06/39.13    (52)   ~ (all_53_12 = e3)
% 227.06/39.13    (53)   ~ (all_53_4 = e2)
% 227.06/39.13    (54)  all_57_8 = e0
% 227.06/39.13    (55)  op(all_52_15, all_52_15) = e0
% 227.06/39.13    (56)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 227.06/39.13          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 227.06/39.13    (57)  op(e2, e2) = e3
% 227.06/39.13    (58)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 227.06/39.13          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 227.06/39.13    (59)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 227.06/39.13          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 227.06/39.13    (60)   ~ (e2 = e1)
% 227.06/39.13    (61)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 227.06/39.13          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 227.06/39.13    (62)  op(e1, e2) = all_53_6
% 227.06/39.13    (63)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 227.06/39.13          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 227.06/39.13    (64)   ~ (all_53_12 = e2)
% 227.06/39.13    (65)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 227.06/39.13          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 227.06/39.13    (66)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 227.06/39.13          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 227.06/39.13    (67)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 227.06/39.13          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 227.06/39.13    (68)  op(all_52_11, all_52_11) = e2
% 227.06/39.13    (69)   ~ (all_52_15 = e3)
% 227.06/39.13    (70)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 227.06/39.13          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 227.06/39.13    (71)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 227.06/39.13          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 227.06/39.13    (72)  op(e3, e0) = all_53_12
% 227.06/39.13  
% 227.06/39.13  Begin of proof
% 227.06/39.13  | 
% 227.06/39.13  | BETA: splitting (5) gives:
% 227.06/39.13  | 
% 227.06/39.13  | Case 1:
% 227.06/39.13  | | 
% 227.06/39.13  | |   (73)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) =
% 227.06/39.13  | |           e1)
% 227.06/39.13  | | 
% 227.06/39.13  | | BETA: splitting (73) gives:
% 227.06/39.13  | | 
% 227.06/39.13  | | Case 1:
% 227.06/39.13  | | | 
% 227.06/39.13  | | |   (74)  all_57_0 = e1 & op(e3, e3) = e1
% 227.06/39.13  | | | 
% 227.06/39.13  | | | ALPHA: (74) implies:
% 227.06/39.13  | | |   (75)  op(e3, e3) = e1
% 227.06/39.13  | | | 
% 227.06/39.13  | | | REF_CLOSE: (9), (17), (20), (21), (34), (53), (60), (64), (72), (75) are
% 227.06/39.13  | | |            inconsistent by sub-proof #234.
% 227.06/39.13  | | | 
% 227.06/39.13  | | Case 2:
% 227.06/39.13  | | | 
% 227.06/39.13  | | |   (76)  all_57_2 = e1 & op(e2, e3) = e1
% 227.06/39.13  | | | 
% 227.06/39.13  | | | ALPHA: (76) implies:
% 227.06/39.13  | | |   (77)  all_57_2 = e1
% 227.06/39.13  | | | 
% 227.06/39.13  | | | REF_CLOSE: (39), (51), (77) are inconsistent by sub-proof #2473.
% 227.06/39.13  | | | 
% 227.06/39.13  | | End of split
% 227.06/39.13  | | 
% 227.06/39.13  | Case 2:
% 227.06/39.13  | | 
% 227.06/39.13  | |   (78)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) =
% 227.06/39.13  | |           e1)
% 227.06/39.13  | | 
% 227.06/39.13  | | BETA: splitting (78) gives:
% 227.06/39.13  | | 
% 227.06/39.13  | | Case 1:
% 227.06/39.13  | | | 
% 227.06/39.13  | | |   (79)  all_57_6 = e1 & op(e1, e3) = e1
% 227.06/39.13  | | | 
% 227.06/39.13  | | | ALPHA: (79) implies:
% 227.06/39.13  | | |   (80)  all_57_6 = e1
% 227.06/39.13  | | | 
% 227.06/39.13  | | | REF_CLOSE: (7), (41), (80) are inconsistent by sub-proof #2017.
% 227.06/39.13  | | | 
% 227.06/39.13  | | Case 2:
% 227.06/39.13  | | | 
% 227.06/39.13  | | |   (81)  all_57_12 = e1 & op(e0, e3) = e1
% 227.06/39.13  | | | 
% 227.06/39.13  | | | ALPHA: (81) implies:
% 227.06/39.13  | | |   (82)  all_57_12 = e1
% 227.06/39.13  | | |   (83)  op(e0, e3) = e1
% 227.06/39.13  | | | 
% 227.06/39.13  | | | BETA: splitting (3) gives:
% 227.06/39.13  | | | 
% 227.06/39.13  | | | Case 1:
% 227.06/39.13  | | | | 
% 227.06/39.13  | | | |   (84)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2)
% 227.06/39.13  | | | |           = e1)
% 227.06/39.13  | | | | 
% 227.06/39.13  | | | | BETA: splitting (84) gives:
% 227.06/39.13  | | | | 
% 227.06/39.13  | | | | Case 1:
% 227.06/39.13  | | | | | 
% 227.06/39.13  | | | | |   (85)  all_57_2 = e1 & op(e2, e3) = e1
% 227.06/39.13  | | | | | 
% 227.06/39.13  | | | | | ALPHA: (85) implies:
% 227.06/39.13  | | | | |   (86)  all_57_2 = e1
% 227.06/39.13  | | | | | 
% 227.06/39.13  | | | | | REF_CLOSE: (39), (51), (86) are inconsistent by sub-proof #2473.
% 227.06/39.13  | | | | | 
% 227.06/39.13  | | | | Case 2:
% 227.06/39.13  | | | | | 
% 227.06/39.13  | | | | |   (87)  all_57_3 = e1 & op(e2, e2) = e1
% 227.06/39.13  | | | | | 
% 227.06/39.13  | | | | | ALPHA: (87) implies:
% 227.06/39.13  | | | | |   (88)  op(e2, e2) = e1
% 227.06/39.13  | | | | | 
% 227.06/39.13  | | | | | REF_CLOSE: (9), (28), (36), (49), (68), (88) are inconsistent by
% 227.06/39.13  | | | | |            sub-proof #1843.
% 227.06/39.13  | | | | | 
% 227.06/39.13  | | | | End of split
% 227.06/39.13  | | | | 
% 227.06/39.13  | | | Case 2:
% 227.06/39.13  | | | | 
% 227.06/39.13  | | | |   (89)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0)
% 227.06/39.13  | | | |           = e1)
% 227.06/39.13  | | | | 
% 227.06/39.13  | | | | BETA: splitting (89) gives:
% 227.06/39.13  | | | | 
% 227.06/39.13  | | | | Case 1:
% 227.06/39.13  | | | | | 
% 227.06/39.13  | | | | |   (90)  all_57_5 = e1 & op(e2, e1) = e1
% 227.06/39.13  | | | | | 
% 227.06/39.13  | | | | | ALPHA: (90) implies:
% 227.06/39.13  | | | | |   (91)  all_57_5 = e1
% 227.06/39.13  | | | | | 
% 227.06/39.13  | | | | | BETA: splitting (47) gives:
% 227.06/39.13  | | | | | 
% 227.06/39.13  | | | | | Case 1:
% 227.06/39.13  | | | | | | 
% 227.06/39.13  | | | | | |   (92)  all_57_15 = e0 & op(e0, e0) = e0
% 227.06/39.13  | | | | | | 
% 227.06/39.13  | | | | | | ALPHA: (92) implies:
% 227.06/39.13  | | | | | |   (93)  op(e0, e0) = e0
% 227.06/39.13  | | | | | | 
% 227.06/39.13  | | | | | | REF_CLOSE: (9), (23), (45), (93) are inconsistent by sub-proof
% 227.06/39.13  | | | | | |            #2304.
% 227.06/39.13  | | | | | | 
% 227.06/39.13  | | | | | Case 2:
% 227.06/39.13  | | | | | | 
% 227.06/39.13  | | | | | |   (94)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 &
% 227.06/39.13  | | | | | |             op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) &
% 227.06/39.13  | | | | | |         ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 227.06/39.13  | | | | | |             op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 227.06/39.13  | | | | | | 
% 227.06/39.13  | | | | | | ALPHA: (94) implies:
% 227.06/39.13  | | | | | |   (95)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 227.06/39.13  | | | | | |           op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 227.06/39.13  | | | | | |   (96)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2,
% 227.06/39.13  | | | | | |             e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 227.06/39.13  | | | | | | 
% 227.06/39.13  | | | | | | BETA: splitting (95) gives:
% 227.06/39.13  | | | | | | 
% 227.06/39.13  | | | | | | Case 1:
% 227.06/39.13  | | | | | | | 
% 227.06/39.13  | | | | | | |   (97)  all_57_12 = e0 & op(e0, e3) = e0
% 227.06/39.13  | | | | | | | 
% 227.06/39.13  | | | | | | | REF_CLOSE: (39), (82), (97) are inconsistent by sub-proof #1279.
% 227.06/39.13  | | | | | | | 
% 227.06/39.13  | | | | | | Case 2:
% 227.06/39.13  | | | | | | | 
% 227.06/39.13  | | | | | | |   (98)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 &
% 227.06/39.13  | | | | | | |           op(e0, e1) = e0)
% 227.06/39.13  | | | | | | | 
% 227.06/39.13  | | | | | | | BETA: splitting (98) gives:
% 227.06/39.13  | | | | | | | 
% 227.06/39.13  | | | | | | | Case 1:
% 227.06/39.13  | | | | | | | | 
% 227.06/39.13  | | | | | | | |   (99)  all_57_13 = e0 & op(e0, e2) = e0
% 227.06/39.13  | | | | | | | | 
% 227.06/39.13  | | | | | | | | ALPHA: (99) implies:
% 227.06/39.13  | | | | | | | |   (100)  all_57_13 = e0
% 227.06/39.13  | | | | | | | | 
% 227.06/39.13  | | | | | | | | REF_CLOSE: (6), (7), (8), (9), (10), (11), (12), (13), (14),
% 227.06/39.13  | | | | | | | |            (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 227.06/39.13  | | | | | | | |            (27), (28), (29), (31), (32), (33), (36), (37), (38),
% 227.06/39.13  | | | | | | | |            (39), (40), (41), (43), (45), (46), (47), (48), (49),
% 227.06/39.13  | | | | | | | |            (52), (54), (55), (57), (60), (61), (65), (66), (67),
% 227.06/39.13  | | | | | | | |            (68), (69), (70), (71), (72), (83), (91), (96), (100)
% 227.06/39.13  | | | | | | | |            are inconsistent by sub-proof #197.
% 227.06/39.13  | | | | | | | | 
% 227.06/39.13  | | | | | | | Case 2:
% 227.06/39.13  | | | | | | | | 
% 227.06/39.13  | | | | | | | |   (101)  all_57_14 = e0 & op(e0, e1) = e0
% 227.06/39.13  | | | | | | | | 
% 227.06/39.13  | | | | | | | | ALPHA: (101) implies:
% 227.06/39.13  | | | | | | | |   (102)  all_57_14 = e0
% 227.06/39.13  | | | | | | | | 
% 227.06/39.13  | | | | | | | | BETA: splitting (46) gives:
% 227.06/39.13  | | | | | | | | 
% 227.06/39.13  | | | | | | | | Case 1:
% 227.06/39.13  | | | | | | | | | 
% 227.06/39.13  | | | | | | | | |   (103)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2
% 227.06/39.13  | | | | | | | | |            & op(e0, e2) = e2)
% 227.06/39.13  | | | | | | | | | 
% 227.06/39.13  | | | | | | | | | BETA: splitting (103) gives:
% 227.06/39.13  | | | | | | | | | 
% 227.06/39.13  | | | | | | | | | Case 1:
% 227.06/39.13  | | | | | | | | | | 
% 227.06/39.13  | | | | | | | | | |   (104)  all_57_12 = e2 & op(e0, e3) = e2
% 227.06/39.13  | | | | | | | | | | 
% 227.06/39.13  | | | | | | | | | | ALPHA: (104) implies:
% 227.06/39.13  | | | | | | | | | |   (105)  op(e0, e3) = e2
% 227.06/39.13  | | | | | | | | | | 
% 227.06/39.13  | | | | | | | | | | REF_CLOSE: (9), (26), (30), (105) are inconsistent by
% 227.06/39.13  | | | | | | | | | |            sub-proof #1980.
% 227.06/39.13  | | | | | | | | | | 
% 227.06/39.13  | | | | | | | | | Case 2:
% 227.06/39.13  | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | |   (106)  all_57_13 = e2 & op(e0, e2) = e2
% 227.06/39.14  | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | ALPHA: (106) implies:
% 227.06/39.14  | | | | | | | | | |   (107)  all_57_13 = e2
% 227.06/39.14  | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | BETA: splitting (35) gives:
% 227.06/39.14  | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | Case 1:
% 227.06/39.14  | | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | |   (108)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 227.06/39.14  | | | | | | | | | | |            & op(e2, e2) = e0)
% 227.06/39.14  | | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | | BETA: splitting (108) gives:
% 227.06/39.14  | | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | | Case 1:
% 227.06/39.14  | | | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | | |   (109)  all_57_1 = e0 & op(e3, e2) = e0
% 227.06/39.14  | | | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | | | ALPHA: (109) implies:
% 227.06/39.14  | | | | | | | | | | | |   (110)  all_57_1 = e0
% 227.06/39.14  | | | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | | | BETA: splitting (13) gives:
% 227.06/39.14  | | | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | | | Case 1:
% 227.06/39.14  | | | | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | | | |   (111)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 227.06/39.14  | | | | | | | | | | | | |            & op(e3, e2) = e1)
% 227.06/39.14  | | | | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | | | | REF_CLOSE: (9), (17), (20), (21), (34), (39), (53), (60),
% 227.06/39.14  | | | | | | | | | | | | |            (64), (72), (110), (111) are inconsistent by
% 227.06/39.14  | | | | | | | | | | | | |            sub-proof #233.
% 227.06/39.14  | | | | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | | | Case 2:
% 227.06/39.14  | | | | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | | | |   (112)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 227.06/39.14  | | | | | | | | | | | | |            & op(e3, e0) = e1)
% 227.06/39.14  | | | | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | | | | BETA: splitting (112) gives:
% 227.06/39.14  | | | | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | | | | Case 1:
% 227.06/39.14  | | | | | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | | | | |   (113)  all_57_4 = e1 & op(e3, e1) = e1
% 227.06/39.14  | | | | | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | | | | | ALPHA: (113) implies:
% 227.06/39.14  | | | | | | | | | | | | | |   (114)  all_57_4 = e1
% 227.06/39.14  | | | | | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | | | | | COMBINE_EQS: (20), (114) imply:
% 227.06/39.14  | | | | | | | | | | | | | |   (115)  e3 = e1
% 227.06/39.14  | | | | | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | | | | | COMBINE_EQS: (41), (115) imply:
% 227.06/39.14  | | | | | | | | | | | | | |   (116)  all_57_6 = e1
% 227.06/39.14  | | | | | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (10), (11), (12), (21), (23), (27),
% 227.06/39.14  | | | | | | | | | | | | | |            (29), (36), (39), (47), (51), (58), (60), (61),
% 227.06/39.14  | | | | | | | | | | | | | |            (66), (82), (96), (116) are inconsistent by
% 227.06/39.14  | | | | | | | | | | | | | |            sub-proof #760.
% 227.06/39.14  | | | | | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | | | | Case 2:
% 227.06/39.14  | | | | | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | | | | |   (117)  all_57_9 = e1 & op(e3, e0) = e1
% 227.06/39.14  | | | | | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | | | | | ALPHA: (117) implies:
% 227.06/39.14  | | | | | | | | | | | | | |   (118)  all_57_9 = e1
% 227.06/39.14  | | | | | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | | | | | BETA: splitting (65) gives:
% 227.06/39.14  | | | | | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | | | | | Case 1:
% 227.06/39.14  | | | | | | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | | | | | |   (119)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 227.06/39.14  | | | | | | | | | | | | | | |            & op(e2, e1) = e2)
% 227.06/39.14  | | | | | | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | | | | | | BETA: splitting (119) gives:
% 227.06/39.14  | | | | | | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | | | | | | Case 1:
% 227.06/39.14  | | | | | | | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | | | | | | |   (120)  all_57_4 = e2 & op(e3, e1) = e2
% 227.06/39.14  | | | | | | | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | | | | | | | ALPHA: (120) implies:
% 227.06/39.14  | | | | | | | | | | | | | | | |   (121)  all_57_4 = e2
% 227.06/39.14  | | | | | | | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (21), (23), (29), (38), (110), (118),
% 227.06/39.14  | | | | | | | | | | | | | | | |            (121) are inconsistent by sub-proof #1608.
% 227.06/39.14  | | | | | | | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | | | | | | Case 2:
% 227.06/39.14  | | | | | | | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | | | | | | |   (122)  all_57_5 = e2 & op(e2, e1) = e2
% 227.06/39.14  | | | | | | | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | | | | | | | ALPHA: (122) implies:
% 227.06/39.14  | | | | | | | | | | | | | | | |   (123)  all_57_5 = e2
% 227.06/39.14  | | | | | | | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (9), (10), (11),
% 227.06/39.14  | | | | | | | | | | | | | | | |            (12), (16), (17), (20), (21), (23), (24), (25),
% 227.06/39.14  | | | | | | | | | | | | | | | |            (26), (27), (28), (30), (31), (34), (35), (36),
% 227.06/39.14  | | | | | | | | | | | | | | | |            (39), (41), (42), (44), (45), (46), (47), (49),
% 227.06/39.14  | | | | | | | | | | | | | | | |            (53), (54), (55), (59), (60), (61), (62), (63),
% 227.06/39.14  | | | | | | | | | | | | | | | |            (64), (65), (66), (67), (68), (69), (70), (72),
% 227.06/39.14  | | | | | | | | | | | | | | | |            (123) are inconsistent by sub-proof #198.
% 227.06/39.14  | | | | | | | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | | | | | | End of split
% 227.06/39.14  | | | | | | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | | | | | Case 2:
% 227.06/39.14  | | | | | | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | | | | | |   (124)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 227.06/39.14  | | | | | | | | | | | | | | |            e2 & op(e0, e1) = e2)
% 227.06/39.14  | | | | | | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | | | | | | BETA: splitting (124) gives:
% 227.06/39.14  | | | | | | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | | | | | | Case 1:
% 227.06/39.14  | | | | | | | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | | | | | | |   (125)  all_57_8 = e2 & op(e1, e1) = e2
% 227.06/39.14  | | | | | | | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | | | | | | | ALPHA: (125) implies:
% 227.06/39.14  | | | | | | | | | | | | | | | |   (126)  all_57_8 = e2
% 227.06/39.14  | | | | | | | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | | | | | | | COMBINE_EQS: (54), (126) imply:
% 227.06/39.14  | | | | | | | | | | | | | | | |   (127)  e2 = e0
% 227.06/39.14  | | | | | | | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | | | | | | | SIMP: (127) implies:
% 227.06/39.14  | | | | | | | | | | | | | | | |   (128)  e2 = e0
% 227.06/39.14  | | | | | | | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | | | | | | | COMBINE_EQS: (32), (128) imply:
% 227.06/39.14  | | | | | | | | | | | | | | | |   (129)  all_57_10 = e0
% 227.06/39.14  | | | | | | | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | | | | | | | REF_CLOSE: (9), (14), (21), (27), (36), (37), (60), (61),
% 227.06/39.14  | | | | | | | | | | | | | | | |            (83), (118), (129) are inconsistent by sub-proof
% 227.06/39.14  | | | | | | | | | | | | | | | |            #1018.
% 227.06/39.14  | | | | | | | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | | | | | | Case 2:
% 227.06/39.14  | | | | | | | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | | | | | | |   (130)  all_57_14 = e2 & op(e0, e1) = e2
% 227.06/39.14  | | | | | | | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | | | | | | | ALPHA: (130) implies:
% 227.06/39.14  | | | | | | | | | | | | | | | |   (131)  all_57_14 = e2
% 227.06/39.14  | | | | | | | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | | | | | | | REF_CLOSE: (36), (39), (82), (95), (107), (131) are
% 227.06/39.14  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1584.
% 227.06/39.14  | | | | | | | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | | | | | | End of split
% 227.06/39.14  | | | | | | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | | | | | End of split
% 227.06/39.14  | | | | | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | | | | End of split
% 227.06/39.14  | | | | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | | | End of split
% 227.06/39.14  | | | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | | Case 2:
% 227.06/39.14  | | | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | | |   (132)  all_57_3 = e0 & op(e2, e2) = e0
% 227.06/39.14  | | | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | | | ALPHA: (132) implies:
% 227.06/39.14  | | | | | | | | | | | |   (133)  all_57_3 = e0
% 227.06/39.14  | | | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | | | REF_CLOSE: (3), (7), (21), (23), (36), (39), (50), (51),
% 227.06/39.14  | | | | | | | | | | | |            (56), (60), (133) are inconsistent by sub-proof
% 227.06/39.14  | | | | | | | | | | | |            #2246.
% 227.06/39.14  | | | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | | End of split
% 227.06/39.14  | | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | Case 2:
% 227.06/39.14  | | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | |   (134)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 227.06/39.14  | | | | | | | | | | |            e0 & op(e0, e2) = e0)
% 227.06/39.14  | | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | | BETA: splitting (134) gives:
% 227.06/39.14  | | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | | Case 1:
% 227.06/39.14  | | | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | | |   (135)  all_57_7 = e0 & op(e1, e2) = e0
% 227.06/39.14  | | | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | | | REF_CLOSE: (4), (9), (62), (135) are inconsistent by
% 227.06/39.14  | | | | | | | | | | | |            sub-proof #2039.
% 227.06/39.14  | | | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | | Case 2:
% 227.06/39.14  | | | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | | |   (136)  all_57_13 = e0 & op(e0, e2) = e0
% 227.06/39.14  | | | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | | | ALPHA: (136) implies:
% 227.06/39.14  | | | | | | | | | | | |   (137)  all_57_13 = e0
% 227.06/39.14  | | | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | | | REF_CLOSE: (6), (7), (8), (9), (10), (11), (12), (13), (14),
% 227.06/39.14  | | | | | | | | | | | |            (15), (16), (17), (18), (19), (20), (21), (22),
% 227.06/39.14  | | | | | | | | | | | |            (23), (27), (28), (29), (31), (32), (33), (36),
% 227.06/39.14  | | | | | | | | | | | |            (37), (38), (39), (40), (41), (43), (45), (46),
% 227.06/39.14  | | | | | | | | | | | |            (47), (48), (49), (52), (54), (55), (57), (60),
% 227.06/39.14  | | | | | | | | | | | |            (61), (65), (66), (67), (68), (69), (70), (71),
% 227.06/39.14  | | | | | | | | | | | |            (72), (83), (91), (96), (137) are inconsistent by
% 227.06/39.14  | | | | | | | | | | | |            sub-proof #197.
% 227.06/39.14  | | | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | | End of split
% 227.06/39.14  | | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | End of split
% 227.06/39.14  | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | End of split
% 227.06/39.14  | | | | | | | | | 
% 227.06/39.14  | | | | | | | | Case 2:
% 227.06/39.14  | | | | | | | | | 
% 227.06/39.14  | | | | | | | | |   (138)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2
% 227.06/39.14  | | | | | | | | |            & op(e0, e0) = e2)
% 227.06/39.14  | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | REF_CLOSE: (1), (9), (25), (36), (102), (138) are inconsistent
% 227.06/39.14  | | | | | | | | |            by sub-proof #2127.
% 227.06/39.14  | | | | | | | | | 
% 227.06/39.14  | | | | | | | | End of split
% 227.06/39.14  | | | | | | | | 
% 227.06/39.14  | | | | | | | End of split
% 227.06/39.14  | | | | | | | 
% 227.06/39.14  | | | | | | End of split
% 227.06/39.14  | | | | | | 
% 227.06/39.14  | | | | | End of split
% 227.06/39.14  | | | | | 
% 227.06/39.14  | | | | Case 2:
% 227.06/39.14  | | | | | 
% 227.06/39.14  | | | | |   (139)  all_57_10 = e1 & op(e2, e0) = e1
% 227.06/39.14  | | | | | 
% 227.06/39.14  | | | | | ALPHA: (139) implies:
% 227.06/39.14  | | | | |   (140)  all_57_10 = e1
% 227.06/39.14  | | | | | 
% 227.06/39.14  | | | | | REF_CLOSE: (32), (60), (140) are inconsistent by sub-proof #2144.
% 227.06/39.14  | | | | | 
% 227.06/39.14  | | | | End of split
% 227.06/39.14  | | | | 
% 227.06/39.14  | | | End of split
% 227.06/39.14  | | | 
% 227.06/39.14  | | End of split
% 227.06/39.14  | | 
% 227.06/39.14  | End of split
% 227.06/39.14  | 
% 227.06/39.14  End of proof
% 227.06/39.14  
% 227.06/39.14  Sub-proof #197 shows that the following formulas are inconsistent:
% 227.06/39.14  ----------------------------------------------------------------
% 227.06/39.14    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 227.06/39.14         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.06/39.14    (2)   ~ (e3 = e1)
% 227.06/39.14    (3)  op(e2, e3) = e0
% 227.06/39.14    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.06/39.14           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.06/39.14    (5)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 227.06/39.14         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 227.06/39.14    (6)   ~ (all_6_2 = e3)
% 227.06/39.14    (7)  op(e1, e1) = all_6_2
% 227.06/39.14    (8)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 227.06/39.14         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 227.06/39.14    (9)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) = all_22_1
% 227.06/39.14           & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0, e3) =
% 227.06/39.14           all_22_1 & $i(all_22_1))
% 227.06/39.14    (10)  op(e2, e3) = all_52_9
% 227.06/39.14    (11)  op(e2, e0) = all_52_15
% 227.06/39.14    (12)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 227.06/39.14          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 227.06/39.14    (13)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 227.06/39.14          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 227.06/39.14    (14)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 227.06/39.14          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 227.06/39.14    (15)  all_57_4 = e3
% 227.06/39.14    (16)   ~ (e3 = e2)
% 227.06/39.14    (17)  op(e1, e0) = all_53_14
% 227.06/39.14    (18)   ~ (e3 = e0)
% 227.06/39.14    (19)  op(e0, e3) = e1
% 227.06/39.14    (20)  all_57_15 = e3
% 227.06/39.14    (21)  op(e2, e2) = all_52_11
% 227.06/39.14    (22)  op(e3, e3) = e2
% 227.06/39.14    (23)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 227.06/39.14          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 227.06/39.14            e1)
% 227.06/39.14    (24)  all_57_10 = e2
% 227.06/39.14    (25)  op(e2, e0) = e2
% 227.06/39.14    (26)   ~ (e2 = e0)
% 227.06/39.14    (27)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 227.06/39.14            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 227.06/39.14              e3) = all_12_1 & $i(all_12_1))
% 227.06/39.14    (28)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 227.06/39.14          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 227.06/39.14    (29)   ~ (e1 = e0)
% 227.06/39.14    (30)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 227.06/39.14          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 227.06/39.14    (31)  all_57_6 = e3
% 227.06/39.14    (32)   ~ (all_53_14 = e0)
% 227.06/39.14    (33)  op(e0, e0) = e3
% 227.06/39.14    (34)  all_57_5 = e1
% 227.06/39.14    (35)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.06/39.14          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 227.06/39.14            e2)
% 227.06/39.14    (36)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 227.06/39.14              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 227.06/39.14                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 227.06/39.14                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 227.06/39.14    (37)  op(all_52_9, all_52_9) = e3
% 227.06/39.14    (38)  op(e1, e1) = e0
% 227.06/39.14    (39)  all_57_13 = e0
% 227.06/39.14    (40)   ~ (all_53_12 = e3)
% 227.06/39.14    (41)  all_57_8 = e0
% 227.06/39.14    (42)  op(all_52_15, all_52_15) = e0
% 227.06/39.14    (43)  op(e2, e2) = e3
% 227.06/39.14    (44)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) |
% 227.06/39.14          (all_57_11 = e0 & op(e1, e0) = e0)
% 227.06/39.14    (45)   ~ (e2 = e1)
% 227.06/39.14    (46)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 227.06/39.14          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 227.06/39.14    (47)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 227.06/39.14          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 227.06/39.14    (48)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 227.06/39.14          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 227.06/39.14    (49)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 227.06/39.14          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 227.06/39.14    (50)  op(all_52_11, all_52_11) = e2
% 227.06/39.14    (51)   ~ (all_52_15 = e3)
% 227.06/39.14    (52)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 227.06/39.14          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 227.06/39.14    (53)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 227.06/39.14          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 227.06/39.14    (54)  op(e3, e0) = all_53_12
% 227.06/39.14  
% 227.06/39.14  Begin of proof
% 227.06/39.14  | 
% 227.06/39.14  | BETA: splitting (1) gives:
% 227.06/39.14  | 
% 227.06/39.14  | Case 1:
% 227.06/39.14  | | 
% 227.06/39.14  | |   (55)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 227.06/39.14  | |           e2)
% 227.06/39.14  | | 
% 227.06/39.14  | | REF_CLOSE: (2), (4), (8), (13), (16), (18), (22), (26), (28), (29), (40),
% 227.06/39.14  | |            (43), (45), (54), (55) are inconsistent by sub-proof #205.
% 227.06/39.14  | | 
% 227.06/39.14  | Case 2:
% 227.06/39.14  | | 
% 227.06/39.14  | |   (56)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 227.06/39.14  | |           e2)
% 227.06/39.14  | | 
% 227.06/39.14  | | BETA: splitting (56) gives:
% 227.06/39.14  | | 
% 227.06/39.14  | | Case 1:
% 227.06/39.14  | | | 
% 227.06/39.14  | | |   (57)  all_57_7 = e2 & op(e1, e2) = e2
% 227.06/39.14  | | | 
% 227.06/39.14  | | | ALPHA: (57) implies:
% 227.06/39.14  | | |   (58)  all_57_7 = e2
% 227.06/39.14  | | | 
% 227.06/39.14  | | | BETA: splitting (52) gives:
% 227.06/39.14  | | | 
% 227.06/39.14  | | | Case 1:
% 227.06/39.14  | | | | 
% 227.06/39.14  | | | |   (59)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2)
% 227.06/39.14  | | | |           = e1)
% 227.06/39.14  | | | | 
% 227.06/39.14  | | | | BETA: splitting (59) gives:
% 227.06/39.14  | | | | 
% 227.06/39.14  | | | | Case 1:
% 227.06/39.14  | | | | | 
% 227.06/39.14  | | | | |   (60)  all_57_1 = e1 & op(e3, e2) = e1
% 227.06/39.14  | | | | | 
% 227.06/39.14  | | | | | ALPHA: (60) implies:
% 227.06/39.14  | | | | |   (61)  all_57_1 = e1
% 227.06/39.14  | | | | | 
% 227.06/39.14  | | | | | BETA: splitting (49) gives:
% 227.06/39.14  | | | | | 
% 227.06/39.14  | | | | | Case 1:
% 227.06/39.14  | | | | | | 
% 227.06/39.14  | | | | | |   (62)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1,
% 227.06/39.14  | | | | | |             e2) = e1)
% 227.06/39.14  | | | | | | 
% 227.06/39.14  | | | | | | BETA: splitting (62) gives:
% 227.06/39.14  | | | | | | 
% 227.06/39.14  | | | | | | Case 1:
% 227.06/39.14  | | | | | | | 
% 227.06/39.14  | | | | | | |   (63)  all_57_6 = e1 & op(e1, e3) = e1
% 227.06/39.14  | | | | | | | 
% 227.06/39.14  | | | | | | | ALPHA: (63) implies:
% 227.06/39.14  | | | | | | |   (64)  all_57_6 = e1
% 227.06/39.14  | | | | | | | 
% 227.06/39.14  | | | | | | | REF_CLOSE: (2), (4), (5), (6), (7), (16), (18), (20), (26), (29),
% 227.06/39.14  | | | | | | |            (33), (36), (45), (46), (48), (58), (64) are
% 227.06/39.14  | | | | | | |            inconsistent by sub-proof #1078.
% 227.06/39.14  | | | | | | | 
% 227.06/39.14  | | | | | | Case 2:
% 227.06/39.14  | | | | | | | 
% 227.06/39.14  | | | | | | |   (65)  all_57_7 = e1 & op(e1, e2) = e1
% 227.06/39.14  | | | | | | | 
% 227.06/39.14  | | | | | | | ALPHA: (65) implies:
% 227.06/39.14  | | | | | | |   (66)  all_57_7 = e1
% 227.06/39.14  | | | | | | | 
% 227.06/39.14  | | | | | | | REF_CLOSE: (2), (4), (5), (6), (7), (9), (16), (18), (19), (20),
% 227.06/39.14  | | | | | | |            (26), (27), (29), (36), (41), (45), (46), (48), (53),
% 227.06/39.14  | | | | | | |            (66) are inconsistent by sub-proof #643.
% 227.06/39.14  | | | | | | | 
% 227.06/39.14  | | | | | | End of split
% 227.06/39.14  | | | | | | 
% 227.06/39.14  | | | | | Case 2:
% 227.06/39.14  | | | | | | 
% 227.06/39.14  | | | | | |   (67)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1,
% 227.06/39.14  | | | | | |             e0) = e1)
% 227.06/39.14  | | | | | | 
% 227.06/39.14  | | | | | | BETA: splitting (67) gives:
% 227.06/39.14  | | | | | | 
% 227.06/39.14  | | | | | | Case 1:
% 227.06/39.14  | | | | | | | 
% 227.06/39.14  | | | | | | |   (68)  all_57_8 = e1 & op(e1, e1) = e1
% 227.06/39.14  | | | | | | | 
% 227.06/39.14  | | | | | | | ALPHA: (68) implies:
% 227.06/39.14  | | | | | | |   (69)  op(e1, e1) = e1
% 227.06/39.14  | | | | | | | 
% 227.06/39.14  | | | | | | | REF_CLOSE: (2), (4), (6), (7), (14), (16), (18), (20), (23), (26),
% 227.06/39.14  | | | | | | |            (29), (30), (34), (35), (36), (45), (47), (69) are
% 227.06/39.14  | | | | | | |            inconsistent by sub-proof #941.
% 227.06/39.14  | | | | | | | 
% 227.06/39.14  | | | | | | Case 2:
% 227.06/39.14  | | | | | | | 
% 227.06/39.14  | | | | | | |   (70)  all_57_11 = e1 & op(e1, e0) = e1
% 227.06/39.14  | | | | | | | 
% 227.06/39.14  | | | | | | | ALPHA: (70) implies:
% 227.06/39.14  | | | | | | |   (71)  all_57_11 = e1
% 227.06/39.14  | | | | | | | 
% 227.06/39.14  | | | | | | | BETA: splitting (44) gives:
% 227.06/39.14  | | | | | | | 
% 227.06/39.14  | | | | | | | Case 1:
% 227.06/39.14  | | | | | | | | 
% 227.06/39.14  | | | | | | | |   (72)  all_57_9 = e0 & op(e3, e0) = e0
% 227.06/39.14  | | | | | | | | 
% 227.06/39.14  | | | | | | | | ALPHA: (72) implies:
% 227.06/39.14  | | | | | | | |   (73)  all_57_9 = e0
% 227.06/39.14  | | | | | | | | 
% 227.06/39.14  | | | | | | | | BETA: splitting (8) gives:
% 227.06/39.14  | | | | | | | | 
% 227.06/39.14  | | | | | | | | Case 1:
% 227.06/39.14  | | | | | | | | | 
% 227.06/39.14  | | | | | | | | |   (74)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 &
% 227.06/39.14  | | | | | | | | |           op(e3, e2) = e1)
% 227.06/39.14  | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | BETA: splitting (74) gives:
% 227.06/39.14  | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | Case 1:
% 227.06/39.14  | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | |   (75)  all_57_0 = e1 & op(e3, e3) = e1
% 227.06/39.14  | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | ALPHA: (75) implies:
% 227.06/39.14  | | | | | | | | | |   (76)  op(e3, e3) = e1
% 227.06/39.14  | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | REF_CLOSE: (2), (4), (12), (16), (18), (26), (28), (45),
% 227.06/39.14  | | | | | | | | | |            (61), (73), (76) are inconsistent by sub-proof
% 227.06/39.14  | | | | | | | | | |            #295.
% 227.06/39.14  | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | Case 2:
% 227.06/39.14  | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | GROUND_INST: instantiating (4) with all_52_15, e2, e0, e2,
% 227.06/39.14  | | | | | | | | | |              simplifying with (11), (25) gives:
% 227.06/39.14  | | | | | | | | | |   (77)  all_52_15 = e2
% 227.06/39.14  | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | GROUND_INST: instantiating (4) with all_52_9, e0, e3, e2,
% 227.06/39.14  | | | | | | | | | |              simplifying with (3), (10) gives:
% 227.06/39.14  | | | | | | | | | |   (78)  all_52_9 = e0
% 227.06/39.14  | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | REDUCE: (51), (77) imply:
% 227.06/39.14  | | | | | | | | | |   (79)   ~ (e3 = e2)
% 227.06/39.14  | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | REDUCE: (42), (77) imply:
% 227.06/39.14  | | | | | | | | | |   (80)  op(e2, e2) = e0
% 227.06/39.14  | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | REF_CLOSE: (4), (16), (21), (33), (50), (80) are inconsistent
% 227.06/39.14  | | | | | | | | | |            by sub-proof #1229.
% 227.06/39.14  | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | End of split
% 227.06/39.14  | | | | | | | | | 
% 227.06/39.14  | | | | | | | | Case 2:
% 227.06/39.14  | | | | | | | | | 
% 227.06/39.14  | | | | | | | | |   (81)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 &
% 227.06/39.14  | | | | | | | | |           op(e3, e0) = e1)
% 227.06/39.14  | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | BETA: splitting (81) gives:
% 227.06/39.14  | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | Case 1:
% 227.06/39.14  | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | |   (82)  all_57_4 = e1 & op(e3, e1) = e1
% 227.06/39.14  | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | ALPHA: (82) implies:
% 227.06/39.14  | | | | | | | | | |   (83)  all_57_4 = e1
% 227.06/39.14  | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | COMBINE_EQS: (15), (83) imply:
% 227.06/39.14  | | | | | | | | | |   (84)  e3 = e1
% 227.06/39.14  | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | COMBINE_EQS: (31), (84) imply:
% 227.06/39.14  | | | | | | | | | |   (85)  all_57_6 = e1
% 227.06/39.14  | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | REF_CLOSE: (2), (4), (5), (6), (7), (16), (26), (41), (45),
% 227.06/39.14  | | | | | | | | | |            (53), (71), (85) are inconsistent by sub-proof
% 227.06/39.14  | | | | | | | | | |            #2003.
% 227.06/39.14  | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | Case 2:
% 227.06/39.14  | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | |   (86)  all_57_9 = e1 & op(e3, e0) = e1
% 227.06/39.14  | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | ALPHA: (86) implies:
% 227.06/39.14  | | | | | | | | | |   (87)  all_57_9 = e1
% 227.06/39.14  | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | COMBINE_EQS: (73), (87) imply:
% 227.06/39.14  | | | | | | | | | |   (88)  e1 = e0
% 227.06/39.14  | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | SIMP: (88) implies:
% 227.06/39.14  | | | | | | | | | |   (89)  e1 = e0
% 227.06/39.14  | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | COMBINE_EQS: (71), (89) imply:
% 227.06/39.14  | | | | | | | | | |   (90)  all_57_11 = e0
% 227.06/39.14  | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | | REF_CLOSE: (2), (16), (20), (26), (29), (45), (46), (48),
% 227.06/39.14  | | | | | | | | | |            (73), (90) are inconsistent by sub-proof #1144.
% 227.06/39.14  | | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | End of split
% 227.06/39.14  | | | | | | | | | 
% 227.06/39.14  | | | | | | | | End of split
% 227.06/39.14  | | | | | | | | 
% 227.06/39.14  | | | | | | | Case 2:
% 227.06/39.14  | | | | | | | | 
% 227.06/39.14  | | | | | | | |   (91)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 227.06/39.14  | | | | | | | |           op(e1, e0) = e0)
% 227.06/39.14  | | | | | | | | 
% 227.06/39.14  | | | | | | | | BETA: splitting (91) gives:
% 227.06/39.14  | | | | | | | | 
% 227.06/39.14  | | | | | | | | Case 1:
% 227.06/39.14  | | | | | | | | | 
% 227.06/39.14  | | | | | | | | |   (92)  all_57_10 = e0 & op(e2, e0) = e0
% 227.06/39.14  | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | REF_CLOSE: (24), (26), (92) are inconsistent by sub-proof
% 227.06/39.14  | | | | | | | | |            #1751.
% 227.06/39.14  | | | | | | | | | 
% 227.06/39.14  | | | | | | | | Case 2:
% 227.06/39.14  | | | | | | | | | 
% 227.06/39.14  | | | | | | | | |   (93)  all_57_11 = e0 & op(e1, e0) = e0
% 227.06/39.14  | | | | | | | | | 
% 227.06/39.14  | | | | | | | | | REF_CLOSE: (4), (17), (32), (93) are inconsistent by sub-proof
% 227.06/39.14  | | | | | | | | |            #2341.
% 227.06/39.14  | | | | | | | | | 
% 227.06/39.14  | | | | | | | | End of split
% 227.06/39.14  | | | | | | | | 
% 227.06/39.14  | | | | | | | End of split
% 227.06/39.14  | | | | | | | 
% 227.06/39.14  | | | | | | End of split
% 227.06/39.14  | | | | | | 
% 227.06/39.14  | | | | | End of split
% 227.06/39.14  | | | | | 
% 227.06/39.14  | | | | Case 2:
% 227.06/39.14  | | | | | 
% 227.06/39.14  | | | | |   (94)  all_57_3 = e1 & op(e2, e2) = e1
% 227.06/39.14  | | | | | 
% 227.06/39.14  | | | | | ALPHA: (94) implies:
% 227.06/39.14  | | | | |   (95)  op(e2, e2) = e1
% 227.06/39.14  | | | | | 
% 227.06/39.14  | | | | | REF_CLOSE: (4), (21), (26), (38), (50), (95) are inconsistent by
% 227.06/39.14  | | | | |            sub-proof #1843.
% 227.06/39.14  | | | | | 
% 227.06/39.14  | | | | End of split
% 227.06/39.14  | | | | 
% 227.06/39.14  | | | Case 2:
% 227.06/39.14  | | | | 
% 227.06/39.14  | | | |   (96)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2)
% 227.06/39.14  | | | |           = e1)
% 227.06/39.14  | | | | 
% 227.06/39.14  | | | | BETA: splitting (96) gives:
% 227.06/39.14  | | | | 
% 227.06/39.14  | | | | Case 1:
% 227.06/39.14  | | | | | 
% 227.06/39.14  | | | | |   (97)  all_57_7 = e1 & op(e1, e2) = e1
% 227.06/39.14  | | | | | 
% 227.06/39.14  | | | | | ALPHA: (97) implies:
% 227.06/39.14  | | | | |   (98)  all_57_7 = e1
% 227.06/39.14  | | | | | 
% 227.06/39.14  | | | | | REF_CLOSE: (2), (4), (5), (6), (7), (9), (16), (18), (19), (20), (26),
% 227.06/39.14  | | | | |            (27), (29), (36), (41), (45), (46), (48), (53), (98) are
% 227.06/39.14  | | | | |            inconsistent by sub-proof #643.
% 227.06/39.14  | | | | | 
% 227.06/39.14  | | | | Case 2:
% 227.06/39.14  | | | | | 
% 227.06/39.14  | | | | |   (99)  all_57_13 = e1 & op(e0, e2) = e1
% 227.06/39.14  | | | | | 
% 227.06/39.14  | | | | | ALPHA: (99) implies:
% 227.06/39.14  | | | | |   (100)  all_57_13 = e1
% 227.06/39.14  | | | | | 
% 227.06/39.14  | | | | | REF_CLOSE: (29), (39), (100) are inconsistent by sub-proof #1760.
% 227.06/39.14  | | | | | 
% 227.06/39.14  | | | | End of split
% 227.06/39.14  | | | | 
% 227.06/39.14  | | | End of split
% 227.06/39.14  | | | 
% 227.06/39.14  | | Case 2:
% 227.06/39.14  | | | 
% 227.06/39.14  | | |   (101)  all_57_13 = e2 & op(e0, e2) = e2
% 227.06/39.14  | | | 
% 227.06/39.14  | | | ALPHA: (101) implies:
% 227.06/39.14  | | |   (102)  all_57_13 = e2
% 227.06/39.14  | | | 
% 227.06/39.14  | | | REF_CLOSE: (26), (39), (102) are inconsistent by sub-proof #1911.
% 227.06/39.14  | | | 
% 227.06/39.14  | | End of split
% 227.06/39.14  | | 
% 227.06/39.14  | End of split
% 227.06/39.14  | 
% 227.06/39.14  End of proof
% 227.06/39.14  
% 227.06/39.14  Sub-proof #198 shows that the following formulas are inconsistent:
% 227.06/39.14  ----------------------------------------------------------------
% 227.06/39.14    (1)  op(e0, e0) = all_4_2
% 227.06/39.14    (2)  all_57_0 = e2
% 227.06/39.14    (3)   ~ (all_53_6 = e0)
% 227.06/39.14    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 227.06/39.14         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 227.06/39.14    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 227.06/39.14         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.06/39.14    (6)   ~ (e3 = e1)
% 227.06/39.14    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.06/39.14           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.06/39.14    (8)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 227.06/39.14         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 227.06/39.14    (9)   ~ (all_6_2 = e3)
% 227.06/39.14    (10)  op(e1, e1) = all_6_2
% 227.06/39.14    (11)  op(e2, e0) = all_52_15
% 227.06/39.14    (12)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 227.06/39.14          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 227.06/39.14    (13)  all_57_4 = e3
% 227.06/39.14    (14)   ~ (e3 = e2)
% 227.06/39.14    (15)   ~ (e3 = e0)
% 227.06/39.14    (16)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 227.06/39.14          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 227.06/39.14    (17)   ~ (all_4_2 = e2)
% 227.06/39.14    (18)  op(e0, e3) = all_53_3
% 227.06/39.14    (19)  all_57_15 = e3
% 227.06/39.14    (20)  op(e2, e2) = all_52_11
% 227.06/39.14    (21)   ~ (all_53_3 = e2)
% 227.06/39.14    (22)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 227.06/39.14          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 227.06/39.14            e1)
% 227.06/39.14    (23)  op(e3, e2) = all_53_4
% 227.06/39.14    (24)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 227.06/39.14          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 227.06/39.14    (25)   ~ (e2 = e0)
% 227.06/39.14    (26)   ~ (e1 = e0)
% 227.06/39.14    (27)  all_57_5 = e2
% 227.06/39.14    (28)  all_57_6 = e3
% 227.06/39.14    (29)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 227.06/39.14          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 227.06/39.14    (30)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 227.06/39.14          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 227.06/39.14            e3)
% 227.06/39.14    (31)  op(e0, e0) = e3
% 227.06/39.14    (32)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.06/39.14          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 227.06/39.14            e2)
% 227.06/39.15    (33)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 227.06/39.15              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 227.06/39.15                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 227.06/39.15                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 227.06/39.15    (34)  op(e1, e1) = e0
% 227.06/39.15    (35)   ~ (all_53_4 = e2)
% 227.06/39.15    (36)  all_57_8 = e0
% 227.06/39.15    (37)  op(all_52_15, all_52_15) = e0
% 227.06/39.15    (38)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 227.06/39.15          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 227.06/39.15    (39)   ~ (e2 = e1)
% 227.06/39.15    (40)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 227.06/39.15          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 227.06/39.15    (41)  op(e1, e2) = all_53_6
% 227.06/39.15    (42)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 227.06/39.15          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 227.06/39.15    (43)   ~ (all_53_12 = e2)
% 227.06/39.15    (44)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 227.06/39.15          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 227.06/39.15    (45)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 227.06/39.15          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 227.06/39.15    (46)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 227.06/39.15          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 227.06/39.15    (47)  op(all_52_11, all_52_11) = e2
% 227.06/39.15    (48)   ~ (all_52_15 = e3)
% 227.06/39.15    (49)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 227.06/39.15          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 227.06/39.15    (50)  op(e3, e0) = all_53_12
% 227.06/39.15  
% 227.06/39.15  Begin of proof
% 227.06/39.15  | 
% 227.06/39.15  | BETA: splitting (16) gives:
% 227.06/39.15  | 
% 227.06/39.15  | Case 1:
% 227.06/39.15  | | 
% 227.06/39.15  | |   (51)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) =
% 227.06/39.15  | |           e1)
% 227.06/39.15  | | 
% 227.06/39.15  | | REF_CLOSE: (6), (13), (27), (39), (51) are inconsistent by sub-proof #200.
% 227.06/39.15  | | 
% 227.06/39.15  | Case 2:
% 227.06/39.15  | | 
% 227.06/39.15  | |   (52)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) =
% 227.06/39.15  | |           e1)
% 227.06/39.15  | | 
% 227.06/39.15  | | BETA: splitting (52) gives:
% 227.06/39.15  | | 
% 227.06/39.15  | | Case 1:
% 227.06/39.15  | | | 
% 227.06/39.15  | | |   (53)  all_57_8 = e1 & op(e1, e1) = e1
% 227.06/39.15  | | | 
% 227.06/39.15  | | | ALPHA: (53) implies:
% 227.06/39.15  | | |   (54)  op(e1, e1) = e1
% 227.06/39.15  | | | 
% 227.06/39.15  | | | REF_CLOSE: (7), (26), (34), (54) are inconsistent by sub-proof #2427.
% 227.06/39.15  | | | 
% 227.06/39.15  | | Case 2:
% 227.06/39.15  | | | 
% 227.06/39.15  | | |   (55)  all_57_14 = e1 & op(e0, e1) = e1
% 227.06/39.15  | | | 
% 227.06/39.15  | | | ALPHA: (55) implies:
% 227.06/39.15  | | |   (56)  all_57_14 = e1
% 227.06/39.15  | | | 
% 227.06/39.15  | | | BETA: splitting (32) gives:
% 227.06/39.15  | | | 
% 227.06/39.15  | | | Case 1:
% 227.06/39.15  | | | | 
% 227.06/39.15  | | | |   (57)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0,
% 227.06/39.15  | | | |             e2) = e2)
% 227.06/39.15  | | | | 
% 227.06/39.15  | | | | BETA: splitting (57) gives:
% 227.06/39.15  | | | | 
% 227.06/39.15  | | | | Case 1:
% 227.06/39.15  | | | | | 
% 227.06/39.15  | | | | |   (58)  all_57_12 = e2 & op(e0, e3) = e2
% 227.06/39.15  | | | | | 
% 227.06/39.15  | | | | | ALPHA: (58) implies:
% 227.06/39.15  | | | | |   (59)  op(e0, e3) = e2
% 227.06/39.15  | | | | | 
% 227.06/39.15  | | | | | REF_CLOSE: (7), (18), (21), (59) are inconsistent by sub-proof #1980.
% 227.06/39.15  | | | | | 
% 227.06/39.15  | | | | Case 2:
% 227.06/39.15  | | | | | 
% 227.06/39.15  | | | | |   (60)  all_57_13 = e2 & op(e0, e2) = e2
% 227.06/39.15  | | | | | 
% 227.06/39.15  | | | | | ALPHA: (60) implies:
% 227.06/39.15  | | | | |   (61)  all_57_13 = e2
% 227.06/39.15  | | | | | 
% 227.06/39.15  | | | | | BETA: splitting (33) gives:
% 227.06/39.15  | | | | | 
% 227.06/39.15  | | | | | Case 1:
% 227.06/39.15  | | | | | | 
% 227.06/39.15  | | | | | |   (62)  all_57_15 = e0 & op(e0, e0) = e0
% 227.06/39.15  | | | | | | 
% 227.06/39.15  | | | | | | ALPHA: (62) implies:
% 227.06/39.15  | | | | | |   (63)  op(e0, e0) = e0
% 227.06/39.15  | | | | | | 
% 227.06/39.15  | | | | | | REF_CLOSE: (7), (15), (31), (63) are inconsistent by sub-proof
% 227.06/39.15  | | | | | |            #2304.
% 227.06/39.15  | | | | | | 
% 227.06/39.15  | | | | | Case 2:
% 227.06/39.15  | | | | | | 
% 227.06/39.15  | | | | | |   (64)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 &
% 227.06/39.15  | | | | | |             op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) &
% 227.06/39.15  | | | | | |         ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 227.06/39.15  | | | | | |             op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 227.06/39.15  | | | | | | 
% 227.06/39.15  | | | | | | ALPHA: (64) implies:
% 227.06/39.15  | | | | | |   (65)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 227.06/39.15  | | | | | |           op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 227.06/39.15  | | | | | | 
% 227.06/39.15  | | | | | | BETA: splitting (65) gives:
% 227.06/39.15  | | | | | | 
% 227.06/39.15  | | | | | | Case 1:
% 227.06/39.15  | | | | | | | 
% 227.06/39.15  | | | | | | |   (66)  all_57_12 = e0 & op(e0, e3) = e0
% 227.06/39.15  | | | | | | | 
% 227.06/39.15  | | | | | | | ALPHA: (66) implies:
% 227.06/39.15  | | | | | | |   (67)  all_57_12 = e0
% 227.06/39.15  | | | | | | | 
% 227.06/39.15  | | | | | | | BETA: splitting (4) gives:
% 227.06/39.15  | | | | | | | 
% 227.06/39.15  | | | | | | | Case 1:
% 227.06/39.15  | | | | | | | | 
% 227.06/39.15  | | | | | | | |   (68)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 &
% 227.06/39.15  | | | | | | | |           op(e2, e3) = e1)
% 227.06/39.15  | | | | | | | | 
% 227.06/39.15  | | | | | | | | BETA: splitting (68) gives:
% 227.06/39.15  | | | | | | | | 
% 227.06/39.15  | | | | | | | | Case 1:
% 227.06/39.15  | | | | | | | | | 
% 227.06/39.15  | | | | | | | | |   (69)  all_57_0 = e1 & op(e3, e3) = e1
% 227.06/39.15  | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | ALPHA: (69) implies:
% 227.06/39.15  | | | | | | | | |   (70)  op(e3, e3) = e1
% 227.06/39.15  | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | REF_CLOSE: (7), (12), (13), (14), (23), (35), (39), (43),
% 227.06/39.15  | | | | | | | | |            (50), (70) are inconsistent by sub-proof #234.
% 227.06/39.15  | | | | | | | | | 
% 227.06/39.15  | | | | | | | | Case 2:
% 227.06/39.15  | | | | | | | | | 
% 227.06/39.15  | | | | | | | | |   (71)  all_57_2 = e1 & op(e2, e3) = e1
% 227.06/39.15  | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | ALPHA: (71) implies:
% 227.06/39.15  | | | | | | | | |   (72)  all_57_2 = e1
% 227.06/39.15  | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | BETA: splitting (24) gives:
% 227.06/39.15  | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | Case 1:
% 227.06/39.15  | | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | |   (73)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 &
% 227.06/39.15  | | | | | | | | | |           op(e2, e2) = e0)
% 227.06/39.15  | | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | | BETA: splitting (73) gives:
% 227.06/39.15  | | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | | Case 1:
% 227.06/39.15  | | | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | | |   (74)  all_57_1 = e0 & op(e3, e2) = e0
% 227.06/39.15  | | | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | | | ALPHA: (74) implies:
% 227.06/39.15  | | | | | | | | | | |   (75)  all_57_1 = e0
% 227.06/39.15  | | | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | | | BETA: splitting (38) gives:
% 227.06/39.15  | | | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | | | Case 1:
% 227.06/39.15  | | | | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | | | |   (76)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 227.06/39.15  | | | | | | | | | | | |           & op(e2, e2) = e0)
% 227.06/39.15  | | | | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | | | | BETA: splitting (76) gives:
% 227.06/39.15  | | | | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | | | | Case 1:
% 227.06/39.15  | | | | | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | | | | |   (77)  all_57_2 = e0 & op(e2, e3) = e0
% 227.06/39.15  | | | | | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | | | | | ALPHA: (77) implies:
% 227.06/39.15  | | | | | | | | | | | | |   (78)  all_57_2 = e0
% 227.06/39.15  | | | | | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | | | | | REF_CLOSE: (26), (72), (78) are inconsistent by sub-proof
% 227.06/39.15  | | | | | | | | | | | | |            #2473.
% 227.06/39.15  | | | | | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | | | | Case 2:
% 227.06/39.15  | | | | | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | | | | |   (79)  all_57_3 = e0 & op(e2, e2) = e0
% 227.06/39.15  | | | | | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | | | | | ALPHA: (79) implies:
% 227.06/39.15  | | | | | | | | | | | | |   (80)  all_57_3 = e0
% 227.06/39.15  | | | | | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | | | | | REF_CLOSE: (5), (6), (14), (15), (19), (22), (25), (26),
% 227.06/39.15  | | | | | | | | | | | | |            (29), (32), (39), (49), (67), (75), (80) are
% 227.06/39.15  | | | | | | | | | | | | |            inconsistent by sub-proof #694.
% 227.06/39.15  | | | | | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | | | | End of split
% 227.06/39.15  | | | | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | | | Case 2:
% 227.06/39.15  | | | | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | | | |   (81)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 227.06/39.15  | | | | | | | | | | | |           e0 & op(e2, e0) = e0)
% 227.06/39.15  | | | | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | | | | BETA: splitting (81) gives:
% 227.06/39.15  | | | | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | | | | Case 1:
% 227.06/39.15  | | | | | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | | | | |   (82)  all_57_5 = e0 & op(e2, e1) = e0
% 227.06/39.15  | | | | | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | | | | | ALPHA: (82) implies:
% 227.06/39.15  | | | | | | | | | | | | |   (83)  all_57_5 = e0
% 227.06/39.15  | | | | | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | | | | | COMBINE_EQS: (27), (83) imply:
% 227.06/39.15  | | | | | | | | | | | | |   (84)  e2 = e0
% 227.06/39.15  | | | | | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | | | | | SIMP: (84) implies:
% 227.06/39.15  | | | | | | | | | | | | |   (85)  e2 = e0
% 227.06/39.15  | | | | | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | | | | | COMBINE_EQS: (2), (85) imply:
% 227.06/39.15  | | | | | | | | | | | | |   (86)  all_57_0 = e0
% 227.06/39.15  | | | | | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | | | | | REF_CLOSE: (14), (25), (28), (39), (42), (67), (72), (86) are
% 227.06/39.15  | | | | | | | | | | | | |            inconsistent by sub-proof #1426.
% 227.06/39.15  | | | | | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | | | | Case 2:
% 227.06/39.15  | | | | | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | | | | |   (87)  all_57_10 = e0 & op(e2, e0) = e0
% 227.06/39.15  | | | | | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | | | | | ALPHA: (87) implies:
% 227.06/39.15  | | | | | | | | | | | | |   (88)  all_57_10 = e0
% 227.06/39.15  | | | | | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | | | | | BETA: splitting (40) gives:
% 227.06/39.15  | | | | | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | | | | | Case 1:
% 227.06/39.15  | | | | | | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | | | | | |   (89)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 227.06/39.15  | | | | | | | | | | | | | |           e2 & op(e2, e0) = e2)
% 227.06/39.15  | | | | | | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | | | | | | BETA: splitting (89) gives:
% 227.06/39.15  | | | | | | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | | | | | | Case 1:
% 227.06/39.15  | | | | | | | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | | | | | | |   (90)  all_57_9 = e2 & op(e3, e0) = e2
% 227.06/39.15  | | | | | | | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | | | | | | | ALPHA: (90) implies:
% 227.06/39.15  | | | | | | | | | | | | | | |   (91)  op(e3, e0) = e2
% 227.06/39.15  | | | | | | | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | | | | | | | REF_CLOSE: (7), (43), (50), (91) are inconsistent by
% 227.06/39.15  | | | | | | | | | | | | | | |            sub-proof #2331.
% 227.06/39.15  | | | | | | | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | | | | | | Case 2:
% 227.06/39.15  | | | | | | | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | | | | | | |   (92)  all_57_10 = e2 & op(e2, e0) = e2
% 227.06/39.15  | | | | | | | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | | | | | | | ALPHA: (92) implies:
% 227.06/39.15  | | | | | | | | | | | | | | |   (93)  all_57_10 = e2
% 227.06/39.15  | | | | | | | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | | | | | | | COMBINE_EQS: (88), (93) imply:
% 227.06/39.15  | | | | | | | | | | | | | | |   (94)  e2 = e0
% 227.06/39.15  | | | | | | | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | | | | | | | SIMP: (94) implies:
% 227.06/39.15  | | | | | | | | | | | | | | |   (95)  e2 = e0
% 227.06/39.15  | | | | | | | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | | | | | | | COMBINE_EQS: (2), (95) imply:
% 227.06/39.15  | | | | | | | | | | | | | | |   (96)  all_57_0 = e0
% 227.06/39.15  | | | | | | | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | | | | | | | REF_CLOSE: (14), (25), (28), (39), (42), (67), (72), (96) are
% 227.06/39.15  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1426.
% 227.06/39.15  | | | | | | | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | | | | | | End of split
% 227.06/39.15  | | | | | | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | | | | | Case 2:
% 227.06/39.15  | | | | | | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | | | | | |   (97)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 227.06/39.15  | | | | | | | | | | | | | |           e2 & op(e0, e0) = e2)
% 227.06/39.15  | | | | | | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | | | | | | BETA: splitting (97) gives:
% 227.06/39.15  | | | | | | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | | | | | | Case 1:
% 227.06/39.15  | | | | | | | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | | | | | | |   (98)  all_57_11 = e2 & op(e1, e0) = e2
% 227.06/39.15  | | | | | | | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | | | | | | | ALPHA: (98) implies:
% 227.06/39.15  | | | | | | | | | | | | | | |   (99)  all_57_11 = e2
% 227.06/39.15  | | | | | | | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | | | | | | | BETA: splitting (46) gives:
% 227.06/39.15  | | | | | | | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | | | | | | | Case 1:
% 227.06/39.15  | | | | | | | | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | | | | | | | |   (100)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 227.06/39.15  | | | | | | | | | | | | | | | |            & op(e1, e2) = e1)
% 227.06/39.15  | | | | | | | | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | | | | | | | | BETA: splitting (100) gives:
% 227.06/39.15  | | | | | | | | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.15  | | | | | | | | | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | | | | | | | | |   (101)  all_57_6 = e1 & op(e1, e3) = e1
% 227.06/39.15  | | | | | | | | | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | | | | | | | | | ALPHA: (101) implies:
% 227.06/39.15  | | | | | | | | | | | | | | | | |   (102)  all_57_6 = e1
% 227.06/39.15  | | | | | | | | | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (28), (102) are inconsistent by sub-proof
% 227.06/39.15  | | | | | | | | | | | | | | | | |            #2017.
% 227.06/39.15  | | | | | | | | | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | | | | | | | | Case 2:
% 227.06/39.15  | | | | | | | | | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | | | | | | | | |   (103)  all_57_7 = e1 & op(e1, e2) = e1
% 227.06/39.15  | | | | | | | | | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | | | | | | | | | ALPHA: (103) implies:
% 227.06/39.15  | | | | | | | | | | | | | | | | |   (104)  all_57_7 = e1
% 227.06/39.15  | | | | | | | | | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | | | | | | | | | BETA: splitting (45) gives:
% 227.06/39.15  | | | | | | | | | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | | | | | | | | | Case 1:
% 227.06/39.15  | | | | | | | | | | | | | | | | | | 
% 227.06/39.15  | | | | | | | | | | | | | | | | | |   (105)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 227.06/39.15  | | | | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 227.06/39.15  | | | | | | | | | | | | | | | | | | 
% 227.35/39.15  | | | | | | | | | | | | | | | | | | BETA: splitting (105) gives:
% 227.35/39.15  | | | | | | | | | | | | | | | | | | 
% 227.35/39.15  | | | | | | | | | | | | | | | | | | Case 1:
% 227.35/39.15  | | | | | | | | | | | | | | | | | | | 
% 227.35/39.15  | | | | | | | | | | | | | | | | | | | 
% 227.35/39.15  | | | | | | | | | | | | | | | | | | | ALPHA: (87) implies:
% 227.35/39.15  | | | | | | | | | | | | | | | | | | |   (106)  op(e2, e0) = e0
% 227.35/39.15  | | | | | | | | | | | | | | | | | | | 
% 227.35/39.15  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_52_15, e0, e0, e2,
% 227.35/39.15  | | | | | | | | | | | | | | | | | | |              simplifying with (11), (106) gives:
% 227.35/39.15  | | | | | | | | | | | | | | | | | | |   (107)  all_52_15 = e0
% 227.35/39.15  | | | | | | | | | | | | | | | | | | | 
% 227.35/39.15  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (31), (37), (48), (107) are inconsistent by
% 227.35/39.15  | | | | | | | | | | | | | | | | | | |            sub-proof #277.
% 227.35/39.15  | | | | | | | | | | | | | | | | | | | 
% 227.35/39.15  | | | | | | | | | | | | | | | | | | Case 2:
% 227.35/39.15  | | | | | | | | | | | | | | | | | | | 
% 227.35/39.15  | | | | | | | | | | | | | | | | | | |   (108)  all_57_10 = e1 & op(e2, e0) = e1
% 227.35/39.15  | | | | | | | | | | | | | | | | | | | 
% 227.35/39.15  | | | | | | | | | | | | | | | | | | | ALPHA: (108) implies:
% 227.35/39.15  | | | | | | | | | | | | | | | | | | |   (109)  all_57_10 = e1
% 227.35/39.15  | | | | | | | | | | | | | | | | | | | 
% 227.35/39.15  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (88), (109) imply:
% 227.35/39.15  | | | | | | | | | | | | | | | | | | |   (110)  e1 = e0
% 227.35/39.15  | | | | | | | | | | | | | | | | | | | 
% 227.35/39.15  | | | | | | | | | | | | | | | | | | | SIMP: (110) implies:
% 227.35/39.15  | | | | | | | | | | | | | | | | | | |   (111)  e1 = e0
% 227.35/39.15  | | | | | | | | | | | | | | | | | | | 
% 227.35/39.15  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (104), (111) imply:
% 227.35/39.15  | | | | | | | | | | | | | | | | | | |   (112)  all_57_7 = e0
% 227.35/39.15  | | | | | | | | | | | | | | | | | | | 
% 227.35/39.15  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (8), (9), (10), (14), (15), (19), (25),
% 227.35/39.15  | | | | | | | | | | | | | | | | | | |            (26), (33), (34), (39), (40), (45), (46), (99),
% 227.35/39.15  | | | | | | | | | | | | | | | | | | |            (112) are inconsistent by sub-proof #947.
% 227.35/39.15  | | | | | | | | | | | | | | | | | | | 
% 227.35/39.15  | | | | | | | | | | | | | | | | | | End of split
% 227.35/39.15  | | | | | | | | | | | | | | | | | | 
% 227.35/39.15  | | | | | | | | | | | | | | | | | Case 2:
% 227.35/39.15  | | | | | | | | | | | | | | | | | | 
% 227.35/39.15  | | | | | | | | | | | | | | | | | |   (113)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 227.35/39.15  | | | | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 227.35/39.15  | | | | | | | | | | | | | | | | | | 
% 227.35/39.15  | | | | | | | | | | | | | | | | | | BETA: splitting (113) gives:
% 227.35/39.15  | | | | | | | | | | | | | | | | | | 
% 227.35/39.15  | | | | | | | | | | | | | | | | | | Case 1:
% 227.35/39.15  | | | | | | | | | | | | | | | | | | | 
% 227.35/39.15  | | | | | | | | | | | | | | | | | | |   (114)  all_57_11 = e1 & op(e1, e0) = e1
% 227.35/39.15  | | | | | | | | | | | | | | | | | | | 
% 227.35/39.15  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (14), (25), (27), (36), (39), (44), (56),
% 227.35/39.15  | | | | | | | | | | | | | | | | | | |            (99), (114) are inconsistent by sub-proof #199.
% 227.35/39.15  | | | | | | | | | | | | | | | | | | | 
% 227.35/39.15  | | | | | | | | | | | | | | | | | | Case 2:
% 227.35/39.15  | | | | | | | | | | | | | | | | | | | 
% 227.35/39.15  | | | | | | | | | | | | | | | | | | |   (115)  all_57_15 = e1 & op(e0, e0) = e1
% 227.35/39.15  | | | | | | | | | | | | | | | | | | | 
% 227.35/39.15  | | | | | | | | | | | | | | | | | | | ALPHA: (115) implies:
% 227.35/39.15  | | | | | | | | | | | | | | | | | | |   (116)  op(e0, e0) = e1
% 227.35/39.15  | | | | | | | | | | | | | | | | | | | 
% 227.35/39.15  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (14), (15), (18), (21), (30), (32),
% 227.35/39.15  | | | | | | | | | | | | | | | | | | |            (39), (56), (67), (116) are inconsistent by
% 227.35/39.15  | | | | | | | | | | | | | | | | | | |            sub-proof #1964.
% 227.35/39.15  | | | | | | | | | | | | | | | | | | | 
% 227.35/39.15  | | | | | | | | | | | | | | | | | | End of split
% 227.35/39.15  | | | | | | | | | | | | | | | | | | 
% 227.35/39.15  | | | | | | | | | | | | | | | | | End of split
% 227.35/39.15  | | | | | | | | | | | | | | | | | 
% 227.35/39.15  | | | | | | | | | | | | | | | | End of split
% 227.35/39.15  | | | | | | | | | | | | | | | | 
% 227.35/39.15  | | | | | | | | | | | | | | | Case 2:
% 227.35/39.15  | | | | | | | | | | | | | | | | 
% 227.35/39.15  | | | | | | | | | | | | | | | |   (117)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 227.35/39.15  | | | | | | | | | | | | | | | |            e1 & op(e1, e0) = e1)
% 227.35/39.15  | | | | | | | | | | | | | | | | 
% 227.35/39.15  | | | | | | | | | | | | | | | | BETA: splitting (117) gives:
% 227.35/39.15  | | | | | | | | | | | | | | | | 
% 227.35/39.15  | | | | | | | | | | | | | | | | Case 1:
% 227.35/39.15  | | | | | | | | | | | | | | | | | 
% 227.35/39.15  | | | | | | | | | | | | | | | | |   (118)  all_57_8 = e1 & op(e1, e1) = e1
% 227.35/39.15  | | | | | | | | | | | | | | | | | 
% 227.35/39.15  | | | | | | | | | | | | | | | | | ALPHA: (118) implies:
% 227.35/39.15  | | | | | | | | | | | | | | | | |   (119)  op(e1, e1) = e1
% 227.35/39.15  | | | | | | | | | | | | | | | | | 
% 227.35/39.15  | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (26), (34), (119) are inconsistent by
% 227.35/39.15  | | | | | | | | | | | | | | | | |            sub-proof #2427.
% 227.35/39.15  | | | | | | | | | | | | | | | | | 
% 227.35/39.15  | | | | | | | | | | | | | | | | Case 2:
% 227.35/39.15  | | | | | | | | | | | | | | | | | 
% 227.35/39.15  | | | | | | | | | | | | | | | | |   (120)  all_57_11 = e1 & op(e1, e0) = e1
% 227.35/39.15  | | | | | | | | | | | | | | | | | 
% 227.35/39.15  | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (14), (25), (27), (36), (39), (44), (56),
% 227.35/39.15  | | | | | | | | | | | | | | | | |            (99), (120) are inconsistent by sub-proof #199.
% 227.35/39.15  | | | | | | | | | | | | | | | | | 
% 227.35/39.15  | | | | | | | | | | | | | | | | End of split
% 227.35/39.15  | | | | | | | | | | | | | | | | 
% 227.35/39.15  | | | | | | | | | | | | | | | End of split
% 227.35/39.15  | | | | | | | | | | | | | | | 
% 227.35/39.15  | | | | | | | | | | | | | | Case 2:
% 227.35/39.15  | | | | | | | | | | | | | | | 
% 227.35/39.15  | | | | | | | | | | | | | | |   (121)  all_57_15 = e2 & op(e0, e0) = e2
% 227.35/39.15  | | | | | | | | | | | | | | | 
% 227.35/39.15  | | | | | | | | | | | | | | | ALPHA: (121) implies:
% 227.35/39.15  | | | | | | | | | | | | | | |   (122)  op(e0, e0) = e2
% 227.35/39.15  | | | | | | | | | | | | | | | 
% 227.35/39.15  | | | | | | | | | | | | | | | REF_CLOSE: (1), (7), (17), (122) are inconsistent by
% 227.35/39.15  | | | | | | | | | | | | | | |            sub-proof #2334.
% 227.35/39.15  | | | | | | | | | | | | | | | 
% 227.35/39.15  | | | | | | | | | | | | | | End of split
% 227.35/39.15  | | | | | | | | | | | | | | 
% 227.35/39.15  | | | | | | | | | | | | | End of split
% 227.35/39.15  | | | | | | | | | | | | | 
% 227.35/39.15  | | | | | | | | | | | | End of split
% 227.35/39.15  | | | | | | | | | | | | 
% 227.35/39.15  | | | | | | | | | | | End of split
% 227.35/39.15  | | | | | | | | | | | 
% 227.35/39.15  | | | | | | | | | | Case 2:
% 227.35/39.15  | | | | | | | | | | | 
% 227.35/39.15  | | | | | | | | | | |   (123)  all_57_3 = e0 & op(e2, e2) = e0
% 227.35/39.15  | | | | | | | | | | | 
% 227.35/39.15  | | | | | | | | | | | ALPHA: (123) implies:
% 227.35/39.15  | | | | | | | | | | |   (124)  op(e2, e2) = e0
% 227.35/39.15  | | | | | | | | | | | 
% 227.35/39.15  | | | | | | | | | | | REF_CLOSE: (7), (14), (20), (31), (47), (124) are
% 227.35/39.15  | | | | | | | | | | |            inconsistent by sub-proof #1229.
% 227.35/39.15  | | | | | | | | | | | 
% 227.35/39.15  | | | | | | | | | | End of split
% 227.35/39.15  | | | | | | | | | | 
% 227.35/39.15  | | | | | | | | | Case 2:
% 227.35/39.15  | | | | | | | | | | 
% 227.35/39.15  | | | | | | | | | |   (125)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0
% 227.35/39.15  | | | | | | | | | |            & op(e0, e2) = e0)
% 227.35/39.15  | | | | | | | | | | 
% 227.35/39.15  | | | | | | | | | | BETA: splitting (125) gives:
% 227.35/39.15  | | | | | | | | | | 
% 227.35/39.15  | | | | | | | | | | Case 1:
% 227.35/39.15  | | | | | | | | | | | 
% 227.35/39.15  | | | | | | | | | | |   (126)  all_57_7 = e0 & op(e1, e2) = e0
% 227.35/39.15  | | | | | | | | | | | 
% 227.35/39.15  | | | | | | | | | | | REF_CLOSE: (3), (7), (41), (126) are inconsistent by
% 227.35/39.15  | | | | | | | | | | |            sub-proof #2039.
% 227.35/39.15  | | | | | | | | | | | 
% 227.35/39.15  | | | | | | | | | | Case 2:
% 227.35/39.15  | | | | | | | | | | | 
% 227.35/39.15  | | | | | | | | | | |   (127)  all_57_13 = e0 & op(e0, e2) = e0
% 227.35/39.15  | | | | | | | | | | | 
% 227.35/39.15  | | | | | | | | | | | ALPHA: (127) implies:
% 227.35/39.15  | | | | | | | | | | |   (128)  all_57_13 = e0
% 227.35/39.15  | | | | | | | | | | | 
% 227.35/39.15  | | | | | | | | | | | COMBINE_EQS: (61), (128) imply:
% 227.35/39.15  | | | | | | | | | | |   (129)  e2 = e0
% 227.35/39.15  | | | | | | | | | | | 
% 227.35/39.15  | | | | | | | | | | | COMBINE_EQS: (2), (129) imply:
% 227.35/39.15  | | | | | | | | | | |   (130)  all_57_0 = e0
% 227.35/39.15  | | | | | | | | | | | 
% 227.35/39.15  | | | | | | | | | | | REF_CLOSE: (14), (25), (28), (39), (42), (67), (72), (130)
% 227.35/39.15  | | | | | | | | | | |            are inconsistent by sub-proof #1426.
% 227.35/39.15  | | | | | | | | | | | 
% 227.35/39.15  | | | | | | | | | | End of split
% 227.35/39.15  | | | | | | | | | | 
% 227.35/39.15  | | | | | | | | | End of split
% 227.35/39.15  | | | | | | | | | 
% 227.35/39.15  | | | | | | | | End of split
% 227.35/39.15  | | | | | | | | 
% 227.35/39.15  | | | | | | | Case 2:
% 227.35/39.15  | | | | | | | | 
% 227.35/39.15  | | | | | | | |   (131)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 &
% 227.35/39.15  | | | | | | | |            op(e0, e3) = e1)
% 227.35/39.15  | | | | | | | | 
% 227.35/39.15  | | | | | | | | BETA: splitting (131) gives:
% 227.35/39.15  | | | | | | | | 
% 227.35/39.15  | | | | | | | | Case 1:
% 227.35/39.15  | | | | | | | | | 
% 227.35/39.15  | | | | | | | | |   (132)  all_57_6 = e1 & op(e1, e3) = e1
% 227.35/39.15  | | | | | | | | | 
% 227.35/39.15  | | | | | | | | | REF_CLOSE: (6), (28), (132) are inconsistent by sub-proof
% 227.35/39.15  | | | | | | | | |            #2117.
% 227.35/39.15  | | | | | | | | | 
% 227.35/39.15  | | | | | | | | Case 2:
% 227.35/39.15  | | | | | | | | | 
% 227.35/39.15  | | | | | | | | |   (133)  all_57_12 = e1 & op(e0, e3) = e1
% 227.35/39.15  | | | | | | | | | 
% 227.35/39.15  | | | | | | | | | REF_CLOSE: (26), (67), (133) are inconsistent by sub-proof
% 227.35/39.15  | | | | | | | | |            #2328.
% 227.35/39.15  | | | | | | | | | 
% 227.35/39.15  | | | | | | | | End of split
% 227.35/39.15  | | | | | | | | 
% 227.35/39.15  | | | | | | | End of split
% 227.35/39.15  | | | | | | | 
% 227.35/39.15  | | | | | | Case 2:
% 227.35/39.15  | | | | | | | 
% 227.35/39.15  | | | | | | |   (134)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 &
% 227.35/39.15  | | | | | | |            op(e0, e1) = e0)
% 227.35/39.15  | | | | | | | 
% 227.35/39.15  | | | | | | | BETA: splitting (134) gives:
% 227.35/39.15  | | | | | | | 
% 227.35/39.15  | | | | | | | Case 1:
% 227.35/39.15  | | | | | | | | 
% 227.35/39.15  | | | | | | | |   (135)  all_57_13 = e0 & op(e0, e2) = e0
% 227.35/39.15  | | | | | | | | 
% 227.35/39.15  | | | | | | | | ALPHA: (135) implies:
% 227.35/39.15  | | | | | | | |   (136)  all_57_13 = e0
% 227.35/39.15  | | | | | | | | 
% 227.35/39.15  | | | | | | | | REF_CLOSE: (25), (61), (136) are inconsistent by sub-proof
% 227.35/39.15  | | | | | | | |            #1911.
% 227.35/39.15  | | | | | | | | 
% 227.35/39.15  | | | | | | | Case 2:
% 227.35/39.15  | | | | | | | | 
% 227.35/39.15  | | | | | | | |   (137)  all_57_14 = e0 & op(e0, e1) = e0
% 227.35/39.15  | | | | | | | | 
% 227.35/39.15  | | | | | | | | REF_CLOSE: (26), (56), (137) are inconsistent by sub-proof
% 227.35/39.15  | | | | | | | |            #2181.
% 227.35/39.15  | | | | | | | | 
% 227.35/39.15  | | | | | | | End of split
% 227.35/39.15  | | | | | | | 
% 227.35/39.15  | | | | | | End of split
% 227.35/39.15  | | | | | | 
% 227.35/39.15  | | | | | End of split
% 227.35/39.15  | | | | | 
% 227.35/39.15  | | | | End of split
% 227.35/39.15  | | | | 
% 227.35/39.15  | | | Case 2:
% 227.35/39.15  | | | | 
% 227.35/39.15  | | | |   (138)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0,
% 227.35/39.15  | | | |              e0) = e2)
% 227.35/39.15  | | | | 
% 227.35/39.15  | | | | BETA: splitting (138) gives:
% 227.35/39.15  | | | | 
% 227.35/39.15  | | | | Case 1:
% 227.35/39.15  | | | | | 
% 227.35/39.15  | | | | |   (139)  all_57_14 = e2 & op(e0, e1) = e2
% 227.35/39.15  | | | | | 
% 227.35/39.15  | | | | | ALPHA: (139) implies:
% 227.35/39.15  | | | | |   (140)  all_57_14 = e2
% 227.35/39.15  | | | | | 
% 227.35/39.15  | | | | | COMBINE_EQS: (56), (140) imply:
% 227.35/39.15  | | | | |   (141)  e2 = e1
% 227.35/39.15  | | | | | 
% 227.35/39.15  | | | | | COMBINE_EQS: (27), (141) imply:
% 227.35/39.15  | | | | |   (142)  all_57_5 = e1
% 227.35/39.15  | | | | | 
% 227.35/39.15  | | | | | REF_CLOSE: (13), (14), (25), (36), (39), (44), (56), (142) are
% 227.35/39.15  | | | | |            inconsistent by sub-proof #1187.
% 227.35/39.15  | | | | | 
% 227.35/39.15  | | | | Case 2:
% 227.35/39.15  | | | | | 
% 227.35/39.15  | | | | |   (143)  all_57_15 = e2 & op(e0, e0) = e2
% 227.35/39.15  | | | | | 
% 227.35/39.15  | | | | | ALPHA: (143) implies:
% 227.35/39.15  | | | | |   (144)  op(e0, e0) = e2
% 227.35/39.15  | | | | | 
% 227.35/39.15  | | | | | REF_CLOSE: (1), (7), (17), (144) are inconsistent by sub-proof #2334.
% 227.35/39.15  | | | | | 
% 227.35/39.15  | | | | End of split
% 227.35/39.15  | | | | 
% 227.35/39.15  | | | End of split
% 227.35/39.15  | | | 
% 227.35/39.15  | | End of split
% 227.35/39.15  | | 
% 227.35/39.15  | End of split
% 227.35/39.15  | 
% 227.35/39.15  End of proof
% 227.35/39.15  
% 227.35/39.15  Sub-proof #199 shows that the following formulas are inconsistent:
% 227.35/39.15  ----------------------------------------------------------------
% 227.35/39.15    (1)  all_57_4 = e3
% 227.35/39.15    (2)   ~ (e3 = e2)
% 227.35/39.15    (3)  all_57_11 = e1 & op(e1, e0) = e1
% 227.35/39.15    (4)  all_57_11 = e2
% 227.35/39.15    (5)   ~ (e2 = e0)
% 227.35/39.15    (6)  all_57_5 = e2
% 227.35/39.15    (7)  all_57_14 = e1
% 227.35/39.15    (8)  all_57_8 = e0
% 227.35/39.15    (9)   ~ (e2 = e1)
% 227.35/39.15    (10)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 227.35/39.15          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 227.35/39.15  
% 227.35/39.15  Begin of proof
% 227.35/39.15  | 
% 227.35/39.15  | ALPHA: (3) implies:
% 227.35/39.15  |   (11)  all_57_11 = e1
% 227.35/39.15  | 
% 227.35/39.15  | COMBINE_EQS: (4), (11) imply:
% 227.35/39.15  |   (12)  e2 = e1
% 227.35/39.15  | 
% 227.35/39.15  | COMBINE_EQS: (6), (12) imply:
% 227.35/39.15  |   (13)  all_57_5 = e1
% 227.35/39.15  | 
% 227.35/39.15  | REF_CLOSE: (1), (2), (5), (7), (8), (9), (10), (13) are inconsistent by
% 227.35/39.15  |            sub-proof #1187.
% 227.35/39.15  | 
% 227.35/39.15  End of proof
% 227.35/39.15  
% 227.35/39.15  Sub-proof #200 shows that the following formulas are inconsistent:
% 227.35/39.15  ----------------------------------------------------------------
% 227.35/39.15    (1)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1)
% 227.35/39.15    (2)   ~ (e3 = e1)
% 227.35/39.15    (3)  all_57_4 = e3
% 227.35/39.15    (4)  all_57_5 = e2
% 227.35/39.15    (5)   ~ (e2 = e1)
% 227.35/39.15  
% 227.35/39.15  Begin of proof
% 227.35/39.15  | 
% 227.35/39.15  | BETA: splitting (1) gives:
% 227.35/39.15  | 
% 227.35/39.15  | Case 1:
% 227.35/39.15  | | 
% 227.35/39.15  | |   (6)  all_57_4 = e1 & op(e3, e1) = e1
% 227.35/39.15  | | 
% 227.35/39.15  | | ALPHA: (6) implies:
% 227.35/39.15  | |   (7)  all_57_4 = e1
% 227.35/39.15  | | 
% 227.35/39.15  | | REF_CLOSE: (2), (3), (7) are inconsistent by sub-proof #2426.
% 227.35/39.15  | | 
% 227.35/39.15  | Case 2:
% 227.35/39.15  | | 
% 227.35/39.15  | |   (8)  all_57_5 = e1 & op(e2, e1) = e1
% 227.35/39.15  | | 
% 227.35/39.15  | | REF_CLOSE: (4), (5), (8) are inconsistent by sub-proof #1886.
% 227.35/39.15  | | 
% 227.35/39.15  | End of split
% 227.35/39.15  | 
% 227.35/39.15  End of proof
% 227.35/39.15  
% 227.35/39.15  Sub-proof #201 shows that the following formulas are inconsistent:
% 227.35/39.15  ----------------------------------------------------------------
% 227.35/39.15    (1)  op(e0, e0) = all_4_2
% 227.35/39.15    (2)   ~ (e3 = e1)
% 227.35/39.15    (3)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 227.35/39.15         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 227.35/39.15    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.35/39.15           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.35/39.15    (5)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 227.35/39.15         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 227.35/39.15    (6)   ~ (all_6_2 = e3)
% 227.35/39.15    (7)  op(e1, e1) = all_6_2
% 227.35/39.15    (8)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 227.35/39.15    (9)   ~ (e3 = e2)
% 227.35/39.15    (10)   ~ (e3 = e0)
% 227.35/39.15    (11)   ~ (all_4_2 = e2)
% 227.35/39.15    (12)   ~ (e2 = e0)
% 227.35/39.15    (13)   ~ (e1 = e0)
% 227.35/39.15    (14)  all_57_6 = e3
% 227.35/39.15    (15)  op(e1, e1) = e2
% 227.35/39.15    (16)   ~ (e2 = e1)
% 227.35/39.15    (17)   ~ (all_6_2 = e0)
% 227.35/39.15    (18)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 227.35/39.15          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 227.35/39.15  
% 227.35/39.15  Begin of proof
% 227.35/39.15  | 
% 227.35/39.15  | BETA: splitting (8) gives:
% 227.35/39.15  | 
% 227.35/39.15  | Case 1:
% 227.35/39.15  | | 
% 227.35/39.15  | |   (19)  all_57_11 = e2 & op(e1, e0) = e2
% 227.35/39.15  | | 
% 227.35/39.15  | | ALPHA: (19) implies:
% 227.35/39.15  | |   (20)  all_57_11 = e2
% 227.35/39.15  | | 
% 227.35/39.15  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (9), (10), (12), (13), (14), (15),
% 227.35/39.15  | |            (16), (17), (18), (20) are inconsistent by sub-proof #229.
% 227.35/39.15  | | 
% 227.35/39.15  | Case 2:
% 227.35/39.15  | | 
% 227.35/39.15  | |   (21)  all_57_15 = e2 & op(e0, e0) = e2
% 227.35/39.15  | | 
% 227.35/39.15  | | ALPHA: (21) implies:
% 227.35/39.15  | |   (22)  op(e0, e0) = e2
% 227.35/39.15  | | 
% 227.35/39.15  | | REF_CLOSE: (1), (4), (11), (22) are inconsistent by sub-proof #2334.
% 227.35/39.15  | | 
% 227.35/39.15  | End of split
% 227.35/39.15  | 
% 227.35/39.15  End of proof
% 227.35/39.15  
% 227.35/39.15  Sub-proof #202 shows that the following formulas are inconsistent:
% 227.35/39.15  ----------------------------------------------------------------
% 227.35/39.15    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 227.35/39.15         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.35/39.15    (2)   ~ (e3 = e1)
% 227.35/39.15    (3)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 227.35/39.15         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 227.35/39.15    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.35/39.15           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.35/39.15    (5)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 227.35/39.15         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 227.35/39.15    (6)   ~ (all_6_2 = e3)
% 227.35/39.15    (7)  op(e1, e1) = all_6_2
% 227.35/39.15    (8)  op(e2, e0) = all_52_15
% 227.35/39.15    (9)   ~ (e3 = e2)
% 227.35/39.15    (10)   ~ (e3 = e0)
% 227.35/39.15    (11)  all_57_15 = e3
% 227.35/39.15    (12)  op(e2, e2) = all_52_11
% 227.35/39.15    (13)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 227.35/39.15          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 227.35/39.15            e1)
% 227.35/39.15    (14)  all_57_10 = e2
% 227.35/39.15    (15)  op(e2, e0) = e2
% 227.35/39.15    (16)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 227.35/39.15          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 227.35/39.15    (17)   ~ (e2 = e0)
% 227.35/39.15    (18)   ~ (e1 = e0)
% 227.35/39.15    (19)  all_57_6 = e3
% 227.35/39.15    (20)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 227.35/39.15          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 227.35/39.15    (21)  op(e0, e0) = e3
% 227.35/39.15    (22)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.35/39.15          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 227.35/39.15            e2)
% 227.35/39.15    (23)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 227.35/39.15              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 227.35/39.15                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 227.35/39.15                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 227.35/39.15    (24)  op(e1, e1) = e2
% 227.35/39.15    (25)  op(all_52_15, all_52_15) = e0
% 227.35/39.15    (26)   ~ (e2 = e1)
% 227.35/39.15    (27)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 227.35/39.15          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 227.35/39.15    (28)   ~ (all_6_2 = e0)
% 227.35/39.15    (29)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 227.35/39.15          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 227.35/39.15    (30)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 227.35/39.15          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 227.35/39.15    (31)  op(all_52_11, all_52_11) = e2
% 227.35/39.15    (32)   ~ (all_52_15 = e3)
% 227.35/39.15    (33)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 227.35/39.16          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 227.35/39.16    (34)  all_57_13 = e2 & op(e0, e2) = e2
% 227.35/39.16    (35)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 227.35/39.16          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 227.35/39.16  
% 227.35/39.16  Begin of proof
% 227.35/39.16  | 
% 227.35/39.16  | ALPHA: (34) implies:
% 227.35/39.16  |   (36)  all_57_13 = e2
% 227.35/39.16  | 
% 227.35/39.16  | BETA: splitting (35) gives:
% 227.35/39.16  | 
% 227.35/39.16  | Case 1:
% 227.35/39.16  | | 
% 227.35/39.16  | |   (37)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) =
% 227.35/39.16  | |           e2)
% 227.35/39.16  | | 
% 227.35/39.16  | | BETA: splitting (37) gives:
% 227.35/39.16  | | 
% 227.35/39.16  | | Case 1:
% 227.35/39.16  | | | 
% 227.35/39.16  | | |   (38)  all_57_6 = e2 & op(e1, e3) = e2
% 227.35/39.16  | | | 
% 227.35/39.16  | | | ALPHA: (38) implies:
% 227.35/39.16  | | |   (39)  all_57_6 = e2
% 227.35/39.16  | | | 
% 227.35/39.16  | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (9), (10), (11), (17), (18),
% 227.35/39.16  | | |            (23), (24), (26), (27), (28), (29), (30), (39) are inconsistent
% 227.35/39.16  | | |            by sub-proof #203.
% 227.35/39.16  | | | 
% 227.35/39.16  | | Case 2:
% 227.35/39.16  | | | 
% 227.35/39.16  | | |   (40)  all_57_7 = e2 & op(e1, e2) = e2
% 227.35/39.16  | | | 
% 227.35/39.16  | | | ALPHA: (40) implies:
% 227.35/39.16  | | |   (41)  all_57_7 = e2
% 227.35/39.16  | | | 
% 227.35/39.16  | | | BETA: splitting (3) gives:
% 227.35/39.16  | | | 
% 227.35/39.16  | | | Case 1:
% 227.35/39.16  | | | | 
% 227.35/39.16  | | | |   (42)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2)
% 227.35/39.16  | | | |           = e0)
% 227.35/39.16  | | | | 
% 227.35/39.16  | | | | REF_CLOSE: (2), (4), (5), (6), (7), (9), (10), (11), (17), (18), (23),
% 227.35/39.16  | | | |            (26), (27), (29), (41), (42) are inconsistent by sub-proof
% 227.35/39.16  | | | |            #960.
% 227.35/39.16  | | | | 
% 227.35/39.16  | | | Case 2:
% 227.35/39.16  | | | | 
% 227.35/39.16  | | | |   (43)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0)
% 227.35/39.16  | | | |           = e0)
% 227.35/39.16  | | | | 
% 227.35/39.16  | | | | BETA: splitting (43) gives:
% 227.35/39.16  | | | | 
% 227.35/39.16  | | | | Case 1:
% 227.35/39.16  | | | | | 
% 227.35/39.16  | | | | |   (44)  all_57_8 = e0 & op(e1, e1) = e0
% 227.35/39.16  | | | | | 
% 227.35/39.16  | | | | | REF_CLOSE: (4), (7), (28), (44) are inconsistent by sub-proof #2412.
% 227.35/39.16  | | | | | 
% 227.35/39.16  | | | | Case 2:
% 227.35/39.16  | | | | | 
% 227.35/39.16  | | | | |   (45)  all_57_11 = e0 & op(e1, e0) = e0
% 227.35/39.16  | | | | | 
% 227.35/39.16  | | | | | ALPHA: (45) implies:
% 227.35/39.16  | | | | |   (46)  all_57_11 = e0
% 227.35/39.16  | | | | | 
% 227.35/39.16  | | | | | BETA: splitting (29) gives:
% 227.35/39.16  | | | | | 
% 227.35/39.16  | | | | | Case 1:
% 227.35/39.16  | | | | | | 
% 227.35/39.16  | | | | | |   (47)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2,
% 227.35/39.16  | | | | | |             e0) = e1)
% 227.35/39.16  | | | | | | 
% 227.35/39.16  | | | | | | BETA: splitting (47) gives:
% 227.35/39.16  | | | | | | 
% 227.35/39.16  | | | | | | Case 1:
% 227.35/39.16  | | | | | | | 
% 227.35/39.16  | | | | | | |   (48)  all_57_9 = e1 & op(e3, e0) = e1
% 227.35/39.16  | | | | | | | 
% 227.35/39.16  | | | | | | | ALPHA: (48) implies:
% 227.35/39.16  | | | | | | |   (49)  all_57_9 = e1
% 227.35/39.16  | | | | | | | 
% 227.35/39.16  | | | | | | | BETA: splitting (33) gives:
% 227.35/39.16  | | | | | | | 
% 227.35/39.16  | | | | | | | Case 1:
% 227.35/39.16  | | | | | | | | 
% 227.35/39.16  | | | | | | | |   (50)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 &
% 227.35/39.16  | | | | | | | |           op(e2, e2) = e1)
% 227.35/39.16  | | | | | | | | 
% 227.35/39.16  | | | | | | | | BETA: splitting (50) gives:
% 227.35/39.16  | | | | | | | | 
% 227.35/39.16  | | | | | | | | Case 1:
% 227.35/39.16  | | | | | | | | | 
% 227.35/39.16  | | | | | | | | |   (51)  all_57_1 = e1 & op(e3, e2) = e1
% 227.35/39.16  | | | | | | | | | 
% 227.35/39.16  | | | | | | | | | ALPHA: (51) implies:
% 227.35/39.16  | | | | | | | | |   (52)  all_57_1 = e1
% 227.35/39.16  | | | | | | | | | 
% 227.35/39.16  | | | | | | | | | BETA: splitting (16) gives:
% 227.35/39.16  | | | | | | | | | 
% 227.35/39.16  | | | | | | | | | Case 1:
% 227.35/39.16  | | | | | | | | | | 
% 227.35/39.16  | | | | | | | | | |   (53)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 &
% 227.35/39.16  | | | | | | | | | |           op(e2, e2) = e0)
% 227.35/39.16  | | | | | | | | | | 
% 227.35/39.16  | | | | | | | | | | BETA: splitting (53) gives:
% 227.35/39.16  | | | | | | | | | | 
% 227.35/39.16  | | | | | | | | | | Case 1:
% 227.35/39.16  | | | | | | | | | | | 
% 227.35/39.16  | | | | | | | | | | |   (54)  all_57_1 = e0 & op(e3, e2) = e0
% 227.35/39.16  | | | | | | | | | | | 
% 227.35/39.16  | | | | | | | | | | | ALPHA: (54) implies:
% 227.35/39.16  | | | | | | | | | | |   (55)  all_57_1 = e0
% 227.35/39.16  | | | | | | | | | | | 
% 227.35/39.16  | | | | | | | | | | | COMBINE_EQS: (52), (55) imply:
% 227.35/39.16  | | | | | | | | | | |   (56)  e1 = e0
% 227.35/39.16  | | | | | | | | | | | 
% 227.35/39.16  | | | | | | | | | | | COMBINE_EQS: (49), (56) imply:
% 227.35/39.16  | | | | | | | | | | |   (57)  all_57_9 = e0
% 227.35/39.16  | | | | | | | | | | | 
% 227.35/39.16  | | | | | | | | | | | REF_CLOSE: (2), (9), (11), (17), (18), (26), (27), (29),
% 227.35/39.16  | | | | | | | | | | |            (46), (57) are inconsistent by sub-proof #1144.
% 227.35/39.16  | | | | | | | | | | | 
% 227.35/39.16  | | | | | | | | | | Case 2:
% 227.35/39.16  | | | | | | | | | | | 
% 227.35/39.16  | | | | | | | | | | |   (58)  all_57_3 = e0 & op(e2, e2) = e0
% 227.35/39.16  | | | | | | | | | | | 
% 227.35/39.16  | | | | | | | | | | | ALPHA: (58) implies:
% 227.35/39.16  | | | | | | | | | | |   (59)  op(e2, e2) = e0
% 227.35/39.16  | | | | | | | | | | | 
% 227.35/39.16  | | | | | | | | | | | REF_CLOSE: (4), (9), (12), (21), (31), (59) are inconsistent
% 227.35/39.16  | | | | | | | | | | |            by sub-proof #1229.
% 227.35/39.16  | | | | | | | | | | | 
% 227.35/39.16  | | | | | | | | | | End of split
% 227.35/39.16  | | | | | | | | | | 
% 227.35/39.16  | | | | | | | | | Case 2:
% 227.35/39.16  | | | | | | | | | | 
% 227.35/39.16  | | | | | | | | | |   (60)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0
% 227.35/39.16  | | | | | | | | | |           & op(e0, e2) = e0)
% 227.35/39.16  | | | | | | | | | | 
% 227.35/39.16  | | | | | | | | | | BETA: splitting (60) gives:
% 227.35/39.16  | | | | | | | | | | 
% 227.35/39.16  | | | | | | | | | | Case 1:
% 227.35/39.16  | | | | | | | | | | | 
% 227.35/39.16  | | | | | | | | | | |   (61)  all_57_7 = e0 & op(e1, e2) = e0
% 227.35/39.16  | | | | | | | | | | | 
% 227.35/39.16  | | | | | | | | | | | ALPHA: (61) implies:
% 227.35/39.16  | | | | | | | | | | |   (62)  all_57_7 = e0
% 227.35/39.16  | | | | | | | | | | | 
% 227.35/39.16  | | | | | | | | | | | COMBINE_EQS: (41), (62) imply:
% 227.35/39.16  | | | | | | | | | | |   (63)  e2 = e0
% 227.35/39.16  | | | | | | | | | | | 
% 227.35/39.16  | | | | | | | | | | | COMBINE_EQS: (14), (63) imply:
% 227.35/39.16  | | | | | | | | | | |   (64)  all_57_10 = e0
% 227.35/39.16  | | | | | | | | | | | 
% 227.35/39.16  | | | | | | | | | | | REF_CLOSE: (2), (4), (9), (11), (17), (18), (21), (26), (27),
% 227.35/39.16  | | | | | | | | | | |            (29), (46), (64) are inconsistent by sub-proof
% 227.35/39.16  | | | | | | | | | | |            #1087.
% 227.35/39.16  | | | | | | | | | | | 
% 227.35/39.16  | | | | | | | | | | Case 2:
% 227.35/39.16  | | | | | | | | | | | 
% 227.35/39.16  | | | | | | | | | | |   (65)  all_57_13 = e0 & op(e0, e2) = e0
% 227.35/39.16  | | | | | | | | | | | 
% 227.35/39.16  | | | | | | | | | | | ALPHA: (65) implies:
% 227.35/39.16  | | | | | | | | | | |   (66)  all_57_13 = e0
% 227.35/39.16  | | | | | | | | | | | 
% 227.35/39.16  | | | | | | | | | | | REF_CLOSE: (2), (4), (9), (11), (14), (17), (18), (21), (26),
% 227.35/39.16  | | | | | | | | | | |            (27), (29), (36), (46), (66) are inconsistent by
% 227.35/39.16  | | | | | | | | | | |            sub-proof #918.
% 227.35/39.16  | | | | | | | | | | | 
% 227.35/39.16  | | | | | | | | | | End of split
% 227.35/39.16  | | | | | | | | | | 
% 227.35/39.16  | | | | | | | | | End of split
% 227.35/39.16  | | | | | | | | | 
% 227.35/39.16  | | | | | | | | Case 2:
% 227.35/39.16  | | | | | | | | | 
% 227.35/39.16  | | | | | | | | |   (67)  all_57_3 = e1 & op(e2, e2) = e1
% 227.35/39.16  | | | | | | | | | 
% 227.35/39.16  | | | | | | | | | ALPHA: (67) implies:
% 227.35/39.16  | | | | | | | | |   (68)  op(e2, e2) = e1
% 227.35/39.16  | | | | | | | | | 
% 227.35/39.16  | | | | | | | | | REF_CLOSE: (1), (2), (4), (9), (10), (11), (13), (16), (17),
% 227.35/39.16  | | | | | | | | |            (18), (20), (21), (22), (23), (26), (33), (36),
% 227.35/39.16  | | | | | | | | |            (41), (68) are inconsistent by sub-proof #712.
% 227.35/39.16  | | | | | | | | | 
% 227.35/39.16  | | | | | | | | End of split
% 227.35/39.16  | | | | | | | | 
% 227.35/39.16  | | | | | | | Case 2:
% 227.35/39.16  | | | | | | | | 
% 227.35/39.16  | | | | | | | |   (69)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 &
% 227.35/39.16  | | | | | | | |           op(e0, e2) = e1)
% 227.35/39.16  | | | | | | | | 
% 227.35/39.16  | | | | | | | | BETA: splitting (69) gives:
% 227.35/39.16  | | | | | | | | 
% 227.35/39.16  | | | | | | | | Case 1:
% 227.35/39.16  | | | | | | | | | 
% 227.35/39.16  | | | | | | | | |   (70)  all_57_7 = e1 & op(e1, e2) = e1
% 227.35/39.16  | | | | | | | | | 
% 227.35/39.16  | | | | | | | | | REF_CLOSE: (26), (41), (70) are inconsistent by sub-proof
% 227.35/39.16  | | | | | | | | |            #2190.
% 227.35/39.16  | | | | | | | | | 
% 227.35/39.16  | | | | | | | | Case 2:
% 227.35/39.16  | | | | | | | | | 
% 227.35/39.16  | | | | | | | | |   (71)  all_57_13 = e1 & op(e0, e2) = e1
% 227.35/39.16  | | | | | | | | | 
% 227.35/39.16  | | | | | | | | | REF_CLOSE: (26), (36), (71) are inconsistent by sub-proof
% 227.35/39.16  | | | | | | | | |            #2205.
% 227.35/39.16  | | | | | | | | | 
% 227.35/39.16  | | | | | | | | End of split
% 227.35/39.16  | | | | | | | | 
% 227.35/39.16  | | | | | | | End of split
% 227.35/39.16  | | | | | | | 
% 227.35/39.16  | | | | | | Case 2:
% 227.35/39.16  | | | | | | | 
% 227.35/39.16  | | | | | | |   (72)  all_57_10 = e1 & op(e2, e0) = e1
% 227.35/39.16  | | | | | | | 
% 227.35/39.16  | | | | | | | REF_CLOSE: (14), (26), (72) are inconsistent by sub-proof #2360.
% 227.35/39.16  | | | | | | | 
% 227.35/39.16  | | | | | | End of split
% 227.35/39.16  | | | | | | 
% 227.35/39.16  | | | | | Case 2:
% 227.35/39.16  | | | | | | 
% 227.35/39.16  | | | | | |   (73)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 &
% 227.35/39.16  | | | | | |           op(e0, e0) = e1)
% 227.35/39.16  | | | | | | 
% 227.35/39.16  | | | | | | REF_CLOSE: (2), (4), (18), (21), (46), (73) are inconsistent by
% 227.35/39.16  | | | | | |            sub-proof #1749.
% 227.35/39.16  | | | | | | 
% 227.35/39.16  | | | | | End of split
% 227.35/39.16  | | | | | 
% 227.35/39.16  | | | | End of split
% 227.35/39.16  | | | | 
% 227.35/39.16  | | | End of split
% 227.35/39.16  | | | 
% 227.35/39.16  | | End of split
% 227.35/39.16  | | 
% 227.35/39.16  | Case 2:
% 227.35/39.16  | | 
% 227.35/39.16  | |   (74)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) =
% 227.35/39.16  | |           e2)
% 227.35/39.16  | | 
% 227.35/39.16  | | BETA: splitting (74) gives:
% 227.35/39.16  | | 
% 227.35/39.16  | | Case 1:
% 227.35/39.16  | | | 
% 227.35/39.16  | | | 
% 227.35/39.16  | | | REF_CLOSE: (4), (8), (12), (15), (21), (25), (31), (32) are inconsistent
% 227.35/39.16  | | |            by sub-proof #204.
% 227.35/39.16  | | | 
% 227.35/39.16  | | Case 2:
% 227.35/39.16  | | | 
% 227.35/39.16  | | |   (75)  all_57_11 = e2 & op(e1, e0) = e2
% 227.35/39.16  | | | 
% 227.35/39.16  | | | ALPHA: (75) implies:
% 227.35/39.16  | | |   (76)  all_57_11 = e2
% 227.35/39.16  | | | 
% 227.35/39.16  | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (9), (10), (17), (18), (19),
% 227.35/39.16  | | |            (24), (26), (28), (30), (76) are inconsistent by sub-proof
% 227.35/39.16  | | |            #229.
% 227.35/39.16  | | | 
% 227.35/39.16  | | End of split
% 227.35/39.16  | | 
% 227.35/39.16  | End of split
% 227.35/39.16  | 
% 227.35/39.16  End of proof
% 227.35/39.16  
% 227.35/39.16  Sub-proof #203 shows that the following formulas are inconsistent:
% 227.35/39.16  ----------------------------------------------------------------
% 227.35/39.16    (1)   ~ (e3 = e1)
% 227.35/39.16    (2)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 227.35/39.16         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 227.35/39.16    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.35/39.16           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.35/39.16    (4)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 227.35/39.16         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 227.35/39.16    (5)   ~ (all_6_2 = e3)
% 227.35/39.16    (6)  op(e1, e1) = all_6_2
% 227.35/39.16    (7)   ~ (e3 = e2)
% 227.35/39.16    (8)   ~ (e3 = e0)
% 227.35/39.16    (9)  all_57_15 = e3
% 227.35/39.16    (10)  all_57_6 = e2
% 227.35/39.16    (11)   ~ (e2 = e0)
% 227.35/39.16    (12)   ~ (e1 = e0)
% 227.35/39.16    (13)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 227.35/39.16              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 227.35/39.16                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 227.35/39.16                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 227.35/39.16    (14)  op(e1, e1) = e2
% 227.35/39.16    (15)   ~ (e2 = e1)
% 227.35/39.16    (16)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 227.35/39.16          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 227.35/39.16    (17)   ~ (all_6_2 = e0)
% 227.35/39.16    (18)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 227.35/39.16          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 227.35/39.16    (19)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 227.35/39.16          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 227.35/39.16  
% 227.35/39.16  Begin of proof
% 227.35/39.16  | 
% 227.35/39.16  | BETA: splitting (4) gives:
% 227.35/39.16  | 
% 227.35/39.16  | Case 1:
% 227.35/39.16  | | 
% 227.35/39.16  | |   (20)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 227.35/39.16  | |           e3)
% 227.35/39.16  | | 
% 227.35/39.16  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 227.35/39.16  | |            (13), (14), (15), (16), (17), (18), (19), (20) are inconsistent
% 227.35/39.16  | |            by sub-proof #336.
% 227.35/39.16  | | 
% 227.35/39.16  | Case 2:
% 227.35/39.16  | | 
% 227.35/39.16  | |   (21)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 227.35/39.16  | |           e3)
% 227.35/39.16  | | 
% 227.35/39.16  | | REF_CLOSE: (1), (3), (5), (6), (7), (8), (9), (11), (12), (13), (15), (16),
% 227.35/39.16  | |            (18), (21) are inconsistent by sub-proof #1786.
% 227.35/39.16  | | 
% 227.35/39.16  | End of split
% 227.35/39.16  | 
% 227.35/39.16  End of proof
% 227.35/39.16  
% 227.35/39.16  Sub-proof #204 shows that the following formulas are inconsistent:
% 227.35/39.16  ----------------------------------------------------------------
% 227.35/39.16    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.35/39.16           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.35/39.16    (2)  op(e2, e0) = all_52_15
% 227.35/39.16    (3)  op(e2, e2) = all_52_11
% 227.35/39.16    (4)  op(e2, e0) = e2
% 227.35/39.16    (5)  op(e0, e0) = e3
% 227.35/39.16    (6)  op(all_52_15, all_52_15) = e0
% 227.35/39.16    (7)  op(all_52_11, all_52_11) = e2
% 227.35/39.16    (8)   ~ (all_52_15 = e3)
% 227.35/39.16  
% 227.35/39.16  Begin of proof
% 227.35/39.16  | 
% 227.35/39.16  | GROUND_INST: instantiating (1) with all_52_15, e2, e0, e2, simplifying with
% 227.35/39.16  |              (2), (4) gives:
% 227.35/39.16  |   (9)  all_52_15 = e2
% 227.35/39.16  | 
% 227.35/39.16  | REDUCE: (8), (9) imply:
% 227.35/39.16  |   (10)   ~ (e3 = e2)
% 227.35/39.16  | 
% 227.35/39.16  | SIMP: (10) implies:
% 227.35/39.16  |   (11)   ~ (e3 = e2)
% 227.35/39.16  | 
% 227.35/39.16  | REDUCE: (6), (9) imply:
% 227.35/39.16  |   (12)  op(e2, e2) = e0
% 227.35/39.16  | 
% 227.35/39.16  | REF_CLOSE: (1), (3), (5), (7), (11), (12) are inconsistent by sub-proof #1229.
% 227.35/39.16  | 
% 227.35/39.16  End of proof
% 227.35/39.16  
% 227.35/39.16  Sub-proof #205 shows that the following formulas are inconsistent:
% 227.35/39.16  ----------------------------------------------------------------
% 227.35/39.16    (1)   ~ (e3 = e1)
% 227.35/39.16    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.35/39.16           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.35/39.16    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 227.35/39.16         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 227.35/39.16    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2)
% 227.35/39.16    (5)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 227.35/39.16         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 227.35/39.16    (6)   ~ (e3 = e2)
% 227.35/39.16    (7)   ~ (e3 = e0)
% 227.35/39.16    (8)  op(e3, e3) = e2
% 227.35/39.16    (9)   ~ (e2 = e0)
% 227.35/39.16    (10)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 227.35/39.16          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 227.35/39.16    (11)   ~ (e1 = e0)
% 227.35/39.16    (12)   ~ (all_53_12 = e3)
% 227.35/39.16    (13)  op(e2, e2) = e3
% 227.35/39.16    (14)   ~ (e2 = e1)
% 227.35/39.16    (15)  op(e3, e0) = all_53_12
% 227.35/39.16  
% 227.35/39.16  Begin of proof
% 227.35/39.16  | 
% 227.35/39.16  | BETA: splitting (4) gives:
% 227.35/39.16  | 
% 227.35/39.16  | Case 1:
% 227.35/39.16  | | 
% 227.35/39.16  | |   (16)  all_57_1 = e2 & op(e3, e2) = e2
% 227.35/39.16  | | 
% 227.35/39.16  | | ALPHA: (16) implies:
% 227.35/39.16  | |   (17)  all_57_1 = e2
% 227.35/39.16  | | 
% 227.35/39.16  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (14),
% 227.35/39.16  | |            (15), (17) are inconsistent by sub-proof #1650.
% 227.35/39.16  | | 
% 227.35/39.16  | Case 2:
% 227.35/39.16  | | 
% 227.35/39.16  | |   (18)  all_57_3 = e2 & op(e2, e2) = e2
% 227.35/39.16  | | 
% 227.35/39.16  | | ALPHA: (18) implies:
% 227.35/39.16  | |   (19)  op(e2, e2) = e2
% 227.35/39.16  | | 
% 227.35/39.16  | | REF_CLOSE: (2), (6), (13), (19) are inconsistent by sub-proof #2298.
% 227.35/39.16  | | 
% 227.35/39.16  | End of split
% 227.35/39.16  | 
% 227.35/39.16  End of proof
% 227.35/39.16  
% 227.35/39.16  Sub-proof #206 shows that the following formulas are inconsistent:
% 227.35/39.16  ----------------------------------------------------------------
% 227.35/39.16    (1)  all_38_2 = e2
% 227.35/39.16    (2)   ~ (e3 = e1)
% 227.35/39.16    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.35/39.16           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.35/39.16    (4)  op(all_6_2, all_6_2) = e1
% 227.35/39.16    (5)  all_38_2 = all_6_2
% 227.35/39.16    (6)  op(e2, e2) = e3
% 227.35/39.16  
% 227.35/39.16  Begin of proof
% 227.35/39.16  | 
% 227.35/39.16  | COMBINE_EQS: (1), (5) imply:
% 227.35/39.16  |   (7)  all_6_2 = e2
% 227.35/39.16  | 
% 227.35/39.16  | SIMP: (7) implies:
% 227.35/39.16  |   (8)  all_6_2 = e2
% 227.35/39.16  | 
% 227.35/39.16  | REDUCE: (4), (8) imply:
% 227.35/39.16  |   (9)  op(e2, e2) = e1
% 227.35/39.16  | 
% 227.35/39.16  | REF_CLOSE: (2), (3), (6), (9) are inconsistent by sub-proof #1912.
% 227.35/39.16  | 
% 227.35/39.16  End of proof
% 227.35/39.16  
% 227.35/39.16  Sub-proof #207 shows that the following formulas are inconsistent:
% 227.35/39.16  ----------------------------------------------------------------
% 227.35/39.16    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.35/39.16           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.35/39.16    (2)  all_57_1 = e1
% 227.35/39.16    (3)  op(e3, e3) = e0
% 227.35/39.16    (4)   ~ (e2 = e0)
% 227.35/39.16    (5)   ~ (e2 = e1)
% 227.35/39.16    (6)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2)
% 227.35/39.16  
% 227.35/39.16  Begin of proof
% 227.35/39.16  | 
% 227.35/39.16  | BETA: splitting (6) gives:
% 227.35/39.16  | 
% 227.35/39.16  | Case 1:
% 227.35/39.16  | | 
% 227.35/39.16  | |   (7)  all_57_0 = e2 & op(e3, e3) = e2
% 227.35/39.16  | | 
% 227.35/39.16  | | ALPHA: (7) implies:
% 227.35/39.16  | |   (8)  op(e3, e3) = e2
% 227.35/39.16  | | 
% 227.35/39.16  | | REF_CLOSE: (1), (3), (4), (8) are inconsistent by sub-proof #2403.
% 227.35/39.16  | | 
% 227.35/39.16  | Case 2:
% 227.35/39.16  | | 
% 227.35/39.16  | |   (9)  all_57_1 = e2 & op(e3, e2) = e2
% 227.35/39.16  | | 
% 227.35/39.16  | | REF_CLOSE: (2), (5), (9) are inconsistent by sub-proof #2489.
% 227.35/39.16  | | 
% 227.35/39.16  | End of split
% 227.35/39.16  | 
% 227.35/39.16  End of proof
% 227.35/39.16  
% 227.35/39.16  Sub-proof #208 shows that the following formulas are inconsistent:
% 227.35/39.16  ----------------------------------------------------------------
% 227.35/39.16    (1)  ( ~ (all_44_0 = e1) & op(all_44_1, e2) = all_44_0 & op(e2, e3) = all_44_1
% 227.35/39.16           & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 = e0) & op(e2, e3) =
% 227.35/39.16           all_44_1 & $i(all_44_1))
% 227.35/39.16    (2)   ~ (all_52_19 = e3)
% 227.35/39.16    (3)  ( ~ (all_8_0 = e0) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 227.35/39.16           $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e1) & op(e2, e3) = all_8_1
% 227.35/39.16           & $i(all_8_1))
% 227.35/39.16    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.35/39.16           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.35/39.16    (5)  all_55_9 = all_52_19
% 227.35/39.16    (6)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 227.35/39.16    (7)  op(e1, e2) = all_52_19
% 227.35/39.16    (8)  op(all_52_19, all_52_19) = e2
% 227.35/39.16    (9)  op(e2, e2) = e3
% 227.35/39.16    (10)  op(e2, e3) = e1
% 227.35/39.16    (11)   ~ (all_52_19 = e1)
% 227.35/39.16  
% 227.35/39.16  Begin of proof
% 227.35/39.16  | 
% 227.35/39.16  | BETA: splitting (1) gives:
% 227.35/39.16  | 
% 227.35/39.16  | Case 1:
% 227.35/39.16  | | 
% 227.35/39.16  | |   (12)   ~ (all_44_0 = e1) & op(all_44_1, e2) = all_44_0 & op(e2, e3) =
% 227.35/39.16  | |         all_44_1 & $i(all_44_0) & $i(all_44_1)
% 227.35/39.16  | | 
% 227.35/39.16  | | ALPHA: (12) implies:
% 227.35/39.16  | |   (13)  op(e2, e3) = all_44_1
% 227.35/39.16  | | 
% 227.35/39.16  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13) are
% 227.35/39.16  | |            inconsistent by sub-proof #246.
% 227.35/39.16  | | 
% 227.35/39.16  | Case 2:
% 227.35/39.16  | | 
% 227.35/39.16  | |   (14)   ~ (all_44_1 = e0) & op(e2, e3) = all_44_1 & $i(all_44_1)
% 227.35/39.16  | | 
% 227.35/39.16  | | ALPHA: (14) implies:
% 227.35/39.16  | |   (15)  op(e2, e3) = all_44_1
% 227.35/39.16  | | 
% 227.35/39.16  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (15) are
% 227.35/39.16  | |            inconsistent by sub-proof #246.
% 227.35/39.16  | | 
% 227.35/39.16  | End of split
% 227.35/39.16  | 
% 227.35/39.16  End of proof
% 227.35/39.16  
% 227.35/39.16  Sub-proof #209 shows that the following formulas are inconsistent:
% 227.35/39.16  ----------------------------------------------------------------
% 227.35/39.16    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.35/39.16           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.35/39.16    (2)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0 &
% 227.35/39.16         op(all_52_9, all_52_9) = e3 & op(all_52_11, all_52_11) = e2 &
% 227.35/39.16         op(all_52_13, all_52_13) = e1 & op(all_52_15, all_52_15) = e0 & op(e2,
% 227.35/39.16           e3) = all_52_9 & op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13 &
% 227.35/39.16         op(e2, e0) = all_52_15 & $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 227.35/39.16         $i(all_52_15)
% 227.35/39.16    (3)  op(e3, e3) = e0
% 227.35/39.16    (4)   ~ (e2 = e0)
% 227.35/39.16    (5)  op(e2, e2) = e3
% 227.35/39.16  
% 227.35/39.16  Begin of proof
% 227.35/39.16  | 
% 227.35/39.16  | ALPHA: (2) implies:
% 227.35/39.16  |   (6)  op(e2, e2) = all_52_11
% 227.35/39.16  |   (7)  op(all_52_11, all_52_11) = e2
% 227.35/39.16  | 
% 227.35/39.16  | GROUND_INST: instantiating (1) with e3, all_52_11, e2, e2, simplifying with
% 227.35/39.16  |              (5), (6) gives:
% 227.35/39.16  |   (8)  all_52_11 = e3
% 227.35/39.16  | 
% 227.35/39.16  | REDUCE: (7), (8) imply:
% 227.35/39.16  |   (9)  op(e3, e3) = e2
% 227.35/39.16  | 
% 227.35/39.16  | REF_CLOSE: (1), (3), (4), (9) are inconsistent by sub-proof #2403.
% 227.35/39.16  | 
% 227.35/39.16  End of proof
% 227.35/39.16  
% 227.35/39.16  Sub-proof #210 shows that the following formulas are inconsistent:
% 227.35/39.16  ----------------------------------------------------------------
% 227.35/39.16    (1)   ~ (all_52_29 = e0)
% 227.35/39.16    (2)   ~ (all_52_29 = e2)
% 227.35/39.16    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.35/39.16           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.35/39.16    (4)  ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 & op(e1, e2) = all_42_1
% 227.35/39.16           & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e0) & op(e1, e2) =
% 227.35/39.16           all_42_1 & $i(all_42_1))
% 227.35/39.16    (5)  all_55_14 = all_52_29
% 227.35/39.16    (6)  op(e1, e2) = e0
% 227.35/39.16    (7)  op(e0, e1) = all_52_29
% 227.35/39.16    (8)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 227.35/39.16    (9)  op(all_52_29, all_52_29) = e1
% 227.35/39.16    (10)  op(e1, e1) = e2
% 227.35/39.16    (11)  op(e1, e2) = all_38_1
% 227.35/39.16  
% 227.35/39.16  Begin of proof
% 227.35/39.16  | 
% 227.35/39.16  | GROUND_INST: instantiating (3) with e0, all_38_1, e2, e1, simplifying with
% 227.35/39.16  |              (6), (11) gives:
% 227.35/39.16  |   (12)  all_38_1 = e0
% 227.35/39.16  | 
% 227.35/39.16  | BETA: splitting (4) gives:
% 227.35/39.16  | 
% 227.35/39.16  | Case 1:
% 227.35/39.16  | | 
% 227.35/39.16  | |   (13)   ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 & op(e1, e2) =
% 227.35/39.16  | |         all_42_1 & $i(all_42_0) & $i(all_42_1)
% 227.35/39.16  | | 
% 227.35/39.16  | | ALPHA: (13) implies:
% 227.35/39.16  | |   (14)   ~ (all_42_0 = e3)
% 227.35/39.16  | |   (15)  op(e1, e2) = all_42_1
% 227.35/39.16  | |   (16)  op(all_42_1, e1) = all_42_0
% 227.35/39.16  | | 
% 227.35/39.16  | | GROUND_INST: instantiating (3) with e0, all_42_1, e2, e1, simplifying with
% 227.35/39.16  | |              (6), (15) gives:
% 227.35/39.16  | |   (17)  all_42_1 = e0
% 227.35/39.16  | | 
% 227.35/39.16  | | REDUCE: (16), (17) imply:
% 227.35/39.16  | |   (18)  op(e0, e1) = all_42_0
% 227.35/39.16  | | 
% 227.35/39.16  | | GROUND_INST: instantiating (3) with all_52_29, all_42_0, e1, e0, simplifying
% 227.35/39.16  | |              with (7), (18) gives:
% 227.35/39.16  | |   (19)  all_52_29 = all_42_0
% 227.35/39.16  | | 
% 227.35/39.16  | | COMBINE_EQS: (5), (19) imply:
% 227.35/39.16  | |   (20)  all_55_14 = all_42_0
% 227.35/39.16  | | 
% 227.35/39.16  | | REDUCE: (2), (19) imply:
% 227.35/39.16  | |   (21)   ~ (all_42_0 = e2)
% 227.35/39.16  | | 
% 227.35/39.16  | | REDUCE: (1), (19) imply:
% 227.35/39.16  | |   (22)   ~ (all_42_0 = e0)
% 227.35/39.16  | | 
% 227.35/39.16  | | REDUCE: (9), (19) imply:
% 227.35/39.16  | |   (23)  op(all_42_0, all_42_0) = e1
% 227.35/39.16  | | 
% 227.35/39.16  | | BETA: splitting (8) gives:
% 227.35/39.16  | | 
% 227.35/39.16  | | Case 1:
% 227.35/39.16  | | | 
% 227.35/39.16  | | |   (24)  all_55_14 = e3
% 227.35/39.16  | | | 
% 227.35/39.16  | | | COMBINE_EQS: (20), (24) imply:
% 227.35/39.16  | | |   (25)  all_42_0 = e3
% 227.35/39.16  | | | 
% 227.35/39.16  | | | REDUCE: (14), (25) imply:
% 227.35/39.16  | | |   (26)  $false
% 227.35/39.16  | | | 
% 227.35/39.16  | | | CLOSE: (26) is inconsistent.
% 227.35/39.16  | | | 
% 227.35/39.16  | | Case 2:
% 227.35/39.16  | | | 
% 227.35/39.16  | | |   (27)  all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 227.35/39.16  | | | 
% 227.35/39.16  | | | BETA: splitting (27) gives:
% 227.35/39.16  | | | 
% 227.35/39.16  | | | Case 1:
% 227.35/39.16  | | | | 
% 227.35/39.16  | | | |   (28)  all_55_14 = e2
% 227.35/39.16  | | | | 
% 227.35/39.16  | | | | COMBINE_EQS: (20), (28) imply:
% 227.35/39.16  | | | |   (29)  all_42_0 = e2
% 227.35/39.16  | | | | 
% 227.35/39.16  | | | | REDUCE: (21), (29) imply:
% 227.35/39.16  | | | |   (30)  $false
% 227.35/39.16  | | | | 
% 227.35/39.16  | | | | CLOSE: (30) is inconsistent.
% 227.35/39.16  | | | | 
% 227.35/39.16  | | | Case 2:
% 227.35/39.16  | | | | 
% 227.35/39.16  | | | |   (31)   ~ (all_55_14 = e2)
% 227.35/39.16  | | | |   (32)  all_55_14 = e1 | all_55_14 = e0
% 227.35/39.16  | | | | 
% 227.35/39.16  | | | | BETA: splitting (32) gives:
% 227.35/39.16  | | | | 
% 227.35/39.16  | | | | Case 1:
% 227.35/39.16  | | | | | 
% 227.35/39.16  | | | | |   (33)  all_55_14 = e1
% 227.35/39.16  | | | | | 
% 227.35/39.16  | | | | | COMBINE_EQS: (20), (33) imply:
% 227.35/39.16  | | | | |   (34)  all_42_0 = e1
% 227.35/39.16  | | | | | 
% 227.35/39.16  | | | | | SIMP: (34) implies:
% 227.35/39.16  | | | | |   (35)  all_42_0 = e1
% 227.35/39.16  | | | | | 
% 227.35/39.16  | | | | | REDUCE: (21), (35) imply:
% 227.35/39.16  | | | | |   (36)   ~ (e2 = e1)
% 227.35/39.16  | | | | | 
% 227.35/39.16  | | | | | SIMP: (36) implies:
% 227.35/39.16  | | | | |   (37)   ~ (e2 = e1)
% 227.35/39.16  | | | | | 
% 227.35/39.16  | | | | | REDUCE: (23), (35) imply:
% 227.35/39.16  | | | | |   (38)  op(e1, e1) = e1
% 227.35/39.16  | | | | | 
% 227.35/39.16  | | | | | REF_CLOSE: (3), (10), (37), (38) are inconsistent by sub-proof #2423.
% 227.35/39.16  | | | | | 
% 227.35/39.16  | | | | Case 2:
% 227.35/39.16  | | | | | 
% 227.35/39.16  | | | | |   (39)  all_55_14 = e0
% 227.35/39.16  | | | | | 
% 227.35/39.16  | | | | | COMBINE_EQS: (20), (39) imply:
% 227.35/39.16  | | | | |   (40)  all_42_0 = e0
% 227.35/39.16  | | | | | 
% 227.35/39.16  | | | | | SIMP: (40) implies:
% 227.35/39.16  | | | | |   (41)  all_42_0 = e0
% 227.35/39.16  | | | | | 
% 227.35/39.16  | | | | | REDUCE: (22), (41) imply:
% 227.35/39.16  | | | | |   (42)  $false
% 227.35/39.16  | | | | | 
% 227.35/39.16  | | | | | CLOSE: (42) is inconsistent.
% 227.35/39.16  | | | | | 
% 227.35/39.16  | | | | End of split
% 227.35/39.16  | | | | 
% 227.35/39.16  | | | End of split
% 227.35/39.16  | | | 
% 227.35/39.16  | | End of split
% 227.35/39.16  | | 
% 227.35/39.16  | Case 2:
% 227.35/39.16  | | 
% 227.35/39.16  | |   (43)   ~ (all_42_1 = e0) & op(e1, e2) = all_42_1 & $i(all_42_1)
% 227.35/39.16  | | 
% 227.35/39.16  | | ALPHA: (43) implies:
% 227.35/39.16  | |   (44)   ~ (all_42_1 = e0)
% 227.35/39.17  | |   (45)  op(e1, e2) = all_42_1
% 227.35/39.17  | | 
% 227.35/39.17  | | REF_CLOSE: (3), (6), (11), (44), (45) are inconsistent by sub-proof #211.
% 227.35/39.17  | | 
% 227.35/39.17  | End of split
% 227.35/39.17  | 
% 227.35/39.17  End of proof
% 227.35/39.17  
% 227.35/39.17  Sub-proof #211 shows that the following formulas are inconsistent:
% 227.35/39.17  ----------------------------------------------------------------
% 227.35/39.17    (1)  op(e1, e2) = all_42_1
% 227.35/39.17    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.35/39.17           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.35/39.17    (3)  op(e1, e2) = e0
% 227.35/39.17    (4)   ~ (all_42_1 = e0)
% 227.35/39.17    (5)  op(e1, e2) = all_38_1
% 227.35/39.17  
% 227.35/39.17  Begin of proof
% 227.35/39.17  | 
% 227.35/39.17  | GROUND_INST: instantiating (2) with all_38_1, all_42_1, e2, e1, simplifying
% 227.35/39.17  |              with (1), (5) gives:
% 227.35/39.17  |   (6)  all_42_1 = all_38_1
% 227.35/39.17  | 
% 227.35/39.17  | GROUND_INST: instantiating (2) with e0, all_42_1, e2, e1, simplifying with
% 227.35/39.17  |              (1), (3) gives:
% 227.35/39.17  |   (7)  all_42_1 = e0
% 227.35/39.17  | 
% 227.35/39.17  | COMBINE_EQS: (6), (7) imply:
% 227.35/39.17  |   (8)  all_38_1 = e0
% 227.35/39.17  | 
% 227.35/39.17  | REDUCE: (4), (7) imply:
% 227.35/39.17  |   (9)  $false
% 227.35/39.17  | 
% 227.35/39.17  | CLOSE: (9) is inconsistent.
% 227.35/39.17  | 
% 227.35/39.17  End of proof
% 227.35/39.17  
% 227.35/39.17  Sub-proof #212 shows that the following formulas are inconsistent:
% 227.35/39.17  ----------------------------------------------------------------
% 227.35/39.17    (1)   ~ (all_52_29 = e0)
% 227.35/39.17    (2)   ~ (all_53_8 = all_52_29)
% 227.35/39.17    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.35/39.17           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.35/39.17    (4)   ~ (all_53_8 = e1)
% 227.35/39.17    (5)  all_55_2 = all_53_8
% 227.35/39.17    (6)  all_55_14 = all_52_29
% 227.35/39.17    (7)   ~ (all_52_29 = e1)
% 227.35/39.17    (8)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 227.35/39.17    (9)  op(all_52_29, all_52_29) = e1
% 227.35/39.17    (10)  op(e2, e2) = e3
% 227.35/39.17    (11)  all_55_2 = e3
% 227.35/39.17  
% 227.35/39.17  Begin of proof
% 227.35/39.17  | 
% 227.35/39.17  | COMBINE_EQS: (5), (11) imply:
% 227.35/39.17  |   (12)  all_53_8 = e3
% 227.35/39.17  | 
% 227.35/39.17  | SIMP: (12) implies:
% 227.35/39.17  |   (13)  all_53_8 = e3
% 227.35/39.17  | 
% 227.35/39.17  | REDUCE: (2), (13) imply:
% 227.35/39.17  |   (14)   ~ (all_52_29 = e3)
% 227.35/39.17  | 
% 227.35/39.17  | SIMP: (14) implies:
% 227.35/39.17  |   (15)   ~ (all_52_29 = e3)
% 227.35/39.17  | 
% 227.35/39.17  | REDUCE: (4), (13) imply:
% 227.35/39.17  |   (16)   ~ (e3 = e1)
% 227.35/39.17  | 
% 227.35/39.17  | BETA: splitting (8) gives:
% 227.35/39.17  | 
% 227.35/39.17  | Case 1:
% 227.35/39.17  | | 
% 227.35/39.17  | |   (17)  all_55_14 = e3
% 227.35/39.17  | | 
% 227.35/39.17  | | COMBINE_EQS: (6), (17) imply:
% 227.35/39.17  | |   (18)  all_52_29 = e3
% 227.35/39.17  | | 
% 227.35/39.17  | | REDUCE: (15), (18) imply:
% 227.35/39.17  | |   (19)  $false
% 227.35/39.17  | | 
% 227.35/39.17  | | CLOSE: (19) is inconsistent.
% 227.35/39.17  | | 
% 227.35/39.17  | Case 2:
% 227.35/39.17  | | 
% 227.35/39.17  | |   (20)  all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 227.35/39.17  | | 
% 227.35/39.17  | | BETA: splitting (20) gives:
% 227.35/39.17  | | 
% 227.35/39.17  | | Case 1:
% 227.35/39.17  | | | 
% 227.35/39.17  | | |   (21)  all_55_14 = e2
% 227.35/39.17  | | | 
% 227.35/39.17  | | | COMBINE_EQS: (6), (21) imply:
% 227.35/39.17  | | |   (22)  all_52_29 = e2
% 227.35/39.17  | | | 
% 227.35/39.17  | | | REDUCE: (9), (22) imply:
% 227.35/39.17  | | |   (23)  op(e2, e2) = e1
% 227.35/39.17  | | | 
% 227.35/39.17  | | | REF_CLOSE: (3), (10), (16), (23) are inconsistent by sub-proof #1912.
% 227.35/39.17  | | | 
% 227.35/39.17  | | Case 2:
% 227.35/39.17  | | | 
% 227.35/39.17  | | |   (24)  all_55_14 = e1 | all_55_14 = e0
% 227.35/39.17  | | | 
% 227.35/39.17  | | | REF_CLOSE: (1), (6), (7), (24) are inconsistent by sub-proof #2035.
% 227.35/39.17  | | | 
% 227.35/39.17  | | End of split
% 227.35/39.17  | | 
% 227.35/39.17  | End of split
% 227.35/39.17  | 
% 227.35/39.17  End of proof
% 227.35/39.17  
% 227.35/39.17  Sub-proof #213 shows that the following formulas are inconsistent:
% 227.35/39.17  ----------------------------------------------------------------
% 227.35/39.17    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.35/39.17           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.35/39.17    (2)  all_57_3 = e3
% 227.35/39.17    (3)   ~ (e3 = e0)
% 227.35/39.17    (4)  op(e3, e2) = all_53_4
% 227.35/39.17    (5)   ~ (all_53_4 = e0)
% 227.35/39.17    (6)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0)
% 227.35/39.17  
% 227.35/39.17  Begin of proof
% 227.35/39.17  | 
% 227.35/39.17  | BETA: splitting (6) gives:
% 227.35/39.17  | 
% 227.35/39.17  | Case 1:
% 227.35/39.17  | | 
% 227.35/39.17  | |   (7)  all_57_1 = e0 & op(e3, e2) = e0
% 227.35/39.17  | | 
% 227.35/39.17  | | ALPHA: (7) implies:
% 227.35/39.17  | |   (8)  op(e3, e2) = e0
% 227.35/39.17  | | 
% 227.35/39.17  | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #1941.
% 227.35/39.17  | | 
% 227.35/39.17  | Case 2:
% 227.35/39.17  | | 
% 227.35/39.17  | |   (9)  all_57_3 = e0 & op(e2, e2) = e0
% 227.35/39.17  | | 
% 227.35/39.17  | | REF_CLOSE: (2), (3), (9) are inconsistent by sub-proof #262.
% 227.35/39.17  | | 
% 227.35/39.17  | End of split
% 227.35/39.17  | 
% 227.35/39.17  End of proof
% 227.35/39.17  
% 227.35/39.17  Sub-proof #214 shows that the following formulas are inconsistent:
% 227.35/39.17  ----------------------------------------------------------------
% 227.35/39.17    (1)  op(e2, e3) = all_53_1
% 227.35/39.17    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.35/39.17           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.35/39.17    (3)  all_57_3 = e3
% 227.35/39.17    (4)   ~ (e3 = e0)
% 227.35/39.17    (5)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0)
% 227.35/39.17    (6)   ~ (all_53_1 = e0)
% 227.35/39.17  
% 227.35/39.17  Begin of proof
% 227.35/39.17  | 
% 227.35/39.17  | BETA: splitting (5) gives:
% 227.35/39.17  | 
% 227.35/39.17  | Case 1:
% 227.35/39.17  | | 
% 227.35/39.17  | |   (7)  all_57_2 = e0 & op(e2, e3) = e0
% 227.35/39.17  | | 
% 227.35/39.17  | | ALPHA: (7) implies:
% 227.35/39.17  | |   (8)  op(e2, e3) = e0
% 227.35/39.17  | | 
% 227.35/39.17  | | REF_CLOSE: (1), (2), (6), (8) are inconsistent by sub-proof #1943.
% 227.35/39.17  | | 
% 227.35/39.17  | Case 2:
% 227.35/39.17  | | 
% 227.35/39.17  | |   (9)  all_57_3 = e0 & op(e2, e2) = e0
% 227.35/39.17  | | 
% 227.35/39.17  | | REF_CLOSE: (3), (4), (9) are inconsistent by sub-proof #262.
% 227.35/39.17  | | 
% 227.35/39.17  | End of split
% 227.35/39.17  | 
% 227.35/39.17  End of proof
% 227.35/39.17  
% 227.35/39.17  Sub-proof #215 shows that the following formulas are inconsistent:
% 227.35/39.17  ----------------------------------------------------------------
% 227.35/39.17    (1)   ~ (e3 = e1)
% 227.35/39.17    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.35/39.17           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.35/39.17    (3)  all_57_4 = e3
% 227.35/39.17    (4)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 227.35/39.17         (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 227.35/39.17    (5)   ~ (e1 = e0)
% 227.35/39.17    (6)  all_57_14 = e2
% 227.35/39.17    (7)  op(e1, e1) = e0
% 227.35/39.17    (8)   ~ (e2 = e1)
% 227.35/39.17    (9)  all_57_5 = e0
% 227.35/39.17  
% 227.35/39.17  Begin of proof
% 227.35/39.17  | 
% 227.35/39.17  | BETA: splitting (4) gives:
% 227.35/39.17  | 
% 227.35/39.17  | Case 1:
% 227.35/39.17  | | 
% 227.35/39.17  | |   (10)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) =
% 227.35/39.17  | |           e1)
% 227.35/39.17  | | 
% 227.35/39.17  | | BETA: splitting (10) gives:
% 227.35/39.17  | | 
% 227.35/39.17  | | Case 1:
% 227.35/39.17  | | | 
% 227.35/39.17  | | |   (11)  all_57_4 = e1 & op(e3, e1) = e1
% 227.35/39.17  | | | 
% 227.35/39.17  | | | REF_CLOSE: (1), (3), (11) are inconsistent by sub-proof #2484.
% 227.35/39.17  | | | 
% 227.35/39.17  | | Case 2:
% 227.35/39.17  | | | 
% 227.35/39.17  | | |   (12)  all_57_5 = e1 & op(e2, e1) = e1
% 227.35/39.17  | | | 
% 227.35/39.17  | | | ALPHA: (12) implies:
% 227.35/39.17  | | |   (13)  all_57_5 = e1
% 227.35/39.17  | | | 
% 227.35/39.17  | | | REF_CLOSE: (5), (9), (13) are inconsistent by sub-proof #2350.
% 227.35/39.17  | | | 
% 227.35/39.17  | | End of split
% 227.35/39.17  | | 
% 227.35/39.17  | Case 2:
% 227.35/39.17  | | 
% 227.35/39.17  | |   (14)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) =
% 227.35/39.17  | |           e1)
% 227.35/39.17  | | 
% 227.35/39.17  | | REF_CLOSE: (2), (5), (6), (7), (8), (14) are inconsistent by sub-proof
% 227.35/39.17  | |            #2374.
% 227.35/39.17  | | 
% 227.35/39.17  | End of split
% 227.35/39.17  | 
% 227.35/39.17  End of proof
% 227.35/39.17  
% 227.35/39.17  Sub-proof #216 shows that the following formulas are inconsistent:
% 227.35/39.17  ----------------------------------------------------------------
% 227.35/39.17    (1)  all_57_10 = e0
% 227.35/39.17    (2)  op(e2, e0) = e0
% 227.35/39.17    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.35/39.17           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.35/39.17    (4)  op(e2, e0) = all_52_15
% 227.35/39.17    (5)  op(e1, e0) = all_53_14
% 227.35/39.17    (6)   ~ (e1 = e0)
% 227.35/39.17    (7)   ~ (all_53_14 = e1)
% 227.35/39.17    (8)   ~ (all_53_12 = e1)
% 227.35/39.17    (9)  op(all_52_15, all_52_15) = e0
% 227.35/39.17    (10)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 227.35/39.17          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 227.35/39.17    (11)  op(e3, e0) = all_53_12
% 227.35/39.17  
% 227.35/39.17  Begin of proof
% 227.35/39.17  | 
% 227.35/39.17  | BETA: splitting (10) gives:
% 227.35/39.17  | 
% 227.35/39.17  | Case 1:
% 227.35/39.17  | | 
% 227.35/39.17  | |   (12)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) =
% 227.35/39.17  | |           e1)
% 227.35/39.17  | | 
% 227.35/39.17  | | REF_CLOSE: (1), (3), (6), (8), (11), (12) are inconsistent by sub-proof
% 227.35/39.17  | |            #218.
% 227.35/39.17  | | 
% 227.35/39.17  | Case 2:
% 227.35/39.17  | | 
% 227.35/39.17  | |   (13)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 227.35/39.17  | |           e1)
% 227.35/39.17  | | 
% 227.35/39.17  | | BETA: splitting (13) gives:
% 227.35/39.17  | | 
% 227.35/39.17  | | Case 1:
% 227.35/39.17  | | | 
% 227.35/39.17  | | |   (14)  all_57_11 = e1 & op(e1, e0) = e1
% 227.35/39.17  | | | 
% 227.35/39.17  | | | REF_CLOSE: (3), (5), (7), (14) are inconsistent by sub-proof #305.
% 227.35/39.17  | | | 
% 227.35/39.17  | | Case 2:
% 227.35/39.17  | | | 
% 227.35/39.17  | | |   (15)  all_57_15 = e1 & op(e0, e0) = e1
% 227.35/39.17  | | | 
% 227.35/39.17  | | | REF_CLOSE: (2), (3), (4), (6), (9), (15) are inconsistent by sub-proof
% 227.35/39.17  | | |            #1897.
% 227.35/39.17  | | | 
% 227.35/39.17  | | End of split
% 227.35/39.17  | | 
% 227.35/39.17  | End of split
% 227.35/39.17  | 
% 227.35/39.17  End of proof
% 227.35/39.17  
% 227.35/39.17  Sub-proof #217 shows that the following formulas are inconsistent:
% 227.35/39.17  ----------------------------------------------------------------
% 227.35/39.17    (1)  all_57_10 = e0
% 227.35/39.17    (2)   ~ (e3 = e1)
% 227.35/39.17    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.35/39.17           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.35/39.17    (4)  op(e1, e0) = all_53_14
% 227.35/39.17    (5)  op(e3, e3) = e0
% 227.35/39.17    (6)  op(e3, e3) = all_52_1
% 227.35/39.17    (7)  op(all_52_1, all_52_1) = e3
% 227.35/39.17    (8)   ~ (e1 = e0)
% 227.35/39.17    (9)   ~ (all_53_14 = e1)
% 227.35/39.17    (10)   ~ (all_53_12 = e1)
% 227.35/39.17    (11)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 227.35/39.17          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 227.35/39.17    (12)  op(e3, e0) = all_53_12
% 227.35/39.17  
% 227.35/39.17  Begin of proof
% 227.35/39.17  | 
% 227.35/39.17  | BETA: splitting (11) gives:
% 227.35/39.17  | 
% 227.35/39.17  | Case 1:
% 227.35/39.17  | | 
% 227.35/39.17  | |   (13)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) =
% 227.35/39.17  | |           e1)
% 227.35/39.17  | | 
% 227.35/39.17  | | REF_CLOSE: (1), (3), (8), (10), (12), (13) are inconsistent by sub-proof
% 227.35/39.17  | |            #218.
% 227.35/39.17  | | 
% 227.35/39.17  | Case 2:
% 227.35/39.17  | | 
% 227.35/39.17  | |   (14)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 227.35/39.17  | |           e1)
% 227.35/39.17  | | 
% 227.35/39.17  | | BETA: splitting (14) gives:
% 227.35/39.17  | | 
% 227.35/39.17  | | Case 1:
% 227.35/39.17  | | | 
% 227.35/39.17  | | |   (15)  all_57_11 = e1 & op(e1, e0) = e1
% 227.35/39.17  | | | 
% 227.35/39.17  | | | REF_CLOSE: (3), (4), (9), (15) are inconsistent by sub-proof #305.
% 227.35/39.17  | | | 
% 227.35/39.17  | | Case 2:
% 227.35/39.17  | | | 
% 227.35/39.17  | | |   (16)  all_57_15 = e1 & op(e0, e0) = e1
% 227.35/39.17  | | | 
% 227.35/39.17  | | | REF_CLOSE: (2), (3), (5), (6), (7), (16) are inconsistent by sub-proof
% 227.35/39.17  | | |            #1916.
% 227.35/39.17  | | | 
% 227.35/39.17  | | End of split
% 227.35/39.17  | | 
% 227.35/39.17  | End of split
% 227.35/39.17  | 
% 227.35/39.17  End of proof
% 227.35/39.17  
% 227.35/39.17  Sub-proof #218 shows that the following formulas are inconsistent:
% 227.35/39.17  ----------------------------------------------------------------
% 227.35/39.17    (1)  all_57_10 = e0
% 227.35/39.17    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.35/39.17           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.35/39.17    (3)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 227.35/39.17    (4)   ~ (e1 = e0)
% 227.35/39.17    (5)   ~ (all_53_12 = e1)
% 227.35/39.17    (6)  op(e3, e0) = all_53_12
% 227.35/39.17  
% 227.35/39.17  Begin of proof
% 227.35/39.17  | 
% 227.35/39.17  | BETA: splitting (3) gives:
% 227.35/39.17  | 
% 227.35/39.17  | Case 1:
% 227.35/39.17  | | 
% 227.35/39.17  | |   (7)  all_57_9 = e1 & op(e3, e0) = e1
% 227.35/39.17  | | 
% 227.35/39.17  | | REF_CLOSE: (2), (5), (6), (7) are inconsistent by sub-proof #2131.
% 227.35/39.17  | | 
% 227.35/39.17  | Case 2:
% 227.35/39.17  | | 
% 227.35/39.17  | |   (8)  all_57_10 = e1 & op(e2, e0) = e1
% 227.35/39.17  | | 
% 227.35/39.17  | | ALPHA: (8) implies:
% 227.35/39.17  | |   (9)  all_57_10 = e1
% 227.35/39.17  | | 
% 227.35/39.17  | | REF_CLOSE: (1), (4), (9) are inconsistent by sub-proof #1531.
% 227.35/39.17  | | 
% 227.35/39.17  | End of split
% 227.35/39.17  | 
% 227.35/39.17  End of proof
% 227.35/39.17  
% 227.35/39.17  Sub-proof #219 shows that the following formulas are inconsistent:
% 227.35/39.17  ----------------------------------------------------------------
% 227.35/39.17    (1)  op(e2, e3) = all_53_1
% 227.35/39.17    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.35/39.17           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.35/39.17    (3)   ~ (all_53_3 = e3)
% 227.35/39.17    (4)   ~ (all_53_1 = all_53_3)
% 227.35/39.17    (5)   ~ (e3 = e0)
% 227.35/39.17    (6)  op(e3, e3) = e2
% 227.35/39.17    (7)   ~ (all_53_3 = e2)
% 227.35/39.17    (8)   ~ (e2 = e0)
% 227.35/39.17    (9)  all_55_12 = all_53_3
% 227.35/39.17    (10)   ~ (all_53_2 = all_53_3)
% 227.35/39.17    (11)   ~ (all_53_3 = e1)
% 227.35/39.17    (12)  op(e1, e3) = all_53_2
% 227.35/39.17    (13)  all_55_12 = e1 | all_55_12 = e0
% 227.35/39.17    (14)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 227.35/39.17    (15)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 227.35/39.17          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 227.35/39.17    (16)  all_57_12 = e3 & op(e0, e3) = e3
% 227.35/39.17  
% 227.35/39.17  Begin of proof
% 227.35/39.17  | 
% 227.35/39.17  | ALPHA: (16) implies:
% 227.35/39.17  |   (17)  all_57_12 = e3
% 227.35/39.17  | 
% 227.35/39.17  | BETA: splitting (15) gives:
% 227.35/39.17  | 
% 227.35/39.17  | Case 1:
% 227.35/39.17  | | 
% 227.35/39.17  | |   (18)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) =
% 227.35/39.17  | |           e0)
% 227.35/39.17  | | 
% 227.35/39.17  | | REF_CLOSE: (1), (2), (4), (6), (8), (9), (11), (13), (18) are inconsistent
% 227.35/39.17  | |            by sub-proof #220.
% 227.35/39.17  | | 
% 227.35/39.17  | Case 2:
% 227.35/39.17  | | 
% 227.35/39.17  | |   (19)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) =
% 227.35/39.17  | |           e0)
% 227.35/39.17  | | 
% 227.35/39.17  | | BETA: splitting (19) gives:
% 227.35/39.17  | | 
% 227.35/39.17  | | Case 1:
% 227.35/39.17  | | | 
% 227.35/39.17  | | |   (20)  all_57_6 = e0 & op(e1, e3) = e0
% 227.35/39.17  | | | 
% 227.35/39.17  | | | ALPHA: (20) implies:
% 227.35/39.17  | | |   (21)  op(e1, e3) = e0
% 227.35/39.17  | | | 
% 227.35/39.17  | | | BETA: splitting (14) gives:
% 227.35/39.17  | | | 
% 227.35/39.17  | | | Case 1:
% 227.35/39.17  | | | | 
% 227.35/39.17  | | | |   (22)  all_55_12 = e3
% 227.35/39.17  | | | | 
% 227.35/39.17  | | | | REF_CLOSE: (3), (9), (22) are inconsistent by sub-proof #2001.
% 227.35/39.17  | | | | 
% 227.35/39.17  | | | Case 2:
% 227.35/39.17  | | | | 
% 227.35/39.17  | | | |   (23)  all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 227.35/39.17  | | | | 
% 227.35/39.17  | | | | REF_CLOSE: (2), (7), (9), (10), (11), (12), (21), (23) are inconsistent
% 227.35/39.17  | | | |            by sub-proof #1336.
% 227.35/39.17  | | | | 
% 227.35/39.17  | | | End of split
% 227.35/39.17  | | | 
% 227.35/39.17  | | Case 2:
% 227.35/39.17  | | | 
% 227.35/39.17  | | |   (24)  all_57_12 = e0 & op(e0, e3) = e0
% 227.35/39.17  | | | 
% 227.35/39.17  | | | REF_CLOSE: (5), (17), (24) are inconsistent by sub-proof #2237.
% 227.35/39.17  | | | 
% 227.35/39.17  | | End of split
% 227.35/39.17  | | 
% 227.35/39.17  | End of split
% 227.35/39.17  | 
% 227.35/39.17  End of proof
% 227.35/39.17  
% 227.35/39.17  Sub-proof #220 shows that the following formulas are inconsistent:
% 227.35/39.17  ----------------------------------------------------------------
% 227.35/39.17    (1)  op(e2, e3) = all_53_1
% 227.35/39.17    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.35/39.17           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.35/39.17    (3)   ~ (all_53_1 = all_53_3)
% 227.35/39.17    (4)  op(e3, e3) = e2
% 227.35/39.17    (5)   ~ (e2 = e0)
% 227.44/39.17    (6)  all_55_12 = all_53_3
% 227.44/39.17    (7)   ~ (all_53_3 = e1)
% 227.44/39.17    (8)  all_55_12 = e1 | all_55_12 = e0
% 227.44/39.17    (9)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0)
% 227.44/39.17  
% 227.44/39.17  Begin of proof
% 227.44/39.17  | 
% 227.44/39.17  | BETA: splitting (9) gives:
% 227.44/39.17  | 
% 227.44/39.17  | Case 1:
% 227.44/39.17  | | 
% 227.44/39.17  | |   (10)  all_57_0 = e0 & op(e3, e3) = e0
% 227.44/39.17  | | 
% 227.44/39.17  | | ALPHA: (10) implies:
% 227.44/39.17  | |   (11)  op(e3, e3) = e0
% 227.44/39.17  | | 
% 227.44/39.17  | | REF_CLOSE: (2), (4), (5), (11) are inconsistent by sub-proof #2403.
% 227.44/39.17  | | 
% 227.44/39.17  | Case 2:
% 227.44/39.17  | | 
% 227.44/39.17  | |   (12)  all_57_2 = e0 & op(e2, e3) = e0
% 227.44/39.17  | | 
% 227.44/39.17  | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (12) are inconsistent by sub-proof
% 227.44/39.17  | |            #221.
% 227.44/39.17  | | 
% 227.44/39.17  | End of split
% 227.44/39.17  | 
% 227.44/39.17  End of proof
% 227.44/39.17  
% 227.44/39.17  Sub-proof #221 shows that the following formulas are inconsistent:
% 227.44/39.17  ----------------------------------------------------------------
% 227.44/39.17    (1)  op(e2, e3) = all_53_1
% 227.44/39.17    (2)  all_57_2 = e0 & op(e2, e3) = e0
% 227.44/39.17    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.44/39.17           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.44/39.17    (4)   ~ (all_53_1 = all_53_3)
% 227.44/39.17    (5)  all_55_12 = all_53_3
% 227.44/39.17    (6)   ~ (all_53_3 = e1)
% 227.44/39.17    (7)  all_55_12 = e1 | all_55_12 = e0
% 227.44/39.17  
% 227.44/39.17  Begin of proof
% 227.44/39.17  | 
% 227.44/39.17  | ALPHA: (2) implies:
% 227.44/39.17  |   (8)  op(e2, e3) = e0
% 227.44/39.17  | 
% 227.44/39.17  | BETA: splitting (7) gives:
% 227.44/39.17  | 
% 227.44/39.17  | Case 1:
% 227.44/39.17  | | 
% 227.44/39.17  | |   (9)  all_55_12 = e1
% 227.44/39.17  | | 
% 227.44/39.17  | | REF_CLOSE: (5), (6), (9) are inconsistent by sub-proof #1994.
% 227.44/39.17  | | 
% 227.44/39.17  | Case 2:
% 227.44/39.17  | | 
% 227.44/39.17  | |   (10)  all_55_12 = e0
% 227.44/39.17  | | 
% 227.44/39.17  | | COMBINE_EQS: (5), (10) imply:
% 227.44/39.17  | |   (11)  all_53_3 = e0
% 227.44/39.17  | | 
% 227.44/39.17  | | SIMP: (11) implies:
% 227.44/39.17  | |   (12)  all_53_3 = e0
% 227.44/39.17  | | 
% 227.44/39.17  | | REDUCE: (4), (12) imply:
% 227.44/39.17  | |   (13)   ~ (all_53_1 = e0)
% 227.44/39.17  | | 
% 227.44/39.17  | | REF_CLOSE: (1), (3), (8), (13) are inconsistent by sub-proof #1943.
% 227.44/39.17  | | 
% 227.44/39.17  | End of split
% 227.44/39.17  | 
% 227.44/39.17  End of proof
% 227.44/39.17  
% 227.44/39.17  Sub-proof #222 shows that the following formulas are inconsistent:
% 227.44/39.17  ----------------------------------------------------------------
% 227.44/39.17    (1)  op(e0, e1) = all_53_11
% 227.44/39.17    (2)   ~ (e3 = e1)
% 227.44/39.17    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.44/39.17           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.44/39.17    (4)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 227.44/39.17         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 227.44/39.17    (5)   ~ (all_6_2 = e3)
% 227.44/39.17    (6)  op(e1, e1) = all_6_2
% 227.44/39.17    (7)  all_57_4 = e3
% 227.44/39.17    (8)   ~ (e3 = e2)
% 227.44/39.17    (9)  op(e1, e0) = all_53_14
% 227.44/39.17    (10)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 227.44/39.17          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 227.44/39.17    (11)   ~ (e2 = e0)
% 227.44/39.17    (12)   ~ (e1 = e0)
% 227.44/39.17    (13)  all_57_5 = e2
% 227.44/39.17    (14)  all_57_6 = e3
% 227.44/39.17    (15)   ~ (all_53_14 = e1)
% 227.44/39.17    (16)  op(e1, e1) = e0
% 227.44/39.17    (17)   ~ (all_53_11 = e1)
% 227.44/39.17    (18)  all_57_8 = e0
% 227.44/39.17    (19)   ~ (e2 = e1)
% 227.44/39.17    (20)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 227.44/39.17          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 227.44/39.17    (21)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 227.44/39.17          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 227.44/39.17  
% 227.44/39.17  Begin of proof
% 227.44/39.17  | 
% 227.44/39.17  | BETA: splitting (20) gives:
% 227.44/39.17  | 
% 227.44/39.17  | Case 1:
% 227.44/39.17  | | 
% 227.44/39.17  | |   (22)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) =
% 227.44/39.17  | |           e1)
% 227.44/39.17  | | 
% 227.44/39.17  | | BETA: splitting (22) gives:
% 227.44/39.17  | | 
% 227.44/39.17  | | Case 1:
% 227.44/39.17  | | | 
% 227.44/39.17  | | |   (23)  all_57_6 = e1 & op(e1, e3) = e1
% 227.44/39.17  | | | 
% 227.44/39.17  | | | REF_CLOSE: (2), (14), (23) are inconsistent by sub-proof #2117.
% 227.44/39.17  | | | 
% 227.44/39.17  | | Case 2:
% 227.44/39.17  | | | 
% 227.44/39.17  | | |   (24)  all_57_7 = e1 & op(e1, e2) = e1
% 227.44/39.17  | | | 
% 227.44/39.17  | | | ALPHA: (24) implies:
% 227.44/39.17  | | |   (25)  all_57_7 = e1
% 227.44/39.17  | | | 
% 227.44/39.17  | | | BETA: splitting (10) gives:
% 227.44/39.17  | | | 
% 227.44/39.17  | | | Case 1:
% 227.44/39.17  | | | | 
% 227.44/39.17  | | | |   (26)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1)
% 227.44/39.17  | | | |           = e1)
% 227.44/39.17  | | | | 
% 227.44/39.17  | | | | BETA: splitting (26) gives:
% 227.44/39.17  | | | | 
% 227.44/39.17  | | | | Case 1:
% 227.44/39.17  | | | | | 
% 227.44/39.17  | | | | |   (27)  all_57_4 = e1 & op(e3, e1) = e1
% 227.44/39.17  | | | | | 
% 227.44/39.17  | | | | | ALPHA: (27) implies:
% 227.44/39.17  | | | | |   (28)  all_57_4 = e1
% 227.44/39.17  | | | | | 
% 227.44/39.17  | | | | | COMBINE_EQS: (7), (28) imply:
% 227.44/39.17  | | | | |   (29)  e3 = e1
% 227.44/39.17  | | | | | 
% 227.44/39.17  | | | | | SIMP: (29) implies:
% 227.44/39.17  | | | | |   (30)  e3 = e1
% 227.44/39.17  | | | | | 
% 227.44/39.17  | | | | | COMBINE_EQS: (14), (30) imply:
% 227.44/39.17  | | | | |   (31)  all_57_6 = e1
% 227.44/39.17  | | | | | 
% 227.44/39.17  | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (11), (18), (19), (21), (25),
% 227.44/39.17  | | | | |            (31) are inconsistent by sub-proof #325.
% 227.44/39.17  | | | | | 
% 227.44/39.17  | | | | Case 2:
% 227.44/39.17  | | | | | 
% 227.44/39.17  | | | | |   (32)  all_57_5 = e1 & op(e2, e1) = e1
% 227.44/39.17  | | | | | 
% 227.44/39.17  | | | | | REF_CLOSE: (13), (19), (32) are inconsistent by sub-proof #1886.
% 227.44/39.17  | | | | | 
% 227.44/39.17  | | | | End of split
% 227.44/39.17  | | | | 
% 227.44/39.17  | | | Case 2:
% 227.44/39.17  | | | | 
% 227.44/39.17  | | | |   (33)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1)
% 227.44/39.17  | | | |           = e1)
% 227.44/39.17  | | | | 
% 227.44/39.17  | | | | REF_CLOSE: (1), (3), (12), (16), (17), (33) are inconsistent by
% 227.44/39.17  | | | |            sub-proof #224.
% 227.44/39.17  | | | | 
% 227.44/39.17  | | | End of split
% 227.44/39.17  | | | 
% 227.44/39.17  | | End of split
% 227.44/39.17  | | 
% 227.44/39.17  | Case 2:
% 227.44/39.17  | | 
% 227.44/39.17  | |   (34)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) =
% 227.44/39.17  | |           e1)
% 227.44/39.17  | | 
% 227.44/39.17  | | REF_CLOSE: (3), (9), (12), (15), (16), (34) are inconsistent by sub-proof
% 227.44/39.17  | |            #223.
% 227.44/39.17  | | 
% 227.44/39.17  | End of split
% 227.44/39.17  | 
% 227.44/39.17  End of proof
% 227.44/39.17  
% 227.44/39.17  Sub-proof #223 shows that the following formulas are inconsistent:
% 227.44/39.17  ----------------------------------------------------------------
% 227.44/39.17    (1)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 227.44/39.17    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.44/39.17           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.44/39.17    (3)  op(e1, e0) = all_53_14
% 227.44/39.17    (4)   ~ (e1 = e0)
% 227.44/39.17    (5)   ~ (all_53_14 = e1)
% 227.44/39.17    (6)  op(e1, e1) = e0
% 227.44/39.17  
% 227.44/39.17  Begin of proof
% 227.44/39.17  | 
% 227.44/39.17  | BETA: splitting (1) gives:
% 227.44/39.17  | 
% 227.44/39.17  | Case 1:
% 227.44/39.17  | | 
% 227.44/39.17  | |   (7)  all_57_8 = e1 & op(e1, e1) = e1
% 227.44/39.17  | | 
% 227.44/39.17  | | ALPHA: (7) implies:
% 227.44/39.17  | |   (8)  op(e1, e1) = e1
% 227.44/39.17  | | 
% 227.44/39.17  | | REF_CLOSE: (2), (4), (6), (8) are inconsistent by sub-proof #2427.
% 227.44/39.17  | | 
% 227.44/39.17  | Case 2:
% 227.44/39.17  | | 
% 227.44/39.17  | |   (9)  all_57_11 = e1 & op(e1, e0) = e1
% 227.44/39.17  | | 
% 227.44/39.17  | | REF_CLOSE: (2), (3), (5), (9) are inconsistent by sub-proof #305.
% 227.44/39.17  | | 
% 227.44/39.17  | End of split
% 227.44/39.17  | 
% 227.44/39.17  End of proof
% 227.44/39.17  
% 227.44/39.17  Sub-proof #224 shows that the following formulas are inconsistent:
% 227.44/39.17  ----------------------------------------------------------------
% 227.44/39.17    (1)  op(e0, e1) = all_53_11
% 227.44/39.17    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.44/39.17           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.44/39.17    (3)   ~ (e1 = e0)
% 227.44/39.17    (4)  op(e1, e1) = e0
% 227.44/39.17    (5)   ~ (all_53_11 = e1)
% 227.44/39.17    (6)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 227.44/39.17  
% 227.44/39.17  Begin of proof
% 227.44/39.17  | 
% 227.44/39.17  | BETA: splitting (6) gives:
% 227.44/39.17  | 
% 227.44/39.17  | Case 1:
% 227.44/39.17  | | 
% 227.44/39.17  | |   (7)  all_57_8 = e1 & op(e1, e1) = e1
% 227.44/39.17  | | 
% 227.44/39.17  | | ALPHA: (7) implies:
% 227.44/39.17  | |   (8)  op(e1, e1) = e1
% 227.44/39.17  | | 
% 227.44/39.17  | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #2427.
% 227.44/39.17  | | 
% 227.44/39.17  | Case 2:
% 227.44/39.17  | | 
% 227.44/39.17  | |   (9)  all_57_14 = e1 & op(e0, e1) = e1
% 227.44/39.17  | | 
% 227.44/39.17  | | REF_CLOSE: (1), (2), (5), (9) are inconsistent by sub-proof #225.
% 227.44/39.17  | | 
% 227.44/39.17  | End of split
% 227.44/39.17  | 
% 227.44/39.17  End of proof
% 227.44/39.17  
% 227.44/39.17  Sub-proof #225 shows that the following formulas are inconsistent:
% 227.44/39.17  ----------------------------------------------------------------
% 227.44/39.17    (1)  all_57_14 = e1 & op(e0, e1) = e1
% 227.44/39.17    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.44/39.17           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.44/39.17    (3)  op(e0, e1) = all_53_11
% 227.44/39.17    (4)   ~ (all_53_11 = e1)
% 227.44/39.17  
% 227.44/39.17  Begin of proof
% 227.44/39.17  | 
% 227.44/39.17  | ALPHA: (1) implies:
% 227.44/39.17  |   (5)  op(e0, e1) = e1
% 227.44/39.17  | 
% 227.44/39.17  | GROUND_INST: instantiating (2) with all_53_11, e1, e1, e0, simplifying with
% 227.44/39.17  |              (3), (5) gives:
% 227.44/39.17  |   (6)  all_53_11 = e1
% 227.44/39.17  | 
% 227.44/39.17  | REDUCE: (4), (6) imply:
% 227.44/39.17  |   (7)  $false
% 227.44/39.17  | 
% 227.44/39.17  | CLOSE: (7) is inconsistent.
% 227.44/39.17  | 
% 227.44/39.17  End of proof
% 227.44/39.17  
% 227.44/39.17  Sub-proof #226 shows that the following formulas are inconsistent:
% 227.44/39.17  ----------------------------------------------------------------
% 227.44/39.17    (1)   ~ (e3 = e1)
% 227.44/39.17    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.44/39.17           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.44/39.17    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 227.44/39.17         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 227.44/39.17    (4)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 227.44/39.17         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 227.44/39.17    (5)   ~ (e3 = e2)
% 227.44/39.17    (6)   ~ (e3 = e0)
% 227.44/39.17    (7)  op(e3, e3) = e2
% 227.44/39.17    (8)   ~ (e2 = e0)
% 227.44/39.17    (9)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 227.44/39.18         (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 227.44/39.18    (10)   ~ (e1 = e0)
% 227.44/39.18    (11)  all_57_4 = e2 & op(e3, e1) = e2
% 227.44/39.18    (12)   ~ (e2 = e1)
% 227.44/39.18  
% 227.44/39.18  Begin of proof
% 227.44/39.18  | 
% 227.44/39.18  | ALPHA: (11) implies:
% 227.44/39.18  |   (13)  all_57_4 = e2
% 227.44/39.18  | 
% 227.44/39.18  | BETA: splitting (4) gives:
% 227.44/39.18  | 
% 227.44/39.18  | Case 1:
% 227.44/39.18  | | 
% 227.44/39.18  | |   (14)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) =
% 227.44/39.18  | |           e0)
% 227.44/39.18  | | 
% 227.44/39.18  | | BETA: splitting (14) gives:
% 227.44/39.18  | | 
% 227.44/39.18  | | Case 1:
% 227.44/39.18  | | | 
% 227.44/39.18  | | |   (15)  all_57_0 = e0 & op(e3, e3) = e0
% 227.44/39.18  | | | 
% 227.44/39.18  | | | ALPHA: (15) implies:
% 227.44/39.18  | | |   (16)  op(e3, e3) = e0
% 227.44/39.18  | | | 
% 227.44/39.18  | | | REF_CLOSE: (2), (7), (8), (16) are inconsistent by sub-proof #2403.
% 227.44/39.18  | | | 
% 227.44/39.18  | | Case 2:
% 227.44/39.18  | | | 
% 227.44/39.18  | | |   (17)  all_57_1 = e0 & op(e3, e2) = e0
% 227.44/39.18  | | | 
% 227.44/39.18  | | | ALPHA: (17) implies:
% 227.44/39.18  | | |   (18)  all_57_1 = e0
% 227.44/39.18  | | | 
% 227.44/39.18  | | | BETA: splitting (3) gives:
% 227.44/39.18  | | | 
% 227.44/39.18  | | | Case 1:
% 227.44/39.18  | | | | 
% 227.44/39.18  | | | |   (19)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2)
% 227.44/39.18  | | | |           = e1)
% 227.44/39.18  | | | | 
% 227.44/39.18  | | | | REF_CLOSE: (2), (7), (10), (12), (18), (19) are inconsistent by
% 227.44/39.18  | | | |            sub-proof #452.
% 227.44/39.18  | | | | 
% 227.44/39.18  | | | Case 2:
% 227.44/39.18  | | | | 
% 227.44/39.18  | | | |   (20)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0)
% 227.44/39.18  | | | |           = e1)
% 227.44/39.18  | | | | 
% 227.44/39.18  | | | | BETA: splitting (20) gives:
% 227.44/39.18  | | | | 
% 227.44/39.18  | | | | Case 1:
% 227.44/39.18  | | | | | 
% 227.44/39.18  | | | | |   (21)  all_57_4 = e1 & op(e3, e1) = e1
% 227.44/39.18  | | | | | 
% 227.44/39.18  | | | | | REF_CLOSE: (12), (13), (21) are inconsistent by sub-proof #2452.
% 227.44/39.18  | | | | | 
% 227.44/39.18  | | | | Case 2:
% 227.44/39.18  | | | | | 
% 227.44/39.18  | | | | |   (22)  all_57_9 = e1 & op(e3, e0) = e1
% 227.44/39.18  | | | | | 
% 227.44/39.18  | | | | | ALPHA: (22) implies:
% 227.44/39.18  | | | | |   (23)  all_57_9 = e1
% 227.44/39.18  | | | | | 
% 227.44/39.18  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12),
% 227.44/39.18  | | | | |            (13), (23) are inconsistent by sub-proof #1604.
% 227.44/39.18  | | | | | 
% 227.44/39.18  | | | | End of split
% 227.44/39.18  | | | | 
% 227.44/39.18  | | | End of split
% 227.44/39.18  | | | 
% 227.44/39.18  | | End of split
% 227.44/39.18  | | 
% 227.44/39.18  | Case 2:
% 227.44/39.18  | | 
% 227.44/39.18  | |   (24)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) =
% 227.44/39.18  | |           e0)
% 227.44/39.18  | | 
% 227.44/39.18  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (12), (13), (24)
% 227.44/39.18  | |            are inconsistent by sub-proof #1605.
% 227.44/39.18  | | 
% 227.44/39.18  | End of split
% 227.44/39.18  | 
% 227.44/39.18  End of proof
% 227.44/39.18  
% 227.44/39.18  Sub-proof #227 shows that the following formulas are inconsistent:
% 227.44/39.18  ----------------------------------------------------------------
% 227.44/39.18    (1)  ( ~ (all_8_0 = e0) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 227.44/39.18           $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e1) & op(e2, e3) = all_8_1
% 227.44/39.18           & $i(all_8_1))
% 227.44/39.18    (2)  op(e2, e3) = e0
% 227.44/39.18    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.44/39.18           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.44/39.18    (4)  op(e1, e1) = all_52_21
% 227.44/39.18    (5)   ~ (e1 = e0)
% 227.44/39.18    (6)  op(e0, e0) = e0
% 227.44/39.18    (7)  op(e1, e1) = e0
% 227.44/39.18    (8)  op(all_52_21, all_52_21) = e1
% 227.44/39.18  
% 227.44/39.18  Begin of proof
% 227.44/39.18  | 
% 227.44/39.18  | BETA: splitting (1) gives:
% 227.44/39.18  | 
% 227.44/39.18  | Case 1:
% 227.44/39.18  | | 
% 227.44/39.18  | | 
% 227.44/39.18  | | GROUND_INST: instantiating (3) with e0, all_52_21, e1, e1, simplifying with
% 227.44/39.18  | |              (4), (7) gives:
% 227.44/39.18  | |   (9)  all_52_21 = e0
% 227.44/39.18  | | 
% 227.44/39.18  | | REDUCE: (8), (9) imply:
% 227.44/39.18  | |   (10)  op(e0, e0) = e1
% 227.44/39.18  | | 
% 227.44/39.18  | | REF_CLOSE: (3), (5), (6), (10) are inconsistent by sub-proof #2290.
% 227.44/39.18  | | 
% 227.44/39.18  | Case 2:
% 227.44/39.18  | | 
% 227.44/39.18  | |   (11)   ~ (all_8_1 = e1) & op(e2, e3) = all_8_1 & $i(all_8_1)
% 227.44/39.18  | | 
% 227.44/39.18  | | ALPHA: (11) implies:
% 227.44/39.18  | |   (12)   ~ (all_8_1 = e1)
% 227.44/39.18  | |   (13)  op(e2, e3) = all_8_1
% 227.44/39.18  | | 
% 227.44/39.18  | | GROUND_INST: instantiating (3) with e0, all_52_21, e1, e1, simplifying with
% 227.44/39.18  | |              (4), (7) gives:
% 227.44/39.18  | |   (14)  all_52_21 = e0
% 227.44/39.18  | | 
% 227.44/39.18  | | GROUND_INST: instantiating (3) with e0, all_8_1, e3, e2, simplifying with
% 227.44/39.18  | |              (2), (13) gives:
% 227.44/39.18  | |   (15)  all_8_1 = e0
% 227.44/39.18  | | 
% 227.44/39.18  | | REDUCE: (12), (15) imply:
% 227.44/39.18  | |   (16)   ~ (e1 = e0)
% 227.44/39.18  | | 
% 227.44/39.18  | | REDUCE: (8), (14) imply:
% 227.44/39.18  | |   (17)  op(e0, e0) = e1
% 227.44/39.18  | | 
% 227.44/39.18  | | REF_CLOSE: (3), (5), (6), (17) are inconsistent by sub-proof #2290.
% 227.44/39.18  | | 
% 227.44/39.18  | End of split
% 227.44/39.18  | 
% 227.44/39.18  End of proof
% 227.44/39.18  
% 227.44/39.18  Sub-proof #228 shows that the following formulas are inconsistent:
% 227.44/39.18  ----------------------------------------------------------------
% 227.44/39.18    (1)  op(e0, e0) = all_4_2
% 227.44/39.18    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 227.44/39.18         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 227.44/39.18    (3)   ~ (all_53_6 = e0)
% 227.44/39.18    (4)   ~ (e3 = e1)
% 227.44/39.18    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.44/39.18           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.44/39.18    (6)  all_55_15 = all_4_2
% 227.44/39.18    (7)  all_57_3 = e3
% 227.44/39.18    (8)  op(e3, e2) = all_52_3
% 227.44/39.18    (9)   ~ (all_53_9 = e0)
% 227.44/39.18    (10)  op(all_52_3, all_52_3) = e2
% 227.44/39.18    (11)   ~ (e3 = e2)
% 227.44/39.18    (12)   ~ (all_4_2 = e2)
% 227.44/39.18    (13)   ~ (all_53_7 = all_4_2)
% 227.44/39.18    (14)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 227.44/39.18          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 227.44/39.18    (15)   ~ (all_53_13 = all_4_2)
% 227.44/39.18    (16)  op(e0, e2) = all_53_7
% 227.44/39.18    (17)  op(e2, e0) = all_53_13
% 227.44/39.18    (18)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 227.44/39.18          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 227.44/39.18    (19)  all_55_15 = e1 | all_55_15 = e0
% 227.44/39.18    (20)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 227.44/39.18          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 227.44/39.18    (21)   ~ (all_4_2 = e3)
% 227.44/39.18    (22)   ~ (all_4_2 = e1)
% 227.44/39.18    (23)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 227.44/39.18          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 227.44/39.18    (24)   ~ (e2 = e1)
% 227.44/39.18    (25)  op(e2, e1) = all_53_9
% 227.44/39.18    (26)  op(e1, e2) = all_53_6
% 227.44/39.18  
% 227.44/39.18  Begin of proof
% 227.44/39.18  | 
% 227.44/39.18  | BETA: splitting (19) gives:
% 227.44/39.18  | 
% 227.44/39.18  | Case 1:
% 227.44/39.18  | | 
% 227.44/39.18  | |   (27)  all_55_15 = e1
% 227.44/39.18  | | 
% 227.44/39.18  | | REF_CLOSE: (6), (22), (27) are inconsistent by sub-proof #2501.
% 227.44/39.18  | | 
% 227.44/39.18  | Case 2:
% 227.44/39.18  | | 
% 227.44/39.18  | |   (28)  all_55_15 = e0
% 227.44/39.18  | | 
% 227.44/39.18  | | COMBINE_EQS: (6), (28) imply:
% 227.44/39.18  | |   (29)  all_4_2 = e0
% 227.44/39.18  | | 
% 227.44/39.18  | | SIMP: (29) implies:
% 227.44/39.18  | |   (30)  all_4_2 = e0
% 227.44/39.18  | | 
% 227.44/39.18  | | REDUCE: (13), (30) imply:
% 227.44/39.18  | |   (31)   ~ (all_53_7 = e0)
% 227.44/39.18  | | 
% 227.44/39.18  | | REDUCE: (15), (30) imply:
% 227.44/39.18  | |   (32)   ~ (all_53_13 = e0)
% 227.44/39.18  | | 
% 227.44/39.18  | | REDUCE: (21), (30) imply:
% 227.44/39.18  | |   (33)   ~ (e3 = e0)
% 227.44/39.18  | | 
% 227.44/39.18  | | SIMP: (33) implies:
% 227.44/39.18  | |   (34)   ~ (e3 = e0)
% 227.44/39.18  | | 
% 227.44/39.18  | | REDUCE: (12), (30) imply:
% 227.44/39.18  | |   (35)   ~ (e2 = e0)
% 227.44/39.18  | | 
% 227.44/39.18  | | SIMP: (35) implies:
% 227.44/39.18  | |   (36)   ~ (e2 = e0)
% 227.44/39.18  | | 
% 227.44/39.18  | | REDUCE: (22), (30) imply:
% 227.44/39.18  | |   (37)   ~ (e1 = e0)
% 227.44/39.18  | | 
% 227.44/39.18  | | SIMP: (37) implies:
% 227.44/39.18  | |   (38)   ~ (e1 = e0)
% 227.44/39.18  | | 
% 227.44/39.18  | | REDUCE: (1), (30) imply:
% 227.44/39.18  | |   (39)  op(e0, e0) = e0
% 227.44/39.18  | | 
% 227.44/39.18  | | BETA: splitting (23) gives:
% 227.44/39.18  | | 
% 227.44/39.18  | | Case 1:
% 227.44/39.18  | | | 
% 227.44/39.18  | | |   (40)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) =
% 227.44/39.18  | | |           e0)
% 227.44/39.18  | | | 
% 227.44/39.18  | | | BETA: splitting (40) gives:
% 227.44/39.18  | | | 
% 227.44/39.18  | | | Case 1:
% 227.44/39.18  | | | | 
% 227.44/39.18  | | | |   (41)  all_57_2 = e0 & op(e2, e3) = e0
% 227.44/39.18  | | | | 
% 227.44/39.18  | | | | ALPHA: (41) implies:
% 227.44/39.18  | | | |   (42)  all_57_2 = e0
% 227.44/39.18  | | | | 
% 227.44/39.18  | | | | BETA: splitting (14) gives:
% 227.44/39.18  | | | | 
% 227.44/39.18  | | | | Case 1:
% 227.44/39.18  | | | | | 
% 227.44/39.18  | | | | |   (43)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2,
% 227.44/39.18  | | | | |             e2) = e0)
% 227.44/39.18  | | | | | 
% 227.44/39.18  | | | | | BETA: splitting (43) gives:
% 227.44/39.18  | | | | | 
% 227.44/39.18  | | | | | Case 1:
% 227.44/39.18  | | | | | | 
% 227.44/39.18  | | | | | |   (44)  all_57_1 = e0 & op(e3, e2) = e0
% 227.44/39.18  | | | | | | 
% 227.44/39.18  | | | | | | ALPHA: (44) implies:
% 227.44/39.18  | | | | | |   (45)  op(e3, e2) = e0
% 227.44/39.18  | | | | | | 
% 227.44/39.18  | | | | | | REF_CLOSE: (5), (8), (10), (36), (39), (45) are inconsistent by
% 227.44/39.18  | | | | | |            sub-proof #2399.
% 227.44/39.18  | | | | | | 
% 227.44/39.18  | | | | | Case 2:
% 227.44/39.18  | | | | | | 
% 227.44/39.18  | | | | | |   (46)  all_57_3 = e0 & op(e2, e2) = e0
% 227.44/39.18  | | | | | | 
% 227.44/39.18  | | | | | | ALPHA: (46) implies:
% 227.44/39.18  | | | | | |   (47)  all_57_3 = e0
% 227.44/39.18  | | | | | | 
% 227.44/39.18  | | | | | | REF_CLOSE: (2), (4), (11), (18), (20), (24), (34), (36), (38), (42),
% 227.44/39.18  | | | | | |            (47) are inconsistent by sub-proof #2246.
% 227.44/39.18  | | | | | | 
% 227.44/39.18  | | | | | End of split
% 227.44/39.18  | | | | | 
% 227.44/39.18  | | | | Case 2:
% 227.44/39.18  | | | | | 
% 227.44/39.18  | | | | |   (48)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0,
% 227.44/39.18  | | | | |             e2) = e0)
% 227.44/39.18  | | | | | 
% 227.44/39.18  | | | | | REF_CLOSE: (3), (5), (16), (26), (31), (48) are inconsistent by
% 227.44/39.18  | | | | |            sub-proof #2024.
% 227.44/39.18  | | | | | 
% 227.44/39.18  | | | | End of split
% 227.44/39.18  | | | | 
% 227.44/39.18  | | | Case 2:
% 227.44/39.18  | | | | 
% 227.44/39.18  | | | |   (49)  all_57_3 = e0 & op(e2, e2) = e0
% 227.44/39.18  | | | | 
% 227.44/39.18  | | | | REF_CLOSE: (7), (34), (49) are inconsistent by sub-proof #262.
% 227.44/39.18  | | | | 
% 227.44/39.18  | | | End of split
% 227.44/39.18  | | | 
% 227.44/39.18  | | Case 2:
% 227.44/39.18  | | | 
% 227.44/39.18  | | |   (50)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 227.44/39.18  | | |           e0)
% 227.44/39.18  | | | 
% 227.44/39.18  | | | REF_CLOSE: (5), (9), (17), (25), (32), (50) are inconsistent by sub-proof
% 227.44/39.18  | | |            #2022.
% 227.44/39.18  | | | 
% 227.44/39.18  | | End of split
% 227.44/39.18  | | 
% 227.44/39.18  | End of split
% 227.44/39.18  | 
% 227.44/39.18  End of proof
% 227.44/39.18  
% 227.44/39.18  Sub-proof #229 shows that the following formulas are inconsistent:
% 227.44/39.18  ----------------------------------------------------------------
% 227.44/39.18    (1)   ~ (e3 = e1)
% 227.44/39.18    (2)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 227.44/39.18         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 227.44/39.18    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.44/39.18           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.44/39.18    (4)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 227.44/39.18         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 227.44/39.18    (5)   ~ (all_6_2 = e3)
% 227.44/39.18    (6)  op(e1, e1) = all_6_2
% 227.44/39.18    (7)   ~ (e3 = e2)
% 227.44/39.18    (8)   ~ (e3 = e0)
% 227.44/39.18    (9)  all_57_11 = e2
% 227.44/39.18    (10)   ~ (e2 = e0)
% 227.44/39.18    (11)   ~ (e1 = e0)
% 227.44/39.18    (12)  all_57_6 = e3
% 227.44/39.18    (13)  op(e1, e1) = e2
% 227.44/39.18    (14)   ~ (e2 = e1)
% 227.44/39.18    (15)   ~ (all_6_2 = e0)
% 227.44/39.18    (16)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 227.44/39.18          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 227.44/39.18  
% 227.44/39.18  Begin of proof
% 227.44/39.18  | 
% 227.44/39.18  | BETA: splitting (16) gives:
% 227.44/39.18  | 
% 227.44/39.18  | Case 1:
% 227.44/39.18  | | 
% 227.44/39.18  | |   (17)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) =
% 227.44/39.18  | |           e1)
% 227.44/39.18  | | 
% 227.44/39.18  | | BETA: splitting (17) gives:
% 227.44/39.18  | | 
% 227.44/39.18  | | Case 1:
% 227.44/39.18  | | | 
% 227.44/39.18  | | |   (18)  all_57_6 = e1 & op(e1, e3) = e1
% 227.44/39.18  | | | 
% 227.44/39.18  | | | REF_CLOSE: (1), (12), (18) are inconsistent by sub-proof #2117.
% 227.44/39.18  | | | 
% 227.44/39.18  | | Case 2:
% 227.44/39.18  | | | 
% 227.44/39.18  | | |   (19)  all_57_7 = e1 & op(e1, e2) = e1
% 227.44/39.18  | | | 
% 227.44/39.18  | | | ALPHA: (19) implies:
% 227.44/39.18  | | |   (20)  all_57_7 = e1
% 227.44/39.18  | | | 
% 227.44/39.18  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (15),
% 227.44/39.18  | | |            (20) are inconsistent by sub-proof #348.
% 227.44/39.18  | | | 
% 227.44/39.18  | | End of split
% 227.44/39.18  | | 
% 227.44/39.18  | Case 2:
% 227.44/39.18  | | 
% 227.44/39.18  | |   (21)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) =
% 227.44/39.18  | |           e1)
% 227.44/39.18  | | 
% 227.44/39.18  | | REF_CLOSE: (3), (9), (13), (14), (21) are inconsistent by sub-proof #1725.
% 227.44/39.18  | | 
% 227.44/39.18  | End of split
% 227.44/39.18  | 
% 227.44/39.18  End of proof
% 227.44/39.18  
% 227.44/39.18  Sub-proof #230 shows that the following formulas are inconsistent:
% 227.44/39.18  ----------------------------------------------------------------
% 227.44/39.18    (1)  all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 227.44/39.18    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.44/39.18           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.44/39.18    (3)  op(all_52_7, all_52_7) = e0
% 227.44/39.18    (4)  all_55_3 = all_52_7
% 227.44/39.18    (5)   ~ (all_52_7 = e1)
% 227.44/39.18    (6)  op(e0, e0) = e1
% 227.44/39.18    (7)  op(e3, e0) = all_52_7
% 227.44/39.18    (8)   ~ (all_52_7 = e2)
% 227.44/39.18  
% 227.44/39.18  Begin of proof
% 227.44/39.18  | 
% 227.44/39.18  | BETA: splitting (1) gives:
% 227.44/39.18  | 
% 227.44/39.18  | Case 1:
% 227.44/39.18  | | 
% 227.44/39.18  | |   (9)  all_55_3 = e2
% 227.44/39.18  | | 
% 227.44/39.18  | | REF_CLOSE: (4), (8), (9) are inconsistent by sub-proof #1450.
% 227.44/39.18  | | 
% 227.44/39.18  | Case 2:
% 227.44/39.18  | | 
% 227.44/39.18  | |   (10)  all_55_3 = e1 | all_55_3 = e0
% 227.44/39.18  | | 
% 227.44/39.18  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (10) are inconsistent by sub-proof
% 227.44/39.18  | |            #259.
% 227.44/39.18  | | 
% 227.44/39.18  | End of split
% 227.44/39.18  | 
% 227.44/39.18  End of proof
% 227.44/39.18  
% 227.44/39.18  Sub-proof #231 shows that the following formulas are inconsistent:
% 227.44/39.18  ----------------------------------------------------------------
% 227.44/39.18    (1)  ( ~ (all_8_0 = e0) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 227.44/39.18           $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e1) & op(e2, e3) = all_8_1
% 227.44/39.18           & $i(all_8_1))
% 227.44/39.18    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.44/39.18           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.44/39.18    (3)  op(e3, e2) = e1
% 227.44/39.18    (4)  op(e3, e2) = all_52_3
% 227.44/39.18    (5)  op(all_52_3, all_52_3) = e2
% 227.44/39.18    (6)  op(e1, e1) = e1
% 227.44/39.18    (7)  op(e2, e3) = all_44_1
% 227.44/39.18    (8)   ~ (e2 = e1)
% 227.44/39.18    (9)  op(e2, e3) = e1
% 227.44/39.18  
% 227.44/39.18  Begin of proof
% 227.44/39.18  | 
% 227.44/39.18  | BETA: splitting (1) gives:
% 227.44/39.18  | 
% 227.44/39.18  | Case 1:
% 227.44/39.18  | | 
% 227.44/39.18  | | 
% 227.44/39.18  | | GROUND_INST: instantiating (2) with e1, all_52_3, e2, e3, simplifying with
% 227.44/39.18  | |              (3), (4) gives:
% 227.44/39.18  | |   (10)  all_52_3 = e1
% 227.44/39.18  | | 
% 227.44/39.18  | | REDUCE: (5), (10) imply:
% 227.44/39.18  | |   (11)  op(e1, e1) = e2
% 227.44/39.18  | | 
% 227.44/39.18  | | REF_CLOSE: (2), (6), (8), (11) are inconsistent by sub-proof #2423.
% 227.44/39.18  | | 
% 227.44/39.18  | Case 2:
% 227.44/39.18  | | 
% 227.44/39.18  | |   (12)   ~ (all_8_1 = e1) & op(e2, e3) = all_8_1 & $i(all_8_1)
% 227.44/39.18  | | 
% 227.44/39.18  | | ALPHA: (12) implies:
% 227.44/39.18  | |   (13)   ~ (all_8_1 = e1)
% 227.44/39.18  | |   (14)  op(e2, e3) = all_8_1
% 227.44/39.18  | | 
% 227.44/39.18  | | REF_CLOSE: (2), (7), (9), (13), (14) are inconsistent by sub-proof #247.
% 227.44/39.18  | | 
% 227.44/39.18  | End of split
% 227.44/39.18  | 
% 227.44/39.18  End of proof
% 227.44/39.18  
% 227.44/39.18  Sub-proof #232 shows that the following formulas are inconsistent:
% 227.44/39.18  ----------------------------------------------------------------
% 227.44/39.18    (1)   ~ (e3 = e1)
% 227.44/39.18    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.44/39.18           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.44/39.18    (3)   ~ (e3 = e0)
% 227.44/39.18    (4)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 227.44/39.18    (5)  op(e0, e0) = e0
% 227.44/39.18    (6)  all_57_11 = e1
% 227.44/39.18  
% 227.44/39.18  Begin of proof
% 227.44/39.18  | 
% 227.44/39.18  | BETA: splitting (4) gives:
% 227.44/39.18  | 
% 227.44/39.18  | Case 1:
% 227.44/39.18  | | 
% 227.44/39.18  | |   (7)  all_57_11 = e3 & op(e1, e0) = e3
% 227.44/39.18  | | 
% 227.44/39.18  | | ALPHA: (7) implies:
% 227.44/39.18  | |   (8)  all_57_11 = e3
% 227.44/39.18  | | 
% 227.44/39.18  | | REF_CLOSE: (1), (6), (8) are inconsistent by sub-proof #2218.
% 227.44/39.18  | | 
% 227.44/39.18  | Case 2:
% 227.44/39.18  | | 
% 227.44/39.18  | |   (9)  all_57_15 = e3 & op(e0, e0) = e3
% 227.44/39.18  | | 
% 227.44/39.18  | | ALPHA: (9) implies:
% 227.44/39.18  | |   (10)  op(e0, e0) = e3
% 227.44/39.18  | | 
% 227.44/39.18  | | REF_CLOSE: (2), (3), (5), (10) are inconsistent by sub-proof #2304.
% 227.44/39.18  | | 
% 227.44/39.18  | End of split
% 227.44/39.18  | 
% 227.44/39.18  End of proof
% 227.44/39.18  
% 227.44/39.18  Sub-proof #233 shows that the following formulas are inconsistent:
% 227.44/39.18  ----------------------------------------------------------------
% 227.44/39.18    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.44/39.18           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.44/39.18    (2)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 227.44/39.18         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 227.44/39.18    (3)  all_57_4 = e3
% 227.44/39.18    (4)   ~ (e3 = e2)
% 227.44/39.18    (5)  all_57_1 = e0
% 227.44/39.18    (6)  op(e3, e2) = all_53_4
% 227.44/39.18    (7)   ~ (e1 = e0)
% 227.44/39.18    (8)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1)
% 227.44/39.18    (9)   ~ (all_53_4 = e2)
% 227.44/39.18    (10)   ~ (e2 = e1)
% 227.44/39.18    (11)   ~ (all_53_12 = e2)
% 227.44/39.18    (12)  op(e3, e0) = all_53_12
% 227.44/39.18  
% 227.44/39.18  Begin of proof
% 227.44/39.18  | 
% 227.44/39.18  | BETA: splitting (8) gives:
% 227.44/39.18  | 
% 227.44/39.18  | Case 1:
% 227.44/39.18  | | 
% 227.44/39.18  | |   (13)  all_57_0 = e1 & op(e3, e3) = e1
% 227.44/39.18  | | 
% 227.44/39.18  | | ALPHA: (13) implies:
% 227.44/39.18  | |   (14)  op(e3, e3) = e1
% 227.44/39.18  | | 
% 227.44/39.18  | | REF_CLOSE: (1), (2), (3), (4), (6), (9), (10), (11), (12), (14) are
% 227.44/39.18  | |            inconsistent by sub-proof #234.
% 227.44/39.18  | | 
% 227.44/39.18  | Case 2:
% 227.44/39.18  | | 
% 227.44/39.18  | |   (15)  all_57_1 = e1 & op(e3, e2) = e1
% 227.44/39.18  | | 
% 227.44/39.18  | | REF_CLOSE: (5), (7), (15) are inconsistent by sub-proof #2446.
% 227.44/39.18  | | 
% 227.44/39.18  | End of split
% 227.44/39.18  | 
% 227.44/39.18  End of proof
% 227.44/39.18  
% 227.44/39.18  Sub-proof #234 shows that the following formulas are inconsistent:
% 227.44/39.18  ----------------------------------------------------------------
% 227.44/39.18    (1)  op(e3, e3) = e1
% 227.44/39.18    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.44/39.18           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.44/39.18    (3)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 227.44/39.18         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 227.44/39.18    (4)  all_57_4 = e3
% 227.44/39.18    (5)   ~ (e3 = e2)
% 227.44/39.18    (6)  op(e3, e2) = all_53_4
% 227.44/39.18    (7)   ~ (all_53_4 = e2)
% 227.44/39.18    (8)   ~ (e2 = e1)
% 227.44/39.18    (9)   ~ (all_53_12 = e2)
% 227.44/39.18    (10)  op(e3, e0) = all_53_12
% 227.44/39.18  
% 227.44/39.18  Begin of proof
% 227.44/39.18  | 
% 227.44/39.18  | BETA: splitting (3) gives:
% 227.44/39.18  | 
% 227.44/39.18  | Case 1:
% 227.44/39.18  | | 
% 227.44/39.18  | |   (11)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) =
% 227.44/39.18  | |           e2)
% 227.44/39.18  | | 
% 227.44/39.18  | | REF_CLOSE: (1), (2), (6), (7), (8), (11) are inconsistent by sub-proof #331.
% 227.44/39.18  | | 
% 227.44/39.18  | Case 2:
% 227.44/39.18  | | 
% 227.44/39.18  | |   (12)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) =
% 227.44/39.18  | |           e2)
% 227.44/39.18  | | 
% 227.44/39.18  | | BETA: splitting (12) gives:
% 227.44/39.18  | | 
% 227.44/39.18  | | Case 1:
% 227.44/39.18  | | | 
% 227.44/39.18  | | |   (13)  all_57_4 = e2 & op(e3, e1) = e2
% 227.44/39.18  | | | 
% 227.44/39.18  | | | REF_CLOSE: (4), (5), (13) are inconsistent by sub-proof #2487.
% 227.44/39.18  | | | 
% 227.44/39.18  | | Case 2:
% 227.44/39.18  | | | 
% 227.44/39.18  | | |   (14)  all_57_9 = e2 & op(e3, e0) = e2
% 227.44/39.18  | | | 
% 227.44/39.18  | | | ALPHA: (14) implies:
% 227.44/39.18  | | |   (15)  op(e3, e0) = e2
% 227.44/39.18  | | | 
% 227.44/39.18  | | | REF_CLOSE: (2), (9), (10), (15) are inconsistent by sub-proof #2331.
% 227.44/39.18  | | | 
% 227.44/39.18  | | End of split
% 227.44/39.18  | | 
% 227.44/39.18  | End of split
% 227.44/39.18  | 
% 227.44/39.18  End of proof
% 227.44/39.18  
% 227.44/39.18  Sub-proof #235 shows that the following formulas are inconsistent:
% 227.44/39.18  ----------------------------------------------------------------
% 227.44/39.18    (1)   ~ (e3 = e1)
% 227.44/39.18    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.44/39.18           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.44/39.18    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 227.44/39.18         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 227.44/39.18    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2)
% 227.44/39.18    (5)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 227.44/39.18         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 227.44/39.18    (6)  all_57_4 = e3
% 227.44/39.18    (7)   ~ (e3 = e2)
% 227.44/39.18    (8)   ~ (e3 = e0)
% 227.44/39.18    (9)  op(e3, e3) = e2
% 227.44/39.18    (10)   ~ (e2 = e0)
% 227.44/39.18    (11)   ~ (e1 = e0)
% 227.44/39.18    (12)  op(e2, e2) = e3
% 227.44/39.18    (13)   ~ (e2 = e1)
% 227.44/39.18  
% 227.44/39.18  Begin of proof
% 227.44/39.18  | 
% 227.44/39.18  | BETA: splitting (4) gives:
% 227.44/39.18  | 
% 227.44/39.18  | Case 1:
% 227.44/39.18  | | 
% 227.44/39.18  | |   (14)  all_57_1 = e2 & op(e3, e2) = e2
% 227.44/39.18  | | 
% 227.44/39.18  | | ALPHA: (14) implies:
% 227.44/39.18  | |   (15)  all_57_1 = e2
% 227.44/39.18  | | 
% 227.44/39.18  | | REF_CLOSE: (1), (2), (3), (5), (6), (8), (9), (10), (11), (13), (15) are
% 227.44/39.18  | |            inconsistent by sub-proof #1659.
% 227.44/39.18  | | 
% 227.44/39.18  | Case 2:
% 227.44/39.18  | | 
% 227.44/39.18  | |   (16)  all_57_3 = e2 & op(e2, e2) = e2
% 227.44/39.18  | | 
% 227.44/39.18  | | ALPHA: (16) implies:
% 227.44/39.18  | |   (17)  op(e2, e2) = e2
% 227.44/39.18  | | 
% 227.44/39.18  | | REF_CLOSE: (2), (7), (12), (17) are inconsistent by sub-proof #2298.
% 227.44/39.18  | | 
% 227.44/39.18  | End of split
% 227.44/39.18  | 
% 227.44/39.18  End of proof
% 227.44/39.18  
% 227.44/39.18  Sub-proof #236 shows that the following formulas are inconsistent:
% 227.44/39.18  ----------------------------------------------------------------
% 227.44/39.18    (1)   ~ (e3 = e1)
% 227.44/39.18    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.44/39.18           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.44/39.18    (3)  op(e1, e1) = e2
% 227.44/39.18    (4)  op(e2, e2) = e3
% 227.44/39.18    (5)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 &
% 227.44/39.18         op(all_52_17, all_52_17) = e3 & op(all_52_19, all_52_19) = e2 &
% 227.44/39.18         op(all_52_21, all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1,
% 227.44/39.18           e3) = all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 &
% 227.44/39.18         op(e1, e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 227.44/39.18         $i(all_52_23)
% 227.44/39.18  
% 227.44/39.18  Begin of proof
% 227.44/39.18  | 
% 227.44/39.18  | ALPHA: (5) implies:
% 227.44/39.18  |   (6)  op(e1, e1) = all_52_21
% 227.44/39.18  |   (7)  op(all_52_21, all_52_21) = e1
% 227.44/39.18  | 
% 227.44/39.18  | GROUND_INST: instantiating (2) with e2, all_52_21, e1, e1, simplifying with
% 227.44/39.18  |              (3), (6) gives:
% 227.44/39.18  |   (8)  all_52_21 = e2
% 227.44/39.18  | 
% 227.44/39.18  | REDUCE: (7), (8) imply:
% 227.44/39.18  |   (9)  op(e2, e2) = e1
% 227.44/39.18  | 
% 227.44/39.18  | REF_CLOSE: (1), (2), (4), (9) are inconsistent by sub-proof #1912.
% 227.44/39.18  | 
% 227.44/39.18  End of proof
% 227.44/39.18  
% 227.44/39.18  Sub-proof #237 shows that the following formulas are inconsistent:
% 227.44/39.18  ----------------------------------------------------------------
% 227.44/39.18    (1)  op(e3, e1) = e3
% 227.44/39.18    (2)  op(e3, e1) = all_52_5
% 227.44/39.18    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.44/39.18           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.44/39.18    (4)  op(all_52_5, all_52_5) = e1
% 227.44/39.18    (5)  op(e3, e3) = e0
% 227.44/39.18    (6)  op(e3, e3) = all_52_1
% 227.44/39.18    (7)   ~ (e1 = e0)
% 227.44/39.18  
% 227.44/39.18  Begin of proof
% 227.44/39.18  | 
% 227.44/39.18  | GROUND_INST: instantiating (3) with e3, all_52_5, e1, e3, simplifying with
% 227.44/39.18  |              (1), (2) gives:
% 227.44/39.18  |   (8)  all_52_5 = e3
% 227.44/39.18  | 
% 227.44/39.18  | GROUND_INST: instantiating (3) with e0, all_52_1, e3, e3, simplifying with
% 227.44/39.18  |              (5), (6) gives:
% 227.44/39.18  |   (9)  all_52_1 = e0
% 227.44/39.18  | 
% 227.44/39.18  | REDUCE: (4), (8) imply:
% 227.44/39.18  |   (10)  op(e3, e3) = e1
% 227.44/39.18  | 
% 227.44/39.18  | GROUND_INST: instantiating (3) with e0, e1, e3, e3, simplifying with (5), (10)
% 227.44/39.18  |              gives:
% 227.44/39.18  |   (11)  e1 = e0
% 227.44/39.18  | 
% 227.44/39.18  | REDUCE: (7), (11) imply:
% 227.44/39.18  |   (12)  $false
% 227.44/39.18  | 
% 227.44/39.18  | CLOSE: (12) is inconsistent.
% 227.44/39.18  | 
% 227.44/39.18  End of proof
% 227.44/39.18  
% 227.44/39.18  Sub-proof #238 shows that the following formulas are inconsistent:
% 227.44/39.18  ----------------------------------------------------------------
% 227.44/39.18    (1)   ~ (all_53_2 = e1)
% 227.44/39.18    (2)  op(e2, e3) = all_53_1
% 227.44/39.18    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 227.44/39.18         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 227.44/39.18    (4)   ~ (e3 = e1)
% 227.44/39.18    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.44/39.18           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.44/39.18    (6)  op(e3, e3) = e2
% 227.44/39.18    (7)   ~ (all_53_1 = e1)
% 227.44/39.18    (8)  all_57_12 = e3
% 227.44/39.18    (9)  op(e1, e3) = all_53_2
% 227.44/39.18    (10)   ~ (e2 = e1)
% 227.44/39.18  
% 227.44/39.18  Begin of proof
% 227.44/39.18  | 
% 227.44/39.18  | BETA: splitting (3) gives:
% 227.44/39.18  | 
% 227.44/39.18  | Case 1:
% 227.44/39.18  | | 
% 227.44/39.18  | |   (11)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) =
% 227.44/39.19  | |           e1)
% 227.44/39.19  | | 
% 227.44/39.19  | | REF_CLOSE: (2), (5), (6), (7), (10), (11) are inconsistent by sub-proof
% 227.44/39.19  | |            #1598.
% 227.44/39.19  | | 
% 227.44/39.19  | Case 2:
% 227.44/39.19  | | 
% 227.44/39.19  | |   (12)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) =
% 227.44/39.19  | |           e1)
% 227.44/39.19  | | 
% 227.44/39.19  | | BETA: splitting (12) gives:
% 227.44/39.19  | | 
% 227.44/39.19  | | Case 1:
% 227.44/39.19  | | | 
% 227.44/39.19  | | |   (13)  all_57_6 = e1 & op(e1, e3) = e1
% 227.44/39.19  | | | 
% 227.44/39.19  | | | REF_CLOSE: (1), (5), (9), (13) are inconsistent by sub-proof #316.
% 227.44/39.19  | | | 
% 227.44/39.19  | | Case 2:
% 227.44/39.19  | | | 
% 227.44/39.19  | | |   (14)  all_57_12 = e1 & op(e0, e3) = e1
% 227.44/39.19  | | | 
% 227.44/39.19  | | | ALPHA: (14) implies:
% 227.44/39.19  | | |   (15)  all_57_12 = e1
% 227.44/39.19  | | | 
% 227.44/39.19  | | | REF_CLOSE: (4), (8), (15) are inconsistent by sub-proof #2151.
% 227.44/39.19  | | | 
% 227.44/39.19  | | End of split
% 227.44/39.19  | | 
% 227.44/39.19  | End of split
% 227.44/39.19  | 
% 227.44/39.19  End of proof
% 227.44/39.19  
% 227.44/39.19  Sub-proof #239 shows that the following formulas are inconsistent:
% 227.44/39.19  ----------------------------------------------------------------
% 227.44/39.19    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.44/39.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.44/39.19    (2)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 227.44/39.19    (3)   ~ (e1 = e0)
% 227.44/39.19    (4)  all_57_5 = e1
% 227.44/39.19    (5)   ~ (all_53_13 = e0)
% 227.44/39.19    (6)  op(e2, e0) = all_53_13
% 227.44/39.19  
% 227.44/39.19  Begin of proof
% 227.44/39.19  | 
% 227.44/39.19  | BETA: splitting (2) gives:
% 227.44/39.19  | 
% 227.44/39.19  | Case 1:
% 227.44/39.19  | | 
% 227.44/39.19  | |   (7)  all_57_5 = e0 & op(e2, e1) = e0
% 227.44/39.19  | | 
% 227.44/39.19  | | REF_CLOSE: (3), (4), (7) are inconsistent by sub-proof #942.
% 227.44/39.19  | | 
% 227.44/39.19  | Case 2:
% 227.44/39.19  | | 
% 227.44/39.19  | |   (8)  all_57_10 = e0 & op(e2, e0) = e0
% 227.44/39.19  | | 
% 227.44/39.19  | | ALPHA: (8) implies:
% 227.44/39.19  | |   (9)  op(e2, e0) = e0
% 227.44/39.19  | | 
% 227.44/39.19  | | REF_CLOSE: (1), (5), (6), (9) are inconsistent by sub-proof #2470.
% 227.44/39.19  | | 
% 227.44/39.19  | End of split
% 227.44/39.19  | 
% 227.44/39.19  End of proof
% 227.44/39.19  
% 227.44/39.19  Sub-proof #240 shows that the following formulas are inconsistent:
% 227.44/39.19  ----------------------------------------------------------------
% 227.44/39.19    (1)  op(e2, e3) = all_53_1
% 227.44/39.19    (2)   ~ (e3 = e1)
% 227.44/39.19    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.44/39.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.44/39.19    (4)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1)
% 227.44/39.19    (5)   ~ (all_53_1 = e1)
% 227.44/39.19    (6)  op(e2, e2) = e3
% 227.44/39.19  
% 227.44/39.19  Begin of proof
% 227.44/39.19  | 
% 227.44/39.19  | BETA: splitting (4) gives:
% 227.44/39.19  | 
% 227.44/39.19  | Case 1:
% 227.44/39.19  | | 
% 227.44/39.19  | |   (7)  all_57_2 = e1 & op(e2, e3) = e1
% 227.44/39.19  | | 
% 227.44/39.19  | | REF_CLOSE: (1), (3), (5), (7) are inconsistent by sub-proof #2156.
% 227.44/39.19  | | 
% 227.44/39.19  | Case 2:
% 227.44/39.19  | | 
% 227.44/39.19  | |   (8)  all_57_3 = e1 & op(e2, e2) = e1
% 227.44/39.19  | | 
% 227.44/39.19  | | ALPHA: (8) implies:
% 227.44/39.19  | |   (9)  op(e2, e2) = e1
% 227.44/39.19  | | 
% 227.44/39.19  | | REF_CLOSE: (2), (3), (6), (9) are inconsistent by sub-proof #1912.
% 227.44/39.19  | | 
% 227.44/39.19  | End of split
% 227.44/39.19  | 
% 227.44/39.19  End of proof
% 227.44/39.19  
% 227.44/39.19  Sub-proof #241 shows that the following formulas are inconsistent:
% 227.44/39.19  ----------------------------------------------------------------
% 227.44/39.19    (1)  op(e2, e3) = all_53_1
% 227.44/39.19    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.44/39.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.44/39.19    (3)   ~ (e3 = e2)
% 227.44/39.19    (4)  op(e3, e3) = e2
% 227.44/39.19    (5)   ~ (all_53_1 = e3)
% 227.44/39.19    (6)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3)
% 227.44/39.19  
% 227.44/39.19  Begin of proof
% 227.44/39.19  | 
% 227.44/39.19  | BETA: splitting (6) gives:
% 227.44/39.19  | 
% 227.44/39.19  | Case 1:
% 227.44/39.19  | | 
% 227.44/39.19  | |   (7)  all_57_0 = e3 & op(e3, e3) = e3
% 227.44/39.19  | | 
% 227.44/39.19  | | ALPHA: (7) implies:
% 227.44/39.19  | |   (8)  op(e3, e3) = e3
% 227.44/39.19  | | 
% 227.44/39.19  | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #2490.
% 227.44/39.19  | | 
% 227.44/39.19  | Case 2:
% 227.44/39.19  | | 
% 227.44/39.19  | |   (9)  all_57_2 = e3 & op(e2, e3) = e3
% 227.44/39.19  | | 
% 227.44/39.19  | | REF_CLOSE: (1), (2), (5), (9) are inconsistent by sub-proof #2299.
% 227.44/39.19  | | 
% 227.44/39.19  | End of split
% 227.44/39.19  | 
% 227.44/39.19  End of proof
% 227.44/39.19  
% 227.44/39.19  Sub-proof #242 shows that the following formulas are inconsistent:
% 227.44/39.19  ----------------------------------------------------------------
% 227.44/39.19    (1)  op(e2, e3) = all_53_1
% 227.44/39.19    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.44/39.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.44/39.19    (3)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2)
% 227.44/39.19    (4)   ~ (e3 = e2)
% 227.44/39.19    (5)  op(e2, e2) = e3
% 227.44/39.19    (6)   ~ (all_53_1 = e2)
% 227.44/39.19  
% 227.44/39.19  Begin of proof
% 227.44/39.19  | 
% 227.44/39.19  | BETA: splitting (3) gives:
% 227.44/39.19  | 
% 227.44/39.19  | Case 1:
% 227.44/39.19  | | 
% 227.44/39.19  | |   (7)  all_57_2 = e2 & op(e2, e3) = e2
% 227.44/39.19  | | 
% 227.44/39.19  | | REF_CLOSE: (1), (2), (6), (7) are inconsistent by sub-proof #2504.
% 227.44/39.19  | | 
% 227.44/39.19  | Case 2:
% 227.44/39.19  | | 
% 227.44/39.19  | |   (8)  all_57_3 = e2 & op(e2, e2) = e2
% 227.44/39.19  | | 
% 227.44/39.19  | | ALPHA: (8) implies:
% 227.44/39.19  | |   (9)  op(e2, e2) = e2
% 227.44/39.19  | | 
% 227.44/39.19  | | REF_CLOSE: (2), (4), (5), (9) are inconsistent by sub-proof #2298.
% 227.44/39.19  | | 
% 227.44/39.19  | End of split
% 227.44/39.19  | 
% 227.44/39.19  End of proof
% 227.44/39.19  
% 227.44/39.19  Sub-proof #243 shows that the following formulas are inconsistent:
% 227.44/39.19  ----------------------------------------------------------------
% 227.44/39.19    (1)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 227.44/39.19    (2)  op(e2, e1) = e1
% 227.44/39.19    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.44/39.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.44/39.19    (4)   ~ (all_6_2 = e3)
% 227.44/39.19    (5)  op(e1, e1) = all_6_2
% 227.44/39.19    (6)   ~ (all_53_9 = all_6_2)
% 227.44/39.19    (7)  op(e1, e1) = all_52_21
% 227.44/39.19    (8)   ~ (all_53_9 = e3)
% 227.44/39.19    (9)  all_55_10 = all_6_2
% 227.44/39.19    (10)  op(e2, e2) = e3
% 227.44/39.19    (11)  op(e2, e1) = all_53_9
% 227.44/39.19    (12)   ~ (all_6_2 = e0)
% 227.44/39.19    (13)  op(all_52_21, all_52_21) = e1
% 227.44/39.19  
% 227.44/39.19  Begin of proof
% 227.44/39.19  | 
% 227.44/39.19  | GROUND_INST: instantiating (3) with all_6_2, all_52_21, e1, e1, simplifying
% 227.44/39.19  |              with (5), (7) gives:
% 227.44/39.19  |   (14)  all_52_21 = all_6_2
% 227.44/39.19  | 
% 227.44/39.19  | GROUND_INST: instantiating (3) with all_53_9, e1, e1, e2, simplifying with
% 227.44/39.19  |              (2), (11) gives:
% 227.44/39.19  |   (15)  all_53_9 = e1
% 227.44/39.19  | 
% 227.44/39.19  | REDUCE: (6), (15) imply:
% 227.44/39.19  |   (16)   ~ (all_6_2 = e1)
% 227.44/39.19  | 
% 227.44/39.19  | SIMP: (16) implies:
% 227.44/39.19  |   (17)   ~ (all_6_2 = e1)
% 227.44/39.19  | 
% 227.44/39.19  | REDUCE: (8), (15) imply:
% 227.44/39.19  |   (18)   ~ (e3 = e1)
% 227.44/39.19  | 
% 227.44/39.19  | SIMP: (18) implies:
% 227.44/39.19  |   (19)   ~ (e3 = e1)
% 227.44/39.19  | 
% 227.44/39.19  | REDUCE: (13), (14) imply:
% 227.44/39.19  |   (20)  op(all_6_2, all_6_2) = e1
% 227.44/39.19  | 
% 227.44/39.19  | BETA: splitting (1) gives:
% 227.44/39.19  | 
% 227.44/39.19  | Case 1:
% 227.44/39.19  | | 
% 227.44/39.19  | |   (21)  all_55_10 = e3
% 227.44/39.19  | | 
% 227.44/39.19  | | REF_CLOSE: (4), (9), (21) are inconsistent by sub-proof #2500.
% 227.44/39.19  | | 
% 227.44/39.19  | Case 2:
% 227.44/39.19  | | 
% 227.44/39.19  | |   (22)  all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 227.44/39.19  | | 
% 227.44/39.19  | | BETA: splitting (22) gives:
% 227.44/39.19  | | 
% 227.44/39.19  | | Case 1:
% 227.44/39.19  | | | 
% 227.44/39.19  | | |   (23)  all_55_10 = e2
% 227.44/39.19  | | | 
% 227.44/39.19  | | | COMBINE_EQS: (9), (23) imply:
% 227.44/39.19  | | |   (24)  all_6_2 = e2
% 227.44/39.19  | | | 
% 227.44/39.19  | | | SIMP: (24) implies:
% 227.44/39.19  | | |   (25)  all_6_2 = e2
% 227.44/39.19  | | | 
% 227.44/39.19  | | | REDUCE: (20), (25) imply:
% 227.44/39.19  | | |   (26)  op(e2, e2) = e1
% 227.44/39.19  | | | 
% 227.44/39.19  | | | REF_CLOSE: (3), (10), (19), (26) are inconsistent by sub-proof #1912.
% 227.44/39.19  | | | 
% 227.44/39.19  | | Case 2:
% 227.44/39.19  | | | 
% 227.44/39.19  | | |   (27)  all_55_10 = e1 | all_55_10 = e0
% 227.44/39.19  | | | 
% 227.44/39.19  | | | REF_CLOSE: (9), (12), (17), (27) are inconsistent by sub-proof #1685.
% 227.44/39.19  | | | 
% 227.44/39.19  | | End of split
% 227.44/39.19  | | 
% 227.44/39.19  | End of split
% 227.44/39.19  | 
% 227.44/39.19  End of proof
% 227.44/39.19  
% 227.44/39.19  Sub-proof #244 shows that the following formulas are inconsistent:
% 227.44/39.19  ----------------------------------------------------------------
% 227.44/39.19    (1)  ( ~ (all_44_0 = e1) & op(all_44_1, e2) = all_44_0 & op(e2, e3) = all_44_1
% 227.44/39.19           & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 = e0) & op(e2, e3) =
% 227.44/39.19           all_44_1 & $i(all_44_1))
% 227.44/39.19    (2)  ( ~ (all_8_0 = e0) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 227.44/39.19           $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e1) & op(e2, e3) = all_8_1
% 227.44/39.19           & $i(all_8_1))
% 227.44/39.19    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.44/39.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.44/39.19    (4)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 227.44/39.19    (5)  all_55_9 = all_53_6
% 227.44/39.19    (6)   ~ (all_53_6 = e1)
% 227.44/39.19    (7)  op(e1, e2) = all_52_19
% 227.44/39.19    (8)  op(all_52_19, all_52_19) = e2
% 227.44/39.19    (9)  op(e2, e2) = e3
% 227.44/39.19    (10)   ~ (all_53_6 = e3)
% 227.44/39.19    (11)  op(e1, e2) = all_53_6
% 227.44/39.19    (12)  op(e2, e3) = e1
% 227.44/39.19  
% 227.44/39.19  Begin of proof
% 227.44/39.19  | 
% 227.44/39.19  | BETA: splitting (1) gives:
% 227.44/39.19  | 
% 227.44/39.19  | Case 1:
% 227.44/39.19  | | 
% 227.44/39.19  | |   (13)   ~ (all_44_0 = e1) & op(all_44_1, e2) = all_44_0 & op(e2, e3) =
% 227.44/39.19  | |         all_44_1 & $i(all_44_0) & $i(all_44_1)
% 227.44/39.19  | | 
% 227.44/39.19  | | ALPHA: (13) implies:
% 227.44/39.19  | |   (14)  op(e2, e3) = all_44_1
% 227.44/39.19  | | 
% 227.44/39.19  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (14)
% 227.44/39.19  | |            are inconsistent by sub-proof #245.
% 227.44/39.19  | | 
% 227.44/39.19  | Case 2:
% 227.44/39.19  | | 
% 227.44/39.19  | |   (15)   ~ (all_44_1 = e0) & op(e2, e3) = all_44_1 & $i(all_44_1)
% 227.44/39.19  | | 
% 227.44/39.19  | | ALPHA: (15) implies:
% 227.44/39.19  | |   (16)  op(e2, e3) = all_44_1
% 227.44/39.19  | | 
% 227.44/39.19  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (16)
% 227.44/39.19  | |            are inconsistent by sub-proof #245.
% 227.44/39.19  | | 
% 227.44/39.19  | End of split
% 227.44/39.19  | 
% 227.44/39.19  End of proof
% 227.44/39.19  
% 227.44/39.19  Sub-proof #245 shows that the following formulas are inconsistent:
% 227.44/39.19  ----------------------------------------------------------------
% 227.44/39.19    (1)  ( ~ (all_8_0 = e0) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 227.44/39.19           $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e1) & op(e2, e3) = all_8_1
% 227.44/39.19           & $i(all_8_1))
% 227.44/39.19    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.44/39.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.44/39.19    (3)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 227.44/39.19    (4)  all_55_9 = all_53_6
% 227.44/39.19    (5)   ~ (all_53_6 = e1)
% 227.44/39.19    (6)  op(e2, e3) = all_44_1
% 227.44/39.19    (7)  op(e1, e2) = all_52_19
% 227.44/39.19    (8)  op(all_52_19, all_52_19) = e2
% 227.44/39.19    (9)  op(e2, e2) = e3
% 227.44/39.19    (10)   ~ (all_53_6 = e3)
% 227.44/39.19    (11)  op(e1, e2) = all_53_6
% 227.44/39.19    (12)  op(e2, e3) = e1
% 227.44/39.19  
% 227.44/39.19  Begin of proof
% 227.44/39.19  | 
% 227.44/39.19  | BETA: splitting (1) gives:
% 227.44/39.19  | 
% 227.44/39.19  | Case 1:
% 227.44/39.19  | | 
% 227.44/39.19  | |   (13)   ~ (all_8_0 = e0) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1
% 227.44/39.19  | |         & $i(all_8_0) & $i(all_8_1)
% 227.44/39.19  | | 
% 227.44/39.19  | | ALPHA: (13) implies:
% 227.44/39.19  | |   (14)  op(e2, e3) = all_8_1
% 227.44/39.19  | | 
% 227.44/39.19  | | GROUND_INST: instantiating (2) with all_53_6, all_52_19, e2, e1, simplifying
% 227.44/39.19  | |              with (7), (11) gives:
% 227.44/39.19  | |   (15)  all_53_6 = all_52_19
% 227.44/39.19  | | 
% 227.44/39.19  | | GROUND_INST: instantiating (2) with e1, all_44_1, e3, e2, simplifying with
% 227.44/39.19  | |              (6), (12) gives:
% 227.44/39.19  | |   (16)  all_44_1 = e1
% 227.44/39.19  | | 
% 227.44/39.19  | | GROUND_INST: instantiating (2) with all_8_1, all_44_1, e3, e2, simplifying
% 227.44/39.19  | |              with (6), (14) gives:
% 227.44/39.19  | |   (17)  all_44_1 = all_8_1
% 227.44/39.19  | | 
% 227.44/39.19  | | COMBINE_EQS: (16), (17) imply:
% 227.44/39.19  | |   (18)  all_8_1 = e1
% 227.44/39.19  | | 
% 227.44/39.19  | | SIMP: (18) implies:
% 227.44/39.19  | |   (19)  all_8_1 = e1
% 227.44/39.19  | | 
% 227.44/39.19  | | COMBINE_EQS: (4), (15) imply:
% 227.44/39.19  | |   (20)  all_55_9 = all_52_19
% 227.44/39.19  | | 
% 227.44/39.19  | | REDUCE: (10), (15) imply:
% 227.44/39.19  | |   (21)   ~ (all_52_19 = e3)
% 227.44/39.19  | | 
% 227.44/39.19  | | REDUCE: (5), (15) imply:
% 227.44/39.19  | |   (22)   ~ (all_52_19 = e1)
% 227.44/39.19  | | 
% 227.44/39.19  | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (9), (12), (20), (21), (22) are
% 227.44/39.19  | |            inconsistent by sub-proof #246.
% 227.44/39.19  | | 
% 227.44/39.19  | Case 2:
% 227.44/39.19  | | 
% 227.44/39.19  | |   (23)   ~ (all_8_1 = e1) & op(e2, e3) = all_8_1 & $i(all_8_1)
% 227.44/39.19  | | 
% 227.44/39.19  | | ALPHA: (23) implies:
% 227.44/39.19  | |   (24)   ~ (all_8_1 = e1)
% 227.44/39.19  | |   (25)  op(e2, e3) = all_8_1
% 227.44/39.19  | | 
% 227.44/39.19  | | REF_CLOSE: (2), (6), (12), (24), (25) are inconsistent by sub-proof #247.
% 227.44/39.19  | | 
% 227.44/39.19  | End of split
% 227.44/39.19  | 
% 227.44/39.19  End of proof
% 227.44/39.19  
% 227.44/39.19  Sub-proof #246 shows that the following formulas are inconsistent:
% 227.44/39.19  ----------------------------------------------------------------
% 227.44/39.19    (1)   ~ (all_52_19 = e3)
% 227.44/39.19    (2)  ( ~ (all_8_0 = e0) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 227.44/39.19           $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e1) & op(e2, e3) = all_8_1
% 227.44/39.19           & $i(all_8_1))
% 227.44/39.19    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.44/39.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.44/39.19    (4)  all_55_9 = all_52_19
% 227.44/39.19    (5)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 227.44/39.19    (6)  op(e2, e3) = all_44_1
% 227.44/39.19    (7)  op(e1, e2) = all_52_19
% 227.44/39.19    (8)  op(all_52_19, all_52_19) = e2
% 227.44/39.19    (9)  op(e2, e2) = e3
% 227.44/39.19    (10)  op(e2, e3) = e1
% 227.44/39.19    (11)   ~ (all_52_19 = e1)
% 227.44/39.19  
% 227.44/39.19  Begin of proof
% 227.44/39.19  | 
% 227.44/39.19  | BETA: splitting (2) gives:
% 227.44/39.19  | 
% 227.44/39.19  | Case 1:
% 227.44/39.19  | | 
% 227.44/39.19  | |   (12)   ~ (all_8_0 = e0) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1
% 227.44/39.19  | |         & $i(all_8_0) & $i(all_8_1)
% 227.44/39.19  | | 
% 227.44/39.19  | | ALPHA: (12) implies:
% 227.44/39.19  | |   (13)   ~ (all_8_0 = e0)
% 227.44/39.19  | |   (14)  op(e2, e3) = all_8_1
% 227.44/39.19  | |   (15)  op(all_8_1, e2) = all_8_0
% 227.44/39.19  | | 
% 227.44/39.19  | | GROUND_INST: instantiating (3) with e1, all_44_1, e3, e2, simplifying with
% 227.44/39.19  | |              (6), (10) gives:
% 227.44/39.19  | |   (16)  all_44_1 = e1
% 227.44/39.19  | | 
% 227.44/39.19  | | GROUND_INST: instantiating (3) with all_8_1, all_44_1, e3, e2, simplifying
% 227.44/39.19  | |              with (6), (14) gives:
% 227.44/39.19  | |   (17)  all_44_1 = all_8_1
% 227.44/39.19  | | 
% 227.44/39.19  | | COMBINE_EQS: (16), (17) imply:
% 227.44/39.19  | |   (18)  all_8_1 = e1
% 227.44/39.19  | | 
% 227.44/39.19  | | REDUCE: (15), (18) imply:
% 227.44/39.19  | |   (19)  op(e1, e2) = all_8_0
% 227.44/39.19  | | 
% 227.44/39.19  | | GROUND_INST: instantiating (3) with all_52_19, all_8_0, e2, e1, simplifying
% 227.44/39.19  | |              with (7), (19) gives:
% 227.44/39.19  | |   (20)  all_52_19 = all_8_0
% 227.44/39.19  | | 
% 227.44/39.19  | | COMBINE_EQS: (4), (20) imply:
% 227.44/39.19  | |   (21)  all_55_9 = all_8_0
% 227.44/39.19  | | 
% 227.44/39.19  | | REDUCE: (1), (20) imply:
% 227.44/39.19  | |   (22)   ~ (all_8_0 = e3)
% 227.44/39.19  | | 
% 227.44/39.19  | | REDUCE: (11), (20) imply:
% 227.44/39.19  | |   (23)   ~ (all_8_0 = e1)
% 227.44/39.19  | | 
% 227.44/39.19  | | REDUCE: (8), (20) imply:
% 227.44/39.19  | |   (24)  op(all_8_0, all_8_0) = e2
% 227.44/39.19  | | 
% 227.44/39.19  | | BETA: splitting (5) gives:
% 227.44/39.19  | | 
% 227.44/39.19  | | Case 1:
% 227.44/39.19  | | | 
% 227.44/39.19  | | |   (25)  all_55_9 = e3
% 227.44/39.19  | | | 
% 227.44/39.19  | | | COMBINE_EQS: (21), (25) imply:
% 227.44/39.19  | | |   (26)  all_8_0 = e3
% 227.44/39.19  | | | 
% 227.44/39.19  | | | SIMP: (26) implies:
% 227.44/39.19  | | |   (27)  all_8_0 = e3
% 227.44/39.19  | | | 
% 227.44/39.19  | | | REDUCE: (22), (27) imply:
% 227.44/39.19  | | |   (28)  $false
% 227.44/39.19  | | | 
% 227.44/39.19  | | | CLOSE: (28) is inconsistent.
% 227.44/39.19  | | | 
% 227.44/39.19  | | Case 2:
% 227.44/39.19  | | | 
% 227.44/39.19  | | |   (29)   ~ (all_55_9 = e3)
% 227.44/39.19  | | |   (30)  all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 227.44/39.19  | | | 
% 227.44/39.19  | | | BETA: splitting (30) gives:
% 227.44/39.19  | | | 
% 227.44/39.19  | | | Case 1:
% 227.44/39.19  | | | | 
% 227.44/39.19  | | | |   (31)  all_55_9 = e2
% 227.44/39.19  | | | | 
% 227.44/39.19  | | | | COMBINE_EQS: (21), (31) imply:
% 227.44/39.19  | | | |   (32)  all_8_0 = e2
% 227.44/39.19  | | | | 
% 227.44/39.19  | | | | SIMP: (32) implies:
% 227.44/39.19  | | | |   (33)  all_8_0 = e2
% 227.44/39.19  | | | | 
% 227.44/39.19  | | | | REF_CLOSE: (3), (9), (22), (24), (33) are inconsistent by sub-proof
% 227.44/39.19  | | | |            #253.
% 227.44/39.19  | | | | 
% 227.44/39.19  | | | Case 2:
% 227.44/39.19  | | | | 
% 227.44/39.19  | | | |   (34)  all_55_9 = e1 | all_55_9 = e0
% 227.44/39.19  | | | | 
% 227.44/39.19  | | | | BETA: splitting (34) gives:
% 227.44/39.19  | | | | 
% 227.44/39.19  | | | | Case 1:
% 227.44/39.19  | | | | | 
% 227.44/39.19  | | | | |   (35)  all_55_9 = e1
% 227.44/39.19  | | | | | 
% 227.44/39.19  | | | | | COMBINE_EQS: (21), (35) imply:
% 227.44/39.19  | | | | |   (36)  all_8_0 = e1
% 227.44/39.19  | | | | | 
% 227.44/39.19  | | | | | REDUCE: (23), (36) imply:
% 227.44/39.19  | | | | |   (37)  $false
% 227.44/39.19  | | | | | 
% 227.44/39.19  | | | | | CLOSE: (37) is inconsistent.
% 227.44/39.19  | | | | | 
% 227.44/39.19  | | | | Case 2:
% 227.44/39.19  | | | | | 
% 227.44/39.19  | | | | |   (38)  all_55_9 = e0
% 227.44/39.19  | | | | | 
% 227.44/39.19  | | | | | COMBINE_EQS: (21), (38) imply:
% 227.44/39.19  | | | | |   (39)  all_8_0 = e0
% 227.44/39.19  | | | | | 
% 227.44/39.19  | | | | | REDUCE: (13), (39) imply:
% 227.44/39.19  | | | | |   (40)  $false
% 227.44/39.19  | | | | | 
% 227.44/39.19  | | | | | CLOSE: (40) is inconsistent.
% 227.44/39.19  | | | | | 
% 227.44/39.19  | | | | End of split
% 227.44/39.19  | | | | 
% 227.44/39.19  | | | End of split
% 227.44/39.19  | | | 
% 227.44/39.19  | | End of split
% 227.44/39.19  | | 
% 227.44/39.19  | Case 2:
% 227.44/39.19  | | 
% 227.44/39.19  | |   (41)   ~ (all_8_1 = e1) & op(e2, e3) = all_8_1 & $i(all_8_1)
% 227.44/39.19  | | 
% 227.44/39.19  | | ALPHA: (41) implies:
% 227.44/39.19  | |   (42)   ~ (all_8_1 = e1)
% 227.44/39.19  | |   (43)  op(e2, e3) = all_8_1
% 227.44/39.19  | | 
% 227.44/39.19  | | REF_CLOSE: (3), (6), (10), (42), (43) are inconsistent by sub-proof #247.
% 227.44/39.19  | | 
% 227.44/39.19  | End of split
% 227.44/39.19  | 
% 227.44/39.19  End of proof
% 227.44/39.19  
% 227.44/39.19  Sub-proof #247 shows that the following formulas are inconsistent:
% 227.44/39.19  ----------------------------------------------------------------
% 227.44/39.19    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.44/39.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.44/39.19    (2)  op(e2, e3) = all_8_1
% 227.44/39.19    (3)   ~ (all_8_1 = e1)
% 227.44/39.19    (4)  op(e2, e3) = all_44_1
% 227.44/39.19    (5)  op(e2, e3) = e1
% 227.44/39.19  
% 227.44/39.19  Begin of proof
% 227.44/39.19  | 
% 227.44/39.19  | GROUND_INST: instantiating (1) with e1, all_44_1, e3, e2, simplifying with
% 227.44/39.19  |              (4), (5) gives:
% 227.44/39.19  |   (6)  all_44_1 = e1
% 227.44/39.19  | 
% 227.44/39.19  | GROUND_INST: instantiating (1) with all_8_1, all_44_1, e3, e2, simplifying
% 227.44/39.19  |              with (2), (4) gives:
% 227.44/39.19  |   (7)  all_44_1 = all_8_1
% 227.44/39.19  | 
% 227.44/39.19  | COMBINE_EQS: (6), (7) imply:
% 227.44/39.19  |   (8)  all_8_1 = e1
% 227.44/39.19  | 
% 227.44/39.19  | REDUCE: (3), (8) imply:
% 227.44/39.19  |   (9)  $false
% 227.44/39.19  | 
% 227.44/39.19  | CLOSE: (9) is inconsistent.
% 227.44/39.19  | 
% 227.44/39.19  End of proof
% 227.44/39.19  
% 227.44/39.19  Sub-proof #248 shows that the following formulas are inconsistent:
% 227.44/39.19  ----------------------------------------------------------------
% 227.44/39.19    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.44/39.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.44/39.19    (2)  op(e2, e0) = all_52_15
% 227.44/39.19    (3)   ~ (e3 = e0)
% 227.44/39.19    (4)  op(e2, e2) = all_52_11
% 227.44/39.19    (5)  op(e2, e0) = e2
% 227.44/39.19    (6)  op(all_52_15, all_52_15) = e0
% 227.44/39.19    (7)  op(e2, e2) = e3
% 227.44/39.19  
% 227.44/39.19  Begin of proof
% 227.44/39.19  | 
% 227.44/39.19  | GROUND_INST: instantiating (1) with e2, all_52_15, e0, e2, simplifying with
% 227.44/39.19  |              (2), (5) gives:
% 227.44/39.19  |   (8)  all_52_15 = e2
% 227.44/39.19  | 
% 227.44/39.19  | GROUND_INST: instantiating (1) with e3, all_52_11, e2, e2, simplifying with
% 227.44/39.19  |              (4), (7) gives:
% 227.44/39.19  |   (9)  all_52_11 = e3
% 227.44/39.19  | 
% 227.44/39.19  | REDUCE: (6), (8) imply:
% 227.44/39.19  |   (10)  op(e2, e2) = e0
% 227.44/39.19  | 
% 227.44/39.19  | GROUND_INST: instantiating (1) with e3, e0, e2, e2, simplifying with (7), (10)
% 227.44/39.19  |              gives:
% 227.44/39.19  |   (11)  e3 = e0
% 227.44/39.19  | 
% 227.44/39.19  | REDUCE: (3), (11) imply:
% 227.44/39.19  |   (12)  $false
% 227.44/39.19  | 
% 227.44/39.19  | CLOSE: (12) is inconsistent.
% 227.44/39.19  | 
% 227.44/39.19  End of proof
% 227.44/39.19  
% 227.44/39.19  Sub-proof #249 shows that the following formulas are inconsistent:
% 227.44/39.19  ----------------------------------------------------------------
% 227.44/39.19    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.44/39.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.44/39.19    (2)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3)
% 227.44/39.19    (3)   ~ (e3 = e2)
% 227.44/39.19    (4)  op(e3, e3) = e2
% 227.44/39.19    (5)  op(e3, e2) = all_53_4
% 227.44/39.19    (6)   ~ (all_53_4 = e3)
% 227.44/39.19  
% 227.44/39.19  Begin of proof
% 227.44/39.19  | 
% 227.44/39.19  | BETA: splitting (2) gives:
% 227.44/39.19  | 
% 227.44/39.19  | Case 1:
% 227.44/39.19  | | 
% 227.44/39.19  | |   (7)  all_57_0 = e3 & op(e3, e3) = e3
% 227.44/39.19  | | 
% 227.44/39.19  | | ALPHA: (7) implies:
% 227.44/39.19  | |   (8)  op(e3, e3) = e3
% 227.44/39.19  | | 
% 227.44/39.19  | | REF_CLOSE: (1), (3), (4), (8) are inconsistent by sub-proof #2490.
% 227.44/39.19  | | 
% 227.44/39.19  | Case 2:
% 227.44/39.19  | | 
% 227.44/39.19  | |   (9)  all_57_1 = e3 & op(e3, e2) = e3
% 227.44/39.19  | | 
% 227.44/39.19  | | REF_CLOSE: (1), (5), (6), (9) are inconsistent by sub-proof #2286.
% 227.44/39.19  | | 
% 227.44/39.19  | End of split
% 227.44/39.19  | 
% 227.44/39.19  End of proof
% 227.44/39.19  
% 227.44/39.19  Sub-proof #250 shows that the following formulas are inconsistent:
% 227.44/39.19  ----------------------------------------------------------------
% 227.44/39.19    (1)  all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 227.44/39.19    (2)   ~ (all_53_7 = e3)
% 227.44/39.19    (3)  op(e3, e1) = e0
% 227.44/39.19    (4)  op(e2, e3) = all_53_1
% 227.44/39.19    (5)  ( ~ (all_8_0 = e0) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 227.44/39.19           $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e1) & op(e2, e3) = all_8_1
% 227.44/39.19           & $i(all_8_1))
% 227.44/39.19    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.44/39.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.44/39.19    (7)  all_55_15 = all_4_2
% 227.44/39.19    (8)   ~ (all_44_2 = e3) | ( ~ (all_44_0 = e1) & op(all_44_1, e2) = all_44_0 &
% 227.44/39.19           op(e2, e3) = all_44_1 & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 =
% 227.44/39.19             e0) & op(e2, e3) = all_44_1 & $i(all_44_1))
% 227.44/39.19    (9)  all_57_3 = e3
% 227.44/39.19    (10)   ~ (all_53_9 = e0)
% 227.44/39.19    (11)   ~ (e3 = e0)
% 227.44/39.19    (12)  op(e0, e3) = all_53_3
% 227.44/39.19    (13)   ~ (all_53_2 = e0)
% 227.44/39.19    (14)   ~ (all_53_7 = all_4_2)
% 227.44/39.19    (15)  op(e3, e3) = e2
% 227.44/39.19    (16)  op(e1, e2) = e0
% 227.44/39.19    (17)   ~ (e2 = e0)
% 227.44/39.19    (18)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 227.44/39.19            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 227.44/39.19            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 227.44/39.19            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 227.44/39.19              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 227.44/39.19            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 227.44/39.19            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 227.44/39.19              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 227.44/39.19              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 227.44/39.19            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 227.44/39.19            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 227.44/39.19            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 227.44/39.19              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 227.44/39.19              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 227.44/39.19            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 227.44/39.19              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 227.44/39.19            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 227.44/39.19            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 227.44/39.19              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 227.44/39.19              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 227.44/39.19            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 227.44/39.19            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 227.44/39.19    (19)   ~ (e1 = e0)
% 227.44/39.19    (20)  op(e0, e0) = e0
% 227.44/39.19    (21)   ~ (all_53_13 = all_4_2)
% 227.44/39.19    (22)  op(e0, e2) = all_53_7
% 227.44/39.19    (23)  all_44_2 = e3
% 227.44/39.19    (24)   ~ (all_53_3 = e0)
% 227.44/39.19    (25)  all_55_13 = all_53_7
% 227.44/39.19    (26)  op(e2, e0) = all_53_13
% 227.44/39.19    (27)  all_55_15 = e1 | all_55_15 = e0
% 227.44/39.19    (28)  op(e1, e3) = all_53_2
% 227.44/39.19    (29)   ~ (all_4_2 = e3)
% 227.44/39.19    (30)  op(e2, e2) = e3
% 227.44/39.19    (31)   ~ (all_4_2 = e1)
% 227.44/39.19    (32)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 227.44/39.19          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 227.44/39.19    (33)  op(e2, e1) = all_53_9
% 227.44/39.19    (34)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 227.44/39.19          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 227.44/39.19  
% 227.44/39.19  Begin of proof
% 227.44/39.19  | 
% 227.44/39.19  | BETA: splitting (18) gives:
% 227.44/39.19  | 
% 227.44/39.19  | Case 1:
% 227.44/39.19  | | 
% 227.44/39.19  | |   (35)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 227.44/39.19  | |           op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 227.44/39.19  | |           op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3,
% 227.44/39.19  | |             e3) = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 &
% 227.44/39.19  | |           op(e3, e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5)
% 227.44/39.19  | |           & $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1
% 227.44/39.19  | |           & all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 227.44/39.19  | |             all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 227.44/39.19  | |             all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11
% 227.44/39.19  | |           & op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 227.44/39.19  | |           $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 227.44/39.19  | | 
% 227.44/39.19  | | BETA: splitting (35) gives:
% 227.44/39.19  | | 
% 227.44/39.19  | | Case 1:
% 227.44/39.19  | | | 
% 227.44/39.20  | | |   (36)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 227.44/39.20  | | |         op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 227.44/39.20  | | |         op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3,
% 227.44/39.20  | | |           e3) = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 &
% 227.44/39.20  | | |         op(e3, e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5)
% 227.44/39.20  | | |         & $i(all_52_7)
% 227.44/39.20  | | | 
% 227.44/39.20  | | | ALPHA: (36) implies:
% 227.44/39.20  | | |   (37)  op(e3, e1) = all_52_5
% 227.44/39.20  | | |   (38)  op(all_52_5, all_52_5) = e1
% 227.44/39.20  | | | 
% 227.44/39.20  | | | REF_CLOSE: (3), (6), (19), (20), (37), (38) are inconsistent by sub-proof
% 227.44/39.20  | | |            #2167.
% 227.44/39.20  | | | 
% 227.44/39.20  | | Case 2:
% 227.44/39.20  | | | 
% 227.44/39.20  | | |   (39)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0 &
% 227.44/39.20  | | |         op(all_52_9, all_52_9) = e3 & op(all_52_11, all_52_11) = e2 &
% 227.44/39.20  | | |         op(all_52_13, all_52_13) = e1 & op(all_52_15, all_52_15) = e0 &
% 227.44/39.20  | | |         op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 & op(e2, e1) =
% 227.44/39.20  | | |         all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) & $i(all_52_11)
% 227.44/39.20  | | |         & $i(all_52_13) & $i(all_52_15)
% 227.44/39.20  | | | 
% 227.44/39.20  | | | ALPHA: (39) implies:
% 227.44/39.20  | | |   (40)  op(e2, e3) = all_52_9
% 227.44/39.20  | | |   (41)  op(all_52_9, all_52_9) = e3
% 227.44/39.20  | | | 
% 227.44/39.20  | | | REF_CLOSE: (4), (6), (11), (12), (13), (15), (17), (20), (24), (28), (34),
% 227.44/39.20  | | |            (40), (41) are inconsistent by sub-proof #1571.
% 227.44/39.20  | | | 
% 227.44/39.20  | | End of split
% 227.44/39.20  | | 
% 227.44/39.20  | Case 2:
% 227.44/39.20  | | 
% 227.44/39.20  | |   (42)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 &
% 227.44/39.20  | |           op(all_52_17, all_52_17) = e3 & op(all_52_19, all_52_19) = e2 &
% 227.44/39.20  | |           op(all_52_21, all_52_21) = e1 & op(all_52_23, all_52_23) = e0 &
% 227.44/39.20  | |           op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) =
% 227.44/39.20  | |           all_52_21 & op(e1, e0) = all_52_23 & $i(all_52_17) & $i(all_52_19)
% 227.44/39.20  | |           & $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3 & all_52_26 =
% 227.44/39.20  | |           e2 & all_52_28 = e1 & all_52_30 = e0 & op(all_52_25, all_52_25) =
% 227.44/39.20  | |           e3 & op(all_52_27, all_52_27) = e2 & op(all_52_29, all_52_29) = e1
% 227.44/39.20  | |           & op(all_52_31, all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0,
% 227.44/39.20  | |             e2) = all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0) =
% 227.44/39.20  | |           all_52_31 & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 227.44/39.20  | |           $i(all_52_31))
% 227.44/39.20  | | 
% 227.44/39.20  | | BETA: splitting (42) gives:
% 227.44/39.20  | | 
% 227.44/39.20  | | Case 1:
% 227.44/39.20  | | | 
% 227.44/39.20  | | |   (43)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 227.44/39.20  | | |         & op(all_52_17, all_52_17) = e3 & op(all_52_19, all_52_19) = e2 &
% 227.44/39.20  | | |         op(all_52_21, all_52_21) = e1 & op(all_52_23, all_52_23) = e0 &
% 227.44/39.20  | | |         op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) =
% 227.44/39.20  | | |         all_52_21 & op(e1, e0) = all_52_23 & $i(all_52_17) & $i(all_52_19)
% 227.44/39.20  | | |         & $i(all_52_21) & $i(all_52_23)
% 227.44/39.20  | | | 
% 227.44/39.20  | | | ALPHA: (43) implies:
% 227.44/39.20  | | |   (44)  op(e1, e2) = all_52_19
% 227.44/39.20  | | |   (45)  op(all_52_19, all_52_19) = e2
% 227.44/39.20  | | | 
% 227.44/39.20  | | | REF_CLOSE: (6), (16), (17), (20), (44), (45) are inconsistent by sub-proof
% 227.44/39.20  | | |            #2158.
% 227.44/39.20  | | | 
% 227.44/39.20  | | Case 2:
% 227.44/39.20  | | | 
% 227.44/39.20  | | |   (46)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 227.44/39.20  | | |         & op(all_52_25, all_52_25) = e3 & op(all_52_27, all_52_27) = e2 &
% 227.44/39.20  | | |         op(all_52_29, all_52_29) = e1 & op(all_52_31, all_52_31) = e0 &
% 227.44/39.20  | | |         op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 & op(e0, e1) =
% 227.44/39.20  | | |         all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) & $i(all_52_27)
% 227.44/39.20  | | |         & $i(all_52_29) & $i(all_52_31)
% 227.44/39.20  | | | 
% 227.44/39.20  | | | ALPHA: (46) implies:
% 227.44/39.20  | | |   (47)  op(e0, e2) = all_52_27
% 227.44/39.20  | | |   (48)  op(all_52_27, all_52_27) = e2
% 227.44/39.20  | | | 
% 227.44/39.20  | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (14), (21), (22),
% 227.44/39.20  | | |            (23), (25), (26), (27), (29), (30), (31), (32), (33), (47),
% 227.44/39.20  | | |            (48) are inconsistent by sub-proof #251.
% 227.44/39.20  | | | 
% 227.44/39.20  | | End of split
% 227.44/39.20  | | 
% 227.44/39.20  | End of split
% 227.44/39.20  | 
% 227.44/39.20  End of proof
% 227.44/39.20  
% 227.44/39.20  Sub-proof #251 shows that the following formulas are inconsistent:
% 227.44/39.20  ----------------------------------------------------------------
% 227.44/39.20    (1)  all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 227.44/39.20    (2)   ~ (all_53_7 = e3)
% 227.44/39.20    (3)  op(e2, e3) = all_53_1
% 227.44/39.20    (4)  ( ~ (all_8_0 = e0) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 227.44/39.20           $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e1) & op(e2, e3) = all_8_1
% 227.44/39.20           & $i(all_8_1))
% 227.44/39.20    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.44/39.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.44/39.20    (6)  all_55_15 = all_4_2
% 227.44/39.20    (7)   ~ (all_44_2 = e3) | ( ~ (all_44_0 = e1) & op(all_44_1, e2) = all_44_0 &
% 227.44/39.20           op(e2, e3) = all_44_1 & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 =
% 227.44/39.20             e0) & op(e2, e3) = all_44_1 & $i(all_44_1))
% 227.44/39.20    (8)  all_57_3 = e3
% 227.44/39.20    (9)   ~ (all_53_9 = e0)
% 227.44/39.20    (10)   ~ (all_53_7 = all_4_2)
% 227.44/39.20    (11)   ~ (all_53_13 = all_4_2)
% 227.44/39.20    (12)  op(e0, e2) = all_53_7
% 227.44/39.20    (13)  all_44_2 = e3
% 227.44/39.20    (14)  all_55_13 = all_53_7
% 227.44/39.20    (15)  op(e2, e0) = all_53_13
% 227.44/39.20    (16)  all_55_15 = e1 | all_55_15 = e0
% 227.44/39.20    (17)   ~ (all_4_2 = e3)
% 227.44/39.20    (18)  op(e0, e2) = all_52_27
% 227.44/39.20    (19)  op(e2, e2) = e3
% 227.44/39.20    (20)   ~ (all_4_2 = e1)
% 227.44/39.20    (21)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 227.44/39.20          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 227.44/39.20    (22)  op(e2, e1) = all_53_9
% 227.44/39.20    (23)  op(all_52_27, all_52_27) = e2
% 227.44/39.20  
% 227.44/39.20  Begin of proof
% 227.44/39.20  | 
% 227.44/39.20  | BETA: splitting (16) gives:
% 227.44/39.20  | 
% 227.44/39.20  | Case 1:
% 227.44/39.20  | | 
% 227.44/39.20  | |   (24)  all_55_15 = e1
% 227.44/39.20  | | 
% 227.44/39.20  | | REF_CLOSE: (6), (20), (24) are inconsistent by sub-proof #2501.
% 227.44/39.20  | | 
% 227.44/39.20  | Case 2:
% 227.44/39.20  | | 
% 227.44/39.20  | |   (25)  all_55_15 = e0
% 227.44/39.20  | | 
% 227.44/39.20  | | COMBINE_EQS: (6), (25) imply:
% 227.44/39.20  | |   (26)  all_4_2 = e0
% 227.44/39.20  | | 
% 227.44/39.20  | | SIMP: (26) implies:
% 227.44/39.20  | |   (27)  all_4_2 = e0
% 227.44/39.20  | | 
% 227.44/39.20  | | REDUCE: (10), (27) imply:
% 227.44/39.20  | |   (28)   ~ (all_53_7 = e0)
% 227.44/39.20  | | 
% 227.44/39.20  | | REDUCE: (11), (27) imply:
% 227.44/39.20  | |   (29)   ~ (all_53_13 = e0)
% 227.44/39.20  | | 
% 227.44/39.20  | | REDUCE: (17), (27) imply:
% 227.44/39.20  | |   (30)   ~ (e3 = e0)
% 227.44/39.20  | | 
% 227.44/39.20  | | SIMP: (30) implies:
% 227.44/39.20  | |   (31)   ~ (e3 = e0)
% 227.44/39.20  | | 
% 227.44/39.20  | | BETA: splitting (21) gives:
% 227.44/39.20  | | 
% 227.44/39.20  | | Case 1:
% 227.44/39.20  | | | 
% 227.44/39.20  | | |   (32)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) =
% 227.44/39.20  | | |           e0)
% 227.44/39.20  | | | 
% 227.44/39.20  | | | BETA: splitting (32) gives:
% 227.44/39.20  | | | 
% 227.44/39.20  | | | Case 1:
% 227.44/39.20  | | | | 
% 227.44/39.20  | | | |   (33)  all_57_2 = e0 & op(e2, e3) = e0
% 227.44/39.20  | | | | 
% 227.44/39.20  | | | | ALPHA: (33) implies:
% 227.44/39.20  | | | |   (34)  op(e2, e3) = e0
% 227.44/39.20  | | | | 
% 227.44/39.20  | | | | GROUND_INST: instantiating (5) with all_53_7, all_52_27, e2, e0,
% 227.44/39.20  | | | |              simplifying with (12), (18) gives:
% 227.44/39.20  | | | |   (35)  all_53_7 = all_52_27
% 227.44/39.20  | | | | 
% 227.44/39.20  | | | | GROUND_INST: instantiating (5) with all_53_1, e0, e3, e2, simplifying
% 227.44/39.20  | | | |              with (3), (34) gives:
% 227.44/39.20  | | | |   (36)  all_53_1 = e0
% 227.44/39.20  | | | | 
% 227.44/39.20  | | | | COMBINE_EQS: (14), (35) imply:
% 227.44/39.20  | | | |   (37)  all_55_13 = all_52_27
% 227.44/39.20  | | | | 
% 227.44/39.20  | | | | REDUCE: (2), (35) imply:
% 227.44/39.20  | | | |   (38)   ~ (all_52_27 = e3)
% 227.44/39.20  | | | | 
% 227.44/39.20  | | | | REDUCE: (28), (35) imply:
% 227.44/39.20  | | | |   (39)   ~ (all_52_27 = e0)
% 227.44/39.20  | | | | 
% 227.44/39.20  | | | | BETA: splitting (7) gives:
% 227.44/39.20  | | | | 
% 227.44/39.20  | | | | Case 1:
% 227.44/39.20  | | | | | 
% 227.44/39.20  | | | | |   (40)   ~ (all_44_2 = e3)
% 227.44/39.20  | | | | | 
% 227.44/39.20  | | | | | REDUCE: (13), (40) imply:
% 227.44/39.20  | | | | |   (41)  $false
% 227.44/39.20  | | | | | 
% 227.44/39.20  | | | | | CLOSE: (41) is inconsistent.
% 227.44/39.20  | | | | | 
% 227.44/39.20  | | | | Case 2:
% 227.44/39.20  | | | | | 
% 227.44/39.20  | | | | |   (42)  ( ~ (all_44_0 = e1) & op(all_44_1, e2) = all_44_0 & op(e2, e3)
% 227.44/39.20  | | | | |           = all_44_1 & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 =
% 227.44/39.20  | | | | |             e0) & op(e2, e3) = all_44_1 & $i(all_44_1))
% 227.44/39.20  | | | | | 
% 227.44/39.20  | | | | | REF_CLOSE: (1), (4), (5), (18), (19), (23), (34), (37), (38), (39),
% 227.44/39.20  | | | | |            (42) are inconsistent by sub-proof #252.
% 227.44/39.20  | | | | | 
% 227.44/39.20  | | | | End of split
% 227.44/39.20  | | | | 
% 227.44/39.20  | | | Case 2:
% 227.44/39.20  | | | | 
% 227.44/39.20  | | | |   (43)  all_57_3 = e0 & op(e2, e2) = e0
% 227.44/39.20  | | | | 
% 227.44/39.20  | | | | REF_CLOSE: (8), (31), (43) are inconsistent by sub-proof #262.
% 227.44/39.20  | | | | 
% 227.44/39.20  | | | End of split
% 227.44/39.20  | | | 
% 227.44/39.20  | | Case 2:
% 227.44/39.20  | | | 
% 227.44/39.20  | | |   (44)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 227.44/39.20  | | |           e0)
% 227.44/39.20  | | | 
% 227.44/39.20  | | | REF_CLOSE: (5), (9), (15), (22), (29), (44) are inconsistent by sub-proof
% 227.44/39.20  | | |            #2022.
% 227.44/39.20  | | | 
% 227.44/39.20  | | End of split
% 227.44/39.20  | | 
% 227.44/39.20  | End of split
% 227.44/39.20  | 
% 227.44/39.20  End of proof
% 227.44/39.20  
% 227.44/39.20  Sub-proof #252 shows that the following formulas are inconsistent:
% 227.44/39.20  ----------------------------------------------------------------
% 227.44/39.20    (1)  all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 227.44/39.20    (2)  ( ~ (all_44_0 = e1) & op(all_44_1, e2) = all_44_0 & op(e2, e3) = all_44_1
% 227.44/39.20           & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 = e0) & op(e2, e3) =
% 227.44/39.20           all_44_1 & $i(all_44_1))
% 227.44/39.20    (3)  ( ~ (all_8_0 = e0) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1 &
% 227.44/39.20           $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e1) & op(e2, e3) = all_8_1
% 227.44/39.20           & $i(all_8_1))
% 227.44/39.20    (4)  op(e2, e3) = e0
% 227.44/39.20    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.44/39.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.44/39.20    (6)  all_55_13 = all_52_27
% 227.44/39.20    (7)   ~ (all_52_27 = e0)
% 227.44/39.20    (8)  op(e0, e2) = all_52_27
% 227.44/39.20    (9)  op(e2, e2) = e3
% 227.44/39.20    (10)  op(all_52_27, all_52_27) = e2
% 227.44/39.20    (11)   ~ (all_52_27 = e3)
% 227.44/39.20  
% 227.44/39.20  Begin of proof
% 227.44/39.20  | 
% 227.44/39.20  | BETA: splitting (3) gives:
% 227.44/39.20  | 
% 227.44/39.20  | Case 1:
% 227.44/39.20  | | 
% 227.44/39.20  | |   (12)   ~ (all_8_0 = e0) & op(all_8_1, e2) = all_8_0 & op(e2, e3) = all_8_1
% 227.44/39.20  | |         & $i(all_8_0) & $i(all_8_1)
% 227.44/39.20  | | 
% 227.44/39.20  | | ALPHA: (12) implies:
% 227.44/39.20  | |   (13)  op(e2, e3) = all_8_1
% 227.44/39.20  | |   (14)  op(all_8_1, e2) = all_8_0
% 227.44/39.20  | | 
% 227.44/39.20  | | GROUND_INST: instantiating (5) with e0, all_8_1, e3, e2, simplifying with
% 227.44/39.20  | |              (4), (13) gives:
% 227.44/39.20  | |   (15)  all_8_1 = e0
% 227.44/39.20  | | 
% 227.44/39.20  | | REDUCE: (14), (15) imply:
% 227.44/39.20  | |   (16)  op(e0, e2) = all_8_0
% 227.44/39.20  | | 
% 227.44/39.20  | | BETA: splitting (2) gives:
% 227.44/39.20  | | 
% 227.44/39.20  | | Case 1:
% 227.44/39.20  | | | 
% 227.44/39.20  | | |   (17)   ~ (all_44_0 = e1) & op(all_44_1, e2) = all_44_0 & op(e2, e3) =
% 227.44/39.20  | | |         all_44_1 & $i(all_44_0) & $i(all_44_1)
% 227.44/39.20  | | | 
% 227.44/39.20  | | | ALPHA: (17) implies:
% 227.44/39.20  | | |   (18)   ~ (all_44_0 = e1)
% 227.44/39.20  | | |   (19)  op(e2, e3) = all_44_1
% 227.44/39.20  | | |   (20)  op(all_44_1, e2) = all_44_0
% 227.44/39.20  | | | 
% 227.44/39.20  | | | GROUND_INST: instantiating (5) with all_52_27, all_8_0, e2, e0,
% 227.44/39.20  | | |              simplifying with (8), (16) gives:
% 227.44/39.20  | | |   (21)  all_52_27 = all_8_0
% 227.44/39.20  | | | 
% 227.44/39.20  | | | GROUND_INST: instantiating (5) with e0, all_44_1, e3, e2, simplifying with
% 227.44/39.20  | | |              (4), (19) gives:
% 227.44/39.20  | | |   (22)  all_44_1 = e0
% 227.44/39.20  | | | 
% 227.44/39.20  | | | COMBINE_EQS: (6), (21) imply:
% 227.44/39.20  | | |   (23)  all_55_13 = all_8_0
% 227.44/39.20  | | | 
% 227.44/39.20  | | | REDUCE: (11), (21) imply:
% 227.44/39.20  | | |   (24)   ~ (all_8_0 = e3)
% 227.44/39.20  | | | 
% 227.44/39.20  | | | REDUCE: (7), (21) imply:
% 227.44/39.20  | | |   (25)   ~ (all_8_0 = e0)
% 227.44/39.20  | | | 
% 227.44/39.20  | | | REDUCE: (10), (21) imply:
% 227.44/39.20  | | |   (26)  op(all_8_0, all_8_0) = e2
% 227.44/39.20  | | | 
% 227.44/39.20  | | | REDUCE: (20), (22) imply:
% 227.44/39.20  | | |   (27)  op(e0, e2) = all_44_0
% 227.44/39.20  | | | 
% 227.44/39.20  | | | GROUND_INST: instantiating (5) with all_8_0, all_44_0, e2, e0, simplifying
% 227.44/39.20  | | |              with (16), (27) gives:
% 227.44/39.20  | | |   (28)  all_44_0 = all_8_0
% 227.44/39.20  | | | 
% 227.44/39.20  | | | REDUCE: (18), (28) imply:
% 227.44/39.20  | | |   (29)   ~ (all_8_0 = e1)
% 227.44/39.20  | | | 
% 227.44/39.20  | | | BETA: splitting (1) gives:
% 227.44/39.20  | | | 
% 227.44/39.20  | | | Case 1:
% 227.44/39.20  | | | | 
% 227.44/39.20  | | | |   (30)  all_55_13 = e3
% 227.44/39.20  | | | | 
% 227.44/39.20  | | | | COMBINE_EQS: (23), (30) imply:
% 227.44/39.20  | | | |   (31)  all_8_0 = e3
% 227.44/39.20  | | | | 
% 227.44/39.20  | | | | REDUCE: (24), (31) imply:
% 227.44/39.20  | | | |   (32)  $false
% 227.44/39.20  | | | | 
% 227.44/39.20  | | | | CLOSE: (32) is inconsistent.
% 227.44/39.20  | | | | 
% 227.44/39.20  | | | Case 2:
% 227.44/39.20  | | | | 
% 227.44/39.20  | | | |   (33)   ~ (all_55_13 = e3)
% 227.44/39.20  | | | |   (34)  all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 227.44/39.20  | | | | 
% 227.44/39.20  | | | | BETA: splitting (34) gives:
% 227.44/39.20  | | | | 
% 227.44/39.20  | | | | Case 1:
% 227.44/39.20  | | | | | 
% 227.44/39.20  | | | | |   (35)  all_55_13 = e2
% 227.44/39.20  | | | | | 
% 227.44/39.20  | | | | | COMBINE_EQS: (23), (35) imply:
% 227.44/39.20  | | | | |   (36)  all_8_0 = e2
% 227.44/39.20  | | | | | 
% 227.44/39.20  | | | | | REF_CLOSE: (5), (9), (24), (26), (36) are inconsistent by sub-proof
% 227.44/39.20  | | | | |            #253.
% 227.44/39.20  | | | | | 
% 227.44/39.20  | | | | Case 2:
% 227.44/39.20  | | | | | 
% 227.44/39.20  | | | | |   (37)  all_55_13 = e1 | all_55_13 = e0
% 227.44/39.20  | | | | | 
% 227.44/39.20  | | | | | BETA: splitting (37) gives:
% 227.44/39.20  | | | | | 
% 227.44/39.20  | | | | | Case 1:
% 227.44/39.20  | | | | | | 
% 227.44/39.20  | | | | | |   (38)  all_55_13 = e1
% 227.44/39.20  | | | | | | 
% 227.44/39.20  | | | | | | COMBINE_EQS: (23), (38) imply:
% 227.44/39.20  | | | | | |   (39)  all_8_0 = e1
% 227.44/39.20  | | | | | | 
% 227.44/39.20  | | | | | | REDUCE: (29), (39) imply:
% 227.44/39.20  | | | | | |   (40)  $false
% 227.44/39.20  | | | | | | 
% 227.44/39.20  | | | | | | CLOSE: (40) is inconsistent.
% 227.44/39.20  | | | | | | 
% 227.44/39.20  | | | | | Case 2:
% 227.44/39.20  | | | | | | 
% 227.44/39.20  | | | | | |   (41)  all_55_13 = e0
% 227.44/39.20  | | | | | | 
% 227.44/39.20  | | | | | | COMBINE_EQS: (23), (41) imply:
% 227.44/39.20  | | | | | |   (42)  all_8_0 = e0
% 227.44/39.20  | | | | | | 
% 227.44/39.20  | | | | | | REDUCE: (25), (42) imply:
% 227.44/39.20  | | | | | |   (43)  $false
% 227.44/39.20  | | | | | | 
% 227.44/39.20  | | | | | | CLOSE: (43) is inconsistent.
% 227.44/39.20  | | | | | | 
% 227.44/39.20  | | | | | End of split
% 227.44/39.20  | | | | | 
% 227.44/39.20  | | | | End of split
% 227.44/39.20  | | | | 
% 227.44/39.20  | | | End of split
% 227.44/39.20  | | | 
% 227.44/39.20  | | Case 2:
% 227.44/39.20  | | | 
% 227.44/39.20  | | |   (44)   ~ (all_44_1 = e0) & op(e2, e3) = all_44_1 & $i(all_44_1)
% 227.44/39.20  | | | 
% 227.44/39.20  | | | ALPHA: (44) implies:
% 227.44/39.20  | | |   (45)   ~ (all_44_1 = e0)
% 227.44/39.20  | | |   (46)  op(e2, e3) = all_44_1
% 227.44/39.20  | | | 
% 227.44/39.20  | | | GROUND_INST: instantiating (5) with e0, all_44_1, e3, e2, simplifying with
% 227.44/39.20  | | |              (4), (46) gives:
% 227.44/39.20  | | |   (47)  all_44_1 = e0
% 227.44/39.20  | | | 
% 227.44/39.20  | | | REDUCE: (45), (47) imply:
% 227.44/39.20  | | |   (48)  $false
% 227.44/39.20  | | | 
% 227.44/39.20  | | | CLOSE: (48) is inconsistent.
% 227.44/39.20  | | | 
% 227.44/39.20  | | End of split
% 227.44/39.20  | | 
% 227.44/39.20  | Case 2:
% 227.44/39.20  | | 
% 227.44/39.20  | |   (49)   ~ (all_8_1 = e1) & op(e2, e3) = all_8_1 & $i(all_8_1)
% 227.44/39.20  | | 
% 227.44/39.20  | | ALPHA: (49) implies:
% 227.44/39.20  | |   (50)  op(e2, e3) = all_8_1
% 227.44/39.20  | | 
% 227.44/39.20  | | GROUND_INST: instantiating (5) with e0, all_8_1, e3, e2, simplifying with
% 227.44/39.20  | |              (4), (50) gives:
% 227.44/39.20  | |   (51)  all_8_1 = e0
% 227.44/39.20  | | 
% 227.44/39.20  | | BETA: splitting (2) gives:
% 227.44/39.20  | | 
% 227.44/39.20  | | Case 1:
% 227.44/39.20  | | | 
% 227.44/39.20  | | |   (52)   ~ (all_44_0 = e1) & op(all_44_1, e2) = all_44_0 & op(e2, e3) =
% 227.44/39.20  | | |         all_44_1 & $i(all_44_0) & $i(all_44_1)
% 227.44/39.20  | | | 
% 227.44/39.20  | | | ALPHA: (52) implies:
% 227.44/39.20  | | |   (53)   ~ (all_44_0 = e1)
% 227.44/39.20  | | |   (54)  op(e2, e3) = all_44_1
% 227.44/39.20  | | |   (55)  op(all_44_1, e2) = all_44_0
% 227.44/39.20  | | | 
% 227.44/39.20  | | | GROUND_INST: instantiating (5) with e0, all_44_1, e3, e2, simplifying with
% 227.44/39.20  | | |              (4), (54) gives:
% 227.44/39.20  | | |   (56)  all_44_1 = e0
% 227.44/39.20  | | | 
% 227.44/39.20  | | | REDUCE: (55), (56) imply:
% 227.44/39.20  | | |   (57)  op(e0, e2) = all_44_0
% 227.44/39.20  | | | 
% 227.44/39.20  | | | GROUND_INST: instantiating (5) with all_52_27, all_44_0, e2, e0,
% 227.44/39.20  | | |              simplifying with (8), (57) gives:
% 227.44/39.20  | | |   (58)  all_52_27 = all_44_0
% 227.44/39.20  | | | 
% 227.44/39.20  | | | COMBINE_EQS: (6), (58) imply:
% 227.44/39.20  | | |   (59)  all_55_13 = all_44_0
% 227.44/39.20  | | | 
% 227.44/39.20  | | | REDUCE: (11), (58) imply:
% 227.44/39.20  | | |   (60)   ~ (all_44_0 = e3)
% 227.44/39.20  | | | 
% 227.44/39.20  | | | REDUCE: (7), (58) imply:
% 227.44/39.20  | | |   (61)   ~ (all_44_0 = e0)
% 227.44/39.20  | | | 
% 227.44/39.20  | | | REDUCE: (10), (58) imply:
% 227.44/39.20  | | |   (62)  op(all_44_0, all_44_0) = e2
% 227.44/39.20  | | | 
% 227.44/39.20  | | | BETA: splitting (1) gives:
% 227.44/39.20  | | | 
% 227.44/39.20  | | | Case 1:
% 227.44/39.20  | | | | 
% 227.44/39.20  | | | |   (63)  all_55_13 = e3
% 227.44/39.20  | | | | 
% 227.44/39.20  | | | | COMBINE_EQS: (59), (63) imply:
% 227.44/39.20  | | | |   (64)  all_44_0 = e3
% 227.44/39.20  | | | | 
% 227.44/39.20  | | | | REDUCE: (60), (64) imply:
% 227.44/39.20  | | | |   (65)  $false
% 227.44/39.20  | | | | 
% 227.44/39.20  | | | | CLOSE: (65) is inconsistent.
% 227.44/39.20  | | | | 
% 227.44/39.20  | | | Case 2:
% 227.44/39.20  | | | | 
% 227.44/39.20  | | | |   (66)   ~ (all_55_13 = e3)
% 227.44/39.20  | | | |   (67)  all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 227.44/39.20  | | | | 
% 227.44/39.20  | | | | BETA: splitting (67) gives:
% 227.44/39.20  | | | | 
% 227.44/39.20  | | | | Case 1:
% 227.44/39.20  | | | | | 
% 227.44/39.20  | | | | |   (68)  all_55_13 = e2
% 227.44/39.20  | | | | | 
% 227.44/39.20  | | | | | COMBINE_EQS: (59), (68) imply:
% 227.44/39.20  | | | | |   (69)  all_44_0 = e2
% 227.44/39.20  | | | | | 
% 227.44/39.20  | | | | | REDUCE: (60), (69) imply:
% 227.44/39.20  | | | | |   (70)   ~ (e3 = e2)
% 227.44/39.20  | | | | | 
% 227.44/39.20  | | | | | SIMP: (70) implies:
% 227.44/39.20  | | | | |   (71)   ~ (e3 = e2)
% 227.44/39.20  | | | | | 
% 227.44/39.20  | | | | | REDUCE: (62), (69) imply:
% 227.44/39.20  | | | | |   (72)  op(e2, e2) = e2
% 227.44/39.20  | | | | | 
% 227.44/39.20  | | | | | REF_CLOSE: (5), (9), (71), (72) are inconsistent by sub-proof #2298.
% 227.44/39.20  | | | | | 
% 227.44/39.20  | | | | Case 2:
% 227.44/39.20  | | | | | 
% 227.44/39.20  | | | | |   (73)  all_55_13 = e1 | all_55_13 = e0
% 227.44/39.20  | | | | | 
% 227.44/39.20  | | | | | BETA: splitting (73) gives:
% 227.44/39.20  | | | | | 
% 227.44/39.20  | | | | | Case 1:
% 227.44/39.20  | | | | | | 
% 227.44/39.20  | | | | | |   (74)  all_55_13 = e1
% 227.44/39.20  | | | | | | 
% 227.44/39.20  | | | | | | COMBINE_EQS: (59), (74) imply:
% 227.44/39.20  | | | | | |   (75)  all_44_0 = e1
% 227.44/39.20  | | | | | | 
% 227.44/39.20  | | | | | | SIMP: (75) implies:
% 227.44/39.20  | | | | | |   (76)  all_44_0 = e1
% 227.44/39.20  | | | | | | 
% 227.44/39.20  | | | | | | REDUCE: (53), (76) imply:
% 227.44/39.20  | | | | | |   (77)  $false
% 227.44/39.20  | | | | | | 
% 227.44/39.20  | | | | | | CLOSE: (77) is inconsistent.
% 227.44/39.20  | | | | | | 
% 227.44/39.20  | | | | | Case 2:
% 227.44/39.20  | | | | | | 
% 227.44/39.20  | | | | | |   (78)  all_55_13 = e0
% 227.44/39.20  | | | | | | 
% 227.44/39.20  | | | | | | COMBINE_EQS: (59), (78) imply:
% 227.44/39.20  | | | | | |   (79)  all_44_0 = e0
% 227.44/39.20  | | | | | | 
% 227.44/39.20  | | | | | | SIMP: (79) implies:
% 227.44/39.20  | | | | | |   (80)  all_44_0 = e0
% 227.44/39.20  | | | | | | 
% 227.44/39.20  | | | | | | REDUCE: (61), (80) imply:
% 227.44/39.20  | | | | | |   (81)  $false
% 227.44/39.20  | | | | | | 
% 227.44/39.20  | | | | | | CLOSE: (81) is inconsistent.
% 227.44/39.20  | | | | | | 
% 227.44/39.20  | | | | | End of split
% 227.44/39.20  | | | | | 
% 227.44/39.20  | | | | End of split
% 227.44/39.20  | | | | 
% 227.44/39.20  | | | End of split
% 227.44/39.20  | | | 
% 227.44/39.20  | | Case 2:
% 227.44/39.20  | | | 
% 227.44/39.20  | | |   (82)   ~ (all_44_1 = e0) & op(e2, e3) = all_44_1 & $i(all_44_1)
% 227.44/39.20  | | | 
% 227.44/39.20  | | | ALPHA: (82) implies:
% 227.44/39.20  | | |   (83)   ~ (all_44_1 = e0)
% 227.44/39.20  | | |   (84)  op(e2, e3) = all_44_1
% 227.44/39.20  | | | 
% 227.44/39.20  | | | GROUND_INST: instantiating (5) with e0, all_44_1, e3, e2, simplifying with
% 227.44/39.20  | | |              (4), (84) gives:
% 227.44/39.20  | | |   (85)  all_44_1 = e0
% 227.44/39.20  | | | 
% 227.44/39.20  | | | REDUCE: (83), (85) imply:
% 227.44/39.20  | | |   (86)  $false
% 227.44/39.20  | | | 
% 227.44/39.20  | | | CLOSE: (86) is inconsistent.
% 227.44/39.20  | | | 
% 227.44/39.20  | | End of split
% 227.44/39.20  | | 
% 227.44/39.20  | End of split
% 227.44/39.20  | 
% 227.44/39.20  End of proof
% 227.44/39.20  
% 227.44/39.20  Sub-proof #253 shows that the following formulas are inconsistent:
% 227.44/39.20  ----------------------------------------------------------------
% 227.44/39.20    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.44/39.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.44/39.20    (2)  all_8_0 = e2
% 227.44/39.20    (3)  op(all_8_0, all_8_0) = e2
% 227.44/39.20    (4)  op(e2, e2) = e3
% 227.44/39.20    (5)   ~ (all_8_0 = e3)
% 227.44/39.20  
% 227.44/39.20  Begin of proof
% 227.44/39.20  | 
% 227.44/39.20  | REDUCE: (2), (5) imply:
% 227.44/39.20  |   (6)   ~ (e3 = e2)
% 227.44/39.20  | 
% 227.44/39.20  | SIMP: (6) implies:
% 227.44/39.20  |   (7)   ~ (e3 = e2)
% 227.44/39.20  | 
% 227.44/39.20  | REDUCE: (2), (3) imply:
% 227.44/39.20  |   (8)  op(e2, e2) = e2
% 227.44/39.20  | 
% 227.44/39.20  | REF_CLOSE: (1), (4), (7), (8) are inconsistent by sub-proof #2298.
% 227.44/39.20  | 
% 227.44/39.20  End of proof
% 227.44/39.20  
% 227.44/39.20  Sub-proof #254 shows that the following formulas are inconsistent:
% 227.44/39.20  ----------------------------------------------------------------
% 227.44/39.20    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.44/39.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.44/39.20    (2)   ~ (e3 = e0)
% 227.44/39.20    (3)  op(e3, e3) = e3
% 227.44/39.20    (4)  op(e1, e0) = e3
% 227.44/39.20    (5)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 &
% 227.44/39.20         op(all_52_17, all_52_17) = e3 & op(all_52_19, all_52_19) = e2 &
% 227.44/39.20         op(all_52_21, all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1,
% 227.44/39.20           e3) = all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 &
% 227.44/39.20         op(e1, e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 227.44/39.20         $i(all_52_23)
% 227.44/39.20  
% 227.44/39.20  Begin of proof
% 227.44/39.20  | 
% 227.44/39.20  | ALPHA: (5) implies:
% 227.44/39.20  |   (6)  op(e1, e0) = all_52_23
% 227.44/39.20  |   (7)  op(all_52_23, all_52_23) = e0
% 227.44/39.20  | 
% 227.44/39.20  | GROUND_INST: instantiating (1) with e3, all_52_23, e0, e1, simplifying with
% 227.44/39.20  |              (4), (6) gives:
% 227.44/39.20  |   (8)  all_52_23 = e3
% 227.44/39.20  | 
% 227.44/39.20  | REDUCE: (7), (8) imply:
% 227.44/39.20  |   (9)  op(e3, e3) = e0
% 227.44/39.20  | 
% 227.44/39.20  | REF_CLOSE: (1), (2), (3), (9) are inconsistent by sub-proof #2494.
% 227.44/39.20  | 
% 227.44/39.20  End of proof
% 227.44/39.20  
% 227.44/39.20  Sub-proof #255 shows that the following formulas are inconsistent:
% 227.44/39.20  ----------------------------------------------------------------
% 227.44/39.20    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.44/39.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.44/39.20    (2)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0 &
% 227.44/39.20         op(all_52_9, all_52_9) = e3 & op(all_52_11, all_52_11) = e2 &
% 227.44/39.20         op(all_52_13, all_52_13) = e1 & op(all_52_15, all_52_15) = e0 & op(e2,
% 227.44/39.20           e3) = all_52_9 & op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13 &
% 227.44/39.20         op(e2, e0) = all_52_15 & $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 227.44/39.20         $i(all_52_15)
% 227.44/39.20    (3)   ~ (e3 = e2)
% 227.44/39.20    (4)  op(e3, e3) = e3
% 227.44/39.20    (5)  op(e2, e2) = e3
% 227.44/39.20  
% 227.44/39.20  Begin of proof
% 227.44/39.20  | 
% 227.44/39.20  | ALPHA: (2) implies:
% 227.44/39.20  |   (6)  op(e2, e2) = all_52_11
% 227.44/39.20  |   (7)  op(all_52_11, all_52_11) = e2
% 227.44/39.20  | 
% 227.44/39.20  | GROUND_INST: instantiating (1) with e3, all_52_11, e2, e2, simplifying with
% 227.44/39.20  |              (5), (6) gives:
% 227.44/39.20  |   (8)  all_52_11 = e3
% 227.44/39.20  | 
% 227.44/39.20  | REDUCE: (7), (8) imply:
% 227.44/39.20  |   (9)  op(e3, e3) = e2
% 227.44/39.20  | 
% 227.44/39.20  | REF_CLOSE: (1), (3), (4), (9) are inconsistent by sub-proof #2490.
% 227.44/39.20  | 
% 227.44/39.20  End of proof
% 227.44/39.20  
% 227.44/39.20  Sub-proof #256 shows that the following formulas are inconsistent:
% 227.44/39.20  ----------------------------------------------------------------
% 227.44/39.20    (1)  op(e3, e1) = all_52_5
% 227.44/39.20    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.44/39.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.44/39.20    (3)  op(all_52_5, all_52_5) = e1
% 227.44/39.20    (4)  ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 & op(e1, e0) = all_24_1
% 227.44/39.20           & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 = e3) & op(e1, e0) =
% 227.44/39.20           all_24_1 & $i(all_24_1))
% 227.44/39.20    (5)  ( ~ (all_34_0 = e3) & op(all_34_1, e1) = all_34_0 & op(e1, e0) = all_34_1
% 227.44/39.20           & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 = e2) & op(e1, e0) =
% 227.44/39.20           all_34_1 & $i(all_34_1))
% 227.44/39.20    (6)   ~ (all_52_5 = e3)
% 227.44/39.20    (7)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 227.44/39.20    (8)  all_55_2 = all_52_5
% 227.44/39.20    (9)  op(e1, e1) = e0
% 227.44/39.20    (10)   ~ (all_52_5 = e0)
% 227.44/39.20    (11)  op(e1, e0) = e3
% 227.44/39.20  
% 227.44/39.20  Begin of proof
% 227.44/39.20  | 
% 227.44/39.20  | BETA: splitting (5) gives:
% 227.44/39.20  | 
% 227.44/39.20  | Case 1:
% 227.44/39.20  | | 
% 227.44/39.20  | |   (12)   ~ (all_34_0 = e3) & op(all_34_1, e1) = all_34_0 & op(e1, e0) =
% 227.44/39.20  | |         all_34_1 & $i(all_34_0) & $i(all_34_1)
% 227.44/39.20  | | 
% 227.44/39.20  | | ALPHA: (12) implies:
% 227.44/39.20  | |   (13)  op(e1, e0) = all_34_1
% 227.44/39.20  | |   (14)  op(all_34_1, e1) = all_34_0
% 227.44/39.20  | | 
% 227.44/39.20  | | GROUND_INST: instantiating (2) with e3, all_34_1, e0, e1, simplifying with
% 227.44/39.20  | |              (11), (13) gives:
% 227.44/39.20  | |   (15)  all_34_1 = e3
% 227.44/39.20  | | 
% 227.44/39.20  | | REDUCE: (14), (15) imply:
% 227.44/39.20  | |   (16)  op(e3, e1) = all_34_0
% 227.44/39.20  | | 
% 227.44/39.20  | | BETA: splitting (4) gives:
% 227.44/39.20  | | 
% 227.44/39.20  | | Case 1:
% 227.44/39.20  | | | 
% 227.44/39.20  | | |   (17)   ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 & op(e1, e0) =
% 227.44/39.20  | | |         all_24_1 & $i(all_24_0) & $i(all_24_1)
% 227.44/39.21  | | | 
% 227.44/39.21  | | | ALPHA: (17) implies:
% 227.44/39.21  | | |   (18)   ~ (all_24_0 = e2)
% 227.44/39.21  | | |   (19)  op(e1, e0) = all_24_1
% 227.44/39.21  | | |   (20)  op(all_24_1, e1) = all_24_0
% 227.44/39.21  | | | 
% 227.44/39.21  | | | GROUND_INST: instantiating (2) with e3, all_24_1, e0, e1, simplifying with
% 227.44/39.21  | | |              (11), (19) gives:
% 227.44/39.21  | | |   (21)  all_24_1 = e3
% 227.44/39.21  | | | 
% 227.44/39.21  | | | GROUND_INST: instantiating (2) with all_52_5, all_34_0, e1, e3,
% 227.44/39.21  | | |              simplifying with (1), (16) gives:
% 227.44/39.21  | | |   (22)  all_52_5 = all_34_0
% 227.44/39.21  | | | 
% 227.44/39.21  | | | COMBINE_EQS: (8), (22) imply:
% 227.44/39.21  | | |   (23)  all_55_2 = all_34_0
% 227.44/39.21  | | | 
% 227.44/39.21  | | | REDUCE: (6), (22) imply:
% 227.44/39.21  | | |   (24)   ~ (all_34_0 = e3)
% 227.44/39.21  | | | 
% 227.44/39.21  | | | REDUCE: (10), (22) imply:
% 227.44/39.21  | | |   (25)   ~ (all_34_0 = e0)
% 227.44/39.21  | | | 
% 227.44/39.21  | | | REDUCE: (3), (22) imply:
% 227.44/39.21  | | |   (26)  op(all_34_0, all_34_0) = e1
% 227.44/39.21  | | | 
% 227.44/39.21  | | | REDUCE: (20), (21) imply:
% 227.44/39.21  | | |   (27)  op(e3, e1) = all_24_0
% 227.44/39.21  | | | 
% 227.44/39.21  | | | GROUND_INST: instantiating (2) with all_34_0, all_24_0, e1, e3,
% 227.44/39.21  | | |              simplifying with (16), (27) gives:
% 227.44/39.21  | | |   (28)  all_34_0 = all_24_0
% 227.44/39.21  | | | 
% 227.44/39.21  | | | COMBINE_EQS: (23), (28) imply:
% 227.44/39.21  | | |   (29)  all_55_2 = all_24_0
% 227.44/39.21  | | | 
% 227.44/39.21  | | | REDUCE: (24), (28) imply:
% 227.44/39.21  | | |   (30)   ~ (all_24_0 = e3)
% 227.44/39.21  | | | 
% 227.44/39.21  | | | REDUCE: (25), (28) imply:
% 227.44/39.21  | | |   (31)   ~ (all_24_0 = e0)
% 227.44/39.21  | | | 
% 227.44/39.21  | | | REDUCE: (26), (28) imply:
% 227.44/39.21  | | |   (32)  op(all_24_0, all_24_0) = e1
% 227.44/39.21  | | | 
% 227.44/39.21  | | | BETA: splitting (7) gives:
% 227.44/39.21  | | | 
% 227.44/39.21  | | | Case 1:
% 227.44/39.21  | | | | 
% 227.44/39.21  | | | |   (33)  all_55_2 = e3
% 227.44/39.21  | | | | 
% 227.44/39.21  | | | | COMBINE_EQS: (29), (33) imply:
% 227.44/39.21  | | | |   (34)  all_24_0 = e3
% 227.44/39.21  | | | | 
% 227.44/39.21  | | | | REDUCE: (30), (34) imply:
% 227.44/39.21  | | | |   (35)  $false
% 227.44/39.21  | | | | 
% 227.44/39.21  | | | | CLOSE: (35) is inconsistent.
% 227.44/39.21  | | | | 
% 227.44/39.21  | | | Case 2:
% 227.44/39.21  | | | | 
% 227.44/39.21  | | | |   (36)  all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 227.44/39.21  | | | | 
% 227.44/39.21  | | | | REF_CLOSE: (2), (9), (18), (29), (31), (32), (36) are inconsistent by
% 227.44/39.21  | | | |            sub-proof #257.
% 227.44/39.21  | | | | 
% 227.44/39.21  | | | End of split
% 227.44/39.21  | | | 
% 227.44/39.21  | | Case 2:
% 227.44/39.21  | | | 
% 227.44/39.21  | | |   (37)   ~ (all_24_1 = e3) & op(e1, e0) = all_24_1 & $i(all_24_1)
% 227.44/39.21  | | | 
% 227.44/39.21  | | | ALPHA: (37) implies:
% 227.44/39.21  | | |   (38)   ~ (all_24_1 = e3)
% 227.44/39.21  | | |   (39)  op(e1, e0) = all_24_1
% 227.44/39.21  | | | 
% 227.44/39.21  | | | REF_CLOSE: (2), (11), (13), (38), (39) are inconsistent by sub-proof
% 227.44/39.21  | | |            #1961.
% 227.44/39.21  | | | 
% 227.44/39.21  | | End of split
% 227.44/39.21  | | 
% 227.44/39.21  | Case 2:
% 227.44/39.21  | | 
% 227.44/39.21  | |   (40)   ~ (all_34_1 = e2) & op(e1, e0) = all_34_1 & $i(all_34_1)
% 227.44/39.21  | | 
% 227.44/39.21  | | ALPHA: (40) implies:
% 227.44/39.21  | |   (41)  op(e1, e0) = all_34_1
% 227.44/39.21  | | 
% 227.44/39.21  | | GROUND_INST: instantiating (2) with e3, all_34_1, e0, e1, simplifying with
% 227.44/39.21  | |              (11), (41) gives:
% 227.44/39.21  | |   (42)  all_34_1 = e3
% 227.44/39.21  | | 
% 227.44/39.21  | | BETA: splitting (4) gives:
% 227.44/39.21  | | 
% 227.44/39.21  | | Case 1:
% 227.44/39.21  | | | 
% 227.44/39.21  | | |   (43)   ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 & op(e1, e0) =
% 227.44/39.21  | | |         all_24_1 & $i(all_24_0) & $i(all_24_1)
% 227.44/39.21  | | | 
% 227.44/39.21  | | | ALPHA: (43) implies:
% 227.44/39.21  | | |   (44)   ~ (all_24_0 = e2)
% 227.44/39.21  | | |   (45)  op(e1, e0) = all_24_1
% 227.44/39.21  | | |   (46)  op(all_24_1, e1) = all_24_0
% 227.44/39.21  | | | 
% 227.44/39.21  | | | GROUND_INST: instantiating (2) with e3, all_24_1, e0, e1, simplifying with
% 227.44/39.21  | | |              (11), (45) gives:
% 227.44/39.21  | | |   (47)  all_24_1 = e3
% 227.44/39.21  | | | 
% 227.44/39.21  | | | REDUCE: (46), (47) imply:
% 227.44/39.21  | | |   (48)  op(e3, e1) = all_24_0
% 227.44/39.21  | | | 
% 227.44/39.21  | | | GROUND_INST: instantiating (2) with all_52_5, all_24_0, e1, e3,
% 227.44/39.21  | | |              simplifying with (1), (48) gives:
% 227.44/39.21  | | |   (49)  all_52_5 = all_24_0
% 227.44/39.21  | | | 
% 227.44/39.21  | | | COMBINE_EQS: (8), (49) imply:
% 227.44/39.21  | | |   (50)  all_55_2 = all_24_0
% 227.44/39.21  | | | 
% 227.44/39.21  | | | REDUCE: (6), (49) imply:
% 227.44/39.21  | | |   (51)   ~ (all_24_0 = e3)
% 227.44/39.21  | | | 
% 227.44/39.21  | | | REDUCE: (10), (49) imply:
% 227.44/39.21  | | |   (52)   ~ (all_24_0 = e0)
% 227.44/39.21  | | | 
% 227.44/39.21  | | | REDUCE: (3), (49) imply:
% 227.44/39.21  | | |   (53)  op(all_24_0, all_24_0) = e1
% 227.44/39.21  | | | 
% 227.44/39.21  | | | BETA: splitting (7) gives:
% 227.44/39.21  | | | 
% 227.44/39.21  | | | Case 1:
% 227.44/39.21  | | | | 
% 227.44/39.21  | | | |   (54)  all_55_2 = e3
% 227.44/39.21  | | | | 
% 227.44/39.21  | | | | COMBINE_EQS: (50), (54) imply:
% 227.44/39.21  | | | |   (55)  all_24_0 = e3
% 227.44/39.21  | | | | 
% 227.44/39.21  | | | | REDUCE: (51), (55) imply:
% 227.44/39.21  | | | |   (56)  $false
% 227.44/39.21  | | | | 
% 227.44/39.21  | | | | CLOSE: (56) is inconsistent.
% 227.44/39.21  | | | | 
% 227.44/39.21  | | | Case 2:
% 227.44/39.21  | | | | 
% 227.44/39.21  | | | |   (57)  all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 227.44/39.21  | | | | 
% 227.44/39.21  | | | | REF_CLOSE: (2), (9), (44), (50), (52), (53), (57) are inconsistent by
% 227.44/39.21  | | | |            sub-proof #257.
% 227.44/39.21  | | | | 
% 227.44/39.21  | | | End of split
% 227.44/39.21  | | | 
% 227.44/39.21  | | Case 2:
% 227.44/39.21  | | | 
% 227.44/39.21  | | |   (58)   ~ (all_24_1 = e3) & op(e1, e0) = all_24_1 & $i(all_24_1)
% 227.44/39.21  | | | 
% 227.44/39.21  | | | ALPHA: (58) implies:
% 227.44/39.21  | | |   (59)   ~ (all_24_1 = e3)
% 227.44/39.21  | | |   (60)  op(e1, e0) = all_24_1
% 227.44/39.21  | | | 
% 227.44/39.21  | | | REF_CLOSE: (2), (11), (41), (59), (60) are inconsistent by sub-proof
% 227.44/39.21  | | |            #1961.
% 227.44/39.21  | | | 
% 227.44/39.21  | | End of split
% 227.44/39.21  | | 
% 227.44/39.21  | End of split
% 227.44/39.21  | 
% 227.44/39.21  End of proof
% 227.44/39.21  
% 227.44/39.21  Sub-proof #257 shows that the following formulas are inconsistent:
% 227.44/39.21  ----------------------------------------------------------------
% 227.44/39.21    (1)  op(all_24_0, all_24_0) = e1
% 227.44/39.21    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.44/39.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.44/39.21    (3)   ~ (all_24_0 = e0)
% 227.44/39.21    (4)   ~ (all_24_0 = e2)
% 227.44/39.21    (5)  all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 227.44/39.21    (6)  all_55_2 = all_24_0
% 227.44/39.21    (7)  op(e1, e1) = e0
% 227.44/39.21  
% 227.44/39.21  Begin of proof
% 227.44/39.21  | 
% 227.44/39.21  | BETA: splitting (5) gives:
% 227.44/39.21  | 
% 227.44/39.21  | Case 1:
% 227.44/39.21  | | 
% 227.44/39.21  | |   (8)  all_55_2 = e2
% 227.44/39.21  | | 
% 227.44/39.21  | | COMBINE_EQS: (6), (8) imply:
% 227.44/39.21  | |   (9)  all_24_0 = e2
% 227.44/39.21  | | 
% 227.44/39.21  | | REDUCE: (4), (9) imply:
% 227.44/39.21  | |   (10)  $false
% 227.44/39.21  | | 
% 227.44/39.21  | | CLOSE: (10) is inconsistent.
% 227.44/39.21  | | 
% 227.44/39.21  | Case 2:
% 227.44/39.21  | | 
% 227.44/39.21  | |   (11)  all_55_2 = e1 | all_55_2 = e0
% 227.44/39.21  | | 
% 227.44/39.21  | | BETA: splitting (11) gives:
% 227.44/39.21  | | 
% 227.44/39.21  | | Case 1:
% 227.44/39.21  | | | 
% 227.44/39.21  | | |   (12)  all_55_2 = e1
% 227.44/39.21  | | | 
% 227.44/39.21  | | | COMBINE_EQS: (6), (12) imply:
% 227.44/39.21  | | |   (13)  all_24_0 = e1
% 227.44/39.21  | | | 
% 227.44/39.21  | | | REDUCE: (3), (13) imply:
% 227.44/39.21  | | |   (14)   ~ (e1 = e0)
% 227.44/39.21  | | | 
% 227.44/39.21  | | | REDUCE: (1), (13) imply:
% 227.44/39.21  | | |   (15)  op(e1, e1) = e1
% 227.44/39.21  | | | 
% 227.44/39.21  | | | REF_CLOSE: (2), (7), (14), (15) are inconsistent by sub-proof #2427.
% 227.44/39.21  | | | 
% 227.44/39.21  | | Case 2:
% 227.44/39.21  | | | 
% 227.44/39.21  | | |   (16)  all_55_2 = e0
% 227.44/39.21  | | | 
% 227.44/39.21  | | | COMBINE_EQS: (6), (16) imply:
% 227.44/39.21  | | |   (17)  all_24_0 = e0
% 227.44/39.21  | | | 
% 227.44/39.21  | | | REDUCE: (3), (17) imply:
% 227.44/39.21  | | |   (18)  $false
% 227.44/39.21  | | | 
% 227.44/39.21  | | | CLOSE: (18) is inconsistent.
% 227.44/39.21  | | | 
% 227.44/39.21  | | End of split
% 227.44/39.21  | | 
% 227.44/39.21  | End of split
% 227.44/39.21  | 
% 227.44/39.21  End of proof
% 227.44/39.21  
% 227.44/39.21  Sub-proof #258 shows that the following formulas are inconsistent:
% 227.44/39.21  ----------------------------------------------------------------
% 227.44/39.21    (1)   ~ (all_52_7 = e3)
% 227.44/39.21    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.44/39.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.44/39.21    (3)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 227.44/39.21    (4)  op(all_52_7, all_52_7) = e0
% 227.44/39.21    (5)  all_55_3 = all_52_7
% 227.44/39.21    (6)  ( ~ (all_30_0 = e2) & op(all_30_1, e0) = all_30_0 & op(e0, e1) = all_30_1
% 227.44/39.21           & $i(all_30_0) & $i(all_30_1)) | ( ~ (all_30_1 = e3) & op(e0, e1) =
% 227.44/39.21           all_30_1 & $i(all_30_1))
% 227.44/39.21    (7)  op(e0, e1) = e3
% 227.44/39.21    (8)   ~ (all_52_7 = e1)
% 227.44/39.21    (9)  op(e0, e1) = all_40_1
% 227.44/39.21    (10)  op(e0, e0) = e1
% 227.44/39.21    (11)  op(e3, e0) = all_52_7
% 227.44/39.21  
% 227.44/39.21  Begin of proof
% 227.44/39.21  | 
% 227.44/39.21  | GROUND_INST: instantiating (2) with e3, all_40_1, e1, e0, simplifying with
% 227.44/39.21  |              (7), (9) gives:
% 227.44/39.21  |   (12)  all_40_1 = e3
% 227.44/39.21  | 
% 227.44/39.21  | BETA: splitting (6) gives:
% 227.44/39.21  | 
% 227.44/39.21  | Case 1:
% 227.44/39.21  | | 
% 227.44/39.21  | |   (13)   ~ (all_30_0 = e2) & op(all_30_1, e0) = all_30_0 & op(e0, e1) =
% 227.44/39.21  | |         all_30_1 & $i(all_30_0) & $i(all_30_1)
% 227.44/39.21  | | 
% 227.44/39.21  | | ALPHA: (13) implies:
% 227.44/39.21  | |   (14)   ~ (all_30_0 = e2)
% 227.44/39.21  | |   (15)  op(e0, e1) = all_30_1
% 227.44/39.21  | |   (16)  op(all_30_1, e0) = all_30_0
% 227.44/39.21  | | 
% 227.44/39.21  | | GROUND_INST: instantiating (2) with e3, all_30_1, e1, e0, simplifying with
% 227.44/39.21  | |              (7), (15) gives:
% 227.44/39.21  | |   (17)  all_30_1 = e3
% 227.44/39.21  | | 
% 227.44/39.21  | | REDUCE: (16), (17) imply:
% 227.44/39.21  | |   (18)  op(e3, e0) = all_30_0
% 227.44/39.21  | | 
% 227.44/39.21  | | GROUND_INST: instantiating (2) with all_52_7, all_30_0, e0, e3, simplifying
% 227.44/39.21  | |              with (11), (18) gives:
% 227.44/39.21  | |   (19)  all_52_7 = all_30_0
% 227.44/39.21  | | 
% 227.44/39.21  | | COMBINE_EQS: (5), (19) imply:
% 227.44/39.21  | |   (20)  all_55_3 = all_30_0
% 227.44/39.21  | | 
% 227.44/39.21  | | REDUCE: (1), (19) imply:
% 227.44/39.21  | |   (21)   ~ (all_30_0 = e3)
% 227.44/39.21  | | 
% 227.44/39.21  | | BETA: splitting (3) gives:
% 227.44/39.21  | | 
% 227.44/39.21  | | Case 1:
% 227.44/39.21  | | | 
% 227.44/39.21  | | |   (22)  all_55_3 = e3
% 227.44/39.21  | | | 
% 227.44/39.21  | | | COMBINE_EQS: (20), (22) imply:
% 227.44/39.21  | | |   (23)  all_30_0 = e3
% 227.44/39.21  | | | 
% 227.44/39.21  | | | REDUCE: (21), (23) imply:
% 227.44/39.21  | | |   (24)  $false
% 227.44/39.21  | | | 
% 227.44/39.21  | | | CLOSE: (24) is inconsistent.
% 227.44/39.21  | | | 
% 227.44/39.21  | | Case 2:
% 227.44/39.21  | | | 
% 227.44/39.21  | | |   (25)  all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 227.44/39.21  | | | 
% 227.44/39.21  | | | BETA: splitting (25) gives:
% 227.44/39.21  | | | 
% 227.44/39.21  | | | Case 1:
% 227.44/39.21  | | | | 
% 227.44/39.21  | | | |   (26)  all_55_3 = e2
% 227.44/39.21  | | | | 
% 227.44/39.21  | | | | COMBINE_EQS: (20), (26) imply:
% 227.44/39.21  | | | |   (27)  all_30_0 = e2
% 227.44/39.21  | | | | 
% 227.44/39.21  | | | | REDUCE: (14), (27) imply:
% 227.44/39.21  | | | |   (28)  $false
% 227.44/39.21  | | | | 
% 227.44/39.21  | | | | CLOSE: (28) is inconsistent.
% 227.44/39.21  | | | | 
% 227.44/39.21  | | | Case 2:
% 227.44/39.21  | | | | 
% 227.44/39.21  | | | |   (29)  all_55_3 = e1 | all_55_3 = e0
% 227.44/39.21  | | | | 
% 227.44/39.21  | | | | REF_CLOSE: (2), (4), (5), (8), (10), (11), (29) are inconsistent by
% 227.44/39.21  | | | |            sub-proof #259.
% 227.44/39.21  | | | | 
% 227.44/39.21  | | | End of split
% 227.44/39.21  | | | 
% 227.44/39.21  | | End of split
% 227.44/39.21  | | 
% 227.44/39.21  | Case 2:
% 227.44/39.21  | | 
% 227.44/39.21  | |   (30)   ~ (all_30_1 = e3) & op(e0, e1) = all_30_1 & $i(all_30_1)
% 227.44/39.21  | | 
% 227.44/39.21  | | ALPHA: (30) implies:
% 227.44/39.21  | |   (31)   ~ (all_30_1 = e3)
% 227.44/39.21  | |   (32)  op(e0, e1) = all_30_1
% 227.44/39.21  | | 
% 227.44/39.21  | | REF_CLOSE: (2), (7), (9), (31), (32) are inconsistent by sub-proof #1995.
% 227.44/39.21  | | 
% 227.44/39.21  | End of split
% 227.44/39.21  | 
% 227.44/39.21  End of proof
% 227.44/39.21  
% 227.44/39.21  Sub-proof #259 shows that the following formulas are inconsistent:
% 227.44/39.21  ----------------------------------------------------------------
% 227.44/39.21    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.44/39.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.44/39.21    (2)  op(all_52_7, all_52_7) = e0
% 227.44/39.21    (3)  all_55_3 = all_52_7
% 227.44/39.21    (4)   ~ (all_52_7 = e1)
% 227.44/39.21    (5)  all_55_3 = e1 | all_55_3 = e0
% 227.44/39.21    (6)  op(e0, e0) = e1
% 227.44/39.21    (7)  op(e3, e0) = all_52_7
% 227.44/39.21  
% 227.44/39.21  Begin of proof
% 227.44/39.21  | 
% 227.44/39.21  | BETA: splitting (5) gives:
% 227.44/39.21  | 
% 227.44/39.21  | Case 1:
% 227.44/39.21  | | 
% 227.44/39.21  | |   (8)  all_55_3 = e1
% 227.44/39.21  | | 
% 227.44/39.21  | | REF_CLOSE: (3), (4), (8) are inconsistent by sub-proof #1449.
% 227.44/39.21  | | 
% 227.44/39.21  | Case 2:
% 227.44/39.21  | | 
% 227.44/39.21  | |   (9)  all_55_3 = e0
% 227.44/39.21  | | 
% 227.44/39.21  | | COMBINE_EQS: (3), (9) imply:
% 227.44/39.21  | |   (10)  all_52_7 = e0
% 227.44/39.21  | | 
% 227.44/39.21  | | SIMP: (10) implies:
% 227.44/39.21  | |   (11)  all_52_7 = e0
% 227.44/39.21  | | 
% 227.44/39.21  | | REDUCE: (4), (11) imply:
% 227.44/39.21  | |   (12)   ~ (e1 = e0)
% 227.44/39.21  | | 
% 227.44/39.21  | | SIMP: (12) implies:
% 227.44/39.21  | |   (13)   ~ (e1 = e0)
% 227.44/39.21  | | 
% 227.44/39.21  | | REDUCE: (7), (11) imply:
% 227.44/39.21  | |   (14)  op(e3, e0) = e0
% 227.44/39.21  | | 
% 227.44/39.21  | | REF_CLOSE: (1), (2), (6), (7), (13), (14) are inconsistent by sub-proof
% 227.44/39.21  | |            #2000.
% 227.44/39.21  | | 
% 227.44/39.21  | End of split
% 227.44/39.21  | 
% 227.44/39.21  End of proof
% 227.44/39.21  
% 227.44/39.21  Sub-proof #260 shows that the following formulas are inconsistent:
% 227.44/39.21  ----------------------------------------------------------------
% 227.44/39.21    (1)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 227.44/39.21    (2)   ~ (e3 = e1)
% 227.44/39.21    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.44/39.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.44/39.21    (4)  op(e1, e1) = e2
% 227.44/39.21    (5)  all_57_11 = e3
% 227.44/39.21    (6)   ~ (e2 = e1)
% 227.44/39.21  
% 227.44/39.21  Begin of proof
% 227.44/39.21  | 
% 227.44/39.21  | BETA: splitting (1) gives:
% 227.44/39.21  | 
% 227.44/39.21  | Case 1:
% 227.44/39.21  | | 
% 227.44/39.21  | |   (7)  all_57_8 = e1 & op(e1, e1) = e1
% 227.44/39.21  | | 
% 227.44/39.21  | | ALPHA: (7) implies:
% 227.44/39.21  | |   (8)  op(e1, e1) = e1
% 227.44/39.21  | | 
% 227.44/39.21  | | REF_CLOSE: (3), (4), (6), (8) are inconsistent by sub-proof #2423.
% 227.44/39.21  | | 
% 227.44/39.21  | Case 2:
% 227.44/39.21  | | 
% 227.44/39.21  | |   (9)  all_57_11 = e1 & op(e1, e0) = e1
% 227.44/39.21  | | 
% 227.44/39.21  | | REF_CLOSE: (2), (5), (9) are inconsistent by sub-proof #2143.
% 227.44/39.21  | | 
% 227.44/39.21  | End of split
% 227.44/39.21  | 
% 227.44/39.21  End of proof
% 227.44/39.21  
% 227.44/39.21  Sub-proof #261 shows that the following formulas are inconsistent:
% 227.44/39.21  ----------------------------------------------------------------
% 227.44/39.21    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.44/39.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.44/39.21    (2)  all_57_7 = e1
% 227.44/39.21    (3)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 227.44/39.21    (4)   ~ (all_53_7 = e0)
% 227.44/39.21    (5)   ~ (e1 = e0)
% 227.44/39.21    (6)  op(e0, e2) = all_53_7
% 227.44/39.21  
% 227.44/39.21  Begin of proof
% 227.44/39.21  | 
% 227.44/39.21  | BETA: splitting (3) gives:
% 227.44/39.21  | 
% 227.44/39.21  | Case 1:
% 227.44/39.21  | | 
% 227.44/39.21  | |   (7)  all_57_7 = e0 & op(e1, e2) = e0
% 227.44/39.21  | | 
% 227.44/39.21  | | REF_CLOSE: (2), (5), (7) are inconsistent by sub-proof #509.
% 227.44/39.21  | | 
% 227.44/39.21  | Case 2:
% 227.44/39.21  | | 
% 227.44/39.21  | |   (8)  all_57_13 = e0 & op(e0, e2) = e0
% 227.44/39.21  | | 
% 227.44/39.21  | | ALPHA: (8) implies:
% 227.44/39.21  | |   (9)  op(e0, e2) = e0
% 227.44/39.21  | | 
% 227.44/39.21  | | REF_CLOSE: (1), (4), (6), (9) are inconsistent by sub-proof #2332.
% 227.44/39.21  | | 
% 227.44/39.21  | End of split
% 227.44/39.21  | 
% 227.44/39.21  End of proof
% 227.44/39.21  
% 227.44/39.21  Sub-proof #262 shows that the following formulas are inconsistent:
% 227.44/39.21  ----------------------------------------------------------------
% 227.44/39.21    (1)  all_57_3 = e0 & op(e2, e2) = e0
% 227.44/39.21    (2)  all_57_3 = e3
% 227.44/39.21    (3)   ~ (e3 = e0)
% 227.44/39.21  
% 227.44/39.21  Begin of proof
% 227.44/39.21  | 
% 227.44/39.21  | ALPHA: (1) implies:
% 227.44/39.21  |   (4)  all_57_3 = e0
% 227.44/39.21  | 
% 227.44/39.21  | COMBINE_EQS: (2), (4) imply:
% 227.44/39.21  |   (5)  e3 = e0
% 227.44/39.21  | 
% 227.44/39.21  | REDUCE: (3), (5) imply:
% 227.44/39.21  |   (6)  $false
% 227.44/39.21  | 
% 227.44/39.21  | CLOSE: (6) is inconsistent.
% 227.44/39.21  | 
% 227.44/39.21  End of proof
% 227.44/39.21  
% 227.44/39.21  Sub-proof #263 shows that the following formulas are inconsistent:
% 227.44/39.21  ----------------------------------------------------------------
% 227.44/39.21    (1)  op(e3, e1) = all_52_5
% 227.44/39.21    (2)   ~ (e3 = e1)
% 227.44/39.21    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.44/39.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.44/39.21    (4)  op(all_52_5, all_52_5) = e1
% 227.44/39.21    (5)  op(e3, e2) = all_52_3
% 227.44/39.21    (6)  op(all_52_3, all_52_3) = e2
% 227.44/39.21    (7)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 227.44/39.21         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 227.44/39.21    (8)   ~ (e3 = e0)
% 227.44/39.21    (9)  op(e3, e3) = e3
% 227.44/39.21    (10)  all_57_10 = e2
% 227.44/39.21    (11)   ~ (e2 = e0)
% 227.44/39.21    (12)   ~ (e1 = e0)
% 227.44/39.21    (13)  op(e0, e0) = e0
% 227.44/39.21    (14)  all_57_11 = e3
% 227.44/39.21    (15)   ~ (e2 = e1)
% 227.44/39.21    (16)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 227.44/39.21          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 227.44/39.21  
% 227.44/39.21  Begin of proof
% 227.44/39.21  | 
% 227.44/39.21  | BETA: splitting (16) gives:
% 227.44/39.21  | 
% 227.44/39.21  | Case 1:
% 227.44/39.21  | | 
% 227.44/39.21  | |   (17)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) =
% 227.44/39.21  | |           e1)
% 227.44/39.21  | | 
% 227.44/39.21  | | BETA: splitting (17) gives:
% 227.44/39.21  | | 
% 227.44/39.21  | | Case 1:
% 227.44/39.21  | | | 
% 227.44/39.21  | | |   (18)  all_57_9 = e1 & op(e3, e0) = e1
% 227.44/39.21  | | | 
% 227.44/39.21  | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13), (18)
% 227.44/39.21  | | |            are inconsistent by sub-proof #264.
% 227.44/39.21  | | | 
% 227.44/39.21  | | Case 2:
% 227.44/39.21  | | | 
% 227.44/39.21  | | |   (19)  all_57_10 = e1 & op(e2, e0) = e1
% 227.44/39.21  | | | 
% 227.44/39.21  | | | ALPHA: (19) implies:
% 227.44/39.21  | | |   (20)  all_57_10 = e1
% 227.44/39.21  | | | 
% 227.44/39.21  | | | REF_CLOSE: (10), (15), (20) are inconsistent by sub-proof #2144.
% 227.44/39.21  | | | 
% 227.44/39.21  | | End of split
% 227.44/39.21  | | 
% 227.44/39.21  | Case 2:
% 227.44/39.21  | | 
% 227.44/39.21  | |   (21)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 227.44/39.21  | |           e1)
% 227.44/39.21  | | 
% 227.44/39.21  | | REF_CLOSE: (2), (3), (12), (13), (14), (21) are inconsistent by sub-proof
% 227.44/39.21  | |            #1727.
% 227.44/39.21  | | 
% 227.44/39.21  | End of split
% 227.44/39.21  | 
% 227.44/39.21  End of proof
% 227.44/39.21  
% 227.44/39.21  Sub-proof #264 shows that the following formulas are inconsistent:
% 227.44/39.21  ----------------------------------------------------------------
% 227.44/39.21    (1)  op(e3, e1) = all_52_5
% 227.44/39.21    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.44/39.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.44/39.21    (3)  op(all_52_5, all_52_5) = e1
% 227.44/39.21    (4)  op(e3, e2) = all_52_3
% 227.44/39.21    (5)  op(all_52_3, all_52_3) = e2
% 227.44/39.21    (6)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 227.44/39.21         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 227.44/39.21    (7)   ~ (e3 = e0)
% 227.44/39.21    (8)  op(e3, e3) = e3
% 227.44/39.21    (9)   ~ (e2 = e0)
% 227.44/39.21    (10)   ~ (e1 = e0)
% 227.44/39.21    (11)  op(e0, e0) = e0
% 227.44/39.21    (12)  all_57_9 = e1 & op(e3, e0) = e1
% 227.44/39.21  
% 227.44/39.21  Begin of proof
% 227.44/39.21  | 
% 227.44/39.21  | ALPHA: (12) implies:
% 227.44/39.21  |   (13)  all_57_9 = e1
% 227.44/39.21  | 
% 227.44/39.21  | BETA: splitting (6) gives:
% 227.44/39.21  | 
% 227.44/39.21  | Case 1:
% 227.44/39.21  | | 
% 227.44/39.21  | |   (14)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) =
% 227.44/39.21  | |           e0)
% 227.44/39.21  | | 
% 227.44/39.21  | | REF_CLOSE: (2), (4), (5), (7), (8), (9), (11), (14) are inconsistent by
% 227.44/39.21  | |            sub-proof #266.
% 227.44/39.21  | | 
% 227.44/39.21  | Case 2:
% 227.44/39.21  | | 
% 227.44/39.21  | |   (15)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) =
% 227.44/39.21  | |           e0)
% 227.44/39.21  | | 
% 227.44/39.21  | | BETA: splitting (15) gives:
% 227.44/39.21  | | 
% 227.44/39.21  | | Case 1:
% 227.44/39.21  | | | 
% 227.44/39.21  | | |   (16)  all_57_4 = e0 & op(e3, e1) = e0
% 227.44/39.21  | | | 
% 227.44/39.21  | | | ALPHA: (16) implies:
% 227.44/39.21  | | |   (17)  op(e3, e1) = e0
% 227.44/39.21  | | | 
% 227.44/39.21  | | | REF_CLOSE: (1), (2), (3), (10), (11), (17) are inconsistent by sub-proof
% 227.44/39.21  | | |            #2167.
% 227.44/39.21  | | | 
% 227.44/39.21  | | Case 2:
% 227.44/39.21  | | | 
% 227.44/39.21  | | |   (18)  all_57_9 = e0 & op(e3, e0) = e0
% 227.44/39.21  | | | 
% 227.44/39.21  | | | REF_CLOSE: (10), (13), (18) are inconsistent by sub-proof #1990.
% 227.44/39.21  | | | 
% 227.44/39.21  | | End of split
% 227.44/39.21  | | 
% 227.44/39.21  | End of split
% 227.44/39.21  | 
% 227.44/39.21  End of proof
% 227.44/39.21  
% 227.44/39.21  Sub-proof #265 shows that the following formulas are inconsistent:
% 227.44/39.21  ----------------------------------------------------------------
% 227.44/39.21    (1)   ~ (e3 = e1)
% 227.44/39.21    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.44/39.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.44/39.21    (3)   ~ (all_6_2 = e3)
% 227.44/39.21    (4)  op(e1, e1) = all_6_2
% 227.44/39.21    (5)  all_57_4 = e2
% 227.44/39.21    (6)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 227.44/39.21         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 227.44/39.21    (7)   ~ (e3 = e2)
% 227.44/39.21    (8)   ~ (e3 = e0)
% 227.44/39.21    (9)  all_57_2 = e2 & op(e2, e3) = e2
% 227.44/39.21    (10)  op(e1, e1) = e1
% 227.44/39.21    (11)   ~ (e2 = e0)
% 227.44/39.21    (12)   ~ (e1 = e0)
% 227.44/39.21    (13)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 227.44/39.21          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 227.44/39.21    (14)  all_57_2 = e1
% 227.44/39.21    (15)   ~ (e2 = e1)
% 227.44/39.21    (16)   ~ (all_6_2 = e0)
% 227.44/39.21    (17)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 227.44/39.21          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 227.44/39.21  
% 227.44/39.21  Begin of proof
% 227.44/39.21  | 
% 227.44/39.21  | ALPHA: (9) implies:
% 227.44/39.21  |   (18)  all_57_2 = e2
% 227.44/39.21  | 
% 227.44/39.21  | COMBINE_EQS: (14), (18) imply:
% 227.44/39.21  |   (19)  e2 = e1
% 227.44/39.21  | 
% 227.44/39.21  | SIMP: (19) implies:
% 227.44/39.21  |   (20)  e2 = e1
% 227.44/39.21  | 
% 227.44/39.21  | COMBINE_EQS: (5), (20) imply:
% 227.44/39.21  |   (21)  all_57_4 = e1
% 227.44/39.21  | 
% 227.44/39.21  | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (10), (11), (12), (13), (15),
% 227.44/39.21  |            (16), (17), (21) are inconsistent by sub-proof #2407.
% 227.44/39.21  | 
% 227.44/39.21  End of proof
% 227.44/39.21  
% 227.44/39.21  Sub-proof #266 shows that the following formulas are inconsistent:
% 227.44/39.21  ----------------------------------------------------------------
% 227.44/39.21    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.44/39.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.44/39.21    (2)  op(e3, e2) = all_52_3
% 227.44/39.21    (3)  op(all_52_3, all_52_3) = e2
% 227.44/39.21    (4)   ~ (e3 = e0)
% 227.44/39.21    (5)  op(e3, e3) = e3
% 227.44/39.21    (6)   ~ (e2 = e0)
% 227.44/39.21    (7)  op(e0, e0) = e0
% 227.44/39.21    (8)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0)
% 227.44/39.21  
% 227.44/39.21  Begin of proof
% 227.44/39.21  | 
% 227.44/39.21  | BETA: splitting (8) gives:
% 227.44/39.21  | 
% 227.44/39.21  | Case 1:
% 227.44/39.21  | | 
% 227.44/39.21  | |   (9)  all_57_0 = e0 & op(e3, e3) = e0
% 227.44/39.21  | | 
% 227.44/39.21  | | ALPHA: (9) implies:
% 227.44/39.21  | |   (10)  op(e3, e3) = e0
% 227.44/39.21  | | 
% 227.44/39.21  | | REF_CLOSE: (1), (4), (5), (10) are inconsistent by sub-proof #2494.
% 227.44/39.21  | | 
% 227.44/39.21  | Case 2:
% 227.44/39.21  | | 
% 227.44/39.21  | |   (11)  all_57_1 = e0 & op(e3, e2) = e0
% 227.44/39.21  | | 
% 227.44/39.21  | | ALPHA: (11) implies:
% 227.44/39.21  | |   (12)  op(e3, e2) = e0
% 227.44/39.21  | | 
% 227.44/39.21  | | REF_CLOSE: (1), (2), (3), (6), (7), (12) are inconsistent by sub-proof
% 227.44/39.21  | |            #2399.
% 227.44/39.21  | | 
% 227.44/39.21  | End of split
% 227.44/39.21  | 
% 227.44/39.21  End of proof
% 227.44/39.21  
% 227.44/39.21  Sub-proof #267 shows that the following formulas are inconsistent:
% 227.44/39.21  ----------------------------------------------------------------
% 227.44/39.21    (1)  all_57_7 = e3 & op(e1, e2) = e3
% 227.44/39.21    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.44/39.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.44/39.21    (3)  op(e1, e2) = all_53_6
% 227.44/39.21    (4)   ~ (all_53_6 = e3)
% 227.44/39.21  
% 227.44/39.21  Begin of proof
% 227.44/39.21  | 
% 227.44/39.21  | ALPHA: (1) implies:
% 227.44/39.21  |   (5)  op(e1, e2) = e3
% 227.44/39.21  | 
% 227.44/39.21  | GROUND_INST: instantiating (2) with all_53_6, e3, e2, e1, simplifying with
% 227.44/39.21  |              (3), (5) gives:
% 227.44/39.21  |   (6)  all_53_6 = e3
% 227.44/39.21  | 
% 227.44/39.21  | REDUCE: (4), (6) imply:
% 227.44/39.21  |   (7)  $false
% 227.44/39.21  | 
% 227.44/39.21  | CLOSE: (7) is inconsistent.
% 227.44/39.21  | 
% 227.44/39.21  End of proof
% 227.44/39.21  
% 227.44/39.21  Sub-proof #268 shows that the following formulas are inconsistent:
% 227.44/39.21  ----------------------------------------------------------------
% 227.44/39.21    (1)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 227.44/39.21         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 227.44/39.21    (2)   ~ (e3 = e1)
% 227.44/39.21    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.44/39.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.44/39.21    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 227.44/39.21         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 227.44/39.21    (5)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 227.44/39.21         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 227.44/39.21    (6)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 227.44/39.21         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 227.44/39.21    (7)   ~ (e3 = e2)
% 227.44/39.21    (8)   ~ (e3 = e0)
% 227.44/39.21    (9)  op(e3, e3) = e3
% 227.44/39.21    (10)  op(e3, e2) = all_53_4
% 227.44/39.21    (11)   ~ (e2 = e0)
% 227.44/39.22    (12)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 227.44/39.22          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 227.44/39.22    (13)   ~ (e1 = e0)
% 227.44/39.22    (14)  all_57_6 = e3
% 227.44/39.22    (15)   ~ (all_53_12 = e3)
% 227.44/39.22    (16)   ~ (e2 = e1)
% 227.44/39.22    (17)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 227.44/39.22          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 227.44/39.22    (18)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 227.44/39.22          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 227.44/39.22    (19)   ~ (all_53_4 = e3)
% 227.44/39.22    (20)  op(e3, e0) = all_53_12
% 227.44/39.22  
% 227.44/39.22  Begin of proof
% 227.44/39.22  | 
% 227.44/39.22  | BETA: splitting (12) gives:
% 227.44/39.22  | 
% 227.44/39.22  | Case 1:
% 227.44/39.22  | | 
% 227.44/39.22  | |   (21)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) =
% 227.44/39.22  | |           e3)
% 227.44/39.22  | | 
% 227.44/39.22  | | REF_CLOSE: (1), (2), (3), (7), (8), (10), (11), (13), (14), (16), (17),
% 227.44/39.22  | |            (18), (19), (21) are inconsistent by sub-proof #269.
% 227.44/39.22  | | 
% 227.44/39.22  | Case 2:
% 227.44/39.22  | | 
% 227.44/39.22  | |   (22)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) =
% 227.44/39.22  | |           e3)
% 227.44/39.22  | | 
% 227.44/39.22  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (11), (13), (15), (16),
% 227.44/39.22  | |            (20), (22) are inconsistent by sub-proof #1955.
% 227.44/39.22  | | 
% 227.44/39.22  | End of split
% 227.44/39.22  | 
% 227.44/39.22  End of proof
% 227.44/39.22  
% 227.44/39.22  Sub-proof #269 shows that the following formulas are inconsistent:
% 227.44/39.22  ----------------------------------------------------------------
% 227.44/39.22    (1)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 227.44/39.22         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 227.44/39.22    (2)   ~ (e3 = e1)
% 227.44/39.22    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.44/39.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.44/39.22    (4)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3)
% 227.44/39.22    (5)   ~ (e3 = e2)
% 227.44/39.22    (6)   ~ (e3 = e0)
% 227.44/39.22    (7)  op(e3, e2) = all_53_4
% 227.44/39.22    (8)   ~ (e2 = e0)
% 227.44/39.22    (9)   ~ (e1 = e0)
% 227.44/39.22    (10)  all_57_6 = e3
% 227.44/39.22    (11)   ~ (e2 = e1)
% 227.44/39.22    (12)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 227.44/39.22          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 227.44/39.22    (13)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 227.44/39.22          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 227.44/39.22    (14)   ~ (all_53_4 = e3)
% 227.44/39.22  
% 227.44/39.22  Begin of proof
% 227.44/39.22  | 
% 227.44/39.22  | BETA: splitting (4) gives:
% 227.44/39.22  | 
% 227.44/39.22  | Case 1:
% 227.44/39.22  | | 
% 227.44/39.22  | |   (15)  all_57_0 = e3 & op(e3, e3) = e3
% 227.44/39.22  | | 
% 227.44/39.22  | | ALPHA: (15) implies:
% 227.44/39.22  | |   (16)  all_57_0 = e3
% 227.44/39.22  | | 
% 227.44/39.22  | | REF_CLOSE: (1), (2), (5), (6), (8), (9), (10), (11), (12), (13), (16) are
% 227.44/39.22  | |            inconsistent by sub-proof #2010.
% 227.44/39.22  | | 
% 227.44/39.22  | Case 2:
% 227.44/39.22  | | 
% 227.44/39.22  | |   (17)  all_57_1 = e3 & op(e3, e2) = e3
% 227.44/39.22  | | 
% 227.44/39.22  | | REF_CLOSE: (3), (7), (14), (17) are inconsistent by sub-proof #2286.
% 227.44/39.22  | | 
% 227.44/39.22  | End of split
% 227.44/39.22  | 
% 227.44/39.22  End of proof
% 227.44/39.22  
% 227.44/39.22  Sub-proof #270 shows that the following formulas are inconsistent:
% 227.44/39.22  ----------------------------------------------------------------
% 227.44/39.22    (1)  all_57_5 = e3 & op(e2, e1) = e3
% 227.44/39.22    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.44/39.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.44/39.22    (3)  op(e2, e1) = all_53_9
% 227.44/39.22    (4)   ~ (all_53_9 = e3)
% 227.44/39.22  
% 227.44/39.22  Begin of proof
% 227.44/39.22  | 
% 227.44/39.22  | ALPHA: (1) implies:
% 227.44/39.22  |   (5)  op(e2, e1) = e3
% 227.44/39.22  | 
% 227.44/39.22  | GROUND_INST: instantiating (2) with all_53_9, e3, e1, e2, simplifying with
% 227.44/39.22  |              (3), (5) gives:
% 227.44/39.22  |   (6)  all_53_9 = e3
% 227.44/39.22  | 
% 227.44/39.22  | REDUCE: (4), (6) imply:
% 227.44/39.22  |   (7)  $false
% 227.44/39.22  | 
% 227.44/39.22  | CLOSE: (7) is inconsistent.
% 227.44/39.22  | 
% 227.44/39.22  End of proof
% 227.44/39.22  
% 227.44/39.22  Sub-proof #271 shows that the following formulas are inconsistent:
% 227.44/39.22  ----------------------------------------------------------------
% 227.44/39.22    (1)  ( ~ (all_50_0 = e3) & op(all_50_1, e2) = all_50_0 & op(e2, e0) = all_50_1
% 227.44/39.22           & $i(all_50_0) & $i(all_50_1)) | ( ~ (all_50_1 = e1) & op(e2, e0) =
% 227.44/39.22           all_50_1 & $i(all_50_1))
% 227.44/39.22    (2)  ( ~ (all_14_0 = e1) & op(all_14_1, e2) = all_14_0 & op(e2, e0) = all_14_1
% 227.44/39.22           & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e3) & op(e2, e0) =
% 227.44/39.22           all_14_1 & $i(all_14_1))
% 227.44/39.22    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.44/39.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.44/39.22    (4)  all_55_9 = all_52_19
% 227.44/39.22    (5)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 227.44/39.22    (6)  op(e2, e2) = e0
% 227.44/39.22    (7)  op(e2, e0) = e1
% 227.44/39.22    (8)   ~ (all_52_19 = e0)
% 227.44/39.22    (9)  op(e1, e2) = all_52_19
% 227.44/39.22    (10)  op(all_52_19, all_52_19) = e2
% 227.44/39.22    (11)   ~ (all_52_19 = e1)
% 227.44/39.22  
% 227.44/39.22  Begin of proof
% 227.44/39.22  | 
% 227.44/39.22  | BETA: splitting (1) gives:
% 227.44/39.22  | 
% 227.44/39.22  | Case 1:
% 227.44/39.22  | | 
% 227.44/39.22  | |   (12)   ~ (all_50_0 = e3) & op(all_50_1, e2) = all_50_0 & op(e2, e0) =
% 227.44/39.22  | |         all_50_1 & $i(all_50_0) & $i(all_50_1)
% 227.44/39.22  | | 
% 227.44/39.22  | | ALPHA: (12) implies:
% 227.44/39.22  | |   (13)   ~ (all_50_0 = e3)
% 227.44/39.22  | |   (14)  op(e2, e0) = all_50_1
% 227.44/39.22  | |   (15)  op(all_50_1, e2) = all_50_0
% 227.44/39.22  | | 
% 227.44/39.22  | | BETA: splitting (2) gives:
% 227.44/39.22  | | 
% 227.44/39.22  | | Case 1:
% 227.44/39.22  | | | 
% 227.44/39.22  | | |   (16)   ~ (all_14_0 = e1) & op(all_14_1, e2) = all_14_0 & op(e2, e0) =
% 227.44/39.22  | | |         all_14_1 & $i(all_14_0) & $i(all_14_1)
% 227.44/39.22  | | | 
% 227.44/39.22  | | | ALPHA: (16) implies:
% 227.44/39.22  | | |   (17)  op(e2, e0) = all_14_1
% 227.44/39.22  | | | 
% 227.44/39.22  | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (10), (11), (13), (14),
% 227.44/39.22  | | |            (15), (17) are inconsistent by sub-proof #274.
% 227.44/39.22  | | | 
% 227.44/39.22  | | Case 2:
% 227.44/39.22  | | | 
% 227.44/39.22  | | |   (18)   ~ (all_14_1 = e3) & op(e2, e0) = all_14_1 & $i(all_14_1)
% 227.44/39.22  | | | 
% 227.44/39.22  | | | ALPHA: (18) implies:
% 227.44/39.22  | | |   (19)  op(e2, e0) = all_14_1
% 227.44/39.22  | | | 
% 227.44/39.22  | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (10), (11), (13), (14),
% 227.44/39.22  | | |            (15), (19) are inconsistent by sub-proof #274.
% 227.44/39.22  | | | 
% 227.44/39.22  | | End of split
% 227.44/39.22  | | 
% 227.44/39.22  | Case 2:
% 227.44/39.22  | | 
% 227.44/39.22  | |   (20)   ~ (all_50_1 = e1) & op(e2, e0) = all_50_1 & $i(all_50_1)
% 227.44/39.22  | | 
% 227.44/39.22  | | REF_CLOSE: (2), (3), (7), (20) are inconsistent by sub-proof #272.
% 227.44/39.22  | | 
% 227.44/39.22  | End of split
% 227.44/39.22  | 
% 227.44/39.22  End of proof
% 227.44/39.22  
% 227.44/39.22  Sub-proof #272 shows that the following formulas are inconsistent:
% 227.44/39.22  ----------------------------------------------------------------
% 227.44/39.22    (1)   ~ (all_50_1 = e1) & op(e2, e0) = all_50_1 & $i(all_50_1)
% 227.44/39.22    (2)  ( ~ (all_14_0 = e1) & op(all_14_1, e2) = all_14_0 & op(e2, e0) = all_14_1
% 227.44/39.22           & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e3) & op(e2, e0) =
% 227.44/39.22           all_14_1 & $i(all_14_1))
% 227.44/39.22    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.44/39.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.44/39.22    (4)  op(e2, e0) = e1
% 227.44/39.22  
% 227.44/39.22  Begin of proof
% 227.44/39.22  | 
% 227.44/39.22  | ALPHA: (1) implies:
% 227.44/39.22  |   (5)   ~ (all_50_1 = e1)
% 227.44/39.22  |   (6)  op(e2, e0) = all_50_1
% 227.44/39.22  | 
% 227.44/39.22  | BETA: splitting (2) gives:
% 227.44/39.22  | 
% 227.44/39.22  | Case 1:
% 227.44/39.22  | | 
% 227.44/39.22  | |   (7)   ~ (all_14_0 = e1) & op(all_14_1, e2) = all_14_0 & op(e2, e0) =
% 227.44/39.22  | |        all_14_1 & $i(all_14_0) & $i(all_14_1)
% 227.44/39.22  | | 
% 227.44/39.22  | | ALPHA: (7) implies:
% 227.44/39.22  | |   (8)  op(e2, e0) = all_14_1
% 227.44/39.22  | | 
% 227.44/39.22  | | REF_CLOSE: (3), (4), (5), (6), (8) are inconsistent by sub-proof #273.
% 227.44/39.22  | | 
% 227.44/39.22  | Case 2:
% 227.44/39.22  | | 
% 227.44/39.22  | |   (9)   ~ (all_14_1 = e3) & op(e2, e0) = all_14_1 & $i(all_14_1)
% 227.44/39.22  | | 
% 227.44/39.22  | | ALPHA: (9) implies:
% 227.44/39.22  | |   (10)  op(e2, e0) = all_14_1
% 227.44/39.22  | | 
% 227.44/39.22  | | REF_CLOSE: (3), (4), (5), (6), (10) are inconsistent by sub-proof #273.
% 227.44/39.22  | | 
% 227.44/39.22  | End of split
% 227.44/39.22  | 
% 227.44/39.22  End of proof
% 227.44/39.22  
% 227.59/39.22  Sub-proof #273 shows that the following formulas are inconsistent:
% 227.59/39.22  ----------------------------------------------------------------
% 227.59/39.22    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.59/39.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.59/39.22    (2)   ~ (all_50_1 = e1)
% 227.59/39.22    (3)  op(e2, e0) = e1
% 227.59/39.22    (4)  op(e2, e0) = all_14_1
% 227.59/39.22    (5)  op(e2, e0) = all_50_1
% 227.59/39.22  
% 227.59/39.22  Begin of proof
% 227.59/39.22  | 
% 227.59/39.22  | GROUND_INST: instantiating (1) with all_14_1, all_50_1, e0, e2, simplifying
% 227.59/39.22  |              with (4), (5) gives:
% 227.59/39.22  |   (6)  all_50_1 = all_14_1
% 227.59/39.22  | 
% 227.59/39.22  | GROUND_INST: instantiating (1) with e1, all_50_1, e0, e2, simplifying with
% 227.59/39.22  |              (3), (5) gives:
% 227.59/39.22  |   (7)  all_50_1 = e1
% 227.59/39.22  | 
% 227.59/39.22  | COMBINE_EQS: (6), (7) imply:
% 227.59/39.22  |   (8)  all_14_1 = e1
% 227.59/39.22  | 
% 227.59/39.22  | REDUCE: (2), (7) imply:
% 227.59/39.22  |   (9)  $false
% 227.59/39.22  | 
% 227.59/39.22  | CLOSE: (9) is inconsistent.
% 227.59/39.22  | 
% 227.59/39.22  End of proof
% 227.59/39.22  
% 227.59/39.22  Sub-proof #274 shows that the following formulas are inconsistent:
% 227.59/39.22  ----------------------------------------------------------------
% 227.59/39.22    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.59/39.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.59/39.22    (2)  op(all_50_1, e2) = all_50_0
% 227.59/39.22    (3)  all_55_9 = all_52_19
% 227.59/39.22    (4)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 227.59/39.22    (5)  op(e2, e2) = e0
% 227.59/39.22    (6)  op(e2, e0) = e1
% 227.59/39.22    (7)  op(e2, e0) = all_14_1
% 227.59/39.22    (8)   ~ (all_52_19 = e0)
% 227.59/39.22    (9)  op(e1, e2) = all_52_19
% 227.59/39.22    (10)  op(all_52_19, all_52_19) = e2
% 227.59/39.22    (11)   ~ (all_50_0 = e3)
% 227.59/39.22    (12)  op(e2, e0) = all_50_1
% 227.59/39.22    (13)   ~ (all_52_19 = e1)
% 227.59/39.22  
% 227.59/39.22  Begin of proof
% 227.59/39.22  | 
% 227.59/39.22  | GROUND_INST: instantiating (1) with e1, all_50_1, e0, e2, simplifying with
% 227.59/39.22  |              (6), (12) gives:
% 227.59/39.22  |   (14)  all_50_1 = e1
% 227.59/39.22  | 
% 227.59/39.22  | GROUND_INST: instantiating (1) with all_14_1, all_50_1, e0, e2, simplifying
% 227.59/39.22  |              with (7), (12) gives:
% 227.59/39.22  |   (15)  all_50_1 = all_14_1
% 227.59/39.22  | 
% 227.59/39.22  | COMBINE_EQS: (14), (15) imply:
% 227.59/39.22  |   (16)  all_14_1 = e1
% 227.59/39.22  | 
% 227.59/39.22  | REDUCE: (2), (14) imply:
% 227.59/39.22  |   (17)  op(e1, e2) = all_50_0
% 227.59/39.22  | 
% 227.59/39.22  | GROUND_INST: instantiating (1) with all_52_19, all_50_0, e2, e1, simplifying
% 227.59/39.22  |              with (9), (17) gives:
% 227.59/39.22  |   (18)  all_52_19 = all_50_0
% 227.59/39.22  | 
% 227.59/39.22  | COMBINE_EQS: (3), (18) imply:
% 227.59/39.22  |   (19)  all_55_9 = all_50_0
% 227.59/39.22  | 
% 227.59/39.22  | BETA: splitting (4) gives:
% 227.59/39.22  | 
% 227.59/39.22  | Case 1:
% 227.59/39.22  | | 
% 227.59/39.22  | |   (20)  all_55_9 = e3
% 227.59/39.22  | | 
% 227.59/39.22  | | COMBINE_EQS: (19), (20) imply:
% 227.59/39.22  | |   (21)  all_50_0 = e3
% 227.59/39.22  | | 
% 227.59/39.22  | | SIMP: (21) implies:
% 227.59/39.22  | |   (22)  all_50_0 = e3
% 227.59/39.22  | | 
% 227.59/39.22  | | REDUCE: (11), (22) imply:
% 227.59/39.22  | |   (23)  $false
% 227.59/39.22  | | 
% 227.59/39.22  | | CLOSE: (23) is inconsistent.
% 227.59/39.22  | | 
% 227.59/39.22  | Case 2:
% 227.59/39.22  | | 
% 227.59/39.22  | |   (24)  all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 227.59/39.22  | | 
% 227.59/39.22  | | REF_CLOSE: (1), (3), (5), (8), (10), (13), (24) are inconsistent by
% 227.59/39.22  | |            sub-proof #1371.
% 227.59/39.22  | | 
% 227.59/39.22  | End of split
% 227.59/39.22  | 
% 227.59/39.22  End of proof
% 227.59/39.22  
% 227.59/39.22  Sub-proof #275 shows that the following formulas are inconsistent:
% 227.59/39.22  ----------------------------------------------------------------
% 227.59/39.22    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 227.59/39.22         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.59/39.22    (2)   ~ (e3 = e1)
% 227.59/39.22    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.59/39.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.59/39.22    (4)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 227.59/39.22         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 227.59/39.22    (5)   ~ (all_6_2 = e3)
% 227.59/39.22    (6)  op(e1, e1) = all_6_2
% 227.59/39.22    (7)  all_57_7 = e2
% 227.59/39.22    (8)   ~ (e3 = e2)
% 227.59/39.22    (9)   ~ (e3 = e0)
% 227.59/39.22    (10)  all_57_15 = e3
% 227.59/39.22    (11)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 227.59/39.22          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 227.59/39.22            e1)
% 227.59/39.22    (12)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 227.59/39.22          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 227.59/39.22    (13)   ~ (e2 = e0)
% 227.59/39.22    (14)  op(e2, e2) = e2
% 227.59/39.22    (15)   ~ (e1 = e0)
% 227.59/39.22    (16)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 227.59/39.22          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 227.59/39.22    (17)  op(e0, e0) = e3
% 227.59/39.22    (18)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.59/39.22          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 227.59/39.22            e2)
% 227.59/39.22    (19)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 227.59/39.22              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 227.59/39.22                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 227.59/39.22                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 227.59/39.22    (20)   ~ (e2 = e1)
% 227.59/39.22    (21)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 227.59/39.22          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 227.59/39.22    (22)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 227.59/39.22          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 227.59/39.22    (23)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 227.59/39.22          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 227.59/39.22  
% 227.59/39.22  Begin of proof
% 227.59/39.22  | 
% 227.59/39.22  | BETA: splitting (23) gives:
% 227.59/39.22  | 
% 227.59/39.22  | Case 1:
% 227.59/39.22  | | 
% 227.59/39.22  | |   (24)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) =
% 227.59/39.22  | |           e1)
% 227.59/39.22  | | 
% 227.59/39.22  | | BETA: splitting (24) gives:
% 227.59/39.22  | | 
% 227.59/39.22  | | Case 1:
% 227.59/39.22  | | | 
% 227.59/39.22  | | |   (25)  all_57_1 = e1 & op(e3, e2) = e1
% 227.59/39.22  | | | 
% 227.59/39.22  | | | ALPHA: (25) implies:
% 227.59/39.22  | | |   (26)  all_57_1 = e1
% 227.59/39.22  | | | 
% 227.59/39.22  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 227.59/39.22  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 227.59/39.22  | | |            (23), (26) are inconsistent by sub-proof #289.
% 227.59/39.22  | | | 
% 227.59/39.22  | | Case 2:
% 227.59/39.22  | | | 
% 227.59/39.22  | | |   (27)  all_57_3 = e1 & op(e2, e2) = e1
% 227.59/39.22  | | | 
% 227.59/39.22  | | | ALPHA: (27) implies:
% 227.59/39.22  | | |   (28)  op(e2, e2) = e1
% 227.59/39.22  | | | 
% 227.59/39.22  | | | REF_CLOSE: (3), (14), (20), (28) are inconsistent by sub-proof #2306.
% 227.59/39.22  | | | 
% 227.59/39.22  | | End of split
% 227.59/39.22  | | 
% 227.59/39.22  | Case 2:
% 227.59/39.22  | | 
% 227.59/39.22  | |   (29)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 227.59/39.22  | |           e1)
% 227.59/39.22  | | 
% 227.59/39.22  | | BETA: splitting (29) gives:
% 227.59/39.22  | | 
% 227.59/39.22  | | Case 1:
% 227.59/39.22  | | | 
% 227.59/39.22  | | |   (30)  all_57_7 = e1 & op(e1, e2) = e1
% 227.59/39.22  | | | 
% 227.59/39.22  | | | REF_CLOSE: (7), (20), (30) are inconsistent by sub-proof #2190.
% 227.59/39.22  | | | 
% 227.59/39.22  | | Case 2:
% 227.59/39.22  | | | 
% 227.59/39.22  | | |   (31)  all_57_13 = e1 & op(e0, e2) = e1
% 227.59/39.22  | | | 
% 227.59/39.22  | | | ALPHA: (31) implies:
% 227.59/39.22  | | |   (32)  all_57_13 = e1
% 227.59/39.22  | | | 
% 227.59/39.22  | | | BETA: splitting (4) gives:
% 227.59/39.22  | | | 
% 227.59/39.22  | | | Case 1:
% 227.59/39.22  | | | | 
% 227.59/39.22  | | | |   (33)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2)
% 227.59/39.22  | | | |           = e3)
% 227.59/39.22  | | | | 
% 227.59/39.22  | | | | BETA: splitting (33) gives:
% 227.59/39.22  | | | | 
% 227.59/39.22  | | | | Case 1:
% 227.59/39.22  | | | | | 
% 227.59/39.22  | | | | |   (34)  all_57_6 = e3 & op(e1, e3) = e3
% 227.59/39.22  | | | | | 
% 227.59/39.22  | | | | | ALPHA: (34) implies:
% 227.59/39.22  | | | | |   (35)  all_57_6 = e3
% 227.59/39.22  | | | | | 
% 227.59/39.22  | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 227.59/39.22  | | | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 227.59/39.22  | | | | |            (32), (35) are inconsistent by sub-proof #285.
% 227.59/39.22  | | | | | 
% 227.59/39.22  | | | | Case 2:
% 227.59/39.22  | | | | | 
% 227.59/39.22  | | | | |   (36)  all_57_7 = e3 & op(e1, e2) = e3
% 227.59/39.22  | | | | | 
% 227.59/39.22  | | | | | ALPHA: (36) implies:
% 227.59/39.22  | | | | |   (37)  all_57_7 = e3
% 227.59/39.22  | | | | | 
% 227.59/39.22  | | | | | REF_CLOSE: (7), (8), (37) are inconsistent by sub-proof #2102.
% 227.59/39.22  | | | | | 
% 227.59/39.22  | | | | End of split
% 227.59/39.22  | | | | 
% 227.59/39.22  | | | Case 2:
% 227.59/39.22  | | | | 
% 227.59/39.22  | | | |   (38)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0)
% 227.59/39.22  | | | |           = e3)
% 227.59/39.22  | | | | 
% 227.59/39.22  | | | | REF_CLOSE: (2), (3), (5), (6), (8), (9), (10), (13), (15), (19), (20),
% 227.59/39.22  | | | |            (21), (22), (38) are inconsistent by sub-proof #1786.
% 227.59/39.22  | | | | 
% 227.59/39.22  | | | End of split
% 227.59/39.22  | | | 
% 227.59/39.22  | | End of split
% 227.59/39.22  | | 
% 227.59/39.22  | End of split
% 227.59/39.22  | 
% 227.59/39.22  End of proof
% 227.59/39.22  
% 227.59/39.22  Sub-proof #276 shows that the following formulas are inconsistent:
% 227.59/39.22  ----------------------------------------------------------------
% 227.59/39.22    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.59/39.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.59/39.22    (2)  all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 227.59/39.22    (3)  all_55_7 = all_52_15
% 227.59/39.22    (4)   ~ (all_52_15 = e1)
% 227.59/39.22    (5)  op(e0, e0) = e3
% 227.59/39.22    (6)  op(all_52_15, all_52_15) = e0
% 227.59/39.22    (7)   ~ (all_52_15 = e2)
% 227.59/39.22    (8)   ~ (all_52_15 = e3)
% 227.59/39.22  
% 227.59/39.22  Begin of proof
% 227.59/39.22  | 
% 227.59/39.22  | BETA: splitting (2) gives:
% 227.59/39.22  | 
% 227.59/39.22  | Case 1:
% 227.59/39.22  | | 
% 227.59/39.22  | |   (9)  all_55_7 = e2
% 227.59/39.22  | | 
% 227.59/39.22  | | REF_CLOSE: (3), (7), (9) are inconsistent by sub-proof #2278.
% 227.59/39.22  | | 
% 227.59/39.22  | Case 2:
% 227.59/39.22  | | 
% 227.59/39.22  | |   (10)  all_55_7 = e1 | all_55_7 = e0
% 227.59/39.22  | | 
% 227.59/39.22  | | BETA: splitting (10) gives:
% 227.59/39.22  | | 
% 227.59/39.22  | | Case 1:
% 227.59/39.22  | | | 
% 227.59/39.22  | | |   (11)  all_55_7 = e1
% 227.59/39.22  | | | 
% 227.59/39.22  | | | REF_CLOSE: (3), (4), (11) are inconsistent by sub-proof #2277.
% 227.59/39.22  | | | 
% 227.59/39.22  | | Case 2:
% 227.59/39.22  | | | 
% 227.59/39.22  | | |   (12)  all_55_7 = e0
% 227.59/39.22  | | | 
% 227.59/39.22  | | | COMBINE_EQS: (3), (12) imply:
% 227.59/39.22  | | |   (13)  all_52_15 = e0
% 227.59/39.22  | | | 
% 227.59/39.22  | | | SIMP: (13) implies:
% 227.59/39.22  | | |   (14)  all_52_15 = e0
% 227.59/39.22  | | | 
% 227.59/39.22  | | | REF_CLOSE: (1), (5), (6), (8), (14) are inconsistent by sub-proof #277.
% 227.59/39.22  | | | 
% 227.59/39.22  | | End of split
% 227.59/39.22  | | 
% 227.59/39.22  | End of split
% 227.59/39.22  | 
% 227.59/39.22  End of proof
% 227.59/39.22  
% 227.59/39.22  Sub-proof #277 shows that the following formulas are inconsistent:
% 227.59/39.22  ----------------------------------------------------------------
% 227.59/39.22    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.59/39.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.59/39.22    (2)  op(e0, e0) = e3
% 227.59/39.22    (3)  op(all_52_15, all_52_15) = e0
% 227.59/39.22    (4)  all_52_15 = e0
% 227.59/39.22    (5)   ~ (all_52_15 = e3)
% 227.59/39.22  
% 227.59/39.22  Begin of proof
% 227.59/39.22  | 
% 227.59/39.22  | REDUCE: (4), (5) imply:
% 227.59/39.22  |   (6)   ~ (e3 = e0)
% 227.59/39.22  | 
% 227.59/39.22  | SIMP: (6) implies:
% 227.59/39.22  |   (7)   ~ (e3 = e0)
% 227.59/39.22  | 
% 227.59/39.22  | REDUCE: (3), (4) imply:
% 227.59/39.22  |   (8)  op(e0, e0) = e0
% 227.59/39.22  | 
% 227.59/39.22  | REF_CLOSE: (1), (2), (7), (8) are inconsistent by sub-proof #2304.
% 227.59/39.22  | 
% 227.59/39.22  End of proof
% 227.59/39.22  
% 227.59/39.22  Sub-proof #278 shows that the following formulas are inconsistent:
% 227.59/39.22  ----------------------------------------------------------------
% 227.59/39.22    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.59/39.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.59/39.22    (2)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) = all_22_1
% 227.59/39.22           & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0, e3) =
% 227.59/39.22           all_22_1 & $i(all_22_1))
% 227.59/39.22    (3)   ~ (all_53_13 = e2)
% 227.59/39.22    (4)   ~ (all_53_7 = e2)
% 227.59/39.22    (5)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.59/39.22    (6)   ~ (all_53_13 = e3)
% 227.59/39.22    (7)  op(e2, e0) = all_52_15
% 227.59/39.22    (8)  all_55_7 = e3 | all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 227.59/39.22    (9)  op(e0, e3) = all_53_3
% 227.59/39.22    (10)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 227.59/39.22            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 227.59/39.22              e3) = all_12_1 & $i(all_12_1))
% 227.59/39.22    (11)  op(e0, e0) = e3
% 227.59/39.22    (12)  op(e0, e2) = all_53_7
% 227.59/39.22    (13)  op(e2, e0) = all_53_13
% 227.59/39.22    (14)  op(all_52_15, all_52_15) = e0
% 227.59/39.22    (15)  all_55_7 = all_53_13
% 227.59/39.22  
% 227.59/39.22  Begin of proof
% 227.59/39.22  | 
% 227.59/39.22  | BETA: splitting (5) gives:
% 227.59/39.22  | 
% 227.59/39.22  | Case 1:
% 227.59/39.22  | | 
% 227.59/39.22  | |   (16)  all_57_12 = e2 & op(e0, e3) = e2
% 227.59/39.22  | | 
% 227.59/39.22  | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (9), (10), (11), (13), (14), (15),
% 227.59/39.22  | |            (16) are inconsistent by sub-proof #279.
% 227.59/39.22  | | 
% 227.59/39.22  | Case 2:
% 227.59/39.22  | | 
% 227.59/39.22  | |   (17)  all_57_13 = e2 & op(e0, e2) = e2
% 227.59/39.22  | | 
% 227.59/39.22  | | ALPHA: (17) implies:
% 227.59/39.22  | |   (18)  op(e0, e2) = e2
% 227.59/39.22  | | 
% 227.59/39.22  | | REF_CLOSE: (1), (4), (12), (18) are inconsistent by sub-proof #2335.
% 227.59/39.22  | | 
% 227.59/39.22  | End of split
% 227.59/39.22  | 
% 227.59/39.22  End of proof
% 227.59/39.22  
% 227.59/39.22  Sub-proof #279 shows that the following formulas are inconsistent:
% 227.59/39.22  ----------------------------------------------------------------
% 227.59/39.22    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.59/39.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.59/39.22    (2)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) = all_22_1
% 227.59/39.22           & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0, e3) =
% 227.59/39.22           all_22_1 & $i(all_22_1))
% 227.59/39.22    (3)   ~ (all_53_13 = e2)
% 227.59/39.22    (4)  all_57_12 = e2 & op(e0, e3) = e2
% 227.59/39.22    (5)   ~ (all_53_13 = e3)
% 227.59/39.22    (6)  op(e2, e0) = all_52_15
% 227.59/39.22    (7)  all_55_7 = e3 | all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 227.59/39.22    (8)  op(e0, e3) = all_53_3
% 227.59/39.22    (9)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) = all_12_1
% 227.59/39.22           & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0, e3) =
% 227.59/39.22           all_12_1 & $i(all_12_1))
% 227.59/39.22    (10)  op(e0, e0) = e3
% 227.59/39.22    (11)  op(e2, e0) = all_53_13
% 227.59/39.22    (12)  op(all_52_15, all_52_15) = e0
% 227.59/39.22    (13)  all_55_7 = all_53_13
% 227.59/39.22  
% 227.59/39.22  Begin of proof
% 227.59/39.22  | 
% 227.59/39.22  | ALPHA: (4) implies:
% 227.59/39.22  |   (14)  op(e0, e3) = e2
% 227.59/39.22  | 
% 227.59/39.22  | GROUND_INST: instantiating (1) with all_53_3, e2, e3, e0, simplifying with
% 227.59/39.22  |              (8), (14) gives:
% 227.59/39.22  |   (15)  all_53_3 = e2
% 227.59/39.22  | 
% 227.59/39.22  | GROUND_INST: instantiating (1) with all_53_13, all_52_15, e0, e2, simplifying
% 227.59/39.22  |              with (6), (11) gives:
% 227.59/39.22  |   (16)  all_53_13 = all_52_15
% 227.59/39.22  | 
% 227.59/39.22  | COMBINE_EQS: (13), (16) imply:
% 227.59/39.22  |   (17)  all_55_7 = all_52_15
% 227.59/39.22  | 
% 227.59/39.22  | REDUCE: (5), (16) imply:
% 227.59/39.22  |   (18)   ~ (all_52_15 = e3)
% 227.59/39.22  | 
% 227.59/39.22  | REDUCE: (3), (16) imply:
% 227.59/39.22  |   (19)   ~ (all_52_15 = e2)
% 227.59/39.22  | 
% 227.59/39.22  | BETA: splitting (9) gives:
% 227.59/39.22  | 
% 227.59/39.22  | Case 1:
% 227.59/39.22  | | 
% 227.59/39.22  | |   (20)   ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 227.59/39.22  | |         all_12_1 & $i(all_12_0) & $i(all_12_1)
% 227.59/39.22  | | 
% 227.59/39.22  | | ALPHA: (20) implies:
% 227.59/39.22  | |   (21)  op(e0, e3) = all_12_1
% 227.59/39.22  | | 
% 227.59/39.22  | | REF_CLOSE: (1), (2), (6), (7), (10), (12), (14), (17), (18), (19), (21) are
% 227.59/39.22  | |            inconsistent by sub-proof #280.
% 227.59/39.22  | | 
% 227.59/39.22  | Case 2:
% 227.59/39.22  | | 
% 227.59/39.22  | |   (22)   ~ (all_12_1 = e1) & op(e0, e3) = all_12_1 & $i(all_12_1)
% 227.59/39.22  | | 
% 227.59/39.22  | | ALPHA: (22) implies:
% 227.59/39.22  | |   (23)  op(e0, e3) = all_12_1
% 227.59/39.22  | | 
% 227.59/39.22  | | REF_CLOSE: (1), (2), (6), (7), (10), (12), (14), (17), (18), (19), (23) are
% 227.59/39.22  | |            inconsistent by sub-proof #280.
% 227.59/39.22  | | 
% 227.59/39.22  | End of split
% 227.59/39.22  | 
% 227.59/39.22  End of proof
% 227.59/39.22  
% 227.59/39.22  Sub-proof #280 shows that the following formulas are inconsistent:
% 227.59/39.22  ----------------------------------------------------------------
% 227.59/39.22    (1)  op(e0, e3) = all_12_1
% 227.59/39.22    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.59/39.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.59/39.22    (3)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) = all_22_1
% 227.59/39.22           & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0, e3) =
% 227.59/39.22           all_22_1 & $i(all_22_1))
% 227.59/39.22    (4)  all_55_7 = all_52_15
% 227.59/39.22    (5)  op(e2, e0) = all_52_15
% 227.59/39.23    (6)  all_55_7 = e3 | all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 227.59/39.23    (7)  op(e0, e0) = e3
% 227.59/39.23    (8)  op(all_52_15, all_52_15) = e0
% 227.59/39.23    (9)  op(e0, e3) = e2
% 227.59/39.23    (10)   ~ (all_52_15 = e2)
% 227.59/39.23    (11)   ~ (all_52_15 = e3)
% 227.59/39.23  
% 227.59/39.23  Begin of proof
% 227.59/39.23  | 
% 227.59/39.23  | BETA: splitting (3) gives:
% 227.59/39.23  | 
% 227.59/39.23  | Case 1:
% 227.59/39.23  | | 
% 227.59/39.23  | |   (12)   ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 227.59/39.23  | |         all_22_1 & $i(all_22_0) & $i(all_22_1)
% 227.59/39.23  | | 
% 227.59/39.23  | | ALPHA: (12) implies:
% 227.59/39.23  | |   (13)   ~ (all_22_0 = e1)
% 227.59/39.23  | |   (14)  op(e0, e3) = all_22_1
% 227.59/39.23  | |   (15)  op(all_22_1, e0) = all_22_0
% 227.59/39.23  | | 
% 227.59/39.23  | | GROUND_INST: instantiating (2) with e2, all_22_1, e3, e0, simplifying with
% 227.59/39.23  | |              (9), (14) gives:
% 227.59/39.23  | |   (16)  all_22_1 = e2
% 227.59/39.23  | | 
% 227.59/39.23  | | GROUND_INST: instantiating (2) with all_12_1, all_22_1, e3, e0, simplifying
% 227.59/39.23  | |              with (1), (14) gives:
% 227.59/39.23  | |   (17)  all_22_1 = all_12_1
% 227.59/39.23  | | 
% 227.59/39.23  | | COMBINE_EQS: (16), (17) imply:
% 227.59/39.23  | |   (18)  all_12_1 = e2
% 227.59/39.23  | | 
% 227.59/39.23  | | REDUCE: (15), (16) imply:
% 227.59/39.23  | |   (19)  op(e2, e0) = all_22_0
% 227.59/39.23  | | 
% 227.59/39.23  | | GROUND_INST: instantiating (2) with all_52_15, all_22_0, e0, e2, simplifying
% 227.59/39.23  | |              with (5), (19) gives:
% 227.59/39.23  | |   (20)  all_52_15 = all_22_0
% 227.59/39.23  | | 
% 227.59/39.23  | | COMBINE_EQS: (4), (20) imply:
% 227.59/39.23  | |   (21)  all_55_7 = all_22_0
% 227.59/39.23  | | 
% 227.59/39.23  | | REDUCE: (11), (20) imply:
% 227.59/39.23  | |   (22)   ~ (all_22_0 = e3)
% 227.59/39.23  | | 
% 227.59/39.23  | | REDUCE: (10), (20) imply:
% 227.59/39.23  | |   (23)   ~ (all_22_0 = e2)
% 227.59/39.23  | | 
% 227.59/39.23  | | REDUCE: (8), (20) imply:
% 227.59/39.23  | |   (24)  op(all_22_0, all_22_0) = e0
% 227.59/39.23  | | 
% 227.59/39.23  | | BETA: splitting (6) gives:
% 227.59/39.23  | | 
% 227.59/39.23  | | Case 1:
% 227.59/39.23  | | | 
% 227.59/39.23  | | |   (25)  all_55_7 = e3
% 227.59/39.23  | | | 
% 227.59/39.23  | | | COMBINE_EQS: (21), (25) imply:
% 227.59/39.23  | | |   (26)  all_22_0 = e3
% 227.59/39.23  | | | 
% 227.59/39.23  | | | SIMP: (26) implies:
% 227.59/39.23  | | |   (27)  all_22_0 = e3
% 227.59/39.23  | | | 
% 227.59/39.23  | | | REDUCE: (22), (27) imply:
% 227.59/39.23  | | |   (28)  $false
% 227.59/39.23  | | | 
% 227.59/39.23  | | | CLOSE: (28) is inconsistent.
% 227.59/39.23  | | | 
% 227.59/39.23  | | Case 2:
% 227.59/39.23  | | | 
% 227.59/39.23  | | |   (29)   ~ (all_55_7 = e3)
% 227.59/39.23  | | |   (30)  all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 227.59/39.23  | | | 
% 227.59/39.23  | | | BETA: splitting (30) gives:
% 227.59/39.23  | | | 
% 227.59/39.23  | | | Case 1:
% 227.59/39.23  | | | | 
% 227.59/39.23  | | | |   (31)  all_55_7 = e2
% 227.59/39.23  | | | | 
% 227.59/39.23  | | | | COMBINE_EQS: (21), (31) imply:
% 227.59/39.23  | | | |   (32)  all_22_0 = e2
% 227.59/39.23  | | | | 
% 227.59/39.23  | | | | SIMP: (32) implies:
% 227.59/39.23  | | | |   (33)  all_22_0 = e2
% 227.59/39.23  | | | | 
% 227.59/39.23  | | | | REDUCE: (23), (33) imply:
% 227.59/39.23  | | | |   (34)  $false
% 227.59/39.23  | | | | 
% 227.59/39.23  | | | | CLOSE: (34) is inconsistent.
% 227.59/39.23  | | | | 
% 227.59/39.23  | | | Case 2:
% 227.59/39.23  | | | | 
% 227.59/39.23  | | | |   (35)  all_55_7 = e1 | all_55_7 = e0
% 227.59/39.23  | | | | 
% 227.59/39.23  | | | | BETA: splitting (35) gives:
% 227.59/39.23  | | | | 
% 227.59/39.23  | | | | Case 1:
% 227.59/39.23  | | | | | 
% 227.59/39.23  | | | | |   (36)  all_55_7 = e1
% 227.59/39.23  | | | | | 
% 227.59/39.23  | | | | | COMBINE_EQS: (21), (36) imply:
% 227.59/39.23  | | | | |   (37)  all_22_0 = e1
% 227.59/39.23  | | | | | 
% 227.59/39.23  | | | | | SIMP: (37) implies:
% 227.59/39.23  | | | | |   (38)  all_22_0 = e1
% 227.59/39.23  | | | | | 
% 227.59/39.23  | | | | | REDUCE: (13), (38) imply:
% 227.59/39.23  | | | | |   (39)  $false
% 227.59/39.23  | | | | | 
% 227.59/39.23  | | | | | CLOSE: (39) is inconsistent.
% 227.59/39.23  | | | | | 
% 227.59/39.23  | | | | Case 2:
% 227.59/39.23  | | | | | 
% 227.59/39.23  | | | | |   (40)  all_55_7 = e0
% 227.59/39.23  | | | | | 
% 227.59/39.23  | | | | | COMBINE_EQS: (21), (40) imply:
% 227.59/39.23  | | | | |   (41)  all_22_0 = e0
% 227.59/39.23  | | | | | 
% 227.59/39.23  | | | | | SIMP: (41) implies:
% 227.59/39.23  | | | | |   (42)  all_22_0 = e0
% 227.59/39.23  | | | | | 
% 227.59/39.23  | | | | | REDUCE: (22), (42) imply:
% 227.59/39.23  | | | | |   (43)   ~ (e3 = e0)
% 227.59/39.23  | | | | | 
% 227.59/39.23  | | | | | SIMP: (43) implies:
% 227.59/39.23  | | | | |   (44)   ~ (e3 = e0)
% 227.59/39.23  | | | | | 
% 227.59/39.23  | | | | | REDUCE: (24), (42) imply:
% 227.59/39.23  | | | | |   (45)  op(e0, e0) = e0
% 227.59/39.23  | | | | | 
% 227.59/39.23  | | | | | REF_CLOSE: (2), (7), (44), (45) are inconsistent by sub-proof #2304.
% 227.59/39.23  | | | | | 
% 227.59/39.23  | | | | End of split
% 227.59/39.23  | | | | 
% 227.59/39.23  | | | End of split
% 227.59/39.23  | | | 
% 227.59/39.23  | | End of split
% 227.59/39.23  | | 
% 227.59/39.23  | Case 2:
% 227.59/39.23  | | 
% 227.59/39.23  | |   (46)   ~ (all_22_1 = e2) & op(e0, e3) = all_22_1 & $i(all_22_1)
% 227.59/39.23  | | 
% 227.59/39.23  | | REF_CLOSE: (2), (9), (46) are inconsistent by sub-proof #836.
% 227.59/39.23  | | 
% 227.59/39.23  | End of split
% 227.59/39.23  | 
% 227.59/39.23  End of proof
% 227.59/39.23  
% 227.59/39.23  Sub-proof #281 shows that the following formulas are inconsistent:
% 227.59/39.23  ----------------------------------------------------------------
% 227.59/39.23    (1)  all_57_9 = e2
% 227.59/39.23    (2)   ~ (e3 = e1)
% 227.59/39.23    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.59/39.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.59/39.23    (4)  all_57_10 = e1
% 227.59/39.23    (5)   ~ (e1 = e0)
% 227.59/39.23    (6)  e1 = e0
% 227.59/39.23    (7)  op(e0, e0) = e3
% 227.59/39.23    (8)  all_57_11 = e1
% 227.59/39.23    (9)   ~ (e2 = e1)
% 227.59/39.23    (10)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 227.59/39.23          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 227.59/39.23  
% 227.59/39.23  Begin of proof
% 227.59/39.23  | 
% 227.59/39.23  | COMBINE_EQS: (6), (8) imply:
% 227.59/39.23  |   (11)  all_57_11 = e0
% 227.59/39.23  | 
% 227.59/39.23  | COMBINE_EQS: (4), (6) imply:
% 227.59/39.23  |   (12)  all_57_10 = e0
% 227.59/39.23  | 
% 227.59/39.23  | REF_CLOSE: (1), (2), (3), (5), (7), (9), (10), (11), (12) are inconsistent by
% 227.59/39.23  |            sub-proof #1104.
% 227.59/39.23  | 
% 227.59/39.23  End of proof
% 227.59/39.23  
% 227.59/39.23  Sub-proof #282 shows that the following formulas are inconsistent:
% 227.59/39.23  ----------------------------------------------------------------
% 227.59/39.23    (1)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 227.59/39.23    (2)   ~ (e3 = e1)
% 227.59/39.23    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.59/39.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.59/39.23    (4)  all_57_10 = e1
% 227.59/39.23    (5)   ~ (e3 = e2)
% 227.59/39.23    (6)  all_57_15 = e3
% 227.59/39.23    (7)  op(e1, e1) = e1
% 227.59/39.23    (8)   ~ (e2 = e0)
% 227.59/39.23    (9)   ~ (e1 = e0)
% 227.59/39.23    (10)  op(e0, e0) = e3
% 227.59/39.23    (11)  all_57_11 = e1
% 227.59/39.23    (12)   ~ (e2 = e1)
% 227.59/39.23    (13)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 227.59/39.23          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 227.59/39.23    (14)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 227.59/39.23          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 227.59/39.23  
% 227.59/39.23  Begin of proof
% 227.59/39.23  | 
% 227.59/39.23  | BETA: splitting (1) gives:
% 227.59/39.23  | 
% 227.59/39.23  | Case 1:
% 227.59/39.23  | | 
% 227.59/39.23  | |   (15)  all_57_8 = e0 & op(e1, e1) = e0
% 227.59/39.23  | | 
% 227.59/39.23  | | ALPHA: (15) implies:
% 227.59/39.23  | |   (16)  op(e1, e1) = e0
% 227.59/39.23  | | 
% 227.59/39.23  | | REF_CLOSE: (3), (7), (9), (16) are inconsistent by sub-proof #2427.
% 227.59/39.23  | | 
% 227.59/39.23  | Case 2:
% 227.59/39.23  | | 
% 227.59/39.23  | |   (17)  all_57_11 = e0 & op(e1, e0) = e0
% 227.59/39.23  | | 
% 227.59/39.23  | | ALPHA: (17) implies:
% 227.59/39.23  | |   (18)  all_57_11 = e0
% 227.59/39.23  | | 
% 227.59/39.23  | | COMBINE_EQS: (11), (18) imply:
% 227.59/39.23  | |   (19)  e1 = e0
% 227.59/39.23  | | 
% 227.59/39.23  | | COMBINE_EQS: (4), (19) imply:
% 227.59/39.23  | |   (20)  all_57_10 = e0
% 227.59/39.23  | | 
% 227.59/39.23  | | REF_CLOSE: (2), (3), (5), (6), (8), (9), (10), (12), (13), (14), (18), (20)
% 227.59/39.23  | |            are inconsistent by sub-proof #1087.
% 227.59/39.23  | | 
% 227.59/39.23  | End of split
% 227.59/39.23  | 
% 227.59/39.23  End of proof
% 227.59/39.23  
% 227.59/39.23  Sub-proof #283 shows that the following formulas are inconsistent:
% 227.59/39.23  ----------------------------------------------------------------
% 227.59/39.23    (1)  op(e3, e3) = e1
% 227.59/39.23    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.59/39.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.59/39.23    (3)  op(e0, e0) = all_52_31
% 227.59/39.23    (4)   ~ (e1 = e0)
% 227.59/39.23    (5)  op(e0, e0) = e3
% 227.59/39.23    (6)  op(all_52_31, all_52_31) = e0
% 227.59/39.23  
% 227.59/39.23  Begin of proof
% 227.59/39.23  | 
% 227.59/39.23  | GROUND_INST: instantiating (2) with e3, all_52_31, e0, e0, simplifying with
% 227.59/39.23  |              (3), (5) gives:
% 227.59/39.23  |   (7)  all_52_31 = e3
% 227.59/39.23  | 
% 227.59/39.23  | REDUCE: (6), (7) imply:
% 227.59/39.23  |   (8)  op(e3, e3) = e0
% 227.59/39.23  | 
% 227.59/39.23  | GROUND_INST: instantiating (2) with e1, e0, e3, e3, simplifying with (1), (8)
% 227.59/39.23  |              gives:
% 227.59/39.23  |   (9)  e1 = e0
% 227.59/39.23  | 
% 227.59/39.23  | REDUCE: (4), (9) imply:
% 227.59/39.23  |   (10)  $false
% 227.59/39.23  | 
% 227.59/39.23  | CLOSE: (10) is inconsistent.
% 227.59/39.23  | 
% 227.59/39.23  End of proof
% 227.59/39.23  
% 227.59/39.23  Sub-proof #284 shows that the following formulas are inconsistent:
% 227.59/39.23  ----------------------------------------------------------------
% 227.59/39.23    (1)  op(e3, e3) = e1
% 227.59/39.23    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 227.59/39.23         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 227.59/39.23    (3)   ~ (e3 = e1)
% 227.59/39.23    (4)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 227.59/39.23         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 227.59/39.23    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.59/39.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.59/39.23    (6)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 227.59/39.23         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 227.59/39.23    (7)   ~ (all_6_2 = e3)
% 227.59/39.23    (8)  op(e1, e1) = all_6_2
% 227.59/39.23    (9)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) = all_22_1
% 227.59/39.23           & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0, e3) =
% 227.59/39.23           all_22_1 & $i(all_22_1))
% 227.59/39.23    (10)   ~ (e3 = e2)
% 227.59/39.23    (11)   ~ (e3 = e0)
% 227.59/39.23    (12)  all_57_15 = e3
% 227.59/39.23    (13)  op(e1, e1) = all_52_21
% 227.59/39.23    (14)   ~ (e2 = e0)
% 227.59/39.23    (15)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 227.59/39.23            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 227.59/39.23              e3) = all_12_1 & $i(all_12_1))
% 227.59/39.23    (16)  op(e2, e2) = e2
% 227.59/39.23    (17)   ~ (e1 = e0)
% 227.59/39.23    (18)  op(e0, e0) = e3
% 227.59/39.23    (19)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 227.59/39.23              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 227.59/39.23                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 227.59/39.23                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 227.59/39.23    (20)  op(e1, e1) = e2
% 227.59/39.23    (21)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 227.59/39.23          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 227.59/39.23    (22)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 227.59/39.23          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 227.59/39.23    (23)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 227.59/39.23          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 227.59/39.23    (24)   ~ (e2 = e1)
% 227.59/39.23    (25)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 227.59/39.23          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 227.59/39.23    (26)   ~ (all_6_2 = e0)
% 227.59/39.23    (27)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 227.59/39.23          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 227.59/39.23    (28)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 227.59/39.23          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 227.59/39.23    (29)  op(all_52_21, all_52_21) = e1
% 227.59/39.23    (30)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 227.59/39.23          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 227.59/39.23    (31)  all_57_3 = e2
% 227.59/39.23  
% 227.59/39.23  Begin of proof
% 227.59/39.23  | 
% 227.59/39.23  | BETA: splitting (19) gives:
% 227.59/39.23  | 
% 227.59/39.23  | Case 1:
% 227.59/39.23  | | 
% 227.59/39.23  | |   (32)  all_57_15 = e0 & op(e0, e0) = e0
% 227.59/39.23  | | 
% 227.59/39.23  | | ALPHA: (32) implies:
% 227.59/39.23  | |   (33)  op(e0, e0) = e0
% 227.59/39.23  | | 
% 227.59/39.23  | | REF_CLOSE: (5), (11), (18), (33) are inconsistent by sub-proof #2304.
% 227.59/39.23  | | 
% 227.59/39.23  | Case 2:
% 227.59/39.23  | | 
% 227.59/39.23  | |   (34)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 227.59/39.23  | |             e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0 &
% 227.59/39.23  | |             op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 227.59/39.23  | |           (all_57_14 = e0 & op(e0, e1) = e0))
% 227.59/39.23  | | 
% 227.59/39.23  | | ALPHA: (34) implies:
% 227.59/39.23  | |   (35)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 227.59/39.23  | |           e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 227.59/39.23  | | 
% 227.59/39.23  | | BETA: splitting (27) gives:
% 227.59/39.23  | | 
% 227.59/39.23  | | Case 1:
% 227.59/39.23  | | | 
% 227.59/39.23  | | |   (36)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) =
% 227.59/39.23  | | |           e2)
% 227.59/39.23  | | | 
% 227.59/39.23  | | | REF_CLOSE: (1), (2), (3), (5), (10), (11), (12), (14), (16), (17), (18),
% 227.59/39.23  | | |            (19), (21), (22), (23), (24), (25), (28), (31), (36) are
% 227.59/39.23  | | |            inconsistent by sub-proof #337.
% 227.59/39.23  | | | 
% 227.59/39.23  | | Case 2:
% 227.59/39.23  | | | 
% 227.59/39.23  | | |   (37)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) =
% 227.59/39.23  | | |           e2)
% 227.59/39.23  | | | 
% 227.59/39.23  | | | BETA: splitting (37) gives:
% 227.59/39.23  | | | 
% 227.59/39.23  | | | Case 1:
% 227.59/39.23  | | | | 
% 227.59/39.23  | | | |   (38)  all_57_6 = e2 & op(e1, e3) = e2
% 227.59/39.23  | | | | 
% 227.59/39.23  | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (10), (11), (12), (14), (17),
% 227.59/39.23  | | | |            (19), (20), (24), (25), (26), (28), (30), (35), (38) are
% 227.59/39.23  | | | |            inconsistent by sub-proof #335.
% 227.59/39.23  | | | | 
% 227.59/39.23  | | | Case 2:
% 227.59/39.23  | | | | 
% 227.59/39.23  | | | |   (39)  all_57_12 = e2 & op(e0, e3) = e2
% 227.59/39.23  | | | | 
% 227.59/39.23  | | | | ALPHA: (39) implies:
% 227.59/39.23  | | | |   (40)  op(e0, e3) = e2
% 227.59/39.23  | | | | 
% 227.59/39.23  | | | | REF_CLOSE: (5), (9), (13), (15), (16), (20), (24), (29), (40) are
% 227.59/39.23  | | | |            inconsistent by sub-proof #835.
% 227.59/39.23  | | | | 
% 227.59/39.23  | | | End of split
% 227.59/39.23  | | | 
% 227.59/39.23  | | End of split
% 227.59/39.23  | | 
% 227.59/39.23  | End of split
% 227.59/39.23  | 
% 227.59/39.23  End of proof
% 227.59/39.23  
% 227.59/39.23  Sub-proof #285 shows that the following formulas are inconsistent:
% 227.59/39.23  ----------------------------------------------------------------
% 227.59/39.23    (1)  all_57_13 = e1
% 227.59/39.23    (2)   ~ (e3 = e1)
% 227.59/39.23    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.59/39.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.59/39.23    (4)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 227.59/39.23         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 227.59/39.23    (5)   ~ (all_6_2 = e3)
% 227.59/39.23    (6)  op(e1, e1) = all_6_2
% 227.59/39.23    (7)  all_57_7 = e2
% 227.59/39.23    (8)   ~ (e3 = e2)
% 227.59/39.23    (9)   ~ (e3 = e0)
% 227.59/39.23    (10)  all_57_15 = e3
% 227.59/39.23    (11)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 227.59/39.23          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 227.59/39.23            e1)
% 227.59/39.23    (12)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 227.59/39.23          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 227.59/39.23    (13)   ~ (e2 = e0)
% 227.59/39.23    (14)  op(e2, e2) = e2
% 227.59/39.23    (15)   ~ (e1 = e0)
% 227.59/39.23    (16)  all_57_6 = e3
% 227.59/39.23    (17)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 227.59/39.23          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 227.59/39.23    (18)  op(e0, e0) = e3
% 227.59/39.23    (19)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.59/39.23          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 227.59/39.23            e2)
% 227.59/39.23    (20)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 227.59/39.23              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 227.59/39.23                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 227.59/39.23                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 227.59/39.23    (21)   ~ (e2 = e1)
% 227.59/39.23    (22)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 227.59/39.23          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 227.59/39.23    (23)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 227.59/39.23          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 227.59/39.23  
% 227.59/39.23  Begin of proof
% 227.59/39.23  | 
% 227.59/39.23  | BETA: splitting (12) gives:
% 227.59/39.23  | 
% 227.59/39.23  | Case 1:
% 227.59/39.23  | | 
% 227.59/39.23  | |   (24)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) =
% 227.59/39.23  | |           e0)
% 227.59/39.23  | | 
% 227.59/39.23  | | BETA: splitting (24) gives:
% 227.59/39.23  | | 
% 227.59/39.23  | | Case 1:
% 227.59/39.23  | | | 
% 227.59/39.23  | | |   (25)  all_57_1 = e0 & op(e3, e2) = e0
% 227.59/39.23  | | | 
% 227.59/39.23  | | | ALPHA: (25) implies:
% 227.59/39.23  | | |   (26)  all_57_1 = e0
% 227.59/39.23  | | | 
% 227.59/39.23  | | | BETA: splitting (17) gives:
% 227.59/39.23  | | | 
% 227.59/39.23  | | | Case 1:
% 227.59/39.23  | | | | 
% 227.59/39.23  | | | |   (27)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2)
% 227.59/39.23  | | | |           = e3)
% 227.59/39.23  | | | | 
% 227.59/39.23  | | | | BETA: splitting (27) gives:
% 227.59/39.23  | | | | 
% 227.59/39.23  | | | | Case 1:
% 227.59/39.23  | | | | | 
% 227.59/39.23  | | | | |   (28)  all_57_1 = e3 & op(e3, e2) = e3
% 227.59/39.23  | | | | | 
% 227.59/39.23  | | | | | ALPHA: (28) implies:
% 227.59/39.23  | | | | |   (29)  all_57_1 = e3
% 227.59/39.23  | | | | | 
% 227.59/39.23  | | | | | COMBINE_EQS: (26), (29) imply:
% 227.59/39.23  | | | | |   (30)  e3 = e0
% 227.59/39.23  | | | | | 
% 227.59/39.23  | | | | | SIMP: (30) implies:
% 227.59/39.23  | | | | |   (31)  e3 = e0
% 227.59/39.23  | | | | | 
% 227.59/39.23  | | | | | COMBINE_EQS: (16), (31) imply:
% 227.59/39.23  | | | | |   (32)  all_57_6 = e0
% 227.59/39.23  | | | | | 
% 227.59/39.23  | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (13), (15),
% 227.59/39.23  | | | | |            (20), (21), (22), (23), (32) are inconsistent by sub-proof
% 227.59/39.23  | | | | |            #1775.
% 227.59/39.23  | | | | | 
% 227.59/39.23  | | | | Case 2:
% 227.59/39.23  | | | | | 
% 227.59/39.23  | | | | |   (33)  all_57_3 = e3 & op(e2, e2) = e3
% 227.59/39.23  | | | | | 
% 227.59/39.23  | | | | | ALPHA: (33) implies:
% 227.59/39.23  | | | | |   (34)  op(e2, e2) = e3
% 227.59/39.23  | | | | | 
% 227.59/39.23  | | | | | REF_CLOSE: (3), (8), (14), (34) are inconsistent by sub-proof #2298.
% 227.59/39.23  | | | | | 
% 227.59/39.23  | | | | End of split
% 227.59/39.23  | | | | 
% 227.59/39.23  | | | Case 2:
% 227.59/39.23  | | | | 
% 227.59/39.23  | | | |   (35)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2)
% 227.59/39.23  | | | |           = e3)
% 227.59/39.23  | | | | 
% 227.59/39.23  | | | | REF_CLOSE: (2), (3), (7), (8), (9), (10), (11), (13), (15), (18), (19),
% 227.59/39.23  | | | |            (20), (21), (35) are inconsistent by sub-proof #776.
% 227.59/39.23  | | | | 
% 227.59/39.23  | | | End of split
% 227.59/39.23  | | | 
% 227.59/39.23  | | Case 2:
% 227.59/39.23  | | | 
% 227.59/39.23  | | |   (36)  all_57_3 = e0 & op(e2, e2) = e0
% 227.59/39.23  | | | 
% 227.59/39.23  | | | ALPHA: (36) implies:
% 227.59/39.23  | | |   (37)  op(e2, e2) = e0
% 227.59/39.23  | | | 
% 227.59/39.23  | | | REF_CLOSE: (3), (13), (14), (37) are inconsistent by sub-proof #2472.
% 227.59/39.23  | | | 
% 227.59/39.23  | | End of split
% 227.59/39.23  | | 
% 227.59/39.23  | Case 2:
% 227.59/39.23  | | 
% 227.59/39.23  | |   (38)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 227.59/39.23  | |           e0)
% 227.59/39.23  | | 
% 227.59/39.23  | | BETA: splitting (38) gives:
% 227.59/39.23  | | 
% 227.59/39.23  | | Case 1:
% 227.59/39.23  | | | 
% 227.59/39.23  | | |   (39)  all_57_7 = e0 & op(e1, e2) = e0
% 227.59/39.23  | | | 
% 227.59/39.23  | | | REF_CLOSE: (7), (13), (39) are inconsistent by sub-proof #2148.
% 227.59/39.23  | | | 
% 227.59/39.23  | | Case 2:
% 227.59/39.23  | | | 
% 227.59/39.23  | | |   (40)  all_57_13 = e0 & op(e0, e2) = e0
% 227.59/39.23  | | | 
% 227.59/39.23  | | | REF_CLOSE: (1), (15), (40) are inconsistent by sub-proof #1920.
% 227.59/39.23  | | | 
% 227.59/39.23  | | End of split
% 227.59/39.23  | | 
% 227.59/39.23  | End of split
% 227.59/39.23  | 
% 227.59/39.23  End of proof
% 227.59/39.23  
% 227.59/39.23  Sub-proof #286 shows that the following formulas are inconsistent:
% 227.59/39.23  ----------------------------------------------------------------
% 227.59/39.23    (1)  op(e0, e0) = all_4_2
% 227.59/39.23    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.59/39.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.59/39.23    (3)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 227.59/39.23    (4)   ~ (all_4_2 = e2)
% 227.59/39.23    (5)  all_57_14 = e1
% 227.59/39.23    (6)   ~ (e2 = e1)
% 227.59/39.23  
% 227.59/39.23  Begin of proof
% 227.59/39.23  | 
% 227.59/39.23  | BETA: splitting (3) gives:
% 227.59/39.23  | 
% 227.59/39.23  | Case 1:
% 227.59/39.23  | | 
% 227.59/39.23  | |   (7)  all_57_14 = e2 & op(e0, e1) = e2
% 227.59/39.23  | | 
% 227.59/39.23  | | ALPHA: (7) implies:
% 227.59/39.23  | |   (8)  all_57_14 = e2
% 227.59/39.23  | | 
% 227.59/39.23  | | REF_CLOSE: (5), (6), (8) are inconsistent by sub-proof #2178.
% 227.59/39.23  | | 
% 227.59/39.23  | Case 2:
% 227.59/39.23  | | 
% 227.59/39.23  | |   (9)  all_57_15 = e2 & op(e0, e0) = e2
% 227.59/39.23  | | 
% 227.59/39.23  | | ALPHA: (9) implies:
% 227.59/39.23  | |   (10)  op(e0, e0) = e2
% 227.59/39.23  | | 
% 227.59/39.23  | | REF_CLOSE: (1), (2), (4), (10) are inconsistent by sub-proof #2334.
% 227.59/39.23  | | 
% 227.59/39.23  | End of split
% 227.59/39.23  | 
% 227.59/39.23  End of proof
% 227.59/39.23  
% 227.59/39.23  Sub-proof #287 shows that the following formulas are inconsistent:
% 227.59/39.23  ----------------------------------------------------------------
% 227.59/39.23    (1)  all_57_9 = e2
% 227.59/39.23    (2)   ~ (e3 = e1)
% 227.59/39.23    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.59/39.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.59/39.23    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 227.59/39.23         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 227.59/39.23    (5)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 227.59/39.23         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 227.59/39.23    (6)   ~ (e3 = e2)
% 227.59/39.23    (7)   ~ (e3 = e0)
% 227.59/39.23    (8)   ~ (e2 = e0)
% 227.59/39.23    (9)   ~ (all_53_9 = e2)
% 227.59/39.23    (10)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2)
% 227.59/39.23    (11)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 227.59/39.23          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 227.59/39.23    (12)   ~ (e1 = e0)
% 227.59/39.23    (13)   ~ (all_53_12 = e3)
% 227.59/39.23    (14)   ~ (e2 = e1)
% 227.59/39.23    (15)  op(e2, e1) = all_53_9
% 227.59/39.23    (16)  op(e3, e0) = all_53_12
% 227.59/39.23  
% 227.59/39.23  Begin of proof
% 227.59/39.23  | 
% 227.59/39.23  | BETA: splitting (10) gives:
% 227.59/39.23  | 
% 227.59/39.23  | Case 1:
% 227.59/39.23  | | 
% 227.59/39.23  | |   (17)  all_57_4 = e2 & op(e3, e1) = e2
% 227.59/39.23  | | 
% 227.59/39.23  | | ALPHA: (17) implies:
% 227.59/39.23  | |   (18)  all_57_4 = e2
% 227.59/39.23  | | 
% 227.59/39.23  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (11), (12), (13), (14),
% 227.59/39.23  | |            (16), (18) are inconsistent by sub-proof #288.
% 227.59/39.23  | | 
% 227.59/39.23  | Case 2:
% 227.59/39.23  | | 
% 227.59/39.23  | |   (19)  all_57_5 = e2 & op(e2, e1) = e2
% 227.59/39.23  | | 
% 227.59/39.23  | | REF_CLOSE: (3), (9), (15), (19) are inconsistent by sub-proof #1858.
% 227.59/39.23  | | 
% 227.59/39.23  | End of split
% 227.59/39.23  | 
% 227.59/39.23  End of proof
% 227.59/39.23  
% 227.59/39.23  Sub-proof #288 shows that the following formulas are inconsistent:
% 227.59/39.23  ----------------------------------------------------------------
% 227.59/39.23    (1)  all_57_9 = e2
% 227.59/39.23    (2)   ~ (e3 = e1)
% 227.59/39.23    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.59/39.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.59/39.23    (4)  all_57_4 = e2
% 227.59/39.23    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 227.59/39.23         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 227.59/39.23    (6)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 227.59/39.23         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 227.59/39.23    (7)   ~ (e3 = e2)
% 227.59/39.23    (8)   ~ (e3 = e0)
% 227.59/39.23    (9)   ~ (e2 = e0)
% 227.59/39.23    (10)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 227.59/39.23          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 227.59/39.23    (11)   ~ (e1 = e0)
% 227.59/39.23    (12)   ~ (all_53_12 = e3)
% 227.59/39.23    (13)   ~ (e2 = e1)
% 227.59/39.23    (14)  op(e3, e0) = all_53_12
% 227.59/39.23  
% 227.59/39.23  Begin of proof
% 227.59/39.23  | 
% 227.59/39.23  | BETA: splitting (6) gives:
% 227.59/39.23  | 
% 227.59/39.23  | Case 1:
% 227.59/39.23  | | 
% 227.59/39.23  | |   (15)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) =
% 227.59/39.23  | |           e0)
% 227.59/39.23  | | 
% 227.59/39.23  | | BETA: splitting (15) gives:
% 227.59/39.23  | | 
% 227.59/39.23  | | Case 1:
% 227.59/39.23  | | | 
% 227.59/39.23  | | |   (16)  all_57_0 = e0 & op(e3, e3) = e0
% 227.59/39.23  | | | 
% 227.59/39.23  | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (10), (11), (12), (13),
% 227.59/39.23  | | |            (14), (16) are inconsistent by sub-proof #2447.
% 227.59/39.23  | | | 
% 227.59/39.23  | | Case 2:
% 227.59/39.23  | | | 
% 227.59/39.23  | | |   (17)  all_57_1 = e0 & op(e3, e2) = e0
% 227.59/39.23  | | | 
% 227.59/39.23  | | | ALPHA: (17) implies:
% 227.59/39.23  | | |   (18)  all_57_1 = e0
% 227.59/39.23  | | | 
% 227.59/39.23  | | | BETA: splitting (10) gives:
% 227.59/39.23  | | | 
% 227.59/39.23  | | | Case 1:
% 227.59/39.23  | | | | 
% 227.59/39.23  | | | |   (19)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2)
% 227.59/39.23  | | | |           = e3)
% 227.59/39.23  | | | | 
% 227.59/39.23  | | | | BETA: splitting (19) gives:
% 227.59/39.23  | | | | 
% 227.59/39.23  | | | | Case 1:
% 227.59/39.23  | | | | | 
% 227.59/39.23  | | | | |   (20)  all_57_0 = e3 & op(e3, e3) = e3
% 227.59/39.23  | | | | | 
% 227.59/39.23  | | | | | ALPHA: (20) implies:
% 227.59/39.23  | | | | |   (21)  op(e3, e3) = e3
% 227.59/39.23  | | | | | 
% 227.59/39.23  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (11), (13), (18), (21) are
% 227.59/39.23  | | | | |            inconsistent by sub-proof #2442.
% 227.59/39.23  | | | | | 
% 227.59/39.23  | | | | Case 2:
% 227.59/39.23  | | | | | 
% 227.59/39.24  | | | | |   (22)  all_57_1 = e3 & op(e3, e2) = e3
% 227.59/39.24  | | | | | 
% 227.59/39.24  | | | | | REF_CLOSE: (8), (18), (22) are inconsistent by sub-proof #2405.
% 227.59/39.24  | | | | | 
% 227.59/39.24  | | | | End of split
% 227.59/39.24  | | | | 
% 227.59/39.24  | | | Case 2:
% 227.59/39.24  | | | | 
% 227.59/39.24  | | | |   (23)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0)
% 227.59/39.24  | | | |           = e3)
% 227.59/39.24  | | | | 
% 227.59/39.24  | | | | REF_CLOSE: (3), (4), (7), (12), (14), (23) are inconsistent by sub-proof
% 227.59/39.24  | | | |            #2448.
% 227.59/39.24  | | | | 
% 227.59/39.24  | | | End of split
% 227.59/39.24  | | | 
% 227.59/39.24  | | End of split
% 227.59/39.24  | | 
% 227.59/39.24  | Case 2:
% 227.59/39.24  | | 
% 227.59/39.24  | |   (24)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) =
% 227.59/39.24  | |           e0)
% 227.59/39.24  | | 
% 227.59/39.24  | | BETA: splitting (24) gives:
% 227.59/39.24  | | 
% 227.59/39.24  | | Case 1:
% 227.59/39.24  | | | 
% 227.59/39.24  | | |   (25)  all_57_4 = e0 & op(e3, e1) = e0
% 227.59/39.24  | | | 
% 227.59/39.24  | | | REF_CLOSE: (4), (9), (25) are inconsistent by sub-proof #2045.
% 227.59/39.24  | | | 
% 227.59/39.24  | | Case 2:
% 227.59/39.24  | | | 
% 227.59/39.24  | | |   (26)  all_57_9 = e0 & op(e3, e0) = e0
% 227.59/39.24  | | | 
% 227.59/39.24  | | | REF_CLOSE: (1), (9), (26) are inconsistent by sub-proof #1973.
% 227.59/39.24  | | | 
% 227.59/39.24  | | End of split
% 227.59/39.24  | | 
% 227.59/39.24  | End of split
% 227.59/39.24  | 
% 227.59/39.24  End of proof
% 227.59/39.24  
% 227.59/39.24  Sub-proof #289 shows that the following formulas are inconsistent:
% 227.59/39.24  ----------------------------------------------------------------
% 227.59/39.24    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 227.59/39.24         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.59/39.24    (2)   ~ (e3 = e1)
% 227.59/39.24    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.59/39.24           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.59/39.24    (4)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 227.59/39.24         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 227.59/39.24    (5)   ~ (all_6_2 = e3)
% 227.59/39.24    (6)  op(e1, e1) = all_6_2
% 227.59/39.24    (7)  all_57_7 = e2
% 227.59/39.24    (8)   ~ (e3 = e2)
% 227.59/39.24    (9)   ~ (e3 = e0)
% 227.59/39.24    (10)  all_57_15 = e3
% 227.59/39.24    (11)  all_57_1 = e1
% 227.59/39.24    (12)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 227.59/39.24          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 227.59/39.24            e1)
% 227.59/39.24    (13)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 227.59/39.24          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 227.59/39.24    (14)   ~ (e2 = e0)
% 227.59/39.24    (15)  op(e2, e2) = e2
% 227.59/39.24    (16)   ~ (e1 = e0)
% 227.59/39.24    (17)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 227.59/39.24          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 227.59/39.24    (18)  op(e0, e0) = e3
% 227.59/39.24    (19)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.59/39.24          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 227.59/39.24            e2)
% 227.59/39.24    (20)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 227.59/39.24              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 227.59/39.24                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 227.59/39.24                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 227.59/39.24    (21)   ~ (e2 = e1)
% 227.59/39.24    (22)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 227.59/39.24          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 227.59/39.24    (23)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 227.59/39.24          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 227.59/39.24    (24)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 227.59/39.24          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 227.59/39.24  
% 227.59/39.24  Begin of proof
% 227.59/39.24  | 
% 227.59/39.24  | BETA: splitting (4) gives:
% 227.59/39.24  | 
% 227.59/39.24  | Case 1:
% 227.59/39.24  | | 
% 227.59/39.24  | |   (25)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 227.59/39.24  | |           e3)
% 227.59/39.24  | | 
% 227.59/39.24  | | BETA: splitting (25) gives:
% 227.59/39.24  | | 
% 227.59/39.24  | | Case 1:
% 227.59/39.24  | | | 
% 227.59/39.24  | | |   (26)  all_57_6 = e3 & op(e1, e3) = e3
% 227.59/39.24  | | | 
% 227.59/39.24  | | | ALPHA: (26) implies:
% 227.59/39.24  | | |   (27)  all_57_6 = e3
% 227.59/39.24  | | | 
% 227.59/39.24  | | | BETA: splitting (17) gives:
% 227.59/39.24  | | | 
% 227.59/39.24  | | | Case 1:
% 227.59/39.24  | | | | 
% 227.59/39.24  | | | |   (28)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2)
% 227.59/39.24  | | | |           = e3)
% 227.59/39.24  | | | | 
% 227.59/39.24  | | | | BETA: splitting (28) gives:
% 227.59/39.24  | | | | 
% 227.59/39.24  | | | | Case 1:
% 227.59/39.24  | | | | | 
% 227.59/39.24  | | | | |   (29)  all_57_1 = e3 & op(e3, e2) = e3
% 227.59/39.24  | | | | | 
% 227.59/39.24  | | | | | ALPHA: (29) implies:
% 227.59/39.24  | | | | |   (30)  all_57_1 = e3
% 227.59/39.24  | | | | | 
% 227.59/39.24  | | | | | COMBINE_EQS: (11), (30) imply:
% 227.59/39.24  | | | | |   (31)  e3 = e1
% 227.59/39.24  | | | | | 
% 227.59/39.24  | | | | | SIMP: (31) implies:
% 227.59/39.24  | | | | |   (32)  e3 = e1
% 227.59/39.24  | | | | | 
% 227.59/39.24  | | | | | COMBINE_EQS: (27), (32) imply:
% 227.59/39.24  | | | | |   (33)  all_57_6 = e1
% 227.59/39.24  | | | | | 
% 227.59/39.24  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (13), (14),
% 227.59/39.24  | | | | |            (15), (16), (20), (21), (22), (23), (24), (30), (33) are
% 227.59/39.24  | | | | |            inconsistent by sub-proof #1071.
% 227.59/39.24  | | | | | 
% 227.59/39.24  | | | | Case 2:
% 227.59/39.24  | | | | | 
% 227.59/39.24  | | | | |   (34)  all_57_3 = e3 & op(e2, e2) = e3
% 227.59/39.24  | | | | | 
% 227.59/39.24  | | | | | ALPHA: (34) implies:
% 227.59/39.24  | | | | |   (35)  op(e2, e2) = e3
% 227.59/39.24  | | | | | 
% 227.59/39.24  | | | | | REF_CLOSE: (3), (8), (15), (35) are inconsistent by sub-proof #2298.
% 227.59/39.24  | | | | | 
% 227.59/39.24  | | | | End of split
% 227.59/39.24  | | | | 
% 227.59/39.24  | | | Case 2:
% 227.59/39.24  | | | | 
% 227.59/39.24  | | | |   (36)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2)
% 227.59/39.24  | | | |           = e3)
% 227.59/39.24  | | | | 
% 227.59/39.24  | | | | REF_CLOSE: (2), (3), (7), (8), (9), (10), (12), (14), (16), (18), (19),
% 227.59/39.24  | | | |            (20), (21), (36) are inconsistent by sub-proof #776.
% 227.59/39.24  | | | | 
% 227.59/39.24  | | | End of split
% 227.59/39.24  | | | 
% 227.59/39.24  | | Case 2:
% 227.59/39.24  | | | 
% 227.59/39.24  | | |   (37)  all_57_7 = e3 & op(e1, e2) = e3
% 227.59/39.24  | | | 
% 227.59/39.24  | | | ALPHA: (37) implies:
% 227.59/39.24  | | |   (38)  all_57_7 = e3
% 227.59/39.24  | | | 
% 227.59/39.24  | | | REF_CLOSE: (7), (8), (38) are inconsistent by sub-proof #2102.
% 227.59/39.24  | | | 
% 227.59/39.24  | | End of split
% 227.59/39.24  | | 
% 227.59/39.24  | Case 2:
% 227.59/39.24  | | 
% 227.59/39.24  | |   (39)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 227.59/39.24  | |           e3)
% 227.59/39.24  | | 
% 227.59/39.24  | | REF_CLOSE: (2), (3), (5), (6), (8), (9), (10), (14), (16), (20), (21), (22),
% 227.59/39.24  | |            (23), (39) are inconsistent by sub-proof #1786.
% 227.59/39.24  | | 
% 227.59/39.24  | End of split
% 227.59/39.24  | 
% 227.59/39.24  End of proof
% 227.59/39.24  
% 227.59/39.24  Sub-proof #290 shows that the following formulas are inconsistent:
% 227.59/39.24  ----------------------------------------------------------------
% 227.59/39.24    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 227.59/39.24         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.59/39.24    (2)   ~ (e3 = e1)
% 227.59/39.24    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.59/39.24           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.59/39.24    (4)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 227.59/39.24    (5)   ~ (e3 = e2)
% 227.59/39.24    (6)   ~ (e3 = e0)
% 227.59/39.24    (7)  op(e0, e3) = all_53_3
% 227.59/39.24    (8)  all_57_15 = e3
% 227.59/39.24    (9)  all_57_1 = e1
% 227.59/39.24    (10)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 227.59/39.24          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 227.59/39.24            e1)
% 227.59/39.24    (11)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 227.59/39.24          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 227.59/39.24    (12)   ~ (e2 = e0)
% 227.59/39.24    (13)  op(e2, e2) = e2
% 227.59/39.24    (14)   ~ (e1 = e0)
% 227.59/39.24    (15)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 227.59/39.24          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 227.59/39.24    (16)  op(e0, e0) = e3
% 227.59/39.24    (17)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.59/39.24          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 227.59/39.24            e2)
% 227.59/39.24    (18)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 227.59/39.24              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 227.59/39.24                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 227.59/39.24                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 227.59/39.24    (19)   ~ (all_53_3 = e1)
% 227.59/39.24    (20)   ~ (e2 = e1)
% 227.59/39.24  
% 227.59/39.24  Begin of proof
% 227.59/39.24  | 
% 227.59/39.24  | BETA: splitting (4) gives:
% 227.59/39.24  | 
% 227.59/39.24  | Case 1:
% 227.59/39.24  | | 
% 227.59/39.24  | |   (21)  all_57_12 = e1 & op(e0, e3) = e1
% 227.59/39.24  | | 
% 227.59/39.24  | | REF_CLOSE: (3), (7), (19), (21) are inconsistent by sub-proof #1947.
% 227.59/39.24  | | 
% 227.59/39.24  | Case 2:
% 227.59/39.24  | | 
% 227.59/39.24  | |   (22)  all_57_13 = e1 & op(e0, e2) = e1
% 227.59/39.24  | | 
% 227.59/39.24  | | ALPHA: (22) implies:
% 227.59/39.24  | |   (23)  all_57_13 = e1
% 227.59/39.24  | | 
% 227.59/39.24  | | BETA: splitting (15) gives:
% 227.59/39.24  | | 
% 227.59/39.24  | | Case 1:
% 227.59/39.24  | | | 
% 227.59/39.24  | | |   (24)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 227.59/39.24  | | |           e3)
% 227.59/39.24  | | | 
% 227.59/39.24  | | | REF_CLOSE: (2), (3), (5), (9), (13), (24) are inconsistent by sub-proof
% 227.59/39.24  | | |            #292.
% 227.59/39.24  | | | 
% 227.59/39.24  | | Case 2:
% 227.59/39.24  | | | 
% 227.59/39.24  | | |   (25)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 227.59/39.24  | | |           e3)
% 227.59/39.24  | | | 
% 227.59/39.24  | | | BETA: splitting (25) gives:
% 227.59/39.24  | | | 
% 227.59/39.24  | | | Case 1:
% 227.59/39.24  | | | | 
% 227.59/39.24  | | | |   (26)  all_57_7 = e3 & op(e1, e2) = e3
% 227.59/39.24  | | | | 
% 227.59/39.24  | | | | ALPHA: (26) implies:
% 227.59/39.24  | | | |   (27)  all_57_7 = e3
% 227.59/39.24  | | | | 
% 227.59/39.24  | | | | REF_CLOSE: (1), (2), (3), (5), (6), (9), (11), (12), (14), (15), (20),
% 227.59/39.24  | | | |            (23), (27) are inconsistent by sub-proof #291.
% 227.59/39.24  | | | | 
% 227.59/39.24  | | | Case 2:
% 227.59/39.24  | | | | 
% 227.59/39.24  | | | |   (28)  all_57_13 = e3 & op(e0, e2) = e3
% 227.59/39.24  | | | | 
% 227.59/39.24  | | | | ALPHA: (28) implies:
% 227.59/39.24  | | | |   (29)  all_57_13 = e3
% 227.59/39.24  | | | | 
% 227.59/39.24  | | | | REF_CLOSE: (2), (3), (5), (6), (8), (10), (12), (14), (16), (17), (18),
% 227.59/39.24  | | | |            (20), (29) are inconsistent by sub-proof #1792.
% 227.59/39.24  | | | | 
% 227.59/39.24  | | | End of split
% 227.59/39.24  | | | 
% 227.59/39.24  | | End of split
% 227.59/39.24  | | 
% 227.59/39.24  | End of split
% 227.59/39.24  | 
% 227.59/39.24  End of proof
% 227.59/39.24  
% 227.59/39.24  Sub-proof #291 shows that the following formulas are inconsistent:
% 227.59/39.24  ----------------------------------------------------------------
% 227.59/39.24    (1)  all_57_13 = e1
% 227.59/39.24    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 227.59/39.24         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.59/39.24    (3)   ~ (e3 = e1)
% 227.59/39.24    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.59/39.24           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.59/39.24    (5)   ~ (e3 = e2)
% 227.59/39.24    (6)   ~ (e3 = e0)
% 227.59/39.24    (7)  all_57_1 = e1
% 227.59/39.24    (8)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 227.59/39.24         (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 227.59/39.24    (9)   ~ (e2 = e0)
% 227.59/39.24    (10)   ~ (e1 = e0)
% 227.59/39.24    (11)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 227.59/39.24          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 227.59/39.24    (12)  all_57_7 = e3
% 227.59/39.24    (13)   ~ (e2 = e1)
% 227.59/39.24  
% 227.59/39.24  Begin of proof
% 227.59/39.24  | 
% 227.59/39.24  | BETA: splitting (8) gives:
% 227.59/39.24  | 
% 227.59/39.24  | Case 1:
% 227.59/39.24  | | 
% 227.59/39.24  | |   (14)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) =
% 227.59/39.24  | |           e0)
% 227.59/39.24  | | 
% 227.59/39.24  | | BETA: splitting (14) gives:
% 227.59/39.24  | | 
% 227.59/39.24  | | Case 1:
% 227.59/39.24  | | | 
% 227.59/39.24  | | |   (15)  all_57_1 = e0 & op(e3, e2) = e0
% 227.59/39.24  | | | 
% 227.59/39.24  | | | REF_CLOSE: (7), (10), (15) are inconsistent by sub-proof #2493.
% 227.59/39.24  | | | 
% 227.59/39.24  | | Case 2:
% 227.59/39.24  | | | 
% 227.59/39.24  | | |   (16)  all_57_3 = e0 & op(e2, e2) = e0
% 227.59/39.24  | | | 
% 227.59/39.24  | | | ALPHA: (16) implies:
% 227.59/39.24  | | |   (17)  all_57_3 = e0
% 227.59/39.24  | | |   (18)  op(e2, e2) = e0
% 227.59/39.24  | | | 
% 227.59/39.24  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (11), (13), (17), (18)
% 227.59/39.24  | | |            are inconsistent by sub-proof #1193.
% 227.59/39.24  | | | 
% 227.59/39.24  | | End of split
% 227.59/39.24  | | 
% 227.59/39.24  | Case 2:
% 227.59/39.24  | | 
% 227.59/39.24  | |   (19)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 227.59/39.24  | |           e0)
% 227.59/39.24  | | 
% 227.59/39.24  | | BETA: splitting (19) gives:
% 227.59/39.24  | | 
% 227.59/39.24  | | Case 1:
% 227.59/39.24  | | | 
% 227.59/39.24  | | |   (20)  all_57_7 = e0 & op(e1, e2) = e0
% 227.59/39.24  | | | 
% 227.59/39.24  | | | REF_CLOSE: (6), (12), (20) are inconsistent by sub-proof #2042.
% 227.59/39.24  | | | 
% 227.59/39.24  | | Case 2:
% 227.59/39.24  | | | 
% 227.59/39.24  | | |   (21)  all_57_13 = e0 & op(e0, e2) = e0
% 227.59/39.24  | | | 
% 227.59/39.24  | | | REF_CLOSE: (1), (10), (21) are inconsistent by sub-proof #1920.
% 227.59/39.24  | | | 
% 227.59/39.24  | | End of split
% 227.59/39.24  | | 
% 227.59/39.24  | End of split
% 227.59/39.24  | 
% 227.59/39.24  End of proof
% 227.59/39.24  
% 227.59/39.24  Sub-proof #292 shows that the following formulas are inconsistent:
% 227.59/39.24  ----------------------------------------------------------------
% 227.59/39.24    (1)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3)
% 227.59/39.24    (2)   ~ (e3 = e1)
% 227.59/39.24    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.59/39.24           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.59/39.24    (4)   ~ (e3 = e2)
% 227.59/39.24    (5)  all_57_1 = e1
% 227.59/39.24    (6)  op(e2, e2) = e2
% 227.59/39.24  
% 227.59/39.24  Begin of proof
% 227.59/39.24  | 
% 227.59/39.24  | BETA: splitting (1) gives:
% 227.59/39.24  | 
% 227.59/39.24  | Case 1:
% 227.59/39.24  | | 
% 227.59/39.24  | |   (7)  all_57_1 = e3 & op(e3, e2) = e3
% 227.59/39.24  | | 
% 227.59/39.24  | | REF_CLOSE: (2), (5), (7) are inconsistent by sub-proof #2196.
% 227.59/39.24  | | 
% 227.59/39.24  | Case 2:
% 227.59/39.24  | | 
% 227.59/39.24  | |   (8)  all_57_3 = e3 & op(e2, e2) = e3
% 227.59/39.24  | | 
% 227.59/39.24  | | ALPHA: (8) implies:
% 227.59/39.24  | |   (9)  op(e2, e2) = e3
% 227.59/39.24  | | 
% 227.59/39.24  | | REF_CLOSE: (3), (4), (6), (9) are inconsistent by sub-proof #2298.
% 227.59/39.24  | | 
% 227.59/39.24  | End of split
% 227.59/39.24  | 
% 227.59/39.24  End of proof
% 227.59/39.24  
% 227.59/39.24  Sub-proof #293 shows that the following formulas are inconsistent:
% 227.59/39.24  ----------------------------------------------------------------
% 227.59/39.24    (1)  all_55_5 = all_8_2
% 227.59/39.24    (2)  all_55_5 = e3
% 227.59/39.24    (3)   ~ (all_8_2 = e3)
% 227.59/39.24  
% 227.59/39.24  Begin of proof
% 227.59/39.24  | 
% 227.59/39.24  | COMBINE_EQS: (1), (2) imply:
% 227.59/39.24  |   (4)  all_8_2 = e3
% 227.59/39.24  | 
% 227.59/39.24  | SIMP: (4) implies:
% 227.59/39.24  |   (5)  all_8_2 = e3
% 227.59/39.24  | 
% 227.59/39.24  | REDUCE: (3), (5) imply:
% 227.59/39.24  |   (6)  $false
% 227.59/39.24  | 
% 227.59/39.24  | CLOSE: (6) is inconsistent.
% 227.59/39.24  | 
% 227.59/39.24  End of proof
% 227.59/39.24  
% 227.59/39.24  Sub-proof #294 shows that the following formulas are inconsistent:
% 227.59/39.24  ----------------------------------------------------------------
% 227.59/39.24    (1)  op(e3, e3) = e1
% 227.59/39.24    (2)   ~ (e3 = e1)
% 227.59/39.24    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.59/39.24           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.59/39.24    (4)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1)
% 227.59/39.24    (5)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 227.59/39.24         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 227.59/39.24    (6)  op(e2, e2) = e0
% 227.59/39.24    (7)   ~ (e3 = e2)
% 227.59/39.24    (8)   ~ (e3 = e0)
% 227.59/39.24    (9)  all_57_9 = e0
% 227.59/39.24    (10)   ~ (e2 = e0)
% 227.59/39.24    (11)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 227.59/39.24          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 227.59/39.24    (12)   ~ (e1 = e0)
% 227.59/39.24    (13)   ~ (e2 = e1)
% 227.59/39.24  
% 227.59/39.24  Begin of proof
% 227.59/39.24  | 
% 227.59/39.24  | BETA: splitting (4) gives:
% 227.59/39.24  | 
% 227.59/39.24  | Case 1:
% 227.59/39.24  | | 
% 227.59/39.24  | |   (14)  all_57_1 = e1 & op(e3, e2) = e1
% 227.59/39.24  | | 
% 227.59/39.24  | | ALPHA: (14) implies:
% 227.59/39.24  | |   (15)  all_57_1 = e1
% 227.59/39.24  | | 
% 227.59/39.24  | | REF_CLOSE: (1), (2), (3), (5), (7), (8), (9), (10), (11), (13), (15) are
% 227.59/39.24  | |            inconsistent by sub-proof #295.
% 227.59/39.24  | | 
% 227.59/39.24  | Case 2:
% 227.59/39.24  | | 
% 227.59/39.24  | |   (16)  all_57_3 = e1 & op(e2, e2) = e1
% 227.59/39.24  | | 
% 227.59/39.24  | | ALPHA: (16) implies:
% 227.59/39.24  | |   (17)  op(e2, e2) = e1
% 227.59/39.24  | | 
% 227.59/39.24  | | REF_CLOSE: (3), (6), (12), (17) are inconsistent by sub-proof #2352.
% 227.59/39.24  | | 
% 227.59/39.24  | End of split
% 227.59/39.24  | 
% 227.59/39.24  End of proof
% 227.59/39.24  
% 227.59/39.24  Sub-proof #295 shows that the following formulas are inconsistent:
% 227.59/39.24  ----------------------------------------------------------------
% 227.59/39.24    (1)  op(e3, e3) = e1
% 227.59/39.24    (2)   ~ (e3 = e1)
% 227.59/39.24    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.59/39.24           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.59/39.24    (4)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 227.59/39.24         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 227.59/39.24    (5)   ~ (e3 = e2)
% 227.59/39.24    (6)   ~ (e3 = e0)
% 227.59/39.24    (7)  all_57_1 = e1
% 227.59/39.24    (8)  all_57_9 = e0
% 227.59/39.24    (9)   ~ (e2 = e0)
% 227.59/39.24    (10)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 227.59/39.24          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 227.59/39.24    (11)   ~ (e2 = e1)
% 227.59/39.24  
% 227.59/39.24  Begin of proof
% 227.59/39.24  | 
% 227.59/39.24  | BETA: splitting (10) gives:
% 227.59/39.24  | 
% 227.59/39.24  | Case 1:
% 227.59/39.24  | | 
% 227.59/39.24  | |   (12)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) =
% 227.59/39.24  | |           e3)
% 227.59/39.24  | | 
% 227.59/39.24  | | BETA: splitting (12) gives:
% 227.59/39.24  | | 
% 227.59/39.24  | | Case 1:
% 227.59/39.24  | | | 
% 227.59/39.24  | | |   (13)  all_57_0 = e3 & op(e3, e3) = e3
% 227.59/39.24  | | | 
% 227.59/39.24  | | | ALPHA: (13) implies:
% 227.59/39.24  | | |   (14)  op(e3, e3) = e3
% 227.59/39.24  | | | 
% 227.59/39.24  | | | REF_CLOSE: (1), (2), (3), (14) are inconsistent by sub-proof #2495.
% 227.59/39.24  | | | 
% 227.59/39.24  | | Case 2:
% 227.59/39.24  | | | 
% 227.59/39.24  | | |   (15)  all_57_1 = e3 & op(e3, e2) = e3
% 227.59/39.24  | | | 
% 227.59/39.24  | | | REF_CLOSE: (2), (7), (15) are inconsistent by sub-proof #2196.
% 227.59/39.24  | | | 
% 227.59/39.24  | | End of split
% 227.59/39.24  | | 
% 227.59/39.24  | Case 2:
% 227.59/39.24  | | 
% 227.59/39.24  | |   (16)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) =
% 227.59/39.24  | |           e3)
% 227.59/39.24  | | 
% 227.59/39.24  | | BETA: splitting (16) gives:
% 227.59/39.24  | | 
% 227.59/39.24  | | Case 1:
% 227.59/39.24  | | | 
% 227.59/39.24  | | |   (17)  all_57_4 = e3 & op(e3, e1) = e3
% 227.59/39.24  | | | 
% 227.59/39.24  | | | ALPHA: (17) implies:
% 227.59/39.24  | | |   (18)  all_57_4 = e3
% 227.59/39.24  | | | 
% 227.59/39.24  | | | REF_CLOSE: (1), (3), (4), (5), (7), (8), (9), (11), (18) are inconsistent
% 227.59/39.24  | | |            by sub-proof #296.
% 227.59/39.24  | | | 
% 227.59/39.24  | | Case 2:
% 227.59/39.24  | | | 
% 227.59/39.24  | | |   (19)  all_57_9 = e3 & op(e3, e0) = e3
% 227.59/39.24  | | | 
% 227.59/39.24  | | | REF_CLOSE: (6), (8), (19) are inconsistent by sub-proof #2052.
% 227.59/39.24  | | | 
% 227.59/39.24  | | End of split
% 227.59/39.24  | | 
% 227.59/39.24  | End of split
% 227.59/39.24  | 
% 227.59/39.24  End of proof
% 227.59/39.24  
% 227.59/39.24  Sub-proof #296 shows that the following formulas are inconsistent:
% 227.59/39.24  ----------------------------------------------------------------
% 227.59/39.24    (1)  op(e3, e3) = e1
% 227.59/39.24    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.59/39.24           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.59/39.24    (3)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 227.59/39.24         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 227.59/39.24    (4)  all_57_4 = e3
% 227.59/39.24    (5)   ~ (e3 = e2)
% 227.59/39.24    (6)  all_57_1 = e1
% 227.59/39.24    (7)  all_57_9 = e0
% 227.59/39.24    (8)   ~ (e2 = e0)
% 227.59/39.24    (9)   ~ (e2 = e1)
% 227.59/39.24  
% 227.59/39.24  Begin of proof
% 227.59/39.24  | 
% 227.59/39.24  | BETA: splitting (3) gives:
% 227.59/39.24  | 
% 227.59/39.24  | Case 1:
% 227.59/39.24  | | 
% 227.59/39.24  | |   (10)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) =
% 227.59/39.24  | |           e2)
% 227.59/39.24  | | 
% 227.59/39.24  | | BETA: splitting (10) gives:
% 227.59/39.24  | | 
% 227.59/39.24  | | Case 1:
% 227.59/39.24  | | | 
% 227.59/39.24  | | |   (11)  all_57_0 = e2 & op(e3, e3) = e2
% 227.59/39.24  | | | 
% 227.59/39.24  | | | ALPHA: (11) implies:
% 227.59/39.24  | | |   (12)  op(e3, e3) = e2
% 227.59/39.24  | | | 
% 227.59/39.24  | | | REF_CLOSE: (1), (2), (9), (12) are inconsistent by sub-proof #1950.
% 227.59/39.24  | | | 
% 227.59/39.24  | | Case 2:
% 227.59/39.24  | | | 
% 227.59/39.24  | | |   (13)  all_57_1 = e2 & op(e3, e2) = e2
% 227.59/39.24  | | | 
% 227.59/39.24  | | | REF_CLOSE: (6), (9), (13) are inconsistent by sub-proof #2489.
% 227.59/39.24  | | | 
% 227.59/39.24  | | End of split
% 227.59/39.24  | | 
% 227.59/39.24  | Case 2:
% 227.59/39.24  | | 
% 227.59/39.24  | |   (14)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) =
% 227.59/39.24  | |           e2)
% 227.59/39.24  | | 
% 227.59/39.24  | | BETA: splitting (14) gives:
% 227.59/39.24  | | 
% 227.59/39.24  | | Case 1:
% 227.59/39.24  | | | 
% 227.59/39.24  | | |   (15)  all_57_4 = e2 & op(e3, e1) = e2
% 227.59/39.24  | | | 
% 227.59/39.24  | | | REF_CLOSE: (4), (5), (15) are inconsistent by sub-proof #2487.
% 227.59/39.24  | | | 
% 227.59/39.24  | | Case 2:
% 227.59/39.24  | | | 
% 227.59/39.24  | | |   (16)  all_57_9 = e2 & op(e3, e0) = e2
% 227.59/39.24  | | | 
% 227.59/39.24  | | | REF_CLOSE: (7), (8), (16) are inconsistent by sub-proof #2486.
% 227.59/39.24  | | | 
% 227.59/39.24  | | End of split
% 227.59/39.24  | | 
% 227.59/39.24  | End of split
% 227.59/39.24  | 
% 227.59/39.24  End of proof
% 227.59/39.24  
% 227.59/39.24  Sub-proof #297 shows that the following formulas are inconsistent:
% 227.59/39.24  ----------------------------------------------------------------
% 227.59/39.24    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 227.59/39.24         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 227.59/39.24    (2)   ~ (e3 = e1)
% 227.59/39.24    (3)  all_57_3 = e0
% 227.59/39.24    (4)   ~ (e3 = e2)
% 227.59/39.24    (5)   ~ (e3 = e0)
% 227.59/39.24    (6)  all_57_0 = e1
% 227.59/39.24    (7)   ~ (e2 = e0)
% 227.59/39.24    (8)   ~ (e1 = e0)
% 227.59/39.24    (9)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 227.59/39.24         (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 227.59/39.24    (10)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 227.59/39.24          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 227.59/39.24    (11)   ~ (e2 = e1)
% 227.59/39.24    (12)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0)
% 227.59/39.24  
% 227.59/39.24  Begin of proof
% 227.59/39.24  | 
% 227.59/39.24  | BETA: splitting (12) gives:
% 227.59/39.24  | 
% 227.59/39.24  | Case 1:
% 227.59/39.24  | | 
% 227.59/39.24  | |   (13)  all_57_0 = e0 & op(e3, e3) = e0
% 227.59/39.24  | | 
% 227.59/39.24  | | REF_CLOSE: (6), (8), (13) are inconsistent by sub-proof #1812.
% 227.59/39.24  | | 
% 227.59/39.24  | Case 2:
% 227.59/39.24  | | 
% 227.59/39.24  | |   (14)  all_57_2 = e0 & op(e2, e3) = e0
% 227.59/39.24  | | 
% 227.59/39.24  | | ALPHA: (14) implies:
% 227.59/39.24  | |   (15)  all_57_2 = e0
% 227.59/39.24  | | 
% 227.59/39.24  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (15) are
% 227.59/39.24  | |            inconsistent by sub-proof #2246.
% 227.59/39.24  | | 
% 227.59/39.24  | End of split
% 227.59/39.24  | 
% 227.59/39.24  End of proof
% 227.59/39.24  
% 227.59/39.24  Sub-proof #298 shows that the following formulas are inconsistent:
% 227.59/39.24  ----------------------------------------------------------------
% 227.59/39.24    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.59/39.24           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.67/39.24    (2)  all_57_0 = e1
% 227.67/39.24    (3)  op(e3, e2) = all_53_4
% 227.67/39.24    (4)   ~ (e1 = e0)
% 227.67/39.24    (5)   ~ (all_53_4 = e0)
% 227.67/39.24    (6)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0)
% 227.67/39.24  
% 227.67/39.24  Begin of proof
% 227.67/39.24  | 
% 227.67/39.24  | BETA: splitting (6) gives:
% 227.67/39.24  | 
% 227.67/39.24  | Case 1:
% 227.67/39.24  | | 
% 227.67/39.24  | |   (7)  all_57_0 = e0 & op(e3, e3) = e0
% 227.67/39.24  | | 
% 227.67/39.24  | | REF_CLOSE: (2), (4), (7) are inconsistent by sub-proof #1812.
% 227.67/39.24  | | 
% 227.67/39.24  | Case 2:
% 227.67/39.24  | | 
% 227.67/39.24  | |   (8)  all_57_1 = e0 & op(e3, e2) = e0
% 227.67/39.24  | | 
% 227.67/39.24  | | ALPHA: (8) implies:
% 227.67/39.24  | |   (9)  op(e3, e2) = e0
% 227.67/39.24  | | 
% 227.67/39.24  | | REF_CLOSE: (1), (3), (5), (9) are inconsistent by sub-proof #1941.
% 227.67/39.24  | | 
% 227.67/39.24  | End of split
% 227.67/39.24  | 
% 227.67/39.24  End of proof
% 227.67/39.24  
% 227.67/39.24  Sub-proof #299 shows that the following formulas are inconsistent:
% 227.67/39.24  ----------------------------------------------------------------
% 227.67/39.24    (1)  op(e2, e3) = all_53_1
% 227.67/39.24    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.67/39.24           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.67/39.24    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1)
% 227.67/39.24    (4)  op(e2, e2) = e0
% 227.67/39.24    (5)   ~ (all_53_1 = e1)
% 227.67/39.24    (6)   ~ (e1 = e0)
% 227.67/39.24  
% 227.67/39.24  Begin of proof
% 227.67/39.24  | 
% 227.67/39.24  | BETA: splitting (3) gives:
% 227.67/39.24  | 
% 227.67/39.24  | Case 1:
% 227.67/39.24  | | 
% 227.67/39.24  | |   (7)  all_57_2 = e1 & op(e2, e3) = e1
% 227.67/39.24  | | 
% 227.67/39.24  | | REF_CLOSE: (1), (2), (5), (7) are inconsistent by sub-proof #2156.
% 227.67/39.24  | | 
% 227.67/39.24  | Case 2:
% 227.67/39.24  | | 
% 227.67/39.24  | |   (8)  all_57_3 = e1 & op(e2, e2) = e1
% 227.67/39.24  | | 
% 227.67/39.24  | | ALPHA: (8) implies:
% 227.67/39.24  | |   (9)  op(e2, e2) = e1
% 227.67/39.24  | | 
% 227.67/39.24  | | REF_CLOSE: (2), (4), (6), (9) are inconsistent by sub-proof #2352.
% 227.67/39.24  | | 
% 227.67/39.24  | End of split
% 227.67/39.24  | 
% 227.67/39.24  End of proof
% 227.67/39.24  
% 227.67/39.24  Sub-proof #300 shows that the following formulas are inconsistent:
% 227.67/39.24  ----------------------------------------------------------------
% 227.67/39.24    (1)  op(e3, e3) = e1
% 227.67/39.24    (2)  all_57_15 = e0
% 227.67/39.24    (3)   ~ (all_53_6 = e0)
% 227.67/39.24    (4)   ~ (e3 = e1)
% 227.67/39.24    (5)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 227.67/39.24         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 227.67/39.24    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.67/39.24           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.67/39.24    (7)   ~ (all_36_2 = e1) | ( ~ (all_36_0 = e0) & op(all_36_1, e3) = all_36_0 &
% 227.67/39.24           op(e3, e1) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 =
% 227.67/39.24             e2) & op(e3, e1) = all_36_1 & $i(all_36_1))
% 227.67/39.24    (8)  op(e1, e1) = all_6_2
% 227.67/39.24    (9)   ~ (all_53_9 = e0)
% 227.67/39.24    (10)   ~ (all_53_8 = e1)
% 227.67/39.24    (11)  op(e2, e2) = e0
% 227.67/39.24    (12)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 227.67/39.24          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 227.67/39.24    (13)   ~ (e3 = e2)
% 227.67/39.24    (14)  op(e1, e0) = all_53_14
% 227.67/39.24    (15)   ~ (e3 = e0)
% 227.67/39.24    (16)  op(e0, e3) = all_53_3
% 227.67/39.24    (17)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 227.67/39.24          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 227.67/39.24            e1)
% 227.67/39.24    (18)  ( ~ (all_10_0 = e2) & op(all_10_1, e3) = all_10_0 & op(e3, e1) =
% 227.67/39.24            all_10_1 & $i(all_10_0) & $i(all_10_1)) | ( ~ (all_10_1 = e0) & op(e3,
% 227.67/39.24              e1) = all_10_1 & $i(all_10_1))
% 227.67/39.24    (19)   ~ (e2 = e0)
% 227.67/39.25    (20)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 227.67/39.25            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 227.67/39.25            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 227.67/39.25            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 227.67/39.25              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 227.67/39.25            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 227.67/39.25            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 227.67/39.25              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 227.67/39.25              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 227.67/39.25            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 227.67/39.25            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 227.67/39.25            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 227.67/39.25              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 227.67/39.25              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 227.67/39.25            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 227.67/39.25              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 227.67/39.25            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 227.67/39.25            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 227.67/39.25              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 227.67/39.25              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 227.67/39.25            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 227.67/39.25            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 227.67/39.25    (21)  all_55_12 = all_53_3
% 227.67/39.25    (22)   ~ (e1 = e0)
% 227.67/39.25    (23)   ~ (all_53_2 = all_53_3)
% 227.67/39.25    (24)  op(e0, e0) = e0
% 227.67/39.25    (25)   ~ (all_53_14 = e0)
% 227.67/39.25    (26)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 227.67/39.25          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 227.67/39.25            e3)
% 227.67/39.25    (27)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.67/39.25          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 227.67/39.25            e2)
% 227.67/39.25    (28)   ~ (all_53_3 = e1)
% 227.67/39.25    (29)  all_36_2 = e1
% 227.67/39.25    (30)  op(e1, e3) = all_53_2
% 227.67/39.25    (31)   ~ (e2 = e1)
% 227.67/39.25    (32)  op(e2, e1) = all_53_9
% 227.67/39.25    (33)  op(e1, e2) = all_53_6
% 227.67/39.25    (34)   ~ (all_6_2 = e0)
% 227.67/39.25    (35)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 227.67/39.25    (36)  op(e3, e1) = all_53_8
% 227.67/39.25  
% 227.67/39.25  Begin of proof
% 227.67/39.25  | 
% 227.67/39.25  | BETA: splitting (5) gives:
% 227.67/39.25  | 
% 227.67/39.25  | Case 1:
% 227.67/39.25  | | 
% 227.67/39.25  | |   (37)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) =
% 227.67/39.25  | |           e0)
% 227.67/39.25  | | 
% 227.67/39.25  | | BETA: splitting (37) gives:
% 227.67/39.25  | | 
% 227.67/39.25  | | Case 1:
% 227.67/39.25  | | | 
% 227.67/39.25  | | |   (38)  all_57_6 = e0 & op(e1, e3) = e0
% 227.67/39.25  | | | 
% 227.67/39.25  | | | ALPHA: (38) implies:
% 227.67/39.25  | | |   (39)  op(e1, e3) = e0
% 227.67/39.25  | | | 
% 227.67/39.25  | | | BETA: splitting (12) gives:
% 227.67/39.25  | | | 
% 227.67/39.25  | | | Case 1:
% 227.67/39.25  | | | | 
% 227.67/39.25  | | | |   (40)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1)
% 227.67/39.25  | | | |           = e0)
% 227.67/39.25  | | | | 
% 227.67/39.25  | | | | REF_CLOSE: (1), (6), (7), (9), (10), (11), (15), (16), (18), (19), (20),
% 227.67/39.25  | | | |            (21), (23), (24), (28), (29), (30), (32), (35), (36), (39),
% 227.67/39.25  | | | |            (40) are inconsistent by sub-proof #301.
% 227.67/39.25  | | | | 
% 227.67/39.25  | | | Case 2:
% 227.67/39.25  | | | | 
% 227.67/39.25  | | | |   (41)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1)
% 227.67/39.25  | | | |           = e0)
% 227.67/39.25  | | | | 
% 227.67/39.25  | | | | BETA: splitting (41) gives:
% 227.67/39.25  | | | | 
% 227.67/39.25  | | | | Case 1:
% 227.67/39.25  | | | | | 
% 227.67/39.25  | | | | |   (42)  all_57_8 = e0 & op(e1, e1) = e0
% 227.67/39.25  | | | | | 
% 227.67/39.25  | | | | | REF_CLOSE: (6), (8), (34), (42) are inconsistent by sub-proof #2412.
% 227.67/39.25  | | | | | 
% 227.67/39.25  | | | | Case 2:
% 227.67/39.25  | | | | | 
% 227.67/39.25  | | | | |   (43)  all_57_14 = e0 & op(e0, e1) = e0
% 227.67/39.25  | | | | | 
% 227.67/39.25  | | | | | ALPHA: (43) implies:
% 227.67/39.25  | | | | |   (44)  all_57_14 = e0
% 227.67/39.25  | | | | | 
% 227.67/39.25  | | | | | REF_CLOSE: (2), (4), (6), (13), (15), (16), (17), (19), (22), (24),
% 227.67/39.25  | | | | |            (26), (27), (28), (31), (44) are inconsistent by sub-proof
% 227.67/39.25  | | | | |            #320.
% 227.67/39.25  | | | | | 
% 227.67/39.25  | | | | End of split
% 227.67/39.25  | | | | 
% 227.67/39.25  | | | End of split
% 227.67/39.25  | | | 
% 227.67/39.25  | | Case 2:
% 227.67/39.25  | | | 
% 227.67/39.25  | | |   (45)  all_57_7 = e0 & op(e1, e2) = e0
% 227.67/39.25  | | | 
% 227.67/39.25  | | | REF_CLOSE: (3), (6), (33), (45) are inconsistent by sub-proof #2039.
% 227.67/39.25  | | | 
% 227.67/39.25  | | End of split
% 227.67/39.25  | | 
% 227.67/39.25  | Case 2:
% 227.67/39.25  | | 
% 227.67/39.25  | |   (46)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 227.67/39.25  | |           e0)
% 227.67/39.25  | | 
% 227.67/39.25  | | BETA: splitting (46) gives:
% 227.67/39.25  | | 
% 227.67/39.25  | | Case 1:
% 227.67/39.25  | | | 
% 227.67/39.25  | | |   (47)  all_57_8 = e0 & op(e1, e1) = e0
% 227.67/39.25  | | | 
% 227.67/39.25  | | | REF_CLOSE: (6), (8), (34), (47) are inconsistent by sub-proof #2412.
% 227.67/39.25  | | | 
% 227.67/39.25  | | Case 2:
% 227.67/39.25  | | | 
% 227.67/39.25  | | |   (48)  all_57_11 = e0 & op(e1, e0) = e0
% 227.67/39.25  | | | 
% 227.67/39.25  | | | REF_CLOSE: (6), (14), (25), (48) are inconsistent by sub-proof #2341.
% 227.67/39.25  | | | 
% 227.67/39.25  | | End of split
% 227.67/39.25  | | 
% 227.67/39.25  | End of split
% 227.67/39.25  | 
% 227.67/39.25  End of proof
% 227.67/39.25  
% 227.67/39.25  Sub-proof #301 shows that the following formulas are inconsistent:
% 227.67/39.25  ----------------------------------------------------------------
% 227.67/39.25    (1)  op(e1, e3) = e0
% 227.67/39.25    (2)  op(e3, e3) = e1
% 227.67/39.25    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.67/39.25           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.67/39.25    (4)   ~ (all_36_2 = e1) | ( ~ (all_36_0 = e0) & op(all_36_1, e3) = all_36_0 &
% 227.67/39.25           op(e3, e1) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 =
% 227.67/39.25             e2) & op(e3, e1) = all_36_1 & $i(all_36_1))
% 227.67/39.25    (5)   ~ (all_53_9 = e0)
% 227.67/39.25    (6)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0)
% 227.67/39.25    (7)   ~ (all_53_8 = e1)
% 227.67/39.25    (8)  op(e2, e2) = e0
% 227.67/39.25    (9)   ~ (e3 = e0)
% 227.67/39.25    (10)  op(e0, e3) = all_53_3
% 227.67/39.25    (11)  ( ~ (all_10_0 = e2) & op(all_10_1, e3) = all_10_0 & op(e3, e1) =
% 227.67/39.25            all_10_1 & $i(all_10_0) & $i(all_10_1)) | ( ~ (all_10_1 = e0) & op(e3,
% 227.67/39.25              e1) = all_10_1 & $i(all_10_1))
% 227.67/39.25    (12)   ~ (e2 = e0)
% 227.67/39.25    (13)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 227.67/39.25            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 227.67/39.25            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 227.67/39.25            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 227.67/39.25              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 227.67/39.25            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 227.67/39.25            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 227.67/39.25              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 227.67/39.25              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 227.67/39.25            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 227.67/39.25            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 227.67/39.25            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 227.67/39.25              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 227.67/39.25              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 227.67/39.25            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 227.67/39.25              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 227.67/39.25            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 227.67/39.25            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 227.67/39.25              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 227.67/39.25              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 227.67/39.25            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 227.67/39.25            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 227.67/39.25    (14)  all_55_12 = all_53_3
% 227.67/39.25    (15)   ~ (all_53_2 = all_53_3)
% 227.67/39.25    (16)  op(e0, e0) = e0
% 227.67/39.25    (17)   ~ (all_53_3 = e1)
% 227.67/39.25    (18)  all_36_2 = e1
% 227.67/39.25    (19)  op(e1, e3) = all_53_2
% 227.67/39.25    (20)  op(e2, e1) = all_53_9
% 227.67/39.25    (21)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 227.67/39.25    (22)  op(e3, e1) = all_53_8
% 227.67/39.25  
% 227.67/39.25  Begin of proof
% 227.67/39.25  | 
% 227.67/39.25  | BETA: splitting (6) gives:
% 227.67/39.25  | 
% 227.67/39.25  | Case 1:
% 227.67/39.25  | | 
% 227.67/39.25  | |   (23)  all_57_4 = e0 & op(e3, e1) = e0
% 227.67/39.25  | | 
% 227.67/39.25  | | ALPHA: (23) implies:
% 227.67/39.25  | |   (24)  op(e3, e1) = e0
% 227.67/39.25  | | 
% 227.67/39.25  | | GROUND_INST: instantiating (3) with all_53_2, e0, e3, e1, simplifying with
% 227.67/39.25  | |              (1), (19) gives:
% 227.67/39.25  | |   (25)  all_53_2 = e0
% 227.67/39.25  | | 
% 227.67/39.25  | | GROUND_INST: instantiating (3) with all_53_8, e0, e1, e3, simplifying with
% 227.67/39.25  | |              (22), (24) gives:
% 227.67/39.25  | |   (26)  all_53_8 = e0
% 227.67/39.25  | | 
% 227.67/39.25  | | REDUCE: (15), (25) imply:
% 227.67/39.25  | |   (27)   ~ (all_53_3 = e0)
% 227.67/39.25  | | 
% 227.67/39.25  | | SIMP: (27) implies:
% 227.67/39.25  | |   (28)   ~ (all_53_3 = e0)
% 227.67/39.25  | | 
% 227.67/39.25  | | REDUCE: (7), (26) imply:
% 227.67/39.25  | |   (29)   ~ (e1 = e0)
% 227.67/39.25  | | 
% 227.67/39.25  | | SIMP: (29) implies:
% 227.67/39.25  | |   (30)   ~ (e1 = e0)
% 227.67/39.25  | | 
% 227.67/39.25  | | BETA: splitting (4) gives:
% 227.67/39.25  | | 
% 227.67/39.25  | | Case 1:
% 227.67/39.25  | | | 
% 227.67/39.25  | | |   (31)   ~ (all_36_2 = e1)
% 227.67/39.25  | | | 
% 227.67/39.25  | | | REDUCE: (18), (31) imply:
% 227.67/39.25  | | |   (32)  $false
% 227.67/39.25  | | | 
% 227.67/39.25  | | | CLOSE: (32) is inconsistent.
% 227.67/39.25  | | | 
% 227.67/39.25  | | Case 2:
% 227.67/39.25  | | | 
% 227.67/39.25  | | |   (33)  ( ~ (all_36_0 = e0) & op(all_36_1, e3) = all_36_0 & op(e3, e1) =
% 227.67/39.25  | | |           all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e2) &
% 227.67/39.25  | | |           op(e3, e1) = all_36_1 & $i(all_36_1))
% 227.67/39.25  | | | 
% 227.67/39.25  | | | BETA: splitting (13) gives:
% 227.67/39.25  | | | 
% 227.67/39.25  | | | Case 1:
% 227.67/39.25  | | | | 
% 227.67/39.25  | | | |   (34)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 227.67/39.25  | | | |           op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 227.67/39.25  | | | |           op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 227.67/39.25  | | | |           op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) =
% 227.67/39.25  | | | |           all_52_5 & op(e3, e0) = all_52_7 & $i(all_52_1) & $i(all_52_3)
% 227.67/39.25  | | | |           & $i(all_52_5) & $i(all_52_7)) | (all_52_8 = e3 & all_52_10 =
% 227.67/39.25  | | | |           e2 & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9, all_52_9)
% 227.67/39.25  | | | |           = e3 & op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 227.67/39.25  | | | |             all_52_13) = e1 & op(all_52_15, all_52_15) = e0 & op(e2, e3)
% 227.67/39.25  | | | |           = all_52_9 & op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13 &
% 227.67/39.25  | | | |           op(e2, e0) = all_52_15 & $i(all_52_9) & $i(all_52_11) &
% 227.67/39.25  | | | |           $i(all_52_13) & $i(all_52_15))
% 227.67/39.25  | | | | 
% 227.67/39.25  | | | | BETA: splitting (34) gives:
% 227.67/39.25  | | | | 
% 227.67/39.25  | | | | Case 1:
% 227.67/39.25  | | | | | 
% 227.67/39.25  | | | | |   (35)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 227.67/39.25  | | | | |         & op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 227.67/39.25  | | | | |         op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 227.67/39.25  | | | | |         op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) =
% 227.67/39.25  | | | | |         all_52_5 & op(e3, e0) = all_52_7 & $i(all_52_1) & $i(all_52_3)
% 227.67/39.25  | | | | |         & $i(all_52_5) & $i(all_52_7)
% 227.67/39.25  | | | | | 
% 227.67/39.25  | | | | | ALPHA: (35) implies:
% 227.67/39.25  | | | | |   (36)  op(e3, e1) = all_52_5
% 227.67/39.25  | | | | |   (37)  op(all_52_5, all_52_5) = e1
% 227.67/39.25  | | | | | 
% 227.67/39.25  | | | | | REF_CLOSE: (3), (16), (24), (30), (36), (37) are inconsistent by
% 227.67/39.25  | | | | |            sub-proof #2167.
% 227.67/39.25  | | | | | 
% 227.67/39.25  | | | | Case 2:
% 227.67/39.25  | | | | | 
% 227.67/39.25  | | | | |   (38)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 227.67/39.25  | | | | |         e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11, all_52_11) =
% 227.67/39.25  | | | | |         e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15, all_52_15)
% 227.67/39.25  | | | | |         = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 & op(e2,
% 227.67/39.25  | | | | |           e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 227.67/39.25  | | | | |         $i(all_52_11) & $i(all_52_13) & $i(all_52_15)
% 227.67/39.25  | | | | | 
% 227.67/39.25  | | | | | ALPHA: (38) implies:
% 227.67/39.25  | | | | |   (39)  op(e2, e2) = all_52_11
% 227.67/39.25  | | | | |   (40)  op(all_52_11, all_52_11) = e2
% 227.67/39.25  | | | | | 
% 227.67/39.25  | | | | | REF_CLOSE: (3), (8), (12), (16), (39), (40) are inconsistent by
% 227.67/39.25  | | | | |            sub-proof #2270.
% 227.67/39.25  | | | | | 
% 227.67/39.25  | | | | End of split
% 227.67/39.25  | | | | 
% 227.67/39.25  | | | Case 2:
% 227.67/39.25  | | | | 
% 227.67/39.25  | | | |   (41)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 227.67/39.25  | | | |           e0 & op(all_52_17, all_52_17) = e3 & op(all_52_19, all_52_19)
% 227.67/39.25  | | | |           = e2 & op(all_52_21, all_52_21) = e1 & op(all_52_23,
% 227.67/39.25  | | | |             all_52_23) = e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 227.67/39.25  | | | |           all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23 &
% 227.67/39.25  | | | |           $i(all_52_17) & $i(all_52_19) & $i(all_52_21) & $i(all_52_23))
% 227.67/39.25  | | | |         | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30
% 227.67/39.25  | | | |           = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 227.67/39.25  | | | |             all_52_27) = e2 & op(all_52_29, all_52_29) = e1 &
% 227.67/39.25  | | | |           op(all_52_31, all_52_31) = e0 & op(e0, e3) = all_52_25 &
% 227.67/39.25  | | | |           op(e0, e2) = all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0) =
% 227.67/39.25  | | | |           all_52_31 & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 227.67/39.25  | | | |           $i(all_52_31))
% 227.67/39.25  | | | | 
% 227.67/39.25  | | | | BETA: splitting (41) gives:
% 227.67/39.25  | | | | 
% 227.67/39.25  | | | | Case 1:
% 227.67/39.25  | | | | | 
% 227.67/39.25  | | | | |   (42)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 227.67/39.25  | | | | |         e0 & op(all_52_17, all_52_17) = e3 & op(all_52_19, all_52_19)
% 227.67/39.25  | | | | |         = e2 & op(all_52_21, all_52_21) = e1 & op(all_52_23,
% 227.67/39.25  | | | | |           all_52_23) = e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 227.67/39.25  | | | | |         all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23 &
% 227.67/39.25  | | | | |         $i(all_52_17) & $i(all_52_19) & $i(all_52_21) & $i(all_52_23)
% 227.67/39.25  | | | | | 
% 227.67/39.25  | | | | | ALPHA: (42) implies:
% 227.67/39.25  | | | | |   (43)  op(e1, e3) = all_52_17
% 227.67/39.25  | | | | |   (44)  op(all_52_17, all_52_17) = e3
% 227.67/39.25  | | | | | 
% 227.67/39.25  | | | | | BETA: splitting (33) gives:
% 227.67/39.25  | | | | | 
% 227.67/39.25  | | | | | Case 1:
% 227.67/39.25  | | | | | | 
% 227.67/39.25  | | | | | |   (45)   ~ (all_36_0 = e0) & op(all_36_1, e3) = all_36_0 & op(e3,
% 227.67/39.25  | | | | | |           e1) = all_36_1 & $i(all_36_0) & $i(all_36_1)
% 227.67/39.25  | | | | | | 
% 227.67/39.25  | | | | | | ALPHA: (45) implies:
% 227.67/39.25  | | | | | |   (46)  op(e3, e1) = all_36_1
% 227.67/39.25  | | | | | | 
% 227.67/39.25  | | | | | | REF_CLOSE: (1), (3), (9), (11), (16), (24), (43), (44), (46) are
% 227.67/39.25  | | | | | |            inconsistent by sub-proof #304.
% 227.67/39.25  | | | | | | 
% 227.67/39.25  | | | | | Case 2:
% 227.67/39.25  | | | | | | 
% 227.67/39.25  | | | | | |   (47)   ~ (all_36_1 = e2) & op(e3, e1) = all_36_1 & $i(all_36_1)
% 227.67/39.25  | | | | | | 
% 227.67/39.25  | | | | | | ALPHA: (47) implies:
% 227.67/39.25  | | | | | |   (48)  op(e3, e1) = all_36_1
% 227.67/39.25  | | | | | | 
% 227.67/39.25  | | | | | | REF_CLOSE: (1), (3), (9), (11), (16), (24), (43), (44), (48) are
% 227.67/39.25  | | | | | |            inconsistent by sub-proof #304.
% 227.67/39.25  | | | | | | 
% 227.67/39.25  | | | | | End of split
% 227.67/39.25  | | | | | 
% 227.67/39.25  | | | | Case 2:
% 227.67/39.25  | | | | | 
% 227.67/39.25  | | | | |   (49)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 227.67/39.25  | | | | |         e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27, all_52_27)
% 227.67/39.25  | | | | |         = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 227.67/39.25  | | | | |           all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 227.67/39.25  | | | | |         all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 &
% 227.67/39.25  | | | | |         $i(all_52_25) & $i(all_52_27) & $i(all_52_29) & $i(all_52_31)
% 227.67/39.25  | | | | | 
% 227.67/39.25  | | | | | ALPHA: (49) implies:
% 227.67/39.25  | | | | |   (50)  op(e0, e3) = all_52_25
% 227.67/39.25  | | | | |   (51)  op(all_52_25, all_52_25) = e3
% 227.67/39.25  | | | | | 
% 227.67/39.25  | | | | | REF_CLOSE: (2), (3), (10), (11), (14), (17), (21), (24), (28), (33),
% 227.67/39.25  | | | | |            (50), (51) are inconsistent by sub-proof #302.
% 227.67/39.25  | | | | | 
% 227.67/39.25  | | | | End of split
% 227.67/39.25  | | | | 
% 227.67/39.25  | | | End of split
% 227.67/39.25  | | | 
% 227.67/39.25  | | End of split
% 227.67/39.25  | | 
% 227.67/39.25  | Case 2:
% 227.67/39.25  | | 
% 227.67/39.25  | |   (52)  all_57_5 = e0 & op(e2, e1) = e0
% 227.67/39.25  | | 
% 227.67/39.25  | | REF_CLOSE: (3), (5), (20), (52) are inconsistent by sub-proof #2023.
% 227.67/39.25  | | 
% 227.67/39.25  | End of split
% 227.67/39.25  | 
% 227.67/39.25  End of proof
% 227.67/39.25  
% 227.67/39.25  Sub-proof #302 shows that the following formulas are inconsistent:
% 227.67/39.25  ----------------------------------------------------------------
% 227.67/39.25    (1)  ( ~ (all_36_0 = e0) & op(all_36_1, e3) = all_36_0 & op(e3, e1) = all_36_1
% 227.67/39.25           & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e2) & op(e3, e1) =
% 227.67/39.25           all_36_1 & $i(all_36_1))
% 227.67/39.25    (2)  op(e3, e3) = e1
% 227.67/39.25    (3)  op(e3, e1) = e0
% 227.67/39.25    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.67/39.25           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.67/39.25    (5)  op(e0, e3) = all_52_25
% 227.67/39.25    (6)  op(e0, e3) = all_53_3
% 227.67/39.25    (7)  ( ~ (all_10_0 = e2) & op(all_10_1, e3) = all_10_0 & op(e3, e1) = all_10_1
% 227.67/39.25           & $i(all_10_0) & $i(all_10_1)) | ( ~ (all_10_1 = e0) & op(e3, e1) =
% 227.67/39.25           all_10_1 & $i(all_10_1))
% 227.67/39.25    (8)  op(all_52_25, all_52_25) = e3
% 227.67/39.25    (9)  all_55_12 = all_53_3
% 227.67/39.25    (10)   ~ (all_53_3 = e0)
% 227.67/39.25    (11)   ~ (all_53_3 = e1)
% 227.67/39.25    (12)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 227.67/39.25  
% 227.67/39.25  Begin of proof
% 227.67/39.25  | 
% 227.67/39.25  | BETA: splitting (1) gives:
% 227.67/39.25  | 
% 227.67/39.25  | Case 1:
% 227.67/39.25  | | 
% 227.67/39.25  | |   (13)   ~ (all_36_0 = e0) & op(all_36_1, e3) = all_36_0 & op(e3, e1) =
% 227.67/39.25  | |         all_36_1 & $i(all_36_0) & $i(all_36_1)
% 227.67/39.25  | | 
% 227.67/39.25  | | ALPHA: (13) implies:
% 227.67/39.25  | |   (14)  op(e3, e1) = all_36_1
% 227.67/39.25  | | 
% 227.67/39.25  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (14)
% 227.67/39.25  | |            are inconsistent by sub-proof #303.
% 227.67/39.25  | | 
% 227.67/39.25  | Case 2:
% 227.67/39.25  | | 
% 227.67/39.25  | |   (15)   ~ (all_36_1 = e2) & op(e3, e1) = all_36_1 & $i(all_36_1)
% 227.67/39.25  | | 
% 227.67/39.25  | | ALPHA: (15) implies:
% 227.67/39.25  | |   (16)  op(e3, e1) = all_36_1
% 227.67/39.25  | | 
% 227.67/39.25  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (16)
% 227.67/39.25  | |            are inconsistent by sub-proof #303.
% 227.67/39.25  | | 
% 227.67/39.25  | End of split
% 227.67/39.25  | 
% 227.67/39.25  End of proof
% 227.67/39.25  
% 227.67/39.25  Sub-proof #303 shows that the following formulas are inconsistent:
% 227.67/39.25  ----------------------------------------------------------------
% 227.67/39.25    (1)  op(e3, e3) = e1
% 227.67/39.25    (2)  op(e3, e1) = e0
% 227.67/39.25    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.67/39.25           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.67/39.25    (4)  op(e0, e3) = all_52_25
% 227.67/39.25    (5)  op(e0, e3) = all_53_3
% 227.67/39.25    (6)  ( ~ (all_10_0 = e2) & op(all_10_1, e3) = all_10_0 & op(e3, e1) = all_10_1
% 227.67/39.25           & $i(all_10_0) & $i(all_10_1)) | ( ~ (all_10_1 = e0) & op(e3, e1) =
% 227.67/39.25           all_10_1 & $i(all_10_1))
% 227.67/39.25    (7)  op(all_52_25, all_52_25) = e3
% 227.67/39.25    (8)  all_55_12 = all_53_3
% 227.67/39.25    (9)   ~ (all_53_3 = e0)
% 227.67/39.25    (10)   ~ (all_53_3 = e1)
% 227.67/39.25    (11)  op(e3, e1) = all_36_1
% 227.67/39.25    (12)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 227.67/39.25  
% 227.67/39.25  Begin of proof
% 227.67/39.25  | 
% 227.67/39.25  | BETA: splitting (6) gives:
% 227.67/39.25  | 
% 227.67/39.25  | Case 1:
% 227.67/39.25  | | 
% 227.67/39.25  | |   (13)   ~ (all_10_0 = e2) & op(all_10_1, e3) = all_10_0 & op(e3, e1) =
% 227.67/39.25  | |         all_10_1 & $i(all_10_0) & $i(all_10_1)
% 227.67/39.25  | | 
% 227.67/39.25  | | ALPHA: (13) implies:
% 227.67/39.25  | |   (14)   ~ (all_10_0 = e2)
% 227.67/39.25  | |   (15)  op(e3, e1) = all_10_1
% 227.67/39.25  | |   (16)  op(all_10_1, e3) = all_10_0
% 227.67/39.25  | | 
% 227.67/39.25  | | GROUND_INST: instantiating (3) with all_53_3, all_52_25, e3, e0, simplifying
% 227.67/39.25  | |              with (4), (5) gives:
% 227.67/39.25  | |   (17)  all_53_3 = all_52_25
% 227.67/39.25  | | 
% 227.67/39.25  | | GROUND_INST: instantiating (3) with e0, all_36_1, e1, e3, simplifying with
% 227.67/39.25  | |              (2), (11) gives:
% 227.67/39.25  | |   (18)  all_36_1 = e0
% 227.67/39.25  | | 
% 227.67/39.25  | | GROUND_INST: instantiating (3) with all_10_1, all_36_1, e1, e3, simplifying
% 227.67/39.25  | |              with (11), (15) gives:
% 227.67/39.25  | |   (19)  all_36_1 = all_10_1
% 227.67/39.25  | | 
% 227.67/39.25  | | COMBINE_EQS: (18), (19) imply:
% 227.67/39.25  | |   (20)  all_10_1 = e0
% 227.67/39.25  | | 
% 227.67/39.25  | | COMBINE_EQS: (8), (17) imply:
% 227.67/39.25  | |   (21)  all_55_12 = all_52_25
% 227.67/39.25  | | 
% 227.67/39.25  | | REDUCE: (10), (17) imply:
% 227.67/39.25  | |   (22)   ~ (all_52_25 = e1)
% 227.67/39.25  | | 
% 227.67/39.25  | | REDUCE: (9), (17) imply:
% 227.67/39.25  | |   (23)   ~ (all_52_25 = e0)
% 227.67/39.25  | | 
% 227.67/39.25  | | REDUCE: (16), (20) imply:
% 227.67/39.25  | |   (24)  op(e0, e3) = all_10_0
% 227.67/39.25  | | 
% 227.67/39.25  | | GROUND_INST: instantiating (3) with all_52_25, all_10_0, e3, e0, simplifying
% 227.67/39.25  | |              with (4), (24) gives:
% 227.67/39.25  | |   (25)  all_52_25 = all_10_0
% 227.67/39.25  | | 
% 227.67/39.25  | | COMBINE_EQS: (21), (25) imply:
% 227.67/39.25  | |   (26)  all_55_12 = all_10_0
% 227.67/39.25  | | 
% 227.67/39.25  | | REDUCE: (22), (25) imply:
% 227.67/39.25  | |   (27)   ~ (all_10_0 = e1)
% 227.67/39.25  | | 
% 227.67/39.25  | | REDUCE: (7), (25) imply:
% 227.67/39.25  | |   (28)  op(all_10_0, all_10_0) = e3
% 227.67/39.25  | | 
% 227.67/39.25  | | BETA: splitting (12) gives:
% 227.67/39.25  | | 
% 227.67/39.25  | | Case 1:
% 227.67/39.25  | | | 
% 227.67/39.25  | | |   (29)  all_55_12 = e3
% 227.67/39.25  | | | 
% 227.67/39.25  | | | COMBINE_EQS: (26), (29) imply:
% 227.67/39.25  | | |   (30)  all_10_0 = e3
% 227.67/39.25  | | | 
% 227.67/39.25  | | | REDUCE: (27), (30) imply:
% 227.67/39.25  | | |   (31)   ~ (e3 = e1)
% 227.67/39.25  | | | 
% 227.67/39.25  | | | REDUCE: (28), (30) imply:
% 227.67/39.25  | | |   (32)  op(e3, e3) = e3
% 227.67/39.25  | | | 
% 227.67/39.25  | | | REF_CLOSE: (1), (3), (31), (32) are inconsistent by sub-proof #2495.
% 227.67/39.25  | | | 
% 227.67/39.25  | | Case 2:
% 227.67/39.25  | | | 
% 227.67/39.25  | | |   (33)  all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 227.67/39.25  | | | 
% 227.67/39.25  | | | BETA: splitting (33) gives:
% 227.67/39.25  | | | 
% 227.67/39.25  | | | Case 1:
% 227.67/39.25  | | | | 
% 227.67/39.25  | | | |   (34)  all_55_12 = e2
% 227.67/39.25  | | | | 
% 227.67/39.25  | | | | COMBINE_EQS: (26), (34) imply:
% 227.67/39.25  | | | |   (35)  all_10_0 = e2
% 227.67/39.25  | | | | 
% 227.67/39.25  | | | | REDUCE: (14), (35) imply:
% 227.67/39.25  | | | |   (36)  $false
% 227.67/39.25  | | | | 
% 227.67/39.25  | | | | CLOSE: (36) is inconsistent.
% 227.67/39.25  | | | | 
% 227.67/39.25  | | | Case 2:
% 227.67/39.25  | | | | 
% 227.67/39.25  | | | |   (37)  all_55_12 = e1 | all_55_12 = e0
% 227.67/39.25  | | | | 
% 227.67/39.25  | | | | REF_CLOSE: (21), (22), (23), (37) are inconsistent by sub-proof #323.
% 227.67/39.25  | | | | 
% 227.67/39.25  | | | End of split
% 227.67/39.25  | | | 
% 227.67/39.25  | | End of split
% 227.67/39.25  | | 
% 227.67/39.25  | Case 2:
% 227.67/39.25  | | 
% 227.67/39.25  | |   (38)   ~ (all_10_1 = e0) & op(e3, e1) = all_10_1 & $i(all_10_1)
% 227.67/39.25  | | 
% 227.67/39.25  | | ALPHA: (38) implies:
% 227.67/39.25  | |   (39)   ~ (all_10_1 = e0)
% 227.67/39.25  | |   (40)  op(e3, e1) = all_10_1
% 227.67/39.25  | | 
% 227.67/39.25  | | REF_CLOSE: (2), (3), (11), (39), (40) are inconsistent by sub-proof #309.
% 227.67/39.25  | | 
% 227.67/39.25  | End of split
% 227.67/39.25  | 
% 227.67/39.25  End of proof
% 227.67/39.25  
% 227.67/39.25  Sub-proof #304 shows that the following formulas are inconsistent:
% 227.67/39.25  ----------------------------------------------------------------
% 227.67/39.25    (1)  op(e1, e3) = e0
% 227.67/39.25    (2)  op(e1, e3) = all_52_17
% 227.67/39.25    (3)  op(e3, e1) = e0
% 227.67/39.25    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.67/39.25           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.67/39.25    (5)  op(all_52_17, all_52_17) = e3
% 227.67/39.25    (6)   ~ (e3 = e0)
% 227.67/39.25    (7)  ( ~ (all_10_0 = e2) & op(all_10_1, e3) = all_10_0 & op(e3, e1) = all_10_1
% 227.67/39.25           & $i(all_10_0) & $i(all_10_1)) | ( ~ (all_10_1 = e0) & op(e3, e1) =
% 227.67/39.25           all_10_1 & $i(all_10_1))
% 227.67/39.25    (8)  op(e0, e0) = e0
% 227.67/39.25    (9)  op(e3, e1) = all_36_1
% 227.67/39.25  
% 227.67/39.25  Begin of proof
% 227.67/39.25  | 
% 227.67/39.25  | BETA: splitting (7) gives:
% 227.67/39.25  | 
% 227.67/39.25  | Case 1:
% 227.67/39.25  | | 
% 227.67/39.25  | | 
% 227.67/39.25  | | GROUND_INST: instantiating (4) with e0, all_52_17, e3, e1, simplifying with
% 227.67/39.25  | |              (1), (2) gives:
% 227.67/39.25  | |   (10)  all_52_17 = e0
% 227.67/39.25  | | 
% 227.67/39.25  | | REDUCE: (5), (10) imply:
% 227.67/39.25  | |   (11)  op(e0, e0) = e3
% 227.67/39.25  | | 
% 227.67/39.25  | | REF_CLOSE: (4), (6), (8), (11) are inconsistent by sub-proof #2304.
% 227.67/39.25  | | 
% 227.67/39.25  | Case 2:
% 227.67/39.25  | | 
% 227.67/39.25  | |   (12)   ~ (all_10_1 = e0) & op(e3, e1) = all_10_1 & $i(all_10_1)
% 227.67/39.25  | | 
% 227.67/39.25  | | ALPHA: (12) implies:
% 227.67/39.25  | |   (13)   ~ (all_10_1 = e0)
% 227.67/39.25  | |   (14)  op(e3, e1) = all_10_1
% 227.67/39.25  | | 
% 227.67/39.25  | | REF_CLOSE: (3), (4), (9), (13), (14) are inconsistent by sub-proof #309.
% 227.67/39.25  | | 
% 227.67/39.25  | End of split
% 227.67/39.25  | 
% 227.67/39.25  End of proof
% 227.67/39.25  
% 227.67/39.25  Sub-proof #305 shows that the following formulas are inconsistent:
% 227.67/39.25  ----------------------------------------------------------------
% 227.67/39.25    (1)  all_57_11 = e1 & op(e1, e0) = e1
% 227.67/39.25    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.67/39.25           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.67/39.25    (3)  op(e1, e0) = all_53_14
% 227.67/39.25    (4)   ~ (all_53_14 = e1)
% 227.67/39.25  
% 227.67/39.25  Begin of proof
% 227.67/39.25  | 
% 227.67/39.25  | ALPHA: (1) implies:
% 227.67/39.25  |   (5)  op(e1, e0) = e1
% 227.67/39.25  | 
% 227.67/39.25  | GROUND_INST: instantiating (2) with all_53_14, e1, e0, e1, simplifying with
% 227.67/39.25  |              (3), (5) gives:
% 227.67/39.25  |   (6)  all_53_14 = e1
% 227.67/39.25  | 
% 227.67/39.25  | REDUCE: (4), (6) imply:
% 227.67/39.25  |   (7)  $false
% 227.67/39.25  | 
% 227.67/39.25  | CLOSE: (7) is inconsistent.
% 227.67/39.25  | 
% 227.67/39.25  End of proof
% 227.67/39.25  
% 227.67/39.25  Sub-proof #306 shows that the following formulas are inconsistent:
% 227.67/39.25  ----------------------------------------------------------------
% 227.67/39.25    (1)  all_57_9 = e2 & op(e3, e0) = e2
% 227.67/39.25    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.67/39.25           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.67/39.25    (3)  op(e3, e0) = e3
% 227.67/39.25    (4)   ~ (e3 = e2)
% 227.67/39.25  
% 227.67/39.25  Begin of proof
% 227.67/39.25  | 
% 227.67/39.25  | ALPHA: (1) implies:
% 227.67/39.25  |   (5)  op(e3, e0) = e2
% 227.67/39.25  | 
% 227.67/39.25  | GROUND_INST: instantiating (2) with e2, e3, e0, e3, simplifying with (3), (5)
% 227.67/39.25  |              gives:
% 227.67/39.25  |   (6)  e3 = e2
% 227.67/39.25  | 
% 227.67/39.25  | REDUCE: (4), (6) imply:
% 227.67/39.25  |   (7)  $false
% 227.67/39.25  | 
% 227.67/39.25  | CLOSE: (7) is inconsistent.
% 227.67/39.25  | 
% 227.67/39.25  End of proof
% 227.67/39.25  
% 227.67/39.25  Sub-proof #307 shows that the following formulas are inconsistent:
% 227.67/39.25  ----------------------------------------------------------------
% 227.67/39.25    (1)   ~ (all_36_1 = e2) & op(e3, e1) = all_36_1 & $i(all_36_1)
% 227.67/39.25    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.67/39.25           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.67/39.25    (3)  op(e3, e1) = e2
% 227.67/39.25  
% 227.67/39.25  Begin of proof
% 227.67/39.25  | 
% 227.67/39.25  | ALPHA: (1) implies:
% 227.67/39.25  |   (4)   ~ (all_36_1 = e2)
% 227.67/39.25  |   (5)  op(e3, e1) = all_36_1
% 227.67/39.25  | 
% 227.67/39.25  | GROUND_INST: instantiating (2) with e2, all_36_1, e1, e3, simplifying with
% 227.67/39.25  |              (3), (5) gives:
% 227.67/39.25  |   (6)  all_36_1 = e2
% 227.67/39.25  | 
% 227.67/39.25  | REDUCE: (4), (6) imply:
% 227.67/39.25  |   (7)  $false
% 227.67/39.25  | 
% 227.67/39.25  | CLOSE: (7) is inconsistent.
% 227.67/39.25  | 
% 227.67/39.25  End of proof
% 227.67/39.25  
% 227.67/39.25  Sub-proof #308 shows that the following formulas are inconsistent:
% 227.67/39.25  ----------------------------------------------------------------
% 227.67/39.25    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 227.67/39.25    (2)  op(e3, e3) = e1
% 227.67/39.25    (3)   ~ (all_53_7 = all_52_19)
% 227.67/39.25    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.67/39.25           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.67/39.25    (5)   ~ (all_53_7 = e1)
% 227.67/39.25    (6)  all_55_9 = all_52_19
% 227.67/39.25    (7)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 227.67/39.25    (8)   ~ (all_53_4 = e1)
% 227.67/39.25    (9)  all_55_1 = all_53_4
% 227.67/39.25    (10)   ~ (all_53_4 = all_53_7)
% 227.67/39.25    (11)  all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 227.67/39.25    (12)   ~ (all_53_7 = e0)
% 227.67/39.25    (13)   ~ (all_53_4 = all_52_19)
% 227.67/39.25    (14)  all_55_13 = all_53_7
% 227.67/39.25    (15)  op(all_52_19, all_52_19) = e2
% 227.67/39.26    (16)   ~ (all_52_19 = e1)
% 227.67/39.26    (17)   ~ (all_53_4 = e3)
% 227.67/39.26  
% 227.67/39.26  Begin of proof
% 227.67/39.26  | 
% 227.67/39.26  | BETA: splitting (11) gives:
% 227.67/39.26  | 
% 227.67/39.26  | Case 1:
% 227.67/39.26  | | 
% 227.67/39.26  | |   (18)  all_55_13 = e2
% 227.67/39.26  | | 
% 227.67/39.26  | | COMBINE_EQS: (14), (18) imply:
% 227.67/39.26  | |   (19)  all_53_7 = e2
% 227.67/39.26  | | 
% 227.67/39.26  | | REDUCE: (10), (19) imply:
% 227.67/39.26  | |   (20)   ~ (all_53_4 = e2)
% 227.67/39.26  | | 
% 227.67/39.26  | | REDUCE: (3), (19) imply:
% 227.67/39.26  | |   (21)   ~ (all_52_19 = e2)
% 227.67/39.26  | | 
% 227.67/39.26  | | SIMP: (21) implies:
% 227.67/39.26  | |   (22)   ~ (all_52_19 = e2)
% 227.67/39.26  | | 
% 227.67/39.26  | | REDUCE: (5), (19) imply:
% 227.67/39.26  | |   (23)   ~ (e2 = e1)
% 227.67/39.26  | | 
% 227.67/39.26  | | BETA: splitting (1) gives:
% 227.67/39.26  | | 
% 227.67/39.26  | | Case 1:
% 227.67/39.26  | | | 
% 227.67/39.26  | | |   (24)  all_55_1 = e3
% 227.67/39.26  | | | 
% 227.67/39.26  | | | REF_CLOSE: (9), (17), (24) are inconsistent by sub-proof #2295.
% 227.67/39.26  | | | 
% 227.67/39.26  | | Case 2:
% 227.67/39.26  | | | 
% 227.67/39.26  | | |   (25)  all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 227.67/39.26  | | | 
% 227.67/39.26  | | | REF_CLOSE: (2), (4), (6), (7), (8), (9), (13), (15), (16), (20), (22),
% 227.67/39.26  | | |            (23), (25) are inconsistent by sub-proof #357.
% 227.67/39.26  | | | 
% 227.67/39.26  | | End of split
% 227.67/39.26  | | 
% 227.67/39.26  | Case 2:
% 227.67/39.26  | | 
% 227.67/39.26  | |   (26)  all_55_13 = e1 | all_55_13 = e0
% 227.67/39.26  | | 
% 227.67/39.26  | | REF_CLOSE: (5), (12), (14), (26) are inconsistent by sub-proof #1837.
% 227.67/39.26  | | 
% 227.67/39.26  | End of split
% 227.67/39.26  | 
% 227.67/39.26  End of proof
% 227.67/39.26  
% 227.67/39.26  Sub-proof #309 shows that the following formulas are inconsistent:
% 227.67/39.26  ----------------------------------------------------------------
% 227.67/39.26    (1)  op(e3, e1) = e0
% 227.67/39.26    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.67/39.26           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.67/39.26    (3)   ~ (all_10_1 = e0)
% 227.67/39.26    (4)  op(e3, e1) = all_10_1
% 227.67/39.26    (5)  op(e3, e1) = all_36_1
% 227.67/39.26  
% 227.67/39.26  Begin of proof
% 227.67/39.26  | 
% 227.67/39.26  | GROUND_INST: instantiating (2) with e0, all_36_1, e1, e3, simplifying with
% 227.67/39.26  |              (1), (5) gives:
% 227.67/39.26  |   (6)  all_36_1 = e0
% 227.67/39.26  | 
% 227.67/39.26  | GROUND_INST: instantiating (2) with all_10_1, all_36_1, e1, e3, simplifying
% 227.67/39.26  |              with (4), (5) gives:
% 227.67/39.26  |   (7)  all_36_1 = all_10_1
% 227.67/39.26  | 
% 227.67/39.26  | COMBINE_EQS: (6), (7) imply:
% 227.67/39.26  |   (8)  all_10_1 = e0
% 227.67/39.26  | 
% 227.67/39.26  | REDUCE: (3), (8) imply:
% 227.67/39.26  |   (9)  $false
% 227.67/39.26  | 
% 227.67/39.26  | CLOSE: (9) is inconsistent.
% 227.67/39.26  | 
% 227.67/39.26  End of proof
% 227.67/39.26  
% 227.67/39.26  Sub-proof #310 shows that the following formulas are inconsistent:
% 227.67/39.26  ----------------------------------------------------------------
% 227.67/39.26    (1)  all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 227.67/39.26    (2)  op(e0, e1) = all_53_11
% 227.67/39.26    (3)  op(e3, e3) = e1
% 227.67/39.26    (4)  op(e1, e3) = all_52_17
% 227.67/39.26    (5)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 227.67/39.26    (6)   ~ (all_53_7 = all_52_19)
% 227.67/39.26    (7)   ~ (all_10_0 = e1)
% 227.67/39.26    (8)  op(e2, e3) = all_53_1
% 227.67/39.26    (9)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 227.67/39.26         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 227.67/39.26    (10)   ~ (all_53_7 = all_10_0)
% 227.67/39.26    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.67/39.26            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.67/39.26    (12)   ~ (all_53_7 = e1)
% 227.67/39.26    (13)   ~ (all_6_2 = e3)
% 227.67/39.26    (14)  op(e1, e1) = all_6_2
% 227.67/39.26    (15)   ~ (all_53_1 = all_53_9)
% 227.67/39.26    (16)  all_55_9 = all_52_19
% 227.67/39.26    (17)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 227.67/39.26    (18)  op(all_52_17, all_52_17) = e3
% 227.67/39.26    (19)   ~ (all_52_17 = e1)
% 227.67/39.26    (20)  all_55_4 = all_53_1
% 227.67/39.26    (21)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 227.67/39.26          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 227.67/39.26    (22)   ~ (e3 = e2)
% 227.67/39.26    (23)   ~ (all_53_1 = all_52_17)
% 227.67/39.26    (24)   ~ (e3 = e0)
% 227.67/39.26    (25)  all_57_1 = e2
% 227.67/39.26    (26)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 227.67/39.26    (27)  op(e0, e3) = all_53_3
% 227.67/39.26    (28)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 227.67/39.26    (29)   ~ (all_53_3 = all_52_17)
% 227.67/39.26    (30)   ~ (all_53_1 = e1)
% 227.67/39.26    (31)  op(e3, e0) = e3
% 227.67/39.26    (32)   ~ (e2 = e0)
% 227.67/39.26    (33)  all_55_12 = all_53_3
% 227.67/39.26    (34)   ~ (e1 = e0)
% 227.67/39.26    (35)  all_57_14 = e2
% 227.67/39.26    (36)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 227.67/39.26          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 227.67/39.26    (37)   ~ (all_53_7 = all_53_11)
% 227.67/39.26    (38)   ~ (all_53_11 = all_10_0)
% 227.67/39.26    (39)  all_55_10 = all_6_2
% 227.67/39.26    (40)   ~ (all_53_3 = e1)
% 227.67/39.26    (41)  all_55_12 = all_10_0
% 227.67/39.26    (42)   ~ (all_53_11 = e1)
% 227.67/39.26    (43)  all_55_13 = all_53_7
% 227.67/39.26    (44)  all_55_8 = all_52_17
% 227.67/39.26    (45)  op(all_52_19, all_52_19) = e2
% 227.67/39.26    (46)   ~ (all_52_19 = e2)
% 227.67/39.26    (47)  op(e2, e1) = all_53_9
% 227.67/39.26    (48)  all_57_14 = e2 & op(e0, e1) = e2
% 227.67/39.26    (49)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 227.67/39.26    (50)   ~ (all_52_19 = e1)
% 227.67/39.26    (51)   ~ (all_53_1 = all_10_0)
% 227.67/39.26  
% 227.67/39.26  Begin of proof
% 227.67/39.26  | 
% 227.67/39.26  | BETA: splitting (36) gives:
% 227.67/39.26  | 
% 227.67/39.26  | Case 1:
% 227.67/39.26  | | 
% 227.67/39.26  | |   (52)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) =
% 227.67/39.26  | |           e3)
% 227.67/39.26  | | 
% 227.67/39.26  | | BETA: splitting (52) gives:
% 227.67/39.26  | | 
% 227.67/39.26  | | Case 1:
% 227.67/39.26  | | | 
% 227.67/39.26  | | |   (53)  all_57_4 = e3 & op(e3, e1) = e3
% 227.67/39.26  | | | 
% 227.67/39.26  | | | ALPHA: (53) implies:
% 227.67/39.26  | | |   (54)  all_57_4 = e3
% 227.67/39.26  | | | 
% 227.67/39.26  | | | BETA: splitting (21) gives:
% 227.67/39.26  | | | 
% 227.67/39.26  | | | Case 1:
% 227.67/39.26  | | | | 
% 227.67/39.26  | | | |   (55)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2)
% 227.67/39.26  | | | |           = e0)
% 227.67/39.26  | | | | 
% 227.67/39.26  | | | | REF_CLOSE: (4), (5), (8), (9), (11), (13), (14), (18), (25), (27), (30),
% 227.67/39.26  | | | |            (32), (34), (39), (40), (55) are inconsistent by sub-proof
% 227.67/39.26  | | | |            #315.
% 227.67/39.26  | | | | 
% 227.67/39.26  | | | Case 2:
% 227.67/39.26  | | | | 
% 227.67/39.26  | | | |   (56)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0)
% 227.67/39.26  | | | |           = e0)
% 227.67/39.26  | | | | 
% 227.67/39.26  | | | | BETA: splitting (56) gives:
% 227.67/39.26  | | | | 
% 227.67/39.26  | | | | Case 1:
% 227.67/39.26  | | | | | 
% 227.67/39.26  | | | | |   (57)  all_57_4 = e0 & op(e3, e1) = e0
% 227.67/39.26  | | | | | 
% 227.67/39.26  | | | | | REF_CLOSE: (24), (54), (57) are inconsistent by sub-proof #2491.
% 227.67/39.26  | | | | | 
% 227.67/39.26  | | | | Case 2:
% 227.67/39.26  | | | | | 
% 227.67/39.26  | | | | |   (58)  all_57_9 = e0 & op(e3, e0) = e0
% 227.67/39.26  | | | | | 
% 227.67/39.26  | | | | | ALPHA: (58) implies:
% 227.67/39.26  | | | | |   (59)  op(e3, e0) = e0
% 227.67/39.26  | | | | | 
% 227.67/39.26  | | | | | REF_CLOSE: (11), (24), (31), (59) are inconsistent by sub-proof #313.
% 227.67/39.26  | | | | | 
% 227.67/39.26  | | | | End of split
% 227.67/39.26  | | | | 
% 227.67/39.26  | | | End of split
% 227.67/39.26  | | | 
% 227.67/39.26  | | Case 2:
% 227.67/39.26  | | | 
% 227.67/39.26  | | |   (60)  all_57_5 = e3 & op(e2, e1) = e3
% 227.67/39.26  | | | 
% 227.67/39.26  | | | ALPHA: (60) implies:
% 227.67/39.26  | | |   (61)  op(e2, e1) = e3
% 227.67/39.26  | | | 
% 227.67/39.26  | | | ALPHA: (48) implies:
% 227.67/39.26  | | |   (62)  op(e0, e1) = e2
% 227.67/39.26  | | | 
% 227.67/39.26  | | | GROUND_INST: instantiating (11) with all_53_11, e2, e1, e0, simplifying
% 227.67/39.26  | | |              with (2), (62) gives:
% 227.67/39.26  | | |   (63)  all_53_11 = e2
% 227.67/39.26  | | | 
% 227.67/39.26  | | | GROUND_INST: instantiating (11) with all_53_9, e3, e1, e2, simplifying
% 227.67/39.26  | | |              with (47), (61) gives:
% 227.67/39.26  | | |   (64)  all_53_9 = e3
% 227.67/39.26  | | | 
% 227.67/39.26  | | | REDUCE: (15), (64) imply:
% 227.67/39.26  | | |   (65)   ~ (all_53_1 = e3)
% 227.67/39.26  | | | 
% 227.67/39.26  | | | REDUCE: (37), (63) imply:
% 227.67/39.26  | | |   (66)   ~ (all_53_7 = e2)
% 227.67/39.26  | | | 
% 227.67/39.26  | | | REDUCE: (38), (63) imply:
% 227.67/39.26  | | |   (67)   ~ (all_10_0 = e2)
% 227.67/39.26  | | | 
% 227.67/39.26  | | | SIMP: (67) implies:
% 227.67/39.26  | | |   (68)   ~ (all_10_0 = e2)
% 227.67/39.26  | | | 
% 227.67/39.26  | | | REDUCE: (42), (63) imply:
% 227.67/39.26  | | |   (69)   ~ (e2 = e1)
% 227.67/39.26  | | | 
% 227.67/39.26  | | | BETA: splitting (49) gives:
% 227.67/39.26  | | | 
% 227.67/39.26  | | | Case 1:
% 227.67/39.26  | | | | 
% 227.67/39.26  | | | |   (70)  all_55_12 = e3
% 227.67/39.26  | | | | 
% 227.67/39.26  | | | | COMBINE_EQS: (41), (70) imply:
% 227.67/39.26  | | | |   (71)  all_10_0 = e3
% 227.67/39.26  | | | | 
% 227.67/39.26  | | | | SIMP: (71) implies:
% 227.67/39.26  | | | |   (72)  all_10_0 = e3
% 227.67/39.26  | | | | 
% 227.67/39.26  | | | | REDUCE: (10), (72) imply:
% 227.67/39.26  | | | |   (73)   ~ (all_53_7 = e3)
% 227.67/39.26  | | | | 
% 227.67/39.26  | | | | BETA: splitting (1) gives:
% 227.67/39.26  | | | | 
% 227.67/39.26  | | | | Case 1:
% 227.67/39.26  | | | | | 
% 227.67/39.26  | | | | |   (74)  all_55_13 = e3
% 227.67/39.26  | | | | | 
% 227.67/39.26  | | | | | REF_CLOSE: (43), (73), (74) are inconsistent by sub-proof #2080.
% 227.67/39.26  | | | | | 
% 227.67/39.26  | | | | Case 2:
% 227.67/39.26  | | | | | 
% 227.67/39.26  | | | | |   (75)  all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 227.67/39.26  | | | | | 
% 227.67/39.26  | | | | | BETA: splitting (75) gives:
% 227.67/39.26  | | | | | 
% 227.67/39.26  | | | | | Case 1:
% 227.67/39.26  | | | | | | 
% 227.67/39.26  | | | | | |   (76)  all_55_13 = e2
% 227.67/39.26  | | | | | | 
% 227.67/39.26  | | | | | | REF_CLOSE: (43), (66), (76) are inconsistent by sub-proof #2287.
% 227.67/39.26  | | | | | | 
% 227.67/39.26  | | | | | Case 2:
% 227.67/39.26  | | | | | | 
% 227.67/39.26  | | | | | |   (77)  all_55_13 = e1 | all_55_13 = e0
% 227.67/39.26  | | | | | | 
% 227.67/39.26  | | | | | | BETA: splitting (77) gives:
% 227.67/39.26  | | | | | | 
% 227.67/39.26  | | | | | | Case 1:
% 227.67/39.26  | | | | | | | 
% 227.67/39.26  | | | | | | |   (78)  all_55_13 = e1
% 227.67/39.26  | | | | | | | 
% 227.67/39.26  | | | | | | | REF_CLOSE: (12), (43), (78) are inconsistent by sub-proof #2002.
% 227.67/39.26  | | | | | | | 
% 227.67/39.26  | | | | | | Case 2:
% 227.67/39.26  | | | | | | | 
% 227.67/39.26  | | | | | | |   (79)  all_55_13 = e0
% 227.67/39.26  | | | | | | | 
% 227.67/39.26  | | | | | | | COMBINE_EQS: (43), (79) imply:
% 227.67/39.26  | | | | | | |   (80)  all_53_7 = e0
% 227.67/39.26  | | | | | | | 
% 227.67/39.26  | | | | | | | SIMP: (80) implies:
% 227.67/39.26  | | | | | | |   (81)  all_53_7 = e0
% 227.67/39.26  | | | | | | | 
% 227.67/39.26  | | | | | | | REDUCE: (6), (81) imply:
% 227.67/39.26  | | | | | | |   (82)   ~ (all_52_19 = e0)
% 227.67/39.26  | | | | | | | 
% 227.67/39.26  | | | | | | | SIMP: (82) implies:
% 227.67/39.26  | | | | | | |   (83)   ~ (all_52_19 = e0)
% 227.67/39.26  | | | | | | | 
% 227.67/39.26  | | | | | | | REF_CLOSE: (3), (11), (16), (17), (45), (46), (50), (69), (83) are
% 227.67/39.26  | | | | | | |            inconsistent by sub-proof #358.
% 227.67/39.26  | | | | | | | 
% 227.67/39.26  | | | | | | End of split
% 227.67/39.26  | | | | | | 
% 227.67/39.26  | | | | | End of split
% 227.67/39.26  | | | | | 
% 227.67/39.26  | | | | End of split
% 227.67/39.26  | | | | 
% 227.67/39.26  | | | Case 2:
% 227.67/39.26  | | | | 
% 227.67/39.26  | | | |   (84)  all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 227.67/39.26  | | | | 
% 227.67/39.26  | | | | BETA: splitting (84) gives:
% 227.67/39.26  | | | | 
% 227.67/39.26  | | | | Case 1:
% 227.67/39.26  | | | | | 
% 227.67/39.26  | | | | |   (85)  all_55_12 = e2
% 227.67/39.26  | | | | | 
% 227.67/39.26  | | | | | COMBINE_EQS: (41), (85) imply:
% 227.67/39.26  | | | | |   (86)  all_10_0 = e2
% 227.67/39.26  | | | | | 
% 227.67/39.26  | | | | | REDUCE: (68), (86) imply:
% 227.67/39.26  | | | | |   (87)  $false
% 227.67/39.26  | | | | | 
% 227.67/39.26  | | | | | CLOSE: (87) is inconsistent.
% 227.67/39.26  | | | | | 
% 227.67/39.26  | | | | Case 2:
% 227.67/39.26  | | | | | 
% 227.67/39.26  | | | | |   (88)  all_55_12 = e1 | all_55_12 = e0
% 227.67/39.26  | | | | | 
% 227.67/39.26  | | | | | BETA: splitting (88) gives:
% 227.67/39.26  | | | | | 
% 227.67/39.26  | | | | | Case 1:
% 227.67/39.26  | | | | | | 
% 227.67/39.26  | | | | | |   (89)  all_55_12 = e1
% 227.67/39.26  | | | | | | 
% 227.67/39.26  | | | | | | COMBINE_EQS: (41), (89) imply:
% 227.67/39.26  | | | | | |   (90)  all_10_0 = e1
% 227.67/39.26  | | | | | | 
% 227.67/39.26  | | | | | | REDUCE: (7), (90) imply:
% 227.67/39.26  | | | | | |   (91)  $false
% 227.67/39.26  | | | | | | 
% 227.67/39.26  | | | | | | CLOSE: (91) is inconsistent.
% 227.67/39.26  | | | | | | 
% 227.67/39.26  | | | | | Case 2:
% 227.67/39.26  | | | | | | 
% 227.67/39.26  | | | | | |   (92)  all_55_12 = e0
% 227.67/39.26  | | | | | | 
% 227.67/39.26  | | | | | | COMBINE_EQS: (41), (92) imply:
% 227.67/39.26  | | | | | |   (93)  all_10_0 = e0
% 227.67/39.26  | | | | | | 
% 227.67/39.26  | | | | | | REDUCE: (51), (93) imply:
% 227.67/39.26  | | | | | |   (94)   ~ (all_53_1 = e0)
% 227.67/39.26  | | | | | | 
% 227.67/39.26  | | | | | | BETA: splitting (28) gives:
% 227.67/39.26  | | | | | | 
% 227.67/39.26  | | | | | | Case 1:
% 227.67/39.26  | | | | | | | 
% 227.67/39.26  | | | | | | |   (95)  all_55_4 = e3
% 227.67/39.26  | | | | | | | 
% 227.67/39.26  | | | | | | | REF_CLOSE: (20), (65), (95) are inconsistent by sub-proof #2170.
% 227.67/39.26  | | | | | | | 
% 227.67/39.26  | | | | | | Case 2:
% 227.67/39.26  | | | | | | | 
% 227.67/39.26  | | | | | | |   (96)  all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 227.67/39.26  | | | | | | | 
% 227.67/39.26  | | | | | | | BETA: splitting (96) gives:
% 227.67/39.26  | | | | | | | 
% 227.67/39.26  | | | | | | | Case 1:
% 227.67/39.26  | | | | | | | | 
% 227.67/39.26  | | | | | | | |   (97)  all_55_4 = e2
% 227.67/39.26  | | | | | | | | 
% 227.67/39.26  | | | | | | | | COMBINE_EQS: (20), (97) imply:
% 227.67/39.26  | | | | | | | |   (98)  all_53_1 = e2
% 227.67/39.26  | | | | | | | | 
% 227.67/39.26  | | | | | | | | SIMP: (98) implies:
% 227.67/39.26  | | | | | | | |   (99)  all_53_1 = e2
% 227.67/39.26  | | | | | | | | 
% 227.67/39.26  | | | | | | | | REDUCE: (23), (99) imply:
% 227.67/39.26  | | | | | | | |   (100)   ~ (all_52_17 = e2)
% 227.67/39.26  | | | | | | | | 
% 227.67/39.26  | | | | | | | | SIMP: (100) implies:
% 227.67/39.26  | | | | | | | |   (101)   ~ (all_52_17 = e2)
% 227.67/39.26  | | | | | | | | 
% 227.67/39.26  | | | | | | | | REF_CLOSE: (3), (11), (18), (19), (26), (29), (33), (40), (44),
% 227.67/39.26  | | | | | | | |            (88), (101) are inconsistent by sub-proof #311.
% 227.67/39.26  | | | | | | | | 
% 227.67/39.26  | | | | | | | Case 2:
% 227.67/39.26  | | | | | | | | 
% 227.67/39.26  | | | | | | | |   (102)  all_55_4 = e1 | all_55_4 = e0
% 227.67/39.26  | | | | | | | | 
% 227.67/39.26  | | | | | | | | REF_CLOSE: (20), (30), (94), (102) are inconsistent by sub-proof
% 227.67/39.26  | | | | | | | |            #773.
% 227.67/39.26  | | | | | | | | 
% 227.67/39.26  | | | | | | | End of split
% 227.67/39.26  | | | | | | | 
% 227.67/39.26  | | | | | | End of split
% 227.67/39.26  | | | | | | 
% 227.67/39.26  | | | | | End of split
% 227.67/39.26  | | | | | 
% 227.67/39.26  | | | | End of split
% 227.67/39.26  | | | | 
% 227.67/39.26  | | | End of split
% 227.67/39.26  | | | 
% 227.67/39.26  | | End of split
% 227.67/39.26  | | 
% 227.67/39.26  | Case 2:
% 227.67/39.26  | | 
% 227.67/39.26  | |   (103)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) =
% 227.67/39.26  | |            e3)
% 227.67/39.26  | | 
% 227.67/39.26  | | REF_CLOSE: (11), (13), (14), (22), (35), (103) are inconsistent by sub-proof
% 227.67/39.26  | |            #1890.
% 227.67/39.26  | | 
% 227.67/39.26  | End of split
% 227.67/39.26  | 
% 227.67/39.26  End of proof
% 227.67/39.26  
% 227.67/39.26  Sub-proof #311 shows that the following formulas are inconsistent:
% 227.67/39.26  ----------------------------------------------------------------
% 227.67/39.26    (1)  op(e3, e3) = e1
% 227.67/39.26    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.67/39.26           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.67/39.26    (3)   ~ (all_52_17 = e2)
% 227.67/39.26    (4)  op(all_52_17, all_52_17) = e3
% 227.67/39.26    (5)   ~ (all_52_17 = e1)
% 227.67/39.26    (6)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 227.67/39.26    (7)   ~ (all_53_3 = all_52_17)
% 227.67/39.26    (8)  all_55_12 = all_53_3
% 227.67/39.26    (9)   ~ (all_53_3 = e1)
% 227.67/39.26    (10)  all_55_8 = all_52_17
% 227.67/39.26    (11)  all_55_12 = e1 | all_55_12 = e0
% 227.67/39.26  
% 227.67/39.26  Begin of proof
% 227.67/39.26  | 
% 227.67/39.26  | BETA: splitting (11) gives:
% 227.67/39.26  | 
% 227.67/39.26  | Case 1:
% 227.67/39.26  | | 
% 227.67/39.26  | |   (12)  all_55_12 = e1
% 227.67/39.26  | | 
% 227.67/39.26  | | REF_CLOSE: (8), (9), (12) are inconsistent by sub-proof #1994.
% 227.67/39.26  | | 
% 227.67/39.26  | Case 2:
% 227.67/39.26  | | 
% 227.67/39.26  | |   (13)  all_55_12 = e0
% 227.67/39.26  | | 
% 227.67/39.26  | | COMBINE_EQS: (8), (13) imply:
% 227.67/39.26  | |   (14)  all_53_3 = e0
% 227.67/39.26  | | 
% 227.67/39.26  | | SIMP: (14) implies:
% 227.67/39.26  | |   (15)  all_53_3 = e0
% 227.67/39.26  | | 
% 227.67/39.26  | | REDUCE: (7), (15) imply:
% 227.67/39.26  | |   (16)   ~ (all_52_17 = e0)
% 227.67/39.26  | | 
% 227.67/39.26  | | SIMP: (16) implies:
% 227.67/39.26  | |   (17)   ~ (all_52_17 = e0)
% 227.67/39.26  | | 
% 227.67/39.26  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (10), (17) are inconsistent by
% 227.67/39.26  | |            sub-proof #312.
% 227.67/39.26  | | 
% 227.67/39.26  | End of split
% 227.67/39.26  | 
% 227.67/39.26  End of proof
% 227.67/39.26  
% 227.67/39.26  Sub-proof #312 shows that the following formulas are inconsistent:
% 227.67/39.26  ----------------------------------------------------------------
% 227.67/39.26    (1)  op(e3, e3) = e1
% 227.67/39.26    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.67/39.26           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.67/39.26    (3)   ~ (all_52_17 = e2)
% 227.67/39.26    (4)  op(all_52_17, all_52_17) = e3
% 227.67/39.26    (5)   ~ (all_52_17 = e1)
% 227.67/39.26    (6)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 227.67/39.26    (7)   ~ (all_52_17 = e0)
% 227.67/39.26    (8)  all_55_8 = all_52_17
% 227.67/39.26  
% 227.67/39.26  Begin of proof
% 227.67/39.26  | 
% 227.67/39.26  | BETA: splitting (6) gives:
% 227.67/39.26  | 
% 227.67/39.26  | Case 1:
% 227.67/39.26  | | 
% 227.67/39.26  | |   (9)  all_55_8 = e3
% 227.67/39.26  | | 
% 227.67/39.26  | | COMBINE_EQS: (8), (9) imply:
% 227.67/39.26  | |   (10)  all_52_17 = e3
% 227.67/39.26  | | 
% 227.67/39.26  | | REDUCE: (5), (10) imply:
% 227.67/39.26  | |   (11)   ~ (e3 = e1)
% 227.67/39.26  | | 
% 227.67/39.26  | | REDUCE: (4), (10) imply:
% 227.67/39.26  | |   (12)  op(e3, e3) = e3
% 227.67/39.26  | | 
% 227.67/39.26  | | REF_CLOSE: (1), (2), (11), (12) are inconsistent by sub-proof #2495.
% 227.67/39.26  | | 
% 227.67/39.26  | Case 2:
% 227.67/39.26  | | 
% 227.67/39.26  | |   (13)  all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 227.67/39.26  | | 
% 227.67/39.26  | | REF_CLOSE: (3), (5), (7), (8), (13) are inconsistent by sub-proof #1867.
% 227.67/39.26  | | 
% 227.67/39.26  | End of split
% 227.67/39.26  | 
% 227.67/39.26  End of proof
% 227.67/39.26  
% 227.67/39.26  Sub-proof #313 shows that the following formulas are inconsistent:
% 227.67/39.26  ----------------------------------------------------------------
% 227.67/39.26    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.67/39.26           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.67/39.26    (2)  op(e3, e0) = e3
% 227.67/39.26    (3)  op(e3, e0) = e0
% 227.67/39.26    (4)   ~ (e3 = e0)
% 227.67/39.26  
% 227.67/39.26  Begin of proof
% 227.67/39.26  | 
% 227.67/39.26  | GROUND_INST: instantiating (1) with e0, e3, e0, e3, simplifying with (2), (3)
% 227.67/39.26  |              gives:
% 227.67/39.26  |   (5)  e3 = e0
% 227.67/39.26  | 
% 227.67/39.26  | REDUCE: (4), (5) imply:
% 227.67/39.26  |   (6)  $false
% 227.67/39.26  | 
% 227.67/39.26  | CLOSE: (6) is inconsistent.
% 227.67/39.26  | 
% 227.67/39.26  End of proof
% 227.67/39.26  
% 227.67/39.26  Sub-proof #314 shows that the following formulas are inconsistent:
% 227.67/39.26  ----------------------------------------------------------------
% 227.67/39.26    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.67/39.26           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.67/39.26    (2)   ~ (all_53_7 = e2)
% 227.67/39.26    (3)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.67/39.26    (4)   ~ (all_10_0 = e2)
% 227.67/39.26    (5)  op(e0, e2) = all_53_7
% 227.67/39.26    (6)  op(e0, e3) = all_10_0
% 227.67/39.26  
% 227.67/39.26  Begin of proof
% 227.67/39.26  | 
% 227.67/39.26  | BETA: splitting (3) gives:
% 227.67/39.26  | 
% 227.67/39.26  | Case 1:
% 227.67/39.26  | | 
% 227.67/39.26  | |   (7)  all_57_12 = e2 & op(e0, e3) = e2
% 227.67/39.26  | | 
% 227.67/39.26  | | ALPHA: (7) implies:
% 227.67/39.26  | |   (8)  op(e0, e3) = e2
% 227.67/39.26  | | 
% 227.67/39.26  | | GROUND_INST: instantiating (1) with all_10_0, e2, e3, e0, simplifying with
% 227.67/39.26  | |              (6), (8) gives:
% 227.67/39.26  | |   (9)  all_10_0 = e2
% 227.67/39.26  | | 
% 227.67/39.26  | | REDUCE: (4), (9) imply:
% 227.67/39.26  | |   (10)  $false
% 227.67/39.26  | | 
% 227.67/39.26  | | CLOSE: (10) is inconsistent.
% 227.67/39.26  | | 
% 227.67/39.26  | Case 2:
% 227.67/39.26  | | 
% 227.67/39.26  | |   (11)  all_57_13 = e2 & op(e0, e2) = e2
% 227.67/39.26  | | 
% 227.67/39.26  | | ALPHA: (11) implies:
% 227.67/39.26  | |   (12)  op(e0, e2) = e2
% 227.67/39.26  | | 
% 227.67/39.26  | | REF_CLOSE: (1), (2), (5), (12) are inconsistent by sub-proof #2335.
% 227.67/39.26  | | 
% 227.67/39.26  | End of split
% 227.67/39.26  | 
% 227.67/39.26  End of proof
% 227.67/39.26  
% 227.67/39.26  Sub-proof #315 shows that the following formulas are inconsistent:
% 227.67/39.26  ----------------------------------------------------------------
% 227.67/39.26    (1)  op(e1, e3) = all_52_17
% 227.67/39.26    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 227.67/39.26    (3)  op(e2, e3) = all_53_1
% 227.67/39.26    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 227.67/39.26         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 227.67/39.26    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.67/39.26           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.67/39.26    (6)   ~ (all_6_2 = e3)
% 227.67/39.26    (7)  op(e1, e1) = all_6_2
% 227.67/39.26    (8)  op(all_52_17, all_52_17) = e3
% 227.67/39.26    (9)  all_57_1 = e2
% 227.67/39.26    (10)  op(e0, e3) = all_53_3
% 227.67/39.26    (11)   ~ (all_53_1 = e1)
% 227.67/39.26    (12)   ~ (e2 = e0)
% 227.67/39.26    (13)   ~ (e1 = e0)
% 227.67/39.26    (14)  all_55_10 = all_6_2
% 227.67/39.26    (15)   ~ (all_53_3 = e1)
% 227.67/39.26    (16)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0)
% 227.67/39.26  
% 227.67/39.26  Begin of proof
% 227.67/39.26  | 
% 227.67/39.26  | BETA: splitting (16) gives:
% 227.67/39.26  | 
% 227.67/39.26  | Case 1:
% 227.67/39.26  | | 
% 227.67/39.26  | |   (17)  all_57_0 = e0 & op(e3, e3) = e0
% 227.67/39.26  | | 
% 227.67/39.26  | | ALPHA: (17) implies:
% 227.67/39.26  | |   (18)  all_57_0 = e0
% 227.67/39.26  | | 
% 227.67/39.26  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (13), (14),
% 227.67/39.26  | |            (15), (18) are inconsistent by sub-proof #1545.
% 227.67/39.26  | | 
% 227.67/39.26  | Case 2:
% 227.67/39.26  | | 
% 227.67/39.26  | |   (19)  all_57_1 = e0 & op(e3, e2) = e0
% 227.67/39.26  | | 
% 227.67/39.26  | | REF_CLOSE: (9), (12), (19) are inconsistent by sub-proof #1723.
% 227.67/39.26  | | 
% 227.67/39.26  | End of split
% 227.67/39.26  | 
% 227.67/39.26  End of proof
% 227.67/39.26  
% 227.67/39.26  Sub-proof #316 shows that the following formulas are inconsistent:
% 227.67/39.26  ----------------------------------------------------------------
% 227.67/39.26    (1)  all_57_6 = e1 & op(e1, e3) = e1
% 227.67/39.26    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.67/39.26           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.67/39.26    (3)  op(e1, e3) = all_53_2
% 227.67/39.26    (4)   ~ (all_53_2 = e1)
% 227.67/39.26  
% 227.67/39.26  Begin of proof
% 227.67/39.26  | 
% 227.67/39.26  | ALPHA: (1) implies:
% 227.67/39.26  |   (5)  op(e1, e3) = e1
% 227.67/39.26  | 
% 227.67/39.26  | GROUND_INST: instantiating (2) with all_53_2, e1, e3, e1, simplifying with
% 227.67/39.26  |              (3), (5) gives:
% 227.67/39.26  |   (6)  all_53_2 = e1
% 227.67/39.26  | 
% 227.67/39.26  | REDUCE: (4), (6) imply:
% 227.67/39.26  |   (7)  $false
% 227.67/39.26  | 
% 227.67/39.26  | CLOSE: (7) is inconsistent.
% 227.67/39.26  | 
% 227.67/39.26  End of proof
% 227.67/39.26  
% 227.67/39.26  Sub-proof #317 shows that the following formulas are inconsistent:
% 227.67/39.26  ----------------------------------------------------------------
% 227.67/39.26    (1)  op(e0, e0) = all_4_2
% 227.67/39.26    (2)  all_55_15 = e3 | all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 227.67/39.26    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.67/39.26           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.67/39.26    (4)  all_55_15 = all_4_2
% 227.67/39.26    (5)   ~ (all_4_2 = e2)
% 227.67/39.26    (6)  op(e0, e0) = e1
% 227.67/39.26    (7)   ~ (all_4_2 = e3)
% 227.67/39.26    (8)   ~ (all_4_2 = e1)
% 227.67/39.26  
% 227.67/39.26  Begin of proof
% 227.67/39.26  | 
% 227.67/39.26  | BETA: splitting (2) gives:
% 227.67/39.26  | 
% 227.67/39.26  | Case 1:
% 227.67/39.26  | | 
% 227.67/39.26  | |   (9)  all_55_15 = e3
% 227.67/39.26  | | 
% 227.67/39.26  | | COMBINE_EQS: (4), (9) imply:
% 227.67/39.26  | |   (10)  all_4_2 = e3
% 227.67/39.26  | | 
% 227.67/39.26  | | REDUCE: (7), (10) imply:
% 227.67/39.26  | |   (11)  $false
% 227.67/39.26  | | 
% 227.67/39.26  | | CLOSE: (11) is inconsistent.
% 227.67/39.26  | | 
% 227.67/39.26  | Case 2:
% 227.67/39.26  | | 
% 227.67/39.26  | |   (12)  all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 227.67/39.26  | | 
% 227.67/39.26  | | BETA: splitting (12) gives:
% 227.67/39.26  | | 
% 227.67/39.26  | | Case 1:
% 227.67/39.26  | | | 
% 227.67/39.26  | | |   (13)  all_55_15 = e2
% 227.67/39.26  | | | 
% 227.67/39.26  | | | COMBINE_EQS: (4), (13) imply:
% 227.67/39.26  | | |   (14)  all_4_2 = e2
% 227.67/39.26  | | | 
% 227.67/39.26  | | | REDUCE: (5), (14) imply:
% 227.67/39.26  | | |   (15)  $false
% 227.67/39.26  | | | 
% 227.67/39.26  | | | CLOSE: (15) is inconsistent.
% 227.67/39.26  | | | 
% 227.67/39.26  | | Case 2:
% 227.67/39.26  | | | 
% 227.67/39.26  | | |   (16)  all_55_15 = e1 | all_55_15 = e0
% 227.67/39.26  | | | 
% 227.67/39.26  | | | BETA: splitting (16) gives:
% 227.67/39.26  | | | 
% 227.67/39.26  | | | Case 1:
% 227.67/39.26  | | | | 
% 227.67/39.26  | | | |   (17)  all_55_15 = e1
% 227.67/39.26  | | | | 
% 227.67/39.26  | | | | COMBINE_EQS: (4), (17) imply:
% 227.67/39.26  | | | |   (18)  all_4_2 = e1
% 227.67/39.26  | | | | 
% 227.67/39.26  | | | | REDUCE: (8), (18) imply:
% 227.67/39.26  | | | |   (19)  $false
% 227.67/39.26  | | | | 
% 227.67/39.26  | | | | CLOSE: (19) is inconsistent.
% 227.67/39.26  | | | | 
% 227.67/39.26  | | | Case 2:
% 227.67/39.26  | | | | 
% 227.67/39.26  | | | |   (20)  all_55_15 = e0
% 227.67/39.26  | | | | 
% 227.67/39.26  | | | | COMBINE_EQS: (4), (20) imply:
% 227.67/39.26  | | | |   (21)  all_4_2 = e0
% 227.67/39.26  | | | | 
% 227.67/39.26  | | | | REDUCE: (8), (21) imply:
% 227.67/39.26  | | | |   (22)   ~ (e1 = e0)
% 227.67/39.26  | | | | 
% 227.67/39.26  | | | | SIMP: (22) implies:
% 227.67/39.26  | | | |   (23)   ~ (e1 = e0)
% 227.67/39.26  | | | | 
% 227.67/39.26  | | | | REDUCE: (1), (21) imply:
% 227.67/39.26  | | | |   (24)  op(e0, e0) = e0
% 227.67/39.26  | | | | 
% 227.67/39.26  | | | | REF_CLOSE: (3), (6), (23), (24) are inconsistent by sub-proof #2290.
% 227.67/39.26  | | | | 
% 227.67/39.26  | | | End of split
% 227.67/39.26  | | | 
% 227.67/39.26  | | End of split
% 227.67/39.26  | | 
% 227.67/39.26  | End of split
% 227.67/39.26  | 
% 227.67/39.26  End of proof
% 227.67/39.26  
% 227.67/39.26  Sub-proof #318 shows that the following formulas are inconsistent:
% 227.67/39.26  ----------------------------------------------------------------
% 227.67/39.26    (1)  all_55_6 = all_52_13
% 227.67/39.26    (2)  all_55_6 = e3
% 227.67/39.26    (3)   ~ (all_52_13 = e3)
% 227.67/39.26  
% 227.67/39.26  Begin of proof
% 227.67/39.26  | 
% 227.67/39.26  | COMBINE_EQS: (1), (2) imply:
% 227.67/39.26  |   (4)  all_52_13 = e3
% 227.67/39.26  | 
% 227.67/39.26  | SIMP: (4) implies:
% 227.67/39.26  |   (5)  all_52_13 = e3
% 227.67/39.26  | 
% 227.67/39.26  | REDUCE: (3), (5) imply:
% 227.67/39.26  |   (6)  $false
% 227.67/39.26  | 
% 227.67/39.26  | CLOSE: (6) is inconsistent.
% 227.67/39.26  | 
% 227.67/39.26  End of proof
% 227.67/39.26  
% 227.67/39.26  Sub-proof #319 shows that the following formulas are inconsistent:
% 227.67/39.26  ----------------------------------------------------------------
% 227.67/39.26    (1)  all_57_15 = e0
% 227.67/39.26    (2)  op(e3, e1) = all_52_5
% 227.67/39.26    (3)   ~ (e3 = e1)
% 227.67/39.26    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.67/39.26           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.67/39.26    (5)  op(all_52_5, all_52_5) = e1
% 227.67/39.26    (6)  op(e3, e2) = all_52_3
% 227.67/39.26    (7)  op(all_52_3, all_52_3) = e2
% 227.67/39.26    (8)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 227.67/39.26         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 227.67/39.26    (9)   ~ (e3 = e2)
% 227.67/39.26    (10)   ~ (e3 = e0)
% 227.67/39.26    (11)  all_57_0 = e1
% 227.67/39.26    (12)  op(e0, e3) = all_53_3
% 227.67/39.26    (13)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 227.67/39.26          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 227.67/39.26            e1)
% 227.67/39.26    (14)   ~ (e2 = e0)
% 227.67/39.26    (15)   ~ (e1 = e0)
% 227.67/39.26    (16)  all_57_14 = e1
% 227.67/39.26    (17)  op(e0, e0) = e0
% 227.67/39.26    (18)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 227.67/39.26          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 227.67/39.26            e3)
% 227.67/39.26    (19)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.67/39.26          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 227.67/39.26            e2)
% 227.67/39.26    (20)   ~ (all_53_3 = e1)
% 227.67/39.26    (21)   ~ (all_53_12 = e0)
% 227.67/39.26    (22)   ~ (e2 = e1)
% 227.67/39.26    (23)  op(e3, e0) = all_53_12
% 227.67/39.26  
% 227.67/39.26  Begin of proof
% 227.67/39.26  | 
% 227.67/39.26  | BETA: splitting (8) gives:
% 227.67/39.26  | 
% 227.67/39.26  | Case 1:
% 227.67/39.26  | | 
% 227.67/39.26  | |   (24)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) =
% 227.67/39.26  | |           e0)
% 227.67/39.26  | | 
% 227.67/39.26  | | BETA: splitting (24) gives:
% 227.67/39.26  | | 
% 227.67/39.26  | | Case 1:
% 227.67/39.26  | | | 
% 227.67/39.26  | | |   (25)  all_57_0 = e0 & op(e3, e3) = e0
% 227.67/39.26  | | | 
% 227.67/39.26  | | | ALPHA: (25) implies:
% 227.67/39.26  | | |   (26)  all_57_0 = e0
% 227.67/39.26  | | | 
% 227.67/39.26  | | | COMBINE_EQS: (11), (26) imply:
% 227.67/39.26  | | |   (27)  e1 = e0
% 227.67/39.26  | | | 
% 227.67/39.26  | | | COMBINE_EQS: (16), (27) imply:
% 227.67/39.26  | | |   (28)  all_57_14 = e0
% 227.67/39.26  | | | 
% 227.67/39.26  | | | REF_CLOSE: (1), (3), (4), (9), (10), (12), (13), (14), (15), (17), (18),
% 227.67/39.26  | | |            (19), (20), (22), (28) are inconsistent by sub-proof #320.
% 227.67/39.26  | | | 
% 227.67/39.26  | | Case 2:
% 227.67/39.26  | | | 
% 227.67/39.26  | | |   (29)  all_57_1 = e0 & op(e3, e2) = e0
% 227.67/39.26  | | | 
% 227.67/39.26  | | | ALPHA: (29) implies:
% 227.67/39.26  | | |   (30)  op(e3, e2) = e0
% 227.67/39.26  | | | 
% 227.67/39.26  | | | REF_CLOSE: (4), (6), (7), (14), (17), (30) are inconsistent by sub-proof
% 227.67/39.26  | | |            #2399.
% 227.67/39.26  | | | 
% 227.67/39.26  | | End of split
% 227.67/39.26  | | 
% 227.67/39.26  | Case 2:
% 227.67/39.26  | | 
% 227.67/39.26  | |   (31)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) =
% 227.67/39.26  | |           e0)
% 227.67/39.26  | | 
% 227.67/39.26  | | BETA: splitting (31) gives:
% 227.67/39.26  | | 
% 227.67/39.26  | | Case 1:
% 227.67/39.26  | | | 
% 227.67/39.26  | | |   (32)  all_57_4 = e0 & op(e3, e1) = e0
% 227.67/39.26  | | | 
% 227.67/39.27  | | | ALPHA: (32) implies:
% 227.67/39.27  | | |   (33)  op(e3, e1) = e0
% 227.67/39.27  | | | 
% 227.67/39.27  | | | REF_CLOSE: (2), (4), (5), (15), (17), (33) are inconsistent by sub-proof
% 227.67/39.27  | | |            #2167.
% 227.67/39.27  | | | 
% 227.67/39.27  | | Case 2:
% 227.67/39.27  | | | 
% 227.67/39.27  | | |   (34)  all_57_9 = e0 & op(e3, e0) = e0
% 227.67/39.27  | | | 
% 227.67/39.27  | | | REF_CLOSE: (4), (21), (23), (34) are inconsistent by sub-proof #2434.
% 227.67/39.27  | | | 
% 227.67/39.27  | | End of split
% 227.67/39.27  | | 
% 227.67/39.27  | End of split
% 227.67/39.27  | 
% 227.67/39.27  End of proof
% 227.67/39.27  
% 227.67/39.27  Sub-proof #320 shows that the following formulas are inconsistent:
% 227.67/39.27  ----------------------------------------------------------------
% 227.67/39.27    (1)  all_57_15 = e0
% 227.67/39.27    (2)   ~ (e3 = e1)
% 227.67/39.27    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.67/39.27           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.67/39.27    (4)   ~ (e3 = e2)
% 227.67/39.27    (5)   ~ (e3 = e0)
% 227.67/39.27    (6)  op(e0, e3) = all_53_3
% 227.67/39.27    (7)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 227.67/39.27         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 227.67/39.27    (8)   ~ (e2 = e0)
% 227.67/39.27    (9)   ~ (e1 = e0)
% 227.67/39.27    (10)  op(e0, e0) = e0
% 227.67/39.27    (11)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 227.67/39.27          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 227.67/39.27            e3)
% 227.67/39.27    (12)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.67/39.27          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 227.67/39.27            e2)
% 227.67/39.27    (13)   ~ (all_53_3 = e1)
% 227.67/39.27    (14)   ~ (e2 = e1)
% 227.67/39.27    (15)  all_57_14 = e0
% 227.67/39.27  
% 227.67/39.27  Begin of proof
% 227.67/39.27  | 
% 227.67/39.27  | BETA: splitting (7) gives:
% 227.67/39.27  | 
% 227.67/39.27  | Case 1:
% 227.67/39.27  | | 
% 227.67/39.27  | |   (16)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 227.67/39.27  | |           e1)
% 227.67/39.27  | | 
% 227.67/39.27  | | BETA: splitting (16) gives:
% 227.67/39.27  | | 
% 227.67/39.27  | | Case 1:
% 227.67/39.27  | | | 
% 227.67/39.27  | | |   (17)  all_57_12 = e1 & op(e0, e3) = e1
% 227.67/39.27  | | | 
% 227.67/39.27  | | | REF_CLOSE: (3), (6), (13), (17) are inconsistent by sub-proof #1947.
% 227.67/39.27  | | | 
% 227.67/39.27  | | Case 2:
% 227.67/39.27  | | | 
% 227.67/39.27  | | |   (18)  all_57_13 = e1 & op(e0, e2) = e1
% 227.67/39.27  | | | 
% 227.67/39.27  | | | ALPHA: (18) implies:
% 227.67/39.27  | | |   (19)  all_57_13 = e1
% 227.67/39.27  | | | 
% 227.67/39.27  | | | REF_CLOSE: (1), (2), (3), (4), (5), (8), (10), (11), (12), (14), (15),
% 227.67/39.27  | | |            (19) are inconsistent by sub-proof #2123.
% 227.67/39.27  | | | 
% 227.67/39.27  | | End of split
% 227.67/39.27  | | 
% 227.67/39.27  | Case 2:
% 227.67/39.27  | | 
% 227.67/39.27  | |   (20)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 227.67/39.27  | |           e1)
% 227.67/39.27  | | 
% 227.67/39.27  | | REF_CLOSE: (3), (9), (10), (15), (20) are inconsistent by sub-proof #2121.
% 227.67/39.27  | | 
% 227.67/39.27  | End of split
% 227.67/39.27  | 
% 227.67/39.27  End of proof
% 227.67/39.27  
% 227.67/39.27  Sub-proof #321 shows that the following formulas are inconsistent:
% 227.67/39.27  ----------------------------------------------------------------
% 227.67/39.27    (1)   ~ (all_53_13 = e1)
% 227.67/39.27    (2)  all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 227.67/39.27    (3)   ~ (all_53_13 = e2)
% 227.67/39.27    (4)   ~ (all_53_13 = e0)
% 227.67/39.27    (5)  all_55_7 = all_53_13
% 227.67/39.27  
% 227.67/39.27  Begin of proof
% 227.67/39.27  | 
% 227.67/39.27  | BETA: splitting (2) gives:
% 227.67/39.27  | 
% 227.67/39.27  | Case 1:
% 227.67/39.27  | | 
% 227.67/39.27  | |   (6)  all_55_7 = e2
% 227.67/39.27  | | 
% 227.67/39.27  | | REF_CLOSE: (3), (5), (6) are inconsistent by sub-proof #2171.
% 227.67/39.27  | | 
% 227.67/39.27  | Case 2:
% 227.67/39.27  | | 
% 227.67/39.27  | |   (7)  all_55_7 = e1 | all_55_7 = e0
% 227.67/39.27  | | 
% 227.67/39.27  | | REF_CLOSE: (1), (4), (5), (7) are inconsistent by sub-proof #1322.
% 227.67/39.27  | | 
% 227.67/39.27  | End of split
% 227.67/39.27  | 
% 227.67/39.27  End of proof
% 227.67/39.27  
% 227.67/39.27  Sub-proof #322 shows that the following formulas are inconsistent:
% 227.67/39.27  ----------------------------------------------------------------
% 227.67/39.27    (1)   ~ (all_52_25 = e1)
% 227.67/39.27    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.67/39.27           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.67/39.27    (3)   ~ (all_52_25 = e3)
% 227.67/39.27    (4)  all_55_12 = all_52_25
% 227.67/39.27    (5)  op(all_52_25, all_52_25) = e3
% 227.67/39.27    (6)  op(e2, e2) = e2
% 227.67/39.27    (7)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 227.67/39.27    (8)   ~ (all_52_25 = e0)
% 227.67/39.27  
% 227.67/39.27  Begin of proof
% 227.67/39.27  | 
% 227.67/39.27  | BETA: splitting (7) gives:
% 227.67/39.27  | 
% 227.67/39.27  | Case 1:
% 227.67/39.27  | | 
% 227.67/39.27  | |   (9)  all_55_12 = e3
% 227.67/39.27  | | 
% 227.67/39.27  | | REF_CLOSE: (3), (4), (9) are inconsistent by sub-proof #1683.
% 227.67/39.27  | | 
% 227.67/39.27  | Case 2:
% 227.67/39.27  | | 
% 227.67/39.27  | |   (10)   ~ (all_55_12 = e3)
% 227.67/39.27  | |   (11)  all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 227.67/39.27  | | 
% 227.67/39.27  | | BETA: splitting (11) gives:
% 227.67/39.27  | | 
% 227.67/39.27  | | Case 1:
% 227.67/39.27  | | | 
% 227.67/39.27  | | |   (12)  all_55_12 = e2
% 227.67/39.27  | | | 
% 227.67/39.27  | | | COMBINE_EQS: (4), (12) imply:
% 227.67/39.27  | | |   (13)  all_52_25 = e2
% 227.67/39.27  | | | 
% 227.67/39.27  | | | SIMP: (13) implies:
% 227.67/39.27  | | |   (14)  all_52_25 = e2
% 227.67/39.27  | | | 
% 227.67/39.27  | | | REDUCE: (3), (14) imply:
% 227.67/39.27  | | |   (15)   ~ (e3 = e2)
% 227.67/39.27  | | | 
% 227.67/39.27  | | | SIMP: (15) implies:
% 227.67/39.27  | | |   (16)   ~ (e3 = e2)
% 227.67/39.27  | | | 
% 227.67/39.27  | | | REDUCE: (5), (14) imply:
% 227.67/39.27  | | |   (17)  op(e2, e2) = e3
% 227.67/39.27  | | | 
% 227.67/39.27  | | | REF_CLOSE: (2), (6), (16), (17) are inconsistent by sub-proof #2298.
% 227.67/39.27  | | | 
% 227.67/39.27  | | Case 2:
% 227.67/39.27  | | | 
% 227.67/39.27  | | |   (18)  all_55_12 = e1 | all_55_12 = e0
% 227.67/39.27  | | | 
% 227.67/39.27  | | | REF_CLOSE: (1), (4), (8), (18) are inconsistent by sub-proof #323.
% 227.67/39.27  | | | 
% 227.67/39.27  | | End of split
% 227.67/39.27  | | 
% 227.67/39.27  | End of split
% 227.67/39.27  | 
% 227.67/39.27  End of proof
% 227.67/39.27  
% 227.67/39.27  Sub-proof #323 shows that the following formulas are inconsistent:
% 227.67/39.27  ----------------------------------------------------------------
% 227.67/39.27    (1)  all_55_12 = e1 | all_55_12 = e0
% 227.67/39.27    (2)  all_55_12 = all_52_25
% 227.67/39.27    (3)   ~ (all_52_25 = e1)
% 227.67/39.27    (4)   ~ (all_52_25 = e0)
% 227.67/39.27  
% 227.67/39.27  Begin of proof
% 227.67/39.27  | 
% 227.67/39.27  | BETA: splitting (1) gives:
% 227.67/39.27  | 
% 227.67/39.27  | Case 1:
% 227.67/39.27  | | 
% 227.67/39.27  | |   (5)  all_55_12 = e1
% 227.67/39.27  | | 
% 227.67/39.27  | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #1681.
% 227.67/39.27  | | 
% 227.67/39.27  | Case 2:
% 227.67/39.27  | | 
% 227.67/39.27  | |   (6)  all_55_12 = e0
% 227.67/39.27  | | 
% 227.67/39.27  | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #1564.
% 227.67/39.27  | | 
% 227.67/39.27  | End of split
% 227.67/39.27  | 
% 227.67/39.27  End of proof
% 227.67/39.27  
% 227.67/39.27  Sub-proof #324 shows that the following formulas are inconsistent:
% 227.67/39.27  ----------------------------------------------------------------
% 227.67/39.27    (1)  all_55_3 = all_53_12
% 227.67/39.27    (2)  all_55_3 = e1
% 227.67/39.27    (3)   ~ (all_53_12 = e1)
% 227.67/39.27  
% 227.67/39.27  Begin of proof
% 227.67/39.27  | 
% 227.67/39.27  | COMBINE_EQS: (1), (2) imply:
% 227.67/39.27  |   (4)  all_53_12 = e1
% 227.67/39.27  | 
% 227.67/39.27  | SIMP: (4) implies:
% 227.67/39.27  |   (5)  all_53_12 = e1
% 227.67/39.27  | 
% 227.67/39.27  | REDUCE: (3), (5) imply:
% 227.67/39.27  |   (6)  $false
% 227.67/39.27  | 
% 227.67/39.27  | CLOSE: (6) is inconsistent.
% 227.67/39.27  | 
% 227.67/39.27  End of proof
% 227.67/39.27  
% 227.67/39.27  Sub-proof #325 shows that the following formulas are inconsistent:
% 227.67/39.27  ----------------------------------------------------------------
% 227.67/39.27    (1)   ~ (e3 = e1)
% 227.67/39.27    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.67/39.27           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.67/39.27    (3)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 227.67/39.27         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 227.67/39.27    (4)   ~ (all_6_2 = e3)
% 227.67/39.27    (5)  op(e1, e1) = all_6_2
% 227.67/39.27    (6)  all_57_7 = e1
% 227.67/39.27    (7)  all_57_6 = e1
% 227.67/39.27    (8)   ~ (e3 = e2)
% 227.67/39.27    (9)   ~ (e2 = e0)
% 227.67/39.27    (10)  all_57_8 = e0
% 227.67/39.27    (11)   ~ (e2 = e1)
% 227.67/39.27    (12)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 227.67/39.27          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 227.67/39.27  
% 227.67/39.27  Begin of proof
% 227.67/39.27  | 
% 227.67/39.27  | BETA: splitting (12) gives:
% 227.67/39.27  | 
% 227.67/39.27  | Case 1:
% 227.67/39.27  | | 
% 227.67/39.27  | |   (13)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) =
% 227.67/39.27  | |           e2)
% 227.67/39.27  | | 
% 227.67/39.27  | | BETA: splitting (13) gives:
% 227.67/39.27  | | 
% 227.67/39.27  | | Case 1:
% 227.67/39.27  | | | 
% 227.67/39.27  | | |   (14)  all_57_6 = e2 & op(e1, e3) = e2
% 227.67/39.27  | | | 
% 227.67/39.27  | | | ALPHA: (14) implies:
% 227.67/39.27  | | |   (15)  all_57_6 = e2
% 227.67/39.27  | | | 
% 227.67/39.27  | | | REF_CLOSE: (7), (11), (15) are inconsistent by sub-proof #2233.
% 227.67/39.27  | | | 
% 227.67/39.27  | | Case 2:
% 227.67/39.27  | | | 
% 227.67/39.27  | | |   (16)  all_57_7 = e2 & op(e1, e2) = e2
% 227.67/39.27  | | | 
% 227.67/39.27  | | | ALPHA: (16) implies:
% 227.67/39.27  | | |   (17)  all_57_7 = e2
% 227.67/39.27  | | | 
% 227.67/39.27  | | | REF_CLOSE: (6), (11), (17) are inconsistent by sub-proof #1761.
% 227.67/39.27  | | | 
% 227.67/39.27  | | End of split
% 227.67/39.27  | | 
% 227.67/39.27  | Case 2:
% 227.67/39.27  | | 
% 227.67/39.27  | |   (18)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) =
% 227.67/39.27  | |           e2)
% 227.67/39.27  | | 
% 227.67/39.27  | | BETA: splitting (18) gives:
% 227.67/39.27  | | 
% 227.67/39.27  | | Case 1:
% 227.67/39.27  | | | 
% 227.67/39.27  | | |   (19)  all_57_8 = e2 & op(e1, e1) = e2
% 227.67/39.27  | | | 
% 227.67/39.27  | | | ALPHA: (19) implies:
% 227.67/39.27  | | |   (20)  all_57_8 = e2
% 227.67/39.27  | | | 
% 227.67/39.27  | | | REF_CLOSE: (9), (10), (20) are inconsistent by sub-proof #1957.
% 227.67/39.27  | | | 
% 227.67/39.27  | | Case 2:
% 227.67/39.27  | | | 
% 227.67/39.27  | | |   (21)  all_57_11 = e2 & op(e1, e0) = e2
% 227.67/39.27  | | | 
% 227.67/39.27  | | | ALPHA: (21) implies:
% 227.67/39.27  | | |   (22)  all_57_11 = e2
% 227.67/39.27  | | | 
% 227.67/39.27  | | | BETA: splitting (3) gives:
% 227.67/39.27  | | | 
% 227.67/39.27  | | | Case 1:
% 227.67/39.27  | | | | 
% 227.67/39.27  | | | |   (23)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2)
% 227.67/39.27  | | | |           = e3)
% 227.67/39.27  | | | | 
% 227.67/39.27  | | | | BETA: splitting (23) gives:
% 227.67/39.27  | | | | 
% 227.67/39.27  | | | | Case 1:
% 227.67/39.27  | | | | | 
% 227.67/39.27  | | | | |   (24)  all_57_6 = e3 & op(e1, e3) = e3
% 227.67/39.27  | | | | | 
% 227.67/39.27  | | | | | ALPHA: (24) implies:
% 227.67/39.27  | | | | |   (25)  all_57_6 = e3
% 227.67/39.27  | | | | | 
% 227.67/39.27  | | | | | REF_CLOSE: (1), (7), (25) are inconsistent by sub-proof #2017.
% 227.67/39.27  | | | | | 
% 227.67/39.27  | | | | Case 2:
% 227.67/39.27  | | | | | 
% 227.67/39.27  | | | | |   (26)  all_57_7 = e3 & op(e1, e2) = e3
% 227.67/39.27  | | | | | 
% 227.67/39.27  | | | | | ALPHA: (26) implies:
% 227.67/39.27  | | | | |   (27)  all_57_7 = e3
% 227.67/39.27  | | | | | 
% 227.67/39.27  | | | | | REF_CLOSE: (1), (6), (27) are inconsistent by sub-proof #2115.
% 227.67/39.27  | | | | | 
% 227.67/39.27  | | | | End of split
% 227.67/39.27  | | | | 
% 227.67/39.27  | | | Case 2:
% 227.67/39.27  | | | | 
% 227.67/39.27  | | | |   (28)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0)
% 227.67/39.27  | | | |           = e3)
% 227.67/39.27  | | | | 
% 227.67/39.27  | | | | REF_CLOSE: (2), (4), (5), (8), (22), (28) are inconsistent by sub-proof
% 227.67/39.27  | | | |            #2040.
% 227.67/39.27  | | | | 
% 227.67/39.27  | | | End of split
% 227.67/39.27  | | | 
% 227.67/39.27  | | End of split
% 227.67/39.27  | | 
% 227.67/39.27  | End of split
% 227.67/39.27  | 
% 227.67/39.27  End of proof
% 227.67/39.27  
% 227.67/39.27  Sub-proof #326 shows that the following formulas are inconsistent:
% 227.67/39.27  ----------------------------------------------------------------
% 227.67/39.27    (1)  all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 227.67/39.27    (2)  op(e3, e3) = e1
% 227.67/39.27    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.67/39.27           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.67/39.27    (4)   ~ (all_53_7 = e1)
% 227.67/39.27    (5)   ~ (all_53_7 = e2)
% 227.67/39.27    (6)   ~ (all_53_4 = all_53_7)
% 227.67/39.27    (7)  op(e3, e2) = all_53_4
% 227.67/39.27    (8)  all_55_13 = all_52_27
% 227.67/39.27    (9)  all_55_13 = all_53_7
% 227.67/39.27    (10)   ~ (e2 = e1)
% 227.67/39.27    (11)  op(e3, e2) = e0
% 227.67/39.27    (12)  op(all_52_27, all_52_27) = e2
% 227.67/39.27  
% 227.67/39.27  Begin of proof
% 227.67/39.27  | 
% 227.67/39.27  | BETA: splitting (1) gives:
% 227.67/39.27  | 
% 227.67/39.27  | Case 1:
% 227.67/39.27  | | 
% 227.67/39.27  | |   (13)  all_55_13 = e3
% 227.67/39.27  | | 
% 227.67/39.27  | | COMBINE_EQS: (8), (13) imply:
% 227.67/39.27  | |   (14)  all_52_27 = e3
% 227.67/39.27  | | 
% 227.67/39.27  | | SIMP: (14) implies:
% 227.67/39.27  | |   (15)  all_52_27 = e3
% 227.67/39.27  | | 
% 227.67/39.27  | | REDUCE: (12), (15) imply:
% 227.67/39.27  | |   (16)  op(e3, e3) = e2
% 227.67/39.27  | | 
% 227.67/39.27  | | REF_CLOSE: (2), (3), (10), (16) are inconsistent by sub-proof #1950.
% 227.67/39.27  | | 
% 227.67/39.27  | Case 2:
% 227.67/39.27  | | 
% 227.67/39.27  | |   (17)  all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 227.67/39.27  | | 
% 227.67/39.27  | | REF_CLOSE: (3), (4), (5), (6), (7), (9), (11), (17) are inconsistent by
% 227.67/39.27  | |            sub-proof #327.
% 227.67/39.27  | | 
% 227.67/39.27  | End of split
% 227.67/39.27  | 
% 227.67/39.27  End of proof
% 227.67/39.27  
% 227.67/39.27  Sub-proof #327 shows that the following formulas are inconsistent:
% 227.67/39.27  ----------------------------------------------------------------
% 227.67/39.27    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.67/39.27           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.67/39.27    (2)   ~ (all_53_7 = e1)
% 227.67/39.27    (3)   ~ (all_53_7 = e2)
% 227.67/39.27    (4)   ~ (all_53_4 = all_53_7)
% 227.67/39.27    (5)  all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 227.67/39.27    (6)  op(e3, e2) = all_53_4
% 227.67/39.27    (7)  all_55_13 = all_53_7
% 227.67/39.27    (8)  op(e3, e2) = e0
% 227.67/39.27  
% 227.67/39.27  Begin of proof
% 227.67/39.27  | 
% 227.67/39.27  | BETA: splitting (5) gives:
% 227.67/39.27  | 
% 227.67/39.27  | Case 1:
% 227.67/39.27  | | 
% 227.67/39.27  | |   (9)  all_55_13 = e2
% 227.67/39.27  | | 
% 227.67/39.27  | | REF_CLOSE: (3), (7), (9) are inconsistent by sub-proof #2287.
% 227.67/39.27  | | 
% 227.67/39.27  | Case 2:
% 227.67/39.27  | | 
% 227.67/39.27  | |   (10)  all_55_13 = e1 | all_55_13 = e0
% 227.67/39.27  | | 
% 227.67/39.27  | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (10) are inconsistent by sub-proof
% 227.67/39.27  | |            #328.
% 227.67/39.27  | | 
% 227.67/39.27  | End of split
% 227.67/39.27  | 
% 227.67/39.27  End of proof
% 227.67/39.27  
% 227.67/39.27  Sub-proof #328 shows that the following formulas are inconsistent:
% 227.67/39.27  ----------------------------------------------------------------
% 227.67/39.27    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.67/39.27           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.67/39.27    (2)   ~ (all_53_7 = e1)
% 227.67/39.27    (3)  all_55_13 = e1 | all_55_13 = e0
% 227.67/39.27    (4)   ~ (all_53_4 = all_53_7)
% 227.67/39.27    (5)  op(e3, e2) = all_53_4
% 227.67/39.27    (6)  all_55_13 = all_53_7
% 227.67/39.27    (7)  op(e3, e2) = e0
% 227.67/39.27  
% 227.67/39.27  Begin of proof
% 227.67/39.27  | 
% 227.67/39.27  | BETA: splitting (3) gives:
% 227.67/39.27  | 
% 227.67/39.27  | Case 1:
% 227.67/39.27  | | 
% 227.67/39.27  | |   (8)  all_55_13 = e1
% 227.67/39.27  | | 
% 227.67/39.27  | | REF_CLOSE: (2), (6), (8) are inconsistent by sub-proof #2002.
% 227.67/39.27  | | 
% 227.67/39.27  | Case 2:
% 227.67/39.27  | | 
% 227.67/39.27  | |   (9)  all_55_13 = e0
% 227.67/39.27  | | 
% 227.67/39.27  | | COMBINE_EQS: (6), (9) imply:
% 227.67/39.27  | |   (10)  all_53_7 = e0
% 227.67/39.27  | | 
% 227.67/39.27  | | SIMP: (10) implies:
% 227.67/39.27  | |   (11)  all_53_7 = e0
% 227.67/39.27  | | 
% 227.67/39.27  | | REDUCE: (4), (11) imply:
% 227.67/39.27  | |   (12)   ~ (all_53_4 = e0)
% 227.67/39.27  | | 
% 227.67/39.27  | | REF_CLOSE: (1), (5), (7), (12) are inconsistent by sub-proof #1941.
% 227.67/39.27  | | 
% 227.67/39.27  | End of split
% 227.67/39.27  | 
% 227.67/39.27  End of proof
% 227.67/39.27  
% 227.67/39.27  Sub-proof #329 shows that the following formulas are inconsistent:
% 227.67/39.27  ----------------------------------------------------------------
% 227.67/39.27    (1)  op(e3, e3) = e1
% 227.67/39.27    (2)  op(e2, e1) = e1
% 227.67/39.27    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.67/39.27           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.67/39.27    (4)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 227.67/39.27           op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 227.67/39.27           op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 227.67/39.27           = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3, e0)
% 227.67/39.27           = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) & $i(all_52_7))
% 227.67/39.27         | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0 &
% 227.67/39.27           op(all_52_9, all_52_9) = e3 & op(all_52_11, all_52_11) = e2 &
% 227.67/39.27           op(all_52_13, all_52_13) = e1 & op(all_52_15, all_52_15) = e0 & op(e2,
% 227.67/39.27             e3) = all_52_9 & op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13 &
% 227.67/39.27           op(e2, e0) = all_52_15 & $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 227.67/39.27           $i(all_52_15))
% 227.67/39.27    (5)   ~ (all_6_2 = e3)
% 227.67/39.27    (6)  op(e1, e1) = all_6_2
% 227.67/39.27    (7)   ~ (e1 = e0)
% 227.67/39.27    (8)  op(e1, e1) = e0
% 227.67/39.27  
% 227.67/39.27  Begin of proof
% 227.67/39.27  | 
% 227.67/39.27  | BETA: splitting (4) gives:
% 227.67/39.27  | 
% 227.67/39.27  | Case 1:
% 227.67/39.27  | | 
% 227.67/39.27  | |   (9)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 227.67/39.27  | |        op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 227.67/39.27  | |        op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3,
% 227.67/39.27  | |          e3) = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 &
% 227.67/39.27  | |        op(e3, e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 227.67/39.27  | |        $i(all_52_7)
% 227.67/39.27  | | 
% 227.67/39.27  | | REF_CLOSE: (1), (3), (5), (6), (9) are inconsistent by sub-proof #360.
% 227.67/39.27  | | 
% 227.67/39.27  | Case 2:
% 227.67/39.27  | | 
% 227.67/39.27  | |   (10)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0 &
% 227.67/39.27  | |         op(all_52_9, all_52_9) = e3 & op(all_52_11, all_52_11) = e2 &
% 227.67/39.27  | |         op(all_52_13, all_52_13) = e1 & op(all_52_15, all_52_15) = e0 &
% 227.67/39.27  | |         op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 & op(e2, e1) =
% 227.67/39.27  | |         all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) & $i(all_52_11) &
% 227.67/39.27  | |         $i(all_52_13) & $i(all_52_15)
% 227.67/39.27  | | 
% 227.67/39.27  | | ALPHA: (10) implies:
% 227.67/39.27  | |   (11)  op(e2, e1) = all_52_13
% 227.67/39.27  | |   (12)  op(all_52_13, all_52_13) = e1
% 227.67/39.27  | | 
% 227.67/39.27  | | GROUND_INST: instantiating (3) with e1, all_52_13, e1, e2, simplifying with
% 227.67/39.27  | |              (2), (11) gives:
% 227.67/39.27  | |   (13)  all_52_13 = e1
% 227.67/39.27  | | 
% 227.67/39.27  | | REDUCE: (12), (13) imply:
% 227.67/39.27  | |   (14)  op(e1, e1) = e1
% 227.67/39.27  | | 
% 227.67/39.27  | | REF_CLOSE: (3), (7), (8), (14) are inconsistent by sub-proof #2427.
% 227.67/39.27  | | 
% 227.67/39.27  | End of split
% 227.67/39.27  | 
% 227.67/39.27  End of proof
% 227.67/39.27  
% 227.67/39.27  Sub-proof #330 shows that the following formulas are inconsistent:
% 227.67/39.27  ----------------------------------------------------------------
% 227.67/39.27    (1)  all_57_13 = e1 & op(e0, e2) = e1
% 227.67/39.27    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.67/39.27           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.67/39.27    (3)  op(e0, e2) = all_53_7
% 227.67/39.27    (4)   ~ (all_53_7 = e1)
% 227.67/39.27  
% 227.67/39.27  Begin of proof
% 227.67/39.27  | 
% 227.67/39.27  | ALPHA: (1) implies:
% 227.67/39.27  |   (5)  op(e0, e2) = e1
% 227.67/39.27  | 
% 227.67/39.27  | GROUND_INST: instantiating (2) with all_53_7, e1, e2, e0, simplifying with
% 227.67/39.27  |              (3), (5) gives:
% 227.67/39.27  |   (6)  all_53_7 = e1
% 227.67/39.27  | 
% 227.67/39.27  | REDUCE: (4), (6) imply:
% 227.67/39.27  |   (7)  $false
% 227.67/39.27  | 
% 227.67/39.27  | CLOSE: (7) is inconsistent.
% 227.67/39.27  | 
% 227.67/39.27  End of proof
% 227.67/39.27  
% 227.67/39.27  Sub-proof #331 shows that the following formulas are inconsistent:
% 227.67/39.27  ----------------------------------------------------------------
% 227.67/39.27    (1)  op(e3, e3) = e1
% 227.67/39.27    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.67/39.27           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.67/39.27    (3)  op(e3, e2) = all_53_4
% 227.67/39.27    (4)   ~ (all_53_4 = e2)
% 227.67/39.27    (5)   ~ (e2 = e1)
% 227.67/39.27    (6)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2)
% 227.67/39.27  
% 227.67/39.27  Begin of proof
% 227.67/39.27  | 
% 227.67/39.27  | BETA: splitting (6) gives:
% 227.67/39.27  | 
% 227.67/39.27  | Case 1:
% 227.67/39.27  | | 
% 227.67/39.27  | |   (7)  all_57_0 = e2 & op(e3, e3) = e2
% 227.67/39.27  | | 
% 227.67/39.27  | | ALPHA: (7) implies:
% 227.67/39.27  | |   (8)  op(e3, e3) = e2
% 227.67/39.27  | | 
% 227.67/39.27  | | REF_CLOSE: (1), (2), (5), (8) are inconsistent by sub-proof #1950.
% 227.67/39.27  | | 
% 227.67/39.27  | Case 2:
% 227.67/39.27  | | 
% 227.67/39.27  | |   (9)  all_57_1 = e2 & op(e3, e2) = e2
% 227.67/39.27  | | 
% 227.67/39.27  | | REF_CLOSE: (2), (3), (4), (9) are inconsistent by sub-proof #2456.
% 227.67/39.27  | | 
% 227.67/39.27  | End of split
% 227.67/39.27  | 
% 227.67/39.27  End of proof
% 227.67/39.27  
% 227.67/39.27  Sub-proof #332 shows that the following formulas are inconsistent:
% 227.67/39.27  ----------------------------------------------------------------
% 227.67/39.27    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.67/39.27           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.67/39.27    (2)  op(e1, e1) = all_52_21
% 227.67/39.27    (3)   ~ (e2 = e0)
% 227.67/39.27    (4)  op(e1, e2) = e1
% 227.67/39.27    (5)  op(e1, e1) = e0
% 227.67/39.27    (6)  op(e1, e2) = all_52_19
% 227.67/39.27    (7)  op(all_52_19, all_52_19) = e2
% 227.67/39.27    (8)  op(e1, e2) = all_53_6
% 227.67/39.27  
% 227.67/39.27  Begin of proof
% 227.67/39.27  | 
% 227.67/39.27  | GROUND_INST: instantiating (1) with e0, all_52_21, e1, e1, simplifying with
% 227.67/39.27  |              (2), (5) gives:
% 227.67/39.27  |   (9)  all_52_21 = e0
% 227.67/39.27  | 
% 227.67/39.27  | GROUND_INST: instantiating (1) with all_53_6, e1, e2, e1, simplifying with
% 227.67/39.27  |              (4), (8) gives:
% 227.67/39.27  |   (10)  all_53_6 = e1
% 227.67/39.27  | 
% 227.67/39.27  | GROUND_INST: instantiating (1) with all_53_6, all_52_19, e2, e1, simplifying
% 227.67/39.27  |              with (6), (8) gives:
% 227.67/39.27  |   (11)  all_53_6 = all_52_19
% 227.67/39.27  | 
% 227.67/39.27  | COMBINE_EQS: (10), (11) imply:
% 227.67/39.27  |   (12)  all_52_19 = e1
% 227.67/39.27  | 
% 227.67/39.27  | REDUCE: (7), (12) imply:
% 227.67/39.27  |   (13)  op(e1, e1) = e2
% 227.67/39.27  | 
% 227.67/39.27  | GROUND_INST: instantiating (1) with e0, e2, e1, e1, simplifying with (5), (13)
% 227.67/39.27  |              gives:
% 227.67/39.27  |   (14)  e2 = e0
% 227.67/39.27  | 
% 227.67/39.27  | REDUCE: (3), (14) imply:
% 227.67/39.27  |   (15)  $false
% 227.67/39.27  | 
% 227.67/39.27  | CLOSE: (15) is inconsistent.
% 227.67/39.27  | 
% 227.67/39.27  End of proof
% 227.67/39.27  
% 227.67/39.27  Sub-proof #333 shows that the following formulas are inconsistent:
% 227.67/39.27  ----------------------------------------------------------------
% 227.67/39.27    (1)  op(e3, e3) = e1
% 227.67/39.27    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 227.67/39.27         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 227.67/39.27    (3)   ~ (e3 = e1)
% 227.67/39.27    (4)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 227.67/39.27         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 227.67/39.27    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.67/39.27           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.67/39.27    (6)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 227.67/39.27         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 227.67/39.27    (7)   ~ (all_6_2 = e3)
% 227.67/39.27    (8)  op(e1, e1) = all_6_2
% 227.67/39.27    (9)   ~ (e3 = e2)
% 227.67/39.27    (10)   ~ (e3 = e0)
% 227.67/39.27    (11)  op(e0, e3) = all_53_3
% 227.67/39.27    (12)  all_57_15 = e3
% 227.67/39.27    (13)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 227.67/39.27          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 227.67/39.27            e1)
% 227.67/39.27    (14)   ~ (e2 = e0)
% 227.67/39.27    (15)  op(e2, e2) = e2
% 227.67/39.27    (16)   ~ (e1 = e0)
% 227.67/39.27    (17)  all_57_14 = e2
% 227.67/39.27    (18)  op(e0, e0) = e3
% 227.67/39.27    (19)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 227.67/39.27              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 227.67/39.27                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 227.67/39.27                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 227.67/39.27    (20)   ~ (all_53_3 = e1)
% 227.67/39.27    (21)  op(e1, e1) = e2
% 227.67/39.27    (22)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 227.67/39.27          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 227.67/39.27    (23)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 227.67/39.27          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 227.67/39.27    (24)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 227.67/39.27          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 227.67/39.27    (25)   ~ (e2 = e1)
% 227.67/39.27    (26)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 227.67/39.27          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 227.67/39.27    (27)   ~ (all_6_2 = e0)
% 227.67/39.27    (28)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 227.67/39.27          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 227.67/39.27    (29)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 227.67/39.27          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 227.67/39.27    (30)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 227.67/39.27          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 227.67/39.27    (31)  all_57_3 = e2
% 227.67/39.27  
% 227.67/39.27  Begin of proof
% 227.67/39.27  | 
% 227.67/39.27  | BETA: splitting (13) gives:
% 227.67/39.27  | 
% 227.67/39.27  | Case 1:
% 227.67/39.27  | | 
% 227.67/39.27  | |   (32)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 227.67/39.27  | |           e1)
% 227.67/39.27  | | 
% 227.67/39.27  | | BETA: splitting (32) gives:
% 227.67/39.27  | | 
% 227.67/39.27  | | Case 1:
% 227.67/39.27  | | | 
% 227.67/39.27  | | |   (33)  all_57_12 = e1 & op(e0, e3) = e1
% 227.67/39.27  | | | 
% 227.67/39.27  | | | REF_CLOSE: (5), (11), (20), (33) are inconsistent by sub-proof #1947.
% 227.67/39.27  | | | 
% 227.67/39.27  | | Case 2:
% 227.67/39.27  | | | 
% 227.67/39.27  | | |   (34)  all_57_13 = e1 & op(e0, e2) = e1
% 227.67/39.27  | | | 
% 227.67/39.27  | | | ALPHA: (34) implies:
% 227.67/39.27  | | |   (35)  all_57_13 = e1
% 227.67/39.27  | | | 
% 227.67/39.27  | | | BETA: splitting (19) gives:
% 227.67/39.27  | | | 
% 227.67/39.27  | | | Case 1:
% 227.67/39.27  | | | | 
% 227.67/39.27  | | | |   (36)  all_57_15 = e0 & op(e0, e0) = e0
% 227.67/39.27  | | | | 
% 227.67/39.27  | | | | ALPHA: (36) implies:
% 227.67/39.27  | | | |   (37)  op(e0, e0) = e0
% 227.67/39.27  | | | | 
% 227.67/39.27  | | | | REF_CLOSE: (5), (10), (18), (37) are inconsistent by sub-proof #2304.
% 227.67/39.27  | | | | 
% 227.67/39.27  | | | Case 2:
% 227.67/39.27  | | | | 
% 227.67/39.27  | | | |   (38)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2,
% 227.67/39.27  | | | |               e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) &
% 227.67/39.27  | | | |         ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0,
% 227.67/39.27  | | | |               e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 227.67/39.27  | | | | 
% 227.67/39.27  | | | | ALPHA: (38) implies:
% 227.67/39.27  | | | |   (39)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0,
% 227.67/39.27  | | | |             e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 227.67/39.27  | | | |   (40)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0)
% 227.67/39.27  | | | |           = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 227.67/39.27  | | | | 
% 227.67/39.27  | | | | BETA: splitting (28) gives:
% 227.67/39.27  | | | | 
% 227.67/39.27  | | | | Case 1:
% 227.67/39.27  | | | | | 
% 227.67/39.27  | | | | |   (41)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2,
% 227.67/39.27  | | | | |             e3) = e2)
% 227.67/39.27  | | | | | 
% 227.67/39.27  | | | | | REF_CLOSE: (1), (2), (3), (5), (9), (10), (12), (14), (15), (16),
% 227.67/39.27  | | | | |            (18), (19), (22), (23), (24), (25), (26), (29), (31), (41)
% 227.67/39.27  | | | | |            are inconsistent by sub-proof #337.
% 227.67/39.27  | | | | | 
% 227.67/39.27  | | | | Case 2:
% 227.67/39.27  | | | | | 
% 227.67/39.27  | | | | |   (42)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0,
% 227.67/39.27  | | | | |             e3) = e2)
% 227.67/39.27  | | | | | 
% 227.67/39.27  | | | | | BETA: splitting (42) gives:
% 227.67/39.27  | | | | | 
% 227.67/39.27  | | | | | Case 1:
% 227.67/39.27  | | | | | | 
% 227.67/39.27  | | | | | |   (43)  all_57_6 = e2 & op(e1, e3) = e2
% 227.67/39.27  | | | | | | 
% 227.67/39.27  | | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (10), (12), (14),
% 227.67/39.27  | | | | | |            (16), (19), (21), (25), (26), (27), (29), (30), (40),
% 227.67/39.27  | | | | | |            (43) are inconsistent by sub-proof #335.
% 227.67/39.27  | | | | | | 
% 227.67/39.27  | | | | | Case 2:
% 227.67/39.27  | | | | | | 
% 227.67/39.27  | | | | | |   (44)  all_57_12 = e2 & op(e0, e3) = e2
% 227.67/39.27  | | | | | | 
% 227.67/39.27  | | | | | | ALPHA: (44) implies:
% 227.67/39.27  | | | | | |   (45)  all_57_12 = e2
% 227.67/39.27  | | | | | | 
% 227.67/39.27  | | | | | | REF_CLOSE: (14), (16), (17), (35), (39), (45) are inconsistent by
% 227.67/39.27  | | | | | |            sub-proof #334.
% 227.67/39.27  | | | | | | 
% 227.67/39.27  | | | | | End of split
% 227.67/39.28  | | | | | 
% 227.67/39.28  | | | | End of split
% 227.67/39.28  | | | | 
% 227.67/39.28  | | | End of split
% 227.67/39.28  | | | 
% 227.67/39.28  | | End of split
% 227.67/39.28  | | 
% 227.67/39.28  | Case 2:
% 227.67/39.28  | | 
% 227.67/39.28  | |   (46)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 227.67/39.28  | |           e1)
% 227.67/39.28  | | 
% 227.67/39.28  | | REF_CLOSE: (3), (5), (17), (18), (25), (46) are inconsistent by sub-proof
% 227.67/39.28  | |            #1139.
% 227.67/39.28  | | 
% 227.67/39.28  | End of split
% 227.67/39.28  | 
% 227.67/39.28  End of proof
% 227.67/39.28  
% 227.67/39.28  Sub-proof #334 shows that the following formulas are inconsistent:
% 227.67/39.28  ----------------------------------------------------------------
% 227.67/39.28    (1)  all_57_13 = e1
% 227.67/39.28    (2)  all_57_12 = e2
% 227.67/39.28    (3)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 227.67/39.28         (all_57_14 = e0 & op(e0, e1) = e0)
% 227.67/39.28    (4)   ~ (e2 = e0)
% 227.67/39.28    (5)   ~ (e1 = e0)
% 227.67/39.28    (6)  all_57_14 = e2
% 227.67/39.28  
% 227.67/39.28  Begin of proof
% 227.67/39.28  | 
% 227.67/39.28  | BETA: splitting (3) gives:
% 227.67/39.28  | 
% 227.67/39.28  | Case 1:
% 227.67/39.28  | | 
% 227.67/39.28  | |   (7)  all_57_12 = e0 & op(e0, e3) = e0
% 227.67/39.28  | | 
% 227.67/39.28  | | REF_CLOSE: (2), (4), (7) are inconsistent by sub-proof #2185.
% 227.67/39.28  | | 
% 227.67/39.28  | Case 2:
% 227.67/39.28  | | 
% 227.67/39.28  | |   (8)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 227.67/39.28  | |          e0)
% 227.67/39.28  | | 
% 227.67/39.28  | | BETA: splitting (8) gives:
% 227.67/39.28  | | 
% 227.67/39.28  | | Case 1:
% 227.67/39.28  | | | 
% 227.67/39.28  | | |   (9)  all_57_13 = e0 & op(e0, e2) = e0
% 227.67/39.28  | | | 
% 227.67/39.28  | | | REF_CLOSE: (1), (5), (9) are inconsistent by sub-proof #1920.
% 227.67/39.28  | | | 
% 227.67/39.28  | | Case 2:
% 227.67/39.28  | | | 
% 227.67/39.28  | | |   (10)  all_57_14 = e0 & op(e0, e1) = e0
% 227.67/39.28  | | | 
% 227.67/39.28  | | | REF_CLOSE: (4), (6), (10) are inconsistent by sub-proof #2173.
% 227.67/39.28  | | | 
% 227.67/39.28  | | End of split
% 227.67/39.28  | | 
% 227.67/39.28  | End of split
% 227.67/39.28  | 
% 227.67/39.28  End of proof
% 227.67/39.28  
% 227.67/39.28  Sub-proof #335 shows that the following formulas are inconsistent:
% 227.67/39.28  ----------------------------------------------------------------
% 227.67/39.28    (1)   ~ (e3 = e1)
% 227.67/39.28    (2)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 227.67/39.28         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 227.67/39.28    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.67/39.28           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.67/39.28    (4)  all_57_6 = e2 & op(e1, e3) = e2
% 227.67/39.28    (5)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 227.67/39.28         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 227.67/39.28    (6)   ~ (all_6_2 = e3)
% 227.67/39.28    (7)  op(e1, e1) = all_6_2
% 227.67/39.28    (8)   ~ (e3 = e2)
% 227.67/39.28    (9)   ~ (e3 = e0)
% 227.67/39.28    (10)  all_57_15 = e3
% 227.67/39.28    (11)   ~ (e2 = e0)
% 227.67/39.28    (12)   ~ (e1 = e0)
% 227.67/39.28    (13)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 227.67/39.28              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 227.67/39.28                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 227.67/39.28                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 227.67/39.28    (14)  op(e1, e1) = e2
% 227.67/39.28    (15)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) |
% 227.67/39.28          (all_57_11 = e0 & op(e1, e0) = e0)
% 227.67/39.28    (16)   ~ (e2 = e1)
% 227.67/39.28    (17)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 227.67/39.28          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 227.67/39.28    (18)   ~ (all_6_2 = e0)
% 227.67/39.28    (19)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 227.67/39.28          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 227.67/39.28    (20)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 227.67/39.28          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 227.67/39.28  
% 227.67/39.28  Begin of proof
% 227.67/39.28  | 
% 227.67/39.28  | ALPHA: (4) implies:
% 227.67/39.28  |   (21)  all_57_6 = e2
% 227.67/39.28  | 
% 227.67/39.28  | BETA: splitting (5) gives:
% 227.67/39.28  | 
% 227.67/39.28  | Case 1:
% 227.67/39.28  | | 
% 227.67/39.28  | |   (22)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 227.67/39.28  | |           e3)
% 227.67/39.28  | | 
% 227.67/39.28  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 227.67/39.28  | |            (14), (16), (17), (18), (19), (20), (21), (22) are inconsistent
% 227.67/39.28  | |            by sub-proof #336.
% 227.67/39.28  | | 
% 227.67/39.28  | Case 2:
% 227.67/39.28  | | 
% 227.67/39.28  | |   (23)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 227.67/39.28  | |           e3)
% 227.67/39.28  | | 
% 227.67/39.28  | | REF_CLOSE: (1), (3), (6), (7), (8), (9), (10), (11), (12), (15), (16), (17),
% 227.67/39.28  | |            (19), (23) are inconsistent by sub-proof #1080.
% 227.67/39.28  | | 
% 227.67/39.28  | End of split
% 227.67/39.28  | 
% 227.67/39.28  End of proof
% 227.67/39.28  
% 227.67/39.28  Sub-proof #336 shows that the following formulas are inconsistent:
% 227.67/39.28  ----------------------------------------------------------------
% 227.67/39.28    (1)   ~ (e3 = e1)
% 227.67/39.28    (2)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 227.67/39.28         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 227.67/39.28    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.67/39.28           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.67/39.28    (4)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 227.67/39.28         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 227.67/39.28    (5)   ~ (all_6_2 = e3)
% 227.67/39.28    (6)  op(e1, e1) = all_6_2
% 227.67/39.28    (7)   ~ (e3 = e2)
% 227.67/39.28    (8)   ~ (e3 = e0)
% 227.67/39.28    (9)  all_57_15 = e3
% 227.67/39.28    (10)  all_57_6 = e2
% 227.67/39.28    (11)   ~ (e2 = e0)
% 227.67/39.28    (12)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3)
% 227.67/39.28    (13)   ~ (e1 = e0)
% 227.67/39.28    (14)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 227.67/39.28              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 227.67/39.28                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 227.67/39.28                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 227.67/39.28    (15)  op(e1, e1) = e2
% 227.67/39.28    (16)   ~ (e2 = e1)
% 227.67/39.28    (17)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 227.67/39.28          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 227.67/39.28    (18)   ~ (all_6_2 = e0)
% 227.67/39.28    (19)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 227.67/39.28          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 227.67/39.28    (20)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 227.67/39.28          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 227.67/39.28  
% 227.67/39.28  Begin of proof
% 227.67/39.28  | 
% 227.67/39.28  | BETA: splitting (12) gives:
% 227.67/39.28  | 
% 227.67/39.28  | Case 1:
% 227.67/39.28  | | 
% 227.67/39.28  | |   (21)  all_57_6 = e3 & op(e1, e3) = e3
% 227.67/39.28  | | 
% 227.67/39.28  | | ALPHA: (21) implies:
% 227.67/39.28  | |   (22)  all_57_6 = e3
% 227.67/39.28  | | 
% 227.67/39.28  | | REF_CLOSE: (7), (10), (22) are inconsistent by sub-proof #2463.
% 227.67/39.28  | | 
% 227.67/39.28  | Case 2:
% 227.67/39.28  | | 
% 227.67/39.28  | |   (23)  all_57_7 = e3 & op(e1, e2) = e3
% 227.67/39.28  | | 
% 227.67/39.28  | | ALPHA: (23) implies:
% 227.67/39.28  | |   (24)  all_57_7 = e3
% 227.67/39.28  | | 
% 227.67/39.28  | | BETA: splitting (2) gives:
% 227.67/39.28  | | 
% 227.67/39.28  | | Case 1:
% 227.67/39.28  | | | 
% 227.67/39.28  | | |   (25)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) =
% 227.67/39.28  | | |           e0)
% 227.67/39.28  | | | 
% 227.67/39.28  | | | BETA: splitting (25) gives:
% 227.67/39.28  | | | 
% 227.67/39.28  | | | Case 1:
% 227.67/39.28  | | | | 
% 227.67/39.28  | | | |   (26)  all_57_6 = e0 & op(e1, e3) = e0
% 227.67/39.28  | | | | 
% 227.67/39.28  | | | | REF_CLOSE: (10), (11), (26) are inconsistent by sub-proof #2386.
% 227.67/39.28  | | | | 
% 227.67/39.28  | | | Case 2:
% 227.67/39.28  | | | | 
% 227.67/39.28  | | | |   (27)  all_57_7 = e0 & op(e1, e2) = e0
% 227.67/39.28  | | | | 
% 227.67/39.28  | | | | REF_CLOSE: (8), (24), (27) are inconsistent by sub-proof #2042.
% 227.67/39.28  | | | | 
% 227.67/39.28  | | | End of split
% 227.67/39.28  | | | 
% 227.67/39.28  | | Case 2:
% 227.67/39.28  | | | 
% 227.67/39.28  | | |   (28)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 227.67/39.28  | | |           e0)
% 227.67/39.28  | | | 
% 227.67/39.28  | | | BETA: splitting (28) gives:
% 227.67/39.28  | | | 
% 227.67/39.28  | | | Case 1:
% 227.67/39.28  | | | | 
% 227.67/39.28  | | | |   (29)  all_57_8 = e0 & op(e1, e1) = e0
% 227.67/39.28  | | | | 
% 227.67/39.28  | | | | REF_CLOSE: (3), (6), (18), (29) are inconsistent by sub-proof #2412.
% 227.67/39.28  | | | | 
% 227.67/39.28  | | | Case 2:
% 227.67/39.28  | | | | 
% 227.67/39.28  | | | |   (30)  all_57_11 = e0 & op(e1, e0) = e0
% 227.67/39.28  | | | | 
% 227.67/39.28  | | | | ALPHA: (30) implies:
% 227.67/39.28  | | | |   (31)  all_57_11 = e0
% 227.67/39.28  | | | | 
% 227.67/39.28  | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 227.67/39.28  | | | |            (14), (15), (16), (17), (19), (20), (31) are inconsistent by
% 227.67/39.28  | | | |            sub-proof #1122.
% 227.67/39.28  | | | | 
% 227.67/39.28  | | | End of split
% 227.67/39.28  | | | 
% 227.67/39.28  | | End of split
% 227.67/39.28  | | 
% 227.67/39.28  | End of split
% 227.67/39.28  | 
% 227.67/39.28  End of proof
% 227.67/39.28  
% 227.67/39.28  Sub-proof #337 shows that the following formulas are inconsistent:
% 227.67/39.28  ----------------------------------------------------------------
% 227.67/39.28    (1)  op(e3, e3) = e1
% 227.67/39.28    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 227.67/39.28         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 227.67/39.28    (3)   ~ (e3 = e1)
% 227.67/39.28    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.67/39.28           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.67/39.28    (5)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2)
% 227.67/39.28    (6)   ~ (e3 = e2)
% 227.67/39.28    (7)   ~ (e3 = e0)
% 227.67/39.28    (8)  all_57_15 = e3
% 227.67/39.28    (9)   ~ (e2 = e0)
% 227.67/39.28    (10)  op(e2, e2) = e2
% 227.67/39.28    (11)   ~ (e1 = e0)
% 227.67/39.28    (12)  op(e0, e0) = e3
% 227.67/39.28    (13)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 227.67/39.28              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 227.67/39.28                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 227.67/39.28                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 227.67/39.28    (14)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 227.67/39.28          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 227.67/39.28    (15)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 227.67/39.28          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 227.67/39.28    (16)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 227.67/39.28          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 227.67/39.28    (17)   ~ (e2 = e1)
% 227.67/39.28    (18)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 227.67/39.28          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 227.67/39.28    (19)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 227.67/39.28          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 227.67/39.28    (20)  all_57_3 = e2
% 227.67/39.28  
% 227.67/39.28  Begin of proof
% 227.67/39.28  | 
% 227.67/39.28  | BETA: splitting (5) gives:
% 227.67/39.28  | 
% 227.67/39.28  | Case 1:
% 227.67/39.28  | | 
% 227.67/39.28  | |   (21)  all_57_0 = e2 & op(e3, e3) = e2
% 227.67/39.28  | | 
% 227.67/39.28  | | ALPHA: (21) implies:
% 227.67/39.28  | |   (22)  op(e3, e3) = e2
% 227.67/39.28  | | 
% 227.67/39.28  | | REF_CLOSE: (1), (4), (17), (22) are inconsistent by sub-proof #1950.
% 227.67/39.28  | | 
% 227.67/39.28  | Case 2:
% 227.67/39.28  | | 
% 227.67/39.28  | |   (23)  all_57_2 = e2 & op(e2, e3) = e2
% 227.67/39.28  | | 
% 227.67/39.28  | | ALPHA: (23) implies:
% 227.67/39.28  | |   (24)  all_57_2 = e2
% 227.67/39.28  | | 
% 227.67/39.28  | | REF_CLOSE: (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13), (14),
% 227.67/39.28  | |            (15), (16), (17), (18), (19), (20), (24) are inconsistent by
% 227.67/39.28  | |            sub-proof #844.
% 227.67/39.28  | | 
% 227.67/39.28  | End of split
% 227.67/39.28  | 
% 227.67/39.28  End of proof
% 227.67/39.28  
% 227.67/39.28  Sub-proof #338 shows that the following formulas are inconsistent:
% 227.67/39.28  ----------------------------------------------------------------
% 227.67/39.28    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.67/39.28           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.67/39.28    (2)  op(all_52_7, all_52_7) = e0
% 227.67/39.28    (3)   ~ (e2 = e0)
% 227.67/39.28    (4)  op(e2, e2) = e2
% 227.67/39.28    (5)  all_53_12 = e2
% 227.67/39.28    (6)  op(e3, e0) = all_52_7
% 227.67/39.28    (7)  op(e3, e0) = all_53_12
% 227.67/39.28  
% 227.67/39.28  Begin of proof
% 227.67/39.28  | 
% 227.67/39.28  | GROUND_INST: instantiating (1) with all_53_12, all_52_7, e0, e3, simplifying
% 227.67/39.28  |              with (6), (7) gives:
% 227.67/39.28  |   (8)  all_53_12 = all_52_7
% 227.67/39.28  | 
% 227.67/39.28  | COMBINE_EQS: (5), (8) imply:
% 227.67/39.28  |   (9)  all_52_7 = e2
% 227.67/39.28  | 
% 227.67/39.28  | REDUCE: (2), (9) imply:
% 227.67/39.28  |   (10)  op(e2, e2) = e0
% 227.67/39.28  | 
% 227.67/39.28  | REF_CLOSE: (1), (3), (4), (10) are inconsistent by sub-proof #2472.
% 227.67/39.28  | 
% 227.67/39.28  End of proof
% 227.67/39.28  
% 227.67/39.28  Sub-proof #339 shows that the following formulas are inconsistent:
% 227.67/39.28  ----------------------------------------------------------------
% 227.67/39.28    (1)   ~ (e3 = e1)
% 227.67/39.28    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.67/39.28           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.67/39.28    (3)   ~ (all_6_2 = e3)
% 227.67/39.28    (4)  op(e1, e1) = all_6_2
% 227.67/39.28    (5)  all_57_4 = e2
% 227.67/39.28    (6)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 227.67/39.28         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 227.67/39.28    (7)   ~ (e3 = e2)
% 227.67/39.28    (8)   ~ (e3 = e0)
% 227.67/39.28    (9)   ~ (e2 = e0)
% 227.67/39.28    (10)   ~ (e1 = e0)
% 227.67/39.28    (11)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 227.67/39.28          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 227.67/39.28    (12)  all_57_5 = e1
% 227.67/39.28    (13)   ~ (all_6_2 = e0)
% 227.67/39.28  
% 227.67/39.28  Begin of proof
% 227.67/39.28  | 
% 227.67/39.28  | BETA: splitting (11) gives:
% 227.67/39.28  | 
% 227.67/39.28  | Case 1:
% 227.67/39.28  | | 
% 227.67/39.28  | |   (14)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) =
% 227.67/39.28  | |           e3)
% 227.67/39.28  | | 
% 227.67/39.28  | | BETA: splitting (14) gives:
% 227.67/39.28  | | 
% 227.67/39.28  | | Case 1:
% 227.67/39.28  | | | 
% 227.67/39.28  | | |   (15)  all_57_4 = e3 & op(e3, e1) = e3
% 227.67/39.28  | | | 
% 227.67/39.28  | | | REF_CLOSE: (5), (7), (15) are inconsistent by sub-proof #877.
% 227.67/39.28  | | | 
% 227.67/39.28  | | Case 2:
% 227.67/39.28  | | | 
% 227.67/39.28  | | |   (16)  all_57_5 = e3 & op(e2, e1) = e3
% 227.67/39.28  | | | 
% 227.67/39.28  | | | ALPHA: (16) implies:
% 227.67/39.28  | | |   (17)  all_57_5 = e3
% 227.67/39.28  | | | 
% 227.67/39.28  | | | REF_CLOSE: (1), (12), (17) are inconsistent by sub-proof #2382.
% 227.67/39.28  | | | 
% 227.67/39.28  | | End of split
% 227.67/39.28  | | 
% 227.67/39.28  | Case 2:
% 227.67/39.28  | | 
% 227.67/39.28  | |   (18)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) =
% 227.67/39.28  | |           e3)
% 227.67/39.28  | | 
% 227.67/39.28  | | BETA: splitting (18) gives:
% 227.67/39.28  | | 
% 227.67/39.28  | | Case 1:
% 227.67/39.28  | | | 
% 227.67/39.28  | | |   (19)  all_57_8 = e3 & op(e1, e1) = e3
% 227.67/39.28  | | | 
% 227.67/39.28  | | | ALPHA: (19) implies:
% 227.67/39.28  | | |   (20)  op(e1, e1) = e3
% 227.67/39.28  | | | 
% 227.67/39.28  | | | REF_CLOSE: (2), (3), (4), (20) are inconsistent by sub-proof #2468.
% 227.67/39.28  | | | 
% 227.67/39.28  | | Case 2:
% 227.67/39.28  | | | 
% 227.67/39.28  | | |   (21)  all_57_14 = e3 & op(e0, e1) = e3
% 227.67/39.28  | | | 
% 227.67/39.28  | | | ALPHA: (21) implies:
% 227.67/39.28  | | |   (22)  all_57_14 = e3
% 227.67/39.28  | | | 
% 227.67/39.28  | | | REF_CLOSE: (2), (4), (5), (6), (8), (9), (10), (12), (13), (22) are
% 227.67/39.28  | | |            inconsistent by sub-proof #340.
% 227.67/39.28  | | | 
% 227.67/39.28  | | End of split
% 227.67/39.28  | | 
% 227.67/39.28  | End of split
% 227.67/39.28  | 
% 227.67/39.28  End of proof
% 227.67/39.28  
% 227.67/39.28  Sub-proof #340 shows that the following formulas are inconsistent:
% 227.67/39.28  ----------------------------------------------------------------
% 227.67/39.28    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.67/39.28           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.67/39.28    (2)  op(e1, e1) = all_6_2
% 227.67/39.28    (3)  all_57_4 = e2
% 227.67/39.28    (4)  all_57_14 = e3
% 227.67/39.28    (5)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 227.67/39.28         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 227.67/39.28    (6)   ~ (e3 = e0)
% 227.67/39.28    (7)   ~ (e2 = e0)
% 227.67/39.28    (8)   ~ (e1 = e0)
% 227.67/39.28    (9)  all_57_5 = e1
% 227.67/39.28    (10)   ~ (all_6_2 = e0)
% 227.67/39.28  
% 227.67/39.28  Begin of proof
% 227.67/39.28  | 
% 227.67/39.28  | BETA: splitting (5) gives:
% 227.67/39.28  | 
% 227.67/39.28  | Case 1:
% 227.67/39.28  | | 
% 227.67/39.28  | |   (11)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) =
% 227.67/39.28  | |           e0)
% 227.67/39.28  | | 
% 227.67/39.28  | | BETA: splitting (11) gives:
% 227.67/39.28  | | 
% 227.67/39.28  | | Case 1:
% 227.67/39.28  | | | 
% 227.67/39.28  | | |   (12)  all_57_4 = e0 & op(e3, e1) = e0
% 227.67/39.28  | | | 
% 227.67/39.28  | | | REF_CLOSE: (3), (7), (12) are inconsistent by sub-proof #2045.
% 227.67/39.28  | | | 
% 227.67/39.28  | | Case 2:
% 227.67/39.28  | | | 
% 227.67/39.28  | | |   (13)  all_57_5 = e0 & op(e2, e1) = e0
% 227.67/39.28  | | | 
% 227.67/39.28  | | | ALPHA: (13) implies:
% 227.67/39.28  | | |   (14)  all_57_5 = e0
% 227.67/39.28  | | | 
% 227.67/39.28  | | | REF_CLOSE: (8), (9), (14) are inconsistent by sub-proof #2350.
% 227.67/39.28  | | | 
% 227.67/39.28  | | End of split
% 227.67/39.28  | | 
% 227.67/39.28  | Case 2:
% 227.67/39.28  | | 
% 227.67/39.28  | |   (15)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 227.67/39.28  | |           e0)
% 227.67/39.28  | | 
% 227.67/39.28  | | REF_CLOSE: (1), (2), (4), (6), (10), (15) are inconsistent by sub-proof
% 227.67/39.28  | |            #1717.
% 227.67/39.28  | | 
% 227.67/39.28  | End of split
% 227.67/39.28  | 
% 227.67/39.28  End of proof
% 227.67/39.28  
% 227.67/39.28  Sub-proof #341 shows that the following formulas are inconsistent:
% 227.67/39.28  ----------------------------------------------------------------
% 227.67/39.28    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.67/39.28           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.67/39.28    (2)   ~ (e3 = e2)
% 227.67/39.28    (3)  op(e3, e3) = all_52_1
% 227.67/39.28    (4)  op(e3, e2) = all_53_4
% 227.67/39.28    (5)  op(all_52_1, all_52_1) = e3
% 227.67/39.28    (6)  op(e2, e2) = e2
% 227.67/39.28    (7)   ~ (all_53_4 = e2)
% 227.67/39.28    (8)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2)
% 227.67/39.28  
% 227.67/39.28  Begin of proof
% 227.67/39.28  | 
% 227.67/39.28  | BETA: splitting (8) gives:
% 227.67/39.28  | 
% 227.67/39.28  | Case 1:
% 227.67/39.28  | | 
% 227.67/39.28  | |   (9)  all_57_0 = e2 & op(e3, e3) = e2
% 227.67/39.28  | | 
% 227.67/39.28  | | ALPHA: (9) implies:
% 227.67/39.28  | |   (10)  op(e3, e3) = e2
% 227.67/39.28  | | 
% 227.67/39.28  | | REF_CLOSE: (1), (2), (3), (5), (6), (10) are inconsistent by sub-proof
% 227.67/39.28  | |            #1951.
% 227.67/39.28  | | 
% 227.67/39.28  | Case 2:
% 227.67/39.28  | | 
% 227.67/39.28  | |   (11)  all_57_1 = e2 & op(e3, e2) = e2
% 227.67/39.28  | | 
% 227.67/39.28  | | REF_CLOSE: (1), (4), (7), (11) are inconsistent by sub-proof #2456.
% 227.67/39.28  | | 
% 227.67/39.28  | End of split
% 227.67/39.28  | 
% 227.67/39.28  End of proof
% 227.67/39.28  
% 227.67/39.28  Sub-proof #342 shows that the following formulas are inconsistent:
% 227.67/39.28  ----------------------------------------------------------------
% 227.67/39.28    (1)   ~ (e3 = e1)
% 227.67/39.28    (2)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 227.67/39.28         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 227.67/39.28    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.67/39.28           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.67/39.28    (4)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 227.67/39.28         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 227.67/39.28    (5)   ~ (all_6_2 = e3)
% 227.67/39.28    (6)  op(e1, e1) = all_6_2
% 227.67/39.28    (7)  all_57_7 = e1
% 227.67/39.28    (8)   ~ (e3 = e2)
% 227.67/39.28    (9)   ~ (e3 = e0)
% 227.67/39.28    (10)  all_57_6 = e2
% 227.67/39.28    (11)   ~ (e2 = e0)
% 227.67/39.28    (12)   ~ (e1 = e0)
% 227.67/39.28    (13)   ~ (all_6_2 = e0)
% 227.67/39.28  
% 227.67/39.28  Begin of proof
% 227.67/39.28  | 
% 227.67/39.28  | BETA: splitting (4) gives:
% 227.67/39.28  | 
% 227.67/39.28  | Case 1:
% 227.67/39.28  | | 
% 227.67/39.28  | |   (14)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 227.67/39.28  | |           e3)
% 227.67/39.28  | | 
% 227.67/39.28  | | REF_CLOSE: (1), (7), (8), (10), (14) are inconsistent by sub-proof #1246.
% 227.67/39.28  | | 
% 227.67/39.28  | Case 2:
% 227.67/39.28  | | 
% 227.67/39.28  | |   (15)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 227.67/39.28  | |           e3)
% 227.67/39.28  | | 
% 227.67/39.28  | | BETA: splitting (15) gives:
% 227.67/39.28  | | 
% 227.67/39.28  | | Case 1:
% 227.67/39.28  | | | 
% 227.67/39.28  | | |   (16)  all_57_8 = e3 & op(e1, e1) = e3
% 227.67/39.28  | | | 
% 227.67/39.28  | | | ALPHA: (16) implies:
% 227.67/39.28  | | |   (17)  op(e1, e1) = e3
% 227.67/39.28  | | | 
% 227.67/39.28  | | | REF_CLOSE: (3), (5), (6), (17) are inconsistent by sub-proof #2468.
% 227.67/39.28  | | | 
% 227.67/39.28  | | Case 2:
% 227.67/39.28  | | | 
% 227.67/39.28  | | |   (18)  all_57_11 = e3 & op(e1, e0) = e3
% 227.67/39.28  | | | 
% 227.67/39.28  | | | ALPHA: (18) implies:
% 227.67/39.28  | | |   (19)  all_57_11 = e3
% 227.67/39.28  | | | 
% 227.67/39.28  | | | REF_CLOSE: (2), (3), (6), (7), (9), (10), (11), (12), (13), (19) are
% 227.67/39.28  | | |            inconsistent by sub-proof #349.
% 227.67/39.28  | | | 
% 227.67/39.28  | | End of split
% 227.67/39.28  | | 
% 227.67/39.28  | End of split
% 227.67/39.28  | 
% 227.67/39.28  End of proof
% 227.67/39.28  
% 227.67/39.28  Sub-proof #343 shows that the following formulas are inconsistent:
% 227.67/39.28  ----------------------------------------------------------------
% 227.67/39.28    (1)  all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 227.67/39.28    (2)   ~ (all_52_9 = e2)
% 227.67/39.28    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.67/39.28           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.67/39.28    (4)  all_55_4 = all_52_9
% 227.67/39.28    (5)   ~ (all_52_9 = e1)
% 227.67/39.28    (6)  op(e0, e0) = e0
% 227.67/39.28    (7)  op(all_52_9, all_52_9) = e3
% 227.67/39.28    (8)   ~ (all_52_9 = e3)
% 227.67/39.28  
% 227.67/39.28  Begin of proof
% 227.67/39.28  | 
% 227.67/39.28  | BETA: splitting (1) gives:
% 227.67/39.28  | 
% 227.67/39.28  | Case 1:
% 227.67/39.28  | | 
% 227.67/39.28  | |   (9)  all_55_4 = e2
% 227.67/39.28  | | 
% 227.67/39.28  | | REF_CLOSE: (2), (4), (9) are inconsistent by sub-proof #345.
% 227.67/39.28  | | 
% 227.67/39.28  | Case 2:
% 227.67/39.28  | | 
% 227.67/39.28  | |   (10)  all_55_4 = e1 | all_55_4 = e0
% 227.67/39.28  | | 
% 227.67/39.28  | | BETA: splitting (10) gives:
% 227.67/39.28  | | 
% 227.67/39.28  | | Case 1:
% 227.67/39.28  | | | 
% 227.67/39.28  | | |   (11)  all_55_4 = e1
% 227.67/39.28  | | | 
% 227.67/39.28  | | | REF_CLOSE: (4), (5), (11) are inconsistent by sub-proof #344.
% 227.67/39.28  | | | 
% 227.67/39.28  | | Case 2:
% 227.67/39.28  | | | 
% 227.67/39.28  | | |   (12)  all_55_4 = e0
% 227.67/39.28  | | | 
% 227.67/39.28  | | | COMBINE_EQS: (4), (12) imply:
% 227.67/39.28  | | |   (13)  all_52_9 = e0
% 227.67/39.28  | | | 
% 227.67/39.28  | | | SIMP: (13) implies:
% 227.67/39.28  | | |   (14)  all_52_9 = e0
% 227.67/39.28  | | | 
% 227.67/39.28  | | | REDUCE: (8), (14) imply:
% 227.67/39.28  | | |   (15)   ~ (e3 = e0)
% 227.67/39.28  | | | 
% 227.67/39.28  | | | SIMP: (15) implies:
% 227.67/39.28  | | |   (16)   ~ (e3 = e0)
% 227.67/39.28  | | | 
% 227.67/39.28  | | | REDUCE: (7), (14) imply:
% 227.67/39.28  | | |   (17)  op(e0, e0) = e3
% 227.67/39.28  | | | 
% 227.67/39.28  | | | REF_CLOSE: (3), (6), (16), (17) are inconsistent by sub-proof #2304.
% 227.67/39.28  | | | 
% 227.67/39.28  | | End of split
% 227.67/39.28  | | 
% 227.67/39.28  | End of split
% 227.67/39.28  | 
% 227.67/39.28  End of proof
% 227.67/39.28  
% 227.67/39.28  Sub-proof #344 shows that the following formulas are inconsistent:
% 227.67/39.28  ----------------------------------------------------------------
% 227.67/39.28    (1)  all_55_4 = all_52_9
% 227.67/39.28    (2)  all_55_4 = e1
% 227.67/39.28    (3)   ~ (all_52_9 = e1)
% 227.67/39.28  
% 227.67/39.28  Begin of proof
% 227.67/39.28  | 
% 227.67/39.28  | COMBINE_EQS: (1), (2) imply:
% 227.67/39.28  |   (4)  all_52_9 = e1
% 227.67/39.28  | 
% 227.67/39.28  | SIMP: (4) implies:
% 227.67/39.28  |   (5)  all_52_9 = e1
% 227.67/39.28  | 
% 227.67/39.28  | REDUCE: (3), (5) imply:
% 227.67/39.28  |   (6)  $false
% 227.67/39.28  | 
% 227.67/39.28  | CLOSE: (6) is inconsistent.
% 227.67/39.28  | 
% 227.67/39.28  End of proof
% 227.67/39.28  
% 227.67/39.28  Sub-proof #345 shows that the following formulas are inconsistent:
% 227.67/39.28  ----------------------------------------------------------------
% 227.67/39.28    (1)  all_55_4 = all_52_9
% 227.67/39.28    (2)  all_55_4 = e2
% 227.67/39.28    (3)   ~ (all_52_9 = e2)
% 227.67/39.28  
% 227.67/39.28  Begin of proof
% 227.67/39.28  | 
% 227.67/39.28  | COMBINE_EQS: (1), (2) imply:
% 227.67/39.28  |   (4)  all_52_9 = e2
% 227.67/39.28  | 
% 227.67/39.28  | SIMP: (4) implies:
% 227.67/39.28  |   (5)  all_52_9 = e2
% 227.67/39.28  | 
% 227.67/39.28  | REDUCE: (3), (5) imply:
% 227.67/39.28  |   (6)  $false
% 227.67/39.28  | 
% 227.67/39.28  | CLOSE: (6) is inconsistent.
% 227.67/39.28  | 
% 227.67/39.28  End of proof
% 227.67/39.28  
% 227.67/39.28  Sub-proof #346 shows that the following formulas are inconsistent:
% 227.67/39.28  ----------------------------------------------------------------
% 227.67/39.28    (1)  op(e0, e0) = all_4_2
% 227.67/39.28    (2)   ~ (e3 = e1)
% 227.67/39.28    (3)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 227.67/39.28         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 227.67/39.28    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.67/39.28           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.67/39.28    (5)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 227.67/39.28         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 227.67/39.28    (6)   ~ (all_6_2 = e3)
% 227.67/39.28    (7)  op(e1, e1) = all_6_2
% 227.67/39.28    (8)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 227.67/39.28    (9)   ~ (e3 = e2)
% 227.67/39.28    (10)  op(e1, e0) = all_53_14
% 227.67/39.28    (11)   ~ (e3 = e0)
% 227.67/39.28    (12)   ~ (all_4_2 = e2)
% 227.67/39.28    (13)   ~ (e2 = e0)
% 227.67/39.28    (14)   ~ (e1 = e0)
% 227.67/39.28    (15)   ~ (all_53_14 = e0)
% 227.67/39.28    (16)  op(e1, e1) = e2
% 227.67/39.28    (17)   ~ (e2 = e1)
% 227.67/39.28    (18)   ~ (all_6_2 = e0)
% 227.67/39.28    (19)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 227.67/39.28          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 227.67/39.28  
% 227.67/39.28  Begin of proof
% 227.67/39.28  | 
% 227.67/39.28  | BETA: splitting (8) gives:
% 227.67/39.28  | 
% 227.67/39.28  | Case 1:
% 227.67/39.28  | | 
% 227.67/39.28  | |   (20)  all_57_11 = e2 & op(e1, e0) = e2
% 227.67/39.28  | | 
% 227.67/39.28  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (9), (10), (11), (13), (14), (15),
% 227.67/39.28  | |            (16), (17), (18), (19), (20) are inconsistent by sub-proof #347.
% 227.67/39.28  | | 
% 227.67/39.28  | Case 2:
% 227.67/39.28  | | 
% 227.67/39.28  | |   (21)  all_57_15 = e2 & op(e0, e0) = e2
% 227.67/39.28  | | 
% 227.67/39.28  | | ALPHA: (21) implies:
% 227.67/39.28  | |   (22)  op(e0, e0) = e2
% 227.67/39.28  | | 
% 227.67/39.28  | | REF_CLOSE: (1), (4), (12), (22) are inconsistent by sub-proof #2334.
% 227.67/39.28  | | 
% 227.67/39.28  | End of split
% 227.67/39.28  | 
% 227.67/39.28  End of proof
% 227.67/39.28  
% 227.67/39.28  Sub-proof #347 shows that the following formulas are inconsistent:
% 227.67/39.28  ----------------------------------------------------------------
% 227.67/39.28    (1)   ~ (e3 = e1)
% 227.67/39.28    (2)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 227.67/39.28         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 227.67/39.28    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.67/39.28           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.67/39.28    (4)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 227.67/39.28         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 227.67/39.28    (5)   ~ (all_6_2 = e3)
% 227.67/39.28    (6)  op(e1, e1) = all_6_2
% 227.67/39.28    (7)  all_57_11 = e2 & op(e1, e0) = e2
% 227.67/39.28    (8)   ~ (e3 = e2)
% 227.67/39.28    (9)  op(e1, e0) = all_53_14
% 227.67/39.28    (10)   ~ (e3 = e0)
% 227.67/39.28    (11)   ~ (e2 = e0)
% 227.67/39.28    (12)   ~ (e1 = e0)
% 227.67/39.28    (13)   ~ (all_53_14 = e0)
% 227.67/39.28    (14)  op(e1, e1) = e2
% 227.67/39.28    (15)   ~ (e2 = e1)
% 227.67/39.28    (16)   ~ (all_6_2 = e0)
% 227.67/39.28    (17)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 227.67/39.28          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 227.67/39.28  
% 227.67/39.28  Begin of proof
% 227.67/39.28  | 
% 227.67/39.28  | ALPHA: (7) implies:
% 227.67/39.28  |   (18)  all_57_11 = e2
% 227.67/39.28  | 
% 227.67/39.28  | BETA: splitting (17) gives:
% 227.67/39.28  | 
% 227.67/39.28  | Case 1:
% 227.67/39.28  | | 
% 227.67/39.28  | |   (19)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) =
% 227.67/39.28  | |           e1)
% 227.67/39.28  | | 
% 227.67/39.28  | | BETA: splitting (19) gives:
% 227.67/39.28  | | 
% 227.67/39.28  | | Case 1:
% 227.67/39.28  | | | 
% 227.67/39.28  | | |   (20)  all_57_6 = e1 & op(e1, e3) = e1
% 227.67/39.28  | | | 
% 227.67/39.28  | | | ALPHA: (20) implies:
% 227.67/39.28  | | |   (21)  all_57_6 = e1
% 227.67/39.28  | | | 
% 227.67/39.29  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (12), (13), (16),
% 227.67/39.29  | | |            (18), (21) are inconsistent by sub-proof #2340.
% 227.67/39.29  | | | 
% 227.67/39.29  | | Case 2:
% 227.67/39.29  | | | 
% 227.67/39.29  | | |   (22)  all_57_7 = e1 & op(e1, e2) = e1
% 227.67/39.29  | | | 
% 227.67/39.29  | | | ALPHA: (22) implies:
% 227.67/39.29  | | |   (23)  all_57_7 = e1
% 227.67/39.29  | | | 
% 227.67/39.29  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (10), (11), (12), (16),
% 227.67/39.29  | | |            (18), (23) are inconsistent by sub-proof #348.
% 227.67/39.29  | | | 
% 227.67/39.29  | | End of split
% 227.67/39.29  | | 
% 227.67/39.29  | Case 2:
% 227.67/39.29  | | 
% 227.67/39.29  | |   (24)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) =
% 227.67/39.29  | |           e1)
% 227.67/39.29  | | 
% 227.67/39.29  | | REF_CLOSE: (3), (14), (15), (18), (24) are inconsistent by sub-proof #1725.
% 227.67/39.29  | | 
% 227.67/39.29  | End of split
% 227.67/39.29  | 
% 227.67/39.29  End of proof
% 227.67/39.29  
% 227.67/39.29  Sub-proof #348 shows that the following formulas are inconsistent:
% 227.67/39.29  ----------------------------------------------------------------
% 227.67/39.29    (1)   ~ (e3 = e1)
% 227.67/39.29    (2)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 227.67/39.29         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 227.67/39.29    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.67/39.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.67/39.29    (4)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 227.67/39.29         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 227.67/39.29    (5)   ~ (all_6_2 = e3)
% 227.67/39.29    (6)  op(e1, e1) = all_6_2
% 227.67/39.29    (7)  all_57_7 = e1
% 227.67/39.29    (8)   ~ (e3 = e2)
% 227.67/39.29    (9)   ~ (e3 = e0)
% 227.67/39.29    (10)  all_57_11 = e2
% 227.67/39.29    (11)   ~ (e2 = e0)
% 227.67/39.29    (12)   ~ (e1 = e0)
% 227.67/39.29    (13)   ~ (all_6_2 = e0)
% 227.67/39.29  
% 227.67/39.29  Begin of proof
% 227.67/39.29  | 
% 227.67/39.29  | BETA: splitting (2) gives:
% 227.67/39.29  | 
% 227.67/39.29  | Case 1:
% 227.67/39.29  | | 
% 227.67/39.29  | |   (14)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) =
% 227.67/39.29  | |           e0)
% 227.67/39.29  | | 
% 227.67/39.29  | | BETA: splitting (14) gives:
% 227.67/39.29  | | 
% 227.67/39.29  | | Case 1:
% 227.67/39.29  | | | 
% 227.67/39.29  | | |   (15)  all_57_6 = e0 & op(e1, e3) = e0
% 227.67/39.29  | | | 
% 227.67/39.29  | | | ALPHA: (15) implies:
% 227.67/39.29  | | |   (16)  all_57_6 = e0
% 227.67/39.29  | | | 
% 227.67/39.29  | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (16) are
% 227.67/39.29  | | |            inconsistent by sub-proof #2114.
% 227.67/39.29  | | | 
% 227.67/39.29  | | Case 2:
% 227.67/39.29  | | | 
% 227.67/39.29  | | |   (17)  all_57_7 = e0 & op(e1, e2) = e0
% 227.67/39.29  | | | 
% 227.67/39.29  | | | ALPHA: (17) implies:
% 227.67/39.29  | | |   (18)  all_57_7 = e0
% 227.67/39.29  | | | 
% 227.67/39.29  | | | REF_CLOSE: (7), (12), (18) are inconsistent by sub-proof #2211.
% 227.67/39.29  | | | 
% 227.67/39.29  | | End of split
% 227.67/39.29  | | 
% 227.67/39.29  | Case 2:
% 227.67/39.29  | | 
% 227.67/39.29  | |   (19)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 227.67/39.29  | |           e0)
% 227.67/39.29  | | 
% 227.67/39.29  | | BETA: splitting (19) gives:
% 227.67/39.29  | | 
% 227.67/39.29  | | Case 1:
% 227.67/39.29  | | | 
% 227.67/39.29  | | |   (20)  all_57_8 = e0 & op(e1, e1) = e0
% 227.67/39.29  | | | 
% 227.67/39.29  | | | REF_CLOSE: (3), (6), (13), (20) are inconsistent by sub-proof #2412.
% 227.67/39.29  | | | 
% 227.67/39.29  | | Case 2:
% 227.67/39.29  | | | 
% 227.67/39.29  | | |   (21)  all_57_11 = e0 & op(e1, e0) = e0
% 227.67/39.29  | | | 
% 227.67/39.29  | | | REF_CLOSE: (10), (11), (21) are inconsistent by sub-proof #2041.
% 227.67/39.29  | | | 
% 227.67/39.29  | | End of split
% 227.67/39.29  | | 
% 227.67/39.29  | End of split
% 227.67/39.29  | 
% 227.67/39.29  End of proof
% 227.67/39.29  
% 227.67/39.29  Sub-proof #349 shows that the following formulas are inconsistent:
% 227.67/39.29  ----------------------------------------------------------------
% 227.67/39.29    (1)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 227.67/39.29         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 227.67/39.29    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.67/39.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.67/39.29    (3)  op(e1, e1) = all_6_2
% 227.67/39.29    (4)  all_57_7 = e1
% 227.67/39.29    (5)   ~ (e3 = e0)
% 227.67/39.29    (6)  all_57_6 = e2
% 227.67/39.29    (7)   ~ (e2 = e0)
% 227.67/39.29    (8)   ~ (e1 = e0)
% 227.67/39.29    (9)  all_57_11 = e3
% 227.67/39.29    (10)   ~ (all_6_2 = e0)
% 227.67/39.29  
% 227.67/39.29  Begin of proof
% 227.67/39.29  | 
% 227.67/39.29  | BETA: splitting (1) gives:
% 227.67/39.29  | 
% 227.67/39.29  | Case 1:
% 227.67/39.29  | | 
% 227.67/39.29  | |   (11)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) =
% 227.67/39.29  | |           e0)
% 227.67/39.29  | | 
% 227.67/39.29  | | BETA: splitting (11) gives:
% 227.67/39.29  | | 
% 227.67/39.29  | | Case 1:
% 227.67/39.29  | | | 
% 227.67/39.29  | | |   (12)  all_57_6 = e0 & op(e1, e3) = e0
% 227.67/39.29  | | | 
% 227.67/39.29  | | | ALPHA: (12) implies:
% 227.67/39.29  | | |   (13)  all_57_6 = e0
% 227.67/39.29  | | | 
% 227.67/39.29  | | | REF_CLOSE: (6), (7), (13) are inconsistent by sub-proof #1846.
% 227.67/39.29  | | | 
% 227.67/39.29  | | Case 2:
% 227.67/39.29  | | | 
% 227.67/39.29  | | |   (14)  all_57_7 = e0 & op(e1, e2) = e0
% 227.67/39.29  | | | 
% 227.67/39.29  | | | ALPHA: (14) implies:
% 227.67/39.29  | | |   (15)  all_57_7 = e0
% 227.67/39.29  | | | 
% 227.67/39.29  | | | REF_CLOSE: (4), (8), (15) are inconsistent by sub-proof #2211.
% 227.67/39.29  | | | 
% 227.67/39.29  | | End of split
% 227.67/39.29  | | 
% 227.67/39.29  | Case 2:
% 227.67/39.29  | | 
% 227.67/39.29  | |   (16)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 227.67/39.29  | |           e0)
% 227.67/39.29  | | 
% 227.67/39.29  | | BETA: splitting (16) gives:
% 227.67/39.29  | | 
% 227.67/39.29  | | Case 1:
% 227.67/39.29  | | | 
% 227.67/39.29  | | |   (17)  all_57_8 = e0 & op(e1, e1) = e0
% 227.67/39.29  | | | 
% 227.67/39.29  | | | REF_CLOSE: (2), (3), (10), (17) are inconsistent by sub-proof #2412.
% 227.67/39.29  | | | 
% 227.67/39.29  | | Case 2:
% 227.67/39.29  | | | 
% 227.67/39.29  | | |   (18)  all_57_11 = e0 & op(e1, e0) = e0
% 227.67/39.29  | | | 
% 227.67/39.29  | | | REF_CLOSE: (5), (9), (18) are inconsistent by sub-proof #2136.
% 227.67/39.29  | | | 
% 227.67/39.29  | | End of split
% 227.67/39.29  | | 
% 227.67/39.29  | End of split
% 227.67/39.29  | 
% 227.67/39.29  End of proof
% 227.67/39.29  
% 227.67/39.29  Sub-proof #350 shows that the following formulas are inconsistent:
% 227.67/39.29  ----------------------------------------------------------------
% 227.67/39.29    (1)  op(e3, e3) = e1
% 227.67/39.29    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.67/39.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.67/39.29    (3)  all_57_6 = e1
% 227.67/39.29    (4)   ~ (e3 = e2)
% 227.67/39.29    (5)   ~ (e2 = e0)
% 227.67/39.29    (6)  all_57_12 = e3
% 227.67/39.29    (7)  all_57_2 = e0
% 227.67/39.29    (8)   ~ (e2 = e1)
% 227.67/39.29    (9)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 227.67/39.29         (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 227.67/39.29  
% 227.67/39.29  Begin of proof
% 227.67/39.29  | 
% 227.67/39.29  | BETA: splitting (9) gives:
% 227.67/39.29  | 
% 227.67/39.29  | Case 1:
% 227.67/39.29  | | 
% 227.67/39.29  | |   (10)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) =
% 227.67/39.29  | |           e2)
% 227.67/39.29  | | 
% 227.67/39.29  | | REF_CLOSE: (1), (2), (5), (7), (8), (10) are inconsistent by sub-proof
% 227.67/39.29  | |            #1063.
% 227.67/39.29  | | 
% 227.67/39.29  | Case 2:
% 227.67/39.29  | | 
% 227.67/39.29  | |   (11)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) =
% 227.67/39.29  | |           e2)
% 227.67/39.29  | | 
% 227.67/39.29  | | BETA: splitting (11) gives:
% 227.67/39.29  | | 
% 227.67/39.29  | | Case 1:
% 227.67/39.29  | | | 
% 227.67/39.29  | | |   (12)  all_57_6 = e2 & op(e1, e3) = e2
% 227.67/39.29  | | | 
% 227.67/39.29  | | | REF_CLOSE: (3), (8), (12) are inconsistent by sub-proof #1317.
% 227.67/39.29  | | | 
% 227.67/39.29  | | Case 2:
% 227.67/39.29  | | | 
% 227.67/39.29  | | |   (13)  all_57_12 = e2 & op(e0, e3) = e2
% 227.67/39.29  | | | 
% 227.67/39.29  | | | ALPHA: (13) implies:
% 227.67/39.29  | | |   (14)  all_57_12 = e2
% 227.67/39.29  | | | 
% 227.67/39.29  | | | REF_CLOSE: (4), (6), (14) are inconsistent by sub-proof #2392.
% 227.67/39.29  | | | 
% 227.67/39.29  | | End of split
% 227.67/39.29  | | 
% 227.67/39.29  | End of split
% 227.67/39.29  | 
% 227.67/39.29  End of proof
% 227.67/39.29  
% 227.67/39.29  Sub-proof #351 shows that the following formulas are inconsistent:
% 227.67/39.29  ----------------------------------------------------------------
% 227.67/39.29    (1)  all_57_9 = e2
% 227.67/39.29    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 227.67/39.29         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 227.67/39.29    (3)   ~ (e3 = e1)
% 227.67/39.29    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.67/39.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.67/39.29    (5)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 227.67/39.29         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 227.67/39.29    (6)   ~ (all_6_2 = e3)
% 227.67/39.29    (7)  op(e1, e1) = all_6_2
% 227.67/39.29    (8)  all_57_12 = e2
% 227.67/39.29    (9)   ~ (e3 = e2)
% 227.67/39.29    (10)   ~ (e3 = e0)
% 227.67/39.29    (11)  all_57_6 = e2
% 227.67/39.29    (12)   ~ (e2 = e0)
% 227.67/39.29    (13)   ~ (e1 = e0)
% 227.67/39.29    (14)   ~ (all_53_12 = e1)
% 227.67/39.29    (15)  op(e0, e0) = e0
% 227.67/39.29    (16)  all_57_2 = e0
% 227.67/39.29    (17)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 227.67/39.29          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 227.67/39.29    (18)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 227.67/39.29          (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 227.67/39.29    (19)   ~ (e2 = e1)
% 227.67/39.29    (20)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 227.67/39.29          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 227.67/39.29    (21)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 227.67/39.29          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 227.67/39.29    (22)  all_57_7 = e0
% 227.67/39.29    (23)  op(e3, e0) = all_53_12
% 227.67/39.29  
% 227.67/39.29  Begin of proof
% 227.67/39.29  | 
% 227.67/39.29  | BETA: splitting (5) gives:
% 227.67/39.29  | 
% 227.67/39.29  | Case 1:
% 227.67/39.29  | | 
% 227.67/39.29  | |   (24)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 227.67/39.29  | |           e3)
% 227.67/39.29  | | 
% 227.67/39.29  | | REF_CLOSE: (9), (10), (11), (22), (24) are inconsistent by sub-proof #353.
% 227.67/39.29  | | 
% 227.67/39.29  | Case 2:
% 227.67/39.29  | | 
% 227.67/39.29  | |   (25)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 227.67/39.29  | |           e3)
% 227.67/39.29  | | 
% 227.67/39.29  | | BETA: splitting (25) gives:
% 227.67/39.29  | | 
% 227.67/39.29  | | Case 1:
% 227.67/39.29  | | | 
% 227.67/39.29  | | |   (26)  all_57_8 = e3 & op(e1, e1) = e3
% 227.67/39.29  | | | 
% 227.67/39.29  | | | ALPHA: (26) implies:
% 227.67/39.29  | | |   (27)  op(e1, e1) = e3
% 227.67/39.29  | | | 
% 227.67/39.29  | | | REF_CLOSE: (4), (6), (7), (27) are inconsistent by sub-proof #2468.
% 227.67/39.29  | | | 
% 227.67/39.29  | | Case 2:
% 227.67/39.29  | | | 
% 227.67/39.29  | | |   (28)  all_57_11 = e3 & op(e1, e0) = e3
% 227.67/39.29  | | | 
% 227.67/39.29  | | | ALPHA: (28) implies:
% 227.67/39.29  | | |   (29)  all_57_11 = e3
% 227.67/39.29  | | | 
% 227.67/39.29  | | | BETA: splitting (21) gives:
% 227.67/39.29  | | | 
% 227.67/39.29  | | | Case 1:
% 227.67/39.29  | | | | 
% 227.67/39.29  | | | |   (30)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0)
% 227.67/39.29  | | | |           = e1)
% 227.67/39.29  | | | | 
% 227.67/39.29  | | | | BETA: splitting (30) gives:
% 227.67/39.29  | | | | 
% 227.67/39.29  | | | | Case 1:
% 227.67/39.29  | | | | | 
% 227.67/39.29  | | | | |   (31)  all_57_9 = e1 & op(e3, e0) = e1
% 227.67/39.29  | | | | | 
% 227.67/39.29  | | | | | REF_CLOSE: (4), (14), (23), (31) are inconsistent by sub-proof #2131.
% 227.67/39.29  | | | | | 
% 227.67/39.29  | | | | Case 2:
% 227.67/39.29  | | | | | 
% 227.67/39.29  | | | | |   (32)  all_57_10 = e1 & op(e2, e0) = e1
% 227.67/39.29  | | | | | 
% 227.67/39.29  | | | | | ALPHA: (32) implies:
% 227.67/39.29  | | | | |   (33)  all_57_10 = e1
% 227.67/39.29  | | | | | 
% 227.67/39.29  | | | | | BETA: splitting (17) gives:
% 227.67/39.29  | | | | | 
% 227.67/39.29  | | | | | Case 1:
% 227.67/39.29  | | | | | | 
% 227.67/39.29  | | | | | |   (34)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2,
% 227.67/39.29  | | | | | |             e3) = e3)
% 227.67/39.29  | | | | | | 
% 227.67/39.29  | | | | | | BETA: splitting (34) gives:
% 227.67/39.29  | | | | | | 
% 227.67/39.29  | | | | | | Case 1:
% 227.67/39.29  | | | | | | | 
% 227.67/39.29  | | | | | | |   (35)  all_57_0 = e3 & op(e3, e3) = e3
% 227.67/39.29  | | | | | | | 
% 227.67/39.29  | | | | | | | ALPHA: (35) implies:
% 227.67/39.29  | | | | | | |   (36)  op(e3, e3) = e3
% 227.67/39.29  | | | | | | | 
% 227.67/39.29  | | | | | | | REF_CLOSE: (2), (3), (4), (8), (10), (11), (12), (13), (19), (20),
% 227.67/39.29  | | | | | | |            (36) are inconsistent by sub-proof #2384.
% 227.67/39.29  | | | | | | | 
% 227.67/39.29  | | | | | | Case 2:
% 227.67/39.29  | | | | | | | 
% 227.67/39.29  | | | | | | |   (37)  all_57_2 = e3 & op(e2, e3) = e3
% 227.67/39.29  | | | | | | | 
% 227.67/39.29  | | | | | | | ALPHA: (37) implies:
% 227.67/39.29  | | | | | | |   (38)  all_57_2 = e3
% 227.67/39.29  | | | | | | | 
% 227.67/39.29  | | | | | | | REF_CLOSE: (10), (16), (38) are inconsistent by sub-proof #2258.
% 227.67/39.29  | | | | | | | 
% 227.67/39.29  | | | | | | End of split
% 227.67/39.29  | | | | | | 
% 227.67/39.29  | | | | | Case 2:
% 227.67/39.29  | | | | | | 
% 227.67/39.29  | | | | | |   (39)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0,
% 227.67/39.29  | | | | | |             e3) = e3)
% 227.67/39.29  | | | | | | 
% 227.67/39.29  | | | | | | BETA: splitting (39) gives:
% 227.67/39.29  | | | | | | 
% 227.67/39.29  | | | | | | Case 1:
% 227.67/39.29  | | | | | | | 
% 227.67/39.29  | | | | | | |   (40)  all_57_6 = e3 & op(e1, e3) = e3
% 227.67/39.29  | | | | | | | 
% 227.67/39.29  | | | | | | | ALPHA: (40) implies:
% 227.67/39.29  | | | | | | |   (41)  all_57_6 = e3
% 227.67/39.29  | | | | | | | 
% 227.67/39.29  | | | | | | | COMBINE_EQS: (11), (41) imply:
% 227.67/39.29  | | | | | | |   (42)  e3 = e2
% 227.67/39.29  | | | | | | | 
% 227.67/39.29  | | | | | | | SIMP: (42) implies:
% 227.67/39.29  | | | | | | |   (43)  e3 = e2
% 227.67/39.29  | | | | | | | 
% 227.67/39.29  | | | | | | | COMBINE_EQS: (29), (43) imply:
% 227.67/39.29  | | | | | | |   (44)  all_57_11 = e2
% 227.67/39.29  | | | | | | | 
% 227.67/39.29  | | | | | | | REF_CLOSE: (1), (3), (4), (9), (10), (15), (18), (33), (44) are
% 227.67/39.29  | | | | | | |            inconsistent by sub-proof #352.
% 227.67/39.29  | | | | | | | 
% 227.67/39.29  | | | | | | Case 2:
% 227.67/39.29  | | | | | | | 
% 227.67/39.29  | | | | | | |   (45)  all_57_12 = e3 & op(e0, e3) = e3
% 227.67/39.29  | | | | | | | 
% 227.67/39.29  | | | | | | | ALPHA: (45) implies:
% 227.67/39.29  | | | | | | |   (46)  all_57_12 = e3
% 227.67/39.29  | | | | | | | 
% 227.67/39.29  | | | | | | | COMBINE_EQS: (8), (46) imply:
% 227.67/39.29  | | | | | | |   (47)  e3 = e2
% 227.67/39.29  | | | | | | | 
% 227.67/39.29  | | | | | | | SIMP: (47) implies:
% 227.67/39.29  | | | | | | |   (48)  e3 = e2
% 227.67/39.29  | | | | | | | 
% 227.67/39.29  | | | | | | | COMBINE_EQS: (29), (48) imply:
% 227.67/39.29  | | | | | | |   (49)  all_57_11 = e2
% 227.67/39.29  | | | | | | | 
% 227.67/39.29  | | | | | | | REF_CLOSE: (1), (3), (4), (9), (10), (15), (18), (33), (49) are
% 227.67/39.29  | | | | | | |            inconsistent by sub-proof #352.
% 227.67/39.29  | | | | | | | 
% 227.67/39.29  | | | | | | End of split
% 227.67/39.29  | | | | | | 
% 227.67/39.29  | | | | | End of split
% 227.67/39.29  | | | | | 
% 227.67/39.29  | | | | End of split
% 227.67/39.29  | | | | 
% 227.67/39.29  | | | Case 2:
% 227.67/39.29  | | | | 
% 227.67/39.29  | | | |   (50)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0,
% 227.67/39.29  | | | |             e0) = e1)
% 227.67/39.29  | | | | 
% 227.67/39.29  | | | | REF_CLOSE: (3), (4), (13), (15), (29), (50) are inconsistent by
% 227.67/39.29  | | | |            sub-proof #1727.
% 227.67/39.29  | | | | 
% 227.67/39.29  | | | End of split
% 227.67/39.29  | | | 
% 227.67/39.29  | | End of split
% 227.67/39.29  | | 
% 227.67/39.29  | End of split
% 227.67/39.29  | 
% 227.67/39.29  End of proof
% 227.67/39.29  
% 227.67/39.29  Sub-proof #352 shows that the following formulas are inconsistent:
% 227.67/39.29  ----------------------------------------------------------------
% 227.67/39.29    (1)  all_57_9 = e2
% 227.67/39.29    (2)   ~ (e3 = e1)
% 227.67/39.29    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.67/39.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.67/39.29    (4)  all_57_10 = e1
% 227.67/39.29    (5)   ~ (e3 = e2)
% 227.67/39.29    (6)   ~ (e3 = e0)
% 227.67/39.29    (7)  all_57_11 = e2
% 227.67/39.29    (8)  op(e0, e0) = e0
% 227.67/39.29    (9)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 227.67/39.29         (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 227.67/39.29  
% 227.67/39.29  Begin of proof
% 227.67/39.29  | 
% 227.67/39.29  | BETA: splitting (9) gives:
% 227.67/39.29  | 
% 227.67/39.29  | Case 1:
% 227.67/39.29  | | 
% 227.67/39.29  | |   (10)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 227.67/39.29  | |           e3)
% 227.67/39.29  | | 
% 227.67/39.29  | | BETA: splitting (10) gives:
% 227.67/39.29  | | 
% 227.67/39.29  | | Case 1:
% 227.67/39.29  | | | 
% 227.67/39.29  | | |   (11)  all_57_9 = e3 & op(e3, e0) = e3
% 227.67/39.29  | | | 
% 227.67/39.29  | | | ALPHA: (11) implies:
% 227.67/39.29  | | |   (12)  all_57_9 = e3
% 227.67/39.29  | | | 
% 227.67/39.29  | | | REF_CLOSE: (1), (5), (12) are inconsistent by sub-proof #1192.
% 227.67/39.29  | | | 
% 227.67/39.29  | | Case 2:
% 227.67/39.29  | | | 
% 227.67/39.29  | | |   (13)  all_57_10 = e3 & op(e2, e0) = e3
% 227.67/39.29  | | | 
% 227.67/39.29  | | | ALPHA: (13) implies:
% 227.67/39.29  | | |   (14)  all_57_10 = e3
% 227.67/39.29  | | | 
% 227.67/39.29  | | | REF_CLOSE: (2), (4), (14) are inconsistent by sub-proof #2248.
% 227.67/39.29  | | | 
% 227.67/39.29  | | End of split
% 227.67/39.29  | | 
% 227.67/39.29  | Case 2:
% 227.67/39.29  | | 
% 227.67/39.29  | |   (15)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 227.67/39.29  | |           e3)
% 227.67/39.29  | | 
% 227.67/39.29  | | REF_CLOSE: (3), (5), (6), (7), (8), (15) are inconsistent by sub-proof
% 227.67/39.29  | |            #1667.
% 227.67/39.29  | | 
% 227.67/39.29  | End of split
% 227.67/39.29  | 
% 227.67/39.29  End of proof
% 227.67/39.29  
% 227.67/39.29  Sub-proof #353 shows that the following formulas are inconsistent:
% 227.67/39.29  ----------------------------------------------------------------
% 227.67/39.29    (1)   ~ (e3 = e2)
% 227.67/39.29    (2)   ~ (e3 = e0)
% 227.67/39.29    (3)  all_57_6 = e2
% 227.67/39.29    (4)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3)
% 227.67/39.29    (5)  all_57_7 = e0
% 227.67/39.29  
% 227.67/39.29  Begin of proof
% 227.67/39.29  | 
% 227.67/39.29  | BETA: splitting (4) gives:
% 227.67/39.29  | 
% 227.67/39.29  | Case 1:
% 227.67/39.29  | | 
% 227.67/39.29  | |   (6)  all_57_6 = e3 & op(e1, e3) = e3
% 227.67/39.29  | | 
% 227.67/39.29  | | ALPHA: (6) implies:
% 227.67/39.29  | |   (7)  all_57_6 = e3
% 227.67/39.29  | | 
% 227.67/39.29  | | REF_CLOSE: (1), (3), (7) are inconsistent by sub-proof #2463.
% 227.67/39.29  | | 
% 227.67/39.29  | Case 2:
% 227.67/39.29  | | 
% 227.67/39.29  | |   (8)  all_57_7 = e3 & op(e1, e2) = e3
% 227.67/39.29  | | 
% 227.67/39.29  | | ALPHA: (8) implies:
% 227.67/39.29  | |   (9)  all_57_7 = e3
% 227.67/39.29  | | 
% 227.67/39.29  | | REF_CLOSE: (2), (5), (9) are inconsistent by sub-proof #2269.
% 227.67/39.29  | | 
% 227.67/39.29  | End of split
% 227.67/39.29  | 
% 227.67/39.29  End of proof
% 227.67/39.29  
% 227.67/39.29  Sub-proof #354 shows that the following formulas are inconsistent:
% 227.67/39.29  ----------------------------------------------------------------
% 227.67/39.29    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 227.67/39.29         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 227.67/39.29    (2)   ~ (e3 = e1)
% 227.67/39.29    (3)   ~ (e3 = e2)
% 227.67/39.29    (4)   ~ (e3 = e0)
% 227.67/39.29    (5)  all_57_6 = e2
% 227.67/39.29    (6)   ~ (e2 = e0)
% 227.67/39.29    (7)   ~ (e1 = e0)
% 227.67/39.29    (8)  all_57_6 = e0 & op(e1, e3) = e0
% 227.67/39.29    (9)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 227.67/39.29         (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 227.67/39.29    (10)  all_57_2 = e0
% 227.67/39.29    (11)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 227.67/39.29          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 227.67/39.29    (12)   ~ (e2 = e1)
% 227.67/39.29    (13)  all_57_3 = e2
% 227.67/39.29  
% 227.67/39.29  Begin of proof
% 227.67/39.29  | 
% 227.67/39.29  | ALPHA: (8) implies:
% 227.67/39.29  |   (14)  all_57_6 = e0
% 227.67/39.29  | 
% 227.67/39.29  | COMBINE_EQS: (5), (14) imply:
% 227.67/39.29  |   (15)  e2 = e0
% 227.67/39.29  | 
% 227.67/39.29  | COMBINE_EQS: (13), (15) imply:
% 227.67/39.29  |   (16)  all_57_3 = e0
% 227.67/39.29  | 
% 227.67/39.29  | REF_CLOSE: (1), (2), (3), (4), (6), (7), (9), (10), (11), (12), (16) are
% 227.67/39.29  |            inconsistent by sub-proof #2246.
% 227.67/39.29  | 
% 227.67/39.29  End of proof
% 227.67/39.29  
% 227.67/39.29  Sub-proof #355 shows that the following formulas are inconsistent:
% 227.67/39.29  ----------------------------------------------------------------
% 227.67/39.29    (1)  op(e3, e3) = e1
% 227.67/39.29    (2)  op(e2, e3) = all_53_1
% 227.67/39.29    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.67/39.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.67/39.29    (4)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2)
% 227.67/39.29    (5)   ~ (all_53_1 = e2)
% 227.67/39.29    (6)   ~ (e2 = e1)
% 227.67/39.29  
% 227.67/39.29  Begin of proof
% 227.67/39.29  | 
% 227.67/39.29  | BETA: splitting (4) gives:
% 227.67/39.29  | 
% 227.67/39.29  | Case 1:
% 227.67/39.29  | | 
% 227.67/39.29  | |   (7)  all_57_0 = e2 & op(e3, e3) = e2
% 227.67/39.29  | | 
% 227.67/39.29  | | ALPHA: (7) implies:
% 227.67/39.29  | |   (8)  op(e3, e3) = e2
% 227.67/39.29  | | 
% 227.67/39.29  | | REF_CLOSE: (1), (3), (6), (8) are inconsistent by sub-proof #1950.
% 227.67/39.29  | | 
% 227.67/39.29  | Case 2:
% 227.67/39.29  | | 
% 227.67/39.29  | |   (9)  all_57_2 = e2 & op(e2, e3) = e2
% 227.67/39.29  | | 
% 227.67/39.29  | | REF_CLOSE: (2), (3), (5), (9) are inconsistent by sub-proof #2504.
% 227.67/39.29  | | 
% 227.67/39.29  | End of split
% 227.67/39.29  | 
% 227.67/39.29  End of proof
% 227.67/39.29  
% 227.67/39.29  Sub-proof #356 shows that the following formulas are inconsistent:
% 227.67/39.29  ----------------------------------------------------------------
% 227.67/39.29    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.67/39.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.67/39.29    (2)  op(e0, e2) = e1
% 227.67/39.29    (3)  op(e1, e1) = e1
% 227.67/39.29    (4)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0 &
% 227.67/39.29         op(all_52_25, all_52_25) = e3 & op(all_52_27, all_52_27) = e2 &
% 227.67/39.29         op(all_52_29, all_52_29) = e1 & op(all_52_31, all_52_31) = e0 & op(e0,
% 227.67/39.29           e3) = all_52_25 & op(e0, e2) = all_52_27 & op(e0, e1) = all_52_29 &
% 227.67/39.29         op(e0, e0) = all_52_31 & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 227.67/39.29         $i(all_52_31)
% 227.67/39.29    (5)   ~ (e2 = e1)
% 227.67/39.29  
% 227.67/39.29  Begin of proof
% 227.67/39.29  | 
% 227.67/39.29  | ALPHA: (4) implies:
% 227.67/39.29  |   (6)  op(e0, e2) = all_52_27
% 227.67/39.29  |   (7)  op(all_52_27, all_52_27) = e2
% 227.67/39.29  | 
% 227.67/39.29  | GROUND_INST: instantiating (1) with e1, all_52_27, e2, e0, simplifying with
% 227.67/39.29  |              (2), (6) gives:
% 227.67/39.29  |   (8)  all_52_27 = e1
% 227.67/39.29  | 
% 227.67/39.29  | REDUCE: (7), (8) imply:
% 227.67/39.29  |   (9)  op(e1, e1) = e2
% 227.67/39.29  | 
% 227.67/39.29  | REF_CLOSE: (1), (3), (5), (9) are inconsistent by sub-proof #2423.
% 227.67/39.29  | 
% 227.67/39.29  End of proof
% 227.67/39.29  
% 227.67/39.29  Sub-proof #357 shows that the following formulas are inconsistent:
% 227.67/39.29  ----------------------------------------------------------------
% 227.67/39.29    (1)  op(e3, e3) = e1
% 227.67/39.29    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.67/39.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.67/39.29    (3)  all_55_9 = all_52_19
% 227.67/39.29    (4)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 227.67/39.29    (5)   ~ (all_53_4 = e1)
% 227.67/39.29    (6)  all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 227.67/39.29    (7)  all_55_1 = all_53_4
% 227.67/39.29    (8)   ~ (all_53_4 = all_52_19)
% 227.67/39.29    (9)   ~ (all_53_4 = e2)
% 227.67/39.29    (10)  op(all_52_19, all_52_19) = e2
% 227.67/39.29    (11)   ~ (all_52_19 = e2)
% 227.67/39.29    (12)   ~ (e2 = e1)
% 227.67/39.29    (13)   ~ (all_52_19 = e1)
% 227.67/39.29  
% 227.67/39.29  Begin of proof
% 227.67/39.29  | 
% 227.67/39.29  | BETA: splitting (6) gives:
% 227.67/39.29  | 
% 227.67/39.29  | Case 1:
% 227.67/39.29  | | 
% 227.67/39.29  | |   (14)  all_55_1 = e2
% 227.67/39.29  | | 
% 227.67/39.29  | | REF_CLOSE: (7), (9), (14) are inconsistent by sub-proof #2284.
% 227.67/39.29  | | 
% 227.67/39.29  | Case 2:
% 227.67/39.29  | | 
% 227.67/39.29  | |   (15)  all_55_1 = e1 | all_55_1 = e0
% 227.67/39.29  | | 
% 227.67/39.29  | | BETA: splitting (15) gives:
% 227.67/39.29  | | 
% 227.67/39.29  | | Case 1:
% 227.67/39.29  | | | 
% 227.67/39.29  | | |   (16)  all_55_1 = e1
% 227.67/39.29  | | | 
% 227.67/39.29  | | | REF_CLOSE: (5), (7), (16) are inconsistent by sub-proof #2283.
% 227.67/39.29  | | | 
% 227.67/39.29  | | Case 2:
% 227.67/39.29  | | | 
% 227.67/39.29  | | |   (17)  all_55_1 = e0
% 227.67/39.29  | | | 
% 227.67/39.29  | | | COMBINE_EQS: (7), (17) imply:
% 227.67/39.29  | | |   (18)  all_53_4 = e0
% 227.67/39.29  | | | 
% 227.67/39.29  | | | SIMP: (18) implies:
% 227.67/39.29  | | |   (19)  all_53_4 = e0
% 227.67/39.29  | | | 
% 227.67/39.29  | | | REDUCE: (8), (19) imply:
% 227.67/39.29  | | |   (20)   ~ (all_52_19 = e0)
% 227.67/39.29  | | | 
% 227.67/39.29  | | | SIMP: (20) implies:
% 227.67/39.29  | | |   (21)   ~ (all_52_19 = e0)
% 227.67/39.29  | | | 
% 227.67/39.29  | | | REF_CLOSE: (1), (2), (3), (4), (10), (11), (12), (13), (21) are
% 227.67/39.29  | | |            inconsistent by sub-proof #358.
% 227.67/39.29  | | | 
% 227.67/39.29  | | End of split
% 227.67/39.29  | | 
% 227.67/39.29  | End of split
% 227.67/39.29  | 
% 227.67/39.29  End of proof
% 227.67/39.29  
% 227.67/39.29  Sub-proof #358 shows that the following formulas are inconsistent:
% 227.67/39.29  ----------------------------------------------------------------
% 227.67/39.29    (1)  op(e3, e3) = e1
% 227.67/39.29    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.67/39.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.67/39.29    (3)  all_55_9 = all_52_19
% 227.67/39.29    (4)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 227.67/39.29    (5)   ~ (all_52_19 = e0)
% 227.67/39.29    (6)  op(all_52_19, all_52_19) = e2
% 227.67/39.29    (7)   ~ (all_52_19 = e2)
% 227.67/39.29    (8)   ~ (e2 = e1)
% 227.67/39.29    (9)   ~ (all_52_19 = e1)
% 227.67/39.29  
% 227.67/39.29  Begin of proof
% 227.67/39.29  | 
% 227.67/39.29  | BETA: splitting (4) gives:
% 227.67/39.29  | 
% 227.67/39.29  | Case 1:
% 227.67/39.29  | | 
% 227.67/39.29  | |   (10)  all_55_9 = e3
% 227.67/39.29  | | 
% 227.67/39.29  | | COMBINE_EQS: (3), (10) imply:
% 227.67/39.29  | |   (11)  all_52_19 = e3
% 227.67/39.29  | | 
% 227.67/39.29  | | SIMP: (11) implies:
% 227.67/39.29  | |   (12)  all_52_19 = e3
% 227.67/39.29  | | 
% 227.67/39.29  | | REDUCE: (6), (12) imply:
% 227.67/39.29  | |   (13)  op(e3, e3) = e2
% 227.67/39.29  | | 
% 227.67/39.29  | | REF_CLOSE: (1), (2), (8), (13) are inconsistent by sub-proof #1950.
% 227.67/39.29  | | 
% 227.67/39.29  | Case 2:
% 227.67/39.29  | | 
% 227.67/39.29  | |   (14)  all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 227.67/39.29  | | 
% 227.67/39.29  | | REF_CLOSE: (3), (5), (7), (9), (14) are inconsistent by sub-proof #1882.
% 227.67/39.29  | | 
% 227.67/39.29  | End of split
% 227.67/39.29  | 
% 227.67/39.29  End of proof
% 227.67/39.29  
% 227.67/39.29  Sub-proof #359 shows that the following formulas are inconsistent:
% 227.67/39.29  ----------------------------------------------------------------
% 227.67/39.29    (1)  op(e3, e3) = e1
% 227.67/39.29    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.67/39.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.67/39.29    (3)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 227.67/39.29           op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 227.67/39.29           op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 227.67/39.29           = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3, e0)
% 227.67/39.29           = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) & $i(all_52_7))
% 227.67/39.29         | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0 &
% 227.67/39.29           op(all_52_9, all_52_9) = e3 & op(all_52_11, all_52_11) = e2 &
% 227.67/39.29           op(all_52_13, all_52_13) = e1 & op(all_52_15, all_52_15) = e0 & op(e2,
% 227.67/39.29             e3) = all_52_9 & op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13 &
% 227.67/39.29           op(e2, e0) = all_52_15 & $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 227.67/39.29           $i(all_52_15))
% 227.67/39.29    (4)   ~ (all_6_2 = e3)
% 227.67/39.29    (5)  op(e1, e1) = all_6_2
% 227.67/39.29    (6)  op(e2, e0) = e1
% 227.67/39.29    (7)  op(e1, e1) = e1
% 227.67/39.29    (8)   ~ (e1 = e0)
% 227.67/39.29  
% 227.67/39.29  Begin of proof
% 227.67/39.29  | 
% 227.67/39.29  | BETA: splitting (3) gives:
% 227.67/39.29  | 
% 227.67/39.29  | Case 1:
% 227.67/39.29  | | 
% 227.67/39.29  | |   (9)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 227.67/39.29  | |        op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 227.67/39.29  | |        op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3,
% 227.67/39.29  | |          e3) = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 &
% 227.67/39.29  | |        op(e3, e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 227.67/39.29  | |        $i(all_52_7)
% 227.67/39.29  | | 
% 227.67/39.29  | | REF_CLOSE: (1), (2), (4), (5), (9) are inconsistent by sub-proof #360.
% 227.67/39.29  | | 
% 227.67/39.29  | Case 2:
% 227.67/39.29  | | 
% 227.67/39.29  | |   (10)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0 &
% 227.67/39.29  | |         op(all_52_9, all_52_9) = e3 & op(all_52_11, all_52_11) = e2 &
% 227.67/39.29  | |         op(all_52_13, all_52_13) = e1 & op(all_52_15, all_52_15) = e0 &
% 227.67/39.29  | |         op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 & op(e2, e1) =
% 227.67/39.29  | |         all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) & $i(all_52_11) &
% 227.67/39.29  | |         $i(all_52_13) & $i(all_52_15)
% 227.67/39.29  | | 
% 227.67/39.29  | | ALPHA: (10) implies:
% 227.67/39.29  | |   (11)  op(e2, e0) = all_52_15
% 227.67/39.29  | |   (12)  op(all_52_15, all_52_15) = e0
% 227.67/39.29  | | 
% 227.67/39.29  | | GROUND_INST: instantiating (2) with e1, all_52_15, e0, e2, simplifying with
% 227.67/39.29  | |              (6), (11) gives:
% 227.67/39.29  | |   (13)  all_52_15 = e1
% 227.67/39.29  | | 
% 227.67/39.29  | | REDUCE: (12), (13) imply:
% 227.67/39.29  | |   (14)  op(e1, e1) = e0
% 227.67/39.29  | | 
% 227.67/39.29  | | REF_CLOSE: (2), (7), (8), (14) are inconsistent by sub-proof #2427.
% 227.67/39.29  | | 
% 227.67/39.29  | End of split
% 227.67/39.29  | 
% 227.67/39.29  End of proof
% 227.67/39.29  
% 227.67/39.29  Sub-proof #360 shows that the following formulas are inconsistent:
% 227.67/39.29  ----------------------------------------------------------------
% 227.67/39.29    (1)  op(e3, e3) = e1
% 227.67/39.29    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.67/39.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.67/39.29    (3)   ~ (all_6_2 = e3)
% 227.67/39.29    (4)  op(e1, e1) = all_6_2
% 227.67/39.29    (5)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 227.67/39.29         op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 227.67/39.29           all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3) = all_52_1 &
% 227.67/39.29         op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 227.67/39.29         $i(all_52_1) & $i(all_52_3) & $i(all_52_5) & $i(all_52_7)
% 227.67/39.29  
% 227.67/39.29  Begin of proof
% 227.67/39.29  | 
% 227.67/39.29  | ALPHA: (5) implies:
% 227.67/39.29  |   (6)  op(e3, e3) = all_52_1
% 227.67/39.29  |   (7)  op(all_52_1, all_52_1) = e3
% 227.67/39.29  | 
% 227.67/39.29  | GROUND_INST: instantiating (2) with e1, all_52_1, e3, e3, simplifying with
% 227.67/39.29  |              (1), (6) gives:
% 227.67/39.29  |   (8)  all_52_1 = e1
% 227.67/39.29  | 
% 227.67/39.29  | REDUCE: (7), (8) imply:
% 227.67/39.29  |   (9)  op(e1, e1) = e3
% 227.67/39.29  | 
% 227.67/39.29  | REF_CLOSE: (2), (3), (4), (9) are inconsistent by sub-proof #2468.
% 227.67/39.29  | 
% 227.67/39.29  End of proof
% 227.67/39.29  
% 227.67/39.29  Sub-proof #361 shows that the following formulas are inconsistent:
% 227.67/39.29  ----------------------------------------------------------------
% 227.67/39.29    (1)  op(e2, e3) = all_53_1
% 227.67/39.29    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.67/39.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.67/39.29    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1)
% 227.67/39.29    (4)   ~ (all_53_1 = e1)
% 227.67/39.29    (5)  op(e2, e2) = e2
% 227.67/39.29    (6)   ~ (e2 = e1)
% 227.67/39.29  
% 227.67/39.29  Begin of proof
% 227.67/39.29  | 
% 227.67/39.29  | BETA: splitting (3) gives:
% 227.67/39.29  | 
% 227.67/39.29  | Case 1:
% 227.67/39.29  | | 
% 227.67/39.29  | |   (7)  all_57_2 = e1 & op(e2, e3) = e1
% 227.67/39.29  | | 
% 227.67/39.29  | | REF_CLOSE: (1), (2), (4), (7) are inconsistent by sub-proof #2156.
% 227.67/39.29  | | 
% 227.67/39.29  | Case 2:
% 227.67/39.29  | | 
% 227.67/39.29  | |   (8)  all_57_3 = e1 & op(e2, e2) = e1
% 227.67/39.29  | | 
% 227.67/39.29  | | ALPHA: (8) implies:
% 227.67/39.29  | |   (9)  op(e2, e2) = e1
% 227.67/39.29  | | 
% 227.67/39.29  | | REF_CLOSE: (2), (5), (6), (9) are inconsistent by sub-proof #2306.
% 227.67/39.29  | | 
% 227.67/39.29  | End of split
% 227.67/39.29  | 
% 227.67/39.29  End of proof
% 227.67/39.29  
% 227.67/39.29  Sub-proof #362 shows that the following formulas are inconsistent:
% 227.67/39.29  ----------------------------------------------------------------
% 227.67/39.30    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.67/39.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.67/39.30    (2)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1)
% 227.67/39.30    (3)   ~ (all_53_4 = e1)
% 227.67/39.30    (4)  op(e3, e2) = all_53_4
% 227.67/39.30    (5)  op(e2, e2) = e2
% 227.67/39.30    (6)   ~ (e2 = e1)
% 227.67/39.30  
% 227.67/39.30  Begin of proof
% 227.67/39.30  | 
% 227.67/39.30  | BETA: splitting (2) gives:
% 227.67/39.30  | 
% 227.67/39.30  | Case 1:
% 227.67/39.30  | | 
% 227.67/39.30  | |   (7)  all_57_1 = e1 & op(e3, e2) = e1
% 227.67/39.30  | | 
% 227.67/39.30  | | ALPHA: (7) implies:
% 227.67/39.30  | |   (8)  op(e3, e2) = e1
% 227.67/39.30  | | 
% 227.67/39.30  | | REF_CLOSE: (1), (3), (4), (8) are inconsistent by sub-proof #363.
% 227.67/39.30  | | 
% 227.67/39.30  | Case 2:
% 227.67/39.30  | | 
% 227.67/39.30  | |   (9)  all_57_3 = e1 & op(e2, e2) = e1
% 227.67/39.30  | | 
% 227.67/39.30  | | ALPHA: (9) implies:
% 227.67/39.30  | |   (10)  op(e2, e2) = e1
% 227.67/39.30  | | 
% 227.67/39.30  | | REF_CLOSE: (1), (5), (6), (10) are inconsistent by sub-proof #2306.
% 227.67/39.30  | | 
% 227.67/39.30  | End of split
% 227.67/39.30  | 
% 227.67/39.30  End of proof
% 227.67/39.30  
% 227.67/39.30  Sub-proof #363 shows that the following formulas are inconsistent:
% 227.67/39.30  ----------------------------------------------------------------
% 227.67/39.30    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.67/39.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.67/39.30    (2)  op(e3, e2) = all_53_4
% 227.67/39.30    (3)  op(e3, e2) = e1
% 227.67/39.30    (4)   ~ (all_53_4 = e1)
% 227.67/39.30  
% 227.67/39.30  Begin of proof
% 227.67/39.30  | 
% 227.67/39.30  | GROUND_INST: instantiating (1) with all_53_4, e1, e2, e3, simplifying with
% 227.67/39.30  |              (2), (3) gives:
% 227.67/39.30  |   (5)  all_53_4 = e1
% 227.67/39.30  | 
% 227.67/39.30  | REDUCE: (4), (5) imply:
% 227.67/39.30  |   (6)  $false
% 227.67/39.30  | 
% 227.67/39.30  | CLOSE: (6) is inconsistent.
% 227.67/39.30  | 
% 227.67/39.30  End of proof
% 227.67/39.30  
% 227.67/39.30  Sub-proof #364 shows that the following formulas are inconsistent:
% 227.67/39.30  ----------------------------------------------------------------
% 227.67/39.30    (1)  all_57_7 = e2 & op(e1, e2) = e2
% 227.67/39.30    (2)  all_57_7 = e0
% 227.67/39.30    (3)   ~ (e2 = e0)
% 227.67/39.30  
% 227.67/39.30  Begin of proof
% 227.67/39.30  | 
% 227.67/39.30  | ALPHA: (1) implies:
% 227.67/39.30  |   (4)  all_57_7 = e2
% 227.67/39.30  | 
% 227.67/39.30  | COMBINE_EQS: (2), (4) imply:
% 227.67/39.30  |   (5)  e2 = e0
% 227.67/39.30  | 
% 227.67/39.30  | REDUCE: (3), (5) imply:
% 227.67/39.30  |   (6)  $false
% 227.67/39.30  | 
% 227.67/39.30  | CLOSE: (6) is inconsistent.
% 227.67/39.30  | 
% 227.67/39.30  End of proof
% 227.67/39.30  
% 227.67/39.30  Sub-proof #365 shows that the following formulas are inconsistent:
% 227.67/39.30  ----------------------------------------------------------------
% 227.67/39.30    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 227.67/39.30         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 227.67/39.30    (2)   ~ (e3 = e1)
% 227.67/39.30    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.67/39.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.67/39.30    (4)  all_57_12 = e2
% 227.67/39.30    (5)  op(e2, e2) = e0
% 227.67/39.30    (6)   ~ (e3 = e2)
% 227.67/39.30    (7)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 227.67/39.30         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 227.67/39.30    (8)  all_57_5 = e3
% 227.67/39.30    (9)   ~ (e2 = e0)
% 227.67/39.30    (10)  op(e2, e2) = e2
% 227.67/39.30    (11)   ~ (e1 = e0)
% 227.67/39.30    (12)  op(e0, e0) = e3
% 227.67/39.30    (13)  all_57_2 = e0
% 227.67/39.30    (14)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 227.67/39.30          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 227.67/39.30    (15)   ~ (e2 = e1)
% 227.67/39.30    (16)  all_57_14 = e0
% 227.67/39.30    (17)  all_57_3 = e2
% 227.67/39.30  
% 227.67/39.30  Begin of proof
% 227.67/39.30  | 
% 227.67/39.30  | BETA: splitting (7) gives:
% 227.67/39.30  | 
% 227.67/39.30  | Case 1:
% 227.67/39.30  | | 
% 227.67/39.30  | |   (18)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 227.67/39.30  | |           e1)
% 227.67/39.30  | | 
% 227.67/39.30  | | BETA: splitting (18) gives:
% 227.67/39.30  | | 
% 227.67/39.30  | | Case 1:
% 227.67/39.30  | | | 
% 227.67/39.30  | | |   (19)  all_57_12 = e1 & op(e0, e3) = e1
% 227.67/39.30  | | | 
% 227.67/39.30  | | | REF_CLOSE: (4), (15), (19) are inconsistent by sub-proof #2388.
% 227.67/39.30  | | | 
% 227.67/39.30  | | Case 2:
% 227.67/39.30  | | | 
% 227.67/39.30  | | | 
% 227.67/39.30  | | | GROUND_INST: instantiating (3) with e0, e2, e2, e2, simplifying with (5),
% 227.67/39.30  | | |              (10) gives:
% 227.67/39.30  | | |   (20)  e2 = e0
% 227.67/39.30  | | | 
% 227.67/39.30  | | | COMBINE_EQS: (17), (20) imply:
% 227.67/39.30  | | |   (21)  all_57_3 = e0
% 227.67/39.30  | | | 
% 227.67/39.30  | | | REF_CLOSE: (1), (2), (6), (8), (9), (11), (13), (14), (15), (21) are
% 227.67/39.30  | | |            inconsistent by sub-proof #2253.
% 227.67/39.30  | | | 
% 227.67/39.30  | | End of split
% 227.67/39.30  | | 
% 227.67/39.30  | Case 2:
% 227.67/39.30  | | 
% 227.67/39.30  | |   (22)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 227.67/39.30  | |           e1)
% 227.67/39.30  | | 
% 227.67/39.30  | | BETA: splitting (22) gives:
% 227.67/39.30  | | 
% 227.67/39.30  | | Case 1:
% 227.67/39.30  | | | 
% 227.67/39.30  | | |   (23)  all_57_14 = e1 & op(e0, e1) = e1
% 227.67/39.30  | | | 
% 227.67/39.30  | | | REF_CLOSE: (11), (16), (23) are inconsistent by sub-proof #2381.
% 227.67/39.30  | | | 
% 227.67/39.30  | | Case 2:
% 227.67/39.30  | | | 
% 227.67/39.30  | | |   (24)  all_57_15 = e1 & op(e0, e0) = e1
% 227.67/39.30  | | | 
% 227.67/39.30  | | | ALPHA: (24) implies:
% 227.67/39.30  | | |   (25)  op(e0, e0) = e1
% 227.67/39.30  | | | 
% 227.67/39.30  | | | REF_CLOSE: (2), (3), (12), (25) are inconsistent by sub-proof #2183.
% 227.67/39.30  | | | 
% 227.67/39.30  | | End of split
% 227.67/39.30  | | 
% 227.67/39.30  | End of split
% 227.67/39.30  | 
% 227.67/39.30  End of proof
% 227.67/39.30  
% 227.67/39.30  Sub-proof #366 shows that the following formulas are inconsistent:
% 227.67/39.30  ----------------------------------------------------------------
% 227.67/39.30    (1)   ~ (e3 = e1)
% 227.67/39.30    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.67/39.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.67/39.30    (3)   ~ (e3 = e2)
% 227.67/39.30    (4)   ~ (e3 = e0)
% 227.67/39.30    (5)  all_57_15 = e3
% 227.67/39.30    (6)   ~ (all_53_7 = e0)
% 227.67/39.30    (7)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 227.67/39.30         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 227.67/39.30    (8)   ~ (e2 = e0)
% 227.67/39.30    (9)   ~ (e1 = e0)
% 227.67/39.30    (10)  all_57_13 = e3
% 227.67/39.30    (11)  op(e0, e0) = e3
% 227.67/39.30    (12)  op(e0, e2) = all_53_7
% 227.67/39.30    (13)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.67/39.30          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 227.67/39.30            e2)
% 227.67/39.30    (14)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 227.67/39.30              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 227.67/39.30                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 227.67/39.30                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 227.67/39.30    (15)   ~ (e2 = e1)
% 227.67/39.30  
% 227.67/39.30  Begin of proof
% 227.67/39.30  | 
% 227.67/39.30  | BETA: splitting (14) gives:
% 227.67/39.30  | 
% 227.67/39.30  | Case 1:
% 227.67/39.30  | | 
% 227.67/39.30  | |   (16)  all_57_15 = e0 & op(e0, e0) = e0
% 227.67/39.30  | | 
% 227.67/39.30  | | ALPHA: (16) implies:
% 227.67/39.30  | |   (17)  op(e0, e0) = e0
% 227.67/39.30  | | 
% 227.67/39.30  | | REF_CLOSE: (2), (4), (11), (17) are inconsistent by sub-proof #2304.
% 227.67/39.30  | | 
% 227.67/39.30  | Case 2:
% 227.67/39.30  | | 
% 227.67/39.30  | |   (18)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 227.67/39.30  | |             e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0 &
% 227.67/39.30  | |             op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 227.67/39.30  | |           (all_57_14 = e0 & op(e0, e1) = e0))
% 227.67/39.30  | | 
% 227.67/39.30  | | ALPHA: (18) implies:
% 227.67/39.30  | |   (19)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 227.67/39.30  | |           e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 227.67/39.30  | | 
% 227.67/39.30  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 227.67/39.30  | |            (13), (15), (19) are inconsistent by sub-proof #372.
% 227.67/39.30  | | 
% 227.67/39.30  | End of split
% 227.67/39.30  | 
% 227.67/39.30  End of proof
% 227.67/39.30  
% 227.67/39.30  Sub-proof #367 shows that the following formulas are inconsistent:
% 227.67/39.30  ----------------------------------------------------------------
% 227.67/39.30    (1)   ~ (e3 = e1)
% 227.67/39.30    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.67/39.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.67/39.30    (3)  all_57_9 = e1
% 227.67/39.30    (4)   ~ (e3 = e2)
% 227.67/39.30    (5)  all_57_15 = e3
% 227.67/39.30    (6)  op(e3, e3) = e2
% 227.67/39.30    (7)  all_57_11 = e0
% 227.67/39.30    (8)   ~ (e2 = e0)
% 227.67/39.30    (9)   ~ (e1 = e0)
% 227.67/39.30    (10)  all_57_2 = e1
% 227.67/39.30    (11)   ~ (e2 = e1)
% 227.67/39.30    (12)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 227.67/39.30          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 227.67/39.30    (13)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 227.67/39.30          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 227.67/39.30    (14)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0)
% 227.67/39.30  
% 227.67/39.30  Begin of proof
% 227.67/39.30  | 
% 227.67/39.30  | BETA: splitting (14) gives:
% 227.67/39.30  | 
% 227.67/39.30  | Case 1:
% 227.67/39.30  | | 
% 227.67/39.30  | |   (15)  all_57_0 = e0 & op(e3, e3) = e0
% 227.67/39.30  | | 
% 227.67/39.30  | | ALPHA: (15) implies:
% 227.67/39.30  | |   (16)  op(e3, e3) = e0
% 227.67/39.30  | | 
% 227.67/39.30  | | REF_CLOSE: (2), (6), (8), (16) are inconsistent by sub-proof #2403.
% 227.67/39.30  | | 
% 227.67/39.30  | Case 2:
% 227.67/39.30  | | 
% 227.67/39.30  | |   (17)  all_57_2 = e0 & op(e2, e3) = e0
% 227.67/39.30  | | 
% 227.67/39.30  | | ALPHA: (17) implies:
% 227.67/39.30  | |   (18)  all_57_2 = e0
% 227.67/39.30  | | 
% 227.67/39.30  | | COMBINE_EQS: (10), (18) imply:
% 227.67/39.30  | |   (19)  e1 = e0
% 227.67/39.30  | | 
% 227.67/39.30  | | SIMP: (19) implies:
% 227.67/39.30  | |   (20)  e1 = e0
% 227.67/39.30  | | 
% 227.67/39.30  | | COMBINE_EQS: (3), (20) imply:
% 227.67/39.30  | |   (21)  all_57_9 = e0
% 227.67/39.30  | | 
% 227.67/39.30  | | REF_CLOSE: (1), (4), (5), (7), (8), (9), (11), (12), (13), (21) are
% 227.67/39.30  | |            inconsistent by sub-proof #1144.
% 227.67/39.30  | | 
% 227.67/39.30  | End of split
% 227.67/39.30  | 
% 227.67/39.30  End of proof
% 227.67/39.30  
% 227.67/39.30  Sub-proof #368 shows that the following formulas are inconsistent:
% 227.67/39.30  ----------------------------------------------------------------
% 227.67/39.30    (1)  all_57_9 = e2
% 227.67/39.30    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 227.67/39.30         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.67/39.30    (3)   ~ (e3 = e1)
% 227.67/39.30    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.67/39.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.67/39.30    (5)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 227.67/39.30         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 227.67/39.30    (6)   ~ (all_6_2 = e3)
% 227.67/39.30    (7)  all_57_9 = e2 & op(e3, e0) = e2
% 227.67/39.30    (8)  op(e1, e1) = all_6_2
% 227.67/39.30    (9)  all_57_3 = e3
% 227.67/39.30    (10)  op(e2, e2) = e0
% 227.67/39.30    (11)   ~ (e3 = e2)
% 227.67/39.30    (12)   ~ (e3 = e0)
% 227.67/39.30    (13)  all_57_1 = e0
% 227.67/39.30    (14)  all_57_0 = e1
% 227.67/39.30    (15)  all_57_15 = e3
% 227.67/39.30    (16)   ~ (all_53_7 = e0)
% 227.67/39.30    (17)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 227.67/39.30          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 227.67/39.30            e1)
% 227.67/39.30    (18)   ~ (e2 = e0)
% 227.67/39.30    (19)   ~ (e1 = e0)
% 227.67/39.30    (20)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 227.67/39.30          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 227.67/39.30    (21)  op(e0, e0) = e3
% 227.67/39.30    (22)  op(e0, e2) = all_53_7
% 227.67/39.30    (23)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.67/39.30          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 227.67/39.30            e2)
% 227.67/39.30    (24)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 227.67/39.30              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 227.67/39.30                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 227.67/39.30                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 227.67/39.30    (25)   ~ (all_53_13 = e0)
% 227.67/39.30    (26)  op(e2, e0) = all_53_13
% 227.67/39.30    (27)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 227.67/39.30          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 227.67/39.30    (28)  op(e2, e2) = e3
% 227.67/39.30    (29)   ~ (e2 = e1)
% 227.67/39.30    (30)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 227.67/39.30          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 227.67/39.30    (31)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 227.67/39.30          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 227.67/39.30    (32)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 227.67/39.30          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 227.67/39.30    (33)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 227.67/39.30          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 227.67/39.30    (34)  all_57_5 = e0
% 227.67/39.30  
% 227.67/39.30  Begin of proof
% 227.67/39.30  | 
% 227.67/39.30  | BETA: splitting (24) gives:
% 227.67/39.30  | 
% 227.67/39.30  | Case 1:
% 227.67/39.30  | | 
% 227.67/39.30  | |   (35)  all_57_15 = e0 & op(e0, e0) = e0
% 227.67/39.30  | | 
% 227.67/39.30  | | ALPHA: (35) implies:
% 227.67/39.30  | |   (36)  op(e0, e0) = e0
% 227.67/39.30  | | 
% 227.67/39.30  | | REF_CLOSE: (4), (12), (21), (36) are inconsistent by sub-proof #2304.
% 227.67/39.30  | | 
% 227.67/39.30  | Case 2:
% 227.67/39.30  | | 
% 227.67/39.30  | |   (37)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 227.67/39.30  | |             e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0 &
% 227.67/39.30  | |             op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 227.67/39.30  | |           (all_57_14 = e0 & op(e0, e1) = e0))
% 227.67/39.30  | | 
% 227.67/39.30  | | ALPHA: (37) implies:
% 227.67/39.30  | |   (38)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 227.67/39.30  | |           e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 227.67/39.30  | |   (39)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 227.67/39.30  | |           e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 227.67/39.30  | | 
% 227.67/39.30  | | BETA: splitting (39) gives:
% 227.67/39.30  | | 
% 227.67/39.30  | | Case 1:
% 227.67/39.30  | | | 
% 227.67/39.30  | | |   (40)  all_57_9 = e0 & op(e3, e0) = e0
% 227.67/39.30  | | | 
% 227.67/39.30  | | | ALPHA: (40) implies:
% 227.67/39.30  | | |   (41)  all_57_9 = e0
% 227.67/39.30  | | | 
% 227.67/39.30  | | | REF_CLOSE: (1), (18), (41) are inconsistent by sub-proof #2440.
% 227.67/39.30  | | | 
% 227.67/39.30  | | Case 2:
% 227.67/39.30  | | | 
% 227.67/39.30  | | |   (42)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 227.67/39.30  | | |           = e0)
% 227.67/39.30  | | | 
% 227.67/39.30  | | | BETA: splitting (42) gives:
% 227.67/39.30  | | | 
% 227.67/39.30  | | | Case 1:
% 227.67/39.30  | | | | 
% 227.67/39.30  | | | |   (43)  all_57_10 = e0 & op(e2, e0) = e0
% 227.67/39.30  | | | | 
% 227.67/39.30  | | | | ALPHA: (43) implies:
% 227.67/39.30  | | | |   (44)  op(e2, e0) = e0
% 227.67/39.30  | | | | 
% 227.67/39.30  | | | | REF_CLOSE: (4), (25), (26), (44) are inconsistent by sub-proof #2470.
% 227.67/39.30  | | | | 
% 227.67/39.30  | | | Case 2:
% 227.67/39.30  | | | | 
% 227.67/39.30  | | | |   (45)  all_57_11 = e0 & op(e1, e0) = e0
% 227.67/39.30  | | | | 
% 227.67/39.30  | | | | ALPHA: (45) implies:
% 227.67/39.30  | | | |   (46)  all_57_11 = e0
% 227.67/39.30  | | | | 
% 227.67/39.30  | | | | BETA: splitting (32) gives:
% 227.67/39.30  | | | | 
% 227.67/39.30  | | | | Case 1:
% 227.67/39.30  | | | | | 
% 227.67/39.30  | | | | |   (47)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2,
% 227.67/39.30  | | | | |             e0) = e1)
% 227.67/39.30  | | | | | 
% 227.67/39.30  | | | | | BETA: splitting (47) gives:
% 227.67/39.30  | | | | | 
% 227.67/39.30  | | | | | Case 1:
% 227.67/39.30  | | | | | | 
% 227.67/39.30  | | | | | |   (48)  all_57_9 = e1 & op(e3, e0) = e1
% 227.67/39.30  | | | | | | 
% 227.67/39.30  | | | | | | ALPHA: (48) implies:
% 227.67/39.30  | | | | | |   (49)  all_57_9 = e1
% 227.67/39.30  | | | | | | 
% 227.67/39.30  | | | | | | REF_CLOSE: (1), (29), (49) are inconsistent by sub-proof #2444.
% 227.67/39.30  | | | | | | 
% 227.67/39.30  | | | | | Case 2:
% 227.67/39.30  | | | | | | 
% 227.67/39.30  | | | | | |   (50)  all_57_10 = e1 & op(e2, e0) = e1
% 227.67/39.30  | | | | | | 
% 227.67/39.30  | | | | | | ALPHA: (50) implies:
% 227.67/39.30  | | | | | |   (51)  all_57_10 = e1
% 227.67/39.30  | | | | | | 
% 227.67/39.30  | | | | | | BETA: splitting (27) gives:
% 227.67/39.30  | | | | | | 
% 227.67/39.30  | | | | | | Case 1:
% 227.67/39.30  | | | | | | | 
% 227.67/39.30  | | | | | | |   (52)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 &
% 227.67/39.30  | | | | | | |           op(e2, e2) = e2)
% 227.67/39.30  | | | | | | | 
% 227.67/39.30  | | | | | | | BETA: splitting (52) gives:
% 227.67/39.30  | | | | | | | 
% 227.67/39.30  | | | | | | | Case 1:
% 227.67/39.30  | | | | | | | | 
% 227.67/39.30  | | | | | | | |   (53)  all_57_2 = e2 & op(e2, e3) = e2
% 227.67/39.30  | | | | | | | | 
% 227.67/39.30  | | | | | | | | ALPHA: (53) implies:
% 227.67/39.30  | | | | | | | |   (54)  all_57_2 = e2
% 227.67/39.30  | | | | | | | | 
% 227.67/39.30  | | | | | | | | BETA: splitting (31) gives:
% 227.67/39.30  | | | | | | | | 
% 227.67/39.30  | | | | | | | | Case 1:
% 227.67/39.30  | | | | | | | | | 
% 227.67/39.30  | | | | | | | | |   (55)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 &
% 227.67/39.30  | | | | | | | | |           op(e2, e3) = e0)
% 227.67/39.30  | | | | | | | | | 
% 227.67/39.30  | | | | | | | | | BETA: splitting (55) gives:
% 227.67/39.30  | | | | | | | | | 
% 227.67/39.30  | | | | | | | | | Case 1:
% 227.67/39.30  | | | | | | | | | | 
% 227.67/39.30  | | | | | | | | | |   (56)  all_57_0 = e0 & op(e3, e3) = e0
% 227.67/39.30  | | | | | | | | | | 
% 227.67/39.30  | | | | | | | | | | REF_CLOSE: (14), (19), (56) are inconsistent by sub-proof
% 227.67/39.30  | | | | | | | | | |            #1812.
% 227.67/39.30  | | | | | | | | | | 
% 227.67/39.30  | | | | | | | | | Case 2:
% 227.67/39.30  | | | | | | | | | | 
% 227.67/39.30  | | | | | | | | | |   (57)  all_57_2 = e0 & op(e2, e3) = e0
% 227.67/39.30  | | | | | | | | | | 
% 227.67/39.30  | | | | | | | | | | ALPHA: (57) implies:
% 227.67/39.30  | | | | | | | | | |   (58)  all_57_2 = e0
% 227.67/39.30  | | | | | | | | | | 
% 227.67/39.30  | | | | | | | | | | COMBINE_EQS: (54), (58) imply:
% 227.67/39.30  | | | | | | | | | |   (59)  e2 = e0
% 227.67/39.30  | | | | | | | | | | 
% 227.67/39.30  | | | | | | | | | | SIMP: (59) implies:
% 227.67/39.30  | | | | | | | | | |   (60)  e2 = e0
% 227.67/39.30  | | | | | | | | | | 
% 227.67/39.30  | | | | | | | | | | COMBINE_EQS: (1), (60) imply:
% 227.67/39.30  | | | | | | | | | |   (61)  all_57_9 = e0
% 227.67/39.30  | | | | | | | | | | 
% 227.67/39.30  | | | | | | | | | | REF_CLOSE: (11), (15), (18), (29), (30), (46), (51), (61) are
% 227.67/39.30  | | | | | | | | | |            inconsistent by sub-proof #1145.
% 227.67/39.30  | | | | | | | | | | 
% 227.67/39.30  | | | | | | | | | End of split
% 227.67/39.30  | | | | | | | | | 
% 227.67/39.30  | | | | | | | | Case 2:
% 227.67/39.30  | | | | | | | | | 
% 227.67/39.30  | | | | | | | | |   (62)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 &
% 227.67/39.30  | | | | | | | | |           op(e0, e3) = e0)
% 227.67/39.30  | | | | | | | | | 
% 227.67/39.30  | | | | | | | | | BETA: splitting (62) gives:
% 227.67/39.30  | | | | | | | | | 
% 227.67/39.30  | | | | | | | | | Case 1:
% 227.67/39.30  | | | | | | | | | | 
% 227.67/39.30  | | | | | | | | | |   (63)  all_57_6 = e0 & op(e1, e3) = e0
% 227.67/39.30  | | | | | | | | | | 
% 227.67/39.30  | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (9), (10), (11),
% 227.67/39.30  | | | | | | | | | |            (12), (13), (15), (16), (17), (18), (19), (20),
% 227.67/39.30  | | | | | | | | | |            (21), (22), (23), (29), (30), (32), (33), (38),
% 227.67/39.30  | | | | | | | | | |            (39), (63) are inconsistent by sub-proof #369.
% 227.67/39.30  | | | | | | | | | | 
% 227.67/39.30  | | | | | | | | | Case 2:
% 227.67/39.30  | | | | | | | | | | 
% 227.67/39.30  | | | | | | | | | |   (64)  all_57_12 = e0 & op(e0, e3) = e0
% 227.67/39.30  | | | | | | | | | | 
% 227.67/39.30  | | | | | | | | | | ALPHA: (64) implies:
% 227.67/39.30  | | | | | | | | | |   (65)  all_57_12 = e0
% 227.67/39.30  | | | | | | | | | | 
% 227.67/39.30  | | | | | | | | | | GROUND_INST: instantiating (4) with e0, e3, e2, e2, simplifying
% 227.67/39.30  | | | | | | | | | |              with (10), (28) gives:
% 227.67/39.30  | | | | | | | | | |   (66)  e3 = e0
% 227.67/39.30  | | | | | | | | | | 
% 227.67/39.30  | | | | | | | | | | COMBINE_EQS: (9), (66) imply:
% 227.67/39.30  | | | | | | | | | |   (67)  all_57_3 = e0
% 227.67/39.30  | | | | | | | | | | 
% 227.67/39.30  | | | | | | | | | | BETA: splitting (20) gives:
% 227.67/39.30  | | | | | | | | | | 
% 227.67/39.30  | | | | | | | | | | Case 1:
% 227.67/39.30  | | | | | | | | | | | 
% 227.67/39.30  | | | | | | | | | | |   (68)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 227.67/39.30  | | | | | | | | | | |           & op(e2, e2) = e3)
% 227.67/39.30  | | | | | | | | | | | 
% 227.67/39.30  | | | | | | | | | | | REF_CLOSE: (12), (13), (67), (68) are inconsistent by
% 227.67/39.30  | | | | | | | | | | |            sub-proof #1284.
% 227.67/39.30  | | | | | | | | | | | 
% 227.67/39.30  | | | | | | | | | | Case 2:
% 227.67/39.30  | | | | | | | | | | | 
% 227.67/39.30  | | | | | | | | | | |   (69)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 227.67/39.30  | | | | | | | | | | |           e3 & op(e0, e2) = e3)
% 227.67/39.30  | | | | | | | | | | | 
% 227.67/39.30  | | | | | | | | | | | BETA: splitting (69) gives:
% 227.67/39.30  | | | | | | | | | | | 
% 227.67/39.30  | | | | | | | | | | | Case 1:
% 227.67/39.30  | | | | | | | | | | | | 
% 227.67/39.30  | | | | | | | | | | | |   (70)  all_57_7 = e3 & op(e1, e2) = e3
% 227.67/39.30  | | | | | | | | | | | | 
% 227.67/39.30  | | | | | | | | | | | | ALPHA: (70) implies:
% 227.67/39.30  | | | | | | | | | | | |   (71)  all_57_7 = e3
% 227.67/39.30  | | | | | | | | | | | | 
% 227.67/39.30  | | | | | | | | | | | | REF_CLOSE: (2), (3), (11), (13), (18), (19), (29), (33),
% 227.67/39.30  | | | | | | | | | | | |            (67), (71) are inconsistent by sub-proof #2098.
% 227.67/39.30  | | | | | | | | | | | | 
% 227.67/39.30  | | | | | | | | | | | Case 2:
% 227.67/39.30  | | | | | | | | | | | | 
% 227.67/39.30  | | | | | | | | | | | |   (72)  all_57_13 = e3 & op(e0, e2) = e3
% 227.67/39.30  | | | | | | | | | | | | 
% 227.67/39.30  | | | | | | | | | | | | ALPHA: (72) implies:
% 227.67/39.30  | | | | | | | | | | | |   (73)  all_57_13 = e3
% 227.67/39.30  | | | | | | | | | | | | 
% 227.67/39.30  | | | | | | | | | | | | BETA: splitting (23) gives:
% 227.67/39.30  | | | | | | | | | | | | 
% 227.67/39.30  | | | | | | | | | | | | Case 1:
% 227.67/39.30  | | | | | | | | | | | | | 
% 227.67/39.30  | | | | | | | | | | | | |   (74)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 227.67/39.30  | | | | | | | | | | | | |           e2 & op(e0, e2) = e2)
% 227.67/39.30  | | | | | | | | | | | | | 
% 227.67/39.30  | | | | | | | | | | | | | BETA: splitting (74) gives:
% 227.67/39.30  | | | | | | | | | | | | | 
% 227.67/39.30  | | | | | | | | | | | | | Case 1:
% 227.67/39.30  | | | | | | | | | | | | | | 
% 227.67/39.30  | | | | | | | | | | | | | |   (75)  all_57_12 = e2 & op(e0, e3) = e2
% 227.67/39.30  | | | | | | | | | | | | | | 
% 227.67/39.30  | | | | | | | | | | | | | | ALPHA: (75) implies:
% 227.67/39.30  | | | | | | | | | | | | | |   (76)  all_57_12 = e2
% 227.67/39.30  | | | | | | | | | | | | | | 
% 227.67/39.30  | | | | | | | | | | | | | | COMBINE_EQS: (65), (76) imply:
% 227.67/39.30  | | | | | | | | | | | | | |   (77)  e2 = e0
% 227.67/39.30  | | | | | | | | | | | | | | 
% 227.67/39.30  | | | | | | | | | | | | | | SIMP: (77) implies:
% 227.67/39.30  | | | | | | | | | | | | | |   (78)  e2 = e0
% 227.67/39.30  | | | | | | | | | | | | | | 
% 227.67/39.30  | | | | | | | | | | | | | | COMBINE_EQS: (1), (78) imply:
% 227.67/39.30  | | | | | | | | | | | | | |   (79)  all_57_9 = e0
% 227.67/39.30  | | | | | | | | | | | | | | 
% 227.67/39.30  | | | | | | | | | | | | | | REF_CLOSE: (3), (11), (15), (18), (19), (29), (30), (32),
% 227.67/39.30  | | | | | | | | | | | | | |            (46), (79) are inconsistent by sub-proof #1144.
% 227.67/39.30  | | | | | | | | | | | | | | 
% 227.67/39.30  | | | | | | | | | | | | | Case 2:
% 227.67/39.30  | | | | | | | | | | | | | | 
% 227.67/39.30  | | | | | | | | | | | | | |   (80)  all_57_13 = e2 & op(e0, e2) = e2
% 227.67/39.30  | | | | | | | | | | | | | | 
% 227.67/39.30  | | | | | | | | | | | | | | REF_CLOSE: (11), (73), (80) are inconsistent by sub-proof
% 227.67/39.30  | | | | | | | | | | | | | |            #2146.
% 227.67/39.30  | | | | | | | | | | | | | | 
% 227.67/39.30  | | | | | | | | | | | | | End of split
% 227.67/39.30  | | | | | | | | | | | | | 
% 227.67/39.30  | | | | | | | | | | | | Case 2:
% 227.67/39.30  | | | | | | | | | | | | | 
% 227.67/39.30  | | | | | | | | | | | | |   (81)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 227.67/39.30  | | | | | | | | | | | | |           e2 & op(e0, e0) = e2)
% 227.67/39.30  | | | | | | | | | | | | | 
% 227.67/39.30  | | | | | | | | | | | | | REF_CLOSE: (3), (11), (15), (17), (19), (29), (65), (73),
% 227.67/39.30  | | | | | | | | | | | | |            (81) are inconsistent by sub-proof #2060.
% 227.67/39.30  | | | | | | | | | | | | | 
% 227.67/39.30  | | | | | | | | | | | | End of split
% 227.67/39.30  | | | | | | | | | | | | 
% 227.67/39.30  | | | | | | | | | | | End of split
% 227.67/39.30  | | | | | | | | | | | 
% 227.67/39.30  | | | | | | | | | | End of split
% 227.67/39.30  | | | | | | | | | | 
% 227.67/39.30  | | | | | | | | | End of split
% 227.67/39.30  | | | | | | | | | 
% 227.67/39.30  | | | | | | | | End of split
% 227.67/39.30  | | | | | | | | 
% 227.67/39.30  | | | | | | | Case 2:
% 227.67/39.30  | | | | | | | | 
% 227.67/39.30  | | | | | | | |   (82)  all_57_3 = e2 & op(e2, e2) = e2
% 227.67/39.30  | | | | | | | | 
% 227.67/39.30  | | | | | | | | ALPHA: (82) implies:
% 227.67/39.30  | | | | | | | |   (83)  all_57_3 = e2
% 227.67/39.30  | | | | | | | | 
% 227.67/39.30  | | | | | | | | REF_CLOSE: (9), (11), (83) are inconsistent by sub-proof #1166.
% 227.67/39.30  | | | | | | | | 
% 227.67/39.30  | | | | | | | End of split
% 227.67/39.30  | | | | | | | 
% 227.67/39.30  | | | | | | Case 2:
% 227.67/39.30  | | | | | | | 
% 227.67/39.30  | | | | | | |   (84)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 &
% 227.67/39.30  | | | | | | |           op(e2, e0) = e2)
% 227.67/39.30  | | | | | | | 
% 227.67/39.30  | | | | | | | BETA: splitting (84) gives:
% 227.67/39.30  | | | | | | | 
% 227.67/39.30  | | | | | | | Case 1:
% 227.67/39.30  | | | | | | | | 
% 227.67/39.30  | | | | | | | |   (85)  all_57_5 = e2 & op(e2, e1) = e2
% 227.67/39.30  | | | | | | | | 
% 227.67/39.30  | | | | | | | | ALPHA: (85) implies:
% 227.67/39.30  | | | | | | | |   (86)  all_57_5 = e2
% 227.67/39.30  | | | | | | | | 
% 227.67/39.30  | | | | | | | | COMBINE_EQS: (34), (86) imply:
% 227.67/39.30  | | | | | | | |   (87)  e2 = e0
% 227.67/39.30  | | | | | | | | 
% 227.67/39.30  | | | | | | | | COMBINE_EQS: (1), (87) imply:
% 227.67/39.30  | | | | | | | |   (88)  all_57_9 = e0
% 227.67/39.30  | | | | | | | | 
% 227.67/39.30  | | | | | | | | REF_CLOSE: (11), (15), (18), (29), (30), (46), (51), (88) are
% 227.67/39.30  | | | | | | | |            inconsistent by sub-proof #1145.
% 227.67/39.30  | | | | | | | | 
% 227.67/39.30  | | | | | | | Case 2:
% 227.67/39.30  | | | | | | | | 
% 227.67/39.30  | | | | | | | |   (89)  all_57_10 = e2 & op(e2, e0) = e2
% 227.67/39.30  | | | | | | | | 
% 227.67/39.30  | | | | | | | | REF_CLOSE: (29), (51), (89) are inconsistent by sub-proof #2255.
% 227.67/39.30  | | | | | | | | 
% 227.67/39.30  | | | | | | | End of split
% 227.67/39.30  | | | | | | | 
% 227.67/39.30  | | | | | | End of split
% 227.67/39.30  | | | | | | 
% 227.67/39.30  | | | | | End of split
% 227.67/39.30  | | | | | 
% 227.67/39.30  | | | | Case 2:
% 227.67/39.30  | | | | | 
% 227.67/39.30  | | | | |   (90)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0,
% 227.67/39.30  | | | | |             e0) = e1)
% 227.67/39.30  | | | | | 
% 227.67/39.30  | | | | | REF_CLOSE: (3), (4), (19), (21), (46), (90) are inconsistent by
% 227.67/39.30  | | | | |            sub-proof #1749.
% 227.67/39.30  | | | | | 
% 227.67/39.30  | | | | End of split
% 227.67/39.30  | | | | 
% 227.67/39.30  | | | End of split
% 227.67/39.30  | | | 
% 227.67/39.30  | | End of split
% 227.67/39.30  | | 
% 227.67/39.30  | End of split
% 227.67/39.30  | 
% 227.67/39.30  End of proof
% 227.67/39.30  
% 227.67/39.30  Sub-proof #369 shows that the following formulas are inconsistent:
% 227.67/39.30  ----------------------------------------------------------------
% 227.67/39.30    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 227.67/39.30         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.67/39.30    (2)   ~ (e3 = e1)
% 227.67/39.30    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.67/39.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.67/39.30    (4)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 227.67/39.30         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 227.67/39.30    (5)   ~ (all_6_2 = e3)
% 227.67/39.30    (6)  op(e1, e1) = all_6_2
% 227.67/39.30    (7)  all_57_3 = e3
% 227.67/39.30    (8)  op(e2, e2) = e0
% 227.67/39.30    (9)   ~ (e3 = e2)
% 227.67/39.30    (10)   ~ (e3 = e0)
% 227.67/39.30    (11)  all_57_1 = e0
% 227.67/39.30    (12)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 227.67/39.30          | (all_57_14 = e0 & op(e0, e1) = e0)
% 227.67/39.30    (13)  all_57_15 = e3
% 227.67/39.30    (14)   ~ (all_53_7 = e0)
% 227.67/39.30    (15)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 227.67/39.30          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 227.67/39.30            e1)
% 227.67/39.30    (16)   ~ (e2 = e0)
% 227.67/39.30    (17)   ~ (e1 = e0)
% 227.67/39.30    (18)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 227.67/39.30          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 227.67/39.30    (19)  op(e0, e0) = e3
% 227.67/39.30    (20)  op(e0, e2) = all_53_7
% 227.67/39.30    (21)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.67/39.30          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 227.67/39.30            e2)
% 227.67/39.30    (22)  all_57_6 = e0 & op(e1, e3) = e0
% 227.67/39.30    (23)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) |
% 227.67/39.30          (all_57_11 = e0 & op(e1, e0) = e0)
% 227.67/39.30    (24)   ~ (e2 = e1)
% 227.67/39.30    (25)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 227.67/39.30          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 227.67/39.30    (26)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 227.67/39.30          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 227.67/39.30    (27)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 227.67/39.30          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 227.67/39.30  
% 227.67/39.30  Begin of proof
% 227.67/39.30  | 
% 227.67/39.30  | ALPHA: (22) implies:
% 227.67/39.30  |   (28)  all_57_6 = e0
% 227.67/39.30  | 
% 227.67/39.30  | BETA: splitting (4) gives:
% 227.67/39.30  | 
% 227.67/39.30  | Case 1:
% 227.67/39.30  | | 
% 227.67/39.30  | |   (29)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 227.67/39.30  | |           e3)
% 227.67/39.30  | | 
% 227.67/39.30  | | BETA: splitting (29) gives:
% 227.67/39.30  | | 
% 227.67/39.30  | | Case 1:
% 227.67/39.30  | | | 
% 227.67/39.30  | | |   (30)  all_57_6 = e3 & op(e1, e3) = e3
% 227.67/39.30  | | | 
% 227.67/39.30  | | | ALPHA: (30) implies:
% 227.67/39.30  | | |   (31)  all_57_6 = e3
% 227.67/39.30  | | | 
% 227.67/39.30  | | | COMBINE_EQS: (28), (31) imply:
% 227.67/39.30  | | |   (32)  e3 = e0
% 227.67/39.30  | | | 
% 227.67/39.30  | | | COMBINE_EQS: (7), (32) imply:
% 227.67/39.30  | | |   (33)  all_57_3 = e0
% 227.67/39.30  | | | 
% 227.67/39.30  | | | REF_CLOSE: (1), (2), (3), (9), (10), (11), (12), (13), (14), (15), (16),
% 227.67/39.30  | | |            (17), (18), (19), (20), (21), (24), (27), (33) are inconsistent
% 227.67/39.30  | | |            by sub-proof #371.
% 227.67/39.30  | | | 
% 227.67/39.30  | | Case 2:
% 227.67/39.30  | | | 
% 227.67/39.30  | | |   (34)  all_57_7 = e3 & op(e1, e2) = e3
% 227.67/39.30  | | | 
% 227.67/39.30  | | | ALPHA: (34) implies:
% 227.67/39.30  | | |   (35)  all_57_7 = e3
% 227.67/39.30  | | | 
% 227.67/39.30  | | | REF_CLOSE: (1), (2), (3), (8), (9), (11), (16), (17), (24), (27), (35) are
% 227.67/39.30  | | |            inconsistent by sub-proof #1282.
% 227.67/39.30  | | | 
% 227.67/39.30  | | End of split
% 227.67/39.30  | | 
% 227.67/39.30  | Case 2:
% 227.67/39.30  | | 
% 227.67/39.30  | |   (36)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 227.67/39.30  | |           e3)
% 227.67/39.30  | | 
% 227.67/39.30  | | REF_CLOSE: (2), (3), (5), (6), (9), (10), (13), (16), (17), (23), (24),
% 227.67/39.30  | |            (25), (26), (36) are inconsistent by sub-proof #1080.
% 227.67/39.30  | | 
% 227.67/39.30  | End of split
% 227.67/39.30  | 
% 227.67/39.30  End of proof
% 227.67/39.30  
% 227.67/39.30  Sub-proof #370 shows that the following formulas are inconsistent:
% 227.67/39.30  ----------------------------------------------------------------
% 227.67/39.30    (1)  all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 227.67/39.30    (2)  op(e3, e3) = all_10_2
% 227.67/39.30    (3)   ~ (all_53_7 = e3)
% 227.67/39.30    (4)  all_28_2 = all_10_2
% 227.67/39.30    (5)  op(e0, e1) = all_53_11
% 227.67/39.30    (6)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 227.67/39.30    (7)   ~ (all_20_2 = e2) | ( ~ (all_20_0 = e1) & op(all_20_1, e3) = all_20_0 &
% 227.67/39.30           op(e3, e2) = all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 =
% 227.67/39.30             e0) & op(e3, e2) = all_20_1 & $i(all_20_1))
% 227.67/39.30    (8)   ~ (all_53_3 = all_10_2)
% 227.67/39.30    (9)   ~ (all_53_6 = all_53_14)
% 227.67/39.30    (10)   ~ (all_53_1 = all_10_2)
% 227.67/39.30    (11)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 227.67/39.30    (12)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 227.67/39.30          (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 227.67/39.31    (13)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 227.67/39.31          (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 227.67/39.31    (14)   ~ (all_53_8 = all_53_12)
% 227.67/39.31    (15)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 227.67/39.31          (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.67/39.31    (16)   ~ (all_53_8 = all_53_11)
% 227.67/39.31    (17)   ~ (e3 = e1)
% 227.67/39.31    (18)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 227.67/39.31          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 227.67/39.31    (19)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.67/39.31            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.67/39.31    (20)  all_55_0 = all_10_2
% 227.67/39.31    (21)  all_22_2 = e3
% 227.67/39.31    (22)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 227.67/39.31          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 227.67/39.31    (23)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 227.67/39.31            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 227.67/39.31              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 227.67/39.31    (24)   ~ (all_53_3 = e3)
% 227.67/39.31    (25)   ~ (all_53_3 = all_53_7)
% 227.67/39.31    (26)   ~ (all_6_2 = e3)
% 227.67/39.31    (27)  op(e1, e1) = all_6_2
% 227.67/39.31    (28)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 227.67/39.31    (29)   ~ (all_53_1 = all_53_9)
% 227.67/39.31    (30)   ~ (all_53_9 = e0)
% 227.67/39.31    (31)  all_55_0 = e3 | all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 227.67/39.31    (32)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 227.67/39.31    (33)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 227.67/39.31          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 227.67/39.31    (34)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 227.67/39.31    (35)  all_55_9 = all_53_6
% 227.67/39.31    (36)   ~ (all_53_11 = all_6_2)
% 227.67/39.31    (37)   ~ (all_18_2 = e0) | ( ~ (all_18_0 = e1) & op(all_18_1, e3) = all_18_0 &
% 227.67/39.31            op(e3, e0) = all_18_1 & $i(all_18_0) & $i(all_18_1)) | ( ~ (all_18_1 =
% 227.67/39.31              e2) & op(e3, e0) = all_18_1 & $i(all_18_1))
% 227.67/39.31    (38)   ~ (all_53_4 = all_53_12)
% 227.67/39.31    (39)   ~ (all_53_2 = all_6_2)
% 227.67/39.31    (40)   ~ (all_53_13 = e3)
% 227.67/39.31    (41)   ~ (all_53_8 = all_53_9)
% 227.67/39.31    (42)   ~ (all_28_2 = e2) | ( ~ (all_28_0 = e0) & op(all_28_1, e3) = all_28_0 &
% 227.67/39.31            op(e3, e2) = all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 =
% 227.67/39.31              e1) & op(e3, e2) = all_28_1 & $i(all_28_1))
% 227.67/39.31    (43)  all_42_2 = all_6_2
% 227.67/39.31    (44)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 227.67/39.31          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 227.67/39.31    (45)  op(e2, e2) = e0
% 227.67/39.31    (46)   ~ (all_53_9 = all_53_11)
% 227.67/39.31    (47)  all_55_4 = all_53_1
% 227.67/39.31    (48)   ~ (all_53_9 = all_6_2)
% 227.67/39.31    (49)   ~ (all_53_12 = all_53_13)
% 227.67/39.31    (50)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 227.67/39.31          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 227.67/39.31    (51)   ~ (all_53_14 = all_6_2)
% 227.67/39.31    (52)  all_57_3 = e0
% 227.67/39.31    (53)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 227.67/39.31          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 227.67/39.31    (54)   ~ (e3 = e2)
% 227.67/39.31    (55)   ~ (all_53_4 = all_10_2)
% 227.67/39.31    (56)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 227.67/39.31    (57)  all_55_1 = all_53_4
% 227.67/39.31    (58)   ~ (all_53_1 = all_53_3)
% 227.67/39.31    (59)  op(e1, e0) = all_53_14
% 227.67/39.31    (60)  all_55_7 = e3 | all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 227.67/39.31    (61)   ~ (e3 = e0)
% 227.67/39.31    (62)  all_20_2 = all_10_2
% 227.67/39.31    (63)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 227.67/39.31          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 227.67/39.31    (64)   ~ (all_53_8 = all_6_2)
% 227.67/39.31    (65)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 227.67/39.31    (66)  op(e0, e3) = all_53_3
% 227.67/39.31    (67)  all_55_2 = all_53_8
% 227.67/39.31    (68)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 227.67/39.31    (69)   ~ (all_53_4 = all_53_7)
% 227.67/39.31    (70)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 227.67/39.31    (71)  all_57_15 = e3
% 227.67/39.31    (72)   ~ (all_53_9 = all_53_13)
% 227.67/39.31    (73)   ~ (all_53_7 = e0)
% 227.67/39.31    (74)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 227.67/39.31          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 227.67/39.31            e1)
% 227.67/39.31    (75)   ~ (all_53_4 = all_53_8)
% 227.67/39.31    (76)   ~ (all_53_14 = e3)
% 227.67/39.31    (77)  all_55_6 = all_53_9
% 227.67/39.31    (78)  op(e3, e2) = all_53_4
% 227.67/39.31    (79)   ~ (all_53_1 = all_53_2)
% 227.67/39.31    (80)   ~ (all_53_2 = all_10_2)
% 227.67/39.31    (81)   ~ (e2 = e0)
% 227.67/39.31    (82)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 227.67/39.31            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 227.67/39.31            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 227.67/39.31            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 227.67/39.31              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 227.67/39.31            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 227.67/39.31            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 227.67/39.31              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 227.67/39.31              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 227.67/39.31            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 227.67/39.31            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 227.67/39.31            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 227.67/39.31              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 227.67/39.31              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 227.67/39.31            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 227.67/39.31              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 227.67/39.31            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 227.67/39.31            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 227.67/39.31              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 227.67/39.31              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 227.67/39.31            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 227.67/39.31            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 227.67/39.31    (83)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 227.67/39.31            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 227.67/39.31              e3) = all_12_1 & $i(all_12_1))
% 227.67/39.31    (84)  all_55_12 = all_53_3
% 227.67/39.31    (85)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 227.67/39.31          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 227.67/39.31    (86)   ~ (all_53_1 = e0)
% 227.67/39.31    (87)   ~ (all_53_2 = all_53_14)
% 227.67/39.31    (88)   ~ (e1 = e0)
% 227.67/39.31    (89)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 227.67/39.31            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 227.67/39.31              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 227.67/39.31    (90)   ~ (all_53_3 = all_53_11)
% 227.67/39.31    (91)   ~ (all_53_4 = e0)
% 227.67/39.31    (92)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 227.67/39.31          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 227.67/39.31    (93)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 227.67/39.31          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 227.67/39.31    (94)   ~ (all_53_2 = all_53_3)
% 227.67/39.31    (95)   ~ (all_10_2 = e1)
% 227.67/39.31    (96)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 227.67/39.31    (97)   ~ (all_53_7 = all_53_11)
% 227.67/39.31    (98)  all_55_8 = all_53_2
% 227.67/39.31    (99)  op(e0, e0) = e3
% 227.67/39.31    (100)   ~ (all_53_4 = all_53_6)
% 227.67/39.31    (101)  op(e0, e2) = all_53_7
% 227.67/39.31    (102)  all_18_2 = all_10_2
% 227.67/39.31    (103)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.67/39.31           | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 227.67/39.31             e2)
% 227.67/39.31    (104)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) =
% 227.67/39.31                 e0) | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 227.67/39.31                 op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) |
% 227.67/39.31               (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 227.67/39.31                 e0)))
% 227.67/39.31    (105)  all_55_10 = all_6_2
% 227.67/39.31    (106)   ~ (all_53_6 = all_6_2)
% 227.67/39.31    (107)   ~ (all_53_13 = e0)
% 227.67/39.31    (108)   ~ (all_53_1 = all_53_13)
% 227.67/39.31    (109)  all_55_13 = all_53_7
% 227.67/39.31    (110)  op(e2, e0) = all_53_13
% 227.67/39.31    (111)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 227.67/39.31           (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 227.67/39.31    (112)  all_38_2 = all_6_2
% 227.67/39.31    (113)  all_55_11 = all_53_14
% 227.67/39.31    (114)  all_55_3 = all_53_12
% 227.67/39.31    (115)   ~ (all_53_12 = e3)
% 227.67/39.31    (116)  op(e1, e3) = all_53_2
% 227.67/39.31    (117)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0
% 227.67/39.31             & op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~
% 227.67/39.31             (all_42_1 = e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 227.67/39.31    (118)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 227.67/39.31           (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 227.67/39.31    (119)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 227.67/39.31           (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 227.67/39.31    (120)   ~ (all_53_12 = all_10_2)
% 227.67/39.31    (121)   ~ (all_53_13 = all_53_14)
% 227.67/39.31    (122)   ~ (e2 = e1)
% 227.67/39.31    (123)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 227.67/39.31           | (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 227.67/39.31             e2)
% 227.67/39.31    (124)  op(e2, e1) = all_53_9
% 227.67/39.31    (125)  op(e1, e2) = all_53_6
% 227.67/39.31    (126)   ~ (all_53_2 = all_53_6)
% 227.67/39.31    (127)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 227.67/39.31           (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 227.67/39.31    (128)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 227.67/39.31    (129)  all_24_2 = all_6_2
% 227.67/39.31    (130)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 227.67/39.31           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 227.67/39.31    (131)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 227.67/39.31           (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 227.67/39.31    (132)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 227.67/39.31           | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 227.67/39.31             e1)
% 227.67/39.31    (133)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 227.67/39.31           (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 227.67/39.31    (134)   ~ (all_53_12 = all_53_14)
% 227.67/39.31    (135)  all_55_14 = all_53_11
% 227.67/39.31    (136)   ~ (all_22_2 = e3) | ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0
% 227.67/39.31             & op(e0, e3) = all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~
% 227.67/39.31             (all_22_1 = e2) & op(e0, e3) = all_22_1 & $i(all_22_1))
% 227.67/39.31    (137)  op(e3, e1) = all_53_8
% 227.67/39.31    (138)  all_55_7 = all_53_13
% 227.67/39.31    (139)   ~ (all_53_11 = e3)
% 227.67/39.31    (140)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 227.67/39.31           (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 227.67/39.31    (141)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 227.67/39.31           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 227.67/39.31    (142)  op(e3, e0) = all_53_12
% 227.67/39.31  
% 227.67/39.31  Begin of proof
% 227.67/39.31  | 
% 227.67/39.31  | BETA: splitting (37) gives:
% 227.67/39.31  | 
% 227.67/39.31  | Case 1:
% 227.67/39.31  | | 
% 227.67/39.31  | |   (143)   ~ (all_18_2 = e0)
% 227.67/39.31  | | 
% 227.67/39.31  | | REDUCE: (102), (143) imply:
% 227.67/39.31  | |   (144)   ~ (all_10_2 = e0)
% 227.67/39.31  | | 
% 227.67/39.31  | | BETA: splitting (7) gives:
% 227.67/39.31  | | 
% 227.67/39.31  | | Case 1:
% 227.67/39.31  | | | 
% 227.67/39.31  | | |   (145)   ~ (all_20_2 = e2)
% 227.67/39.31  | | | 
% 227.67/39.31  | | | REDUCE: (62), (145) imply:
% 227.67/39.31  | | |   (146)   ~ (all_10_2 = e2)
% 227.67/39.31  | | | 
% 227.67/39.31  | | | REF_CLOSE: (2), (6), (11), (12), (13), (14), (15), (18), (19), (20), (22),
% 227.67/39.31  | | |            (23), (26), (27), (28), (30), (31), (33), (38), (41), (43),
% 227.67/39.31  | | |            (44), (48), (50), (52), (53), (57), (63), (64), (67), (70),
% 227.67/39.31  | | |            (71), (74), (75), (78), (81), (82), (85), (88), (89), (91),
% 227.67/39.31  | | |            (92), (93), (95), (99), (100), (103), (104), (105), (111),
% 227.67/39.31  | | |            (112), (114), (117), (118), (119), (120), (122), (123), (124),
% 227.67/39.31  | | |            (125), (127), (129), (130), (131), (132), (133), (137), (140),
% 227.67/39.31  | | |            (141), (142), (144), (146) are inconsistent by sub-proof #1414.
% 227.67/39.31  | | | 
% 227.67/39.31  | | Case 2:
% 227.67/39.31  | | | 
% 227.67/39.31  | | |   (147)  all_20_2 = e2
% 227.67/39.31  | | |   (148)  ( ~ (all_20_0 = e1) & op(all_20_1, e3) = all_20_0 & op(e3, e2) =
% 227.67/39.31  | | |            all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e0) &
% 227.67/39.31  | | |            op(e3, e2) = all_20_1 & $i(all_20_1))
% 227.67/39.31  | | | 
% 227.67/39.31  | | | COMBINE_EQS: (62), (147) imply:
% 227.67/39.31  | | |   (149)  all_10_2 = e2
% 227.67/39.31  | | | 
% 227.67/39.31  | | | SIMP: (149) implies:
% 227.67/39.31  | | |   (150)  all_10_2 = e2
% 227.67/39.31  | | | 
% 227.67/39.31  | | | COMBINE_EQS: (4), (150) imply:
% 227.67/39.31  | | |   (151)  all_28_2 = e2
% 227.67/39.31  | | | 
% 227.67/39.31  | | | REDUCE: (10), (150) imply:
% 227.67/39.31  | | |   (152)   ~ (all_53_1 = e2)
% 227.67/39.31  | | | 
% 227.67/39.31  | | | REDUCE: (80), (150) imply:
% 227.67/39.31  | | |   (153)   ~ (all_53_2 = e2)
% 227.67/39.31  | | | 
% 227.67/39.31  | | | REDUCE: (8), (150) imply:
% 227.67/39.31  | | |   (154)   ~ (all_53_3 = e2)
% 227.67/39.31  | | | 
% 227.67/39.31  | | | REDUCE: (55), (150) imply:
% 227.67/39.31  | | |   (155)   ~ (all_53_4 = e2)
% 227.67/39.31  | | | 
% 227.67/39.31  | | | REDUCE: (2), (150) imply:
% 227.67/39.31  | | |   (156)  op(e3, e3) = e2
% 227.67/39.31  | | | 
% 227.67/39.31  | | | BETA: splitting (82) gives:
% 227.67/39.31  | | | 
% 227.67/39.31  | | | Case 1:
% 227.67/39.31  | | | | 
% 227.67/39.31  | | | |   (157)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 227.67/39.31  | | | |            & op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 227.67/39.31  | | | |            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 227.67/39.31  | | | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) =
% 227.67/39.31  | | | |            all_52_5 & op(e3, e0) = all_52_7 & $i(all_52_1) &
% 227.67/39.31  | | | |            $i(all_52_3) & $i(all_52_5) & $i(all_52_7)) | (all_52_8 = e3
% 227.67/39.31  | | | |            & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0 &
% 227.67/39.31  | | | |            op(all_52_9, all_52_9) = e3 & op(all_52_11, all_52_11) = e2 &
% 227.67/39.31  | | | |            op(all_52_13, all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 227.67/39.31  | | | |            & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 & op(e2, e1)
% 227.67/39.31  | | | |            = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 227.67/39.31  | | | |            $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 227.67/39.31  | | | | 
% 227.67/39.31  | | | | BETA: splitting (157) gives:
% 227.67/39.31  | | | | 
% 227.67/39.31  | | | | Case 1:
% 227.67/39.31  | | | | | 
% 227.67/39.31  | | | | |   (158)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 227.67/39.31  | | | | |          & op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 227.67/39.31  | | | | |          op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 227.67/39.31  | | | | |          op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) =
% 227.67/39.31  | | | | |          all_52_5 & op(e3, e0) = all_52_7 & $i(all_52_1) &
% 227.67/39.31  | | | | |          $i(all_52_3) & $i(all_52_5) & $i(all_52_7)
% 227.67/39.31  | | | | | 
% 227.67/39.31  | | | | | ALPHA: (158) implies:
% 227.67/39.31  | | | | |   (159)  op(e3, e3) = all_52_1
% 227.67/39.31  | | | | |   (160)  op(all_52_1, all_52_1) = e3
% 227.67/39.31  | | | | | 
% 227.67/39.31  | | | | | REF_CLOSE: (19), (45), (61), (156), (159), (160) are inconsistent by
% 227.67/39.31  | | | | |            sub-proof #1653.
% 227.67/39.31  | | | | | 
% 227.67/39.31  | | | | Case 2:
% 227.67/39.31  | | | | | 
% 227.67/39.31  | | | | |   (161)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 227.67/39.31  | | | | |          e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11, all_52_11) =
% 227.67/39.31  | | | | |          e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15, all_52_15)
% 227.67/39.31  | | | | |          = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 227.67/39.31  | | | | |          op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 227.67/39.31  | | | | |          $i(all_52_9) & $i(all_52_11) & $i(all_52_13) & $i(all_52_15)
% 227.67/39.31  | | | | | 
% 227.67/39.31  | | | | | ALPHA: (161) implies:
% 227.67/39.31  | | | | |   (162)  op(e2, e2) = all_52_11
% 227.67/39.31  | | | | |   (163)  op(all_52_11, all_52_11) = e2
% 227.67/39.31  | | | | | 
% 227.67/39.31  | | | | | REF_CLOSE: (19), (45), (54), (99), (162), (163) are inconsistent by
% 227.67/39.31  | | | | |            sub-proof #1229.
% 227.67/39.31  | | | | | 
% 227.67/39.31  | | | | End of split
% 227.67/39.31  | | | | 
% 227.67/39.31  | | | Case 2:
% 227.67/39.31  | | | | 
% 227.67/39.31  | | | |   (164)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 227.67/39.31  | | | |            e0 & op(all_52_17, all_52_17) = e3 & op(all_52_19, all_52_19)
% 227.67/39.31  | | | |            = e2 & op(all_52_21, all_52_21) = e1 & op(all_52_23,
% 227.67/39.31  | | | |              all_52_23) = e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 227.67/39.31  | | | |            all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23 &
% 227.67/39.31  | | | |            $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 227.67/39.31  | | | |            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28
% 227.67/39.31  | | | |            = e1 & all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 227.67/39.31  | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29, all_52_29) = e1
% 227.67/39.31  | | | |            & op(all_52_31, all_52_31) = e0 & op(e0, e3) = all_52_25 &
% 227.67/39.31  | | | |            op(e0, e2) = all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 227.67/39.31  | | | |            = all_52_31 & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 227.67/39.31  | | | |            $i(all_52_31))
% 227.67/39.31  | | | | 
% 227.67/39.31  | | | | BETA: splitting (164) gives:
% 227.67/39.31  | | | | 
% 227.67/39.31  | | | | Case 1:
% 227.67/39.31  | | | | | 
% 227.67/39.31  | | | | |   (165)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22
% 227.67/39.31  | | | | |          = e0 & op(all_52_17, all_52_17) = e3 & op(all_52_19,
% 227.67/39.31  | | | | |            all_52_19) = e2 & op(all_52_21, all_52_21) = e1 &
% 227.67/39.31  | | | | |          op(all_52_23, all_52_23) = e0 & op(e1, e3) = all_52_17 &
% 227.67/39.31  | | | | |          op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 227.67/39.31  | | | | |          = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 227.67/39.31  | | | | |          $i(all_52_23)
% 227.67/39.31  | | | | | 
% 227.67/39.31  | | | | | ALPHA: (165) implies:
% 227.67/39.31  | | | | |   (166)  op(e1, e0) = all_52_23
% 227.67/39.31  | | | | |   (167)  op(e1, e1) = all_52_21
% 227.67/39.31  | | | | |   (168)  op(e1, e3) = all_52_17
% 227.67/39.31  | | | | |   (169)  op(all_52_21, all_52_21) = e1
% 227.67/39.31  | | | | |   (170)  op(all_52_17, all_52_17) = e3
% 227.67/39.31  | | | | | 
% 227.67/39.31  | | | | | BETA: splitting (127) gives:
% 227.67/39.31  | | | | | 
% 227.67/39.31  | | | | | Case 1:
% 227.67/39.31  | | | | | | 
% 227.67/39.31  | | | | | |   (171)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2,
% 227.67/39.31  | | | | | |              e3) = e2)
% 227.67/39.31  | | | | | | 
% 227.67/39.31  | | | | | | BETA: splitting (171) gives:
% 227.67/39.31  | | | | | | 
% 227.67/39.31  | | | | | | Case 1:
% 227.67/39.31  | | | | | | | 
% 227.67/39.31  | | | | | | |   (172)  all_57_0 = e2 & op(e3, e3) = e2
% 227.67/39.31  | | | | | | | 
% 227.67/39.31  | | | | | | | ALPHA: (172) implies:
% 227.67/39.31  | | | | | | |   (173)  all_57_0 = e2
% 227.67/39.31  | | | | | | | 
% 227.67/39.31  | | | | | | | GROUND_INST: instantiating (19) with all_53_14, all_52_23, e0, e1,
% 227.67/39.31  | | | | | | |              simplifying with (59), (166) gives:
% 227.67/39.31  | | | | | | |   (174)  all_53_14 = all_52_23
% 227.67/39.31  | | | | | | | 
% 227.67/39.31  | | | | | | | GROUND_INST: instantiating (19) with all_6_2, all_52_21, e1, e1,
% 227.67/39.31  | | | | | | |              simplifying with (27), (167) gives:
% 227.67/39.31  | | | | | | |   (175)  all_52_21 = all_6_2
% 227.67/39.31  | | | | | | | 
% 227.67/39.31  | | | | | | | GROUND_INST: instantiating (19) with all_53_2, all_52_17, e3, e1,
% 227.67/39.31  | | | | | | |              simplifying with (116), (168) gives:
% 227.67/39.31  | | | | | | |   (176)  all_53_2 = all_52_17
% 227.67/39.31  | | | | | | | 
% 227.67/39.31  | | | | | | | COMBINE_EQS: (113), (174) imply:
% 227.67/39.31  | | | | | | |   (177)  all_55_11 = all_52_23
% 227.67/39.31  | | | | | | | 
% 227.67/39.31  | | | | | | | COMBINE_EQS: (98), (176) imply:
% 227.67/39.31  | | | | | | |   (178)  all_55_8 = all_52_17
% 227.67/39.31  | | | | | | | 
% 227.67/39.31  | | | | | | | REDUCE: (79), (176) imply:
% 227.67/39.31  | | | | | | |   (179)   ~ (all_53_1 = all_52_17)
% 227.67/39.31  | | | | | | | 
% 227.67/39.31  | | | | | | | REDUCE: (94), (176) imply:
% 227.67/39.31  | | | | | | |   (180)   ~ (all_53_3 = all_52_17)
% 227.67/39.31  | | | | | | | 
% 227.67/39.31  | | | | | | | SIMP: (180) implies:
% 227.67/39.31  | | | | | | |   (181)   ~ (all_53_3 = all_52_17)
% 227.67/39.31  | | | | | | | 
% 227.67/39.31  | | | | | | | REDUCE: (87), (174), (176) imply:
% 227.67/39.31  | | | | | | |   (182)   ~ (all_52_17 = all_52_23)
% 227.67/39.31  | | | | | | | 
% 227.67/39.31  | | | | | | | REDUCE: (39), (176) imply:
% 227.67/39.31  | | | | | | |   (183)   ~ (all_52_17 = all_6_2)
% 227.67/39.31  | | | | | | | 
% 227.67/39.31  | | | | | | | REDUCE: (153), (176) imply:
% 227.67/39.31  | | | | | | |   (184)   ~ (all_52_17 = e2)
% 227.67/39.31  | | | | | | | 
% 227.67/39.31  | | | | | | | REDUCE: (51), (174) imply:
% 227.67/39.31  | | | | | | |   (185)   ~ (all_52_23 = all_6_2)
% 227.67/39.31  | | | | | | | 
% 227.67/39.31  | | | | | | | REDUCE: (76), (174) imply:
% 227.67/39.31  | | | | | | |   (186)   ~ (all_52_23 = e3)
% 227.67/39.31  | | | | | | | 
% 227.67/39.31  | | | | | | | REDUCE: (169), (175) imply:
% 227.67/39.31  | | | | | | |   (187)  op(all_6_2, all_6_2) = e1
% 227.67/39.31  | | | | | | | 
% 227.67/39.31  | | | | | | | BETA: splitting (136) gives:
% 227.67/39.31  | | | | | | | 
% 227.67/39.31  | | | | | | | Case 1:
% 227.67/39.31  | | | | | | | | 
% 227.67/39.31  | | | | | | | |   (188)   ~ (all_22_2 = e3)
% 227.67/39.31  | | | | | | | | 
% 227.67/39.31  | | | | | | | | REDUCE: (21), (188) imply:
% 227.67/39.31  | | | | | | | |   (189)  $false
% 227.67/39.31  | | | | | | | | 
% 227.67/39.31  | | | | | | | | CLOSE: (189) is inconsistent.
% 227.67/39.31  | | | | | | | | 
% 227.67/39.31  | | | | | | | Case 2:
% 227.67/39.31  | | | | | | | | 
% 227.67/39.31  | | | | | | | |   (190)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 &
% 227.67/39.31  | | | | | | | |            op(e0, e3) = all_22_1 & $i(all_22_0) & $i(all_22_1))
% 227.67/39.31  | | | | | | | |          | ( ~ (all_22_1 = e2) & op(e0, e3) = all_22_1 &
% 227.67/39.31  | | | | | | | |            $i(all_22_1))
% 227.67/39.31  | | | | | | | | 
% 227.67/39.31  | | | | | | | | BETA: splitting (23) gives:
% 227.67/39.31  | | | | | | | | 
% 227.67/39.31  | | | | | | | | Case 1:
% 227.67/39.31  | | | | | | | | | 
% 227.67/39.31  | | | | | | | | |   (191)   ~ (all_24_2 = e0)
% 227.67/39.31  | | | | | | | | | 
% 227.67/39.31  | | | | | | | | | REDUCE: (129), (191) imply:
% 227.67/39.31  | | | | | | | | |   (192)   ~ (all_6_2 = e0)
% 227.67/39.31  | | | | | | | | | 
% 227.67/39.31  | | | | | | | | | BETA: splitting (42) gives:
% 227.67/39.31  | | | | | | | | | 
% 227.67/39.31  | | | | | | | | | Case 1:
% 227.67/39.31  | | | | | | | | | | 
% 227.67/39.31  | | | | | | | | | |   (193)   ~ (all_28_2 = e2)
% 227.67/39.31  | | | | | | | | | | 
% 227.67/39.31  | | | | | | | | | | REDUCE: (151), (193) imply:
% 227.67/39.31  | | | | | | | | | |   (194)  $false
% 227.67/39.31  | | | | | | | | | | 
% 227.67/39.31  | | | | | | | | | | CLOSE: (194) is inconsistent.
% 227.67/39.31  | | | | | | | | | | 
% 227.67/39.31  | | | | | | | | | Case 2:
% 227.67/39.31  | | | | | | | | | | 
% 227.67/39.31  | | | | | | | | | |   (195)  ( ~ (all_28_0 = e0) & op(all_28_1, e3) = all_28_0 &
% 227.67/39.31  | | | | | | | | | |            op(e3, e2) = all_28_1 & $i(all_28_0) &
% 227.67/39.31  | | | | | | | | | |            $i(all_28_1)) | ( ~ (all_28_1 = e1) & op(e3, e2)
% 227.67/39.31  | | | | | | | | | |            = all_28_1 & $i(all_28_1))
% 227.67/39.31  | | | | | | | | | | 
% 227.67/39.31  | | | | | | | | | | BETA: splitting (89) gives:
% 227.67/39.31  | | | | | | | | | | 
% 227.67/39.31  | | | | | | | | | | Case 1:
% 227.67/39.31  | | | | | | | | | | | 
% 227.67/39.31  | | | | | | | | | | |   (196)   ~ (all_38_2 = e2)
% 227.67/39.31  | | | | | | | | | | | 
% 227.67/39.31  | | | | | | | | | | | REDUCE: (112), (196) imply:
% 227.67/39.31  | | | | | | | | | | |   (197)   ~ (all_6_2 = e2)
% 227.67/39.31  | | | | | | | | | | | 
% 227.67/39.31  | | | | | | | | | | | BETA: splitting (11) gives:
% 227.67/39.31  | | | | | | | | | | | 
% 227.67/39.31  | | | | | | | | | | | Case 1:
% 227.67/39.31  | | | | | | | | | | | | 
% 227.67/39.31  | | | | | | | | | | | |   (198)  all_55_10 = e3
% 227.67/39.31  | | | | | | | | | | | | 
% 227.67/39.31  | | | | | | | | | | | | REF_CLOSE: (26), (105), (198) are inconsistent by sub-proof
% 227.67/39.31  | | | | | | | | | | | |            #2500.
% 227.67/39.31  | | | | | | | | | | | | 
% 227.67/39.31  | | | | | | | | | | | Case 2:
% 227.67/39.31  | | | | | | | | | | | | 
% 227.67/39.31  | | | | | | | | | | | |   (199)   ~ (all_55_10 = e3)
% 227.67/39.31  | | | | | | | | | | | |   (200)  all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 227.67/39.31  | | | | | | | | | | | | 
% 227.67/39.31  | | | | | | | | | | | | BETA: splitting (200) gives:
% 227.67/39.31  | | | | | | | | | | | | 
% 227.67/39.31  | | | | | | | | | | | | Case 1:
% 227.67/39.31  | | | | | | | | | | | | | 
% 227.67/39.31  | | | | | | | | | | | | |   (201)  all_55_10 = e2
% 227.67/39.31  | | | | | | | | | | | | | 
% 227.67/39.31  | | | | | | | | | | | | | REF_CLOSE: (105), (197), (201) are inconsistent by sub-proof
% 227.67/39.31  | | | | | | | | | | | | |            #2499.
% 227.67/39.31  | | | | | | | | | | | | | 
% 227.67/39.31  | | | | | | | | | | | | Case 2:
% 227.67/39.31  | | | | | | | | | | | | | 
% 227.67/39.31  | | | | | | | | | | | | |   (202)   ~ (all_55_10 = e2)
% 227.67/39.31  | | | | | | | | | | | | |   (203)  all_55_10 = e1 | all_55_10 = e0
% 227.67/39.31  | | | | | | | | | | | | | 
% 227.67/39.31  | | | | | | | | | | | | | BETA: splitting (203) gives:
% 227.67/39.31  | | | | | | | | | | | | | 
% 227.67/39.31  | | | | | | | | | | | | | Case 1:
% 227.67/39.31  | | | | | | | | | | | | | | 
% 227.67/39.31  | | | | | | | | | | | | | |   (204)  all_55_10 = e1
% 227.67/39.31  | | | | | | | | | | | | | | 
% 227.67/39.31  | | | | | | | | | | | | | | COMBINE_EQS: (105), (204) imply:
% 227.67/39.31  | | | | | | | | | | | | | |   (205)  all_6_2 = e1
% 227.67/39.31  | | | | | | | | | | | | | | 
% 227.67/39.31  | | | | | | | | | | | | | | SIMP: (205) implies:
% 227.67/39.31  | | | | | | | | | | | | | |   (206)  all_6_2 = e1
% 227.67/39.31  | | | | | | | | | | | | | | 
% 227.67/39.31  | | | | | | | | | | | | | | REDUCE: (64), (206) imply:
% 227.67/39.31  | | | | | | | | | | | | | |   (207)   ~ (all_53_8 = e1)
% 227.67/39.31  | | | | | | | | | | | | | | 
% 227.67/39.31  | | | | | | | | | | | | | | REDUCE: (48), (206) imply:
% 227.67/39.31  | | | | | | | | | | | | | |   (208)   ~ (all_53_9 = e1)
% 227.67/39.31  | | | | | | | | | | | | | | 
% 227.67/39.31  | | | | | | | | | | | | | | REDUCE: (36), (206) imply:
% 227.67/39.31  | | | | | | | | | | | | | |   (209)   ~ (all_53_11 = e1)
% 227.67/39.31  | | | | | | | | | | | | | | 
% 227.67/39.31  | | | | | | | | | | | | | | REDUCE: (183), (206) imply:
% 227.67/39.31  | | | | | | | | | | | | | |   (210)   ~ (all_52_17 = e1)
% 227.67/39.31  | | | | | | | | | | | | | | 
% 227.67/39.31  | | | | | | | | | | | | | | REDUCE: (185), (206) imply:
% 227.67/39.31  | | | | | | | | | | | | | |   (211)   ~ (all_52_23 = e1)
% 227.67/39.31  | | | | | | | | | | | | | | 
% 227.67/39.31  | | | | | | | | | | | | | | REDUCE: (26), (206) imply:
% 227.67/39.31  | | | | | | | | | | | | | |   (212)   ~ (e3 = e1)
% 227.67/39.31  | | | | | | | | | | | | | | 
% 227.67/39.31  | | | | | | | | | | | | | | REDUCE: (197), (206) imply:
% 227.67/39.31  | | | | | | | | | | | | | |   (213)   ~ (e2 = e1)
% 227.67/39.31  | | | | | | | | | | | | | | 
% 227.67/39.31  | | | | | | | | | | | | | | REDUCE: (27), (206) imply:
% 227.67/39.31  | | | | | | | | | | | | | |   (214)  op(e1, e1) = e1
% 227.67/39.31  | | | | | | | | | | | | | | 
% 227.67/39.31  | | | | | | | | | | | | | | BETA: splitting (133) gives:
% 227.67/39.31  | | | | | | | | | | | | | | 
% 227.67/39.31  | | | | | | | | | | | | | | Case 1:
% 227.67/39.31  | | | | | | | | | | | | | | | 
% 227.67/39.31  | | | | | | | | | | | | | | |   (215)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 227.67/39.31  | | | | | | | | | | | | | | |            & op(e1, e2) = e1)
% 227.67/39.31  | | | | | | | | | | | | | | | 
% 227.67/39.31  | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 227.67/39.31  | | | | | | | | | | | | | | | 
% 227.67/39.31  | | | | | | | | | | | | | | | Case 1:
% 227.67/39.31  | | | | | | | | | | | | | | | | 
% 227.67/39.31  | | | | | | | | | | | | | | | |   (216)  all_57_6 = e1 & op(e1, e3) = e1
% 227.67/39.31  | | | | | | | | | | | | | | | | 
% 227.67/39.31  | | | | | | | | | | | | | | | | ALPHA: (216) implies:
% 227.67/39.31  | | | | | | | | | | | | | | | |   (217)  all_57_6 = e1
% 227.67/39.31  | | | | | | | | | | | | | | | | 
% 227.67/39.31  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (12), (13), (14), (15), (17), (18),
% 227.67/39.31  | | | | | | | | | | | | | | | |            (19), (22), (23), (26), (27), (28), (30), (33),
% 227.67/39.31  | | | | | | | | | | | | | | | |            (38), (41), (43), (44), (48), (50), (52), (53),
% 227.67/39.31  | | | | | | | | | | | | | | | |            (54), (57), (61), (63), (64), (67), (70), (71),
% 227.67/39.31  | | | | | | | | | | | | | | | |            (74), (75), (78), (81), (82), (85), (88), (89),
% 227.67/39.31  | | | | | | | | | | | | | | | |            (91), (92), (93), (99), (100), (103), (104),
% 227.67/39.31  | | | | | | | | | | | | | | | |            (105), (111), (112), (114), (115), (117), (118),
% 227.67/39.31  | | | | | | | | | | | | | | | |            (119), (122), (123), (124), (125), (127), (129),
% 227.67/39.31  | | | | | | | | | | | | | | | |            (130), (131), (132), (133), (137), (140), (141),
% 227.67/39.31  | | | | | | | | | | | | | | | |            (142), (156), (214), (217) are inconsistent by
% 227.67/39.31  | | | | | | | | | | | | | | | |            sub-proof #523.
% 227.67/39.31  | | | | | | | | | | | | | | | | 
% 227.67/39.31  | | | | | | | | | | | | | | | Case 2:
% 227.67/39.31  | | | | | | | | | | | | | | | | 
% 227.67/39.31  | | | | | | | | | | | | | | | |   (218)  all_57_7 = e1 & op(e1, e2) = e1
% 227.67/39.31  | | | | | | | | | | | | | | | | 
% 227.67/39.31  | | | | | | | | | | | | | | | | ALPHA: (218) implies:
% 227.67/39.31  | | | | | | | | | | | | | | | |   (219)  all_57_7 = e1
% 227.67/39.31  | | | | | | | | | | | | | | | | 
% 227.67/39.31  | | | | | | | | | | | | | | | | BETA: splitting (15) gives:
% 227.67/39.31  | | | | | | | | | | | | | | | | 
% 227.67/39.31  | | | | | | | | | | | | | | | | Case 1:
% 227.67/39.31  | | | | | | | | | | | | | | | | | 
% 227.67/39.31  | | | | | | | | | | | | | | | | |   (220)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 227.67/39.31  | | | | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 227.67/39.31  | | | | | | | | | | | | | | | | | 
% 227.67/39.31  | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 227.67/39.31  | | | | | | | | | | | | | | | | | 
% 227.67/39.31  | | | | | | | | | | | | | | | | | Case 1:
% 227.67/39.31  | | | | | | | | | | | | | | | | | | 
% 227.67/39.31  | | | | | | | | | | | | | | | | | |   (221)  all_57_1 = e2 & op(e3, e2) = e2
% 227.67/39.31  | | | | | | | | | | | | | | | | | | 
% 227.67/39.31  | | | | | | | | | | | | | | | | | | ALPHA: (221) implies:
% 227.67/39.31  | | | | | | | | | | | | | | | | | |   (222)  all_57_1 = e2
% 227.67/39.31  | | | | | | | | | | | | | | | | | | 
% 227.67/39.31  | | | | | | | | | | | | | | | | | | BETA: splitting (33) gives:
% 227.67/39.31  | | | | | | | | | | | | | | | | | | 
% 227.67/39.31  | | | | | | | | | | | | | | | | | | Case 1:
% 227.67/39.31  | | | | | | | | | | | | | | | | | | | 
% 227.67/39.31  | | | | | | | | | | | | | | | | | | |   (223)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 227.67/39.31  | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e1)
% 227.67/39.31  | | | | | | | | | | | | | | | | | | | 
% 227.67/39.31  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (122), (156), (222), (223) are inconsistent
% 227.67/39.31  | | | | | | | | | | | | | | | | | | |            by sub-proof #1662.
% 227.67/39.31  | | | | | | | | | | | | | | | | | | | 
% 227.67/39.31  | | | | | | | | | | | | | | | | | | Case 2:
% 227.67/39.31  | | | | | | | | | | | | | | | | | | | 
% 227.67/39.31  | | | | | | | | | | | | | | | | | | |   (224)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 227.67/39.31  | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e1)
% 227.67/39.31  | | | | | | | | | | | | | | | | | | | 
% 227.67/39.31  | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 227.67/39.31  | | | | | | | | | | | | | | | | | | | 
% 227.67/39.31  | | | | | | | | | | | | | | | | | | | Case 1:
% 227.67/39.31  | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.31  | | | | | | | | | | | | | | | | | | | |   (225)  all_57_4 = e1 & op(e3, e1) = e1
% 227.67/39.31  | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.31  | | | | | | | | | | | | | | | | | | | | ALPHA: (225) implies:
% 227.67/39.31  | | | | | | | | | | | | | | | | | | | |   (226)  all_57_4 = e1
% 227.67/39.31  | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.31  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (12), (13), (14), (15), (17), (18),
% 227.67/39.31  | | | | | | | | | | | | | | | | | | | |            (19), (22), (23), (26), (27), (28), (30), (33),
% 227.67/39.31  | | | | | | | | | | | | | | | | | | | |            (38), (41), (43), (44), (48), (50), (52), (53),
% 227.67/39.31  | | | | | | | | | | | | | | | | | | | |            (54), (57), (61), (63), (64), (67), (70), (71),
% 227.67/39.31  | | | | | | | | | | | | | | | | | | | |            (74), (75), (78), (81), (82), (85), (88), (89),
% 227.67/39.31  | | | | | | | | | | | | | | | | | | | |            (91), (92), (93), (99), (100), (103), (104),
% 227.67/39.31  | | | | | | | | | | | | | | | | | | | |            (105), (111), (112), (114), (115), (117), (118),
% 227.67/39.31  | | | | | | | | | | | | | | | | | | | |            (119), (122), (123), (124), (125), (127), (129),
% 227.67/39.31  | | | | | | | | | | | | | | | | | | | |            (130), (131), (132), (133), (137), (140), (141),
% 227.67/39.31  | | | | | | | | | | | | | | | | | | | |            (142), (156), (214), (219), (222), (226) are
% 227.67/39.31  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #515.
% 227.67/39.31  | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.31  | | | | | | | | | | | | | | | | | | | Case 2:
% 227.67/39.31  | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.31  | | | | | | | | | | | | | | | | | | | |   (227)  all_57_9 = e1 & op(e3, e0) = e1
% 227.67/39.31  | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.31  | | | | | | | | | | | | | | | | | | | | ALPHA: (227) implies:
% 227.67/39.31  | | | | | | | | | | | | | | | | | | | |   (228)  all_57_9 = e1
% 227.67/39.31  | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (12), (13), (14), (15), (17), (18),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | |            (19), (22), (23), (26), (27), (28), (30), (33),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | |            (38), (41), (43), (44), (48), (50), (52), (53),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | |            (54), (57), (61), (63), (64), (67), (70), (71),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | |            (74), (75), (78), (81), (82), (85), (88), (89),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | |            (91), (92), (93), (99), (100), (103), (104),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | |            (105), (111), (112), (114), (115), (117), (118),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | |            (119), (122), (123), (124), (125), (127), (129),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | |            (130), (131), (132), (133), (137), (140), (141),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | |            (142), (156), (214), (219), (222), (228) are
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #512.
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | End of split
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | End of split
% 227.67/39.32  | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | Case 2:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | |   (229)  all_57_3 = e2 & op(e2, e2) = e2
% 227.67/39.32  | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | REF_CLOSE: (52), (81), (229) are inconsistent by sub-proof
% 227.67/39.32  | | | | | | | | | | | | | | | | | |            #2103.
% 227.67/39.32  | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | End of split
% 227.67/39.32  | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | Case 2:
% 227.67/39.32  | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | |   (230)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 227.67/39.32  | | | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 227.67/39.32  | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 227.67/39.32  | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | Case 1:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | |   (231)  all_57_7 = e2 & op(e1, e2) = e2
% 227.67/39.32  | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | REF_CLOSE: (122), (219), (231) are inconsistent by sub-proof
% 227.67/39.32  | | | | | | | | | | | | | | | | | |            #1268.
% 227.67/39.32  | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | Case 2:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | |   (232)  all_57_13 = e2 & op(e0, e2) = e2
% 227.67/39.32  | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | ALPHA: (232) implies:
% 227.67/39.32  | | | | | | | | | | | | | | | | | |   (233)  all_57_13 = e2
% 227.67/39.32  | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | BETA: splitting (22) gives:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | Case 1:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | |   (234)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 227.67/39.32  | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e3)
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | Case 1:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | |   (235)  all_57_6 = e3 & op(e1, e3) = e3
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | ALPHA: (235) implies:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | |   (236)  all_57_6 = e3
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | BETA: splitting (93) gives:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | |   (237)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e3)
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | |   (238)  all_57_1 = e3 & op(e3, e2) = e3
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (238) implies:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | |   (239)  all_57_1 = e3
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (131) gives:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | |   (240)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e0)
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (17), (19), (52), (54), (61), (81), (88),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | |            (111), (118), (122), (156), (240) are inconsistent
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1654.
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | |   (241)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e3) = e0)
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | |   (242)  all_57_6 = e0 & op(e1, e3) = e0
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (12), (13), (14), (15), (17), (18),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | |            (19), (22), (23), (26), (27), (28), (30), (33),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | |            (38), (41), (43), (44), (48), (50), (52), (53),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | |            (54), (57), (61), (63), (64), (67), (70), (71),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | |            (74), (75), (78), (81), (82), (85), (88), (89),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | |            (91), (92), (93), (99), (100), (103), (104),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | |            (105), (111), (112), (114), (115), (117), (118),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | |            (119), (122), (123), (124), (125), (127), (129),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | |            (130), (131), (132), (133), (137), (140), (141),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | |            (142), (156), (214), (236), (239), (242) are
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #510.
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | |   (243)  all_57_12 = e0 & op(e0, e3) = e0
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (243) implies:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | |   (244)  all_57_12 = e0
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (141) gives:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | |   (245)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e2)
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | |   (246)  all_57_6 = e2 & op(e1, e3) = e2
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (246) implies:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | |   (247)  all_57_6 = e2
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (13), (15), (17), (19), (22), (26), (27),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | |            (33), (44), (50), (52), (54), (61), (71), (81),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | |            (85), (88), (104), (111), (115), (118), (119),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | |            (122), (123), (131), (132), (140), (142), (156),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | |            (247) are inconsistent by sub-proof #728.
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | |   (248)  all_57_7 = e2 & op(e1, e2) = e2
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (248) implies:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | |   (249)  all_57_7 = e2
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (52), (88), (122), (140), (233), (239),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | |            (249) are inconsistent by sub-proof #1698.
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | |   (250)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e1, e0) = e2)
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (250) gives:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | |   (251)  all_57_8 = e2 & op(e1, e1) = e2
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (251) implies:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | |   (252)  all_57_8 = e2
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | |   (253)  op(e1, e1) = e2
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (33) gives:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (254)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e1)
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (254) gives:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (255)  all_57_0 = e1 & op(e3, e3) = e1
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (255) implies:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (256)  op(e3, e3) = e1
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (122), (156), (256) are inconsistent by
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1950.
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (257)  all_57_1 = e1 & op(e3, e2) = e1
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (257) implies:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (258)  all_57_1 = e1
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (239), (258) imply:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (259)  e3 = e1
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (236), (259) imply:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (260)  all_57_6 = e1
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (12), (13), (14), (15), (17), (18),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19), (22), (23), (26), (27), (28), (30), (33),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (38), (41), (43), (44), (48), (50), (52), (53),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (54), (57), (61), (63), (64), (67), (70), (71),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (74), (75), (78), (81), (82), (85), (88), (89),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (91), (92), (93), (99), (100), (103), (104),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (105), (111), (112), (114), (115), (117), (118),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (122), (123), (124), (125), (127), (129),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (130), (131), (132), (133), (137), (140), (141),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (142), (156), (214), (260) are inconsistent by
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #523.
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (261)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e1)
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (261) gives:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (262)  all_57_4 = e1 & op(e3, e1) = e1
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (262) implies:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (263)  all_57_4 = e1
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18) gives:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (264)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e0)
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (264) gives:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (265)  all_57_6 = e0 & op(e1, e3) = e0
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (12), (13), (14), (15), (17), (18),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19), (22), (23), (26), (27), (28), (30), (33),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (38), (41), (43), (44), (48), (50), (52), (53),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (54), (57), (61), (63), (64), (67), (70), (71),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (74), (75), (78), (81), (82), (85), (88), (89),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (91), (92), (93), (99), (100), (103), (104),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (105), (111), (112), (114), (115), (117), (118),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (122), (123), (124), (125), (127), (129),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (130), (131), (132), (133), (137), (140), (141),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (142), (156), (214), (236), (239), (265) are
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #510.
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (266)  all_57_7 = e0 & op(e1, e2) = e0
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (88), (219), (266) are inconsistent by sub-proof
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #509.
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (267)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (267) gives:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (268)  all_57_8 = e0 & op(e1, e1) = e0
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (17), (54), (81), (88), (122), (127), (173),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (236), (244), (252), (268) are inconsistent by
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #508.
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (269)  all_57_11 = e0 & op(e1, e0) = e0
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (269) implies:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (270)  all_57_11 = e0
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (123) gives:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (271)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (271) gives:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (272)  all_57_9 = e2 & op(e3, e0) = e2
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (272) implies:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (273)  all_57_9 = e2
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (132) gives:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (274)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (274) gives:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (275)  all_57_9 = e1 & op(e3, e0) = e1
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (275) implies:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (276)  all_57_9 = e1
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (12), (13), (14), (15), (16), (17),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18), (19), (22), (23), (24), (26), (27), (28),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (29), (30), (32), (33), (38), (41), (43), (44),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (46), (47), (48), (50), (52), (53), (54), (56),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (57), (58), (61), (63), (64), (65), (67), (68),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (70), (71), (74), (75), (77), (78), (81), (82),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (83), (84), (85), (86), (88), (89), (91), (92),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (93), (96), (99), (100), (103), (104), (105),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (111), (112), (114), (115), (117), (118), (119),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (122), (123), (124), (125), (127), (128), (129),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (130), (131), (132), (133), (135), (137), (139),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (140), (141), (142), (148), (152), (154), (155),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (156), (166), (170), (173), (177), (178), (179),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (181), (182), (184), (186), (190), (195), (207),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (208), (209), (210), (211), (214), (219), (232),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (235), (236), (239), (244), (252), (253),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (270), (276) are inconsistent by sub-proof #458.
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (277)  all_57_10 = e1 & op(e2, e0) = e1
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (277) implies:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (278)  all_57_10 = e1
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (104) gives:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (279)  all_57_15 = e0 & op(e0, e0) = e0
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (279) implies:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (280)  op(e0, e0) = e0
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (61), (99), (280) are inconsistent by
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2304.
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (281)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (281) implies:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (282)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e0)
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (50) gives:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (283)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e0)
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (283) gives:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (284)  all_57_0 = e0 & op(e3, e3) = e0
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (284) implies:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (285)  all_57_0 = e0
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (17), (54), (81), (88), (122), (127), (236),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (244), (285) are inconsistent by sub-proof #1425.
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (286)  all_57_1 = e0 & op(e3, e2) = e0
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (286) implies:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (287)  all_57_1 = e0
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (12), (13), (14), (15), (17), (18),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19), (22), (23), (26), (27), (28), (30), (33),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (38), (41), (43), (44), (48), (50), (52), (53),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (54), (57), (61), (63), (64), (67), (70), (71),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (74), (75), (78), (81), (82), (85), (88), (89),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (91), (92), (93), (99), (100), (103), (104),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (105), (111), (112), (114), (115), (117), (118),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (122), (123), (124), (125), (127), (129),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (130), (131), (132), (133), (137), (140), (141),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (142), (156), (214), (287) are inconsistent by
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #511.
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (288)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e0)
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (288) gives:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (289)  all_57_4 = e0 & op(e3, e1) = e0
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (289) implies:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (290)  all_57_4 = e0
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (263), (290) imply:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (291)  e1 = e0
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (278), (291) imply:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (292)  all_57_10 = e0
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (17), (19), (26), (27), (52), (54), (61),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (71), (74), (81), (88), (92), (103), (118), (122),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (282), (290), (292) are inconsistent by sub-proof
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1043.
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (293)  all_57_9 = e0 & op(e3, e0) = e0
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (17), (54), (81), (88), (122), (127), (173),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (236), (244), (273), (293) are inconsistent by
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #457.
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (294)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (294) gives:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (295)  all_57_11 = e1 & op(e1, e0) = e1
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (295) implies:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (296)  all_57_11 = e1
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (12), (13), (14), (15), (17), (18),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19), (22), (23), (26), (27), (28), (30), (33),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (38), (41), (43), (44), (48), (50), (52), (53),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (54), (57), (61), (63), (64), (67), (70), (71),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (74), (75), (78), (81), (82), (85), (88), (89),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (91), (92), (93), (99), (100), (103), (104),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (105), (111), (112), (114), (115), (117), (118),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (122), (123), (124), (125), (127), (129),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (130), (131), (132), (133), (137), (140), (141),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (142), (156), (214), (273), (296) are inconsistent
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #456.
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (297)  all_57_15 = e1 & op(e0, e0) = e1
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (12), (13), (14), (15), (17), (18),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19), (22), (23), (26), (27), (28), (30), (33),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (38), (41), (43), (44), (48), (50), (52), (53),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (54), (57), (61), (63), (64), (67), (70), (71),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (74), (75), (78), (81), (82), (85), (88), (89),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (91), (92), (93), (99), (100), (103), (104),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (105), (111), (112), (114), (115), (117), (118),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (122), (123), (124), (125), (127), (129),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (130), (131), (132), (133), (137), (140), (141),
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (142), (156), (214), (236), (297) are inconsistent
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #459.
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (298)  all_57_10 = e2 & op(e2, e0) = e2
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (298) implies:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (299)  all_57_10 = e2
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (132) gives:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (300)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (300) gives:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (301)  all_57_9 = e1 & op(e3, e0) = e1
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (301) implies:
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (302)  all_57_9 = e1
% 227.67/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (12), (13), (14), (15), (16), (17),
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18), (19), (22), (23), (24), (26), (27), (28),
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (29), (30), (32), (33), (38), (41), (43), (44),
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (46), (47), (48), (50), (52), (53), (54), (56),
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (57), (58), (61), (63), (64), (65), (67), (68),
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (70), (71), (74), (75), (77), (78), (81), (82),
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (83), (84), (85), (86), (88), (89), (91), (92),
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (93), (96), (99), (100), (103), (104), (105),
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (111), (112), (114), (115), (117), (118), (119),
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (122), (123), (124), (125), (127), (128), (129),
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (130), (131), (132), (133), (135), (137), (139),
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (140), (141), (142), (148), (152), (154), (155),
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (156), (166), (170), (173), (177), (178), (179),
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (181), (182), (184), (186), (190), (195), (207),
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (208), (209), (210), (211), (214), (219), (232),
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (235), (236), (239), (244), (252), (253),
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (270), (302) are inconsistent by sub-proof #458.
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (303)  all_57_10 = e1 & op(e2, e0) = e1
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (303) implies:
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (304)  all_57_10 = e1
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (299), (304) imply:
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (305)  e2 = e1
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (252), (305) imply:
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (306)  all_57_8 = e1
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (12), (13), (14), (15), (16), (17),
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18), (19), (22), (23), (24), (26), (27), (28),
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (29), (30), (32), (33), (38), (41), (43), (44),
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (46), (47), (48), (50), (52), (53), (54), (56),
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (57), (58), (61), (63), (64), (65), (67), (68),
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (70), (71), (74), (75), (77), (78), (81), (82),
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (83), (84), (85), (86), (88), (89), (91), (92),
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (93), (96), (99), (100), (103), (104), (105),
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (111), (112), (114), (115), (117), (118), (119),
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (123), (124), (125), (127), (128), (129), (130),
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (131), (132), (133), (135), (137), (139), (140),
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (141), (142), (148), (152), (154), (155), (156),
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (166), (170), (173), (177), (178), (179), (181),
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (182), (184), (186), (190), (195), (207), (208),
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (209), (210), (211), (306) are inconsistent by
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #474.
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (307)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (307) gives:
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (308)  all_57_11 = e1 & op(e1, e0) = e1
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (308) implies:
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (309)  all_57_11 = e1
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (12), (13), (14), (15), (16), (17),
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18), (19), (22), (23), (24), (26), (27), (28),
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (29), (30), (32), (33), (38), (41), (43), (44),
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (46), (47), (48), (50), (52), (53), (54), (56),
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (57), (58), (61), (63), (64), (65), (67), (68),
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (70), (71), (74), (75), (77), (78), (81), (82),
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (83), (84), (85), (86), (88), (89), (91), (92),
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (93), (96), (99), (100), (103), (104), (105),
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (111), (112), (114), (115), (117), (118), (119),
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (122), (123), (124), (125), (127), (128), (129),
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (130), (131), (132), (133), (135), (137), (139),
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (140), (141), (142), (148), (152), (154), (155),
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (156), (166), (170), (173), (177), (178), (179),
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (181), (182), (184), (186), (190), (195), (207),
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (208), (209), (210), (211), (252), (263), (299),
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (309) are inconsistent by sub-proof #454.
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (310)  all_57_15 = e1 & op(e0, e0) = e1
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (12), (13), (14), (15), (17), (18),
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19), (22), (23), (26), (27), (28), (30), (33),
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (38), (41), (43), (44), (48), (50), (52), (53),
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (54), (57), (61), (63), (64), (67), (70), (71),
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (74), (75), (78), (81), (82), (85), (88), (89),
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (91), (92), (93), (99), (100), (103), (104),
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (105), (111), (112), (114), (115), (117), (118),
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (122), (123), (124), (125), (127), (129),
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (130), (131), (132), (133), (137), (140), (141),
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (142), (156), (214), (236), (310) are inconsistent
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #459.
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (311)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (311) gives:
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (312)  all_57_11 = e2 & op(e1, e0) = e2
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (17), (54), (81), (88), (122), (127), (173),
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (236), (244), (270), (312) are inconsistent by
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #461.
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (313)  all_57_15 = e2 & op(e0, e0) = e2
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (313) implies:
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (314)  all_57_15 = e2
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (71), (314) imply:
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (315)  e3 = e2
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (239), (315) imply:
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (316)  all_57_1 = e2
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (12), (13), (14), (15), (17), (18),
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19), (22), (23), (26), (27), (28), (30), (33),
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (38), (41), (43), (44), (48), (50), (52), (53),
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (54), (57), (61), (63), (64), (67), (70), (71),
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (74), (75), (78), (81), (82), (85), (88), (89),
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (91), (92), (93), (99), (100), (103), (104),
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (105), (111), (112), (114), (115), (117), (118),
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (122), (123), (124), (125), (127), (129),
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (130), (131), (132), (133), (137), (140), (141),
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (142), (156), (214), (219), (263), (316) are
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #515.
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (317)  all_57_9 = e1 & op(e3, e0) = e1
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (317) implies:
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (318)  all_57_9 = e1
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18) gives:
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (319)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e0)
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (319) gives:
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (320)  all_57_6 = e0 & op(e1, e3) = e0
% 227.78/39.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (12), (13), (14), (15), (17), (18),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19), (22), (23), (26), (27), (28), (30), (33),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (38), (41), (43), (44), (48), (50), (52), (53),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (54), (57), (61), (63), (64), (67), (70), (71),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (74), (75), (78), (81), (82), (85), (88), (89),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (91), (92), (93), (99), (100), (103), (104),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (105), (111), (112), (114), (115), (117), (118),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (122), (123), (124), (125), (127), (129),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (130), (131), (132), (133), (137), (140), (141),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (142), (156), (214), (236), (239), (320) are
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #510.
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (321)  all_57_7 = e0 & op(e1, e2) = e0
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (88), (219), (321) are inconsistent by sub-proof
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #509.
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (322)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (322) gives:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (323)  all_57_8 = e0 & op(e1, e1) = e0
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (17), (54), (81), (88), (122), (127), (173),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (236), (244), (252), (323) are inconsistent by
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #508.
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (324)  all_57_11 = e0 & op(e1, e0) = e0
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (324) implies:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (325)  all_57_11 = e0
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (12), (13), (14), (15), (16), (17),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18), (19), (22), (23), (24), (26), (27), (28),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (29), (30), (32), (33), (38), (41), (43), (44),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (46), (47), (48), (50), (52), (53), (54), (56),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (57), (58), (61), (63), (64), (65), (67), (68),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (70), (71), (74), (75), (77), (78), (81), (82),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (83), (84), (85), (86), (88), (89), (91), (92),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (93), (96), (99), (100), (103), (104), (105),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (111), (112), (114), (115), (117), (118), (119),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (122), (123), (124), (125), (127), (128), (129),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (130), (131), (132), (133), (135), (137), (139),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (140), (141), (142), (148), (152), (154), (155),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (156), (166), (170), (173), (177), (178), (179),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (181), (182), (184), (186), (190), (195), (207),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (208), (209), (210), (211), (214), (219), (232),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (235), (236), (239), (244), (252), (253),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (318), (325) are inconsistent by sub-proof #458.
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | |   (326)  all_57_11 = e2 & op(e1, e0) = e2
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (326) implies:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | |   (327)  all_57_11 = e2
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18) gives:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (328)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e0)
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (328) gives:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (329)  all_57_6 = e0 & op(e1, e3) = e0
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (12), (13), (14), (15), (17), (18),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19), (22), (23), (26), (27), (28), (30), (33),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (38), (41), (43), (44), (48), (50), (52), (53),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (54), (57), (61), (63), (64), (67), (70), (71),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (74), (75), (78), (81), (82), (85), (88), (89),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (91), (92), (93), (99), (100), (103), (104),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (105), (111), (112), (114), (115), (117), (118),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (122), (123), (124), (125), (127), (129),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (130), (131), (132), (133), (137), (140), (141),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (142), (156), (214), (236), (239), (329) are
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #510.
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (330)  all_57_7 = e0 & op(e1, e2) = e0
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (88), (219), (330) are inconsistent by sub-proof
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #509.
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (331)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (331) gives:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (332)  all_57_8 = e0 & op(e1, e1) = e0
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (332) implies:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (333)  op(e1, e1) = e0
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (111) gives:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (334)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e3)
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (334) gives:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (335)  all_57_2 = e3 & op(e2, e3) = e3
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (335) implies:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (336)  all_57_2 = e3
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (17), (88), (122), (173), (236), (244),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (336) are inconsistent by sub-proof #1535.
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (337)  all_57_3 = e3 & op(e2, e2) = e3
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (12), (13), (14), (15), (17), (18),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19), (22), (23), (26), (27), (28), (30), (33),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (38), (41), (43), (44), (48), (50), (52), (53),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (54), (57), (61), (63), (64), (67), (70), (71),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (74), (75), (78), (81), (82), (85), (88), (89),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (91), (92), (93), (99), (100), (103), (104),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (105), (111), (112), (114), (115), (117), (118),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (122), (123), (124), (125), (127), (129),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (130), (131), (132), (133), (137), (140), (141),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (142), (156), (214), (239), (337) are inconsistent
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #473.
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (338)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e2, e0) = e3)
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (338) gives:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (339)  all_57_5 = e3 & op(e2, e1) = e3
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (339) implies:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (340)  all_57_5 = e3
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (12), (13), (14), (15), (17), (18),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19), (22), (23), (26), (27), (28), (30), (33),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (38), (41), (43), (44), (48), (50), (52), (53),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (54), (57), (61), (63), (64), (67), (70), (71),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (74), (75), (78), (81), (82), (85), (88), (89),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (91), (92), (93), (99), (100), (103), (104),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (105), (111), (112), (114), (115), (117), (118),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (122), (123), (124), (125), (127), (129),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (130), (131), (132), (133), (137), (140), (141),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (142), (156), (214), (236), (333), (340) are
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #453.
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (341)  all_57_10 = e3 & op(e2, e0) = e3
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (341) implies:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (342)  all_57_10 = e3
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (54), (61), (71), (81), (88), (104), (122),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (123), (132), (327), (342) are inconsistent by
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1983.
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (343)  all_57_11 = e0 & op(e1, e0) = e0
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (17), (54), (81), (88), (122), (127), (173),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (236), (244), (327), (343) are inconsistent by
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #491.
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | |   (344)  all_57_3 = e3 & op(e2, e2) = e3
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (344) implies:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | |   (345)  all_57_3 = e3
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (52), (61), (345) are inconsistent by sub-proof
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | |            #2358.
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | |   (346)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (346) gives:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | |   (347)  all_57_7 = e3 & op(e1, e2) = e3
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (347) implies:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | |   (348)  all_57_7 = e3
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (219), (348) imply:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | |   (349)  e3 = e1
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (12), (13), (14), (15), (17), (18),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | |            (19), (22), (23), (26), (27), (28), (30), (33),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | |            (38), (41), (43), (44), (48), (50), (52), (53),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | |            (54), (57), (61), (63), (64), (67), (70), (71),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | |            (74), (75), (78), (81), (82), (85), (88), (89),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | |            (91), (92), (93), (99), (100), (103), (104),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | |            (105), (111), (112), (114), (115), (117), (118),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | |            (119), (122), (123), (124), (125), (127), (129),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | |            (130), (131), (132), (133), (137), (140), (141),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | |            (142), (156), (214), (236), (349) are inconsistent
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #472.
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | |   (350)  all_57_13 = e3 & op(e0, e2) = e3
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (350) implies:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | |   (351)  all_57_13 = e3
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (233), (351) imply:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | |   (352)  e3 = e2
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (13), (15), (17), (19), (22), (26), (27),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | |            (33), (44), (50), (52), (54), (61), (71), (81),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | |            (85), (88), (104), (111), (115), (118), (119),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | |            (122), (123), (131), (132), (140), (142), (156),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | |            (236), (352) are inconsistent by sub-proof #604.
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | |   (353)  all_57_7 = e3 & op(e1, e2) = e3
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (219), (353) are inconsistent by sub-proof
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | |            #1247.
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | |   (354)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 227.78/39.33  | | | | | | | | | | | | | | | | | | |            e3 & op(e1, e0) = e3)
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (19), (26), (27), (54), (61), (71), (81),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | |            (88), (104), (122), (123), (132), (354) are
% 227.78/39.33  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1786.
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.33  | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | End of split
% 227.78/39.33  | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | End of split
% 227.78/39.33  | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | End of split
% 227.78/39.33  | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | Case 2:
% 227.78/39.33  | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | |   (355)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 227.78/39.33  | | | | | | | | | | | | | | |            e1 & op(e1, e0) = e1)
% 227.78/39.33  | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | BETA: splitting (355) gives:
% 227.78/39.33  | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | Case 1:
% 227.78/39.33  | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | |   (356)  all_57_8 = e1 & op(e1, e1) = e1
% 227.78/39.33  | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | ALPHA: (356) implies:
% 227.78/39.33  | | | | | | | | | | | | | | | |   (357)  all_57_8 = e1
% 227.78/39.33  | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (12), (13), (14), (15), (16), (17),
% 227.78/39.33  | | | | | | | | | | | | | | | |            (18), (19), (22), (23), (24), (26), (27), (28),
% 227.78/39.33  | | | | | | | | | | | | | | | |            (29), (30), (32), (33), (38), (41), (43), (44),
% 227.78/39.33  | | | | | | | | | | | | | | | |            (46), (47), (48), (50), (52), (53), (54), (56),
% 227.78/39.33  | | | | | | | | | | | | | | | |            (57), (58), (61), (63), (64), (65), (67), (68),
% 227.78/39.33  | | | | | | | | | | | | | | | |            (70), (71), (74), (75), (77), (78), (81), (82),
% 227.78/39.33  | | | | | | | | | | | | | | | |            (83), (84), (85), (86), (88), (89), (91), (92),
% 227.78/39.33  | | | | | | | | | | | | | | | |            (93), (96), (99), (100), (103), (104), (105),
% 227.78/39.33  | | | | | | | | | | | | | | | |            (111), (112), (114), (115), (117), (118), (119),
% 227.78/39.33  | | | | | | | | | | | | | | | |            (123), (124), (125), (127), (128), (129), (130),
% 227.78/39.33  | | | | | | | | | | | | | | | |            (131), (132), (133), (135), (137), (139), (140),
% 227.78/39.33  | | | | | | | | | | | | | | | |            (141), (142), (148), (152), (154), (155), (156),
% 227.78/39.33  | | | | | | | | | | | | | | | |            (166), (170), (173), (177), (178), (179), (181),
% 227.78/39.33  | | | | | | | | | | | | | | | |            (182), (184), (186), (190), (195), (207), (208),
% 227.78/39.33  | | | | | | | | | | | | | | | |            (209), (210), (211), (357) are inconsistent by
% 227.78/39.33  | | | | | | | | | | | | | | | |            sub-proof #474.
% 227.78/39.33  | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | Case 2:
% 227.78/39.33  | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | |   (358)  all_57_11 = e1 & op(e1, e0) = e1
% 227.78/39.33  | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | ALPHA: (358) implies:
% 227.78/39.33  | | | | | | | | | | | | | | | |   (359)  all_57_11 = e1
% 227.78/39.33  | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | BETA: splitting (141) gives:
% 227.78/39.33  | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.33  | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | |   (360)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 227.78/39.33  | | | | | | | | | | | | | | | | |            & op(e1, e2) = e2)
% 227.78/39.33  | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | BETA: splitting (360) gives:
% 227.78/39.33  | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | |   (361)  all_57_6 = e2 & op(e1, e3) = e2
% 227.78/39.33  | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | ALPHA: (361) implies:
% 227.78/39.33  | | | | | | | | | | | | | | | | | |   (362)  all_57_6 = e2
% 227.78/39.33  | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (13), (15), (17), (19), (22), (26), (27),
% 227.78/39.33  | | | | | | | | | | | | | | | | | |            (33), (44), (50), (52), (54), (61), (71), (81),
% 227.78/39.33  | | | | | | | | | | | | | | | | | |            (85), (88), (104), (111), (115), (118), (119),
% 227.78/39.33  | | | | | | | | | | | | | | | | | |            (122), (123), (131), (132), (140), (142), (156),
% 227.78/39.33  | | | | | | | | | | | | | | | | | |            (362) are inconsistent by sub-proof #728.
% 227.78/39.33  | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | |   (363)  all_57_7 = e2 & op(e1, e2) = e2
% 227.78/39.33  | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | ALPHA: (363) implies:
% 227.78/39.33  | | | | | | | | | | | | | | | | | |   (364)  all_57_7 = e2
% 227.78/39.33  | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | BETA: splitting (123) gives:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | |   (365)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 227.78/39.33  | | | | | | | | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | BETA: splitting (365) gives:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | |   (366)  all_57_9 = e2 & op(e3, e0) = e2
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | ALPHA: (366) implies:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | |   (367)  all_57_9 = e2
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (12), (13), (14), (15), (17), (18),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | |            (19), (22), (23), (26), (27), (28), (30), (33),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | |            (38), (41), (43), (44), (48), (50), (52), (53),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | |            (54), (57), (61), (63), (64), (67), (70), (71),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | |            (74), (75), (78), (81), (82), (85), (88), (89),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | |            (91), (92), (93), (99), (100), (103), (104),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | |            (105), (111), (112), (114), (115), (117), (118),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | |            (119), (122), (123), (124), (125), (127), (129),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | |            (130), (131), (132), (133), (137), (140), (141),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | |            (142), (156), (214), (359), (367) are inconsistent
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | |            by sub-proof #456.
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | |   (368)  all_57_10 = e2 & op(e2, e0) = e2
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | ALPHA: (368) implies:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | |   (369)  all_57_10 = e2
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | BETA: splitting (63) gives:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | |   (370)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e1)
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (370) gives:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | |   (371)  all_57_4 = e1 & op(e3, e1) = e1
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (371) implies:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | |   (372)  all_57_4 = e1
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (92) gives:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | |   (373)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e3)
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (373) gives:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | |   (374)  all_57_4 = e3 & op(e3, e1) = e3
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (374) implies:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | |   (375)  all_57_4 = e3
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (372), (375) are inconsistent by sub-proof
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | |            #2426.
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | |   (376)  all_57_5 = e3 & op(e2, e1) = e3
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (376) implies:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | |   (377)  all_57_5 = e3
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | |   (378)  op(e2, e1) = e3
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (85) gives:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | |   (379)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e3)
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (379) gives:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | |   (380)  all_57_0 = e3 & op(e3, e3) = e3
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (380) implies:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | |   (381)  op(e3, e3) = e3
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (12), (13), (14), (15), (17), (18),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | |            (19), (22), (23), (26), (27), (28), (30), (33),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | |            (38), (41), (43), (44), (48), (50), (52), (53),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | |            (54), (57), (61), (63), (64), (67), (70), (71),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | |            (74), (75), (78), (81), (82), (85), (88), (89),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | |            (91), (99), (100), (103), (104), (105), (112),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | |            (114), (115), (117), (118), (122), (123), (124),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | |            (125), (127), (129), (130), (131), (132), (133),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | |            (137), (140), (141), (142), (377), (378), (381)
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1438.
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | |   (382)  all_57_1 = e3 & op(e3, e2) = e3
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (382) implies:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | |   (383)  all_57_1 = e3
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18) gives:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (384)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e0)
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (384) gives:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (385)  all_57_6 = e0 & op(e1, e3) = e0
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (13), (15), (17), (19), (22), (26), (27),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (52), (54), (61), (71), (74), (81), (88), (92),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (103), (104), (119), (122), (123), (127), (131),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (132), (140), (369), (372), (383), (385) are
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #666.
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (386)  all_57_7 = e0 & op(e1, e2) = e0
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (386) implies:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (387)  all_57_7 = e0
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (17), (52), (54), (81), (88), (118), (122),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (364), (369), (377), (387) are inconsistent by
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #466.
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (388)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (388) gives:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (389)  all_57_8 = e0 & op(e1, e1) = e0
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (389) implies:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (390)  op(e1, e1) = e0
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (119) gives:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (391)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e3)
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (13), (15), (17), (19), (22), (26), (27),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (52), (54), (61), (71), (74), (81), (88), (92),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (103), (104), (122), (123), (127), (131), (132),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (140), (369), (372), (383), (391) are inconsistent
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #667.
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (392)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e3) = e3)
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (392) gives:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (393)  all_57_6 = e3 & op(e1, e3) = e3
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (393) implies:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (394)  all_57_6 = e3
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (12), (13), (14), (15), (17), (18),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19), (22), (23), (26), (27), (28), (30), (33),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (38), (41), (43), (44), (48), (50), (52), (53),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (54), (57), (61), (63), (64), (67), (70), (71),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (74), (75), (78), (81), (82), (85), (88), (89),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (91), (92), (93), (99), (100), (103), (104),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (105), (111), (112), (114), (115), (117), (118),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (122), (123), (124), (125), (127), (129),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (130), (131), (132), (133), (137), (140), (141),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (142), (156), (214), (377), (390), (394) are
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #453.
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (395)  all_57_12 = e3 & op(e0, e3) = e3
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (395) implies:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (396)  all_57_12 = e3
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (17), (52), (54), (61), (71), (74), (81),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (88), (103), (104), (122), (140), (383), (396) are
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1037.
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (397)  all_57_11 = e0 & op(e1, e0) = e0
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (88), (359), (397) are inconsistent by sub-proof
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1257.
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | |   (398)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e3)
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (398) gives:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | |   (399)  all_57_4 = e3 & op(e3, e1) = e3
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (399) implies:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | |   (400)  all_57_4 = e3
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (372), (400) imply:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | |   (401)  e3 = e1
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (401) implies:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | |   (402)  e3 = e1
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (377), (402) imply:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | |   (403)  all_57_5 = e1
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (12), (13), (14), (15), (17), (18),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | |            (19), (22), (23), (26), (27), (28), (30), (33),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | |            (38), (41), (43), (44), (48), (50), (52), (53),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | |            (54), (57), (61), (63), (64), (67), (70), (71),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | |            (74), (75), (78), (81), (82), (85), (88), (89),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | |            (91), (92), (93), (99), (100), (103), (104),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | |            (105), (111), (112), (114), (115), (117), (118),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (122), (123), (124), (125), (127), (129),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | |            (130), (131), (132), (133), (137), (140), (141),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | |            (142), (156), (173), (364), (369), (400), (403)
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #449.
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | |   (404)  all_57_9 = e3 & op(e3, e0) = e3
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (404) implies:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | |   (405)  op(e3, e0) = e3
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (115), (142), (405) are inconsistent by
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2458.
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | |   (406)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e1) = e3)
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (19), (26), (27), (54), (61), (71), (74),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | |            (81), (88), (103), (104), (122), (406) are
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1794.
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | |   (407)  all_57_5 = e1 & op(e2, e1) = e1
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (407) implies:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | |   (408)  all_57_5 = e1
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (12), (13), (14), (15), (17), (18),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | |            (19), (22), (23), (26), (27), (28), (30), (33),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | |            (38), (41), (43), (44), (48), (50), (52), (53),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | |            (54), (57), (61), (63), (64), (67), (70), (71),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | |            (74), (75), (78), (81), (82), (85), (88), (89),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | |            (91), (92), (93), (99), (100), (103), (104),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | |            (105), (111), (112), (114), (115), (117), (118),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | |            (119), (122), (123), (124), (125), (127), (129),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | |            (130), (131), (132), (133), (137), (140), (141),
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | |            (142), (156), (173), (364), (369), (408) are
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #448.
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | |   (409)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e1) = e1)
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (409) gives:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | |   (410)  all_57_8 = e1 & op(e1, e1) = e1
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (410) implies:
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | |   (411)  all_57_8 = e1
% 227.78/39.33  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (12), (13), (14), (15), (16), (17),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | |            (18), (19), (22), (23), (24), (26), (27), (28),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | |            (29), (30), (32), (33), (38), (41), (43), (44),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | |            (46), (47), (48), (50), (52), (53), (54), (56),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | |            (57), (58), (61), (63), (64), (65), (67), (68),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | |            (70), (71), (74), (75), (77), (78), (81), (82),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | |            (83), (84), (85), (86), (88), (89), (91), (92),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | |            (93), (96), (99), (100), (103), (104), (105),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | |            (111), (112), (114), (115), (117), (118), (119),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | |            (123), (124), (125), (127), (128), (129), (130),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | |            (131), (132), (133), (135), (137), (139), (140),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | |            (141), (142), (148), (152), (154), (155), (156),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | |            (166), (170), (173), (177), (178), (179), (181),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | |            (182), (184), (186), (190), (195), (207), (208),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | |            (209), (210), (211), (411) are inconsistent by
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #474.
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | |   (412)  all_57_14 = e1 & op(e0, e1) = e1
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (412) implies:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | |   (413)  all_57_14 = e1
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (93) gives:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | |   (414)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e3)
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (414) gives:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | |   (415)  all_57_1 = e3 & op(e3, e2) = e3
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (415) implies:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | |   (416)  all_57_1 = e3
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (33) gives:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | |   (417)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e1)
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (19), (122), (156), (416), (417) are
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1607.
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | |   (418)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e1)
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (418) gives:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | |   (419)  all_57_4 = e1 & op(e3, e1) = e1
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (419) implies:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | |   (420)  all_57_4 = e1
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (103) gives:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (421)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (421) gives:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (422)  all_57_12 = e2 & op(e0, e3) = e2
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (422) implies:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (423)  all_57_12 = e2
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13) gives:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (424)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e1)
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (424) gives:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (425)  all_57_0 = e1 & op(e3, e3) = e1
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (425) implies:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (426)  op(e3, e3) = e1
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (122), (156), (426) are inconsistent by
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1950.
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (427)  all_57_2 = e1 & op(e2, e3) = e1
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (427) implies:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (428)  all_57_2 = e1
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (92) gives:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (429)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e3)
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (429) gives:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (430)  all_57_4 = e3 & op(e3, e1) = e3
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (430) implies:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (431)  all_57_4 = e3
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (420), (431) are inconsistent by sub-proof
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2426.
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (432)  all_57_5 = e3 & op(e2, e1) = e3
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (432) implies:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (433)  all_57_5 = e3
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (119) gives:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (434)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e3)
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (434) gives:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (435)  all_57_0 = e3 & op(e3, e3) = e3
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (15), (17), (19), (22), (26), (27), (52),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (54), (61), (71), (81), (88), (104), (122), (123),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (127), (131), (132), (140), (416), (435) are
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #791.
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (436)  all_57_2 = e3 & op(e2, e3) = e3
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (436) implies:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (437)  all_57_2 = e3
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (17), (52), (88), (122), (369), (433), (437)
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1804.
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (438)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e3) = e3)
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (438) gives:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (439)  all_57_6 = e3 & op(e1, e3) = e3
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (439) implies:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (440)  all_57_6 = e3
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (13), (15), (17), (19), (22), (26), (27),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (52), (54), (61), (71), (74), (81), (88), (92),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (103), (104), (118), (119), (122), (123), (127),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (131), (132), (140), (156), (173), (369), (416),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (420), (423), (428), (433), (440) are inconsistent
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #664.
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (441)  all_57_12 = e3 & op(e0, e3) = e3
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (441) implies:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (442)  all_57_12 = e3
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (17), (52), (54), (61), (71), (74), (81),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (88), (103), (104), (122), (140), (416), (442) are
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1037.
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (443)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e1) = e3)
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (19), (26), (27), (54), (61), (71), (74),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (81), (88), (103), (104), (122), (443) are
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1794.
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (444)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e3) = e1)
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (12), (13), (14), (15), (17), (18),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19), (22), (23), (26), (27), (28), (30), (33),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (38), (41), (43), (44), (48), (50), (52), (53),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (54), (57), (61), (63), (64), (67), (70), (71),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (74), (75), (78), (81), (82), (85), (88), (89),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (91), (92), (93), (99), (100), (103), (104),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (105), (111), (112), (114), (115), (117), (118),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (122), (123), (124), (125), (127), (129),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (130), (131), (132), (133), (137), (140), (141),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (142), (156), (214), (423), (444) are inconsistent
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #520.
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (445)  all_57_13 = e2 & op(e0, e2) = e2
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (445) implies:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (446)  all_57_13 = e2
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (52), (88), (122), (140), (364), (416),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (446) are inconsistent by sub-proof #1698.
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (447)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (54), (71), (122), (413), (447) are inconsistent
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1529.
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | |   (448)  all_57_9 = e1 & op(e3, e0) = e1
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (448) implies:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | |   (449)  all_57_9 = e1
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (103) gives:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (450)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (450) gives:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (451)  all_57_12 = e2 & op(e0, e3) = e2
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (451) implies:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (452)  all_57_12 = e2
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13) gives:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (453)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e1)
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (453) gives:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (454)  all_57_0 = e1 & op(e3, e3) = e1
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (454) implies:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (455)  op(e3, e3) = e1
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (122), (156), (455) are inconsistent by
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1950.
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (456)  all_57_2 = e1 & op(e2, e3) = e1
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (456) implies:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (457)  all_57_2 = e1
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (13), (15), (17), (19), (22), (26), (27),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (52), (54), (61), (71), (81), (88), (104), (111),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (118), (122), (123), (127), (131), (132), (140),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (156), (173), (369), (416), (449), (452), (457)
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #447.
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (458)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e3) = e1)
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (12), (13), (14), (15), (17), (18),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19), (22), (23), (26), (27), (28), (30), (33),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (38), (41), (43), (44), (48), (50), (52), (53),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (54), (57), (61), (63), (64), (67), (70), (71),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (74), (75), (78), (81), (82), (85), (88), (89),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (91), (92), (93), (99), (100), (103), (104),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (105), (111), (112), (114), (115), (117), (118),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (122), (123), (124), (125), (127), (129),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (130), (131), (132), (133), (137), (140), (141),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (142), (156), (214), (452), (458) are inconsistent
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #520.
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (459)  all_57_13 = e2 & op(e0, e2) = e2
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (459) implies:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (460)  all_57_13 = e2
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (52), (88), (122), (140), (364), (416),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (460) are inconsistent by sub-proof #1698.
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (461)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (54), (71), (122), (413), (461) are inconsistent
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1529.
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | |   (462)  all_57_3 = e3 & op(e2, e2) = e3
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (462) implies:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | |   (463)  all_57_3 = e3
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (52), (61), (463) are inconsistent by sub-proof
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | |            #2358.
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | |   (464)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (464) gives:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | |   (465)  all_57_7 = e3 & op(e1, e2) = e3
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (465) implies:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | |   (466)  all_57_7 = e3
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (54), (364), (466) are inconsistent by sub-proof
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | |            #2102.
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | |   (467)  all_57_13 = e3 & op(e0, e2) = e3
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (467) implies:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | |   (468)  all_57_13 = e3
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (12), (13), (14), (15), (17), (18),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | |            (19), (22), (23), (26), (27), (28), (30), (33),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | |            (38), (41), (43), (44), (48), (50), (52), (53),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | |            (54), (57), (61), (63), (64), (67), (70), (71),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | |            (74), (75), (78), (81), (82), (85), (88), (89),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | |            (91), (92), (93), (99), (100), (103), (104),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | |            (105), (111), (112), (114), (115), (117), (118),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | |            (119), (122), (123), (124), (125), (127), (129),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | |            (130), (131), (132), (133), (137), (140), (141),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | |            (142), (156), (214), (413), (468) are inconsistent
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #518.
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | |   (469)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 227.78/39.34  | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (54), (71), (122), (359), (469) are inconsistent
% 227.78/39.34  | | | | | | | | | | | | | | | | | | |            by sub-proof #717.
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.34  | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | End of split
% 227.78/39.34  | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.34  | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | |   (470)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 227.78/39.34  | | | | | | | | | | | | | | | | |            e2 & op(e1, e0) = e2)
% 227.78/39.34  | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | BETA: splitting (470) gives:
% 227.78/39.34  | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | |   (471)  all_57_8 = e2 & op(e1, e1) = e2
% 227.78/39.34  | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | ALPHA: (471) implies:
% 227.78/39.34  | | | | | | | | | | | | | | | | | |   (472)  all_57_8 = e2
% 227.78/39.34  | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | BETA: splitting (123) gives:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | |   (473)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 227.78/39.34  | | | | | | | | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | BETA: splitting (473) gives:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | |   (474)  all_57_9 = e2 & op(e3, e0) = e2
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | ALPHA: (474) implies:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | |   (475)  all_57_9 = e2
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | BETA: splitting (50) gives:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | |   (476)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e0)
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (476) gives:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | |   (477)  all_57_0 = e0 & op(e3, e3) = e0
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (477) implies:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | |   (478)  op(e3, e3) = e0
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (81), (156), (478) are inconsistent by
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2403.
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | |   (479)  all_57_1 = e0 & op(e3, e2) = e0
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (479) implies:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | |   (480)  all_57_1 = e0
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (93) gives:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | |   (481)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e3)
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (52), (61), (480), (481) are inconsistent by
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1284.
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | |   (482)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (482) gives:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | |   (483)  all_57_7 = e3 & op(e1, e2) = e3
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (483) implies:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | |   (484)  all_57_7 = e3
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (17), (52), (54), (81), (88), (122), (140),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | |            (480), (484) are inconsistent by sub-proof #2098.
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | |   (485)  all_57_13 = e3 & op(e0, e2) = e3
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (485) implies:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | |   (486)  all_57_13 = e3
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (74) gives:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | |   (487)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (13), (15), (17), (19), (22), (26), (27),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | |            (52), (54), (61), (71), (74), (81), (88), (103),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | |            (104), (111), (118), (119), (122), (123), (127),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | |            (131), (132), (140), (156), (480), (486), (487)
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #521.
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | |   (488)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (488) gives:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | |   (489)  all_57_14 = e1 & op(e0, e1) = e1
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (489) implies:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | |   (490)  all_57_14 = e1
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18) gives:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (491)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e0)
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (491) gives:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (492)  all_57_6 = e0 & op(e1, e3) = e0
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (492) implies:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (493)  all_57_6 = e0
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (13), (15), (17), (19), (22), (26), (27),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (52), (54), (61), (71), (74), (81), (88), (103),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (104), (111), (118), (119), (122), (123), (127),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (131), (132), (140), (480), (486), (493) are
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #691.
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (494)  all_57_7 = e0 & op(e1, e2) = e0
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (494) implies:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (495)  all_57_7 = e0
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (103) gives:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (496)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (496) gives:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (497)  all_57_12 = e2 & op(e0, e3) = e2
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (497) implies:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (498)  all_57_12 = e2
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13) gives:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (499)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e1)
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (499) gives:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (500)  all_57_0 = e1 & op(e3, e3) = e1
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (500) implies:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (501)  op(e3, e3) = e1
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (122), (156), (501) are inconsistent by
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1950.
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (502)  all_57_2 = e1 & op(e2, e3) = e1
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (502) implies:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (503)  all_57_2 = e1
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (140) gives:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (504)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (504) gives:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (505)  all_57_1 = e1 & op(e3, e2) = e1
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (505) implies:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (506)  all_57_1 = e1
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (480), (506) imply:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (507)  e1 = e0
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (17), (52), (54), (61), (81), (88), (111),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (118), (122), (503), (507) are inconsistent by
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1252.
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (508)  all_57_3 = e1 & op(e2, e2) = e1
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (508) implies:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (509)  all_57_3 = e1
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (52), (509) imply:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (510)  e1 = e0
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (17), (52), (54), (61), (81), (88), (111),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (118), (122), (503), (510) are inconsistent by
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1252.
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (511)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (511) gives:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (512)  all_57_7 = e1 & op(e1, e2) = e1
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (512) implies:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (513)  all_57_7 = e1
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (495), (513) imply:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (514)  e1 = e0
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (17), (52), (54), (61), (81), (88), (111),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (118), (122), (503), (514) are inconsistent by
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1252.
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (515)  all_57_13 = e1 & op(e0, e2) = e1
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (486), (515) are inconsistent by sub-proof
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2264.
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (516)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e3) = e1)
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (516) gives:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (517)  all_57_6 = e1 & op(e1, e3) = e1
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (517) implies:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (518)  all_57_6 = e1
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (19), (22), (26), (27), (54), (61), (71),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (81), (88), (104), (122), (123), (132), (495),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (518) are inconsistent by sub-proof #1735.
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (519)  all_57_12 = e1 & op(e0, e3) = e1
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (519) implies:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (520)  all_57_12 = e1
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (498), (520) imply:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (521)  e2 = e1
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (472), (521) imply:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (522)  all_57_8 = e1
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (12), (13), (14), (15), (16), (17),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18), (19), (22), (23), (24), (26), (27), (28),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (29), (30), (32), (33), (38), (41), (43), (44),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (46), (47), (48), (50), (52), (53), (54), (56),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (57), (58), (61), (63), (64), (65), (67), (68),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (70), (71), (74), (75), (77), (78), (81), (82),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (83), (84), (85), (86), (88), (89), (91), (92),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (93), (96), (99), (100), (103), (104), (105),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (111), (112), (114), (115), (117), (118), (119),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (123), (124), (125), (127), (128), (129), (130),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (131), (132), (133), (135), (137), (139), (140),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (141), (142), (148), (152), (154), (155), (156),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (166), (170), (173), (177), (178), (179), (181),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (182), (184), (186), (190), (195), (207), (208),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (209), (210), (211), (522) are inconsistent by
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #474.
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (523)  all_57_13 = e2 & op(e0, e2) = e2
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (54), (486), (523) are inconsistent by sub-proof
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2146.
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (524)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (12), (13), (14), (15), (16), (17),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18), (19), (22), (23), (24), (26), (27), (28),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (29), (30), (32), (33), (38), (41), (43), (44),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (46), (47), (48), (50), (52), (53), (54), (56),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (57), (58), (61), (63), (64), (65), (67), (68),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (70), (71), (74), (75), (77), (78), (81), (82),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (83), (84), (85), (86), (88), (89), (91), (92),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (93), (96), (99), (100), (103), (104), (105),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (111), (112), (114), (115), (117), (118), (119),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (123), (124), (125), (127), (128), (129), (130),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (131), (132), (133), (135), (137), (139), (140),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (141), (142), (148), (152), (154), (155), (156),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (166), (170), (173), (177), (178), (179), (181),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (182), (184), (186), (190), (195), (207), (208),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (209), (210), (211), (472), (490), (524) are
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #468.
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (525)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (525) gives:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (526)  all_57_8 = e0 & op(e1, e1) = e0
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (81), (472), (526) are inconsistent by sub-proof
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #917.
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (527)  all_57_11 = e0 & op(e1, e0) = e0
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (88), (359), (527) are inconsistent by sub-proof
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1257.
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | |   (528)  all_57_15 = e1 & op(e0, e0) = e1
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (71), (528) are inconsistent by sub-proof
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | |            #2325.
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | |   (529)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e0)
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (529) gives:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | |   (530)  all_57_4 = e0 & op(e3, e1) = e0
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (530) implies:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | |   (531)  all_57_4 = e0
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (17), (19), (26), (27), (52), (54), (61),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | |            (71), (74), (81), (88), (92), (99), (103), (104),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | |            (118), (122), (359), (475), (531) are inconsistent
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1041.
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | |   (532)  all_57_9 = e0 & op(e3, e0) = e0
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (81), (475), (532) are inconsistent by sub-proof
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | |            #1973.
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | |   (533)  all_57_10 = e2 & op(e2, e0) = e2
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | ALPHA: (533) implies:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | |   (534)  all_57_10 = e2
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | BETA: splitting (63) gives:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | |   (535)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e1)
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (535) gives:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | |   (536)  all_57_4 = e1 & op(e3, e1) = e1
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (536) implies:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | |   (537)  all_57_4 = e1
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (12), (13), (14), (15), (16), (17),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | |            (18), (19), (22), (23), (24), (26), (27), (28),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | |            (29), (30), (32), (33), (38), (41), (43), (44),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | |            (46), (47), (48), (50), (52), (53), (54), (56),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | |            (57), (58), (61), (63), (64), (65), (67), (68),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | |            (70), (71), (74), (75), (77), (78), (81), (82),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | |            (83), (84), (85), (86), (88), (89), (91), (92),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | |            (93), (96), (99), (100), (103), (104), (105),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | |            (111), (112), (114), (115), (117), (118), (119),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | |            (122), (123), (124), (125), (127), (128), (129),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | |            (130), (131), (132), (133), (135), (137), (139),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | |            (140), (141), (142), (148), (152), (154), (155),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | |            (156), (166), (170), (173), (177), (178), (179),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | |            (181), (182), (184), (186), (190), (195), (207),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | |            (208), (209), (210), (211), (359), (472), (534),
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | |            (537) are inconsistent by sub-proof #454.
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.34  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | |   (538)  all_57_5 = e1 & op(e2, e1) = e1
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (538) implies:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | |   (539)  all_57_5 = e1
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (92) gives:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | |   (540)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e3)
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (540) gives:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | |   (541)  all_57_4 = e3 & op(e3, e1) = e3
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (541) implies:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | |   (542)  all_57_4 = e3
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (50) gives:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (543)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e0)
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (543) gives:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | |   (544)  all_57_0 = e0 & op(e3, e3) = e0
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (544) implies:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | |   (545)  op(e3, e3) = e0
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (81), (156), (545) are inconsistent by
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2403.
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | |   (546)  all_57_1 = e0 & op(e3, e2) = e0
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (546) implies:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | |   (547)  all_57_1 = e0
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18) gives:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (548)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e0)
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (548) gives:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (549)  all_57_6 = e0 & op(e1, e3) = e0
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (549) implies:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (550)  all_57_6 = e0
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (33) gives:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (551)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e1)
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (88), (122), (156), (547), (551) are
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #452.
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (552)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e1)
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (552) gives:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (553)  all_57_4 = e1 & op(e3, e1) = e1
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (553) implies:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (554)  all_57_4 = e1
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (12), (13), (14), (15), (16), (17),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18), (19), (22), (23), (24), (26), (27), (28),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (29), (30), (32), (33), (38), (41), (43), (44),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (46), (47), (48), (50), (52), (53), (54), (56),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (57), (58), (61), (63), (64), (65), (67), (68),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (70), (71), (74), (75), (77), (78), (81), (82),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (83), (84), (85), (86), (88), (89), (91), (92),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (93), (96), (99), (100), (103), (104), (105),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (111), (112), (114), (115), (117), (118), (119),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (122), (123), (124), (125), (127), (128), (129),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (130), (131), (132), (133), (135), (137), (139),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (140), (141), (142), (148), (152), (154), (155),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (156), (166), (170), (173), (177), (178), (179),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (181), (182), (184), (186), (190), (195), (207),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (208), (209), (210), (211), (359), (472), (534),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (554) are inconsistent by sub-proof #454.
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (555)  all_57_9 = e1 & op(e3, e0) = e1
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (555) implies:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (556)  all_57_9 = e1
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (111) gives:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (557)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e3)
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (557) gives:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (558)  all_57_2 = e3 & op(e2, e3) = e3
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (558) implies:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (559)  all_57_2 = e3
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (15), (17), (19), (22), (26), (27), (52),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (54), (61), (71), (81), (88), (104), (111), (118),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (122), (123), (132), (140), (547), (550), (559)
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #826.
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (560)  all_57_3 = e3 & op(e2, e2) = e3
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (560) implies:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (561)  all_57_3 = e3
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (52), (61), (561) are inconsistent by sub-proof
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2358.
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (562)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e2, e0) = e3)
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (12), (13), (14), (15), (16), (17),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18), (19), (22), (23), (24), (26), (27), (28),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (29), (30), (32), (33), (38), (41), (43), (44),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (46), (47), (48), (50), (52), (53), (54), (56),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (57), (58), (61), (63), (64), (65), (67), (68),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (70), (71), (74), (75), (77), (78), (81), (82),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (83), (84), (85), (86), (88), (89), (91), (92),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (93), (96), (99), (100), (103), (104), (105),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (111), (112), (114), (115), (117), (118), (119),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (122), (123), (124), (125), (127), (128), (129),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (130), (131), (132), (133), (135), (137), (139),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (140), (141), (142), (148), (152), (154), (155),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (156), (166), (170), (173), (177), (178), (179),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (181), (182), (184), (186), (190), (195), (207),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (208), (209), (210), (211), (359), (472), (534),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (539), (542), (556), (562) are inconsistent by
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #445.
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (563)  all_57_7 = e0 & op(e1, e2) = e0
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (563) implies:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (564)  all_57_7 = e0
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (140) gives:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (565)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (565) gives:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (566)  all_57_1 = e1 & op(e3, e2) = e1
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (88), (547), (566) are inconsistent by sub-proof
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2446.
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (567)  all_57_3 = e1 & op(e2, e2) = e1
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (52), (88), (567) are inconsistent by sub-proof
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2362.
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (568)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (568) gives:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (569)  all_57_7 = e1 & op(e1, e2) = e1
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (569) implies:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (570)  all_57_7 = e1
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (88), (564), (570) are inconsistent by sub-proof
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2211.
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (571)  all_57_13 = e1 & op(e0, e2) = e1
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (571) implies:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (572)  all_57_13 = e1
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (33) gives:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (573)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e1)
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (88), (122), (156), (547), (573) are
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #452.
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (574)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e1)
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (574) gives:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (575)  all_57_4 = e1 & op(e3, e1) = e1
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (575) implies:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (576)  all_57_4 = e1
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (12), (13), (14), (15), (16), (17),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18), (19), (22), (23), (24), (26), (27), (28),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (29), (30), (32), (33), (38), (41), (43), (44),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (46), (47), (48), (50), (52), (53), (54), (56),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (57), (58), (61), (63), (64), (65), (67), (68),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (70), (71), (74), (75), (77), (78), (81), (82),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (83), (84), (85), (86), (88), (89), (91), (92),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (93), (96), (99), (100), (103), (104), (105),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (111), (112), (114), (115), (117), (118), (119),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (122), (123), (124), (125), (127), (128), (129),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (130), (131), (132), (133), (135), (137), (139),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (140), (141), (142), (148), (152), (154), (155),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (156), (166), (170), (173), (177), (178), (179),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (181), (182), (184), (186), (190), (195), (207),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (208), (209), (210), (211), (359), (472), (534),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (576) are inconsistent by sub-proof #454.
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (577)  all_57_9 = e1 & op(e3, e0) = e1
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (577) implies:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (578)  all_57_9 = e1
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (103) gives:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (579)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (579) gives:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (580)  all_57_12 = e2 & op(e0, e3) = e2
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (580) implies:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (581)  all_57_12 = e2
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (111) gives:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (582)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e3)
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (582) gives:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (583)  all_57_2 = e3 & op(e2, e3) = e3
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (583) implies:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (584)  all_57_2 = e3
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13) gives:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (585)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e1)
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (17), (19), (26), (27), (52), (54), (61),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (71), (74), (81), (88), (92), (103), (104), (122),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (156), (534), (542), (584), (585) are inconsistent
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #450.
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (586)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e3) = e1)
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (586) gives:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (587)  all_57_6 = e1 & op(e1, e3) = e1
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (587) implies:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (588)  all_57_6 = e1
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (12), (13), (14), (15), (17), (18),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19), (22), (23), (26), (27), (28), (30), (33),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (38), (41), (43), (44), (48), (50), (52), (53),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (54), (57), (61), (63), (64), (67), (70), (71),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (74), (75), (78), (81), (82), (85), (88), (89),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (91), (92), (93), (99), (100), (103), (104),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (105), (111), (112), (114), (115), (117), (118),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (122), (123), (124), (125), (127), (129),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (130), (131), (132), (133), (137), (140), (141),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (142), (156), (214), (584), (588) are inconsistent
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #524.
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (589)  all_57_12 = e1 & op(e0, e3) = e1
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (589) implies:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (590)  all_57_12 = e1
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (581), (590) imply:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (591)  e2 = e1
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (591) implies:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (592)  e2 = e1
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (472), (592) imply:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (593)  all_57_8 = e1
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (12), (13), (14), (15), (17), (18),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19), (22), (23), (26), (27), (28), (30), (33),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (38), (41), (43), (44), (48), (50), (52), (53),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (54), (57), (61), (63), (64), (67), (70), (71),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (74), (75), (78), (81), (82), (85), (88), (89),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (91), (92), (93), (99), (100), (103), (104),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (105), (111), (112), (114), (115), (117), (118),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (122), (123), (124), (125), (127), (129),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (130), (131), (132), (133), (137), (140), (141),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (142), (156), (534), (584), (593) are inconsistent
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #501.
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (594)  all_57_3 = e3 & op(e2, e2) = e3
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (594) implies:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (595)  all_57_3 = e3
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (52), (61), (595) are inconsistent by sub-proof
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2358.
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (596)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e2, e0) = e3)
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (12), (13), (14), (15), (16), (17),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18), (19), (22), (23), (24), (26), (27), (28),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (29), (30), (32), (33), (38), (41), (43), (44),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (46), (47), (48), (50), (52), (53), (54), (56),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (57), (58), (61), (63), (64), (65), (67), (68),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (70), (71), (74), (75), (77), (78), (81), (82),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (83), (84), (85), (86), (88), (89), (91), (92),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (93), (96), (99), (100), (103), (104), (105),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (111), (112), (114), (115), (117), (118), (119),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (122), (123), (124), (125), (127), (128), (129),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (130), (131), (132), (133), (135), (137), (139),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (140), (141), (142), (148), (152), (154), (155),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (156), (166), (170), (173), (177), (178), (179),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (181), (182), (184), (186), (190), (195), (207),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (208), (209), (210), (211), (359), (472), (534),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (539), (542), (578), (596) are inconsistent by
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #445.
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (597)  all_57_13 = e2 & op(e0, e2) = e2
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (597) implies:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (598)  all_57_13 = e2
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (572), (598) imply:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (599)  e2 = e1
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (599) implies:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (600)  e2 = e1
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (472), (600) imply:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (601)  all_57_8 = e1
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (12), (13), (14), (15), (16), (17),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18), (19), (22), (23), (24), (26), (27), (28),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (29), (30), (32), (33), (38), (41), (43), (44),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (46), (47), (48), (50), (52), (53), (54), (56),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (57), (58), (61), (63), (64), (65), (67), (68),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (70), (71), (74), (75), (77), (78), (81), (82),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (83), (84), (85), (86), (88), (89), (91), (92),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (93), (96), (99), (100), (103), (104), (105),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (111), (112), (114), (115), (117), (118), (119),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (123), (124), (125), (127), (128), (129), (130),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (131), (132), (133), (135), (137), (139), (140),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (141), (142), (148), (152), (154), (155), (156),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (166), (170), (173), (177), (178), (179), (181),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (182), (184), (186), (190), (195), (207), (208),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (209), (210), (211), (601) are inconsistent by
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #474.
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (602)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (602) gives:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (603)  all_57_14 = e2 & op(e0, e1) = e2
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (603) implies:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (604)  all_57_14 = e2
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (111) gives:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (605)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e3)
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (605) gives:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (606)  all_57_2 = e3 & op(e2, e3) = e3
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (606) implies:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (607)  all_57_2 = e3
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (17), (19), (26), (27), (52), (53), (54),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (61), (71), (74), (81), (88), (92), (103), (104),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (111), (118), (122), (472), (534), (604), (607)
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #591.
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (608)  all_57_3 = e3 & op(e2, e2) = e3
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (608) implies:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (609)  all_57_3 = e3
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (52), (61), (609) are inconsistent by sub-proof
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2358.
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (610)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e2, e0) = e3)
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (12), (13), (14), (15), (16), (17),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18), (19), (22), (23), (24), (26), (27), (28),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (29), (30), (32), (33), (38), (41), (43), (44),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (46), (47), (48), (50), (52), (53), (54), (56),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (57), (58), (61), (63), (64), (65), (67), (68),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (70), (71), (74), (75), (77), (78), (81), (82),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (83), (84), (85), (86), (88), (89), (91), (92),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (93), (96), (99), (100), (103), (104), (105),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (111), (112), (114), (115), (117), (118), (119),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (122), (123), (124), (125), (127), (128), (129),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (130), (131), (132), (133), (135), (137), (139),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (140), (141), (142), (148), (152), (154), (155),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (156), (166), (170), (173), (177), (178), (179),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (181), (182), (184), (186), (190), (195), (207),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (208), (209), (210), (211), (359), (472), (534),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (539), (542), (578), (610) are inconsistent by
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #445.
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (611)  all_57_15 = e2 & op(e0, e0) = e2
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (54), (71), (611) are inconsistent by sub-proof
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2323.
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (612)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (612) gives:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (613)  all_57_8 = e0 & op(e1, e1) = e0
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (81), (472), (613) are inconsistent by sub-proof
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #917.
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (614)  all_57_11 = e0 & op(e1, e0) = e0
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (88), (359), (614) are inconsistent by sub-proof
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1257.
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (615)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e0)
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (615) gives:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | |   (616)  all_57_4 = e0 & op(e3, e1) = e0
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (61), (542), (616) are inconsistent by sub-proof
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | |            #2491.
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | |   (617)  all_57_9 = e0 & op(e3, e0) = e0
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (617) implies:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | |   (618)  all_57_9 = e0
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (111) gives:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (619)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e3)
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (619) gives:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (620)  all_57_2 = e3 & op(e2, e3) = e3
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (620) implies:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (621)  all_57_2 = e3
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22) gives:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (622)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e3)
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (622) gives:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (623)  all_57_6 = e3 & op(e1, e3) = e3
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (623) implies:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (624)  all_57_6 = e3
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (13), (17), (19), (52), (54), (61), (81),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (88), (111), (118), (122), (131), (156), (173),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (621), (624) are inconsistent by sub-proof #794.
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (625)  all_57_7 = e3 & op(e1, e2) = e3
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (625) implies:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (626)  all_57_7 = e3
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15) gives:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (627)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (627) gives:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (628)  all_57_1 = e2 & op(e3, e2) = e2
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (628) implies:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (629)  all_57_1 = e2
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (19), (33), (88), (122), (156), (542),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (618), (629) are inconsistent by sub-proof #1661.
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (630)  all_57_3 = e2 & op(e2, e2) = e2
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (52), (81), (630) are inconsistent by sub-proof
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2103.
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (631)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (631) gives:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (632)  all_57_7 = e2 & op(e1, e2) = e2
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (632) implies:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (633)  all_57_7 = e2
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (12), (13), (14), (15), (17), (18),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19), (22), (23), (26), (27), (28), (30), (33),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (38), (41), (43), (44), (48), (50), (52), (53),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (54), (57), (61), (63), (64), (67), (70), (71),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (74), (75), (78), (81), (82), (85), (88), (89),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (91), (92), (93), (99), (100), (103), (104),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (105), (111), (112), (114), (115), (117), (118),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (122), (123), (124), (125), (127), (129),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (130), (131), (132), (133), (137), (140), (141),
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (142), (156), (621), (626), (633) are inconsistent
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #532.
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (471) implies:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (634)  op(e1, e1) = e2
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with e1, e2, e1, e1,
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (214), (634) gives:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (635)  e2 = e1
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (472), (635) imply:
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (636)  all_57_8 = e1
% 227.78/39.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (12), (13), (14), (15), (17), (18),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19), (22), (23), (26), (27), (28), (30), (33),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (38), (41), (43), (44), (48), (50), (52), (53),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (54), (57), (61), (63), (64), (67), (70), (71),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (74), (75), (78), (81), (82), (85), (88), (89),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (91), (92), (99), (100), (103), (104), (105),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (111), (112), (114), (115), (117), (118), (119),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (122), (123), (124), (125), (127), (129), (130),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (131), (132), (133), (137), (140), (141), (142),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (156), (359), (542), (626), (636) are inconsistent
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #499.
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (637)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e1, e0) = e3)
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (19), (26), (27), (71), (88), (122), (132),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (534), (618), (637) are inconsistent by sub-proof
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #731.
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (638)  all_57_3 = e3 & op(e2, e2) = e3
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (638) implies:
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (639)  all_57_3 = e3
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (52), (61), (639) are inconsistent by sub-proof
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2358.
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (640)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e2, e0) = e3)
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (640) gives:
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (641)  all_57_5 = e3 & op(e2, e1) = e3
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (12), (13), (14), (15), (16), (17),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18), (19), (22), (23), (24), (26), (27), (28),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (29), (30), (32), (33), (38), (41), (43), (44),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (46), (47), (48), (50), (52), (53), (54), (56),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (57), (58), (61), (63), (64), (65), (67), (68),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (70), (71), (74), (75), (77), (78), (81), (82),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (83), (84), (85), (86), (88), (89), (91), (92),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (93), (96), (99), (100), (103), (104), (105),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (111), (112), (114), (115), (117), (118), (119),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (122), (123), (124), (125), (127), (128), (129),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (130), (131), (132), (133), (135), (137), (139),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (140), (141), (142), (148), (152), (154), (155),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (156), (166), (170), (173), (177), (178), (179),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (181), (182), (184), (186), (190), (195), (207),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (208), (209), (210), (211), (359), (472), (534),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (539), (542), (641) are inconsistent by sub-proof
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #446.
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (642)  all_57_10 = e3 & op(e2, e0) = e3
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (642) implies:
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (643)  all_57_10 = e3
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (54), (61), (71), (81), (88), (104), (122),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (123), (132), (618), (643) are inconsistent by
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1982.
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | |   (644)  all_57_5 = e3 & op(e2, e1) = e3
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (644) implies:
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | |   (645)  all_57_5 = e3
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (539), (645) are inconsistent by sub-proof
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | |            #2382.
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | |   (646)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e1) = e3)
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (19), (26), (27), (54), (61), (71), (74),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | |            (81), (88), (103), (104), (122), (646) are
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1794.
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | |   (647)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e1) = e1)
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (647) gives:
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | |   (648)  all_57_8 = e1 & op(e1, e1) = e1
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (648) implies:
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | |   (649)  all_57_8 = e1
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (12), (13), (14), (15), (16), (17),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | |            (18), (19), (22), (23), (24), (26), (27), (28),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | |            (29), (30), (32), (33), (38), (41), (43), (44),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | |            (46), (47), (48), (50), (52), (53), (54), (56),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | |            (57), (58), (61), (63), (64), (65), (67), (68),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | |            (70), (71), (74), (75), (77), (78), (81), (82),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | |            (83), (84), (85), (86), (88), (89), (91), (92),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | |            (93), (96), (99), (100), (103), (104), (105),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | |            (111), (112), (114), (115), (117), (118), (119),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | |            (123), (124), (125), (127), (128), (129), (130),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | |            (131), (132), (133), (135), (137), (139), (140),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | |            (141), (142), (148), (152), (154), (155), (156),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | |            (166), (170), (173), (177), (178), (179), (181),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | |            (182), (184), (186), (190), (195), (207), (208),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | |            (209), (210), (211), (649) are inconsistent by
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #474.
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | |   (650)  all_57_14 = e1 & op(e0, e1) = e1
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (650) implies:
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | |   (651)  all_57_14 = e1
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18) gives:
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | |   (652)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e0)
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (652) gives:
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | |   (653)  all_57_6 = e0 & op(e1, e3) = e0
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (653) implies:
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | |   (654)  all_57_6 = e0
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (12), (13), (14), (15), (16), (17),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | |            (18), (19), (22), (23), (24), (26), (27), (28),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | |            (29), (30), (32), (33), (38), (41), (43), (44),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | |            (46), (47), (48), (50), (52), (53), (54), (56),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | |            (57), (58), (61), (63), (64), (65), (67), (68),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | |            (70), (71), (74), (75), (77), (78), (81), (82),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | |            (83), (84), (85), (86), (88), (89), (91), (92),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | |            (93), (96), (99), (100), (103), (104), (105),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | |            (111), (112), (114), (115), (117), (118), (119),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | |            (122), (123), (124), (125), (127), (128), (129),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | |            (130), (131), (132), (133), (135), (137), (139),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | |            (140), (141), (142), (148), (152), (154), (155),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | |            (156), (166), (170), (173), (177), (178), (179),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | |            (181), (182), (184), (186), (190), (195), (207),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | |            (208), (209), (210), (211), (472), (534), (651),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | |            (654) are inconsistent by sub-proof #467.
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | |   (655)  all_57_7 = e0 & op(e1, e2) = e0
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (655) implies:
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | |   (656)  all_57_7 = e0
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (12), (13), (14), (15), (16), (17),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | |            (18), (19), (22), (23), (24), (26), (27), (28),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | |            (29), (30), (32), (33), (38), (41), (43), (44),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | |            (46), (47), (48), (50), (52), (53), (54), (56),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | |            (57), (58), (61), (63), (64), (65), (67), (68),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | |            (70), (71), (74), (75), (77), (78), (81), (82),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | |            (83), (84), (85), (86), (88), (89), (91), (92),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | |            (93), (96), (99), (100), (103), (104), (105),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | |            (111), (112), (114), (115), (117), (118), (119),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | |            (122), (123), (124), (125), (127), (128), (129),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | |            (130), (131), (132), (133), (135), (137), (139),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | |            (140), (141), (142), (148), (152), (154), (155),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | |            (156), (166), (170), (173), (177), (178), (179),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | |            (181), (182), (184), (186), (190), (195), (207),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | |            (208), (209), (210), (211), (472), (534), (651),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | |            (656) are inconsistent by sub-proof #462.
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | |   (657)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (657) gives:
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | |   (658)  all_57_8 = e0 & op(e1, e1) = e0
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (81), (472), (658) are inconsistent by sub-proof
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | |            #917.
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | |   (659)  all_57_11 = e0 & op(e1, e0) = e0
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (88), (359), (659) are inconsistent by sub-proof
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | |            #1257.
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | |   (660)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 227.78/39.36  | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | BETA: splitting (660) gives:
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | |   (661)  all_57_11 = e2 & op(e1, e0) = e2
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | ALPHA: (661) implies:
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | |   (662)  all_57_11 = e2
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (359), (662) imply:
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | |   (663)  e2 = e1
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | SIMP: (663) implies:
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | |   (664)  e2 = e1
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (472), (664) imply:
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | |   (665)  all_57_8 = e1
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (12), (13), (14), (15), (16), (17),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | |            (18), (19), (22), (23), (24), (26), (27), (28),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | |            (29), (30), (32), (33), (38), (41), (43), (44),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | |            (46), (47), (48), (50), (52), (53), (54), (56),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | |            (57), (58), (61), (63), (64), (65), (67), (68),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | |            (70), (71), (74), (75), (77), (78), (81), (82),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | |            (83), (84), (85), (86), (88), (89), (91), (92),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | |            (93), (96), (99), (100), (103), (104), (105),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | |            (111), (112), (114), (115), (117), (118), (119),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | |            (123), (124), (125), (127), (128), (129), (130),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | |            (131), (132), (133), (135), (137), (139), (140),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | |            (141), (142), (148), (152), (154), (155), (156),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | |            (166), (170), (173), (177), (178), (179), (181),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | |            (182), (184), (186), (190), (195), (207), (208),
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | |            (209), (210), (211), (665) are inconsistent by
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | |            sub-proof #474.
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | |   (666)  all_57_15 = e2 & op(e0, e0) = e2
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (54), (71), (666) are inconsistent by sub-proof
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | |            #2323.
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.36  | | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.36  | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.36  | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | |   (667)  all_57_11 = e2 & op(e1, e0) = e2
% 227.78/39.36  | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | | REF_CLOSE: (122), (359), (667) are inconsistent by sub-proof
% 227.78/39.36  | | | | | | | | | | | | | | | | | |            #2048.
% 227.78/39.36  | | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | | End of split
% 227.78/39.36  | | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | | End of split
% 227.78/39.36  | | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | | End of split
% 227.78/39.36  | | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | End of split
% 227.78/39.36  | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | Case 2:
% 227.78/39.36  | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | |   (668)  all_55_10 = e0
% 227.78/39.36  | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | | REF_CLOSE: (105), (192), (668) are inconsistent by sub-proof
% 227.78/39.36  | | | | | | | | | | | | | |            #2118.
% 227.78/39.36  | | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | | End of split
% 227.78/39.36  | | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | | End of split
% 227.78/39.36  | | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | End of split
% 227.78/39.36  | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | Case 2:
% 227.78/39.36  | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | |   (669)  all_38_2 = e2
% 227.78/39.36  | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | COMBINE_EQS: (112), (669) imply:
% 227.78/39.36  | | | | | | | | | | |   (670)  all_6_2 = e2
% 227.78/39.36  | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | REDUCE: (187), (670) imply:
% 227.78/39.36  | | | | | | | | | | |   (671)  op(e2, e2) = e1
% 227.78/39.36  | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | | REF_CLOSE: (19), (45), (88), (671) are inconsistent by
% 227.78/39.36  | | | | | | | | | | |            sub-proof #2352.
% 227.78/39.36  | | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | End of split
% 227.78/39.36  | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | End of split
% 227.78/39.36  | | | | | | | | | 
% 227.78/39.36  | | | | | | | | Case 2:
% 227.78/39.36  | | | | | | | | | 
% 227.78/39.36  | | | | | | | | |   (672)  all_24_2 = e0
% 227.78/39.36  | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | REF_CLOSE: (17), (19), (99), (129), (187), (672) are
% 227.78/39.36  | | | | | | | | |            inconsistent by sub-proof #444.
% 227.78/39.36  | | | | | | | | | 
% 227.78/39.36  | | | | | | | | End of split
% 227.78/39.36  | | | | | | | | 
% 227.78/39.36  | | | | | | | End of split
% 227.78/39.36  | | | | | | | 
% 227.78/39.36  | | | | | | Case 2:
% 227.78/39.36  | | | | | | | 
% 227.78/39.36  | | | | | | |   (673)  all_57_2 = e2 & op(e2, e3) = e2
% 227.78/39.36  | | | | | | | 
% 227.78/39.36  | | | | | | | ALPHA: (673) implies:
% 227.78/39.36  | | | | | | |   (674)  all_57_2 = e2
% 227.78/39.36  | | | | | | | 
% 227.78/39.36  | | | | | | | REF_CLOSE: (6), (11), (12), (13), (14), (15), (17), (18), (19),
% 227.78/39.36  | | | | | | |            (22), (23), (26), (27), (28), (30), (33), (38), (41),
% 227.78/39.36  | | | | | | |            (43), (44), (48), (50), (52), (53), (54), (57), (61),
% 227.78/39.36  | | | | | | |            (63), (64), (67), (70), (71), (74), (75), (78), (81),
% 227.78/39.36  | | | | | | |            (82), (85), (88), (89), (91), (92), (93), (99), (100),
% 227.78/39.36  | | | | | | |            (103), (104), (105), (111), (112), (114), (115), (117),
% 227.78/39.36  | | | | | | |            (118), (119), (122), (123), (124), (125), (127), (129),
% 227.78/39.36  | | | | | | |            (130), (131), (132), (133), (137), (140), (141), (142),
% 227.78/39.36  | | | | | | |            (156), (674) are inconsistent by sub-proof #544.
% 227.78/39.36  | | | | | | | 
% 227.78/39.36  | | | | | | End of split
% 227.78/39.36  | | | | | | 
% 227.78/39.36  | | | | | Case 2:
% 227.78/39.36  | | | | | | 
% 227.78/39.36  | | | | | |   (675)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 &
% 227.78/39.36  | | | | | |            op(e0, e3) = e2)
% 227.78/39.36  | | | | | | 
% 227.78/39.36  | | | | | | BETA: splitting (675) gives:
% 227.78/39.36  | | | | | | 
% 227.78/39.36  | | | | | | Case 1:
% 227.78/39.36  | | | | | | | 
% 227.78/39.36  | | | | | | |   (676)  all_57_6 = e2 & op(e1, e3) = e2
% 227.78/39.36  | | | | | | | 
% 227.78/39.36  | | | | | | | ALPHA: (676) implies:
% 227.78/39.36  | | | | | | |   (677)  all_57_6 = e2
% 227.78/39.36  | | | | | | | 
% 227.78/39.36  | | | | | | | REF_CLOSE: (12), (13), (15), (17), (19), (22), (26), (27), (33),
% 227.78/39.36  | | | | | | |            (44), (50), (52), (54), (61), (71), (81), (85), (88),
% 227.78/39.36  | | | | | | |            (104), (111), (115), (118), (119), (122), (123), (131),
% 227.78/39.36  | | | | | | |            (132), (140), (142), (156), (677) are inconsistent by
% 227.78/39.36  | | | | | | |            sub-proof #728.
% 227.78/39.36  | | | | | | | 
% 227.78/39.36  | | | | | | Case 2:
% 227.78/39.36  | | | | | | | 
% 227.78/39.36  | | | | | | |   (678)  all_57_12 = e2 & op(e0, e3) = e2
% 227.78/39.36  | | | | | | | 
% 227.78/39.36  | | | | | | | ALPHA: (678) implies:
% 227.78/39.36  | | | | | | |   (679)  all_57_12 = e2
% 227.78/39.36  | | | | | | | 
% 227.78/39.36  | | | | | | | REF_CLOSE: (6), (11), (12), (13), (14), (15), (17), (18), (19),
% 227.78/39.36  | | | | | | |            (22), (23), (26), (27), (28), (30), (33), (38), (41),
% 227.78/39.36  | | | | | | |            (43), (44), (48), (50), (52), (53), (54), (57), (61),
% 227.78/39.36  | | | | | | |            (63), (64), (67), (70), (71), (74), (75), (78), (81),
% 227.78/39.36  | | | | | | |            (82), (85), (88), (89), (91), (92), (93), (99), (100),
% 227.78/39.36  | | | | | | |            (103), (104), (105), (111), (112), (114), (115), (117),
% 227.78/39.36  | | | | | | |            (118), (119), (122), (123), (124), (125), (127), (129),
% 227.78/39.36  | | | | | | |            (130), (131), (132), (133), (137), (140), (141), (142),
% 227.78/39.36  | | | | | | |            (156), (679) are inconsistent by sub-proof #442.
% 227.78/39.36  | | | | | | | 
% 227.78/39.36  | | | | | | End of split
% 227.78/39.36  | | | | | | 
% 227.78/39.36  | | | | | End of split
% 227.78/39.36  | | | | | 
% 227.78/39.36  | | | | Case 2:
% 227.78/39.36  | | | | | 
% 227.78/39.36  | | | | |   (680)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30
% 227.78/39.36  | | | | |          = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 227.78/39.36  | | | | |            all_52_27) = e2 & op(all_52_29, all_52_29) = e1 &
% 227.78/39.36  | | | | |          op(all_52_31, all_52_31) = e0 & op(e0, e3) = all_52_25 &
% 227.78/39.36  | | | | |          op(e0, e2) = all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 227.78/39.36  | | | | |          = all_52_31 & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 227.78/39.36  | | | | |          $i(all_52_31)
% 227.78/39.36  | | | | | 
% 227.78/39.36  | | | | | ALPHA: (680) implies:
% 227.78/39.36  | | | | |   (681)  op(e0, e0) = all_52_31
% 227.78/39.36  | | | | |   (682)  op(all_52_31, all_52_31) = e0
% 227.78/39.36  | | | | | 
% 227.78/39.36  | | | | | BETA: splitting (127) gives:
% 227.78/39.36  | | | | | 
% 227.78/39.36  | | | | | Case 1:
% 227.78/39.36  | | | | | | 
% 227.78/39.36  | | | | | |   (683)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2,
% 227.78/39.36  | | | | | |              e3) = e2)
% 227.78/39.36  | | | | | | 
% 227.78/39.36  | | | | | | BETA: splitting (683) gives:
% 227.78/39.36  | | | | | | 
% 227.78/39.36  | | | | | | Case 1:
% 227.78/39.36  | | | | | | | 
% 227.78/39.36  | | | | | | |   (684)  all_57_0 = e2 & op(e3, e3) = e2
% 227.78/39.36  | | | | | | | 
% 227.78/39.36  | | | | | | | REF_CLOSE: (19), (81), (99), (681), (682), (684) are inconsistent
% 227.78/39.36  | | | | | | |            by sub-proof #441.
% 227.78/39.36  | | | | | | | 
% 227.78/39.36  | | | | | | Case 2:
% 227.78/39.36  | | | | | | | 
% 227.78/39.36  | | | | | | |   (685)  all_57_2 = e2 & op(e2, e3) = e2
% 227.78/39.36  | | | | | | | 
% 227.78/39.36  | | | | | | | ALPHA: (685) implies:
% 227.78/39.36  | | | | | | |   (686)  all_57_2 = e2
% 227.78/39.36  | | | | | | | 
% 227.78/39.36  | | | | | | | REF_CLOSE: (6), (11), (12), (13), (14), (15), (17), (18), (19),
% 227.78/39.36  | | | | | | |            (22), (23), (26), (27), (28), (30), (33), (38), (41),
% 227.78/39.36  | | | | | | |            (43), (44), (48), (50), (52), (53), (54), (57), (61),
% 227.78/39.36  | | | | | | |            (63), (64), (67), (70), (71), (74), (75), (78), (81),
% 227.78/39.36  | | | | | | |            (82), (85), (88), (89), (91), (92), (93), (99), (100),
% 227.78/39.36  | | | | | | |            (103), (104), (105), (111), (112), (114), (115), (117),
% 227.78/39.36  | | | | | | |            (118), (119), (122), (123), (124), (125), (127), (129),
% 227.78/39.36  | | | | | | |            (130), (131), (132), (133), (137), (140), (141), (142),
% 227.78/39.36  | | | | | | |            (156), (686) are inconsistent by sub-proof #544.
% 227.78/39.36  | | | | | | | 
% 227.78/39.36  | | | | | | End of split
% 227.78/39.36  | | | | | | 
% 227.78/39.36  | | | | | Case 2:
% 227.78/39.36  | | | | | | 
% 227.78/39.36  | | | | | |   (687)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 &
% 227.78/39.36  | | | | | |            op(e0, e3) = e2)
% 227.78/39.36  | | | | | | 
% 227.78/39.36  | | | | | | BETA: splitting (687) gives:
% 227.78/39.36  | | | | | | 
% 227.78/39.36  | | | | | | Case 1:
% 227.78/39.36  | | | | | | | 
% 227.78/39.36  | | | | | | |   (688)  all_57_6 = e2 & op(e1, e3) = e2
% 227.78/39.36  | | | | | | | 
% 227.78/39.36  | | | | | | | ALPHA: (688) implies:
% 227.78/39.36  | | | | | | |   (689)  all_57_6 = e2
% 227.78/39.36  | | | | | | | 
% 227.78/39.36  | | | | | | | REF_CLOSE: (12), (13), (15), (17), (19), (22), (26), (27), (33),
% 227.78/39.36  | | | | | | |            (44), (50), (52), (54), (61), (71), (81), (85), (88),
% 227.78/39.36  | | | | | | |            (104), (111), (115), (118), (119), (122), (123), (131),
% 227.78/39.36  | | | | | | |            (132), (140), (142), (156), (689) are inconsistent by
% 227.78/39.36  | | | | | | |            sub-proof #728.
% 227.78/39.36  | | | | | | | 
% 227.78/39.36  | | | | | | Case 2:
% 227.78/39.36  | | | | | | | 
% 227.78/39.36  | | | | | | |   (690)  all_57_12 = e2 & op(e0, e3) = e2
% 227.78/39.36  | | | | | | | 
% 227.78/39.36  | | | | | | | ALPHA: (690) implies:
% 227.78/39.36  | | | | | | |   (691)  all_57_12 = e2
% 227.78/39.36  | | | | | | | 
% 227.78/39.36  | | | | | | | REF_CLOSE: (6), (11), (12), (13), (14), (15), (17), (18), (19),
% 227.78/39.36  | | | | | | |            (22), (23), (26), (27), (28), (30), (33), (38), (41),
% 227.78/39.36  | | | | | | |            (43), (44), (48), (50), (52), (53), (54), (57), (61),
% 227.78/39.36  | | | | | | |            (63), (64), (67), (70), (71), (74), (75), (78), (81),
% 227.78/39.36  | | | | | | |            (82), (85), (88), (89), (91), (92), (93), (99), (100),
% 227.78/39.36  | | | | | | |            (103), (104), (105), (111), (112), (114), (115), (117),
% 227.78/39.36  | | | | | | |            (118), (119), (122), (123), (124), (125), (127), (129),
% 227.78/39.36  | | | | | | |            (130), (131), (132), (133), (137), (140), (141), (142),
% 227.78/39.36  | | | | | | |            (156), (691) are inconsistent by sub-proof #442.
% 227.78/39.36  | | | | | | | 
% 227.78/39.36  | | | | | | End of split
% 227.78/39.36  | | | | | | 
% 227.78/39.36  | | | | | End of split
% 227.78/39.36  | | | | | 
% 227.78/39.36  | | | | End of split
% 227.78/39.36  | | | | 
% 227.78/39.36  | | | End of split
% 227.78/39.36  | | | 
% 227.78/39.36  | | End of split
% 227.78/39.36  | | 
% 227.78/39.36  | Case 2:
% 227.78/39.36  | | 
% 227.78/39.36  | |   (692)  all_18_2 = e0
% 227.78/39.36  | | 
% 227.78/39.36  | | COMBINE_EQS: (102), (692) imply:
% 227.78/39.36  | |   (693)  all_10_2 = e0
% 227.78/39.36  | | 
% 227.78/39.36  | | SIMP: (693) implies:
% 227.78/39.36  | |   (694)  all_10_2 = e0
% 227.78/39.36  | | 
% 227.78/39.36  | | REDUCE: (8), (694) imply:
% 227.78/39.36  | |   (695)   ~ (all_53_3 = e0)
% 227.78/39.36  | | 
% 227.78/39.36  | | REDUCE: (120), (694) imply:
% 227.78/39.36  | |   (696)   ~ (all_53_12 = e0)
% 227.78/39.36  | | 
% 227.78/39.36  | | REDUCE: (95), (694) imply:
% 227.78/39.36  | |   (697)   ~ (e1 = e0)
% 227.78/39.36  | | 
% 227.78/39.36  | | BETA: splitting (104) gives:
% 227.78/39.36  | | 
% 227.78/39.36  | | Case 1:
% 227.78/39.36  | | | 
% 227.78/39.36  | | |   (698)  all_57_15 = e0 & op(e0, e0) = e0
% 227.78/39.36  | | | 
% 227.78/39.36  | | | ALPHA: (698) implies:
% 227.78/39.36  | | |   (699)  op(e0, e0) = e0
% 227.78/39.36  | | | 
% 227.78/39.36  | | | REF_CLOSE: (19), (61), (99), (699) are inconsistent by sub-proof #2304.
% 227.78/39.36  | | | 
% 227.78/39.36  | | Case 2:
% 227.78/39.36  | | | 
% 227.78/39.36  | | |   (700)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0)
% 227.78/39.36  | | |              = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 =
% 227.78/39.36  | | |              e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 227.78/39.36  | | |            (all_57_14 = e0 & op(e0, e1) = e0))
% 227.78/39.36  | | | 
% 227.78/39.36  | | | ALPHA: (700) implies:
% 227.78/39.36  | | |   (701)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2)
% 227.78/39.36  | | |            = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 227.78/39.36  | | |   (702)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0)
% 227.78/39.36  | | |            = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 227.78/39.36  | | | 
% 227.78/39.36  | | | BETA: splitting (50) gives:
% 227.78/39.36  | | | 
% 227.78/39.36  | | | Case 1:
% 227.78/39.36  | | | | 
% 227.78/39.36  | | | |   (703)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2)
% 227.78/39.36  | | | |            = e0)
% 227.78/39.36  | | | | 
% 227.78/39.36  | | | | BETA: splitting (703) gives:
% 227.78/39.36  | | | | 
% 227.78/39.36  | | | | Case 1:
% 227.78/39.36  | | | | | 
% 227.78/39.36  | | | | |   (704)  all_57_0 = e0 & op(e3, e3) = e0
% 227.78/39.36  | | | | | 
% 227.78/39.36  | | | | | ALPHA: (704) implies:
% 227.78/39.36  | | | | |   (705)  all_57_0 = e0
% 227.78/39.36  | | | | |   (706)  op(e3, e3) = e0
% 227.78/39.36  | | | | | 
% 227.78/39.36  | | | | | BETA: splitting (701) gives:
% 227.78/39.36  | | | | | 
% 227.78/39.36  | | | | | Case 1:
% 227.78/39.36  | | | | | | 
% 227.78/39.36  | | | | | |   (707)  all_57_12 = e0 & op(e0, e3) = e0
% 227.78/39.36  | | | | | | 
% 227.78/39.36  | | | | | | ALPHA: (707) implies:
% 227.78/39.36  | | | | | |   (708)  op(e0, e3) = e0
% 227.78/39.36  | | | | | | 
% 227.78/39.36  | | | | | | REF_CLOSE: (19), (66), (695), (708) are inconsistent by sub-proof
% 227.78/39.36  | | | | | |            #2366.
% 227.78/39.36  | | | | | | 
% 227.78/39.36  | | | | | Case 2:
% 227.78/39.36  | | | | | | 
% 227.78/39.36  | | | | | |   (709)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 &
% 227.78/39.36  | | | | | |            op(e0, e1) = e0)
% 227.78/39.36  | | | | | | 
% 227.78/39.36  | | | | | | BETA: splitting (709) gives:
% 227.78/39.36  | | | | | | 
% 227.78/39.36  | | | | | | Case 1:
% 227.78/39.36  | | | | | | | 
% 227.78/39.36  | | | | | | |   (710)  all_57_13 = e0 & op(e0, e2) = e0
% 227.78/39.36  | | | | | | | 
% 227.78/39.36  | | | | | | | ALPHA: (710) implies:
% 227.78/39.36  | | | | | | |   (711)  op(e0, e2) = e0
% 227.78/39.36  | | | | | | | 
% 227.78/39.36  | | | | | | | REF_CLOSE: (19), (73), (101), (711) are inconsistent by sub-proof
% 227.78/39.36  | | | | | | |            #2332.
% 227.78/39.36  | | | | | | | 
% 227.78/39.36  | | | | | | Case 2:
% 227.78/39.36  | | | | | | | 
% 227.78/39.36  | | | | | | |   (712)  all_57_14 = e0 & op(e0, e1) = e0
% 227.78/39.36  | | | | | | | 
% 227.78/39.36  | | | | | | | ALPHA: (712) implies:
% 227.78/39.36  | | | | | | |   (713)  all_57_14 = e0
% 227.78/39.36  | | | | | | |   (714)  op(e0, e1) = e0
% 227.78/39.36  | | | | | | | 
% 227.78/39.36  | | | | | | | BETA: splitting (702) gives:
% 227.78/39.36  | | | | | | | 
% 227.78/39.36  | | | | | | | Case 1:
% 227.78/39.36  | | | | | | | | 
% 227.78/39.36  | | | | | | | |   (715)  all_57_9 = e0 & op(e3, e0) = e0
% 227.78/39.36  | | | | | | | | 
% 227.78/39.36  | | | | | | | | ALPHA: (715) implies:
% 227.78/39.36  | | | | | | | |   (716)  op(e3, e0) = e0
% 227.78/39.36  | | | | | | | | 
% 227.78/39.36  | | | | | | | | GROUND_INST: instantiating (19) with all_53_12, e0, e0, e3,
% 227.78/39.36  | | | | | | | |              simplifying with (142), (716) gives:
% 227.78/39.36  | | | | | | | |   (717)  all_53_12 = e0
% 227.78/39.36  | | | | | | | | 
% 227.78/39.36  | | | | | | | | REDUCE: (696), (717) imply:
% 227.78/39.36  | | | | | | | |   (718)  $false
% 227.78/39.36  | | | | | | | | 
% 227.78/39.36  | | | | | | | | CLOSE: (718) is inconsistent.
% 227.78/39.36  | | | | | | | | 
% 227.78/39.36  | | | | | | | Case 2:
% 227.78/39.36  | | | | | | | | 
% 227.78/39.36  | | | | | | | |   (719)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 227.78/39.36  | | | | | | | |            op(e1, e0) = e0)
% 227.78/39.36  | | | | | | | | 
% 227.78/39.36  | | | | | | | | BETA: splitting (719) gives:
% 227.78/39.36  | | | | | | | | 
% 227.78/39.36  | | | | | | | | Case 1:
% 227.78/39.36  | | | | | | | | | 
% 227.78/39.36  | | | | | | | | |   (720)  all_57_10 = e0 & op(e2, e0) = e0
% 227.78/39.36  | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | ALPHA: (720) implies:
% 227.78/39.36  | | | | | | | | |   (721)  op(e2, e0) = e0
% 227.78/39.36  | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | GROUND_INST: instantiating (19) with all_53_13, e0, e0, e2,
% 227.78/39.36  | | | | | | | | |              simplifying with (110), (721) gives:
% 227.78/39.36  | | | | | | | | |   (722)  all_53_13 = e0
% 227.78/39.36  | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | REDUCE: (107), (722) imply:
% 227.78/39.36  | | | | | | | | |   (723)  $false
% 227.78/39.36  | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | CLOSE: (723) is inconsistent.
% 227.78/39.36  | | | | | | | | | 
% 227.78/39.36  | | | | | | | | Case 2:
% 227.78/39.36  | | | | | | | | | 
% 227.78/39.36  | | | | | | | | |   (724)  all_57_11 = e0 & op(e1, e0) = e0
% 227.78/39.36  | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | ALPHA: (724) implies:
% 227.78/39.36  | | | | | | | | |   (725)  all_57_11 = e0
% 227.78/39.36  | | | | | | | | |   (726)  op(e1, e0) = e0
% 227.78/39.36  | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | GROUND_INST: instantiating (19) with all_53_11, e0, e1, e0,
% 227.78/39.36  | | | | | | | | |              simplifying with (5), (714) gives:
% 227.78/39.36  | | | | | | | | |   (727)  all_53_11 = e0
% 227.78/39.36  | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | GROUND_INST: instantiating (19) with all_53_14, e0, e0, e1,
% 227.78/39.36  | | | | | | | | |              simplifying with (59), (726) gives:
% 227.78/39.36  | | | | | | | | |   (728)  all_53_14 = e0
% 227.78/39.36  | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | REDUCE: (87), (728) imply:
% 227.78/39.36  | | | | | | | | |   (729)   ~ (all_53_2 = e0)
% 227.78/39.36  | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | REDUCE: (9), (728) imply:
% 227.78/39.36  | | | | | | | | |   (730)   ~ (all_53_6 = e0)
% 227.78/39.36  | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | REDUCE: (16), (727) imply:
% 227.78/39.36  | | | | | | | | |   (731)   ~ (all_53_8 = e0)
% 227.78/39.36  | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | REDUCE: (51), (728) imply:
% 227.78/39.36  | | | | | | | | |   (732)   ~ (all_6_2 = e0)
% 227.78/39.36  | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | SIMP: (732) implies:
% 227.78/39.36  | | | | | | | | |   (733)   ~ (all_6_2 = e0)
% 227.78/39.36  | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | REDUCE: (76), (728) imply:
% 227.78/39.36  | | | | | | | | |   (734)   ~ (e3 = e0)
% 227.78/39.36  | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | BETA: splitting (82) gives:
% 227.78/39.36  | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | Case 1:
% 227.78/39.36  | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | |   (735)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 227.78/39.36  | | | | | | | | | |            all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 227.78/39.36  | | | | | | | | | |            op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 227.78/39.36  | | | | | | | | | |              all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 227.78/39.36  | | | | | | | | | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 227.78/39.36  | | | | | | | | | |            op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 227.78/39.36  | | | | | | | | | |            $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 227.78/39.36  | | | | | | | | | |            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 &
% 227.78/39.36  | | | | | | | | | |            all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 227.78/39.36  | | | | | | | | | |              all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 227.78/39.36  | | | | | | | | | |            & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 227.78/39.36  | | | | | | | | | |              all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 227.78/39.36  | | | | | | | | | |            op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13 &
% 227.78/39.36  | | | | | | | | | |            op(e2, e0) = all_52_15 & $i(all_52_9) &
% 227.78/39.36  | | | | | | | | | |            $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 227.78/39.36  | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | BETA: splitting (735) gives:
% 227.78/39.36  | | | | | | | | | | 
% 227.78/39.36  | | | | | | | | | | Case 1:
% 227.78/39.36  | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | |   (736)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 227.78/39.37  | | | | | | | | | | |          all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 227.78/39.37  | | | | | | | | | | |          op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 227.78/39.37  | | | | | | | | | | |            all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 227.78/39.37  | | | | | | | | | | |          op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 227.78/39.37  | | | | | | | | | | |          op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 227.78/39.37  | | | | | | | | | | |          $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 227.78/39.37  | | | | | | | | | | |          $i(all_52_7)
% 227.78/39.37  | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | ALPHA: (736) implies:
% 227.78/39.37  | | | | | | | | | | |   (737)  op(e3, e0) = all_52_7
% 227.78/39.37  | | | | | | | | | | |   (738)  op(e3, e1) = all_52_5
% 227.78/39.37  | | | | | | | | | | |   (739)  op(e3, e2) = all_52_3
% 227.78/39.37  | | | | | | | | | | |   (740)  op(e3, e3) = all_52_1
% 227.78/39.37  | | | | | | | | | | |   (741)  op(all_52_7, all_52_7) = e0
% 227.78/39.37  | | | | | | | | | | |   (742)  op(all_52_5, all_52_5) = e1
% 227.78/39.37  | | | | | | | | | | |   (743)  op(all_52_3, all_52_3) = e2
% 227.78/39.37  | | | | | | | | | | |   (744)  op(all_52_1, all_52_1) = e3
% 227.78/39.37  | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | GROUND_INST: instantiating (19) with all_53_12, all_52_7, e0,
% 227.78/39.37  | | | | | | | | | | |              e3, simplifying with (142), (737) gives:
% 227.78/39.37  | | | | | | | | | | |   (745)  all_53_12 = all_52_7
% 227.78/39.37  | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | GROUND_INST: instantiating (19) with all_53_8, all_52_5, e1,
% 227.78/39.37  | | | | | | | | | | |              e3, simplifying with (137), (738) gives:
% 227.78/39.37  | | | | | | | | | | |   (746)  all_53_8 = all_52_5
% 227.78/39.37  | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | GROUND_INST: instantiating (19) with all_53_4, all_52_3, e2,
% 227.78/39.37  | | | | | | | | | | |              e3, simplifying with (78), (739) gives:
% 227.78/39.37  | | | | | | | | | | |   (747)  all_53_4 = all_52_3
% 227.78/39.37  | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | GROUND_INST: instantiating (19) with e0, all_52_1, e3, e3,
% 227.78/39.37  | | | | | | | | | | |              simplifying with (706), (740) gives:
% 227.78/39.37  | | | | | | | | | | |   (748)  all_52_1 = e0
% 227.78/39.37  | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | COMBINE_EQS: (114), (745) imply:
% 227.78/39.37  | | | | | | | | | | |   (749)  all_55_3 = all_52_7
% 227.78/39.37  | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | COMBINE_EQS: (67), (746) imply:
% 227.78/39.37  | | | | | | | | | | |   (750)  all_55_2 = all_52_5
% 227.78/39.37  | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | COMBINE_EQS: (57), (747) imply:
% 227.78/39.37  | | | | | | | | | | |   (751)  all_55_1 = all_52_3
% 227.78/39.37  | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | REDUCE: (100), (747) imply:
% 227.78/39.37  | | | | | | | | | | |   (752)   ~ (all_53_6 = all_52_3)
% 227.78/39.37  | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | SIMP: (752) implies:
% 227.78/39.37  | | | | | | | | | | |   (753)   ~ (all_53_6 = all_52_3)
% 227.78/39.37  | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | REDUCE: (69), (747) imply:
% 227.78/39.37  | | | | | | | | | | |   (754)   ~ (all_53_7 = all_52_3)
% 227.78/39.37  | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | SIMP: (754) implies:
% 227.78/39.37  | | | | | | | | | | |   (755)   ~ (all_53_7 = all_52_3)
% 227.78/39.37  | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | REDUCE: (75), (746), (747) imply:
% 227.78/39.37  | | | | | | | | | | |   (756)   ~ (all_52_3 = all_52_5)
% 227.78/39.37  | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | REDUCE: (38), (745), (747) imply:
% 227.78/39.37  | | | | | | | | | | |   (757)   ~ (all_52_3 = all_52_7)
% 227.78/39.37  | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | REDUCE: (91), (747) imply:
% 227.78/39.37  | | | | | | | | | | |   (758)   ~ (all_52_3 = e0)
% 227.78/39.37  | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | REDUCE: (41), (746) imply:
% 227.78/39.37  | | | | | | | | | | |   (759)   ~ (all_53_9 = all_52_5)
% 227.78/39.37  | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | SIMP: (759) implies:
% 227.78/39.37  | | | | | | | | | | |   (760)   ~ (all_53_9 = all_52_5)
% 227.78/39.37  | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | REDUCE: (14), (745), (746) imply:
% 227.78/39.37  | | | | | | | | | | |   (761)   ~ (all_52_5 = all_52_7)
% 227.78/39.37  | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | REDUCE: (64), (746) imply:
% 227.78/39.37  | | | | | | | | | | |   (762)   ~ (all_52_5 = all_6_2)
% 227.78/39.37  | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | REDUCE: (731), (746) imply:
% 227.78/39.37  | | | | | | | | | | |   (763)   ~ (all_52_5 = e0)
% 227.78/39.37  | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | REDUCE: (49), (745) imply:
% 227.78/39.37  | | | | | | | | | | |   (764)   ~ (all_53_13 = all_52_7)
% 227.78/39.37  | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | SIMP: (764) implies:
% 227.78/39.37  | | | | | | | | | | |   (765)   ~ (all_53_13 = all_52_7)
% 227.78/39.37  | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | REDUCE: (115), (745) imply:
% 227.78/39.37  | | | | | | | | | | |   (766)   ~ (all_52_7 = e3)
% 227.78/39.37  | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | REDUCE: (696), (745) imply:
% 227.78/39.37  | | | | | | | | | | |   (767)   ~ (all_52_7 = e0)
% 227.78/39.37  | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | BETA: splitting (136) gives:
% 227.78/39.37  | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | Case 1:
% 227.78/39.37  | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | |   (768)   ~ (all_22_2 = e3)
% 227.78/39.37  | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | REDUCE: (21), (768) imply:
% 227.78/39.37  | | | | | | | | | | | |   (769)  $false
% 227.78/39.37  | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | CLOSE: (769) is inconsistent.
% 227.78/39.37  | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | Case 2:
% 227.78/39.37  | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | |   (770)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0
% 227.78/39.37  | | | | | | | | | | | |            & op(e0, e3) = all_22_1 & $i(all_22_0) &
% 227.78/39.37  | | | | | | | | | | | |            $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0, e3)
% 227.78/39.37  | | | | | | | | | | | |            = all_22_1 & $i(all_22_1))
% 227.78/39.37  | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | BETA: splitting (89) gives:
% 227.78/39.37  | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | Case 1:
% 227.78/39.37  | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | |   (771)   ~ (all_38_2 = e2)
% 227.78/39.37  | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | REDUCE: (112), (771) imply:
% 227.78/39.37  | | | | | | | | | | | | |   (772)   ~ (all_6_2 = e2)
% 227.78/39.37  | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | BETA: splitting (11) gives:
% 227.78/39.37  | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | Case 1:
% 227.78/39.37  | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | |   (773)  all_55_10 = e3
% 227.78/39.37  | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | REF_CLOSE: (26), (105), (773) are inconsistent by sub-proof
% 227.78/39.37  | | | | | | | | | | | | | |            #2500.
% 227.78/39.37  | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | Case 2:
% 227.78/39.37  | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | |   (774)   ~ (all_55_10 = e3)
% 227.78/39.37  | | | | | | | | | | | | | |   (775)  all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 227.78/39.37  | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | BETA: splitting (775) gives:
% 227.78/39.37  | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | Case 1:
% 227.78/39.37  | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | |   (776)  all_55_10 = e2
% 227.78/39.37  | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | REF_CLOSE: (105), (772), (776) are inconsistent by sub-proof
% 227.78/39.37  | | | | | | | | | | | | | | |            #2499.
% 227.78/39.37  | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | Case 2:
% 227.78/39.37  | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | |   (777)   ~ (all_55_10 = e2)
% 227.78/39.37  | | | | | | | | | | | | | | |   (778)  all_55_10 = e1 | all_55_10 = e0
% 227.78/39.37  | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | BETA: splitting (778) gives:
% 227.78/39.37  | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | Case 1:
% 227.78/39.37  | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | |   (779)  all_55_10 = e1
% 227.78/39.37  | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | COMBINE_EQS: (105), (779) imply:
% 227.78/39.37  | | | | | | | | | | | | | | | |   (780)  all_6_2 = e1
% 227.78/39.37  | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | SIMP: (780) implies:
% 227.78/39.37  | | | | | | | | | | | | | | | |   (781)  all_6_2 = e1
% 227.78/39.37  | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | REDUCE: (39), (781) imply:
% 227.78/39.37  | | | | | | | | | | | | | | | |   (782)   ~ (all_53_2 = e1)
% 227.78/39.37  | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | REDUCE: (48), (781) imply:
% 227.78/39.37  | | | | | | | | | | | | | | | |   (783)   ~ (all_53_9 = e1)
% 227.78/39.37  | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | REDUCE: (762), (781) imply:
% 227.78/39.37  | | | | | | | | | | | | | | | |   (784)   ~ (all_52_5 = e1)
% 227.78/39.37  | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | REDUCE: (26), (781) imply:
% 227.78/39.37  | | | | | | | | | | | | | | | |   (785)   ~ (e3 = e1)
% 227.78/39.37  | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | REDUCE: (772), (781) imply:
% 227.78/39.37  | | | | | | | | | | | | | | | |   (786)   ~ (e2 = e1)
% 227.78/39.37  | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | REDUCE: (27), (781) imply:
% 227.78/39.37  | | | | | | | | | | | | | | | |   (787)  op(e1, e1) = e1
% 227.78/39.37  | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | BETA: splitting (63) gives:
% 227.78/39.37  | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.37  | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | |   (788)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 227.78/39.37  | | | | | | | | | | | | | | | | |            & op(e2, e1) = e1)
% 227.78/39.37  | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | BETA: splitting (788) gives:
% 227.78/39.37  | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | |   (789)  all_57_4 = e1 & op(e3, e1) = e1
% 227.78/39.37  | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | ALPHA: (789) implies:
% 227.78/39.37  | | | | | | | | | | | | | | | | | |   (790)  all_57_4 = e1
% 227.78/39.37  | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (6), (11), (12), (13), (14), (15), (17),
% 227.78/39.37  | | | | | | | | | | | | | | | | | |            (18), (19), (22), (23), (24), (25), (26), (27),
% 227.78/39.37  | | | | | | | | | | | | | | | | | |            (28), (29), (30), (33), (38), (40), (41), (43),
% 227.78/39.37  | | | | | | | | | | | | | | | | | |            (44), (45), (47), (48), (50), (52), (53), (54),
% 227.78/39.37  | | | | | | | | | | | | | | | | | |            (56), (57), (60), (61), (63), (64), (65), (67),
% 227.78/39.37  | | | | | | | | | | | | | | | | | |            (68), (70), (71), (72), (73), (74), (75), (77),
% 227.78/39.37  | | | | | | | | | | | | | | | | | |            (78), (79), (81), (82), (83), (84), (85), (86),
% 227.78/39.37  | | | | | | | | | | | | | | | | | |            (88), (89), (91), (92), (93), (98), (99), (100),
% 227.78/39.37  | | | | | | | | | | | | | | | | | |            (103), (104), (105), (107), (108), (109), (111),
% 227.78/39.37  | | | | | | | | | | | | | | | | | |            (112), (114), (115), (117), (118), (119), (122),
% 227.78/39.37  | | | | | | | | | | | | | | | | | |            (123), (124), (125), (127), (128), (129), (130),
% 227.78/39.37  | | | | | | | | | | | | | | | | | |            (131), (132), (133), (137), (138), (140), (141),
% 227.78/39.37  | | | | | | | | | | | | | | | | | |            (142), (695), (701), (702), (705), (706), (713),
% 227.78/39.37  | | | | | | | | | | | | | | | | | |            (725), (729), (733), (737), (738), (739), (740),
% 227.78/39.37  | | | | | | | | | | | | | | | | | |            (741), (742), (744), (749), (750), (751), (755),
% 227.78/39.37  | | | | | | | | | | | | | | | | | |            (756), (757), (758), (760), (761), (762), (763),
% 227.78/39.37  | | | | | | | | | | | | | | | | | |            (765), (766), (770), (772), (775), (782), (783),
% 227.78/39.37  | | | | | | | | | | | | | | | | | |            (784), (787), (790) are inconsistent by sub-proof
% 227.78/39.37  | | | | | | | | | | | | | | | | | |            #397.
% 227.78/39.37  | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | |   (791)  all_57_5 = e1 & op(e2, e1) = e1
% 227.78/39.37  | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | ALPHA: (791) implies:
% 227.78/39.37  | | | | | | | | | | | | | | | | | |   (792)  all_57_5 = e1
% 227.78/39.37  | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | BETA: splitting (111) gives:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | |   (793)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 227.78/39.37  | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e3)
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | BETA: splitting (793) gives:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | |   (794)  all_57_2 = e3 & op(e2, e3) = e3
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | ALPHA: (794) implies:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | |   (795)  all_57_2 = e3
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | BETA: splitting (92) gives:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | |   (796)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e3)
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (796) gives:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | |   (797)  all_57_4 = e3 & op(e3, e1) = e3
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (797) implies:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | |   (798)  all_57_4 = e3
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (118) gives:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | |   (799)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (799) gives:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | |   (800)  all_57_2 = e2 & op(e2, e3) = e2
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (54), (795), (800) are inconsistent by sub-proof
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | |            #1925.
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | |   (801)  all_57_3 = e2 & op(e2, e2) = e2
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (52), (81), (801) are inconsistent by sub-proof
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | |            #2103.
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | |   (802)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (802) gives:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | |   (803)  all_57_5 = e2 & op(e2, e1) = e2
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (803) implies:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | |   (804)  all_57_5 = e2
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (122), (792), (804) are inconsistent by sub-proof
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | |            #1885.
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | |   (805)  all_57_10 = e2 & op(e2, e0) = e2
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (805) implies:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | |   (806)  all_57_10 = e2
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13) gives:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | |   (807)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e1)
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (807) gives:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | |   (808)  all_57_0 = e1 & op(e3, e3) = e1
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (17), (52), (88), (122), (705), (792),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | |            (795), (806), (808) are inconsistent by sub-proof
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | |            #396.
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | |   (809)  all_57_2 = e1 & op(e2, e3) = e1
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (17), (19), (26), (27), (52), (54), (61),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | |            (71), (74), (81), (88), (92), (103), (104), (122),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | |            (795), (798), (806), (809) are inconsistent by
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1754.
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | |   (810)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e3) = e1)
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (810) gives:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | |   (811)  all_57_6 = e1 & op(e1, e3) = e1
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (811) implies:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | |   (812)  all_57_6 = e1
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (141) gives:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (813)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e2)
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (813) gives:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (814)  all_57_6 = e2 & op(e1, e3) = e2
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (814) implies:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (815)  all_57_6 = e2
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (122), (812), (815) are inconsistent by sub-proof
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2233.
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (816)  all_57_7 = e2 & op(e1, e2) = e2
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (12), (13), (14), (15), (17), (18),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19), (22), (23), (26), (27), (28), (30), (33),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (38), (41), (43), (44), (48), (50), (52), (53),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (54), (57), (61), (63), (64), (67), (70), (71),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (74), (75), (78), (81), (82), (85), (88), (89),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (91), (92), (99), (100), (103), (104), (105),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (112), (114), (115), (117), (118), (119), (122),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (123), (124), (125), (127), (129), (130), (131),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (132), (133), (137), (140), (141), (142), (701),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (702), (713), (798), (812), (816) are inconsistent
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #393.
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (817)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e1, e0) = e2)
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (817) gives:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (818)  all_57_8 = e2 & op(e1, e1) = e2
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (818) implies:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (819)  all_57_8 = e2
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (820)  op(e1, e1) = e2
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22) gives:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (821)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e3)
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (821) gives:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (822)  all_57_6 = e3 & op(e1, e3) = e3
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (12), (13), (14), (15), (17), (18),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19), (22), (23), (26), (27), (28), (30), (33),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (38), (41), (43), (44), (48), (50), (52), (53),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (54), (57), (61), (63), (64), (67), (70), (71),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (74), (75), (78), (81), (82), (85), (88), (89),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (91), (92), (99), (100), (103), (104), (105),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (112), (114), (115), (117), (118), (119), (122),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (123), (124), (125), (127), (129), (130), (131),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (132), (133), (137), (140), (141), (142), (701),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (713), (798), (812), (822) are inconsistent by
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #395.
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (823)  all_57_7 = e3 & op(e1, e2) = e3
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (823) implies:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (824)  all_57_7 = e3
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (132) gives:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (825)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (825) gives:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (826)  all_57_9 = e1 & op(e3, e0) = e1
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (826) implies:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (827)  all_57_9 = e1
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (74) gives:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (828)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (828) gives:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (829)  all_57_12 = e1 & op(e0, e3) = e1
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (829) implies:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (830)  all_57_12 = e1
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (6), (11), (12), (13), (14), (15), (17),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18), (19), (22), (23), (24), (25), (26), (27),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (28), (29), (30), (33), (38), (40), (41), (43),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (44), (45), (47), (48), (50), (52), (53), (54),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (56), (57), (60), (61), (63), (64), (65), (67),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (68), (70), (71), (72), (73), (74), (75), (77),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (78), (79), (81), (82), (83), (84), (85), (86),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (88), (89), (91), (92), (93), (98), (99), (100),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (103), (104), (105), (107), (108), (109), (111),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (112), (114), (115), (117), (118), (119), (122),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (123), (124), (125), (127), (128), (129), (130),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (131), (132), (133), (137), (138), (140), (141),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (142), (695), (701), (702), (705), (706), (713),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (725), (729), (733), (737), (738), (739), (740),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (741), (742), (744), (749), (750), (751), (755),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (756), (757), (758), (760), (761), (762), (763),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (765), (766), (770), (772), (775), (782), (783),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (784), (787), (795), (798), (806), (819), (830)
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #389.
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (831)  all_57_13 = e1 & op(e0, e2) = e1
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (831) implies:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (832)  all_57_13 = e1
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (12), (13), (14), (15), (17), (18),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19), (22), (23), (26), (27), (28), (30), (33),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (38), (41), (43), (44), (48), (50), (52), (53),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (54), (57), (61), (63), (64), (67), (70), (71),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (74), (75), (78), (81), (82), (85), (88), (89),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (91), (92), (93), (99), (100), (103), (104),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (105), (111), (112), (114), (115), (117), (118),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (122), (123), (124), (125), (127), (129),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (130), (131), (132), (133), (137), (140), (141),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (142), (701), (702), (713), (725), (787), (795),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (798), (806), (812), (819), (820), (824), (827),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (832) are inconsistent by sub-proof #388.
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (833)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (17), (19), (26), (27), (52), (53), (54),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (61), (71), (74), (81), (88), (92), (99), (103),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (104), (111), (118), (122), (795), (806), (819),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (833) are inconsistent by sub-proof #387.
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (834)  all_57_10 = e1 & op(e2, e0) = e1
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (834) implies:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (835)  all_57_10 = e1
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (806), (835) imply:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (836)  e2 = e1
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (819), (836) imply:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (837)  all_57_8 = e1
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (12), (13), (14), (15), (17), (18),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19), (22), (23), (26), (27), (28), (30), (33),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (38), (41), (43), (44), (48), (50), (52), (53),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (54), (57), (61), (63), (64), (67), (70), (71),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (74), (75), (78), (81), (82), (85), (88), (89),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (91), (92), (93), (99), (100), (103), (104),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (105), (111), (112), (114), (115), (117), (118),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (122), (123), (124), (125), (127), (129),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (130), (131), (132), (133), (137), (140), (141),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (142), (705), (725), (795), (798), (806), (824),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (837) are inconsistent by sub-proof #425.
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (838)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (838) gives:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (839)  all_57_11 = e1 & op(e1, e0) = e1
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (839) implies:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (840)  all_57_11 = e1
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (725), (840) imply:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (841)  e1 = e0
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (841) implies:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (842)  e1 = e0
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (792), (842) imply:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (843)  all_57_5 = e0
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (12), (13), (14), (15), (17), (18),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19), (22), (23), (26), (27), (28), (30), (33),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (38), (41), (43), (44), (48), (50), (52), (53),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (54), (57), (61), (63), (64), (67), (70), (71),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (74), (75), (78), (81), (82), (85), (88), (89),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (91), (92), (99), (100), (103), (104), (105),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (111), (112), (114), (115), (117), (118), (122),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (123), (124), (125), (127), (129), (130), (131),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (132), (133), (137), (140), (141), (142), (798),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (806), (824), (843) are inconsistent by sub-proof
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #469.
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (844)  all_57_15 = e1 & op(e0, e0) = e1
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (844) implies:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (845)  op(e0, e0) = e1
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (19), (99), (845) are inconsistent by
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2183.
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (846)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e1, e0) = e3)
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (19), (26), (27), (54), (61), (71), (81),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (88), (122), (123), (132), (702), (846) are
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1080.
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (847)  all_57_11 = e2 & op(e1, e0) = e2
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (847) implies:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (848)  all_57_11 = e2
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (81), (725), (848) are inconsistent by sub-proof
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1949.
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | |   (849)  all_57_12 = e1 & op(e0, e3) = e1
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (849) implies:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | |   (850)  all_57_12 = e1
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (130) gives:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (851)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e2)
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (851) gives:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (852)  all_57_4 = e2 & op(e3, e1) = e2
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (54), (798), (852) are inconsistent by sub-proof
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2487.
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (853)  all_57_5 = e2 & op(e2, e1) = e2
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (853) implies:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (854)  all_57_5 = e2
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (17), (19), (26), (27), (52), (54), (61),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (71), (74), (81), (88), (92), (103), (104), (122),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (795), (798), (806), (854) are inconsistent by
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1753.
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (855)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e1) = e2)
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (855) gives:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (856)  all_57_8 = e2 & op(e1, e1) = e2
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (856) implies:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (857)  all_57_8 = e2
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (6), (11), (12), (13), (14), (15), (17),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18), (19), (22), (23), (24), (25), (26), (27),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (28), (29), (30), (33), (38), (40), (41), (43),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (44), (45), (47), (48), (50), (52), (53), (54),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (56), (57), (60), (61), (63), (64), (65), (67),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (68), (70), (71), (72), (73), (74), (75), (77),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (78), (79), (81), (82), (83), (84), (85), (86),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (88), (89), (91), (92), (93), (98), (99), (100),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (103), (104), (105), (107), (108), (109), (111),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (112), (114), (115), (117), (118), (119), (122),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (123), (124), (125), (127), (128), (129), (130),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (131), (132), (133), (137), (138), (140), (141),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (142), (695), (701), (702), (705), (706), (713),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (725), (729), (733), (737), (738), (739), (740),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (741), (742), (744), (749), (750), (751), (755),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (756), (757), (758), (760), (761), (762), (763),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (765), (766), (770), (772), (775), (782), (783),
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (784), (787), (795), (798), (806), (850), (857)
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #389.
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (858)  all_57_14 = e2 & op(e0, e1) = e2
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (858) implies:
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (859)  all_57_14 = e2
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (81), (713), (859) are inconsistent by sub-proof
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2422.
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.38  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.38  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.38  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.38  | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.38  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.38  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.38  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.38  | | | | | | | | | | | | | | | | | | | | | |   (860)  all_57_5 = e3 & op(e2, e1) = e3
% 227.78/39.38  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.38  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (860) implies:
% 227.78/39.38  | | | | | | | | | | | | | | | | | | | | | |   (861)  all_57_5 = e3
% 227.78/39.38  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.38  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (17), (52), (54), (81), (88), (118), (122),
% 227.78/39.38  | | | | | | | | | | | | | | | | | | | | | |            (795), (861) are inconsistent by sub-proof #1802.
% 227.78/39.38  | | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.38  | | | | | | | | | | | | | | | | | | | | | End of split
% 227.78/39.38  | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.38  | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.78/39.38  | | | | | | | | | | | | | | | | | | | | | 
% 227.78/39.38  | | | | | | | | | | | | | | | | | | | | |   (862)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 227.78/39.38  | | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e1) = e3)
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (19), (26), (27), (54), (61), (71), (74),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | |            (81), (88), (103), (122), (701), (862) are
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1044.
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | |   (863)  all_57_3 = e3 & op(e2, e2) = e3
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | ALPHA: (863) implies:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | |   (864)  all_57_3 = e3
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (52), (61), (864) are inconsistent by sub-proof
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | |            #2358.
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | |   (865)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 227.83/39.38  | | | | | | | | | | | | | | | | | | |            e3 & op(e2, e0) = e3)
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | BETA: splitting (865) gives:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | |   (866)  all_57_5 = e3 & op(e2, e1) = e3
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (792), (866) are inconsistent by sub-proof
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | |            #386.
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | |   (867)  all_57_10 = e3 & op(e2, e0) = e3
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | ALPHA: (867) implies:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | |   (868)  all_57_10 = e3
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | BETA: splitting (92) gives:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | |   (869)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e3)
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (869) gives:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | |   (870)  all_57_4 = e3 & op(e3, e1) = e3
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (870) implies:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | |   (871)  all_57_4 = e3
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (118) gives:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | |   (872)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (872) gives:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | |   (873)  all_57_2 = e2 & op(e2, e3) = e2
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (873) implies:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | |   (874)  all_57_2 = e2
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13) gives:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | |   (875)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e1)
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (875) gives:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | |   (876)  all_57_0 = e1 & op(e3, e3) = e1
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (88), (705), (876) are inconsistent by sub-proof
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | |            #2454.
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | |   (877)  all_57_2 = e1 & op(e2, e3) = e1
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (122), (874), (877) are inconsistent by sub-proof
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | |            #2244.
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | |   (878)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e3) = e1)
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (878) gives:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | |   (879)  all_57_6 = e1 & op(e1, e3) = e1
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (879) implies:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | |   (880)  all_57_6 = e1
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (132) gives:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (881)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (881) gives:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (882)  all_57_9 = e1 & op(e3, e0) = e1
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (882) implies:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (883)  all_57_9 = e1
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (54), (71), (81), (122), (123), (725), (868),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (883) are inconsistent by sub-proof #1987.
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (884)  all_57_10 = e1 & op(e2, e0) = e1
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (884) implies:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (885)  all_57_10 = e1
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (868), (885) imply:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (886)  e3 = e1
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (871), (886) imply:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (887)  all_57_4 = e1
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (12), (13), (14), (15), (17), (18),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19), (22), (23), (26), (27), (28), (30), (33),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (38), (41), (43), (44), (48), (50), (52), (53),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (54), (57), (61), (63), (64), (67), (70), (71),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (74), (75), (78), (81), (82), (85), (88), (89),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (91), (92), (99), (100), (103), (104), (105),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (112), (114), (115), (117), (118), (119), (122),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (123), (124), (125), (127), (129), (130), (131),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (132), (133), (137), (140), (141), (142), (701),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (713), (880), (887) are inconsistent by sub-proof
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #438.
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (888)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (19), (88), (99), (725), (888) are
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1105.
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | |   (889)  all_57_12 = e1 & op(e0, e3) = e1
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (889) implies:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | |   (890)  all_57_12 = e1
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (130) gives:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (891)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e2)
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (54), (122), (792), (871), (891) are inconsistent
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1232.
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (892)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e1) = e2)
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (892) gives:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (893)  all_57_8 = e2 & op(e1, e1) = e2
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (893) implies:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (894)  all_57_8 = e2
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (103) gives:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (895)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (895) gives:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (896)  all_57_12 = e2 & op(e0, e3) = e2
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (6), (11), (12), (13), (14), (15), (17),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18), (19), (22), (23), (24), (25), (26), (27),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (28), (29), (30), (33), (38), (40), (41), (43),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (44), (45), (47), (48), (50), (52), (53), (56),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (57), (60), (61), (63), (64), (65), (67), (68),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (70), (71), (72), (73), (74), (75), (77), (78),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (79), (82), (83), (84), (85), (86), (88), (89),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (91), (92), (93), (98), (99), (100), (103), (104),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (105), (107), (108), (109), (111), (112), (114),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (115), (117), (118), (119), (123), (124), (125),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (127), (128), (129), (130), (131), (132), (133),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (137), (138), (140), (141), (142), (695), (701),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (702), (705), (706), (713), (725), (729), (733),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (737), (738), (739), (741), (742), (749), (750),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (751), (755), (756), (757), (758), (760), (761),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (762), (763), (765), (766), (770), (772), (775),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (782), (783), (784), (890), (894), (896) are
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #392.
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (897)  all_57_13 = e2 & op(e0, e2) = e2
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (897) implies:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (898)  all_57_13 = e2
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (140) gives:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (899)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (899) gives:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (900)  all_57_1 = e1 & op(e3, e2) = e1
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (900) implies:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (901)  all_57_1 = e1
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (93) gives:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (902)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e3)
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (902) gives:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (903)  all_57_1 = e3 & op(e3, e2) = e3
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (903) implies:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (904)  all_57_1 = e3
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (33), (44), (50), (54), (61), (71), (81),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (88), (104), (122), (123), (868), (871), (904) are
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1436.
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (905)  all_57_3 = e3 & op(e2, e2) = e3
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (905) implies:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (906)  all_57_3 = e3
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (52), (906) imply:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (907)  e3 = e0
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (907) implies:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (908)  e3 = e0
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (868), (908) imply:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (909)  all_57_10 = e0
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (871), (908) imply:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (910)  all_57_4 = e0
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (17), (19), (26), (27), (52), (54), (61),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (71), (74), (81), (88), (92), (103), (118), (122),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (701), (909), (910) are inconsistent by sub-proof
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1043.
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (911)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (911) gives:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (912)  all_57_7 = e3 & op(e1, e2) = e3
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (912) implies:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (913)  all_57_7 = e3
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (132) gives:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (914)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (914) gives:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (915)  all_57_9 = e1 & op(e3, e0) = e1
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (915) implies:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (916)  all_57_9 = e1
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (54), (71), (81), (122), (123), (725), (868),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (916) are inconsistent by sub-proof #1987.
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (917)  all_57_10 = e1 & op(e2, e0) = e1
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (917) implies:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (918)  all_57_10 = e1
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (868), (918) imply:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (919)  e3 = e1
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (919) implies:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (920)  e3 = e1
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (871), (920) imply:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (921)  all_57_4 = e1
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (6), (11), (12), (13), (14), (15), (17),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18), (19), (22), (23), (24), (25), (26), (27),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (28), (29), (30), (33), (38), (40), (41), (43),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (44), (45), (47), (48), (50), (52), (53), (54),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (56), (57), (60), (61), (63), (64), (65), (67),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (68), (70), (71), (72), (73), (74), (75), (77),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (78), (79), (81), (82), (83), (84), (85), (86),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (88), (89), (91), (92), (93), (98), (99), (100),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (103), (104), (105), (107), (108), (109), (111),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (112), (114), (115), (117), (118), (119), (122),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (123), (124), (125), (127), (128), (129), (130),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (131), (132), (133), (137), (138), (140), (141),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (142), (695), (701), (702), (705), (706), (713),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (725), (729), (733), (737), (738), (739), (740),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (741), (742), (744), (749), (750), (751), (755),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (756), (757), (758), (760), (761), (762), (763),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (765), (766), (770), (772), (775), (782), (783),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (784), (787), (921) are inconsistent by sub-proof
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #397.
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (922)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (922) gives:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (923)  all_57_11 = e1 & op(e1, e0) = e1
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (923) implies:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (924)  all_57_11 = e1
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (17), (52), (54), (81), (88), (122), (140),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (725), (901), (913), (924) are inconsistent by
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1377.
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (925)  all_57_15 = e1 & op(e0, e0) = e1
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (925) implies:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (926)  op(e0, e0) = e1
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (19), (99), (926) are inconsistent by
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2183.
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (927)  all_57_13 = e3 & op(e0, e2) = e3
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (927) implies:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (928)  all_57_13 = e3
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (54), (61), (71), (74), (81), (88), (103),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (122), (701), (890), (928) are inconsistent by
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2057.
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (929)  all_57_3 = e1 & op(e2, e2) = e1
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (929) implies:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (930)  op(e2, e2) = e1
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (45), (88), (930) are inconsistent by
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2352.
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (931)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (931) gives:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (932)  all_57_7 = e1 & op(e1, e2) = e1
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (932) implies:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (933)  all_57_7 = e1
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (93) gives:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (934)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e3)
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (934) gives:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (935)  all_57_1 = e3 & op(e3, e2) = e3
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (935) implies:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (936)  all_57_1 = e3
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (33), (44), (50), (54), (61), (71), (81),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (88), (104), (122), (123), (868), (871), (936) are
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1436.
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (937)  all_57_3 = e3 & op(e2, e2) = e3
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (937) implies:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (938)  all_57_3 = e3
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (52), (938) imply:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (939)  e3 = e0
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (868), (939) imply:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (940)  all_57_10 = e0
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (871), (939) imply:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (941)  all_57_4 = e0
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (17), (19), (26), (27), (52), (54), (61),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (71), (74), (81), (88), (92), (103), (118), (122),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (701), (940), (941) are inconsistent by sub-proof
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1043.
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (942)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (942) gives:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (943)  all_57_7 = e3 & op(e1, e2) = e3
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (943) implies:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (944)  all_57_7 = e3
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (933), (944) imply:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (945)  e3 = e1
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (871), (945) imply:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (946)  all_57_4 = e1
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (6), (11), (12), (13), (14), (15), (17),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18), (19), (22), (23), (24), (25), (26), (27),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (28), (29), (30), (33), (38), (40), (41), (43),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (44), (45), (47), (48), (50), (52), (53), (54),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (56), (57), (60), (61), (63), (64), (65), (67),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (68), (70), (71), (72), (73), (74), (75), (77),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (78), (79), (81), (82), (83), (84), (85), (86),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (88), (89), (91), (92), (93), (98), (99), (100),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (103), (104), (105), (107), (108), (109), (111),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (112), (114), (115), (117), (118), (119), (122),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (123), (124), (125), (127), (128), (129), (130),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (131), (132), (133), (137), (138), (140), (141),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (142), (695), (701), (702), (705), (706), (713),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (725), (729), (733), (737), (738), (739), (740),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (741), (742), (744), (749), (750), (751), (755),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (756), (757), (758), (760), (761), (762), (763),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (765), (766), (770), (772), (775), (782), (783),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (784), (787), (933), (946) are inconsistent by
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #398.
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (947)  all_57_13 = e3 & op(e0, e2) = e3
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (947) implies:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (948)  all_57_13 = e3
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (54), (61), (71), (74), (81), (88), (103),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (122), (701), (890), (948) are inconsistent by
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2057.
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (949)  all_57_13 = e1 & op(e0, e2) = e1
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (6), (11), (12), (13), (14), (15), (17),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18), (19), (22), (23), (24), (25), (26), (27),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (28), (29), (30), (33), (38), (40), (41), (43),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (44), (45), (47), (48), (50), (52), (53), (56),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (57), (60), (61), (63), (64), (65), (67), (68),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (70), (71), (72), (73), (74), (75), (77), (78),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (79), (82), (83), (84), (85), (86), (88), (89),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (91), (92), (93), (98), (99), (100), (103), (104),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (105), (107), (108), (109), (111), (112), (114),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (115), (117), (118), (119), (123), (124), (125),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (127), (128), (129), (130), (131), (132), (133),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (137), (138), (140), (141), (142), (695), (701),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (702), (705), (706), (713), (725), (729), (733),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (737), (738), (739), (741), (742), (749), (750),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (751), (755), (756), (757), (758), (760), (761),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (762), (763), (765), (766), (770), (772), (775),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (782), (783), (784), (894), (898), (949) are
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #400.
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (950)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (950) gives:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (951)  all_57_14 = e2 & op(e0, e1) = e2
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (52), (54), (81), (118), (122), (713), (792),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (868), (874), (951) are inconsistent by sub-proof
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #385.
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (952)  all_57_15 = e2 & op(e0, e0) = e2
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (54), (71), (952) are inconsistent by sub-proof
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2323.
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (953)  all_57_14 = e2 & op(e0, e1) = e2
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (52), (54), (81), (118), (122), (713), (792),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (868), (874), (953) are inconsistent by sub-proof
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #385.
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | |   (954)  all_57_3 = e2 & op(e2, e2) = e2
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (52), (81), (954) are inconsistent by sub-proof
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | |            #2103.
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | |   (955)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (955) gives:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | |   (956)  all_57_5 = e2 & op(e2, e1) = e2
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (956) implies:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | |   (957)  all_57_5 = e2
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (122), (792), (957) are inconsistent by sub-proof
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | |            #1885.
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | |   (958)  all_57_10 = e2 & op(e2, e0) = e2
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (54), (868), (958) are inconsistent by sub-proof
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | |            #2250.
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | |   (959)  all_57_5 = e3 & op(e2, e1) = e3
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (959) implies:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | |   (960)  all_57_5 = e3
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (17), (52), (54), (81), (88), (118), (122),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | |            (868), (960) are inconsistent by sub-proof #1693.
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | |   (961)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e1) = e3)
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (19), (26), (27), (54), (61), (71), (74),
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | |            (81), (88), (103), (122), (701), (961) are
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1044.
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.38  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.38  | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | End of split
% 227.83/39.38  | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.38  | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | |   (962)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 227.83/39.38  | | | | | | | | | | | | | | | | |            e1 & op(e0, e1) = e1)
% 227.83/39.38  | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | BETA: splitting (962) gives:
% 227.83/39.38  | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.38  | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | |   (963)  all_57_8 = e1 & op(e1, e1) = e1
% 227.83/39.38  | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | ALPHA: (963) implies:
% 227.83/39.38  | | | | | | | | | | | | | | | | | |   (964)  all_57_8 = e1
% 227.83/39.38  | | | | | | | | | | | | | | | | | | 
% 227.83/39.38  | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (6), (11), (12), (13), (14), (15), (17),
% 227.83/39.38  | | | | | | | | | | | | | | | | | |            (18), (19), (22), (23), (24), (25), (26), (27),
% 227.83/39.38  | | | | | | | | | | | | | | | | | |            (28), (29), (30), (33), (38), (40), (41), (43),
% 227.83/39.38  | | | | | | | | | | | | | | | | | |            (44), (45), (47), (48), (50), (52), (53), (56),
% 227.83/39.38  | | | | | | | | | | | | | | | | | |            (57), (60), (61), (63), (64), (65), (67), (68),
% 227.83/39.38  | | | | | | | | | | | | | | | | | |            (70), (71), (72), (73), (74), (75), (77), (78),
% 227.83/39.39  | | | | | | | | | | | | | | | | | |            (79), (82), (83), (84), (85), (86), (88), (89),
% 227.83/39.39  | | | | | | | | | | | | | | | | | |            (91), (92), (93), (98), (99), (100), (103), (104),
% 227.83/39.39  | | | | | | | | | | | | | | | | | |            (105), (107), (108), (109), (111), (112), (114),
% 227.83/39.39  | | | | | | | | | | | | | | | | | |            (115), (117), (118), (119), (123), (124), (125),
% 227.83/39.39  | | | | | | | | | | | | | | | | | |            (127), (128), (129), (130), (131), (132), (133),
% 227.83/39.39  | | | | | | | | | | | | | | | | | |            (137), (138), (140), (141), (142), (695), (701),
% 227.83/39.39  | | | | | | | | | | | | | | | | | |            (702), (705), (706), (713), (725), (729), (733),
% 227.83/39.39  | | | | | | | | | | | | | | | | | |            (737), (738), (739), (741), (742), (749), (750),
% 227.83/39.39  | | | | | | | | | | | | | | | | | |            (751), (755), (756), (757), (758), (760), (761),
% 227.83/39.39  | | | | | | | | | | | | | | | | | |            (762), (763), (765), (766), (770), (772), (775),
% 227.83/39.39  | | | | | | | | | | | | | | | | | |            (782), (783), (784), (964) are inconsistent by
% 227.83/39.39  | | | | | | | | | | | | | | | | | |            sub-proof #403.
% 227.83/39.39  | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | |   (965)  all_57_14 = e1 & op(e0, e1) = e1
% 227.83/39.39  | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | ALPHA: (965) implies:
% 227.83/39.39  | | | | | | | | | | | | | | | | | |   (966)  all_57_14 = e1
% 227.83/39.39  | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | REF_CLOSE: (88), (713), (966) are inconsistent by sub-proof
% 227.83/39.39  | | | | | | | | | | | | | | | | | |            #2122.
% 227.83/39.39  | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | End of split
% 227.83/39.39  | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | End of split
% 227.83/39.39  | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | Case 2:
% 227.83/39.39  | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | |   (967)  all_55_10 = e0
% 227.83/39.39  | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | REF_CLOSE: (105), (733), (967) are inconsistent by sub-proof
% 227.83/39.39  | | | | | | | | | | | | | | | |            #2118.
% 227.83/39.39  | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | End of split
% 227.83/39.39  | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | End of split
% 227.83/39.39  | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | End of split
% 227.83/39.39  | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | Case 2:
% 227.83/39.39  | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | |   (968)  all_38_2 = e2
% 227.83/39.39  | | | | | | | | | | | | |   (969)  ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0
% 227.83/39.39  | | | | | | | | | | | | |            & op(e1, e2) = all_38_1 & $i(all_38_0) &
% 227.83/39.39  | | | | | | | | | | | | |            $i(all_38_1)) | ( ~ (all_38_1 = e3) & op(e1, e2)
% 227.83/39.39  | | | | | | | | | | | | |            = all_38_1 & $i(all_38_1))
% 227.83/39.39  | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | COMBINE_EQS: (112), (968) imply:
% 227.83/39.39  | | | | | | | | | | | | |   (970)  all_6_2 = e2
% 227.83/39.39  | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | SIMP: (970) implies:
% 227.83/39.39  | | | | | | | | | | | | |   (971)  all_6_2 = e2
% 227.83/39.39  | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | COMBINE_EQS: (43), (971) imply:
% 227.83/39.39  | | | | | | | | | | | | |   (972)  all_42_2 = e2
% 227.83/39.39  | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | REDUCE: (39), (971) imply:
% 227.83/39.39  | | | | | | | | | | | | |   (973)   ~ (all_53_2 = e2)
% 227.83/39.39  | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | REDUCE: (106), (971) imply:
% 227.83/39.39  | | | | | | | | | | | | |   (974)   ~ (all_53_6 = e2)
% 227.83/39.39  | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | REDUCE: (48), (971) imply:
% 227.83/39.39  | | | | | | | | | | | | |   (975)   ~ (all_53_9 = e2)
% 227.83/39.39  | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | REDUCE: (762), (971) imply:
% 227.83/39.39  | | | | | | | | | | | | |   (976)   ~ (all_52_5 = e2)
% 227.83/39.39  | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | REDUCE: (26), (971) imply:
% 227.83/39.39  | | | | | | | | | | | | |   (977)   ~ (e3 = e2)
% 227.83/39.39  | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | REDUCE: (27), (971) imply:
% 227.83/39.39  | | | | | | | | | | | | |   (978)  op(e1, e1) = e2
% 227.83/39.39  | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | BETA: splitting (141) gives:
% 227.83/39.39  | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | Case 1:
% 227.83/39.39  | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | |   (979)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 227.83/39.39  | | | | | | | | | | | | | |            & op(e1, e2) = e2)
% 227.83/39.39  | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | BETA: splitting (979) gives:
% 227.83/39.39  | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | Case 1:
% 227.83/39.39  | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | |   (980)  all_57_6 = e2 & op(e1, e3) = e2
% 227.83/39.39  | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | ALPHA: (980) implies:
% 227.83/39.39  | | | | | | | | | | | | | | |   (981)  all_57_6 = e2
% 227.83/39.39  | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | BETA: splitting (119) gives:
% 227.83/39.39  | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | Case 1:
% 227.83/39.39  | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | |   (982)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 227.83/39.39  | | | | | | | | | | | | | | | |            & op(e2, e3) = e3)
% 227.83/39.39  | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | BETA: splitting (982) gives:
% 227.83/39.39  | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.39  | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | |   (983)  all_57_0 = e3 & op(e3, e3) = e3
% 227.83/39.39  | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | ALPHA: (983) implies:
% 227.83/39.39  | | | | | | | | | | | | | | | | |   (984)  op(e3, e3) = e3
% 227.83/39.39  | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (61), (706), (984) are inconsistent by
% 227.83/39.39  | | | | | | | | | | | | | | | | |            sub-proof #2494.
% 227.83/39.39  | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.39  | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | |   (985)  all_57_2 = e3 & op(e2, e3) = e3
% 227.83/39.39  | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | ALPHA: (985) implies:
% 227.83/39.39  | | | | | | | | | | | | | | | | |   (986)  all_57_2 = e3
% 227.83/39.39  | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | BETA: splitting (118) gives:
% 227.83/39.39  | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | |   (987)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 227.83/39.39  | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 227.83/39.39  | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | BETA: splitting (987) gives:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | |   (988)  all_57_2 = e2 & op(e2, e3) = e2
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (54), (986), (988) are inconsistent by sub-proof
% 227.83/39.39  | | | | | | | | | | | | | | | | | | |            #1925.
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | |   (989)  all_57_3 = e2 & op(e2, e2) = e2
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (52), (81), (989) are inconsistent by sub-proof
% 227.83/39.39  | | | | | | | | | | | | | | | | | | |            #2103.
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.39  | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | |   (990)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 227.83/39.39  | | | | | | | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 227.83/39.39  | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | BETA: splitting (990) gives:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | |   (991)  all_57_5 = e2 & op(e2, e1) = e2
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | ALPHA: (991) implies:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | |   (992)  all_57_5 = e2
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | BETA: splitting (63) gives:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | |   (993)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e1)
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | BETA: splitting (993) gives:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | |   (994)  all_57_4 = e1 & op(e3, e1) = e1
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | ALPHA: (994) implies:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | |   (995)  all_57_4 = e1
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13) gives:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | |   (996)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e1)
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (996) gives:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | |   (997)  all_57_0 = e1 & op(e3, e3) = e1
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (88), (705), (997) are inconsistent by sub-proof
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | |            #2454.
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | |   (998)  all_57_2 = e1 & op(e2, e3) = e1
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (986), (998) are inconsistent by sub-proof
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | |            #1928.
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | |   (999)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e3) = e1)
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (999) gives:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | |   (1000)  all_57_6 = e1 & op(e1, e3) = e1
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1000) implies:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | |   (1001)  all_57_6 = e1
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (12), (13), (14), (15), (17), (18),
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | |            (19), (22), (23), (26), (27), (28), (30), (33),
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | |            (38), (41), (43), (44), (48), (50), (52), (53),
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | |            (54), (57), (61), (63), (64), (67), (70), (71),
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | |            (74), (75), (78), (81), (82), (85), (88), (89),
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | |            (91), (92), (99), (100), (103), (104), (105),
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | |            (112), (114), (115), (117), (118), (119), (122),
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | |            (123), (124), (125), (127), (129), (130), (131),
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | |            (132), (133), (137), (140), (141), (142), (701),
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | |            (713), (995), (1001) are inconsistent by sub-proof
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | |            #438.
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | |   (1002)  all_57_12 = e1 & op(e0, e3) = e1
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1002) implies:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | |   (1003)  all_57_12 = e1
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (85) gives:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | |   (1004)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e3)
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (12), (13), (14), (15), (17), (18),
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | |            (19), (22), (23), (26), (27), (28), (30), (33),
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | |            (38), (41), (43), (44), (48), (50), (52), (53),
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | |            (54), (57), (61), (63), (64), (67), (70), (71),
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | |            (74), (75), (78), (81), (82), (85), (88), (89),
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | |            (91), (92), (99), (100), (103), (104), (105),
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | |            (111), (112), (114), (115), (117), (118), (122),
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | |            (123), (124), (125), (127), (129), (130), (131),
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | |            (132), (133), (137), (140), (141), (142), (702),
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | |            (713), (986), (1003), (1004) are inconsistent by
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #384.
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | |   (1005)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e3)
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (19), (115), (142), (995), (1005) are
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2281.
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | |   (1006)  all_57_5 = e1 & op(e2, e1) = e1
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (122), (992), (1006) are inconsistent by sub-proof
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | |            #1886.
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | |   (1007)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e1)
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (88), (122), (713), (978), (1007) are
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2380.
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | |   (1008)  all_57_10 = e2 & op(e2, e0) = e2
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | ALPHA: (1008) implies:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | |   (1009)  all_57_10 = e2
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | BETA: splitting (13) gives:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | |   (1010)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e1)
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | BETA: splitting (1010) gives:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | |   (1011)  all_57_0 = e1 & op(e3, e3) = e1
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (88), (705), (1011) are inconsistent by sub-proof
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | |            #2454.
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | |   (1012)  all_57_2 = e1 & op(e2, e3) = e1
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (986), (1012) are inconsistent by sub-proof
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | |            #1928.
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | |   (1013)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e3) = e1)
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | BETA: splitting (1013) gives:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | |   (1014)  all_57_6 = e1 & op(e1, e3) = e1
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (122), (981), (1014) are inconsistent by sub-proof
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | |            #2389.
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | |   (1015)  all_57_12 = e1 & op(e0, e3) = e1
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | ALPHA: (1015) implies:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | |   (1016)  all_57_12 = e1
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (130) gives:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | |   (1017)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e2)
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1017) gives:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | |   (1018)  all_57_4 = e2 & op(e3, e1) = e2
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1018) implies:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | |   (1019)  all_57_4 = e2
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (85) gives:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | |   (1020)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e3)
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (12), (13), (14), (15), (17), (18),
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | |            (19), (22), (23), (26), (27), (28), (30), (33),
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | |            (38), (41), (43), (44), (48), (50), (52), (53),
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | |            (54), (57), (61), (63), (64), (67), (70), (71),
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | |            (74), (75), (78), (81), (82), (85), (88), (89),
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | |            (91), (92), (99), (100), (103), (104), (105),
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | |            (111), (112), (114), (115), (117), (118), (122),
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | |            (123), (124), (125), (127), (129), (130), (131),
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | |            (132), (133), (137), (140), (141), (142), (702),
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | |            (713), (986), (1016), (1020) are inconsistent by
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #384.
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | |   (1021)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e3)
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (54), (115), (142), (1019), (1021) are
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2448.
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | |   (1022)  all_57_5 = e2 & op(e2, e1) = e2
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1022) implies:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | |   (1023)  all_57_5 = e2
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (17), (19), (26), (27), (52), (54), (61),
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | |            (71), (74), (81), (88), (92), (103), (104), (122),
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | |            (986), (1009), (1023) are inconsistent by
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1752.
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | |   (1024)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e1) = e2)
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1024) gives:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | |   (1025)  all_57_8 = e2 & op(e1, e1) = e2
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1025) implies:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | |   (1026)  all_57_8 = e2
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (17), (19), (22), (26), (27), (52), (54),
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | |            (61), (63), (71), (74), (81), (88), (92), (103),
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | |            (104), (118), (122), (123), (132), (133), (701),
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | |            (702), (713), (725), (981), (986), (1026) are
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #382.
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | |   (1027)  all_57_14 = e2 & op(e0, e1) = e2
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1027) implies:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | |   (1028)  all_57_14 = e2
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (81), (713), (1028) are inconsistent by sub-proof
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | |            #2422.
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.39  | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | End of split
% 227.83/39.39  | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | End of split
% 227.83/39.39  | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | Case 2:
% 227.83/39.39  | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | |   (1029)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 227.83/39.39  | | | | | | | | | | | | | | | |             e3 & op(e0, e3) = e3)
% 227.83/39.39  | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | REF_CLOSE: (17), (54), (71), (74), (81), (88), (103), (122),
% 227.83/39.39  | | | | | | | | | | | | | | | |            (713), (981), (1029) are inconsistent by sub-proof
% 227.83/39.39  | | | | | | | | | | | | | | | |            #1557.
% 227.83/39.39  | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | End of split
% 227.83/39.39  | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | Case 2:
% 227.83/39.39  | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | |   (1030)  all_57_7 = e2 & op(e1, e2) = e2
% 227.83/39.39  | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | ALPHA: (1030) implies:
% 227.83/39.39  | | | | | | | | | | | | | | |   (1031)  all_57_7 = e2
% 227.83/39.39  | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | BETA: splitting (22) gives:
% 227.83/39.39  | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | Case 1:
% 227.83/39.39  | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | |   (1032)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 227.83/39.39  | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 227.83/39.39  | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | BETA: splitting (1032) gives:
% 227.83/39.39  | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.39  | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | |   (1033)  all_57_6 = e3 & op(e1, e3) = e3
% 227.83/39.39  | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | ALPHA: (1033) implies:
% 227.83/39.39  | | | | | | | | | | | | | | | | |   (1034)  all_57_6 = e3
% 227.83/39.39  | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | BETA: splitting (93) gives:
% 227.83/39.39  | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | |   (1035)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 227.83/39.39  | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 227.83/39.39  | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | BETA: splitting (1035) gives:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | |   (1036)  all_57_1 = e3 & op(e3, e2) = e3
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | ALPHA: (1036) implies:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | |   (1037)  all_57_1 = e3
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | BETA: splitting (130) gives:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | |   (1038)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e2)
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | BETA: splitting (1038) gives:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | |   (1039)  all_57_4 = e2 & op(e3, e1) = e2
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | ALPHA: (1039) implies:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | |   (1040)  all_57_4 = e2
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (140) gives:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | |   (1041)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (19), (45), (88), (1037), (1041) are
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2206.
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | |   (1042)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1042) gives:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | |   (1043)  all_57_7 = e1 & op(e1, e2) = e1
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (122), (1031), (1043) are inconsistent by
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2190.
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | |   (1044)  all_57_13 = e1 & op(e0, e2) = e1
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1044) implies:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | |   (1045)  all_57_13 = e1
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (133) gives:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | |   (1046)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1046) gives:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | |   (1047)  all_57_6 = e1 & op(e1, e3) = e1
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (1034), (1047) are inconsistent by sub-proof
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | |            #2117.
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | |   (1048)  all_57_7 = e1 & op(e1, e2) = e1
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (122), (1031), (1048) are inconsistent by
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2190.
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | |   (1049)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1049) gives:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | |   (1050)  all_57_8 = e1 & op(e1, e1) = e1
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1050) implies:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | |   (1051)  all_57_8 = e1
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | |   (1052)  op(e1, e1) = e1
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (103) gives:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1053)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1053) gives:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1054)  all_57_12 = e2 & op(e0, e3) = e2
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1054) implies:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1055)  all_57_12 = e2
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (92) gives:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1056)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e3)
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1056) gives:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1057)  all_57_4 = e3 & op(e3, e1) = e3
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1057) implies:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1058)  all_57_4 = e3
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (54), (1040), (1058) are inconsistent by sub-proof
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2482.
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1059)  all_57_5 = e3 & op(e2, e1) = e3
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1059) implies:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1060)  all_57_5 = e3
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1061)  op(e2, e1) = e3
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13) gives:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1062)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e1)
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1062) gives:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1063)  all_57_0 = e1 & op(e3, e3) = e1
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (17), (52), (54), (81), (88), (122), (140),
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (705), (1037), (1045), (1063) are inconsistent by
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #381.
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1064)  all_57_2 = e1 & op(e2, e3) = e1
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1064) implies:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1065)  all_57_2 = e1
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (118) gives:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1066)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1066) gives:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1067)  all_57_2 = e2 & op(e2, e3) = e2
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1067) implies:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1068)  all_57_2 = e2
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (122), (1065), (1068) are inconsistent by
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2464.
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1069)  all_57_3 = e2 & op(e2, e2) = e2
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1069) implies:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1070)  all_57_3 = e2
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (52), (1070) imply:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1071)  e2 = e0
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1071) implies:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1072)  e2 = e0
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1055), (1072) imply:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1073)  all_57_12 = e0
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (54), (81), (122), (127), (705), (1034), (1065),
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1073) are inconsistent by sub-proof #1426.
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1074)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1074) gives:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1075)  all_57_5 = e2 & op(e2, e1) = e2
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (54), (1060), (1075) are inconsistent by sub-proof
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2425.
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1076)  all_57_10 = e2 & op(e2, e0) = e2
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1076) implies:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1077)  all_57_10 = e2
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (119) gives:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1078)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e3)
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1078) gives:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1079)  all_57_0 = e3 & op(e3, e3) = e3
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1079) implies:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1080)  all_57_0 = e3
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (17), (54), (61), (81), (88), (122), (127),
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (131), (1034), (1080) are inconsistent by
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2010.
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1081)  all_57_2 = e3 & op(e2, e3) = e3
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1081) implies:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1082)  all_57_2 = e3
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (17), (52), (88), (122), (1060), (1077),
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1082) are inconsistent by sub-proof #1804.
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1083)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e3) = e3)
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1083) gives:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with e1, e2, e1, e1,
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (978), (1052) gives:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1084)  e2 = e1
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1031), (1084) imply:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1085)  all_57_7 = e1
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1040), (1084) imply:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1086)  all_57_4 = e1
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (44) gives:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1087)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e2)
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1087) gives:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1088)  all_57_0 = e2 & op(e3, e3) = e2
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1088) implies:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1089)  all_57_0 = e2
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1090)  op(e3, e3) = e2
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (131) gives:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1091)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e0)
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (17), (19), (52), (54), (61), (81), (88),
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (111), (118), (122), (1090), (1091) are
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1654.
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1092)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = e0)
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1092) gives:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1093)  all_57_6 = e0 & op(e1, e3) = e0
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1093) implies:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1094)  all_57_6 = e0
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (13), (15), (17), (19), (22), (26), (27),
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (52), (54), (61), (71), (74), (81), (88), (99),
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (103), (104), (111), (118), (119), (122), (123),
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (127), (131), (132), (140), (1037), (1089),
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1090), (1094) are inconsistent by sub-proof #789.
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1095)  all_57_12 = e0 & op(e0, e3) = e0
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1095) implies:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1096)  all_57_12 = e0
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (81), (1055), (1096) are inconsistent by sub-proof
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2385.
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1097)  all_57_1 = e2 & op(e3, e2) = e2
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (54), (1037), (1097) are inconsistent by sub-proof
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1809.
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1098)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e2)
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1098) gives:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (122), (1040), (1086) are inconsistent by
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2430.
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1099)  all_57_9 = e2 & op(e3, e0) = e2
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1099) implies:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1100)  all_57_9 = e2
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (17), (18), (52), (54), (61), (71), (81),
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (88), (118), (122), (132), (1034), (1051), (1060),
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1065), (1077), (1085), (1100) are inconsistent by
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #404.
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1101)  all_57_12 = e3 & op(e0, e3) = e3
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1101) implies:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1102)  all_57_12 = e3
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (17), (52), (54), (61), (71), (74), (81),
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (88), (103), (122), (140), (701), (1037), (1102)
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1038.
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1103)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e3) = e1)
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1103) gives:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1104)  all_57_6 = e1 & op(e1, e3) = e1
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1104) implies:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1105)  all_57_6 = e1
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (12), (13), (14), (15), (17), (18),
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19), (22), (23), (26), (27), (28), (30), (33),
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (38), (41), (43), (44), (48), (50), (52), (53),
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (54), (57), (61), (63), (64), (67), (70), (71),
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (74), (75), (78), (81), (82), (85), (88), (89),
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (91), (99), (100), (103), (104), (105), (112),
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (114), (115), (117), (118), (119), (122), (123),
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (124), (125), (127), (129), (130), (131), (132),
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (133), (137), (140), (141), (142), (713), (1060),
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1061), (1105) are inconsistent by sub-proof #439.
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1106)  all_57_12 = e1 & op(e0, e3) = e1
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (122), (1055), (1106) are inconsistent by
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2388.
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1107)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e1) = e3)
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (19), (26), (27), (54), (61), (71), (74),
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (81), (88), (103), (122), (701), (1107) are
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1044.
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1108)  all_57_13 = e2 & op(e0, e2) = e2
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1108) implies:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1109)  all_57_13 = e2
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (52), (88), (122), (140), (1031), (1037),
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1109) are inconsistent by sub-proof #1698.
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.39  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1110)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1110) gives:
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1111)  all_57_14 = e2 & op(e0, e1) = e2
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1111) implies:
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1112)  all_57_14 = e2
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (81), (713), (1112) are inconsistent by sub-proof
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2422.
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1113)  all_57_15 = e2 & op(e0, e0) = e2
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (54), (71), (1113) are inconsistent by sub-proof
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2323.
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | |   (1114)  all_57_11 = e1 & op(e1, e0) = e1
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1114) implies:
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | |   (1115)  all_57_11 = e1
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (725), (1115) imply:
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | |   (1116)  e1 = e0
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1045), (1116) imply:
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | |   (1117)  all_57_13 = e0
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (17), (52), (54), (81), (88), (122), (140),
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | |            (1037), (1117) are inconsistent by sub-proof
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | |            #1758.
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | |   (1118)  all_57_5 = e2 & op(e2, e1) = e2
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | ALPHA: (1118) implies:
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | |   (1119)  all_57_5 = e2
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (111) gives:
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | |   (1120)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1120) gives:
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | |   (1121)  all_57_2 = e3 & op(e2, e3) = e3
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1121) implies:
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | |   (1122)  all_57_2 = e3
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (140) gives:
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | |   (1123)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (19), (45), (88), (1037), (1123) are
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2206.
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | |   (1124)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1124) gives:
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | |   (1125)  all_57_7 = e1 & op(e1, e2) = e1
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (122), (1031), (1125) are inconsistent by
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2190.
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | |   (1126)  all_57_13 = e1 & op(e0, e2) = e1
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1126) implies:
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | |   (1127)  all_57_13 = e1
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13) gives:
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1128)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e1)
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1128) gives:
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1129)  all_57_0 = e1 & op(e3, e3) = e1
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (17), (52), (54), (81), (88), (122), (140),
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (705), (1037), (1127), (1129) are inconsistent by
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #381.
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1130)  all_57_2 = e1 & op(e2, e3) = e1
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (1122), (1130) are inconsistent by sub-proof
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1928.
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1131)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e3) = e1)
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1131) gives:
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1132)  all_57_6 = e1 & op(e1, e3) = e1
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (1034), (1132) are inconsistent by sub-proof
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2117.
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1133)  all_57_12 = e1 & op(e0, e3) = e1
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1133) implies:
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1134)  all_57_12 = e1
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (13), (15), (17), (19), (22), (26), (27),
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (52), (54), (61), (71), (81), (88), (103), (111),
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (118), (122), (123), (127), (131), (132), (140),
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (702), (713), (1037), (1122), (1134) are
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #417.
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | |   (1135)  all_57_3 = e3 & op(e2, e2) = e3
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (19), (22), (26), (27), (52), (54), (61),
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | |            (71), (81), (88), (104), (122), (123), (132),
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | |            (1031), (1034), (1135) are inconsistent by
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #380.
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | |   (1136)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (19), (54), (71), (81), (88), (99), (122),
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | |            (123), (132), (725), (1119), (1136) are
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #866.
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | |   (1137)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e1) = e2)
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | BETA: splitting (1137) gives:
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | |   (1138)  all_57_8 = e2 & op(e1, e1) = e2
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | ALPHA: (1138) implies:
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | |   (1139)  all_57_8 = e2
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (12), (13), (14), (15), (17), (18),
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | |            (19), (22), (23), (26), (27), (28), (29), (30),
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | |            (33), (34), (35), (38), (40), (41), (43), (44),
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | |            (45), (47), (48), (50), (52), (53), (54), (56),
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | |            (57), (60), (61), (63), (64), (65), (67), (68),
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | |            (70), (71), (72), (74), (75), (77), (78), (79),
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | |            (81), (82), (83), (85), (86), (88), (89), (91),
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | |            (92), (93), (98), (99), (100), (103), (104),
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | |            (105), (107), (108), (111), (112), (114), (115),
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | |            (117), (118), (119), (122), (123), (124), (125),
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | |            (126), (127), (129), (130), (131), (132), (133),
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | |            (137), (138), (140), (141), (142), (701), (702),
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | |            (705), (713), (725), (729), (730), (739), (740),
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | |            (742), (743), (744), (749), (750), (751), (753),
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | |            (756), (757), (758), (760), (763), (765), (766),
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | |            (767), (770), (969), (972), (973), (974), (975),
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | |            (976), (978), (1139) are inconsistent by sub-proof
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | |            #373.
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | |   (1140)  all_57_14 = e2 & op(e0, e1) = e2
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (81), (713), (1140) are inconsistent by sub-proof
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | |            #2074.
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | |   (1141)  all_57_3 = e3 & op(e2, e2) = e3
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (19), (22), (26), (27), (52), (54), (61),
% 227.83/39.40  | | | | | | | | | | | | | | | | | | |            (71), (81), (88), (104), (122), (123), (132),
% 227.83/39.40  | | | | | | | | | | | | | | | | | | |            (1031), (1034), (1141) are inconsistent by
% 227.83/39.40  | | | | | | | | | | | | | | | | | | |            sub-proof #380.
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.40  | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.40  | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | |   (1142)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 227.83/39.40  | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 227.83/39.40  | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | BETA: splitting (1142) gives:
% 227.83/39.40  | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | |   (1143)  all_57_7 = e3 & op(e1, e2) = e3
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | ALPHA: (1143) implies:
% 227.83/39.40  | | | | | | | | | | | | | | | | | | |   (1144)  all_57_7 = e3
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (54), (1031), (1144) are inconsistent by sub-proof
% 227.83/39.40  | | | | | | | | | | | | | | | | | | |            #2102.
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | |   (1145)  all_57_13 = e3 & op(e0, e2) = e3
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | ALPHA: (1145) implies:
% 227.83/39.40  | | | | | | | | | | | | | | | | | | |   (1146)  all_57_13 = e3
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (19), (54), (61), (71), (74), (81), (88),
% 227.83/39.40  | | | | | | | | | | | | | | | | | | |            (99), (103), (122), (701), (713), (1146) are
% 227.83/39.40  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2055.
% 227.83/39.40  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.40  | | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | End of split
% 227.83/39.40  | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.40  | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | |   (1147)  all_57_7 = e3 & op(e1, e2) = e3
% 227.83/39.40  | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | | REF_CLOSE: (54), (1031), (1147) are inconsistent by sub-proof
% 227.83/39.40  | | | | | | | | | | | | | | | | |            #2194.
% 227.83/39.40  | | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | End of split
% 227.83/39.40  | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | Case 2:
% 227.83/39.40  | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | |   (1148)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 227.83/39.40  | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 227.83/39.40  | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | | REF_CLOSE: (17), (19), (26), (27), (54), (61), (71), (81),
% 227.83/39.40  | | | | | | | | | | | | | | | |            (88), (122), (123), (132), (702), (1148) are
% 227.83/39.40  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1080.
% 227.83/39.40  | | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | End of split
% 227.83/39.40  | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | End of split
% 227.83/39.40  | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | Case 2:
% 227.83/39.40  | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | |   (1149)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 227.83/39.40  | | | | | | | | | | | | | |             e2 & op(e1, e0) = e2)
% 227.83/39.40  | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | BETA: splitting (1149) gives:
% 227.83/39.40  | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | Case 1:
% 227.83/39.40  | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | |   (1150)  all_57_8 = e2 & op(e1, e1) = e2
% 227.83/39.40  | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | ALPHA: (1150) implies:
% 227.83/39.40  | | | | | | | | | | | | | | |   (1151)  all_57_8 = e2
% 227.83/39.40  | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (12), (13), (14), (15), (17), (18),
% 227.83/39.40  | | | | | | | | | | | | | | |            (19), (22), (23), (26), (27), (28), (29), (30),
% 227.83/39.40  | | | | | | | | | | | | | | |            (33), (34), (35), (38), (40), (41), (43), (44),
% 227.83/39.40  | | | | | | | | | | | | | | |            (45), (47), (48), (50), (52), (53), (54), (56),
% 227.83/39.40  | | | | | | | | | | | | | | |            (57), (60), (61), (63), (64), (65), (67), (68),
% 227.83/39.40  | | | | | | | | | | | | | | |            (70), (71), (72), (74), (75), (77), (78), (79),
% 227.83/39.40  | | | | | | | | | | | | | | |            (81), (82), (83), (85), (86), (88), (89), (91),
% 227.83/39.40  | | | | | | | | | | | | | | |            (92), (93), (98), (99), (100), (103), (104),
% 227.83/39.40  | | | | | | | | | | | | | | |            (105), (107), (108), (111), (112), (114), (115),
% 227.83/39.40  | | | | | | | | | | | | | | |            (117), (118), (119), (122), (123), (124), (125),
% 227.83/39.40  | | | | | | | | | | | | | | |            (126), (127), (129), (130), (131), (132), (133),
% 227.83/39.40  | | | | | | | | | | | | | | |            (137), (138), (140), (141), (142), (701), (702),
% 227.83/39.40  | | | | | | | | | | | | | | |            (705), (713), (725), (729), (730), (739), (740),
% 227.83/39.40  | | | | | | | | | | | | | | |            (742), (743), (744), (749), (750), (751), (753),
% 227.83/39.40  | | | | | | | | | | | | | | |            (756), (757), (758), (760), (763), (765), (766),
% 227.83/39.40  | | | | | | | | | | | | | | |            (767), (770), (969), (972), (973), (974), (975),
% 227.83/39.40  | | | | | | | | | | | | | | |            (976), (978), (1151) are inconsistent by sub-proof
% 227.83/39.40  | | | | | | | | | | | | | | |            #373.
% 227.83/39.40  | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | Case 2:
% 227.83/39.40  | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | |   (1152)  all_57_11 = e2 & op(e1, e0) = e2
% 227.83/39.40  | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | | REF_CLOSE: (81), (725), (1152) are inconsistent by sub-proof
% 227.83/39.40  | | | | | | | | | | | | | | |            #1988.
% 227.83/39.40  | | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | | End of split
% 227.83/39.40  | | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | | End of split
% 227.83/39.40  | | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | | End of split
% 227.83/39.40  | | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | End of split
% 227.83/39.40  | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | Case 2:
% 227.83/39.40  | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | |   (1153)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 227.83/39.40  | | | | | | | | | | |           all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 227.83/39.40  | | | | | | | | | | |           op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 227.83/39.40  | | | | | | | | | | |             all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 227.83/39.40  | | | | | | | | | | |           & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 227.83/39.40  | | | | | | | | | | |           op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 227.83/39.40  | | | | | | | | | | |           $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 227.83/39.40  | | | | | | | | | | |           $i(all_52_15)
% 227.83/39.40  | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | ALPHA: (1153) implies:
% 227.83/39.40  | | | | | | | | | | |   (1154)  op(e2, e2) = all_52_11
% 227.83/39.40  | | | | | | | | | | |   (1155)  op(all_52_11, all_52_11) = e2
% 227.83/39.40  | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | REF_CLOSE: (19), (45), (54), (99), (1154), (1155) are
% 227.83/39.40  | | | | | | | | | | |            inconsistent by sub-proof #1229.
% 227.83/39.40  | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | End of split
% 227.83/39.40  | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | Case 2:
% 227.83/39.40  | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | |   (1156)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 227.83/39.40  | | | | | | | | | |             & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 227.83/39.40  | | | | | | | | | |             & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 227.83/39.40  | | | | | | | | | |               all_52_21) = e1 & op(all_52_23, all_52_23) =
% 227.83/39.40  | | | | | | | | | |             e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 227.83/39.40  | | | | | | | | | |             all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 227.83/39.40  | | | | | | | | | |             = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 227.83/39.40  | | | | | | | | | |             $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 227.83/39.40  | | | | | | | | | |             & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 227.83/39.40  | | | | | | | | | |             e0 & op(all_52_25, all_52_25) = e3 &
% 227.83/39.40  | | | | | | | | | |             op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 227.83/39.40  | | | | | | | | | |               all_52_29) = e1 & op(all_52_31, all_52_31) =
% 227.83/39.40  | | | | | | | | | |             e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 227.83/39.40  | | | | | | | | | |             all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 227.83/39.40  | | | | | | | | | |             = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 227.83/39.40  | | | | | | | | | |             $i(all_52_29) & $i(all_52_31))
% 227.83/39.40  | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | BETA: splitting (1156) gives:
% 227.83/39.40  | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | Case 1:
% 227.83/39.40  | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | |   (1157)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 227.83/39.40  | | | | | | | | | | |           all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 227.83/39.40  | | | | | | | | | | |           op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 227.83/39.40  | | | | | | | | | | |             all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 227.83/39.40  | | | | | | | | | | |           & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 227.83/39.40  | | | | | | | | | | |           & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 227.83/39.40  | | | | | | | | | | |           & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 227.83/39.40  | | | | | | | | | | |           $i(all_52_23)
% 227.83/39.40  | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | ALPHA: (1157) implies:
% 227.83/39.40  | | | | | | | | | | |   (1158)  op(e1, e0) = all_52_23
% 227.83/39.40  | | | | | | | | | | |   (1159)  op(all_52_23, all_52_23) = e0
% 227.83/39.40  | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | GROUND_INST: instantiating (19) with e0, all_52_23, e0, e1,
% 227.83/39.40  | | | | | | | | | | |              simplifying with (726), (1158) gives:
% 227.83/39.40  | | | | | | | | | | |   (1160)  all_52_23 = e0
% 227.83/39.40  | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | REDUCE: (1159), (1160) imply:
% 227.83/39.40  | | | | | | | | | | |   (1161)  op(e0, e0) = e0
% 227.83/39.40  | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | REF_CLOSE: (19), (61), (99), (1161) are inconsistent by
% 227.83/39.40  | | | | | | | | | | |            sub-proof #2304.
% 227.83/39.40  | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | Case 2:
% 227.83/39.40  | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | |   (1162)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 227.83/39.40  | | | | | | | | | | |           all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 227.83/39.40  | | | | | | | | | | |           op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 227.83/39.40  | | | | | | | | | | |             all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 227.83/39.40  | | | | | | | | | | |           & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 227.83/39.40  | | | | | | | | | | |           & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 227.83/39.40  | | | | | | | | | | |           & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 227.83/39.40  | | | | | | | | | | |           $i(all_52_31)
% 227.83/39.40  | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | ALPHA: (1162) implies:
% 227.83/39.40  | | | | | | | | | | |   (1163)  op(e0, e0) = all_52_31
% 227.83/39.40  | | | | | | | | | | |   (1164)  op(e0, e1) = all_52_29
% 227.83/39.40  | | | | | | | | | | |   (1165)  op(all_52_29, all_52_29) = e1
% 227.83/39.40  | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | | REF_CLOSE: (17), (19), (99), (714), (1163), (1164), (1165)
% 227.83/39.40  | | | | | | | | | | |            are inconsistent by sub-proof #887.
% 227.83/39.40  | | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | | End of split
% 227.83/39.40  | | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | End of split
% 227.83/39.40  | | | | | | | | | 
% 227.83/39.40  | | | | | | | | End of split
% 227.83/39.40  | | | | | | | | 
% 227.83/39.40  | | | | | | | End of split
% 227.83/39.40  | | | | | | | 
% 227.83/39.40  | | | | | | End of split
% 227.83/39.40  | | | | | | 
% 227.83/39.40  | | | | | End of split
% 227.83/39.40  | | | | | 
% 227.83/39.40  | | | | Case 2:
% 227.83/39.40  | | | | | 
% 227.83/39.40  | | | | |   (1166)  all_57_1 = e0 & op(e3, e2) = e0
% 227.83/39.40  | | | | | 
% 227.83/39.40  | | | | | ALPHA: (1166) implies:
% 227.83/39.40  | | | | |   (1167)  all_57_1 = e0
% 227.83/39.40  | | | | | 
% 227.83/39.40  | | | | | REF_CLOSE: (15), (17), (19), (52), (54), (61), (71), (73), (74), (81),
% 227.83/39.40  | | | | |            (88), (93), (99), (101), (103), (122), (140), (701), (1167)
% 227.83/39.40  | | | | |            are inconsistent by sub-proof #371.
% 227.83/39.40  | | | | | 
% 227.83/39.40  | | | | End of split
% 227.83/39.40  | | | | 
% 227.83/39.40  | | | Case 2:
% 227.83/39.40  | | | | 
% 227.83/39.40  | | | |   (1168)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3,
% 227.83/39.40  | | | |               e0) = e0)
% 227.83/39.40  | | | | 
% 227.83/39.40  | | | | BETA: splitting (1168) gives:
% 227.83/39.40  | | | | 
% 227.83/39.40  | | | | Case 1:
% 227.83/39.40  | | | | | 
% 227.83/39.40  | | | | |   (1169)  all_57_4 = e0 & op(e3, e1) = e0
% 227.83/39.40  | | | | | 
% 227.83/39.40  | | | | | ALPHA: (1169) implies:
% 227.83/39.40  | | | | |   (1170)  all_57_4 = e0
% 227.83/39.40  | | | | | 
% 227.83/39.40  | | | | | BETA: splitting (701) gives:
% 227.83/39.40  | | | | | 
% 227.83/39.40  | | | | | Case 1:
% 227.83/39.40  | | | | | | 
% 227.83/39.40  | | | | | |   (1171)  all_57_12 = e0 & op(e0, e3) = e0
% 227.83/39.40  | | | | | | 
% 227.83/39.40  | | | | | | ALPHA: (1171) implies:
% 227.83/39.40  | | | | | |   (1172)  op(e0, e3) = e0
% 227.83/39.40  | | | | | | 
% 227.83/39.40  | | | | | | REF_CLOSE: (19), (66), (695), (1172) are inconsistent by sub-proof
% 227.83/39.40  | | | | | |            #2366.
% 227.83/39.40  | | | | | | 
% 227.83/39.40  | | | | | Case 2:
% 227.83/39.40  | | | | | | 
% 227.83/39.40  | | | | | |   (1173)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 &
% 227.83/39.40  | | | | | |             op(e0, e1) = e0)
% 227.83/39.40  | | | | | | 
% 227.83/39.40  | | | | | | BETA: splitting (1173) gives:
% 227.83/39.40  | | | | | | 
% 227.83/39.40  | | | | | | Case 1:
% 227.83/39.40  | | | | | | | 
% 227.83/39.40  | | | | | | |   (1174)  all_57_13 = e0 & op(e0, e2) = e0
% 227.83/39.40  | | | | | | | 
% 227.83/39.40  | | | | | | | ALPHA: (1174) implies:
% 227.83/39.40  | | | | | | |   (1175)  op(e0, e2) = e0
% 227.83/39.40  | | | | | | | 
% 227.83/39.40  | | | | | | | REF_CLOSE: (19), (73), (101), (1175) are inconsistent by sub-proof
% 227.83/39.40  | | | | | | |            #2332.
% 227.83/39.40  | | | | | | | 
% 227.83/39.40  | | | | | | Case 2:
% 227.83/39.40  | | | | | | | 
% 227.83/39.40  | | | | | | |   (1176)  all_57_14 = e0 & op(e0, e1) = e0
% 227.83/39.40  | | | | | | | 
% 227.83/39.40  | | | | | | | ALPHA: (1176) implies:
% 227.83/39.40  | | | | | | |   (1177)  all_57_14 = e0
% 227.83/39.40  | | | | | | | 
% 227.83/39.40  | | | | | | | BETA: splitting (92) gives:
% 227.83/39.40  | | | | | | | 
% 227.83/39.40  | | | | | | | Case 1:
% 227.83/39.40  | | | | | | | | 
% 227.83/39.40  | | | | | | | |   (1178)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 &
% 227.83/39.40  | | | | | | | |             op(e2, e1) = e3)
% 227.83/39.40  | | | | | | | | 
% 227.83/39.40  | | | | | | | | BETA: splitting (1178) gives:
% 227.83/39.40  | | | | | | | | 
% 227.83/39.40  | | | | | | | | Case 1:
% 227.83/39.40  | | | | | | | | | 
% 227.83/39.40  | | | | | | | | |   (1179)  all_57_4 = e3 & op(e3, e1) = e3
% 227.83/39.40  | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | ALPHA: (1179) implies:
% 227.83/39.40  | | | | | | | | |   (1180)  all_57_4 = e3
% 227.83/39.40  | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | REF_CLOSE: (61), (1170), (1180) are inconsistent by sub-proof
% 227.83/39.40  | | | | | | | | |            #2372.
% 227.83/39.40  | | | | | | | | | 
% 227.83/39.40  | | | | | | | | Case 2:
% 227.83/39.40  | | | | | | | | | 
% 227.83/39.40  | | | | | | | | |   (1181)  all_57_5 = e3 & op(e2, e1) = e3
% 227.83/39.40  | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | ALPHA: (1181) implies:
% 227.83/39.40  | | | | | | | | |   (1182)  all_57_5 = e3
% 227.83/39.40  | | | | | | | | | 
% 227.83/39.40  | | | | | | | | | REF_CLOSE: (17), (19), (54), (63), (81), (88), (122), (130),
% 227.83/39.40  | | | | | | | | |            (1170), (1177), (1182) are inconsistent by
% 227.83/39.40  | | | | | | | | |            sub-proof #2378.
% 227.83/39.40  | | | | | | | | | 
% 227.83/39.40  | | | | | | | | End of split
% 227.83/39.40  | | | | | | | | 
% 227.83/39.40  | | | | | | | Case 2:
% 227.83/39.40  | | | | | | | | 
% 227.83/39.40  | | | | | | | |   (1183)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 &
% 227.83/39.40  | | | | | | | |             op(e0, e1) = e3)
% 227.83/39.40  | | | | | | | | 
% 227.83/39.40  | | | | | | | | REF_CLOSE: (17), (19), (26), (27), (54), (61), (71), (74), (81),
% 227.83/39.40  | | | | | | | |            (88), (103), (122), (701), (1183) are inconsistent by
% 227.83/39.40  | | | | | | | |            sub-proof #1044.
% 227.83/39.40  | | | | | | | | 
% 227.83/39.40  | | | | | | | End of split
% 227.83/39.40  | | | | | | | 
% 227.83/39.40  | | | | | | End of split
% 227.83/39.40  | | | | | | 
% 227.83/39.40  | | | | | End of split
% 227.83/39.40  | | | | | 
% 227.83/39.40  | | | | Case 2:
% 227.83/39.40  | | | | | 
% 227.83/39.40  | | | | |   (1184)  all_57_9 = e0 & op(e3, e0) = e0
% 227.83/39.40  | | | | | 
% 227.83/39.40  | | | | | REF_CLOSE: (19), (142), (696), (1184) are inconsistent by sub-proof
% 227.83/39.40  | | | | |            #2434.
% 227.83/39.40  | | | | | 
% 227.83/39.40  | | | | End of split
% 227.83/39.40  | | | | 
% 227.83/39.40  | | | End of split
% 227.83/39.40  | | | 
% 227.83/39.40  | | End of split
% 227.83/39.40  | | 
% 227.83/39.40  | End of split
% 227.83/39.40  | 
% 227.83/39.40  End of proof
% 227.83/39.40  
% 227.83/39.40  Sub-proof #371 shows that the following formulas are inconsistent:
% 227.83/39.40  ----------------------------------------------------------------
% 227.83/39.40    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 227.83/39.40         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.83/39.40    (2)   ~ (e3 = e1)
% 227.83/39.40    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.83/39.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.83/39.40    (4)  all_57_3 = e0
% 227.83/39.40    (5)   ~ (e3 = e2)
% 227.83/39.40    (6)   ~ (e3 = e0)
% 227.83/39.40    (7)  all_57_1 = e0
% 227.83/39.40    (8)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 227.83/39.40         (all_57_14 = e0 & op(e0, e1) = e0)
% 227.83/39.40    (9)  all_57_15 = e3
% 227.83/39.40    (10)   ~ (all_53_7 = e0)
% 227.83/39.40    (11)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 227.83/39.40          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 227.83/39.40            e1)
% 227.83/39.40    (12)   ~ (e2 = e0)
% 227.83/39.40    (13)   ~ (e1 = e0)
% 227.83/39.40    (14)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 227.83/39.40          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 227.83/39.40    (15)  op(e0, e0) = e3
% 227.83/39.40    (16)  op(e0, e2) = all_53_7
% 227.83/39.40    (17)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.83/39.40          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 227.83/39.40            e2)
% 227.83/39.40    (18)   ~ (e2 = e1)
% 227.83/39.40    (19)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 227.83/39.40          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 227.83/39.40  
% 227.83/39.40  Begin of proof
% 227.83/39.40  | 
% 227.83/39.40  | BETA: splitting (14) gives:
% 227.83/39.40  | 
% 227.83/39.40  | Case 1:
% 227.83/39.40  | | 
% 227.83/39.40  | |   (20)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 227.83/39.40  | |           e3)
% 227.83/39.40  | | 
% 227.83/39.40  | | REF_CLOSE: (4), (6), (7), (20) are inconsistent by sub-proof #1284.
% 227.83/39.40  | | 
% 227.83/39.40  | Case 2:
% 227.83/39.40  | | 
% 227.83/39.40  | |   (21)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 227.83/39.40  | |           e3)
% 227.83/39.40  | | 
% 227.83/39.40  | | BETA: splitting (21) gives:
% 227.83/39.40  | | 
% 227.83/39.40  | | Case 1:
% 227.83/39.40  | | | 
% 227.83/39.40  | | |   (22)  all_57_7 = e3 & op(e1, e2) = e3
% 227.83/39.40  | | | 
% 227.83/39.40  | | | ALPHA: (22) implies:
% 227.83/39.40  | | |   (23)  all_57_7 = e3
% 227.83/39.40  | | | 
% 227.83/39.40  | | | REF_CLOSE: (1), (2), (4), (5), (7), (12), (13), (18), (19), (23) are
% 227.83/39.40  | | |            inconsistent by sub-proof #2098.
% 227.83/39.40  | | | 
% 227.83/39.40  | | Case 2:
% 227.83/39.40  | | | 
% 227.83/39.40  | | |   (24)  all_57_13 = e3 & op(e0, e2) = e3
% 227.83/39.40  | | | 
% 227.83/39.40  | | | ALPHA: (24) implies:
% 227.83/39.40  | | |   (25)  all_57_13 = e3
% 227.83/39.40  | | | 
% 227.83/39.40  | | | REF_CLOSE: (2), (3), (5), (6), (8), (9), (10), (11), (12), (13), (15),
% 227.83/39.40  | | |            (16), (17), (18), (25) are inconsistent by sub-proof #372.
% 227.83/39.40  | | | 
% 227.83/39.40  | | End of split
% 227.83/39.40  | | 
% 227.83/39.40  | End of split
% 227.83/39.40  | 
% 227.83/39.40  End of proof
% 227.83/39.40  
% 227.83/39.40  Sub-proof #372 shows that the following formulas are inconsistent:
% 227.83/39.40  ----------------------------------------------------------------
% 227.83/39.40    (1)   ~ (e3 = e1)
% 227.83/39.40    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.83/39.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.83/39.40    (3)   ~ (e3 = e2)
% 227.83/39.40    (4)   ~ (e3 = e0)
% 227.83/39.40    (5)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 227.83/39.40         (all_57_14 = e0 & op(e0, e1) = e0)
% 227.83/39.40    (6)  all_57_15 = e3
% 227.83/39.40    (7)   ~ (all_53_7 = e0)
% 227.83/39.40    (8)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 227.83/39.40         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 227.83/39.40    (9)   ~ (e2 = e0)
% 227.83/39.40    (10)   ~ (e1 = e0)
% 227.83/39.40    (11)  all_57_13 = e3
% 227.83/39.40    (12)  op(e0, e0) = e3
% 227.83/39.40    (13)  op(e0, e2) = all_53_7
% 227.83/39.40    (14)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.83/39.40          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 227.83/39.40            e2)
% 227.83/39.40    (15)   ~ (e2 = e1)
% 227.83/39.40  
% 227.83/39.40  Begin of proof
% 227.83/39.40  | 
% 227.83/39.40  | BETA: splitting (5) gives:
% 227.83/39.40  | 
% 227.83/39.40  | Case 1:
% 227.83/39.40  | | 
% 227.83/39.40  | |   (16)  all_57_12 = e0 & op(e0, e3) = e0
% 227.83/39.40  | | 
% 227.83/39.40  | | ALPHA: (16) implies:
% 227.83/39.40  | |   (17)  all_57_12 = e0
% 227.83/39.40  | | 
% 227.83/39.40  | | REF_CLOSE: (1), (3), (6), (8), (9), (10), (11), (14), (15), (17) are
% 227.83/39.40  | |            inconsistent by sub-proof #2059.
% 227.83/39.40  | | 
% 227.83/39.40  | Case 2:
% 227.83/39.40  | | 
% 227.83/39.40  | |   (18)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 227.83/39.40  | |           e0)
% 227.83/39.40  | | 
% 227.83/39.40  | | BETA: splitting (18) gives:
% 227.83/39.40  | | 
% 227.83/39.40  | | Case 1:
% 227.83/39.40  | | | 
% 227.83/39.40  | | |   (19)  all_57_13 = e0 & op(e0, e2) = e0
% 227.83/39.40  | | | 
% 227.83/39.40  | | | ALPHA: (19) implies:
% 227.83/39.40  | | |   (20)  op(e0, e2) = e0
% 227.83/39.40  | | | 
% 227.83/39.40  | | | REF_CLOSE: (2), (7), (13), (20) are inconsistent by sub-proof #2332.
% 227.83/39.40  | | | 
% 227.83/39.40  | | Case 2:
% 227.83/39.40  | | | 
% 227.83/39.40  | | |   (21)  all_57_14 = e0 & op(e0, e1) = e0
% 227.83/39.40  | | | 
% 227.83/39.40  | | | ALPHA: (21) implies:
% 227.83/39.40  | | |   (22)  all_57_14 = e0
% 227.83/39.40  | | | 
% 227.83/39.40  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (14),
% 227.83/39.40  | | |            (15), (22) are inconsistent by sub-proof #2055.
% 227.83/39.40  | | | 
% 227.83/39.40  | | End of split
% 227.83/39.40  | | 
% 227.83/39.40  | End of split
% 227.83/39.40  | 
% 227.83/39.40  End of proof
% 227.83/39.40  
% 227.83/39.40  Sub-proof #373 shows that the following formulas are inconsistent:
% 227.83/39.40  ----------------------------------------------------------------
% 227.83/39.40    (1)   ~ (all_53_2 = e2)
% 227.83/39.40    (2)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 227.83/39.40    (3)  all_42_2 = e2
% 227.83/39.40    (4)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 227.83/39.40    (5)   ~ (all_53_6 = e2)
% 227.83/39.40    (6)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 227.83/39.40         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 227.83/39.40    (7)   ~ (all_52_7 = e3)
% 227.83/39.40    (8)   ~ (all_53_6 = e0)
% 227.83/39.41    (9)   ~ (all_52_3 = all_52_5)
% 227.83/39.41    (10)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 227.83/39.41          (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 227.83/39.41    (11)   ~ (all_53_8 = all_53_12)
% 227.83/39.41    (12)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 227.83/39.41          (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.83/39.41    (13)   ~ (e3 = e1)
% 227.83/39.41    (14)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 227.83/39.41          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 227.83/39.41    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.83/39.41            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.83/39.41    (16)  op(all_52_5, all_52_5) = e1
% 227.83/39.41    (17)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 227.83/39.41          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 227.83/39.41    (18)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 227.83/39.41            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 227.83/39.41              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 227.83/39.41    (19)   ~ (all_6_2 = e3)
% 227.83/39.41    (20)   ~ (all_52_3 = e0)
% 227.83/39.41    (21)  op(e1, e1) = all_6_2
% 227.83/39.41    (22)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 227.83/39.41    (23)   ~ (all_53_6 = all_52_3)
% 227.83/39.41    (24)   ~ (all_53_1 = all_53_9)
% 227.83/39.41    (25)  op(e3, e2) = all_52_3
% 227.83/39.41    (26)   ~ (all_53_9 = e0)
% 227.83/39.41    (27)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 227.83/39.41          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 227.83/39.41    (28)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 227.83/39.41            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 227.83/39.41              e3) = all_22_1 & $i(all_22_1))
% 227.83/39.41    (29)  all_55_3 = all_52_7
% 227.83/39.41    (30)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 227.83/39.41    (31)  all_55_9 = all_53_6
% 227.83/39.41    (32)   ~ (all_53_4 = all_53_12)
% 227.83/39.41    (33)   ~ (all_53_13 = e3)
% 227.83/39.41    (34)   ~ (all_53_8 = all_53_9)
% 227.83/39.41    (35)  op(all_52_3, all_52_3) = e2
% 227.83/39.41    (36)  all_42_2 = all_6_2
% 227.83/39.41    (37)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 227.83/39.41          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 227.83/39.41    (38)  op(e2, e2) = e0
% 227.83/39.41    (39)  all_55_4 = all_53_1
% 227.83/39.41    (40)   ~ (all_53_9 = all_6_2)
% 227.83/39.41    (41)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 227.83/39.41          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 227.83/39.41    (42)  all_57_3 = e0
% 227.83/39.41    (43)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 227.83/39.41          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 227.83/39.41    (44)   ~ (e3 = e2)
% 227.83/39.41    (45)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 227.83/39.41    (46)  all_55_1 = all_53_4
% 227.83/39.41    (47)   ~ (all_53_13 = all_52_7)
% 227.83/39.41    (48)  all_55_7 = e3 | all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 227.83/39.41    (49)   ~ (e3 = e0)
% 227.83/39.41    (50)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 227.83/39.41          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 227.83/39.41    (51)   ~ (all_53_8 = all_6_2)
% 227.83/39.41    (52)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 227.83/39.41    (53)   ~ (all_53_2 = e0)
% 227.83/39.41    (54)  all_57_0 = e0
% 227.83/39.41    (55)  all_55_2 = all_53_8
% 227.83/39.41    (56)   ~ (all_52_5 = e2)
% 227.83/39.41    (57)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 227.83/39.41    (58)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 227.83/39.41          | (all_57_14 = e0 & op(e0, e1) = e0)
% 227.83/39.41    (59)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 227.83/39.41    (60)  all_57_15 = e3
% 227.83/39.41    (61)   ~ (all_53_9 = all_53_13)
% 227.83/39.41    (62)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 227.83/39.41          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 227.83/39.41            e1)
% 227.83/39.41    (63)  op(e3, e3) = all_52_1
% 227.83/39.41    (64)  all_57_11 = e0
% 227.83/39.41    (65)   ~ (all_53_4 = all_53_8)
% 227.83/39.41    (66)  all_55_6 = all_53_9
% 227.83/39.41    (67)  op(e3, e2) = all_53_4
% 227.83/39.41    (68)   ~ (all_53_1 = all_53_2)
% 227.83/39.41    (69)  op(all_52_1, all_52_1) = e3
% 227.83/39.41    (70)   ~ (e2 = e0)
% 227.83/39.41    (71)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 227.83/39.41            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 227.83/39.41            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 227.83/39.41            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 227.83/39.41              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 227.83/39.41            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 227.83/39.41            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 227.83/39.41              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 227.83/39.41              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 227.83/39.41            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 227.83/39.41            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 227.83/39.41            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 227.83/39.41              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 227.83/39.41              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 227.83/39.41            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 227.83/39.41              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 227.83/39.41            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 227.83/39.41            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 227.83/39.41              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 227.83/39.41              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 227.83/39.41            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 227.83/39.41            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 227.83/39.41    (72)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 227.83/39.41            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 227.83/39.41              e3) = all_12_1 & $i(all_12_1))
% 227.83/39.41    (73)   ~ (all_53_9 = e2)
% 227.83/39.41    (74)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 227.83/39.41          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 227.83/39.41    (75)   ~ (all_53_1 = e0)
% 227.83/39.41    (76)   ~ (e1 = e0)
% 227.83/39.41    (77)   ~ (all_52_3 = all_52_7)
% 227.83/39.41    (78)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 227.83/39.41            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 227.83/39.41              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 227.83/39.41    (79)   ~ (all_53_4 = e0)
% 227.83/39.41    (80)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 227.83/39.41          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 227.83/39.41    (81)  all_57_8 = e2
% 227.83/39.41    (82)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 227.83/39.41          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 227.83/39.41    (83)  all_55_8 = all_53_2
% 227.83/39.41    (84)  op(e0, e0) = e3
% 227.83/39.41    (85)   ~ (all_53_4 = all_53_6)
% 227.83/39.41    (86)  all_55_2 = all_52_5
% 227.83/39.41    (87)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.83/39.41          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 227.83/39.41            e2)
% 227.83/39.41    (88)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 227.83/39.41              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 227.83/39.41                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 227.83/39.41                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 227.83/39.41    (89)  all_55_10 = all_6_2
% 227.83/39.41    (90)   ~ (all_53_13 = e0)
% 227.83/39.41    (91)  op(e1, e1) = e2
% 227.83/39.41    (92)   ~ (all_53_1 = all_53_13)
% 227.83/39.41    (93)   ~ (all_53_9 = all_52_5)
% 227.83/39.41    (94)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 227.83/39.41          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 227.83/39.41    (95)  all_38_2 = all_6_2
% 227.83/39.41    (96)  all_55_3 = all_53_12
% 227.83/39.41    (97)   ~ (all_53_12 = e3)
% 227.83/39.41    (98)   ~ (all_52_7 = e0)
% 227.83/39.41    (99)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 227.83/39.41            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 227.83/39.41              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 227.83/39.41    (100)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 227.83/39.41           (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 227.83/39.41    (101)  all_55_1 = all_52_3
% 227.83/39.41    (102)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 227.83/39.41           (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 227.83/39.41    (103)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 227.83/39.41           | (all_57_11 = e0 & op(e1, e0) = e0)
% 227.83/39.41    (104)   ~ (all_52_5 = e0)
% 227.83/39.41    (105)   ~ (e2 = e1)
% 227.83/39.41    (106)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 227.83/39.41           | (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 227.83/39.41             e2)
% 227.83/39.41    (107)  op(e2, e1) = all_53_9
% 227.83/39.41    (108)  op(e1, e2) = all_53_6
% 227.83/39.41    (109)   ~ (all_53_2 = all_53_6)
% 227.83/39.41    (110)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 227.83/39.41           (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 227.83/39.41    (111)  all_24_2 = all_6_2
% 227.83/39.41    (112)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 227.83/39.41           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 227.83/39.41    (113)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 227.83/39.41           (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 227.83/39.41    (114)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 227.83/39.41           | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 227.83/39.41             e1)
% 227.83/39.41    (115)  all_57_14 = e0
% 227.83/39.41    (116)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 227.83/39.41           (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 227.83/39.41    (117)  op(e3, e1) = all_53_8
% 227.83/39.41    (118)  all_55_7 = all_53_13
% 227.83/39.41    (119)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 227.83/39.41           (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 227.83/39.41    (120)  ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 & op(e1, e2) =
% 227.83/39.41             all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 = e3) &
% 227.83/39.41             op(e1, e2) = all_38_1 & $i(all_38_1))
% 227.83/39.41    (121)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 227.83/39.41           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 227.83/39.41    (122)  op(e3, e0) = all_53_12
% 227.83/39.41  
% 227.83/39.41  Begin of proof
% 227.83/39.41  | 
% 227.83/39.41  | BETA: splitting (99) gives:
% 227.83/39.41  | 
% 227.83/39.41  | Case 1:
% 227.83/39.41  | | 
% 227.83/39.41  | |   (123)   ~ (all_42_2 = e2)
% 227.83/39.41  | | 
% 227.83/39.41  | | REDUCE: (3), (123) imply:
% 227.83/39.41  | |   (124)  $false
% 227.83/39.41  | | 
% 227.83/39.41  | | CLOSE: (124) is inconsistent.
% 227.83/39.41  | | 
% 227.83/39.41  | Case 2:
% 227.83/39.41  | | 
% 227.83/39.41  | |   (125)  ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 & op(e1, e2) =
% 227.83/39.41  | |            all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e0) &
% 227.83/39.41  | |            op(e1, e2) = all_42_1 & $i(all_42_1))
% 227.83/39.41  | | 
% 227.83/39.41  | | BETA: splitting (48) gives:
% 227.83/39.41  | | 
% 227.83/39.41  | | Case 1:
% 227.83/39.41  | | | 
% 227.83/39.41  | | |   (126)  all_55_7 = e3
% 227.83/39.41  | | | 
% 227.83/39.41  | | | REF_CLOSE: (33), (118), (126) are inconsistent by sub-proof #2109.
% 227.83/39.41  | | | 
% 227.83/39.41  | | Case 2:
% 227.83/39.41  | | | 
% 227.83/39.41  | | |   (127)  all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 227.83/39.41  | | | 
% 227.83/39.41  | | | BETA: splitting (22) gives:
% 227.83/39.41  | | | 
% 227.83/39.41  | | | Case 1:
% 227.83/39.41  | | | | 
% 227.83/39.41  | | | |   (128)  all_55_3 = e3
% 227.83/39.41  | | | | 
% 227.83/39.41  | | | | REF_CLOSE: (7), (29), (128) are inconsistent by sub-proof #1451.
% 227.83/39.41  | | | | 
% 227.83/39.41  | | | Case 2:
% 227.83/39.41  | | | | 
% 227.83/39.41  | | | |   (129)  all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 227.83/39.41  | | | | 
% 227.83/39.41  | | | | BETA: splitting (45) gives:
% 227.83/39.41  | | | | 
% 227.83/39.41  | | | | Case 1:
% 227.83/39.41  | | | | | 
% 227.83/39.41  | | | | |   (130)  all_55_6 = e3
% 227.83/39.41  | | | | | 
% 227.83/39.41  | | | | | COMBINE_EQS: (66), (130) imply:
% 227.83/39.41  | | | | |   (131)  all_53_9 = e3
% 227.83/39.41  | | | | | 
% 227.83/39.41  | | | | | REDUCE: (93), (131) imply:
% 227.83/39.41  | | | | |   (132)   ~ (all_52_5 = e3)
% 227.83/39.41  | | | | | 
% 227.83/39.41  | | | | | SIMP: (132) implies:
% 227.83/39.41  | | | | |   (133)   ~ (all_52_5 = e3)
% 227.83/39.41  | | | | | 
% 227.83/39.41  | | | | | BETA: splitting (94) gives:
% 227.83/39.41  | | | | | 
% 227.83/39.41  | | | | | Case 1:
% 227.83/39.41  | | | | | | 
% 227.83/39.41  | | | | | |   (134)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2,
% 227.83/39.41  | | | | | |              e2) = e3)
% 227.83/39.41  | | | | | | 
% 227.83/39.41  | | | | | | BETA: splitting (134) gives:
% 227.83/39.41  | | | | | | 
% 227.83/39.41  | | | | | | Case 1:
% 227.83/39.41  | | | | | | | 
% 227.83/39.41  | | | | | | |   (135)  all_57_2 = e3 & op(e2, e3) = e3
% 227.83/39.41  | | | | | | | 
% 227.83/39.41  | | | | | | | ALPHA: (135) implies:
% 227.83/39.41  | | | | | | |   (136)  all_57_2 = e3
% 227.83/39.41  | | | | | | | 
% 227.83/39.41  | | | | | | | BETA: splitting (80) gives:
% 227.83/39.41  | | | | | | | 
% 227.83/39.41  | | | | | | | Case 1:
% 227.83/39.41  | | | | | | | | 
% 227.83/39.41  | | | | | | | |   (137)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 &
% 227.83/39.41  | | | | | | | |            op(e2, e1) = e3)
% 227.83/39.41  | | | | | | | | 
% 227.83/39.41  | | | | | | | | BETA: splitting (137) gives:
% 227.83/39.41  | | | | | | | | 
% 227.83/39.41  | | | | | | | | Case 1:
% 227.83/39.41  | | | | | | | | | 
% 227.83/39.41  | | | | | | | | |   (138)  all_57_4 = e3 & op(e3, e1) = e3
% 227.83/39.41  | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | ALPHA: (138) implies:
% 227.83/39.41  | | | | | | | | |   (139)  all_57_4 = e3
% 227.83/39.41  | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | BETA: splitting (59) gives:
% 227.83/39.41  | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | Case 1:
% 227.83/39.41  | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | |   (140)  all_55_2 = e3
% 227.83/39.41  | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | REF_CLOSE: (86), (133), (140) are inconsistent by sub-proof
% 227.83/39.41  | | | | | | | | | |            #437.
% 227.83/39.41  | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | Case 2:
% 227.83/39.41  | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | |   (141)   ~ (all_55_2 = e3)
% 227.83/39.41  | | | | | | | | | |   (142)  all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 227.83/39.41  | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | BETA: splitting (142) gives:
% 227.83/39.41  | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | Case 1:
% 227.83/39.41  | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | |   (143)  all_55_2 = e2
% 227.83/39.41  | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | REF_CLOSE: (56), (86), (143) are inconsistent by sub-proof
% 227.83/39.41  | | | | | | | | | | |            #561.
% 227.83/39.41  | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | Case 2:
% 227.83/39.41  | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | |   (144)   ~ (all_55_2 = e2)
% 227.83/39.41  | | | | | | | | | | |   (145)  all_55_2 = e1 | all_55_2 = e0
% 227.83/39.41  | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | BETA: splitting (100) gives:
% 227.83/39.41  | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | Case 1:
% 227.83/39.41  | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | |   (146)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 227.83/39.41  | | | | | | | | | | | |            & op(e2, e2) = e2)
% 227.83/39.41  | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | BETA: splitting (146) gives:
% 227.83/39.41  | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | Case 1:
% 227.83/39.41  | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | |   (147)  all_57_2 = e2 & op(e2, e3) = e2
% 227.83/39.41  | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | REF_CLOSE: (44), (136), (147) are inconsistent by sub-proof
% 227.83/39.41  | | | | | | | | | | | | |            #1925.
% 227.83/39.41  | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | Case 2:
% 227.83/39.41  | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | |   (148)  all_57_3 = e2 & op(e2, e2) = e2
% 227.83/39.41  | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | REF_CLOSE: (42), (70), (148) are inconsistent by sub-proof
% 227.83/39.41  | | | | | | | | | | | | |            #2256.
% 227.83/39.41  | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | End of split
% 227.83/39.41  | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | Case 2:
% 227.83/39.41  | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | |   (149)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 227.83/39.41  | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 227.83/39.41  | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | BETA: splitting (149) gives:
% 227.83/39.41  | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | Case 1:
% 227.83/39.41  | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | |   (150)  all_57_5 = e2 & op(e2, e1) = e2
% 227.83/39.41  | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | ALPHA: (150) implies:
% 227.83/39.41  | | | | | | | | | | | | |   (151)  all_57_5 = e2
% 227.83/39.41  | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | REF_CLOSE: (13), (50), (76), (81), (105), (115), (139), (151)
% 227.83/39.41  | | | | | | | | | | | | |            are inconsistent by sub-proof #925.
% 227.83/39.41  | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | Case 2:
% 227.83/39.41  | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | |   (152)  all_57_10 = e2 & op(e2, e0) = e2
% 227.83/39.41  | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | ALPHA: (152) implies:
% 227.83/39.41  | | | | | | | | | | | | |   (153)  all_57_10 = e2
% 227.83/39.41  | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | BETA: splitting (50) gives:
% 227.83/39.41  | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | Case 1:
% 227.83/39.41  | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | |   (154)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 227.83/39.41  | | | | | | | | | | | | | |            & op(e2, e1) = e1)
% 227.83/39.41  | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | BETA: splitting (154) gives:
% 227.83/39.41  | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | Case 1:
% 227.83/39.41  | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | |   (155)  all_57_4 = e1 & op(e3, e1) = e1
% 227.83/39.41  | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | ALPHA: (155) implies:
% 227.83/39.41  | | | | | | | | | | | | | | |   (156)  all_57_4 = e1
% 227.83/39.41  | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | REF_CLOSE: (6), (13), (15), (19), (21), (42), (44), (49),
% 227.83/39.41  | | | | | | | | | | | | | | |            (60), (62), (70), (76), (80), (87), (88), (105),
% 227.83/39.41  | | | | | | | | | | | | | | |            (136), (153), (156) are inconsistent by sub-proof
% 227.83/39.41  | | | | | | | | | | | | | | |            #1755.
% 227.83/39.41  | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | Case 2:
% 227.83/39.41  | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | |   (157)  all_57_5 = e1 & op(e2, e1) = e1
% 227.83/39.41  | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | ALPHA: (157) implies:
% 227.83/39.41  | | | | | | | | | | | | | | |   (158)  all_57_5 = e1
% 227.83/39.41  | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | BETA: splitting (110) gives:
% 227.83/39.41  | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | Case 1:
% 227.83/39.41  | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | |   (159)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 227.83/39.41  | | | | | | | | | | | | | | | |            & op(e2, e3) = e2)
% 227.83/39.41  | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | REF_CLOSE: (15), (38), (44), (49), (63), (69), (136), (159)
% 227.83/39.41  | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #391.
% 227.83/39.41  | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | Case 2:
% 227.83/39.41  | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | |   (160)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 227.83/39.41  | | | | | | | | | | | | | | | |            e2 & op(e0, e3) = e2)
% 227.83/39.41  | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | BETA: splitting (160) gives:
% 227.83/39.41  | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.41  | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | |   (161)  all_57_6 = e2 & op(e1, e3) = e2
% 227.83/39.41  | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | ALPHA: (161) implies:
% 227.83/39.41  | | | | | | | | | | | | | | | | |   (162)  all_57_6 = e2
% 227.83/39.41  | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (13), (15), (17), (19), (21), (42), (44),
% 227.83/39.41  | | | | | | | | | | | | | | | | |            (49), (50), (60), (62), (64), (70), (76), (80),
% 227.83/39.41  | | | | | | | | | | | | | | | | |            (81), (87), (88), (100), (103), (105), (106),
% 227.83/39.41  | | | | | | | | | | | | | | | | |            (114), (115), (116), (136), (139), (162) are
% 227.83/39.41  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #383.
% 227.83/39.41  | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.41  | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | |   (163)  all_57_12 = e2 & op(e0, e3) = e2
% 227.83/39.41  | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | ALPHA: (163) implies:
% 227.83/39.41  | | | | | | | | | | | | | | | | |   (164)  all_57_12 = e2
% 227.83/39.41  | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | BETA: splitting (62) gives:
% 227.83/39.41  | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.41  | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | |   (165)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 227.83/39.41  | | | | | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 227.83/39.41  | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | BETA: splitting (165) gives:
% 227.83/39.41  | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | |   (166)  all_57_12 = e1 & op(e0, e3) = e1
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (105), (164), (166) are inconsistent by sub-proof
% 227.83/39.41  | | | | | | | | | | | | | | | | | | |            #2388.
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | |   (167)  all_57_13 = e1 & op(e0, e2) = e1
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | ALPHA: (167) implies:
% 227.83/39.41  | | | | | | | | | | | | | | | | | | |   (168)  all_57_13 = e1
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | BETA: splitting (12) gives:
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | |   (169)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | BETA: splitting (169) gives:
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | |   (170)  all_57_1 = e2 & op(e3, e2) = e2
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | ALPHA: (170) implies:
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | |   (171)  all_57_1 = e2
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (27) gives:
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | |   (172)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e1)
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (172) gives:
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | |   (173)  all_57_0 = e1 & op(e3, e3) = e1
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (13), (42), (54), (76), (105), (136), (153),
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | |            (158), (173) are inconsistent by sub-proof #396.
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | |   (174)  all_57_1 = e1 & op(e3, e2) = e1
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (105), (171), (174) are inconsistent by sub-proof
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | |            #2210.
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | |   (175)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e1)
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (175) gives:
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | |   (176)  all_57_4 = e1 & op(e3, e1) = e1
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (176) implies:
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | |   (177)  all_57_4 = e1
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (13), (15), (19), (21), (42), (44), (49),
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | |            (60), (62), (70), (76), (80), (87), (88), (105),
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | |            (136), (153), (177) are inconsistent by sub-proof
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | |            #1755.
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | |   (178)  all_57_9 = e1 & op(e3, e0) = e1
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (178) implies:
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | |   (179)  all_57_9 = e1
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (82) gives:
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | |   (180)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e3)
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (13), (42), (44), (49), (70), (76), (94),
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | |            (100), (105), (136), (171), (180) are inconsistent
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #379.
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | |   (181)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (181) gives:
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | |   (182)  all_57_7 = e3 & op(e1, e2) = e3
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (182) implies:
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | |   (183)  all_57_7 = e3
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (116) gives:
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | |   (184)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e1)
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (184) gives:
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (185)  all_57_6 = e1 & op(e1, e3) = e1
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (185) implies:
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (186)  all_57_6 = e1
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (145) gives:
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (187)  all_55_2 = e1
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (86), (187) imply:
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (188)  all_52_5 = e1
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (188) implies:
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (189)  all_52_5 = e1
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (133), (189) imply:
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (190)   ~ (e3 = e1)
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (56), (189) imply:
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (191)   ~ (e2 = e1)
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (16), (189) imply:
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (192)  op(e1, e1) = e1
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (6), (10), (11), (12), (13), (14), (15),
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17), (18), (19), (21), (22), (26), (27), (32),
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (34), (36), (37), (40), (41), (42), (43), (44),
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (46), (49), (50), (51), (55), (58), (59), (60),
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (62), (64), (65), (67), (70), (71), (74), (76),
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (78), (79), (80), (81), (82), (84), (85), (87),
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (88), (89), (91), (94), (95), (96), (97), (99),
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (100), (102), (103), (105), (106), (107), (108),
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (110), (111), (112), (113), (114), (115), (116),
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (117), (119), (121), (122), (136), (139), (153),
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (168), (179), (183), (186), (192) are inconsistent
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #388.
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (193)  all_55_2 = e0
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (86), (104), (193) are inconsistent by sub-proof
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #560.
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (194)  all_57_7 = e1 & op(e1, e2) = e1
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (194) implies:
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (195)  all_57_7 = e1
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (183), (195) imply:
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (196)  e3 = e1
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (196) implies:
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (197)  e3 = e1
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (139), (197) imply:
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (198)  all_57_4 = e1
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (13), (15), (19), (21), (42), (44), (49),
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (60), (62), (70), (76), (80), (87), (88), (105),
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (136), (153), (198) are inconsistent by sub-proof
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1755.
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | |   (199)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e1, e0) = e1)
% 227.83/39.41  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (6), (10), (11), (12), (13), (14), (15),
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | | | |            (17), (18), (19), (21), (22), (26), (27), (32),
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | | | |            (34), (36), (37), (40), (41), (42), (43), (44),
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | | | |            (46), (49), (50), (51), (54), (55), (59), (60),
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | | | |            (62), (64), (65), (67), (70), (71), (74), (76),
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | | | |            (78), (79), (80), (82), (84), (85), (87), (88),
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | | | |            (89), (94), (95), (96), (97), (99), (100), (102),
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | | | |            (105), (106), (107), (108), (110), (111), (112),
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | | | |            (113), (114), (116), (117), (119), (121), (122),
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | | | |            (136), (139), (153), (158), (168), (171), (183),
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | | | |            (199) are inconsistent by sub-proof #378.
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | | |   (200)  all_57_13 = e3 & op(e0, e2) = e3
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (200) implies:
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | | |   (201)  all_57_13 = e3
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (13), (15), (19), (21), (42), (44), (49),
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | | |            (58), (60), (62), (70), (76), (80), (84), (87),
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | | |            (88), (105), (115), (136), (139), (153), (201) are
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #424.
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | |   (202)  all_57_3 = e2 & op(e2, e2) = e2
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (70), (202) are inconsistent by sub-proof
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | |            #2103.
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | |   (203)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | |   (204)  all_57_7 = e2 & op(e1, e2) = e2
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | ALPHA: (204) implies:
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | |   (205)  all_57_7 = e2
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (82) gives:
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | |   (206)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e3)
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | |   (207)  all_57_1 = e3 & op(e3, e2) = e3
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (207) implies:
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | |   (208)  all_57_1 = e3
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (37) gives:
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | |   (209)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e2)
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | | |   (210)  all_57_0 = e2 & op(e3, e3) = e2
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (210) implies:
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | | |   (211)  all_57_0 = e2
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | | |   (212)  op(e3, e3) = e2
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (6), (10), (11), (12), (13), (14), (15),
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | | |            (17), (18), (19), (21), (22), (26), (27), (32),
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | | |            (34), (36), (37), (40), (41), (42), (43), (44),
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | | |            (46), (49), (50), (51), (55), (59), (60), (62),
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | | |            (65), (67), (70), (71), (74), (76), (78), (79),
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | | |            (80), (82), (84), (85), (87), (88), (89), (94),
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | | |            (95), (96), (97), (99), (100), (102), (105),
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | | |            (106), (107), (108), (110), (111), (112), (113),
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | | |            (114), (116), (117), (119), (121), (122), (153),
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | | |            (158), (205), (211), (212) are inconsistent by
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #448.
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | | |   (213)  all_57_1 = e2 & op(e3, e2) = e2
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (44), (208), (213) are inconsistent by sub-proof
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | | |            #1809.
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | |   (214)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e2)
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (27), (37), (41), (44), (49), (70), (76),
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | |            (105), (139), (208), (214) are inconsistent by
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1221.
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | |   (215)  all_57_3 = e3 & op(e2, e2) = e3
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (215) implies:
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | |   (216)  all_57_3 = e3
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (42), (216) imply:
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | |   (217)  e3 = e0
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (13), (42), (44), (49), (70), (76), (94),
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | |            (100), (105), (136), (217) are inconsistent by
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1333.
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | |   (218)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | |   (219)  all_57_7 = e3 & op(e1, e2) = e3
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (6), (10), (11), (12), (13), (14), (15),
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | |            (17), (18), (19), (21), (22), (26), (27), (32),
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | |            (34), (36), (37), (40), (41), (42), (43), (44),
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | |            (46), (49), (50), (51), (55), (59), (60), (62),
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | |            (65), (67), (70), (71), (74), (76), (78), (79),
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | |            (80), (84), (85), (87), (88), (89), (95), (96),
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | |            (97), (99), (100), (105), (106), (107), (108),
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | |            (110), (111), (112), (113), (114), (116), (117),
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | |            (119), (121), (122), (139), (205), (219) are
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #394.
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | |   (220)  all_57_13 = e3 & op(e0, e2) = e3
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (220) implies:
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | |   (221)  all_57_13 = e3
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (13), (15), (19), (21), (42), (44), (49),
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | |            (58), (60), (62), (70), (76), (80), (84), (87),
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | |            (88), (105), (115), (136), (139), (153), (221) are
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #424.
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | |   (222)  all_57_13 = e2 & op(e0, e2) = e2
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | ALPHA: (222) implies:
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | |   (223)  all_57_13 = e2
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (105), (168), (223) are inconsistent by sub-proof
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | |            #2327.
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.42  | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.42  | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | |   (224)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 227.83/39.42  | | | | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 227.83/39.42  | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (13), (15), (19), (21), (42), (43), (44),
% 227.83/39.42  | | | | | | | | | | | | | | | | | |            (49), (60), (62), (70), (76), (80), (81), (84),
% 227.83/39.42  | | | | | | | | | | | | | | | | | |            (87), (88), (94), (100), (105), (136), (153),
% 227.83/39.42  | | | | | | | | | | | | | | | | | |            (224) are inconsistent by sub-proof #387.
% 227.83/39.42  | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | End of split
% 227.83/39.42  | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | End of split
% 227.83/39.42  | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | End of split
% 227.83/39.42  | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | End of split
% 227.83/39.42  | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | Case 2:
% 227.83/39.42  | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | |   (225)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 227.83/39.42  | | | | | | | | | | | | | |            e1 & op(e0, e1) = e1)
% 227.83/39.42  | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | REF_CLOSE: (6), (13), (15), (19), (21), (42), (43), (44),
% 227.83/39.42  | | | | | | | | | | | | | |            (49), (60), (62), (70), (76), (80), (81), (87),
% 227.83/39.42  | | | | | | | | | | | | | |            (88), (94), (100), (105), (136), (153), (225) are
% 227.83/39.42  | | | | | | | | | | | | | |            inconsistent by sub-proof #377.
% 227.83/39.42  | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | End of split
% 227.83/39.42  | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | End of split
% 227.83/39.42  | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | End of split
% 227.83/39.42  | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | End of split
% 227.83/39.42  | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | End of split
% 227.83/39.42  | | | | | | | | | 
% 227.83/39.42  | | | | | | | | Case 2:
% 227.83/39.42  | | | | | | | | | 
% 227.83/39.42  | | | | | | | | |   (226)  all_57_5 = e3 & op(e2, e1) = e3
% 227.83/39.42  | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | ALPHA: (226) implies:
% 227.83/39.42  | | | | | | | | |   (227)  all_57_5 = e3
% 227.83/39.42  | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | REF_CLOSE: (6), (13), (42), (44), (70), (76), (100), (105),
% 227.83/39.42  | | | | | | | | |            (136), (227) are inconsistent by sub-proof #1802.
% 227.83/39.42  | | | | | | | | | 
% 227.83/39.42  | | | | | | | | End of split
% 227.83/39.42  | | | | | | | | 
% 227.83/39.42  | | | | | | | Case 2:
% 227.83/39.42  | | | | | | | | 
% 227.83/39.42  | | | | | | | |   (228)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 &
% 227.83/39.42  | | | | | | | |            op(e0, e1) = e3)
% 227.83/39.42  | | | | | | | | 
% 227.83/39.42  | | | | | | | | REF_CLOSE: (13), (15), (19), (21), (44), (49), (58), (60), (62),
% 227.83/39.42  | | | | | | | |            (70), (76), (87), (105), (228) are inconsistent by
% 227.83/39.42  | | | | | | | |            sub-proof #1044.
% 227.83/39.42  | | | | | | | | 
% 227.83/39.42  | | | | | | | End of split
% 227.83/39.42  | | | | | | | 
% 227.83/39.42  | | | | | | Case 2:
% 227.83/39.42  | | | | | | | 
% 227.83/39.42  | | | | | | |   (229)  all_57_3 = e3 & op(e2, e2) = e3
% 227.83/39.42  | | | | | | | 
% 227.83/39.42  | | | | | | | ALPHA: (229) implies:
% 227.83/39.42  | | | | | | |   (230)  all_57_3 = e3
% 227.83/39.42  | | | | | | | 
% 227.83/39.42  | | | | | | | REF_CLOSE: (42), (49), (230) are inconsistent by sub-proof #2358.
% 227.83/39.42  | | | | | | | 
% 227.83/39.42  | | | | | | End of split
% 227.83/39.42  | | | | | | 
% 227.83/39.42  | | | | | Case 2:
% 227.83/39.42  | | | | | | 
% 227.83/39.42  | | | | | |   (231)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 &
% 227.83/39.42  | | | | | |            op(e2, e0) = e3)
% 227.83/39.42  | | | | | | 
% 227.83/39.42  | | | | | | BETA: splitting (231) gives:
% 227.83/39.42  | | | | | | 
% 227.83/39.42  | | | | | | Case 1:
% 227.83/39.42  | | | | | | | 
% 227.83/39.42  | | | | | | |   (232)  all_57_5 = e3 & op(e2, e1) = e3
% 227.83/39.42  | | | | | | | 
% 227.83/39.42  | | | | | | | ALPHA: (232) implies:
% 227.83/39.42  | | | | | | |   (233)  all_57_5 = e3
% 227.83/39.42  | | | | | | |   (234)  op(e2, e1) = e3
% 227.83/39.42  | | | | | | | 
% 227.83/39.42  | | | | | | | BETA: splitting (50) gives:
% 227.83/39.42  | | | | | | | 
% 227.83/39.42  | | | | | | | Case 1:
% 227.83/39.42  | | | | | | | | 
% 227.83/39.42  | | | | | | | |   (235)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 &
% 227.83/39.42  | | | | | | | |            op(e2, e1) = e1)
% 227.83/39.42  | | | | | | | | 
% 227.83/39.42  | | | | | | | | BETA: splitting (235) gives:
% 227.83/39.42  | | | | | | | | 
% 227.83/39.42  | | | | | | | | Case 1:
% 227.83/39.42  | | | | | | | | | 
% 227.83/39.42  | | | | | | | | |   (236)  all_57_4 = e1 & op(e3, e1) = e1
% 227.83/39.42  | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | ALPHA: (236) implies:
% 227.83/39.42  | | | | | | | | |   (237)  all_57_4 = e1
% 227.83/39.42  | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | BETA: splitting (59) gives:
% 227.83/39.42  | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | Case 1:
% 227.83/39.42  | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | |   (238)  all_55_2 = e3
% 227.83/39.42  | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | REF_CLOSE: (86), (133), (238) are inconsistent by sub-proof
% 227.83/39.42  | | | | | | | | | |            #437.
% 227.83/39.42  | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | Case 2:
% 227.83/39.42  | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | |   (239)   ~ (all_55_2 = e3)
% 227.83/39.42  | | | | | | | | | |   (240)  all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 227.83/39.42  | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | BETA: splitting (240) gives:
% 227.83/39.42  | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | Case 1:
% 227.83/39.42  | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | |   (241)  all_55_2 = e2
% 227.83/39.42  | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | REF_CLOSE: (56), (86), (241) are inconsistent by sub-proof
% 227.83/39.42  | | | | | | | | | | |            #561.
% 227.83/39.42  | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | Case 2:
% 227.83/39.42  | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | |   (242)   ~ (all_55_2 = e2)
% 227.83/39.42  | | | | | | | | | | |   (243)  all_55_2 = e1 | all_55_2 = e0
% 227.83/39.42  | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | BETA: splitting (74) gives:
% 227.83/39.42  | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | Case 1:
% 227.83/39.42  | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | |   (244)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 227.83/39.42  | | | | | | | | | | | |            & op(e3, e2) = e3)
% 227.83/39.42  | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | BETA: splitting (244) gives:
% 227.83/39.42  | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | Case 1:
% 227.83/39.42  | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | |   (245)  all_57_0 = e3 & op(e3, e3) = e3
% 227.83/39.42  | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | ALPHA: (245) implies:
% 227.83/39.42  | | | | | | | | | | | | |   (246)  all_57_0 = e3
% 227.83/39.42  | | | | | | | | | | | | |   (247)  op(e3, e3) = e3
% 227.83/39.42  | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | REF_CLOSE: (2), (4), (6), (10), (11), (12), (13), (14), (15),
% 227.83/39.42  | | | | | | | | | | | | |            (17), (18), (19), (21), (22), (26), (27), (32),
% 227.83/39.42  | | | | | | | | | | | | |            (34), (36), (37), (40), (41), (42), (43), (44),
% 227.83/39.42  | | | | | | | | | | | | |            (46), (49), (50), (51), (55), (59), (60), (62),
% 227.83/39.42  | | | | | | | | | | | | |            (65), (67), (70), (71), (76), (78), (79), (84),
% 227.83/39.42  | | | | | | | | | | | | |            (85), (87), (88), (89), (95), (96), (97), (99),
% 227.83/39.42  | | | | | | | | | | | | |            (100), (105), (106), (107), (108), (110), (111),
% 227.83/39.42  | | | | | | | | | | | | |            (112), (113), (114), (116), (117), (119), (121),
% 227.83/39.42  | | | | | | | | | | | | |            (122), (233), (234), (246), (247) are inconsistent
% 227.83/39.42  | | | | | | | | | | | | |            by sub-proof #1440.
% 227.83/39.42  | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | Case 2:
% 227.83/39.42  | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | |   (248)  all_57_1 = e3 & op(e3, e2) = e3
% 227.83/39.42  | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | ALPHA: (248) implies:
% 227.83/39.42  | | | | | | | | | | | | |   (249)  all_57_1 = e3
% 227.83/39.42  | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | BETA: splitting (37) gives:
% 227.83/39.42  | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | Case 1:
% 227.83/39.42  | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | |   (250)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 227.83/39.42  | | | | | | | | | | | | | |            & op(e3, e2) = e2)
% 227.83/39.42  | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | REF_CLOSE: (15), (38), (44), (49), (63), (69), (249), (250)
% 227.83/39.42  | | | | | | | | | | | | | |            are inconsistent by sub-proof #1363.
% 227.83/39.42  | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | Case 2:
% 227.83/39.42  | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | |   (251)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 227.83/39.42  | | | | | | | | | | | | | |            & op(e3, e0) = e2)
% 227.83/39.42  | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | BETA: splitting (251) gives:
% 227.83/39.42  | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | Case 1:
% 227.83/39.42  | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | |   (252)  all_57_4 = e2 & op(e3, e1) = e2
% 227.83/39.42  | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | ALPHA: (252) implies:
% 227.83/39.42  | | | | | | | | | | | | | | |   (253)  all_57_4 = e2
% 227.83/39.42  | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | REF_CLOSE: (13), (50), (76), (81), (105), (115), (233), (253)
% 227.83/39.42  | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1456.
% 227.83/39.42  | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | Case 2:
% 227.83/39.42  | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | |   (254)  all_57_9 = e2 & op(e3, e0) = e2
% 227.83/39.42  | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | ALPHA: (254) implies:
% 227.83/39.42  | | | | | | | | | | | | | | |   (255)  all_57_9 = e2
% 227.83/39.42  | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | BETA: splitting (114) gives:
% 227.83/39.42  | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | Case 1:
% 227.83/39.42  | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | |   (256)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 227.83/39.42  | | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 227.83/39.42  | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | BETA: splitting (256) gives:
% 227.83/39.42  | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.42  | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | |   (257)  all_57_9 = e1 & op(e3, e0) = e1
% 227.83/39.42  | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | REF_CLOSE: (105), (255), (257) are inconsistent by sub-proof
% 227.83/39.42  | | | | | | | | | | | | | | | | |            #2451.
% 227.83/39.42  | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.42  | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | |   (258)  all_57_10 = e1 & op(e2, e0) = e1
% 227.83/39.42  | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | ALPHA: (258) implies:
% 227.83/39.42  | | | | | | | | | | | | | | | | |   (259)  all_57_10 = e1
% 227.83/39.42  | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | BETA: splitting (100) gives:
% 227.83/39.42  | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.42  | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | |   (260)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 227.83/39.42  | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 227.83/39.42  | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | BETA: splitting (260) gives:
% 227.83/39.42  | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | |   (261)  all_57_2 = e2 & op(e2, e3) = e2
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | |   (262)  all_55_2 = e1
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (86), (262) imply:
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | |   (263)  all_52_5 = e1
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | SIMP: (263) implies:
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | |   (264)  all_52_5 = e1
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | REDUCE: (133), (264) imply:
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | |   (265)   ~ (e3 = e1)
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | REDUCE: (56), (264) imply:
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | |   (266)   ~ (e2 = e1)
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | REDUCE: (16), (264) imply:
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | |   (267)  op(e1, e1) = e1
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (6), (10), (11), (12), (13), (14), (15),
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | |            (17), (18), (19), (21), (22), (26), (27), (32),
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | |            (34), (36), (37), (40), (41), (42), (43), (44),
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | |            (46), (49), (50), (51), (54), (55), (59), (60),
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | |            (62), (64), (65), (67), (70), (71), (74), (76),
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | |            (78), (79), (84), (85), (87), (88), (89), (91),
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | |            (95), (96), (97), (99), (100), (102), (105),
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | |            (106), (107), (108), (110), (111), (112), (113),
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | |            (114), (115), (116), (117), (119), (121), (122),
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | |            (232), (233), (234), (255), (259), (261), (267)
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #401.
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | |   (268)  all_55_2 = e0
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (86), (104), (268) are inconsistent by sub-proof
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | |            #560.
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | |   (269)  all_57_3 = e2 & op(e2, e2) = e2
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (42), (44), (60), (64), (70), (76), (105),
% 227.83/39.42  | | | | | | | | | | | | | | | | | | |            (106), (114), (255), (269) are inconsistent by
% 227.83/39.42  | | | | | | | | | | | | | | | | | | |            sub-proof #1096.
% 227.83/39.42  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.42  | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.42  | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | |   (270)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 227.83/39.42  | | | | | | | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 227.83/39.42  | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | | REF_CLOSE: (44), (105), (233), (259), (270) are inconsistent
% 227.83/39.42  | | | | | | | | | | | | | | | | | |            by sub-proof #1523.
% 227.83/39.42  | | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | | End of split
% 227.83/39.42  | | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | End of split
% 227.83/39.42  | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | Case 2:
% 227.83/39.42  | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | |   (271)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 227.83/39.42  | | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 227.83/39.42  | | | | | | | | | | | | | | | | 
% 227.83/39.42  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (13), (15), (19), (21), (42), (44), (49),
% 227.83/39.42  | | | | | | | | | | | | | | | |            (60), (62), (64), (70), (76), (80), (84), (87),
% 227.83/39.42  | | | | | | | | | | | | | | | |            (88), (100), (105), (237), (255), (271) are
% 227.83/39.43  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #399.
% 227.83/39.43  | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | End of split
% 227.83/39.43  | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | End of split
% 227.83/39.43  | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | End of split
% 227.83/39.43  | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | End of split
% 227.83/39.43  | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | Case 2:
% 227.83/39.43  | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | |   (272)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 227.83/39.43  | | | | | | | | | | | |            & op(e3, e0) = e3)
% 227.83/39.43  | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | REF_CLOSE: (13), (15), (97), (122), (237), (272) are
% 227.83/39.43  | | | | | | | | | | | |            inconsistent by sub-proof #1004.
% 227.83/39.43  | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | End of split
% 227.83/39.43  | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | End of split
% 227.83/39.43  | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | End of split
% 227.83/39.43  | | | | | | | | | 
% 227.83/39.43  | | | | | | | | Case 2:
% 227.83/39.43  | | | | | | | | | 
% 227.83/39.43  | | | | | | | | |   (273)  all_57_5 = e1 & op(e2, e1) = e1
% 227.83/39.43  | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | ALPHA: (273) implies:
% 227.83/39.43  | | | | | | | | |   (274)  all_57_5 = e1
% 227.83/39.43  | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | REF_CLOSE: (13), (233), (274) are inconsistent by sub-proof
% 227.83/39.43  | | | | | | | | |            #2382.
% 227.83/39.43  | | | | | | | | | 
% 227.83/39.43  | | | | | | | | End of split
% 227.83/39.43  | | | | | | | | 
% 227.83/39.43  | | | | | | | Case 2:
% 227.83/39.43  | | | | | | | | 
% 227.83/39.43  | | | | | | | |   (275)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 &
% 227.83/39.43  | | | | | | | |            op(e0, e1) = e1)
% 227.83/39.43  | | | | | | | | 
% 227.83/39.43  | | | | | | | | BETA: splitting (275) gives:
% 227.83/39.43  | | | | | | | | 
% 227.83/39.43  | | | | | | | | Case 1:
% 227.83/39.43  | | | | | | | | | 
% 227.83/39.43  | | | | | | | | |   (276)  all_57_8 = e1 & op(e1, e1) = e1
% 227.83/39.43  | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | REF_CLOSE: (81), (105), (276) are inconsistent by sub-proof
% 227.83/39.43  | | | | | | | | |            #1533.
% 227.83/39.43  | | | | | | | | | 
% 227.83/39.43  | | | | | | | | Case 2:
% 227.83/39.43  | | | | | | | | | 
% 227.83/39.43  | | | | | | | | |   (277)  all_57_14 = e1 & op(e0, e1) = e1
% 227.83/39.43  | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | REF_CLOSE: (76), (115), (277) are inconsistent by sub-proof
% 227.83/39.43  | | | | | | | | |            #2381.
% 227.83/39.43  | | | | | | | | | 
% 227.83/39.43  | | | | | | | | End of split
% 227.83/39.43  | | | | | | | | 
% 227.83/39.43  | | | | | | | End of split
% 227.83/39.43  | | | | | | | 
% 227.83/39.43  | | | | | | Case 2:
% 227.83/39.43  | | | | | | | 
% 227.83/39.43  | | | | | | |   (278)  all_57_10 = e3 & op(e2, e0) = e3
% 227.83/39.43  | | | | | | | 
% 227.83/39.43  | | | | | | | ALPHA: (278) implies:
% 227.83/39.43  | | | | | | |   (279)  all_57_10 = e3
% 227.83/39.43  | | | | | | | 
% 227.83/39.43  | | | | | | | REF_CLOSE: (13), (15), (44), (60), (64), (70), (76), (84), (105),
% 227.83/39.43  | | | | | | |            (106), (114), (279) are inconsistent by sub-proof
% 227.83/39.43  | | | | | | |            #1748.
% 227.83/39.43  | | | | | | | 
% 227.83/39.43  | | | | | | End of split
% 227.83/39.43  | | | | | | 
% 227.83/39.43  | | | | | End of split
% 227.83/39.43  | | | | | 
% 227.83/39.43  | | | | Case 2:
% 227.83/39.43  | | | | | 
% 227.83/39.43  | | | | |   (280)  all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 227.83/39.43  | | | | | 
% 227.83/39.43  | | | | | BETA: splitting (94) gives:
% 227.83/39.43  | | | | | 
% 227.83/39.43  | | | | | Case 1:
% 227.83/39.43  | | | | | | 
% 227.83/39.43  | | | | | |   (281)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2,
% 227.83/39.43  | | | | | |              e2) = e3)
% 227.83/39.43  | | | | | | 
% 227.83/39.43  | | | | | | BETA: splitting (281) gives:
% 227.83/39.43  | | | | | | 
% 227.83/39.43  | | | | | | Case 1:
% 227.83/39.43  | | | | | | | 
% 227.83/39.43  | | | | | | |   (282)  all_57_2 = e3 & op(e2, e3) = e3
% 227.83/39.43  | | | | | | | 
% 227.83/39.43  | | | | | | | ALPHA: (282) implies:
% 227.83/39.43  | | | | | | |   (283)  all_57_2 = e3
% 227.83/39.43  | | | | | | | 
% 227.83/39.43  | | | | | | | BETA: splitting (110) gives:
% 227.83/39.43  | | | | | | | 
% 227.83/39.43  | | | | | | | Case 1:
% 227.83/39.43  | | | | | | | | 
% 227.83/39.43  | | | | | | | |   (284)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 &
% 227.83/39.43  | | | | | | | |            op(e2, e3) = e2)
% 227.83/39.43  | | | | | | | | 
% 227.83/39.43  | | | | | | | | REF_CLOSE: (15), (38), (44), (49), (63), (69), (283), (284) are
% 227.83/39.43  | | | | | | | |            inconsistent by sub-proof #391.
% 227.83/39.43  | | | | | | | | 
% 227.83/39.43  | | | | | | | Case 2:
% 227.83/39.43  | | | | | | | | 
% 227.83/39.43  | | | | | | | |   (285)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 &
% 227.83/39.43  | | | | | | | |            op(e0, e3) = e2)
% 227.83/39.43  | | | | | | | | 
% 227.83/39.43  | | | | | | | | BETA: splitting (285) gives:
% 227.83/39.43  | | | | | | | | 
% 227.83/39.43  | | | | | | | | Case 1:
% 227.83/39.43  | | | | | | | | | 
% 227.83/39.43  | | | | | | | | |   (286)  all_57_6 = e2 & op(e1, e3) = e2
% 227.83/39.43  | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | ALPHA: (286) implies:
% 227.83/39.43  | | | | | | | | |   (287)  all_57_6 = e2
% 227.83/39.43  | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | REF_CLOSE: (6), (13), (15), (17), (19), (21), (42), (44),
% 227.83/39.43  | | | | | | | | |            (49), (50), (58), (60), (62), (64), (70), (76),
% 227.83/39.43  | | | | | | | | |            (80), (81), (87), (88), (100), (103), (105), (106),
% 227.83/39.43  | | | | | | | | |            (114), (115), (116), (283), (287) are inconsistent
% 227.83/39.43  | | | | | | | | |            by sub-proof #382.
% 227.83/39.43  | | | | | | | | | 
% 227.83/39.43  | | | | | | | | Case 2:
% 227.83/39.43  | | | | | | | | | 
% 227.83/39.43  | | | | | | | | |   (288)  all_57_12 = e2 & op(e0, e3) = e2
% 227.83/39.43  | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | ALPHA: (288) implies:
% 227.83/39.43  | | | | | | | | |   (289)  all_57_12 = e2
% 227.83/39.43  | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | BETA: splitting (280) gives:
% 227.83/39.43  | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | Case 1:
% 227.83/39.43  | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | |   (290)  all_55_6 = e2
% 227.83/39.43  | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | REF_CLOSE: (66), (73), (290) are inconsistent by sub-proof
% 227.83/39.43  | | | | | | | | | |            #2398.
% 227.83/39.43  | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | Case 2:
% 227.83/39.43  | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | |   (291)   ~ (all_55_6 = e2)
% 227.83/39.43  | | | | | | | | | |   (292)  all_55_6 = e1 | all_55_6 = e0
% 227.83/39.43  | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | BETA: splitting (80) gives:
% 227.83/39.43  | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | Case 1:
% 227.83/39.43  | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | |   (293)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 227.83/39.43  | | | | | | | | | | |            & op(e2, e1) = e3)
% 227.83/39.43  | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | BETA: splitting (293) gives:
% 227.83/39.43  | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | Case 1:
% 227.83/39.43  | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | |   (294)  all_57_4 = e3 & op(e3, e1) = e3
% 227.83/39.43  | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | ALPHA: (294) implies:
% 227.83/39.43  | | | | | | | | | | | |   (295)  all_57_4 = e3
% 227.83/39.43  | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | BETA: splitting (100) gives:
% 227.83/39.43  | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | Case 1:
% 227.83/39.43  | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | |   (296)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 227.83/39.43  | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 227.83/39.43  | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | BETA: splitting (296) gives:
% 227.83/39.43  | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | Case 1:
% 227.83/39.43  | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | |   (297)  all_57_2 = e2 & op(e2, e3) = e2
% 227.83/39.43  | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | REF_CLOSE: (44), (283), (297) are inconsistent by sub-proof
% 227.83/39.43  | | | | | | | | | | | | | |            #1925.
% 227.83/39.43  | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | Case 2:
% 227.83/39.43  | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | |   (298)  all_57_3 = e2 & op(e2, e2) = e2
% 227.83/39.43  | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | REF_CLOSE: (42), (70), (298) are inconsistent by sub-proof
% 227.83/39.43  | | | | | | | | | | | | | |            #2256.
% 227.83/39.43  | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | End of split
% 227.83/39.43  | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | Case 2:
% 227.83/39.43  | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | |   (299)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 227.83/39.43  | | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 227.83/39.43  | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | BETA: splitting (299) gives:
% 227.83/39.43  | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | Case 1:
% 227.83/39.43  | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | |   (300)  all_57_5 = e2 & op(e2, e1) = e2
% 227.83/39.43  | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | ALPHA: (300) implies:
% 227.83/39.43  | | | | | | | | | | | | | |   (301)  all_57_5 = e2
% 227.83/39.43  | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | REF_CLOSE: (13), (50), (76), (81), (105), (115), (295), (301)
% 227.83/39.43  | | | | | | | | | | | | | |            are inconsistent by sub-proof #925.
% 227.83/39.43  | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | Case 2:
% 227.83/39.43  | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | |   (302)  all_57_10 = e2 & op(e2, e0) = e2
% 227.83/39.43  | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | ALPHA: (302) implies:
% 227.83/39.43  | | | | | | | | | | | | | |   (303)  all_57_10 = e2
% 227.83/39.43  | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | BETA: splitting (114) gives:
% 227.83/39.43  | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | Case 1:
% 227.83/39.43  | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | |   (304)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 227.83/39.43  | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 227.83/39.43  | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | BETA: splitting (304) gives:
% 227.83/39.43  | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | Case 1:
% 227.83/39.43  | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | |   (305)  all_57_9 = e1 & op(e3, e0) = e1
% 227.83/39.43  | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | ALPHA: (305) implies:
% 227.83/39.43  | | | | | | | | | | | | | | | |   (306)  all_57_9 = e1
% 227.83/39.43  | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | BETA: splitting (50) gives:
% 227.83/39.43  | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.43  | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | |   (307)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 227.83/39.43  | | | | | | | | | | | | | | | | |            & op(e2, e1) = e1)
% 227.83/39.43  | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | BETA: splitting (307) gives:
% 227.83/39.43  | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | |   (308)  all_57_4 = e1 & op(e3, e1) = e1
% 227.83/39.43  | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | ALPHA: (308) implies:
% 227.83/39.43  | | | | | | | | | | | | | | | | | |   (309)  all_57_4 = e1
% 227.83/39.43  | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (13), (15), (19), (21), (42), (44), (49),
% 227.83/39.43  | | | | | | | | | | | | | | | | | |            (60), (62), (70), (76), (80), (87), (88), (105),
% 227.83/39.43  | | | | | | | | | | | | | | | | | |            (283), (303), (309) are inconsistent by sub-proof
% 227.83/39.43  | | | | | | | | | | | | | | | | | |            #1755.
% 227.83/39.43  | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | |   (310)  all_57_5 = e1 & op(e2, e1) = e1
% 227.83/39.43  | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | ALPHA: (310) implies:
% 227.83/39.43  | | | | | | | | | | | | | | | | | |   (311)  all_57_5 = e1
% 227.83/39.43  | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | BETA: splitting (62) gives:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | |   (312)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 227.83/39.43  | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | BETA: splitting (312) gives:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | |   (313)  all_57_12 = e1 & op(e0, e3) = e1
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (105), (289), (313) are inconsistent by sub-proof
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | |            #2388.
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | |   (314)  all_57_13 = e1 & op(e0, e2) = e1
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | ALPHA: (314) implies:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | |   (315)  all_57_13 = e1
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | BETA: splitting (37) gives:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | |   (316)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e2)
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (316) gives:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | |   (317)  all_57_0 = e2 & op(e3, e3) = e2
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (317) implies:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | |   (318)  op(e3, e3) = e2
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (6), (10), (11), (12), (13), (14), (15),
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | |            (17), (18), (19), (21), (22), (26), (27), (32),
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | |            (34), (36), (37), (40), (41), (42), (43), (44),
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | |            (46), (49), (50), (51), (55), (59), (60), (62),
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | |            (65), (67), (70), (71), (74), (76), (78), (79),
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | |            (80), (82), (84), (85), (87), (88), (89), (94),
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | |            (95), (96), (97), (99), (100), (102), (105),
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | |            (106), (107), (108), (110), (111), (112), (113),
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | |            (114), (116), (117), (119), (121), (122), (289),
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | |            (318) are inconsistent by sub-proof #442.
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | |   (319)  all_57_1 = e2 & op(e3, e2) = e2
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (319) implies:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | |   (320)  all_57_1 = e2
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (292) gives:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | |   (321)  all_55_6 = e1
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (66), (321) imply:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | |   (322)  all_53_9 = e1
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (322) implies:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | |   (323)  all_53_9 = e1
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (24), (323) imply:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | |   (324)   ~ (all_53_1 = e1)
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (61), (323) imply:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | |   (325)   ~ (all_53_13 = e1)
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (325) implies:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | |   (326)   ~ (all_53_13 = e1)
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (93), (323) imply:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | |   (327)   ~ (all_52_5 = e1)
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (327) implies:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | |   (328)   ~ (all_52_5 = e1)
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (73), (323) imply:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | |   (329)   ~ (e2 = e1)
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (59) gives:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | |   (330)  all_55_2 = e3
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (86), (330) imply:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | |   (331)  all_52_5 = e3
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (331) implies:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | |   (332)  all_52_5 = e3
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (332) imply:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | |   (333)   ~ (all_52_3 = e3)
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (82) gives:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | |   (334)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e3)
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (13), (42), (44), (49), (70), (76), (94),
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | |            (100), (105), (283), (320), (334) are inconsistent
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #379.
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | |   (335)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (335) gives:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | |   (336)  all_57_7 = e3 & op(e1, e2) = e3
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (336) implies:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | |   (337)  all_57_7 = e3
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (116) gives:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (338)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e1)
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (338) gives:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (339)  all_57_6 = e1 & op(e1, e3) = e1
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (339) implies:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (340)  all_57_6 = e1
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (127) gives:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (341)  all_55_7 = e2
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (118), (341) imply:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (342)  all_53_13 = e2
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (342) implies:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (343)  all_53_13 = e2
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (92), (343) imply:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (344)   ~ (all_53_1 = e2)
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (47), (343) imply:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (345)   ~ (all_52_7 = e2)
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (345) implies:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (346)   ~ (all_52_7 = e2)
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (57) gives:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (347)  all_55_4 = e3
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (39), (347) imply:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (348)  all_53_1 = e3
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (348) implies:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (349)  all_53_1 = e3
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (68), (349) imply:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (350)   ~ (all_53_2 = e3)
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (350) implies:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (351)   ~ (all_53_2 = e3)
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (52) gives:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (352)  all_55_8 = e3
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (83), (351), (352) are inconsistent by sub-proof
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2496.
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (353)   ~ (all_55_8 = e3)
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (354)  all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (129) gives:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (355)  all_55_3 = e2
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (29), (346), (355) are inconsistent by sub-proof
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1450.
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (356)  all_55_3 = e1 | all_55_3 = e0
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (356) gives:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (357)  all_55_3 = e1
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (29), (357) imply:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (358)  all_52_7 = e1
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (358) implies:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (359)  all_52_7 = e1
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (77), (359) imply:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (360)   ~ (all_52_3 = e1)
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2) gives:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (361)  all_55_1 = e3
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (101), (333), (361) are inconsistent by sub-proof
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #562.
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (362)   ~ (all_55_1 = e3)
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (363)  all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (363) gives:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (364)  all_55_1 = e2
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (101), (364) imply:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (365)  all_52_3 = e2
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (365) implies:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (366)  all_52_3 = e2
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (333), (366) imply:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (367)   ~ (e3 = e2)
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (35), (366) imply:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (368)  op(e2, e2) = e2
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (354) gives:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (369)  all_55_8 = e2
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (83), (369) are inconsistent by sub-proof
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2406.
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (370)   ~ (all_55_8 = e2)
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (371)  all_55_8 = e1 | all_55_8 = e0
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (371) gives:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (372)  all_55_8 = e1
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (83), (372) imply:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (373)  all_53_2 = e1
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (373) implies:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (374)  all_53_2 = e1
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (351), (374) imply:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (375)   ~ (e3 = e1)
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (15) with e0, e2, e2, e2,
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (38), (368) gives:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (376)  e2 = e0
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (320), (376) imply:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (377)  all_57_1 = e0
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10), (12), (13), (15), (17), (19), (21),
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (42), (44), (49), (60), (70), (74), (76), (80),
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (82), (87), (88), (94), (97), (100), (105), (106),
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (110), (113), (114), (119), (122), (283), (303),
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (340), (377) are inconsistent by sub-proof #537.
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (378)  all_55_8 = e0
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (53), (83), (378) are inconsistent by sub-proof
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1997.
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (379)  all_55_1 = e1 | all_55_1 = e0
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (101), (360), (379) are inconsistent by
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1447.
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (380)  all_55_3 = e0
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (29), (98), (380) are inconsistent by sub-proof
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #376.
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (381)  all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (75), (324), (344), (381) are inconsistent
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #772.
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (382)  all_55_7 = e1 | all_55_7 = e0
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (90), (118), (326), (382) are inconsistent by
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1322.
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (383)  all_57_7 = e1 & op(e1, e2) = e1
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (383) implies:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (384)  all_57_7 = e1
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (337), (384) imply:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (385)  e3 = e1
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (295), (385) imply:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (386)  all_57_4 = e1
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (13), (15), (19), (21), (42), (44), (49),
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (60), (62), (70), (76), (80), (87), (88), (105),
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (283), (303), (386) are inconsistent by sub-proof
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1755.
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (387)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e1, e0) = e1)
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (6), (10), (11), (12), (13), (14), (15),
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17), (18), (19), (21), (22), (26), (27), (32),
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (34), (36), (37), (40), (41), (42), (43), (44),
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (46), (49), (50), (51), (54), (55), (59), (60),
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (62), (64), (65), (67), (70), (71), (74), (76),
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (78), (79), (80), (82), (84), (85), (87), (88),
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (89), (94), (95), (96), (97), (99), (100), (102),
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (105), (106), (107), (108), (110), (111), (112),
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (113), (114), (116), (117), (119), (121), (122),
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (283), (295), (303), (311), (315), (320), (337),
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (387) are inconsistent by sub-proof #378.
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | |   (388)  all_57_13 = e3 & op(e0, e2) = e3
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (388) implies:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | |   (389)  all_57_13 = e3
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (13), (15), (19), (21), (42), (44), (49),
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | |            (58), (60), (62), (70), (76), (80), (84), (87),
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | |            (88), (105), (115), (283), (295), (303), (389) are
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #424.
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | |   (390)  all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (38), (76), (86), (104), (328), (390)
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #436.
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | |   (391)  all_55_6 = e0
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (26), (66), (391) are inconsistent by sub-proof
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | |            #2162.
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | |   (392)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e2)
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (392) gives:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | |   (393)  all_57_4 = e2 & op(e3, e1) = e2
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (44), (295), (393) are inconsistent by sub-proof
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | |            #2487.
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | |   (394)  all_57_9 = e2 & op(e3, e0) = e2
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (105), (306), (394) are inconsistent by sub-proof
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | |            #2481.
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | |   (395)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 227.83/39.43  | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (13), (15), (19), (21), (42), (43), (44),
% 227.83/39.43  | | | | | | | | | | | | | | | | | | |            (49), (60), (62), (70), (76), (80), (81), (84),
% 227.83/39.43  | | | | | | | | | | | | | | | | | | |            (87), (88), (94), (100), (105), (283), (303),
% 227.83/39.43  | | | | | | | | | | | | | | | | | | |            (395) are inconsistent by sub-proof #387.
% 227.83/39.43  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.43  | | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | End of split
% 227.83/39.43  | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.43  | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | |   (396)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 227.83/39.43  | | | | | | | | | | | | | | | | |            e1 & op(e0, e1) = e1)
% 227.83/39.43  | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (13), (15), (19), (21), (42), (43), (44),
% 227.83/39.43  | | | | | | | | | | | | | | | | |            (49), (60), (62), (70), (76), (80), (81), (87),
% 227.83/39.43  | | | | | | | | | | | | | | | | |            (88), (94), (100), (105), (283), (303), (396) are
% 227.83/39.43  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #377.
% 227.83/39.43  | | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | End of split
% 227.83/39.43  | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | Case 2:
% 227.83/39.43  | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | |   (397)  all_57_10 = e1 & op(e2, e0) = e1
% 227.83/39.43  | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | ALPHA: (397) implies:
% 227.83/39.43  | | | | | | | | | | | | | | | |   (398)  all_57_10 = e1
% 227.83/39.43  | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | | REF_CLOSE: (105), (303), (398) are inconsistent by sub-proof
% 227.83/39.43  | | | | | | | | | | | | | | | |            #2144.
% 227.83/39.43  | | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | End of split
% 227.83/39.43  | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | Case 2:
% 227.83/39.43  | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | |   (399)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 227.83/39.43  | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 227.83/39.43  | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | | REF_CLOSE: (13), (15), (64), (76), (84), (399) are
% 227.83/39.43  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1749.
% 227.83/39.43  | | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | End of split
% 227.83/39.43  | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | End of split
% 227.83/39.43  | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | End of split
% 227.83/39.43  | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | Case 2:
% 227.83/39.43  | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | |   (400)  all_57_5 = e3 & op(e2, e1) = e3
% 227.83/39.43  | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | ALPHA: (400) implies:
% 227.83/39.43  | | | | | | | | | | | |   (401)  all_57_5 = e3
% 227.83/39.43  | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | REF_CLOSE: (6), (13), (42), (44), (70), (76), (100), (105),
% 227.83/39.43  | | | | | | | | | | | |            (283), (401) are inconsistent by sub-proof #1802.
% 227.83/39.43  | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | End of split
% 227.83/39.43  | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | Case 2:
% 227.83/39.43  | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | |   (402)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 227.83/39.43  | | | | | | | | | | |            e3 & op(e0, e1) = e3)
% 227.83/39.43  | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | REF_CLOSE: (13), (15), (19), (21), (44), (49), (58), (60),
% 227.83/39.43  | | | | | | | | | | |            (62), (70), (76), (87), (105), (402) are
% 227.83/39.43  | | | | | | | | | | |            inconsistent by sub-proof #1044.
% 227.83/39.43  | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | End of split
% 227.83/39.43  | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | End of split
% 227.83/39.43  | | | | | | | | | 
% 227.83/39.43  | | | | | | | | End of split
% 227.83/39.43  | | | | | | | | 
% 227.83/39.43  | | | | | | | End of split
% 227.83/39.43  | | | | | | | 
% 227.83/39.43  | | | | | | Case 2:
% 227.83/39.43  | | | | | | | 
% 227.83/39.43  | | | | | | |   (403)  all_57_3 = e3 & op(e2, e2) = e3
% 227.83/39.43  | | | | | | | 
% 227.83/39.43  | | | | | | | ALPHA: (403) implies:
% 227.83/39.43  | | | | | | |   (404)  all_57_3 = e3
% 227.83/39.43  | | | | | | | 
% 227.83/39.43  | | | | | | | REF_CLOSE: (42), (49), (404) are inconsistent by sub-proof #2358.
% 227.83/39.43  | | | | | | | 
% 227.83/39.43  | | | | | | End of split
% 227.83/39.43  | | | | | | 
% 227.83/39.43  | | | | | Case 2:
% 227.83/39.43  | | | | | | 
% 227.83/39.43  | | | | | |   (405)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 &
% 227.83/39.43  | | | | | |            op(e2, e0) = e3)
% 227.83/39.43  | | | | | | 
% 227.83/39.43  | | | | | | BETA: splitting (405) gives:
% 227.83/39.43  | | | | | | 
% 227.83/39.43  | | | | | | Case 1:
% 227.83/39.43  | | | | | | | 
% 227.83/39.43  | | | | | | |   (406)  all_57_5 = e3 & op(e2, e1) = e3
% 227.83/39.43  | | | | | | | 
% 227.83/39.43  | | | | | | | ALPHA: (406) implies:
% 227.83/39.43  | | | | | | |   (407)  all_57_5 = e3
% 227.83/39.43  | | | | | | |   (408)  op(e2, e1) = e3
% 227.83/39.43  | | | | | | | 
% 227.83/39.43  | | | | | | | BETA: splitting (280) gives:
% 227.83/39.43  | | | | | | | 
% 227.83/39.43  | | | | | | | Case 1:
% 227.83/39.43  | | | | | | | | 
% 227.83/39.43  | | | | | | | |   (409)  all_55_6 = e2
% 227.83/39.43  | | | | | | | | 
% 227.83/39.43  | | | | | | | | REF_CLOSE: (66), (73), (409) are inconsistent by sub-proof
% 227.83/39.43  | | | | | | | |            #2398.
% 227.83/39.43  | | | | | | | | 
% 227.83/39.43  | | | | | | | Case 2:
% 227.83/39.43  | | | | | | | | 
% 227.83/39.43  | | | | | | | |   (410)   ~ (all_55_6 = e2)
% 227.83/39.43  | | | | | | | |   (411)  all_55_6 = e1 | all_55_6 = e0
% 227.83/39.43  | | | | | | | | 
% 227.83/39.43  | | | | | | | | BETA: splitting (50) gives:
% 227.83/39.43  | | | | | | | | 
% 227.83/39.43  | | | | | | | | Case 1:
% 227.83/39.43  | | | | | | | | | 
% 227.83/39.43  | | | | | | | | |   (412)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 &
% 227.83/39.43  | | | | | | | | |            op(e2, e1) = e1)
% 227.83/39.43  | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | BETA: splitting (412) gives:
% 227.83/39.43  | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | Case 1:
% 227.83/39.43  | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | |   (413)  all_57_4 = e1 & op(e3, e1) = e1
% 227.83/39.43  | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | ALPHA: (413) implies:
% 227.83/39.43  | | | | | | | | | |   (414)  all_57_4 = e1
% 227.83/39.43  | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | BETA: splitting (74) gives:
% 227.83/39.43  | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | Case 1:
% 227.83/39.43  | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | |   (415)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 227.83/39.43  | | | | | | | | | | |            & op(e3, e2) = e3)
% 227.83/39.43  | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | BETA: splitting (415) gives:
% 227.83/39.43  | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | Case 1:
% 227.83/39.43  | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | |   (416)  all_57_0 = e3 & op(e3, e3) = e3
% 227.83/39.43  | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | ALPHA: (416) implies:
% 227.83/39.43  | | | | | | | | | | | |   (417)  op(e3, e3) = e3
% 227.83/39.43  | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | REF_CLOSE: (2), (4), (6), (10), (11), (12), (13), (14), (15),
% 227.83/39.43  | | | | | | | | | | | |            (17), (18), (19), (21), (22), (26), (27), (32),
% 227.83/39.43  | | | | | | | | | | | |            (34), (36), (37), (40), (41), (42), (43), (44),
% 227.83/39.43  | | | | | | | | | | | |            (46), (49), (50), (51), (55), (59), (60), (62),
% 227.83/39.43  | | | | | | | | | | | |            (65), (67), (70), (71), (74), (76), (78), (79),
% 227.83/39.43  | | | | | | | | | | | |            (84), (85), (87), (88), (89), (95), (96), (97),
% 227.83/39.43  | | | | | | | | | | | |            (99), (100), (105), (106), (107), (108), (110),
% 227.83/39.43  | | | | | | | | | | | |            (111), (112), (113), (114), (116), (117), (119),
% 227.83/39.43  | | | | | | | | | | | |            (121), (122), (407), (408), (417) are inconsistent
% 227.83/39.43  | | | | | | | | | | | |            by sub-proof #1438.
% 227.83/39.43  | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | Case 2:
% 227.83/39.43  | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | |   (418)  all_57_1 = e3 & op(e3, e2) = e3
% 227.83/39.43  | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | ALPHA: (418) implies:
% 227.83/39.43  | | | | | | | | | | | |   (419)  all_57_1 = e3
% 227.83/39.43  | | | | | | | | | | | |   (420)  op(e3, e2) = e3
% 227.83/39.43  | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | BETA: splitting (12) gives:
% 227.83/39.43  | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | Case 1:
% 227.83/39.43  | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | |   (421)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 227.83/39.43  | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 227.83/39.43  | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | BETA: splitting (421) gives:
% 227.83/39.43  | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | Case 1:
% 227.83/39.43  | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | |   (422)  all_57_1 = e2 & op(e3, e2) = e2
% 227.83/39.43  | | | | | | | | | | | | | | 
% 227.83/39.43  | | | | | | | | | | | | | | REF_CLOSE: (44), (419), (422) are inconsistent by sub-proof
% 227.83/39.44  | | | | | | | | | | | | | |            #1809.
% 227.83/39.44  | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | Case 2:
% 227.83/39.44  | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | |   (423)  all_57_3 = e2 & op(e2, e2) = e2
% 227.83/39.44  | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | REF_CLOSE: (42), (70), (423) are inconsistent by sub-proof
% 227.83/39.44  | | | | | | | | | | | | | |            #2256.
% 227.83/39.44  | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | End of split
% 227.83/39.44  | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | Case 2:
% 227.83/39.44  | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | |   (424)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 227.83/39.44  | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 227.83/39.44  | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | BETA: splitting (424) gives:
% 227.83/39.44  | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | Case 1:
% 227.83/39.44  | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | |   (425)  all_57_7 = e2 & op(e1, e2) = e2
% 227.83/39.44  | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | ALPHA: (425) implies:
% 227.83/39.44  | | | | | | | | | | | | | |   (426)  all_57_7 = e2
% 227.83/39.44  | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | BETA: splitting (37) gives:
% 227.83/39.44  | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | Case 1:
% 227.83/39.44  | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | |   (427)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 227.83/39.44  | | | | | | | | | | | | | | |            & op(e3, e2) = e2)
% 227.83/39.44  | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | REF_CLOSE: (15), (38), (44), (49), (63), (69), (419), (427)
% 227.83/39.44  | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1363.
% 227.83/39.44  | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | Case 2:
% 227.83/39.44  | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | |   (428)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 227.83/39.44  | | | | | | | | | | | | | | |            & op(e3, e0) = e2)
% 227.83/39.44  | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | BETA: splitting (428) gives:
% 227.83/39.44  | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | Case 1:
% 227.83/39.44  | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | |   (429)  all_57_4 = e2 & op(e3, e1) = e2
% 227.83/39.44  | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | ALPHA: (429) implies:
% 227.83/39.44  | | | | | | | | | | | | | | | |   (430)  all_57_4 = e2
% 227.83/39.44  | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | REF_CLOSE: (13), (50), (76), (81), (105), (115), (407), (430)
% 227.83/39.44  | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1456.
% 227.83/39.44  | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | Case 2:
% 227.83/39.44  | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | |   (431)  all_57_9 = e2 & op(e3, e0) = e2
% 227.83/39.44  | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | ALPHA: (431) implies:
% 227.83/39.44  | | | | | | | | | | | | | | | |   (432)  all_57_9 = e2
% 227.83/39.44  | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | BETA: splitting (411) gives:
% 227.83/39.44  | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.44  | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | |   (433)  all_55_6 = e1
% 227.83/39.44  | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | COMBINE_EQS: (66), (433) imply:
% 227.83/39.44  | | | | | | | | | | | | | | | | |   (434)  all_53_9 = e1
% 227.83/39.44  | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | REDUCE: (93), (434) imply:
% 227.83/39.44  | | | | | | | | | | | | | | | | |   (435)   ~ (all_52_5 = e1)
% 227.83/39.44  | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | SIMP: (435) implies:
% 227.83/39.44  | | | | | | | | | | | | | | | | |   (436)   ~ (all_52_5 = e1)
% 227.83/39.44  | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | REDUCE: (73), (434) imply:
% 227.83/39.44  | | | | | | | | | | | | | | | | |   (437)   ~ (e2 = e1)
% 227.83/39.44  | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | BETA: splitting (59) gives:
% 227.83/39.44  | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | |   (438)  all_55_2 = e3
% 227.83/39.44  | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (86), (438) imply:
% 227.83/39.44  | | | | | | | | | | | | | | | | | |   (439)  all_52_5 = e3
% 227.83/39.44  | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | SIMP: (439) implies:
% 227.83/39.44  | | | | | | | | | | | | | | | | | |   (440)  all_52_5 = e3
% 227.83/39.44  | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | REDUCE: (16), (440) imply:
% 227.83/39.44  | | | | | | | | | | | | | | | | | |   (441)  op(e3, e3) = e1
% 227.83/39.44  | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | BETA: splitting (116) gives:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | |   (442)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 227.83/39.44  | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e1)
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | BETA: splitting (442) gives:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | |   (443)  all_57_6 = e1 & op(e1, e3) = e1
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | ALPHA: (443) implies:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | |   (444)  all_57_6 = e1
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (13), (15), (42), (44), (60), (62), (64),
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | |            (70), (76), (87), (100), (102), (105), (106),
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | |            (114), (115), (407), (432), (441), (444) are
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #406.
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | |   (445)  all_57_7 = e1 & op(e1, e2) = e1
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (105), (426), (445) are inconsistent by sub-proof
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | |            #2190.
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | |   (446)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 227.83/39.44  | | | | | | | | | | | | | | | | | | |            e1 & op(e1, e0) = e1)
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | BETA: splitting (446) gives:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | |   (447)  all_57_8 = e1 & op(e1, e1) = e1
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (81), (105), (447) are inconsistent by sub-proof
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | |            #1533.
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | |   (448)  all_57_11 = e1 & op(e1, e0) = e1
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (13), (15), (19), (21), (42), (44), (49),
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | |            (58), (60), (62), (64), (70), (76), (80), (87),
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | |            (100), (103), (105), (414), (432), (448) are
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #375.
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.44  | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | |   (449)  all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 227.83/39.44  | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (38), (76), (86), (104), (436), (449)
% 227.83/39.44  | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #436.
% 227.83/39.44  | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | End of split
% 227.83/39.44  | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.44  | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | |   (450)  all_55_6 = e0
% 227.83/39.44  | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | COMBINE_EQS: (66), (450) imply:
% 227.83/39.44  | | | | | | | | | | | | | | | | |   (451)  all_53_9 = e0
% 227.83/39.44  | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | REDUCE: (26), (451) imply:
% 227.83/39.44  | | | | | | | | | | | | | | | | |   (452)  $false
% 227.83/39.44  | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | CLOSE: (452) is inconsistent.
% 227.83/39.44  | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | End of split
% 227.83/39.44  | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | End of split
% 227.83/39.44  | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | End of split
% 227.83/39.44  | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | Case 2:
% 227.83/39.44  | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | |   (453)  all_57_13 = e2 & op(e0, e2) = e2
% 227.83/39.44  | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | ALPHA: (453) implies:
% 227.83/39.44  | | | | | | | | | | | | | |   (454)  all_57_13 = e2
% 227.83/39.44  | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | BETA: splitting (62) gives:
% 227.83/39.44  | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | Case 1:
% 227.83/39.44  | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | |   (455)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 227.83/39.44  | | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 227.83/39.44  | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | BETA: splitting (455) gives:
% 227.83/39.44  | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | Case 1:
% 227.83/39.44  | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | |   (456)  all_57_12 = e1 & op(e0, e3) = e1
% 227.83/39.44  | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | ALPHA: (456) implies:
% 227.83/39.44  | | | | | | | | | | | | | | | |   (457)  all_57_12 = e1
% 227.83/39.44  | | | | | | | | | | | | | | | |   (458)  op(e0, e3) = e1
% 227.83/39.44  | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | BETA: splitting (110) gives:
% 227.83/39.44  | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.44  | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | |   (459)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 227.83/39.44  | | | | | | | | | | | | | | | | |            & op(e2, e3) = e2)
% 227.83/39.44  | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | BETA: splitting (459) gives:
% 227.83/39.44  | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | |   (460)  all_57_0 = e2 & op(e3, e3) = e2
% 227.83/39.44  | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | ALPHA: (460) implies:
% 227.83/39.44  | | | | | | | | | | | | | | | | | |   (461)  op(e3, e3) = e2
% 227.83/39.44  | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (38), (49), (63), (69), (461) are
% 227.83/39.44  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1653.
% 227.83/39.44  | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | |   (462)  all_57_2 = e2 & op(e2, e3) = e2
% 227.83/39.44  | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | ALPHA: (462) implies:
% 227.83/39.44  | | | | | | | | | | | | | | | | | |   (463)  all_57_2 = e2
% 227.83/39.44  | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | BETA: splitting (37) gives:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | |   (464)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 227.83/39.44  | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e2)
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | BETA: splitting (464) gives:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | |   (465)  all_57_0 = e2 & op(e3, e3) = e2
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | ALPHA: (465) implies:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | |   (466)  op(e3, e3) = e2
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (6), (10), (11), (12), (13), (14), (15),
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | |            (17), (18), (19), (21), (22), (26), (27), (32),
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | |            (34), (36), (37), (40), (41), (42), (43), (44),
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | |            (46), (49), (50), (51), (55), (59), (60), (62),
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | |            (65), (67), (70), (71), (76), (78), (79), (84),
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | |            (85), (87), (88), (89), (95), (96), (97), (99),
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | |            (100), (102), (105), (106), (107), (108), (110),
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | |            (111), (112), (113), (114), (116), (117), (119),
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | |            (121), (122), (407), (408), (463), (466) are
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #554.
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | |   (467)  all_57_1 = e2 & op(e3, e2) = e2
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (44), (419), (467) are inconsistent by sub-proof
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | |            #1809.
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | |   (468)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 227.83/39.44  | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e2)
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | BETA: splitting (468) gives:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | |   (469)  all_57_4 = e2 & op(e3, e1) = e2
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | ALPHA: (469) implies:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | |   (470)  all_57_4 = e2
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (50), (76), (81), (105), (115), (407), (470)
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1456.
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | |   (471)  all_57_9 = e2 & op(e3, e0) = e2
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | ALPHA: (471) implies:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | |   (472)  all_57_9 = e2
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | BETA: splitting (114) gives:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | |   (473)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (473) gives:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | |   (474)  all_57_9 = e1 & op(e3, e0) = e1
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (474) implies:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | |   (475)  all_57_9 = e1
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (472), (475) imply:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | |   (476)  e2 = e1
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (463), (476) imply:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | |   (477)  all_57_2 = e1
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (13), (15), (42), (44), (60), (64), (70),
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | |            (76), (84), (100), (105), (106), (114), (407),
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | |            (472), (477) are inconsistent by sub-proof #1093.
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | |   (478)  all_57_10 = e1 & op(e2, e0) = e1
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (478) implies:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | |   (479)  all_57_10 = e1
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (116) gives:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | |   (480)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e1)
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (480) gives:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | |   (481)  all_57_6 = e1 & op(e1, e3) = e1
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (481) implies:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | |   (482)  all_57_6 = e1
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (6), (10), (11), (12), (13), (14), (15),
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | |            (17), (18), (19), (21), (22), (26), (27), (32),
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | |            (34), (36), (37), (40), (41), (42), (43), (44),
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | |            (46), (49), (50), (51), (55), (58), (59), (60),
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | |            (62), (65), (67), (70), (71), (74), (76), (78),
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | |            (79), (80), (84), (85), (87), (88), (89), (95),
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | |            (96), (97), (99), (100), (102), (105), (106),
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | |            (107), (108), (110), (111), (112), (113), (114),
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | |            (115), (116), (117), (119), (121), (122), (414),
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | |            (482) are inconsistent by sub-proof #438.
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | |   (483)  all_57_7 = e1 & op(e1, e2) = e1
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (483) implies:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | |   (484)  op(e1, e2) = e1
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (411) gives:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | |   (485)  all_55_6 = e1
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (66), (485) imply:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | |   (486)  all_53_9 = e1
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (486) implies:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | |   (487)  all_53_9 = e1
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (24), (487) imply:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | |   (488)   ~ (all_53_1 = e1)
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (61), (487) imply:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | |   (489)   ~ (all_53_13 = e1)
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (489) implies:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | |   (490)   ~ (all_53_13 = e1)
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (127) gives:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | |   (491)  all_55_7 = e2
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (118), (491) imply:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | |   (492)  all_53_13 = e2
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (492) implies:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | |   (493)  all_53_13 = e2
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (92), (493) imply:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | |   (494)   ~ (all_53_1 = e2)
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (47), (493) imply:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | |   (495)   ~ (all_52_7 = e2)
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (495) implies:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | |   (496)   ~ (all_52_7 = e2)
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (57) gives:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (497)  all_55_4 = e3
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (39), (497) imply:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (498)  all_53_1 = e3
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (498) implies:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (499)  all_53_1 = e3
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (68), (499) imply:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (500)   ~ (all_53_2 = e3)
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (500) implies:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (501)   ~ (all_53_2 = e3)
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (129) gives:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (502)  all_55_3 = e2
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (29), (496), (502) are inconsistent by sub-proof
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1450.
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (503)  all_55_3 = e1 | all_55_3 = e0
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (52) gives:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (504)  all_55_8 = e3
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (83), (501), (504) are inconsistent by sub-proof
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2496.
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (505)  all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (505) gives:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (506)  all_55_8 = e2
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (83), (506) are inconsistent by sub-proof
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2406.
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (507)  all_55_8 = e1 | all_55_8 = e0
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (507) gives:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (508)  all_55_8 = e1
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (83), (508) imply:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (509)  all_53_2 = e1
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (509) implies:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (510)  all_53_2 = e1
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (109), (510) imply:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (511)   ~ (all_53_6 = e1)
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (511) implies:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (512)   ~ (all_53_6 = e1)
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (30) gives:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (513)  all_55_9 = e3
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (31), (513) imply:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (514)  all_53_6 = e3
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (514) implies:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (515)  all_53_6 = e3
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (23), (515) imply:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (516)   ~ (all_52_3 = e3)
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (516) implies:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (517)   ~ (all_52_3 = e3)
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (108), (515) imply:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (518)  op(e1, e2) = e3
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (125) gives:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (519)   ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e1, e2) = all_42_1 & $i(all_42_0) &
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_42_1)
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (519) implies:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (520)  op(e1, e2) = all_42_1
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (15), (20), (25), (28), (29), (35), (38),
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (42), (72), (77), (98), (100), (101), (120),
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (407), (420), (458), (463), (479), (484), (503),
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (517), (518), (520) are inconsistent by sub-proof
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #374.
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (521)   ~ (all_42_1 = e0) & op(e1, e2) = all_42_1 &
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_42_1)
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (521) implies:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (522)  op(e1, e2) = all_42_1
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (15), (20), (25), (28), (29), (35), (38),
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (42), (72), (77), (98), (100), (101), (120),
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (407), (420), (458), (463), (479), (484), (503),
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (517), (518), (522) are inconsistent by sub-proof
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #374.
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (523)  all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (31), (512), (523) are inconsistent by
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2271.
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (524)  all_55_8 = e0
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (53), (83), (524) are inconsistent by sub-proof
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1997.
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (525)  all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (75), (488), (494), (525) are inconsistent
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #772.
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | |   (526)  all_55_7 = e1 | all_55_7 = e0
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (90), (118), (490), (526) are inconsistent by
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1322.
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | |   (527)  all_55_6 = e0
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (26), (66), (527) are inconsistent by sub-proof
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | |            #2162.
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | |   (528)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e1, e0) = e1)
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (528) gives:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | |   (529)  all_57_8 = e1 & op(e1, e1) = e1
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (529) implies:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | |   (530)  op(e1, e1) = e1
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (6), (10), (11), (12), (13), (14), (15),
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | |            (17), (18), (19), (21), (22), (26), (27), (32),
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | |            (34), (36), (37), (40), (41), (42), (43), (44),
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | |            (46), (49), (50), (51), (54), (55), (59), (60),
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | |            (62), (64), (65), (67), (70), (71), (74), (76),
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | |            (78), (79), (84), (85), (87), (88), (89), (91),
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | |            (95), (96), (97), (99), (100), (102), (105),
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | |            (106), (107), (108), (110), (111), (112), (113),
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | |            (114), (115), (116), (117), (119), (121), (122),
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | |            (406), (407), (408), (462), (472), (479), (530)
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #401.
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | |   (531)  all_57_11 = e1 & op(e1, e0) = e1
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (13), (15), (19), (21), (42), (44), (49),
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | |            (58), (60), (62), (64), (70), (76), (80), (87),
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | |            (100), (103), (105), (414), (472), (531) are
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #375.
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | |   (532)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (532) gives:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | |   (533)  all_57_11 = e1 & op(e1, e0) = e1
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (13), (15), (19), (21), (42), (44), (49),
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | |            (58), (60), (62), (64), (70), (76), (80), (87),
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | |            (100), (103), (105), (414), (472), (533) are
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #375.
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | |   (534)  all_57_15 = e1 & op(e0, e0) = e1
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (534) implies:
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | |   (535)  op(e0, e0) = e1
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (15), (84), (535) are inconsistent by
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2183.
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.44  | | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | | End of split
% 227.83/39.44  | | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | End of split
% 227.83/39.44  | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | Case 2:
% 227.83/39.44  | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | |   (536)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 227.83/39.44  | | | | | | | | | | | | | | | | |            e2 & op(e0, e3) = e2)
% 227.83/39.44  | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (15), (17), (19), (21), (42), (44), (49),
% 227.83/39.44  | | | | | | | | | | | | | | | | |            (60), (70), (76), (103), (105), (106), (114),
% 227.83/39.44  | | | | | | | | | | | | | | | | |            (119), (419), (454), (457), (536) are inconsistent
% 227.83/39.44  | | | | | | | | | | | | | | | | |            by sub-proof #418.
% 227.83/39.44  | | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | End of split
% 227.83/39.44  | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | Case 2:
% 227.83/39.44  | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | |   (537)  all_57_13 = e1 & op(e0, e2) = e1
% 227.83/39.44  | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | | REF_CLOSE: (105), (454), (537) are inconsistent by sub-proof
% 227.83/39.44  | | | | | | | | | | | | | | | |            #2205.
% 227.83/39.44  | | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | End of split
% 227.83/39.44  | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | Case 2:
% 227.83/39.44  | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | |   (538)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 227.83/39.44  | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 227.83/39.44  | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | | REF_CLOSE: (13), (15), (76), (84), (115), (538) are
% 227.83/39.44  | | | | | | | | | | | | | | |            inconsistent by sub-proof #2056.
% 227.83/39.44  | | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | | End of split
% 227.83/39.44  | | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | | End of split
% 227.83/39.44  | | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | | End of split
% 227.83/39.44  | | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | End of split
% 227.83/39.44  | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | Case 2:
% 227.83/39.44  | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | |   (539)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 227.83/39.44  | | | | | | | | | | |            & op(e3, e0) = e3)
% 227.83/39.44  | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | | REF_CLOSE: (13), (15), (97), (122), (414), (539) are
% 227.83/39.44  | | | | | | | | | | |            inconsistent by sub-proof #1004.
% 227.83/39.44  | | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | End of split
% 227.83/39.44  | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | Case 2:
% 227.83/39.44  | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | |   (540)  all_57_5 = e1 & op(e2, e1) = e1
% 227.83/39.44  | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | ALPHA: (540) implies:
% 227.83/39.44  | | | | | | | | | |   (541)  all_57_5 = e1
% 227.83/39.44  | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | REF_CLOSE: (13), (407), (541) are inconsistent by sub-proof
% 227.83/39.44  | | | | | | | | | |            #2382.
% 227.83/39.44  | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | End of split
% 227.83/39.44  | | | | | | | | | 
% 227.83/39.44  | | | | | | | | Case 2:
% 227.83/39.44  | | | | | | | | | 
% 227.83/39.44  | | | | | | | | |   (542)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 &
% 227.83/39.44  | | | | | | | | |            op(e0, e1) = e1)
% 227.83/39.44  | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | BETA: splitting (542) gives:
% 227.83/39.44  | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | Case 1:
% 227.83/39.44  | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | |   (543)  all_57_8 = e1 & op(e1, e1) = e1
% 227.83/39.44  | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | REF_CLOSE: (81), (105), (543) are inconsistent by sub-proof
% 227.83/39.44  | | | | | | | | | |            #1533.
% 227.83/39.44  | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | Case 2:
% 227.83/39.44  | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | |   (544)  all_57_14 = e1 & op(e0, e1) = e1
% 227.83/39.44  | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | | REF_CLOSE: (76), (115), (544) are inconsistent by sub-proof
% 227.83/39.44  | | | | | | | | | |            #2381.
% 227.83/39.44  | | | | | | | | | | 
% 227.83/39.44  | | | | | | | | | End of split
% 227.83/39.44  | | | | | | | | | 
% 227.83/39.44  | | | | | | | | End of split
% 227.83/39.44  | | | | | | | | 
% 227.83/39.44  | | | | | | | End of split
% 227.83/39.44  | | | | | | | 
% 227.83/39.44  | | | | | | Case 2:
% 227.83/39.44  | | | | | | | 
% 227.83/39.44  | | | | | | |   (545)  all_57_10 = e3 & op(e2, e0) = e3
% 227.83/39.44  | | | | | | | 
% 227.83/39.44  | | | | | | | ALPHA: (545) implies:
% 227.83/39.44  | | | | | | |   (546)  all_57_10 = e3
% 227.83/39.44  | | | | | | | 
% 227.83/39.44  | | | | | | | REF_CLOSE: (13), (15), (44), (60), (64), (70), (76), (84), (105),
% 227.83/39.44  | | | | | | |            (106), (114), (546) are inconsistent by sub-proof
% 227.83/39.44  | | | | | | |            #1748.
% 227.83/39.44  | | | | | | | 
% 227.83/39.44  | | | | | | End of split
% 227.83/39.44  | | | | | | 
% 227.83/39.44  | | | | | End of split
% 227.83/39.44  | | | | | 
% 227.83/39.44  | | | | End of split
% 227.83/39.44  | | | | 
% 227.83/39.44  | | | End of split
% 227.83/39.44  | | | 
% 227.83/39.44  | | End of split
% 227.83/39.44  | | 
% 227.83/39.44  | End of split
% 227.83/39.44  | 
% 227.83/39.44  End of proof
% 227.83/39.44  
% 227.83/39.44  Sub-proof #374 shows that the following formulas are inconsistent:
% 227.83/39.44  ----------------------------------------------------------------
% 227.83/39.44    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 227.83/39.44    (2)  op(e1, e2) = all_42_1
% 227.83/39.44    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.83/39.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.83/39.44    (4)  op(e1, e2) = e3
% 227.83/39.44    (5)   ~ (all_52_3 = e0)
% 227.83/39.44    (6)  all_57_10 = e1
% 227.83/39.44    (7)  op(e3, e2) = all_52_3
% 227.83/39.44    (8)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) = all_22_1
% 227.83/39.44           & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0, e3) =
% 227.83/39.44           all_22_1 & $i(all_22_1))
% 227.83/39.44    (9)  all_55_3 = all_52_7
% 227.83/39.44    (10)  all_57_2 = e2
% 227.83/39.44    (11)  op(all_52_3, all_52_3) = e2
% 227.83/39.44    (12)  op(e2, e2) = e0
% 227.83/39.44    (13)  all_57_3 = e0
% 227.83/39.44    (14)  op(e0, e3) = e1
% 227.83/39.44    (15)   ~ (all_52_3 = e3)
% 227.83/39.44    (16)  all_57_5 = e3
% 227.83/39.44    (17)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 227.83/39.44            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 227.83/39.44              e3) = all_12_1 & $i(all_12_1))
% 227.83/39.44    (18)  op(e1, e2) = e1
% 227.83/39.44    (19)   ~ (all_52_3 = all_52_7)
% 227.83/39.44    (20)  all_55_3 = e1 | all_55_3 = e0
% 227.83/39.44    (21)   ~ (all_52_7 = e0)
% 227.83/39.44    (22)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 227.83/39.44          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 227.83/39.44    (23)  all_55_1 = all_52_3
% 227.83/39.44    (24)  op(e3, e2) = e3
% 227.83/39.44    (25)  ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 & op(e1, e2) =
% 227.83/39.44            all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 = e3) & op(e1,
% 227.83/39.44              e2) = all_38_1 & $i(all_38_1))
% 227.83/39.44  
% 227.83/39.44  Begin of proof
% 227.83/39.44  | 
% 227.83/39.44  | BETA: splitting (25) gives:
% 227.83/39.44  | 
% 227.83/39.44  | Case 1:
% 227.83/39.44  | | 
% 227.83/39.44  | |   (26)   ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 & op(e1, e2) =
% 227.83/39.44  | |         all_38_1 & $i(all_38_0) & $i(all_38_1)
% 227.83/39.44  | | 
% 227.83/39.44  | | ALPHA: (26) implies:
% 227.83/39.44  | |   (27)  op(e1, e2) = all_38_1
% 227.83/39.44  | | 
% 227.83/39.44  | | BETA: splitting (20) gives:
% 227.83/39.44  | | 
% 227.83/39.44  | | Case 1:
% 227.83/39.44  | | | 
% 227.83/39.44  | | |   (28)  all_55_3 = e1
% 227.83/39.44  | | | 
% 227.83/39.44  | | | COMBINE_EQS: (9), (28) imply:
% 227.83/39.44  | | |   (29)  all_52_7 = e1
% 227.83/39.44  | | | 
% 227.83/39.44  | | | SIMP: (29) implies:
% 227.83/39.44  | | |   (30)  all_52_7 = e1
% 227.83/39.44  | | | 
% 227.83/39.44  | | | REDUCE: (19), (30) imply:
% 227.83/39.44  | | |   (31)   ~ (all_52_3 = e1)
% 227.83/39.44  | | | 
% 227.83/39.44  | | | BETA: splitting (1) gives:
% 227.83/39.44  | | | 
% 227.83/39.44  | | | Case 1:
% 227.83/39.44  | | | | 
% 227.83/39.44  | | | |   (32)  all_55_1 = e3
% 227.83/39.44  | | | | 
% 227.83/39.44  | | | | REF_CLOSE: (15), (23), (32) are inconsistent by sub-proof #562.
% 227.83/39.44  | | | | 
% 227.83/39.44  | | | Case 2:
% 227.83/39.44  | | | | 
% 227.83/39.44  | | | |   (33)   ~ (all_55_1 = e3)
% 227.83/39.45  | | | |   (34)  all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 227.83/39.45  | | | | 
% 227.83/39.45  | | | | BETA: splitting (34) gives:
% 227.83/39.45  | | | | 
% 227.83/39.45  | | | | Case 1:
% 227.83/39.45  | | | | | 
% 227.83/39.45  | | | | |   (35)  all_55_1 = e2
% 227.83/39.45  | | | | | 
% 227.83/39.45  | | | | | COMBINE_EQS: (23), (35) imply:
% 227.83/39.45  | | | | |   (36)  all_52_3 = e2
% 227.83/39.45  | | | | | 
% 227.83/39.45  | | | | | SIMP: (36) implies:
% 227.83/39.45  | | | | |   (37)  all_52_3 = e2
% 227.83/39.45  | | | | | 
% 227.83/39.45  | | | | | REDUCE: (15), (37) imply:
% 227.83/39.45  | | | | |   (38)   ~ (e3 = e2)
% 227.83/39.45  | | | | | 
% 227.83/39.45  | | | | | SIMP: (38) implies:
% 227.83/39.45  | | | | |   (39)   ~ (e3 = e2)
% 227.83/39.45  | | | | | 
% 227.83/39.45  | | | | | REDUCE: (31), (37) imply:
% 227.83/39.45  | | | | |   (40)   ~ (e2 = e1)
% 227.83/39.45  | | | | | 
% 227.83/39.45  | | | | | REDUCE: (5), (37) imply:
% 227.83/39.45  | | | | |   (41)   ~ (e2 = e0)
% 227.83/39.45  | | | | | 
% 227.83/39.45  | | | | | REDUCE: (11), (37) imply:
% 227.83/39.45  | | | | |   (42)  op(e2, e2) = e2
% 227.83/39.45  | | | | | 
% 227.83/39.45  | | | | | REDUCE: (7), (37) imply:
% 227.83/39.45  | | | | |   (43)  op(e3, e2) = e2
% 227.83/39.45  | | | | | 
% 227.83/39.45  | | | | | BETA: splitting (17) gives:
% 227.83/39.45  | | | | | 
% 227.83/39.45  | | | | | Case 1:
% 227.83/39.45  | | | | | | 
% 227.83/39.45  | | | | | | 
% 227.83/39.45  | | | | | | GROUND_INST: instantiating (3) with e1, all_38_1, e2, e1,
% 227.83/39.45  | | | | | |              simplifying with (18), (27) gives:
% 227.83/39.45  | | | | | |   (44)  all_38_1 = e1
% 227.83/39.45  | | | | | | 
% 227.83/39.45  | | | | | | GROUND_INST: instantiating (3) with all_38_1, all_42_1, e2, e1,
% 227.83/39.45  | | | | | |              simplifying with (2), (27) gives:
% 227.83/39.45  | | | | | |   (45)  all_42_1 = all_38_1
% 227.83/39.45  | | | | | | 
% 227.83/39.45  | | | | | | GROUND_INST: instantiating (3) with e3, all_42_1, e2, e1,
% 227.83/39.45  | | | | | |              simplifying with (2), (4) gives:
% 227.83/39.45  | | | | | |   (46)  all_42_1 = e3
% 227.83/39.45  | | | | | | 
% 227.83/39.45  | | | | | | GROUND_INST: instantiating (3) with e0, e2, e2, e2, simplifying with
% 227.83/39.45  | | | | | |              (12), (42) gives:
% 227.83/39.45  | | | | | |   (47)  e2 = e0
% 227.83/39.45  | | | | | | 
% 227.83/39.45  | | | | | | GROUND_INST: instantiating (3) with e2, e3, e2, e3, simplifying with
% 227.83/39.45  | | | | | |              (24), (43) gives:
% 227.83/39.45  | | | | | |   (48)  e3 = e2
% 227.83/39.45  | | | | | | 
% 227.83/39.45  | | | | | | COMBINE_EQS: (45), (46) imply:
% 227.83/39.45  | | | | | |   (49)  all_38_1 = e3
% 227.83/39.45  | | | | | | 
% 227.83/39.45  | | | | | | SIMP: (49) implies:
% 227.83/39.45  | | | | | |   (50)  all_38_1 = e3
% 227.83/39.45  | | | | | | 
% 227.83/39.45  | | | | | | COMBINE_EQS: (44), (50) imply:
% 227.83/39.45  | | | | | |   (51)  e3 = e1
% 227.83/39.45  | | | | | | 
% 227.83/39.45  | | | | | | SIMP: (51) implies:
% 227.83/39.45  | | | | | |   (52)  e3 = e1
% 227.83/39.45  | | | | | | 
% 227.83/39.45  | | | | | | COMBINE_EQS: (48), (52) imply:
% 227.83/39.45  | | | | | |   (53)  e2 = e1
% 227.83/39.45  | | | | | | 
% 227.83/39.45  | | | | | | SIMP: (53) implies:
% 227.83/39.45  | | | | | |   (54)  e2 = e1
% 227.83/39.45  | | | | | | 
% 227.83/39.45  | | | | | | COMBINE_EQS: (47), (54) imply:
% 227.83/39.45  | | | | | |   (55)  e1 = e0
% 227.83/39.45  | | | | | | 
% 227.83/39.45  | | | | | | COMBINE_EQS: (10), (47) imply:
% 227.83/39.45  | | | | | |   (56)  all_57_2 = e0
% 227.83/39.45  | | | | | | 
% 227.83/39.45  | | | | | | REF_CLOSE: (6), (13), (16), (22), (39), (40), (41), (56) are
% 227.83/39.45  | | | | | |            inconsistent by sub-proof #2254.
% 227.83/39.45  | | | | | | 
% 227.83/39.45  | | | | | Case 2:
% 227.83/39.45  | | | | | | 
% 227.83/39.45  | | | | | |   (57)   ~ (all_12_1 = e1) & op(e0, e3) = all_12_1 & $i(all_12_1)
% 227.83/39.45  | | | | | | 
% 227.83/39.45  | | | | | | REF_CLOSE: (3), (8), (14), (57) are inconsistent by sub-proof #1148.
% 227.83/39.45  | | | | | | 
% 227.83/39.45  | | | | | End of split
% 227.83/39.45  | | | | | 
% 227.83/39.45  | | | | Case 2:
% 227.83/39.45  | | | | | 
% 227.83/39.45  | | | | |   (58)  all_55_1 = e1 | all_55_1 = e0
% 227.83/39.45  | | | | | 
% 227.83/39.45  | | | | | REF_CLOSE: (5), (23), (31), (58) are inconsistent by sub-proof #1447.
% 227.83/39.45  | | | | | 
% 227.83/39.45  | | | | End of split
% 227.83/39.45  | | | | 
% 227.83/39.45  | | | End of split
% 227.83/39.45  | | | 
% 227.83/39.45  | | Case 2:
% 227.83/39.45  | | | 
% 227.83/39.45  | | |   (59)  all_55_3 = e0
% 227.83/39.45  | | | 
% 227.83/39.45  | | | REF_CLOSE: (9), (21), (59) are inconsistent by sub-proof #376.
% 227.83/39.45  | | | 
% 227.83/39.45  | | End of split
% 227.83/39.45  | | 
% 227.83/39.45  | Case 2:
% 227.83/39.45  | | 
% 227.83/39.45  | |   (60)   ~ (all_38_1 = e3) & op(e1, e2) = all_38_1 & $i(all_38_1)
% 227.83/39.45  | | 
% 227.83/39.45  | | REF_CLOSE: (3), (4), (60) are inconsistent by sub-proof #1444.
% 227.83/39.45  | | 
% 227.83/39.45  | End of split
% 227.83/39.45  | 
% 227.83/39.45  End of proof
% 227.83/39.45  
% 227.83/39.45  Sub-proof #375 shows that the following formulas are inconsistent:
% 227.83/39.45  ----------------------------------------------------------------
% 227.83/39.45    (1)  all_57_9 = e2
% 227.83/39.45    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 227.83/39.45         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 227.83/39.45    (3)   ~ (e3 = e1)
% 227.83/39.45    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.83/39.45           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.83/39.45    (5)   ~ (all_6_2 = e3)
% 227.83/39.45    (6)  op(e1, e1) = all_6_2
% 227.83/39.45    (7)  all_57_3 = e0
% 227.83/39.45    (8)   ~ (e3 = e2)
% 227.83/39.45    (9)   ~ (e3 = e0)
% 227.83/39.45    (10)  all_57_11 = e1 & op(e1, e0) = e1
% 227.83/39.45    (11)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 227.83/39.45          | (all_57_14 = e0 & op(e0, e1) = e0)
% 227.83/39.45    (12)  all_57_15 = e3
% 227.83/39.45    (13)  all_57_4 = e1
% 227.83/39.45    (14)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 227.83/39.45          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 227.83/39.45            e1)
% 227.83/39.45    (15)  all_57_11 = e0
% 227.83/39.45    (16)   ~ (e2 = e0)
% 227.83/39.45    (17)   ~ (e1 = e0)
% 227.83/39.45    (18)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 227.83/39.45          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 227.83/39.45    (19)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.83/39.45          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 227.83/39.45            e2)
% 227.83/39.45    (20)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 227.83/39.45          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 227.83/39.45    (21)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) |
% 227.83/39.45          (all_57_11 = e0 & op(e1, e0) = e0)
% 227.83/39.45    (22)   ~ (e2 = e1)
% 227.83/39.45  
% 227.83/39.45  Begin of proof
% 227.83/39.45  | 
% 227.83/39.45  | ALPHA: (10) implies:
% 227.83/39.45  |   (23)  all_57_11 = e1
% 227.83/39.45  | 
% 227.83/39.45  | COMBINE_EQS: (15), (23) imply:
% 227.83/39.45  |   (24)  e1 = e0
% 227.83/39.45  | 
% 227.83/39.45  | SIMP: (24) implies:
% 227.83/39.45  |   (25)  e1 = e0
% 227.83/39.45  | 
% 227.83/39.45  | COMBINE_EQS: (13), (25) imply:
% 227.83/39.45  |   (26)  all_57_4 = e0
% 227.83/39.45  | 
% 227.83/39.45  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (14),
% 227.83/39.45  |            (16), (17), (18), (19), (20), (21), (22), (23), (26) are
% 227.83/39.45  |            inconsistent by sub-proof #1042.
% 227.83/39.45  | 
% 227.83/39.45  End of proof
% 227.83/39.45  
% 227.83/39.45  Sub-proof #376 shows that the following formulas are inconsistent:
% 227.83/39.45  ----------------------------------------------------------------
% 227.83/39.45    (1)  all_55_3 = all_52_7
% 227.83/39.45    (2)  all_55_3 = e0
% 227.83/39.45    (3)   ~ (all_52_7 = e0)
% 227.83/39.45  
% 227.83/39.45  Begin of proof
% 227.83/39.45  | 
% 227.83/39.45  | COMBINE_EQS: (1), (2) imply:
% 227.83/39.45  |   (4)  all_52_7 = e0
% 227.83/39.45  | 
% 227.83/39.45  | SIMP: (4) implies:
% 227.83/39.45  |   (5)  all_52_7 = e0
% 227.83/39.45  | 
% 227.83/39.45  | REDUCE: (3), (5) imply:
% 227.83/39.45  |   (6)  $false
% 227.83/39.45  | 
% 227.83/39.45  | CLOSE: (6) is inconsistent.
% 227.83/39.45  | 
% 227.83/39.45  End of proof
% 227.83/39.45  
% 227.83/39.45  Sub-proof #377 shows that the following formulas are inconsistent:
% 227.83/39.45  ----------------------------------------------------------------
% 227.83/39.45    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 227.83/39.45         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 227.83/39.45    (2)   ~ (e3 = e1)
% 227.83/39.45    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.83/39.45           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.83/39.45    (4)   ~ (all_6_2 = e3)
% 227.83/39.45    (5)  op(e1, e1) = all_6_2
% 227.83/39.45    (6)  all_57_3 = e0
% 227.83/39.45    (7)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 227.83/39.45         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 227.83/39.45    (8)   ~ (e3 = e2)
% 227.83/39.45    (9)   ~ (e3 = e0)
% 227.83/39.45    (10)  all_57_15 = e3
% 227.83/39.45    (11)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 227.83/39.45          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 227.83/39.45            e1)
% 227.83/39.45    (12)  all_57_10 = e2
% 227.83/39.45    (13)   ~ (e2 = e0)
% 227.83/39.45    (14)  all_57_2 = e3
% 227.83/39.45    (15)   ~ (e1 = e0)
% 227.83/39.45    (16)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 227.83/39.45          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 227.83/39.45    (17)  all_57_8 = e2
% 227.83/39.45    (18)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.83/39.45          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 227.83/39.45            e2)
% 227.83/39.45    (19)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 227.83/39.45              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 227.83/39.45                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 227.83/39.45                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 227.83/39.45    (20)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 227.83/39.45          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 227.83/39.45    (21)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 227.83/39.45          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 227.83/39.45    (22)   ~ (e2 = e1)
% 227.83/39.45    (23)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 227.83/39.45  
% 227.83/39.45  Begin of proof
% 227.83/39.45  | 
% 227.83/39.45  | BETA: splitting (23) gives:
% 227.83/39.45  | 
% 227.83/39.45  | Case 1:
% 227.83/39.45  | | 
% 227.83/39.45  | |   (24)  all_57_8 = e1 & op(e1, e1) = e1
% 227.83/39.45  | | 
% 227.83/39.45  | | REF_CLOSE: (17), (22), (24) are inconsistent by sub-proof #1533.
% 227.83/39.45  | | 
% 227.83/39.45  | Case 2:
% 227.83/39.45  | | 
% 227.83/39.45  | |   (25)  all_57_14 = e1 & op(e0, e1) = e1
% 227.83/39.45  | | 
% 227.83/39.45  | | ALPHA: (25) implies:
% 227.83/39.45  | |   (26)  all_57_14 = e1
% 227.83/39.45  | | 
% 227.83/39.45  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 227.83/39.45  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (26)
% 227.83/39.45  | |            are inconsistent by sub-proof #745.
% 227.83/39.45  | | 
% 227.83/39.45  | End of split
% 227.83/39.45  | 
% 227.83/39.45  End of proof
% 227.83/39.45  
% 227.83/39.45  Sub-proof #378 shows that the following formulas are inconsistent:
% 227.83/39.45  ----------------------------------------------------------------
% 227.83/39.45    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 227.83/39.45    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 227.83/39.45    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 227.83/39.45         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 227.83/39.45    (4)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 227.83/39.45    (5)  all_57_13 = e1
% 227.83/39.45    (6)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 227.83/39.45         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 227.83/39.45    (7)   ~ (all_53_8 = all_53_12)
% 227.83/39.45    (8)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 227.83/39.45         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.83/39.45    (9)   ~ (e3 = e1)
% 227.83/39.45    (10)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 227.83/39.45          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 227.83/39.45    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.83/39.45            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.83/39.45    (12)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 227.83/39.45          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 227.83/39.45    (13)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 227.83/39.45            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 227.83/39.45              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 227.83/39.45    (14)   ~ (all_6_2 = e3)
% 227.83/39.45    (15)  op(e1, e1) = all_6_2
% 227.83/39.45    (16)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 227.83/39.45    (17)   ~ (all_53_9 = e0)
% 227.83/39.45    (18)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 227.83/39.45          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 227.83/39.45    (19)   ~ (all_53_4 = all_53_12)
% 227.83/39.45    (20)   ~ (all_53_8 = all_53_9)
% 227.83/39.45    (21)  all_42_2 = all_6_2
% 227.83/39.45    (22)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 227.83/39.45          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 227.83/39.45    (23)   ~ (all_53_9 = all_6_2)
% 227.83/39.45    (24)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 227.83/39.45          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 227.83/39.45    (25)  all_57_3 = e0
% 227.83/39.45    (26)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 227.83/39.45          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 227.83/39.45    (27)  all_57_4 = e3
% 227.83/39.45    (28)   ~ (e3 = e2)
% 227.92/39.45    (29)  all_55_1 = all_53_4
% 227.92/39.45    (30)   ~ (e3 = e0)
% 227.92/39.45    (31)  all_57_1 = e2
% 227.92/39.45    (32)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 227.92/39.45          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 227.92/39.45    (33)   ~ (all_53_8 = all_6_2)
% 227.92/39.45    (34)  all_57_0 = e0
% 227.92/39.45    (35)  all_55_2 = all_53_8
% 227.92/39.45    (36)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 227.92/39.45    (37)  all_57_15 = e3
% 227.92/39.45    (38)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 227.92/39.45          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 227.92/39.45            e1)
% 227.92/39.45    (39)  all_57_10 = e2
% 227.92/39.45    (40)  all_57_11 = e0
% 227.92/39.45    (41)   ~ (all_53_4 = all_53_8)
% 227.92/39.45    (42)  op(e3, e2) = all_53_4
% 227.92/39.45    (43)   ~ (e2 = e0)
% 227.92/39.45    (44)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 227.92/39.45            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 227.92/39.45            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 227.92/39.45            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 227.92/39.45              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 227.92/39.45            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 227.92/39.45            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 227.92/39.45              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 227.92/39.45              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 227.92/39.45            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 227.92/39.45            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 227.92/39.45            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 227.92/39.45              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 227.92/39.45              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 227.92/39.45            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 227.92/39.45              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 227.92/39.45            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 227.92/39.45            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 227.92/39.45              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 227.92/39.45              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 227.92/39.45            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 227.92/39.45            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 227.92/39.45    (45)  all_57_2 = e3
% 227.92/39.45    (46)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 227.92/39.45          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 227.92/39.45    (47)   ~ (e1 = e0)
% 227.92/39.45    (48)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 227.92/39.45            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 227.92/39.45              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 227.92/39.45    (49)   ~ (all_53_4 = e0)
% 227.92/39.45    (50)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 227.92/39.45          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 227.92/39.45    (51)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 227.92/39.45          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 227.92/39.45    (52)  op(e0, e0) = e3
% 227.92/39.45    (53)   ~ (all_53_4 = all_53_6)
% 227.92/39.45    (54)  all_57_5 = e1
% 227.92/39.45    (55)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.92/39.45          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 227.92/39.45            e2)
% 227.92/39.45    (56)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 227.92/39.45              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 227.92/39.45                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 227.92/39.45                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 227.92/39.45    (57)  all_55_10 = all_6_2
% 227.92/39.45    (58)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 227.92/39.45          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 227.92/39.45    (59)  all_38_2 = all_6_2
% 227.92/39.45    (60)  all_55_3 = all_53_12
% 227.92/39.45    (61)   ~ (all_53_12 = e3)
% 227.92/39.45    (62)  all_57_7 = e3
% 227.92/39.45    (63)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 227.92/39.45            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 227.92/39.45              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 227.92/39.45    (64)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 227.92/39.45          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 227.92/39.45    (65)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 227.92/39.45          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 227.92/39.45    (66)   ~ (e2 = e1)
% 227.92/39.45    (67)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 227.92/39.45          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 227.92/39.45    (68)  op(e2, e1) = all_53_9
% 227.92/39.45    (69)  op(e1, e2) = all_53_6
% 227.92/39.45    (70)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 227.92/39.45          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 227.92/39.45    (71)  all_24_2 = all_6_2
% 227.92/39.45    (72)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 227.92/39.45          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 227.92/39.45    (73)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 227.92/39.45          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 227.92/39.45    (74)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 227.92/39.45          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 227.92/39.45    (75)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 227.92/39.45          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 227.92/39.45    (76)  op(e3, e1) = all_53_8
% 227.92/39.45    (77)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 227.92/39.45          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 227.92/39.45    (78)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 227.92/39.45          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 227.92/39.45    (79)  op(e3, e0) = all_53_12
% 227.92/39.45  
% 227.92/39.45  Begin of proof
% 227.92/39.45  | 
% 227.92/39.45  | BETA: splitting (4) gives:
% 227.92/39.45  | 
% 227.92/39.45  | Case 1:
% 227.92/39.45  | | 
% 227.92/39.45  | |   (80)  all_57_8 = e1 & op(e1, e1) = e1
% 227.92/39.45  | | 
% 227.92/39.45  | | ALPHA: (80) implies:
% 227.92/39.45  | |   (81)  all_57_8 = e1
% 227.92/39.45  | | 
% 227.92/39.45  | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (9), (10), (11), (12), (13), (14),
% 227.92/39.45  | |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 227.92/39.45  | |            (26), (27), (28), (29), (30), (32), (33), (34), (35), (36), (37),
% 227.92/39.45  | |            (38), (39), (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 227.92/39.45  | |            (49), (50), (51), (52), (53), (55), (56), (57), (58), (59), (60),
% 227.92/39.45  | |            (61), (62), (63), (64), (65), (66), (67), (68), (69), (70), (71),
% 227.92/39.45  | |            (72), (73), (74), (75), (76), (77), (78), (79), (81) are
% 227.92/39.45  | |            inconsistent by sub-proof #425.
% 227.92/39.45  | | 
% 227.92/39.45  | Case 2:
% 227.92/39.45  | | 
% 227.92/39.45  | |   (82)  all_57_11 = e1 & op(e1, e0) = e1
% 227.92/39.45  | | 
% 227.92/39.45  | | ALPHA: (82) implies:
% 227.92/39.45  | |   (83)  all_57_11 = e1
% 227.92/39.45  | | 
% 227.92/39.45  | | COMBINE_EQS: (40), (83) imply:
% 227.92/39.45  | |   (84)  e1 = e0
% 227.92/39.45  | | 
% 227.92/39.45  | | SIMP: (84) implies:
% 227.92/39.45  | |   (85)  e1 = e0
% 227.92/39.45  | | 
% 227.92/39.45  | | COMBINE_EQS: (54), (85) imply:
% 227.92/39.45  | |   (86)  all_57_5 = e0
% 227.92/39.45  | | 
% 227.92/39.45  | | REF_CLOSE: (3), (5), (8), (9), (25), (28), (31), (43), (45), (47), (62),
% 227.92/39.45  | |            (64), (66), (86) are inconsistent by sub-proof #571.
% 227.92/39.45  | | 
% 227.92/39.45  | End of split
% 227.92/39.45  | 
% 227.92/39.45  End of proof
% 227.92/39.45  
% 227.92/39.45  Sub-proof #379 shows that the following formulas are inconsistent:
% 227.92/39.45  ----------------------------------------------------------------
% 227.92/39.45    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 227.92/39.45         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 227.92/39.45    (2)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3)
% 227.92/39.45    (3)   ~ (e3 = e1)
% 227.92/39.45    (4)  all_57_3 = e0
% 227.92/39.45    (5)   ~ (e3 = e2)
% 227.92/39.45    (6)   ~ (e3 = e0)
% 227.92/39.45    (7)  all_57_1 = e2
% 227.92/39.45    (8)   ~ (e2 = e0)
% 227.92/39.45    (9)  all_57_2 = e3
% 227.92/39.45    (10)   ~ (e1 = e0)
% 227.92/39.45    (11)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 227.92/39.45          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 227.92/39.45    (12)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 227.92/39.45          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 227.92/39.45    (13)   ~ (e2 = e1)
% 227.92/39.45  
% 227.92/39.45  Begin of proof
% 227.92/39.45  | 
% 227.92/39.45  | BETA: splitting (2) gives:
% 227.92/39.45  | 
% 227.92/39.45  | Case 1:
% 227.92/39.45  | | 
% 227.92/39.45  | |   (14)  all_57_1 = e3 & op(e3, e2) = e3
% 227.92/39.45  | | 
% 227.92/39.45  | | REF_CLOSE: (5), (7), (14) are inconsistent by sub-proof #1664.
% 227.92/39.45  | | 
% 227.92/39.45  | Case 2:
% 227.92/39.45  | | 
% 227.92/39.45  | |   (15)  all_57_3 = e3 & op(e2, e2) = e3
% 227.92/39.45  | | 
% 227.92/39.45  | | ALPHA: (15) implies:
% 227.92/39.45  | |   (16)  all_57_3 = e3
% 227.92/39.45  | | 
% 227.92/39.45  | | COMBINE_EQS: (4), (16) imply:
% 227.92/39.45  | |   (17)  e3 = e0
% 227.92/39.45  | | 
% 227.92/39.45  | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13), (17)
% 227.92/39.45  | |            are inconsistent by sub-proof #1333.
% 227.92/39.45  | | 
% 227.92/39.45  | End of split
% 227.92/39.45  | 
% 227.92/39.45  End of proof
% 227.92/39.45  
% 227.92/39.45  Sub-proof #380 shows that the following formulas are inconsistent:
% 227.92/39.45  ----------------------------------------------------------------
% 227.92/39.45    (1)   ~ (e3 = e1)
% 227.92/39.45    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.92/39.45           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.92/39.45    (3)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 227.92/39.45         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 227.92/39.45    (4)   ~ (all_6_2 = e3)
% 227.92/39.45    (5)  op(e1, e1) = all_6_2
% 227.92/39.45    (6)  all_57_7 = e2
% 227.92/39.45    (7)  all_57_3 = e0
% 227.92/39.45    (8)   ~ (e3 = e2)
% 227.92/39.45    (9)   ~ (e3 = e0)
% 227.92/39.45    (10)  all_57_15 = e3
% 227.92/39.45    (11)   ~ (e2 = e0)
% 227.92/39.45    (12)  all_57_3 = e3 & op(e2, e2) = e3
% 227.92/39.45    (13)   ~ (e1 = e0)
% 227.92/39.45    (14)  all_57_6 = e3
% 227.92/39.45    (15)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 227.92/39.45              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 227.92/39.45                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 227.92/39.45                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 227.92/39.45    (16)   ~ (e2 = e1)
% 227.92/39.46    (17)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 227.92/39.46          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 227.92/39.46    (18)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 227.92/39.46          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 227.92/39.46  
% 227.92/39.46  Begin of proof
% 227.92/39.46  | 
% 227.92/39.46  | ALPHA: (12) implies:
% 227.92/39.46  |   (19)  all_57_3 = e3
% 227.92/39.46  | 
% 227.92/39.46  | COMBINE_EQS: (7), (19) imply:
% 227.92/39.46  |   (20)  e3 = e0
% 227.92/39.46  | 
% 227.92/39.46  | SIMP: (20) implies:
% 227.92/39.46  |   (21)  e3 = e0
% 227.92/39.46  | 
% 227.92/39.46  | COMBINE_EQS: (14), (21) imply:
% 227.92/39.46  |   (22)  all_57_6 = e0
% 227.92/39.46  | 
% 227.92/39.46  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (13), (15),
% 227.92/39.46  |            (16), (17), (18), (22) are inconsistent by sub-proof #1775.
% 227.92/39.46  | 
% 227.92/39.46  End of proof
% 227.92/39.46  
% 227.92/39.46  Sub-proof #381 shows that the following formulas are inconsistent:
% 227.92/39.46  ----------------------------------------------------------------
% 227.92/39.46    (1)  all_57_13 = e1
% 227.92/39.46    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 227.92/39.46         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.92/39.46    (3)   ~ (e3 = e1)
% 227.92/39.46    (4)  all_57_0 = e1 & op(e3, e3) = e1
% 227.92/39.46    (5)  all_57_3 = e0
% 227.92/39.46    (6)   ~ (e3 = e2)
% 227.92/39.46    (7)  all_57_0 = e0
% 227.92/39.46    (8)   ~ (e2 = e0)
% 227.92/39.46    (9)   ~ (e1 = e0)
% 227.92/39.46    (10)  all_57_1 = e3
% 227.92/39.46    (11)   ~ (e2 = e1)
% 227.92/39.46    (12)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 227.92/39.46          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 227.92/39.46  
% 227.92/39.46  Begin of proof
% 227.92/39.46  | 
% 227.92/39.46  | ALPHA: (4) implies:
% 227.92/39.46  |   (13)  all_57_0 = e1
% 227.92/39.46  | 
% 227.92/39.46  | COMBINE_EQS: (7), (13) imply:
% 227.92/39.46  |   (14)  e1 = e0
% 227.92/39.46  | 
% 227.92/39.46  | SIMP: (14) implies:
% 227.92/39.46  |   (15)  e1 = e0
% 227.92/39.46  | 
% 227.92/39.46  | COMBINE_EQS: (1), (15) imply:
% 227.92/39.46  |   (16)  all_57_13 = e0
% 227.92/39.46  | 
% 227.92/39.46  | REF_CLOSE: (2), (3), (5), (6), (8), (9), (10), (11), (12), (16) are
% 227.92/39.46  |            inconsistent by sub-proof #1758.
% 227.92/39.46  | 
% 227.92/39.46  End of proof
% 227.92/39.46  
% 227.92/39.46  Sub-proof #382 shows that the following formulas are inconsistent:
% 227.92/39.46  ----------------------------------------------------------------
% 227.92/39.46    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 227.92/39.46         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 227.92/39.46    (2)   ~ (e3 = e1)
% 227.92/39.46    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.92/39.46           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.92/39.46    (4)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 227.92/39.46         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 227.92/39.46    (5)   ~ (all_6_2 = e3)
% 227.92/39.46    (6)  op(e1, e1) = all_6_2
% 227.92/39.46    (7)  all_57_3 = e0
% 227.92/39.46    (8)   ~ (e3 = e2)
% 227.92/39.46    (9)   ~ (e3 = e0)
% 227.92/39.46    (10)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 227.92/39.46          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 227.92/39.46    (11)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 227.92/39.46          | (all_57_14 = e0 & op(e0, e1) = e0)
% 227.92/39.46    (12)  all_57_15 = e3
% 227.92/39.46    (13)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 227.92/39.46          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 227.92/39.46            e1)
% 227.92/39.46    (14)  all_57_6 = e2
% 227.92/39.46    (15)  all_57_11 = e0
% 227.92/39.46    (16)   ~ (e2 = e0)
% 227.92/39.46    (17)  all_57_2 = e3
% 227.92/39.46    (18)   ~ (e1 = e0)
% 227.92/39.46    (19)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 227.92/39.46          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 227.92/39.46    (20)  all_57_8 = e2
% 227.92/39.46    (21)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.92/39.46          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 227.92/39.46            e2)
% 227.92/39.46    (22)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 227.92/39.46              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 227.92/39.46                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 227.92/39.46                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 227.92/39.46    (23)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 227.92/39.46          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 227.92/39.46    (24)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) |
% 227.92/39.46          (all_57_11 = e0 & op(e1, e0) = e0)
% 227.92/39.46    (25)   ~ (e2 = e1)
% 227.92/39.46    (26)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 227.92/39.46          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 227.92/39.46    (27)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 227.92/39.46          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 227.92/39.46    (28)  all_57_14 = e0
% 227.92/39.46    (29)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 227.92/39.46          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 227.92/39.46  
% 227.92/39.46  Begin of proof
% 227.92/39.46  | 
% 227.92/39.46  | BETA: splitting (19) gives:
% 227.92/39.46  | 
% 227.92/39.46  | Case 1:
% 227.92/39.46  | | 
% 227.92/39.46  | |   (30)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) =
% 227.92/39.46  | |           e3)
% 227.92/39.46  | | 
% 227.92/39.46  | | BETA: splitting (30) gives:
% 227.92/39.46  | | 
% 227.92/39.46  | | Case 1:
% 227.92/39.46  | | | 
% 227.92/39.46  | | |   (31)  all_57_4 = e3 & op(e3, e1) = e3
% 227.92/39.46  | | | 
% 227.92/39.46  | | | ALPHA: (31) implies:
% 227.92/39.46  | | |   (32)  all_57_4 = e3
% 227.92/39.46  | | | 
% 227.92/39.46  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 227.92/39.46  | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 227.92/39.46  | | |            (24), (25), (26), (27), (28), (29), (32) are inconsistent by
% 227.92/39.46  | | |            sub-proof #383.
% 227.92/39.46  | | | 
% 227.92/39.46  | | Case 2:
% 227.92/39.46  | | | 
% 227.92/39.46  | | |   (33)  all_57_5 = e3 & op(e2, e1) = e3
% 227.92/39.46  | | | 
% 227.92/39.46  | | | ALPHA: (33) implies:
% 227.92/39.46  | | |   (34)  all_57_5 = e3
% 227.92/39.46  | | | 
% 227.92/39.46  | | | REF_CLOSE: (1), (2), (7), (8), (16), (17), (18), (23), (25), (34) are
% 227.92/39.46  | | |            inconsistent by sub-proof #1802.
% 227.92/39.46  | | | 
% 227.92/39.46  | | End of split
% 227.92/39.46  | | 
% 227.92/39.46  | Case 2:
% 227.92/39.46  | | 
% 227.92/39.46  | |   (35)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) =
% 227.92/39.46  | |           e3)
% 227.92/39.46  | | 
% 227.92/39.46  | | REF_CLOSE: (2), (3), (5), (6), (8), (9), (11), (12), (13), (16), (18), (21),
% 227.92/39.46  | |            (25), (35) are inconsistent by sub-proof #1044.
% 227.92/39.46  | | 
% 227.92/39.46  | End of split
% 227.92/39.46  | 
% 227.92/39.46  End of proof
% 227.92/39.46  
% 227.92/39.46  Sub-proof #383 shows that the following formulas are inconsistent:
% 227.92/39.46  ----------------------------------------------------------------
% 227.92/39.46    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 227.92/39.46         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 227.92/39.46    (2)   ~ (e3 = e1)
% 227.92/39.46    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.92/39.46           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.92/39.46    (4)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 227.92/39.46         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 227.92/39.46    (5)   ~ (all_6_2 = e3)
% 227.92/39.46    (6)  op(e1, e1) = all_6_2
% 227.92/39.46    (7)  all_57_3 = e0
% 227.92/39.46    (8)  all_57_4 = e3
% 227.92/39.46    (9)   ~ (e3 = e2)
% 227.92/39.46    (10)   ~ (e3 = e0)
% 227.92/39.46    (11)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 227.92/39.46          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 227.92/39.46    (12)  all_57_15 = e3
% 227.92/39.46    (13)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 227.92/39.46          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 227.92/39.46            e1)
% 227.92/39.46    (14)  all_57_6 = e2
% 227.92/39.46    (15)  all_57_11 = e0
% 227.92/39.46    (16)   ~ (e2 = e0)
% 227.92/39.46    (17)  all_57_2 = e3
% 227.92/39.46    (18)   ~ (e1 = e0)
% 227.92/39.46    (19)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 227.92/39.46          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 227.92/39.46    (20)  all_57_8 = e2
% 227.92/39.46    (21)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.92/39.46          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 227.92/39.46            e2)
% 227.92/39.46    (22)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 227.92/39.46              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 227.92/39.46                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 227.92/39.46                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 227.92/39.46    (23)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 227.92/39.46          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 227.92/39.46    (24)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) |
% 227.92/39.46          (all_57_11 = e0 & op(e1, e0) = e0)
% 227.92/39.46    (25)   ~ (e2 = e1)
% 227.92/39.46    (26)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 227.92/39.46          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 227.92/39.46    (27)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 227.92/39.46          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 227.92/39.46    (28)  all_57_14 = e0
% 227.92/39.46    (29)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 227.92/39.46          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 227.92/39.46  
% 227.92/39.46  Begin of proof
% 227.92/39.46  | 
% 227.92/39.46  | BETA: splitting (29) gives:
% 227.92/39.46  | 
% 227.92/39.46  | Case 1:
% 227.92/39.46  | | 
% 227.92/39.46  | |   (30)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) =
% 227.92/39.46  | |           e1)
% 227.92/39.46  | | 
% 227.92/39.46  | | BETA: splitting (30) gives:
% 227.92/39.46  | | 
% 227.92/39.46  | | Case 1:
% 227.92/39.46  | | | 
% 227.92/39.46  | | |   (31)  all_57_6 = e1 & op(e1, e3) = e1
% 227.92/39.46  | | | 
% 227.92/39.46  | | | REF_CLOSE: (14), (25), (31) are inconsistent by sub-proof #2389.
% 227.92/39.46  | | | 
% 227.92/39.46  | | Case 2:
% 227.92/39.46  | | | 
% 227.92/39.46  | | |   (32)  all_57_7 = e1 & op(e1, e2) = e1
% 227.92/39.46  | | | 
% 227.92/39.46  | | | ALPHA: (32) implies:
% 227.92/39.46  | | |   (33)  all_57_7 = e1
% 227.92/39.46  | | | 
% 227.92/39.46  | | | BETA: splitting (23) gives:
% 227.92/39.46  | | | 
% 227.92/39.46  | | | Case 1:
% 227.92/39.46  | | | | 
% 227.92/39.46  | | | |   (34)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2)
% 227.92/39.46  | | | |           = e2)
% 227.92/39.46  | | | | 
% 227.92/39.46  | | | | BETA: splitting (34) gives:
% 227.92/39.46  | | | | 
% 227.92/39.46  | | | | Case 1:
% 227.92/39.46  | | | | | 
% 227.92/39.46  | | | | |   (35)  all_57_2 = e2 & op(e2, e3) = e2
% 227.92/39.46  | | | | | 
% 227.92/39.46  | | | | | REF_CLOSE: (9), (17), (35) are inconsistent by sub-proof #1925.
% 227.92/39.46  | | | | | 
% 227.92/39.46  | | | | Case 2:
% 227.92/39.46  | | | | | 
% 227.92/39.46  | | | | |   (36)  all_57_3 = e2 & op(e2, e2) = e2
% 227.92/39.46  | | | | | 
% 227.92/39.46  | | | | | REF_CLOSE: (7), (16), (36) are inconsistent by sub-proof #2256.
% 227.92/39.46  | | | | | 
% 227.92/39.46  | | | | End of split
% 227.92/39.46  | | | | 
% 227.92/39.46  | | | Case 2:
% 227.92/39.46  | | | | 
% 227.92/39.46  | | | |   (37)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0)
% 227.92/39.46  | | | |           = e2)
% 227.92/39.46  | | | | 
% 227.92/39.46  | | | | BETA: splitting (37) gives:
% 227.92/39.46  | | | | 
% 227.92/39.46  | | | | Case 1:
% 227.92/39.46  | | | | | 
% 227.92/39.46  | | | | |   (38)  all_57_5 = e2 & op(e2, e1) = e2
% 227.92/39.46  | | | | | 
% 227.92/39.46  | | | | | ALPHA: (38) implies:
% 227.92/39.46  | | | | |   (39)  all_57_5 = e2
% 227.92/39.46  | | | | | 
% 227.92/39.46  | | | | | REF_CLOSE: (2), (8), (11), (18), (20), (25), (28), (39) are
% 227.92/39.46  | | | | |            inconsistent by sub-proof #925.
% 227.92/39.46  | | | | | 
% 227.92/39.46  | | | | Case 2:
% 227.92/39.46  | | | | | 
% 227.92/39.46  | | | | |   (40)  all_57_10 = e2 & op(e2, e0) = e2
% 227.92/39.46  | | | | | 
% 227.92/39.46  | | | | | ALPHA: (40) implies:
% 227.92/39.46  | | | | |   (41)  all_57_10 = e2
% 227.92/39.46  | | | | | 
% 227.92/39.46  | | | | | BETA: splitting (4) gives:
% 227.92/39.46  | | | | | 
% 227.92/39.46  | | | | | Case 1:
% 227.92/39.46  | | | | | | 
% 227.92/39.46  | | | | | |   (42)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1,
% 227.92/39.46  | | | | | |             e2) = e3)
% 227.92/39.46  | | | | | | 
% 227.92/39.46  | | | | | | BETA: splitting (42) gives:
% 227.92/39.46  | | | | | | 
% 227.92/39.46  | | | | | | Case 1:
% 227.92/39.46  | | | | | | | 
% 227.92/39.46  | | | | | | |   (43)  all_57_6 = e3 & op(e1, e3) = e3
% 227.92/39.46  | | | | | | | 
% 227.92/39.46  | | | | | | | REF_CLOSE: (9), (14), (43) are inconsistent by sub-proof #1558.
% 227.92/39.46  | | | | | | | 
% 227.92/39.46  | | | | | | Case 2:
% 227.92/39.46  | | | | | | | 
% 227.92/39.46  | | | | | | |   (44)  all_57_7 = e3 & op(e1, e2) = e3
% 227.92/39.46  | | | | | | | 
% 227.92/39.46  | | | | | | | ALPHA: (44) implies:
% 227.92/39.46  | | | | | | |   (45)  all_57_7 = e3
% 227.92/39.46  | | | | | | | 
% 227.92/39.46  | | | | | | | COMBINE_EQS: (33), (45) imply:
% 227.92/39.46  | | | | | | |   (46)  e3 = e1
% 227.92/39.46  | | | | | | | 
% 227.92/39.46  | | | | | | | COMBINE_EQS: (8), (46) imply:
% 227.92/39.46  | | | | | | |   (47)  all_57_4 = e1
% 227.92/39.46  | | | | | | | 
% 227.92/39.46  | | | | | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (9), (10), (12), (13),
% 227.92/39.46  | | | | | | |            (16), (17), (18), (19), (21), (22), (25), (41), (47)
% 227.92/39.46  | | | | | | |            are inconsistent by sub-proof #1755.
% 227.92/39.46  | | | | | | | 
% 227.92/39.46  | | | | | | End of split
% 227.92/39.46  | | | | | | 
% 227.92/39.46  | | | | | Case 2:
% 227.92/39.46  | | | | | | 
% 227.92/39.46  | | | | | |   (48)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1,
% 227.92/39.46  | | | | | |             e0) = e3)
% 227.92/39.46  | | | | | | 
% 227.92/39.46  | | | | | | REF_CLOSE: (2), (3), (5), (6), (9), (10), (12), (16), (18), (24),
% 227.92/39.46  | | | | | |            (25), (26), (27), (48) are inconsistent by sub-proof
% 227.92/39.46  | | | | | |            #1080.
% 227.92/39.46  | | | | | | 
% 227.92/39.46  | | | | | End of split
% 227.92/39.46  | | | | | 
% 227.92/39.46  | | | | End of split
% 227.92/39.46  | | | | 
% 227.92/39.46  | | | End of split
% 227.92/39.46  | | | 
% 227.92/39.46  | | End of split
% 227.92/39.46  | | 
% 227.92/39.46  | Case 2:
% 227.92/39.46  | | 
% 227.92/39.46  | |   (49)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) =
% 227.92/39.46  | |           e1)
% 227.92/39.46  | | 
% 227.92/39.46  | | BETA: splitting (49) gives:
% 227.92/39.46  | | 
% 227.92/39.46  | | Case 1:
% 227.92/39.46  | | | 
% 227.92/39.46  | | |   (50)  all_57_8 = e1 & op(e1, e1) = e1
% 227.92/39.46  | | | 
% 227.92/39.46  | | | ALPHA: (50) implies:
% 227.92/39.46  | | |   (51)  all_57_8 = e1
% 227.92/39.46  | | | 
% 227.92/39.46  | | | REF_CLOSE: (20), (25), (51) are inconsistent by sub-proof #1485.
% 227.92/39.46  | | | 
% 227.92/39.46  | | Case 2:
% 227.92/39.46  | | | 
% 227.92/39.46  | | |   (52)  all_57_11 = e1 & op(e1, e0) = e1
% 227.92/39.46  | | | 
% 227.92/39.46  | | | REF_CLOSE: (15), (18), (52) are inconsistent by sub-proof #1750.
% 227.92/39.46  | | | 
% 227.92/39.46  | | End of split
% 227.92/39.46  | | 
% 227.92/39.46  | End of split
% 227.92/39.46  | 
% 227.92/39.46  End of proof
% 227.92/39.46  
% 227.92/39.46  Sub-proof #384 shows that the following formulas are inconsistent:
% 227.92/39.46  ----------------------------------------------------------------
% 227.92/39.46    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 227.92/39.46    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 227.92/39.46    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 227.92/39.46         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 227.92/39.46    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 227.92/39.46         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 227.92/39.46    (5)   ~ (all_53_8 = all_53_12)
% 227.92/39.46    (6)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 227.92/39.46         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.92/39.46    (7)   ~ (e3 = e1)
% 227.92/39.46    (8)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 227.92/39.46         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 227.92/39.46    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.92/39.46           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.92/39.46    (10)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 227.92/39.46          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 227.92/39.46    (11)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 227.92/39.46            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 227.92/39.46              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 227.92/39.46    (12)   ~ (all_6_2 = e3)
% 227.92/39.46    (13)  op(e1, e1) = all_6_2
% 227.92/39.46    (14)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 227.92/39.46    (15)   ~ (all_53_9 = e0)
% 227.92/39.46    (16)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 227.92/39.46          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 227.92/39.46    (17)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3)
% 227.92/39.46    (18)   ~ (all_53_4 = all_53_12)
% 227.92/39.46    (19)   ~ (all_53_8 = all_53_9)
% 227.92/39.46    (20)  all_42_2 = all_6_2
% 227.92/39.46    (21)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 227.92/39.46          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 227.92/39.46    (22)   ~ (all_53_9 = all_6_2)
% 227.92/39.46    (23)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 227.92/39.46          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 227.92/39.46    (24)  all_57_3 = e0
% 227.92/39.46    (25)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 227.92/39.46          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 227.92/39.46    (26)   ~ (e3 = e2)
% 227.92/39.46    (27)  all_55_1 = all_53_4
% 227.92/39.46    (28)   ~ (e3 = e0)
% 227.92/39.46    (29)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 227.92/39.46          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 227.92/39.46    (30)   ~ (all_53_8 = all_6_2)
% 227.92/39.46    (31)  all_55_2 = all_53_8
% 227.92/39.46    (32)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 227.92/39.46    (33)  all_57_15 = e3
% 227.92/39.46    (34)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 227.92/39.46          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 227.92/39.46            e1)
% 227.92/39.46    (35)  all_57_12 = e1
% 227.92/39.46    (36)   ~ (all_53_4 = all_53_8)
% 227.92/39.46    (37)  op(e3, e2) = all_53_4
% 227.92/39.46    (38)   ~ (e2 = e0)
% 227.92/39.46    (39)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 227.92/39.46            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 227.92/39.46            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 227.92/39.46            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 227.92/39.46              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 227.92/39.46            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 227.92/39.46            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 227.92/39.46              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 227.92/39.46              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 227.92/39.46            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 227.92/39.46            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 227.92/39.46            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 227.92/39.46              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 227.92/39.46              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 227.92/39.46            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 227.92/39.46              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 227.92/39.46            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 227.92/39.46            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 227.92/39.46              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 227.92/39.46              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 227.92/39.46            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 227.92/39.46            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 227.92/39.46    (40)  all_57_2 = e3
% 227.92/39.46    (41)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 227.92/39.46          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 227.92/39.46    (42)   ~ (e1 = e0)
% 227.92/39.46    (43)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 227.92/39.46            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 227.92/39.46              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 227.92/39.46    (44)   ~ (all_53_4 = e0)
% 227.92/39.46    (45)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 227.92/39.46          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 227.92/39.46    (46)  op(e0, e0) = e3
% 227.92/39.46    (47)   ~ (all_53_4 = all_53_6)
% 227.92/39.46    (48)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.92/39.46          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 227.92/39.46            e2)
% 227.92/39.46    (49)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 227.92/39.46              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 227.92/39.46                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 227.92/39.46                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 227.92/39.46    (50)  all_55_10 = all_6_2
% 227.92/39.46    (51)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 227.92/39.46          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 227.92/39.46    (52)  all_38_2 = all_6_2
% 227.92/39.46    (53)  all_55_3 = all_53_12
% 227.92/39.46    (54)   ~ (all_53_12 = e3)
% 227.92/39.46    (55)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 227.92/39.46            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 227.92/39.46              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 227.92/39.46    (56)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 227.92/39.46          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 227.92/39.46    (57)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) |
% 227.92/39.46          (all_57_11 = e0 & op(e1, e0) = e0)
% 227.92/39.46    (58)   ~ (e2 = e1)
% 227.92/39.46    (59)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 227.92/39.46          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 227.92/39.46    (60)  op(e2, e1) = all_53_9
% 227.92/39.46    (61)  op(e1, e2) = all_53_6
% 227.92/39.46    (62)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 227.92/39.46          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 227.92/39.46    (63)  all_24_2 = all_6_2
% 227.92/39.46    (64)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 227.92/39.46          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 227.92/39.46    (65)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 227.92/39.46          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 227.92/39.46    (66)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 227.92/39.46          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 227.92/39.46    (67)  all_57_14 = e0
% 227.92/39.46    (68)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 227.92/39.46          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 227.92/39.46    (69)  op(e3, e1) = all_53_8
% 227.92/39.46    (70)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 227.92/39.46          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 227.92/39.46    (71)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 227.92/39.46          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 227.92/39.46    (72)  op(e3, e0) = all_53_12
% 227.92/39.46  
% 227.92/39.46  Begin of proof
% 227.92/39.46  | 
% 227.92/39.46  | BETA: splitting (17) gives:
% 227.92/39.46  | 
% 227.92/39.46  | Case 1:
% 227.92/39.46  | | 
% 227.92/39.46  | |   (73)  all_57_0 = e3 & op(e3, e3) = e3
% 227.92/39.46  | | 
% 227.92/39.46  | | ALPHA: (73) implies:
% 227.92/39.46  | |   (74)  op(e3, e3) = e3
% 227.92/39.46  | | 
% 227.92/39.46  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 227.92/39.46  | |            (13), (14), (15), (16), (18), (19), (20), (21), (22), (23), (24),
% 227.92/39.46  | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (36),
% 227.92/39.46  | |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 227.92/39.46  | |            (48), (49), (50), (52), (53), (54), (55), (56), (58), (59), (60),
% 227.92/39.46  | |            (61), (62), (63), (64), (65), (66), (68), (69), (70), (71), (72),
% 227.92/39.46  | |            (74) are inconsistent by sub-proof #1437.
% 227.92/39.46  | | 
% 227.92/39.46  | Case 2:
% 227.92/39.46  | | 
% 227.92/39.46  | |   (75)  all_57_1 = e3 & op(e3, e2) = e3
% 227.92/39.46  | | 
% 227.92/39.46  | | ALPHA: (75) implies:
% 227.92/39.46  | |   (76)  all_57_1 = e3
% 227.92/39.46  | | 
% 227.92/39.47  | | REF_CLOSE: (3), (4), (6), (7), (9), (10), (12), (13), (24), (26), (28),
% 227.92/39.47  | |            (33), (35), (38), (40), (42), (48), (51), (56), (57), (58), (59),
% 227.92/39.47  | |            (62), (65), (66), (67), (70), (76) are inconsistent by sub-proof
% 227.92/39.47  | |            #417.
% 227.92/39.47  | | 
% 227.92/39.47  | End of split
% 227.92/39.47  | 
% 227.92/39.47  End of proof
% 227.92/39.47  
% 227.92/39.47  Sub-proof #385 shows that the following formulas are inconsistent:
% 227.92/39.47  ----------------------------------------------------------------
% 227.92/39.47    (1)  all_57_2 = e2
% 227.92/39.47    (2)  all_57_3 = e0
% 227.92/39.47    (3)   ~ (e3 = e2)
% 227.92/39.47    (4)   ~ (e2 = e0)
% 227.92/39.47    (5)  all_57_10 = e3
% 227.92/39.47    (6)  all_57_5 = e1
% 227.92/39.47    (7)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 227.92/39.47         (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 227.92/39.47    (8)   ~ (e2 = e1)
% 227.92/39.47    (9)  all_57_14 = e2 & op(e0, e1) = e2
% 227.92/39.47    (10)  all_57_14 = e0
% 227.92/39.47  
% 227.92/39.47  Begin of proof
% 227.92/39.47  | 
% 227.92/39.47  | ALPHA: (9) implies:
% 227.92/39.47  |   (11)  all_57_14 = e2
% 227.92/39.47  | 
% 227.92/39.47  | COMBINE_EQS: (10), (11) imply:
% 227.92/39.47  |   (12)  e2 = e0
% 227.92/39.47  | 
% 227.92/39.47  | SIMP: (12) implies:
% 227.92/39.47  |   (13)  e2 = e0
% 227.92/39.47  | 
% 227.92/39.47  | COMBINE_EQS: (1), (13) imply:
% 227.92/39.47  |   (14)  all_57_2 = e0
% 227.92/39.47  | 
% 227.92/39.47  | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (14) are inconsistent by
% 227.92/39.47  |            sub-proof #2249.
% 227.92/39.47  | 
% 227.92/39.47  End of proof
% 227.92/39.47  
% 227.92/39.47  Sub-proof #386 shows that the following formulas are inconsistent:
% 227.92/39.47  ----------------------------------------------------------------
% 227.92/39.47    (1)  all_57_5 = e3 & op(e2, e1) = e3
% 227.92/39.47    (2)  all_57_5 = e1
% 227.92/39.47    (3)   ~ (e3 = e1)
% 227.92/39.47  
% 227.92/39.47  Begin of proof
% 227.92/39.47  | 
% 227.92/39.47  | ALPHA: (1) implies:
% 227.92/39.47  |   (4)  all_57_5 = e3
% 227.92/39.47  | 
% 227.92/39.47  | COMBINE_EQS: (2), (4) imply:
% 227.92/39.47  |   (5)  e3 = e1
% 227.92/39.47  | 
% 227.92/39.47  | REDUCE: (3), (5) imply:
% 227.92/39.47  |   (6)  $false
% 227.92/39.47  | 
% 227.92/39.47  | CLOSE: (6) is inconsistent.
% 227.92/39.47  | 
% 227.92/39.47  End of proof
% 227.92/39.47  
% 227.92/39.47  Sub-proof #387 shows that the following formulas are inconsistent:
% 227.92/39.47  ----------------------------------------------------------------
% 227.92/39.47    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 227.92/39.47         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 227.92/39.47    (2)   ~ (e3 = e1)
% 227.92/39.47    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.92/39.47           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.92/39.47    (4)   ~ (all_6_2 = e3)
% 227.92/39.47    (5)  op(e1, e1) = all_6_2
% 227.92/39.47    (6)  all_57_3 = e0
% 227.92/39.47    (7)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 227.92/39.47         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 227.92/39.47    (8)   ~ (e3 = e2)
% 227.92/39.47    (9)   ~ (e3 = e0)
% 227.92/39.47    (10)  all_57_15 = e3
% 227.92/39.47    (11)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 227.92/39.47          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 227.92/39.47            e1)
% 227.92/39.47    (12)  all_57_10 = e2
% 227.92/39.47    (13)   ~ (e2 = e0)
% 227.92/39.47    (14)  all_57_2 = e3
% 227.92/39.47    (15)   ~ (e1 = e0)
% 227.92/39.47    (16)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 227.92/39.47          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 227.92/39.47    (17)  all_57_8 = e2
% 227.92/39.47    (18)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 227.92/39.47    (19)  op(e0, e0) = e3
% 227.92/39.47    (20)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.92/39.47          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 227.92/39.47            e2)
% 227.92/39.47    (21)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 227.92/39.47              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 227.92/39.47                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 227.92/39.47                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 227.92/39.47    (22)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 227.92/39.47          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 227.92/39.47    (23)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 227.92/39.47          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 227.92/39.47    (24)   ~ (e2 = e1)
% 227.92/39.47  
% 227.92/39.47  Begin of proof
% 227.92/39.47  | 
% 227.92/39.47  | BETA: splitting (18) gives:
% 227.92/39.47  | 
% 227.92/39.47  | Case 1:
% 227.92/39.47  | | 
% 227.92/39.47  | |   (25)  all_57_14 = e1 & op(e0, e1) = e1
% 227.92/39.47  | | 
% 227.92/39.47  | | ALPHA: (25) implies:
% 227.92/39.47  | |   (26)  all_57_14 = e1
% 227.92/39.47  | | 
% 227.92/39.47  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 227.92/39.47  | |            (13), (14), (15), (16), (17), (20), (21), (22), (23), (24), (26)
% 227.92/39.47  | |            are inconsistent by sub-proof #745.
% 227.92/39.47  | | 
% 227.92/39.47  | Case 2:
% 227.92/39.47  | | 
% 227.92/39.47  | |   (27)  all_57_15 = e1 & op(e0, e0) = e1
% 227.92/39.47  | | 
% 227.92/39.47  | | ALPHA: (27) implies:
% 227.92/39.47  | |   (28)  op(e0, e0) = e1
% 227.92/39.47  | | 
% 227.92/39.47  | | REF_CLOSE: (2), (3), (19), (28) are inconsistent by sub-proof #2183.
% 227.92/39.47  | | 
% 227.92/39.47  | End of split
% 227.92/39.47  | 
% 227.92/39.47  End of proof
% 227.92/39.47  
% 227.92/39.47  Sub-proof #388 shows that the following formulas are inconsistent:
% 227.92/39.47  ----------------------------------------------------------------
% 227.92/39.47    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 227.92/39.47    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 227.92/39.47    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 227.92/39.47         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 227.92/39.47    (4)  all_57_13 = e1
% 227.92/39.47    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 227.92/39.47         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 227.92/39.47    (6)   ~ (all_53_8 = all_53_12)
% 227.92/39.47    (7)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 227.92/39.47         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.92/39.47    (8)   ~ (e3 = e1)
% 227.92/39.47    (9)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 227.92/39.47         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 227.92/39.47    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.92/39.47            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.92/39.47    (11)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 227.92/39.47          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 227.92/39.47    (12)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 227.92/39.47            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 227.92/39.47              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 227.92/39.47    (13)   ~ (all_6_2 = e3)
% 227.92/39.47    (14)  op(e1, e1) = all_6_2
% 227.92/39.47    (15)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 227.92/39.47    (16)   ~ (all_53_9 = e0)
% 227.92/39.47    (17)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 227.92/39.47          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 227.92/39.47    (18)  all_57_9 = e1
% 227.92/39.47    (19)   ~ (all_53_4 = all_53_12)
% 227.92/39.47    (20)   ~ (all_53_8 = all_53_9)
% 227.92/39.47    (21)  all_42_2 = all_6_2
% 227.92/39.47    (22)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 227.92/39.47          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 227.92/39.47    (23)  all_57_6 = e1
% 227.92/39.47    (24)   ~ (all_53_9 = all_6_2)
% 227.92/39.47    (25)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 227.92/39.47          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 227.92/39.47    (26)  all_57_3 = e0
% 227.92/39.47    (27)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 227.92/39.47          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 227.92/39.47    (28)  all_57_4 = e3
% 227.92/39.47    (29)   ~ (e3 = e2)
% 227.92/39.47    (30)  all_55_1 = all_53_4
% 227.92/39.47    (31)   ~ (e3 = e0)
% 227.92/39.47    (32)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 227.92/39.47          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 227.92/39.47    (33)   ~ (all_53_8 = all_6_2)
% 227.92/39.47    (34)  all_55_2 = all_53_8
% 227.92/39.47    (35)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 227.92/39.47          | (all_57_14 = e0 & op(e0, e1) = e0)
% 227.92/39.47    (36)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 227.92/39.47    (37)  all_57_15 = e3
% 227.92/39.47    (38)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 227.92/39.47          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 227.92/39.47            e1)
% 227.92/39.47    (39)  all_57_10 = e2
% 227.92/39.47    (40)  all_57_11 = e0
% 227.92/39.47    (41)   ~ (all_53_4 = all_53_8)
% 227.92/39.47    (42)  op(e3, e2) = all_53_4
% 227.92/39.47    (43)  op(e1, e1) = e1
% 227.92/39.47    (44)   ~ (e2 = e0)
% 227.92/39.47    (45)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 227.92/39.47            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 227.92/39.47            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 227.92/39.47            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 227.92/39.47              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 227.92/39.47            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 227.92/39.47            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 227.92/39.47              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 227.92/39.47              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 227.92/39.47            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 227.92/39.47            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 227.92/39.47            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 227.92/39.47              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 227.92/39.47              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 227.92/39.47            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 227.92/39.47              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 227.92/39.47            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 227.92/39.47            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 227.92/39.47              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 227.92/39.47              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 227.92/39.47            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 227.92/39.47            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 227.92/39.47    (46)  all_57_2 = e3
% 227.92/39.47    (47)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 227.92/39.47          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 227.92/39.47    (48)   ~ (e1 = e0)
% 227.92/39.47    (49)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 227.92/39.47            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 227.92/39.47              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 227.92/39.47    (50)   ~ (all_53_4 = e0)
% 227.92/39.47    (51)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 227.92/39.47          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 227.92/39.47    (52)  all_57_8 = e2
% 227.92/39.47    (53)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 227.92/39.47          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 227.92/39.47    (54)  op(e0, e0) = e3
% 227.92/39.47    (55)   ~ (all_53_4 = all_53_6)
% 227.92/39.47    (56)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.92/39.47          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 227.92/39.47            e2)
% 227.92/39.47    (57)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 227.92/39.47              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 227.92/39.47                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 227.92/39.47                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 227.92/39.47    (58)  all_55_10 = all_6_2
% 227.92/39.47    (59)  op(e1, e1) = e2
% 227.92/39.47    (60)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 227.92/39.47          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 227.92/39.47    (61)  all_38_2 = all_6_2
% 227.92/39.47    (62)  all_55_3 = all_53_12
% 227.92/39.47    (63)   ~ (all_53_12 = e3)
% 227.92/39.47    (64)  all_57_7 = e3
% 227.92/39.47    (65)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 227.92/39.47            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 227.92/39.47              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 227.92/39.47    (66)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 227.92/39.47          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 227.92/39.47    (67)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 227.92/39.47          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 227.92/39.47    (68)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) |
% 227.92/39.47          (all_57_11 = e0 & op(e1, e0) = e0)
% 227.92/39.47    (69)   ~ (e2 = e1)
% 227.92/39.47    (70)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 227.92/39.47          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 227.92/39.47    (71)  op(e2, e1) = all_53_9
% 227.92/39.47    (72)  op(e1, e2) = all_53_6
% 227.92/39.47    (73)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 227.92/39.47          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 227.92/39.47    (74)  all_24_2 = all_6_2
% 227.92/39.47    (75)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 227.92/39.47          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 227.92/39.47    (76)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 227.92/39.47          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 227.92/39.47    (77)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 227.92/39.47          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 227.92/39.47    (78)  all_57_14 = e0
% 227.92/39.47    (79)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 227.92/39.47          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 227.92/39.47    (80)  op(e3, e1) = all_53_8
% 227.92/39.47    (81)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 227.92/39.47          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 227.92/39.47    (82)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 227.92/39.47          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 227.92/39.47    (83)  op(e3, e0) = all_53_12
% 227.92/39.47  
% 227.92/39.47  Begin of proof
% 227.92/39.47  | 
% 227.92/39.47  | BETA: splitting (7) gives:
% 227.92/39.47  | 
% 227.92/39.47  | Case 1:
% 227.92/39.47  | | 
% 227.92/39.47  | |   (84)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 227.92/39.47  | |           e2)
% 227.92/39.47  | | 
% 227.92/39.47  | | BETA: splitting (84) gives:
% 227.92/39.47  | | 
% 227.92/39.47  | | Case 1:
% 227.92/39.47  | | | 
% 227.92/39.47  | | |   (85)  all_57_1 = e2 & op(e3, e2) = e2
% 227.92/39.47  | | | 
% 227.92/39.47  | | | BETA: splitting (53) gives:
% 227.92/39.47  | | | 
% 227.92/39.47  | | | Case 1:
% 227.92/39.47  | | | | 
% 227.92/39.47  | | | |   (86)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2)
% 227.92/39.47  | | | |           = e3)
% 227.92/39.47  | | | | 
% 227.92/39.47  | | | | BETA: splitting (86) gives:
% 227.92/39.47  | | | | 
% 227.92/39.47  | | | | Case 1:
% 227.92/39.47  | | | | | 
% 227.92/39.47  | | | | |   (87)  all_57_1 = e3 & op(e3, e2) = e3
% 227.92/39.47  | | | | | 
% 227.92/39.47  | | | | | ALPHA: (87) implies:
% 227.92/39.47  | | | | |   (88)  all_57_1 = e3
% 227.92/39.47  | | | | | 
% 227.92/39.47  | | | | | REF_CLOSE: (7), (8), (26), (29), (44), (48), (64), (69), (81), (88)
% 227.92/39.47  | | | | |            are inconsistent by sub-proof #1778.
% 227.92/39.47  | | | | | 
% 227.92/39.47  | | | | Case 2:
% 227.92/39.47  | | | | | 
% 227.92/39.47  | | | | |   (89)  all_57_3 = e3 & op(e2, e2) = e3
% 227.92/39.47  | | | | | 
% 227.92/39.47  | | | | | ALPHA: (89) implies:
% 227.92/39.47  | | | | |   (90)  all_57_3 = e3
% 227.92/39.47  | | | | | 
% 227.92/39.47  | | | | | COMBINE_EQS: (26), (90) imply:
% 227.92/39.47  | | | | |   (91)  e3 = e0
% 227.92/39.47  | | | | | 
% 227.92/39.47  | | | | | REF_CLOSE: (3), (8), (26), (29), (31), (44), (46), (48), (60), (66),
% 227.92/39.47  | | | | |            (69), (91) are inconsistent by sub-proof #1333.
% 227.92/39.47  | | | | | 
% 227.92/39.47  | | | | End of split
% 227.92/39.47  | | | | 
% 227.92/39.47  | | | Case 2:
% 227.92/39.47  | | | | 
% 227.92/39.47  | | | |   (92)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2)
% 227.92/39.47  | | | |           = e3)
% 227.92/39.47  | | | | 
% 227.92/39.47  | | | | BETA: splitting (92) gives:
% 227.92/39.47  | | | | 
% 227.92/39.47  | | | | Case 1:
% 227.92/39.47  | | | | | 
% 227.92/39.47  | | | | |   (93)  all_57_7 = e3 & op(e1, e2) = e3
% 227.92/39.47  | | | | | 
% 227.92/39.47  | | | | | ALPHA: (85) implies:
% 227.92/39.47  | | | | |   (94)  all_57_1 = e2
% 227.92/39.47  | | | | | 
% 227.92/39.47  | | | | | GROUND_INST: instantiating (10) with e1, e2, e1, e1, simplifying with
% 227.92/39.47  | | | | |              (43), (59) gives:
% 227.92/39.47  | | | | |   (95)  e2 = e1
% 227.92/39.47  | | | | | 
% 227.92/39.47  | | | | | COMBINE_EQS: (52), (95) imply:
% 227.92/39.47  | | | | |   (96)  all_57_8 = e1
% 227.92/39.47  | | | | | 
% 227.92/39.47  | | | | | COMBINE_EQS: (94), (95) imply:
% 227.92/39.47  | | | | |   (97)  all_57_1 = e1
% 227.92/39.47  | | | | | 
% 227.92/39.47  | | | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12),
% 227.92/39.47  | | | | |            (13), (14), (15), (16), (17), (19), (20), (21), (22), (24),
% 227.92/39.47  | | | | |            (25), (26), (27), (29), (30), (31), (32), (33), (34), (36),
% 227.92/39.47  | | | | |            (37), (38), (39), (40), (41), (42), (44), (45), (46), (47),
% 227.92/39.47  | | | | |            (48), (49), (50), (51), (53), (54), (55), (56), (57), (58),
% 227.92/39.47  | | | | |            (60), (61), (62), (63), (64), (65), (66), (67), (69), (70),
% 227.92/39.47  | | | | |            (71), (72), (73), (74), (75), (76), (77), (79), (80), (81),
% 227.92/39.47  | | | | |            (82), (83), (96), (97) are inconsistent by sub-proof #427.
% 227.92/39.47  | | | | | 
% 227.92/39.47  | | | | Case 2:
% 227.92/39.47  | | | | | 
% 227.92/39.47  | | | | |   (98)  all_57_13 = e3 & op(e0, e2) = e3
% 227.92/39.47  | | | | | 
% 227.92/39.47  | | | | | ALPHA: (98) implies:
% 227.92/39.47  | | | | |   (99)  all_57_13 = e3
% 227.92/39.47  | | | | | 
% 227.92/39.47  | | | | | REF_CLOSE: (3), (8), (10), (13), (14), (26), (28), (29), (31), (35),
% 227.92/39.47  | | | | |            (37), (38), (39), (44), (46), (48), (51), (54), (56), (57),
% 227.92/39.47  | | | | |            (69), (78), (99) are inconsistent by sub-proof #424.
% 227.92/39.47  | | | | | 
% 227.92/39.47  | | | | End of split
% 227.92/39.47  | | | | 
% 227.92/39.47  | | | End of split
% 227.92/39.47  | | | 
% 227.92/39.47  | | Case 2:
% 227.92/39.47  | | | 
% 227.92/39.47  | | |   (100)  all_57_3 = e2 & op(e2, e2) = e2
% 227.92/39.47  | | | 
% 227.92/39.47  | | | REF_CLOSE: (26), (44), (100) are inconsistent by sub-proof #2256.
% 227.92/39.47  | | | 
% 227.92/39.47  | | End of split
% 227.92/39.47  | | 
% 227.92/39.47  | Case 2:
% 227.92/39.47  | | 
% 227.92/39.47  | |   (101)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 227.92/39.47  | |            e2)
% 227.92/39.47  | | 
% 227.92/39.47  | | BETA: splitting (101) gives:
% 227.92/39.47  | | 
% 227.92/39.47  | | Case 1:
% 227.92/39.47  | | | 
% 227.92/39.47  | | |   (102)  all_57_7 = e2 & op(e1, e2) = e2
% 227.92/39.47  | | | 
% 227.92/39.47  | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 227.92/39.47  | | |            (14), (15), (16), (17), (19), (20), (21), (22), (23), (24),
% 227.92/39.47  | | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 227.92/39.47  | | |            (35), (36), (37), (38), (41), (42), (44), (45), (47), (48),
% 227.92/39.47  | | |            (49), (50), (51), (54), (55), (56), (57), (58), (61), (62),
% 227.92/39.47  | | |            (63), (65), (66), (67), (68), (69), (70), (71), (72), (73),
% 227.92/39.47  | | |            (74), (75), (76), (77), (78), (79), (80), (81), (82), (83),
% 227.92/39.47  | | |            (102) are inconsistent by sub-proof #393.
% 227.92/39.47  | | | 
% 227.92/39.47  | | Case 2:
% 227.92/39.47  | | | 
% 227.92/39.47  | | |   (103)  all_57_13 = e2 & op(e0, e2) = e2
% 227.92/39.47  | | | 
% 227.92/39.47  | | | ALPHA: (103) implies:
% 227.92/39.47  | | |   (104)  all_57_13 = e2
% 227.92/39.47  | | | 
% 227.92/39.47  | | | COMBINE_EQS: (4), (104) imply:
% 227.92/39.47  | | |   (105)  e2 = e1
% 227.92/39.47  | | | 
% 227.92/39.47  | | | COMBINE_EQS: (52), (105) imply:
% 227.92/39.47  | | |   (106)  all_57_8 = e1
% 227.92/39.47  | | | 
% 227.92/39.47  | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 227.92/39.47  | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (24),
% 227.92/39.47  | | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 227.92/39.47  | | |            (36), (37), (38), (39), (40), (41), (42), (44), (45), (46),
% 227.92/39.47  | | |            (47), (48), (49), (50), (51), (53), (54), (55), (56), (57),
% 227.92/39.47  | | |            (58), (60), (61), (62), (63), (64), (65), (66), (67), (69),
% 227.92/39.47  | | |            (70), (71), (72), (73), (74), (75), (76), (77), (79), (80),
% 227.92/39.47  | | |            (81), (82), (83), (106) are inconsistent by sub-proof #428.
% 227.92/39.47  | | | 
% 227.92/39.47  | | End of split
% 227.92/39.47  | | 
% 227.92/39.47  | End of split
% 227.92/39.47  | 
% 227.92/39.47  End of proof
% 227.92/39.47  
% 227.92/39.47  Sub-proof #389 shows that the following formulas are inconsistent:
% 227.92/39.47  ----------------------------------------------------------------
% 227.92/39.47    (1)  all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 227.92/39.47    (2)   ~ (all_53_7 = e3)
% 227.92/39.47    (3)   ~ (all_53_2 = e1)
% 227.92/39.47    (4)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 227.92/39.47    (5)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 227.92/39.47    (6)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 227.92/39.47         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 227.92/39.47    (7)  op(e3, e1) = all_52_5
% 227.92/39.47    (8)   ~ (all_52_7 = e3)
% 227.92/39.47    (9)   ~ (all_52_3 = all_52_5)
% 227.92/39.47    (10)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 227.92/39.47          (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 227.92/39.47    (11)   ~ (all_53_8 = all_53_12)
% 227.92/39.47    (12)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 227.92/39.47          (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.92/39.47    (13)   ~ (e3 = e1)
% 227.92/39.47    (14)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 227.92/39.47          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 227.92/39.47    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.92/39.47            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.92/39.47    (16)  op(all_52_5, all_52_5) = e1
% 227.92/39.47    (17)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 227.92/39.47          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 227.92/39.47    (18)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 227.92/39.47            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 227.92/39.47              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 227.92/39.47    (19)   ~ (all_53_3 = e3)
% 227.92/39.47    (20)   ~ (all_53_3 = all_53_7)
% 227.92/39.47    (21)   ~ (all_6_2 = e3)
% 227.92/39.47    (22)   ~ (all_52_3 = e0)
% 227.92/39.47    (23)   ~ (all_53_9 = e1)
% 227.92/39.47    (24)  op(e1, e1) = all_6_2
% 227.92/39.47    (25)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 227.92/39.47    (26)  op(all_52_7, all_52_7) = e0
% 227.92/39.47    (27)   ~ (all_53_1 = all_53_9)
% 227.92/39.47    (28)  op(e3, e2) = all_52_3
% 227.92/39.47    (29)   ~ (all_53_9 = e0)
% 227.92/39.47    (30)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 227.92/39.47          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 227.92/39.47    (31)   ~ (all_52_5 = all_52_7)
% 227.92/39.47    (32)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 227.92/39.47            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 227.92/39.47              e3) = all_22_1 & $i(all_22_1))
% 227.92/39.47    (33)  all_55_3 = all_52_7
% 227.92/39.47    (34)   ~ (all_53_4 = all_53_12)
% 227.92/39.47    (35)   ~ (all_53_13 = e3)
% 227.92/39.47    (36)   ~ (all_53_8 = all_53_9)
% 227.92/39.47    (37)   ~ (all_53_7 = all_52_3)
% 227.92/39.47    (38)  all_42_2 = all_6_2
% 227.92/39.47    (39)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 227.92/39.47          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 227.92/39.47    (40)  op(e2, e2) = e0
% 227.92/39.47    (41)  all_55_4 = all_53_1
% 227.92/39.47    (42)   ~ (all_53_9 = all_6_2)
% 227.92/39.47    (43)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 227.92/39.47          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 227.92/39.47    (44)  all_57_3 = e0
% 227.92/39.47    (45)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 227.92/39.47          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 227.92/39.47    (46)  all_57_4 = e3
% 227.92/39.47    (47)   ~ (e3 = e2)
% 227.92/39.47    (48)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 227.92/39.47    (49)  all_55_1 = all_53_4
% 227.92/39.47    (50)   ~ (all_53_13 = all_52_7)
% 227.92/39.47    (51)  all_55_7 = e3 | all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 227.92/39.47    (52)  all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 227.92/39.47    (53)   ~ (e3 = e0)
% 227.92/39.47    (54)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 227.92/39.47          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 227.92/39.47    (55)   ~ (all_6_2 = e2)
% 227.92/39.47    (56)   ~ (all_53_8 = all_6_2)
% 227.92/39.48    (57)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 227.92/39.48    (58)   ~ (all_53_2 = e0)
% 227.92/39.48    (59)  all_57_0 = e0
% 227.92/39.48    (60)  all_55_2 = all_53_8
% 227.92/39.48    (61)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 227.92/39.48    (62)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 227.92/39.48          | (all_57_14 = e0 & op(e0, e1) = e0)
% 227.92/39.48    (63)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 227.92/39.48    (64)  all_57_15 = e3
% 227.92/39.48    (65)   ~ (all_53_9 = all_53_13)
% 227.92/39.48    (66)   ~ (all_53_7 = e0)
% 227.92/39.48    (67)  op(e3, e3) = e0
% 227.92/39.48    (68)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 227.92/39.48          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 227.92/39.48            e1)
% 227.92/39.48    (69)  all_57_10 = e2
% 227.92/39.48    (70)  op(e3, e3) = all_52_1
% 227.92/39.48    (71)  all_57_11 = e0
% 227.92/39.48    (72)  all_57_12 = e1
% 227.92/39.48    (73)   ~ (all_53_4 = all_53_8)
% 227.92/39.48    (74)  all_55_6 = all_53_9
% 227.92/39.48    (75)  op(e3, e2) = all_53_4
% 227.92/39.48    (76)   ~ (all_53_1 = all_53_2)
% 227.92/39.48    (77)  op(e1, e1) = e1
% 227.92/39.48    (78)  op(all_52_1, all_52_1) = e3
% 227.92/39.48    (79)   ~ (e2 = e0)
% 227.92/39.48    (80)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 227.92/39.48            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 227.92/39.48            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 227.92/39.48            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 227.92/39.48              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 227.92/39.48            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 227.92/39.48            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 227.92/39.48              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 227.92/39.48              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 227.92/39.48            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 227.92/39.48            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 227.92/39.48            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 227.92/39.48              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 227.92/39.48              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 227.92/39.48            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 227.92/39.48              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 227.92/39.48            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 227.92/39.48            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 227.92/39.48              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 227.92/39.48              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 227.92/39.48            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 227.92/39.48            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 227.92/39.48    (81)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 227.92/39.48            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 227.92/39.48              e3) = all_12_1 & $i(all_12_1))
% 227.92/39.48    (82)  all_55_12 = all_53_3
% 227.92/39.48    (83)  all_57_2 = e3
% 227.92/39.48    (84)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 227.92/39.48          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 227.92/39.48    (85)   ~ (all_53_1 = e0)
% 227.92/39.48    (86)   ~ (e1 = e0)
% 227.92/39.48    (87)   ~ (all_52_3 = all_52_7)
% 227.92/39.48    (88)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 227.92/39.48            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 227.92/39.48              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 227.92/39.48    (89)   ~ (all_53_4 = e0)
% 227.92/39.48    (90)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 227.92/39.48          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 227.92/39.48    (91)  all_57_8 = e2
% 227.92/39.48    (92)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 227.92/39.48          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 227.92/39.48    (93)  all_55_8 = all_53_2
% 227.92/39.48    (94)  op(e0, e0) = e3
% 227.92/39.48    (95)   ~ (all_53_4 = all_53_6)
% 227.92/39.48    (96)  all_55_2 = all_52_5
% 227.92/39.48    (97)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.92/39.48          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 227.92/39.48            e2)
% 227.92/39.48    (98)   ~ (all_53_3 = e0)
% 227.92/39.48    (99)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 227.92/39.48              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 227.92/39.48                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 227.92/39.48                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 227.92/39.48    (100)  all_55_10 = all_6_2
% 227.92/39.48    (101)   ~ (all_53_13 = e0)
% 227.92/39.48    (102)   ~ (all_53_1 = all_53_13)
% 227.92/39.48    (103)  all_55_13 = all_53_7
% 227.92/39.48    (104)   ~ (all_53_9 = all_52_5)
% 227.92/39.48    (105)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 227.92/39.48           (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 227.92/39.48    (106)  all_38_2 = all_6_2
% 227.92/39.48    (107)  all_55_3 = all_53_12
% 227.92/39.48    (108)   ~ (all_53_12 = e3)
% 227.92/39.48    (109)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0
% 227.92/39.48             & op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~
% 227.92/39.48             (all_42_1 = e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 227.92/39.48    (110)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 227.92/39.48           (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 227.92/39.48    (111)  all_55_1 = all_52_3
% 227.92/39.48    (112)   ~ (all_52_5 = all_6_2)
% 227.92/39.48    (113)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 227.92/39.48           (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 227.92/39.48    (114)   ~ (all_52_5 = e1)
% 227.92/39.48    (115)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 227.92/39.48           | (all_57_11 = e0 & op(e1, e0) = e0)
% 227.92/39.48    (116)   ~ (all_52_5 = e0)
% 227.92/39.48    (117)   ~ (e2 = e1)
% 227.92/39.48    (118)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 227.92/39.48           | (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 227.92/39.48             e2)
% 227.92/39.48    (119)  op(e2, e1) = all_53_9
% 227.92/39.48    (120)  op(e1, e2) = all_53_6
% 227.92/39.48    (121)   ~ (all_6_2 = e0)
% 227.92/39.48    (122)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 227.92/39.48           (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 227.92/39.48    (123)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 227.92/39.48    (124)  all_24_2 = all_6_2
% 227.92/39.48    (125)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 227.92/39.48           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 227.92/39.48    (126)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 227.92/39.48           (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 227.92/39.48    (127)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 227.92/39.48           | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 227.92/39.48             e1)
% 227.92/39.48    (128)  all_57_14 = e0
% 227.92/39.48    (129)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 227.92/39.48           (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 227.92/39.48    (130)  op(e3, e0) = all_52_7
% 227.92/39.48    (131)  op(e3, e1) = all_53_8
% 227.92/39.48    (132)  all_55_7 = all_53_13
% 227.92/39.48    (133)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 227.92/39.48           (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 227.92/39.48    (134)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 227.92/39.48           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 227.92/39.48    (135)  op(e3, e0) = all_53_12
% 227.92/39.48  
% 227.92/39.48  Begin of proof
% 227.92/39.48  | 
% 227.92/39.48  | BETA: splitting (97) gives:
% 227.92/39.48  | 
% 227.92/39.48  | Case 1:
% 227.92/39.48  | | 
% 227.92/39.48  | |   (136)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 227.92/39.48  | |            e2)
% 227.92/39.48  | | 
% 227.92/39.48  | | BETA: splitting (136) gives:
% 227.92/39.48  | | 
% 227.92/39.48  | | Case 1:
% 227.92/39.48  | | | 
% 227.92/39.48  | | |   (137)  all_57_12 = e2 & op(e0, e3) = e2
% 227.92/39.48  | | | 
% 227.92/39.48  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 227.92/39.48  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 227.92/39.48  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 227.92/39.48  | | |            (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 227.92/39.48  | | |            (43), (44), (45), (48), (49), (50), (51), (52), (53), (54),
% 227.92/39.48  | | |            (55), (56), (57), (58), (59), (60), (61), (62), (63), (64),
% 227.92/39.48  | | |            (65), (66), (67), (68), (71), (72), (73), (74), (75), (76),
% 227.92/39.48  | | |            (80), (81), (82), (84), (85), (86), (87), (88), (89), (90),
% 227.92/39.48  | | |            (91), (92), (93), (94), (95), (96), (97), (98), (99), (100),
% 227.92/39.48  | | |            (101), (102), (103), (104), (105), (106), (107), (108), (109),
% 227.92/39.48  | | |            (110), (111), (112), (113), (114), (115), (116), (118), (119),
% 227.92/39.48  | | |            (120), (121), (122), (123), (124), (125), (126), (127), (128),
% 227.92/39.48  | | |            (129), (130), (131), (132), (133), (134), (135), (137) are
% 227.92/39.48  | | |            inconsistent by sub-proof #392.
% 227.92/39.48  | | | 
% 227.92/39.48  | | Case 2:
% 227.92/39.48  | | | 
% 227.92/39.48  | | |   (138)  all_57_13 = e2 & op(e0, e2) = e2
% 227.92/39.48  | | | 
% 227.92/39.48  | | | ALPHA: (138) implies:
% 227.92/39.48  | | |   (139)  all_57_13 = e2
% 227.92/39.48  | | | 
% 227.92/39.48  | | | BETA: splitting (133) gives:
% 227.92/39.48  | | | 
% 227.92/39.48  | | | Case 1:
% 227.92/39.48  | | | | 
% 227.92/39.48  | | | |   (140)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2)
% 227.92/39.48  | | | |            = e1)
% 227.92/39.48  | | | | 
% 227.92/39.48  | | | | BETA: splitting (140) gives:
% 227.92/39.48  | | | | 
% 227.92/39.48  | | | | Case 1:
% 227.92/39.48  | | | | | 
% 227.92/39.48  | | | | |   (141)  all_57_1 = e1 & op(e3, e2) = e1
% 227.92/39.48  | | | | | 
% 227.92/39.48  | | | | | ALPHA: (141) implies:
% 227.92/39.48  | | | | |   (142)  all_57_1 = e1
% 227.92/39.48  | | | | | 
% 227.92/39.48  | | | | | BETA: splitting (122) gives:
% 227.92/39.48  | | | | | 
% 227.92/39.48  | | | | | Case 1:
% 227.92/39.48  | | | | | | 
% 227.92/39.48  | | | | | |   (143)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2,
% 227.92/39.48  | | | | | |              e3) = e2)
% 227.92/39.48  | | | | | | 
% 227.92/39.48  | | | | | | REF_CLOSE: (15), (40), (47), (53), (70), (78), (83), (143) are
% 227.92/39.48  | | | | | |            inconsistent by sub-proof #391.
% 227.92/39.48  | | | | | | 
% 227.92/39.48  | | | | | Case 2:
% 227.92/39.48  | | | | | | 
% 227.92/39.48  | | | | | |   (144)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 &
% 227.92/39.48  | | | | | |            op(e0, e3) = e2)
% 227.92/39.48  | | | | | | 
% 227.92/39.48  | | | | | | BETA: splitting (144) gives:
% 227.92/39.48  | | | | | | 
% 227.92/39.48  | | | | | | Case 1:
% 227.92/39.48  | | | | | | | 
% 227.92/39.48  | | | | | | |   (145)  all_57_6 = e2 & op(e1, e3) = e2
% 227.92/39.48  | | | | | | | 
% 227.92/39.48  | | | | | | | ALPHA: (145) implies:
% 227.92/39.48  | | | | | | |   (146)  all_57_6 = e2
% 227.92/39.48  | | | | | | | 
% 227.92/39.48  | | | | | | | BETA: splitting (92) gives:
% 227.92/39.48  | | | | | | | 
% 227.92/39.48  | | | | | | | Case 1:
% 227.92/39.48  | | | | | | | | 
% 227.92/39.48  | | | | | | | |   (147)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 &
% 227.92/39.48  | | | | | | | |            op(e2, e2) = e3)
% 227.92/39.48  | | | | | | | | 
% 227.92/39.48  | | | | | | | | REF_CLOSE: (6), (13), (15), (17), (21), (24), (44), (47), (53),
% 227.92/39.48  | | | | | | | |            (64), (79), (83), (86), (105), (110), (115), (117),
% 227.92/39.48  | | | | | | | |            (118), (127), (133), (139), (146), (147) are
% 227.92/39.48  | | | | | | | |            inconsistent by sub-proof #390.
% 227.92/39.48  | | | | | | | | 
% 227.92/39.48  | | | | | | | Case 2:
% 227.92/39.48  | | | | | | | | 
% 227.92/39.48  | | | | | | | |   (148)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 &
% 227.92/39.48  | | | | | | | |            op(e0, e2) = e3)
% 227.92/39.48  | | | | | | | | 
% 227.92/39.48  | | | | | | | | BETA: splitting (148) gives:
% 227.92/39.48  | | | | | | | | 
% 227.92/39.48  | | | | | | | | Case 1:
% 227.92/39.48  | | | | | | | | | 
% 227.92/39.48  | | | | | | | | |   (149)  all_57_7 = e3 & op(e1, e2) = e3
% 227.92/39.48  | | | | | | | | | 
% 227.92/39.48  | | | | | | | | | ALPHA: (149) implies:
% 227.92/39.48  | | | | | | | | |   (150)  all_57_7 = e3
% 227.92/39.48  | | | | | | | | | 
% 227.92/39.48  | | | | | | | | | REF_CLOSE: (12), (13), (44), (47), (71), (79), (86), (91),
% 227.92/39.48  | | | | | | | | |            (117), (129), (133), (142), (146), (150) are
% 227.92/39.48  | | | | | | | | |            inconsistent by sub-proof #430.
% 227.92/39.48  | | | | | | | | | 
% 227.92/39.48  | | | | | | | | Case 2:
% 227.92/39.48  | | | | | | | | | 
% 227.92/39.48  | | | | | | | | |   (151)  all_57_13 = e3 & op(e0, e2) = e3
% 227.92/39.48  | | | | | | | | | 
% 227.92/39.48  | | | | | | | | | ALPHA: (151) implies:
% 227.92/39.48  | | | | | | | | |   (152)  all_57_13 = e3
% 227.92/39.48  | | | | | | | | | 
% 227.92/39.48  | | | | | | | | | REF_CLOSE: (13), (47), (53), (62), (64), (68), (72), (79),
% 227.92/39.48  | | | | | | | | |            (86), (97), (117), (152) are inconsistent by
% 227.92/39.48  | | | | | | | | |            sub-proof #2057.
% 227.92/39.48  | | | | | | | | | 
% 227.92/39.48  | | | | | | | | End of split
% 227.92/39.48  | | | | | | | | 
% 227.92/39.48  | | | | | | | End of split
% 227.92/39.48  | | | | | | | 
% 227.92/39.48  | | | | | | Case 2:
% 227.92/39.48  | | | | | | | 
% 227.92/39.48  | | | | | | |   (153)  all_57_12 = e2 & op(e0, e3) = e2
% 227.92/39.48  | | | | | | | 
% 227.92/39.48  | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 227.92/39.48  | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18), (19),
% 227.92/39.48  | | | | | | |            (20), (21), (22), (23), (24), (25), (26), (27), (28),
% 227.92/39.48  | | | | | | |            (29), (30), (31), (32), (33), (34), (35), (36), (37),
% 227.92/39.48  | | | | | | |            (38), (39), (40), (41), (42), (43), (44), (45), (48),
% 227.92/39.48  | | | | | | |            (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 227.92/39.48  | | | | | | |            (58), (59), (60), (61), (62), (63), (64), (65), (66),
% 227.92/39.48  | | | | | | |            (67), (68), (71), (72), (73), (74), (75), (76), (80),
% 227.92/39.48  | | | | | | |            (81), (82), (84), (85), (86), (87), (88), (89), (90),
% 227.92/39.48  | | | | | | |            (91), (92), (93), (94), (95), (96), (97), (98), (99),
% 227.92/39.48  | | | | | | |            (100), (101), (102), (103), (104), (105), (106), (107),
% 227.92/39.48  | | | | | | |            (108), (109), (110), (111), (112), (113), (114), (115),
% 227.92/39.48  | | | | | | |            (116), (118), (119), (120), (121), (122), (123), (124),
% 227.92/39.48  | | | | | | |            (125), (126), (127), (128), (129), (130), (131), (132),
% 227.92/39.48  | | | | | | |            (133), (134), (135), (153) are inconsistent by
% 227.92/39.48  | | | | | | |            sub-proof #392.
% 227.92/39.48  | | | | | | | 
% 227.92/39.48  | | | | | | End of split
% 227.92/39.48  | | | | | | 
% 227.92/39.48  | | | | | End of split
% 227.92/39.48  | | | | | 
% 227.92/39.48  | | | | Case 2:
% 227.92/39.48  | | | | | 
% 227.92/39.48  | | | | |   (154)  all_57_3 = e1 & op(e2, e2) = e1
% 227.92/39.48  | | | | | 
% 227.92/39.48  | | | | | ALPHA: (154) implies:
% 227.92/39.48  | | | | |   (155)  op(e2, e2) = e1
% 227.92/39.48  | | | | | 
% 227.92/39.48  | | | | | REF_CLOSE: (15), (40), (86), (155) are inconsistent by sub-proof
% 227.92/39.48  | | | | |            #2352.
% 227.92/39.48  | | | | | 
% 227.92/39.48  | | | | End of split
% 227.92/39.48  | | | | 
% 227.92/39.48  | | | Case 2:
% 227.92/39.48  | | | | 
% 227.92/39.48  | | | |   (156)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0,
% 227.92/39.48  | | | |              e2) = e1)
% 227.92/39.48  | | | | 
% 227.92/39.48  | | | | BETA: splitting (156) gives:
% 227.92/39.48  | | | | 
% 227.92/39.48  | | | | Case 1:
% 227.92/39.48  | | | | | 
% 227.92/39.48  | | | | |   (157)  all_57_7 = e1 & op(e1, e2) = e1
% 227.92/39.48  | | | | | 
% 227.92/39.48  | | | | | ALPHA: (157) implies:
% 227.92/39.48  | | | | |   (158)  all_57_7 = e1
% 227.92/39.48  | | | | | 
% 227.92/39.48  | | | | | BETA: splitting (122) gives:
% 227.92/39.48  | | | | | 
% 227.92/39.48  | | | | | Case 1:
% 227.92/39.48  | | | | | | 
% 227.92/39.48  | | | | | |   (159)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2,
% 227.92/39.48  | | | | | |              e3) = e2)
% 227.92/39.48  | | | | | | 
% 227.92/39.48  | | | | | | REF_CLOSE: (15), (40), (47), (53), (70), (78), (83), (159) are
% 227.92/39.48  | | | | | |            inconsistent by sub-proof #391.
% 227.92/39.48  | | | | | | 
% 227.92/39.48  | | | | | Case 2:
% 227.92/39.48  | | | | | | 
% 227.92/39.48  | | | | | |   (160)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 &
% 227.92/39.48  | | | | | |            op(e0, e3) = e2)
% 227.92/39.48  | | | | | | 
% 227.92/39.48  | | | | | | BETA: splitting (160) gives:
% 227.92/39.48  | | | | | | 
% 227.92/39.48  | | | | | | Case 1:
% 227.92/39.48  | | | | | | | 
% 227.92/39.48  | | | | | | |   (161)  all_57_6 = e2 & op(e1, e3) = e2
% 227.92/39.48  | | | | | | | 
% 227.92/39.48  | | | | | | | ALPHA: (161) implies:
% 227.92/39.48  | | | | | | |   (162)  all_57_6 = e2
% 227.92/39.48  | | | | | | | 
% 227.92/39.48  | | | | | | | BETA: splitting (92) gives:
% 227.92/39.48  | | | | | | | 
% 227.92/39.48  | | | | | | | Case 1:
% 227.92/39.48  | | | | | | | | 
% 227.92/39.48  | | | | | | | |   (163)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 &
% 227.92/39.48  | | | | | | | |            op(e2, e2) = e3)
% 227.92/39.48  | | | | | | | | 
% 227.92/39.48  | | | | | | | | REF_CLOSE: (6), (13), (15), (17), (21), (24), (44), (47), (53),
% 227.92/39.48  | | | | | | | |            (64), (79), (83), (86), (105), (110), (115), (117),
% 227.92/39.48  | | | | | | | |            (118), (127), (133), (139), (162), (163) are
% 227.92/39.48  | | | | | | | |            inconsistent by sub-proof #390.
% 227.92/39.48  | | | | | | | | 
% 227.92/39.48  | | | | | | | Case 2:
% 227.92/39.48  | | | | | | | | 
% 227.92/39.48  | | | | | | | |   (164)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 &
% 227.92/39.48  | | | | | | | |            op(e0, e2) = e3)
% 227.92/39.48  | | | | | | | | 
% 227.92/39.48  | | | | | | | | BETA: splitting (164) gives:
% 227.92/39.48  | | | | | | | | 
% 227.92/39.48  | | | | | | | | Case 1:
% 227.92/39.48  | | | | | | | | | 
% 227.92/39.48  | | | | | | | | |   (165)  all_57_7 = e3 & op(e1, e2) = e3
% 227.92/39.48  | | | | | | | | | 
% 227.92/39.48  | | | | | | | | | ALPHA: (165) implies:
% 227.92/39.48  | | | | | | | | |   (166)  all_57_7 = e3
% 227.92/39.48  | | | | | | | | | 
% 227.92/39.48  | | | | | | | | | COMBINE_EQS: (158), (166) imply:
% 227.92/39.48  | | | | | | | | |   (167)  e3 = e1
% 227.92/39.48  | | | | | | | | | 
% 227.92/39.48  | | | | | | | | | SIMP: (167) implies:
% 227.92/39.48  | | | | | | | | |   (168)  e3 = e1
% 227.92/39.48  | | | | | | | | | 
% 227.92/39.48  | | | | | | | | | COMBINE_EQS: (46), (168) imply:
% 227.92/39.48  | | | | | | | | |   (169)  all_57_4 = e1
% 227.92/39.48  | | | | | | | | | 
% 227.92/39.48  | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 227.92/39.48  | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 227.92/39.48  | | | | | | | | |            (19), (20), (21), (22), (23), (24), (25), (26),
% 227.92/39.48  | | | | | | | | |            (27), (28), (29), (30), (31), (32), (33), (34),
% 227.92/39.48  | | | | | | | | |            (35), (36), (37), (38), (39), (40), (41), (42),
% 227.92/39.48  | | | | | | | | |            (43), (44), (45), (47), (48), (49), (50), (51),
% 227.92/39.48  | | | | | | | | |            (52), (53), (54), (55), (56), (57), (58), (59),
% 227.92/39.48  | | | | | | | | |            (60), (61), (62), (63), (64), (65), (66), (67),
% 227.92/39.48  | | | | | | | | |            (68), (70), (71), (73), (74), (75), (76), (77),
% 227.92/39.48  | | | | | | | | |            (78), (79), (80), (81), (82), (84), (85), (86),
% 227.92/39.48  | | | | | | | | |            (87), (88), (89), (90), (92), (93), (94), (95),
% 227.92/39.48  | | | | | | | | |            (96), (97), (98), (99), (100), (101), (102), (103),
% 227.92/39.48  | | | | | | | | |            (104), (105), (106), (107), (108), (109), (110),
% 227.92/39.48  | | | | | | | | |            (111), (112), (113), (114), (115), (116), (117),
% 227.92/39.48  | | | | | | | | |            (118), (119), (120), (121), (122), (123), (124),
% 227.92/39.48  | | | | | | | | |            (125), (126), (127), (128), (129), (130), (131),
% 227.92/39.48  | | | | | | | | |            (132), (133), (134), (135), (158), (169) are
% 227.92/39.48  | | | | | | | | |            inconsistent by sub-proof #398.
% 227.92/39.48  | | | | | | | | | 
% 227.92/39.48  | | | | | | | | Case 2:
% 227.92/39.48  | | | | | | | | | 
% 227.92/39.48  | | | | | | | | |   (170)  all_57_13 = e3 & op(e0, e2) = e3
% 227.92/39.48  | | | | | | | | | 
% 227.92/39.48  | | | | | | | | | ALPHA: (170) implies:
% 227.92/39.48  | | | | | | | | |   (171)  all_57_13 = e3
% 227.92/39.48  | | | | | | | | | 
% 227.92/39.48  | | | | | | | | | REF_CLOSE: (13), (47), (53), (62), (64), (68), (72), (79),
% 227.92/39.48  | | | | | | | | |            (86), (97), (117), (171) are inconsistent by
% 227.92/39.48  | | | | | | | | |            sub-proof #2057.
% 227.92/39.48  | | | | | | | | | 
% 227.92/39.48  | | | | | | | | End of split
% 227.92/39.48  | | | | | | | | 
% 227.92/39.48  | | | | | | | End of split
% 227.92/39.48  | | | | | | | 
% 227.92/39.48  | | | | | | Case 2:
% 227.92/39.48  | | | | | | | 
% 227.92/39.48  | | | | | | |   (172)  all_57_12 = e2 & op(e0, e3) = e2
% 227.92/39.48  | | | | | | | 
% 227.92/39.48  | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 227.92/39.48  | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18), (19),
% 227.92/39.48  | | | | | | |            (20), (21), (22), (23), (24), (25), (26), (27), (28),
% 227.92/39.48  | | | | | | |            (29), (30), (31), (32), (33), (34), (35), (36), (37),
% 227.92/39.48  | | | | | | |            (38), (39), (40), (41), (42), (43), (44), (45), (48),
% 227.92/39.48  | | | | | | |            (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 227.92/39.48  | | | | | | |            (58), (59), (60), (61), (62), (63), (64), (65), (66),
% 227.92/39.48  | | | | | | |            (67), (68), (71), (72), (73), (74), (75), (76), (80),
% 227.92/39.48  | | | | | | |            (81), (82), (84), (85), (86), (87), (88), (89), (90),
% 227.92/39.48  | | | | | | |            (91), (92), (93), (94), (95), (96), (97), (98), (99),
% 227.92/39.48  | | | | | | |            (100), (101), (102), (103), (104), (105), (106), (107),
% 227.92/39.48  | | | | | | |            (108), (109), (110), (111), (112), (113), (114), (115),
% 227.92/39.48  | | | | | | |            (116), (118), (119), (120), (121), (122), (123), (124),
% 227.92/39.48  | | | | | | |            (125), (126), (127), (128), (129), (130), (131), (132),
% 227.92/39.48  | | | | | | |            (133), (134), (135), (172) are inconsistent by
% 227.92/39.48  | | | | | | |            sub-proof #392.
% 227.92/39.48  | | | | | | | 
% 227.92/39.48  | | | | | | End of split
% 227.92/39.48  | | | | | | 
% 227.92/39.48  | | | | | End of split
% 227.92/39.48  | | | | | 
% 227.92/39.48  | | | | Case 2:
% 227.92/39.48  | | | | | 
% 227.92/39.48  | | | | |   (173)  all_57_13 = e1 & op(e0, e2) = e1
% 227.92/39.48  | | | | | 
% 227.92/39.48  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 227.92/39.48  | | | | |            (12), (13), (14), (15), (16), (17), (18), (19), (20), (21),
% 227.92/39.48  | | | | |            (22), (23), (24), (25), (26), (27), (28), (29), (30), (31),
% 227.92/39.48  | | | | |            (32), (33), (34), (35), (36), (37), (38), (39), (40), (41),
% 227.92/39.48  | | | | |            (42), (43), (44), (45), (48), (49), (50), (51), (52), (53),
% 227.92/39.48  | | | | |            (54), (55), (56), (57), (58), (59), (60), (61), (62), (63),
% 227.92/39.48  | | | | |            (64), (65), (66), (67), (68), (71), (73), (74), (75), (76),
% 227.92/39.48  | | | | |            (80), (81), (82), (84), (85), (86), (87), (88), (89), (90),
% 227.92/39.48  | | | | |            (91), (92), (93), (94), (95), (96), (97), (98), (99),
% 227.92/39.48  | | | | |            (100), (101), (102), (103), (104), (105), (106), (107),
% 227.92/39.48  | | | | |            (108), (109), (110), (111), (112), (113), (114), (115),
% 227.92/39.48  | | | | |            (116), (118), (119), (120), (121), (122), (123), (124),
% 227.92/39.48  | | | | |            (125), (126), (127), (128), (129), (130), (131), (132),
% 227.92/39.48  | | | | |            (133), (134), (135), (139), (173) are inconsistent by
% 227.92/39.48  | | | | |            sub-proof #400.
% 227.92/39.48  | | | | | 
% 227.92/39.48  | | | | End of split
% 227.92/39.48  | | | | 
% 227.92/39.48  | | | End of split
% 227.92/39.48  | | | 
% 227.92/39.48  | | End of split
% 227.92/39.48  | | 
% 227.92/39.48  | Case 2:
% 227.92/39.48  | | 
% 227.92/39.48  | |   (174)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 227.92/39.48  | |            e2)
% 227.92/39.48  | | 
% 227.92/39.48  | | BETA: splitting (174) gives:
% 227.92/39.48  | | 
% 227.92/39.48  | | Case 1:
% 227.92/39.48  | | | 
% 227.92/39.48  | | |   (175)  all_57_14 = e2 & op(e0, e1) = e2
% 227.92/39.48  | | | 
% 227.92/39.48  | | | ALPHA: (175) implies:
% 227.92/39.48  | | |   (176)  all_57_14 = e2
% 227.92/39.48  | | | 
% 227.92/39.48  | | | REF_CLOSE: (6), (13), (15), (21), (24), (44), (45), (47), (53), (64),
% 227.92/39.48  | | |            (68), (69), (79), (83), (86), (90), (91), (97), (99), (105),
% 227.92/39.48  | | |            (110), (117), (176) are inconsistent by sub-proof #591.
% 227.92/39.48  | | | 
% 227.92/39.48  | | Case 2:
% 227.92/39.48  | | | 
% 227.92/39.48  | | |   (177)  all_57_15 = e2 & op(e0, e0) = e2
% 227.92/39.48  | | | 
% 227.92/39.48  | | | REF_CLOSE: (47), (64), (177) are inconsistent by sub-proof #2323.
% 227.92/39.48  | | | 
% 227.92/39.48  | | End of split
% 227.92/39.48  | | 
% 227.92/39.48  | End of split
% 227.92/39.48  | 
% 227.92/39.48  End of proof
% 227.92/39.48  
% 227.92/39.48  Sub-proof #390 shows that the following formulas are inconsistent:
% 227.92/39.48  ----------------------------------------------------------------
% 227.92/39.48    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 227.92/39.48         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 227.92/39.48    (2)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3)
% 227.92/39.48    (3)   ~ (e3 = e1)
% 227.92/39.48    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.92/39.48           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.92/39.48    (5)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 227.92/39.48         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 227.92/39.48    (6)   ~ (all_6_2 = e3)
% 227.92/39.48    (7)  op(e1, e1) = all_6_2
% 227.92/39.48    (8)  all_57_3 = e0
% 227.92/39.48    (9)   ~ (e3 = e2)
% 227.92/39.48    (10)   ~ (e3 = e0)
% 227.92/39.48    (11)  all_57_15 = e3
% 227.92/39.48    (12)  all_57_6 = e2
% 227.92/39.48    (13)   ~ (e2 = e0)
% 227.92/39.48    (14)  all_57_13 = e2
% 227.92/39.48    (15)  all_57_2 = e3
% 227.92/39.48    (16)   ~ (e1 = e0)
% 227.92/39.48    (17)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 227.92/39.48          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 227.92/39.48    (18)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 227.92/39.48          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 227.92/39.48    (19)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) |
% 227.92/39.48          (all_57_11 = e0 & op(e1, e0) = e0)
% 227.92/39.48    (20)   ~ (e2 = e1)
% 227.92/39.48    (21)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 227.92/39.48          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 227.92/39.48    (22)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 227.92/39.48          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 227.92/39.48    (23)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 227.92/39.48          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 227.92/39.48  
% 227.92/39.48  Begin of proof
% 227.92/39.48  | 
% 227.92/39.48  | BETA: splitting (2) gives:
% 227.92/39.48  | 
% 227.92/39.48  | Case 1:
% 227.92/39.48  | | 
% 227.92/39.48  | |   (24)  all_57_1 = e3 & op(e3, e2) = e3
% 227.92/39.48  | | 
% 227.92/39.48  | | ALPHA: (24) implies:
% 227.92/39.48  | |   (25)  all_57_1 = e3
% 227.92/39.48  | | 
% 227.92/39.48  | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), (14),
% 227.92/39.48  | |            (16), (19), (20), (21), (22), (23), (25) are inconsistent by
% 227.92/39.48  | |            sub-proof #419.
% 227.92/39.48  | | 
% 227.92/39.48  | Case 2:
% 227.92/39.48  | | 
% 227.92/39.48  | |   (26)  all_57_3 = e3 & op(e2, e2) = e3
% 227.92/39.48  | | 
% 227.92/39.48  | | ALPHA: (26) implies:
% 227.92/39.48  | |   (27)  all_57_3 = e3
% 227.92/39.48  | | 
% 227.92/39.48  | | COMBINE_EQS: (8), (27) imply:
% 227.92/39.48  | |   (28)  e3 = e0
% 227.92/39.48  | | 
% 227.92/39.48  | | REF_CLOSE: (1), (3), (8), (9), (10), (13), (15), (16), (17), (18), (20),
% 227.92/39.48  | |            (28) are inconsistent by sub-proof #1333.
% 227.92/39.48  | | 
% 227.92/39.48  | End of split
% 227.92/39.48  | 
% 227.92/39.48  End of proof
% 227.92/39.48  
% 227.92/39.48  Sub-proof #391 shows that the following formulas are inconsistent:
% 227.92/39.48  ----------------------------------------------------------------
% 227.92/39.48    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.92/39.48           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.92/39.48    (2)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2)
% 227.92/39.48    (3)  op(e2, e2) = e0
% 227.92/39.48    (4)   ~ (e3 = e2)
% 227.92/39.48    (5)   ~ (e3 = e0)
% 227.92/39.48    (6)  op(e3, e3) = all_52_1
% 227.92/39.48    (7)  op(all_52_1, all_52_1) = e3
% 227.92/39.48    (8)  all_57_2 = e3
% 227.92/39.48  
% 227.92/39.48  Begin of proof
% 227.92/39.48  | 
% 227.92/39.48  | BETA: splitting (2) gives:
% 227.92/39.48  | 
% 227.92/39.48  | Case 1:
% 227.92/39.48  | | 
% 227.92/39.48  | |   (9)  all_57_0 = e2 & op(e3, e3) = e2
% 227.92/39.48  | | 
% 227.92/39.48  | | ALPHA: (9) implies:
% 227.92/39.48  | |   (10)  op(e3, e3) = e2
% 227.92/39.48  | | 
% 227.92/39.48  | | REF_CLOSE: (1), (3), (5), (6), (7), (10) are inconsistent by sub-proof
% 227.92/39.48  | |            #1653.
% 227.92/39.48  | | 
% 227.92/39.48  | Case 2:
% 227.92/39.48  | | 
% 227.92/39.48  | |   (11)  all_57_2 = e2 & op(e2, e3) = e2
% 227.92/39.48  | | 
% 227.92/39.48  | | REF_CLOSE: (4), (8), (11) are inconsistent by sub-proof #1925.
% 227.92/39.48  | | 
% 227.92/39.48  | End of split
% 227.92/39.48  | 
% 227.92/39.48  End of proof
% 227.92/39.48  
% 227.92/39.48  Sub-proof #392 shows that the following formulas are inconsistent:
% 227.92/39.48  ----------------------------------------------------------------
% 227.92/39.48    (1)  all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 227.92/39.48    (2)   ~ (all_53_7 = e3)
% 227.92/39.48    (3)   ~ (all_53_2 = e1)
% 227.92/39.48    (4)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 227.92/39.48    (5)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 227.92/39.48    (6)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 227.92/39.48         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 227.92/39.48    (7)  op(e3, e1) = all_52_5
% 227.92/39.48    (8)   ~ (all_52_7 = e3)
% 227.92/39.48    (9)   ~ (all_52_3 = all_52_5)
% 227.92/39.48    (10)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 227.92/39.48          (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 227.92/39.48    (11)   ~ (all_53_8 = all_53_12)
% 227.92/39.48    (12)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 227.92/39.48          (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.92/39.48    (13)   ~ (e3 = e1)
% 227.92/39.49    (14)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 227.92/39.49          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 227.92/39.49    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.92/39.49            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.92/39.49    (16)  op(all_52_5, all_52_5) = e1
% 227.92/39.49    (17)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 227.92/39.49          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 227.92/39.49    (18)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 227.92/39.49            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 227.92/39.49              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 227.92/39.49    (19)   ~ (all_53_3 = e3)
% 227.92/39.49    (20)   ~ (all_53_3 = all_53_7)
% 227.92/39.49    (21)   ~ (all_6_2 = e3)
% 227.92/39.49    (22)   ~ (all_52_3 = e0)
% 227.92/39.49    (23)   ~ (all_53_9 = e1)
% 227.92/39.49    (24)  op(e1, e1) = all_6_2
% 227.92/39.49    (25)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 227.92/39.49    (26)  op(all_52_7, all_52_7) = e0
% 227.92/39.49    (27)   ~ (all_53_1 = all_53_9)
% 227.92/39.49    (28)  op(e3, e2) = all_52_3
% 227.92/39.49    (29)   ~ (all_53_9 = e0)
% 227.92/39.49    (30)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 227.92/39.49          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 227.92/39.49    (31)   ~ (all_52_5 = all_52_7)
% 227.92/39.49    (32)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 227.92/39.49            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 227.92/39.49              e3) = all_22_1 & $i(all_22_1))
% 227.92/39.49    (33)  all_55_3 = all_52_7
% 227.92/39.49    (34)   ~ (all_53_4 = all_53_12)
% 227.92/39.49    (35)  all_57_12 = e2 & op(e0, e3) = e2
% 227.92/39.49    (36)   ~ (all_53_13 = e3)
% 227.92/39.49    (37)   ~ (all_53_8 = all_53_9)
% 227.92/39.49    (38)   ~ (all_53_7 = all_52_3)
% 227.92/39.49    (39)  all_42_2 = all_6_2
% 227.92/39.49    (40)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 227.92/39.49          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 227.92/39.49    (41)  op(e2, e2) = e0
% 227.92/39.49    (42)  all_55_4 = all_53_1
% 227.92/39.49    (43)   ~ (all_53_9 = all_6_2)
% 227.92/39.49    (44)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 227.92/39.49          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 227.92/39.49    (45)  all_57_3 = e0
% 227.92/39.49    (46)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 227.92/39.49          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 227.92/39.49    (47)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 227.92/39.49    (48)  all_55_1 = all_53_4
% 227.92/39.49    (49)   ~ (all_53_13 = all_52_7)
% 227.92/39.49    (50)  all_55_7 = e3 | all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 227.92/39.49    (51)  all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 227.92/39.49    (52)   ~ (e3 = e0)
% 227.92/39.49    (53)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 227.92/39.49          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 227.92/39.49    (54)   ~ (all_6_2 = e2)
% 227.92/39.49    (55)   ~ (all_53_8 = all_6_2)
% 227.92/39.49    (56)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 227.92/39.49    (57)   ~ (all_53_2 = e0)
% 227.92/39.49    (58)  all_57_0 = e0
% 227.92/39.49    (59)  all_55_2 = all_53_8
% 227.92/39.49    (60)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 227.92/39.49    (61)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 227.92/39.49          | (all_57_14 = e0 & op(e0, e1) = e0)
% 227.92/39.49    (62)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 227.92/39.49    (63)  all_57_15 = e3
% 227.92/39.49    (64)   ~ (all_53_9 = all_53_13)
% 227.92/39.49    (65)   ~ (all_53_7 = e0)
% 227.92/39.49    (66)  op(e3, e3) = e0
% 227.92/39.49    (67)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 227.92/39.49          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 227.92/39.49            e1)
% 227.92/39.49    (68)  all_57_11 = e0
% 227.92/39.49    (69)  all_57_12 = e1
% 227.92/39.49    (70)   ~ (all_53_4 = all_53_8)
% 227.92/39.49    (71)  all_55_6 = all_53_9
% 227.92/39.49    (72)  op(e3, e2) = all_53_4
% 227.92/39.49    (73)   ~ (all_53_1 = all_53_2)
% 227.92/39.49    (74)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 227.92/39.49            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 227.92/39.49            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 227.92/39.49            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 227.92/39.49              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 227.92/39.49            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 227.92/39.49            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 227.92/39.49              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 227.92/39.49              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 227.92/39.49            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 227.92/39.49            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 227.92/39.49            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 227.92/39.49              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 227.92/39.49              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 227.92/39.49            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 227.92/39.49              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 227.92/39.49            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 227.92/39.49            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 227.92/39.49              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 227.92/39.49              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 227.92/39.49            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 227.92/39.49            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 227.92/39.49    (75)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 227.92/39.49            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 227.92/39.49              e3) = all_12_1 & $i(all_12_1))
% 227.92/39.49    (76)  all_55_12 = all_53_3
% 227.92/39.49    (77)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 227.92/39.49          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 227.92/39.49    (78)   ~ (all_53_1 = e0)
% 227.92/39.49    (79)   ~ (e1 = e0)
% 227.92/39.49    (80)   ~ (all_52_3 = all_52_7)
% 227.92/39.49    (81)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 227.92/39.49            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 227.92/39.49              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 227.92/39.49    (82)   ~ (all_53_4 = e0)
% 227.92/39.49    (83)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 227.92/39.49          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 227.92/39.49    (84)  all_57_8 = e2
% 227.92/39.49    (85)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 227.92/39.49          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 227.92/39.49    (86)  all_55_8 = all_53_2
% 227.92/39.49    (87)  op(e0, e0) = e3
% 227.92/39.49    (88)   ~ (all_53_4 = all_53_6)
% 227.92/39.49    (89)  all_55_2 = all_52_5
% 227.92/39.49    (90)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.92/39.49          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 227.92/39.49            e2)
% 227.92/39.49    (91)   ~ (all_53_3 = e0)
% 227.92/39.49    (92)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 227.92/39.49              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 227.92/39.49                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 227.92/39.49                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 227.92/39.49    (93)  all_55_10 = all_6_2
% 227.92/39.49    (94)   ~ (all_53_13 = e0)
% 227.92/39.49    (95)   ~ (all_53_1 = all_53_13)
% 227.92/39.49    (96)  all_55_13 = all_53_7
% 227.92/39.49    (97)   ~ (all_53_9 = all_52_5)
% 227.92/39.49    (98)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 227.92/39.49          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 227.92/39.49    (99)  all_38_2 = all_6_2
% 227.92/39.49    (100)  all_55_3 = all_53_12
% 227.92/39.49    (101)   ~ (all_53_12 = e3)
% 227.92/39.49    (102)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0
% 227.92/39.49             & op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~
% 227.92/39.49             (all_42_1 = e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 227.92/39.49    (103)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 227.92/39.49           (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 227.92/39.49    (104)  all_55_1 = all_52_3
% 227.92/39.49    (105)   ~ (all_52_5 = all_6_2)
% 227.92/39.49    (106)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 227.92/39.49           (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 227.92/39.49    (107)   ~ (all_52_5 = e1)
% 227.92/39.49    (108)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 227.92/39.49           | (all_57_11 = e0 & op(e1, e0) = e0)
% 227.92/39.49    (109)   ~ (all_52_5 = e0)
% 227.92/39.49    (110)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 227.92/39.49           | (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 227.92/39.49             e2)
% 227.92/39.49    (111)  op(e2, e1) = all_53_9
% 227.92/39.49    (112)  op(e1, e2) = all_53_6
% 227.92/39.49    (113)   ~ (all_6_2 = e0)
% 227.92/39.49    (114)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 227.92/39.49           (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 227.92/39.49    (115)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 227.92/39.49    (116)  all_24_2 = all_6_2
% 227.92/39.49    (117)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 227.92/39.49           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 227.92/39.49    (118)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 227.92/39.49           (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 227.92/39.49    (119)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 227.92/39.49           | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 227.92/39.49             e1)
% 227.92/39.49    (120)  all_57_14 = e0
% 227.92/39.49    (121)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 227.92/39.49           (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 227.92/39.49    (122)  op(e3, e0) = all_52_7
% 227.92/39.49    (123)  op(e3, e1) = all_53_8
% 227.92/39.49    (124)  all_55_7 = all_53_13
% 227.92/39.49    (125)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 227.92/39.49           (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 227.92/39.49    (126)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 227.92/39.49           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 227.92/39.49    (127)  op(e3, e0) = all_53_12
% 227.92/39.49  
% 227.92/39.49  Begin of proof
% 227.92/39.49  | 
% 227.92/39.49  | ALPHA: (35) implies:
% 227.92/39.49  |   (128)  all_57_12 = e2
% 227.92/39.49  | 
% 227.92/39.49  | COMBINE_EQS: (69), (128) imply:
% 227.92/39.49  |   (129)  e2 = e1
% 227.92/39.49  | 
% 227.92/39.49  | SIMP: (129) implies:
% 227.92/39.49  |   (130)  e2 = e1
% 227.92/39.49  | 
% 227.92/39.49  | COMBINE_EQS: (84), (130) imply:
% 227.92/39.49  |   (131)  all_57_8 = e1
% 227.92/39.49  | 
% 227.92/39.49  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 227.92/39.49  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 227.92/39.49  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 227.92/39.49  |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 227.92/39.49  |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 227.92/39.49  |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 227.92/39.49  |            (70), (71), (72), (73), (74), (75), (76), (77), (78), (79), (80),
% 227.92/39.49  |            (81), (82), (83), (85), (86), (87), (88), (89), (90), (91), (92),
% 227.92/39.49  |            (93), (94), (95), (96), (97), (98), (99), (100), (101), (102),
% 227.92/39.49  |            (103), (104), (105), (106), (107), (108), (109), (110), (111),
% 227.92/39.49  |            (112), (113), (114), (115), (116), (117), (118), (119), (120),
% 227.92/39.49  |            (121), (122), (123), (124), (125), (126), (127), (131) are
% 227.92/39.49  |            inconsistent by sub-proof #403.
% 227.92/39.49  | 
% 227.92/39.49  End of proof
% 227.92/39.49  
% 227.92/39.49  Sub-proof #393 shows that the following formulas are inconsistent:
% 227.92/39.49  ----------------------------------------------------------------
% 227.92/39.49    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 227.92/39.49    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 227.92/39.49    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 227.92/39.49         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 227.92/39.49    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 227.92/39.49         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 227.92/39.49    (5)   ~ (all_53_8 = all_53_12)
% 227.92/39.49    (6)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 227.92/39.49         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.92/39.49    (7)   ~ (e3 = e1)
% 227.92/39.49    (8)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 227.92/39.49         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 227.92/39.49    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.92/39.49           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.92/39.49    (10)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 227.92/39.49          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 227.92/39.49    (11)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 227.92/39.49            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 227.92/39.49              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 227.92/39.49    (12)   ~ (all_6_2 = e3)
% 227.92/39.49    (13)  op(e1, e1) = all_6_2
% 227.92/39.49    (14)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 227.92/39.49    (15)   ~ (all_53_9 = e0)
% 227.92/39.49    (16)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 227.92/39.49          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 227.92/39.49    (17)   ~ (all_53_4 = all_53_12)
% 227.92/39.49    (18)   ~ (all_53_8 = all_53_9)
% 227.92/39.49    (19)  all_42_2 = all_6_2
% 227.92/39.49    (20)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 227.92/39.49          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 227.92/39.49    (21)  all_57_6 = e1
% 227.92/39.49    (22)   ~ (all_53_9 = all_6_2)
% 227.92/39.49    (23)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 227.92/39.49          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 227.92/39.49    (24)  all_57_3 = e0
% 227.92/39.49    (25)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 227.92/39.49          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 227.92/39.49    (26)  all_57_4 = e3
% 227.92/39.49    (27)   ~ (e3 = e2)
% 227.92/39.49    (28)  all_55_1 = all_53_4
% 227.92/39.49    (29)   ~ (e3 = e0)
% 227.92/39.49    (30)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 227.92/39.49          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 227.92/39.49    (31)   ~ (all_53_8 = all_6_2)
% 227.92/39.49    (32)  all_55_2 = all_53_8
% 227.92/39.49    (33)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 227.92/39.49          | (all_57_14 = e0 & op(e0, e1) = e0)
% 227.92/39.49    (34)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 227.92/39.49    (35)  all_57_15 = e3
% 227.92/39.49    (36)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 227.92/39.49          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 227.92/39.49            e1)
% 227.92/39.49    (37)   ~ (all_53_4 = all_53_8)
% 227.92/39.49    (38)  op(e3, e2) = all_53_4
% 227.92/39.49    (39)   ~ (e2 = e0)
% 227.92/39.49    (40)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 227.92/39.49            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 227.92/39.49            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 227.92/39.49            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 227.92/39.49              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 227.92/39.49            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 227.92/39.49            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 227.92/39.49              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 227.92/39.49              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 227.92/39.49            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 227.92/39.49            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 227.92/39.49            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 227.92/39.49              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 227.92/39.49              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 227.92/39.49            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 227.92/39.49              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 227.92/39.49            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 227.92/39.49            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 227.92/39.49              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 227.92/39.49              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 227.92/39.49            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 227.92/39.49            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 227.92/39.49    (41)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 227.92/39.49          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 227.92/39.49    (42)   ~ (e1 = e0)
% 227.92/39.49    (43)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 227.92/39.49            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 227.92/39.49              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 227.92/39.49    (44)   ~ (all_53_4 = e0)
% 227.92/39.49    (45)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 227.92/39.49          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 227.92/39.49    (46)  op(e0, e0) = e3
% 227.92/39.49    (47)  all_57_7 = e2 & op(e1, e2) = e2
% 227.92/39.49    (48)   ~ (all_53_4 = all_53_6)
% 227.92/39.49    (49)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.92/39.49          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 227.92/39.49            e2)
% 227.92/39.49    (50)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 227.92/39.49              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 227.92/39.49                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 227.92/39.49                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 227.92/39.49    (51)  all_55_10 = all_6_2
% 227.92/39.49    (52)  all_38_2 = all_6_2
% 227.92/39.49    (53)  all_55_3 = all_53_12
% 227.92/39.49    (54)   ~ (all_53_12 = e3)
% 227.92/39.49    (55)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 227.92/39.49            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 227.92/39.49              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 227.92/39.49    (56)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 227.92/39.49          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 227.92/39.49    (57)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 227.92/39.49          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 227.92/39.49    (58)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) |
% 227.92/39.49          (all_57_11 = e0 & op(e1, e0) = e0)
% 227.92/39.49    (59)   ~ (e2 = e1)
% 227.92/39.49    (60)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 227.92/39.49          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 227.92/39.49    (61)  op(e2, e1) = all_53_9
% 227.92/39.49    (62)  op(e1, e2) = all_53_6
% 227.92/39.49    (63)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 227.92/39.49          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 227.92/39.49    (64)  all_24_2 = all_6_2
% 227.92/39.49    (65)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 227.92/39.49          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 227.92/39.49    (66)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 227.92/39.49          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 227.92/39.49    (67)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 227.92/39.49          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 227.92/39.49    (68)  all_57_14 = e0
% 227.92/39.49    (69)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 227.92/39.49          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 227.92/39.49    (70)  op(e3, e1) = all_53_8
% 227.92/39.49    (71)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 227.92/39.49          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 227.92/39.49    (72)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 227.92/39.49          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 227.92/39.49    (73)  op(e3, e0) = all_53_12
% 227.92/39.49  
% 227.92/39.49  Begin of proof
% 227.92/39.49  | 
% 227.92/39.49  | ALPHA: (47) implies:
% 227.92/39.49  |   (74)  all_57_7 = e2
% 227.92/39.49  | 
% 227.92/39.49  | BETA: splitting (10) gives:
% 227.92/39.49  | 
% 227.92/39.49  | Case 1:
% 227.92/39.49  | | 
% 227.92/39.49  | |   (75)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 227.92/39.49  | |           e3)
% 227.92/39.49  | | 
% 227.92/39.49  | | BETA: splitting (75) gives:
% 227.92/39.49  | | 
% 227.92/39.49  | | Case 1:
% 227.92/39.49  | | | 
% 227.92/39.49  | | |   (76)  all_57_6 = e3 & op(e1, e3) = e3
% 227.92/39.49  | | | 
% 227.92/39.49  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 227.92/39.49  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 227.92/39.49  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 227.92/39.49  | | |            (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 227.92/39.49  | | |            (43), (44), (45), (46), (48), (49), (50), (51), (52), (53),
% 227.92/39.49  | | |            (54), (55), (56), (57), (59), (60), (61), (62), (63), (64),
% 227.92/39.49  | | |            (65), (66), (67), (68), (69), (70), (71), (72), (73), (76) are
% 227.92/39.49  | | |            inconsistent by sub-proof #395.
% 227.92/39.49  | | | 
% 227.92/39.49  | | Case 2:
% 227.92/39.49  | | | 
% 227.92/39.49  | | |   (77)  all_57_7 = e3 & op(e1, e2) = e3
% 227.92/39.49  | | | 
% 227.92/39.49  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 227.92/39.49  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (22), (23),
% 227.92/39.49  | | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (34),
% 227.92/39.49  | | |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44),
% 227.92/39.49  | | |            (45), (46), (48), (49), (50), (51), (52), (53), (54), (55),
% 227.92/39.49  | | |            (56), (59), (60), (61), (62), (63), (64), (65), (66), (67),
% 227.92/39.49  | | |            (69), (70), (71), (72), (73), (74), (77) are inconsistent by
% 227.92/39.49  | | |            sub-proof #394.
% 227.92/39.49  | | | 
% 227.92/39.49  | | End of split
% 227.92/39.49  | | 
% 227.92/39.49  | Case 2:
% 227.92/39.49  | | 
% 227.92/39.49  | |   (78)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 227.92/39.49  | |           e3)
% 227.92/39.49  | | 
% 227.92/39.50  | | REF_CLOSE: (7), (9), (12), (13), (27), (29), (35), (39), (42), (58), (59),
% 227.92/39.50  | |            (60), (67), (78) are inconsistent by sub-proof #1080.
% 227.92/39.50  | | 
% 227.92/39.50  | End of split
% 227.92/39.50  | 
% 227.92/39.50  End of proof
% 227.92/39.50  
% 227.92/39.50  Sub-proof #394 shows that the following formulas are inconsistent:
% 227.92/39.50  ----------------------------------------------------------------
% 227.92/39.50    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 227.92/39.50    (2)  all_57_7 = e3 & op(e1, e2) = e3
% 227.92/39.50    (3)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 227.92/39.50    (4)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 227.92/39.50         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 227.92/39.50    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 227.92/39.50         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 227.92/39.50    (6)   ~ (all_53_8 = all_53_12)
% 227.92/39.50    (7)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 227.92/39.50         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.92/39.50    (8)   ~ (e3 = e1)
% 227.92/39.50    (9)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 227.92/39.50         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 227.92/39.50    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.92/39.50            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.92/39.50    (11)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 227.92/39.50          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 227.92/39.50    (12)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 227.92/39.50            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 227.92/39.50              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 227.92/39.50    (13)   ~ (all_6_2 = e3)
% 227.92/39.50    (14)  op(e1, e1) = all_6_2
% 227.92/39.50    (15)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 227.92/39.50    (16)   ~ (all_53_9 = e0)
% 227.92/39.50    (17)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 227.92/39.50          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 227.92/39.50    (18)  all_57_7 = e2
% 227.92/39.50    (19)   ~ (all_53_4 = all_53_12)
% 227.92/39.50    (20)   ~ (all_53_8 = all_53_9)
% 227.92/39.50    (21)  all_42_2 = all_6_2
% 227.92/39.50    (22)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 227.92/39.50          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 227.92/39.50    (23)   ~ (all_53_9 = all_6_2)
% 227.92/39.50    (24)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 227.92/39.50          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 227.92/39.50    (25)  all_57_3 = e0
% 227.92/39.50    (26)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 227.92/39.50          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 227.92/39.50    (27)  all_57_4 = e3
% 227.92/39.50    (28)   ~ (e3 = e2)
% 227.92/39.50    (29)  all_55_1 = all_53_4
% 227.92/39.50    (30)   ~ (e3 = e0)
% 227.92/39.50    (31)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 227.92/39.50          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 227.92/39.50    (32)   ~ (all_53_8 = all_6_2)
% 227.92/39.50    (33)  all_55_2 = all_53_8
% 227.92/39.50    (34)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 227.92/39.50    (35)  all_57_15 = e3
% 227.92/39.50    (36)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 227.92/39.50          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 227.92/39.50            e1)
% 227.92/39.50    (37)   ~ (all_53_4 = all_53_8)
% 227.92/39.50    (38)  op(e3, e2) = all_53_4
% 227.92/39.50    (39)   ~ (e2 = e0)
% 227.92/39.50    (40)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 227.92/39.50            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 227.92/39.50            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 227.92/39.50            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 227.92/39.50              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 227.92/39.50            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 227.92/39.50            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 227.92/39.50              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 227.92/39.50              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 227.92/39.50            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 227.92/39.50            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 227.92/39.50            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 227.92/39.50              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 227.92/39.50              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 227.92/39.50            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 227.92/39.50              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 227.92/39.50            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 227.92/39.50            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 227.92/39.50              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 227.92/39.50              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 227.92/39.50            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 227.92/39.50            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 227.92/39.50    (41)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 227.92/39.50          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 227.92/39.50    (42)   ~ (e1 = e0)
% 227.92/39.50    (43)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 227.92/39.50            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 227.92/39.50              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 227.92/39.50    (44)   ~ (all_53_4 = e0)
% 227.92/39.50    (45)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 227.92/39.50          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 227.92/39.50    (46)  op(e0, e0) = e3
% 227.92/39.50    (47)   ~ (all_53_4 = all_53_6)
% 227.92/39.50    (48)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.92/39.50          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 227.92/39.50            e2)
% 227.92/39.50    (49)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 227.92/39.50              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 227.92/39.50                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 227.92/39.50                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 227.92/39.50    (50)  all_55_10 = all_6_2
% 227.92/39.50    (51)  all_38_2 = all_6_2
% 227.92/39.50    (52)  all_55_3 = all_53_12
% 227.92/39.50    (53)   ~ (all_53_12 = e3)
% 227.92/39.50    (54)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 227.92/39.50            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 227.92/39.50              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 227.92/39.50    (55)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 227.92/39.50          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 227.92/39.50    (56)   ~ (e2 = e1)
% 227.92/39.50    (57)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 227.92/39.50          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 227.92/39.50    (58)  op(e2, e1) = all_53_9
% 227.92/39.50    (59)  op(e1, e2) = all_53_6
% 227.92/39.50    (60)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 227.92/39.50          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 227.92/39.50    (61)  all_24_2 = all_6_2
% 227.92/39.50    (62)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 227.92/39.50          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 227.92/39.50    (63)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 227.92/39.50          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 227.92/39.50    (64)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 227.92/39.50          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 227.92/39.50    (65)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 227.92/39.50          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 227.92/39.50    (66)  op(e3, e1) = all_53_8
% 227.92/39.50    (67)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 227.92/39.50          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 227.92/39.50    (68)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 227.92/39.50          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 227.92/39.50    (69)  op(e3, e0) = all_53_12
% 227.92/39.50  
% 227.92/39.50  Begin of proof
% 227.92/39.50  | 
% 227.92/39.50  | ALPHA: (2) implies:
% 227.92/39.50  |   (70)  all_57_7 = e3
% 227.92/39.50  | 
% 227.92/39.50  | COMBINE_EQS: (18), (70) imply:
% 227.92/39.50  |   (71)  e3 = e2
% 227.92/39.50  | 
% 227.92/39.50  | SIMP: (71) implies:
% 227.92/39.50  |   (72)  e3 = e2
% 227.92/39.50  | 
% 227.92/39.50  | COMBINE_EQS: (27), (72) imply:
% 227.92/39.50  |   (73)  all_57_4 = e2
% 227.92/39.50  | 
% 227.92/39.50  | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 227.92/39.50  |            (14), (15), (16), (17), (19), (20), (21), (22), (23), (24), (25),
% 227.92/39.50  |            (26), (28), (29), (30), (31), (32), (33), (34), (35), (36), (37),
% 227.92/39.50  |            (38), (39), (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 227.92/39.50  |            (49), (50), (51), (52), (53), (54), (55), (56), (57), (58), (59),
% 227.92/39.50  |            (60), (61), (62), (63), (64), (65), (66), (67), (68), (69), (70),
% 227.92/39.50  |            (73) are inconsistent by sub-proof #546.
% 227.92/39.50  | 
% 227.92/39.50  End of proof
% 227.92/39.50  
% 227.92/39.50  Sub-proof #395 shows that the following formulas are inconsistent:
% 227.92/39.50  ----------------------------------------------------------------
% 227.92/39.50    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 227.92/39.50    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 227.92/39.50    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 227.92/39.50         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 227.92/39.50    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 227.92/39.50         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 227.92/39.50    (5)   ~ (all_53_8 = all_53_12)
% 227.92/39.50    (6)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 227.92/39.50         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.92/39.50    (7)   ~ (e3 = e1)
% 227.92/39.50    (8)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 227.92/39.50         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 227.92/39.50    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.92/39.50           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.92/39.50    (10)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 227.92/39.50          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 227.92/39.50    (11)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 227.92/39.50            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 227.92/39.50              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 227.92/39.50    (12)   ~ (all_6_2 = e3)
% 227.92/39.50    (13)  op(e1, e1) = all_6_2
% 227.92/39.50    (14)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 227.92/39.50    (15)   ~ (all_53_9 = e0)
% 227.92/39.50    (16)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 227.92/39.50          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 227.92/39.50    (17)   ~ (all_53_4 = all_53_12)
% 227.92/39.50    (18)   ~ (all_53_8 = all_53_9)
% 227.92/39.50    (19)  all_42_2 = all_6_2
% 227.92/39.50    (20)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 227.92/39.50          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 227.92/39.50    (21)  all_57_6 = e1
% 227.92/39.50    (22)   ~ (all_53_9 = all_6_2)
% 227.92/39.50    (23)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 227.92/39.50          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 227.92/39.50    (24)  all_57_3 = e0
% 227.92/39.50    (25)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 227.92/39.50          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 227.92/39.50    (26)  all_57_4 = e3
% 227.92/39.50    (27)   ~ (e3 = e2)
% 227.92/39.50    (28)  all_55_1 = all_53_4
% 227.92/39.50    (29)   ~ (e3 = e0)
% 227.92/39.50    (30)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 227.92/39.50          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 227.92/39.50    (31)   ~ (all_53_8 = all_6_2)
% 227.92/39.50    (32)  all_55_2 = all_53_8
% 227.92/39.50    (33)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 227.92/39.50          | (all_57_14 = e0 & op(e0, e1) = e0)
% 227.92/39.50    (34)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 227.92/39.50    (35)  all_57_15 = e3
% 227.92/39.50    (36)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 227.92/39.50          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 227.92/39.50            e1)
% 227.92/39.50    (37)   ~ (all_53_4 = all_53_8)
% 227.92/39.50    (38)  op(e3, e2) = all_53_4
% 227.92/39.50    (39)   ~ (e2 = e0)
% 227.92/39.50    (40)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 227.92/39.50            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 227.92/39.50            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 227.92/39.50            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 227.92/39.50              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 227.92/39.50            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 227.92/39.50            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 227.92/39.50              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 227.92/39.50              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 227.92/39.50            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 227.92/39.50            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 227.92/39.50            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 227.92/39.50              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 227.92/39.50              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 227.92/39.50            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 227.92/39.50              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 227.92/39.50            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 227.92/39.50            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 227.92/39.50              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 227.92/39.50              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 227.92/39.50            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 227.92/39.50            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 227.92/39.50    (41)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 227.92/39.50          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 227.92/39.50    (42)   ~ (e1 = e0)
% 227.92/39.50    (43)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 227.92/39.50            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 227.92/39.50              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 227.92/39.50    (44)   ~ (all_53_4 = e0)
% 227.92/39.50    (45)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 227.92/39.50          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 227.92/39.50    (46)  op(e0, e0) = e3
% 227.92/39.50    (47)   ~ (all_53_4 = all_53_6)
% 227.92/39.50    (48)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.92/39.50          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 227.92/39.50            e2)
% 227.92/39.50    (49)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 227.92/39.50              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 227.92/39.50                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 227.92/39.50                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 227.92/39.50    (50)  all_55_10 = all_6_2
% 227.92/39.50    (51)  all_38_2 = all_6_2
% 227.92/39.50    (52)  all_55_3 = all_53_12
% 227.92/39.50    (53)   ~ (all_53_12 = e3)
% 227.92/39.50    (54)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 227.92/39.50            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 227.92/39.50              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 227.92/39.50    (55)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 227.92/39.50          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 227.92/39.50    (56)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 227.92/39.50          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 227.92/39.50    (57)   ~ (e2 = e1)
% 227.92/39.50    (58)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 227.92/39.50          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 227.92/39.50    (59)  op(e2, e1) = all_53_9
% 227.92/39.50    (60)  op(e1, e2) = all_53_6
% 227.92/39.50    (61)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 227.92/39.50          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 227.92/39.50    (62)  all_57_6 = e3 & op(e1, e3) = e3
% 227.92/39.50    (63)  all_24_2 = all_6_2
% 227.92/39.50    (64)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 227.92/39.50          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 227.92/39.50    (65)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 227.92/39.50          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 227.92/39.50    (66)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 227.92/39.50          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 227.92/39.50    (67)  all_57_14 = e0
% 227.92/39.50    (68)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 227.92/39.50          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 227.92/39.50    (69)  op(e3, e1) = all_53_8
% 227.92/39.50    (70)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 227.92/39.50          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 227.92/39.50    (71)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 227.92/39.50          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 227.92/39.50    (72)  op(e3, e0) = all_53_12
% 227.92/39.50  
% 227.92/39.50  Begin of proof
% 227.92/39.50  | 
% 227.92/39.50  | ALPHA: (62) implies:
% 227.92/39.50  |   (73)  all_57_6 = e3
% 227.92/39.50  | 
% 227.92/39.50  | COMBINE_EQS: (21), (73) imply:
% 227.92/39.50  |   (74)  e3 = e1
% 227.92/39.50  | 
% 227.92/39.50  | SIMP: (74) implies:
% 227.92/39.50  |   (75)  e3 = e1
% 227.92/39.50  | 
% 227.92/39.50  | COMBINE_EQS: (26), (75) imply:
% 227.92/39.50  |   (76)  all_57_4 = e1
% 227.92/39.50  | 
% 227.92/39.50  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 227.92/39.50  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 227.92/39.50  |            (24), (25), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 227.92/39.50  |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 227.92/39.50  |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 227.92/39.50  |            (58), (59), (60), (61), (63), (64), (65), (66), (67), (68), (69),
% 227.92/39.50  |            (70), (71), (72), (76) are inconsistent by sub-proof #438.
% 227.92/39.50  | 
% 227.92/39.50  End of proof
% 227.92/39.50  
% 227.92/39.50  Sub-proof #396 shows that the following formulas are inconsistent:
% 227.92/39.50  ----------------------------------------------------------------
% 227.92/39.50    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 227.92/39.50         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 227.92/39.50    (2)   ~ (e3 = e1)
% 227.92/39.50    (3)  all_57_0 = e1 & op(e3, e3) = e1
% 227.92/39.50    (4)  all_57_3 = e0
% 227.92/39.50    (5)  all_57_0 = e0
% 227.92/39.50    (6)  all_57_10 = e2
% 227.92/39.50    (7)  all_57_2 = e3
% 227.92/39.50    (8)   ~ (e1 = e0)
% 227.92/39.50    (9)  all_57_5 = e1
% 227.92/39.50    (10)   ~ (e2 = e1)
% 227.92/39.50  
% 227.92/39.50  Begin of proof
% 227.92/39.50  | 
% 227.92/39.50  | ALPHA: (3) implies:
% 227.92/39.50  |   (11)  all_57_0 = e1
% 227.92/39.50  | 
% 227.92/39.50  | COMBINE_EQS: (5), (11) imply:
% 227.92/39.50  |   (12)  e1 = e0
% 227.92/39.50  | 
% 227.92/39.50  | SIMP: (12) implies:
% 227.92/39.50  |   (13)  e1 = e0
% 227.92/39.50  | 
% 227.92/39.50  | COMBINE_EQS: (9), (13) imply:
% 227.92/39.50  |   (14)  all_57_5 = e0
% 227.92/39.50  | 
% 227.92/39.50  | REF_CLOSE: (1), (2), (4), (6), (7), (8), (10), (14) are inconsistent by
% 227.92/39.50  |            sub-proof #2359.
% 227.92/39.50  | 
% 227.92/39.50  End of proof
% 227.92/39.50  
% 227.92/39.50  Sub-proof #397 shows that the following formulas are inconsistent:
% 227.92/39.50  ----------------------------------------------------------------
% 227.92/39.50    (1)  all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 227.92/39.50    (2)   ~ (all_53_7 = e3)
% 227.92/39.50    (3)   ~ (all_53_2 = e1)
% 227.92/39.50    (4)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 227.92/39.50    (5)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 227.92/39.50    (6)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 227.92/39.50         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 227.92/39.50    (7)  op(e3, e1) = all_52_5
% 227.92/39.50    (8)   ~ (all_52_7 = e3)
% 227.92/39.50    (9)   ~ (all_52_3 = all_52_5)
% 227.92/39.50    (10)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 227.92/39.50          (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 227.92/39.50    (11)   ~ (all_53_8 = all_53_12)
% 227.92/39.50    (12)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 227.92/39.50          (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.92/39.50    (13)   ~ (e3 = e1)
% 227.92/39.50    (14)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 227.92/39.50          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 227.92/39.50    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.92/39.50            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.92/39.50    (16)  op(all_52_5, all_52_5) = e1
% 227.92/39.50    (17)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 227.92/39.50          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 227.92/39.50    (18)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 227.92/39.50            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 227.92/39.50              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 227.92/39.50    (19)   ~ (all_53_3 = e3)
% 227.92/39.50    (20)   ~ (all_53_3 = all_53_7)
% 227.92/39.50    (21)   ~ (all_6_2 = e3)
% 227.92/39.50    (22)   ~ (all_52_3 = e0)
% 227.92/39.50    (23)   ~ (all_53_9 = e1)
% 227.92/39.50    (24)  op(e1, e1) = all_6_2
% 227.92/39.50    (25)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 227.92/39.50    (26)  op(all_52_7, all_52_7) = e0
% 227.92/39.50    (27)   ~ (all_53_1 = all_53_9)
% 227.92/39.50    (28)  op(e3, e2) = all_52_3
% 227.92/39.50    (29)   ~ (all_53_9 = e0)
% 227.92/39.50    (30)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 227.92/39.50          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 227.92/39.50    (31)   ~ (all_52_5 = all_52_7)
% 227.92/39.51    (32)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 227.92/39.51            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 227.92/39.51              e3) = all_22_1 & $i(all_22_1))
% 227.92/39.51    (33)  all_55_3 = all_52_7
% 227.92/39.51    (34)   ~ (all_53_4 = all_53_12)
% 227.92/39.51    (35)   ~ (all_53_13 = e3)
% 227.92/39.51    (36)   ~ (all_53_8 = all_53_9)
% 227.92/39.51    (37)   ~ (all_53_7 = all_52_3)
% 227.92/39.51    (38)  all_42_2 = all_6_2
% 227.92/39.51    (39)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 227.92/39.51          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 227.92/39.51    (40)  op(e2, e2) = e0
% 227.92/39.51    (41)  all_55_4 = all_53_1
% 227.92/39.51    (42)   ~ (all_53_9 = all_6_2)
% 227.92/39.51    (43)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 227.92/39.51          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 227.92/39.51    (44)  all_57_3 = e0
% 227.92/39.51    (45)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 227.92/39.51          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 227.92/39.51    (46)   ~ (e3 = e2)
% 227.92/39.51    (47)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 227.92/39.51    (48)  all_55_1 = all_53_4
% 227.92/39.51    (49)   ~ (all_53_13 = all_52_7)
% 227.92/39.51    (50)  all_55_7 = e3 | all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 227.92/39.51    (51)  all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 227.92/39.51    (52)   ~ (e3 = e0)
% 227.92/39.51    (53)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 227.92/39.51          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 227.92/39.51    (54)   ~ (all_6_2 = e2)
% 227.92/39.51    (55)   ~ (all_53_8 = all_6_2)
% 227.92/39.51    (56)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 227.92/39.51    (57)   ~ (all_53_2 = e0)
% 227.92/39.51    (58)  all_57_0 = e0
% 227.92/39.51    (59)  all_55_2 = all_53_8
% 227.92/39.51    (60)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 227.92/39.51    (61)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 227.92/39.51          | (all_57_14 = e0 & op(e0, e1) = e0)
% 227.92/39.51    (62)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 227.92/39.51    (63)  all_57_15 = e3
% 227.92/39.51    (64)   ~ (all_53_9 = all_53_13)
% 227.92/39.51    (65)   ~ (all_53_7 = e0)
% 227.92/39.51    (66)  all_57_4 = e1
% 227.92/39.51    (67)  op(e3, e3) = e0
% 227.92/39.51    (68)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 227.92/39.51          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 227.92/39.51            e1)
% 227.92/39.51    (69)  op(e3, e3) = all_52_1
% 227.92/39.51    (70)  all_57_11 = e0
% 227.92/39.51    (71)   ~ (all_53_4 = all_53_8)
% 227.92/39.51    (72)  all_55_6 = all_53_9
% 227.92/39.51    (73)  op(e3, e2) = all_53_4
% 227.92/39.51    (74)   ~ (all_53_1 = all_53_2)
% 227.92/39.51    (75)  op(e1, e1) = e1
% 227.92/39.51    (76)  op(all_52_1, all_52_1) = e3
% 227.92/39.51    (77)   ~ (e2 = e0)
% 227.92/39.51    (78)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 227.92/39.51            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 227.92/39.51            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 227.92/39.51            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 227.92/39.51              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 227.92/39.51            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 227.92/39.51            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 227.92/39.51              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 227.92/39.51              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 227.92/39.51            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 227.92/39.51            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 227.92/39.51            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 227.92/39.51              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 227.92/39.51              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 227.92/39.51            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 227.92/39.51              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 227.92/39.51            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 227.92/39.51            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 227.92/39.51              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 227.92/39.51              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 227.92/39.51            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 227.92/39.51            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 227.92/39.51    (79)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 227.92/39.51            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 227.92/39.51              e3) = all_12_1 & $i(all_12_1))
% 227.92/39.51    (80)  all_55_12 = all_53_3
% 227.92/39.51    (81)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 227.92/39.51          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 227.92/39.51    (82)   ~ (all_53_1 = e0)
% 227.92/39.51    (83)   ~ (e1 = e0)
% 227.92/39.51    (84)   ~ (all_52_3 = all_52_7)
% 227.92/39.51    (85)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 227.92/39.51            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 227.92/39.51              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 227.92/39.51    (86)   ~ (all_53_4 = e0)
% 227.92/39.51    (87)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 227.92/39.51          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 227.92/39.51    (88)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 227.92/39.51          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 227.92/39.51    (89)  all_55_8 = all_53_2
% 227.92/39.51    (90)  op(e0, e0) = e3
% 227.92/39.51    (91)   ~ (all_53_4 = all_53_6)
% 227.92/39.51    (92)  all_55_2 = all_52_5
% 227.92/39.51    (93)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.92/39.51          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 227.92/39.51            e2)
% 227.92/39.51    (94)   ~ (all_53_3 = e0)
% 227.92/39.51    (95)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 227.92/39.51              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 227.92/39.51                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 227.92/39.51                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 227.92/39.51    (96)  all_55_10 = all_6_2
% 227.92/39.51    (97)   ~ (all_53_13 = e0)
% 227.92/39.51    (98)   ~ (all_53_1 = all_53_13)
% 227.92/39.51    (99)  all_55_13 = all_53_7
% 227.92/39.51    (100)   ~ (all_53_9 = all_52_5)
% 227.92/39.51    (101)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 227.92/39.51           (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 227.92/39.51    (102)  all_38_2 = all_6_2
% 227.92/39.51    (103)  all_55_3 = all_53_12
% 227.92/39.51    (104)   ~ (all_53_12 = e3)
% 227.92/39.51    (105)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0
% 227.92/39.51             & op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~
% 227.92/39.51             (all_42_1 = e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 227.92/39.51    (106)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 227.92/39.51           (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 227.92/39.51    (107)  all_55_1 = all_52_3
% 227.92/39.51    (108)   ~ (all_52_5 = all_6_2)
% 227.92/39.51    (109)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 227.92/39.51           (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 227.92/39.51    (110)   ~ (all_52_5 = e1)
% 227.92/39.51    (111)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 227.92/39.51           | (all_57_11 = e0 & op(e1, e0) = e0)
% 227.92/39.51    (112)   ~ (all_52_5 = e0)
% 227.92/39.51    (113)   ~ (e2 = e1)
% 227.92/39.51    (114)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 227.92/39.51           | (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 227.92/39.51             e2)
% 227.92/39.51    (115)  op(e2, e1) = all_53_9
% 227.92/39.51    (116)  op(e1, e2) = all_53_6
% 227.92/39.51    (117)   ~ (all_6_2 = e0)
% 227.92/39.51    (118)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 227.92/39.51           (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 227.92/39.51    (119)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 227.92/39.51    (120)  all_24_2 = all_6_2
% 227.92/39.51    (121)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 227.92/39.51           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 227.92/39.51    (122)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 227.92/39.51           (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 227.92/39.51    (123)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 227.92/39.51           | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 227.92/39.51             e1)
% 227.92/39.51    (124)  all_57_14 = e0
% 227.92/39.51    (125)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 227.92/39.51           (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 227.92/39.51    (126)  op(e3, e0) = all_52_7
% 227.92/39.51    (127)  op(e3, e1) = all_53_8
% 227.92/39.51    (128)  all_55_7 = all_53_13
% 227.92/39.51    (129)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 227.92/39.51           (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 227.92/39.51    (130)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 227.92/39.51           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 227.92/39.51    (131)  op(e3, e0) = all_53_12
% 227.92/39.51  
% 227.92/39.51  Begin of proof
% 227.92/39.51  | 
% 227.92/39.51  | BETA: splitting (125) gives:
% 227.92/39.51  | 
% 227.92/39.51  | Case 1:
% 227.92/39.51  | | 
% 227.92/39.51  | |   (132)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) =
% 227.92/39.51  | |            e1)
% 227.92/39.51  | | 
% 227.92/39.51  | | BETA: splitting (132) gives:
% 227.92/39.51  | | 
% 227.92/39.51  | | Case 1:
% 227.92/39.51  | | | 
% 227.92/39.51  | | |   (133)  all_57_6 = e1 & op(e1, e3) = e1
% 227.92/39.51  | | | 
% 227.92/39.51  | | | ALPHA: (133) implies:
% 227.92/39.51  | | |   (134)  all_57_6 = e1
% 227.92/39.51  | | | 
% 227.92/39.51  | | | REF_CLOSE: (4), (5), (6), (10), (11), (12), (13), (14), (15), (17), (18),
% 227.92/39.51  | | |            (21), (24), (25), (29), (30), (34), (36), (38), (39), (42),
% 227.92/39.51  | | |            (43), (44), (45), (46), (48), (52), (53), (55), (59), (61),
% 227.92/39.51  | | |            (62), (63), (66), (68), (71), (73), (77), (78), (81), (83),
% 227.92/39.51  | | |            (85), (86), (87), (90), (91), (93), (95), (96), (102), (103),
% 227.92/39.51  | | |            (104), (105), (106), (109), (113), (114), (115), (116), (118),
% 227.92/39.51  | | |            (120), (121), (122), (123), (124), (125), (127), (129), (130),
% 227.92/39.51  | | |            (131), (134) are inconsistent by sub-proof #438.
% 227.92/39.51  | | | 
% 227.92/39.51  | | Case 2:
% 227.92/39.51  | | | 
% 227.92/39.51  | | |   (135)  all_57_7 = e1 & op(e1, e2) = e1
% 227.92/39.51  | | | 
% 227.92/39.51  | | | ALPHA: (135) implies:
% 227.92/39.51  | | |   (136)  all_57_7 = e1
% 227.92/39.51  | | | 
% 227.92/39.51  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 227.92/39.51  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 227.92/39.51  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 227.92/39.51  | | |            (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 227.92/39.51  | | |            (43), (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 227.92/39.51  | | |            (53), (54), (55), (56), (57), (58), (59), (60), (61), (62),
% 227.92/39.51  | | |            (63), (64), (65), (66), (67), (68), (69), (70), (71), (72),
% 227.92/39.51  | | |            (73), (74), (75), (76), (77), (78), (79), (80), (81), (82),
% 227.92/39.51  | | |            (83), (84), (85), (86), (87), (88), (89), (90), (91), (92),
% 227.92/39.51  | | |            (93), (94), (95), (96), (97), (98), (99), (100), (101), (102),
% 227.92/39.51  | | |            (103), (104), (105), (106), (107), (108), (109), (110), (111),
% 227.92/39.51  | | |            (112), (113), (114), (115), (116), (117), (118), (119), (120),
% 227.92/39.51  | | |            (121), (122), (123), (124), (125), (126), (127), (128), (129),
% 227.92/39.51  | | |            (130), (131), (136) are inconsistent by sub-proof #398.
% 227.92/39.51  | | | 
% 227.92/39.51  | | End of split
% 227.92/39.51  | | 
% 227.92/39.51  | Case 2:
% 227.92/39.51  | | 
% 227.92/39.51  | |   (137)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) =
% 227.92/39.51  | |            e1)
% 227.92/39.51  | | 
% 227.92/39.51  | | BETA: splitting (137) gives:
% 227.92/39.51  | | 
% 227.92/39.51  | | Case 1:
% 227.92/39.51  | | | 
% 227.92/39.51  | | |   (138)  all_57_8 = e1 & op(e1, e1) = e1
% 227.92/39.51  | | | 
% 227.92/39.51  | | | ALPHA: (138) implies:
% 227.92/39.51  | | |   (139)  all_57_8 = e1
% 227.92/39.51  | | | 
% 227.92/39.51  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 227.92/39.51  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 227.92/39.51  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 227.92/39.51  | | |            (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 227.92/39.51  | | |            (43), (44), (45), (47), (48), (49), (50), (51), (52), (53),
% 227.92/39.51  | | |            (54), (55), (56), (57), (58), (59), (60), (61), (62), (63),
% 227.92/39.51  | | |            (64), (65), (67), (68), (70), (71), (72), (73), (74), (78),
% 227.92/39.51  | | |            (79), (80), (81), (82), (83), (84), (85), (86), (87), (88),
% 227.92/39.51  | | |            (89), (90), (91), (92), (93), (94), (95), (96), (97), (98),
% 227.92/39.51  | | |            (99), (100), (101), (102), (103), (104), (105), (106), (107),
% 227.92/39.51  | | |            (108), (109), (110), (111), (112), (114), (115), (116), (117),
% 227.92/39.51  | | |            (118), (119), (120), (121), (122), (123), (124), (125), (126),
% 227.92/39.51  | | |            (127), (128), (129), (130), (131), (139) are inconsistent by
% 227.92/39.51  | | |            sub-proof #403.
% 227.92/39.51  | | | 
% 227.92/39.51  | | Case 2:
% 227.92/39.51  | | | 
% 227.92/39.51  | | |   (140)  all_57_11 = e1 & op(e1, e0) = e1
% 227.92/39.51  | | | 
% 227.92/39.51  | | | ALPHA: (140) implies:
% 227.92/39.51  | | |   (141)  all_57_11 = e1
% 227.92/39.51  | | | 
% 227.92/39.51  | | | REF_CLOSE: (70), (83), (141) are inconsistent by sub-proof #1862.
% 227.92/39.51  | | | 
% 227.92/39.51  | | End of split
% 227.92/39.51  | | 
% 227.92/39.51  | End of split
% 227.92/39.51  | 
% 227.92/39.51  End of proof
% 227.92/39.51  
% 227.92/39.51  Sub-proof #398 shows that the following formulas are inconsistent:
% 227.92/39.51  ----------------------------------------------------------------
% 227.92/39.51    (1)  all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 227.92/39.51    (2)   ~ (all_53_7 = e3)
% 227.92/39.51    (3)   ~ (all_53_2 = e1)
% 227.92/39.51    (4)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 227.92/39.51    (5)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 227.92/39.51    (6)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 227.92/39.51         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 227.92/39.51    (7)  op(e3, e1) = all_52_5
% 227.92/39.51    (8)   ~ (all_52_7 = e3)
% 227.92/39.51    (9)   ~ (all_52_3 = all_52_5)
% 227.92/39.51    (10)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 227.92/39.51          (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 227.92/39.51    (11)   ~ (all_53_8 = all_53_12)
% 227.92/39.51    (12)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 227.92/39.51          (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.92/39.51    (13)   ~ (e3 = e1)
% 227.92/39.51    (14)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 227.92/39.51          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 227.92/39.51    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.92/39.51            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.92/39.51    (16)  op(all_52_5, all_52_5) = e1
% 227.92/39.51    (17)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 227.92/39.51          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 227.92/39.51    (18)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 227.92/39.51            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 227.92/39.51              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 227.92/39.51    (19)   ~ (all_53_3 = e3)
% 227.92/39.51    (20)   ~ (all_53_3 = all_53_7)
% 227.92/39.51    (21)   ~ (all_6_2 = e3)
% 227.92/39.51    (22)   ~ (all_52_3 = e0)
% 227.92/39.51    (23)   ~ (all_53_9 = e1)
% 227.92/39.51    (24)  op(e1, e1) = all_6_2
% 227.92/39.51    (25)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 227.92/39.51    (26)  op(all_52_7, all_52_7) = e0
% 227.92/39.51    (27)   ~ (all_53_1 = all_53_9)
% 227.92/39.51    (28)  op(e3, e2) = all_52_3
% 227.92/39.51    (29)   ~ (all_53_9 = e0)
% 227.92/39.51    (30)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 227.92/39.51          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 227.92/39.51    (31)   ~ (all_52_5 = all_52_7)
% 227.92/39.51    (32)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 227.92/39.51            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 227.92/39.51              e3) = all_22_1 & $i(all_22_1))
% 227.92/39.51    (33)  all_55_3 = all_52_7
% 227.92/39.51    (34)   ~ (all_53_4 = all_53_12)
% 227.92/39.51    (35)   ~ (all_53_13 = e3)
% 227.92/39.51    (36)   ~ (all_53_8 = all_53_9)
% 227.92/39.51    (37)   ~ (all_53_7 = all_52_3)
% 227.92/39.51    (38)  all_57_7 = e1
% 227.92/39.51    (39)  all_42_2 = all_6_2
% 227.92/39.51    (40)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 227.92/39.51          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 227.92/39.51    (41)  op(e2, e2) = e0
% 227.92/39.51    (42)  all_55_4 = all_53_1
% 227.92/39.51    (43)   ~ (all_53_9 = all_6_2)
% 227.92/39.51    (44)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 227.92/39.51          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 227.92/39.51    (45)  all_57_3 = e0
% 227.92/39.51    (46)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 227.92/39.51          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 227.92/39.51    (47)   ~ (e3 = e2)
% 227.92/39.51    (48)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 227.92/39.51    (49)  all_55_1 = all_53_4
% 227.92/39.51    (50)   ~ (all_53_13 = all_52_7)
% 227.92/39.51    (51)  all_55_7 = e3 | all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 227.92/39.51    (52)  all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 227.92/39.51    (53)   ~ (e3 = e0)
% 227.92/39.51    (54)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 227.92/39.51          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 227.92/39.51    (55)   ~ (all_6_2 = e2)
% 227.92/39.51    (56)   ~ (all_53_8 = all_6_2)
% 227.92/39.51    (57)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 227.92/39.51    (58)   ~ (all_53_2 = e0)
% 227.92/39.51    (59)  all_57_0 = e0
% 227.92/39.51    (60)  all_55_2 = all_53_8
% 227.92/39.51    (61)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 227.92/39.51    (62)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 227.92/39.51          | (all_57_14 = e0 & op(e0, e1) = e0)
% 227.92/39.51    (63)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 227.92/39.51    (64)  all_57_15 = e3
% 227.92/39.51    (65)   ~ (all_53_9 = all_53_13)
% 227.92/39.51    (66)   ~ (all_53_7 = e0)
% 227.92/39.51    (67)  all_57_4 = e1
% 227.92/39.51    (68)  op(e3, e3) = e0
% 227.92/39.51    (69)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 227.92/39.51          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 227.92/39.51            e1)
% 227.92/39.51    (70)  op(e3, e3) = all_52_1
% 227.92/39.51    (71)  all_57_11 = e0
% 227.92/39.51    (72)   ~ (all_53_4 = all_53_8)
% 227.92/39.51    (73)  all_55_6 = all_53_9
% 227.92/39.51    (74)  op(e3, e2) = all_53_4
% 227.92/39.51    (75)   ~ (all_53_1 = all_53_2)
% 227.92/39.51    (76)  op(e1, e1) = e1
% 227.92/39.51    (77)  op(all_52_1, all_52_1) = e3
% 227.92/39.51    (78)   ~ (e2 = e0)
% 227.92/39.51    (79)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 227.92/39.51            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 227.92/39.51            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 227.92/39.51            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 227.92/39.51              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 227.92/39.51            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 227.92/39.51            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 227.92/39.51              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 227.92/39.51              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 227.92/39.51            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 227.92/39.51            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 227.92/39.51            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 227.92/39.51              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 227.92/39.51              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 227.92/39.51            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 227.92/39.51              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 227.92/39.51            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 227.92/39.51            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 227.92/39.51              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 227.92/39.51              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 227.92/39.51            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 227.92/39.51            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 227.92/39.51    (80)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 227.92/39.51            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 227.92/39.51              e3) = all_12_1 & $i(all_12_1))
% 227.92/39.51    (81)  all_55_12 = all_53_3
% 227.92/39.51    (82)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 227.92/39.51          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 227.92/39.51    (83)   ~ (all_53_1 = e0)
% 227.92/39.51    (84)   ~ (e1 = e0)
% 227.92/39.51    (85)   ~ (all_52_3 = all_52_7)
% 227.92/39.51    (86)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 227.92/39.51            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 227.92/39.51              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 227.92/39.51    (87)   ~ (all_53_4 = e0)
% 227.92/39.51    (88)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 227.92/39.51          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 227.92/39.51    (89)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 227.92/39.51          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 227.92/39.51    (90)  all_55_8 = all_53_2
% 227.92/39.51    (91)  op(e0, e0) = e3
% 227.92/39.51    (92)   ~ (all_53_4 = all_53_6)
% 227.92/39.51    (93)  all_55_2 = all_52_5
% 227.92/39.51    (94)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.92/39.51          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 227.92/39.51            e2)
% 227.92/39.51    (95)   ~ (all_53_3 = e0)
% 227.92/39.51    (96)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 227.92/39.51              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 227.92/39.51                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 227.92/39.51                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 227.92/39.51    (97)  all_55_10 = all_6_2
% 227.92/39.51    (98)   ~ (all_53_13 = e0)
% 227.92/39.51    (99)   ~ (all_53_1 = all_53_13)
% 227.92/39.51    (100)  all_55_13 = all_53_7
% 227.92/39.51    (101)   ~ (all_53_9 = all_52_5)
% 227.92/39.51    (102)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 227.92/39.51           (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 227.92/39.51    (103)  all_38_2 = all_6_2
% 227.92/39.51    (104)  all_55_3 = all_53_12
% 227.92/39.51    (105)   ~ (all_53_12 = e3)
% 227.92/39.51    (106)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0
% 227.92/39.51             & op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~
% 227.92/39.51             (all_42_1 = e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 227.92/39.51    (107)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 227.92/39.51           (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 227.92/39.51    (108)  all_55_1 = all_52_3
% 227.92/39.51    (109)   ~ (all_52_5 = all_6_2)
% 227.92/39.51    (110)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 227.92/39.51           (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 227.92/39.51    (111)   ~ (all_52_5 = e1)
% 227.92/39.51    (112)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 227.92/39.51           | (all_57_11 = e0 & op(e1, e0) = e0)
% 227.92/39.52    (113)   ~ (all_52_5 = e0)
% 227.92/39.52    (114)   ~ (e2 = e1)
% 227.92/39.52    (115)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 227.92/39.52           | (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 227.92/39.52             e2)
% 227.92/39.52    (116)  op(e2, e1) = all_53_9
% 227.92/39.52    (117)  op(e1, e2) = all_53_6
% 227.92/39.52    (118)   ~ (all_6_2 = e0)
% 227.92/39.52    (119)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 227.92/39.52           (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 227.92/39.52    (120)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 227.92/39.52    (121)  all_24_2 = all_6_2
% 227.92/39.52    (122)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 227.92/39.52           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 227.92/39.52    (123)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 227.92/39.52           (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 227.92/39.52    (124)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 227.92/39.52           | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 227.92/39.52             e1)
% 227.92/39.52    (125)  all_57_14 = e0
% 227.92/39.52    (126)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 227.92/39.52           (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 227.92/39.52    (127)  op(e3, e0) = all_52_7
% 227.92/39.52    (128)  op(e3, e1) = all_53_8
% 227.92/39.52    (129)  all_55_7 = all_53_13
% 227.92/39.52    (130)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 227.92/39.52           (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 227.92/39.52    (131)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 227.92/39.52           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 227.92/39.52    (132)  op(e3, e0) = all_53_12
% 227.92/39.52  
% 227.92/39.52  Begin of proof
% 227.92/39.52  | 
% 227.92/39.52  | BETA: splitting (88) gives:
% 227.92/39.52  | 
% 227.92/39.52  | Case 1:
% 227.92/39.52  | | 
% 227.92/39.52  | |   (133)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) =
% 227.92/39.52  | |            e3)
% 227.92/39.52  | | 
% 227.92/39.52  | | BETA: splitting (133) gives:
% 227.92/39.52  | | 
% 227.92/39.52  | | Case 1:
% 227.92/39.52  | | | 
% 227.92/39.52  | | |   (134)  all_57_4 = e3 & op(e3, e1) = e3
% 227.92/39.52  | | | 
% 227.92/39.52  | | | ALPHA: (134) implies:
% 227.92/39.52  | | |   (135)  all_57_4 = e3
% 227.92/39.52  | | | 
% 227.92/39.52  | | | REF_CLOSE: (13), (67), (135) are inconsistent by sub-proof #2426.
% 227.92/39.52  | | | 
% 227.92/39.52  | | Case 2:
% 227.92/39.52  | | | 
% 227.92/39.52  | | |   (136)  all_57_5 = e3 & op(e2, e1) = e3
% 227.92/39.52  | | | 
% 227.92/39.52  | | | ALPHA: (136) implies:
% 227.92/39.52  | | |   (137)  all_57_5 = e3
% 227.92/39.52  | | |   (138)  op(e2, e1) = e3
% 227.92/39.52  | | | 
% 227.92/39.52  | | | BETA: splitting (89) gives:
% 227.92/39.52  | | | 
% 227.92/39.52  | | | Case 1:
% 227.92/39.52  | | | | 
% 227.92/39.52  | | | |   (139)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2)
% 227.92/39.52  | | | |            = e3)
% 227.92/39.52  | | | | 
% 227.92/39.52  | | | | BETA: splitting (139) gives:
% 227.92/39.52  | | | | 
% 227.92/39.52  | | | | Case 1:
% 227.92/39.52  | | | | | 
% 227.92/39.52  | | | | |   (140)  all_57_1 = e3 & op(e3, e2) = e3
% 227.92/39.52  | | | | | 
% 227.92/39.52  | | | | | ALPHA: (140) implies:
% 227.92/39.52  | | | | |   (141)  all_57_1 = e3
% 227.92/39.52  | | | | | 
% 227.92/39.52  | | | | | BETA: splitting (17) gives:
% 227.92/39.52  | | | | | 
% 227.92/39.52  | | | | | Case 1:
% 227.92/39.52  | | | | | | 
% 227.92/39.52  | | | | | |   (142)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1,
% 227.92/39.52  | | | | | |              e2) = e3)
% 227.92/39.52  | | | | | | 
% 227.92/39.52  | | | | | | BETA: splitting (142) gives:
% 227.92/39.52  | | | | | | 
% 227.92/39.52  | | | | | | Case 1:
% 227.92/39.52  | | | | | | | 
% 227.92/39.52  | | | | | | |   (143)  all_57_6 = e3 & op(e1, e3) = e3
% 227.92/39.52  | | | | | | | 
% 227.92/39.52  | | | | | | | ALPHA: (143) implies:
% 227.92/39.52  | | | | | | |   (144)  all_57_6 = e3
% 227.92/39.52  | | | | | | | 
% 227.92/39.52  | | | | | | | BETA: splitting (40) gives:
% 227.92/39.52  | | | | | | | 
% 227.92/39.52  | | | | | | | Case 1:
% 227.92/39.52  | | | | | | | | 
% 227.92/39.52  | | | | | | | |   (145)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 &
% 227.92/39.52  | | | | | | | |            op(e3, e2) = e2)
% 227.92/39.52  | | | | | | | | 
% 227.92/39.52  | | | | | | | | REF_CLOSE: (15), (41), (47), (53), (70), (77), (141), (145) are
% 227.92/39.52  | | | | | | | |            inconsistent by sub-proof #1363.
% 227.92/39.52  | | | | | | | | 
% 227.92/39.52  | | | | | | | Case 2:
% 227.92/39.52  | | | | | | | | 
% 227.92/39.52  | | | | | | | |   (146)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 &
% 227.92/39.52  | | | | | | | |            op(e3, e0) = e2)
% 227.92/39.52  | | | | | | | | 
% 227.92/39.52  | | | | | | | | BETA: splitting (146) gives:
% 227.92/39.52  | | | | | | | | 
% 227.92/39.52  | | | | | | | | Case 1:
% 227.92/39.52  | | | | | | | | | 
% 227.92/39.52  | | | | | | | | |   (147)  all_57_4 = e2 & op(e3, e1) = e2
% 227.92/39.52  | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | ALPHA: (147) implies:
% 227.92/39.52  | | | | | | | | |   (148)  all_57_4 = e2
% 227.92/39.52  | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | REF_CLOSE: (67), (114), (148) are inconsistent by sub-proof
% 227.92/39.52  | | | | | | | | |            #2430.
% 227.92/39.52  | | | | | | | | | 
% 227.92/39.52  | | | | | | | | Case 2:
% 227.92/39.52  | | | | | | | | | 
% 227.92/39.52  | | | | | | | | |   (149)  all_57_9 = e2 & op(e3, e0) = e2
% 227.92/39.52  | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | ALPHA: (149) implies:
% 227.92/39.52  | | | | | | | | |   (150)  all_57_9 = e2
% 227.92/39.52  | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | BETA: splitting (124) gives:
% 227.92/39.52  | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | Case 1:
% 227.92/39.52  | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | |   (151)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1
% 227.92/39.52  | | | | | | | | | |            & op(e2, e0) = e1)
% 227.92/39.52  | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | BETA: splitting (151) gives:
% 227.92/39.52  | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | Case 1:
% 227.92/39.52  | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | |   (152)  all_57_9 = e1 & op(e3, e0) = e1
% 227.92/39.52  | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | ALPHA: (152) implies:
% 227.92/39.52  | | | | | | | | | | |   (153)  all_57_9 = e1
% 227.92/39.52  | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 227.92/39.52  | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 227.92/39.52  | | | | | | | | | | |            (19), (20), (21), (22), (23), (24), (25), (26),
% 227.92/39.52  | | | | | | | | | | |            (27), (28), (29), (30), (31), (32), (33), (34),
% 227.92/39.52  | | | | | | | | | | |            (35), (36), (37), (38), (39), (40), (41), (42),
% 227.92/39.52  | | | | | | | | | | |            (43), (44), (45), (46), (47), (48), (49), (50),
% 227.92/39.52  | | | | | | | | | | |            (51), (52), (53), (54), (55), (56), (57), (58),
% 227.92/39.52  | | | | | | | | | | |            (59), (60), (61), (62), (63), (64), (65), (66),
% 227.92/39.52  | | | | | | | | | | |            (68), (69), (70), (71), (72), (73), (74), (75),
% 227.92/39.52  | | | | | | | | | | |            (77), (78), (79), (80), (81), (82), (83), (84),
% 227.92/39.52  | | | | | | | | | | |            (85), (86), (87), (88), (89), (90), (91), (92),
% 227.92/39.52  | | | | | | | | | | |            (93), (94), (95), (96), (97), (98), (99), (100),
% 227.92/39.52  | | | | | | | | | | |            (101), (102), (103), (104), (105), (106), (107),
% 227.92/39.52  | | | | | | | | | | |            (108), (109), (110), (111), (112), (113), (114),
% 227.92/39.52  | | | | | | | | | | |            (115), (116), (117), (118), (119), (120), (121),
% 227.92/39.52  | | | | | | | | | | |            (122), (123), (124), (125), (126), (127), (128),
% 227.92/39.52  | | | | | | | | | | |            (129), (130), (131), (132), (137), (141), (144),
% 227.92/39.52  | | | | | | | | | | |            (153) are inconsistent by sub-proof #402.
% 227.92/39.52  | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | Case 2:
% 227.92/39.52  | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | |   (154)  all_57_10 = e1 & op(e2, e0) = e1
% 227.92/39.52  | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | ALPHA: (154) implies:
% 227.92/39.52  | | | | | | | | | | |   (155)  all_57_10 = e1
% 227.92/39.52  | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | BETA: splitting (131) gives:
% 227.92/39.52  | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | Case 1:
% 227.92/39.52  | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | |   (156)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 227.92/39.52  | | | | | | | | | | | |            & op(e1, e2) = e2)
% 227.92/39.52  | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | BETA: splitting (156) gives:
% 227.92/39.52  | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | Case 1:
% 227.92/39.52  | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | |   (157)  all_57_6 = e2 & op(e1, e3) = e2
% 227.92/39.52  | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | REF_CLOSE: (47), (144), (157) are inconsistent by sub-proof
% 227.92/39.52  | | | | | | | | | | | | |            #2012.
% 227.92/39.52  | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | Case 2:
% 227.92/39.52  | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | |   (158)  all_57_7 = e2 & op(e1, e2) = e2
% 227.92/39.52  | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | ALPHA: (158) implies:
% 227.92/39.52  | | | | | | | | | | | | |   (159)  all_57_7 = e2
% 227.92/39.52  | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | COMBINE_EQS: (38), (159) imply:
% 227.92/39.52  | | | | | | | | | | | | |   (160)  e2 = e1
% 227.92/39.52  | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | SIMP: (160) implies:
% 227.92/39.52  | | | | | | | | | | | | |   (161)  e2 = e1
% 227.92/39.52  | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | COMBINE_EQS: (150), (161) imply:
% 227.92/39.52  | | | | | | | | | | | | |   (162)  all_57_9 = e1
% 227.92/39.52  | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 227.92/39.52  | | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 227.92/39.52  | | | | | | | | | | | | |            (19), (20), (21), (22), (23), (24), (25), (26),
% 227.92/39.52  | | | | | | | | | | | | |            (27), (28), (29), (30), (31), (32), (33), (34),
% 227.92/39.52  | | | | | | | | | | | | |            (35), (36), (37), (38), (39), (40), (41), (42),
% 227.92/39.52  | | | | | | | | | | | | |            (43), (44), (45), (46), (47), (48), (49), (50),
% 227.92/39.52  | | | | | | | | | | | | |            (51), (52), (53), (54), (55), (56), (57), (58),
% 227.92/39.52  | | | | | | | | | | | | |            (59), (60), (61), (62), (63), (64), (65), (66),
% 227.92/39.52  | | | | | | | | | | | | |            (68), (69), (70), (71), (72), (73), (74), (75),
% 227.92/39.52  | | | | | | | | | | | | |            (77), (78), (79), (80), (81), (82), (83), (84),
% 227.92/39.52  | | | | | | | | | | | | |            (85), (86), (87), (88), (89), (90), (91), (92),
% 227.92/39.52  | | | | | | | | | | | | |            (93), (94), (95), (96), (97), (98), (99), (100),
% 227.92/39.52  | | | | | | | | | | | | |            (101), (102), (103), (104), (105), (106), (107),
% 227.92/39.52  | | | | | | | | | | | | |            (108), (109), (110), (111), (112), (113), (114),
% 227.92/39.52  | | | | | | | | | | | | |            (115), (116), (117), (118), (119), (120), (121),
% 227.92/39.52  | | | | | | | | | | | | |            (122), (123), (124), (125), (126), (127), (128),
% 227.92/39.52  | | | | | | | | | | | | |            (129), (130), (131), (132), (137), (141), (144),
% 227.92/39.52  | | | | | | | | | | | | |            (162) are inconsistent by sub-proof #402.
% 227.92/39.52  | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | End of split
% 227.92/39.52  | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | Case 2:
% 227.92/39.52  | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | |   (163)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 227.92/39.52  | | | | | | | | | | | |            e2 & op(e1, e0) = e2)
% 227.92/39.52  | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | BETA: splitting (163) gives:
% 227.92/39.52  | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | Case 1:
% 227.92/39.52  | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | |   (164)  all_57_8 = e2 & op(e1, e1) = e2
% 227.92/39.52  | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | ALPHA: (164) implies:
% 227.92/39.52  | | | | | | | | | | | | |   (165)  all_57_8 = e2
% 227.92/39.52  | | | | | | | | | | | | |   (166)  op(e1, e1) = e2
% 227.92/39.52  | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | BETA: splitting (12) gives:
% 227.92/39.52  | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | Case 1:
% 227.92/39.52  | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | |   (167)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 227.92/39.52  | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 227.92/39.52  | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | BETA: splitting (167) gives:
% 227.92/39.52  | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | Case 1:
% 227.92/39.52  | | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | |   (168)  all_57_1 = e2 & op(e3, e2) = e2
% 227.92/39.52  | | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | | REF_CLOSE: (47), (141), (168) are inconsistent by sub-proof
% 227.92/39.52  | | | | | | | | | | | | | | |            #1809.
% 227.92/39.52  | | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | Case 2:
% 227.92/39.52  | | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | |   (169)  all_57_3 = e2 & op(e2, e2) = e2
% 227.92/39.52  | | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | | REF_CLOSE: (13), (45), (47), (64), (71), (78), (84), (114),
% 227.92/39.52  | | | | | | | | | | | | | | |            (115), (124), (150), (169) are inconsistent by
% 227.92/39.52  | | | | | | | | | | | | | | |            sub-proof #1096.
% 227.92/39.52  | | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | End of split
% 227.92/39.52  | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | Case 2:
% 227.92/39.52  | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | |   (170)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 227.92/39.52  | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 227.92/39.52  | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | BETA: splitting (170) gives:
% 227.92/39.52  | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | Case 1:
% 227.92/39.52  | | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | |   (171)  all_57_7 = e2 & op(e1, e2) = e2
% 227.92/39.52  | | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | | ALPHA: (171) implies:
% 227.92/39.52  | | | | | | | | | | | | | | |   (172)  all_57_7 = e2
% 227.92/39.52  | | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | | COMBINE_EQS: (38), (172) imply:
% 227.92/39.52  | | | | | | | | | | | | | | |   (173)  e2 = e1
% 227.92/39.52  | | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | | SIMP: (173) implies:
% 227.92/39.52  | | | | | | | | | | | | | | |   (174)  e2 = e1
% 227.92/39.52  | | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | | COMBINE_EQS: (165), (174) imply:
% 227.92/39.52  | | | | | | | | | | | | | | |   (175)  all_57_8 = e1
% 227.92/39.52  | | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 227.92/39.52  | | | | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 227.92/39.52  | | | | | | | | | | | | | | |            (19), (20), (21), (22), (23), (24), (25), (26),
% 227.92/39.52  | | | | | | | | | | | | | | |            (27), (28), (29), (30), (31), (32), (33), (34),
% 227.92/39.52  | | | | | | | | | | | | | | |            (35), (36), (37), (39), (40), (41), (42), (43),
% 227.92/39.52  | | | | | | | | | | | | | | |            (44), (45), (46), (48), (49), (50), (51), (52),
% 227.92/39.52  | | | | | | | | | | | | | | |            (53), (54), (55), (56), (57), (58), (59), (60),
% 227.92/39.52  | | | | | | | | | | | | | | |            (61), (62), (63), (64), (65), (66), (68), (69),
% 227.92/39.52  | | | | | | | | | | | | | | |            (71), (72), (73), (74), (75), (79), (80), (81),
% 227.92/39.52  | | | | | | | | | | | | | | |            (82), (83), (84), (85), (86), (87), (88), (89),
% 227.92/39.52  | | | | | | | | | | | | | | |            (90), (91), (92), (93), (94), (95), (96), (97),
% 227.92/39.52  | | | | | | | | | | | | | | |            (98), (99), (100), (101), (102), (103), (104),
% 227.92/39.52  | | | | | | | | | | | | | | |            (105), (106), (107), (108), (109), (110), (111),
% 227.92/39.52  | | | | | | | | | | | | | | |            (112), (113), (115), (116), (117), (118), (119),
% 227.92/39.52  | | | | | | | | | | | | | | |            (120), (121), (122), (123), (124), (125), (126),
% 227.92/39.52  | | | | | | | | | | | | | | |            (127), (128), (129), (130), (131), (132), (175)
% 227.92/39.52  | | | | | | | | | | | | | | |            are inconsistent by sub-proof #403.
% 227.92/39.52  | | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | Case 2:
% 227.92/39.52  | | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | |   (176)  all_57_13 = e2 & op(e0, e2) = e2
% 227.92/39.52  | | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | | ALPHA: (176) implies:
% 227.92/39.52  | | | | | | | | | | | | | | |   (177)  all_57_13 = e2
% 227.92/39.52  | | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | | BETA: splitting (69) gives:
% 227.92/39.52  | | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | | Case 1:
% 227.92/39.52  | | | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | | |   (178)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 227.92/39.52  | | | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 227.92/39.52  | | | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | | | BETA: splitting (178) gives:
% 227.92/39.52  | | | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.52  | | | | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | | | |   (179)  all_57_12 = e1 & op(e0, e3) = e1
% 227.92/39.52  | | | | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | | | | ALPHA: (179) implies:
% 227.92/39.52  | | | | | | | | | | | | | | | | |   (180)  all_57_12 = e1
% 227.92/39.52  | | | | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | | | | BETA: splitting (119) gives:
% 227.92/39.52  | | | | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.52  | | | | | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | | | | |   (181)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 227.92/39.52  | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e2)
% 227.92/39.52  | | | | | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | | | | | BETA: splitting (181) gives:
% 227.92/39.52  | | | | | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.52  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | | | | | |   (182)  all_57_0 = e2 & op(e3, e3) = e2
% 227.92/39.52  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | | | | | | ALPHA: (182) implies:
% 227.92/39.52  | | | | | | | | | | | | | | | | | | |   (183)  op(e3, e3) = e2
% 227.92/39.52  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (13), (15), (45), (47), (53), (78), (84),
% 227.92/39.52  | | | | | | | | | | | | | | | | | | |            (107), (114), (123), (137), (144), (180), (183)
% 227.92/39.52  | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #810.
% 227.92/39.52  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.52  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | | | | | |   (184)  all_57_2 = e2 & op(e2, e3) = e2
% 227.92/39.52  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (10), (11), (12), (13), (14), (15),
% 227.92/39.52  | | | | | | | | | | | | | | | | | | |            (17), (18), (21), (24), (25), (29), (30), (34),
% 227.92/39.52  | | | | | | | | | | | | | | | | | | |            (36), (39), (40), (43), (44), (45), (46), (47),
% 227.92/39.52  | | | | | | | | | | | | | | | | | | |            (49), (53), (54), (56), (59), (60), (63), (64),
% 227.92/39.52  | | | | | | | | | | | | | | | | | | |            (69), (71), (72), (74), (76), (78), (79), (82),
% 227.92/39.52  | | | | | | | | | | | | | | | | | | |            (84), (86), (87), (91), (92), (94), (96), (97),
% 227.92/39.52  | | | | | | | | | | | | | | | | | | |            (103), (104), (105), (106), (107), (110), (114),
% 227.92/39.52  | | | | | | | | | | | | | | | | | | |            (115), (116), (117), (119), (121), (122), (123),
% 227.92/39.52  | | | | | | | | | | | | | | | | | | |            (124), (125), (126), (128), (130), (131), (132),
% 227.92/39.52  | | | | | | | | | | | | | | | | | | |            (136), (137), (138), (150), (155), (166), (184)
% 227.92/39.52  | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #401.
% 227.92/39.52  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.52  | | | | | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.52  | | | | | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | | | | |   (185)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 227.92/39.52  | | | | | | | | | | | | | | | | | |            e2 & op(e0, e3) = e2)
% 227.92/39.52  | | | | | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 227.92/39.52  | | | | | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.52  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | | | | | |   (186)  all_57_6 = e2 & op(e1, e3) = e2
% 227.92/39.52  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | | | | | | ALPHA: (186) implies:
% 227.92/39.52  | | | | | | | | | | | | | | | | | | |   (187)  all_57_6 = e2
% 227.92/39.52  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (15), (17), (21), (24), (45), (47), (53),
% 227.92/39.52  | | | | | | | | | | | | | | | | | | |            (64), (78), (84), (112), (114), (115), (124),
% 227.92/39.52  | | | | | | | | | | | | | | | | | | |            (130), (141), (177), (187) are inconsistent by
% 227.92/39.52  | | | | | | | | | | | | | | | | | | |            sub-proof #419.
% 227.92/39.52  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.52  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | | | | | |   (188)  all_57_12 = e2 & op(e0, e3) = e2
% 227.92/39.52  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | | | | | | ALPHA: (188) implies:
% 227.92/39.52  | | | | | | | | | | | | | | | | | | |   (189)  all_57_12 = e2
% 227.92/39.52  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (180), (189) imply:
% 227.92/39.52  | | | | | | | | | | | | | | | | | | |   (190)  e2 = e1
% 227.92/39.52  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (165), (190) imply:
% 227.92/39.52  | | | | | | | | | | | | | | | | | | |   (191)  all_57_8 = e1
% 227.92/39.52  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 227.92/39.52  | | | | | | | | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 227.92/39.52  | | | | | | | | | | | | | | | | | | |            (19), (20), (21), (22), (23), (24), (25), (26),
% 227.92/39.52  | | | | | | | | | | | | | | | | | | |            (27), (28), (29), (30), (31), (32), (33), (34),
% 227.92/39.52  | | | | | | | | | | | | | | | | | | |            (35), (36), (37), (39), (40), (41), (42), (43),
% 227.92/39.52  | | | | | | | | | | | | | | | | | | |            (44), (45), (46), (48), (49), (50), (51), (52),
% 227.92/39.52  | | | | | | | | | | | | | | | | | | |            (53), (54), (55), (56), (57), (58), (59), (60),
% 227.92/39.52  | | | | | | | | | | | | | | | | | | |            (61), (62), (63), (64), (65), (66), (68), (69),
% 227.92/39.52  | | | | | | | | | | | | | | | | | | |            (71), (72), (73), (74), (75), (79), (80), (81),
% 227.92/39.52  | | | | | | | | | | | | | | | | | | |            (82), (83), (84), (85), (86), (87), (88), (89),
% 227.92/39.52  | | | | | | | | | | | | | | | | | | |            (90), (91), (92), (93), (94), (95), (96), (97),
% 227.92/39.52  | | | | | | | | | | | | | | | | | | |            (98), (99), (100), (101), (102), (103), (104),
% 227.92/39.52  | | | | | | | | | | | | | | | | | | |            (105), (106), (107), (108), (109), (110), (111),
% 227.92/39.52  | | | | | | | | | | | | | | | | | | |            (112), (113), (115), (116), (117), (118), (119),
% 227.92/39.52  | | | | | | | | | | | | | | | | | | |            (120), (121), (122), (123), (124), (125), (126),
% 227.92/39.52  | | | | | | | | | | | | | | | | | | |            (127), (128), (129), (130), (131), (132), (191)
% 227.92/39.52  | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #403.
% 227.92/39.52  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.52  | | | | | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | | | | End of split
% 227.92/39.52  | | | | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.52  | | | | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | | | |   (192)  all_57_13 = e1 & op(e0, e2) = e1
% 227.92/39.52  | | | | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 227.92/39.52  | | | | | | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 227.92/39.52  | | | | | | | | | | | | | | | | |            (19), (20), (21), (22), (23), (24), (25), (26),
% 227.92/39.52  | | | | | | | | | | | | | | | | |            (27), (28), (29), (30), (31), (32), (33), (34),
% 227.92/39.52  | | | | | | | | | | | | | | | | |            (35), (36), (37), (39), (40), (41), (42), (43),
% 227.92/39.52  | | | | | | | | | | | | | | | | |            (44), (45), (46), (48), (49), (50), (51), (52),
% 227.92/39.52  | | | | | | | | | | | | | | | | |            (53), (54), (55), (56), (57), (58), (59), (60),
% 227.92/39.52  | | | | | | | | | | | | | | | | |            (61), (62), (63), (64), (65), (66), (68), (69),
% 227.92/39.52  | | | | | | | | | | | | | | | | |            (71), (72), (73), (74), (75), (79), (80), (81),
% 227.92/39.52  | | | | | | | | | | | | | | | | |            (82), (83), (84), (85), (86), (87), (88), (89),
% 227.92/39.52  | | | | | | | | | | | | | | | | |            (90), (91), (92), (93), (94), (95), (96), (97),
% 227.92/39.52  | | | | | | | | | | | | | | | | |            (98), (99), (100), (101), (102), (103), (104),
% 227.92/39.52  | | | | | | | | | | | | | | | | |            (105), (106), (107), (108), (109), (110), (111),
% 227.92/39.52  | | | | | | | | | | | | | | | | |            (112), (113), (115), (116), (117), (118), (119),
% 227.92/39.52  | | | | | | | | | | | | | | | | |            (120), (121), (122), (123), (124), (125), (126),
% 227.92/39.52  | | | | | | | | | | | | | | | | |            (127), (128), (129), (130), (131), (132), (165),
% 227.92/39.52  | | | | | | | | | | | | | | | | |            (177), (192) are inconsistent by sub-proof #400.
% 227.92/39.52  | | | | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | | | End of split
% 227.92/39.52  | | | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | | Case 2:
% 227.92/39.52  | | | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | | |   (193)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 227.92/39.52  | | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 227.92/39.52  | | | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 227.92/39.52  | | | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.52  | | | | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | | | |   (194)  all_57_14 = e1 & op(e0, e1) = e1
% 227.92/39.52  | | | | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | | | | ALPHA: (194) implies:
% 227.92/39.52  | | | | | | | | | | | | | | | | |   (195)  all_57_14 = e1
% 227.92/39.52  | | | | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | | | | COMBINE_EQS: (125), (195) imply:
% 227.92/39.52  | | | | | | | | | | | | | | | | |   (196)  e1 = e0
% 227.92/39.52  | | | | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (13), (45), (47), (78), (84), (107), (114),
% 227.92/39.52  | | | | | | | | | | | | | | | | |            (137), (155), (196) are inconsistent by sub-proof
% 227.92/39.52  | | | | | | | | | | | | | | | | |            #1506.
% 227.92/39.52  | | | | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.52  | | | | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | | | |   (197)  all_57_15 = e1 & op(e0, e0) = e1
% 227.92/39.52  | | | | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | | | | ALPHA: (197) implies:
% 227.92/39.52  | | | | | | | | | | | | | | | | |   (198)  op(e0, e0) = e1
% 227.92/39.52  | | | | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (15), (91), (198) are inconsistent by
% 227.92/39.52  | | | | | | | | | | | | | | | | |            sub-proof #2183.
% 227.92/39.52  | | | | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | | | End of split
% 227.92/39.52  | | | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | | End of split
% 227.92/39.52  | | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | | End of split
% 227.92/39.52  | | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | End of split
% 227.92/39.52  | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | Case 2:
% 227.92/39.52  | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | |   (199)  all_57_11 = e2 & op(e1, e0) = e2
% 227.92/39.52  | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | ALPHA: (199) implies:
% 227.92/39.52  | | | | | | | | | | | | |   (200)  all_57_11 = e2
% 227.92/39.52  | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | | REF_CLOSE: (13), (47), (64), (71), (78), (84), (114), (115),
% 227.92/39.52  | | | | | | | | | | | | |            (124), (150), (200) are inconsistent by sub-proof
% 227.92/39.52  | | | | | | | | | | | | |            #1136.
% 227.92/39.52  | | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | | End of split
% 227.92/39.52  | | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | | End of split
% 227.92/39.52  | | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | End of split
% 227.92/39.52  | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | Case 2:
% 227.92/39.52  | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | |   (201)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 227.92/39.52  | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 227.92/39.52  | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | | REF_CLOSE: (6), (13), (15), (21), (24), (45), (47), (53),
% 227.92/39.52  | | | | | | | | | |            (64), (67), (69), (71), (78), (84), (88), (91),
% 227.92/39.52  | | | | | | | | | |            (94), (96), (107), (114), (150), (201) are
% 227.92/39.52  | | | | | | | | | |            inconsistent by sub-proof #399.
% 227.92/39.52  | | | | | | | | | | 
% 227.92/39.52  | | | | | | | | | End of split
% 227.92/39.52  | | | | | | | | | 
% 227.92/39.52  | | | | | | | | End of split
% 227.92/39.52  | | | | | | | | 
% 227.92/39.52  | | | | | | | End of split
% 227.92/39.52  | | | | | | | 
% 227.92/39.52  | | | | | | Case 2:
% 227.92/39.52  | | | | | | | 
% 227.92/39.52  | | | | | | |   (202)  all_57_7 = e3 & op(e1, e2) = e3
% 227.92/39.52  | | | | | | | 
% 227.92/39.52  | | | | | | | ALPHA: (202) implies:
% 227.92/39.52  | | | | | | |   (203)  all_57_7 = e3
% 227.92/39.52  | | | | | | | 
% 227.92/39.52  | | | | | | | REF_CLOSE: (12), (13), (45), (47), (78), (84), (114), (130),
% 227.92/39.52  | | | | | | |            (141), (203) are inconsistent by sub-proof #1778.
% 227.92/39.52  | | | | | | | 
% 227.92/39.52  | | | | | | End of split
% 227.92/39.52  | | | | | | 
% 227.92/39.52  | | | | | Case 2:
% 227.92/39.52  | | | | | | 
% 227.92/39.52  | | | | | |   (204)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 &
% 227.92/39.52  | | | | | |            op(e1, e0) = e3)
% 227.92/39.52  | | | | | | 
% 227.92/39.52  | | | | | | REF_CLOSE: (13), (15), (21), (24), (47), (53), (64), (78), (84),
% 227.92/39.52  | | | | | |            (112), (114), (115), (124), (204) are inconsistent by
% 227.92/39.52  | | | | | |            sub-proof #1080.
% 227.92/39.52  | | | | | | 
% 227.92/39.52  | | | | | End of split
% 227.92/39.52  | | | | | 
% 227.92/39.52  | | | | Case 2:
% 227.92/39.52  | | | | | 
% 227.92/39.52  | | | | |   (205)  all_57_3 = e3 & op(e2, e2) = e3
% 227.92/39.52  | | | | | 
% 227.92/39.52  | | | | | ALPHA: (205) implies:
% 227.92/39.52  | | | | |   (206)  all_57_3 = e3
% 227.92/39.52  | | | | | 
% 227.92/39.52  | | | | | REF_CLOSE: (45), (53), (206) are inconsistent by sub-proof #2358.
% 227.92/39.52  | | | | | 
% 227.92/39.52  | | | | End of split
% 227.92/39.52  | | | | 
% 227.92/39.52  | | | Case 2:
% 227.92/39.52  | | | | 
% 227.92/39.52  | | | |   (207)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0,
% 227.92/39.52  | | | |              e2) = e3)
% 227.92/39.52  | | | | 
% 227.92/39.52  | | | | BETA: splitting (207) gives:
% 227.92/39.52  | | | | 
% 227.92/39.52  | | | | Case 1:
% 227.92/39.52  | | | | | 
% 227.92/39.52  | | | | |   (208)  all_57_7 = e3 & op(e1, e2) = e3
% 227.92/39.52  | | | | | 
% 227.92/39.52  | | | | | ALPHA: (208) implies:
% 227.92/39.52  | | | | |   (209)  all_57_7 = e3
% 227.92/39.52  | | | | | 
% 227.92/39.52  | | | | | REF_CLOSE: (13), (38), (209) are inconsistent by sub-proof #2115.
% 227.92/39.52  | | | | | 
% 227.92/39.52  | | | | Case 2:
% 227.92/39.52  | | | | | 
% 227.92/39.52  | | | | |   (210)  all_57_13 = e3 & op(e0, e2) = e3
% 227.92/39.52  | | | | | 
% 227.92/39.52  | | | | | ALPHA: (210) implies:
% 227.92/39.52  | | | | |   (211)  all_57_13 = e3
% 227.92/39.52  | | | | | 
% 227.92/39.52  | | | | | REF_CLOSE: (13), (15), (47), (53), (62), (64), (69), (78), (84), (91),
% 227.92/39.52  | | | | |            (94), (114), (125), (211) are inconsistent by sub-proof
% 227.92/39.52  | | | | |            #2055.
% 227.92/39.52  | | | | | 
% 227.92/39.52  | | | | End of split
% 227.92/39.52  | | | | 
% 227.92/39.52  | | | End of split
% 227.92/39.52  | | | 
% 227.92/39.52  | | End of split
% 227.92/39.52  | | 
% 227.92/39.52  | Case 2:
% 227.92/39.52  | | 
% 227.92/39.52  | |   (212)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) =
% 227.92/39.52  | |            e3)
% 227.92/39.52  | | 
% 227.92/39.52  | | REF_CLOSE: (13), (15), (21), (24), (47), (53), (62), (64), (69), (78), (84),
% 227.92/39.52  | |            (94), (114), (212) are inconsistent by sub-proof #1044.
% 227.92/39.52  | | 
% 227.92/39.52  | End of split
% 227.92/39.52  | 
% 227.92/39.52  End of proof
% 227.92/39.52  
% 227.92/39.52  Sub-proof #399 shows that the following formulas are inconsistent:
% 227.92/39.52  ----------------------------------------------------------------
% 227.92/39.52    (1)  all_57_9 = e2
% 227.92/39.52    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 227.92/39.52         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 227.92/39.52    (3)   ~ (e3 = e1)
% 227.92/39.52    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.92/39.52           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.92/39.52    (5)   ~ (all_6_2 = e3)
% 227.92/39.52    (6)  op(e1, e1) = all_6_2
% 227.92/39.52    (7)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 227.92/39.52    (8)  all_57_3 = e0
% 227.92/39.52    (9)   ~ (e3 = e2)
% 227.92/39.52    (10)   ~ (e3 = e0)
% 227.92/39.52    (11)  all_57_15 = e3
% 227.92/39.52    (12)  all_57_4 = e1
% 227.92/39.52    (13)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 227.92/39.52          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 227.92/39.52            e1)
% 227.92/39.52    (14)  all_57_11 = e0
% 227.92/39.52    (15)   ~ (e2 = e0)
% 227.92/39.52    (16)   ~ (e1 = e0)
% 227.92/39.52    (17)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 227.92/39.52          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 227.92/39.52    (18)  op(e0, e0) = e3
% 227.92/39.52    (19)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.92/39.52          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 227.92/39.52            e2)
% 227.92/39.52    (20)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 227.92/39.52              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 227.92/39.52                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 227.92/39.52                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 227.92/39.52    (21)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 227.92/39.52          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 227.92/39.52    (22)   ~ (e2 = e1)
% 227.92/39.52  
% 227.92/39.52  Begin of proof
% 227.92/39.52  | 
% 227.92/39.52  | BETA: splitting (7) gives:
% 227.92/39.52  | 
% 227.92/39.52  | Case 1:
% 227.92/39.52  | | 
% 227.92/39.52  | |   (23)  all_57_11 = e1 & op(e1, e0) = e1
% 227.92/39.52  | | 
% 227.92/39.52  | | ALPHA: (23) implies:
% 227.92/39.52  | |   (24)  all_57_11 = e1
% 227.92/39.52  | | 
% 227.92/39.52  | | COMBINE_EQS: (14), (24) imply:
% 227.92/39.52  | |   (25)  e1 = e0
% 227.92/39.52  | | 
% 227.92/39.52  | | SIMP: (25) implies:
% 227.92/39.52  | |   (26)  e1 = e0
% 227.92/39.52  | | 
% 227.92/39.52  | | COMBINE_EQS: (12), (26) imply:
% 227.92/39.52  | |   (27)  all_57_4 = e0
% 227.92/39.52  | | 
% 227.92/39.52  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (13), (15),
% 227.92/39.52  | |            (16), (17), (18), (19), (20), (21), (22), (24), (27) are
% 227.92/39.52  | |            inconsistent by sub-proof #1041.
% 227.92/39.52  | | 
% 227.92/39.52  | Case 2:
% 227.92/39.52  | | 
% 227.92/39.52  | |   (28)  all_57_15 = e1 & op(e0, e0) = e1
% 227.92/39.52  | | 
% 227.92/39.52  | | ALPHA: (28) implies:
% 227.92/39.52  | |   (29)  op(e0, e0) = e1
% 227.92/39.52  | | 
% 227.92/39.52  | | REF_CLOSE: (3), (4), (18), (29) are inconsistent by sub-proof #2183.
% 227.92/39.52  | | 
% 227.92/39.52  | End of split
% 227.92/39.52  | 
% 227.92/39.52  End of proof
% 227.92/39.52  
% 227.92/39.52  Sub-proof #400 shows that the following formulas are inconsistent:
% 227.92/39.52  ----------------------------------------------------------------
% 227.92/39.52    (1)  all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 227.92/39.52    (2)   ~ (all_53_7 = e3)
% 227.92/39.52    (3)   ~ (all_53_2 = e1)
% 227.92/39.52    (4)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 227.92/39.52    (5)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 227.92/39.52    (6)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 227.92/39.52         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 227.92/39.52    (7)  op(e3, e1) = all_52_5
% 227.92/39.52    (8)   ~ (all_52_7 = e3)
% 227.92/39.52    (9)   ~ (all_52_3 = all_52_5)
% 227.92/39.52    (10)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 227.92/39.52          (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 227.92/39.52    (11)   ~ (all_53_8 = all_53_12)
% 227.92/39.52    (12)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 227.92/39.52          (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.92/39.52    (13)   ~ (e3 = e1)
% 227.92/39.52    (14)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 227.92/39.52          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 227.92/39.52    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.92/39.52            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.92/39.52    (16)  op(all_52_5, all_52_5) = e1
% 227.92/39.52    (17)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 227.92/39.52          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 227.92/39.53    (18)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 227.92/39.53            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 227.92/39.53              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 227.92/39.53    (19)   ~ (all_53_3 = e3)
% 227.92/39.53    (20)   ~ (all_53_3 = all_53_7)
% 227.92/39.53    (21)   ~ (all_6_2 = e3)
% 227.92/39.53    (22)   ~ (all_52_3 = e0)
% 227.92/39.53    (23)   ~ (all_53_9 = e1)
% 227.92/39.53    (24)  op(e1, e1) = all_6_2
% 227.92/39.53    (25)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 227.92/39.53    (26)  all_57_13 = e1 & op(e0, e2) = e1
% 227.92/39.53    (27)  op(all_52_7, all_52_7) = e0
% 227.92/39.53    (28)   ~ (all_53_1 = all_53_9)
% 227.92/39.53    (29)  op(e3, e2) = all_52_3
% 227.92/39.53    (30)   ~ (all_53_9 = e0)
% 227.92/39.53    (31)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 227.92/39.53          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 227.92/39.53    (32)   ~ (all_52_5 = all_52_7)
% 227.92/39.53    (33)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 227.92/39.53            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 227.92/39.53              e3) = all_22_1 & $i(all_22_1))
% 227.92/39.53    (34)  all_55_3 = all_52_7
% 227.92/39.53    (35)   ~ (all_53_4 = all_53_12)
% 227.92/39.53    (36)   ~ (all_53_13 = e3)
% 227.92/39.53    (37)   ~ (all_53_8 = all_53_9)
% 227.92/39.53    (38)   ~ (all_53_7 = all_52_3)
% 227.92/39.53    (39)  all_42_2 = all_6_2
% 227.92/39.53    (40)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 227.92/39.53          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 227.92/39.53    (41)  op(e2, e2) = e0
% 227.92/39.53    (42)  all_55_4 = all_53_1
% 227.92/39.53    (43)   ~ (all_53_9 = all_6_2)
% 227.92/39.53    (44)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 227.92/39.53          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 227.92/39.53    (45)  all_57_3 = e0
% 227.92/39.53    (46)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 227.92/39.53          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 227.92/39.53    (47)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 227.92/39.53    (48)  all_55_1 = all_53_4
% 227.92/39.53    (49)   ~ (all_53_13 = all_52_7)
% 227.92/39.53    (50)  all_55_7 = e3 | all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 227.92/39.53    (51)  all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 227.92/39.53    (52)   ~ (e3 = e0)
% 227.92/39.53    (53)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 227.92/39.53          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 227.92/39.53    (54)   ~ (all_6_2 = e2)
% 227.92/39.53    (55)   ~ (all_53_8 = all_6_2)
% 227.92/39.53    (56)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 227.92/39.53    (57)   ~ (all_53_2 = e0)
% 227.92/39.53    (58)  all_57_0 = e0
% 227.92/39.53    (59)  all_55_2 = all_53_8
% 227.92/39.53    (60)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 227.92/39.53    (61)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 227.92/39.53          | (all_57_14 = e0 & op(e0, e1) = e0)
% 227.92/39.53    (62)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 227.92/39.53    (63)  all_57_15 = e3
% 227.92/39.53    (64)   ~ (all_53_9 = all_53_13)
% 227.92/39.53    (65)   ~ (all_53_7 = e0)
% 227.92/39.53    (66)  op(e3, e3) = e0
% 227.92/39.53    (67)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 227.92/39.53          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 227.92/39.53            e1)
% 227.92/39.53    (68)  all_57_11 = e0
% 227.92/39.53    (69)   ~ (all_53_4 = all_53_8)
% 227.92/39.53    (70)  all_55_6 = all_53_9
% 227.92/39.53    (71)  op(e3, e2) = all_53_4
% 227.92/39.53    (72)   ~ (all_53_1 = all_53_2)
% 227.92/39.53    (73)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 227.92/39.53            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 227.92/39.53            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 227.92/39.53            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 227.92/39.53              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 227.92/39.53            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 227.92/39.53            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 227.92/39.53              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 227.92/39.53              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 227.92/39.53            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 227.92/39.53            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 227.92/39.53            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 227.92/39.53              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 227.92/39.53              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 227.92/39.53            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 227.92/39.53              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 227.92/39.53            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 227.92/39.53            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 227.92/39.53              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 227.92/39.53              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 227.92/39.53            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 227.92/39.53            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 227.92/39.53    (74)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 227.92/39.53            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 227.92/39.53              e3) = all_12_1 & $i(all_12_1))
% 227.92/39.53    (75)  all_55_12 = all_53_3
% 227.92/39.53    (76)  all_57_13 = e2
% 227.92/39.53    (77)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 227.92/39.53          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 227.92/39.53    (78)   ~ (all_53_1 = e0)
% 227.92/39.53    (79)   ~ (e1 = e0)
% 227.92/39.53    (80)   ~ (all_52_3 = all_52_7)
% 227.92/39.53    (81)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 227.92/39.53            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 227.92/39.53              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 227.92/39.53    (82)   ~ (all_53_4 = e0)
% 227.92/39.53    (83)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 227.92/39.53          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 227.92/39.53    (84)  all_57_8 = e2
% 227.92/39.53    (85)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 227.92/39.53          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 227.92/39.53    (86)  all_55_8 = all_53_2
% 227.92/39.53    (87)  op(e0, e0) = e3
% 227.92/39.53    (88)   ~ (all_53_4 = all_53_6)
% 227.92/39.53    (89)  all_55_2 = all_52_5
% 227.92/39.53    (90)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.92/39.53          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 227.92/39.53            e2)
% 227.92/39.53    (91)   ~ (all_53_3 = e0)
% 227.92/39.53    (92)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 227.92/39.53              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 227.92/39.53                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 227.92/39.53                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 227.92/39.53    (93)  all_55_10 = all_6_2
% 227.92/39.53    (94)   ~ (all_53_13 = e0)
% 227.92/39.53    (95)   ~ (all_53_1 = all_53_13)
% 227.92/39.53    (96)  all_55_13 = all_53_7
% 227.92/39.53    (97)   ~ (all_53_9 = all_52_5)
% 227.92/39.53    (98)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 227.92/39.53          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 227.92/39.53    (99)  all_38_2 = all_6_2
% 227.92/39.53    (100)  all_55_3 = all_53_12
% 227.92/39.53    (101)   ~ (all_53_12 = e3)
% 227.92/39.53    (102)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0
% 227.92/39.53             & op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~
% 227.92/39.53             (all_42_1 = e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 227.92/39.53    (103)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 227.92/39.53           (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 227.92/39.53    (104)  all_55_1 = all_52_3
% 227.92/39.53    (105)   ~ (all_52_5 = all_6_2)
% 227.92/39.53    (106)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 227.92/39.53           (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 227.92/39.53    (107)   ~ (all_52_5 = e1)
% 227.92/39.53    (108)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 227.92/39.53           | (all_57_11 = e0 & op(e1, e0) = e0)
% 227.92/39.53    (109)   ~ (all_52_5 = e0)
% 227.92/39.53    (110)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 227.92/39.53           | (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 227.92/39.53             e2)
% 227.92/39.53    (111)  op(e2, e1) = all_53_9
% 227.92/39.53    (112)  op(e1, e2) = all_53_6
% 227.92/39.53    (113)   ~ (all_6_2 = e0)
% 227.92/39.53    (114)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 227.92/39.53           (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 227.92/39.53    (115)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 227.92/39.53    (116)  all_24_2 = all_6_2
% 227.92/39.53    (117)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 227.92/39.53           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 227.92/39.53    (118)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 227.92/39.53           (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 227.92/39.53    (119)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 227.92/39.53           | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 227.92/39.53             e1)
% 227.92/39.53    (120)  all_57_14 = e0
% 227.92/39.53    (121)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 227.92/39.53           (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 227.92/39.53    (122)  op(e3, e0) = all_52_7
% 227.92/39.53    (123)  op(e3, e1) = all_53_8
% 227.92/39.53    (124)  all_55_7 = all_53_13
% 227.92/39.53    (125)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 227.92/39.53           (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 227.92/39.53    (126)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 227.92/39.53           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 227.92/39.53    (127)  op(e3, e0) = all_53_12
% 227.92/39.53  
% 227.92/39.53  Begin of proof
% 227.92/39.53  | 
% 227.92/39.53  | ALPHA: (26) implies:
% 227.92/39.53  |   (128)  all_57_13 = e1
% 227.92/39.53  | 
% 227.92/39.53  | COMBINE_EQS: (76), (128) imply:
% 227.92/39.53  |   (129)  e2 = e1
% 227.92/39.53  | 
% 227.92/39.53  | COMBINE_EQS: (84), (129) imply:
% 227.92/39.53  |   (130)  all_57_8 = e1
% 227.92/39.53  | 
% 227.92/39.53  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 227.92/39.53  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 227.92/39.53  |            (24), (25), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 227.92/39.53  |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 227.92/39.53  |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 227.92/39.53  |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 227.92/39.53  |            (69), (70), (71), (72), (73), (74), (75), (77), (78), (79), (80),
% 227.92/39.53  |            (81), (82), (83), (85), (86), (87), (88), (89), (90), (91), (92),
% 227.92/39.53  |            (93), (94), (95), (96), (97), (98), (99), (100), (101), (102),
% 227.92/39.53  |            (103), (104), (105), (106), (107), (108), (109), (110), (111),
% 227.92/39.53  |            (112), (113), (114), (115), (116), (117), (118), (119), (120),
% 227.92/39.53  |            (121), (122), (123), (124), (125), (126), (127), (130) are
% 227.92/39.53  |            inconsistent by sub-proof #403.
% 227.92/39.53  | 
% 227.92/39.53  End of proof
% 227.92/39.53  
% 227.92/39.53  Sub-proof #401 shows that the following formulas are inconsistent:
% 227.92/39.53  ----------------------------------------------------------------
% 227.92/39.53    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 227.92/39.53    (2)  all_57_9 = e2
% 227.92/39.53    (3)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 227.92/39.53    (4)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 227.92/39.53         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 227.92/39.53    (5)  all_57_5 = e3 & op(e2, e1) = e3
% 227.92/39.53    (6)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 227.92/39.53         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 227.92/39.53    (7)  op(e2, e1) = e3
% 227.92/39.53    (8)   ~ (all_53_8 = all_53_12)
% 227.92/39.53    (9)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 227.92/39.53         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.92/39.53    (10)   ~ (e3 = e1)
% 227.92/39.53    (11)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 227.92/39.53          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 227.92/39.53    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.92/39.53            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.92/39.53    (13)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 227.92/39.53          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 227.92/39.53    (14)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 227.92/39.53            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 227.92/39.53              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 227.92/39.53    (15)   ~ (all_6_2 = e3)
% 227.92/39.53    (16)  all_57_10 = e1
% 227.92/39.53    (17)  op(e1, e1) = all_6_2
% 227.92/39.53    (18)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 227.92/39.53    (19)   ~ (all_53_9 = e0)
% 227.92/39.53    (20)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 227.92/39.53          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 227.92/39.53    (21)   ~ (all_53_4 = all_53_12)
% 227.92/39.53    (22)   ~ (all_53_8 = all_53_9)
% 227.92/39.53    (23)  all_42_2 = all_6_2
% 227.92/39.53    (24)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 227.92/39.53          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 227.92/39.53    (25)   ~ (all_53_9 = all_6_2)
% 227.92/39.53    (26)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 227.92/39.53          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 227.92/39.53    (27)  all_57_3 = e0
% 227.92/39.53    (28)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 227.92/39.53          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 227.92/39.53    (29)   ~ (e3 = e2)
% 227.92/39.53    (30)  all_55_1 = all_53_4
% 227.92/39.53    (31)   ~ (e3 = e0)
% 227.92/39.53    (32)  all_57_2 = e2 & op(e2, e3) = e2
% 227.92/39.53    (33)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 227.92/39.53          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 227.92/39.53    (34)   ~ (all_53_8 = all_6_2)
% 227.92/39.53    (35)  all_57_0 = e0
% 227.92/39.53    (36)  all_55_2 = all_53_8
% 227.92/39.53    (37)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 227.92/39.53    (38)  all_57_15 = e3
% 227.92/39.53    (39)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 227.92/39.53          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 227.92/39.53            e1)
% 227.92/39.53    (40)  all_57_5 = e3
% 227.92/39.53    (41)  all_57_11 = e0
% 227.92/39.53    (42)   ~ (all_53_4 = all_53_8)
% 227.92/39.53    (43)  op(e3, e2) = all_53_4
% 227.92/39.53    (44)  op(e1, e1) = e1
% 227.92/39.53    (45)   ~ (e2 = e0)
% 227.92/39.53    (46)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 227.92/39.53            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 227.92/39.53            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 227.92/39.53            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 227.92/39.53              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 227.92/39.53            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 227.92/39.53            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 227.92/39.53              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 227.92/39.53              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 227.92/39.53            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 227.92/39.53            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 227.92/39.53            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 227.92/39.53              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 227.92/39.53              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 227.92/39.53            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 227.92/39.53              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 227.92/39.53            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 227.92/39.53            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 227.92/39.53              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 227.92/39.53              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 227.92/39.53            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 227.92/39.53            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 227.92/39.53    (47)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 227.92/39.53          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 227.92/39.53    (48)   ~ (e1 = e0)
% 227.92/39.53    (49)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 227.92/39.53            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 227.92/39.53              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 227.92/39.53    (50)   ~ (all_53_4 = e0)
% 227.92/39.53    (51)  op(e0, e0) = e3
% 227.92/39.53    (52)   ~ (all_53_4 = all_53_6)
% 227.92/39.53    (53)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.92/39.53          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 227.92/39.53            e2)
% 227.92/39.53    (54)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 227.92/39.53              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 227.92/39.53                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 227.92/39.53                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 227.92/39.53    (55)  all_55_10 = all_6_2
% 227.92/39.53    (56)  op(e1, e1) = e2
% 227.92/39.53    (57)  all_38_2 = all_6_2
% 227.92/39.53    (58)  all_55_3 = all_53_12
% 227.92/39.53    (59)   ~ (all_53_12 = e3)
% 227.92/39.53    (60)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 227.92/39.53            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 227.92/39.53              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 227.92/39.53    (61)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 227.92/39.53          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 227.92/39.53    (62)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 227.92/39.53          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 227.92/39.53    (63)   ~ (e2 = e1)
% 227.92/39.53    (64)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 227.92/39.53          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 227.92/39.53    (65)  op(e2, e1) = all_53_9
% 227.92/39.53    (66)  op(e1, e2) = all_53_6
% 227.92/39.53    (67)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 227.92/39.53          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 227.92/39.53    (68)  all_24_2 = all_6_2
% 227.92/39.53    (69)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 227.92/39.53          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 227.92/39.53    (70)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 227.92/39.53          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 227.92/39.53    (71)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 227.92/39.53          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 227.92/39.53    (72)  all_57_14 = e0
% 227.92/39.53    (73)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 227.92/39.53          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 227.92/39.53    (74)  op(e3, e1) = all_53_8
% 227.92/39.53    (75)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 227.92/39.53          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 227.92/39.53    (76)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 227.92/39.53          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 227.92/39.53    (77)  op(e3, e0) = all_53_12
% 227.92/39.53  
% 227.92/39.53  Begin of proof
% 227.92/39.53  | 
% 227.92/39.53  | BETA: splitting (6) gives:
% 227.92/39.53  | 
% 227.92/39.53  | Case 1:
% 227.92/39.53  | | 
% 227.92/39.53  | |   (78)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) =
% 227.92/39.53  | |           e1)
% 227.92/39.53  | | 
% 227.92/39.53  | | BETA: splitting (78) gives:
% 227.92/39.53  | | 
% 227.92/39.53  | | Case 1:
% 227.92/39.53  | | | 
% 227.92/39.53  | | |   (79)  all_57_0 = e1 & op(e3, e3) = e1
% 227.92/39.53  | | | 
% 227.92/39.53  | | | ALPHA: (79) implies:
% 227.92/39.53  | | |   (80)  all_57_0 = e1
% 227.92/39.53  | | | 
% 227.92/39.53  | | | COMBINE_EQS: (35), (80) imply:
% 227.92/39.53  | | |   (81)  e1 = e0
% 227.92/39.53  | | | 
% 227.92/39.53  | | | REF_CLOSE: (4), (10), (16), (27), (29), (40), (45), (48), (61), (63), (81)
% 227.92/39.53  | | |            are inconsistent by sub-proof #1506.
% 227.92/39.53  | | | 
% 227.92/39.53  | | Case 2:
% 227.92/39.53  | | | 
% 227.92/39.53  | | |   (82)  all_57_2 = e1 & op(e2, e3) = e1
% 227.92/39.53  | | | 
% 227.92/39.53  | | | ALPHA: (82) implies:
% 227.92/39.53  | | |   (83)  all_57_2 = e1
% 227.92/39.53  | | | 
% 227.92/39.53  | | | REF_CLOSE: (2), (4), (10), (12), (27), (29), (38), (40), (41), (45), (48),
% 227.92/39.53  | | |            (51), (61), (63), (64), (71), (83) are inconsistent by
% 227.92/39.53  | | |            sub-proof #1093.
% 227.92/39.53  | | | 
% 227.92/39.53  | | End of split
% 227.92/39.53  | | 
% 227.92/39.53  | Case 2:
% 227.92/39.53  | | 
% 227.92/39.53  | |   (84)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) =
% 227.92/39.53  | |           e1)
% 227.92/39.53  | | 
% 227.92/39.53  | | BETA: splitting (84) gives:
% 227.92/39.53  | | 
% 227.92/39.53  | | Case 1:
% 227.92/39.53  | | | 
% 227.92/39.53  | | |   (85)  all_57_6 = e1 & op(e1, e3) = e1
% 227.92/39.53  | | | 
% 227.92/39.53  | | | ALPHA: (85) implies:
% 227.92/39.53  | | |   (86)  all_57_6 = e1
% 227.92/39.53  | | | 
% 227.92/39.53  | | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13),
% 227.92/39.53  | | |            (14), (15), (17), (18), (19), (20), (21), (22), (23), (24),
% 227.92/39.53  | | |            (25), (26), (27), (28), (29), (30), (31), (33), (34), (36),
% 227.92/39.53  | | |            (37), (38), (39), (40), (42), (43), (45), (46), (47), (48),
% 227.92/39.53  | | |            (49), (50), (51), (52), (53), (54), (55), (57), (58), (59),
% 227.92/39.53  | | |            (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 227.92/39.53  | | |            (70), (71), (72), (73), (74), (75), (76), (77), (86) are
% 227.92/39.53  | | |            inconsistent by sub-proof #439.
% 227.92/39.53  | | | 
% 227.92/39.53  | | Case 2:
% 227.92/39.53  | | | 
% 227.92/39.53  | | | 
% 227.92/39.53  | | | ALPHA: (32) implies:
% 227.92/39.53  | | |   (87)  all_57_2 = e2
% 227.92/39.53  | | | 
% 227.92/39.53  | | | GROUND_INST: instantiating (12) with e1, e2, e1, e1, simplifying with
% 227.92/39.53  | | |              (44), (56) gives:
% 227.92/39.53  | | |   (88)  e2 = e1
% 227.92/39.53  | | | 
% 227.92/39.53  | | | COMBINE_EQS: (87), (88) imply:
% 227.92/39.53  | | |   (89)  all_57_2 = e1
% 227.92/39.53  | | | 
% 227.92/39.53  | | | REF_CLOSE: (2), (4), (10), (12), (27), (29), (38), (40), (41), (45), (48),
% 227.92/39.53  | | |            (51), (61), (63), (64), (71), (89) are inconsistent by
% 227.92/39.53  | | |            sub-proof #1093.
% 227.92/39.53  | | | 
% 227.92/39.53  | | End of split
% 227.92/39.53  | | 
% 227.92/39.53  | End of split
% 227.92/39.53  | 
% 227.92/39.53  End of proof
% 227.92/39.53  
% 227.92/39.53  Sub-proof #402 shows that the following formulas are inconsistent:
% 227.92/39.53  ----------------------------------------------------------------
% 227.92/39.53    (1)  all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 227.92/39.53    (2)   ~ (all_53_7 = e3)
% 227.92/39.53    (3)   ~ (all_53_2 = e1)
% 227.92/39.53    (4)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 227.92/39.53    (5)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 227.92/39.53    (6)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 227.92/39.53         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 227.92/39.54    (7)  op(e3, e1) = all_52_5
% 227.92/39.54    (8)   ~ (all_52_7 = e3)
% 227.92/39.54    (9)   ~ (all_52_3 = all_52_5)
% 227.92/39.54    (10)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 227.92/39.54          (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 227.92/39.54    (11)   ~ (all_53_8 = all_53_12)
% 227.92/39.54    (12)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 227.92/39.54          (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.92/39.54    (13)   ~ (e3 = e1)
% 227.92/39.54    (14)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 227.92/39.54          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 227.92/39.54    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.92/39.54            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.92/39.54    (16)  op(all_52_5, all_52_5) = e1
% 227.92/39.54    (17)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 227.92/39.54          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 227.92/39.54    (18)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 227.92/39.54            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 227.92/39.54              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 227.92/39.54    (19)   ~ (all_53_3 = e3)
% 227.92/39.54    (20)   ~ (all_53_3 = all_53_7)
% 227.92/39.54    (21)   ~ (all_6_2 = e3)
% 227.92/39.54    (22)   ~ (all_52_3 = e0)
% 227.92/39.54    (23)   ~ (all_53_9 = e1)
% 227.92/39.54    (24)  op(e1, e1) = all_6_2
% 227.92/39.54    (25)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 227.92/39.54    (26)  op(all_52_7, all_52_7) = e0
% 227.92/39.54    (27)   ~ (all_53_1 = all_53_9)
% 227.92/39.54    (28)  op(e3, e2) = all_52_3
% 227.92/39.54    (29)   ~ (all_53_9 = e0)
% 227.92/39.54    (30)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 227.92/39.54          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 227.92/39.54    (31)   ~ (all_52_5 = all_52_7)
% 227.92/39.54    (32)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 227.92/39.54            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 227.92/39.54              e3) = all_22_1 & $i(all_22_1))
% 227.92/39.54    (33)  all_55_3 = all_52_7
% 227.92/39.54    (34)  all_57_9 = e1
% 227.92/39.54    (35)   ~ (all_53_4 = all_53_12)
% 227.92/39.54    (36)   ~ (all_53_13 = e3)
% 227.92/39.54    (37)   ~ (all_53_8 = all_53_9)
% 227.92/39.54    (38)   ~ (all_53_7 = all_52_3)
% 227.92/39.54    (39)  all_57_7 = e1
% 227.92/39.54    (40)  all_42_2 = all_6_2
% 227.92/39.54    (41)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 227.92/39.54          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 227.92/39.54    (42)  op(e2, e2) = e0
% 227.92/39.54    (43)  all_55_4 = all_53_1
% 227.92/39.54    (44)   ~ (all_53_9 = all_6_2)
% 227.92/39.54    (45)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 227.92/39.54          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 227.92/39.54    (46)  all_57_3 = e0
% 227.92/39.54    (47)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 227.92/39.54          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 227.92/39.54    (48)   ~ (e3 = e2)
% 227.92/39.54    (49)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 227.92/39.54    (50)  all_55_1 = all_53_4
% 227.92/39.54    (51)   ~ (all_53_13 = all_52_7)
% 227.92/39.54    (52)  all_55_7 = e3 | all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 227.92/39.54    (53)  all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 227.92/39.54    (54)   ~ (e3 = e0)
% 227.92/39.54    (55)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 227.92/39.54          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 227.92/39.54    (56)   ~ (all_6_2 = e2)
% 227.92/39.54    (57)   ~ (all_53_8 = all_6_2)
% 227.92/39.54    (58)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 227.92/39.54    (59)   ~ (all_53_2 = e0)
% 227.92/39.54    (60)  all_57_0 = e0
% 227.92/39.54    (61)  all_55_2 = all_53_8
% 227.92/39.54    (62)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 227.92/39.54    (63)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 227.92/39.54          | (all_57_14 = e0 & op(e0, e1) = e0)
% 227.92/39.54    (64)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 227.92/39.54    (65)  all_57_15 = e3
% 227.92/39.54    (66)   ~ (all_53_9 = all_53_13)
% 227.92/39.54    (67)   ~ (all_53_7 = e0)
% 227.92/39.54    (68)  op(e3, e3) = e0
% 227.92/39.54    (69)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 227.92/39.54          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 227.92/39.54            e1)
% 227.92/39.54    (70)  all_57_5 = e3
% 227.92/39.54    (71)  op(e3, e3) = all_52_1
% 227.92/39.54    (72)  all_57_11 = e0
% 227.92/39.54    (73)   ~ (all_53_4 = all_53_8)
% 227.92/39.54    (74)  all_55_6 = all_53_9
% 227.92/39.54    (75)  op(e3, e2) = all_53_4
% 227.92/39.54    (76)   ~ (all_53_1 = all_53_2)
% 227.92/39.54    (77)  op(all_52_1, all_52_1) = e3
% 227.92/39.54    (78)   ~ (e2 = e0)
% 227.92/39.54    (79)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 227.92/39.54            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 227.92/39.54            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 227.92/39.54            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 227.92/39.54              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 227.92/39.54            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 227.92/39.54            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 227.92/39.54              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 227.92/39.54              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 227.92/39.54            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 227.92/39.54            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 227.92/39.54            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 227.92/39.54              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 227.92/39.54              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 227.92/39.54            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 227.92/39.54              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 227.92/39.54            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 227.92/39.54            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 227.92/39.54              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 227.92/39.54              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 227.92/39.54            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 227.92/39.54            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 227.92/39.54    (80)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 227.92/39.54            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 227.92/39.54              e3) = all_12_1 & $i(all_12_1))
% 227.92/39.54    (81)  all_55_12 = all_53_3
% 227.92/39.54    (82)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 227.92/39.54          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 227.92/39.54    (83)   ~ (all_53_1 = e0)
% 227.92/39.54    (84)   ~ (e1 = e0)
% 227.92/39.54    (85)   ~ (all_52_3 = all_52_7)
% 227.92/39.54    (86)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 227.92/39.54            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 227.92/39.54              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 227.92/39.54    (87)   ~ (all_53_4 = e0)
% 227.92/39.54    (88)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 227.92/39.54          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 227.92/39.54    (89)  all_57_6 = e3
% 227.92/39.54    (90)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 227.92/39.54          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 227.92/39.54    (91)  all_55_8 = all_53_2
% 227.92/39.54    (92)  op(e0, e0) = e3
% 227.92/39.54    (93)   ~ (all_53_4 = all_53_6)
% 227.92/39.54    (94)  all_55_2 = all_52_5
% 227.92/39.54    (95)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.92/39.54          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 227.92/39.54            e2)
% 227.92/39.54    (96)   ~ (all_53_3 = e0)
% 227.92/39.54    (97)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 227.92/39.54              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 227.92/39.54                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 227.92/39.54                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 227.92/39.54    (98)  all_55_10 = all_6_2
% 227.92/39.54    (99)   ~ (all_53_13 = e0)
% 227.92/39.54    (100)   ~ (all_53_1 = all_53_13)
% 227.92/39.54    (101)  all_55_13 = all_53_7
% 227.92/39.54    (102)   ~ (all_53_9 = all_52_5)
% 227.92/39.54    (103)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 227.92/39.54           (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 227.92/39.54    (104)  all_38_2 = all_6_2
% 227.92/39.54    (105)  all_55_3 = all_53_12
% 227.92/39.54    (106)   ~ (all_53_12 = e3)
% 227.92/39.54    (107)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0
% 227.92/39.54             & op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~
% 227.92/39.54             (all_42_1 = e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 227.92/39.54    (108)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 227.92/39.54           (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 227.92/39.54    (109)  all_55_1 = all_52_3
% 227.92/39.54    (110)   ~ (all_52_5 = all_6_2)
% 227.92/39.54    (111)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 227.92/39.54           (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 227.92/39.54    (112)  all_57_1 = e3
% 227.92/39.54    (113)   ~ (all_52_5 = e1)
% 227.92/39.54    (114)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 227.92/39.54           | (all_57_11 = e0 & op(e1, e0) = e0)
% 227.92/39.54    (115)   ~ (all_52_5 = e0)
% 227.92/39.54    (116)   ~ (e2 = e1)
% 227.92/39.54    (117)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 227.92/39.54           | (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 227.92/39.54             e2)
% 227.92/39.54    (118)  op(e2, e1) = all_53_9
% 227.92/39.54    (119)  op(e1, e2) = all_53_6
% 227.92/39.54    (120)   ~ (all_6_2 = e0)
% 227.92/39.54    (121)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 227.92/39.54           (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 227.92/39.54    (122)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 227.92/39.54    (123)  all_24_2 = all_6_2
% 227.92/39.54    (124)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 227.92/39.54           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 227.92/39.54    (125)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 227.92/39.54           (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 227.92/39.54    (126)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 227.92/39.54           | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 227.92/39.54             e1)
% 227.92/39.54    (127)  all_57_14 = e0
% 227.92/39.54    (128)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 227.92/39.54           (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 227.92/39.54    (129)  op(e3, e0) = all_52_7
% 227.92/39.54    (130)  op(e3, e1) = all_53_8
% 227.92/39.54    (131)  all_55_7 = all_53_13
% 227.92/39.54    (132)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 227.92/39.54           (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 227.92/39.54    (133)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 227.92/39.54           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 227.92/39.54    (134)  op(e3, e0) = all_53_12
% 227.92/39.54  
% 227.92/39.54  Begin of proof
% 227.92/39.54  | 
% 227.92/39.54  | BETA: splitting (117) gives:
% 227.92/39.54  | 
% 227.92/39.54  | Case 1:
% 227.92/39.54  | | 
% 227.92/39.54  | |   (135)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 227.92/39.54  | |            e2)
% 227.92/39.54  | | 
% 227.92/39.54  | | BETA: splitting (135) gives:
% 227.92/39.54  | | 
% 227.92/39.54  | | Case 1:
% 227.92/39.54  | | | 
% 227.92/39.54  | | |   (136)  all_57_9 = e2 & op(e3, e0) = e2
% 227.92/39.54  | | | 
% 227.92/39.54  | | | ALPHA: (136) implies:
% 227.92/39.54  | | |   (137)  all_57_9 = e2
% 227.92/39.54  | | | 
% 227.92/39.54  | | | REF_CLOSE: (34), (116), (137) are inconsistent by sub-proof #2444.
% 227.92/39.54  | | | 
% 227.92/39.54  | | Case 2:
% 227.92/39.54  | | | 
% 227.92/39.54  | | |   (138)  all_57_10 = e2 & op(e2, e0) = e2
% 227.92/39.54  | | | 
% 227.92/39.54  | | | ALPHA: (138) implies:
% 227.92/39.54  | | |   (139)  all_57_10 = e2
% 227.92/39.54  | | | 
% 227.92/39.54  | | | BETA: splitting (133) gives:
% 227.92/39.54  | | | 
% 227.92/39.54  | | | Case 1:
% 227.92/39.54  | | | | 
% 227.92/39.54  | | | |   (140)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2)
% 227.92/39.54  | | | |            = e2)
% 227.92/39.54  | | | | 
% 227.92/39.54  | | | | BETA: splitting (140) gives:
% 227.92/39.54  | | | | 
% 227.92/39.54  | | | | Case 1:
% 227.92/39.54  | | | | | 
% 227.92/39.54  | | | | |   (141)  all_57_6 = e2 & op(e1, e3) = e2
% 227.92/39.54  | | | | | 
% 227.92/39.54  | | | | | REF_CLOSE: (48), (89), (141) are inconsistent by sub-proof #2012.
% 227.92/39.54  | | | | | 
% 227.92/39.54  | | | | Case 2:
% 227.92/39.54  | | | | | 
% 227.92/39.54  | | | | |   (142)  all_57_7 = e2 & op(e1, e2) = e2
% 227.92/39.54  | | | | | 
% 227.92/39.54  | | | | | ALPHA: (142) implies:
% 227.92/39.54  | | | | |   (143)  all_57_7 = e2
% 227.92/39.54  | | | | | 
% 227.92/39.54  | | | | | REF_CLOSE: (39), (116), (143) are inconsistent by sub-proof #1761.
% 227.92/39.54  | | | | | 
% 227.92/39.54  | | | | End of split
% 227.92/39.54  | | | | 
% 227.92/39.54  | | | Case 2:
% 227.92/39.54  | | | | 
% 227.92/39.54  | | | |   (144)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1,
% 227.92/39.54  | | | |              e0) = e2)
% 227.92/39.54  | | | | 
% 227.92/39.54  | | | | BETA: splitting (144) gives:
% 227.92/39.54  | | | | 
% 227.92/39.54  | | | | Case 1:
% 227.92/39.54  | | | | | 
% 227.92/39.54  | | | | |   (145)  all_57_8 = e2 & op(e1, e1) = e2
% 227.92/39.54  | | | | | 
% 227.92/39.54  | | | | | ALPHA: (145) implies:
% 227.92/39.54  | | | | |   (146)  all_57_8 = e2
% 227.92/39.54  | | | | | 
% 227.92/39.54  | | | | | BETA: splitting (41) gives:
% 227.92/39.54  | | | | | 
% 227.92/39.54  | | | | | Case 1:
% 227.92/39.54  | | | | | | 
% 227.92/39.54  | | | | | |   (147)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3,
% 227.92/39.54  | | | | | |              e2) = e2)
% 227.92/39.54  | | | | | | 
% 227.92/39.54  | | | | | | REF_CLOSE: (15), (42), (48), (54), (71), (77), (112), (147) are
% 227.92/39.54  | | | | | |            inconsistent by sub-proof #1363.
% 227.92/39.54  | | | | | | 
% 227.92/39.54  | | | | | Case 2:
% 227.92/39.54  | | | | | | 
% 227.92/39.54  | | | | | |   (148)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3,
% 227.92/39.54  | | | | | |              e0) = e2)
% 227.92/39.54  | | | | | | 
% 227.92/39.54  | | | | | | BETA: splitting (148) gives:
% 227.92/39.54  | | | | | | 
% 227.92/39.54  | | | | | | Case 1:
% 227.92/39.54  | | | | | | | 
% 227.92/39.54  | | | | | | |   (149)  all_57_4 = e2 & op(e3, e1) = e2
% 227.92/39.54  | | | | | | | 
% 227.92/39.54  | | | | | | | ALPHA: (149) implies:
% 227.92/39.54  | | | | | | |   (150)  all_57_4 = e2
% 227.92/39.54  | | | | | | | 
% 227.92/39.54  | | | | | | | REF_CLOSE: (13), (55), (70), (84), (116), (127), (146), (150) are
% 227.92/39.54  | | | | | | |            inconsistent by sub-proof #1456.
% 227.92/39.54  | | | | | | | 
% 227.92/39.54  | | | | | | Case 2:
% 227.92/39.54  | | | | | | | 
% 227.92/39.54  | | | | | | |   (151)  all_57_9 = e2 & op(e3, e0) = e2
% 227.92/39.54  | | | | | | | 
% 227.92/39.54  | | | | | | | ALPHA: (151) implies:
% 227.92/39.54  | | | | | | |   (152)  all_57_9 = e2
% 227.92/39.54  | | | | | | | 
% 227.92/39.54  | | | | | | | COMBINE_EQS: (34), (152) imply:
% 227.92/39.54  | | | | | | |   (153)  e2 = e1
% 227.92/39.54  | | | | | | | 
% 227.92/39.54  | | | | | | | SIMP: (153) implies:
% 227.92/39.54  | | | | | | |   (154)  e2 = e1
% 227.92/39.54  | | | | | | | 
% 227.92/39.54  | | | | | | | COMBINE_EQS: (146), (154) imply:
% 227.92/39.54  | | | | | | |   (155)  all_57_8 = e1
% 227.92/39.54  | | | | | | | 
% 227.92/39.54  | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 227.92/39.54  | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18), (19),
% 227.92/39.54  | | | | | | |            (20), (21), (22), (23), (24), (25), (26), (27), (28),
% 227.92/39.54  | | | | | | |            (29), (30), (31), (32), (33), (35), (36), (37), (38),
% 227.92/39.54  | | | | | | |            (40), (41), (42), (43), (44), (45), (46), (47), (49),
% 227.92/39.54  | | | | | | |            (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 227.92/39.54  | | | | | | |            (59), (60), (61), (62), (63), (64), (65), (66), (67),
% 227.92/39.54  | | | | | | |            (68), (69), (72), (73), (74), (75), (76), (79), (80),
% 227.92/39.54  | | | | | | |            (81), (82), (83), (84), (85), (86), (87), (88), (90),
% 227.92/39.54  | | | | | | |            (91), (92), (93), (94), (95), (96), (97), (98), (99),
% 227.92/39.54  | | | | | | |            (100), (101), (102), (103), (104), (105), (106), (107),
% 227.92/39.54  | | | | | | |            (108), (109), (110), (111), (113), (114), (115), (117),
% 227.92/39.54  | | | | | | |            (118), (119), (120), (121), (122), (123), (124), (125),
% 227.92/39.54  | | | | | | |            (126), (127), (128), (129), (130), (131), (132), (133),
% 227.92/39.54  | | | | | | |            (134), (155) are inconsistent by sub-proof #403.
% 227.92/39.54  | | | | | | | 
% 227.92/39.54  | | | | | | End of split
% 227.92/39.54  | | | | | | 
% 227.92/39.54  | | | | | End of split
% 227.92/39.54  | | | | | 
% 227.92/39.54  | | | | Case 2:
% 227.92/39.54  | | | | | 
% 227.92/39.54  | | | | |   (156)  all_57_11 = e2 & op(e1, e0) = e2
% 227.92/39.54  | | | | | 
% 227.92/39.54  | | | | | ALPHA: (156) implies:
% 227.92/39.54  | | | | |   (157)  all_57_11 = e2
% 227.92/39.54  | | | | | 
% 227.92/39.54  | | | | | COMBINE_EQS: (72), (157) imply:
% 227.92/39.54  | | | | |   (158)  e2 = e0
% 227.92/39.54  | | | | | 
% 227.92/39.54  | | | | | REF_CLOSE: (6), (13), (46), (48), (70), (78), (84), (108), (116),
% 227.92/39.54  | | | | |            (139), (158) are inconsistent by sub-proof #1517.
% 227.92/39.54  | | | | | 
% 227.92/39.54  | | | | End of split
% 227.92/39.54  | | | | 
% 227.92/39.54  | | | End of split
% 227.92/39.54  | | | 
% 227.92/39.54  | | End of split
% 227.92/39.54  | | 
% 227.92/39.54  | Case 2:
% 227.92/39.54  | | 
% 227.92/39.54  | |   (159)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 227.92/39.54  | |            e2)
% 227.92/39.54  | | 
% 227.92/39.54  | | REF_CLOSE: (48), (65), (72), (78), (159) are inconsistent by sub-proof
% 227.92/39.54  | |            #1146.
% 227.92/39.54  | | 
% 227.92/39.54  | End of split
% 227.92/39.54  | 
% 227.92/39.54  End of proof
% 227.92/39.54  
% 227.92/39.54  Sub-proof #403 shows that the following formulas are inconsistent:
% 227.92/39.54  ----------------------------------------------------------------
% 227.92/39.54    (1)  all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 227.92/39.54    (2)   ~ (all_53_7 = e3)
% 227.92/39.54    (3)   ~ (all_53_2 = e1)
% 227.92/39.54    (4)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 227.92/39.54    (5)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 227.92/39.54    (6)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 227.92/39.54         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 227.92/39.54    (7)  op(e3, e1) = all_52_5
% 227.92/39.54    (8)   ~ (all_52_7 = e3)
% 227.92/39.54    (9)   ~ (all_52_3 = all_52_5)
% 227.92/39.54    (10)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 227.92/39.54          (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 227.92/39.54    (11)   ~ (all_53_8 = all_53_12)
% 227.92/39.54    (12)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 227.92/39.54          (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.92/39.54    (13)   ~ (e3 = e1)
% 227.92/39.54    (14)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 227.92/39.54          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 227.92/39.54    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.92/39.54            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.92/39.54    (16)  op(all_52_5, all_52_5) = e1
% 227.92/39.54    (17)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 227.92/39.54          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 227.92/39.54    (18)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 227.92/39.54            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 227.92/39.54              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 227.92/39.54    (19)   ~ (all_53_3 = e3)
% 227.92/39.54    (20)   ~ (all_53_3 = all_53_7)
% 227.92/39.54    (21)   ~ (all_6_2 = e3)
% 227.92/39.54    (22)   ~ (all_52_3 = e0)
% 227.92/39.54    (23)   ~ (all_53_9 = e1)
% 227.92/39.54    (24)  op(e1, e1) = all_6_2
% 227.92/39.54    (25)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 227.92/39.54    (26)  op(all_52_7, all_52_7) = e0
% 227.92/39.54    (27)   ~ (all_53_1 = all_53_9)
% 227.92/39.54    (28)  op(e3, e2) = all_52_3
% 227.92/39.54    (29)   ~ (all_53_9 = e0)
% 227.92/39.54    (30)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 227.92/39.54          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 227.92/39.54    (31)   ~ (all_52_5 = all_52_7)
% 227.92/39.54    (32)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 227.92/39.54            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 227.92/39.54              e3) = all_22_1 & $i(all_22_1))
% 227.92/39.54    (33)  all_55_3 = all_52_7
% 227.92/39.54    (34)   ~ (all_53_4 = all_53_12)
% 227.92/39.54    (35)   ~ (all_53_13 = e3)
% 227.92/39.54    (36)   ~ (all_53_8 = all_53_9)
% 227.92/39.54    (37)   ~ (all_53_7 = all_52_3)
% 227.92/39.54    (38)  all_42_2 = all_6_2
% 227.92/39.54    (39)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 227.92/39.54          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 227.92/39.54    (40)  op(e2, e2) = e0
% 227.92/39.54    (41)  all_55_4 = all_53_1
% 227.92/39.54    (42)  all_57_8 = e1
% 227.92/39.54    (43)   ~ (all_53_9 = all_6_2)
% 227.92/39.54    (44)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 227.92/39.54          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 227.92/39.54    (45)  all_57_3 = e0
% 227.92/39.54    (46)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 227.92/39.54          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 227.92/39.54    (47)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 227.92/39.54    (48)  all_55_1 = all_53_4
% 227.92/39.54    (49)   ~ (all_53_13 = all_52_7)
% 227.92/39.54    (50)  all_55_7 = e3 | all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 227.92/39.54    (51)  all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 227.92/39.54    (52)   ~ (e3 = e0)
% 227.92/39.54    (53)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 227.92/39.54          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 227.92/39.54    (54)   ~ (all_6_2 = e2)
% 227.92/39.54    (55)   ~ (all_53_8 = all_6_2)
% 227.92/39.54    (56)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 227.92/39.54    (57)   ~ (all_53_2 = e0)
% 227.92/39.54    (58)  all_57_0 = e0
% 227.92/39.54    (59)  all_55_2 = all_53_8
% 227.92/39.54    (60)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 227.92/39.54    (61)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 227.92/39.54          | (all_57_14 = e0 & op(e0, e1) = e0)
% 227.92/39.54    (62)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 227.92/39.54    (63)  all_57_15 = e3
% 227.92/39.54    (64)   ~ (all_53_9 = all_53_13)
% 227.92/39.54    (65)   ~ (all_53_7 = e0)
% 227.92/39.54    (66)  op(e3, e3) = e0
% 227.92/39.54    (67)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 227.92/39.54          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 227.92/39.54            e1)
% 227.92/39.54    (68)  all_57_11 = e0
% 227.92/39.54    (69)   ~ (all_53_4 = all_53_8)
% 227.92/39.54    (70)  all_55_6 = all_53_9
% 227.92/39.54    (71)  op(e3, e2) = all_53_4
% 227.92/39.54    (72)   ~ (all_53_1 = all_53_2)
% 227.92/39.54    (73)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 227.92/39.54            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 227.92/39.54            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 227.92/39.54            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 227.92/39.54              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 227.92/39.54            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 227.92/39.54            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 227.92/39.54              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 227.92/39.54              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 227.92/39.54            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 227.92/39.54            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 227.92/39.54            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 227.92/39.54              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 227.92/39.54              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 227.92/39.54            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 227.92/39.54              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 227.92/39.54            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 227.92/39.54            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 227.92/39.54              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 227.92/39.54              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 227.92/39.54            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 227.92/39.54            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 227.92/39.54    (74)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 227.92/39.54            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 227.92/39.54              e3) = all_12_1 & $i(all_12_1))
% 227.92/39.54    (75)  all_55_12 = all_53_3
% 227.92/39.54    (76)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 227.92/39.54          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 227.92/39.54    (77)   ~ (all_53_1 = e0)
% 227.92/39.54    (78)   ~ (e1 = e0)
% 227.92/39.54    (79)   ~ (all_52_3 = all_52_7)
% 227.92/39.54    (80)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 227.92/39.54            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 227.92/39.54              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 227.92/39.54    (81)   ~ (all_53_4 = e0)
% 227.92/39.54    (82)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 227.92/39.54          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 227.92/39.54    (83)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 227.92/39.54          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 227.92/39.54    (84)  all_55_8 = all_53_2
% 227.92/39.54    (85)  op(e0, e0) = e3
% 227.92/39.54    (86)   ~ (all_53_4 = all_53_6)
% 227.92/39.54    (87)  all_55_2 = all_52_5
% 227.92/39.54    (88)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.92/39.54          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 227.92/39.54            e2)
% 227.92/39.54    (89)   ~ (all_53_3 = e0)
% 227.92/39.55    (90)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 227.92/39.55              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 227.92/39.55                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 227.92/39.55                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 227.92/39.55    (91)  all_55_10 = all_6_2
% 227.92/39.55    (92)   ~ (all_53_13 = e0)
% 227.92/39.55    (93)   ~ (all_53_1 = all_53_13)
% 227.92/39.55    (94)  all_55_13 = all_53_7
% 227.92/39.55    (95)   ~ (all_53_9 = all_52_5)
% 227.92/39.55    (96)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 227.92/39.55          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 227.92/39.55    (97)  all_38_2 = all_6_2
% 227.92/39.55    (98)  all_55_3 = all_53_12
% 227.92/39.55    (99)   ~ (all_53_12 = e3)
% 227.92/39.55    (100)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0
% 227.92/39.55             & op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~
% 227.92/39.55             (all_42_1 = e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 227.92/39.55    (101)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 227.92/39.55           (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 227.92/39.55    (102)  all_55_1 = all_52_3
% 227.92/39.55    (103)   ~ (all_52_5 = all_6_2)
% 227.92/39.55    (104)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 227.92/39.55           (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 227.92/39.55    (105)   ~ (all_52_5 = e1)
% 227.92/39.55    (106)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 227.92/39.55           | (all_57_11 = e0 & op(e1, e0) = e0)
% 227.92/39.55    (107)   ~ (all_52_5 = e0)
% 227.92/39.55    (108)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 227.92/39.55           | (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 227.92/39.55             e2)
% 227.92/39.55    (109)  op(e2, e1) = all_53_9
% 227.92/39.55    (110)  op(e1, e2) = all_53_6
% 227.92/39.55    (111)   ~ (all_6_2 = e0)
% 227.92/39.55    (112)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 227.92/39.55           (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 227.92/39.55    (113)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 227.92/39.55    (114)  all_24_2 = all_6_2
% 227.92/39.55    (115)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 227.92/39.55           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 227.92/39.55    (116)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 227.92/39.55           (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 227.92/39.55    (117)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 227.92/39.55           | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 227.92/39.55             e1)
% 227.92/39.55    (118)  all_57_14 = e0
% 227.92/39.55    (119)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 227.92/39.55           (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 227.92/39.55    (120)  op(e3, e0) = all_52_7
% 227.92/39.55    (121)  op(e3, e1) = all_53_8
% 227.92/39.55    (122)  all_55_7 = all_53_13
% 227.92/39.55    (123)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 227.92/39.55           (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 227.92/39.55    (124)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 227.92/39.55           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 227.92/39.55    (125)  op(e3, e0) = all_53_12
% 227.92/39.55  
% 227.92/39.55  Begin of proof
% 227.92/39.55  | 
% 227.92/39.55  | BETA: splitting (113) gives:
% 227.92/39.55  | 
% 227.92/39.55  | Case 1:
% 227.92/39.55  | | 
% 227.92/39.55  | |   (126)  all_55_12 = e3
% 227.92/39.55  | | 
% 227.92/39.55  | | REF_CLOSE: (19), (75), (126) are inconsistent by sub-proof #2001.
% 227.92/39.55  | | 
% 227.92/39.55  | Case 2:
% 227.92/39.55  | | 
% 227.92/39.55  | |   (127)   ~ (all_55_12 = e3)
% 227.92/39.55  | |   (128)  all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 227.92/39.55  | | 
% 227.92/39.55  | | BETA: splitting (25) gives:
% 227.92/39.55  | | 
% 227.92/39.55  | | Case 1:
% 227.92/39.55  | | | 
% 227.92/39.55  | | |   (129)  all_55_3 = e3
% 227.92/39.55  | | | 
% 227.92/39.55  | | | REF_CLOSE: (8), (33), (129) are inconsistent by sub-proof #1451.
% 227.92/39.55  | | | 
% 227.92/39.55  | | Case 2:
% 227.92/39.55  | | | 
% 227.92/39.55  | | |   (130)  all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 227.92/39.55  | | | 
% 227.92/39.55  | | | BETA: splitting (1) gives:
% 227.92/39.55  | | | 
% 227.92/39.55  | | | Case 1:
% 227.92/39.55  | | | | 
% 227.92/39.55  | | | |   (131)  all_55_13 = e3
% 227.92/39.55  | | | | 
% 227.92/39.55  | | | | COMBINE_EQS: (94), (131) imply:
% 227.92/39.55  | | | |   (132)  all_53_7 = e3
% 227.92/39.55  | | | | 
% 227.92/39.55  | | | | REDUCE: (2), (132) imply:
% 227.92/39.55  | | | |   (133)  $false
% 227.92/39.55  | | | | 
% 227.92/39.55  | | | | CLOSE: (133) is inconsistent.
% 227.92/39.55  | | | | 
% 227.92/39.55  | | | Case 2:
% 227.92/39.55  | | | | 
% 227.92/39.55  | | | |   (134)   ~ (all_55_13 = e3)
% 227.92/39.55  | | | |   (135)  all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 227.92/39.55  | | | | 
% 227.92/39.55  | | | | BETA: splitting (47) gives:
% 227.92/39.55  | | | | 
% 227.92/39.55  | | | | Case 1:
% 227.92/39.55  | | | | | 
% 227.92/39.55  | | | | |   (136)  all_55_6 = e3
% 227.92/39.55  | | | | | 
% 227.92/39.55  | | | | | COMBINE_EQS: (70), (136) imply:
% 227.92/39.55  | | | | |   (137)  all_53_9 = e3
% 227.92/39.55  | | | | | 
% 227.92/39.55  | | | | | REDUCE: (95), (137) imply:
% 227.92/39.55  | | | | |   (138)   ~ (all_52_5 = e3)
% 227.92/39.55  | | | | | 
% 227.92/39.55  | | | | | SIMP: (138) implies:
% 227.92/39.55  | | | | |   (139)   ~ (all_52_5 = e3)
% 227.92/39.55  | | | | | 
% 227.92/39.55  | | | | | BETA: splitting (62) gives:
% 227.92/39.55  | | | | | 
% 227.92/39.55  | | | | | Case 1:
% 227.92/39.55  | | | | | | 
% 227.92/39.55  | | | | | |   (140)  all_55_2 = e3
% 227.92/39.55  | | | | | | 
% 227.92/39.55  | | | | | | REF_CLOSE: (87), (139), (140) are inconsistent by sub-proof #437.
% 227.92/39.55  | | | | | | 
% 227.92/39.55  | | | | | Case 2:
% 227.92/39.55  | | | | | | 
% 227.92/39.55  | | | | | |   (141)  all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 227.92/39.55  | | | | | | 
% 227.92/39.55  | | | | | | REF_CLOSE: (15), (16), (40), (78), (87), (105), (107), (141) are
% 227.92/39.55  | | | | | |            inconsistent by sub-proof #436.
% 227.92/39.55  | | | | | | 
% 227.92/39.55  | | | | | End of split
% 227.92/39.55  | | | | | 
% 227.92/39.55  | | | | Case 2:
% 227.92/39.55  | | | | | 
% 227.92/39.55  | | | | |   (142)   ~ (all_55_6 = e3)
% 227.92/39.55  | | | | |   (143)  all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 227.92/39.55  | | | | | 
% 227.92/39.55  | | | | | REDUCE: (70), (142) imply:
% 227.92/39.55  | | | | |   (144)   ~ (all_53_9 = e3)
% 227.92/39.55  | | | | | 
% 227.92/39.55  | | | | | BETA: splitting (143) gives:
% 227.92/39.55  | | | | | 
% 227.92/39.55  | | | | | Case 1:
% 227.92/39.55  | | | | | | 
% 227.92/39.55  | | | | | |   (145)  all_55_6 = e2
% 227.92/39.55  | | | | | | 
% 227.92/39.55  | | | | | | COMBINE_EQS: (70), (145) imply:
% 227.92/39.55  | | | | | |   (146)  all_53_9 = e2
% 227.92/39.55  | | | | | | 
% 227.92/39.55  | | | | | | REDUCE: (27), (146) imply:
% 227.92/39.55  | | | | | |   (147)   ~ (all_53_1 = e2)
% 227.92/39.55  | | | | | | 
% 227.92/39.55  | | | | | | REDUCE: (64), (146) imply:
% 227.92/39.55  | | | | | |   (148)   ~ (all_53_13 = e2)
% 227.92/39.55  | | | | | | 
% 227.92/39.55  | | | | | | SIMP: (148) implies:
% 227.92/39.55  | | | | | |   (149)   ~ (all_53_13 = e2)
% 227.92/39.55  | | | | | | 
% 227.92/39.55  | | | | | | REDUCE: (95), (146) imply:
% 227.92/39.55  | | | | | |   (150)   ~ (all_52_5 = e2)
% 227.92/39.55  | | | | | | 
% 227.92/39.55  | | | | | | SIMP: (150) implies:
% 227.92/39.55  | | | | | |   (151)   ~ (all_52_5 = e2)
% 227.92/39.55  | | | | | | 
% 227.92/39.55  | | | | | | REDUCE: (144), (146) imply:
% 227.92/39.55  | | | | | |   (152)   ~ (e3 = e2)
% 227.92/39.55  | | | | | | 
% 227.92/39.55  | | | | | | SIMP: (152) implies:
% 227.92/39.55  | | | | | |   (153)   ~ (e3 = e2)
% 227.92/39.55  | | | | | | 
% 227.92/39.55  | | | | | | REDUCE: (23), (146) imply:
% 227.92/39.55  | | | | | |   (154)   ~ (e2 = e1)
% 227.92/39.55  | | | | | | 
% 227.92/39.55  | | | | | | REDUCE: (29), (146) imply:
% 227.92/39.55  | | | | | |   (155)   ~ (e2 = e0)
% 227.92/39.55  | | | | | | 
% 227.92/39.55  | | | | | | BETA: splitting (82) gives:
% 227.92/39.55  | | | | | | 
% 227.92/39.55  | | | | | | Case 1:
% 227.92/39.55  | | | | | | | 
% 227.92/39.55  | | | | | | |   (156)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 &
% 227.92/39.55  | | | | | | |            op(e2, e1) = e3)
% 227.92/39.55  | | | | | | | 
% 227.92/39.55  | | | | | | | BETA: splitting (156) gives:
% 227.92/39.55  | | | | | | | 
% 227.92/39.55  | | | | | | | Case 1:
% 227.92/39.55  | | | | | | | | 
% 227.92/39.55  | | | | | | | |   (157)  all_57_4 = e3 & op(e3, e1) = e3
% 227.92/39.55  | | | | | | | | 
% 227.92/39.55  | | | | | | | | ALPHA: (157) implies:
% 227.92/39.55  | | | | | | | |   (158)  all_57_4 = e3
% 227.92/39.55  | | | | | | | | 
% 227.92/39.55  | | | | | | | | BETA: splitting (62) gives:
% 227.92/39.55  | | | | | | | | 
% 227.92/39.55  | | | | | | | | Case 1:
% 227.92/39.55  | | | | | | | | | 
% 227.92/39.55  | | | | | | | | |   (159)  all_55_2 = e3
% 227.92/39.55  | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | COMBINE_EQS: (87), (159) imply:
% 227.92/39.55  | | | | | | | | |   (160)  all_52_5 = e3
% 227.92/39.55  | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | SIMP: (160) implies:
% 227.92/39.55  | | | | | | | | |   (161)  all_52_5 = e3
% 227.92/39.55  | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | REDUCE: (9), (161) imply:
% 227.92/39.55  | | | | | | | | |   (162)   ~ (all_52_3 = e3)
% 227.92/39.55  | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | REDUCE: (31), (161) imply:
% 227.92/39.55  | | | | | | | | |   (163)   ~ (all_52_7 = e3)
% 227.92/39.55  | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | REDUCE: (16), (161) imply:
% 227.92/39.55  | | | | | | | | |   (164)  op(e3, e3) = e1
% 227.92/39.55  | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | BETA: splitting (50) gives:
% 227.92/39.55  | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | Case 1:
% 227.92/39.55  | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | |   (165)  all_55_7 = e3
% 227.92/39.55  | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | REF_CLOSE: (35), (122), (165) are inconsistent by sub-proof
% 227.92/39.55  | | | | | | | | | |            #2109.
% 227.92/39.55  | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | Case 2:
% 227.92/39.55  | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | |   (166)   ~ (all_55_7 = e3)
% 227.92/39.55  | | | | | | | | | |   (167)  all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 227.92/39.55  | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | BETA: splitting (167) gives:
% 227.92/39.55  | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | Case 1:
% 227.92/39.55  | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | |   (168)  all_55_7 = e2
% 227.92/39.55  | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | REF_CLOSE: (122), (149), (168) are inconsistent by sub-proof
% 227.92/39.55  | | | | | | | | | | |            #2171.
% 227.92/39.55  | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | Case 2:
% 227.92/39.55  | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | |   (169)   ~ (all_55_7 = e2)
% 227.92/39.55  | | | | | | | | | | |   (170)  all_55_7 = e1 | all_55_7 = e0
% 227.92/39.55  | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | BETA: splitting (170) gives:
% 227.92/39.55  | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | Case 1:
% 227.92/39.55  | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | |   (171)  all_55_7 = e1
% 227.92/39.55  | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | COMBINE_EQS: (122), (171) imply:
% 227.92/39.55  | | | | | | | | | | | |   (172)  all_53_13 = e1
% 227.92/39.55  | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | SIMP: (172) implies:
% 227.92/39.55  | | | | | | | | | | | |   (173)  all_53_13 = e1
% 227.92/39.55  | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | REDUCE: (93), (173) imply:
% 227.92/39.55  | | | | | | | | | | | |   (174)   ~ (all_53_1 = e1)
% 227.92/39.55  | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | REDUCE: (35), (173) imply:
% 227.92/39.55  | | | | | | | | | | | |   (175)   ~ (e3 = e1)
% 227.92/39.55  | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | REDUCE: (149), (173) imply:
% 227.92/39.55  | | | | | | | | | | | |   (176)   ~ (e2 = e1)
% 227.92/39.55  | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | BETA: splitting (10) gives:
% 227.92/39.55  | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | Case 1:
% 227.92/39.55  | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | |   (177)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 227.92/39.55  | | | | | | | | | | | | |            & op(e2, e3) = e1)
% 227.92/39.55  | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | BETA: splitting (177) gives:
% 227.92/39.55  | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | Case 1:
% 227.92/39.55  | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | |   (178)  all_57_0 = e1 & op(e3, e3) = e1
% 227.92/39.55  | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | REF_CLOSE: (58), (78), (178) are inconsistent by sub-proof
% 227.92/39.55  | | | | | | | | | | | | | |            #2454.
% 227.92/39.55  | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | Case 2:
% 227.92/39.55  | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | |   (179)  all_57_2 = e1 & op(e2, e3) = e1
% 227.92/39.55  | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | ALPHA: (179) implies:
% 227.92/39.55  | | | | | | | | | | | | | |   (180)  all_57_2 = e1
% 227.92/39.55  | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | BETA: splitting (108) gives:
% 227.92/39.55  | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | Case 1:
% 227.92/39.55  | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | |   (181)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 227.92/39.55  | | | | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 227.92/39.55  | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | BETA: splitting (181) gives:
% 227.92/39.55  | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | Case 1:
% 227.92/39.55  | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | |   (182)  all_57_9 = e2 & op(e3, e0) = e2
% 227.92/39.55  | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | ALPHA: (182) implies:
% 227.92/39.55  | | | | | | | | | | | | | | | |   (183)  all_57_9 = e2
% 227.92/39.55  | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | BETA: splitting (83) gives:
% 227.92/39.55  | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.55  | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | |   (184)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 227.92/39.55  | | | | | | | | | | | | | | | | |            & op(e2, e2) = e3)
% 227.92/39.55  | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (30), (39), (44), (45), (52), (78), (153),
% 227.92/39.55  | | | | | | | | | | | | | | | | |            (154), (155), (158), (183), (184) are inconsistent
% 227.92/39.55  | | | | | | | | | | | | | | | | |            by sub-proof #435.
% 227.92/39.55  | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.55  | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | |   (185)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 227.92/39.55  | | | | | | | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 227.92/39.55  | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 227.92/39.55  | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | |   (186)  all_57_7 = e3 & op(e1, e2) = e3
% 227.92/39.55  | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | ALPHA: (186) implies:
% 227.92/39.55  | | | | | | | | | | | | | | | | | |   (187)  all_57_7 = e3
% 227.92/39.55  | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (12), (13), (15), (30), (41), (45), (56),
% 227.92/39.55  | | | | | | | | | | | | | | | | | |            (57), (58), (60), (66), (72), (77), (78), (84),
% 227.92/39.55  | | | | | | | | | | | | | | | | | |            (123), (147), (154), (158), (164), (174), (183),
% 227.92/39.55  | | | | | | | | | | | | | | | | | |            (187) are inconsistent by sub-proof #433.
% 227.92/39.55  | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | |   (188)  all_57_13 = e3 & op(e0, e2) = e3
% 227.92/39.55  | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | ALPHA: (188) implies:
% 227.92/39.55  | | | | | | | | | | | | | | | | | |   (189)  all_57_13 = e3
% 227.92/39.55  | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (12), (13), (15), (30), (39), (41), (44),
% 227.92/39.55  | | | | | | | | | | | | | | | | | |            (45), (52), (56), (57), (58), (60), (61), (63),
% 227.92/39.55  | | | | | | | | | | | | | | | | | |            (66), (67), (72), (77), (78), (83), (84), (85),
% 227.92/39.55  | | | | | | | | | | | | | | | | | |            (88), (118), (123), (147), (153), (154), (155),
% 227.92/39.55  | | | | | | | | | | | | | | | | | |            (158), (164), (174), (183), (189) are inconsistent
% 227.92/39.55  | | | | | | | | | | | | | | | | | |            by sub-proof #431.
% 227.92/39.55  | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | End of split
% 227.92/39.55  | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | End of split
% 227.92/39.55  | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | Case 2:
% 227.92/39.55  | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | |   (190)  all_57_10 = e2 & op(e2, e0) = e2
% 227.92/39.55  | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | ALPHA: (190) implies:
% 227.92/39.55  | | | | | | | | | | | | | | | |   (191)  all_57_10 = e2
% 227.92/39.55  | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | BETA: splitting (104) gives:
% 227.92/39.55  | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.55  | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | |   (192)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 227.92/39.55  | | | | | | | | | | | | | | | | |            & op(e2, e3) = e3)
% 227.92/39.55  | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 227.92/39.55  | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | |   (193)  all_57_0 = e3 & op(e3, e3) = e3
% 227.92/39.55  | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | ALPHA: (193) implies:
% 227.92/39.55  | | | | | | | | | | | | | | | | | |   (194)  op(e3, e3) = e3
% 227.92/39.55  | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (15), (164), (194) are inconsistent by
% 227.92/39.55  | | | | | | | | | | | | | | | | | |            sub-proof #2495.
% 227.92/39.55  | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | |   (195)  all_57_2 = e3 & op(e2, e3) = e3
% 227.92/39.55  | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | ALPHA: (195) implies:
% 227.92/39.55  | | | | | | | | | | | | | | | | | |   (196)  all_57_2 = e3
% 227.92/39.55  | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (13), (15), (21), (24), (45), (52), (63),
% 227.92/39.55  | | | | | | | | | | | | | | | | | |            (67), (78), (82), (88), (90), (153), (154), (155),
% 227.92/39.55  | | | | | | | | | | | | | | | | | |            (158), (180), (191), (196) are inconsistent by
% 227.92/39.55  | | | | | | | | | | | | | | | | | |            sub-proof #451.
% 227.92/39.55  | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | End of split
% 227.92/39.55  | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.55  | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | |   (197)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 227.92/39.55  | | | | | | | | | | | | | | | | |            e3 & op(e0, e3) = e3)
% 227.92/39.55  | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 227.92/39.55  | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | |   (198)  all_57_6 = e3 & op(e1, e3) = e3
% 227.92/39.55  | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | ALPHA: (198) implies:
% 227.92/39.55  | | | | | | | | | | | | | | | | | |   (199)  all_57_6 = e3
% 227.92/39.55  | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | BETA: splitting (83) gives:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | |   (200)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 227.92/39.55  | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e3)
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | |   (201)  all_57_1 = e3 & op(e3, e2) = e3
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | ALPHA: (201) implies:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | |   (202)  all_57_1 = e3
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | BETA: splitting (30) gives:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | |   (203)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e1)
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | |   (204)  all_57_0 = e1 & op(e3, e3) = e1
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (204) implies:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | |   (205)  all_57_0 = e1
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (44), (52), (78), (153), (154), (155),
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | |            (158), (202), (205) are inconsistent by sub-proof
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | |            #1808.
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | |   (206)  all_57_1 = e1 & op(e3, e2) = e1
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (206) implies:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | |   (207)  all_57_1 = e1
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (202), (207) imply:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | |   (208)  e3 = e1
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (199), (208) imply:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | |   (209)  all_57_6 = e1
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (10), (11), (12), (13), (14), (15),
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | |            (17), (18), (21), (24), (25), (29), (30), (34),
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | |            (36), (38), (39), (42), (43), (44), (45), (46),
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | |            (48), (52), (53), (55), (58), (59), (61), (62),
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | |            (63), (67), (68), (69), (71), (73), (76), (78),
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | |            (80), (81), (82), (83), (85), (86), (88), (90),
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | |            (91), (96), (97), (98), (99), (100), (101), (104),
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | |            (106), (108), (109), (110), (112), (114), (115),
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | |            (116), (117), (118), (119), (121), (123), (124),
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | |            (125), (153), (154), (155), (158), (164), (191),
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | |            (209) are inconsistent by sub-proof #423.
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | |   (210)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e1)
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | |   (211)  all_57_4 = e1 & op(e3, e1) = e1
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (10), (11), (12), (13), (14), (15),
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | |            (17), (18), (21), (24), (25), (29), (30), (34),
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | |            (36), (38), (39), (42), (43), (44), (45), (46),
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | |            (48), (52), (53), (55), (58), (59), (61), (62),
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | |            (63), (67), (68), (69), (71), (73), (76), (78),
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | |            (80), (81), (82), (83), (85), (86), (88), (90),
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | |            (91), (96), (97), (98), (99), (100), (101), (104),
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | |            (106), (108), (109), (110), (112), (114), (115),
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | |            (116), (117), (118), (119), (121), (123), (124),
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | |            (125), (153), (154), (155), (158), (164), (191),
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | |            (199), (211) are inconsistent by sub-proof #422.
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | |   (212)  all_57_9 = e1 & op(e3, e0) = e1
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (212) implies:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | |   (213)  all_57_9 = e1
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (112) gives:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | |   (214)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e2)
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (154), (164), (180), (214) are inconsistent
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #421.
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | |   (215)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e3) = e2)
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | |   (216)  all_57_6 = e2 & op(e1, e3) = e2
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (153), (199), (216) are inconsistent by sub-proof
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | |            #2012.
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | |   (217)  all_57_12 = e2 & op(e0, e3) = e2
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (217) implies:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | |   (218)  all_57_12 = e2
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (39) gives:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | |   (219)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e2)
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | |   (220)  all_57_0 = e2 & op(e3, e3) = e2
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (220) implies:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | |   (221)  all_57_0 = e2
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | |   (222)  op(e3, e3) = e2
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10), (12), (13), (15), (17), (21), (24),
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | |            (45), (52), (63), (78), (90), (96), (101), (108),
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | |            (112), (116), (117), (123), (153), (154), (155),
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | |            (180), (191), (202), (213), (218), (221), (222)
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #447.
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | |   (223)  all_57_1 = e2 & op(e3, e2) = e2
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (153), (202), (223) are inconsistent by sub-proof
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | |            #1809.
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | |   (224)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e2)
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (30), (39), (44), (52), (78), (153), (154),
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | |            (155), (158), (202), (224) are inconsistent by
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1221.
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | |   (225)  all_57_3 = e3 & op(e2, e2) = e3
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | ALPHA: (225) implies:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | |   (226)  all_57_3 = e3
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (52), (226) are inconsistent by sub-proof
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | |            #2358.
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | |   (227)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 227.92/39.55  | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | |   (228)  all_57_7 = e3 & op(e1, e2) = e3
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | ALPHA: (228) implies:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | |   (229)  all_57_7 = e3
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | BETA: splitting (30) gives:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | |   (230)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e1)
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | |   (231)  all_57_0 = e1 & op(e3, e3) = e1
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (231) implies:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | |   (232)  all_57_0 = e1
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (58), (232) imply:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | |   (233)  e1 = e0
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (13), (45), (52), (78), (96), (101), (153),
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | |            (154), (155), (180), (233) are inconsistent by
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1252.
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | |   (234)  all_57_1 = e1 & op(e3, e2) = e1
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (12), (15), (41), (45), (56), (57), (60),
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | |            (66), (72), (77), (78), (84), (123), (147), (164),
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | |            (174), (229), (234) are inconsistent by sub-proof
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | |            #434.
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | |   (235)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e1)
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | |   (236)  all_57_4 = e1 & op(e3, e1) = e1
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (10), (11), (12), (13), (14), (15),
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | |            (17), (18), (21), (24), (25), (29), (30), (34),
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | |            (36), (38), (39), (42), (43), (44), (45), (46),
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | |            (48), (52), (53), (55), (58), (59), (61), (62),
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | |            (63), (67), (68), (69), (71), (73), (76), (78),
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | |            (80), (81), (82), (83), (85), (86), (88), (90),
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | |            (91), (96), (97), (98), (99), (100), (101), (104),
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | |            (106), (108), (109), (110), (112), (114), (115),
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | |            (116), (117), (118), (119), (121), (123), (124),
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | |            (125), (153), (154), (155), (158), (164), (191),
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | |            (199), (236) are inconsistent by sub-proof #422.
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | |   (237)  all_57_9 = e1 & op(e3, e0) = e1
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (237) implies:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | |   (238)  all_57_9 = e1
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (112) gives:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | |   (239)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e2)
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (154), (164), (180), (239) are inconsistent
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #421.
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | |   (240)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e3) = e2)
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (240) gives:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | |   (241)  all_57_6 = e2 & op(e1, e3) = e2
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (241) implies:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | |   (242)  all_57_6 = e2
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (199), (242) imply:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | |   (243)  e3 = e2
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (158), (243) imply:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | |   (244)  all_57_4 = e2
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (10), (11), (12), (13), (14), (15),
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | |            (17), (18), (21), (24), (25), (29), (30), (34),
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | |            (36), (38), (39), (43), (44), (45), (46), (48),
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | |            (52), (53), (55), (59), (62), (63), (67), (69),
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | |            (71), (73), (76), (78), (80), (81), (82), (85),
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | |            (86), (88), (90), (91), (97), (98), (99), (100),
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | |            (101), (108), (109), (110), (112), (114), (115),
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | |            (116), (117), (119), (121), (123), (124), (125),
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | |            (153), (154), (155), (229), (244) are inconsistent
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #546.
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | |   (245)  all_57_12 = e2 & op(e0, e3) = e2
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (245) implies:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | |   (246)  all_57_12 = e2
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (96) gives:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | |   (247)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e3)
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (247) gives:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | |   (248)  all_57_2 = e3 & op(e2, e3) = e3
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (248) implies:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | |   (249)  all_57_2 = e3
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (10), (11), (12), (13), (14), (15),
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | |            (17), (18), (21), (24), (25), (29), (30), (34),
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | |            (36), (38), (39), (42), (43), (44), (45), (46),
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | |            (48), (52), (53), (55), (58), (59), (62), (63),
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | |            (67), (68), (69), (71), (73), (76), (78), (80),
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | |            (81), (82), (83), (85), (86), (88), (90), (91),
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | |            (96), (97), (98), (99), (100), (101), (104),
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | |            (108), (109), (110), (112), (114), (115), (116),
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | |            (117), (119), (121), (123), (124), (125), (153),
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | |            (154), (155), (158), (191), (229), (249) are
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #425.
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | |   (250)  all_57_3 = e3 & op(e2, e2) = e3
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (250) implies:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | |   (251)  all_57_3 = e3
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (45), (251) imply:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | |   (252)  e3 = e0
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (252) implies:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | |   (253)  e3 = e0
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (199), (253) imply:
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | |   (254)  all_57_6 = e0
% 227.92/39.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (10), (11), (12), (13), (14), (15),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | |            (17), (18), (21), (24), (25), (29), (30), (34),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | |            (36), (38), (39), (43), (44), (45), (46), (48),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | |            (52), (53), (55), (59), (62), (63), (67), (69),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | |            (71), (73), (76), (78), (80), (81), (82), (83),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | |            (85), (86), (88), (90), (91), (96), (97), (98),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | |            (99), (100), (101), (104), (108), (109), (110),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | |            (112), (114), (115), (116), (117), (119), (121),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | |            (123), (124), (125), (153), (154), (155), (180),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | |            (246), (254) are inconsistent by sub-proof #443.
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | |   (255)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e2, e0) = e3)
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (255) gives:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | |   (256)  all_57_5 = e3 & op(e2, e1) = e3
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (256) implies:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | |   (257)  all_57_5 = e3
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | |   (258)  op(e2, e1) = e3
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (124) gives:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (259)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e2)
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (259) gives:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (260)  all_57_6 = e2 & op(e1, e3) = e2
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (10), (11), (12), (13), (14), (15),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17), (18), (21), (24), (25), (29), (30), (34),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (36), (38), (39), (43), (44), (45), (46), (48),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (52), (53), (55), (59), (62), (63), (67), (69),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (71), (73), (76), (78), (80), (81), (85), (86),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (88), (90), (91), (97), (98), (99), (100), (101),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (108), (109), (110), (112), (114), (115), (116),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (117), (119), (121), (123), (124), (125), (153),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (154), (155), (158), (199), (229), (257), (258),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (260) are inconsistent by sub-proof #420.
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (261)  all_57_7 = e2 & op(e1, e2) = e2
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (261) implies:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (262)  all_57_7 = e2
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (229), (262) imply:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (263)  e3 = e2
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (158), (263) imply:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (264)  all_57_4 = e2
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (10), (11), (12), (13), (14), (15),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (17), (18), (21), (24), (25), (29), (30), (34),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (36), (38), (39), (43), (44), (45), (46), (48),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (52), (53), (55), (59), (62), (63), (67), (69),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (71), (73), (76), (78), (80), (81), (85), (86),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (88), (90), (91), (97), (98), (99), (100), (101),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (108), (109), (110), (112), (114), (115), (116),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (117), (119), (121), (123), (124), (125), (153),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (154), (155), (229), (257), (258), (264) are
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #547.
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (265)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e1, e0) = e2)
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (265) gives:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (266)  all_57_8 = e2 & op(e1, e1) = e2
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (266) implies:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (267)  all_57_8 = e2
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (154), (267) are inconsistent by sub-proof
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1485.
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (268)  all_57_11 = e2 & op(e1, e0) = e2
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (268) implies:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (269)  all_57_11 = e2
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (68), (269) imply:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (270)  e2 = e0
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (13), (45), (78), (101), (153), (154), (155),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (191), (257), (270) are inconsistent by sub-proof
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1517.
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | |   (271)  all_57_10 = e3 & op(e2, e0) = e3
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (271) implies:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | |   (272)  all_57_10 = e3
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (52), (63), (78), (106), (108), (153), (154),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | |            (155), (238), (272) are inconsistent by sub-proof
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | |            #1986.
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | |   (273)  all_57_13 = e3 & op(e0, e2) = e3
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | ALPHA: (273) implies:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | |   (274)  all_57_13 = e3
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | |   (275)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (275) gives:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | |   (276)  all_57_12 = e1 & op(e0, e3) = e1
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (276) implies:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | |   (277)  all_57_12 = e1
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (52), (61), (63), (67), (78), (88), (153),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | |            (154), (155), (274), (277) are inconsistent by
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2057.
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | |   (278)  all_57_13 = e1 & op(e0, e2) = e1
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (278) implies:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | |   (279)  all_57_13 = e1
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (274), (279) imply:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | |   (280)  e3 = e1
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (199), (280) imply:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | |   (281)  all_57_6 = e1
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (10), (11), (12), (13), (14), (15),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | |            (17), (18), (21), (24), (25), (29), (30), (34),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | |            (36), (38), (39), (42), (43), (44), (45), (46),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | |            (48), (52), (53), (55), (58), (59), (61), (62),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | |            (63), (67), (68), (69), (71), (73), (76), (78),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | |            (80), (81), (82), (83), (85), (86), (88), (90),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | |            (91), (96), (97), (98), (99), (100), (101), (104),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | |            (106), (108), (109), (110), (112), (114), (115),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | |            (116), (117), (118), (119), (121), (123), (124),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | |            (125), (153), (154), (155), (158), (164), (191),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | |            (281) are inconsistent by sub-proof #423.
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | |   (282)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (282) gives:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | |   (283)  all_57_14 = e1 & op(e0, e1) = e1
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (283) implies:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | |   (284)  all_57_14 = e1
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (118), (284) imply:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | |   (285)  e1 = e0
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (13), (45), (52), (78), (96), (101), (153),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | |            (154), (155), (180), (285) are inconsistent by
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1252.
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | |   (286)  all_57_15 = e1 & op(e0, e0) = e1
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (286) implies:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | |   (287)  op(e0, e0) = e1
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (15), (85), (287) are inconsistent by
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2183.
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.56  | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | |   (288)  all_57_12 = e3 & op(e0, e3) = e3
% 227.92/39.56  | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | ALPHA: (288) implies:
% 227.92/39.56  | | | | | | | | | | | | | | | | | |   (289)  all_57_12 = e3
% 227.92/39.56  | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (63), (67), (78), (88), (118), (153), (154),
% 227.92/39.56  | | | | | | | | | | | | | | | | | |            (155), (289) are inconsistent by sub-proof #1763.
% 227.92/39.56  | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | End of split
% 227.92/39.56  | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | End of split
% 227.92/39.56  | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | End of split
% 227.92/39.56  | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | Case 2:
% 227.92/39.56  | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | |   (290)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 227.92/39.56  | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 227.92/39.56  | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | BETA: splitting (290) gives:
% 227.92/39.56  | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | Case 1:
% 227.92/39.56  | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | |   (291)  all_57_11 = e2 & op(e1, e0) = e2
% 227.92/39.56  | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | REF_CLOSE: (68), (155), (291) are inconsistent by sub-proof
% 227.92/39.56  | | | | | | | | | | | | | | | |            #1988.
% 227.92/39.56  | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | Case 2:
% 227.92/39.56  | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | |   (292)  all_57_15 = e2 & op(e0, e0) = e2
% 227.92/39.56  | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | REF_CLOSE: (63), (153), (292) are inconsistent by sub-proof
% 227.92/39.56  | | | | | | | | | | | | | | | |            #2323.
% 227.92/39.56  | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | End of split
% 227.92/39.56  | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | End of split
% 227.92/39.56  | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | End of split
% 227.92/39.56  | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | Case 2:
% 227.92/39.56  | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | |   (293)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 227.92/39.56  | | | | | | | | | | | | |            e1 & op(e0, e3) = e1)
% 227.92/39.56  | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | BETA: splitting (293) gives:
% 227.92/39.56  | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | Case 1:
% 227.92/39.56  | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | |   (294)  all_57_6 = e1 & op(e1, e3) = e1
% 227.92/39.56  | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | ALPHA: (294) implies:
% 227.92/39.56  | | | | | | | | | | | | | |   (295)  all_57_6 = e1
% 227.92/39.56  | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | BETA: splitting (108) gives:
% 227.92/39.56  | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | Case 1:
% 227.92/39.56  | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | |   (296)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 227.92/39.56  | | | | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 227.92/39.56  | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | BETA: splitting (296) gives:
% 227.92/39.56  | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | Case 1:
% 227.92/39.56  | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | |   (297)  all_57_9 = e2 & op(e3, e0) = e2
% 227.92/39.56  | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | ALPHA: (297) implies:
% 227.92/39.56  | | | | | | | | | | | | | | | |   (298)  all_57_9 = e2
% 227.92/39.56  | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | BETA: splitting (104) gives:
% 227.92/39.56  | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.56  | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | |   (299)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 227.92/39.56  | | | | | | | | | | | | | | | | |            & op(e2, e3) = e3)
% 227.92/39.56  | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | BETA: splitting (299) gives:
% 227.92/39.56  | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | |   (300)  all_57_0 = e3 & op(e3, e3) = e3
% 227.92/39.56  | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | ALPHA: (300) implies:
% 227.92/39.56  | | | | | | | | | | | | | | | | | |   (301)  op(e3, e3) = e3
% 227.92/39.56  | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (15), (164), (301) are inconsistent by
% 227.92/39.56  | | | | | | | | | | | | | | | | | |            sub-proof #2495.
% 227.92/39.56  | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | |   (302)  all_57_2 = e3 & op(e2, e3) = e3
% 227.92/39.56  | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | ALPHA: (302) implies:
% 227.92/39.56  | | | | | | | | | | | | | | | | | |   (303)  all_57_2 = e3
% 227.92/39.56  | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | BETA: splitting (83) gives:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | |   (304)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 227.92/39.56  | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e3)
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | BETA: splitting (304) gives:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | |   (305)  all_57_1 = e3 & op(e3, e2) = e3
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | ALPHA: (305) implies:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | |   (306)  all_57_1 = e3
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (30), (39), (44), (52), (78), (153), (154),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | |            (155), (158), (298), (306) are inconsistent by
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | |            sub-proof #1222.
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | |   (307)  all_57_3 = e3 & op(e2, e2) = e3
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | ALPHA: (307) implies:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | |   (308)  all_57_3 = e3
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (45), (308) imply:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | |   (309)  e3 = e0
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (13), (45), (52), (78), (96), (101), (153),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | |            (154), (155), (303), (309) are inconsistent by
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | |            sub-proof #1333.
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | |   (310)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 227.92/39.56  | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | BETA: splitting (310) gives:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | |   (311)  all_57_7 = e3 & op(e1, e2) = e3
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | ALPHA: (311) implies:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | |   (312)  all_57_7 = e3
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (12), (13), (15), (30), (41), (45), (56),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | |            (57), (58), (60), (66), (72), (77), (78), (84),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | |            (123), (147), (154), (158), (164), (174), (298),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | |            (312) are inconsistent by sub-proof #433.
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | |   (313)  all_57_13 = e3 & op(e0, e2) = e3
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | ALPHA: (313) implies:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | |   (314)  all_57_13 = e3
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (12), (13), (15), (30), (39), (41), (44),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | |            (45), (52), (56), (57), (58), (60), (61), (63),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | |            (66), (67), (72), (77), (78), (83), (84), (85),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | |            (88), (118), (123), (147), (153), (154), (155),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | |            (158), (164), (174), (298), (314) are inconsistent
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | |            by sub-proof #431.
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.56  | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | End of split
% 227.92/39.56  | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.56  | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | |   (315)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 227.92/39.56  | | | | | | | | | | | | | | | | |            e3 & op(e0, e3) = e3)
% 227.92/39.56  | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (63), (67), (78), (88), (118), (153), (154),
% 227.92/39.56  | | | | | | | | | | | | | | | | |            (155), (295), (315) are inconsistent by sub-proof
% 227.92/39.56  | | | | | | | | | | | | | | | | |            #440.
% 227.92/39.56  | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | End of split
% 227.92/39.56  | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | Case 2:
% 227.92/39.56  | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | |   (316)  all_57_10 = e2 & op(e2, e0) = e2
% 227.92/39.56  | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | ALPHA: (316) implies:
% 227.92/39.56  | | | | | | | | | | | | | | | |   (317)  all_57_10 = e2
% 227.92/39.56  | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (10), (11), (12), (13), (14), (15),
% 227.92/39.56  | | | | | | | | | | | | | | | |            (17), (18), (21), (24), (25), (29), (30), (34),
% 227.92/39.56  | | | | | | | | | | | | | | | |            (36), (38), (39), (42), (43), (44), (45), (46),
% 227.92/39.56  | | | | | | | | | | | | | | | |            (48), (52), (53), (55), (58), (59), (61), (62),
% 227.92/39.56  | | | | | | | | | | | | | | | |            (63), (67), (68), (69), (71), (73), (76), (78),
% 227.92/39.56  | | | | | | | | | | | | | | | |            (80), (81), (82), (83), (85), (86), (88), (90),
% 227.92/39.56  | | | | | | | | | | | | | | | |            (91), (96), (97), (98), (99), (100), (101), (104),
% 227.92/39.56  | | | | | | | | | | | | | | | |            (106), (108), (109), (110), (112), (114), (115),
% 227.92/39.56  | | | | | | | | | | | | | | | |            (116), (117), (118), (119), (121), (123), (124),
% 227.92/39.56  | | | | | | | | | | | | | | | |            (125), (153), (154), (155), (158), (164), (295),
% 227.92/39.56  | | | | | | | | | | | | | | | |            (317) are inconsistent by sub-proof #423.
% 227.92/39.56  | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | End of split
% 227.92/39.56  | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | Case 2:
% 227.92/39.56  | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | |   (318)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 227.92/39.56  | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 227.92/39.56  | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | BETA: splitting (318) gives:
% 227.92/39.56  | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | Case 1:
% 227.92/39.56  | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | |   (319)  all_57_11 = e2 & op(e1, e0) = e2
% 227.92/39.56  | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | REF_CLOSE: (68), (155), (319) are inconsistent by sub-proof
% 227.92/39.56  | | | | | | | | | | | | | | | |            #1988.
% 227.92/39.56  | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | Case 2:
% 227.92/39.56  | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | |   (320)  all_57_15 = e2 & op(e0, e0) = e2
% 227.92/39.56  | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | REF_CLOSE: (63), (153), (320) are inconsistent by sub-proof
% 227.92/39.56  | | | | | | | | | | | | | | | |            #2323.
% 227.92/39.56  | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | End of split
% 227.92/39.56  | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | End of split
% 227.92/39.56  | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | Case 2:
% 227.92/39.56  | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | |   (321)  all_57_12 = e1 & op(e0, e3) = e1
% 227.92/39.56  | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | ALPHA: (321) implies:
% 227.92/39.56  | | | | | | | | | | | | | |   (322)  all_57_12 = e1
% 227.92/39.56  | | | | | | | | | | | | | |   (323)  op(e0, e3) = e1
% 227.92/39.56  | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | BETA: splitting (108) gives:
% 227.92/39.56  | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | Case 1:
% 227.92/39.56  | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | |   (324)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 227.92/39.56  | | | | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 227.92/39.56  | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | BETA: splitting (324) gives:
% 227.92/39.56  | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | Case 1:
% 227.92/39.56  | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | |   (325)  all_57_9 = e2 & op(e3, e0) = e2
% 227.92/39.56  | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | ALPHA: (325) implies:
% 227.92/39.56  | | | | | | | | | | | | | | | |   (326)  all_57_9 = e2
% 227.92/39.56  | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | REF_CLOSE: (3), (12), (13), (15), (30), (39), (41), (44),
% 227.92/39.56  | | | | | | | | | | | | | | | |            (45), (52), (56), (57), (58), (60), (61), (63),
% 227.92/39.56  | | | | | | | | | | | | | | | |            (66), (67), (72), (77), (78), (83), (84), (88),
% 227.92/39.56  | | | | | | | | | | | | | | | |            (123), (147), (153), (154), (155), (158), (164),
% 227.92/39.56  | | | | | | | | | | | | | | | |            (174), (322), (326) are inconsistent by sub-proof
% 227.92/39.56  | | | | | | | | | | | | | | | |            #432.
% 227.92/39.56  | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | Case 2:
% 227.92/39.56  | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | |   (327)  all_57_10 = e2 & op(e2, e0) = e2
% 227.92/39.56  | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | ALPHA: (327) implies:
% 227.92/39.56  | | | | | | | | | | | | | | | |   (328)  all_57_10 = e2
% 227.92/39.56  | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | BETA: splitting (83) gives:
% 227.92/39.56  | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.56  | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | |   (329)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 227.92/39.56  | | | | | | | | | | | | | | | | |            & op(e2, e2) = e3)
% 227.92/39.56  | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | BETA: splitting (329) gives:
% 227.92/39.56  | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | |   (330)  all_57_1 = e3 & op(e3, e2) = e3
% 227.92/39.56  | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | ALPHA: (330) implies:
% 227.92/39.56  | | | | | | | | | | | | | | | | | |   (331)  all_57_1 = e3
% 227.92/39.56  | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | BETA: splitting (96) gives:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | |   (332)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 227.92/39.56  | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e3)
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | BETA: splitting (332) gives:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | |   (333)  all_57_2 = e3 & op(e2, e3) = e3
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | ALPHA: (333) implies:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | |   (334)  all_57_2 = e3
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10), (12), (13), (15), (17), (21), (24),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | |            (45), (52), (63), (78), (88), (96), (101), (106),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | |            (108), (112), (116), (117), (118), (123), (153),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | |            (154), (155), (322), (331), (334) are inconsistent
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | |            by sub-proof #417.
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | |   (335)  all_57_3 = e3 & op(e2, e2) = e3
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | ALPHA: (335) implies:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | |   (336)  all_57_3 = e3
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (52), (336) are inconsistent by sub-proof
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | |            #2358.
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | |   (337)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 227.92/39.56  | | | | | | | | | | | | | | | | | | |            e3 & op(e2, e0) = e3)
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | BETA: splitting (337) gives:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | |   (338)  all_57_5 = e3 & op(e2, e1) = e3
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | ALPHA: (338) implies:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | |   (339)  all_57_5 = e3
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | |   (340)  op(e2, e1) = e3
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (10), (11), (12), (13), (14), (15),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | |            (17), (18), (21), (24), (25), (29), (30), (32),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | |            (34), (36), (38), (39), (40), (42), (43), (44),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | |            (45), (46), (48), (52), (53), (55), (59), (62),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | |            (63), (67), (69), (71), (73), (74), (76), (78),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | |            (80), (81), (82), (83), (85), (86), (88), (90),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | |            (91), (96), (97), (98), (99), (100), (101), (104),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | |            (106), (108), (109), (110), (112), (114), (115),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | |            (116), (117), (118), (119), (121), (123), (124),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | |            (125), (153), (154), (155), (322), (323), (328),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | |            (331), (339), (340) are inconsistent by sub-proof
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | |            #410.
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | |   (341)  all_57_10 = e3 & op(e2, e0) = e3
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | ALPHA: (341) implies:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | |   (342)  all_57_10 = e3
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (30), (39), (44), (52), (63), (78), (90),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | |            (108), (153), (154), (155), (158), (331), (342)
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1436.
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.56  | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | |   (343)  all_57_3 = e3 & op(e2, e2) = e3
% 227.92/39.56  | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | ALPHA: (343) implies:
% 227.92/39.56  | | | | | | | | | | | | | | | | | |   (344)  all_57_3 = e3
% 227.92/39.56  | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (52), (344) are inconsistent by sub-proof
% 227.92/39.56  | | | | | | | | | | | | | | | | | |            #2358.
% 227.92/39.56  | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | End of split
% 227.92/39.56  | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.56  | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | |   (345)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 227.92/39.56  | | | | | | | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 227.92/39.56  | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | BETA: splitting (345) gives:
% 227.92/39.56  | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | |   (346)  all_57_7 = e3 & op(e1, e2) = e3
% 227.92/39.56  | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | ALPHA: (346) implies:
% 227.92/39.56  | | | | | | | | | | | | | | | | | |   (347)  all_57_7 = e3
% 227.92/39.56  | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | BETA: splitting (96) gives:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | |   (348)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 227.92/39.56  | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e3)
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | BETA: splitting (348) gives:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | |   (349)  all_57_2 = e3 & op(e2, e3) = e3
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | ALPHA: (349) implies:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | |   (350)  all_57_2 = e3
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | BETA: splitting (124) gives:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | |   (351)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e2)
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (351) gives:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | |   (352)  all_57_6 = e2 & op(e1, e3) = e2
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (352) implies:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | |   (353)  all_57_6 = e2
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (30) gives:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | |   (354)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e1)
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (10), (11), (12), (13), (14), (15),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | |            (17), (18), (21), (24), (25), (29), (30), (34),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | |            (36), (38), (39), (42), (43), (44), (45), (46),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | |            (48), (52), (53), (55), (58), (59), (62), (63),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | |            (67), (68), (69), (71), (73), (76), (78), (80),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | |            (81), (82), (83), (85), (86), (88), (90), (91),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | |            (96), (97), (98), (99), (100), (101), (104),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | |            (108), (109), (110), (112), (114), (115), (116),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | |            (117), (119), (121), (123), (124), (125), (153),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | |            (154), (155), (328), (347), (350), (354) are
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #426.
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | |   (355)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e1)
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (355) gives:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | |   (356)  all_57_4 = e1 & op(e3, e1) = e1
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (356) implies:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | |   (357)  all_57_4 = e1
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (13), (15), (21), (24), (45), (52), (63),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | |            (67), (78), (82), (88), (90), (153), (154), (155),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | |            (328), (350), (357) are inconsistent by sub-proof
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | |            #1755.
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | |   (358)  all_57_9 = e1 & op(e3, e0) = e1
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (358) implies:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | |   (359)  all_57_9 = e1
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (10), (11), (12), (13), (14), (15),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | |            (17), (18), (21), (24), (25), (29), (30), (34),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | |            (36), (38), (39), (42), (43), (44), (45), (46),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | |            (48), (52), (53), (55), (59), (62), (63), (67),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | |            (68), (69), (71), (73), (76), (78), (80), (81),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | |            (82), (83), (85), (86), (88), (90), (91), (96),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | |            (97), (98), (99), (100), (101), (104), (108),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | |            (109), (110), (112), (114), (115), (116), (117),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | |            (119), (121), (123), (124), (125), (153), (154),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | |            (155), (328), (347), (350), (353), (359) are
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #429.
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | |   (360)  all_57_7 = e2 & op(e1, e2) = e2
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (360) implies:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | |   (361)  all_57_7 = e2
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (347), (361) imply:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | |   (362)  e3 = e2
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (350), (362) imply:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | |   (363)  all_57_2 = e2
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (96) gives:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (348) gives:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (350), (363) imply:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | |   (364)  e3 = e2
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (158), (362) imply:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | |   (365)  all_57_4 = e2
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (10), (11), (12), (13), (14), (15),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | |            (17), (18), (21), (24), (25), (29), (30), (34),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | |            (36), (38), (39), (43), (44), (45), (46), (48),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | |            (52), (53), (55), (59), (62), (63), (67), (69),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | |            (71), (73), (76), (78), (80), (81), (82), (85),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | |            (86), (88), (90), (91), (97), (98), (99), (100),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | |            (101), (108), (109), (110), (112), (114), (115),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | |            (116), (117), (119), (121), (123), (124), (125),
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | |            (153), (154), (155), (347), (365) are inconsistent
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #546.
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | |   (366)  all_57_3 = e3 & op(e2, e2) = e3
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (366) implies:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | |   (367)  all_57_3 = e3
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (52), (367) are inconsistent by sub-proof
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | |            #2358.
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | |   (368)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e2, e0) = e3)
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (368) gives:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | |   (369)  all_57_5 = e3 & op(e2, e1) = e3
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (369) implies:
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | |   (370)  all_57_5 = e3
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | |   (371)  op(e2, e1) = e3
% 227.92/39.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (10), (11), (12), (13),
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | |            (14), (15), (17), (18), (21), (22), (24), (25),
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | |            (26), (28), (29), (30), (32), (34), (36), (38),
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | |            (39), (42), (43), (44), (45), (46), (48), (51),
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | |            (52), (53), (54), (55), (59), (62), (63), (67),
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | |            (69), (71), (73), (74), (76), (78), (79), (80),
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | |            (81), (85), (86), (88), (90), (91), (97), (98),
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | |            (99), (100), (101), (103), (104), (108), (109),
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | |            (110), (111), (112), (114), (115), (116), (117),
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | |            (118), (119), (120), (121), (123), (124), (125),
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | |            (153), (154), (155), (158), (162), (323), (328),
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | |            (347), (370), (371) are inconsistent by sub-proof
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | |            #408.
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | |   (372)  all_57_10 = e3 & op(e2, e0) = e3
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (10), (11), (12), (13), (14), (15),
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | |            (17), (18), (21), (24), (25), (29), (30), (34),
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | |            (36), (38), (39), (43), (44), (45), (46), (48),
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | |            (52), (53), (55), (59), (62), (63), (67), (69),
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | |            (71), (73), (76), (78), (80), (81), (82), (85),
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | |            (86), (88), (90), (91), (97), (98), (99), (100),
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | |            (101), (108), (109), (110), (112), (114), (115),
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | |            (116), (117), (119), (121), (123), (124), (125),
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | |            (153), (154), (155), (158), (328), (347), (372)
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #470.
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | |   (373)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | |            e2 & op(e1, e0) = e2)
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (32), (42), (74), (154), (323), (373) are
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #409.
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | |   (374)  all_57_3 = e3 & op(e2, e2) = e3
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | ALPHA: (374) implies:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | |   (375)  all_57_3 = e3
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (52), (375) are inconsistent by sub-proof
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | |            #2358.
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | |   (376)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 227.92/39.57  | | | | | | | | | | | | | | | | | | |            e3 & op(e2, e0) = e3)
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | BETA: splitting (376) gives:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | |   (377)  all_57_5 = e3 & op(e2, e1) = e3
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | ALPHA: (377) implies:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | |   (378)  all_57_5 = e3
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | |   (379)  op(e2, e1) = e3
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (10), (11), (12), (13),
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | |            (14), (15), (17), (18), (21), (22), (24), (25),
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | |            (26), (28), (29), (30), (32), (34), (36), (38),
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | |            (39), (42), (43), (44), (45), (46), (48), (51),
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | |            (52), (53), (54), (55), (59), (62), (63), (67),
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | |            (69), (71), (73), (74), (76), (78), (79), (80),
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | |            (81), (85), (86), (88), (90), (91), (97), (98),
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | |            (99), (100), (101), (103), (104), (108), (109),
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | |            (110), (111), (112), (114), (115), (116), (117),
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | |            (118), (119), (120), (121), (123), (124), (125),
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | |            (153), (154), (155), (158), (162), (323), (328),
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | |            (347), (378), (379) are inconsistent by sub-proof
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | |            #408.
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | |   (380)  all_57_10 = e3 & op(e2, e0) = e3
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | ALPHA: (380) implies:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | |   (381)  all_57_10 = e3
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (10), (11), (12), (13), (14), (15),
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | |            (17), (18), (21), (24), (25), (29), (30), (34),
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | |            (36), (38), (39), (43), (44), (45), (46), (48),
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | |            (52), (53), (55), (59), (62), (63), (67), (69),
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | |            (71), (73), (76), (78), (80), (81), (82), (85),
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | |            (86), (88), (90), (91), (97), (98), (99), (100),
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | |            (101), (108), (109), (110), (112), (114), (115),
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | |            (116), (117), (119), (121), (123), (124), (125),
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | |            (153), (154), (155), (158), (328), (347), (381)
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #545.
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.57  | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | |   (382)  all_57_13 = e3 & op(e0, e2) = e3
% 227.92/39.57  | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | ALPHA: (382) implies:
% 227.92/39.57  | | | | | | | | | | | | | | | | | |   (383)  all_57_13 = e3
% 227.92/39.57  | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (52), (61), (63), (67), (78), (88), (153),
% 227.92/39.57  | | | | | | | | | | | | | | | | | |            (154), (155), (322), (383) are inconsistent by
% 227.92/39.57  | | | | | | | | | | | | | | | | | |            sub-proof #2057.
% 227.92/39.57  | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | End of split
% 227.92/39.57  | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | End of split
% 227.92/39.57  | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | End of split
% 227.92/39.57  | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | Case 2:
% 227.92/39.57  | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | |   (384)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 227.92/39.57  | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 227.92/39.57  | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | REF_CLOSE: (15), (32), (63), (74), (153), (323), (384) are
% 227.92/39.57  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1019.
% 227.92/39.57  | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | End of split
% 227.92/39.57  | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | End of split
% 227.92/39.57  | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | End of split
% 227.92/39.57  | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | Case 2:
% 227.92/39.57  | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | |   (385)  all_55_7 = e0
% 227.92/39.57  | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | REF_CLOSE: (92), (122), (385) are inconsistent by sub-proof
% 227.92/39.57  | | | | | | | | | | | |            #2130.
% 227.92/39.57  | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | End of split
% 227.92/39.57  | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | End of split
% 227.92/39.57  | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | End of split
% 227.92/39.57  | | | | | | | | | 
% 227.92/39.57  | | | | | | | | Case 2:
% 227.92/39.57  | | | | | | | | | 
% 227.92/39.57  | | | | | | | | |   (386)  all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 227.92/39.57  | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | REF_CLOSE: (15), (16), (40), (78), (87), (105), (107), (386)
% 227.92/39.57  | | | | | | | | |            are inconsistent by sub-proof #436.
% 227.92/39.57  | | | | | | | | | 
% 227.92/39.57  | | | | | | | | End of split
% 227.92/39.57  | | | | | | | | 
% 227.92/39.57  | | | | | | | Case 2:
% 227.92/39.57  | | | | | | | | 
% 227.92/39.57  | | | | | | | |   (387)  all_57_5 = e3 & op(e2, e1) = e3
% 227.92/39.57  | | | | | | | | 
% 227.92/39.57  | | | | | | | | ALPHA: (387) implies:
% 227.92/39.57  | | | | | | | |   (388)  all_57_5 = e3
% 227.92/39.57  | | | | | | | |   (389)  op(e2, e1) = e3
% 227.92/39.57  | | | | | | | | 
% 227.92/39.57  | | | | | | | | BETA: splitting (62) gives:
% 227.92/39.57  | | | | | | | | 
% 227.92/39.57  | | | | | | | | Case 1:
% 227.92/39.57  | | | | | | | | | 
% 227.92/39.57  | | | | | | | | |   (390)  all_55_2 = e3
% 227.92/39.57  | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | COMBINE_EQS: (87), (390) imply:
% 227.92/39.57  | | | | | | | | |   (391)  all_52_5 = e3
% 227.92/39.57  | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | SIMP: (391) implies:
% 227.92/39.57  | | | | | | | | |   (392)  all_52_5 = e3
% 227.92/39.57  | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | REDUCE: (9), (392) imply:
% 227.92/39.57  | | | | | | | | |   (393)   ~ (all_52_3 = e3)
% 227.92/39.57  | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | REDUCE: (31), (392) imply:
% 227.92/39.57  | | | | | | | | |   (394)   ~ (all_52_7 = e3)
% 227.92/39.57  | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | REDUCE: (16), (392) imply:
% 227.92/39.57  | | | | | | | | |   (395)  op(e3, e3) = e1
% 227.92/39.57  | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | BETA: splitting (50) gives:
% 227.92/39.57  | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | Case 1:
% 227.92/39.57  | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | |   (396)  all_55_7 = e3
% 227.92/39.57  | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | REF_CLOSE: (35), (122), (396) are inconsistent by sub-proof
% 227.92/39.57  | | | | | | | | | |            #2109.
% 227.92/39.57  | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | Case 2:
% 227.92/39.57  | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | |   (397)   ~ (all_55_7 = e3)
% 227.92/39.57  | | | | | | | | | |   (398)  all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 227.92/39.57  | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | BETA: splitting (398) gives:
% 227.92/39.57  | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | Case 1:
% 227.92/39.57  | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | |   (399)  all_55_7 = e2
% 227.92/39.57  | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | REF_CLOSE: (122), (149), (399) are inconsistent by sub-proof
% 227.92/39.57  | | | | | | | | | | |            #2171.
% 227.92/39.57  | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | Case 2:
% 227.92/39.57  | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | |   (400)   ~ (all_55_7 = e2)
% 227.92/39.57  | | | | | | | | | | |   (401)  all_55_7 = e1 | all_55_7 = e0
% 227.92/39.57  | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | BETA: splitting (401) gives:
% 227.92/39.57  | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | Case 1:
% 227.92/39.57  | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | |   (402)  all_55_7 = e1
% 227.92/39.57  | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | COMBINE_EQS: (122), (402) imply:
% 227.92/39.57  | | | | | | | | | | | |   (403)  all_53_13 = e1
% 227.92/39.57  | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | SIMP: (403) implies:
% 227.92/39.57  | | | | | | | | | | | |   (404)  all_53_13 = e1
% 227.92/39.57  | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | REDUCE: (93), (404) imply:
% 227.92/39.57  | | | | | | | | | | | |   (405)   ~ (all_53_1 = e1)
% 227.92/39.57  | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | REDUCE: (49), (404) imply:
% 227.92/39.57  | | | | | | | | | | | |   (406)   ~ (all_52_7 = e1)
% 227.92/39.57  | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | SIMP: (406) implies:
% 227.92/39.57  | | | | | | | | | | | |   (407)   ~ (all_52_7 = e1)
% 227.92/39.57  | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | REDUCE: (35), (404) imply:
% 227.92/39.57  | | | | | | | | | | | |   (408)   ~ (e3 = e1)
% 227.92/39.57  | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | REDUCE: (149), (404) imply:
% 227.92/39.57  | | | | | | | | | | | |   (409)   ~ (e2 = e1)
% 227.92/39.57  | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | BETA: splitting (10) gives:
% 227.92/39.57  | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | Case 1:
% 227.92/39.57  | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | |   (410)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 227.92/39.57  | | | | | | | | | | | | |            & op(e2, e3) = e1)
% 227.92/39.57  | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | BETA: splitting (410) gives:
% 227.92/39.57  | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | Case 1:
% 227.92/39.57  | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | |   (411)  all_57_0 = e1 & op(e3, e3) = e1
% 227.92/39.57  | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | REF_CLOSE: (58), (78), (411) are inconsistent by sub-proof
% 227.92/39.57  | | | | | | | | | | | | | |            #2454.
% 227.92/39.57  | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | Case 2:
% 227.92/39.57  | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | |   (412)  all_57_2 = e1 & op(e2, e3) = e1
% 227.92/39.57  | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | ALPHA: (412) implies:
% 227.92/39.57  | | | | | | | | | | | | | |   (413)  all_57_2 = e1
% 227.92/39.57  | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | BETA: splitting (130) gives:
% 227.92/39.57  | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | Case 1:
% 227.92/39.57  | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | |   (414)  all_55_3 = e2
% 227.92/39.57  | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | COMBINE_EQS: (33), (414) imply:
% 227.92/39.57  | | | | | | | | | | | | | | |   (415)  all_52_7 = e2
% 227.92/39.57  | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | SIMP: (415) implies:
% 227.92/39.57  | | | | | | | | | | | | | | |   (416)  all_52_7 = e2
% 227.92/39.57  | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | REDUCE: (79), (416) imply:
% 227.92/39.57  | | | | | | | | | | | | | | |   (417)   ~ (all_52_3 = e2)
% 227.92/39.57  | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | BETA: splitting (4) gives:
% 227.92/39.57  | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | Case 1:
% 227.92/39.57  | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | |   (418)  all_55_1 = e3
% 227.92/39.57  | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | REF_CLOSE: (102), (393), (418) are inconsistent by sub-proof
% 227.92/39.57  | | | | | | | | | | | | | | | |            #562.
% 227.92/39.57  | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | Case 2:
% 227.92/39.57  | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | |   (419)  all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 227.92/39.57  | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | BETA: splitting (419) gives:
% 227.92/39.57  | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.57  | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | |   (420)  all_55_1 = e2
% 227.92/39.57  | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | REF_CLOSE: (102), (417), (420) are inconsistent by sub-proof
% 227.92/39.57  | | | | | | | | | | | | | | | | |            #851.
% 227.92/39.57  | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.57  | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | |   (421)  all_55_1 = e1 | all_55_1 = e0
% 227.92/39.57  | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | BETA: splitting (421) gives:
% 227.92/39.57  | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | |   (422)  all_55_1 = e1
% 227.92/39.57  | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (102), (422) imply:
% 227.92/39.57  | | | | | | | | | | | | | | | | | |   (423)  all_52_3 = e1
% 227.92/39.57  | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | SIMP: (423) implies:
% 227.92/39.57  | | | | | | | | | | | | | | | | | |   (424)  all_52_3 = e1
% 227.92/39.57  | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | REDUCE: (37), (424) imply:
% 227.92/39.57  | | | | | | | | | | | | | | | | | |   (425)   ~ (all_53_7 = e1)
% 227.92/39.57  | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | BETA: splitting (135) gives:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | |   (426)  all_55_13 = e2
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (94), (426) imply:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | |   (427)  all_53_7 = e2
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | SIMP: (427) implies:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | |   (428)  all_53_7 = e2
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | REDUCE: (20), (428) imply:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | |   (429)   ~ (all_53_3 = e2)
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | BETA: splitting (128) gives:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | |   (430)  all_55_12 = e2
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (75), (429), (430) are inconsistent by sub-proof
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | |            #1337.
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | |   (431)   ~ (all_55_12 = e2)
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | |   (432)  all_55_12 = e1 | all_55_12 = e0
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | BETA: splitting (432) gives:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | |   (433)  all_55_12 = e1
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (75), (433) imply:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | |   (434)  all_53_3 = e1
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | SIMP: (434) implies:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | |   (435)  all_53_3 = e1
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (15) with e0, e1, e3, e3,
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | |              simplifying with (66), (395) gives:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | |   (436)  e1 = e0
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (413), (436) imply:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | |   (437)  all_57_2 = e0
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (13), (45), (78), (101), (153), (154), (155),
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | |            (388), (437) are inconsistent by sub-proof #2253.
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | |   (438)  all_55_12 = e0
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (75), (89), (438) are inconsistent by sub-proof
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | |            #1993.
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | |   (439)  all_55_13 = e1 | all_55_13 = e0
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (65), (94), (425), (439) are inconsistent by
% 227.92/39.57  | | | | | | | | | | | | | | | | | | |            sub-proof #1837.
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.57  | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | |   (440)  all_55_1 = e0
% 227.92/39.57  | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | REF_CLOSE: (22), (102), (440) are inconsistent by sub-proof
% 227.92/39.57  | | | | | | | | | | | | | | | | | |            #849.
% 227.92/39.57  | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | End of split
% 227.92/39.57  | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | End of split
% 227.92/39.57  | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | End of split
% 227.92/39.57  | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | Case 2:
% 227.92/39.57  | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | |   (441)  all_55_3 = e1 | all_55_3 = e0
% 227.92/39.57  | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | REF_CLOSE: (8), (15), (26), (33), (85), (407), (441) are
% 227.92/39.57  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1448.
% 227.92/39.57  | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | End of split
% 227.92/39.57  | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | End of split
% 227.92/39.57  | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | Case 2:
% 227.92/39.57  | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | |   (442)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 227.92/39.57  | | | | | | | | | | | | |            e1 & op(e0, e3) = e1)
% 227.92/39.57  | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | BETA: splitting (442) gives:
% 227.92/39.57  | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | Case 1:
% 227.92/39.57  | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | |   (443)  all_57_6 = e1 & op(e1, e3) = e1
% 227.92/39.57  | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | ALPHA: (443) implies:
% 227.92/39.57  | | | | | | | | | | | | | |   (444)  all_57_6 = e1
% 227.92/39.57  | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | BETA: splitting (108) gives:
% 227.92/39.57  | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | Case 1:
% 227.92/39.57  | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | |   (445)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 227.92/39.57  | | | | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 227.92/39.57  | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | BETA: splitting (445) gives:
% 227.92/39.57  | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | Case 1:
% 227.92/39.57  | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | |   (446)  all_57_9 = e2 & op(e3, e0) = e2
% 227.92/39.57  | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | ALPHA: (446) implies:
% 227.92/39.57  | | | | | | | | | | | | | | | |   (447)  all_57_9 = e2
% 227.92/39.57  | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (13), (15), (45), (63), (67), (68), (78),
% 227.92/39.57  | | | | | | | | | | | | | | | |            (88), (101), (104), (108), (117), (118), (153),
% 227.92/39.57  | | | | | | | | | | | | | | | |            (154), (155), (388), (395), (444), (447) are
% 227.92/39.57  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #406.
% 227.92/39.57  | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | Case 2:
% 227.92/39.57  | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | |   (448)  all_57_10 = e2 & op(e2, e0) = e2
% 227.92/39.57  | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | ALPHA: (448) implies:
% 227.92/39.57  | | | | | | | | | | | | | | | |   (449)  all_57_10 = e2
% 227.92/39.57  | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (13), (15), (45), (63), (67), (78), (88),
% 227.92/39.57  | | | | | | | | | | | | | | | |            (104), (118), (153), (154), (155), (388), (395),
% 227.92/39.57  | | | | | | | | | | | | | | | |            (444), (449) are inconsistent by sub-proof #405.
% 227.92/39.57  | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | End of split
% 227.92/39.57  | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | Case 2:
% 227.92/39.57  | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | |   (450)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 227.92/39.57  | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 227.92/39.57  | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | BETA: splitting (450) gives:
% 227.92/39.57  | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | Case 1:
% 227.92/39.57  | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | |   (451)  all_57_11 = e2 & op(e1, e0) = e2
% 227.92/39.57  | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | REF_CLOSE: (68), (155), (451) are inconsistent by sub-proof
% 227.92/39.57  | | | | | | | | | | | | | | | |            #1988.
% 227.92/39.57  | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | Case 2:
% 227.92/39.57  | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | |   (452)  all_57_15 = e2 & op(e0, e0) = e2
% 227.92/39.57  | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | REF_CLOSE: (63), (153), (452) are inconsistent by sub-proof
% 227.92/39.57  | | | | | | | | | | | | | | | |            #2323.
% 227.92/39.57  | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | End of split
% 227.92/39.57  | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | End of split
% 227.92/39.57  | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | Case 2:
% 227.92/39.57  | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | |   (453)  all_57_12 = e1 & op(e0, e3) = e1
% 227.92/39.57  | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | ALPHA: (453) implies:
% 227.92/39.57  | | | | | | | | | | | | | |   (454)  all_57_12 = e1
% 227.92/39.57  | | | | | | | | | | | | | |   (455)  op(e0, e3) = e1
% 227.92/39.57  | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | BETA: splitting (108) gives:
% 227.92/39.57  | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | Case 1:
% 227.92/39.57  | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | |   (456)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 227.92/39.57  | | | | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 227.92/39.57  | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | BETA: splitting (456) gives:
% 227.92/39.57  | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | Case 1:
% 227.92/39.57  | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | |   (457)  all_57_9 = e2 & op(e3, e0) = e2
% 227.92/39.57  | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | ALPHA: (457) implies:
% 227.92/39.57  | | | | | | | | | | | | | | | |   (458)  all_57_9 = e2
% 227.92/39.57  | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | BETA: splitting (83) gives:
% 227.92/39.57  | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.57  | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | |   (459)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 227.92/39.57  | | | | | | | | | | | | | | | | |            & op(e2, e2) = e3)
% 227.92/39.57  | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | BETA: splitting (459) gives:
% 227.92/39.57  | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | |   (460)  all_57_1 = e3 & op(e3, e2) = e3
% 227.92/39.57  | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | ALPHA: (460) implies:
% 227.92/39.57  | | | | | | | | | | | | | | | | | |   (461)  all_57_1 = e3
% 227.92/39.57  | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | BETA: splitting (6) gives:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | |   (462)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 227.92/39.57  | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | BETA: splitting (462) gives:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | |   (463)  all_57_2 = e1 & op(e2, e3) = e1
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | ALPHA: (463) implies:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | |   (464)  all_57_2 = e1
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (13), (15), (45), (63), (68), (78), (85),
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | |            (101), (108), (117), (153), (154), (155), (388),
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | |            (458), (464) are inconsistent by sub-proof #1093.
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | |   (465)  all_57_3 = e1 & op(e2, e2) = e1
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | ALPHA: (465) implies:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | |   (466)  op(e2, e2) = e1
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (40), (78), (466) are inconsistent by
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | |            sub-proof #2352.
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | |   (467)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 227.92/39.57  | | | | | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | BETA: splitting (467) gives:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | |   (468)  all_57_5 = e1 & op(e2, e1) = e1
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (388), (468) are inconsistent by sub-proof
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | |            #2376.
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | |   (469)  all_57_10 = e1 & op(e2, e0) = e1
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | ALPHA: (469) implies:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | |   (470)  all_57_10 = e1
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | BETA: splitting (88) gives:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | |   (471)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (471) gives:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | |   (472)  all_57_12 = e2 & op(e0, e3) = e2
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (472) implies:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | |   (473)  all_57_12 = e2
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (154), (454), (473) are inconsistent by sub-proof
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | |            #2321.
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | |   (474)  all_57_13 = e2 & op(e0, e2) = e2
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (474) implies:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | |   (475)  all_57_13 = e2
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (112) gives:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | |   (476)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e2)
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (476) gives:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | |   (477)  all_57_0 = e2 & op(e3, e3) = e2
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (477) implies:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | |   (478)  all_57_0 = e2
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | |   (479)  op(e3, e3) = e2
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (108) gives:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (456) gives:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (10), (11), (12), (13), (14), (15),
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | |            (17), (18), (21), (24), (25), (29), (30), (32),
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | |            (34), (36), (38), (39), (42), (43), (44), (45),
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | |            (46), (48), (52), (53), (55), (59), (62), (63),
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | |            (67), (69), (71), (73), (74), (76), (78), (80),
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | |            (81), (82), (83), (85), (86), (88), (90), (91),
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | |            (96), (97), (98), (99), (100), (101), (104),
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | |            (108), (109), (110), (112), (114), (115), (116),
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | |            (117), (119), (121), (123), (124), (125), (153),
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | |            (154), (155), (388), (389), (457), (478), (479)
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #411.
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | |   (480)  all_57_10 = e2 & op(e2, e0) = e2
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (480) implies:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | |   (481)  all_57_10 = e2
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (154), (470), (481) are inconsistent by sub-proof
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | |            #2144.
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | |   (482)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (482) gives:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | |   (483)  all_57_11 = e2 & op(e1, e0) = e2
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (483) implies:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | |   (484)  op(e1, e0) = e2
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (32), (74), (455), (484) are inconsistent by
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1147.
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | |   (485)  all_57_15 = e2 & op(e0, e0) = e2
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (485) implies:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | |   (486)  all_57_15 = e2
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (63), (486) imply:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | |   (487)  e3 = e2
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (487) implies:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | |   (488)  e3 = e2
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (388), (488) imply:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | |   (489)  all_57_5 = e2
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (10), (11), (12), (13), (14), (15),
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | |            (17), (18), (21), (24), (25), (29), (30), (32),
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | |            (34), (36), (38), (39), (42), (43), (44), (45),
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | |            (46), (48), (52), (53), (55), (59), (62), (63),
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | |            (67), (69), (71), (73), (74), (76), (78), (80),
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | |            (81), (82), (83), (85), (86), (88), (90), (91),
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | |            (96), (97), (98), (99), (100), (101), (104),
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | |            (108), (109), (110), (112), (114), (115), (116),
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | |            (117), (119), (121), (123), (124), (125), (153),
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | |            (154), (155), (478), (479), (489) are inconsistent
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #496.
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | |   (490)  all_57_2 = e2 & op(e2, e3) = e2
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (490) implies:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | |   (491)  all_57_2 = e2
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17) gives:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | |   (492)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e3)
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (492) gives:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | |   (493)  all_57_6 = e3 & op(e1, e3) = e3
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (493) implies:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | |   (494)  all_57_6 = e3
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (124) gives:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (495)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e2)
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (495) gives:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (496)  all_57_6 = e2 & op(e1, e3) = e2
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (496) implies:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (497)  all_57_6 = e2
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (15), (17), (21), (24), (45), (52), (63),
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (78), (106), (108), (117), (123), (153), (154),
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (155), (461), (475), (497) are inconsistent by
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #419.
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (498)  all_57_7 = e2 & op(e1, e2) = e2
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (498) implies:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (499)  all_57_7 = e2
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (45), (78), (123), (154), (461), (475),
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (499) are inconsistent by sub-proof #1698.
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (500)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e1, e0) = e2)
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (500) gives:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (501)  all_57_8 = e2 & op(e1, e1) = e2
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (501) implies:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (502)  all_57_8 = e2
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (42), (502) imply:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (503)  e2 = e1
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (503) implies:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (504)  e2 = e1
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (491), (504) imply:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (505)  all_57_2 = e1
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (101) gives:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (506)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (45), (63), (68), (78), (108), (117), (153),
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (154), (155), (458), (505), (506) are inconsistent
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1095.
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (507)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (507) gives:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (508)  all_57_5 = e2 & op(e2, e1) = e2
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (153), (388), (508) are inconsistent by sub-proof
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2425.
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (509)  all_57_10 = e2 & op(e2, e0) = e2
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (509) implies:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (510)  all_57_10 = e2
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (123) gives:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (511)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (511) gives:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (512)  all_57_1 = e1 & op(e3, e2) = e1
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (512) implies:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (513)  all_57_1 = e1
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (461), (513) imply:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (514)  e3 = e1
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (494), (514) imply:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (515)  all_57_6 = e1
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (13), (15), (45), (63), (67), (78), (88),
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (104), (118), (153), (154), (155), (388), (395),
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (510), (515) are inconsistent by sub-proof #405.
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (516)  all_57_3 = e1 & op(e2, e2) = e1
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (516) implies:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (517)  op(e2, e2) = e1
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (40), (78), (517) are inconsistent by
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2352.
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (518)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (518) gives:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (519)  all_57_7 = e1 & op(e1, e2) = e1
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (519) implies:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (520)  all_57_7 = e1
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (13), (14), (42), (45), (52), (63), (78),
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (101), (117), (153), (154), (155), (388), (458),
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (494), (505), (510), (520) are inconsistent by
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #404.
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (521)  all_57_13 = e1 & op(e0, e2) = e1
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (521) implies:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (522)  all_57_13 = e1
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12) gives:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (523)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (523) gives:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (524)  all_57_1 = e2 & op(e3, e2) = e2
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (153), (461), (524) are inconsistent by sub-proof
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1809.
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (525)  all_57_3 = e2 & op(e2, e2) = e2
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (45), (63), (68), (78), (108), (117), (153),
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (154), (155), (458), (525) are inconsistent by
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1096.
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (526)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 227.92/39.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (526) gives:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (527)  all_57_7 = e2 & op(e1, e2) = e2
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (527) implies:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (528)  all_57_7 = e2
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (117) gives:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (529)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (529) gives:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (530)  all_57_9 = e1 & op(e3, e0) = e1
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (530) implies:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (531)  all_57_9 = e1
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (504), (528) imply:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (532)  all_57_7 = e1
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (13), (14), (42), (45), (52), (63), (78),
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (101), (117), (153), (154), (155), (388), (458),
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (494), (505), (510), (532) are inconsistent by
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #404.
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (504), (528) imply:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (533)  all_57_7 = e1
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (13), (14), (42), (45), (52), (63), (78),
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (101), (117), (153), (154), (155), (388), (458),
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (494), (505), (510), (533) are inconsistent by
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #404.
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (534)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (13), (15), (45), (68), (78), (85), (101),
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (153), (154), (155), (388), (505), (534) are
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1094.
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (154), (475), (522) are inconsistent by sub-proof
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2327.
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (535)  all_57_11 = e2 & op(e1, e0) = e2
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (535) implies:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (536)  op(e1, e0) = e2
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (32), (74), (455), (536) are inconsistent by
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1147.
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | |   (537)  all_57_7 = e3 & op(e1, e2) = e3
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (537) implies:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | |   (538)  all_57_7 = e3
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (45), (78), (123), (154), (461), (475),
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | |            (538) are inconsistent by sub-proof #1779.
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | |   (539)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e1, e0) = e3)
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (15), (21), (24), (52), (63), (78), (106),
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | |            (108), (117), (153), (154), (155), (539) are
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1080.
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | |   (540)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e3) = e2)
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (15), (17), (21), (24), (45), (52), (63),
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | |            (78), (106), (108), (117), (123), (153), (154),
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | |            (155), (454), (461), (475), (540) are inconsistent
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #418.
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | |   (541)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (541) gives:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | |   (542)  all_57_14 = e2 & op(e0, e1) = e2
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (542) implies:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | |   (543)  all_57_14 = e2
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (118), (543) imply:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | |   (544)  e2 = e0
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | SIMP: (544) implies:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | |   (545)  e2 = e0
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (458), (545) imply:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | |   (546)  all_57_9 = e0
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (63), (68), (78), (108), (117), (153),
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | |            (154), (155), (546) are inconsistent by sub-proof
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | |            #1144.
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | |   (547)  all_57_15 = e2 & op(e0, e0) = e2
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (547) implies:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | |   (548)  all_57_15 = e2
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (63), (153), (548) are inconsistent by sub-proof
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | |            #2058.
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.58  | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | |   (549)  all_57_3 = e3 & op(e2, e2) = e3
% 227.92/39.58  | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | ALPHA: (549) implies:
% 227.92/39.58  | | | | | | | | | | | | | | | | | |   (550)  all_57_3 = e3
% 227.92/39.58  | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (52), (550) are inconsistent by sub-proof
% 227.92/39.58  | | | | | | | | | | | | | | | | | |            #2358.
% 227.92/39.58  | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | End of split
% 227.92/39.58  | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.58  | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | |   (551)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 227.92/39.58  | | | | | | | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 227.92/39.58  | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | BETA: splitting (551) gives:
% 227.92/39.58  | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | |   (552)  all_57_7 = e3 & op(e1, e2) = e3
% 227.92/39.58  | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | ALPHA: (552) implies:
% 227.92/39.58  | | | | | | | | | | | | | | | | | |   (553)  all_57_7 = e3
% 227.92/39.58  | | | | | | | | | | | | | | | | | |   (554)  op(e1, e2) = e3
% 227.92/39.58  | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | BETA: splitting (104) gives:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | |   (555)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 227.92/39.58  | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e3)
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | BETA: splitting (555) gives:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | |   (556)  all_57_0 = e3 & op(e3, e3) = e3
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | ALPHA: (556) implies:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | |   (557)  op(e3, e3) = e3
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (10), (11), (12), (13), (14), (15),
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | |            (18), (24), (25), (29), (30), (34), (36), (38),
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | |            (39), (43), (44), (45), (46), (48), (53), (55),
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | |            (59), (62), (63), (67), (69), (71), (73), (78),
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | |            (80), (81), (85), (86), (88), (90), (91), (97),
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | |            (98), (99), (100), (101), (108), (109), (110),
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | |            (112), (114), (115), (116), (117), (119), (121),
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | |            (123), (124), (125), (153), (154), (155), (388),
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | |            (389), (553), (554), (557) are inconsistent by
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | |            sub-proof #1441.
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | |   (558)  all_57_2 = e3 & op(e2, e3) = e3
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (13), (45), (63), (68), (78), (101), (108),
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | |            (117), (153), (154), (155), (388), (458), (558)
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #407.
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | |   (559)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 227.92/39.58  | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e3) = e3)
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | BETA: splitting (559) gives:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | |   (560)  all_57_6 = e3 & op(e1, e3) = e3
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | ALPHA: (560) implies:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | |   (561)  all_57_6 = e3
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | BETA: splitting (76) gives:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | |   (562)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e3)
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (562) gives:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | |   (563)  all_57_0 = e3 & op(e3, e3) = e3
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (563) implies:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | |   (564)  all_57_0 = e3
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (13), (52), (78), (112), (116), (153),
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | |            (154), (155), (561), (564) are inconsistent by
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2010.
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | |   (565)  all_57_1 = e3 & op(e3, e2) = e3
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (565) implies:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | |   (566)  all_57_1 = e3
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (13), (45), (78), (123), (153), (154),
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | |            (155), (553), (566) are inconsistent by sub-proof
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | |            #1778.
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | |   (567)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e3)
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (567) gives:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | |   (568)  all_57_4 = e3 & op(e3, e1) = e3
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (568) implies:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | |   (569)  all_57_4 = e3
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (12), (13), (15), (30), (41), (45), (56),
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | |            (57), (58), (60), (66), (72), (77), (78), (84),
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | |            (123), (147), (154), (395), (405), (458), (553),
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | |            (569) are inconsistent by sub-proof #433.
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | |   (570)  all_57_9 = e3 & op(e3, e0) = e3
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (570) implies:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | |   (571)  op(e3, e0) = e3
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (99), (125), (571) are inconsistent by
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2458.
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | |   (572)  all_57_12 = e3 & op(e0, e3) = e3
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | ALPHA: (572) implies:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | |   (573)  all_57_12 = e3
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (63), (67), (78), (88), (118), (153), (154),
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | |            (155), (573) are inconsistent by sub-proof #1763.
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.58  | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | |   (574)  all_57_13 = e3 & op(e0, e2) = e3
% 227.92/39.58  | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | ALPHA: (574) implies:
% 227.92/39.58  | | | | | | | | | | | | | | | | | |   (575)  all_57_13 = e3
% 227.92/39.58  | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (52), (61), (63), (67), (78), (88), (153),
% 227.92/39.58  | | | | | | | | | | | | | | | | | |            (154), (155), (454), (575) are inconsistent by
% 227.92/39.58  | | | | | | | | | | | | | | | | | |            sub-proof #2057.
% 227.92/39.58  | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | End of split
% 227.92/39.58  | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | End of split
% 227.92/39.58  | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | Case 2:
% 227.92/39.58  | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | |   (576)  all_57_10 = e2 & op(e2, e0) = e2
% 227.92/39.58  | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | ALPHA: (576) implies:
% 227.92/39.58  | | | | | | | | | | | | | | | |   (577)  all_57_10 = e2
% 227.92/39.58  | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | BETA: splitting (83) gives:
% 227.92/39.58  | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.58  | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | |   (578)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 227.92/39.58  | | | | | | | | | | | | | | | | |            & op(e2, e2) = e3)
% 227.92/39.58  | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | BETA: splitting (578) gives:
% 227.92/39.58  | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | |   (579)  all_57_1 = e3 & op(e3, e2) = e3
% 227.92/39.58  | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | ALPHA: (579) implies:
% 227.92/39.58  | | | | | | | | | | | | | | | | | |   (580)  all_57_1 = e3
% 227.92/39.58  | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (10), (11), (12), (13), (14), (15),
% 227.92/39.58  | | | | | | | | | | | | | | | | | |            (17), (18), (21), (24), (25), (29), (30), (32),
% 227.92/39.58  | | | | | | | | | | | | | | | | | |            (34), (36), (38), (39), (40), (42), (43), (44),
% 227.92/39.58  | | | | | | | | | | | | | | | | | |            (45), (46), (48), (52), (53), (55), (59), (62),
% 227.92/39.58  | | | | | | | | | | | | | | | | | |            (63), (67), (69), (71), (73), (74), (76), (78),
% 227.92/39.58  | | | | | | | | | | | | | | | | | |            (80), (81), (82), (83), (85), (86), (88), (90),
% 227.92/39.58  | | | | | | | | | | | | | | | | | |            (91), (96), (97), (98), (99), (100), (101), (104),
% 227.92/39.58  | | | | | | | | | | | | | | | | | |            (106), (108), (109), (110), (112), (114), (115),
% 227.92/39.58  | | | | | | | | | | | | | | | | | |            (116), (117), (118), (119), (121), (123), (124),
% 227.92/39.58  | | | | | | | | | | | | | | | | | |            (125), (153), (154), (155), (388), (389), (454),
% 227.92/39.58  | | | | | | | | | | | | | | | | | |            (455), (577), (580) are inconsistent by sub-proof
% 227.92/39.58  | | | | | | | | | | | | | | | | | |            #410.
% 227.92/39.58  | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | |   (581)  all_57_3 = e3 & op(e2, e2) = e3
% 227.92/39.58  | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | ALPHA: (581) implies:
% 227.92/39.58  | | | | | | | | | | | | | | | | | |   (582)  all_57_3 = e3
% 227.92/39.58  | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (52), (582) are inconsistent by sub-proof
% 227.92/39.58  | | | | | | | | | | | | | | | | | |            #2358.
% 227.92/39.58  | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | End of split
% 227.92/39.58  | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.58  | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | |   (583)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 227.92/39.58  | | | | | | | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 227.92/39.58  | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | BETA: splitting (583) gives:
% 227.92/39.58  | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | |   (584)  all_57_7 = e3 & op(e1, e2) = e3
% 227.92/39.58  | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | ALPHA: (584) implies:
% 227.92/39.58  | | | | | | | | | | | | | | | | | |   (585)  all_57_7 = e3
% 227.92/39.58  | | | | | | | | | | | | | | | | | |   (586)  op(e1, e2) = e3
% 227.92/39.58  | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | BETA: splitting (104) gives:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | |   (587)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 227.92/39.58  | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e3)
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | BETA: splitting (587) gives:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | |   (588)  all_57_0 = e3 & op(e3, e3) = e3
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | ALPHA: (588) implies:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | |   (589)  op(e3, e3) = e3
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (10), (11), (12), (13), (14), (15),
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | |            (18), (24), (25), (29), (30), (34), (36), (38),
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | |            (39), (43), (44), (45), (46), (48), (53), (55),
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | |            (59), (62), (63), (67), (69), (71), (73), (78),
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | |            (80), (81), (85), (86), (88), (90), (91), (97),
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | |            (98), (99), (100), (101), (108), (109), (110),
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | |            (112), (114), (115), (116), (117), (119), (121),
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | |            (123), (124), (125), (153), (154), (155), (388),
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | |            (389), (585), (586), (589) are inconsistent by
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | |            sub-proof #1441.
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | |   (590)  all_57_2 = e3 & op(e2, e3) = e3
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | ALPHA: (590) implies:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | |   (591)  all_57_2 = e3
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (13), (45), (78), (154), (388), (577), (591)
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1804.
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | |   (592)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 227.92/39.58  | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e3) = e3)
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | BETA: splitting (592) gives:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | |   (593)  all_57_6 = e3 & op(e1, e3) = e3
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | ALPHA: (593) implies:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | |   (594)  all_57_6 = e3
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | BETA: splitting (76) gives:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | |   (595)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e3)
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (595) gives:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | |   (596)  all_57_0 = e3 & op(e3, e3) = e3
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (596) implies:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | |   (597)  all_57_0 = e3
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (13), (52), (78), (112), (116), (153),
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | |            (154), (155), (594), (597) are inconsistent by
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2010.
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | |   (598)  all_57_1 = e3 & op(e3, e2) = e3
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (598) implies:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | |   (599)  all_57_1 = e3
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (10), (11), (12), (13), (14), (15),
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | |            (17), (18), (21), (24), (25), (29), (30), (32),
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | |            (34), (36), (38), (39), (40), (42), (43), (44),
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | |            (45), (46), (48), (52), (53), (55), (59), (62),
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | |            (63), (67), (69), (71), (73), (74), (76), (78),
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | |            (80), (81), (82), (83), (85), (86), (88), (90),
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | |            (91), (96), (97), (98), (99), (100), (101), (104),
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | |            (106), (108), (109), (110), (112), (114), (115),
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | |            (116), (117), (118), (119), (121), (123), (124),
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | |            (125), (153), (154), (155), (388), (389), (454),
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | |            (455), (577), (599) are inconsistent by sub-proof
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | |            #410.
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | |   (600)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e3)
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (600) gives:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | |   (601)  all_57_4 = e3 & op(e3, e1) = e3
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (601) implies:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | |   (602)  all_57_4 = e3
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (10), (11), (12), (13),
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | |            (14), (15), (17), (18), (21), (22), (24), (25),
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | |            (26), (28), (29), (30), (32), (34), (36), (38),
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | |            (39), (42), (43), (44), (45), (46), (48), (51),
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | |            (52), (53), (54), (55), (59), (62), (63), (67),
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | |            (69), (71), (73), (74), (76), (78), (79), (80),
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | |            (81), (85), (86), (88), (90), (91), (97), (98),
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | |            (99), (100), (101), (103), (104), (108), (109),
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | |            (110), (111), (112), (114), (115), (116), (117),
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | |            (118), (119), (120), (121), (123), (124), (125),
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | |            (153), (154), (155), (388), (389), (393), (455),
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | |            (577), (585), (602) are inconsistent by sub-proof
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | |            #408.
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | |   (603)  all_57_9 = e3 & op(e3, e0) = e3
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (603) implies:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | |   (604)  op(e3, e0) = e3
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (99), (125), (604) are inconsistent by
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2458.
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | |   (605)  all_57_12 = e3 & op(e0, e3) = e3
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | ALPHA: (605) implies:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | |   (606)  all_57_12 = e3
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (63), (67), (78), (88), (118), (153), (154),
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | |            (155), (606) are inconsistent by sub-proof #1763.
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.58  | | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | End of split
% 227.92/39.58  | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | Case 2:
% 227.92/39.58  | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | |   (607)  all_57_13 = e3 & op(e0, e2) = e3
% 227.92/39.58  | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | ALPHA: (607) implies:
% 227.92/39.58  | | | | | | | | | | | | | | | | | |   (608)  all_57_13 = e3
% 227.92/39.58  | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (52), (61), (63), (67), (78), (88), (153),
% 227.92/39.58  | | | | | | | | | | | | | | | | | |            (154), (155), (454), (608) are inconsistent by
% 227.92/39.58  | | | | | | | | | | | | | | | | | |            sub-proof #2057.
% 227.92/39.58  | | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | | End of split
% 227.92/39.58  | | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | | End of split
% 227.92/39.58  | | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | End of split
% 227.92/39.58  | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | Case 2:
% 227.92/39.58  | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | |   (609)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 227.92/39.58  | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 227.92/39.58  | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | | REF_CLOSE: (15), (32), (63), (74), (153), (455), (609) are
% 227.92/39.58  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1019.
% 227.92/39.58  | | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | | End of split
% 227.92/39.58  | | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | | End of split
% 227.92/39.58  | | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | End of split
% 227.92/39.58  | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | Case 2:
% 227.92/39.58  | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | |   (610)  all_55_7 = e0
% 227.92/39.58  | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | | REF_CLOSE: (92), (122), (610) are inconsistent by sub-proof
% 227.92/39.58  | | | | | | | | | | | |            #2130.
% 227.92/39.58  | | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | | End of split
% 227.92/39.58  | | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | | End of split
% 227.92/39.58  | | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | End of split
% 227.92/39.58  | | | | | | | | | 
% 227.92/39.58  | | | | | | | | Case 2:
% 227.92/39.58  | | | | | | | | | 
% 227.92/39.58  | | | | | | | | |   (611)  all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 227.92/39.58  | | | | | | | | | 
% 227.92/39.58  | | | | | | | | | REF_CLOSE: (15), (16), (40), (78), (87), (105), (107), (611)
% 227.92/39.58  | | | | | | | | |            are inconsistent by sub-proof #436.
% 227.92/39.58  | | | | | | | | | 
% 227.92/39.58  | | | | | | | | End of split
% 227.92/39.58  | | | | | | | | 
% 227.92/39.58  | | | | | | | End of split
% 227.92/39.58  | | | | | | | 
% 227.92/39.58  | | | | | | Case 2:
% 227.92/39.58  | | | | | | | 
% 227.92/39.58  | | | | | | |   (612)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 &
% 227.92/39.58  | | | | | | |            op(e0, e1) = e3)
% 227.92/39.58  | | | | | | | 
% 227.92/39.58  | | | | | | | REF_CLOSE: (13), (15), (21), (24), (52), (61), (63), (67), (78),
% 227.92/39.58  | | | | | | |            (88), (153), (154), (155), (612) are inconsistent by
% 227.92/39.58  | | | | | | |            sub-proof #1044.
% 227.92/39.58  | | | | | | | 
% 227.92/39.58  | | | | | | End of split
% 227.92/39.58  | | | | | | 
% 227.92/39.58  | | | | | Case 2:
% 227.92/39.58  | | | | | | 
% 227.92/39.58  | | | | | |   (613)  all_55_6 = e1 | all_55_6 = e0
% 227.92/39.58  | | | | | | 
% 227.92/39.58  | | | | | | REF_CLOSE: (23), (29), (70), (613) are inconsistent by sub-proof
% 227.92/39.58  | | | | | |            #2161.
% 227.92/39.58  | | | | | | 
% 227.92/39.58  | | | | | End of split
% 227.92/39.58  | | | | | 
% 227.92/39.58  | | | | End of split
% 227.92/39.58  | | | | 
% 227.92/39.58  | | | End of split
% 227.92/39.58  | | | 
% 227.92/39.58  | | End of split
% 227.92/39.58  | | 
% 227.92/39.58  | End of split
% 227.92/39.58  | 
% 227.92/39.58  End of proof
% 227.92/39.58  
% 227.92/39.58  Sub-proof #404 shows that the following formulas are inconsistent:
% 227.92/39.58  ----------------------------------------------------------------
% 227.92/39.58    (1)  all_57_9 = e2
% 227.92/39.58    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 227.92/39.58         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 227.92/39.58    (3)   ~ (e3 = e1)
% 227.92/39.58    (4)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 227.92/39.58         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 227.92/39.58    (5)  all_57_7 = e1
% 227.92/39.58    (6)  all_57_8 = e1
% 227.92/39.58    (7)  all_57_3 = e0
% 227.92/39.58    (8)   ~ (e3 = e2)
% 227.92/39.58    (9)   ~ (e3 = e0)
% 227.92/39.58    (10)  all_57_15 = e3
% 227.92/39.58    (11)  all_57_10 = e2
% 227.92/39.58    (12)  all_57_5 = e3
% 227.92/39.58    (13)   ~ (e2 = e0)
% 227.92/39.58    (14)   ~ (e1 = e0)
% 227.92/39.58    (15)  all_57_6 = e3
% 227.92/39.58    (16)  all_57_2 = e1
% 227.92/39.58    (17)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 227.92/39.58          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 227.92/39.58    (18)   ~ (e2 = e1)
% 227.92/39.58    (19)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 227.92/39.58          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 227.92/39.58  
% 227.92/39.58  Begin of proof
% 227.92/39.58  | 
% 227.92/39.58  | BETA: splitting (19) gives:
% 227.92/39.58  | 
% 227.92/39.58  | Case 1:
% 227.92/39.58  | | 
% 227.92/39.58  | |   (20)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) =
% 227.92/39.58  | |           e1)
% 227.92/39.58  | | 
% 227.92/39.58  | | BETA: splitting (20) gives:
% 227.92/39.58  | | 
% 227.92/39.58  | | Case 1:
% 227.92/39.58  | | | 
% 227.92/39.58  | | |   (21)  all_57_9 = e1 & op(e3, e0) = e1
% 227.92/39.58  | | | 
% 227.92/39.58  | | | REF_CLOSE: (1), (18), (21) are inconsistent by sub-proof #2451.
% 227.92/39.58  | | | 
% 227.92/39.58  | | Case 2:
% 227.92/39.58  | | | 
% 227.92/39.58  | | |   (22)  all_57_10 = e1 & op(e2, e0) = e1
% 227.92/39.58  | | | 
% 227.92/39.58  | | | REF_CLOSE: (11), (18), (22) are inconsistent by sub-proof #2360.
% 227.92/39.58  | | | 
% 227.92/39.58  | | End of split
% 227.92/39.58  | | 
% 227.92/39.58  | Case 2:
% 227.92/39.58  | | 
% 227.92/39.58  | |   (23)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 227.92/39.58  | |           e1)
% 227.92/39.58  | | 
% 227.92/39.58  | | BETA: splitting (23) gives:
% 227.92/39.58  | | 
% 227.92/39.58  | | Case 1:
% 227.92/39.58  | | | 
% 227.92/39.58  | | |   (24)  all_57_11 = e1 & op(e1, e0) = e1
% 227.92/39.58  | | | 
% 227.92/39.58  | | | ALPHA: (24) implies:
% 227.92/39.58  | | |   (25)  all_57_11 = e1
% 227.92/39.58  | | | 
% 227.92/39.58  | | | BETA: splitting (4) gives:
% 227.92/39.58  | | | 
% 227.92/39.58  | | | Case 1:
% 227.92/39.58  | | | | 
% 227.92/39.58  | | | |   (26)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2)
% 227.92/39.58  | | | |           = e0)
% 227.92/39.58  | | | | 
% 227.92/39.58  | | | | REF_CLOSE: (2), (3), (5), (7), (8), (9), (12), (13), (14), (15), (16),
% 227.92/39.58  | | | |            (17), (18), (26) are inconsistent by sub-proof #493.
% 227.92/39.58  | | | | 
% 227.92/39.58  | | | Case 2:
% 227.92/39.58  | | | | 
% 227.92/39.58  | | | |   (27)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0)
% 227.92/39.58  | | | |           = e0)
% 227.92/39.58  | | | | 
% 227.92/39.58  | | | | BETA: splitting (27) gives:
% 227.92/39.58  | | | | 
% 227.92/39.58  | | | | Case 1:
% 227.92/39.58  | | | | | 
% 227.92/39.58  | | | | |   (28)  all_57_8 = e0 & op(e1, e1) = e0
% 227.92/39.58  | | | | | 
% 227.92/39.58  | | | | | REF_CLOSE: (2), (3), (6), (7), (8), (12), (13), (14), (16), (17),
% 227.92/39.58  | | | | |            (18), (28) are inconsistent by sub-proof #492.
% 227.92/39.58  | | | | | 
% 227.92/39.58  | | | | Case 2:
% 227.92/39.58  | | | | | 
% 227.92/39.58  | | | | |   (29)  all_57_11 = e0 & op(e1, e0) = e0
% 227.92/39.58  | | | | | 
% 227.92/39.58  | | | | | REF_CLOSE: (2), (3), (7), (8), (12), (13), (14), (16), (17), (18),
% 227.92/39.58  | | | | |            (25), (29) are inconsistent by sub-proof #1465.
% 227.92/39.58  | | | | | 
% 227.92/39.58  | | | | End of split
% 227.92/39.58  | | | | 
% 227.92/39.58  | | | End of split
% 227.92/39.58  | | | 
% 227.92/39.58  | | Case 2:
% 227.92/39.58  | | | 
% 227.92/39.58  | | |   (30)  all_57_15 = e1 & op(e0, e0) = e1
% 227.92/39.58  | | | 
% 227.92/39.58  | | | REF_CLOSE: (3), (10), (30) are inconsistent by sub-proof #2325.
% 227.92/39.58  | | | 
% 227.92/39.58  | | End of split
% 227.92/39.58  | | 
% 227.92/39.58  | End of split
% 227.92/39.58  | 
% 227.92/39.58  End of proof
% 227.92/39.58  
% 227.92/39.58  Sub-proof #405 shows that the following formulas are inconsistent:
% 227.92/39.58  ----------------------------------------------------------------
% 227.92/39.58    (1)  op(e3, e3) = e1
% 227.92/39.58    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 227.92/39.58         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 227.92/39.58    (3)   ~ (e3 = e1)
% 227.92/39.58    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.92/39.58           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.92/39.58    (5)  all_57_6 = e1
% 227.92/39.58    (6)  all_57_3 = e0
% 227.92/39.58    (7)   ~ (e3 = e2)
% 227.92/39.58    (8)  all_57_15 = e3
% 227.92/39.58    (9)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 227.92/39.58         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 227.92/39.58    (10)  all_57_10 = e2
% 227.92/39.58    (11)  all_57_5 = e3
% 227.92/39.58    (12)   ~ (e2 = e0)
% 227.92/39.58    (13)   ~ (e1 = e0)
% 227.92/39.58    (14)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.92/39.58          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 227.92/39.58            e2)
% 227.92/39.58    (15)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 227.92/39.58          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 227.92/39.58    (16)   ~ (e2 = e1)
% 227.92/39.58    (17)  all_57_14 = e0
% 227.92/39.58  
% 227.92/39.58  Begin of proof
% 227.92/39.58  | 
% 227.92/39.58  | BETA: splitting (15) gives:
% 227.92/39.58  | 
% 227.92/39.58  | Case 1:
% 227.92/39.58  | | 
% 227.92/39.58  | |   (18)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) =
% 227.92/39.58  | |           e3)
% 227.92/39.58  | | 
% 227.92/39.58  | | BETA: splitting (18) gives:
% 227.92/39.58  | | 
% 227.92/39.58  | | Case 1:
% 227.92/39.58  | | | 
% 227.92/39.58  | | |   (19)  all_57_0 = e3 & op(e3, e3) = e3
% 227.92/39.58  | | | 
% 227.92/39.58  | | | ALPHA: (19) implies:
% 227.92/39.58  | | |   (20)  op(e3, e3) = e3
% 227.92/39.58  | | | 
% 227.92/39.58  | | | REF_CLOSE: (1), (3), (4), (20) are inconsistent by sub-proof #2495.
% 227.92/39.58  | | | 
% 227.92/39.58  | | Case 2:
% 227.92/39.58  | | | 
% 227.92/39.58  | | |   (21)  all_57_2 = e3 & op(e2, e3) = e3
% 227.92/39.58  | | | 
% 227.92/39.58  | | | ALPHA: (21) implies:
% 227.92/39.58  | | |   (22)  all_57_2 = e3
% 227.92/39.58  | | | 
% 227.92/39.58  | | | REF_CLOSE: (2), (3), (6), (10), (11), (13), (16), (22) are inconsistent by
% 227.92/39.58  | | |            sub-proof #1804.
% 227.92/39.58  | | | 
% 227.92/39.58  | | End of split
% 227.92/39.58  | | 
% 227.92/39.58  | Case 2:
% 227.92/39.58  | | 
% 227.92/39.58  | |   (23)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) =
% 227.92/39.58  | |           e3)
% 227.92/39.58  | | 
% 227.92/39.58  | | REF_CLOSE: (3), (5), (7), (8), (9), (12), (13), (14), (16), (17), (23) are
% 227.92/39.58  | |            inconsistent by sub-proof #440.
% 227.92/39.58  | | 
% 227.92/39.58  | End of split
% 227.92/39.58  | 
% 227.92/39.58  End of proof
% 227.92/39.58  
% 227.92/39.58  Sub-proof #406 shows that the following formulas are inconsistent:
% 227.92/39.58  ----------------------------------------------------------------
% 227.92/39.58    (1)  all_57_9 = e2
% 227.92/39.58    (2)  op(e3, e3) = e1
% 227.92/39.58    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 227.92/39.58         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 227.92/39.58    (4)   ~ (e3 = e1)
% 227.92/39.59    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 227.92/39.59           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 227.92/39.59    (6)  all_57_6 = e1
% 227.92/39.59    (7)  all_57_3 = e0
% 227.92/39.59    (8)   ~ (e3 = e2)
% 227.92/39.59    (9)  all_57_15 = e3
% 227.92/39.59    (10)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 227.92/39.59          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 227.92/39.59            e1)
% 227.92/39.59    (11)  all_57_5 = e3
% 227.92/39.59    (12)  all_57_11 = e0
% 227.92/39.59    (13)   ~ (e2 = e0)
% 227.92/39.59    (14)   ~ (e1 = e0)
% 227.92/39.59    (15)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 227.92/39.59          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 227.92/39.59            e2)
% 227.92/39.59    (16)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 227.92/39.59          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 227.92/39.59    (17)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 227.92/39.59          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 227.92/39.59    (18)   ~ (e2 = e1)
% 227.92/39.59    (19)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 227.92/39.59          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 227.92/39.59    (20)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 227.92/39.59          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 227.92/39.59    (21)  all_57_14 = e0
% 227.92/39.59  
% 227.92/39.59  Begin of proof
% 227.92/39.59  | 
% 227.92/39.59  | BETA: splitting (17) gives:
% 227.92/39.59  | 
% 227.92/39.59  | Case 1:
% 227.92/39.59  | | 
% 227.92/39.59  | |   (22)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) =
% 227.92/39.59  | |           e3)
% 227.92/39.59  | | 
% 227.92/39.59  | | BETA: splitting (22) gives:
% 227.92/39.59  | | 
% 227.92/39.59  | | Case 1:
% 227.92/39.59  | | | 
% 227.92/39.59  | | |   (23)  all_57_0 = e3 & op(e3, e3) = e3
% 227.92/39.59  | | | 
% 227.92/39.59  | | | ALPHA: (23) implies:
% 227.92/39.59  | | |   (24)  op(e3, e3) = e3
% 227.92/39.59  | | | 
% 227.92/39.59  | | | REF_CLOSE: (2), (4), (5), (24) are inconsistent by sub-proof #2495.
% 227.92/39.59  | | | 
% 227.92/39.59  | | Case 2:
% 227.92/39.59  | | | 
% 227.92/39.59  | | |   (25)  all_57_2 = e3 & op(e2, e3) = e3
% 227.92/39.59  | | | 
% 227.92/39.59  | | | REF_CLOSE: (1), (3), (4), (7), (8), (9), (11), (12), (13), (14), (16),
% 227.92/39.59  | | |            (18), (19), (20), (25) are inconsistent by sub-proof #407.
% 227.92/39.59  | | | 
% 227.92/39.59  | | End of split
% 227.92/39.59  | | 
% 227.92/39.59  | Case 2:
% 227.92/39.59  | | 
% 228.06/39.59  | |   (26)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) =
% 228.06/39.59  | |           e3)
% 228.06/39.59  | | 
% 228.06/39.59  | | REF_CLOSE: (4), (6), (8), (9), (10), (13), (14), (15), (18), (21), (26) are
% 228.06/39.59  | |            inconsistent by sub-proof #440.
% 228.06/39.59  | | 
% 228.06/39.59  | End of split
% 228.06/39.59  | 
% 228.06/39.59  End of proof
% 228.06/39.59  
% 228.06/39.59  Sub-proof #407 shows that the following formulas are inconsistent:
% 228.06/39.59  ----------------------------------------------------------------
% 228.06/39.59    (1)  all_57_9 = e2
% 228.06/39.59    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.06/39.59         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.06/39.59    (3)   ~ (e3 = e1)
% 228.06/39.59    (4)  all_57_2 = e3 & op(e2, e3) = e3
% 228.06/39.59    (5)  all_57_3 = e0
% 228.06/39.59    (6)   ~ (e3 = e2)
% 228.06/39.59    (7)  all_57_15 = e3
% 228.06/39.59    (8)  all_57_5 = e3
% 228.06/39.59    (9)  all_57_11 = e0
% 228.06/39.59    (10)   ~ (e2 = e0)
% 228.06/39.59    (11)   ~ (e1 = e0)
% 228.06/39.59    (12)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.06/39.59          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.06/39.59    (13)   ~ (e2 = e1)
% 228.06/39.59    (14)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.06/39.59          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.06/39.59    (15)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.06/39.59          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.06/39.59  
% 228.06/39.59  Begin of proof
% 228.06/39.59  | 
% 228.06/39.59  | ALPHA: (4) implies:
% 228.06/39.59  |   (16)  all_57_2 = e3
% 228.06/39.59  | 
% 228.06/39.59  | BETA: splitting (12) gives:
% 228.06/39.59  | 
% 228.06/39.59  | Case 1:
% 228.06/39.59  | | 
% 228.06/39.59  | |   (17)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 228.06/39.59  | |           e2)
% 228.06/39.59  | | 
% 228.06/39.59  | | BETA: splitting (17) gives:
% 228.06/39.59  | | 
% 228.06/39.59  | | Case 1:
% 228.06/39.59  | | | 
% 228.06/39.59  | | |   (18)  all_57_2 = e2 & op(e2, e3) = e2
% 228.06/39.59  | | | 
% 228.06/39.59  | | | REF_CLOSE: (6), (16), (18) are inconsistent by sub-proof #1925.
% 228.06/39.59  | | | 
% 228.06/39.59  | | Case 2:
% 228.06/39.59  | | | 
% 228.06/39.59  | | |   (19)  all_57_3 = e2 & op(e2, e2) = e2
% 228.06/39.59  | | | 
% 228.06/39.59  | | | REF_CLOSE: (1), (3), (5), (6), (7), (9), (10), (11), (13), (14), (15),
% 228.06/39.59  | | |            (19) are inconsistent by sub-proof #1096.
% 228.06/39.59  | | | 
% 228.06/39.59  | | End of split
% 228.06/39.59  | | 
% 228.06/39.59  | Case 2:
% 228.06/39.59  | | 
% 228.06/39.59  | |   (20)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 228.06/39.59  | |           e2)
% 228.06/39.59  | | 
% 228.06/39.59  | | REF_CLOSE: (2), (3), (5), (6), (8), (11), (13), (16), (20) are inconsistent
% 228.06/39.59  | |            by sub-proof #1803.
% 228.06/39.59  | | 
% 228.06/39.59  | End of split
% 228.06/39.59  | 
% 228.06/39.59  End of proof
% 228.06/39.59  
% 228.06/39.59  Sub-proof #408 shows that the following formulas are inconsistent:
% 228.06/39.59  ----------------------------------------------------------------
% 228.06/39.59    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.06/39.59    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.06/39.59    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.06/39.59         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.06/39.59    (4)  op(e3, e1) = all_52_5
% 228.06/39.59    (5)   ~ (all_52_7 = e3)
% 228.06/39.59    (6)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.06/39.59         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.06/39.59    (7)  op(e2, e1) = e3
% 228.06/39.59    (8)   ~ (all_53_8 = all_53_12)
% 228.06/39.59    (9)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.06/39.59         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.06/39.59    (10)   ~ (e3 = e1)
% 228.06/39.59    (11)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.06/39.59          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.06/39.59    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.06/39.59            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.06/39.59    (13)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.06/39.59          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.06/39.59    (14)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.06/39.59            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.06/39.59              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.06/39.59    (15)   ~ (all_6_2 = e3)
% 228.06/39.59    (16)   ~ (all_52_3 = e0)
% 228.06/39.59    (17)  op(e1, e1) = all_6_2
% 228.06/39.59    (18)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.06/39.59    (19)  op(all_52_7, all_52_7) = e0
% 228.06/39.59    (20)  op(e3, e2) = all_52_3
% 228.06/39.59    (21)   ~ (all_53_9 = e0)
% 228.06/39.59    (22)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.06/39.59          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.06/39.59    (23)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 228.06/39.59            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 228.06/39.59              e3) = all_22_1 & $i(all_22_1))
% 228.06/39.59    (24)   ~ (all_53_4 = all_53_12)
% 228.06/39.59    (25)   ~ (all_53_8 = all_53_9)
% 228.06/39.59    (26)  all_42_2 = all_6_2
% 228.06/39.59    (27)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.06/39.59          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.06/39.59    (28)  all_57_8 = e1
% 228.06/39.59    (29)   ~ (all_53_9 = all_6_2)
% 228.06/39.59    (30)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.06/39.59          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.06/39.59    (31)  all_57_3 = e0
% 228.06/39.59    (32)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.06/39.59          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.06/39.59    (33)  all_57_4 = e3
% 228.06/39.59    (34)   ~ (e3 = e2)
% 228.06/39.59    (35)  all_55_1 = all_53_4
% 228.06/39.59    (36)  all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.06/39.59    (37)   ~ (e3 = e0)
% 228.06/39.59    (38)  op(e0, e3) = e1
% 228.06/39.59    (39)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.06/39.59          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.06/39.59    (40)   ~ (all_6_2 = e2)
% 228.06/39.59    (41)   ~ (all_53_8 = all_6_2)
% 228.06/39.59    (42)  all_55_2 = all_53_8
% 228.06/39.59    (43)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.06/39.59    (44)  all_57_15 = e3
% 228.06/39.59    (45)   ~ (all_52_3 = e3)
% 228.06/39.59    (46)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.06/39.59          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.06/39.59            e1)
% 228.06/39.59    (47)  all_57_10 = e2
% 228.06/39.59    (48)  all_57_5 = e3
% 228.06/39.59    (49)   ~ (all_53_4 = all_53_8)
% 228.06/39.59    (50)  op(e3, e2) = all_53_4
% 228.06/39.59    (51)   ~ (e2 = e0)
% 228.06/39.59    (52)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.06/39.59            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.06/39.59            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.06/39.59            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.06/39.59              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.06/39.59            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.06/39.59            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.06/39.59              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.06/39.59              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.06/39.59            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.06/39.59            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.06/39.59            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.06/39.59              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.06/39.59              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.06/39.59            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.06/39.59              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.06/39.59            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.06/39.59            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.06/39.59              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.06/39.59              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.06/39.59            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.06/39.59            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.06/39.59    (53)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 228.06/39.59            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 228.06/39.59              e3) = all_12_1 & $i(all_12_1))
% 228.06/39.59    (54)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.06/39.59          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.06/39.59    (55)   ~ (e1 = e0)
% 228.06/39.59    (56)   ~ (all_52_3 = all_52_7)
% 228.06/39.59    (57)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.06/39.59            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.06/39.59              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.06/39.59    (58)   ~ (all_53_4 = e0)
% 228.06/39.59    (59)  op(e0, e0) = e3
% 228.06/39.59    (60)   ~ (all_53_4 = all_53_6)
% 228.06/39.59    (61)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.06/39.59          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.06/39.59            e2)
% 228.06/39.59    (62)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.06/39.59              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.06/39.59                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.06/39.59                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.06/39.59    (63)  all_55_10 = all_6_2
% 228.06/39.59    (64)  all_38_2 = all_6_2
% 228.06/39.59    (65)  all_55_3 = all_53_12
% 228.06/39.59    (66)   ~ (all_53_12 = e3)
% 228.06/39.59    (67)  all_57_7 = e3
% 228.06/39.59    (68)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.06/39.59            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.06/39.59              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.06/39.59    (69)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.06/39.59          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.06/39.59    (70)   ~ (all_52_5 = all_6_2)
% 228.06/39.59    (71)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.06/39.59          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.06/39.59    (72)   ~ (e2 = e1)
% 228.06/39.59    (73)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.06/39.59          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.06/39.59    (74)  op(e2, e1) = all_53_9
% 228.06/39.59    (75)  op(e1, e2) = all_53_6
% 228.06/39.59    (76)   ~ (all_6_2 = e0)
% 228.06/39.59    (77)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.06/39.59          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.06/39.59    (78)  all_24_2 = all_6_2
% 228.06/39.59    (79)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.06/39.59          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.06/39.59    (80)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.06/39.59          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.06/39.59    (81)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.06/39.59          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.06/39.59    (82)  all_57_14 = e0
% 228.06/39.59    (83)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.06/39.59          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.06/39.59    (84)  op(e3, e0) = all_52_7
% 228.06/39.59    (85)  op(e3, e1) = all_53_8
% 228.06/39.59    (86)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.06/39.59          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.06/39.59    (87)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.06/39.59          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.06/39.59    (88)  op(e3, e0) = all_53_12
% 228.06/39.59  
% 228.06/39.59  Begin of proof
% 228.06/39.59  | 
% 228.06/39.59  | BETA: splitting (71) gives:
% 228.06/39.59  | 
% 228.06/39.59  | Case 1:
% 228.06/39.59  | | 
% 228.06/39.59  | |   (89)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) =
% 228.06/39.59  | |           e3)
% 228.06/39.59  | | 
% 228.06/39.59  | | BETA: splitting (89) gives:
% 228.06/39.59  | | 
% 228.06/39.59  | | Case 1:
% 228.06/39.59  | | | 
% 228.06/39.59  | | |   (90)  all_57_0 = e3 & op(e3, e3) = e3
% 228.06/39.59  | | | 
% 228.06/39.59  | | | ALPHA: (90) implies:
% 228.06/39.59  | | |   (91)  op(e3, e3) = e3
% 228.06/39.59  | | | 
% 228.06/39.59  | | | REF_CLOSE: (3), (4), (5), (6), (9), (11), (12), (15), (16), (17), (19),
% 228.06/39.59  | | |            (20), (22), (27), (30), (31), (32), (34), (36), (37), (39),
% 228.06/39.59  | | |            (40), (44), (45), (46), (48), (51), (56), (59), (61), (62),
% 228.06/39.59  | | |            (63), (67), (69), (70), (73), (76), (77), (79), (80), (81),
% 228.06/39.59  | | |            (83), (84), (86), (87), (91) are inconsistent by sub-proof
% 228.06/39.59  | | |            #1453.
% 228.06/39.59  | | | 
% 228.06/39.59  | | Case 2:
% 228.06/39.59  | | | 
% 228.06/39.59  | | |   (92)  all_57_2 = e3 & op(e2, e3) = e3
% 228.06/39.59  | | | 
% 228.06/39.59  | | | ALPHA: (92) implies:
% 228.06/39.59  | | |   (93)  all_57_2 = e3
% 228.06/39.59  | | | 
% 228.06/39.59  | | | REF_CLOSE: (3), (10), (31), (47), (48), (55), (72), (93) are inconsistent
% 228.06/39.59  | | |            by sub-proof #1804.
% 228.06/39.59  | | | 
% 228.06/39.59  | | End of split
% 228.06/39.59  | | 
% 228.06/39.59  | Case 2:
% 228.06/39.59  | | 
% 228.06/39.59  | |   (94)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) =
% 228.06/39.59  | |           e3)
% 228.06/39.59  | | 
% 228.06/39.59  | | BETA: splitting (94) gives:
% 228.06/39.59  | | 
% 228.06/39.59  | | Case 1:
% 228.06/39.59  | | | 
% 228.06/39.59  | | |   (95)  all_57_6 = e3 & op(e1, e3) = e3
% 228.06/39.59  | | | 
% 228.06/39.59  | | | ALPHA: (95) implies:
% 228.06/39.59  | | |   (96)  all_57_6 = e3
% 228.06/39.59  | | | 
% 228.06/39.59  | | | BETA: splitting (87) gives:
% 228.06/39.59  | | | 
% 228.06/39.59  | | | Case 1:
% 228.06/39.59  | | | | 
% 228.06/39.59  | | | |   (97)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2)
% 228.06/39.59  | | | |           = e2)
% 228.06/39.59  | | | | 
% 228.06/39.59  | | | | BETA: splitting (97) gives:
% 228.06/39.59  | | | | 
% 228.06/39.59  | | | | Case 1:
% 228.06/39.59  | | | | | 
% 228.06/39.59  | | | | |   (98)  all_57_6 = e2 & op(e1, e3) = e2
% 228.06/39.59  | | | | | 
% 228.06/39.59  | | | | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (9), (10), (11), (12), (13),
% 228.06/39.59  | | | | |            (14), (15), (17), (18), (21), (22), (24), (25), (26), (27),
% 228.06/39.59  | | | | |            (29), (30), (31), (32), (33), (34), (35), (37), (39), (41),
% 228.06/39.59  | | | | |            (42), (43), (44), (46), (48), (49), (50), (51), (52), (54),
% 228.06/39.59  | | | | |            (55), (57), (58), (59), (60), (61), (62), (63), (64), (65),
% 228.06/39.59  | | | | |            (66), (67), (68), (69), (72), (73), (74), (75), (77), (78),
% 228.06/39.59  | | | | |            (79), (80), (81), (83), (85), (86), (87), (88), (96), (98)
% 228.06/39.59  | | | | |            are inconsistent by sub-proof #420.
% 228.06/39.59  | | | | | 
% 228.06/39.59  | | | | Case 2:
% 228.06/39.59  | | | | | 
% 228.06/39.59  | | | | |   (99)  all_57_7 = e2 & op(e1, e2) = e2
% 228.06/39.59  | | | | | 
% 228.06/39.59  | | | | | ALPHA: (99) implies:
% 228.06/39.59  | | | | |   (100)  all_57_7 = e2
% 228.06/39.59  | | | | | 
% 228.06/39.59  | | | | | COMBINE_EQS: (67), (100) imply:
% 228.06/39.59  | | | | |   (101)  e3 = e2
% 228.06/39.59  | | | | | 
% 228.06/39.59  | | | | | SIMP: (101) implies:
% 228.06/39.59  | | | | |   (102)  e3 = e2
% 228.06/39.59  | | | | | 
% 228.06/39.59  | | | | | COMBINE_EQS: (33), (102) imply:
% 228.06/39.59  | | | | |   (103)  all_57_4 = e2
% 228.06/39.59  | | | | | 
% 228.06/39.59  | | | | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (9), (10), (11), (12), (13),
% 228.06/39.59  | | | | |            (14), (15), (17), (18), (21), (22), (24), (25), (26), (27),
% 228.06/39.59  | | | | |            (29), (30), (31), (32), (34), (35), (37), (39), (41), (42),
% 228.06/39.59  | | | | |            (43), (44), (46), (48), (49), (50), (51), (52), (54), (55),
% 228.06/39.59  | | | | |            (57), (58), (59), (60), (61), (62), (63), (64), (65), (66),
% 228.06/39.59  | | | | |            (67), (68), (69), (72), (73), (74), (75), (77), (78), (79),
% 228.06/39.59  | | | | |            (80), (81), (83), (85), (86), (87), (88), (103) are
% 228.06/39.59  | | | | |            inconsistent by sub-proof #547.
% 228.06/39.59  | | | | | 
% 228.06/39.59  | | | | End of split
% 228.06/39.59  | | | | 
% 228.06/39.59  | | | Case 2:
% 228.06/39.59  | | | | 
% 228.06/39.59  | | | |   (104)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1,
% 228.06/39.59  | | | |              e0) = e2)
% 228.06/39.59  | | | | 
% 228.06/39.59  | | | | REF_CLOSE: (12), (23), (28), (38), (53), (72), (104) are inconsistent by
% 228.06/39.59  | | | |            sub-proof #409.
% 228.06/39.59  | | | | 
% 228.06/39.59  | | | End of split
% 228.06/39.59  | | | 
% 228.06/39.59  | | Case 2:
% 228.06/39.59  | | | 
% 228.06/39.59  | | |   (105)  all_57_12 = e3 & op(e0, e3) = e3
% 228.06/39.59  | | | 
% 228.06/39.59  | | | ALPHA: (105) implies:
% 228.06/39.59  | | |   (106)  all_57_12 = e3
% 228.06/39.59  | | | 
% 228.06/39.59  | | | REF_CLOSE: (10), (34), (44), (46), (51), (55), (61), (72), (82), (106) are
% 228.06/39.59  | | |            inconsistent by sub-proof #1763.
% 228.06/39.59  | | | 
% 228.06/39.59  | | End of split
% 228.06/39.59  | | 
% 228.06/39.59  | End of split
% 228.06/39.59  | 
% 228.06/39.59  End of proof
% 228.06/39.59  
% 228.06/39.59  Sub-proof #409 shows that the following formulas are inconsistent:
% 228.06/39.59  ----------------------------------------------------------------
% 228.06/39.59    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.06/39.59           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.06/39.59    (2)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) = all_22_1
% 228.06/39.59           & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0, e3) =
% 228.06/39.59           all_22_1 & $i(all_22_1))
% 228.06/39.59    (3)  all_57_8 = e1
% 228.06/39.59    (4)  op(e0, e3) = e1
% 228.06/39.59    (5)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) = all_12_1
% 228.06/39.59           & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0, e3) =
% 228.06/39.59           all_12_1 & $i(all_12_1))
% 228.06/39.59    (6)   ~ (e2 = e1)
% 228.06/39.59    (7)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.06/39.59  
% 228.06/39.59  Begin of proof
% 228.06/39.59  | 
% 228.06/39.59  | BETA: splitting (7) gives:
% 228.06/39.59  | 
% 228.06/39.59  | Case 1:
% 228.06/39.59  | | 
% 228.06/39.59  | |   (8)  all_57_8 = e2 & op(e1, e1) = e2
% 228.06/39.59  | | 
% 228.06/39.59  | | ALPHA: (8) implies:
% 228.06/39.59  | |   (9)  all_57_8 = e2
% 228.06/39.59  | | 
% 228.06/39.59  | | REF_CLOSE: (3), (6), (9) are inconsistent by sub-proof #1485.
% 228.06/39.59  | | 
% 228.06/39.59  | Case 2:
% 228.06/39.59  | | 
% 228.06/39.59  | |   (10)  all_57_11 = e2 & op(e1, e0) = e2
% 228.06/39.59  | | 
% 228.06/39.59  | | ALPHA: (10) implies:
% 228.06/39.59  | |   (11)  op(e1, e0) = e2
% 228.06/39.59  | | 
% 228.06/39.59  | | REF_CLOSE: (1), (2), (4), (5), (11) are inconsistent by sub-proof #1147.
% 228.06/39.59  | | 
% 228.06/39.59  | End of split
% 228.06/39.59  | 
% 228.06/39.59  End of proof
% 228.06/39.59  
% 228.06/39.59  Sub-proof #410 shows that the following formulas are inconsistent:
% 228.06/39.59  ----------------------------------------------------------------
% 228.06/39.59    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.06/39.59    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.06/39.59    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.06/39.59         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.06/39.59    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.06/39.59         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.06/39.59    (5)  op(e2, e1) = e3
% 228.06/39.59    (6)   ~ (all_53_8 = all_53_12)
% 228.06/39.59    (7)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.06/39.59         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.06/39.59    (8)   ~ (e3 = e1)
% 228.06/39.59    (9)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.06/39.59         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.06/39.59    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.06/39.59            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.06/39.59    (11)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.06/39.59          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.06/39.59    (12)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.06/39.59            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.06/39.59              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.06/39.59    (13)   ~ (all_6_2 = e3)
% 228.06/39.59    (14)  op(e1, e1) = all_6_2
% 228.06/39.59    (15)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.06/39.59    (16)   ~ (all_53_9 = e0)
% 228.06/39.59    (17)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.06/39.59          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.06/39.59    (18)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 228.06/39.59            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 228.06/39.59              e3) = all_22_1 & $i(all_22_1))
% 228.06/39.59    (19)   ~ (all_53_4 = all_53_12)
% 228.06/39.59    (20)   ~ (all_53_8 = all_53_9)
% 228.06/39.59    (21)  all_42_2 = all_6_2
% 228.06/39.59    (22)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.06/39.59          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.06/39.59    (23)  op(e2, e2) = e0
% 228.06/39.59    (24)  all_57_8 = e1
% 228.06/39.59    (25)   ~ (all_53_9 = all_6_2)
% 228.06/39.59    (26)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.06/39.59          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.06/39.59    (27)  all_57_3 = e0
% 228.06/39.59    (28)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.06/39.59          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.06/39.59    (29)   ~ (e3 = e2)
% 228.06/39.59    (30)  all_55_1 = all_53_4
% 228.06/39.59    (31)   ~ (e3 = e0)
% 228.06/39.59    (32)  op(e0, e3) = e1
% 228.06/39.59    (33)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.06/39.59          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.06/39.59    (34)   ~ (all_53_8 = all_6_2)
% 228.06/39.59    (35)  all_55_2 = all_53_8
% 228.06/39.59    (36)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.06/39.59    (37)  all_57_15 = e3
% 228.06/39.59    (38)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.06/39.59          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.06/39.59            e1)
% 228.06/39.59    (39)  all_57_10 = e2
% 228.06/39.59    (40)  all_57_5 = e3
% 228.06/39.59    (41)  all_57_12 = e1
% 228.06/39.59    (42)   ~ (all_53_4 = all_53_8)
% 228.06/39.59    (43)  op(e3, e2) = all_53_4
% 228.06/39.59    (44)   ~ (e2 = e0)
% 228.06/39.59    (45)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.06/39.59            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.06/39.59            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.06/39.59            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.06/39.59              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.06/39.59            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.06/39.59            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.06/39.59              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.06/39.59              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.06/39.59            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.06/39.59            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.06/39.59            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.06/39.59              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.06/39.59              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.06/39.59            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.06/39.59              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.06/39.59            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.06/39.59            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.06/39.59              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.06/39.59              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.06/39.59            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.06/39.59            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.06/39.59    (46)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 228.06/39.59            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 228.06/39.59              e3) = all_12_1 & $i(all_12_1))
% 228.06/39.59    (47)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.06/39.59          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.06/39.59    (48)   ~ (e1 = e0)
% 228.06/39.60    (49)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.06/39.60            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.06/39.60              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.06/39.60    (50)   ~ (all_53_4 = e0)
% 228.06/39.60    (51)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.06/39.60          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.06/39.60    (52)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.06/39.60          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.06/39.60    (53)  op(e0, e0) = e3
% 228.06/39.60    (54)   ~ (all_53_4 = all_53_6)
% 228.06/39.60    (55)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.06/39.60          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.06/39.60            e2)
% 228.06/39.60    (56)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.06/39.60              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.06/39.60                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.06/39.60                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.06/39.60    (57)  all_55_10 = all_6_2
% 228.06/39.60    (58)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.06/39.60          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.06/39.60    (59)  all_38_2 = all_6_2
% 228.06/39.60    (60)  all_55_3 = all_53_12
% 228.06/39.60    (61)   ~ (all_53_12 = e3)
% 228.06/39.60    (62)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.06/39.60            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.06/39.60              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.06/39.60    (63)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.06/39.60          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.06/39.60    (64)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.06/39.60          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.06/39.60    (65)  all_57_1 = e3
% 228.06/39.60    (66)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) |
% 228.06/39.60          (all_57_11 = e0 & op(e1, e0) = e0)
% 228.06/39.60    (67)   ~ (e2 = e1)
% 228.06/39.60    (68)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.06/39.60          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.06/39.60    (69)  op(e2, e1) = all_53_9
% 228.06/39.60    (70)  op(e1, e2) = all_53_6
% 228.06/39.60    (71)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.06/39.60          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.06/39.60    (72)  all_24_2 = all_6_2
% 228.06/39.60    (73)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.06/39.60          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.06/39.60    (74)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.06/39.60          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.06/39.60    (75)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.06/39.60          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.06/39.60    (76)  all_57_14 = e0
% 228.06/39.60    (77)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.06/39.60          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.06/39.60    (78)  op(e3, e1) = all_53_8
% 228.06/39.60    (79)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.06/39.60          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.06/39.60    (80)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.06/39.60          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.06/39.60    (81)  op(e3, e0) = all_53_12
% 228.06/39.60  
% 228.06/39.60  Begin of proof
% 228.06/39.60  | 
% 228.06/39.60  | BETA: splitting (3) gives:
% 228.06/39.60  | 
% 228.06/39.60  | Case 1:
% 228.06/39.60  | | 
% 228.06/39.60  | |   (82)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) =
% 228.06/39.60  | |           e1)
% 228.06/39.60  | | 
% 228.06/39.60  | | BETA: splitting (82) gives:
% 228.06/39.60  | | 
% 228.06/39.60  | | Case 1:
% 228.06/39.60  | | | 
% 228.06/39.60  | | |   (83)  all_57_2 = e1 & op(e2, e3) = e1
% 228.06/39.60  | | | 
% 228.06/39.60  | | | ALPHA: (83) implies:
% 228.06/39.60  | | |   (84)  all_57_2 = e1
% 228.06/39.60  | | | 
% 228.06/39.60  | | | BETA: splitting (55) gives:
% 228.06/39.60  | | | 
% 228.06/39.60  | | | Case 1:
% 228.06/39.60  | | | | 
% 228.06/39.60  | | | |   (85)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0,
% 228.06/39.60  | | | |             e2) = e2)
% 228.06/39.60  | | | | 
% 228.06/39.60  | | | | BETA: splitting (85) gives:
% 228.06/39.60  | | | | 
% 228.06/39.60  | | | | Case 1:
% 228.06/39.60  | | | | | 
% 228.06/39.60  | | | | |   (86)  all_57_12 = e2 & op(e0, e3) = e2
% 228.06/39.60  | | | | | 
% 228.06/39.60  | | | | | ALPHA: (86) implies:
% 228.06/39.60  | | | | |   (87)  all_57_12 = e2
% 228.06/39.60  | | | | | 
% 228.06/39.60  | | | | | REF_CLOSE: (41), (67), (87) are inconsistent by sub-proof #2321.
% 228.06/39.60  | | | | | 
% 228.06/39.60  | | | | Case 2:
% 228.06/39.60  | | | | | 
% 228.06/39.60  | | | | |   (88)  all_57_13 = e2 & op(e0, e2) = e2
% 228.06/39.60  | | | | | 
% 228.06/39.60  | | | | | ALPHA: (88) implies:
% 228.06/39.60  | | | | |   (89)  all_57_13 = e2
% 228.06/39.60  | | | | | 
% 228.06/39.60  | | | | | BETA: splitting (71) gives:
% 228.06/39.60  | | | | | 
% 228.06/39.60  | | | | | Case 1:
% 228.06/39.60  | | | | | | 
% 228.06/39.60  | | | | | |   (90)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2,
% 228.06/39.60  | | | | | |             e3) = e2)
% 228.06/39.60  | | | | | | 
% 228.06/39.60  | | | | | | BETA: splitting (90) gives:
% 228.06/39.60  | | | | | | 
% 228.06/39.60  | | | | | | Case 1:
% 228.06/39.60  | | | | | | | 
% 228.06/39.60  | | | | | | |   (91)  all_57_0 = e2 & op(e3, e3) = e2
% 228.06/39.60  | | | | | | | 
% 228.06/39.60  | | | | | | | ALPHA: (91) implies:
% 228.06/39.60  | | | | | | |   (92)  all_57_0 = e2
% 228.06/39.60  | | | | | | |   (93)  op(e3, e3) = e2
% 228.06/39.60  | | | | | | | 
% 228.06/39.60  | | | | | | | BETA: splitting (11) gives:
% 228.06/39.60  | | | | | | | 
% 228.06/39.60  | | | | | | | Case 1:
% 228.06/39.60  | | | | | | | | 
% 228.06/39.60  | | | | | | | |   (94)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 &
% 228.06/39.60  | | | | | | | |           op(e1, e2) = e3)
% 228.06/39.60  | | | | | | | | 
% 228.06/39.60  | | | | | | | | BETA: splitting (94) gives:
% 228.06/39.60  | | | | | | | | 
% 228.06/39.60  | | | | | | | | Case 1:
% 228.06/39.60  | | | | | | | | | 
% 228.06/39.60  | | | | | | | | |   (95)  all_57_6 = e3 & op(e1, e3) = e3
% 228.06/39.60  | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | ALPHA: (95) implies:
% 228.06/39.60  | | | | | | | | |   (96)  all_57_6 = e3
% 228.06/39.60  | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | REF_CLOSE: (3), (8), (10), (27), (29), (31), (40), (41), (44),
% 228.06/39.60  | | | | | | | | |            (48), (63), (67), (74), (93), (96) are inconsistent
% 228.06/39.60  | | | | | | | | |            by sub-proof #810.
% 228.06/39.60  | | | | | | | | | 
% 228.06/39.60  | | | | | | | | Case 2:
% 228.06/39.60  | | | | | | | | | 
% 228.06/39.60  | | | | | | | | |   (97)  all_57_7 = e3 & op(e1, e2) = e3
% 228.06/39.60  | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | ALPHA: (97) implies:
% 228.06/39.60  | | | | | | | | |   (98)  all_57_7 = e3
% 228.06/39.60  | | | | | | | | |   (99)  op(e1, e2) = e3
% 228.06/39.60  | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | BETA: splitting (68) gives:
% 228.06/39.60  | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | Case 1:
% 228.06/39.60  | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | |   (100)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2
% 228.06/39.60  | | | | | | | | | |            & op(e2, e0) = e2)
% 228.06/39.60  | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | BETA: splitting (100) gives:
% 228.06/39.60  | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | Case 1:
% 228.06/39.60  | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | |   (101)  all_57_9 = e2 & op(e3, e0) = e2
% 228.06/39.60  | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 228.06/39.60  | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 228.06/39.60  | | | | | | | | | | |            (19), (20), (21), (22), (24), (25), (26), (27),
% 228.06/39.60  | | | | | | | | | | |            (28), (29), (30), (31), (33), (34), (35), (36),
% 228.06/39.60  | | | | | | | | | | |            (37), (38), (40), (42), (43), (44), (45), (46),
% 228.06/39.60  | | | | | | | | | | |            (47), (48), (49), (50), (51), (52), (53), (54),
% 228.06/39.60  | | | | | | | | | | |            (55), (56), (57), (58), (59), (60), (61), (62),
% 228.06/39.60  | | | | | | | | | | |            (63), (64), (67), (68), (69), (70), (71), (72),
% 228.06/39.60  | | | | | | | | | | |            (73), (74), (75), (77), (78), (79), (80), (81),
% 228.06/39.60  | | | | | | | | | | |            (92), (93), (101) are inconsistent by sub-proof
% 228.06/39.60  | | | | | | | | | | |            #411.
% 228.06/39.60  | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | Case 2:
% 228.06/39.60  | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | |   (102)  all_57_10 = e2 & op(e2, e0) = e2
% 228.06/39.60  | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | BETA: splitting (28) gives:
% 228.06/39.60  | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | Case 1:
% 228.06/39.60  | | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | |   (103)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 228.06/39.60  | | | | | | | | | | | |            & op(e2, e1) = e0)
% 228.06/39.60  | | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | | BETA: splitting (103) gives:
% 228.06/39.60  | | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | | Case 1:
% 228.06/39.60  | | | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | | |   (104)  all_57_4 = e0 & op(e3, e1) = e0
% 228.06/39.60  | | | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | | | ALPHA: (104) implies:
% 228.06/39.60  | | | | | | | | | | | | |   (105)  all_57_4 = e0
% 228.06/39.60  | | | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | | | BETA: splitting (64) gives:
% 228.06/39.60  | | | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | | | Case 1:
% 228.06/39.60  | | | | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | | | |   (106)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 228.06/39.60  | | | | | | | | | | | | | |            & op(e2, e3) = e3)
% 228.06/39.60  | | | | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | | | | BETA: splitting (106) gives:
% 228.06/39.60  | | | | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | | | | Case 1:
% 228.06/39.60  | | | | | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | | | | |   (107)  all_57_0 = e3 & op(e3, e3) = e3
% 228.06/39.60  | | | | | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | | | | | ALPHA: (107) implies:
% 228.06/39.60  | | | | | | | | | | | | | | |   (108)  all_57_0 = e3
% 228.06/39.60  | | | | | | | | | | | | | | |   (109)  op(e3, e3) = e3
% 228.06/39.60  | | | | | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 228.06/39.60  | | | | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (19),
% 228.06/39.60  | | | | | | | | | | | | | | |            (20), (21), (22), (25), (26), (27), (28), (29),
% 228.06/39.60  | | | | | | | | | | | | | | |            (30), (31), (33), (34), (35), (36), (37), (38),
% 228.06/39.60  | | | | | | | | | | | | | | |            (40), (42), (43), (44), (45), (48), (49), (50),
% 228.06/39.60  | | | | | | | | | | | | | | |            (53), (54), (55), (56), (57), (59), (60), (61),
% 228.06/39.60  | | | | | | | | | | | | | | |            (62), (63), (67), (68), (69), (70), (71), (72),
% 228.06/39.60  | | | | | | | | | | | | | | |            (73), (74), (75), (77), (78), (79), (80), (81),
% 228.06/39.60  | | | | | | | | | | | | | | |            (108), (109) are inconsistent by sub-proof #1440.
% 228.06/39.60  | | | | | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | | | | Case 2:
% 228.06/39.60  | | | | | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | | | | |   (110)  all_57_2 = e3 & op(e2, e3) = e3
% 228.06/39.60  | | | | | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | | | | | ALPHA: (110) implies:
% 228.06/39.60  | | | | | | | | | | | | | | |   (111)  all_57_2 = e3
% 228.06/39.60  | | | | | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | | | | | REF_CLOSE: (3), (8), (10), (13), (14), (27), (29), (31),
% 228.06/39.60  | | | | | | | | | | | | | | |            (37), (38), (39), (44), (48), (51), (55), (56),
% 228.06/39.60  | | | | | | | | | | | | | | |            (58), (63), (67), (105), (111) are inconsistent by
% 228.06/39.60  | | | | | | | | | | | | | | |            sub-proof #747.
% 228.06/39.60  | | | | | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | | | | End of split
% 228.06/39.60  | | | | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | | | Case 2:
% 228.06/39.60  | | | | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | | | |   (112)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 228.06/39.60  | | | | | | | | | | | | | |            e3 & op(e0, e3) = e3)
% 228.06/39.60  | | | | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | | | | BETA: splitting (112) gives:
% 228.06/39.60  | | | | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | | | | Case 1:
% 228.06/39.60  | | | | | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | | | | |   (113)  all_57_6 = e3 & op(e1, e3) = e3
% 228.06/39.60  | | | | | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | | | | | ALPHA: (113) implies:
% 228.06/39.60  | | | | | | | | | | | | | | |   (114)  all_57_6 = e3
% 228.06/39.60  | | | | | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | | | | | REF_CLOSE: (3), (8), (10), (27), (29), (31), (40), (41),
% 228.06/39.60  | | | | | | | | | | | | | | |            (44), (48), (63), (67), (74), (93), (114) are
% 228.06/39.60  | | | | | | | | | | | | | | |            inconsistent by sub-proof #810.
% 228.06/39.60  | | | | | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | | | | Case 2:
% 228.06/39.60  | | | | | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | | | | |   (115)  all_57_12 = e3 & op(e0, e3) = e3
% 228.06/39.60  | | | | | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | | | | | ALPHA: (115) implies:
% 228.06/39.60  | | | | | | | | | | | | | | |   (116)  all_57_12 = e3
% 228.06/39.60  | | | | | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 228.06/39.60  | | | | | | | | | | | | | | |            (12), (14), (15), (16), (17), (19), (20), (21),
% 228.06/39.60  | | | | | | | | | | | | | | |            (22), (24), (25), (26), (27), (28), (29), (30),
% 228.06/39.60  | | | | | | | | | | | | | | |            (31), (33), (34), (35), (36), (37), (38), (40),
% 228.06/39.60  | | | | | | | | | | | | | | |            (42), (43), (44), (45), (47), (48), (49), (50),
% 228.06/39.60  | | | | | | | | | | | | | | |            (53), (54), (55), (56), (57), (59), (60), (61),
% 228.06/39.60  | | | | | | | | | | | | | | |            (62), (63), (67), (68), (69), (70), (71), (72),
% 228.06/39.60  | | | | | | | | | | | | | | |            (73), (74), (75), (77), (78), (79), (80), (81),
% 228.06/39.60  | | | | | | | | | | | | | | |            (84), (98), (99), (116) are inconsistent by
% 228.06/39.60  | | | | | | | | | | | | | | |            sub-proof #475.
% 228.06/39.60  | | | | | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | | | | End of split
% 228.06/39.60  | | | | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | | | End of split
% 228.06/39.60  | | | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | | Case 2:
% 228.06/39.60  | | | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | | |   (117)  all_57_5 = e0 & op(e2, e1) = e0
% 228.06/39.60  | | | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | | | REF_CLOSE: (31), (40), (117) are inconsistent by sub-proof
% 228.06/39.60  | | | | | | | | | | | | |            #2414.
% 228.06/39.60  | | | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | | End of split
% 228.06/39.60  | | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | Case 2:
% 228.06/39.60  | | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | |   (118)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 228.06/39.60  | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 228.06/39.60  | | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | | BETA: splitting (118) gives:
% 228.06/39.60  | | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | | Case 1:
% 228.06/39.60  | | | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | | |   (119)  all_57_8 = e0 & op(e1, e1) = e0
% 228.06/39.60  | | | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | | | REF_CLOSE: (3), (8), (24), (27), (29), (40), (44), (48),
% 228.06/39.60  | | | | | | | | | | | | |            (63), (67), (84), (119) are inconsistent by
% 228.06/39.60  | | | | | | | | | | | | |            sub-proof #492.
% 228.06/39.60  | | | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | | Case 2:
% 228.06/39.60  | | | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | | |   (120)  all_57_14 = e0 & op(e0, e1) = e0
% 228.06/39.60  | | | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | | | BETA: splitting (64) gives:
% 228.06/39.60  | | | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | | | Case 1:
% 228.06/39.60  | | | | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | | | |   (121)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 228.06/39.60  | | | | | | | | | | | | | |            & op(e2, e3) = e3)
% 228.06/39.60  | | | | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 228.06/39.60  | | | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (19),
% 228.06/39.60  | | | | | | | | | | | | | |            (20), (21), (22), (25), (26), (27), (28), (29),
% 228.06/39.60  | | | | | | | | | | | | | |            (30), (31), (33), (34), (35), (36), (37), (38),
% 228.06/39.60  | | | | | | | | | | | | | |            (39), (40), (42), (43), (44), (45), (48), (49),
% 228.06/39.60  | | | | | | | | | | | | | |            (50), (53), (54), (55), (56), (57), (59), (60),
% 228.06/39.60  | | | | | | | | | | | | | |            (61), (62), (63), (67), (68), (69), (70), (71),
% 228.06/39.60  | | | | | | | | | | | | | |            (72), (73), (74), (75), (77), (78), (79), (80),
% 228.06/39.60  | | | | | | | | | | | | | |            (81), (121) are inconsistent by sub-proof #495.
% 228.06/39.60  | | | | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | | | Case 2:
% 228.06/39.60  | | | | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | | | |   (122)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 228.06/39.60  | | | | | | | | | | | | | |            e3 & op(e0, e3) = e3)
% 228.06/39.60  | | | | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | | | | BETA: splitting (122) gives:
% 228.06/39.60  | | | | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | | | | Case 1:
% 228.06/39.60  | | | | | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | | | | |   (123)  all_57_6 = e3 & op(e1, e3) = e3
% 228.06/39.60  | | | | | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | | | | | ALPHA: (123) implies:
% 228.06/39.60  | | | | | | | | | | | | | | |   (124)  all_57_6 = e3
% 228.06/39.60  | | | | | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | | | | | REF_CLOSE: (3), (8), (10), (27), (29), (31), (40), (41),
% 228.06/39.60  | | | | | | | | | | | | | | |            (44), (48), (63), (67), (74), (93), (124) are
% 228.06/39.60  | | | | | | | | | | | | | | |            inconsistent by sub-proof #810.
% 228.06/39.60  | | | | | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | | | | Case 2:
% 228.06/39.60  | | | | | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | | | | |   (125)  all_57_12 = e3 & op(e0, e3) = e3
% 228.06/39.60  | | | | | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | | | | | ALPHA: (125) implies:
% 228.06/39.60  | | | | | | | | | | | | | | |   (126)  all_57_12 = e3
% 228.06/39.60  | | | | | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | | | | | REF_CLOSE: (8), (29), (37), (38), (44), (48), (55), (67),
% 228.06/39.60  | | | | | | | | | | | | | | |            (76), (126) are inconsistent by sub-proof #1763.
% 228.06/39.60  | | | | | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | | | | End of split
% 228.06/39.60  | | | | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | | | End of split
% 228.06/39.60  | | | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | | End of split
% 228.06/39.60  | | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | End of split
% 228.06/39.60  | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | End of split
% 228.06/39.60  | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | Case 2:
% 228.06/39.60  | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | |   (127)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 228.06/39.60  | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 228.06/39.60  | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | BETA: splitting (127) gives:
% 228.06/39.60  | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | Case 1:
% 228.06/39.60  | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | |   (128)  all_57_11 = e2 & op(e1, e0) = e2
% 228.06/39.60  | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | ALPHA: (128) implies:
% 228.06/39.60  | | | | | | | | | | |   (129)  op(e1, e0) = e2
% 228.06/39.60  | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | REF_CLOSE: (10), (18), (32), (46), (129) are inconsistent by
% 228.06/39.60  | | | | | | | | | | |            sub-proof #1147.
% 228.06/39.60  | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | Case 2:
% 228.06/39.60  | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | |   (130)  all_57_15 = e2 & op(e0, e0) = e2
% 228.06/39.60  | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | ALPHA: (130) implies:
% 228.06/39.60  | | | | | | | | | | |   (131)  all_57_15 = e2
% 228.06/39.60  | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | COMBINE_EQS: (37), (131) imply:
% 228.06/39.60  | | | | | | | | | | |   (132)  e3 = e2
% 228.06/39.60  | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | COMBINE_EQS: (40), (132) imply:
% 228.06/39.60  | | | | | | | | | | |   (133)  all_57_5 = e2
% 228.06/39.60  | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10),
% 228.06/39.60  | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 228.06/39.60  | | | | | | | | | | |            (19), (20), (21), (22), (24), (25), (26), (27),
% 228.06/39.60  | | | | | | | | | | |            (28), (29), (30), (31), (33), (34), (35), (36),
% 228.06/39.60  | | | | | | | | | | |            (37), (38), (42), (43), (44), (45), (46), (47),
% 228.06/39.60  | | | | | | | | | | |            (48), (49), (50), (51), (52), (53), (54), (55),
% 228.06/39.60  | | | | | | | | | | |            (56), (57), (58), (59), (60), (61), (62), (63),
% 228.06/39.60  | | | | | | | | | | |            (64), (67), (68), (69), (70), (71), (72), (73),
% 228.06/39.60  | | | | | | | | | | |            (74), (75), (77), (78), (79), (80), (81), (92),
% 228.06/39.60  | | | | | | | | | | |            (93), (133) are inconsistent by sub-proof #496.
% 228.06/39.60  | | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | | End of split
% 228.06/39.60  | | | | | | | | | | 
% 228.06/39.60  | | | | | | | | | End of split
% 228.06/39.60  | | | | | | | | | 
% 228.06/39.60  | | | | | | | | End of split
% 228.06/39.60  | | | | | | | | 
% 228.06/39.60  | | | | | | | Case 2:
% 228.06/39.60  | | | | | | | | 
% 228.06/39.60  | | | | | | | |   (134)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 &
% 228.06/39.60  | | | | | | | |            op(e1, e0) = e3)
% 228.06/39.60  | | | | | | | | 
% 228.06/39.60  | | | | | | | | REF_CLOSE: (8), (10), (13), (14), (29), (31), (37), (44), (48),
% 228.06/39.60  | | | | | | | |            (56), (67), (68), (75), (134) are inconsistent by
% 228.06/39.60  | | | | | | | |            sub-proof #1786.
% 228.06/39.60  | | | | | | | | 
% 228.06/39.60  | | | | | | | End of split
% 228.06/39.60  | | | | | | | 
% 228.06/39.60  | | | | | | Case 2:
% 228.06/39.60  | | | | | | | 
% 228.06/39.60  | | | | | | |   (135)  all_57_2 = e2 & op(e2, e3) = e2
% 228.06/39.60  | | | | | | | 
% 228.06/39.60  | | | | | | | ALPHA: (135) implies:
% 228.06/39.60  | | | | | | |   (136)  all_57_2 = e2
% 228.06/39.60  | | | | | | | 
% 228.06/39.60  | | | | | | | REF_CLOSE: (67), (84), (136) are inconsistent by sub-proof #2464.
% 228.06/39.60  | | | | | | | 
% 228.06/39.60  | | | | | | End of split
% 228.06/39.60  | | | | | | 
% 228.06/39.60  | | | | | Case 2:
% 228.06/39.60  | | | | | | 
% 228.06/39.60  | | | | | |   (137)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 &
% 228.06/39.60  | | | | | |            op(e0, e3) = e2)
% 228.06/39.60  | | | | | | 
% 228.06/39.60  | | | | | | REF_CLOSE: (8), (10), (11), (13), (14), (27), (29), (31), (37),
% 228.06/39.60  | | | | | |            (41), (44), (48), (65), (66), (67), (68), (75), (79),
% 228.06/39.60  | | | | | |            (89), (137) are inconsistent by sub-proof #418.
% 228.06/39.60  | | | | | | 
% 228.06/39.60  | | | | | End of split
% 228.06/39.60  | | | | | 
% 228.06/39.60  | | | | End of split
% 228.06/39.60  | | | | 
% 228.06/39.60  | | | Case 2:
% 228.06/39.60  | | | | 
% 228.06/39.60  | | | |   (138)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0,
% 228.06/39.60  | | | |              e0) = e2)
% 228.06/39.60  | | | | 
% 228.06/39.60  | | | | BETA: splitting (138) gives:
% 228.06/39.60  | | | | 
% 228.06/39.60  | | | | Case 1:
% 228.06/39.60  | | | | | 
% 228.06/39.60  | | | | |   (139)  all_57_14 = e2 & op(e0, e1) = e2
% 228.06/39.60  | | | | | 
% 228.06/39.60  | | | | | ALPHA: (139) implies:
% 228.06/39.60  | | | | |   (140)  all_57_14 = e2
% 228.06/39.60  | | | | | 
% 228.06/39.60  | | | | | COMBINE_EQS: (76), (140) imply:
% 228.06/39.60  | | | | |   (141)  e2 = e0
% 228.06/39.60  | | | | | 
% 228.06/39.60  | | | | | REF_CLOSE: (3), (8), (27), (29), (39), (40), (44), (48), (63), (67),
% 228.06/39.60  | | | | |            (141) are inconsistent by sub-proof #1517.
% 228.06/39.60  | | | | | 
% 228.06/39.60  | | | | Case 2:
% 228.06/39.60  | | | | | 
% 228.06/39.60  | | | | |   (142)  all_57_15 = e2 & op(e0, e0) = e2
% 228.06/39.60  | | | | | 
% 228.06/39.60  | | | | | ALPHA: (142) implies:
% 228.06/39.60  | | | | |   (143)  all_57_15 = e2
% 228.06/39.60  | | | | | 
% 228.06/39.60  | | | | | REF_CLOSE: (29), (37), (143) are inconsistent by sub-proof #2058.
% 228.06/39.60  | | | | | 
% 228.06/39.60  | | | | End of split
% 228.06/39.60  | | | | 
% 228.06/39.60  | | | End of split
% 228.06/39.60  | | | 
% 228.06/39.60  | | Case 2:
% 228.06/39.60  | | | 
% 228.06/39.60  | | |   (144)  all_57_3 = e1 & op(e2, e2) = e1
% 228.06/39.60  | | | 
% 228.06/39.60  | | | ALPHA: (144) implies:
% 228.06/39.60  | | |   (145)  op(e2, e2) = e1
% 228.06/39.60  | | | 
% 228.06/39.60  | | | REF_CLOSE: (10), (23), (48), (145) are inconsistent by sub-proof #2352.
% 228.06/39.60  | | | 
% 228.06/39.60  | | End of split
% 228.06/39.60  | | 
% 228.06/39.60  | Case 2:
% 228.06/39.60  | | 
% 228.06/39.60  | |   (146)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) =
% 228.06/39.60  | |            e1)
% 228.06/39.60  | | 
% 228.06/39.60  | | BETA: splitting (146) gives:
% 228.06/39.60  | | 
% 228.06/39.60  | | Case 1:
% 228.06/39.60  | | | 
% 228.06/39.60  | | |   (147)  all_57_5 = e1 & op(e2, e1) = e1
% 228.06/39.60  | | | 
% 228.06/39.60  | | | REF_CLOSE: (8), (40), (147) are inconsistent by sub-proof #2376.
% 228.06/39.60  | | | 
% 228.06/39.60  | | Case 2:
% 228.06/39.60  | | | 
% 228.06/39.60  | | |   (148)  all_57_10 = e1 & op(e2, e0) = e1
% 228.06/39.60  | | | 
% 228.06/39.60  | | | REF_CLOSE: (39), (67), (148) are inconsistent by sub-proof #2360.
% 228.06/39.60  | | | 
% 228.06/39.60  | | End of split
% 228.06/39.60  | | 
% 228.06/39.60  | End of split
% 228.06/39.60  | 
% 228.06/39.60  End of proof
% 228.06/39.60  
% 228.06/39.60  Sub-proof #411 shows that the following formulas are inconsistent:
% 228.06/39.60  ----------------------------------------------------------------
% 228.06/39.60    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.06/39.60    (2)  all_57_0 = e2
% 228.06/39.60    (3)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.06/39.60    (4)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.06/39.60         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.06/39.60    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.06/39.60         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.06/39.60    (6)  op(e2, e1) = e3
% 228.06/39.60    (7)   ~ (all_53_8 = all_53_12)
% 228.06/39.60    (8)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.06/39.60         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.06/39.60    (9)   ~ (e3 = e1)
% 228.06/39.60    (10)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.06/39.60          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.06/39.60    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.06/39.60            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.06/39.60    (12)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.06/39.60          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.06/39.60    (13)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.06/39.60            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.06/39.60              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.06/39.60    (14)   ~ (all_6_2 = e3)
% 228.06/39.60    (15)  all_57_9 = e2 & op(e3, e0) = e2
% 228.06/39.60    (16)  op(e1, e1) = all_6_2
% 228.06/39.60    (17)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.06/39.60    (18)   ~ (all_53_9 = e0)
% 228.06/39.60    (19)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.06/39.60          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.06/39.60    (20)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 228.06/39.60            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 228.06/39.60              e3) = all_22_1 & $i(all_22_1))
% 228.06/39.60    (21)   ~ (all_53_4 = all_53_12)
% 228.06/39.60    (22)   ~ (all_53_8 = all_53_9)
% 228.06/39.60    (23)  all_42_2 = all_6_2
% 228.06/39.60    (24)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.06/39.60          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.06/39.60    (25)  all_57_8 = e1
% 228.06/39.60    (26)   ~ (all_53_9 = all_6_2)
% 228.06/39.60    (27)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.06/39.60          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.06/39.60    (28)  all_57_3 = e0
% 228.06/39.60    (29)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.06/39.60          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.06/39.60    (30)   ~ (e3 = e2)
% 228.06/39.60    (31)  all_55_1 = all_53_4
% 228.06/39.60    (32)   ~ (e3 = e0)
% 228.06/39.60    (33)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.06/39.60          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.06/39.60    (34)   ~ (all_53_8 = all_6_2)
% 228.06/39.60    (35)  all_55_2 = all_53_8
% 228.06/39.60    (36)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.06/39.60    (37)  all_57_15 = e3
% 228.06/39.60    (38)  op(e3, e3) = e2
% 228.06/39.60    (39)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.06/39.60          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.06/39.60            e1)
% 228.06/39.60    (40)  all_57_5 = e3
% 228.06/39.60    (41)   ~ (all_53_4 = all_53_8)
% 228.06/39.60    (42)  op(e3, e2) = all_53_4
% 228.06/39.60    (43)   ~ (e2 = e0)
% 228.06/39.60    (44)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.06/39.60            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.06/39.60            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.06/39.60            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.06/39.60              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.06/39.60            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.06/39.60            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.06/39.60              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.06/39.60              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.06/39.60            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.06/39.60            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.06/39.60            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.06/39.60              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.06/39.60              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.06/39.60            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.06/39.60              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.06/39.60            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.06/39.60            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.06/39.60              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.06/39.60              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.06/39.60            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.06/39.60            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.06/39.60    (45)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 228.06/39.60            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 228.06/39.60              e3) = all_12_1 & $i(all_12_1))
% 228.06/39.60    (46)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.06/39.60          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.06/39.60    (47)   ~ (e1 = e0)
% 228.06/39.60    (48)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.06/39.60            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.06/39.60              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.06/39.60    (49)   ~ (all_53_4 = e0)
% 228.06/39.60    (50)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.06/39.60          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.06/39.60    (51)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.06/39.60          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.06/39.60    (52)  op(e0, e0) = e3
% 228.06/39.60    (53)   ~ (all_53_4 = all_53_6)
% 228.06/39.60    (54)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.06/39.60          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.06/39.60            e2)
% 228.06/39.60    (55)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.06/39.60              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.06/39.60                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.06/39.60                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.06/39.60    (56)  all_55_10 = all_6_2
% 228.06/39.60    (57)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.06/39.60          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.06/39.60    (58)  all_38_2 = all_6_2
% 228.06/39.60    (59)  all_55_3 = all_53_12
% 228.06/39.60    (60)   ~ (all_53_12 = e3)
% 228.06/39.60    (61)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.06/39.60            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.06/39.60              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.06/39.60    (62)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.06/39.60          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.06/39.60    (63)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.06/39.60          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.06/39.60    (64)   ~ (e2 = e1)
% 228.06/39.60    (65)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.06/39.60          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.06/39.60    (66)  op(e2, e1) = all_53_9
% 228.06/39.60    (67)  op(e1, e2) = all_53_6
% 228.06/39.60    (68)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.06/39.60          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.06/39.60    (69)  all_24_2 = all_6_2
% 228.06/39.60    (70)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.06/39.60          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.06/39.60    (71)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.06/39.60          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.06/39.60    (72)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.06/39.60          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.06/39.61    (73)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.06/39.61          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.06/39.61    (74)  op(e3, e1) = all_53_8
% 228.06/39.61    (75)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.06/39.61          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.06/39.61    (76)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.06/39.61          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.06/39.61    (77)  op(e3, e0) = all_53_12
% 228.06/39.61  
% 228.06/39.61  Begin of proof
% 228.06/39.61  | 
% 228.06/39.61  | ALPHA: (15) implies:
% 228.06/39.61  |   (78)  all_57_9 = e2
% 228.06/39.61  | 
% 228.06/39.61  | BETA: splitting (62) gives:
% 228.06/39.61  | 
% 228.06/39.61  | Case 1:
% 228.06/39.61  | | 
% 228.06/39.61  | |   (79)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 228.06/39.61  | |           e2)
% 228.06/39.61  | | 
% 228.06/39.61  | | BETA: splitting (79) gives:
% 228.06/39.61  | | 
% 228.06/39.61  | | Case 1:
% 228.06/39.61  | | | 
% 228.06/39.61  | | |   (80)  all_57_2 = e2 & op(e2, e3) = e2
% 228.06/39.61  | | | 
% 228.06/39.61  | | | ALPHA: (80) implies:
% 228.06/39.61  | | |   (81)  all_57_2 = e2
% 228.06/39.61  | | | 
% 228.06/39.61  | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 228.06/39.61  | | |            (14), (16), (17), (18), (19), (21), (22), (23), (24), (26),
% 228.06/39.61  | | |            (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 228.06/39.61  | | |            (37), (38), (39), (40), (41), (42), (43), (44), (47), (48),
% 228.06/39.61  | | |            (49), (52), (53), (54), (55), (56), (58), (59), (60), (61),
% 228.06/39.61  | | |            (62), (63), (64), (65), (66), (67), (68), (69), (70), (71),
% 228.06/39.61  | | |            (72), (73), (74), (75), (76), (77), (81) are inconsistent by
% 228.06/39.61  | | |            sub-proof #554.
% 228.06/39.61  | | | 
% 228.06/39.61  | | Case 2:
% 228.06/39.61  | | | 
% 228.06/39.61  | | |   (82)  all_57_3 = e2 & op(e2, e2) = e2
% 228.06/39.61  | | | 
% 228.06/39.61  | | | REF_CLOSE: (28), (43), (82) are inconsistent by sub-proof #2103.
% 228.06/39.61  | | | 
% 228.06/39.61  | | End of split
% 228.06/39.61  | | 
% 228.06/39.61  | Case 2:
% 228.06/39.61  | | 
% 228.06/39.61  | |   (83)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 228.06/39.61  | |           e2)
% 228.06/39.61  | | 
% 228.06/39.61  | | BETA: splitting (83) gives:
% 228.06/39.61  | | 
% 228.06/39.61  | | Case 1:
% 228.06/39.61  | | | 
% 228.06/39.61  | | |   (84)  all_57_5 = e2 & op(e2, e1) = e2
% 228.06/39.61  | | | 
% 228.06/39.61  | | | ALPHA: (84) implies:
% 228.06/39.61  | | |   (85)  all_57_5 = e2
% 228.06/39.61  | | | 
% 228.06/39.61  | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 228.06/39.61  | | |            (14), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 228.06/39.61  | | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 228.06/39.61  | | |            (35), (36), (37), (38), (39), (41), (42), (43), (44), (45),
% 228.06/39.61  | | |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (55),
% 228.06/39.61  | | |            (56), (57), (58), (59), (60), (61), (62), (63), (64), (65),
% 228.06/39.61  | | |            (66), (67), (68), (69), (70), (71), (72), (73), (74), (75),
% 228.06/39.61  | | |            (76), (77), (85) are inconsistent by sub-proof #496.
% 228.06/39.61  | | | 
% 228.06/39.61  | | Case 2:
% 228.06/39.61  | | | 
% 228.06/39.61  | | |   (86)  all_57_10 = e2 & op(e2, e0) = e2
% 228.06/39.61  | | | 
% 228.06/39.61  | | | ALPHA: (86) implies:
% 228.06/39.61  | | |   (87)  all_57_10 = e2
% 228.06/39.61  | | | 
% 228.06/39.61  | | | BETA: splitting (63) gives:
% 228.06/39.61  | | | 
% 228.06/39.61  | | | Case 1:
% 228.06/39.61  | | | | 
% 228.06/39.61  | | | |   (88)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3)
% 228.06/39.61  | | | |           = e3)
% 228.06/39.61  | | | | 
% 228.06/39.61  | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.06/39.61  | | | |            (13), (14), (16), (17), (18), (19), (21), (22), (23), (24),
% 228.06/39.61  | | | |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 228.06/39.61  | | | |            (36), (37), (39), (40), (41), (42), (43), (44), (47), (48),
% 228.06/39.61  | | | |            (49), (52), (53), (54), (55), (56), (58), (59), (60), (61),
% 228.06/39.61  | | | |            (62), (64), (65), (66), (67), (68), (69), (70), (71), (72),
% 228.06/39.61  | | | |            (73), (74), (75), (76), (77), (87), (88) are inconsistent by
% 228.06/39.61  | | | |            sub-proof #495.
% 228.06/39.61  | | | | 
% 228.06/39.61  | | | Case 2:
% 228.06/39.61  | | | | 
% 228.06/39.61  | | | |   (89)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3)
% 228.06/39.61  | | | |           = e3)
% 228.06/39.61  | | | | 
% 228.06/39.61  | | | | BETA: splitting (89) gives:
% 228.06/39.61  | | | | 
% 228.06/39.61  | | | | Case 1:
% 228.06/39.61  | | | | | 
% 228.06/39.61  | | | | |   (90)  all_57_6 = e3 & op(e1, e3) = e3
% 228.06/39.61  | | | | | 
% 228.06/39.61  | | | | | ALPHA: (90) implies:
% 228.06/39.61  | | | | |   (91)  all_57_6 = e3
% 228.06/39.61  | | | | | 
% 228.06/39.61  | | | | | BETA: splitting (71) gives:
% 228.06/39.61  | | | | | 
% 228.06/39.61  | | | | | Case 1:
% 228.06/39.61  | | | | | | 
% 228.06/39.61  | | | | | |   (92)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2,
% 228.06/39.61  | | | | | |             e3) = e0)
% 228.06/39.61  | | | | | | 
% 228.06/39.61  | | | | | | REF_CLOSE: (4), (9), (11), (28), (30), (38), (40), (43), (47), (62),
% 228.06/39.61  | | | | | |            (64), (92) are inconsistent by sub-proof #1644.
% 228.06/39.61  | | | | | | 
% 228.06/39.61  | | | | | Case 2:
% 228.06/39.61  | | | | | | 
% 228.06/39.61  | | | | | |   (93)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0,
% 228.06/39.61  | | | | | |             e3) = e0)
% 228.06/39.61  | | | | | | 
% 228.06/39.61  | | | | | | BETA: splitting (93) gives:
% 228.06/39.61  | | | | | | 
% 228.06/39.61  | | | | | | Case 1:
% 228.06/39.61  | | | | | | | 
% 228.06/39.61  | | | | | | |   (94)  all_57_6 = e0 & op(e1, e3) = e0
% 228.06/39.61  | | | | | | | 
% 228.06/39.61  | | | | | | | REF_CLOSE: (32), (91), (94) are inconsistent by sub-proof #2465.
% 228.06/39.61  | | | | | | | 
% 228.06/39.61  | | | | | | Case 2:
% 228.06/39.61  | | | | | | | 
% 228.06/39.61  | | | | | | |   (95)  all_57_12 = e0 & op(e0, e3) = e0
% 228.06/39.61  | | | | | | | 
% 228.06/39.61  | | | | | | | ALPHA: (95) implies:
% 228.06/39.61  | | | | | | |   (96)  all_57_12 = e0
% 228.06/39.61  | | | | | | | 
% 228.06/39.61  | | | | | | | BETA: splitting (5) gives:
% 228.06/39.61  | | | | | | | 
% 228.06/39.61  | | | | | | | Case 1:
% 228.06/39.61  | | | | | | | | 
% 228.06/39.61  | | | | | | | |   (97)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 &
% 228.06/39.61  | | | | | | | |           op(e2, e3) = e1)
% 228.06/39.61  | | | | | | | | 
% 228.06/39.61  | | | | | | | | BETA: splitting (97) gives:
% 228.06/39.61  | | | | | | | | 
% 228.06/39.61  | | | | | | | | Case 1:
% 228.06/39.61  | | | | | | | | | 
% 228.06/39.61  | | | | | | | | |   (98)  all_57_0 = e1 & op(e3, e3) = e1
% 228.06/39.61  | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | ALPHA: (98) implies:
% 228.06/39.61  | | | | | | | | |   (99)  op(e3, e3) = e1
% 228.06/39.61  | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | REF_CLOSE: (11), (38), (64), (99) are inconsistent by
% 228.06/39.61  | | | | | | | | |            sub-proof #1950.
% 228.06/39.61  | | | | | | | | | 
% 228.06/39.61  | | | | | | | | Case 2:
% 228.06/39.61  | | | | | | | | | 
% 228.06/39.61  | | | | | | | | |   (100)  all_57_2 = e1 & op(e2, e3) = e1
% 228.06/39.61  | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | ALPHA: (100) implies:
% 228.06/39.61  | | | | | | | | |   (101)  all_57_2 = e1
% 228.06/39.61  | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | BETA: splitting (54) gives:
% 228.06/39.61  | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | Case 1:
% 228.06/39.61  | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | |   (102)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 228.06/39.61  | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 228.06/39.61  | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | BETA: splitting (102) gives:
% 228.06/39.61  | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | Case 1:
% 228.06/39.61  | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | |   (103)  all_57_12 = e2 & op(e0, e3) = e2
% 228.06/39.61  | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | REF_CLOSE: (2), (5), (9), (30), (43), (47), (64), (68), (91),
% 228.06/39.61  | | | | | | | | | | |            (96), (103) are inconsistent by sub-proof #494.
% 228.06/39.61  | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | Case 2:
% 228.06/39.61  | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | |   (104)  all_57_13 = e2 & op(e0, e2) = e2
% 228.06/39.61  | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | ALPHA: (104) implies:
% 228.06/39.61  | | | | | | | | | | |   (105)  all_57_13 = e2
% 228.06/39.61  | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | BETA: splitting (19) gives:
% 228.06/39.61  | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | Case 1:
% 228.06/39.61  | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | |   (106)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 228.06/39.61  | | | | | | | | | | | |            & op(e3, e2) = e1)
% 228.06/39.61  | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | BETA: splitting (106) gives:
% 228.06/39.61  | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | Case 1:
% 228.06/39.61  | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | |   (107)  all_57_0 = e1 & op(e3, e3) = e1
% 228.06/39.61  | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | ALPHA: (107) implies:
% 228.06/39.61  | | | | | | | | | | | | |   (108)  op(e3, e3) = e1
% 228.06/39.61  | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | REF_CLOSE: (11), (38), (64), (108) are inconsistent by
% 228.06/39.61  | | | | | | | | | | | | |            sub-proof #1950.
% 228.06/39.61  | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | Case 2:
% 228.06/39.61  | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | |   (109)  all_57_1 = e1 & op(e3, e2) = e1
% 228.06/39.61  | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | ALPHA: (109) implies:
% 228.06/39.61  | | | | | | | | | | | | |   (110)  all_57_1 = e1
% 228.06/39.61  | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | BETA: splitting (72) gives:
% 228.06/39.61  | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | Case 1:
% 228.06/39.61  | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | |   (111)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 228.06/39.61  | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 228.06/39.61  | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | BETA: splitting (111) gives:
% 228.06/39.61  | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | Case 1:
% 228.06/39.61  | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | |   (112)  all_57_9 = e1 & op(e3, e0) = e1
% 228.06/39.61  | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | REF_CLOSE: (64), (78), (112) are inconsistent by sub-proof
% 228.06/39.61  | | | | | | | | | | | | | | |            #2451.
% 228.06/39.61  | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | Case 2:
% 228.06/39.61  | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | |   (113)  all_57_10 = e1 & op(e2, e0) = e1
% 228.06/39.61  | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | REF_CLOSE: (64), (87), (113) are inconsistent by sub-proof
% 228.06/39.61  | | | | | | | | | | | | | | |            #2360.
% 228.06/39.61  | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | End of split
% 228.06/39.61  | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | Case 2:
% 228.06/39.61  | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | |   (114)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 228.06/39.61  | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 228.06/39.61  | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | BETA: splitting (114) gives:
% 228.06/39.61  | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | Case 1:
% 228.06/39.61  | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | |   (115)  all_57_11 = e1 & op(e1, e0) = e1
% 228.06/39.61  | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | ALPHA: (115) implies:
% 228.06/39.61  | | | | | | | | | | | | | | |   (116)  all_57_11 = e1
% 228.06/39.61  | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | BETA: splitting (46) gives:
% 228.06/39.61  | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | Case 1:
% 228.06/39.61  | | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | |   (117)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 228.06/39.61  | | | | | | | | | | | | | | | |            & op(e3, e2) = e3)
% 228.06/39.61  | | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (30), (43), (47), (64), (68), (91),
% 228.06/39.61  | | | | | | | | | | | | | | | |            (96), (110), (117) are inconsistent by sub-proof
% 228.06/39.61  | | | | | | | | | | | | | | | |            #488.
% 228.06/39.61  | | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | Case 2:
% 228.06/39.61  | | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | |   (118)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 228.06/39.61  | | | | | | | | | | | | | | | |            & op(e3, e0) = e3)
% 228.06/39.61  | | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | | BETA: splitting (118) gives:
% 228.06/39.61  | | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | | Case 1:
% 228.06/39.61  | | | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | | |   (119)  all_57_4 = e3 & op(e3, e1) = e3
% 228.06/39.61  | | | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | | | ALPHA: (119) implies:
% 228.06/39.61  | | | | | | | | | | | | | | | | |   (120)  all_57_4 = e3
% 228.06/39.61  | | | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | | | BETA: splitting (51) gives:
% 228.06/39.61  | | | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | | | Case 1:
% 228.06/39.61  | | | | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | | | |   (121)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 228.06/39.61  | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e3)
% 228.06/39.61  | | | | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | | | | BETA: splitting (121) gives:
% 228.06/39.61  | | | | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | | | | Case 1:
% 228.06/39.61  | | | | | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | | | | |   (122)  all_57_1 = e3 & op(e3, e2) = e3
% 228.06/39.61  | | | | | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | | | | | ALPHA: (122) implies:
% 228.06/39.61  | | | | | | | | | | | | | | | | | | |   (123)  all_57_1 = e3
% 228.06/39.61  | | | | | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (110), (123) imply:
% 228.06/39.61  | | | | | | | | | | | | | | | | | | |   (124)  e3 = e1
% 228.06/39.61  | | | | | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | | | | | SIMP: (124) implies:
% 228.06/39.61  | | | | | | | | | | | | | | | | | | |   (125)  e3 = e1
% 228.06/39.61  | | | | | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (120), (125) imply:
% 228.06/39.61  | | | | | | | | | | | | | | | | | | |   (126)  all_57_4 = e1
% 228.06/39.61  | | | | | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (5), (9), (27), (28), (30), (32), (40),
% 228.06/39.61  | | | | | | | | | | | | | | | | | | |            (43), (47), (62), (64), (68), (78), (91), (96),
% 228.06/39.61  | | | | | | | | | | | | | | | | | | |            (101), (123), (126) are inconsistent by sub-proof
% 228.06/39.61  | | | | | | | | | | | | | | | | | | |            #416.
% 228.06/39.61  | | | | | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | | | | Case 2:
% 228.06/39.61  | | | | | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | | | | |   (127)  all_57_3 = e3 & op(e2, e2) = e3
% 228.06/39.61  | | | | | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | | | | | ALPHA: (127) implies:
% 228.06/39.61  | | | | | | | | | | | | | | | | | | |   (128)  all_57_3 = e3
% 228.06/39.61  | | | | | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (28), (32), (128) are inconsistent by sub-proof
% 228.06/39.61  | | | | | | | | | | | | | | | | | | |            #2358.
% 228.06/39.61  | | | | | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | | | | End of split
% 228.06/39.61  | | | | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | | | Case 2:
% 228.06/39.61  | | | | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | | | |   (129)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 228.06/39.61  | | | | | | | | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 228.06/39.61  | | | | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | | | | BETA: splitting (129) gives:
% 228.06/39.61  | | | | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | | | | Case 1:
% 228.06/39.61  | | | | | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | | | | |   (130)  all_57_7 = e3 & op(e1, e2) = e3
% 228.06/39.61  | | | | | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | | | | | ALPHA: (130) implies:
% 228.06/39.61  | | | | | | | | | | | | | | | | | | |   (131)  all_57_7 = e3
% 228.06/39.61  | | | | | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (7), (8), (9), (10), (11),
% 228.06/39.61  | | | | | | | | | | | | | | | | | | |            (12), (13), (14), (16), (17), (18), (19), (21),
% 228.06/39.61  | | | | | | | | | | | | | | | | | | |            (22), (23), (24), (25), (26), (27), (28), (29),
% 228.06/39.61  | | | | | | | | | | | | | | | | | | |            (30), (31), (32), (33), (34), (35), (36), (37),
% 228.06/39.61  | | | | | | | | | | | | | | | | | | |            (38), (39), (41), (42), (43), (44), (46), (47),
% 228.06/39.61  | | | | | | | | | | | | | | | | | | |            (48), (49), (50), (52), (53), (54), (55), (56),
% 228.06/39.61  | | | | | | | | | | | | | | | | | | |            (57), (58), (59), (60), (61), (62), (63), (64),
% 228.06/39.61  | | | | | | | | | | | | | | | | | | |            (65), (66), (67), (68), (69), (70), (71), (72),
% 228.06/39.61  | | | | | | | | | | | | | | | | | | |            (73), (74), (75), (76), (77), (116), (120), (131)
% 228.06/39.61  | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #499.
% 228.06/39.61  | | | | | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | | | | Case 2:
% 228.06/39.61  | | | | | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | | | | |   (132)  all_57_13 = e3 & op(e0, e2) = e3
% 228.06/39.61  | | | | | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | | | | | ALPHA: (132) implies:
% 228.06/39.61  | | | | | | | | | | | | | | | | | | |   (133)  all_57_13 = e3
% 228.06/39.61  | | | | | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (105), (133) imply:
% 228.06/39.61  | | | | | | | | | | | | | | | | | | |   (134)  e3 = e2
% 228.06/39.61  | | | | | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (8), (9), (11), (12), (14), (16), (19),
% 228.06/39.61  | | | | | | | | | | | | | | | | | | |            (24), (27), (28), (30), (32), (37), (38), (43),
% 228.06/39.61  | | | | | | | | | | | | | | | | | | |            (46), (47), (55), (57), (60), (62), (63), (64),
% 228.06/39.61  | | | | | | | | | | | | | | | | | | |            (65), (71), (72), (75), (77), (91), (134) are
% 228.06/39.61  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #604.
% 228.06/39.61  | | | | | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | | | | End of split
% 228.06/39.61  | | | | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | | | End of split
% 228.06/39.61  | | | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | | Case 2:
% 228.06/39.61  | | | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | | |   (135)  all_57_9 = e3 & op(e3, e0) = e3
% 228.06/39.61  | | | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | | | ALPHA: (135) implies:
% 228.06/39.61  | | | | | | | | | | | | | | | | |   (136)  op(e3, e0) = e3
% 228.06/39.61  | | | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (60), (77), (136) are inconsistent by
% 228.06/39.61  | | | | | | | | | | | | | | | | |            sub-proof #2458.
% 228.06/39.61  | | | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | | End of split
% 228.06/39.61  | | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | End of split
% 228.06/39.61  | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | Case 2:
% 228.06/39.61  | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | |   (137)  all_57_15 = e1 & op(e0, e0) = e1
% 228.06/39.61  | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | REF_CLOSE: (9), (37), (137) are inconsistent by sub-proof
% 228.06/39.61  | | | | | | | | | | | | | | |            #2325.
% 228.06/39.61  | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | End of split
% 228.06/39.61  | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | End of split
% 228.06/39.61  | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | End of split
% 228.06/39.61  | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | Case 2:
% 228.06/39.61  | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | |   (138)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 228.06/39.61  | | | | | | | | | | | |            & op(e3, e0) = e1)
% 228.06/39.61  | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | REF_CLOSE: (2), (4), (5), (9), (11), (27), (28), (30), (32),
% 228.06/39.61  | | | | | | | | | | | |            (40), (43), (46), (47), (60), (62), (64), (68),
% 228.06/39.61  | | | | | | | | | | | |            (77), (78), (91), (96), (101), (138) are
% 228.06/39.61  | | | | | | | | | | | |            inconsistent by sub-proof #415.
% 228.06/39.61  | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | End of split
% 228.06/39.61  | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | End of split
% 228.06/39.61  | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | Case 2:
% 228.06/39.61  | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | |   (139)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 228.06/39.61  | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 228.06/39.61  | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | BETA: splitting (139) gives:
% 228.06/39.61  | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | Case 1:
% 228.06/39.61  | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | |   (140)  all_57_14 = e2 & op(e0, e1) = e2
% 228.06/39.61  | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | ALPHA: (140) implies:
% 228.06/39.61  | | | | | | | | | | |   (141)  all_57_14 = e2
% 228.06/39.61  | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | BETA: splitting (19) gives:
% 228.06/39.61  | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | Case 1:
% 228.06/39.61  | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | |   (142)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 228.06/39.61  | | | | | | | | | | | |            & op(e3, e2) = e1)
% 228.06/39.61  | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | BETA: splitting (142) gives:
% 228.06/39.61  | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | Case 1:
% 228.06/39.61  | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | |   (143)  all_57_0 = e1 & op(e3, e3) = e1
% 228.06/39.61  | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | ALPHA: (143) implies:
% 228.06/39.61  | | | | | | | | | | | | |   (144)  op(e3, e3) = e1
% 228.06/39.61  | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | REF_CLOSE: (11), (38), (64), (144) are inconsistent by
% 228.06/39.61  | | | | | | | | | | | | |            sub-proof #1950.
% 228.06/39.61  | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | Case 2:
% 228.06/39.61  | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | |   (145)  all_57_1 = e1 & op(e3, e2) = e1
% 228.06/39.61  | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | ALPHA: (145) implies:
% 228.06/39.61  | | | | | | | | | | | | |   (146)  all_57_1 = e1
% 228.06/39.61  | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | BETA: splitting (46) gives:
% 228.06/39.61  | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | Case 1:
% 228.06/39.61  | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | |   (147)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 228.06/39.61  | | | | | | | | | | | | | |            & op(e3, e2) = e3)
% 228.06/39.61  | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (30), (43), (47), (64), (68), (91),
% 228.06/39.61  | | | | | | | | | | | | | |            (96), (146), (147) are inconsistent by sub-proof
% 228.06/39.61  | | | | | | | | | | | | | |            #488.
% 228.06/39.61  | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | Case 2:
% 228.06/39.61  | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | |   (148)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 228.06/39.61  | | | | | | | | | | | | | |            & op(e3, e0) = e3)
% 228.06/39.61  | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | BETA: splitting (148) gives:
% 228.06/39.61  | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | Case 1:
% 228.06/39.61  | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | |   (149)  all_57_4 = e3 & op(e3, e1) = e3
% 228.06/39.61  | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | ALPHA: (149) implies:
% 228.06/39.61  | | | | | | | | | | | | | | |   (150)  all_57_4 = e3
% 228.06/39.61  | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | BETA: splitting (72) gives:
% 228.06/39.61  | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | Case 1:
% 228.06/39.61  | | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | |   (151)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 228.06/39.61  | | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 228.06/39.61  | | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | | BETA: splitting (151) gives:
% 228.06/39.61  | | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | | Case 1:
% 228.06/39.61  | | | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | | |   (152)  all_57_9 = e1 & op(e3, e0) = e1
% 228.06/39.61  | | | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | | | REF_CLOSE: (64), (78), (152) are inconsistent by sub-proof
% 228.06/39.61  | | | | | | | | | | | | | | | | |            #2451.
% 228.06/39.61  | | | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | | Case 2:
% 228.06/39.61  | | | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | | |   (153)  all_57_10 = e1 & op(e2, e0) = e1
% 228.06/39.61  | | | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | | | REF_CLOSE: (64), (87), (153) are inconsistent by sub-proof
% 228.06/39.61  | | | | | | | | | | | | | | | | |            #2360.
% 228.06/39.61  | | | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | | End of split
% 228.06/39.61  | | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | Case 2:
% 228.06/39.61  | | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | |   (154)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 228.06/39.61  | | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 228.06/39.61  | | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (7), (8), (9), (10), (11),
% 228.06/39.61  | | | | | | | | | | | | | | | |            (12), (13), (14), (16), (17), (18), (19), (21),
% 228.06/39.61  | | | | | | | | | | | | | | | |            (22), (23), (24), (25), (26), (27), (28), (29),
% 228.06/39.61  | | | | | | | | | | | | | | | |            (30), (31), (32), (33), (34), (35), (36), (37),
% 228.06/39.61  | | | | | | | | | | | | | | | |            (38), (39), (41), (42), (43), (44), (46), (47),
% 228.06/39.61  | | | | | | | | | | | | | | | |            (48), (49), (50), (51), (52), (53), (54), (55),
% 228.06/39.61  | | | | | | | | | | | | | | | |            (56), (57), (58), (59), (60), (61), (62), (63),
% 228.06/39.61  | | | | | | | | | | | | | | | |            (64), (65), (66), (67), (68), (69), (70), (71),
% 228.06/39.61  | | | | | | | | | | | | | | | |            (72), (73), (74), (75), (76), (77), (96), (141),
% 228.06/39.61  | | | | | | | | | | | | | | | |            (146), (150), (154) are inconsistent by sub-proof
% 228.06/39.61  | | | | | | | | | | | | | | | |            #498.
% 228.06/39.61  | | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | End of split
% 228.06/39.61  | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | Case 2:
% 228.06/39.61  | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | |   (155)  all_57_9 = e3 & op(e3, e0) = e3
% 228.06/39.61  | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | ALPHA: (155) implies:
% 228.06/39.61  | | | | | | | | | | | | | | |   (156)  op(e3, e0) = e3
% 228.06/39.61  | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | REF_CLOSE: (11), (60), (77), (156) are inconsistent by
% 228.06/39.61  | | | | | | | | | | | | | | |            sub-proof #2458.
% 228.06/39.61  | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | End of split
% 228.06/39.61  | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | End of split
% 228.06/39.61  | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | End of split
% 228.06/39.61  | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | Case 2:
% 228.06/39.61  | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | |   (157)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 228.06/39.61  | | | | | | | | | | | |            & op(e3, e0) = e1)
% 228.06/39.61  | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | REF_CLOSE: (2), (4), (5), (9), (11), (27), (28), (30), (32),
% 228.06/39.61  | | | | | | | | | | | |            (40), (43), (46), (47), (60), (62), (64), (68),
% 228.06/39.61  | | | | | | | | | | | |            (77), (78), (91), (96), (101), (157) are
% 228.06/39.61  | | | | | | | | | | | |            inconsistent by sub-proof #415.
% 228.06/39.61  | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | End of split
% 228.06/39.61  | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | Case 2:
% 228.06/39.61  | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | |   (158)  all_57_15 = e2 & op(e0, e0) = e2
% 228.06/39.61  | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | REF_CLOSE: (4), (5), (8), (9), (11), (12), (14), (16), (19),
% 228.06/39.61  | | | | | | | | | | |            (24), (27), (28), (30), (32), (37), (38), (43),
% 228.06/39.61  | | | | | | | | | | |            (46), (47), (55), (57), (60), (62), (63), (64),
% 228.06/39.61  | | | | | | | | | | |            (65), (71), (72), (75), (77), (91), (158) are
% 228.06/39.61  | | | | | | | | | | |            inconsistent by sub-proof #477.
% 228.06/39.61  | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | End of split
% 228.06/39.61  | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | End of split
% 228.06/39.61  | | | | | | | | | 
% 228.06/39.61  | | | | | | | | End of split
% 228.06/39.61  | | | | | | | | 
% 228.06/39.61  | | | | | | | Case 2:
% 228.06/39.61  | | | | | | | | 
% 228.06/39.61  | | | | | | | |   (159)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 &
% 228.06/39.61  | | | | | | | |            op(e0, e3) = e1)
% 228.06/39.61  | | | | | | | | 
% 228.06/39.61  | | | | | | | | REF_CLOSE: (4), (9), (11), (28), (30), (32), (38), (40), (43),
% 228.06/39.61  | | | | | | | |            (47), (62), (64), (71), (91), (159) are inconsistent
% 228.06/39.61  | | | | | | | |            by sub-proof #809.
% 228.06/39.61  | | | | | | | | 
% 228.06/39.61  | | | | | | | End of split
% 228.06/39.61  | | | | | | | 
% 228.06/39.61  | | | | | | End of split
% 228.06/39.61  | | | | | | 
% 228.06/39.61  | | | | | End of split
% 228.06/39.61  | | | | | 
% 228.06/39.61  | | | | Case 2:
% 228.06/39.61  | | | | | 
% 228.06/39.61  | | | | |   (160)  all_57_12 = e3 & op(e0, e3) = e3
% 228.06/39.61  | | | | | 
% 228.06/39.61  | | | | | ALPHA: (160) implies:
% 228.06/39.61  | | | | |   (161)  all_57_12 = e3
% 228.06/39.61  | | | | | 
% 228.06/39.61  | | | | | BETA: splitting (54) gives:
% 228.06/39.61  | | | | | 
% 228.06/39.61  | | | | | Case 1:
% 228.06/39.61  | | | | | | 
% 228.06/39.61  | | | | | |   (162)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 &
% 228.06/39.61  | | | | | |            op(e0, e2) = e2)
% 228.06/39.61  | | | | | | 
% 228.06/39.61  | | | | | | BETA: splitting (162) gives:
% 228.06/39.61  | | | | | | 
% 228.06/39.61  | | | | | | Case 1:
% 228.06/39.61  | | | | | | | 
% 228.06/39.61  | | | | | | |   (163)  all_57_12 = e2 & op(e0, e3) = e2
% 228.06/39.61  | | | | | | | 
% 228.06/39.61  | | | | | | | REF_CLOSE: (30), (161), (163) are inconsistent by sub-proof #2232.
% 228.06/39.61  | | | | | | | 
% 228.06/39.61  | | | | | | Case 2:
% 228.06/39.61  | | | | | | | 
% 228.06/39.61  | | | | | | |   (164)  all_57_13 = e2 & op(e0, e2) = e2
% 228.06/39.61  | | | | | | | 
% 228.06/39.61  | | | | | | | ALPHA: (164) implies:
% 228.06/39.61  | | | | | | |   (165)  all_57_13 = e2
% 228.06/39.61  | | | | | | | 
% 228.06/39.61  | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 228.06/39.61  | | | | | | |            (12), (13), (14), (16), (17), (18), (19), (21), (22),
% 228.06/39.61  | | | | | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31),
% 228.06/39.61  | | | | | | |            (32), (33), (34), (35), (36), (37), (38), (39), (40),
% 228.06/39.61  | | | | | | |            (41), (42), (43), (44), (46), (47), (48), (49), (50),
% 228.06/39.61  | | | | | | |            (51), (52), (53), (54), (55), (56), (57), (58), (59),
% 228.06/39.61  | | | | | | |            (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 228.06/39.61  | | | | | | |            (69), (70), (71), (72), (73), (74), (75), (76), (77),
% 228.06/39.61  | | | | | | |            (78), (87), (161), (165) are inconsistent by sub-proof
% 228.06/39.61  | | | | | | |            #413.
% 228.06/39.61  | | | | | | | 
% 228.06/39.61  | | | | | | End of split
% 228.06/39.61  | | | | | | 
% 228.06/39.61  | | | | | Case 2:
% 228.06/39.61  | | | | | | 
% 228.06/39.61  | | | | | |   (166)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 &
% 228.06/39.61  | | | | | |            op(e0, e0) = e2)
% 228.06/39.61  | | | | | | 
% 228.06/39.61  | | | | | | BETA: splitting (166) gives:
% 228.06/39.61  | | | | | | 
% 228.06/39.61  | | | | | | Case 1:
% 228.06/39.61  | | | | | | | 
% 228.06/39.61  | | | | | | |   (167)  all_57_14 = e2 & op(e0, e1) = e2
% 228.06/39.61  | | | | | | | 
% 228.06/39.61  | | | | | | | ALPHA: (167) implies:
% 228.06/39.61  | | | | | | |   (168)  all_57_14 = e2
% 228.06/39.61  | | | | | | | 
% 228.06/39.61  | | | | | | | BETA: splitting (12) gives:
% 228.06/39.61  | | | | | | | 
% 228.06/39.61  | | | | | | | Case 1:
% 228.06/39.61  | | | | | | | | 
% 228.06/39.61  | | | | | | | |   (169)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 &
% 228.06/39.61  | | | | | | | |            op(e1, e2) = e3)
% 228.06/39.61  | | | | | | | | 
% 228.06/39.61  | | | | | | | | BETA: splitting (169) gives:
% 228.06/39.61  | | | | | | | | 
% 228.06/39.61  | | | | | | | | Case 1:
% 228.06/39.61  | | | | | | | | | 
% 228.06/39.61  | | | | | | | | |   (170)  all_57_6 = e3 & op(e1, e3) = e3
% 228.06/39.61  | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (7), (8), (9), (10), (11),
% 228.06/39.61  | | | | | | | | |            (12), (13), (14), (16), (17), (18), (19), (21),
% 228.06/39.61  | | | | | | | | |            (22), (23), (24), (25), (26), (27), (28), (29),
% 228.06/39.61  | | | | | | | | |            (30), (31), (32), (33), (34), (35), (36), (37),
% 228.06/39.61  | | | | | | | | |            (38), (39), (40), (41), (42), (43), (44), (46),
% 228.06/39.61  | | | | | | | | |            (47), (48), (49), (50), (51), (52), (53), (54),
% 228.06/39.61  | | | | | | | | |            (55), (56), (57), (58), (59), (60), (61), (62),
% 228.06/39.61  | | | | | | | | |            (63), (64), (65), (66), (67), (68), (69), (70),
% 228.06/39.61  | | | | | | | | |            (71), (72), (73), (74), (75), (76), (77), (78),
% 228.06/39.61  | | | | | | | | |            (87), (161), (170) are inconsistent by sub-proof
% 228.06/39.61  | | | | | | | | |            #414.
% 228.06/39.61  | | | | | | | | | 
% 228.06/39.61  | | | | | | | | Case 2:
% 228.06/39.61  | | | | | | | | | 
% 228.06/39.61  | | | | | | | | |   (171)  all_57_7 = e3 & op(e1, e2) = e3
% 228.06/39.61  | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | ALPHA: (171) implies:
% 228.06/39.61  | | | | | | | | |   (172)  all_57_7 = e3
% 228.06/39.61  | | | | | | | | |   (173)  op(e1, e2) = e3
% 228.06/39.61  | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | BETA: splitting (19) gives:
% 228.06/39.61  | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | Case 1:
% 228.06/39.61  | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | |   (174)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 228.06/39.61  | | | | | | | | | |            & op(e3, e2) = e1)
% 228.06/39.61  | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | BETA: splitting (174) gives:
% 228.06/39.61  | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | Case 1:
% 228.06/39.61  | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | |   (175)  all_57_0 = e1 & op(e3, e3) = e1
% 228.06/39.61  | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | ALPHA: (175) implies:
% 228.06/39.61  | | | | | | | | | | |   (176)  op(e3, e3) = e1
% 228.06/39.61  | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | REF_CLOSE: (11), (38), (64), (176) are inconsistent by
% 228.06/39.61  | | | | | | | | | | |            sub-proof #1950.
% 228.06/39.61  | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | Case 2:
% 228.06/39.61  | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | |   (177)  all_57_1 = e1 & op(e3, e2) = e1
% 228.06/39.61  | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | ALPHA: (177) implies:
% 228.06/39.61  | | | | | | | | | | |   (178)  all_57_1 = e1
% 228.06/39.61  | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | BETA: splitting (46) gives:
% 228.06/39.61  | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | Case 1:
% 228.06/39.61  | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | |   (179)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 228.06/39.61  | | | | | | | | | | | |            & op(e3, e2) = e3)
% 228.06/39.61  | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10),
% 228.06/39.61  | | | | | | | | | | | |            (11), (13), (16), (17), (18), (19), (21), (22),
% 228.06/39.61  | | | | | | | | | | | |            (23), (24), (26), (27), (28), (29), (30), (31),
% 228.06/39.61  | | | | | | | | | | | |            (32), (33), (34), (35), (36), (37), (39), (40),
% 228.06/39.61  | | | | | | | | | | | |            (41), (42), (43), (44), (47), (48), (49), (52),
% 228.06/39.61  | | | | | | | | | | | |            (53), (54), (55), (56), (58), (59), (60), (61),
% 228.06/39.61  | | | | | | | | | | | |            (62), (64), (65), (66), (67), (68), (69), (70),
% 228.06/39.61  | | | | | | | | | | | |            (71), (72), (73), (74), (75), (76), (77), (161),
% 228.06/39.61  | | | | | | | | | | | |            (172), (173), (179) are inconsistent by sub-proof
% 228.06/39.61  | | | | | | | | | | | |            #412.
% 228.06/39.61  | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | Case 2:
% 228.06/39.61  | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | |   (180)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 228.06/39.61  | | | | | | | | | | | |            & op(e3, e0) = e3)
% 228.06/39.61  | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | BETA: splitting (180) gives:
% 228.06/39.61  | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | Case 1:
% 228.06/39.61  | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | |   (181)  all_57_4 = e3 & op(e3, e1) = e3
% 228.06/39.61  | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | ALPHA: (181) implies:
% 228.06/39.61  | | | | | | | | | | | | |   (182)  all_57_4 = e3
% 228.06/39.61  | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | BETA: splitting (29) gives:
% 228.06/39.61  | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | Case 1:
% 228.06/39.61  | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | |   (183)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 228.06/39.61  | | | | | | | | | | | | | |            & op(e2, e1) = e0)
% 228.06/39.61  | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | BETA: splitting (183) gives:
% 228.06/39.61  | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | Case 1:
% 228.06/39.61  | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | |   (184)  all_57_4 = e0 & op(e3, e1) = e0
% 228.06/39.61  | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | ALPHA: (184) implies:
% 228.06/39.61  | | | | | | | | | | | | | | |   (185)  all_57_4 = e0
% 228.06/39.61  | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | REF_CLOSE: (32), (182), (185) are inconsistent by sub-proof
% 228.06/39.61  | | | | | | | | | | | | | | |            #2372.
% 228.06/39.61  | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | Case 2:
% 228.06/39.61  | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | |   (186)  all_57_5 = e0 & op(e2, e1) = e0
% 228.06/39.61  | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | ALPHA: (186) implies:
% 228.06/39.61  | | | | | | | | | | | | | | |   (187)  all_57_5 = e0
% 228.06/39.61  | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | REF_CLOSE: (32), (40), (187) are inconsistent by sub-proof
% 228.06/39.61  | | | | | | | | | | | | | | |            #2471.
% 228.06/39.61  | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | End of split
% 228.06/39.61  | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | Case 2:
% 228.06/39.61  | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | |   (188)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 228.06/39.61  | | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 228.06/39.61  | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | BETA: splitting (188) gives:
% 228.06/39.61  | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | Case 1:
% 228.06/39.61  | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | |   (189)  all_57_8 = e0 & op(e1, e1) = e0
% 228.06/39.61  | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | ALPHA: (189) implies:
% 228.06/39.61  | | | | | | | | | | | | | | |   (190)  all_57_8 = e0
% 228.06/39.61  | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | COMBINE_EQS: (25), (190) imply:
% 228.06/39.61  | | | | | | | | | | | | | | |   (191)  e1 = e0
% 228.06/39.61  | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (28), (30), (43), (47), (64), (75),
% 228.06/39.61  | | | | | | | | | | | | | | |            (172), (178), (191) are inconsistent by sub-proof
% 228.06/39.61  | | | | | | | | | | | | | | |            #1626.
% 228.06/39.61  | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | Case 2:
% 228.06/39.61  | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | |   (192)  all_57_14 = e0 & op(e0, e1) = e0
% 228.06/39.61  | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | ALPHA: (192) implies:
% 228.06/39.61  | | | | | | | | | | | | | | |   (193)  all_57_14 = e0
% 228.06/39.61  | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | | REF_CLOSE: (9), (30), (37), (39), (43), (47), (54), (64),
% 228.06/39.61  | | | | | | | | | | | | | | |            (161), (193) are inconsistent by sub-proof #1763.
% 228.06/39.61  | | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | | End of split
% 228.06/39.61  | | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | End of split
% 228.06/39.61  | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | Case 2:
% 228.06/39.61  | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | |   (194)  all_57_9 = e3 & op(e3, e0) = e3
% 228.06/39.61  | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | ALPHA: (194) implies:
% 228.06/39.61  | | | | | | | | | | | | |   (195)  op(e3, e0) = e3
% 228.06/39.61  | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | REF_CLOSE: (11), (60), (77), (195) are inconsistent by
% 228.06/39.61  | | | | | | | | | | | | |            sub-proof #2458.
% 228.06/39.61  | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | End of split
% 228.06/39.61  | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | End of split
% 228.06/39.61  | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | End of split
% 228.06/39.61  | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | Case 2:
% 228.06/39.61  | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | |   (196)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 228.06/39.61  | | | | | | | | | |            & op(e3, e0) = e1)
% 228.06/39.61  | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | BETA: splitting (196) gives:
% 228.06/39.61  | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | Case 1:
% 228.06/39.61  | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | |   (197)  all_57_4 = e1 & op(e3, e1) = e1
% 228.06/39.61  | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | ALPHA: (197) implies:
% 228.06/39.61  | | | | | | | | | | |   (198)  all_57_4 = e1
% 228.06/39.61  | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | BETA: splitting (46) gives:
% 228.06/39.61  | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | Case 1:
% 228.06/39.61  | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | |   (199)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 228.06/39.61  | | | | | | | | | | | |            & op(e3, e2) = e3)
% 228.06/39.61  | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10),
% 228.06/39.61  | | | | | | | | | | | |            (11), (13), (16), (17), (18), (19), (21), (22),
% 228.06/39.61  | | | | | | | | | | | |            (23), (24), (26), (27), (28), (29), (30), (31),
% 228.06/39.61  | | | | | | | | | | | |            (32), (33), (34), (35), (36), (37), (39), (40),
% 228.06/39.61  | | | | | | | | | | | |            (41), (42), (43), (44), (47), (48), (49), (52),
% 228.06/39.61  | | | | | | | | | | | |            (53), (54), (55), (56), (58), (59), (60), (61),
% 228.06/39.61  | | | | | | | | | | | |            (62), (64), (65), (66), (67), (68), (69), (70),
% 228.06/39.61  | | | | | | | | | | | |            (71), (72), (73), (74), (75), (76), (77), (161),
% 228.06/39.61  | | | | | | | | | | | |            (172), (173), (199) are inconsistent by sub-proof
% 228.06/39.61  | | | | | | | | | | | |            #412.
% 228.06/39.61  | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | Case 2:
% 228.06/39.61  | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | |   (200)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 228.06/39.61  | | | | | | | | | | | |            & op(e3, e0) = e3)
% 228.06/39.61  | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | REF_CLOSE: (9), (11), (60), (77), (198), (200) are
% 228.06/39.61  | | | | | | | | | | | |            inconsistent by sub-proof #2281.
% 228.06/39.61  | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | End of split
% 228.06/39.61  | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | Case 2:
% 228.06/39.61  | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | |   (201)  all_57_9 = e1 & op(e3, e0) = e1
% 228.06/39.61  | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | ALPHA: (201) implies:
% 228.06/39.61  | | | | | | | | | | |   (202)  all_57_9 = e1
% 228.06/39.61  | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | COMBINE_EQS: (78), (202) imply:
% 228.06/39.61  | | | | | | | | | | |   (203)  e2 = e1
% 228.06/39.61  | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | SIMP: (203) implies:
% 228.06/39.61  | | | | | | | | | | |   (204)  e2 = e1
% 228.06/39.61  | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | COMBINE_EQS: (168), (204) imply:
% 228.06/39.61  | | | | | | | | | | |   (205)  all_57_14 = e1
% 228.06/39.61  | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | BETA: splitting (54) gives:
% 228.06/39.61  | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | Case 1:
% 228.06/39.61  | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | |   (206)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 228.06/39.61  | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 228.06/39.61  | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | BETA: splitting (206) gives:
% 228.06/39.61  | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | Case 1:
% 228.06/39.61  | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | |   (207)  all_57_12 = e2 & op(e0, e3) = e2
% 228.06/39.61  | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | REF_CLOSE: (30), (161), (207) are inconsistent by sub-proof
% 228.06/39.61  | | | | | | | | | | | | |            #2232.
% 228.06/39.61  | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | Case 2:
% 228.06/39.61  | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | |   (208)  all_57_13 = e2 & op(e0, e2) = e2
% 228.06/39.61  | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | ALPHA: (208) implies:
% 228.06/39.61  | | | | | | | | | | | | |   (209)  all_57_13 = e2
% 228.06/39.61  | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10),
% 228.06/39.61  | | | | | | | | | | | | |            (11), (12), (13), (14), (16), (17), (18), (19),
% 228.06/39.61  | | | | | | | | | | | | |            (21), (22), (23), (24), (25), (26), (27), (28),
% 228.06/39.61  | | | | | | | | | | | | |            (29), (30), (31), (32), (33), (34), (35), (36),
% 228.06/39.61  | | | | | | | | | | | | |            (37), (38), (39), (40), (41), (42), (43), (44),
% 228.06/39.61  | | | | | | | | | | | | |            (46), (47), (48), (49), (50), (51), (52), (53),
% 228.06/39.61  | | | | | | | | | | | | |            (54), (55), (56), (57), (58), (59), (60), (61),
% 228.06/39.61  | | | | | | | | | | | | |            (62), (63), (64), (65), (66), (67), (68), (69),
% 228.06/39.61  | | | | | | | | | | | | |            (70), (71), (72), (73), (74), (75), (76), (77),
% 228.06/39.61  | | | | | | | | | | | | |            (78), (87), (161), (209) are inconsistent by
% 228.06/39.61  | | | | | | | | | | | | |            sub-proof #413.
% 228.06/39.61  | | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | End of split
% 228.06/39.61  | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | Case 2:
% 228.06/39.61  | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | | REF_CLOSE: (30), (37), (64), (166), (205) are inconsistent by
% 228.06/39.61  | | | | | | | | | | | |            sub-proof #1529.
% 228.06/39.61  | | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | | End of split
% 228.06/39.61  | | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | | End of split
% 228.06/39.61  | | | | | | | | | | 
% 228.06/39.61  | | | | | | | | | End of split
% 228.06/39.61  | | | | | | | | | 
% 228.06/39.61  | | | | | | | | End of split
% 228.06/39.61  | | | | | | | | 
% 228.06/39.61  | | | | | | | Case 2:
% 228.06/39.61  | | | | | | | | 
% 228.06/39.61  | | | | | | | |   (210)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 &
% 228.06/39.61  | | | | | | | |            op(e1, e0) = e3)
% 228.06/39.61  | | | | | | | | 
% 228.06/39.62  | | | | | | | | REF_CLOSE: (9), (11), (14), (16), (30), (32), (37), (43), (47),
% 228.06/39.62  | | | | | | | |            (55), (64), (65), (72), (210) are inconsistent by
% 228.06/39.62  | | | | | | | |            sub-proof #1786.
% 228.06/39.62  | | | | | | | | 
% 228.06/39.62  | | | | | | | End of split
% 228.06/39.62  | | | | | | | 
% 228.06/39.62  | | | | | | Case 2:
% 228.06/39.62  | | | | | | | 
% 228.06/39.62  | | | | | | |   (211)  all_57_15 = e2 & op(e0, e0) = e2
% 228.06/39.62  | | | | | | | 
% 228.06/39.62  | | | | | | | REF_CLOSE: (30), (37), (211) are inconsistent by sub-proof #2323.
% 228.06/39.62  | | | | | | | 
% 228.06/39.62  | | | | | | End of split
% 228.06/39.62  | | | | | | 
% 228.06/39.62  | | | | | End of split
% 228.06/39.62  | | | | | 
% 228.06/39.62  | | | | End of split
% 228.06/39.62  | | | | 
% 228.06/39.62  | | | End of split
% 228.06/39.62  | | | 
% 228.06/39.62  | | End of split
% 228.06/39.62  | | 
% 228.06/39.62  | End of split
% 228.06/39.62  | 
% 228.06/39.62  End of proof
% 228.06/39.62  
% 228.06/39.62  Sub-proof #412 shows that the following formulas are inconsistent:
% 228.06/39.62  ----------------------------------------------------------------
% 228.06/39.62    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.06/39.62    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.06/39.62    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.06/39.62         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.06/39.62    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.06/39.62         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.06/39.62    (5)  op(e2, e1) = e3
% 228.06/39.62    (6)   ~ (all_53_8 = all_53_12)
% 228.06/39.62    (7)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.06/39.62         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.06/39.62    (8)   ~ (e3 = e1)
% 228.06/39.62    (9)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.06/39.62         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.06/39.62    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.06/39.62            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.06/39.62    (11)  op(e1, e2) = e3
% 228.06/39.62    (12)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.06/39.62            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.06/39.62              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.06/39.62    (13)  op(e1, e1) = all_6_2
% 228.06/39.62    (14)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.06/39.62    (15)   ~ (all_53_9 = e0)
% 228.06/39.62    (16)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.06/39.62          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.06/39.62    (17)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3)
% 228.06/39.62    (18)   ~ (all_53_4 = all_53_12)
% 228.06/39.62    (19)   ~ (all_53_8 = all_53_9)
% 228.06/39.62    (20)  all_42_2 = all_6_2
% 228.06/39.62    (21)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.06/39.62          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.06/39.62    (22)   ~ (all_53_9 = all_6_2)
% 228.06/39.62    (23)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.06/39.62          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.06/39.62    (24)  all_57_3 = e0
% 228.06/39.62    (25)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.06/39.62          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.06/39.62    (26)   ~ (e3 = e2)
% 228.06/39.62    (27)  all_55_1 = all_53_4
% 228.06/39.62    (28)   ~ (e3 = e0)
% 228.06/39.62    (29)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.06/39.62          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.06/39.62    (30)   ~ (all_53_8 = all_6_2)
% 228.06/39.62    (31)  all_55_2 = all_53_8
% 228.06/39.62    (32)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.06/39.62    (33)  all_57_15 = e3
% 228.06/39.62    (34)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.06/39.62          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.06/39.62            e1)
% 228.06/39.62    (35)  all_57_5 = e3
% 228.06/39.62    (36)   ~ (all_53_4 = all_53_8)
% 228.06/39.62    (37)  op(e3, e2) = all_53_4
% 228.06/39.62    (38)   ~ (e2 = e0)
% 228.06/39.62    (39)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.06/39.62            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.06/39.62            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.06/39.62            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.06/39.62              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.06/39.62            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.06/39.62            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.06/39.62              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.06/39.62              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.06/39.62            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.06/39.62            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.06/39.62            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.06/39.62              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.06/39.62              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.06/39.62            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.06/39.62              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.06/39.62            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.06/39.62            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.06/39.62              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.06/39.62              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.06/39.62            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.06/39.62            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.06/39.62    (40)   ~ (e1 = e0)
% 228.06/39.62    (41)  all_57_12 = e3
% 228.06/39.62    (42)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.06/39.62            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.06/39.62              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.06/39.62    (43)   ~ (all_53_4 = e0)
% 228.06/39.62    (44)  op(e0, e0) = e3
% 228.06/39.62    (45)   ~ (all_53_4 = all_53_6)
% 228.06/39.62    (46)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.06/39.62          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.06/39.62            e2)
% 228.06/39.62    (47)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.06/39.62              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.06/39.62                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.06/39.62                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.06/39.62    (48)  all_55_10 = all_6_2
% 228.06/39.62    (49)  all_38_2 = all_6_2
% 228.06/39.62    (50)  all_55_3 = all_53_12
% 228.06/39.62    (51)   ~ (all_53_12 = e3)
% 228.06/39.62    (52)  all_57_7 = e3
% 228.06/39.62    (53)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.06/39.62            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.06/39.62              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.06/39.62    (54)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.06/39.62          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.06/39.62    (55)   ~ (e2 = e1)
% 228.06/39.62    (56)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.06/39.62          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.06/39.62    (57)  op(e2, e1) = all_53_9
% 228.06/39.62    (58)  op(e1, e2) = all_53_6
% 228.06/39.62    (59)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.06/39.62          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.06/39.62    (60)  all_24_2 = all_6_2
% 228.06/39.62    (61)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.06/39.62          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.06/39.62    (62)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.06/39.62          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.06/39.62    (63)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.06/39.62          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.06/39.62    (64)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.06/39.62          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.06/39.62    (65)  op(e3, e1) = all_53_8
% 228.06/39.62    (66)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.06/39.62          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.06/39.62    (67)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.06/39.62          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.06/39.62    (68)  op(e3, e0) = all_53_12
% 228.06/39.62  
% 228.06/39.62  Begin of proof
% 228.06/39.62  | 
% 228.06/39.62  | BETA: splitting (17) gives:
% 228.06/39.62  | 
% 228.06/39.62  | Case 1:
% 228.06/39.62  | | 
% 228.06/39.62  | |   (69)  all_57_0 = e3 & op(e3, e3) = e3
% 228.06/39.62  | | 
% 228.06/39.62  | | ALPHA: (69) implies:
% 228.06/39.62  | |   (70)  op(e3, e3) = e3
% 228.06/39.62  | | 
% 228.06/39.62  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.06/39.62  | |            (13), (14), (15), (16), (18), (19), (20), (21), (22), (23), (24),
% 228.06/39.62  | |            (25), (26), (27), (29), (30), (31), (32), (33), (34), (35), (36),
% 228.06/39.62  | |            (37), (38), (39), (40), (42), (43), (44), (45), (46), (47), (48),
% 228.06/39.62  | |            (49), (50), (51), (52), (53), (54), (55), (56), (57), (58), (59),
% 228.06/39.62  | |            (60), (61), (62), (63), (64), (65), (66), (67), (68), (70) are
% 228.06/39.62  | |            inconsistent by sub-proof #1441.
% 228.06/39.62  | | 
% 228.06/39.62  | Case 2:
% 228.06/39.62  | | 
% 228.06/39.62  | |   (71)  all_57_1 = e3 & op(e3, e2) = e3
% 228.06/39.62  | | 
% 228.06/39.62  | | ALPHA: (71) implies:
% 228.06/39.62  | |   (72)  all_57_1 = e3
% 228.06/39.62  | | 
% 228.06/39.62  | | REF_CLOSE: (7), (8), (24), (26), (28), (33), (34), (38), (40), (41), (46),
% 228.06/39.62  | |            (47), (55), (66), (72) are inconsistent by sub-proof #1037.
% 228.06/39.62  | | 
% 228.06/39.62  | End of split
% 228.06/39.62  | 
% 228.06/39.62  End of proof
% 228.06/39.62  
% 228.06/39.62  Sub-proof #413 shows that the following formulas are inconsistent:
% 228.06/39.62  ----------------------------------------------------------------
% 228.06/39.62    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.06/39.62    (2)  all_57_9 = e2
% 228.06/39.62    (3)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.06/39.62    (4)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.06/39.62         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.06/39.62    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.06/39.62         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.06/39.62    (6)  op(e2, e1) = e3
% 228.06/39.62    (7)   ~ (all_53_8 = all_53_12)
% 228.06/39.62    (8)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.06/39.62         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.06/39.62    (9)   ~ (e3 = e1)
% 228.06/39.62    (10)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.06/39.62          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.06/39.62    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.06/39.62            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.06/39.62    (12)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.06/39.62          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.06/39.62    (13)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.06/39.62            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.06/39.62              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.06/39.62    (14)   ~ (all_6_2 = e3)
% 228.06/39.62    (15)  op(e1, e1) = all_6_2
% 228.06/39.62    (16)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.06/39.62    (17)   ~ (all_53_9 = e0)
% 228.06/39.62    (18)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.06/39.62          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.06/39.62    (19)   ~ (all_53_4 = all_53_12)
% 228.06/39.62    (20)   ~ (all_53_8 = all_53_9)
% 228.06/39.62    (21)  all_42_2 = all_6_2
% 228.06/39.62    (22)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.06/39.62          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.06/39.62    (23)  all_57_8 = e1
% 228.06/39.62    (24)   ~ (all_53_9 = all_6_2)
% 228.06/39.62    (25)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.06/39.62          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.06/39.62    (26)  all_57_3 = e0
% 228.06/39.62    (27)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.06/39.62          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.06/39.62    (28)   ~ (e3 = e2)
% 228.06/39.62    (29)  all_55_1 = all_53_4
% 228.06/39.62    (30)   ~ (e3 = e0)
% 228.06/39.62    (31)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.06/39.62          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.06/39.62    (32)   ~ (all_53_8 = all_6_2)
% 228.06/39.62    (33)  all_55_2 = all_53_8
% 228.06/39.62    (34)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.06/39.62    (35)  all_57_15 = e3
% 228.06/39.62    (36)  op(e3, e3) = e2
% 228.06/39.62    (37)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.06/39.62          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.06/39.62            e1)
% 228.06/39.62    (38)  all_57_10 = e2
% 228.06/39.62    (39)  all_57_5 = e3
% 228.06/39.62    (40)   ~ (all_53_4 = all_53_8)
% 228.06/39.62    (41)  op(e3, e2) = all_53_4
% 228.06/39.62    (42)   ~ (e2 = e0)
% 228.06/39.62    (43)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.06/39.62            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.06/39.62            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.06/39.62            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.06/39.62              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.06/39.62            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.06/39.62            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.06/39.62              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.06/39.62              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.06/39.62            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.06/39.62            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.06/39.62            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.06/39.62              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.06/39.62              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.06/39.62            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.06/39.62              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.06/39.62            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.06/39.62            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.06/39.62              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.06/39.62              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.06/39.62            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.06/39.62            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.06/39.62    (44)  all_57_13 = e2
% 228.06/39.62    (45)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.06/39.62          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.06/39.62    (46)   ~ (e1 = e0)
% 228.06/39.62    (47)  all_57_12 = e3
% 228.06/39.62    (48)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.06/39.62            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.06/39.62              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.06/39.62    (49)   ~ (all_53_4 = e0)
% 228.06/39.62    (50)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.06/39.62          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.06/39.62    (51)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.06/39.62          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.06/39.62    (52)  op(e0, e0) = e3
% 228.06/39.62    (53)   ~ (all_53_4 = all_53_6)
% 228.06/39.62    (54)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.06/39.62          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.06/39.62            e2)
% 228.06/39.62    (55)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.06/39.62              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.06/39.62                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.06/39.62                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.06/39.62    (56)  all_55_10 = all_6_2
% 228.06/39.62    (57)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.06/39.62          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.06/39.62    (58)  all_38_2 = all_6_2
% 228.06/39.62    (59)  all_55_3 = all_53_12
% 228.06/39.62    (60)   ~ (all_53_12 = e3)
% 228.06/39.62    (61)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.06/39.62            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.06/39.62              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.06/39.62    (62)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.06/39.62          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.06/39.62    (63)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.06/39.62          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.06/39.62    (64)   ~ (e2 = e1)
% 228.06/39.62    (65)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.06/39.62          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.06/39.62    (66)  op(e2, e1) = all_53_9
% 228.06/39.62    (67)  op(e1, e2) = all_53_6
% 228.06/39.62    (68)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.06/39.62          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.06/39.62    (69)  all_24_2 = all_6_2
% 228.06/39.62    (70)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.06/39.62          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.06/39.62    (71)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.06/39.62          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.06/39.62    (72)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.06/39.62          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.06/39.62    (73)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.06/39.62          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.06/39.62    (74)  op(e3, e1) = all_53_8
% 228.06/39.62    (75)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.06/39.62          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.06/39.62    (76)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.06/39.62          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.06/39.62    (77)  op(e3, e0) = all_53_12
% 228.06/39.62  
% 228.06/39.62  Begin of proof
% 228.06/39.62  | 
% 228.06/39.62  | BETA: splitting (12) gives:
% 228.06/39.62  | 
% 228.06/39.62  | Case 1:
% 228.06/39.62  | | 
% 228.06/39.62  | |   (78)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 228.06/39.62  | |           e3)
% 228.06/39.62  | | 
% 228.06/39.62  | | BETA: splitting (78) gives:
% 228.06/39.62  | | 
% 228.06/39.62  | | Case 1:
% 228.06/39.62  | | | 
% 228.06/39.62  | | |   (79)  all_57_6 = e3 & op(e1, e3) = e3
% 228.06/39.62  | | | 
% 228.06/39.62  | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 228.06/39.62  | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 228.06/39.62  | | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 228.06/39.62  | | |            (34), (35), (36), (37), (38), (39), (40), (41), (42), (43),
% 228.06/39.62  | | |            (45), (46), (47), (48), (49), (50), (51), (52), (53), (54),
% 228.06/39.62  | | |            (55), (56), (57), (58), (59), (60), (61), (62), (63), (64),
% 228.06/39.62  | | |            (65), (66), (67), (68), (69), (70), (71), (72), (73), (74),
% 228.06/39.62  | | |            (75), (76), (77), (79) are inconsistent by sub-proof #414.
% 228.06/39.62  | | | 
% 228.06/39.62  | | Case 2:
% 228.06/39.62  | | | 
% 228.06/39.62  | | |   (80)  all_57_7 = e3 & op(e1, e2) = e3
% 228.06/39.62  | | | 
% 228.06/39.62  | | | ALPHA: (80) implies:
% 228.06/39.62  | | |   (81)  all_57_7 = e3
% 228.06/39.62  | | |   (82)  op(e1, e2) = e3
% 228.06/39.62  | | | 
% 228.06/39.62  | | | BETA: splitting (72) gives:
% 228.06/39.62  | | | 
% 228.06/39.62  | | | Case 1:
% 228.06/39.62  | | | | 
% 228.06/39.62  | | | |   (83)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0)
% 228.06/39.62  | | | |           = e1)
% 228.06/39.62  | | | | 
% 228.06/39.62  | | | | BETA: splitting (83) gives:
% 228.06/39.62  | | | | 
% 228.06/39.62  | | | | Case 1:
% 228.06/39.62  | | | | | 
% 228.06/39.62  | | | | |   (84)  all_57_9 = e1 & op(e3, e0) = e1
% 228.06/39.62  | | | | | 
% 228.06/39.62  | | | | | REF_CLOSE: (2), (64), (84) are inconsistent by sub-proof #2451.
% 228.06/39.62  | | | | | 
% 228.06/39.62  | | | | Case 2:
% 228.06/39.62  | | | | | 
% 228.06/39.62  | | | | |   (85)  all_57_10 = e1 & op(e2, e0) = e1
% 228.06/39.62  | | | | | 
% 228.06/39.62  | | | | | REF_CLOSE: (38), (64), (85) are inconsistent by sub-proof #2360.
% 228.06/39.62  | | | | | 
% 228.06/39.62  | | | | End of split
% 228.06/39.62  | | | | 
% 228.06/39.62  | | | Case 2:
% 228.06/39.62  | | | | 
% 228.06/39.62  | | | |   (86)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0,
% 228.06/39.62  | | | |             e0) = e1)
% 228.06/39.62  | | | | 
% 228.06/39.62  | | | | BETA: splitting (86) gives:
% 228.06/39.62  | | | | 
% 228.06/39.62  | | | | Case 1:
% 228.06/39.62  | | | | | 
% 228.06/39.62  | | | | |   (87)  all_57_11 = e1 & op(e1, e0) = e1
% 228.06/39.62  | | | | | 
% 228.06/39.62  | | | | | ALPHA: (87) implies:
% 228.06/39.62  | | | | |   (88)  all_57_11 = e1
% 228.06/39.62  | | | | | 
% 228.06/39.62  | | | | | BETA: splitting (45) gives:
% 228.06/39.62  | | | | | 
% 228.06/39.62  | | | | | Case 1:
% 228.06/39.62  | | | | | | 
% 228.06/39.62  | | | | | |   (89)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3,
% 228.06/39.62  | | | | | |             e2) = e3)
% 228.06/39.62  | | | | | | 
% 228.06/39.62  | | | | | | BETA: splitting (89) gives:
% 228.06/39.62  | | | | | | 
% 228.06/39.62  | | | | | | Case 1:
% 228.06/39.62  | | | | | | | 
% 228.06/39.62  | | | | | | |   (90)  all_57_0 = e3 & op(e3, e3) = e3
% 228.06/39.62  | | | | | | | 
% 228.06/39.62  | | | | | | | ALPHA: (90) implies:
% 228.06/39.62  | | | | | | |   (91)  op(e3, e3) = e3
% 228.06/39.62  | | | | | | | 
% 228.06/39.62  | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 228.06/39.62  | | | | | | |            (13), (15), (16), (17), (18), (19), (20), (21), (22),
% 228.06/39.62  | | | | | | |            (24), (25), (26), (27), (28), (29), (31), (32), (33),
% 228.06/39.62  | | | | | | |            (34), (35), (37), (39), (40), (41), (42), (43), (46),
% 228.06/39.62  | | | | | | |            (48), (49), (52), (53), (54), (55), (56), (58), (59),
% 228.06/39.62  | | | | | | |            (60), (61), (62), (64), (65), (66), (67), (68), (69),
% 228.06/39.62  | | | | | | |            (70), (71), (72), (73), (74), (75), (76), (77), (81),
% 228.06/39.62  | | | | | | |            (82), (91) are inconsistent by sub-proof #1441.
% 228.06/39.62  | | | | | | | 
% 228.06/39.62  | | | | | | Case 2:
% 228.06/39.62  | | | | | | | 
% 228.06/39.62  | | | | | | |   (92)  all_57_1 = e3 & op(e3, e2) = e3
% 228.06/39.62  | | | | | | | 
% 228.06/39.62  | | | | | | | ALPHA: (92) implies:
% 228.06/39.62  | | | | | | |   (93)  all_57_1 = e3
% 228.06/39.62  | | | | | | | 
% 228.06/39.62  | | | | | | | REF_CLOSE: (9), (26), (44), (46), (64), (75), (81), (93) are
% 228.06/39.62  | | | | | | |            inconsistent by sub-proof #1779.
% 228.06/39.62  | | | | | | | 
% 228.06/39.62  | | | | | | End of split
% 228.06/39.62  | | | | | | 
% 228.06/39.62  | | | | | Case 2:
% 228.06/39.62  | | | | | | 
% 228.06/39.62  | | | | | |   (94)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3,
% 228.06/39.62  | | | | | |             e0) = e3)
% 228.06/39.62  | | | | | | 
% 228.06/39.62  | | | | | | BETA: splitting (94) gives:
% 228.06/39.62  | | | | | | 
% 228.06/39.62  | | | | | | Case 1:
% 228.06/39.62  | | | | | | | 
% 228.06/39.62  | | | | | | |   (95)  all_57_4 = e3 & op(e3, e1) = e3
% 228.06/39.62  | | | | | | | 
% 228.06/39.62  | | | | | | | ALPHA: (95) implies:
% 228.06/39.62  | | | | | | |   (96)  all_57_4 = e3
% 228.06/39.62  | | | | | | | 
% 228.06/39.62  | | | | | | | REF_CLOSE: (1), (3), (4), (5), (7), (8), (9), (10), (11), (12),
% 228.06/39.62  | | | | | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21),
% 228.06/39.62  | | | | | | |            (22), (23), (24), (25), (26), (27), (28), (29), (30),
% 228.06/39.62  | | | | | | |            (31), (32), (33), (34), (35), (36), (37), (40), (41),
% 228.06/39.62  | | | | | | |            (42), (43), (45), (46), (48), (49), (50), (52), (53),
% 228.06/39.62  | | | | | | |            (54), (55), (56), (57), (58), (59), (60), (61), (62),
% 228.06/39.62  | | | | | | |            (63), (64), (65), (66), (67), (68), (69), (70), (71),
% 228.06/39.62  | | | | | | |            (72), (73), (74), (75), (76), (77), (81), (88), (96)
% 228.06/39.62  | | | | | | |            are inconsistent by sub-proof #499.
% 228.06/39.62  | | | | | | | 
% 228.06/39.62  | | | | | | Case 2:
% 228.06/39.62  | | | | | | | 
% 228.06/39.62  | | | | | | |   (97)  all_57_9 = e3 & op(e3, e0) = e3
% 228.06/39.62  | | | | | | | 
% 228.06/39.62  | | | | | | | ALPHA: (97) implies:
% 228.06/39.62  | | | | | | |   (98)  op(e3, e0) = e3
% 228.06/39.62  | | | | | | | 
% 228.06/39.62  | | | | | | | REF_CLOSE: (11), (60), (77), (98) are inconsistent by sub-proof
% 228.06/39.62  | | | | | | |            #2458.
% 228.06/39.62  | | | | | | | 
% 228.06/39.62  | | | | | | End of split
% 228.06/39.62  | | | | | | 
% 228.06/39.62  | | | | | End of split
% 228.06/39.62  | | | | | 
% 228.06/39.62  | | | | Case 2:
% 228.06/39.62  | | | | | 
% 228.06/39.62  | | | | |   (99)  all_57_15 = e1 & op(e0, e0) = e1
% 228.06/39.62  | | | | | 
% 228.06/39.62  | | | | | REF_CLOSE: (9), (35), (99) are inconsistent by sub-proof #2325.
% 228.06/39.62  | | | | | 
% 228.06/39.62  | | | | End of split
% 228.06/39.62  | | | | 
% 228.06/39.62  | | | End of split
% 228.06/39.62  | | | 
% 228.06/39.62  | | End of split
% 228.06/39.62  | | 
% 228.06/39.62  | Case 2:
% 228.06/39.62  | | 
% 228.06/39.62  | |   (100)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 228.06/39.62  | |            e3)
% 228.06/39.62  | | 
% 228.06/39.62  | | REF_CLOSE: (9), (11), (14), (15), (28), (30), (35), (42), (46), (55), (64),
% 228.06/39.62  | |            (65), (72), (100) are inconsistent by sub-proof #1786.
% 228.06/39.62  | | 
% 228.06/39.62  | End of split
% 228.06/39.62  | 
% 228.06/39.62  End of proof
% 228.06/39.62  
% 228.06/39.62  Sub-proof #414 shows that the following formulas are inconsistent:
% 228.06/39.62  ----------------------------------------------------------------
% 228.06/39.62    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.06/39.62    (2)  all_57_9 = e2
% 228.06/39.62    (3)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.06/39.62    (4)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.06/39.62         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.06/39.62    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.06/39.62         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.06/39.62    (6)   ~ (all_53_8 = all_53_12)
% 228.06/39.62    (7)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.06/39.62         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.06/39.62    (8)   ~ (e3 = e1)
% 228.06/39.62    (9)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.06/39.62         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.06/39.62    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.06/39.62            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.06/39.62    (11)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.06/39.62          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.06/39.62    (12)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.06/39.62            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.06/39.62              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.06/39.62    (13)   ~ (all_6_2 = e3)
% 228.06/39.62    (14)  op(e1, e1) = all_6_2
% 228.06/39.62    (15)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.06/39.62    (16)   ~ (all_53_9 = e0)
% 228.06/39.62    (17)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.06/39.62          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.06/39.62    (18)   ~ (all_53_4 = all_53_12)
% 228.06/39.62    (19)   ~ (all_53_8 = all_53_9)
% 228.06/39.62    (20)  all_42_2 = all_6_2
% 228.06/39.62    (21)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.06/39.62          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.06/39.62    (22)  all_57_8 = e1
% 228.06/39.62    (23)   ~ (all_53_9 = all_6_2)
% 228.06/39.62    (24)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.06/39.62          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.06/39.62    (25)  all_57_3 = e0
% 228.06/39.62    (26)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.06/39.62          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.06/39.63    (27)   ~ (e3 = e2)
% 228.06/39.63    (28)  all_55_1 = all_53_4
% 228.06/39.63    (29)   ~ (e3 = e0)
% 228.06/39.63    (30)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.06/39.63          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.06/39.63    (31)   ~ (all_53_8 = all_6_2)
% 228.06/39.63    (32)  all_55_2 = all_53_8
% 228.06/39.63    (33)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.06/39.63    (34)  all_57_15 = e3
% 228.06/39.63    (35)  op(e3, e3) = e2
% 228.06/39.63    (36)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.06/39.63          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.06/39.63            e1)
% 228.06/39.63    (37)  all_57_10 = e2
% 228.06/39.63    (38)  all_57_5 = e3
% 228.06/39.63    (39)   ~ (all_53_4 = all_53_8)
% 228.06/39.63    (40)  op(e3, e2) = all_53_4
% 228.06/39.63    (41)   ~ (e2 = e0)
% 228.06/39.63    (42)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.06/39.63            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.06/39.63            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.06/39.63            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.06/39.63              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.06/39.63            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.06/39.63            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.06/39.63              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.06/39.63              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.06/39.63            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.06/39.63            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.06/39.63            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.06/39.63              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.06/39.63              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.06/39.63            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.06/39.63              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.06/39.63            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.06/39.63            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.06/39.63              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.06/39.63              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.06/39.63            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.06/39.63            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.06/39.63    (43)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.06/39.63          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.06/39.63    (44)   ~ (e1 = e0)
% 228.06/39.63    (45)  all_57_12 = e3
% 228.06/39.63    (46)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.06/39.63            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.06/39.63              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.06/39.63    (47)   ~ (all_53_4 = e0)
% 228.06/39.63    (48)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.06/39.63          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.06/39.63    (49)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.06/39.63          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.06/39.63    (50)  op(e0, e0) = e3
% 228.06/39.63    (51)   ~ (all_53_4 = all_53_6)
% 228.06/39.63    (52)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.06/39.63          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.06/39.63            e2)
% 228.06/39.63    (53)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.06/39.63              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.06/39.63                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.06/39.63                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.06/39.63    (54)  all_55_10 = all_6_2
% 228.06/39.63    (55)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.06/39.63          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.06/39.63    (56)  all_38_2 = all_6_2
% 228.06/39.63    (57)  all_55_3 = all_53_12
% 228.06/39.63    (58)   ~ (all_53_12 = e3)
% 228.06/39.63    (59)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.06/39.63            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.06/39.63              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.06/39.63    (60)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.06/39.63          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.06/39.63    (61)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.06/39.63          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.06/39.63    (62)   ~ (e2 = e1)
% 228.06/39.63    (63)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.06/39.63          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.06/39.63    (64)  op(e2, e1) = all_53_9
% 228.06/39.63    (65)  op(e1, e2) = all_53_6
% 228.06/39.63    (66)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.06/39.63          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.06/39.63    (67)  all_57_6 = e3 & op(e1, e3) = e3
% 228.06/39.63    (68)  all_24_2 = all_6_2
% 228.06/39.63    (69)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.06/39.63          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.06/39.63    (70)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.06/39.63          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.06/39.63    (71)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.06/39.63          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.06/39.63    (72)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.06/39.63          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.06/39.63    (73)  op(e3, e1) = all_53_8
% 228.06/39.63    (74)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.06/39.63          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.06/39.63    (75)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.06/39.63          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.06/39.63    (76)  op(e3, e0) = all_53_12
% 228.06/39.63  
% 228.06/39.63  Begin of proof
% 228.06/39.63  | 
% 228.06/39.63  | ALPHA: (67) implies:
% 228.06/39.63  |   (77)  all_57_6 = e3
% 228.06/39.63  | 
% 228.06/39.63  | BETA: splitting (71) gives:
% 228.06/39.63  | 
% 228.06/39.63  | Case 1:
% 228.06/39.63  | | 
% 228.06/39.63  | |   (78)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) =
% 228.06/39.63  | |           e1)
% 228.06/39.63  | | 
% 228.06/39.63  | | BETA: splitting (78) gives:
% 228.06/39.63  | | 
% 228.06/39.63  | | Case 1:
% 228.06/39.63  | | | 
% 228.06/39.63  | | |   (79)  all_57_9 = e1 & op(e3, e0) = e1
% 228.06/39.63  | | | 
% 228.06/39.63  | | | REF_CLOSE: (2), (62), (79) are inconsistent by sub-proof #2451.
% 228.06/39.63  | | | 
% 228.06/39.63  | | Case 2:
% 228.06/39.63  | | | 
% 228.06/39.63  | | |   (80)  all_57_10 = e1 & op(e2, e0) = e1
% 228.06/39.63  | | | 
% 228.06/39.63  | | | REF_CLOSE: (37), (62), (80) are inconsistent by sub-proof #2360.
% 228.06/39.63  | | | 
% 228.06/39.63  | | End of split
% 228.06/39.63  | | 
% 228.06/39.63  | Case 2:
% 228.06/39.63  | | 
% 228.06/39.63  | |   (81)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.06/39.63  | |           e1)
% 228.06/39.63  | | 
% 228.06/39.63  | | BETA: splitting (81) gives:
% 228.06/39.63  | | 
% 228.06/39.63  | | Case 1:
% 228.06/39.63  | | | 
% 228.06/39.63  | | |   (82)  all_57_11 = e1 & op(e1, e0) = e1
% 228.06/39.63  | | | 
% 228.06/39.63  | | | ALPHA: (82) implies:
% 228.06/39.63  | | |   (83)  all_57_11 = e1
% 228.06/39.63  | | | 
% 228.06/39.63  | | | BETA: splitting (43) gives:
% 228.06/39.63  | | | 
% 228.06/39.63  | | | Case 1:
% 228.06/39.63  | | | | 
% 228.06/39.63  | | | |   (84)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2)
% 228.06/39.63  | | | |           = e3)
% 228.06/39.63  | | | | 
% 228.06/39.63  | | | | BETA: splitting (84) gives:
% 228.06/39.63  | | | | 
% 228.06/39.63  | | | | Case 1:
% 228.06/39.63  | | | | | 
% 228.06/39.63  | | | | |   (85)  all_57_0 = e3 & op(e3, e3) = e3
% 228.06/39.63  | | | | | 
% 228.06/39.63  | | | | | ALPHA: (85) implies:
% 228.06/39.63  | | | | |   (86)  all_57_0 = e3
% 228.06/39.63  | | | | | 
% 228.06/39.63  | | | | | REF_CLOSE: (5), (8), (27), (29), (41), (44), (62), (66), (70), (77),
% 228.06/39.63  | | | | |            (86) are inconsistent by sub-proof #2010.
% 228.06/39.63  | | | | | 
% 228.06/39.63  | | | | Case 2:
% 228.06/39.63  | | | | | 
% 228.06/39.63  | | | | |   (87)  all_57_1 = e3 & op(e3, e2) = e3
% 228.06/39.63  | | | | | 
% 228.06/39.63  | | | | | ALPHA: (87) implies:
% 228.06/39.63  | | | | |   (88)  all_57_1 = e3
% 228.06/39.63  | | | | | 
% 228.06/39.63  | | | | | REF_CLOSE: (7), (8), (25), (27), (29), (34), (36), (41), (44), (45),
% 228.06/39.63  | | | | |            (52), (53), (62), (74), (88) are inconsistent by sub-proof
% 228.06/39.63  | | | | |            #1037.
% 228.06/39.63  | | | | | 
% 228.06/39.63  | | | | End of split
% 228.06/39.63  | | | | 
% 228.06/39.63  | | | Case 2:
% 228.06/39.63  | | | | 
% 228.06/39.63  | | | |   (89)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0)
% 228.06/39.63  | | | |           = e3)
% 228.06/39.63  | | | | 
% 228.06/39.63  | | | | BETA: splitting (89) gives:
% 228.06/39.63  | | | | 
% 228.06/39.63  | | | | Case 1:
% 228.06/39.63  | | | | | 
% 228.06/39.63  | | | | |   (90)  all_57_4 = e3 & op(e3, e1) = e3
% 228.06/39.63  | | | | | 
% 228.06/39.63  | | | | | ALPHA: (90) implies:
% 228.06/39.63  | | | | |   (91)  all_57_4 = e3
% 228.06/39.63  | | | | | 
% 228.06/39.63  | | | | | BETA: splitting (49) gives:
% 228.06/39.63  | | | | | 
% 228.06/39.63  | | | | | Case 1:
% 228.06/39.63  | | | | | | 
% 228.06/39.63  | | | | | |   (92)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2,
% 228.06/39.63  | | | | | |             e2) = e3)
% 228.06/39.63  | | | | | | 
% 228.06/39.63  | | | | | | BETA: splitting (92) gives:
% 228.06/39.63  | | | | | | 
% 228.06/39.63  | | | | | | Case 1:
% 228.06/39.63  | | | | | | | 
% 228.06/39.63  | | | | | | |   (93)  all_57_1 = e3 & op(e3, e2) = e3
% 228.06/39.63  | | | | | | | 
% 228.06/39.63  | | | | | | | ALPHA: (93) implies:
% 228.06/39.63  | | | | | | |   (94)  all_57_1 = e3
% 228.06/39.63  | | | | | | | 
% 228.06/39.63  | | | | | | | REF_CLOSE: (7), (8), (25), (27), (29), (34), (36), (41), (44),
% 228.06/39.63  | | | | | | |            (45), (52), (53), (62), (74), (94) are inconsistent by
% 228.06/39.63  | | | | | | |            sub-proof #1037.
% 228.06/39.63  | | | | | | | 
% 228.06/39.63  | | | | | | Case 2:
% 228.06/39.63  | | | | | | | 
% 228.06/39.63  | | | | | | |   (95)  all_57_3 = e3 & op(e2, e2) = e3
% 228.06/39.63  | | | | | | | 
% 228.06/39.63  | | | | | | | ALPHA: (95) implies:
% 228.06/39.63  | | | | | | |   (96)  all_57_3 = e3
% 228.06/39.63  | | | | | | | 
% 228.06/39.63  | | | | | | | REF_CLOSE: (25), (29), (96) are inconsistent by sub-proof #2358.
% 228.06/39.63  | | | | | | | 
% 228.06/39.63  | | | | | | End of split
% 228.06/39.63  | | | | | | 
% 228.06/39.63  | | | | | Case 2:
% 228.06/39.63  | | | | | | 
% 228.06/39.63  | | | | | |   (97)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0,
% 228.06/39.63  | | | | | |             e2) = e3)
% 228.06/39.63  | | | | | | 
% 228.06/39.63  | | | | | | BETA: splitting (97) gives:
% 228.06/39.63  | | | | | | 
% 228.06/39.63  | | | | | | Case 1:
% 228.06/39.63  | | | | | | | 
% 228.06/39.63  | | | | | | |   (98)  all_57_7 = e3 & op(e1, e2) = e3
% 228.06/39.63  | | | | | | | 
% 228.06/39.63  | | | | | | | ALPHA: (98) implies:
% 228.06/39.63  | | | | | | |   (99)  all_57_7 = e3
% 228.06/39.63  | | | | | | | 
% 228.06/39.63  | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 228.06/39.63  | | | | | | |            (12), (13), (14), (15), (16), (17), (18), (19), (20),
% 228.06/39.63  | | | | | | |            (21), (22), (23), (24), (25), (26), (27), (28), (29),
% 228.06/39.63  | | | | | | |            (30), (31), (32), (33), (34), (35), (36), (39), (40),
% 228.06/39.63  | | | | | | |            (41), (42), (43), (44), (46), (47), (48), (50), (51),
% 228.06/39.63  | | | | | | |            (52), (53), (54), (55), (56), (57), (58), (59), (60),
% 228.06/39.63  | | | | | | |            (61), (62), (63), (64), (65), (66), (68), (69), (70),
% 228.06/39.63  | | | | | | |            (71), (72), (73), (74), (75), (76), (83), (91), (99)
% 228.06/39.63  | | | | | | |            are inconsistent by sub-proof #499.
% 228.06/39.63  | | | | | | | 
% 228.06/39.63  | | | | | | Case 2:
% 228.06/39.63  | | | | | | | 
% 228.06/39.63  | | | | | | |   (100)  all_57_13 = e3 & op(e0, e2) = e3
% 228.06/39.63  | | | | | | | 
% 228.06/39.63  | | | | | | | ALPHA: (100) implies:
% 228.06/39.63  | | | | | | |   (101)  all_57_13 = e3
% 228.06/39.63  | | | | | | | 
% 228.06/39.63  | | | | | | | REF_CLOSE: (8), (27), (34), (36), (41), (44), (45), (52), (53),
% 228.06/39.63  | | | | | | |            (62), (101) are inconsistent by sub-proof #1733.
% 228.06/39.63  | | | | | | | 
% 228.06/39.63  | | | | | | End of split
% 228.06/39.63  | | | | | | 
% 228.06/39.63  | | | | | End of split
% 228.06/39.63  | | | | | 
% 228.06/39.63  | | | | Case 2:
% 228.06/39.63  | | | | | 
% 228.06/39.63  | | | | |   (102)  all_57_9 = e3 & op(e3, e0) = e3
% 228.06/39.63  | | | | | 
% 228.06/39.63  | | | | | ALPHA: (102) implies:
% 228.06/39.63  | | | | |   (103)  op(e3, e0) = e3
% 228.06/39.63  | | | | | 
% 228.06/39.63  | | | | | REF_CLOSE: (10), (58), (76), (103) are inconsistent by sub-proof
% 228.06/39.63  | | | | |            #2458.
% 228.06/39.63  | | | | | 
% 228.06/39.63  | | | | End of split
% 228.06/39.63  | | | | 
% 228.06/39.63  | | | End of split
% 228.06/39.63  | | | 
% 228.06/39.63  | | Case 2:
% 228.06/39.63  | | | 
% 228.06/39.63  | | |   (104)  all_57_15 = e1 & op(e0, e0) = e1
% 228.06/39.63  | | | 
% 228.06/39.63  | | | ALPHA: (104) implies:
% 228.06/39.63  | | |   (105)  all_57_15 = e1
% 228.06/39.63  | | | 
% 228.06/39.63  | | | COMBINE_EQS: (34), (105) imply:
% 228.06/39.63  | | |   (106)  e3 = e1
% 228.06/39.63  | | | 
% 228.06/39.63  | | | COMBINE_EQS: (77), (106) imply:
% 228.06/39.63  | | |   (107)  all_57_6 = e1
% 228.06/39.63  | | | 
% 228.06/39.63  | | | REF_CLOSE: (4), (8), (10), (25), (27), (29), (35), (38), (41), (44), (45),
% 228.06/39.63  | | |            (60), (62), (70), (107) are inconsistent by sub-proof #1643.
% 228.06/39.63  | | | 
% 228.06/39.63  | | End of split
% 228.06/39.63  | | 
% 228.06/39.63  | End of split
% 228.06/39.63  | 
% 228.06/39.63  End of proof
% 228.06/39.63  
% 228.06/39.63  Sub-proof #415 shows that the following formulas are inconsistent:
% 228.06/39.63  ----------------------------------------------------------------
% 228.06/39.63    (1)  all_57_9 = e2
% 228.06/39.63    (2)  all_57_0 = e2
% 228.06/39.63    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.06/39.63         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.06/39.63    (4)  all_57_12 = e0
% 228.06/39.63    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.06/39.63         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.06/39.63    (6)   ~ (e3 = e1)
% 228.06/39.63    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.06/39.63           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.06/39.63    (8)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.06/39.63    (9)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.06/39.63         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.06/39.63    (10)  all_57_3 = e0
% 228.06/39.63    (11)   ~ (e3 = e2)
% 228.06/39.63    (12)   ~ (e3 = e0)
% 228.06/39.63    (13)  all_57_5 = e3
% 228.06/39.63    (14)   ~ (e2 = e0)
% 228.06/39.63    (15)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.06/39.63          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.06/39.63    (16)   ~ (e1 = e0)
% 228.06/39.63    (17)  all_57_6 = e3
% 228.06/39.63    (18)  all_57_2 = e1
% 228.06/39.63    (19)   ~ (all_53_12 = e3)
% 228.06/39.63    (20)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.06/39.63          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.06/39.63    (21)   ~ (e2 = e1)
% 228.06/39.63    (22)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.06/39.63          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.06/39.63    (23)  op(e3, e0) = all_53_12
% 228.06/39.63  
% 228.06/39.63  Begin of proof
% 228.06/39.63  | 
% 228.06/39.63  | BETA: splitting (8) gives:
% 228.06/39.63  | 
% 228.06/39.63  | Case 1:
% 228.06/39.63  | | 
% 228.06/39.63  | |   (24)  all_57_4 = e1 & op(e3, e1) = e1
% 228.06/39.63  | | 
% 228.06/39.63  | | ALPHA: (24) implies:
% 228.06/39.63  | |   (25)  all_57_4 = e1
% 228.06/39.63  | | 
% 228.06/39.63  | | BETA: splitting (15) gives:
% 228.06/39.63  | | 
% 228.06/39.63  | | Case 1:
% 228.06/39.63  | | | 
% 228.06/39.63  | | |   (26)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) =
% 228.06/39.63  | | |           e3)
% 228.06/39.63  | | | 
% 228.06/39.63  | | | BETA: splitting (26) gives:
% 228.06/39.63  | | | 
% 228.06/39.63  | | | Case 1:
% 228.06/39.63  | | | | 
% 228.06/39.63  | | | |   (27)  all_57_0 = e3 & op(e3, e3) = e3
% 228.06/39.63  | | | | 
% 228.06/39.63  | | | | ALPHA: (27) implies:
% 228.06/39.63  | | | |   (28)  all_57_0 = e3
% 228.06/39.63  | | | | 
% 228.06/39.63  | | | | REF_CLOSE: (4), (5), (6), (11), (14), (16), (17), (21), (22), (28) are
% 228.06/39.63  | | | |            inconsistent by sub-proof #2011.
% 228.06/39.63  | | | | 
% 228.06/39.63  | | | Case 2:
% 228.06/39.63  | | | | 
% 228.06/39.63  | | | |   (29)  all_57_1 = e3 & op(e3, e2) = e3
% 228.06/39.63  | | | | 
% 228.06/39.63  | | | | ALPHA: (29) implies:
% 228.06/39.63  | | | |   (30)  all_57_1 = e3
% 228.06/39.63  | | | | 
% 228.06/39.63  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (9), (10), (11), (12), (13),
% 228.06/39.63  | | | |            (14), (16), (17), (18), (20), (21), (22), (25), (30) are
% 228.06/39.63  | | | |            inconsistent by sub-proof #416.
% 228.06/39.63  | | | | 
% 228.06/39.63  | | | End of split
% 228.06/39.63  | | | 
% 228.06/39.63  | | Case 2:
% 228.06/39.63  | | | 
% 228.06/39.63  | | |   (31)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) =
% 228.06/39.63  | | |           e3)
% 228.06/39.63  | | | 
% 228.06/39.63  | | | REF_CLOSE: (6), (7), (19), (23), (25), (31) are inconsistent by sub-proof
% 228.06/39.63  | | |            #2281.
% 228.06/39.63  | | | 
% 228.06/39.63  | | End of split
% 228.06/39.63  | | 
% 228.06/39.63  | Case 2:
% 228.06/39.63  | | 
% 228.06/39.63  | |   (32)  all_57_9 = e1 & op(e3, e0) = e1
% 228.06/39.63  | | 
% 228.06/39.63  | | ALPHA: (32) implies:
% 228.06/39.63  | |   (33)  all_57_9 = e1
% 228.06/39.63  | | 
% 228.06/39.63  | | REF_CLOSE: (1), (21), (33) are inconsistent by sub-proof #2444.
% 228.06/39.63  | | 
% 228.06/39.63  | End of split
% 228.06/39.63  | 
% 228.06/39.63  End of proof
% 228.06/39.63  
% 228.06/39.63  Sub-proof #416 shows that the following formulas are inconsistent:
% 228.06/39.63  ----------------------------------------------------------------
% 228.06/39.63    (1)  all_57_9 = e2
% 228.06/39.63    (2)  all_57_0 = e2
% 228.06/39.63    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.06/39.63         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.06/39.63    (4)  all_57_12 = e0
% 228.06/39.63    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.06/39.63         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.06/39.63    (6)   ~ (e3 = e1)
% 228.06/39.63    (7)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.06/39.63         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.06/39.63    (8)  all_57_3 = e0
% 228.06/39.63    (9)   ~ (e3 = e2)
% 228.06/39.63    (10)   ~ (e3 = e0)
% 228.06/39.63    (11)  all_57_4 = e1
% 228.06/39.63    (12)  all_57_5 = e3
% 228.06/39.63    (13)   ~ (e2 = e0)
% 228.06/39.63    (14)   ~ (e1 = e0)
% 228.06/39.63    (15)  all_57_6 = e3
% 228.06/39.63    (16)  all_57_2 = e1
% 228.06/39.63    (17)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.06/39.63          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.06/39.63    (18)  all_57_1 = e3
% 228.06/39.63    (19)   ~ (e2 = e1)
% 228.06/39.63    (20)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.06/39.63          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.06/39.63  
% 228.06/39.63  Begin of proof
% 228.06/39.63  | 
% 228.06/39.63  | BETA: splitting (7) gives:
% 228.06/39.63  | 
% 228.06/39.63  | Case 1:
% 228.06/39.63  | | 
% 228.06/39.63  | |   (21)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) =
% 228.06/39.63  | |           e0)
% 228.06/39.63  | | 
% 228.06/39.63  | | BETA: splitting (21) gives:
% 228.06/39.63  | | 
% 228.06/39.63  | | Case 1:
% 228.06/39.63  | | | 
% 228.06/39.63  | | |   (22)  all_57_0 = e0 & op(e3, e3) = e0
% 228.06/39.63  | | | 
% 228.06/39.63  | | | ALPHA: (22) implies:
% 228.06/39.63  | | |   (23)  all_57_0 = e0
% 228.06/39.63  | | | 
% 228.06/39.63  | | | REF_CLOSE: (4), (5), (6), (9), (13), (14), (15), (19), (20), (23) are
% 228.06/39.63  | | |            inconsistent by sub-proof #1425.
% 228.06/39.63  | | | 
% 228.06/39.63  | | Case 2:
% 228.06/39.63  | | | 
% 228.06/39.63  | | |   (24)  all_57_1 = e0 & op(e3, e2) = e0
% 228.06/39.63  | | | 
% 228.06/39.63  | | | REF_CLOSE: (10), (18), (24) are inconsistent by sub-proof #1811.
% 228.06/39.63  | | | 
% 228.06/39.63  | | End of split
% 228.06/39.63  | | 
% 228.06/39.63  | Case 2:
% 228.06/39.63  | | 
% 228.06/39.63  | |   (25)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) =
% 228.06/39.63  | |           e0)
% 228.06/39.63  | | 
% 228.06/39.63  | | BETA: splitting (25) gives:
% 228.06/39.63  | | 
% 228.06/39.63  | | Case 1:
% 228.06/39.63  | | | 
% 228.06/39.63  | | |   (26)  all_57_4 = e0 & op(e3, e1) = e0
% 228.06/39.63  | | | 
% 228.06/39.63  | | | ALPHA: (26) implies:
% 228.06/39.63  | | |   (27)  all_57_4 = e0
% 228.06/39.63  | | | 
% 228.06/39.63  | | | REF_CLOSE: (3), (6), (8), (9), (11), (12), (13), (14), (16), (17), (19),
% 228.06/39.63  | | |            (27) are inconsistent by sub-proof #1537.
% 228.06/39.63  | | | 
% 228.06/39.63  | | Case 2:
% 228.06/39.63  | | | 
% 228.06/39.63  | | |   (28)  all_57_9 = e0 & op(e3, e0) = e0
% 228.06/39.63  | | | 
% 228.06/39.63  | | | REF_CLOSE: (1), (2), (4), (5), (6), (9), (13), (14), (15), (19), (20),
% 228.06/39.63  | | |            (28) are inconsistent by sub-proof #457.
% 228.06/39.63  | | | 
% 228.06/39.63  | | End of split
% 228.06/39.63  | | 
% 228.06/39.63  | End of split
% 228.06/39.63  | 
% 228.06/39.63  End of proof
% 228.06/39.63  
% 228.06/39.63  Sub-proof #417 shows that the following formulas are inconsistent:
% 228.06/39.63  ----------------------------------------------------------------
% 228.06/39.63    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.06/39.63         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.06/39.63    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.06/39.63         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.06/39.63    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.06/39.63         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.06/39.63    (4)   ~ (e3 = e1)
% 228.06/39.63    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.06/39.63           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.06/39.63    (6)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.06/39.63         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.06/39.63    (7)   ~ (all_6_2 = e3)
% 228.06/39.63    (8)  op(e1, e1) = all_6_2
% 228.06/39.63    (9)  all_57_3 = e0
% 228.06/39.63    (10)   ~ (e3 = e2)
% 228.06/39.63    (11)   ~ (e3 = e0)
% 228.06/39.63    (12)  all_57_15 = e3
% 228.06/39.63    (13)  all_57_12 = e1
% 228.06/39.63    (14)   ~ (e2 = e0)
% 228.06/39.63    (15)  all_57_2 = e3
% 228.06/39.63    (16)   ~ (e1 = e0)
% 228.06/39.63    (17)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.06/39.63          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.06/39.63            e2)
% 228.06/39.63    (18)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.06/39.63          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.06/39.63    (19)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.06/39.63          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.06/39.63    (20)  all_57_1 = e3
% 228.06/39.63    (21)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) |
% 228.11/39.63          (all_57_11 = e0 & op(e1, e0) = e0)
% 228.11/39.63    (22)   ~ (e2 = e1)
% 228.11/39.63    (23)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.11/39.63          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.11/39.63    (24)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.11/39.63          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.11/39.63    (25)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.11/39.63          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.11/39.63    (26)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.11/39.63          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.11/39.63    (27)  all_57_14 = e0
% 228.11/39.63    (28)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.11/39.63          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.11/39.63  
% 228.11/39.63  Begin of proof
% 228.11/39.63  | 
% 228.11/39.63  | BETA: splitting (17) gives:
% 228.11/39.63  | 
% 228.11/39.63  | Case 1:
% 228.11/39.63  | | 
% 228.11/39.63  | |   (29)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 228.11/39.63  | |           e2)
% 228.11/39.63  | | 
% 228.11/39.63  | | BETA: splitting (29) gives:
% 228.11/39.63  | | 
% 228.11/39.63  | | Case 1:
% 228.11/39.63  | | | 
% 228.11/39.63  | | |   (30)  all_57_12 = e2 & op(e0, e3) = e2
% 228.11/39.63  | | | 
% 228.11/39.63  | | | ALPHA: (30) implies:
% 228.11/39.63  | | |   (31)  all_57_12 = e2
% 228.11/39.63  | | | 
% 228.11/39.63  | | | REF_CLOSE: (13), (22), (31) are inconsistent by sub-proof #2321.
% 228.11/39.63  | | | 
% 228.11/39.63  | | Case 2:
% 228.11/39.63  | | | 
% 228.11/39.63  | | |   (32)  all_57_13 = e2 & op(e0, e2) = e2
% 228.11/39.63  | | | 
% 228.11/39.63  | | | ALPHA: (32) implies:
% 228.11/39.63  | | |   (33)  all_57_13 = e2
% 228.11/39.63  | | | 
% 228.11/39.63  | | | BETA: splitting (24) gives:
% 228.11/39.63  | | | 
% 228.11/39.63  | | | Case 1:
% 228.11/39.63  | | | | 
% 228.11/39.63  | | | |   (34)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3)
% 228.11/39.63  | | | |           = e2)
% 228.11/39.63  | | | | 
% 228.11/39.63  | | | | BETA: splitting (34) gives:
% 228.11/39.63  | | | | 
% 228.11/39.63  | | | | Case 1:
% 228.11/39.63  | | | | | 
% 228.11/39.63  | | | | |   (35)  all_57_0 = e2 & op(e3, e3) = e2
% 228.11/39.63  | | | | | 
% 228.11/39.63  | | | | | ALPHA: (35) implies:
% 228.11/39.63  | | | | |   (36)  all_57_0 = e2
% 228.11/39.63  | | | | |   (37)  op(e3, e3) = e2
% 228.11/39.63  | | | | | 
% 228.11/39.63  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 228.11/39.63  | | | | |            (12), (14), (15), (16), (18), (19), (20), (21), (22), (23),
% 228.11/39.63  | | | | |            (25), (26), (28), (36), (37) are inconsistent by sub-proof
% 228.11/39.63  | | | | |            #793.
% 228.11/39.63  | | | | | 
% 228.11/39.63  | | | | Case 2:
% 228.11/39.63  | | | | | 
% 228.11/39.63  | | | | |   (38)  all_57_2 = e2 & op(e2, e3) = e2
% 228.11/39.63  | | | | | 
% 228.11/39.63  | | | | | REF_CLOSE: (10), (15), (38) are inconsistent by sub-proof #1925.
% 228.11/39.63  | | | | | 
% 228.11/39.63  | | | | End of split
% 228.11/39.63  | | | | 
% 228.11/39.63  | | | Case 2:
% 228.11/39.63  | | | | 
% 228.11/39.63  | | | |   (39)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3)
% 228.11/39.63  | | | |           = e2)
% 228.11/39.63  | | | | 
% 228.11/39.63  | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), (14),
% 228.11/39.63  | | | |            (16), (20), (21), (22), (23), (26), (28), (33), (39) are
% 228.11/39.63  | | | |            inconsistent by sub-proof #418.
% 228.11/39.63  | | | | 
% 228.11/39.63  | | | End of split
% 228.11/39.63  | | | 
% 228.11/39.63  | | End of split
% 228.11/39.63  | | 
% 228.11/39.63  | Case 2:
% 228.11/39.63  | | 
% 228.11/39.63  | |   (40)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.11/39.63  | |           e2)
% 228.11/39.63  | | 
% 228.11/39.63  | | BETA: splitting (40) gives:
% 228.11/39.63  | | 
% 228.11/39.63  | | Case 1:
% 228.11/39.63  | | | 
% 228.11/39.63  | | |   (41)  all_57_14 = e2 & op(e0, e1) = e2
% 228.11/39.63  | | | 
% 228.11/39.63  | | | ALPHA: (41) implies:
% 228.11/39.63  | | |   (42)  all_57_14 = e2
% 228.11/39.63  | | | 
% 228.11/39.63  | | | REF_CLOSE: (14), (27), (42) are inconsistent by sub-proof #2422.
% 228.11/39.63  | | | 
% 228.11/39.63  | | Case 2:
% 228.11/39.63  | | | 
% 228.11/39.63  | | |   (43)  all_57_15 = e2 & op(e0, e0) = e2
% 228.11/39.63  | | | 
% 228.11/39.63  | | | ALPHA: (43) implies:
% 228.11/39.63  | | |   (44)  all_57_15 = e2
% 228.11/39.63  | | | 
% 228.11/39.63  | | | REF_CLOSE: (10), (12), (44) are inconsistent by sub-proof #2058.
% 228.11/39.63  | | | 
% 228.11/39.63  | | End of split
% 228.11/39.63  | | 
% 228.11/39.63  | End of split
% 228.11/39.63  | 
% 228.11/39.63  End of proof
% 228.11/39.63  
% 228.11/39.63  Sub-proof #418 shows that the following formulas are inconsistent:
% 228.11/39.63  ----------------------------------------------------------------
% 228.11/39.63    (1)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.11/39.63    (2)   ~ (e3 = e1)
% 228.11/39.63    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.11/39.63           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.11/39.63    (4)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.11/39.63         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.11/39.63    (5)   ~ (all_6_2 = e3)
% 228.11/39.63    (6)  op(e1, e1) = all_6_2
% 228.11/39.63    (7)  all_57_3 = e0
% 228.11/39.63    (8)   ~ (e3 = e2)
% 228.11/39.63    (9)   ~ (e3 = e0)
% 228.11/39.63    (10)  all_57_15 = e3
% 228.11/39.63    (11)  all_57_12 = e1
% 228.11/39.63    (12)   ~ (e2 = e0)
% 228.11/39.63    (13)  all_57_13 = e2
% 228.11/39.63    (14)   ~ (e1 = e0)
% 228.11/39.63    (15)  all_57_1 = e3
% 228.11/39.63    (16)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) |
% 228.11/39.63          (all_57_11 = e0 & op(e1, e0) = e0)
% 228.11/39.63    (17)   ~ (e2 = e1)
% 228.11/39.63    (18)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.11/39.63          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.11/39.63    (19)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.11/39.63          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.11/39.63    (20)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.11/39.63          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.11/39.63  
% 228.11/39.63  Begin of proof
% 228.11/39.63  | 
% 228.11/39.63  | BETA: splitting (1) gives:
% 228.11/39.63  | 
% 228.11/39.63  | Case 1:
% 228.11/39.63  | | 
% 228.11/39.63  | |   (21)  all_57_6 = e2 & op(e1, e3) = e2
% 228.11/39.63  | | 
% 228.11/39.63  | | ALPHA: (21) implies:
% 228.11/39.63  | |   (22)  all_57_6 = e2
% 228.11/39.63  | | 
% 228.11/39.63  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13), (14),
% 228.11/39.63  | |            (15), (16), (17), (18), (19), (20), (22) are inconsistent by
% 228.11/39.63  | |            sub-proof #419.
% 228.11/39.63  | | 
% 228.11/39.63  | Case 2:
% 228.11/39.63  | | 
% 228.11/39.63  | |   (23)  all_57_12 = e2 & op(e0, e3) = e2
% 228.11/39.63  | | 
% 228.11/39.63  | | ALPHA: (23) implies:
% 228.11/39.63  | |   (24)  all_57_12 = e2
% 228.11/39.63  | | 
% 228.11/39.63  | | REF_CLOSE: (11), (17), (24) are inconsistent by sub-proof #2321.
% 228.11/39.63  | | 
% 228.11/39.63  | End of split
% 228.11/39.63  | 
% 228.11/39.63  End of proof
% 228.11/39.63  
% 228.11/39.63  Sub-proof #419 shows that the following formulas are inconsistent:
% 228.11/39.63  ----------------------------------------------------------------
% 228.11/39.63    (1)   ~ (e3 = e1)
% 228.11/39.64    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.11/39.64           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.11/39.64    (3)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.11/39.64         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.11/39.64    (4)   ~ (all_6_2 = e3)
% 228.11/39.64    (5)  op(e1, e1) = all_6_2
% 228.11/39.64    (6)  all_57_3 = e0
% 228.11/39.64    (7)   ~ (e3 = e2)
% 228.11/39.64    (8)   ~ (e3 = e0)
% 228.11/39.64    (9)  all_57_15 = e3
% 228.11/39.64    (10)  all_57_6 = e2
% 228.11/39.64    (11)   ~ (e2 = e0)
% 228.11/39.64    (12)  all_57_13 = e2
% 228.11/39.64    (13)   ~ (e1 = e0)
% 228.11/39.64    (14)  all_57_1 = e3
% 228.11/39.64    (15)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) |
% 228.11/39.64          (all_57_11 = e0 & op(e1, e0) = e0)
% 228.11/39.64    (16)   ~ (e2 = e1)
% 228.11/39.64    (17)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.11/39.64          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.11/39.64    (18)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.11/39.64          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.11/39.64    (19)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.11/39.64          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.11/39.64  
% 228.11/39.64  Begin of proof
% 228.11/39.64  | 
% 228.11/39.64  | BETA: splitting (3) gives:
% 228.11/39.64  | 
% 228.11/39.64  | Case 1:
% 228.11/39.64  | | 
% 228.11/39.64  | |   (20)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 228.11/39.64  | |           e3)
% 228.11/39.64  | | 
% 228.11/39.64  | | BETA: splitting (20) gives:
% 228.11/39.64  | | 
% 228.11/39.64  | | Case 1:
% 228.11/39.64  | | | 
% 228.11/39.64  | | |   (21)  all_57_6 = e3 & op(e1, e3) = e3
% 228.11/39.64  | | | 
% 228.11/39.64  | | | ALPHA: (21) implies:
% 228.11/39.64  | | |   (22)  all_57_6 = e3
% 228.11/39.64  | | | 
% 228.11/39.64  | | | REF_CLOSE: (7), (10), (22) are inconsistent by sub-proof #2463.
% 228.11/39.64  | | | 
% 228.11/39.64  | | Case 2:
% 228.11/39.64  | | | 
% 228.11/39.64  | | |   (23)  all_57_7 = e3 & op(e1, e2) = e3
% 228.11/39.64  | | | 
% 228.11/39.64  | | | ALPHA: (23) implies:
% 228.11/39.64  | | |   (24)  all_57_7 = e3
% 228.11/39.64  | | | 
% 228.11/39.64  | | | REF_CLOSE: (1), (6), (12), (13), (14), (16), (19), (24) are inconsistent
% 228.11/39.64  | | |            by sub-proof #1779.
% 228.11/39.64  | | | 
% 228.11/39.64  | | End of split
% 228.11/39.64  | | 
% 228.11/39.64  | Case 2:
% 228.11/39.64  | | 
% 228.11/39.64  | |   (25)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 228.11/39.64  | |           e3)
% 228.11/39.64  | | 
% 228.11/39.64  | | REF_CLOSE: (1), (2), (4), (5), (7), (8), (9), (11), (13), (15), (16), (17),
% 228.11/39.64  | |            (18), (25) are inconsistent by sub-proof #1080.
% 228.11/39.64  | | 
% 228.11/39.64  | End of split
% 228.11/39.64  | 
% 228.11/39.64  End of proof
% 228.11/39.64  
% 228.11/39.64  Sub-proof #420 shows that the following formulas are inconsistent:
% 228.11/39.64  ----------------------------------------------------------------
% 228.11/39.64    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.11/39.64    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.11/39.64    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.11/39.64         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.11/39.64    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.11/39.64         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.11/39.64    (5)  op(e2, e1) = e3
% 228.11/39.64    (6)   ~ (all_53_8 = all_53_12)
% 228.11/39.64    (7)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.11/39.64         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.11/39.64    (8)   ~ (e3 = e1)
% 228.11/39.64    (9)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.11/39.64         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.11/39.64    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.11/39.64            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.11/39.64    (11)  all_57_6 = e2 & op(e1, e3) = e2
% 228.11/39.64    (12)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.11/39.64          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.11/39.64    (13)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.11/39.64            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.11/39.64              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.11/39.64    (14)   ~ (all_6_2 = e3)
% 228.11/39.64    (15)  op(e1, e1) = all_6_2
% 228.11/39.64    (16)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.11/39.64    (17)   ~ (all_53_9 = e0)
% 228.11/39.64    (18)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.11/39.64          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.11/39.64    (19)   ~ (all_53_4 = all_53_12)
% 228.11/39.64    (20)   ~ (all_53_8 = all_53_9)
% 228.11/39.64    (21)  all_42_2 = all_6_2
% 228.11/39.64    (22)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.11/39.64          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.11/39.64    (23)   ~ (all_53_9 = all_6_2)
% 228.11/39.64    (24)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.11/39.64          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.11/39.64    (25)  all_57_3 = e0
% 228.11/39.64    (26)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.11/39.64          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.11/39.64    (27)  all_57_4 = e3
% 228.11/39.64    (28)   ~ (e3 = e2)
% 228.11/39.64    (29)  all_55_1 = all_53_4
% 228.11/39.64    (30)   ~ (e3 = e0)
% 228.11/39.64    (31)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.11/39.64          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.11/39.64    (32)   ~ (all_53_8 = all_6_2)
% 228.11/39.64    (33)  all_55_2 = all_53_8
% 228.11/39.64    (34)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.11/39.64    (35)  all_57_15 = e3
% 228.11/39.64    (36)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.11/39.64          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.11/39.64            e1)
% 228.11/39.64    (37)  all_57_5 = e3
% 228.11/39.64    (38)   ~ (all_53_4 = all_53_8)
% 228.11/39.64    (39)  op(e3, e2) = all_53_4
% 228.11/39.64    (40)   ~ (e2 = e0)
% 228.11/39.64    (41)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.11/39.64            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.11/39.64            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.11/39.64            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.11/39.64              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.11/39.64            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.11/39.64            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.11/39.64              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.11/39.64              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.11/39.64            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.11/39.64            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.11/39.64            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.11/39.64              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.11/39.64              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.11/39.64            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.11/39.64              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.11/39.64            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.11/39.64            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.11/39.64              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.11/39.64              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.11/39.64            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.11/39.64            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.11/39.64    (42)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.11/39.64          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.11/39.64    (43)   ~ (e1 = e0)
% 228.11/39.64    (44)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.11/39.64            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.11/39.64              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.11/39.64    (45)   ~ (all_53_4 = e0)
% 228.11/39.64    (46)  all_57_6 = e3
% 228.11/39.64    (47)  op(e0, e0) = e3
% 228.11/39.64    (48)   ~ (all_53_4 = all_53_6)
% 228.11/39.64    (49)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.11/39.64          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.11/39.64            e2)
% 228.11/39.64    (50)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.11/39.64              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.11/39.64                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.11/39.64                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.11/39.64    (51)  all_55_10 = all_6_2
% 228.11/39.64    (52)  all_38_2 = all_6_2
% 228.11/39.64    (53)  all_55_3 = all_53_12
% 228.11/39.64    (54)   ~ (all_53_12 = e3)
% 228.11/39.64    (55)  all_57_7 = e3
% 228.11/39.64    (56)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.11/39.64            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.11/39.64              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.11/39.64    (57)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.11/39.64          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.11/39.64    (58)   ~ (e2 = e1)
% 228.11/39.64    (59)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.11/39.64          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.11/39.64    (60)  op(e2, e1) = all_53_9
% 228.11/39.64    (61)  op(e1, e2) = all_53_6
% 228.11/39.64    (62)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.11/39.64          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.11/39.64    (63)  all_24_2 = all_6_2
% 228.11/39.64    (64)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.11/39.64          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.11/39.64    (65)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.11/39.64          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.11/39.64    (66)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.11/39.64          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.11/39.64    (67)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.11/39.64          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.11/39.64    (68)  op(e3, e1) = all_53_8
% 228.11/39.64    (69)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.11/39.64          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.11/39.64    (70)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.11/39.64          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.11/39.64    (71)  op(e3, e0) = all_53_12
% 228.11/39.64  
% 228.11/39.64  Begin of proof
% 228.11/39.64  | 
% 228.11/39.64  | ALPHA: (11) implies:
% 228.11/39.64  |   (72)  all_57_6 = e2
% 228.11/39.64  | 
% 228.11/39.64  | COMBINE_EQS: (46), (72) imply:
% 228.11/39.64  |   (73)  e3 = e2
% 228.11/39.64  | 
% 228.11/39.64  | COMBINE_EQS: (27), (73) imply:
% 228.11/39.64  |   (74)  all_57_4 = e2
% 228.11/39.64  | 
% 228.11/39.64  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 228.11/39.64  |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 228.11/39.64  |            (25), (26), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 228.11/39.64  |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (47), (48),
% 228.11/39.64  |            (49), (50), (51), (52), (53), (54), (55), (56), (57), (58), (59),
% 228.11/39.64  |            (60), (61), (62), (63), (64), (65), (66), (67), (68), (69), (70),
% 228.11/39.64  |            (71), (74) are inconsistent by sub-proof #547.
% 228.11/39.64  | 
% 228.11/39.64  End of proof
% 228.11/39.64  
% 228.11/39.64  Sub-proof #421 shows that the following formulas are inconsistent:
% 228.11/39.64  ----------------------------------------------------------------
% 228.11/39.64    (1)  op(e3, e3) = e1
% 228.11/39.64    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.11/39.64           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.11/39.64    (3)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2)
% 228.11/39.64    (4)  all_57_2 = e1
% 228.11/39.64    (5)   ~ (e2 = e1)
% 228.11/39.64  
% 228.11/39.64  Begin of proof
% 228.11/39.64  | 
% 228.11/39.64  | BETA: splitting (3) gives:
% 228.11/39.64  | 
% 228.11/39.64  | Case 1:
% 228.11/39.64  | | 
% 228.11/39.64  | |   (6)  all_57_0 = e2 & op(e3, e3) = e2
% 228.11/39.64  | | 
% 228.11/39.64  | | ALPHA: (6) implies:
% 228.11/39.64  | |   (7)  op(e3, e3) = e2
% 228.11/39.64  | | 
% 228.11/39.64  | | REF_CLOSE: (1), (2), (5), (7) are inconsistent by sub-proof #1950.
% 228.11/39.64  | | 
% 228.11/39.64  | Case 2:
% 228.11/39.64  | | 
% 228.11/39.64  | |   (8)  all_57_2 = e2 & op(e2, e3) = e2
% 228.11/39.64  | | 
% 228.11/39.64  | | ALPHA: (8) implies:
% 228.11/39.64  | |   (9)  all_57_2 = e2
% 228.11/39.64  | | 
% 228.11/39.64  | | REF_CLOSE: (4), (5), (9) are inconsistent by sub-proof #2464.
% 228.11/39.64  | | 
% 228.11/39.64  | End of split
% 228.11/39.64  | 
% 228.11/39.64  End of proof
% 228.11/39.64  
% 228.11/39.64  Sub-proof #422 shows that the following formulas are inconsistent:
% 228.11/39.64  ----------------------------------------------------------------
% 228.11/39.64    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.11/39.64    (2)  op(e3, e3) = e1
% 228.11/39.64    (3)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.11/39.64    (4)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.11/39.64         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.11/39.64    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.11/39.64         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.11/39.64    (6)   ~ (all_53_8 = all_53_12)
% 228.11/39.64    (7)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.11/39.64         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.11/39.64    (8)   ~ (e3 = e1)
% 228.11/39.64    (9)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.11/39.64         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.11/39.64    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.11/39.64            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.11/39.64    (11)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.11/39.64          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.11/39.64    (12)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.11/39.64            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.11/39.64              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.11/39.64    (13)   ~ (all_6_2 = e3)
% 228.11/39.64    (14)  op(e1, e1) = all_6_2
% 228.11/39.64    (15)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.11/39.64    (16)   ~ (all_53_9 = e0)
% 228.11/39.64    (17)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.11/39.64          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.11/39.64    (18)   ~ (all_53_4 = all_53_12)
% 228.11/39.64    (19)   ~ (all_53_8 = all_53_9)
% 228.11/39.64    (20)  all_42_2 = all_6_2
% 228.11/39.64    (21)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.11/39.64          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.11/39.64    (22)  all_57_4 = e1 & op(e3, e1) = e1
% 228.11/39.64    (23)  all_57_8 = e1
% 228.11/39.64    (24)   ~ (all_53_9 = all_6_2)
% 228.11/39.64    (25)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.11/39.64          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.11/39.64    (26)  all_57_3 = e0
% 228.11/39.64    (27)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.11/39.64          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.11/39.64    (28)  all_57_4 = e3
% 228.11/39.64    (29)   ~ (e3 = e2)
% 228.11/39.64    (30)  all_55_1 = all_53_4
% 228.11/39.64    (31)   ~ (e3 = e0)
% 228.11/39.64    (32)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.11/39.64          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.11/39.64    (33)   ~ (all_53_8 = all_6_2)
% 228.11/39.64    (34)  all_57_0 = e0
% 228.11/39.64    (35)  all_55_2 = all_53_8
% 228.11/39.64    (36)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 228.11/39.64          | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.11/39.64    (37)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.11/39.64    (38)  all_57_15 = e3
% 228.11/39.64    (39)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.11/39.64          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.11/39.64            e1)
% 228.11/39.64    (40)  all_57_10 = e2
% 228.11/39.64    (41)  all_57_11 = e0
% 228.11/39.64    (42)   ~ (all_53_4 = all_53_8)
% 228.11/39.64    (43)  op(e3, e2) = all_53_4
% 228.11/39.64    (44)   ~ (e2 = e0)
% 228.11/39.64    (45)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.11/39.64            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.11/39.64            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.11/39.64            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.11/39.64              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.11/39.64            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.11/39.64            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.11/39.64              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.11/39.64              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.11/39.64            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.11/39.64            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.11/39.64            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.11/39.64              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.11/39.64              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.11/39.64            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.11/39.64              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.11/39.64            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.11/39.64            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.11/39.64              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.11/39.64              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.11/39.64            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.11/39.64            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.11/39.64    (46)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.11/39.64          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.11/39.64    (47)   ~ (e1 = e0)
% 228.11/39.64    (48)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.11/39.64            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.11/39.64              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.11/39.64    (49)   ~ (all_53_4 = e0)
% 228.11/39.64    (50)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.11/39.64          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.11/39.64    (51)  all_57_6 = e3
% 228.11/39.64    (52)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.11/39.64          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.11/39.64    (53)  op(e0, e0) = e3
% 228.11/39.64    (54)   ~ (all_53_4 = all_53_6)
% 228.11/39.64    (55)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.11/39.64          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.11/39.64            e2)
% 228.11/39.64    (56)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.11/39.64              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.11/39.64                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.11/39.64                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.11/39.64    (57)  all_55_10 = all_6_2
% 228.11/39.64    (58)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.11/39.64          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.11/39.64    (59)  all_38_2 = all_6_2
% 228.11/39.64    (60)  all_55_3 = all_53_12
% 228.11/39.64    (61)   ~ (all_53_12 = e3)
% 228.11/39.64    (62)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.11/39.64            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.11/39.64              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.11/39.64    (63)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.11/39.64          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.11/39.64    (64)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.11/39.64          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.11/39.64    (65)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) |
% 228.11/39.64          (all_57_11 = e0 & op(e1, e0) = e0)
% 228.11/39.64    (66)   ~ (e2 = e1)
% 228.11/39.64    (67)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.11/39.64          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.11/39.64    (68)  op(e2, e1) = all_53_9
% 228.11/39.64    (69)  op(e1, e2) = all_53_6
% 228.11/39.64    (70)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.11/39.64          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.11/39.64    (71)  all_24_2 = all_6_2
% 228.11/39.64    (72)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.11/39.64          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.11/39.64    (73)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.11/39.64          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.11/39.64    (74)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.11/39.64          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.11/39.64    (75)  all_57_14 = e0
% 228.11/39.64    (76)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.11/39.64          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.11/39.64    (77)  op(e3, e1) = all_53_8
% 228.11/39.64    (78)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.11/39.64          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.11/39.64    (79)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.11/39.64          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.11/39.64    (80)  op(e3, e0) = all_53_12
% 228.11/39.64  
% 228.11/39.64  Begin of proof
% 228.11/39.64  | 
% 228.11/39.64  | ALPHA: (22) implies:
% 228.11/39.64  |   (81)  all_57_4 = e1
% 228.11/39.64  | 
% 228.11/39.64  | COMBINE_EQS: (28), (81) imply:
% 228.11/39.64  |   (82)  e3 = e1
% 228.11/39.64  | 
% 228.11/39.64  | COMBINE_EQS: (51), (82) imply:
% 228.11/39.64  |   (83)  all_57_6 = e1
% 228.11/39.64  | 
% 228.11/39.64  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.11/39.64  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (23), (24),
% 228.11/39.64  |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 228.11/39.64  |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 228.11/39.64  |            (47), (48), (49), (50), (52), (53), (54), (55), (56), (57), (58),
% 228.11/39.64  |            (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 228.11/39.64  |            (70), (71), (72), (73), (74), (75), (76), (77), (78), (79), (80),
% 228.11/39.64  |            (83) are inconsistent by sub-proof #423.
% 228.11/39.64  | 
% 228.11/39.64  End of proof
% 228.11/39.64  
% 228.11/39.64  Sub-proof #423 shows that the following formulas are inconsistent:
% 228.11/39.64  ----------------------------------------------------------------
% 228.11/39.64    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.11/39.64    (2)  op(e3, e3) = e1
% 228.11/39.64    (3)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.11/39.64    (4)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.11/39.64         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.11/39.64    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.11/39.64         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.11/39.64    (6)   ~ (all_53_8 = all_53_12)
% 228.11/39.64    (7)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.11/39.64         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.11/39.64    (8)   ~ (e3 = e1)
% 228.11/39.64    (9)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.11/39.64         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.11/39.64    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.11/39.64            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.11/39.64    (11)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.11/39.64          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.11/39.64    (12)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.11/39.64            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.11/39.64              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.11/39.64    (13)   ~ (all_6_2 = e3)
% 228.11/39.64    (14)  op(e1, e1) = all_6_2
% 228.11/39.64    (15)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.11/39.64    (16)   ~ (all_53_9 = e0)
% 228.11/39.64    (17)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.11/39.64          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.11/39.64    (18)   ~ (all_53_4 = all_53_12)
% 228.11/39.64    (19)   ~ (all_53_8 = all_53_9)
% 228.11/39.64    (20)  all_42_2 = all_6_2
% 228.11/39.64    (21)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.11/39.64          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.11/39.64    (22)  all_57_6 = e1
% 228.11/39.64    (23)  all_57_8 = e1
% 228.11/39.65    (24)   ~ (all_53_9 = all_6_2)
% 228.11/39.65    (25)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.11/39.65          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.11/39.65    (26)  all_57_3 = e0
% 228.11/39.65    (27)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.11/39.65          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.11/39.65    (28)  all_57_4 = e3
% 228.11/39.65    (29)   ~ (e3 = e2)
% 228.11/39.65    (30)  all_55_1 = all_53_4
% 228.11/39.65    (31)   ~ (e3 = e0)
% 228.11/39.65    (32)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.11/39.65          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.11/39.65    (33)   ~ (all_53_8 = all_6_2)
% 228.11/39.65    (34)  all_57_0 = e0
% 228.11/39.65    (35)  all_55_2 = all_53_8
% 228.11/39.65    (36)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 228.11/39.65          | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.11/39.65    (37)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.11/39.65    (38)  all_57_15 = e3
% 228.11/39.65    (39)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.11/39.65          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.11/39.65            e1)
% 228.11/39.65    (40)  all_57_10 = e2
% 228.11/39.65    (41)  all_57_11 = e0
% 228.11/39.65    (42)   ~ (all_53_4 = all_53_8)
% 228.11/39.65    (43)  op(e3, e2) = all_53_4
% 228.11/39.65    (44)   ~ (e2 = e0)
% 228.11/39.65    (45)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.11/39.65            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.11/39.65            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.11/39.65            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.11/39.65              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.11/39.65            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.11/39.65            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.11/39.65              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.11/39.65              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.11/39.65            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.11/39.65            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.11/39.65            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.11/39.65              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.11/39.65              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.11/39.65            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.11/39.65              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.11/39.65            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.11/39.65            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.11/39.65              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.11/39.65              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.11/39.65            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.11/39.65            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.11/39.65    (46)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.11/39.65          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.11/39.65    (47)   ~ (e1 = e0)
% 228.11/39.65    (48)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.11/39.65            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.11/39.65              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.11/39.65    (49)   ~ (all_53_4 = e0)
% 228.11/39.65    (50)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.11/39.65          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.11/39.65    (51)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.11/39.65          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.11/39.65    (52)  op(e0, e0) = e3
% 228.11/39.65    (53)   ~ (all_53_4 = all_53_6)
% 228.11/39.65    (54)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.11/39.65          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.11/39.65            e2)
% 228.11/39.65    (55)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.11/39.65              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.11/39.65                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.11/39.65                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.11/39.65    (56)  all_55_10 = all_6_2
% 228.11/39.65    (57)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.11/39.65          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.11/39.65    (58)  all_38_2 = all_6_2
% 228.11/39.65    (59)  all_55_3 = all_53_12
% 228.11/39.65    (60)   ~ (all_53_12 = e3)
% 228.11/39.65    (61)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.11/39.65            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.11/39.65              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.11/39.65    (62)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.11/39.65          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.11/39.65    (63)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.11/39.65          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.11/39.65    (64)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) |
% 228.11/39.65          (all_57_11 = e0 & op(e1, e0) = e0)
% 228.11/39.65    (65)   ~ (e2 = e1)
% 228.11/39.65    (66)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.11/39.65          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.11/39.65    (67)  op(e2, e1) = all_53_9
% 228.11/39.65    (68)  op(e1, e2) = all_53_6
% 228.11/39.65    (69)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.11/39.65          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.11/39.65    (70)  all_24_2 = all_6_2
% 228.11/39.65    (71)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.11/39.65          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.11/39.65    (72)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.11/39.65          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.11/39.65    (73)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.11/39.65          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.11/39.65    (74)  all_57_14 = e0
% 228.11/39.65    (75)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.11/39.65          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.11/39.65    (76)  op(e3, e1) = all_53_8
% 228.11/39.65    (77)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.11/39.65          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.11/39.65    (78)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.11/39.65          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.11/39.65    (79)  op(e3, e0) = all_53_12
% 228.11/39.65  
% 228.11/39.65  Begin of proof
% 228.11/39.65  | 
% 228.11/39.65  | BETA: splitting (63) gives:
% 228.11/39.65  | 
% 228.11/39.65  | Case 1:
% 228.11/39.65  | | 
% 228.11/39.65  | |   (80)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) =
% 228.11/39.65  | |           e3)
% 228.11/39.65  | | 
% 228.11/39.65  | | BETA: splitting (80) gives:
% 228.11/39.65  | | 
% 228.11/39.65  | | Case 1:
% 228.11/39.65  | | | 
% 228.11/39.65  | | |   (81)  all_57_0 = e3 & op(e3, e3) = e3
% 228.11/39.65  | | | 
% 228.11/39.65  | | | ALPHA: (81) implies:
% 228.11/39.65  | | |   (82)  op(e3, e3) = e3
% 228.11/39.65  | | | 
% 228.11/39.65  | | | REF_CLOSE: (2), (8), (10), (82) are inconsistent by sub-proof #2495.
% 228.11/39.65  | | | 
% 228.11/39.65  | | Case 2:
% 228.11/39.65  | | | 
% 228.11/39.65  | | |   (83)  all_57_2 = e3 & op(e2, e3) = e3
% 228.11/39.65  | | | 
% 228.11/39.65  | | | ALPHA: (83) implies:
% 228.11/39.65  | | |   (84)  all_57_2 = e3
% 228.11/39.65  | | | 
% 228.11/39.65  | | | BETA: splitting (51) gives:
% 228.11/39.65  | | | 
% 228.11/39.65  | | | Case 1:
% 228.11/39.65  | | | | 
% 228.11/39.65  | | | |   (85)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2)
% 228.11/39.65  | | | |           = e3)
% 228.11/39.65  | | | | 
% 228.11/39.65  | | | | BETA: splitting (85) gives:
% 228.11/39.65  | | | | 
% 228.11/39.65  | | | | Case 1:
% 228.11/39.65  | | | | | 
% 228.11/39.65  | | | | |   (86)  all_57_1 = e3 & op(e3, e2) = e3
% 228.11/39.65  | | | | | 
% 228.11/39.65  | | | | | ALPHA: (86) implies:
% 228.11/39.65  | | | | |   (87)  all_57_1 = e3
% 228.11/39.65  | | | | | 
% 228.11/39.65  | | | | | BETA: splitting (17) gives:
% 228.11/39.65  | | | | | 
% 228.11/39.65  | | | | | Case 1:
% 228.11/39.65  | | | | | | 
% 228.11/39.65  | | | | | |   (88)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3,
% 228.11/39.65  | | | | | |             e2) = e1)
% 228.11/39.65  | | | | | | 
% 228.11/39.65  | | | | | | BETA: splitting (88) gives:
% 228.11/39.65  | | | | | | 
% 228.11/39.65  | | | | | | Case 1:
% 228.11/39.65  | | | | | | | 
% 228.11/39.65  | | | | | | |   (89)  all_57_0 = e1 & op(e3, e3) = e1
% 228.11/39.65  | | | | | | | 
% 228.11/39.65  | | | | | | | ALPHA: (89) implies:
% 228.11/39.65  | | | | | | |   (90)  all_57_0 = e1
% 228.11/39.65  | | | | | | | 
% 228.11/39.65  | | | | | | | REF_CLOSE: (21), (25), (28), (29), (31), (44), (47), (65), (87),
% 228.11/39.65  | | | | | | |            (90) are inconsistent by sub-proof #1808.
% 228.11/39.65  | | | | | | | 
% 228.11/39.65  | | | | | | Case 2:
% 228.11/39.65  | | | | | | | 
% 228.11/39.65  | | | | | | |   (91)  all_57_1 = e1 & op(e3, e2) = e1
% 228.11/39.65  | | | | | | | 
% 228.11/39.65  | | | | | | | ALPHA: (91) implies:
% 228.11/39.65  | | | | | | |   (92)  all_57_1 = e1
% 228.11/39.65  | | | | | | | 
% 228.11/39.65  | | | | | | | COMBINE_EQS: (87), (92) imply:
% 228.11/39.65  | | | | | | |   (93)  e3 = e1
% 228.11/39.65  | | | | | | | 
% 228.11/39.65  | | | | | | | COMBINE_EQS: (28), (93) imply:
% 228.11/39.65  | | | | | | |   (94)  all_57_4 = e1
% 228.11/39.65  | | | | | | | 
% 228.11/39.65  | | | | | | | REF_CLOSE: (4), (8), (10), (13), (14), (26), (29), (31), (38),
% 228.11/39.65  | | | | | | |            (39), (40), (44), (47), (50), (54), (55), (65), (84),
% 228.11/39.65  | | | | | | |            (94) are inconsistent by sub-proof #1755.
% 228.11/39.65  | | | | | | | 
% 228.11/39.65  | | | | | | End of split
% 228.11/39.65  | | | | | | 
% 228.11/39.65  | | | | | Case 2:
% 228.11/39.65  | | | | | | 
% 228.11/39.65  | | | | | |   (95)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3,
% 228.11/39.65  | | | | | |             e0) = e1)
% 228.11/39.65  | | | | | | 
% 228.11/39.65  | | | | | | BETA: splitting (95) gives:
% 228.11/39.65  | | | | | | 
% 228.11/39.65  | | | | | | Case 1:
% 228.11/39.65  | | | | | | | 
% 228.11/39.65  | | | | | | |   (96)  all_57_4 = e1 & op(e3, e1) = e1
% 228.11/39.65  | | | | | | | 
% 228.11/39.65  | | | | | | | ALPHA: (96) implies:
% 228.11/39.65  | | | | | | |   (97)  all_57_4 = e1
% 228.11/39.65  | | | | | | | 
% 228.11/39.65  | | | | | | | REF_CLOSE: (4), (8), (10), (13), (14), (26), (29), (31), (38),
% 228.11/39.65  | | | | | | |            (39), (40), (44), (47), (50), (54), (55), (65), (84),
% 228.11/39.65  | | | | | | |            (97) are inconsistent by sub-proof #1755.
% 228.11/39.65  | | | | | | | 
% 228.11/39.65  | | | | | | Case 2:
% 228.11/39.65  | | | | | | | 
% 228.11/39.65  | | | | | | |   (98)  all_57_9 = e1 & op(e3, e0) = e1
% 228.11/39.65  | | | | | | | 
% 228.11/39.65  | | | | | | | ALPHA: (98) implies:
% 228.11/39.65  | | | | | | |   (99)  all_57_9 = e1
% 228.11/39.65  | | | | | | | 
% 228.11/39.65  | | | | | | | BETA: splitting (11) gives:
% 228.11/39.65  | | | | | | | 
% 228.11/39.65  | | | | | | | Case 1:
% 228.11/39.65  | | | | | | | | 
% 228.11/39.65  | | | | | | | |   (100)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 &
% 228.11/39.65  | | | | | | | |            op(e1, e2) = e3)
% 228.11/39.65  | | | | | | | | 
% 228.11/39.65  | | | | | | | | BETA: splitting (100) gives:
% 228.11/39.65  | | | | | | | | 
% 228.11/39.65  | | | | | | | | Case 1:
% 228.11/39.65  | | | | | | | | | 
% 228.11/39.65  | | | | | | | | |   (101)  all_57_6 = e3 & op(e1, e3) = e3
% 228.11/39.65  | | | | | | | | | 
% 228.11/39.65  | | | | | | | | | REF_CLOSE: (4), (8), (10), (13), (14), (22), (26), (28), (29),
% 228.11/39.65  | | | | | | | | |            (31), (38), (39), (40), (44), (47), (50), (54),
% 228.11/39.65  | | | | | | | | |            (55), (65), (84), (101) are inconsistent by
% 228.11/39.65  | | | | | | | | |            sub-proof #536.
% 228.11/39.65  | | | | | | | | | 
% 228.11/39.65  | | | | | | | | Case 2:
% 228.11/39.65  | | | | | | | | | 
% 228.11/39.65  | | | | | | | | |   (102)  all_57_7 = e3 & op(e1, e2) = e3
% 228.11/39.65  | | | | | | | | | 
% 228.11/39.65  | | | | | | | | | ALPHA: (102) implies:
% 228.11/39.65  | | | | | | | | |   (103)  all_57_7 = e3
% 228.11/39.65  | | | | | | | | | 
% 228.11/39.65  | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 228.11/39.65  | | | | | | | | |            (12), (13), (14), (15), (16), (17), (18), (19),
% 228.11/39.65  | | | | | | | | |            (20), (21), (23), (24), (25), (26), (27), (28),
% 228.11/39.65  | | | | | | | | |            (29), (30), (31), (32), (33), (35), (37), (38),
% 228.11/39.65  | | | | | | | | |            (39), (40), (41), (42), (43), (44), (45), (46),
% 228.11/39.65  | | | | | | | | |            (47), (48), (49), (50), (51), (52), (53), (54),
% 228.11/39.65  | | | | | | | | |            (55), (56), (57), (58), (59), (60), (61), (62),
% 228.11/39.65  | | | | | | | | |            (63), (65), (66), (67), (68), (69), (70), (71),
% 228.11/39.65  | | | | | | | | |            (72), (73), (75), (76), (77), (78), (79), (84),
% 228.11/39.65  | | | | | | | | |            (99), (103) are inconsistent by sub-proof #428.
% 228.11/39.65  | | | | | | | | | 
% 228.11/39.65  | | | | | | | | End of split
% 228.11/39.65  | | | | | | | | 
% 228.11/39.65  | | | | | | | Case 2:
% 228.11/39.65  | | | | | | | | 
% 228.11/39.65  | | | | | | | |   (104)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 &
% 228.11/39.65  | | | | | | | |            op(e1, e0) = e3)
% 228.11/39.65  | | | | | | | | 
% 228.11/39.65  | | | | | | | | REF_CLOSE: (8), (10), (13), (14), (29), (31), (38), (44), (47),
% 228.11/39.65  | | | | | | | |            (64), (65), (66), (73), (104) are inconsistent by
% 228.11/39.65  | | | | | | | |            sub-proof #1080.
% 228.11/39.65  | | | | | | | | 
% 228.11/39.65  | | | | | | | End of split
% 228.11/39.65  | | | | | | | 
% 228.11/39.65  | | | | | | End of split
% 228.11/39.65  | | | | | | 
% 228.11/39.65  | | | | | End of split
% 228.11/39.65  | | | | | 
% 228.11/39.65  | | | | Case 2:
% 228.11/39.65  | | | | | 
% 228.11/39.65  | | | | |   (105)  all_57_3 = e3 & op(e2, e2) = e3
% 228.11/39.65  | | | | | 
% 228.11/39.65  | | | | | ALPHA: (105) implies:
% 228.11/39.65  | | | | |   (106)  all_57_3 = e3
% 228.11/39.65  | | | | | 
% 228.11/39.65  | | | | | COMBINE_EQS: (26), (106) imply:
% 228.11/39.65  | | | | |   (107)  e3 = e0
% 228.11/39.65  | | | | | 
% 228.11/39.65  | | | | | REF_CLOSE: (4), (8), (26), (29), (31), (44), (47), (57), (62), (65),
% 228.11/39.65  | | | | |            (84), (107) are inconsistent by sub-proof #1333.
% 228.11/39.65  | | | | | 
% 228.11/39.65  | | | | End of split
% 228.11/39.65  | | | | 
% 228.11/39.65  | | | Case 2:
% 228.11/39.65  | | | | 
% 228.11/39.65  | | | |   (108)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0,
% 228.11/39.65  | | | |              e2) = e3)
% 228.11/39.65  | | | | 
% 228.11/39.65  | | | | BETA: splitting (108) gives:
% 228.11/39.65  | | | | 
% 228.11/39.65  | | | | Case 1:
% 228.11/39.65  | | | | | 
% 228.11/39.65  | | | | |   (109)  all_57_7 = e3 & op(e1, e2) = e3
% 228.11/39.65  | | | | | 
% 228.11/39.65  | | | | | ALPHA: (109) implies:
% 228.11/39.65  | | | | |   (110)  all_57_7 = e3
% 228.11/39.65  | | | | | 
% 228.11/39.65  | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.11/39.65  | | | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (23),
% 228.11/39.65  | | | | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 228.11/39.65  | | | | |            (34), (35), (37), (38), (39), (40), (41), (42), (43), (44),
% 228.11/39.65  | | | | |            (45), (46), (47), (48), (49), (50), (51), (52), (53), (54),
% 228.11/39.65  | | | | |            (55), (56), (57), (58), (59), (60), (61), (62), (63), (65),
% 228.11/39.65  | | | | |            (66), (67), (68), (69), (70), (71), (72), (73), (75), (76),
% 228.11/39.65  | | | | |            (77), (78), (79), (84), (110) are inconsistent by sub-proof
% 228.11/39.65  | | | | |            #425.
% 228.11/39.65  | | | | | 
% 228.11/39.65  | | | | Case 2:
% 228.11/39.65  | | | | | 
% 228.11/39.65  | | | | |   (111)  all_57_13 = e3 & op(e0, e2) = e3
% 228.11/39.65  | | | | | 
% 228.11/39.65  | | | | | ALPHA: (111) implies:
% 228.11/39.65  | | | | |   (112)  all_57_13 = e3
% 228.11/39.65  | | | | | 
% 228.11/39.65  | | | | | REF_CLOSE: (4), (8), (10), (13), (14), (26), (28), (29), (31), (36),
% 228.11/39.65  | | | | |            (38), (39), (40), (44), (47), (50), (52), (54), (55), (65),
% 228.11/39.65  | | | | |            (74), (84), (112) are inconsistent by sub-proof #424.
% 228.11/39.65  | | | | | 
% 228.11/39.65  | | | | End of split
% 228.11/39.65  | | | | 
% 228.11/39.65  | | | End of split
% 228.11/39.65  | | | 
% 228.11/39.65  | | End of split
% 228.11/39.65  | | 
% 228.11/39.65  | Case 2:
% 228.11/39.65  | | 
% 228.11/39.65  | |   (113)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) =
% 228.11/39.65  | |            e3)
% 228.11/39.65  | | 
% 228.11/39.65  | | REF_CLOSE: (8), (22), (29), (38), (39), (44), (47), (54), (65), (74), (113)
% 228.11/39.65  | |            are inconsistent by sub-proof #440.
% 228.11/39.65  | | 
% 228.11/39.65  | End of split
% 228.11/39.65  | 
% 228.11/39.65  End of proof
% 228.11/39.65  
% 228.11/39.65  Sub-proof #424 shows that the following formulas are inconsistent:
% 228.11/39.65  ----------------------------------------------------------------
% 228.11/39.65    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.11/39.65         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.11/39.65    (2)   ~ (e3 = e1)
% 228.11/39.65    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.11/39.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.11/39.65    (4)   ~ (all_6_2 = e3)
% 228.11/39.65    (5)  op(e1, e1) = all_6_2
% 228.11/39.65    (6)  all_57_3 = e0
% 228.11/39.65    (7)  all_57_4 = e3
% 228.11/39.65    (8)   ~ (e3 = e2)
% 228.11/39.65    (9)   ~ (e3 = e0)
% 228.11/39.65    (10)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 228.11/39.65          | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.11/39.65    (11)  all_57_15 = e3
% 228.11/39.65    (12)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.11/39.65          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.11/39.65            e1)
% 228.11/39.65    (13)  all_57_10 = e2
% 228.11/39.65    (14)   ~ (e2 = e0)
% 228.11/39.65    (15)  all_57_2 = e3
% 228.11/39.65    (16)   ~ (e1 = e0)
% 228.11/39.65    (17)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.11/39.65          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.11/39.65    (18)  all_57_13 = e3
% 228.11/39.65    (19)  op(e0, e0) = e3
% 228.11/39.65    (20)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.11/39.65          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.11/39.65            e2)
% 228.11/39.65    (21)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.11/39.65              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.11/39.65                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.11/39.65                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.11/39.65    (22)   ~ (e2 = e1)
% 228.11/39.65    (23)  all_57_14 = e0
% 228.11/39.65  
% 228.11/39.65  Begin of proof
% 228.11/39.65  | 
% 228.11/39.65  | BETA: splitting (12) gives:
% 228.11/39.65  | 
% 228.11/39.65  | Case 1:
% 228.11/39.65  | | 
% 228.11/39.65  | |   (24)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 228.11/39.65  | |           e1)
% 228.11/39.65  | | 
% 228.11/39.65  | | BETA: splitting (24) gives:
% 228.11/39.65  | | 
% 228.11/39.65  | | Case 1:
% 228.11/39.65  | | | 
% 228.11/39.65  | | |   (25)  all_57_12 = e1 & op(e0, e3) = e1
% 228.11/39.65  | | | 
% 228.11/39.65  | | | ALPHA: (25) implies:
% 228.11/39.65  | | |   (26)  all_57_12 = e1
% 228.11/39.65  | | | 
% 228.11/39.65  | | | REF_CLOSE: (2), (8), (9), (10), (11), (12), (14), (16), (18), (20), (22),
% 228.11/39.65  | | |            (26) are inconsistent by sub-proof #2057.
% 228.11/39.65  | | | 
% 228.11/39.65  | | Case 2:
% 228.11/39.65  | | | 
% 228.11/39.65  | | |   (27)  all_57_13 = e1 & op(e0, e2) = e1
% 228.11/39.65  | | | 
% 228.11/39.65  | | | ALPHA: (27) implies:
% 228.11/39.65  | | |   (28)  all_57_13 = e1
% 228.11/39.65  | | | 
% 228.11/39.65  | | | COMBINE_EQS: (18), (28) imply:
% 228.11/39.65  | | |   (29)  e3 = e1
% 228.11/39.65  | | | 
% 228.11/39.65  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (13), (14),
% 228.11/39.65  | | |            (15), (16), (17), (18), (20), (21), (22), (29) are inconsistent
% 228.11/39.65  | | |            by sub-proof #539.
% 228.11/39.65  | | | 
% 228.11/39.65  | | End of split
% 228.11/39.65  | | 
% 228.11/39.65  | Case 2:
% 228.11/39.65  | | 
% 228.11/39.65  | |   (30)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.11/39.65  | |           e1)
% 228.11/39.65  | | 
% 228.11/39.65  | | REF_CLOSE: (2), (3), (16), (19), (23), (30) are inconsistent by sub-proof
% 228.11/39.65  | |            #2056.
% 228.11/39.65  | | 
% 228.11/39.65  | End of split
% 228.11/39.65  | 
% 228.11/39.65  End of proof
% 228.11/39.65  
% 228.11/39.65  Sub-proof #425 shows that the following formulas are inconsistent:
% 228.11/39.65  ----------------------------------------------------------------
% 228.11/39.65    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.11/39.65    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.11/39.65    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.11/39.65         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.11/39.65    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.11/39.65         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.11/39.65    (5)   ~ (all_53_8 = all_53_12)
% 228.11/39.65    (6)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.11/39.65         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.11/39.65    (7)   ~ (e3 = e1)
% 228.11/39.65    (8)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.11/39.65         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.11/39.65    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.11/39.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.11/39.65    (10)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.11/39.65          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.11/39.65    (11)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.11/39.65            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.11/39.65              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.11/39.65    (12)   ~ (all_6_2 = e3)
% 228.11/39.65    (13)  op(e1, e1) = all_6_2
% 228.11/39.65    (14)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.11/39.65    (15)   ~ (all_53_9 = e0)
% 228.11/39.65    (16)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.11/39.65          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.11/39.65    (17)   ~ (all_53_4 = all_53_12)
% 228.11/39.65    (18)   ~ (all_53_8 = all_53_9)
% 228.11/39.65    (19)  all_42_2 = all_6_2
% 228.11/39.65    (20)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.11/39.65          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.11/39.65    (21)  all_57_8 = e1
% 228.11/39.65    (22)   ~ (all_53_9 = all_6_2)
% 228.11/39.65    (23)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.11/39.65          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.11/39.65    (24)  all_57_3 = e0
% 228.11/39.65    (25)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.11/39.65          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.11/39.65    (26)  all_57_4 = e3
% 228.11/39.65    (27)   ~ (e3 = e2)
% 228.11/39.65    (28)  all_55_1 = all_53_4
% 228.11/39.65    (29)   ~ (e3 = e0)
% 228.11/39.65    (30)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.11/39.65          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.11/39.65    (31)   ~ (all_53_8 = all_6_2)
% 228.11/39.65    (32)  all_57_0 = e0
% 228.11/39.65    (33)  all_55_2 = all_53_8
% 228.11/39.65    (34)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.11/39.65    (35)  all_57_15 = e3
% 228.11/39.65    (36)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.11/39.65          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.11/39.65            e1)
% 228.11/39.65    (37)  all_57_10 = e2
% 228.11/39.65    (38)  all_57_11 = e0
% 228.11/39.65    (39)   ~ (all_53_4 = all_53_8)
% 228.11/39.65    (40)  op(e3, e2) = all_53_4
% 228.11/39.65    (41)   ~ (e2 = e0)
% 228.11/39.65    (42)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.11/39.65            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.11/39.65            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.11/39.65            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.11/39.65              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.11/39.65            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.11/39.65            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.11/39.65              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.11/39.65              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.11/39.65            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.11/39.65            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.11/39.65            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.11/39.65              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.11/39.65              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.11/39.65            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.11/39.65              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.11/39.65            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.11/39.65            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.11/39.65              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.11/39.65              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.11/39.65            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.11/39.65            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.11/39.65    (43)  all_57_2 = e3
% 228.11/39.65    (44)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.11/39.65          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.11/39.65    (45)   ~ (e1 = e0)
% 228.11/39.65    (46)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.11/39.65            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.11/39.65              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.11/39.65    (47)   ~ (all_53_4 = e0)
% 228.11/39.65    (48)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.11/39.65          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.11/39.65    (49)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.11/39.65          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.11/39.65    (50)  op(e0, e0) = e3
% 228.11/39.65    (51)   ~ (all_53_4 = all_53_6)
% 228.11/39.65    (52)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.11/39.65          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.11/39.65            e2)
% 228.11/39.65    (53)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.11/39.65              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.11/39.65                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.11/39.65                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.11/39.65    (54)  all_55_10 = all_6_2
% 228.11/39.65    (55)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.11/39.65          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.11/39.65    (56)  all_38_2 = all_6_2
% 228.11/39.65    (57)  all_55_3 = all_53_12
% 228.11/39.65    (58)   ~ (all_53_12 = e3)
% 228.11/39.65    (59)  all_57_7 = e3
% 228.11/39.65    (60)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.11/39.65            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.11/39.65              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.11/39.65    (61)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.11/39.65          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.11/39.65    (62)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.11/39.65          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.11/39.65    (63)   ~ (e2 = e1)
% 228.11/39.65    (64)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.11/39.65          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.11/39.65    (65)  op(e2, e1) = all_53_9
% 228.11/39.65    (66)  op(e1, e2) = all_53_6
% 228.11/39.65    (67)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.11/39.65          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.11/39.65    (68)  all_24_2 = all_6_2
% 228.11/39.65    (69)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.11/39.65          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.11/39.65    (70)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.11/39.65          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.11/39.65    (71)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.11/39.65          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.11/39.65    (72)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.11/39.65          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.11/39.65    (73)  op(e3, e1) = all_53_8
% 228.11/39.66    (74)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.11/39.66          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.11/39.66    (75)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.11/39.66          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.11/39.66    (76)  op(e3, e0) = all_53_12
% 228.11/39.66  
% 228.11/39.66  Begin of proof
% 228.11/39.66  | 
% 228.11/39.66  | BETA: splitting (16) gives:
% 228.11/39.66  | 
% 228.11/39.66  | Case 1:
% 228.11/39.66  | | 
% 228.11/39.66  | |   (77)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) =
% 228.11/39.66  | |           e1)
% 228.11/39.66  | | 
% 228.11/39.66  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.11/39.66  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 228.11/39.66  | |            (24), (25), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 228.11/39.66  | |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 228.11/39.66  | |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 228.11/39.66  | |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 228.11/39.66  | |            (69), (70), (71), (72), (73), (74), (75), (76), (77) are
% 228.11/39.66  | |            inconsistent by sub-proof #426.
% 228.11/39.66  | | 
% 228.11/39.66  | Case 2:
% 228.11/39.66  | | 
% 228.11/39.66  | |   (78)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) =
% 228.11/39.66  | |           e1)
% 228.11/39.66  | | 
% 228.11/39.66  | | BETA: splitting (78) gives:
% 228.11/39.66  | | 
% 228.11/39.66  | | Case 1:
% 228.11/39.66  | | | 
% 228.11/39.66  | | |   (79)  all_57_4 = e1 & op(e3, e1) = e1
% 228.11/39.66  | | | 
% 228.11/39.66  | | | ALPHA: (79) implies:
% 228.11/39.66  | | |   (80)  all_57_4 = e1
% 228.11/39.66  | | | 
% 228.11/39.66  | | | REF_CLOSE: (3), (7), (9), (12), (13), (24), (27), (29), (35), (36), (37),
% 228.11/39.66  | | |            (41), (43), (45), (48), (52), (53), (63), (80) are inconsistent
% 228.11/39.66  | | |            by sub-proof #1755.
% 228.11/39.66  | | | 
% 228.11/39.66  | | Case 2:
% 228.11/39.66  | | | 
% 228.11/39.66  | | |   (81)  all_57_9 = e1 & op(e3, e0) = e1
% 228.11/39.66  | | | 
% 228.11/39.66  | | | ALPHA: (81) implies:
% 228.11/39.66  | | |   (82)  all_57_9 = e1
% 228.11/39.66  | | | 
% 228.11/39.66  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.11/39.66  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 228.11/39.66  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (33),
% 228.11/39.66  | | |            (34), (35), (36), (37), (38), (39), (40), (41), (42), (43),
% 228.11/39.66  | | |            (44), (45), (46), (47), (48), (49), (50), (51), (52), (53),
% 228.11/39.66  | | |            (54), (55), (56), (57), (58), (59), (60), (61), (62), (63),
% 228.11/39.66  | | |            (64), (65), (66), (67), (68), (69), (70), (71), (72), (73),
% 228.11/39.66  | | |            (74), (75), (76), (82) are inconsistent by sub-proof #428.
% 228.11/39.66  | | | 
% 228.11/39.66  | | End of split
% 228.11/39.66  | | 
% 228.11/39.66  | End of split
% 228.11/39.66  | 
% 228.11/39.66  End of proof
% 228.11/39.66  
% 228.11/39.66  Sub-proof #426 shows that the following formulas are inconsistent:
% 228.11/39.66  ----------------------------------------------------------------
% 228.11/39.66    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.11/39.66    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.11/39.66    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.11/39.66         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.11/39.66    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.11/39.66         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.11/39.66    (5)   ~ (all_53_8 = all_53_12)
% 228.11/39.66    (6)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.11/39.66         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.11/39.66    (7)   ~ (e3 = e1)
% 228.11/39.66    (8)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.11/39.66         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.11/39.66    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.11/39.66           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.11/39.66    (10)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.11/39.66          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.11/39.66    (11)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.11/39.66            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.11/39.66              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.11/39.66    (12)   ~ (all_6_2 = e3)
% 228.11/39.66    (13)  op(e1, e1) = all_6_2
% 228.11/39.66    (14)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.11/39.66    (15)   ~ (all_53_9 = e0)
% 228.11/39.66    (16)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.11/39.66          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.11/39.66    (17)   ~ (all_53_4 = all_53_12)
% 228.11/39.66    (18)   ~ (all_53_8 = all_53_9)
% 228.11/39.66    (19)  all_42_2 = all_6_2
% 228.11/39.66    (20)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.11/39.66          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.11/39.66    (21)  all_57_8 = e1
% 228.11/39.66    (22)   ~ (all_53_9 = all_6_2)
% 228.11/39.66    (23)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.11/39.66          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.11/39.66    (24)  all_57_3 = e0
% 228.11/39.66    (25)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.11/39.66          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.11/39.66    (26)   ~ (e3 = e2)
% 228.11/39.66    (27)  all_55_1 = all_53_4
% 228.11/39.66    (28)   ~ (e3 = e0)
% 228.11/39.66    (29)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.11/39.66          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.11/39.66    (30)   ~ (all_53_8 = all_6_2)
% 228.11/39.66    (31)  all_57_0 = e0
% 228.13/39.66    (32)  all_55_2 = all_53_8
% 228.13/39.66    (33)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.13/39.66    (34)  all_57_15 = e3
% 228.13/39.66    (35)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.13/39.66          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.13/39.66            e1)
% 228.13/39.66    (36)  all_57_10 = e2
% 228.13/39.66    (37)  all_57_11 = e0
% 228.13/39.66    (38)   ~ (all_53_4 = all_53_8)
% 228.13/39.66    (39)  op(e3, e2) = all_53_4
% 228.13/39.66    (40)   ~ (e2 = e0)
% 228.13/39.66    (41)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.13/39.66            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.13/39.66            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.13/39.66            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.13/39.66              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.13/39.66            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.13/39.66            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.13/39.66              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.13/39.66              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.13/39.66            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.13/39.66            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.13/39.66            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.13/39.66              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.13/39.66              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.13/39.66            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.13/39.66              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.13/39.66            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.13/39.66            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.13/39.66              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.13/39.66              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.13/39.66            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.13/39.66            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.13/39.66    (42)  all_57_2 = e3
% 228.13/39.66    (43)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.13/39.66          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.13/39.66    (44)   ~ (e1 = e0)
% 228.13/39.66    (45)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.13/39.66            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.13/39.66              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.13/39.66    (46)   ~ (all_53_4 = e0)
% 228.13/39.66    (47)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.13/39.66          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.13/39.66    (48)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.13/39.66          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.13/39.66    (49)  op(e0, e0) = e3
% 228.13/39.66    (50)   ~ (all_53_4 = all_53_6)
% 228.13/39.66    (51)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.13/39.66          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.13/39.66            e2)
% 228.13/39.66    (52)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.13/39.66              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.13/39.66                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.13/39.66                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.13/39.66    (53)  all_55_10 = all_6_2
% 228.13/39.66    (54)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1)
% 228.13/39.66    (55)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.13/39.66          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.13/39.66    (56)  all_38_2 = all_6_2
% 228.13/39.66    (57)  all_55_3 = all_53_12
% 228.13/39.66    (58)   ~ (all_53_12 = e3)
% 228.13/39.66    (59)  all_57_7 = e3
% 228.13/39.66    (60)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.13/39.66            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.13/39.66              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.13/39.66    (61)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.13/39.66          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.13/39.66    (62)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.13/39.66          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.13/39.66    (63)   ~ (e2 = e1)
% 228.13/39.66    (64)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.13/39.66          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.13/39.66    (65)  op(e2, e1) = all_53_9
% 228.13/39.66    (66)  op(e1, e2) = all_53_6
% 228.13/39.66    (67)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.13/39.66          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.13/39.66    (68)  all_24_2 = all_6_2
% 228.13/39.66    (69)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.13/39.66          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.13/39.66    (70)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.13/39.66          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.13/39.66    (71)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.13/39.66          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.13/39.66    (72)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.13/39.66          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.13/39.66    (73)  op(e3, e1) = all_53_8
% 228.13/39.66    (74)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.13/39.66          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.13/39.66    (75)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.13/39.66          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.13/39.66    (76)  op(e3, e0) = all_53_12
% 228.13/39.66  
% 228.13/39.66  Begin of proof
% 228.13/39.66  | 
% 228.13/39.66  | BETA: splitting (54) gives:
% 228.13/39.66  | 
% 228.13/39.66  | Case 1:
% 228.13/39.66  | | 
% 228.13/39.66  | |   (77)  all_57_0 = e1 & op(e3, e3) = e1
% 228.13/39.66  | | 
% 228.13/39.66  | | REF_CLOSE: (31), (44), (77) are inconsistent by sub-proof #2454.
% 228.13/39.66  | | 
% 228.13/39.66  | Case 2:
% 228.13/39.66  | | 
% 228.13/39.66  | |   (78)  all_57_1 = e1 & op(e3, e2) = e1
% 228.13/39.66  | | 
% 228.13/39.66  | | ALPHA: (78) implies:
% 228.13/39.66  | |   (79)  all_57_1 = e1
% 228.13/39.66  | | 
% 228.13/39.66  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.13/39.66  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 228.13/39.66  | |            (24), (25), (26), (27), (28), (29), (30), (32), (33), (34), (35),
% 228.13/39.66  | |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 228.13/39.66  | |            (47), (48), (49), (50), (51), (52), (53), (55), (56), (57), (58),
% 228.13/39.66  | |            (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 228.13/39.66  | |            (70), (71), (72), (73), (74), (75), (76), (79) are inconsistent
% 228.13/39.66  | |            by sub-proof #427.
% 228.13/39.66  | | 
% 228.13/39.66  | End of split
% 228.13/39.66  | 
% 228.13/39.66  End of proof
% 228.13/39.66  
% 228.13/39.66  Sub-proof #427 shows that the following formulas are inconsistent:
% 228.13/39.66  ----------------------------------------------------------------
% 228.13/39.66    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.13/39.66    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.13/39.66    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.13/39.66         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.13/39.66    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.13/39.66         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.13/39.66    (5)   ~ (all_53_8 = all_53_12)
% 228.13/39.66    (6)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.13/39.66         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.13/39.66    (7)   ~ (e3 = e1)
% 228.13/39.66    (8)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.13/39.66         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.13/39.66    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.13/39.66           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.13/39.66    (10)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.13/39.66          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.13/39.66    (11)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.13/39.66            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.13/39.66              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.13/39.66    (12)   ~ (all_6_2 = e3)
% 228.13/39.66    (13)  op(e1, e1) = all_6_2
% 228.13/39.66    (14)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.13/39.66    (15)   ~ (all_53_9 = e0)
% 228.13/39.66    (16)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.13/39.66          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.13/39.66    (17)   ~ (all_53_4 = all_53_12)
% 228.13/39.66    (18)   ~ (all_53_8 = all_53_9)
% 228.13/39.66    (19)  all_42_2 = all_6_2
% 228.13/39.66    (20)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.13/39.66          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.13/39.66    (21)  all_57_8 = e1
% 228.13/39.66    (22)   ~ (all_53_9 = all_6_2)
% 228.13/39.66    (23)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.13/39.66          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.13/39.66    (24)  all_57_3 = e0
% 228.13/39.66    (25)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.13/39.66          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.13/39.66    (26)   ~ (e3 = e2)
% 228.13/39.66    (27)  all_55_1 = all_53_4
% 228.13/39.66    (28)   ~ (e3 = e0)
% 228.13/39.66    (29)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.13/39.66          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.13/39.66    (30)   ~ (all_53_8 = all_6_2)
% 228.13/39.66    (31)  all_55_2 = all_53_8
% 228.13/39.66    (32)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.13/39.66    (33)  all_57_15 = e3
% 228.13/39.66    (34)  all_57_1 = e1
% 228.13/39.66    (35)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.13/39.66          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.13/39.66            e1)
% 228.13/39.66    (36)  all_57_10 = e2
% 228.13/39.66    (37)  all_57_11 = e0
% 228.13/39.66    (38)   ~ (all_53_4 = all_53_8)
% 228.13/39.66    (39)  op(e3, e2) = all_53_4
% 228.13/39.66    (40)   ~ (e2 = e0)
% 228.13/39.66    (41)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.13/39.66            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.13/39.66            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.13/39.66            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.13/39.66              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.13/39.66            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.13/39.66            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.13/39.66              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.13/39.66              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.13/39.66            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.13/39.66            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.13/39.66            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.13/39.66              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.13/39.66              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.13/39.66            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.13/39.66              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.13/39.66            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.13/39.66            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.13/39.66              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.13/39.66              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.13/39.66            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.13/39.66            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.13/39.66    (42)  all_57_2 = e3
% 228.13/39.66    (43)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.13/39.66          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.13/39.66    (44)   ~ (e1 = e0)
% 228.13/39.66    (45)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.13/39.66            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.13/39.66              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.13/39.66    (46)   ~ (all_53_4 = e0)
% 228.13/39.66    (47)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.13/39.66          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.13/39.66    (48)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.13/39.66          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.13/39.66    (49)  op(e0, e0) = e3
% 228.13/39.66    (50)   ~ (all_53_4 = all_53_6)
% 228.13/39.66    (51)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.13/39.66          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.13/39.66            e2)
% 228.13/39.66    (52)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.13/39.66              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.13/39.66                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.13/39.66                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.13/39.66    (53)  all_55_10 = all_6_2
% 228.13/39.66    (54)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.13/39.66          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.13/39.66    (55)  all_38_2 = all_6_2
% 228.13/39.66    (56)  all_55_3 = all_53_12
% 228.13/39.66    (57)   ~ (all_53_12 = e3)
% 228.13/39.66    (58)  all_57_7 = e3
% 228.13/39.66    (59)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.13/39.66            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.13/39.66              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.13/39.66    (60)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.13/39.66          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.13/39.66    (61)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.13/39.66          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.13/39.66    (62)   ~ (e2 = e1)
% 228.13/39.66    (63)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.13/39.66          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.13/39.66    (64)  op(e2, e1) = all_53_9
% 228.13/39.66    (65)  op(e1, e2) = all_53_6
% 228.13/39.66    (66)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.13/39.66          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.13/39.66    (67)  all_24_2 = all_6_2
% 228.13/39.66    (68)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.13/39.66          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.13/39.66    (69)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.13/39.66          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.13/39.66    (70)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.13/39.66          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.13/39.66    (71)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.13/39.66          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.13/39.66    (72)  op(e3, e1) = all_53_8
% 228.13/39.66    (73)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.13/39.66          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.13/39.66    (74)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.13/39.66          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.13/39.66    (75)  op(e3, e0) = all_53_12
% 228.13/39.66  
% 228.13/39.66  Begin of proof
% 228.13/39.66  | 
% 228.13/39.66  | BETA: splitting (20) gives:
% 228.13/39.66  | 
% 228.13/39.66  | Case 1:
% 228.13/39.66  | | 
% 228.13/39.66  | |   (76)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) =
% 228.13/39.66  | |           e2)
% 228.13/39.66  | | 
% 228.13/39.66  | | BETA: splitting (76) gives:
% 228.13/39.66  | | 
% 228.13/39.66  | | Case 1:
% 228.13/39.66  | | | 
% 228.13/39.66  | | |   (77)  all_57_0 = e2 & op(e3, e3) = e2
% 228.13/39.66  | | | 
% 228.13/39.66  | | | ALPHA: (77) implies:
% 228.13/39.66  | | |   (78)  op(e3, e3) = e2
% 228.13/39.66  | | | 
% 228.13/39.66  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.13/39.66  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 228.13/39.66  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 228.13/39.66  | | |            (33), (35), (36), (38), (39), (40), (41), (42), (43), (44),
% 228.13/39.66  | | |            (45), (46), (47), (48), (49), (50), (51), (52), (53), (54),
% 228.13/39.66  | | |            (55), (56), (57), (59), (60), (61), (62), (63), (64), (65),
% 228.13/39.66  | | |            (66), (67), (68), (69), (70), (71), (72), (73), (74), (75),
% 228.13/39.66  | | |            (78) are inconsistent by sub-proof #501.
% 228.13/39.66  | | | 
% 228.13/39.66  | | Case 2:
% 228.13/39.66  | | | 
% 228.13/39.66  | | |   (79)  all_57_1 = e2 & op(e3, e2) = e2
% 228.13/39.66  | | | 
% 228.13/39.66  | | | REF_CLOSE: (34), (62), (79) are inconsistent by sub-proof #2489.
% 228.13/39.66  | | | 
% 228.13/39.66  | | End of split
% 228.13/39.66  | | 
% 228.13/39.66  | Case 2:
% 228.13/39.66  | | 
% 228.13/39.66  | |   (80)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) =
% 228.13/39.66  | |           e2)
% 228.13/39.66  | | 
% 228.13/39.66  | | BETA: splitting (80) gives:
% 228.13/39.66  | | 
% 228.13/39.66  | | Case 1:
% 228.13/39.66  | | | 
% 228.13/39.66  | | |   (81)  all_57_4 = e2 & op(e3, e1) = e2
% 228.13/39.66  | | | 
% 228.13/39.66  | | | ALPHA: (81) implies:
% 228.13/39.66  | | |   (82)  all_57_4 = e2
% 228.13/39.66  | | | 
% 228.13/39.66  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.13/39.66  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (22), (23),
% 228.13/39.66  | | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 228.13/39.66  | | |            (35), (38), (39), (40), (41), (43), (44), (45), (46), (47),
% 228.13/39.66  | | |            (49), (50), (51), (52), (53), (55), (56), (57), (58), (59),
% 228.13/39.66  | | |            (60), (62), (63), (64), (65), (66), (67), (68), (69), (70),
% 228.13/39.66  | | |            (71), (72), (73), (74), (75), (82) are inconsistent by
% 228.13/39.66  | | |            sub-proof #546.
% 228.13/39.66  | | | 
% 228.13/39.66  | | Case 2:
% 228.13/39.66  | | | 
% 228.13/39.66  | | |   (83)  all_57_9 = e2 & op(e3, e0) = e2
% 228.13/39.66  | | | 
% 228.13/39.66  | | | ALPHA: (83) implies:
% 228.13/39.66  | | |   (84)  all_57_9 = e2
% 228.13/39.66  | | | 
% 228.13/39.66  | | | BETA: splitting (70) gives:
% 228.13/39.66  | | | 
% 228.13/39.66  | | | Case 1:
% 228.13/39.66  | | | | 
% 228.13/39.66  | | | |   (85)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0)
% 228.13/39.66  | | | |           = e1)
% 228.13/39.66  | | | | 
% 228.13/39.66  | | | | BETA: splitting (85) gives:
% 228.13/39.66  | | | | 
% 228.13/39.66  | | | | Case 1:
% 228.13/39.66  | | | | | 
% 228.13/39.66  | | | | |   (86)  all_57_9 = e1 & op(e3, e0) = e1
% 228.13/39.66  | | | | | 
% 228.13/39.66  | | | | | REF_CLOSE: (62), (84), (86) are inconsistent by sub-proof #2451.
% 228.13/39.66  | | | | | 
% 228.13/39.66  | | | | Case 2:
% 228.13/39.66  | | | | | 
% 228.13/39.66  | | | | |   (87)  all_57_10 = e1 & op(e2, e0) = e1
% 228.13/39.66  | | | | | 
% 228.13/39.66  | | | | | REF_CLOSE: (36), (62), (87) are inconsistent by sub-proof #2360.
% 228.13/39.66  | | | | | 
% 228.13/39.66  | | | | End of split
% 228.13/39.66  | | | | 
% 228.13/39.66  | | | Case 2:
% 228.13/39.66  | | | | 
% 228.13/39.66  | | | |   (88)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0,
% 228.13/39.66  | | | |             e0) = e1)
% 228.13/39.66  | | | | 
% 228.13/39.66  | | | | BETA: splitting (88) gives:
% 228.13/39.66  | | | | 
% 228.13/39.66  | | | | Case 1:
% 228.13/39.66  | | | | | 
% 228.13/39.66  | | | | |   (89)  all_57_11 = e1 & op(e1, e0) = e1
% 228.13/39.66  | | | | | 
% 228.13/39.66  | | | | | ALPHA: (89) implies:
% 228.13/39.66  | | | | |   (90)  all_57_11 = e1
% 228.13/39.66  | | | | | 
% 228.13/39.66  | | | | | COMBINE_EQS: (37), (90) imply:
% 228.13/39.66  | | | | |   (91)  e1 = e0
% 228.13/39.66  | | | | | 
% 228.13/39.66  | | | | | REF_CLOSE: (6), (7), (24), (26), (34), (40), (44), (58), (62), (73),
% 228.13/39.66  | | | | |            (91) are inconsistent by sub-proof #1626.
% 228.13/39.66  | | | | | 
% 228.13/39.66  | | | | Case 2:
% 228.13/39.66  | | | | | 
% 228.13/39.66  | | | | |   (92)  all_57_15 = e1 & op(e0, e0) = e1
% 228.13/39.66  | | | | | 
% 228.13/39.66  | | | | | ALPHA: (92) implies:
% 228.13/39.66  | | | | |   (93)  op(e0, e0) = e1
% 228.13/39.66  | | | | | 
% 228.13/39.66  | | | | | REF_CLOSE: (7), (9), (49), (93) are inconsistent by sub-proof #2183.
% 228.13/39.66  | | | | | 
% 228.13/39.66  | | | | End of split
% 228.13/39.66  | | | | 
% 228.13/39.66  | | | End of split
% 228.13/39.66  | | | 
% 228.13/39.66  | | End of split
% 228.13/39.66  | | 
% 228.13/39.66  | End of split
% 228.13/39.66  | 
% 228.13/39.66  End of proof
% 228.13/39.66  
% 228.13/39.66  Sub-proof #428 shows that the following formulas are inconsistent:
% 228.13/39.66  ----------------------------------------------------------------
% 228.13/39.66    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.13/39.66    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.13/39.66    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.13/39.66         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.13/39.66    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.13/39.66         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.13/39.66    (5)   ~ (all_53_8 = all_53_12)
% 228.13/39.66    (6)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.13/39.66         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.13/39.66    (7)   ~ (e3 = e1)
% 228.13/39.66    (8)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.13/39.66         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.13/39.66    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.13/39.66           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.13/39.67    (10)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.13/39.67          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.13/39.67    (11)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.13/39.67            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.13/39.67              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.13/39.67    (12)   ~ (all_6_2 = e3)
% 228.13/39.67    (13)  op(e1, e1) = all_6_2
% 228.13/39.67    (14)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.13/39.67    (15)   ~ (all_53_9 = e0)
% 228.13/39.67    (16)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.13/39.67          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.13/39.67    (17)  all_57_9 = e1
% 228.13/39.67    (18)   ~ (all_53_4 = all_53_12)
% 228.13/39.67    (19)   ~ (all_53_8 = all_53_9)
% 228.13/39.67    (20)  all_42_2 = all_6_2
% 228.13/39.67    (21)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.13/39.67          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.13/39.67    (22)  all_57_8 = e1
% 228.13/39.67    (23)   ~ (all_53_9 = all_6_2)
% 228.13/39.67    (24)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.13/39.67          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.13/39.67    (25)  all_57_3 = e0
% 228.13/39.67    (26)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.13/39.67          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.13/39.67    (27)  all_57_4 = e3
% 228.13/39.67    (28)   ~ (e3 = e2)
% 228.13/39.67    (29)  all_55_1 = all_53_4
% 228.13/39.67    (30)   ~ (e3 = e0)
% 228.13/39.67    (31)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.13/39.67          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.13/39.67    (32)   ~ (all_53_8 = all_6_2)
% 228.13/39.67    (33)  all_55_2 = all_53_8
% 228.13/39.67    (34)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.13/39.67    (35)  all_57_15 = e3
% 228.13/39.67    (36)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.13/39.67          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.13/39.67            e1)
% 228.13/39.67    (37)  all_57_10 = e2
% 228.13/39.67    (38)  all_57_11 = e0
% 228.13/39.67    (39)   ~ (all_53_4 = all_53_8)
% 228.13/39.67    (40)  op(e3, e2) = all_53_4
% 228.13/39.67    (41)   ~ (e2 = e0)
% 228.13/39.67    (42)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.13/39.67            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.13/39.67            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.13/39.67            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.13/39.67              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.13/39.67            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.13/39.67            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.13/39.67              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.13/39.67              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.13/39.67            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.13/39.67            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.13/39.67            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.13/39.67              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.13/39.67              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.13/39.67            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.13/39.67              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.13/39.67            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.13/39.67            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.13/39.67              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.13/39.67              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.13/39.67            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.13/39.67            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.13/39.67    (43)  all_57_2 = e3
% 228.13/39.67    (44)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.13/39.67          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.13/39.67    (45)   ~ (e1 = e0)
% 228.13/39.67    (46)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.13/39.67            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.13/39.67              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.13/39.67    (47)   ~ (all_53_4 = e0)
% 228.13/39.67    (48)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.13/39.67          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.13/39.67    (49)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.13/39.67          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.13/39.67    (50)  op(e0, e0) = e3
% 228.13/39.67    (51)   ~ (all_53_4 = all_53_6)
% 228.13/39.67    (52)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.13/39.67          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.13/39.67            e2)
% 228.13/39.67    (53)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.13/39.67              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.13/39.67                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.13/39.67                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.13/39.67    (54)  all_55_10 = all_6_2
% 228.13/39.67    (55)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.13/39.67          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.13/39.67    (56)  all_38_2 = all_6_2
% 228.13/39.67    (57)  all_55_3 = all_53_12
% 228.13/39.67    (58)   ~ (all_53_12 = e3)
% 228.13/39.67    (59)  all_57_7 = e3
% 228.13/39.67    (60)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.13/39.67            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.13/39.67              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.13/39.67    (61)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.13/39.67          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.13/39.67    (62)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.13/39.67          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.13/39.67    (63)   ~ (e2 = e1)
% 228.13/39.67    (64)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.13/39.67          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.13/39.67    (65)  op(e2, e1) = all_53_9
% 228.13/39.67    (66)  op(e1, e2) = all_53_6
% 228.13/39.67    (67)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.13/39.67          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.13/39.67    (68)  all_24_2 = all_6_2
% 228.13/39.67    (69)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.13/39.67          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.13/39.67    (70)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.13/39.67          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.13/39.67    (71)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.13/39.67          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.13/39.67    (72)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.13/39.67          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.13/39.67    (73)  op(e3, e1) = all_53_8
% 228.13/39.67    (74)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.13/39.67          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.13/39.67    (75)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.13/39.67          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.13/39.67    (76)  op(e3, e0) = all_53_12
% 228.13/39.67  
% 228.13/39.67  Begin of proof
% 228.13/39.67  | 
% 228.13/39.67  | BETA: splitting (75) gives:
% 228.13/39.67  | 
% 228.13/39.67  | Case 1:
% 228.13/39.67  | | 
% 228.13/39.67  | |   (77)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) =
% 228.13/39.67  | |           e2)
% 228.13/39.67  | | 
% 228.13/39.67  | | BETA: splitting (77) gives:
% 228.13/39.67  | | 
% 228.13/39.67  | | Case 1:
% 228.13/39.67  | | | 
% 228.13/39.67  | | |   (78)  all_57_6 = e2 & op(e1, e3) = e2
% 228.13/39.67  | | | 
% 228.13/39.67  | | | ALPHA: (78) implies:
% 228.13/39.67  | | |   (79)  all_57_6 = e2
% 228.13/39.67  | | | 
% 228.13/39.67  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.13/39.67  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 228.13/39.67  | | |            (23), (24), (25), (26), (28), (29), (30), (31), (32), (33),
% 228.13/39.67  | | |            (34), (35), (36), (37), (38), (39), (40), (41), (42), (43),
% 228.13/39.67  | | |            (44), (45), (46), (47), (48), (49), (50), (51), (52), (53),
% 228.13/39.67  | | |            (54), (55), (56), (57), (58), (59), (60), (61), (62), (63),
% 228.13/39.67  | | |            (64), (65), (66), (67), (68), (69), (70), (71), (72), (73),
% 228.13/39.67  | | |            (74), (75), (76), (79) are inconsistent by sub-proof #429.
% 228.13/39.67  | | | 
% 228.13/39.67  | | Case 2:
% 228.13/39.67  | | | 
% 228.13/39.67  | | |   (80)  all_57_7 = e2 & op(e1, e2) = e2
% 228.13/39.67  | | | 
% 228.13/39.67  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.13/39.67  | | |            (13), (14), (15), (16), (18), (19), (20), (21), (23), (24),
% 228.13/39.67  | | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 228.13/39.67  | | |            (35), (36), (39), (40), (41), (42), (44), (45), (46), (47),
% 228.13/39.67  | | |            (48), (50), (51), (52), (53), (54), (56), (57), (58), (59),
% 228.13/39.67  | | |            (60), (61), (63), (64), (65), (66), (67), (68), (69), (70),
% 228.13/39.67  | | |            (71), (72), (73), (74), (75), (76), (80) are inconsistent by
% 228.13/39.67  | | |            sub-proof #500.
% 228.13/39.67  | | | 
% 228.13/39.67  | | End of split
% 228.13/39.67  | | 
% 228.13/39.67  | Case 2:
% 228.13/39.67  | | 
% 228.13/39.67  | |   (81)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) =
% 228.13/39.67  | |           e2)
% 228.13/39.67  | | 
% 228.13/39.67  | | BETA: splitting (81) gives:
% 228.13/39.67  | | 
% 228.13/39.67  | | Case 1:
% 228.13/39.67  | | | 
% 228.13/39.67  | | |   (82)  all_57_8 = e2 & op(e1, e1) = e2
% 228.13/39.67  | | | 
% 228.13/39.67  | | | ALPHA: (82) implies:
% 228.13/39.67  | | |   (83)  all_57_8 = e2
% 228.13/39.67  | | | 
% 228.13/39.67  | | | REF_CLOSE: (22), (63), (83) are inconsistent by sub-proof #1485.
% 228.13/39.67  | | | 
% 228.13/39.67  | | Case 2:
% 228.13/39.67  | | | 
% 228.13/39.67  | | |   (84)  all_57_11 = e2 & op(e1, e0) = e2
% 228.13/39.67  | | | 
% 228.13/39.67  | | | ALPHA: (84) implies:
% 228.13/39.67  | | |   (85)  all_57_11 = e2
% 228.13/39.67  | | | 
% 228.13/39.67  | | | REF_CLOSE: (38), (41), (85) are inconsistent by sub-proof #1949.
% 228.13/39.67  | | | 
% 228.13/39.67  | | End of split
% 228.13/39.67  | | 
% 228.13/39.67  | End of split
% 228.13/39.67  | 
% 228.13/39.67  End of proof
% 228.13/39.67  
% 228.13/39.67  Sub-proof #429 shows that the following formulas are inconsistent:
% 228.13/39.67  ----------------------------------------------------------------
% 228.13/39.67    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.13/39.67    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.13/39.67    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.13/39.67         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.13/39.67    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.13/39.67         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.13/39.67    (5)   ~ (all_53_8 = all_53_12)
% 228.13/39.67    (6)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.13/39.67         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.13/39.67    (7)   ~ (e3 = e1)
% 228.13/39.67    (8)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.13/39.67         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.13/39.67    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.13/39.67           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.13/39.67    (10)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.13/39.67          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.13/39.67    (11)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.13/39.67            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.13/39.67              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.13/39.67    (12)   ~ (all_6_2 = e3)
% 228.13/39.67    (13)  op(e1, e1) = all_6_2
% 228.13/39.67    (14)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.13/39.67    (15)   ~ (all_53_9 = e0)
% 228.13/39.67    (16)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.13/39.67          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.13/39.67    (17)  all_57_9 = e1
% 228.13/39.67    (18)   ~ (all_53_4 = all_53_12)
% 228.13/39.67    (19)   ~ (all_53_8 = all_53_9)
% 228.13/39.67    (20)  all_42_2 = all_6_2
% 228.13/39.67    (21)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.13/39.67          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.13/39.67    (22)  all_57_8 = e1
% 228.13/39.67    (23)   ~ (all_53_9 = all_6_2)
% 228.13/39.67    (24)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.13/39.67          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.13/39.67    (25)  all_57_3 = e0
% 228.13/39.67    (26)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.13/39.67          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.13/39.67    (27)   ~ (e3 = e2)
% 228.13/39.67    (28)  all_55_1 = all_53_4
% 228.13/39.67    (29)   ~ (e3 = e0)
% 228.13/39.67    (30)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.13/39.67          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.13/39.67    (31)   ~ (all_53_8 = all_6_2)
% 228.13/39.67    (32)  all_55_2 = all_53_8
% 228.13/39.67    (33)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.13/39.67    (34)  all_57_15 = e3
% 228.13/39.67    (35)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.13/39.67          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.13/39.67            e1)
% 228.13/39.67    (36)  all_57_10 = e2
% 228.13/39.67    (37)  all_57_6 = e2
% 228.13/39.67    (38)  all_57_11 = e0
% 228.13/39.67    (39)   ~ (all_53_4 = all_53_8)
% 228.13/39.67    (40)  op(e3, e2) = all_53_4
% 228.13/39.67    (41)   ~ (e2 = e0)
% 228.13/39.67    (42)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.13/39.67            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.13/39.67            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.13/39.67            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.13/39.67              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.13/39.67            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.13/39.67            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.13/39.67              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.13/39.67              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.13/39.67            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.13/39.67            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.13/39.67            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.13/39.67              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.13/39.67              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.13/39.67            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.13/39.67              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.13/39.67            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.13/39.67            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.13/39.67              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.13/39.67              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.13/39.67            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.13/39.67            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.13/39.67    (43)  all_57_2 = e3
% 228.13/39.67    (44)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.13/39.67          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.13/39.67    (45)   ~ (e1 = e0)
% 228.13/39.67    (46)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.13/39.67            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.13/39.67              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.13/39.67    (47)   ~ (all_53_4 = e0)
% 228.13/39.67    (48)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.13/39.67          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.13/39.67    (49)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.13/39.67          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.13/39.67    (50)  op(e0, e0) = e3
% 228.13/39.67    (51)   ~ (all_53_4 = all_53_6)
% 228.13/39.67    (52)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.13/39.67          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.13/39.67            e2)
% 228.13/39.67    (53)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.13/39.67              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.13/39.67                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.13/39.67                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.13/39.67    (54)  all_55_10 = all_6_2
% 228.13/39.67    (55)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.13/39.67          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.13/39.67    (56)  all_38_2 = all_6_2
% 228.13/39.67    (57)  all_55_3 = all_53_12
% 228.13/39.67    (58)   ~ (all_53_12 = e3)
% 228.13/39.67    (59)  all_57_7 = e3
% 228.13/39.67    (60)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.13/39.67            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.13/39.67              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.13/39.67    (61)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.13/39.67          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.13/39.67    (62)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.13/39.67          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.13/39.67    (63)   ~ (e2 = e1)
% 228.13/39.67    (64)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.13/39.67          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.13/39.67    (65)  op(e2, e1) = all_53_9
% 228.13/39.67    (66)  op(e1, e2) = all_53_6
% 228.13/39.67    (67)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.13/39.67          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.13/39.67    (68)  all_24_2 = all_6_2
% 228.13/39.67    (69)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.13/39.67          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.13/39.67    (70)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.13/39.67          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.13/39.67    (71)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.13/39.67          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.13/39.67    (72)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.13/39.67          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.13/39.67    (73)  op(e3, e1) = all_53_8
% 228.13/39.67    (74)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.13/39.67          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.13/39.67    (75)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.13/39.67          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.13/39.67    (76)  op(e3, e0) = all_53_12
% 228.13/39.67  
% 228.13/39.67  Begin of proof
% 228.13/39.67  | 
% 228.13/39.67  | BETA: splitting (21) gives:
% 228.13/39.67  | 
% 228.13/39.67  | Case 1:
% 228.13/39.67  | | 
% 228.13/39.67  | |   (77)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) =
% 228.13/39.67  | |           e2)
% 228.13/39.67  | | 
% 228.13/39.67  | | BETA: splitting (77) gives:
% 228.13/39.67  | | 
% 228.13/39.67  | | Case 1:
% 228.13/39.67  | | | 
% 228.13/39.67  | | |   (78)  all_57_0 = e2 & op(e3, e3) = e2
% 228.13/39.67  | | | 
% 228.13/39.67  | | | ALPHA: (78) implies:
% 228.13/39.67  | | |   (79)  op(e3, e3) = e2
% 228.13/39.67  | | | 
% 228.13/39.67  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.13/39.67  | | |            (13), (14), (15), (16), (18), (19), (20), (21), (22), (23),
% 228.13/39.67  | | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 228.13/39.67  | | |            (34), (35), (36), (39), (40), (41), (42), (43), (44), (45),
% 228.13/39.67  | | |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (55),
% 228.13/39.67  | | |            (56), (57), (58), (60), (61), (62), (63), (64), (65), (66),
% 228.13/39.67  | | |            (67), (68), (69), (70), (71), (72), (73), (74), (75), (76),
% 228.13/39.67  | | |            (79) are inconsistent by sub-proof #501.
% 228.13/39.67  | | | 
% 228.13/39.67  | | Case 2:
% 228.13/39.67  | | | 
% 228.13/39.67  | | |   (80)  all_57_1 = e2 & op(e3, e2) = e2
% 228.13/39.67  | | | 
% 228.13/39.67  | | | ALPHA: (80) implies:
% 228.13/39.67  | | |   (81)  all_57_1 = e2
% 228.13/39.67  | | | 
% 228.13/39.67  | | | BETA: splitting (69) gives:
% 228.13/39.67  | | | 
% 228.13/39.67  | | | Case 1:
% 228.13/39.67  | | | | 
% 228.13/39.67  | | | |   (82)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1)
% 228.13/39.67  | | | |           = e2)
% 228.13/39.67  | | | | 
% 228.13/39.67  | | | | BETA: splitting (82) gives:
% 228.13/39.67  | | | | 
% 228.13/39.67  | | | | Case 1:
% 228.13/39.67  | | | | | 
% 228.13/39.67  | | | | |   (83)  all_57_4 = e2 & op(e3, e1) = e2
% 228.13/39.67  | | | | | 
% 228.13/39.67  | | | | | ALPHA: (83) implies:
% 228.13/39.67  | | | | |   (84)  all_57_4 = e2
% 228.13/39.67  | | | | | 
% 228.13/39.67  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 228.13/39.67  | | | | |            (12), (13), (14), (15), (16), (18), (19), (20), (21), (23),
% 228.13/39.67  | | | | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 228.13/39.67  | | | | |            (34), (35), (39), (40), (41), (42), (44), (45), (46), (47),
% 228.13/39.67  | | | | |            (48), (50), (51), (52), (53), (54), (56), (57), (58), (59),
% 228.13/39.67  | | | | |            (60), (61), (63), (64), (65), (66), (67), (68), (69), (70),
% 228.13/39.67  | | | | |            (71), (72), (73), (74), (75), (76), (84) are inconsistent
% 228.13/39.67  | | | | |            by sub-proof #546.
% 228.13/39.67  | | | | | 
% 228.13/39.67  | | | | Case 2:
% 228.13/39.67  | | | | | 
% 228.13/39.67  | | | | |   (85)  all_57_5 = e2 & op(e2, e1) = e2
% 228.13/39.67  | | | | | 
% 228.13/39.67  | | | | | ALPHA: (85) implies:
% 228.13/39.67  | | | | |   (86)  all_57_5 = e2
% 228.13/39.67  | | | | | 
% 228.13/39.67  | | | | | BETA: splitting (44) gives:
% 228.13/39.67  | | | | | 
% 228.13/39.67  | | | | | Case 1:
% 228.13/39.67  | | | | | | 
% 228.13/39.67  | | | | | |   (87)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3,
% 228.13/39.67  | | | | | |             e2) = e3)
% 228.13/39.67  | | | | | | 
% 228.13/39.67  | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 228.13/39.67  | | | | | |            (12), (13), (14), (15), (16), (18), (19), (20), (21),
% 228.13/39.67  | | | | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31),
% 228.13/39.67  | | | | | |            (32), (33), (34), (35), (39), (40), (41), (42), (43),
% 228.13/39.67  | | | | | |            (44), (45), (46), (47), (48), (50), (51), (52), (53),
% 228.13/39.67  | | | | | |            (54), (56), (57), (58), (59), (60), (61), (63), (64),
% 228.13/39.67  | | | | | |            (65), (66), (67), (68), (69), (70), (71), (72), (73),
% 228.13/39.67  | | | | | |            (74), (75), (76), (87) are inconsistent by sub-proof
% 228.13/39.67  | | | | | |            #514.
% 228.13/39.67  | | | | | | 
% 228.13/39.67  | | | | | Case 2:
% 228.13/39.67  | | | | | | 
% 228.13/39.67  | | | | | |   (88)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3,
% 228.13/39.67  | | | | | |             e0) = e3)
% 228.13/39.67  | | | | | | 
% 228.13/39.67  | | | | | | BETA: splitting (88) gives:
% 228.13/39.67  | | | | | | 
% 228.13/39.67  | | | | | | Case 1:
% 228.13/39.67  | | | | | | | 
% 228.13/39.67  | | | | | | |   (89)  all_57_4 = e3 & op(e3, e1) = e3
% 228.13/39.67  | | | | | | | 
% 228.13/39.67  | | | | | | | ALPHA: (89) implies:
% 228.13/39.67  | | | | | | |   (90)  all_57_4 = e3
% 228.13/39.67  | | | | | | | 
% 228.13/39.67  | | | | | | | REF_CLOSE: (3), (7), (9), (12), (13), (25), (27), (29), (34),
% 228.13/39.67  | | | | | | |            (35), (36), (41), (43), (45), (48), (52), (53), (63),
% 228.13/39.67  | | | | | | |            (86), (90) are inconsistent by sub-proof #1753.
% 228.13/39.67  | | | | | | | 
% 228.13/39.67  | | | | | | Case 2:
% 228.13/39.67  | | | | | | | 
% 228.13/39.67  | | | | | | |   (91)  all_57_9 = e3 & op(e3, e0) = e3
% 228.13/39.67  | | | | | | | 
% 228.13/39.67  | | | | | | | ALPHA: (91) implies:
% 228.13/39.67  | | | | | | |   (92)  op(e3, e0) = e3
% 228.13/39.67  | | | | | | | 
% 228.13/39.67  | | | | | | | REF_CLOSE: (9), (58), (76), (92) are inconsistent by sub-proof
% 228.13/39.67  | | | | | | |            #2458.
% 228.13/39.67  | | | | | | | 
% 228.13/39.67  | | | | | | End of split
% 228.13/39.67  | | | | | | 
% 228.13/39.67  | | | | | End of split
% 228.13/39.67  | | | | | 
% 228.13/39.67  | | | | End of split
% 228.13/39.67  | | | | 
% 228.13/39.67  | | | Case 2:
% 228.13/39.67  | | | | 
% 228.13/39.67  | | | |   (93)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1)
% 228.13/39.67  | | | |           = e2)
% 228.13/39.67  | | | | 
% 228.13/39.67  | | | | BETA: splitting (93) gives:
% 228.13/39.67  | | | | 
% 228.13/39.67  | | | | Case 1:
% 228.13/39.67  | | | | | 
% 228.13/39.67  | | | | |   (94)  all_57_8 = e2 & op(e1, e1) = e2
% 228.13/39.67  | | | | | 
% 228.13/39.67  | | | | | ALPHA: (94) implies:
% 228.13/39.67  | | | | |   (95)  all_57_8 = e2
% 228.13/39.67  | | | | | 
% 228.13/39.67  | | | | | COMBINE_EQS: (22), (95) imply:
% 228.13/39.67  | | | | |   (96)  e2 = e1
% 228.13/39.67  | | | | | 
% 228.13/39.67  | | | | | SIMP: (96) implies:
% 228.13/39.67  | | | | |   (97)  e2 = e1
% 228.13/39.67  | | | | | 
% 228.13/39.67  | | | | | COMBINE_EQS: (81), (97) imply:
% 228.13/39.67  | | | | |   (98)  all_57_1 = e1
% 228.13/39.67  | | | | | 
% 228.13/39.67  | | | | | REF_CLOSE: (6), (7), (25), (27), (37), (38), (41), (45), (59), (63),
% 228.13/39.67  | | | | |            (72), (74), (95), (98) are inconsistent by sub-proof #430.
% 228.13/39.67  | | | | | 
% 228.13/39.67  | | | | Case 2:
% 228.13/39.67  | | | | | 
% 228.13/39.67  | | | | |   (99)  all_57_14 = e2 & op(e0, e1) = e2
% 228.13/39.67  | | | | | 
% 228.13/39.67  | | | | | ALPHA: (99) implies:
% 228.13/39.67  | | | | |   (100)  all_57_14 = e2
% 228.13/39.67  | | | | | 
% 228.13/39.67  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 228.13/39.67  | | | | |            (12), (13), (14), (15), (16), (18), (19), (20), (21), (22),
% 228.13/39.67  | | | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 228.13/39.67  | | | | |            (33), (34), (35), (36), (39), (40), (41), (42), (43), (44),
% 228.13/39.67  | | | | |            (45), (46), (47), (48), (50), (51), (52), (53), (54), (55),
% 228.13/39.67  | | | | |            (56), (57), (58), (59), (60), (61), (63), (64), (65), (66),
% 228.13/39.67  | | | | |            (67), (68), (69), (70), (71), (72), (73), (74), (75), (76),
% 228.13/39.67  | | | | |            (100) are inconsistent by sub-proof #502.
% 228.13/39.67  | | | | | 
% 228.13/39.67  | | | | End of split
% 228.13/39.67  | | | | 
% 228.13/39.67  | | | End of split
% 228.13/39.67  | | | 
% 228.13/39.67  | | End of split
% 228.13/39.67  | | 
% 228.13/39.67  | Case 2:
% 228.13/39.67  | | 
% 228.13/39.67  | |   (101)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) =
% 228.13/39.67  | |            e2)
% 228.13/39.67  | | 
% 228.13/39.67  | | BETA: splitting (101) gives:
% 228.13/39.67  | | 
% 228.13/39.67  | | Case 1:
% 228.13/39.67  | | | 
% 228.13/39.67  | | |   (102)  all_57_4 = e2 & op(e3, e1) = e2
% 228.13/39.67  | | | 
% 228.13/39.67  | | | ALPHA: (102) implies:
% 228.13/39.67  | | |   (103)  all_57_4 = e2
% 228.13/39.67  | | | 
% 228.13/39.67  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.13/39.67  | | |            (13), (14), (15), (16), (18), (19), (20), (21), (23), (24),
% 228.13/39.67  | | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 228.13/39.67  | | |            (35), (39), (40), (41), (42), (44), (45), (46), (47), (48),
% 228.13/39.67  | | |            (50), (51), (52), (53), (54), (56), (57), (58), (59), (60),
% 228.13/39.67  | | |            (61), (63), (64), (65), (66), (67), (68), (69), (70), (71),
% 228.13/39.67  | | |            (72), (73), (74), (75), (76), (103) are inconsistent by
% 228.13/39.67  | | |            sub-proof #546.
% 228.13/39.67  | | | 
% 228.13/39.67  | | Case 2:
% 228.13/39.67  | | | 
% 228.13/39.67  | | |   (104)  all_57_9 = e2 & op(e3, e0) = e2
% 228.13/39.67  | | | 
% 228.13/39.67  | | | ALPHA: (104) implies:
% 228.13/39.67  | | |   (105)  all_57_9 = e2
% 228.13/39.67  | | | 
% 228.13/39.67  | | | REF_CLOSE: (17), (63), (105) are inconsistent by sub-proof #2444.
% 228.13/39.67  | | | 
% 228.13/39.67  | | End of split
% 228.13/39.67  | | 
% 228.13/39.67  | End of split
% 228.13/39.67  | 
% 228.13/39.67  End of proof
% 228.13/39.67  
% 228.13/39.67  Sub-proof #430 shows that the following formulas are inconsistent:
% 228.13/39.67  ----------------------------------------------------------------
% 228.13/39.67    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.13/39.67         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.13/39.67    (2)   ~ (e3 = e1)
% 228.13/39.67    (3)  all_57_3 = e0
% 228.13/39.67    (4)   ~ (e3 = e2)
% 228.13/39.67    (5)  all_57_1 = e1
% 228.13/39.67    (6)  all_57_6 = e2
% 228.13/39.67    (7)  all_57_11 = e0
% 228.13/39.67    (8)   ~ (e2 = e0)
% 228.13/39.67    (9)   ~ (e1 = e0)
% 228.13/39.67    (10)  all_57_8 = e2
% 228.13/39.67    (11)  all_57_7 = e3
% 228.13/39.67    (12)   ~ (e2 = e1)
% 228.13/39.67    (13)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.13/39.67          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.13/39.67    (14)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.13/39.67          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.13/39.67  
% 228.13/39.67  Begin of proof
% 228.13/39.67  | 
% 228.13/39.67  | BETA: splitting (13) gives:
% 228.13/39.67  | 
% 228.13/39.67  | Case 1:
% 228.13/39.67  | | 
% 228.13/39.67  | |   (15)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) =
% 228.13/39.67  | |           e1)
% 228.13/39.67  | | 
% 228.13/39.67  | | BETA: splitting (15) gives:
% 228.13/39.67  | | 
% 228.13/39.67  | | Case 1:
% 228.13/39.67  | | | 
% 228.13/39.67  | | |   (16)  all_57_6 = e1 & op(e1, e3) = e1
% 228.13/39.67  | | | 
% 228.13/39.67  | | | ALPHA: (16) implies:
% 228.13/39.67  | | |   (17)  all_57_6 = e1
% 228.13/39.67  | | | 
% 228.13/39.67  | | | REF_CLOSE: (6), (12), (17) are inconsistent by sub-proof #2233.
% 228.13/39.67  | | | 
% 228.13/39.67  | | Case 2:
% 228.13/39.67  | | | 
% 228.13/39.67  | | |   (18)  all_57_7 = e1 & op(e1, e2) = e1
% 228.13/39.67  | | | 
% 228.13/39.67  | | | ALPHA: (18) implies:
% 228.13/39.67  | | |   (19)  all_57_7 = e1
% 228.13/39.67  | | | 
% 228.13/39.67  | | | REF_CLOSE: (2), (11), (19) are inconsistent by sub-proof #2115.
% 228.13/39.67  | | | 
% 228.13/39.67  | | End of split
% 228.13/39.67  | | 
% 228.13/39.67  | Case 2:
% 228.13/39.67  | | 
% 228.13/39.67  | |   (20)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) =
% 228.13/39.67  | |           e1)
% 228.13/39.67  | | 
% 228.13/39.67  | | BETA: splitting (20) gives:
% 228.13/39.67  | | 
% 228.13/39.67  | | Case 1:
% 228.13/39.67  | | | 
% 228.13/39.68  | | |   (21)  all_57_8 = e1 & op(e1, e1) = e1
% 228.13/39.68  | | | 
% 228.13/39.68  | | | REF_CLOSE: (10), (12), (21) are inconsistent by sub-proof #1533.
% 228.13/39.68  | | | 
% 228.13/39.68  | | Case 2:
% 228.13/39.68  | | | 
% 228.13/39.68  | | |   (22)  all_57_11 = e1 & op(e1, e0) = e1
% 228.13/39.68  | | | 
% 228.13/39.68  | | | ALPHA: (22) implies:
% 228.13/39.68  | | |   (23)  all_57_11 = e1
% 228.13/39.68  | | | 
% 228.13/39.68  | | | COMBINE_EQS: (7), (23) imply:
% 228.13/39.68  | | |   (24)  e1 = e0
% 228.13/39.68  | | | 
% 228.13/39.68  | | | REF_CLOSE: (1), (2), (3), (4), (5), (8), (9), (11), (12), (14), (24) are
% 228.13/39.68  | | |            inconsistent by sub-proof #1626.
% 228.13/39.68  | | | 
% 228.13/39.68  | | End of split
% 228.13/39.68  | | 
% 228.13/39.68  | End of split
% 228.13/39.68  | 
% 228.13/39.68  End of proof
% 228.13/39.68  
% 228.13/39.68  Sub-proof #431 shows that the following formulas are inconsistent:
% 228.13/39.68  ----------------------------------------------------------------
% 228.13/39.68    (1)   ~ (all_53_2 = e1)
% 228.13/39.68    (2)  all_57_9 = e2
% 228.13/39.68    (3)  op(e3, e3) = e1
% 228.13/39.68    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.13/39.68         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.13/39.68    (5)   ~ (e3 = e1)
% 228.13/39.68    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.13/39.68           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.13/39.68    (7)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.13/39.68         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.13/39.68    (8)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.13/39.68         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.13/39.68    (9)  all_55_4 = all_53_1
% 228.13/39.68    (10)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.13/39.68          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.13/39.68    (11)  all_57_3 = e0
% 228.13/39.68    (12)  all_57_4 = e3
% 228.13/39.68    (13)   ~ (e3 = e2)
% 228.13/39.68    (14)   ~ (e3 = e0)
% 228.13/39.68    (15)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.13/39.68    (16)   ~ (all_53_2 = e0)
% 228.13/39.68    (17)  all_57_0 = e0
% 228.13/39.68    (18)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 228.13/39.68    (19)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 228.13/39.68          | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.13/39.68    (20)  all_57_15 = e3
% 228.13/39.68    (21)  op(e3, e3) = e0
% 228.13/39.68    (22)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.13/39.68          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.13/39.68            e1)
% 228.13/39.68    (23)   ~ (all_53_1 = e1)
% 228.13/39.68    (24)   ~ (all_53_1 = all_53_2)
% 228.13/39.68    (25)   ~ (e2 = e0)
% 228.13/39.68    (26)   ~ (all_53_1 = e0)
% 228.13/39.68    (27)   ~ (e1 = e0)
% 228.13/39.68    (28)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.13/39.68          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.13/39.68    (29)  all_57_13 = e3
% 228.13/39.68    (30)  all_55_8 = all_53_2
% 228.13/39.68    (31)  op(e0, e0) = e3
% 228.13/39.68    (32)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.13/39.68          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.13/39.68            e2)
% 228.13/39.68    (33)   ~ (all_53_1 = e2)
% 228.13/39.68    (34)   ~ (e2 = e1)
% 228.13/39.68    (35)  all_57_14 = e0
% 228.13/39.68    (36)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.13/39.68          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.13/39.68  
% 228.13/39.68  Begin of proof
% 228.13/39.68  | 
% 228.13/39.68  | BETA: splitting (22) gives:
% 228.13/39.68  | 
% 228.13/39.68  | Case 1:
% 228.13/39.68  | | 
% 228.13/39.68  | |   (37)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 228.13/39.68  | |           e1)
% 228.13/39.68  | | 
% 228.13/39.68  | | BETA: splitting (37) gives:
% 228.13/39.68  | | 
% 228.13/39.68  | | Case 1:
% 228.13/39.68  | | | 
% 228.13/39.68  | | |   (38)  all_57_12 = e1 & op(e0, e3) = e1
% 228.13/39.68  | | | 
% 228.13/39.68  | | | ALPHA: (38) implies:
% 228.13/39.68  | | |   (39)  all_57_12 = e1
% 228.13/39.68  | | | 
% 228.13/39.68  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.13/39.68  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 228.13/39.68  | | |            (23), (24), (25), (26), (27), (28), (30), (32), (33), (34),
% 228.13/39.68  | | |            (36), (39) are inconsistent by sub-proof #432.
% 228.13/39.68  | | | 
% 228.13/39.68  | | Case 2:
% 228.13/39.68  | | | 
% 228.13/39.68  | | |   (40)  all_57_13 = e1 & op(e0, e2) = e1
% 228.13/39.68  | | | 
% 228.13/39.68  | | | REF_CLOSE: (5), (29), (40) are inconsistent by sub-proof #2264.
% 228.13/39.68  | | | 
% 228.13/39.68  | | End of split
% 228.13/39.68  | | 
% 228.13/39.68  | Case 2:
% 228.13/39.68  | | 
% 228.13/39.68  | |   (41)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.13/39.68  | |           e1)
% 228.13/39.68  | | 
% 228.13/39.68  | | REF_CLOSE: (5), (6), (27), (31), (35), (41) are inconsistent by sub-proof
% 228.13/39.68  | |            #2056.
% 228.13/39.68  | | 
% 228.13/39.68  | End of split
% 228.13/39.68  | 
% 228.13/39.68  End of proof
% 228.13/39.68  
% 228.13/39.68  Sub-proof #432 shows that the following formulas are inconsistent:
% 228.13/39.68  ----------------------------------------------------------------
% 228.13/39.68    (1)   ~ (all_53_2 = e1)
% 228.13/39.68    (2)  all_57_9 = e2
% 228.13/39.68    (3)  op(e3, e3) = e1
% 228.13/39.68    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.13/39.68         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.13/39.68    (5)   ~ (e3 = e1)
% 228.13/39.68    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.13/39.68           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.13/39.68    (7)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.13/39.68         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.13/39.68    (8)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.13/39.68         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.13/39.68    (9)  all_55_4 = all_53_1
% 228.13/39.68    (10)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.13/39.68          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.13/39.68    (11)  all_57_3 = e0
% 228.13/39.68    (12)  all_57_4 = e3
% 228.13/39.68    (13)   ~ (e3 = e2)
% 228.13/39.68    (14)   ~ (e3 = e0)
% 228.13/39.68    (15)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.13/39.68    (16)   ~ (all_53_2 = e0)
% 228.13/39.68    (17)  all_57_0 = e0
% 228.13/39.68    (18)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 228.13/39.68    (19)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 228.13/39.68          | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.13/39.68    (20)  all_57_15 = e3
% 228.13/39.68    (21)  op(e3, e3) = e0
% 228.13/39.68    (22)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.13/39.68          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.13/39.68            e1)
% 228.13/39.68    (23)   ~ (all_53_1 = e1)
% 228.13/39.68    (24)  all_57_12 = e1
% 228.13/39.68    (25)   ~ (all_53_1 = all_53_2)
% 228.13/39.68    (26)   ~ (e2 = e0)
% 228.13/39.68    (27)   ~ (all_53_1 = e0)
% 228.13/39.68    (28)   ~ (e1 = e0)
% 228.13/39.68    (29)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.13/39.68          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.13/39.68    (30)  all_55_8 = all_53_2
% 228.13/39.68    (31)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.13/39.68          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.13/39.68            e2)
% 228.13/39.68    (32)   ~ (all_53_1 = e2)
% 228.13/39.68    (33)   ~ (e2 = e1)
% 228.13/39.68    (34)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.13/39.68          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.13/39.68  
% 228.13/39.68  Begin of proof
% 228.13/39.68  | 
% 228.13/39.68  | BETA: splitting (29) gives:
% 228.13/39.68  | 
% 228.13/39.68  | Case 1:
% 228.13/39.68  | | 
% 228.13/39.68  | |   (35)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 228.13/39.68  | |           e3)
% 228.13/39.68  | | 
% 228.13/39.68  | | REF_CLOSE: (2), (5), (7), (8), (10), (11), (12), (13), (14), (26), (28),
% 228.13/39.68  | |            (33), (35) are inconsistent by sub-proof #435.
% 228.13/39.68  | | 
% 228.13/39.68  | Case 2:
% 228.13/39.68  | | 
% 228.13/39.68  | |   (36)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 228.13/39.68  | |           e3)
% 228.13/39.68  | | 
% 228.13/39.68  | | BETA: splitting (36) gives:
% 228.13/39.68  | | 
% 228.13/39.68  | | Case 1:
% 228.13/39.68  | | | 
% 228.13/39.68  | | |   (37)  all_57_7 = e3 & op(e1, e2) = e3
% 228.13/39.68  | | | 
% 228.13/39.68  | | | ALPHA: (37) implies:
% 228.13/39.68  | | |   (38)  all_57_7 = e3
% 228.13/39.68  | | | 
% 228.13/39.68  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (11), (12), (15), (16),
% 228.13/39.68  | | |            (17), (18), (21), (23), (25), (27), (28), (30), (32), (33),
% 228.13/39.68  | | |            (34), (38) are inconsistent by sub-proof #433.
% 228.13/39.68  | | | 
% 228.13/39.68  | | Case 2:
% 228.13/39.68  | | | 
% 228.13/39.68  | | |   (39)  all_57_13 = e3 & op(e0, e2) = e3
% 228.13/39.68  | | | 
% 228.13/39.68  | | | ALPHA: (39) implies:
% 228.13/39.68  | | |   (40)  all_57_13 = e3
% 228.13/39.68  | | | 
% 228.13/39.68  | | | REF_CLOSE: (5), (13), (14), (19), (20), (22), (24), (26), (28), (31),
% 228.13/39.68  | | |            (33), (40) are inconsistent by sub-proof #2057.
% 228.13/39.68  | | | 
% 228.13/39.68  | | End of split
% 228.13/39.68  | | 
% 228.13/39.68  | End of split
% 228.13/39.68  | 
% 228.13/39.68  End of proof
% 228.13/39.68  
% 228.13/39.68  Sub-proof #433 shows that the following formulas are inconsistent:
% 228.13/39.68  ----------------------------------------------------------------
% 228.13/39.68    (1)   ~ (all_53_2 = e1)
% 228.13/39.68    (2)  all_57_9 = e2
% 228.13/39.68    (3)  op(e3, e3) = e1
% 228.13/39.68    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.13/39.68         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.13/39.68    (5)   ~ (e3 = e1)
% 228.13/39.68    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.13/39.68           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.13/39.68    (7)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.13/39.68         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.13/39.68    (8)  all_55_4 = all_53_1
% 228.13/39.68    (9)  all_57_3 = e0
% 228.13/39.68    (10)  all_57_4 = e3
% 228.13/39.68    (11)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.13/39.68    (12)   ~ (all_53_2 = e0)
% 228.13/39.68    (13)  all_57_0 = e0
% 228.13/39.68    (14)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 228.13/39.68    (15)  op(e3, e3) = e0
% 228.13/39.68    (16)   ~ (all_53_1 = e1)
% 228.13/39.68    (17)   ~ (all_53_1 = all_53_2)
% 228.13/39.68    (18)   ~ (all_53_1 = e0)
% 228.13/39.68    (19)   ~ (e1 = e0)
% 228.13/39.68    (20)  all_55_8 = all_53_2
% 228.13/39.68    (21)  all_57_7 = e3
% 228.13/39.68    (22)   ~ (all_53_1 = e2)
% 228.13/39.68    (23)   ~ (e2 = e1)
% 228.13/39.68    (24)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.13/39.68          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.13/39.68  
% 228.13/39.68  Begin of proof
% 228.13/39.68  | 
% 228.13/39.68  | BETA: splitting (7) gives:
% 228.13/39.68  | 
% 228.13/39.68  | Case 1:
% 228.13/39.68  | | 
% 228.13/39.68  | |   (25)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) =
% 228.13/39.68  | |           e1)
% 228.13/39.68  | | 
% 228.13/39.68  | | BETA: splitting (25) gives:
% 228.13/39.68  | | 
% 228.13/39.68  | | Case 1:
% 228.13/39.68  | | | 
% 228.13/39.68  | | |   (26)  all_57_0 = e1 & op(e3, e3) = e1
% 228.13/39.68  | | | 
% 228.13/39.68  | | | REF_CLOSE: (13), (19), (26) are inconsistent by sub-proof #2454.
% 228.13/39.68  | | | 
% 228.13/39.68  | | Case 2:
% 228.13/39.68  | | | 
% 228.13/39.68  | | |   (27)  all_57_1 = e1 & op(e3, e2) = e1
% 228.13/39.68  | | | 
% 228.13/39.68  | | | REF_CLOSE: (1), (3), (4), (6), (8), (9), (11), (12), (14), (15), (16),
% 228.13/39.68  | | |            (17), (18), (19), (20), (21), (22), (24), (27) are inconsistent
% 228.13/39.68  | | |            by sub-proof #434.
% 228.13/39.68  | | | 
% 228.13/39.68  | | End of split
% 228.13/39.68  | | 
% 228.13/39.68  | Case 2:
% 228.13/39.68  | | 
% 228.13/39.68  | |   (28)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) =
% 228.13/39.68  | |           e1)
% 228.13/39.68  | | 
% 228.13/39.68  | | BETA: splitting (28) gives:
% 228.13/39.68  | | 
% 228.13/39.68  | | Case 1:
% 228.13/39.68  | | | 
% 228.13/39.68  | | |   (29)  all_57_4 = e1 & op(e3, e1) = e1
% 228.13/39.68  | | | 
% 228.13/39.68  | | | REF_CLOSE: (5), (10), (29) are inconsistent by sub-proof #2484.
% 228.13/39.68  | | | 
% 228.13/39.68  | | Case 2:
% 228.13/39.68  | | | 
% 228.13/39.68  | | |   (30)  all_57_9 = e1 & op(e3, e0) = e1
% 228.13/39.68  | | | 
% 228.13/39.68  | | | REF_CLOSE: (2), (23), (30) are inconsistent by sub-proof #2451.
% 228.13/39.68  | | | 
% 228.13/39.68  | | End of split
% 228.13/39.68  | | 
% 228.13/39.68  | End of split
% 228.13/39.68  | 
% 228.13/39.68  End of proof
% 228.13/39.68  
% 228.13/39.68  Sub-proof #434 shows that the following formulas are inconsistent:
% 228.13/39.68  ----------------------------------------------------------------
% 228.13/39.68    (1)   ~ (all_53_2 = e1)
% 228.13/39.68    (2)  op(e3, e3) = e1
% 228.13/39.68    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.13/39.68         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.13/39.68    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.13/39.68           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.13/39.68    (5)  all_57_1 = e1 & op(e3, e2) = e1
% 228.13/39.68    (6)  all_55_4 = all_53_1
% 228.13/39.68    (7)  all_57_3 = e0
% 228.13/39.68    (8)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.13/39.68    (9)   ~ (all_53_2 = e0)
% 228.13/39.68    (10)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 228.13/39.68    (11)  op(e3, e3) = e0
% 228.13/39.68    (12)   ~ (all_53_1 = e1)
% 228.13/39.68    (13)   ~ (all_53_1 = all_53_2)
% 228.13/39.68    (14)   ~ (all_53_1 = e0)
% 228.13/39.68    (15)   ~ (e1 = e0)
% 228.13/39.68    (16)  all_55_8 = all_53_2
% 228.13/39.68    (17)  all_57_7 = e3
% 228.13/39.68    (18)   ~ (all_53_1 = e2)
% 228.13/39.68    (19)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.13/39.68          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.13/39.68  
% 228.13/39.68  Begin of proof
% 228.13/39.68  | 
% 228.13/39.68  | ALPHA: (5) implies:
% 228.13/39.68  |   (20)  all_57_1 = e1
% 228.13/39.68  | 
% 228.13/39.68  | BETA: splitting (10) gives:
% 228.13/39.68  | 
% 228.13/39.68  | Case 1:
% 228.13/39.68  | | 
% 228.13/39.68  | |   (21)  all_55_4 = e3
% 228.13/39.68  | | 
% 228.13/39.68  | | COMBINE_EQS: (6), (21) imply:
% 228.13/39.68  | |   (22)  all_53_1 = e3
% 228.13/39.68  | | 
% 228.13/39.68  | | SIMP: (22) implies:
% 228.13/39.68  | |   (23)  all_53_1 = e3
% 228.13/39.68  | | 
% 228.13/39.68  | | REDUCE: (13), (23) imply:
% 228.13/39.68  | |   (24)   ~ (all_53_2 = e3)
% 228.13/39.68  | | 
% 228.13/39.68  | | SIMP: (24) implies:
% 228.13/39.68  | |   (25)   ~ (all_53_2 = e3)
% 228.13/39.68  | | 
% 228.13/39.68  | | REDUCE: (12), (23) imply:
% 228.13/39.68  | |   (26)   ~ (e3 = e1)
% 228.13/39.68  | | 
% 228.13/39.68  | | BETA: splitting (8) gives:
% 228.13/39.68  | | 
% 228.13/39.68  | | Case 1:
% 228.13/39.68  | | | 
% 228.13/39.68  | | |   (27)  all_55_8 = e3
% 228.13/39.68  | | | 
% 228.13/39.68  | | | REF_CLOSE: (16), (25), (27) are inconsistent by sub-proof #2496.
% 228.13/39.68  | | | 
% 228.13/39.68  | | Case 2:
% 228.13/39.68  | | | 
% 228.13/39.68  | | |   (28)   ~ (all_55_8 = e3)
% 228.13/39.68  | | |   (29)  all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.13/39.68  | | | 
% 228.13/39.68  | | | BETA: splitting (29) gives:
% 228.13/39.68  | | | 
% 228.13/39.68  | | | Case 1:
% 228.13/39.68  | | | | 
% 228.13/39.68  | | | |   (30)  all_55_8 = e2
% 228.13/39.68  | | | | 
% 228.13/39.68  | | | | COMBINE_EQS: (16), (30) imply:
% 228.13/39.68  | | | |   (31)  all_53_2 = e2
% 228.13/39.68  | | | | 
% 228.13/39.68  | | | | SIMP: (31) implies:
% 228.13/39.68  | | | |   (32)  all_53_2 = e2
% 228.13/39.68  | | | | 
% 228.13/39.68  | | | | REDUCE: (25), (32) imply:
% 228.13/39.68  | | | |   (33)   ~ (e3 = e2)
% 228.13/39.68  | | | | 
% 228.13/39.68  | | | | SIMP: (33) implies:
% 228.13/39.68  | | | |   (34)   ~ (e3 = e2)
% 228.13/39.68  | | | | 
% 228.13/39.68  | | | | REDUCE: (1), (32) imply:
% 228.13/39.68  | | | |   (35)   ~ (e2 = e1)
% 228.13/39.68  | | | | 
% 228.13/39.68  | | | | REDUCE: (9), (32) imply:
% 228.13/39.68  | | | |   (36)   ~ (e2 = e0)
% 228.13/39.68  | | | | 
% 228.13/39.68  | | | | GROUND_INST: instantiating (4) with e0, e1, e3, e3, simplifying with
% 228.13/39.68  | | | |              (2), (11) gives:
% 228.13/39.68  | | | |   (37)  e1 = e0
% 228.13/39.68  | | | | 
% 228.13/39.68  | | | | COMBINE_EQS: (20), (37) imply:
% 228.13/39.68  | | | |   (38)  all_57_1 = e0
% 228.13/39.68  | | | | 
% 228.13/39.68  | | | | REF_CLOSE: (3), (7), (15), (17), (19), (26), (34), (35), (36), (38) are
% 228.13/39.68  | | | |            inconsistent by sub-proof #2098.
% 228.13/39.68  | | | | 
% 228.13/39.68  | | | Case 2:
% 228.13/39.68  | | | | 
% 228.13/39.68  | | | |   (39)  all_55_8 = e1 | all_55_8 = e0
% 228.13/39.68  | | | | 
% 228.13/39.68  | | | | BETA: splitting (39) gives:
% 228.13/39.68  | | | | 
% 228.13/39.68  | | | | Case 1:
% 228.13/39.68  | | | | | 
% 228.13/39.68  | | | | |   (40)  all_55_8 = e1
% 228.13/39.68  | | | | | 
% 228.13/39.68  | | | | | REF_CLOSE: (1), (16), (40) are inconsistent by sub-proof #2367.
% 228.13/39.68  | | | | | 
% 228.13/39.68  | | | | Case 2:
% 228.13/39.68  | | | | | 
% 228.13/39.68  | | | | |   (41)  all_55_8 = e0
% 228.13/39.68  | | | | | 
% 228.13/39.68  | | | | | REF_CLOSE: (9), (16), (41) are inconsistent by sub-proof #1997.
% 228.13/39.68  | | | | | 
% 228.13/39.68  | | | | End of split
% 228.13/39.68  | | | | 
% 228.13/39.68  | | | End of split
% 228.13/39.68  | | | 
% 228.13/39.68  | | End of split
% 228.13/39.68  | | 
% 228.13/39.68  | Case 2:
% 228.13/39.68  | | 
% 228.13/39.68  | |   (42)  all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 228.13/39.68  | | 
% 228.13/39.68  | | BETA: splitting (42) gives:
% 228.13/39.68  | | 
% 228.13/39.68  | | Case 1:
% 228.13/39.68  | | | 
% 228.13/39.68  | | |   (43)  all_55_4 = e2
% 228.13/39.68  | | | 
% 228.13/39.68  | | | REF_CLOSE: (6), (18), (43) are inconsistent by sub-proof #2168.
% 228.13/39.68  | | | 
% 228.13/39.68  | | Case 2:
% 228.13/39.68  | | | 
% 228.13/39.68  | | |   (44)  all_55_4 = e1 | all_55_4 = e0
% 228.13/39.68  | | | 
% 228.13/39.68  | | | REF_CLOSE: (6), (12), (14), (44) are inconsistent by sub-proof #773.
% 228.13/39.68  | | | 
% 228.13/39.68  | | End of split
% 228.13/39.68  | | 
% 228.13/39.68  | End of split
% 228.13/39.68  | 
% 228.13/39.68  End of proof
% 228.13/39.68  
% 228.13/39.68  Sub-proof #435 shows that the following formulas are inconsistent:
% 228.13/39.68  ----------------------------------------------------------------
% 228.13/39.68    (1)  all_57_9 = e2
% 228.13/39.68    (2)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3)
% 228.13/39.68    (3)   ~ (e3 = e1)
% 228.13/39.68    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.13/39.68         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.13/39.68    (5)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.13/39.68         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.13/39.68    (6)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.13/39.68         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.13/39.68    (7)  all_57_3 = e0
% 228.13/39.68    (8)  all_57_4 = e3
% 228.13/39.68    (9)   ~ (e3 = e2)
% 228.13/39.68    (10)   ~ (e3 = e0)
% 228.13/39.68    (11)   ~ (e2 = e0)
% 228.13/39.68    (12)   ~ (e1 = e0)
% 228.13/39.68    (13)   ~ (e2 = e1)
% 228.13/39.68  
% 228.13/39.68  Begin of proof
% 228.13/39.68  | 
% 228.13/39.68  | BETA: splitting (2) gives:
% 228.13/39.68  | 
% 228.13/39.68  | Case 1:
% 228.13/39.68  | | 
% 228.13/39.68  | |   (14)  all_57_1 = e3 & op(e3, e2) = e3
% 228.13/39.68  | | 
% 228.13/39.68  | | ALPHA: (14) implies:
% 228.13/39.68  | |   (15)  all_57_1 = e3
% 228.13/39.68  | | 
% 228.13/39.68  | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13), (15)
% 228.13/39.68  | |            are inconsistent by sub-proof #1222.
% 228.13/39.68  | | 
% 228.13/39.68  | Case 2:
% 228.13/39.68  | | 
% 228.13/39.68  | |   (16)  all_57_3 = e3 & op(e2, e2) = e3
% 228.13/39.68  | | 
% 228.13/39.68  | | ALPHA: (16) implies:
% 228.13/39.68  | |   (17)  all_57_3 = e3
% 228.13/39.68  | | 
% 228.13/39.68  | | REF_CLOSE: (7), (10), (17) are inconsistent by sub-proof #2358.
% 228.13/39.68  | | 
% 228.13/39.68  | End of split
% 228.13/39.68  | 
% 228.13/39.68  End of proof
% 228.13/39.68  
% 228.13/39.68  Sub-proof #436 shows that the following formulas are inconsistent:
% 228.13/39.68  ----------------------------------------------------------------
% 228.13/39.68    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.13/39.68           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.13/39.68    (2)  op(all_52_5, all_52_5) = e1
% 228.13/39.68    (3)  op(e2, e2) = e0
% 228.13/39.68    (4)  all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.13/39.68    (5)   ~ (e1 = e0)
% 228.13/39.68    (6)  all_55_2 = all_52_5
% 228.13/39.68    (7)   ~ (all_52_5 = e1)
% 228.13/39.68    (8)   ~ (all_52_5 = e0)
% 228.13/39.68  
% 228.13/39.68  Begin of proof
% 228.13/39.68  | 
% 228.13/39.68  | BETA: splitting (4) gives:
% 228.13/39.68  | 
% 228.13/39.68  | Case 1:
% 228.13/39.68  | | 
% 228.13/39.68  | |   (9)  all_55_2 = e2
% 228.13/39.68  | | 
% 228.13/39.68  | | COMBINE_EQS: (6), (9) imply:
% 228.13/39.68  | |   (10)  all_52_5 = e2
% 228.13/39.68  | | 
% 228.13/39.68  | | SIMP: (10) implies:
% 228.13/39.68  | |   (11)  all_52_5 = e2
% 228.13/39.68  | | 
% 228.13/39.68  | | REDUCE: (2), (11) imply:
% 228.13/39.68  | |   (12)  op(e2, e2) = e1
% 228.13/39.68  | | 
% 228.13/39.68  | | REF_CLOSE: (1), (3), (5), (12) are inconsistent by sub-proof #2352.
% 228.13/39.68  | | 
% 228.13/39.68  | Case 2:
% 228.13/39.68  | | 
% 228.13/39.68  | |   (13)  all_55_2 = e1 | all_55_2 = e0
% 228.13/39.68  | | 
% 228.13/39.68  | | REF_CLOSE: (6), (7), (8), (13) are inconsistent by sub-proof #559.
% 228.13/39.68  | | 
% 228.13/39.68  | End of split
% 228.13/39.68  | 
% 228.13/39.68  End of proof
% 228.13/39.68  
% 228.13/39.68  Sub-proof #437 shows that the following formulas are inconsistent:
% 228.13/39.68  ----------------------------------------------------------------
% 228.13/39.68    (1)  all_55_2 = all_52_5
% 228.13/39.68    (2)  all_55_2 = e3
% 228.13/39.68    (3)   ~ (all_52_5 = e3)
% 228.13/39.68  
% 228.13/39.68  Begin of proof
% 228.13/39.68  | 
% 228.13/39.68  | COMBINE_EQS: (1), (2) imply:
% 228.13/39.68  |   (4)  all_52_5 = e3
% 228.13/39.68  | 
% 228.13/39.68  | SIMP: (4) implies:
% 228.13/39.68  |   (5)  all_52_5 = e3
% 228.13/39.68  | 
% 228.13/39.68  | REDUCE: (3), (5) imply:
% 228.13/39.68  |   (6)  $false
% 228.13/39.68  | 
% 228.13/39.68  | CLOSE: (6) is inconsistent.
% 228.13/39.68  | 
% 228.13/39.68  End of proof
% 228.13/39.68  
% 228.13/39.68  Sub-proof #438 shows that the following formulas are inconsistent:
% 228.13/39.68  ----------------------------------------------------------------
% 228.13/39.68    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.13/39.68    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.13/39.68    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.13/39.68         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.13/39.68    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.13/39.68         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.13/39.68    (5)   ~ (all_53_8 = all_53_12)
% 228.13/39.68    (6)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.13/39.68         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.13/39.68    (7)   ~ (e3 = e1)
% 228.13/39.68    (8)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.13/39.68         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.13/39.68    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.13/39.68           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.13/39.68    (10)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.13/39.68          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.13/39.68    (11)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.13/39.68            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.13/39.68              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.13/39.68    (12)   ~ (all_6_2 = e3)
% 228.13/39.68    (13)  op(e1, e1) = all_6_2
% 228.13/39.68    (14)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.13/39.68    (15)   ~ (all_53_9 = e0)
% 228.13/39.68    (16)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.13/39.68          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.13/39.68    (17)   ~ (all_53_4 = all_53_12)
% 228.13/39.68    (18)   ~ (all_53_8 = all_53_9)
% 228.13/39.68    (19)  all_42_2 = all_6_2
% 228.13/39.68    (20)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.13/39.68          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.13/39.68    (21)  all_57_6 = e1
% 228.13/39.68    (22)   ~ (all_53_9 = all_6_2)
% 228.13/39.68    (23)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.13/39.68          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.13/39.68    (24)  all_57_3 = e0
% 228.13/39.68    (25)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.13/39.68          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.13/39.68    (26)   ~ (e3 = e2)
% 228.13/39.68    (27)  all_55_1 = all_53_4
% 228.13/39.68    (28)   ~ (e3 = e0)
% 228.13/39.68    (29)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.13/39.68          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.13/39.68    (30)   ~ (all_53_8 = all_6_2)
% 228.13/39.68    (31)  all_55_2 = all_53_8
% 228.13/39.68    (32)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 228.13/39.68          | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.13/39.68    (33)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.13/39.68    (34)  all_57_15 = e3
% 228.13/39.68    (35)  all_57_4 = e1
% 228.13/39.68    (36)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.13/39.68          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.13/39.68            e1)
% 228.13/39.68    (37)   ~ (all_53_4 = all_53_8)
% 228.13/39.68    (38)  op(e3, e2) = all_53_4
% 228.13/39.68    (39)   ~ (e2 = e0)
% 228.13/39.68    (40)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.13/39.68            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.13/39.68            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.13/39.68            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.13/39.68              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.13/39.68            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.13/39.68            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.13/39.68              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.13/39.68              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.13/39.68            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.13/39.68            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.13/39.68            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.13/39.68              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.13/39.68              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.13/39.68            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.13/39.68              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.13/39.68            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.13/39.68            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.13/39.68              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.13/39.68              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.13/39.68            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.13/39.68            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.13/39.68    (41)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.13/39.68          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.13/39.68    (42)   ~ (e1 = e0)
% 228.13/39.68    (43)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.13/39.68            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.13/39.68              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.13/39.68    (44)   ~ (all_53_4 = e0)
% 228.13/39.68    (45)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.13/39.68          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.13/39.68    (46)  op(e0, e0) = e3
% 228.13/39.68    (47)   ~ (all_53_4 = all_53_6)
% 228.13/39.68    (48)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.13/39.68          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.13/39.68            e2)
% 228.13/39.68    (49)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.13/39.68              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.13/39.68                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.13/39.68                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.13/39.68    (50)  all_55_10 = all_6_2
% 228.13/39.68    (51)  all_38_2 = all_6_2
% 228.13/39.68    (52)  all_55_3 = all_53_12
% 228.13/39.68    (53)   ~ (all_53_12 = e3)
% 228.13/39.68    (54)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.13/39.68            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.13/39.68              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.13/39.68    (55)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.13/39.68          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.13/39.68    (56)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.13/39.68          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.13/39.68    (57)   ~ (e2 = e1)
% 228.13/39.69    (58)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.13/39.69          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.13/39.69    (59)  op(e2, e1) = all_53_9
% 228.13/39.69    (60)  op(e1, e2) = all_53_6
% 228.13/39.69    (61)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.13/39.69          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.13/39.69    (62)  all_24_2 = all_6_2
% 228.13/39.69    (63)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.13/39.69          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.13/39.69    (64)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.13/39.69          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.13/39.69    (65)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.13/39.69          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.13/39.69    (66)  all_57_14 = e0
% 228.13/39.69    (67)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.13/39.69          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.13/39.69    (68)  op(e3, e1) = all_53_8
% 228.13/39.69    (69)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.13/39.69          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.13/39.69    (70)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.13/39.69          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.13/39.69    (71)  op(e3, e0) = all_53_12
% 228.13/39.69  
% 228.13/39.69  Begin of proof
% 228.13/39.69  | 
% 228.13/39.69  | BETA: splitting (45) gives:
% 228.13/39.69  | 
% 228.13/39.69  | Case 1:
% 228.13/39.69  | | 
% 228.13/39.69  | |   (72)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) =
% 228.13/39.69  | |           e3)
% 228.13/39.69  | | 
% 228.13/39.69  | | BETA: splitting (72) gives:
% 228.13/39.69  | | 
% 228.13/39.69  | | Case 1:
% 228.13/39.69  | | | 
% 228.13/39.69  | | |   (73)  all_57_4 = e3 & op(e3, e1) = e3
% 228.13/39.69  | | | 
% 228.13/39.69  | | | ALPHA: (73) implies:
% 228.13/39.69  | | |   (74)  all_57_4 = e3
% 228.13/39.69  | | | 
% 228.13/39.69  | | | REF_CLOSE: (7), (35), (74) are inconsistent by sub-proof #2426.
% 228.13/39.69  | | | 
% 228.13/39.69  | | Case 2:
% 228.13/39.69  | | | 
% 228.13/39.69  | | |   (75)  all_57_5 = e3 & op(e2, e1) = e3
% 228.13/39.69  | | | 
% 228.13/39.69  | | | ALPHA: (75) implies:
% 228.13/39.69  | | |   (76)  all_57_5 = e3
% 228.13/39.69  | | |   (77)  op(e2, e1) = e3
% 228.13/39.69  | | | 
% 228.13/39.69  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.13/39.69  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 228.13/39.69  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (33),
% 228.13/39.69  | | |            (34), (36), (37), (38), (39), (40), (41), (42), (43), (44),
% 228.13/39.69  | | |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (55),
% 228.13/39.69  | | |            (56), (57), (58), (59), (60), (61), (62), (63), (64), (65),
% 228.13/39.69  | | |            (66), (67), (68), (69), (70), (71), (76), (77) are inconsistent
% 228.13/39.69  | | |            by sub-proof #439.
% 228.13/39.69  | | | 
% 228.13/39.69  | | End of split
% 228.13/39.69  | | 
% 228.13/39.69  | Case 2:
% 228.13/39.69  | | 
% 228.13/39.69  | |   (78)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) =
% 228.13/39.69  | |           e3)
% 228.13/39.69  | | 
% 228.13/39.69  | | REF_CLOSE: (7), (9), (12), (13), (26), (28), (32), (34), (36), (39), (42),
% 228.13/39.69  | |            (48), (57), (78) are inconsistent by sub-proof #1044.
% 228.13/39.69  | | 
% 228.13/39.69  | End of split
% 228.13/39.69  | 
% 228.13/39.69  End of proof
% 228.13/39.69  
% 228.13/39.69  Sub-proof #439 shows that the following formulas are inconsistent:
% 228.13/39.69  ----------------------------------------------------------------
% 228.13/39.69    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.13/39.69    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.13/39.69    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.13/39.69         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.13/39.69    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.13/39.69         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.13/39.69    (5)  op(e2, e1) = e3
% 228.13/39.69    (6)   ~ (all_53_8 = all_53_12)
% 228.13/39.69    (7)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.13/39.69         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.13/39.69    (8)   ~ (e3 = e1)
% 228.13/39.69    (9)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.13/39.69         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.13/39.69    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.13/39.69            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.13/39.69    (11)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.13/39.69          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.13/39.69    (12)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.13/39.69            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.13/39.69              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.13/39.69    (13)   ~ (all_6_2 = e3)
% 228.13/39.69    (14)  op(e1, e1) = all_6_2
% 228.13/39.69    (15)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.13/39.69    (16)   ~ (all_53_9 = e0)
% 228.13/39.69    (17)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.13/39.69          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.13/39.69    (18)   ~ (all_53_4 = all_53_12)
% 228.13/39.69    (19)   ~ (all_53_8 = all_53_9)
% 228.13/39.69    (20)  all_42_2 = all_6_2
% 228.13/39.69    (21)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.13/39.69          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.13/39.69    (22)  all_57_6 = e1
% 228.13/39.69    (23)   ~ (all_53_9 = all_6_2)
% 228.13/39.69    (24)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.13/39.69          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.13/39.69    (25)  all_57_3 = e0
% 228.13/39.69    (26)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.13/39.69          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.13/39.69    (27)   ~ (e3 = e2)
% 228.13/39.69    (28)  all_55_1 = all_53_4
% 228.13/39.69    (29)   ~ (e3 = e0)
% 228.13/39.69    (30)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.13/39.69          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.13/39.69    (31)   ~ (all_53_8 = all_6_2)
% 228.13/39.69    (32)  all_55_2 = all_53_8
% 228.13/39.69    (33)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.13/39.69    (34)  all_57_15 = e3
% 228.13/39.69    (35)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.13/39.69          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.13/39.69            e1)
% 228.13/39.69    (36)  all_57_5 = e3
% 228.13/39.69    (37)   ~ (all_53_4 = all_53_8)
% 228.13/39.69    (38)  op(e3, e2) = all_53_4
% 228.13/39.69    (39)   ~ (e2 = e0)
% 228.13/39.69    (40)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.13/39.69            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.13/39.69            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.13/39.69            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.13/39.69              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.13/39.69            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.13/39.69            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.13/39.69              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.13/39.69              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.13/39.69            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.13/39.69            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.13/39.69            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.13/39.69              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.13/39.69              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.13/39.69            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.13/39.69              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.13/39.69            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.13/39.69            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.13/39.69              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.13/39.69              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.13/39.69            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.13/39.69            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.13/39.69    (41)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.13/39.69          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.13/39.69    (42)   ~ (e1 = e0)
% 228.13/39.69    (43)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.13/39.69            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.13/39.69              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.13/39.69    (44)   ~ (all_53_4 = e0)
% 228.13/39.69    (45)  op(e0, e0) = e3
% 228.13/39.69    (46)   ~ (all_53_4 = all_53_6)
% 228.13/39.69    (47)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.13/39.69          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.13/39.69            e2)
% 228.13/39.69    (48)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.13/39.69              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.13/39.69                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.13/39.69                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.13/39.69    (49)  all_55_10 = all_6_2
% 228.13/39.69    (50)  all_38_2 = all_6_2
% 228.13/39.69    (51)  all_55_3 = all_53_12
% 228.13/39.69    (52)   ~ (all_53_12 = e3)
% 228.13/39.69    (53)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.13/39.69            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.13/39.69              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.13/39.69    (54)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.13/39.69          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.13/39.69    (55)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.13/39.69          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.13/39.69    (56)   ~ (e2 = e1)
% 228.13/39.69    (57)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.13/39.69          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.13/39.69    (58)  op(e2, e1) = all_53_9
% 228.13/39.69    (59)  op(e1, e2) = all_53_6
% 228.13/39.69    (60)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.13/39.69          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.13/39.69    (61)  all_24_2 = all_6_2
% 228.13/39.69    (62)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.13/39.69          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.13/39.69    (63)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.13/39.69          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.13/39.69    (64)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.13/39.69          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.13/39.69    (65)  all_57_14 = e0
% 228.13/39.69    (66)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.13/39.69          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.13/39.69    (67)  op(e3, e1) = all_53_8
% 228.13/39.69    (68)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.13/39.69          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.13/39.69    (69)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.13/39.69          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.13/39.69    (70)  op(e3, e0) = all_53_12
% 228.13/39.69  
% 228.13/39.69  Begin of proof
% 228.13/39.69  | 
% 228.13/39.69  | BETA: splitting (55) gives:
% 228.13/39.69  | 
% 228.13/39.69  | Case 1:
% 228.13/39.69  | | 
% 228.13/39.69  | |   (71)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) =
% 228.13/39.69  | |           e3)
% 228.13/39.69  | | 
% 228.13/39.69  | | BETA: splitting (71) gives:
% 228.13/39.69  | | 
% 228.13/39.69  | | Case 1:
% 228.13/39.69  | | | 
% 228.13/39.69  | | |   (72)  all_57_0 = e3 & op(e3, e3) = e3
% 228.13/39.69  | | | 
% 228.13/39.69  | | | ALPHA: (72) implies:
% 228.13/39.69  | | |   (73)  op(e3, e3) = e3
% 228.13/39.69  | | | 
% 228.13/39.69  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.13/39.69  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (23),
% 228.13/39.69  | | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 228.13/39.69  | | |            (34), (35), (36), (37), (38), (39), (40), (41), (42), (43),
% 228.13/39.69  | | |            (44), (45), (46), (47), (48), (49), (50), (51), (52), (53),
% 228.13/39.69  | | |            (54), (56), (57), (58), (59), (60), (61), (62), (63), (64),
% 228.13/39.69  | | |            (66), (67), (68), (69), (70), (73) are inconsistent by
% 228.13/39.69  | | |            sub-proof #1438.
% 228.13/39.69  | | | 
% 228.13/39.69  | | Case 2:
% 228.13/39.69  | | | 
% 228.13/39.69  | | |   (74)  all_57_2 = e3 & op(e2, e3) = e3
% 228.13/39.69  | | | 
% 228.13/39.69  | | | ALPHA: (74) implies:
% 228.13/39.69  | | |   (75)  all_57_2 = e3
% 228.13/39.69  | | | 
% 228.13/39.69  | | | REF_CLOSE: (3), (8), (25), (27), (36), (39), (42), (54), (56), (75) are
% 228.13/39.69  | | |            inconsistent by sub-proof #1802.
% 228.13/39.69  | | | 
% 228.13/39.69  | | End of split
% 228.13/39.69  | | 
% 228.13/39.69  | Case 2:
% 228.13/39.69  | | 
% 228.13/39.69  | |   (76)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) =
% 228.13/39.69  | |           e3)
% 228.13/39.69  | | 
% 228.13/39.69  | | REF_CLOSE: (8), (22), (27), (34), (35), (39), (42), (47), (56), (65), (76)
% 228.13/39.69  | |            are inconsistent by sub-proof #440.
% 228.13/39.69  | | 
% 228.13/39.69  | End of split
% 228.13/39.69  | 
% 228.13/39.69  End of proof
% 228.13/39.69  
% 228.13/39.69  Sub-proof #440 shows that the following formulas are inconsistent:
% 228.13/39.69  ----------------------------------------------------------------
% 228.13/39.69    (1)   ~ (e3 = e1)
% 228.13/39.69    (2)  all_57_6 = e1
% 228.13/39.69    (3)   ~ (e3 = e2)
% 228.13/39.69    (4)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.13/39.69    (5)  all_57_15 = e3
% 228.13/39.69    (6)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 228.13/39.69         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.13/39.69    (7)   ~ (e2 = e0)
% 228.13/39.69    (8)   ~ (e1 = e0)
% 228.13/39.69    (9)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2) |
% 228.13/39.69         (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.13/39.69    (10)   ~ (e2 = e1)
% 228.13/39.69    (11)  all_57_14 = e0
% 228.13/39.69  
% 228.13/39.69  Begin of proof
% 228.13/39.69  | 
% 228.13/39.69  | BETA: splitting (4) gives:
% 228.13/39.69  | 
% 228.13/39.69  | Case 1:
% 228.13/39.69  | | 
% 228.13/39.69  | |   (12)  all_57_6 = e3 & op(e1, e3) = e3
% 228.13/39.69  | | 
% 228.13/39.69  | | ALPHA: (12) implies:
% 228.13/39.69  | |   (13)  all_57_6 = e3
% 228.13/39.69  | | 
% 228.13/39.69  | | REF_CLOSE: (1), (2), (13) are inconsistent by sub-proof #2017.
% 228.13/39.69  | | 
% 228.13/39.69  | Case 2:
% 228.13/39.69  | | 
% 228.13/39.69  | |   (14)  all_57_12 = e3 & op(e0, e3) = e3
% 228.13/39.69  | | 
% 228.13/39.69  | | ALPHA: (14) implies:
% 228.13/39.69  | |   (15)  all_57_12 = e3
% 228.13/39.69  | | 
% 228.13/39.69  | | REF_CLOSE: (1), (3), (5), (6), (7), (8), (9), (10), (11), (15) are
% 228.13/39.69  | |            inconsistent by sub-proof #1763.
% 228.13/39.69  | | 
% 228.13/39.69  | End of split
% 228.13/39.69  | 
% 228.13/39.69  End of proof
% 228.13/39.69  
% 228.13/39.69  Sub-proof #441 shows that the following formulas are inconsistent:
% 228.13/39.69  ----------------------------------------------------------------
% 228.13/39.69    (1)  all_57_0 = e2 & op(e3, e3) = e2
% 228.13/39.69    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.13/39.69           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.13/39.69    (3)  op(e0, e0) = all_52_31
% 228.13/39.69    (4)   ~ (e2 = e0)
% 228.13/39.69    (5)  op(e0, e0) = e3
% 228.13/39.69    (6)  op(all_52_31, all_52_31) = e0
% 228.13/39.69  
% 228.13/39.69  Begin of proof
% 228.13/39.69  | 
% 228.13/39.69  | ALPHA: (1) implies:
% 228.13/39.69  |   (7)  op(e3, e3) = e2
% 228.13/39.69  | 
% 228.13/39.69  | GROUND_INST: instantiating (2) with e3, all_52_31, e0, e0, simplifying with
% 228.13/39.69  |              (3), (5) gives:
% 228.13/39.69  |   (8)  all_52_31 = e3
% 228.13/39.69  | 
% 228.13/39.69  | REDUCE: (6), (8) imply:
% 228.13/39.69  |   (9)  op(e3, e3) = e0
% 228.13/39.69  | 
% 228.13/39.69  | REF_CLOSE: (2), (4), (7), (9) are inconsistent by sub-proof #2403.
% 228.13/39.69  | 
% 228.13/39.69  End of proof
% 228.13/39.69  
% 228.13/39.69  Sub-proof #442 shows that the following formulas are inconsistent:
% 228.13/39.69  ----------------------------------------------------------------
% 228.13/39.69    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.13/39.69    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.13/39.69    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.13/39.69         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.13/39.69    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.13/39.69         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.13/39.69    (5)   ~ (all_53_8 = all_53_12)
% 228.13/39.69    (6)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.13/39.69         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.13/39.69    (7)   ~ (e3 = e1)
% 228.13/39.69    (8)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.13/39.69         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.13/39.69    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.13/39.69           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.13/39.69    (10)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.13/39.69          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.13/39.69    (11)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.13/39.69            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.13/39.69              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.13/39.69    (12)   ~ (all_6_2 = e3)
% 228.13/39.69    (13)  op(e1, e1) = all_6_2
% 228.13/39.69    (14)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.13/39.69    (15)   ~ (all_53_9 = e0)
% 228.13/39.69    (16)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.13/39.69          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.13/39.69    (17)   ~ (all_53_4 = all_53_12)
% 228.13/39.69    (18)   ~ (all_53_8 = all_53_9)
% 228.13/39.69    (19)  all_57_12 = e2
% 228.13/39.69    (20)  all_42_2 = all_6_2
% 228.13/39.69    (21)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.13/39.69          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.13/39.69    (22)   ~ (all_53_9 = all_6_2)
% 228.13/39.69    (23)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.13/39.69          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.13/39.69    (24)  all_57_3 = e0
% 228.13/39.69    (25)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.13/39.69          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.13/39.69    (26)   ~ (e3 = e2)
% 228.13/39.69    (27)  all_55_1 = all_53_4
% 228.13/39.69    (28)   ~ (e3 = e0)
% 228.13/39.69    (29)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.13/39.69          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.13/39.69    (30)   ~ (all_53_8 = all_6_2)
% 228.13/39.69    (31)  all_55_2 = all_53_8
% 228.13/39.69    (32)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.13/39.69    (33)  all_57_15 = e3
% 228.13/39.69    (34)  op(e3, e3) = e2
% 228.13/39.69    (35)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.13/39.69          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.13/39.69            e1)
% 228.13/39.69    (36)   ~ (all_53_4 = all_53_8)
% 228.13/39.69    (37)  op(e3, e2) = all_53_4
% 228.13/39.69    (38)   ~ (e2 = e0)
% 228.13/39.69    (39)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.13/39.69            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.13/39.69            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.13/39.69            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.13/39.69              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.13/39.69            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.13/39.69            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.13/39.69              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.13/39.69              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.13/39.69            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.13/39.69            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.13/39.69            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.13/39.69              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.13/39.69              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.13/39.69            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.13/39.69              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.13/39.69            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.13/39.69            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.13/39.69              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.13/39.69              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.13/39.69            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.13/39.69            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.13/39.69    (40)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.13/39.69          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.13/39.69    (41)   ~ (e1 = e0)
% 228.13/39.69    (42)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.13/39.69            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.13/39.69              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.13/39.69    (43)   ~ (all_53_4 = e0)
% 228.13/39.69    (44)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.13/39.69          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.13/39.69    (45)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.13/39.69          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.13/39.69    (46)  op(e0, e0) = e3
% 228.13/39.69    (47)   ~ (all_53_4 = all_53_6)
% 228.13/39.69    (48)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.13/39.69          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.13/39.69            e2)
% 228.13/39.69    (49)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.13/39.69              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.13/39.69                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.13/39.69                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.13/39.69    (50)  all_55_10 = all_6_2
% 228.13/39.69    (51)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.13/39.69          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.13/39.69    (52)  all_38_2 = all_6_2
% 228.13/39.69    (53)  all_55_3 = all_53_12
% 228.13/39.69    (54)   ~ (all_53_12 = e3)
% 228.13/39.69    (55)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.13/39.69            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.13/39.69              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.13/39.69    (56)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.13/39.69          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.13/39.69    (57)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.13/39.69          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.13/39.69    (58)   ~ (e2 = e1)
% 228.13/39.69    (59)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.13/39.69          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.13/39.69    (60)  op(e2, e1) = all_53_9
% 228.13/39.69    (61)  op(e1, e2) = all_53_6
% 228.13/39.69    (62)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.13/39.69          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.13/39.69    (63)  all_24_2 = all_6_2
% 228.13/39.69    (64)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.13/39.69          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.13/39.69    (65)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.13/39.69          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.13/39.69    (66)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.13/39.69          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.13/39.69    (67)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.13/39.69          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.13/39.69    (68)  op(e3, e1) = all_53_8
% 228.13/39.69    (69)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.13/39.69          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.13/39.69    (70)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.13/39.69          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.13/39.69    (71)  op(e3, e0) = all_53_12
% 228.13/39.69  
% 228.13/39.69  Begin of proof
% 228.13/39.69  | 
% 228.13/39.69  | BETA: splitting (65) gives:
% 228.13/39.69  | 
% 228.13/39.69  | Case 1:
% 228.13/39.69  | | 
% 228.13/39.69  | |   (72)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) =
% 228.13/39.69  | |           e0)
% 228.13/39.69  | | 
% 228.13/39.69  | | REF_CLOSE: (3), (7), (9), (24), (26), (28), (34), (38), (41), (51), (56),
% 228.13/39.69  | |            (58), (72) are inconsistent by sub-proof #1654.
% 228.13/39.69  | | 
% 228.13/39.69  | Case 2:
% 228.13/39.69  | | 
% 228.13/39.69  | |   (73)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) =
% 228.13/39.69  | |           e0)
% 228.13/39.69  | | 
% 228.13/39.69  | | BETA: splitting (73) gives:
% 228.13/39.69  | | 
% 228.13/39.69  | | Case 1:
% 228.13/39.69  | | | 
% 228.13/39.69  | | |   (74)  all_57_6 = e0 & op(e1, e3) = e0
% 228.13/39.69  | | | 
% 228.13/39.69  | | | ALPHA: (74) implies:
% 228.13/39.69  | | |   (75)  all_57_6 = e0
% 228.13/39.69  | | | 
% 228.13/39.69  | | | BETA: splitting (4) gives:
% 228.13/39.69  | | | 
% 228.13/39.69  | | | Case 1:
% 228.13/39.69  | | | | 
% 228.13/39.69  | | | |   (76)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3)
% 228.13/39.69  | | | |           = e1)
% 228.13/39.69  | | | | 
% 228.13/39.69  | | | | BETA: splitting (76) gives:
% 228.13/39.69  | | | | 
% 228.13/39.69  | | | | Case 1:
% 228.13/39.69  | | | | | 
% 228.13/39.69  | | | | |   (77)  all_57_0 = e1 & op(e3, e3) = e1
% 228.13/39.69  | | | | | 
% 228.13/39.69  | | | | | ALPHA: (77) implies:
% 228.13/39.69  | | | | |   (78)  op(e3, e3) = e1
% 228.13/39.69  | | | | | 
% 228.13/39.69  | | | | | REF_CLOSE: (9), (34), (58), (78) are inconsistent by sub-proof #1950.
% 228.13/39.69  | | | | | 
% 228.13/39.69  | | | | Case 2:
% 228.13/39.69  | | | | | 
% 228.13/39.69  | | | | |   (79)  all_57_2 = e1 & op(e2, e3) = e1
% 228.13/39.69  | | | | | 
% 228.13/39.69  | | | | | ALPHA: (79) implies:
% 228.13/39.69  | | | | |   (80)  all_57_2 = e1
% 228.13/39.69  | | | | | 
% 228.13/39.69  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 228.13/39.69  | | | | |            (12), (13), (14), (15), (16), (17), (18), (19), (20), (21),
% 228.13/39.69  | | | | |            (22), (23), (24), (25), (26), (27), (28), (29), (30), (31),
% 228.13/39.69  | | | | |            (32), (33), (35), (36), (37), (38), (39), (40), (41), (42),
% 228.13/39.69  | | | | |            (43), (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 228.13/39.69  | | | | |            (53), (54), (55), (56), (57), (58), (59), (60), (61), (62),
% 228.13/39.70  | | | | |            (63), (64), (65), (66), (67), (68), (69), (70), (71), (75),
% 228.13/39.70  | | | | |            (80) are inconsistent by sub-proof #443.
% 228.13/39.70  | | | | | 
% 228.13/39.70  | | | | End of split
% 228.13/39.70  | | | | 
% 228.13/39.70  | | | Case 2:
% 228.13/39.70  | | | | 
% 228.13/39.70  | | | |   (81)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3)
% 228.13/39.70  | | | |           = e1)
% 228.13/39.70  | | | | 
% 228.13/39.70  | | | | BETA: splitting (81) gives:
% 228.13/39.70  | | | | 
% 228.13/39.70  | | | | Case 1:
% 228.13/39.70  | | | | | 
% 228.13/39.70  | | | | |   (82)  all_57_6 = e1 & op(e1, e3) = e1
% 228.13/39.70  | | | | | 
% 228.13/39.70  | | | | | ALPHA: (82) implies:
% 228.13/39.70  | | | | |   (83)  all_57_6 = e1
% 228.13/39.70  | | | | | 
% 228.13/39.70  | | | | | REF_CLOSE: (41), (75), (83) are inconsistent by sub-proof #2227.
% 228.13/39.70  | | | | | 
% 228.13/39.70  | | | | Case 2:
% 228.13/39.70  | | | | | 
% 228.13/39.70  | | | | |   (84)  all_57_12 = e1 & op(e0, e3) = e1
% 228.13/39.70  | | | | | 
% 228.13/39.70  | | | | | ALPHA: (84) implies:
% 228.13/39.70  | | | | |   (85)  all_57_12 = e1
% 228.13/39.70  | | | | | 
% 228.13/39.70  | | | | | REF_CLOSE: (19), (58), (85) are inconsistent by sub-proof #2321.
% 228.13/39.70  | | | | | 
% 228.13/39.70  | | | | End of split
% 228.13/39.70  | | | | 
% 228.13/39.70  | | | End of split
% 228.13/39.70  | | | 
% 228.13/39.70  | | Case 2:
% 228.13/39.70  | | | 
% 228.13/39.70  | | |   (86)  all_57_12 = e0 & op(e0, e3) = e0
% 228.13/39.70  | | | 
% 228.13/39.70  | | | REF_CLOSE: (19), (38), (86) are inconsistent by sub-proof #2185.
% 228.13/39.70  | | | 
% 228.13/39.70  | | End of split
% 228.13/39.70  | | 
% 228.13/39.70  | End of split
% 228.13/39.70  | 
% 228.13/39.70  End of proof
% 228.13/39.70  
% 228.13/39.70  Sub-proof #443 shows that the following formulas are inconsistent:
% 228.13/39.70  ----------------------------------------------------------------
% 228.13/39.70    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.13/39.70    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.13/39.70    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.13/39.70         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.13/39.70    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.13/39.70         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.13/39.70    (5)   ~ (all_53_8 = all_53_12)
% 228.13/39.70    (6)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.13/39.70         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.13/39.70    (7)   ~ (e3 = e1)
% 228.13/39.70    (8)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.13/39.70         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.13/39.70    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.13/39.70           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.13/39.70    (10)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.13/39.70          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.13/39.70    (11)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.13/39.70            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.13/39.70              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.13/39.70    (12)   ~ (all_6_2 = e3)
% 228.13/39.70    (13)  op(e1, e1) = all_6_2
% 228.13/39.70    (14)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.13/39.70    (15)   ~ (all_53_9 = e0)
% 228.13/39.70    (16)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.13/39.70          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.13/39.70    (17)   ~ (all_53_4 = all_53_12)
% 228.13/39.70    (18)   ~ (all_53_8 = all_53_9)
% 228.13/39.70    (19)  all_57_12 = e2
% 228.13/39.70    (20)  all_42_2 = all_6_2
% 228.13/39.70    (21)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.13/39.70          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.13/39.70    (22)   ~ (all_53_9 = all_6_2)
% 228.13/39.70    (23)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.13/39.70          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.13/39.70    (24)  all_57_3 = e0
% 228.13/39.70    (25)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.13/39.70          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.13/39.70    (26)   ~ (e3 = e2)
% 228.13/39.70    (27)  all_55_1 = all_53_4
% 228.13/39.70    (28)   ~ (e3 = e0)
% 228.13/39.70    (29)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.13/39.70          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.13/39.70    (30)  all_57_6 = e0
% 228.13/39.70    (31)   ~ (all_53_8 = all_6_2)
% 228.13/39.70    (32)  all_55_2 = all_53_8
% 228.13/39.70    (33)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.13/39.70    (34)  all_57_15 = e3
% 228.13/39.70    (35)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.13/39.70          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.13/39.70            e1)
% 228.13/39.70    (36)   ~ (all_53_4 = all_53_8)
% 228.13/39.70    (37)  op(e3, e2) = all_53_4
% 228.13/39.70    (38)   ~ (e2 = e0)
% 228.13/39.70    (39)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.13/39.70            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.13/39.70            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.13/39.70            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.13/39.70              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.13/39.70            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.13/39.70            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.13/39.70              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.13/39.70              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.13/39.70            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.13/39.70            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.13/39.70            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.13/39.70              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.13/39.70              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.13/39.70            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.13/39.70              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.13/39.70            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.13/39.70            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.13/39.70              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.13/39.70              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.13/39.70            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.13/39.70            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.13/39.70    (40)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.13/39.70          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.13/39.70    (41)   ~ (e1 = e0)
% 228.13/39.70    (42)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.13/39.70            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.13/39.70              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.13/39.70    (43)   ~ (all_53_4 = e0)
% 228.13/39.70    (44)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.13/39.70          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.13/39.70    (45)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.13/39.70          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.13/39.70    (46)  op(e0, e0) = e3
% 228.13/39.70    (47)   ~ (all_53_4 = all_53_6)
% 228.13/39.70    (48)  all_57_2 = e1
% 228.13/39.70    (49)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.13/39.70          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.13/39.70            e2)
% 228.13/39.70    (50)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.13/39.70              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.13/39.70                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.13/39.70                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.13/39.70    (51)  all_55_10 = all_6_2
% 228.13/39.70    (52)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.13/39.70          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.13/39.70    (53)  all_38_2 = all_6_2
% 228.13/39.70    (54)  all_55_3 = all_53_12
% 228.13/39.70    (55)   ~ (all_53_12 = e3)
% 228.13/39.70    (56)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.13/39.70            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.13/39.70              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.13/39.70    (57)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.13/39.70          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.13/39.70    (58)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.13/39.70          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.13/39.70    (59)   ~ (e2 = e1)
% 228.13/39.70    (60)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.13/39.70          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.13/39.70    (61)  op(e2, e1) = all_53_9
% 228.13/39.70    (62)  op(e1, e2) = all_53_6
% 228.13/39.70    (63)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.13/39.70          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.13/39.70    (64)  all_24_2 = all_6_2
% 228.13/39.70    (65)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.13/39.70          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.13/39.70    (66)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.13/39.70          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.13/39.70    (67)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.13/39.70          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.13/39.70    (68)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.13/39.70          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.13/39.70    (69)  op(e3, e1) = all_53_8
% 228.13/39.70    (70)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.13/39.70          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.13/39.70    (71)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.13/39.70          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.13/39.70    (72)  op(e3, e0) = all_53_12
% 228.13/39.70  
% 228.13/39.70  Begin of proof
% 228.13/39.70  | 
% 228.13/39.70  | BETA: splitting (52) gives:
% 228.13/39.70  | 
% 228.13/39.70  | Case 1:
% 228.13/39.70  | | 
% 228.13/39.70  | |   (73)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 228.13/39.70  | |           e3)
% 228.13/39.70  | | 
% 228.13/39.70  | | REF_CLOSE: (7), (24), (28), (48), (73) are inconsistent by sub-proof #1646.
% 228.13/39.70  | | 
% 228.13/39.70  | Case 2:
% 228.13/39.70  | | 
% 228.13/39.70  | |   (74)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 228.13/39.70  | |           e3)
% 228.13/39.70  | | 
% 228.13/39.70  | | BETA: splitting (74) gives:
% 228.13/39.70  | | 
% 228.13/39.70  | | Case 1:
% 228.13/39.70  | | | 
% 228.13/39.70  | | |   (75)  all_57_5 = e3 & op(e2, e1) = e3
% 228.13/39.70  | | | 
% 228.13/39.70  | | | ALPHA: (75) implies:
% 228.13/39.70  | | |   (76)  all_57_5 = e3
% 228.13/39.70  | | |   (77)  op(e2, e1) = e3
% 228.13/39.70  | | | 
% 228.13/39.70  | | | BETA: splitting (58) gives:
% 228.13/39.70  | | | 
% 228.13/39.70  | | | Case 1:
% 228.13/39.70  | | | | 
% 228.13/39.70  | | | |   (78)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3)
% 228.13/39.70  | | | |           = e3)
% 228.13/39.70  | | | | 
% 228.13/39.70  | | | | BETA: splitting (78) gives:
% 228.13/39.70  | | | | 
% 228.13/39.70  | | | | Case 1:
% 228.13/39.70  | | | | | 
% 228.13/39.70  | | | | |   (79)  all_57_0 = e3 & op(e3, e3) = e3
% 228.13/39.70  | | | | | 
% 228.13/39.70  | | | | | ALPHA: (79) implies:
% 228.13/39.70  | | | | |   (80)  op(e3, e3) = e3
% 228.13/39.70  | | | | | 
% 228.13/39.70  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 228.13/39.70  | | | | |            (12), (13), (14), (15), (16), (17), (18), (20), (21), (22),
% 228.13/39.70  | | | | |            (23), (24), (25), (26), (27), (28), (29), (31), (32), (33),
% 228.13/39.70  | | | | |            (34), (35), (36), (37), (38), (39), (40), (41), (42), (43),
% 228.13/39.70  | | | | |            (46), (47), (49), (50), (51), (53), (54), (55), (56), (57),
% 228.13/39.70  | | | | |            (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 228.13/39.70  | | | | |            (69), (70), (71), (72), (76), (77), (80) are inconsistent
% 228.13/39.70  | | | | |            by sub-proof #1438.
% 228.13/39.70  | | | | | 
% 228.13/39.70  | | | | Case 2:
% 228.13/39.70  | | | | | 
% 228.13/39.70  | | | | |   (81)  all_57_2 = e3 & op(e2, e3) = e3
% 228.13/39.70  | | | | | 
% 228.13/39.70  | | | | | ALPHA: (81) implies:
% 228.13/39.70  | | | | |   (82)  all_57_2 = e3
% 228.13/39.70  | | | | | 
% 228.13/39.70  | | | | | REF_CLOSE: (7), (48), (82) are inconsistent by sub-proof #2397.
% 228.13/39.70  | | | | | 
% 228.13/39.70  | | | | End of split
% 228.13/39.70  | | | | 
% 228.13/39.70  | | | Case 2:
% 228.13/39.70  | | | | 
% 228.13/39.70  | | | |   (83)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3)
% 228.13/39.70  | | | |           = e3)
% 228.13/39.70  | | | | 
% 228.13/39.70  | | | | BETA: splitting (83) gives:
% 228.13/39.70  | | | | 
% 228.13/39.70  | | | | Case 1:
% 228.13/39.70  | | | | | 
% 228.13/39.70  | | | | |   (84)  all_57_6 = e3 & op(e1, e3) = e3
% 228.13/39.70  | | | | | 
% 228.13/39.70  | | | | | ALPHA: (84) implies:
% 228.13/39.70  | | | | |   (85)  all_57_6 = e3
% 228.13/39.70  | | | | | 
% 228.13/39.70  | | | | | REF_CLOSE: (28), (30), (85) are inconsistent by sub-proof #1822.
% 228.13/39.70  | | | | | 
% 228.13/39.70  | | | | Case 2:
% 228.13/39.70  | | | | | 
% 228.13/39.70  | | | | |   (86)  all_57_12 = e3 & op(e0, e3) = e3
% 228.13/39.70  | | | | | 
% 228.13/39.70  | | | | | REF_CLOSE: (19), (26), (86) are inconsistent by sub-proof #2075.
% 228.13/39.70  | | | | | 
% 228.13/39.70  | | | | End of split
% 228.13/39.70  | | | | 
% 228.13/39.70  | | | End of split
% 228.13/39.70  | | | 
% 228.13/39.70  | | Case 2:
% 228.13/39.70  | | | 
% 228.13/39.70  | | |   (87)  all_57_10 = e3 & op(e2, e0) = e3
% 228.13/39.70  | | | 
% 228.13/39.70  | | | ALPHA: (87) implies:
% 228.13/39.70  | | |   (88)  all_57_10 = e3
% 228.13/39.70  | | | 
% 228.13/39.70  | | | BETA: splitting (58) gives:
% 228.13/39.70  | | | 
% 228.13/39.70  | | | Case 1:
% 228.13/39.70  | | | | 
% 228.13/39.70  | | | |   (89)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3)
% 228.13/39.70  | | | |           = e3)
% 228.13/39.70  | | | | 
% 228.13/39.70  | | | | REF_CLOSE: (3), (4), (6), (7), (8), (9), (10), (12), (13), (16), (21),
% 228.13/39.70  | | | |            (23), (24), (25), (26), (28), (34), (35), (38), (41), (44),
% 228.13/39.70  | | | |            (45), (49), (50), (57), (58), (59), (60), (63), (65), (66),
% 228.13/39.70  | | | |            (67), (70), (88), (89) are inconsistent by sub-proof #553.
% 228.13/39.70  | | | | 
% 228.13/39.70  | | | Case 2:
% 228.13/39.70  | | | | 
% 228.13/39.70  | | | |   (90)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3)
% 228.13/39.70  | | | |           = e3)
% 228.13/39.70  | | | | 
% 228.13/39.70  | | | | BETA: splitting (90) gives:
% 228.13/39.70  | | | | 
% 228.13/39.70  | | | | Case 1:
% 228.13/39.70  | | | | | 
% 228.13/39.70  | | | | |   (91)  all_57_6 = e3 & op(e1, e3) = e3
% 228.13/39.70  | | | | | 
% 228.13/39.70  | | | | | REF_CLOSE: (28), (30), (91) are inconsistent by sub-proof #2395.
% 228.13/39.70  | | | | | 
% 228.13/39.70  | | | | Case 2:
% 228.13/39.70  | | | | | 
% 228.13/39.70  | | | | |   (92)  all_57_12 = e3 & op(e0, e3) = e3
% 228.13/39.70  | | | | | 
% 228.13/39.70  | | | | | REF_CLOSE: (19), (26), (92) are inconsistent by sub-proof #2075.
% 228.13/39.70  | | | | | 
% 228.13/39.70  | | | | End of split
% 228.13/39.70  | | | | 
% 228.13/39.70  | | | End of split
% 228.13/39.70  | | | 
% 228.13/39.70  | | End of split
% 228.13/39.70  | | 
% 228.13/39.70  | End of split
% 228.13/39.70  | 
% 228.13/39.70  End of proof
% 228.13/39.70  
% 228.13/39.70  Sub-proof #444 shows that the following formulas are inconsistent:
% 228.13/39.70  ----------------------------------------------------------------
% 228.13/39.70    (1)  all_24_2 = e0
% 228.13/39.70    (2)   ~ (e3 = e1)
% 228.13/39.70    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.13/39.70           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.13/39.70    (4)  op(all_6_2, all_6_2) = e1
% 228.13/39.70    (5)  op(e0, e0) = e3
% 228.13/39.70    (6)  all_24_2 = all_6_2
% 228.13/39.70  
% 228.13/39.70  Begin of proof
% 228.13/39.70  | 
% 228.13/39.70  | COMBINE_EQS: (1), (6) imply:
% 228.13/39.70  |   (7)  all_6_2 = e0
% 228.13/39.70  | 
% 228.13/39.70  | SIMP: (7) implies:
% 228.13/39.70  |   (8)  all_6_2 = e0
% 228.13/39.70  | 
% 228.13/39.70  | REDUCE: (4), (8) imply:
% 228.13/39.70  |   (9)  op(e0, e0) = e1
% 228.13/39.70  | 
% 228.13/39.70  | REF_CLOSE: (2), (3), (5), (9) are inconsistent by sub-proof #2183.
% 228.13/39.70  | 
% 228.13/39.70  End of proof
% 228.13/39.70  
% 228.13/39.70  Sub-proof #445 shows that the following formulas are inconsistent:
% 228.13/39.70  ----------------------------------------------------------------
% 228.13/39.70    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.13/39.70    (2)  all_57_0 = e2
% 228.13/39.70    (3)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.13/39.70    (4)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.13/39.70         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.13/39.70    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.13/39.70         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.13/39.70    (6)   ~ (all_53_8 = all_53_12)
% 228.13/39.70    (7)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.13/39.70         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.13/39.70    (8)   ~ (all_53_8 = all_53_11)
% 228.13/39.70    (9)   ~ (e3 = e1)
% 228.13/39.70    (10)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.13/39.70          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.13/39.70    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.13/39.70            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.13/39.70    (12)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.13/39.70          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.13/39.70    (13)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.13/39.70            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.13/39.70              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.13/39.70    (14)   ~ (all_53_3 = e3)
% 228.13/39.70    (15)   ~ (all_6_2 = e3)
% 228.13/39.70    (16)  ( ~ (all_28_0 = e0) & op(all_28_1, e3) = all_28_0 & op(e3, e2) =
% 228.13/39.70            all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 = e1) & op(e3,
% 228.13/39.70              e2) = all_28_1 & $i(all_28_1))
% 228.13/39.70    (17)   ~ (all_53_9 = e1)
% 228.13/39.70    (18)  op(e1, e1) = all_6_2
% 228.13/39.70    (19)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.13/39.70    (20)   ~ (all_53_1 = all_53_9)
% 228.13/39.70    (21)   ~ (all_53_9 = e0)
% 228.13/39.70    (22)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 228.13/39.70    (23)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.13/39.70          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.13/39.70    (24)   ~ (all_52_17 = e2)
% 228.13/39.70    (25)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 228.13/39.70            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 228.13/39.70              e3) = all_22_1 & $i(all_22_1))
% 228.13/39.70    (26)   ~ (all_53_8 = e1)
% 228.13/39.70    (27)  all_57_9 = e1
% 228.13/39.70    (28)  op(all_52_17, all_52_17) = e3
% 228.13/39.70    (29)   ~ (all_53_4 = all_53_12)
% 228.13/39.70    (30)   ~ (all_52_17 = all_52_23)
% 228.13/39.70    (31)   ~ (all_52_17 = e1)
% 228.13/39.70    (32)   ~ (all_53_8 = all_53_9)
% 228.13/39.70    (33)  all_42_2 = all_6_2
% 228.13/39.70    (34)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.13/39.70          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.13/39.70    (35)   ~ (all_53_9 = all_53_11)
% 228.13/39.70    (36)  all_55_4 = all_53_1
% 228.13/39.70    (37)   ~ (all_53_9 = all_6_2)
% 228.13/39.70    (38)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.13/39.70          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.13/39.70    (39)  all_57_3 = e0
% 228.13/39.70    (40)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.13/39.70          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.13/39.70    (41)  all_57_4 = e3
% 228.13/39.70    (42)   ~ (e3 = e2)
% 228.13/39.70    (43)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 228.13/39.70    (44)  all_55_1 = all_53_4
% 228.13/39.70    (45)   ~ (all_53_1 = all_53_3)
% 228.13/39.70    (46)   ~ (all_53_1 = all_52_17)
% 228.13/39.70    (47)   ~ (e3 = e0)
% 228.13/39.70    (48)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.13/39.70          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.13/39.70    (49)   ~ (all_53_8 = all_6_2)
% 228.13/39.70    (50)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.13/39.70    (51)  all_55_11 = all_52_23
% 228.13/39.70    (52)  all_55_2 = all_53_8
% 228.13/39.70    (53)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 228.13/39.70    (54)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.13/39.70    (55)  all_57_15 = e3
% 228.13/39.70    (56)  op(e3, e3) = e2
% 228.13/39.70    (57)   ~ (all_53_3 = e2)
% 228.13/39.70    (58)   ~ (all_53_3 = all_52_17)
% 228.13/39.70    (59)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.13/39.70          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.13/39.70            e1)
% 228.13/39.70    (60)  all_57_10 = e2
% 228.13/39.70    (61)   ~ (all_52_23 = e3)
% 228.13/39.70    (62)  op(e1, e0) = all_52_23
% 228.13/39.70    (63)   ~ (all_53_4 = all_53_8)
% 228.13/39.70    (64)  all_55_6 = all_53_9
% 228.13/39.70    (65)  op(e3, e2) = all_53_4
% 228.13/39.70    (66)   ~ (e2 = e0)
% 228.13/39.70    (67)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.13/39.70            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.13/39.70            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.13/39.70            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.13/39.70              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.13/39.70            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.13/39.70            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.13/39.70              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.13/39.70              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.13/39.70            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.13/39.70            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.13/39.70            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.13/39.70              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.13/39.70              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.13/39.70            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.13/39.70              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.13/39.70            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.13/39.70            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.13/39.70              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.13/39.70              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.13/39.70            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.13/39.70            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.13/39.70    (68)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 228.13/39.70            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 228.13/39.70              e3) = all_12_1 & $i(all_12_1))
% 228.13/39.70    (69)  all_55_12 = all_53_3
% 228.13/39.70    (70)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.13/39.70          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.13/39.70    (71)   ~ (all_53_1 = e0)
% 228.13/39.70    (72)   ~ (e1 = e0)
% 228.13/39.70    (73)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.13/39.70            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.13/39.70              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.13/39.70    (74)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.13/39.70    (75)   ~ (all_53_4 = e0)
% 228.13/39.70    (76)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.13/39.70          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.13/39.70    (77)  all_57_8 = e2
% 228.13/39.70    (78)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.13/39.70          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.13/39.70    (79)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 228.13/39.70    (80)  op(e0, e0) = e3
% 228.13/39.70    (81)   ~ (all_53_4 = all_53_6)
% 228.13/39.70    (82)  ( ~ (all_20_0 = e1) & op(all_20_1, e3) = all_20_0 & op(e3, e2) =
% 228.13/39.70            all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e0) & op(e3,
% 228.13/39.70              e2) = all_20_1 & $i(all_20_1))
% 228.13/39.70    (83)  all_57_5 = e1
% 228.13/39.70    (84)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.13/39.70          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.13/39.70            e2)
% 228.13/39.70    (85)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.13/39.70              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.13/39.70                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.13/39.70                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.13/39.70    (86)  all_55_10 = all_6_2
% 228.13/39.70    (87)   ~ (all_53_11 = e1)
% 228.13/39.70    (88)  all_55_8 = all_52_17
% 228.13/39.70    (89)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.13/39.70          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.13/39.70    (90)  all_38_2 = all_6_2
% 228.13/39.70    (91)  all_55_3 = all_53_12
% 228.13/39.70    (92)   ~ (all_53_12 = e3)
% 228.13/39.70    (93)   ~ (all_53_4 = e2)
% 228.13/39.70    (94)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.13/39.70            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.13/39.70              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.13/39.70    (95)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.13/39.70          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.13/39.70    (96)  all_57_11 = e1
% 228.13/39.70    (97)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.13/39.70          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.13/39.70    (98)   ~ (all_52_23 = e1)
% 228.13/39.70    (99)   ~ (all_53_1 = e2)
% 228.13/39.70    (100)   ~ (e2 = e1)
% 228.13/39.70    (101)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.13/39.70           | (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.13/39.70             e2)
% 228.13/39.70    (102)  op(e2, e1) = all_53_9
% 228.13/39.70    (103)  op(e1, e2) = all_53_6
% 228.13/39.70    (104)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.13/39.70           (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.13/39.70    (105)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 228.13/39.70    (106)  all_24_2 = all_6_2
% 228.13/39.71    (107)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.13/39.71           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.13/39.71    (108)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.13/39.71           (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.13/39.71    (109)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.13/39.71           | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.13/39.71             e1)
% 228.13/39.71    (110)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.13/39.71           (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.13/39.71    (111)  all_55_14 = all_53_11
% 228.13/39.71    (112)  op(e3, e1) = all_53_8
% 228.13/39.71    (113)   ~ (all_53_11 = e3)
% 228.13/39.71    (114)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.13/39.71           (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.13/39.71    (115)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.13/39.71           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.13/39.71    (116)  op(e3, e0) = all_53_12
% 228.13/39.71  
% 228.13/39.71  Begin of proof
% 228.13/39.71  | 
% 228.13/39.71  | BETA: splitting (74) gives:
% 228.13/39.71  | 
% 228.13/39.71  | Case 1:
% 228.13/39.71  | | 
% 228.13/39.71  | |   (117)  all_57_5 = e3 & op(e2, e1) = e3
% 228.13/39.71  | | 
% 228.13/39.71  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.13/39.71  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 228.13/39.71  | |            (24), (25), (26), (28), (29), (30), (31), (32), (33), (34), (35),
% 228.13/39.71  | |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 228.13/39.71  | |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 228.13/39.71  | |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 228.13/39.71  | |            (69), (70), (71), (72), (73), (75), (76), (77), (78), (79), (80),
% 228.13/39.71  | |            (81), (82), (83), (84), (85), (86), (87), (88), (89), (90), (91),
% 228.13/39.71  | |            (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 228.13/39.71  | |            (102), (103), (104), (105), (106), (107), (108), (109), (110),
% 228.13/39.71  | |            (111), (112), (113), (114), (115), (116), (117) are inconsistent
% 228.13/39.71  | |            by sub-proof #446.
% 228.13/39.71  | | 
% 228.13/39.71  | Case 2:
% 228.13/39.71  | | 
% 228.13/39.71  | |   (118)  all_57_10 = e3 & op(e2, e0) = e3
% 228.13/39.71  | | 
% 228.13/39.71  | | ALPHA: (118) implies:
% 228.13/39.71  | |   (119)  all_57_10 = e3
% 228.13/39.71  | | 
% 228.13/39.71  | | REF_CLOSE: (27), (42), (47), (55), (66), (72), (85), (100), (101), (119) are
% 228.13/39.71  | |            inconsistent by sub-proof #1985.
% 228.13/39.71  | | 
% 228.13/39.71  | End of split
% 228.13/39.71  | 
% 228.13/39.71  End of proof
% 228.13/39.71  
% 228.13/39.71  Sub-proof #446 shows that the following formulas are inconsistent:
% 228.13/39.71  ----------------------------------------------------------------
% 228.13/39.71    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.13/39.71    (2)  all_57_0 = e2
% 228.13/39.71    (3)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.13/39.71    (4)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.13/39.71         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.13/39.71    (5)  all_57_5 = e3 & op(e2, e1) = e3
% 228.13/39.71    (6)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.13/39.71         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.13/39.71    (7)   ~ (all_53_8 = all_53_12)
% 228.13/39.71    (8)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.13/39.71         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.13/39.71    (9)   ~ (all_53_8 = all_53_11)
% 228.13/39.71    (10)   ~ (e3 = e1)
% 228.13/39.71    (11)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.13/39.71          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.13/39.71    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.13/39.71            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.13/39.71    (13)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.13/39.71          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.13/39.71    (14)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.13/39.71            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.13/39.71              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.13/39.71    (15)   ~ (all_53_3 = e3)
% 228.13/39.71    (16)   ~ (all_6_2 = e3)
% 228.13/39.71    (17)  ( ~ (all_28_0 = e0) & op(all_28_1, e3) = all_28_0 & op(e3, e2) =
% 228.13/39.71            all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 = e1) & op(e3,
% 228.13/39.71              e2) = all_28_1 & $i(all_28_1))
% 228.13/39.71    (18)   ~ (all_53_9 = e1)
% 228.13/39.71    (19)  op(e1, e1) = all_6_2
% 228.13/39.71    (20)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.13/39.71    (21)   ~ (all_53_1 = all_53_9)
% 228.13/39.71    (22)   ~ (all_53_9 = e0)
% 228.13/39.71    (23)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 228.13/39.71    (24)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.13/39.71          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.13/39.71    (25)   ~ (all_52_17 = e2)
% 228.13/39.71    (26)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 228.13/39.71            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 228.13/39.71              e3) = all_22_1 & $i(all_22_1))
% 228.13/39.71    (27)   ~ (all_53_8 = e1)
% 228.13/39.71    (28)  op(all_52_17, all_52_17) = e3
% 228.13/39.71    (29)   ~ (all_53_4 = all_53_12)
% 228.13/39.71    (30)   ~ (all_52_17 = all_52_23)
% 228.13/39.71    (31)   ~ (all_52_17 = e1)
% 228.13/39.71    (32)   ~ (all_53_8 = all_53_9)
% 228.13/39.71    (33)  all_42_2 = all_6_2
% 228.13/39.71    (34)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.13/39.71          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.13/39.71    (35)   ~ (all_53_9 = all_53_11)
% 228.13/39.71    (36)  all_55_4 = all_53_1
% 228.13/39.71    (37)   ~ (all_53_9 = all_6_2)
% 228.13/39.71    (38)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.13/39.71          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.13/39.71    (39)  all_57_3 = e0
% 228.13/39.71    (40)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.13/39.71          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.13/39.71    (41)  all_57_4 = e3
% 228.13/39.71    (42)   ~ (e3 = e2)
% 228.13/39.71    (43)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 228.13/39.71    (44)  all_55_1 = all_53_4
% 228.13/39.71    (45)   ~ (all_53_1 = all_53_3)
% 228.13/39.71    (46)   ~ (all_53_1 = all_52_17)
% 228.13/39.71    (47)   ~ (e3 = e0)
% 228.13/39.71    (48)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.13/39.71          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.13/39.71    (49)   ~ (all_53_8 = all_6_2)
% 228.13/39.71    (50)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.13/39.71    (51)  all_55_11 = all_52_23
% 228.13/39.71    (52)  all_55_2 = all_53_8
% 228.13/39.71    (53)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 228.13/39.71    (54)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.13/39.71    (55)  all_57_15 = e3
% 228.13/39.71    (56)  op(e3, e3) = e2
% 228.13/39.71    (57)   ~ (all_53_3 = e2)
% 228.13/39.71    (58)   ~ (all_53_3 = all_52_17)
% 228.13/39.71    (59)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.13/39.71          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.13/39.71            e1)
% 228.13/39.71    (60)  all_57_10 = e2
% 228.13/39.71    (61)   ~ (all_52_23 = e3)
% 228.13/39.71    (62)  op(e1, e0) = all_52_23
% 228.13/39.71    (63)   ~ (all_53_4 = all_53_8)
% 228.13/39.71    (64)  all_55_6 = all_53_9
% 228.13/39.71    (65)  op(e3, e2) = all_53_4
% 228.13/39.71    (66)   ~ (e2 = e0)
% 228.13/39.71    (67)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.13/39.71            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.13/39.71            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.13/39.71            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.13/39.71              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.13/39.71            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.13/39.71            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.13/39.71              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.13/39.71              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.13/39.71            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.13/39.71            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.13/39.71            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.13/39.71              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.13/39.71              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.13/39.71            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.13/39.71              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.13/39.71            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.13/39.71            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.13/39.71              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.13/39.71              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.13/39.71            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.13/39.71            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.13/39.71    (68)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 228.13/39.71            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 228.13/39.71              e3) = all_12_1 & $i(all_12_1))
% 228.13/39.71    (69)  all_55_12 = all_53_3
% 228.13/39.71    (70)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.13/39.71          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.13/39.71    (71)   ~ (all_53_1 = e0)
% 228.13/39.71    (72)   ~ (e1 = e0)
% 228.13/39.71    (73)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.13/39.71            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.13/39.71              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.13/39.71    (74)   ~ (all_53_4 = e0)
% 228.13/39.71    (75)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.13/39.71          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.13/39.71    (76)  all_57_8 = e2
% 228.13/39.71    (77)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.13/39.71          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.13/39.71    (78)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 228.13/39.71    (79)  op(e0, e0) = e3
% 228.13/39.71    (80)   ~ (all_53_4 = all_53_6)
% 228.13/39.71    (81)  ( ~ (all_20_0 = e1) & op(all_20_1, e3) = all_20_0 & op(e3, e2) =
% 228.13/39.71            all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e0) & op(e3,
% 228.13/39.71              e2) = all_20_1 & $i(all_20_1))
% 228.13/39.71    (82)  all_57_5 = e1
% 228.13/39.71    (83)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.13/39.71          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.13/39.71            e2)
% 228.13/39.71    (84)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.13/39.71              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.13/39.71                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.13/39.71                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.13/39.71    (85)  all_55_10 = all_6_2
% 228.13/39.71    (86)   ~ (all_53_11 = e1)
% 228.13/39.71    (87)  all_55_8 = all_52_17
% 228.13/39.71    (88)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.13/39.71          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.13/39.71    (89)  all_38_2 = all_6_2
% 228.13/39.71    (90)  all_55_3 = all_53_12
% 228.13/39.71    (91)   ~ (all_53_12 = e3)
% 228.13/39.71    (92)   ~ (all_53_4 = e2)
% 228.13/39.71    (93)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.13/39.71            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.13/39.71              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.13/39.71    (94)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.13/39.71          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.13/39.71    (95)  all_57_11 = e1
% 228.13/39.71    (96)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.13/39.71          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.13/39.71    (97)   ~ (all_52_23 = e1)
% 228.13/39.71    (98)   ~ (all_53_1 = e2)
% 228.13/39.71    (99)   ~ (e2 = e1)
% 228.13/39.71    (100)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.13/39.71           | (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.13/39.71             e2)
% 228.13/39.71    (101)  op(e2, e1) = all_53_9
% 228.13/39.71    (102)  op(e1, e2) = all_53_6
% 228.13/39.71    (103)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.13/39.71           (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.13/39.71    (104)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 228.13/39.71    (105)  all_24_2 = all_6_2
% 228.13/39.71    (106)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.13/39.71           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.13/39.71    (107)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.13/39.71           (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.13/39.71    (108)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.13/39.71           | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.13/39.71             e1)
% 228.13/39.71    (109)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.13/39.71           (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.13/39.71    (110)  all_55_14 = all_53_11
% 228.13/39.71    (111)  op(e3, e1) = all_53_8
% 228.13/39.71    (112)   ~ (all_53_11 = e3)
% 228.13/39.71    (113)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.13/39.71           (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.13/39.71    (114)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.13/39.71           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.13/39.71    (115)  op(e3, e0) = all_53_12
% 228.13/39.71  
% 228.13/39.71  Begin of proof
% 228.13/39.71  | 
% 228.13/39.71  | ALPHA: (5) implies:
% 228.13/39.71  |   (116)  all_57_5 = e3
% 228.13/39.71  |   (117)  op(e2, e1) = e3
% 228.13/39.71  | 
% 228.13/39.71  | COMBINE_EQS: (82), (116) imply:
% 228.13/39.71  |   (118)  e3 = e1
% 228.13/39.71  | 
% 228.13/39.71  | SIMP: (118) implies:
% 228.13/39.71  |   (119)  e3 = e1
% 228.13/39.71  | 
% 228.13/39.71  | COMBINE_EQS: (41), (119) imply:
% 228.13/39.71  |   (120)  all_57_4 = e1
% 228.13/39.71  | 
% 228.13/39.71  | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13),
% 228.13/39.71  |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 228.13/39.71  |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 228.13/39.71  |            (36), (37), (38), (39), (40), (42), (43), (44), (45), (46), (47),
% 228.13/39.71  |            (48), (49), (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 228.13/39.71  |            (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 228.13/39.71  |            (70), (71), (72), (73), (74), (75), (76), (77), (78), (79), (80),
% 228.13/39.71  |            (81), (83), (84), (85), (86), (87), (88), (89), (90), (91), (92),
% 228.13/39.71  |            (93), (94), (95), (96), (97), (98), (99), (100), (101), (102),
% 228.13/39.71  |            (103), (104), (105), (106), (107), (108), (109), (110), (111),
% 228.13/39.71  |            (112), (113), (114), (115), (116), (117), (120) are inconsistent by
% 228.13/39.71  |            sub-proof #455.
% 228.13/39.71  | 
% 228.13/39.71  End of proof
% 228.13/39.71  
% 228.13/39.71  Sub-proof #447 shows that the following formulas are inconsistent:
% 228.13/39.71  ----------------------------------------------------------------
% 228.13/39.71    (1)  all_57_0 = e2
% 228.13/39.71    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.13/39.71         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.13/39.71    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.13/39.71         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.13/39.71    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.13/39.71         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.13/39.71    (5)   ~ (e3 = e1)
% 228.13/39.71    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.13/39.71           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.13/39.71    (7)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.13/39.71         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.13/39.71    (8)   ~ (all_6_2 = e3)
% 228.13/39.71    (9)  op(e1, e1) = all_6_2
% 228.13/39.71    (10)  all_57_9 = e1
% 228.13/39.71    (11)  all_57_12 = e2
% 228.13/39.71    (12)  all_57_3 = e0
% 228.13/39.71    (13)   ~ (e3 = e2)
% 228.13/39.71    (14)   ~ (e3 = e0)
% 228.13/39.71    (15)  all_57_15 = e3
% 228.13/39.71    (16)  op(e3, e3) = e2
% 228.13/39.71    (17)  all_57_10 = e2
% 228.13/39.71    (18)   ~ (e2 = e0)
% 228.13/39.71    (19)   ~ (e1 = e0)
% 228.13/39.71    (20)  all_57_2 = e1
% 228.13/39.71    (21)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.13/39.71              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.13/39.71                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.13/39.71                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.13/39.71    (22)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.13/39.71          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.13/39.71    (23)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.13/39.71          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.13/39.71    (24)  all_57_1 = e3
% 228.13/39.71    (25)   ~ (e2 = e1)
% 228.13/39.71    (26)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.13/39.71          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.13/39.71    (27)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.13/39.71          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.13/39.71    (28)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.13/39.71          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.13/39.71    (29)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.13/39.71          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.13/39.71    (30)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.13/39.71          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.13/39.71  
% 228.13/39.71  Begin of proof
% 228.13/39.71  | 
% 228.13/39.71  | BETA: splitting (7) gives:
% 228.13/39.71  | 
% 228.13/39.71  | Case 1:
% 228.13/39.71  | | 
% 228.13/39.71  | |   (31)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 228.13/39.71  | |           e3)
% 228.13/39.71  | | 
% 228.13/39.71  | | BETA: splitting (31) gives:
% 228.13/39.71  | | 
% 228.13/39.71  | | Case 1:
% 228.13/39.71  | | | 
% 228.13/39.71  | | |   (32)  all_57_6 = e3 & op(e1, e3) = e3
% 228.13/39.71  | | | 
% 228.13/39.71  | | | ALPHA: (32) implies:
% 228.13/39.71  | | |   (33)  all_57_6 = e3
% 228.13/39.71  | | | 
% 228.13/39.71  | | | BETA: splitting (22) gives:
% 228.13/39.71  | | | 
% 228.13/39.71  | | | Case 1:
% 228.13/39.71  | | | | 
% 228.13/39.71  | | | |   (34)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2)
% 228.13/39.71  | | | |           = e3)
% 228.13/39.71  | | | | 
% 228.13/39.71  | | | | BETA: splitting (34) gives:
% 228.13/39.71  | | | | 
% 228.13/39.71  | | | | Case 1:
% 228.13/39.71  | | | | | 
% 228.13/39.71  | | | | |   (35)  all_57_2 = e3 & op(e2, e3) = e3
% 228.13/39.71  | | | | | 
% 228.13/39.71  | | | | | ALPHA: (35) implies:
% 228.13/39.71  | | | | |   (36)  all_57_2 = e3
% 228.13/39.71  | | | | | 
% 228.13/39.71  | | | | | REF_CLOSE: (1), (2), (3), (5), (6), (12), (13), (14), (16), (18),
% 228.13/39.71  | | | | |            (19), (22), (23), (25), (28), (33), (36) are inconsistent
% 228.13/39.71  | | | | |            by sub-proof #794.
% 228.13/39.71  | | | | | 
% 228.13/39.71  | | | | Case 2:
% 228.13/39.71  | | | | | 
% 228.13/39.71  | | | | |   (37)  all_57_3 = e3 & op(e2, e2) = e3
% 228.13/39.71  | | | | | 
% 228.13/39.71  | | | | | ALPHA: (37) implies:
% 228.13/39.71  | | | | |   (38)  all_57_3 = e3
% 228.13/39.71  | | | | | 
% 228.13/39.71  | | | | | REF_CLOSE: (12), (14), (38) are inconsistent by sub-proof #2358.
% 228.13/39.71  | | | | | 
% 228.13/39.71  | | | | End of split
% 228.13/39.71  | | | | 
% 228.13/39.71  | | | Case 2:
% 228.13/39.71  | | | | 
% 228.13/39.71  | | | |   (39)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0)
% 228.13/39.71  | | | |           = e3)
% 228.13/39.71  | | | | 
% 228.13/39.71  | | | | BETA: splitting (39) gives:
% 228.13/39.71  | | | | 
% 228.13/39.71  | | | | Case 1:
% 228.13/39.71  | | | | | 
% 228.13/39.71  | | | | |   (40)  all_57_5 = e3 & op(e2, e1) = e3
% 228.13/39.71  | | | | | 
% 228.13/39.71  | | | | | ALPHA: (40) implies:
% 228.13/39.71  | | | | |   (41)  all_57_5 = e3
% 228.13/39.71  | | | | | 
% 228.13/39.71  | | | | | BETA: splitting (28) gives:
% 228.13/39.71  | | | | | 
% 228.13/39.71  | | | | | Case 1:
% 228.13/39.71  | | | | | | 
% 228.13/39.71  | | | | | |   (42)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2,
% 228.13/39.71  | | | | | |             e3) = e0)
% 228.13/39.71  | | | | | | 
% 228.13/39.71  | | | | | | REF_CLOSE: (2), (5), (6), (12), (13), (16), (18), (19), (23), (25),
% 228.13/39.71  | | | | | |            (41), (42) are inconsistent by sub-proof #1644.
% 228.13/39.71  | | | | | | 
% 228.13/39.71  | | | | | Case 2:
% 228.13/39.71  | | | | | | 
% 228.13/39.71  | | | | | |   (43)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0,
% 228.13/39.71  | | | | | |             e3) = e0)
% 228.13/39.71  | | | | | | 
% 228.13/39.71  | | | | | | BETA: splitting (43) gives:
% 228.13/39.71  | | | | | | 
% 228.13/39.71  | | | | | | Case 1:
% 228.13/39.71  | | | | | | | 
% 228.13/39.71  | | | | | | |   (44)  all_57_6 = e0 & op(e1, e3) = e0
% 228.13/39.71  | | | | | | | 
% 228.13/39.71  | | | | | | | ALPHA: (44) implies:
% 228.13/39.71  | | | | | | |   (45)  all_57_6 = e0
% 228.13/39.71  | | | | | | | 
% 228.13/39.71  | | | | | | | COMBINE_EQS: (33), (45) imply:
% 228.13/39.71  | | | | | | |   (46)  e3 = e0
% 228.13/39.71  | | | | | | | 
% 228.13/39.71  | | | | | | | SIMP: (46) implies:
% 228.13/39.71  | | | | | | |   (47)  e3 = e0
% 228.13/39.71  | | | | | | | 
% 228.13/39.71  | | | | | | | COMBINE_EQS: (41), (47) imply:
% 228.13/39.71  | | | | | | |   (48)  all_57_5 = e0
% 228.13/39.71  | | | | | | | 
% 228.13/39.71  | | | | | | | REF_CLOSE: (2), (5), (10), (12), (13), (14), (15), (17), (18),
% 228.13/39.71  | | | | | | |            (19), (21), (22), (25), (26), (48) are inconsistent by
% 228.13/39.71  | | | | | | |            sub-proof #967.
% 228.13/39.71  | | | | | | | 
% 228.13/39.71  | | | | | | Case 2:
% 228.13/39.71  | | | | | | | 
% 228.13/39.71  | | | | | | |   (49)  all_57_12 = e0 & op(e0, e3) = e0
% 228.13/39.71  | | | | | | | 
% 228.13/39.71  | | | | | | | ALPHA: (49) implies:
% 228.13/39.71  | | | | | | |   (50)  all_57_12 = e0
% 228.13/39.71  | | | | | | | 
% 228.13/39.71  | | | | | | | REF_CLOSE: (1), (11), (13), (18), (20), (25), (27), (33), (50) are
% 228.13/39.71  | | | | | | |            inconsistent by sub-proof #665.
% 228.13/39.71  | | | | | | | 
% 228.13/39.71  | | | | | | End of split
% 228.13/39.71  | | | | | | 
% 228.13/39.71  | | | | | End of split
% 228.13/39.71  | | | | | 
% 228.13/39.71  | | | | Case 2:
% 228.13/39.71  | | | | | 
% 228.13/39.71  | | | | |   (51)  all_57_10 = e3 & op(e2, e0) = e3
% 228.13/39.71  | | | | | 
% 228.13/39.71  | | | | | ALPHA: (51) implies:
% 228.13/39.71  | | | | |   (52)  all_57_10 = e3
% 228.13/39.71  | | | | | 
% 228.13/39.71  | | | | | REF_CLOSE: (10), (13), (14), (15), (18), (19), (21), (25), (26), (52)
% 228.13/39.71  | | | | |            are inconsistent by sub-proof #1985.
% 228.13/39.71  | | | | | 
% 228.13/39.71  | | | | End of split
% 228.13/39.71  | | | | 
% 228.13/39.71  | | | End of split
% 228.13/39.71  | | | 
% 228.13/39.71  | | Case 2:
% 228.13/39.71  | | | 
% 228.13/39.71  | | |   (53)  all_57_7 = e3 & op(e1, e2) = e3
% 228.13/39.71  | | | 
% 228.13/39.71  | | | ALPHA: (53) implies:
% 228.13/39.71  | | |   (54)  all_57_7 = e3
% 228.13/39.71  | | | 
% 228.13/39.71  | | | REF_CLOSE: (4), (5), (12), (13), (18), (19), (24), (25), (30), (54) are
% 228.13/39.71  | | |            inconsistent by sub-proof #1778.
% 228.13/39.71  | | | 
% 228.13/39.71  | | End of split
% 228.13/39.71  | | 
% 228.13/39.71  | Case 2:
% 228.13/39.71  | | 
% 228.13/39.71  | |   (55)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 228.13/39.71  | |           e3)
% 228.13/39.71  | | 
% 228.13/39.71  | | REF_CLOSE: (5), (6), (8), (9), (13), (14), (15), (18), (19), (21), (25),
% 228.13/39.71  | |            (26), (29), (55) are inconsistent by sub-proof #1786.
% 228.13/39.71  | | 
% 228.13/39.71  | End of split
% 228.13/39.71  | 
% 228.13/39.71  End of proof
% 228.13/39.71  
% 228.13/39.71  Sub-proof #448 shows that the following formulas are inconsistent:
% 228.13/39.71  ----------------------------------------------------------------
% 228.13/39.71    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.13/39.71    (2)  all_57_0 = e2
% 228.13/39.71    (3)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.13/39.71    (4)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.13/39.71         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.13/39.71    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.13/39.71         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.13/39.71    (6)   ~ (all_53_8 = all_53_12)
% 228.13/39.71    (7)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.13/39.71         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.13/39.71    (8)   ~ (e3 = e1)
% 228.13/39.71    (9)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.13/39.71         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.13/39.71    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.13/39.71            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.13/39.71    (11)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.13/39.71          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.13/39.72    (12)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.13/39.72            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.13/39.72              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.13/39.72    (13)   ~ (all_6_2 = e3)
% 228.13/39.72    (14)  op(e1, e1) = all_6_2
% 228.13/39.72    (15)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.13/39.72    (16)   ~ (all_53_9 = e0)
% 228.13/39.72    (17)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.13/39.72          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.13/39.72    (18)  all_57_7 = e2
% 228.13/39.72    (19)   ~ (all_53_4 = all_53_12)
% 228.13/39.72    (20)   ~ (all_53_8 = all_53_9)
% 228.13/39.72    (21)  all_42_2 = all_6_2
% 228.13/39.72    (22)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.13/39.72          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.13/39.72    (23)   ~ (all_53_9 = all_6_2)
% 228.13/39.72    (24)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.13/39.72          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.13/39.72    (25)  all_57_3 = e0
% 228.13/39.72    (26)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.13/39.72          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.13/39.72    (27)   ~ (e3 = e2)
% 228.13/39.72    (28)  all_55_1 = all_53_4
% 228.13/39.72    (29)   ~ (e3 = e0)
% 228.13/39.72    (30)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.13/39.72          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.13/39.72    (31)   ~ (all_53_8 = all_6_2)
% 228.13/39.72    (32)  all_55_2 = all_53_8
% 228.13/39.72    (33)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.13/39.72    (34)  all_57_15 = e3
% 228.13/39.72    (35)  op(e3, e3) = e2
% 228.13/39.72    (36)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.13/39.72          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.13/39.72            e1)
% 228.13/39.72    (37)  all_57_10 = e2
% 228.13/39.72    (38)   ~ (all_53_4 = all_53_8)
% 228.13/39.72    (39)  op(e3, e2) = all_53_4
% 228.13/39.72    (40)   ~ (e2 = e0)
% 228.13/39.72    (41)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.13/39.72            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.13/39.72            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.13/39.72            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.13/39.72              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.13/39.72            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.13/39.72            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.13/39.72              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.13/39.72              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.13/39.72            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.13/39.72            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.13/39.72            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.13/39.72              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.13/39.72              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.13/39.72            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.13/39.72              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.13/39.72            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.13/39.72            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.13/39.72              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.13/39.72              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.13/39.72            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.13/39.72            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.13/39.72    (42)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.13/39.72          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.13/39.72    (43)   ~ (e1 = e0)
% 228.13/39.72    (44)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.13/39.72            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.13/39.72              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.13/39.72    (45)   ~ (all_53_4 = e0)
% 228.13/39.72    (46)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.13/39.72          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.13/39.72    (47)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.13/39.72          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.13/39.72    (48)  op(e0, e0) = e3
% 228.13/39.72    (49)   ~ (all_53_4 = all_53_6)
% 228.13/39.72    (50)  all_57_5 = e1
% 228.13/39.72    (51)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.13/39.72          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.13/39.72            e2)
% 228.13/39.72    (52)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.13/39.72              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.13/39.72                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.13/39.72                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.13/39.72    (53)  all_55_10 = all_6_2
% 228.13/39.72    (54)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.13/39.72          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.13/39.72    (55)  all_38_2 = all_6_2
% 228.13/39.72    (56)  all_55_3 = all_53_12
% 228.13/39.72    (57)   ~ (all_53_12 = e3)
% 228.13/39.72    (58)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.13/39.72            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.13/39.72              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.13/39.72    (59)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.13/39.72          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.13/39.72    (60)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.13/39.72          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.13/39.72    (61)   ~ (e2 = e1)
% 228.13/39.72    (62)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.13/39.72          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.13/39.72    (63)  op(e2, e1) = all_53_9
% 228.13/39.72    (64)  op(e1, e2) = all_53_6
% 228.13/39.72    (65)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.13/39.72          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.13/39.72    (66)  all_24_2 = all_6_2
% 228.13/39.72    (67)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.13/39.72          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.13/39.72    (68)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.13/39.72          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.13/39.72    (69)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.13/39.72          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.13/39.72    (70)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.13/39.72          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.13/39.72    (71)  op(e3, e1) = all_53_8
% 228.13/39.72    (72)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.13/39.72          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.13/39.72    (73)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.13/39.72          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.13/39.72    (74)  op(e3, e0) = all_53_12
% 228.13/39.72  
% 228.13/39.72  Begin of proof
% 228.13/39.72  | 
% 228.13/39.72  | BETA: splitting (46) gives:
% 228.13/39.72  | 
% 228.13/39.72  | Case 1:
% 228.13/39.72  | | 
% 228.13/39.72  | |   (75)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) =
% 228.13/39.72  | |           e3)
% 228.13/39.72  | | 
% 228.13/39.72  | | BETA: splitting (75) gives:
% 228.13/39.72  | | 
% 228.13/39.72  | | Case 1:
% 228.13/39.72  | | | 
% 228.13/39.72  | | |   (76)  all_57_4 = e3 & op(e3, e1) = e3
% 228.13/39.72  | | | 
% 228.13/39.72  | | | ALPHA: (76) implies:
% 228.13/39.72  | | |   (77)  all_57_4 = e3
% 228.13/39.72  | | | 
% 228.13/39.72  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.13/39.72  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 228.13/39.72  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 228.13/39.72  | | |            (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 228.13/39.72  | | |            (43), (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 228.13/39.72  | | |            (53), (54), (55), (56), (57), (58), (59), (60), (61), (62),
% 228.13/39.72  | | |            (63), (64), (65), (66), (67), (68), (69), (70), (71), (72),
% 228.13/39.72  | | |            (73), (74), (77) are inconsistent by sub-proof #449.
% 228.13/39.72  | | | 
% 228.13/39.72  | | Case 2:
% 228.13/39.72  | | | 
% 228.13/39.72  | | |   (78)  all_57_5 = e3 & op(e2, e1) = e3
% 228.13/39.72  | | | 
% 228.13/39.72  | | | ALPHA: (78) implies:
% 228.13/39.72  | | |   (79)  all_57_5 = e3
% 228.13/39.72  | | | 
% 228.13/39.72  | | | REF_CLOSE: (8), (50), (79) are inconsistent by sub-proof #2382.
% 228.13/39.72  | | | 
% 228.13/39.72  | | End of split
% 228.13/39.72  | | 
% 228.13/39.72  | Case 2:
% 228.13/39.72  | | 
% 228.13/39.72  | |   (80)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) =
% 228.13/39.72  | |           e3)
% 228.13/39.72  | | 
% 228.13/39.72  | | REF_CLOSE: (8), (10), (13), (14), (27), (29), (34), (36), (40), (43), (51),
% 228.13/39.72  | |            (52), (61), (80) are inconsistent by sub-proof #1794.
% 228.13/39.72  | | 
% 228.13/39.72  | End of split
% 228.13/39.72  | 
% 228.13/39.72  End of proof
% 228.13/39.72  
% 228.13/39.72  Sub-proof #449 shows that the following formulas are inconsistent:
% 228.13/39.72  ----------------------------------------------------------------
% 228.13/39.72    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.13/39.72    (2)  all_57_0 = e2
% 228.13/39.72    (3)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.13/39.72    (4)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.13/39.72         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.13/39.72    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.13/39.72         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.13/39.72    (6)   ~ (all_53_8 = all_53_12)
% 228.13/39.72    (7)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.13/39.72         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.13/39.72    (8)   ~ (e3 = e1)
% 228.13/39.72    (9)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.13/39.72         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.13/39.72    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.13/39.72            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.13/39.72    (11)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.13/39.72          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.13/39.72    (12)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.13/39.72            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.13/39.72              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.13/39.72    (13)   ~ (all_6_2 = e3)
% 228.13/39.72    (14)  op(e1, e1) = all_6_2
% 228.13/39.72    (15)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.13/39.72    (16)   ~ (all_53_9 = e0)
% 228.13/39.72    (17)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.13/39.72          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.13/39.72    (18)  all_57_7 = e2
% 228.13/39.72    (19)   ~ (all_53_4 = all_53_12)
% 228.13/39.72    (20)   ~ (all_53_8 = all_53_9)
% 228.13/39.72    (21)  all_42_2 = all_6_2
% 228.13/39.72    (22)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.13/39.72          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.13/39.72    (23)   ~ (all_53_9 = all_6_2)
% 228.13/39.72    (24)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.13/39.72          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.13/39.72    (25)  all_57_3 = e0
% 228.13/39.72    (26)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.13/39.72          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.13/39.72    (27)  all_57_4 = e3
% 228.13/39.72    (28)   ~ (e3 = e2)
% 228.13/39.72    (29)  all_55_1 = all_53_4
% 228.13/39.72    (30)   ~ (e3 = e0)
% 228.13/39.72    (31)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.13/39.72          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.13/39.72    (32)   ~ (all_53_8 = all_6_2)
% 228.13/39.72    (33)  all_55_2 = all_53_8
% 228.13/39.72    (34)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.13/39.72    (35)  all_57_15 = e3
% 228.13/39.72    (36)  op(e3, e3) = e2
% 228.13/39.72    (37)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.13/39.72          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.13/39.72            e1)
% 228.13/39.72    (38)  all_57_10 = e2
% 228.13/39.72    (39)   ~ (all_53_4 = all_53_8)
% 228.13/39.72    (40)  op(e3, e2) = all_53_4
% 228.13/39.72    (41)   ~ (e2 = e0)
% 228.13/39.72    (42)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.13/39.72            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.13/39.72            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.13/39.72            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.13/39.72              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.13/39.72            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.13/39.72            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.13/39.72              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.13/39.72              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.13/39.72            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.13/39.72            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.13/39.72            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.13/39.72              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.13/39.72              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.13/39.72            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.13/39.72              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.13/39.72            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.13/39.72            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.13/39.72              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.13/39.72              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.13/39.72            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.13/39.72            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.13/39.72    (43)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.13/39.72          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.13/39.72    (44)   ~ (e1 = e0)
% 228.13/39.72    (45)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.13/39.72            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.13/39.72              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.13/39.72    (46)   ~ (all_53_4 = e0)
% 228.13/39.72    (47)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.13/39.72          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.13/39.72    (48)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.13/39.72          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.13/39.72    (49)  op(e0, e0) = e3
% 228.13/39.72    (50)   ~ (all_53_4 = all_53_6)
% 228.13/39.72    (51)  all_57_5 = e1
% 228.13/39.72    (52)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.13/39.72          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.13/39.72            e2)
% 228.13/39.72    (53)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.13/39.72              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.13/39.72                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.13/39.72                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.13/39.72    (54)  all_55_10 = all_6_2
% 228.13/39.72    (55)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.13/39.72          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.13/39.72    (56)  all_38_2 = all_6_2
% 228.13/39.72    (57)  all_55_3 = all_53_12
% 228.13/39.72    (58)   ~ (all_53_12 = e3)
% 228.13/39.72    (59)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.13/39.72            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.13/39.72              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.13/39.72    (60)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.13/39.72          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.20/39.72    (61)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.20/39.72          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.20/39.72    (62)   ~ (e2 = e1)
% 228.20/39.72    (63)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.20/39.72          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.20/39.72    (64)  op(e2, e1) = all_53_9
% 228.20/39.72    (65)  op(e1, e2) = all_53_6
% 228.20/39.72    (66)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.20/39.72          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.20/39.72    (67)  all_24_2 = all_6_2
% 228.20/39.72    (68)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.20/39.72          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.20/39.72    (69)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.20/39.72          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.20/39.72    (70)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.20/39.72          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.20/39.72    (71)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.20/39.72          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.20/39.72    (72)  op(e3, e1) = all_53_8
% 228.20/39.72    (73)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.20/39.72          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.20/39.72    (74)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.20/39.72          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.20/39.72    (75)  op(e3, e0) = all_53_12
% 228.20/39.72  
% 228.20/39.72  Begin of proof
% 228.20/39.72  | 
% 228.20/39.72  | BETA: splitting (24) gives:
% 228.20/39.72  | 
% 228.20/39.72  | Case 1:
% 228.20/39.72  | | 
% 228.20/39.72  | |   (76)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) =
% 228.20/39.72  | |           e0)
% 228.20/39.72  | | 
% 228.20/39.72  | | BETA: splitting (76) gives:
% 228.20/39.72  | | 
% 228.20/39.72  | | Case 1:
% 228.20/39.72  | | | 
% 228.20/39.72  | | |   (77)  all_57_0 = e0 & op(e3, e3) = e0
% 228.20/39.72  | | | 
% 228.20/39.72  | | | ALPHA: (77) implies:
% 228.20/39.72  | | |   (78)  op(e3, e3) = e0
% 228.20/39.72  | | | 
% 228.20/39.72  | | | REF_CLOSE: (10), (36), (41), (78) are inconsistent by sub-proof #2403.
% 228.20/39.72  | | | 
% 228.20/39.72  | | Case 2:
% 228.20/39.72  | | | 
% 228.20/39.72  | | |   (79)  all_57_1 = e0 & op(e3, e2) = e0
% 228.20/39.72  | | | 
% 228.20/39.72  | | | ALPHA: (79) implies:
% 228.20/39.72  | | |   (80)  all_57_1 = e0
% 228.20/39.72  | | | 
% 228.20/39.72  | | | BETA: splitting (73) gives:
% 228.20/39.72  | | | 
% 228.20/39.72  | | | Case 1:
% 228.20/39.72  | | | | 
% 228.20/39.72  | | | |   (81)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2)
% 228.20/39.72  | | | |           = e1)
% 228.20/39.72  | | | | 
% 228.20/39.72  | | | | BETA: splitting (81) gives:
% 228.20/39.72  | | | | 
% 228.20/39.72  | | | | Case 1:
% 228.20/39.72  | | | | | 
% 228.20/39.72  | | | | |   (82)  all_57_1 = e1 & op(e3, e2) = e1
% 228.20/39.72  | | | | | 
% 228.20/39.72  | | | | | REF_CLOSE: (44), (80), (82) are inconsistent by sub-proof #2446.
% 228.20/39.72  | | | | | 
% 228.20/39.72  | | | | Case 2:
% 228.20/39.72  | | | | | 
% 228.20/39.72  | | | | |   (83)  all_57_3 = e1 & op(e2, e2) = e1
% 228.20/39.72  | | | | | 
% 228.20/39.72  | | | | | REF_CLOSE: (25), (44), (83) are inconsistent by sub-proof #2362.
% 228.20/39.72  | | | | | 
% 228.20/39.72  | | | | End of split
% 228.20/39.72  | | | | 
% 228.20/39.72  | | | Case 2:
% 228.20/39.72  | | | | 
% 228.20/39.72  | | | |   (84)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2)
% 228.20/39.72  | | | |           = e1)
% 228.20/39.72  | | | | 
% 228.20/39.72  | | | | BETA: splitting (84) gives:
% 228.20/39.72  | | | | 
% 228.20/39.72  | | | | Case 1:
% 228.20/39.72  | | | | | 
% 228.20/39.72  | | | | |   (85)  all_57_7 = e1 & op(e1, e2) = e1
% 228.20/39.72  | | | | | 
% 228.20/39.72  | | | | | REF_CLOSE: (18), (62), (85) are inconsistent by sub-proof #2190.
% 228.20/39.72  | | | | | 
% 228.20/39.72  | | | | Case 2:
% 228.20/39.72  | | | | | 
% 228.20/39.72  | | | | |   (86)  all_57_13 = e1 & op(e0, e2) = e1
% 228.20/39.72  | | | | | 
% 228.20/39.72  | | | | | ALPHA: (86) implies:
% 228.20/39.72  | | | | |   (87)  all_57_13 = e1
% 228.20/39.72  | | | | | 
% 228.20/39.72  | | | | | BETA: splitting (17) gives:
% 228.20/39.72  | | | | | 
% 228.20/39.72  | | | | | Case 1:
% 228.20/39.72  | | | | | | 
% 228.20/39.72  | | | | | |   (88)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3,
% 228.20/39.72  | | | | | |             e2) = e1)
% 228.20/39.72  | | | | | | 
% 228.20/39.72  | | | | | | REF_CLOSE: (10), (36), (44), (62), (80), (88) are inconsistent by
% 228.20/39.72  | | | | | |            sub-proof #452.
% 228.20/39.72  | | | | | | 
% 228.20/39.72  | | | | | Case 2:
% 228.20/39.72  | | | | | | 
% 228.20/39.72  | | | | | |   (89)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3,
% 228.20/39.72  | | | | | |             e0) = e1)
% 228.20/39.72  | | | | | | 
% 228.20/39.72  | | | | | | BETA: splitting (89) gives:
% 228.20/39.72  | | | | | | 
% 228.20/39.72  | | | | | | Case 1:
% 228.20/39.72  | | | | | | | 
% 228.20/39.72  | | | | | | |   (90)  all_57_4 = e1 & op(e3, e1) = e1
% 228.20/39.72  | | | | | | | 
% 228.20/39.72  | | | | | | | REF_CLOSE: (8), (27), (90) are inconsistent by sub-proof #2484.
% 228.20/39.72  | | | | | | | 
% 228.20/39.72  | | | | | | Case 2:
% 228.20/39.72  | | | | | | | 
% 228.20/39.72  | | | | | | |   (91)  all_57_9 = e1 & op(e3, e0) = e1
% 228.20/39.72  | | | | | | | 
% 228.20/39.72  | | | | | | | ALPHA: (91) implies:
% 228.20/39.72  | | | | | | |   (92)  all_57_9 = e1
% 228.20/39.72  | | | | | | | 
% 228.20/39.72  | | | | | | | BETA: splitting (55) gives:
% 228.20/39.72  | | | | | | | 
% 228.20/39.72  | | | | | | | Case 1:
% 228.20/39.72  | | | | | | | | 
% 228.20/39.72  | | | | | | | |   (93)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 &
% 228.20/39.72  | | | | | | | |           op(e2, e2) = e3)
% 228.20/39.72  | | | | | | | | 
% 228.20/39.72  | | | | | | | | BETA: splitting (93) gives:
% 228.20/39.72  | | | | | | | | 
% 228.20/39.72  | | | | | | | | Case 1:
% 228.20/39.72  | | | | | | | | | 
% 228.20/39.72  | | | | | | | | |   (94)  all_57_2 = e3 & op(e2, e3) = e3
% 228.20/39.72  | | | | | | | | | 
% 228.20/39.72  | | | | | | | | | ALPHA: (94) implies:
% 228.20/39.72  | | | | | | | | |   (95)  all_57_2 = e3
% 228.20/39.72  | | | | | | | | | 
% 228.20/39.72  | | | | | | | | | BETA: splitting (5) gives:
% 228.20/39.72  | | | | | | | | | 
% 228.20/39.72  | | | | | | | | | Case 1:
% 228.20/39.72  | | | | | | | | | | 
% 228.20/39.72  | | | | | | | | | |   (96)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 &
% 228.20/39.72  | | | | | | | | | |           op(e2, e3) = e1)
% 228.20/39.72  | | | | | | | | | | 
% 228.20/39.72  | | | | | | | | | | REF_CLOSE: (4), (8), (10), (13), (14), (25), (27), (28),
% 228.20/39.72  | | | | | | | | | |            (30), (35), (36), (37), (38), (41), (44), (47),
% 228.20/39.72  | | | | | | | | | |            (52), (53), (62), (95), (96) are inconsistent by
% 228.20/39.72  | | | | | | | | | |            sub-proof #450.
% 228.20/39.72  | | | | | | | | | | 
% 228.20/39.72  | | | | | | | | | Case 2:
% 228.20/39.72  | | | | | | | | | | 
% 228.20/39.72  | | | | | | | | | |   (97)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1
% 228.20/39.72  | | | | | | | | | |           & op(e0, e3) = e1)
% 228.20/39.72  | | | | | | | | | | 
% 228.20/39.72  | | | | | | | | | | BETA: splitting (97) gives:
% 228.20/39.72  | | | | | | | | | | 
% 228.20/39.72  | | | | | | | | | | Case 1:
% 228.20/39.72  | | | | | | | | | | | 
% 228.20/39.72  | | | | | | | | | | |   (98)  all_57_6 = e1 & op(e1, e3) = e1
% 228.20/39.72  | | | | | | | | | | | 
% 228.20/39.72  | | | | | | | | | | | ALPHA: (98) implies:
% 228.20/39.72  | | | | | | | | | | |   (99)  all_57_6 = e1
% 228.20/39.72  | | | | | | | | | | | 
% 228.20/39.72  | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (10), (11), (13), (14), (25),
% 228.20/39.72  | | | | | | | | | | |            (28), (30), (35), (38), (41), (43), (44), (47),
% 228.20/39.72  | | | | | | | | | | |            (48), (52), (53), (55), (58), (60), (62), (63),
% 228.20/39.72  | | | | | | | | | | |            (66), (69), (70), (73), (75), (80), (95), (99) are
% 228.20/39.72  | | | | | | | | | | |            inconsistent by sub-proof #537.
% 228.20/39.72  | | | | | | | | | | | 
% 228.20/39.72  | | | | | | | | | | Case 2:
% 228.20/39.72  | | | | | | | | | | | 
% 228.20/39.72  | | | | | | | | | | |   (100)  all_57_12 = e1 & op(e0, e3) = e1
% 228.20/39.72  | | | | | | | | | | | 
% 228.20/39.72  | | | | | | | | | | | ALPHA: (100) implies:
% 228.20/39.72  | | | | | | | | | | |   (101)  all_57_12 = e1
% 228.20/39.72  | | | | | | | | | | | 
% 228.20/39.72  | | | | | | | | | | | BETA: splitting (48) gives:
% 228.20/39.72  | | | | | | | | | | | 
% 228.20/39.72  | | | | | | | | | | | Case 1:
% 228.20/39.72  | | | | | | | | | | | | 
% 228.20/39.72  | | | | | | | | | | | |   (102)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 228.20/39.72  | | | | | | | | | | | |            & op(e2, e2) = e3)
% 228.20/39.72  | | | | | | | | | | | | 
% 228.20/39.72  | | | | | | | | | | | | REF_CLOSE: (4), (8), (25), (28), (30), (41), (44), (55),
% 228.20/39.72  | | | | | | | | | | | |            (60), (62), (80), (95), (102) are inconsistent by
% 228.20/39.72  | | | | | | | | | | | |            sub-proof #542.
% 228.20/39.72  | | | | | | | | | | | | 
% 228.20/39.72  | | | | | | | | | | | Case 2:
% 228.20/39.72  | | | | | | | | | | | | 
% 228.20/39.72  | | | | | | | | | | | |   (103)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 228.20/39.72  | | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 228.20/39.72  | | | | | | | | | | | | 
% 228.20/39.72  | | | | | | | | | | | | BETA: splitting (103) gives:
% 228.20/39.72  | | | | | | | | | | | | 
% 228.20/39.72  | | | | | | | | | | | | Case 1:
% 228.20/39.72  | | | | | | | | | | | | | 
% 228.20/39.72  | | | | | | | | | | | | |   (104)  all_57_7 = e3 & op(e1, e2) = e3
% 228.20/39.72  | | | | | | | | | | | | | 
% 228.20/39.72  | | | | | | | | | | | | | ALPHA: (104) implies:
% 228.20/39.72  | | | | | | | | | | | | |   (105)  all_57_7 = e3
% 228.20/39.72  | | | | | | | | | | | | | 
% 228.20/39.72  | | | | | | | | | | | | | REF_CLOSE: (7), (25), (28), (41), (62), (80), (87), (105) are
% 228.20/39.72  | | | | | | | | | | | | |            inconsistent by sub-proof #2099.
% 228.20/39.72  | | | | | | | | | | | | | 
% 228.20/39.72  | | | | | | | | | | | | Case 2:
% 228.20/39.72  | | | | | | | | | | | | | 
% 228.20/39.72  | | | | | | | | | | | | |   (106)  all_57_13 = e3 & op(e0, e2) = e3
% 228.20/39.72  | | | | | | | | | | | | | 
% 228.20/39.72  | | | | | | | | | | | | | ALPHA: (106) implies:
% 228.20/39.72  | | | | | | | | | | | | |   (107)  all_57_13 = e3
% 228.20/39.72  | | | | | | | | | | | | | 
% 228.20/39.72  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (10), (11), (13), (14), (25),
% 228.20/39.72  | | | | | | | | | | | | |            (28), (30), (35), (36), (37), (41), (44), (52),
% 228.20/39.72  | | | | | | | | | | | | |            (53), (55), (60), (61), (62), (63), (66), (69),
% 228.20/39.72  | | | | | | | | | | | | |            (70), (73), (80), (101), (107) are inconsistent by
% 228.20/39.72  | | | | | | | | | | | | |            sub-proof #522.
% 228.20/39.72  | | | | | | | | | | | | | 
% 228.20/39.72  | | | | | | | | | | | | End of split
% 228.20/39.72  | | | | | | | | | | | | 
% 228.20/39.72  | | | | | | | | | | | End of split
% 228.20/39.72  | | | | | | | | | | | 
% 228.20/39.72  | | | | | | | | | | End of split
% 228.20/39.72  | | | | | | | | | | 
% 228.20/39.72  | | | | | | | | | End of split
% 228.20/39.72  | | | | | | | | | 
% 228.20/39.72  | | | | | | | | Case 2:
% 228.20/39.72  | | | | | | | | | 
% 228.20/39.72  | | | | | | | | |   (108)  all_57_3 = e3 & op(e2, e2) = e3
% 228.20/39.72  | | | | | | | | | 
% 228.20/39.72  | | | | | | | | | ALPHA: (108) implies:
% 228.20/39.72  | | | | | | | | |   (109)  all_57_3 = e3
% 228.20/39.72  | | | | | | | | | 
% 228.20/39.72  | | | | | | | | | REF_CLOSE: (25), (30), (109) are inconsistent by sub-proof
% 228.20/39.72  | | | | | | | | |            #2358.
% 228.20/39.72  | | | | | | | | | 
% 228.20/39.72  | | | | | | | | End of split
% 228.20/39.72  | | | | | | | | 
% 228.20/39.72  | | | | | | | Case 2:
% 228.20/39.72  | | | | | | | | 
% 228.20/39.72  | | | | | | | |   (110)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 &
% 228.20/39.72  | | | | | | | |            op(e2, e0) = e3)
% 228.20/39.72  | | | | | | | | 
% 228.20/39.72  | | | | | | | | BETA: splitting (110) gives:
% 228.20/39.72  | | | | | | | | 
% 228.20/39.72  | | | | | | | | Case 1:
% 228.20/39.72  | | | | | | | | | 
% 228.20/39.72  | | | | | | | | |   (111)  all_57_5 = e3 & op(e2, e1) = e3
% 228.20/39.72  | | | | | | | | | 
% 228.20/39.72  | | | | | | | | | ALPHA: (111) implies:
% 228.20/39.72  | | | | | | | | |   (112)  all_57_5 = e3
% 228.20/39.72  | | | | | | | | | 
% 228.20/39.72  | | | | | | | | | REF_CLOSE: (8), (51), (112) are inconsistent by sub-proof
% 228.20/39.72  | | | | | | | | |            #2382.
% 228.20/39.72  | | | | | | | | | 
% 228.20/39.72  | | | | | | | | Case 2:
% 228.20/39.72  | | | | | | | | | 
% 228.20/39.72  | | | | | | | | |   (113)  all_57_10 = e3 & op(e2, e0) = e3
% 228.20/39.72  | | | | | | | | | 
% 228.20/39.72  | | | | | | | | | ALPHA: (113) implies:
% 228.20/39.72  | | | | | | | | |   (114)  all_57_10 = e3
% 228.20/39.72  | | | | | | | | | 
% 228.20/39.72  | | | | | | | | | REF_CLOSE: (28), (30), (35), (41), (44), (53), (62), (63),
% 228.20/39.72  | | | | | | | | |            (92), (114) are inconsistent by sub-proof #1985.
% 228.20/39.72  | | | | | | | | | 
% 228.20/39.72  | | | | | | | | End of split
% 228.20/39.72  | | | | | | | | 
% 228.20/39.72  | | | | | | | End of split
% 228.20/39.72  | | | | | | | 
% 228.20/39.72  | | | | | | End of split
% 228.20/39.72  | | | | | | 
% 228.20/39.72  | | | | | End of split
% 228.20/39.72  | | | | | 
% 228.20/39.72  | | | | End of split
% 228.20/39.72  | | | | 
% 228.20/39.72  | | | End of split
% 228.20/39.72  | | | 
% 228.20/39.72  | | End of split
% 228.20/39.72  | | 
% 228.20/39.72  | Case 2:
% 228.20/39.72  | | 
% 228.20/39.72  | |   (115)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) =
% 228.20/39.72  | |            e0)
% 228.20/39.72  | | 
% 228.20/39.72  | | BETA: splitting (115) gives:
% 228.20/39.72  | | 
% 228.20/39.72  | | Case 1:
% 228.20/39.72  | | | 
% 228.20/39.73  | | |   (116)  all_57_4 = e0 & op(e3, e1) = e0
% 228.20/39.73  | | | 
% 228.20/39.73  | | | REF_CLOSE: (27), (30), (116) are inconsistent by sub-proof #2491.
% 228.20/39.73  | | | 
% 228.20/39.73  | | Case 2:
% 228.20/39.73  | | | 
% 228.20/39.73  | | |   (117)  all_57_9 = e0 & op(e3, e0) = e0
% 228.20/39.73  | | | 
% 228.20/39.73  | | | ALPHA: (117) implies:
% 228.20/39.73  | | |   (118)  all_57_9 = e0
% 228.20/39.73  | | | 
% 228.20/39.73  | | | BETA: splitting (55) gives:
% 228.20/39.73  | | | 
% 228.20/39.73  | | | Case 1:
% 228.20/39.73  | | | | 
% 228.20/39.73  | | | |   (119)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2)
% 228.20/39.73  | | | |            = e3)
% 228.20/39.73  | | | | 
% 228.20/39.73  | | | | BETA: splitting (119) gives:
% 228.20/39.73  | | | | 
% 228.20/39.73  | | | | Case 1:
% 228.20/39.73  | | | | | 
% 228.20/39.73  | | | | |   (120)  all_57_2 = e3 & op(e2, e3) = e3
% 228.20/39.73  | | | | | 
% 228.20/39.73  | | | | | ALPHA: (120) implies:
% 228.20/39.73  | | | | |   (121)  all_57_2 = e3
% 228.20/39.73  | | | | | 
% 228.20/39.73  | | | | | BETA: splitting (11) gives:
% 228.20/39.73  | | | | | 
% 228.20/39.73  | | | | | Case 1:
% 228.20/39.73  | | | | | | 
% 228.20/39.73  | | | | | |   (122)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1,
% 228.20/39.73  | | | | | |              e2) = e3)
% 228.20/39.73  | | | | | | 
% 228.20/39.73  | | | | | | BETA: splitting (122) gives:
% 228.20/39.73  | | | | | | 
% 228.20/39.73  | | | | | | Case 1:
% 228.20/39.73  | | | | | | | 
% 228.20/39.73  | | | | | | |   (123)  all_57_6 = e3 & op(e1, e3) = e3
% 228.20/39.73  | | | | | | | 
% 228.20/39.73  | | | | | | | ALPHA: (123) implies:
% 228.20/39.73  | | | | | | |   (124)  all_57_6 = e3
% 228.20/39.73  | | | | | | | 
% 228.20/39.73  | | | | | | | REF_CLOSE: (2), (4), (5), (8), (10), (25), (28), (30), (36), (41),
% 228.20/39.73  | | | | | | |            (44), (55), (60), (62), (69), (121), (124) are
% 228.20/39.73  | | | | | | |            inconsistent by sub-proof #794.
% 228.20/39.73  | | | | | | | 
% 228.20/39.73  | | | | | | Case 2:
% 228.20/39.73  | | | | | | | 
% 228.20/39.73  | | | | | | |   (125)  all_57_7 = e3 & op(e1, e2) = e3
% 228.20/39.73  | | | | | | | 
% 228.20/39.73  | | | | | | | ALPHA: (125) implies:
% 228.20/39.73  | | | | | | |   (126)  all_57_7 = e3
% 228.20/39.73  | | | | | | | 
% 228.20/39.73  | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 228.20/39.73  | | | | | | |            (12), (13), (14), (15), (16), (17), (18), (19), (20),
% 228.20/39.73  | | | | | | |            (21), (22), (23), (24), (25), (26), (28), (29), (30),
% 228.20/39.73  | | | | | | |            (31), (32), (33), (34), (35), (36), (37), (39), (40),
% 228.20/39.73  | | | | | | |            (41), (42), (43), (44), (45), (46), (47), (48), (49),
% 228.20/39.73  | | | | | | |            (50), (52), (53), (54), (55), (56), (57), (58), (59),
% 228.20/39.73  | | | | | | |            (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 228.20/39.73  | | | | | | |            (69), (70), (71), (72), (73), (74), (75), (121), (126)
% 228.20/39.73  | | | | | | |            are inconsistent by sub-proof #532.
% 228.20/39.73  | | | | | | | 
% 228.20/39.73  | | | | | | End of split
% 228.20/39.73  | | | | | | 
% 228.20/39.73  | | | | | Case 2:
% 228.20/39.73  | | | | | | 
% 228.20/39.73  | | | | | |   (127)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 &
% 228.20/39.73  | | | | | |            op(e1, e0) = e3)
% 228.20/39.73  | | | | | | 
% 228.20/39.73  | | | | | | REF_CLOSE: (8), (10), (13), (14), (35), (38), (44), (62), (70),
% 228.20/39.73  | | | | | |            (118), (127) are inconsistent by sub-proof #731.
% 228.20/39.73  | | | | | | 
% 228.20/39.73  | | | | | End of split
% 228.20/39.73  | | | | | 
% 228.20/39.73  | | | | Case 2:
% 228.20/39.73  | | | | | 
% 228.20/39.73  | | | | |   (128)  all_57_3 = e3 & op(e2, e2) = e3
% 228.20/39.73  | | | | | 
% 228.20/39.73  | | | | | ALPHA: (128) implies:
% 228.20/39.73  | | | | |   (129)  all_57_3 = e3
% 228.20/39.73  | | | | | 
% 228.20/39.73  | | | | | REF_CLOSE: (25), (30), (129) are inconsistent by sub-proof #2358.
% 228.20/39.73  | | | | | 
% 228.20/39.73  | | | | End of split
% 228.20/39.73  | | | | 
% 228.20/39.73  | | | Case 2:
% 228.20/39.73  | | | | 
% 228.20/39.73  | | | |   (130)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2,
% 228.20/39.73  | | | |              e0) = e3)
% 228.20/39.73  | | | | 
% 228.20/39.73  | | | | BETA: splitting (130) gives:
% 228.20/39.73  | | | | 
% 228.20/39.73  | | | | Case 1:
% 228.20/39.73  | | | | | 
% 228.20/39.73  | | | | |   (131)  all_57_5 = e3 & op(e2, e1) = e3
% 228.20/39.73  | | | | | 
% 228.20/39.73  | | | | | ALPHA: (131) implies:
% 228.20/39.73  | | | | |   (132)  all_57_5 = e3
% 228.20/39.73  | | | | | 
% 228.20/39.73  | | | | | REF_CLOSE: (8), (51), (132) are inconsistent by sub-proof #2382.
% 228.20/39.73  | | | | | 
% 228.20/39.73  | | | | Case 2:
% 228.20/39.73  | | | | | 
% 228.20/39.73  | | | | |   (133)  all_57_10 = e3 & op(e2, e0) = e3
% 228.20/39.73  | | | | | 
% 228.20/39.73  | | | | | ALPHA: (133) implies:
% 228.20/39.73  | | | | |   (134)  all_57_10 = e3
% 228.20/39.73  | | | | | 
% 228.20/39.73  | | | | | REF_CLOSE: (8), (28), (30), (35), (41), (44), (53), (62), (63), (70),
% 228.20/39.73  | | | | |            (118), (134) are inconsistent by sub-proof #1982.
% 228.20/39.73  | | | | | 
% 228.20/39.73  | | | | End of split
% 228.20/39.73  | | | | 
% 228.20/39.73  | | | End of split
% 228.20/39.73  | | | 
% 228.20/39.73  | | End of split
% 228.20/39.73  | | 
% 228.20/39.73  | End of split
% 228.20/39.73  | 
% 228.20/39.73  End of proof
% 228.20/39.73  
% 228.20/39.73  Sub-proof #450 shows that the following formulas are inconsistent:
% 228.20/39.73  ----------------------------------------------------------------
% 228.20/39.73    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.20/39.73         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.20/39.73    (2)   ~ (e3 = e1)
% 228.20/39.73    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.20/39.73           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.20/39.73    (4)   ~ (all_6_2 = e3)
% 228.20/39.73    (5)  op(e1, e1) = all_6_2
% 228.20/39.73    (6)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1)
% 228.20/39.73    (7)  all_57_3 = e0
% 228.20/39.73    (8)  all_57_4 = e3
% 228.20/39.73    (9)   ~ (e3 = e2)
% 228.20/39.73    (10)   ~ (e3 = e0)
% 228.20/39.73    (11)  all_57_15 = e3
% 228.20/39.73    (12)  op(e3, e3) = e2
% 228.20/39.73    (13)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.20/39.73          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.20/39.73            e1)
% 228.20/39.73    (14)  all_57_10 = e2
% 228.20/39.73    (15)   ~ (e2 = e0)
% 228.20/39.73    (16)  all_57_2 = e3
% 228.20/39.73    (17)   ~ (e1 = e0)
% 228.20/39.73    (18)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.20/39.73          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.20/39.73    (19)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.20/39.73          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.20/39.73            e2)
% 228.20/39.73    (20)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.20/39.73              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.20/39.73                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.20/39.73                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.20/39.73    (21)   ~ (e2 = e1)
% 228.20/39.73  
% 228.20/39.73  Begin of proof
% 228.20/39.73  | 
% 228.20/39.73  | BETA: splitting (6) gives:
% 228.20/39.73  | 
% 228.20/39.73  | Case 1:
% 228.20/39.73  | | 
% 228.20/39.73  | |   (22)  all_57_0 = e1 & op(e3, e3) = e1
% 228.20/39.73  | | 
% 228.20/39.73  | | ALPHA: (22) implies:
% 228.20/39.73  | |   (23)  op(e3, e3) = e1
% 228.20/39.73  | | 
% 228.20/39.73  | | REF_CLOSE: (3), (12), (21), (23) are inconsistent by sub-proof #1950.
% 228.20/39.73  | | 
% 228.20/39.73  | Case 2:
% 228.20/39.73  | | 
% 228.20/39.73  | |   (24)  all_57_2 = e1 & op(e2, e3) = e1
% 228.20/39.73  | | 
% 228.20/39.73  | | ALPHA: (24) implies:
% 228.20/39.73  | |   (25)  all_57_2 = e1
% 228.20/39.73  | | 
% 228.20/39.73  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (13), (14),
% 228.20/39.73  | |            (15), (16), (17), (18), (19), (20), (21), (25) are inconsistent
% 228.20/39.73  | |            by sub-proof #451.
% 228.20/39.73  | | 
% 228.20/39.73  | End of split
% 228.20/39.73  | 
% 228.20/39.73  End of proof
% 228.20/39.73  
% 228.20/39.73  Sub-proof #451 shows that the following formulas are inconsistent:
% 228.20/39.73  ----------------------------------------------------------------
% 228.20/39.73    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.20/39.73         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.20/39.73    (2)   ~ (e3 = e1)
% 228.20/39.73    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.20/39.73           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.20/39.73    (4)   ~ (all_6_2 = e3)
% 228.20/39.73    (5)  op(e1, e1) = all_6_2
% 228.20/39.73    (6)  all_57_3 = e0
% 228.20/39.73    (7)  all_57_4 = e3
% 228.20/39.73    (8)   ~ (e3 = e2)
% 228.20/39.73    (9)   ~ (e3 = e0)
% 228.20/39.73    (10)  all_57_15 = e3
% 228.20/39.73    (11)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.20/39.73          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.20/39.73            e1)
% 228.20/39.73    (12)  all_57_10 = e2
% 228.20/39.73    (13)   ~ (e2 = e0)
% 228.20/39.73    (14)  all_57_2 = e3
% 228.20/39.73    (15)   ~ (e1 = e0)
% 228.20/39.73    (16)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.20/39.73          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.20/39.73    (17)  all_57_2 = e1
% 228.20/39.73    (18)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.20/39.73          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.20/39.73            e2)
% 228.20/39.73    (19)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.20/39.73              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.20/39.73                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.20/39.73                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.20/39.73    (20)   ~ (e2 = e1)
% 228.20/39.73  
% 228.20/39.73  Begin of proof
% 228.20/39.73  | 
% 228.20/39.73  | COMBINE_EQS: (14), (17) imply:
% 228.20/39.73  |   (21)  e3 = e1
% 228.20/39.73  | 
% 228.20/39.73  | SIMP: (21) implies:
% 228.20/39.73  |   (22)  e3 = e1
% 228.20/39.73  | 
% 228.20/39.73  | COMBINE_EQS: (7), (22) imply:
% 228.20/39.73  |   (23)  all_57_4 = e1
% 228.20/39.73  | 
% 228.20/39.73  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13),
% 228.20/39.73  |            (14), (15), (16), (18), (19), (20), (23) are inconsistent by
% 228.20/39.73  |            sub-proof #1755.
% 228.20/39.73  | 
% 228.20/39.73  End of proof
% 228.20/39.73  
% 228.20/39.73  Sub-proof #452 shows that the following formulas are inconsistent:
% 228.20/39.73  ----------------------------------------------------------------
% 228.20/39.73    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.20/39.73           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.20/39.73    (2)  all_57_1 = e0
% 228.20/39.73    (3)  op(e3, e3) = e2
% 228.20/39.73    (4)   ~ (e1 = e0)
% 228.20/39.73    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1)
% 228.20/39.73    (6)   ~ (e2 = e1)
% 228.20/39.73  
% 228.20/39.73  Begin of proof
% 228.20/39.73  | 
% 228.20/39.73  | BETA: splitting (5) gives:
% 228.20/39.73  | 
% 228.20/39.73  | Case 1:
% 228.20/39.73  | | 
% 228.20/39.73  | |   (7)  all_57_0 = e1 & op(e3, e3) = e1
% 228.20/39.73  | | 
% 228.20/39.73  | | ALPHA: (7) implies:
% 228.20/39.73  | |   (8)  op(e3, e3) = e1
% 228.20/39.73  | | 
% 228.20/39.73  | | REF_CLOSE: (1), (3), (6), (8) are inconsistent by sub-proof #1950.
% 228.20/39.73  | | 
% 228.20/39.73  | Case 2:
% 228.20/39.73  | | 
% 228.20/39.73  | |   (9)  all_57_1 = e1 & op(e3, e2) = e1
% 228.20/39.73  | | 
% 228.20/39.73  | | REF_CLOSE: (2), (4), (9) are inconsistent by sub-proof #2446.
% 228.20/39.73  | | 
% 228.20/39.73  | End of split
% 228.20/39.73  | 
% 228.20/39.73  End of proof
% 228.20/39.73  
% 228.20/39.73  Sub-proof #453 shows that the following formulas are inconsistent:
% 228.20/39.73  ----------------------------------------------------------------
% 228.20/39.73    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.20/39.73    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.20/39.73    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.20/39.73         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.20/39.73    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.20/39.73         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.20/39.73    (5)   ~ (all_53_8 = all_53_12)
% 228.20/39.73    (6)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.20/39.73         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.20/39.73    (7)   ~ (e3 = e1)
% 228.20/39.73    (8)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.20/39.73         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.20/39.73    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.20/39.73           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.20/39.73    (10)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.20/39.73          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.20/39.73    (11)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.20/39.73            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.20/39.73              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.20/39.73    (12)   ~ (all_6_2 = e3)
% 228.20/39.73    (13)  op(e1, e1) = all_6_2
% 228.20/39.73    (14)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.20/39.73    (15)   ~ (all_53_9 = e0)
% 228.20/39.73    (16)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.20/39.73          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.20/39.73    (17)   ~ (all_53_4 = all_53_12)
% 228.20/39.73    (18)   ~ (all_53_8 = all_53_9)
% 228.20/39.73    (19)  all_42_2 = all_6_2
% 228.20/39.73    (20)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.20/39.73          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.20/39.73    (21)   ~ (all_53_9 = all_6_2)
% 228.20/39.73    (22)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.20/39.73          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.20/39.73    (23)  all_57_3 = e0
% 228.20/39.73    (24)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.20/39.73          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.20/39.73    (25)   ~ (e3 = e2)
% 228.20/39.73    (26)  all_55_1 = all_53_4
% 228.20/39.73    (27)   ~ (e3 = e0)
% 228.20/39.73    (28)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.20/39.73          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.20/39.73    (29)   ~ (all_53_8 = all_6_2)
% 228.20/39.73    (30)  all_55_2 = all_53_8
% 228.20/39.73    (31)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.20/39.73    (32)  all_57_15 = e3
% 228.20/39.73    (33)  op(e3, e3) = e2
% 228.20/39.73    (34)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.20/39.73          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.20/39.73            e1)
% 228.20/39.73    (35)  all_57_5 = e3
% 228.20/39.73    (36)   ~ (all_53_4 = all_53_8)
% 228.20/39.73    (37)  op(e3, e2) = all_53_4
% 228.20/39.73    (38)  op(e1, e1) = e1
% 228.20/39.73    (39)   ~ (e2 = e0)
% 228.20/39.73    (40)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.20/39.73            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.20/39.73            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.20/39.73            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.20/39.73              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.20/39.73            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.20/39.73            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.20/39.73              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.20/39.73              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.20/39.73            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.20/39.73            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.20/39.73            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.20/39.73              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.20/39.73              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.20/39.73            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.20/39.73              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.20/39.73            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.20/39.73            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.20/39.73              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.20/39.73              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.20/39.73            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.20/39.73            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.20/39.73    (41)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.20/39.73          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.20/39.73    (42)   ~ (e1 = e0)
% 228.20/39.73    (43)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.20/39.73            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.20/39.73              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.20/39.73    (44)   ~ (all_53_4 = e0)
% 228.20/39.73    (45)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.20/39.73          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.20/39.73    (46)  all_57_6 = e3
% 228.20/39.73    (47)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.20/39.73          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.20/39.73    (48)  op(e0, e0) = e3
% 228.20/39.73    (49)   ~ (all_53_4 = all_53_6)
% 228.20/39.73    (50)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.20/39.73          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.20/39.73            e2)
% 228.20/39.73    (51)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.20/39.73              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.20/39.73                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.20/39.73                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.20/39.73    (52)  op(e1, e1) = e0
% 228.20/39.73    (53)  all_55_10 = all_6_2
% 228.20/39.73    (54)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.20/39.73          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.20/39.73    (55)  all_38_2 = all_6_2
% 228.20/39.73    (56)  all_55_3 = all_53_12
% 228.20/39.73    (57)   ~ (all_53_12 = e3)
% 228.20/39.73    (58)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.20/39.73            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.20/39.73              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.20/39.73    (59)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.20/39.73          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.20/39.73    (60)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.20/39.73          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.20/39.73    (61)   ~ (e2 = e1)
% 228.20/39.73    (62)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.20/39.73          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.20/39.73    (63)  op(e2, e1) = all_53_9
% 228.20/39.73    (64)  op(e1, e2) = all_53_6
% 228.20/39.73    (65)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.20/39.73          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.20/39.73    (66)  all_24_2 = all_6_2
% 228.20/39.73    (67)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.20/39.73          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.20/39.73    (68)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.20/39.73          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.20/39.73    (69)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.20/39.73          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.20/39.73    (70)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.20/39.73          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.20/39.73    (71)  op(e3, e1) = all_53_8
% 228.20/39.73    (72)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.20/39.73          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.20/39.73    (73)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.20/39.73          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.20/39.73    (74)  op(e3, e0) = all_53_12
% 228.20/39.73  
% 228.20/39.73  Begin of proof
% 228.20/39.73  | 
% 228.20/39.73  | BETA: splitting (4) gives:
% 228.20/39.73  | 
% 228.20/39.73  | Case 1:
% 228.20/39.73  | | 
% 228.20/39.73  | |   (75)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) =
% 228.20/39.73  | |           e1)
% 228.20/39.73  | | 
% 228.20/39.73  | | BETA: splitting (75) gives:
% 228.20/39.73  | | 
% 228.20/39.73  | | Case 1:
% 228.20/39.73  | | | 
% 228.20/39.73  | | |   (76)  all_57_0 = e1 & op(e3, e3) = e1
% 228.20/39.73  | | | 
% 228.20/39.73  | | | ALPHA: (76) implies:
% 228.20/39.73  | | |   (77)  op(e3, e3) = e1
% 228.20/39.73  | | | 
% 228.20/39.73  | | | REF_CLOSE: (9), (33), (61), (77) are inconsistent by sub-proof #1950.
% 228.20/39.73  | | | 
% 228.20/39.73  | | Case 2:
% 228.20/39.73  | | | 
% 228.20/39.73  | | |   (78)  all_57_2 = e1 & op(e2, e3) = e1
% 228.20/39.73  | | | 
% 228.20/39.73  | | | ALPHA: (78) implies:
% 228.20/39.73  | | |   (79)  all_57_2 = e1
% 228.20/39.73  | | | 
% 228.20/39.73  | | | GROUND_INST: instantiating (9) with e0, e1, e1, e1, simplifying with (38),
% 228.20/39.73  | | |              (52) gives:
% 228.20/39.73  | | |   (80)  e1 = e0
% 228.20/39.73  | | | 
% 228.20/39.73  | | | COMBINE_EQS: (79), (80) imply:
% 228.20/39.73  | | |   (81)  all_57_2 = e0
% 228.20/39.73  | | | 
% 228.20/39.73  | | | REF_CLOSE: (3), (7), (23), (25), (35), (39), (42), (59), (61), (81) are
% 228.20/39.73  | | |            inconsistent by sub-proof #2253.
% 228.20/39.73  | | | 
% 228.20/39.73  | | End of split
% 228.20/39.73  | | 
% 228.20/39.73  | Case 2:
% 228.20/39.73  | | 
% 228.20/39.73  | |   (82)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) =
% 228.20/39.73  | |           e1)
% 228.20/39.73  | | 
% 228.20/39.73  | | BETA: splitting (82) gives:
% 228.20/39.73  | | 
% 228.20/39.73  | | Case 1:
% 228.20/39.73  | | | 
% 228.20/39.73  | | |   (83)  all_57_6 = e1 & op(e1, e3) = e1
% 228.20/39.73  | | | 
% 228.20/39.73  | | | ALPHA: (83) implies:
% 228.20/39.73  | | |   (84)  all_57_6 = e1
% 228.20/39.73  | | | 
% 228.20/39.73  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.20/39.73  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 228.20/39.73  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 228.20/39.73  | | |            (33), (34), (36), (37), (38), (39), (40), (41), (42), (43),
% 228.20/39.73  | | |            (44), (45), (47), (48), (49), (50), (51), (53), (54), (55),
% 228.20/39.73  | | |            (56), (57), (58), (59), (60), (61), (62), (63), (64), (65),
% 228.20/39.73  | | |            (66), (67), (68), (69), (70), (71), (72), (73), (74), (84) are
% 228.20/39.73  | | |            inconsistent by sub-proof #523.
% 228.20/39.73  | | | 
% 228.20/39.73  | | Case 2:
% 228.20/39.73  | | | 
% 228.20/39.73  | | |   (85)  all_57_12 = e1 & op(e0, e3) = e1
% 228.20/39.73  | | | 
% 228.20/39.73  | | | ALPHA: (85) implies:
% 228.20/39.73  | | |   (86)  all_57_12 = e1
% 228.20/39.73  | | | 
% 228.20/39.73  | | | REF_CLOSE: (3), (7), (9), (23), (25), (27), (33), (35), (39), (42), (46),
% 228.20/39.73  | | |            (59), (61), (68), (86) are inconsistent by sub-proof #810.
% 228.20/39.73  | | | 
% 228.20/39.73  | | End of split
% 228.20/39.73  | | 
% 228.20/39.73  | End of split
% 228.20/39.73  | 
% 228.20/39.73  End of proof
% 228.20/39.73  
% 228.20/39.73  Sub-proof #454 shows that the following formulas are inconsistent:
% 228.20/39.73  ----------------------------------------------------------------
% 228.20/39.73    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.20/39.73    (2)  all_57_0 = e2
% 228.20/39.73    (3)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.20/39.73    (4)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.20/39.73         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.20/39.73    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.20/39.73         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.20/39.73    (6)   ~ (all_53_8 = all_53_12)
% 228.20/39.73    (7)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.20/39.73         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.20/39.73    (8)   ~ (all_53_8 = all_53_11)
% 228.20/39.73    (9)   ~ (e3 = e1)
% 228.20/39.73    (10)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.20/39.73          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.20/39.73    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.20/39.73            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.20/39.73    (12)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.20/39.73          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.20/39.73    (13)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.20/39.73            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.20/39.73              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.20/39.73    (14)   ~ (all_53_3 = e3)
% 228.20/39.73    (15)   ~ (all_6_2 = e3)
% 228.20/39.73    (16)  ( ~ (all_28_0 = e0) & op(all_28_1, e3) = all_28_0 & op(e3, e2) =
% 228.20/39.73            all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 = e1) & op(e3,
% 228.20/39.73              e2) = all_28_1 & $i(all_28_1))
% 228.20/39.73    (17)   ~ (all_53_9 = e1)
% 228.20/39.73    (18)  op(e1, e1) = all_6_2
% 228.20/39.73    (19)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.20/39.73    (20)   ~ (all_53_1 = all_53_9)
% 228.20/39.73    (21)   ~ (all_53_9 = e0)
% 228.20/39.73    (22)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 228.20/39.73    (23)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.20/39.73          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.20/39.73    (24)   ~ (all_52_17 = e2)
% 228.20/39.73    (25)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 228.20/39.73            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 228.20/39.73              e3) = all_22_1 & $i(all_22_1))
% 228.20/39.73    (26)   ~ (all_53_8 = e1)
% 228.20/39.73    (27)  op(all_52_17, all_52_17) = e3
% 228.20/39.73    (28)   ~ (all_53_4 = all_53_12)
% 228.20/39.73    (29)   ~ (all_52_17 = all_52_23)
% 228.20/39.73    (30)   ~ (all_52_17 = e1)
% 228.20/39.73    (31)   ~ (all_53_8 = all_53_9)
% 228.20/39.73    (32)  all_42_2 = all_6_2
% 228.20/39.73    (33)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.20/39.73          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.20/39.73    (34)   ~ (all_53_9 = all_53_11)
% 228.20/39.73    (35)  all_55_4 = all_53_1
% 228.20/39.73    (36)   ~ (all_53_9 = all_6_2)
% 228.20/39.73    (37)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.20/39.73          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.20/39.73    (38)  all_57_3 = e0
% 228.20/39.73    (39)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.20/39.73          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.20/39.73    (40)   ~ (e3 = e2)
% 228.20/39.73    (41)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 228.20/39.73    (42)  all_55_1 = all_53_4
% 228.20/39.73    (43)   ~ (all_53_1 = all_53_3)
% 228.20/39.73    (44)   ~ (all_53_1 = all_52_17)
% 228.20/39.73    (45)   ~ (e3 = e0)
% 228.20/39.73    (46)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.20/39.73          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.20/39.73    (47)   ~ (all_53_8 = all_6_2)
% 228.20/39.73    (48)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.20/39.74    (49)  all_55_11 = all_52_23
% 228.20/39.74    (50)  all_55_2 = all_53_8
% 228.20/39.74    (51)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 228.20/39.74    (52)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.20/39.74    (53)  all_57_15 = e3
% 228.20/39.74    (54)  op(e3, e3) = e2
% 228.20/39.74    (55)   ~ (all_53_3 = e2)
% 228.20/39.74    (56)   ~ (all_53_3 = all_52_17)
% 228.20/39.74    (57)  all_57_4 = e1
% 228.20/39.74    (58)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.20/39.74          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.20/39.74            e1)
% 228.20/39.74    (59)  all_57_10 = e2
% 228.20/39.74    (60)   ~ (all_52_23 = e3)
% 228.20/39.74    (61)  op(e1, e0) = all_52_23
% 228.20/39.74    (62)   ~ (all_53_4 = all_53_8)
% 228.20/39.74    (63)  all_55_6 = all_53_9
% 228.20/39.74    (64)  op(e3, e2) = all_53_4
% 228.20/39.74    (65)   ~ (e2 = e0)
% 228.20/39.74    (66)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.20/39.74            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.20/39.74            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.20/39.74            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.20/39.74              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.20/39.74            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.20/39.74            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.20/39.74              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.20/39.74              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.20/39.74            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.20/39.74            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.20/39.74            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.20/39.74              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.20/39.74              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.20/39.74            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.20/39.74              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.20/39.74            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.20/39.74            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.20/39.74              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.20/39.74              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.20/39.74            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.20/39.74            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.20/39.74    (67)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 228.20/39.74            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 228.20/39.74              e3) = all_12_1 & $i(all_12_1))
% 228.20/39.74    (68)  all_55_12 = all_53_3
% 228.20/39.74    (69)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.20/39.74          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.20/39.74    (70)   ~ (all_53_1 = e0)
% 228.20/39.74    (71)   ~ (e1 = e0)
% 228.20/39.74    (72)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.20/39.74            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.20/39.74              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.20/39.74    (73)   ~ (all_53_4 = e0)
% 228.20/39.74    (74)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.20/39.74          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.20/39.74    (75)  all_57_8 = e2
% 228.20/39.74    (76)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.20/39.74          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.20/39.74    (77)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 228.20/39.74    (78)  op(e0, e0) = e3
% 228.20/39.74    (79)   ~ (all_53_4 = all_53_6)
% 228.20/39.74    (80)  ( ~ (all_20_0 = e1) & op(all_20_1, e3) = all_20_0 & op(e3, e2) =
% 228.20/39.74            all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e0) & op(e3,
% 228.20/39.74              e2) = all_20_1 & $i(all_20_1))
% 228.20/39.74    (81)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.20/39.74          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.20/39.74            e2)
% 228.20/39.74    (82)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.20/39.74              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.20/39.74                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.20/39.74                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.20/39.74    (83)  all_55_10 = all_6_2
% 228.20/39.74    (84)   ~ (all_53_11 = e1)
% 228.20/39.74    (85)  all_55_8 = all_52_17
% 228.20/39.74    (86)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.20/39.74          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.20/39.74    (87)  all_38_2 = all_6_2
% 228.20/39.74    (88)  all_55_3 = all_53_12
% 228.20/39.74    (89)   ~ (all_53_12 = e3)
% 228.20/39.74    (90)   ~ (all_53_4 = e2)
% 228.20/39.74    (91)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.20/39.74            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.20/39.74              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.20/39.74    (92)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.20/39.74          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.20/39.74    (93)  all_57_11 = e1
% 228.20/39.74    (94)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.20/39.74          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.20/39.74    (95)   ~ (all_52_23 = e1)
% 228.20/39.74    (96)   ~ (all_53_1 = e2)
% 228.20/39.74    (97)   ~ (e2 = e1)
% 228.20/39.74    (98)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.20/39.74          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.20/39.74    (99)  op(e2, e1) = all_53_9
% 228.20/39.74    (100)  op(e1, e2) = all_53_6
% 228.20/39.74    (101)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.20/39.74           (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.20/39.74    (102)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 228.20/39.74    (103)  all_24_2 = all_6_2
% 228.20/39.74    (104)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.20/39.74           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.20/39.74    (105)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.20/39.74           (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.20/39.74    (106)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.20/39.74           | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.20/39.74             e1)
% 228.20/39.74    (107)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.20/39.74           (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.20/39.74    (108)  all_55_14 = all_53_11
% 228.20/39.74    (109)  op(e3, e1) = all_53_8
% 228.20/39.74    (110)   ~ (all_53_11 = e3)
% 228.20/39.74    (111)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.20/39.74           (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.20/39.74    (112)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.20/39.74           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.20/39.74    (113)  op(e3, e0) = all_53_12
% 228.20/39.74  
% 228.20/39.74  Begin of proof
% 228.20/39.74  | 
% 228.20/39.74  | BETA: splitting (74) gives:
% 228.20/39.74  | 
% 228.20/39.74  | Case 1:
% 228.20/39.74  | | 
% 228.20/39.74  | |   (114)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) =
% 228.20/39.74  | |            e3)
% 228.20/39.74  | | 
% 228.20/39.74  | | BETA: splitting (114) gives:
% 228.20/39.74  | | 
% 228.20/39.74  | | Case 1:
% 228.20/39.74  | | | 
% 228.20/39.74  | | |   (115)  all_57_4 = e3 & op(e3, e1) = e3
% 228.20/39.74  | | | 
% 228.20/39.74  | | | ALPHA: (115) implies:
% 228.20/39.74  | | |   (116)  all_57_4 = e3
% 228.20/39.74  | | | 
% 228.20/39.74  | | | REF_CLOSE: (9), (57), (116) are inconsistent by sub-proof #2426.
% 228.20/39.74  | | | 
% 228.20/39.74  | | Case 2:
% 228.20/39.74  | | | 
% 228.20/39.74  | | |   (117)  all_57_5 = e3 & op(e2, e1) = e3
% 228.20/39.74  | | | 
% 228.20/39.74  | | | ALPHA: (117) implies:
% 228.20/39.74  | | |   (118)  all_57_5 = e3
% 228.20/39.74  | | |   (119)  op(e2, e1) = e3
% 228.20/39.74  | | | 
% 228.20/39.74  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.20/39.74  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 228.20/39.74  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 228.20/39.74  | | |            (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 228.20/39.74  | | |            (43), (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 228.20/39.74  | | |            (53), (54), (55), (56), (57), (58), (59), (60), (61), (62),
% 228.20/39.74  | | |            (63), (64), (65), (66), (67), (68), (69), (70), (71), (72),
% 228.20/39.74  | | |            (73), (74), (75), (76), (77), (78), (79), (80), (81), (82),
% 228.20/39.74  | | |            (83), (84), (85), (86), (87), (88), (89), (90), (91), (92),
% 228.20/39.74  | | |            (93), (94), (95), (96), (97), (98), (99), (100), (101), (102),
% 228.20/39.74  | | |            (103), (104), (105), (106), (107), (108), (109), (110), (111),
% 228.20/39.74  | | |            (112), (113), (118), (119) are inconsistent by sub-proof #455.
% 228.20/39.74  | | | 
% 228.20/39.74  | | End of split
% 228.20/39.74  | | 
% 228.20/39.74  | Case 2:
% 228.20/39.74  | | 
% 228.20/39.74  | |   (120)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) =
% 228.20/39.74  | |            e3)
% 228.20/39.74  | | 
% 228.20/39.74  | | REF_CLOSE: (9), (11), (15), (18), (40), (45), (53), (58), (65), (71), (81),
% 228.20/39.74  | |            (82), (97), (120) are inconsistent by sub-proof #1794.
% 228.20/39.74  | | 
% 228.20/39.74  | End of split
% 228.20/39.74  | 
% 228.20/39.74  End of proof
% 228.20/39.74  
% 228.20/39.74  Sub-proof #455 shows that the following formulas are inconsistent:
% 228.20/39.74  ----------------------------------------------------------------
% 228.20/39.74    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.20/39.74    (2)  all_57_0 = e2
% 228.20/39.74    (3)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.20/39.74    (4)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.20/39.74         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.20/39.74    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.20/39.74         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.20/39.74    (6)  op(e2, e1) = e3
% 228.20/39.74    (7)   ~ (all_53_8 = all_53_12)
% 228.20/39.74    (8)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.20/39.74         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.20/39.74    (9)   ~ (all_53_8 = all_53_11)
% 228.20/39.74    (10)   ~ (e3 = e1)
% 228.20/39.74    (11)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.20/39.74          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.20/39.74    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.20/39.74            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.20/39.74    (13)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.20/39.74          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.20/39.74    (14)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.20/39.74            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.20/39.74              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.20/39.74    (15)   ~ (all_53_3 = e3)
% 228.20/39.74    (16)   ~ (all_6_2 = e3)
% 228.20/39.74    (17)  ( ~ (all_28_0 = e0) & op(all_28_1, e3) = all_28_0 & op(e3, e2) =
% 228.20/39.74            all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 = e1) & op(e3,
% 228.20/39.74              e2) = all_28_1 & $i(all_28_1))
% 228.20/39.74    (18)   ~ (all_53_9 = e1)
% 228.20/39.74    (19)  op(e1, e1) = all_6_2
% 228.20/39.74    (20)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.20/39.74    (21)   ~ (all_53_1 = all_53_9)
% 228.20/39.74    (22)   ~ (all_53_9 = e0)
% 228.20/39.74    (23)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 228.20/39.74    (24)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.20/39.74          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.20/39.74    (25)   ~ (all_52_17 = e2)
% 228.20/39.74    (26)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 228.20/39.74            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 228.20/39.74              e3) = all_22_1 & $i(all_22_1))
% 228.20/39.74    (27)   ~ (all_53_8 = e1)
% 228.20/39.74    (28)  op(all_52_17, all_52_17) = e3
% 228.20/39.74    (29)   ~ (all_53_4 = all_53_12)
% 228.20/39.74    (30)   ~ (all_52_17 = all_52_23)
% 228.20/39.74    (31)   ~ (all_52_17 = e1)
% 228.20/39.74    (32)   ~ (all_53_8 = all_53_9)
% 228.20/39.74    (33)  all_42_2 = all_6_2
% 228.20/39.74    (34)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.20/39.74          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.20/39.74    (35)   ~ (all_53_9 = all_53_11)
% 228.20/39.74    (36)  all_55_4 = all_53_1
% 228.20/39.74    (37)   ~ (all_53_9 = all_6_2)
% 228.20/39.74    (38)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.20/39.74          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.20/39.74    (39)  all_57_3 = e0
% 228.20/39.74    (40)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.20/39.74          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.20/39.74    (41)   ~ (e3 = e2)
% 228.20/39.74    (42)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 228.20/39.74    (43)  all_55_1 = all_53_4
% 228.20/39.74    (44)   ~ (all_53_1 = all_53_3)
% 228.20/39.74    (45)   ~ (all_53_1 = all_52_17)
% 228.20/39.74    (46)   ~ (e3 = e0)
% 228.20/39.74    (47)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.20/39.74          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.20/39.74    (48)   ~ (all_53_8 = all_6_2)
% 228.20/39.74    (49)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.20/39.74    (50)  all_55_11 = all_52_23
% 228.20/39.74    (51)  all_55_2 = all_53_8
% 228.20/39.74    (52)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 228.20/39.74    (53)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.20/39.74    (54)  all_57_15 = e3
% 228.20/39.74    (55)  op(e3, e3) = e2
% 228.20/39.74    (56)   ~ (all_53_3 = e2)
% 228.20/39.74    (57)   ~ (all_53_3 = all_52_17)
% 228.20/39.74    (58)  all_57_4 = e1
% 228.20/39.74    (59)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.20/39.74          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.20/39.74            e1)
% 228.20/39.74    (60)  all_57_10 = e2
% 228.20/39.74    (61)  all_57_5 = e3
% 228.20/39.74    (62)   ~ (all_52_23 = e3)
% 228.20/39.74    (63)  op(e1, e0) = all_52_23
% 228.20/39.74    (64)   ~ (all_53_4 = all_53_8)
% 228.20/39.74    (65)  all_55_6 = all_53_9
% 228.20/39.74    (66)  op(e3, e2) = all_53_4
% 228.20/39.74    (67)   ~ (e2 = e0)
% 228.20/39.74    (68)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.20/39.74            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.20/39.74            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.20/39.74            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.20/39.74              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.20/39.74            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.20/39.74            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.20/39.74              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.20/39.74              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.20/39.74            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.20/39.74            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.20/39.74            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.20/39.74              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.20/39.74              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.20/39.74            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.20/39.74              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.20/39.74            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.20/39.74            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.20/39.74              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.20/39.74              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.20/39.74            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.20/39.74            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.20/39.74    (69)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 228.20/39.74            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 228.20/39.74              e3) = all_12_1 & $i(all_12_1))
% 228.20/39.74    (70)  all_55_12 = all_53_3
% 228.20/39.74    (71)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.20/39.74          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.20/39.74    (72)   ~ (all_53_1 = e0)
% 228.20/39.74    (73)   ~ (e1 = e0)
% 228.20/39.74    (74)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.20/39.74            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.20/39.74              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.20/39.74    (75)   ~ (all_53_4 = e0)
% 228.20/39.74    (76)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.20/39.74          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.20/39.74    (77)  all_57_8 = e2
% 228.20/39.74    (78)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.20/39.74          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.20/39.74    (79)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 228.20/39.74    (80)  op(e0, e0) = e3
% 228.20/39.74    (81)   ~ (all_53_4 = all_53_6)
% 228.20/39.74    (82)  ( ~ (all_20_0 = e1) & op(all_20_1, e3) = all_20_0 & op(e3, e2) =
% 228.20/39.74            all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e0) & op(e3,
% 228.20/39.74              e2) = all_20_1 & $i(all_20_1))
% 228.20/39.74    (83)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.20/39.74          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.20/39.74            e2)
% 228.20/39.74    (84)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.20/39.74              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.20/39.74                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.20/39.74                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.20/39.74    (85)  all_55_10 = all_6_2
% 228.20/39.74    (86)   ~ (all_53_11 = e1)
% 228.20/39.74    (87)  all_55_8 = all_52_17
% 228.20/39.74    (88)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.20/39.74          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.20/39.74    (89)  all_38_2 = all_6_2
% 228.20/39.74    (90)  all_55_3 = all_53_12
% 228.20/39.74    (91)   ~ (all_53_12 = e3)
% 228.20/39.74    (92)   ~ (all_53_4 = e2)
% 228.20/39.74    (93)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.20/39.74            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.20/39.74              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.20/39.74    (94)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.20/39.74          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.20/39.74    (95)  all_57_11 = e1
% 228.20/39.74    (96)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.20/39.74          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.20/39.74    (97)   ~ (all_52_23 = e1)
% 228.20/39.74    (98)   ~ (all_53_1 = e2)
% 228.20/39.74    (99)   ~ (e2 = e1)
% 228.20/39.74    (100)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.20/39.74           | (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.20/39.74             e2)
% 228.20/39.74    (101)  op(e2, e1) = all_53_9
% 228.20/39.74    (102)  op(e1, e2) = all_53_6
% 228.20/39.74    (103)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.20/39.74           (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.20/39.74    (104)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 228.20/39.74    (105)  all_24_2 = all_6_2
% 228.20/39.74    (106)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.20/39.74           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.20/39.74    (107)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.20/39.74           (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.20/39.74    (108)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.20/39.74           | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.20/39.74             e1)
% 228.20/39.74    (109)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.20/39.74           (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.20/39.74    (110)  all_55_14 = all_53_11
% 228.20/39.74    (111)  op(e3, e1) = all_53_8
% 228.20/39.74    (112)   ~ (all_53_11 = e3)
% 228.20/39.74    (113)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.20/39.74           (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.20/39.74    (114)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.20/39.74           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.20/39.74    (115)  op(e3, e0) = all_53_12
% 228.20/39.74  
% 228.20/39.74  Begin of proof
% 228.20/39.74  | 
% 228.20/39.74  | BETA: splitting (71) gives:
% 228.20/39.74  | 
% 228.20/39.74  | Case 1:
% 228.20/39.74  | | 
% 228.20/39.74  | |   (116)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) =
% 228.20/39.74  | |            e3)
% 228.20/39.74  | | 
% 228.20/39.74  | | BETA: splitting (116) gives:
% 228.20/39.74  | | 
% 228.20/39.74  | | Case 1:
% 228.20/39.74  | | | 
% 228.20/39.74  | | |   (117)  all_57_0 = e3 & op(e3, e3) = e3
% 228.20/39.74  | | | 
% 228.20/39.74  | | | ALPHA: (117) implies:
% 228.20/39.74  | | |   (118)  op(e3, e3) = e3
% 228.20/39.74  | | | 
% 228.20/39.74  | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13),
% 228.20/39.74  | | |            (14), (16), (19), (20), (22), (24), (29), (32), (33), (34),
% 228.20/39.74  | | |            (37), (38), (39), (40), (41), (43), (46), (47), (48), (51),
% 228.20/39.74  | | |            (53), (54), (59), (61), (64), (66), (67), (68), (71), (73),
% 228.20/39.74  | | |            (74), (75), (80), (81), (83), (84), (85), (89), (90), (91),
% 228.20/39.74  | | |            (93), (94), (99), (100), (101), (102), (103), (105), (106),
% 228.20/39.74  | | |            (107), (108), (109), (111), (113), (114), (115), (118) are
% 228.20/39.74  | | |            inconsistent by sub-proof #1438.
% 228.20/39.74  | | | 
% 228.20/39.74  | | Case 2:
% 228.20/39.74  | | | 
% 228.20/39.74  | | |   (119)  all_57_1 = e3 & op(e3, e2) = e3
% 228.20/39.74  | | | 
% 228.20/39.74  | | | ALPHA: (119) implies:
% 228.20/39.74  | | |   (120)  all_57_1 = e3
% 228.20/39.74  | | | 
% 228.20/39.74  | | | BETA: splitting (11) gives:
% 228.20/39.74  | | | 
% 228.20/39.74  | | | Case 1:
% 228.20/39.74  | | | | 
% 228.20/39.74  | | | |   (121)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2)
% 228.20/39.74  | | | |            = e0)
% 228.20/39.74  | | | | 
% 228.20/39.74  | | | | BETA: splitting (121) gives:
% 228.20/39.74  | | | | 
% 228.20/39.74  | | | | Case 1:
% 228.20/39.74  | | | | | 
% 228.20/39.74  | | | | |   (122)  all_57_6 = e0 & op(e1, e3) = e0
% 228.20/39.74  | | | | | 
% 228.20/39.74  | | | | | REF_CLOSE: (4), (5), (8), (10), (12), (13), (16), (19), (39), (41),
% 228.20/39.74  | | | | |            (46), (54), (58), (59), (60), (67), (73), (76), (83), (84),
% 228.20/39.74  | | | | |            (96), (99), (100), (103), (107), (108), (113), (120), (122)
% 228.20/39.74  | | | | |            are inconsistent by sub-proof #666.
% 228.20/39.74  | | | | | 
% 228.20/39.74  | | | | Case 2:
% 228.20/39.74  | | | | | 
% 228.20/39.74  | | | | |   (123)  all_57_7 = e0 & op(e1, e2) = e0
% 228.20/39.74  | | | | | 
% 228.20/39.74  | | | | | ALPHA: (123) implies:
% 228.20/39.74  | | | | |   (124)  all_57_7 = e0
% 228.20/39.74  | | | | | 
% 228.20/39.74  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12),
% 228.20/39.74  | | | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 228.20/39.74  | | | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 228.20/39.74  | | | | |            (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 228.20/39.74  | | | | |            (43), (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 228.20/39.74  | | | | |            (53), (54), (55), (56), (57), (59), (60), (61), (62), (63),
% 228.20/39.74  | | | | |            (64), (65), (66), (67), (68), (69), (70), (71), (72), (73),
% 228.20/39.74  | | | | |            (74), (75), (76), (77), (78), (79), (80), (81), (82), (83),
% 228.20/39.74  | | | | |            (84), (85), (86), (87), (88), (89), (90), (91), (92), (93),
% 228.20/39.74  | | | | |            (94), (96), (97), (98), (99), (100), (101), (102), (103),
% 228.20/39.74  | | | | |            (104), (105), (106), (107), (108), (109), (110), (111),
% 228.20/39.74  | | | | |            (112), (113), (114), (115), (120), (124) are inconsistent
% 228.20/39.74  | | | | |            by sub-proof #465.
% 228.20/39.74  | | | | | 
% 228.20/39.74  | | | | End of split
% 228.20/39.74  | | | | 
% 228.20/39.74  | | | Case 2:
% 228.20/39.74  | | | | 
% 228.20/39.74  | | | |   (125)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1,
% 228.20/39.74  | | | |              e0) = e0)
% 228.20/39.74  | | | | 
% 228.20/39.74  | | | | BETA: splitting (125) gives:
% 228.20/39.74  | | | | 
% 228.20/39.74  | | | | Case 1:
% 228.20/39.74  | | | | | 
% 228.20/39.74  | | | | |   (126)  all_57_8 = e0 & op(e1, e1) = e0
% 228.20/39.74  | | | | | 
% 228.20/39.74  | | | | | ALPHA: (126) implies:
% 228.20/39.74  | | | | |   (127)  all_57_8 = e0
% 228.20/39.74  | | | | | 
% 228.20/39.74  | | | | | REF_CLOSE: (4), (10), (39), (41), (60), (61), (67), (73), (77), (94),
% 228.20/39.74  | | | | |            (99), (127) are inconsistent by sub-proof #1272.
% 228.20/39.74  | | | | | 
% 228.20/39.74  | | | | Case 2:
% 228.20/39.74  | | | | | 
% 228.20/39.74  | | | | |   (128)  all_57_11 = e0 & op(e1, e0) = e0
% 228.20/39.74  | | | | | 
% 228.20/39.74  | | | | | REF_CLOSE: (73), (95), (128) are inconsistent by sub-proof #1257.
% 228.20/39.74  | | | | | 
% 228.20/39.75  | | | | End of split
% 228.20/39.75  | | | | 
% 228.20/39.75  | | | End of split
% 228.20/39.75  | | | 
% 228.20/39.75  | | End of split
% 228.20/39.75  | | 
% 228.20/39.75  | Case 2:
% 228.20/39.75  | | 
% 228.20/39.75  | |   (129)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) =
% 228.20/39.75  | |            e3)
% 228.20/39.75  | | 
% 228.20/39.75  | | REF_CLOSE: (10), (12), (58), (91), (115), (129) are inconsistent by
% 228.20/39.75  | |            sub-proof #2281.
% 228.20/39.75  | | 
% 228.20/39.75  | End of split
% 228.20/39.75  | 
% 228.20/39.75  End of proof
% 228.20/39.75  
% 228.20/39.75  Sub-proof #456 shows that the following formulas are inconsistent:
% 228.20/39.75  ----------------------------------------------------------------
% 228.20/39.75    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.20/39.75    (2)  all_57_9 = e2
% 228.20/39.75    (3)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.20/39.75    (4)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.20/39.75         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.20/39.75    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.20/39.75         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.20/39.75    (6)   ~ (all_53_8 = all_53_12)
% 228.20/39.75    (7)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.20/39.75         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.20/39.75    (8)   ~ (e3 = e1)
% 228.20/39.75    (9)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.20/39.75         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.20/39.75    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.20/39.75            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.20/39.75    (11)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.20/39.75          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.20/39.75    (12)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.20/39.75            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.20/39.75              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.20/39.75    (13)   ~ (all_6_2 = e3)
% 228.20/39.75    (14)  op(e1, e1) = all_6_2
% 228.20/39.75    (15)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.20/39.75    (16)   ~ (all_53_9 = e0)
% 228.20/39.75    (17)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.20/39.75          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.20/39.75    (18)   ~ (all_53_4 = all_53_12)
% 228.20/39.75    (19)   ~ (all_53_8 = all_53_9)
% 228.20/39.75    (20)  all_42_2 = all_6_2
% 228.20/39.75    (21)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.20/39.75          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.20/39.75    (22)   ~ (all_53_9 = all_6_2)
% 228.20/39.75    (23)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.20/39.75          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.20/39.75    (24)  all_57_3 = e0
% 228.20/39.75    (25)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.20/39.75          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.20/39.75    (26)   ~ (e3 = e2)
% 228.20/39.75    (27)  all_55_1 = all_53_4
% 228.20/39.75    (28)   ~ (e3 = e0)
% 228.20/39.75    (29)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.20/39.75          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.20/39.75    (30)   ~ (all_53_8 = all_6_2)
% 228.20/39.75    (31)  all_55_2 = all_53_8
% 228.20/39.75    (32)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.20/39.75    (33)  all_57_15 = e3
% 228.20/39.75    (34)  op(e3, e3) = e2
% 228.20/39.75    (35)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.20/39.75          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.20/39.75            e1)
% 228.20/39.75    (36)   ~ (all_53_4 = all_53_8)
% 228.20/39.75    (37)  op(e3, e2) = all_53_4
% 228.20/39.75    (38)  op(e1, e1) = e1
% 228.20/39.75    (39)   ~ (e2 = e0)
% 228.20/39.75    (40)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.20/39.75            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.20/39.75            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.20/39.75            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.20/39.75              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.20/39.75            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.20/39.75            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.20/39.75              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.20/39.75              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.20/39.75            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.20/39.75            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.20/39.75            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.20/39.75              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.20/39.75              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.20/39.75            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.20/39.75              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.20/39.75            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.20/39.75            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.20/39.75              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.20/39.75              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.20/39.75            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.20/39.75            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.20/39.75    (41)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.20/39.75          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.20/39.75    (42)   ~ (e1 = e0)
% 228.20/39.75    (43)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.20/39.75            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.20/39.75              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.20/39.75    (44)   ~ (all_53_4 = e0)
% 228.20/39.75    (45)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.20/39.75          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.20/39.75    (46)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.20/39.75          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.20/39.75    (47)  op(e0, e0) = e3
% 228.20/39.75    (48)   ~ (all_53_4 = all_53_6)
% 228.20/39.75    (49)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.20/39.75          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.20/39.75            e2)
% 228.20/39.75    (50)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.20/39.75              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.20/39.75                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.20/39.75                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.20/39.75    (51)  all_55_10 = all_6_2
% 228.20/39.75    (52)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.20/39.75          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.20/39.75    (53)  all_38_2 = all_6_2
% 228.20/39.75    (54)  all_55_3 = all_53_12
% 228.20/39.75    (55)   ~ (all_53_12 = e3)
% 228.20/39.75    (56)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.20/39.75            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.20/39.75              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.20/39.75    (57)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.20/39.75          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.20/39.75    (58)  all_57_11 = e1
% 228.20/39.75    (59)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.20/39.75          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.20/39.75    (60)   ~ (e2 = e1)
% 228.20/39.75    (61)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.20/39.75          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.20/39.75    (62)  op(e2, e1) = all_53_9
% 228.20/39.75    (63)  op(e1, e2) = all_53_6
% 228.20/39.75    (64)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.20/39.75          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.20/39.75    (65)  all_24_2 = all_6_2
% 228.20/39.75    (66)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.20/39.75          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.20/39.75    (67)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.20/39.75          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.20/39.75    (68)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.20/39.75          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.20/39.75    (69)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.20/39.75          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.20/39.75    (70)  op(e3, e1) = all_53_8
% 228.20/39.75    (71)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.20/39.75          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.20/39.75    (72)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.20/39.75          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.20/39.75    (73)  op(e3, e0) = all_53_12
% 228.20/39.75  
% 228.20/39.75  Begin of proof
% 228.20/39.75  | 
% 228.20/39.75  | BETA: splitting (23) gives:
% 228.20/39.75  | 
% 228.20/39.75  | Case 1:
% 228.20/39.75  | | 
% 228.20/39.75  | |   (74)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) =
% 228.20/39.75  | |           e0)
% 228.20/39.75  | | 
% 228.20/39.75  | | BETA: splitting (74) gives:
% 228.20/39.75  | | 
% 228.20/39.75  | | Case 1:
% 228.20/39.75  | | | 
% 228.20/39.75  | | |   (75)  all_57_0 = e0 & op(e3, e3) = e0
% 228.20/39.75  | | | 
% 228.20/39.75  | | | ALPHA: (75) implies:
% 228.20/39.75  | | |   (76)  op(e3, e3) = e0
% 228.20/39.75  | | | 
% 228.20/39.75  | | | REF_CLOSE: (10), (34), (39), (76) are inconsistent by sub-proof #2403.
% 228.20/39.75  | | | 
% 228.20/39.75  | | Case 2:
% 228.20/39.75  | | | 
% 228.20/39.75  | | |   (77)  all_57_1 = e0 & op(e3, e2) = e0
% 228.20/39.75  | | | 
% 228.20/39.75  | | | ALPHA: (77) implies:
% 228.20/39.75  | | |   (78)  all_57_1 = e0
% 228.20/39.75  | | | 
% 228.20/39.75  | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 228.20/39.75  | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 228.20/39.75  | | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 228.20/39.75  | | |            (34), (35), (36), (37), (38), (39), (40), (41), (42), (43),
% 228.20/39.75  | | |            (44), (45), (46), (47), (48), (49), (50), (51), (52), (53),
% 228.20/39.75  | | |            (54), (55), (56), (57), (59), (60), (61), (62), (63), (64),
% 228.20/39.75  | | |            (65), (66), (67), (68), (69), (70), (71), (72), (73), (78) are
% 228.20/39.75  | | |            inconsistent by sub-proof #511.
% 228.20/39.75  | | | 
% 228.20/39.75  | | End of split
% 228.20/39.75  | | 
% 228.20/39.75  | Case 2:
% 228.20/39.75  | | 
% 228.20/39.75  | |   (79)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) =
% 228.20/39.75  | |           e0)
% 228.20/39.75  | | 
% 228.20/39.75  | | BETA: splitting (79) gives:
% 228.20/39.75  | | 
% 228.20/39.75  | | Case 1:
% 228.20/39.75  | | | 
% 228.20/39.75  | | |   (80)  all_57_4 = e0 & op(e3, e1) = e0
% 228.20/39.75  | | | 
% 228.20/39.75  | | | ALPHA: (80) implies:
% 228.20/39.75  | | |   (81)  all_57_4 = e0
% 228.20/39.75  | | | 
% 228.20/39.75  | | | REF_CLOSE: (2), (4), (8), (10), (13), (14), (24), (26), (28), (33), (35),
% 228.20/39.75  | | |            (39), (42), (45), (47), (49), (50), (57), (58), (60), (81) are
% 228.20/39.75  | | |            inconsistent by sub-proof #1041.
% 228.20/39.75  | | | 
% 228.20/39.75  | | Case 2:
% 228.20/39.75  | | | 
% 228.20/39.75  | | |   (82)  all_57_9 = e0 & op(e3, e0) = e0
% 228.20/39.75  | | | 
% 228.20/39.75  | | | REF_CLOSE: (2), (39), (82) are inconsistent by sub-proof #1973.
% 228.20/39.75  | | | 
% 228.20/39.75  | | End of split
% 228.20/39.75  | | 
% 228.20/39.75  | End of split
% 228.20/39.75  | 
% 228.20/39.75  End of proof
% 228.20/39.75  
% 228.20/39.75  Sub-proof #457 shows that the following formulas are inconsistent:
% 228.20/39.75  ----------------------------------------------------------------
% 228.20/39.75    (1)  all_57_9 = e2
% 228.20/39.75    (2)  all_57_0 = e2
% 228.20/39.75    (3)  all_57_12 = e0
% 228.20/39.75    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.20/39.75         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.20/39.75    (5)   ~ (e3 = e1)
% 228.20/39.75    (6)  all_57_9 = e0 & op(e3, e0) = e0
% 228.20/39.75    (7)   ~ (e3 = e2)
% 228.20/39.75    (8)   ~ (e2 = e0)
% 228.20/39.75    (9)   ~ (e1 = e0)
% 228.20/39.75    (10)  all_57_6 = e3
% 228.20/39.75    (11)   ~ (e2 = e1)
% 228.20/39.75    (12)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.20/39.75          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.20/39.75  
% 228.20/39.75  Begin of proof
% 228.20/39.75  | 
% 228.20/39.75  | ALPHA: (6) implies:
% 228.20/39.75  |   (13)  all_57_9 = e0
% 228.20/39.75  | 
% 228.20/39.75  | COMBINE_EQS: (1), (13) imply:
% 228.20/39.75  |   (14)  e2 = e0
% 228.20/39.75  | 
% 228.20/39.75  | SIMP: (14) implies:
% 228.20/39.75  |   (15)  e2 = e0
% 228.20/39.75  | 
% 228.20/39.75  | COMBINE_EQS: (2), (15) imply:
% 228.20/39.75  |   (16)  all_57_0 = e0
% 228.20/39.75  | 
% 228.20/39.75  | REF_CLOSE: (3), (4), (5), (7), (8), (9), (10), (11), (12), (16) are
% 228.20/39.75  |            inconsistent by sub-proof #1425.
% 228.20/39.75  | 
% 228.20/39.75  End of proof
% 228.20/39.75  
% 228.20/39.75  Sub-proof #458 shows that the following formulas are inconsistent:
% 228.20/39.75  ----------------------------------------------------------------
% 228.20/39.75    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.20/39.75    (2)  all_57_0 = e2
% 228.20/39.75    (3)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.20/39.75    (4)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.20/39.75         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.20/39.75    (5)  all_57_12 = e0
% 228.20/39.75    (6)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.20/39.75         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.20/39.75    (7)   ~ (all_53_8 = all_53_12)
% 228.20/39.75    (8)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.20/39.75         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.20/39.75    (9)   ~ (all_53_8 = all_53_11)
% 228.20/39.75    (10)   ~ (e3 = e1)
% 228.20/39.75    (11)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.20/39.75          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.20/39.75    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.20/39.75            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.20/39.75    (13)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.20/39.75          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.20/39.75    (14)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.20/39.75            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.20/39.75              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.20/39.75    (15)   ~ (all_53_3 = e3)
% 228.20/39.75    (16)   ~ (all_6_2 = e3)
% 228.20/39.75    (17)  ( ~ (all_28_0 = e0) & op(all_28_1, e3) = all_28_0 & op(e3, e2) =
% 228.20/39.75            all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 = e1) & op(e3,
% 228.20/39.75              e2) = all_28_1 & $i(all_28_1))
% 228.20/39.75    (18)   ~ (all_53_9 = e1)
% 228.20/39.75    (19)  op(e1, e1) = all_6_2
% 228.20/39.75    (20)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.20/39.75    (21)   ~ (all_53_1 = all_53_9)
% 228.20/39.75    (22)   ~ (all_53_9 = e0)
% 228.20/39.75    (23)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 228.20/39.75    (24)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.20/39.75          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.20/39.75    (25)   ~ (all_52_17 = e2)
% 228.20/39.75    (26)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 228.20/39.75            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 228.20/39.75              e3) = all_22_1 & $i(all_22_1))
% 228.20/39.75    (27)   ~ (all_53_8 = e1)
% 228.20/39.75    (28)  all_57_9 = e1
% 228.20/39.75    (29)  op(all_52_17, all_52_17) = e3
% 228.20/39.75    (30)   ~ (all_53_4 = all_53_12)
% 228.20/39.75    (31)   ~ (all_52_17 = all_52_23)
% 228.20/39.75    (32)   ~ (all_52_17 = e1)
% 228.20/39.75    (33)   ~ (all_53_8 = all_53_9)
% 228.20/39.75    (34)  all_57_7 = e1
% 228.20/39.75    (35)  all_42_2 = all_6_2
% 228.20/39.75    (36)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.20/39.75          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.20/39.75    (37)   ~ (all_53_9 = all_53_11)
% 228.20/39.75    (38)  all_55_4 = all_53_1
% 228.20/39.75    (39)   ~ (all_53_9 = all_6_2)
% 228.20/39.75    (40)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.20/39.75          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.20/39.75    (41)  all_57_3 = e0
% 228.20/39.75    (42)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.20/39.75          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.20/39.75    (43)   ~ (e3 = e2)
% 228.20/39.75    (44)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 228.20/39.75    (45)  all_55_1 = all_53_4
% 228.20/39.75    (46)   ~ (all_53_1 = all_53_3)
% 228.20/39.75    (47)   ~ (all_53_1 = all_52_17)
% 228.20/39.75    (48)   ~ (e3 = e0)
% 228.20/39.75    (49)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.20/39.75          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.20/39.75    (50)   ~ (all_53_8 = all_6_2)
% 228.20/39.75    (51)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.20/39.75    (52)  all_55_11 = all_52_23
% 228.20/39.75    (53)  all_55_2 = all_53_8
% 228.20/39.75    (54)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 228.20/39.75    (55)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.20/39.75    (56)  all_57_15 = e3
% 228.20/39.75    (57)  op(e3, e3) = e2
% 228.20/39.75    (58)   ~ (all_53_3 = e2)
% 228.20/39.75    (59)   ~ (all_53_3 = all_52_17)
% 228.20/39.75    (60)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.20/39.75          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.20/39.75            e1)
% 228.20/39.75    (61)  all_57_11 = e0
% 228.20/39.75    (62)   ~ (all_52_23 = e3)
% 228.20/39.75    (63)  op(e1, e0) = all_52_23
% 228.20/39.75    (64)   ~ (all_53_4 = all_53_8)
% 228.20/39.75    (65)  all_55_6 = all_53_9
% 228.20/39.75    (66)  op(e3, e2) = all_53_4
% 228.20/39.75    (67)  op(e1, e1) = e1
% 228.20/39.75    (68)   ~ (e2 = e0)
% 228.20/39.75    (69)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.20/39.75            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.20/39.75            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.20/39.75            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.20/39.75              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.20/39.75            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.20/39.75            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.20/39.75              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.20/39.75              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.20/39.75            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.20/39.75            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.20/39.75            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.20/39.75              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.20/39.75              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.20/39.75            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.20/39.75              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.20/39.75            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.20/39.75            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.20/39.75              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.20/39.75              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.20/39.75            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.20/39.75            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.20/39.75    (70)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 228.20/39.75            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 228.20/39.75              e3) = all_12_1 & $i(all_12_1))
% 228.20/39.75    (71)  all_55_12 = all_53_3
% 228.20/39.75    (72)  all_57_13 = e2
% 228.20/39.75    (73)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.20/39.75          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.20/39.75    (74)   ~ (all_53_1 = e0)
% 228.20/39.75    (75)   ~ (e1 = e0)
% 228.20/39.75    (76)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.20/39.75            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.20/39.75              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.20/39.75    (77)   ~ (all_53_4 = e0)
% 228.20/39.75    (78)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.20/39.75          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.20/39.75    (79)  all_57_8 = e2
% 228.20/39.75    (80)  all_57_6 = e3
% 228.20/39.75    (81)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.20/39.75          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.20/39.75    (82)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 228.20/39.75    (83)  op(e0, e0) = e3
% 228.20/39.75    (84)   ~ (all_53_4 = all_53_6)
% 228.20/39.75    (85)  ( ~ (all_20_0 = e1) & op(all_20_1, e3) = all_20_0 & op(e3, e2) =
% 228.20/39.75            all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e0) & op(e3,
% 228.20/39.75              e2) = all_20_1 & $i(all_20_1))
% 228.20/39.75    (86)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.20/39.75          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.20/39.75            e2)
% 228.20/39.75    (87)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.20/39.75              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.20/39.75                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.20/39.75                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.20/39.75    (88)  all_55_10 = all_6_2
% 228.20/39.75    (89)  op(e1, e1) = e2
% 228.20/39.75    (90)   ~ (all_53_11 = e1)
% 228.20/39.75    (91)  all_55_8 = all_52_17
% 228.20/39.75    (92)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.20/39.75          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.20/39.75    (93)  all_38_2 = all_6_2
% 228.20/39.75    (94)  all_55_3 = all_53_12
% 228.20/39.75    (95)   ~ (all_53_12 = e3)
% 228.20/39.75    (96)   ~ (all_53_4 = e2)
% 228.20/39.75    (97)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.20/39.75            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.20/39.75              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.20/39.75    (98)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.20/39.75          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.20/39.75    (99)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.20/39.75          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.20/39.75    (100)  all_57_1 = e3
% 228.20/39.75    (101)   ~ (all_52_23 = e1)
% 228.20/39.75    (102)   ~ (all_53_1 = e2)
% 228.20/39.75    (103)   ~ (e2 = e1)
% 228.20/39.75    (104)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.20/39.75           | (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.20/39.75             e2)
% 228.20/39.75    (105)  op(e2, e1) = all_53_9
% 228.20/39.75    (106)  op(e1, e2) = all_53_6
% 228.20/39.75    (107)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.20/39.75           (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.20/39.75    (108)  all_57_6 = e3 & op(e1, e3) = e3
% 228.20/39.75    (109)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 228.20/39.75    (110)  all_24_2 = all_6_2
% 228.20/39.75    (111)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.20/39.75           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.20/39.76    (112)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.20/39.76           (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.20/39.76    (113)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.20/39.76           | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.20/39.76             e1)
% 228.20/39.76    (114)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.20/39.76           (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.20/39.76    (115)  all_55_14 = all_53_11
% 228.20/39.76    (116)  op(e3, e1) = all_53_8
% 228.20/39.76    (117)   ~ (all_53_11 = e3)
% 228.20/39.76    (118)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.20/39.76           (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.20/39.76    (119)  all_57_13 = e2 & op(e0, e2) = e2
% 228.20/39.76    (120)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.20/39.76           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.20/39.76    (121)  op(e3, e0) = all_53_12
% 228.20/39.76  
% 228.20/39.76  Begin of proof
% 228.20/39.76  | 
% 228.20/39.76  | BETA: splitting (60) gives:
% 228.20/39.76  | 
% 228.20/39.76  | Case 1:
% 228.20/39.76  | | 
% 228.20/39.76  | |   (122)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 228.20/39.76  | |            e1)
% 228.20/39.76  | | 
% 228.20/39.76  | | BETA: splitting (122) gives:
% 228.20/39.76  | | 
% 228.20/39.76  | | Case 1:
% 228.20/39.76  | | | 
% 228.20/39.76  | | |   (123)  all_57_12 = e1 & op(e0, e3) = e1
% 228.20/39.76  | | | 
% 228.20/39.76  | | | ALPHA: (123) implies:
% 228.20/39.76  | | |   (124)  all_57_12 = e1
% 228.20/39.76  | | | 
% 228.20/39.76  | | | REF_CLOSE: (5), (75), (124) are inconsistent by sub-proof #2014.
% 228.20/39.76  | | | 
% 228.20/39.76  | | Case 2:
% 228.20/39.76  | | | 
% 228.20/39.76  | | |   (125)  all_57_13 = e1 & op(e0, e2) = e1
% 228.20/39.76  | | | 
% 228.20/39.76  | | | ALPHA: (125) implies:
% 228.20/39.76  | | |   (126)  all_57_13 = e1
% 228.20/39.76  | | | 
% 228.20/39.76  | | | COMBINE_EQS: (72), (126) imply:
% 228.20/39.76  | | |   (127)  e2 = e1
% 228.20/39.76  | | | 
% 228.20/39.76  | | | COMBINE_EQS: (79), (127) imply:
% 228.20/39.76  | | |   (128)  all_57_8 = e1
% 228.20/39.76  | | | 
% 228.20/39.76  | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13),
% 228.20/39.76  | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 228.20/39.76  | | |            (24), (25), (26), (27), (29), (30), (31), (32), (33), (35),
% 228.20/39.76  | | |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 228.20/39.76  | | |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (55),
% 228.20/39.76  | | |            (56), (57), (58), (59), (60), (62), (63), (64), (65), (66),
% 228.20/39.76  | | |            (68), (69), (70), (71), (73), (74), (75), (76), (77), (78),
% 228.20/39.76  | | |            (81), (82), (83), (84), (85), (86), (87), (88), (90), (91),
% 228.20/39.76  | | |            (92), (93), (94), (95), (96), (97), (98), (99), (101), (102),
% 228.20/39.76  | | |            (104), (105), (106), (107), (109), (110), (111), (112), (113),
% 228.20/39.76  | | |            (114), (115), (116), (117), (118), (120), (121), (128) are
% 228.20/39.76  | | |            inconsistent by sub-proof #474.
% 228.20/39.76  | | | 
% 228.20/39.76  | | End of split
% 228.20/39.76  | | 
% 228.20/39.76  | Case 2:
% 228.20/39.76  | | 
% 228.20/39.76  | |   (129)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.20/39.76  | |            e1)
% 228.20/39.76  | | 
% 228.20/39.76  | | BETA: splitting (129) gives:
% 228.20/39.76  | | 
% 228.20/39.76  | | Case 1:
% 228.20/39.76  | | | 
% 228.20/39.76  | | |   (130)  all_57_14 = e1 & op(e0, e1) = e1
% 228.20/39.76  | | | 
% 228.20/39.76  | | | ALPHA: (130) implies:
% 228.20/39.76  | | |   (131)  all_57_14 = e1
% 228.20/39.76  | | | 
% 228.20/39.76  | | | BETA: splitting (42) gives:
% 228.20/39.76  | | | 
% 228.20/39.76  | | | Case 1:
% 228.20/39.76  | | | | 
% 228.20/39.76  | | | |   (132)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1)
% 228.20/39.76  | | | |            = e0)
% 228.20/39.76  | | | | 
% 228.20/39.76  | | | | BETA: splitting (132) gives:
% 228.20/39.76  | | | | 
% 228.20/39.76  | | | | Case 1:
% 228.20/39.76  | | | | | 
% 228.20/39.76  | | | | |   (133)  all_57_4 = e0 & op(e3, e1) = e0
% 228.20/39.76  | | | | | 
% 228.20/39.76  | | | | | ALPHA: (133) implies:
% 228.20/39.76  | | | | |   (134)  all_57_4 = e0
% 228.20/39.76  | | | | | 
% 228.20/39.76  | | | | | BETA: splitting (104) gives:
% 228.20/39.76  | | | | | 
% 228.20/39.76  | | | | | Case 1:
% 228.20/39.76  | | | | | | 
% 228.20/39.76  | | | | | |   (135)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 &
% 228.20/39.76  | | | | | |            op(e2, e0) = e2)
% 228.20/39.76  | | | | | | 
% 228.20/39.76  | | | | | | BETA: splitting (135) gives:
% 228.20/39.76  | | | | | | 
% 228.20/39.76  | | | | | | Case 1:
% 228.20/39.76  | | | | | | | 
% 228.20/39.76  | | | | | | |   (136)  all_57_9 = e2 & op(e3, e0) = e2
% 228.20/39.76  | | | | | | | 
% 228.20/39.76  | | | | | | | ALPHA: (136) implies:
% 228.20/39.76  | | | | | | |   (137)  all_57_9 = e2
% 228.20/39.76  | | | | | | | 
% 228.20/39.76  | | | | | | | COMBINE_EQS: (28), (137) imply:
% 228.20/39.76  | | | | | | |   (138)  e2 = e1
% 228.20/39.76  | | | | | | | 
% 228.20/39.76  | | | | | | | SIMP: (138) implies:
% 228.20/39.76  | | | | | | |   (139)  e2 = e1
% 228.20/39.76  | | | | | | | 
% 228.20/39.76  | | | | | | | COMBINE_EQS: (79), (139) imply:
% 228.20/39.76  | | | | | | |   (140)  all_57_8 = e1
% 228.20/39.76  | | | | | | | 
% 228.20/39.76  | | | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11),
% 228.20/39.76  | | | | | | |            (12), (13), (14), (15), (16), (17), (18), (19), (20),
% 228.20/39.76  | | | | | | |            (21), (22), (23), (24), (25), (26), (27), (29), (30),
% 228.20/39.76  | | | | | | |            (31), (32), (33), (35), (36), (37), (38), (39), (40),
% 228.20/39.76  | | | | | | |            (41), (42), (43), (44), (45), (46), (47), (48), (49),
% 228.20/39.76  | | | | | | |            (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 228.20/39.76  | | | | | | |            (59), (60), (62), (63), (64), (65), (66), (68), (69),
% 228.20/39.76  | | | | | | |            (70), (71), (73), (74), (75), (76), (77), (78), (81),
% 228.20/39.76  | | | | | | |            (82), (83), (84), (85), (86), (87), (88), (90), (91),
% 228.20/39.76  | | | | | | |            (92), (93), (94), (95), (96), (97), (98), (99), (101),
% 228.20/39.76  | | | | | | |            (102), (104), (105), (106), (107), (109), (110), (111),
% 228.20/39.76  | | | | | | |            (112), (113), (114), (115), (116), (117), (118), (120),
% 228.20/39.76  | | | | | | |            (121), (140) are inconsistent by sub-proof #474.
% 228.20/39.76  | | | | | | | 
% 228.20/39.76  | | | | | | Case 2:
% 228.20/39.76  | | | | | | | 
% 228.20/39.76  | | | | | | |   (141)  all_57_10 = e2 & op(e2, e0) = e2
% 228.20/39.76  | | | | | | | 
% 228.20/39.76  | | | | | | | ALPHA: (141) implies:
% 228.20/39.76  | | | | | | |   (142)  all_57_10 = e2
% 228.20/39.76  | | | | | | | 
% 228.20/39.76  | | | | | | | BETA: splitting (87) gives:
% 228.20/39.76  | | | | | | | 
% 228.20/39.76  | | | | | | | Case 1:
% 228.20/39.76  | | | | | | | | 
% 228.20/39.76  | | | | | | | |   (143)  all_57_15 = e0 & op(e0, e0) = e0
% 228.20/39.76  | | | | | | | | 
% 228.20/39.76  | | | | | | | | ALPHA: (143) implies:
% 228.20/39.76  | | | | | | | |   (144)  op(e0, e0) = e0
% 228.20/39.76  | | | | | | | | 
% 228.20/39.76  | | | | | | | | REF_CLOSE: (12), (48), (83), (144) are inconsistent by sub-proof
% 228.20/39.76  | | | | | | | |            #2304.
% 228.20/39.76  | | | | | | | | 
% 228.20/39.76  | | | | | | | Case 2:
% 228.20/39.76  | | | | | | | | 
% 228.20/39.76  | | | | | | | |   (145)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 &
% 228.20/39.76  | | | | | | | |              op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 228.20/39.76  | | | | | | | |              e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) |
% 228.20/39.76  | | | | | | | |            (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0
% 228.20/39.76  | | | | | | | |              & op(e0, e1) = e0))
% 228.20/39.76  | | | | | | | | 
% 228.20/39.76  | | | | | | | | ALPHA: (145) implies:
% 228.20/39.76  | | | | | | | |   (146)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 &
% 228.20/39.76  | | | | | | | |            op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.20/39.76  | | | | | | | | 
% 228.20/39.76  | | | | | | | | BETA: splitting (6) gives:
% 228.20/39.76  | | | | | | | | 
% 228.20/39.76  | | | | | | | | Case 1:
% 228.20/39.76  | | | | | | | | | 
% 228.20/39.76  | | | | | | | | |   (147)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 &
% 228.20/39.76  | | | | | | | | |            op(e2, e3) = e1)
% 228.20/39.76  | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | BETA: splitting (147) gives:
% 228.20/39.76  | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | Case 1:
% 228.20/39.76  | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | |   (148)  all_57_0 = e1 & op(e3, e3) = e1
% 228.20/39.76  | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | | ALPHA: (148) implies:
% 228.20/39.76  | | | | | | | | | |   (149)  op(e3, e3) = e1
% 228.20/39.76  | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | | REF_CLOSE: (12), (57), (103), (149) are inconsistent by
% 228.20/39.76  | | | | | | | | | |            sub-proof #1950.
% 228.20/39.76  | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | Case 2:
% 228.20/39.76  | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | |   (150)  all_57_2 = e1 & op(e2, e3) = e1
% 228.20/39.76  | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | | ALPHA: (150) implies:
% 228.20/39.76  | | | | | | | | | |   (151)  all_57_2 = e1
% 228.20/39.76  | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | | BETA: splitting (92) gives:
% 228.20/39.76  | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | | Case 1:
% 228.20/39.76  | | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | | |   (152)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 228.20/39.76  | | | | | | | | | | |            & op(e2, e2) = e3)
% 228.20/39.76  | | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | | | BETA: splitting (152) gives:
% 228.20/39.76  | | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | | | Case 1:
% 228.20/39.76  | | | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | | | |   (153)  all_57_2 = e3 & op(e2, e3) = e3
% 228.20/39.76  | | | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | | | | ALPHA: (153) implies:
% 228.20/39.76  | | | | | | | | | | | |   (154)  all_57_2 = e3
% 228.20/39.76  | | | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | | | | REF_CLOSE: (4), (10), (12), (16), (19), (41), (43), (48),
% 228.20/39.76  | | | | | | | | | | | |            (56), (60), (68), (75), (78), (86), (87), (92),
% 228.20/39.76  | | | | | | | | | | | |            (98), (103), (134), (142), (154) are inconsistent
% 228.20/39.76  | | | | | | | | | | | |            by sub-proof #747.
% 228.20/39.76  | | | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | | | Case 2:
% 228.20/39.76  | | | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | | | |   (155)  all_57_3 = e3 & op(e2, e2) = e3
% 228.20/39.76  | | | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (10), (11), (12),
% 228.20/39.76  | | | | | | | | | | | |            (13), (14), (16), (19), (20), (22), (24), (30),
% 228.20/39.76  | | | | | | | | | | | |            (33), (35), (36), (39), (40), (41), (42), (43),
% 228.20/39.76  | | | | | | | | | | | |            (45), (48), (49), (50), (53), (55), (56), (57),
% 228.20/39.76  | | | | | | | | | | | |            (60), (64), (66), (67), (68), (69), (73), (75),
% 228.20/39.76  | | | | | | | | | | | |            (76), (77), (78), (81), (83), (84), (86), (87),
% 228.20/39.76  | | | | | | | | | | | |            (88), (92), (93), (94), (95), (97), (98), (99),
% 228.20/39.76  | | | | | | | | | | | |            (100), (103), (104), (105), (106), (107), (110),
% 228.20/39.76  | | | | | | | | | | | |            (111), (112), (113), (114), (116), (118), (120),
% 228.20/39.76  | | | | | | | | | | | |            (121), (155) are inconsistent by sub-proof #473.
% 228.20/39.76  | | | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | | | End of split
% 228.20/39.76  | | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | | Case 2:
% 228.20/39.76  | | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | | |   (156)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 228.20/39.76  | | | | | | | | | | |            e3 & op(e2, e0) = e3)
% 228.20/39.76  | | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | | | BETA: splitting (156) gives:
% 228.20/39.76  | | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | | | Case 1:
% 228.20/39.76  | | | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | | | |   (157)  all_57_5 = e3 & op(e2, e1) = e3
% 228.20/39.76  | | | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | | | | ALPHA: (157) implies:
% 228.20/39.76  | | | | | | | | | | | |   (158)  all_57_5 = e3
% 228.20/39.76  | | | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | | | | BETA: splitting (4) gives:
% 228.20/39.76  | | | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | | | | Case 1:
% 228.20/39.76  | | | | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | | | | |   (159)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 228.20/39.76  | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 228.20/39.76  | | | | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | | | | | BETA: splitting (159) gives:
% 228.20/39.76  | | | | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | | | | | Case 1:
% 228.20/39.76  | | | | | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | | | | | | GROUND_INST: instantiating (12) with e1, e2, e1, e1,
% 228.20/39.76  | | | | | | | | | | | | | |              simplifying with (67), (89) gives:
% 228.20/39.76  | | | | | | | | | | | | | |   (160)  e2 = e1
% 228.20/39.76  | | | | | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | | | | | | COMBINE_EQS: (79), (160) imply:
% 228.20/39.76  | | | | | | | | | | | | | |   (161)  all_57_8 = e1
% 228.20/39.76  | | | | | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (5), (6), (8), (10), (11), (12), (13),
% 228.20/39.76  | | | | | | | | | | | | | |            (16), (19), (24), (36), (40), (41), (43), (48),
% 228.20/39.76  | | | | | | | | | | | | | |            (56), (57), (60), (68), (72), (73), (75), (80),
% 228.20/39.76  | | | | | | | | | | | | | |            (87), (92), (95), (98), (99), (103), (104), (107),
% 228.20/39.76  | | | | | | | | | | | | | |            (111), (112), (113), (118), (120), (121), (151),
% 228.20/39.76  | | | | | | | | | | | | | |            (158), (161) are inconsistent by sub-proof #489.
% 228.20/39.76  | | | | | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | | | | | Case 2:
% 228.20/39.76  | | | | | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | | | | | |   (162)  all_57_3 = e1 & op(e2, e2) = e1
% 228.20/39.76  | | | | | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | | | | | | REF_CLOSE: (4), (10), (41), (43), (68), (75), (98), (103),
% 228.20/39.76  | | | | | | | | | | | | | |            (151), (158), (162) are inconsistent by sub-proof
% 228.20/39.76  | | | | | | | | | | | | | |            #1520.
% 228.20/39.76  | | | | | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | | | | | End of split
% 228.20/39.76  | | | | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | | | | Case 2:
% 228.20/39.76  | | | | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | | | | |   (163)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 228.20/39.76  | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 228.20/39.76  | | | | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | | | | | BETA: splitting (163) gives:
% 228.20/39.76  | | | | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | | | | | Case 1:
% 228.20/39.76  | | | | | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | | | | | |   (164)  all_57_5 = e1 & op(e2, e1) = e1
% 228.20/39.76  | | | | | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | | | | | | ALPHA: (164) implies:
% 228.20/39.76  | | | | | | | | | | | | | |   (165)  all_57_5 = e1
% 228.20/39.76  | | | | | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | | | | | | COMBINE_EQS: (158), (165) imply:
% 228.20/39.76  | | | | | | | | | | | | | |   (166)  e3 = e1
% 228.20/39.76  | | | | | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (10), (11), (12),
% 228.20/39.76  | | | | | | | | | | | | | |            (13), (14), (16), (19), (20), (22), (24), (30),
% 228.20/39.76  | | | | | | | | | | | | | |            (33), (35), (36), (39), (40), (41), (42), (43),
% 228.20/39.76  | | | | | | | | | | | | | |            (45), (48), (49), (50), (53), (55), (56), (57),
% 228.20/39.76  | | | | | | | | | | | | | |            (60), (64), (66), (67), (68), (69), (73), (75),
% 228.20/39.76  | | | | | | | | | | | | | |            (76), (77), (78), (80), (81), (83), (84), (86),
% 228.20/39.76  | | | | | | | | | | | | | |            (87), (88), (92), (93), (94), (95), (97), (98),
% 228.20/39.76  | | | | | | | | | | | | | |            (99), (103), (104), (105), (106), (107), (110),
% 228.20/39.76  | | | | | | | | | | | | | |            (111), (112), (113), (114), (116), (118), (120),
% 228.20/39.76  | | | | | | | | | | | | | |            (121), (166) are inconsistent by sub-proof #472.
% 228.20/39.76  | | | | | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | | | | | Case 2:
% 228.20/39.76  | | | | | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | | | | | |   (167)  all_57_10 = e1 & op(e2, e0) = e1
% 228.20/39.76  | | | | | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | | | | | | ALPHA: (167) implies:
% 228.20/39.76  | | | | | | | | | | | | | |   (168)  all_57_10 = e1
% 228.20/39.76  | | | | | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | | | | | | COMBINE_EQS: (142), (168) imply:
% 228.20/39.76  | | | | | | | | | | | | | |   (169)  e2 = e1
% 228.20/39.76  | | | | | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | | | | | | SIMP: (169) implies:
% 228.20/39.76  | | | | | | | | | | | | | |   (170)  e2 = e1
% 228.20/39.76  | | | | | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | | | | | | COMBINE_EQS: (79), (170) imply:
% 228.20/39.76  | | | | | | | | | | | | | |   (171)  all_57_8 = e1
% 228.20/39.76  | | | | | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (5), (6), (8), (10), (11), (12), (13),
% 228.20/39.76  | | | | | | | | | | | | | |            (16), (19), (24), (36), (40), (41), (43), (48),
% 228.20/39.76  | | | | | | | | | | | | | |            (56), (57), (60), (68), (72), (73), (75), (80),
% 228.20/39.76  | | | | | | | | | | | | | |            (87), (92), (95), (98), (99), (103), (104), (107),
% 228.20/39.76  | | | | | | | | | | | | | |            (111), (112), (113), (118), (120), (121), (151),
% 228.20/39.76  | | | | | | | | | | | | | |            (158), (171) are inconsistent by sub-proof #489.
% 228.20/39.76  | | | | | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | | | | | End of split
% 228.20/39.76  | | | | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | | | | End of split
% 228.20/39.76  | | | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | | | Case 2:
% 228.20/39.76  | | | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | | | |   (172)  all_57_10 = e3 & op(e2, e0) = e3
% 228.20/39.76  | | | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | | | | ALPHA: (172) implies:
% 228.20/39.76  | | | | | | | | | | | |   (173)  all_57_10 = e3
% 228.20/39.76  | | | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | | | | REF_CLOSE: (28), (43), (48), (56), (68), (75), (103), (104),
% 228.20/39.76  | | | | | | | | | | | |            (146), (173) are inconsistent by sub-proof #1986.
% 228.20/39.76  | | | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | | | End of split
% 228.20/39.76  | | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | | End of split
% 228.20/39.76  | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | End of split
% 228.20/39.76  | | | | | | | | | 
% 228.20/39.76  | | | | | | | | Case 2:
% 228.20/39.76  | | | | | | | | | 
% 228.20/39.76  | | | | | | | | |   (174)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 &
% 228.20/39.76  | | | | | | | | |            op(e0, e3) = e1)
% 228.20/39.76  | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | BETA: splitting (174) gives:
% 228.20/39.76  | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | Case 1:
% 228.20/39.76  | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | |   (175)  all_57_6 = e1 & op(e1, e3) = e1
% 228.20/39.76  | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | | ALPHA: (175) implies:
% 228.20/39.76  | | | | | | | | | |   (176)  all_57_6 = e1
% 228.20/39.76  | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (10), (11), (12),
% 228.20/39.76  | | | | | | | | | |            (13), (14), (16), (19), (20), (22), (24), (30),
% 228.20/39.76  | | | | | | | | | |            (33), (35), (36), (39), (40), (41), (42), (43),
% 228.20/39.76  | | | | | | | | | |            (45), (48), (49), (50), (53), (55), (56), (57),
% 228.20/39.76  | | | | | | | | | |            (60), (64), (66), (67), (68), (69), (73), (75),
% 228.20/39.76  | | | | | | | | | |            (76), (77), (78), (81), (83), (84), (86), (87),
% 228.20/39.76  | | | | | | | | | |            (88), (92), (93), (94), (95), (97), (98), (99),
% 228.20/39.76  | | | | | | | | | |            (103), (104), (105), (106), (107), (110), (111),
% 228.20/39.76  | | | | | | | | | |            (112), (113), (114), (116), (118), (120), (121),
% 228.20/39.76  | | | | | | | | | |            (176) are inconsistent by sub-proof #523.
% 228.20/39.76  | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | Case 2:
% 228.20/39.76  | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | |   (177)  all_57_12 = e1 & op(e0, e3) = e1
% 228.20/39.76  | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | | ALPHA: (177) implies:
% 228.20/39.76  | | | | | | | | | |   (178)  all_57_12 = e1
% 228.20/39.76  | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | | COMBINE_EQS: (5), (178) imply:
% 228.20/39.76  | | | | | | | | | |   (179)  e1 = e0
% 228.20/39.76  | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | | COMBINE_EQS: (34), (179) imply:
% 228.20/39.76  | | | | | | | | | |   (180)  all_57_7 = e0
% 228.20/39.76  | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10),
% 228.20/39.76  | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 228.20/39.76  | | | | | | | | | |            (19), (20), (21), (22), (23), (24), (25), (26),
% 228.20/39.76  | | | | | | | | | |            (27), (29), (30), (31), (32), (33), (35), (36),
% 228.20/39.76  | | | | | | | | | |            (37), (38), (39), (40), (41), (42), (43), (44),
% 228.20/39.76  | | | | | | | | | |            (45), (46), (47), (48), (49), (50), (51), (52),
% 228.20/39.76  | | | | | | | | | |            (53), (54), (55), (56), (57), (58), (59), (60),
% 228.20/39.76  | | | | | | | | | |            (62), (63), (64), (65), (66), (68), (69), (70),
% 228.20/39.76  | | | | | | | | | |            (71), (73), (74), (75), (76), (77), (78), (79),
% 228.20/39.76  | | | | | | | | | |            (81), (82), (83), (84), (85), (86), (87), (88),
% 228.20/39.76  | | | | | | | | | |            (90), (91), (92), (93), (94), (95), (96), (97),
% 228.20/39.76  | | | | | | | | | |            (98), (99), (101), (102), (103), (104), (105),
% 228.20/39.76  | | | | | | | | | |            (106), (107), (109), (110), (111), (112), (113),
% 228.20/39.76  | | | | | | | | | |            (114), (115), (116), (117), (118), (120), (121),
% 228.20/39.76  | | | | | | | | | |            (131), (142), (180) are inconsistent by sub-proof
% 228.20/39.76  | | | | | | | | | |            #462.
% 228.20/39.76  | | | | | | | | | | 
% 228.20/39.76  | | | | | | | | | End of split
% 228.20/39.76  | | | | | | | | | 
% 228.20/39.76  | | | | | | | | End of split
% 228.20/39.76  | | | | | | | | 
% 228.20/39.76  | | | | | | | End of split
% 228.20/39.76  | | | | | | | 
% 228.20/39.76  | | | | | | End of split
% 228.20/39.76  | | | | | | 
% 228.20/39.76  | | | | | Case 2:
% 228.20/39.76  | | | | | | 
% 228.20/39.76  | | | | | |   (181)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 &
% 228.20/39.76  | | | | | |            op(e0, e0) = e2)
% 228.20/39.76  | | | | | | 
% 228.20/39.76  | | | | | | BETA: splitting (181) gives:
% 228.20/39.76  | | | | | | 
% 228.20/39.76  | | | | | | Case 1:
% 228.20/39.76  | | | | | | | 
% 228.20/39.76  | | | | | | |   (182)  all_57_11 = e2 & op(e1, e0) = e2
% 228.20/39.76  | | | | | | | 
% 228.20/39.76  | | | | | | | REF_CLOSE: (2), (5), (6), (10), (43), (61), (68), (75), (80),
% 228.20/39.76  | | | | | | |            (103), (107), (182) are inconsistent by sub-proof #461.
% 228.20/39.76  | | | | | | | 
% 228.20/39.76  | | | | | | Case 2:
% 228.20/39.76  | | | | | | | 
% 228.20/39.76  | | | | | | |   (183)  all_57_15 = e2 & op(e0, e0) = e2
% 228.20/39.76  | | | | | | | 
% 228.20/39.76  | | | | | | | ALPHA: (183) implies:
% 228.20/39.76  | | | | | | |   (184)  all_57_15 = e2
% 228.20/39.76  | | | | | | | 
% 228.20/39.76  | | | | | | | COMBINE_EQS: (56), (184) imply:
% 228.20/39.76  | | | | | | |   (185)  e3 = e2
% 228.20/39.76  | | | | | | | 
% 228.20/39.76  | | | | | | | COMBINE_EQS: (100), (185) imply:
% 228.20/39.76  | | | | | | |   (186)  all_57_1 = e2
% 228.20/39.76  | | | | | | | 
% 228.20/39.76  | | | | | | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (10), (11), (12), (13),
% 228.20/39.76  | | | | | | |            (14), (16), (19), (20), (22), (24), (28), (30), (33),
% 228.20/39.76  | | | | | | |            (34), (35), (36), (39), (40), (41), (42), (43), (45),
% 228.20/39.76  | | | | | | |            (48), (49), (50), (53), (55), (56), (57), (60), (64),
% 228.20/39.76  | | | | | | |            (66), (67), (68), (69), (73), (75), (76), (77), (78),
% 228.20/39.76  | | | | | | |            (81), (83), (84), (86), (87), (88), (92), (93), (94),
% 228.20/39.76  | | | | | | |            (95), (97), (98), (99), (103), (104), (105), (106),
% 228.20/39.76  | | | | | | |            (107), (110), (111), (112), (113), (114), (116), (118),
% 228.20/39.76  | | | | | | |            (120), (121), (186) are inconsistent by sub-proof #512.
% 228.20/39.76  | | | | | | | 
% 228.20/39.76  | | | | | | End of split
% 228.20/39.76  | | | | | | 
% 228.20/39.76  | | | | | End of split
% 228.20/39.76  | | | | | 
% 228.20/39.76  | | | | Case 2:
% 228.20/39.76  | | | | | 
% 228.20/39.76  | | | | |   (187)  all_57_5 = e0 & op(e2, e1) = e0
% 228.20/39.76  | | | | | 
% 228.20/39.76  | | | | | ALPHA: (187) implies:
% 228.20/39.76  | | | | |   (188)  all_57_5 = e0
% 228.20/39.76  | | | | | 
% 228.20/39.76  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12),
% 228.20/39.76  | | | | |            (13), (14), (16), (19), (20), (22), (24), (28), (30), (33),
% 228.20/39.76  | | | | |            (35), (36), (39), (40), (41), (42), (43), (45), (48), (49),
% 228.20/39.76  | | | | |            (50), (53), (55), (56), (57), (60), (64), (66), (68), (69),
% 228.20/39.76  | | | | |            (73), (75), (76), (77), (78), (80), (81), (83), (84), (86),
% 228.20/39.76  | | | | |            (87), (88), (92), (93), (94), (95), (97), (98), (99),
% 228.20/39.76  | | | | |            (103), (104), (105), (106), (107), (110), (111), (112),
% 228.20/39.76  | | | | |            (113), (114), (116), (118), (120), (121), (188) are
% 228.20/39.76  | | | | |            inconsistent by sub-proof #460.
% 228.20/39.76  | | | | | 
% 228.20/39.76  | | | | End of split
% 228.20/39.76  | | | | 
% 228.20/39.76  | | | Case 2:
% 228.20/39.76  | | | | 
% 228.20/39.76  | | | |   (189)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0,
% 228.20/39.76  | | | |              e1) = e0)
% 228.20/39.76  | | | | 
% 228.20/39.76  | | | | BETA: splitting (189) gives:
% 228.20/39.76  | | | | 
% 228.20/39.76  | | | | Case 1:
% 228.20/39.76  | | | | | 
% 228.20/39.76  | | | | |   (190)  all_57_8 = e0 & op(e1, e1) = e0
% 228.20/39.76  | | | | | 
% 228.20/39.76  | | | | | REF_CLOSE: (2), (5), (6), (10), (43), (68), (75), (79), (80), (103),
% 228.20/39.76  | | | | |            (107), (190) are inconsistent by sub-proof #508.
% 228.20/39.76  | | | | | 
% 228.20/39.76  | | | | Case 2:
% 228.20/39.76  | | | | | 
% 228.20/39.76  | | | | |   (191)  all_57_14 = e0 & op(e0, e1) = e0
% 228.20/39.76  | | | | | 
% 228.20/39.76  | | | | | REF_CLOSE: (75), (131), (191) are inconsistent by sub-proof #2181.
% 228.20/39.76  | | | | | 
% 228.20/39.76  | | | | End of split
% 228.20/39.76  | | | | 
% 228.20/39.76  | | | End of split
% 228.20/39.76  | | | 
% 228.20/39.76  | | Case 2:
% 228.20/39.76  | | | 
% 228.20/39.76  | | |   (192)  all_57_15 = e1 & op(e0, e0) = e1
% 228.20/39.76  | | | 
% 228.20/39.76  | | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (10), (11), (12), (13), (14),
% 228.20/39.76  | | |            (16), (19), (20), (22), (24), (30), (33), (35), (36), (39),
% 228.20/39.76  | | |            (40), (41), (42), (43), (45), (48), (49), (50), (53), (55),
% 228.20/39.76  | | |            (56), (57), (60), (64), (66), (67), (68), (69), (73), (75),
% 228.20/39.76  | | |            (76), (77), (78), (80), (81), (83), (84), (86), (87), (88),
% 228.20/39.76  | | |            (92), (93), (94), (95), (97), (98), (99), (103), (104), (105),
% 228.20/39.76  | | |            (106), (107), (110), (111), (112), (113), (114), (116), (118),
% 228.20/39.76  | | |            (120), (121), (192) are inconsistent by sub-proof #459.
% 228.20/39.76  | | | 
% 228.20/39.76  | | End of split
% 228.20/39.76  | | 
% 228.20/39.76  | End of split
% 228.20/39.76  | 
% 228.20/39.76  End of proof
% 228.20/39.76  
% 228.20/39.76  Sub-proof #459 shows that the following formulas are inconsistent:
% 228.20/39.76  ----------------------------------------------------------------
% 228.23/39.76    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.23/39.76    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.23/39.76    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.23/39.76         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.23/39.76    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.23/39.76         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.23/39.76    (5)   ~ (all_53_8 = all_53_12)
% 228.23/39.76    (6)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.23/39.76         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.23/39.76    (7)   ~ (e3 = e1)
% 228.23/39.76    (8)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.23/39.76         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.23/39.76    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.23/39.76           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.23/39.76    (10)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.23/39.76          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.23/39.76    (11)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.23/39.76            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.23/39.76              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.23/39.76    (12)   ~ (all_6_2 = e3)
% 228.23/39.76    (13)  op(e1, e1) = all_6_2
% 228.23/39.76    (14)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.23/39.76    (15)   ~ (all_53_9 = e0)
% 228.23/39.76    (16)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.23/39.76          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.23/39.76    (17)  all_57_15 = e1 & op(e0, e0) = e1
% 228.23/39.76    (18)   ~ (all_53_4 = all_53_12)
% 228.23/39.76    (19)   ~ (all_53_8 = all_53_9)
% 228.23/39.76    (20)  all_42_2 = all_6_2
% 228.23/39.76    (21)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.23/39.76          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.23/39.76    (22)   ~ (all_53_9 = all_6_2)
% 228.23/39.76    (23)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.23/39.76          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.23/39.76    (24)  all_57_3 = e0
% 228.23/39.76    (25)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.23/39.76          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.23/39.76    (26)   ~ (e3 = e2)
% 228.23/39.76    (27)  all_55_1 = all_53_4
% 228.23/39.76    (28)   ~ (e3 = e0)
% 228.23/39.76    (29)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.23/39.76          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.23/39.76    (30)   ~ (all_53_8 = all_6_2)
% 228.23/39.76    (31)  all_55_2 = all_53_8
% 228.23/39.76    (32)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.23/39.76    (33)  all_57_15 = e3
% 228.23/39.76    (34)  op(e3, e3) = e2
% 228.23/39.76    (35)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.23/39.76          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.23/39.76            e1)
% 228.23/39.76    (36)   ~ (all_53_4 = all_53_8)
% 228.23/39.76    (37)  op(e3, e2) = all_53_4
% 228.23/39.76    (38)  op(e1, e1) = e1
% 228.23/39.76    (39)   ~ (e2 = e0)
% 228.23/39.76    (40)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.23/39.76            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.23/39.76            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.23/39.76            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.23/39.76              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.23/39.76            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.23/39.76            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.23/39.76              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.23/39.76              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.23/39.76            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.23/39.76            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.23/39.76            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.23/39.76              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.23/39.76              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.23/39.76            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.23/39.76              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.23/39.76            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.23/39.76            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.23/39.76              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.23/39.76              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.23/39.76            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.23/39.76            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.23/39.76    (41)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.23/39.76          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.23/39.76    (42)   ~ (e1 = e0)
% 228.23/39.76    (43)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.23/39.76            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.23/39.76              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.23/39.76    (44)   ~ (all_53_4 = e0)
% 228.23/39.76    (45)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.23/39.76          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.23/39.76    (46)  all_57_6 = e3
% 228.23/39.76    (47)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.23/39.76          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.23/39.76    (48)  op(e0, e0) = e3
% 228.23/39.76    (49)   ~ (all_53_4 = all_53_6)
% 228.23/39.76    (50)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.23/39.76          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.23/39.76            e2)
% 228.23/39.76    (51)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.23/39.76              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.23/39.76                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.23/39.76                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.23/39.76    (52)  all_55_10 = all_6_2
% 228.23/39.76    (53)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.23/39.76          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.23/39.76    (54)  all_38_2 = all_6_2
% 228.23/39.76    (55)  all_55_3 = all_53_12
% 228.23/39.76    (56)   ~ (all_53_12 = e3)
% 228.23/39.76    (57)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.23/39.76            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.23/39.76              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.23/39.76    (58)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.23/39.76          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.23/39.76    (59)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.23/39.76          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.23/39.76    (60)   ~ (e2 = e1)
% 228.23/39.76    (61)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.23/39.76          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.23/39.76    (62)  op(e2, e1) = all_53_9
% 228.23/39.76    (63)  op(e1, e2) = all_53_6
% 228.23/39.76    (64)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.23/39.76          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.23/39.76    (65)  all_24_2 = all_6_2
% 228.23/39.77    (66)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.23/39.77          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.23/39.77    (67)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.23/39.77          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.23/39.77    (68)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.23/39.77          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.23/39.77    (69)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.23/39.77          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.23/39.77    (70)  op(e3, e1) = all_53_8
% 228.23/39.77    (71)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.23/39.77          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.23/39.77    (72)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.23/39.77          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.23/39.77    (73)  op(e3, e0) = all_53_12
% 228.23/39.77  
% 228.23/39.77  Begin of proof
% 228.23/39.77  | 
% 228.23/39.77  | ALPHA: (17) implies:
% 228.23/39.77  |   (74)  all_57_15 = e1
% 228.23/39.77  | 
% 228.23/39.77  | COMBINE_EQS: (33), (74) imply:
% 228.23/39.77  |   (75)  e3 = e1
% 228.23/39.77  | 
% 228.23/39.77  | COMBINE_EQS: (46), (75) imply:
% 228.23/39.77  |   (76)  all_57_6 = e1
% 228.23/39.77  | 
% 228.23/39.77  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.23/39.77  |            (13), (14), (15), (16), (18), (19), (20), (21), (22), (23), (24),
% 228.23/39.77  |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 228.23/39.77  |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (47),
% 228.23/39.77  |            (48), (49), (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 228.23/39.77  |            (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 228.23/39.77  |            (70), (71), (72), (73), (76) are inconsistent by sub-proof #523.
% 228.23/39.77  | 
% 228.23/39.77  End of proof
% 228.23/39.77  
% 228.23/39.77  Sub-proof #460 shows that the following formulas are inconsistent:
% 228.23/39.77  ----------------------------------------------------------------
% 228.23/39.77    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.23/39.77    (2)  all_57_0 = e2
% 228.23/39.77    (3)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.23/39.77    (4)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.23/39.77         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.23/39.77    (5)  all_57_12 = e0
% 228.23/39.77    (6)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.23/39.77         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.23/39.77    (7)   ~ (all_53_8 = all_53_12)
% 228.23/39.77    (8)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.23/39.77         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.23/39.77    (9)   ~ (e3 = e1)
% 228.23/39.77    (10)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.23/39.77          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.23/39.77    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.23/39.77            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.23/39.77    (12)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.23/39.77          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.23/39.77    (13)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.23/39.77            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.23/39.77              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.23/39.77    (14)   ~ (all_6_2 = e3)
% 228.23/39.77    (15)  op(e1, e1) = all_6_2
% 228.23/39.77    (16)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.23/39.77    (17)   ~ (all_53_9 = e0)
% 228.23/39.77    (18)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.23/39.77          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.23/39.77    (19)  all_57_9 = e1
% 228.23/39.77    (20)   ~ (all_53_4 = all_53_12)
% 228.23/39.77    (21)   ~ (all_53_8 = all_53_9)
% 228.23/39.77    (22)  all_42_2 = all_6_2
% 228.23/39.77    (23)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.23/39.77          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.23/39.77    (24)   ~ (all_53_9 = all_6_2)
% 228.23/39.77    (25)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.23/39.77          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.23/39.77    (26)  all_57_3 = e0
% 228.23/39.77    (27)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.23/39.77          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.23/39.77    (28)   ~ (e3 = e2)
% 228.23/39.77    (29)  all_55_1 = all_53_4
% 228.23/39.77    (30)   ~ (e3 = e0)
% 228.23/39.77    (31)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.23/39.77          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.23/39.77    (32)   ~ (all_53_8 = all_6_2)
% 228.23/39.77    (33)  all_55_2 = all_53_8
% 228.23/39.77    (34)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.23/39.77    (35)  all_57_15 = e3
% 228.23/39.77    (36)  op(e3, e3) = e2
% 228.23/39.77    (37)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.23/39.77          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.23/39.77            e1)
% 228.23/39.77    (38)   ~ (all_53_4 = all_53_8)
% 228.23/39.77    (39)  op(e3, e2) = all_53_4
% 228.23/39.77    (40)   ~ (e2 = e0)
% 228.23/39.77    (41)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.23/39.77            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.23/39.77            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.23/39.77            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.23/39.77              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.23/39.77            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.23/39.77            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.23/39.77              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.23/39.77              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.23/39.77            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.23/39.77            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.23/39.77            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.23/39.77              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.23/39.77              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.23/39.77            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.23/39.77              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.23/39.77            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.23/39.77            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.23/39.77              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.23/39.77              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.23/39.77            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.23/39.77            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.23/39.77    (42)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.23/39.77          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.23/39.77    (43)   ~ (e1 = e0)
% 228.23/39.77    (44)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.23/39.77            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.23/39.77              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.23/39.77    (45)   ~ (all_53_4 = e0)
% 228.23/39.77    (46)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.23/39.77          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.23/39.77    (47)  all_57_6 = e3
% 228.23/39.77    (48)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.23/39.77          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.23/39.77    (49)  op(e0, e0) = e3
% 228.23/39.77    (50)   ~ (all_53_4 = all_53_6)
% 228.23/39.77    (51)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.23/39.77          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.23/39.77            e2)
% 228.23/39.77    (52)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.23/39.77              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.23/39.77                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.23/39.77                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.23/39.77    (53)  all_55_10 = all_6_2
% 228.23/39.77    (54)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.23/39.77          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.23/39.77    (55)  all_38_2 = all_6_2
% 228.23/39.77    (56)  all_55_3 = all_53_12
% 228.23/39.77    (57)   ~ (all_53_12 = e3)
% 228.23/39.77    (58)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.23/39.77            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.23/39.77              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.23/39.77    (59)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.23/39.77          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.23/39.77    (60)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.23/39.77          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.23/39.77    (61)   ~ (e2 = e1)
% 228.23/39.77    (62)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.23/39.77          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.23/39.77    (63)  op(e2, e1) = all_53_9
% 228.23/39.77    (64)  op(e1, e2) = all_53_6
% 228.23/39.77    (65)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.23/39.77          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.23/39.77    (66)  all_24_2 = all_6_2
% 228.23/39.77    (67)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.23/39.77          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.23/39.77    (68)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.23/39.77          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.23/39.77    (69)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.23/39.77          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.23/39.77    (70)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.23/39.77          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.23/39.77    (71)  op(e3, e1) = all_53_8
% 228.23/39.77    (72)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.23/39.77          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.23/39.77    (73)  all_57_5 = e0
% 228.23/39.77    (74)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.23/39.77          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.23/39.77    (75)  op(e3, e0) = all_53_12
% 228.23/39.77  
% 228.23/39.77  Begin of proof
% 228.23/39.77  | 
% 228.23/39.77  | BETA: splitting (59) gives:
% 228.23/39.77  | 
% 228.23/39.77  | Case 1:
% 228.23/39.77  | | 
% 228.23/39.77  | |   (76)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 228.23/39.77  | |           e2)
% 228.23/39.77  | | 
% 228.23/39.77  | | BETA: splitting (76) gives:
% 228.23/39.77  | | 
% 228.23/39.77  | | Case 1:
% 228.23/39.77  | | | 
% 228.23/39.77  | | |   (77)  all_57_2 = e2 & op(e2, e3) = e2
% 228.23/39.77  | | | 
% 228.23/39.77  | | | ALPHA: (77) implies:
% 228.23/39.77  | | |   (78)  all_57_2 = e2
% 228.23/39.77  | | | 
% 228.23/39.77  | | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13),
% 228.23/39.77  | | |            (14), (15), (16), (17), (18), (20), (21), (22), (23), (24),
% 228.23/39.77  | | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 228.23/39.77  | | |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44),
% 228.23/39.77  | | |            (45), (46), (48), (49), (50), (51), (52), (53), (54), (55),
% 228.23/39.77  | | |            (56), (57), (58), (59), (60), (61), (62), (63), (64), (65),
% 228.23/39.77  | | |            (66), (67), (68), (69), (70), (71), (72), (74), (75), (78) are
% 228.23/39.77  | | |            inconsistent by sub-proof #544.
% 228.23/39.77  | | | 
% 228.23/39.77  | | Case 2:
% 228.23/39.77  | | | 
% 228.23/39.77  | | |   (79)  all_57_3 = e2 & op(e2, e2) = e2
% 228.23/39.77  | | | 
% 228.23/39.77  | | | REF_CLOSE: (2), (5), (6), (9), (26), (28), (40), (43), (47), (61), (65),
% 228.23/39.77  | | |            (79) are inconsistent by sub-proof #784.
% 228.23/39.77  | | | 
% 228.23/39.77  | | End of split
% 228.23/39.77  | | 
% 228.23/39.77  | Case 2:
% 228.23/39.77  | | 
% 228.23/39.77  | |   (80)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 228.23/39.77  | |           e2)
% 228.23/39.77  | | 
% 228.23/39.77  | | BETA: splitting (80) gives:
% 228.23/39.77  | | 
% 228.23/39.77  | | Case 1:
% 228.23/39.77  | | | 
% 228.23/39.77  | | |   (81)  all_57_5 = e2 & op(e2, e1) = e2
% 228.23/39.77  | | | 
% 228.23/39.77  | | | ALPHA: (81) implies:
% 228.23/39.77  | | |   (82)  all_57_5 = e2
% 228.23/39.77  | | | 
% 228.23/39.77  | | | COMBINE_EQS: (73), (82) imply:
% 228.23/39.77  | | |   (83)  e2 = e0
% 228.23/39.77  | | | 
% 228.23/39.77  | | | SIMP: (83) implies:
% 228.23/39.77  | | |   (84)  e2 = e0
% 228.23/39.77  | | | 
% 228.23/39.77  | | | COMBINE_EQS: (2), (84) imply:
% 228.23/39.77  | | |   (85)  all_57_0 = e0
% 228.23/39.77  | | | 
% 228.23/39.77  | | | REF_CLOSE: (5), (6), (9), (28), (40), (43), (47), (61), (65), (85) are
% 228.23/39.77  | | |            inconsistent by sub-proof #1425.
% 228.23/39.77  | | | 
% 228.23/39.77  | | Case 2:
% 228.23/39.77  | | | 
% 228.23/39.77  | | |   (86)  all_57_10 = e2 & op(e2, e0) = e2
% 228.23/39.77  | | | 
% 228.23/39.77  | | | ALPHA: (86) implies:
% 228.23/39.77  | | |   (87)  all_57_10 = e2
% 228.23/39.77  | | | 
% 228.23/39.77  | | | REF_CLOSE: (4), (9), (19), (26), (28), (30), (35), (40), (43), (52), (54),
% 228.23/39.77  | | |            (61), (62), (73), (87) are inconsistent by sub-proof #967.
% 228.23/39.77  | | | 
% 228.23/39.77  | | End of split
% 228.23/39.77  | | 
% 228.23/39.77  | End of split
% 228.23/39.77  | 
% 228.23/39.77  End of proof
% 228.23/39.77  
% 228.23/39.77  Sub-proof #461 shows that the following formulas are inconsistent:
% 228.23/39.77  ----------------------------------------------------------------
% 228.23/39.77    (1)  all_57_0 = e2
% 228.23/39.77    (2)  all_57_12 = e0
% 228.23/39.77    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.23/39.77         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.23/39.77    (4)   ~ (e3 = e1)
% 228.23/39.77    (5)  all_57_11 = e2 & op(e1, e0) = e2
% 228.23/39.77    (6)   ~ (e3 = e2)
% 228.23/39.77    (7)  all_57_11 = e0
% 228.23/39.77    (8)   ~ (e2 = e0)
% 228.23/39.77    (9)   ~ (e1 = e0)
% 228.23/39.77    (10)  all_57_6 = e3
% 228.23/39.77    (11)   ~ (e2 = e1)
% 228.23/39.77    (12)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.23/39.77          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.23/39.77  
% 228.23/39.77  Begin of proof
% 228.23/39.77  | 
% 228.23/39.77  | ALPHA: (5) implies:
% 228.23/39.77  |   (13)  all_57_11 = e2
% 228.23/39.77  | 
% 228.23/39.77  | COMBINE_EQS: (7), (13) imply:
% 228.23/39.77  |   (14)  e2 = e0
% 228.23/39.77  | 
% 228.23/39.77  | SIMP: (14) implies:
% 228.23/39.77  |   (15)  e2 = e0
% 228.23/39.77  | 
% 228.23/39.77  | COMBINE_EQS: (1), (15) imply:
% 228.23/39.77  |   (16)  all_57_0 = e0
% 228.23/39.77  | 
% 228.23/39.77  | REF_CLOSE: (2), (3), (4), (6), (8), (9), (10), (11), (12), (16) are
% 228.23/39.77  |            inconsistent by sub-proof #1425.
% 228.23/39.77  | 
% 228.23/39.77  End of proof
% 228.23/39.77  
% 228.23/39.77  Sub-proof #462 shows that the following formulas are inconsistent:
% 228.23/39.77  ----------------------------------------------------------------
% 228.23/39.77    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.23/39.77    (2)  all_57_0 = e2
% 228.23/39.77    (3)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.23/39.77    (4)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.23/39.77         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.23/39.77    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.23/39.77         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.23/39.77    (6)   ~ (all_53_8 = all_53_12)
% 228.23/39.77    (7)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.23/39.77         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.23/39.77    (8)   ~ (all_53_8 = all_53_11)
% 228.23/39.77    (9)   ~ (e3 = e1)
% 228.23/39.77    (10)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.23/39.77          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.23/39.77    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.23/39.77            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.23/39.77    (12)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.23/39.77          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.23/39.77    (13)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.23/39.77            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.23/39.77              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.23/39.77    (14)   ~ (all_53_3 = e3)
% 228.23/39.77    (15)   ~ (all_6_2 = e3)
% 228.23/39.77    (16)  ( ~ (all_28_0 = e0) & op(all_28_1, e3) = all_28_0 & op(e3, e2) =
% 228.23/39.77            all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 = e1) & op(e3,
% 228.23/39.77              e2) = all_28_1 & $i(all_28_1))
% 228.23/39.77    (17)   ~ (all_53_9 = e1)
% 228.23/39.77    (18)  op(e1, e1) = all_6_2
% 228.23/39.77    (19)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.23/39.77    (20)   ~ (all_53_1 = all_53_9)
% 228.23/39.77    (21)   ~ (all_53_9 = e0)
% 228.23/39.77    (22)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 228.23/39.77    (23)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.23/39.77          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.23/39.77    (24)   ~ (all_52_17 = e2)
% 228.23/39.77    (25)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 228.23/39.77            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 228.23/39.77              e3) = all_22_1 & $i(all_22_1))
% 228.23/39.77    (26)   ~ (all_53_8 = e1)
% 228.23/39.77    (27)  op(all_52_17, all_52_17) = e3
% 228.23/39.77    (28)   ~ (all_53_4 = all_53_12)
% 228.23/39.77    (29)   ~ (all_52_17 = all_52_23)
% 228.23/39.77    (30)   ~ (all_52_17 = e1)
% 228.23/39.77    (31)   ~ (all_53_8 = all_53_9)
% 228.23/39.77    (32)  all_42_2 = all_6_2
% 228.23/39.77    (33)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.23/39.77          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.23/39.77    (34)   ~ (all_53_9 = all_53_11)
% 228.23/39.77    (35)  all_55_4 = all_53_1
% 228.23/39.77    (36)   ~ (all_53_9 = all_6_2)
% 228.23/39.77    (37)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.23/39.77          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.23/39.77    (38)  all_57_3 = e0
% 228.23/39.77    (39)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.23/39.77          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.23/39.77    (40)   ~ (e3 = e2)
% 228.23/39.77    (41)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 228.23/39.77    (42)  all_55_1 = all_53_4
% 228.23/39.77    (43)   ~ (all_53_1 = all_53_3)
% 228.23/39.77    (44)   ~ (all_53_1 = all_52_17)
% 228.23/39.77    (45)   ~ (e3 = e0)
% 228.23/39.77    (46)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.23/39.77          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.23/39.77    (47)   ~ (all_53_8 = all_6_2)
% 228.23/39.77    (48)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.23/39.77    (49)  all_55_11 = all_52_23
% 228.23/39.77    (50)  all_55_2 = all_53_8
% 228.23/39.77    (51)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 228.23/39.77    (52)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.23/39.77    (53)  all_57_15 = e3
% 228.23/39.77    (54)  op(e3, e3) = e2
% 228.23/39.77    (55)   ~ (all_53_3 = e2)
% 228.23/39.77    (56)   ~ (all_53_3 = all_52_17)
% 228.23/39.77    (57)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.23/39.77          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.23/39.77            e1)
% 228.23/39.77    (58)  all_57_10 = e2
% 228.23/39.77    (59)   ~ (all_52_23 = e3)
% 228.23/39.77    (60)  op(e1, e0) = all_52_23
% 228.23/39.77    (61)   ~ (all_53_4 = all_53_8)
% 228.23/39.77    (62)  all_55_6 = all_53_9
% 228.23/39.77    (63)  op(e3, e2) = all_53_4
% 228.23/39.77    (64)   ~ (e2 = e0)
% 228.23/39.77    (65)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.23/39.77            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.23/39.77            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.23/39.77            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.23/39.77              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.23/39.77            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.23/39.77            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.23/39.77              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.23/39.77              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.23/39.77            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.23/39.77            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.23/39.77            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.23/39.77              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.23/39.77              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.23/39.77            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.23/39.77              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.23/39.77            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.23/39.77            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.23/39.77              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.23/39.77              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.23/39.77            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.23/39.77            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.23/39.77    (66)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 228.23/39.77            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 228.23/39.77              e3) = all_12_1 & $i(all_12_1))
% 228.23/39.77    (67)  all_55_12 = all_53_3
% 228.23/39.77    (68)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.23/39.77          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.23/39.77    (69)   ~ (all_53_1 = e0)
% 228.23/39.77    (70)   ~ (e1 = e0)
% 228.23/39.77    (71)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.23/39.77            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.23/39.77              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.23/39.77    (72)   ~ (all_53_4 = e0)
% 228.23/39.77    (73)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.23/39.77          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.23/39.77    (74)  all_57_8 = e2
% 228.23/39.77    (75)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.23/39.77          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.23/39.77    (76)  all_57_14 = e1
% 228.23/39.77    (77)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 228.23/39.77    (78)  op(e0, e0) = e3
% 228.23/39.77    (79)   ~ (all_53_4 = all_53_6)
% 228.23/39.77    (80)  ( ~ (all_20_0 = e1) & op(all_20_1, e3) = all_20_0 & op(e3, e2) =
% 228.23/39.77            all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e0) & op(e3,
% 228.23/39.77              e2) = all_20_1 & $i(all_20_1))
% 228.23/39.77    (81)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.23/39.77          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.23/39.77            e2)
% 228.23/39.77    (82)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.23/39.77              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.23/39.77                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.23/39.77                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.23/39.77    (83)  all_55_10 = all_6_2
% 228.23/39.77    (84)   ~ (all_53_11 = e1)
% 228.23/39.77    (85)  all_55_8 = all_52_17
% 228.23/39.77    (86)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.23/39.77          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.23/39.77    (87)  all_38_2 = all_6_2
% 228.23/39.77    (88)  all_55_3 = all_53_12
% 228.23/39.77    (89)   ~ (all_53_12 = e3)
% 228.23/39.77    (90)   ~ (all_53_4 = e2)
% 228.23/39.77    (91)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.23/39.77            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.23/39.77              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.23/39.77    (92)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.23/39.77          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.23/39.78    (93)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.23/39.78          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.23/39.78    (94)   ~ (all_52_23 = e1)
% 228.23/39.78    (95)   ~ (all_53_1 = e2)
% 228.23/39.78    (96)   ~ (e2 = e1)
% 228.23/39.78    (97)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.23/39.78          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.23/39.78    (98)  op(e2, e1) = all_53_9
% 228.23/39.78    (99)  op(e1, e2) = all_53_6
% 228.23/39.78    (100)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.23/39.78           (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.23/39.78    (101)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 228.23/39.78    (102)  all_24_2 = all_6_2
% 228.23/39.78    (103)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.23/39.78           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.23/39.78    (104)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.23/39.78           (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.23/39.78    (105)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.23/39.78           | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.23/39.78             e1)
% 228.23/39.78    (106)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.23/39.78           (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.23/39.78    (107)  all_55_14 = all_53_11
% 228.23/39.78    (108)  op(e3, e1) = all_53_8
% 228.23/39.78    (109)   ~ (all_53_11 = e3)
% 228.23/39.78    (110)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.23/39.78           (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.23/39.78    (111)  all_57_7 = e0
% 228.23/39.78    (112)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.23/39.78           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.23/39.78    (113)  op(e3, e0) = all_53_12
% 228.23/39.78  
% 228.23/39.78  Begin of proof
% 228.23/39.78  | 
% 228.23/39.78  | BETA: splitting (39) gives:
% 228.23/39.78  | 
% 228.23/39.78  | Case 1:
% 228.23/39.78  | | 
% 228.23/39.78  | |   (114)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) =
% 228.23/39.78  | |            e0)
% 228.23/39.78  | | 
% 228.23/39.78  | | BETA: splitting (114) gives:
% 228.23/39.78  | | 
% 228.23/39.78  | | Case 1:
% 228.23/39.78  | | | 
% 228.23/39.78  | | |   (115)  all_57_4 = e0 & op(e3, e1) = e0
% 228.23/39.78  | | | 
% 228.23/39.78  | | | ALPHA: (115) implies:
% 228.23/39.78  | | |   (116)  all_57_4 = e0
% 228.23/39.78  | | | 
% 228.23/39.78  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.23/39.78  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 228.23/39.78  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 228.23/39.78  | | |            (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 228.23/39.78  | | |            (43), (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 228.23/39.78  | | |            (53), (54), (55), (56), (57), (58), (59), (60), (61), (62),
% 228.23/39.78  | | |            (63), (64), (65), (66), (67), (68), (69), (70), (71), (72),
% 228.23/39.78  | | |            (73), (74), (75), (76), (77), (78), (79), (80), (81), (82),
% 228.23/39.78  | | |            (83), (84), (85), (86), (87), (88), (89), (90), (91), (92),
% 228.23/39.78  | | |            (93), (94), (95), (96), (97), (98), (99), (100), (101), (102),
% 228.23/39.78  | | |            (103), (104), (105), (106), (107), (108), (109), (110), (111),
% 228.23/39.78  | | |            (112), (113), (116) are inconsistent by sub-proof #463.
% 228.23/39.78  | | | 
% 228.23/39.78  | | Case 2:
% 228.23/39.78  | | | 
% 228.23/39.78  | | |   (117)  all_57_5 = e0 & op(e2, e1) = e0
% 228.23/39.78  | | | 
% 228.23/39.78  | | | ALPHA: (117) implies:
% 228.23/39.78  | | |   (118)  all_57_5 = e0
% 228.23/39.78  | | | 
% 228.23/39.78  | | | BETA: splitting (73) gives:
% 228.23/39.78  | | | 
% 228.23/39.78  | | | Case 1:
% 228.23/39.78  | | | | 
% 228.23/39.78  | | | |   (119)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1)
% 228.23/39.78  | | | |            = e3)
% 228.23/39.78  | | | | 
% 228.23/39.78  | | | | BETA: splitting (119) gives:
% 228.23/39.78  | | | | 
% 228.23/39.78  | | | | Case 1:
% 228.23/39.78  | | | | | 
% 228.23/39.78  | | | | |   (120)  all_57_4 = e3 & op(e3, e1) = e3
% 228.23/39.78  | | | | | 
% 228.23/39.78  | | | | | ALPHA: (120) implies:
% 228.23/39.78  | | | | |   (121)  all_57_4 = e3
% 228.23/39.78  | | | | | 
% 228.23/39.78  | | | | | BETA: splitting (12) gives:
% 228.23/39.78  | | | | | 
% 228.23/39.78  | | | | | Case 1:
% 228.23/39.78  | | | | | | 
% 228.23/39.78  | | | | | |   (122)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1,
% 228.23/39.78  | | | | | |              e2) = e3)
% 228.23/39.78  | | | | | | 
% 228.23/39.78  | | | | | | BETA: splitting (122) gives:
% 228.23/39.78  | | | | | | 
% 228.23/39.78  | | | | | | Case 1:
% 228.23/39.78  | | | | | | | 
% 228.23/39.78  | | | | | | |   (123)  all_57_6 = e3 & op(e1, e3) = e3
% 228.23/39.78  | | | | | | | 
% 228.23/39.78  | | | | | | | ALPHA: (123) implies:
% 228.23/39.78  | | | | | | |   (124)  all_57_6 = e3
% 228.23/39.78  | | | | | | | 
% 228.23/39.78  | | | | | | | BETA: splitting (86) gives:
% 228.23/39.78  | | | | | | | 
% 228.23/39.78  | | | | | | | Case 1:
% 228.23/39.78  | | | | | | | | 
% 228.23/39.78  | | | | | | | |   (125)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 &
% 228.23/39.78  | | | | | | | |            op(e2, e2) = e3)
% 228.23/39.78  | | | | | | | | 
% 228.23/39.78  | | | | | | | | BETA: splitting (125) gives:
% 228.23/39.78  | | | | | | | | 
% 228.23/39.78  | | | | | | | | Case 1:
% 228.23/39.78  | | | | | | | | | 
% 228.23/39.78  | | | | | | | | |   (126)  all_57_2 = e3 & op(e2, e3) = e3
% 228.23/39.78  | | | | | | | | | 
% 228.23/39.78  | | | | | | | | | ALPHA: (126) implies:
% 228.23/39.78  | | | | | | | | |   (127)  all_57_2 = e3
% 228.23/39.78  | | | | | | | | | 
% 228.23/39.78  | | | | | | | | | REF_CLOSE: (2), (4), (5), (9), (11), (38), (40), (45), (54),
% 228.23/39.78  | | | | | | | | |            (64), (70), (86), (92), (96), (104), (124), (127)
% 228.23/39.78  | | | | | | | | |            are inconsistent by sub-proof #794.
% 228.23/39.78  | | | | | | | | | 
% 228.23/39.78  | | | | | | | | Case 2:
% 228.23/39.78  | | | | | | | | | 
% 228.23/39.78  | | | | | | | | |   (128)  all_57_3 = e3 & op(e2, e2) = e3
% 228.23/39.78  | | | | | | | | | 
% 228.23/39.78  | | | | | | | | | ALPHA: (128) implies:
% 228.23/39.78  | | | | | | | | |   (129)  all_57_3 = e3
% 228.23/39.78  | | | | | | | | | 
% 228.23/39.78  | | | | | | | | | COMBINE_EQS: (38), (129) imply:
% 228.23/39.78  | | | | | | | | |   (130)  e3 = e0
% 228.23/39.78  | | | | | | | | | 
% 228.23/39.78  | | | | | | | | | SIMP: (130) implies:
% 228.23/39.78  | | | | | | | | |   (131)  e3 = e0
% 228.23/39.78  | | | | | | | | | 
% 228.23/39.78  | | | | | | | | | COMBINE_EQS: (121), (131) imply:
% 228.23/39.78  | | | | | | | | |   (132)  all_57_4 = e0
% 228.23/39.78  | | | | | | | | | 
% 228.23/39.78  | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 228.23/39.78  | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 228.23/39.78  | | | | | | | | |            (19), (20), (21), (22), (23), (24), (25), (26),
% 228.23/39.78  | | | | | | | | |            (27), (28), (29), (30), (31), (32), (33), (34),
% 228.23/39.78  | | | | | | | | |            (35), (36), (37), (38), (39), (40), (41), (42),
% 228.23/39.78  | | | | | | | | |            (43), (44), (45), (46), (47), (48), (49), (50),
% 228.23/39.78  | | | | | | | | |            (51), (52), (53), (54), (55), (56), (57), (58),
% 228.23/39.78  | | | | | | | | |            (59), (60), (61), (62), (63), (64), (65), (66),
% 228.23/39.78  | | | | | | | | |            (67), (68), (69), (70), (71), (72), (73), (74),
% 228.23/39.78  | | | | | | | | |            (75), (76), (77), (78), (79), (80), (81), (82),
% 228.23/39.78  | | | | | | | | |            (83), (84), (85), (86), (87), (88), (89), (90),
% 228.23/39.78  | | | | | | | | |            (91), (92), (93), (94), (95), (96), (97), (98),
% 228.23/39.78  | | | | | | | | |            (99), (100), (101), (102), (103), (104), (105),
% 228.23/39.78  | | | | | | | | |            (106), (107), (108), (109), (110), (111), (112),
% 228.23/39.78  | | | | | | | | |            (113), (132) are inconsistent by sub-proof #463.
% 228.23/39.78  | | | | | | | | | 
% 228.23/39.78  | | | | | | | | End of split
% 228.23/39.78  | | | | | | | | 
% 228.23/39.78  | | | | | | | Case 2:
% 228.23/39.78  | | | | | | | | 
% 228.23/39.78  | | | | | | | |   (133)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 &
% 228.23/39.78  | | | | | | | |            op(e2, e0) = e3)
% 228.23/39.78  | | | | | | | | 
% 228.23/39.78  | | | | | | | | BETA: splitting (133) gives:
% 228.23/39.78  | | | | | | | | 
% 228.23/39.78  | | | | | | | | Case 1:
% 228.23/39.78  | | | | | | | | | 
% 228.23/39.78  | | | | | | | | |   (134)  all_57_5 = e3 & op(e2, e1) = e3
% 228.23/39.78  | | | | | | | | | 
% 228.23/39.78  | | | | | | | | | ALPHA: (134) implies:
% 228.23/39.78  | | | | | | | | |   (135)  all_57_5 = e3
% 228.23/39.78  | | | | | | | | | 
% 228.23/39.78  | | | | | | | | | COMBINE_EQS: (118), (135) imply:
% 228.23/39.78  | | | | | | | | |   (136)  e3 = e0
% 228.23/39.78  | | | | | | | | | 
% 228.23/39.78  | | | | | | | | | SIMP: (136) implies:
% 228.23/39.78  | | | | | | | | |   (137)  e3 = e0
% 228.23/39.78  | | | | | | | | | 
% 228.23/39.78  | | | | | | | | | COMBINE_EQS: (121), (137) imply:
% 228.23/39.78  | | | | | | | | |   (138)  all_57_4 = e0
% 228.23/39.78  | | | | | | | | | 
% 228.23/39.78  | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 228.23/39.78  | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 228.23/39.78  | | | | | | | | |            (19), (20), (21), (22), (23), (24), (25), (26),
% 228.23/39.78  | | | | | | | | |            (27), (28), (29), (30), (31), (32), (33), (34),
% 228.23/39.78  | | | | | | | | |            (35), (36), (37), (38), (39), (40), (41), (42),
% 228.23/39.78  | | | | | | | | |            (43), (44), (45), (46), (47), (48), (49), (50),
% 228.23/39.78  | | | | | | | | |            (51), (52), (53), (54), (55), (56), (57), (58),
% 228.23/39.78  | | | | | | | | |            (59), (60), (61), (62), (63), (64), (65), (66),
% 228.23/39.78  | | | | | | | | |            (67), (68), (69), (70), (71), (72), (73), (74),
% 228.23/39.78  | | | | | | | | |            (75), (76), (77), (78), (79), (80), (81), (82),
% 228.23/39.78  | | | | | | | | |            (83), (84), (85), (86), (87), (88), (89), (90),
% 228.23/39.78  | | | | | | | | |            (91), (92), (93), (94), (95), (96), (97), (98),
% 228.23/39.78  | | | | | | | | |            (99), (100), (101), (102), (103), (104), (105),
% 228.23/39.78  | | | | | | | | |            (106), (107), (108), (109), (110), (111), (112),
% 228.23/39.78  | | | | | | | | |            (113), (135), (138) are inconsistent by sub-proof
% 228.23/39.78  | | | | | | | | |            #464.
% 228.23/39.78  | | | | | | | | | 
% 228.23/39.78  | | | | | | | | Case 2:
% 228.23/39.78  | | | | | | | | | 
% 228.23/39.78  | | | | | | | | |   (139)  all_57_10 = e3 & op(e2, e0) = e3
% 228.23/39.78  | | | | | | | | | 
% 228.23/39.78  | | | | | | | | | ALPHA: (139) implies:
% 228.23/39.78  | | | | | | | | |   (140)  all_57_10 = e3
% 228.23/39.78  | | | | | | | | | 
% 228.23/39.78  | | | | | | | | | COMBINE_EQS: (58), (140) imply:
% 228.23/39.78  | | | | | | | | |   (141)  e3 = e2
% 228.23/39.78  | | | | | | | | | 
% 228.23/39.78  | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (11), (12), (15), (18), (23),
% 228.23/39.78  | | | | | | | | |            (33), (37), (38), (40), (45), (53), (54), (64),
% 228.23/39.78  | | | | | | | | |            (68), (70), (82), (86), (89), (92), (93), (96),
% 228.23/39.78  | | | | | | | | |            (97), (104), (105), (110), (113), (124), (141) are
% 228.23/39.78  | | | | | | | | |            inconsistent by sub-proof #604.
% 228.23/39.78  | | | | | | | | | 
% 228.23/39.78  | | | | | | | | End of split
% 228.23/39.78  | | | | | | | | 
% 228.23/39.78  | | | | | | | End of split
% 228.23/39.78  | | | | | | | 
% 228.23/39.78  | | | | | | Case 2:
% 228.23/39.78  | | | | | | | 
% 228.23/39.78  | | | | | | |   (142)  all_57_7 = e3 & op(e1, e2) = e3
% 228.23/39.78  | | | | | | | 
% 228.23/39.78  | | | | | | | ALPHA: (142) implies:
% 228.23/39.78  | | | | | | |   (143)  all_57_7 = e3
% 228.23/39.78  | | | | | | | 
% 228.23/39.78  | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (9), (10), (11), (12),
% 228.23/39.78  | | | | | | |            (13), (15), (18), (19), (21), (23), (28), (31), (32),
% 228.23/39.78  | | | | | | |            (33), (36), (37), (38), (39), (40), (42), (45), (46),
% 228.23/39.78  | | | | | | |            (47), (50), (52), (53), (57), (58), (61), (63), (64),
% 228.23/39.78  | | | | | | |            (65), (68), (70), (71), (72), (73), (78), (79), (81),
% 228.23/39.78  | | | | | | |            (82), (83), (86), (87), (88), (89), (91), (92), (96),
% 228.23/39.78  | | | | | | |            (97), (98), (99), (100), (102), (103), (104), (105),
% 228.23/39.78  | | | | | | |            (106), (108), (110), (112), (113), (118), (121), (143)
% 228.23/39.78  | | | | | | |            are inconsistent by sub-proof #469.
% 228.23/39.78  | | | | | | | 
% 228.23/39.78  | | | | | | End of split
% 228.23/39.78  | | | | | | 
% 228.23/39.78  | | | | | Case 2:
% 228.23/39.78  | | | | | | 
% 228.23/39.78  | | | | | |   (144)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 &
% 228.23/39.78  | | | | | |            op(e1, e0) = e3)
% 228.23/39.78  | | | | | | 
% 228.23/39.78  | | | | | | REF_CLOSE: (9), (11), (15), (18), (40), (45), (53), (64), (70),
% 228.23/39.78  | | | | | |            (82), (96), (97), (105), (144) are inconsistent by
% 228.23/39.78  | | | | | |            sub-proof #1786.
% 228.23/39.78  | | | | | | 
% 228.23/39.78  | | | | | End of split
% 228.23/39.78  | | | | | 
% 228.23/39.78  | | | | Case 2:
% 228.23/39.78  | | | | | 
% 228.23/39.78  | | | | |   (145)  all_57_5 = e3 & op(e2, e1) = e3
% 228.23/39.78  | | | | | 
% 228.23/39.78  | | | | | ALPHA: (145) implies:
% 228.23/39.78  | | | | |   (146)  all_57_5 = e3
% 228.23/39.78  | | | | | 
% 228.23/39.78  | | | | | REF_CLOSE: (45), (118), (146) are inconsistent by sub-proof #2471.
% 228.23/39.78  | | | | | 
% 228.23/39.78  | | | | End of split
% 228.23/39.78  | | | | 
% 228.23/39.78  | | | Case 2:
% 228.23/39.78  | | | | 
% 228.23/39.78  | | | |   (147)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0,
% 228.23/39.78  | | | |              e1) = e3)
% 228.23/39.78  | | | | 
% 228.23/39.78  | | | | REF_CLOSE: (9), (11), (15), (18), (40), (45), (53), (57), (64), (70),
% 228.23/39.78  | | | |            (81), (82), (96), (147) are inconsistent by sub-proof #1794.
% 228.23/39.78  | | | | 
% 228.23/39.78  | | | End of split
% 228.23/39.78  | | | 
% 228.23/39.78  | | End of split
% 228.23/39.78  | | 
% 228.23/39.78  | Case 2:
% 228.23/39.78  | | 
% 228.23/39.78  | |   (148)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 228.23/39.78  | |            e0)
% 228.23/39.78  | | 
% 228.23/39.78  | | BETA: splitting (148) gives:
% 228.23/39.78  | | 
% 228.23/39.78  | | Case 1:
% 228.23/39.78  | | | 
% 228.23/39.78  | | |   (149)  all_57_8 = e0 & op(e1, e1) = e0
% 228.23/39.78  | | | 
% 228.23/39.78  | | | REF_CLOSE: (64), (74), (149) are inconsistent by sub-proof #917.
% 228.23/39.78  | | | 
% 228.23/39.78  | | Case 2:
% 228.23/39.78  | | | 
% 228.23/39.78  | | |   (150)  all_57_14 = e0 & op(e0, e1) = e0
% 228.23/39.78  | | | 
% 228.23/39.78  | | | REF_CLOSE: (70), (76), (150) are inconsistent by sub-proof #2181.
% 228.23/39.78  | | | 
% 228.23/39.78  | | End of split
% 228.23/39.78  | | 
% 228.23/39.78  | End of split
% 228.23/39.78  | 
% 228.23/39.78  End of proof
% 228.23/39.78  
% 228.23/39.78  Sub-proof #463 shows that the following formulas are inconsistent:
% 228.23/39.78  ----------------------------------------------------------------
% 228.23/39.78    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.23/39.78    (2)  all_57_0 = e2
% 228.23/39.78    (3)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.23/39.78    (4)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.23/39.78         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.23/39.78    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.23/39.78         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.23/39.78    (6)   ~ (all_53_8 = all_53_12)
% 228.23/39.78    (7)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.23/39.78         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.23/39.78    (8)   ~ (all_53_8 = all_53_11)
% 228.23/39.78    (9)   ~ (e3 = e1)
% 228.23/39.78    (10)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.23/39.78          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.23/39.78    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.23/39.78            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.23/39.78    (12)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.23/39.78          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.23/39.78    (13)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.23/39.78            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.23/39.78              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.23/39.78    (14)   ~ (all_53_3 = e3)
% 228.23/39.78    (15)   ~ (all_6_2 = e3)
% 228.23/39.78    (16)  ( ~ (all_28_0 = e0) & op(all_28_1, e3) = all_28_0 & op(e3, e2) =
% 228.23/39.78            all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 = e1) & op(e3,
% 228.23/39.78              e2) = all_28_1 & $i(all_28_1))
% 228.23/39.78    (17)   ~ (all_53_9 = e1)
% 228.23/39.78    (18)  op(e1, e1) = all_6_2
% 228.23/39.78    (19)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.23/39.78    (20)   ~ (all_53_1 = all_53_9)
% 228.23/39.78    (21)   ~ (all_53_9 = e0)
% 228.23/39.78    (22)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 228.23/39.78    (23)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.23/39.78          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.23/39.78    (24)   ~ (all_52_17 = e2)
% 228.23/39.78    (25)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 228.23/39.78            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 228.23/39.78              e3) = all_22_1 & $i(all_22_1))
% 228.23/39.78    (26)   ~ (all_53_8 = e1)
% 228.23/39.78    (27)  op(all_52_17, all_52_17) = e3
% 228.23/39.78    (28)   ~ (all_53_4 = all_53_12)
% 228.23/39.78    (29)   ~ (all_52_17 = all_52_23)
% 228.23/39.78    (30)  all_57_4 = e0
% 228.23/39.78    (31)   ~ (all_52_17 = e1)
% 228.23/39.78    (32)   ~ (all_53_8 = all_53_9)
% 228.23/39.78    (33)  all_42_2 = all_6_2
% 228.23/39.78    (34)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.23/39.78          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.23/39.78    (35)   ~ (all_53_9 = all_53_11)
% 228.23/39.78    (36)  all_55_4 = all_53_1
% 228.23/39.78    (37)   ~ (all_53_9 = all_6_2)
% 228.23/39.78    (38)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.23/39.78          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.23/39.78    (39)  all_57_3 = e0
% 228.23/39.78    (40)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.23/39.78          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.23/39.78    (41)   ~ (e3 = e2)
% 228.23/39.78    (42)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 228.23/39.78    (43)  all_55_1 = all_53_4
% 228.23/39.78    (44)   ~ (all_53_1 = all_53_3)
% 228.23/39.78    (45)   ~ (all_53_1 = all_52_17)
% 228.23/39.78    (46)   ~ (e3 = e0)
% 228.23/39.78    (47)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.23/39.78          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.23/39.78    (48)   ~ (all_53_8 = all_6_2)
% 228.23/39.78    (49)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.23/39.78    (50)  all_55_11 = all_52_23
% 228.23/39.78    (51)  all_55_2 = all_53_8
% 228.23/39.78    (52)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 228.23/39.78    (53)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.23/39.78    (54)  all_57_15 = e3
% 228.23/39.78    (55)  op(e3, e3) = e2
% 228.23/39.78    (56)   ~ (all_53_3 = e2)
% 228.23/39.78    (57)   ~ (all_53_3 = all_52_17)
% 228.23/39.78    (58)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.23/39.78          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.23/39.78            e1)
% 228.23/39.78    (59)  all_57_10 = e2
% 228.23/39.78    (60)   ~ (all_52_23 = e3)
% 228.23/39.78    (61)  op(e1, e0) = all_52_23
% 228.23/39.78    (62)   ~ (all_53_4 = all_53_8)
% 228.23/39.78    (63)  all_55_6 = all_53_9
% 228.23/39.78    (64)  op(e3, e2) = all_53_4
% 228.23/39.78    (65)   ~ (e2 = e0)
% 228.23/39.78    (66)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.23/39.78            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.23/39.78            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.23/39.78            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.23/39.78              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.23/39.78            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.23/39.78            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.23/39.78              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.23/39.78              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.23/39.78            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.23/39.78            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.23/39.78            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.23/39.78              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.23/39.78              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.23/39.78            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.23/39.78              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.23/39.78            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.23/39.78            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.23/39.78              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.23/39.78              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.23/39.78            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.23/39.78            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.23/39.78    (67)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 228.23/39.78            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 228.23/39.78              e3) = all_12_1 & $i(all_12_1))
% 228.23/39.78    (68)  all_55_12 = all_53_3
% 228.23/39.78    (69)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.23/39.78          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.23/39.78    (70)   ~ (all_53_1 = e0)
% 228.23/39.78    (71)   ~ (e1 = e0)
% 228.23/39.78    (72)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.23/39.78            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.23/39.78              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.23/39.78    (73)   ~ (all_53_4 = e0)
% 228.23/39.78    (74)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.23/39.78          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.23/39.78    (75)  all_57_8 = e2
% 228.23/39.78    (76)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.23/39.78          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.23/39.78    (77)  all_57_14 = e1
% 228.23/39.78    (78)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 228.23/39.78    (79)  op(e0, e0) = e3
% 228.23/39.78    (80)   ~ (all_53_4 = all_53_6)
% 228.23/39.78    (81)  ( ~ (all_20_0 = e1) & op(all_20_1, e3) = all_20_0 & op(e3, e2) =
% 228.23/39.78            all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e0) & op(e3,
% 228.23/39.78              e2) = all_20_1 & $i(all_20_1))
% 228.23/39.78    (82)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.23/39.78          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.23/39.78            e2)
% 228.23/39.78    (83)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.23/39.78              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.23/39.78                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.23/39.78                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.23/39.78    (84)  all_55_10 = all_6_2
% 228.23/39.78    (85)   ~ (all_53_11 = e1)
% 228.23/39.78    (86)  all_55_8 = all_52_17
% 228.23/39.78    (87)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.23/39.78          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.23/39.78    (88)  all_38_2 = all_6_2
% 228.23/39.78    (89)  all_55_3 = all_53_12
% 228.23/39.78    (90)   ~ (all_53_12 = e3)
% 228.23/39.78    (91)   ~ (all_53_4 = e2)
% 228.23/39.78    (92)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.23/39.78            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.23/39.78              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.23/39.78    (93)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.23/39.78          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.23/39.78    (94)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.23/39.78          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.23/39.78    (95)   ~ (all_52_23 = e1)
% 228.23/39.78    (96)   ~ (all_53_1 = e2)
% 228.23/39.78    (97)   ~ (e2 = e1)
% 228.23/39.78    (98)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.23/39.78          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.23/39.78    (99)  op(e2, e1) = all_53_9
% 228.23/39.78    (100)  op(e1, e2) = all_53_6
% 228.23/39.78    (101)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.23/39.78           (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.23/39.78    (102)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 228.23/39.78    (103)  all_24_2 = all_6_2
% 228.23/39.78    (104)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.23/39.78           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.23/39.78    (105)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.23/39.78           (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.23/39.78    (106)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.23/39.78           | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.23/39.78             e1)
% 228.23/39.78    (107)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.23/39.78           (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.23/39.78    (108)  all_55_14 = all_53_11
% 228.23/39.78    (109)  op(e3, e1) = all_53_8
% 228.23/39.78    (110)   ~ (all_53_11 = e3)
% 228.23/39.78    (111)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.23/39.78           (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.23/39.78    (112)  all_57_7 = e0
% 228.23/39.78    (113)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.23/39.78           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.23/39.78    (114)  op(e3, e0) = all_53_12
% 228.23/39.78  
% 228.23/39.78  Begin of proof
% 228.23/39.78  | 
% 228.23/39.78  | BETA: splitting (74) gives:
% 228.23/39.78  | 
% 228.23/39.78  | Case 1:
% 228.23/39.78  | | 
% 228.23/39.78  | |   (115)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) =
% 228.23/39.78  | |            e3)
% 228.23/39.78  | | 
% 228.23/39.78  | | BETA: splitting (115) gives:
% 228.23/39.78  | | 
% 228.23/39.78  | | Case 1:
% 228.23/39.78  | | | 
% 228.23/39.78  | | |   (116)  all_57_4 = e3 & op(e3, e1) = e3
% 228.23/39.78  | | | 
% 228.23/39.78  | | | ALPHA: (116) implies:
% 228.23/39.78  | | |   (117)  all_57_4 = e3
% 228.23/39.78  | | | 
% 228.23/39.78  | | | REF_CLOSE: (30), (46), (117) are inconsistent by sub-proof #2372.
% 228.23/39.78  | | | 
% 228.23/39.78  | | Case 2:
% 228.23/39.78  | | | 
% 228.23/39.78  | | |   (118)  all_57_5 = e3 & op(e2, e1) = e3
% 228.23/39.78  | | | 
% 228.23/39.78  | | | ALPHA: (118) implies:
% 228.23/39.78  | | |   (119)  all_57_5 = e3
% 228.23/39.78  | | | 
% 228.23/39.78  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.23/39.78  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 228.23/39.78  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 228.23/39.78  | | |            (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 228.23/39.78  | | |            (43), (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 228.23/39.78  | | |            (53), (54), (55), (56), (57), (58), (59), (60), (61), (62),
% 228.23/39.78  | | |            (63), (64), (65), (66), (67), (68), (69), (70), (71), (72),
% 228.23/39.78  | | |            (73), (74), (75), (76), (77), (78), (79), (80), (81), (82),
% 228.23/39.78  | | |            (83), (84), (85), (86), (87), (88), (89), (90), (91), (92),
% 228.23/39.78  | | |            (93), (94), (95), (96), (97), (98), (99), (100), (101), (102),
% 228.23/39.78  | | |            (103), (104), (105), (106), (107), (108), (109), (110), (111),
% 228.23/39.78  | | |            (112), (113), (114), (119) are inconsistent by sub-proof #464.
% 228.23/39.78  | | | 
% 228.23/39.78  | | End of split
% 228.23/39.78  | | 
% 228.23/39.78  | Case 2:
% 228.23/39.78  | | 
% 228.23/39.78  | |   (120)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) =
% 228.23/39.78  | |            e3)
% 228.23/39.78  | | 
% 228.23/39.78  | | REF_CLOSE: (9), (11), (15), (18), (41), (46), (54), (58), (65), (71), (82),
% 228.23/39.78  | |            (83), (97), (120) are inconsistent by sub-proof #1794.
% 228.23/39.78  | | 
% 228.23/39.78  | End of split
% 228.23/39.78  | 
% 228.23/39.78  End of proof
% 228.23/39.78  
% 228.23/39.78  Sub-proof #464 shows that the following formulas are inconsistent:
% 228.23/39.78  ----------------------------------------------------------------
% 228.23/39.78    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.23/39.78    (2)  all_57_0 = e2
% 228.23/39.78    (3)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.23/39.78    (4)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.23/39.78         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.23/39.78    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.23/39.78         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.23/39.78    (6)   ~ (all_53_8 = all_53_12)
% 228.23/39.78    (7)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.23/39.78         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.23/39.78    (8)   ~ (all_53_8 = all_53_11)
% 228.23/39.79    (9)   ~ (e3 = e1)
% 228.23/39.79    (10)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.23/39.79          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.23/39.79    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.23/39.79            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.23/39.79    (12)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.23/39.79          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.23/39.79    (13)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.23/39.79            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.23/39.79              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.23/39.79    (14)   ~ (all_53_3 = e3)
% 228.23/39.79    (15)   ~ (all_6_2 = e3)
% 228.23/39.79    (16)  ( ~ (all_28_0 = e0) & op(all_28_1, e3) = all_28_0 & op(e3, e2) =
% 228.23/39.79            all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 = e1) & op(e3,
% 228.23/39.79              e2) = all_28_1 & $i(all_28_1))
% 228.23/39.79    (17)   ~ (all_53_9 = e1)
% 228.23/39.79    (18)  op(e1, e1) = all_6_2
% 228.23/39.79    (19)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.23/39.79    (20)   ~ (all_53_1 = all_53_9)
% 228.23/39.79    (21)   ~ (all_53_9 = e0)
% 228.23/39.79    (22)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 228.23/39.79    (23)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.23/39.79          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.23/39.79    (24)   ~ (all_52_17 = e2)
% 228.23/39.79    (25)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 228.23/39.79            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 228.23/39.79              e3) = all_22_1 & $i(all_22_1))
% 228.23/39.79    (26)   ~ (all_53_8 = e1)
% 228.23/39.79    (27)  op(all_52_17, all_52_17) = e3
% 228.23/39.79    (28)   ~ (all_53_4 = all_53_12)
% 228.23/39.79    (29)   ~ (all_52_17 = all_52_23)
% 228.23/39.79    (30)  all_57_4 = e0
% 228.23/39.79    (31)   ~ (all_52_17 = e1)
% 228.23/39.79    (32)   ~ (all_53_8 = all_53_9)
% 228.23/39.79    (33)  all_42_2 = all_6_2
% 228.23/39.79    (34)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.23/39.79          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.23/39.79    (35)   ~ (all_53_9 = all_53_11)
% 228.23/39.79    (36)  all_55_4 = all_53_1
% 228.23/39.79    (37)   ~ (all_53_9 = all_6_2)
% 228.23/39.79    (38)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.23/39.79          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.23/39.79    (39)  all_57_3 = e0
% 228.23/39.79    (40)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.23/39.79          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.23/39.79    (41)   ~ (e3 = e2)
% 228.23/39.79    (42)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 228.23/39.79    (43)  all_55_1 = all_53_4
% 228.23/39.79    (44)   ~ (all_53_1 = all_53_3)
% 228.23/39.79    (45)   ~ (all_53_1 = all_52_17)
% 228.23/39.79    (46)   ~ (e3 = e0)
% 228.23/39.79    (47)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.23/39.79          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.23/39.79    (48)   ~ (all_53_8 = all_6_2)
% 228.23/39.79    (49)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.23/39.79    (50)  all_55_11 = all_52_23
% 228.23/39.79    (51)  all_55_2 = all_53_8
% 228.23/39.79    (52)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 228.23/39.79    (53)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.23/39.79    (54)  all_57_15 = e3
% 228.23/39.79    (55)  op(e3, e3) = e2
% 228.23/39.79    (56)   ~ (all_53_3 = e2)
% 228.23/39.79    (57)   ~ (all_53_3 = all_52_17)
% 228.23/39.79    (58)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.23/39.79          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.23/39.79            e1)
% 228.23/39.79    (59)  all_57_10 = e2
% 228.23/39.79    (60)  all_57_5 = e3
% 228.23/39.79    (61)   ~ (all_52_23 = e3)
% 228.23/39.79    (62)  op(e1, e0) = all_52_23
% 228.23/39.79    (63)   ~ (all_53_4 = all_53_8)
% 228.23/39.79    (64)  all_55_6 = all_53_9
% 228.23/39.79    (65)  op(e3, e2) = all_53_4
% 228.23/39.79    (66)   ~ (e2 = e0)
% 228.23/39.79    (67)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.23/39.79            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.23/39.79            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.23/39.79            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.23/39.79              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.23/39.79            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.23/39.79            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.23/39.79              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.23/39.79              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.23/39.79            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.23/39.79            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.23/39.79            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.23/39.79              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.23/39.79              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.23/39.79            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.23/39.79              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.23/39.79            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.23/39.79            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.23/39.79              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.23/39.79              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.23/39.79            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.23/39.79            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.23/39.79    (68)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 228.23/39.79            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 228.23/39.79              e3) = all_12_1 & $i(all_12_1))
% 228.23/39.79    (69)  all_55_12 = all_53_3
% 228.23/39.79    (70)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.23/39.79          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.23/39.79    (71)   ~ (all_53_1 = e0)
% 228.23/39.79    (72)   ~ (e1 = e0)
% 228.23/39.79    (73)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.23/39.79            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.23/39.79              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.23/39.79    (74)   ~ (all_53_4 = e0)
% 228.23/39.79    (75)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.23/39.79          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.23/39.79    (76)  all_57_8 = e2
% 228.23/39.79    (77)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.23/39.79          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.23/39.79    (78)  all_57_14 = e1
% 228.23/39.79    (79)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 228.23/39.79    (80)  op(e0, e0) = e3
% 228.23/39.79    (81)   ~ (all_53_4 = all_53_6)
% 228.23/39.79    (82)  ( ~ (all_20_0 = e1) & op(all_20_1, e3) = all_20_0 & op(e3, e2) =
% 228.23/39.79            all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e0) & op(e3,
% 228.23/39.79              e2) = all_20_1 & $i(all_20_1))
% 228.23/39.79    (83)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.23/39.79          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.23/39.79            e2)
% 228.23/39.79    (84)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.23/39.79              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.23/39.79                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.23/39.79                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.23/39.79    (85)  all_55_10 = all_6_2
% 228.23/39.79    (86)   ~ (all_53_11 = e1)
% 228.23/39.79    (87)  all_55_8 = all_52_17
% 228.23/39.79    (88)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.23/39.79          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.23/39.79    (89)  all_38_2 = all_6_2
% 228.23/39.79    (90)  all_55_3 = all_53_12
% 228.23/39.79    (91)   ~ (all_53_12 = e3)
% 228.23/39.79    (92)   ~ (all_53_4 = e2)
% 228.23/39.79    (93)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.23/39.79            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.23/39.79              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.23/39.79    (94)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.23/39.79          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.23/39.79    (95)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.23/39.79          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.23/39.79    (96)   ~ (all_52_23 = e1)
% 228.23/39.79    (97)   ~ (all_53_1 = e2)
% 228.23/39.79    (98)   ~ (e2 = e1)
% 228.23/39.79    (99)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.23/39.79          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.23/39.79    (100)  op(e2, e1) = all_53_9
% 228.23/39.79    (101)  op(e1, e2) = all_53_6
% 228.23/39.79    (102)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.23/39.79           (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.23/39.79    (103)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 228.23/39.79    (104)  all_24_2 = all_6_2
% 228.23/39.79    (105)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.23/39.79           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.23/39.79    (106)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.23/39.79           (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.23/39.79    (107)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.23/39.79           | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.23/39.79             e1)
% 228.23/39.79    (108)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.23/39.79           (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.23/39.79    (109)  all_55_14 = all_53_11
% 228.23/39.79    (110)  op(e3, e1) = all_53_8
% 228.23/39.79    (111)   ~ (all_53_11 = e3)
% 228.23/39.79    (112)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.23/39.79           (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.23/39.79    (113)  all_57_7 = e0
% 228.23/39.79    (114)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.23/39.79           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.23/39.79    (115)  op(e3, e0) = all_53_12
% 228.23/39.79  
% 228.23/39.79  Begin of proof
% 228.23/39.79  | 
% 228.23/39.79  | BETA: splitting (12) gives:
% 228.23/39.79  | 
% 228.23/39.79  | Case 1:
% 228.23/39.79  | | 
% 228.23/39.79  | |   (116)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 228.23/39.79  | |            e3)
% 228.23/39.79  | | 
% 228.23/39.79  | | BETA: splitting (116) gives:
% 228.23/39.79  | | 
% 228.23/39.79  | | Case 1:
% 228.23/39.79  | | | 
% 228.23/39.79  | | |   (117)  all_57_6 = e3 & op(e1, e3) = e3
% 228.23/39.79  | | | 
% 228.23/39.79  | | | ALPHA: (117) implies:
% 228.23/39.79  | | |   (118)  all_57_6 = e3
% 228.23/39.79  | | | 
% 228.23/39.79  | | | BETA: splitting (106) gives:
% 228.23/39.79  | | | 
% 228.23/39.79  | | | Case 1:
% 228.23/39.79  | | | | 
% 228.23/39.79  | | | |   (119)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3)
% 228.23/39.79  | | | |            = e0)
% 228.23/39.79  | | | | 
% 228.23/39.79  | | | | REF_CLOSE: (4), (9), (11), (39), (41), (55), (60), (66), (72), (94),
% 228.23/39.79  | | | |            (98), (119) are inconsistent by sub-proof #1644.
% 228.23/39.79  | | | | 
% 228.23/39.79  | | | Case 2:
% 228.23/39.79  | | | | 
% 228.23/39.79  | | | |   (120)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0,
% 228.23/39.79  | | | |              e3) = e0)
% 228.23/39.79  | | | | 
% 228.23/39.79  | | | | BETA: splitting (120) gives:
% 228.23/39.79  | | | | 
% 228.23/39.79  | | | | Case 1:
% 228.23/39.79  | | | | | 
% 228.23/39.79  | | | | |   (121)  all_57_6 = e0 & op(e1, e3) = e0
% 228.23/39.79  | | | | | 
% 228.23/39.79  | | | | | ALPHA: (121) implies:
% 228.23/39.79  | | | | |   (122)  all_57_6 = e0
% 228.23/39.79  | | | | | 
% 228.23/39.79  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 228.23/39.79  | | | | |            (12), (13), (14), (15), (16), (17), (18), (19), (20), (21),
% 228.23/39.79  | | | | |            (22), (23), (24), (25), (26), (27), (28), (29), (31), (32),
% 228.23/39.79  | | | | |            (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 228.23/39.79  | | | | |            (43), (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 228.23/39.79  | | | | |            (53), (54), (55), (56), (57), (58), (59), (61), (62), (63),
% 228.23/39.79  | | | | |            (64), (65), (66), (67), (68), (69), (70), (71), (72), (73),
% 228.23/39.79  | | | | |            (74), (75), (76), (77), (78), (79), (80), (81), (82), (83),
% 228.23/39.79  | | | | |            (84), (85), (86), (87), (88), (89), (90), (91), (92), (93),
% 228.23/39.79  | | | | |            (94), (95), (96), (97), (98), (99), (100), (101), (102),
% 228.23/39.79  | | | | |            (103), (104), (105), (106), (107), (108), (109), (110),
% 228.23/39.79  | | | | |            (111), (112), (114), (115), (122) are inconsistent by
% 228.23/39.79  | | | | |            sub-proof #467.
% 228.23/39.79  | | | | | 
% 228.23/39.79  | | | | Case 2:
% 228.23/39.79  | | | | | 
% 228.23/39.79  | | | | |   (123)  all_57_12 = e0 & op(e0, e3) = e0
% 228.23/39.79  | | | | | 
% 228.23/39.79  | | | | | ALPHA: (123) implies:
% 228.23/39.79  | | | | |   (124)  all_57_12 = e0
% 228.23/39.79  | | | | | 
% 228.23/39.79  | | | | | BETA: splitting (70) gives:
% 228.23/39.79  | | | | | 
% 228.23/39.79  | | | | | Case 1:
% 228.23/39.79  | | | | | | 
% 228.23/39.79  | | | | | |   (125)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3,
% 228.23/39.79  | | | | | |              e2) = e3)
% 228.23/39.79  | | | | | | 
% 228.23/39.79  | | | | | | BETA: splitting (125) gives:
% 228.23/39.79  | | | | | | 
% 228.23/39.79  | | | | | | Case 1:
% 228.23/39.79  | | | | | | | 
% 228.23/39.79  | | | | | | |   (126)  all_57_0 = e3 & op(e3, e3) = e3
% 228.23/39.79  | | | | | | | 
% 228.23/39.79  | | | | | | | ALPHA: (126) implies:
% 228.23/39.79  | | | | | | |   (127)  all_57_0 = e3
% 228.23/39.79  | | | | | | | 
% 228.23/39.79  | | | | | | | REF_CLOSE: (5), (9), (41), (66), (72), (98), (102), (118), (124),
% 228.23/39.79  | | | | | | |            (127) are inconsistent by sub-proof #2011.
% 228.23/39.79  | | | | | | | 
% 228.23/39.79  | | | | | | Case 2:
% 228.23/39.79  | | | | | | | 
% 228.23/39.79  | | | | | | |   (128)  all_57_1 = e3 & op(e3, e2) = e3
% 228.23/39.79  | | | | | | | 
% 228.23/39.79  | | | | | | | ALPHA: (128) implies:
% 228.23/39.79  | | | | | | |   (129)  all_57_1 = e3
% 228.23/39.79  | | | | | | | 
% 228.23/39.79  | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 228.23/39.79  | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18), (19),
% 228.23/39.79  | | | | | | |            (20), (21), (22), (23), (24), (25), (26), (27), (28),
% 228.23/39.79  | | | | | | |            (29), (31), (32), (33), (34), (35), (36), (37), (38),
% 228.23/39.79  | | | | | | |            (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 228.23/39.79  | | | | | | |            (48), (49), (50), (51), (52), (53), (54), (55), (56),
% 228.23/39.79  | | | | | | |            (57), (58), (59), (60), (61), (62), (63), (64), (65),
% 228.23/39.79  | | | | | | |            (66), (67), (68), (69), (70), (71), (72), (73), (74),
% 228.23/39.79  | | | | | | |            (75), (76), (77), (79), (80), (81), (82), (83), (84),
% 228.23/39.79  | | | | | | |            (85), (86), (87), (88), (89), (90), (91), (92), (93),
% 228.23/39.79  | | | | | | |            (94), (95), (96), (97), (98), (99), (100), (101),
% 228.23/39.79  | | | | | | |            (102), (103), (104), (105), (106), (107), (108), (109),
% 228.23/39.79  | | | | | | |            (110), (111), (112), (113), (114), (115), (129) are
% 228.23/39.79  | | | | | | |            inconsistent by sub-proof #465.
% 228.23/39.79  | | | | | | | 
% 228.23/39.79  | | | | | | End of split
% 228.23/39.79  | | | | | | 
% 228.23/39.79  | | | | | Case 2:
% 228.23/39.79  | | | | | | 
% 228.23/39.79  | | | | | |   (130)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3,
% 228.23/39.79  | | | | | |              e0) = e3)
% 228.23/39.79  | | | | | | 
% 228.23/39.79  | | | | | | BETA: splitting (130) gives:
% 228.23/39.79  | | | | | | 
% 228.23/39.79  | | | | | | Case 1:
% 228.23/39.79  | | | | | | | 
% 228.23/39.79  | | | | | | |   (131)  all_57_4 = e3 & op(e3, e1) = e3
% 228.23/39.79  | | | | | | | 
% 228.23/39.79  | | | | | | | ALPHA: (131) implies:
% 228.23/39.79  | | | | | | |   (132)  all_57_4 = e3
% 228.23/39.79  | | | | | | | 
% 228.23/39.79  | | | | | | | COMBINE_EQS: (30), (132) imply:
% 228.23/39.79  | | | | | | |   (133)  e3 = e0
% 228.23/39.79  | | | | | | | 
% 228.23/39.79  | | | | | | | SIMP: (133) implies:
% 228.23/39.79  | | | | | | |   (134)  e3 = e0
% 228.23/39.79  | | | | | | | 
% 228.23/39.79  | | | | | | | COMBINE_EQS: (118), (134) imply:
% 228.23/39.79  | | | | | | |   (135)  all_57_6 = e0
% 228.23/39.79  | | | | | | | 
% 228.23/39.79  | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 228.23/39.79  | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18), (19),
% 228.23/39.79  | | | | | | |            (20), (21), (22), (23), (24), (25), (26), (27), (28),
% 228.23/39.79  | | | | | | |            (29), (31), (32), (33), (34), (35), (36), (37), (38),
% 228.23/39.79  | | | | | | |            (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 228.23/39.79  | | | | | | |            (48), (49), (50), (51), (52), (53), (54), (55), (56),
% 228.23/39.79  | | | | | | |            (57), (58), (59), (61), (62), (63), (64), (65), (66),
% 228.23/39.79  | | | | | | |            (67), (68), (69), (70), (71), (72), (73), (74), (75),
% 228.23/39.79  | | | | | | |            (76), (77), (78), (79), (80), (81), (82), (83), (84),
% 228.23/39.79  | | | | | | |            (85), (86), (87), (88), (89), (90), (91), (92), (93),
% 228.23/39.79  | | | | | | |            (94), (95), (96), (97), (98), (99), (100), (101),
% 228.23/39.79  | | | | | | |            (102), (103), (104), (105), (106), (107), (108), (109),
% 228.23/39.79  | | | | | | |            (110), (111), (112), (114), (115), (135) are
% 228.23/39.79  | | | | | | |            inconsistent by sub-proof #467.
% 228.23/39.79  | | | | | | | 
% 228.23/39.79  | | | | | | Case 2:
% 228.23/39.79  | | | | | | | 
% 228.23/39.79  | | | | | | |   (136)  all_57_9 = e3 & op(e3, e0) = e3
% 228.23/39.79  | | | | | | | 
% 228.23/39.79  | | | | | | | ALPHA: (136) implies:
% 228.23/39.79  | | | | | | |   (137)  op(e3, e0) = e3
% 228.23/39.79  | | | | | | | 
% 228.23/39.79  | | | | | | | REF_CLOSE: (11), (91), (115), (137) are inconsistent by sub-proof
% 228.23/39.79  | | | | | | |            #2458.
% 228.23/39.79  | | | | | | | 
% 228.23/39.79  | | | | | | End of split
% 228.23/39.79  | | | | | | 
% 228.23/39.79  | | | | | End of split
% 228.23/39.79  | | | | | 
% 228.23/39.79  | | | | End of split
% 228.23/39.79  | | | | 
% 228.23/39.79  | | | End of split
% 228.23/39.79  | | | 
% 228.23/39.79  | | Case 2:
% 228.23/39.79  | | | 
% 228.23/39.79  | | |   (138)  all_57_7 = e3 & op(e1, e2) = e3
% 228.23/39.79  | | | 
% 228.23/39.79  | | | ALPHA: (138) implies:
% 228.23/39.79  | | |   (139)  all_57_7 = e3
% 228.23/39.79  | | | 
% 228.23/39.79  | | | REF_CLOSE: (46), (113), (139) are inconsistent by sub-proof #2269.
% 228.23/39.79  | | | 
% 228.23/39.79  | | End of split
% 228.23/39.79  | | 
% 228.23/39.79  | Case 2:
% 228.23/39.79  | | 
% 228.23/39.79  | |   (140)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 228.23/39.79  | |            e3)
% 228.23/39.79  | | 
% 228.23/39.79  | | REF_CLOSE: (9), (11), (15), (18), (41), (46), (54), (66), (72), (84), (98),
% 228.23/39.79  | |            (99), (107), (140) are inconsistent by sub-proof #1786.
% 228.23/39.79  | | 
% 228.23/39.79  | End of split
% 228.23/39.79  | 
% 228.23/39.79  End of proof
% 228.23/39.79  
% 228.23/39.79  Sub-proof #465 shows that the following formulas are inconsistent:
% 228.23/39.79  ----------------------------------------------------------------
% 228.23/39.79    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.23/39.79    (2)  all_57_0 = e2
% 228.23/39.79    (3)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.23/39.79    (4)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.23/39.79         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.23/39.79    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.23/39.79         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.23/39.79    (6)   ~ (all_53_8 = all_53_12)
% 228.23/39.79    (7)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.23/39.79         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.23/39.79    (8)   ~ (all_53_8 = all_53_11)
% 228.23/39.79    (9)   ~ (e3 = e1)
% 228.23/39.79    (10)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.23/39.79          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.23/39.79    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.23/39.79            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.23/39.79    (12)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.23/39.79          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.23/39.79    (13)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.23/39.79            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.23/39.79              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.23/39.79    (14)   ~ (all_53_3 = e3)
% 228.23/39.79    (15)   ~ (all_6_2 = e3)
% 228.23/39.79    (16)  ( ~ (all_28_0 = e0) & op(all_28_1, e3) = all_28_0 & op(e3, e2) =
% 228.23/39.79            all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 = e1) & op(e3,
% 228.23/39.79              e2) = all_28_1 & $i(all_28_1))
% 228.23/39.79    (17)   ~ (all_53_9 = e1)
% 228.23/39.79    (18)  op(e1, e1) = all_6_2
% 228.23/39.79    (19)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.23/39.79    (20)   ~ (all_53_1 = all_53_9)
% 228.23/39.79    (21)   ~ (all_53_9 = e0)
% 228.23/39.79    (22)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 228.23/39.79    (23)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.23/39.79          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.23/39.79    (24)   ~ (all_52_17 = e2)
% 228.23/39.79    (25)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 228.23/39.79            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 228.23/39.79              e3) = all_22_1 & $i(all_22_1))
% 228.23/39.79    (26)   ~ (all_53_8 = e1)
% 228.23/39.79    (27)  op(all_52_17, all_52_17) = e3
% 228.23/39.79    (28)   ~ (all_53_4 = all_53_12)
% 228.23/39.79    (29)   ~ (all_52_17 = all_52_23)
% 228.23/39.79    (30)   ~ (all_52_17 = e1)
% 228.23/39.79    (31)   ~ (all_53_8 = all_53_9)
% 228.23/39.79    (32)  all_42_2 = all_6_2
% 228.23/39.79    (33)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.23/39.79          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.23/39.79    (34)   ~ (all_53_9 = all_53_11)
% 228.23/39.79    (35)  all_55_4 = all_53_1
% 228.23/39.79    (36)   ~ (all_53_9 = all_6_2)
% 228.23/39.79    (37)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.23/39.79          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.23/39.79    (38)  all_57_3 = e0
% 228.23/39.79    (39)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.23/39.79          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.23/39.79    (40)   ~ (e3 = e2)
% 228.23/39.79    (41)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 228.23/39.79    (42)  all_55_1 = all_53_4
% 228.23/39.79    (43)   ~ (all_53_1 = all_53_3)
% 228.23/39.79    (44)   ~ (all_53_1 = all_52_17)
% 228.23/39.79    (45)   ~ (e3 = e0)
% 228.23/39.79    (46)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.23/39.79          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.23/39.79    (47)   ~ (all_53_8 = all_6_2)
% 228.23/39.79    (48)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.23/39.79    (49)  all_55_11 = all_52_23
% 228.23/39.79    (50)  all_55_2 = all_53_8
% 228.23/39.79    (51)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 228.23/39.79    (52)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.23/39.79    (53)  all_57_15 = e3
% 228.23/39.79    (54)  op(e3, e3) = e2
% 228.23/39.79    (55)   ~ (all_53_3 = e2)
% 228.23/39.79    (56)   ~ (all_53_3 = all_52_17)
% 228.23/39.79    (57)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.23/39.79          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.23/39.79            e1)
% 228.23/39.79    (58)  all_57_10 = e2
% 228.23/39.79    (59)  all_57_5 = e3
% 228.23/39.79    (60)   ~ (all_52_23 = e3)
% 228.23/39.79    (61)  op(e1, e0) = all_52_23
% 228.23/39.79    (62)   ~ (all_53_4 = all_53_8)
% 228.23/39.79    (63)  all_55_6 = all_53_9
% 228.23/39.79    (64)  op(e3, e2) = all_53_4
% 228.23/39.79    (65)   ~ (e2 = e0)
% 228.23/39.79    (66)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.23/39.79            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.23/39.79            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.23/39.79            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.23/39.79              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.23/39.79            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.23/39.79            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.23/39.79              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.23/39.79              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.23/39.79            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.23/39.79            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.23/39.79            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.23/39.79              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.23/39.79              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.23/39.79            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.23/39.79              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.23/39.79            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.23/39.79            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.23/39.79              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.23/39.79              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.23/39.79            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.23/39.79            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.23/39.79    (67)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 228.23/39.79            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 228.23/39.79              e3) = all_12_1 & $i(all_12_1))
% 228.23/39.79    (68)  all_55_12 = all_53_3
% 228.23/39.79    (69)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.23/39.79          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.23/39.79    (70)   ~ (all_53_1 = e0)
% 228.23/39.79    (71)   ~ (e1 = e0)
% 228.23/39.79    (72)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.23/39.79            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.23/39.79              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.23/39.79    (73)   ~ (all_53_4 = e0)
% 228.23/39.79    (74)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.23/39.79          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.23/39.79    (75)  all_57_8 = e2
% 228.23/39.79    (76)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.23/39.79          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.23/39.79    (77)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 228.23/39.79    (78)  op(e0, e0) = e3
% 228.23/39.79    (79)   ~ (all_53_4 = all_53_6)
% 228.23/39.79    (80)  ( ~ (all_20_0 = e1) & op(all_20_1, e3) = all_20_0 & op(e3, e2) =
% 228.23/39.79            all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e0) & op(e3,
% 228.23/39.79              e2) = all_20_1 & $i(all_20_1))
% 228.23/39.80    (81)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.23/39.80          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.23/39.80            e2)
% 228.23/39.80    (82)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.23/39.80              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.23/39.80                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.23/39.80                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.23/39.80    (83)  all_55_10 = all_6_2
% 228.23/39.80    (84)   ~ (all_53_11 = e1)
% 228.23/39.80    (85)  all_55_8 = all_52_17
% 228.23/39.80    (86)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.23/39.80          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.23/39.80    (87)  all_38_2 = all_6_2
% 228.23/39.80    (88)  all_55_3 = all_53_12
% 228.23/39.80    (89)   ~ (all_53_12 = e3)
% 228.23/39.80    (90)   ~ (all_53_4 = e2)
% 228.23/39.80    (91)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.23/39.80            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.23/39.80              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.23/39.80    (92)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.23/39.80          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.23/39.80    (93)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.23/39.80          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.23/39.80    (94)  all_57_1 = e3
% 228.23/39.80    (95)   ~ (all_52_23 = e1)
% 228.23/39.80    (96)   ~ (all_53_1 = e2)
% 228.23/39.80    (97)   ~ (e2 = e1)
% 228.23/39.80    (98)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.23/39.80          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.23/39.80    (99)  op(e2, e1) = all_53_9
% 228.23/39.80    (100)  op(e1, e2) = all_53_6
% 228.23/39.80    (101)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.23/39.80           (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.23/39.80    (102)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 228.23/39.80    (103)  all_24_2 = all_6_2
% 228.23/39.80    (104)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.23/39.80           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.23/39.80    (105)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.23/39.80           (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.23/39.80    (106)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.23/39.80           | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.23/39.80             e1)
% 228.23/39.80    (107)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.23/39.80           (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.23/39.80    (108)  all_55_14 = all_53_11
% 228.23/39.80    (109)  op(e3, e1) = all_53_8
% 228.23/39.80    (110)   ~ (all_53_11 = e3)
% 228.23/39.80    (111)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.23/39.80           (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.23/39.80    (112)  all_57_7 = e0
% 228.23/39.80    (113)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.23/39.80           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.23/39.80    (114)  op(e3, e0) = all_53_12
% 228.23/39.80  
% 228.23/39.80  Begin of proof
% 228.23/39.80  | 
% 228.23/39.80  | BETA: splitting (111) gives:
% 228.23/39.80  | 
% 228.23/39.80  | Case 1:
% 228.23/39.80  | | 
% 228.23/39.80  | |   (115)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) =
% 228.23/39.80  | |            e1)
% 228.23/39.80  | | 
% 228.23/39.80  | | BETA: splitting (115) gives:
% 228.23/39.80  | | 
% 228.23/39.80  | | Case 1:
% 228.23/39.80  | | | 
% 228.23/39.80  | | |   (116)  all_57_1 = e1 & op(e3, e2) = e1
% 228.23/39.80  | | | 
% 228.23/39.80  | | | REF_CLOSE: (9), (94), (116) are inconsistent by sub-proof #2453.
% 228.23/39.80  | | | 
% 228.23/39.80  | | Case 2:
% 228.23/39.80  | | | 
% 228.23/39.80  | | |   (117)  all_57_3 = e1 & op(e2, e2) = e1
% 228.23/39.80  | | | 
% 228.23/39.80  | | | REF_CLOSE: (38), (71), (117) are inconsistent by sub-proof #2362.
% 228.23/39.80  | | | 
% 228.23/39.80  | | End of split
% 228.23/39.80  | | 
% 228.23/39.80  | Case 2:
% 228.23/39.80  | | 
% 228.23/39.80  | |   (118)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 228.23/39.80  | |            e1)
% 228.23/39.80  | | 
% 228.23/39.80  | | BETA: splitting (118) gives:
% 228.23/39.80  | | 
% 228.23/39.80  | | Case 1:
% 228.23/39.80  | | | 
% 228.23/39.80  | | |   (119)  all_57_7 = e1 & op(e1, e2) = e1
% 228.23/39.80  | | | 
% 228.23/39.80  | | | ALPHA: (119) implies:
% 228.23/39.80  | | |   (120)  all_57_7 = e1
% 228.23/39.80  | | | 
% 228.23/39.80  | | | REF_CLOSE: (71), (112), (120) are inconsistent by sub-proof #2211.
% 228.23/39.80  | | | 
% 228.23/39.80  | | Case 2:
% 228.23/39.80  | | | 
% 228.23/39.80  | | |   (121)  all_57_13 = e1 & op(e0, e2) = e1
% 228.23/39.80  | | | 
% 228.23/39.80  | | | ALPHA: (121) implies:
% 228.23/39.80  | | |   (122)  all_57_13 = e1
% 228.23/39.80  | | | 
% 228.23/39.80  | | | BETA: splitting (7) gives:
% 228.23/39.80  | | | 
% 228.23/39.80  | | | Case 1:
% 228.23/39.80  | | | | 
% 228.23/39.80  | | | |   (123)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2)
% 228.23/39.80  | | | |            = e2)
% 228.23/39.80  | | | | 
% 228.23/39.80  | | | | BETA: splitting (123) gives:
% 228.23/39.80  | | | | 
% 228.23/39.80  | | | | Case 1:
% 228.23/39.80  | | | | | 
% 228.23/39.80  | | | | |   (124)  all_57_1 = e2 & op(e3, e2) = e2
% 228.23/39.80  | | | | | 
% 228.23/39.80  | | | | | REF_CLOSE: (40), (94), (124) are inconsistent by sub-proof #1809.
% 228.23/39.80  | | | | | 
% 228.23/39.80  | | | | Case 2:
% 228.23/39.80  | | | | | 
% 228.23/39.80  | | | | |   (125)  all_57_3 = e2 & op(e2, e2) = e2
% 228.23/39.80  | | | | | 
% 228.23/39.80  | | | | | ALPHA: (125) implies:
% 228.23/39.80  | | | | |   (126)  all_57_3 = e2
% 228.23/39.80  | | | | | 
% 228.23/39.80  | | | | | COMBINE_EQS: (38), (126) imply:
% 228.23/39.80  | | | | |   (127)  e2 = e0
% 228.23/39.80  | | | | | 
% 228.23/39.80  | | | | | REF_CLOSE: (4), (9), (38), (40), (58), (59), (65), (71), (92), (97),
% 228.23/39.80  | | | | |            (127) are inconsistent by sub-proof #1517.
% 228.23/39.80  | | | | | 
% 228.23/39.80  | | | | End of split
% 228.23/39.80  | | | | 
% 228.23/39.80  | | | Case 2:
% 228.23/39.80  | | | | 
% 228.23/39.80  | | | |   (128)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0,
% 228.23/39.80  | | | |              e2) = e2)
% 228.23/39.80  | | | | 
% 228.23/39.80  | | | | BETA: splitting (128) gives:
% 228.23/39.80  | | | | 
% 228.23/39.80  | | | | Case 1:
% 228.23/39.80  | | | | | 
% 228.23/39.80  | | | | |   (129)  all_57_7 = e2 & op(e1, e2) = e2
% 228.23/39.80  | | | | | 
% 228.23/39.80  | | | | | ALPHA: (129) implies:
% 228.23/39.80  | | | | |   (130)  all_57_7 = e2
% 228.23/39.80  | | | | | 
% 228.23/39.80  | | | | | REF_CLOSE: (4), (9), (38), (40), (58), (59), (65), (71), (92), (97),
% 228.23/39.80  | | | | |            (112), (130) are inconsistent by sub-proof #466.
% 228.23/39.80  | | | | | 
% 228.23/39.80  | | | | Case 2:
% 228.23/39.80  | | | | | 
% 228.23/39.80  | | | | |   (131)  all_57_13 = e2 & op(e0, e2) = e2
% 228.23/39.80  | | | | | 
% 228.23/39.80  | | | | | ALPHA: (131) implies:
% 228.23/39.80  | | | | |   (132)  all_57_13 = e2
% 228.23/39.80  | | | | | 
% 228.23/39.80  | | | | | COMBINE_EQS: (122), (132) imply:
% 228.23/39.80  | | | | |   (133)  e2 = e1
% 228.23/39.80  | | | | | 
% 228.23/39.80  | | | | | COMBINE_EQS: (75), (133) imply:
% 228.23/39.80  | | | | |   (134)  all_57_8 = e1
% 228.23/39.80  | | | | | 
% 228.23/39.80  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 228.23/39.80  | | | | |            (12), (13), (14), (15), (16), (17), (18), (19), (20), (21),
% 228.23/39.80  | | | | |            (22), (23), (24), (25), (26), (27), (28), (29), (30), (31),
% 228.23/39.80  | | | | |            (32), (33), (34), (35), (36), (37), (38), (39), (40), (41),
% 228.23/39.80  | | | | |            (42), (43), (44), (45), (46), (47), (48), (49), (50), (51),
% 228.23/39.80  | | | | |            (52), (53), (54), (55), (56), (57), (60), (61), (62), (63),
% 228.23/39.80  | | | | |            (64), (65), (66), (67), (68), (69), (70), (71), (72), (73),
% 228.23/39.80  | | | | |            (74), (76), (77), (78), (79), (80), (81), (82), (83), (84),
% 228.23/39.80  | | | | |            (85), (86), (87), (88), (89), (90), (91), (92), (93), (95),
% 228.23/39.80  | | | | |            (96), (98), (99), (100), (101), (102), (103), (104), (105),
% 228.23/39.80  | | | | |            (106), (107), (108), (109), (110), (111), (113), (114),
% 228.23/39.80  | | | | |            (134) are inconsistent by sub-proof #474.
% 228.23/39.80  | | | | | 
% 228.23/39.80  | | | | End of split
% 228.23/39.80  | | | | 
% 228.23/39.80  | | | End of split
% 228.23/39.80  | | | 
% 228.23/39.80  | | End of split
% 228.23/39.80  | | 
% 228.23/39.80  | End of split
% 228.23/39.80  | 
% 228.23/39.80  End of proof
% 228.23/39.80  
% 228.23/39.80  Sub-proof #466 shows that the following formulas are inconsistent:
% 228.23/39.80  ----------------------------------------------------------------
% 228.23/39.80    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.23/39.80         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.23/39.80    (2)   ~ (e3 = e1)
% 228.23/39.80    (3)  all_57_7 = e2
% 228.23/39.80    (4)  all_57_3 = e0
% 228.23/39.80    (5)   ~ (e3 = e2)
% 228.23/39.80    (6)  all_57_10 = e2
% 228.23/39.80    (7)  all_57_5 = e3
% 228.23/39.80    (8)   ~ (e2 = e0)
% 228.23/39.80    (9)   ~ (e1 = e0)
% 228.23/39.80    (10)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.23/39.80          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.23/39.80    (11)   ~ (e2 = e1)
% 228.23/39.80    (12)  all_57_7 = e0
% 228.23/39.80  
% 228.23/39.80  Begin of proof
% 228.23/39.80  | 
% 228.23/39.80  | COMBINE_EQS: (3), (12) imply:
% 228.23/39.80  |   (13)  e2 = e0
% 228.23/39.80  | 
% 228.23/39.80  | COMBINE_EQS: (6), (13) imply:
% 228.23/39.80  |   (14)  all_57_10 = e0
% 228.23/39.80  | 
% 228.23/39.80  | REF_CLOSE: (1), (2), (4), (5), (7), (8), (9), (10), (11), (14) are
% 228.23/39.80  |            inconsistent by sub-proof #1518.
% 228.23/39.80  | 
% 228.23/39.80  End of proof
% 228.23/39.80  
% 228.23/39.80  Sub-proof #467 shows that the following formulas are inconsistent:
% 228.23/39.80  ----------------------------------------------------------------
% 228.23/39.80    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.23/39.80    (2)  all_57_0 = e2
% 228.23/39.80    (3)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.23/39.80    (4)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.23/39.80         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.23/39.80    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.23/39.80         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.23/39.80    (6)   ~ (all_53_8 = all_53_12)
% 228.23/39.80    (7)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.23/39.80         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.23/39.80    (8)   ~ (all_53_8 = all_53_11)
% 228.23/39.80    (9)   ~ (e3 = e1)
% 228.23/39.80    (10)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.23/39.80          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.23/39.80    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.23/39.80            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.23/39.80    (12)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.23/39.80          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.23/39.80    (13)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.23/39.80            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.23/39.80              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.23/39.80    (14)   ~ (all_53_3 = e3)
% 228.23/39.80    (15)   ~ (all_6_2 = e3)
% 228.23/39.80    (16)  ( ~ (all_28_0 = e0) & op(all_28_1, e3) = all_28_0 & op(e3, e2) =
% 228.23/39.80            all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 = e1) & op(e3,
% 228.23/39.80              e2) = all_28_1 & $i(all_28_1))
% 228.23/39.80    (17)   ~ (all_53_9 = e1)
% 228.23/39.80    (18)  op(e1, e1) = all_6_2
% 228.23/39.80    (19)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.23/39.80    (20)   ~ (all_53_1 = all_53_9)
% 228.23/39.80    (21)   ~ (all_53_9 = e0)
% 228.23/39.80    (22)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 228.23/39.80    (23)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.23/39.80          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.23/39.80    (24)   ~ (all_52_17 = e2)
% 228.23/39.80    (25)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 228.23/39.80            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 228.23/39.80              e3) = all_22_1 & $i(all_22_1))
% 228.23/39.80    (26)   ~ (all_53_8 = e1)
% 228.23/39.80    (27)  op(all_52_17, all_52_17) = e3
% 228.23/39.80    (28)   ~ (all_53_4 = all_53_12)
% 228.23/39.80    (29)   ~ (all_52_17 = all_52_23)
% 228.23/39.80    (30)   ~ (all_52_17 = e1)
% 228.23/39.80    (31)   ~ (all_53_8 = all_53_9)
% 228.23/39.80    (32)  all_42_2 = all_6_2
% 228.23/39.80    (33)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.23/39.80          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.23/39.80    (34)   ~ (all_53_9 = all_53_11)
% 228.23/39.80    (35)  all_55_4 = all_53_1
% 228.23/39.80    (36)   ~ (all_53_9 = all_6_2)
% 228.23/39.80    (37)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.23/39.80          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.23/39.80    (38)  all_57_3 = e0
% 228.23/39.80    (39)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.23/39.80          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.23/39.80    (40)   ~ (e3 = e2)
% 228.23/39.80    (41)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 228.23/39.80    (42)  all_55_1 = all_53_4
% 228.23/39.80    (43)   ~ (all_53_1 = all_53_3)
% 228.23/39.80    (44)   ~ (all_53_1 = all_52_17)
% 228.23/39.80    (45)   ~ (e3 = e0)
% 228.23/39.80    (46)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.23/39.80          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.23/39.80    (47)  all_57_6 = e0
% 228.23/39.80    (48)   ~ (all_53_8 = all_6_2)
% 228.23/39.80    (49)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.23/39.80    (50)  all_55_11 = all_52_23
% 228.23/39.80    (51)  all_55_2 = all_53_8
% 228.23/39.80    (52)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 228.23/39.80    (53)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.23/39.80    (54)  all_57_15 = e3
% 228.23/39.80    (55)  op(e3, e3) = e2
% 228.23/39.80    (56)   ~ (all_53_3 = e2)
% 228.23/39.80    (57)   ~ (all_53_3 = all_52_17)
% 228.23/39.80    (58)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.23/39.80          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.23/39.80            e1)
% 228.23/39.80    (59)  all_57_10 = e2
% 228.23/39.80    (60)   ~ (all_52_23 = e3)
% 228.23/39.80    (61)  op(e1, e0) = all_52_23
% 228.23/39.80    (62)   ~ (all_53_4 = all_53_8)
% 228.23/39.80    (63)  all_55_6 = all_53_9
% 228.23/39.80    (64)  op(e3, e2) = all_53_4
% 228.23/39.80    (65)   ~ (e2 = e0)
% 228.23/39.80    (66)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.23/39.80            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.23/39.80            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.23/39.80            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.23/39.80              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.23/39.80            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.23/39.80            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.23/39.80              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.23/39.80              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.23/39.80            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.23/39.80            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.23/39.80            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.23/39.80              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.23/39.80              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.23/39.80            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.23/39.80              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.23/39.80            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.23/39.80            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.23/39.80              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.23/39.80              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.23/39.80            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.23/39.80            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.23/39.80    (67)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 228.23/39.80            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 228.23/39.80              e3) = all_12_1 & $i(all_12_1))
% 228.23/39.80    (68)  all_55_12 = all_53_3
% 228.23/39.80    (69)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.23/39.80          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.23/39.80    (70)   ~ (all_53_1 = e0)
% 228.23/39.80    (71)   ~ (e1 = e0)
% 228.23/39.80    (72)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.23/39.80            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.23/39.80              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.23/39.80    (73)   ~ (all_53_4 = e0)
% 228.23/39.80    (74)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.23/39.80          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.23/39.80    (75)  all_57_8 = e2
% 228.23/39.80    (76)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.23/39.80          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.23/39.80    (77)  all_57_14 = e1
% 228.23/39.80    (78)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 228.23/39.80    (79)  op(e0, e0) = e3
% 228.23/39.80    (80)   ~ (all_53_4 = all_53_6)
% 228.23/39.80    (81)  ( ~ (all_20_0 = e1) & op(all_20_1, e3) = all_20_0 & op(e3, e2) =
% 228.23/39.80            all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e0) & op(e3,
% 228.23/39.80              e2) = all_20_1 & $i(all_20_1))
% 228.23/39.80    (82)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.23/39.80          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.23/39.80            e2)
% 228.23/39.80    (83)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.23/39.80              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.23/39.80                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.23/39.80                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.23/39.80    (84)  all_55_10 = all_6_2
% 228.23/39.80    (85)   ~ (all_53_11 = e1)
% 228.23/39.80    (86)  all_55_8 = all_52_17
% 228.23/39.80    (87)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.23/39.80          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.23/39.80    (88)  all_38_2 = all_6_2
% 228.23/39.80    (89)  all_55_3 = all_53_12
% 228.23/39.80    (90)   ~ (all_53_12 = e3)
% 228.23/39.80    (91)   ~ (all_53_4 = e2)
% 228.23/39.80    (92)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.23/39.80            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.23/39.80              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.23/39.80    (93)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.23/39.80          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.23/39.80    (94)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.23/39.80          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.23/39.80    (95)   ~ (all_52_23 = e1)
% 228.23/39.80    (96)   ~ (all_53_1 = e2)
% 228.23/39.80    (97)   ~ (e2 = e1)
% 228.23/39.80    (98)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.23/39.80          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.23/39.80    (99)  op(e2, e1) = all_53_9
% 228.23/39.80    (100)  op(e1, e2) = all_53_6
% 228.23/39.80    (101)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.23/39.80           (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.23/39.80    (102)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 228.23/39.80    (103)  all_24_2 = all_6_2
% 228.23/39.80    (104)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.23/39.80           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.23/39.80    (105)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.23/39.80           (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.23/39.80    (106)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.23/39.80           | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.23/39.80             e1)
% 228.23/39.80    (107)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.23/39.80           (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.23/39.80    (108)  all_55_14 = all_53_11
% 228.23/39.80    (109)  op(e3, e1) = all_53_8
% 228.23/39.80    (110)   ~ (all_53_11 = e3)
% 228.23/39.80    (111)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.23/39.80           (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.23/39.80    (112)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.23/39.80           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.23/39.80    (113)  op(e3, e0) = all_53_12
% 228.23/39.80  
% 228.23/39.80  Begin of proof
% 228.23/39.80  | 
% 228.23/39.80  | BETA: splitting (94) gives:
% 228.23/39.80  | 
% 228.23/39.80  | Case 1:
% 228.23/39.80  | | 
% 228.23/39.80  | |   (114)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) =
% 228.23/39.80  | |            e3)
% 228.23/39.80  | | 
% 228.23/39.80  | | BETA: splitting (114) gives:
% 228.23/39.80  | | 
% 228.23/39.80  | | Case 1:
% 228.23/39.80  | | | 
% 228.23/39.80  | | |   (115)  all_57_0 = e3 & op(e3, e3) = e3
% 228.23/39.80  | | | 
% 228.23/39.80  | | | ALPHA: (115) implies:
% 228.23/39.80  | | |   (116)  op(e3, e3) = e3
% 228.23/39.80  | | | 
% 228.23/39.80  | | | REF_CLOSE: (11), (40), (55), (116) are inconsistent by sub-proof #2490.
% 228.23/39.80  | | | 
% 228.23/39.80  | | Case 2:
% 228.23/39.80  | | | 
% 228.23/39.80  | | |   (117)  all_57_2 = e3 & op(e2, e3) = e3
% 228.23/39.80  | | | 
% 228.23/39.80  | | | ALPHA: (117) implies:
% 228.23/39.80  | | |   (118)  all_57_2 = e3
% 228.23/39.80  | | | 
% 228.23/39.80  | | | REF_CLOSE: (4), (9), (11), (15), (18), (38), (39), (40), (45), (54), (58),
% 228.23/39.80  | | |            (59), (65), (71), (74), (75), (77), (82), (83), (87), (93),
% 228.23/39.80  | | |            (97), (118) are inconsistent by sub-proof #745.
% 228.23/39.80  | | | 
% 228.23/39.80  | | End of split
% 228.23/39.80  | | 
% 228.23/39.80  | Case 2:
% 228.23/39.80  | | 
% 228.23/39.80  | |   (119)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) =
% 228.23/39.80  | |            e3)
% 228.23/39.80  | | 
% 228.23/39.80  | | BETA: splitting (119) gives:
% 228.23/39.80  | | 
% 228.23/39.80  | | Case 1:
% 228.23/39.80  | | | 
% 228.23/39.80  | | |   (120)  all_57_6 = e3 & op(e1, e3) = e3
% 228.23/39.80  | | | 
% 228.23/39.80  | | | ALPHA: (120) implies:
% 228.23/39.80  | | |   (121)  all_57_6 = e3
% 228.23/39.80  | | | 
% 228.23/39.80  | | | REF_CLOSE: (45), (47), (121) are inconsistent by sub-proof #1822.
% 228.23/39.80  | | | 
% 228.23/39.80  | | Case 2:
% 228.23/39.80  | | | 
% 228.23/39.80  | | |   (122)  all_57_12 = e3 & op(e0, e3) = e3
% 228.23/39.80  | | | 
% 228.23/39.80  | | | ALPHA: (122) implies:
% 228.23/39.80  | | |   (123)  all_57_12 = e3
% 228.23/39.80  | | | 
% 228.23/39.80  | | | BETA: splitting (82) gives:
% 228.23/39.80  | | | 
% 228.23/39.80  | | | Case 1:
% 228.23/39.80  | | | | 
% 228.23/39.80  | | | |   (124)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0,
% 228.23/39.80  | | | |              e2) = e2)
% 228.23/39.80  | | | | 
% 228.23/39.80  | | | | BETA: splitting (124) gives:
% 228.23/39.80  | | | | 
% 228.23/39.80  | | | | Case 1:
% 228.23/39.80  | | | | | 
% 228.23/39.80  | | | | |   (125)  all_57_12 = e2 & op(e0, e3) = e2
% 228.23/39.80  | | | | | 
% 228.23/39.80  | | | | | REF_CLOSE: (40), (123), (125) are inconsistent by sub-proof #2232.
% 228.23/39.80  | | | | | 
% 228.23/39.80  | | | | Case 2:
% 228.23/39.80  | | | | | 
% 228.23/39.80  | | | | |   (126)  all_57_13 = e2 & op(e0, e2) = e2
% 228.23/39.80  | | | | | 
% 228.23/39.80  | | | | | ALPHA: (126) implies:
% 228.23/39.80  | | | | |   (127)  all_57_13 = e2
% 228.23/39.80  | | | | | 
% 228.23/39.80  | | | | | BETA: splitting (39) gives:
% 228.23/39.80  | | | | | 
% 228.23/39.80  | | | | | Case 1:
% 228.23/39.80  | | | | | | 
% 228.23/39.80  | | | | | |   (128)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2,
% 228.23/39.80  | | | | | |              e1) = e0)
% 228.23/39.80  | | | | | | 
% 228.23/39.80  | | | | | | BETA: splitting (128) gives:
% 228.23/39.80  | | | | | | 
% 228.23/39.80  | | | | | | Case 1:
% 228.23/39.80  | | | | | | | 
% 228.23/39.80  | | | | | | |   (129)  all_57_4 = e0 & op(e3, e1) = e0
% 228.23/39.80  | | | | | | | 
% 228.23/39.80  | | | | | | | ALPHA: (129) implies:
% 228.23/39.80  | | | | | | |   (130)  all_57_4 = e0
% 228.23/39.80  | | | | | | | 
% 228.23/39.80  | | | | | | | BETA: splitting (69) gives:
% 228.23/39.80  | | | | | | | 
% 228.23/39.80  | | | | | | | Case 1:
% 228.23/39.80  | | | | | | | | 
% 228.23/39.80  | | | | | | | |   (131)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 &
% 228.23/39.80  | | | | | | | |            op(e3, e2) = e3)
% 228.23/39.80  | | | | | | | | 
% 228.23/39.80  | | | | | | | | REF_CLOSE: (7), (9), (11), (38), (40), (45), (54), (55), (58),
% 228.23/39.80  | | | | | | | |            (65), (71), (82), (83), (97), (111), (123), (131) are
% 228.23/39.80  | | | | | | | |            inconsistent by sub-proof #471.
% 228.23/39.80  | | | | | | | | 
% 228.23/39.80  | | | | | | | Case 2:
% 228.23/39.80  | | | | | | | | 
% 228.23/39.80  | | | | | | | |   (132)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 &
% 228.23/39.80  | | | | | | | |            op(e3, e0) = e3)
% 228.23/39.80  | | | | | | | | 
% 228.23/39.80  | | | | | | | | REF_CLOSE: (11), (45), (90), (113), (130), (132) are
% 228.23/39.80  | | | | | | | |            inconsistent by sub-proof #1617.
% 228.23/39.80  | | | | | | | | 
% 228.23/39.80  | | | | | | | End of split
% 228.23/39.80  | | | | | | | 
% 228.23/39.80  | | | | | | Case 2:
% 228.23/39.80  | | | | | | | 
% 228.23/39.80  | | | | | | |   (133)  all_57_5 = e0 & op(e2, e1) = e0
% 228.23/39.80  | | | | | | | 
% 228.23/39.80  | | | | | | | ALPHA: (133) implies:
% 228.23/39.80  | | | | | | |   (134)  all_57_5 = e0
% 228.23/39.80  | | | | | | | 
% 228.23/39.80  | | | | | | | BETA: splitting (12) gives:
% 228.23/39.80  | | | | | | | 
% 228.23/39.80  | | | | | | | Case 1:
% 228.23/39.80  | | | | | | | | 
% 228.23/39.80  | | | | | | | |   (135)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 &
% 228.23/39.80  | | | | | | | |            op(e1, e2) = e3)
% 228.23/39.80  | | | | | | | | 
% 228.23/39.80  | | | | | | | | BETA: splitting (135) gives:
% 228.23/39.80  | | | | | | | | 
% 228.23/39.80  | | | | | | | | Case 1:
% 228.23/39.80  | | | | | | | | | 
% 228.23/39.80  | | | | | | | | |   (136)  all_57_6 = e3 & op(e1, e3) = e3
% 228.23/39.80  | | | | | | | | | 
% 228.23/39.80  | | | | | | | | | ALPHA: (136) implies:
% 228.23/39.80  | | | | | | | | |   (137)  all_57_6 = e3
% 228.23/39.80  | | | | | | | | | 
% 228.23/39.80  | | | | | | | | | REF_CLOSE: (45), (47), (137) are inconsistent by sub-proof
% 228.23/39.80  | | | | | | | | |            #1822.
% 228.23/39.80  | | | | | | | | | 
% 228.23/39.80  | | | | | | | | Case 2:
% 228.23/39.80  | | | | | | | | | 
% 228.23/39.80  | | | | | | | | |   (138)  all_57_7 = e3 & op(e1, e2) = e3
% 228.23/39.80  | | | | | | | | | 
% 228.23/39.80  | | | | | | | | | ALPHA: (138) implies:
% 228.23/39.80  | | | | | | | | |   (139)  all_57_7 = e3
% 228.23/39.80  | | | | | | | | | 
% 228.23/39.80  | | | | | | | | | BETA: splitting (69) gives:
% 228.23/39.80  | | | | | | | | | 
% 228.23/39.80  | | | | | | | | | Case 1:
% 228.23/39.80  | | | | | | | | | | 
% 228.23/39.80  | | | | | | | | | |   (140)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 228.23/39.80  | | | | | | | | | |            & op(e3, e2) = e3)
% 228.23/39.80  | | | | | | | | | | 
% 228.23/39.80  | | | | | | | | | | REF_CLOSE: (7), (9), (11), (38), (40), (45), (54), (55),
% 228.23/39.80  | | | | | | | | | |            (58), (65), (71), (82), (83), (97), (111), (123),
% 228.23/39.80  | | | | | | | | | |            (140) are inconsistent by sub-proof #471.
% 228.23/39.80  | | | | | | | | | | 
% 228.23/39.80  | | | | | | | | | Case 2:
% 228.23/39.80  | | | | | | | | | | 
% 228.23/39.80  | | | | | | | | | |   (141)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 228.23/39.80  | | | | | | | | | |            & op(e3, e0) = e3)
% 228.23/39.80  | | | | | | | | | | 
% 228.23/39.80  | | | | | | | | | | BETA: splitting (141) gives:
% 228.23/39.80  | | | | | | | | | | 
% 228.23/39.80  | | | | | | | | | | Case 1:
% 228.23/39.80  | | | | | | | | | | | 
% 228.23/39.80  | | | | | | | | | | |   (142)  all_57_4 = e3 & op(e3, e1) = e3
% 228.23/39.80  | | | | | | | | | | | 
% 228.23/39.80  | | | | | | | | | | | ALPHA: (142) implies:
% 228.23/39.80  | | | | | | | | | | |   (143)  all_57_4 = e3
% 228.23/39.80  | | | | | | | | | | | 
% 228.23/39.80  | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (9), (10), (11),
% 228.23/39.80  | | | | | | | | | | |            (12), (13), (15), (18), (19), (21), (23), (28),
% 228.23/39.80  | | | | | | | | | | |            (31), (32), (33), (36), (37), (38), (39), (40),
% 228.23/39.80  | | | | | | | | | | |            (42), (45), (46), (48), (51), (53), (54), (58),
% 228.23/39.80  | | | | | | | | | | |            (59), (62), (64), (65), (66), (69), (71), (72),
% 228.23/39.80  | | | | | | | | | | |            (73), (74), (79), (80), (82), (83), (84), (87),
% 228.23/39.80  | | | | | | | | | | |            (88), (89), (90), (92), (93), (97), (98), (99),
% 228.23/39.80  | | | | | | | | | | |            (100), (101), (103), (104), (105), (106), (107),
% 228.23/39.80  | | | | | | | | | | |            (109), (111), (112), (113), (134), (139), (143)
% 228.23/39.80  | | | | | | | | | | |            are inconsistent by sub-proof #469.
% 228.23/39.80  | | | | | | | | | | | 
% 228.23/39.80  | | | | | | | | | | Case 2:
% 228.23/39.80  | | | | | | | | | | | 
% 228.23/39.80  | | | | | | | | | | |   (144)  all_57_9 = e3 & op(e3, e0) = e3
% 228.23/39.81  | | | | | | | | | | | 
% 228.23/39.81  | | | | | | | | | | | ALPHA: (144) implies:
% 228.23/39.81  | | | | | | | | | | |   (145)  op(e3, e0) = e3
% 228.23/39.81  | | | | | | | | | | | 
% 228.23/39.81  | | | | | | | | | | | REF_CLOSE: (11), (90), (113), (145) are inconsistent by
% 228.23/39.81  | | | | | | | | | | |            sub-proof #2458.
% 228.23/39.81  | | | | | | | | | | | 
% 228.23/39.81  | | | | | | | | | | End of split
% 228.23/39.81  | | | | | | | | | | 
% 228.23/39.81  | | | | | | | | | End of split
% 228.23/39.81  | | | | | | | | | 
% 228.23/39.81  | | | | | | | | End of split
% 228.23/39.81  | | | | | | | | 
% 228.23/39.81  | | | | | | | Case 2:
% 228.23/39.81  | | | | | | | | 
% 228.23/39.81  | | | | | | | |   (146)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 &
% 228.23/39.81  | | | | | | | |            op(e1, e0) = e3)
% 228.23/39.81  | | | | | | | | 
% 228.23/39.81  | | | | | | | | REF_CLOSE: (9), (11), (15), (18), (40), (45), (54), (65), (71),
% 228.23/39.81  | | | | | | | |            (83), (97), (98), (106), (146) are inconsistent by
% 228.23/39.81  | | | | | | | |            sub-proof #1786.
% 228.23/39.81  | | | | | | | | 
% 228.23/39.81  | | | | | | | End of split
% 228.23/39.81  | | | | | | | 
% 228.23/39.81  | | | | | | End of split
% 228.23/39.81  | | | | | | 
% 228.23/39.81  | | | | | Case 2:
% 228.23/39.81  | | | | | | 
% 228.23/39.81  | | | | | |   (147)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 &
% 228.23/39.81  | | | | | |            op(e0, e1) = e0)
% 228.23/39.81  | | | | | | 
% 228.23/39.81  | | | | | | BETA: splitting (147) gives:
% 228.23/39.81  | | | | | | 
% 228.23/39.81  | | | | | | Case 1:
% 228.23/39.81  | | | | | | | 
% 228.23/39.81  | | | | | | |   (148)  all_57_8 = e0 & op(e1, e1) = e0
% 228.23/39.81  | | | | | | | 
% 228.23/39.81  | | | | | | | REF_CLOSE: (65), (75), (148) are inconsistent by sub-proof #917.
% 228.23/39.81  | | | | | | | 
% 228.23/39.81  | | | | | | Case 2:
% 228.23/39.81  | | | | | | | 
% 228.23/39.81  | | | | | | |   (149)  all_57_14 = e0 & op(e0, e1) = e0
% 228.23/39.81  | | | | | | | 
% 228.23/39.81  | | | | | | | ALPHA: (149) implies:
% 228.23/39.81  | | | | | | |   (150)  all_57_14 = e0
% 228.23/39.81  | | | | | | | 
% 228.23/39.81  | | | | | | | REF_CLOSE: (9), (54), (58), (71), (97), (123), (127), (150) are
% 228.23/39.81  | | | | | | |            inconsistent by sub-proof #1764.
% 228.23/39.81  | | | | | | | 
% 228.23/39.81  | | | | | | End of split
% 228.23/39.81  | | | | | | 
% 228.23/39.81  | | | | | End of split
% 228.23/39.81  | | | | | 
% 228.23/39.81  | | | | End of split
% 228.23/39.81  | | | | 
% 228.23/39.81  | | | Case 2:
% 228.23/39.81  | | | | 
% 228.23/39.81  | | | |   (151)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0,
% 228.23/39.81  | | | |              e0) = e2)
% 228.23/39.81  | | | | 
% 228.23/39.81  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 228.23/39.81  | | | |            (12), (13), (14), (15), (16), (17), (18), (19), (20), (21),
% 228.23/39.81  | | | |            (22), (23), (24), (25), (26), (27), (28), (29), (30), (31),
% 228.23/39.81  | | | |            (32), (33), (34), (35), (36), (37), (38), (39), (40), (41),
% 228.23/39.81  | | | |            (42), (43), (44), (45), (46), (48), (49), (50), (51), (52),
% 228.23/39.81  | | | |            (53), (54), (55), (56), (57), (58), (60), (61), (62), (63),
% 228.23/39.81  | | | |            (64), (65), (66), (67), (68), (69), (70), (71), (72), (73),
% 228.23/39.81  | | | |            (74), (75), (76), (77), (78), (79), (80), (81), (82), (83),
% 228.23/39.81  | | | |            (84), (85), (86), (87), (88), (89), (90), (91), (92), (93),
% 228.23/39.81  | | | |            (94), (95), (96), (98), (99), (100), (101), (102), (103),
% 228.23/39.81  | | | |            (104), (105), (106), (107), (108), (109), (110), (111),
% 228.23/39.81  | | | |            (112), (113), (151) are inconsistent by sub-proof #468.
% 228.23/39.81  | | | | 
% 228.23/39.81  | | | End of split
% 228.23/39.81  | | | 
% 228.23/39.81  | | End of split
% 228.23/39.81  | | 
% 228.23/39.81  | End of split
% 228.23/39.81  | 
% 228.23/39.81  End of proof
% 228.23/39.81  
% 228.23/39.81  Sub-proof #468 shows that the following formulas are inconsistent:
% 228.23/39.81  ----------------------------------------------------------------
% 228.23/39.81    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.23/39.81    (2)  all_57_0 = e2
% 228.23/39.81    (3)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.23/39.81    (4)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.23/39.81         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.23/39.81    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.23/39.81         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.23/39.81    (6)   ~ (all_53_8 = all_53_12)
% 228.23/39.81    (7)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.23/39.81         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.23/39.81    (8)   ~ (all_53_8 = all_53_11)
% 228.23/39.81    (9)   ~ (e3 = e1)
% 228.23/39.81    (10)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.23/39.81          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.23/39.81    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.23/39.81            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.23/39.81    (12)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.23/39.81          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.23/39.81    (13)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.23/39.81            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.23/39.81              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.23/39.81    (14)   ~ (all_53_3 = e3)
% 228.23/39.81    (15)   ~ (all_6_2 = e3)
% 228.23/39.81    (16)  ( ~ (all_28_0 = e0) & op(all_28_1, e3) = all_28_0 & op(e3, e2) =
% 228.23/39.81            all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 = e1) & op(e3,
% 228.23/39.81              e2) = all_28_1 & $i(all_28_1))
% 228.23/39.81    (17)   ~ (all_53_9 = e1)
% 228.23/39.81    (18)  op(e1, e1) = all_6_2
% 228.23/39.81    (19)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.23/39.81    (20)   ~ (all_53_1 = all_53_9)
% 228.23/39.81    (21)   ~ (all_53_9 = e0)
% 228.23/39.81    (22)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 228.23/39.81    (23)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.23/39.81          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.23/39.81    (24)   ~ (all_52_17 = e2)
% 228.23/39.81    (25)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 228.23/39.81            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 228.23/39.81              e3) = all_22_1 & $i(all_22_1))
% 228.23/39.81    (26)   ~ (all_53_8 = e1)
% 228.23/39.81    (27)  op(all_52_17, all_52_17) = e3
% 228.23/39.81    (28)   ~ (all_53_4 = all_53_12)
% 228.23/39.81    (29)   ~ (all_52_17 = all_52_23)
% 228.23/39.81    (30)   ~ (all_52_17 = e1)
% 228.23/39.81    (31)   ~ (all_53_8 = all_53_9)
% 228.23/39.81    (32)  all_42_2 = all_6_2
% 228.23/39.81    (33)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.23/39.81          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.23/39.81    (34)   ~ (all_53_9 = all_53_11)
% 228.23/39.81    (35)  all_55_4 = all_53_1
% 228.23/39.81    (36)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.23/39.81    (37)   ~ (all_53_9 = all_6_2)
% 228.23/39.81    (38)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.23/39.81          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.23/39.81    (39)  all_57_3 = e0
% 228.23/39.81    (40)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.23/39.81          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.23/39.81    (41)   ~ (e3 = e2)
% 228.23/39.81    (42)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 228.23/39.81    (43)  all_55_1 = all_53_4
% 228.23/39.81    (44)   ~ (all_53_1 = all_53_3)
% 228.23/39.81    (45)   ~ (all_53_1 = all_52_17)
% 228.23/39.81    (46)   ~ (e3 = e0)
% 228.23/39.81    (47)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.23/39.81          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.23/39.81    (48)   ~ (all_53_8 = all_6_2)
% 228.23/39.81    (49)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.23/39.81    (50)  all_55_11 = all_52_23
% 228.23/39.81    (51)  all_55_2 = all_53_8
% 228.23/39.81    (52)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 228.23/39.81    (53)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.23/39.81    (54)  all_57_15 = e3
% 228.23/39.81    (55)  op(e3, e3) = e2
% 228.23/39.81    (56)   ~ (all_53_3 = e2)
% 228.23/39.81    (57)   ~ (all_53_3 = all_52_17)
% 228.23/39.81    (58)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.23/39.81          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.23/39.81            e1)
% 228.23/39.81    (59)   ~ (all_52_23 = e3)
% 228.23/39.81    (60)  op(e1, e0) = all_52_23
% 228.23/39.81    (61)   ~ (all_53_4 = all_53_8)
% 228.23/39.81    (62)  all_55_6 = all_53_9
% 228.23/39.81    (63)  op(e3, e2) = all_53_4
% 228.23/39.81    (64)   ~ (e2 = e0)
% 228.23/39.81    (65)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.23/39.81            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.23/39.81            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.23/39.81            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.23/39.81              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.23/39.81            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.23/39.81            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.23/39.81              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.23/39.81              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.23/39.81            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.23/39.81            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.23/39.81            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.23/39.81              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.23/39.81              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.23/39.81            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.23/39.81              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.23/39.81            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.23/39.81            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.23/39.81              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.23/39.81              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.23/39.81            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.23/39.81            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.23/39.81    (66)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 228.23/39.81            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 228.23/39.81              e3) = all_12_1 & $i(all_12_1))
% 228.23/39.81    (67)  all_55_12 = all_53_3
% 228.23/39.81    (68)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.23/39.81          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.23/39.81    (69)   ~ (all_53_1 = e0)
% 228.23/39.81    (70)   ~ (e1 = e0)
% 228.23/39.81    (71)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.23/39.81            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.23/39.81              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.23/39.81    (72)   ~ (all_53_4 = e0)
% 228.23/39.81    (73)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.23/39.81          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.23/39.81    (74)  all_57_8 = e2
% 228.23/39.81    (75)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.23/39.81          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.23/39.81    (76)  all_57_14 = e1
% 228.23/39.81    (77)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 228.23/39.81    (78)  op(e0, e0) = e3
% 228.23/39.81    (79)   ~ (all_53_4 = all_53_6)
% 228.23/39.81    (80)  ( ~ (all_20_0 = e1) & op(all_20_1, e3) = all_20_0 & op(e3, e2) =
% 228.23/39.81            all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e0) & op(e3,
% 228.23/39.81              e2) = all_20_1 & $i(all_20_1))
% 228.23/39.81    (81)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.23/39.81          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.23/39.81            e2)
% 228.23/39.81    (82)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.23/39.81              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.23/39.81                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.23/39.81                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.23/39.81    (83)  all_55_10 = all_6_2
% 228.23/39.81    (84)   ~ (all_53_11 = e1)
% 228.23/39.81    (85)  all_55_8 = all_52_17
% 228.23/39.81    (86)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.23/39.81          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.23/39.81    (87)  all_38_2 = all_6_2
% 228.23/39.81    (88)  all_55_3 = all_53_12
% 228.23/39.81    (89)   ~ (all_53_12 = e3)
% 228.23/39.81    (90)   ~ (all_53_4 = e2)
% 228.23/39.81    (91)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.23/39.81            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.23/39.81              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.23/39.81    (92)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.23/39.81          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.23/39.81    (93)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.23/39.81          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.23/39.81    (94)   ~ (all_52_23 = e1)
% 228.23/39.81    (95)   ~ (all_53_1 = e2)
% 228.23/39.81    (96)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.23/39.81          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.23/39.81    (97)  op(e2, e1) = all_53_9
% 228.23/39.81    (98)  op(e1, e2) = all_53_6
% 228.23/39.81    (99)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.23/39.81          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.23/39.81    (100)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 228.23/39.81    (101)  all_24_2 = all_6_2
% 228.23/39.81    (102)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.23/39.81           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.23/39.81    (103)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.23/39.81           (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.23/39.81    (104)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.23/39.81           | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.23/39.81             e1)
% 228.23/39.81    (105)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.23/39.81           (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.23/39.81    (106)  all_55_14 = all_53_11
% 228.23/39.81    (107)  op(e3, e1) = all_53_8
% 228.23/39.81    (108)   ~ (all_53_11 = e3)
% 228.23/39.81    (109)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.23/39.81           (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.23/39.81    (110)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.23/39.81           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.23/39.81    (111)  op(e3, e0) = all_53_12
% 228.23/39.81  
% 228.23/39.81  Begin of proof
% 228.23/39.81  | 
% 228.23/39.81  | BETA: splitting (36) gives:
% 228.23/39.81  | 
% 228.23/39.81  | Case 1:
% 228.23/39.81  | | 
% 228.23/39.81  | |   (112)  all_57_14 = e2 & op(e0, e1) = e2
% 228.23/39.81  | | 
% 228.23/39.81  | | ALPHA: (112) implies:
% 228.23/39.81  | |   (113)  all_57_14 = e2
% 228.23/39.81  | | 
% 228.23/39.81  | | COMBINE_EQS: (76), (113) imply:
% 228.23/39.81  | |   (114)  e2 = e1
% 228.23/39.81  | | 
% 228.23/39.81  | | SIMP: (114) implies:
% 228.23/39.81  | |   (115)  e2 = e1
% 228.23/39.81  | | 
% 228.23/39.81  | | COMBINE_EQS: (74), (115) imply:
% 228.23/39.81  | |   (116)  all_57_8 = e1
% 228.23/39.81  | | 
% 228.23/39.81  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.23/39.81  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 228.23/39.81  | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 228.23/39.81  | |            (35), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 228.23/39.81  | |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 228.23/39.81  | |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 228.23/39.81  | |            (69), (70), (71), (72), (73), (75), (77), (78), (79), (80), (81),
% 228.23/39.81  | |            (82), (83), (84), (85), (86), (87), (88), (89), (90), (91), (92),
% 228.23/39.81  | |            (93), (94), (95), (96), (97), (98), (99), (100), (101), (102),
% 228.23/39.81  | |            (103), (104), (105), (106), (107), (108), (109), (110), (111),
% 228.23/39.81  | |            (116) are inconsistent by sub-proof #474.
% 228.23/39.81  | | 
% 228.23/39.81  | Case 2:
% 228.23/39.81  | | 
% 228.23/39.81  | |   (117)  all_57_15 = e2 & op(e0, e0) = e2
% 228.23/39.81  | | 
% 228.23/39.81  | | REF_CLOSE: (41), (54), (117) are inconsistent by sub-proof #2323.
% 228.23/39.81  | | 
% 228.23/39.81  | End of split
% 228.23/39.81  | 
% 228.23/39.81  End of proof
% 228.23/39.81  
% 228.23/39.81  Sub-proof #469 shows that the following formulas are inconsistent:
% 228.23/39.81  ----------------------------------------------------------------
% 228.23/39.81    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.23/39.81    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.23/39.81    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.23/39.81         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.23/39.81    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.23/39.81         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.23/39.81    (5)   ~ (all_53_8 = all_53_12)
% 228.23/39.81    (6)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.23/39.81         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.23/39.81    (7)   ~ (e3 = e1)
% 228.23/39.81    (8)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.23/39.81         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.23/39.81    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.23/39.81           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.23/39.81    (10)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.23/39.81          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.23/39.81    (11)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.23/39.81            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.23/39.81              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.23/39.81    (12)   ~ (all_6_2 = e3)
% 228.23/39.81    (13)  op(e1, e1) = all_6_2
% 228.23/39.81    (14)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.23/39.81    (15)   ~ (all_53_9 = e0)
% 228.23/39.81    (16)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.23/39.81          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.23/39.81    (17)   ~ (all_53_4 = all_53_12)
% 228.23/39.81    (18)   ~ (all_53_8 = all_53_9)
% 228.23/39.81    (19)  all_42_2 = all_6_2
% 228.23/39.81    (20)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.23/39.81          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.23/39.81    (21)   ~ (all_53_9 = all_6_2)
% 228.23/39.81    (22)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.23/39.81          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.23/39.81    (23)  all_57_3 = e0
% 228.23/39.81    (24)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.23/39.81          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.23/39.81    (25)  all_57_4 = e3
% 228.23/39.81    (26)   ~ (e3 = e2)
% 228.23/39.81    (27)  all_55_1 = all_53_4
% 228.23/39.81    (28)   ~ (e3 = e0)
% 228.23/39.81    (29)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.23/39.81          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.23/39.81    (30)   ~ (all_53_8 = all_6_2)
% 228.23/39.81    (31)  all_55_2 = all_53_8
% 228.23/39.81    (32)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.23/39.81    (33)  all_57_15 = e3
% 228.23/39.81    (34)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.23/39.81          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.23/39.81            e1)
% 228.23/39.81    (35)  all_57_10 = e2
% 228.23/39.81    (36)   ~ (all_53_4 = all_53_8)
% 228.23/39.81    (37)  op(e3, e2) = all_53_4
% 228.23/39.81    (38)   ~ (e2 = e0)
% 228.23/39.81    (39)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.23/39.81            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.23/39.81            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.23/39.81            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.23/39.81              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.23/39.81            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.23/39.81            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.23/39.81              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.23/39.81              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.23/39.81            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.23/39.81            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.23/39.81            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.23/39.81              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.23/39.81              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.23/39.81            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.23/39.81              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.23/39.81            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.23/39.81            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.23/39.81              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.23/39.81              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.23/39.81            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.23/39.81            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.23/39.81    (40)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.23/39.81          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.23/39.81    (41)   ~ (e1 = e0)
% 228.23/39.81    (42)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.23/39.81            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.23/39.81              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.23/39.81    (43)   ~ (all_53_4 = e0)
% 228.23/39.81    (44)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.23/39.81          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.23/39.81    (45)  op(e0, e0) = e3
% 228.23/39.81    (46)   ~ (all_53_4 = all_53_6)
% 228.23/39.81    (47)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.23/39.81          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.23/39.81            e2)
% 228.23/39.81    (48)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.23/39.81              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.23/39.81                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.23/39.81                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.23/39.81    (49)  all_55_10 = all_6_2
% 228.23/39.81    (50)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.23/39.81          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.23/39.81    (51)  all_38_2 = all_6_2
% 228.23/39.81    (52)  all_55_3 = all_53_12
% 228.23/39.81    (53)   ~ (all_53_12 = e3)
% 228.23/39.81    (54)  all_57_7 = e3
% 228.23/39.81    (55)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.23/39.81            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.23/39.81              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.23/39.81    (56)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.23/39.81          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.23/39.81    (57)   ~ (e2 = e1)
% 228.23/39.81    (58)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.23/39.81          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.23/39.81    (59)  op(e2, e1) = all_53_9
% 228.23/39.81    (60)  op(e1, e2) = all_53_6
% 228.23/39.81    (61)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.23/39.81          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.23/39.81    (62)  all_24_2 = all_6_2
% 228.23/39.81    (63)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.23/39.81          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.23/39.81    (64)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.23/39.81          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.23/39.81    (65)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.23/39.81          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.23/39.81    (66)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.23/39.81          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.23/39.81    (67)  op(e3, e1) = all_53_8
% 228.23/39.81    (68)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.23/39.81          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.23/39.81    (69)  all_57_5 = e0
% 228.23/39.81    (70)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.23/39.81          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.23/39.81    (71)  op(e3, e0) = all_53_12
% 228.23/39.81  
% 228.23/39.81  Begin of proof
% 228.23/39.81  | 
% 228.23/39.81  | BETA: splitting (50) gives:
% 228.23/39.81  | 
% 228.23/39.81  | Case 1:
% 228.23/39.81  | | 
% 228.23/39.81  | |   (72)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 228.23/39.81  | |           e3)
% 228.23/39.81  | | 
% 228.23/39.81  | | REF_CLOSE: (3), (7), (23), (28), (35), (41), (57), (69), (72) are
% 228.23/39.81  | |            inconsistent by sub-proof #2357.
% 228.23/39.81  | | 
% 228.23/39.81  | Case 2:
% 228.23/39.81  | | 
% 228.23/39.81  | |   (73)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 228.23/39.81  | |           e3)
% 228.23/39.81  | | 
% 228.23/39.81  | | BETA: splitting (73) gives:
% 228.23/39.81  | | 
% 228.23/39.81  | | Case 1:
% 228.23/39.81  | | | 
% 228.23/39.81  | | |   (74)  all_57_5 = e3 & op(e2, e1) = e3
% 228.23/39.81  | | | 
% 228.23/39.81  | | | REF_CLOSE: (28), (69), (74) are inconsistent by sub-proof #1936.
% 228.23/39.81  | | | 
% 228.23/39.81  | | Case 2:
% 228.23/39.81  | | | 
% 228.23/39.81  | | |   (75)  all_57_10 = e3 & op(e2, e0) = e3
% 228.23/39.81  | | | 
% 228.23/39.82  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.23/39.82  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 228.23/39.82  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 228.23/39.82  | | |            (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 228.23/39.82  | | |            (43), (44), (45), (46), (47), (48), (49), (51), (52), (53),
% 228.23/39.82  | | |            (54), (55), (56), (57), (58), (59), (60), (61), (62), (63),
% 228.23/39.82  | | |            (64), (65), (66), (67), (68), (70), (71), (75) are inconsistent
% 228.23/39.82  | | |            by sub-proof #470.
% 228.23/39.82  | | | 
% 228.23/39.82  | | End of split
% 228.23/39.82  | | 
% 228.23/39.82  | End of split
% 228.23/39.82  | 
% 228.23/39.82  End of proof
% 228.23/39.82  
% 228.23/39.82  Sub-proof #470 shows that the following formulas are inconsistent:
% 228.23/39.82  ----------------------------------------------------------------
% 228.23/39.82    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.23/39.82    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.23/39.82    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.23/39.82         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.23/39.82    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.23/39.82         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.23/39.82    (5)   ~ (all_53_8 = all_53_12)
% 228.23/39.82    (6)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.23/39.82         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.23/39.82    (7)   ~ (e3 = e1)
% 228.23/39.82    (8)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.23/39.82         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.23/39.82    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.23/39.82           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.23/39.82    (10)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.23/39.82          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.23/39.82    (11)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.23/39.82            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.23/39.82              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.23/39.82    (12)   ~ (all_6_2 = e3)
% 228.23/39.82    (13)  op(e1, e1) = all_6_2
% 228.23/39.82    (14)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.23/39.82    (15)   ~ (all_53_9 = e0)
% 228.23/39.82    (16)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.23/39.82          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.23/39.82    (17)   ~ (all_53_4 = all_53_12)
% 228.23/39.82    (18)   ~ (all_53_8 = all_53_9)
% 228.23/39.82    (19)  all_42_2 = all_6_2
% 228.23/39.82    (20)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.23/39.82          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.23/39.82    (21)   ~ (all_53_9 = all_6_2)
% 228.23/39.82    (22)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.23/39.82          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.23/39.82    (23)  all_57_3 = e0
% 228.23/39.82    (24)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.23/39.82          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.23/39.82    (25)  all_57_4 = e3
% 228.23/39.82    (26)   ~ (e3 = e2)
% 228.23/39.82    (27)  all_55_1 = all_53_4
% 228.23/39.82    (28)   ~ (e3 = e0)
% 228.23/39.82    (29)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.23/39.82          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.23/39.82    (30)   ~ (all_53_8 = all_6_2)
% 228.23/39.82    (31)  all_55_2 = all_53_8
% 228.23/39.82    (32)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.23/39.82    (33)  all_57_15 = e3
% 228.23/39.82    (34)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.23/39.82          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.23/39.82            e1)
% 228.23/39.82    (35)  all_57_10 = e2
% 228.23/39.82    (36)   ~ (all_53_4 = all_53_8)
% 228.23/39.82    (37)  op(e3, e2) = all_53_4
% 228.23/39.82    (38)   ~ (e2 = e0)
% 228.23/39.82    (39)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.23/39.82            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.23/39.82            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.23/39.82            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.23/39.82              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.23/39.82            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.23/39.82            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.23/39.82              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.23/39.82              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.23/39.82            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.23/39.82            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.23/39.82            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.23/39.82              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.23/39.82              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.23/39.82            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.23/39.82              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.23/39.82            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.23/39.82            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.23/39.82              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.23/39.82              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.23/39.82            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.23/39.82            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.23/39.82    (40)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.23/39.82          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.23/39.82    (41)   ~ (e1 = e0)
% 228.23/39.82    (42)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.23/39.82            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.23/39.82              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.23/39.82    (43)   ~ (all_53_4 = e0)
% 228.23/39.82    (44)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.23/39.82          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.23/39.82    (45)  op(e0, e0) = e3
% 228.23/39.82    (46)   ~ (all_53_4 = all_53_6)
% 228.23/39.82    (47)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.23/39.82          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.23/39.82            e2)
% 228.23/39.82    (48)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.23/39.82              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.23/39.82                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.23/39.82                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.23/39.82    (49)  all_55_10 = all_6_2
% 228.23/39.82    (50)  all_38_2 = all_6_2
% 228.23/39.82    (51)  all_55_3 = all_53_12
% 228.23/39.82    (52)   ~ (all_53_12 = e3)
% 228.23/39.82    (53)  all_57_7 = e3
% 228.23/39.82    (54)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.23/39.82            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.23/39.82              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.23/39.82    (55)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.23/39.82          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.23/39.82    (56)   ~ (e2 = e1)
% 228.23/39.82    (57)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.23/39.82          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.23/39.82    (58)  op(e2, e1) = all_53_9
% 228.23/39.82    (59)  op(e1, e2) = all_53_6
% 228.23/39.82    (60)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.23/39.82          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.23/39.82    (61)  all_24_2 = all_6_2
% 228.23/39.82    (62)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.23/39.82          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.23/39.82    (63)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.23/39.82          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.23/39.82    (64)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.23/39.82          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.23/39.82    (65)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.23/39.82          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.23/39.82    (66)  op(e3, e1) = all_53_8
% 228.23/39.82    (67)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.23/39.82          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.23/39.82    (68)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.23/39.82          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.23/39.82    (69)  all_57_10 = e3 & op(e2, e0) = e3
% 228.23/39.82    (70)  op(e3, e0) = all_53_12
% 228.23/39.82  
% 228.23/39.82  Begin of proof
% 228.23/39.82  | 
% 228.23/39.82  | ALPHA: (69) implies:
% 228.23/39.82  |   (71)  all_57_10 = e3
% 228.23/39.82  | 
% 228.23/39.82  | COMBINE_EQS: (35), (71) imply:
% 228.23/39.82  |   (72)  e3 = e2
% 228.23/39.82  | 
% 228.23/39.82  | COMBINE_EQS: (25), (72) imply:
% 228.23/39.82  |   (73)  all_57_4 = e2
% 228.23/39.82  | 
% 228.23/39.82  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.23/39.82  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 228.23/39.82  |            (24), (26), (27), (28), (29), (30), (31), (32), (33), (34), (36),
% 228.23/39.82  |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 228.23/39.82  |            (48), (49), (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 228.23/39.82  |            (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), (70),
% 228.23/39.82  |            (73) are inconsistent by sub-proof #546.
% 228.23/39.82  | 
% 228.23/39.82  End of proof
% 228.23/39.82  
% 228.23/39.82  Sub-proof #471 shows that the following formulas are inconsistent:
% 228.23/39.82  ----------------------------------------------------------------
% 228.23/39.82    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.23/39.82         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.23/39.82    (2)   ~ (e3 = e1)
% 228.23/39.82    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.23/39.82           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.23/39.82    (4)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3)
% 228.23/39.82    (5)  all_57_3 = e0
% 228.23/39.82    (6)   ~ (e3 = e2)
% 228.23/39.82    (7)   ~ (e3 = e0)
% 228.23/39.82    (8)  all_57_15 = e3
% 228.23/39.82    (9)  op(e3, e3) = e2
% 228.23/39.82    (10)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.23/39.82          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.23/39.82            e1)
% 228.23/39.82    (11)   ~ (e2 = e0)
% 228.23/39.82    (12)   ~ (e1 = e0)
% 228.23/39.82    (13)  all_57_12 = e3
% 228.23/39.82    (14)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.23/39.82          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.23/39.82            e2)
% 228.23/39.82    (15)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.23/39.82              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.23/39.82                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.23/39.82                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.23/39.82    (16)   ~ (e2 = e1)
% 228.23/39.82    (17)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.23/39.82          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.23/39.82  
% 228.23/39.82  Begin of proof
% 228.23/39.82  | 
% 228.23/39.82  | BETA: splitting (4) gives:
% 228.23/39.82  | 
% 228.23/39.82  | Case 1:
% 228.23/39.82  | | 
% 228.23/39.82  | |   (18)  all_57_0 = e3 & op(e3, e3) = e3
% 228.23/39.82  | | 
% 228.23/39.82  | | ALPHA: (18) implies:
% 228.23/39.82  | |   (19)  op(e3, e3) = e3
% 228.23/39.82  | | 
% 228.23/39.82  | | REF_CLOSE: (3), (6), (9), (19) are inconsistent by sub-proof #2490.
% 228.23/39.82  | | 
% 228.23/39.82  | Case 2:
% 228.23/39.82  | | 
% 228.23/39.82  | |   (20)  all_57_1 = e3 & op(e3, e2) = e3
% 228.23/39.82  | | 
% 228.23/39.82  | | ALPHA: (20) implies:
% 228.23/39.82  | |   (21)  all_57_1 = e3
% 228.23/39.82  | | 
% 228.23/39.82  | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (10), (11), (12), (13), (14), (15),
% 228.23/39.82  | |            (16), (17), (21) are inconsistent by sub-proof #1037.
% 228.23/39.82  | | 
% 228.23/39.82  | End of split
% 228.23/39.82  | 
% 228.23/39.82  End of proof
% 228.23/39.82  
% 228.23/39.82  Sub-proof #472 shows that the following formulas are inconsistent:
% 228.23/39.82  ----------------------------------------------------------------
% 228.23/39.82    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.23/39.82    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.23/39.82    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.23/39.82         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.23/39.82    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.23/39.82         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.23/39.82    (5)   ~ (all_53_8 = all_53_12)
% 228.23/39.82    (6)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.23/39.82         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.23/39.82    (7)   ~ (e3 = e1)
% 228.23/39.82    (8)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.23/39.82         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.23/39.82    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.23/39.82           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.23/39.82    (10)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.23/39.82          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.23/39.82    (11)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.23/39.82            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.23/39.82              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.23/39.82    (12)   ~ (all_6_2 = e3)
% 228.23/39.82    (13)  op(e1, e1) = all_6_2
% 228.23/39.82    (14)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.23/39.82    (15)   ~ (all_53_9 = e0)
% 228.23/39.82    (16)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.23/39.82          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.23/39.82    (17)   ~ (all_53_4 = all_53_12)
% 228.23/39.82    (18)   ~ (all_53_8 = all_53_9)
% 228.23/39.82    (19)  all_42_2 = all_6_2
% 228.23/39.82    (20)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.23/39.82          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.23/39.82    (21)   ~ (all_53_9 = all_6_2)
% 228.23/39.82    (22)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.23/39.82          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.23/39.82    (23)  all_57_3 = e0
% 228.23/39.82    (24)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.23/39.82          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.23/39.82    (25)   ~ (e3 = e2)
% 228.23/39.82    (26)  all_55_1 = all_53_4
% 228.23/39.82    (27)   ~ (e3 = e0)
% 228.23/39.82    (28)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.23/39.82          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.23/39.82    (29)   ~ (all_53_8 = all_6_2)
% 228.23/39.82    (30)  all_55_2 = all_53_8
% 228.23/39.82    (31)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.23/39.82    (32)  all_57_15 = e3
% 228.23/39.82    (33)  op(e3, e3) = e2
% 228.23/39.82    (34)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.23/39.82          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.23/39.82            e1)
% 228.23/39.82    (35)   ~ (all_53_4 = all_53_8)
% 228.23/39.82    (36)  op(e3, e2) = all_53_4
% 228.23/39.82    (37)  op(e1, e1) = e1
% 228.23/39.82    (38)   ~ (e2 = e0)
% 228.23/39.82    (39)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.23/39.82            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.23/39.82            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.23/39.82            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.23/39.82              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.23/39.82            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.23/39.82            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.23/39.82              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.23/39.82              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.23/39.82            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.23/39.82            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.23/39.82            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.23/39.82              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.23/39.82              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.23/39.82            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.23/39.82              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.23/39.82            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.23/39.82            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.23/39.82              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.23/39.82              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.23/39.82            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.23/39.82            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.23/39.82    (40)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.23/39.82          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.23/39.82    (41)   ~ (e1 = e0)
% 228.23/39.82    (42)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.23/39.82            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.23/39.82              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.23/39.82    (43)   ~ (all_53_4 = e0)
% 228.23/39.82    (44)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.23/39.82          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.23/39.82    (45)  all_57_6 = e3
% 228.23/39.82    (46)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.23/39.82          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.23/39.82    (47)  op(e0, e0) = e3
% 228.23/39.82    (48)   ~ (all_53_4 = all_53_6)
% 228.23/39.82    (49)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.23/39.82          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.23/39.82            e2)
% 228.23/39.82    (50)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.23/39.82              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.23/39.82                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.23/39.82                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.23/39.82    (51)  all_55_10 = all_6_2
% 228.23/39.82    (52)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.23/39.82          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.23/39.82    (53)  all_38_2 = all_6_2
% 228.23/39.82    (54)  all_55_3 = all_53_12
% 228.23/39.82    (55)   ~ (all_53_12 = e3)
% 228.23/39.82    (56)  e3 = e1
% 228.23/39.82    (57)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.23/39.82            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.23/39.82              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.23/39.82    (58)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.23/39.82          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.23/39.82    (59)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.23/39.82          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.23/39.82    (60)   ~ (e2 = e1)
% 228.23/39.82    (61)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.23/39.82          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.23/39.82    (62)  op(e2, e1) = all_53_9
% 228.23/39.82    (63)  op(e1, e2) = all_53_6
% 228.23/39.82    (64)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.23/39.82          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.23/39.82    (65)  all_24_2 = all_6_2
% 228.23/39.82    (66)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.23/39.82          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.23/39.82    (67)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.23/39.82          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.23/39.82    (68)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.23/39.82          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.23/39.82    (69)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.23/39.82          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.23/39.82    (70)  op(e3, e1) = all_53_8
% 228.23/39.82    (71)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.23/39.82          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.23/39.82    (72)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.23/39.82          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.23/39.82    (73)  op(e3, e0) = all_53_12
% 228.23/39.82  
% 228.23/39.82  Begin of proof
% 228.23/39.82  | 
% 228.23/39.82  | SIMP: (56) implies:
% 228.23/39.82  |   (74)  e3 = e1
% 228.23/39.82  | 
% 228.23/39.82  | COMBINE_EQS: (45), (74) imply:
% 228.23/39.82  |   (75)  all_57_6 = e1
% 228.23/39.82  | 
% 228.23/39.82  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.23/39.82  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 228.23/39.82  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 228.23/39.82  |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (46),
% 228.23/39.82  |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (57), (58),
% 228.23/39.82  |            (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 228.23/39.82  |            (70), (71), (72), (73), (75) are inconsistent by sub-proof #523.
% 228.23/39.82  | 
% 228.23/39.82  End of proof
% 228.23/39.82  
% 228.23/39.82  Sub-proof #473 shows that the following formulas are inconsistent:
% 228.23/39.82  ----------------------------------------------------------------
% 228.23/39.82    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.23/39.82    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.23/39.82    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.23/39.82         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.23/39.82    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.23/39.82         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.23/39.82    (5)   ~ (all_53_8 = all_53_12)
% 228.23/39.82    (6)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.23/39.82         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.23/39.82    (7)   ~ (e3 = e1)
% 228.23/39.82    (8)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.23/39.82         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.23/39.82    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.23/39.82           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.23/39.82    (10)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.23/39.82          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.23/39.82    (11)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.23/39.82            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.23/39.82              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.23/39.82    (12)   ~ (all_6_2 = e3)
% 228.23/39.82    (13)  op(e1, e1) = all_6_2
% 228.23/39.82    (14)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.23/39.82    (15)   ~ (all_53_9 = e0)
% 228.23/39.82    (16)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.23/39.82          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.23/39.82    (17)   ~ (all_53_4 = all_53_12)
% 228.23/39.82    (18)   ~ (all_53_8 = all_53_9)
% 228.23/39.82    (19)  all_42_2 = all_6_2
% 228.23/39.82    (20)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.23/39.82          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.23/39.82    (21)   ~ (all_53_9 = all_6_2)
% 228.23/39.82    (22)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.23/39.82          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.23/39.82    (23)  all_57_3 = e0
% 228.23/39.82    (24)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.23/39.82          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.23/39.82    (25)   ~ (e3 = e2)
% 228.23/39.82    (26)  all_55_1 = all_53_4
% 228.23/39.82    (27)   ~ (e3 = e0)
% 228.23/39.82    (28)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.23/39.82          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.23/39.82    (29)   ~ (all_53_8 = all_6_2)
% 228.23/39.82    (30)  all_55_2 = all_53_8
% 228.23/39.82    (31)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.23/39.83    (32)  all_57_15 = e3
% 228.23/39.83    (33)  op(e3, e3) = e2
% 228.23/39.83    (34)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.23/39.83          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.23/39.83            e1)
% 228.23/39.83    (35)   ~ (all_53_4 = all_53_8)
% 228.23/39.83    (36)  op(e3, e2) = all_53_4
% 228.23/39.83    (37)  op(e1, e1) = e1
% 228.23/39.83    (38)   ~ (e2 = e0)
% 228.23/39.83    (39)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.23/39.83            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.23/39.83            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.23/39.83            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.23/39.83              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.23/39.83            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.23/39.83            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.23/39.83              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.23/39.83              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.23/39.83            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.23/39.83            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.23/39.83            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.23/39.83              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.23/39.83              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.23/39.83            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.23/39.83              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.23/39.83            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.23/39.83            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.23/39.83              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.23/39.83              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.23/39.83            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.23/39.83            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.23/39.83    (40)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.23/39.83          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.23/39.83    (41)  all_57_3 = e3 & op(e2, e2) = e3
% 228.23/39.83    (42)   ~ (e1 = e0)
% 228.23/39.83    (43)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.23/39.83            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.23/39.83              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.23/39.83    (44)   ~ (all_53_4 = e0)
% 228.23/39.83    (45)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.23/39.83          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.23/39.83    (46)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.23/39.83          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.23/39.83    (47)  op(e0, e0) = e3
% 228.23/39.83    (48)   ~ (all_53_4 = all_53_6)
% 228.23/39.83    (49)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.23/39.83          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.23/39.83            e2)
% 228.23/39.83    (50)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.23/39.83              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.23/39.83                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.23/39.83                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.23/39.83    (51)  all_55_10 = all_6_2
% 228.23/39.83    (52)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.23/39.83          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.23/39.83    (53)  all_38_2 = all_6_2
% 228.23/39.83    (54)  all_55_3 = all_53_12
% 228.23/39.83    (55)   ~ (all_53_12 = e3)
% 228.23/39.83    (56)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.23/39.83            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.23/39.83              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.23/39.83    (57)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.23/39.83          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.23/39.83    (58)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.23/39.83          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.23/39.83    (59)  all_57_1 = e3
% 228.23/39.83    (60)   ~ (e2 = e1)
% 228.23/39.83    (61)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.23/39.83          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.23/39.83    (62)  op(e2, e1) = all_53_9
% 228.23/39.83    (63)  op(e1, e2) = all_53_6
% 228.23/39.83    (64)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.23/39.83          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.23/39.83    (65)  all_24_2 = all_6_2
% 228.23/39.83    (66)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.23/39.83          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.23/39.83    (67)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.23/39.83          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.23/39.83    (68)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.23/39.83          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.23/39.83    (69)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.23/39.83          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.23/39.83    (70)  op(e3, e1) = all_53_8
% 228.23/39.83    (71)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.23/39.83          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.23/39.83    (72)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.23/39.83          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.23/39.83    (73)  op(e3, e0) = all_53_12
% 228.23/39.83  
% 228.23/39.83  Begin of proof
% 228.23/39.83  | 
% 228.23/39.83  | ALPHA: (41) implies:
% 228.23/39.83  |   (74)  all_57_3 = e3
% 228.23/39.83  | 
% 228.23/39.83  | COMBINE_EQS: (23), (74) imply:
% 228.23/39.83  |   (75)  e3 = e0
% 228.23/39.83  | 
% 228.23/39.83  | SIMP: (75) implies:
% 228.23/39.83  |   (76)  e3 = e0
% 228.23/39.83  | 
% 228.23/39.83  | COMBINE_EQS: (59), (76) imply:
% 228.23/39.83  |   (77)  all_57_1 = e0
% 228.23/39.83  | 
% 228.23/39.83  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.23/39.83  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 228.23/39.83  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 228.23/39.83  |            (35), (36), (37), (38), (39), (40), (42), (43), (44), (45), (46),
% 228.23/39.83  |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 228.23/39.83  |            (58), (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 228.23/39.83  |            (70), (71), (72), (73), (77) are inconsistent by sub-proof #511.
% 228.23/39.83  | 
% 228.23/39.83  End of proof
% 228.23/39.83  
% 228.23/39.83  Sub-proof #474 shows that the following formulas are inconsistent:
% 228.23/39.83  ----------------------------------------------------------------
% 228.23/39.83    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.23/39.83    (2)  all_57_0 = e2
% 228.23/39.83    (3)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.23/39.83    (4)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.23/39.83         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.23/39.83    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.23/39.83         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.23/39.83    (6)   ~ (all_53_8 = all_53_12)
% 228.23/39.83    (7)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.23/39.83         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.23/39.83    (8)   ~ (all_53_8 = all_53_11)
% 228.23/39.83    (9)   ~ (e3 = e1)
% 228.23/39.83    (10)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.23/39.83          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.23/39.83    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.23/39.83            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.23/39.83    (12)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.23/39.83          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.23/39.83    (13)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.23/39.83            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.23/39.83              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.23/39.83    (14)   ~ (all_53_3 = e3)
% 228.23/39.83    (15)   ~ (all_6_2 = e3)
% 228.23/39.83    (16)  ( ~ (all_28_0 = e0) & op(all_28_1, e3) = all_28_0 & op(e3, e2) =
% 228.23/39.83            all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 = e1) & op(e3,
% 228.23/39.83              e2) = all_28_1 & $i(all_28_1))
% 228.23/39.83    (17)   ~ (all_53_9 = e1)
% 228.23/39.83    (18)  op(e1, e1) = all_6_2
% 228.23/39.83    (19)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.23/39.83    (20)   ~ (all_53_1 = all_53_9)
% 228.23/39.83    (21)   ~ (all_53_9 = e0)
% 228.23/39.83    (22)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 228.23/39.83    (23)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.23/39.83          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.23/39.83    (24)   ~ (all_52_17 = e2)
% 228.23/39.83    (25)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 228.23/39.83            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 228.23/39.83              e3) = all_22_1 & $i(all_22_1))
% 228.23/39.83    (26)   ~ (all_53_8 = e1)
% 228.23/39.83    (27)  op(all_52_17, all_52_17) = e3
% 228.23/39.83    (28)   ~ (all_53_4 = all_53_12)
% 228.23/39.83    (29)   ~ (all_52_17 = all_52_23)
% 228.23/39.83    (30)   ~ (all_52_17 = e1)
% 228.23/39.83    (31)   ~ (all_53_8 = all_53_9)
% 228.23/39.83    (32)  all_42_2 = all_6_2
% 228.23/39.83    (33)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.23/39.83          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.23/39.83    (34)   ~ (all_53_9 = all_53_11)
% 228.23/39.83    (35)  all_55_4 = all_53_1
% 228.23/39.83    (36)  all_57_8 = e1
% 228.23/39.83    (37)   ~ (all_53_9 = all_6_2)
% 228.23/39.83    (38)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.23/39.83          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.23/39.83    (39)  all_57_3 = e0
% 228.23/39.83    (40)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.23/39.83          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.23/39.83    (41)   ~ (e3 = e2)
% 228.23/39.83    (42)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 228.23/39.83    (43)  all_55_1 = all_53_4
% 228.23/39.83    (44)   ~ (all_53_1 = all_53_3)
% 228.23/39.83    (45)   ~ (all_53_1 = all_52_17)
% 228.23/39.83    (46)   ~ (e3 = e0)
% 228.23/39.83    (47)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.23/39.83          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.23/39.83    (48)   ~ (all_53_8 = all_6_2)
% 228.23/39.83    (49)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.23/39.83    (50)  all_55_11 = all_52_23
% 228.23/39.83    (51)  all_55_2 = all_53_8
% 228.23/39.83    (52)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 228.23/39.83    (53)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.23/39.83    (54)  all_57_15 = e3
% 228.23/39.83    (55)  op(e3, e3) = e2
% 228.23/39.83    (56)   ~ (all_53_3 = e2)
% 228.23/39.83    (57)   ~ (all_53_3 = all_52_17)
% 228.23/39.83    (58)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.23/39.83          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.23/39.83            e1)
% 228.23/39.83    (59)   ~ (all_52_23 = e3)
% 228.23/39.83    (60)  op(e1, e0) = all_52_23
% 228.23/39.83    (61)   ~ (all_53_4 = all_53_8)
% 228.23/39.83    (62)  all_55_6 = all_53_9
% 228.23/39.83    (63)  op(e3, e2) = all_53_4
% 228.23/39.83    (64)   ~ (e2 = e0)
% 228.23/39.83    (65)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.23/39.83            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.23/39.83            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.23/39.83            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.23/39.83              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.23/39.83            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.23/39.83            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.23/39.83              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.23/39.83              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.23/39.83            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.23/39.83            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.23/39.83            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.23/39.83              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.23/39.83              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.23/39.83            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.23/39.83              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.23/39.83            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.23/39.83            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.23/39.83              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.23/39.83              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.23/39.83            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.23/39.83            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.23/39.83    (66)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 228.23/39.83            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 228.23/39.83              e3) = all_12_1 & $i(all_12_1))
% 228.23/39.83    (67)  all_55_12 = all_53_3
% 228.23/39.83    (68)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.23/39.83          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.23/39.83    (69)   ~ (all_53_1 = e0)
% 228.23/39.83    (70)   ~ (e1 = e0)
% 228.23/39.83    (71)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.23/39.83            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.23/39.83              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.23/39.83    (72)   ~ (all_53_4 = e0)
% 228.23/39.83    (73)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.23/39.83          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.23/39.83    (74)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.23/39.83          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.23/39.83    (75)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 228.23/39.83    (76)  op(e0, e0) = e3
% 228.23/39.83    (77)   ~ (all_53_4 = all_53_6)
% 228.23/39.83    (78)  ( ~ (all_20_0 = e1) & op(all_20_1, e3) = all_20_0 & op(e3, e2) =
% 228.23/39.83            all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e0) & op(e3,
% 228.23/39.83              e2) = all_20_1 & $i(all_20_1))
% 228.23/39.83    (79)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.23/39.83          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.23/39.83            e2)
% 228.23/39.83    (80)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.23/39.83              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.23/39.83                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.23/39.83                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.23/39.83    (81)  all_55_10 = all_6_2
% 228.23/39.83    (82)   ~ (all_53_11 = e1)
% 228.23/39.83    (83)  all_55_8 = all_52_17
% 228.23/39.83    (84)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.23/39.83          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.23/39.83    (85)  all_38_2 = all_6_2
% 228.23/39.83    (86)  all_55_3 = all_53_12
% 228.23/39.83    (87)   ~ (all_53_12 = e3)
% 228.23/39.83    (88)   ~ (all_53_4 = e2)
% 228.23/39.83    (89)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.23/39.83            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.23/39.83              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.23/39.83    (90)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.23/39.83          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.23/39.83    (91)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.23/39.83          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.23/39.83    (92)   ~ (all_52_23 = e1)
% 228.23/39.83    (93)   ~ (all_53_1 = e2)
% 228.23/39.83    (94)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.23/39.83          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.23/39.83    (95)  op(e2, e1) = all_53_9
% 228.23/39.83    (96)  op(e1, e2) = all_53_6
% 228.23/39.83    (97)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.23/39.83          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.23/39.83    (98)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 228.23/39.83    (99)  all_24_2 = all_6_2
% 228.23/39.83    (100)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.23/39.83           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.23/39.83    (101)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.23/39.83           (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.23/39.83    (102)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.23/39.83           | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.23/39.83             e1)
% 228.23/39.83    (103)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.23/39.83           (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.23/39.83    (104)  all_55_14 = all_53_11
% 228.23/39.83    (105)  op(e3, e1) = all_53_8
% 228.23/39.83    (106)   ~ (all_53_11 = e3)
% 228.23/39.83    (107)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.23/39.83           (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.23/39.83    (108)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.23/39.83           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.23/39.83    (109)  op(e3, e0) = all_53_12
% 228.23/39.83  
% 228.23/39.83  Begin of proof
% 228.23/39.83  | 
% 228.23/39.83  | BETA: splitting (52) gives:
% 228.23/39.83  | 
% 228.23/39.83  | Case 1:
% 228.23/39.83  | | 
% 228.23/39.83  | |   (110)  all_55_4 = e3
% 228.23/39.83  | | 
% 228.23/39.83  | | COMBINE_EQS: (35), (110) imply:
% 228.23/39.83  | |   (111)  all_53_1 = e3
% 228.23/39.83  | | 
% 228.23/39.83  | | SIMP: (111) implies:
% 228.23/39.83  | |   (112)  all_53_1 = e3
% 228.23/39.83  | | 
% 228.23/39.83  | | REDUCE: (20), (112) imply:
% 228.23/39.83  | |   (113)   ~ (all_53_9 = e3)
% 228.23/39.83  | | 
% 228.23/39.83  | | SIMP: (113) implies:
% 228.23/39.83  | |   (114)   ~ (all_53_9 = e3)
% 228.23/39.83  | | 
% 228.23/39.83  | | REDUCE: (45), (112) imply:
% 228.23/39.83  | |   (115)   ~ (all_52_17 = e3)
% 228.23/39.83  | | 
% 228.23/39.83  | | SIMP: (115) implies:
% 228.23/39.83  | |   (116)   ~ (all_52_17 = e3)
% 228.23/39.83  | | 
% 228.23/39.83  | | BETA: splitting (42) gives:
% 228.23/39.83  | | 
% 228.23/39.83  | | Case 1:
% 228.23/39.83  | | | 
% 228.23/39.83  | | |   (117)  all_55_6 = e3
% 228.23/39.83  | | | 
% 228.23/39.83  | | | REF_CLOSE: (62), (114), (117) are inconsistent by sub-proof #2498.
% 228.23/39.83  | | | 
% 228.23/39.83  | | Case 2:
% 228.23/39.83  | | | 
% 228.23/39.83  | | |   (118)   ~ (all_55_6 = e3)
% 228.23/39.83  | | |   (119)  all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 228.23/39.83  | | | 
% 228.23/39.83  | | | BETA: splitting (119) gives:
% 228.23/39.83  | | | 
% 228.23/39.83  | | | Case 1:
% 228.23/39.83  | | | | 
% 228.23/39.83  | | | |   (120)  all_55_6 = e2
% 228.23/39.83  | | | | 
% 228.23/39.83  | | | | COMBINE_EQS: (62), (120) imply:
% 228.23/39.83  | | | |   (121)  all_53_9 = e2
% 228.23/39.83  | | | | 
% 228.23/39.83  | | | | SIMP: (121) implies:
% 228.23/39.83  | | | |   (122)  all_53_9 = e2
% 228.23/39.83  | | | | 
% 228.23/39.83  | | | | REDUCE: (31), (122) imply:
% 228.23/39.83  | | | |   (123)   ~ (all_53_8 = e2)
% 228.23/39.83  | | | | 
% 228.23/39.83  | | | | REDUCE: (34), (122) imply:
% 228.23/39.83  | | | |   (124)   ~ (all_53_11 = e2)
% 228.23/39.83  | | | | 
% 228.23/39.83  | | | | SIMP: (124) implies:
% 228.23/39.83  | | | |   (125)   ~ (all_53_11 = e2)
% 228.23/39.83  | | | | 
% 228.23/39.83  | | | | REDUCE: (114), (122) imply:
% 228.23/39.83  | | | |   (126)   ~ (e3 = e2)
% 228.23/39.83  | | | | 
% 228.23/39.83  | | | | REDUCE: (17), (122) imply:
% 228.23/39.83  | | | |   (127)   ~ (e2 = e1)
% 228.23/39.83  | | | | 
% 228.23/39.83  | | | | REDUCE: (95), (122) imply:
% 228.23/39.83  | | | |   (128)  op(e2, e1) = e2
% 228.23/39.83  | | | | 
% 228.23/39.83  | | | | BETA: splitting (90) gives:
% 228.23/39.83  | | | | 
% 228.23/39.83  | | | | Case 1:
% 228.23/39.83  | | | | | 
% 228.23/39.83  | | | | |   (129)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2,
% 228.23/39.83  | | | | |              e2) = e2)
% 228.23/39.83  | | | | | 
% 228.23/39.83  | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13),
% 228.23/39.83  | | | | |            (15), (18), (19), (21), (23), (28), (31), (32), (33), (37),
% 228.23/39.83  | | | | |            (38), (39), (40), (41), (43), (46), (47), (48), (51), (53),
% 228.23/39.83  | | | | |            (54), (55), (58), (61), (63), (64), (65), (68), (70), (71),
% 228.23/39.83  | | | | |            (72), (73), (74), (76), (77), (79), (80), (81), (84), (85),
% 228.23/39.83  | | | | |            (86), (87), (89), (90), (91), (94), (95), (96), (97), (99),
% 228.23/39.83  | | | | |            (100), (101), (102), (103), (105), (107), (108), (109),
% 228.23/39.83  | | | | |            (127), (129) are inconsistent by sub-proof #543.
% 228.23/39.83  | | | | | 
% 228.23/39.83  | | | | Case 2:
% 228.23/39.83  | | | | | 
% 228.23/39.83  | | | | |   (130)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2,
% 228.23/39.83  | | | | |              e0) = e2)
% 228.23/39.83  | | | | | 
% 228.23/39.83  | | | | | BETA: splitting (130) gives:
% 228.23/39.83  | | | | | 
% 228.23/39.83  | | | | | Case 1:
% 228.23/39.83  | | | | | | 
% 228.23/39.83  | | | | | |   (131)  all_57_5 = e2 & op(e2, e1) = e2
% 228.23/39.83  | | | | | | 
% 228.23/39.83  | | | | | | ALPHA: (131) implies:
% 228.23/39.83  | | | | | |   (132)  all_57_5 = e2
% 228.23/39.83  | | | | | | 
% 228.23/39.83  | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12),
% 228.23/39.83  | | | | | |            (13), (15), (18), (19), (21), (23), (25), (28), (31),
% 228.23/39.83  | | | | | |            (32), (33), (36), (37), (38), (39), (40), (41), (43),
% 228.23/39.83  | | | | | |            (46), (47), (48), (51), (53), (54), (55), (58), (61),
% 228.23/39.83  | | | | | |            (63), (64), (65), (66), (68), (70), (71), (72), (73),
% 228.23/39.83  | | | | | |            (74), (76), (77), (79), (80), (81), (84), (85), (86),
% 228.23/39.83  | | | | | |            (87), (89), (90), (91), (94), (95), (96), (97), (99),
% 228.23/39.83  | | | | | |            (100), (101), (102), (103), (105), (107), (108), (109),
% 228.23/39.83  | | | | | |            (127), (132) are inconsistent by sub-proof #496.
% 228.23/39.83  | | | | | | 
% 228.23/39.83  | | | | | Case 2:
% 228.23/39.83  | | | | | | 
% 228.23/39.83  | | | | | |   (133)  all_57_10 = e2 & op(e2, e0) = e2
% 228.23/39.83  | | | | | | 
% 228.23/39.83  | | | | | | ALPHA: (133) implies:
% 228.23/39.83  | | | | | |   (134)  all_57_10 = e2
% 228.23/39.83  | | | | | | 
% 228.23/39.83  | | | | | | BETA: splitting (75) gives:
% 228.23/39.83  | | | | | | 
% 228.23/39.83  | | | | | | Case 1:
% 228.23/39.83  | | | | | | | 
% 228.23/39.83  | | | | | | |   (135)  all_55_14 = e3
% 228.23/39.83  | | | | | | | 
% 228.23/39.83  | | | | | | | COMBINE_EQS: (104), (135) imply:
% 228.23/39.83  | | | | | | |   (136)  all_53_11 = e3
% 228.23/39.83  | | | | | | | 
% 228.23/39.83  | | | | | | | REDUCE: (106), (136) imply:
% 228.23/39.83  | | | | | | |   (137)  $false
% 228.23/39.83  | | | | | | | 
% 228.23/39.83  | | | | | | | CLOSE: (137) is inconsistent.
% 228.23/39.83  | | | | | | | 
% 228.23/39.83  | | | | | | Case 2:
% 228.23/39.83  | | | | | | | 
% 228.23/39.83  | | | | | | |   (138)  all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 228.23/39.83  | | | | | | | 
% 228.23/39.83  | | | | | | | BETA: splitting (84) gives:
% 228.23/39.83  | | | | | | | 
% 228.23/39.83  | | | | | | | Case 1:
% 228.23/39.83  | | | | | | | | 
% 228.23/39.83  | | | | | | | |   (139)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 &
% 228.23/39.83  | | | | | | | |            op(e2, e2) = e3)
% 228.23/39.83  | | | | | | | | 
% 228.23/39.83  | | | | | | | | BETA: splitting (139) gives:
% 228.23/39.83  | | | | | | | | 
% 228.23/39.83  | | | | | | | | Case 1:
% 228.23/39.83  | | | | | | | | | 
% 228.23/39.83  | | | | | | | | |   (140)  all_57_2 = e3 & op(e2, e3) = e3
% 228.23/39.83  | | | | | | | | | 
% 228.23/39.83  | | | | | | | | | ALPHA: (140) implies:
% 228.23/39.83  | | | | | | | | |   (141)  all_57_2 = e3
% 228.23/39.83  | | | | | | | | | 
% 228.23/39.83  | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (9), (10), (11),
% 228.23/39.83  | | | | | | | | |            (12), (13), (15), (18), (19), (21), (23), (28),
% 228.23/39.83  | | | | | | | | |            (31), (32), (33), (36), (37), (38), (39), (40),
% 228.23/39.83  | | | | | | | | |            (41), (43), (46), (47), (48), (51), (53), (54),
% 228.23/39.83  | | | | | | | | |            (55), (58), (61), (63), (64), (65), (68), (70),
% 228.23/39.83  | | | | | | | | |            (71), (72), (73), (74), (76), (77), (79), (80),
% 228.23/39.83  | | | | | | | | |            (81), (84), (85), (86), (87), (89), (90), (91),
% 228.23/39.83  | | | | | | | | |            (94), (95), (96), (97), (99), (100), (101), (102),
% 228.23/39.83  | | | | | | | | |            (103), (105), (107), (108), (109), (127), (134),
% 228.23/39.83  | | | | | | | | |            (141) are inconsistent by sub-proof #501.
% 228.23/39.83  | | | | | | | | | 
% 228.23/39.83  | | | | | | | | Case 2:
% 228.23/39.83  | | | | | | | | | 
% 228.23/39.83  | | | | | | | | |   (142)  all_57_3 = e3 & op(e2, e2) = e3
% 228.23/39.83  | | | | | | | | | 
% 228.23/39.83  | | | | | | | | | ALPHA: (142) implies:
% 228.23/39.83  | | | | | | | | |   (143)  all_57_3 = e3
% 228.23/39.83  | | | | | | | | | 
% 228.23/39.83  | | | | | | | | | REF_CLOSE: (39), (46), (143) are inconsistent by sub-proof
% 228.23/39.83  | | | | | | | | |            #2358.
% 228.23/39.83  | | | | | | | | | 
% 228.23/39.83  | | | | | | | | End of split
% 228.23/39.83  | | | | | | | | 
% 228.23/39.83  | | | | | | | Case 2:
% 228.23/39.83  | | | | | | | | 
% 228.23/39.83  | | | | | | | |   (144)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 &
% 228.23/39.83  | | | | | | | |            op(e2, e0) = e3)
% 228.23/39.83  | | | | | | | | 
% 228.23/39.83  | | | | | | | | BETA: splitting (144) gives:
% 228.23/39.83  | | | | | | | | 
% 228.23/39.83  | | | | | | | | Case 1:
% 228.23/39.83  | | | | | | | | | 
% 228.23/39.83  | | | | | | | | |   (145)  all_57_5 = e3 & op(e2, e1) = e3
% 228.23/39.83  | | | | | | | | | 
% 228.23/39.83  | | | | | | | | | ALPHA: (145) implies:
% 228.23/39.83  | | | | | | | | |   (146)  all_57_5 = e3
% 228.23/39.83  | | | | | | | | |   (147)  op(e2, e1) = e3
% 228.23/39.83  | | | | | | | | | 
% 228.23/39.83  | | | | | | | | | BETA: splitting (49) gives:
% 228.23/39.83  | | | | | | | | | 
% 228.23/39.83  | | | | | | | | | Case 1:
% 228.23/39.83  | | | | | | | | | | 
% 228.23/39.83  | | | | | | | | | |   (148)  all_55_8 = e3
% 228.23/39.83  | | | | | | | | | | 
% 228.23/39.83  | | | | | | | | | | REF_CLOSE: (83), (116), (148) are inconsistent by sub-proof
% 228.23/39.83  | | | | | | | | | |            #1881.
% 228.23/39.83  | | | | | | | | | | 
% 228.23/39.83  | | | | | | | | | Case 2:
% 228.23/39.83  | | | | | | | | | | 
% 228.23/39.83  | | | | | | | | | |   (149)  all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.23/39.83  | | | | | | | | | | 
% 228.23/39.83  | | | | | | | | | | BETA: splitting (138) gives:
% 228.23/39.83  | | | | | | | | | | 
% 228.23/39.83  | | | | | | | | | | Case 1:
% 228.23/39.83  | | | | | | | | | | | 
% 228.23/39.83  | | | | | | | | | | |   (150)  all_55_14 = e2
% 228.23/39.83  | | | | | | | | | | | 
% 228.23/39.83  | | | | | | | | | | | REF_CLOSE: (104), (125), (150) are inconsistent by sub-proof
% 228.23/39.83  | | | | | | | | | | |            #2293.
% 228.23/39.83  | | | | | | | | | | | 
% 228.23/39.83  | | | | | | | | | | Case 2:
% 228.23/39.83  | | | | | | | | | | | 
% 228.23/39.83  | | | | | | | | | | |   (151)  all_55_14 = e1 | all_55_14 = e0
% 228.23/39.83  | | | | | | | | | | | 
% 228.23/39.83  | | | | | | | | | | | BETA: splitting (91) gives:
% 228.23/39.83  | | | | | | | | | | | 
% 228.23/39.83  | | | | | | | | | | | Case 1:
% 228.23/39.83  | | | | | | | | | | | | 
% 228.23/39.83  | | | | | | | | | | | |   (152)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 228.23/39.83  | | | | | | | | | | | |            & op(e2, e3) = e3)
% 228.23/39.83  | | | | | | | | | | | | 
% 228.23/39.83  | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (9), (10), (11),
% 228.23/39.83  | | | | | | | | | | | |            (12), (13), (15), (18), (19), (21), (23), (28),
% 228.23/39.83  | | | | | | | | | | | |            (31), (32), (33), (37), (38), (39), (40), (41),
% 228.23/39.83  | | | | | | | | | | | |            (43), (46), (47), (48), (51), (53), (54), (58),
% 228.23/39.83  | | | | | | | | | | | |            (61), (63), (64), (65), (70), (71), (72), (76),
% 228.23/39.83  | | | | | | | | | | | |            (77), (79), (80), (81), (85), (86), (87), (89),
% 228.23/39.83  | | | | | | | | | | | |            (90), (94), (95), (96), (97), (99), (100), (101),
% 228.23/39.83  | | | | | | | | | | | |            (102), (103), (105), (107), (108), (109), (127),
% 228.23/39.83  | | | | | | | | | | | |            (134), (146), (147), (152) are inconsistent by
% 228.23/39.83  | | | | | | | | | | | |            sub-proof #495.
% 228.23/39.83  | | | | | | | | | | | | 
% 228.23/39.83  | | | | | | | | | | | Case 2:
% 228.23/39.83  | | | | | | | | | | | | 
% 228.23/39.83  | | | | | | | | | | | |   (153)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 228.23/39.83  | | | | | | | | | | | |            e3 & op(e0, e3) = e3)
% 228.23/39.83  | | | | | | | | | | | | 
% 228.23/39.83  | | | | | | | | | | | | BETA: splitting (153) gives:
% 228.23/39.83  | | | | | | | | | | | | 
% 228.23/39.84  | | | | | | | | | | | | Case 1:
% 228.23/39.84  | | | | | | | | | | | | | 
% 228.23/39.84  | | | | | | | | | | | | |   (154)  all_57_6 = e3 & op(e1, e3) = e3
% 228.23/39.84  | | | | | | | | | | | | | 
% 228.23/39.84  | | | | | | | | | | | | | ALPHA: (154) implies:
% 228.23/39.84  | | | | | | | | | | | | |   (155)  all_57_6 = e3
% 228.23/39.84  | | | | | | | | | | | | | 
% 228.23/39.84  | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 228.23/39.84  | | | | | | | | | | | | |            (11), (12), (13), (15), (16), (18), (19), (21),
% 228.23/39.84  | | | | | | | | | | | | |            (22), (23), (24), (26), (28), (29), (30), (31),
% 228.23/39.84  | | | | | | | | | | | | |            (32), (33), (36), (37), (38), (39), (40), (41),
% 228.23/39.84  | | | | | | | | | | | | |            (43), (46), (47), (48), (50), (51), (53), (54),
% 228.23/39.84  | | | | | | | | | | | | |            (55), (58), (59), (60), (61), (63), (64), (65),
% 228.23/39.84  | | | | | | | | | | | | |            (68), (70), (71), (72), (73), (74), (76), (77),
% 228.23/39.84  | | | | | | | | | | | | |            (78), (79), (80), (81), (82), (83), (84), (85),
% 228.23/39.84  | | | | | | | | | | | | |            (86), (87), (88), (89), (90), (91), (92), (94),
% 228.23/39.84  | | | | | | | | | | | | |            (95), (96), (97), (99), (100), (101), (102),
% 228.23/39.84  | | | | | | | | | | | | |            (103), (104), (105), (107), (108), (109), (123),
% 228.23/39.84  | | | | | | | | | | | | |            (127), (128), (134), (146), (147), (149), (151),
% 228.23/39.84  | | | | | | | | | | | | |            (155) are inconsistent by sub-proof #476.
% 228.23/39.84  | | | | | | | | | | | | | 
% 228.23/39.84  | | | | | | | | | | | | Case 2:
% 228.23/39.84  | | | | | | | | | | | | | 
% 228.23/39.84  | | | | | | | | | | | | |   (156)  all_57_12 = e3 & op(e0, e3) = e3
% 228.23/39.84  | | | | | | | | | | | | | 
% 228.23/39.84  | | | | | | | | | | | | | ALPHA: (156) implies:
% 228.23/39.84  | | | | | | | | | | | | |   (157)  all_57_12 = e3
% 228.23/39.84  | | | | | | | | | | | | | 
% 228.23/39.84  | | | | | | | | | | | | | BETA: splitting (5) gives:
% 228.23/39.84  | | | | | | | | | | | | | 
% 228.23/39.84  | | | | | | | | | | | | | Case 1:
% 228.23/39.84  | | | | | | | | | | | | | | 
% 228.23/39.84  | | | | | | | | | | | | | |   (158)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 228.23/39.84  | | | | | | | | | | | | | |            & op(e2, e3) = e1)
% 228.23/39.84  | | | | | | | | | | | | | | 
% 228.23/39.84  | | | | | | | | | | | | | | BETA: splitting (158) gives:
% 228.23/39.84  | | | | | | | | | | | | | | 
% 228.23/39.84  | | | | | | | | | | | | | | Case 1:
% 228.23/39.84  | | | | | | | | | | | | | | | 
% 228.23/39.84  | | | | | | | | | | | | | | |   (159)  all_57_0 = e1 & op(e3, e3) = e1
% 228.23/39.84  | | | | | | | | | | | | | | | 
% 228.23/39.84  | | | | | | | | | | | | | | | ALPHA: (159) implies:
% 228.23/39.84  | | | | | | | | | | | | | | |   (160)  op(e3, e3) = e1
% 228.23/39.84  | | | | | | | | | | | | | | | 
% 228.23/39.84  | | | | | | | | | | | | | | | REF_CLOSE: (11), (55), (127), (160) are inconsistent by
% 228.23/39.84  | | | | | | | | | | | | | | |            sub-proof #1950.
% 228.23/39.84  | | | | | | | | | | | | | | | 
% 228.23/39.84  | | | | | | | | | | | | | | Case 2:
% 228.23/39.84  | | | | | | | | | | | | | | | 
% 228.23/39.84  | | | | | | | | | | | | | | |   (161)  all_57_2 = e1 & op(e2, e3) = e1
% 228.23/39.84  | | | | | | | | | | | | | | | 
% 228.23/39.84  | | | | | | | | | | | | | | | ALPHA: (161) implies:
% 228.23/39.84  | | | | | | | | | | | | | | |   (162)  all_57_2 = e1
% 228.23/39.84  | | | | | | | | | | | | | | | 
% 228.23/39.84  | | | | | | | | | | | | | | | BETA: splitting (12) gives:
% 228.23/39.84  | | | | | | | | | | | | | | | 
% 228.23/39.84  | | | | | | | | | | | | | | | Case 1:
% 228.23/39.84  | | | | | | | | | | | | | | | | 
% 228.23/39.84  | | | | | | | | | | | | | | | |   (163)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 228.23/39.84  | | | | | | | | | | | | | | | |            & op(e1, e2) = e3)
% 228.23/39.84  | | | | | | | | | | | | | | | | 
% 228.23/39.84  | | | | | | | | | | | | | | | | BETA: splitting (163) gives:
% 228.23/39.84  | | | | | | | | | | | | | | | | 
% 228.23/39.84  | | | | | | | | | | | | | | | | Case 1:
% 228.23/39.84  | | | | | | | | | | | | | | | | | 
% 228.23/39.84  | | | | | | | | | | | | | | | | |   (164)  all_57_6 = e3 & op(e1, e3) = e3
% 228.23/39.84  | | | | | | | | | | | | | | | | | 
% 228.23/39.84  | | | | | | | | | | | | | | | | | ALPHA: (164) implies:
% 228.23/39.84  | | | | | | | | | | | | | | | | |   (165)  all_57_6 = e3
% 228.23/39.84  | | | | | | | | | | | | | | | | | 
% 228.23/39.84  | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 228.23/39.84  | | | | | | | | | | | | | | | | |            (11), (12), (13), (15), (16), (18), (19), (21),
% 228.23/39.84  | | | | | | | | | | | | | | | | |            (22), (23), (24), (26), (28), (29), (30), (31),
% 228.23/39.84  | | | | | | | | | | | | | | | | |            (32), (33), (36), (37), (38), (39), (40), (41),
% 228.23/39.84  | | | | | | | | | | | | | | | | |            (43), (46), (47), (48), (50), (51), (53), (54),
% 228.23/39.84  | | | | | | | | | | | | | | | | |            (55), (58), (59), (60), (61), (63), (64), (65),
% 228.23/39.84  | | | | | | | | | | | | | | | | |            (68), (70), (71), (72), (73), (74), (76), (77),
% 228.23/39.84  | | | | | | | | | | | | | | | | |            (78), (79), (80), (81), (82), (83), (84), (85),
% 228.23/39.84  | | | | | | | | | | | | | | | | |            (86), (87), (88), (89), (90), (91), (92), (94),
% 228.23/39.84  | | | | | | | | | | | | | | | | |            (95), (96), (97), (99), (100), (101), (102),
% 228.23/39.84  | | | | | | | | | | | | | | | | |            (103), (104), (105), (107), (108), (109), (123),
% 228.23/39.84  | | | | | | | | | | | | | | | | |            (127), (128), (134), (146), (147), (149), (151),
% 228.23/39.84  | | | | | | | | | | | | | | | | |            (165) are inconsistent by sub-proof #476.
% 228.23/39.84  | | | | | | | | | | | | | | | | | 
% 228.23/39.84  | | | | | | | | | | | | | | | | Case 2:
% 228.23/39.84  | | | | | | | | | | | | | | | | | 
% 228.23/39.84  | | | | | | | | | | | | | | | | |   (166)  all_57_7 = e3 & op(e1, e2) = e3
% 228.23/39.84  | | | | | | | | | | | | | | | | | 
% 228.23/39.84  | | | | | | | | | | | | | | | | | ALPHA: (166) implies:
% 228.23/39.84  | | | | | | | | | | | | | | | | |   (167)  all_57_7 = e3
% 228.23/39.84  | | | | | | | | | | | | | | | | |   (168)  op(e1, e2) = e3
% 228.23/39.84  | | | | | | | | | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (9), (10), (11),
% 228.31/39.84  | | | | | | | | | | | | | | | | |            (13), (18), (19), (21), (23), (28), (31), (32),
% 228.31/39.84  | | | | | | | | | | | | | | | | |            (33), (36), (37), (38), (39), (40), (41), (43),
% 228.31/39.84  | | | | | | | | | | | | | | | | |            (46), (47), (48), (51), (53), (54), (58), (61),
% 228.31/39.84  | | | | | | | | | | | | | | | | |            (63), (64), (65), (68), (70), (71), (72), (76),
% 228.31/39.84  | | | | | | | | | | | | | | | | |            (77), (79), (80), (81), (85), (86), (87), (89),
% 228.31/39.84  | | | | | | | | | | | | | | | | |            (90), (94), (95), (96), (97), (99), (100), (101),
% 228.31/39.84  | | | | | | | | | | | | | | | | |            (102), (103), (105), (107), (108), (109), (127),
% 228.31/39.84  | | | | | | | | | | | | | | | | |            (146), (147), (157), (162), (167), (168) are
% 228.31/39.84  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #475.
% 228.31/39.84  | | | | | | | | | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | | | | | | | | End of split
% 228.31/39.84  | | | | | | | | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | | | | | | | Case 2:
% 228.31/39.84  | | | | | | | | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | | | | | | | |   (169)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 228.31/39.84  | | | | | | | | | | | | | | | |            e3 & op(e1, e0) = e3)
% 228.31/39.84  | | | | | | | | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11), (15), (18), (41), (46), (54), (64),
% 228.31/39.84  | | | | | | | | | | | | | | | |            (70), (80), (94), (102), (127), (169) are
% 228.31/39.84  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1786.
% 228.31/39.84  | | | | | | | | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | | | | | | | End of split
% 228.31/39.84  | | | | | | | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | | | | | | End of split
% 228.31/39.84  | | | | | | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | | | | | Case 2:
% 228.31/39.84  | | | | | | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | | | | | |   (170)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 228.31/39.84  | | | | | | | | | | | | | |            e1 & op(e0, e3) = e1)
% 228.31/39.84  | | | | | | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | | | | | | BETA: splitting (170) gives:
% 228.31/39.84  | | | | | | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | | | | | | Case 1:
% 228.31/39.84  | | | | | | | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | | | | | | |   (171)  all_57_6 = e1 & op(e1, e3) = e1
% 228.31/39.84  | | | | | | | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | | | | | | | ALPHA: (171) implies:
% 228.31/39.84  | | | | | | | | | | | | | | |   (172)  all_57_6 = e1
% 228.31/39.84  | | | | | | | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | | | | | | | REF_CLOSE: (4), (9), (11), (39), (41), (46), (55), (64),
% 228.31/39.84  | | | | | | | | | | | | | | |            (70), (90), (101), (127), (146), (157), (172) are
% 228.31/39.84  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1643.
% 228.31/39.84  | | | | | | | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | | | | | | Case 2:
% 228.31/39.84  | | | | | | | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | | | | | | |   (173)  all_57_12 = e1 & op(e0, e3) = e1
% 228.31/39.84  | | | | | | | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | | | | | | | ALPHA: (173) implies:
% 228.31/39.84  | | | | | | | | | | | | | | |   (174)  all_57_12 = e1
% 228.31/39.84  | | | | | | | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | | | | | | | REF_CLOSE: (9), (157), (174) are inconsistent by sub-proof
% 228.31/39.84  | | | | | | | | | | | | | | |            #2151.
% 228.31/39.84  | | | | | | | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | | | | | | End of split
% 228.31/39.84  | | | | | | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | | | | | End of split
% 228.31/39.84  | | | | | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | | | | End of split
% 228.31/39.84  | | | | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | | | End of split
% 228.31/39.84  | | | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | | End of split
% 228.31/39.84  | | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | End of split
% 228.31/39.84  | | | | | | | | | 
% 228.31/39.84  | | | | | | | | Case 2:
% 228.31/39.84  | | | | | | | | | 
% 228.31/39.84  | | | | | | | | |   (175)  all_57_10 = e3 & op(e2, e0) = e3
% 228.31/39.84  | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | ALPHA: (175) implies:
% 228.31/39.84  | | | | | | | | |   (176)  all_57_10 = e3
% 228.31/39.84  | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | REF_CLOSE: (41), (134), (176) are inconsistent by sub-proof
% 228.31/39.84  | | | | | | | | |            #2356.
% 228.31/39.84  | | | | | | | | | 
% 228.31/39.84  | | | | | | | | End of split
% 228.31/39.84  | | | | | | | | 
% 228.31/39.84  | | | | | | | End of split
% 228.31/39.84  | | | | | | | 
% 228.31/39.84  | | | | | | End of split
% 228.31/39.84  | | | | | | 
% 228.31/39.84  | | | | | End of split
% 228.31/39.84  | | | | | 
% 228.31/39.84  | | | | End of split
% 228.31/39.84  | | | | 
% 228.31/39.84  | | | Case 2:
% 228.31/39.84  | | | | 
% 228.31/39.84  | | | |   (177)  all_55_6 = e1 | all_55_6 = e0
% 228.31/39.84  | | | | 
% 228.31/39.84  | | | | BETA: splitting (177) gives:
% 228.31/39.84  | | | | 
% 228.31/39.84  | | | | Case 1:
% 228.31/39.84  | | | | | 
% 228.31/39.84  | | | | |   (178)  all_55_6 = e1
% 228.31/39.84  | | | | | 
% 228.31/39.84  | | | | | REF_CLOSE: (17), (62), (178) are inconsistent by sub-proof #2163.
% 228.31/39.84  | | | | | 
% 228.31/39.84  | | | | Case 2:
% 228.31/39.84  | | | | | 
% 228.31/39.84  | | | | |   (179)  all_55_6 = e0
% 228.31/39.84  | | | | | 
% 228.31/39.84  | | | | | REF_CLOSE: (21), (62), (179) are inconsistent by sub-proof #2162.
% 228.31/39.84  | | | | | 
% 228.31/39.84  | | | | End of split
% 228.31/39.84  | | | | 
% 228.31/39.84  | | | End of split
% 228.31/39.84  | | | 
% 228.31/39.84  | | End of split
% 228.31/39.84  | | 
% 228.31/39.84  | Case 2:
% 228.31/39.84  | | 
% 228.31/39.84  | |   (180)   ~ (all_55_4 = e3)
% 228.31/39.84  | |   (181)  all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 228.31/39.84  | | 
% 228.31/39.84  | | REDUCE: (35), (180) imply:
% 228.31/39.84  | |   (182)   ~ (all_53_1 = e3)
% 228.31/39.84  | | 
% 228.31/39.84  | | BETA: splitting (181) gives:
% 228.31/39.84  | | 
% 228.31/39.84  | | Case 1:
% 228.31/39.84  | | | 
% 228.31/39.84  | | |   (183)  all_55_4 = e2
% 228.31/39.84  | | | 
% 228.31/39.84  | | | REF_CLOSE: (35), (93), (183) are inconsistent by sub-proof #2168.
% 228.31/39.84  | | | 
% 228.31/39.84  | | Case 2:
% 228.31/39.84  | | | 
% 228.31/39.84  | | |   (184)   ~ (all_55_4 = e2)
% 228.31/39.84  | | |   (185)  all_55_4 = e1 | all_55_4 = e0
% 228.31/39.84  | | | 
% 228.31/39.84  | | | BETA: splitting (185) gives:
% 228.31/39.84  | | | 
% 228.31/39.84  | | | Case 1:
% 228.31/39.84  | | | | 
% 228.31/39.84  | | | |   (186)  all_55_4 = e1
% 228.31/39.84  | | | | 
% 228.31/39.84  | | | | COMBINE_EQS: (35), (186) imply:
% 228.31/39.84  | | | |   (187)  all_53_1 = e1
% 228.31/39.84  | | | | 
% 228.31/39.84  | | | | SIMP: (187) implies:
% 228.31/39.84  | | | |   (188)  all_53_1 = e1
% 228.31/39.84  | | | | 
% 228.31/39.84  | | | | REDUCE: (44), (188) imply:
% 228.31/39.84  | | | |   (189)   ~ (all_53_3 = e1)
% 228.31/39.84  | | | | 
% 228.31/39.84  | | | | SIMP: (189) implies:
% 228.31/39.84  | | | |   (190)   ~ (all_53_3 = e1)
% 228.31/39.84  | | | | 
% 228.31/39.84  | | | | REDUCE: (45), (188) imply:
% 228.31/39.84  | | | |   (191)   ~ (all_52_17 = e1)
% 228.31/39.84  | | | | 
% 228.31/39.84  | | | | REDUCE: (182), (188) imply:
% 228.31/39.84  | | | |   (192)   ~ (e3 = e1)
% 228.31/39.84  | | | | 
% 228.31/39.84  | | | | REDUCE: (93), (188) imply:
% 228.31/39.84  | | | |   (193)   ~ (e2 = e1)
% 228.31/39.84  | | | | 
% 228.31/39.84  | | | | SIMP: (193) implies:
% 228.31/39.84  | | | |   (194)   ~ (e2 = e1)
% 228.31/39.84  | | | | 
% 228.31/39.84  | | | | BETA: splitting (84) gives:
% 228.31/39.84  | | | | 
% 228.31/39.84  | | | | Case 1:
% 228.31/39.84  | | | | | 
% 228.31/39.84  | | | | |   (195)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2,
% 228.31/39.84  | | | | |              e2) = e3)
% 228.31/39.84  | | | | | 
% 228.31/39.84  | | | | | BETA: splitting (195) gives:
% 228.31/39.84  | | | | | 
% 228.31/39.84  | | | | | Case 1:
% 228.31/39.84  | | | | | | 
% 228.31/39.84  | | | | | |   (196)  all_57_2 = e3 & op(e2, e3) = e3
% 228.31/39.84  | | | | | | 
% 228.31/39.84  | | | | | | ALPHA: (196) implies:
% 228.31/39.84  | | | | | |   (197)  all_57_2 = e3
% 228.31/39.84  | | | | | | 
% 228.31/39.84  | | | | | | BETA: splitting (98) gives:
% 228.31/39.84  | | | | | | 
% 228.31/39.84  | | | | | | Case 1:
% 228.31/39.84  | | | | | | | 
% 228.31/39.84  | | | | | | |   (198)  all_55_12 = e3
% 228.31/39.84  | | | | | | | 
% 228.31/39.84  | | | | | | | COMBINE_EQS: (67), (198) imply:
% 228.31/39.84  | | | | | | |   (199)  all_53_3 = e3
% 228.31/39.84  | | | | | | | 
% 228.31/39.84  | | | | | | | REDUCE: (14), (199) imply:
% 228.31/39.84  | | | | | | |   (200)  $false
% 228.31/39.84  | | | | | | | 
% 228.31/39.84  | | | | | | | CLOSE: (200) is inconsistent.
% 228.31/39.84  | | | | | | | 
% 228.31/39.84  | | | | | | Case 2:
% 228.31/39.84  | | | | | | | 
% 228.31/39.84  | | | | | | |   (201)  all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 228.31/39.84  | | | | | | | 
% 228.31/39.84  | | | | | | | BETA: splitting (201) gives:
% 228.31/39.84  | | | | | | | 
% 228.31/39.84  | | | | | | | Case 1:
% 228.31/39.84  | | | | | | | | 
% 228.31/39.84  | | | | | | | |   (202)  all_55_12 = e2
% 228.31/39.84  | | | | | | | | 
% 228.31/39.84  | | | | | | | | COMBINE_EQS: (67), (202) imply:
% 228.31/39.84  | | | | | | | |   (203)  all_53_3 = e2
% 228.31/39.84  | | | | | | | | 
% 228.31/39.84  | | | | | | | | REDUCE: (56), (203) imply:
% 228.31/39.84  | | | | | | | |   (204)  $false
% 228.31/39.84  | | | | | | | | 
% 228.31/39.84  | | | | | | | | CLOSE: (204) is inconsistent.
% 228.31/39.84  | | | | | | | | 
% 228.31/39.84  | | | | | | | Case 2:
% 228.31/39.84  | | | | | | | | 
% 228.31/39.84  | | | | | | | |   (205)   ~ (all_55_12 = e2)
% 228.31/39.84  | | | | | | | |   (206)  all_55_12 = e1 | all_55_12 = e0
% 228.31/39.84  | | | | | | | | 
% 228.31/39.84  | | | | | | | | BETA: splitting (206) gives:
% 228.31/39.84  | | | | | | | | 
% 228.31/39.84  | | | | | | | | Case 1:
% 228.31/39.84  | | | | | | | | | 
% 228.31/39.84  | | | | | | | | |   (207)  all_55_12 = e1
% 228.31/39.84  | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | COMBINE_EQS: (67), (207) imply:
% 228.31/39.84  | | | | | | | | |   (208)  all_53_3 = e1
% 228.31/39.84  | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | REDUCE: (190), (208) imply:
% 228.31/39.84  | | | | | | | | |   (209)  $false
% 228.31/39.84  | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | CLOSE: (209) is inconsistent.
% 228.31/39.84  | | | | | | | | | 
% 228.31/39.84  | | | | | | | | Case 2:
% 228.31/39.84  | | | | | | | | | 
% 228.31/39.84  | | | | | | | | |   (210)  all_55_12 = e0
% 228.31/39.84  | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | COMBINE_EQS: (67), (210) imply:
% 228.31/39.84  | | | | | | | | |   (211)  all_53_3 = e0
% 228.31/39.84  | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | REDUCE: (57), (211) imply:
% 228.31/39.84  | | | | | | | | |   (212)   ~ (all_52_17 = e0)
% 228.31/39.84  | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | SIMP: (212) implies:
% 228.31/39.84  | | | | | | | | |   (213)   ~ (all_52_17 = e0)
% 228.31/39.84  | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | REDUCE: (56), (211) imply:
% 228.31/39.84  | | | | | | | | |   (214)   ~ (e2 = e0)
% 228.31/39.84  | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | REDUCE: (190), (211) imply:
% 228.31/39.84  | | | | | | | | |   (215)   ~ (e1 = e0)
% 228.31/39.84  | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | BETA: splitting (49) gives:
% 228.31/39.84  | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | Case 1:
% 228.31/39.84  | | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | |   (216)  all_55_8 = e3
% 228.31/39.84  | | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | | COMBINE_EQS: (83), (216) imply:
% 228.31/39.84  | | | | | | | | | |   (217)  all_52_17 = e3
% 228.31/39.84  | | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | | SIMP: (217) implies:
% 228.31/39.84  | | | | | | | | | |   (218)  all_52_17 = e3
% 228.31/39.84  | | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | | REDUCE: (27), (218) imply:
% 228.31/39.84  | | | | | | | | | |   (219)  op(e3, e3) = e3
% 228.31/39.84  | | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (9), (10), (11),
% 228.31/39.84  | | | | | | | | | |            (12), (13), (15), (18), (19), (21), (23), (28),
% 228.31/39.84  | | | | | | | | | |            (31), (32), (33), (37), (38), (39), (40), (41),
% 228.31/39.84  | | | | | | | | | |            (43), (46), (47), (48), (51), (53), (54), (58),
% 228.31/39.84  | | | | | | | | | |            (61), (63), (64), (65), (68), (70), (71), (72),
% 228.31/39.84  | | | | | | | | | |            (73), (76), (77), (79), (80), (81), (85), (86),
% 228.31/39.84  | | | | | | | | | |            (87), (89), (90), (94), (95), (96), (97), (99),
% 228.31/39.84  | | | | | | | | | |            (100), (101), (102), (103), (105), (107), (108),
% 228.31/39.84  | | | | | | | | | |            (109), (194), (197), (219) are inconsistent by
% 228.31/39.84  | | | | | | | | | |            sub-proof #1437.
% 228.31/39.84  | | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | Case 2:
% 228.31/39.84  | | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | |   (220)  all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.31/39.84  | | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | | REF_CLOSE: (24), (30), (83), (213), (220) are inconsistent by
% 228.31/39.84  | | | | | | | | | |            sub-proof #1867.
% 228.31/39.84  | | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | End of split
% 228.31/39.84  | | | | | | | | | 
% 228.31/39.84  | | | | | | | | End of split
% 228.31/39.84  | | | | | | | | 
% 228.31/39.84  | | | | | | | End of split
% 228.31/39.84  | | | | | | | 
% 228.31/39.84  | | | | | | End of split
% 228.31/39.84  | | | | | | 
% 228.31/39.84  | | | | | Case 2:
% 228.31/39.84  | | | | | | 
% 228.31/39.84  | | | | | |   (221)  all_57_3 = e3 & op(e2, e2) = e3
% 228.31/39.84  | | | | | | 
% 228.31/39.84  | | | | | | ALPHA: (221) implies:
% 228.31/39.84  | | | | | |   (222)  all_57_3 = e3
% 228.31/39.84  | | | | | | 
% 228.31/39.84  | | | | | | REF_CLOSE: (39), (46), (222) are inconsistent by sub-proof #2358.
% 228.31/39.84  | | | | | | 
% 228.31/39.84  | | | | | End of split
% 228.31/39.84  | | | | | 
% 228.31/39.84  | | | | Case 2:
% 228.31/39.84  | | | | | 
% 228.31/39.84  | | | | |   (223)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2,
% 228.31/39.84  | | | | |              e0) = e3)
% 228.31/39.84  | | | | | 
% 228.31/39.84  | | | | | BETA: splitting (223) gives:
% 228.31/39.84  | | | | | 
% 228.31/39.84  | | | | | Case 1:
% 228.31/39.84  | | | | | | 
% 228.31/39.84  | | | | | |   (224)  all_57_5 = e3 & op(e2, e1) = e3
% 228.31/39.84  | | | | | | 
% 228.31/39.84  | | | | | | ALPHA: (224) implies:
% 228.31/39.84  | | | | | |   (225)  all_57_5 = e3
% 228.31/39.84  | | | | | |   (226)  op(e2, e1) = e3
% 228.31/39.84  | | | | | | 
% 228.31/39.84  | | | | | | BETA: splitting (98) gives:
% 228.31/39.84  | | | | | | 
% 228.31/39.84  | | | | | | Case 1:
% 228.31/39.84  | | | | | | | 
% 228.31/39.84  | | | | | | |   (227)  all_55_12 = e3
% 228.31/39.84  | | | | | | | 
% 228.31/39.84  | | | | | | | COMBINE_EQS: (67), (227) imply:
% 228.31/39.84  | | | | | | |   (228)  all_53_3 = e3
% 228.31/39.84  | | | | | | | 
% 228.31/39.84  | | | | | | | REDUCE: (14), (228) imply:
% 228.31/39.84  | | | | | | |   (229)  $false
% 228.31/39.84  | | | | | | | 
% 228.31/39.84  | | | | | | | CLOSE: (229) is inconsistent.
% 228.31/39.84  | | | | | | | 
% 228.31/39.84  | | | | | | Case 2:
% 228.31/39.84  | | | | | | | 
% 228.31/39.84  | | | | | | |   (230)  all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 228.31/39.84  | | | | | | | 
% 228.31/39.84  | | | | | | | BETA: splitting (230) gives:
% 228.31/39.84  | | | | | | | 
% 228.31/39.84  | | | | | | | Case 1:
% 228.31/39.84  | | | | | | | | 
% 228.31/39.84  | | | | | | | |   (231)  all_55_12 = e2
% 228.31/39.84  | | | | | | | | 
% 228.31/39.84  | | | | | | | | COMBINE_EQS: (67), (231) imply:
% 228.31/39.84  | | | | | | | |   (232)  all_53_3 = e2
% 228.31/39.84  | | | | | | | | 
% 228.31/39.84  | | | | | | | | REDUCE: (56), (232) imply:
% 228.31/39.84  | | | | | | | |   (233)  $false
% 228.31/39.84  | | | | | | | | 
% 228.31/39.84  | | | | | | | | CLOSE: (233) is inconsistent.
% 228.31/39.84  | | | | | | | | 
% 228.31/39.84  | | | | | | | Case 2:
% 228.31/39.84  | | | | | | | | 
% 228.31/39.84  | | | | | | | |   (234)   ~ (all_55_12 = e2)
% 228.31/39.84  | | | | | | | |   (235)  all_55_12 = e1 | all_55_12 = e0
% 228.31/39.84  | | | | | | | | 
% 228.31/39.84  | | | | | | | | BETA: splitting (235) gives:
% 228.31/39.84  | | | | | | | | 
% 228.31/39.84  | | | | | | | | Case 1:
% 228.31/39.84  | | | | | | | | | 
% 228.31/39.84  | | | | | | | | |   (236)  all_55_12 = e1
% 228.31/39.84  | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | COMBINE_EQS: (67), (236) imply:
% 228.31/39.84  | | | | | | | | |   (237)  all_53_3 = e1
% 228.31/39.84  | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | REDUCE: (190), (237) imply:
% 228.31/39.84  | | | | | | | | |   (238)  $false
% 228.31/39.84  | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | CLOSE: (238) is inconsistent.
% 228.31/39.84  | | | | | | | | | 
% 228.31/39.84  | | | | | | | | Case 2:
% 228.31/39.84  | | | | | | | | | 
% 228.31/39.84  | | | | | | | | |   (239)  all_55_12 = e0
% 228.31/39.84  | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | COMBINE_EQS: (67), (239) imply:
% 228.31/39.84  | | | | | | | | |   (240)  all_53_3 = e0
% 228.31/39.84  | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | REDUCE: (57), (240) imply:
% 228.31/39.84  | | | | | | | | |   (241)   ~ (all_52_17 = e0)
% 228.31/39.84  | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | SIMP: (241) implies:
% 228.31/39.84  | | | | | | | | |   (242)   ~ (all_52_17 = e0)
% 228.31/39.84  | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | REDUCE: (56), (240) imply:
% 228.31/39.84  | | | | | | | | |   (243)   ~ (e2 = e0)
% 228.31/39.84  | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | REDUCE: (190), (240) imply:
% 228.31/39.84  | | | | | | | | |   (244)   ~ (e1 = e0)
% 228.31/39.84  | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | BETA: splitting (49) gives:
% 228.31/39.84  | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | Case 1:
% 228.31/39.84  | | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | |   (245)  all_55_8 = e3
% 228.31/39.84  | | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | | COMBINE_EQS: (83), (245) imply:
% 228.31/39.84  | | | | | | | | | |   (246)  all_52_17 = e3
% 228.31/39.84  | | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | | SIMP: (246) implies:
% 228.31/39.84  | | | | | | | | | |   (247)  all_52_17 = e3
% 228.31/39.84  | | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | | REDUCE: (27), (247) imply:
% 228.31/39.84  | | | | | | | | | |   (248)  op(e3, e3) = e3
% 228.31/39.84  | | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (9), (10), (11),
% 228.31/39.84  | | | | | | | | | |            (12), (13), (15), (18), (19), (21), (23), (28),
% 228.31/39.84  | | | | | | | | | |            (31), (32), (33), (37), (38), (39), (40), (41),
% 228.31/39.84  | | | | | | | | | |            (43), (46), (47), (48), (51), (53), (54), (58),
% 228.31/39.84  | | | | | | | | | |            (61), (63), (64), (65), (68), (70), (71), (72),
% 228.31/39.84  | | | | | | | | | |            (76), (77), (79), (80), (81), (85), (86), (87),
% 228.31/39.84  | | | | | | | | | |            (89), (90), (94), (95), (96), (97), (99), (100),
% 228.31/39.84  | | | | | | | | | |            (101), (102), (103), (105), (107), (108), (109),
% 228.31/39.84  | | | | | | | | | |            (194), (225), (226), (248) are inconsistent by
% 228.31/39.84  | | | | | | | | | |            sub-proof #1438.
% 228.31/39.84  | | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | Case 2:
% 228.31/39.84  | | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | |   (249)  all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.31/39.84  | | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | | BETA: splitting (249) gives:
% 228.31/39.84  | | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | | Case 1:
% 228.31/39.84  | | | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | | |   (250)  all_55_8 = e2
% 228.31/39.84  | | | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | | | REF_CLOSE: (24), (83), (250) are inconsistent by sub-proof
% 228.31/39.84  | | | | | | | | | | |            #1869.
% 228.31/39.84  | | | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | | Case 2:
% 228.31/39.84  | | | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | | |   (251)  all_55_8 = e1 | all_55_8 = e0
% 228.31/39.84  | | | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | | | REF_CLOSE: (30), (83), (242), (251) are inconsistent by
% 228.31/39.84  | | | | | | | | | | |            sub-proof #1878.
% 228.31/39.84  | | | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | | End of split
% 228.31/39.84  | | | | | | | | | | 
% 228.31/39.84  | | | | | | | | | End of split
% 228.31/39.84  | | | | | | | | | 
% 228.31/39.84  | | | | | | | | End of split
% 228.31/39.84  | | | | | | | | 
% 228.31/39.84  | | | | | | | End of split
% 228.31/39.84  | | | | | | | 
% 228.31/39.84  | | | | | | End of split
% 228.31/39.84  | | | | | | 
% 228.31/39.84  | | | | | Case 2:
% 228.31/39.84  | | | | | | 
% 228.31/39.84  | | | | | |   (252)  all_57_10 = e3 & op(e2, e0) = e3
% 228.31/39.84  | | | | | | 
% 228.31/39.84  | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12),
% 228.31/39.84  | | | | | |            (13), (15), (18), (19), (21), (23), (28), (31), (32),
% 228.31/39.84  | | | | | |            (33), (36), (37), (38), (39), (40), (41), (43), (46),
% 228.31/39.84  | | | | | |            (47), (48), (51), (53), (54), (55), (58), (61), (63),
% 228.31/39.84  | | | | | |            (64), (65), (68), (70), (71), (72), (73), (74), (76),
% 228.31/39.84  | | | | | |            (77), (79), (80), (81), (84), (85), (86), (87), (89),
% 228.31/39.84  | | | | | |            (90), (91), (94), (95), (96), (97), (99), (100), (101),
% 228.31/39.84  | | | | | |            (102), (103), (105), (107), (108), (109), (194), (252)
% 228.31/39.84  | | | | | |            are inconsistent by sub-proof #497.
% 228.31/39.84  | | | | | | 
% 228.31/39.84  | | | | | End of split
% 228.31/39.84  | | | | | 
% 228.31/39.84  | | | | End of split
% 228.31/39.84  | | | | 
% 228.31/39.84  | | | Case 2:
% 228.31/39.84  | | | | 
% 228.31/39.84  | | | |   (253)  all_55_4 = e0
% 228.31/39.84  | | | | 
% 228.31/39.84  | | | | REF_CLOSE: (35), (69), (253) are inconsistent by sub-proof #1865.
% 228.31/39.84  | | | | 
% 228.31/39.84  | | | End of split
% 228.31/39.84  | | | 
% 228.31/39.84  | | End of split
% 228.31/39.84  | | 
% 228.31/39.84  | End of split
% 228.31/39.84  | 
% 228.31/39.84  End of proof
% 228.31/39.84  
% 228.31/39.84  Sub-proof #475 shows that the following formulas are inconsistent:
% 228.31/39.84  ----------------------------------------------------------------
% 228.31/39.84    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.31/39.84    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.31/39.84    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.31/39.84         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.31/39.84    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.31/39.84         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.31/39.84    (5)  op(e2, e1) = e3
% 228.31/39.84    (6)   ~ (all_53_8 = all_53_12)
% 228.31/39.84    (7)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.31/39.84         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.31/39.84    (8)   ~ (e3 = e1)
% 228.31/39.84    (9)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.31/39.84         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.31/39.84    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.31/39.84            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.31/39.84    (11)  op(e1, e2) = e3
% 228.31/39.84    (12)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.31/39.84            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.31/39.84              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.31/39.84    (13)  op(e1, e1) = all_6_2
% 228.31/39.84    (14)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.31/39.84    (15)   ~ (all_53_9 = e0)
% 228.31/39.84    (16)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.31/39.84          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.31/39.84    (17)   ~ (all_53_4 = all_53_12)
% 228.31/39.84    (18)   ~ (all_53_8 = all_53_9)
% 228.31/39.84    (19)  all_42_2 = all_6_2
% 228.31/39.84    (20)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.31/39.84          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.31/39.84    (21)  all_57_8 = e1
% 228.31/39.84    (22)   ~ (all_53_9 = all_6_2)
% 228.31/39.84    (23)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.31/39.84          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.31/39.84    (24)  all_57_3 = e0
% 228.31/39.84    (25)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.31/39.84          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.31/39.84    (26)   ~ (e3 = e2)
% 228.31/39.84    (27)  all_55_1 = all_53_4
% 228.31/39.84    (28)   ~ (e3 = e0)
% 228.31/39.84    (29)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.31/39.84          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.31/39.84    (30)   ~ (all_53_8 = all_6_2)
% 228.31/39.84    (31)  all_55_2 = all_53_8
% 228.31/39.84    (32)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.31/39.84    (33)  all_57_15 = e3
% 228.31/39.84    (34)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.31/39.84          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.31/39.84            e1)
% 228.31/39.84    (35)  all_57_5 = e3
% 228.31/39.84    (36)   ~ (all_53_4 = all_53_8)
% 228.31/39.84    (37)  op(e3, e2) = all_53_4
% 228.31/39.84    (38)   ~ (e2 = e0)
% 228.31/39.84    (39)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.31/39.84            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.31/39.84            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.31/39.84            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.31/39.84              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.31/39.84            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.31/39.84            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.31/39.84              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.31/39.84              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.31/39.84            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.31/39.84            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.31/39.84            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.31/39.84              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.31/39.84              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.31/39.84            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.31/39.84              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.31/39.84            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.31/39.84            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.31/39.84              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.31/39.84              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.31/39.84            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.31/39.84            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.31/39.84    (40)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.31/39.84          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.31/39.84    (41)   ~ (e1 = e0)
% 228.31/39.84    (42)  all_57_12 = e3
% 228.31/39.84    (43)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.31/39.84            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.31/39.84              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.31/39.84    (44)   ~ (all_53_4 = e0)
% 228.31/39.84    (45)  op(e0, e0) = e3
% 228.31/39.84    (46)   ~ (all_53_4 = all_53_6)
% 228.31/39.84    (47)  all_57_2 = e1
% 228.31/39.84    (48)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.31/39.84          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.31/39.84            e2)
% 228.31/39.84    (49)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.31/39.84              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.31/39.84                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.31/39.84                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.31/39.84    (50)  all_55_10 = all_6_2
% 228.31/39.84    (51)  all_38_2 = all_6_2
% 228.31/39.84    (52)  all_55_3 = all_53_12
% 228.31/39.84    (53)   ~ (all_53_12 = e3)
% 228.31/39.84    (54)  all_57_7 = e3
% 228.31/39.84    (55)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.31/39.84            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.31/39.84              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.31/39.84    (56)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.31/39.84          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.31/39.84    (57)   ~ (e2 = e1)
% 228.31/39.84    (58)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.31/39.84          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.31/39.84    (59)  op(e2, e1) = all_53_9
% 228.31/39.84    (60)  op(e1, e2) = all_53_6
% 228.31/39.84    (61)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.31/39.84          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.31/39.84    (62)  all_24_2 = all_6_2
% 228.31/39.84    (63)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.31/39.84          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.31/39.84    (64)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.31/39.84          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.31/39.84    (65)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.31/39.84          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.31/39.84    (66)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.31/39.84          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.31/39.84    (67)  op(e3, e1) = all_53_8
% 228.31/39.84    (68)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.31/39.84          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.31/39.84    (69)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.31/39.84          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.31/39.84    (70)  op(e3, e0) = all_53_12
% 228.31/39.84  
% 228.31/39.84  Begin of proof
% 228.31/39.84  | 
% 228.31/39.84  | BETA: splitting (40) gives:
% 228.31/39.84  | 
% 228.31/39.84  | Case 1:
% 228.31/39.84  | | 
% 228.31/39.84  | |   (71)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) =
% 228.31/39.84  | |           e3)
% 228.31/39.84  | | 
% 228.31/39.84  | | BETA: splitting (71) gives:
% 228.31/39.84  | | 
% 228.31/39.84  | | Case 1:
% 228.31/39.84  | | | 
% 228.31/39.84  | | |   (72)  all_57_0 = e3 & op(e3, e3) = e3
% 228.31/39.84  | | | 
% 228.31/39.84  | | | ALPHA: (72) implies:
% 228.31/39.85  | | |   (73)  op(e3, e3) = e3
% 228.31/39.85  | | | 
% 228.31/39.85  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.31/39.85  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (22), (23),
% 228.31/39.85  | | |            (24), (25), (26), (27), (29), (30), (31), (32), (33), (34),
% 228.31/39.85  | | |            (35), (36), (37), (38), (39), (41), (43), (44), (45), (46),
% 228.31/39.85  | | |            (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 228.31/39.85  | | |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67),
% 228.31/39.85  | | |            (68), (69), (70), (73) are inconsistent by sub-proof #1441.
% 228.31/39.85  | | | 
% 228.31/39.85  | | Case 2:
% 228.31/39.85  | | | 
% 228.31/39.85  | | |   (74)  all_57_1 = e3 & op(e3, e2) = e3
% 228.31/39.85  | | | 
% 228.31/39.85  | | | ALPHA: (74) implies:
% 228.31/39.85  | | |   (75)  all_57_1 = e3
% 228.31/39.85  | | | 
% 228.31/39.85  | | | REF_CLOSE: (7), (8), (24), (26), (38), (41), (54), (57), (68), (75) are
% 228.31/39.85  | | |            inconsistent by sub-proof #1778.
% 228.31/39.85  | | | 
% 228.31/39.85  | | End of split
% 228.31/39.85  | | 
% 228.31/39.85  | Case 2:
% 228.31/39.85  | | 
% 228.31/39.85  | |   (76)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) =
% 228.31/39.85  | |           e3)
% 228.31/39.85  | | 
% 228.31/39.85  | | BETA: splitting (76) gives:
% 228.31/39.85  | | 
% 228.31/39.85  | | Case 1:
% 228.31/39.85  | | | 
% 228.31/39.85  | | |   (77)  all_57_4 = e3 & op(e3, e1) = e3
% 228.31/39.85  | | | 
% 228.31/39.85  | | | ALPHA: (77) implies:
% 228.31/39.85  | | |   (78)  all_57_4 = e3
% 228.31/39.85  | | | 
% 228.31/39.85  | | | BETA: splitting (25) gives:
% 228.31/39.85  | | | 
% 228.31/39.85  | | | Case 1:
% 228.31/39.85  | | | | 
% 228.31/39.85  | | | |   (79)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1)
% 228.31/39.85  | | | |           = e0)
% 228.31/39.85  | | | | 
% 228.31/39.85  | | | | BETA: splitting (79) gives:
% 228.31/39.85  | | | | 
% 228.31/39.85  | | | | Case 1:
% 228.31/39.85  | | | | | 
% 228.31/39.85  | | | | |   (80)  all_57_4 = e0 & op(e3, e1) = e0
% 228.31/39.85  | | | | | 
% 228.31/39.85  | | | | | REF_CLOSE: (28), (78), (80) are inconsistent by sub-proof #2491.
% 228.31/39.85  | | | | | 
% 228.31/39.85  | | | | Case 2:
% 228.31/39.85  | | | | | 
% 228.31/39.85  | | | | |   (81)  all_57_5 = e0 & op(e2, e1) = e0
% 228.31/39.85  | | | | | 
% 228.31/39.85  | | | | | REF_CLOSE: (28), (35), (81) are inconsistent by sub-proof #2414.
% 228.31/39.85  | | | | | 
% 228.31/39.85  | | | | End of split
% 228.31/39.85  | | | | 
% 228.31/39.85  | | | Case 2:
% 228.31/39.85  | | | | 
% 228.31/39.85  | | | |   (82)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1)
% 228.31/39.85  | | | |           = e0)
% 228.31/39.85  | | | | 
% 228.31/39.85  | | | | BETA: splitting (82) gives:
% 228.31/39.85  | | | | 
% 228.31/39.85  | | | | Case 1:
% 228.31/39.85  | | | | | 
% 228.31/39.85  | | | | |   (83)  all_57_8 = e0 & op(e1, e1) = e0
% 228.31/39.85  | | | | | 
% 228.31/39.85  | | | | | REF_CLOSE: (3), (8), (21), (24), (26), (35), (38), (41), (47), (56),
% 228.31/39.85  | | | | |            (57), (83) are inconsistent by sub-proof #492.
% 228.31/39.85  | | | | | 
% 228.31/39.85  | | | | Case 2:
% 228.31/39.85  | | | | | 
% 228.31/39.85  | | | | |   (84)  all_57_14 = e0 & op(e0, e1) = e0
% 228.31/39.85  | | | | | 
% 228.31/39.85  | | | | | ALPHA: (84) implies:
% 228.31/39.85  | | | | |   (85)  all_57_14 = e0
% 228.31/39.85  | | | | | 
% 228.31/39.85  | | | | | REF_CLOSE: (8), (26), (33), (34), (38), (41), (42), (48), (57), (85)
% 228.31/39.85  | | | | |            are inconsistent by sub-proof #1763.
% 228.31/39.85  | | | | | 
% 228.31/39.85  | | | | End of split
% 228.31/39.85  | | | | 
% 228.31/39.85  | | | End of split
% 228.31/39.85  | | | 
% 228.31/39.85  | | Case 2:
% 228.31/39.85  | | | 
% 228.31/39.85  | | |   (86)  all_57_9 = e3 & op(e3, e0) = e3
% 228.31/39.85  | | | 
% 228.31/39.85  | | | ALPHA: (86) implies:
% 228.31/39.85  | | |   (87)  op(e3, e0) = e3
% 228.31/39.85  | | | 
% 228.31/39.85  | | | REF_CLOSE: (10), (53), (70), (87) are inconsistent by sub-proof #2458.
% 228.31/39.85  | | | 
% 228.31/39.85  | | End of split
% 228.31/39.85  | | 
% 228.31/39.85  | End of split
% 228.31/39.85  | 
% 228.31/39.85  End of proof
% 228.31/39.85  
% 228.31/39.85  Sub-proof #476 shows that the following formulas are inconsistent:
% 228.31/39.85  ----------------------------------------------------------------
% 228.31/39.85    (1)  all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.31/39.85    (2)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.31/39.85    (3)  all_57_0 = e2
% 228.31/39.85    (4)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.31/39.85    (5)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.31/39.85         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.31/39.85    (6)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.31/39.85         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.31/39.85    (7)  op(e2, e1) = e3
% 228.31/39.85    (8)   ~ (all_53_8 = all_53_12)
% 228.31/39.85    (9)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.31/39.85         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.31/39.85    (10)   ~ (all_53_8 = all_53_11)
% 228.31/39.85    (11)   ~ (e3 = e1)
% 228.31/39.85    (12)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.31/39.85          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.31/39.85    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.31/39.85            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.31/39.85    (14)  all_55_14 = e1 | all_55_14 = e0
% 228.31/39.85    (15)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.31/39.85          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.31/39.85    (16)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.31/39.85            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.31/39.85              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.31/39.85    (17)   ~ (all_6_2 = e3)
% 228.31/39.85    (18)  ( ~ (all_28_0 = e0) & op(all_28_1, e3) = all_28_0 & op(e3, e2) =
% 228.31/39.85            all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 = e1) & op(e3,
% 228.31/39.85              e2) = all_28_1 & $i(all_28_1))
% 228.31/39.85    (19)  op(e1, e1) = all_6_2
% 228.31/39.85    (20)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.31/39.85    (21)  op(e2, e1) = e2
% 228.31/39.85    (22)   ~ (all_53_9 = e0)
% 228.31/39.85    (23)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 228.31/39.85    (24)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.31/39.85          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.31/39.85    (25)   ~ (all_52_17 = e2)
% 228.31/39.85    (26)   ~ (all_53_8 = e1)
% 228.31/39.85    (27)   ~ (all_53_4 = all_53_12)
% 228.31/39.85    (28)   ~ (all_52_17 = all_52_23)
% 228.31/39.85    (29)   ~ (all_52_17 = e1)
% 228.31/39.85    (30)   ~ (all_53_8 = all_53_9)
% 228.31/39.85    (31)  all_42_2 = all_6_2
% 228.31/39.85    (32)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.31/39.85          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.31/39.85    (33)  all_57_8 = e1
% 228.31/39.85    (34)   ~ (all_53_9 = all_6_2)
% 228.31/39.85    (35)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.31/39.85          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.31/39.85    (36)  all_57_3 = e0
% 228.31/39.85    (37)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.31/39.85          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.31/39.85    (38)   ~ (e3 = e2)
% 228.31/39.85    (39)  all_55_1 = all_53_4
% 228.31/39.85    (40)   ~ (e3 = e0)
% 228.31/39.85    (41)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.31/39.85          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.31/39.85    (42)   ~ (all_53_8 = all_6_2)
% 228.31/39.85    (43)  all_55_11 = all_52_23
% 228.31/39.85    (44)  all_55_2 = all_53_8
% 228.31/39.85    (45)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.31/39.85    (46)  all_57_15 = e3
% 228.31/39.85    (47)  op(e3, e3) = e2
% 228.31/39.85    (48)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.31/39.85          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.31/39.85            e1)
% 228.31/39.85    (49)  all_57_10 = e2
% 228.31/39.85    (50)  all_57_5 = e3
% 228.31/39.85    (51)   ~ (all_52_23 = e3)
% 228.31/39.85    (52)  op(e1, e0) = all_52_23
% 228.31/39.85    (53)   ~ (all_53_4 = all_53_8)
% 228.31/39.85    (54)  op(e3, e2) = all_53_4
% 228.31/39.85    (55)   ~ (e2 = e0)
% 228.31/39.85    (56)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.31/39.85            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.31/39.85            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.31/39.85            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.31/39.85              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.31/39.85            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.31/39.85            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.31/39.85              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.31/39.85              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.31/39.85            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.31/39.85            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.31/39.85            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.31/39.85              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.31/39.85              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.31/39.85            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.31/39.85              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.31/39.85            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.31/39.85            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.31/39.85              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.31/39.85              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.31/39.85            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.31/39.85            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.31/39.85    (57)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.31/39.85          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.31/39.85    (58)   ~ (e1 = e0)
% 228.31/39.85    (59)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.31/39.85            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.31/39.85              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.31/39.85    (60)   ~ (all_53_4 = e0)
% 228.31/39.85    (61)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.31/39.85          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.31/39.85    (62)  all_57_6 = e3
% 228.31/39.85    (63)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.31/39.85          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.31/39.85    (64)  op(e0, e0) = e3
% 228.31/39.85    (65)   ~ (all_53_4 = all_53_6)
% 228.31/39.85    (66)  ( ~ (all_20_0 = e1) & op(all_20_1, e3) = all_20_0 & op(e3, e2) =
% 228.31/39.85            all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e0) & op(e3,
% 228.31/39.85              e2) = all_20_1 & $i(all_20_1))
% 228.31/39.85    (67)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.31/39.85          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.31/39.85            e2)
% 228.31/39.85    (68)   ~ (all_53_8 = e2)
% 228.31/39.85    (69)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.31/39.85              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.31/39.85                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.31/39.85                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.31/39.85    (70)  all_55_10 = all_6_2
% 228.31/39.85    (71)   ~ (all_53_11 = e1)
% 228.31/39.85    (72)  all_55_8 = all_52_17
% 228.31/39.85    (73)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.31/39.85          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.31/39.85    (74)  all_38_2 = all_6_2
% 228.31/39.85    (75)  all_55_3 = all_53_12
% 228.31/39.85    (76)   ~ (all_53_12 = e3)
% 228.31/39.85    (77)   ~ (all_53_4 = e2)
% 228.31/39.85    (78)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.31/39.85            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.31/39.85              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.31/39.85    (79)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.31/39.85          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.31/39.85    (80)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.31/39.85          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.31/39.85    (81)   ~ (all_52_23 = e1)
% 228.31/39.85    (82)   ~ (e2 = e1)
% 228.31/39.85    (83)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.31/39.85          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.31/39.85    (84)  op(e2, e1) = all_53_9
% 228.31/39.85    (85)  op(e1, e2) = all_53_6
% 228.31/39.85    (86)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.31/39.85          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.31/39.85    (87)  all_24_2 = all_6_2
% 228.31/39.85    (88)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.31/39.85          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.31/39.85    (89)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.31/39.85          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.31/39.85    (90)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.31/39.85          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.31/39.85    (91)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.31/39.85          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.31/39.85    (92)  all_55_14 = all_53_11
% 228.31/39.85    (93)  op(e3, e1) = all_53_8
% 228.31/39.85    (94)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.31/39.85          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.31/39.85    (95)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.31/39.85          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.31/39.85    (96)  op(e3, e0) = all_53_12
% 228.31/39.85  
% 228.31/39.85  Begin of proof
% 228.31/39.85  | 
% 228.31/39.85  | BETA: splitting (89) gives:
% 228.31/39.85  | 
% 228.31/39.85  | Case 1:
% 228.31/39.85  | | 
% 228.31/39.85  | |   (97)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) =
% 228.31/39.85  | |           e0)
% 228.31/39.85  | | 
% 228.31/39.85  | | REF_CLOSE: (5), (11), (13), (36), (38), (47), (50), (55), (58), (79), (82),
% 228.31/39.85  | |            (97) are inconsistent by sub-proof #1644.
% 228.31/39.85  | | 
% 228.31/39.85  | Case 2:
% 228.31/39.85  | | 
% 228.31/39.85  | |   (98)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) =
% 228.31/39.85  | |           e0)
% 228.31/39.85  | | 
% 228.31/39.85  | | BETA: splitting (98) gives:
% 228.31/39.85  | | 
% 228.31/39.85  | | Case 1:
% 228.31/39.85  | | | 
% 228.31/39.85  | | |   (99)  all_57_6 = e0 & op(e1, e3) = e0
% 228.31/39.85  | | | 
% 228.31/39.85  | | | REF_CLOSE: (40), (62), (99) are inconsistent by sub-proof #2465.
% 228.31/39.85  | | | 
% 228.31/39.85  | | Case 2:
% 228.31/39.85  | | | 
% 228.31/39.85  | | |   (100)  all_57_12 = e0 & op(e0, e3) = e0
% 228.31/39.85  | | | 
% 228.31/39.85  | | | ALPHA: (100) implies:
% 228.31/39.85  | | |   (101)  all_57_12 = e0
% 228.31/39.85  | | | 
% 228.31/39.85  | | | BETA: splitting (6) gives:
% 228.31/39.85  | | | 
% 228.31/39.85  | | | Case 1:
% 228.31/39.85  | | | | 
% 228.31/39.85  | | | |   (102)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3)
% 228.31/39.85  | | | |            = e1)
% 228.31/39.85  | | | | 
% 228.31/39.85  | | | | BETA: splitting (102) gives:
% 228.31/39.85  | | | | 
% 228.31/39.85  | | | | Case 1:
% 228.31/39.85  | | | | | 
% 228.31/39.85  | | | | |   (103)  all_57_0 = e1 & op(e3, e3) = e1
% 228.31/39.85  | | | | | 
% 228.31/39.85  | | | | | ALPHA: (103) implies:
% 228.31/39.85  | | | | |   (104)  op(e3, e3) = e1
% 228.31/39.85  | | | | | 
% 228.31/39.85  | | | | | REF_CLOSE: (13), (47), (82), (104) are inconsistent by sub-proof
% 228.31/39.85  | | | | |            #1950.
% 228.31/39.85  | | | | | 
% 228.31/39.85  | | | | Case 2:
% 228.31/39.85  | | | | | 
% 228.31/39.85  | | | | |   (105)  all_57_2 = e1 & op(e2, e3) = e1
% 228.31/39.85  | | | | | 
% 228.31/39.85  | | | | | ALPHA: (105) implies:
% 228.31/39.85  | | | | |   (106)  all_57_2 = e1
% 228.31/39.85  | | | | | 
% 228.31/39.85  | | | | | BETA: splitting (67) gives:
% 228.31/39.85  | | | | | 
% 228.31/39.85  | | | | | Case 1:
% 228.31/39.85  | | | | | | 
% 228.31/39.85  | | | | | |   (107)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 &
% 228.31/39.85  | | | | | |            op(e0, e2) = e2)
% 228.31/39.85  | | | | | | 
% 228.31/39.85  | | | | | | BETA: splitting (107) gives:
% 228.31/39.85  | | | | | | 
% 228.31/39.85  | | | | | | Case 1:
% 228.31/39.85  | | | | | | | 
% 228.31/39.85  | | | | | | |   (108)  all_57_12 = e2 & op(e0, e3) = e2
% 228.31/39.85  | | | | | | | 
% 228.31/39.85  | | | | | | | REF_CLOSE: (3), (6), (11), (38), (55), (58), (62), (82), (86),
% 228.31/39.85  | | | | | | |            (101), (108) are inconsistent by sub-proof #494.
% 228.31/39.85  | | | | | | | 
% 228.31/39.85  | | | | | | Case 2:
% 228.31/39.85  | | | | | | | 
% 228.31/39.85  | | | | | | |   (109)  all_57_13 = e2 & op(e0, e2) = e2
% 228.31/39.85  | | | | | | | 
% 228.31/39.85  | | | | | | | ALPHA: (109) implies:
% 228.31/39.85  | | | | | | |   (110)  all_57_13 = e2
% 228.31/39.85  | | | | | | | 
% 228.31/39.85  | | | | | | | REF_CLOSE: (3), (5), (6), (9), (11), (12), (13), (15), (17), (19),
% 228.31/39.85  | | | | | | |            (24), (32), (33), (35), (36), (38), (40), (46), (47),
% 228.31/39.85  | | | | | | |            (48), (50), (55), (57), (58), (62), (69), (73), (76),
% 228.31/39.85  | | | | | | |            (79), (80), (82), (83), (86), (88), (89), (90), (94),
% 228.31/39.85  | | | | | | |            (95), (96), (101), (106), (110) are inconsistent by
% 228.31/39.85  | | | | | | |            sub-proof #489.
% 228.31/39.85  | | | | | | | 
% 228.31/39.85  | | | | | | End of split
% 228.31/39.85  | | | | | | 
% 228.31/39.85  | | | | | Case 2:
% 228.31/39.85  | | | | | | 
% 228.31/39.85  | | | | | |   (111)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 &
% 228.31/39.85  | | | | | |            op(e0, e0) = e2)
% 228.31/39.85  | | | | | | 
% 228.31/39.85  | | | | | | BETA: splitting (111) gives:
% 228.31/39.85  | | | | | | 
% 228.31/39.85  | | | | | | Case 1:
% 228.31/39.85  | | | | | | | 
% 228.31/39.85  | | | | | | |   (112)  all_57_14 = e2 & op(e0, e1) = e2
% 228.31/39.85  | | | | | | | 
% 228.31/39.85  | | | | | | | ALPHA: (112) implies:
% 228.31/39.85  | | | | | | |   (113)  all_57_14 = e2
% 228.31/39.85  | | | | | | | 
% 228.31/39.85  | | | | | | | BETA: splitting (24) gives:
% 228.31/39.85  | | | | | | | 
% 228.31/39.85  | | | | | | | Case 1:
% 228.31/39.85  | | | | | | | | 
% 228.31/39.85  | | | | | | | |   (114)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 &
% 228.31/39.85  | | | | | | | |            op(e3, e2) = e1)
% 228.31/39.85  | | | | | | | | 
% 228.31/39.85  | | | | | | | | BETA: splitting (114) gives:
% 228.31/39.85  | | | | | | | | 
% 228.31/39.85  | | | | | | | | Case 1:
% 228.31/39.85  | | | | | | | | | 
% 228.31/39.85  | | | | | | | | |   (115)  all_57_0 = e1 & op(e3, e3) = e1
% 228.31/39.85  | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | ALPHA: (115) implies:
% 228.31/39.85  | | | | | | | | |   (116)  op(e3, e3) = e1
% 228.31/39.85  | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | REF_CLOSE: (13), (47), (82), (116) are inconsistent by
% 228.31/39.85  | | | | | | | | |            sub-proof #1950.
% 228.31/39.85  | | | | | | | | | 
% 228.31/39.85  | | | | | | | | Case 2:
% 228.31/39.85  | | | | | | | | | 
% 228.31/39.85  | | | | | | | | |   (117)  all_57_1 = e1 & op(e3, e2) = e1
% 228.31/39.85  | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | ALPHA: (117) implies:
% 228.31/39.85  | | | | | | | | |   (118)  all_57_1 = e1
% 228.31/39.85  | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | REF_CLOSE: (2), (4), (5), (6), (8), (9), (11), (12), (13),
% 228.31/39.85  | | | | | | | | |            (15), (16), (17), (19), (20), (22), (24), (27),
% 228.31/39.85  | | | | | | | | |            (30), (31), (32), (33), (34), (35), (36), (37),
% 228.31/39.85  | | | | | | | | |            (38), (39), (40), (41), (42), (44), (45), (46),
% 228.31/39.85  | | | | | | | | |            (47), (48), (49), (50), (53), (54), (55), (56),
% 228.31/39.85  | | | | | | | | |            (57), (58), (59), (60), (61), (62), (63), (64),
% 228.31/39.85  | | | | | | | | |            (65), (67), (69), (70), (73), (74), (75), (76),
% 228.31/39.85  | | | | | | | | |            (78), (79), (80), (82), (83), (84), (85), (86),
% 228.31/39.85  | | | | | | | | |            (87), (88), (89), (90), (91), (93), (94), (95),
% 228.31/39.85  | | | | | | | | |            (96), (101), (106), (113), (118) are inconsistent
% 228.31/39.85  | | | | | | | | |            by sub-proof #485.
% 228.31/39.85  | | | | | | | | | 
% 228.31/39.85  | | | | | | | | End of split
% 228.31/39.85  | | | | | | | | 
% 228.31/39.85  | | | | | | | Case 2:
% 228.31/39.85  | | | | | | | | 
% 228.31/39.85  | | | | | | | |   (119)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 &
% 228.31/39.85  | | | | | | | |            op(e3, e0) = e1)
% 228.31/39.85  | | | | | | | | 
% 228.31/39.85  | | | | | | | | BETA: splitting (119) gives:
% 228.31/39.85  | | | | | | | | 
% 228.31/39.85  | | | | | | | | Case 1:
% 228.31/39.85  | | | | | | | | | 
% 228.31/39.85  | | | | | | | | |   (120)  all_57_4 = e1 & op(e3, e1) = e1
% 228.31/39.85  | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | ALPHA: (120) implies:
% 228.31/39.85  | | | | | | | | |   (121)  all_57_4 = e1
% 228.31/39.85  | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | BETA: splitting (35) gives:
% 228.31/39.85  | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | Case 1:
% 228.31/39.85  | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | |   (122)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 228.31/39.85  | | | | | | | | | |            & op(e3, e2) = e0)
% 228.31/39.85  | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | REF_CLOSE: (6), (9), (11), (36), (38), (40), (46), (48),
% 228.31/39.85  | | | | | | | | | |            (55), (58), (62), (63), (82), (86), (94), (101),
% 228.31/39.85  | | | | | | | | | |            (113), (122) are inconsistent by sub-proof #483.
% 228.31/39.85  | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | Case 2:
% 228.31/39.85  | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | |   (123)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 228.31/39.85  | | | | | | | | | |            & op(e3, e0) = e0)
% 228.31/39.85  | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | BETA: splitting (123) gives:
% 228.31/39.85  | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | Case 1:
% 228.31/39.85  | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | |   (124)  all_57_4 = e0 & op(e3, e1) = e0
% 228.31/39.85  | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | REF_CLOSE: (5), (11), (36), (38), (50), (55), (58), (79),
% 228.31/39.85  | | | | | | | | | | |            (82), (106), (121), (124) are inconsistent by
% 228.31/39.85  | | | | | | | | | | |            sub-proof #1355.
% 228.31/39.85  | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | Case 2:
% 228.31/39.85  | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | |   (125)  all_57_9 = e0 & op(e3, e0) = e0
% 228.31/39.85  | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | ALPHA: (125) implies:
% 228.31/39.85  | | | | | | | | | | |   (126)  all_57_9 = e0
% 228.31/39.85  | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | BETA: splitting (57) gives:
% 228.31/39.85  | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | Case 1:
% 228.31/39.85  | | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | |   (127)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 228.31/39.85  | | | | | | | | | | | |            & op(e3, e2) = e3)
% 228.31/39.85  | | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | | BETA: splitting (127) gives:
% 228.31/39.85  | | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | | Case 1:
% 228.31/39.85  | | | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | | |   (128)  all_57_0 = e3 & op(e3, e3) = e3
% 228.31/39.85  | | | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | | | ALPHA: (128) implies:
% 228.31/39.85  | | | | | | | | | | | | |   (129)  all_57_0 = e3
% 228.31/39.85  | | | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | | | REF_CLOSE: (6), (11), (38), (55), (58), (62), (82), (86),
% 228.31/39.85  | | | | | | | | | | | | |            (101), (129) are inconsistent by sub-proof #2011.
% 228.31/39.85  | | | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | | Case 2:
% 228.31/39.85  | | | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | | |   (130)  all_57_1 = e3 & op(e3, e2) = e3
% 228.31/39.85  | | | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | | | ALPHA: (130) implies:
% 228.31/39.85  | | | | | | | | | | | | |   (131)  all_57_1 = e3
% 228.31/39.85  | | | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | | | BETA: splitting (12) gives:
% 228.31/39.85  | | | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | | | Case 1:
% 228.31/39.85  | | | | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | | | |   (132)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 228.31/39.85  | | | | | | | | | | | | | |            & op(e1, e2) = e0)
% 228.31/39.85  | | | | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | | | | BETA: splitting (132) gives:
% 228.31/39.85  | | | | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | | | | Case 1:
% 228.31/39.85  | | | | | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | | | | |   (133)  all_57_6 = e0 & op(e1, e3) = e0
% 228.31/39.85  | | | | | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | | | | | REF_CLOSE: (9), (11), (36), (38), (40), (46), (48), (55),
% 228.31/39.85  | | | | | | | | | | | | | | |            (58), (62), (63), (82), (94), (101), (113), (131),
% 228.31/39.85  | | | | | | | | | | | | | | |            (133) are inconsistent by sub-proof #482.
% 228.31/39.85  | | | | | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | | | | Case 2:
% 228.31/39.85  | | | | | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | | | | |   (134)  all_57_7 = e0 & op(e1, e2) = e0
% 228.31/39.85  | | | | | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | | | | | ALPHA: (134) implies:
% 228.31/39.85  | | | | | | | | | | | | | | |   (135)  all_57_7 = e0
% 228.31/39.85  | | | | | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | | | | | REF_CLOSE: (3), (5), (6), (9), (11), (12), (13), (15), (17),
% 228.31/39.85  | | | | | | | | | | | | | | |            (19), (24), (32), (33), (35), (36), (38), (40),
% 228.31/39.85  | | | | | | | | | | | | | | |            (46), (47), (50), (55), (57), (58), (62), (69),
% 228.31/39.85  | | | | | | | | | | | | | | |            (73), (76), (79), (80), (82), (83), (86), (89),
% 228.31/39.85  | | | | | | | | | | | | | | |            (90), (94), (95), (96), (101), (106), (131), (135)
% 228.31/39.85  | | | | | | | | | | | | | | |            are inconsistent by sub-proof #481.
% 228.31/39.85  | | | | | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | | | | End of split
% 228.31/39.85  | | | | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | | | Case 2:
% 228.31/39.85  | | | | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | | | |   (136)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 228.31/39.85  | | | | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 228.31/39.85  | | | | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | | | | BETA: splitting (136) gives:
% 228.31/39.85  | | | | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | | | | Case 1:
% 228.31/39.85  | | | | | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | | | | |   (137)  all_57_8 = e0 & op(e1, e1) = e0
% 228.31/39.85  | | | | | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | | | | | REF_CLOSE: (5), (11), (33), (36), (38), (50), (55), (58),
% 228.31/39.85  | | | | | | | | | | | | | | |            (79), (82), (106), (137) are inconsistent by
% 228.31/39.85  | | | | | | | | | | | | | | |            sub-proof #492.
% 228.31/39.85  | | | | | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | | | | Case 2:
% 228.31/39.85  | | | | | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | | | | |   (138)  all_57_11 = e0 & op(e1, e0) = e0
% 228.31/39.85  | | | | | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | | | | | ALPHA: (138) implies:
% 228.31/39.85  | | | | | | | | | | | | | | |   (139)  all_57_11 = e0
% 228.31/39.85  | | | | | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | | | | | BETA: splitting (90) gives:
% 228.31/39.85  | | | | | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | | | | | Case 1:
% 228.31/39.85  | | | | | | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | | | | | |   (140)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 228.31/39.85  | | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 228.31/39.85  | | | | | | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | | | | | | REF_CLOSE: (5), (11), (36), (38), (49), (50), (55), (58),
% 228.31/39.85  | | | | | | | | | | | | | | | |            (79), (82), (106), (126), (140) are inconsistent
% 228.31/39.85  | | | | | | | | | | | | | | | |            by sub-proof #487.
% 228.31/39.85  | | | | | | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | | | | | Case 2:
% 228.31/39.85  | | | | | | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | | | | | |   (141)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 228.31/39.85  | | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 228.31/39.85  | | | | | | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | | | | | | BETA: splitting (141) gives:
% 228.31/39.85  | | | | | | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | | | | | | Case 1:
% 228.31/39.85  | | | | | | | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | | | | | | |   (142)  all_57_11 = e1 & op(e1, e0) = e1
% 228.31/39.85  | | | | | | | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (11), (36), (38), (50), (55), (58), (79),
% 228.31/39.85  | | | | | | | | | | | | | | | | |            (82), (106), (139), (142) are inconsistent by
% 228.31/39.85  | | | | | | | | | | | | | | | | |            sub-proof #1515.
% 228.31/39.85  | | | | | | | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | | | | | | Case 2:
% 228.31/39.85  | | | | | | | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | | | | | | |   (143)  all_57_15 = e1 & op(e0, e0) = e1
% 228.31/39.85  | | | | | | | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | | | | | | | ALPHA: (143) implies:
% 228.31/39.85  | | | | | | | | | | | | | | | | |   (144)  all_57_15 = e1
% 228.31/39.85  | | | | | | | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | | | | | | | COMBINE_EQS: (46), (144) imply:
% 228.31/39.85  | | | | | | | | | | | | | | | | |   (145)  e3 = e1
% 228.31/39.85  | | | | | | | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | | | | | | | COMBINE_EQS: (131), (145) imply:
% 228.31/39.85  | | | | | | | | | | | | | | | | |   (146)  all_57_1 = e1
% 228.31/39.85  | | | | | | | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (5), (6), (8), (9), (11), (12), (13),
% 228.31/39.85  | | | | | | | | | | | | | | | | |            (15), (16), (17), (19), (20), (22), (24), (27),
% 228.31/39.85  | | | | | | | | | | | | | | | | |            (30), (31), (32), (33), (34), (35), (36), (37),
% 228.31/39.85  | | | | | | | | | | | | | | | | |            (38), (39), (40), (41), (42), (44), (45), (46),
% 228.31/39.85  | | | | | | | | | | | | | | | | |            (47), (48), (49), (50), (53), (54), (55), (56),
% 228.31/39.85  | | | | | | | | | | | | | | | | |            (57), (58), (59), (60), (61), (62), (63), (64),
% 228.31/39.85  | | | | | | | | | | | | | | | | |            (65), (67), (69), (70), (73), (74), (75), (76),
% 228.31/39.85  | | | | | | | | | | | | | | | | |            (78), (79), (80), (82), (83), (84), (85), (86),
% 228.31/39.85  | | | | | | | | | | | | | | | | |            (87), (88), (89), (90), (91), (93), (94), (95),
% 228.31/39.85  | | | | | | | | | | | | | | | | |            (96), (101), (106), (113), (146) are inconsistent
% 228.31/39.85  | | | | | | | | | | | | | | | | |            by sub-proof #485.
% 228.31/39.85  | | | | | | | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | | | | | | End of split
% 228.31/39.85  | | | | | | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | | | | | End of split
% 228.31/39.85  | | | | | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | | | | End of split
% 228.31/39.85  | | | | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | | | End of split
% 228.31/39.85  | | | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | | End of split
% 228.31/39.85  | | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | Case 2:
% 228.31/39.85  | | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | |   (147)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 228.31/39.85  | | | | | | | | | | | |            & op(e3, e0) = e3)
% 228.31/39.85  | | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | | BETA: splitting (147) gives:
% 228.31/39.85  | | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | | Case 1:
% 228.31/39.85  | | | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | | |   (148)  all_57_4 = e3 & op(e3, e1) = e3
% 228.31/39.85  | | | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | | | ALPHA: (148) implies:
% 228.31/39.85  | | | | | | | | | | | | |   (149)  all_57_4 = e3
% 228.31/39.85  | | | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | | | BETA: splitting (24) gives:
% 228.31/39.85  | | | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | | | Case 1:
% 228.31/39.85  | | | | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | | | |   (150)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 228.31/39.85  | | | | | | | | | | | | | |            & op(e3, e2) = e1)
% 228.31/39.85  | | | | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | | | | BETA: splitting (150) gives:
% 228.31/39.85  | | | | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | | | | Case 1:
% 228.31/39.85  | | | | | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | | | | |   (151)  all_57_0 = e1 & op(e3, e3) = e1
% 228.31/39.85  | | | | | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | | | | | ALPHA: (151) implies:
% 228.31/39.85  | | | | | | | | | | | | | | |   (152)  op(e3, e3) = e1
% 228.31/39.85  | | | | | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | | | | | REF_CLOSE: (13), (47), (82), (152) are inconsistent by
% 228.31/39.85  | | | | | | | | | | | | | | |            sub-proof #1950.
% 228.31/39.85  | | | | | | | | | | | | | | | 
% 228.31/39.85  | | | | | | | | | | | | | | Case 2:
% 228.31/39.85  | | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | |   (153)  all_57_1 = e1 & op(e3, e2) = e1
% 228.31/39.86  | | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | | ALPHA: (153) implies:
% 228.31/39.86  | | | | | | | | | | | | | | |   (154)  all_57_1 = e1
% 228.31/39.86  | | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (5), (6), (8), (9), (11), (12), (13),
% 228.31/39.86  | | | | | | | | | | | | | | |            (15), (16), (17), (19), (20), (22), (24), (27),
% 228.31/39.86  | | | | | | | | | | | | | | |            (30), (31), (32), (33), (34), (35), (36), (37),
% 228.31/39.86  | | | | | | | | | | | | | | |            (38), (39), (40), (41), (42), (44), (45), (46),
% 228.31/39.86  | | | | | | | | | | | | | | |            (47), (48), (49), (50), (53), (54), (55), (56),
% 228.31/39.86  | | | | | | | | | | | | | | |            (57), (58), (59), (60), (61), (62), (63), (64),
% 228.31/39.86  | | | | | | | | | | | | | | |            (65), (67), (69), (70), (73), (74), (75), (76),
% 228.31/39.86  | | | | | | | | | | | | | | |            (78), (79), (80), (82), (83), (84), (85), (86),
% 228.31/39.86  | | | | | | | | | | | | | | |            (87), (88), (89), (90), (91), (93), (94), (95),
% 228.31/39.86  | | | | | | | | | | | | | | |            (96), (101), (106), (113), (149), (154) are
% 228.31/39.86  | | | | | | | | | | | | | | |            inconsistent by sub-proof #486.
% 228.31/39.86  | | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | End of split
% 228.31/39.86  | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | Case 2:
% 228.31/39.86  | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | BETA: splitting (119) gives:
% 228.31/39.86  | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | Case 1:
% 228.31/39.86  | | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | | REF_CLOSE: (11), (120), (149) are inconsistent by sub-proof
% 228.31/39.86  | | | | | | | | | | | | | | |            #2484.
% 228.31/39.86  | | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | Case 2:
% 228.31/39.86  | | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | |   (155)  all_57_9 = e1 & op(e3, e0) = e1
% 228.31/39.86  | | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | | ALPHA: (155) implies:
% 228.31/39.86  | | | | | | | | | | | | | | |   (156)  all_57_9 = e1
% 228.31/39.86  | | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (11), (35), (36), (38), (40), (46),
% 228.31/39.86  | | | | | | | | | | | | | | |            (48), (50), (55), (58), (62), (63), (79), (82),
% 228.31/39.86  | | | | | | | | | | | | | | |            (86), (94), (101), (106), (113), (149), (156) are
% 228.31/39.86  | | | | | | | | | | | | | | |            inconsistent by sub-proof #480.
% 228.31/39.86  | | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | End of split
% 228.31/39.86  | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | End of split
% 228.31/39.86  | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | Case 2:
% 228.31/39.86  | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | |   (157)  all_57_9 = e3 & op(e3, e0) = e3
% 228.31/39.86  | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | ALPHA: (157) implies:
% 228.31/39.86  | | | | | | | | | | | | |   (158)  op(e3, e0) = e3
% 228.31/39.86  | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | REF_CLOSE: (13), (76), (96), (158) are inconsistent by
% 228.31/39.86  | | | | | | | | | | | | |            sub-proof #2458.
% 228.31/39.86  | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | End of split
% 228.31/39.86  | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | End of split
% 228.31/39.86  | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | End of split
% 228.31/39.86  | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | End of split
% 228.31/39.86  | | | | | | | | | 
% 228.31/39.86  | | | | | | | | Case 2:
% 228.31/39.86  | | | | | | | | | 
% 228.31/39.86  | | | | | | | | |   (159)  all_57_9 = e1 & op(e3, e0) = e1
% 228.31/39.86  | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | ALPHA: (159) implies:
% 228.31/39.86  | | | | | | | | |   (160)  all_57_9 = e1
% 228.31/39.86  | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | BETA: splitting (57) gives:
% 228.31/39.86  | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | Case 1:
% 228.31/39.86  | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | |   (161)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 228.31/39.86  | | | | | | | | | |            & op(e3, e2) = e3)
% 228.31/39.86  | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | BETA: splitting (161) gives:
% 228.31/39.86  | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | Case 1:
% 228.31/39.86  | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | |   (162)  all_57_0 = e3 & op(e3, e3) = e3
% 228.31/39.86  | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | ALPHA: (162) implies:
% 228.31/39.86  | | | | | | | | | | |   (163)  all_57_0 = e3
% 228.31/39.86  | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | REF_CLOSE: (6), (11), (38), (55), (58), (62), (82), (86),
% 228.31/39.86  | | | | | | | | | | |            (101), (163) are inconsistent by sub-proof #2011.
% 228.31/39.86  | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | Case 2:
% 228.31/39.86  | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | |   (164)  all_57_1 = e3 & op(e3, e2) = e3
% 228.31/39.86  | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | ALPHA: (164) implies:
% 228.31/39.86  | | | | | | | | | | |   (165)  all_57_1 = e3
% 228.31/39.86  | | | | | | | | | | |   (166)  op(e3, e2) = e3
% 228.31/39.86  | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | BETA: splitting (12) gives:
% 228.31/39.86  | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | Case 1:
% 228.31/39.86  | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | |   (167)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 228.31/39.86  | | | | | | | | | | | |            & op(e1, e2) = e0)
% 228.31/39.86  | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | BETA: splitting (167) gives:
% 228.31/39.86  | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | Case 1:
% 228.31/39.86  | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | |   (168)  all_57_6 = e0 & op(e1, e3) = e0
% 228.31/39.86  | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | REF_CLOSE: (9), (11), (36), (38), (40), (46), (48), (55),
% 228.31/39.86  | | | | | | | | | | | | |            (58), (62), (63), (82), (94), (101), (113), (165),
% 228.31/39.86  | | | | | | | | | | | | |            (168) are inconsistent by sub-proof #482.
% 228.31/39.86  | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | Case 2:
% 228.31/39.86  | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | |   (169)  all_57_7 = e0 & op(e1, e2) = e0
% 228.31/39.86  | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | ALPHA: (169) implies:
% 228.31/39.86  | | | | | | | | | | | | |   (170)  all_57_7 = e0
% 228.31/39.86  | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | REF_CLOSE: (3), (5), (6), (9), (11), (12), (13), (15), (17),
% 228.31/39.86  | | | | | | | | | | | | |            (19), (24), (32), (33), (35), (36), (38), (40),
% 228.31/39.86  | | | | | | | | | | | | |            (46), (47), (50), (55), (57), (58), (62), (69),
% 228.31/39.86  | | | | | | | | | | | | |            (73), (76), (79), (80), (82), (83), (86), (89),
% 228.31/39.86  | | | | | | | | | | | | |            (90), (94), (95), (96), (101), (106), (165), (170)
% 228.31/39.86  | | | | | | | | | | | | |            are inconsistent by sub-proof #481.
% 228.31/39.86  | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | End of split
% 228.31/39.86  | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | Case 2:
% 228.31/39.86  | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | |   (171)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 228.31/39.86  | | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 228.31/39.86  | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | BETA: splitting (171) gives:
% 228.31/39.86  | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | Case 1:
% 228.31/39.86  | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | |   (172)  all_57_8 = e0 & op(e1, e1) = e0
% 228.31/39.86  | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | REF_CLOSE: (5), (11), (33), (36), (38), (50), (55), (58),
% 228.31/39.86  | | | | | | | | | | | | |            (79), (82), (106), (172) are inconsistent by
% 228.31/39.86  | | | | | | | | | | | | |            sub-proof #492.
% 228.31/39.86  | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | Case 2:
% 228.31/39.86  | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | |   (173)  all_57_11 = e0 & op(e1, e0) = e0
% 228.31/39.86  | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | ALPHA: (173) implies:
% 228.31/39.86  | | | | | | | | | | | | |   (174)  op(e1, e0) = e0
% 228.31/39.86  | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | BETA: splitting (14) gives:
% 228.31/39.86  | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | Case 1:
% 228.31/39.86  | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | |   (175)  all_55_14 = e1
% 228.31/39.86  | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | REF_CLOSE: (71), (92), (175) are inconsistent by sub-proof
% 228.31/39.86  | | | | | | | | | | | | | |            #2165.
% 228.31/39.86  | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | Case 2:
% 228.31/39.86  | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | |   (176)  all_55_14 = e0
% 228.31/39.86  | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | COMBINE_EQS: (92), (176) imply:
% 228.31/39.86  | | | | | | | | | | | | | |   (177)  all_53_11 = e0
% 228.31/39.86  | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | SIMP: (177) implies:
% 228.31/39.86  | | | | | | | | | | | | | |   (178)  all_53_11 = e0
% 228.31/39.86  | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | REDUCE: (10), (178) imply:
% 228.31/39.86  | | | | | | | | | | | | | |   (179)   ~ (all_53_8 = e0)
% 228.31/39.86  | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | BETA: splitting (45) gives:
% 228.31/39.86  | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | Case 1:
% 228.31/39.86  | | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | |   (180)  all_55_2 = e3
% 228.31/39.86  | | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | | COMBINE_EQS: (44), (180) imply:
% 228.31/39.86  | | | | | | | | | | | | | | |   (181)  all_53_8 = e3
% 228.31/39.86  | | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | | SIMP: (181) implies:
% 228.31/39.86  | | | | | | | | | | | | | | |   (182)  all_53_8 = e3
% 228.31/39.86  | | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | | REDUCE: (53), (182) imply:
% 228.31/39.86  | | | | | | | | | | | | | | |   (183)   ~ (all_53_4 = e3)
% 228.31/39.86  | | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | | BETA: splitting (2) gives:
% 228.31/39.86  | | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | | Case 1:
% 228.31/39.86  | | | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | | |   (184)  all_55_1 = e3
% 228.31/39.86  | | | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | | | REF_CLOSE: (39), (183), (184) are inconsistent by sub-proof
% 228.31/39.86  | | | | | | | | | | | | | | | |            #2295.
% 228.31/39.86  | | | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | | Case 2:
% 228.31/39.86  | | | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | | |   (185)   ~ (all_55_1 = e3)
% 228.31/39.86  | | | | | | | | | | | | | | | |   (186)  all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.31/39.86  | | | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | | | BETA: splitting (186) gives:
% 228.31/39.86  | | | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | | | Case 1:
% 228.31/39.86  | | | | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | | | |   (187)  all_55_1 = e2
% 228.31/39.86  | | | | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (77), (187) are inconsistent by sub-proof
% 228.31/39.86  | | | | | | | | | | | | | | | | |            #2284.
% 228.31/39.86  | | | | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | | | Case 2:
% 228.31/39.86  | | | | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | | | |   (188)  all_55_1 = e1 | all_55_1 = e0
% 228.31/39.86  | | | | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | | | | BETA: splitting (188) gives:
% 228.31/39.86  | | | | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | | | | Case 1:
% 228.31/39.86  | | | | | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | | | | |   (189)  all_55_1 = e1
% 228.31/39.86  | | | | | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (39), (189) imply:
% 228.31/39.86  | | | | | | | | | | | | | | | | | |   (190)  all_53_4 = e1
% 228.31/39.86  | | | | | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | | | | | SIMP: (190) implies:
% 228.31/39.86  | | | | | | | | | | | | | | | | | |   (191)  all_53_4 = e1
% 228.31/39.86  | | | | | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | | | | | REDUCE: (183), (191) imply:
% 228.31/39.86  | | | | | | | | | | | | | | | | | |   (192)   ~ (e3 = e1)
% 228.31/39.86  | | | | | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | | | | | REDUCE: (54), (191) imply:
% 228.31/39.86  | | | | | | | | | | | | | | | | | |   (193)  op(e3, e2) = e1
% 228.31/39.86  | | | | | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | | | | | BETA: splitting (66) gives:
% 228.31/39.86  | | | | | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | | | | | Case 1:
% 228.31/39.86  | | | | | | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | | | | | |   (194)   ~ (all_20_0 = e1) & op(all_20_1, e3) = all_20_0 &
% 228.31/39.86  | | | | | | | | | | | | | | | | | | |          op(e3, e2) = all_20_1 & $i(all_20_0) &
% 228.31/39.86  | | | | | | | | | | | | | | | | | | |          $i(all_20_1)
% 228.31/39.86  | | | | | | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | | | | | | ALPHA: (194) implies:
% 228.31/39.86  | | | | | | | | | | | | | | | | | | |   (195)  op(e3, e2) = all_20_1
% 228.31/39.86  | | | | | | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (6), (7), (11), (13), (18), (21), (23),
% 228.31/39.86  | | | | | | | | | | | | | | | | | | |            (25), (28), (29), (43), (51), (52), (62), (72),
% 228.31/39.86  | | | | | | | | | | | | | | | | | | |            (81), (86), (101), (166), (174), (193), (195) are
% 228.31/39.86  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #478.
% 228.31/39.86  | | | | | | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | | | | | Case 2:
% 228.31/39.86  | | | | | | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | | | | | |   (196)   ~ (all_20_1 = e0) & op(e3, e2) = all_20_1 &
% 228.31/39.86  | | | | | | | | | | | | | | | | | | |          $i(all_20_1)
% 228.31/39.86  | | | | | | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | | | | | | ALPHA: (196) implies:
% 228.31/39.86  | | | | | | | | | | | | | | | | | | |   (197)  op(e3, e2) = all_20_1
% 228.31/39.86  | | | | | | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (6), (7), (11), (13), (18), (21), (23),
% 228.31/39.86  | | | | | | | | | | | | | | | | | | |            (25), (28), (29), (43), (51), (52), (62), (72),
% 228.31/39.86  | | | | | | | | | | | | | | | | | | |            (81), (86), (101), (166), (174), (193), (197) are
% 228.31/39.86  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #478.
% 228.31/39.86  | | | | | | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | | | | | End of split
% 228.31/39.86  | | | | | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | | | | Case 2:
% 228.31/39.86  | | | | | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | | | | |   (198)  all_55_1 = e0
% 228.31/39.86  | | | | | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (60), (198) are inconsistent by sub-proof
% 228.31/39.86  | | | | | | | | | | | | | | | | | |            #2076.
% 228.31/39.86  | | | | | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | | | | End of split
% 228.31/39.86  | | | | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | | | End of split
% 228.31/39.86  | | | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | | End of split
% 228.31/39.86  | | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | Case 2:
% 228.31/39.86  | | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | |   (199)  all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.31/39.86  | | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 228.31/39.86  | | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | | Case 1:
% 228.31/39.86  | | | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | | |   (200)  all_55_2 = e2
% 228.31/39.86  | | | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | | | REF_CLOSE: (44), (68), (200) are inconsistent by sub-proof
% 228.31/39.86  | | | | | | | | | | | | | | | |            #2027.
% 228.31/39.86  | | | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | | Case 2:
% 228.31/39.86  | | | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | | |   (201)  all_55_2 = e1 | all_55_2 = e0
% 228.31/39.86  | | | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | | | REF_CLOSE: (26), (44), (179), (201) are inconsistent by
% 228.31/39.86  | | | | | | | | | | | | | | | |            sub-proof #2030.
% 228.31/39.86  | | | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | | End of split
% 228.31/39.86  | | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | | End of split
% 228.31/39.86  | | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | | End of split
% 228.31/39.86  | | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | | End of split
% 228.31/39.86  | | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | End of split
% 228.31/39.86  | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | End of split
% 228.31/39.86  | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | Case 2:
% 228.31/39.86  | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | |   (202)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 228.31/39.86  | | | | | | | | | |            & op(e3, e0) = e3)
% 228.31/39.86  | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | BETA: splitting (202) gives:
% 228.31/39.86  | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | Case 1:
% 228.31/39.86  | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | |   (203)  all_57_4 = e3 & op(e3, e1) = e3
% 228.31/39.86  | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | ALPHA: (203) implies:
% 228.31/39.86  | | | | | | | | | | |   (204)  all_57_4 = e3
% 228.31/39.86  | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (11), (35), (36), (38), (40), (46),
% 228.31/39.86  | | | | | | | | | | |            (48), (50), (55), (58), (62), (63), (79), (82),
% 228.31/39.86  | | | | | | | | | | |            (86), (94), (101), (106), (113), (160), (204) are
% 228.31/39.86  | | | | | | | | | | |            inconsistent by sub-proof #480.
% 228.31/39.86  | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | Case 2:
% 228.31/39.86  | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | |   (205)  all_57_9 = e3 & op(e3, e0) = e3
% 228.31/39.86  | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | ALPHA: (205) implies:
% 228.31/39.86  | | | | | | | | | | |   (206)  op(e3, e0) = e3
% 228.31/39.86  | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | | REF_CLOSE: (13), (76), (96), (206) are inconsistent by
% 228.31/39.86  | | | | | | | | | | |            sub-proof #2458.
% 228.31/39.86  | | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | | End of split
% 228.31/39.86  | | | | | | | | | | 
% 228.31/39.86  | | | | | | | | | End of split
% 228.31/39.86  | | | | | | | | | 
% 228.31/39.86  | | | | | | | | End of split
% 228.31/39.86  | | | | | | | | 
% 228.31/39.86  | | | | | | | End of split
% 228.31/39.86  | | | | | | | 
% 228.31/39.86  | | | | | | Case 2:
% 228.31/39.86  | | | | | | | 
% 228.31/39.86  | | | | | | |   (207)  all_57_15 = e2 & op(e0, e0) = e2
% 228.31/39.86  | | | | | | | 
% 228.31/39.86  | | | | | | | REF_CLOSE: (5), (6), (9), (11), (13), (15), (17), (19), (24),
% 228.31/39.86  | | | | | | |            (32), (35), (36), (38), (40), (46), (47), (55), (57),
% 228.31/39.86  | | | | | | |            (58), (62), (69), (73), (76), (79), (80), (82), (83),
% 228.31/39.86  | | | | | | |            (89), (90), (94), (96), (207) are inconsistent by
% 228.31/39.86  | | | | | | |            sub-proof #477.
% 228.31/39.86  | | | | | | | 
% 228.31/39.86  | | | | | | End of split
% 228.31/39.86  | | | | | | 
% 228.31/39.86  | | | | | End of split
% 228.31/39.86  | | | | | 
% 228.31/39.86  | | | | End of split
% 228.31/39.86  | | | | 
% 228.31/39.86  | | | Case 2:
% 228.31/39.86  | | | | 
% 228.31/39.86  | | | |   (208)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0,
% 228.31/39.86  | | | |              e3) = e1)
% 228.31/39.86  | | | | 
% 228.31/39.86  | | | | REF_CLOSE: (5), (11), (13), (36), (38), (40), (47), (50), (55), (58),
% 228.31/39.86  | | | |            (62), (79), (82), (89), (208) are inconsistent by sub-proof
% 228.31/39.86  | | | |            #809.
% 228.31/39.86  | | | | 
% 228.31/39.86  | | | End of split
% 228.31/39.86  | | | 
% 228.31/39.86  | | End of split
% 228.31/39.86  | | 
% 228.31/39.86  | End of split
% 228.31/39.86  | 
% 228.31/39.86  End of proof
% 228.31/39.86  
% 228.31/39.86  Sub-proof #477 shows that the following formulas are inconsistent:
% 228.31/39.86  ----------------------------------------------------------------
% 228.31/39.86    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.31/39.86         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.31/39.86    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.31/39.86         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.31/39.86    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.31/39.86         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.31/39.86    (4)   ~ (e3 = e1)
% 228.31/39.86    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.31/39.86           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.31/39.86    (6)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.31/39.86         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.31/39.86    (7)   ~ (all_6_2 = e3)
% 228.31/39.86    (8)  op(e1, e1) = all_6_2
% 228.31/39.86    (9)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.31/39.86         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.31/39.86    (10)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.31/39.86          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.31/39.86    (11)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.31/39.86          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.31/39.86    (12)  all_57_3 = e0
% 228.31/39.86    (13)   ~ (e3 = e2)
% 228.31/39.86    (14)   ~ (e3 = e0)
% 228.31/39.86    (15)  all_57_15 = e3
% 228.31/39.86    (16)  op(e3, e3) = e2
% 228.31/39.86    (17)   ~ (e2 = e0)
% 228.31/39.86    (18)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.31/39.86          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.31/39.86    (19)   ~ (e1 = e0)
% 228.31/39.86    (20)  all_57_6 = e3
% 228.31/39.86    (21)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.31/39.86              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.31/39.86                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.31/39.86                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.31/39.86    (22)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.31/39.86          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.31/39.86    (23)   ~ (all_53_12 = e3)
% 228.31/39.86    (24)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.31/39.86          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.31/39.86    (25)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.31/39.86          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.31/39.86    (26)   ~ (e2 = e1)
% 228.31/39.86    (27)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.31/39.86          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.31/39.86    (28)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.31/39.86          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.31/39.86    (29)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.31/39.86          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.31/39.86    (30)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.31/39.86          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.31/39.86    (31)  all_57_15 = e2 & op(e0, e0) = e2
% 228.31/39.86    (32)  op(e3, e0) = all_53_12
% 228.31/39.86  
% 228.31/39.86  Begin of proof
% 228.31/39.86  | 
% 228.31/39.86  | ALPHA: (31) implies:
% 228.31/39.86  |   (33)  all_57_15 = e2
% 228.31/39.86  | 
% 228.31/39.86  | COMBINE_EQS: (15), (33) imply:
% 228.31/39.86  |   (34)  e3 = e2
% 228.31/39.86  | 
% 228.31/39.86  | COMBINE_EQS: (20), (34) imply:
% 228.31/39.86  |   (35)  all_57_6 = e2
% 228.31/39.86  | 
% 228.31/39.86  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.31/39.86  |            (13), (14), (15), (16), (17), (18), (19), (21), (22), (23), (24),
% 228.31/39.86  |            (25), (26), (27), (28), (29), (30), (32), (35) are inconsistent by
% 228.31/39.86  |            sub-proof #728.
% 228.31/39.86  | 
% 228.31/39.86  End of proof
% 228.31/39.86  
% 228.31/39.86  Sub-proof #478 shows that the following formulas are inconsistent:
% 228.31/39.86  ----------------------------------------------------------------
% 228.31/39.86    (1)  all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.31/39.86    (2)  all_57_0 = e2
% 228.31/39.86    (3)  all_57_12 = e0
% 228.31/39.86    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.31/39.86         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.31/39.86    (5)  op(e2, e1) = e3
% 228.31/39.86    (6)   ~ (e3 = e1)
% 228.31/39.86    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.31/39.86           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.31/39.86    (8)  ( ~ (all_28_0 = e0) & op(all_28_1, e3) = all_28_0 & op(e3, e2) = all_28_1
% 228.31/39.86           & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 = e1) & op(e3, e2) =
% 228.31/39.86           all_28_1 & $i(all_28_1))
% 228.31/39.86    (9)  op(e3, e2) = e1
% 228.31/39.86    (10)  op(e2, e1) = e2
% 228.31/39.86    (11)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 228.31/39.86    (12)   ~ (all_52_17 = e2)
% 228.31/39.86    (13)  op(e3, e2) = all_20_1
% 228.31/39.86    (14)   ~ (all_52_17 = all_52_23)
% 228.31/39.86    (15)   ~ (all_52_17 = e1)
% 228.31/39.86    (16)  all_55_11 = all_52_23
% 228.31/39.86    (17)   ~ (all_52_23 = e3)
% 228.31/39.86    (18)  op(e1, e0) = all_52_23
% 228.31/39.86    (19)  all_57_6 = e3
% 228.31/39.86    (20)  all_55_8 = all_52_17
% 228.31/39.86    (21)  op(e3, e2) = e3
% 228.31/39.86    (22)   ~ (all_52_23 = e1)
% 228.31/39.86    (23)  op(e1, e0) = e0
% 228.31/39.86    (24)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.31/39.86          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.31/39.86  
% 228.31/39.86  Begin of proof
% 228.31/39.86  | 
% 228.31/39.86  | BETA: splitting (8) gives:
% 228.31/39.86  | 
% 228.31/39.86  | Case 1:
% 228.31/39.86  | | 
% 228.31/39.86  | |   (25)   ~ (all_28_0 = e0) & op(all_28_1, e3) = all_28_0 & op(e3, e2) =
% 228.31/39.86  | |         all_28_1 & $i(all_28_0) & $i(all_28_1)
% 228.31/39.86  | | 
% 228.31/39.86  | | ALPHA: (25) implies:
% 228.31/39.86  | |   (26)  op(e3, e2) = all_28_1
% 228.31/39.86  | | 
% 228.31/39.86  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13),
% 228.31/39.86  | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 228.31/39.86  | |            (26) are inconsistent by sub-proof #479.
% 228.31/39.86  | | 
% 228.31/39.86  | Case 2:
% 228.31/39.86  | | 
% 228.31/39.86  | |   (27)   ~ (all_28_1 = e1) & op(e3, e2) = all_28_1 & $i(all_28_1)
% 228.31/39.86  | | 
% 228.31/39.86  | | ALPHA: (27) implies:
% 228.31/39.86  | |   (28)  op(e3, e2) = all_28_1
% 228.31/39.86  | | 
% 228.31/39.86  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13),
% 228.31/39.86  | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 228.31/39.86  | |            (28) are inconsistent by sub-proof #479.
% 228.31/39.86  | | 
% 228.31/39.86  | End of split
% 228.31/39.86  | 
% 228.31/39.86  End of proof
% 228.31/39.86  
% 228.31/39.86  Sub-proof #479 shows that the following formulas are inconsistent:
% 228.31/39.86  ----------------------------------------------------------------
% 228.31/39.86    (1)  all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.31/39.86    (2)  all_57_0 = e2
% 228.31/39.86    (3)  all_57_12 = e0
% 228.31/39.86    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.31/39.86         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.31/39.86    (5)  op(e2, e1) = e3
% 228.31/39.86    (6)   ~ (e3 = e1)
% 228.31/39.86    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.31/39.86           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.31/39.86    (8)  op(e3, e2) = e1
% 228.31/39.86    (9)  op(e2, e1) = e2
% 228.31/39.86    (10)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 228.31/39.86    (11)   ~ (all_52_17 = e2)
% 228.31/39.86    (12)  op(e3, e2) = all_20_1
% 228.31/39.86    (13)   ~ (all_52_17 = all_52_23)
% 228.31/39.86    (14)   ~ (all_52_17 = e1)
% 228.31/39.86    (15)  op(e3, e2) = all_28_1
% 228.31/39.86    (16)  all_55_11 = all_52_23
% 228.31/39.86    (17)   ~ (all_52_23 = e3)
% 228.31/39.86    (18)  op(e1, e0) = all_52_23
% 228.31/39.86    (19)  all_57_6 = e3
% 228.31/39.86    (20)  all_55_8 = all_52_17
% 228.31/39.86    (21)  op(e3, e2) = e3
% 228.31/39.86    (22)   ~ (all_52_23 = e1)
% 228.31/39.86    (23)  op(e1, e0) = e0
% 228.31/39.86    (24)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.31/39.86          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.31/39.86  
% 228.31/39.86  Begin of proof
% 228.31/39.86  | 
% 228.31/39.86  | BETA: splitting (1) gives:
% 228.31/39.86  | 
% 228.31/39.86  | Case 1:
% 228.31/39.86  | | 
% 228.31/39.86  | |   (25)  all_55_8 = e2
% 228.31/39.86  | | 
% 228.31/39.86  | | REF_CLOSE: (11), (20), (25) are inconsistent by sub-proof #1869.
% 228.31/39.86  | | 
% 228.31/39.86  | Case 2:
% 228.31/39.86  | | 
% 228.31/39.86  | |   (26)  all_55_8 = e1 | all_55_8 = e0
% 228.31/39.86  | | 
% 228.31/39.86  | | BETA: splitting (26) gives:
% 228.31/39.86  | | 
% 228.31/39.86  | | Case 1:
% 228.31/39.86  | | | 
% 228.31/39.86  | | |   (27)  all_55_8 = e1
% 228.31/39.86  | | | 
% 228.31/39.86  | | | REF_CLOSE: (14), (20), (27) are inconsistent by sub-proof #1880.
% 228.31/39.86  | | | 
% 228.31/39.86  | | Case 2:
% 228.31/39.86  | | | 
% 228.31/39.86  | | |   (28)  all_55_8 = e0
% 228.31/39.86  | | | 
% 228.31/39.86  | | | COMBINE_EQS: (20), (28) imply:
% 228.31/39.86  | | |   (29)  all_52_17 = e0
% 228.31/39.86  | | | 
% 228.31/39.86  | | | SIMP: (29) implies:
% 228.31/39.86  | | |   (30)  all_52_17 = e0
% 228.31/39.86  | | | 
% 228.31/39.86  | | | REDUCE: (13), (30) imply:
% 228.31/39.86  | | |   (31)   ~ (all_52_23 = e0)
% 228.31/39.86  | | | 
% 228.31/39.86  | | | SIMP: (31) implies:
% 228.31/39.86  | | |   (32)   ~ (all_52_23 = e0)
% 228.31/39.86  | | | 
% 228.31/39.86  | | | REDUCE: (14), (30) imply:
% 228.31/39.86  | | |   (33)   ~ (e1 = e0)
% 228.31/39.86  | | | 
% 228.31/39.86  | | | SIMP: (33) implies:
% 228.31/39.86  | | |   (34)   ~ (e1 = e0)
% 228.31/39.86  | | | 
% 228.31/39.86  | | | BETA: splitting (10) gives:
% 228.31/39.86  | | | 
% 228.31/39.86  | | | Case 1:
% 228.31/39.86  | | | | 
% 228.31/39.86  | | | |   (35)  all_55_11 = e3
% 228.31/39.86  | | | | 
% 228.31/39.86  | | | | REF_CLOSE: (16), (17), (35) are inconsistent by sub-proof #1914.
% 228.31/39.86  | | | | 
% 228.31/39.86  | | | Case 2:
% 228.31/39.86  | | | | 
% 228.31/39.86  | | | |   (36)   ~ (all_55_11 = e3)
% 228.31/39.86  | | | |   (37)  all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 228.31/39.86  | | | | 
% 228.31/39.86  | | | | BETA: splitting (37) gives:
% 228.31/39.86  | | | | 
% 228.31/39.86  | | | | Case 1:
% 228.31/39.86  | | | | | 
% 228.31/39.86  | | | | |   (38)  all_55_11 = e2
% 228.31/39.86  | | | | | 
% 228.31/39.86  | | | | | COMBINE_EQS: (16), (38) imply:
% 228.31/39.86  | | | | |   (39)  all_52_23 = e2
% 228.31/39.86  | | | | | 
% 228.31/39.86  | | | | | SIMP: (39) implies:
% 228.31/39.86  | | | | |   (40)  all_52_23 = e2
% 228.31/39.86  | | | | | 
% 228.31/39.86  | | | | | REDUCE: (17), (40) imply:
% 228.31/39.86  | | | | |   (41)   ~ (e3 = e2)
% 228.31/39.86  | | | | | 
% 228.31/39.86  | | | | | SIMP: (41) implies:
% 228.31/39.86  | | | | |   (42)   ~ (e3 = e2)
% 228.31/39.86  | | | | | 
% 228.31/39.86  | | | | | REDUCE: (22), (40) imply:
% 228.31/39.86  | | | | |   (43)   ~ (e2 = e1)
% 228.31/39.86  | | | | | 
% 228.31/39.86  | | | | | REDUCE: (32), (40) imply:
% 228.31/39.86  | | | | |   (44)   ~ (e2 = e0)
% 228.31/39.86  | | | | | 
% 228.31/39.86  | | | | | REDUCE: (18), (40) imply:
% 228.31/39.86  | | | | |   (45)  op(e1, e0) = e2
% 228.31/39.86  | | | | | 
% 228.31/39.86  | | | | | GROUND_INST: instantiating (7) with e0, e2, e0, e1, simplifying with
% 228.31/39.86  | | | | |              (23), (45) gives:
% 228.31/39.86  | | | | |   (46)  e2 = e0
% 228.31/39.86  | | | | | 
% 228.31/39.86  | | | | | GROUND_INST: instantiating (7) with e2, e3, e1, e2, simplifying with
% 228.31/39.86  | | | | |              (5), (9) gives:
% 228.31/39.86  | | | | |   (47)  e3 = e2
% 228.31/39.86  | | | | | 
% 228.31/39.86  | | | | | GROUND_INST: instantiating (7) with e3, all_20_1, e2, e3, simplifying
% 228.31/39.86  | | | | |              with (12), (21) gives:
% 228.31/39.86  | | | | |   (48)  all_20_1 = e3
% 228.31/39.86  | | | | | 
% 228.31/39.86  | | | | | GROUND_INST: instantiating (7) with all_20_1, all_28_1, e2, e3,
% 228.31/39.86  | | | | |              simplifying with (12), (15) gives:
% 228.31/39.86  | | | | |   (49)  all_28_1 = all_20_1
% 228.31/39.86  | | | | | 
% 228.31/39.86  | | | | | GROUND_INST: instantiating (7) with e1, all_28_1, e2, e3, simplifying
% 228.31/39.86  | | | | |              with (8), (15) gives:
% 228.31/39.86  | | | | |   (50)  all_28_1 = e1
% 228.31/39.86  | | | | | 
% 228.31/39.86  | | | | | COMBINE_EQS: (49), (50) imply:
% 228.31/39.86  | | | | |   (51)  all_20_1 = e1
% 228.31/39.86  | | | | | 
% 228.31/39.86  | | | | | SIMP: (51) implies:
% 228.31/39.86  | | | | |   (52)  all_20_1 = e1
% 228.31/39.86  | | | | | 
% 228.31/39.86  | | | | | COMBINE_EQS: (48), (52) imply:
% 228.31/39.86  | | | | |   (53)  e3 = e1
% 228.31/39.86  | | | | | 
% 228.31/39.86  | | | | | SIMP: (53) implies:
% 228.31/39.86  | | | | |   (54)  e3 = e1
% 228.31/39.86  | | | | | 
% 228.31/39.86  | | | | | COMBINE_EQS: (47), (54) imply:
% 228.31/39.86  | | | | |   (55)  e2 = e1
% 228.31/39.86  | | | | | 
% 228.31/39.86  | | | | | SIMP: (55) implies:
% 228.31/39.86  | | | | |   (56)  e2 = e1
% 228.31/39.86  | | | | | 
% 228.31/39.86  | | | | | COMBINE_EQS: (46), (56) imply:
% 228.31/39.86  | | | | |   (57)  e1 = e0
% 228.31/39.86  | | | | | 
% 228.31/39.86  | | | | | COMBINE_EQS: (2), (46) imply:
% 228.31/39.86  | | | | |   (58)  all_57_0 = e0
% 228.31/39.86  | | | | | 
% 228.31/39.86  | | | | | REF_CLOSE: (3), (4), (6), (19), (24), (34), (42), (43), (44), (58) are
% 228.31/39.86  | | | | |            inconsistent by sub-proof #1425.
% 228.31/39.86  | | | | | 
% 228.31/39.86  | | | | Case 2:
% 228.31/39.86  | | | | | 
% 228.31/39.86  | | | | |   (59)  all_55_11 = e1 | all_55_11 = e0
% 228.31/39.86  | | | | | 
% 228.31/39.86  | | | | | REF_CLOSE: (16), (22), (32), (59) are inconsistent by sub-proof #2107.
% 228.31/39.86  | | | | | 
% 228.31/39.86  | | | | End of split
% 228.31/39.86  | | | | 
% 228.31/39.86  | | | End of split
% 228.31/39.86  | | | 
% 228.31/39.86  | | End of split
% 228.31/39.86  | | 
% 228.31/39.86  | End of split
% 228.31/39.86  | 
% 228.31/39.86  End of proof
% 228.31/39.86  
% 228.31/39.86  Sub-proof #480 shows that the following formulas are inconsistent:
% 228.31/39.86  ----------------------------------------------------------------
% 228.31/39.86    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.31/39.87         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.31/39.87    (2)  all_57_12 = e0
% 228.31/39.87    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.31/39.87         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.31/39.87    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.31/39.87         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.31/39.87    (5)   ~ (e3 = e1)
% 228.31/39.87    (6)  all_57_9 = e1
% 228.31/39.87    (7)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.31/39.87         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.31/39.87    (8)  all_57_3 = e0
% 228.31/39.87    (9)  all_57_4 = e3
% 228.31/39.87    (10)   ~ (e3 = e2)
% 228.31/39.87    (11)   ~ (e3 = e0)
% 228.31/39.87    (12)  all_57_15 = e3
% 228.31/39.87    (13)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.31/39.87          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.31/39.87            e1)
% 228.31/39.87    (14)  all_57_5 = e3
% 228.31/39.87    (15)   ~ (e2 = e0)
% 228.31/39.87    (16)   ~ (e1 = e0)
% 228.31/39.87    (17)  all_57_14 = e2
% 228.31/39.87    (18)  all_57_6 = e3
% 228.31/39.87    (19)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.31/39.87          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.31/39.87    (20)  all_57_2 = e1
% 228.31/39.87    (21)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.31/39.87          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.31/39.87    (22)   ~ (e2 = e1)
% 228.31/39.87    (23)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.31/39.87          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.31/39.87    (24)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.31/39.87          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.31/39.87  
% 228.31/39.87  Begin of proof
% 228.31/39.87  | 
% 228.31/39.87  | BETA: splitting (7) gives:
% 228.31/39.87  | 
% 228.31/39.87  | Case 1:
% 228.31/39.87  | | 
% 228.31/39.87  | |   (25)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) =
% 228.31/39.87  | |           e0)
% 228.31/39.87  | | 
% 228.31/39.87  | | REF_CLOSE: (2), (3), (4), (5), (8), (10), (11), (12), (13), (15), (16),
% 228.31/39.87  | |            (17), (18), (19), (22), (23), (24), (25) are inconsistent by
% 228.31/39.87  | |            sub-proof #483.
% 228.31/39.87  | | 
% 228.31/39.87  | Case 2:
% 228.31/39.87  | | 
% 228.31/39.87  | |   (26)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) =
% 228.31/39.87  | |           e0)
% 228.31/39.87  | | 
% 228.31/39.87  | | BETA: splitting (26) gives:
% 228.31/39.87  | | 
% 228.31/39.87  | | Case 1:
% 228.31/39.87  | | | 
% 228.31/39.87  | | |   (27)  all_57_4 = e0 & op(e3, e1) = e0
% 228.31/39.87  | | | 
% 228.31/39.87  | | | REF_CLOSE: (9), (11), (27) are inconsistent by sub-proof #2491.
% 228.31/39.87  | | | 
% 228.31/39.87  | | Case 2:
% 228.31/39.87  | | | 
% 228.31/39.87  | | |   (28)  all_57_9 = e0 & op(e3, e0) = e0
% 228.31/39.87  | | | 
% 228.31/39.87  | | | ALPHA: (28) implies:
% 228.31/39.87  | | |   (29)  all_57_9 = e0
% 228.31/39.87  | | | 
% 228.31/39.87  | | | COMBINE_EQS: (6), (29) imply:
% 228.31/39.87  | | |   (30)  e1 = e0
% 228.31/39.87  | | | 
% 228.31/39.87  | | | COMBINE_EQS: (20), (30) imply:
% 228.31/39.87  | | |   (31)  all_57_2 = e0
% 228.31/39.87  | | | 
% 228.31/39.87  | | | REF_CLOSE: (1), (5), (8), (10), (14), (15), (16), (21), (22), (31) are
% 228.31/39.87  | | |            inconsistent by sub-proof #2253.
% 228.31/39.87  | | | 
% 228.31/39.87  | | End of split
% 228.31/39.87  | | 
% 228.31/39.87  | End of split
% 228.31/39.87  | 
% 228.31/39.87  End of proof
% 228.31/39.87  
% 228.31/39.87  Sub-proof #481 shows that the following formulas are inconsistent:
% 228.31/39.87  ----------------------------------------------------------------
% 228.31/39.87    (1)  all_57_0 = e2
% 228.31/39.87    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.31/39.87         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.31/39.87    (3)  all_57_12 = e0
% 228.31/39.87    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.31/39.87         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.31/39.87    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.31/39.87         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.31/39.87    (6)   ~ (e3 = e1)
% 228.31/39.87    (7)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.31/39.87         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.31/39.87    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.31/39.87           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.31/39.87    (9)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.31/39.87         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.31/39.87    (10)   ~ (all_6_2 = e3)
% 228.31/39.87    (11)  op(e1, e1) = all_6_2
% 228.31/39.87    (12)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.31/39.87          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.31/39.87    (13)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.31/39.87          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.31/39.87    (14)  all_57_8 = e1
% 228.31/39.87    (15)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.31/39.87          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.31/39.87    (16)  all_57_3 = e0
% 228.31/39.87    (17)   ~ (e3 = e2)
% 228.31/39.87    (18)   ~ (e3 = e0)
% 228.31/39.87    (19)  all_57_15 = e3
% 228.31/39.87    (20)  op(e3, e3) = e2
% 228.31/39.87    (21)  all_57_5 = e3
% 228.31/39.87    (22)   ~ (e2 = e0)
% 228.31/39.87    (23)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.31/39.87          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.31/39.87    (24)   ~ (e1 = e0)
% 228.31/39.87    (25)  all_57_6 = e3
% 228.31/39.87    (26)  all_57_2 = e1
% 228.31/39.87    (27)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.31/39.87              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.31/39.87                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.31/39.87                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.31/39.87    (28)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.31/39.87          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.31/39.87    (29)   ~ (all_53_12 = e3)
% 228.31/39.87    (30)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.31/39.87          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.31/39.87    (31)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.31/39.87          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.31/39.87    (32)  all_57_1 = e3
% 228.31/39.87    (33)   ~ (e2 = e1)
% 228.31/39.87    (34)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.31/39.87          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.31/39.87    (35)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.31/39.87          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.31/39.87    (36)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.31/39.87          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.31/39.87    (37)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.31/39.87          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.31/39.87    (38)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.31/39.87          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.31/39.87    (39)  all_57_7 = e0
% 228.31/39.87    (40)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.31/39.87          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.31/39.87    (41)  op(e3, e0) = all_53_12
% 228.31/39.87  
% 228.31/39.87  Begin of proof
% 228.31/39.87  | 
% 228.31/39.87  | BETA: splitting (5) gives:
% 228.31/39.87  | 
% 228.31/39.87  | Case 1:
% 228.31/39.87  | | 
% 228.31/39.87  | |   (42)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 228.31/39.87  | |           e2)
% 228.31/39.87  | | 
% 228.31/39.87  | | BETA: splitting (42) gives:
% 228.31/39.87  | | 
% 228.31/39.87  | | Case 1:
% 228.31/39.87  | | | 
% 228.31/39.87  | | |   (43)  all_57_1 = e2 & op(e3, e2) = e2
% 228.31/39.87  | | | 
% 228.31/39.87  | | | ALPHA: (43) implies:
% 228.31/39.87  | | |   (44)  all_57_1 = e2
% 228.31/39.87  | | | 
% 228.31/39.87  | | | COMBINE_EQS: (32), (44) imply:
% 228.31/39.87  | | |   (45)  e3 = e2
% 228.31/39.87  | | | 
% 228.31/39.87  | | | COMBINE_EQS: (25), (45) imply:
% 228.31/39.87  | | |   (46)  all_57_6 = e2
% 228.31/39.87  | | | 
% 228.31/39.87  | | | REF_CLOSE: (2), (4), (5), (6), (8), (9), (10), (11), (12), (13), (15),
% 228.31/39.87  | | |            (16), (17), (18), (19), (20), (22), (23), (24), (27), (28),
% 228.31/39.87  | | |            (29), (30), (31), (33), (34), (36), (37), (38), (41), (46) are
% 228.31/39.87  | | |            inconsistent by sub-proof #728.
% 228.31/39.87  | | | 
% 228.31/39.87  | | Case 2:
% 228.31/39.87  | | | 
% 228.31/39.87  | | |   (47)  all_57_3 = e2 & op(e2, e2) = e2
% 228.31/39.87  | | | 
% 228.31/39.87  | | | REF_CLOSE: (1), (3), (4), (6), (16), (17), (22), (24), (25), (33), (35),
% 228.31/39.87  | | |            (47) are inconsistent by sub-proof #784.
% 228.31/39.87  | | | 
% 228.31/39.87  | | End of split
% 228.31/39.87  | | 
% 228.31/39.87  | Case 2:
% 228.31/39.87  | | 
% 228.31/39.87  | |   (48)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 228.31/39.87  | |           e2)
% 228.31/39.87  | | 
% 228.31/39.87  | | BETA: splitting (48) gives:
% 228.31/39.87  | | 
% 228.31/39.87  | | Case 1:
% 228.31/39.87  | | | 
% 228.31/39.87  | | |   (49)  all_57_7 = e2 & op(e1, e2) = e2
% 228.31/39.87  | | | 
% 228.31/39.87  | | | REF_CLOSE: (1), (3), (4), (6), (17), (22), (24), (25), (33), (35), (39),
% 228.31/39.87  | | |            (49) are inconsistent by sub-proof #783.
% 228.31/39.87  | | | 
% 228.31/39.87  | | Case 2:
% 228.31/39.87  | | | 
% 228.31/39.87  | | |   (50)  all_57_13 = e2 & op(e0, e2) = e2
% 228.31/39.87  | | | 
% 228.31/39.87  | | | ALPHA: (50) implies:
% 228.31/39.87  | | |   (51)  all_57_13 = e2
% 228.31/39.87  | | | 
% 228.31/39.87  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.31/39.87  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 228.31/39.87  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 228.31/39.87  | | |            (33), (34), (35), (36), (37), (38), (40), (41), (51) are
% 228.31/39.87  | | |            inconsistent by sub-proof #490.
% 228.31/39.87  | | | 
% 228.31/39.87  | | End of split
% 228.31/39.87  | | 
% 228.31/39.87  | End of split
% 228.31/39.87  | 
% 228.31/39.87  End of proof
% 228.31/39.87  
% 228.31/39.87  Sub-proof #482 shows that the following formulas are inconsistent:
% 228.31/39.87  ----------------------------------------------------------------
% 228.31/39.87    (1)  all_57_12 = e0
% 228.31/39.87    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.31/39.87         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.31/39.87    (3)   ~ (e3 = e1)
% 228.31/39.87    (4)  all_57_3 = e0
% 228.31/39.87    (5)   ~ (e3 = e2)
% 228.31/39.87    (6)   ~ (e3 = e0)
% 228.31/39.87    (7)  all_57_15 = e3
% 228.31/39.87    (8)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 228.31/39.87         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.31/39.87    (9)   ~ (e2 = e0)
% 228.31/39.87    (10)   ~ (e1 = e0)
% 228.31/39.87    (11)  all_57_14 = e2
% 228.31/39.87    (12)  all_57_6 = e3
% 228.31/39.87    (13)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.31/39.87          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.31/39.87    (14)  all_57_6 = e0 & op(e1, e3) = e0
% 228.31/39.87    (15)  all_57_1 = e3
% 228.31/39.87    (16)   ~ (e2 = e1)
% 228.31/39.87    (17)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.31/39.87          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.31/39.87  
% 228.31/39.87  Begin of proof
% 228.31/39.87  | 
% 228.31/39.87  | ALPHA: (14) implies:
% 228.31/39.87  |   (18)  all_57_6 = e0
% 228.31/39.87  | 
% 228.31/39.87  | COMBINE_EQS: (12), (18) imply:
% 228.31/39.87  |   (19)  e3 = e0
% 228.31/39.87  | 
% 228.31/39.87  | COMBINE_EQS: (15), (19) imply:
% 228.31/39.87  |   (20)  all_57_1 = e0
% 228.31/39.87  | 
% 228.31/39.87  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 228.31/39.87  |            (16), (17), (20) are inconsistent by sub-proof #484.
% 228.31/39.87  | 
% 228.31/39.87  End of proof
% 228.31/39.87  
% 228.31/39.87  Sub-proof #483 shows that the following formulas are inconsistent:
% 228.31/39.87  ----------------------------------------------------------------
% 228.31/39.87    (1)  all_57_12 = e0
% 228.31/39.87    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.31/39.87         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.31/39.87    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.31/39.87         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.31/39.87    (4)   ~ (e3 = e1)
% 228.31/39.87    (5)  all_57_3 = e0
% 228.31/39.87    (6)   ~ (e3 = e2)
% 228.31/39.87    (7)   ~ (e3 = e0)
% 228.31/39.87    (8)  all_57_15 = e3
% 228.31/39.87    (9)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 228.31/39.87         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.31/39.87    (10)   ~ (e2 = e0)
% 228.31/39.87    (11)   ~ (e1 = e0)
% 228.31/39.87    (12)  all_57_14 = e2
% 228.31/39.87    (13)  all_57_6 = e3
% 228.31/39.87    (14)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.31/39.87          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.31/39.87    (15)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0)
% 228.31/39.87    (16)   ~ (e2 = e1)
% 228.31/39.87    (17)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.31/39.87          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.31/39.87    (18)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.31/39.87          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.31/39.87  
% 228.31/39.87  Begin of proof
% 228.31/39.87  | 
% 228.31/39.87  | BETA: splitting (15) gives:
% 228.31/39.87  | 
% 228.31/39.87  | Case 1:
% 228.31/39.87  | | 
% 228.31/39.87  | |   (19)  all_57_0 = e0 & op(e3, e3) = e0
% 228.31/39.87  | | 
% 228.31/39.87  | | ALPHA: (19) implies:
% 228.31/39.87  | |   (20)  all_57_0 = e0
% 228.31/39.87  | | 
% 228.31/39.87  | | REF_CLOSE: (1), (2), (4), (6), (10), (11), (13), (16), (17), (20) are
% 228.31/39.87  | |            inconsistent by sub-proof #1425.
% 228.31/39.87  | | 
% 228.31/39.87  | Case 2:
% 228.31/39.87  | | 
% 228.31/39.87  | |   (21)  all_57_1 = e0 & op(e3, e2) = e0
% 228.31/39.87  | | 
% 228.31/39.87  | | ALPHA: (21) implies:
% 228.31/39.87  | |   (22)  all_57_1 = e0
% 228.31/39.87  | | 
% 228.31/39.87  | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (14),
% 228.31/39.87  | |            (16), (18), (22) are inconsistent by sub-proof #484.
% 228.31/39.87  | | 
% 228.31/39.87  | End of split
% 228.31/39.87  | 
% 228.31/39.87  End of proof
% 228.31/39.87  
% 228.31/39.87  Sub-proof #484 shows that the following formulas are inconsistent:
% 228.31/39.87  ----------------------------------------------------------------
% 228.31/39.87    (1)  all_57_12 = e0
% 228.31/39.87    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.31/39.87         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.31/39.87    (3)   ~ (e3 = e1)
% 228.31/39.87    (4)  all_57_3 = e0
% 228.31/39.87    (5)   ~ (e3 = e2)
% 228.31/39.87    (6)   ~ (e3 = e0)
% 228.31/39.87    (7)  all_57_1 = e0
% 228.31/39.87    (8)  all_57_15 = e3
% 228.31/39.87    (9)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 228.31/39.87         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.31/39.87    (10)   ~ (e2 = e0)
% 228.31/39.87    (11)   ~ (e1 = e0)
% 228.31/39.87    (12)  all_57_14 = e2
% 228.31/39.87    (13)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.31/39.87          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.31/39.87    (14)   ~ (e2 = e1)
% 228.31/39.87    (15)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.31/39.87          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.31/39.87  
% 228.31/39.87  Begin of proof
% 228.31/39.87  | 
% 228.31/39.87  | BETA: splitting (13) gives:
% 228.31/39.87  | 
% 228.31/39.87  | Case 1:
% 228.31/39.87  | | 
% 228.31/39.87  | |   (16)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 228.31/39.87  | |           e3)
% 228.31/39.87  | | 
% 228.31/39.87  | | REF_CLOSE: (4), (6), (7), (16) are inconsistent by sub-proof #1284.
% 228.31/39.87  | | 
% 228.31/39.87  | Case 2:
% 228.31/39.87  | | 
% 228.31/39.87  | |   (17)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 228.31/39.87  | |           e3)
% 228.31/39.87  | | 
% 228.31/39.87  | | BETA: splitting (17) gives:
% 228.31/39.87  | | 
% 228.31/39.87  | | Case 1:
% 228.31/39.87  | | | 
% 228.31/39.87  | | |   (18)  all_57_7 = e3 & op(e1, e2) = e3
% 228.31/39.87  | | | 
% 228.31/39.87  | | | ALPHA: (18) implies:
% 228.31/39.87  | | |   (19)  all_57_7 = e3
% 228.31/39.87  | | | 
% 228.31/39.87  | | | REF_CLOSE: (2), (3), (4), (5), (7), (10), (11), (14), (15), (19) are
% 228.31/39.87  | | |            inconsistent by sub-proof #2098.
% 228.31/39.87  | | | 
% 228.31/39.87  | | Case 2:
% 228.31/39.87  | | | 
% 228.31/39.87  | | |   (20)  all_57_13 = e3 & op(e0, e2) = e3
% 228.31/39.87  | | | 
% 228.31/39.87  | | | ALPHA: (20) implies:
% 228.31/39.87  | | |   (21)  all_57_13 = e3
% 228.31/39.87  | | | 
% 228.31/39.87  | | | REF_CLOSE: (1), (3), (8), (9), (11), (12), (14), (21) are inconsistent by
% 228.31/39.87  | | |            sub-proof #2215.
% 228.31/39.87  | | | 
% 228.31/39.87  | | End of split
% 228.31/39.87  | | 
% 228.31/39.87  | End of split
% 228.31/39.87  | 
% 228.31/39.87  End of proof
% 228.31/39.87  
% 228.31/39.87  Sub-proof #485 shows that the following formulas are inconsistent:
% 228.31/39.87  ----------------------------------------------------------------
% 228.31/39.87    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.31/39.87    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.31/39.87    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.31/39.87         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.31/39.87    (4)  all_57_12 = e0
% 228.31/39.87    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.31/39.87         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.31/39.87    (6)   ~ (all_53_8 = all_53_12)
% 228.31/39.87    (7)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.31/39.87         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.31/39.87    (8)   ~ (e3 = e1)
% 228.31/39.87    (9)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.31/39.87         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.31/39.87    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.31/39.87            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.31/39.87    (11)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.31/39.87          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.31/39.87    (12)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.31/39.87            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.31/39.87              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.31/39.87    (13)   ~ (all_6_2 = e3)
% 228.31/39.87    (14)  op(e1, e1) = all_6_2
% 228.31/39.87    (15)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.31/39.87    (16)   ~ (all_53_9 = e0)
% 228.31/39.87    (17)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.31/39.87          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.31/39.87    (18)   ~ (all_53_4 = all_53_12)
% 228.31/39.87    (19)   ~ (all_53_8 = all_53_9)
% 228.34/39.87    (20)  all_42_2 = all_6_2
% 228.34/39.87    (21)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.34/39.87          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.34/39.87    (22)  all_57_8 = e1
% 228.34/39.87    (23)   ~ (all_53_9 = all_6_2)
% 228.34/39.87    (24)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.34/39.87          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.34/39.87    (25)  all_57_3 = e0
% 228.34/39.87    (26)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.34/39.87          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.34/39.87    (27)   ~ (e3 = e2)
% 228.34/39.87    (28)  all_55_1 = all_53_4
% 228.34/39.87    (29)   ~ (e3 = e0)
% 228.34/39.87    (30)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.34/39.87          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.34/39.87    (31)   ~ (all_53_8 = all_6_2)
% 228.34/39.87    (32)  all_55_2 = all_53_8
% 228.34/39.87    (33)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.34/39.87    (34)  all_57_15 = e3
% 228.34/39.87    (35)  all_57_1 = e1
% 228.34/39.87    (36)  op(e3, e3) = e2
% 228.34/39.87    (37)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.34/39.87          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.34/39.87            e1)
% 228.34/39.87    (38)  all_57_10 = e2
% 228.34/39.87    (39)  all_57_5 = e3
% 228.34/39.87    (40)   ~ (all_53_4 = all_53_8)
% 228.34/39.87    (41)  op(e3, e2) = all_53_4
% 228.34/39.87    (42)   ~ (e2 = e0)
% 228.34/39.87    (43)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.34/39.87            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.34/39.87            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.34/39.87            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.34/39.87              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.34/39.87            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.34/39.87            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.34/39.87              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.34/39.87              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.34/39.87            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.34/39.87            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.34/39.87            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.34/39.87              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.34/39.87              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.34/39.87            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.34/39.87              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.34/39.87            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.34/39.87            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.34/39.87              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.34/39.87              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.34/39.87            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.34/39.87            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.34/39.87    (44)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.34/39.87          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.34/39.87    (45)   ~ (e1 = e0)
% 228.34/39.87    (46)  all_57_14 = e2
% 228.34/39.87    (47)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.34/39.87            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.34/39.87              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.34/39.87    (48)   ~ (all_53_4 = e0)
% 228.34/39.87    (49)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.34/39.87          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.34/39.87    (50)  all_57_6 = e3
% 228.34/39.87    (51)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.34/39.87          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.34/39.87    (52)  op(e0, e0) = e3
% 228.34/39.87    (53)   ~ (all_53_4 = all_53_6)
% 228.34/39.87    (54)  all_57_2 = e1
% 228.34/39.87    (55)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.34/39.87          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.34/39.87            e2)
% 228.34/39.87    (56)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.34/39.87              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.34/39.87                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.34/39.87                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.34/39.87    (57)  all_55_10 = all_6_2
% 228.34/39.87    (58)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.34/39.87          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.34/39.87    (59)  all_38_2 = all_6_2
% 228.34/39.87    (60)  all_55_3 = all_53_12
% 228.34/39.87    (61)   ~ (all_53_12 = e3)
% 228.34/39.87    (62)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.34/39.87            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.34/39.87              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.34/39.87    (63)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.34/39.87          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.34/39.87    (64)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.34/39.87          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.34/39.87    (65)   ~ (e2 = e1)
% 228.34/39.87    (66)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.34/39.87          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.34/39.87    (67)  op(e2, e1) = all_53_9
% 228.34/39.87    (68)  op(e1, e2) = all_53_6
% 228.34/39.87    (69)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.34/39.87          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.34/39.87    (70)  all_24_2 = all_6_2
% 228.34/39.87    (71)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.34/39.87          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.34/39.87    (72)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.34/39.87          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.34/39.87    (73)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.34/39.88          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.34/39.88    (74)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.34/39.88          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.34/39.88    (75)  op(e3, e1) = all_53_8
% 228.34/39.88    (76)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.34/39.88          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.34/39.88    (77)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.34/39.88          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.34/39.88    (78)  op(e3, e0) = all_53_12
% 228.34/39.88  
% 228.34/39.88  Begin of proof
% 228.34/39.88  | 
% 228.34/39.88  | BETA: splitting (44) gives:
% 228.34/39.88  | 
% 228.34/39.88  | Case 1:
% 228.34/39.88  | | 
% 228.34/39.88  | |   (79)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) =
% 228.34/39.88  | |           e3)
% 228.34/39.88  | | 
% 228.34/39.88  | | REF_CLOSE: (4), (5), (8), (27), (35), (42), (45), (50), (65), (69), (79) are
% 228.34/39.88  | |            inconsistent by sub-proof #488.
% 228.34/39.88  | | 
% 228.34/39.88  | Case 2:
% 228.34/39.88  | | 
% 228.34/39.88  | |   (80)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) =
% 228.34/39.88  | |           e3)
% 228.34/39.88  | | 
% 228.34/39.88  | | BETA: splitting (80) gives:
% 228.34/39.88  | | 
% 228.34/39.88  | | Case 1:
% 228.34/39.88  | | | 
% 228.34/39.88  | | |   (81)  all_57_4 = e3 & op(e3, e1) = e3
% 228.34/39.88  | | | 
% 228.34/39.88  | | | ALPHA: (81) implies:
% 228.34/39.88  | | |   (82)  all_57_4 = e3
% 228.34/39.88  | | | 
% 228.34/39.88  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.34/39.88  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 228.34/39.88  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 228.34/39.88  | | |            (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 228.34/39.88  | | |            (43), (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 228.34/39.88  | | |            (53), (54), (55), (56), (57), (58), (59), (60), (61), (62),
% 228.34/39.88  | | |            (63), (64), (65), (66), (67), (68), (69), (70), (71), (72),
% 228.34/39.88  | | |            (73), (74), (75), (76), (77), (78), (82) are inconsistent by
% 228.34/39.88  | | |            sub-proof #486.
% 228.34/39.88  | | | 
% 228.34/39.88  | | Case 2:
% 228.34/39.88  | | | 
% 228.34/39.88  | | |   (83)  all_57_9 = e3 & op(e3, e0) = e3
% 228.34/39.88  | | | 
% 228.34/39.88  | | | ALPHA: (83) implies:
% 228.34/39.88  | | |   (84)  op(e3, e0) = e3
% 228.34/39.88  | | | 
% 228.34/39.88  | | | REF_CLOSE: (10), (61), (78), (84) are inconsistent by sub-proof #2458.
% 228.34/39.88  | | | 
% 228.34/39.88  | | End of split
% 228.34/39.88  | | 
% 228.34/39.88  | End of split
% 228.34/39.88  | 
% 228.34/39.88  End of proof
% 228.34/39.88  
% 228.34/39.88  Sub-proof #486 shows that the following formulas are inconsistent:
% 228.34/39.88  ----------------------------------------------------------------
% 228.34/39.88    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.34/39.88    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.34/39.88    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.34/39.88         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.34/39.88    (4)  all_57_12 = e0
% 228.34/39.88    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.34/39.88         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.34/39.88    (6)   ~ (all_53_8 = all_53_12)
% 228.34/39.88    (7)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.34/39.88         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.34/39.88    (8)   ~ (e3 = e1)
% 228.34/39.88    (9)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.34/39.88         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.34/39.88    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.34/39.88            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.34/39.88    (11)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.34/39.88          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.34/39.88    (12)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.34/39.88            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.34/39.88              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.34/39.88    (13)   ~ (all_6_2 = e3)
% 228.34/39.88    (14)  op(e1, e1) = all_6_2
% 228.34/39.88    (15)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.34/39.88    (16)   ~ (all_53_9 = e0)
% 228.34/39.88    (17)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.34/39.88          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.34/39.88    (18)   ~ (all_53_4 = all_53_12)
% 228.34/39.88    (19)   ~ (all_53_8 = all_53_9)
% 228.34/39.88    (20)  all_42_2 = all_6_2
% 228.34/39.88    (21)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.34/39.88          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.34/39.88    (22)  all_57_8 = e1
% 228.34/39.88    (23)   ~ (all_53_9 = all_6_2)
% 228.34/39.88    (24)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.34/39.88          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.34/39.88    (25)  all_57_3 = e0
% 228.34/39.88    (26)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.34/39.88          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.34/39.88    (27)  all_57_4 = e3
% 228.34/39.88    (28)   ~ (e3 = e2)
% 228.34/39.88    (29)  all_55_1 = all_53_4
% 228.34/39.88    (30)   ~ (e3 = e0)
% 228.34/39.88    (31)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.34/39.88          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.34/39.88    (32)   ~ (all_53_8 = all_6_2)
% 228.34/39.88    (33)  all_55_2 = all_53_8
% 228.34/39.88    (34)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.34/39.88    (35)  all_57_15 = e3
% 228.34/39.88    (36)  all_57_1 = e1
% 228.34/39.88    (37)  op(e3, e3) = e2
% 228.34/39.88    (38)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.34/39.88          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.34/39.88            e1)
% 228.34/39.88    (39)  all_57_10 = e2
% 228.34/39.88    (40)  all_57_5 = e3
% 228.34/39.88    (41)   ~ (all_53_4 = all_53_8)
% 228.34/39.88    (42)  op(e3, e2) = all_53_4
% 228.34/39.88    (43)   ~ (e2 = e0)
% 228.34/39.88    (44)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.34/39.88            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.34/39.88            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.34/39.88            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.34/39.88              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.34/39.88            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.34/39.88            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.34/39.88              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.34/39.88              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.34/39.88            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.34/39.88            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.34/39.88            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.34/39.88              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.34/39.88              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.34/39.88            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.34/39.88              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.34/39.88            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.34/39.88            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.34/39.88              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.34/39.88              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.34/39.88            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.34/39.88            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.34/39.88    (45)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.34/39.88          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.34/39.88    (46)   ~ (e1 = e0)
% 228.34/39.88    (47)  all_57_14 = e2
% 228.34/39.88    (48)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.34/39.88            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.34/39.88              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.34/39.88    (49)   ~ (all_53_4 = e0)
% 228.34/39.88    (50)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.34/39.88          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.34/39.88    (51)  all_57_6 = e3
% 228.34/39.88    (52)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.34/39.88          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.34/39.88    (53)  op(e0, e0) = e3
% 228.34/39.88    (54)   ~ (all_53_4 = all_53_6)
% 228.34/39.88    (55)  all_57_2 = e1
% 228.34/39.88    (56)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.34/39.88          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.34/39.88            e2)
% 228.34/39.88    (57)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.34/39.88              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.34/39.88                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.34/39.88                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.34/39.88    (58)  all_55_10 = all_6_2
% 228.34/39.88    (59)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.34/39.88          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.34/39.88    (60)  all_38_2 = all_6_2
% 228.34/39.88    (61)  all_55_3 = all_53_12
% 228.34/39.88    (62)   ~ (all_53_12 = e3)
% 228.34/39.88    (63)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.34/39.88            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.34/39.88              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.34/39.88    (64)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.34/39.88          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.34/39.88    (65)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.34/39.88          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.34/39.88    (66)   ~ (e2 = e1)
% 228.34/39.88    (67)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.34/39.88          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.34/39.88    (68)  op(e2, e1) = all_53_9
% 228.34/39.88    (69)  op(e1, e2) = all_53_6
% 228.34/39.88    (70)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.34/39.88          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.34/39.88    (71)  all_24_2 = all_6_2
% 228.34/39.88    (72)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.34/39.88          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.34/39.88    (73)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.34/39.88          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.34/39.88    (74)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.34/39.88          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.34/39.88    (75)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.34/39.88          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.34/39.88    (76)  op(e3, e1) = all_53_8
% 228.34/39.88    (77)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.34/39.88          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.34/39.88    (78)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.34/39.88          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.34/39.88    (79)  op(e3, e0) = all_53_12
% 228.34/39.88  
% 228.34/39.88  Begin of proof
% 228.34/39.88  | 
% 228.34/39.88  | BETA: splitting (24) gives:
% 228.34/39.88  | 
% 228.34/39.88  | Case 1:
% 228.34/39.88  | | 
% 228.34/39.88  | |   (80)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) =
% 228.34/39.88  | |           e0)
% 228.34/39.88  | | 
% 228.34/39.88  | | BETA: splitting (80) gives:
% 228.34/39.88  | | 
% 228.34/39.88  | | Case 1:
% 228.34/39.88  | | | 
% 228.34/39.88  | | |   (81)  all_57_0 = e0 & op(e3, e3) = e0
% 228.34/39.88  | | | 
% 228.34/39.88  | | | ALPHA: (81) implies:
% 228.34/39.88  | | |   (82)  all_57_0 = e0
% 228.34/39.88  | | | 
% 228.34/39.88  | | | REF_CLOSE: (4), (5), (8), (28), (43), (46), (51), (66), (70), (82) are
% 228.34/39.88  | | |            inconsistent by sub-proof #1425.
% 228.34/39.88  | | | 
% 228.34/39.88  | | Case 2:
% 228.34/39.88  | | | 
% 228.34/39.88  | | |   (83)  all_57_1 = e0 & op(e3, e2) = e0
% 228.34/39.88  | | | 
% 228.34/39.88  | | | ALPHA: (83) implies:
% 228.34/39.88  | | |   (84)  all_57_1 = e0
% 228.34/39.88  | | | 
% 228.34/39.88  | | | COMBINE_EQS: (36), (84) imply:
% 228.34/39.88  | | |   (85)  e1 = e0
% 228.34/39.88  | | | 
% 228.34/39.88  | | | COMBINE_EQS: (55), (85) imply:
% 228.34/39.88  | | |   (86)  all_57_2 = e0
% 228.34/39.88  | | | 
% 228.34/39.88  | | | REF_CLOSE: (3), (8), (25), (28), (40), (43), (46), (64), (66), (86) are
% 228.34/39.88  | | |            inconsistent by sub-proof #2253.
% 228.34/39.88  | | | 
% 228.34/39.88  | | End of split
% 228.34/39.88  | | 
% 228.34/39.88  | Case 2:
% 228.34/39.88  | | 
% 228.34/39.88  | |   (87)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) =
% 228.34/39.88  | |           e0)
% 228.34/39.88  | | 
% 228.34/39.88  | | BETA: splitting (87) gives:
% 228.34/39.88  | | 
% 228.34/39.88  | | Case 1:
% 228.34/39.88  | | | 
% 228.34/39.88  | | |   (88)  all_57_4 = e0 & op(e3, e1) = e0
% 228.34/39.88  | | | 
% 228.34/39.88  | | | REF_CLOSE: (27), (30), (88) are inconsistent by sub-proof #2491.
% 228.34/39.88  | | | 
% 228.34/39.88  | | Case 2:
% 228.34/39.88  | | | 
% 228.34/39.88  | | |   (89)  all_57_9 = e0 & op(e3, e0) = e0
% 228.34/39.88  | | | 
% 228.34/39.88  | | | ALPHA: (89) implies:
% 228.34/39.88  | | |   (90)  all_57_9 = e0
% 228.34/39.88  | | | 
% 228.34/39.88  | | | BETA: splitting (74) gives:
% 228.34/39.88  | | | 
% 228.34/39.88  | | | Case 1:
% 228.34/39.88  | | | | 
% 228.34/39.88  | | | |   (91)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0)
% 228.34/39.88  | | | |           = e1)
% 228.34/39.88  | | | | 
% 228.34/39.88  | | | | REF_CLOSE: (3), (8), (25), (28), (39), (40), (43), (46), (55), (64),
% 228.34/39.88  | | | |            (66), (90), (91) are inconsistent by sub-proof #487.
% 228.34/39.88  | | | | 
% 228.34/39.88  | | | Case 2:
% 228.34/39.88  | | | | 
% 228.34/39.88  | | | |   (92)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0,
% 228.34/39.88  | | | |             e0) = e1)
% 228.34/39.88  | | | | 
% 228.34/39.88  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 228.34/39.88  | | | |            (12), (13), (14), (15), (16), (17), (18), (19), (20), (21),
% 228.34/39.88  | | | |            (22), (23), (24), (25), (26), (27), (28), (29), (30), (31),
% 228.34/39.88  | | | |            (32), (33), (34), (35), (36), (37), (38), (41), (42), (43),
% 228.34/39.88  | | | |            (44), (45), (46), (47), (48), (49), (50), (52), (53), (54),
% 228.34/39.88  | | | |            (56), (57), (58), (59), (60), (61), (62), (63), (64), (65),
% 228.34/39.88  | | | |            (66), (67), (68), (69), (70), (71), (72), (73), (74), (75),
% 228.34/39.88  | | | |            (76), (77), (78), (79), (92) are inconsistent by sub-proof
% 228.34/39.88  | | | |            #498.
% 228.34/39.88  | | | | 
% 228.34/39.88  | | | End of split
% 228.34/39.88  | | | 
% 228.34/39.88  | | End of split
% 228.34/39.88  | | 
% 228.34/39.88  | End of split
% 228.34/39.88  | 
% 228.34/39.88  End of proof
% 228.34/39.88  
% 228.34/39.88  Sub-proof #487 shows that the following formulas are inconsistent:
% 228.34/39.88  ----------------------------------------------------------------
% 228.34/39.88    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.34/39.88         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.34/39.88    (2)   ~ (e3 = e1)
% 228.34/39.88    (3)  all_57_3 = e0
% 228.34/39.88    (4)   ~ (e3 = e2)
% 228.34/39.88    (5)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.34/39.88    (6)  all_57_10 = e2
% 228.34/39.88    (7)  all_57_5 = e3
% 228.34/39.88    (8)  all_57_9 = e0
% 228.34/39.88    (9)   ~ (e2 = e0)
% 228.34/39.88    (10)   ~ (e1 = e0)
% 228.34/39.88    (11)  all_57_2 = e1
% 228.34/39.88    (12)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.34/39.88          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.34/39.88    (13)   ~ (e2 = e1)
% 228.34/39.88  
% 228.34/39.88  Begin of proof
% 228.34/39.88  | 
% 228.34/39.88  | BETA: splitting (5) gives:
% 228.34/39.88  | 
% 228.34/39.88  | Case 1:
% 228.34/39.88  | | 
% 228.34/39.88  | |   (14)  all_57_9 = e1 & op(e3, e0) = e1
% 228.34/39.88  | | 
% 228.34/39.88  | | ALPHA: (14) implies:
% 228.34/39.88  | |   (15)  all_57_9 = e1
% 228.34/39.88  | | 
% 228.34/39.88  | | REF_CLOSE: (1), (2), (3), (4), (7), (8), (9), (10), (11), (12), (13), (15)
% 228.34/39.88  | |            are inconsistent by sub-proof #1467.
% 228.34/39.88  | | 
% 228.34/39.88  | Case 2:
% 228.34/39.88  | | 
% 228.34/39.88  | |   (16)  all_57_10 = e1 & op(e2, e0) = e1
% 228.34/39.88  | | 
% 228.34/39.88  | | REF_CLOSE: (6), (13), (16) are inconsistent by sub-proof #2360.
% 228.34/39.88  | | 
% 228.34/39.88  | End of split
% 228.34/39.88  | 
% 228.34/39.88  End of proof
% 228.34/39.88  
% 228.34/39.88  Sub-proof #488 shows that the following formulas are inconsistent:
% 228.34/39.88  ----------------------------------------------------------------
% 228.34/39.88    (1)  all_57_12 = e0
% 228.34/39.88    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.34/39.88         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.34/39.88    (3)   ~ (e3 = e1)
% 228.34/39.88    (4)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3)
% 228.34/39.88    (5)   ~ (e3 = e2)
% 228.34/39.88    (6)  all_57_1 = e1
% 228.34/39.88    (7)   ~ (e2 = e0)
% 228.34/39.88    (8)   ~ (e1 = e0)
% 228.34/39.88    (9)  all_57_6 = e3
% 228.34/39.88    (10)   ~ (e2 = e1)
% 228.34/39.88    (11)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.34/39.88          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.34/39.88  
% 228.34/39.88  Begin of proof
% 228.34/39.88  | 
% 228.34/39.88  | BETA: splitting (4) gives:
% 228.34/39.88  | 
% 228.34/39.88  | Case 1:
% 228.34/39.88  | | 
% 228.34/39.88  | |   (12)  all_57_0 = e3 & op(e3, e3) = e3
% 228.34/39.88  | | 
% 228.34/39.88  | | ALPHA: (12) implies:
% 228.34/39.88  | |   (13)  all_57_0 = e3
% 228.34/39.88  | | 
% 228.34/39.88  | | REF_CLOSE: (1), (2), (3), (5), (7), (8), (9), (10), (11), (13) are
% 228.34/39.88  | |            inconsistent by sub-proof #2011.
% 228.34/39.88  | | 
% 228.34/39.88  | Case 2:
% 228.34/39.88  | | 
% 228.34/39.88  | |   (14)  all_57_1 = e3 & op(e3, e2) = e3
% 228.34/39.88  | | 
% 228.34/39.88  | | REF_CLOSE: (3), (6), (14) are inconsistent by sub-proof #2196.
% 228.34/39.88  | | 
% 228.34/39.88  | End of split
% 228.34/39.88  | 
% 228.34/39.88  End of proof
% 228.34/39.88  
% 228.34/39.88  Sub-proof #489 shows that the following formulas are inconsistent:
% 228.34/39.88  ----------------------------------------------------------------
% 228.34/39.88    (1)  all_57_0 = e2
% 228.34/39.88    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.34/39.88         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.34/39.88    (3)  all_57_12 = e0
% 228.34/39.88    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.34/39.88         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.34/39.88    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.34/39.88         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.34/39.88    (6)   ~ (e3 = e1)
% 228.34/39.88    (7)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.34/39.88         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.34/39.88    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.34/39.88           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.34/39.88    (9)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.34/39.88         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.34/39.88    (10)   ~ (all_6_2 = e3)
% 228.34/39.88    (11)  op(e1, e1) = all_6_2
% 228.34/39.88    (12)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.34/39.88          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.34/39.88    (13)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.34/39.88          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.34/39.88    (14)  all_57_8 = e1
% 228.34/39.88    (15)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.34/39.88          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.34/39.88    (16)  all_57_3 = e0
% 228.34/39.88    (17)   ~ (e3 = e2)
% 228.34/39.88    (18)   ~ (e3 = e0)
% 228.34/39.88    (19)  all_57_15 = e3
% 228.34/39.88    (20)  op(e3, e3) = e2
% 228.34/39.88    (21)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.34/39.88          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.34/39.88            e1)
% 228.34/39.88    (22)  all_57_5 = e3
% 228.34/39.88    (23)   ~ (e2 = e0)
% 228.34/39.88    (24)  all_57_13 = e2
% 228.34/39.88    (25)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.34/39.88          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.34/39.88    (26)   ~ (e1 = e0)
% 228.34/39.88    (27)  all_57_6 = e3
% 228.34/39.88    (28)  all_57_2 = e1
% 228.34/39.88    (29)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.34/39.88              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.34/39.88                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.34/39.88                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.34/39.88    (30)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.34/39.88          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.34/39.88    (31)   ~ (all_53_12 = e3)
% 228.34/39.88    (32)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.34/39.88          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.34/39.88    (33)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.34/39.88          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.34/39.88    (34)   ~ (e2 = e1)
% 228.34/39.88    (35)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.34/39.88          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.34/39.88    (36)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.34/39.88          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.34/39.88    (37)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.34/39.88          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.34/39.88    (38)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.34/39.88          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.34/39.88    (39)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.34/39.88          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.34/39.88    (40)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.34/39.88          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.34/39.88    (41)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.34/39.88          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.34/39.88    (42)  op(e3, e0) = all_53_12
% 228.34/39.88  
% 228.34/39.88  Begin of proof
% 228.34/39.88  | 
% 228.34/39.88  | BETA: splitting (25) gives:
% 228.34/39.88  | 
% 228.34/39.88  | Case 1:
% 228.34/39.88  | | 
% 228.34/39.88  | |   (43)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) =
% 228.34/39.88  | |           e3)
% 228.34/39.88  | | 
% 228.34/39.88  | | BETA: splitting (43) gives:
% 228.34/39.88  | | 
% 228.34/39.88  | | Case 1:
% 228.34/39.88  | | | 
% 228.34/39.88  | | |   (44)  all_57_0 = e3 & op(e3, e3) = e3
% 228.34/39.88  | | | 
% 228.34/39.88  | | | ALPHA: (44) implies:
% 228.34/39.88  | | |   (45)  all_57_0 = e3
% 228.34/39.88  | | | 
% 228.34/39.88  | | | REF_CLOSE: (3), (4), (6), (17), (23), (26), (27), (34), (36), (45) are
% 228.34/39.88  | | |            inconsistent by sub-proof #2011.
% 228.34/39.88  | | | 
% 228.34/39.88  | | Case 2:
% 228.34/39.88  | | | 
% 228.34/39.88  | | |   (46)  all_57_1 = e3 & op(e3, e2) = e3
% 228.34/39.88  | | | 
% 228.34/39.88  | | | ALPHA: (46) implies:
% 228.34/39.88  | | |   (47)  all_57_1 = e3
% 228.34/39.88  | | | 
% 228.34/39.88  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.34/39.88  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (22), (23),
% 228.34/39.88  | | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 228.34/39.88  | | |            (34), (35), (36), (38), (39), (40), (41), (42), (47) are
% 228.34/39.88  | | |            inconsistent by sub-proof #490.
% 228.34/39.88  | | | 
% 228.34/39.88  | | End of split
% 228.34/39.88  | | 
% 228.34/39.88  | Case 2:
% 228.34/39.88  | | 
% 228.34/39.88  | |   (48)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) =
% 228.34/39.88  | |           e3)
% 228.34/39.88  | | 
% 228.34/39.88  | | BETA: splitting (48) gives:
% 228.34/39.88  | | 
% 228.34/39.88  | | Case 1:
% 228.34/39.88  | | | 
% 228.34/39.88  | | |   (49)  all_57_4 = e3 & op(e3, e1) = e3
% 228.34/39.88  | | | 
% 228.34/39.88  | | | ALPHA: (49) implies:
% 228.34/39.88  | | |   (50)  all_57_4 = e3
% 228.34/39.88  | | | 
% 228.34/39.88  | | | BETA: splitting (37) gives:
% 228.34/39.88  | | | 
% 228.34/39.88  | | | Case 1:
% 228.34/39.88  | | | | 
% 228.34/39.88  | | | |   (51)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1)
% 228.34/39.88  | | | |           = e2)
% 228.34/39.88  | | | | 
% 228.34/39.88  | | | | BETA: splitting (51) gives:
% 228.34/39.88  | | | | 
% 228.34/39.88  | | | | Case 1:
% 228.34/39.88  | | | | | 
% 228.34/39.88  | | | | |   (52)  all_57_4 = e2 & op(e3, e1) = e2
% 228.34/39.88  | | | | | 
% 228.34/39.88  | | | | | ALPHA: (52) implies:
% 228.34/39.88  | | | | |   (53)  all_57_4 = e2
% 228.34/39.88  | | | | | 
% 228.34/39.88  | | | | | COMBINE_EQS: (50), (53) imply:
% 228.34/39.88  | | | | |   (54)  e3 = e2
% 228.34/39.88  | | | | | 
% 228.34/39.88  | | | | | COMBINE_EQS: (27), (54) imply:
% 228.34/39.88  | | | | |   (55)  all_57_6 = e2
% 228.34/39.88  | | | | | 
% 228.34/39.88  | | | | | REF_CLOSE: (2), (4), (5), (6), (8), (9), (10), (11), (12), (13), (15),
% 228.34/39.88  | | | | |            (16), (17), (18), (19), (20), (23), (25), (26), (29), (30),
% 228.34/39.88  | | | | |            (31), (32), (33), (34), (35), (38), (39), (40), (42), (55)
% 228.34/39.88  | | | | |            are inconsistent by sub-proof #728.
% 228.34/39.88  | | | | | 
% 228.34/39.88  | | | | Case 2:
% 228.34/39.88  | | | | | 
% 228.34/39.88  | | | | |   (56)  all_57_5 = e2 & op(e2, e1) = e2
% 228.34/39.88  | | | | | 
% 228.34/39.88  | | | | | ALPHA: (56) implies:
% 228.34/39.88  | | | | |   (57)  all_57_5 = e2
% 228.34/39.88  | | | | | 
% 228.34/39.88  | | | | | COMBINE_EQS: (22), (57) imply:
% 228.34/39.88  | | | | |   (58)  e3 = e2
% 228.34/39.88  | | | | | 
% 228.34/39.88  | | | | | COMBINE_EQS: (27), (58) imply:
% 228.34/39.88  | | | | |   (59)  all_57_6 = e2
% 228.34/39.88  | | | | | 
% 228.34/39.88  | | | | | REF_CLOSE: (2), (4), (5), (6), (8), (9), (10), (11), (12), (13), (15),
% 228.34/39.88  | | | | |            (16), (17), (18), (19), (20), (23), (25), (26), (29), (30),
% 228.34/39.88  | | | | |            (31), (32), (33), (34), (35), (38), (39), (40), (42), (59)
% 228.34/39.88  | | | | |            are inconsistent by sub-proof #728.
% 228.34/39.88  | | | | | 
% 228.34/39.88  | | | | End of split
% 228.34/39.88  | | | | 
% 228.34/39.88  | | | Case 2:
% 228.34/39.88  | | | | 
% 228.34/39.88  | | | |   (60)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1)
% 228.34/39.88  | | | |           = e2)
% 228.34/39.88  | | | | 
% 228.34/39.88  | | | | BETA: splitting (60) gives:
% 228.34/39.88  | | | | 
% 228.34/39.88  | | | | Case 1:
% 228.34/39.88  | | | | | 
% 228.34/39.88  | | | | |   (61)  all_57_8 = e2 & op(e1, e1) = e2
% 228.34/39.88  | | | | | 
% 228.34/39.88  | | | | | REF_CLOSE: (14), (34), (61) are inconsistent by sub-proof #1501.
% 228.34/39.88  | | | | | 
% 228.34/39.88  | | | | Case 2:
% 228.34/39.89  | | | | | 
% 228.34/39.89  | | | | |   (62)  all_57_14 = e2 & op(e0, e1) = e2
% 228.34/39.89  | | | | | 
% 228.34/39.89  | | | | | ALPHA: (62) implies:
% 228.34/39.89  | | | | |   (63)  all_57_14 = e2
% 228.34/39.89  | | | | | 
% 228.34/39.89  | | | | | BETA: splitting (21) gives:
% 228.34/39.89  | | | | | 
% 228.34/39.89  | | | | | Case 1:
% 228.34/39.89  | | | | | | 
% 228.34/39.89  | | | | | |   (64)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 &
% 228.34/39.89  | | | | | |           op(e0, e2) = e1)
% 228.34/39.89  | | | | | | 
% 228.34/39.89  | | | | | | BETA: splitting (64) gives:
% 228.34/39.89  | | | | | | 
% 228.34/39.89  | | | | | | Case 1:
% 228.34/39.89  | | | | | | | 
% 228.34/39.89  | | | | | | |   (65)  all_57_12 = e1 & op(e0, e3) = e1
% 228.34/39.89  | | | | | | | 
% 228.34/39.89  | | | | | | | ALPHA: (65) implies:
% 228.34/39.89  | | | | | | |   (66)  all_57_12 = e1
% 228.34/39.89  | | | | | | | 
% 228.34/39.89  | | | | | | | REF_CLOSE: (2), (6), (8), (16), (17), (18), (20), (22), (23),
% 228.34/39.89  | | | | | | |            (26), (27), (32), (34), (38), (66) are inconsistent by
% 228.34/39.89  | | | | | | |            sub-proof #810.
% 228.34/39.89  | | | | | | | 
% 228.34/39.89  | | | | | | Case 2:
% 228.34/39.89  | | | | | | | 
% 228.34/39.89  | | | | | | |   (67)  all_57_13 = e1 & op(e0, e2) = e1
% 228.34/39.89  | | | | | | | 
% 228.34/39.89  | | | | | | | REF_CLOSE: (24), (34), (67) are inconsistent by sub-proof #2205.
% 228.34/39.89  | | | | | | | 
% 228.34/39.89  | | | | | | End of split
% 228.34/39.89  | | | | | | 
% 228.34/39.89  | | | | | Case 2:
% 228.34/39.89  | | | | | | 
% 228.34/39.89  | | | | | |   (68)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 &
% 228.34/39.89  | | | | | |           op(e0, e0) = e1)
% 228.34/39.89  | | | | | | 
% 228.34/39.89  | | | | | | BETA: splitting (68) gives:
% 228.34/39.89  | | | | | | 
% 228.34/39.89  | | | | | | Case 1:
% 228.34/39.89  | | | | | | | 
% 228.34/39.89  | | | | | | |   (69)  all_57_14 = e1 & op(e0, e1) = e1
% 228.34/39.89  | | | | | | | 
% 228.34/39.89  | | | | | | | REF_CLOSE: (34), (63), (69) are inconsistent by sub-proof #2375.
% 228.34/39.89  | | | | | | | 
% 228.34/39.89  | | | | | | Case 2:
% 228.34/39.89  | | | | | | | 
% 228.34/39.89  | | | | | | |   (70)  all_57_15 = e1 & op(e0, e0) = e1
% 228.34/39.89  | | | | | | | 
% 228.34/39.89  | | | | | | | REF_CLOSE: (6), (19), (70) are inconsistent by sub-proof #2325.
% 228.34/39.89  | | | | | | | 
% 228.34/39.89  | | | | | | End of split
% 228.34/39.89  | | | | | | 
% 228.34/39.89  | | | | | End of split
% 228.34/39.89  | | | | | 
% 228.34/39.89  | | | | End of split
% 228.34/39.89  | | | | 
% 228.34/39.89  | | | End of split
% 228.34/39.89  | | | 
% 228.34/39.89  | | Case 2:
% 228.34/39.89  | | | 
% 228.34/39.89  | | |   (71)  all_57_9 = e3 & op(e3, e0) = e3
% 228.34/39.89  | | | 
% 228.34/39.89  | | | ALPHA: (71) implies:
% 228.34/39.89  | | |   (72)  op(e3, e0) = e3
% 228.34/39.89  | | | 
% 228.34/39.89  | | | REF_CLOSE: (8), (31), (42), (72) are inconsistent by sub-proof #2458.
% 228.34/39.89  | | | 
% 228.34/39.89  | | End of split
% 228.34/39.89  | | 
% 228.34/39.89  | End of split
% 228.34/39.89  | 
% 228.34/39.89  End of proof
% 228.34/39.89  
% 228.34/39.89  Sub-proof #490 shows that the following formulas are inconsistent:
% 228.34/39.89  ----------------------------------------------------------------
% 228.34/39.89    (1)  all_57_0 = e2
% 228.34/39.89    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.34/39.89         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.34/39.89    (3)  all_57_12 = e0
% 228.34/39.89    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.34/39.89         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.34/39.89    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.34/39.89         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.34/39.89    (6)   ~ (e3 = e1)
% 228.34/39.89    (7)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.34/39.89         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.34/39.89    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.34/39.89           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.34/39.89    (9)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.34/39.89         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.34/39.89    (10)   ~ (all_6_2 = e3)
% 228.34/39.89    (11)  op(e1, e1) = all_6_2
% 228.34/39.89    (12)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.34/39.89          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.34/39.89    (13)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.34/39.89          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.34/39.89    (14)  all_57_8 = e1
% 228.34/39.89    (15)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.34/39.89          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.34/39.89    (16)  all_57_3 = e0
% 228.34/39.89    (17)   ~ (e3 = e2)
% 228.34/39.89    (18)   ~ (e3 = e0)
% 228.34/39.89    (19)  all_57_15 = e3
% 228.34/39.89    (20)  op(e3, e3) = e2
% 228.34/39.89    (21)  all_57_5 = e3
% 228.34/39.89    (22)   ~ (e2 = e0)
% 228.34/39.89    (23)  all_57_13 = e2
% 228.34/39.89    (24)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.34/39.89          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.34/39.89    (25)   ~ (e1 = e0)
% 228.34/39.89    (26)  all_57_6 = e3
% 228.34/39.89    (27)  all_57_2 = e1
% 228.34/39.89    (28)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.34/39.89              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.34/39.89                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.34/39.89                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.34/39.89    (29)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.34/39.89          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.34/39.89    (30)   ~ (all_53_12 = e3)
% 228.34/39.89    (31)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.34/39.89          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.34/39.89    (32)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.34/39.89          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.34/39.89    (33)  all_57_1 = e3
% 228.34/39.89    (34)   ~ (e2 = e1)
% 228.34/39.89    (35)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.34/39.89          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.34/39.89    (36)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.34/39.89          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.34/39.89    (37)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.34/39.89          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.34/39.89    (38)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.34/39.89          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.34/39.89    (39)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.34/39.89          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.34/39.89    (40)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.34/39.89          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.34/39.89    (41)  op(e3, e0) = all_53_12
% 228.34/39.89  
% 228.34/39.89  Begin of proof
% 228.34/39.89  | 
% 228.34/39.89  | BETA: splitting (39) gives:
% 228.34/39.89  | 
% 228.34/39.89  | Case 1:
% 228.34/39.89  | | 
% 228.34/39.89  | |   (42)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) =
% 228.34/39.89  | |           e1)
% 228.34/39.89  | | 
% 228.34/39.89  | | BETA: splitting (42) gives:
% 228.34/39.89  | | 
% 228.34/39.89  | | Case 1:
% 228.34/39.89  | | | 
% 228.34/39.89  | | |   (43)  all_57_1 = e1 & op(e3, e2) = e1
% 228.34/39.89  | | | 
% 228.34/39.89  | | | REF_CLOSE: (6), (33), (43) are inconsistent by sub-proof #2453.
% 228.34/39.89  | | | 
% 228.34/39.89  | | Case 2:
% 228.34/39.89  | | | 
% 228.34/39.89  | | |   (44)  all_57_3 = e1 & op(e2, e2) = e1
% 228.34/39.89  | | | 
% 228.34/39.89  | | | REF_CLOSE: (2), (6), (16), (17), (21), (22), (25), (27), (31), (34), (44)
% 228.34/39.89  | | |            are inconsistent by sub-proof #1520.
% 228.34/39.89  | | | 
% 228.34/39.89  | | End of split
% 228.34/39.89  | | 
% 228.34/39.89  | Case 2:
% 228.34/39.89  | | 
% 228.34/39.89  | |   (45)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 228.34/39.89  | |           e1)
% 228.34/39.89  | | 
% 228.34/39.89  | | BETA: splitting (45) gives:
% 228.34/39.89  | | 
% 228.34/39.89  | | Case 1:
% 228.34/39.89  | | | 
% 228.34/39.89  | | |   (46)  all_57_7 = e1 & op(e1, e2) = e1
% 228.34/39.89  | | | 
% 228.34/39.89  | | | ALPHA: (46) implies:
% 228.34/39.89  | | |   (47)  all_57_7 = e1
% 228.34/39.89  | | | 
% 228.34/39.89  | | | BETA: splitting (40) gives:
% 228.34/39.89  | | | 
% 228.34/39.89  | | | Case 1:
% 228.34/39.89  | | | | 
% 228.34/39.89  | | | |   (48)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2)
% 228.34/39.89  | | | |           = e2)
% 228.34/39.89  | | | | 
% 228.34/39.89  | | | | BETA: splitting (48) gives:
% 228.34/39.89  | | | | 
% 228.34/39.89  | | | | Case 1:
% 228.34/39.89  | | | | | 
% 228.34/39.89  | | | | |   (49)  all_57_6 = e2 & op(e1, e3) = e2
% 228.34/39.89  | | | | | 
% 228.34/39.89  | | | | | ALPHA: (49) implies:
% 228.34/39.89  | | | | |   (50)  all_57_6 = e2
% 228.34/39.89  | | | | | 
% 228.34/39.89  | | | | | REF_CLOSE: (2), (4), (5), (6), (8), (9), (10), (11), (12), (13), (15),
% 228.34/39.89  | | | | |            (16), (17), (18), (19), (20), (22), (24), (25), (28), (29),
% 228.34/39.89  | | | | |            (30), (31), (32), (34), (35), (37), (38), (39), (41), (50)
% 228.34/39.89  | | | | |            are inconsistent by sub-proof #728.
% 228.34/39.89  | | | | | 
% 228.34/39.89  | | | | Case 2:
% 228.34/39.89  | | | | | 
% 228.34/39.89  | | | | |   (51)  all_57_7 = e2 & op(e1, e2) = e2
% 228.34/39.89  | | | | | 
% 228.34/39.89  | | | | | ALPHA: (51) implies:
% 228.34/39.89  | | | | |   (52)  all_57_7 = e2
% 228.34/39.89  | | | | | 
% 228.34/39.89  | | | | | REF_CLOSE: (34), (47), (52) are inconsistent by sub-proof #1761.
% 228.34/39.89  | | | | | 
% 228.34/39.89  | | | | End of split
% 228.34/39.89  | | | | 
% 228.34/39.89  | | | Case 2:
% 228.34/39.89  | | | | 
% 228.34/39.89  | | | |   (53)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0)
% 228.34/39.89  | | | |           = e2)
% 228.34/39.89  | | | | 
% 228.34/39.89  | | | | BETA: splitting (53) gives:
% 228.34/39.89  | | | | 
% 228.34/39.89  | | | | Case 1:
% 228.34/39.89  | | | | | 
% 228.34/39.89  | | | | |   (54)  all_57_8 = e2 & op(e1, e1) = e2
% 228.34/39.89  | | | | | 
% 228.34/39.89  | | | | | ALPHA: (54) implies:
% 228.34/39.89  | | | | |   (55)  all_57_8 = e2
% 228.34/39.89  | | | | | 
% 228.34/39.89  | | | | | REF_CLOSE: (14), (34), (55) are inconsistent by sub-proof #1485.
% 228.34/39.89  | | | | | 
% 228.34/39.89  | | | | Case 2:
% 228.34/39.89  | | | | | 
% 228.34/39.89  | | | | |   (56)  all_57_11 = e2 & op(e1, e0) = e2
% 228.34/39.89  | | | | | 
% 228.34/39.89  | | | | | ALPHA: (56) implies:
% 228.34/39.89  | | | | |   (57)  all_57_11 = e2
% 228.34/39.89  | | | | | 
% 228.34/39.89  | | | | | BETA: splitting (7) gives:
% 228.34/39.89  | | | | | 
% 228.34/39.89  | | | | | Case 1:
% 228.34/39.89  | | | | | | 
% 228.34/39.89  | | | | | |   (58)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1,
% 228.34/39.89  | | | | | |             e2) = e0)
% 228.34/39.89  | | | | | | 
% 228.34/39.89  | | | | | | REF_CLOSE: (2), (6), (16), (17), (18), (21), (22), (25), (26), (27),
% 228.34/39.89  | | | | | |            (31), (34), (47), (58) are inconsistent by sub-proof
% 228.34/39.89  | | | | | |            #493.
% 228.34/39.89  | | | | | | 
% 228.34/39.89  | | | | | Case 2:
% 228.34/39.89  | | | | | | 
% 228.34/39.89  | | | | | |   (59)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1,
% 228.34/39.89  | | | | | |             e0) = e0)
% 228.34/39.89  | | | | | | 
% 228.34/39.89  | | | | | | BETA: splitting (59) gives:
% 228.34/39.89  | | | | | | 
% 228.34/39.89  | | | | | | Case 1:
% 228.34/39.89  | | | | | | | 
% 228.34/39.89  | | | | | | |   (60)  all_57_8 = e0 & op(e1, e1) = e0
% 228.34/39.89  | | | | | | | 
% 228.34/39.89  | | | | | | | REF_CLOSE: (2), (6), (14), (16), (17), (21), (22), (25), (27),
% 228.34/39.89  | | | | | | |            (31), (34), (60) are inconsistent by sub-proof #492.
% 228.34/39.89  | | | | | | | 
% 228.34/39.89  | | | | | | Case 2:
% 228.34/39.89  | | | | | | | 
% 228.34/39.89  | | | | | | |   (61)  all_57_11 = e0 & op(e1, e0) = e0
% 228.34/39.89  | | | | | | | 
% 228.34/39.89  | | | | | | | REF_CLOSE: (1), (3), (4), (6), (17), (22), (25), (26), (34), (36),
% 228.34/39.89  | | | | | | |            (57), (61) are inconsistent by sub-proof #491.
% 228.34/39.89  | | | | | | | 
% 228.34/39.89  | | | | | | End of split
% 228.34/39.89  | | | | | | 
% 228.34/39.89  | | | | | End of split
% 228.34/39.89  | | | | | 
% 228.34/39.89  | | | | End of split
% 228.34/39.89  | | | | 
% 228.34/39.89  | | | End of split
% 228.34/39.89  | | | 
% 228.34/39.89  | | Case 2:
% 228.34/39.89  | | | 
% 228.34/39.89  | | |   (62)  all_57_13 = e1 & op(e0, e2) = e1
% 228.34/39.89  | | | 
% 228.34/39.89  | | | REF_CLOSE: (23), (34), (62) are inconsistent by sub-proof #2205.
% 228.34/39.89  | | | 
% 228.34/39.89  | | End of split
% 228.34/39.89  | | 
% 228.34/39.89  | End of split
% 228.34/39.89  | 
% 228.34/39.89  End of proof
% 228.34/39.89  
% 228.34/39.89  Sub-proof #491 shows that the following formulas are inconsistent:
% 228.34/39.89  ----------------------------------------------------------------
% 228.34/39.89    (1)  all_57_11 = e0 & op(e1, e0) = e0
% 228.34/39.89    (2)  all_57_0 = e2
% 228.34/39.89    (3)  all_57_12 = e0
% 228.34/39.89    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.34/39.89         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.34/39.89    (5)   ~ (e3 = e1)
% 228.34/39.89    (6)   ~ (e3 = e2)
% 228.34/39.89    (7)  all_57_11 = e2
% 228.34/39.89    (8)   ~ (e2 = e0)
% 228.34/39.89    (9)   ~ (e1 = e0)
% 228.34/39.89    (10)  all_57_6 = e3
% 228.34/39.89    (11)   ~ (e2 = e1)
% 228.34/39.89    (12)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.34/39.89          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.34/39.89  
% 228.34/39.89  Begin of proof
% 228.34/39.89  | 
% 228.34/39.89  | ALPHA: (1) implies:
% 228.34/39.89  |   (13)  all_57_11 = e0
% 228.34/39.89  | 
% 228.34/39.89  | COMBINE_EQS: (7), (13) imply:
% 228.34/39.89  |   (14)  e2 = e0
% 228.34/39.89  | 
% 228.34/39.89  | COMBINE_EQS: (2), (14) imply:
% 228.34/39.89  |   (15)  all_57_0 = e0
% 228.34/39.89  | 
% 228.34/39.89  | REF_CLOSE: (3), (4), (5), (6), (8), (9), (10), (11), (12), (15) are
% 228.34/39.89  |            inconsistent by sub-proof #1425.
% 228.34/39.89  | 
% 228.34/39.89  End of proof
% 228.34/39.89  
% 228.34/39.89  Sub-proof #492 shows that the following formulas are inconsistent:
% 228.34/39.89  ----------------------------------------------------------------
% 228.34/39.89    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.34/39.89         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.34/39.89    (2)   ~ (e3 = e1)
% 228.34/39.89    (3)  all_57_8 = e0 & op(e1, e1) = e0
% 228.34/39.89    (4)  all_57_8 = e1
% 228.34/39.89    (5)  all_57_3 = e0
% 228.34/39.89    (6)   ~ (e3 = e2)
% 228.34/39.89    (7)  all_57_5 = e3
% 228.34/39.89    (8)   ~ (e2 = e0)
% 228.34/39.89    (9)   ~ (e1 = e0)
% 228.34/39.89    (10)  all_57_2 = e1
% 228.34/39.89    (11)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.34/39.89          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.34/39.89    (12)   ~ (e2 = e1)
% 228.34/39.89  
% 228.34/39.89  Begin of proof
% 228.34/39.89  | 
% 228.34/39.89  | ALPHA: (3) implies:
% 228.34/39.89  |   (13)  all_57_8 = e0
% 228.34/39.89  | 
% 228.34/39.89  | COMBINE_EQS: (4), (13) imply:
% 228.34/39.89  |   (14)  e1 = e0
% 228.34/39.89  | 
% 228.34/39.89  | COMBINE_EQS: (10), (14) imply:
% 228.34/39.89  |   (15)  all_57_2 = e0
% 228.34/39.89  | 
% 228.34/39.89  | REF_CLOSE: (1), (2), (5), (6), (7), (8), (9), (11), (12), (15) are
% 228.34/39.89  |            inconsistent by sub-proof #2253.
% 228.34/39.89  | 
% 228.34/39.89  End of proof
% 228.34/39.89  
% 228.34/39.89  Sub-proof #493 shows that the following formulas are inconsistent:
% 228.34/39.89  ----------------------------------------------------------------
% 228.34/39.89    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.34/39.89         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.34/39.89    (2)   ~ (e3 = e1)
% 228.34/39.89    (3)  all_57_7 = e1
% 228.34/39.89    (4)  all_57_3 = e0
% 228.34/39.89    (5)   ~ (e3 = e2)
% 228.34/39.89    (6)   ~ (e3 = e0)
% 228.34/39.89    (7)  all_57_5 = e3
% 228.34/39.89    (8)   ~ (e2 = e0)
% 228.34/39.89    (9)   ~ (e1 = e0)
% 228.34/39.89    (10)  all_57_6 = e3
% 228.34/39.89    (11)  all_57_2 = e1
% 228.34/39.89    (12)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.34/39.89          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.34/39.89    (13)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0)
% 228.34/39.89    (14)   ~ (e2 = e1)
% 228.34/39.89  
% 228.34/39.89  Begin of proof
% 228.34/39.89  | 
% 228.34/39.89  | BETA: splitting (13) gives:
% 228.34/39.89  | 
% 228.34/39.89  | Case 1:
% 228.34/39.89  | | 
% 228.34/39.89  | |   (15)  all_57_6 = e0 & op(e1, e3) = e0
% 228.34/39.89  | | 
% 228.34/39.89  | | REF_CLOSE: (6), (10), (15) are inconsistent by sub-proof #2465.
% 228.34/39.89  | | 
% 228.34/39.89  | Case 2:
% 228.34/39.89  | | 
% 228.34/39.89  | |   (16)  all_57_7 = e0 & op(e1, e2) = e0
% 228.34/39.89  | | 
% 228.34/39.89  | | ALPHA: (16) implies:
% 228.34/39.89  | |   (17)  all_57_7 = e0
% 228.34/39.89  | | 
% 228.34/39.89  | | COMBINE_EQS: (3), (17) imply:
% 228.34/39.89  | |   (18)  e1 = e0
% 228.34/39.89  | | 
% 228.34/39.89  | | COMBINE_EQS: (11), (18) imply:
% 228.34/39.89  | |   (19)  all_57_2 = e0
% 228.34/39.89  | | 
% 228.34/39.89  | | REF_CLOSE: (1), (2), (4), (5), (7), (8), (9), (12), (14), (19) are
% 228.34/39.89  | |            inconsistent by sub-proof #2253.
% 228.34/39.89  | | 
% 228.34/39.89  | End of split
% 228.34/39.89  | 
% 228.34/39.89  End of proof
% 228.34/39.89  
% 228.34/39.89  Sub-proof #494 shows that the following formulas are inconsistent:
% 228.34/39.89  ----------------------------------------------------------------
% 228.34/39.89    (1)  all_57_0 = e2
% 228.34/39.89    (2)  all_57_12 = e0
% 228.34/39.89    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.34/39.89         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.34/39.89    (4)   ~ (e3 = e1)
% 228.34/39.89    (5)  all_57_12 = e2 & op(e0, e3) = e2
% 228.34/39.89    (6)   ~ (e3 = e2)
% 228.34/39.89    (7)   ~ (e2 = e0)
% 228.34/39.89    (8)   ~ (e1 = e0)
% 228.34/39.89    (9)  all_57_6 = e3
% 228.34/39.89    (10)   ~ (e2 = e1)
% 228.34/39.89    (11)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.34/39.89          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.34/39.89  
% 228.34/39.89  Begin of proof
% 228.34/39.89  | 
% 228.34/39.89  | ALPHA: (5) implies:
% 228.34/39.89  |   (12)  all_57_12 = e2
% 228.34/39.89  | 
% 228.34/39.89  | COMBINE_EQS: (2), (12) imply:
% 228.34/39.89  |   (13)  e2 = e0
% 228.34/39.89  | 
% 228.34/39.89  | SIMP: (13) implies:
% 228.34/39.89  |   (14)  e2 = e0
% 228.34/39.89  | 
% 228.34/39.89  | COMBINE_EQS: (1), (14) imply:
% 228.34/39.89  |   (15)  all_57_0 = e0
% 228.34/39.89  | 
% 228.34/39.89  | REF_CLOSE: (2), (3), (4), (6), (7), (8), (9), (10), (11), (15) are
% 228.34/39.89  |            inconsistent by sub-proof #1425.
% 228.34/39.89  | 
% 228.34/39.89  End of proof
% 228.34/39.89  
% 228.34/39.89  Sub-proof #495 shows that the following formulas are inconsistent:
% 228.34/39.89  ----------------------------------------------------------------
% 228.34/39.89    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.34/39.89    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.34/39.89    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.34/39.89         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.34/39.89    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.34/39.89         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.34/39.89    (5)  op(e2, e1) = e3
% 228.34/39.89    (6)   ~ (all_53_8 = all_53_12)
% 228.34/39.89    (7)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.34/39.89         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.34/39.89    (8)   ~ (e3 = e1)
% 228.34/39.89    (9)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.34/39.89         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.34/39.89    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.34/39.89            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.34/39.89    (11)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.34/39.89          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.34/39.89    (12)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.34/39.89            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.34/39.89              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.34/39.89    (13)   ~ (all_6_2 = e3)
% 228.34/39.89    (14)  op(e1, e1) = all_6_2
% 228.34/39.89    (15)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.34/39.89    (16)   ~ (all_53_9 = e0)
% 228.34/39.89    (17)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.34/39.89          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.34/39.89    (18)   ~ (all_53_4 = all_53_12)
% 228.34/39.89    (19)   ~ (all_53_8 = all_53_9)
% 228.34/39.89    (20)  all_42_2 = all_6_2
% 228.34/39.89    (21)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.34/39.89          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.34/39.89    (22)   ~ (all_53_9 = all_6_2)
% 228.34/39.89    (23)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.34/39.89          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.34/39.89    (24)  all_57_3 = e0
% 228.34/39.89    (25)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.34/39.89          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.34/39.89    (26)   ~ (e3 = e2)
% 228.34/39.89    (27)  all_55_1 = all_53_4
% 228.34/39.89    (28)   ~ (e3 = e0)
% 228.34/39.89    (29)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.34/39.89          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.34/39.89    (30)   ~ (all_53_8 = all_6_2)
% 228.34/39.89    (31)  all_55_2 = all_53_8
% 228.34/39.89    (32)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.34/39.89    (33)  all_57_15 = e3
% 228.34/39.89    (34)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.34/39.89          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.34/39.89            e1)
% 228.34/39.89    (35)  all_57_10 = e2
% 228.34/39.89    (36)  all_57_5 = e3
% 228.34/39.89    (37)   ~ (all_53_4 = all_53_8)
% 228.34/39.89    (38)  op(e3, e2) = all_53_4
% 228.34/39.89    (39)   ~ (e2 = e0)
% 228.34/39.89    (40)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.34/39.89            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.34/39.89            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.34/39.89            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.34/39.89              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.34/39.89            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.34/39.89            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.34/39.89              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.34/39.89              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.34/39.89            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.34/39.89            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.34/39.89            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.34/39.89              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.34/39.89              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.34/39.89            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.34/39.89              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.34/39.89            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.34/39.89            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.34/39.89              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.34/39.89              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.34/39.89            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.34/39.89            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.34/39.89    (41)   ~ (e1 = e0)
% 228.34/39.89    (42)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.34/39.89            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.34/39.89              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.34/39.89    (43)   ~ (all_53_4 = e0)
% 228.34/39.89    (44)  op(e0, e0) = e3
% 228.34/39.89    (45)   ~ (all_53_4 = all_53_6)
% 228.34/39.89    (46)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.34/39.89          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.34/39.89            e2)
% 228.34/39.89    (47)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.34/39.89              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.34/39.89                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.34/39.89                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.34/39.89    (48)  all_55_10 = all_6_2
% 228.34/39.89    (49)  all_38_2 = all_6_2
% 228.34/39.89    (50)  all_55_3 = all_53_12
% 228.34/39.89    (51)   ~ (all_53_12 = e3)
% 228.34/39.89    (52)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.34/39.89            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.34/39.89              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.34/39.89    (53)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.34/39.89          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.34/39.89    (54)   ~ (e2 = e1)
% 228.34/39.89    (55)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.34/39.89          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.34/39.89    (56)  op(e2, e1) = all_53_9
% 228.34/39.89    (57)  op(e1, e2) = all_53_6
% 228.34/39.90    (58)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.34/39.90          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.34/39.90    (59)  all_24_2 = all_6_2
% 228.34/39.90    (60)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.34/39.90          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.34/39.90    (61)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.34/39.90          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.34/39.90    (62)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.34/39.90          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.34/39.90    (63)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.34/39.90          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.34/39.90    (64)  op(e3, e1) = all_53_8
% 228.34/39.90    (65)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3)
% 228.34/39.90    (66)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.34/39.90          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.34/39.90    (67)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.34/39.90          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.34/39.90    (68)  op(e3, e0) = all_53_12
% 228.34/39.90  
% 228.34/39.90  Begin of proof
% 228.34/39.90  | 
% 228.34/39.90  | BETA: splitting (65) gives:
% 228.34/39.90  | 
% 228.34/39.90  | Case 1:
% 228.34/39.90  | | 
% 228.34/39.90  | |   (69)  all_57_0 = e3 & op(e3, e3) = e3
% 228.34/39.90  | | 
% 228.34/39.90  | | ALPHA: (69) implies:
% 228.34/39.90  | |   (70)  all_57_0 = e3
% 228.34/39.90  | |   (71)  op(e3, e3) = e3
% 228.34/39.90  | | 
% 228.34/39.90  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.34/39.90  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 228.34/39.90  | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 228.34/39.90  | |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 228.34/39.90  | |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 228.34/39.90  | |            (58), (59), (60), (61), (62), (63), (64), (66), (67), (68), (70),
% 228.34/39.90  | |            (71) are inconsistent by sub-proof #1440.
% 228.34/39.90  | | 
% 228.34/39.90  | Case 2:
% 228.34/39.90  | | 
% 228.34/39.90  | |   (72)  all_57_2 = e3 & op(e2, e3) = e3
% 228.34/39.90  | | 
% 228.34/39.90  | | ALPHA: (72) implies:
% 228.34/39.90  | |   (73)  all_57_2 = e3
% 228.34/39.90  | | 
% 228.34/39.90  | | REF_CLOSE: (3), (8), (24), (35), (36), (41), (54), (73) are inconsistent by
% 228.34/39.90  | |            sub-proof #1804.
% 228.34/39.90  | | 
% 228.34/39.90  | End of split
% 228.34/39.90  | 
% 228.34/39.90  End of proof
% 228.34/39.90  
% 228.34/39.90  Sub-proof #496 shows that the following formulas are inconsistent:
% 228.34/39.90  ----------------------------------------------------------------
% 228.34/39.90    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.34/39.90    (2)  all_57_0 = e2
% 228.34/39.90    (3)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.34/39.90    (4)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.34/39.90         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.34/39.90    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.34/39.90         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.34/39.90    (6)   ~ (all_53_8 = all_53_12)
% 228.34/39.90    (7)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.34/39.90         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.34/39.90    (8)   ~ (e3 = e1)
% 228.34/39.90    (9)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.34/39.90         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.34/39.90    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.34/39.90            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.34/39.90    (11)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.34/39.90          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.34/39.90    (12)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.34/39.90            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.34/39.90              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.34/39.90    (13)   ~ (all_6_2 = e3)
% 228.34/39.90    (14)  op(e1, e1) = all_6_2
% 228.34/39.90    (15)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.34/39.90    (16)   ~ (all_53_9 = e0)
% 228.34/39.90    (17)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.34/39.90          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.34/39.90    (18)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 228.34/39.90            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 228.34/39.90              e3) = all_22_1 & $i(all_22_1))
% 228.34/39.90    (19)   ~ (all_53_4 = all_53_12)
% 228.34/39.90    (20)   ~ (all_53_8 = all_53_9)
% 228.34/39.90    (21)  all_42_2 = all_6_2
% 228.34/39.90    (22)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.34/39.90          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.34/39.90    (23)  all_57_8 = e1
% 228.34/39.90    (24)   ~ (all_53_9 = all_6_2)
% 228.34/39.90    (25)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.34/39.90          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.34/39.90    (26)  all_57_3 = e0
% 228.34/39.90    (27)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.34/39.90          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.34/39.90    (28)   ~ (e3 = e2)
% 228.34/39.90    (29)  all_55_1 = all_53_4
% 228.34/39.90    (30)   ~ (e3 = e0)
% 228.34/39.90    (31)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.34/39.90          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.34/39.90    (32)   ~ (all_53_8 = all_6_2)
% 228.34/39.90    (33)  all_55_2 = all_53_8
% 228.34/39.90    (34)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.34/39.90    (35)  all_57_15 = e3
% 228.34/39.90    (36)  op(e3, e3) = e2
% 228.34/39.90    (37)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.34/39.90          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.34/39.90            e1)
% 228.34/39.90    (38)   ~ (all_53_4 = all_53_8)
% 228.34/39.90    (39)  op(e3, e2) = all_53_4
% 228.34/39.90    (40)   ~ (e2 = e0)
% 228.34/39.90    (41)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.34/39.90            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.34/39.90            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.34/39.90            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.34/39.90              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.34/39.90            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.34/39.90            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.34/39.90              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.34/39.90              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.34/39.90            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.34/39.90            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.34/39.90            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.34/39.90              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.34/39.90              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.34/39.90            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.34/39.90              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.34/39.90            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.34/39.90            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.34/39.90              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.34/39.90              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.34/39.90            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.34/39.90            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.34/39.90    (42)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 228.34/39.90            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 228.34/39.90              e3) = all_12_1 & $i(all_12_1))
% 228.34/39.90    (43)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.34/39.90          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.34/39.90    (44)   ~ (e1 = e0)
% 228.34/39.90    (45)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.34/39.90            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.34/39.90              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.34/39.90    (46)  all_57_5 = e2
% 228.34/39.90    (47)   ~ (all_53_4 = e0)
% 228.34/39.90    (48)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.34/39.90          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.34/39.90    (49)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.34/39.90          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.34/39.90    (50)  op(e0, e0) = e3
% 228.34/39.90    (51)   ~ (all_53_4 = all_53_6)
% 228.34/39.90    (52)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.34/39.90          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.34/39.90            e2)
% 228.34/39.90    (53)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.34/39.90              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.34/39.90                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.34/39.90                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.34/39.90    (54)  all_55_10 = all_6_2
% 228.34/39.90    (55)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.34/39.90          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.34/39.90    (56)  all_38_2 = all_6_2
% 228.34/39.90    (57)  all_55_3 = all_53_12
% 228.34/39.90    (58)   ~ (all_53_12 = e3)
% 228.34/39.90    (59)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.34/39.90            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.34/39.90              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.34/39.90    (60)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.34/39.90          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.34/39.90    (61)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.34/39.90          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.34/39.90    (62)   ~ (e2 = e1)
% 228.34/39.90    (63)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.34/39.90          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.34/39.90    (64)  op(e2, e1) = all_53_9
% 228.34/39.90    (65)  op(e1, e2) = all_53_6
% 228.34/39.90    (66)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.34/39.90          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.34/39.90    (67)  all_24_2 = all_6_2
% 228.34/39.90    (68)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.34/39.90          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.34/39.90    (69)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.34/39.90          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.34/39.90    (70)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.34/39.90          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.34/39.90    (71)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.34/39.90          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.34/39.90    (72)  op(e3, e1) = all_53_8
% 228.34/39.90    (73)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.34/39.90          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.34/39.91    (74)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.34/39.91          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.34/39.91    (75)  op(e3, e0) = all_53_12
% 228.34/39.91  
% 228.34/39.91  Begin of proof
% 228.34/39.91  | 
% 228.34/39.91  | BETA: splitting (55) gives:
% 228.34/39.91  | 
% 228.34/39.91  | Case 1:
% 228.34/39.91  | | 
% 228.34/39.91  | |   (76)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 228.34/39.91  | |           e3)
% 228.34/39.91  | | 
% 228.34/39.91  | | BETA: splitting (76) gives:
% 228.34/39.91  | | 
% 228.34/39.91  | | Case 1:
% 228.34/39.91  | | | 
% 228.34/39.91  | | |   (77)  all_57_2 = e3 & op(e2, e3) = e3
% 228.34/39.91  | | | 
% 228.34/39.91  | | | ALPHA: (77) implies:
% 228.34/39.91  | | |   (78)  all_57_2 = e3
% 228.34/39.91  | | | 
% 228.34/39.91  | | | BETA: splitting (63) gives:
% 228.34/39.91  | | | 
% 228.34/39.91  | | | Case 1:
% 228.34/39.91  | | | | 
% 228.34/39.91  | | | |   (79)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0)
% 228.34/39.91  | | | |           = e2)
% 228.34/39.91  | | | | 
% 228.34/39.91  | | | | BETA: splitting (79) gives:
% 228.34/39.91  | | | | 
% 228.34/39.91  | | | | Case 1:
% 228.34/39.91  | | | | | 
% 228.34/39.91  | | | | |   (80)  all_57_9 = e2 & op(e3, e0) = e2
% 228.34/39.91  | | | | | 
% 228.34/39.91  | | | | | ALPHA: (80) implies:
% 228.34/39.91  | | | | |   (81)  all_57_9 = e2
% 228.34/39.91  | | | | | 
% 228.34/39.91  | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.34/39.91  | | | | |            (13), (14), (15), (16), (17), (19), (20), (21), (22), (24),
% 228.34/39.91  | | | | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 228.34/39.91  | | | | |            (35), (36), (37), (38), (39), (40), (41), (43), (44), (45),
% 228.34/39.91  | | | | |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (55),
% 228.34/39.91  | | | | |            (56), (57), (58), (59), (60), (61), (62), (63), (64), (65),
% 228.34/39.91  | | | | |            (66), (67), (68), (69), (70), (71), (72), (73), (74), (75),
% 228.34/39.91  | | | | |            (78), (81) are inconsistent by sub-proof #527.
% 228.34/39.91  | | | | | 
% 228.34/39.91  | | | | Case 2:
% 228.34/39.91  | | | | | 
% 228.34/39.91  | | | | |   (82)  all_57_10 = e2 & op(e2, e0) = e2
% 228.34/39.91  | | | | | 
% 228.34/39.91  | | | | | ALPHA: (82) implies:
% 228.34/39.91  | | | | |   (83)  all_57_10 = e2
% 228.34/39.91  | | | | | 
% 228.34/39.91  | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.34/39.91  | | | | |            (13), (14), (15), (16), (17), (19), (20), (21), (22), (23),
% 228.34/39.91  | | | | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 228.34/39.91  | | | | |            (34), (35), (36), (37), (38), (39), (40), (41), (43), (44),
% 228.34/39.91  | | | | |            (45), (47), (48), (49), (50), (51), (52), (53), (54), (55),
% 228.34/39.91  | | | | |            (56), (57), (58), (59), (60), (61), (62), (63), (64), (65),
% 228.34/39.91  | | | | |            (66), (67), (68), (69), (70), (71), (72), (73), (74), (75),
% 228.34/39.91  | | | | |            (78), (83) are inconsistent by sub-proof #501.
% 228.34/39.91  | | | | | 
% 228.34/39.91  | | | | End of split
% 228.34/39.91  | | | | 
% 228.34/39.91  | | | Case 2:
% 228.34/39.91  | | | | 
% 228.34/39.91  | | | |   (84)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0,
% 228.34/39.91  | | | |             e0) = e2)
% 228.34/39.91  | | | | 
% 228.34/39.91  | | | | BETA: splitting (84) gives:
% 228.34/39.91  | | | | 
% 228.34/39.91  | | | | Case 1:
% 228.34/39.91  | | | | | 
% 228.34/39.91  | | | | |   (85)  all_57_11 = e2 & op(e1, e0) = e2
% 228.34/39.91  | | | | | 
% 228.34/39.91  | | | | | ALPHA: (85) implies:
% 228.34/39.91  | | | | |   (86)  all_57_11 = e2
% 228.34/39.91  | | | | |   (87)  op(e1, e0) = e2
% 228.34/39.91  | | | | | 
% 228.34/39.91  | | | | | BETA: splitting (53) gives:
% 228.34/39.91  | | | | | 
% 228.34/39.91  | | | | | Case 1:
% 228.34/39.91  | | | | | | 
% 228.34/39.91  | | | | | |   (88)  all_57_15 = e0 & op(e0, e0) = e0
% 228.34/39.91  | | | | | | 
% 228.34/39.91  | | | | | | ALPHA: (88) implies:
% 228.34/39.91  | | | | | |   (89)  op(e0, e0) = e0
% 228.34/39.91  | | | | | | 
% 228.34/39.91  | | | | | | REF_CLOSE: (10), (30), (50), (89) are inconsistent by sub-proof
% 228.34/39.91  | | | | | |            #2304.
% 228.34/39.91  | | | | | | 
% 228.34/39.91  | | | | | Case 2:
% 228.34/39.91  | | | | | | 
% 228.34/39.91  | | | | | |   (90)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 &
% 228.34/39.91  | | | | | |             op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) &
% 228.34/39.91  | | | | | |         ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.34/39.91  | | | | | |             op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 228.34/39.91  | | | | | | 
% 228.34/39.91  | | | | | | ALPHA: (90) implies:
% 228.34/39.91  | | | | | |   (91)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2,
% 228.34/39.91  | | | | | |             e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.34/39.91  | | | | | | 
% 228.34/39.91  | | | | | | BETA: splitting (5) gives:
% 228.34/39.91  | | | | | | 
% 228.34/39.91  | | | | | | Case 1:
% 228.34/39.91  | | | | | | | 
% 228.34/39.91  | | | | | | |   (92)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 &
% 228.34/39.91  | | | | | | |           op(e2, e3) = e1)
% 228.34/39.91  | | | | | | | 
% 228.34/39.91  | | | | | | | REF_CLOSE: (8), (10), (36), (62), (78), (92) are inconsistent by
% 228.34/39.91  | | | | | | |            sub-proof #753.
% 228.34/39.91  | | | | | | | 
% 228.34/39.91  | | | | | | Case 2:
% 228.34/39.91  | | | | | | | 
% 228.34/39.91  | | | | | | |   (93)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 &
% 228.34/39.91  | | | | | | |           op(e0, e3) = e1)
% 228.34/39.91  | | | | | | | 
% 228.34/39.91  | | | | | | | BETA: splitting (93) gives:
% 228.34/39.91  | | | | | | | 
% 228.34/39.91  | | | | | | | Case 1:
% 228.34/39.91  | | | | | | | | 
% 228.34/39.91  | | | | | | | |   (94)  all_57_6 = e1 & op(e1, e3) = e1
% 228.34/39.91  | | | | | | | | 
% 228.34/39.91  | | | | | | | | ALPHA: (94) implies:
% 228.34/39.91  | | | | | | | |   (95)  all_57_6 = e1
% 228.34/39.91  | | | | | | | | 
% 228.34/39.91  | | | | | | | | BETA: splitting (4) gives:
% 228.34/39.91  | | | | | | | | 
% 228.34/39.91  | | | | | | | | Case 1:
% 228.34/39.91  | | | | | | | | | 
% 228.34/39.91  | | | | | | | | |   (96)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 &
% 228.34/39.91  | | | | | | | | |           op(e2, e2) = e1)
% 228.34/39.91  | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | BETA: splitting (96) gives:
% 228.34/39.91  | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | Case 1:
% 228.34/39.91  | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | |   (97)  all_57_2 = e1 & op(e2, e3) = e1
% 228.34/39.91  | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | REF_CLOSE: (8), (78), (97) are inconsistent by sub-proof
% 228.34/39.91  | | | | | | | | | |            #1928.
% 228.34/39.91  | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | Case 2:
% 228.34/39.91  | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | |   (98)  all_57_3 = e1 & op(e2, e2) = e1
% 228.34/39.91  | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | REF_CLOSE: (26), (44), (98) are inconsistent by sub-proof
% 228.34/39.91  | | | | | | | | | |            #2252.
% 228.34/39.91  | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | End of split
% 228.34/39.91  | | | | | | | | | 
% 228.34/39.91  | | | | | | | | Case 2:
% 228.34/39.91  | | | | | | | | | 
% 228.34/39.91  | | | | | | | | |   (99)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 &
% 228.34/39.91  | | | | | | | | |           op(e2, e0) = e1)
% 228.34/39.91  | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | BETA: splitting (99) gives:
% 228.34/39.91  | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | Case 1:
% 228.34/39.91  | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | |   (100)  all_57_5 = e1 & op(e2, e1) = e1
% 228.34/39.91  | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | REF_CLOSE: (46), (62), (100) are inconsistent by sub-proof
% 228.34/39.91  | | | | | | | | | |            #1886.
% 228.34/39.91  | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | Case 2:
% 228.34/39.91  | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | |   (101)  all_57_10 = e1 & op(e2, e0) = e1
% 228.34/39.91  | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | ALPHA: (101) implies:
% 228.34/39.91  | | | | | | | | | |   (102)  all_57_10 = e1
% 228.34/39.91  | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | BETA: splitting (69) gives:
% 228.34/39.91  | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | Case 1:
% 228.34/39.91  | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | |   (103)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 228.34/39.91  | | | | | | | | | | |            & op(e2, e3) = e0)
% 228.34/39.91  | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | REF_CLOSE: (4), (8), (10), (26), (28), (30), (36), (40),
% 228.34/39.91  | | | | | | | | | | |            (44), (55), (60), (62), (103) are inconsistent by
% 228.34/39.91  | | | | | | | | | | |            sub-proof #1654.
% 228.34/39.91  | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | Case 2:
% 228.34/39.91  | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | |   (104)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 228.34/39.91  | | | | | | | | | | |            e0 & op(e0, e3) = e0)
% 228.34/39.91  | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | BETA: splitting (104) gives:
% 228.34/39.91  | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | Case 1:
% 228.34/39.91  | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | |   (105)  all_57_6 = e0 & op(e1, e3) = e0
% 228.34/39.91  | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | REF_CLOSE: (44), (95), (105) are inconsistent by sub-proof
% 228.34/39.91  | | | | | | | | | | | |            #2347.
% 228.34/39.91  | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | Case 2:
% 228.34/39.91  | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | |   (106)  all_57_12 = e0 & op(e0, e3) = e0
% 228.34/39.91  | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | ALPHA: (106) implies:
% 228.34/39.91  | | | | | | | | | | | |   (107)  all_57_12 = e0
% 228.34/39.91  | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | BETA: splitting (91) gives:
% 228.34/39.91  | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | Case 1:
% 228.34/39.91  | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | |   (108)  all_57_9 = e0 & op(e3, e0) = e0
% 228.34/39.91  | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | ALPHA: (108) implies:
% 228.34/39.91  | | | | | | | | | | | | |   (109)  all_57_9 = e0
% 228.34/39.91  | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | BETA: splitting (48) gives:
% 228.34/39.91  | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | Case 1:
% 228.34/39.91  | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | |   (110)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 228.34/39.91  | | | | | | | | | | | | | |            & op(e2, e1) = e3)
% 228.34/39.91  | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | BETA: splitting (110) gives:
% 228.34/39.91  | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | Case 1:
% 228.34/39.91  | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | |   (111)  all_57_4 = e3 & op(e3, e1) = e3
% 228.34/39.91  | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | | ALPHA: (111) implies:
% 228.34/39.91  | | | | | | | | | | | | | | |   (112)  all_57_4 = e3
% 228.34/39.91  | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | | BETA: splitting (11) gives:
% 228.34/39.91  | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | | Case 1:
% 228.34/39.91  | | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | | |   (113)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 228.34/39.91  | | | | | | | | | | | | | | | |            & op(e1, e2) = e3)
% 228.34/39.91  | | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | | | BETA: splitting (113) gives:
% 228.34/39.91  | | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | | | Case 1:
% 228.34/39.91  | | | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | | | |   (114)  all_57_6 = e3 & op(e1, e3) = e3
% 228.34/39.91  | | | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | | | | ALPHA: (114) implies:
% 228.34/39.91  | | | | | | | | | | | | | | | | |   (115)  all_57_6 = e3
% 228.34/39.91  | | | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (5), (8), (44), (62), (78), (107), (115) are
% 228.34/39.91  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1535.
% 228.34/39.91  | | | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | | | Case 2:
% 228.34/39.91  | | | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | | | |   (116)  all_57_7 = e3 & op(e1, e2) = e3
% 228.34/39.91  | | | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | | | | ALPHA: (116) implies:
% 228.34/39.91  | | | | | | | | | | | | | | | | |   (117)  all_57_7 = e3
% 228.34/39.91  | | | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | | | | BETA: splitting (17) gives:
% 228.34/39.91  | | | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | | | | Case 1:
% 228.34/39.91  | | | | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | | | | |   (118)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 228.34/39.91  | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e1)
% 228.34/39.91  | | | | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | | | | | BETA: splitting (118) gives:
% 228.34/39.91  | | | | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | | | | | Case 1:
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | | | | | |   (119)  all_57_0 = e1 & op(e3, e3) = e1
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | ALPHA: (119) implies:
% 228.34/39.91  | | | | | | | | | | | | | | | | | | |   (120)  op(e3, e3) = e1
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (36), (62), (120) are inconsistent by
% 228.34/39.91  | | | | | | | | | | | | | | | | | | |            sub-proof #1950.
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | | | | | Case 2:
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | | | | | |   (121)  all_57_1 = e1 & op(e3, e2) = e1
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | ALPHA: (121) implies:
% 228.34/39.91  | | | | | | | | | | | | | | | | | | |   (122)  all_57_1 = e1
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | BETA: splitting (9) gives:
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | Case 1:
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | |   (123)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e0)
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | BETA: splitting (123) gives:
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | Case 1:
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | |   (124)  all_57_6 = e0 & op(e1, e3) = e0
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | | ALPHA: (124) implies:
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | |   (125)  all_57_6 = e0
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (95), (125) imply:
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | |   (126)  e1 = e0
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | | SIMP: (126) implies:
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | |   (127)  e1 = e0
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (122), (127) imply:
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | |   (128)  all_57_1 = e0
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (10), (11), (13), (14), (26), (28),
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | |            (30), (35), (40), (44), (53), (55), (60), (62),
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | |            (63), (70), (73), (78), (125), (128) are
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #826.
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | Case 2:
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | |   (129)  all_57_7 = e0 & op(e1, e2) = e0
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | | ALPHA: (129) implies:
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | |   (130)  all_57_7 = e0
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (117), (130) imply:
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | |   (131)  e3 = e0
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (78), (131) imply:
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | |   (132)  all_57_2 = e0
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (26), (28), (30), (40), (44), (55),
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | |            (60), (62), (132) are inconsistent by sub-proof
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | |            #2246.
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | End of split
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | Case 2:
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | |   (133)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | BETA: splitting (133) gives:
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | Case 1:
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | |   (134)  all_57_8 = e0 & op(e1, e1) = e0
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | | ALPHA: (134) implies:
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | |   (135)  all_57_8 = e0
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (23), (135) imply:
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | |   (136)  e1 = e0
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (26), (28), (40), (44), (62), (73),
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | |            (117), (122), (136) are inconsistent by sub-proof
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | |            #1626.
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | Case 2:
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | |   (137)  all_57_11 = e0 & op(e1, e0) = e0
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | | ALPHA: (137) implies:
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | |   (138)  all_57_11 = e0
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (40), (86), (138) are inconsistent by sub-proof
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | |            #1949.
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | End of split
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | End of split
% 228.34/39.91  | | | | | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | | | | | End of split
% 228.34/39.91  | | | | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | | | | Case 2:
% 228.34/39.91  | | | | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | | | | |   (139)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 228.34/39.91  | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e1)
% 228.34/39.91  | | | | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (44), (109), (112), (139) are inconsistent by
% 228.34/39.91  | | | | | | | | | | | | | | | | | |            sub-proof #2478.
% 228.34/39.91  | | | | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | | | | End of split
% 228.34/39.91  | | | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | | | End of split
% 228.34/39.91  | | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | | Case 2:
% 228.34/39.91  | | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | | |   (140)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 228.34/39.91  | | | | | | | | | | | | | | | |            e3 & op(e1, e0) = e3)
% 228.34/39.91  | | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10), (13), (14), (28), (35), (40), (44),
% 228.34/39.91  | | | | | | | | | | | | | | | |            (62), (63), (70), (109), (140) are inconsistent by
% 228.34/39.91  | | | | | | | | | | | | | | | |            sub-proof #781.
% 228.34/39.91  | | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | | End of split
% 228.34/39.91  | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | Case 2:
% 228.34/39.91  | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | |   (141)  all_57_5 = e3 & op(e2, e1) = e3
% 228.34/39.91  | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10),
% 228.34/39.91  | | | | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (19),
% 228.34/39.91  | | | | | | | | | | | | | | |            (20), (21), (22), (24), (25), (26), (27), (28),
% 228.34/39.91  | | | | | | | | | | | | | | |            (29), (30), (31), (32), (33), (34), (35), (36),
% 228.34/39.91  | | | | | | | | | | | | | | |            (37), (38), (39), (40), (41), (44), (45), (46),
% 228.34/39.91  | | | | | | | | | | | | | | |            (47), (50), (51), (52), (53), (54), (56), (57),
% 228.34/39.91  | | | | | | | | | | | | | | |            (58), (59), (60), (61), (62), (63), (64), (65),
% 228.34/39.91  | | | | | | | | | | | | | | |            (66), (67), (68), (69), (70), (71), (72), (73),
% 228.34/39.91  | | | | | | | | | | | | | | |            (74), (75), (78), (141) are inconsistent by
% 228.34/39.91  | | | | | | | | | | | | | | |            sub-proof #531.
% 228.34/39.91  | | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | End of split
% 228.34/39.91  | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | Case 2:
% 228.34/39.91  | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | |   (142)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 228.34/39.91  | | | | | | | | | | | | | |            e3 & op(e0, e1) = e3)
% 228.34/39.91  | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | REF_CLOSE: (8), (10), (13), (14), (28), (35), (37), (40),
% 228.34/39.91  | | | | | | | | | | | | | |            (44), (52), (62), (107), (142) are inconsistent by
% 228.34/39.91  | | | | | | | | | | | | | |            sub-proof #530.
% 228.34/39.91  | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | End of split
% 228.34/39.91  | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | Case 2:
% 228.34/39.91  | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | |   (143)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 =
% 228.34/39.91  | | | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 228.34/39.91  | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | BETA: splitting (143) gives:
% 228.34/39.91  | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | Case 1:
% 228.34/39.91  | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | |   (144)  all_57_10 = e0 & op(e2, e0) = e0
% 228.34/39.91  | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | ALPHA: (144) implies:
% 228.34/39.91  | | | | | | | | | | | | | |   (145)  all_57_10 = e0
% 228.34/39.91  | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | REF_CLOSE: (44), (102), (145) are inconsistent by sub-proof
% 228.34/39.91  | | | | | | | | | | | | | |            #1531.
% 228.34/39.91  | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | Case 2:
% 228.34/39.91  | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | |   (146)  all_57_11 = e0 & op(e1, e0) = e0
% 228.34/39.91  | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | | REF_CLOSE: (40), (86), (146) are inconsistent by sub-proof
% 228.34/39.91  | | | | | | | | | | | | | |            #2041.
% 228.34/39.91  | | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | | End of split
% 228.34/39.91  | | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | | End of split
% 228.34/39.91  | | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | | End of split
% 228.34/39.91  | | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | | End of split
% 228.34/39.91  | | | | | | | | | | 
% 228.34/39.91  | | | | | | | | | End of split
% 228.34/39.91  | | | | | | | | | 
% 228.34/39.91  | | | | | | | | End of split
% 228.34/39.91  | | | | | | | | 
% 228.34/39.91  | | | | | | | Case 2:
% 228.34/39.91  | | | | | | | | 
% 228.34/39.91  | | | | | | | |   (147)  all_57_12 = e1 & op(e0, e3) = e1
% 228.34/39.91  | | | | | | | | 
% 228.34/39.91  | | | | | | | | ALPHA: (147) implies:
% 228.34/39.91  | | | | | | | |   (148)  op(e0, e3) = e1
% 228.34/39.91  | | | | | | | | 
% 228.34/39.91  | | | | | | | | REF_CLOSE: (10), (18), (42), (87), (148) are inconsistent by
% 228.34/39.91  | | | | | | | |            sub-proof #1147.
% 228.34/39.91  | | | | | | | | 
% 228.34/39.91  | | | | | | | End of split
% 228.34/39.91  | | | | | | | 
% 228.34/39.91  | | | | | | End of split
% 228.34/39.91  | | | | | | 
% 228.34/39.91  | | | | | End of split
% 228.34/39.91  | | | | | 
% 228.34/39.91  | | | | Case 2:
% 228.34/39.91  | | | | | 
% 228.34/39.91  | | | | |   (149)  all_57_15 = e2 & op(e0, e0) = e2
% 228.34/39.91  | | | | | 
% 228.34/39.91  | | | | | ALPHA: (149) implies:
% 228.34/39.91  | | | | |   (150)  all_57_15 = e2
% 228.34/39.91  | | | | | 
% 228.34/39.91  | | | | | COMBINE_EQS: (35), (150) imply:
% 228.34/39.91  | | | | |   (151)  e3 = e2
% 228.34/39.91  | | | | | 
% 228.34/39.91  | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.34/39.91  | | | | |            (13), (14), (15), (16), (17), (19), (20), (21), (22), (24),
% 228.34/39.91  | | | | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 228.34/39.91  | | | | |            (35), (36), (37), (38), (39), (40), (41), (43), (44), (45),
% 228.34/39.91  | | | | |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56),
% 228.34/39.91  | | | | |            (57), (58), (59), (60), (61), (62), (63), (64), (65), (66),
% 228.34/39.91  | | | | |            (67), (68), (69), (70), (71), (72), (73), (74), (75), (78),
% 228.34/39.91  | | | | |            (151) are inconsistent by sub-proof #534.
% 228.34/39.91  | | | | | 
% 228.34/39.91  | | | | End of split
% 228.34/39.91  | | | | 
% 228.34/39.91  | | | End of split
% 228.34/39.91  | | | 
% 228.34/39.91  | | Case 2:
% 228.34/39.91  | | | 
% 228.34/39.91  | | |   (152)  all_57_3 = e3 & op(e2, e2) = e3
% 228.34/39.91  | | | 
% 228.34/39.91  | | | ALPHA: (152) implies:
% 228.34/39.91  | | |   (153)  all_57_3 = e3
% 228.34/39.91  | | | 
% 228.34/39.91  | | | REF_CLOSE: (26), (30), (153) are inconsistent by sub-proof #2358.
% 228.34/39.91  | | | 
% 228.34/39.91  | | End of split
% 228.34/39.91  | | 
% 228.34/39.91  | Case 2:
% 228.34/39.91  | | 
% 228.34/39.91  | |   (154)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 228.34/39.91  | |            e3)
% 228.34/39.91  | | 
% 228.34/39.91  | | BETA: splitting (154) gives:
% 228.34/39.91  | | 
% 228.34/39.91  | | Case 1:
% 228.34/39.91  | | | 
% 228.34/39.91  | | |   (155)  all_57_5 = e3 & op(e2, e1) = e3
% 228.34/39.91  | | | 
% 228.34/39.91  | | | REF_CLOSE: (28), (46), (155) are inconsistent by sub-proof #1893.
% 228.34/39.91  | | | 
% 228.34/39.91  | | Case 2:
% 228.34/39.91  | | | 
% 228.34/39.91  | | |   (156)  all_57_10 = e3 & op(e2, e0) = e3
% 228.34/39.91  | | | 
% 228.34/39.91  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.34/39.91  | | |            (13), (14), (15), (16), (17), (19), (20), (21), (22), (23),
% 228.34/39.91  | | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 228.34/39.91  | | |            (34), (35), (36), (37), (38), (39), (40), (41), (43), (44),
% 228.34/39.91  | | |            (45), (47), (48), (49), (50), (51), (52), (53), (54), (55),
% 228.34/39.91  | | |            (56), (57), (58), (59), (60), (61), (62), (63), (64), (65),
% 228.34/39.91  | | |            (66), (67), (68), (69), (70), (71), (72), (73), (74), (75),
% 228.34/39.91  | | |            (156) are inconsistent by sub-proof #497.
% 228.34/39.91  | | | 
% 228.34/39.91  | | End of split
% 228.34/39.91  | | 
% 228.34/39.91  | End of split
% 228.34/39.91  | 
% 228.34/39.91  End of proof
% 228.34/39.91  
% 228.34/39.91  Sub-proof #497 shows that the following formulas are inconsistent:
% 228.34/39.91  ----------------------------------------------------------------
% 228.34/39.91    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.34/39.91    (2)  all_57_0 = e2
% 228.34/39.91    (3)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.34/39.91    (4)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.34/39.91         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.34/39.91    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.34/39.91         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.34/39.91    (6)   ~ (all_53_8 = all_53_12)
% 228.34/39.91    (7)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.34/39.91         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.34/39.91    (8)   ~ (e3 = e1)
% 228.34/39.91    (9)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.34/39.91         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.34/39.91    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.34/39.91            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.34/39.91    (11)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.34/39.91          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.34/39.91    (12)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.34/39.91            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.34/39.91              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.34/39.91    (13)   ~ (all_6_2 = e3)
% 228.34/39.91    (14)  op(e1, e1) = all_6_2
% 228.34/39.91    (15)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.34/39.91    (16)   ~ (all_53_9 = e0)
% 228.34/39.91    (17)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.34/39.91          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.34/39.91    (18)   ~ (all_53_4 = all_53_12)
% 228.34/39.91    (19)   ~ (all_53_8 = all_53_9)
% 228.34/39.91    (20)  all_42_2 = all_6_2
% 228.34/39.91    (21)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.34/39.91          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.34/39.91    (22)  all_57_8 = e1
% 228.34/39.91    (23)   ~ (all_53_9 = all_6_2)
% 228.34/39.91    (24)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.34/39.91          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.34/39.91    (25)  all_57_3 = e0
% 228.34/39.91    (26)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.34/39.91          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.34/39.91    (27)   ~ (e3 = e2)
% 228.34/39.91    (28)  all_55_1 = all_53_4
% 228.34/39.91    (29)   ~ (e3 = e0)
% 228.34/39.91    (30)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.34/39.91          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.34/39.91    (31)   ~ (all_53_8 = all_6_2)
% 228.34/39.91    (32)  all_55_2 = all_53_8
% 228.34/39.91    (33)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.34/39.91    (34)  all_57_15 = e3
% 228.34/39.91    (35)  op(e3, e3) = e2
% 228.34/39.91    (36)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.34/39.91          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.34/39.91            e1)
% 228.34/39.91    (37)   ~ (all_53_4 = all_53_8)
% 228.34/39.91    (38)  op(e3, e2) = all_53_4
% 228.34/39.91    (39)   ~ (e2 = e0)
% 228.34/39.91    (40)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.34/39.91            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.34/39.91            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.34/39.91            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.34/39.91              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.34/39.91            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.34/39.91            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.34/39.91              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.34/39.91              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.34/39.91            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.34/39.91            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.34/39.91            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.34/39.91              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.34/39.91              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.34/39.91            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.34/39.91              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.34/39.91            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.34/39.91            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.34/39.91              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.34/39.91              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.34/39.91            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.34/39.91            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.34/39.91    (41)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.34/39.91          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.34/39.91    (42)   ~ (e1 = e0)
% 228.34/39.91    (43)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.34/39.91            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.34/39.91              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.34/39.91    (44)   ~ (all_53_4 = e0)
% 228.34/39.91    (45)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.34/39.91          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.34/39.91    (46)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.34/39.91          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.34/39.91    (47)  op(e0, e0) = e3
% 228.34/39.91    (48)   ~ (all_53_4 = all_53_6)
% 228.34/39.91    (49)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.34/39.91          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.34/39.91            e2)
% 228.34/39.91    (50)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.34/39.91              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.34/39.91                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.34/39.91                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.34/39.91    (51)  all_55_10 = all_6_2
% 228.34/39.91    (52)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.34/39.91          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.34/39.91    (53)  all_38_2 = all_6_2
% 228.34/39.91    (54)  all_55_3 = all_53_12
% 228.34/39.91    (55)   ~ (all_53_12 = e3)
% 228.34/39.91    (56)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.34/39.91            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.34/39.91              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.34/39.91    (57)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.34/39.91          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.34/39.91    (58)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.34/39.91          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.34/39.91    (59)   ~ (e2 = e1)
% 228.34/39.91    (60)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.34/39.91          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.34/39.91    (61)  op(e2, e1) = all_53_9
% 228.34/39.91    (62)  op(e1, e2) = all_53_6
% 228.34/39.91    (63)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.34/39.91          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.34/39.91    (64)  all_24_2 = all_6_2
% 228.34/39.91    (65)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.34/39.91          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.34/39.91    (66)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.34/39.91          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.34/39.91    (67)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.34/39.91          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.34/39.91    (68)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.34/39.91          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.34/39.91    (69)  op(e3, e1) = all_53_8
% 228.34/39.91    (70)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.34/39.91          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.34/39.91    (71)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.34/39.91          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.34/39.91    (72)  all_57_10 = e3 & op(e2, e0) = e3
% 228.34/39.91    (73)  op(e3, e0) = all_53_12
% 228.34/39.91  
% 228.34/39.91  Begin of proof
% 228.34/39.91  | 
% 228.34/39.91  | ALPHA: (72) implies:
% 228.34/39.91  |   (74)  all_57_10 = e3
% 228.34/39.91  | 
% 228.34/39.91  | BETA: splitting (45) gives:
% 228.34/39.91  | 
% 228.34/39.91  | Case 1:
% 228.34/39.91  | | 
% 228.34/39.91  | |   (75)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) =
% 228.34/39.91  | |           e3)
% 228.34/39.91  | | 
% 228.34/39.91  | | BETA: splitting (75) gives:
% 228.34/39.91  | | 
% 228.34/39.91  | | Case 1:
% 228.34/39.91  | | | 
% 228.34/39.91  | | |   (76)  all_57_4 = e3 & op(e3, e1) = e3
% 228.34/39.91  | | | 
% 228.34/39.91  | | | ALPHA: (76) implies:
% 228.34/39.91  | | |   (77)  all_57_4 = e3
% 228.34/39.91  | | | 
% 228.34/39.91  | | | BETA: splitting (11) gives:
% 228.34/39.91  | | | 
% 228.34/39.91  | | | Case 1:
% 228.34/39.91  | | | | 
% 228.34/39.91  | | | |   (78)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2)
% 228.34/39.91  | | | |           = e3)
% 228.34/39.91  | | | | 
% 228.34/39.91  | | | | BETA: splitting (78) gives:
% 228.34/39.91  | | | | 
% 228.34/39.91  | | | | Case 1:
% 228.34/39.91  | | | | | 
% 228.34/39.91  | | | | |   (79)  all_57_6 = e3 & op(e1, e3) = e3
% 228.34/39.91  | | | | | 
% 228.34/39.91  | | | | | ALPHA: (79) implies:
% 228.34/39.91  | | | | |   (80)  all_57_6 = e3
% 228.34/39.91  | | | | | 
% 228.34/39.91  | | | | | BETA: splitting (66) gives:
% 228.34/39.91  | | | | | 
% 228.34/39.91  | | | | | Case 1:
% 228.34/39.91  | | | | | | 
% 228.34/39.91  | | | | | |   (81)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2,
% 228.34/39.91  | | | | | |             e3) = e0)
% 228.34/39.91  | | | | | | 
% 228.34/39.91  | | | | | | REF_CLOSE: (4), (8), (10), (25), (27), (35), (39), (42), (57), (59),
% 228.34/39.91  | | | | | |            (74), (81) are inconsistent by sub-proof #552.
% 228.34/39.91  | | | | | | 
% 228.34/39.91  | | | | | Case 2:
% 228.34/39.91  | | | | | | 
% 228.34/39.91  | | | | | |   (82)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0,
% 228.34/39.91  | | | | | |             e3) = e0)
% 228.34/39.91  | | | | | | 
% 228.34/39.91  | | | | | | BETA: splitting (82) gives:
% 228.34/39.91  | | | | | | 
% 228.34/39.91  | | | | | | Case 1:
% 228.34/39.91  | | | | | | | 
% 228.34/39.91  | | | | | | |   (83)  all_57_6 = e0 & op(e1, e3) = e0
% 228.34/39.91  | | | | | | | 
% 228.34/39.91  | | | | | | | REF_CLOSE: (29), (80), (83) are inconsistent by sub-proof #2465.
% 228.34/39.91  | | | | | | | 
% 228.34/39.91  | | | | | | Case 2:
% 228.34/39.91  | | | | | | | 
% 228.34/39.91  | | | | | | |   (84)  all_57_12 = e0 & op(e0, e3) = e0
% 228.34/39.91  | | | | | | | 
% 228.34/39.91  | | | | | | | ALPHA: (84) implies:
% 228.34/39.91  | | | | | | |   (85)  all_57_12 = e0
% 228.34/39.91  | | | | | | | 
% 228.34/39.91  | | | | | | | BETA: splitting (5) gives:
% 228.34/39.91  | | | | | | | 
% 228.34/39.91  | | | | | | | Case 1:
% 228.34/39.91  | | | | | | | | 
% 228.34/39.91  | | | | | | | |   (86)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 &
% 228.34/39.91  | | | | | | | |           op(e2, e3) = e1)
% 228.34/39.91  | | | | | | | | 
% 228.34/39.91  | | | | | | | | BETA: splitting (86) gives:
% 228.34/39.91  | | | | | | | | 
% 228.34/39.91  | | | | | | | | Case 1:
% 228.34/39.91  | | | | | | | | | 
% 228.34/39.92  | | | | | | | | |   (87)  all_57_0 = e1 & op(e3, e3) = e1
% 228.34/39.92  | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | ALPHA: (87) implies:
% 228.34/39.92  | | | | | | | | |   (88)  op(e3, e3) = e1
% 228.34/39.92  | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | REF_CLOSE: (10), (35), (59), (88) are inconsistent by
% 228.34/39.92  | | | | | | | | |            sub-proof #1950.
% 228.34/39.92  | | | | | | | | | 
% 228.34/39.92  | | | | | | | | Case 2:
% 228.34/39.92  | | | | | | | | | 
% 228.34/39.92  | | | | | | | | |   (89)  all_57_2 = e1 & op(e2, e3) = e1
% 228.34/39.92  | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | ALPHA: (89) implies:
% 228.34/39.92  | | | | | | | | |   (90)  all_57_2 = e1
% 228.34/39.92  | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | BETA: splitting (45) gives:
% 228.34/39.92  | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | Case 1:
% 228.34/39.92  | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | BETA: splitting (75) gives:
% 228.34/39.92  | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | Case 1:
% 228.34/39.92  | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | BETA: splitting (49) gives:
% 228.34/39.92  | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | Case 1:
% 228.34/39.92  | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | |   (91)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 228.34/39.92  | | | | | | | | | | | |           e2 & op(e0, e2) = e2)
% 228.34/39.92  | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | BETA: splitting (91) gives:
% 228.34/39.92  | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | Case 1:
% 228.34/39.92  | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | |   (92)  all_57_12 = e2 & op(e0, e3) = e2
% 228.34/39.92  | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | ALPHA: (92) implies:
% 228.34/39.92  | | | | | | | | | | | | |   (93)  all_57_12 = e2
% 228.34/39.92  | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | REF_CLOSE: (2), (27), (39), (59), (63), (80), (85), (90),
% 228.34/39.92  | | | | | | | | | | | | |            (93) are inconsistent by sub-proof #665.
% 228.34/39.92  | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | Case 2:
% 228.34/39.92  | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | |   (94)  all_57_13 = e2 & op(e0, e2) = e2
% 228.34/39.92  | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | ALPHA: (94) implies:
% 228.34/39.92  | | | | | | | | | | | | |   (95)  all_57_13 = e2
% 228.34/39.92  | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | BETA: splitting (67) gives:
% 228.34/39.92  | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | Case 1:
% 228.34/39.92  | | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | |   (96)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 228.34/39.92  | | | | | | | | | | | | | |           e1 & op(e2, e0) = e1)
% 228.34/39.92  | | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | | REF_CLOSE: (8), (27), (29), (34), (39), (42), (50), (59),
% 228.34/39.92  | | | | | | | | | | | | | |            (60), (74), (96) are inconsistent by sub-proof
% 228.34/39.92  | | | | | | | | | | | | | |            #1984.
% 228.34/39.92  | | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | Case 2:
% 228.34/39.92  | | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | |   (97)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 228.34/39.92  | | | | | | | | | | | | | |           e1 & op(e0, e0) = e1)
% 228.34/39.92  | | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | | BETA: splitting (97) gives:
% 228.34/39.92  | | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | | Case 1:
% 228.34/39.92  | | | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | | |   (98)  all_57_11 = e1 & op(e1, e0) = e1
% 228.34/39.92  | | | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | | | ALPHA: (98) implies:
% 228.34/39.92  | | | | | | | | | | | | | | |   (99)  all_57_11 = e1
% 228.34/39.92  | | | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | | | BETA: splitting (46) gives:
% 228.34/39.92  | | | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | | | Case 1:
% 228.34/39.92  | | | | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | | | |   (100)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 228.34/39.92  | | | | | | | | | | | | | | | |            & op(e2, e2) = e3)
% 228.34/39.92  | | | | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | | | | REF_CLOSE: (8), (17), (21), (24), (25), (27), (29), (34),
% 228.34/39.92  | | | | | | | | | | | | | | | |            (39), (42), (50), (59), (60), (74), (77), (100)
% 228.34/39.92  | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1435.
% 228.34/39.92  | | | | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | | | Case 2:
% 228.34/39.92  | | | | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | | | |   (101)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 228.34/39.92  | | | | | | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 228.34/39.92  | | | | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | | | | BETA: splitting (101) gives:
% 228.34/39.92  | | | | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | | | | Case 1:
% 228.34/39.92  | | | | | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | | | | |   (102)  all_57_7 = e3 & op(e1, e2) = e3
% 228.34/39.92  | | | | | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | | | | | ALPHA: (102) implies:
% 228.34/39.92  | | | | | | | | | | | | | | | | |   (103)  all_57_7 = e3
% 228.34/39.92  | | | | | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10),
% 228.34/39.92  | | | | | | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 228.34/39.92  | | | | | | | | | | | | | | | | |            (19), (20), (21), (22), (23), (24), (25), (26),
% 228.34/39.92  | | | | | | | | | | | | | | | | |            (27), (28), (29), (30), (31), (32), (33), (34),
% 228.34/39.92  | | | | | | | | | | | | | | | | |            (35), (36), (37), (38), (39), (40), (41), (42),
% 228.34/39.92  | | | | | | | | | | | | | | | | |            (43), (44), (45), (47), (48), (49), (50), (51),
% 228.34/39.92  | | | | | | | | | | | | | | | | |            (52), (53), (54), (55), (56), (57), (58), (59),
% 228.34/39.92  | | | | | | | | | | | | | | | | |            (60), (61), (62), (63), (64), (65), (66), (67),
% 228.34/39.92  | | | | | | | | | | | | | | | | |            (68), (69), (70), (71), (73), (77), (99), (103)
% 228.34/39.92  | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #499.
% 228.34/39.92  | | | | | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | | | | Case 2:
% 228.34/39.92  | | | | | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | | | | |   (104)  all_57_13 = e3 & op(e0, e2) = e3
% 228.34/39.92  | | | | | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | | | | | ALPHA: (104) implies:
% 228.34/39.92  | | | | | | | | | | | | | | | | |   (105)  all_57_13 = e3
% 228.34/39.92  | | | | | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | | | | | COMBINE_EQS: (95), (105) imply:
% 228.34/39.92  | | | | | | | | | | | | | | | | |   (106)  e3 = e2
% 228.34/39.92  | | | | | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | | | | | SIMP: (106) implies:
% 228.34/39.92  | | | | | | | | | | | | | | | | |   (107)  e3 = e2
% 228.34/39.92  | | | | | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (10), (11), (13), (14),
% 228.34/39.92  | | | | | | | | | | | | | | | | |            (17), (21), (24), (25), (26), (27), (29), (34),
% 228.34/39.92  | | | | | | | | | | | | | | | | |            (36), (39), (42), (45), (46), (49), (50), (57),
% 228.34/39.92  | | | | | | | | | | | | | | | | |            (58), (59), (60), (63), (65), (66), (67), (70),
% 228.34/39.92  | | | | | | | | | | | | | | | | |            (74), (80), (85), (107) are inconsistent by
% 228.34/39.92  | | | | | | | | | | | | | | | | |            sub-proof #549.
% 228.34/39.92  | | | | | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | | | | End of split
% 228.34/39.92  | | | | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | | | End of split
% 228.34/39.92  | | | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | | Case 2:
% 228.34/39.92  | | | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | | |   (108)  all_57_15 = e1 & op(e0, e0) = e1
% 228.34/39.92  | | | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | | | REF_CLOSE: (8), (34), (108) are inconsistent by sub-proof
% 228.34/39.92  | | | | | | | | | | | | | | |            #2325.
% 228.34/39.92  | | | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | | End of split
% 228.34/39.92  | | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | End of split
% 228.34/39.92  | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | End of split
% 228.34/39.92  | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | Case 2:
% 228.34/39.92  | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | |   (109)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 228.34/39.92  | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 228.34/39.92  | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | BETA: splitting (109) gives:
% 228.34/39.92  | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | Case 1:
% 228.34/39.92  | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | |   (110)  all_57_14 = e2 & op(e0, e1) = e2
% 228.34/39.92  | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | ALPHA: (110) implies:
% 228.34/39.92  | | | | | | | | | | | | |   (111)  all_57_14 = e2
% 228.34/39.92  | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | BETA: splitting (17) gives:
% 228.34/39.92  | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | Case 1:
% 228.34/39.92  | | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | |   (112)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 228.34/39.92  | | | | | | | | | | | | | |            & op(e3, e2) = e1)
% 228.34/39.92  | | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | | BETA: splitting (112) gives:
% 228.34/39.92  | | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | | Case 1:
% 228.34/39.92  | | | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | | |   (113)  all_57_0 = e1 & op(e3, e3) = e1
% 228.34/39.92  | | | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | | | ALPHA: (113) implies:
% 228.34/39.92  | | | | | | | | | | | | | | |   (114)  op(e3, e3) = e1
% 228.34/39.92  | | | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | | | REF_CLOSE: (10), (35), (59), (114) are inconsistent by
% 228.34/39.92  | | | | | | | | | | | | | | |            sub-proof #1950.
% 228.34/39.92  | | | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | | Case 2:
% 228.34/39.92  | | | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | | |   (115)  all_57_1 = e1 & op(e3, e2) = e1
% 228.34/39.92  | | | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | | | ALPHA: (115) implies:
% 228.34/39.92  | | | | | | | | | | | | | | |   (116)  all_57_1 = e1
% 228.34/39.92  | | | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 228.34/39.92  | | | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | | | Case 1:
% 228.34/39.92  | | | | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | | | |   (117)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 228.34/39.92  | | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 228.34/39.92  | | | | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | | | | REF_CLOSE: (8), (27), (29), (34), (39), (42), (50), (59),
% 228.34/39.92  | | | | | | | | | | | | | | | |            (60), (74), (117) are inconsistent by sub-proof
% 228.34/39.92  | | | | | | | | | | | | | | | |            #1984.
% 228.34/39.92  | | | | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | | | Case 2:
% 228.34/39.92  | | | | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | | | |   (118)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 228.34/39.92  | | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 228.34/39.92  | | | | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10),
% 228.34/39.92  | | | | | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 228.34/39.92  | | | | | | | | | | | | | | | |            (19), (20), (21), (22), (23), (24), (25), (26),
% 228.34/39.92  | | | | | | | | | | | | | | | |            (27), (28), (29), (30), (31), (32), (33), (34),
% 228.34/39.92  | | | | | | | | | | | | | | | |            (35), (36), (37), (38), (39), (40), (41), (42),
% 228.34/39.92  | | | | | | | | | | | | | | | |            (43), (44), (45), (46), (47), (48), (49), (50),
% 228.34/39.92  | | | | | | | | | | | | | | | |            (51), (52), (53), (54), (55), (56), (57), (58),
% 228.34/39.92  | | | | | | | | | | | | | | | |            (59), (60), (61), (62), (63), (64), (65), (66),
% 228.34/39.92  | | | | | | | | | | | | | | | |            (67), (68), (69), (70), (71), (73), (77), (85),
% 228.34/39.92  | | | | | | | | | | | | | | | |            (111), (116), (118) are inconsistent by sub-proof
% 228.34/39.92  | | | | | | | | | | | | | | | |            #498.
% 228.34/39.92  | | | | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | | | End of split
% 228.34/39.92  | | | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | | End of split
% 228.34/39.92  | | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | Case 2:
% 228.34/39.92  | | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | |   (119)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 228.34/39.92  | | | | | | | | | | | | | |            & op(e3, e0) = e1)
% 228.34/39.92  | | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | | BETA: splitting (119) gives:
% 228.34/39.92  | | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | | Case 1:
% 228.34/39.92  | | | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | | |   (120)  all_57_4 = e1 & op(e3, e1) = e1
% 228.34/39.92  | | | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | | | REF_CLOSE: (8), (77), (120) are inconsistent by sub-proof
% 228.34/39.92  | | | | | | | | | | | | | | |            #2484.
% 228.34/39.92  | | | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | | Case 2:
% 228.34/39.92  | | | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | | |   (121)  all_57_9 = e1 & op(e3, e0) = e1
% 228.34/39.92  | | | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | | | ALPHA: (121) implies:
% 228.34/39.92  | | | | | | | | | | | | | | |   (122)  all_57_9 = e1
% 228.34/39.92  | | | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | | | REF_CLOSE: (27), (29), (34), (39), (42), (50), (59), (60),
% 228.34/39.92  | | | | | | | | | | | | | | |            (74), (122) are inconsistent by sub-proof #1985.
% 228.34/39.92  | | | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | | End of split
% 228.34/39.92  | | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | End of split
% 228.34/39.92  | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | Case 2:
% 228.34/39.92  | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | |   (123)  all_57_15 = e2 & op(e0, e0) = e2
% 228.34/39.92  | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | ALPHA: (123) implies:
% 228.34/39.92  | | | | | | | | | | | | |   (124)  all_57_15 = e2
% 228.34/39.92  | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | COMBINE_EQS: (34), (124) imply:
% 228.34/39.92  | | | | | | | | | | | | |   (125)  e3 = e2
% 228.34/39.92  | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (10), (11), (13), (14),
% 228.34/39.92  | | | | | | | | | | | | |            (17), (21), (24), (25), (26), (27), (29), (34),
% 228.34/39.92  | | | | | | | | | | | | |            (36), (39), (42), (45), (46), (49), (50), (57),
% 228.34/39.92  | | | | | | | | | | | | |            (58), (59), (60), (63), (65), (66), (67), (70),
% 228.34/39.92  | | | | | | | | | | | | |            (74), (80), (85), (125) are inconsistent by
% 228.34/39.92  | | | | | | | | | | | | |            sub-proof #549.
% 228.34/39.92  | | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | | End of split
% 228.34/39.92  | | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | End of split
% 228.34/39.92  | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | Case 2:
% 228.34/39.92  | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | |   (126)  all_57_5 = e3 & op(e2, e1) = e3
% 228.34/39.92  | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | ALPHA: (126) implies:
% 228.34/39.92  | | | | | | | | | | |   (127)  all_57_5 = e3
% 228.34/39.92  | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | | REF_CLOSE: (4), (8), (25), (27), (39), (42), (57), (59),
% 228.34/39.92  | | | | | | | | | | |            (74), (127) are inconsistent by sub-proof #1693.
% 228.34/39.92  | | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | End of split
% 228.34/39.92  | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | Case 2:
% 228.34/39.92  | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | |   (128)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3
% 228.34/39.92  | | | | | | | | | |            & op(e0, e1) = e3)
% 228.34/39.92  | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | | REF_CLOSE: (8), (10), (13), (14), (27), (34), (36), (39),
% 228.34/39.92  | | | | | | | | | |            (42), (49), (59), (85), (128) are inconsistent by
% 228.34/39.92  | | | | | | | | | |            sub-proof #530.
% 228.34/39.92  | | | | | | | | | | 
% 228.34/39.92  | | | | | | | | | End of split
% 228.34/39.92  | | | | | | | | | 
% 228.34/39.92  | | | | | | | | End of split
% 228.34/39.92  | | | | | | | | 
% 228.34/39.92  | | | | | | | Case 2:
% 228.34/39.92  | | | | | | | | 
% 228.34/39.92  | | | | | | | |   (129)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 &
% 228.34/39.92  | | | | | | | |            op(e0, e3) = e1)
% 228.34/39.92  | | | | | | | | 
% 228.34/39.92  | | | | | | | | REF_CLOSE: (8), (42), (80), (85), (129) are inconsistent by
% 228.34/39.92  | | | | | | | |            sub-proof #1783.
% 228.34/39.92  | | | | | | | | 
% 228.34/39.92  | | | | | | | End of split
% 228.34/39.92  | | | | | | | 
% 228.34/39.92  | | | | | | End of split
% 228.34/39.92  | | | | | | 
% 228.34/39.92  | | | | | End of split
% 228.34/39.92  | | | | | 
% 228.34/39.92  | | | | Case 2:
% 228.34/39.92  | | | | | 
% 228.34/39.92  | | | | |   (130)  all_57_7 = e3 & op(e1, e2) = e3
% 228.34/39.92  | | | | | 
% 228.34/39.92  | | | | | ALPHA: (130) implies:
% 228.34/39.92  | | | | |   (131)  all_57_7 = e3
% 228.34/39.92  | | | | | 
% 228.34/39.92  | | | | | BETA: splitting (67) gives:
% 228.34/39.92  | | | | | 
% 228.34/39.92  | | | | | Case 1:
% 228.34/39.92  | | | | | | 
% 228.34/39.92  | | | | | |   (132)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 &
% 228.34/39.92  | | | | | |            op(e2, e0) = e1)
% 228.34/39.92  | | | | | | 
% 228.34/39.92  | | | | | | REF_CLOSE: (8), (27), (29), (34), (39), (42), (50), (59), (60),
% 228.34/39.92  | | | | | |            (74), (132) are inconsistent by sub-proof #1984.
% 228.34/39.92  | | | | | | 
% 228.34/39.92  | | | | | Case 2:
% 228.34/39.92  | | | | | | 
% 228.34/39.92  | | | | | |   (133)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 &
% 228.34/39.92  | | | | | |            op(e0, e0) = e1)
% 228.34/39.92  | | | | | | 
% 228.34/39.92  | | | | | | BETA: splitting (133) gives:
% 228.34/39.92  | | | | | | 
% 228.34/39.92  | | | | | | Case 1:
% 228.34/39.92  | | | | | | | 
% 228.34/39.92  | | | | | | |   (134)  all_57_11 = e1 & op(e1, e0) = e1
% 228.34/39.92  | | | | | | | 
% 228.34/39.92  | | | | | | | ALPHA: (134) implies:
% 228.34/39.92  | | | | | | |   (135)  all_57_11 = e1
% 228.34/39.92  | | | | | | | 
% 228.34/39.92  | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 228.34/39.92  | | | | | | |            (12), (13), (14), (15), (16), (17), (18), (19), (20),
% 228.34/39.92  | | | | | | |            (21), (22), (23), (24), (25), (26), (27), (28), (29),
% 228.34/39.92  | | | | | | |            (30), (31), (32), (33), (34), (35), (36), (37), (38),
% 228.34/39.92  | | | | | | |            (39), (40), (41), (42), (43), (44), (45), (47), (48),
% 228.34/39.92  | | | | | | |            (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 228.34/39.92  | | | | | | |            (58), (59), (60), (61), (62), (63), (64), (65), (66),
% 228.34/39.92  | | | | | | |            (67), (68), (69), (70), (71), (73), (77), (131), (135)
% 228.34/39.92  | | | | | | |            are inconsistent by sub-proof #499.
% 228.34/39.92  | | | | | | | 
% 228.34/39.92  | | | | | | Case 2:
% 228.34/39.92  | | | | | | | 
% 228.34/39.92  | | | | | | |   (136)  all_57_15 = e1 & op(e0, e0) = e1
% 228.34/39.92  | | | | | | | 
% 228.34/39.92  | | | | | | | REF_CLOSE: (8), (34), (136) are inconsistent by sub-proof #2325.
% 228.34/39.92  | | | | | | | 
% 228.34/39.92  | | | | | | End of split
% 228.34/39.92  | | | | | | 
% 228.34/39.92  | | | | | End of split
% 228.34/39.92  | | | | | 
% 228.34/39.92  | | | | End of split
% 228.34/39.92  | | | | 
% 228.34/39.92  | | | Case 2:
% 228.34/39.92  | | | | 
% 228.34/39.92  | | | |   (137)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1,
% 228.34/39.92  | | | |              e0) = e3)
% 228.34/39.92  | | | | 
% 228.34/39.92  | | | | REF_CLOSE: (8), (10), (13), (14), (27), (29), (34), (39), (42), (50),
% 228.34/39.92  | | | |            (59), (60), (67), (74), (137) are inconsistent by sub-proof
% 228.34/39.92  | | | |            #1417.
% 228.34/39.92  | | | | 
% 228.34/39.92  | | | End of split
% 228.34/39.92  | | | 
% 228.34/39.92  | | Case 2:
% 228.34/39.92  | | | 
% 228.34/39.92  | | |   (138)  all_57_5 = e3 & op(e2, e1) = e3
% 228.34/39.92  | | | 
% 228.34/39.92  | | | ALPHA: (138) implies:
% 228.34/39.92  | | |   (139)  all_57_5 = e3
% 228.34/39.92  | | | 
% 228.34/39.92  | | | REF_CLOSE: (4), (8), (25), (27), (39), (42), (57), (59), (74), (139) are
% 228.34/39.92  | | |            inconsistent by sub-proof #1693.
% 228.34/39.92  | | | 
% 228.34/39.92  | | End of split
% 228.34/39.92  | | 
% 228.34/39.92  | Case 2:
% 228.34/39.92  | | 
% 228.34/39.92  | |   (140)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) =
% 228.34/39.92  | |            e3)
% 228.34/39.92  | | 
% 228.34/39.92  | | REF_CLOSE: (8), (10), (13), (14), (27), (29), (34), (36), (39), (42), (49),
% 228.34/39.92  | |            (50), (59), (140) are inconsistent by sub-proof #1794.
% 228.34/39.92  | | 
% 228.34/39.92  | End of split
% 228.34/39.92  | 
% 228.34/39.92  End of proof
% 228.34/39.92  
% 228.34/39.92  Sub-proof #498 shows that the following formulas are inconsistent:
% 228.34/39.92  ----------------------------------------------------------------
% 228.34/39.92    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.34/39.92    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.34/39.92    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.34/39.92         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.34/39.92    (4)  all_57_12 = e0
% 228.34/39.92    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.34/39.92         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.34/39.92    (6)   ~ (all_53_8 = all_53_12)
% 228.34/39.92    (7)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.34/39.92         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.34/39.92    (8)   ~ (e3 = e1)
% 228.34/39.92    (9)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.34/39.92         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.34/39.92    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.34/39.92            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.34/39.92    (11)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.34/39.92          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.34/39.92    (12)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.34/39.92            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.34/39.92              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.34/39.92    (13)   ~ (all_6_2 = e3)
% 228.34/39.92    (14)  op(e1, e1) = all_6_2
% 228.34/39.92    (15)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.34/39.92    (16)   ~ (all_53_9 = e0)
% 228.34/39.92    (17)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.34/39.92          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.34/39.92    (18)   ~ (all_53_4 = all_53_12)
% 228.34/39.92    (19)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.34/39.92    (20)   ~ (all_53_8 = all_53_9)
% 228.34/39.92    (21)  all_42_2 = all_6_2
% 228.34/39.92    (22)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.34/39.92          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.34/39.92    (23)  all_57_8 = e1
% 228.34/39.92    (24)   ~ (all_53_9 = all_6_2)
% 228.34/39.92    (25)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.34/39.92          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.34/39.92    (26)  all_57_3 = e0
% 228.34/39.92    (27)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.34/39.92          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.34/39.92    (28)  all_57_4 = e3
% 228.34/39.92    (29)   ~ (e3 = e2)
% 228.34/39.92    (30)  all_55_1 = all_53_4
% 228.34/39.92    (31)   ~ (e3 = e0)
% 228.34/39.92    (32)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.34/39.92          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.34/39.92    (33)   ~ (all_53_8 = all_6_2)
% 228.34/39.92    (34)  all_55_2 = all_53_8
% 228.34/39.92    (35)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.34/39.92    (36)  all_57_15 = e3
% 228.34/39.92    (37)  all_57_1 = e1
% 228.34/39.92    (38)  op(e3, e3) = e2
% 228.34/39.92    (39)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.34/39.92          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.34/39.92            e1)
% 228.34/39.92    (40)   ~ (all_53_4 = all_53_8)
% 228.34/39.92    (41)  op(e3, e2) = all_53_4
% 228.34/39.92    (42)   ~ (e2 = e0)
% 228.34/39.92    (43)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.34/39.92            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.34/39.92            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.34/39.92            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.34/39.92              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.34/39.92            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.34/39.92            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.34/39.92              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.34/39.92              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.34/39.92            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.34/39.92            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.34/39.92            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.34/39.92              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.34/39.92              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.34/39.92            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.34/39.92              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.34/39.92            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.34/39.92            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.34/39.92              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.34/39.92              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.34/39.92            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.34/39.92            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.34/39.92    (44)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.34/39.92          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.34/39.92    (45)   ~ (e1 = e0)
% 228.34/39.92    (46)  all_57_14 = e2
% 228.34/39.92    (47)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.34/39.92            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.34/39.92              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.34/39.92    (48)   ~ (all_53_4 = e0)
% 228.34/39.92    (49)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.34/39.92          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.34/39.92    (50)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.34/39.92          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.34/39.92    (51)  op(e0, e0) = e3
% 228.34/39.92    (52)   ~ (all_53_4 = all_53_6)
% 228.34/39.92    (53)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.34/39.92          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.34/39.92            e2)
% 228.34/39.92    (54)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.34/39.92              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.34/39.92                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.34/39.92                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.34/39.92    (55)  all_55_10 = all_6_2
% 228.34/39.92    (56)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.34/39.92          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.34/39.92    (57)  all_38_2 = all_6_2
% 228.34/39.92    (58)  all_55_3 = all_53_12
% 228.34/39.92    (59)   ~ (all_53_12 = e3)
% 228.34/39.92    (60)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.34/39.92            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.34/39.92              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.34/39.92    (61)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.34/39.92          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.34/39.92    (62)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.34/39.92          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.34/39.92    (63)   ~ (e2 = e1)
% 228.34/39.92    (64)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.34/39.92          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.34/39.92    (65)  op(e2, e1) = all_53_9
% 228.34/39.92    (66)  op(e1, e2) = all_53_6
% 228.34/39.92    (67)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.34/39.92          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.34/39.92    (68)  all_24_2 = all_6_2
% 228.34/39.92    (69)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.34/39.92          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.34/39.92    (70)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.34/39.92          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.34/39.92    (71)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.34/39.92          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.34/39.92    (72)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.34/39.92          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.34/39.92    (73)  op(e3, e1) = all_53_8
% 228.34/39.92    (74)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.34/39.92          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.34/39.92    (75)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.34/39.92          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.34/39.92    (76)  op(e3, e0) = all_53_12
% 228.34/39.92  
% 228.34/39.92  Begin of proof
% 228.34/39.92  | 
% 228.34/39.92  | BETA: splitting (19) gives:
% 228.34/39.92  | 
% 228.34/39.92  | Case 1:
% 228.34/39.92  | | 
% 228.34/39.92  | |   (77)  all_57_11 = e1 & op(e1, e0) = e1
% 228.34/39.92  | | 
% 228.34/39.92  | | ALPHA: (77) implies:
% 228.34/39.92  | |   (78)  all_57_11 = e1
% 228.34/39.92  | | 
% 228.34/39.92  | | BETA: splitting (50) gives:
% 228.34/39.92  | | 
% 228.34/39.92  | | Case 1:
% 228.34/39.92  | | | 
% 228.34/39.92  | | |   (79)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 228.34/39.92  | | |           e3)
% 228.34/39.92  | | | 
% 228.34/39.92  | | | REF_CLOSE: (8), (26), (31), (37), (79) are inconsistent by sub-proof
% 228.34/39.92  | | |            #2195.
% 228.34/39.92  | | | 
% 228.34/39.92  | | Case 2:
% 228.34/39.92  | | | 
% 228.34/39.92  | | |   (80)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 228.34/39.92  | | |           e3)
% 228.34/39.92  | | | 
% 228.34/39.92  | | | BETA: splitting (80) gives:
% 228.34/39.92  | | | 
% 228.34/39.92  | | | Case 1:
% 228.34/39.92  | | | | 
% 228.34/39.92  | | | |   (81)  all_57_7 = e3 & op(e1, e2) = e3
% 228.34/39.92  | | | | 
% 228.34/39.92  | | | | ALPHA: (81) implies:
% 228.34/39.92  | | | |   (82)  all_57_7 = e3
% 228.34/39.92  | | | | 
% 228.34/39.92  | | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.34/39.92  | | | |            (13), (14), (15), (16), (17), (18), (20), (21), (22), (23),
% 228.34/39.92  | | | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 228.34/39.92  | | | |            (34), (35), (36), (38), (39), (40), (41), (42), (43), (44),
% 228.34/39.92  | | | |            (45), (47), (48), (49), (51), (52), (53), (54), (55), (56),
% 228.34/39.92  | | | |            (57), (58), (59), (60), (61), (62), (63), (64), (65), (66),
% 228.34/39.92  | | | |            (67), (68), (69), (70), (71), (72), (73), (74), (75), (76),
% 228.34/39.92  | | | |            (78), (82) are inconsistent by sub-proof #499.
% 228.34/39.92  | | | | 
% 228.34/39.92  | | | Case 2:
% 228.34/39.92  | | | | 
% 228.34/39.92  | | | |   (83)  all_57_13 = e3 & op(e0, e2) = e3
% 228.34/39.92  | | | | 
% 228.34/39.92  | | | | ALPHA: (83) implies:
% 228.34/39.92  | | | |   (84)  all_57_13 = e3
% 228.34/39.92  | | | | 
% 228.34/39.92  | | | | REF_CLOSE: (4), (8), (36), (39), (45), (46), (63), (84) are inconsistent
% 228.34/39.92  | | | |            by sub-proof #2215.
% 228.34/39.92  | | | | 
% 228.34/39.92  | | | End of split
% 228.34/39.92  | | | 
% 228.34/39.92  | | End of split
% 228.34/39.92  | | 
% 228.34/39.92  | Case 2:
% 228.34/39.92  | | 
% 228.34/39.92  | |   (85)  all_57_15 = e1 & op(e0, e0) = e1
% 228.34/39.92  | | 
% 228.34/39.92  | | REF_CLOSE: (8), (36), (85) are inconsistent by sub-proof #2325.
% 228.34/39.92  | | 
% 228.34/39.92  | End of split
% 228.34/39.92  | 
% 228.34/39.92  End of proof
% 228.34/39.92  
% 228.34/39.92  Sub-proof #499 shows that the following formulas are inconsistent:
% 228.34/39.92  ----------------------------------------------------------------
% 228.34/39.92    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.34/39.92    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.34/39.92    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.34/39.92         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.34/39.92    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.34/39.92         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.34/39.92    (5)   ~ (all_53_8 = all_53_12)
% 228.34/39.92    (6)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.34/39.92         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.34/39.92    (7)   ~ (e3 = e1)
% 228.34/39.92    (8)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.34/39.92         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.34/39.92    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.34/39.92           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.34/39.92    (10)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.34/39.92          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.34/39.92    (11)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.34/39.92            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.34/39.92              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.34/39.92    (12)   ~ (all_6_2 = e3)
% 228.34/39.92    (13)  op(e1, e1) = all_6_2
% 228.34/39.92    (14)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.34/39.92    (15)   ~ (all_53_9 = e0)
% 228.34/39.92    (16)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.34/39.92          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.34/39.92    (17)   ~ (all_53_4 = all_53_12)
% 228.34/39.92    (18)   ~ (all_53_8 = all_53_9)
% 228.34/39.92    (19)  all_42_2 = all_6_2
% 228.34/39.92    (20)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.34/39.92          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.34/39.92    (21)  all_57_8 = e1
% 228.34/39.92    (22)   ~ (all_53_9 = all_6_2)
% 228.34/39.92    (23)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.34/39.92          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.34/39.92    (24)  all_57_3 = e0
% 228.34/39.92    (25)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.34/39.92          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.34/39.92    (26)  all_57_4 = e3
% 228.34/39.92    (27)   ~ (e3 = e2)
% 228.34/39.92    (28)  all_55_1 = all_53_4
% 228.34/39.92    (29)   ~ (e3 = e0)
% 228.34/39.92    (30)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.34/39.92          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.34/39.92    (31)   ~ (all_53_8 = all_6_2)
% 228.34/39.92    (32)  all_55_2 = all_53_8
% 228.34/39.92    (33)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.34/39.92    (34)  all_57_15 = e3
% 228.34/39.92    (35)  op(e3, e3) = e2
% 228.34/39.92    (36)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.34/39.92          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.34/39.92            e1)
% 228.34/39.92    (37)   ~ (all_53_4 = all_53_8)
% 228.34/39.92    (38)  op(e3, e2) = all_53_4
% 228.34/39.92    (39)   ~ (e2 = e0)
% 228.34/39.93    (40)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.34/39.93            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.34/39.93            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.34/39.93            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.34/39.93              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.34/39.93            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.34/39.93            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.34/39.93              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.34/39.93              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.34/39.93            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.34/39.93            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.34/39.93            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.34/39.93              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.34/39.93              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.34/39.93            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.34/39.93              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.34/39.93            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.34/39.93            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.34/39.93              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.34/39.93              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.34/39.93            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.34/39.93            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.34/39.93    (41)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.34/39.93          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.34/39.93    (42)   ~ (e1 = e0)
% 228.34/39.93    (43)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.34/39.93            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.34/39.93              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.34/39.93    (44)   ~ (all_53_4 = e0)
% 228.34/39.93    (45)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.34/39.93          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.34/39.93    (46)  op(e0, e0) = e3
% 228.34/39.93    (47)   ~ (all_53_4 = all_53_6)
% 228.34/39.93    (48)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.34/39.93          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.34/39.93            e2)
% 228.34/39.93    (49)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.34/39.93              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.34/39.93                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.34/39.93                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.34/39.93    (50)  all_55_10 = all_6_2
% 228.34/39.93    (51)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.34/39.93          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.34/39.93    (52)  all_38_2 = all_6_2
% 228.34/39.93    (53)  all_55_3 = all_53_12
% 228.34/39.93    (54)   ~ (all_53_12 = e3)
% 228.34/39.93    (55)  all_57_7 = e3
% 228.34/39.93    (56)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.34/39.93            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.34/39.93              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.34/39.93    (57)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.34/39.93          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.34/39.93    (58)  all_57_11 = e1
% 228.34/39.93    (59)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.34/39.93          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.34/39.93    (60)   ~ (e2 = e1)
% 228.34/39.93    (61)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.34/39.93          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.34/39.93    (62)  op(e2, e1) = all_53_9
% 228.34/39.93    (63)  op(e1, e2) = all_53_6
% 228.34/39.93    (64)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.34/39.93          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.34/39.93    (65)  all_24_2 = all_6_2
% 228.34/39.93    (66)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.34/39.93          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.34/39.93    (67)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.34/39.93          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.34/39.93    (68)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.34/39.93          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.34/39.93    (69)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.34/39.93          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.34/39.93    (70)  op(e3, e1) = all_53_8
% 228.34/39.93    (71)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.34/39.93          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.34/39.93    (72)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.34/39.93          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.34/39.93    (73)  op(e3, e0) = all_53_12
% 228.34/39.93  
% 228.34/39.93  Begin of proof
% 228.34/39.93  | 
% 228.34/39.93  | BETA: splitting (72) gives:
% 228.34/39.93  | 
% 228.34/39.93  | Case 1:
% 228.34/39.93  | | 
% 228.34/39.93  | |   (74)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) =
% 228.34/39.93  | |           e2)
% 228.34/39.93  | | 
% 228.34/39.93  | | BETA: splitting (74) gives:
% 228.34/39.93  | | 
% 228.34/39.93  | | Case 1:
% 228.34/39.93  | | | 
% 228.34/39.93  | | |   (75)  all_57_6 = e2 & op(e1, e3) = e2
% 228.34/39.93  | | | 
% 228.34/39.93  | | | ALPHA: (75) implies:
% 228.34/39.93  | | |   (76)  all_57_6 = e2
% 228.34/39.93  | | | 
% 228.34/39.93  | | | REF_CLOSE: (3), (4), (6), (7), (9), (16), (20), (23), (24), (27), (29),
% 228.34/39.93  | | |            (35), (39), (41), (42), (51), (54), (55), (57), (59), (60),
% 228.34/39.93  | | |            (67), (71), (73), (76) are inconsistent by sub-proof #729.
% 228.34/39.93  | | | 
% 228.34/39.93  | | Case 2:
% 228.34/39.93  | | | 
% 228.34/39.93  | | |   (77)  all_57_7 = e2 & op(e1, e2) = e2
% 228.34/39.93  | | | 
% 228.34/39.93  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.34/39.93  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (22), (23),
% 228.34/39.93  | | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 228.34/39.93  | | |            (34), (36), (37), (38), (39), (40), (41), (42), (43), (44),
% 228.34/39.93  | | |            (45), (46), (47), (48), (49), (50), (52), (53), (54), (55),
% 228.34/39.93  | | |            (56), (57), (60), (61), (62), (63), (64), (65), (66), (67),
% 228.34/39.93  | | |            (68), (69), (70), (71), (72), (73), (77) are inconsistent by
% 228.34/39.93  | | |            sub-proof #500.
% 228.34/39.93  | | | 
% 228.34/39.93  | | End of split
% 228.34/39.93  | | 
% 228.34/39.93  | Case 2:
% 228.34/39.93  | | 
% 228.34/39.93  | |   (78)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) =
% 228.34/39.93  | |           e2)
% 228.34/39.93  | | 
% 228.34/39.93  | | BETA: splitting (78) gives:
% 228.34/39.93  | | 
% 228.34/39.93  | | Case 1:
% 228.34/39.93  | | | 
% 228.34/39.93  | | |   (79)  all_57_8 = e2 & op(e1, e1) = e2
% 228.34/39.93  | | | 
% 228.34/39.93  | | | REF_CLOSE: (21), (60), (79) are inconsistent by sub-proof #1501.
% 228.34/39.93  | | | 
% 228.34/39.93  | | Case 2:
% 228.34/39.93  | | | 
% 228.34/39.93  | | |   (80)  all_57_11 = e2 & op(e1, e0) = e2
% 228.34/39.93  | | | 
% 228.34/39.93  | | | REF_CLOSE: (58), (60), (80) are inconsistent by sub-proof #2048.
% 228.34/39.93  | | | 
% 228.34/39.93  | | End of split
% 228.34/39.93  | | 
% 228.34/39.93  | End of split
% 228.34/39.93  | 
% 228.34/39.93  End of proof
% 228.34/39.93  
% 228.34/39.93  Sub-proof #500 shows that the following formulas are inconsistent:
% 228.34/39.93  ----------------------------------------------------------------
% 228.34/39.93    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.34/39.93    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.34/39.93    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.34/39.93         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.34/39.93    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.34/39.93         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.34/39.93    (5)   ~ (all_53_8 = all_53_12)
% 228.34/39.93    (6)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.34/39.93         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.34/39.93    (7)   ~ (e3 = e1)
% 228.34/39.93    (8)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.34/39.93         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.34/39.93    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.34/39.93           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.34/39.93    (10)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.34/39.93          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.34/39.93    (11)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.34/39.93            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.34/39.93              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.34/39.93    (12)   ~ (all_6_2 = e3)
% 228.34/39.93    (13)  op(e1, e1) = all_6_2
% 228.34/39.93    (14)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.34/39.93    (15)   ~ (all_53_9 = e0)
% 228.34/39.93    (16)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.34/39.93          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.34/39.93    (17)   ~ (all_53_4 = all_53_12)
% 228.34/39.93    (18)   ~ (all_53_8 = all_53_9)
% 228.34/39.93    (19)  all_42_2 = all_6_2
% 228.34/39.93    (20)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.34/39.93          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.34/39.93    (21)   ~ (all_53_9 = all_6_2)
% 228.34/39.93    (22)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.34/39.93          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.34/39.93    (23)  all_57_3 = e0
% 228.34/39.93    (24)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.34/39.93          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.34/39.93    (25)  all_57_4 = e3
% 228.34/39.93    (26)   ~ (e3 = e2)
% 228.34/39.93    (27)  all_55_1 = all_53_4
% 228.34/39.93    (28)   ~ (e3 = e0)
% 228.34/39.93    (29)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.34/39.93          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.34/39.93    (30)   ~ (all_53_8 = all_6_2)
% 228.34/39.93    (31)  all_55_2 = all_53_8
% 228.34/39.93    (32)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.34/39.93    (33)  all_57_15 = e3
% 228.34/39.93    (34)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.34/39.93          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.34/39.93            e1)
% 228.34/39.93    (35)   ~ (all_53_4 = all_53_8)
% 228.34/39.93    (36)  op(e3, e2) = all_53_4
% 228.34/39.93    (37)   ~ (e2 = e0)
% 228.34/39.93    (38)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.34/39.93            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.34/39.93            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.34/39.93            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.34/39.93              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.34/39.93            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.34/39.93            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.34/39.93              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.34/39.93              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.34/39.93            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.34/39.93            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.34/39.93            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.34/39.93              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.34/39.93              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.34/39.93            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.34/39.93              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.34/39.93            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.34/39.93            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.34/39.93              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.34/39.93              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.34/39.93            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.34/39.93            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.34/39.93    (39)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.34/39.93          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.34/39.93    (40)   ~ (e1 = e0)
% 228.34/39.93    (41)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.34/39.93            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.34/39.93              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.34/39.93    (42)   ~ (all_53_4 = e0)
% 228.34/39.93    (43)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.34/39.93          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.34/39.93    (44)  op(e0, e0) = e3
% 228.34/39.93    (45)  all_57_7 = e2 & op(e1, e2) = e2
% 228.34/39.93    (46)   ~ (all_53_4 = all_53_6)
% 228.34/39.93    (47)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.34/39.93          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.34/39.93            e2)
% 228.34/39.93    (48)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.34/39.93              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.34/39.93                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.34/39.93                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.34/39.93    (49)  all_55_10 = all_6_2
% 228.34/39.93    (50)  all_38_2 = all_6_2
% 228.34/39.93    (51)  all_55_3 = all_53_12
% 228.34/39.93    (52)   ~ (all_53_12 = e3)
% 228.34/39.93    (53)  all_57_7 = e3
% 228.34/39.93    (54)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.34/39.93            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.34/39.93              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.34/39.93    (55)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.34/39.93          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.34/39.93    (56)   ~ (e2 = e1)
% 228.34/39.93    (57)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.34/39.93          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.34/39.93    (58)  op(e2, e1) = all_53_9
% 228.34/39.93    (59)  op(e1, e2) = all_53_6
% 228.34/39.93    (60)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.34/39.93          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.34/39.93    (61)  all_24_2 = all_6_2
% 228.34/39.93    (62)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.34/39.93          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.34/39.93    (63)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.34/39.93          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.34/39.93    (64)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.34/39.93          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.34/39.93    (65)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.34/39.93          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.34/39.93    (66)  op(e3, e1) = all_53_8
% 228.34/39.93    (67)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.34/39.93          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.34/39.93    (68)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.34/39.93          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.34/39.93    (69)  op(e3, e0) = all_53_12
% 228.34/39.93  
% 228.34/39.93  Begin of proof
% 228.34/39.93  | 
% 228.34/39.93  | ALPHA: (45) implies:
% 228.34/39.93  |   (70)  all_57_7 = e2
% 228.34/39.93  | 
% 228.34/39.93  | COMBINE_EQS: (53), (70) imply:
% 228.34/39.93  |   (71)  e3 = e2
% 228.34/39.93  | 
% 228.34/39.93  | COMBINE_EQS: (25), (71) imply:
% 228.34/39.93  |   (72)  all_57_4 = e2
% 228.34/39.93  | 
% 228.34/39.93  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.34/39.93  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 228.34/39.93  |            (24), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 228.34/39.93  |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (46), (47),
% 228.34/39.93  |            (48), (49), (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 228.34/39.93  |            (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 228.34/39.93  |            (72) are inconsistent by sub-proof #546.
% 228.34/39.93  | 
% 228.34/39.93  End of proof
% 228.34/39.93  
% 228.34/39.93  Sub-proof #501 shows that the following formulas are inconsistent:
% 228.34/39.93  ----------------------------------------------------------------
% 228.34/39.93    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.34/39.93    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.34/39.93    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.34/39.93         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.34/39.93    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.34/39.93         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.34/39.93    (5)   ~ (all_53_8 = all_53_12)
% 228.34/39.93    (6)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.34/39.93         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.34/39.93    (7)   ~ (e3 = e1)
% 228.34/39.93    (8)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.34/39.93         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.34/39.93    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.34/39.93           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.34/39.93    (10)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.34/39.93          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.34/39.93    (11)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.34/39.93            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.34/39.93              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.34/39.93    (12)   ~ (all_6_2 = e3)
% 228.34/39.93    (13)  op(e1, e1) = all_6_2
% 228.34/39.93    (14)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.34/39.93    (15)   ~ (all_53_9 = e0)
% 228.34/39.93    (16)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.34/39.93          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.34/39.93    (17)   ~ (all_53_4 = all_53_12)
% 228.34/39.93    (18)   ~ (all_53_8 = all_53_9)
% 228.34/39.93    (19)  all_42_2 = all_6_2
% 228.34/39.93    (20)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.34/39.93          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.34/39.93    (21)  all_57_8 = e1
% 228.34/39.93    (22)   ~ (all_53_9 = all_6_2)
% 228.34/39.93    (23)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.34/39.93          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.44/39.93    (24)  all_57_3 = e0
% 228.44/39.93    (25)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.44/39.93          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.44/39.93    (26)   ~ (e3 = e2)
% 228.44/39.93    (27)  all_55_1 = all_53_4
% 228.44/39.93    (28)   ~ (e3 = e0)
% 228.44/39.93    (29)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.44/39.93          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.44/39.93    (30)   ~ (all_53_8 = all_6_2)
% 228.44/39.93    (31)  all_55_2 = all_53_8
% 228.44/39.93    (32)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.44/39.93    (33)  all_57_15 = e3
% 228.44/39.93    (34)  op(e3, e3) = e2
% 228.44/39.93    (35)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.44/39.93          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.44/39.93            e1)
% 228.44/39.93    (36)  all_57_10 = e2
% 228.44/39.93    (37)   ~ (all_53_4 = all_53_8)
% 228.44/39.93    (38)  op(e3, e2) = all_53_4
% 228.44/39.93    (39)   ~ (e2 = e0)
% 228.44/39.93    (40)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.44/39.93            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.44/39.93            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.44/39.93            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.44/39.93              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.44/39.93            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.44/39.93            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.44/39.93              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.44/39.93              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.44/39.93            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.44/39.93            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.44/39.93            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.44/39.93              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.44/39.93              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.44/39.93            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.44/39.93              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.44/39.93            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.44/39.93            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.44/39.93              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.44/39.93              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.44/39.93            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.44/39.93            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.44/39.93    (41)  all_57_2 = e3
% 228.44/39.93    (42)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.44/39.93          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.44/39.93    (43)   ~ (e1 = e0)
% 228.44/39.93    (44)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.44/39.93            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.44/39.93              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.44/39.93    (45)   ~ (all_53_4 = e0)
% 228.44/39.93    (46)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.44/39.93          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.44/39.93    (47)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.44/39.93          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.44/39.93    (48)  op(e0, e0) = e3
% 228.44/39.93    (49)   ~ (all_53_4 = all_53_6)
% 228.44/39.93    (50)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.44/39.93          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.44/39.93            e2)
% 228.44/39.93    (51)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.44/39.93              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.44/39.93                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.44/39.93                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.44/39.93    (52)  all_55_10 = all_6_2
% 228.44/39.93    (53)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.44/39.93          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.44/39.93    (54)  all_38_2 = all_6_2
% 228.44/39.93    (55)  all_55_3 = all_53_12
% 228.44/39.93    (56)   ~ (all_53_12 = e3)
% 228.44/39.93    (57)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.44/39.93            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.44/39.93              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.44/39.93    (58)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.44/39.93          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.44/39.93    (59)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.44/39.93          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.44/39.93    (60)   ~ (e2 = e1)
% 228.44/39.93    (61)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.44/39.93          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.44/39.93    (62)  op(e2, e1) = all_53_9
% 228.44/39.93    (63)  op(e1, e2) = all_53_6
% 228.44/39.93    (64)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.44/39.93          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.44/39.93    (65)  all_24_2 = all_6_2
% 228.44/39.93    (66)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.44/39.93          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.44/39.93    (67)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.44/39.93          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.44/39.93    (68)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.44/39.93          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.44/39.93    (69)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.44/39.93          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.44/39.93    (70)  op(e3, e1) = all_53_8
% 228.44/39.93    (71)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.44/39.93          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.44/39.93    (72)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.44/39.93          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.44/39.93    (73)  op(e3, e0) = all_53_12
% 228.44/39.93  
% 228.44/39.93  Begin of proof
% 228.44/39.93  | 
% 228.44/39.93  | BETA: splitting (66) gives:
% 228.44/39.93  | 
% 228.44/39.93  | Case 1:
% 228.44/39.93  | | 
% 228.44/39.93  | |   (74)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) =
% 228.44/39.93  | |           e2)
% 228.44/39.93  | | 
% 228.44/39.93  | | BETA: splitting (74) gives:
% 228.44/39.93  | | 
% 228.44/39.93  | | Case 1:
% 228.44/39.93  | | | 
% 228.44/39.93  | | |   (75)  all_57_4 = e2 & op(e3, e1) = e2
% 228.44/39.93  | | | 
% 228.44/39.93  | | | ALPHA: (75) implies:
% 228.44/39.93  | | |   (76)  all_57_4 = e2
% 228.44/39.93  | | | 
% 228.44/39.93  | | | BETA: splitting (23) gives:
% 228.44/39.93  | | | 
% 228.44/39.93  | | | Case 1:
% 228.44/39.93  | | | | 
% 228.44/39.93  | | | |   (77)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2)
% 228.44/39.93  | | | |           = e0)
% 228.44/39.93  | | | | 
% 228.44/39.93  | | | | BETA: splitting (77) gives:
% 228.44/39.93  | | | | 
% 228.44/39.93  | | | | Case 1:
% 228.44/39.93  | | | | | 
% 228.44/39.93  | | | | |   (78)  all_57_0 = e0 & op(e3, e3) = e0
% 228.44/39.93  | | | | | 
% 228.44/39.93  | | | | | ALPHA: (78) implies:
% 228.44/39.93  | | | | |   (79)  op(e3, e3) = e0
% 228.44/39.93  | | | | | 
% 228.44/39.93  | | | | | REF_CLOSE: (9), (34), (39), (79) are inconsistent by sub-proof #2403.
% 228.44/39.93  | | | | | 
% 228.44/39.93  | | | | Case 2:
% 228.44/39.93  | | | | | 
% 228.44/39.93  | | | | |   (80)  all_57_1 = e0 & op(e3, e2) = e0
% 228.44/39.93  | | | | | 
% 228.44/39.93  | | | | | ALPHA: (80) implies:
% 228.44/39.93  | | | | |   (81)  all_57_1 = e0
% 228.44/39.93  | | | | | 
% 228.44/39.93  | | | | | BETA: splitting (42) gives:
% 228.44/39.93  | | | | | 
% 228.44/39.93  | | | | | Case 1:
% 228.44/39.93  | | | | | | 
% 228.44/39.93  | | | | | |   (82)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3,
% 228.44/39.93  | | | | | |             e2) = e3)
% 228.44/39.93  | | | | | | 
% 228.44/39.94  | | | | | | REF_CLOSE: (3), (4), (6), (7), (9), (10), (12), (13), (24), (26),
% 228.44/39.94  | | | | | |            (28), (33), (39), (41), (43), (51), (53), (58), (60),
% 228.44/39.94  | | | | | |            (61), (64), (67), (68), (71), (81), (82) are inconsistent
% 228.44/39.94  | | | | | |            by sub-proof #541.
% 228.44/39.94  | | | | | | 
% 228.44/39.94  | | | | | Case 2:
% 228.44/39.94  | | | | | | 
% 228.44/39.94  | | | | | |   (83)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3,
% 228.44/39.94  | | | | | |             e0) = e3)
% 228.44/39.94  | | | | | | 
% 228.44/39.94  | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 228.44/39.94  | | | | | |            (12), (13), (14), (15), (16), (17), (18), (19), (20),
% 228.44/39.94  | | | | | |            (22), (23), (24), (25), (26), (27), (28), (29), (30),
% 228.44/39.94  | | | | | |            (31), (32), (33), (34), (35), (37), (38), (39), (40),
% 228.44/39.94  | | | | | |            (41), (42), (43), (44), (45), (46), (47), (48), (49),
% 228.44/39.94  | | | | | |            (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 228.44/39.94  | | | | | |            (59), (60), (61), (62), (63), (64), (65), (66), (67),
% 228.44/39.94  | | | | | |            (68), (69), (70), (71), (72), (73), (76), (83) are
% 228.44/39.94  | | | | | |            inconsistent by sub-proof #507.
% 228.44/39.94  | | | | | | 
% 228.44/39.94  | | | | | End of split
% 228.44/39.94  | | | | | 
% 228.44/39.94  | | | | End of split
% 228.44/39.94  | | | | 
% 228.44/39.94  | | | Case 2:
% 228.44/39.94  | | | | 
% 228.44/39.94  | | | |   (84)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0)
% 228.44/39.94  | | | |           = e0)
% 228.44/39.94  | | | | 
% 228.44/39.94  | | | | BETA: splitting (84) gives:
% 228.44/39.94  | | | | 
% 228.44/39.94  | | | | Case 1:
% 228.44/39.94  | | | | | 
% 228.44/39.94  | | | | |   (85)  all_57_4 = e0 & op(e3, e1) = e0
% 228.44/39.94  | | | | | 
% 228.44/39.94  | | | | | REF_CLOSE: (39), (76), (85) are inconsistent by sub-proof #2045.
% 228.44/39.94  | | | | | 
% 228.44/39.94  | | | | Case 2:
% 228.44/39.94  | | | | | 
% 228.44/39.94  | | | | |   (86)  all_57_9 = e0 & op(e3, e0) = e0
% 228.44/39.94  | | | | | 
% 228.44/39.94  | | | | | ALPHA: (86) implies:
% 228.44/39.94  | | | | |   (87)  all_57_9 = e0
% 228.44/39.94  | | | | | 
% 228.44/39.94  | | | | | BETA: splitting (42) gives:
% 228.44/39.94  | | | | | 
% 228.44/39.94  | | | | | Case 1:
% 228.44/39.94  | | | | | | 
% 228.44/39.94  | | | | | |   (88)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3,
% 228.44/39.94  | | | | | |             e2) = e3)
% 228.44/39.94  | | | | | | 
% 228.44/39.94  | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 228.44/39.94  | | | | | |            (12), (13), (14), (15), (16), (17), (18), (19), (20),
% 228.44/39.94  | | | | | |            (22), (23), (24), (25), (26), (27), (28), (29), (30),
% 228.44/39.94  | | | | | |            (31), (32), (33), (34), (35), (36), (37), (38), (39),
% 228.44/39.94  | | | | | |            (40), (41), (42), (43), (44), (45), (46), (48), (49),
% 228.44/39.94  | | | | | |            (50), (51), (52), (54), (55), (56), (57), (58), (60),
% 228.44/39.94  | | | | | |            (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 228.44/39.94  | | | | | |            (70), (71), (72), (73), (87), (88) are inconsistent by
% 228.44/39.94  | | | | | |            sub-proof #505.
% 228.44/39.94  | | | | | | 
% 228.44/39.94  | | | | | Case 2:
% 228.44/39.94  | | | | | | 
% 228.44/39.94  | | | | | |   (89)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3,
% 228.44/39.94  | | | | | |             e0) = e3)
% 228.44/39.94  | | | | | | 
% 228.44/39.94  | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 228.44/39.94  | | | | | |            (12), (13), (14), (15), (16), (17), (18), (19), (20),
% 228.44/39.94  | | | | | |            (22), (23), (24), (25), (26), (27), (28), (29), (30),
% 228.44/39.94  | | | | | |            (31), (32), (33), (34), (35), (37), (38), (39), (40),
% 228.44/39.94  | | | | | |            (41), (42), (43), (44), (45), (46), (47), (48), (49),
% 228.44/39.94  | | | | | |            (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 228.44/39.94  | | | | | |            (59), (60), (61), (62), (63), (64), (65), (66), (67),
% 228.44/39.94  | | | | | |            (68), (69), (70), (71), (72), (73), (76), (89) are
% 228.44/39.94  | | | | | |            inconsistent by sub-proof #507.
% 228.44/39.94  | | | | | | 
% 228.44/39.94  | | | | | End of split
% 228.44/39.94  | | | | | 
% 228.44/39.94  | | | | End of split
% 228.44/39.94  | | | | 
% 228.44/39.94  | | | End of split
% 228.44/39.94  | | | 
% 228.44/39.94  | | Case 2:
% 228.44/39.94  | | | 
% 228.44/39.94  | | |   (90)  all_57_5 = e2 & op(e2, e1) = e2
% 228.44/39.94  | | | 
% 228.44/39.94  | | | ALPHA: (90) implies:
% 228.44/39.94  | | |   (91)  all_57_5 = e2
% 228.44/39.94  | | | 
% 228.44/39.94  | | | REF_CLOSE: (3), (7), (9), (12), (13), (24), (26), (28), (33), (35), (36),
% 228.44/39.94  | | |            (39), (41), (43), (46), (50), (51), (60), (91) are inconsistent
% 228.44/39.94  | | |            by sub-proof #1752.
% 228.44/39.94  | | | 
% 228.44/39.94  | | End of split
% 228.44/39.94  | | 
% 228.44/39.94  | Case 2:
% 228.44/39.94  | | 
% 228.44/39.94  | |   (92)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) =
% 228.44/39.94  | |           e2)
% 228.44/39.94  | | 
% 228.44/39.94  | | BETA: splitting (92) gives:
% 228.44/39.94  | | 
% 228.44/39.94  | | Case 1:
% 228.44/39.94  | | | 
% 228.44/39.94  | | |   (93)  all_57_8 = e2 & op(e1, e1) = e2
% 228.44/39.94  | | | 
% 228.44/39.94  | | | ALPHA: (93) implies:
% 228.44/39.94  | | |   (94)  all_57_8 = e2
% 228.44/39.94  | | | 
% 228.44/39.94  | | | REF_CLOSE: (21), (60), (94) are inconsistent by sub-proof #1485.
% 228.44/39.94  | | | 
% 228.44/39.94  | | Case 2:
% 228.44/39.94  | | | 
% 228.44/39.94  | | |   (95)  all_57_14 = e2 & op(e0, e1) = e2
% 228.44/39.94  | | | 
% 228.44/39.94  | | | ALPHA: (95) implies:
% 228.44/39.94  | | |   (96)  all_57_14 = e2
% 228.44/39.94  | | | 
% 228.44/39.94  | | | BETA: splitting (23) gives:
% 228.44/39.94  | | | 
% 228.44/39.94  | | | Case 1:
% 228.44/39.94  | | | | 
% 228.44/39.94  | | | |   (97)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2)
% 228.44/39.94  | | | |           = e0)
% 228.44/39.94  | | | | 
% 228.44/39.94  | | | | BETA: splitting (97) gives:
% 228.44/39.94  | | | | 
% 228.44/39.94  | | | | Case 1:
% 228.44/39.94  | | | | | 
% 228.44/39.94  | | | | |   (98)  all_57_0 = e0 & op(e3, e3) = e0
% 228.44/39.94  | | | | | 
% 228.44/39.94  | | | | | ALPHA: (98) implies:
% 228.44/39.94  | | | | |   (99)  op(e3, e3) = e0
% 228.44/39.94  | | | | | 
% 228.44/39.94  | | | | | REF_CLOSE: (9), (34), (39), (99) are inconsistent by sub-proof #2403.
% 228.44/39.94  | | | | | 
% 228.44/39.94  | | | | Case 2:
% 228.44/39.94  | | | | | 
% 228.44/39.94  | | | | |   (100)  all_57_1 = e0 & op(e3, e2) = e0
% 228.44/39.94  | | | | | 
% 228.44/39.94  | | | | | ALPHA: (100) implies:
% 228.44/39.94  | | | | |   (101)  all_57_1 = e0
% 228.44/39.94  | | | | | 
% 228.44/39.94  | | | | | BETA: splitting (4) gives:
% 228.44/39.94  | | | | | 
% 228.44/39.94  | | | | | Case 1:
% 228.44/39.94  | | | | | | 
% 228.44/39.94  | | | | | |   (102)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2,
% 228.44/39.94  | | | | | |              e3) = e1)
% 228.44/39.94  | | | | | | 
% 228.44/39.94  | | | | | | REF_CLOSE: (7), (9), (34), (41), (60), (102) are inconsistent by
% 228.44/39.94  | | | | | |            sub-proof #753.
% 228.44/39.94  | | | | | | 
% 228.44/39.94  | | | | | Case 2:
% 228.44/39.94  | | | | | | 
% 228.44/39.94  | | | | | |   (103)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 &
% 228.44/39.94  | | | | | |            op(e0, e3) = e1)
% 228.44/39.94  | | | | | | 
% 228.44/39.94  | | | | | | BETA: splitting (103) gives:
% 228.44/39.94  | | | | | | 
% 228.44/39.94  | | | | | | Case 1:
% 228.44/39.94  | | | | | | | 
% 228.44/39.94  | | | | | | |   (104)  all_57_6 = e1 & op(e1, e3) = e1
% 228.44/39.94  | | | | | | | 
% 228.44/39.94  | | | | | | | ALPHA: (104) implies:
% 228.44/39.94  | | | | | | |   (105)  all_57_6 = e1
% 228.44/39.94  | | | | | | | 
% 228.44/39.94  | | | | | | | REF_CLOSE: (3), (4), (6), (7), (9), (10), (12), (13), (24), (26),
% 228.44/39.94  | | | | | | |            (28), (33), (36), (39), (41), (42), (43), (46), (47),
% 228.44/39.94  | | | | | | |            (50), (51), (53), (56), (58), (60), (61), (64), (67),
% 228.44/39.94  | | | | | | |            (68), (71), (73), (101), (105) are inconsistent by
% 228.44/39.94  | | | | | | |            sub-proof #537.
% 228.44/39.94  | | | | | | | 
% 228.44/39.94  | | | | | | Case 2:
% 228.44/39.94  | | | | | | | 
% 228.44/39.94  | | | | | | |   (106)  all_57_12 = e1 & op(e0, e3) = e1
% 228.44/39.94  | | | | | | | 
% 228.44/39.94  | | | | | | | ALPHA: (106) implies:
% 228.44/39.94  | | | | | | |   (107)  all_57_12 = e1
% 228.44/39.94  | | | | | | | 
% 228.44/39.94  | | | | | | | BETA: splitting (47) gives:
% 228.44/39.94  | | | | | | | 
% 228.44/39.94  | | | | | | | Case 1:
% 228.44/39.94  | | | | | | | | 
% 228.44/39.94  | | | | | | | |   (108)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 &
% 228.44/39.94  | | | | | | | |            op(e2, e2) = e3)
% 228.44/39.94  | | | | | | | | 
% 228.44/39.94  | | | | | | | | REF_CLOSE: (3), (7), (24), (26), (28), (39), (41), (43), (53),
% 228.44/39.94  | | | | | | | |            (58), (60), (101), (108) are inconsistent by
% 228.44/39.94  | | | | | | | |            sub-proof #542.
% 228.44/39.94  | | | | | | | | 
% 228.44/39.94  | | | | | | | Case 2:
% 228.44/39.94  | | | | | | | | 
% 228.44/39.94  | | | | | | | |   (109)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 &
% 228.44/39.94  | | | | | | | |            op(e0, e2) = e3)
% 228.44/39.94  | | | | | | | | 
% 228.44/39.94  | | | | | | | | BETA: splitting (109) gives:
% 228.44/39.94  | | | | | | | | 
% 228.44/39.94  | | | | | | | | Case 1:
% 228.44/39.94  | | | | | | | | | 
% 228.44/39.94  | | | | | | | | |   (110)  all_57_7 = e3 & op(e1, e2) = e3
% 228.44/39.94  | | | | | | | | | 
% 228.44/39.94  | | | | | | | | | ALPHA: (110) implies:
% 228.44/39.94  | | | | | | | | |   (111)  all_57_7 = e3
% 228.44/39.94  | | | | | | | | | 
% 228.44/39.94  | | | | | | | | | REF_CLOSE: (6), (7), (24), (26), (39), (43), (60), (71),
% 228.44/39.94  | | | | | | | | |            (101), (111) are inconsistent by sub-proof #2098.
% 228.44/39.94  | | | | | | | | | 
% 228.44/39.94  | | | | | | | | Case 2:
% 228.44/39.94  | | | | | | | | | 
% 228.44/39.94  | | | | | | | | |   (112)  all_57_13 = e3 & op(e0, e2) = e3
% 228.44/39.94  | | | | | | | | | 
% 228.44/39.94  | | | | | | | | | REF_CLOSE: (3), (7), (9), (12), (13), (21), (24), (25), (26),
% 228.44/39.94  | | | | | | | | |            (28), (33), (35), (36), (39), (41), (43), (46),
% 228.44/39.94  | | | | | | | | |            (50), (51), (53), (58), (60), (96), (107), (112)
% 228.44/39.94  | | | | | | | | |            are inconsistent by sub-proof #504.
% 228.44/39.94  | | | | | | | | | 
% 228.44/39.94  | | | | | | | | End of split
% 228.44/39.94  | | | | | | | | 
% 228.44/39.94  | | | | | | | End of split
% 228.44/39.94  | | | | | | | 
% 228.44/39.94  | | | | | | End of split
% 228.44/39.94  | | | | | | 
% 228.44/39.94  | | | | | End of split
% 228.44/39.94  | | | | | 
% 228.44/39.94  | | | | End of split
% 228.44/39.94  | | | | 
% 228.44/39.94  | | | Case 2:
% 228.44/39.94  | | | | 
% 228.44/39.94  | | | |   (113)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0)
% 228.44/39.94  | | | |            = e0)
% 228.44/39.94  | | | | 
% 228.44/39.94  | | | | BETA: splitting (113) gives:
% 228.44/39.94  | | | | 
% 228.44/39.94  | | | | Case 1:
% 228.44/39.94  | | | | | 
% 228.44/39.94  | | | | |   (114)  all_57_4 = e0 & op(e3, e1) = e0
% 228.44/39.94  | | | | | 
% 228.44/39.94  | | | | | ALPHA: (114) implies:
% 228.44/39.94  | | | | |   (115)  all_57_4 = e0
% 228.44/39.94  | | | | | 
% 228.44/39.94  | | | | | REF_CLOSE: (3), (7), (9), (12), (13), (24), (26), (28), (33), (35),
% 228.44/39.94  | | | | |            (36), (39), (41), (43), (46), (50), (51), (53), (58), (60),
% 228.44/39.94  | | | | |            (115) are inconsistent by sub-proof #747.
% 228.44/39.94  | | | | | 
% 228.44/39.94  | | | | Case 2:
% 228.44/39.94  | | | | | 
% 228.44/39.94  | | | | |   (116)  all_57_9 = e0 & op(e3, e0) = e0
% 228.44/39.94  | | | | | 
% 228.44/39.94  | | | | | ALPHA: (116) implies:
% 228.44/39.94  | | | | |   (117)  all_57_9 = e0
% 228.44/39.94  | | | | | 
% 228.44/39.94  | | | | | BETA: splitting (4) gives:
% 228.44/39.94  | | | | | 
% 228.44/39.94  | | | | | Case 1:
% 228.44/39.94  | | | | | | 
% 228.44/39.94  | | | | | |   (118)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2,
% 228.44/39.94  | | | | | |              e3) = e1)
% 228.44/39.94  | | | | | | 
% 228.44/39.94  | | | | | | REF_CLOSE: (7), (9), (34), (41), (60), (118) are inconsistent by
% 228.44/39.94  | | | | | |            sub-proof #753.
% 228.44/39.94  | | | | | | 
% 228.44/39.94  | | | | | Case 2:
% 228.44/39.94  | | | | | | 
% 228.44/39.94  | | | | | |   (119)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 &
% 228.44/39.94  | | | | | |            op(e0, e3) = e1)
% 228.44/39.94  | | | | | | 
% 228.44/39.94  | | | | | | BETA: splitting (119) gives:
% 228.44/39.94  | | | | | | 
% 228.44/39.94  | | | | | | Case 1:
% 228.44/39.94  | | | | | | | 
% 228.44/39.94  | | | | | | |   (120)  all_57_6 = e1 & op(e1, e3) = e1
% 228.44/39.94  | | | | | | | 
% 228.44/39.94  | | | | | | | ALPHA: (120) implies:
% 228.44/39.94  | | | | | | |   (121)  all_57_6 = e1
% 228.44/39.94  | | | | | | | 
% 228.44/39.94  | | | | | | | BETA: splitting (47) gives:
% 228.44/39.94  | | | | | | | 
% 228.44/39.94  | | | | | | | Case 1:
% 228.44/39.94  | | | | | | | | 
% 228.44/39.94  | | | | | | | |   (122)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 &
% 228.44/39.94  | | | | | | | |            op(e2, e2) = e3)
% 228.44/39.94  | | | | | | | | 
% 228.44/39.94  | | | | | | | | REF_CLOSE: (3), (7), (9), (12), (13), (16), (24), (26), (28),
% 228.44/39.94  | | | | | | | |            (33), (34), (35), (36), (39), (41), (43), (46), (50),
% 228.44/39.94  | | | | | | | |            (51), (53), (58), (60), (117), (122) are inconsistent
% 228.44/39.94  | | | | | | | |            by sub-proof #503.
% 228.44/39.94  | | | | | | | | 
% 228.44/39.94  | | | | | | | Case 2:
% 228.44/39.94  | | | | | | | | 
% 228.44/39.94  | | | | | | | |   (123)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 &
% 228.44/39.94  | | | | | | | |            op(e0, e2) = e3)
% 228.44/39.94  | | | | | | | | 
% 228.44/39.94  | | | | | | | | BETA: splitting (123) gives:
% 228.44/39.94  | | | | | | | | 
% 228.44/39.94  | | | | | | | | Case 1:
% 228.44/39.94  | | | | | | | | | 
% 228.44/39.94  | | | | | | | | |   (124)  all_57_7 = e3 & op(e1, e2) = e3
% 228.44/39.94  | | | | | | | | | 
% 228.44/39.94  | | | | | | | | | ALPHA: (124) implies:
% 228.44/39.94  | | | | | | | | |   (125)  all_57_7 = e3
% 228.44/39.94  | | | | | | | | | 
% 228.44/39.94  | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 228.44/39.94  | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 228.44/39.94  | | | | | | | | |            (19), (20), (21), (22), (23), (24), (25), (26),
% 228.44/39.94  | | | | | | | | |            (27), (28), (29), (30), (31), (32), (33), (35),
% 228.44/39.94  | | | | | | | | |            (36), (37), (38), (39), (40), (41), (42), (43),
% 228.44/39.94  | | | | | | | | |            (44), (45), (46), (48), (49), (50), (51), (52),
% 228.44/39.94  | | | | | | | | |            (53), (54), (55), (56), (57), (58), (60), (61),
% 228.44/39.94  | | | | | | | | |            (62), (63), (64), (65), (66), (67), (68), (69),
% 228.44/39.94  | | | | | | | | |            (70), (71), (72), (73), (96), (125) are
% 228.44/39.94  | | | | | | | | |            inconsistent by sub-proof #502.
% 228.44/39.94  | | | | | | | | | 
% 228.44/39.94  | | | | | | | | Case 2:
% 228.44/39.94  | | | | | | | | | 
% 228.44/39.94  | | | | | | | | |   (126)  all_57_13 = e3 & op(e0, e2) = e3
% 228.44/39.94  | | | | | | | | | 
% 228.44/39.94  | | | | | | | | | ALPHA: (126) implies:
% 228.44/39.94  | | | | | | | | |   (127)  all_57_13 = e3
% 228.44/39.94  | | | | | | | | | 
% 228.44/39.94  | | | | | | | | | BETA: splitting (42) gives:
% 228.44/39.94  | | | | | | | | | 
% 228.44/39.94  | | | | | | | | | Case 1:
% 228.44/39.94  | | | | | | | | | | 
% 228.44/39.94  | | | | | | | | | |   (128)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 228.44/39.94  | | | | | | | | | |            & op(e3, e2) = e3)
% 228.44/39.94  | | | | | | | | | | 
% 228.44/39.94  | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 228.44/39.94  | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 228.44/39.94  | | | | | | | | | |            (19), (20), (22), (23), (24), (25), (26), (27),
% 228.44/39.94  | | | | | | | | | |            (28), (29), (30), (31), (32), (33), (34), (35),
% 228.44/39.94  | | | | | | | | | |            (36), (37), (38), (39), (40), (41), (42), (43),
% 228.44/39.94  | | | | | | | | | |            (44), (45), (46), (48), (49), (50), (51), (52),
% 228.44/39.94  | | | | | | | | | |            (54), (55), (56), (57), (58), (60), (61), (62),
% 228.44/39.94  | | | | | | | | | |            (63), (64), (65), (66), (67), (68), (69), (70),
% 228.44/39.94  | | | | | | | | | |            (71), (72), (73), (117), (128) are inconsistent by
% 228.44/39.94  | | | | | | | | | |            sub-proof #505.
% 228.44/39.94  | | | | | | | | | | 
% 228.44/39.94  | | | | | | | | | Case 2:
% 228.44/39.94  | | | | | | | | | | 
% 228.44/39.94  | | | | | | | | | |   (129)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 228.44/39.94  | | | | | | | | | |            & op(e3, e0) = e3)
% 228.44/39.94  | | | | | | | | | | 
% 228.44/39.94  | | | | | | | | | | BETA: splitting (129) gives:
% 228.44/39.94  | | | | | | | | | | 
% 228.44/39.94  | | | | | | | | | | Case 1:
% 228.44/39.94  | | | | | | | | | | | 
% 228.44/39.94  | | | | | | | | | | |   (130)  all_57_4 = e3 & op(e3, e1) = e3
% 228.44/39.94  | | | | | | | | | | | 
% 228.44/39.94  | | | | | | | | | | | ALPHA: (130) implies:
% 228.44/39.94  | | | | | | | | | | |   (131)  all_57_4 = e3
% 228.44/39.94  | | | | | | | | | | | 
% 228.44/39.94  | | | | | | | | | | | BETA: splitting (10) gives:
% 228.44/39.94  | | | | | | | | | | | 
% 228.44/39.94  | | | | | | | | | | | Case 1:
% 228.44/39.94  | | | | | | | | | | | | 
% 228.44/39.94  | | | | | | | | | | | |   (132)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 228.44/39.94  | | | | | | | | | | | |            & op(e1, e2) = e3)
% 228.44/39.94  | | | | | | | | | | | | 
% 228.44/39.94  | | | | | | | | | | | | BETA: splitting (132) gives:
% 228.44/39.94  | | | | | | | | | | | | 
% 228.44/39.94  | | | | | | | | | | | | Case 1:
% 228.44/39.94  | | | | | | | | | | | | | 
% 228.44/39.94  | | | | | | | | | | | | |   (133)  all_57_6 = e3 & op(e1, e3) = e3
% 228.44/39.94  | | | | | | | | | | | | | 
% 228.44/39.94  | | | | | | | | | | | | | REF_CLOSE: (3), (7), (9), (12), (13), (24), (26), (28), (33),
% 228.44/39.94  | | | | | | | | | | | | |            (36), (39), (41), (43), (46), (50), (51), (60),
% 228.44/39.94  | | | | | | | | | | | | |            (121), (127), (131), (133) are inconsistent by
% 228.44/39.94  | | | | | | | | | | | | |            sub-proof #538.
% 228.44/39.94  | | | | | | | | | | | | | 
% 228.44/39.94  | | | | | | | | | | | | Case 2:
% 228.44/39.94  | | | | | | | | | | | | | 
% 228.44/39.94  | | | | | | | | | | | | |   (134)  all_57_7 = e3 & op(e1, e2) = e3
% 228.44/39.94  | | | | | | | | | | | | | 
% 228.44/39.94  | | | | | | | | | | | | | ALPHA: (134) implies:
% 228.44/39.94  | | | | | | | | | | | | |   (135)  all_57_7 = e3
% 228.44/39.94  | | | | | | | | | | | | | 
% 228.44/39.94  | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 228.44/39.94  | | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 228.44/39.94  | | | | | | | | | | | | |            (19), (20), (21), (22), (23), (24), (25), (26),
% 228.44/39.94  | | | | | | | | | | | | |            (27), (28), (29), (30), (31), (32), (33), (35),
% 228.44/39.94  | | | | | | | | | | | | |            (36), (37), (38), (39), (40), (41), (42), (43),
% 228.44/39.94  | | | | | | | | | | | | |            (44), (45), (46), (48), (49), (50), (51), (52),
% 228.44/39.94  | | | | | | | | | | | | |            (53), (54), (55), (56), (57), (58), (60), (61),
% 228.44/39.94  | | | | | | | | | | | | |            (62), (63), (64), (65), (66), (67), (68), (69),
% 228.44/39.94  | | | | | | | | | | | | |            (70), (71), (72), (73), (96), (135) are
% 228.44/39.94  | | | | | | | | | | | | |            inconsistent by sub-proof #502.
% 228.44/39.94  | | | | | | | | | | | | | 
% 228.44/39.94  | | | | | | | | | | | | End of split
% 228.44/39.94  | | | | | | | | | | | | 
% 228.44/39.94  | | | | | | | | | | | Case 2:
% 228.44/39.94  | | | | | | | | | | | | 
% 228.44/39.94  | | | | | | | | | | | |   (136)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 228.44/39.94  | | | | | | | | | | | |            e3 & op(e1, e0) = e3)
% 228.44/39.94  | | | | | | | | | | | | 
% 228.44/39.94  | | | | | | | | | | | | REF_CLOSE: (7), (9), (12), (13), (26), (33), (39), (43),
% 228.44/39.94  | | | | | | | | | | | |            (60), (61), (68), (117), (136) are inconsistent by
% 228.44/39.94  | | | | | | | | | | | |            sub-proof #781.
% 228.44/39.94  | | | | | | | | | | | | 
% 228.44/39.94  | | | | | | | | | | | End of split
% 228.44/39.94  | | | | | | | | | | | 
% 228.44/39.94  | | | | | | | | | | Case 2:
% 228.44/39.94  | | | | | | | | | | | 
% 228.44/39.94  | | | | | | | | | | |   (137)  all_57_9 = e3 & op(e3, e0) = e3
% 228.44/39.94  | | | | | | | | | | | 
% 228.44/39.94  | | | | | | | | | | | ALPHA: (137) implies:
% 228.44/39.94  | | | | | | | | | | |   (138)  op(e3, e0) = e3
% 228.44/39.94  | | | | | | | | | | | 
% 228.44/39.94  | | | | | | | | | | | REF_CLOSE: (9), (56), (73), (138) are inconsistent by
% 228.44/39.94  | | | | | | | | | | |            sub-proof #2458.
% 228.44/39.94  | | | | | | | | | | | 
% 228.44/39.94  | | | | | | | | | | End of split
% 228.44/39.94  | | | | | | | | | | 
% 228.44/39.94  | | | | | | | | | End of split
% 228.44/39.94  | | | | | | | | | 
% 228.44/39.94  | | | | | | | | End of split
% 228.44/39.94  | | | | | | | | 
% 228.44/39.94  | | | | | | | End of split
% 228.44/39.94  | | | | | | | 
% 228.44/39.94  | | | | | | Case 2:
% 228.44/39.94  | | | | | | | 
% 228.44/39.94  | | | | | | |   (139)  all_57_12 = e1 & op(e0, e3) = e1
% 228.44/39.94  | | | | | | | 
% 228.44/39.94  | | | | | | | ALPHA: (139) implies:
% 228.44/39.94  | | | | | | |   (140)  all_57_12 = e1
% 228.44/39.94  | | | | | | | 
% 228.44/39.94  | | | | | | | BETA: splitting (47) gives:
% 228.44/39.94  | | | | | | | 
% 228.44/39.94  | | | | | | | Case 1:
% 228.44/39.94  | | | | | | | | 
% 228.44/39.94  | | | | | | | |   (141)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 &
% 228.44/39.94  | | | | | | | |            op(e2, e2) = e3)
% 228.44/39.94  | | | | | | | | 
% 228.44/39.94  | | | | | | | | REF_CLOSE: (3), (7), (9), (12), (13), (16), (24), (26), (28),
% 228.44/39.94  | | | | | | | |            (33), (34), (35), (36), (39), (41), (43), (46), (50),
% 228.44/39.94  | | | | | | | |            (51), (53), (58), (60), (117), (141) are inconsistent
% 228.44/39.94  | | | | | | | |            by sub-proof #503.
% 228.44/39.94  | | | | | | | | 
% 228.44/39.94  | | | | | | | Case 2:
% 228.44/39.94  | | | | | | | | 
% 228.44/39.94  | | | | | | | |   (142)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 &
% 228.44/39.94  | | | | | | | |            op(e0, e2) = e3)
% 228.44/39.94  | | | | | | | | 
% 228.44/39.94  | | | | | | | | BETA: splitting (142) gives:
% 228.44/39.94  | | | | | | | | 
% 228.44/39.94  | | | | | | | | Case 1:
% 228.44/39.94  | | | | | | | | | 
% 228.44/39.94  | | | | | | | | |   (143)  all_57_7 = e3 & op(e1, e2) = e3
% 228.44/39.94  | | | | | | | | | 
% 228.44/39.94  | | | | | | | | | ALPHA: (143) implies:
% 228.44/39.94  | | | | | | | | |   (144)  all_57_7 = e3
% 228.44/39.94  | | | | | | | | | 
% 228.44/39.94  | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 228.44/39.94  | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 228.44/39.94  | | | | | | | | |            (19), (20), (21), (22), (23), (24), (25), (26),
% 228.44/39.94  | | | | | | | | |            (27), (28), (29), (30), (31), (32), (33), (35),
% 228.44/39.94  | | | | | | | | |            (36), (37), (38), (39), (40), (41), (42), (43),
% 228.44/39.94  | | | | | | | | |            (44), (45), (46), (48), (49), (50), (51), (52),
% 228.44/39.94  | | | | | | | | |            (53), (54), (55), (56), (57), (58), (60), (61),
% 228.44/39.94  | | | | | | | | |            (62), (63), (64), (65), (66), (67), (68), (69),
% 228.44/39.94  | | | | | | | | |            (70), (71), (72), (73), (96), (144) are
% 228.44/39.94  | | | | | | | | |            inconsistent by sub-proof #502.
% 228.44/39.94  | | | | | | | | | 
% 228.44/39.94  | | | | | | | | Case 2:
% 228.44/39.94  | | | | | | | | | 
% 228.44/39.94  | | | | | | | | |   (145)  all_57_13 = e3 & op(e0, e2) = e3
% 228.44/39.94  | | | | | | | | | 
% 228.44/39.94  | | | | | | | | | REF_CLOSE: (3), (7), (9), (12), (13), (21), (24), (25), (26),
% 228.44/39.94  | | | | | | | | |            (28), (33), (35), (36), (39), (41), (43), (46),
% 228.44/39.94  | | | | | | | | |            (50), (51), (53), (58), (60), (96), (140), (145)
% 228.44/39.94  | | | | | | | | |            are inconsistent by sub-proof #504.
% 228.44/39.94  | | | | | | | | | 
% 228.44/39.94  | | | | | | | | End of split
% 228.44/39.94  | | | | | | | | 
% 228.44/39.94  | | | | | | | End of split
% 228.44/39.94  | | | | | | | 
% 228.44/39.94  | | | | | | End of split
% 228.44/39.94  | | | | | | 
% 228.44/39.94  | | | | | End of split
% 228.44/39.94  | | | | | 
% 228.44/39.94  | | | | End of split
% 228.44/39.94  | | | | 
% 228.44/39.94  | | | End of split
% 228.44/39.94  | | | 
% 228.44/39.94  | | End of split
% 228.44/39.94  | | 
% 228.44/39.94  | End of split
% 228.44/39.94  | 
% 228.44/39.94  End of proof
% 228.44/39.94  
% 228.44/39.94  Sub-proof #502 shows that the following formulas are inconsistent:
% 228.44/39.94  ----------------------------------------------------------------
% 228.44/39.94    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.44/39.94    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.44/39.94    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.44/39.94         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.44/39.94    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.44/39.94         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.44/39.94    (5)   ~ (all_53_8 = all_53_12)
% 228.44/39.94    (6)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.44/39.94         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.44/39.94    (7)   ~ (e3 = e1)
% 228.44/39.94    (8)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.44/39.94         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.44/39.94    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.44/39.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.44/39.94    (10)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.44/39.94          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.44/39.94    (11)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.44/39.94            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.44/39.94              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.44/39.94    (12)   ~ (all_6_2 = e3)
% 228.44/39.94    (13)  op(e1, e1) = all_6_2
% 228.44/39.94    (14)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.44/39.94    (15)   ~ (all_53_9 = e0)
% 228.44/39.94    (16)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.44/39.94          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.44/39.94    (17)   ~ (all_53_4 = all_53_12)
% 228.44/39.94    (18)   ~ (all_53_8 = all_53_9)
% 228.44/39.94    (19)  all_42_2 = all_6_2
% 228.44/39.94    (20)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.44/39.94          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.44/39.94    (21)  all_57_8 = e1
% 228.44/39.94    (22)   ~ (all_53_9 = all_6_2)
% 228.44/39.94    (23)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.44/39.94          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.44/39.94    (24)  all_57_3 = e0
% 228.44/39.94    (25)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.44/39.94          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.44/39.94    (26)   ~ (e3 = e2)
% 228.44/39.94    (27)  all_55_1 = all_53_4
% 228.44/39.94    (28)   ~ (e3 = e0)
% 228.44/39.94    (29)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.44/39.94          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.44/39.94    (30)   ~ (all_53_8 = all_6_2)
% 228.44/39.94    (31)  all_55_2 = all_53_8
% 228.44/39.94    (32)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.44/39.94    (33)  all_57_15 = e3
% 228.44/39.94    (34)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.44/39.94          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.44/39.94            e1)
% 228.44/39.94    (35)  all_57_10 = e2
% 228.44/39.94    (36)   ~ (all_53_4 = all_53_8)
% 228.44/39.94    (37)  op(e3, e2) = all_53_4
% 228.44/39.94    (38)   ~ (e2 = e0)
% 228.44/39.94    (39)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.44/39.94            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.44/39.94            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.44/39.94            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.44/39.94              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.44/39.94            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.44/39.94            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.44/39.94              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.44/39.94              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.44/39.94            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.44/39.94            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.44/39.94            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.44/39.94              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.44/39.94              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.44/39.94            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.44/39.94              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.44/39.94            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.44/39.94            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.44/39.94              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.44/39.94              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.44/39.94            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.44/39.94            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.44/39.94    (40)  all_57_2 = e3
% 228.44/39.94    (41)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.44/39.94          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.44/39.94    (42)   ~ (e1 = e0)
% 228.44/39.94    (43)  all_57_14 = e2
% 228.44/39.94    (44)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.44/39.94            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.44/39.94              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.44/39.94    (45)   ~ (all_53_4 = e0)
% 228.44/39.94    (46)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.44/39.94          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.44/39.94    (47)  op(e0, e0) = e3
% 228.44/39.94    (48)   ~ (all_53_4 = all_53_6)
% 228.44/39.94    (49)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.44/39.94          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.44/39.94            e2)
% 228.44/39.94    (50)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.44/39.94              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.44/39.94                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.44/39.94                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.44/39.94    (51)  all_55_10 = all_6_2
% 228.44/39.94    (52)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.44/39.94          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.44/39.94    (53)  all_38_2 = all_6_2
% 228.44/39.94    (54)  all_55_3 = all_53_12
% 228.44/39.94    (55)   ~ (all_53_12 = e3)
% 228.44/39.94    (56)  all_57_7 = e3
% 228.44/39.94    (57)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.44/39.94            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.44/39.94              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.44/39.94    (58)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.44/39.94          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.44/39.94    (59)   ~ (e2 = e1)
% 228.44/39.94    (60)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.44/39.94          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.44/39.94    (61)  op(e2, e1) = all_53_9
% 228.44/39.94    (62)  op(e1, e2) = all_53_6
% 228.44/39.94    (63)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.44/39.94          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.44/39.94    (64)  all_24_2 = all_6_2
% 228.44/39.94    (65)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.44/39.94          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.44/39.94    (66)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.44/39.94          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.44/39.94    (67)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.44/39.94          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.44/39.94    (68)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.44/39.94          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.44/39.94    (69)  op(e3, e1) = all_53_8
% 228.44/39.94    (70)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.44/39.94          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.44/39.94    (71)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.44/39.94          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.44/39.94    (72)  op(e3, e0) = all_53_12
% 228.44/39.94  
% 228.44/39.94  Begin of proof
% 228.44/39.94  | 
% 228.44/39.94  | BETA: splitting (25) gives:
% 228.44/39.94  | 
% 228.44/39.94  | Case 1:
% 228.44/39.94  | | 
% 228.44/39.94  | |   (73)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) =
% 228.44/39.94  | |           e0)
% 228.44/39.94  | | 
% 228.44/39.94  | | BETA: splitting (73) gives:
% 228.44/39.94  | | 
% 228.44/39.94  | | Case 1:
% 228.44/39.94  | | | 
% 228.44/39.94  | | |   (74)  all_57_4 = e0 & op(e3, e1) = e0
% 228.44/39.94  | | | 
% 228.44/39.94  | | | ALPHA: (74) implies:
% 228.44/39.94  | | |   (75)  all_57_4 = e0
% 228.44/39.94  | | | 
% 228.44/39.94  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.44/39.94  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (22), (23),
% 228.44/39.94  | | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 228.44/39.94  | | |            (34), (36), (37), (38), (39), (40), (41), (42), (44), (45),
% 228.44/39.94  | | |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (55),
% 228.44/39.94  | | |            (56), (57), (58), (59), (60), (61), (62), (63), (64), (65),
% 228.44/39.94  | | |            (66), (67), (68), (69), (70), (71), (72), (75) are inconsistent
% 228.44/39.94  | | |            by sub-proof #513.
% 228.44/39.94  | | | 
% 228.44/39.95  | | Case 2:
% 228.44/39.95  | | | 
% 228.44/39.95  | | |   (76)  all_57_5 = e0 & op(e2, e1) = e0
% 228.44/39.95  | | | 
% 228.44/39.95  | | | ALPHA: (76) implies:
% 228.44/39.95  | | |   (77)  all_57_5 = e0
% 228.44/39.95  | | | 
% 228.44/39.95  | | | REF_CLOSE: (3), (7), (24), (35), (40), (42), (59), (77) are inconsistent
% 228.44/39.95  | | |            by sub-proof #2359.
% 228.44/39.95  | | | 
% 228.44/39.95  | | End of split
% 228.44/39.95  | | 
% 228.44/39.95  | Case 2:
% 228.44/39.95  | | 
% 228.44/39.95  | |   (78)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 228.44/39.95  | |           e0)
% 228.44/39.95  | | 
% 228.44/39.95  | | BETA: splitting (78) gives:
% 228.44/39.95  | | 
% 228.44/39.95  | | Case 1:
% 228.44/39.95  | | | 
% 228.44/39.95  | | |   (79)  all_57_8 = e0 & op(e1, e1) = e0
% 228.44/39.95  | | | 
% 228.44/39.95  | | | ALPHA: (79) implies:
% 228.44/39.95  | | |   (80)  all_57_8 = e0
% 228.44/39.95  | | | 
% 228.44/39.95  | | | COMBINE_EQS: (21), (80) imply:
% 228.44/39.95  | | |   (81)  e1 = e0
% 228.44/39.95  | | | 
% 228.44/39.95  | | | REDUCE: (42), (81) imply:
% 228.44/39.95  | | |   (82)  $false
% 228.44/39.95  | | | 
% 228.44/39.95  | | | CLOSE: (82) is inconsistent.
% 228.44/39.95  | | | 
% 228.44/39.95  | | Case 2:
% 228.44/39.95  | | | 
% 228.44/39.95  | | |   (83)  all_57_14 = e0 & op(e0, e1) = e0
% 228.44/39.95  | | | 
% 228.44/39.95  | | | REF_CLOSE: (38), (43), (83) are inconsistent by sub-proof #2173.
% 228.44/39.95  | | | 
% 228.44/39.95  | | End of split
% 228.44/39.95  | | 
% 228.44/39.95  | End of split
% 228.44/39.95  | 
% 228.44/39.95  End of proof
% 228.44/39.95  
% 228.44/39.95  Sub-proof #503 shows that the following formulas are inconsistent:
% 228.44/39.95  ----------------------------------------------------------------
% 228.44/39.95    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.44/39.95         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.44/39.95    (2)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3)
% 228.44/39.95    (3)   ~ (e3 = e1)
% 228.44/39.95    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.44/39.95           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.44/39.95    (5)   ~ (all_6_2 = e3)
% 228.44/39.95    (6)  op(e1, e1) = all_6_2
% 228.44/39.95    (7)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.44/39.95         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.44/39.95    (8)  all_57_3 = e0
% 228.44/39.95    (9)   ~ (e3 = e2)
% 228.44/39.95    (10)   ~ (e3 = e0)
% 228.44/39.95    (11)  all_57_15 = e3
% 228.44/39.95    (12)  op(e3, e3) = e2
% 228.44/39.95    (13)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.44/39.95          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.44/39.95            e1)
% 228.44/39.95    (14)  all_57_10 = e2
% 228.44/39.95    (15)  all_57_9 = e0
% 228.44/39.95    (16)   ~ (e2 = e0)
% 228.44/39.95    (17)  all_57_2 = e3
% 228.44/39.95    (18)   ~ (e1 = e0)
% 228.44/39.95    (19)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.44/39.95          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.44/39.95    (20)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.44/39.95          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.44/39.95            e2)
% 228.44/39.95    (21)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.44/39.95              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.44/39.95                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.44/39.95                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.44/39.95    (22)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.44/39.95          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.44/39.95    (23)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.44/39.95          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.44/39.95    (24)   ~ (e2 = e1)
% 228.44/39.95  
% 228.44/39.95  Begin of proof
% 228.44/39.95  | 
% 228.44/39.95  | BETA: splitting (2) gives:
% 228.44/39.95  | 
% 228.44/39.95  | Case 1:
% 228.44/39.95  | | 
% 228.44/39.95  | |   (25)  all_57_1 = e3 & op(e3, e2) = e3
% 228.44/39.95  | | 
% 228.44/39.95  | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 228.44/39.95  | |            (14), (15), (16), (17), (18), (19), (20), (21), (24), (25) are
% 228.44/39.95  | |            inconsistent by sub-proof #506.
% 228.44/39.95  | | 
% 228.44/39.95  | Case 2:
% 228.44/39.95  | | 
% 228.44/39.95  | |   (26)  all_57_3 = e3 & op(e2, e2) = e3
% 228.44/39.95  | | 
% 228.44/39.95  | | ALPHA: (26) implies:
% 228.44/39.95  | |   (27)  all_57_3 = e3
% 228.44/39.95  | | 
% 228.44/39.95  | | COMBINE_EQS: (8), (27) imply:
% 228.44/39.95  | |   (28)  e3 = e0
% 228.44/39.95  | | 
% 228.44/39.95  | | REF_CLOSE: (1), (3), (8), (9), (10), (16), (17), (18), (22), (23), (24),
% 228.44/39.95  | |            (28) are inconsistent by sub-proof #1333.
% 228.44/39.95  | | 
% 228.44/39.95  | End of split
% 228.44/39.95  | 
% 228.44/39.95  End of proof
% 228.44/39.95  
% 228.44/39.95  Sub-proof #504 shows that the following formulas are inconsistent:
% 228.44/39.95  ----------------------------------------------------------------
% 228.44/39.95    (1)  all_57_13 = e3 & op(e0, e2) = e3
% 228.44/39.95    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.44/39.95         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.44/39.95    (3)   ~ (e3 = e1)
% 228.44/39.95    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.44/39.95           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.44/39.95    (5)   ~ (all_6_2 = e3)
% 228.44/39.95    (6)  op(e1, e1) = all_6_2
% 228.44/39.95    (7)  all_57_8 = e1
% 228.44/39.95    (8)  all_57_3 = e0
% 228.44/39.95    (9)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.44/39.95         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.44/39.95    (10)   ~ (e3 = e2)
% 228.44/39.95    (11)   ~ (e3 = e0)
% 228.44/39.95    (12)  all_57_15 = e3
% 228.44/39.95    (13)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.44/39.95          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.44/39.95            e1)
% 228.44/39.95    (14)  all_57_10 = e2
% 228.44/39.95    (15)  all_57_12 = e1
% 228.44/39.95    (16)   ~ (e2 = e0)
% 228.44/39.95    (17)  all_57_2 = e3
% 228.44/39.95    (18)   ~ (e1 = e0)
% 228.44/39.95    (19)  all_57_14 = e2
% 228.44/39.95    (20)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.44/39.95          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.44/39.95    (21)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.44/39.95          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.44/39.95            e2)
% 228.44/39.95    (22)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.44/39.95              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.44/39.95                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.44/39.95                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.44/39.95    (23)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.44/39.95          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.44/39.95    (24)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.44/39.95          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.44/39.95    (25)   ~ (e2 = e1)
% 228.44/39.95  
% 228.44/39.95  Begin of proof
% 228.44/39.95  | 
% 228.44/39.95  | ALPHA: (1) implies:
% 228.44/39.95  |   (26)  all_57_13 = e3
% 228.44/39.95  | 
% 228.44/39.95  | BETA: splitting (9) gives:
% 228.44/39.95  | 
% 228.44/39.95  | Case 1:
% 228.44/39.95  | | 
% 228.44/39.95  | |   (27)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) =
% 228.44/39.95  | |           e0)
% 228.44/39.95  | | 
% 228.44/39.95  | | BETA: splitting (27) gives:
% 228.44/39.95  | | 
% 228.44/39.95  | | Case 1:
% 228.44/39.95  | | | 
% 228.44/39.95  | | |   (28)  all_57_4 = e0 & op(e3, e1) = e0
% 228.44/39.95  | | | 
% 228.44/39.95  | | | ALPHA: (28) implies:
% 228.44/39.95  | | |   (29)  all_57_4 = e0
% 228.44/39.95  | | | 
% 228.44/39.95  | | | BETA: splitting (20) gives:
% 228.44/39.95  | | | 
% 228.44/39.95  | | | Case 1:
% 228.44/39.95  | | | | 
% 228.44/39.95  | | | |   (30)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1)
% 228.44/39.95  | | | |           = e3)
% 228.44/39.95  | | | | 
% 228.44/39.95  | | | | REF_CLOSE: (2), (3), (8), (10), (11), (14), (16), (17), (18), (23),
% 228.44/39.95  | | | |            (24), (25), (29), (30) are inconsistent by sub-proof #748.
% 228.44/39.95  | | | | 
% 228.44/39.95  | | | Case 2:
% 228.44/39.95  | | | | 
% 228.44/39.95  | | | |   (31)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1)
% 228.44/39.95  | | | |           = e3)
% 228.44/39.95  | | | | 
% 228.44/39.95  | | | | REF_CLOSE: (4), (5), (6), (10), (11), (12), (16), (21), (22), (26), (31)
% 228.44/39.95  | | | |            are inconsistent by sub-proof #540.
% 228.44/39.95  | | | | 
% 228.44/39.95  | | | End of split
% 228.44/39.95  | | | 
% 228.44/39.95  | | Case 2:
% 228.44/39.95  | | | 
% 228.44/39.95  | | |   (32)  all_57_5 = e0 & op(e2, e1) = e0
% 228.44/39.95  | | | 
% 228.44/39.95  | | | ALPHA: (32) implies:
% 228.44/39.95  | | |   (33)  all_57_5 = e0
% 228.44/39.95  | | | 
% 228.44/39.95  | | | REF_CLOSE: (2), (3), (8), (14), (17), (18), (25), (33) are inconsistent by
% 228.44/39.95  | | |            sub-proof #2359.
% 228.44/39.95  | | | 
% 228.44/39.95  | | End of split
% 228.44/39.95  | | 
% 228.44/39.95  | Case 2:
% 228.44/39.95  | | 
% 228.44/39.95  | |   (34)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 228.44/39.95  | |           e0)
% 228.44/39.95  | | 
% 228.44/39.95  | | BETA: splitting (34) gives:
% 228.44/39.95  | | 
% 228.44/39.95  | | Case 1:
% 228.44/39.95  | | | 
% 228.44/39.95  | | |   (35)  all_57_8 = e0 & op(e1, e1) = e0
% 228.44/39.95  | | | 
% 228.44/39.95  | | | ALPHA: (35) implies:
% 228.44/39.95  | | |   (36)  all_57_8 = e0
% 228.44/39.95  | | | 
% 228.44/39.95  | | | COMBINE_EQS: (7), (36) imply:
% 228.44/39.95  | | |   (37)  e1 = e0
% 228.44/39.95  | | | 
% 228.44/39.95  | | | COMBINE_EQS: (15), (37) imply:
% 228.44/39.95  | | |   (38)  all_57_12 = e0
% 228.44/39.95  | | | 
% 228.44/39.95  | | | REF_CLOSE: (3), (12), (13), (18), (19), (25), (26), (38) are inconsistent
% 228.44/39.95  | | |            by sub-proof #2215.
% 228.44/39.95  | | | 
% 228.44/39.95  | | Case 2:
% 228.44/39.95  | | | 
% 228.44/39.95  | | |   (39)  all_57_14 = e0 & op(e0, e1) = e0
% 228.44/39.95  | | | 
% 228.44/39.95  | | | REF_CLOSE: (16), (19), (39) are inconsistent by sub-proof #2173.
% 228.44/39.95  | | | 
% 228.44/39.95  | | End of split
% 228.44/39.95  | | 
% 228.44/39.95  | End of split
% 228.44/39.95  | 
% 228.44/39.95  End of proof
% 228.44/39.95  
% 228.44/39.95  Sub-proof #505 shows that the following formulas are inconsistent:
% 228.44/39.95  ----------------------------------------------------------------
% 228.44/39.95    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.44/39.95    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.44/39.95    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.44/39.95         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.44/39.95    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.44/39.95         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.44/39.95    (5)   ~ (all_53_8 = all_53_12)
% 228.44/39.95    (6)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.44/39.95         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.44/39.95    (7)   ~ (e3 = e1)
% 228.44/39.95    (8)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.44/39.95         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.44/39.95    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.44/39.95           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.44/39.95    (10)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.44/39.95          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.44/39.95    (11)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.44/39.95            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.44/39.95              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.44/39.95    (12)   ~ (all_6_2 = e3)
% 228.44/39.95    (13)  op(e1, e1) = all_6_2
% 228.44/39.95    (14)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.44/39.95    (15)   ~ (all_53_9 = e0)
% 228.44/39.95    (16)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.44/39.95          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.44/39.95    (17)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3)
% 228.44/39.95    (18)   ~ (all_53_4 = all_53_12)
% 228.44/39.95    (19)   ~ (all_53_8 = all_53_9)
% 228.44/39.95    (20)  all_42_2 = all_6_2
% 228.44/39.95    (21)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.44/39.95          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.44/39.95    (22)   ~ (all_53_9 = all_6_2)
% 228.44/39.95    (23)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.44/39.95          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.44/39.95    (24)  all_57_3 = e0
% 228.44/39.95    (25)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.44/39.95          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.44/39.95    (26)   ~ (e3 = e2)
% 228.44/39.95    (27)  all_55_1 = all_53_4
% 228.44/39.95    (28)   ~ (e3 = e0)
% 228.44/39.95    (29)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.44/39.95          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.44/39.95    (30)   ~ (all_53_8 = all_6_2)
% 228.44/39.95    (31)  all_55_2 = all_53_8
% 228.44/39.95    (32)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.44/39.95    (33)  all_57_15 = e3
% 228.44/39.95    (34)  op(e3, e3) = e2
% 228.44/39.95    (35)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.44/39.95          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.44/39.95            e1)
% 228.44/39.95    (36)  all_57_10 = e2
% 228.44/39.95    (37)  all_57_9 = e0
% 228.44/39.95    (38)   ~ (all_53_4 = all_53_8)
% 228.44/39.95    (39)  op(e3, e2) = all_53_4
% 228.44/39.95    (40)   ~ (e2 = e0)
% 228.44/39.95    (41)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.44/39.95            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.44/39.95            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.44/39.95            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.44/39.95              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.44/39.95            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.44/39.95            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.44/39.95              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.44/39.95              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.44/39.95            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.44/39.95            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.44/39.95            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.44/39.95              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.44/39.95              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.44/39.95            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.44/39.95              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.44/39.95            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.44/39.95            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.44/39.95              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.44/39.95              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.44/39.95            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.44/39.95            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.44/39.95    (42)  all_57_2 = e3
% 228.44/39.95    (43)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.44/39.95          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.44/39.95    (44)   ~ (e1 = e0)
% 228.44/39.95    (45)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.44/39.95            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.44/39.95              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.44/39.95    (46)   ~ (all_53_4 = e0)
% 228.44/39.95    (47)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.44/39.95          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.44/39.95    (48)  op(e0, e0) = e3
% 228.44/39.95    (49)   ~ (all_53_4 = all_53_6)
% 228.44/39.95    (50)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.44/39.95          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.44/39.95            e2)
% 228.44/39.95    (51)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.44/39.95              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.44/39.95                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.44/39.95                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.44/39.95    (52)  all_55_10 = all_6_2
% 228.44/39.95    (53)  all_38_2 = all_6_2
% 228.44/39.95    (54)  all_55_3 = all_53_12
% 228.44/39.95    (55)   ~ (all_53_12 = e3)
% 228.44/39.95    (56)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.44/39.95            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.44/39.95              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.44/39.95    (57)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.44/39.95          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.44/39.95    (58)   ~ (e2 = e1)
% 228.44/39.95    (59)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.44/39.95          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.44/39.95    (60)  op(e2, e1) = all_53_9
% 228.44/39.95    (61)  op(e1, e2) = all_53_6
% 228.44/39.95    (62)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.44/39.95          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.44/39.95    (63)  all_24_2 = all_6_2
% 228.44/39.95    (64)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.44/39.95          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.44/39.95    (65)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.44/39.95          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.44/39.95    (66)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.44/39.95          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.44/39.95    (67)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.44/39.95          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.44/39.95    (68)  op(e3, e1) = all_53_8
% 228.44/39.95    (69)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.44/39.95          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.44/39.95    (70)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.44/39.95          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.44/39.95    (71)  op(e3, e0) = all_53_12
% 228.44/39.95  
% 228.44/39.95  Begin of proof
% 228.44/39.95  | 
% 228.44/39.95  | BETA: splitting (17) gives:
% 228.44/39.95  | 
% 228.44/39.95  | Case 1:
% 228.44/39.95  | | 
% 228.44/39.95  | |   (72)  all_57_0 = e3 & op(e3, e3) = e3
% 228.44/39.95  | | 
% 228.44/39.95  | | ALPHA: (72) implies:
% 228.44/39.95  | |   (73)  op(e3, e3) = e3
% 228.44/39.95  | | 
% 228.44/39.95  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.44/39.95  | |            (13), (14), (15), (16), (18), (19), (20), (21), (22), (23), (24),
% 228.44/39.95  | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (35), (38),
% 228.44/39.95  | |            (39), (40), (41), (42), (43), (44), (45), (46), (47), (48), (49),
% 228.44/39.95  | |            (50), (51), (52), (53), (54), (55), (56), (57), (58), (59), (60),
% 228.44/39.95  | |            (61), (62), (63), (64), (65), (66), (67), (68), (69), (70), (71),
% 228.44/39.95  | |            (73) are inconsistent by sub-proof #1437.
% 228.44/39.95  | | 
% 228.44/39.95  | Case 2:
% 228.44/39.95  | | 
% 228.44/39.95  | |   (74)  all_57_1 = e3 & op(e3, e2) = e3
% 228.44/39.95  | | 
% 228.44/39.95  | | REF_CLOSE: (3), (7), (9), (12), (13), (16), (24), (26), (28), (33), (34),
% 228.44/39.95  | |            (35), (36), (37), (40), (42), (44), (47), (50), (51), (58), (74)
% 228.44/39.95  | |            are inconsistent by sub-proof #506.
% 228.44/39.95  | | 
% 228.44/39.95  | End of split
% 228.44/39.95  | 
% 228.44/39.95  End of proof
% 228.44/39.95  
% 228.44/39.95  Sub-proof #506 shows that the following formulas are inconsistent:
% 228.44/39.95  ----------------------------------------------------------------
% 228.44/39.95    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.44/39.95         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.44/39.95    (2)   ~ (e3 = e1)
% 228.44/39.95    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.44/39.95           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.44/39.95    (4)   ~ (all_6_2 = e3)
% 228.44/39.95    (5)  op(e1, e1) = all_6_2
% 228.44/39.95    (6)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.44/39.95         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.44/39.95    (7)  all_57_3 = e0
% 228.44/39.95    (8)   ~ (e3 = e2)
% 228.44/39.95    (9)   ~ (e3 = e0)
% 228.44/39.95    (10)  all_57_15 = e3
% 228.44/39.95    (11)  op(e3, e3) = e2
% 228.44/39.95    (12)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.44/39.95          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.44/39.95            e1)
% 228.44/39.95    (13)  all_57_10 = e2
% 228.44/39.95    (14)  all_57_9 = e0
% 228.44/39.95    (15)   ~ (e2 = e0)
% 228.44/39.95    (16)  all_57_2 = e3
% 228.44/39.95    (17)   ~ (e1 = e0)
% 228.44/39.95    (18)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.44/39.95          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.44/39.95    (19)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.44/39.95          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.44/39.95            e2)
% 228.44/39.95    (20)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.44/39.95              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.44/39.95                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.44/39.95                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.44/39.95    (21)  all_57_1 = e3 & op(e3, e2) = e3
% 228.44/39.95    (22)   ~ (e2 = e1)
% 228.44/39.95  
% 228.44/39.95  Begin of proof
% 228.44/39.95  | 
% 228.44/39.95  | ALPHA: (21) implies:
% 228.44/39.95  |   (23)  all_57_1 = e3
% 228.44/39.95  | 
% 228.44/39.95  | BETA: splitting (6) gives:
% 228.44/39.95  | 
% 228.44/39.95  | Case 1:
% 228.44/39.95  | | 
% 228.44/39.95  | |   (24)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) =
% 228.44/39.95  | |           e1)
% 228.44/39.95  | | 
% 228.44/39.95  | | REF_CLOSE: (2), (3), (11), (22), (23), (24) are inconsistent by sub-proof
% 228.44/39.95  | |            #1607.
% 228.44/39.95  | | 
% 228.44/39.95  | Case 2:
% 228.44/39.95  | | 
% 228.44/39.95  | |   (25)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) =
% 228.44/39.95  | |           e1)
% 228.44/39.95  | | 
% 228.44/39.95  | | BETA: splitting (25) gives:
% 228.44/39.95  | | 
% 228.44/39.95  | | Case 1:
% 228.44/39.95  | | | 
% 228.44/39.95  | | |   (26)  all_57_4 = e1 & op(e3, e1) = e1
% 228.44/39.95  | | | 
% 228.44/39.95  | | | ALPHA: (26) implies:
% 228.44/39.95  | | |   (27)  all_57_4 = e1
% 228.44/39.95  | | | 
% 228.44/39.95  | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (12), (13), (15),
% 228.44/39.95  | | |            (16), (17), (18), (19), (20), (22), (27) are inconsistent by
% 228.44/39.95  | | |            sub-proof #1755.
% 228.44/39.95  | | | 
% 228.44/39.95  | | Case 2:
% 228.44/39.95  | | | 
% 228.44/39.95  | | |   (28)  all_57_9 = e1 & op(e3, e0) = e1
% 228.44/39.95  | | | 
% 228.44/39.95  | | | REF_CLOSE: (14), (17), (28) are inconsistent by sub-proof #2437.
% 228.44/39.95  | | | 
% 228.44/39.95  | | End of split
% 228.44/39.95  | | 
% 228.44/39.95  | End of split
% 228.44/39.95  | 
% 228.44/39.95  End of proof
% 228.44/39.95  
% 228.44/39.95  Sub-proof #507 shows that the following formulas are inconsistent:
% 228.44/39.95  ----------------------------------------------------------------
% 228.44/39.95    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.44/39.95    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.44/39.95    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.44/39.95         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.44/39.95    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.44/39.95         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.44/39.95    (5)   ~ (all_53_8 = all_53_12)
% 228.44/39.95    (6)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.44/39.95         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.44/39.95    (7)   ~ (e3 = e1)
% 228.44/39.95    (8)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.44/39.95         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.44/39.95    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.44/39.95           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.44/39.95    (10)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.44/39.95          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.44/39.95    (11)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.44/39.95            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.44/39.95              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.44/39.95    (12)   ~ (all_6_2 = e3)
% 228.44/39.95    (13)  op(e1, e1) = all_6_2
% 228.44/39.95    (14)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.44/39.95    (15)  all_57_4 = e2
% 228.44/39.95    (16)   ~ (all_53_9 = e0)
% 228.44/39.95    (17)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.44/39.95          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.44/39.95    (18)   ~ (all_53_4 = all_53_12)
% 228.44/39.95    (19)   ~ (all_53_8 = all_53_9)
% 228.44/39.95    (20)  all_42_2 = all_6_2
% 228.44/39.95    (21)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.44/39.95          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.44/39.95    (22)   ~ (all_53_9 = all_6_2)
% 228.44/39.95    (23)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.44/39.95          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.44/39.95    (24)  all_57_3 = e0
% 228.44/39.96    (25)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.44/39.96          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.44/39.96    (26)   ~ (e3 = e2)
% 228.44/39.96    (27)  all_55_1 = all_53_4
% 228.44/39.96    (28)   ~ (e3 = e0)
% 228.44/39.96    (29)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.44/39.96          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.44/39.96    (30)   ~ (all_53_8 = all_6_2)
% 228.44/39.96    (31)  all_55_2 = all_53_8
% 228.44/39.96    (32)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.44/39.96    (33)  all_57_15 = e3
% 228.44/39.96    (34)  op(e3, e3) = e2
% 228.44/39.96    (35)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.44/39.96          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.44/39.96            e1)
% 228.44/39.96    (36)   ~ (all_53_4 = all_53_8)
% 228.44/39.96    (37)  op(e3, e2) = all_53_4
% 228.44/39.96    (38)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.44/39.96    (39)   ~ (e2 = e0)
% 228.44/39.96    (40)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.44/39.96            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.44/39.96            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.44/39.96            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.44/39.96              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.44/39.96            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.44/39.96            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.44/39.96              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.44/39.96              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.44/39.96            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.44/39.96            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.44/39.96            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.44/39.96              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.44/39.96              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.44/39.96            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.44/39.96              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.44/39.96            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.44/39.96            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.44/39.96              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.44/39.96              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.44/39.96            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.44/39.96            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.44/39.96    (41)  all_57_2 = e3
% 228.44/39.96    (42)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.44/39.96          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.44/39.96    (43)   ~ (e1 = e0)
% 228.44/39.96    (44)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.44/39.96            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.44/39.96              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.44/39.96    (45)   ~ (all_53_4 = e0)
% 228.44/39.96    (46)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.44/39.96          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.44/39.96    (47)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.44/39.96          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.44/39.96    (48)  op(e0, e0) = e3
% 228.44/39.96    (49)   ~ (all_53_4 = all_53_6)
% 228.46/39.96    (50)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.46/39.96          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.46/39.96            e2)
% 228.46/39.96    (51)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.46/39.96              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.46/39.96                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.46/39.96                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.46/39.96    (52)  all_55_10 = all_6_2
% 228.46/39.96    (53)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.46/39.96          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.46/39.96    (54)  all_38_2 = all_6_2
% 228.46/39.96    (55)  all_55_3 = all_53_12
% 228.46/39.96    (56)   ~ (all_53_12 = e3)
% 228.46/39.96    (57)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.46/39.96            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.46/39.96              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.46/39.96    (58)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.46/39.96          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.46/39.96    (59)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.46/39.96          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.46/39.96    (60)   ~ (e2 = e1)
% 228.46/39.96    (61)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.46/39.96          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.46/39.96    (62)  op(e2, e1) = all_53_9
% 228.46/39.96    (63)  op(e1, e2) = all_53_6
% 228.46/39.96    (64)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.46/39.96          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.46/39.96    (65)  all_24_2 = all_6_2
% 228.46/39.96    (66)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.46/39.96          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.46/39.96    (67)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.46/39.96          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.46/39.96    (68)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.46/39.96          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.46/39.96    (69)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.46/39.96          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.46/39.96    (70)  op(e3, e1) = all_53_8
% 228.46/39.96    (71)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.46/39.96          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.46/39.96    (72)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.46/39.96          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.46/39.96    (73)  op(e3, e0) = all_53_12
% 228.46/39.96  
% 228.46/39.96  Begin of proof
% 228.46/39.96  | 
% 228.46/39.96  | BETA: splitting (38) gives:
% 228.46/39.96  | 
% 228.46/39.96  | Case 1:
% 228.46/39.96  | | 
% 228.46/39.96  | |   (74)  all_57_4 = e3 & op(e3, e1) = e3
% 228.46/39.96  | | 
% 228.46/39.96  | | ALPHA: (74) implies:
% 228.46/39.96  | |   (75)  all_57_4 = e3
% 228.46/39.96  | | 
% 228.46/39.96  | | COMBINE_EQS: (15), (75) imply:
% 228.46/39.96  | |   (76)  e3 = e2
% 228.46/39.96  | | 
% 228.46/39.96  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.46/39.96  | |            (13), (14), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 228.46/39.96  | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 228.46/39.96  | |            (36), (37), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 228.46/39.96  | |            (48), (49), (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 228.46/39.96  | |            (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 228.46/39.96  | |            (70), (71), (72), (73), (76) are inconsistent by sub-proof #534.
% 228.46/39.96  | | 
% 228.46/39.96  | Case 2:
% 228.46/39.96  | | 
% 228.46/39.96  | |   (77)  all_57_9 = e3 & op(e3, e0) = e3
% 228.46/39.96  | | 
% 228.46/39.96  | | ALPHA: (77) implies:
% 228.46/39.96  | |   (78)  op(e3, e0) = e3
% 228.46/39.96  | | 
% 228.46/39.96  | | REF_CLOSE: (9), (56), (73), (78) are inconsistent by sub-proof #2458.
% 228.46/39.96  | | 
% 228.46/39.96  | End of split
% 228.46/39.96  | 
% 228.46/39.96  End of proof
% 228.46/39.96  
% 228.46/39.96  Sub-proof #508 shows that the following formulas are inconsistent:
% 228.46/39.96  ----------------------------------------------------------------
% 228.46/39.96    (1)  all_57_0 = e2
% 228.46/39.96    (2)  all_57_12 = e0
% 228.46/39.96    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.46/39.96         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.46/39.96    (4)   ~ (e3 = e1)
% 228.46/39.96    (5)  all_57_8 = e0 & op(e1, e1) = e0
% 228.46/39.96    (6)   ~ (e3 = e2)
% 228.46/39.96    (7)   ~ (e2 = e0)
% 228.46/39.96    (8)   ~ (e1 = e0)
% 228.46/39.96    (9)  all_57_8 = e2
% 228.46/39.96    (10)  all_57_6 = e3
% 228.46/39.96    (11)   ~ (e2 = e1)
% 228.46/39.96    (12)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.46/39.96          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.46/39.96  
% 228.46/39.96  Begin of proof
% 228.46/39.96  | 
% 228.46/39.96  | ALPHA: (5) implies:
% 228.46/39.96  |   (13)  all_57_8 = e0
% 228.46/39.96  | 
% 228.46/39.96  | COMBINE_EQS: (9), (13) imply:
% 228.46/39.96  |   (14)  e2 = e0
% 228.46/39.96  | 
% 228.46/39.96  | COMBINE_EQS: (1), (14) imply:
% 228.46/39.96  |   (15)  all_57_0 = e0
% 228.46/39.96  | 
% 228.46/39.96  | REF_CLOSE: (2), (3), (4), (6), (7), (8), (10), (11), (12), (15) are
% 228.46/39.96  |            inconsistent by sub-proof #1425.
% 228.46/39.96  | 
% 228.46/39.96  End of proof
% 228.46/39.96  
% 228.46/39.96  Sub-proof #509 shows that the following formulas are inconsistent:
% 228.46/39.96  ----------------------------------------------------------------
% 228.46/39.96    (1)  all_57_7 = e0 & op(e1, e2) = e0
% 228.46/39.96    (2)  all_57_7 = e1
% 228.46/39.96    (3)   ~ (e1 = e0)
% 228.46/39.96  
% 228.46/39.96  Begin of proof
% 228.46/39.96  | 
% 228.46/39.96  | ALPHA: (1) implies:
% 228.46/39.96  |   (4)  all_57_7 = e0
% 228.46/39.96  | 
% 228.46/39.96  | COMBINE_EQS: (2), (4) imply:
% 228.46/39.96  |   (5)  e1 = e0
% 228.46/39.96  | 
% 228.46/39.96  | REDUCE: (3), (5) imply:
% 228.46/39.96  |   (6)  $false
% 228.46/39.96  | 
% 228.46/39.96  | CLOSE: (6) is inconsistent.
% 228.46/39.96  | 
% 228.46/39.96  End of proof
% 228.46/39.96  
% 228.46/39.96  Sub-proof #510 shows that the following formulas are inconsistent:
% 228.46/39.96  ----------------------------------------------------------------
% 228.46/39.96    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.46/39.96    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.46/39.96    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.46/39.96         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.46/39.96    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.46/39.96         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.46/39.96    (5)   ~ (all_53_8 = all_53_12)
% 228.46/39.96    (6)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.46/39.96         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.46/39.96    (7)   ~ (e3 = e1)
% 228.46/39.96    (8)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.46/39.96         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.46/39.96    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.46/39.96           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.46/39.96    (10)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.46/39.96          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.46/39.96    (11)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.46/39.96            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.46/39.96              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.46/39.96    (12)   ~ (all_6_2 = e3)
% 228.46/39.96    (13)  op(e1, e1) = all_6_2
% 228.46/39.96    (14)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.46/39.96    (15)   ~ (all_53_9 = e0)
% 228.46/39.96    (16)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.46/39.96          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.46/39.96    (17)   ~ (all_53_4 = all_53_12)
% 228.46/39.96    (18)   ~ (all_53_8 = all_53_9)
% 228.46/39.96    (19)  all_42_2 = all_6_2
% 228.46/39.96    (20)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.46/39.96          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.46/39.96    (21)   ~ (all_53_9 = all_6_2)
% 228.46/39.96    (22)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.46/39.96          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.46/39.96    (23)  all_57_3 = e0
% 228.46/39.96    (24)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.46/39.96          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.46/39.96    (25)   ~ (e3 = e2)
% 228.46/39.96    (26)  all_55_1 = all_53_4
% 228.46/39.96    (27)   ~ (e3 = e0)
% 228.46/39.96    (28)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.46/39.96          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.46/39.96    (29)   ~ (all_53_8 = all_6_2)
% 228.46/39.96    (30)  all_55_2 = all_53_8
% 228.46/39.96    (31)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.46/39.96    (32)  all_57_15 = e3
% 228.46/39.96    (33)  op(e3, e3) = e2
% 228.46/39.96    (34)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.46/39.96          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.46/39.96            e1)
% 228.46/39.96    (35)   ~ (all_53_4 = all_53_8)
% 228.46/39.96    (36)  op(e3, e2) = all_53_4
% 228.46/39.96    (37)  op(e1, e1) = e1
% 228.46/39.96    (38)   ~ (e2 = e0)
% 228.46/39.96    (39)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.46/39.96            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.46/39.96            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.46/39.96            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.46/39.96              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.46/39.96            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.46/39.96            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.46/39.96              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.46/39.96              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.46/39.96            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.46/39.96            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.46/39.96            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.46/39.96              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.46/39.96              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.46/39.96            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.46/39.96              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.46/39.96            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.46/39.96            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.46/39.96              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.46/39.96              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.46/39.96            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.46/39.96            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.46/39.96    (40)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.46/39.96          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.46/39.96    (41)   ~ (e1 = e0)
% 228.46/39.96    (42)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.46/39.96            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.46/39.96              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.46/39.96    (43)   ~ (all_53_4 = e0)
% 228.46/39.96    (44)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.46/39.96          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.46/39.96    (45)  all_57_6 = e3
% 228.46/39.96    (46)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.46/39.96          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.46/39.96    (47)  op(e0, e0) = e3
% 228.46/39.96    (48)   ~ (all_53_4 = all_53_6)
% 228.46/39.96    (49)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.46/39.96          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.46/39.96            e2)
% 228.46/39.96    (50)  all_57_6 = e0 & op(e1, e3) = e0
% 228.46/39.96    (51)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.46/39.96              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.46/39.96                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.46/39.96                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.46/39.96    (52)  all_55_10 = all_6_2
% 228.46/39.96    (53)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.46/39.96          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.46/39.96    (54)  all_38_2 = all_6_2
% 228.46/39.96    (55)  all_55_3 = all_53_12
% 228.46/39.96    (56)   ~ (all_53_12 = e3)
% 228.46/39.96    (57)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.46/39.96            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.46/39.96              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.46/39.96    (58)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.46/39.96          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.46/39.96    (59)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.46/39.96          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.46/39.96    (60)  all_57_1 = e3
% 228.46/39.96    (61)   ~ (e2 = e1)
% 228.46/39.96    (62)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.46/39.96          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.46/39.96    (63)  op(e2, e1) = all_53_9
% 228.46/39.96    (64)  op(e1, e2) = all_53_6
% 228.46/39.96    (65)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.46/39.96          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.46/39.96    (66)  all_24_2 = all_6_2
% 228.46/39.96    (67)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.46/39.96          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.46/39.96    (68)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.46/39.96          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.46/39.96    (69)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.46/39.96          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.46/39.96    (70)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.46/39.96          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.46/39.96    (71)  op(e3, e1) = all_53_8
% 228.46/39.96    (72)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.46/39.96          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.46/39.96    (73)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.46/39.96          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.46/39.96    (74)  op(e3, e0) = all_53_12
% 228.46/39.96  
% 228.46/39.96  Begin of proof
% 228.46/39.96  | 
% 228.46/39.96  | ALPHA: (50) implies:
% 228.46/39.96  |   (75)  all_57_6 = e0
% 228.46/39.96  | 
% 228.46/39.96  | COMBINE_EQS: (45), (75) imply:
% 228.46/39.96  |   (76)  e3 = e0
% 228.46/39.96  | 
% 228.46/39.96  | COMBINE_EQS: (60), (76) imply:
% 228.46/39.96  |   (77)  all_57_1 = e0
% 228.46/39.96  | 
% 228.46/39.96  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.46/39.96  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 228.46/39.96  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 228.46/39.96  |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (46),
% 228.46/39.96  |            (47), (48), (49), (51), (52), (53), (54), (55), (56), (57), (58),
% 228.46/39.96  |            (59), (61), (62), (63), (64), (65), (66), (67), (68), (69), (70),
% 228.46/39.96  |            (71), (72), (73), (74), (77) are inconsistent by sub-proof #511.
% 228.46/39.96  | 
% 228.46/39.96  End of proof
% 228.46/39.96  
% 228.46/39.96  Sub-proof #511 shows that the following formulas are inconsistent:
% 228.46/39.96  ----------------------------------------------------------------
% 228.46/39.96    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.46/39.96    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.46/39.96    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.46/39.96         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.46/39.96    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.46/39.96         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.46/39.96    (5)   ~ (all_53_8 = all_53_12)
% 228.46/39.96    (6)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.46/39.96         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.46/39.96    (7)   ~ (e3 = e1)
% 228.46/39.96    (8)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.46/39.96         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.46/39.96    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.46/39.96           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.46/39.96    (10)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.46/39.96          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.46/39.96    (11)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.46/39.96            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.46/39.96              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.46/39.96    (12)   ~ (all_6_2 = e3)
% 228.46/39.96    (13)  op(e1, e1) = all_6_2
% 228.46/39.96    (14)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.46/39.96    (15)   ~ (all_53_9 = e0)
% 228.46/39.96    (16)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.46/39.96          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.46/39.96    (17)   ~ (all_53_4 = all_53_12)
% 228.46/39.96    (18)   ~ (all_53_8 = all_53_9)
% 228.46/39.96    (19)  all_42_2 = all_6_2
% 228.46/39.96    (20)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.46/39.96          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.46/39.96    (21)   ~ (all_53_9 = all_6_2)
% 228.46/39.96    (22)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.46/39.96          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.46/39.96    (23)  all_57_3 = e0
% 228.46/39.96    (24)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.46/39.96          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.46/39.96    (25)   ~ (e3 = e2)
% 228.46/39.96    (26)  all_55_1 = all_53_4
% 228.46/39.96    (27)   ~ (e3 = e0)
% 228.46/39.96    (28)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.46/39.96          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.46/39.96    (29)   ~ (all_53_8 = all_6_2)
% 228.46/39.96    (30)  all_57_1 = e0
% 228.46/39.96    (31)  all_55_2 = all_53_8
% 228.46/39.96    (32)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.46/39.96    (33)  all_57_15 = e3
% 228.46/39.96    (34)  op(e3, e3) = e2
% 228.46/39.96    (35)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.46/39.96          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.46/39.96            e1)
% 228.46/39.96    (36)   ~ (all_53_4 = all_53_8)
% 228.46/39.96    (37)  op(e3, e2) = all_53_4
% 228.46/39.96    (38)  op(e1, e1) = e1
% 228.46/39.96    (39)   ~ (e2 = e0)
% 228.46/39.96    (40)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.46/39.96            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.46/39.96            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.46/39.96            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.46/39.96              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.46/39.96            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.46/39.96            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.46/39.96              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.46/39.96              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.46/39.96            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.46/39.96            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.46/39.96            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.46/39.96              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.46/39.96              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.46/39.96            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.46/39.96              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.46/39.96            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.46/39.96            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.46/39.96              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.46/39.96              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.46/39.96            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.46/39.96            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.46/39.96    (41)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.46/39.96          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.46/39.96    (42)   ~ (e1 = e0)
% 228.46/39.96    (43)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.46/39.96            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.46/39.96              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.46/39.96    (44)   ~ (all_53_4 = e0)
% 228.46/39.97    (45)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.46/39.97          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.46/39.97    (46)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.46/39.97          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.46/39.97    (47)  op(e0, e0) = e3
% 228.46/39.97    (48)   ~ (all_53_4 = all_53_6)
% 228.46/39.97    (49)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.46/39.97          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.46/39.97            e2)
% 228.46/39.97    (50)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.46/39.97              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.46/39.97                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.46/39.97                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.46/39.97    (51)  all_55_10 = all_6_2
% 228.46/39.97    (52)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.46/39.97          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.46/39.97    (53)  all_38_2 = all_6_2
% 228.46/39.97    (54)  all_55_3 = all_53_12
% 228.46/39.97    (55)   ~ (all_53_12 = e3)
% 228.46/39.97    (56)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.46/39.97            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.46/39.97              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.46/39.97    (57)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.46/39.97          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.46/39.97    (58)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.46/39.97          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.46/39.97    (59)   ~ (e2 = e1)
% 228.46/39.97    (60)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.46/39.97          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.46/39.97    (61)  op(e2, e1) = all_53_9
% 228.46/39.97    (62)  op(e1, e2) = all_53_6
% 228.46/39.97    (63)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.46/39.97          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.46/39.97    (64)  all_24_2 = all_6_2
% 228.46/39.97    (65)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.46/39.97          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.46/39.97    (66)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.46/39.97          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.46/39.97    (67)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.46/39.97          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.46/39.97    (68)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.46/39.97          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.46/39.97    (69)  op(e3, e1) = all_53_8
% 228.46/39.97    (70)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.46/39.97          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.46/39.97    (71)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.46/39.97          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.46/39.97    (72)  op(e3, e0) = all_53_12
% 228.46/39.97  
% 228.46/39.97  Begin of proof
% 228.46/39.97  | 
% 228.46/39.97  | BETA: splitting (46) gives:
% 228.46/39.97  | 
% 228.46/39.97  | Case 1:
% 228.46/39.97  | | 
% 228.46/39.97  | |   (73)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 228.46/39.97  | |           e3)
% 228.46/39.97  | | 
% 228.46/39.97  | | REF_CLOSE: (23), (27), (30), (73) are inconsistent by sub-proof #1284.
% 228.46/39.97  | | 
% 228.46/39.97  | Case 2:
% 228.46/39.97  | | 
% 228.46/39.97  | |   (74)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 228.46/39.97  | |           e3)
% 228.46/39.97  | | 
% 228.46/39.97  | | BETA: splitting (74) gives:
% 228.46/39.97  | | 
% 228.46/39.97  | | Case 1:
% 228.46/39.97  | | | 
% 228.46/39.97  | | |   (75)  all_57_7 = e3 & op(e1, e2) = e3
% 228.46/39.97  | | | 
% 228.46/39.97  | | | ALPHA: (75) implies:
% 228.46/39.97  | | |   (76)  all_57_7 = e3
% 228.46/39.97  | | | 
% 228.46/39.97  | | | REF_CLOSE: (6), (7), (23), (25), (30), (39), (42), (59), (70), (76) are
% 228.46/39.97  | | |            inconsistent by sub-proof #2098.
% 228.46/39.97  | | | 
% 228.46/39.97  | | Case 2:
% 228.46/39.97  | | | 
% 228.46/39.97  | | |   (77)  all_57_13 = e3 & op(e0, e2) = e3
% 228.46/39.97  | | | 
% 228.46/39.97  | | | ALPHA: (77) implies:
% 228.46/39.97  | | |   (78)  all_57_13 = e3
% 228.46/39.97  | | | 
% 228.46/39.97  | | | BETA: splitting (35) gives:
% 228.46/39.97  | | | 
% 228.46/39.97  | | | Case 1:
% 228.46/39.97  | | | | 
% 228.46/39.97  | | | |   (79)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0,
% 228.46/39.97  | | | |             e2) = e1)
% 228.46/39.97  | | | | 
% 228.46/39.97  | | | | REF_CLOSE: (3), (4), (6), (7), (9), (10), (12), (13), (23), (25), (27),
% 228.46/39.97  | | | |            (30), (33), (34), (35), (39), (42), (49), (50), (52), (57),
% 228.46/39.97  | | | |            (58), (59), (60), (63), (66), (67), (70), (78), (79) are
% 228.46/39.97  | | | |            inconsistent by sub-proof #521.
% 228.46/39.97  | | | | 
% 228.46/39.97  | | | Case 2:
% 228.46/39.97  | | | | 
% 228.46/39.97  | | | |   (80)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0,
% 228.46/39.97  | | | |             e0) = e1)
% 228.46/39.97  | | | | 
% 228.46/39.97  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 228.46/39.97  | | | |            (12), (13), (14), (15), (16), (17), (18), (19), (20), (21),
% 228.46/39.97  | | | |            (22), (23), (24), (25), (26), (27), (28), (29), (31), (32),
% 228.46/39.97  | | | |            (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 228.46/39.97  | | | |            (43), (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 228.46/39.97  | | | |            (53), (54), (55), (56), (57), (58), (59), (60), (61), (62),
% 228.46/39.97  | | | |            (63), (64), (65), (66), (67), (68), (69), (70), (71), (72),
% 228.46/39.97  | | | |            (78), (80) are inconsistent by sub-proof #517.
% 228.46/39.97  | | | | 
% 228.46/39.97  | | | End of split
% 228.46/39.97  | | | 
% 228.46/39.97  | | End of split
% 228.46/39.97  | | 
% 228.46/39.97  | End of split
% 228.46/39.97  | 
% 228.46/39.97  End of proof
% 228.46/39.97  
% 228.46/39.97  Sub-proof #512 shows that the following formulas are inconsistent:
% 228.46/39.97  ----------------------------------------------------------------
% 228.46/39.97    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.46/39.97    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.46/39.97    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.46/39.97         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.46/39.97    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.46/39.97         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.46/39.97    (5)   ~ (all_53_8 = all_53_12)
% 228.46/39.97    (6)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.46/39.97         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.46/39.97    (7)   ~ (e3 = e1)
% 228.46/39.97    (8)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.46/39.97         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.46/39.97    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.46/39.97           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.46/39.97    (10)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.46/39.97          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.46/39.97    (11)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.46/39.97            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.46/39.97              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.46/39.97    (12)   ~ (all_6_2 = e3)
% 228.46/39.97    (13)  op(e1, e1) = all_6_2
% 228.46/39.97    (14)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.46/39.97    (15)   ~ (all_53_9 = e0)
% 228.46/39.97    (16)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.46/39.97          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.46/39.97    (17)  all_57_9 = e1
% 228.46/39.97    (18)   ~ (all_53_4 = all_53_12)
% 228.46/39.97    (19)   ~ (all_53_8 = all_53_9)
% 228.46/39.97    (20)  all_57_7 = e1
% 228.46/39.97    (21)  all_42_2 = all_6_2
% 228.46/39.97    (22)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.46/39.97          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.46/39.97    (23)   ~ (all_53_9 = all_6_2)
% 228.46/39.97    (24)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.46/39.97          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.46/39.97    (25)  all_57_3 = e0
% 228.46/39.97    (26)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.46/39.97          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.46/39.97    (27)   ~ (e3 = e2)
% 228.46/39.97    (28)  all_55_1 = all_53_4
% 228.46/39.97    (29)   ~ (e3 = e0)
% 228.46/39.97    (30)  all_57_1 = e2
% 228.46/39.97    (31)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.46/39.97          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.46/39.97    (32)   ~ (all_53_8 = all_6_2)
% 228.46/39.97    (33)  all_55_2 = all_53_8
% 228.46/39.97    (34)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.46/39.97    (35)  all_57_15 = e3
% 228.46/39.97    (36)  op(e3, e3) = e2
% 228.46/39.97    (37)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.46/39.97          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.46/39.97            e1)
% 228.46/39.97    (38)   ~ (all_53_4 = all_53_8)
% 228.46/39.97    (39)  op(e3, e2) = all_53_4
% 228.46/39.97    (40)  op(e1, e1) = e1
% 228.46/39.97    (41)   ~ (e2 = e0)
% 228.46/39.97    (42)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.46/39.97            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.46/39.97            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.46/39.97            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.46/39.97              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.46/39.97            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.46/39.97            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.46/39.97              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.46/39.97              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.46/39.97            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.46/39.97            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.46/39.97            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.46/39.97              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.46/39.97              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.46/39.97            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.46/39.97              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.46/39.97            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.46/39.97            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.46/39.97              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.46/39.97              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.46/39.97            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.46/39.97            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.46/39.97    (43)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.46/39.97          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.46/39.97    (44)   ~ (e1 = e0)
% 228.46/39.97    (45)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.46/39.97            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.46/39.97              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.46/39.97    (46)   ~ (all_53_4 = e0)
% 228.46/39.97    (47)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.46/39.97          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.46/39.97    (48)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.46/39.97          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.46/39.97    (49)  op(e0, e0) = e3
% 228.46/39.97    (50)   ~ (all_53_4 = all_53_6)
% 228.46/39.97    (51)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.46/39.97          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.46/39.97            e2)
% 228.46/39.97    (52)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.46/39.97              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.46/39.97                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.46/39.97                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.46/39.97    (53)  all_55_10 = all_6_2
% 228.46/39.97    (54)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.46/39.97          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.46/39.97    (55)  all_38_2 = all_6_2
% 228.46/39.97    (56)  all_55_3 = all_53_12
% 228.46/39.97    (57)   ~ (all_53_12 = e3)
% 228.46/39.97    (58)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.46/39.97            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.46/39.97              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.46/39.97    (59)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.46/39.97          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.46/39.97    (60)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.46/39.97          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.46/39.97    (61)   ~ (e2 = e1)
% 228.46/39.97    (62)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.46/39.97          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.46/39.97    (63)  op(e2, e1) = all_53_9
% 228.46/39.97    (64)  op(e1, e2) = all_53_6
% 228.46/39.97    (65)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.46/39.97          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.46/39.97    (66)  all_24_2 = all_6_2
% 228.46/39.97    (67)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.46/39.97          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.46/39.97    (68)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.46/39.97          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.46/39.97    (69)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.46/39.97          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.46/39.97    (70)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.46/39.97          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.46/39.97    (71)  op(e3, e1) = all_53_8
% 228.46/39.97    (72)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.46/39.97          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.46/39.97    (73)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.46/39.97          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.46/39.97    (74)  op(e3, e0) = all_53_12
% 228.46/39.97  
% 228.46/39.97  Begin of proof
% 228.46/39.97  | 
% 228.46/39.97  | BETA: splitting (48) gives:
% 228.46/39.97  | 
% 228.46/39.97  | Case 1:
% 228.46/39.97  | | 
% 228.46/39.97  | |   (75)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 228.46/39.97  | |           e3)
% 228.46/39.97  | | 
% 228.46/39.97  | | REF_CLOSE: (25), (27), (29), (30), (75) are inconsistent by sub-proof #788.
% 228.46/39.97  | | 
% 228.46/39.97  | Case 2:
% 228.46/39.97  | | 
% 228.46/39.97  | |   (76)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 228.46/39.97  | |           e3)
% 228.46/39.97  | | 
% 228.46/39.97  | | BETA: splitting (76) gives:
% 228.46/39.97  | | 
% 228.46/39.97  | | Case 1:
% 228.46/39.97  | | | 
% 228.46/39.97  | | |   (77)  all_57_7 = e3 & op(e1, e2) = e3
% 228.46/39.97  | | | 
% 228.46/39.97  | | | ALPHA: (77) implies:
% 228.46/39.97  | | |   (78)  all_57_7 = e3
% 228.46/39.97  | | | 
% 228.46/39.97  | | | REF_CLOSE: (7), (20), (78) are inconsistent by sub-proof #2115.
% 228.46/39.97  | | | 
% 228.46/39.97  | | Case 2:
% 228.46/39.97  | | | 
% 228.46/39.97  | | |   (79)  all_57_13 = e3 & op(e0, e2) = e3
% 228.46/39.97  | | | 
% 228.46/39.97  | | | ALPHA: (79) implies:
% 228.46/39.97  | | |   (80)  all_57_13 = e3
% 228.46/39.97  | | | 
% 228.46/39.97  | | | BETA: splitting (51) gives:
% 228.46/39.97  | | | 
% 228.46/39.97  | | | Case 1:
% 228.46/39.97  | | | | 
% 228.46/39.97  | | | |   (81)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0,
% 228.46/39.97  | | | |             e2) = e2)
% 228.46/39.97  | | | | 
% 228.46/39.97  | | | | BETA: splitting (81) gives:
% 228.46/39.97  | | | | 
% 228.46/39.97  | | | | Case 1:
% 228.46/39.97  | | | | | 
% 228.46/39.97  | | | | |   (82)  all_57_12 = e2 & op(e0, e3) = e2
% 228.46/39.97  | | | | | 
% 228.46/39.97  | | | | | ALPHA: (82) implies:
% 228.46/39.97  | | | | |   (83)  all_57_12 = e2
% 228.46/39.97  | | | | | 
% 228.46/39.97  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 228.46/39.97  | | | | |            (12), (13), (14), (15), (16), (18), (19), (21), (22), (23),
% 228.46/39.97  | | | | |            (24), (25), (26), (27), (28), (29), (31), (32), (33), (34),
% 228.46/39.97  | | | | |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44),
% 228.46/39.97  | | | | |            (45), (46), (47), (48), (49), (50), (51), (52), (53), (54),
% 228.46/39.97  | | | | |            (55), (56), (57), (58), (59), (60), (61), (62), (63), (64),
% 228.46/39.97  | | | | |            (65), (66), (67), (68), (69), (70), (71), (72), (73), (74),
% 228.46/39.97  | | | | |            (80), (83) are inconsistent by sub-proof #519.
% 228.46/39.97  | | | | | 
% 228.46/39.97  | | | | Case 2:
% 228.46/39.97  | | | | | 
% 228.46/39.97  | | | | |   (84)  all_57_13 = e2 & op(e0, e2) = e2
% 228.46/39.97  | | | | | 
% 228.46/39.97  | | | | | REF_CLOSE: (27), (80), (84) are inconsistent by sub-proof #2146.
% 228.46/39.97  | | | | | 
% 228.46/39.97  | | | | End of split
% 228.46/39.97  | | | | 
% 228.46/39.97  | | | Case 2:
% 228.46/39.97  | | | | 
% 228.46/39.97  | | | |   (85)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0,
% 228.46/39.97  | | | |             e0) = e2)
% 228.46/39.97  | | | | 
% 228.46/39.97  | | | | BETA: splitting (85) gives:
% 228.46/39.97  | | | | 
% 228.46/39.97  | | | | Case 1:
% 228.46/39.97  | | | | | 
% 228.46/39.97  | | | | |   (86)  all_57_14 = e2 & op(e0, e1) = e2
% 228.46/39.97  | | | | | 
% 228.46/39.97  | | | | | ALPHA: (86) implies:
% 228.46/39.97  | | | | |   (87)  all_57_14 = e2
% 228.46/39.97  | | | | | 
% 228.46/39.97  | | | | | BETA: splitting (37) gives:
% 228.46/39.97  | | | | | 
% 228.46/39.97  | | | | | Case 1:
% 228.46/39.97  | | | | | | 
% 228.46/39.97  | | | | | |   (88)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 &
% 228.46/39.97  | | | | | |           op(e0, e2) = e1)
% 228.46/39.97  | | | | | | 
% 228.46/39.97  | | | | | | BETA: splitting (88) gives:
% 228.46/39.97  | | | | | | 
% 228.46/39.97  | | | | | | Case 1:
% 228.46/39.97  | | | | | | | 
% 228.46/39.97  | | | | | | |   (89)  all_57_12 = e1 & op(e0, e3) = e1
% 228.46/39.97  | | | | | | | 
% 228.46/39.97  | | | | | | | ALPHA: (89) implies:
% 228.46/39.97  | | | | | | |   (90)  all_57_12 = e1
% 228.46/39.97  | | | | | | | 
% 228.46/39.97  | | | | | | | BETA: splitting (24) gives:
% 228.46/39.97  | | | | | | | 
% 228.46/39.97  | | | | | | | Case 1:
% 228.46/39.97  | | | | | | | | 
% 228.46/39.97  | | | | | | | |   (91)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 &
% 228.46/39.97  | | | | | | | |           op(e3, e2) = e0)
% 228.46/39.97  | | | | | | | | 
% 228.46/39.97  | | | | | | | | BETA: splitting (91) gives:
% 228.46/39.97  | | | | | | | | 
% 228.46/39.97  | | | | | | | | Case 1:
% 228.46/39.97  | | | | | | | | | 
% 228.46/39.97  | | | | | | | | |   (92)  all_57_0 = e0 & op(e3, e3) = e0
% 228.46/39.97  | | | | | | | | | 
% 228.46/39.97  | | | | | | | | | ALPHA: (92) implies:
% 228.46/39.97  | | | | | | | | |   (93)  op(e3, e3) = e0
% 228.46/39.97  | | | | | | | | | 
% 228.46/39.97  | | | | | | | | | REF_CLOSE: (9), (36), (41), (93) are inconsistent by sub-proof
% 228.46/39.97  | | | | | | | | |            #2403.
% 228.46/39.97  | | | | | | | | | 
% 228.46/39.97  | | | | | | | | Case 2:
% 228.46/39.97  | | | | | | | | | 
% 228.46/39.97  | | | | | | | | |   (94)  all_57_1 = e0 & op(e3, e2) = e0
% 228.46/39.97  | | | | | | | | | 
% 228.46/39.97  | | | | | | | | | ALPHA: (94) implies:
% 228.46/39.97  | | | | | | | | |   (95)  all_57_1 = e0
% 228.46/39.97  | | | | | | | | | 
% 228.46/39.97  | | | | | | | | | REF_CLOSE: (3), (4), (6), (7), (9), (10), (12), (13), (25),
% 228.46/39.97  | | | | | | | | |            (27), (29), (35), (36), (37), (41), (44), (51),
% 228.46/39.97  | | | | | | | | |            (52), (54), (59), (60), (61), (62), (65), (68),
% 228.46/39.97  | | | | | | | | |            (69), (72), (80), (90), (95) are inconsistent by
% 228.46/39.97  | | | | | | | | |            sub-proof #522.
% 228.46/39.97  | | | | | | | | | 
% 228.46/39.97  | | | | | | | | End of split
% 228.46/39.97  | | | | | | | | 
% 228.46/39.97  | | | | | | | Case 2:
% 228.46/39.97  | | | | | | | | 
% 228.46/39.97  | | | | | | | |   (96)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 &
% 228.46/39.97  | | | | | | | |           op(e3, e0) = e0)
% 228.46/39.97  | | | | | | | | 
% 228.46/39.97  | | | | | | | | BETA: splitting (96) gives:
% 228.46/39.97  | | | | | | | | 
% 228.46/39.97  | | | | | | | | Case 1:
% 228.46/39.97  | | | | | | | | | 
% 228.46/39.97  | | | | | | | | |   (97)  all_57_4 = e0 & op(e3, e1) = e0
% 228.46/39.97  | | | | | | | | | 
% 228.46/39.97  | | | | | | | | | ALPHA: (97) implies:
% 228.46/39.97  | | | | | | | | |   (98)  all_57_4 = e0
% 228.46/39.97  | | | | | | | | | 
% 228.46/39.97  | | | | | | | | | BETA: splitting (47) gives:
% 228.46/39.97  | | | | | | | | | 
% 228.46/39.97  | | | | | | | | | Case 1:
% 228.46/39.97  | | | | | | | | | | 
% 228.46/39.97  | | | | | | | | | |   (99)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 &
% 228.46/39.97  | | | | | | | | | |           op(e2, e1) = e3)
% 228.46/39.97  | | | | | | | | | | 
% 228.46/39.97  | | | | | | | | | | BETA: splitting (99) gives:
% 228.46/39.97  | | | | | | | | | | 
% 228.46/39.97  | | | | | | | | | | Case 1:
% 228.46/39.97  | | | | | | | | | | | 
% 228.46/39.97  | | | | | | | | | | |   (100)  all_57_4 = e3 & op(e3, e1) = e3
% 228.46/39.97  | | | | | | | | | | | 
% 228.46/39.97  | | | | | | | | | | | ALPHA: (100) implies:
% 228.46/39.97  | | | | | | | | | | |   (101)  all_57_4 = e3
% 228.46/39.97  | | | | | | | | | | | 
% 228.46/39.97  | | | | | | | | | | | REF_CLOSE: (29), (98), (101) are inconsistent by sub-proof
% 228.46/39.97  | | | | | | | | | | |            #2372.
% 228.46/39.97  | | | | | | | | | | | 
% 228.46/39.97  | | | | | | | | | | Case 2:
% 228.46/39.97  | | | | | | | | | | | 
% 228.46/39.97  | | | | | | | | | | |   (102)  all_57_5 = e3 & op(e2, e1) = e3
% 228.46/39.97  | | | | | | | | | | | 
% 228.46/39.97  | | | | | | | | | | | ALPHA: (102) implies:
% 228.46/39.97  | | | | | | | | | | |   (103)  all_57_5 = e3
% 228.46/39.97  | | | | | | | | | | |   (104)  op(e2, e1) = e3
% 228.46/39.97  | | | | | | | | | | | 
% 228.46/39.97  | | | | | | | | | | | BETA: splitting (60) gives:
% 228.46/39.97  | | | | | | | | | | | 
% 228.46/39.97  | | | | | | | | | | | Case 1:
% 228.46/39.97  | | | | | | | | | | | | 
% 228.46/39.97  | | | | | | | | | | | |   (105)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 228.46/39.97  | | | | | | | | | | | |            & op(e2, e3) = e3)
% 228.46/39.97  | | | | | | | | | | | | 
% 228.46/39.97  | | | | | | | | | | | | BETA: splitting (105) gives:
% 228.46/39.97  | | | | | | | | | | | | 
% 228.46/39.97  | | | | | | | | | | | | Case 1:
% 228.46/39.97  | | | | | | | | | | | | | 
% 228.46/39.97  | | | | | | | | | | | | |   (106)  all_57_0 = e3 & op(e3, e3) = e3
% 228.46/39.97  | | | | | | | | | | | | | 
% 228.46/39.97  | | | | | | | | | | | | | ALPHA: (106) implies:
% 228.46/39.97  | | | | | | | | | | | | |   (107)  op(e3, e3) = e3
% 228.46/39.97  | | | | | | | | | | | | | 
% 228.46/39.97  | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 228.46/39.97  | | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (18), (19),
% 228.46/39.97  | | | | | | | | | | | | |            (21), (22), (23), (24), (25), (26), (27), (28),
% 228.46/39.97  | | | | | | | | | | | | |            (29), (31), (32), (33), (34), (35), (37), (38),
% 228.46/39.97  | | | | | | | | | | | | |            (39), (41), (42), (43), (44), (45), (46), (49),
% 228.46/39.97  | | | | | | | | | | | | |            (50), (51), (52), (53), (55), (56), (57), (58),
% 228.46/39.97  | | | | | | | | | | | | |            (59), (61), (62), (63), (64), (65), (66), (67),
% 228.46/39.97  | | | | | | | | | | | | |            (68), (69), (70), (71), (72), (73), (74), (103),
% 228.46/39.97  | | | | | | | | | | | | |            (104), (107) are inconsistent by sub-proof #1438.
% 228.46/39.97  | | | | | | | | | | | | | 
% 228.46/39.97  | | | | | | | | | | | | Case 2:
% 228.46/39.97  | | | | | | | | | | | | | 
% 228.46/39.97  | | | | | | | | | | | | |   (108)  all_57_2 = e3 & op(e2, e3) = e3
% 228.46/39.97  | | | | | | | | | | | | | 
% 228.46/39.97  | | | | | | | | | | | | | ALPHA: (108) implies:
% 228.46/39.97  | | | | | | | | | | | | |   (109)  all_57_2 = e3
% 228.46/39.97  | | | | | | | | | | | | | 
% 228.46/39.97  | | | | | | | | | | | | | BETA: splitting (10) gives:
% 228.46/39.97  | | | | | | | | | | | | | 
% 228.46/39.97  | | | | | | | | | | | | | Case 1:
% 228.46/39.97  | | | | | | | | | | | | | | 
% 228.46/39.97  | | | | | | | | | | | | | |   (110)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 228.46/39.97  | | | | | | | | | | | | | |            & op(e1, e2) = e3)
% 228.46/39.97  | | | | | | | | | | | | | | 
% 228.46/39.97  | | | | | | | | | | | | | | BETA: splitting (110) gives:
% 228.46/39.97  | | | | | | | | | | | | | | 
% 228.46/39.97  | | | | | | | | | | | | | | Case 1:
% 228.46/39.97  | | | | | | | | | | | | | | | 
% 228.46/39.97  | | | | | | | | | | | | | | |   (111)  all_57_6 = e3 & op(e1, e3) = e3
% 228.46/39.97  | | | | | | | | | | | | | | | 
% 228.46/39.97  | | | | | | | | | | | | | | | ALPHA: (111) implies:
% 228.46/39.97  | | | | | | | | | | | | | | |   (112)  all_57_6 = e3
% 228.46/39.97  | | | | | | | | | | | | | | | 
% 228.46/39.97  | | | | | | | | | | | | | | | REF_CLOSE: (3), (7), (9), (25), (27), (29), (36), (41), (44),
% 228.46/39.97  | | | | | | | | | | | | | | |            (59), (61), (68), (90), (103), (112) are
% 228.46/39.97  | | | | | | | | | | | | | | |            inconsistent by sub-proof #810.
% 228.46/39.97  | | | | | | | | | | | | | | | 
% 228.46/39.97  | | | | | | | | | | | | | | Case 2:
% 228.46/39.97  | | | | | | | | | | | | | | | 
% 228.46/39.97  | | | | | | | | | | | | | | |   (113)  all_57_7 = e3 & op(e1, e2) = e3
% 228.46/39.97  | | | | | | | | | | | | | | | 
% 228.46/39.97  | | | | | | | | | | | | | | | ALPHA: (113) implies:
% 228.46/39.97  | | | | | | | | | | | | | | |   (114)  all_57_7 = e3
% 228.46/39.97  | | | | | | | | | | | | | | | 
% 228.46/39.97  | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 228.46/39.97  | | | | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (18), (19),
% 228.46/39.97  | | | | | | | | | | | | | | |            (21), (22), (23), (24), (25), (26), (27), (28),
% 228.46/39.97  | | | | | | | | | | | | | | |            (29), (31), (32), (33), (34), (35), (37), (38),
% 228.46/39.97  | | | | | | | | | | | | | | |            (39), (41), (42), (43), (44), (45), (46), (47),
% 228.46/39.97  | | | | | | | | | | | | | | |            (49), (50), (51), (52), (53), (54), (55), (56),
% 228.46/39.97  | | | | | | | | | | | | | | |            (57), (58), (59), (61), (62), (63), (64), (65),
% 228.46/39.97  | | | | | | | | | | | | | | |            (66), (67), (68), (69), (70), (71), (72), (73),
% 228.46/39.97  | | | | | | | | | | | | | | |            (74), (98), (109), (114) are inconsistent by
% 228.46/39.97  | | | | | | | | | | | | | | |            sub-proof #513.
% 228.46/39.97  | | | | | | | | | | | | | | | 
% 228.46/39.97  | | | | | | | | | | | | | | End of split
% 228.46/39.97  | | | | | | | | | | | | | | 
% 228.46/39.97  | | | | | | | | | | | | | Case 2:
% 228.46/39.97  | | | | | | | | | | | | | | 
% 228.46/39.97  | | | | | | | | | | | | | |   (115)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 228.46/39.97  | | | | | | | | | | | | | |            e3 & op(e1, e0) = e3)
% 228.46/39.97  | | | | | | | | | | | | | | 
% 228.46/39.97  | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (12), (13), (27), (29), (35), (41),
% 228.46/39.97  | | | | | | | | | | | | | |            (44), (52), (61), (62), (69), (115) are
% 228.46/39.97  | | | | | | | | | | | | | |            inconsistent by sub-proof #1786.
% 228.46/39.97  | | | | | | | | | | | | | | 
% 228.46/39.97  | | | | | | | | | | | | | End of split
% 228.46/39.97  | | | | | | | | | | | | | 
% 228.46/39.97  | | | | | | | | | | | | End of split
% 228.46/39.97  | | | | | | | | | | | | 
% 228.46/39.97  | | | | | | | | | | | Case 2:
% 228.46/39.97  | | | | | | | | | | | | 
% 228.46/39.97  | | | | | | | | | | | |   (116)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 228.46/39.97  | | | | | | | | | | | |            e3 & op(e0, e3) = e3)
% 228.46/39.97  | | | | | | | | | | | | 
% 228.46/39.97  | | | | | | | | | | | | BETA: splitting (116) gives:
% 228.46/39.97  | | | | | | | | | | | | 
% 228.46/39.97  | | | | | | | | | | | | Case 1:
% 228.46/39.97  | | | | | | | | | | | | | 
% 228.46/39.97  | | | | | | | | | | | | |   (117)  all_57_6 = e3 & op(e1, e3) = e3
% 228.46/39.97  | | | | | | | | | | | | | 
% 228.46/39.97  | | | | | | | | | | | | | ALPHA: (117) implies:
% 228.46/39.97  | | | | | | | | | | | | |   (118)  all_57_6 = e3
% 228.46/39.97  | | | | | | | | | | | | | 
% 228.46/39.97  | | | | | | | | | | | | | REF_CLOSE: (3), (7), (9), (25), (27), (29), (36), (41), (44),
% 228.46/39.97  | | | | | | | | | | | | |            (59), (61), (68), (90), (103), (118) are
% 228.46/39.97  | | | | | | | | | | | | |            inconsistent by sub-proof #810.
% 228.46/39.97  | | | | | | | | | | | | | 
% 228.46/39.97  | | | | | | | | | | | | Case 2:
% 228.46/39.97  | | | | | | | | | | | | | 
% 228.46/39.97  | | | | | | | | | | | | |   (119)  all_57_12 = e3 & op(e0, e3) = e3
% 228.46/39.97  | | | | | | | | | | | | | 
% 228.46/39.97  | | | | | | | | | | | | | ALPHA: (119) implies:
% 228.46/39.97  | | | | | | | | | | | | |   (120)  all_57_12 = e3
% 228.46/39.97  | | | | | | | | | | | | | 
% 228.46/39.97  | | | | | | | | | | | | | REF_CLOSE: (7), (27), (35), (37), (41), (44), (51), (52),
% 228.46/39.97  | | | | | | | | | | | | |            (61), (80), (87), (120) are inconsistent by
% 228.46/39.97  | | | | | | | | | | | | |            sub-proof #1734.
% 228.46/39.97  | | | | | | | | | | | | | 
% 228.46/39.97  | | | | | | | | | | | | End of split
% 228.46/39.97  | | | | | | | | | | | | 
% 228.46/39.97  | | | | | | | | | | | End of split
% 228.46/39.97  | | | | | | | | | | | 
% 228.46/39.97  | | | | | | | | | | End of split
% 228.46/39.97  | | | | | | | | | | 
% 228.46/39.97  | | | | | | | | | Case 2:
% 228.46/39.97  | | | | | | | | | | 
% 228.46/39.97  | | | | | | | | | |   (121)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3
% 228.46/39.97  | | | | | | | | | |            & op(e0, e1) = e3)
% 228.46/39.97  | | | | | | | | | | 
% 228.46/39.97  | | | | | | | | | | REF_CLOSE: (9), (12), (13), (27), (29), (35), (41), (51),
% 228.46/39.97  | | | | | | | | | |            (52), (80), (121) are inconsistent by sub-proof
% 228.46/39.97  | | | | | | | | | |            #540.
% 228.46/39.97  | | | | | | | | | | 
% 228.46/39.97  | | | | | | | | | End of split
% 228.46/39.97  | | | | | | | | | 
% 228.46/39.97  | | | | | | | | Case 2:
% 228.46/39.97  | | | | | | | | | 
% 228.46/39.97  | | | | | | | | |   (122)  all_57_9 = e0 & op(e3, e0) = e0
% 228.46/39.97  | | | | | | | | | 
% 228.46/39.97  | | | | | | | | | ALPHA: (122) implies:
% 228.46/39.97  | | | | | | | | |   (123)  all_57_9 = e0
% 228.46/39.97  | | | | | | | | | 
% 228.46/39.97  | | | | | | | | | COMBINE_EQS: (17), (123) imply:
% 228.46/39.97  | | | | | | | | |   (124)  e1 = e0
% 228.46/39.97  | | | | | | | | | 
% 228.46/39.97  | | | | | | | | | COMBINE_EQS: (90), (124) imply:
% 228.46/39.97  | | | | | | | | |   (125)  all_57_12 = e0
% 228.46/39.97  | | | | | | | | | 
% 228.46/39.97  | | | | | | | | | REF_CLOSE: (7), (35), (37), (44), (61), (80), (87), (125) are
% 228.46/39.97  | | | | | | | | |            inconsistent by sub-proof #2215.
% 228.46/39.97  | | | | | | | | | 
% 228.46/39.97  | | | | | | | | End of split
% 228.46/39.97  | | | | | | | | 
% 228.46/39.97  | | | | | | | End of split
% 228.46/39.97  | | | | | | | 
% 228.46/39.97  | | | | | | Case 2:
% 228.46/39.97  | | | | | | | 
% 228.46/39.97  | | | | | | |   (126)  all_57_13 = e1 & op(e0, e2) = e1
% 228.46/39.97  | | | | | | | 
% 228.46/39.97  | | | | | | | REF_CLOSE: (7), (80), (126) are inconsistent by sub-proof #2264.
% 228.46/39.97  | | | | | | | 
% 228.46/39.97  | | | | | | End of split
% 228.46/39.97  | | | | | | 
% 228.46/39.97  | | | | | Case 2:
% 228.46/39.97  | | | | | | 
% 228.46/39.97  | | | | | |   (127)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 &
% 228.46/39.97  | | | | | |            op(e0, e0) = e1)
% 228.46/39.97  | | | | | | 
% 228.46/39.97  | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 228.46/39.97  | | | | | |            (12), (13), (14), (15), (16), (18), (19), (21), (22),
% 228.46/39.97  | | | | | |            (23), (24), (25), (26), (27), (28), (29), (31), (32),
% 228.46/39.97  | | | | | |            (33), (34), (35), (36), (37), (38), (39), (40), (41),
% 228.46/39.97  | | | | | |            (42), (43), (44), (45), (46), (47), (48), (49), (50),
% 228.46/39.97  | | | | | |            (51), (52), (53), (54), (55), (56), (57), (58), (59),
% 228.46/39.97  | | | | | |            (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 228.46/39.97  | | | | | |            (69), (70), (71), (72), (73), (74), (80), (127) are
% 228.46/39.97  | | | | | |            inconsistent by sub-proof #517.
% 228.46/39.97  | | | | | | 
% 228.46/39.97  | | | | | End of split
% 228.46/39.97  | | | | | 
% 228.46/39.97  | | | | Case 2:
% 228.46/39.97  | | | | | 
% 228.46/39.97  | | | | |   (128)  all_57_15 = e2 & op(e0, e0) = e2
% 228.46/39.97  | | | | | 
% 228.46/39.97  | | | | | ALPHA: (128) implies:
% 228.46/39.97  | | | | |   (129)  all_57_15 = e2
% 228.46/39.97  | | | | | 
% 228.46/39.97  | | | | | REF_CLOSE: (27), (35), (129) are inconsistent by sub-proof #2058.
% 228.46/39.97  | | | | | 
% 228.46/39.97  | | | | End of split
% 228.46/39.97  | | | | 
% 228.46/39.97  | | | End of split
% 228.46/39.97  | | | 
% 228.46/39.97  | | End of split
% 228.46/39.97  | | 
% 228.46/39.97  | End of split
% 228.46/39.97  | 
% 228.46/39.97  End of proof
% 228.46/39.97  
% 228.46/39.97  Sub-proof #513 shows that the following formulas are inconsistent:
% 228.46/39.97  ----------------------------------------------------------------
% 228.46/39.97    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.46/39.97    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.46/39.97    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.46/39.97         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.46/39.98    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.46/39.98         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.46/39.98    (5)   ~ (all_53_8 = all_53_12)
% 228.46/39.98    (6)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.46/39.98         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.46/39.98    (7)   ~ (e3 = e1)
% 228.46/39.98    (8)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.46/39.98         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.46/39.98    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.46/39.98           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.46/39.98    (10)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.46/39.98          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.46/39.98    (11)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.46/39.98            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.46/39.98              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.46/39.98    (12)   ~ (all_6_2 = e3)
% 228.46/39.98    (13)  op(e1, e1) = all_6_2
% 228.46/39.98    (14)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.46/39.98    (15)   ~ (all_53_9 = e0)
% 228.46/39.98    (16)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.46/39.98          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.46/39.98    (17)   ~ (all_53_4 = all_53_12)
% 228.46/39.98    (18)  all_57_4 = e0
% 228.46/39.98    (19)   ~ (all_53_8 = all_53_9)
% 228.46/39.98    (20)  all_42_2 = all_6_2
% 228.46/39.98    (21)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.46/39.98          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.46/39.98    (22)   ~ (all_53_9 = all_6_2)
% 228.46/39.98    (23)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.46/39.98          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.46/39.98    (24)  all_57_3 = e0
% 228.46/39.98    (25)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.46/39.98          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.46/39.98    (26)   ~ (e3 = e2)
% 228.46/39.98    (27)  all_55_1 = all_53_4
% 228.46/39.98    (28)   ~ (e3 = e0)
% 228.46/39.98    (29)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.46/39.98          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.46/39.98    (30)   ~ (all_53_8 = all_6_2)
% 228.46/39.98    (31)  all_55_2 = all_53_8
% 228.46/39.98    (32)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.46/39.98    (33)  all_57_15 = e3
% 228.46/39.98    (34)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.46/39.98          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.46/39.98            e1)
% 228.46/39.98    (35)   ~ (all_53_4 = all_53_8)
% 228.46/39.98    (36)  op(e3, e2) = all_53_4
% 228.46/39.98    (37)   ~ (e2 = e0)
% 228.46/39.98    (38)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.46/39.98            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.46/39.98            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.46/39.98            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.46/39.98              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.46/39.98            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.46/39.98            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.46/39.98              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.46/39.98              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.46/39.98            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.46/39.98            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.46/39.98            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.46/39.98              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.46/39.98              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.46/39.98            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.46/39.98              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.46/39.98            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.46/39.98            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.46/39.98              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.46/39.98              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.46/39.98            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.46/39.98            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.46/39.98    (39)  all_57_2 = e3
% 228.46/39.98    (40)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.46/39.98          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.46/39.98    (41)   ~ (e1 = e0)
% 228.46/39.98    (42)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.46/39.98            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.46/39.98              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.46/39.98    (43)   ~ (all_53_4 = e0)
% 228.46/39.98    (44)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.46/39.98          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.46/39.98    (45)  op(e0, e0) = e3
% 228.46/39.98    (46)   ~ (all_53_4 = all_53_6)
% 228.46/39.98    (47)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.46/39.98          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.46/39.98            e2)
% 228.46/39.98    (48)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.46/39.98              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.46/39.98                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.46/39.98                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.46/39.98    (49)  all_55_10 = all_6_2
% 228.46/39.98    (50)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.46/39.98          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.46/39.98    (51)  all_38_2 = all_6_2
% 228.46/39.98    (52)  all_55_3 = all_53_12
% 228.46/39.98    (53)   ~ (all_53_12 = e3)
% 228.46/39.98    (54)  all_57_7 = e3
% 228.46/39.98    (55)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.46/39.98            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.46/39.98              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.46/39.98    (56)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.46/39.98          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.46/39.98    (57)   ~ (e2 = e1)
% 228.46/39.98    (58)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.46/39.98          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.46/39.98    (59)  op(e2, e1) = all_53_9
% 228.46/39.98    (60)  op(e1, e2) = all_53_6
% 228.46/39.98    (61)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.46/39.98          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.46/39.98    (62)  all_24_2 = all_6_2
% 228.46/39.98    (63)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.46/39.98          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.46/39.98    (64)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.46/39.98          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.46/39.98    (65)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.46/39.98          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.46/39.98    (66)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.46/39.98          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.46/39.98    (67)  op(e3, e1) = all_53_8
% 228.46/39.98    (68)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.46/39.98          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.46/39.98    (69)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.46/39.98          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.46/39.98    (70)  op(e3, e0) = all_53_12
% 228.46/39.98  
% 228.46/39.98  Begin of proof
% 228.46/39.98  | 
% 228.46/39.98  | BETA: splitting (40) gives:
% 228.46/39.98  | 
% 228.46/39.98  | Case 1:
% 228.46/39.98  | | 
% 228.46/39.98  | |   (71)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) =
% 228.46/39.98  | |           e3)
% 228.46/39.98  | | 
% 228.46/39.98  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.46/39.98  | |            (13), (14), (15), (16), (17), (19), (20), (21), (22), (23), (24),
% 228.46/39.98  | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 228.46/39.98  | |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 228.46/39.98  | |            (47), (48), (49), (51), (52), (53), (54), (55), (56), (57), (58),
% 228.46/39.98  | |            (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 228.46/39.98  | |            (70), (71) are inconsistent by sub-proof #514.
% 228.46/39.98  | | 
% 228.46/39.98  | Case 2:
% 228.46/39.98  | | 
% 228.46/39.98  | |   (72)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) =
% 228.46/39.98  | |           e3)
% 228.46/39.98  | | 
% 228.46/39.98  | | REF_CLOSE: (3), (7), (9), (18), (24), (26), (28), (37), (39), (41), (50),
% 228.46/39.98  | |            (53), (56), (57), (70), (72) are inconsistent by sub-proof #528.
% 228.46/39.98  | | 
% 228.46/39.98  | End of split
% 228.46/39.98  | 
% 228.46/39.98  End of proof
% 228.46/39.98  
% 228.46/39.98  Sub-proof #514 shows that the following formulas are inconsistent:
% 228.46/39.98  ----------------------------------------------------------------
% 228.46/39.98    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.46/39.98    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.46/39.98    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.46/39.98         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.46/39.98    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.46/39.98         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.46/39.98    (5)   ~ (all_53_8 = all_53_12)
% 228.46/39.98    (6)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.46/39.98         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.46/39.98    (7)   ~ (e3 = e1)
% 228.46/39.98    (8)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.46/39.98         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.46/39.98    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.46/39.98           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.46/39.98    (10)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.46/39.98          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.46/39.98    (11)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.46/39.98            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.46/39.98              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.46/39.98    (12)   ~ (all_6_2 = e3)
% 228.46/39.98    (13)  op(e1, e1) = all_6_2
% 228.46/39.98    (14)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.46/39.98    (15)   ~ (all_53_9 = e0)
% 228.46/39.98    (16)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.46/39.98          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.46/39.98    (17)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3)
% 228.46/39.98    (18)   ~ (all_53_4 = all_53_12)
% 228.46/39.98    (19)   ~ (all_53_8 = all_53_9)
% 228.46/39.98    (20)  all_42_2 = all_6_2
% 228.46/39.98    (21)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.46/39.98          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.46/39.98    (22)   ~ (all_53_9 = all_6_2)
% 228.46/39.98    (23)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.46/39.98          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.46/39.98    (24)  all_57_3 = e0
% 228.46/39.98    (25)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.46/39.98          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.46/39.98    (26)   ~ (e3 = e2)
% 228.46/39.98    (27)  all_55_1 = all_53_4
% 228.46/39.98    (28)   ~ (e3 = e0)
% 228.46/39.98    (29)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.46/39.98          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.46/39.98    (30)   ~ (all_53_8 = all_6_2)
% 228.46/39.98    (31)  all_55_2 = all_53_8
% 228.46/39.98    (32)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.46/39.98    (33)  all_57_15 = e3
% 228.46/39.98    (34)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.46/39.98          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.46/39.98            e1)
% 228.46/39.98    (35)   ~ (all_53_4 = all_53_8)
% 228.46/39.98    (36)  op(e3, e2) = all_53_4
% 228.46/39.98    (37)   ~ (e2 = e0)
% 228.46/39.98    (38)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.46/39.98            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.46/39.98            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.46/39.98            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.46/39.98              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.46/39.98            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.46/39.98            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.46/39.98              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.46/39.98              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.46/39.98            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.46/39.98            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.46/39.98            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.46/39.98              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.46/39.98              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.46/39.98            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.46/39.98              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.46/39.98            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.46/39.98            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.46/39.98              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.46/39.98              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.46/39.98            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.46/39.98            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.46/39.98    (39)  all_57_2 = e3
% 228.46/39.98    (40)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.46/39.98          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.46/39.98    (41)   ~ (e1 = e0)
% 228.46/39.98    (42)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.46/39.98            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.46/39.98              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.46/39.98    (43)   ~ (all_53_4 = e0)
% 228.46/39.98    (44)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.46/39.98          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.46/39.98    (45)  op(e0, e0) = e3
% 228.46/39.98    (46)   ~ (all_53_4 = all_53_6)
% 228.46/39.98    (47)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.46/39.98          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.46/39.98            e2)
% 228.46/39.98    (48)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.46/39.98              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.46/39.98                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.46/39.98                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.46/39.98    (49)  all_55_10 = all_6_2
% 228.46/39.98    (50)  all_38_2 = all_6_2
% 228.46/39.98    (51)  all_55_3 = all_53_12
% 228.46/39.98    (52)   ~ (all_53_12 = e3)
% 228.46/39.98    (53)  all_57_7 = e3
% 228.46/39.98    (54)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.46/39.98            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.46/39.98              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.46/39.98    (55)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.46/39.98          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.46/39.98    (56)   ~ (e2 = e1)
% 228.46/39.98    (57)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.46/39.98          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.46/39.98    (58)  op(e2, e1) = all_53_9
% 228.46/39.98    (59)  op(e1, e2) = all_53_6
% 228.46/39.98    (60)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.46/39.98          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.46/39.98    (61)  all_24_2 = all_6_2
% 228.46/39.98    (62)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.46/39.98          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.46/39.98    (63)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.46/39.98          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.46/39.98    (64)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.46/39.98          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.46/39.98    (65)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.46/39.98          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.46/39.98    (66)  op(e3, e1) = all_53_8
% 228.46/39.98    (67)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.46/39.98          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.46/39.98    (68)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.46/39.98          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.46/39.98    (69)  op(e3, e0) = all_53_12
% 228.46/39.98  
% 228.46/39.98  Begin of proof
% 228.46/39.98  | 
% 228.46/39.98  | BETA: splitting (17) gives:
% 228.46/39.98  | 
% 228.46/39.98  | Case 1:
% 228.46/39.98  | | 
% 228.46/39.98  | |   (70)  all_57_0 = e3 & op(e3, e3) = e3
% 228.46/39.98  | | 
% 228.46/39.98  | | ALPHA: (70) implies:
% 228.46/39.98  | |   (71)  op(e3, e3) = e3
% 228.46/39.98  | | 
% 228.46/39.98  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.46/39.98  | |            (13), (14), (15), (16), (18), (19), (20), (21), (22), (23), (24),
% 228.46/39.98  | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 228.46/39.98  | |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 228.46/39.98  | |            (47), (48), (49), (50), (51), (52), (54), (55), (56), (57), (58),
% 228.46/39.98  | |            (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 228.46/39.98  | |            (71) are inconsistent by sub-proof #1437.
% 228.46/39.98  | | 
% 228.46/39.98  | Case 2:
% 228.46/39.98  | | 
% 228.46/39.98  | |   (72)  all_57_1 = e3 & op(e3, e2) = e3
% 228.46/39.98  | | 
% 228.46/39.98  | | ALPHA: (72) implies:
% 228.46/39.98  | |   (73)  all_57_1 = e3
% 228.46/39.98  | | 
% 228.46/39.98  | | REF_CLOSE: (6), (7), (24), (26), (37), (41), (53), (56), (67), (73) are
% 228.46/39.98  | |            inconsistent by sub-proof #1778.
% 228.46/39.98  | | 
% 228.46/39.98  | End of split
% 228.46/39.98  | 
% 228.46/39.98  End of proof
% 228.46/39.98  
% 228.46/39.98  Sub-proof #515 shows that the following formulas are inconsistent:
% 228.46/39.98  ----------------------------------------------------------------
% 228.46/39.98    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.46/39.98    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.46/39.98    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.46/39.98         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.46/39.98    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.46/39.98         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.46/39.98    (5)   ~ (all_53_8 = all_53_12)
% 228.46/39.98    (6)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.46/39.98         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.46/39.98    (7)   ~ (e3 = e1)
% 228.46/39.98    (8)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.46/39.98         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.46/39.98    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.46/39.98           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.46/39.98    (10)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.46/39.98          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.46/39.98    (11)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.46/39.98            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.46/39.98              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.46/39.98    (12)   ~ (all_6_2 = e3)
% 228.46/39.98    (13)  op(e1, e1) = all_6_2
% 228.46/39.98    (14)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.46/39.98    (15)   ~ (all_53_9 = e0)
% 228.46/39.98    (16)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.46/39.98          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.46/39.98    (17)   ~ (all_53_4 = all_53_12)
% 228.46/39.98    (18)   ~ (all_53_8 = all_53_9)
% 228.46/39.98    (19)  all_57_7 = e1
% 228.46/39.98    (20)  all_42_2 = all_6_2
% 228.46/39.98    (21)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.46/39.98          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.46/39.98    (22)   ~ (all_53_9 = all_6_2)
% 228.46/39.98    (23)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.46/39.98          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.46/39.98    (24)  all_57_3 = e0
% 228.46/39.98    (25)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.46/39.98          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.46/39.98    (26)   ~ (e3 = e2)
% 228.46/39.98    (27)  all_55_1 = all_53_4
% 228.46/39.98    (28)   ~ (e3 = e0)
% 228.46/39.98    (29)  all_57_1 = e2
% 228.46/39.98    (30)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.46/39.98          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.46/39.98    (31)   ~ (all_53_8 = all_6_2)
% 228.46/39.98    (32)  all_55_2 = all_53_8
% 228.46/39.98    (33)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.46/39.98    (34)  all_57_15 = e3
% 228.46/39.98    (35)  op(e3, e3) = e2
% 228.46/39.98    (36)  all_57_4 = e1
% 228.46/39.98    (37)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.46/39.98          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.46/39.98            e1)
% 228.46/39.98    (38)   ~ (all_53_4 = all_53_8)
% 228.46/39.98    (39)  op(e3, e2) = all_53_4
% 228.46/39.98    (40)  op(e1, e1) = e1
% 228.46/39.98    (41)   ~ (e2 = e0)
% 228.46/39.98    (42)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.46/39.98            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.46/39.98            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.46/39.98            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.46/39.98              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.46/39.98            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.46/39.98            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.46/39.98              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.46/39.98              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.46/39.98            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.46/39.98            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.46/39.98            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.46/39.98              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.46/39.98              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.46/39.98            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.46/39.98              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.46/39.98            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.46/39.98            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.46/39.98              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.46/39.98              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.46/39.98            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.46/39.98            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.46/39.98    (43)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.46/39.98          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.46/39.98    (44)   ~ (e1 = e0)
% 228.46/39.99    (45)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.46/39.99            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.46/39.99              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.46/39.99    (46)   ~ (all_53_4 = e0)
% 228.46/39.99    (47)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.46/39.99          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.46/39.99    (48)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.46/39.99          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.46/39.99    (49)  op(e0, e0) = e3
% 228.46/39.99    (50)   ~ (all_53_4 = all_53_6)
% 228.46/39.99    (51)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.46/39.99          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.46/39.99            e2)
% 228.46/39.99    (52)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.46/39.99              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.46/39.99                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.46/39.99                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.46/39.99    (53)  all_55_10 = all_6_2
% 228.46/39.99    (54)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.46/39.99          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.46/39.99    (55)  all_38_2 = all_6_2
% 228.46/39.99    (56)  all_55_3 = all_53_12
% 228.46/39.99    (57)   ~ (all_53_12 = e3)
% 228.46/39.99    (58)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.46/39.99            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.46/39.99              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.46/39.99    (59)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.46/39.99          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.46/39.99    (60)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.46/39.99          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.46/39.99    (61)   ~ (e2 = e1)
% 228.46/39.99    (62)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.46/39.99          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.46/39.99    (63)  op(e2, e1) = all_53_9
% 228.46/39.99    (64)  op(e1, e2) = all_53_6
% 228.46/39.99    (65)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.46/39.99          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.46/39.99    (66)  all_24_2 = all_6_2
% 228.46/39.99    (67)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.46/39.99          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.46/39.99    (68)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.46/39.99          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.46/39.99    (69)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.46/39.99          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.46/39.99    (70)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.46/39.99          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.46/39.99    (71)  op(e3, e1) = all_53_8
% 228.46/39.99    (72)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.46/39.99          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.46/39.99    (73)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.46/39.99          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.46/39.99    (74)  op(e3, e0) = all_53_12
% 228.46/39.99  
% 228.46/39.99  Begin of proof
% 228.46/39.99  | 
% 228.46/39.99  | BETA: splitting (48) gives:
% 228.46/39.99  | 
% 228.46/39.99  | Case 1:
% 228.46/39.99  | | 
% 228.46/39.99  | |   (75)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 228.46/39.99  | |           e3)
% 228.46/39.99  | | 
% 228.46/39.99  | | REF_CLOSE: (24), (26), (28), (29), (75) are inconsistent by sub-proof #788.
% 228.46/39.99  | | 
% 228.46/39.99  | Case 2:
% 228.46/39.99  | | 
% 228.46/39.99  | |   (76)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 228.46/39.99  | |           e3)
% 228.46/39.99  | | 
% 228.46/39.99  | | BETA: splitting (76) gives:
% 228.46/39.99  | | 
% 228.46/39.99  | | Case 1:
% 228.46/39.99  | | | 
% 228.46/39.99  | | |   (77)  all_57_7 = e3 & op(e1, e2) = e3
% 228.46/39.99  | | | 
% 228.46/39.99  | | | ALPHA: (77) implies:
% 228.46/39.99  | | |   (78)  all_57_7 = e3
% 228.46/39.99  | | | 
% 228.46/39.99  | | | REF_CLOSE: (7), (19), (78) are inconsistent by sub-proof #2115.
% 228.46/39.99  | | | 
% 228.46/39.99  | | Case 2:
% 228.46/39.99  | | | 
% 228.46/39.99  | | |   (79)  all_57_13 = e3 & op(e0, e2) = e3
% 228.46/39.99  | | | 
% 228.46/39.99  | | | ALPHA: (79) implies:
% 228.46/39.99  | | |   (80)  all_57_13 = e3
% 228.46/39.99  | | | 
% 228.46/39.99  | | | BETA: splitting (47) gives:
% 228.46/39.99  | | | 
% 228.46/39.99  | | | Case 1:
% 228.46/39.99  | | | | 
% 228.46/39.99  | | | |   (81)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1)
% 228.46/39.99  | | | |           = e3)
% 228.46/39.99  | | | | 
% 228.46/39.99  | | | | BETA: splitting (81) gives:
% 228.46/39.99  | | | | 
% 228.46/39.99  | | | | Case 1:
% 228.46/39.99  | | | | | 
% 228.46/39.99  | | | | |   (82)  all_57_4 = e3 & op(e3, e1) = e3
% 228.46/39.99  | | | | | 
% 228.46/39.99  | | | | | ALPHA: (82) implies:
% 228.46/39.99  | | | | |   (83)  all_57_4 = e3
% 228.46/39.99  | | | | | 
% 228.46/39.99  | | | | | REF_CLOSE: (7), (36), (83) are inconsistent by sub-proof #2426.
% 228.46/39.99  | | | | | 
% 228.46/39.99  | | | | Case 2:
% 228.46/39.99  | | | | | 
% 228.46/39.99  | | | | |   (84)  all_57_5 = e3 & op(e2, e1) = e3
% 228.46/39.99  | | | | | 
% 228.46/39.99  | | | | | ALPHA: (84) implies:
% 228.46/39.99  | | | | |   (85)  all_57_5 = e3
% 228.46/39.99  | | | | |   (86)  op(e2, e1) = e3
% 228.46/39.99  | | | | | 
% 228.46/39.99  | | | | | BETA: splitting (59) gives:
% 228.46/39.99  | | | | | 
% 228.46/39.99  | | | | | Case 1:
% 228.46/39.99  | | | | | | 
% 228.46/39.99  | | | | | |   (87)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2,
% 228.46/39.99  | | | | | |             e2) = e2)
% 228.46/39.99  | | | | | | 
% 228.46/39.99  | | | | | | BETA: splitting (87) gives:
% 228.46/39.99  | | | | | | 
% 228.46/39.99  | | | | | | Case 1:
% 228.46/39.99  | | | | | | | 
% 228.46/39.99  | | | | | | |   (88)  all_57_2 = e2 & op(e2, e3) = e2
% 228.46/39.99  | | | | | | | 
% 228.46/39.99  | | | | | | | ALPHA: (88) implies:
% 228.46/39.99  | | | | | | |   (89)  all_57_2 = e2
% 228.46/39.99  | | | | | | | 
% 228.46/39.99  | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 228.46/39.99  | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18), (20),
% 228.46/39.99  | | | | | | |            (21), (22), (23), (24), (25), (26), (27), (28), (30),
% 228.46/39.99  | | | | | | |            (31), (32), (33), (34), (35), (37), (38), (39), (41),
% 228.46/39.99  | | | | | | |            (42), (44), (45), (46), (49), (50), (51), (52), (53),
% 228.46/39.99  | | | | | | |            (55), (56), (57), (58), (59), (60), (61), (62), (63),
% 228.46/39.99  | | | | | | |            (64), (65), (66), (67), (68), (69), (70), (71), (72),
% 228.46/39.99  | | | | | | |            (73), (74), (85), (86), (89) are inconsistent by
% 228.46/39.99  | | | | | | |            sub-proof #554.
% 228.46/39.99  | | | | | | | 
% 228.46/39.99  | | | | | | Case 2:
% 228.46/39.99  | | | | | | | 
% 228.46/39.99  | | | | | | |   (90)  all_57_3 = e2 & op(e2, e2) = e2
% 228.46/39.99  | | | | | | | 
% 228.46/39.99  | | | | | | | ALPHA: (90) implies:
% 228.46/39.99  | | | | | | |   (91)  all_57_3 = e2
% 228.46/39.99  | | | | | | | 
% 228.46/39.99  | | | | | | | COMBINE_EQS: (24), (91) imply:
% 228.46/39.99  | | | | | | |   (92)  e2 = e0
% 228.46/39.99  | | | | | | | 
% 228.46/39.99  | | | | | | | SIMP: (92) implies:
% 228.46/39.99  | | | | | | |   (93)  e2 = e0
% 228.46/39.99  | | | | | | | 
% 228.46/39.99  | | | | | | | COMBINE_EQS: (29), (93) imply:
% 228.46/39.99  | | | | | | |   (94)  all_57_1 = e0
% 228.46/39.99  | | | | | | | 
% 228.46/39.99  | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 228.46/39.99  | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18), (20),
% 228.46/39.99  | | | | | | |            (21), (22), (23), (24), (25), (26), (27), (28), (30),
% 228.46/39.99  | | | | | | |            (31), (32), (33), (34), (35), (37), (38), (39), (40),
% 228.46/39.99  | | | | | | |            (41), (42), (43), (44), (45), (46), (47), (48), (49),
% 228.46/39.99  | | | | | | |            (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 228.46/39.99  | | | | | | |            (59), (60), (61), (62), (63), (64), (65), (66), (67),
% 228.46/39.99  | | | | | | |            (68), (69), (70), (71), (72), (73), (74), (80), (94)
% 228.46/39.99  | | | | | | |            are inconsistent by sub-proof #516.
% 228.46/39.99  | | | | | | | 
% 228.46/39.99  | | | | | | End of split
% 228.46/39.99  | | | | | | 
% 228.46/39.99  | | | | | Case 2:
% 228.46/39.99  | | | | | | 
% 228.46/39.99  | | | | | |   (95)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2,
% 228.46/39.99  | | | | | |             e0) = e2)
% 228.46/39.99  | | | | | | 
% 228.46/39.99  | | | | | | BETA: splitting (95) gives:
% 228.46/39.99  | | | | | | 
% 228.46/39.99  | | | | | | Case 1:
% 228.46/39.99  | | | | | | | 
% 228.46/39.99  | | | | | | |   (96)  all_57_5 = e2 & op(e2, e1) = e2
% 228.46/39.99  | | | | | | | 
% 228.46/39.99  | | | | | | | REF_CLOSE: (26), (85), (96) are inconsistent by sub-proof #2425.
% 228.46/39.99  | | | | | | | 
% 228.46/39.99  | | | | | | Case 2:
% 228.46/39.99  | | | | | | | 
% 228.46/39.99  | | | | | | |   (97)  all_57_10 = e2 & op(e2, e0) = e2
% 228.46/39.99  | | | | | | | 
% 228.46/39.99  | | | | | | | ALPHA: (97) implies:
% 228.46/39.99  | | | | | | |   (98)  all_57_10 = e2
% 228.46/39.99  | | | | | | | 
% 228.46/39.99  | | | | | | | BETA: splitting (23) gives:
% 228.46/39.99  | | | | | | | 
% 228.46/39.99  | | | | | | | Case 1:
% 228.46/39.99  | | | | | | | | 
% 228.46/39.99  | | | | | | | |   (99)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 &
% 228.46/39.99  | | | | | | | |           op(e3, e2) = e0)
% 228.46/39.99  | | | | | | | | 
% 228.46/39.99  | | | | | | | | BETA: splitting (99) gives:
% 228.46/39.99  | | | | | | | | 
% 228.46/39.99  | | | | | | | | Case 1:
% 228.46/39.99  | | | | | | | | | 
% 228.46/39.99  | | | | | | | | |   (100)  all_57_0 = e0 & op(e3, e3) = e0
% 228.46/39.99  | | | | | | | | | 
% 228.46/39.99  | | | | | | | | | ALPHA: (100) implies:
% 228.46/39.99  | | | | | | | | |   (101)  op(e3, e3) = e0
% 228.46/39.99  | | | | | | | | | 
% 228.46/39.99  | | | | | | | | | REF_CLOSE: (9), (35), (41), (101) are inconsistent by
% 228.46/39.99  | | | | | | | | |            sub-proof #2403.
% 228.46/39.99  | | | | | | | | | 
% 228.46/39.99  | | | | | | | | Case 2:
% 228.46/39.99  | | | | | | | | | 
% 228.46/39.99  | | | | | | | | |   (102)  all_57_1 = e0 & op(e3, e2) = e0
% 228.46/39.99  | | | | | | | | | 
% 228.46/39.99  | | | | | | | | | ALPHA: (102) implies:
% 228.46/39.99  | | | | | | | | |   (103)  all_57_1 = e0
% 228.46/39.99  | | | | | | | | | 
% 228.46/39.99  | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 228.46/39.99  | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 228.46/39.99  | | | | | | | | |            (20), (21), (22), (23), (24), (25), (26), (27),
% 228.46/39.99  | | | | | | | | |            (28), (30), (31), (32), (33), (34), (35), (37),
% 228.46/39.99  | | | | | | | | |            (38), (39), (40), (41), (42), (43), (44), (45),
% 228.46/39.99  | | | | | | | | |            (46), (47), (48), (49), (50), (51), (52), (53),
% 228.46/39.99  | | | | | | | | |            (54), (55), (56), (57), (58), (59), (60), (61),
% 228.46/39.99  | | | | | | | | |            (62), (63), (64), (65), (66), (67), (68), (69),
% 228.46/39.99  | | | | | | | | |            (70), (71), (72), (73), (74), (80), (103) are
% 228.46/39.99  | | | | | | | | |            inconsistent by sub-proof #516.
% 228.46/39.99  | | | | | | | | | 
% 228.46/39.99  | | | | | | | | End of split
% 228.46/39.99  | | | | | | | | 
% 228.46/39.99  | | | | | | | Case 2:
% 228.46/39.99  | | | | | | | | 
% 228.46/39.99  | | | | | | | |   (104)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 &
% 228.46/39.99  | | | | | | | |            op(e3, e0) = e0)
% 228.46/39.99  | | | | | | | | 
% 228.46/39.99  | | | | | | | | BETA: splitting (104) gives:
% 228.46/39.99  | | | | | | | | 
% 228.46/39.99  | | | | | | | | Case 1:
% 228.46/39.99  | | | | | | | | | 
% 228.46/39.99  | | | | | | | | |   (105)  all_57_4 = e0 & op(e3, e1) = e0
% 228.46/39.99  | | | | | | | | | 
% 228.46/39.99  | | | | | | | | | REF_CLOSE: (36), (44), (105) are inconsistent by sub-proof
% 228.46/39.99  | | | | | | | | |            #2429.
% 228.46/39.99  | | | | | | | | | 
% 228.46/39.99  | | | | | | | | Case 2:
% 228.46/39.99  | | | | | | | | | 
% 228.46/39.99  | | | | | | | | |   (106)  all_57_9 = e0 & op(e3, e0) = e0
% 228.46/39.99  | | | | | | | | | 
% 228.46/39.99  | | | | | | | | | ALPHA: (106) implies:
% 228.46/39.99  | | | | | | | | |   (107)  all_57_9 = e0
% 228.46/39.99  | | | | | | | | | 
% 228.46/39.99  | | | | | | | | | BETA: splitting (37) gives:
% 228.46/39.99  | | | | | | | | | 
% 228.46/39.99  | | | | | | | | | Case 1:
% 228.46/39.99  | | | | | | | | | | 
% 228.46/39.99  | | | | | | | | | |   (108)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 228.46/39.99  | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 228.46/39.99  | | | | | | | | | | 
% 228.46/39.99  | | | | | | | | | | BETA: splitting (108) gives:
% 228.46/39.99  | | | | | | | | | | 
% 228.46/39.99  | | | | | | | | | | Case 1:
% 228.46/39.99  | | | | | | | | | | | 
% 228.46/39.99  | | | | | | | | | | |   (109)  all_57_12 = e1 & op(e0, e3) = e1
% 228.46/39.99  | | | | | | | | | | | 
% 228.46/39.99  | | | | | | | | | | | ALPHA: (109) implies:
% 228.46/39.99  | | | | | | | | | | |   (110)  all_57_12 = e1
% 228.46/39.99  | | | | | | | | | | | 
% 228.46/39.99  | | | | | | | | | | | BETA: splitting (10) gives:
% 228.46/39.99  | | | | | | | | | | | 
% 228.46/39.99  | | | | | | | | | | | Case 1:
% 228.46/39.99  | | | | | | | | | | | | 
% 228.46/39.99  | | | | | | | | | | | |   (111)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 228.46/39.99  | | | | | | | | | | | |            & op(e1, e2) = e3)
% 228.46/39.99  | | | | | | | | | | | | 
% 228.46/39.99  | | | | | | | | | | | | BETA: splitting (111) gives:
% 228.46/39.99  | | | | | | | | | | | | 
% 228.46/39.99  | | | | | | | | | | | | Case 1:
% 228.46/39.99  | | | | | | | | | | | | | 
% 228.46/39.99  | | | | | | | | | | | | |   (112)  all_57_6 = e3 & op(e1, e3) = e3
% 228.46/39.99  | | | | | | | | | | | | | 
% 228.46/39.99  | | | | | | | | | | | | | ALPHA: (112) implies:
% 228.46/39.99  | | | | | | | | | | | | |   (113)  all_57_6 = e3
% 228.46/39.99  | | | | | | | | | | | | | 
% 228.46/39.99  | | | | | | | | | | | | | REF_CLOSE: (3), (7), (9), (24), (26), (28), (35), (41), (44),
% 228.46/39.99  | | | | | | | | | | | | |            (59), (61), (68), (85), (110), (113) are
% 228.46/39.99  | | | | | | | | | | | | |            inconsistent by sub-proof #810.
% 228.46/39.99  | | | | | | | | | | | | | 
% 228.46/39.99  | | | | | | | | | | | | Case 2:
% 228.46/39.99  | | | | | | | | | | | | | 
% 228.46/39.99  | | | | | | | | | | | | |   (114)  all_57_7 = e3 & op(e1, e2) = e3
% 228.46/39.99  | | | | | | | | | | | | | 
% 228.46/39.99  | | | | | | | | | | | | | ALPHA: (114) implies:
% 228.46/39.99  | | | | | | | | | | | | |   (115)  all_57_7 = e3
% 228.46/39.99  | | | | | | | | | | | | | 
% 228.46/39.99  | | | | | | | | | | | | | REF_CLOSE: (7), (24), (29), (44), (61), (72), (80), (115) are
% 228.46/39.99  | | | | | | | | | | | | |            inconsistent by sub-proof #2008.
% 228.46/39.99  | | | | | | | | | | | | | 
% 228.46/39.99  | | | | | | | | | | | | End of split
% 228.46/39.99  | | | | | | | | | | | | 
% 228.46/39.99  | | | | | | | | | | | Case 2:
% 228.46/39.99  | | | | | | | | | | | | 
% 228.46/39.99  | | | | | | | | | | | |   (116)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 228.46/39.99  | | | | | | | | | | | |            e3 & op(e1, e0) = e3)
% 228.46/39.99  | | | | | | | | | | | | 
% 228.46/39.99  | | | | | | | | | | | | REF_CLOSE: (7), (9), (12), (13), (34), (44), (61), (69),
% 228.46/39.99  | | | | | | | | | | | |            (98), (107), (116) are inconsistent by sub-proof
% 228.46/39.99  | | | | | | | | | | | |            #731.
% 228.46/39.99  | | | | | | | | | | | | 
% 228.46/39.99  | | | | | | | | | | | End of split
% 228.46/39.99  | | | | | | | | | | | 
% 228.46/39.99  | | | | | | | | | | Case 2:
% 228.46/39.99  | | | | | | | | | | | 
% 228.46/39.99  | | | | | | | | | | |   (117)  all_57_13 = e1 & op(e0, e2) = e1
% 228.46/39.99  | | | | | | | | | | | 
% 228.46/39.99  | | | | | | | | | | | REF_CLOSE: (7), (80), (117) are inconsistent by sub-proof
% 228.46/39.99  | | | | | | | | | | |            #2264.
% 228.46/39.99  | | | | | | | | | | | 
% 228.46/39.99  | | | | | | | | | | End of split
% 228.46/39.99  | | | | | | | | | | 
% 228.46/39.99  | | | | | | | | | Case 2:
% 228.46/39.99  | | | | | | | | | | 
% 228.46/39.99  | | | | | | | | | |   (118)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 228.46/39.99  | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 228.46/39.99  | | | | | | | | | | 
% 228.46/39.99  | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 228.46/39.99  | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 228.46/39.99  | | | | | | | | | |            (20), (21), (22), (23), (24), (25), (26), (27),
% 228.46/39.99  | | | | | | | | | |            (28), (30), (31), (32), (33), (34), (35), (37),
% 228.46/39.99  | | | | | | | | | |            (38), (39), (40), (41), (42), (43), (44), (45),
% 228.46/39.99  | | | | | | | | | |            (46), (47), (48), (49), (50), (51), (52), (53),
% 228.46/39.99  | | | | | | | | | |            (54), (55), (56), (57), (58), (59), (60), (61),
% 228.46/39.99  | | | | | | | | | |            (62), (63), (64), (65), (66), (67), (68), (69),
% 228.46/39.99  | | | | | | | | | |            (70), (71), (72), (73), (74), (80), (118) are
% 228.46/39.99  | | | | | | | | | |            inconsistent by sub-proof #517.
% 228.46/39.99  | | | | | | | | | | 
% 228.46/39.99  | | | | | | | | | End of split
% 228.46/39.99  | | | | | | | | | 
% 228.46/39.99  | | | | | | | | End of split
% 228.46/39.99  | | | | | | | | 
% 228.46/39.99  | | | | | | | End of split
% 228.46/39.99  | | | | | | | 
% 228.46/39.99  | | | | | | End of split
% 228.46/39.99  | | | | | | 
% 228.46/39.99  | | | | | End of split
% 228.46/39.99  | | | | | 
% 228.46/39.99  | | | | End of split
% 228.46/39.99  | | | | 
% 228.46/39.99  | | | Case 2:
% 228.46/39.99  | | | | 
% 228.46/39.99  | | | |   (119)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0,
% 228.46/39.99  | | | |              e1) = e3)
% 228.46/39.99  | | | | 
% 228.46/39.99  | | | | REF_CLOSE: (9), (12), (13), (26), (28), (34), (41), (51), (52), (80),
% 228.46/39.99  | | | |            (119) are inconsistent by sub-proof #540.
% 228.46/39.99  | | | | 
% 228.46/39.99  | | | End of split
% 228.46/39.99  | | | 
% 228.46/39.99  | | End of split
% 228.46/39.99  | | 
% 228.46/39.99  | End of split
% 228.46/39.99  | 
% 228.46/39.99  End of proof
% 228.46/39.99  
% 228.46/39.99  Sub-proof #516 shows that the following formulas are inconsistent:
% 228.46/39.99  ----------------------------------------------------------------
% 228.46/39.99    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.46/39.99    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.46/39.99    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.46/39.99         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.46/39.99    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.46/39.99         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.46/39.99    (5)   ~ (all_53_8 = all_53_12)
% 228.46/39.99    (6)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.46/39.99         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.46/39.99    (7)   ~ (e3 = e1)
% 228.46/39.99    (8)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.46/39.99         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.46/39.99    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.46/39.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.46/39.99    (10)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.46/39.99          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.46/39.99    (11)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.46/39.99            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.46/39.99              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.46/39.99    (12)   ~ (all_6_2 = e3)
% 228.46/39.99    (13)  op(e1, e1) = all_6_2
% 228.46/39.99    (14)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.46/39.99    (15)   ~ (all_53_9 = e0)
% 228.46/39.99    (16)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.46/39.99          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.46/39.99    (17)   ~ (all_53_4 = all_53_12)
% 228.46/39.99    (18)   ~ (all_53_8 = all_53_9)
% 228.46/39.99    (19)  all_42_2 = all_6_2
% 228.46/39.99    (20)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.46/39.99          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.46/39.99    (21)   ~ (all_53_9 = all_6_2)
% 228.46/39.99    (22)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.46/39.99          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.46/39.99    (23)  all_57_3 = e0
% 228.46/39.99    (24)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.46/39.99          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.46/39.99    (25)   ~ (e3 = e2)
% 228.46/39.99    (26)  all_55_1 = all_53_4
% 228.46/39.99    (27)   ~ (e3 = e0)
% 228.46/39.99    (28)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.46/39.99          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.46/39.99    (29)   ~ (all_53_8 = all_6_2)
% 228.46/39.99    (30)  all_57_1 = e0
% 228.46/39.99    (31)  all_55_2 = all_53_8
% 228.46/39.99    (32)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.46/39.99    (33)  all_57_15 = e3
% 228.46/39.99    (34)  op(e3, e3) = e2
% 228.46/39.99    (35)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.46/39.99          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.46/39.99            e1)
% 228.46/39.99    (36)   ~ (all_53_4 = all_53_8)
% 228.46/39.99    (37)  op(e3, e2) = all_53_4
% 228.46/39.99    (38)  op(e1, e1) = e1
% 228.46/39.99    (39)   ~ (e2 = e0)
% 228.46/39.99    (40)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.46/39.99            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.46/39.99            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.46/39.99            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.46/39.99              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.46/39.99            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.46/39.99            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.46/39.99              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.46/39.99              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.46/39.99            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.46/39.99            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.46/39.99            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.46/39.99              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.46/39.99              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.46/39.99            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.46/39.99              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.46/39.99            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.46/39.99            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.46/39.99              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.46/39.99              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.46/39.99            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.46/39.99            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.46/39.99    (41)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.46/39.99          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.46/39.99    (42)   ~ (e1 = e0)
% 228.46/39.99    (43)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.46/39.99            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.46/39.99              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.46/39.99    (44)   ~ (all_53_4 = e0)
% 228.46/39.99    (45)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.46/39.99          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.46/39.99    (46)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.46/39.99          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.46/39.99    (47)  all_57_13 = e3
% 228.46/39.99    (48)  op(e0, e0) = e3
% 228.46/39.99    (49)   ~ (all_53_4 = all_53_6)
% 228.46/39.99    (50)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.46/39.99          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.46/39.99            e2)
% 228.46/39.99    (51)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.46/39.99              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.46/39.99                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.46/39.99                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.46/39.99    (52)  all_55_10 = all_6_2
% 228.46/39.99    (53)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.46/39.99          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.46/39.99    (54)  all_38_2 = all_6_2
% 228.46/39.99    (55)  all_55_3 = all_53_12
% 228.46/39.99    (56)   ~ (all_53_12 = e3)
% 228.46/39.99    (57)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.46/39.99            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.46/39.99              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.46/39.99    (58)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.46/39.99          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.46/39.99    (59)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.46/39.99          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.46/39.99    (60)   ~ (e2 = e1)
% 228.46/39.99    (61)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.46/39.99          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.46/39.99    (62)  op(e2, e1) = all_53_9
% 228.46/39.99    (63)  op(e1, e2) = all_53_6
% 228.46/39.99    (64)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.46/39.99          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.46/39.99    (65)  all_24_2 = all_6_2
% 228.46/39.99    (66)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.46/39.99          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.46/39.99    (67)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.46/39.99          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.46/39.99    (68)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.46/39.99          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.46/39.99    (69)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.46/39.99          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.46/39.99    (70)  op(e3, e1) = all_53_8
% 228.46/39.99    (71)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.46/39.99          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.46/39.99    (72)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.46/39.99          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.46/39.99    (73)  op(e3, e0) = all_53_12
% 228.46/39.99  
% 228.46/39.99  Begin of proof
% 228.46/39.99  | 
% 228.46/39.99  | BETA: splitting (35) gives:
% 228.46/39.99  | 
% 228.46/39.99  | Case 1:
% 228.46/39.99  | | 
% 228.46/39.99  | |   (74)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 228.46/39.99  | |           e1)
% 228.46/39.99  | | 
% 228.46/39.99  | | REF_CLOSE: (3), (4), (6), (7), (9), (10), (12), (13), (23), (25), (27),
% 228.46/39.99  | |            (30), (33), (34), (35), (39), (42), (47), (50), (51), (53), (58),
% 228.46/39.99  | |            (59), (60), (61), (64), (67), (68), (71), (74) are inconsistent
% 228.46/39.99  | |            by sub-proof #521.
% 228.46/39.99  | | 
% 228.46/39.99  | Case 2:
% 228.46/39.99  | | 
% 228.46/39.99  | |   (75)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.46/39.99  | |           e1)
% 228.46/39.99  | | 
% 228.46/39.99  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.46/39.99  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 228.46/39.99  | |            (24), (25), (26), (27), (28), (29), (31), (32), (33), (34), (35),
% 228.46/39.99  | |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 228.46/39.99  | |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 228.46/39.99  | |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 228.46/39.99  | |            (69), (70), (71), (72), (73), (75) are inconsistent by sub-proof
% 228.46/39.99  | |            #517.
% 228.46/39.99  | | 
% 228.46/39.99  | End of split
% 228.46/39.99  | 
% 228.46/39.99  End of proof
% 228.46/39.99  
% 228.46/39.99  Sub-proof #517 shows that the following formulas are inconsistent:
% 228.46/39.99  ----------------------------------------------------------------
% 228.46/39.99    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.46/39.99    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.46/39.99    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.46/39.99         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.46/39.99    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.46/39.99         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.46/39.99    (5)   ~ (all_53_8 = all_53_12)
% 228.46/39.99    (6)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.46/39.99         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.46/39.99    (7)   ~ (e3 = e1)
% 228.46/39.99    (8)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.46/39.99         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.46/39.99    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.46/39.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.46/39.99    (10)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.46/39.99          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.46/39.99    (11)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.46/39.99            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.46/39.99              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.46/39.99    (12)   ~ (all_6_2 = e3)
% 228.46/39.99    (13)  op(e1, e1) = all_6_2
% 228.46/39.99    (14)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.46/39.99    (15)   ~ (all_53_9 = e0)
% 228.46/40.00    (16)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.46/40.00          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.46/40.00    (17)   ~ (all_53_4 = all_53_12)
% 228.46/40.00    (18)   ~ (all_53_8 = all_53_9)
% 228.46/40.00    (19)  all_42_2 = all_6_2
% 228.46/40.00    (20)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.46/40.00          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.46/40.00    (21)   ~ (all_53_9 = all_6_2)
% 228.46/40.00    (22)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.46/40.00          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.46/40.00    (23)  all_57_3 = e0
% 228.46/40.00    (24)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.46/40.00          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.46/40.00    (25)   ~ (e3 = e2)
% 228.46/40.00    (26)  all_55_1 = all_53_4
% 228.46/40.00    (27)   ~ (e3 = e0)
% 228.46/40.00    (28)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.46/40.00          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.46/40.00    (29)   ~ (all_53_8 = all_6_2)
% 228.46/40.00    (30)  all_55_2 = all_53_8
% 228.46/40.00    (31)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.46/40.00    (32)  all_57_15 = e3
% 228.46/40.00    (33)  op(e3, e3) = e2
% 228.46/40.00    (34)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.46/40.00          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.46/40.00            e1)
% 228.46/40.00    (35)   ~ (all_53_4 = all_53_8)
% 228.46/40.00    (36)  op(e3, e2) = all_53_4
% 228.46/40.00    (37)  op(e1, e1) = e1
% 228.46/40.00    (38)   ~ (e2 = e0)
% 228.46/40.00    (39)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.46/40.00            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.46/40.00            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.46/40.00            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.46/40.00              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.46/40.00            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.46/40.00            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.46/40.00              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.46/40.00              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.46/40.00            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.46/40.00            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.46/40.00            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.46/40.00              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.46/40.00              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.46/40.00            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.46/40.00              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.46/40.00            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.46/40.00            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.46/40.00              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.46/40.00              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.46/40.00            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.46/40.00            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.46/40.00    (40)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.46/40.00          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.46/40.00    (41)   ~ (e1 = e0)
% 228.46/40.00    (42)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.46/40.00            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.46/40.00              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.46/40.00    (43)   ~ (all_53_4 = e0)
% 228.46/40.00    (44)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.46/40.00          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.46/40.00    (45)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.46/40.00          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.46/40.00    (46)  all_57_13 = e3
% 228.46/40.00    (47)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.46/40.00    (48)  op(e0, e0) = e3
% 228.46/40.00    (49)   ~ (all_53_4 = all_53_6)
% 228.46/40.00    (50)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.46/40.00          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.46/40.00            e2)
% 228.46/40.00    (51)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.46/40.00              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.46/40.00                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.46/40.00                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.46/40.00    (52)  all_55_10 = all_6_2
% 228.46/40.00    (53)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.46/40.00          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.46/40.00    (54)  all_38_2 = all_6_2
% 228.46/40.00    (55)  all_55_3 = all_53_12
% 228.46/40.00    (56)   ~ (all_53_12 = e3)
% 228.46/40.00    (57)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.46/40.00            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.46/40.00              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.46/40.00    (58)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.46/40.00          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.46/40.00    (59)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.46/40.00          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.46/40.00    (60)   ~ (e2 = e1)
% 228.46/40.00    (61)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.46/40.00          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.46/40.00    (62)  op(e2, e1) = all_53_9
% 228.46/40.00    (63)  op(e1, e2) = all_53_6
% 228.46/40.00    (64)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.46/40.00          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.46/40.00    (65)  all_24_2 = all_6_2
% 228.46/40.00    (66)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.46/40.00          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.46/40.00    (67)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.46/40.00          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.46/40.00    (68)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.46/40.00          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.46/40.00    (69)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.46/40.00          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.46/40.00    (70)  op(e3, e1) = all_53_8
% 228.46/40.00    (71)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.46/40.00          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.46/40.00    (72)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.46/40.00          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.46/40.00    (73)  op(e3, e0) = all_53_12
% 228.46/40.00  
% 228.46/40.00  Begin of proof
% 228.46/40.00  | 
% 228.46/40.00  | BETA: splitting (47) gives:
% 228.46/40.00  | 
% 228.46/40.00  | Case 1:
% 228.46/40.00  | | 
% 228.46/40.00  | |   (74)  all_57_14 = e1 & op(e0, e1) = e1
% 228.46/40.00  | | 
% 228.46/40.00  | | ALPHA: (74) implies:
% 228.46/40.00  | |   (75)  all_57_14 = e1
% 228.46/40.00  | | 
% 228.46/40.00  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.46/40.00  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 228.46/40.00  | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 228.46/40.00  | |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 228.46/40.00  | |            (46), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 228.46/40.00  | |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 228.46/40.00  | |            (69), (70), (71), (72), (73), (75) are inconsistent by sub-proof
% 228.46/40.00  | |            #518.
% 228.46/40.00  | | 
% 228.46/40.00  | Case 2:
% 228.46/40.00  | | 
% 228.46/40.00  | |   (76)  all_57_15 = e1 & op(e0, e0) = e1
% 228.46/40.00  | | 
% 228.46/40.00  | | REF_CLOSE: (7), (32), (76) are inconsistent by sub-proof #2325.
% 228.46/40.00  | | 
% 228.46/40.00  | End of split
% 228.46/40.00  | 
% 228.46/40.00  End of proof
% 228.46/40.00  
% 228.46/40.00  Sub-proof #518 shows that the following formulas are inconsistent:
% 228.46/40.00  ----------------------------------------------------------------
% 228.46/40.00    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.46/40.00    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.46/40.00    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.46/40.00         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.46/40.00    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.46/40.00         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.46/40.00    (5)   ~ (all_53_8 = all_53_12)
% 228.46/40.00    (6)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.46/40.00         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.46/40.00    (7)   ~ (e3 = e1)
% 228.46/40.00    (8)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.46/40.00         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.46/40.00    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.46/40.00           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.46/40.00    (10)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.46/40.00          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.46/40.00    (11)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.46/40.00            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.46/40.00              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.46/40.00    (12)   ~ (all_6_2 = e3)
% 228.46/40.00    (13)  op(e1, e1) = all_6_2
% 228.46/40.00    (14)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.46/40.00    (15)   ~ (all_53_9 = e0)
% 228.46/40.00    (16)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.46/40.00          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.46/40.00    (17)   ~ (all_53_4 = all_53_12)
% 228.46/40.00    (18)   ~ (all_53_8 = all_53_9)
% 228.46/40.00    (19)  all_42_2 = all_6_2
% 228.46/40.00    (20)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.46/40.00          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.46/40.00    (21)   ~ (all_53_9 = all_6_2)
% 228.46/40.00    (22)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.46/40.00          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.46/40.00    (23)  all_57_3 = e0
% 228.46/40.00    (24)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.46/40.00          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.46/40.00    (25)   ~ (e3 = e2)
% 228.46/40.00    (26)  all_55_1 = all_53_4
% 228.46/40.00    (27)   ~ (e3 = e0)
% 228.46/40.00    (28)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.46/40.00          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.46/40.00    (29)   ~ (all_53_8 = all_6_2)
% 228.46/40.00    (30)  all_55_2 = all_53_8
% 228.46/40.00    (31)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.46/40.00    (32)  all_57_15 = e3
% 228.46/40.00    (33)  op(e3, e3) = e2
% 228.46/40.00    (34)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.46/40.00          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.46/40.00            e1)
% 228.46/40.00    (35)   ~ (all_53_4 = all_53_8)
% 228.46/40.00    (36)  op(e3, e2) = all_53_4
% 228.46/40.00    (37)  op(e1, e1) = e1
% 228.46/40.00    (38)   ~ (e2 = e0)
% 228.46/40.00    (39)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.46/40.00            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.46/40.00            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.46/40.00            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.46/40.00              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.46/40.00            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.46/40.00            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.46/40.00              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.46/40.00              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.46/40.00            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.46/40.00            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.46/40.00            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.46/40.00              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.46/40.00              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.46/40.00            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.46/40.00              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.46/40.00            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.46/40.00            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.46/40.00              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.46/40.00              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.46/40.00            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.46/40.00            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.46/40.00    (40)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.46/40.00          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.46/40.00    (41)   ~ (e1 = e0)
% 228.46/40.00    (42)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.46/40.00            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.46/40.00              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.46/40.00    (43)   ~ (all_53_4 = e0)
% 228.46/40.00    (44)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.46/40.00          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.46/40.00    (45)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.46/40.00          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.46/40.00    (46)  all_57_14 = e1
% 228.46/40.00    (47)  all_57_13 = e3
% 228.46/40.00    (48)  op(e0, e0) = e3
% 228.46/40.00    (49)   ~ (all_53_4 = all_53_6)
% 228.46/40.00    (50)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.46/40.00          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.46/40.00            e2)
% 228.46/40.00    (51)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.46/40.00              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.46/40.00                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.46/40.00                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.46/40.00    (52)  all_55_10 = all_6_2
% 228.46/40.00    (53)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.46/40.00          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.46/40.00    (54)  all_38_2 = all_6_2
% 228.46/40.00    (55)  all_55_3 = all_53_12
% 228.46/40.00    (56)   ~ (all_53_12 = e3)
% 228.46/40.00    (57)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.46/40.00            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.46/40.00              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.46/40.00    (58)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.46/40.00          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.46/40.00    (59)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.46/40.00          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.46/40.00    (60)   ~ (e2 = e1)
% 228.46/40.00    (61)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.46/40.00          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.46/40.00    (62)  op(e2, e1) = all_53_9
% 228.46/40.00    (63)  op(e1, e2) = all_53_6
% 228.46/40.00    (64)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.46/40.00          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.46/40.00    (65)  all_24_2 = all_6_2
% 228.46/40.00    (66)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.46/40.00          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.46/40.00    (67)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.46/40.00          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.46/40.00    (68)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.46/40.00          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.46/40.00    (69)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.46/40.00          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.46/40.00    (70)  op(e3, e1) = all_53_8
% 228.46/40.00    (71)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.46/40.00          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.46/40.00    (72)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.46/40.00          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.46/40.00    (73)  op(e3, e0) = all_53_12
% 228.46/40.00  
% 228.46/40.00  Begin of proof
% 228.46/40.00  | 
% 228.46/40.00  | BETA: splitting (50) gives:
% 228.46/40.00  | 
% 228.46/40.00  | Case 1:
% 228.46/40.00  | | 
% 228.46/40.00  | |   (74)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 228.46/40.00  | |           e2)
% 228.46/40.00  | | 
% 228.46/40.00  | | BETA: splitting (74) gives:
% 228.46/40.00  | | 
% 228.46/40.00  | | Case 1:
% 228.46/40.00  | | | 
% 228.46/40.00  | | |   (75)  all_57_12 = e2 & op(e0, e3) = e2
% 228.46/40.00  | | | 
% 228.46/40.00  | | | ALPHA: (75) implies:
% 228.46/40.00  | | |   (76)  all_57_12 = e2
% 228.46/40.00  | | | 
% 228.46/40.00  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.46/40.00  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 228.46/40.00  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 228.46/40.00  | | |            (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 228.46/40.00  | | |            (43), (44), (45), (47), (48), (49), (50), (51), (52), (53),
% 228.46/40.00  | | |            (54), (55), (56), (57), (58), (59), (60), (61), (62), (63),
% 228.46/40.00  | | |            (64), (65), (66), (67), (68), (69), (70), (71), (72), (73),
% 228.46/40.00  | | |            (76) are inconsistent by sub-proof #519.
% 228.46/40.00  | | | 
% 228.46/40.00  | | Case 2:
% 228.46/40.00  | | | 
% 228.46/40.00  | | |   (77)  all_57_13 = e2 & op(e0, e2) = e2
% 228.46/40.00  | | | 
% 228.46/40.00  | | | ALPHA: (77) implies:
% 228.46/40.00  | | |   (78)  all_57_13 = e2
% 228.46/40.00  | | | 
% 228.46/40.00  | | | REF_CLOSE: (25), (47), (78) are inconsistent by sub-proof #2203.
% 228.46/40.00  | | | 
% 228.46/40.00  | | End of split
% 228.46/40.00  | | 
% 228.46/40.00  | Case 2:
% 228.46/40.00  | | 
% 228.46/40.00  | |   (79)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.46/40.00  | |           e2)
% 228.46/40.00  | | 
% 228.46/40.00  | | REF_CLOSE: (25), (32), (46), (60), (79) are inconsistent by sub-proof #1529.
% 228.46/40.00  | | 
% 228.46/40.00  | End of split
% 228.46/40.00  | 
% 228.46/40.00  End of proof
% 228.46/40.00  
% 228.46/40.00  Sub-proof #519 shows that the following formulas are inconsistent:
% 228.46/40.00  ----------------------------------------------------------------
% 228.46/40.00    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.46/40.00    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.46/40.00    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.46/40.00         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.46/40.00    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.46/40.00         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.46/40.00    (5)   ~ (all_53_8 = all_53_12)
% 228.46/40.00    (6)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.46/40.00         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.46/40.00    (7)   ~ (e3 = e1)
% 228.46/40.00    (8)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.46/40.00         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.46/40.00    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.46/40.00           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.46/40.00    (10)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.46/40.00          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.46/40.00    (11)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.46/40.00            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.46/40.00              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.46/40.00    (12)   ~ (all_6_2 = e3)
% 228.46/40.00    (13)  op(e1, e1) = all_6_2
% 228.46/40.00    (14)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.46/40.00    (15)   ~ (all_53_9 = e0)
% 228.46/40.00    (16)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.46/40.00          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.46/40.00    (17)   ~ (all_53_4 = all_53_12)
% 228.46/40.00    (18)   ~ (all_53_8 = all_53_9)
% 228.46/40.00    (19)  all_57_12 = e2
% 228.46/40.00    (20)  all_42_2 = all_6_2
% 228.46/40.00    (21)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.46/40.00          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.46/40.00    (22)   ~ (all_53_9 = all_6_2)
% 228.46/40.00    (23)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.46/40.00          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.46/40.00    (24)  all_57_3 = e0
% 228.46/40.00    (25)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.46/40.00          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.46/40.00    (26)   ~ (e3 = e2)
% 228.46/40.00    (27)  all_55_1 = all_53_4
% 228.46/40.00    (28)   ~ (e3 = e0)
% 228.46/40.00    (29)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.46/40.00          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.46/40.00    (30)   ~ (all_53_8 = all_6_2)
% 228.46/40.00    (31)  all_55_2 = all_53_8
% 228.46/40.00    (32)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.46/40.00    (33)  all_57_15 = e3
% 228.46/40.00    (34)  op(e3, e3) = e2
% 228.46/40.00    (35)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.46/40.00          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.46/40.00            e1)
% 228.46/40.00    (36)   ~ (all_53_4 = all_53_8)
% 228.46/40.00    (37)  op(e3, e2) = all_53_4
% 228.46/40.00    (38)  op(e1, e1) = e1
% 228.46/40.00    (39)   ~ (e2 = e0)
% 228.46/40.00    (40)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.46/40.00            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.46/40.00            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.46/40.00            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.46/40.00              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.46/40.00            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.46/40.00            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.46/40.00              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.46/40.00              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.46/40.00            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.46/40.00            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.46/40.00            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.46/40.00              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.46/40.00              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.46/40.00            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.46/40.00              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.46/40.00            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.46/40.00            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.46/40.00              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.46/40.00              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.46/40.00            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.46/40.00            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.46/40.00    (41)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.46/40.00          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.46/40.00    (42)   ~ (e1 = e0)
% 228.46/40.00    (43)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.46/40.00            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.46/40.00              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.46/40.00    (44)   ~ (all_53_4 = e0)
% 228.46/40.00    (45)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.46/40.00          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.46/40.00    (46)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.46/40.00          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.46/40.00    (47)  all_57_13 = e3
% 228.46/40.00    (48)  op(e0, e0) = e3
% 228.46/40.00    (49)   ~ (all_53_4 = all_53_6)
% 228.46/40.00    (50)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.46/40.00          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.46/40.00            e2)
% 228.46/40.00    (51)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.46/40.00              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.46/40.00                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.46/40.00                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.46/40.00    (52)  all_55_10 = all_6_2
% 228.46/40.00    (53)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.46/40.00          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.46/40.00    (54)  all_38_2 = all_6_2
% 228.46/40.00    (55)  all_55_3 = all_53_12
% 228.46/40.01    (56)   ~ (all_53_12 = e3)
% 228.46/40.01    (57)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.46/40.01            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.46/40.01              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.46/40.01    (58)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.46/40.01          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.46/40.01    (59)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.46/40.01          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.46/40.01    (60)   ~ (e2 = e1)
% 228.46/40.01    (61)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.46/40.01          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.46/40.01    (62)  op(e2, e1) = all_53_9
% 228.46/40.01    (63)  op(e1, e2) = all_53_6
% 228.46/40.01    (64)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.46/40.01          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.46/40.01    (65)  all_24_2 = all_6_2
% 228.46/40.01    (66)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.46/40.01          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.46/40.01    (67)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.46/40.01          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.46/40.01    (68)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.46/40.01          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.46/40.01    (69)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.46/40.01          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.46/40.01    (70)  op(e3, e1) = all_53_8
% 228.46/40.01    (71)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.46/40.01          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.46/40.01    (72)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.46/40.01          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.46/40.01    (73)  op(e3, e0) = all_53_12
% 228.46/40.01  
% 228.46/40.01  Begin of proof
% 228.46/40.01  | 
% 228.46/40.01  | BETA: splitting (67) gives:
% 228.46/40.01  | 
% 228.46/40.01  | Case 1:
% 228.46/40.01  | | 
% 228.46/40.01  | |   (74)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) =
% 228.46/40.01  | |           e0)
% 228.46/40.01  | | 
% 228.46/40.01  | | REF_CLOSE: (3), (7), (9), (24), (26), (28), (34), (39), (42), (53), (58),
% 228.46/40.01  | |            (60), (74) are inconsistent by sub-proof #1654.
% 228.46/40.01  | | 
% 228.46/40.01  | Case 2:
% 228.46/40.01  | | 
% 228.46/40.01  | |   (75)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) =
% 228.46/40.01  | |           e0)
% 228.46/40.01  | | 
% 228.46/40.01  | | BETA: splitting (75) gives:
% 228.46/40.01  | | 
% 228.46/40.01  | | Case 1:
% 228.46/40.01  | | | 
% 228.46/40.01  | | |   (76)  all_57_6 = e0 & op(e1, e3) = e0
% 228.46/40.01  | | | 
% 228.46/40.01  | | | ALPHA: (76) implies:
% 228.46/40.01  | | |   (77)  all_57_6 = e0
% 228.46/40.01  | | | 
% 228.46/40.01  | | | BETA: splitting (4) gives:
% 228.46/40.01  | | | 
% 228.46/40.01  | | | Case 1:
% 228.46/40.01  | | | | 
% 228.46/40.01  | | | |   (78)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3)
% 228.46/40.01  | | | |           = e1)
% 228.46/40.01  | | | | 
% 228.46/40.01  | | | | BETA: splitting (78) gives:
% 228.46/40.01  | | | | 
% 228.46/40.01  | | | | Case 1:
% 228.46/40.01  | | | | | 
% 228.46/40.01  | | | | |   (79)  all_57_0 = e1 & op(e3, e3) = e1
% 228.46/40.01  | | | | | 
% 228.46/40.01  | | | | | ALPHA: (79) implies:
% 228.46/40.01  | | | | |   (80)  op(e3, e3) = e1
% 228.46/40.01  | | | | | 
% 228.46/40.01  | | | | | REF_CLOSE: (9), (34), (60), (80) are inconsistent by sub-proof #1950.
% 228.46/40.01  | | | | | 
% 228.46/40.01  | | | | Case 2:
% 228.46/40.01  | | | | | 
% 228.46/40.01  | | | | |   (81)  all_57_2 = e1 & op(e2, e3) = e1
% 228.46/40.01  | | | | | 
% 228.46/40.01  | | | | | ALPHA: (81) implies:
% 228.46/40.01  | | | | |   (82)  all_57_2 = e1
% 228.46/40.01  | | | | | 
% 228.46/40.01  | | | | | BETA: splitting (59) gives:
% 228.46/40.01  | | | | | 
% 228.46/40.01  | | | | | Case 1:
% 228.46/40.01  | | | | | | 
% 228.46/40.01  | | | | | |   (83)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2,
% 228.46/40.01  | | | | | |             e3) = e3)
% 228.46/40.01  | | | | | | 
% 228.46/40.01  | | | | | | REF_CLOSE: (7), (9), (26), (34), (82), (83) are inconsistent by
% 228.46/40.01  | | | | | |            sub-proof #765.
% 228.46/40.01  | | | | | | 
% 228.46/40.01  | | | | | Case 2:
% 228.46/40.01  | | | | | | 
% 228.46/40.01  | | | | | |   (84)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0,
% 228.46/40.01  | | | | | |             e3) = e3)
% 228.46/40.01  | | | | | | 
% 228.46/40.01  | | | | | | REF_CLOSE: (7), (26), (28), (33), (35), (39), (42), (47), (50),
% 228.46/40.01  | | | | | |            (51), (60), (77), (84) are inconsistent by sub-proof
% 228.46/40.01  | | | | | |            #786.
% 228.46/40.01  | | | | | | 
% 228.46/40.01  | | | | | End of split
% 228.46/40.01  | | | | | 
% 228.46/40.01  | | | | End of split
% 228.46/40.01  | | | | 
% 228.46/40.01  | | | Case 2:
% 228.46/40.01  | | | | 
% 228.46/40.01  | | | |   (85)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3)
% 228.46/40.01  | | | |           = e1)
% 228.46/40.01  | | | | 
% 228.46/40.01  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 228.46/40.01  | | | |            (12), (13), (14), (15), (16), (17), (18), (19), (20), (21),
% 228.46/40.01  | | | |            (22), (23), (24), (25), (26), (27), (28), (29), (30), (31),
% 228.46/40.01  | | | |            (32), (33), (34), (35), (36), (37), (38), (39), (40), (41),
% 228.46/40.01  | | | |            (42), (43), (44), (45), (46), (48), (49), (50), (51), (52),
% 228.46/40.01  | | | |            (53), (54), (55), (56), (57), (58), (59), (60), (61), (62),
% 228.46/40.01  | | | |            (63), (64), (65), (66), (67), (68), (69), (70), (71), (72),
% 228.46/40.01  | | | |            (73), (85) are inconsistent by sub-proof #520.
% 228.46/40.01  | | | | 
% 228.46/40.01  | | | End of split
% 228.46/40.01  | | | 
% 228.46/40.01  | | Case 2:
% 228.46/40.01  | | | 
% 228.46/40.01  | | |   (86)  all_57_12 = e0 & op(e0, e3) = e0
% 228.46/40.01  | | | 
% 228.46/40.01  | | | REF_CLOSE: (19), (39), (86) are inconsistent by sub-proof #2185.
% 228.46/40.01  | | | 
% 228.46/40.01  | | End of split
% 228.46/40.01  | | 
% 228.46/40.01  | End of split
% 228.46/40.01  | 
% 228.46/40.01  End of proof
% 228.46/40.01  
% 228.46/40.01  Sub-proof #520 shows that the following formulas are inconsistent:
% 228.46/40.01  ----------------------------------------------------------------
% 228.46/40.01    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.46/40.01    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.46/40.01    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.46/40.01         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.46/40.01    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.46/40.01         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.46/40.01    (5)   ~ (all_53_8 = all_53_12)
% 228.46/40.01    (6)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.46/40.01         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.46/40.01    (7)   ~ (e3 = e1)
% 228.46/40.01    (8)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.46/40.01         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.46/40.01    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.46/40.01           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.46/40.01    (10)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.46/40.01          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.46/40.01    (11)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.46/40.01            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.46/40.01              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.46/40.01    (12)   ~ (all_6_2 = e3)
% 228.46/40.01    (13)  op(e1, e1) = all_6_2
% 228.46/40.01    (14)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.46/40.01    (15)   ~ (all_53_9 = e0)
% 228.46/40.01    (16)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.46/40.01          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.46/40.01    (17)   ~ (all_53_4 = all_53_12)
% 228.46/40.01    (18)   ~ (all_53_8 = all_53_9)
% 228.46/40.01    (19)  all_57_12 = e2
% 228.46/40.01    (20)  all_42_2 = all_6_2
% 228.46/40.01    (21)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.46/40.01          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.46/40.01    (22)   ~ (all_53_9 = all_6_2)
% 228.46/40.01    (23)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.46/40.01          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.46/40.01    (24)  all_57_3 = e0
% 228.46/40.01    (25)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.46/40.01          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.46/40.01    (26)   ~ (e3 = e2)
% 228.46/40.01    (27)  all_55_1 = all_53_4
% 228.46/40.01    (28)   ~ (e3 = e0)
% 228.46/40.01    (29)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.46/40.01          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.46/40.01    (30)   ~ (all_53_8 = all_6_2)
% 228.46/40.01    (31)  all_55_2 = all_53_8
% 228.46/40.01    (32)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.46/40.01    (33)  all_57_15 = e3
% 228.46/40.01    (34)  op(e3, e3) = e2
% 228.46/40.01    (35)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.46/40.01          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.46/40.01            e1)
% 228.46/40.01    (36)   ~ (all_53_4 = all_53_8)
% 228.46/40.01    (37)  op(e3, e2) = all_53_4
% 228.46/40.01    (38)  op(e1, e1) = e1
% 228.46/40.01    (39)   ~ (e2 = e0)
% 228.46/40.01    (40)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.46/40.01            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.46/40.01            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.46/40.01            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.46/40.01              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.46/40.01            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.46/40.01            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.46/40.01              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.46/40.01              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.46/40.01            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.46/40.01            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.46/40.01            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.46/40.01              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.46/40.01              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.46/40.01            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.46/40.01              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.46/40.01            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.46/40.01            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.46/40.01              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.46/40.01              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.46/40.01            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.46/40.01            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.46/40.01    (41)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.46/40.01          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.46/40.01    (42)   ~ (e1 = e0)
% 228.46/40.01    (43)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.46/40.01            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.46/40.01              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.46/40.01    (44)   ~ (all_53_4 = e0)
% 228.46/40.01    (45)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.46/40.01          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.46/40.01    (46)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.46/40.01          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.46/40.01    (47)  op(e0, e0) = e3
% 228.46/40.01    (48)   ~ (all_53_4 = all_53_6)
% 228.46/40.01    (49)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.46/40.01          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.46/40.01            e2)
% 228.46/40.01    (50)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.46/40.01    (51)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.46/40.01              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.46/40.01                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.46/40.01                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.46/40.01    (52)  all_55_10 = all_6_2
% 228.46/40.01    (53)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.46/40.01          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.46/40.01    (54)  all_38_2 = all_6_2
% 228.46/40.01    (55)  all_55_3 = all_53_12
% 228.46/40.01    (56)   ~ (all_53_12 = e3)
% 228.46/40.01    (57)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.46/40.01            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.46/40.01              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.46/40.01    (58)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.46/40.01          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.46/40.01    (59)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.46/40.01          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.46/40.01    (60)   ~ (e2 = e1)
% 228.46/40.01    (61)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.46/40.01          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.46/40.01    (62)  op(e2, e1) = all_53_9
% 228.46/40.01    (63)  op(e1, e2) = all_53_6
% 228.46/40.01    (64)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.46/40.01          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.46/40.01    (65)  all_24_2 = all_6_2
% 228.46/40.01    (66)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.46/40.01          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.46/40.01    (67)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.46/40.01          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.46/40.01    (68)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.46/40.01          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.46/40.01    (69)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.46/40.01          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.46/40.01    (70)  op(e3, e1) = all_53_8
% 228.46/40.01    (71)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.46/40.01          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.46/40.01    (72)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.46/40.01          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.46/40.01    (73)  op(e3, e0) = all_53_12
% 228.46/40.01  
% 228.46/40.01  Begin of proof
% 228.46/40.01  | 
% 228.46/40.01  | BETA: splitting (50) gives:
% 228.46/40.01  | 
% 228.46/40.01  | Case 1:
% 228.46/40.01  | | 
% 228.46/40.01  | |   (74)  all_57_6 = e1 & op(e1, e3) = e1
% 228.46/40.01  | | 
% 228.46/40.01  | | ALPHA: (74) implies:
% 228.46/40.01  | |   (75)  all_57_6 = e1
% 228.46/40.01  | | 
% 228.46/40.01  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.46/40.01  | |            (13), (14), (15), (16), (17), (18), (20), (21), (22), (23), (24),
% 228.46/40.01  | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 228.46/40.01  | |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 228.46/40.01  | |            (47), (48), (49), (51), (52), (53), (54), (55), (56), (57), (58),
% 228.46/40.01  | |            (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 228.46/40.01  | |            (70), (71), (72), (73), (75) are inconsistent by sub-proof #523.
% 228.46/40.01  | | 
% 228.46/40.01  | Case 2:
% 228.46/40.01  | | 
% 228.46/40.01  | |   (76)  all_57_12 = e1 & op(e0, e3) = e1
% 228.46/40.01  | | 
% 228.46/40.01  | | REF_CLOSE: (19), (60), (76) are inconsistent by sub-proof #2388.
% 228.46/40.01  | | 
% 228.46/40.01  | End of split
% 228.46/40.01  | 
% 228.46/40.01  End of proof
% 228.46/40.01  
% 228.46/40.01  Sub-proof #521 shows that the following formulas are inconsistent:
% 228.46/40.01  ----------------------------------------------------------------
% 228.46/40.01    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.46/40.01         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.46/40.01    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.46/40.01         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.46/40.01    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.46/40.01         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.46/40.01    (4)   ~ (e3 = e1)
% 228.46/40.01    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.46/40.01           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.46/40.01    (6)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.46/40.01         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.46/40.01    (7)   ~ (all_6_2 = e3)
% 228.46/40.01    (8)  op(e1, e1) = all_6_2
% 228.46/40.01    (9)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.46/40.01    (10)  all_57_3 = e0
% 228.46/40.01    (11)   ~ (e3 = e2)
% 228.46/40.01    (12)   ~ (e3 = e0)
% 228.46/40.01    (13)  all_57_1 = e0
% 228.46/40.01    (14)  all_57_15 = e3
% 228.46/40.01    (15)  op(e3, e3) = e2
% 228.46/40.01    (16)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.46/40.01          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.46/40.01            e1)
% 228.46/40.01    (17)   ~ (e2 = e0)
% 228.46/40.01    (18)   ~ (e1 = e0)
% 228.46/40.01    (19)  all_57_13 = e3
% 228.46/40.01    (20)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.46/40.01          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.46/40.01            e2)
% 228.46/40.01    (21)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.46/40.01              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.46/40.01                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.46/40.01                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.46/40.01    (22)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.46/40.01          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.46/40.01    (23)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.46/40.01          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.46/40.01    (24)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.46/40.01          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.46/40.01    (25)   ~ (e2 = e1)
% 228.46/40.01    (26)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.46/40.01          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.46/40.01    (27)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.46/40.01          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.46/40.01    (28)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.46/40.01          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.46/40.01    (29)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.46/40.01          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.46/40.01    (30)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.46/40.01          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.46/40.01  
% 228.46/40.01  Begin of proof
% 228.46/40.01  | 
% 228.46/40.01  | BETA: splitting (9) gives:
% 228.46/40.01  | 
% 228.46/40.01  | Case 1:
% 228.46/40.01  | | 
% 228.46/40.01  | |   (31)  all_57_12 = e1 & op(e0, e3) = e1
% 228.46/40.01  | | 
% 228.46/40.01  | | ALPHA: (31) implies:
% 228.46/40.01  | |   (32)  all_57_12 = e1
% 228.46/40.01  | | 
% 228.46/40.01  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13),
% 228.46/40.01  | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 228.46/40.01  | |            (25), (26), (27), (28), (29), (30), (32) are inconsistent by
% 228.46/40.01  | |            sub-proof #522.
% 228.46/40.01  | | 
% 228.46/40.01  | Case 2:
% 228.46/40.01  | | 
% 228.46/40.01  | |   (33)  all_57_13 = e1 & op(e0, e2) = e1
% 228.46/40.01  | | 
% 228.46/40.01  | | ALPHA: (33) implies:
% 228.46/40.01  | |   (34)  all_57_13 = e1
% 228.46/40.01  | | 
% 228.46/40.01  | | REF_CLOSE: (4), (19), (34) are inconsistent by sub-proof #2268.
% 228.46/40.01  | | 
% 228.46/40.01  | End of split
% 228.46/40.01  | 
% 228.46/40.01  End of proof
% 228.46/40.01  
% 228.46/40.01  Sub-proof #522 shows that the following formulas are inconsistent:
% 228.46/40.01  ----------------------------------------------------------------
% 228.46/40.01    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.46/40.01         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.46/40.01    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.46/40.01         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.46/40.01    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.46/40.01         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.46/40.01    (4)   ~ (e3 = e1)
% 228.46/40.01    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.46/40.01           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.46/40.01    (6)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.46/40.01         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.46/40.01    (7)   ~ (all_6_2 = e3)
% 228.46/40.01    (8)  op(e1, e1) = all_6_2
% 228.46/40.01    (9)  all_57_3 = e0
% 228.46/40.01    (10)   ~ (e3 = e2)
% 228.46/40.01    (11)   ~ (e3 = e0)
% 228.46/40.01    (12)  all_57_1 = e0
% 228.46/40.01    (13)  all_57_15 = e3
% 228.46/40.01    (14)  op(e3, e3) = e2
% 228.46/40.01    (15)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.46/40.01          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.46/40.01            e1)
% 228.46/40.01    (16)  all_57_12 = e1
% 228.46/40.01    (17)   ~ (e2 = e0)
% 228.46/40.01    (18)   ~ (e1 = e0)
% 228.46/40.01    (19)  all_57_13 = e3
% 228.46/40.01    (20)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.46/40.01          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.46/40.01            e2)
% 228.46/40.01    (21)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.46/40.01              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.46/40.01                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.46/40.01                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.46/40.01    (22)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.46/40.01          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.46/40.01    (23)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.46/40.01          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.46/40.01    (24)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.46/40.01          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.46/40.01    (25)   ~ (e2 = e1)
% 228.46/40.01    (26)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.46/40.01          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.46/40.01    (27)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.46/40.01          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.46/40.01    (28)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.46/40.01          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.46/40.01    (29)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.46/40.01          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.46/40.01    (30)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.46/40.01          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.46/40.01  
% 228.46/40.01  Begin of proof
% 228.46/40.01  | 
% 228.46/40.01  | BETA: splitting (28) gives:
% 228.46/40.01  | 
% 228.46/40.01  | Case 1:
% 228.46/40.01  | | 
% 228.46/40.01  | |   (31)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) =
% 228.46/40.01  | |           e0)
% 228.46/40.01  | | 
% 228.46/40.01  | | REF_CLOSE: (1), (4), (5), (9), (10), (11), (14), (17), (18), (22), (23),
% 228.46/40.01  | |            (25), (31) are inconsistent by sub-proof #1654.
% 228.46/40.01  | | 
% 228.46/40.01  | Case 2:
% 228.46/40.01  | | 
% 228.46/40.01  | |   (32)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) =
% 228.46/40.01  | |           e0)
% 228.46/40.01  | | 
% 228.46/40.01  | | BETA: splitting (32) gives:
% 228.46/40.01  | | 
% 228.46/40.01  | | Case 1:
% 228.46/40.01  | | | 
% 228.46/40.01  | | |   (33)  all_57_6 = e0 & op(e1, e3) = e0
% 228.46/40.01  | | | 
% 228.46/40.01  | | | ALPHA: (33) implies:
% 228.46/40.01  | | |   (34)  all_57_6 = e0
% 228.46/40.01  | | | 
% 228.46/40.01  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.46/40.01  | | |            (13), (15), (17), (18), (19), (20), (21), (22), (23), (24),
% 228.46/40.01  | | |            (25), (26), (27), (28), (29), (30), (34) are inconsistent by
% 228.46/40.01  | | |            sub-proof #691.
% 228.46/40.01  | | | 
% 228.46/40.01  | | Case 2:
% 228.46/40.01  | | | 
% 228.46/40.01  | | |   (35)  all_57_12 = e0 & op(e0, e3) = e0
% 228.46/40.01  | | | 
% 228.46/40.01  | | | REF_CLOSE: (16), (18), (35) are inconsistent by sub-proof #1279.
% 228.46/40.01  | | | 
% 228.46/40.01  | | End of split
% 228.46/40.01  | | 
% 228.46/40.01  | End of split
% 228.46/40.01  | 
% 228.46/40.01  End of proof
% 228.46/40.01  
% 228.46/40.01  Sub-proof #523 shows that the following formulas are inconsistent:
% 228.46/40.01  ----------------------------------------------------------------
% 228.46/40.01    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.46/40.01    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.46/40.02    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.46/40.02         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.46/40.02    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.46/40.02         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.46/40.02    (5)   ~ (all_53_8 = all_53_12)
% 228.46/40.02    (6)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.46/40.02         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.46/40.02    (7)   ~ (e3 = e1)
% 228.46/40.02    (8)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.46/40.02         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.46/40.02    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.46/40.02           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.46/40.02    (10)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.46/40.02          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.46/40.02    (11)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.46/40.02            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.46/40.02              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.46/40.02    (12)   ~ (all_6_2 = e3)
% 228.46/40.02    (13)  op(e1, e1) = all_6_2
% 228.46/40.02    (14)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.46/40.02    (15)   ~ (all_53_9 = e0)
% 228.46/40.02    (16)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.46/40.02          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.46/40.02    (17)   ~ (all_53_4 = all_53_12)
% 228.46/40.02    (18)   ~ (all_53_8 = all_53_9)
% 228.46/40.02    (19)  all_42_2 = all_6_2
% 228.46/40.02    (20)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.46/40.02          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.46/40.02    (21)  all_57_6 = e1
% 228.46/40.02    (22)   ~ (all_53_9 = all_6_2)
% 228.46/40.02    (23)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.46/40.02          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.46/40.02    (24)  all_57_3 = e0
% 228.46/40.02    (25)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.46/40.02          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.46/40.02    (26)   ~ (e3 = e2)
% 228.46/40.02    (27)  all_55_1 = all_53_4
% 228.46/40.02    (28)   ~ (e3 = e0)
% 228.46/40.02    (29)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.46/40.02          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.46/40.02    (30)   ~ (all_53_8 = all_6_2)
% 228.46/40.02    (31)  all_55_2 = all_53_8
% 228.46/40.02    (32)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.46/40.02    (33)  all_57_15 = e3
% 228.46/40.02    (34)  op(e3, e3) = e2
% 228.46/40.02    (35)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.46/40.02          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.46/40.02            e1)
% 228.46/40.02    (36)   ~ (all_53_4 = all_53_8)
% 228.46/40.02    (37)  op(e3, e2) = all_53_4
% 228.46/40.02    (38)  op(e1, e1) = e1
% 228.46/40.02    (39)   ~ (e2 = e0)
% 228.46/40.02    (40)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.46/40.02            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.46/40.02            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.46/40.02            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.46/40.02              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.46/40.02            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.46/40.02            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.46/40.02              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.46/40.02              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.46/40.02            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.46/40.02            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.46/40.02            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.46/40.02              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.46/40.02              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.46/40.02            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.46/40.02              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.46/40.02            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.46/40.02            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.46/40.02              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.46/40.02              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.46/40.02            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.46/40.02            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.46/40.02    (41)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.46/40.02          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.46/40.02    (42)   ~ (e1 = e0)
% 228.46/40.02    (43)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.46/40.02            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.46/40.02              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.46/40.02    (44)   ~ (all_53_4 = e0)
% 228.46/40.02    (45)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.46/40.02          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.46/40.02    (46)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.46/40.02          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.46/40.02    (47)  op(e0, e0) = e3
% 228.46/40.02    (48)   ~ (all_53_4 = all_53_6)
% 228.46/40.02    (49)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.46/40.02          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.46/40.02            e2)
% 228.46/40.02    (50)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.46/40.02              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.46/40.02                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.46/40.02                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.46/40.02    (51)  all_55_10 = all_6_2
% 228.46/40.02    (52)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.46/40.02          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.46/40.02    (53)  all_38_2 = all_6_2
% 228.46/40.02    (54)  all_55_3 = all_53_12
% 228.46/40.02    (55)   ~ (all_53_12 = e3)
% 228.46/40.02    (56)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.46/40.02            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.46/40.02              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.46/40.02    (57)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.46/40.02          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.46/40.02    (58)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.46/40.02          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.46/40.02    (59)   ~ (e2 = e1)
% 228.46/40.02    (60)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.46/40.02          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.46/40.02    (61)  op(e2, e1) = all_53_9
% 228.46/40.02    (62)  op(e1, e2) = all_53_6
% 228.46/40.02    (63)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.46/40.02          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.46/40.02    (64)  all_24_2 = all_6_2
% 228.46/40.02    (65)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.46/40.02          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.46/40.02    (66)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.46/40.02          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.46/40.02    (67)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.46/40.02          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.46/40.02    (68)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.46/40.02          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.46/40.02    (69)  op(e3, e1) = all_53_8
% 228.46/40.02    (70)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.46/40.02          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.46/40.02    (71)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.46/40.02          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.46/40.02    (72)  op(e3, e0) = all_53_12
% 228.46/40.02  
% 228.46/40.02  Begin of proof
% 228.46/40.02  | 
% 228.46/40.02  | BETA: splitting (58) gives:
% 228.46/40.02  | 
% 228.46/40.02  | Case 1:
% 228.46/40.02  | | 
% 228.46/40.02  | |   (73)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) =
% 228.46/40.02  | |           e3)
% 228.46/40.02  | | 
% 228.46/40.02  | | BETA: splitting (73) gives:
% 228.46/40.02  | | 
% 228.46/40.02  | | Case 1:
% 228.46/40.02  | | | 
% 228.46/40.02  | | |   (74)  all_57_0 = e3 & op(e3, e3) = e3
% 228.46/40.02  | | | 
% 228.46/40.02  | | | ALPHA: (74) implies:
% 228.46/40.02  | | |   (75)  op(e3, e3) = e3
% 228.46/40.02  | | | 
% 228.46/40.02  | | | REF_CLOSE: (9), (26), (34), (75) are inconsistent by sub-proof #2490.
% 228.46/40.02  | | | 
% 228.46/40.02  | | Case 2:
% 228.46/40.02  | | | 
% 228.46/40.02  | | |   (76)  all_57_2 = e3 & op(e2, e3) = e3
% 228.46/40.02  | | | 
% 228.46/40.02  | | | ALPHA: (76) implies:
% 228.46/40.02  | | |   (77)  all_57_2 = e3
% 228.46/40.02  | | | 
% 228.46/40.02  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.46/40.02  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 228.46/40.02  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 228.46/40.02  | | |            (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 228.46/40.02  | | |            (43), (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 228.46/40.02  | | |            (53), (54), (55), (56), (57), (58), (59), (60), (61), (62),
% 228.46/40.02  | | |            (63), (64), (65), (66), (67), (68), (69), (70), (71), (72),
% 228.46/40.02  | | |            (77) are inconsistent by sub-proof #524.
% 228.46/40.02  | | | 
% 228.46/40.02  | | End of split
% 228.46/40.02  | | 
% 228.46/40.02  | Case 2:
% 228.46/40.02  | | 
% 228.46/40.02  | |   (78)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) =
% 228.46/40.02  | |           e3)
% 228.46/40.02  | | 
% 228.46/40.02  | | BETA: splitting (78) gives:
% 228.46/40.02  | | 
% 228.46/40.02  | | Case 1:
% 228.46/40.02  | | | 
% 228.46/40.02  | | |   (79)  all_57_6 = e3 & op(e1, e3) = e3
% 228.46/40.02  | | | 
% 228.46/40.02  | | | REF_CLOSE: (7), (21), (79) are inconsistent by sub-proof #2346.
% 228.46/40.02  | | | 
% 228.46/40.02  | | Case 2:
% 228.46/40.02  | | | 
% 228.46/40.02  | | |   (80)  all_57_12 = e3 & op(e0, e3) = e3
% 228.46/40.02  | | | 
% 228.46/40.02  | | | ALPHA: (80) implies:
% 228.46/40.02  | | |   (81)  all_57_12 = e3
% 228.46/40.02  | | | 
% 228.46/40.02  | | | REF_CLOSE: (3), (7), (9), (21), (24), (26), (28), (34), (39), (42), (52),
% 228.46/40.02  | | |            (57), (59), (66), (81) are inconsistent by sub-proof #1632.
% 228.46/40.02  | | | 
% 228.46/40.02  | | End of split
% 228.46/40.02  | | 
% 228.46/40.02  | End of split
% 228.46/40.02  | 
% 228.46/40.02  End of proof
% 228.46/40.02  
% 228.46/40.02  Sub-proof #524 shows that the following formulas are inconsistent:
% 228.46/40.02  ----------------------------------------------------------------
% 228.46/40.02    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.46/40.02    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.46/40.02    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.46/40.02         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.46/40.02    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.46/40.02         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.46/40.02    (5)   ~ (all_53_8 = all_53_12)
% 228.46/40.02    (6)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.46/40.02         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.46/40.02    (7)   ~ (e3 = e1)
% 228.46/40.02    (8)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.46/40.02         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.46/40.02    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.46/40.02           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.46/40.02    (10)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.46/40.02          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.46/40.02    (11)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.46/40.02            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.46/40.02              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.46/40.02    (12)   ~ (all_6_2 = e3)
% 228.46/40.02    (13)  op(e1, e1) = all_6_2
% 228.46/40.02    (14)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.46/40.02    (15)   ~ (all_53_9 = e0)
% 228.46/40.02    (16)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.46/40.02          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.46/40.02    (17)   ~ (all_53_4 = all_53_12)
% 228.46/40.02    (18)   ~ (all_53_8 = all_53_9)
% 228.46/40.02    (19)  all_42_2 = all_6_2
% 228.46/40.02    (20)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.46/40.02          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.46/40.02    (21)  all_57_6 = e1
% 228.46/40.02    (22)   ~ (all_53_9 = all_6_2)
% 228.46/40.02    (23)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.46/40.02          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.46/40.02    (24)  all_57_3 = e0
% 228.46/40.02    (25)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.46/40.02          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.46/40.02    (26)   ~ (e3 = e2)
% 228.46/40.02    (27)  all_55_1 = all_53_4
% 228.46/40.02    (28)   ~ (e3 = e0)
% 228.46/40.02    (29)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.46/40.02          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.46/40.02    (30)   ~ (all_53_8 = all_6_2)
% 228.46/40.02    (31)  all_55_2 = all_53_8
% 228.46/40.02    (32)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.46/40.02    (33)  all_57_15 = e3
% 228.46/40.02    (34)  op(e3, e3) = e2
% 228.46/40.02    (35)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.46/40.02          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.46/40.02            e1)
% 228.46/40.02    (36)   ~ (all_53_4 = all_53_8)
% 228.46/40.02    (37)  op(e3, e2) = all_53_4
% 228.46/40.02    (38)  op(e1, e1) = e1
% 228.46/40.02    (39)   ~ (e2 = e0)
% 228.46/40.02    (40)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.46/40.02            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.46/40.02            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.46/40.02            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.46/40.02              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.46/40.02            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.46/40.02            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.46/40.02              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.46/40.02              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.46/40.02            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.46/40.02            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.46/40.02            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.46/40.02              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.46/40.02              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.46/40.02            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.46/40.02              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.46/40.02            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.46/40.02            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.46/40.02              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.46/40.02              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.46/40.02            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.46/40.02            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.46/40.02    (41)  all_57_2 = e3
% 228.46/40.02    (42)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.46/40.02          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.46/40.02    (43)   ~ (e1 = e0)
% 228.46/40.02    (44)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.46/40.02            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.46/40.02              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.46/40.02    (45)   ~ (all_53_4 = e0)
% 228.52/40.02    (46)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.52/40.02          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.52/40.02    (47)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.52/40.02          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.52/40.02    (48)  op(e0, e0) = e3
% 228.52/40.02    (49)   ~ (all_53_4 = all_53_6)
% 228.52/40.02    (50)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.52/40.02          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.52/40.02            e2)
% 228.52/40.02    (51)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.52/40.02              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.52/40.02                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.52/40.02                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.52/40.02    (52)  all_55_10 = all_6_2
% 228.52/40.02    (53)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.52/40.02          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.52/40.02    (54)  all_38_2 = all_6_2
% 228.52/40.02    (55)  all_55_3 = all_53_12
% 228.52/40.02    (56)   ~ (all_53_12 = e3)
% 228.52/40.02    (57)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.52/40.02            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.52/40.02              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.52/40.02    (58)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.52/40.02          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.52/40.02    (59)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.52/40.02          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.52/40.02    (60)   ~ (e2 = e1)
% 228.52/40.02    (61)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.52/40.02          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.52/40.02    (62)  op(e2, e1) = all_53_9
% 228.52/40.02    (63)  op(e1, e2) = all_53_6
% 228.52/40.02    (64)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.52/40.02          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.52/40.02    (65)  all_24_2 = all_6_2
% 228.52/40.02    (66)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.52/40.02          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.52/40.02    (67)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.52/40.02          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.52/40.02    (68)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.52/40.02          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.52/40.02    (69)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.52/40.02          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.52/40.02    (70)  op(e3, e1) = all_53_8
% 228.52/40.02    (71)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.52/40.02          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.52/40.02    (72)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.52/40.02          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.52/40.02    (73)  op(e3, e0) = all_53_12
% 228.52/40.02  
% 228.52/40.02  Begin of proof
% 228.52/40.02  | 
% 228.52/40.02  | BETA: splitting (3) gives:
% 228.52/40.02  | 
% 228.52/40.02  | Case 1:
% 228.52/40.02  | | 
% 228.52/40.02  | |   (74)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) =
% 228.52/40.02  | |           e1)
% 228.52/40.02  | | 
% 228.52/40.02  | | BETA: splitting (74) gives:
% 228.52/40.02  | | 
% 228.52/40.02  | | Case 1:
% 228.52/40.02  | | | 
% 228.52/40.02  | | |   (75)  all_57_2 = e1 & op(e2, e3) = e1
% 228.52/40.02  | | | 
% 228.52/40.02  | | | REF_CLOSE: (7), (41), (75) are inconsistent by sub-proof #1928.
% 228.52/40.02  | | | 
% 228.52/40.02  | | Case 2:
% 228.52/40.02  | | | 
% 228.52/40.02  | | |   (76)  all_57_3 = e1 & op(e2, e2) = e1
% 228.52/40.02  | | | 
% 228.52/40.02  | | | REF_CLOSE: (24), (43), (76) are inconsistent by sub-proof #2252.
% 228.52/40.02  | | | 
% 228.52/40.02  | | End of split
% 228.52/40.02  | | 
% 228.52/40.02  | Case 2:
% 228.52/40.02  | | 
% 228.52/40.02  | |   (77)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) =
% 228.52/40.02  | |           e1)
% 228.52/40.02  | | 
% 228.52/40.02  | | BETA: splitting (77) gives:
% 228.52/40.02  | | 
% 228.52/40.02  | | Case 1:
% 228.52/40.02  | | | 
% 228.52/40.02  | | |   (78)  all_57_5 = e1 & op(e2, e1) = e1
% 228.52/40.02  | | | 
% 228.52/40.02  | | | ALPHA: (78) implies:
% 228.52/40.02  | | |   (79)  all_57_5 = e1
% 228.52/40.02  | | | 
% 228.52/40.02  | | | BETA: splitting (46) gives:
% 228.52/40.02  | | | 
% 228.52/40.02  | | | Case 1:
% 228.52/40.02  | | | | 
% 228.52/40.02  | | | |   (80)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1)
% 228.52/40.02  | | | |           = e3)
% 228.52/40.02  | | | | 
% 228.52/40.02  | | | | BETA: splitting (80) gives:
% 228.52/40.02  | | | | 
% 228.52/40.02  | | | | Case 1:
% 228.52/40.02  | | | | | 
% 228.52/40.02  | | | | |   (81)  all_57_4 = e3 & op(e3, e1) = e3
% 228.52/40.02  | | | | | 
% 228.52/40.02  | | | | | ALPHA: (81) implies:
% 228.52/40.02  | | | | |   (82)  all_57_4 = e3
% 228.52/40.02  | | | | | 
% 228.52/40.02  | | | | | BETA: splitting (23) gives:
% 228.52/40.02  | | | | | 
% 228.52/40.02  | | | | | Case 1:
% 228.52/40.02  | | | | | | 
% 228.52/40.02  | | | | | |   (83)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3,
% 228.52/40.02  | | | | | |             e2) = e0)
% 228.52/40.02  | | | | | | 
% 228.52/40.02  | | | | | | BETA: splitting (83) gives:
% 228.52/40.02  | | | | | | 
% 228.52/40.02  | | | | | | Case 1:
% 228.52/40.02  | | | | | | | 
% 228.52/40.02  | | | | | | |   (84)  all_57_0 = e0 & op(e3, e3) = e0
% 228.52/40.02  | | | | | | | 
% 228.52/40.02  | | | | | | | ALPHA: (84) implies:
% 228.52/40.02  | | | | | | |   (85)  op(e3, e3) = e0
% 228.52/40.02  | | | | | | | 
% 228.52/40.02  | | | | | | | REF_CLOSE: (9), (34), (39), (85) are inconsistent by sub-proof
% 228.52/40.02  | | | | | | |            #2403.
% 228.52/40.02  | | | | | | | 
% 228.52/40.02  | | | | | | Case 2:
% 228.52/40.02  | | | | | | | 
% 228.52/40.02  | | | | | | |   (86)  all_57_1 = e0 & op(e3, e2) = e0
% 228.52/40.02  | | | | | | | 
% 228.52/40.02  | | | | | | | ALPHA: (86) implies:
% 228.52/40.02  | | | | | | |   (87)  all_57_1 = e0
% 228.52/40.02  | | | | | | | 
% 228.52/40.02  | | | | | | | BETA: splitting (58) gives:
% 228.52/40.02  | | | | | | | 
% 228.52/40.02  | | | | | | | Case 1:
% 228.52/40.02  | | | | | | | | 
% 228.52/40.02  | | | | | | | |   (88)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 &
% 228.52/40.02  | | | | | | | |           op(e2, e2) = e2)
% 228.52/40.02  | | | | | | | | 
% 228.52/40.02  | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 228.52/40.02  | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18), (19),
% 228.52/40.02  | | | | | | | |            (20), (22), (23), (24), (25), (26), (27), (28), (29),
% 228.52/40.02  | | | | | | | |            (30), (31), (32), (33), (34), (35), (36), (37), (39),
% 228.52/40.02  | | | | | | | |            (40), (42), (43), (44), (45), (46), (47), (48), (49),
% 228.52/40.02  | | | | | | | |            (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 228.52/40.02  | | | | | | | |            (59), (60), (61), (62), (63), (64), (65), (66), (67),
% 228.52/40.02  | | | | | | | |            (68), (69), (70), (71), (72), (73), (88) are
% 228.52/40.02  | | | | | | | |            inconsistent by sub-proof #543.
% 228.52/40.02  | | | | | | | | 
% 228.52/40.02  | | | | | | | Case 2:
% 228.52/40.02  | | | | | | | | 
% 228.52/40.02  | | | | | | | |   (89)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 &
% 228.52/40.02  | | | | | | | |           op(e2, e0) = e2)
% 228.52/40.02  | | | | | | | | 
% 228.52/40.02  | | | | | | | | BETA: splitting (89) gives:
% 228.52/40.02  | | | | | | | | 
% 228.52/40.02  | | | | | | | | Case 1:
% 228.52/40.02  | | | | | | | | | 
% 228.52/40.02  | | | | | | | | |   (90)  all_57_5 = e2 & op(e2, e1) = e2
% 228.52/40.02  | | | | | | | | | 
% 228.52/40.02  | | | | | | | | | ALPHA: (90) implies:
% 228.52/40.02  | | | | | | | | |   (91)  all_57_5 = e2
% 228.52/40.02  | | | | | | | | | 
% 228.52/40.02  | | | | | | | | | REF_CLOSE: (60), (79), (91) are inconsistent by sub-proof
% 228.52/40.02  | | | | | | | | |            #1885.
% 228.52/40.02  | | | | | | | | | 
% 228.52/40.02  | | | | | | | | Case 2:
% 228.52/40.02  | | | | | | | | | 
% 228.52/40.02  | | | | | | | | |   (92)  all_57_10 = e2 & op(e2, e0) = e2
% 228.52/40.02  | | | | | | | | | 
% 228.52/40.02  | | | | | | | | | ALPHA: (92) implies:
% 228.52/40.02  | | | | | | | | |   (93)  all_57_10 = e2
% 228.52/40.02  | | | | | | | | | 
% 228.52/40.02  | | | | | | | | | REF_CLOSE: (3), (4), (6), (7), (9), (10), (12), (13), (21),
% 228.52/40.02  | | | | | | | | |            (24), (26), (28), (33), (39), (41), (42), (43),
% 228.52/40.02  | | | | | | | | |            (46), (47), (50), (51), (53), (56), (58), (60),
% 228.52/40.02  | | | | | | | | |            (61), (64), (67), (68), (71), (73), (87), (93) are
% 228.52/40.02  | | | | | | | | |            inconsistent by sub-proof #537.
% 228.52/40.02  | | | | | | | | | 
% 228.52/40.02  | | | | | | | | End of split
% 228.52/40.02  | | | | | | | | 
% 228.52/40.02  | | | | | | | End of split
% 228.52/40.02  | | | | | | | 
% 228.52/40.02  | | | | | | End of split
% 228.52/40.02  | | | | | | 
% 228.52/40.02  | | | | | Case 2:
% 228.52/40.02  | | | | | | 
% 228.52/40.02  | | | | | |   (94)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3,
% 228.52/40.02  | | | | | |             e0) = e0)
% 228.52/40.02  | | | | | | 
% 228.52/40.02  | | | | | | BETA: splitting (94) gives:
% 228.52/40.02  | | | | | | 
% 228.52/40.02  | | | | | | Case 1:
% 228.52/40.02  | | | | | | | 
% 228.52/40.02  | | | | | | |   (95)  all_57_4 = e0 & op(e3, e1) = e0
% 228.52/40.02  | | | | | | | 
% 228.52/40.02  | | | | | | | ALPHA: (95) implies:
% 228.52/40.02  | | | | | | |   (96)  all_57_4 = e0
% 228.52/40.02  | | | | | | | 
% 228.52/40.02  | | | | | | | REF_CLOSE: (3), (7), (24), (26), (28), (39), (41), (43), (53),
% 228.52/40.02  | | | | | | |            (58), (60), (82), (96) are inconsistent by sub-proof
% 228.52/40.02  | | | | | | |            #1292.
% 228.52/40.02  | | | | | | | 
% 228.52/40.02  | | | | | | Case 2:
% 228.52/40.02  | | | | | | | 
% 228.52/40.02  | | | | | | |   (97)  all_57_9 = e0 & op(e3, e0) = e0
% 228.52/40.02  | | | | | | | 
% 228.52/40.02  | | | | | | | ALPHA: (97) implies:
% 228.52/40.02  | | | | | | |   (98)  all_57_9 = e0
% 228.52/40.02  | | | | | | | 
% 228.52/40.02  | | | | | | | BETA: splitting (58) gives:
% 228.52/40.02  | | | | | | | 
% 228.52/40.02  | | | | | | | Case 1:
% 228.52/40.02  | | | | | | | | 
% 228.52/40.02  | | | | | | | |   (99)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 &
% 228.52/40.02  | | | | | | | |           op(e2, e2) = e2)
% 228.52/40.02  | | | | | | | | 
% 228.52/40.02  | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 228.52/40.02  | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18), (19),
% 228.52/40.02  | | | | | | | |            (20), (22), (23), (24), (25), (26), (27), (28), (29),
% 228.52/40.02  | | | | | | | |            (30), (31), (32), (33), (34), (35), (36), (37), (39),
% 228.52/40.02  | | | | | | | |            (40), (42), (43), (44), (45), (46), (47), (48), (49),
% 228.52/40.02  | | | | | | | |            (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 228.52/40.02  | | | | | | | |            (59), (60), (61), (62), (63), (64), (65), (66), (67),
% 228.52/40.02  | | | | | | | |            (68), (69), (70), (71), (72), (73), (99) are
% 228.52/40.02  | | | | | | | |            inconsistent by sub-proof #543.
% 228.52/40.02  | | | | | | | | 
% 228.52/40.02  | | | | | | | Case 2:
% 228.52/40.02  | | | | | | | | 
% 228.52/40.02  | | | | | | | |   (100)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 &
% 228.52/40.02  | | | | | | | |            op(e2, e0) = e2)
% 228.52/40.02  | | | | | | | | 
% 228.52/40.02  | | | | | | | | BETA: splitting (100) gives:
% 228.52/40.02  | | | | | | | | 
% 228.52/40.02  | | | | | | | | Case 1:
% 228.52/40.02  | | | | | | | | | 
% 228.52/40.02  | | | | | | | | |   (101)  all_57_5 = e2 & op(e2, e1) = e2
% 228.52/40.02  | | | | | | | | | 
% 228.52/40.02  | | | | | | | | | ALPHA: (101) implies:
% 228.52/40.02  | | | | | | | | |   (102)  all_57_5 = e2
% 228.52/40.02  | | | | | | | | | 
% 228.52/40.02  | | | | | | | | | REF_CLOSE: (60), (79), (102) are inconsistent by sub-proof
% 228.52/40.02  | | | | | | | | |            #1885.
% 228.52/40.02  | | | | | | | | | 
% 228.52/40.02  | | | | | | | | Case 2:
% 228.52/40.02  | | | | | | | | | 
% 228.52/40.03  | | | | | | | | |   (103)  all_57_10 = e2 & op(e2, e0) = e2
% 228.52/40.03  | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | ALPHA: (103) implies:
% 228.52/40.03  | | | | | | | | |   (104)  all_57_10 = e2
% 228.52/40.03  | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | BETA: splitting (10) gives:
% 228.52/40.03  | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | Case 1:
% 228.52/40.03  | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | |   (105)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 228.52/40.03  | | | | | | | | | |            & op(e1, e2) = e3)
% 228.52/40.03  | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | BETA: splitting (105) gives:
% 228.52/40.03  | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | Case 1:
% 228.52/40.03  | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | |   (106)  all_57_6 = e3 & op(e1, e3) = e3
% 228.52/40.03  | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | REF_CLOSE: (3), (7), (9), (12), (13), (21), (24), (26), (28),
% 228.52/40.03  | | | | | | | | | | |            (33), (35), (39), (41), (43), (46), (50), (51),
% 228.52/40.03  | | | | | | | | | | |            (60), (82), (104), (106) are inconsistent by
% 228.52/40.03  | | | | | | | | | | |            sub-proof #536.
% 228.52/40.03  | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | Case 2:
% 228.52/40.03  | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | |   (107)  all_57_7 = e3 & op(e1, e2) = e3
% 228.52/40.03  | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | ALPHA: (107) implies:
% 228.52/40.03  | | | | | | | | | | |   (108)  all_57_7 = e3
% 228.52/40.03  | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | BETA: splitting (67) gives:
% 228.52/40.03  | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | Case 1:
% 228.52/40.03  | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | |   (109)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 228.52/40.03  | | | | | | | | | | | |            & op(e2, e3) = e0)
% 228.52/40.03  | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | REF_CLOSE: (3), (7), (9), (24), (26), (28), (34), (39), (43),
% 228.52/40.03  | | | | | | | | | | | |            (53), (58), (60), (109) are inconsistent by
% 228.52/40.03  | | | | | | | | | | | |            sub-proof #1654.
% 228.52/40.03  | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | Case 2:
% 228.52/40.03  | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | |   (110)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 228.52/40.03  | | | | | | | | | | | |            e0 & op(e0, e3) = e0)
% 228.52/40.03  | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | BETA: splitting (110) gives:
% 228.52/40.03  | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | Case 1:
% 228.52/40.03  | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | |   (111)  all_57_6 = e0 & op(e1, e3) = e0
% 228.52/40.03  | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | ALPHA: (111) implies:
% 228.52/40.03  | | | | | | | | | | | | |   (112)  all_57_6 = e0
% 228.52/40.03  | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | COMBINE_EQS: (21), (112) imply:
% 228.52/40.03  | | | | | | | | | | | | |   (113)  e1 = e0
% 228.52/40.03  | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | COMBINE_EQS: (79), (113) imply:
% 228.52/40.03  | | | | | | | | | | | | |   (114)  all_57_5 = e0
% 228.52/40.03  | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | REF_CLOSE: (3), (7), (24), (41), (43), (60), (104), (114) are
% 228.52/40.03  | | | | | | | | | | | | |            inconsistent by sub-proof #2359.
% 228.52/40.03  | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | Case 2:
% 228.52/40.03  | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | |   (115)  all_57_12 = e0 & op(e0, e3) = e0
% 228.52/40.03  | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | ALPHA: (115) implies:
% 228.52/40.03  | | | | | | | | | | | | |   (116)  all_57_12 = e0
% 228.52/40.03  | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | BETA: splitting (16) gives:
% 228.52/40.03  | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | Case 1:
% 228.52/40.03  | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | |   (117)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 228.52/40.03  | | | | | | | | | | | | | |            & op(e3, e2) = e1)
% 228.52/40.03  | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | BETA: splitting (117) gives:
% 228.52/40.03  | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | Case 1:
% 228.52/40.03  | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | |   (118)  all_57_0 = e1 & op(e3, e3) = e1
% 228.52/40.03  | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | ALPHA: (118) implies:
% 228.52/40.03  | | | | | | | | | | | | | | |   (119)  op(e3, e3) = e1
% 228.52/40.03  | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | REF_CLOSE: (9), (34), (60), (119) are inconsistent by
% 228.52/40.03  | | | | | | | | | | | | | | |            sub-proof #1950.
% 228.52/40.03  | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | Case 2:
% 228.52/40.03  | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | |   (120)  all_57_1 = e1 & op(e3, e2) = e1
% 228.52/40.03  | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | ALPHA: (120) implies:
% 228.52/40.03  | | | | | | | | | | | | | | |   (121)  all_57_1 = e1
% 228.52/40.03  | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | BETA: splitting (68) gives:
% 228.52/40.03  | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | Case 1:
% 228.52/40.03  | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | |   (122)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 228.52/40.03  | | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 228.52/40.03  | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | BETA: splitting (122) gives:
% 228.52/40.03  | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | Case 1:
% 228.52/40.03  | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | |   (123)  all_57_9 = e1 & op(e3, e0) = e1
% 228.52/40.03  | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | ALPHA: (123) implies:
% 228.52/40.03  | | | | | | | | | | | | | | | | |   (124)  all_57_9 = e1
% 228.52/40.03  | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | COMBINE_EQS: (98), (124) imply:
% 228.52/40.03  | | | | | | | | | | | | | | | | |   (125)  e1 = e0
% 228.52/40.03  | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | COMBINE_EQS: (121), (125) imply:
% 228.52/40.03  | | | | | | | | | | | | | | | | |   (126)  all_57_1 = e0
% 228.52/40.03  | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 228.52/40.03  | | | | | | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 228.52/40.03  | | | | | | | | | | | | | | | | |            (19), (20), (22), (23), (24), (25), (26), (27),
% 228.52/40.03  | | | | | | | | | | | | | | | | |            (28), (29), (30), (31), (32), (33), (34), (35),
% 228.52/40.03  | | | | | | | | | | | | | | | | |            (36), (37), (39), (40), (41), (42), (43), (44),
% 228.52/40.03  | | | | | | | | | | | | | | | | |            (45), (46), (47), (48), (49), (50), (51), (52),
% 228.52/40.03  | | | | | | | | | | | | | | | | |            (53), (54), (55), (56), (57), (58), (59), (60),
% 228.52/40.03  | | | | | | | | | | | | | | | | |            (61), (62), (63), (64), (65), (66), (67), (68),
% 228.52/40.03  | | | | | | | | | | | | | | | | |            (69), (70), (71), (72), (73), (116), (126) are
% 228.52/40.03  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #533.
% 228.52/40.03  | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | Case 2:
% 228.52/40.03  | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | |   (127)  all_57_10 = e1 & op(e2, e0) = e1
% 228.52/40.03  | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | ALPHA: (127) implies:
% 228.52/40.03  | | | | | | | | | | | | | | | | |   (128)  all_57_10 = e1
% 228.52/40.03  | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | REF_CLOSE: (60), (104), (128) are inconsistent by sub-proof
% 228.52/40.03  | | | | | | | | | | | | | | | | |            #2144.
% 228.52/40.03  | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | End of split
% 228.52/40.03  | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | Case 2:
% 228.52/40.03  | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | |   (129)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 228.52/40.03  | | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 228.52/40.03  | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | BETA: splitting (129) gives:
% 228.52/40.03  | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | Case 1:
% 228.52/40.03  | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | |   (130)  all_57_11 = e1 & op(e1, e0) = e1
% 228.52/40.03  | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | ALPHA: (130) implies:
% 228.52/40.03  | | | | | | | | | | | | | | | | |   (131)  all_57_11 = e1
% 228.52/40.03  | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | BETA: splitting (72) gives:
% 228.52/40.03  | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | Case 1:
% 228.52/40.03  | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | |   (132)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 228.52/40.03  | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e2)
% 228.52/40.03  | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | BETA: splitting (132) gives:
% 228.52/40.03  | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | Case 1:
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | |   (133)  all_57_6 = e2 & op(e1, e3) = e2
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | ALPHA: (133) implies:
% 228.52/40.03  | | | | | | | | | | | | | | | | | | |   (134)  all_57_6 = e2
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (9), (16), (20), (23), (24), (26),
% 228.52/40.03  | | | | | | | | | | | | | | | | | | |            (28), (34), (39), (43), (59), (60), (71), (82),
% 228.52/40.03  | | | | | | | | | | | | | | | | | | |            (108), (116), (134) are inconsistent by sub-proof
% 228.52/40.03  | | | | | | | | | | | | | | | | | | |            #730.
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | Case 2:
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | |   (135)  all_57_7 = e2 & op(e1, e2) = e2
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | ALPHA: (135) implies:
% 228.52/40.03  | | | | | | | | | | | | | | | | | | |   (136)  all_57_7 = e2
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 228.52/40.03  | | | | | | | | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 228.52/40.03  | | | | | | | | | | | | | | | | | | |            (19), (20), (22), (23), (24), (25), (26), (27),
% 228.52/40.03  | | | | | | | | | | | | | | | | | | |            (28), (29), (30), (31), (32), (33), (34), (35),
% 228.52/40.03  | | | | | | | | | | | | | | | | | | |            (36), (37), (39), (40), (41), (42), (43), (44),
% 228.52/40.03  | | | | | | | | | | | | | | | | | | |            (45), (46), (47), (48), (49), (50), (51), (52),
% 228.52/40.03  | | | | | | | | | | | | | | | | | | |            (53), (54), (55), (56), (57), (58), (59), (60),
% 228.52/40.03  | | | | | | | | | | | | | | | | | | |            (61), (62), (63), (64), (65), (66), (67), (68),
% 228.52/40.03  | | | | | | | | | | | | | | | | | | |            (69), (70), (71), (72), (73), (108), (136) are
% 228.52/40.03  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #532.
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | End of split
% 228.52/40.03  | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | Case 2:
% 228.52/40.03  | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | |   (137)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 228.52/40.03  | | | | | | | | | | | | | | | | | |            e2 & op(e1, e0) = e2)
% 228.52/40.03  | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | BETA: splitting (137) gives:
% 228.52/40.03  | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | Case 1:
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | |   (138)  all_57_8 = e2 & op(e1, e1) = e2
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | ALPHA: (138) implies:
% 228.52/40.03  | | | | | | | | | | | | | | | | | | |   (139)  all_57_8 = e2
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | BETA: splitting (8) gives:
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | Case 1:
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | |   (140)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e0)
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | BETA: splitting (140) gives:
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | Case 1:
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | |   (141)  all_57_6 = e0 & op(e1, e3) = e0
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | ALPHA: (141) implies:
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | |   (142)  all_57_6 = e0
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (21), (142) imply:
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | |   (143)  e1 = e0
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | SIMP: (143) implies:
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | |   (144)  e1 = e0
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (121), (144) imply:
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | |   (145)  all_57_1 = e0
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | |            (19), (20), (22), (23), (24), (25), (26), (27),
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | |            (28), (29), (30), (31), (32), (33), (34), (35),
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | |            (36), (37), (39), (40), (41), (42), (43), (44),
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | |            (45), (46), (47), (48), (49), (50), (51), (52),
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | |            (53), (54), (55), (56), (57), (58), (59), (60),
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | |            (61), (62), (63), (64), (65), (66), (67), (68),
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | |            (69), (70), (71), (72), (73), (116), (145) are
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #533.
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | Case 2:
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | |   (146)  all_57_7 = e0 & op(e1, e2) = e0
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | ALPHA: (146) implies:
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | |   (147)  all_57_7 = e0
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (10), (12), (13), (21), (26), (28),
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | |            (33), (39), (43), (51), (60), (61), (68), (147)
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1735.
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | End of split
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | Case 2:
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | |   (148)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | BETA: splitting (148) gives:
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | Case 1:
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | |   (149)  all_57_8 = e0 & op(e1, e1) = e0
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | ALPHA: (149) implies:
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | |   (150)  all_57_8 = e0
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (139), (150) are inconsistent by sub-proof
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | |            #1957.
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | Case 2:
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | |   (151)  all_57_11 = e0 & op(e1, e0) = e0
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | ALPHA: (151) implies:
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | |   (152)  all_57_11 = e0
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (131), (152) imply:
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | |   (153)  e1 = e0
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | SIMP: (153) implies:
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | |   (154)  e1 = e0
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (121), (154) imply:
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | |   (155)  all_57_1 = e0
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | |            (19), (20), (22), (23), (24), (25), (26), (27),
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | |            (28), (29), (30), (31), (32), (33), (34), (35),
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | |            (36), (37), (39), (40), (41), (42), (43), (44),
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | |            (45), (46), (47), (48), (49), (50), (51), (52),
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | |            (53), (54), (55), (56), (57), (58), (59), (60),
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | |            (61), (62), (63), (64), (65), (66), (67), (68),
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | |            (69), (70), (71), (72), (73), (116), (155) are
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #533.
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | End of split
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | End of split
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | Case 2:
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | |   (156)  all_57_11 = e2 & op(e1, e0) = e2
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | ALPHA: (156) implies:
% 228.52/40.03  | | | | | | | | | | | | | | | | | | |   (157)  all_57_11 = e2
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | BETA: splitting (10) gives:
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | Case 1:
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | BETA: splitting (105) gives:
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | Case 1:
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | |   (158)  all_57_6 = e3 & op(e1, e3) = e3
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (7), (9), (12), (13), (21), (24), (26), (28),
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | |            (33), (35), (39), (41), (43), (46), (50), (51),
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | |            (60), (82), (104), (158) are inconsistent by
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | |            sub-proof #536.
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | Case 2:
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (68) gives:
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | |   (159)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (159) gives:
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | | |   (160)  all_57_9 = e1 & op(e3, e0) = e1
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (160) implies:
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | | |   (161)  all_57_9 = e1
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (98), (161) imply:
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | | |   (162)  e1 = e0
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (24), (26), (39), (43), (60), (71),
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | | |            (108), (121), (162) are inconsistent by sub-proof
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | | |            #1626.
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | | |   (163)  all_57_10 = e1 & op(e2, e0) = e1
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (60), (104), (163) are inconsistent by sub-proof
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | | |            #2360.
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | | End of split
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (129) gives:
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (60), (130), (157) are inconsistent by sub-proof
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | | |            #1726.
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | | |   (164)  all_57_15 = e1 & op(e0, e0) = e1
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (164) implies:
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | | |   (165)  all_57_15 = e1
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (33), (165) imply:
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | | |   (166)  e3 = e1
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (82), (166) imply:
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | | |   (167)  all_57_4 = e1
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (7), (9), (12), (13), (24), (26), (28), (33),
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | | |            (35), (39), (41), (43), (46), (50), (51), (60),
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | | |            (104), (167) are inconsistent by sub-proof #1755.
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | | End of split
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | End of split
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | End of split
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | Case 2:
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | |   (168)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | |            e3 & op(e1, e0) = e3)
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (12), (13), (26), (33), (39), (43),
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | |            (60), (61), (68), (98), (168) are inconsistent by
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | |            sub-proof #781.
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | End of split
% 228.52/40.03  | | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | End of split
% 228.52/40.03  | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | End of split
% 228.52/40.03  | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | Case 2:
% 228.52/40.03  | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | |   (169)  all_57_15 = e1 & op(e0, e0) = e1
% 228.52/40.03  | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | ALPHA: (169) implies:
% 228.52/40.03  | | | | | | | | | | | | | | | | |   (170)  all_57_15 = e1
% 228.52/40.03  | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | COMBINE_EQS: (33), (170) imply:
% 228.52/40.03  | | | | | | | | | | | | | | | | |   (171)  e3 = e1
% 228.52/40.03  | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | SIMP: (171) implies:
% 228.52/40.03  | | | | | | | | | | | | | | | | |   (172)  e3 = e1
% 228.52/40.03  | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | COMBINE_EQS: (82), (172) imply:
% 228.52/40.03  | | | | | | | | | | | | | | | | |   (173)  all_57_4 = e1
% 228.52/40.03  | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (7), (9), (12), (13), (24), (26), (28), (33),
% 228.52/40.03  | | | | | | | | | | | | | | | | |            (35), (39), (41), (43), (46), (50), (51), (60),
% 228.52/40.03  | | | | | | | | | | | | | | | | |            (104), (173) are inconsistent by sub-proof #1755.
% 228.52/40.03  | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | End of split
% 228.52/40.03  | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | End of split
% 228.52/40.03  | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | End of split
% 228.52/40.03  | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | Case 2:
% 228.52/40.03  | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | |   (174)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 228.52/40.03  | | | | | | | | | | | | | |            & op(e3, e0) = e1)
% 228.52/40.03  | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | BETA: splitting (174) gives:
% 228.52/40.03  | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | Case 1:
% 228.52/40.03  | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | |   (175)  all_57_4 = e1 & op(e3, e1) = e1
% 228.52/40.03  | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | ALPHA: (175) implies:
% 228.52/40.03  | | | | | | | | | | | | | | |   (176)  all_57_4 = e1
% 228.52/40.03  | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | REF_CLOSE: (3), (7), (9), (12), (13), (24), (26), (28), (33),
% 228.52/40.03  | | | | | | | | | | | | | | |            (35), (39), (41), (43), (46), (50), (51), (60),
% 228.52/40.03  | | | | | | | | | | | | | | |            (104), (176) are inconsistent by sub-proof #1755.
% 228.52/40.03  | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | Case 2:
% 228.52/40.03  | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | |   (177)  all_57_9 = e1 & op(e3, e0) = e1
% 228.52/40.03  | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | ALPHA: (177) implies:
% 228.52/40.03  | | | | | | | | | | | | | | |   (178)  all_57_9 = e1
% 228.52/40.03  | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | COMBINE_EQS: (98), (178) imply:
% 228.52/40.03  | | | | | | | | | | | | | | |   (179)  e1 = e0
% 228.52/40.03  | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | SIMP: (179) implies:
% 228.52/40.03  | | | | | | | | | | | | | | |   (180)  e1 = e0
% 228.52/40.03  | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | COMBINE_EQS: (79), (180) imply:
% 228.52/40.03  | | | | | | | | | | | | | | |   (181)  all_57_5 = e0
% 228.52/40.03  | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | REF_CLOSE: (3), (7), (24), (41), (43), (60), (104), (181) are
% 228.52/40.03  | | | | | | | | | | | | | | |            inconsistent by sub-proof #2359.
% 228.52/40.03  | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | End of split
% 228.52/40.03  | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | End of split
% 228.52/40.03  | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | End of split
% 228.52/40.03  | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | End of split
% 228.52/40.03  | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | End of split
% 228.52/40.03  | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | Case 2:
% 228.52/40.03  | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | |   (182)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3
% 228.52/40.03  | | | | | | | | | |            & op(e1, e0) = e3)
% 228.52/40.03  | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | REF_CLOSE: (7), (9), (12), (13), (33), (43), (60), (68),
% 228.52/40.03  | | | | | | | | | |            (98), (104), (182) are inconsistent by sub-proof
% 228.52/40.03  | | | | | | | | | |            #731.
% 228.52/40.03  | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | End of split
% 228.52/40.03  | | | | | | | | | 
% 228.52/40.03  | | | | | | | | End of split
% 228.52/40.03  | | | | | | | | 
% 228.52/40.03  | | | | | | | End of split
% 228.52/40.03  | | | | | | | 
% 228.52/40.03  | | | | | | End of split
% 228.52/40.03  | | | | | | 
% 228.52/40.03  | | | | | End of split
% 228.52/40.03  | | | | | 
% 228.52/40.03  | | | | Case 2:
% 228.52/40.03  | | | | | 
% 228.52/40.03  | | | | |   (183)  all_57_5 = e3 & op(e2, e1) = e3
% 228.52/40.03  | | | | | 
% 228.52/40.03  | | | | | ALPHA: (183) implies:
% 228.52/40.03  | | | | |   (184)  all_57_5 = e3
% 228.52/40.03  | | | | | 
% 228.52/40.03  | | | | | REF_CLOSE: (7), (79), (184) are inconsistent by sub-proof #2382.
% 228.52/40.03  | | | | | 
% 228.52/40.03  | | | | End of split
% 228.52/40.03  | | | | 
% 228.52/40.03  | | | Case 2:
% 228.52/40.03  | | | | 
% 228.52/40.03  | | | |   (185)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0,
% 228.52/40.03  | | | |              e1) = e3)
% 228.52/40.03  | | | | 
% 228.52/40.03  | | | | REF_CLOSE: (7), (9), (12), (13), (26), (28), (33), (35), (39), (43),
% 228.52/40.03  | | | |            (50), (51), (60), (185) are inconsistent by sub-proof #1794.
% 228.52/40.03  | | | | 
% 228.52/40.03  | | | End of split
% 228.52/40.03  | | | 
% 228.52/40.03  | | Case 2:
% 228.52/40.03  | | | 
% 228.52/40.03  | | |   (186)  all_57_10 = e1 & op(e2, e0) = e1
% 228.52/40.03  | | | 
% 228.52/40.03  | | | ALPHA: (186) implies:
% 228.52/40.03  | | |   (187)  all_57_10 = e1
% 228.52/40.03  | | | 
% 228.52/40.03  | | | BETA: splitting (8) gives:
% 228.52/40.03  | | | 
% 228.52/40.03  | | | Case 1:
% 228.52/40.03  | | | | 
% 228.52/40.03  | | | |   (188)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2)
% 228.52/40.03  | | | |            = e0)
% 228.52/40.03  | | | | 
% 228.52/40.03  | | | | REF_CLOSE: (7), (9), (10), (12), (13), (21), (26), (28), (33), (39),
% 228.52/40.03  | | | |            (43), (51), (60), (61), (68), (188) are inconsistent by
% 228.52/40.03  | | | |            sub-proof #755.
% 228.52/40.03  | | | | 
% 228.52/40.03  | | | Case 2:
% 228.52/40.03  | | | | 
% 228.52/40.03  | | | |   (189)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1,
% 228.52/40.03  | | | |              e0) = e0)
% 228.52/40.03  | | | | 
% 228.52/40.03  | | | | BETA: splitting (189) gives:
% 228.52/40.03  | | | | 
% 228.52/40.03  | | | | Case 1:
% 228.52/40.03  | | | | | 
% 228.52/40.03  | | | | |   (190)  all_57_8 = e0 & op(e1, e1) = e0
% 228.52/40.03  | | | | | 
% 228.52/40.03  | | | | | ALPHA: (190) implies:
% 228.52/40.03  | | | | |   (191)  op(e1, e1) = e0
% 228.52/40.03  | | | | | 
% 228.52/40.03  | | | | | BETA: splitting (61) gives:
% 228.52/40.03  | | | | | 
% 228.52/40.03  | | | | | Case 1:
% 228.52/40.03  | | | | | | 
% 228.52/40.03  | | | | | |   (192)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 &
% 228.52/40.03  | | | | | |            op(e2, e0) = e2)
% 228.52/40.03  | | | | | | 
% 228.52/40.03  | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 228.52/40.03  | | | | | |            (12), (13), (14), (15), (16), (17), (18), (19), (20),
% 228.52/40.03  | | | | | |            (22), (23), (24), (25), (26), (27), (28), (29), (30),
% 228.52/40.03  | | | | | |            (31), (32), (33), (34), (35), (36), (37), (39), (40),
% 228.52/40.03  | | | | | |            (41), (42), (43), (44), (45), (46), (47), (48), (49),
% 228.52/40.03  | | | | | |            (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 228.52/40.03  | | | | | |            (59), (60), (61), (62), (63), (64), (65), (66), (67),
% 228.52/40.03  | | | | | |            (68), (69), (70), (71), (72), (73), (187), (192) are
% 228.52/40.03  | | | | | |            inconsistent by sub-proof #526.
% 228.52/40.03  | | | | | | 
% 228.52/40.03  | | | | | Case 2:
% 228.52/40.03  | | | | | | 
% 228.52/40.03  | | | | | |   (193)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 &
% 228.52/40.03  | | | | | |            op(e0, e0) = e2)
% 228.52/40.03  | | | | | | 
% 228.52/40.03  | | | | | | BETA: splitting (193) gives:
% 228.52/40.03  | | | | | | 
% 228.52/40.03  | | | | | | Case 1:
% 228.52/40.03  | | | | | | | 
% 228.52/40.03  | | | | | | |   (194)  all_57_11 = e2 & op(e1, e0) = e2
% 228.52/40.03  | | | | | | | 
% 228.52/40.03  | | | | | | | ALPHA: (194) implies:
% 228.52/40.03  | | | | | | |   (195)  all_57_11 = e2
% 228.52/40.03  | | | | | | | 
% 228.52/40.03  | | | | | | | BETA: splitting (58) gives:
% 228.52/40.03  | | | | | | | 
% 228.52/40.03  | | | | | | | Case 1:
% 228.52/40.03  | | | | | | | | 
% 228.52/40.03  | | | | | | | |   (196)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 &
% 228.52/40.03  | | | | | | | |            op(e2, e2) = e2)
% 228.52/40.03  | | | | | | | | 
% 228.52/40.03  | | | | | | | | BETA: splitting (196) gives:
% 228.52/40.03  | | | | | | | | 
% 228.52/40.03  | | | | | | | | Case 1:
% 228.52/40.03  | | | | | | | | | 
% 228.52/40.03  | | | | | | | | |   (197)  all_57_2 = e2 & op(e2, e3) = e2
% 228.52/40.03  | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | ALPHA: (197) implies:
% 228.52/40.03  | | | | | | | | |   (198)  all_57_2 = e2
% 228.52/40.03  | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 228.52/40.03  | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 228.52/40.03  | | | | | | | | |            (19), (20), (22), (23), (24), (25), (26), (27),
% 228.52/40.03  | | | | | | | | |            (28), (29), (30), (31), (32), (33), (34), (35),
% 228.52/40.03  | | | | | | | | |            (36), (37), (39), (40), (42), (43), (44), (45),
% 228.52/40.03  | | | | | | | | |            (46), (47), (48), (49), (50), (51), (52), (53),
% 228.52/40.03  | | | | | | | | |            (54), (55), (56), (57), (58), (59), (60), (61),
% 228.52/40.03  | | | | | | | | |            (62), (63), (64), (65), (66), (67), (68), (69),
% 228.52/40.03  | | | | | | | | |            (70), (71), (72), (73), (198) are inconsistent by
% 228.52/40.03  | | | | | | | | |            sub-proof #544.
% 228.52/40.03  | | | | | | | | | 
% 228.52/40.03  | | | | | | | | Case 2:
% 228.52/40.03  | | | | | | | | | 
% 228.52/40.03  | | | | | | | | |   (199)  all_57_3 = e2 & op(e2, e2) = e2
% 228.52/40.03  | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | ALPHA: (199) implies:
% 228.52/40.03  | | | | | | | | |   (200)  all_57_3 = e2
% 228.52/40.03  | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | COMBINE_EQS: (24), (200) imply:
% 228.52/40.03  | | | | | | | | |   (201)  e2 = e0
% 228.52/40.03  | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | SIMP: (201) implies:
% 228.52/40.03  | | | | | | | | |   (202)  e2 = e0
% 228.52/40.03  | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | COMBINE_EQS: (195), (202) imply:
% 228.52/40.03  | | | | | | | | |   (203)  all_57_11 = e0
% 228.52/40.03  | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 228.52/40.03  | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 228.52/40.03  | | | | | | | | |            (19), (20), (22), (23), (24), (25), (26), (27),
% 228.52/40.03  | | | | | | | | |            (28), (29), (30), (31), (32), (33), (34), (35),
% 228.52/40.03  | | | | | | | | |            (36), (37), (39), (40), (41), (42), (43), (44),
% 228.52/40.03  | | | | | | | | |            (45), (46), (47), (48), (49), (50), (51), (52),
% 228.52/40.03  | | | | | | | | |            (53), (54), (55), (56), (57), (58), (59), (60),
% 228.52/40.03  | | | | | | | | |            (61), (62), (63), (64), (65), (66), (67), (68),
% 228.52/40.03  | | | | | | | | |            (69), (70), (71), (72), (73), (187), (203) are
% 228.52/40.03  | | | | | | | | |            inconsistent by sub-proof #525.
% 228.52/40.03  | | | | | | | | | 
% 228.52/40.03  | | | | | | | | End of split
% 228.52/40.03  | | | | | | | | 
% 228.52/40.03  | | | | | | | Case 2:
% 228.52/40.03  | | | | | | | | 
% 228.52/40.03  | | | | | | | |   (204)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 &
% 228.52/40.03  | | | | | | | |            op(e2, e0) = e2)
% 228.52/40.03  | | | | | | | | 
% 228.52/40.03  | | | | | | | | BETA: splitting (204) gives:
% 228.52/40.03  | | | | | | | | 
% 228.52/40.03  | | | | | | | | Case 1:
% 228.52/40.03  | | | | | | | | | 
% 228.52/40.03  | | | | | | | | |   (205)  all_57_5 = e2 & op(e2, e1) = e2
% 228.52/40.03  | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | ALPHA: (205) implies:
% 228.52/40.03  | | | | | | | | |   (206)  all_57_5 = e2
% 228.52/40.03  | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | BETA: splitting (46) gives:
% 228.52/40.03  | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | Case 1:
% 228.52/40.03  | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | |   (207)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 228.52/40.03  | | | | | | | | | |            & op(e2, e1) = e3)
% 228.52/40.03  | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | BETA: splitting (207) gives:
% 228.52/40.03  | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | Case 1:
% 228.52/40.03  | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | |   (208)  all_57_4 = e3 & op(e3, e1) = e3
% 228.52/40.03  | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | ALPHA: (208) implies:
% 228.52/40.03  | | | | | | | | | | |   (209)  all_57_4 = e3
% 228.52/40.03  | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | BETA: splitting (67) gives:
% 228.52/40.03  | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | Case 1:
% 228.52/40.03  | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | |   (210)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 228.52/40.03  | | | | | | | | | | | |            & op(e2, e3) = e0)
% 228.52/40.03  | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | REF_CLOSE: (3), (7), (9), (24), (26), (28), (34), (39), (43),
% 228.52/40.03  | | | | | | | | | | | |            (53), (58), (60), (210) are inconsistent by
% 228.52/40.03  | | | | | | | | | | | |            sub-proof #1654.
% 228.52/40.03  | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | Case 2:
% 228.52/40.03  | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | |   (211)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 228.52/40.03  | | | | | | | | | | | |            e0 & op(e0, e3) = e0)
% 228.52/40.03  | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | BETA: splitting (211) gives:
% 228.52/40.03  | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | Case 1:
% 228.52/40.03  | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | |   (212)  all_57_6 = e0 & op(e1, e3) = e0
% 228.52/40.03  | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | REF_CLOSE: (21), (43), (212) are inconsistent by sub-proof
% 228.52/40.03  | | | | | | | | | | | | |            #2347.
% 228.52/40.03  | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | Case 2:
% 228.52/40.03  | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | |   (213)  all_57_12 = e0 & op(e0, e3) = e0
% 228.52/40.03  | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | ALPHA: (213) implies:
% 228.52/40.03  | | | | | | | | | | | | |   (214)  all_57_12 = e0
% 228.52/40.03  | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | BETA: splitting (23) gives:
% 228.52/40.03  | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | Case 1:
% 228.52/40.03  | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | |   (215)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 228.52/40.03  | | | | | | | | | | | | | |            & op(e3, e2) = e0)
% 228.52/40.03  | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 228.52/40.03  | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | Case 1:
% 228.52/40.03  | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | |   (216)  all_57_0 = e0 & op(e3, e3) = e0
% 228.52/40.03  | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | ALPHA: (216) implies:
% 228.52/40.03  | | | | | | | | | | | | | | |   (217)  op(e3, e3) = e0
% 228.52/40.03  | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | REF_CLOSE: (9), (34), (39), (217) are inconsistent by
% 228.52/40.03  | | | | | | | | | | | | | | |            sub-proof #2403.
% 228.52/40.03  | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | Case 2:
% 228.52/40.03  | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | |   (218)  all_57_1 = e0 & op(e3, e2) = e0
% 228.52/40.03  | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | ALPHA: (218) implies:
% 228.52/40.03  | | | | | | | | | | | | | | |   (219)  all_57_1 = e0
% 228.52/40.03  | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 228.52/40.03  | | | | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 228.52/40.03  | | | | | | | | | | | | | | |            (19), (20), (22), (23), (24), (25), (26), (27),
% 228.52/40.03  | | | | | | | | | | | | | | |            (28), (29), (30), (31), (32), (33), (34), (35),
% 228.52/40.03  | | | | | | | | | | | | | | |            (36), (37), (39), (40), (41), (42), (43), (44),
% 228.52/40.03  | | | | | | | | | | | | | | |            (45), (46), (47), (48), (49), (50), (51), (52),
% 228.52/40.03  | | | | | | | | | | | | | | |            (53), (54), (55), (56), (57), (58), (59), (60),
% 228.52/40.03  | | | | | | | | | | | | | | |            (61), (62), (63), (64), (65), (66), (67), (68),
% 228.52/40.03  | | | | | | | | | | | | | | |            (69), (70), (71), (72), (73), (214), (219) are
% 228.52/40.03  | | | | | | | | | | | | | | |            inconsistent by sub-proof #533.
% 228.52/40.03  | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | End of split
% 228.52/40.03  | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | Case 2:
% 228.52/40.03  | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | |   (220)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 228.52/40.03  | | | | | | | | | | | | | |            & op(e3, e0) = e0)
% 228.52/40.03  | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 228.52/40.03  | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | Case 1:
% 228.52/40.03  | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | |   (221)  all_57_4 = e0 & op(e3, e1) = e0
% 228.52/40.03  | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 228.52/40.03  | | | | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 228.52/40.03  | | | | | | | | | | | | | | |            (19), (20), (22), (23), (24), (25), (26), (27),
% 228.52/40.03  | | | | | | | | | | | | | | |            (28), (29), (30), (31), (32), (33), (34), (35),
% 228.52/40.03  | | | | | | | | | | | | | | |            (36), (37), (39), (40), (41), (43), (44), (45),
% 228.52/40.03  | | | | | | | | | | | | | | |            (46), (48), (49), (50), (51), (52), (53), (54),
% 228.52/40.03  | | | | | | | | | | | | | | |            (55), (56), (57), (58), (59), (60), (61), (62),
% 228.52/40.03  | | | | | | | | | | | | | | |            (63), (64), (65), (66), (67), (68), (69), (70),
% 228.52/40.03  | | | | | | | | | | | | | | |            (71), (72), (73), (206), (214), (221) are
% 228.52/40.03  | | | | | | | | | | | | | | |            inconsistent by sub-proof #529.
% 228.52/40.03  | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | Case 2:
% 228.52/40.03  | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | |   (222)  all_57_9 = e0 & op(e3, e0) = e0
% 228.52/40.03  | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | ALPHA: (222) implies:
% 228.52/40.03  | | | | | | | | | | | | | | |   (223)  all_57_9 = e0
% 228.52/40.03  | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | BETA: splitting (16) gives:
% 228.52/40.03  | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | Case 1:
% 228.52/40.03  | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | |   (224)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 228.52/40.03  | | | | | | | | | | | | | | | |            & op(e3, e2) = e1)
% 228.52/40.03  | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 228.52/40.03  | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | Case 1:
% 228.52/40.03  | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | |   (225)  all_57_0 = e1 & op(e3, e3) = e1
% 228.52/40.03  | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | ALPHA: (225) implies:
% 228.52/40.03  | | | | | | | | | | | | | | | | |   (226)  op(e3, e3) = e1
% 228.52/40.03  | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (34), (60), (226) are inconsistent by
% 228.52/40.03  | | | | | | | | | | | | | | | | |            sub-proof #1950.
% 228.52/40.03  | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | Case 2:
% 228.52/40.03  | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | |   (227)  all_57_1 = e1 & op(e3, e2) = e1
% 228.52/40.03  | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | ALPHA: (227) implies:
% 228.52/40.03  | | | | | | | | | | | | | | | | |   (228)  all_57_1 = e1
% 228.52/40.03  | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | BETA: splitting (51) gives:
% 228.52/40.03  | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | Case 1:
% 228.52/40.03  | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | |   (229)  all_57_15 = e0 & op(e0, e0) = e0
% 228.52/40.03  | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | ALPHA: (229) implies:
% 228.52/40.03  | | | | | | | | | | | | | | | | | |   (230)  op(e0, e0) = e0
% 228.52/40.03  | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (28), (48), (230) are inconsistent by
% 228.52/40.03  | | | | | | | | | | | | | | | | | |            sub-proof #2304.
% 228.52/40.03  | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | Case 2:
% 228.52/40.03  | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with e0, e1, e1, e1, simplifying
% 228.52/40.03  | | | | | | | | | | | | | | | | | |              with (38), (191) gives:
% 228.52/40.03  | | | | | | | | | | | | | | | | | |   (231)  e1 = e0
% 228.52/40.03  | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (228), (231) imply:
% 228.52/40.03  | | | | | | | | | | | | | | | | | |   (232)  all_57_1 = e0
% 228.52/40.03  | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 228.52/40.03  | | | | | | | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 228.52/40.03  | | | | | | | | | | | | | | | | | |            (19), (20), (22), (23), (24), (25), (26), (27),
% 228.52/40.03  | | | | | | | | | | | | | | | | | |            (28), (29), (30), (31), (32), (33), (34), (35),
% 228.52/40.03  | | | | | | | | | | | | | | | | | |            (36), (37), (39), (40), (41), (42), (43), (44),
% 228.52/40.03  | | | | | | | | | | | | | | | | | |            (45), (46), (47), (48), (49), (50), (51), (52),
% 228.52/40.03  | | | | | | | | | | | | | | | | | |            (53), (54), (55), (56), (57), (58), (59), (60),
% 228.52/40.03  | | | | | | | | | | | | | | | | | |            (61), (62), (63), (64), (65), (66), (67), (68),
% 228.52/40.03  | | | | | | | | | | | | | | | | | |            (69), (70), (71), (72), (73), (214), (232) are
% 228.52/40.03  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #533.
% 228.52/40.03  | | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | End of split
% 228.52/40.03  | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | End of split
% 228.52/40.03  | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | Case 2:
% 228.52/40.03  | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | |   (233)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 228.52/40.03  | | | | | | | | | | | | | | | |            & op(e3, e0) = e1)
% 228.52/40.03  | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 228.52/40.03  | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | Case 1:
% 228.52/40.03  | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | |   (234)  all_57_4 = e1 & op(e3, e1) = e1
% 228.52/40.03  | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (209), (234) are inconsistent by sub-proof
% 228.52/40.03  | | | | | | | | | | | | | | | | |            #2484.
% 228.52/40.03  | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | Case 2:
% 228.52/40.03  | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | |   (235)  all_57_9 = e1 & op(e3, e0) = e1
% 228.52/40.03  | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (223), (235) are inconsistent by sub-proof
% 228.52/40.03  | | | | | | | | | | | | | | | | |            #2437.
% 228.52/40.03  | | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | | End of split
% 228.52/40.03  | | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | | End of split
% 228.52/40.03  | | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | | End of split
% 228.52/40.03  | | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | | End of split
% 228.52/40.03  | | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | | End of split
% 228.52/40.03  | | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | End of split
% 228.52/40.03  | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | Case 2:
% 228.52/40.03  | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | |   (236)  all_57_5 = e3 & op(e2, e1) = e3
% 228.52/40.03  | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 228.52/40.03  | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 228.52/40.03  | | | | | | | | | | |            (19), (20), (22), (23), (24), (25), (26), (27),
% 228.52/40.03  | | | | | | | | | | |            (28), (29), (30), (31), (32), (33), (34), (35),
% 228.52/40.03  | | | | | | | | | | |            (36), (37), (39), (40), (41), (43), (44), (45),
% 228.52/40.03  | | | | | | | | | | |            (48), (49), (50), (51), (52), (54), (55), (56),
% 228.52/40.03  | | | | | | | | | | |            (57), (58), (59), (60), (61), (62), (63), (64),
% 228.52/40.03  | | | | | | | | | | |            (65), (66), (67), (68), (69), (70), (71), (72),
% 228.52/40.03  | | | | | | | | | | |            (73), (206), (236) are inconsistent by sub-proof
% 228.52/40.03  | | | | | | | | | | |            #531.
% 228.52/40.03  | | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | End of split
% 228.52/40.03  | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | Case 2:
% 228.52/40.03  | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | |   (237)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3
% 228.52/40.03  | | | | | | | | | |            & op(e0, e1) = e3)
% 228.52/40.03  | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | | REF_CLOSE: (7), (9), (12), (13), (26), (28), (33), (35),
% 228.52/40.03  | | | | | | | | | |            (39), (43), (50), (51), (60), (237) are
% 228.52/40.03  | | | | | | | | | |            inconsistent by sub-proof #1794.
% 228.52/40.03  | | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | End of split
% 228.52/40.03  | | | | | | | | | 
% 228.52/40.03  | | | | | | | | Case 2:
% 228.52/40.03  | | | | | | | | | 
% 228.52/40.03  | | | | | | | | |   (238)  all_57_10 = e2 & op(e2, e0) = e2
% 228.52/40.03  | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | ALPHA: (238) implies:
% 228.52/40.03  | | | | | | | | |   (239)  all_57_10 = e2
% 228.52/40.03  | | | | | | | | | 
% 228.52/40.03  | | | | | | | | | REF_CLOSE: (60), (187), (239) are inconsistent by sub-proof
% 228.52/40.03  | | | | | | | | |            #2144.
% 228.52/40.03  | | | | | | | | | 
% 228.52/40.03  | | | | | | | | End of split
% 228.52/40.03  | | | | | | | | 
% 228.52/40.03  | | | | | | | End of split
% 228.52/40.03  | | | | | | | 
% 228.52/40.03  | | | | | | Case 2:
% 228.52/40.03  | | | | | | | 
% 228.52/40.03  | | | | | | |   (240)  all_57_15 = e2 & op(e0, e0) = e2
% 228.52/40.03  | | | | | | | 
% 228.52/40.03  | | | | | | | ALPHA: (240) implies:
% 228.52/40.03  | | | | | | |   (241)  all_57_15 = e2
% 228.52/40.03  | | | | | | | 
% 228.52/40.03  | | | | | | | COMBINE_EQS: (33), (241) imply:
% 228.52/40.03  | | | | | | |   (242)  e3 = e2
% 228.52/40.03  | | | | | | | 
% 228.52/40.04  | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 228.52/40.04  | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18), (19),
% 228.52/40.04  | | | | | | |            (20), (22), (23), (24), (25), (26), (27), (28), (29),
% 228.52/40.04  | | | | | | |            (30), (31), (32), (33), (34), (35), (36), (37), (39),
% 228.52/40.04  | | | | | | |            (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 228.52/40.04  | | | | | | |            (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 228.52/40.04  | | | | | | |            (58), (59), (60), (61), (62), (63), (64), (65), (66),
% 228.52/40.04  | | | | | | |            (67), (68), (69), (70), (71), (72), (73), (242) are
% 228.52/40.04  | | | | | | |            inconsistent by sub-proof #534.
% 228.52/40.04  | | | | | | | 
% 228.52/40.04  | | | | | | End of split
% 228.52/40.04  | | | | | | 
% 228.52/40.04  | | | | | End of split
% 228.52/40.04  | | | | | 
% 228.52/40.04  | | | | Case 2:
% 228.52/40.04  | | | | | 
% 228.52/40.04  | | | | |   (243)  all_57_11 = e0 & op(e1, e0) = e0
% 228.52/40.04  | | | | | 
% 228.52/40.04  | | | | | ALPHA: (243) implies:
% 228.52/40.04  | | | | |   (244)  all_57_11 = e0
% 228.52/40.04  | | | | | 
% 228.52/40.04  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 228.52/40.04  | | | | |            (12), (13), (14), (15), (16), (17), (18), (19), (20), (22),
% 228.52/40.04  | | | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 228.52/40.04  | | | | |            (33), (34), (35), (36), (37), (39), (40), (41), (42), (43),
% 228.52/40.04  | | | | |            (44), (45), (46), (47), (48), (49), (50), (51), (52), (53),
% 228.52/40.04  | | | | |            (54), (55), (56), (57), (58), (59), (60), (61), (62), (63),
% 228.52/40.04  | | | | |            (64), (65), (66), (67), (68), (69), (70), (71), (72), (73),
% 228.52/40.04  | | | | |            (187), (244) are inconsistent by sub-proof #525.
% 228.52/40.04  | | | | | 
% 228.52/40.04  | | | | End of split
% 228.52/40.04  | | | | 
% 228.52/40.04  | | | End of split
% 228.52/40.04  | | | 
% 228.52/40.04  | | End of split
% 228.52/40.04  | | 
% 228.52/40.04  | End of split
% 228.52/40.04  | 
% 228.52/40.04  End of proof
% 228.52/40.04  
% 228.52/40.04  Sub-proof #525 shows that the following formulas are inconsistent:
% 228.52/40.04  ----------------------------------------------------------------
% 228.52/40.04    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.52/40.04    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.52/40.04    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.52/40.04         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.52/40.04    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.52/40.04         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.52/40.04    (5)   ~ (all_53_8 = all_53_12)
% 228.52/40.04    (6)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.52/40.04         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.52/40.04    (7)   ~ (e3 = e1)
% 228.52/40.04    (8)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.52/40.04         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.52/40.04    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.52/40.04           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.52/40.04    (10)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.52/40.04          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.52/40.04    (11)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.52/40.04            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.52/40.04              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.52/40.04    (12)   ~ (all_6_2 = e3)
% 228.52/40.04    (13)  all_57_10 = e1
% 228.52/40.04    (14)  op(e1, e1) = all_6_2
% 228.52/40.04    (15)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.52/40.04    (16)   ~ (all_53_9 = e0)
% 228.52/40.04    (17)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.52/40.04          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.52/40.04    (18)   ~ (all_53_4 = all_53_12)
% 228.52/40.04    (19)   ~ (all_53_8 = all_53_9)
% 228.52/40.04    (20)  all_42_2 = all_6_2
% 228.52/40.04    (21)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.52/40.04          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.52/40.04    (22)   ~ (all_53_9 = all_6_2)
% 228.52/40.04    (23)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.52/40.04          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.52/40.04    (24)  all_57_3 = e0
% 228.52/40.04    (25)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.52/40.04          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.52/40.04    (26)   ~ (e3 = e2)
% 228.52/40.04    (27)  all_55_1 = all_53_4
% 228.52/40.04    (28)   ~ (e3 = e0)
% 228.52/40.04    (29)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.52/40.04          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.52/40.04    (30)   ~ (all_53_8 = all_6_2)
% 228.52/40.04    (31)  all_55_2 = all_53_8
% 228.52/40.04    (32)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.52/40.04    (33)  all_57_15 = e3
% 228.52/40.04    (34)  op(e3, e3) = e2
% 228.52/40.04    (35)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.52/40.04          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.52/40.04            e1)
% 228.52/40.04    (36)  all_57_11 = e0
% 228.52/40.04    (37)   ~ (all_53_4 = all_53_8)
% 228.52/40.04    (38)  op(e3, e2) = all_53_4
% 228.52/40.04    (39)   ~ (e2 = e0)
% 228.52/40.04    (40)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.52/40.04            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.52/40.04            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.52/40.04            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.52/40.04              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.52/40.04            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.52/40.04            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.52/40.04              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.52/40.04              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.52/40.04            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.52/40.04            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.52/40.04            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.52/40.04              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.52/40.04              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.52/40.04            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.52/40.04              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.52/40.04            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.52/40.04            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.52/40.04              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.52/40.04              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.52/40.04            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.52/40.04            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.52/40.04    (41)  all_57_2 = e3
% 228.52/40.04    (42)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.52/40.04          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.52/40.04    (43)   ~ (e1 = e0)
% 228.52/40.04    (44)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.52/40.04            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.52/40.04              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.52/40.04    (45)   ~ (all_53_4 = e0)
% 228.52/40.04    (46)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.52/40.04          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.52/40.04    (47)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.52/40.04          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.52/40.04    (48)  op(e0, e0) = e3
% 228.52/40.04    (49)   ~ (all_53_4 = all_53_6)
% 228.52/40.04    (50)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.52/40.04          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.52/40.04            e2)
% 228.52/40.04    (51)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.52/40.04              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.52/40.04                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.52/40.04                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.52/40.04    (52)  all_55_10 = all_6_2
% 228.52/40.04    (53)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.52/40.04          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.52/40.04    (54)  all_38_2 = all_6_2
% 228.52/40.04    (55)  all_55_3 = all_53_12
% 228.52/40.04    (56)   ~ (all_53_12 = e3)
% 228.52/40.04    (57)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.52/40.04            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.52/40.04              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.52/40.04    (58)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.52/40.04          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.52/40.04    (59)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.52/40.04          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.52/40.04    (60)   ~ (e2 = e1)
% 228.52/40.04    (61)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.52/40.04          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.52/40.04    (62)  op(e2, e1) = all_53_9
% 228.52/40.04    (63)  op(e1, e2) = all_53_6
% 228.52/40.04    (64)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.52/40.04          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.52/40.04    (65)  all_24_2 = all_6_2
% 228.52/40.04    (66)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.52/40.04          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.52/40.04    (67)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.52/40.04          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.52/40.04    (68)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.52/40.04          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.52/40.04    (69)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.52/40.04          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.52/40.04    (70)  op(e3, e1) = all_53_8
% 228.52/40.04    (71)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.52/40.04          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.52/40.04    (72)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.52/40.04          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.52/40.04    (73)  op(e3, e0) = all_53_12
% 228.52/40.04  
% 228.52/40.04  Begin of proof
% 228.52/40.04  | 
% 228.52/40.04  | BETA: splitting (61) gives:
% 228.52/40.04  | 
% 228.52/40.04  | Case 1:
% 228.52/40.04  | | 
% 228.52/40.04  | |   (74)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 228.52/40.04  | |           e2)
% 228.52/40.04  | | 
% 228.52/40.04  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.52/40.04  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 228.52/40.04  | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 228.52/40.04  | |            (35), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 228.52/40.04  | |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 228.52/40.04  | |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 228.52/40.04  | |            (69), (70), (71), (72), (73), (74) are inconsistent by sub-proof
% 228.52/40.04  | |            #526.
% 228.52/40.04  | | 
% 228.52/40.04  | Case 2:
% 228.52/40.04  | | 
% 228.52/40.04  | |   (75)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.52/40.04  | |           e2)
% 228.52/40.04  | | 
% 228.52/40.04  | | BETA: splitting (75) gives:
% 228.52/40.04  | | 
% 228.52/40.04  | | Case 1:
% 228.52/40.04  | | | 
% 228.52/40.04  | | |   (76)  all_57_11 = e2 & op(e1, e0) = e2
% 228.52/40.04  | | | 
% 228.52/40.04  | | | ALPHA: (76) implies:
% 228.52/40.04  | | |   (77)  all_57_11 = e2
% 228.52/40.04  | | | 
% 228.52/40.04  | | | REF_CLOSE: (36), (39), (77) are inconsistent by sub-proof #1949.
% 228.52/40.04  | | | 
% 228.52/40.04  | | Case 2:
% 228.52/40.04  | | | 
% 228.52/40.04  | | |   (78)  all_57_15 = e2 & op(e0, e0) = e2
% 228.52/40.04  | | | 
% 228.52/40.04  | | | ALPHA: (78) implies:
% 228.52/40.04  | | |   (79)  all_57_15 = e2
% 228.52/40.04  | | | 
% 228.52/40.04  | | | COMBINE_EQS: (33), (79) imply:
% 228.52/40.04  | | |   (80)  e3 = e2
% 228.52/40.04  | | | 
% 228.52/40.04  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.52/40.04  | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 228.52/40.04  | | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 228.52/40.04  | | |            (34), (35), (37), (38), (39), (40), (41), (42), (43), (44),
% 228.52/40.04  | | |            (45), (46), (47), (48), (49), (50), (51), (52), (53), (54),
% 228.52/40.04  | | |            (55), (56), (57), (58), (59), (60), (61), (62), (63), (64),
% 228.52/40.04  | | |            (65), (66), (67), (68), (69), (70), (71), (72), (73), (80) are
% 228.52/40.04  | | |            inconsistent by sub-proof #534.
% 228.52/40.04  | | | 
% 228.52/40.04  | | End of split
% 228.52/40.04  | | 
% 228.52/40.04  | End of split
% 228.52/40.04  | 
% 228.52/40.04  End of proof
% 228.52/40.04  
% 228.52/40.04  Sub-proof #526 shows that the following formulas are inconsistent:
% 228.52/40.04  ----------------------------------------------------------------
% 228.52/40.04    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.52/40.04    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.52/40.04    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.52/40.04         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.52/40.04    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.52/40.04         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.52/40.04    (5)   ~ (all_53_8 = all_53_12)
% 228.52/40.04    (6)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.52/40.04         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.52/40.04    (7)   ~ (e3 = e1)
% 228.52/40.04    (8)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.52/40.04         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.52/40.04    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.52/40.04           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.52/40.04    (10)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.52/40.04          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.52/40.04    (11)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.52/40.04            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.52/40.04              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.52/40.04    (12)   ~ (all_6_2 = e3)
% 228.52/40.04    (13)  all_57_10 = e1
% 228.52/40.04    (14)  op(e1, e1) = all_6_2
% 228.52/40.04    (15)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.52/40.04    (16)   ~ (all_53_9 = e0)
% 228.52/40.04    (17)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.52/40.04          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.52/40.04    (18)   ~ (all_53_4 = all_53_12)
% 228.52/40.04    (19)   ~ (all_53_8 = all_53_9)
% 228.52/40.04    (20)  all_42_2 = all_6_2
% 228.52/40.04    (21)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.52/40.04          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.52/40.04    (22)   ~ (all_53_9 = all_6_2)
% 228.52/40.04    (23)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.52/40.04          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.52/40.04    (24)  all_57_3 = e0
% 228.52/40.04    (25)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.52/40.04          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.52/40.04    (26)   ~ (e3 = e2)
% 228.52/40.04    (27)  all_55_1 = all_53_4
% 228.52/40.04    (28)   ~ (e3 = e0)
% 228.52/40.04    (29)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.52/40.04          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.52/40.04    (30)   ~ (all_53_8 = all_6_2)
% 228.52/40.04    (31)  all_55_2 = all_53_8
% 228.52/40.04    (32)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.52/40.04    (33)  all_57_15 = e3
% 228.52/40.04    (34)  op(e3, e3) = e2
% 228.52/40.04    (35)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.52/40.04          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.52/40.04            e1)
% 228.52/40.04    (36)   ~ (all_53_4 = all_53_8)
% 228.52/40.04    (37)  op(e3, e2) = all_53_4
% 228.52/40.04    (38)   ~ (e2 = e0)
% 228.52/40.04    (39)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.52/40.04            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.52/40.04            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.52/40.04            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.52/40.04              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.52/40.04            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.52/40.04            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.52/40.04              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.52/40.04              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.52/40.04            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.52/40.04            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.52/40.04            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.52/40.04              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.52/40.04              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.52/40.04            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.52/40.04              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.52/40.04            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.52/40.04            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.52/40.04              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.52/40.04              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.52/40.04            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.52/40.04            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.52/40.04    (40)  all_57_2 = e3
% 228.52/40.04    (41)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.52/40.04          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.52/40.04    (42)   ~ (e1 = e0)
% 228.52/40.04    (43)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.52/40.04            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.52/40.04              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.52/40.04    (44)   ~ (all_53_4 = e0)
% 228.52/40.04    (45)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.52/40.04          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.52/40.04    (46)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.52/40.04          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.52/40.04    (47)  op(e0, e0) = e3
% 228.52/40.04    (48)   ~ (all_53_4 = all_53_6)
% 228.52/40.04    (49)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.52/40.04          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.52/40.04            e2)
% 228.52/40.04    (50)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.52/40.04              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.52/40.04                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.52/40.04                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.52/40.04    (51)  all_55_10 = all_6_2
% 228.52/40.04    (52)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.52/40.04          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.52/40.04    (53)  all_38_2 = all_6_2
% 228.52/40.04    (54)  all_55_3 = all_53_12
% 228.52/40.04    (55)   ~ (all_53_12 = e3)
% 228.52/40.04    (56)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.52/40.04            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.52/40.04              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.52/40.04    (57)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.52/40.04          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.52/40.04    (58)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.52/40.04          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.52/40.04    (59)   ~ (e2 = e1)
% 228.52/40.04    (60)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.52/40.04          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.52/40.04    (61)  op(e2, e1) = all_53_9
% 228.52/40.04    (62)  op(e1, e2) = all_53_6
% 228.52/40.04    (63)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.52/40.04          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.52/40.04    (64)  all_24_2 = all_6_2
% 228.52/40.04    (65)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.52/40.04          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.52/40.04    (66)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.52/40.04          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.52/40.04    (67)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.52/40.04          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.52/40.04    (68)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.52/40.04          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.52/40.04    (69)  op(e3, e1) = all_53_8
% 228.52/40.04    (70)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.52/40.04    (71)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.52/40.04          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.52/40.04    (72)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.52/40.04          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.52/40.04    (73)  op(e3, e0) = all_53_12
% 228.52/40.04  
% 228.52/40.04  Begin of proof
% 228.52/40.04  | 
% 228.52/40.04  | BETA: splitting (70) gives:
% 228.52/40.04  | 
% 228.52/40.04  | Case 1:
% 228.52/40.04  | | 
% 228.52/40.04  | |   (74)  all_57_9 = e2 & op(e3, e0) = e2
% 228.52/40.04  | | 
% 228.52/40.04  | | ALPHA: (74) implies:
% 228.52/40.04  | |   (75)  all_57_9 = e2
% 228.52/40.04  | | 
% 228.52/40.04  | | BETA: splitting (57) gives:
% 228.52/40.04  | | 
% 228.52/40.04  | | Case 1:
% 228.52/40.04  | | | 
% 228.52/40.04  | | |   (76)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 228.52/40.04  | | |           e2)
% 228.52/40.04  | | | 
% 228.52/40.04  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.52/40.04  | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 228.52/40.04  | | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 228.52/40.04  | | |            (34), (35), (36), (37), (38), (39), (41), (42), (43), (44),
% 228.52/40.04  | | |            (45), (46), (47), (48), (49), (50), (51), (52), (53), (54),
% 228.52/40.04  | | |            (55), (56), (57), (58), (59), (60), (61), (62), (63), (64),
% 228.52/40.04  | | |            (65), (66), (67), (68), (69), (71), (72), (73), (76) are
% 228.52/40.04  | | |            inconsistent by sub-proof #543.
% 228.52/40.04  | | | 
% 228.52/40.04  | | Case 2:
% 228.52/40.04  | | | 
% 228.52/40.04  | | |   (77)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 228.52/40.04  | | |           e2)
% 228.52/40.04  | | | 
% 228.52/40.04  | | | BETA: splitting (77) gives:
% 228.52/40.04  | | | 
% 228.52/40.04  | | | Case 1:
% 228.52/40.04  | | | | 
% 228.52/40.04  | | | |   (78)  all_57_5 = e2 & op(e2, e1) = e2
% 228.52/40.04  | | | | 
% 228.52/40.04  | | | | ALPHA: (78) implies:
% 228.52/40.04  | | | |   (79)  all_57_5 = e2
% 228.52/40.04  | | | | 
% 228.52/40.04  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 228.52/40.04  | | | |            (12), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 228.52/40.04  | | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 228.52/40.04  | | | |            (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 228.52/40.04  | | | |            (43), (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 228.52/40.04  | | | |            (53), (54), (55), (56), (57), (58), (59), (60), (61), (62),
% 228.52/40.04  | | | |            (63), (64), (65), (66), (67), (68), (69), (71), (72), (73),
% 228.52/40.04  | | | |            (75), (79) are inconsistent by sub-proof #527.
% 228.52/40.04  | | | | 
% 228.52/40.04  | | | Case 2:
% 228.52/40.04  | | | | 
% 228.52/40.04  | | | |   (80)  all_57_10 = e2 & op(e2, e0) = e2
% 228.52/40.04  | | | | 
% 228.52/40.04  | | | | REF_CLOSE: (13), (59), (80) are inconsistent by sub-proof #2255.
% 228.52/40.04  | | | | 
% 228.52/40.04  | | | End of split
% 228.52/40.04  | | | 
% 228.52/40.04  | | End of split
% 228.52/40.04  | | 
% 228.52/40.04  | Case 2:
% 228.52/40.04  | | 
% 228.52/40.04  | |   (81)  all_57_10 = e2 & op(e2, e0) = e2
% 228.52/40.04  | | 
% 228.52/40.04  | | ALPHA: (81) implies:
% 228.52/40.04  | |   (82)  all_57_10 = e2
% 228.52/40.04  | | 
% 228.52/40.04  | | REF_CLOSE: (13), (59), (82) are inconsistent by sub-proof #2144.
% 228.52/40.04  | | 
% 228.52/40.04  | End of split
% 228.52/40.04  | 
% 228.52/40.04  End of proof
% 228.52/40.04  
% 228.52/40.04  Sub-proof #527 shows that the following formulas are inconsistent:
% 228.52/40.04  ----------------------------------------------------------------
% 228.52/40.04    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.52/40.04    (2)  all_57_9 = e2
% 228.52/40.04    (3)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.52/40.04    (4)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.52/40.04         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.52/40.04    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.52/40.04         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.52/40.04    (6)   ~ (all_53_8 = all_53_12)
% 228.52/40.04    (7)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.52/40.04         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.52/40.04    (8)   ~ (e3 = e1)
% 228.52/40.04    (9)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.52/40.04         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.52/40.04    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.52/40.04            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.52/40.04    (11)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.52/40.04          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.52/40.04    (12)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.52/40.04            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.52/40.04              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.52/40.04    (13)   ~ (all_6_2 = e3)
% 228.52/40.04    (14)  op(e1, e1) = all_6_2
% 228.52/40.04    (15)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.52/40.04    (16)   ~ (all_53_9 = e0)
% 228.52/40.04    (17)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.52/40.04          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.52/40.04    (18)   ~ (all_53_4 = all_53_12)
% 228.52/40.04    (19)   ~ (all_53_8 = all_53_9)
% 228.52/40.04    (20)  all_42_2 = all_6_2
% 228.52/40.05    (21)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.52/40.05          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.52/40.05    (22)   ~ (all_53_9 = all_6_2)
% 228.52/40.05    (23)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.52/40.05          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.52/40.05    (24)  all_57_3 = e0
% 228.52/40.05    (25)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.52/40.05          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.52/40.05    (26)   ~ (e3 = e2)
% 228.52/40.05    (27)  all_55_1 = all_53_4
% 228.52/40.05    (28)   ~ (e3 = e0)
% 228.52/40.05    (29)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.52/40.05          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.52/40.05    (30)   ~ (all_53_8 = all_6_2)
% 228.52/40.05    (31)  all_55_2 = all_53_8
% 228.52/40.05    (32)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.52/40.05    (33)  all_57_15 = e3
% 228.52/40.05    (34)  op(e3, e3) = e2
% 228.52/40.05    (35)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.52/40.05          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.52/40.05            e1)
% 228.52/40.05    (36)   ~ (all_53_4 = all_53_8)
% 228.52/40.05    (37)  op(e3, e2) = all_53_4
% 228.52/40.05    (38)   ~ (e2 = e0)
% 228.52/40.05    (39)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.52/40.05            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.52/40.05            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.52/40.05            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.52/40.05              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.52/40.05            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.52/40.05            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.52/40.05              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.52/40.05              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.52/40.05            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.52/40.05            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.52/40.05            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.52/40.05              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.52/40.05              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.52/40.05            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.52/40.05              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.52/40.05            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.52/40.05            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.52/40.05              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.52/40.05              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.52/40.05            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.52/40.05            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.52/40.05    (40)  all_57_2 = e3
% 228.52/40.05    (41)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.52/40.05          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.52/40.05    (42)   ~ (e1 = e0)
% 228.52/40.05    (43)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.52/40.05            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.52/40.05              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.52/40.05    (44)  all_57_5 = e2
% 228.52/40.05    (45)   ~ (all_53_4 = e0)
% 228.52/40.05    (46)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.52/40.05          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.52/40.05    (47)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.52/40.05          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.52/40.05    (48)  op(e0, e0) = e3
% 228.52/40.05    (49)   ~ (all_53_4 = all_53_6)
% 228.52/40.05    (50)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.52/40.05          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.52/40.05            e2)
% 228.52/40.05    (51)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.52/40.05              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.52/40.05                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.52/40.05                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.52/40.05    (52)  all_55_10 = all_6_2
% 228.52/40.05    (53)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.52/40.05          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.52/40.05    (54)  all_38_2 = all_6_2
% 228.52/40.05    (55)  all_55_3 = all_53_12
% 228.52/40.05    (56)   ~ (all_53_12 = e3)
% 228.52/40.05    (57)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.52/40.05            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.52/40.05              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.52/40.05    (58)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.52/40.05          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.52/40.05    (59)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.52/40.05          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.52/40.05    (60)   ~ (e2 = e1)
% 228.52/40.05    (61)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.52/40.05          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.52/40.05    (62)  op(e2, e1) = all_53_9
% 228.52/40.05    (63)  op(e1, e2) = all_53_6
% 228.52/40.05    (64)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.52/40.05          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.52/40.05    (65)  all_24_2 = all_6_2
% 228.52/40.05    (66)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.52/40.05          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.52/40.05    (67)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.52/40.05          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.52/40.05    (68)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.52/40.05          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.52/40.05    (69)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.52/40.05          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.52/40.05    (70)  op(e3, e1) = all_53_8
% 228.52/40.05    (71)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.52/40.05          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.52/40.05    (72)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.52/40.05          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.52/40.05    (73)  op(e3, e0) = all_53_12
% 228.52/40.05  
% 228.52/40.05  Begin of proof
% 228.52/40.05  | 
% 228.52/40.05  | BETA: splitting (51) gives:
% 228.52/40.05  | 
% 228.52/40.05  | Case 1:
% 228.52/40.05  | | 
% 228.52/40.05  | |   (74)  all_57_15 = e0 & op(e0, e0) = e0
% 228.52/40.05  | | 
% 228.52/40.05  | | ALPHA: (74) implies:
% 228.52/40.05  | |   (75)  op(e0, e0) = e0
% 228.52/40.05  | | 
% 228.52/40.05  | | REF_CLOSE: (10), (28), (48), (75) are inconsistent by sub-proof #2304.
% 228.52/40.05  | | 
% 228.52/40.05  | Case 2:
% 228.52/40.05  | | 
% 228.52/40.05  | |   (76)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 228.52/40.05  | |             e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0 &
% 228.52/40.05  | |             op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 228.52/40.05  | |           (all_57_14 = e0 & op(e0, e1) = e0))
% 228.52/40.05  | | 
% 228.52/40.05  | | ALPHA: (76) implies:
% 228.52/40.05  | |   (77)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 228.52/40.05  | |           e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.52/40.05  | | 
% 228.52/40.05  | | BETA: splitting (5) gives:
% 228.52/40.05  | | 
% 228.52/40.05  | | Case 1:
% 228.52/40.05  | | | 
% 228.52/40.05  | | |   (78)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) =
% 228.52/40.05  | | |           e1)
% 228.52/40.05  | | | 
% 228.52/40.05  | | | REF_CLOSE: (8), (10), (34), (40), (60), (78) are inconsistent by sub-proof
% 228.52/40.05  | | |            #753.
% 228.52/40.05  | | | 
% 228.52/40.05  | | Case 2:
% 228.52/40.05  | | | 
% 228.52/40.05  | | |   (79)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) =
% 228.52/40.05  | | |           e1)
% 228.52/40.05  | | | 
% 228.52/40.05  | | | BETA: splitting (79) gives:
% 228.52/40.05  | | | 
% 228.52/40.05  | | | Case 1:
% 228.52/40.05  | | | | 
% 228.52/40.05  | | | |   (80)  all_57_6 = e1 & op(e1, e3) = e1
% 228.52/40.05  | | | | 
% 228.52/40.05  | | | | ALPHA: (80) implies:
% 228.52/40.05  | | | |   (81)  all_57_6 = e1
% 228.52/40.05  | | | | 
% 228.52/40.05  | | | | BETA: splitting (67) gives:
% 228.52/40.05  | | | | 
% 228.52/40.05  | | | | Case 1:
% 228.52/40.05  | | | | | 
% 228.52/40.05  | | | | |   (82)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2,
% 228.52/40.05  | | | | |             e3) = e0)
% 228.52/40.05  | | | | | 
% 228.52/40.05  | | | | | REF_CLOSE: (4), (8), (10), (24), (26), (28), (34), (38), (42), (53),
% 228.52/40.05  | | | | |            (58), (60), (82) are inconsistent by sub-proof #1654.
% 228.52/40.05  | | | | | 
% 228.52/40.05  | | | | Case 2:
% 228.52/40.05  | | | | | 
% 228.52/40.05  | | | | |   (83)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0,
% 228.52/40.05  | | | | |             e3) = e0)
% 228.52/40.05  | | | | | 
% 228.52/40.05  | | | | | BETA: splitting (83) gives:
% 228.52/40.05  | | | | | 
% 228.52/40.05  | | | | | Case 1:
% 228.52/40.05  | | | | | | 
% 228.52/40.05  | | | | | |   (84)  all_57_6 = e0 & op(e1, e3) = e0
% 228.52/40.05  | | | | | | 
% 228.52/40.05  | | | | | | REF_CLOSE: (42), (81), (84) are inconsistent by sub-proof #2347.
% 228.52/40.05  | | | | | | 
% 228.52/40.05  | | | | | Case 2:
% 228.52/40.05  | | | | | | 
% 228.52/40.05  | | | | | |   (85)  all_57_12 = e0 & op(e0, e3) = e0
% 228.52/40.05  | | | | | | 
% 228.52/40.05  | | | | | | ALPHA: (85) implies:
% 228.52/40.05  | | | | | |   (86)  all_57_12 = e0
% 228.52/40.05  | | | | | | 
% 228.52/40.05  | | | | | | BETA: splitting (23) gives:
% 228.52/40.05  | | | | | | 
% 228.52/40.05  | | | | | | Case 1:
% 228.52/40.05  | | | | | | | 
% 228.52/40.05  | | | | | | |   (87)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 &
% 228.52/40.05  | | | | | | |           op(e3, e2) = e0)
% 228.52/40.05  | | | | | | | 
% 228.52/40.05  | | | | | | | BETA: splitting (87) gives:
% 228.52/40.05  | | | | | | | 
% 228.52/40.05  | | | | | | | Case 1:
% 228.52/40.05  | | | | | | | | 
% 228.52/40.05  | | | | | | | |   (88)  all_57_0 = e0 & op(e3, e3) = e0
% 228.52/40.05  | | | | | | | | 
% 228.52/40.05  | | | | | | | | ALPHA: (88) implies:
% 228.52/40.05  | | | | | | | |   (89)  op(e3, e3) = e0
% 228.52/40.05  | | | | | | | | 
% 228.52/40.05  | | | | | | | | REF_CLOSE: (10), (34), (38), (89) are inconsistent by sub-proof
% 228.52/40.05  | | | | | | | |            #2403.
% 228.52/40.05  | | | | | | | | 
% 228.52/40.05  | | | | | | | Case 2:
% 228.52/40.05  | | | | | | | | 
% 228.52/40.05  | | | | | | | |   (90)  all_57_1 = e0 & op(e3, e2) = e0
% 228.52/40.05  | | | | | | | | 
% 228.52/40.05  | | | | | | | | ALPHA: (90) implies:
% 228.52/40.05  | | | | | | | |   (91)  all_57_1 = e0
% 228.52/40.05  | | | | | | | | 
% 228.52/40.05  | | | | | | | | BETA: splitting (47) gives:
% 228.52/40.05  | | | | | | | | 
% 228.52/40.05  | | | | | | | | Case 1:
% 228.52/40.05  | | | | | | | | | 
% 228.52/40.05  | | | | | | | | |   (92)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 &
% 228.52/40.05  | | | | | | | | |           op(e2, e2) = e3)
% 228.52/40.05  | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | REF_CLOSE: (4), (8), (24), (26), (28), (38), (40), (42), (53),
% 228.52/40.05  | | | | | | | | |            (58), (60), (91), (92) are inconsistent by
% 228.52/40.05  | | | | | | | | |            sub-proof #542.
% 228.52/40.05  | | | | | | | | | 
% 228.52/40.05  | | | | | | | | Case 2:
% 228.52/40.05  | | | | | | | | | 
% 228.52/40.05  | | | | | | | | |   (93)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 &
% 228.52/40.05  | | | | | | | | |           op(e0, e2) = e3)
% 228.52/40.05  | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | BETA: splitting (93) gives:
% 228.52/40.05  | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | Case 1:
% 228.52/40.05  | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | |   (94)  all_57_7 = e3 & op(e1, e2) = e3
% 228.52/40.05  | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | ALPHA: (94) implies:
% 228.52/40.05  | | | | | | | | | |   (95)  all_57_7 = e3
% 228.52/40.05  | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | REF_CLOSE: (7), (8), (24), (26), (38), (42), (60), (71),
% 228.52/40.05  | | | | | | | | | |            (91), (95) are inconsistent by sub-proof #2098.
% 228.52/40.05  | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | Case 2:
% 228.52/40.05  | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | |   (96)  all_57_13 = e3 & op(e0, e2) = e3
% 228.52/40.05  | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | ALPHA: (96) implies:
% 228.52/40.05  | | | | | | | | | |   (97)  all_57_13 = e3
% 228.52/40.05  | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | BETA: splitting (41) gives:
% 228.52/40.05  | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | Case 1:
% 228.52/40.05  | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | |   (98)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 228.52/40.05  | | | | | | | | | | |           & op(e3, e2) = e3)
% 228.52/40.05  | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (10), (11), (13), (14), (24),
% 228.52/40.05  | | | | | | | | | | |            (26), (28), (33), (38), (40), (42), (51), (53),
% 228.52/40.05  | | | | | | | | | | |            (58), (60), (61), (64), (67), (68), (71), (91),
% 228.52/40.05  | | | | | | | | | | |            (98) are inconsistent by sub-proof #541.
% 228.52/40.05  | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | Case 2:
% 228.52/40.05  | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | |   (99)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 228.52/40.05  | | | | | | | | | | |           & op(e3, e0) = e3)
% 228.52/40.05  | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | BETA: splitting (99) gives:
% 228.52/40.05  | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | Case 1:
% 228.52/40.05  | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | |   (100)  all_57_4 = e3 & op(e3, e1) = e3
% 228.52/40.05  | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | | ALPHA: (100) implies:
% 228.52/40.05  | | | | | | | | | | | |   (101)  all_57_4 = e3
% 228.52/40.05  | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | | BETA: splitting (7) gives:
% 228.52/40.05  | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | | Case 1:
% 228.52/40.05  | | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | | |   (102)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 228.52/40.05  | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 228.52/40.05  | | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | | | BETA: splitting (102) gives:
% 228.52/40.05  | | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | | | Case 1:
% 228.52/40.05  | | | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | | | |   (103)  all_57_1 = e2 & op(e3, e2) = e2
% 228.52/40.05  | | | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | | | | ALPHA: (103) implies:
% 228.52/40.05  | | | | | | | | | | | | | |   (104)  all_57_1 = e2
% 228.52/40.05  | | | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | | | | COMBINE_EQS: (91), (104) imply:
% 228.52/40.05  | | | | | | | | | | | | | |   (105)  e2 = e0
% 228.52/40.05  | | | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | | | | SIMP: (105) implies:
% 228.52/40.05  | | | | | | | | | | | | | |   (106)  e2 = e0
% 228.52/40.05  | | | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | | | | COMBINE_EQS: (2), (106) imply:
% 228.52/40.05  | | | | | | | | | | | | | |   (107)  all_57_9 = e0
% 228.52/40.05  | | | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | | | | REF_CLOSE: (8), (10), (17), (34), (42), (60), (101), (104),
% 228.52/40.05  | | | | | | | | | | | | | |            (107) are inconsistent by sub-proof #1661.
% 228.52/40.05  | | | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | | | Case 2:
% 228.52/40.05  | | | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | | | |   (108)  all_57_3 = e2 & op(e2, e2) = e2
% 228.52/40.05  | | | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | | | | REF_CLOSE: (24), (38), (108) are inconsistent by sub-proof
% 228.52/40.05  | | | | | | | | | | | | | |            #2103.
% 228.52/40.05  | | | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | | | End of split
% 228.52/40.05  | | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | | Case 2:
% 228.52/40.05  | | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | | |   (109)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 228.52/40.05  | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 228.52/40.05  | | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | | | BETA: splitting (109) gives:
% 228.52/40.05  | | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | | | Case 1:
% 228.52/40.05  | | | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | | | |   (110)  all_57_7 = e2 & op(e1, e2) = e2
% 228.52/40.05  | | | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | | | | ALPHA: (110) implies:
% 228.52/40.05  | | | | | | | | | | | | | |   (111)  all_57_7 = e2
% 228.52/40.05  | | | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | | | | BETA: splitting (71) gives:
% 228.52/40.05  | | | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | | | | Case 1:
% 228.52/40.05  | | | | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | | | | |   (112)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 228.52/40.05  | | | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 228.52/40.05  | | | | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | | | | | BETA: splitting (112) gives:
% 228.52/40.05  | | | | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | | | | | Case 1:
% 228.52/40.05  | | | | | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | | | | | |   (113)  all_57_1 = e1 & op(e3, e2) = e1
% 228.52/40.05  | | | | | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | | | | | | ALPHA: (113) implies:
% 228.52/40.05  | | | | | | | | | | | | | | | |   (114)  all_57_1 = e1
% 228.52/40.05  | | | | | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | | | | | | COMBINE_EQS: (91), (114) imply:
% 228.52/40.05  | | | | | | | | | | | | | | | |   (115)  e1 = e0
% 228.52/40.05  | | | | | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | | | | | | SIMP: (115) implies:
% 228.52/40.05  | | | | | | | | | | | | | | | |   (116)  e1 = e0
% 228.52/40.05  | | | | | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | | | | | | COMBINE_EQS: (81), (116) imply:
% 228.52/40.05  | | | | | | | | | | | | | | | |   (117)  all_57_6 = e0
% 228.52/40.05  | | | | | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (10), (11), (13), (14), (24), (26),
% 228.52/40.05  | | | | | | | | | | | | | | | |            (28), (33), (38), (40), (42), (51), (53), (58),
% 228.52/40.05  | | | | | | | | | | | | | | | |            (60), (61), (68), (71), (91), (117) are
% 228.52/40.05  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #826.
% 228.52/40.05  | | | | | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | | | | | Case 2:
% 228.52/40.05  | | | | | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | | | | | |   (118)  all_57_3 = e1 & op(e2, e2) = e1
% 228.52/40.05  | | | | | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | | | | | | ALPHA: (118) implies:
% 228.52/40.05  | | | | | | | | | | | | | | | |   (119)  all_57_3 = e1
% 228.52/40.05  | | | | | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | | | | | | COMBINE_EQS: (24), (119) imply:
% 228.52/40.05  | | | | | | | | | | | | | | | |   (120)  e1 = e0
% 228.52/40.05  | | | | | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | | | | | | SIMP: (120) implies:
% 228.52/40.05  | | | | | | | | | | | | | | | |   (121)  e1 = e0
% 228.52/40.05  | | | | | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | | | | | | COMBINE_EQS: (81), (121) imply:
% 228.52/40.05  | | | | | | | | | | | | | | | |   (122)  all_57_6 = e0
% 228.52/40.05  | | | | | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (10), (11), (13), (14), (24), (26),
% 228.52/40.05  | | | | | | | | | | | | | | | |            (28), (33), (38), (40), (42), (51), (53), (58),
% 228.52/40.05  | | | | | | | | | | | | | | | |            (60), (61), (68), (71), (91), (122) are
% 228.52/40.05  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #826.
% 228.52/40.05  | | | | | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | | | | | End of split
% 228.52/40.05  | | | | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | | | | Case 2:
% 228.52/40.05  | | | | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | | | | |   (123)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 228.52/40.05  | | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 228.52/40.05  | | | | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | | | | | BETA: splitting (123) gives:
% 228.52/40.05  | | | | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | | | | | Case 1:
% 228.52/40.05  | | | | | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | | | | | |   (124)  all_57_7 = e1 & op(e1, e2) = e1
% 228.52/40.05  | | | | | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | | | | | | REF_CLOSE: (60), (111), (124) are inconsistent by sub-proof
% 228.52/40.05  | | | | | | | | | | | | | | | |            #2190.
% 228.52/40.05  | | | | | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | | | | | Case 2:
% 228.52/40.05  | | | | | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | | | | | |   (125)  all_57_13 = e1 & op(e0, e2) = e1
% 228.52/40.05  | | | | | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | | | | | | REF_CLOSE: (8), (97), (125) are inconsistent by sub-proof
% 228.52/40.05  | | | | | | | | | | | | | | | |            #2264.
% 228.52/40.05  | | | | | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | | | | | End of split
% 228.52/40.05  | | | | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | | | | End of split
% 228.52/40.05  | | | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | | | Case 2:
% 228.52/40.05  | | | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | | | |   (126)  all_57_13 = e2 & op(e0, e2) = e2
% 228.52/40.05  | | | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10),
% 228.52/40.05  | | | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 228.52/40.05  | | | | | | | | | | | | | |            (19), (20), (21), (22), (23), (24), (25), (26),
% 228.52/40.05  | | | | | | | | | | | | | |            (27), (28), (29), (30), (31), (32), (33), (34),
% 228.52/40.05  | | | | | | | | | | | | | |            (35), (36), (37), (38), (39), (40), (41), (42),
% 228.52/40.05  | | | | | | | | | | | | | |            (43), (45), (46), (47), (48), (49), (50), (51),
% 228.52/40.05  | | | | | | | | | | | | | |            (52), (53), (54), (55), (56), (57), (58), (59),
% 228.52/40.05  | | | | | | | | | | | | | |            (60), (61), (62), (63), (64), (65), (66), (67),
% 228.52/40.05  | | | | | | | | | | | | | |            (68), (69), (70), (71), (72), (73), (97), (126)
% 228.52/40.05  | | | | | | | | | | | | | |            are inconsistent by sub-proof #535.
% 228.52/40.05  | | | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | | | End of split
% 228.52/40.05  | | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | | End of split
% 228.52/40.05  | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | Case 2:
% 228.52/40.05  | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | |   (127)  all_57_9 = e3 & op(e3, e0) = e3
% 228.52/40.05  | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | | ALPHA: (127) implies:
% 228.52/40.05  | | | | | | | | | | | |   (128)  op(e3, e0) = e3
% 228.52/40.05  | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | | REF_CLOSE: (10), (56), (73), (128) are inconsistent by
% 228.52/40.05  | | | | | | | | | | | |            sub-proof #2458.
% 228.52/40.05  | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | End of split
% 228.52/40.05  | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | End of split
% 228.52/40.05  | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | End of split
% 228.52/40.05  | | | | | | | | | 
% 228.52/40.05  | | | | | | | | End of split
% 228.52/40.05  | | | | | | | | 
% 228.52/40.05  | | | | | | | End of split
% 228.52/40.05  | | | | | | | 
% 228.52/40.05  | | | | | | Case 2:
% 228.52/40.05  | | | | | | | 
% 228.52/40.05  | | | | | | |   (129)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 &
% 228.52/40.05  | | | | | | |            op(e3, e0) = e0)
% 228.52/40.05  | | | | | | | 
% 228.52/40.05  | | | | | | | BETA: splitting (129) gives:
% 228.52/40.05  | | | | | | | 
% 228.52/40.05  | | | | | | | Case 1:
% 228.52/40.05  | | | | | | | | 
% 228.52/40.05  | | | | | | | |   (130)  all_57_4 = e0 & op(e3, e1) = e0
% 228.52/40.05  | | | | | | | | 
% 228.52/40.05  | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 228.52/40.05  | | | | | | | |            (12), (13), (14), (15), (16), (17), (18), (19), (20),
% 228.52/40.05  | | | | | | | |            (21), (22), (23), (24), (25), (26), (27), (28), (29),
% 228.52/40.05  | | | | | | | |            (30), (31), (32), (33), (34), (35), (36), (37), (38),
% 228.52/40.05  | | | | | | | |            (39), (40), (42), (43), (44), (45), (46), (48), (49),
% 228.52/40.05  | | | | | | | |            (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 228.52/40.05  | | | | | | | |            (59), (60), (61), (62), (63), (64), (65), (66), (67),
% 228.52/40.05  | | | | | | | |            (68), (69), (70), (71), (72), (73), (86), (130) are
% 228.52/40.05  | | | | | | | |            inconsistent by sub-proof #529.
% 228.52/40.05  | | | | | | | | 
% 228.52/40.05  | | | | | | | Case 2:
% 228.52/40.05  | | | | | | | | 
% 228.52/40.05  | | | | | | | |   (131)  all_57_9 = e0 & op(e3, e0) = e0
% 228.52/40.05  | | | | | | | | 
% 228.52/40.05  | | | | | | | | ALPHA: (131) implies:
% 228.52/40.05  | | | | | | | |   (132)  all_57_9 = e0
% 228.52/40.05  | | | | | | | | 
% 228.52/40.05  | | | | | | | | REF_CLOSE: (2), (38), (132) are inconsistent by sub-proof #2440.
% 228.52/40.05  | | | | | | | | 
% 228.52/40.05  | | | | | | | End of split
% 228.52/40.05  | | | | | | | 
% 228.52/40.05  | | | | | | End of split
% 228.52/40.05  | | | | | | 
% 228.52/40.05  | | | | | End of split
% 228.52/40.05  | | | | | 
% 228.52/40.05  | | | | End of split
% 228.52/40.05  | | | | 
% 228.52/40.05  | | | Case 2:
% 228.52/40.05  | | | | 
% 228.52/40.05  | | | |   (133)  all_57_12 = e1 & op(e0, e3) = e1
% 228.52/40.05  | | | | 
% 228.52/40.05  | | | | ALPHA: (133) implies:
% 228.52/40.05  | | | |   (134)  all_57_12 = e1
% 228.52/40.05  | | | | 
% 228.52/40.05  | | | | BETA: splitting (67) gives:
% 228.52/40.05  | | | | 
% 228.52/40.05  | | | | Case 1:
% 228.52/40.05  | | | | | 
% 228.52/40.05  | | | | |   (135)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2,
% 228.52/40.05  | | | | |              e3) = e0)
% 228.52/40.05  | | | | | 
% 228.52/40.05  | | | | | REF_CLOSE: (4), (8), (10), (24), (26), (28), (34), (38), (42), (53),
% 228.52/40.05  | | | | |            (58), (60), (135) are inconsistent by sub-proof #1654.
% 228.52/40.05  | | | | | 
% 228.52/40.05  | | | | Case 2:
% 228.52/40.05  | | | | | 
% 228.52/40.05  | | | | |   (136)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0,
% 228.52/40.05  | | | | |              e3) = e0)
% 228.52/40.05  | | | | | 
% 228.52/40.05  | | | | | BETA: splitting (136) gives:
% 228.52/40.05  | | | | | 
% 228.52/40.05  | | | | | Case 1:
% 228.52/40.05  | | | | | | 
% 228.52/40.05  | | | | | |   (137)  all_57_6 = e0 & op(e1, e3) = e0
% 228.52/40.05  | | | | | | 
% 228.52/40.05  | | | | | | ALPHA: (137) implies:
% 228.52/40.05  | | | | | |   (138)  all_57_6 = e0
% 228.52/40.05  | | | | | | 
% 228.52/40.05  | | | | | | BETA: splitting (23) gives:
% 228.52/40.05  | | | | | | 
% 228.52/40.05  | | | | | | Case 1:
% 228.52/40.05  | | | | | | | 
% 228.52/40.05  | | | | | | |   (139)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 &
% 228.52/40.05  | | | | | | |            op(e3, e2) = e0)
% 228.52/40.05  | | | | | | | 
% 228.52/40.05  | | | | | | | BETA: splitting (139) gives:
% 228.52/40.05  | | | | | | | 
% 228.52/40.05  | | | | | | | Case 1:
% 228.52/40.05  | | | | | | | | 
% 228.52/40.05  | | | | | | | |   (140)  all_57_0 = e0 & op(e3, e3) = e0
% 228.52/40.05  | | | | | | | | 
% 228.52/40.05  | | | | | | | | ALPHA: (140) implies:
% 228.52/40.05  | | | | | | | |   (141)  op(e3, e3) = e0
% 228.52/40.05  | | | | | | | | 
% 228.52/40.05  | | | | | | | | REF_CLOSE: (10), (34), (38), (141) are inconsistent by sub-proof
% 228.52/40.05  | | | | | | | |            #2403.
% 228.52/40.05  | | | | | | | | 
% 228.52/40.05  | | | | | | | Case 2:
% 228.52/40.05  | | | | | | | | 
% 228.52/40.05  | | | | | | | |   (142)  all_57_1 = e0 & op(e3, e2) = e0
% 228.52/40.05  | | | | | | | | 
% 228.52/40.05  | | | | | | | | ALPHA: (142) implies:
% 228.52/40.05  | | | | | | | |   (143)  all_57_1 = e0
% 228.52/40.05  | | | | | | | | 
% 228.52/40.05  | | | | | | | | REF_CLOSE: (4), (7), (8), (10), (11), (13), (14), (24), (26),
% 228.52/40.05  | | | | | | | |            (28), (33), (38), (40), (42), (51), (53), (58), (60),
% 228.52/40.05  | | | | | | | |            (61), (68), (71), (138), (143) are inconsistent by
% 228.52/40.05  | | | | | | | |            sub-proof #826.
% 228.52/40.05  | | | | | | | | 
% 228.52/40.05  | | | | | | | End of split
% 228.52/40.05  | | | | | | | 
% 228.52/40.05  | | | | | | Case 2:
% 228.52/40.05  | | | | | | | 
% 228.52/40.05  | | | | | | |   (144)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 &
% 228.52/40.05  | | | | | | |            op(e3, e0) = e0)
% 228.52/40.05  | | | | | | | 
% 228.52/40.05  | | | | | | | BETA: splitting (144) gives:
% 228.52/40.05  | | | | | | | 
% 228.52/40.05  | | | | | | | Case 1:
% 228.52/40.05  | | | | | | | | 
% 228.52/40.05  | | | | | | | |   (145)  all_57_4 = e0 & op(e3, e1) = e0
% 228.52/40.05  | | | | | | | | 
% 228.52/40.05  | | | | | | | | ALPHA: (145) implies:
% 228.52/40.05  | | | | | | | |   (146)  all_57_4 = e0
% 228.52/40.05  | | | | | | | | 
% 228.52/40.05  | | | | | | | | BETA: splitting (41) gives:
% 228.52/40.05  | | | | | | | | 
% 228.52/40.05  | | | | | | | | Case 1:
% 228.52/40.05  | | | | | | | | | 
% 228.52/40.05  | | | | | | | | |   (147)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 &
% 228.52/40.05  | | | | | | | | |            op(e3, e2) = e3)
% 228.52/40.05  | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | BETA: splitting (147) gives:
% 228.52/40.05  | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | Case 1:
% 228.52/40.05  | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | |   (148)  all_57_0 = e3 & op(e3, e3) = e3
% 228.52/40.05  | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | ALPHA: (148) implies:
% 228.52/40.05  | | | | | | | | | |   (149)  op(e3, e3) = e3
% 228.52/40.05  | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10),
% 228.52/40.05  | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 228.52/40.05  | | | | | | | | | |            (19), (20), (21), (22), (23), (24), (25), (26),
% 228.52/40.05  | | | | | | | | | |            (27), (28), (29), (30), (31), (32), (33), (35),
% 228.52/40.05  | | | | | | | | | |            (36), (37), (38), (39), (40), (41), (42), (43),
% 228.52/40.05  | | | | | | | | | |            (45), (46), (48), (49), (50), (51), (52), (54),
% 228.52/40.05  | | | | | | | | | |            (55), (56), (57), (58), (60), (61), (62), (63),
% 228.52/40.05  | | | | | | | | | |            (64), (65), (66), (67), (68), (69), (70), (71),
% 228.52/40.05  | | | | | | | | | |            (72), (73), (149) are inconsistent by sub-proof
% 228.52/40.05  | | | | | | | | | |            #1437.
% 228.52/40.05  | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | Case 2:
% 228.52/40.05  | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | |   (150)  all_57_1 = e3 & op(e3, e2) = e3
% 228.52/40.05  | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | ALPHA: (150) implies:
% 228.52/40.05  | | | | | | | | | |   (151)  all_57_1 = e3
% 228.52/40.05  | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | BETA: splitting (46) gives:
% 228.52/40.05  | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | Case 1:
% 228.52/40.05  | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | |   (152)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 228.52/40.05  | | | | | | | | | | |            & op(e2, e1) = e3)
% 228.52/40.05  | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | BETA: splitting (152) gives:
% 228.52/40.05  | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | Case 1:
% 228.52/40.05  | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | |   (153)  all_57_4 = e3 & op(e3, e1) = e3
% 228.52/40.05  | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | | ALPHA: (153) implies:
% 228.52/40.05  | | | | | | | | | | | |   (154)  all_57_4 = e3
% 228.52/40.05  | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | | COMBINE_EQS: (146), (154) imply:
% 228.52/40.05  | | | | | | | | | | | |   (155)  e3 = e0
% 228.52/40.05  | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | | SIMP: (155) implies:
% 228.52/40.05  | | | | | | | | | | | |   (156)  e3 = e0
% 228.52/40.05  | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | | COMBINE_EQS: (151), (156) imply:
% 228.52/40.05  | | | | | | | | | | | |   (157)  all_57_1 = e0
% 228.52/40.05  | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (10), (11), (13), (14), (24), (26),
% 228.52/40.05  | | | | | | | | | | | |            (28), (33), (38), (40), (42), (51), (53), (58),
% 228.52/40.05  | | | | | | | | | | | |            (60), (61), (68), (71), (138), (157) are
% 228.52/40.05  | | | | | | | | | | | |            inconsistent by sub-proof #826.
% 228.52/40.05  | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | Case 2:
% 228.52/40.05  | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | |   (158)  all_57_5 = e3 & op(e2, e1) = e3
% 228.52/40.05  | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10),
% 228.52/40.05  | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 228.52/40.05  | | | | | | | | | | | |            (19), (20), (21), (22), (23), (24), (25), (26),
% 228.52/40.05  | | | | | | | | | | | |            (27), (28), (29), (30), (31), (32), (33), (34),
% 228.52/40.05  | | | | | | | | | | | |            (35), (36), (37), (38), (39), (40), (42), (43),
% 228.52/40.05  | | | | | | | | | | | |            (44), (45), (48), (49), (50), (51), (52), (54),
% 228.52/40.05  | | | | | | | | | | | |            (55), (56), (57), (58), (59), (60), (61), (62),
% 228.52/40.05  | | | | | | | | | | | |            (63), (64), (65), (66), (67), (68), (69), (70),
% 228.52/40.05  | | | | | | | | | | | |            (71), (72), (73), (158) are inconsistent by
% 228.52/40.05  | | | | | | | | | | | |            sub-proof #531.
% 228.52/40.05  | | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | End of split
% 228.52/40.05  | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | Case 2:
% 228.52/40.05  | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | |   (159)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 228.52/40.05  | | | | | | | | | | |            e3 & op(e0, e1) = e3)
% 228.52/40.05  | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | | REF_CLOSE: (8), (10), (13), (14), (26), (28), (33), (35),
% 228.52/40.05  | | | | | | | | | | |            (38), (42), (50), (60), (77), (159) are
% 228.52/40.05  | | | | | | | | | | |            inconsistent by sub-proof #1044.
% 228.52/40.05  | | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | | End of split
% 228.52/40.05  | | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | End of split
% 228.52/40.05  | | | | | | | | | 
% 228.52/40.05  | | | | | | | | Case 2:
% 228.52/40.05  | | | | | | | | | 
% 228.52/40.05  | | | | | | | | |   (160)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 &
% 228.52/40.05  | | | | | | | | |            op(e3, e0) = e3)
% 228.52/40.05  | | | | | | | | | 
% 228.52/40.05  | | | | | | | | | REF_CLOSE: (4), (8), (10), (24), (26), (28), (38), (40), (42),
% 228.52/40.05  | | | | | | | | |            (53), (56), (58), (60), (73), (146), (160) are
% 228.52/40.05  | | | | | | | | |            inconsistent by sub-proof #528.
% 228.52/40.05  | | | | | | | | | 
% 228.52/40.05  | | | | | | | | End of split
% 228.52/40.05  | | | | | | | | 
% 228.52/40.05  | | | | | | | Case 2:
% 228.52/40.05  | | | | | | | | 
% 228.52/40.05  | | | | | | | |   (161)  all_57_9 = e0 & op(e3, e0) = e0
% 228.52/40.05  | | | | | | | | 
% 228.52/40.05  | | | | | | | | ALPHA: (161) implies:
% 228.52/40.05  | | | | | | | |   (162)  all_57_9 = e0
% 228.52/40.05  | | | | | | | | 
% 228.52/40.05  | | | | | | | | REF_CLOSE: (2), (38), (162) are inconsistent by sub-proof #2440.
% 228.52/40.05  | | | | | | | | 
% 228.52/40.05  | | | | | | | End of split
% 228.52/40.05  | | | | | | | 
% 228.52/40.05  | | | | | | End of split
% 228.52/40.05  | | | | | | 
% 228.52/40.05  | | | | | Case 2:
% 228.52/40.05  | | | | | | 
% 228.52/40.05  | | | | | |   (163)  all_57_12 = e0 & op(e0, e3) = e0
% 228.52/40.05  | | | | | | 
% 228.52/40.05  | | | | | | REF_CLOSE: (42), (134), (163) are inconsistent by sub-proof #1279.
% 228.52/40.05  | | | | | | 
% 228.52/40.05  | | | | | End of split
% 228.52/40.05  | | | | | 
% 228.52/40.05  | | | | End of split
% 228.52/40.05  | | | | 
% 228.52/40.05  | | | End of split
% 228.52/40.05  | | | 
% 228.52/40.05  | | End of split
% 228.52/40.05  | | 
% 228.52/40.05  | End of split
% 228.52/40.05  | 
% 228.52/40.05  End of proof
% 228.52/40.05  
% 228.52/40.05  Sub-proof #528 shows that the following formulas are inconsistent:
% 228.52/40.05  ----------------------------------------------------------------
% 228.52/40.05    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.52/40.05         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.52/40.05    (2)   ~ (e3 = e1)
% 228.52/40.05    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.52/40.05           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.52/40.05    (4)  all_57_4 = e0
% 228.52/40.05    (5)  all_57_3 = e0
% 228.52/40.05    (6)   ~ (e3 = e2)
% 228.52/40.05    (7)   ~ (e3 = e0)
% 228.52/40.05    (8)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.52/40.05    (9)   ~ (e2 = e0)
% 228.52/40.05    (10)  all_57_2 = e3
% 228.52/40.05    (11)   ~ (e1 = e0)
% 228.52/40.05    (12)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.52/40.05          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.52/40.05    (13)   ~ (all_53_12 = e3)
% 228.52/40.05    (14)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.52/40.05          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.52/40.05    (15)   ~ (e2 = e1)
% 228.52/40.05    (16)  op(e3, e0) = all_53_12
% 228.52/40.05  
% 228.52/40.05  Begin of proof
% 228.52/40.05  | 
% 228.52/40.05  | BETA: splitting (8) gives:
% 228.52/40.05  | 
% 228.52/40.05  | Case 1:
% 228.52/40.05  | | 
% 228.52/40.05  | |   (17)  all_57_4 = e3 & op(e3, e1) = e3
% 228.52/40.05  | | 
% 228.52/40.05  | | ALPHA: (17) implies:
% 228.52/40.05  | |   (18)  all_57_4 = e3
% 228.52/40.05  | | 
% 228.52/40.05  | | COMBINE_EQS: (4), (18) imply:
% 228.52/40.05  | |   (19)  e3 = e0
% 228.52/40.05  | | 
% 228.52/40.05  | | REF_CLOSE: (1), (2), (5), (6), (7), (9), (10), (11), (12), (14), (15), (19)
% 228.52/40.05  | |            are inconsistent by sub-proof #1333.
% 228.52/40.05  | | 
% 228.52/40.05  | Case 2:
% 228.52/40.05  | | 
% 228.52/40.05  | |   (20)  all_57_9 = e3 & op(e3, e0) = e3
% 228.52/40.05  | | 
% 228.52/40.05  | | ALPHA: (20) implies:
% 228.52/40.05  | |   (21)  op(e3, e0) = e3
% 228.52/40.05  | | 
% 228.52/40.05  | | REF_CLOSE: (3), (13), (16), (21) are inconsistent by sub-proof #2458.
% 228.52/40.05  | | 
% 228.52/40.05  | End of split
% 228.52/40.05  | 
% 228.52/40.05  End of proof
% 228.52/40.05  
% 228.52/40.05  Sub-proof #529 shows that the following formulas are inconsistent:
% 228.52/40.05  ----------------------------------------------------------------
% 228.52/40.05    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.52/40.05    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.52/40.05    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.52/40.05         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.52/40.05    (4)  all_57_12 = e0
% 228.52/40.05    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.52/40.05         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.52/40.05    (6)   ~ (all_53_8 = all_53_12)
% 228.52/40.05    (7)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.52/40.05         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.52/40.05    (8)   ~ (e3 = e1)
% 228.52/40.05    (9)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.52/40.05         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.52/40.05    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.52/40.05            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.52/40.06    (11)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.52/40.06          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.52/40.06    (12)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.52/40.06            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.52/40.06              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.52/40.06    (13)   ~ (all_6_2 = e3)
% 228.52/40.06    (14)  op(e1, e1) = all_6_2
% 228.52/40.06    (15)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.52/40.06    (16)   ~ (all_53_9 = e0)
% 228.52/40.06    (17)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.52/40.06          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.52/40.06    (18)   ~ (all_53_4 = all_53_12)
% 228.52/40.06    (19)   ~ (all_53_8 = all_53_9)
% 228.52/40.06    (20)  all_42_2 = all_6_2
% 228.52/40.06    (21)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.52/40.06          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.52/40.06    (22)   ~ (all_53_9 = all_6_2)
% 228.52/40.06    (23)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.52/40.06          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.52/40.06    (24)  all_57_3 = e0
% 228.52/40.06    (25)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.52/40.06          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.52/40.06    (26)   ~ (e3 = e2)
% 228.52/40.06    (27)  all_55_1 = all_53_4
% 228.52/40.06    (28)   ~ (e3 = e0)
% 228.52/40.06    (29)  all_57_4 = e0 & op(e3, e1) = e0
% 228.52/40.06    (30)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.52/40.06          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.52/40.06    (31)   ~ (all_53_8 = all_6_2)
% 228.52/40.06    (32)  all_55_2 = all_53_8
% 228.52/40.06    (33)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.52/40.06    (34)  all_57_15 = e3
% 228.52/40.06    (35)  op(e3, e3) = e2
% 228.52/40.06    (36)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.52/40.06          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.52/40.06            e1)
% 228.52/40.06    (37)   ~ (all_53_4 = all_53_8)
% 228.52/40.06    (38)  op(e3, e2) = all_53_4
% 228.52/40.06    (39)   ~ (e2 = e0)
% 228.52/40.06    (40)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.52/40.06            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.52/40.06            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.52/40.06            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.52/40.06              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.52/40.06            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.52/40.06            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.52/40.06              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.52/40.06              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.52/40.06            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.52/40.06            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.52/40.06            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.52/40.06              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.52/40.06              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.52/40.06            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.52/40.06              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.52/40.06            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.52/40.06            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.52/40.06              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.52/40.06              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.52/40.06            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.52/40.06            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.52/40.06    (41)  all_57_2 = e3
% 228.52/40.06    (42)   ~ (e1 = e0)
% 228.52/40.06    (43)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.52/40.06            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.52/40.06              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.52/40.06    (44)  all_57_5 = e2
% 228.52/40.06    (45)   ~ (all_53_4 = e0)
% 228.52/40.06    (46)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.52/40.06          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.52/40.06    (47)  op(e0, e0) = e3
% 228.52/40.06    (48)   ~ (all_53_4 = all_53_6)
% 228.52/40.06    (49)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.52/40.06          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.52/40.06            e2)
% 228.52/40.06    (50)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.52/40.06              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.52/40.06                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.52/40.06                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.52/40.06    (51)  all_55_10 = all_6_2
% 228.52/40.06    (52)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.52/40.06          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.52/40.06    (53)  all_38_2 = all_6_2
% 228.52/40.06    (54)  all_55_3 = all_53_12
% 228.52/40.06    (55)   ~ (all_53_12 = e3)
% 228.52/40.06    (56)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.52/40.06            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.52/40.06              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.52/40.06    (57)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.52/40.06          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.52/40.06    (58)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.52/40.06          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.52/40.06    (59)   ~ (e2 = e1)
% 228.52/40.06    (60)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.52/40.06          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.52/40.06    (61)  op(e2, e1) = all_53_9
% 228.52/40.06    (62)  op(e1, e2) = all_53_6
% 228.52/40.06    (63)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.52/40.06          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.52/40.06    (64)  all_24_2 = all_6_2
% 228.52/40.06    (65)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.52/40.06          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.52/40.06    (66)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.52/40.06          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.52/40.06    (67)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.52/40.06          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.52/40.06    (68)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.52/40.06          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.52/40.06    (69)  op(e3, e1) = all_53_8
% 228.52/40.06    (70)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.52/40.06          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.52/40.06    (71)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.52/40.06          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.52/40.06    (72)  op(e3, e0) = all_53_12
% 228.52/40.06  
% 228.52/40.06  Begin of proof
% 228.52/40.06  | 
% 228.52/40.06  | ALPHA: (29) implies:
% 228.52/40.06  |   (73)  all_57_4 = e0
% 228.52/40.06  | 
% 228.52/40.06  | BETA: splitting (46) gives:
% 228.52/40.06  | 
% 228.52/40.06  | Case 1:
% 228.52/40.06  | | 
% 228.52/40.06  | |   (74)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) =
% 228.52/40.06  | |           e3)
% 228.52/40.06  | | 
% 228.52/40.06  | | BETA: splitting (74) gives:
% 228.52/40.06  | | 
% 228.52/40.06  | | Case 1:
% 228.52/40.06  | | | 
% 228.52/40.06  | | |   (75)  all_57_4 = e3 & op(e3, e1) = e3
% 228.52/40.06  | | | 
% 228.52/40.06  | | | ALPHA: (75) implies:
% 228.52/40.06  | | |   (76)  all_57_4 = e3
% 228.52/40.06  | | | 
% 228.52/40.06  | | | COMBINE_EQS: (73), (76) imply:
% 228.52/40.06  | | |   (77)  e3 = e0
% 228.52/40.06  | | | 
% 228.52/40.06  | | | REF_CLOSE: (3), (8), (24), (26), (28), (39), (41), (42), (52), (57), (59),
% 228.52/40.06  | | |            (77) are inconsistent by sub-proof #1333.
% 228.52/40.06  | | | 
% 228.52/40.06  | | Case 2:
% 228.52/40.06  | | | 
% 228.52/40.06  | | |   (78)  all_57_5 = e3 & op(e2, e1) = e3
% 228.52/40.06  | | | 
% 228.52/40.06  | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 228.52/40.06  | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 228.52/40.06  | | |            (24), (25), (26), (27), (28), (30), (31), (32), (33), (34),
% 228.52/40.06  | | |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44),
% 228.52/40.06  | | |            (45), (47), (48), (49), (50), (51), (53), (54), (55), (56),
% 228.52/40.06  | | |            (57), (58), (59), (60), (61), (62), (63), (64), (65), (66),
% 228.52/40.06  | | |            (67), (68), (69), (70), (71), (72), (78) are inconsistent by
% 228.52/40.06  | | |            sub-proof #531.
% 228.52/40.06  | | | 
% 228.52/40.06  | | End of split
% 228.52/40.06  | | 
% 228.52/40.06  | Case 2:
% 228.52/40.06  | | 
% 228.52/40.06  | |   (79)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) =
% 228.52/40.06  | |           e3)
% 228.52/40.06  | | 
% 228.52/40.06  | | REF_CLOSE: (4), (8), (10), (13), (14), (26), (34), (36), (39), (42), (49),
% 228.52/40.06  | |            (59), (79) are inconsistent by sub-proof #530.
% 228.52/40.06  | | 
% 228.52/40.06  | End of split
% 228.52/40.06  | 
% 228.52/40.06  End of proof
% 228.52/40.06  
% 228.52/40.06  Sub-proof #530 shows that the following formulas are inconsistent:
% 228.52/40.06  ----------------------------------------------------------------
% 228.52/40.06    (1)  all_57_12 = e0
% 228.52/40.06    (2)   ~ (e3 = e1)
% 228.52/40.06    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.52/40.06           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.52/40.06    (4)   ~ (all_6_2 = e3)
% 228.52/40.06    (5)  op(e1, e1) = all_6_2
% 228.52/40.06    (6)   ~ (e3 = e2)
% 228.52/40.06    (7)  all_57_15 = e3
% 228.52/40.06    (8)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 228.52/40.06         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.52/40.06    (9)   ~ (e2 = e0)
% 228.52/40.06    (10)   ~ (e1 = e0)
% 228.52/40.06    (11)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.52/40.06          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.52/40.06            e2)
% 228.52/40.06    (12)   ~ (e2 = e1)
% 228.52/40.06    (13)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.52/40.06  
% 228.52/40.06  Begin of proof
% 228.52/40.06  | 
% 228.52/40.06  | BETA: splitting (13) gives:
% 228.52/40.06  | 
% 228.52/40.06  | Case 1:
% 228.52/40.06  | | 
% 228.52/40.06  | |   (14)  all_57_8 = e3 & op(e1, e1) = e3
% 228.52/40.06  | | 
% 228.52/40.06  | | ALPHA: (14) implies:
% 228.52/40.06  | |   (15)  op(e1, e1) = e3
% 228.52/40.06  | | 
% 228.52/40.06  | | REF_CLOSE: (3), (4), (5), (15) are inconsistent by sub-proof #2468.
% 228.52/40.06  | | 
% 228.52/40.06  | Case 2:
% 228.52/40.06  | | 
% 228.52/40.06  | |   (16)  all_57_14 = e3 & op(e0, e1) = e3
% 228.52/40.06  | | 
% 228.52/40.06  | | ALPHA: (16) implies:
% 228.52/40.06  | |   (17)  all_57_14 = e3
% 228.52/40.06  | | 
% 228.52/40.06  | | REF_CLOSE: (1), (2), (6), (7), (8), (9), (10), (11), (12), (17) are
% 228.52/40.06  | |            inconsistent by sub-proof #2322.
% 228.52/40.06  | | 
% 228.52/40.06  | End of split
% 228.52/40.06  | 
% 228.52/40.06  End of proof
% 228.52/40.06  
% 228.52/40.06  Sub-proof #531 shows that the following formulas are inconsistent:
% 228.52/40.06  ----------------------------------------------------------------
% 228.52/40.06    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.52/40.06    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.52/40.06    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.52/40.06         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.52/40.06    (4)  all_57_5 = e3 & op(e2, e1) = e3
% 228.52/40.06    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.52/40.06         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.52/40.06    (6)   ~ (all_53_8 = all_53_12)
% 228.52/40.06    (7)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.52/40.06         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.52/40.06    (8)   ~ (e3 = e1)
% 228.52/40.06    (9)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.52/40.06         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.52/40.06    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.52/40.06            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.52/40.06    (11)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.52/40.06          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.52/40.06    (12)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.52/40.06            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.52/40.06              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.52/40.06    (13)   ~ (all_6_2 = e3)
% 228.52/40.06    (14)  op(e1, e1) = all_6_2
% 228.52/40.06    (15)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.52/40.06    (16)   ~ (all_53_9 = e0)
% 228.52/40.06    (17)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.52/40.06          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.52/40.06    (18)   ~ (all_53_4 = all_53_12)
% 228.52/40.06    (19)   ~ (all_53_8 = all_53_9)
% 228.52/40.06    (20)  all_42_2 = all_6_2
% 228.52/40.06    (21)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.52/40.06          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.52/40.06    (22)   ~ (all_53_9 = all_6_2)
% 228.52/40.06    (23)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.52/40.06          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.52/40.06    (24)  all_57_3 = e0
% 228.52/40.06    (25)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.52/40.06          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.52/40.06    (26)   ~ (e3 = e2)
% 228.52/40.06    (27)  all_55_1 = all_53_4
% 228.52/40.06    (28)   ~ (e3 = e0)
% 228.52/40.06    (29)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.52/40.06          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.52/40.06    (30)   ~ (all_53_8 = all_6_2)
% 228.52/40.06    (31)  all_55_2 = all_53_8
% 228.52/40.06    (32)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.52/40.06    (33)  all_57_15 = e3
% 228.52/40.06    (34)  op(e3, e3) = e2
% 228.52/40.06    (35)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.52/40.06          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.52/40.06            e1)
% 228.52/40.06    (36)   ~ (all_53_4 = all_53_8)
% 228.52/40.06    (37)  op(e3, e2) = all_53_4
% 228.52/40.06    (38)   ~ (e2 = e0)
% 228.52/40.06    (39)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.52/40.06            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.52/40.06            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.52/40.06            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.52/40.06              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.52/40.06            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.52/40.06            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.52/40.06              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.52/40.06              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.52/40.06            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.52/40.06            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.52/40.06            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.52/40.06              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.52/40.06              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.52/40.06            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.52/40.06              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.52/40.06            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.52/40.06            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.52/40.06              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.52/40.06              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.52/40.06            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.52/40.06            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.52/40.06    (40)  all_57_2 = e3
% 228.52/40.06    (41)   ~ (e1 = e0)
% 228.52/40.06    (42)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.52/40.06            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.52/40.06              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.52/40.06    (43)  all_57_5 = e2
% 228.52/40.06    (44)   ~ (all_53_4 = e0)
% 228.52/40.06    (45)  op(e0, e0) = e3
% 228.52/40.06    (46)   ~ (all_53_4 = all_53_6)
% 228.52/40.06    (47)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.52/40.06          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.52/40.06            e2)
% 228.52/40.06    (48)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.52/40.06              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.52/40.06                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.52/40.06                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.52/40.06    (49)  all_55_10 = all_6_2
% 228.52/40.06    (50)  all_38_2 = all_6_2
% 228.52/40.06    (51)  all_55_3 = all_53_12
% 228.52/40.06    (52)   ~ (all_53_12 = e3)
% 228.52/40.06    (53)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.52/40.06            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.52/40.06              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.57/40.06    (54)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.06          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.57/40.06    (55)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.57/40.06          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.57/40.06    (56)   ~ (e2 = e1)
% 228.57/40.06    (57)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.57/40.06          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.57/40.06    (58)  op(e2, e1) = all_53_9
% 228.57/40.06    (59)  op(e1, e2) = all_53_6
% 228.57/40.06    (60)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.57/40.06          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.57/40.06    (61)  all_24_2 = all_6_2
% 228.57/40.06    (62)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.57/40.06          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.57/40.06    (63)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.57/40.06          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.57/40.06    (64)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.57/40.06          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.57/40.06    (65)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.57/40.06          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.57/40.06    (66)  op(e3, e1) = all_53_8
% 228.57/40.06    (67)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.06          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.57/40.06    (68)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.57/40.06          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.57/40.06    (69)  op(e3, e0) = all_53_12
% 228.57/40.06  
% 228.57/40.06  Begin of proof
% 228.57/40.06  | 
% 228.57/40.06  | ALPHA: (4) implies:
% 228.57/40.06  |   (70)  all_57_5 = e3
% 228.57/40.06  |   (71)  op(e2, e1) = e3
% 228.57/40.06  | 
% 228.57/40.06  | COMBINE_EQS: (43), (70) imply:
% 228.57/40.06  |   (72)  e3 = e2
% 228.57/40.06  | 
% 228.57/40.06  | SIMP: (72) implies:
% 228.57/40.06  |   (73)  e3 = e2
% 228.57/40.06  | 
% 228.57/40.06  | COMBINE_EQS: (40), (73) imply:
% 228.57/40.06  |   (74)  all_57_2 = e2
% 228.57/40.06  | 
% 228.57/40.06  | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 228.57/40.06  |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 228.57/40.06  |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 228.57/40.06  |            (36), (37), (38), (39), (41), (42), (44), (45), (46), (47), (48),
% 228.57/40.06  |            (49), (50), (51), (52), (53), (54), (55), (56), (57), (58), (59),
% 228.57/40.06  |            (60), (61), (62), (63), (64), (65), (66), (67), (68), (69), (70),
% 228.57/40.06  |            (71), (74) are inconsistent by sub-proof #554.
% 228.57/40.06  | 
% 228.57/40.06  End of proof
% 228.57/40.06  
% 228.57/40.06  Sub-proof #532 shows that the following formulas are inconsistent:
% 228.57/40.06  ----------------------------------------------------------------
% 228.57/40.06    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.57/40.06    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.57/40.06    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.06         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.57/40.06    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.57/40.06         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.57/40.06    (5)   ~ (all_53_8 = all_53_12)
% 228.57/40.06    (6)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.06         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.06    (7)   ~ (e3 = e1)
% 228.57/40.06    (8)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.57/40.06         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.57/40.06    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.57/40.06           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.57/40.06    (10)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.57/40.06          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.57/40.06    (11)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.57/40.06            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.57/40.06              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.57/40.06    (12)   ~ (all_6_2 = e3)
% 228.57/40.06    (13)  op(e1, e1) = all_6_2
% 228.57/40.06    (14)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.57/40.06    (15)   ~ (all_53_9 = e0)
% 228.57/40.06    (16)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.57/40.06          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.57/40.06    (17)  all_57_7 = e2
% 228.57/40.06    (18)   ~ (all_53_4 = all_53_12)
% 228.57/40.06    (19)   ~ (all_53_8 = all_53_9)
% 228.57/40.06    (20)  all_42_2 = all_6_2
% 228.57/40.06    (21)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.57/40.06          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.57/40.06    (22)   ~ (all_53_9 = all_6_2)
% 228.57/40.06    (23)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.57/40.06          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.06    (24)  all_57_3 = e0
% 228.57/40.06    (25)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.57/40.06          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.57/40.06    (26)   ~ (e3 = e2)
% 228.57/40.06    (27)  all_55_1 = all_53_4
% 228.57/40.06    (28)   ~ (e3 = e0)
% 228.57/40.06    (29)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.57/40.06          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.57/40.06    (30)   ~ (all_53_8 = all_6_2)
% 228.57/40.06    (31)  all_55_2 = all_53_8
% 228.57/40.06    (32)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.57/40.06    (33)  all_57_15 = e3
% 228.57/40.06    (34)  op(e3, e3) = e2
% 228.57/40.06    (35)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.57/40.06          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.57/40.06            e1)
% 228.57/40.06    (36)   ~ (all_53_4 = all_53_8)
% 228.57/40.06    (37)  op(e3, e2) = all_53_4
% 228.57/40.06    (38)   ~ (e2 = e0)
% 228.57/40.06    (39)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.57/40.06            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.57/40.06            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.57/40.06            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.57/40.06              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.57/40.06            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.57/40.06            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.57/40.06              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.57/40.06              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.57/40.06            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.57/40.06            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.57/40.06            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.57/40.06              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.57/40.06              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.57/40.06            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.57/40.06              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.57/40.06            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.57/40.06            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.57/40.06              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.57/40.06              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.57/40.06            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.57/40.06            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.57/40.06    (40)  all_57_2 = e3
% 228.57/40.07    (41)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.57/40.07          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.57/40.07    (42)   ~ (e1 = e0)
% 228.57/40.07    (43)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.57/40.07            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.57/40.07              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.57/40.07    (44)   ~ (all_53_4 = e0)
% 228.57/40.07    (45)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.57/40.07          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.57/40.07    (46)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.57/40.07          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.57/40.07    (47)  op(e0, e0) = e3
% 228.57/40.07    (48)   ~ (all_53_4 = all_53_6)
% 228.57/40.07    (49)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.07          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.57/40.07            e2)
% 228.57/40.07    (50)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.07              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.57/40.07                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.57/40.07                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.57/40.07    (51)  all_55_10 = all_6_2
% 228.57/40.07    (52)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.57/40.07          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.57/40.07    (53)  all_38_2 = all_6_2
% 228.57/40.07    (54)  all_55_3 = all_53_12
% 228.57/40.07    (55)   ~ (all_53_12 = e3)
% 228.57/40.07    (56)  all_57_7 = e3
% 228.57/40.07    (57)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.57/40.07            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.57/40.07              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.57/40.07    (58)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.07          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.57/40.07    (59)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.57/40.07          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.57/40.07    (60)   ~ (e2 = e1)
% 228.57/40.07    (61)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.57/40.07          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.57/40.07    (62)  op(e2, e1) = all_53_9
% 228.57/40.07    (63)  op(e1, e2) = all_53_6
% 228.57/40.07    (64)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.57/40.07          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.57/40.07    (65)  all_24_2 = all_6_2
% 228.57/40.07    (66)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.57/40.07          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.57/40.07    (67)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.57/40.07          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.57/40.07    (68)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.57/40.07          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.57/40.07    (69)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.57/40.07          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.57/40.07    (70)  op(e3, e1) = all_53_8
% 228.57/40.07    (71)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.07          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.57/40.07    (72)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.57/40.07          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.57/40.07    (73)  op(e3, e0) = all_53_12
% 228.57/40.07  
% 228.57/40.07  Begin of proof
% 228.57/40.07  | 
% 228.57/40.07  | COMBINE_EQS: (17), (56) imply:
% 228.57/40.07  |   (74)  e3 = e2
% 228.57/40.07  | 
% 228.57/40.07  | COMBINE_EQS: (40), (74) imply:
% 228.57/40.07  |   (75)  all_57_2 = e2
% 228.57/40.07  | 
% 228.57/40.07  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.57/40.07  |            (13), (14), (15), (16), (18), (19), (20), (21), (22), (23), (24),
% 228.57/40.07  |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 228.57/40.07  |            (36), (37), (38), (39), (41), (42), (43), (44), (45), (46), (47),
% 228.57/40.07  |            (48), (49), (50), (51), (52), (53), (54), (55), (57), (58), (59),
% 228.57/40.07  |            (60), (61), (62), (63), (64), (65), (66), (67), (68), (69), (70),
% 228.57/40.07  |            (71), (72), (73), (75) are inconsistent by sub-proof #544.
% 228.57/40.07  | 
% 228.57/40.07  End of proof
% 228.57/40.07  
% 228.57/40.07  Sub-proof #533 shows that the following formulas are inconsistent:
% 228.57/40.07  ----------------------------------------------------------------
% 228.57/40.07    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.57/40.07    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.57/40.07    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.07         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.57/40.07    (4)  all_57_12 = e0
% 228.57/40.07    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.57/40.07         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.57/40.07    (6)   ~ (all_53_8 = all_53_12)
% 228.57/40.07    (7)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.07         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.07    (8)   ~ (e3 = e1)
% 228.57/40.07    (9)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.57/40.07         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.57/40.07    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.57/40.07            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.57/40.07    (11)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.57/40.07          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.57/40.07    (12)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.57/40.07            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.57/40.07              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.57/40.07    (13)   ~ (all_6_2 = e3)
% 228.57/40.07    (14)  op(e1, e1) = all_6_2
% 228.57/40.07    (15)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.57/40.07    (16)   ~ (all_53_9 = e0)
% 228.57/40.07    (17)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.57/40.07          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.57/40.07    (18)   ~ (all_53_4 = all_53_12)
% 228.57/40.07    (19)   ~ (all_53_8 = all_53_9)
% 228.57/40.07    (20)  all_42_2 = all_6_2
% 228.57/40.07    (21)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.57/40.07          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.57/40.07    (22)   ~ (all_53_9 = all_6_2)
% 228.57/40.07    (23)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.57/40.07          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.07    (24)  all_57_3 = e0
% 228.57/40.07    (25)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.57/40.07          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.57/40.07    (26)   ~ (e3 = e2)
% 228.57/40.07    (27)  all_55_1 = all_53_4
% 228.57/40.07    (28)   ~ (e3 = e0)
% 228.57/40.07    (29)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.57/40.07          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.57/40.07    (30)   ~ (all_53_8 = all_6_2)
% 228.57/40.07    (31)  all_57_1 = e0
% 228.57/40.07    (32)  all_55_2 = all_53_8
% 228.57/40.07    (33)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.57/40.07    (34)  all_57_15 = e3
% 228.57/40.07    (35)  op(e3, e3) = e2
% 228.57/40.07    (36)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.57/40.07          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.57/40.07            e1)
% 228.57/40.07    (37)   ~ (all_53_4 = all_53_8)
% 228.57/40.07    (38)  op(e3, e2) = all_53_4
% 228.57/40.07    (39)   ~ (e2 = e0)
% 228.57/40.07    (40)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.57/40.07            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.57/40.07            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.57/40.07            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.57/40.07              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.57/40.07            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.57/40.07            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.57/40.07              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.57/40.07              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.57/40.07            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.57/40.07            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.57/40.07            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.57/40.07              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.57/40.07              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.57/40.07            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.57/40.07              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.57/40.07            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.57/40.07            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.57/40.07              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.57/40.07              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.57/40.07            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.57/40.07            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.57/40.07    (41)  all_57_2 = e3
% 228.57/40.07    (42)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.57/40.07          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.57/40.07    (43)   ~ (e1 = e0)
% 228.57/40.07    (44)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.57/40.07            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.57/40.07              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.57/40.07    (45)   ~ (all_53_4 = e0)
% 228.57/40.07    (46)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.57/40.07          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.57/40.07    (47)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.57/40.07          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.57/40.07    (48)  op(e0, e0) = e3
% 228.57/40.07    (49)   ~ (all_53_4 = all_53_6)
% 228.57/40.07    (50)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.07          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.57/40.07            e2)
% 228.57/40.07    (51)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.07              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.57/40.07                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.57/40.07                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.57/40.07    (52)  all_55_10 = all_6_2
% 228.57/40.07    (53)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.57/40.07          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.57/40.07    (54)  all_38_2 = all_6_2
% 228.57/40.07    (55)  all_55_3 = all_53_12
% 228.57/40.07    (56)   ~ (all_53_12 = e3)
% 228.57/40.07    (57)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.57/40.07            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.57/40.07              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.57/40.07    (58)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.07          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.57/40.07    (59)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.57/40.07          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.57/40.07    (60)   ~ (e2 = e1)
% 228.57/40.07    (61)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.57/40.07          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.57/40.07    (62)  op(e2, e1) = all_53_9
% 228.57/40.07    (63)  op(e1, e2) = all_53_6
% 228.57/40.07    (64)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.57/40.07          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.57/40.07    (65)  all_24_2 = all_6_2
% 228.57/40.07    (66)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.57/40.07          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.57/40.07    (67)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.57/40.07          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.57/40.07    (68)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.57/40.07          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.57/40.07    (69)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.57/40.07          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.57/40.07    (70)  op(e3, e1) = all_53_8
% 228.57/40.07    (71)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.07          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.57/40.07    (72)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.57/40.07          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.57/40.07    (73)  op(e3, e0) = all_53_12
% 228.57/40.07  
% 228.57/40.07  Begin of proof
% 228.57/40.07  | 
% 228.57/40.07  | BETA: splitting (47) gives:
% 228.57/40.07  | 
% 228.57/40.07  | Case 1:
% 228.57/40.07  | | 
% 228.57/40.07  | |   (74)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 228.57/40.07  | |           e3)
% 228.57/40.07  | | 
% 228.57/40.07  | | REF_CLOSE: (3), (8), (24), (26), (28), (31), (39), (41), (43), (53), (58),
% 228.57/40.07  | |            (60), (74) are inconsistent by sub-proof #542.
% 228.57/40.07  | | 
% 228.57/40.07  | Case 2:
% 228.57/40.07  | | 
% 228.57/40.07  | |   (75)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 228.57/40.07  | |           e3)
% 228.57/40.07  | | 
% 228.57/40.07  | | BETA: splitting (75) gives:
% 228.57/40.07  | | 
% 228.57/40.07  | | Case 1:
% 228.57/40.07  | | | 
% 228.57/40.07  | | |   (76)  all_57_7 = e3 & op(e1, e2) = e3
% 228.57/40.07  | | | 
% 228.57/40.07  | | | ALPHA: (76) implies:
% 228.57/40.07  | | |   (77)  all_57_7 = e3
% 228.57/40.07  | | | 
% 228.57/40.07  | | | REF_CLOSE: (7), (8), (24), (26), (31), (39), (43), (60), (71), (77) are
% 228.57/40.07  | | |            inconsistent by sub-proof #2098.
% 228.57/40.07  | | | 
% 228.57/40.07  | | Case 2:
% 228.57/40.07  | | | 
% 228.57/40.07  | | |   (78)  all_57_13 = e3 & op(e0, e2) = e3
% 228.57/40.07  | | | 
% 228.57/40.07  | | | ALPHA: (78) implies:
% 228.57/40.07  | | |   (79)  all_57_13 = e3
% 228.57/40.07  | | | 
% 228.57/40.07  | | | BETA: splitting (50) gives:
% 228.57/40.07  | | | 
% 228.57/40.07  | | | Case 1:
% 228.57/40.07  | | | | 
% 228.57/40.07  | | | |   (80)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0,
% 228.57/40.07  | | | |             e2) = e2)
% 228.57/40.07  | | | | 
% 228.57/40.07  | | | | BETA: splitting (80) gives:
% 228.57/40.07  | | | | 
% 228.57/40.07  | | | | Case 1:
% 228.57/40.07  | | | | | 
% 228.57/40.07  | | | | |   (81)  all_57_12 = e2 & op(e0, e3) = e2
% 228.57/40.07  | | | | | 
% 228.57/40.07  | | | | | ALPHA: (81) implies:
% 228.57/40.07  | | | | |   (82)  all_57_12 = e2
% 228.57/40.07  | | | | | 
% 228.57/40.07  | | | | | REF_CLOSE: (4), (39), (82) are inconsistent by sub-proof #2385.
% 228.57/40.07  | | | | | 
% 228.57/40.07  | | | | Case 2:
% 228.57/40.07  | | | | | 
% 228.57/40.07  | | | | |   (83)  all_57_13 = e2 & op(e0, e2) = e2
% 228.57/40.07  | | | | | 
% 228.57/40.07  | | | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.57/40.07  | | | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 228.57/40.07  | | | | |            (23), (24), (25), (26), (27), (28), (29), (30), (32), (33),
% 228.57/40.07  | | | | |            (34), (35), (36), (37), (38), (39), (40), (41), (42), (43),
% 228.57/40.07  | | | | |            (44), (45), (46), (47), (48), (49), (50), (51), (52), (53),
% 228.57/40.07  | | | | |            (54), (55), (56), (57), (58), (59), (60), (61), (62), (63),
% 228.57/40.07  | | | | |            (64), (65), (66), (67), (68), (69), (70), (71), (72), (73),
% 228.57/40.07  | | | | |            (79), (83) are inconsistent by sub-proof #535.
% 228.57/40.07  | | | | | 
% 228.57/40.07  | | | | End of split
% 228.57/40.07  | | | | 
% 228.57/40.07  | | | Case 2:
% 228.57/40.07  | | | | 
% 228.57/40.07  | | | |   (84)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0,
% 228.57/40.07  | | | |             e0) = e2)
% 228.57/40.07  | | | | 
% 228.57/40.07  | | | | BETA: splitting (84) gives:
% 228.57/40.07  | | | | 
% 228.57/40.07  | | | | Case 1:
% 228.57/40.07  | | | | | 
% 228.57/40.07  | | | | |   (85)  all_57_14 = e2 & op(e0, e1) = e2
% 228.57/40.07  | | | | | 
% 228.57/40.07  | | | | | ALPHA: (85) implies:
% 228.57/40.07  | | | | |   (86)  all_57_14 = e2
% 228.57/40.07  | | | | | 
% 228.57/40.07  | | | | | REF_CLOSE: (4), (8), (34), (36), (43), (60), (79), (86) are
% 228.57/40.07  | | | | |            inconsistent by sub-proof #2215.
% 228.57/40.07  | | | | | 
% 228.57/40.07  | | | | Case 2:
% 228.57/40.07  | | | | | 
% 228.57/40.07  | | | | |   (87)  all_57_15 = e2 & op(e0, e0) = e2
% 228.57/40.07  | | | | | 
% 228.57/40.07  | | | | | ALPHA: (87) implies:
% 228.57/40.07  | | | | |   (88)  all_57_15 = e2
% 228.57/40.07  | | | | | 
% 228.57/40.07  | | | | | COMBINE_EQS: (34), (88) imply:
% 228.57/40.07  | | | | |   (89)  e3 = e2
% 228.57/40.07  | | | | | 
% 228.57/40.07  | | | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.57/40.07  | | | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 228.57/40.07  | | | | |            (23), (24), (25), (26), (27), (28), (29), (30), (32), (33),
% 228.57/40.07  | | | | |            (34), (35), (36), (37), (38), (39), (40), (41), (42), (43),
% 228.57/40.07  | | | | |            (44), (45), (46), (47), (48), (49), (50), (51), (52), (53),
% 228.57/40.07  | | | | |            (54), (55), (56), (57), (58), (59), (60), (61), (62), (63),
% 228.57/40.07  | | | | |            (64), (65), (66), (67), (68), (69), (70), (71), (72), (73),
% 228.57/40.07  | | | | |            (89) are inconsistent by sub-proof #534.
% 228.57/40.07  | | | | | 
% 228.57/40.07  | | | | End of split
% 228.57/40.07  | | | | 
% 228.57/40.07  | | | End of split
% 228.57/40.07  | | | 
% 228.57/40.07  | | End of split
% 228.57/40.07  | | 
% 228.57/40.07  | End of split
% 228.57/40.07  | 
% 228.57/40.07  End of proof
% 228.57/40.07  
% 228.57/40.07  Sub-proof #534 shows that the following formulas are inconsistent:
% 228.57/40.07  ----------------------------------------------------------------
% 228.57/40.07    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.57/40.07    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.57/40.07    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.07         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.57/40.07    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.57/40.07         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.57/40.07    (5)   ~ (all_53_8 = all_53_12)
% 228.57/40.07    (6)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.07         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.07    (7)   ~ (e3 = e1)
% 228.57/40.07    (8)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.57/40.07         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.57/40.07    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.57/40.07           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.57/40.07    (10)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.57/40.07          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.57/40.07    (11)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.57/40.07            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.57/40.07              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.57/40.07    (12)   ~ (all_6_2 = e3)
% 228.57/40.07    (13)  op(e1, e1) = all_6_2
% 228.57/40.07    (14)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.57/40.07    (15)   ~ (all_53_9 = e0)
% 228.57/40.07    (16)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.57/40.07          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.57/40.07    (17)   ~ (all_53_4 = all_53_12)
% 228.57/40.07    (18)   ~ (all_53_8 = all_53_9)
% 228.57/40.07    (19)  all_42_2 = all_6_2
% 228.57/40.07    (20)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.57/40.07          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.57/40.07    (21)   ~ (all_53_9 = all_6_2)
% 228.57/40.07    (22)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.57/40.07          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.07    (23)  all_57_3 = e0
% 228.57/40.07    (24)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.57/40.07          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.57/40.07    (25)   ~ (e3 = e2)
% 228.57/40.07    (26)  all_55_1 = all_53_4
% 228.57/40.07    (27)   ~ (e3 = e0)
% 228.57/40.07    (28)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.57/40.07          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.57/40.07    (29)   ~ (all_53_8 = all_6_2)
% 228.57/40.07    (30)  all_55_2 = all_53_8
% 228.57/40.07    (31)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.57/40.07    (32)  all_57_15 = e3
% 228.57/40.07    (33)  op(e3, e3) = e2
% 228.57/40.07    (34)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.57/40.07          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.57/40.07            e1)
% 228.57/40.07    (35)   ~ (all_53_4 = all_53_8)
% 228.57/40.07    (36)  op(e3, e2) = all_53_4
% 228.57/40.07    (37)   ~ (e2 = e0)
% 228.57/40.07    (38)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.57/40.07            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.57/40.07            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.57/40.07            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.57/40.07              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.57/40.07            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.57/40.07            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.57/40.07              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.57/40.07              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.57/40.07            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.57/40.07            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.57/40.07            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.57/40.07              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.57/40.07              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.57/40.07            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.57/40.07              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.57/40.07            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.57/40.07            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.57/40.07              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.57/40.07              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.57/40.07            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.57/40.07            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.57/40.07    (39)  all_57_2 = e3
% 228.57/40.07    (40)  e3 = e2
% 228.57/40.07    (41)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.57/40.07          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.57/40.07    (42)   ~ (e1 = e0)
% 228.57/40.07    (43)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.57/40.07            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.57/40.07              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.57/40.07    (44)   ~ (all_53_4 = e0)
% 228.57/40.07    (45)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.57/40.07          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.57/40.07    (46)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.57/40.07          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.57/40.07    (47)  op(e0, e0) = e3
% 228.57/40.07    (48)   ~ (all_53_4 = all_53_6)
% 228.57/40.07    (49)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.07          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.57/40.07            e2)
% 228.57/40.07    (50)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.07              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.57/40.07                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.57/40.07                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.57/40.07    (51)  all_55_10 = all_6_2
% 228.57/40.07    (52)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.57/40.07          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.57/40.07    (53)  all_38_2 = all_6_2
% 228.57/40.07    (54)  all_55_3 = all_53_12
% 228.57/40.07    (55)   ~ (all_53_12 = e3)
% 228.57/40.07    (56)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.57/40.07            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.57/40.07              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.57/40.07    (57)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.07          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.57/40.07    (58)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.57/40.07          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.57/40.07    (59)   ~ (e2 = e1)
% 228.57/40.07    (60)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.57/40.07          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.57/40.07    (61)  op(e2, e1) = all_53_9
% 228.57/40.07    (62)  op(e1, e2) = all_53_6
% 228.57/40.07    (63)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.57/40.07          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.57/40.07    (64)  all_24_2 = all_6_2
% 228.57/40.07    (65)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.57/40.07          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.57/40.07    (66)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.57/40.07          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.57/40.07    (67)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.57/40.07          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.57/40.07    (68)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.57/40.07          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.57/40.07    (69)  op(e3, e1) = all_53_8
% 228.57/40.08    (70)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.08          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.57/40.08    (71)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.57/40.08          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.57/40.08    (72)  op(e3, e0) = all_53_12
% 228.57/40.08  
% 228.57/40.08  Begin of proof
% 228.57/40.08  | 
% 228.57/40.08  | SIMP: (40) implies:
% 228.57/40.08  |   (73)  e3 = e2
% 228.57/40.08  | 
% 228.57/40.08  | COMBINE_EQS: (39), (73) imply:
% 228.57/40.08  |   (74)  all_57_2 = e2
% 228.57/40.08  | 
% 228.57/40.08  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.57/40.08  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 228.57/40.08  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 228.57/40.08  |            (35), (36), (37), (38), (41), (42), (43), (44), (45), (46), (47),
% 228.57/40.08  |            (48), (49), (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 228.57/40.08  |            (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 228.57/40.08  |            (70), (71), (72), (74) are inconsistent by sub-proof #544.
% 228.57/40.08  | 
% 228.57/40.08  End of proof
% 228.57/40.08  
% 228.57/40.08  Sub-proof #535 shows that the following formulas are inconsistent:
% 228.57/40.08  ----------------------------------------------------------------
% 228.57/40.08    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.57/40.08    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.57/40.08    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.08         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.57/40.08    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.57/40.08         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.57/40.08    (5)   ~ (all_53_8 = all_53_12)
% 228.57/40.08    (6)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.08         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.08    (7)   ~ (e3 = e1)
% 228.57/40.08    (8)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.57/40.08         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.57/40.08    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.57/40.08           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.57/40.08    (10)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.57/40.08          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.57/40.08    (11)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.57/40.08            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.57/40.08              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.57/40.08    (12)   ~ (all_6_2 = e3)
% 228.57/40.08    (13)  op(e1, e1) = all_6_2
% 228.57/40.08    (14)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.57/40.08    (15)   ~ (all_53_9 = e0)
% 228.57/40.08    (16)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.57/40.08          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.57/40.08    (17)   ~ (all_53_4 = all_53_12)
% 228.57/40.08    (18)   ~ (all_53_8 = all_53_9)
% 228.57/40.08    (19)  all_42_2 = all_6_2
% 228.57/40.08    (20)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.57/40.08          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.57/40.08    (21)   ~ (all_53_9 = all_6_2)
% 228.57/40.08    (22)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.57/40.08          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.08    (23)  all_57_3 = e0
% 228.57/40.08    (24)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.57/40.08          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.57/40.08    (25)   ~ (e3 = e2)
% 228.57/40.08    (26)  all_55_1 = all_53_4
% 228.57/40.08    (27)   ~ (e3 = e0)
% 228.57/40.08    (28)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.57/40.08          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.57/40.08    (29)   ~ (all_53_8 = all_6_2)
% 228.57/40.08    (30)  all_55_2 = all_53_8
% 228.57/40.08    (31)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.57/40.08    (32)  all_57_15 = e3
% 228.57/40.08    (33)  op(e3, e3) = e2
% 228.57/40.08    (34)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.57/40.08          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.57/40.08            e1)
% 228.57/40.08    (35)   ~ (all_53_4 = all_53_8)
% 228.57/40.08    (36)  op(e3, e2) = all_53_4
% 228.57/40.08    (37)   ~ (e2 = e0)
% 228.57/40.08    (38)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.57/40.08            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.57/40.08            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.57/40.08            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.57/40.08              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.57/40.08            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.57/40.08            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.57/40.08              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.57/40.08              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.57/40.08            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.57/40.08            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.57/40.08            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.57/40.08              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.57/40.08              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.57/40.08            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.57/40.08              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.57/40.08            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.57/40.08            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.57/40.08              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.57/40.08              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.57/40.08            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.57/40.08            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.57/40.08    (39)  all_57_2 = e3
% 228.57/40.08    (40)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.57/40.08          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.57/40.08    (41)   ~ (e1 = e0)
% 228.57/40.08    (42)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.57/40.08            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.57/40.08              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.57/40.08    (43)   ~ (all_53_4 = e0)
% 228.57/40.08    (44)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.57/40.08          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.57/40.08    (45)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.57/40.08          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.57/40.08    (46)  all_57_13 = e3
% 228.57/40.08    (47)  op(e0, e0) = e3
% 228.57/40.08    (48)   ~ (all_53_4 = all_53_6)
% 228.57/40.08    (49)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.08          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.57/40.08            e2)
% 228.57/40.08    (50)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.08              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.57/40.08                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.57/40.08                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.57/40.08    (51)  all_55_10 = all_6_2
% 228.57/40.08    (52)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.57/40.08          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.57/40.08    (53)  all_38_2 = all_6_2
% 228.57/40.08    (54)  all_55_3 = all_53_12
% 228.57/40.08    (55)   ~ (all_53_12 = e3)
% 228.57/40.08    (56)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.57/40.08            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.57/40.08              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.57/40.08    (57)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.08          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.57/40.08    (58)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.57/40.08          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.57/40.08    (59)   ~ (e2 = e1)
% 228.57/40.08    (60)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.57/40.08          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.57/40.08    (61)  op(e2, e1) = all_53_9
% 228.57/40.08    (62)  op(e1, e2) = all_53_6
% 228.57/40.08    (63)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.57/40.08          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.57/40.08    (64)  all_24_2 = all_6_2
% 228.57/40.08    (65)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.57/40.08          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.57/40.08    (66)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.57/40.08          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.57/40.08    (67)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.57/40.08          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.57/40.08    (68)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.57/40.08          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.57/40.08    (69)  op(e3, e1) = all_53_8
% 228.57/40.08    (70)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.08          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.57/40.08    (71)  all_57_13 = e2 & op(e0, e2) = e2
% 228.57/40.08    (72)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.57/40.08          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.57/40.08    (73)  op(e3, e0) = all_53_12
% 228.57/40.08  
% 228.57/40.08  Begin of proof
% 228.57/40.08  | 
% 228.57/40.08  | ALPHA: (71) implies:
% 228.57/40.08  |   (74)  all_57_13 = e2
% 228.57/40.08  | 
% 228.57/40.08  | COMBINE_EQS: (46), (74) imply:
% 228.57/40.08  |   (75)  e3 = e2
% 228.57/40.08  | 
% 228.57/40.08  | COMBINE_EQS: (39), (75) imply:
% 228.57/40.08  |   (76)  all_57_2 = e2
% 228.57/40.08  | 
% 228.57/40.08  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.57/40.08  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 228.57/40.08  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 228.57/40.08  |            (35), (36), (37), (38), (40), (41), (42), (43), (44), (45), (47),
% 228.57/40.08  |            (48), (49), (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 228.57/40.08  |            (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 228.57/40.08  |            (70), (72), (73), (76) are inconsistent by sub-proof #544.
% 228.57/40.08  | 
% 228.57/40.08  End of proof
% 228.57/40.08  
% 228.57/40.08  Sub-proof #536 shows that the following formulas are inconsistent:
% 228.57/40.08  ----------------------------------------------------------------
% 228.57/40.08    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.08         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.57/40.08    (2)   ~ (e3 = e1)
% 228.57/40.08    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.57/40.08           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.57/40.08    (4)   ~ (all_6_2 = e3)
% 228.57/40.08    (5)  op(e1, e1) = all_6_2
% 228.57/40.08    (6)  all_57_6 = e1
% 228.57/40.08    (7)  all_57_3 = e0
% 228.57/40.08    (8)  all_57_4 = e3
% 228.57/40.08    (9)   ~ (e3 = e2)
% 228.57/40.08    (10)   ~ (e3 = e0)
% 228.57/40.08    (11)  all_57_15 = e3
% 228.57/40.08    (12)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.57/40.08          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.57/40.08            e1)
% 228.57/40.08    (13)  all_57_10 = e2
% 228.57/40.08    (14)   ~ (e2 = e0)
% 228.57/40.08    (15)  all_57_2 = e3
% 228.57/40.08    (16)   ~ (e1 = e0)
% 228.57/40.08    (17)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.57/40.08          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.57/40.08    (18)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.08          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.57/40.08            e2)
% 228.57/40.08    (19)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.08              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.57/40.08                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.57/40.08                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.57/40.08    (20)   ~ (e2 = e1)
% 228.57/40.08    (21)  all_57_6 = e3 & op(e1, e3) = e3
% 228.57/40.08  
% 228.57/40.08  Begin of proof
% 228.57/40.08  | 
% 228.57/40.08  | ALPHA: (21) implies:
% 228.57/40.08  |   (22)  all_57_6 = e3
% 228.57/40.08  | 
% 228.57/40.08  | COMBINE_EQS: (6), (22) imply:
% 228.57/40.08  |   (23)  e3 = e1
% 228.57/40.08  | 
% 228.57/40.08  | SIMP: (23) implies:
% 228.57/40.08  |   (24)  e3 = e1
% 228.57/40.08  | 
% 228.57/40.08  | COMBINE_EQS: (8), (24) imply:
% 228.57/40.08  |   (25)  all_57_4 = e1
% 228.57/40.08  | 
% 228.57/40.08  | REF_CLOSE: (1), (2), (3), (4), (5), (7), (9), (10), (11), (12), (13), (14),
% 228.57/40.08  |            (15), (16), (17), (18), (19), (20), (25) are inconsistent by
% 228.57/40.08  |            sub-proof #1755.
% 228.57/40.08  | 
% 228.57/40.08  End of proof
% 228.57/40.08  
% 228.57/40.08  Sub-proof #537 shows that the following formulas are inconsistent:
% 228.57/40.08  ----------------------------------------------------------------
% 228.57/40.08    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.08         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.57/40.08    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.57/40.08         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.57/40.08    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.08         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.08    (4)   ~ (e3 = e1)
% 228.57/40.08    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.57/40.08           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.57/40.08    (6)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.57/40.08         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.57/40.08    (7)   ~ (all_6_2 = e3)
% 228.57/40.08    (8)  op(e1, e1) = all_6_2
% 228.57/40.08    (9)  all_57_6 = e1
% 228.57/40.08    (10)  all_57_3 = e0
% 228.57/40.08    (11)   ~ (e3 = e2)
% 228.57/40.08    (12)   ~ (e3 = e0)
% 228.57/40.08    (13)  all_57_1 = e0
% 228.57/40.08    (14)  all_57_15 = e3
% 228.57/40.08    (15)  all_57_10 = e2
% 228.57/40.08    (16)   ~ (e2 = e0)
% 228.57/40.08    (17)  all_57_2 = e3
% 228.57/40.08    (18)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.57/40.08          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.57/40.08    (19)   ~ (e1 = e0)
% 228.57/40.08    (20)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.57/40.08          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.57/40.08    (21)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.57/40.08          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.57/40.08    (22)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.08          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.57/40.08            e2)
% 228.57/40.08    (23)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.08              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.57/40.08                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.57/40.08                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.57/40.08    (24)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.57/40.08          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.57/40.08    (25)   ~ (all_53_12 = e3)
% 228.57/40.08    (26)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.08          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.57/40.08    (27)   ~ (e2 = e1)
% 228.57/40.08    (28)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.57/40.08          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.57/40.08    (29)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.57/40.08          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.57/40.08    (30)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.57/40.08          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.57/40.08    (31)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.57/40.08          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.57/40.08    (32)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.08          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.57/40.08    (33)  op(e3, e0) = all_53_12
% 228.57/40.08  
% 228.57/40.08  Begin of proof
% 228.57/40.08  | 
% 228.57/40.08  | BETA: splitting (21) gives:
% 228.57/40.08  | 
% 228.57/40.08  | Case 1:
% 228.57/40.08  | | 
% 228.57/40.08  | |   (34)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 228.57/40.08  | |           e3)
% 228.57/40.08  | | 
% 228.57/40.08  | | REF_CLOSE: (1), (4), (10), (11), (12), (13), (16), (17), (19), (24), (26),
% 228.57/40.08  | |            (27), (34) are inconsistent by sub-proof #542.
% 228.57/40.08  | | 
% 228.57/40.08  | Case 2:
% 228.57/40.08  | | 
% 228.57/40.08  | |   (35)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 228.57/40.08  | |           e3)
% 228.57/40.08  | | 
% 228.57/40.08  | | BETA: splitting (35) gives:
% 228.57/40.08  | | 
% 228.57/40.08  | | Case 1:
% 228.57/40.08  | | | 
% 228.57/40.08  | | |   (36)  all_57_7 = e3 & op(e1, e2) = e3
% 228.57/40.08  | | | 
% 228.57/40.08  | | | ALPHA: (36) implies:
% 228.57/40.08  | | |   (37)  all_57_7 = e3
% 228.57/40.08  | | | 
% 228.57/40.08  | | | REF_CLOSE: (3), (4), (10), (11), (13), (16), (19), (27), (32), (37) are
% 228.57/40.08  | | |            inconsistent by sub-proof #2098.
% 228.57/40.08  | | | 
% 228.57/40.08  | | Case 2:
% 228.57/40.08  | | | 
% 228.57/40.08  | | |   (38)  all_57_13 = e3 & op(e0, e2) = e3
% 228.57/40.08  | | | 
% 228.57/40.08  | | | ALPHA: (38) implies:
% 228.57/40.08  | | |   (39)  all_57_13 = e3
% 228.57/40.08  | | | 
% 228.57/40.08  | | | BETA: splitting (18) gives:
% 228.57/40.08  | | | 
% 228.57/40.08  | | | Case 1:
% 228.57/40.08  | | | | 
% 228.57/40.08  | | | |   (40)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2)
% 228.57/40.08  | | | |           = e3)
% 228.57/40.08  | | | | 
% 228.57/40.08  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12),
% 228.57/40.08  | | | |            (13), (14), (16), (17), (19), (23), (24), (26), (27), (28),
% 228.57/40.08  | | | |            (29), (30), (31), (32), (40) are inconsistent by sub-proof
% 228.57/40.08  | | | |            #541.
% 228.57/40.08  | | | | 
% 228.57/40.08  | | | Case 2:
% 228.57/40.08  | | | | 
% 228.57/40.08  | | | |   (41)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0)
% 228.57/40.08  | | | |           = e3)
% 228.57/40.08  | | | | 
% 228.57/40.08  | | | | BETA: splitting (41) gives:
% 228.57/40.08  | | | | 
% 228.57/40.08  | | | | Case 1:
% 228.57/40.08  | | | | | 
% 228.57/40.08  | | | | |   (42)  all_57_4 = e3 & op(e3, e1) = e3
% 228.57/40.08  | | | | | 
% 228.57/40.08  | | | | | ALPHA: (42) implies:
% 228.57/40.08  | | | | |   (43)  all_57_4 = e3
% 228.57/40.08  | | | | | 
% 228.57/40.08  | | | | | BETA: splitting (6) gives:
% 228.57/40.08  | | | | | 
% 228.57/40.08  | | | | | Case 1:
% 228.57/40.08  | | | | | | 
% 228.57/40.08  | | | | | |   (44)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1,
% 228.57/40.08  | | | | | |             e2) = e3)
% 228.57/40.08  | | | | | | 
% 228.57/40.08  | | | | | | BETA: splitting (44) gives:
% 228.57/40.08  | | | | | | 
% 228.57/40.08  | | | | | | Case 1:
% 228.57/40.08  | | | | | | | 
% 228.57/40.08  | | | | | | |   (45)  all_57_6 = e3 & op(e1, e3) = e3
% 228.57/40.08  | | | | | | | 
% 228.57/40.08  | | | | | | | REF_CLOSE: (1), (4), (5), (7), (8), (9), (10), (11), (12), (14),
% 228.57/40.08  | | | | | | |            (15), (16), (17), (19), (20), (22), (23), (27), (39),
% 228.57/40.08  | | | | | | |            (43), (45) are inconsistent by sub-proof #538.
% 228.57/40.08  | | | | | | | 
% 228.57/40.08  | | | | | | Case 2:
% 228.57/40.08  | | | | | | | 
% 228.57/40.08  | | | | | | |   (46)  all_57_7 = e3 & op(e1, e2) = e3
% 228.57/40.08  | | | | | | | 
% 228.57/40.08  | | | | | | | ALPHA: (46) implies:
% 228.57/40.08  | | | | | | |   (47)  all_57_7 = e3
% 228.57/40.08  | | | | | | | 
% 228.57/40.08  | | | | | | | REF_CLOSE: (3), (4), (10), (11), (13), (16), (19), (27), (32),
% 228.57/40.08  | | | | | | |            (47) are inconsistent by sub-proof #2098.
% 228.57/40.08  | | | | | | | 
% 228.57/40.08  | | | | | | End of split
% 228.57/40.08  | | | | | | 
% 228.57/40.08  | | | | | Case 2:
% 228.57/40.08  | | | | | | 
% 228.57/40.08  | | | | | |   (48)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1,
% 228.57/40.08  | | | | | |             e0) = e3)
% 228.57/40.08  | | | | | | 
% 228.57/40.08  | | | | | | REF_CLOSE: (4), (5), (7), (8), (11), (12), (14), (16), (19), (23),
% 228.57/40.08  | | | | | |            (27), (28), (31), (48) are inconsistent by sub-proof
% 228.57/40.08  | | | | | |            #1786.
% 228.57/40.08  | | | | | | 
% 228.57/40.08  | | | | | End of split
% 228.57/40.08  | | | | | 
% 228.57/40.08  | | | | Case 2:
% 228.57/40.08  | | | | | 
% 228.57/40.08  | | | | |   (49)  all_57_9 = e3 & op(e3, e0) = e3
% 228.57/40.08  | | | | | 
% 228.57/40.08  | | | | | ALPHA: (49) implies:
% 228.57/40.08  | | | | |   (50)  op(e3, e0) = e3
% 228.57/40.08  | | | | | 
% 228.57/40.08  | | | | | REF_CLOSE: (5), (25), (33), (50) are inconsistent by sub-proof #2458.
% 228.57/40.08  | | | | | 
% 228.57/40.08  | | | | End of split
% 228.57/40.08  | | | | 
% 228.57/40.08  | | | End of split
% 228.57/40.08  | | | 
% 228.57/40.08  | | End of split
% 228.57/40.08  | | 
% 228.57/40.08  | End of split
% 228.57/40.08  | 
% 228.57/40.08  End of proof
% 228.57/40.08  
% 228.57/40.08  Sub-proof #538 shows that the following formulas are inconsistent:
% 228.57/40.08  ----------------------------------------------------------------
% 228.57/40.08    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.08         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.57/40.08    (2)   ~ (e3 = e1)
% 228.57/40.08    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.57/40.08           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.57/40.08    (4)   ~ (all_6_2 = e3)
% 228.57/40.08    (5)  op(e1, e1) = all_6_2
% 228.57/40.08    (6)  all_57_6 = e1
% 228.57/40.08    (7)  all_57_3 = e0
% 228.57/40.08    (8)  all_57_4 = e3
% 228.57/40.08    (9)   ~ (e3 = e2)
% 228.57/40.08    (10)   ~ (e3 = e0)
% 228.57/40.08    (11)  all_57_15 = e3
% 228.57/40.08    (12)  all_57_10 = e2
% 228.57/40.08    (13)   ~ (e2 = e0)
% 228.57/40.08    (14)  all_57_2 = e3
% 228.57/40.08    (15)   ~ (e1 = e0)
% 228.57/40.08    (16)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.57/40.08          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.57/40.08    (17)  all_57_13 = e3
% 228.57/40.08    (18)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.08          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.57/40.08            e2)
% 228.57/40.08    (19)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.08              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.57/40.08                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.57/40.08                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.57/40.08    (20)   ~ (e2 = e1)
% 228.57/40.08    (21)  all_57_6 = e3 & op(e1, e3) = e3
% 228.57/40.08  
% 228.57/40.08  Begin of proof
% 228.57/40.08  | 
% 228.57/40.08  | ALPHA: (21) implies:
% 228.57/40.08  |   (22)  all_57_6 = e3
% 228.57/40.08  | 
% 228.57/40.08  | COMBINE_EQS: (6), (22) imply:
% 228.57/40.08  |   (23)  e3 = e1
% 228.57/40.08  | 
% 228.57/40.08  | SIMP: (23) implies:
% 228.57/40.08  |   (24)  e3 = e1
% 228.57/40.08  | 
% 228.57/40.08  | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 228.57/40.08  |            (14), (15), (16), (17), (18), (19), (20), (24) are inconsistent by
% 228.57/40.08  |            sub-proof #539.
% 228.57/40.08  | 
% 228.57/40.08  End of proof
% 228.57/40.08  
% 228.57/40.08  Sub-proof #539 shows that the following formulas are inconsistent:
% 228.57/40.08  ----------------------------------------------------------------
% 228.57/40.08    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.08         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.57/40.08    (2)   ~ (e3 = e1)
% 228.57/40.08    (3)  e3 = e1
% 228.57/40.08    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.57/40.08           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.57/40.08    (5)   ~ (all_6_2 = e3)
% 228.57/40.08    (6)  op(e1, e1) = all_6_2
% 228.57/40.08    (7)  all_57_3 = e0
% 228.57/40.08    (8)  all_57_4 = e3
% 228.57/40.08    (9)   ~ (e3 = e2)
% 228.57/40.08    (10)   ~ (e3 = e0)
% 228.57/40.08    (11)  all_57_15 = e3
% 228.57/40.08    (12)  all_57_10 = e2
% 228.57/40.08    (13)   ~ (e2 = e0)
% 228.57/40.08    (14)  all_57_2 = e3
% 228.57/40.08    (15)   ~ (e1 = e0)
% 228.57/40.08    (16)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.57/40.08          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.57/40.08    (17)  all_57_13 = e3
% 228.57/40.08    (18)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.08          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.57/40.08            e2)
% 228.57/40.08    (19)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.08              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.57/40.08                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.57/40.08                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.57/40.08    (20)   ~ (e2 = e1)
% 228.57/40.08  
% 228.57/40.08  Begin of proof
% 228.57/40.08  | 
% 228.57/40.08  | COMBINE_EQS: (3), (8) imply:
% 228.57/40.08  |   (21)  all_57_4 = e1
% 228.57/40.08  | 
% 228.57/40.08  | BETA: splitting (16) gives:
% 228.57/40.08  | 
% 228.57/40.08  | Case 1:
% 228.57/40.08  | | 
% 228.57/40.08  | |   (22)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) =
% 228.57/40.08  | |           e3)
% 228.57/40.08  | | 
% 228.57/40.08  | | REF_CLOSE: (1), (2), (7), (12), (14), (15), (20), (21), (22) are
% 228.57/40.08  | |            inconsistent by sub-proof #1756.
% 228.57/40.08  | | 
% 228.57/40.08  | Case 2:
% 228.57/40.08  | | 
% 228.57/40.08  | |   (23)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) =
% 228.57/40.08  | |           e3)
% 228.57/40.08  | | 
% 228.57/40.08  | | REF_CLOSE: (4), (5), (6), (9), (10), (11), (13), (17), (18), (19), (23) are
% 228.57/40.08  | |            inconsistent by sub-proof #540.
% 228.57/40.08  | | 
% 228.57/40.08  | End of split
% 228.57/40.08  | 
% 228.57/40.08  End of proof
% 228.57/40.08  
% 228.57/40.08  Sub-proof #540 shows that the following formulas are inconsistent:
% 228.57/40.08  ----------------------------------------------------------------
% 228.57/40.08    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.57/40.08           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.57/40.08    (2)   ~ (all_6_2 = e3)
% 228.57/40.09    (3)  op(e1, e1) = all_6_2
% 228.57/40.09    (4)   ~ (e3 = e2)
% 228.57/40.09    (5)   ~ (e3 = e0)
% 228.57/40.09    (6)  all_57_15 = e3
% 228.57/40.09    (7)   ~ (e2 = e0)
% 228.57/40.09    (8)  all_57_13 = e3
% 228.57/40.09    (9)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2) |
% 228.57/40.09         (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.57/40.09    (10)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.09              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.57/40.09                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.57/40.09                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.57/40.09    (11)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.57/40.09  
% 228.57/40.09  Begin of proof
% 228.57/40.09  | 
% 228.57/40.09  | BETA: splitting (11) gives:
% 228.57/40.09  | 
% 228.57/40.09  | Case 1:
% 228.57/40.09  | | 
% 228.57/40.09  | |   (12)  all_57_8 = e3 & op(e1, e1) = e3
% 228.57/40.09  | | 
% 228.57/40.09  | | ALPHA: (12) implies:
% 228.57/40.09  | |   (13)  op(e1, e1) = e3
% 228.57/40.09  | | 
% 228.57/40.09  | | REF_CLOSE: (1), (2), (3), (13) are inconsistent by sub-proof #2468.
% 228.57/40.09  | | 
% 228.57/40.09  | Case 2:
% 228.57/40.09  | | 
% 228.57/40.09  | |   (14)  all_57_14 = e3 & op(e0, e1) = e3
% 228.57/40.09  | | 
% 228.57/40.09  | | ALPHA: (14) implies:
% 228.57/40.09  | |   (15)  all_57_14 = e3
% 228.57/40.09  | | 
% 228.57/40.09  | | BETA: splitting (10) gives:
% 228.57/40.09  | | 
% 228.57/40.09  | | Case 1:
% 228.57/40.09  | | | 
% 228.57/40.09  | | |   (16)  all_57_15 = e0 & op(e0, e0) = e0
% 228.57/40.09  | | | 
% 228.57/40.09  | | | REF_CLOSE: (5), (6), (16) are inconsistent by sub-proof #2329.
% 228.57/40.09  | | | 
% 228.57/40.09  | | Case 2:
% 228.57/40.09  | | | 
% 228.57/40.09  | | |   (17)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0)
% 228.57/40.09  | | |             = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0
% 228.57/40.09  | | |             & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 228.57/40.09  | | |           (all_57_14 = e0 & op(e0, e1) = e0))
% 228.57/40.09  | | | 
% 228.57/40.09  | | | ALPHA: (17) implies:
% 228.57/40.09  | | |   (18)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2)
% 228.57/40.09  | | |           = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.57/40.09  | | | 
% 228.57/40.09  | | | BETA: splitting (9) gives:
% 228.57/40.09  | | | 
% 228.57/40.09  | | | Case 1:
% 228.57/40.09  | | | | 
% 228.57/40.09  | | | |   (19)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0,
% 228.57/40.09  | | | |             e2) = e2)
% 228.57/40.09  | | | | 
% 228.57/40.09  | | | | BETA: splitting (19) gives:
% 228.57/40.09  | | | | 
% 228.57/40.09  | | | | Case 1:
% 228.57/40.09  | | | | | 
% 228.57/40.09  | | | | |   (20)  all_57_12 = e2 & op(e0, e3) = e2
% 228.57/40.09  | | | | | 
% 228.57/40.09  | | | | | ALPHA: (20) implies:
% 228.57/40.09  | | | | |   (21)  all_57_12 = e2
% 228.57/40.09  | | | | | 
% 228.57/40.09  | | | | | REF_CLOSE: (5), (7), (8), (15), (18), (21) are inconsistent by
% 228.57/40.09  | | | | |            sub-proof #2088.
% 228.57/40.09  | | | | | 
% 228.57/40.09  | | | | Case 2:
% 228.57/40.09  | | | | | 
% 228.57/40.09  | | | | |   (22)  all_57_13 = e2 & op(e0, e2) = e2
% 228.57/40.09  | | | | | 
% 228.57/40.09  | | | | | REF_CLOSE: (4), (8), (22) are inconsistent by sub-proof #2146.
% 228.57/40.09  | | | | | 
% 228.57/40.09  | | | | End of split
% 228.57/40.09  | | | | 
% 228.57/40.09  | | | Case 2:
% 228.57/40.09  | | | | 
% 228.57/40.09  | | | |   (23)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0,
% 228.57/40.09  | | | |             e0) = e2)
% 228.57/40.09  | | | | 
% 228.57/40.09  | | | | BETA: splitting (23) gives:
% 228.57/40.09  | | | | 
% 228.57/40.09  | | | | Case 1:
% 228.57/40.09  | | | | | 
% 228.57/40.09  | | | | |   (24)  all_57_14 = e2 & op(e0, e1) = e2
% 228.57/40.09  | | | | | 
% 228.57/40.09  | | | | | REF_CLOSE: (4), (15), (24) are inconsistent by sub-proof #2324.
% 228.57/40.09  | | | | | 
% 228.57/40.09  | | | | Case 2:
% 228.57/40.09  | | | | | 
% 228.57/40.09  | | | | |   (25)  all_57_15 = e2 & op(e0, e0) = e2
% 228.57/40.09  | | | | | 
% 228.57/40.09  | | | | | REF_CLOSE: (4), (6), (25) are inconsistent by sub-proof #2323.
% 228.57/40.09  | | | | | 
% 228.57/40.09  | | | | End of split
% 228.57/40.09  | | | | 
% 228.57/40.09  | | | End of split
% 228.57/40.09  | | | 
% 228.57/40.09  | | End of split
% 228.57/40.09  | | 
% 228.57/40.09  | End of split
% 228.57/40.09  | 
% 228.57/40.09  End of proof
% 228.57/40.09  
% 228.57/40.09  Sub-proof #541 shows that the following formulas are inconsistent:
% 228.57/40.09  ----------------------------------------------------------------
% 228.57/40.09    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.09         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.57/40.09    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.57/40.09         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.57/40.09    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.09         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.09    (4)   ~ (e3 = e1)
% 228.57/40.09    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.57/40.09           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.57/40.09    (6)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.57/40.09         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.57/40.09    (7)   ~ (all_6_2 = e3)
% 228.57/40.09    (8)  op(e1, e1) = all_6_2
% 228.57/40.09    (9)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3)
% 228.57/40.09    (10)  all_57_3 = e0
% 228.57/40.09    (11)   ~ (e3 = e2)
% 228.57/40.09    (12)   ~ (e3 = e0)
% 228.57/40.09    (13)  all_57_1 = e0
% 228.57/40.09    (14)  all_57_15 = e3
% 228.57/40.09    (15)   ~ (e2 = e0)
% 228.57/40.09    (16)  all_57_2 = e3
% 228.57/40.09    (17)   ~ (e1 = e0)
% 228.57/40.09    (18)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.09              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.57/40.09                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.57/40.09                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.57/40.09    (19)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.57/40.09          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.57/40.09    (20)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.09          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.57/40.09    (21)   ~ (e2 = e1)
% 228.57/40.09    (22)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.57/40.09          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.57/40.09    (23)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.57/40.09          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.57/40.09    (24)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.57/40.09          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.57/40.09    (25)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.57/40.09          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.57/40.09    (26)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.09          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.57/40.09  
% 228.57/40.09  Begin of proof
% 228.57/40.09  | 
% 228.57/40.09  | BETA: splitting (9) gives:
% 228.57/40.09  | 
% 228.57/40.09  | Case 1:
% 228.57/40.09  | | 
% 228.57/40.09  | |   (27)  all_57_0 = e3 & op(e3, e3) = e3
% 228.57/40.09  | | 
% 228.57/40.09  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13), (14),
% 228.57/40.09  | |            (15), (17), (18), (21), (22), (23), (24), (25), (26), (27) are
% 228.57/40.09  | |            inconsistent by sub-proof #692.
% 228.57/40.09  | | 
% 228.57/40.09  | Case 2:
% 228.57/40.09  | | 
% 228.57/40.09  | |   (28)  all_57_1 = e3 & op(e3, e2) = e3
% 228.57/40.09  | | 
% 228.57/40.09  | | ALPHA: (28) implies:
% 228.57/40.09  | |   (29)  all_57_1 = e3
% 228.57/40.09  | | 
% 228.57/40.09  | | COMBINE_EQS: (13), (29) imply:
% 228.57/40.09  | |   (30)  e3 = e0
% 228.57/40.09  | | 
% 228.57/40.09  | | REF_CLOSE: (1), (4), (10), (11), (12), (15), (16), (17), (19), (20), (21),
% 228.57/40.09  | |            (30) are inconsistent by sub-proof #1333.
% 228.57/40.09  | | 
% 228.57/40.09  | End of split
% 228.57/40.09  | 
% 228.57/40.09  End of proof
% 228.57/40.09  
% 228.57/40.09  Sub-proof #542 shows that the following formulas are inconsistent:
% 228.57/40.09  ----------------------------------------------------------------
% 228.57/40.09    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.09         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.57/40.09    (2)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3)
% 228.57/40.09    (3)   ~ (e3 = e1)
% 228.57/40.09    (4)  all_57_3 = e0
% 228.57/40.09    (5)   ~ (e3 = e2)
% 228.57/40.09    (6)   ~ (e3 = e0)
% 228.57/40.09    (7)  all_57_1 = e0
% 228.57/40.09    (8)   ~ (e2 = e0)
% 228.57/40.09    (9)  all_57_2 = e3
% 228.57/40.09    (10)   ~ (e1 = e0)
% 228.57/40.09    (11)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.57/40.09          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.57/40.09    (12)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.09          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.57/40.09    (13)   ~ (e2 = e1)
% 228.57/40.09  
% 228.57/40.09  Begin of proof
% 228.57/40.09  | 
% 228.57/40.09  | BETA: splitting (2) gives:
% 228.57/40.09  | 
% 228.57/40.09  | Case 1:
% 228.57/40.09  | | 
% 228.57/40.09  | |   (14)  all_57_1 = e3 & op(e3, e2) = e3
% 228.57/40.09  | | 
% 228.57/40.09  | | ALPHA: (14) implies:
% 228.57/40.09  | |   (15)  all_57_1 = e3
% 228.57/40.09  | | 
% 228.57/40.09  | | COMBINE_EQS: (7), (15) imply:
% 228.57/40.09  | |   (16)  e3 = e0
% 228.57/40.09  | | 
% 228.57/40.09  | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13), (16)
% 228.57/40.09  | |            are inconsistent by sub-proof #1333.
% 228.57/40.09  | | 
% 228.57/40.09  | Case 2:
% 228.57/40.09  | | 
% 228.57/40.09  | |   (17)  all_57_3 = e3 & op(e2, e2) = e3
% 228.57/40.09  | | 
% 228.57/40.09  | | ALPHA: (17) implies:
% 228.57/40.09  | |   (18)  all_57_3 = e3
% 228.57/40.09  | | 
% 228.57/40.09  | | COMBINE_EQS: (4), (18) imply:
% 228.57/40.09  | |   (19)  e3 = e0
% 228.57/40.09  | | 
% 228.57/40.09  | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13), (19)
% 228.57/40.09  | |            are inconsistent by sub-proof #1333.
% 228.57/40.09  | | 
% 228.57/40.09  | End of split
% 228.57/40.09  | 
% 228.57/40.09  End of proof
% 228.57/40.09  
% 228.57/40.09  Sub-proof #543 shows that the following formulas are inconsistent:
% 228.57/40.09  ----------------------------------------------------------------
% 228.57/40.09    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.57/40.09    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.57/40.09    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.09         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.57/40.09    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.57/40.09         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.57/40.09    (5)   ~ (all_53_8 = all_53_12)
% 228.57/40.09    (6)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.09         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.09    (7)   ~ (e3 = e1)
% 228.57/40.09    (8)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.57/40.09         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.57/40.09    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.57/40.09           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.57/40.09    (10)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.57/40.09          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.57/40.09    (11)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.57/40.09            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.57/40.09              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.57/40.09    (12)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2)
% 228.57/40.09    (13)   ~ (all_6_2 = e3)
% 228.57/40.09    (14)  op(e1, e1) = all_6_2
% 228.57/40.09    (15)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.57/40.09    (16)   ~ (all_53_9 = e0)
% 228.57/40.09    (17)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.57/40.09          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.57/40.09    (18)   ~ (all_53_4 = all_53_12)
% 228.57/40.09    (19)   ~ (all_53_8 = all_53_9)
% 228.57/40.09    (20)  all_42_2 = all_6_2
% 228.57/40.09    (21)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.57/40.09          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.57/40.09    (22)   ~ (all_53_9 = all_6_2)
% 228.57/40.09    (23)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.57/40.09          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.09    (24)  all_57_3 = e0
% 228.57/40.09    (25)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.57/40.09          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.57/40.09    (26)   ~ (e3 = e2)
% 228.57/40.09    (27)  all_55_1 = all_53_4
% 228.57/40.09    (28)   ~ (e3 = e0)
% 228.57/40.09    (29)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.57/40.09          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.57/40.09    (30)   ~ (all_53_8 = all_6_2)
% 228.57/40.09    (31)  all_55_2 = all_53_8
% 228.57/40.09    (32)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.57/40.09    (33)  all_57_15 = e3
% 228.57/40.09    (34)  op(e3, e3) = e2
% 228.57/40.09    (35)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.57/40.09          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.57/40.09            e1)
% 228.57/40.09    (36)   ~ (all_53_4 = all_53_8)
% 228.57/40.09    (37)  op(e3, e2) = all_53_4
% 228.57/40.09    (38)   ~ (e2 = e0)
% 228.57/40.09    (39)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.57/40.09            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.57/40.09            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.57/40.09            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.57/40.09              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.57/40.09            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.57/40.09            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.57/40.09              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.57/40.09              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.57/40.09            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.57/40.09            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.57/40.09            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.57/40.09              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.57/40.09              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.57/40.09            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.57/40.09              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.57/40.09            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.57/40.09            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.57/40.09              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.57/40.09              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.57/40.09            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.57/40.09            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.57/40.09    (40)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.57/40.09          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.57/40.09    (41)   ~ (e1 = e0)
% 228.57/40.09    (42)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.57/40.09            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.57/40.09              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.57/40.09    (43)   ~ (all_53_4 = e0)
% 228.57/40.09    (44)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.57/40.09          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.57/40.09    (45)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.57/40.09          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.57/40.09    (46)  op(e0, e0) = e3
% 228.57/40.09    (47)   ~ (all_53_4 = all_53_6)
% 228.57/40.09    (48)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.09          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.57/40.09            e2)
% 228.57/40.09    (49)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.09              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.57/40.09                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.57/40.09                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.57/40.09    (50)  all_55_10 = all_6_2
% 228.57/40.09    (51)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.57/40.09          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.57/40.09    (52)  all_38_2 = all_6_2
% 228.57/40.09    (53)  all_55_3 = all_53_12
% 228.57/40.09    (54)   ~ (all_53_12 = e3)
% 228.57/40.09    (55)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.57/40.09            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.57/40.09              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.57/40.09    (56)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.09          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.57/40.09    (57)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.57/40.09          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.57/40.09    (58)   ~ (e2 = e1)
% 228.57/40.09    (59)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.57/40.09          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.57/40.09    (60)  op(e2, e1) = all_53_9
% 228.57/40.09    (61)  op(e1, e2) = all_53_6
% 228.57/40.09    (62)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.57/40.09          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.57/40.09    (63)  all_24_2 = all_6_2
% 228.57/40.09    (64)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.57/40.09          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.57/40.09    (65)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.57/40.09          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.57/40.09    (66)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.57/40.09          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.57/40.09    (67)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.57/40.09          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.57/40.09    (68)  op(e3, e1) = all_53_8
% 228.57/40.09    (69)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.09          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.57/40.09    (70)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.57/40.09          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.57/40.09    (71)  op(e3, e0) = all_53_12
% 228.57/40.09  
% 228.57/40.09  Begin of proof
% 228.57/40.09  | 
% 228.57/40.09  | BETA: splitting (12) gives:
% 228.57/40.09  | 
% 228.57/40.09  | Case 1:
% 228.57/40.09  | | 
% 228.57/40.09  | |   (72)  all_57_2 = e2 & op(e2, e3) = e2
% 228.57/40.09  | | 
% 228.57/40.09  | | ALPHA: (72) implies:
% 228.57/40.09  | |   (73)  all_57_2 = e2
% 228.57/40.09  | | 
% 228.57/40.09  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 228.57/40.09  | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 228.57/40.09  | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 228.57/40.09  | |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 228.57/40.09  | |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 228.57/40.09  | |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 228.57/40.09  | |            (69), (70), (71), (73) are inconsistent by sub-proof #544.
% 228.57/40.09  | | 
% 228.57/40.09  | Case 2:
% 228.57/40.09  | | 
% 228.57/40.09  | |   (74)  all_57_3 = e2 & op(e2, e2) = e2
% 228.57/40.09  | | 
% 228.57/40.09  | | REF_CLOSE: (24), (38), (74) are inconsistent by sub-proof #2103.
% 228.57/40.09  | | 
% 228.57/40.09  | End of split
% 228.57/40.09  | 
% 228.57/40.09  End of proof
% 228.57/40.09  
% 228.57/40.09  Sub-proof #544 shows that the following formulas are inconsistent:
% 228.57/40.09  ----------------------------------------------------------------
% 228.57/40.09    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.57/40.09    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.57/40.09    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.09         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.57/40.09    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.57/40.09         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.57/40.09    (5)   ~ (all_53_8 = all_53_12)
% 228.57/40.09    (6)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.09         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.09    (7)   ~ (e3 = e1)
% 228.57/40.09    (8)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.57/40.09         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.57/40.09    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.57/40.09           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.57/40.09    (10)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.57/40.09          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.57/40.09    (11)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.57/40.09            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.57/40.09              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.57/40.09    (12)   ~ (all_6_2 = e3)
% 228.57/40.09    (13)  op(e1, e1) = all_6_2
% 228.57/40.09    (14)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.57/40.09    (15)   ~ (all_53_9 = e0)
% 228.57/40.09    (16)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.57/40.09          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.57/40.09    (17)   ~ (all_53_4 = all_53_12)
% 228.57/40.09    (18)  all_57_2 = e2
% 228.57/40.09    (19)   ~ (all_53_8 = all_53_9)
% 228.57/40.09    (20)  all_42_2 = all_6_2
% 228.57/40.09    (21)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.57/40.09          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.57/40.09    (22)   ~ (all_53_9 = all_6_2)
% 228.57/40.09    (23)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.57/40.09          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.09    (24)  all_57_3 = e0
% 228.57/40.09    (25)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.57/40.09          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.57/40.09    (26)   ~ (e3 = e2)
% 228.57/40.09    (27)  all_55_1 = all_53_4
% 228.57/40.09    (28)   ~ (e3 = e0)
% 228.57/40.09    (29)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.57/40.09          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.57/40.09    (30)   ~ (all_53_8 = all_6_2)
% 228.57/40.09    (31)  all_55_2 = all_53_8
% 228.57/40.09    (32)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.57/40.09    (33)  all_57_15 = e3
% 228.57/40.09    (34)  op(e3, e3) = e2
% 228.57/40.09    (35)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.57/40.09          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.57/40.09            e1)
% 228.57/40.09    (36)   ~ (all_53_4 = all_53_8)
% 228.57/40.09    (37)  op(e3, e2) = all_53_4
% 228.57/40.09    (38)   ~ (e2 = e0)
% 228.57/40.09    (39)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.57/40.09            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.57/40.09            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.57/40.09            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.57/40.09              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.57/40.09            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.57/40.09            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.57/40.09              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.57/40.09              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.57/40.09            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.57/40.09            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.57/40.09            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.57/40.09              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.57/40.09              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.57/40.09            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.57/40.09              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.57/40.09            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.57/40.09            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.57/40.09              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.57/40.09              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.57/40.09            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.57/40.09            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.57/40.09    (40)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.57/40.09          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.57/40.09    (41)   ~ (e1 = e0)
% 228.57/40.09    (42)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.57/40.09            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.57/40.09              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.57/40.09    (43)   ~ (all_53_4 = e0)
% 228.57/40.09    (44)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.57/40.09          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.57/40.09    (45)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.57/40.09          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.57/40.09    (46)  op(e0, e0) = e3
% 228.57/40.09    (47)   ~ (all_53_4 = all_53_6)
% 228.57/40.09    (48)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.09          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.57/40.09            e2)
% 228.57/40.09    (49)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.09              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.57/40.09                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.57/40.09                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.57/40.09    (50)  all_55_10 = all_6_2
% 228.57/40.10    (51)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.57/40.10          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.57/40.10    (52)  all_38_2 = all_6_2
% 228.57/40.10    (53)  all_55_3 = all_53_12
% 228.57/40.10    (54)   ~ (all_53_12 = e3)
% 228.57/40.10    (55)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.57/40.10            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.57/40.10              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.57/40.10    (56)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.10          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.57/40.10    (57)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.57/40.10          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.57/40.10    (58)   ~ (e2 = e1)
% 228.57/40.10    (59)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.57/40.10          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.57/40.10    (60)  op(e2, e1) = all_53_9
% 228.57/40.10    (61)  op(e1, e2) = all_53_6
% 228.57/40.10    (62)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.57/40.10          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.57/40.10    (63)  all_24_2 = all_6_2
% 228.57/40.10    (64)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.57/40.10          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.57/40.10    (65)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.57/40.10          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.57/40.10    (66)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.57/40.10          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.57/40.10    (67)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.57/40.10          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.57/40.10    (68)  op(e3, e1) = all_53_8
% 228.57/40.10    (69)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.10          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.57/40.10    (70)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.57/40.10          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.57/40.10    (71)  op(e3, e0) = all_53_12
% 228.57/40.10  
% 228.57/40.10  Begin of proof
% 228.57/40.10  | 
% 228.57/40.10  | BETA: splitting (51) gives:
% 228.57/40.10  | 
% 228.57/40.10  | Case 1:
% 228.57/40.10  | | 
% 228.57/40.10  | |   (72)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 228.57/40.10  | |           e3)
% 228.57/40.10  | | 
% 228.57/40.10  | | BETA: splitting (72) gives:
% 228.57/40.10  | | 
% 228.57/40.10  | | Case 1:
% 228.57/40.10  | | | 
% 228.57/40.10  | | |   (73)  all_57_2 = e3 & op(e2, e3) = e3
% 228.57/40.10  | | | 
% 228.57/40.10  | | | ALPHA: (73) implies:
% 228.57/40.10  | | |   (74)  all_57_2 = e3
% 228.57/40.10  | | | 
% 228.57/40.10  | | | REF_CLOSE: (18), (26), (74) are inconsistent by sub-proof #1800.
% 228.57/40.10  | | | 
% 228.57/40.10  | | Case 2:
% 228.57/40.10  | | | 
% 228.57/40.10  | | |   (75)  all_57_3 = e3 & op(e2, e2) = e3
% 228.57/40.10  | | | 
% 228.57/40.10  | | | ALPHA: (75) implies:
% 228.57/40.10  | | |   (76)  all_57_3 = e3
% 228.57/40.10  | | | 
% 228.57/40.10  | | | REF_CLOSE: (24), (28), (76) are inconsistent by sub-proof #2358.
% 228.57/40.10  | | | 
% 228.57/40.10  | | End of split
% 228.57/40.10  | | 
% 228.57/40.10  | Case 2:
% 228.57/40.10  | | 
% 228.57/40.10  | |   (77)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 228.57/40.10  | |           e3)
% 228.57/40.10  | | 
% 228.57/40.10  | | BETA: splitting (77) gives:
% 228.57/40.10  | | 
% 228.57/40.10  | | Case 1:
% 228.57/40.10  | | | 
% 228.57/40.10  | | |   (78)  all_57_5 = e3 & op(e2, e1) = e3
% 228.57/40.10  | | | 
% 228.57/40.10  | | | ALPHA: (78) implies:
% 228.57/40.10  | | |   (79)  all_57_5 = e3
% 228.57/40.10  | | |   (80)  op(e2, e1) = e3
% 228.57/40.10  | | | 
% 228.57/40.10  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.57/40.10  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 228.57/40.10  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 228.57/40.10  | | |            (33), (34), (35), (36), (37), (38), (39), (41), (42), (43),
% 228.57/40.10  | | |            (46), (47), (48), (49), (50), (52), (53), (54), (55), (56),
% 228.57/40.10  | | |            (57), (58), (59), (60), (61), (62), (63), (64), (65), (66),
% 228.57/40.10  | | |            (67), (68), (69), (70), (71), (79), (80) are inconsistent by
% 228.57/40.10  | | |            sub-proof #554.
% 228.57/40.10  | | | 
% 228.57/40.10  | | Case 2:
% 228.57/40.10  | | | 
% 228.57/40.10  | | |   (81)  all_57_10 = e3 & op(e2, e0) = e3
% 228.57/40.10  | | | 
% 228.57/40.10  | | | ALPHA: (81) implies:
% 228.57/40.10  | | |   (82)  all_57_10 = e3
% 228.57/40.10  | | | 
% 228.57/40.10  | | | BETA: splitting (57) gives:
% 228.57/40.10  | | | 
% 228.57/40.10  | | | Case 1:
% 228.57/40.10  | | | | 
% 228.57/40.10  | | | |   (83)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3)
% 228.57/40.10  | | | |           = e3)
% 228.57/40.10  | | | | 
% 228.57/40.10  | | | | REF_CLOSE: (3), (4), (6), (7), (8), (9), (10), (12), (13), (16), (21),
% 228.57/40.10  | | | |            (23), (24), (25), (26), (28), (33), (35), (38), (41), (44),
% 228.57/40.10  | | | |            (45), (48), (49), (56), (57), (58), (59), (62), (64), (65),
% 228.57/40.10  | | | |            (66), (69), (82), (83) are inconsistent by sub-proof #553.
% 228.57/40.10  | | | | 
% 228.57/40.10  | | | Case 2:
% 228.57/40.10  | | | | 
% 228.57/40.10  | | | |   (84)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3)
% 228.57/40.10  | | | |           = e3)
% 228.57/40.10  | | | | 
% 228.57/40.10  | | | | BETA: splitting (84) gives:
% 228.57/40.10  | | | | 
% 228.57/40.10  | | | | Case 1:
% 228.57/40.10  | | | | | 
% 228.57/40.10  | | | | |   (85)  all_57_6 = e3 & op(e1, e3) = e3
% 228.57/40.10  | | | | | 
% 228.57/40.10  | | | | | REF_CLOSE: (3), (4), (6), (7), (8), (9), (10), (12), (13), (16), (18),
% 228.57/40.10  | | | | |            (21), (23), (24), (25), (26), (28), (33), (34), (35), (38),
% 228.57/40.10  | | | | |            (41), (44), (45), (48), (49), (56), (57), (58), (59), (62),
% 228.57/40.10  | | | | |            (64), (65), (66), (69), (82), (85) are inconsistent by
% 228.57/40.10  | | | | |            sub-proof #548.
% 228.57/40.10  | | | | | 
% 228.57/40.10  | | | | Case 2:
% 228.57/40.10  | | | | | 
% 228.57/40.10  | | | | |   (86)  all_57_12 = e3 & op(e0, e3) = e3
% 228.57/40.10  | | | | | 
% 228.57/40.10  | | | | | ALPHA: (86) implies:
% 228.57/40.10  | | | | |   (87)  all_57_12 = e3
% 228.57/40.10  | | | | | 
% 228.57/40.10  | | | | | BETA: splitting (44) gives:
% 228.57/40.10  | | | | | 
% 228.57/40.10  | | | | | Case 1:
% 228.57/40.10  | | | | | | 
% 228.57/40.10  | | | | | |   (88)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2,
% 228.57/40.10  | | | | | |             e1) = e3)
% 228.57/40.10  | | | | | | 
% 228.57/40.10  | | | | | | BETA: splitting (88) gives:
% 228.57/40.10  | | | | | | 
% 228.57/40.10  | | | | | | Case 1:
% 228.57/40.10  | | | | | | | 
% 228.57/40.10  | | | | | | |   (89)  all_57_4 = e3 & op(e3, e1) = e3
% 228.57/40.10  | | | | | | | 
% 228.57/40.10  | | | | | | | ALPHA: (89) implies:
% 228.57/40.10  | | | | | | |   (90)  all_57_4 = e3
% 228.57/40.10  | | | | | | | 
% 228.57/40.10  | | | | | | | BETA: splitting (65) gives:
% 228.57/40.10  | | | | | | | 
% 228.57/40.10  | | | | | | | Case 1:
% 228.57/40.10  | | | | | | | | 
% 228.57/40.10  | | | | | | | |   (91)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 &
% 228.57/40.10  | | | | | | | |           op(e2, e3) = e0)
% 228.57/40.10  | | | | | | | | 
% 228.57/40.10  | | | | | | | | REF_CLOSE: (3), (7), (9), (24), (26), (34), (38), (41), (56),
% 228.57/40.10  | | | | | | | |            (58), (82), (91) are inconsistent by sub-proof #552.
% 228.57/40.10  | | | | | | | | 
% 228.57/40.10  | | | | | | | Case 2:
% 228.57/40.10  | | | | | | | | 
% 228.57/40.10  | | | | | | | |   (92)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 &
% 228.57/40.10  | | | | | | | |           op(e0, e3) = e0)
% 228.57/40.10  | | | | | | | | 
% 228.57/40.10  | | | | | | | | BETA: splitting (92) gives:
% 228.57/40.10  | | | | | | | | 
% 228.57/40.10  | | | | | | | | Case 1:
% 228.57/40.10  | | | | | | | | | 
% 228.57/40.10  | | | | | | | | |   (93)  all_57_6 = e0 & op(e1, e3) = e0
% 228.57/40.10  | | | | | | | | | 
% 228.57/40.10  | | | | | | | | | ALPHA: (93) implies:
% 228.57/40.10  | | | | | | | | |   (94)  all_57_6 = e0
% 228.57/40.10  | | | | | | | | | 
% 228.57/40.10  | | | | | | | | | BETA: splitting (10) gives:
% 228.57/40.10  | | | | | | | | | 
% 228.57/40.10  | | | | | | | | | Case 1:
% 228.57/40.10  | | | | | | | | | | 
% 228.57/40.10  | | | | | | | | | |   (95)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 &
% 228.57/40.10  | | | | | | | | | |           op(e1, e2) = e3)
% 228.57/40.10  | | | | | | | | | | 
% 228.57/40.10  | | | | | | | | | | BETA: splitting (95) gives:
% 228.57/40.10  | | | | | | | | | | 
% 228.57/40.10  | | | | | | | | | | Case 1:
% 228.57/40.10  | | | | | | | | | | | 
% 228.57/40.10  | | | | | | | | | | |   (96)  all_57_6 = e3 & op(e1, e3) = e3
% 228.57/40.10  | | | | | | | | | | | 
% 228.57/40.10  | | | | | | | | | | | REF_CLOSE: (3), (4), (6), (7), (8), (9), (10), (12), (13),
% 228.57/40.10  | | | | | | | | | | |            (16), (18), (21), (23), (24), (25), (26), (28),
% 228.57/40.10  | | | | | | | | | | |            (33), (34), (35), (38), (41), (44), (45), (48),
% 228.57/40.10  | | | | | | | | | | |            (49), (56), (57), (58), (59), (62), (64), (65),
% 228.57/40.10  | | | | | | | | | | |            (66), (69), (82), (96) are inconsistent by
% 228.57/40.10  | | | | | | | | | | |            sub-proof #548.
% 228.57/40.10  | | | | | | | | | | | 
% 228.57/40.10  | | | | | | | | | | Case 2:
% 228.57/40.10  | | | | | | | | | | | 
% 228.57/40.10  | | | | | | | | | | |   (97)  all_57_7 = e3 & op(e1, e2) = e3
% 228.57/40.10  | | | | | | | | | | | 
% 228.57/40.10  | | | | | | | | | | | ALPHA: (97) implies:
% 228.57/40.10  | | | | | | | | | | |   (98)  all_57_7 = e3
% 228.57/40.10  | | | | | | | | | | | 
% 228.57/40.10  | | | | | | | | | | | BETA: splitting (59) gives:
% 228.57/40.10  | | | | | | | | | | | 
% 228.57/40.10  | | | | | | | | | | | Case 1:
% 228.57/40.10  | | | | | | | | | | | | 
% 228.57/40.10  | | | | | | | | | | | |   (99)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 228.57/40.10  | | | | | | | | | | | |           e2 & op(e2, e0) = e2)
% 228.57/40.10  | | | | | | | | | | | | 
% 228.57/40.10  | | | | | | | | | | | | BETA: splitting (99) gives:
% 228.57/40.10  | | | | | | | | | | | | 
% 228.57/40.10  | | | | | | | | | | | | Case 1:
% 228.57/40.10  | | | | | | | | | | | | | 
% 228.57/40.10  | | | | | | | | | | | | |   (100)  all_57_9 = e2 & op(e3, e0) = e2
% 228.57/40.10  | | | | | | | | | | | | | 
% 228.57/40.10  | | | | | | | | | | | | | ALPHA: (100) implies:
% 228.57/40.10  | | | | | | | | | | | | |   (101)  all_57_9 = e2
% 228.57/40.10  | | | | | | | | | | | | | 
% 228.57/40.10  | | | | | | | | | | | | | BETA: splitting (4) gives:
% 228.57/40.10  | | | | | | | | | | | | | 
% 228.57/40.10  | | | | | | | | | | | | | Case 1:
% 228.57/40.10  | | | | | | | | | | | | | | 
% 228.57/40.10  | | | | | | | | | | | | | |   (102)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 228.57/40.10  | | | | | | | | | | | | | |            & op(e2, e3) = e1)
% 228.57/40.10  | | | | | | | | | | | | | | 
% 228.57/40.10  | | | | | | | | | | | | | | REF_CLOSE: (9), (18), (26), (28), (33), (34), (38), (41),
% 228.57/40.10  | | | | | | | | | | | | | |            (49), (58), (59), (82), (101), (102) are
% 228.57/40.10  | | | | | | | | | | | | | |            inconsistent by sub-proof #551.
% 228.57/40.10  | | | | | | | | | | | | | | 
% 228.57/40.10  | | | | | | | | | | | | | Case 2:
% 228.57/40.10  | | | | | | | | | | | | | | 
% 228.57/40.10  | | | | | | | | | | | | | |   (103)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 228.57/40.10  | | | | | | | | | | | | | |            e1 & op(e0, e3) = e1)
% 228.57/40.10  | | | | | | | | | | | | | | 
% 228.57/40.10  | | | | | | | | | | | | | | BETA: splitting (103) gives:
% 228.57/40.10  | | | | | | | | | | | | | | 
% 228.57/40.10  | | | | | | | | | | | | | | Case 1:
% 228.57/40.10  | | | | | | | | | | | | | | | 
% 228.57/40.10  | | | | | | | | | | | | | | |   (104)  all_57_6 = e1 & op(e1, e3) = e1
% 228.57/40.10  | | | | | | | | | | | | | | | 
% 228.57/40.10  | | | | | | | | | | | | | | | REF_CLOSE: (41), (94), (104) are inconsistent by sub-proof
% 228.57/40.10  | | | | | | | | | | | | | | |            #2044.
% 228.57/40.10  | | | | | | | | | | | | | | | 
% 228.57/40.10  | | | | | | | | | | | | | | Case 2:
% 228.57/40.10  | | | | | | | | | | | | | | | 
% 228.57/40.10  | | | | | | | | | | | | | | |   (105)  all_57_12 = e1 & op(e0, e3) = e1
% 228.57/40.10  | | | | | | | | | | | | | | | 
% 228.57/40.10  | | | | | | | | | | | | | | | ALPHA: (105) implies:
% 228.57/40.10  | | | | | | | | | | | | | | |   (106)  all_57_12 = e1
% 228.57/40.10  | | | | | | | | | | | | | | | 
% 228.57/40.10  | | | | | | | | | | | | | | | REF_CLOSE: (7), (87), (106) are inconsistent by sub-proof
% 228.57/40.10  | | | | | | | | | | | | | | |            #2151.
% 228.57/40.10  | | | | | | | | | | | | | | | 
% 228.57/40.10  | | | | | | | | | | | | | | End of split
% 228.57/40.10  | | | | | | | | | | | | | | 
% 228.57/40.10  | | | | | | | | | | | | | End of split
% 228.57/40.10  | | | | | | | | | | | | | 
% 228.57/40.10  | | | | | | | | | | | | Case 2:
% 228.57/40.10  | | | | | | | | | | | | | 
% 228.57/40.10  | | | | | | | | | | | | |   (107)  all_57_10 = e2 & op(e2, e0) = e2
% 228.57/40.10  | | | | | | | | | | | | | 
% 228.57/40.10  | | | | | | | | | | | | | ALPHA: (107) implies:
% 228.57/40.10  | | | | | | | | | | | | |   (108)  all_57_10 = e2
% 228.57/40.10  | | | | | | | | | | | | | 
% 228.57/40.10  | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 228.57/40.10  | | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (19),
% 228.57/40.10  | | | | | | | | | | | | |            (20), (21), (22), (23), (24), (25), (26), (27),
% 228.57/40.10  | | | | | | | | | | | | |            (28), (29), (30), (31), (32), (33), (35), (36),
% 228.57/40.10  | | | | | | | | | | | | |            (37), (38), (39), (40), (41), (42), (43), (44),
% 228.57/40.10  | | | | | | | | | | | | |            (46), (47), (48), (49), (50), (52), (53), (54),
% 228.57/40.10  | | | | | | | | | | | | |            (55), (56), (58), (59), (60), (61), (62), (63),
% 228.57/40.10  | | | | | | | | | | | | |            (64), (65), (66), (67), (68), (69), (70), (71),
% 228.57/40.10  | | | | | | | | | | | | |            (82), (90), (98), (108) are inconsistent by
% 228.57/40.10  | | | | | | | | | | | | |            sub-proof #545.
% 228.57/40.10  | | | | | | | | | | | | | 
% 228.57/40.10  | | | | | | | | | | | | End of split
% 228.57/40.10  | | | | | | | | | | | | 
% 228.57/40.10  | | | | | | | | | | | Case 2:
% 228.57/40.10  | | | | | | | | | | | | 
% 228.57/40.10  | | | | | | | | | | | |   (109)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 228.57/40.10  | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 228.57/40.10  | | | | | | | | | | | | 
% 228.57/40.10  | | | | | | | | | | | | BETA: splitting (109) gives:
% 228.57/40.10  | | | | | | | | | | | | 
% 228.57/40.10  | | | | | | | | | | | | Case 1:
% 228.57/40.10  | | | | | | | | | | | | | 
% 228.57/40.10  | | | | | | | | | | | | |   (110)  all_57_11 = e2 & op(e1, e0) = e2
% 228.57/40.10  | | | | | | | | | | | | | 
% 228.57/40.10  | | | | | | | | | | | | | ALPHA: (110) implies:
% 228.57/40.10  | | | | | | | | | | | | |   (111)  all_57_11 = e2
% 228.57/40.10  | | | | | | | | | | | | | 
% 228.57/40.10  | | | | | | | | | | | | | REF_CLOSE: (7), (26), (28), (33), (38), (41), (49), (58),
% 228.57/40.10  | | | | | | | | | | | | |            (59), (66), (82), (111) are inconsistent by
% 228.57/40.10  | | | | | | | | | | | | |            sub-proof #1983.
% 228.57/40.10  | | | | | | | | | | | | | 
% 228.57/40.10  | | | | | | | | | | | | Case 2:
% 228.57/40.10  | | | | | | | | | | | | | 
% 228.57/40.10  | | | | | | | | | | | | |   (112)  all_57_15 = e2 & op(e0, e0) = e2
% 228.57/40.10  | | | | | | | | | | | | | 
% 228.57/40.10  | | | | | | | | | | | | | ALPHA: (112) implies:
% 228.57/40.10  | | | | | | | | | | | | |   (113)  all_57_15 = e2
% 228.57/40.10  | | | | | | | | | | | | | 
% 228.57/40.10  | | | | | | | | | | | | | COMBINE_EQS: (33), (113) imply:
% 228.57/40.10  | | | | | | | | | | | | |   (114)  e3 = e2
% 228.57/40.10  | | | | | | | | | | | | | 
% 228.57/40.10  | | | | | | | | | | | | | COMBINE_EQS: (90), (114) imply:
% 228.57/40.10  | | | | | | | | | | | | |   (115)  all_57_4 = e2
% 228.57/40.10  | | | | | | | | | | | | | 
% 228.57/40.10  | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 228.57/40.10  | | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (19),
% 228.57/40.10  | | | | | | | | | | | | |            (20), (21), (22), (23), (24), (25), (26), (27),
% 228.57/40.10  | | | | | | | | | | | | |            (28), (29), (30), (31), (32), (33), (35), (36),
% 228.57/40.10  | | | | | | | | | | | | |            (37), (38), (39), (40), (41), (42), (43), (44),
% 228.57/40.10  | | | | | | | | | | | | |            (46), (47), (48), (49), (50), (52), (53), (54),
% 228.57/40.10  | | | | | | | | | | | | |            (55), (56), (58), (59), (60), (61), (62), (63),
% 228.57/40.10  | | | | | | | | | | | | |            (64), (65), (66), (67), (68), (69), (70), (71),
% 228.57/40.10  | | | | | | | | | | | | |            (98), (115) are inconsistent by sub-proof #546.
% 228.57/40.10  | | | | | | | | | | | | | 
% 228.57/40.10  | | | | | | | | | | | | End of split
% 228.57/40.10  | | | | | | | | | | | | 
% 228.57/40.10  | | | | | | | | | | | End of split
% 228.57/40.10  | | | | | | | | | | | 
% 228.57/40.10  | | | | | | | | | | End of split
% 228.57/40.10  | | | | | | | | | | 
% 228.57/40.10  | | | | | | | | | Case 2:
% 228.57/40.10  | | | | | | | | | | 
% 228.57/40.10  | | | | | | | | | |   (116)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3
% 228.57/40.10  | | | | | | | | | |            & op(e1, e0) = e3)
% 228.57/40.10  | | | | | | | | | | 
% 228.57/40.10  | | | | | | | | | | REF_CLOSE: (7), (9), (12), (13), (26), (28), (33), (38),
% 228.57/40.10  | | | | | | | | | |            (41), (49), (58), (59), (66), (82), (116) are
% 228.57/40.10  | | | | | | | | | |            inconsistent by sub-proof #1417.
% 228.57/40.10  | | | | | | | | | | 
% 228.57/40.10  | | | | | | | | | End of split
% 228.57/40.10  | | | | | | | | | 
% 228.57/40.10  | | | | | | | | Case 2:
% 228.57/40.10  | | | | | | | | | 
% 228.57/40.10  | | | | | | | | |   (117)  all_57_12 = e0 & op(e0, e3) = e0
% 228.57/40.10  | | | | | | | | | 
% 228.57/40.10  | | | | | | | | | ALPHA: (117) implies:
% 228.57/40.10  | | | | | | | | |   (118)  all_57_12 = e0
% 228.57/40.10  | | | | | | | | | 
% 228.57/40.10  | | | | | | | | | REF_CLOSE: (28), (87), (118) are inconsistent by sub-proof
% 228.57/40.10  | | | | | | | | |            #2153.
% 228.57/40.10  | | | | | | | | | 
% 228.57/40.10  | | | | | | | | End of split
% 228.57/40.10  | | | | | | | | 
% 228.57/40.10  | | | | | | | End of split
% 228.57/40.10  | | | | | | | 
% 228.57/40.10  | | | | | | Case 2:
% 228.57/40.10  | | | | | | | 
% 228.57/40.10  | | | | | | |   (119)  all_57_5 = e3 & op(e2, e1) = e3
% 228.57/40.10  | | | | | | | 
% 228.57/40.10  | | | | | | | ALPHA: (119) implies:
% 228.57/40.10  | | | | | | |   (120)  all_57_5 = e3
% 228.57/40.10  | | | | | | | 
% 228.57/40.10  | | | | | | | REF_CLOSE: (3), (4), (7), (9), (18), (24), (26), (28), (34), (38),
% 228.57/40.10  | | | | | | |            (41), (56), (58), (65), (87), (120) are inconsistent by
% 228.57/40.10  | | | | | | |            sub-proof #1576.
% 228.57/40.10  | | | | | | | 
% 228.57/40.10  | | | | | | End of split
% 228.57/40.10  | | | | | | 
% 228.57/40.10  | | | | | Case 2:
% 228.57/40.10  | | | | | | 
% 228.57/40.10  | | | | | |   (121)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 &
% 228.57/40.10  | | | | | |            op(e0, e1) = e3)
% 228.57/40.10  | | | | | | 
% 228.57/40.10  | | | | | | REF_CLOSE: (7), (9), (12), (13), (26), (28), (33), (35), (38), (41),
% 228.57/40.10  | | | | | |            (48), (49), (58), (121) are inconsistent by sub-proof
% 228.57/40.10  | | | | | |            #1794.
% 228.57/40.10  | | | | | | 
% 228.57/40.10  | | | | | End of split
% 228.57/40.10  | | | | | 
% 228.57/40.10  | | | | End of split
% 228.57/40.10  | | | | 
% 228.57/40.10  | | | End of split
% 228.57/40.10  | | | 
% 228.57/40.10  | | End of split
% 228.57/40.10  | | 
% 228.57/40.10  | End of split
% 228.57/40.10  | 
% 228.57/40.10  End of proof
% 228.57/40.10  
% 228.57/40.10  Sub-proof #545 shows that the following formulas are inconsistent:
% 228.57/40.10  ----------------------------------------------------------------
% 228.57/40.10    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.57/40.10    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.57/40.10    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.10         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.57/40.10    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.57/40.10         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.57/40.10    (5)   ~ (all_53_8 = all_53_12)
% 228.57/40.10    (6)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.10         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.10    (7)   ~ (e3 = e1)
% 228.57/40.10    (8)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.57/40.10         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.57/40.10    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.57/40.10           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.57/40.10    (10)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.57/40.10          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.57/40.10    (11)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.57/40.10            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.57/40.10              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.57/40.10    (12)   ~ (all_6_2 = e3)
% 228.57/40.10    (13)  op(e1, e1) = all_6_2
% 228.57/40.10    (14)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.57/40.10    (15)   ~ (all_53_9 = e0)
% 228.57/40.10    (16)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.57/40.10          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.57/40.10    (17)   ~ (all_53_4 = all_53_12)
% 228.57/40.10    (18)   ~ (all_53_8 = all_53_9)
% 228.57/40.10    (19)  all_42_2 = all_6_2
% 228.57/40.10    (20)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.57/40.10          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.57/40.10    (21)   ~ (all_53_9 = all_6_2)
% 228.57/40.10    (22)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.57/40.10          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.10    (23)  all_57_3 = e0
% 228.57/40.10    (24)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.57/40.10          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.57/40.10    (25)  all_57_4 = e3
% 228.57/40.10    (26)   ~ (e3 = e2)
% 228.57/40.10    (27)  all_55_1 = all_53_4
% 228.57/40.10    (28)   ~ (e3 = e0)
% 228.57/40.10    (29)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.57/40.10          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.57/40.10    (30)   ~ (all_53_8 = all_6_2)
% 228.57/40.10    (31)  all_55_2 = all_53_8
% 228.57/40.10    (32)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.57/40.10    (33)  all_57_15 = e3
% 228.57/40.10    (34)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.57/40.10          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.57/40.10            e1)
% 228.57/40.10    (35)  all_57_10 = e2
% 228.57/40.10    (36)   ~ (all_53_4 = all_53_8)
% 228.57/40.10    (37)  op(e3, e2) = all_53_4
% 228.57/40.10    (38)   ~ (e2 = e0)
% 228.57/40.10    (39)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.57/40.10            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.57/40.10            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.57/40.10            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.57/40.10              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.57/40.10            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.57/40.10            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.57/40.10              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.57/40.10              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.57/40.10            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.57/40.10            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.57/40.10            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.57/40.10              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.57/40.10              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.57/40.10            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.57/40.10              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.57/40.10            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.57/40.10            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.57/40.10              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.57/40.10              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.57/40.10            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.57/40.10            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.57/40.10    (40)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.57/40.10          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.57/40.10    (41)   ~ (e1 = e0)
% 228.57/40.10    (42)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.57/40.10            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.57/40.10              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.57/40.10    (43)   ~ (all_53_4 = e0)
% 228.57/40.10    (44)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.57/40.10          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.57/40.10    (45)  all_57_10 = e3
% 228.57/40.10    (46)  op(e0, e0) = e3
% 228.57/40.10    (47)   ~ (all_53_4 = all_53_6)
% 228.57/40.10    (48)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.10          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.57/40.10            e2)
% 228.57/40.10    (49)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.10              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.57/40.10                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.57/40.10                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.57/40.10    (50)  all_55_10 = all_6_2
% 228.57/40.10    (51)  all_38_2 = all_6_2
% 228.57/40.10    (52)  all_55_3 = all_53_12
% 228.57/40.10    (53)   ~ (all_53_12 = e3)
% 228.57/40.10    (54)  all_57_7 = e3
% 228.57/40.10    (55)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.57/40.10            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.57/40.10              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.57/40.10    (56)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.10          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.57/40.10    (57)   ~ (e2 = e1)
% 228.57/40.10    (58)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.57/40.10          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.57/40.10    (59)  op(e2, e1) = all_53_9
% 228.57/40.10    (60)  op(e1, e2) = all_53_6
% 228.57/40.10    (61)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.57/40.10          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.57/40.10    (62)  all_24_2 = all_6_2
% 228.57/40.10    (63)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.57/40.10          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.57/40.10    (64)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.57/40.10          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.57/40.10    (65)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.57/40.10          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.57/40.10    (66)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.57/40.10          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.57/40.10    (67)  op(e3, e1) = all_53_8
% 228.57/40.10    (68)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.10          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.57/40.10    (69)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.57/40.10          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.57/40.10    (70)  op(e3, e0) = all_53_12
% 228.57/40.10  
% 228.57/40.10  Begin of proof
% 228.57/40.10  | 
% 228.57/40.10  | COMBINE_EQS: (35), (45) imply:
% 228.57/40.10  |   (71)  e3 = e2
% 228.57/40.10  | 
% 228.57/40.10  | SIMP: (71) implies:
% 228.57/40.10  |   (72)  e3 = e2
% 228.57/40.10  | 
% 228.57/40.10  | COMBINE_EQS: (25), (72) imply:
% 228.57/40.10  |   (73)  all_57_4 = e2
% 228.57/40.10  | 
% 228.57/40.10  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.57/40.10  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 228.57/40.10  |            (24), (26), (27), (28), (29), (30), (31), (32), (33), (34), (36),
% 228.57/40.10  |            (37), (38), (39), (40), (41), (42), (43), (44), (46), (47), (48),
% 228.57/40.10  |            (49), (50), (51), (52), (53), (54), (55), (56), (57), (58), (59),
% 228.57/40.10  |            (60), (61), (62), (63), (64), (65), (66), (67), (68), (69), (70),
% 228.57/40.10  |            (73) are inconsistent by sub-proof #546.
% 228.57/40.10  | 
% 228.57/40.10  End of proof
% 228.57/40.10  
% 228.57/40.10  Sub-proof #546 shows that the following formulas are inconsistent:
% 228.57/40.10  ----------------------------------------------------------------
% 228.57/40.10    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.57/40.10    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.57/40.10    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.10         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.57/40.10    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.57/40.10         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.57/40.10    (5)   ~ (all_53_8 = all_53_12)
% 228.57/40.10    (6)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.10         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.10    (7)   ~ (e3 = e1)
% 228.57/40.10    (8)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.57/40.10         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.57/40.10    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.57/40.10           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.57/40.10    (10)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.57/40.10          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.57/40.10    (11)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.57/40.10            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.57/40.10              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.57/40.10    (12)   ~ (all_6_2 = e3)
% 228.57/40.10    (13)  op(e1, e1) = all_6_2
% 228.57/40.10    (14)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.57/40.10    (15)  all_57_4 = e2
% 228.57/40.10    (16)   ~ (all_53_9 = e0)
% 228.57/40.10    (17)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.57/40.10          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.57/40.10    (18)   ~ (all_53_4 = all_53_12)
% 228.57/40.10    (19)   ~ (all_53_8 = all_53_9)
% 228.57/40.10    (20)  all_42_2 = all_6_2
% 228.57/40.10    (21)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.57/40.10          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.57/40.10    (22)   ~ (all_53_9 = all_6_2)
% 228.57/40.10    (23)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.57/40.10          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.10    (24)  all_57_3 = e0
% 228.57/40.10    (25)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.57/40.10          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.57/40.10    (26)   ~ (e3 = e2)
% 228.57/40.10    (27)  all_55_1 = all_53_4
% 228.57/40.10    (28)   ~ (e3 = e0)
% 228.57/40.10    (29)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.57/40.10          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.57/40.10    (30)   ~ (all_53_8 = all_6_2)
% 228.57/40.10    (31)  all_55_2 = all_53_8
% 228.57/40.10    (32)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.57/40.10    (33)  all_57_15 = e3
% 228.57/40.10    (34)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.57/40.10          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.57/40.10            e1)
% 228.57/40.10    (35)   ~ (all_53_4 = all_53_8)
% 228.57/40.10    (36)  op(e3, e2) = all_53_4
% 228.57/40.10    (37)   ~ (e2 = e0)
% 228.57/40.11    (38)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.57/40.11            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.57/40.11            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.57/40.11            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.57/40.11              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.57/40.11            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.57/40.11            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.57/40.11              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.57/40.11              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.57/40.11            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.57/40.11            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.57/40.11            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.57/40.11              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.57/40.11              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.57/40.11            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.57/40.11              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.57/40.11            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.57/40.11            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.57/40.11              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.57/40.11              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.57/40.11            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.57/40.11            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.57/40.11    (39)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.57/40.11          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.57/40.11    (40)   ~ (e1 = e0)
% 228.57/40.11    (41)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.57/40.11            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.57/40.11              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.57/40.11    (42)   ~ (all_53_4 = e0)
% 228.57/40.11    (43)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.57/40.11          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.57/40.11    (44)  op(e0, e0) = e3
% 228.57/40.11    (45)   ~ (all_53_4 = all_53_6)
% 228.57/40.11    (46)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.11          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.57/40.11            e2)
% 228.57/40.11    (47)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.11              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.57/40.11                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.57/40.11                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.57/40.11    (48)  all_55_10 = all_6_2
% 228.57/40.11    (49)  all_38_2 = all_6_2
% 228.57/40.11    (50)  all_55_3 = all_53_12
% 228.57/40.11    (51)   ~ (all_53_12 = e3)
% 228.57/40.11    (52)  all_57_7 = e3
% 228.57/40.11    (53)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.57/40.11            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.57/40.11              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.57/40.11    (54)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.11          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.57/40.11    (55)   ~ (e2 = e1)
% 228.57/40.11    (56)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.57/40.11          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.57/40.11    (57)  op(e2, e1) = all_53_9
% 228.57/40.11    (58)  op(e1, e2) = all_53_6
% 228.57/40.11    (59)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.57/40.11          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.57/40.11    (60)  all_24_2 = all_6_2
% 228.57/40.11    (61)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.57/40.11          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.57/40.11    (62)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.57/40.11          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.57/40.11    (63)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.57/40.11          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.57/40.11    (64)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.57/40.11          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.57/40.11    (65)  op(e3, e1) = all_53_8
% 228.57/40.11    (66)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.11          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.57/40.11    (67)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.57/40.11          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.57/40.11    (68)  op(e3, e0) = all_53_12
% 228.57/40.11  
% 228.57/40.11  Begin of proof
% 228.57/40.11  | 
% 228.57/40.11  | BETA: splitting (43) gives:
% 228.57/40.11  | 
% 228.57/40.11  | Case 1:
% 228.57/40.11  | | 
% 228.57/40.11  | |   (69)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) =
% 228.57/40.11  | |           e3)
% 228.57/40.11  | | 
% 228.57/40.11  | | BETA: splitting (69) gives:
% 228.57/40.11  | | 
% 228.57/40.11  | | Case 1:
% 228.57/40.11  | | | 
% 228.57/40.11  | | |   (70)  all_57_4 = e3 & op(e3, e1) = e3
% 228.57/40.11  | | | 
% 228.57/40.11  | | | REF_CLOSE: (15), (26), (70) are inconsistent by sub-proof #877.
% 228.57/40.11  | | | 
% 228.57/40.11  | | Case 2:
% 228.57/40.11  | | | 
% 228.57/40.11  | | |   (71)  all_57_5 = e3 & op(e2, e1) = e3
% 228.57/40.11  | | | 
% 228.57/40.11  | | | ALPHA: (71) implies:
% 228.57/40.11  | | |   (72)  all_57_5 = e3
% 228.57/40.11  | | |   (73)  op(e2, e1) = e3
% 228.57/40.11  | | | 
% 228.57/40.11  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.57/40.11  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 228.57/40.11  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 228.57/40.11  | | |            (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 228.57/40.11  | | |            (44), (45), (46), (47), (48), (49), (50), (51), (52), (53),
% 228.57/40.11  | | |            (54), (55), (56), (57), (58), (59), (60), (61), (62), (63),
% 228.57/40.11  | | |            (64), (65), (66), (67), (68), (72), (73) are inconsistent by
% 228.57/40.11  | | |            sub-proof #547.
% 228.57/40.11  | | | 
% 228.57/40.11  | | End of split
% 228.57/40.11  | | 
% 228.57/40.11  | Case 2:
% 228.57/40.11  | | 
% 228.57/40.11  | |   (74)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) =
% 228.57/40.11  | |           e3)
% 228.57/40.11  | | 
% 228.57/40.11  | | REF_CLOSE: (7), (9), (12), (13), (26), (28), (33), (34), (37), (40), (46),
% 228.57/40.11  | |            (47), (55), (74) are inconsistent by sub-proof #1794.
% 228.57/40.11  | | 
% 228.57/40.11  | End of split
% 228.57/40.11  | 
% 228.57/40.11  End of proof
% 228.57/40.11  
% 228.57/40.11  Sub-proof #547 shows that the following formulas are inconsistent:
% 228.57/40.11  ----------------------------------------------------------------
% 228.57/40.11    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.57/40.11    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.57/40.11    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.11         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.57/40.11    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.57/40.11         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.57/40.11    (5)  op(e2, e1) = e3
% 228.57/40.11    (6)   ~ (all_53_8 = all_53_12)
% 228.57/40.11    (7)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.11         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.11    (8)   ~ (e3 = e1)
% 228.57/40.11    (9)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.57/40.11         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.57/40.11    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.57/40.11            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.57/40.11    (11)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.57/40.11          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.57/40.11    (12)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.57/40.11            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.57/40.11              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.57/40.11    (13)   ~ (all_6_2 = e3)
% 228.57/40.11    (14)  op(e1, e1) = all_6_2
% 228.57/40.11    (15)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.57/40.11    (16)  all_57_4 = e2
% 228.57/40.11    (17)   ~ (all_53_9 = e0)
% 228.57/40.11    (18)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.57/40.11          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.57/40.11    (19)   ~ (all_53_4 = all_53_12)
% 228.57/40.11    (20)   ~ (all_53_8 = all_53_9)
% 228.57/40.11    (21)  all_42_2 = all_6_2
% 228.57/40.11    (22)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.57/40.11          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.57/40.11    (23)   ~ (all_53_9 = all_6_2)
% 228.57/40.11    (24)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.57/40.11          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.11    (25)  all_57_3 = e0
% 228.57/40.11    (26)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.57/40.11          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.57/40.11    (27)   ~ (e3 = e2)
% 228.57/40.11    (28)  all_55_1 = all_53_4
% 228.57/40.11    (29)   ~ (e3 = e0)
% 228.57/40.11    (30)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.57/40.11          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.57/40.11    (31)   ~ (all_53_8 = all_6_2)
% 228.57/40.11    (32)  all_55_2 = all_53_8
% 228.57/40.11    (33)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.57/40.11    (34)  all_57_15 = e3
% 228.57/40.11    (35)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.57/40.11          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.57/40.11            e1)
% 228.57/40.11    (36)  all_57_5 = e3
% 228.57/40.11    (37)   ~ (all_53_4 = all_53_8)
% 228.57/40.11    (38)  op(e3, e2) = all_53_4
% 228.57/40.11    (39)   ~ (e2 = e0)
% 228.57/40.11    (40)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.57/40.11            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.57/40.11            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.57/40.11            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.57/40.11              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.57/40.11            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.57/40.11            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.57/40.11              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.57/40.11              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.57/40.11            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.57/40.11            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.57/40.11            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.57/40.11              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.57/40.11              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.57/40.11            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.57/40.11              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.57/40.11            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.57/40.11            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.57/40.11              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.57/40.11              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.57/40.11            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.57/40.11            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.57/40.11    (41)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.57/40.11          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.57/40.11    (42)   ~ (e1 = e0)
% 228.57/40.11    (43)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.57/40.11            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.57/40.11              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.57/40.11    (44)   ~ (all_53_4 = e0)
% 228.57/40.11    (45)  op(e0, e0) = e3
% 228.57/40.11    (46)   ~ (all_53_4 = all_53_6)
% 228.57/40.11    (47)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.11          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.57/40.11            e2)
% 228.57/40.11    (48)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.11              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.57/40.11                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.57/40.11                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.57/40.11    (49)  all_55_10 = all_6_2
% 228.57/40.11    (50)  all_38_2 = all_6_2
% 228.57/40.11    (51)  all_55_3 = all_53_12
% 228.57/40.11    (52)   ~ (all_53_12 = e3)
% 228.57/40.11    (53)  all_57_7 = e3
% 228.57/40.11    (54)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.57/40.11            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.57/40.11              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.57/40.11    (55)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.11          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.57/40.11    (56)   ~ (e2 = e1)
% 228.57/40.11    (57)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.57/40.11          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.57/40.11    (58)  op(e2, e1) = all_53_9
% 228.57/40.11    (59)  op(e1, e2) = all_53_6
% 228.57/40.11    (60)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.57/40.11          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.57/40.11    (61)  all_24_2 = all_6_2
% 228.57/40.11    (62)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.57/40.11          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.57/40.11    (63)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.57/40.11          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.57/40.11    (64)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.57/40.11          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.57/40.11    (65)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.57/40.11          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.57/40.11    (66)  op(e3, e1) = all_53_8
% 228.57/40.11    (67)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.11          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.57/40.11    (68)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.57/40.11          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.57/40.11    (69)  op(e3, e0) = all_53_12
% 228.57/40.11  
% 228.57/40.11  Begin of proof
% 228.57/40.11  | 
% 228.57/40.11  | BETA: splitting (41) gives:
% 228.57/40.11  | 
% 228.57/40.11  | Case 1:
% 228.57/40.11  | | 
% 228.57/40.11  | |   (70)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) =
% 228.57/40.11  | |           e3)
% 228.57/40.11  | | 
% 228.57/40.11  | | BETA: splitting (70) gives:
% 228.57/40.11  | | 
% 228.57/40.11  | | Case 1:
% 228.57/40.11  | | | 
% 228.57/40.11  | | |   (71)  all_57_0 = e3 & op(e3, e3) = e3
% 228.57/40.11  | | | 
% 228.57/40.11  | | | ALPHA: (71) implies:
% 228.57/40.11  | | |   (72)  all_57_0 = e3
% 228.57/40.11  | | |   (73)  op(e3, e3) = e3
% 228.57/40.11  | | | 
% 228.57/40.11  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.57/40.11  | | |            (13), (14), (15), (17), (18), (19), (20), (21), (22), (23),
% 228.57/40.11  | | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 228.57/40.11  | | |            (34), (35), (36), (37), (38), (39), (40), (42), (43), (44),
% 228.57/40.11  | | |            (45), (46), (47), (48), (49), (50), (51), (52), (54), (55),
% 228.57/40.11  | | |            (56), (57), (58), (59), (60), (61), (62), (63), (64), (65),
% 228.57/40.11  | | |            (66), (67), (68), (69), (72), (73) are inconsistent by
% 228.57/40.11  | | |            sub-proof #1440.
% 228.57/40.11  | | | 
% 228.57/40.11  | | Case 2:
% 228.57/40.11  | | | 
% 228.57/40.11  | | |   (74)  all_57_1 = e3 & op(e3, e2) = e3
% 228.57/40.11  | | | 
% 228.57/40.11  | | | ALPHA: (74) implies:
% 228.57/40.11  | | |   (75)  all_57_1 = e3
% 228.57/40.11  | | | 
% 228.57/40.11  | | | REF_CLOSE: (7), (8), (25), (27), (39), (42), (53), (56), (67), (75) are
% 228.57/40.11  | | |            inconsistent by sub-proof #1778.
% 228.57/40.11  | | | 
% 228.57/40.11  | | End of split
% 228.57/40.11  | | 
% 228.57/40.11  | Case 2:
% 228.57/40.11  | | 
% 228.57/40.11  | |   (76)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) =
% 228.57/40.11  | |           e3)
% 228.57/40.11  | | 
% 228.57/40.11  | | REF_CLOSE: (10), (16), (27), (52), (69), (76) are inconsistent by sub-proof
% 228.57/40.11  | |            #876.
% 228.57/40.11  | | 
% 228.57/40.11  | End of split
% 228.57/40.11  | 
% 228.57/40.11  End of proof
% 228.57/40.11  
% 228.57/40.11  Sub-proof #548 shows that the following formulas are inconsistent:
% 228.57/40.11  ----------------------------------------------------------------
% 228.57/40.11    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.11         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.57/40.11    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.57/40.11         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.57/40.11    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.11         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.11    (4)   ~ (e3 = e1)
% 228.57/40.11    (5)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.57/40.11         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.57/40.11    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.57/40.11           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.57/40.11    (7)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.57/40.11         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.57/40.11    (8)   ~ (all_6_2 = e3)
% 228.57/40.11    (9)  op(e1, e1) = all_6_2
% 228.57/40.11    (10)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.57/40.11          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.57/40.11    (11)  all_57_2 = e2
% 228.57/40.11    (12)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.57/40.11          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.57/40.11    (13)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.57/40.11          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.11    (14)  all_57_3 = e0
% 228.57/40.11    (15)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.57/40.11          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.57/40.11    (16)   ~ (e3 = e2)
% 228.57/40.11    (17)   ~ (e3 = e0)
% 228.57/40.11    (18)  all_57_15 = e3
% 228.57/40.11    (19)  op(e3, e3) = e2
% 228.57/40.11    (20)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.57/40.11          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.57/40.11            e1)
% 228.57/40.11    (21)   ~ (e2 = e0)
% 228.57/40.11    (22)   ~ (e1 = e0)
% 228.57/40.11    (23)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.57/40.11          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.57/40.11    (24)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.57/40.11          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.57/40.11    (25)  all_57_10 = e3
% 228.57/40.11    (26)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.11          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.57/40.11            e2)
% 228.57/40.11    (27)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.11              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.57/40.11                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.57/40.11                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.57/40.11    (28)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.11          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.57/40.11    (29)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.57/40.11          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.57/40.11    (30)   ~ (e2 = e1)
% 228.57/40.11    (31)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.57/40.11          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.57/40.11    (32)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.57/40.11          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.57/40.11    (33)  all_57_6 = e3 & op(e1, e3) = e3
% 228.57/40.11    (34)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.57/40.11          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.57/40.11    (35)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.57/40.11          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.57/40.11    (36)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.57/40.11          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.57/40.11    (37)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.11          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.57/40.11  
% 228.57/40.11  Begin of proof
% 228.57/40.11  | 
% 228.57/40.11  | ALPHA: (33) implies:
% 228.57/40.11  |   (38)  all_57_6 = e3
% 228.57/40.11  | 
% 228.57/40.11  | BETA: splitting (35) gives:
% 228.57/40.11  | 
% 228.57/40.11  | Case 1:
% 228.57/40.11  | | 
% 228.57/40.11  | |   (39)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) =
% 228.57/40.11  | |           e0)
% 228.57/40.11  | | 
% 228.57/40.11  | | REF_CLOSE: (1), (4), (6), (14), (16), (19), (21), (22), (25), (28), (30),
% 228.57/40.11  | |            (39) are inconsistent by sub-proof #552.
% 228.57/40.11  | | 
% 228.57/40.11  | Case 2:
% 228.57/40.11  | | 
% 228.57/40.11  | |   (40)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) =
% 228.57/40.11  | |           e0)
% 228.57/40.11  | | 
% 228.57/40.11  | | BETA: splitting (40) gives:
% 228.57/40.11  | | 
% 228.57/40.11  | | Case 1:
% 228.57/40.11  | | | 
% 228.57/40.11  | | |   (41)  all_57_6 = e0 & op(e1, e3) = e0
% 228.57/40.11  | | | 
% 228.57/40.11  | | | ALPHA: (41) implies:
% 228.57/40.11  | | |   (42)  all_57_6 = e0
% 228.57/40.11  | | | 
% 228.57/40.11  | | | REF_CLOSE: (17), (38), (42) are inconsistent by sub-proof #1822.
% 228.57/40.11  | | | 
% 228.57/40.11  | | Case 2:
% 228.57/40.11  | | | 
% 228.57/40.11  | | |   (43)  all_57_12 = e0 & op(e0, e3) = e0
% 228.57/40.11  | | | 
% 228.57/40.11  | | | ALPHA: (43) implies:
% 228.57/40.11  | | |   (44)  all_57_12 = e0
% 228.57/40.11  | | | 
% 228.57/40.11  | | | BETA: splitting (31) gives:
% 228.57/40.11  | | | 
% 228.57/40.11  | | | Case 1:
% 228.57/40.11  | | | | 
% 228.57/40.11  | | | |   (45)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0)
% 228.57/40.11  | | | |           = e2)
% 228.57/40.11  | | | | 
% 228.57/40.11  | | | | BETA: splitting (45) gives:
% 228.57/40.11  | | | | 
% 228.57/40.11  | | | | Case 1:
% 228.57/40.11  | | | | | 
% 228.57/40.11  | | | | |   (46)  all_57_9 = e2 & op(e3, e0) = e2
% 228.57/40.11  | | | | | 
% 228.57/40.11  | | | | | ALPHA: (46) implies:
% 228.57/40.11  | | | | |   (47)  all_57_9 = e2
% 228.57/40.11  | | | | | 
% 228.57/40.11  | | | | | BETA: splitting (2) gives:
% 228.57/40.11  | | | | | 
% 228.57/40.11  | | | | | Case 1:
% 228.57/40.11  | | | | | | 
% 228.57/40.11  | | | | | |   (48)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2,
% 228.57/40.11  | | | | | |             e3) = e1)
% 228.57/40.11  | | | | | | 
% 228.57/40.11  | | | | | | REF_CLOSE: (6), (11), (16), (17), (18), (19), (21), (22), (25),
% 228.57/40.11  | | | | | |            (27), (30), (31), (47), (48) are inconsistent by
% 228.57/40.11  | | | | | |            sub-proof #551.
% 228.57/40.11  | | | | | | 
% 228.57/40.11  | | | | | Case 2:
% 228.57/40.11  | | | | | | 
% 228.57/40.11  | | | | | |   (49)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0,
% 228.57/40.11  | | | | | |             e3) = e1)
% 228.57/40.11  | | | | | | 
% 228.57/40.11  | | | | | | REF_CLOSE: (4), (22), (38), (44), (49) are inconsistent by sub-proof
% 228.57/40.11  | | | | | |            #2013.
% 228.57/40.11  | | | | | | 
% 228.57/40.11  | | | | | End of split
% 228.57/40.11  | | | | | 
% 228.57/40.11  | | | | Case 2:
% 228.57/40.11  | | | | | 
% 228.57/40.11  | | | | |   (50)  all_57_10 = e2 & op(e2, e0) = e2
% 228.57/40.11  | | | | | 
% 228.57/40.11  | | | | | ALPHA: (50) implies:
% 228.57/40.11  | | | | |   (51)  all_57_10 = e2
% 228.57/40.11  | | | | | 
% 228.57/40.11  | | | | | COMBINE_EQS: (25), (51) imply:
% 228.57/40.11  | | | | |   (52)  e3 = e2
% 228.57/40.11  | | | | | 
% 228.57/40.11  | | | | | SIMP: (52) implies:
% 228.57/40.11  | | | | |   (53)  e3 = e2
% 228.57/40.11  | | | | | 
% 228.57/40.11  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12),
% 228.57/40.11  | | | | |            (13), (14), (15), (16), (17), (18), (20), (21), (22), (23),
% 228.57/40.11  | | | | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (34),
% 228.57/40.11  | | | | |            (35), (36), (37), (38), (44), (53) are inconsistent by
% 228.57/40.11  | | | | |            sub-proof #549.
% 228.57/40.11  | | | | | 
% 228.57/40.11  | | | | End of split
% 228.57/40.11  | | | | 
% 228.57/40.11  | | | Case 2:
% 228.57/40.11  | | | | 
% 228.57/40.11  | | | |   (54)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0,
% 228.57/40.11  | | | |             e0) = e2)
% 228.57/40.11  | | | | 
% 228.57/40.11  | | | | BETA: splitting (54) gives:
% 228.57/40.11  | | | | 
% 228.57/40.11  | | | | Case 1:
% 228.57/40.11  | | | | | 
% 228.57/40.11  | | | | |   (55)  all_57_11 = e2 & op(e1, e0) = e2
% 228.57/40.11  | | | | | 
% 228.57/40.11  | | | | | ALPHA: (55) implies:
% 228.57/40.11  | | | | |   (56)  all_57_11 = e2
% 228.57/40.11  | | | | | 
% 228.57/40.11  | | | | | REF_CLOSE: (4), (16), (17), (18), (21), (22), (25), (27), (30), (31),
% 228.57/40.11  | | | | |            (36), (56) are inconsistent by sub-proof #1983.
% 228.57/40.11  | | | | | 
% 228.57/40.11  | | | | Case 2:
% 228.57/40.11  | | | | | 
% 228.57/40.11  | | | | |   (57)  all_57_15 = e2 & op(e0, e0) = e2
% 228.57/40.11  | | | | | 
% 228.57/40.11  | | | | | ALPHA: (57) implies:
% 228.57/40.11  | | | | |   (58)  all_57_15 = e2
% 228.57/40.11  | | | | | 
% 228.57/40.11  | | | | | COMBINE_EQS: (18), (58) imply:
% 228.57/40.11  | | | | |   (59)  e3 = e2
% 228.57/40.11  | | | | | 
% 228.57/40.11  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12),
% 228.57/40.11  | | | | |            (13), (14), (15), (16), (17), (18), (20), (21), (22), (23),
% 228.57/40.11  | | | | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (34),
% 228.57/40.11  | | | | |            (35), (36), (37), (38), (44), (59) are inconsistent by
% 228.57/40.11  | | | | |            sub-proof #549.
% 228.57/40.11  | | | | | 
% 228.57/40.11  | | | | End of split
% 228.57/40.11  | | | | 
% 228.57/40.11  | | | End of split
% 228.57/40.11  | | | 
% 228.57/40.11  | | End of split
% 228.57/40.11  | | 
% 228.57/40.11  | End of split
% 228.57/40.11  | 
% 228.57/40.11  End of proof
% 228.57/40.11  
% 228.57/40.11  Sub-proof #549 shows that the following formulas are inconsistent:
% 228.57/40.11  ----------------------------------------------------------------
% 228.57/40.11    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.11         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.57/40.11    (2)  all_57_12 = e0
% 228.57/40.11    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.57/40.11         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.57/40.11    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.11         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.11    (5)   ~ (e3 = e1)
% 228.57/40.11    (6)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.57/40.11         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.57/40.12    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.57/40.12           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.57/40.12    (8)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.57/40.12         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.57/40.12    (9)   ~ (all_6_2 = e3)
% 228.57/40.12    (10)  op(e1, e1) = all_6_2
% 228.57/40.12    (11)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.57/40.12          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.57/40.12    (12)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.57/40.12          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.57/40.12    (13)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.57/40.12          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.12    (14)  all_57_3 = e0
% 228.57/40.12    (15)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.57/40.12          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.57/40.12    (16)   ~ (e3 = e2)
% 228.57/40.12    (17)  e3 = e2
% 228.57/40.12    (18)   ~ (e3 = e0)
% 228.57/40.12    (19)  all_57_15 = e3
% 228.57/40.12    (20)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.57/40.12          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.57/40.12            e1)
% 228.57/40.12    (21)   ~ (e2 = e0)
% 228.57/40.12    (22)   ~ (e1 = e0)
% 228.57/40.12    (23)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.57/40.12          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.57/40.12    (24)  all_57_6 = e3
% 228.57/40.12    (25)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.57/40.12          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.57/40.12    (26)  all_57_10 = e3
% 228.57/40.12    (27)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.12          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.57/40.12            e2)
% 228.57/40.12    (28)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.12              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.57/40.12                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.57/40.12                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.57/40.12    (29)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.12          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.57/40.12    (30)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.57/40.12          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.57/40.12    (31)   ~ (e2 = e1)
% 228.57/40.12    (32)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.57/40.12          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.57/40.12    (33)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.57/40.12          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.57/40.12    (34)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.57/40.12          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.57/40.12    (35)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.57/40.12          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.57/40.12    (36)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.57/40.12          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.57/40.12    (37)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.12          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.57/40.12  
% 228.57/40.12  Begin of proof
% 228.57/40.12  | 
% 228.57/40.12  | COMBINE_EQS: (17), (24) imply:
% 228.57/40.12  |   (38)  all_57_6 = e2
% 228.57/40.12  | 
% 228.57/40.12  | BETA: splitting (30) gives:
% 228.57/40.12  | 
% 228.57/40.12  | Case 1:
% 228.57/40.12  | | 
% 228.57/40.12  | |   (39)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) =
% 228.57/40.12  | |           e3)
% 228.57/40.12  | | 
% 228.57/40.12  | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 228.57/40.12  | |            (14), (15), (16), (18), (19), (20), (21), (22), (23), (25), (26),
% 228.57/40.12  | |            (27), (28), (29), (30), (31), (32), (33), (34), (35), (36), (37),
% 228.57/40.12  | |            (39) are inconsistent by sub-proof #553.
% 228.57/40.12  | | 
% 228.57/40.12  | Case 2:
% 228.57/40.12  | | 
% 228.57/40.12  | |   (40)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) =
% 228.57/40.12  | |           e3)
% 228.57/40.12  | | 
% 228.57/40.12  | | REF_CLOSE: (2), (16), (18), (38), (40) are inconsistent by sub-proof #550.
% 228.57/40.12  | | 
% 228.57/40.12  | End of split
% 228.57/40.12  | 
% 228.57/40.12  End of proof
% 228.57/40.12  
% 228.57/40.12  Sub-proof #550 shows that the following formulas are inconsistent:
% 228.57/40.12  ----------------------------------------------------------------
% 228.57/40.12    (1)  all_57_12 = e0
% 228.57/40.12    (2)   ~ (e3 = e2)
% 228.57/40.12    (3)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.57/40.12    (4)   ~ (e3 = e0)
% 228.57/40.12    (5)  all_57_6 = e2
% 228.57/40.12  
% 228.57/40.12  Begin of proof
% 228.57/40.12  | 
% 228.57/40.12  | BETA: splitting (3) gives:
% 228.57/40.12  | 
% 228.57/40.12  | Case 1:
% 228.57/40.12  | | 
% 228.57/40.12  | |   (6)  all_57_6 = e3 & op(e1, e3) = e3
% 228.57/40.12  | | 
% 228.57/40.12  | | REF_CLOSE: (2), (5), (6) are inconsistent by sub-proof #1558.
% 228.57/40.12  | | 
% 228.57/40.12  | Case 2:
% 228.57/40.12  | | 
% 228.57/40.12  | |   (7)  all_57_12 = e3 & op(e0, e3) = e3
% 228.57/40.12  | | 
% 228.57/40.12  | | ALPHA: (7) implies:
% 228.57/40.12  | |   (8)  all_57_12 = e3
% 228.57/40.12  | | 
% 228.57/40.12  | | REF_CLOSE: (1), (4), (8) are inconsistent by sub-proof #2153.
% 228.57/40.12  | | 
% 228.57/40.12  | End of split
% 228.57/40.12  | 
% 228.57/40.12  End of proof
% 228.57/40.12  
% 228.57/40.12  Sub-proof #551 shows that the following formulas are inconsistent:
% 228.57/40.12  ----------------------------------------------------------------
% 228.57/40.12    (1)  all_57_9 = e2
% 228.57/40.12    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.57/40.12           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.57/40.12    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1)
% 228.57/40.12    (4)  all_57_2 = e2
% 228.57/40.12    (5)   ~ (e3 = e2)
% 228.57/40.12    (6)   ~ (e3 = e0)
% 228.57/40.12    (7)  all_57_15 = e3
% 228.57/40.12    (8)  op(e3, e3) = e2
% 228.57/40.12    (9)   ~ (e2 = e0)
% 228.57/40.12    (10)   ~ (e1 = e0)
% 228.57/40.12    (11)  all_57_10 = e3
% 228.57/40.12    (12)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.12              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.57/40.12                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.57/40.12                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.57/40.12    (13)   ~ (e2 = e1)
% 228.57/40.12    (14)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.57/40.12          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.57/40.12  
% 228.57/40.12  Begin of proof
% 228.57/40.12  | 
% 228.57/40.12  | BETA: splitting (3) gives:
% 228.57/40.12  | 
% 228.57/40.12  | Case 1:
% 228.57/40.12  | | 
% 228.57/40.12  | |   (15)  all_57_0 = e1 & op(e3, e3) = e1
% 228.57/40.12  | | 
% 228.57/40.12  | | ALPHA: (15) implies:
% 228.57/40.12  | |   (16)  op(e3, e3) = e1
% 228.57/40.12  | | 
% 228.57/40.12  | | REF_CLOSE: (2), (8), (13), (16) are inconsistent by sub-proof #1950.
% 228.57/40.12  | | 
% 228.57/40.12  | Case 2:
% 228.57/40.12  | | 
% 228.57/40.12  | |   (17)  all_57_2 = e1 & op(e2, e3) = e1
% 228.57/40.12  | | 
% 228.57/40.12  | | ALPHA: (17) implies:
% 228.57/40.12  | |   (18)  all_57_2 = e1
% 228.57/40.12  | | 
% 228.57/40.12  | | COMBINE_EQS: (4), (18) imply:
% 228.57/40.12  | |   (19)  e2 = e1
% 228.57/40.12  | | 
% 228.57/40.12  | | COMBINE_EQS: (1), (19) imply:
% 228.57/40.12  | |   (20)  all_57_9 = e1
% 228.57/40.12  | | 
% 228.57/40.12  | | REF_CLOSE: (5), (6), (7), (9), (10), (11), (12), (13), (14), (20) are
% 228.57/40.12  | |            inconsistent by sub-proof #1985.
% 228.57/40.12  | | 
% 228.57/40.12  | End of split
% 228.57/40.12  | 
% 228.57/40.12  End of proof
% 228.57/40.12  
% 228.57/40.12  Sub-proof #552 shows that the following formulas are inconsistent:
% 228.57/40.12  ----------------------------------------------------------------
% 228.57/40.12    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.12         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.57/40.12    (2)   ~ (e3 = e1)
% 228.57/40.12    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.57/40.12           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.57/40.12    (4)  all_57_3 = e0
% 228.57/40.12    (5)   ~ (e3 = e2)
% 228.57/40.12    (6)  op(e3, e3) = e2
% 228.57/40.12    (7)   ~ (e2 = e0)
% 228.57/40.12    (8)   ~ (e1 = e0)
% 228.57/40.12    (9)  all_57_10 = e3
% 228.57/40.12    (10)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.12          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.57/40.12    (11)   ~ (e2 = e1)
% 228.57/40.12    (12)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0)
% 228.57/40.12  
% 228.57/40.12  Begin of proof
% 228.57/40.12  | 
% 228.57/40.12  | BETA: splitting (12) gives:
% 228.57/40.12  | 
% 228.57/40.12  | Case 1:
% 228.57/40.12  | | 
% 228.57/40.12  | |   (13)  all_57_0 = e0 & op(e3, e3) = e0
% 228.57/40.12  | | 
% 228.57/40.12  | | ALPHA: (13) implies:
% 228.57/40.12  | |   (14)  op(e3, e3) = e0
% 228.57/40.12  | | 
% 228.57/40.12  | | REF_CLOSE: (3), (6), (7), (14) are inconsistent by sub-proof #2403.
% 228.57/40.12  | | 
% 228.57/40.12  | Case 2:
% 228.57/40.12  | | 
% 228.57/40.12  | |   (15)  all_57_2 = e0 & op(e2, e3) = e0
% 228.57/40.12  | | 
% 228.57/40.12  | | ALPHA: (15) implies:
% 228.57/40.12  | |   (16)  all_57_2 = e0
% 228.57/40.12  | | 
% 228.57/40.12  | | REF_CLOSE: (1), (2), (4), (5), (7), (8), (9), (10), (11), (16) are
% 228.57/40.12  | |            inconsistent by sub-proof #2247.
% 228.57/40.12  | | 
% 228.57/40.12  | End of split
% 228.57/40.12  | 
% 228.57/40.12  End of proof
% 228.57/40.12  
% 228.57/40.12  Sub-proof #553 shows that the following formulas are inconsistent:
% 228.57/40.12  ----------------------------------------------------------------
% 228.57/40.12    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.12         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.57/40.12    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.57/40.12         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.57/40.12    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.12         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.12    (4)   ~ (e3 = e1)
% 228.57/40.12    (5)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.57/40.12         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.57/40.12    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.57/40.12           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.57/40.12    (7)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.57/40.12         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.57/40.12    (8)   ~ (all_6_2 = e3)
% 228.57/40.12    (9)  op(e1, e1) = all_6_2
% 228.57/40.12    (10)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.57/40.12          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.57/40.12    (11)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.57/40.12          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.57/40.12    (12)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.57/40.12          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.12    (13)  all_57_3 = e0
% 228.57/40.12    (14)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.57/40.12          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.57/40.12    (15)   ~ (e3 = e2)
% 228.57/40.12    (16)   ~ (e3 = e0)
% 228.57/40.12    (17)  all_57_15 = e3
% 228.57/40.12    (18)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.57/40.12          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.57/40.12            e1)
% 228.57/40.12    (19)   ~ (e2 = e0)
% 228.57/40.12    (20)   ~ (e1 = e0)
% 228.57/40.12    (21)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.57/40.12          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.57/40.12    (22)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.57/40.12          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.57/40.12    (23)  all_57_10 = e3
% 228.57/40.12    (24)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.12          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.57/40.12            e2)
% 228.57/40.12    (25)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.12              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.57/40.12                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.57/40.12                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.57/40.12    (26)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.12          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.57/40.12    (27)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.57/40.12          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.57/40.12    (28)   ~ (e2 = e1)
% 228.57/40.12    (29)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.57/40.12          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.57/40.12    (30)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.57/40.12          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.57/40.12    (31)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.57/40.12          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.57/40.12    (32)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.57/40.12          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.57/40.12    (33)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.57/40.12          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.57/40.12    (34)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3)
% 228.57/40.12    (35)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.12          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.57/40.12  
% 228.57/40.12  Begin of proof
% 228.57/40.12  | 
% 228.57/40.12  | BETA: splitting (34) gives:
% 228.57/40.12  | 
% 228.57/40.12  | Case 1:
% 228.57/40.12  | | 
% 228.57/40.12  | |   (36)  all_57_0 = e3 & op(e3, e3) = e3
% 228.57/40.12  | | 
% 228.57/40.12  | | ALPHA: (36) implies:
% 228.57/40.12  | |   (37)  op(e3, e3) = e3
% 228.57/40.12  | | 
% 228.57/40.12  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.57/40.12  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 228.57/40.12  | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (35),
% 228.57/40.12  | |            (37) are inconsistent by sub-proof #1416.
% 228.57/40.12  | | 
% 228.57/40.12  | Case 2:
% 228.57/40.12  | | 
% 228.57/40.12  | |   (38)  all_57_2 = e3 & op(e2, e3) = e3
% 228.57/40.12  | | 
% 228.57/40.12  | | ALPHA: (38) implies:
% 228.57/40.12  | |   (39)  all_57_2 = e3
% 228.57/40.12  | | 
% 228.57/40.12  | | REF_CLOSE: (1), (4), (13), (15), (19), (20), (23), (26), (28), (39) are
% 228.57/40.12  | |            inconsistent by sub-proof #1433.
% 228.57/40.12  | | 
% 228.57/40.12  | End of split
% 228.57/40.12  | 
% 228.57/40.12  End of proof
% 228.57/40.12  
% 228.57/40.12  Sub-proof #554 shows that the following formulas are inconsistent:
% 228.57/40.12  ----------------------------------------------------------------
% 228.57/40.12    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.57/40.12    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 228.57/40.12    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.12         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.57/40.12    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.57/40.12         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.57/40.12    (5)  op(e2, e1) = e3
% 228.57/40.12    (6)   ~ (all_53_8 = all_53_12)
% 228.57/40.12    (7)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.12         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.12    (8)   ~ (e3 = e1)
% 228.57/40.12    (9)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.57/40.12         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.57/40.12    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.57/40.12            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.57/40.12    (11)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.57/40.12          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.57/40.12    (12)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 228.57/40.12            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 228.57/40.12              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 228.57/40.12    (13)   ~ (all_6_2 = e3)
% 228.57/40.12    (14)  op(e1, e1) = all_6_2
% 228.57/40.12    (15)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.57/40.12    (16)   ~ (all_53_9 = e0)
% 228.57/40.12    (17)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.57/40.12          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.57/40.12    (18)   ~ (all_53_4 = all_53_12)
% 228.57/40.12    (19)  all_57_2 = e2
% 228.57/40.12    (20)   ~ (all_53_8 = all_53_9)
% 228.57/40.12    (21)  all_42_2 = all_6_2
% 228.57/40.12    (22)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.57/40.12          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.57/40.12    (23)   ~ (all_53_9 = all_6_2)
% 228.57/40.12    (24)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.57/40.12          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.12    (25)  all_57_3 = e0
% 228.57/40.12    (26)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.57/40.12          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.57/40.12    (27)   ~ (e3 = e2)
% 228.57/40.12    (28)  all_55_1 = all_53_4
% 228.57/40.12    (29)   ~ (e3 = e0)
% 228.57/40.12    (30)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.57/40.12          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.57/40.12    (31)   ~ (all_53_8 = all_6_2)
% 228.57/40.12    (32)  all_55_2 = all_53_8
% 228.57/40.12    (33)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.57/40.12    (34)  all_57_15 = e3
% 228.57/40.12    (35)  op(e3, e3) = e2
% 228.57/40.12    (36)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.57/40.12          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.57/40.12            e1)
% 228.57/40.12    (37)  all_57_5 = e3
% 228.57/40.12    (38)   ~ (all_53_4 = all_53_8)
% 228.57/40.12    (39)  op(e3, e2) = all_53_4
% 228.57/40.12    (40)   ~ (e2 = e0)
% 228.57/40.12    (41)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.57/40.12            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.57/40.12            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.57/40.12            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.57/40.12              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.57/40.12            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.57/40.12            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.57/40.12              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.57/40.12              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.57/40.12            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.57/40.12            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.57/40.12            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.57/40.12              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.57/40.12              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.57/40.12            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.57/40.12              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.57/40.12            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.57/40.12            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.57/40.12              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.57/40.12              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.57/40.12            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.57/40.12            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.57/40.12    (42)   ~ (e1 = e0)
% 228.57/40.12    (43)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 228.57/40.12            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 228.57/40.12              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 228.57/40.12    (44)   ~ (all_53_4 = e0)
% 228.57/40.12    (45)  op(e0, e0) = e3
% 228.57/40.12    (46)   ~ (all_53_4 = all_53_6)
% 228.57/40.12    (47)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.12          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.57/40.12            e2)
% 228.57/40.12    (48)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.12              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.57/40.12                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.57/40.12                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.57/40.12    (49)  all_55_10 = all_6_2
% 228.57/40.12    (50)  all_38_2 = all_6_2
% 228.57/40.12    (51)  all_55_3 = all_53_12
% 228.57/40.12    (52)   ~ (all_53_12 = e3)
% 228.57/40.12    (53)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 228.57/40.12            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 228.57/40.12              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 228.57/40.12    (54)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.12          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.57/40.12    (55)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.57/40.12          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.57/40.12    (56)   ~ (e2 = e1)
% 228.57/40.12    (57)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.57/40.12          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.57/40.12    (58)  op(e2, e1) = all_53_9
% 228.57/40.12    (59)  op(e1, e2) = all_53_6
% 228.57/40.12    (60)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.57/40.12          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.57/40.12    (61)  all_24_2 = all_6_2
% 228.57/40.12    (62)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.57/40.12          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.57/40.12    (63)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.57/40.12          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.57/40.12    (64)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.57/40.12          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.57/40.12    (65)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.57/40.12          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.57/40.12    (66)  op(e3, e1) = all_53_8
% 228.57/40.12    (67)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.12          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.57/40.12    (68)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.57/40.12          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.57/40.12    (69)  op(e3, e0) = all_53_12
% 228.57/40.12  
% 228.57/40.12  Begin of proof
% 228.57/40.12  | 
% 228.57/40.12  | BETA: splitting (55) gives:
% 228.57/40.12  | 
% 228.57/40.12  | Case 1:
% 228.57/40.12  | | 
% 228.57/40.12  | |   (70)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) =
% 228.57/40.12  | |           e3)
% 228.57/40.12  | | 
% 228.57/40.12  | | BETA: splitting (70) gives:
% 228.57/40.12  | | 
% 228.57/40.12  | | Case 1:
% 228.57/40.12  | | | 
% 228.57/40.12  | | |   (71)  all_57_0 = e3 & op(e3, e3) = e3
% 228.57/40.12  | | | 
% 228.57/40.12  | | | ALPHA: (71) implies:
% 228.57/40.12  | | |   (72)  all_57_0 = e3
% 228.57/40.12  | | |   (73)  op(e3, e3) = e3
% 228.57/40.12  | | | 
% 228.57/40.12  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.57/40.12  | | |            (13), (14), (15), (16), (17), (18), (20), (21), (22), (23),
% 228.57/40.12  | | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 228.57/40.12  | | |            (34), (36), (37), (38), (39), (40), (41), (42), (43), (44),
% 228.57/40.12  | | |            (45), (46), (47), (48), (49), (50), (51), (52), (53), (54),
% 228.57/40.12  | | |            (56), (57), (58), (59), (60), (61), (62), (63), (64), (65),
% 228.57/40.12  | | |            (66), (67), (68), (69), (72), (73) are inconsistent by
% 228.57/40.12  | | |            sub-proof #1440.
% 228.57/40.12  | | | 
% 228.57/40.12  | | Case 2:
% 228.57/40.12  | | | 
% 228.57/40.12  | | |   (74)  all_57_2 = e3 & op(e2, e3) = e3
% 228.57/40.12  | | | 
% 228.57/40.12  | | | ALPHA: (74) implies:
% 228.57/40.12  | | |   (75)  all_57_2 = e3
% 228.57/40.12  | | | 
% 228.57/40.12  | | | REF_CLOSE: (19), (27), (75) are inconsistent by sub-proof #1800.
% 228.57/40.12  | | | 
% 228.57/40.12  | | End of split
% 228.57/40.12  | | 
% 228.57/40.12  | Case 2:
% 228.57/40.12  | | 
% 228.57/40.12  | |   (76)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) =
% 228.57/40.12  | |           e3)
% 228.57/40.12  | | 
% 228.57/40.12  | | BETA: splitting (76) gives:
% 228.57/40.12  | | 
% 228.57/40.12  | | Case 1:
% 228.57/40.12  | | | 
% 228.57/40.12  | | |   (77)  all_57_6 = e3 & op(e1, e3) = e3
% 228.57/40.12  | | | 
% 228.57/40.12  | | | ALPHA: (77) implies:
% 228.57/40.12  | | |   (78)  all_57_6 = e3
% 228.57/40.12  | | | 
% 228.57/40.12  | | | BETA: splitting (4) gives:
% 228.57/40.12  | | | 
% 228.57/40.12  | | | Case 1:
% 228.57/40.12  | | | | 
% 228.57/40.12  | | | |   (79)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3)
% 228.57/40.12  | | | |           = e1)
% 228.57/40.12  | | | | 
% 228.57/40.12  | | | | REF_CLOSE: (10), (19), (35), (56), (79) are inconsistent by sub-proof
% 228.57/40.12  | | | |            #1633.
% 228.57/40.12  | | | | 
% 228.57/40.12  | | | Case 2:
% 228.57/40.12  | | | | 
% 228.57/40.12  | | | |   (80)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3)
% 228.57/40.12  | | | |           = e1)
% 228.57/40.12  | | | | 
% 228.57/40.12  | | | | REF_CLOSE: (3), (8), (10), (25), (27), (29), (35), (37), (40), (42),
% 228.57/40.12  | | | |            (54), (56), (63), (78), (80) are inconsistent by sub-proof
% 228.57/40.12  | | | |            #809.
% 228.57/40.12  | | | | 
% 228.57/40.12  | | | End of split
% 228.57/40.12  | | | 
% 228.57/40.12  | | Case 2:
% 228.57/40.12  | | | 
% 228.57/40.13  | | |   (81)  all_57_12 = e3 & op(e0, e3) = e3
% 228.57/40.13  | | | 
% 228.57/40.13  | | | ALPHA: (81) implies:
% 228.57/40.13  | | |   (82)  all_57_12 = e3
% 228.57/40.13  | | | 
% 228.57/40.13  | | | REF_CLOSE: (3), (4), (8), (10), (19), (25), (27), (29), (35), (37), (40),
% 228.57/40.13  | | |            (42), (54), (56), (63), (82) are inconsistent by sub-proof
% 228.57/40.13  | | |            #1576.
% 228.57/40.13  | | | 
% 228.57/40.13  | | End of split
% 228.57/40.13  | | 
% 228.57/40.13  | End of split
% 228.57/40.13  | 
% 228.57/40.13  End of proof
% 228.57/40.13  
% 228.57/40.13  Sub-proof #555 shows that the following formulas are inconsistent:
% 228.57/40.13  ----------------------------------------------------------------
% 228.57/40.13    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.57/40.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.57/40.13    (2)  op(e2, e2) = e1
% 228.57/40.13    (3)   ~ (e3 = e2)
% 228.57/40.13    (4)   ~ (e3 = e0)
% 228.57/40.13    (5)   ~ (e2 = e0)
% 228.57/40.13    (6)  all_57_2 = e3
% 228.57/40.13    (7)   ~ (e1 = e0)
% 228.57/40.13    (8)  all_57_5 = e1
% 228.57/40.13    (9)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.13         (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.57/40.13    (10)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.57/40.13          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 228.57/40.13    (11)   ~ (e2 = e1)
% 228.57/40.13  
% 228.57/40.13  Begin of proof
% 228.57/40.13  | 
% 228.57/40.13  | BETA: splitting (10) gives:
% 228.57/40.13  | 
% 228.57/40.13  | Case 1:
% 228.57/40.13  | | 
% 228.57/40.13  | |   (12)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) =
% 228.57/40.13  | |           e0)
% 228.57/40.13  | | 
% 228.57/40.13  | | REF_CLOSE: (1), (2), (4), (6), (7), (12) are inconsistent by sub-proof #658.
% 228.57/40.13  | | 
% 228.57/40.13  | Case 2:
% 228.57/40.13  | | 
% 228.57/40.13  | |   (13)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 228.57/40.13  | |           e0)
% 228.57/40.13  | | 
% 228.57/40.13  | | BETA: splitting (13) gives:
% 228.57/40.13  | | 
% 228.57/40.13  | | Case 1:
% 228.57/40.13  | | | 
% 228.57/40.13  | | |   (14)  all_57_5 = e0 & op(e2, e1) = e0
% 228.57/40.13  | | | 
% 228.57/40.13  | | | ALPHA: (14) implies:
% 228.57/40.13  | | |   (15)  all_57_5 = e0
% 228.57/40.13  | | | 
% 228.57/40.13  | | | REF_CLOSE: (7), (8), (15) are inconsistent by sub-proof #2350.
% 228.57/40.13  | | | 
% 228.57/40.13  | | Case 2:
% 228.57/40.13  | | | 
% 228.57/40.13  | | |   (16)  all_57_10 = e0 & op(e2, e0) = e0
% 228.57/40.13  | | | 
% 228.57/40.13  | | | ALPHA: (16) implies:
% 228.57/40.13  | | |   (17)  all_57_10 = e0
% 228.57/40.13  | | | 
% 228.57/40.13  | | | BETA: splitting (9) gives:
% 228.57/40.13  | | | 
% 228.57/40.13  | | | Case 1:
% 228.57/40.13  | | | | 
% 228.57/40.13  | | | |   (18)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2)
% 228.57/40.13  | | | |           = e2)
% 228.57/40.13  | | | | 
% 228.57/40.13  | | | | REF_CLOSE: (1), (2), (3), (6), (11), (18) are inconsistent by sub-proof
% 228.57/40.13  | | | |            #969.
% 228.57/40.13  | | | | 
% 228.57/40.13  | | | Case 2:
% 228.57/40.13  | | | | 
% 228.57/40.13  | | | |   (19)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0)
% 228.57/40.13  | | | |           = e2)
% 228.57/40.13  | | | | 
% 228.57/40.13  | | | | BETA: splitting (19) gives:
% 228.57/40.13  | | | | 
% 228.57/40.13  | | | | Case 1:
% 228.57/40.13  | | | | | 
% 228.57/40.13  | | | | |   (20)  all_57_5 = e2 & op(e2, e1) = e2
% 228.57/40.13  | | | | | 
% 228.57/40.13  | | | | | REF_CLOSE: (8), (11), (20) are inconsistent by sub-proof #2251.
% 228.57/40.13  | | | | | 
% 228.57/40.13  | | | | Case 2:
% 228.57/40.13  | | | | | 
% 228.57/40.13  | | | | |   (21)  all_57_10 = e2 & op(e2, e0) = e2
% 228.57/40.13  | | | | | 
% 228.57/40.13  | | | | | ALPHA: (21) implies:
% 228.57/40.13  | | | | |   (22)  all_57_10 = e2
% 228.57/40.13  | | | | | 
% 228.57/40.13  | | | | | REF_CLOSE: (5), (17), (22) are inconsistent by sub-proof #2138.
% 228.57/40.13  | | | | | 
% 228.57/40.13  | | | | End of split
% 228.57/40.13  | | | | 
% 228.57/40.13  | | | End of split
% 228.57/40.13  | | | 
% 228.57/40.13  | | End of split
% 228.57/40.13  | | 
% 228.57/40.13  | End of split
% 228.57/40.13  | 
% 228.57/40.13  End of proof
% 228.57/40.13  
% 228.57/40.13  Sub-proof #556 shows that the following formulas are inconsistent:
% 228.57/40.13  ----------------------------------------------------------------
% 228.57/40.13    (1)  all_57_10 = e0
% 228.57/40.13    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.13         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.57/40.13    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.57/40.13         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.57/40.13    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.13         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.13    (5)   ~ (e3 = e1)
% 228.57/40.13    (6)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.57/40.13         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.57/40.13    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.57/40.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.57/40.13    (8)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.57/40.13         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.57/40.13    (9)   ~ (all_6_2 = e3)
% 228.57/40.13    (10)  op(e1, e1) = all_6_2
% 228.57/40.13    (11)  op(e2, e2) = e1
% 228.57/40.13    (12)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.57/40.13          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.57/40.13    (13)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 228.57/40.13            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 228.57/40.13              e3) = all_22_1 & $i(all_22_1))
% 228.57/40.13    (14)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.57/40.13          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.57/40.13    (15)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.57/40.13          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.13    (16)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.57/40.13          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.57/40.13    (17)   ~ (e3 = e2)
% 228.57/40.13    (18)   ~ (e3 = e0)
% 228.57/40.13    (19)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.57/40.13          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.57/40.13    (20)  op(e0, e3) = all_53_3
% 228.57/40.13    (21)  all_57_0 = e0
% 228.57/40.13    (22)  all_57_15 = e3
% 228.57/40.13    (23)   ~ (all_53_3 = e2)
% 228.57/40.13    (24)  op(e3, e3) = e0
% 228.57/40.13    (25)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.57/40.13          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.57/40.13            e1)
% 228.57/40.13    (26)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.57/40.13    (27)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.57/40.13          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 228.57/40.13    (28)   ~ (e2 = e0)
% 228.57/40.13    (29)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 228.57/40.13            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 228.57/40.13              e3) = all_12_1 & $i(all_12_1))
% 228.57/40.13    (30)  all_55_12 = all_53_3
% 228.57/40.13    (31)  all_57_3 = e1
% 228.57/40.13    (32)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.57/40.13          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.57/40.13    (33)   ~ (e1 = e0)
% 228.57/40.13    (34)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.57/40.13          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.57/40.13    (35)  all_57_6 = e3
% 228.57/40.13    (36)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.57/40.13          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.57/40.13    (37)  op(e0, e0) = e3
% 228.57/40.13    (38)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.13          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.57/40.13            e2)
% 228.57/40.13    (39)   ~ (all_53_3 = e0)
% 228.57/40.13    (40)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.13              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.57/40.13                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.57/40.13                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.57/40.13    (41)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.57/40.13          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.57/40.13    (42)   ~ (all_53_12 = e3)
% 228.57/40.13    (43)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.13          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.57/40.13    (44)  all_57_11 = e1
% 228.57/40.13    (45)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.57/40.13          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.57/40.13    (46)   ~ (all_53_12 = e0)
% 228.57/40.13    (47)  all_55_12 = e1 | all_55_12 = e0
% 228.57/40.13    (48)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.57/40.13          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 228.57/40.13    (49)   ~ (e2 = e1)
% 228.57/40.13    (50)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.57/40.13          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.57/40.13    (51)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.57/40.13          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.57/40.13    (52)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.57/40.13          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.57/40.13    (53)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.57/40.13          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.57/40.13    (54)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.57/40.13          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.57/40.13    (55)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.57/40.13          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.57/40.13    (56)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.13          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.57/40.13    (57)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.57/40.13          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.57/40.13    (58)  op(e3, e0) = all_53_12
% 228.57/40.13  
% 228.57/40.13  Begin of proof
% 228.57/40.13  | 
% 228.57/40.13  | BETA: splitting (26) gives:
% 228.57/40.13  | 
% 228.57/40.13  | Case 1:
% 228.57/40.13  | | 
% 228.57/40.13  | |   (59)  all_57_4 = e3 & op(e3, e1) = e3
% 228.57/40.13  | | 
% 228.57/40.13  | | ALPHA: (59) implies:
% 228.57/40.13  | |   (60)  all_57_4 = e3
% 228.57/40.13  | | 
% 228.57/40.13  | | BETA: splitting (50) gives:
% 228.57/40.13  | | 
% 228.57/40.13  | | Case 1:
% 228.57/40.13  | | | 
% 228.57/40.13  | | |   (61)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 228.57/40.13  | | |           e2)
% 228.57/40.13  | | | 
% 228.57/40.13  | | | BETA: splitting (61) gives:
% 228.57/40.13  | | | 
% 228.57/40.13  | | | Case 1:
% 228.57/40.13  | | | | 
% 228.57/40.13  | | | |   (62)  all_57_9 = e2 & op(e3, e0) = e2
% 228.57/40.13  | | | | 
% 228.57/40.13  | | | | ALPHA: (62) implies:
% 228.57/40.13  | | | |   (63)  all_57_9 = e2
% 228.57/40.13  | | | | 
% 228.57/40.13  | | | | BETA: splitting (41) gives:
% 228.57/40.13  | | | | 
% 228.57/40.13  | | | | Case 1:
% 228.57/40.13  | | | | | 
% 228.57/40.13  | | | | |   (64)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2,
% 228.57/40.13  | | | | |             e2) = e3)
% 228.57/40.13  | | | | | 
% 228.57/40.13  | | | | | BETA: splitting (64) gives:
% 228.57/40.13  | | | | | 
% 228.57/40.13  | | | | | Case 1:
% 228.57/40.13  | | | | | | 
% 228.57/40.13  | | | | | |   (65)  all_57_2 = e3 & op(e2, e3) = e3
% 228.57/40.13  | | | | | | 
% 228.57/40.13  | | | | | | ALPHA: (65) implies:
% 228.57/40.13  | | | | | |   (66)  all_57_2 = e3
% 228.57/40.13  | | | | | | 
% 228.57/40.13  | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 228.57/40.13  | | | | | |            (12), (13), (14), (15), (16), (17), (18), (19), (20),
% 228.57/40.13  | | | | | |            (21), (22), (23), (24), (25), (27), (28), (29), (30),
% 228.57/40.13  | | | | | |            (31), (32), (33), (34), (36), (37), (38), (39), (40),
% 228.57/40.13  | | | | | |            (42), (43), (45), (46), (47), (48), (49), (50), (51),
% 228.57/40.13  | | | | | |            (52), (53), (54), (55), (56), (57), (58), (66) are
% 228.57/40.13  | | | | | |            inconsistent by sub-proof #557.
% 228.57/40.13  | | | | | | 
% 228.57/40.13  | | | | | Case 2:
% 228.57/40.13  | | | | | | 
% 228.57/40.13  | | | | | |   (67)  all_57_3 = e3 & op(e2, e2) = e3
% 228.57/40.13  | | | | | | 
% 228.57/40.13  | | | | | | ALPHA: (67) implies:
% 228.57/40.13  | | | | | |   (68)  op(e2, e2) = e3
% 228.57/40.13  | | | | | | 
% 228.57/40.13  | | | | | | REF_CLOSE: (5), (7), (11), (68) are inconsistent by sub-proof #1912.
% 228.57/40.13  | | | | | | 
% 228.57/40.13  | | | | | End of split
% 228.57/40.13  | | | | | 
% 228.57/40.13  | | | | Case 2:
% 228.57/40.13  | | | | | 
% 228.57/40.13  | | | | |   (69)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2,
% 228.57/40.13  | | | | |             e0) = e3)
% 228.57/40.13  | | | | | 
% 228.57/40.13  | | | | | BETA: splitting (69) gives:
% 228.57/40.13  | | | | | 
% 228.57/40.13  | | | | | Case 1:
% 228.57/40.13  | | | | | | 
% 228.57/40.13  | | | | | |   (70)  all_57_5 = e3 & op(e2, e1) = e3
% 228.57/40.13  | | | | | | 
% 228.57/40.13  | | | | | | ALPHA: (70) implies:
% 228.57/40.13  | | | | | |   (71)  all_57_5 = e3
% 228.57/40.13  | | | | | | 
% 228.57/40.13  | | | | | | REF_CLOSE: (1), (2), (4), (5), (7), (11), (12), (17), (18), (21),
% 228.57/40.13  | | | | | |            (27), (28), (31), (33), (36), (43), (49), (60), (63),
% 228.57/40.13  | | | | | |            (71) are inconsistent by sub-proof #586.
% 228.57/40.13  | | | | | | 
% 228.57/40.13  | | | | | Case 2:
% 228.57/40.13  | | | | | | 
% 228.57/40.13  | | | | | |   (72)  all_57_10 = e3 & op(e2, e0) = e3
% 228.57/40.13  | | | | | | 
% 228.57/40.13  | | | | | | REF_CLOSE: (3), (4), (5), (7), (8), (9), (10), (11), (15), (17),
% 228.57/40.13  | | | | | |            (18), (20), (22), (24), (25), (27), (28), (31), (32),
% 228.57/40.13  | | | | | |            (33), (35), (36), (37), (39), (40), (42), (45), (46),
% 228.57/40.13  | | | | | |            (49), (50), (51), (54), (56), (58), (72) are inconsistent
% 228.57/40.13  | | | | | |            by sub-proof #981.
% 228.57/40.13  | | | | | | 
% 228.57/40.13  | | | | | End of split
% 228.57/40.13  | | | | | 
% 228.57/40.13  | | | | End of split
% 228.57/40.13  | | | | 
% 228.57/40.13  | | | Case 2:
% 228.57/40.13  | | | | 
% 228.57/40.13  | | | |   (73)  all_57_10 = e2 & op(e2, e0) = e2
% 228.57/40.13  | | | | 
% 228.57/40.13  | | | | REF_CLOSE: (1), (28), (73) are inconsistent by sub-proof #1798.
% 228.57/40.13  | | | | 
% 228.57/40.13  | | | End of split
% 228.57/40.13  | | | 
% 228.57/40.13  | | Case 2:
% 228.57/40.13  | | | 
% 228.57/40.13  | | |   (74)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0)
% 228.57/40.13  | | |           = e2)
% 228.57/40.13  | | | 
% 228.57/40.13  | | | REF_CLOSE: (17), (22), (44), (49), (74) are inconsistent by sub-proof
% 228.57/40.13  | | |            #717.
% 228.57/40.13  | | | 
% 228.57/40.13  | | End of split
% 228.57/40.13  | | 
% 228.57/40.13  | Case 2:
% 228.57/40.13  | | 
% 228.57/40.13  | |   (75)  all_57_9 = e3 & op(e3, e0) = e3
% 228.57/40.13  | | 
% 228.57/40.13  | | ALPHA: (75) implies:
% 228.57/40.13  | |   (76)  op(e3, e0) = e3
% 228.57/40.13  | | 
% 228.57/40.13  | | REF_CLOSE: (7), (42), (58), (76) are inconsistent by sub-proof #2458.
% 228.57/40.13  | | 
% 228.57/40.13  | End of split
% 228.57/40.13  | 
% 228.57/40.13  End of proof
% 228.57/40.13  
% 228.57/40.13  Sub-proof #557 shows that the following formulas are inconsistent:
% 228.57/40.13  ----------------------------------------------------------------
% 228.57/40.13    (1)  all_57_10 = e0
% 228.57/40.13    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.13         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.57/40.13    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.57/40.13         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.57/40.13    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.13         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.13    (5)   ~ (e3 = e1)
% 228.57/40.13    (6)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.57/40.13         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.57/40.13    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.57/40.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.57/40.13    (8)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.57/40.13         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.57/40.13    (9)   ~ (all_6_2 = e3)
% 228.57/40.13    (10)  op(e1, e1) = all_6_2
% 228.57/40.13    (11)  op(e2, e2) = e1
% 228.57/40.13    (12)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.57/40.13          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.57/40.13    (13)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 228.57/40.13            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 228.57/40.13              e3) = all_22_1 & $i(all_22_1))
% 228.57/40.13    (14)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.57/40.13          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.57/40.13    (15)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.57/40.13          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.13    (16)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.57/40.13          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.57/40.13    (17)   ~ (e3 = e2)
% 228.57/40.13    (18)   ~ (e3 = e0)
% 228.57/40.13    (19)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.57/40.13          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.57/40.13    (20)  op(e0, e3) = all_53_3
% 228.57/40.13    (21)  all_57_0 = e0
% 228.57/40.13    (22)  all_57_15 = e3
% 228.57/40.13    (23)   ~ (all_53_3 = e2)
% 228.57/40.13    (24)  op(e3, e3) = e0
% 228.57/40.13    (25)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.57/40.13          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.57/40.13            e1)
% 228.57/40.13    (26)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.57/40.13          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 228.57/40.13    (27)   ~ (e2 = e0)
% 228.57/40.13    (28)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 228.57/40.13            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 228.57/40.13              e3) = all_12_1 & $i(all_12_1))
% 228.57/40.13    (29)  all_55_12 = all_53_3
% 228.57/40.13    (30)  all_57_2 = e3
% 228.57/40.13    (31)  all_57_3 = e1
% 228.57/40.13    (32)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.57/40.13          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.57/40.13    (33)   ~ (e1 = e0)
% 228.57/40.13    (34)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.57/40.13          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.57/40.13    (35)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.57/40.13          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.57/40.13    (36)  op(e0, e0) = e3
% 228.57/40.13    (37)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.13          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.57/40.13            e2)
% 228.57/40.13    (38)   ~ (all_53_3 = e0)
% 228.57/40.13    (39)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.13              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.57/40.13                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.57/40.13                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.57/40.13    (40)   ~ (all_53_12 = e3)
% 228.57/40.13    (41)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.13          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.57/40.13    (42)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.57/40.13          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.57/40.13    (43)   ~ (all_53_12 = e0)
% 228.57/40.13    (44)  all_55_12 = e1 | all_55_12 = e0
% 228.57/40.13    (45)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.57/40.13          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 228.57/40.13    (46)   ~ (e2 = e1)
% 228.57/40.13    (47)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.57/40.13          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.57/40.13    (48)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.57/40.13          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.57/40.13    (49)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.57/40.13          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.57/40.13    (50)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.57/40.13          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.57/40.13    (51)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.57/40.13          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.57/40.13    (52)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.57/40.13          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.57/40.13    (53)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.13          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.57/40.13    (54)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.57/40.13          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.57/40.13    (55)  op(e3, e0) = all_53_12
% 228.57/40.13  
% 228.57/40.13  Begin of proof
% 228.57/40.13  | 
% 228.57/40.13  | BETA: splitting (12) gives:
% 228.57/40.13  | 
% 228.57/40.13  | Case 1:
% 228.57/40.13  | | 
% 228.57/40.13  | |   (56)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) =
% 228.57/40.13  | |           e1)
% 228.57/40.13  | | 
% 228.57/40.13  | | REF_CLOSE: (4), (5), (7), (11), (17), (18), (21), (26), (27), (33), (35),
% 228.57/40.13  | |            (46), (56) are inconsistent by sub-proof #1551.
% 228.57/40.13  | | 
% 228.57/40.13  | Case 2:
% 228.57/40.13  | | 
% 228.57/40.13  | |   (57)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) =
% 228.57/40.13  | |           e1)
% 228.57/40.13  | | 
% 228.57/40.13  | | BETA: splitting (57) gives:
% 228.57/40.13  | | 
% 228.57/40.13  | | Case 1:
% 228.57/40.13  | | | 
% 228.57/40.13  | | |   (58)  all_57_4 = e1 & op(e3, e1) = e1
% 228.57/40.13  | | | 
% 228.57/40.13  | | | ALPHA: (58) implies:
% 228.57/40.13  | | |   (59)  all_57_4 = e1
% 228.57/40.13  | | | 
% 228.57/40.13  | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (14),
% 228.57/40.13  | | |            (15), (16), (17), (18), (19), (20), (22), (24), (25), (26),
% 228.57/40.13  | | |            (27), (30), (31), (32), (33), (34), (35), (36), (37), (38),
% 228.57/40.13  | | |            (39), (40), (41), (42), (43), (45), (46), (47), (48), (49),
% 228.57/40.13  | | |            (50), (51), (52), (53), (54), (55), (59) are inconsistent by
% 228.57/40.13  | | |            sub-proof #974.
% 228.57/40.13  | | | 
% 228.57/40.13  | | Case 2:
% 228.57/40.13  | | | 
% 228.57/40.13  | | |   (60)  all_57_9 = e1 & op(e3, e0) = e1
% 228.57/40.13  | | | 
% 228.57/40.13  | | | ALPHA: (60) implies:
% 228.57/40.13  | | |   (61)  all_57_9 = e1
% 228.57/40.13  | | | 
% 228.57/40.13  | | | BETA: splitting (44) gives:
% 228.57/40.13  | | | 
% 228.57/40.13  | | | Case 1:
% 228.57/40.13  | | | | 
% 228.57/40.13  | | | |   (62)  all_55_12 = e1
% 228.57/40.13  | | | | 
% 228.57/40.13  | | | | COMBINE_EQS: (29), (62) imply:
% 228.57/40.13  | | | |   (63)  all_53_3 = e1
% 228.57/40.13  | | | | 
% 228.57/40.13  | | | | SIMP: (63) implies:
% 228.57/40.13  | | | |   (64)  all_53_3 = e1
% 228.57/40.13  | | | | 
% 228.57/40.13  | | | | REDUCE: (23), (64) imply:
% 228.57/40.13  | | | |   (65)   ~ (e2 = e1)
% 228.57/40.13  | | | | 
% 228.57/40.13  | | | | REDUCE: (20), (64) imply:
% 228.57/40.13  | | | |   (66)  op(e0, e3) = e1
% 228.57/40.13  | | | | 
% 228.57/40.13  | | | | REF_CLOSE: (1), (7), (13), (17), (22), (27), (28), (46), (47), (61),
% 228.57/40.13  | | | |            (66) are inconsistent by sub-proof #1018.
% 228.57/40.13  | | | | 
% 228.57/40.13  | | | Case 2:
% 228.57/40.13  | | | | 
% 228.57/40.13  | | | |   (67)  all_55_12 = e0
% 228.57/40.13  | | | | 
% 228.57/40.13  | | | | REF_CLOSE: (29), (38), (67) are inconsistent by sub-proof #1993.
% 228.57/40.13  | | | | 
% 228.57/40.13  | | | End of split
% 228.57/40.13  | | | 
% 228.57/40.13  | | End of split
% 228.57/40.13  | | 
% 228.57/40.13  | End of split
% 228.57/40.13  | 
% 228.57/40.13  End of proof
% 228.57/40.13  
% 228.57/40.13  Sub-proof #558 shows that the following formulas are inconsistent:
% 228.57/40.13  ----------------------------------------------------------------
% 228.57/40.13    (1)  all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.57/40.13    (2)   ~ (all_52_5 = e2)
% 228.57/40.13    (3)  all_55_2 = all_52_5
% 228.57/40.13    (4)   ~ (all_52_5 = e1)
% 228.57/40.13    (5)   ~ (all_52_5 = e0)
% 228.57/40.13  
% 228.57/40.13  Begin of proof
% 228.57/40.13  | 
% 228.57/40.13  | BETA: splitting (1) gives:
% 228.57/40.13  | 
% 228.57/40.13  | Case 1:
% 228.57/40.13  | | 
% 228.57/40.13  | |   (6)  all_55_2 = e2
% 228.57/40.13  | | 
% 228.57/40.13  | | REF_CLOSE: (2), (3), (6) are inconsistent by sub-proof #561.
% 228.57/40.13  | | 
% 228.57/40.13  | Case 2:
% 228.57/40.13  | | 
% 228.57/40.13  | |   (7)  all_55_2 = e1 | all_55_2 = e0
% 228.57/40.13  | | 
% 228.57/40.13  | | REF_CLOSE: (3), (4), (5), (7) are inconsistent by sub-proof #559.
% 228.57/40.13  | | 
% 228.57/40.13  | End of split
% 228.57/40.13  | 
% 228.57/40.13  End of proof
% 228.57/40.13  
% 228.57/40.13  Sub-proof #559 shows that the following formulas are inconsistent:
% 228.57/40.13  ----------------------------------------------------------------
% 228.57/40.13    (1)  all_55_2 = e1 | all_55_2 = e0
% 228.57/40.13    (2)  all_55_2 = all_52_5
% 228.57/40.13    (3)   ~ (all_52_5 = e1)
% 228.57/40.13    (4)   ~ (all_52_5 = e0)
% 228.57/40.13  
% 228.57/40.13  Begin of proof
% 228.57/40.13  | 
% 228.57/40.13  | BETA: splitting (1) gives:
% 228.57/40.13  | 
% 228.57/40.13  | Case 1:
% 228.57/40.13  | | 
% 228.57/40.13  | |   (5)  all_55_2 = e1
% 228.57/40.13  | | 
% 228.57/40.13  | | COMBINE_EQS: (2), (5) imply:
% 228.57/40.13  | |   (6)  all_52_5 = e1
% 228.57/40.13  | | 
% 228.57/40.13  | | SIMP: (6) implies:
% 228.57/40.13  | |   (7)  all_52_5 = e1
% 228.57/40.13  | | 
% 228.57/40.13  | | REDUCE: (3), (7) imply:
% 228.57/40.13  | |   (8)  $false
% 228.57/40.13  | | 
% 228.57/40.13  | | CLOSE: (8) is inconsistent.
% 228.57/40.13  | | 
% 228.57/40.13  | Case 2:
% 228.57/40.13  | | 
% 228.57/40.13  | |   (9)  all_55_2 = e0
% 228.57/40.13  | | 
% 228.57/40.13  | | REF_CLOSE: (2), (4), (9) are inconsistent by sub-proof #560.
% 228.57/40.13  | | 
% 228.57/40.13  | End of split
% 228.57/40.13  | 
% 228.57/40.13  End of proof
% 228.57/40.13  
% 228.57/40.13  Sub-proof #560 shows that the following formulas are inconsistent:
% 228.57/40.13  ----------------------------------------------------------------
% 228.57/40.13    (1)  all_55_2 = all_52_5
% 228.57/40.13    (2)  all_55_2 = e0
% 228.57/40.13    (3)   ~ (all_52_5 = e0)
% 228.57/40.13  
% 228.57/40.13  Begin of proof
% 228.57/40.13  | 
% 228.57/40.13  | COMBINE_EQS: (1), (2) imply:
% 228.57/40.13  |   (4)  all_52_5 = e0
% 228.57/40.13  | 
% 228.57/40.13  | SIMP: (4) implies:
% 228.57/40.13  |   (5)  all_52_5 = e0
% 228.57/40.13  | 
% 228.57/40.13  | REDUCE: (3), (5) imply:
% 228.57/40.13  |   (6)  $false
% 228.57/40.13  | 
% 228.57/40.13  | CLOSE: (6) is inconsistent.
% 228.57/40.13  | 
% 228.57/40.13  End of proof
% 228.57/40.13  
% 228.57/40.13  Sub-proof #561 shows that the following formulas are inconsistent:
% 228.57/40.13  ----------------------------------------------------------------
% 228.57/40.13    (1)  all_55_2 = all_52_5
% 228.57/40.13    (2)  all_55_2 = e2
% 228.57/40.13    (3)   ~ (all_52_5 = e2)
% 228.57/40.13  
% 228.57/40.13  Begin of proof
% 228.57/40.13  | 
% 228.57/40.13  | COMBINE_EQS: (1), (2) imply:
% 228.57/40.13  |   (4)  all_52_5 = e2
% 228.57/40.13  | 
% 228.57/40.13  | SIMP: (4) implies:
% 228.57/40.13  |   (5)  all_52_5 = e2
% 228.57/40.13  | 
% 228.57/40.13  | REDUCE: (3), (5) imply:
% 228.57/40.13  |   (6)  $false
% 228.57/40.13  | 
% 228.57/40.13  | CLOSE: (6) is inconsistent.
% 228.57/40.13  | 
% 228.57/40.13  End of proof
% 228.57/40.13  
% 228.57/40.13  Sub-proof #562 shows that the following formulas are inconsistent:
% 228.57/40.13  ----------------------------------------------------------------
% 228.57/40.13    (1)  all_55_1 = all_52_3
% 228.57/40.13    (2)  all_55_1 = e3
% 228.57/40.13    (3)   ~ (all_52_3 = e3)
% 228.57/40.13  
% 228.57/40.13  Begin of proof
% 228.57/40.13  | 
% 228.57/40.13  | COMBINE_EQS: (1), (2) imply:
% 228.57/40.13  |   (4)  all_52_3 = e3
% 228.57/40.13  | 
% 228.57/40.13  | SIMP: (4) implies:
% 228.57/40.13  |   (5)  all_52_3 = e3
% 228.57/40.13  | 
% 228.57/40.13  | REDUCE: (3), (5) imply:
% 228.57/40.13  |   (6)  $false
% 228.57/40.13  | 
% 228.57/40.13  | CLOSE: (6) is inconsistent.
% 228.57/40.13  | 
% 228.57/40.13  End of proof
% 228.57/40.13  
% 228.57/40.13  Sub-proof #563 shows that the following formulas are inconsistent:
% 228.57/40.13  ----------------------------------------------------------------
% 228.57/40.13    (1)   ~ (all_53_2 = e2)
% 228.57/40.13    (2)  op(e0, e1) = all_53_11
% 228.57/40.13    (3)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.57/40.13    (4)   ~ (all_53_6 = all_53_14)
% 228.57/40.13    (5)   ~ (all_53_6 = e2)
% 228.57/40.13    (6)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.13         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.57/40.13    (7)  op(e1, e0) = e2
% 228.57/40.13    (8)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.57/40.13         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.57/40.14    (9)   ~ (all_53_8 = all_53_12)
% 228.57/40.14    (10)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.14          (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.14    (11)   ~ (all_53_8 = all_53_11)
% 228.57/40.14    (12)   ~ (e3 = e1)
% 228.57/40.14    (13)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.57/40.14          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.57/40.14    (14)   ~ (all_53_13 = e1)
% 228.57/40.14    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.57/40.14            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.57/40.14    (16)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.57/40.14          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.57/40.14    (17)   ~ (all_53_3 = e3)
% 228.57/40.14    (18)   ~ (all_6_2 = e3)
% 228.57/40.14    (19)   ~ (all_53_9 = e1)
% 228.57/40.14    (20)  op(e1, e1) = all_6_2
% 228.57/40.14    (21)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.57/40.14    (22)   ~ (all_53_1 = all_53_9)
% 228.57/40.14    (23)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 228.57/40.14    (24)  op(e2, e2) = e1
% 228.57/40.14    (25)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.57/40.14          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.57/40.14    (26)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 228.57/40.14            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 228.57/40.14              e3) = all_22_1 & $i(all_22_1))
% 228.57/40.14    (27)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 228.57/40.14    (28)  all_55_9 = all_53_6
% 228.57/40.14    (29)  all_57_9 = e1
% 228.57/40.14    (30)   ~ (all_53_4 = all_53_12)
% 228.57/40.14    (31)   ~ (all_53_4 = e1)
% 228.57/40.14    (32)   ~ (all_53_13 = e3)
% 228.57/40.14    (33)   ~ (all_53_8 = all_53_9)
% 228.57/40.14    (34)  all_57_7 = e1
% 228.57/40.14    (35)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.57/40.14          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.57/40.14    (36)   ~ (all_53_9 = all_53_11)
% 228.57/40.14    (37)  all_55_4 = all_53_1
% 228.57/40.14    (38)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.57/40.14          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.14    (39)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.57/40.14          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.57/40.14    (40)   ~ (e3 = e2)
% 228.57/40.14    (41)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 228.57/40.14    (42)  all_55_1 = all_53_4
% 228.57/40.14    (43)   ~ (all_53_1 = all_53_3)
% 228.57/40.14    (44)  op(e1, e0) = all_53_14
% 228.57/40.14    (45)   ~ (all_53_6 = all_53_7)
% 228.57/40.14    (46)  all_55_7 = e3 | all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 228.57/40.14    (47)   ~ (e3 = e0)
% 228.57/40.14    (48)  all_57_1 = e2
% 228.57/40.14    (49)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.57/40.14          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.57/40.14    (50)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.57/40.14    (51)  op(e0, e3) = all_53_3
% 228.57/40.14    (52)   ~ (all_53_2 = e0)
% 228.57/40.14    (53)  all_57_0 = e0
% 228.57/40.14    (54)  all_55_2 = all_53_8
% 228.57/40.14    (55)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 228.57/40.14    (56)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.57/40.14    (57)  all_57_15 = e3
% 228.57/40.14    (58)   ~ (all_53_9 = all_53_13)
% 228.57/40.14    (59)  op(e3, e3) = e0
% 228.57/40.14    (60)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.57/40.14          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.57/40.14            e1)
% 228.57/40.14    (61)   ~ (all_53_1 = e1)
% 228.57/40.14    (62)  all_57_11 = e2
% 228.57/40.14    (63)   ~ (all_53_4 = all_53_8)
% 228.57/40.14    (64)   ~ (all_53_14 = e3)
% 228.57/40.14    (65)  all_55_6 = all_53_9
% 228.57/40.14    (66)  op(e3, e2) = all_53_4
% 228.57/40.14    (67)   ~ (all_53_1 = all_53_2)
% 228.57/40.14    (68)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.57/40.14          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 228.57/40.14    (69)   ~ (e2 = e0)
% 228.57/40.14    (70)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.57/40.14            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.57/40.14            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.57/40.14            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.57/40.14              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.57/40.14            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.57/40.14            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.57/40.14              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.57/40.14              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.57/40.14            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.57/40.14            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.57/40.14            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.57/40.14              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.57/40.14              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.57/40.14            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.57/40.14              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.57/40.14            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.57/40.14            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.57/40.14              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.57/40.14              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.57/40.14            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.57/40.14            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.57/40.14    (71)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 228.57/40.14            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 228.57/40.14              e3) = all_12_1 & $i(all_12_1))
% 228.57/40.14    (72)   ~ (all_53_9 = e2)
% 228.57/40.14    (73)   ~ (all_53_6 = e1)
% 228.57/40.14    (74)  all_55_12 = all_53_3
% 228.57/40.14    (75)  all_57_3 = e1
% 228.57/40.14    (76)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.57/40.14          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.57/40.14    (77)   ~ (all_53_1 = e0)
% 228.57/40.14    (78)   ~ (all_53_2 = all_53_14)
% 228.57/40.14    (79)   ~ (e1 = e0)
% 228.57/40.14    (80)   ~ (all_53_4 = e0)
% 228.57/40.14    (81)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.57/40.14          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.57/40.14    (82)  all_57_6 = e3
% 228.57/40.14    (83)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.57/40.14          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.57/40.14    (84)   ~ (all_53_2 = all_53_3)
% 228.57/40.14    (85)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 228.57/40.14    (86)   ~ (all_53_11 = e2)
% 228.57/40.14    (87)  all_55_8 = all_53_2
% 228.57/40.14    (88)  op(e0, e0) = e3
% 228.57/40.14    (89)   ~ (all_53_4 = all_53_6)
% 228.57/40.14    (90)  op(e0, e2) = all_53_7
% 228.57/40.14    (91)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.14          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.57/40.14            e2)
% 228.57/40.14    (92)   ~ (all_53_8 = e2)
% 228.57/40.14    (93)   ~ (all_53_3 = e0)
% 228.57/40.14    (94)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.14              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.57/40.14                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.57/40.14                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.57/40.14    (95)  op(e1, e1) = e0
% 228.57/40.14    (96)  op(e1, e1) = e2
% 228.57/40.14    (97)   ~ (all_53_1 = all_53_13)
% 228.57/40.14    (98)  op(e2, e0) = all_53_13
% 228.57/40.14    (99)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.57/40.14          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.57/40.14    (100)  all_55_11 = all_53_14
% 228.57/40.14    (101)  all_55_3 = all_53_12
% 228.57/40.14    (102)   ~ (all_53_12 = e3)
% 228.57/40.14    (103)  op(e1, e3) = all_53_2
% 228.57/40.14    (104)  all_57_8 = e0
% 228.57/40.14    (105)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.14           (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.57/40.14    (106)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.57/40.14           (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.57/40.14    (107)   ~ (all_53_12 = e0)
% 228.57/40.14    (108)   ~ (all_53_13 = all_53_14)
% 228.57/40.14    (109)   ~ (all_53_8 = e0)
% 228.57/40.14    (110)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.57/40.14           (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 228.57/40.14    (111)   ~ (e2 = e1)
% 228.57/40.14    (112)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.57/40.14           | (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.57/40.14             e2)
% 228.57/40.14    (113)   ~ (all_53_14 = e2)
% 228.57/40.14    (114)   ~ (all_53_2 = all_53_6)
% 228.57/40.14    (115)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.57/40.14           (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.57/40.14    (116)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 228.57/40.14    (117)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.57/40.14           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.57/40.14    (118)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.57/40.14           (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.57/40.14    (119)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.57/40.14           | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.57/40.14             e1)
% 228.57/40.14    (120)  all_57_9 = e1 & op(e3, e0) = e1
% 228.57/40.14    (121)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.57/40.14           (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.57/40.14    (122)  all_55_14 = all_53_11
% 228.57/40.14    (123)  all_55_7 = all_53_13
% 228.57/40.14    (124)   ~ (all_53_11 = e3)
% 228.57/40.14    (125)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.14           (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.57/40.14    (126)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.57/40.14           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.57/40.14    (127)  op(e3, e0) = all_53_12
% 228.57/40.14  
% 228.57/40.14  Begin of proof
% 228.57/40.14  | 
% 228.57/40.14  | BETA: splitting (83) gives:
% 228.57/40.14  | 
% 228.57/40.14  | Case 1:
% 228.57/40.14  | | 
% 228.57/40.14  | |   (128)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 228.57/40.14  | |            e3)
% 228.57/40.14  | | 
% 228.57/40.14  | | BETA: splitting (128) gives:
% 228.57/40.14  | | 
% 228.57/40.14  | | Case 1:
% 228.57/40.14  | | | 
% 228.57/40.14  | | |   (129)  all_57_1 = e3 & op(e3, e2) = e3
% 228.57/40.14  | | | 
% 228.57/40.14  | | | ALPHA: (129) implies:
% 228.57/40.14  | | |   (130)  all_57_1 = e3
% 228.57/40.14  | | | 
% 228.57/40.14  | | | COMBINE_EQS: (48), (130) imply:
% 228.57/40.14  | | |   (131)  e3 = e2
% 228.57/40.14  | | | 
% 228.57/40.14  | | | SIMP: (131) implies:
% 228.57/40.14  | | |   (132)  e3 = e2
% 228.57/40.14  | | | 
% 228.57/40.14  | | | COMBINE_EQS: (82), (132) imply:
% 228.57/40.14  | | |   (133)  all_57_6 = e2
% 228.57/40.14  | | | 
% 228.57/40.14  | | | REF_CLOSE: (12), (15), (16), (18), (20), (34), (40), (47), (57), (69),
% 228.57/40.14  | | |            (79), (94), (111), (112), (119), (133) are inconsistent by
% 228.57/40.14  | | |            sub-proof #1245.
% 228.57/40.14  | | | 
% 228.57/40.14  | | Case 2:
% 228.57/40.14  | | | 
% 228.57/40.14  | | |   (134)  all_57_3 = e3 & op(e2, e2) = e3
% 228.57/40.14  | | | 
% 228.57/40.14  | | | ALPHA: (134) implies:
% 228.57/40.14  | | |   (135)  op(e2, e2) = e3
% 228.57/40.14  | | | 
% 228.57/40.14  | | | REF_CLOSE: (12), (15), (24), (135) are inconsistent by sub-proof #1912.
% 228.57/40.14  | | | 
% 228.57/40.14  | | End of split
% 228.57/40.14  | | 
% 228.57/40.14  | Case 2:
% 228.57/40.14  | | 
% 228.57/40.14  | |   (136)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 228.57/40.14  | |            e3)
% 228.57/40.14  | | 
% 228.57/40.14  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.57/40.14  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 228.57/40.14  | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 228.57/40.14  | |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 228.57/40.14  | |            (46), (47), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 228.57/40.14  | |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 228.57/40.14  | |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 228.57/40.14  | |            (80), (81), (82), (83), (84), (85), (86), (87), (88), (89), (90),
% 228.57/40.14  | |            (91), (92), (93), (94), (95), (96), (97), (98), (99), (100),
% 228.57/40.14  | |            (101), (102), (103), (104), (105), (106), (107), (108), (109),
% 228.57/40.14  | |            (110), (111), (112), (113), (114), (115), (116), (117), (118),
% 228.57/40.14  | |            (119), (120), (121), (122), (123), (124), (125), (126), (127),
% 228.57/40.14  | |            (136) are inconsistent by sub-proof #564.
% 228.57/40.14  | | 
% 228.57/40.14  | End of split
% 228.57/40.14  | 
% 228.57/40.14  End of proof
% 228.57/40.14  
% 228.57/40.14  Sub-proof #564 shows that the following formulas are inconsistent:
% 228.57/40.14  ----------------------------------------------------------------
% 228.57/40.14    (1)   ~ (all_53_2 = e2)
% 228.57/40.14    (2)  op(e0, e1) = all_53_11
% 228.57/40.14    (3)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.57/40.14    (4)   ~ (all_53_6 = all_53_14)
% 228.57/40.14    (5)   ~ (all_53_6 = e2)
% 228.57/40.14    (6)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.14         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.57/40.14    (7)  op(e1, e0) = e2
% 228.57/40.14    (8)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.57/40.14         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.57/40.14    (9)   ~ (all_53_8 = all_53_12)
% 228.57/40.14    (10)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.14          (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.14    (11)   ~ (all_53_8 = all_53_11)
% 228.57/40.14    (12)   ~ (e3 = e1)
% 228.57/40.14    (13)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.57/40.14          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.57/40.14    (14)   ~ (all_53_13 = e1)
% 228.57/40.14    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.57/40.14            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.57/40.14    (16)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.57/40.14          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.57/40.14    (17)   ~ (all_53_3 = e3)
% 228.57/40.14    (18)   ~ (all_6_2 = e3)
% 228.57/40.14    (19)   ~ (all_53_9 = e1)
% 228.57/40.14    (20)  op(e1, e1) = all_6_2
% 228.57/40.14    (21)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.57/40.14    (22)   ~ (all_53_1 = all_53_9)
% 228.57/40.14    (23)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 228.57/40.14    (24)  op(e2, e2) = e1
% 228.57/40.14    (25)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.57/40.14          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.57/40.14    (26)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 228.57/40.14            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 228.57/40.14              e3) = all_22_1 & $i(all_22_1))
% 228.57/40.14    (27)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 228.57/40.14    (28)  all_55_9 = all_53_6
% 228.57/40.14    (29)  all_57_9 = e1
% 228.57/40.14    (30)   ~ (all_53_4 = all_53_12)
% 228.57/40.14    (31)   ~ (all_53_4 = e1)
% 228.57/40.14    (32)   ~ (all_53_13 = e3)
% 228.57/40.14    (33)   ~ (all_53_8 = all_53_9)
% 228.57/40.14    (34)  all_57_7 = e1
% 228.57/40.14    (35)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.57/40.14          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.57/40.14    (36)   ~ (all_53_9 = all_53_11)
% 228.57/40.14    (37)  all_55_4 = all_53_1
% 228.57/40.14    (38)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.57/40.14          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.14    (39)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.57/40.14          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.57/40.14    (40)   ~ (e3 = e2)
% 228.57/40.14    (41)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 228.57/40.14    (42)  all_55_1 = all_53_4
% 228.57/40.14    (43)   ~ (all_53_1 = all_53_3)
% 228.57/40.14    (44)  op(e1, e0) = all_53_14
% 228.57/40.14    (45)   ~ (all_53_6 = all_53_7)
% 228.57/40.14    (46)  all_55_7 = e3 | all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 228.57/40.14    (47)   ~ (e3 = e0)
% 228.57/40.14    (48)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.57/40.14          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.57/40.14    (49)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.57/40.14    (50)  op(e0, e3) = all_53_3
% 228.57/40.14    (51)   ~ (all_53_2 = e0)
% 228.57/40.14    (52)  all_57_0 = e0
% 228.57/40.14    (53)  all_55_2 = all_53_8
% 228.57/40.14    (54)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 228.57/40.14    (55)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.57/40.14    (56)  all_57_15 = e3
% 228.57/40.14    (57)   ~ (all_53_9 = all_53_13)
% 228.57/40.14    (58)  op(e3, e3) = e0
% 228.57/40.14    (59)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.57/40.14          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.57/40.14            e1)
% 228.57/40.14    (60)   ~ (all_53_1 = e1)
% 228.57/40.14    (61)  all_57_11 = e2
% 228.57/40.14    (62)   ~ (all_53_4 = all_53_8)
% 228.57/40.14    (63)   ~ (all_53_14 = e3)
% 228.57/40.14    (64)  all_55_6 = all_53_9
% 228.57/40.14    (65)  op(e3, e2) = all_53_4
% 228.57/40.14    (66)   ~ (all_53_1 = all_53_2)
% 228.57/40.14    (67)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.57/40.14          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 228.57/40.14    (68)   ~ (e2 = e0)
% 228.57/40.14    (69)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.57/40.14            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.57/40.14            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.57/40.14            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.57/40.14              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.57/40.14            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.57/40.14            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.57/40.14              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.57/40.14              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.57/40.14            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.57/40.14            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.57/40.14            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.57/40.14              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.57/40.14              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.57/40.14            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.57/40.14              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.57/40.14            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.57/40.14            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.57/40.14              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.57/40.14              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.57/40.14            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.57/40.14            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.57/40.14    (70)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 228.57/40.14            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 228.57/40.14              e3) = all_12_1 & $i(all_12_1))
% 228.57/40.14    (71)   ~ (all_53_9 = e2)
% 228.57/40.14    (72)   ~ (all_53_6 = e1)
% 228.57/40.14    (73)  all_55_12 = all_53_3
% 228.57/40.14    (74)  all_57_3 = e1
% 228.57/40.14    (75)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.57/40.14          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.57/40.14    (76)   ~ (all_53_1 = e0)
% 228.57/40.14    (77)   ~ (all_53_2 = all_53_14)
% 228.57/40.14    (78)   ~ (e1 = e0)
% 228.57/40.14    (79)   ~ (all_53_4 = e0)
% 228.57/40.14    (80)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.57/40.14          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.57/40.14    (81)  all_57_6 = e3
% 228.57/40.14    (82)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.57/40.14          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.57/40.14    (83)   ~ (all_53_2 = all_53_3)
% 228.57/40.14    (84)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 228.57/40.14    (85)   ~ (all_53_11 = e2)
% 228.57/40.14    (86)  all_55_8 = all_53_2
% 228.57/40.14    (87)  op(e0, e0) = e3
% 228.57/40.14    (88)   ~ (all_53_4 = all_53_6)
% 228.57/40.14    (89)  op(e0, e2) = all_53_7
% 228.57/40.14    (90)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.14          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.57/40.14            e2)
% 228.57/40.14    (91)   ~ (all_53_8 = e2)
% 228.57/40.14    (92)   ~ (all_53_3 = e0)
% 228.57/40.14    (93)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.14              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.57/40.14                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.57/40.14                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.57/40.14    (94)  op(e1, e1) = e0
% 228.57/40.14    (95)  op(e1, e1) = e2
% 228.57/40.14    (96)   ~ (all_53_1 = all_53_13)
% 228.57/40.14    (97)  op(e2, e0) = all_53_13
% 228.57/40.14    (98)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.57/40.14          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.57/40.14    (99)  all_55_11 = all_53_14
% 228.57/40.14    (100)  all_55_3 = all_53_12
% 228.57/40.14    (101)   ~ (all_53_12 = e3)
% 228.57/40.14    (102)  op(e1, e3) = all_53_2
% 228.57/40.14    (103)  all_57_8 = e0
% 228.57/40.14    (104)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.14           (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.57/40.14    (105)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.57/40.14           (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.57/40.14    (106)   ~ (all_53_12 = e0)
% 228.57/40.14    (107)   ~ (all_53_13 = all_53_14)
% 228.57/40.14    (108)   ~ (all_53_8 = e0)
% 228.57/40.14    (109)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.57/40.14           (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 228.57/40.14    (110)   ~ (e2 = e1)
% 228.57/40.14    (111)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.57/40.14           | (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.57/40.14             e2)
% 228.57/40.14    (112)   ~ (all_53_14 = e2)
% 228.57/40.14    (113)   ~ (all_53_2 = all_53_6)
% 228.57/40.14    (114)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.57/40.14           (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.57/40.14    (115)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 228.57/40.14    (116)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.57/40.14           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.57/40.14    (117)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.57/40.14           (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.57/40.14    (118)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.57/40.14           | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.57/40.14             e1)
% 228.57/40.14    (119)  all_57_9 = e1 & op(e3, e0) = e1
% 228.57/40.14    (120)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.57/40.14           (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.57/40.14    (121)  all_55_14 = all_53_11
% 228.57/40.14    (122)  all_55_7 = all_53_13
% 228.57/40.14    (123)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.57/40.14    (124)   ~ (all_53_11 = e3)
% 228.57/40.14    (125)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.14           (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.57/40.14    (126)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.57/40.14           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.57/40.14    (127)  op(e3, e0) = all_53_12
% 228.57/40.14  
% 228.57/40.14  Begin of proof
% 228.57/40.14  | 
% 228.57/40.14  | BETA: splitting (123) gives:
% 228.57/40.14  | 
% 228.57/40.14  | Case 1:
% 228.57/40.14  | | 
% 228.57/40.14  | |   (128)  all_57_7 = e3 & op(e1, e2) = e3
% 228.57/40.14  | | 
% 228.57/40.14  | | ALPHA: (128) implies:
% 228.57/40.14  | |   (129)  all_57_7 = e3
% 228.57/40.14  | | 
% 228.57/40.14  | | COMBINE_EQS: (34), (129) imply:
% 228.57/40.14  | |   (130)  e3 = e1
% 228.57/40.14  | | 
% 228.57/40.15  | | SIMP: (130) implies:
% 228.57/40.15  | |   (131)  e3 = e1
% 228.57/40.15  | | 
% 228.57/40.15  | | COMBINE_EQS: (81), (131) imply:
% 228.57/40.15  | |   (132)  all_57_6 = e1
% 228.57/40.15  | | 
% 228.57/40.15  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.57/40.15  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 228.57/40.15  | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (35),
% 228.57/40.15  | |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 228.57/40.15  | |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 228.57/40.15  | |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 228.57/40.15  | |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 228.57/40.15  | |            (80), (82), (83), (84), (85), (86), (87), (88), (89), (90), (91),
% 228.57/40.15  | |            (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 228.57/40.15  | |            (102), (103), (104), (105), (106), (107), (108), (109), (110),
% 228.57/40.15  | |            (111), (112), (113), (114), (115), (116), (117), (118), (119),
% 228.57/40.15  | |            (120), (121), (122), (124), (125), (126), (127), (129), (132) are
% 228.57/40.15  | |            inconsistent by sub-proof #565.
% 228.57/40.15  | | 
% 228.57/40.15  | Case 2:
% 228.57/40.15  | | 
% 228.57/40.15  | |   (133)  all_57_13 = e3 & op(e0, e2) = e3
% 228.57/40.15  | | 
% 228.57/40.15  | | ALPHA: (133) implies:
% 228.57/40.15  | |   (134)  all_57_13 = e3
% 228.57/40.15  | | 
% 228.57/40.15  | | REF_CLOSE: (12), (15), (40), (47), (56), (59), (68), (78), (87), (90), (93),
% 228.57/40.15  | |            (110), (134) are inconsistent by sub-proof #1792.
% 228.57/40.15  | | 
% 228.57/40.15  | End of split
% 228.57/40.15  | 
% 228.57/40.15  End of proof
% 228.57/40.15  
% 228.57/40.15  Sub-proof #565 shows that the following formulas are inconsistent:
% 228.57/40.15  ----------------------------------------------------------------
% 228.57/40.15    (1)   ~ (all_53_2 = e2)
% 228.57/40.15    (2)  op(e0, e1) = all_53_11
% 228.57/40.15    (3)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.57/40.15    (4)   ~ (all_53_6 = all_53_14)
% 228.57/40.15    (5)   ~ (all_53_6 = e2)
% 228.57/40.15    (6)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.15         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.57/40.15    (7)  op(e1, e0) = e2
% 228.57/40.15    (8)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.57/40.15         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.57/40.15    (9)   ~ (all_53_8 = all_53_12)
% 228.57/40.15    (10)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.15          (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.15    (11)   ~ (all_53_8 = all_53_11)
% 228.57/40.15    (12)   ~ (e3 = e1)
% 228.57/40.15    (13)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.57/40.15          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.57/40.15    (14)   ~ (all_53_13 = e1)
% 228.57/40.15    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.57/40.15            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.57/40.15    (16)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.57/40.15          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.57/40.15    (17)   ~ (all_53_3 = e3)
% 228.57/40.15    (18)   ~ (all_6_2 = e3)
% 228.57/40.15    (19)   ~ (all_53_9 = e1)
% 228.57/40.15    (20)  op(e1, e1) = all_6_2
% 228.57/40.15    (21)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.57/40.15    (22)   ~ (all_53_1 = all_53_9)
% 228.57/40.15    (23)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 228.57/40.15    (24)  op(e2, e2) = e1
% 228.57/40.15    (25)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.57/40.15          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.57/40.15    (26)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 228.57/40.15            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 228.57/40.15              e3) = all_22_1 & $i(all_22_1))
% 228.57/40.15    (27)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 228.57/40.15    (28)  all_55_9 = all_53_6
% 228.57/40.15    (29)  all_57_9 = e1
% 228.57/40.15    (30)   ~ (all_53_4 = all_53_12)
% 228.57/40.15    (31)   ~ (all_53_4 = e1)
% 228.57/40.15    (32)   ~ (all_53_13 = e3)
% 228.57/40.15    (33)   ~ (all_53_8 = all_53_9)
% 228.57/40.15    (34)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.57/40.15          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.57/40.15    (35)  all_57_6 = e1
% 228.57/40.15    (36)   ~ (all_53_9 = all_53_11)
% 228.57/40.15    (37)  all_55_4 = all_53_1
% 228.57/40.15    (38)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.57/40.15          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.15    (39)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.57/40.15          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.57/40.15    (40)   ~ (e3 = e2)
% 228.57/40.15    (41)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 228.57/40.15    (42)  all_55_1 = all_53_4
% 228.57/40.15    (43)   ~ (all_53_1 = all_53_3)
% 228.57/40.15    (44)  op(e1, e0) = all_53_14
% 228.57/40.15    (45)   ~ (all_53_6 = all_53_7)
% 228.57/40.15    (46)  all_55_7 = e3 | all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 228.57/40.15    (47)   ~ (e3 = e0)
% 228.57/40.15    (48)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.57/40.15          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.57/40.15    (49)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.57/40.15    (50)  op(e0, e3) = all_53_3
% 228.57/40.15    (51)   ~ (all_53_2 = e0)
% 228.57/40.15    (52)  all_57_0 = e0
% 228.57/40.15    (53)  all_55_2 = all_53_8
% 228.57/40.15    (54)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 228.57/40.15    (55)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.57/40.15    (56)  all_57_15 = e3
% 228.57/40.15    (57)   ~ (all_53_9 = all_53_13)
% 228.57/40.15    (58)  op(e3, e3) = e0
% 228.57/40.15    (59)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.57/40.15          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.57/40.15            e1)
% 228.57/40.15    (60)   ~ (all_53_1 = e1)
% 228.57/40.15    (61)  all_57_11 = e2
% 228.57/40.15    (62)   ~ (all_53_4 = all_53_8)
% 228.57/40.15    (63)   ~ (all_53_14 = e3)
% 228.57/40.15    (64)  all_55_6 = all_53_9
% 228.57/40.15    (65)  op(e3, e2) = all_53_4
% 228.57/40.15    (66)   ~ (all_53_1 = all_53_2)
% 228.57/40.15    (67)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.57/40.15          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 228.57/40.15    (68)   ~ (e2 = e0)
% 228.57/40.15    (69)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.57/40.15            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.57/40.15            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.57/40.15            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.57/40.15              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.57/40.15            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.57/40.15            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.57/40.15              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.57/40.15              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.57/40.15            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.57/40.15            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.57/40.15            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.57/40.15              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.57/40.15              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.57/40.15            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.57/40.15              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.57/40.15            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.57/40.15            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.57/40.15              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.57/40.15              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.57/40.15            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.57/40.15            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.57/40.15    (70)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 228.57/40.15            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 228.57/40.15              e3) = all_12_1 & $i(all_12_1))
% 228.57/40.15    (71)   ~ (all_53_9 = e2)
% 228.57/40.15    (72)   ~ (all_53_6 = e1)
% 228.57/40.15    (73)  all_55_12 = all_53_3
% 228.57/40.15    (74)  all_57_3 = e1
% 228.57/40.15    (75)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.57/40.15          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.57/40.15    (76)   ~ (all_53_1 = e0)
% 228.57/40.15    (77)   ~ (all_53_2 = all_53_14)
% 228.57/40.15    (78)   ~ (e1 = e0)
% 228.57/40.15    (79)   ~ (all_53_4 = e0)
% 228.57/40.15    (80)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.57/40.15          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.57/40.15    (81)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.57/40.15          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.57/40.15    (82)   ~ (all_53_2 = all_53_3)
% 228.57/40.15    (83)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 228.57/40.15    (84)   ~ (all_53_11 = e2)
% 228.57/40.15    (85)  all_55_8 = all_53_2
% 228.57/40.15    (86)  op(e0, e0) = e3
% 228.57/40.15    (87)   ~ (all_53_4 = all_53_6)
% 228.57/40.15    (88)  op(e0, e2) = all_53_7
% 228.57/40.15    (89)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.15          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.57/40.15            e2)
% 228.57/40.15    (90)   ~ (all_53_8 = e2)
% 228.57/40.15    (91)   ~ (all_53_3 = e0)
% 228.57/40.15    (92)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.15              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.57/40.15                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.57/40.15                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.57/40.15    (93)  op(e1, e1) = e0
% 228.57/40.15    (94)  op(e1, e1) = e2
% 228.57/40.15    (95)   ~ (all_53_1 = all_53_13)
% 228.57/40.15    (96)  op(e2, e0) = all_53_13
% 228.57/40.15    (97)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.57/40.15          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.57/40.15    (98)  all_55_11 = all_53_14
% 228.57/40.15    (99)  all_55_3 = all_53_12
% 228.57/40.15    (100)   ~ (all_53_12 = e3)
% 228.57/40.15    (101)  all_57_7 = e3
% 228.57/40.15    (102)  op(e1, e3) = all_53_2
% 228.57/40.15    (103)  all_57_8 = e0
% 228.57/40.15    (104)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.15           (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.57/40.15    (105)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.57/40.15           (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.57/40.15    (106)   ~ (all_53_12 = e0)
% 228.57/40.15    (107)   ~ (all_53_13 = all_53_14)
% 228.57/40.15    (108)   ~ (all_53_8 = e0)
% 228.57/40.15    (109)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.57/40.15           (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 228.57/40.15    (110)   ~ (e2 = e1)
% 228.57/40.15    (111)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.57/40.15           | (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.57/40.15             e2)
% 228.57/40.15    (112)   ~ (all_53_14 = e2)
% 228.57/40.15    (113)   ~ (all_53_2 = all_53_6)
% 228.57/40.15    (114)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.57/40.15           (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.57/40.15    (115)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 228.57/40.15    (116)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.57/40.15           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.57/40.15    (117)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.57/40.15           (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.57/40.15    (118)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.57/40.15           | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.57/40.15             e1)
% 228.57/40.15    (119)  all_57_9 = e1 & op(e3, e0) = e1
% 228.57/40.15    (120)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.57/40.15           (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.57/40.15    (121)  all_55_14 = all_53_11
% 228.57/40.15    (122)  all_55_7 = all_53_13
% 228.57/40.15    (123)   ~ (all_53_11 = e3)
% 228.57/40.15    (124)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.15           (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.57/40.15    (125)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.57/40.15           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.57/40.15    (126)  op(e3, e0) = all_53_12
% 228.57/40.15  
% 228.57/40.15  Begin of proof
% 228.57/40.15  | 
% 228.57/40.15  | BETA: splitting (105) gives:
% 228.57/40.15  | 
% 228.57/40.15  | Case 1:
% 228.57/40.15  | | 
% 228.57/40.15  | |   (127)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) =
% 228.57/40.15  | |            e3)
% 228.57/40.15  | | 
% 228.57/40.15  | | BETA: splitting (127) gives:
% 228.57/40.15  | | 
% 228.57/40.15  | | Case 1:
% 228.57/40.15  | | | 
% 228.57/40.15  | | |   (128)  all_57_0 = e3 & op(e3, e3) = e3
% 228.57/40.15  | | | 
% 228.57/40.15  | | | ALPHA: (128) implies:
% 228.57/40.15  | | |   (129)  op(e3, e3) = e3
% 228.57/40.15  | | | 
% 228.57/40.15  | | | REF_CLOSE: (15), (47), (58), (129) are inconsistent by sub-proof #2494.
% 228.57/40.15  | | | 
% 228.57/40.15  | | Case 2:
% 228.57/40.15  | | | 
% 228.57/40.15  | | |   (130)  all_57_2 = e3 & op(e2, e3) = e3
% 228.57/40.15  | | | 
% 228.57/40.15  | | | ALPHA: (130) implies:
% 228.57/40.15  | | |   (131)  all_57_2 = e3
% 228.57/40.15  | | | 
% 228.57/40.15  | | | BETA: splitting (67) gives:
% 228.57/40.15  | | | 
% 228.57/40.15  | | | Case 1:
% 228.57/40.15  | | | | 
% 228.57/40.15  | | | |   (132)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2)
% 228.57/40.15  | | | |            = e0)
% 228.57/40.15  | | | | 
% 228.57/40.15  | | | | REF_CLOSE: (12), (15), (16), (18), (20), (24), (29), (34), (35), (40),
% 228.57/40.15  | | | |            (47), (56), (58), (68), (75), (78), (92), (100), (101),
% 228.57/40.15  | | | |            (110), (111), (118), (126), (132) are inconsistent by
% 228.57/40.15  | | | |            sub-proof #567.
% 228.57/40.15  | | | | 
% 228.57/40.15  | | | Case 2:
% 228.57/40.15  | | | | 
% 228.57/40.15  | | | |   (133)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0,
% 228.57/40.15  | | | |              e2) = e0)
% 228.57/40.15  | | | | 
% 228.57/40.15  | | | | BETA: splitting (133) gives:
% 228.57/40.15  | | | | 
% 228.57/40.15  | | | | Case 1:
% 228.57/40.15  | | | | | 
% 228.57/40.15  | | | | |   (134)  all_57_7 = e0 & op(e1, e2) = e0
% 228.57/40.15  | | | | | 
% 228.57/40.15  | | | | | ALPHA: (134) implies:
% 228.57/40.15  | | | | |   (135)  all_57_7 = e0
% 228.57/40.15  | | | | | 
% 228.57/40.15  | | | | | REF_CLOSE: (12), (15), (16), (18), (20), (35), (40), (47), (56), (68),
% 228.57/40.15  | | | | |            (78), (92), (110), (111), (118), (135) are inconsistent by
% 228.57/40.15  | | | | |            sub-proof #1735.
% 228.57/40.15  | | | | | 
% 228.57/40.15  | | | | Case 2:
% 228.57/40.15  | | | | | 
% 228.57/40.15  | | | | |   (136)  all_57_13 = e0 & op(e0, e2) = e0
% 228.57/40.15  | | | | | 
% 228.57/40.15  | | | | | ALPHA: (136) implies:
% 228.57/40.15  | | | | |   (137)  all_57_13 = e0
% 228.57/40.15  | | | | | 
% 228.57/40.15  | | | | | BETA: splitting (92) gives:
% 228.57/40.15  | | | | | 
% 228.57/40.15  | | | | | Case 1:
% 228.57/40.15  | | | | | | 
% 228.57/40.15  | | | | | |   (138)  all_57_15 = e0 & op(e0, e0) = e0
% 228.57/40.15  | | | | | | 
% 228.57/40.15  | | | | | | ALPHA: (138) implies:
% 228.57/40.15  | | | | | |   (139)  op(e0, e0) = e0
% 228.57/40.15  | | | | | | 
% 228.57/40.15  | | | | | | REF_CLOSE: (15), (47), (86), (139) are inconsistent by sub-proof
% 228.57/40.15  | | | | | |            #2304.
% 228.57/40.15  | | | | | | 
% 228.57/40.15  | | | | | Case 2:
% 228.57/40.15  | | | | | | 
% 228.57/40.15  | | | | | |   (140)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 &
% 228.57/40.15  | | | | | |              op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0))
% 228.57/40.15  | | | | | |          & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.57/40.15  | | | | | |              op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 228.57/40.15  | | | | | | 
% 228.57/40.15  | | | | | | ALPHA: (140) implies:
% 228.57/40.15  | | | | | |   (141)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 &
% 228.57/40.15  | | | | | |            op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.57/40.15  | | | | | | 
% 228.57/40.15  | | | | | | BETA: splitting (10) gives:
% 228.57/40.15  | | | | | | 
% 228.57/40.15  | | | | | | Case 1:
% 228.57/40.15  | | | | | | | 
% 228.57/40.15  | | | | | | |   (142)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 &
% 228.57/40.15  | | | | | | |            op(e2, e2) = e2)
% 228.57/40.15  | | | | | | | 
% 228.57/40.15  | | | | | | | BETA: splitting (142) gives:
% 228.57/40.15  | | | | | | | 
% 228.57/40.15  | | | | | | | Case 1:
% 228.57/40.15  | | | | | | | | 
% 228.57/40.15  | | | | | | | |   (143)  all_57_1 = e2 & op(e3, e2) = e2
% 228.57/40.15  | | | | | | | | 
% 228.57/40.15  | | | | | | | | ALPHA: (143) implies:
% 228.57/40.15  | | | | | | | |   (144)  all_57_1 = e2
% 228.57/40.15  | | | | | | | | 
% 228.57/40.15  | | | | | | | | BETA: splitting (75) gives:
% 228.57/40.15  | | | | | | | | 
% 228.57/40.15  | | | | | | | | Case 1:
% 228.57/40.15  | | | | | | | | | 
% 228.57/40.15  | | | | | | | | |   (145)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 &
% 228.57/40.15  | | | | | | | | |            op(e3, e2) = e3)
% 228.57/40.15  | | | | | | | | | 
% 228.57/40.15  | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11),
% 228.57/40.15  | | | | | | | | |            (12), (13), (14), (15), (16), (17), (18), (19),
% 228.57/40.15  | | | | | | | | |            (20), (21), (22), (23), (24), (25), (26), (27),
% 228.57/40.15  | | | | | | | | |            (28), (30), (31), (32), (33), (34), (36), (37),
% 228.57/40.15  | | | | | | | | |            (38), (39), (40), (41), (42), (43), (44), (45),
% 228.57/40.15  | | | | | | | | |            (46), (47), (48), (49), (50), (51), (52), (53),
% 228.57/40.15  | | | | | | | | |            (54), (55), (56), (57), (58), (59), (60), (62),
% 228.57/40.15  | | | | | | | | |            (63), (64), (65), (66), (67), (68), (69), (70),
% 228.57/40.15  | | | | | | | | |            (71), (72), (73), (74), (75), (76), (77), (78),
% 228.57/40.15  | | | | | | | | |            (79), (80), (81), (82), (83), (84), (85), (86),
% 228.57/40.15  | | | | | | | | |            (87), (88), (89), (90), (91), (92), (94), (95),
% 228.57/40.15  | | | | | | | | |            (96), (97), (98), (99), (100), (101), (102), (104),
% 228.57/40.15  | | | | | | | | |            (105), (106), (107), (108), (109), (110), (111),
% 228.57/40.15  | | | | | | | | |            (112), (113), (114), (115), (116), (117), (118),
% 228.57/40.15  | | | | | | | | |            (120), (121), (122), (123), (124), (125), (126),
% 228.57/40.15  | | | | | | | | |            (144), (145) are inconsistent by sub-proof #566.
% 228.57/40.15  | | | | | | | | | 
% 228.57/40.15  | | | | | | | | Case 2:
% 228.57/40.15  | | | | | | | | | 
% 228.57/40.15  | | | | | | | | |   (146)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 &
% 228.57/40.15  | | | | | | | | |            op(e3, e0) = e3)
% 228.57/40.15  | | | | | | | | | 
% 228.57/40.15  | | | | | | | | | BETA: splitting (146) gives:
% 228.57/40.15  | | | | | | | | | 
% 228.57/40.15  | | | | | | | | | Case 1:
% 228.57/40.15  | | | | | | | | | | 
% 228.57/40.15  | | | | | | | | | |   (147)  all_57_4 = e3 & op(e3, e1) = e3
% 228.57/40.15  | | | | | | | | | | 
% 228.57/40.15  | | | | | | | | | | ALPHA: (147) implies:
% 228.57/40.15  | | | | | | | | | |   (148)  all_57_4 = e3
% 228.57/40.15  | | | | | | | | | | 
% 228.57/40.15  | | | | | | | | | | BETA: splitting (104) gives:
% 228.57/40.15  | | | | | | | | | | 
% 228.57/40.15  | | | | | | | | | | Case 1:
% 228.57/40.15  | | | | | | | | | | | 
% 228.57/40.15  | | | | | | | | | | |   (149)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 228.57/40.15  | | | | | | | | | | |            & op(e2, e2) = e2)
% 228.57/40.15  | | | | | | | | | | | 
% 228.57/40.15  | | | | | | | | | | | BETA: splitting (149) gives:
% 228.57/40.15  | | | | | | | | | | | 
% 228.57/40.15  | | | | | | | | | | | Case 1:
% 228.57/40.15  | | | | | | | | | | | | 
% 228.57/40.15  | | | | | | | | | | | |   (150)  all_57_2 = e2 & op(e2, e3) = e2
% 228.57/40.15  | | | | | | | | | | | | 
% 228.57/40.15  | | | | | | | | | | | | ALPHA: (150) implies:
% 228.57/40.15  | | | | | | | | | | | |   (151)  all_57_2 = e2
% 228.57/40.15  | | | | | | | | | | | | 
% 228.57/40.15  | | | | | | | | | | | | COMBINE_EQS: (131), (151) imply:
% 228.57/40.15  | | | | | | | | | | | |   (152)  e3 = e2
% 228.57/40.15  | | | | | | | | | | | | 
% 228.57/40.15  | | | | | | | | | | | | SIMP: (152) implies:
% 228.57/40.15  | | | | | | | | | | | |   (153)  e3 = e2
% 228.57/40.15  | | | | | | | | | | | | 
% 228.57/40.15  | | | | | | | | | | | | COMBINE_EQS: (148), (153) imply:
% 228.57/40.15  | | | | | | | | | | | |   (154)  all_57_4 = e2
% 228.57/40.15  | | | | | | | | | | | | 
% 228.57/40.15  | | | | | | | | | | | | BETA: splitting (75) gives:
% 228.57/40.15  | | | | | | | | | | | | 
% 228.57/40.15  | | | | | | | | | | | | Case 1:
% 228.57/40.15  | | | | | | | | | | | | | 
% 228.57/40.15  | | | | | | | | | | | | |   (155)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 228.57/40.15  | | | | | | | | | | | | |            & op(e3, e2) = e3)
% 228.57/40.15  | | | | | | | | | | | | | 
% 228.57/40.15  | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10),
% 228.57/40.15  | | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 228.57/40.15  | | | | | | | | | | | | |            (19), (20), (21), (22), (23), (24), (25), (26),
% 228.57/40.15  | | | | | | | | | | | | |            (27), (28), (30), (31), (32), (33), (34), (36),
% 228.57/40.15  | | | | | | | | | | | | |            (37), (38), (39), (40), (41), (42), (43), (44),
% 228.57/40.15  | | | | | | | | | | | | |            (45), (46), (47), (48), (49), (50), (51), (52),
% 228.57/40.15  | | | | | | | | | | | | |            (53), (54), (55), (56), (57), (58), (59), (60),
% 228.57/40.15  | | | | | | | | | | | | |            (62), (63), (64), (65), (66), (67), (68), (69),
% 228.57/40.15  | | | | | | | | | | | | |            (70), (71), (72), (73), (74), (75), (76), (77),
% 228.57/40.15  | | | | | | | | | | | | |            (78), (79), (80), (81), (82), (83), (84), (85),
% 228.57/40.15  | | | | | | | | | | | | |            (86), (87), (88), (89), (90), (91), (92), (94),
% 228.57/40.15  | | | | | | | | | | | | |            (95), (96), (97), (98), (99), (100), (101), (102),
% 228.57/40.15  | | | | | | | | | | | | |            (104), (105), (106), (107), (108), (109), (110),
% 228.57/40.15  | | | | | | | | | | | | |            (111), (112), (113), (114), (115), (116), (117),
% 228.57/40.15  | | | | | | | | | | | | |            (118), (120), (121), (122), (123), (124), (125),
% 228.57/40.15  | | | | | | | | | | | | |            (126), (144), (155) are inconsistent by sub-proof
% 228.57/40.15  | | | | | | | | | | | | |            #566.
% 228.57/40.15  | | | | | | | | | | | | | 
% 228.57/40.15  | | | | | | | | | | | | Case 2:
% 228.57/40.15  | | | | | | | | | | | | | 
% 228.57/40.15  | | | | | | | | | | | | | 
% 228.57/40.15  | | | | | | | | | | | | | BETA: splitting (146) gives:
% 228.57/40.15  | | | | | | | | | | | | | 
% 228.57/40.15  | | | | | | | | | | | | | Case 1:
% 228.57/40.15  | | | | | | | | | | | | | | 
% 228.57/40.15  | | | | | | | | | | | | | | 
% 228.57/40.15  | | | | | | | | | | | | | | COMBINE_EQS: (101), (153) imply:
% 228.57/40.15  | | | | | | | | | | | | | |   (156)  all_57_7 = e2
% 228.57/40.15  | | | | | | | | | | | | | | 
% 228.57/40.15  | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10),
% 228.57/40.15  | | | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 228.57/40.15  | | | | | | | | | | | | | |            (19), (20), (21), (22), (23), (24), (25), (26),
% 228.57/40.15  | | | | | | | | | | | | | |            (27), (28), (30), (31), (32), (33), (34), (36),
% 228.57/40.15  | | | | | | | | | | | | | |            (37), (38), (39), (40), (41), (42), (43), (44),
% 228.57/40.15  | | | | | | | | | | | | | |            (45), (46), (47), (48), (49), (50), (51), (52),
% 228.57/40.15  | | | | | | | | | | | | | |            (53), (54), (55), (56), (57), (58), (59), (60),
% 228.57/40.15  | | | | | | | | | | | | | |            (62), (63), (64), (65), (66), (67), (68), (69),
% 228.57/40.15  | | | | | | | | | | | | | |            (70), (71), (72), (73), (74), (75), (76), (77),
% 228.57/40.15  | | | | | | | | | | | | | |            (78), (79), (80), (81), (82), (83), (84), (85),
% 228.57/40.15  | | | | | | | | | | | | | |            (86), (87), (88), (89), (90), (91), (92), (94),
% 228.57/40.15  | | | | | | | | | | | | | |            (95), (96), (97), (98), (99), (100), (102), (104),
% 228.57/40.15  | | | | | | | | | | | | | |            (105), (106), (107), (108), (109), (110), (111),
% 228.57/40.15  | | | | | | | | | | | | | |            (112), (113), (114), (115), (116), (117), (118),
% 228.57/40.15  | | | | | | | | | | | | | |            (120), (121), (122), (123), (124), (125), (126),
% 228.57/40.15  | | | | | | | | | | | | | |            (156) are inconsistent by sub-proof #577.
% 228.57/40.15  | | | | | | | | | | | | | | 
% 228.57/40.15  | | | | | | | | | | | | | Case 2:
% 228.57/40.15  | | | | | | | | | | | | | | 
% 228.57/40.15  | | | | | | | | | | | | | |   (157)  all_57_9 = e3 & op(e3, e0) = e3
% 228.57/40.15  | | | | | | | | | | | | | | 
% 228.57/40.15  | | | | | | | | | | | | | | ALPHA: (157) implies:
% 228.57/40.15  | | | | | | | | | | | | | |   (158)  op(e3, e0) = e3
% 228.57/40.15  | | | | | | | | | | | | | | 
% 228.57/40.15  | | | | | | | | | | | | | | REF_CLOSE: (15), (100), (126), (158) are inconsistent by
% 228.57/40.15  | | | | | | | | | | | | | |            sub-proof #2458.
% 228.57/40.15  | | | | | | | | | | | | | | 
% 228.57/40.15  | | | | | | | | | | | | | End of split
% 228.57/40.15  | | | | | | | | | | | | | 
% 228.57/40.15  | | | | | | | | | | | | End of split
% 228.57/40.15  | | | | | | | | | | | | 
% 228.57/40.15  | | | | | | | | | | | Case 2:
% 228.57/40.15  | | | | | | | | | | | | 
% 228.57/40.15  | | | | | | | | | | | |   (159)  all_57_3 = e2 & op(e2, e2) = e2
% 228.57/40.15  | | | | | | | | | | | | 
% 228.57/40.15  | | | | | | | | | | | | ALPHA: (159) implies:
% 228.57/40.15  | | | | | | | | | | | |   (160)  op(e2, e2) = e2
% 228.57/40.15  | | | | | | | | | | | | 
% 228.57/40.15  | | | | | | | | | | | | REF_CLOSE: (15), (24), (110), (160) are inconsistent by
% 228.57/40.15  | | | | | | | | | | | |            sub-proof #2306.
% 228.57/40.15  | | | | | | | | | | | | 
% 228.57/40.15  | | | | | | | | | | | End of split
% 228.57/40.15  | | | | | | | | | | | 
% 228.57/40.15  | | | | | | | | | | Case 2:
% 228.57/40.15  | | | | | | | | | | | 
% 228.57/40.15  | | | | | | | | | | |   (161)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 228.57/40.15  | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 228.57/40.15  | | | | | | | | | | | 
% 228.57/40.15  | | | | | | | | | | | BETA: splitting (161) gives:
% 228.57/40.15  | | | | | | | | | | | 
% 228.57/40.15  | | | | | | | | | | | Case 1:
% 228.57/40.15  | | | | | | | | | | | | 
% 228.57/40.15  | | | | | | | | | | | | 
% 228.57/40.15  | | | | | | | | | | | | GROUND_INST: instantiating (15) with e0, e2, e1, e1,
% 228.57/40.15  | | | | | | | | | | | |              simplifying with (93), (94) gives:
% 228.57/40.15  | | | | | | | | | | | |   (162)  e2 = e0
% 228.57/40.15  | | | | | | | | | | | | 
% 228.57/40.15  | | | | | | | | | | | | COMBINE_EQS: (144), (162) imply:
% 228.57/40.15  | | | | | | | | | | | |   (163)  all_57_1 = e0
% 228.57/40.15  | | | | | | | | | | | | 
% 228.57/40.15  | | | | | | | | | | | | REF_CLOSE: (15), (29), (34), (40), (58), (68), (110), (148),
% 228.57/40.15  | | | | | | | | | | | |            (163) are inconsistent by sub-proof #2402.
% 228.57/40.15  | | | | | | | | | | | | 
% 228.57/40.15  | | | | | | | | | | | Case 2:
% 228.57/40.15  | | | | | | | | | | | | 
% 228.57/40.15  | | | | | | | | | | | |   (164)  all_57_10 = e2 & op(e2, e0) = e2
% 228.57/40.15  | | | | | | | | | | | | 
% 228.57/40.15  | | | | | | | | | | | | ALPHA: (164) implies:
% 228.57/40.15  | | | | | | | | | | | |   (165)  all_57_10 = e2
% 228.57/40.15  | | | | | | | | | | | | 
% 228.57/40.15  | | | | | | | | | | | | REF_CLOSE: (15), (29), (34), (40), (58), (61), (68), (106),
% 228.57/40.15  | | | | | | | | | | | |            (110), (126), (141), (144), (148), (165) are
% 228.57/40.15  | | | | | | | | | | | |            inconsistent by sub-proof #968.
% 228.57/40.15  | | | | | | | | | | | | 
% 228.57/40.15  | | | | | | | | | | | End of split
% 228.57/40.15  | | | | | | | | | | | 
% 228.57/40.15  | | | | | | | | | | End of split
% 228.57/40.15  | | | | | | | | | | 
% 228.57/40.15  | | | | | | | | | Case 2:
% 228.57/40.15  | | | | | | | | | | 
% 228.57/40.15  | | | | | | | | | |   (166)  all_57_9 = e3 & op(e3, e0) = e3
% 228.57/40.15  | | | | | | | | | | 
% 228.57/40.15  | | | | | | | | | | ALPHA: (166) implies:
% 228.57/40.15  | | | | | | | | | |   (167)  op(e3, e0) = e3
% 228.57/40.15  | | | | | | | | | | 
% 228.57/40.15  | | | | | | | | | | REF_CLOSE: (15), (100), (126), (167) are inconsistent by
% 228.57/40.15  | | | | | | | | | |            sub-proof #2458.
% 228.57/40.15  | | | | | | | | | | 
% 228.57/40.15  | | | | | | | | | End of split
% 228.57/40.15  | | | | | | | | | 
% 228.57/40.15  | | | | | | | | End of split
% 228.57/40.15  | | | | | | | | 
% 228.57/40.15  | | | | | | | Case 2:
% 228.57/40.15  | | | | | | | | 
% 228.57/40.15  | | | | | | | |   (168)  all_57_3 = e2 & op(e2, e2) = e2
% 228.57/40.15  | | | | | | | | 
% 228.57/40.15  | | | | | | | | ALPHA: (168) implies:
% 228.57/40.15  | | | | | | | |   (169)  op(e2, e2) = e2
% 228.57/40.15  | | | | | | | | 
% 228.57/40.15  | | | | | | | | REF_CLOSE: (15), (24), (110), (169) are inconsistent by
% 228.57/40.15  | | | | | | | |            sub-proof #2306.
% 228.57/40.15  | | | | | | | | 
% 228.57/40.15  | | | | | | | End of split
% 228.57/40.15  | | | | | | | 
% 228.57/40.15  | | | | | | Case 2:
% 228.57/40.15  | | | | | | | 
% 228.57/40.15  | | | | | | |   (170)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 &
% 228.57/40.15  | | | | | | |            op(e0, e2) = e2)
% 228.57/40.15  | | | | | | | 
% 228.57/40.15  | | | | | | | BETA: splitting (170) gives:
% 228.57/40.15  | | | | | | | 
% 228.57/40.15  | | | | | | | Case 1:
% 228.57/40.15  | | | | | | | | 
% 228.57/40.15  | | | | | | | |   (171)  all_57_7 = e2 & op(e1, e2) = e2
% 228.57/40.15  | | | | | | | | 
% 228.57/40.15  | | | | | | | | ALPHA: (171) implies:
% 228.57/40.15  | | | | | | | |   (172)  all_57_7 = e2
% 228.57/40.15  | | | | | | | | 
% 228.57/40.15  | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11),
% 228.57/40.15  | | | | | | | |            (12), (13), (14), (15), (16), (17), (18), (19), (20),
% 228.57/40.15  | | | | | | | |            (21), (22), (23), (24), (25), (26), (27), (28), (30),
% 228.57/40.15  | | | | | | | |            (31), (32), (33), (34), (36), (37), (38), (39), (40),
% 228.57/40.15  | | | | | | | |            (41), (42), (43), (44), (45), (46), (47), (48), (49),
% 228.57/40.15  | | | | | | | |            (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 228.57/40.15  | | | | | | | |            (59), (60), (62), (63), (64), (65), (66), (67), (68),
% 228.57/40.15  | | | | | | | |            (69), (70), (71), (72), (73), (74), (75), (76), (77),
% 228.57/40.15  | | | | | | | |            (78), (79), (80), (81), (82), (83), (84), (85), (86),
% 228.57/40.15  | | | | | | | |            (87), (88), (89), (90), (91), (92), (94), (95), (96),
% 228.57/40.15  | | | | | | | |            (97), (98), (99), (100), (102), (104), (105), (106),
% 228.57/40.15  | | | | | | | |            (107), (108), (109), (110), (111), (112), (113),
% 228.57/40.15  | | | | | | | |            (114), (115), (116), (117), (118), (120), (121),
% 228.57/40.15  | | | | | | | |            (122), (123), (124), (125), (126), (172) are
% 228.57/40.15  | | | | | | | |            inconsistent by sub-proof #577.
% 228.57/40.15  | | | | | | | | 
% 228.57/40.15  | | | | | | | Case 2:
% 228.57/40.15  | | | | | | | | 
% 228.57/40.15  | | | | | | | |   (173)  all_57_13 = e2 & op(e0, e2) = e2
% 228.57/40.15  | | | | | | | | 
% 228.57/40.15  | | | | | | | | ALPHA: (173) implies:
% 228.57/40.15  | | | | | | | |   (174)  all_57_13 = e2
% 228.57/40.15  | | | | | | | | 
% 228.57/40.15  | | | | | | | | REF_CLOSE: (68), (137), (174) are inconsistent by sub-proof
% 228.57/40.15  | | | | | | | |            #1911.
% 228.57/40.15  | | | | | | | | 
% 228.57/40.15  | | | | | | | End of split
% 228.57/40.15  | | | | | | | 
% 228.57/40.15  | | | | | | End of split
% 228.57/40.15  | | | | | | 
% 228.57/40.15  | | | | | End of split
% 228.57/40.15  | | | | | 
% 228.57/40.15  | | | | End of split
% 228.57/40.15  | | | | 
% 228.57/40.15  | | | End of split
% 228.57/40.15  | | | 
% 228.57/40.15  | | End of split
% 228.57/40.15  | | 
% 228.57/40.15  | Case 2:
% 228.57/40.15  | | 
% 228.57/40.15  | |   (175)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) =
% 228.57/40.15  | |            e3)
% 228.57/40.15  | | 
% 228.57/40.15  | | BETA: splitting (175) gives:
% 228.57/40.15  | | 
% 228.57/40.15  | | Case 1:
% 228.57/40.15  | | | 
% 228.57/40.15  | | |   (176)  all_57_6 = e3 & op(e1, e3) = e3
% 228.57/40.15  | | | 
% 228.57/40.15  | | | ALPHA: (176) implies:
% 228.57/40.16  | | |   (177)  all_57_6 = e3
% 228.57/40.16  | | | 
% 228.57/40.16  | | | REF_CLOSE: (12), (35), (177) are inconsistent by sub-proof #2017.
% 228.57/40.16  | | | 
% 228.57/40.16  | | Case 2:
% 228.57/40.16  | | | 
% 228.57/40.16  | | |   (178)  all_57_12 = e3 & op(e0, e3) = e3
% 228.57/40.16  | | | 
% 228.57/40.16  | | | ALPHA: (178) implies:
% 228.57/40.16  | | |   (179)  all_57_12 = e3
% 228.57/40.16  | | | 
% 228.57/40.16  | | | BETA: splitting (67) gives:
% 228.57/40.16  | | | 
% 228.57/40.16  | | | Case 1:
% 228.57/40.16  | | | | 
% 228.57/40.16  | | | |   (180)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2)
% 228.57/40.16  | | | |            = e0)
% 228.57/40.16  | | | | 
% 228.57/40.16  | | | | REF_CLOSE: (12), (15), (16), (18), (20), (24), (29), (34), (35), (40),
% 228.57/40.16  | | | |            (47), (56), (58), (68), (75), (78), (92), (100), (101),
% 228.57/40.16  | | | |            (110), (111), (118), (126), (180) are inconsistent by
% 228.57/40.16  | | | |            sub-proof #567.
% 228.57/40.16  | | | | 
% 228.57/40.16  | | | Case 2:
% 228.57/40.16  | | | | 
% 228.57/40.16  | | | |   (181)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0,
% 228.57/40.16  | | | |              e2) = e0)
% 228.57/40.16  | | | | 
% 228.57/40.16  | | | | BETA: splitting (181) gives:
% 228.57/40.16  | | | | 
% 228.57/40.16  | | | | Case 1:
% 228.57/40.16  | | | | | 
% 228.57/40.16  | | | | |   (182)  all_57_7 = e0 & op(e1, e2) = e0
% 228.57/40.16  | | | | | 
% 228.57/40.16  | | | | | ALPHA: (182) implies:
% 228.57/40.16  | | | | |   (183)  all_57_7 = e0
% 228.57/40.16  | | | | | 
% 228.57/40.16  | | | | | REF_CLOSE: (12), (15), (16), (18), (20), (35), (40), (47), (56), (68),
% 228.57/40.16  | | | | |            (78), (92), (110), (111), (118), (183) are inconsistent by
% 228.57/40.16  | | | | |            sub-proof #1735.
% 228.57/40.16  | | | | | 
% 228.57/40.16  | | | | Case 2:
% 228.57/40.16  | | | | | 
% 228.57/40.16  | | | | |   (184)  all_57_13 = e0 & op(e0, e2) = e0
% 228.57/40.16  | | | | | 
% 228.57/40.16  | | | | | ALPHA: (184) implies:
% 228.57/40.16  | | | | |   (185)  all_57_13 = e0
% 228.57/40.16  | | | | | 
% 228.57/40.16  | | | | | BETA: splitting (59) gives:
% 228.57/40.16  | | | | | 
% 228.57/40.16  | | | | | Case 1:
% 228.57/40.16  | | | | | | 
% 228.57/40.16  | | | | | |   (186)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 &
% 228.57/40.16  | | | | | |            op(e0, e2) = e1)
% 228.57/40.16  | | | | | | 
% 228.57/40.16  | | | | | | BETA: splitting (186) gives:
% 228.57/40.16  | | | | | | 
% 228.57/40.16  | | | | | | Case 1:
% 228.57/40.16  | | | | | | | 
% 228.57/40.16  | | | | | | |   (187)  all_57_12 = e1 & op(e0, e3) = e1
% 228.57/40.16  | | | | | | | 
% 228.57/40.16  | | | | | | | ALPHA: (187) implies:
% 228.57/40.16  | | | | | | |   (188)  op(e0, e3) = e1
% 228.57/40.16  | | | | | | | 
% 228.57/40.16  | | | | | | | REF_CLOSE: (7), (15), (26), (70), (188) are inconsistent by
% 228.57/40.16  | | | | | | |            sub-proof #1147.
% 228.57/40.16  | | | | | | | 
% 228.57/40.16  | | | | | | Case 2:
% 228.57/40.16  | | | | | | | 
% 228.57/40.16  | | | | | | |   (189)  all_57_13 = e1 & op(e0, e2) = e1
% 228.57/40.16  | | | | | | | 
% 228.57/40.16  | | | | | | | ALPHA: (189) implies:
% 228.57/40.16  | | | | | | |   (190)  all_57_13 = e1
% 228.57/40.16  | | | | | | | 
% 228.57/40.16  | | | | | | | COMBINE_EQS: (185), (190) imply:
% 228.57/40.16  | | | | | | |   (191)  e1 = e0
% 228.57/40.16  | | | | | | | 
% 228.57/40.16  | | | | | | | REF_CLOSE: (8), (10), (12), (15), (16), (18), (20), (24), (35),
% 228.57/40.16  | | | | | | |            (38), (40), (47), (50), (56), (58), (59), (67), (68),
% 228.57/40.16  | | | | | | |            (74), (75), (78), (81), (86), (91), (92), (100), (105),
% 228.57/40.16  | | | | | | |            (106), (110), (111), (114), (118), (124), (126), (191)
% 228.57/40.16  | | | | | | |            are inconsistent by sub-proof #915.
% 228.57/40.16  | | | | | | | 
% 228.57/40.16  | | | | | | End of split
% 228.57/40.16  | | | | | | 
% 228.57/40.16  | | | | | Case 2:
% 228.57/40.16  | | | | | | 
% 228.57/40.16  | | | | | |   (192)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 &
% 228.57/40.16  | | | | | |            op(e0, e0) = e1)
% 228.57/40.16  | | | | | | 
% 228.57/40.16  | | | | | | BETA: splitting (192) gives:
% 228.57/40.16  | | | | | | 
% 228.57/40.16  | | | | | | Case 1:
% 228.57/40.16  | | | | | | | 
% 228.57/40.16  | | | | | | |   (193)  all_57_14 = e1 & op(e0, e1) = e1
% 228.57/40.16  | | | | | | | 
% 228.57/40.16  | | | | | | | ALPHA: (193) implies:
% 228.57/40.16  | | | | | | |   (194)  all_57_14 = e1
% 228.57/40.16  | | | | | | | 
% 228.57/40.16  | | | | | | | BETA: splitting (89) gives:
% 228.57/40.16  | | | | | | | 
% 228.57/40.16  | | | | | | | Case 1:
% 228.57/40.16  | | | | | | | | 
% 228.57/40.16  | | | | | | | |   (195)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 &
% 228.57/40.16  | | | | | | | |            op(e0, e2) = e2)
% 228.57/40.16  | | | | | | | | 
% 228.57/40.16  | | | | | | | | BETA: splitting (195) gives:
% 228.57/40.16  | | | | | | | | 
% 228.57/40.16  | | | | | | | | Case 1:
% 228.57/40.16  | | | | | | | | | 
% 228.57/40.16  | | | | | | | | |   (196)  all_57_12 = e2 & op(e0, e3) = e2
% 228.57/40.16  | | | | | | | | | 
% 228.57/40.16  | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11),
% 228.57/40.16  | | | | | | | | |            (12), (13), (14), (15), (16), (17), (18), (19),
% 228.57/40.16  | | | | | | | | |            (20), (21), (22), (23), (24), (25), (26), (27),
% 228.57/40.16  | | | | | | | | |            (28), (30), (31), (32), (33), (34), (36), (37),
% 228.57/40.16  | | | | | | | | |            (38), (39), (40), (41), (42), (43), (44), (45),
% 228.57/40.16  | | | | | | | | |            (46), (47), (48), (49), (50), (51), (52), (53),
% 228.57/40.16  | | | | | | | | |            (54), (55), (56), (57), (58), (59), (60), (62),
% 228.57/40.16  | | | | | | | | |            (63), (64), (65), (66), (67), (68), (69), (70),
% 228.57/40.16  | | | | | | | | |            (71), (72), (73), (74), (75), (76), (77), (78),
% 228.57/40.16  | | | | | | | | |            (79), (80), (81), (82), (83), (84), (85), (86),
% 228.57/40.16  | | | | | | | | |            (87), (88), (89), (90), (91), (92), (94), (95),
% 228.57/40.16  | | | | | | | | |            (96), (97), (98), (99), (100), (101), (102), (104),
% 228.57/40.16  | | | | | | | | |            (105), (106), (107), (108), (109), (110), (111),
% 228.57/40.16  | | | | | | | | |            (112), (113), (114), (115), (116), (117), (118),
% 228.57/40.16  | | | | | | | | |            (120), (121), (122), (123), (124), (125), (126),
% 228.57/40.16  | | | | | | | | |            (179), (196) are inconsistent by sub-proof #575.
% 228.57/40.16  | | | | | | | | | 
% 228.57/40.16  | | | | | | | | Case 2:
% 228.57/40.16  | | | | | | | | | 
% 228.57/40.16  | | | | | | | | |   (197)  all_57_13 = e2 & op(e0, e2) = e2
% 228.57/40.16  | | | | | | | | | 
% 228.57/40.16  | | | | | | | | | ALPHA: (197) implies:
% 228.57/40.16  | | | | | | | | |   (198)  all_57_13 = e2
% 228.57/40.16  | | | | | | | | | 
% 228.57/40.16  | | | | | | | | | BETA: splitting (114) gives:
% 228.57/40.16  | | | | | | | | | 
% 228.57/40.16  | | | | | | | | | Case 1:
% 228.57/40.16  | | | | | | | | | | 
% 228.57/40.16  | | | | | | | | | |   (199)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 228.57/40.16  | | | | | | | | | |            & op(e2, e3) = e2)
% 228.57/40.16  | | | | | | | | | | 
% 228.57/40.16  | | | | | | | | | | BETA: splitting (199) gives:
% 228.57/40.16  | | | | | | | | | | 
% 228.57/40.16  | | | | | | | | | | Case 1:
% 228.57/40.16  | | | | | | | | | | | 
% 228.57/40.16  | | | | | | | | | | |   (200)  all_57_0 = e2 & op(e3, e3) = e2
% 228.57/40.16  | | | | | | | | | | | 
% 228.57/40.16  | | | | | | | | | | | ALPHA: (200) implies:
% 228.57/40.16  | | | | | | | | | | |   (201)  op(e3, e3) = e2
% 228.57/40.16  | | | | | | | | | | | 
% 228.57/40.16  | | | | | | | | | | | REF_CLOSE: (15), (58), (68), (201) are inconsistent by
% 228.57/40.16  | | | | | | | | | | |            sub-proof #2403.
% 228.57/40.16  | | | | | | | | | | | 
% 228.57/40.16  | | | | | | | | | | Case 2:
% 228.57/40.16  | | | | | | | | | | | 
% 228.57/40.16  | | | | | | | | | | |   (202)  all_57_2 = e2 & op(e2, e3) = e2
% 228.57/40.16  | | | | | | | | | | | 
% 228.57/40.16  | | | | | | | | | | | ALPHA: (202) implies:
% 228.57/40.16  | | | | | | | | | | |   (203)  all_57_2 = e2
% 228.57/40.16  | | | | | | | | | | | 
% 228.57/40.16  | | | | | | | | | | | BETA: splitting (97) gives:
% 228.57/40.16  | | | | | | | | | | | 
% 228.57/40.16  | | | | | | | | | | | Case 1:
% 228.57/40.16  | | | | | | | | | | | | 
% 228.57/40.16  | | | | | | | | | | | |   (204)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 228.57/40.16  | | | | | | | | | | | |            & op(e2, e2) = e3)
% 228.57/40.16  | | | | | | | | | | | | 
% 228.57/40.16  | | | | | | | | | | | | BETA: splitting (204) gives:
% 228.57/40.16  | | | | | | | | | | | | 
% 228.57/40.16  | | | | | | | | | | | | Case 1:
% 228.57/40.16  | | | | | | | | | | | | | 
% 228.57/40.16  | | | | | | | | | | | | |   (205)  all_57_2 = e3 & op(e2, e3) = e3
% 228.57/40.16  | | | | | | | | | | | | | 
% 228.57/40.16  | | | | | | | | | | | | | ALPHA: (205) implies:
% 228.57/40.16  | | | | | | | | | | | | |   (206)  all_57_2 = e3
% 228.57/40.16  | | | | | | | | | | | | | 
% 228.57/40.16  | | | | | | | | | | | | | COMBINE_EQS: (203), (206) imply:
% 228.57/40.16  | | | | | | | | | | | | |   (207)  e3 = e2
% 228.57/40.16  | | | | | | | | | | | | | 
% 228.57/40.16  | | | | | | | | | | | | | SIMP: (207) implies:
% 228.57/40.16  | | | | | | | | | | | | |   (208)  e3 = e2
% 228.57/40.16  | | | | | | | | | | | | | 
% 228.57/40.16  | | | | | | | | | | | | | COMBINE_EQS: (101), (208) imply:
% 228.57/40.16  | | | | | | | | | | | | |   (209)  all_57_7 = e2
% 228.57/40.16  | | | | | | | | | | | | | 
% 228.57/40.16  | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10),
% 228.57/40.16  | | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 228.57/40.16  | | | | | | | | | | | | |            (19), (20), (21), (22), (23), (24), (25), (26),
% 228.57/40.16  | | | | | | | | | | | | |            (27), (28), (30), (31), (32), (33), (34), (36),
% 228.57/40.16  | | | | | | | | | | | | |            (37), (38), (39), (40), (41), (42), (43), (44),
% 228.57/40.16  | | | | | | | | | | | | |            (45), (46), (47), (48), (49), (50), (51), (52),
% 228.57/40.16  | | | | | | | | | | | | |            (53), (54), (55), (56), (57), (58), (59), (60),
% 228.57/40.16  | | | | | | | | | | | | |            (62), (63), (64), (65), (66), (67), (68), (69),
% 228.57/40.16  | | | | | | | | | | | | |            (70), (71), (72), (73), (74), (75), (76), (77),
% 228.57/40.16  | | | | | | | | | | | | |            (78), (79), (80), (81), (82), (83), (84), (85),
% 228.57/40.16  | | | | | | | | | | | | |            (86), (87), (88), (89), (90), (91), (92), (94),
% 228.57/40.16  | | | | | | | | | | | | |            (95), (96), (97), (98), (99), (100), (102), (104),
% 228.57/40.16  | | | | | | | | | | | | |            (105), (106), (107), (108), (109), (110), (111),
% 228.57/40.16  | | | | | | | | | | | | |            (112), (113), (114), (115), (116), (117), (118),
% 228.57/40.16  | | | | | | | | | | | | |            (120), (121), (122), (123), (124), (125), (126),
% 228.57/40.16  | | | | | | | | | | | | |            (209) are inconsistent by sub-proof #577.
% 228.57/40.16  | | | | | | | | | | | | | 
% 228.57/40.16  | | | | | | | | | | | | Case 2:
% 228.57/40.16  | | | | | | | | | | | | | 
% 228.57/40.16  | | | | | | | | | | | | |   (210)  all_57_3 = e3 & op(e2, e2) = e3
% 228.57/40.16  | | | | | | | | | | | | | 
% 228.57/40.16  | | | | | | | | | | | | | ALPHA: (210) implies:
% 228.57/40.16  | | | | | | | | | | | | |   (211)  op(e2, e2) = e3
% 228.57/40.16  | | | | | | | | | | | | | 
% 228.57/40.16  | | | | | | | | | | | | | REF_CLOSE: (12), (15), (24), (211) are inconsistent by
% 228.57/40.16  | | | | | | | | | | | | |            sub-proof #1912.
% 228.57/40.16  | | | | | | | | | | | | | 
% 228.57/40.16  | | | | | | | | | | | | End of split
% 228.57/40.16  | | | | | | | | | | | | 
% 228.57/40.16  | | | | | | | | | | | Case 2:
% 228.57/40.16  | | | | | | | | | | | | 
% 228.57/40.16  | | | | | | | | | | | |   (212)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 228.57/40.16  | | | | | | | | | | | |            e3 & op(e2, e0) = e3)
% 228.57/40.16  | | | | | | | | | | | | 
% 228.57/40.16  | | | | | | | | | | | | BETA: splitting (212) gives:
% 228.57/40.16  | | | | | | | | | | | | 
% 228.57/40.16  | | | | | | | | | | | | Case 1:
% 228.57/40.16  | | | | | | | | | | | | | 
% 228.57/40.16  | | | | | | | | | | | | |   (213)  all_57_5 = e3 & op(e2, e1) = e3
% 228.57/40.16  | | | | | | | | | | | | | 
% 228.57/40.16  | | | | | | | | | | | | | ALPHA: (213) implies:
% 228.57/40.16  | | | | | | | | | | | | |   (214)  all_57_5 = e3
% 228.57/40.16  | | | | | | | | | | | | | 
% 228.57/40.16  | | | | | | | | | | | | | REF_CLOSE: (6), (8), (10), (12), (13), (15), (16), (18),
% 228.57/40.16  | | | | | | | | | | | | |            (20), (24), (25), (34), (38), (40), (47), (48),
% 228.57/40.16  | | | | | | | | | | | | |            (50), (52), (56), (58), (59), (67), (68), (74),
% 228.57/40.16  | | | | | | | | | | | | |            (75), (78), (80), (81), (86), (89), (91), (92),
% 228.57/40.16  | | | | | | | | | | | | |            (100), (103), (104), (105), (106), (110), (111),
% 228.57/40.16  | | | | | | | | | | | | |            (114), (116), (117), (118), (120), (124), (125),
% 228.57/40.16  | | | | | | | | | | | | |            (126), (179), (194), (198), (203), (214) are
% 228.57/40.16  | | | | | | | | | | | | |            inconsistent by sub-proof #574.
% 228.57/40.16  | | | | | | | | | | | | | 
% 228.57/40.16  | | | | | | | | | | | | Case 2:
% 228.57/40.16  | | | | | | | | | | | | | 
% 228.57/40.16  | | | | | | | | | | | | |   (215)  all_57_10 = e3 & op(e2, e0) = e3
% 228.57/40.16  | | | | | | | | | | | | | 
% 228.57/40.16  | | | | | | | | | | | | | ALPHA: (215) implies:
% 228.57/40.16  | | | | | | | | | | | | |   (216)  all_57_10 = e3
% 228.57/40.16  | | | | | | | | | | | | | 
% 228.57/40.16  | | | | | | | | | | | | | REF_CLOSE: (12), (40), (47), (56), (61), (68), (78), (92),
% 228.57/40.16  | | | | | | | | | | | | |            (110), (111), (118), (216) are inconsistent by
% 228.57/40.16  | | | | | | | | | | | | |            sub-proof #1983.
% 228.57/40.16  | | | | | | | | | | | | | 
% 228.57/40.16  | | | | | | | | | | | | End of split
% 228.57/40.16  | | | | | | | | | | | | 
% 228.57/40.16  | | | | | | | | | | | End of split
% 228.57/40.16  | | | | | | | | | | | 
% 228.57/40.16  | | | | | | | | | | End of split
% 228.57/40.16  | | | | | | | | | | 
% 228.57/40.16  | | | | | | | | | Case 2:
% 228.57/40.16  | | | | | | | | | | 
% 228.57/40.16  | | | | | | | | | |   (217)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2
% 228.57/40.16  | | | | | | | | | |            & op(e0, e3) = e2)
% 228.57/40.16  | | | | | | | | | | 
% 228.57/40.16  | | | | | | | | | | BETA: splitting (217) gives:
% 228.57/40.16  | | | | | | | | | | 
% 228.57/40.16  | | | | | | | | | | Case 1:
% 228.57/40.16  | | | | | | | | | | | 
% 228.57/40.16  | | | | | | | | | | |   (218)  all_57_6 = e2 & op(e1, e3) = e2
% 228.57/40.16  | | | | | | | | | | | 
% 228.57/40.16  | | | | | | | | | | | ALPHA: (218) implies:
% 228.57/40.16  | | | | | | | | | | |   (219)  all_57_6 = e2
% 228.57/40.16  | | | | | | | | | | | 
% 228.57/40.16  | | | | | | | | | | | COMBINE_EQS: (35), (219) imply:
% 228.57/40.16  | | | | | | | | | | |   (220)  e2 = e1
% 228.57/40.16  | | | | | | | | | | | 
% 228.57/40.16  | | | | | | | | | | | SIMP: (220) implies:
% 228.57/40.16  | | | | | | | | | | |   (221)  e2 = e1
% 228.57/40.16  | | | | | | | | | | | 
% 228.57/40.16  | | | | | | | | | | | COMBINE_EQS: (198), (221) imply:
% 228.57/40.16  | | | | | | | | | | |   (222)  all_57_13 = e1
% 228.57/40.16  | | | | | | | | | | | 
% 228.57/40.16  | | | | | | | | | | | REF_CLOSE: (8), (10), (12), (15), (16), (18), (20), (24),
% 228.57/40.16  | | | | | | | | | | |            (35), (38), (40), (47), (50), (56), (58), (59),
% 228.57/40.16  | | | | | | | | | | |            (67), (68), (74), (75), (78), (81), (86), (91),
% 228.57/40.16  | | | | | | | | | | |            (92), (100), (105), (106), (110), (111), (114),
% 228.57/40.16  | | | | | | | | | | |            (118), (124), (126), (194), (222) are inconsistent
% 228.57/40.16  | | | | | | | | | | |            by sub-proof #569.
% 228.57/40.16  | | | | | | | | | | | 
% 228.57/40.16  | | | | | | | | | | Case 2:
% 228.57/40.16  | | | | | | | | | | | 
% 228.57/40.16  | | | | | | | | | | |   (223)  all_57_12 = e2 & op(e0, e3) = e2
% 228.57/40.16  | | | | | | | | | | | 
% 228.57/40.16  | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10),
% 228.57/40.16  | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 228.57/40.16  | | | | | | | | | | |            (19), (20), (21), (22), (23), (24), (25), (26),
% 228.57/40.16  | | | | | | | | | | |            (27), (28), (30), (31), (32), (33), (34), (36),
% 228.57/40.16  | | | | | | | | | | |            (37), (38), (39), (40), (41), (42), (43), (44),
% 228.57/40.16  | | | | | | | | | | |            (45), (46), (47), (48), (49), (50), (51), (52),
% 228.57/40.16  | | | | | | | | | | |            (53), (54), (55), (56), (57), (58), (59), (60),
% 228.57/40.16  | | | | | | | | | | |            (62), (63), (64), (65), (66), (67), (68), (69),
% 228.57/40.16  | | | | | | | | | | |            (70), (71), (72), (73), (74), (75), (76), (77),
% 228.57/40.16  | | | | | | | | | | |            (78), (79), (80), (81), (82), (83), (84), (85),
% 228.57/40.16  | | | | | | | | | | |            (86), (87), (88), (89), (90), (91), (92), (94),
% 228.57/40.16  | | | | | | | | | | |            (95), (96), (97), (98), (99), (100), (101), (102),
% 228.57/40.16  | | | | | | | | | | |            (104), (105), (106), (107), (108), (109), (110),
% 228.57/40.16  | | | | | | | | | | |            (111), (112), (113), (114), (115), (116), (117),
% 228.57/40.16  | | | | | | | | | | |            (118), (120), (121), (122), (123), (124), (125),
% 228.57/40.16  | | | | | | | | | | |            (126), (179), (223) are inconsistent by sub-proof
% 228.57/40.16  | | | | | | | | | | |            #575.
% 228.57/40.16  | | | | | | | | | | | 
% 228.57/40.16  | | | | | | | | | | End of split
% 228.57/40.16  | | | | | | | | | | 
% 228.57/40.16  | | | | | | | | | End of split
% 228.57/40.16  | | | | | | | | | 
% 228.57/40.16  | | | | | | | | End of split
% 228.57/40.16  | | | | | | | | 
% 228.57/40.16  | | | | | | | Case 2:
% 228.57/40.16  | | | | | | | | 
% 228.57/40.16  | | | | | | | |   (224)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 &
% 228.57/40.16  | | | | | | | |            op(e0, e0) = e2)
% 228.57/40.16  | | | | | | | | 
% 228.57/40.16  | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11),
% 228.57/40.16  | | | | | | | |            (12), (13), (14), (15), (16), (17), (18), (19), (20),
% 228.57/40.16  | | | | | | | |            (21), (22), (23), (24), (25), (26), (27), (28), (30),
% 228.57/40.16  | | | | | | | |            (31), (32), (33), (34), (36), (37), (38), (39), (40),
% 228.57/40.16  | | | | | | | |            (41), (42), (43), (44), (45), (46), (47), (48), (49),
% 228.57/40.16  | | | | | | | |            (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 228.57/40.16  | | | | | | | |            (59), (60), (62), (63), (64), (65), (66), (67), (68),
% 228.57/40.16  | | | | | | | |            (69), (70), (71), (72), (73), (74), (75), (76), (77),
% 228.57/40.16  | | | | | | | |            (78), (79), (80), (81), (82), (83), (84), (85), (86),
% 228.57/40.16  | | | | | | | |            (87), (88), (89), (90), (91), (92), (94), (95), (96),
% 228.57/40.16  | | | | | | | |            (97), (98), (99), (100), (101), (102), (104), (105),
% 228.57/40.16  | | | | | | | |            (106), (107), (108), (109), (110), (111), (112),
% 228.57/40.16  | | | | | | | |            (113), (114), (115), (116), (117), (118), (120),
% 228.57/40.16  | | | | | | | |            (121), (122), (123), (124), (125), (126), (194),
% 228.57/40.16  | | | | | | | |            (224) are inconsistent by sub-proof #573.
% 228.57/40.16  | | | | | | | | 
% 228.57/40.16  | | | | | | | End of split
% 228.57/40.16  | | | | | | | 
% 228.57/40.16  | | | | | | Case 2:
% 228.57/40.16  | | | | | | | 
% 228.57/40.16  | | | | | | |   (225)  all_57_15 = e1 & op(e0, e0) = e1
% 228.57/40.16  | | | | | | | 
% 228.57/40.16  | | | | | | | ALPHA: (225) implies:
% 228.57/40.16  | | | | | | |   (226)  op(e0, e0) = e1
% 228.57/40.16  | | | | | | | 
% 228.57/40.16  | | | | | | | REF_CLOSE: (12), (15), (86), (226) are inconsistent by sub-proof
% 228.57/40.16  | | | | | | |            #2183.
% 228.57/40.16  | | | | | | | 
% 228.57/40.16  | | | | | | End of split
% 228.57/40.16  | | | | | | 
% 228.57/40.16  | | | | | End of split
% 228.57/40.16  | | | | | 
% 228.57/40.16  | | | | End of split
% 228.57/40.16  | | | | 
% 228.57/40.16  | | | End of split
% 228.57/40.16  | | | 
% 228.57/40.16  | | End of split
% 228.57/40.16  | | 
% 228.57/40.16  | End of split
% 228.57/40.16  | 
% 228.57/40.16  End of proof
% 228.57/40.16  
% 228.57/40.16  Sub-proof #566 shows that the following formulas are inconsistent:
% 228.57/40.16  ----------------------------------------------------------------
% 228.57/40.16    (1)   ~ (all_53_2 = e2)
% 228.57/40.16    (2)  op(e0, e1) = all_53_11
% 228.57/40.16    (3)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.57/40.16    (4)   ~ (all_53_6 = all_53_14)
% 228.57/40.16    (5)   ~ (all_53_6 = e2)
% 228.57/40.16    (6)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.16         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.57/40.16    (7)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.57/40.16         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.57/40.16    (8)   ~ (all_53_8 = all_53_12)
% 228.57/40.16    (9)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.16         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.16    (10)   ~ (all_53_8 = all_53_11)
% 228.57/40.16    (11)   ~ (e3 = e1)
% 228.57/40.16    (12)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.57/40.16          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.57/40.16    (13)   ~ (all_53_13 = e1)
% 228.57/40.16    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.57/40.16            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.57/40.16    (15)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.57/40.16          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.57/40.16    (16)   ~ (all_53_3 = e3)
% 228.57/40.16    (17)   ~ (all_6_2 = e3)
% 228.57/40.16    (18)   ~ (all_53_9 = e1)
% 228.57/40.16    (19)  op(e1, e1) = all_6_2
% 228.57/40.16    (20)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.57/40.16    (21)   ~ (all_53_1 = all_53_9)
% 228.57/40.16    (22)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 228.57/40.16    (23)  op(e2, e2) = e1
% 228.57/40.16    (24)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.57/40.16          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.57/40.16    (25)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3)
% 228.57/40.16    (26)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 228.57/40.16            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 228.57/40.16              e3) = all_22_1 & $i(all_22_1))
% 228.57/40.16    (27)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 228.57/40.16    (28)  all_55_9 = all_53_6
% 228.57/40.16    (29)   ~ (all_53_4 = all_53_12)
% 228.57/40.16    (30)   ~ (all_53_4 = e1)
% 228.57/40.16    (31)   ~ (all_53_13 = e3)
% 228.57/40.16    (32)   ~ (all_53_8 = all_53_9)
% 228.57/40.16    (33)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.57/40.16          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.57/40.16    (34)   ~ (all_53_9 = all_53_11)
% 228.57/40.16    (35)  all_55_4 = all_53_1
% 228.57/40.16    (36)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.57/40.16          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.16    (37)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.57/40.16          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.57/40.16    (38)   ~ (e3 = e2)
% 228.57/40.16    (39)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 228.57/40.16    (40)  all_55_1 = all_53_4
% 228.57/40.16    (41)   ~ (all_53_1 = all_53_3)
% 228.57/40.16    (42)  op(e1, e0) = all_53_14
% 228.57/40.16    (43)   ~ (all_53_6 = all_53_7)
% 228.57/40.16    (44)  all_55_7 = e3 | all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 228.57/40.16    (45)   ~ (e3 = e0)
% 228.57/40.16    (46)  all_57_1 = e2
% 228.57/40.16    (47)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.57/40.16          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.57/40.16    (48)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.57/40.16    (49)  op(e0, e3) = all_53_3
% 228.57/40.16    (50)   ~ (all_53_2 = e0)
% 228.57/40.16    (51)  all_57_0 = e0
% 228.57/40.16    (52)  all_55_2 = all_53_8
% 228.57/40.16    (53)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 228.57/40.16    (54)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.57/40.16    (55)  all_57_15 = e3
% 228.57/40.16    (56)   ~ (all_53_9 = all_53_13)
% 228.57/40.16    (57)  op(e3, e3) = e0
% 228.57/40.16    (58)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.57/40.16          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.57/40.16            e1)
% 228.57/40.16    (59)   ~ (all_53_1 = e1)
% 228.57/40.16    (60)   ~ (all_53_4 = all_53_8)
% 228.57/40.16    (61)   ~ (all_53_14 = e3)
% 228.57/40.16    (62)  all_55_6 = all_53_9
% 228.57/40.16    (63)  op(e3, e2) = all_53_4
% 228.57/40.16    (64)   ~ (all_53_1 = all_53_2)
% 228.57/40.16    (65)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.57/40.16          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 228.57/40.16    (66)   ~ (e2 = e0)
% 228.57/40.16    (67)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.57/40.16            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.57/40.16            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.57/40.16            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.57/40.16              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.57/40.16            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.57/40.16            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.57/40.16              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.57/40.16              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.57/40.16            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.57/40.16            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.57/40.16            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.57/40.16              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.57/40.16              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.57/40.16            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.57/40.16              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.57/40.16            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.57/40.16            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.57/40.16              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.57/40.16              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.57/40.16            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.57/40.16            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.57/40.16    (68)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 228.57/40.16            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 228.57/40.16              e3) = all_12_1 & $i(all_12_1))
% 228.57/40.16    (69)   ~ (all_53_9 = e2)
% 228.57/40.16    (70)   ~ (all_53_6 = e1)
% 228.57/40.16    (71)  all_55_12 = all_53_3
% 228.57/40.16    (72)  all_57_3 = e1
% 228.57/40.16    (73)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.57/40.16          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.57/40.16    (74)   ~ (all_53_1 = e0)
% 228.57/40.16    (75)   ~ (all_53_2 = all_53_14)
% 228.57/40.16    (76)   ~ (e1 = e0)
% 228.57/40.16    (77)   ~ (all_53_4 = e0)
% 228.57/40.16    (78)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.57/40.16          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.57/40.16    (79)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.57/40.16          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.57/40.16    (80)   ~ (all_53_2 = all_53_3)
% 228.57/40.16    (81)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 228.57/40.16    (82)   ~ (all_53_11 = e2)
% 228.57/40.16    (83)  all_55_8 = all_53_2
% 228.57/40.16    (84)  op(e0, e0) = e3
% 228.57/40.16    (85)   ~ (all_53_4 = all_53_6)
% 228.57/40.16    (86)  op(e0, e2) = all_53_7
% 228.57/40.16    (87)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.16          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.57/40.16            e2)
% 228.57/40.16    (88)   ~ (all_53_8 = e2)
% 228.57/40.16    (89)   ~ (all_53_3 = e0)
% 228.57/40.16    (90)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.16              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.57/40.16                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.57/40.16                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.57/40.16    (91)  op(e1, e1) = e2
% 228.57/40.16    (92)   ~ (all_53_1 = all_53_13)
% 228.57/40.16    (93)  op(e2, e0) = all_53_13
% 228.57/40.16    (94)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.57/40.16          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.57/40.16    (95)  all_55_11 = all_53_14
% 228.57/40.16    (96)  all_55_3 = all_53_12
% 228.57/40.16    (97)   ~ (all_53_12 = e3)
% 228.57/40.16    (98)  all_57_7 = e3
% 228.57/40.16    (99)  op(e1, e3) = all_53_2
% 228.57/40.16    (100)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.16           (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.57/40.16    (101)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.57/40.16           (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.57/40.16    (102)   ~ (all_53_12 = e0)
% 228.57/40.16    (103)   ~ (all_53_13 = all_53_14)
% 228.57/40.16    (104)   ~ (all_53_8 = e0)
% 228.57/40.16    (105)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.57/40.16           (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 228.57/40.16    (106)   ~ (e2 = e1)
% 228.57/40.16    (107)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.57/40.16           | (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.57/40.16             e2)
% 228.57/40.16    (108)   ~ (all_53_14 = e2)
% 228.57/40.16    (109)   ~ (all_53_2 = all_53_6)
% 228.57/40.16    (110)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.57/40.16           (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.57/40.16    (111)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 228.57/40.16    (112)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.57/40.16           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.57/40.16    (113)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.57/40.16           (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.57/40.16    (114)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.57/40.16           | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.57/40.16             e1)
% 228.57/40.16    (115)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.57/40.16           (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.57/40.16    (116)  all_55_14 = all_53_11
% 228.57/40.16    (117)  all_55_7 = all_53_13
% 228.57/40.16    (118)   ~ (all_53_11 = e3)
% 228.57/40.16    (119)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.16           (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.57/40.16    (120)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.57/40.16           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.57/40.16    (121)  op(e3, e0) = all_53_12
% 228.57/40.16  
% 228.57/40.16  Begin of proof
% 228.57/40.16  | 
% 228.57/40.16  | BETA: splitting (25) gives:
% 228.57/40.16  | 
% 228.57/40.16  | Case 1:
% 228.57/40.16  | | 
% 228.57/40.16  | |   (122)  all_57_0 = e3 & op(e3, e3) = e3
% 228.57/40.16  | | 
% 228.57/40.16  | | ALPHA: (122) implies:
% 228.57/40.16  | |   (123)  op(e3, e3) = e3
% 228.57/40.16  | | 
% 228.57/40.16  | | REF_CLOSE: (14), (45), (57), (123) are inconsistent by sub-proof #2494.
% 228.57/40.16  | | 
% 228.57/40.16  | Case 2:
% 228.57/40.16  | | 
% 228.57/40.16  | |   (124)  all_57_1 = e3 & op(e3, e2) = e3
% 228.57/40.16  | | 
% 228.57/40.16  | | ALPHA: (124) implies:
% 228.57/40.16  | |   (125)  all_57_1 = e3
% 228.57/40.16  | | 
% 228.57/40.16  | | COMBINE_EQS: (46), (125) imply:
% 228.57/40.16  | |   (126)  e3 = e2
% 228.57/40.16  | | 
% 228.57/40.16  | | SIMP: (126) implies:
% 228.57/40.16  | |   (127)  e3 = e2
% 228.57/40.16  | | 
% 228.57/40.16  | | COMBINE_EQS: (98), (127) imply:
% 228.57/40.16  | |   (128)  all_57_7 = e2
% 228.57/40.16  | | 
% 228.57/40.16  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.57/40.16  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 228.57/40.16  | |            (24), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 228.57/40.16  | |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (47),
% 228.57/40.16  | |            (48), (49), (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 228.57/40.16  | |            (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 228.57/40.17  | |            (70), (71), (72), (73), (74), (75), (76), (77), (78), (79), (80),
% 228.57/40.17  | |            (81), (82), (83), (84), (85), (86), (87), (88), (89), (90), (91),
% 228.57/40.17  | |            (92), (93), (94), (95), (96), (97), (99), (100), (101), (102),
% 228.57/40.17  | |            (103), (104), (105), (106), (107), (108), (109), (110), (111),
% 228.57/40.17  | |            (112), (113), (114), (115), (116), (117), (118), (119), (120),
% 228.57/40.17  | |            (121), (125), (128) are inconsistent by sub-proof #578.
% 228.57/40.17  | | 
% 228.57/40.17  | End of split
% 228.57/40.17  | 
% 228.57/40.17  End of proof
% 228.57/40.17  
% 228.57/40.17  Sub-proof #567 shows that the following formulas are inconsistent:
% 228.57/40.17  ----------------------------------------------------------------
% 228.57/40.17    (1)   ~ (e3 = e1)
% 228.57/40.17    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.57/40.17           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.57/40.17    (3)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.57/40.17         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.57/40.17    (4)   ~ (all_6_2 = e3)
% 228.57/40.17    (5)  op(e1, e1) = all_6_2
% 228.57/40.17    (6)  op(e2, e2) = e1
% 228.57/40.17    (7)  all_57_9 = e1
% 228.57/40.17    (8)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.57/40.17         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.57/40.17    (9)  all_57_6 = e1
% 228.57/40.17    (10)   ~ (e3 = e2)
% 228.57/40.17    (11)   ~ (e3 = e0)
% 228.57/40.17    (12)  all_57_15 = e3
% 228.57/40.17    (13)  op(e3, e3) = e0
% 228.57/40.17    (14)   ~ (e2 = e0)
% 228.57/40.17    (15)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.57/40.17          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.57/40.17    (16)   ~ (e1 = e0)
% 228.57/40.17    (17)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0)
% 228.57/40.17    (18)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.17              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.57/40.17                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.57/40.17                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.57/40.17    (19)   ~ (all_53_12 = e3)
% 228.57/40.17    (20)  all_57_7 = e3
% 228.57/40.17    (21)   ~ (e2 = e1)
% 228.57/40.17    (22)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.57/40.17          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.57/40.17    (23)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.57/40.17          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.57/40.17    (24)  op(e3, e0) = all_53_12
% 228.57/40.17  
% 228.57/40.17  Begin of proof
% 228.57/40.17  | 
% 228.57/40.17  | BETA: splitting (17) gives:
% 228.57/40.17  | 
% 228.57/40.17  | Case 1:
% 228.57/40.17  | | 
% 228.57/40.17  | |   (25)  all_57_1 = e0 & op(e3, e2) = e0
% 228.57/40.17  | | 
% 228.57/40.17  | | ALPHA: (25) implies:
% 228.57/40.17  | |   (26)  all_57_1 = e0
% 228.57/40.17  | | 
% 228.57/40.17  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 228.57/40.17  | |            (14), (15), (16), (18), (19), (20), (21), (22), (23), (24), (26)
% 228.57/40.17  | |            are inconsistent by sub-proof #920.
% 228.57/40.17  | | 
% 228.57/40.17  | Case 2:
% 228.57/40.17  | | 
% 228.57/40.17  | |   (27)  all_57_3 = e0 & op(e2, e2) = e0
% 228.57/40.17  | | 
% 228.57/40.17  | | ALPHA: (27) implies:
% 228.57/40.17  | |   (28)  op(e2, e2) = e0
% 228.57/40.17  | | 
% 228.57/40.17  | | REF_CLOSE: (2), (6), (16), (28) are inconsistent by sub-proof #2352.
% 228.57/40.17  | | 
% 228.57/40.17  | End of split
% 228.57/40.17  | 
% 228.57/40.17  End of proof
% 228.57/40.17  
% 228.57/40.17  Sub-proof #568 shows that the following formulas are inconsistent:
% 228.57/40.17  ----------------------------------------------------------------
% 228.57/40.17    (1)   ~ (all_53_2 = e2)
% 228.57/40.17    (2)  op(e0, e1) = all_53_11
% 228.57/40.17    (3)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.57/40.17    (4)   ~ (all_53_6 = all_53_14)
% 228.57/40.17    (5)   ~ (all_53_6 = e2)
% 228.57/40.17    (6)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.17         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.57/40.17    (7)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.57/40.17         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.57/40.17    (8)   ~ (all_53_8 = all_53_12)
% 228.57/40.17    (9)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.17         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.17    (10)   ~ (all_53_8 = all_53_11)
% 228.57/40.17    (11)   ~ (e3 = e1)
% 228.57/40.17    (12)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.57/40.17          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.57/40.17    (13)   ~ (all_53_13 = e1)
% 228.57/40.17    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.57/40.17            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.57/40.17    (15)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.57/40.17          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.57/40.17    (16)   ~ (all_53_3 = e3)
% 228.57/40.17    (17)   ~ (all_6_2 = e3)
% 228.57/40.17    (18)   ~ (all_53_9 = e1)
% 228.57/40.17    (19)  op(e1, e1) = all_6_2
% 228.57/40.17    (20)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.57/40.17    (21)   ~ (all_53_1 = all_53_9)
% 228.57/40.17    (22)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 228.57/40.17    (23)  op(e2, e2) = e1
% 228.57/40.17    (24)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.57/40.17          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.57/40.17    (25)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 228.57/40.17            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 228.57/40.17              e3) = all_22_1 & $i(all_22_1))
% 228.57/40.17    (26)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 228.57/40.17    (27)  all_55_9 = all_53_6
% 228.57/40.17    (28)   ~ (all_53_4 = all_53_12)
% 228.57/40.17    (29)   ~ (all_53_4 = e1)
% 228.57/40.17    (30)   ~ (all_53_13 = e3)
% 228.57/40.17    (31)   ~ (all_53_8 = all_53_9)
% 228.57/40.17    (32)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.57/40.17          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.57/40.17    (33)   ~ (all_53_9 = all_53_11)
% 228.57/40.17    (34)  all_55_4 = all_53_1
% 228.57/40.17    (35)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.57/40.17          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.17    (36)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.57/40.17          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.57/40.17    (37)   ~ (e3 = e2)
% 228.57/40.17    (38)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 228.57/40.17    (39)  all_55_1 = all_53_4
% 228.57/40.17    (40)   ~ (all_53_1 = all_53_3)
% 228.57/40.17    (41)  op(e1, e0) = all_53_14
% 228.57/40.17    (42)   ~ (all_53_6 = all_53_7)
% 228.57/40.17    (43)  all_55_7 = e3 | all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 228.57/40.17    (44)   ~ (e3 = e0)
% 228.57/40.17    (45)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.57/40.17          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.57/40.17    (46)  all_57_1 = e0
% 228.57/40.17    (47)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.57/40.17    (48)  op(e0, e3) = all_53_3
% 228.57/40.17    (49)   ~ (all_53_2 = e0)
% 228.57/40.17    (50)  all_57_0 = e0
% 228.57/40.17    (51)  all_55_2 = all_53_8
% 228.57/40.17    (52)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 228.57/40.17    (53)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 228.57/40.17          | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.57/40.17    (54)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.57/40.17    (55)  all_57_15 = e3
% 228.57/40.17    (56)   ~ (all_53_9 = all_53_13)
% 228.57/40.17    (57)  op(e3, e3) = e0
% 228.57/40.17    (58)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.57/40.17          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.57/40.17            e1)
% 228.57/40.17    (59)   ~ (all_53_1 = e1)
% 228.57/40.17    (60)  all_57_6 = e2
% 228.57/40.17    (61)  all_57_12 = e1
% 228.57/40.17    (62)   ~ (all_53_4 = all_53_8)
% 228.57/40.17    (63)   ~ (all_53_14 = e3)
% 228.57/40.17    (64)  all_55_6 = all_53_9
% 228.57/40.17    (65)  op(e3, e2) = all_53_4
% 228.57/40.17    (66)   ~ (all_53_1 = all_53_2)
% 228.57/40.17    (67)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.57/40.17          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 228.57/40.17    (68)   ~ (e2 = e0)
% 228.57/40.17    (69)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.57/40.17            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.57/40.17            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.57/40.17            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.57/40.17              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.57/40.17            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.57/40.17            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.57/40.17              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.57/40.17              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.57/40.17            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.57/40.17            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.57/40.17            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.57/40.17              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.57/40.17              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.57/40.17            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.57/40.17              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.57/40.17            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.57/40.17            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.57/40.17              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.57/40.17              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.57/40.17            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.57/40.17            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.57/40.17    (70)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 228.57/40.17            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 228.57/40.17              e3) = all_12_1 & $i(all_12_1))
% 228.57/40.17    (71)   ~ (all_53_9 = e2)
% 228.57/40.17    (72)   ~ (all_53_6 = e1)
% 228.57/40.17    (73)  all_55_12 = all_53_3
% 228.57/40.17    (74)  all_57_13 = e2
% 228.57/40.17    (75)  all_57_2 = e3
% 228.57/40.17    (76)  all_57_3 = e1
% 228.57/40.17    (77)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.57/40.17          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.57/40.17    (78)   ~ (all_53_1 = e0)
% 228.57/40.17    (79)   ~ (all_53_2 = all_53_14)
% 228.57/40.17    (80)   ~ (e1 = e0)
% 228.57/40.17    (81)   ~ (all_53_4 = e0)
% 228.57/40.17    (82)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.57/40.17          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.57/40.17    (83)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.57/40.17          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.57/40.17    (84)   ~ (all_53_2 = all_53_3)
% 228.57/40.17    (85)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 228.57/40.17    (86)   ~ (all_53_11 = e2)
% 228.57/40.17    (87)  all_55_8 = all_53_2
% 228.57/40.17    (88)  op(e0, e0) = e3
% 228.57/40.17    (89)   ~ (all_53_4 = all_53_6)
% 228.57/40.17    (90)  op(e0, e2) = all_53_7
% 228.57/40.17    (91)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.17          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.57/40.17            e2)
% 228.57/40.17    (92)   ~ (all_53_8 = e2)
% 228.57/40.17    (93)   ~ (all_53_3 = e0)
% 228.57/40.17    (94)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.17              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.57/40.17                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.57/40.17                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.57/40.17    (95)  op(e1, e1) = e2
% 228.57/40.17    (96)   ~ (all_53_1 = all_53_13)
% 228.57/40.17    (97)  op(e2, e0) = all_53_13
% 228.57/40.17    (98)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.57/40.17          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.57/40.17    (99)  all_55_11 = all_53_14
% 228.57/40.17    (100)  all_55_3 = all_53_12
% 228.57/40.17    (101)   ~ (all_53_12 = e3)
% 228.57/40.17    (102)  all_57_7 = e3
% 228.57/40.17    (103)  op(e1, e3) = all_53_2
% 228.57/40.17    (104)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.17           (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.57/40.17    (105)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.57/40.17           (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.57/40.17    (106)   ~ (all_53_12 = e0)
% 228.57/40.17    (107)   ~ (all_53_13 = all_53_14)
% 228.57/40.17    (108)   ~ (all_53_8 = e0)
% 228.57/40.17    (109)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.57/40.17           (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 228.57/40.17    (110)   ~ (e2 = e1)
% 228.57/40.17    (111)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.57/40.17           | (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.57/40.17             e2)
% 228.57/40.17    (112)   ~ (all_53_14 = e2)
% 228.57/40.17    (113)   ~ (all_53_2 = all_53_6)
% 228.57/40.17    (114)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.57/40.17           (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.57/40.17    (115)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 228.57/40.17    (116)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.57/40.17           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.57/40.17    (117)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.57/40.17           (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.57/40.17    (118)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.57/40.17           | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.57/40.17             e1)
% 228.57/40.17    (119)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.57/40.17           (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.57/40.17    (120)  all_55_14 = all_53_11
% 228.57/40.17    (121)  all_55_7 = all_53_13
% 228.57/40.17    (122)   ~ (all_53_11 = e3)
% 228.57/40.17    (123)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.17           (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.57/40.17    (124)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.57/40.17           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.57/40.17    (125)  op(e3, e0) = all_53_12
% 228.57/40.17  
% 228.57/40.17  Begin of proof
% 228.57/40.17  | 
% 228.57/40.17  | BETA: splitting (53) gives:
% 228.57/40.17  | 
% 228.57/40.17  | Case 1:
% 228.57/40.17  | | 
% 228.57/40.17  | |   (126)  all_57_12 = e0 & op(e0, e3) = e0
% 228.57/40.17  | | 
% 228.57/40.17  | | ALPHA: (126) implies:
% 228.57/40.17  | |   (127)  op(e0, e3) = e0
% 228.57/40.17  | | 
% 228.57/40.17  | | REF_CLOSE: (14), (48), (93), (127) are inconsistent by sub-proof #2366.
% 228.57/40.17  | | 
% 228.57/40.17  | Case 2:
% 228.57/40.17  | | 
% 228.57/40.17  | |   (128)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 228.57/40.17  | |            e0)
% 228.57/40.17  | | 
% 228.57/40.17  | | BETA: splitting (128) gives:
% 228.57/40.17  | | 
% 228.57/40.17  | | Case 1:
% 228.57/40.17  | | | 
% 228.57/40.17  | | |   (129)  all_57_13 = e0 & op(e0, e2) = e0
% 228.57/40.17  | | | 
% 228.57/40.17  | | | ALPHA: (129) implies:
% 228.57/40.17  | | |   (130)  all_57_13 = e0
% 228.57/40.17  | | | 
% 228.57/40.17  | | | COMBINE_EQS: (74), (130) imply:
% 228.57/40.17  | | |   (131)  e2 = e0
% 228.57/40.17  | | | 
% 228.57/40.17  | | | COMBINE_EQS: (60), (131) imply:
% 228.57/40.17  | | |   (132)  all_57_6 = e0
% 228.57/40.17  | | | 
% 228.57/40.17  | | | REF_CLOSE: (11), (14), (15), (17), (19), (37), (44), (55), (57), (61),
% 228.57/40.17  | | |            (68), (80), (94), (105), (110), (111), (114), (118), (132) are
% 228.57/40.17  | | |            inconsistent by sub-proof #1028.
% 228.57/40.17  | | | 
% 228.57/40.17  | | Case 2:
% 228.57/40.17  | | | 
% 228.57/40.17  | | |   (133)  all_57_14 = e0 & op(e0, e1) = e0
% 228.57/40.17  | | | 
% 228.57/40.17  | | | ALPHA: (133) implies:
% 228.57/40.17  | | |   (134)  all_57_14 = e0
% 228.57/40.17  | | | 
% 228.57/40.17  | | | BETA: splitting (77) gives:
% 228.57/40.17  | | | 
% 228.57/40.17  | | | Case 1:
% 228.57/40.17  | | | | 
% 228.57/40.17  | | | |   (135)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2)
% 228.57/40.17  | | | |            = e3)
% 228.57/40.17  | | | | 
% 228.57/40.17  | | | | BETA: splitting (135) gives:
% 228.57/40.17  | | | | 
% 228.57/40.17  | | | | Case 1:
% 228.57/40.17  | | | | | 
% 228.57/40.17  | | | | |   (136)  all_57_0 = e3 & op(e3, e3) = e3
% 228.57/40.17  | | | | | 
% 228.57/40.17  | | | | | ALPHA: (136) implies:
% 228.57/40.17  | | | | |   (137)  op(e3, e3) = e3
% 228.57/40.17  | | | | | 
% 228.57/40.17  | | | | | REF_CLOSE: (14), (44), (57), (137) are inconsistent by sub-proof
% 228.57/40.17  | | | | |            #2494.
% 228.57/40.17  | | | | | 
% 228.57/40.17  | | | | Case 2:
% 228.57/40.17  | | | | | 
% 228.57/40.17  | | | | |   (138)  all_57_1 = e3 & op(e3, e2) = e3
% 228.57/40.17  | | | | | 
% 228.57/40.17  | | | | | ALPHA: (138) implies:
% 228.57/40.17  | | | | |   (139)  all_57_1 = e3
% 228.57/40.17  | | | | | 
% 228.57/40.17  | | | | | COMBINE_EQS: (46), (139) imply:
% 228.57/40.17  | | | | |   (140)  e3 = e0
% 228.57/40.17  | | | | | 
% 228.57/40.17  | | | | | SIMP: (140) implies:
% 228.57/40.17  | | | | |   (141)  e3 = e0
% 228.57/40.17  | | | | | 
% 228.57/40.17  | | | | | COMBINE_EQS: (75), (141) imply:
% 228.57/40.17  | | | | |   (142)  all_57_2 = e0
% 228.57/40.17  | | | | | 
% 228.57/40.17  | | | | | REF_CLOSE: (9), (11), (14), (37), (44), (46), (55), (57), (58), (68),
% 228.57/40.17  | | | | |            (74), (76), (80), (88), (91), (102), (105), (110), (114),
% 228.57/40.17  | | | | |            (123), (134), (142) are inconsistent by sub-proof #1061.
% 228.57/40.17  | | | | | 
% 228.57/40.17  | | | | End of split
% 228.57/40.17  | | | | 
% 228.57/40.17  | | | Case 2:
% 228.57/40.17  | | | | 
% 228.57/40.17  | | | |   (143)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0)
% 228.57/40.17  | | | |            = e3)
% 228.57/40.17  | | | | 
% 228.57/40.17  | | | | BETA: splitting (143) gives:
% 228.57/40.17  | | | | 
% 228.57/40.17  | | | | Case 1:
% 228.57/40.17  | | | | | 
% 228.57/40.17  | | | | |   (144)  all_57_4 = e3 & op(e3, e1) = e3
% 228.57/40.17  | | | | | 
% 228.57/40.17  | | | | | ALPHA: (144) implies:
% 228.57/40.17  | | | | |   (145)  all_57_4 = e3
% 228.57/40.17  | | | | | 
% 228.57/40.17  | | | | | BETA: splitting (45) gives:
% 228.57/40.17  | | | | | 
% 228.57/40.17  | | | | | Case 1:
% 228.57/40.17  | | | | | | 
% 228.57/40.17  | | | | | |   (146)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2,
% 228.57/40.17  | | | | | |              e1) = e1)
% 228.57/40.17  | | | | | | 
% 228.57/40.17  | | | | | | BETA: splitting (146) gives:
% 228.57/40.17  | | | | | | 
% 228.57/40.17  | | | | | | Case 1:
% 228.57/40.17  | | | | | | | 
% 228.57/40.17  | | | | | | |   (147)  all_57_4 = e1 & op(e3, e1) = e1
% 228.57/40.17  | | | | | | | 
% 228.57/40.17  | | | | | | | ALPHA: (147) implies:
% 228.57/40.17  | | | | | | |   (148)  all_57_4 = e1
% 228.57/40.17  | | | | | | | 
% 228.57/40.17  | | | | | | | COMBINE_EQS: (145), (148) imply:
% 228.57/40.17  | | | | | | |   (149)  e3 = e1
% 228.57/40.17  | | | | | | | 
% 228.57/40.17  | | | | | | | SIMP: (149) implies:
% 228.57/40.17  | | | | | | |   (150)  e3 = e1
% 228.57/40.17  | | | | | | | 
% 228.57/40.17  | | | | | | | COMBINE_EQS: (75), (150) imply:
% 228.57/40.17  | | | | | | |   (151)  all_57_2 = e1
% 228.57/40.17  | | | | | | | 
% 228.57/40.17  | | | | | | | REF_CLOSE: (11), (14), (37), (44), (55), (57), (58), (60), (68),
% 228.57/40.17  | | | | | | |            (80), (91), (105), (110), (134), (151) are inconsistent
% 228.57/40.17  | | | | | | |            by sub-proof #894.
% 228.57/40.17  | | | | | | | 
% 228.57/40.17  | | | | | | Case 2:
% 228.57/40.17  | | | | | | | 
% 228.57/40.17  | | | | | | |   (152)  all_57_5 = e1 & op(e2, e1) = e1
% 228.57/40.17  | | | | | | | 
% 228.57/40.17  | | | | | | | ALPHA: (152) implies:
% 228.57/40.17  | | | | | | |   (153)  all_57_5 = e1
% 228.57/40.17  | | | | | | | 
% 228.57/40.17  | | | | | | | BETA: splitting (116) gives:
% 228.57/40.17  | | | | | | | 
% 228.57/40.17  | | | | | | | Case 1:
% 228.57/40.17  | | | | | | | | 
% 228.57/40.17  | | | | | | | |   (154)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 &
% 228.57/40.17  | | | | | | | |            op(e2, e1) = e2)
% 228.57/40.17  | | | | | | | | 
% 228.57/40.17  | | | | | | | | BETA: splitting (154) gives:
% 228.57/40.17  | | | | | | | | 
% 228.57/40.17  | | | | | | | | Case 1:
% 228.57/40.17  | | | | | | | | | 
% 228.57/40.17  | | | | | | | | |   (155)  all_57_4 = e2 & op(e3, e1) = e2
% 228.57/40.17  | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | REF_CLOSE: (11), (14), (37), (44), (57), (60), (61), (75),
% 228.57/40.17  | | | | | | | | |            (105), (145), (155) are inconsistent by sub-proof
% 228.57/40.17  | | | | | | | | |            #899.
% 228.57/40.17  | | | | | | | | | 
% 228.57/40.17  | | | | | | | | Case 2:
% 228.57/40.17  | | | | | | | | | 
% 228.57/40.17  | | | | | | | | |   (156)  all_57_5 = e2 & op(e2, e1) = e2
% 228.57/40.17  | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | ALPHA: (156) implies:
% 228.57/40.17  | | | | | | | | |   (157)  all_57_5 = e2
% 228.57/40.17  | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | COMBINE_EQS: (153), (157) imply:
% 228.57/40.17  | | | | | | | | |   (158)  e2 = e1
% 228.57/40.17  | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | COMBINE_EQS: (74), (158) imply:
% 228.57/40.17  | | | | | | | | |   (159)  all_57_13 = e1
% 228.57/40.17  | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | COMBINE_EQS: (60), (158) imply:
% 228.57/40.17  | | | | | | | | |   (160)  all_57_6 = e1
% 228.57/40.17  | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | BETA: splitting (45) gives:
% 228.57/40.17  | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | Case 1:
% 228.57/40.17  | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | BETA: splitting (146) gives:
% 228.57/40.17  | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | Case 1:
% 228.57/40.17  | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | |   (161)  all_57_4 = e1 & op(e3, e1) = e1
% 228.57/40.17  | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | REF_CLOSE: (11), (145), (161) are inconsistent by sub-proof
% 228.57/40.17  | | | | | | | | | | |            #2484.
% 228.57/40.17  | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | Case 2:
% 228.57/40.17  | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | BETA: splitting (94) gives:
% 228.57/40.17  | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | Case 1:
% 228.57/40.17  | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | |   (162)  all_57_15 = e0 & op(e0, e0) = e0
% 228.57/40.17  | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | | ALPHA: (162) implies:
% 228.57/40.17  | | | | | | | | | | | |   (163)  op(e0, e0) = e0
% 228.57/40.17  | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | | REF_CLOSE: (14), (44), (88), (163) are inconsistent by
% 228.57/40.17  | | | | | | | | | | | |            sub-proof #2304.
% 228.57/40.17  | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | Case 2:
% 228.57/40.17  | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | |   (164)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 228.57/40.17  | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 228.57/40.17  | | | | | | | | | | | |              op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 228.57/40.17  | | | | | | | | | | | |                e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 228.57/40.17  | | | | | | | | | | | |              e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 228.57/40.17  | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | | ALPHA: (164) implies:
% 228.57/40.17  | | | | | | | | | | | |   (165)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 228.57/40.17  | | | | | | | | | | | |            e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 228.57/40.17  | | | | | | | | | | | |              e0) = e0)
% 228.57/40.17  | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | | BETA: splitting (15) gives:
% 228.57/40.17  | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | | Case 1:
% 228.57/40.17  | | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | | |   (166)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 228.57/40.17  | | | | | | | | | | | | |            & op(e1, e2) = e3)
% 228.57/40.17  | | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | | | BETA: splitting (166) gives:
% 228.57/40.17  | | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | | | Case 1:
% 228.57/40.17  | | | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | | | |   (167)  all_57_6 = e3 & op(e1, e3) = e3
% 228.57/40.17  | | | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | | | | REF_CLOSE: (11), (160), (167) are inconsistent by sub-proof
% 228.57/40.17  | | | | | | | | | | | | | |            #2346.
% 228.57/40.17  | | | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | | | Case 2:
% 228.57/40.17  | | | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | | | |   (168)  all_57_7 = e3 & op(e1, e2) = e3
% 228.57/40.17  | | | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | | | | BETA: splitting (9) gives:
% 228.57/40.17  | | | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | | | | Case 1:
% 228.57/40.17  | | | | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | | | | |   (169)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 228.57/40.17  | | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 228.57/40.17  | | | | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | | | | | BETA: splitting (169) gives:
% 228.57/40.17  | | | | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | | | | | Case 1:
% 228.57/40.17  | | | | | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | | | | | |   (170)  all_57_1 = e2 & op(e3, e2) = e2
% 228.57/40.17  | | | | | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | | | | | | ALPHA: (170) implies:
% 228.57/40.17  | | | | | | | | | | | | | | | |   (171)  all_57_1 = e2
% 228.57/40.17  | | | | | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | | | | | | BETA: splitting (53) gives:
% 228.57/40.17  | | | | | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | | | | | | Case 1:
% 228.57/40.17  | | | | | | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | | | | | | |   (172)  all_57_12 = e0 & op(e0, e3) = e0
% 228.57/40.17  | | | | | | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | | | | | | | ALPHA: (172) implies:
% 228.57/40.17  | | | | | | | | | | | | | | | | |   (173)  op(e0, e3) = e0
% 228.57/40.17  | | | | | | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (48), (93), (173) are inconsistent by
% 228.57/40.17  | | | | | | | | | | | | | | | | |            sub-proof #2366.
% 228.57/40.17  | | | | | | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | | | | | | Case 2:
% 228.57/40.17  | | | | | | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | | | | | | | BETA: splitting (128) gives:
% 228.57/40.17  | | | | | | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | | | | | | | Case 1:
% 228.57/40.17  | | | | | | | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | | | | | | | |   (174)  all_57_13 = e0 & op(e0, e2) = e0
% 228.57/40.17  | | | | | | | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (11), (37), (68), (75), (76), (80),
% 228.57/40.17  | | | | | | | | | | | | | | | | | |            (102), (104), (110), (153), (159), (171), (174)
% 228.57/40.17  | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #570.
% 228.57/40.17  | | | | | | | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | | | | | | | Case 2:
% 228.57/40.17  | | | | | | | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 228.57/40.17  | | | | | | | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | | | | | | | | Case 1:
% 228.57/40.17  | | | | | | | | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | | | | | | | | |   (175)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 228.57/40.17  | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e0)
% 228.57/40.17  | | | | | | | | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | | | | | | | | | BETA: splitting (175) gives:
% 228.57/40.17  | | | | | | | | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | | | | | | | | | Case 1:
% 228.57/40.17  | | | | | | | | | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | | | | | | | | | |   (176)  all_57_1 = e0 & op(e3, e2) = e0
% 228.57/40.17  | | | | | | | | | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11), (14), (23), (37), (44), (46), (53),
% 228.57/40.17  | | | | | | | | | | | | | | | | | | | |            (55), (58), (68), (80), (83), (88), (91), (110),
% 228.57/40.17  | | | | | | | | | | | | | | | | | | | |            (134), (159) are inconsistent by sub-proof #1736.
% 228.57/40.17  | | | | | | | | | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | | | | | | | | | Case 2:
% 228.57/40.17  | | | | | | | | | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | | | | | | | | | |   (177)  all_57_3 = e0 & op(e2, e2) = e0
% 228.57/40.17  | | | | | | | | | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | | | | | | | | | | ALPHA: (177) implies:
% 228.57/40.17  | | | | | | | | | | | | | | | | | | | |   (178)  op(e2, e2) = e0
% 228.57/40.17  | | | | | | | | | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (23), (80), (178) are inconsistent by
% 228.57/40.17  | | | | | | | | | | | | | | | | | | | |            sub-proof #2352.
% 228.57/40.17  | | | | | | | | | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | | | | | | | | | End of split
% 228.57/40.17  | | | | | | | | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | | | | | | | | Case 2:
% 228.57/40.17  | | | | | | | | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | | | | | | | | |   (179)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 228.57/40.17  | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0)
% 228.57/40.17  | | | | | | | | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | | | | | | | | | BETA: splitting (179) gives:
% 228.57/40.17  | | | | | | | | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | | | | | | | | | Case 1:
% 228.57/40.17  | | | | | | | | | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | | | | | | | | | |   (180)  all_57_7 = e0 & op(e1, e2) = e0
% 228.57/40.17  | | | | | | | | | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | | | | | | | | | | ALPHA: (180) implies:
% 228.57/40.17  | | | | | | | | | | | | | | | | | | | |   (181)  all_57_7 = e0
% 228.57/40.17  | | | | | | | | | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (14), (15), (17), (19), (37), (44), (55),
% 228.57/40.17  | | | | | | | | | | | | | | | | | | | |            (68), (80), (94), (110), (111), (118), (160),
% 228.57/40.17  | | | | | | | | | | | | | | | | | | | |            (181) are inconsistent by sub-proof #1735.
% 228.57/40.17  | | | | | | | | | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | | | | | | | | | Case 2:
% 228.57/40.17  | | | | | | | | | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | | | | | | | | | |   (182)  all_57_13 = e0 & op(e0, e2) = e0
% 228.57/40.17  | | | | | | | | | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (11), (37), (68), (75), (76), (80),
% 228.57/40.17  | | | | | | | | | | | | | | | | | | | |            (102), (104), (110), (153), (159), (171), (182)
% 228.57/40.17  | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #570.
% 228.57/40.17  | | | | | | | | | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | | | | | | | | | End of split
% 228.57/40.17  | | | | | | | | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | | | | | | | | End of split
% 228.57/40.17  | | | | | | | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | | | | | | | End of split
% 228.57/40.17  | | | | | | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | | | | | | End of split
% 228.57/40.17  | | | | | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | | | | | Case 2:
% 228.57/40.17  | | | | | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | | | | | |   (183)  all_57_3 = e2 & op(e2, e2) = e2
% 228.57/40.17  | | | | | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | | | | | | ALPHA: (183) implies:
% 228.57/40.17  | | | | | | | | | | | | | | | |   (184)  op(e2, e2) = e2
% 228.57/40.17  | | | | | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | | | | | | REF_CLOSE: (14), (23), (110), (184) are inconsistent by
% 228.57/40.17  | | | | | | | | | | | | | | | |            sub-proof #2306.
% 228.57/40.17  | | | | | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | | | | | End of split
% 228.57/40.17  | | | | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | | | | Case 2:
% 228.57/40.17  | | | | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | | | | |   (185)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 228.57/40.17  | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 228.57/40.17  | | | | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 228.57/40.17  | | | | | | | | | | | | | | | 
% 228.57/40.17  | | | | | | | | | | | | | | | Case 1:
% 228.57/40.17  | | | | | | | | | | | | | | | | 
% 228.57/40.18  | | | | | | | | | | | | | | | |   (186)  all_57_7 = e2 & op(e1, e2) = e2
% 228.57/40.18  | | | | | | | | | | | | | | | | 
% 228.57/40.18  | | | | | | | | | | | | | | | | ALPHA: (186) implies:
% 228.57/40.18  | | | | | | | | | | | | | | | |   (187)  all_57_7 = e2
% 228.57/40.18  | | | | | | | | | | | | | | | | 
% 228.57/40.18  | | | | | | | | | | | | | | | | REF_CLOSE: (37), (102), (187) are inconsistent by sub-proof
% 228.57/40.18  | | | | | | | | | | | | | | | |            #2102.
% 228.57/40.18  | | | | | | | | | | | | | | | | 
% 228.57/40.18  | | | | | | | | | | | | | | | Case 2:
% 228.57/40.18  | | | | | | | | | | | | | | | | 
% 228.57/40.18  | | | | | | | | | | | | | | | |   (188)  all_57_13 = e2 & op(e0, e2) = e2
% 228.57/40.18  | | | | | | | | | | | | | | | | 
% 228.57/40.18  | | | | | | | | | | | | | | | | REF_CLOSE: (74), (110), (159) are inconsistent by sub-proof
% 228.57/40.18  | | | | | | | | | | | | | | | |            #2327.
% 228.57/40.18  | | | | | | | | | | | | | | | | 
% 228.57/40.18  | | | | | | | | | | | | | | | End of split
% 228.57/40.18  | | | | | | | | | | | | | | | 
% 228.57/40.18  | | | | | | | | | | | | | | End of split
% 228.57/40.18  | | | | | | | | | | | | | | 
% 228.57/40.18  | | | | | | | | | | | | | End of split
% 228.57/40.18  | | | | | | | | | | | | | 
% 228.57/40.18  | | | | | | | | | | | | Case 2:
% 228.57/40.18  | | | | | | | | | | | | | 
% 228.57/40.18  | | | | | | | | | | | | |   (189)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 228.57/40.18  | | | | | | | | | | | | |            e3 & op(e1, e0) = e3)
% 228.57/40.18  | | | | | | | | | | | | | 
% 228.57/40.18  | | | | | | | | | | | | | REF_CLOSE: (11), (14), (17), (19), (37), (44), (55), (68),
% 228.57/40.18  | | | | | | | | | | | | |            (80), (110), (111), (118), (165), (189) are
% 228.57/40.18  | | | | | | | | | | | | |            inconsistent by sub-proof #1080.
% 228.57/40.18  | | | | | | | | | | | | | 
% 228.57/40.18  | | | | | | | | | | | | End of split
% 228.57/40.18  | | | | | | | | | | | | 
% 228.57/40.18  | | | | | | | | | | | End of split
% 228.57/40.18  | | | | | | | | | | | 
% 228.57/40.18  | | | | | | | | | | End of split
% 228.57/40.18  | | | | | | | | | | 
% 228.57/40.18  | | | | | | | | | Case 2:
% 228.57/40.18  | | | | | | | | | | 
% 228.57/40.18  | | | | | | | | | |   (190)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1
% 228.57/40.18  | | | | | | | | | |            & op(e0, e1) = e1)
% 228.57/40.18  | | | | | | | | | | 
% 228.57/40.18  | | | | | | | | | | BETA: splitting (190) gives:
% 228.57/40.18  | | | | | | | | | | 
% 228.57/40.18  | | | | | | | | | | Case 1:
% 228.57/40.18  | | | | | | | | | | | 
% 228.57/40.18  | | | | | | | | | | |   (191)  all_57_8 = e1 & op(e1, e1) = e1
% 228.57/40.18  | | | | | | | | | | | 
% 228.57/40.18  | | | | | | | | | | | ALPHA: (191) implies:
% 228.57/40.18  | | | | | | | | | | |   (192)  op(e1, e1) = e1
% 228.57/40.18  | | | | | | | | | | | 
% 228.57/40.18  | | | | | | | | | | | REF_CLOSE: (14), (95), (110), (192) are inconsistent by
% 228.57/40.18  | | | | | | | | | | |            sub-proof #2423.
% 228.57/40.18  | | | | | | | | | | | 
% 228.57/40.18  | | | | | | | | | | Case 2:
% 228.57/40.18  | | | | | | | | | | | 
% 228.57/40.18  | | | | | | | | | | |   (193)  all_57_14 = e1 & op(e0, e1) = e1
% 228.57/40.18  | | | | | | | | | | | 
% 228.57/40.18  | | | | | | | | | | | ALPHA: (193) implies:
% 228.57/40.18  | | | | | | | | | | |   (194)  all_57_14 = e1
% 228.57/40.18  | | | | | | | | | | | 
% 228.57/40.18  | | | | | | | | | | | REF_CLOSE: (7), (9), (11), (14), (15), (17), (19), (23),
% 228.57/40.18  | | | | | | | | | | |            (35), (37), (44), (48), (55), (57), (58), (67),
% 228.57/40.18  | | | | | | | | | | |            (68), (76), (77), (80), (83), (88), (93), (94),
% 228.57/40.18  | | | | | | | | | | |            (101), (105), (106), (110), (111), (114), (118),
% 228.57/40.18  | | | | | | | | | | |            (123), (125), (159), (160), (194) are inconsistent
% 228.57/40.18  | | | | | | | | | | |            by sub-proof #569.
% 228.57/40.18  | | | | | | | | | | | 
% 228.57/40.18  | | | | | | | | | | End of split
% 228.57/40.18  | | | | | | | | | | 
% 228.57/40.18  | | | | | | | | | End of split
% 228.57/40.18  | | | | | | | | | 
% 228.57/40.18  | | | | | | | | End of split
% 228.57/40.18  | | | | | | | | 
% 228.57/40.18  | | | | | | | Case 2:
% 228.57/40.18  | | | | | | | | 
% 228.57/40.18  | | | | | | | |   (195)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 &
% 228.57/40.18  | | | | | | | |            op(e0, e1) = e2)
% 228.57/40.18  | | | | | | | | 
% 228.57/40.18  | | | | | | | | BETA: splitting (195) gives:
% 228.57/40.18  | | | | | | | | 
% 228.57/40.18  | | | | | | | | Case 1:
% 228.57/40.18  | | | | | | | | | 
% 228.57/40.18  | | | | | | | | |   (196)  all_57_8 = e2 & op(e1, e1) = e2
% 228.57/40.18  | | | | | | | | | 
% 228.57/40.18  | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 228.57/40.18  | | | | | | | | |            (12), (13), (14), (15), (16), (17), (18), (19),
% 228.57/40.18  | | | | | | | | |            (20), (21), (22), (23), (24), (25), (26), (27),
% 228.57/40.18  | | | | | | | | |            (28), (29), (30), (31), (32), (33), (34), (35),
% 228.57/40.18  | | | | | | | | |            (36), (38), (39), (40), (41), (42), (43), (44),
% 228.57/40.18  | | | | | | | | |            (45), (47), (48), (49), (50), (51), (52), (54),
% 228.57/40.18  | | | | | | | | |            (55), (56), (57), (58), (59), (62), (63), (64),
% 228.57/40.18  | | | | | | | | |            (65), (66), (67), (68), (69), (70), (71), (72),
% 228.57/40.18  | | | | | | | | |            (73), (76), (77), (78), (79), (80), (81), (82),
% 228.57/40.18  | | | | | | | | |            (83), (84), (85), (86), (87), (88), (89), (90),
% 228.57/40.18  | | | | | | | | |            (91), (92), (93), (94), (96), (97), (98), (99),
% 228.57/40.18  | | | | | | | | |            (100), (101), (103), (104), (105), (106), (107),
% 228.57/40.18  | | | | | | | | |            (108), (109), (110), (111), (112), (113), (114),
% 228.57/40.18  | | | | | | | | |            (115), (116), (117), (118), (119), (120), (121),
% 228.57/40.18  | | | | | | | | |            (122), (123), (124), (125), (196) are inconsistent
% 228.57/40.18  | | | | | | | | |            by sub-proof #581.
% 228.57/40.18  | | | | | | | | | 
% 228.57/40.18  | | | | | | | | Case 2:
% 228.57/40.18  | | | | | | | | | 
% 228.57/40.18  | | | | | | | | |   (197)  all_57_14 = e2 & op(e0, e1) = e2
% 228.57/40.18  | | | | | | | | | 
% 228.57/40.18  | | | | | | | | | ALPHA: (197) implies:
% 228.57/40.18  | | | | | | | | |   (198)  all_57_14 = e2
% 228.57/40.18  | | | | | | | | | 
% 228.57/40.18  | | | | | | | | | COMBINE_EQS: (134), (198) imply:
% 228.57/40.18  | | | | | | | | |   (199)  e2 = e0
% 228.57/40.18  | | | | | | | | | 
% 228.57/40.18  | | | | | | | | | COMBINE_EQS: (60), (199) imply:
% 228.57/40.18  | | | | | | | | |   (200)  all_57_6 = e0
% 228.57/40.18  | | | | | | | | | 
% 228.57/40.18  | | | | | | | | | REF_CLOSE: (11), (14), (15), (17), (19), (37), (44), (55),
% 228.57/40.18  | | | | | | | | |            (57), (61), (68), (80), (94), (105), (110), (111),
% 228.57/40.18  | | | | | | | | |            (114), (118), (200) are inconsistent by sub-proof
% 228.57/40.18  | | | | | | | | |            #1028.
% 228.57/40.18  | | | | | | | | | 
% 228.57/40.18  | | | | | | | | End of split
% 228.57/40.18  | | | | | | | | 
% 228.57/40.18  | | | | | | | End of split
% 228.57/40.18  | | | | | | | 
% 228.57/40.18  | | | | | | End of split
% 228.57/40.18  | | | | | | 
% 228.57/40.18  | | | | | Case 2:
% 228.57/40.18  | | | | | | 
% 228.57/40.18  | | | | | |   (201)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 &
% 228.57/40.18  | | | | | |            op(e0, e1) = e1)
% 228.57/40.18  | | | | | | 
% 228.57/40.18  | | | | | | BETA: splitting (201) gives:
% 228.57/40.18  | | | | | | 
% 228.57/40.18  | | | | | | Case 1:
% 228.57/40.18  | | | | | | | 
% 228.57/40.18  | | | | | | |   (202)  all_57_8 = e1 & op(e1, e1) = e1
% 228.57/40.18  | | | | | | | 
% 228.57/40.18  | | | | | | | ALPHA: (202) implies:
% 228.57/40.18  | | | | | | |   (203)  op(e1, e1) = e1
% 228.57/40.18  | | | | | | | 
% 228.57/40.18  | | | | | | | REF_CLOSE: (14), (95), (110), (203) are inconsistent by sub-proof
% 228.57/40.18  | | | | | | |            #2423.
% 228.57/40.18  | | | | | | | 
% 228.57/40.18  | | | | | | Case 2:
% 228.57/40.18  | | | | | | | 
% 228.57/40.18  | | | | | | |   (204)  all_57_14 = e1 & op(e0, e1) = e1
% 228.57/40.18  | | | | | | | 
% 228.57/40.18  | | | | | | | REF_CLOSE: (9), (11), (37), (46), (68), (76), (80), (102), (110),
% 228.57/40.18  | | | | | | |            (123), (134), (204) are inconsistent by sub-proof
% 228.57/40.18  | | | | | | |            #1062.
% 228.57/40.18  | | | | | | | 
% 228.57/40.18  | | | | | | End of split
% 228.57/40.18  | | | | | | 
% 228.57/40.18  | | | | | End of split
% 228.57/40.18  | | | | | 
% 228.57/40.18  | | | | Case 2:
% 228.57/40.18  | | | | | 
% 228.57/40.18  | | | | |   (205)  all_57_9 = e3 & op(e3, e0) = e3
% 228.57/40.18  | | | | | 
% 228.57/40.18  | | | | | ALPHA: (205) implies:
% 228.57/40.18  | | | | |   (206)  op(e3, e0) = e3
% 228.57/40.18  | | | | | 
% 228.57/40.18  | | | | | REF_CLOSE: (14), (101), (125), (206) are inconsistent by sub-proof
% 228.57/40.18  | | | | |            #2458.
% 228.57/40.18  | | | | | 
% 228.57/40.18  | | | | End of split
% 228.57/40.18  | | | | 
% 228.57/40.18  | | | End of split
% 228.57/40.18  | | | 
% 228.57/40.18  | | End of split
% 228.57/40.18  | | 
% 228.57/40.18  | End of split
% 228.57/40.18  | 
% 228.57/40.18  End of proof
% 228.57/40.18  
% 228.57/40.18  Sub-proof #569 shows that the following formulas are inconsistent:
% 228.57/40.18  ----------------------------------------------------------------
% 228.57/40.18    (1)  all_57_13 = e1
% 228.57/40.18    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.57/40.18         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.57/40.18    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.18         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.18    (4)   ~ (e3 = e1)
% 228.57/40.18    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.57/40.18           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.57/40.18    (6)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.57/40.18         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.57/40.18    (7)   ~ (all_6_2 = e3)
% 228.57/40.18    (8)  op(e1, e1) = all_6_2
% 228.57/40.18    (9)  op(e2, e2) = e1
% 228.57/40.18    (10)  all_57_6 = e1
% 228.57/40.18    (11)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.57/40.18          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.18    (12)   ~ (e3 = e2)
% 228.57/40.18    (13)   ~ (e3 = e0)
% 228.57/40.18    (14)  op(e0, e3) = all_53_3
% 228.57/40.18    (15)  all_57_15 = e3
% 228.57/40.18    (16)  op(e3, e3) = e0
% 228.57/40.18    (17)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.57/40.18          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.57/40.18            e1)
% 228.57/40.18    (18)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.57/40.18          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 228.57/40.18    (19)   ~ (e2 = e0)
% 228.57/40.18    (20)  all_57_3 = e1
% 228.57/40.18    (21)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.57/40.18          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.57/40.18    (22)   ~ (e1 = e0)
% 228.57/40.18    (23)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.57/40.18          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.57/40.18    (24)  all_57_14 = e1
% 228.57/40.18    (25)  op(e0, e0) = e3
% 228.57/40.18    (26)   ~ (all_53_3 = e0)
% 228.57/40.18    (27)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.18              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.57/40.18                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.57/40.18                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.57/40.18    (28)   ~ (all_53_12 = e3)
% 228.57/40.18    (29)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.57/40.18          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.57/40.18    (30)   ~ (all_53_12 = e0)
% 228.57/40.18    (31)   ~ (e2 = e1)
% 228.57/40.18    (32)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.57/40.18          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.57/40.18    (33)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.57/40.18          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.57/40.18    (34)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.57/40.18          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.57/40.18    (35)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.18          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.57/40.18    (36)  op(e3, e0) = all_53_12
% 228.57/40.18  
% 228.57/40.18  Begin of proof
% 228.57/40.18  | 
% 228.57/40.18  | BETA: splitting (27) gives:
% 228.57/40.18  | 
% 228.57/40.18  | Case 1:
% 228.57/40.18  | | 
% 228.57/40.18  | |   (37)  all_57_15 = e0 & op(e0, e0) = e0
% 228.57/40.18  | | 
% 228.57/40.18  | | ALPHA: (37) implies:
% 228.57/40.18  | |   (38)  op(e0, e0) = e0
% 228.57/40.18  | | 
% 228.57/40.18  | | REF_CLOSE: (5), (13), (25), (38) are inconsistent by sub-proof #2304.
% 228.57/40.18  | | 
% 228.57/40.18  | Case 2:
% 228.57/40.18  | | 
% 228.57/40.18  | |   (39)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 228.57/40.18  | |             e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0 &
% 228.57/40.18  | |             op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 228.57/40.18  | |           (all_57_14 = e0 & op(e0, e1) = e0))
% 228.57/40.18  | | 
% 228.57/40.18  | | ALPHA: (39) implies:
% 228.57/40.18  | |   (40)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 228.57/40.18  | |           e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.57/40.18  | | 
% 228.57/40.18  | | BETA: splitting (40) gives:
% 228.57/40.18  | | 
% 228.57/40.18  | | Case 1:
% 228.57/40.18  | | | 
% 228.57/40.18  | | |   (41)  all_57_12 = e0 & op(e0, e3) = e0
% 228.57/40.18  | | | 
% 228.57/40.18  | | | ALPHA: (41) implies:
% 228.57/40.18  | | |   (42)  op(e0, e3) = e0
% 228.57/40.18  | | | 
% 228.57/40.18  | | | REF_CLOSE: (5), (14), (26), (42) are inconsistent by sub-proof #2366.
% 228.57/40.18  | | | 
% 228.57/40.18  | | Case 2:
% 228.57/40.18  | | | 
% 228.57/40.18  | | |   (43)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1)
% 228.57/40.18  | | |           = e0)
% 228.57/40.18  | | | 
% 228.57/40.18  | | | BETA: splitting (43) gives:
% 228.57/40.18  | | | 
% 228.57/40.18  | | | Case 1:
% 228.57/40.18  | | | | 
% 228.57/40.18  | | | |   (44)  all_57_13 = e0 & op(e0, e2) = e0
% 228.57/40.18  | | | | 
% 228.57/40.18  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 228.57/40.18  | | | |            (12), (13), (14), (15), (16), (17), (18), (19), (20), (21),
% 228.57/40.18  | | | |            (22), (23), (25), (26), (27), (28), (29), (30), (31), (32),
% 228.57/40.18  | | | |            (33), (34), (35), (36), (44) are inconsistent by sub-proof
% 228.57/40.18  | | | |            #977.
% 228.57/40.18  | | | | 
% 228.57/40.18  | | | Case 2:
% 228.57/40.18  | | | | 
% 228.57/40.18  | | | |   (45)  all_57_14 = e0 & op(e0, e1) = e0
% 228.57/40.18  | | | | 
% 228.57/40.18  | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.57/40.18  | | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 228.57/40.18  | | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 228.57/40.18  | | | |            (33), (34), (35), (36), (45) are inconsistent by sub-proof
% 228.57/40.18  | | | |            #964.
% 228.57/40.18  | | | | 
% 228.57/40.18  | | | End of split
% 228.57/40.18  | | | 
% 228.57/40.18  | | End of split
% 228.57/40.18  | | 
% 228.57/40.18  | End of split
% 228.57/40.18  | 
% 228.57/40.18  End of proof
% 228.57/40.18  
% 228.57/40.18  Sub-proof #570 shows that the following formulas are inconsistent:
% 228.57/40.18  ----------------------------------------------------------------
% 228.57/40.18    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.18         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.57/40.18    (2)  all_57_13 = e1
% 228.57/40.18    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.18         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.18    (4)   ~ (e3 = e1)
% 228.57/40.18    (5)  all_57_13 = e0 & op(e0, e2) = e0
% 228.57/40.18    (6)   ~ (e3 = e2)
% 228.57/40.18    (7)  all_57_1 = e2
% 228.57/40.18    (8)   ~ (e2 = e0)
% 228.57/40.18    (9)  all_57_2 = e3
% 228.57/40.18    (10)  all_57_3 = e1
% 228.57/40.18    (11)   ~ (e1 = e0)
% 228.57/40.18    (12)  all_57_5 = e1
% 228.57/40.18    (13)  all_57_7 = e3
% 228.57/40.18    (14)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.18          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.57/40.18    (15)   ~ (e2 = e1)
% 228.57/40.18  
% 228.57/40.18  Begin of proof
% 228.57/40.18  | 
% 228.57/40.18  | ALPHA: (5) implies:
% 228.57/40.18  |   (16)  all_57_13 = e0
% 228.57/40.18  | 
% 228.57/40.18  | COMBINE_EQS: (2), (16) imply:
% 228.57/40.18  |   (17)  e1 = e0
% 228.57/40.18  | 
% 228.57/40.18  | COMBINE_EQS: (12), (17) imply:
% 228.57/40.18  |   (18)  all_57_5 = e0
% 228.57/40.18  | 
% 228.57/40.18  | COMBINE_EQS: (10), (17) imply:
% 228.57/40.18  |   (19)  all_57_3 = e0
% 228.57/40.18  | 
% 228.57/40.18  | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (11), (13), (14), (15),
% 228.57/40.18  |            (18), (19) are inconsistent by sub-proof #571.
% 228.57/40.18  | 
% 228.57/40.18  End of proof
% 228.57/40.18  
% 228.57/40.18  Sub-proof #571 shows that the following formulas are inconsistent:
% 228.57/40.18  ----------------------------------------------------------------
% 228.57/40.18    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.18         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.57/40.18    (2)  all_57_13 = e1
% 228.57/40.18    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.18         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.18    (4)   ~ (e3 = e1)
% 228.57/40.18    (5)  all_57_3 = e0
% 228.57/40.18    (6)   ~ (e3 = e2)
% 228.57/40.18    (7)  all_57_1 = e2
% 228.57/40.18    (8)   ~ (e2 = e0)
% 228.57/40.18    (9)  all_57_2 = e3
% 228.57/40.18    (10)   ~ (e1 = e0)
% 228.57/40.18    (11)  all_57_7 = e3
% 228.57/40.18    (12)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.18          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.57/40.18    (13)   ~ (e2 = e1)
% 228.57/40.18    (14)  all_57_5 = e0
% 228.57/40.18  
% 228.57/40.18  Begin of proof
% 228.57/40.18  | 
% 228.57/40.18  | BETA: splitting (12) gives:
% 228.57/40.18  | 
% 228.57/40.18  | Case 1:
% 228.57/40.18  | | 
% 228.57/40.18  | |   (15)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 228.57/40.18  | |           e2)
% 228.57/40.18  | | 
% 228.57/40.18  | | BETA: splitting (15) gives:
% 228.57/40.18  | | 
% 228.57/40.18  | | Case 1:
% 228.57/40.18  | | | 
% 228.57/40.18  | | |   (16)  all_57_2 = e2 & op(e2, e3) = e2
% 228.57/40.18  | | | 
% 228.57/40.18  | | | ALPHA: (16) implies:
% 228.57/40.18  | | |   (17)  all_57_2 = e2
% 228.57/40.18  | | | 
% 228.57/40.18  | | | REF_CLOSE: (6), (9), (17) are inconsistent by sub-proof #1800.
% 228.57/40.18  | | | 
% 228.57/40.18  | | Case 2:
% 228.57/40.18  | | | 
% 228.57/40.18  | | |   (18)  all_57_3 = e2 & op(e2, e2) = e2
% 228.57/40.18  | | | 
% 228.57/40.18  | | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (11), (13), (18) are inconsistent
% 228.57/40.18  | | |            by sub-proof #1475.
% 228.57/40.18  | | | 
% 228.57/40.18  | | End of split
% 228.57/40.18  | | 
% 228.57/40.18  | Case 2:
% 228.57/40.18  | | 
% 228.57/40.18  | |   (19)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 228.57/40.18  | |           e2)
% 228.57/40.18  | | 
% 228.57/40.18  | | BETA: splitting (19) gives:
% 228.57/40.18  | | 
% 228.57/40.18  | | Case 1:
% 228.57/40.18  | | | 
% 228.57/40.18  | | |   (20)  all_57_5 = e2 & op(e2, e1) = e2
% 228.57/40.18  | | | 
% 228.57/40.18  | | | ALPHA: (20) implies:
% 228.57/40.18  | | |   (21)  all_57_5 = e2
% 228.57/40.18  | | | 
% 228.57/40.18  | | | COMBINE_EQS: (14), (21) imply:
% 228.57/40.18  | | |   (22)  e2 = e0
% 228.57/40.18  | | | 
% 228.57/40.18  | | | COMBINE_EQS: (7), (22) imply:
% 228.57/40.18  | | |   (23)  all_57_1 = e0
% 228.57/40.18  | | | 
% 228.57/40.18  | | | REF_CLOSE: (2), (3), (5), (6), (8), (11), (13), (23) are inconsistent by
% 228.57/40.18  | | |            sub-proof #2099.
% 228.57/40.18  | | | 
% 228.57/40.18  | | Case 2:
% 228.57/40.18  | | | 
% 228.57/40.18  | | |   (24)  all_57_10 = e2 & op(e2, e0) = e2
% 228.57/40.18  | | | 
% 228.57/40.18  | | | ALPHA: (24) implies:
% 228.57/40.18  | | |   (25)  all_57_10 = e2
% 228.57/40.18  | | | 
% 228.57/40.18  | | | REF_CLOSE: (1), (4), (5), (9), (10), (13), (14), (25) are inconsistent by
% 228.57/40.18  | | |            sub-proof #2359.
% 228.57/40.18  | | | 
% 228.57/40.18  | | End of split
% 228.57/40.18  | | 
% 228.57/40.18  | End of split
% 228.57/40.18  | 
% 228.57/40.18  End of proof
% 228.57/40.18  
% 228.57/40.18  Sub-proof #572 shows that the following formulas are inconsistent:
% 228.57/40.18  ----------------------------------------------------------------
% 228.57/40.18    (1)   ~ (all_53_2 = e2)
% 228.57/40.18    (2)  op(e0, e1) = all_53_11
% 228.57/40.18    (3)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.57/40.18    (4)   ~ (all_53_6 = all_53_14)
% 228.57/40.18    (5)   ~ (all_53_6 = e2)
% 228.57/40.18    (6)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.18         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.57/40.18    (7)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.57/40.18         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.57/40.18    (8)   ~ (all_53_8 = all_53_12)
% 228.57/40.18    (9)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.18         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.18    (10)   ~ (all_53_8 = all_53_11)
% 228.57/40.18    (11)   ~ (e3 = e1)
% 228.57/40.18    (12)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.57/40.18          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.57/40.18    (13)   ~ (all_53_13 = e1)
% 228.57/40.18    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.57/40.18            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.57/40.18    (15)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.57/40.18          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.57/40.18    (16)   ~ (all_53_3 = e3)
% 228.57/40.18    (17)   ~ (all_6_2 = e3)
% 228.57/40.18    (18)   ~ (all_53_9 = e1)
% 228.57/40.18    (19)  op(e1, e1) = all_6_2
% 228.57/40.18    (20)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.57/40.18    (21)   ~ (all_53_1 = all_53_9)
% 228.57/40.18    (22)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 228.57/40.18    (23)  op(e2, e2) = e1
% 228.57/40.18    (24)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.57/40.18          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.57/40.18    (25)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 228.57/40.18            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 228.57/40.18              e3) = all_22_1 & $i(all_22_1))
% 228.57/40.18    (26)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 228.57/40.18    (27)  all_55_9 = all_53_6
% 228.57/40.18    (28)   ~ (all_53_4 = all_53_12)
% 228.57/40.18    (29)   ~ (all_53_4 = e1)
% 228.57/40.18    (30)   ~ (all_53_13 = e3)
% 228.57/40.18    (31)   ~ (all_53_8 = all_53_9)
% 228.57/40.18    (32)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.57/40.18          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.57/40.18    (33)   ~ (all_53_9 = all_53_11)
% 228.57/40.18    (34)  all_55_4 = all_53_1
% 228.57/40.18    (35)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.57/40.18          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.18    (36)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.57/40.18          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.57/40.18    (37)   ~ (e3 = e2)
% 228.57/40.18    (38)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 228.57/40.18    (39)  all_55_1 = all_53_4
% 228.57/40.18    (40)   ~ (all_53_1 = all_53_3)
% 228.57/40.18    (41)  op(e1, e0) = all_53_14
% 228.57/40.18    (42)   ~ (all_53_6 = all_53_7)
% 228.57/40.18    (43)  all_55_7 = e3 | all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 228.57/40.18    (44)   ~ (e3 = e0)
% 228.57/40.18    (45)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.57/40.18          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.57/40.18    (46)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.57/40.18    (47)  op(e0, e3) = all_53_3
% 228.57/40.18    (48)   ~ (all_53_2 = e0)
% 228.57/40.18    (49)  all_57_0 = e0
% 228.57/40.18    (50)  all_55_2 = all_53_8
% 228.57/40.18    (51)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 228.57/40.18    (52)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.57/40.18    (53)  all_57_15 = e3
% 228.57/40.18    (54)   ~ (all_53_9 = all_53_13)
% 228.57/40.18    (55)  op(e3, e3) = e0
% 228.57/40.18    (56)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.57/40.18          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.57/40.18            e1)
% 228.57/40.18    (57)   ~ (all_53_1 = e1)
% 228.57/40.18    (58)  all_57_6 = e2
% 228.57/40.18    (59)   ~ (all_53_4 = all_53_8)
% 228.57/40.18    (60)   ~ (all_53_14 = e3)
% 228.57/40.18    (61)  all_55_6 = all_53_9
% 228.57/40.18    (62)  op(e3, e2) = all_53_4
% 228.57/40.18    (63)   ~ (all_53_1 = all_53_2)
% 228.57/40.18    (64)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.57/40.18          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 228.57/40.18    (65)   ~ (e2 = e0)
% 228.57/40.18    (66)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.57/40.18            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.57/40.18            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.57/40.18            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.57/40.18              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.57/40.18            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.57/40.18            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.57/40.18              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.57/40.18              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.57/40.18            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.57/40.18            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.57/40.18            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.57/40.18              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.57/40.18              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.57/40.18            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.57/40.18              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.57/40.18            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.57/40.18            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.57/40.18              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.57/40.18              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.57/40.18            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.57/40.18            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.57/40.18    (67)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 228.57/40.18            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 228.57/40.18              e3) = all_12_1 & $i(all_12_1))
% 228.57/40.18    (68)   ~ (all_53_9 = e2)
% 228.57/40.18    (69)   ~ (all_53_6 = e1)
% 228.57/40.18    (70)  all_55_12 = all_53_3
% 228.57/40.18    (71)  all_57_3 = e1
% 228.57/40.18    (72)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.57/40.18          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.57/40.18    (73)   ~ (all_53_1 = e0)
% 228.57/40.18    (74)   ~ (all_53_2 = all_53_14)
% 228.57/40.18    (75)   ~ (e1 = e0)
% 228.57/40.18    (76)   ~ (all_53_4 = e0)
% 228.57/40.18    (77)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.57/40.18          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.57/40.18    (78)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.57/40.18          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.57/40.18    (79)   ~ (all_53_2 = all_53_3)
% 228.57/40.18    (80)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 228.57/40.18    (81)   ~ (all_53_11 = e2)
% 228.57/40.18    (82)  all_55_8 = all_53_2
% 228.57/40.18    (83)  op(e0, e0) = e3
% 228.57/40.18    (84)   ~ (all_53_4 = all_53_6)
% 228.57/40.18    (85)  op(e0, e2) = all_53_7
% 228.57/40.18    (86)  all_57_2 = e1
% 228.57/40.18    (87)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.18          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.57/40.18            e2)
% 228.57/40.18    (88)   ~ (all_53_8 = e2)
% 228.57/40.18    (89)   ~ (all_53_3 = e0)
% 228.57/40.18    (90)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.18              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.57/40.18                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.57/40.18                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.57/40.18    (91)  op(e1, e1) = e2
% 228.57/40.18    (92)   ~ (all_53_1 = all_53_13)
% 228.57/40.18    (93)  op(e2, e0) = all_53_13
% 228.57/40.19    (94)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.57/40.19          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.57/40.19    (95)  all_55_11 = all_53_14
% 228.57/40.19    (96)  all_55_3 = all_53_12
% 228.57/40.19    (97)   ~ (all_53_12 = e3)
% 228.57/40.19    (98)  op(e1, e3) = all_53_2
% 228.57/40.19    (99)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.19          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.57/40.19    (100)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.57/40.19           (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.57/40.19    (101)   ~ (all_53_12 = e0)
% 228.57/40.19    (102)   ~ (all_53_13 = all_53_14)
% 228.57/40.19    (103)   ~ (all_53_8 = e0)
% 228.57/40.19    (104)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.57/40.19           (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 228.57/40.19    (105)   ~ (e2 = e1)
% 228.57/40.19    (106)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.57/40.19           | (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.57/40.19             e2)
% 228.57/40.19    (107)   ~ (all_53_14 = e2)
% 228.57/40.19    (108)   ~ (all_53_2 = all_53_6)
% 228.57/40.19    (109)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.57/40.19           (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.57/40.19    (110)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 228.57/40.19    (111)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.57/40.19           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.57/40.19    (112)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.57/40.19           (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.57/40.19    (113)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.57/40.19           | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.57/40.19             e1)
% 228.57/40.19    (114)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.57/40.19           (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.57/40.19    (115)  all_55_14 = all_53_11
% 228.57/40.19    (116)  all_55_7 = all_53_13
% 228.57/40.19    (117)   ~ (all_53_11 = e3)
% 228.57/40.19    (118)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.19           (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.57/40.19    (119)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.57/40.19           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.57/40.19    (120)  op(e3, e0) = all_53_12
% 228.57/40.19  
% 228.57/40.19  Begin of proof
% 228.57/40.19  | 
% 228.57/40.19  | BETA: splitting (94) gives:
% 228.57/40.19  | 
% 228.57/40.19  | Case 1:
% 228.57/40.19  | | 
% 228.57/40.19  | |   (121)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 228.57/40.19  | |            e3)
% 228.57/40.19  | | 
% 228.57/40.19  | | REF_CLOSE: (11), (14), (23), (86), (121) are inconsistent by sub-proof #995.
% 228.57/40.19  | | 
% 228.57/40.19  | Case 2:
% 228.57/40.19  | | 
% 228.57/40.19  | |   (122)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 228.57/40.19  | |            e3)
% 228.57/40.19  | | 
% 228.57/40.19  | | BETA: splitting (122) gives:
% 228.57/40.19  | | 
% 228.57/40.19  | | Case 1:
% 228.57/40.19  | | | 
% 228.57/40.19  | | |   (123)  all_57_5 = e3 & op(e2, e1) = e3
% 228.57/40.19  | | | 
% 228.57/40.19  | | | ALPHA: (123) implies:
% 228.57/40.19  | | |   (124)  all_57_5 = e3
% 228.57/40.19  | | | 
% 228.57/40.19  | | | BETA: splitting (36) gives:
% 228.57/40.19  | | | 
% 228.57/40.19  | | | Case 1:
% 228.57/40.19  | | | | 
% 228.57/40.19  | | | |   (125)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1)
% 228.57/40.19  | | | |            = e0)
% 228.57/40.19  | | | | 
% 228.57/40.19  | | | | BETA: splitting (125) gives:
% 228.57/40.19  | | | | 
% 228.57/40.19  | | | | Case 1:
% 228.57/40.19  | | | | | 
% 228.57/40.19  | | | | |   (126)  all_57_4 = e0 & op(e3, e1) = e0
% 228.57/40.19  | | | | | 
% 228.57/40.19  | | | | | REF_CLOSE: (9), (11), (14), (23), (24), (32), (37), (44), (45), (49),
% 228.57/40.19  | | | | |            (55), (64), (65), (72), (75), (78), (91), (97), (105),
% 228.57/40.19  | | | | |            (120), (124), (126) are inconsistent by sub-proof #927.
% 228.57/40.19  | | | | | 
% 228.57/40.19  | | | | Case 2:
% 228.57/40.19  | | | | | 
% 228.57/40.19  | | | | |   (127)  all_57_5 = e0 & op(e2, e1) = e0
% 228.57/40.19  | | | | | 
% 228.57/40.19  | | | | | REF_CLOSE: (44), (124), (127) are inconsistent by sub-proof #2414.
% 228.57/40.19  | | | | | 
% 228.57/40.19  | | | | End of split
% 228.57/40.19  | | | | 
% 228.57/40.19  | | | Case 2:
% 228.57/40.19  | | | | 
% 228.57/40.19  | | | |   (128)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0,
% 228.57/40.19  | | | |              e1) = e0)
% 228.57/40.19  | | | | 
% 228.57/40.19  | | | | BETA: splitting (128) gives:
% 228.57/40.19  | | | | 
% 228.57/40.19  | | | | Case 1:
% 228.57/40.19  | | | | | 
% 228.57/40.19  | | | | |   (129)  all_57_8 = e0 & op(e1, e1) = e0
% 228.57/40.19  | | | | | 
% 228.57/40.19  | | | | | ALPHA: (129) implies:
% 228.57/40.19  | | | | |   (130)  all_57_8 = e0
% 228.57/40.19  | | | | | 
% 228.57/40.19  | | | | | BETA: splitting (100) gives:
% 228.57/40.19  | | | | | 
% 228.57/40.19  | | | | | Case 1:
% 228.57/40.19  | | | | | | 
% 228.57/40.19  | | | | | |   (131)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2,
% 228.57/40.19  | | | | | |              e3) = e3)
% 228.57/40.19  | | | | | | 
% 228.57/40.19  | | | | | | REF_CLOSE: (11), (14), (44), (55), (86), (131) are inconsistent by
% 228.57/40.19  | | | | | |            sub-proof #2396.
% 228.57/40.19  | | | | | | 
% 228.57/40.19  | | | | | Case 2:
% 228.57/40.19  | | | | | | 
% 228.57/40.19  | | | | | |   (132)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 &
% 228.57/40.19  | | | | | |            op(e0, e3) = e3)
% 228.57/40.19  | | | | | | 
% 228.57/40.19  | | | | | | BETA: splitting (132) gives:
% 228.57/40.19  | | | | | | 
% 228.57/40.19  | | | | | | Case 1:
% 228.57/40.19  | | | | | | | 
% 228.57/40.19  | | | | | | |   (133)  all_57_6 = e3 & op(e1, e3) = e3
% 228.57/40.19  | | | | | | | 
% 228.57/40.19  | | | | | | | ALPHA: (133) implies:
% 228.57/40.19  | | | | | | |   (134)  all_57_6 = e3
% 228.57/40.19  | | | | | | | 
% 228.57/40.19  | | | | | | | REF_CLOSE: (37), (58), (134) are inconsistent by sub-proof #2463.
% 228.57/40.19  | | | | | | | 
% 228.57/40.19  | | | | | | Case 2:
% 228.57/40.19  | | | | | | | 
% 228.57/40.19  | | | | | | |   (135)  all_57_12 = e3 & op(e0, e3) = e3
% 228.57/40.19  | | | | | | | 
% 228.57/40.19  | | | | | | | ALPHA: (135) implies:
% 228.57/40.19  | | | | | | |   (136)  all_57_12 = e3
% 228.57/40.19  | | | | | | | 
% 228.57/40.19  | | | | | | | BETA: splitting (56) gives:
% 228.57/40.19  | | | | | | | 
% 228.57/40.19  | | | | | | | Case 1:
% 228.57/40.19  | | | | | | | | 
% 228.57/40.19  | | | | | | | |   (137)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 &
% 228.57/40.19  | | | | | | | |            op(e0, e2) = e1)
% 228.57/40.19  | | | | | | | | 
% 228.57/40.19  | | | | | | | | BETA: splitting (137) gives:
% 228.57/40.19  | | | | | | | | 
% 228.57/40.19  | | | | | | | | Case 1:
% 228.57/40.19  | | | | | | | | | 
% 228.57/40.19  | | | | | | | | |   (138)  all_57_12 = e1 & op(e0, e3) = e1
% 228.57/40.19  | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | REF_CLOSE: (11), (136), (138) are inconsistent by sub-proof
% 228.57/40.19  | | | | | | | | |            #2230.
% 228.57/40.19  | | | | | | | | | 
% 228.57/40.19  | | | | | | | | Case 2:
% 228.57/40.19  | | | | | | | | | 
% 228.57/40.19  | | | | | | | | |   (139)  all_57_13 = e1 & op(e0, e2) = e1
% 228.57/40.19  | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | ALPHA: (139) implies:
% 228.57/40.19  | | | | | | | | |   (140)  all_57_13 = e1
% 228.57/40.19  | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | BETA: splitting (15) gives:
% 228.57/40.19  | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | Case 1:
% 228.57/40.19  | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | |   (141)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 228.57/40.19  | | | | | | | | | |            & op(e1, e2) = e3)
% 228.57/40.19  | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | BETA: splitting (141) gives:
% 228.57/40.19  | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | Case 1:
% 228.57/40.19  | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | |   (142)  all_57_6 = e3 & op(e1, e3) = e3
% 228.57/40.19  | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | ALPHA: (142) implies:
% 228.57/40.19  | | | | | | | | | | |   (143)  all_57_6 = e3
% 228.57/40.19  | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | REF_CLOSE: (37), (58), (143) are inconsistent by sub-proof
% 228.57/40.19  | | | | | | | | | | |            #2463.
% 228.57/40.19  | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | Case 2:
% 228.57/40.19  | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | |   (144)  all_57_7 = e3 & op(e1, e2) = e3
% 228.57/40.19  | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | ALPHA: (144) implies:
% 228.57/40.19  | | | | | | | | | | |   (145)  all_57_7 = e3
% 228.57/40.19  | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | BETA: splitting (104) gives:
% 228.57/40.19  | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | Case 1:
% 228.57/40.19  | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | |   (146)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 228.57/40.19  | | | | | | | | | | | |            & op(e2, e2) = e0)
% 228.57/40.19  | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | BETA: splitting (146) gives:
% 228.57/40.19  | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | Case 1:
% 228.57/40.19  | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | |   (147)  all_57_2 = e0 & op(e2, e3) = e0
% 228.57/40.19  | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | ALPHA: (147) implies:
% 228.57/40.19  | | | | | | | | | | | | |   (148)  all_57_2 = e0
% 228.57/40.19  | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | REF_CLOSE: (6), (11), (14), (37), (44), (47), (53), (56),
% 228.57/40.19  | | | | | | | | | | | | |            (65), (71), (75), (83), (87), (89), (90), (99),
% 228.57/40.19  | | | | | | | | | | | | |            (105), (124), (136), (140), (148) are inconsistent
% 228.57/40.19  | | | | | | | | | | | | |            by sub-proof #1065.
% 228.57/40.19  | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | Case 2:
% 228.57/40.19  | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | |   (149)  all_57_3 = e0 & op(e2, e2) = e0
% 228.57/40.19  | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | ALPHA: (149) implies:
% 228.57/40.19  | | | | | | | | | | | | |   (150)  op(e2, e2) = e0
% 228.57/40.19  | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | REF_CLOSE: (14), (23), (75), (150) are inconsistent by
% 228.57/40.19  | | | | | | | | | | | | |            sub-proof #2352.
% 228.57/40.19  | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | End of split
% 228.57/40.19  | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | Case 2:
% 228.57/40.19  | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | |   (151)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 228.57/40.19  | | | | | | | | | | | |            e0 & op(e2, e0) = e0)
% 228.57/40.19  | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | BETA: splitting (151) gives:
% 228.57/40.19  | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | Case 1:
% 228.57/40.19  | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | |   (152)  all_57_5 = e0 & op(e2, e1) = e0
% 228.57/40.19  | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | REF_CLOSE: (44), (124), (152) are inconsistent by sub-proof
% 228.57/40.19  | | | | | | | | | | | | |            #2414.
% 228.57/40.19  | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | Case 2:
% 228.57/40.19  | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | |   (153)  all_57_10 = e0 & op(e2, e0) = e0
% 228.57/40.19  | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | ALPHA: (153) implies:
% 228.57/40.19  | | | | | | | | | | | | |   (154)  all_57_10 = e0
% 228.57/40.19  | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | BETA: splitting (9) gives:
% 228.57/40.19  | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | Case 1:
% 228.57/40.19  | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | |   (155)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 228.57/40.19  | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 228.57/40.19  | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | | BETA: splitting (155) gives:
% 228.57/40.19  | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | | Case 1:
% 228.57/40.19  | | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | | |   (156)  all_57_1 = e2 & op(e3, e2) = e2
% 228.57/40.19  | | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | | | ALPHA: (156) implies:
% 228.57/40.19  | | | | | | | | | | | | | | |   (157)  all_57_1 = e2
% 228.57/40.19  | | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | | | BETA: splitting (99) gives:
% 228.57/40.19  | | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | | | Case 1:
% 228.57/40.19  | | | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | | | |   (158)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 228.57/40.19  | | | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 228.57/40.19  | | | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | | | | BETA: splitting (158) gives:
% 228.57/40.19  | | | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | | | | Case 1:
% 228.57/40.19  | | | | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | | | | |   (159)  all_57_2 = e2 & op(e2, e3) = e2
% 228.57/40.19  | | | | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | | | | | ALPHA: (159) implies:
% 228.57/40.19  | | | | | | | | | | | | | | | | |   (160)  all_57_2 = e2
% 228.57/40.19  | | | | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | | | | | COMBINE_EQS: (86), (160) imply:
% 228.57/40.19  | | | | | | | | | | | | | | | | |   (161)  e2 = e1
% 228.57/40.19  | | | | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (14), (23), (37), (44), (64), (65), (75),
% 228.57/40.19  | | | | | | | | | | | | | | | | |            (105), (145), (157), (161) are inconsistent by
% 228.57/40.19  | | | | | | | | | | | | | | | | |            sub-proof #593.
% 228.57/40.19  | | | | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | | | | Case 2:
% 228.57/40.19  | | | | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | | | | |   (162)  all_57_3 = e2 & op(e2, e2) = e2
% 228.57/40.19  | | | | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | | | | | ALPHA: (162) implies:
% 228.57/40.19  | | | | | | | | | | | | | | | | |   (163)  op(e2, e2) = e2
% 228.57/40.19  | | | | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (23), (105), (163) are inconsistent by
% 228.57/40.19  | | | | | | | | | | | | | | | | |            sub-proof #2306.
% 228.57/40.19  | | | | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | | | | End of split
% 228.57/40.19  | | | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | | | Case 2:
% 228.57/40.19  | | | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | | | |   (164)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 228.57/40.19  | | | | | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 228.57/40.19  | | | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 228.57/40.19  | | | | | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 228.57/40.19  | | | | | | | | | | | | | | | |            (19), (20), (21), (22), (23), (24), (25), (26),
% 228.57/40.19  | | | | | | | | | | | | | | | |            (27), (28), (29), (30), (31), (32), (33), (34),
% 228.57/40.19  | | | | | | | | | | | | | | | |            (35), (36), (37), (38), (39), (40), (41), (42),
% 228.57/40.19  | | | | | | | | | | | | | | | |            (43), (44), (45), (46), (47), (48), (49), (50),
% 228.57/40.19  | | | | | | | | | | | | | | | |            (51), (52), (53), (54), (55), (56), (57), (58),
% 228.57/40.19  | | | | | | | | | | | | | | | |            (59), (60), (61), (62), (63), (64), (65), (66),
% 228.57/40.19  | | | | | | | | | | | | | | | |            (67), (68), (69), (70), (71), (72), (73), (74),
% 228.57/40.19  | | | | | | | | | | | | | | | |            (75), (76), (77), (78), (79), (80), (81), (82),
% 228.57/40.19  | | | | | | | | | | | | | | | |            (83), (84), (85), (86), (87), (88), (89), (90),
% 228.57/40.19  | | | | | | | | | | | | | | | |            (91), (92), (93), (94), (95), (96), (97), (98),
% 228.57/40.19  | | | | | | | | | | | | | | | |            (99), (100), (101), (102), (103), (104), (105),
% 228.57/40.19  | | | | | | | | | | | | | | | |            (106), (107), (108), (109), (110), (111), (112),
% 228.57/40.19  | | | | | | | | | | | | | | | |            (113), (114), (115), (116), (117), (118), (119),
% 228.57/40.19  | | | | | | | | | | | | | | | |            (120), (124), (136), (145), (154), (164) are
% 228.57/40.19  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #576.
% 228.57/40.19  | | | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | | | End of split
% 228.57/40.19  | | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | | Case 2:
% 228.57/40.19  | | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | | |   (165)  all_57_3 = e2 & op(e2, e2) = e2
% 228.57/40.19  | | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | | | ALPHA: (165) implies:
% 228.57/40.19  | | | | | | | | | | | | | | |   (166)  op(e2, e2) = e2
% 228.57/40.19  | | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | | | REF_CLOSE: (14), (23), (105), (166) are inconsistent by
% 228.57/40.19  | | | | | | | | | | | | | | |            sub-proof #2306.
% 228.57/40.19  | | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | | End of split
% 228.57/40.19  | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | Case 2:
% 228.57/40.19  | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | |   (167)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 228.57/40.19  | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 228.57/40.19  | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | | BETA: splitting (167) gives:
% 228.57/40.19  | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | | Case 1:
% 228.57/40.19  | | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | | |   (168)  all_57_7 = e2 & op(e1, e2) = e2
% 228.57/40.19  | | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | | | ALPHA: (168) implies:
% 228.57/40.19  | | | | | | | | | | | | | | |   (169)  all_57_7 = e2
% 228.57/40.19  | | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 228.57/40.19  | | | | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 228.57/40.19  | | | | | | | | | | | | | | |            (19), (20), (21), (22), (23), (24), (25), (26),
% 228.57/40.19  | | | | | | | | | | | | | | |            (27), (28), (29), (30), (31), (32), (33), (34),
% 228.57/40.19  | | | | | | | | | | | | | | |            (35), (36), (37), (38), (39), (40), (41), (42),
% 228.57/40.19  | | | | | | | | | | | | | | |            (43), (44), (45), (46), (47), (48), (49), (50),
% 228.57/40.19  | | | | | | | | | | | | | | |            (51), (52), (53), (54), (55), (56), (57), (59),
% 228.57/40.19  | | | | | | | | | | | | | | |            (60), (61), (62), (63), (64), (65), (66), (67),
% 228.57/40.19  | | | | | | | | | | | | | | |            (68), (69), (70), (71), (72), (73), (74), (75),
% 228.57/40.19  | | | | | | | | | | | | | | |            (76), (77), (78), (79), (80), (81), (82), (83),
% 228.57/40.19  | | | | | | | | | | | | | | |            (84), (85), (87), (88), (89), (90), (91), (92),
% 228.57/40.19  | | | | | | | | | | | | | | |            (93), (94), (95), (96), (97), (98), (99), (100),
% 228.57/40.19  | | | | | | | | | | | | | | |            (101), (102), (103), (104), (105), (106), (107),
% 228.57/40.19  | | | | | | | | | | | | | | |            (108), (109), (110), (111), (112), (113), (114),
% 228.57/40.19  | | | | | | | | | | | | | | |            (115), (116), (117), (118), (119), (120), (169)
% 228.57/40.19  | | | | | | | | | | | | | | |            are inconsistent by sub-proof #577.
% 228.57/40.19  | | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | | Case 2:
% 228.57/40.19  | | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | | |   (170)  all_57_13 = e2 & op(e0, e2) = e2
% 228.57/40.19  | | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | | | ALPHA: (170) implies:
% 228.57/40.19  | | | | | | | | | | | | | | |   (171)  all_57_13 = e2
% 228.57/40.19  | | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | | | REF_CLOSE: (105), (140), (171) are inconsistent by sub-proof
% 228.57/40.19  | | | | | | | | | | | | | | |            #2327.
% 228.57/40.19  | | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | | End of split
% 228.57/40.19  | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | End of split
% 228.57/40.19  | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | End of split
% 228.57/40.19  | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | End of split
% 228.57/40.19  | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | End of split
% 228.57/40.19  | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | Case 2:
% 228.57/40.19  | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | |   (172)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3
% 228.57/40.19  | | | | | | | | | |            & op(e1, e0) = e3)
% 228.57/40.19  | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | REF_CLOSE: (11), (14), (17), (19), (37), (44), (53), (65),
% 228.57/40.19  | | | | | | | | | |            (75), (90), (105), (106), (113), (172) are
% 228.57/40.19  | | | | | | | | | |            inconsistent by sub-proof #1786.
% 228.57/40.19  | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | End of split
% 228.57/40.19  | | | | | | | | | 
% 228.57/40.19  | | | | | | | | End of split
% 228.57/40.19  | | | | | | | | 
% 228.57/40.19  | | | | | | | Case 2:
% 228.57/40.19  | | | | | | | | 
% 228.57/40.19  | | | | | | | |   (173)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 &
% 228.57/40.19  | | | | | | | |            op(e0, e0) = e1)
% 228.57/40.19  | | | | | | | | 
% 228.57/40.19  | | | | | | | | BETA: splitting (173) gives:
% 228.57/40.19  | | | | | | | | 
% 228.57/40.19  | | | | | | | | Case 1:
% 228.57/40.19  | | | | | | | | | 
% 228.57/40.19  | | | | | | | | |   (174)  all_57_14 = e1 & op(e0, e1) = e1
% 228.57/40.19  | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | ALPHA: (174) implies:
% 228.57/40.19  | | | | | | | | |   (175)  all_57_14 = e1
% 228.57/40.19  | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | BETA: splitting (15) gives:
% 228.57/40.19  | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | Case 1:
% 228.57/40.19  | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | |   (176)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 228.57/40.19  | | | | | | | | | |            & op(e1, e2) = e3)
% 228.57/40.19  | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | BETA: splitting (176) gives:
% 228.57/40.19  | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | Case 1:
% 228.57/40.19  | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | |   (177)  all_57_6 = e3 & op(e1, e3) = e3
% 228.57/40.19  | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | ALPHA: (177) implies:
% 228.57/40.19  | | | | | | | | | | |   (178)  all_57_6 = e3
% 228.57/40.19  | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | REF_CLOSE: (37), (58), (178) are inconsistent by sub-proof
% 228.57/40.19  | | | | | | | | | | |            #2463.
% 228.57/40.19  | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | Case 2:
% 228.57/40.19  | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | |   (179)  all_57_7 = e3 & op(e1, e2) = e3
% 228.57/40.19  | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | ALPHA: (179) implies:
% 228.57/40.19  | | | | | | | | | | |   (180)  all_57_7 = e3
% 228.57/40.19  | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | BETA: splitting (104) gives:
% 228.57/40.19  | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | Case 1:
% 228.57/40.19  | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | |   (181)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 228.57/40.19  | | | | | | | | | | | |            & op(e2, e2) = e0)
% 228.57/40.19  | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | BETA: splitting (181) gives:
% 228.57/40.19  | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | Case 1:
% 228.57/40.19  | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | |   (182)  all_57_2 = e0 & op(e2, e3) = e0
% 228.57/40.19  | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | ALPHA: (182) implies:
% 228.57/40.19  | | | | | | | | | | | | |   (183)  all_57_2 = e0
% 228.57/40.19  | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | REF_CLOSE: (6), (7), (9), (11), (12), (14), (15), (17), (19),
% 228.57/40.19  | | | | | | | | | | | | |            (23), (24), (32), (35), (36), (37), (44), (45),
% 228.57/40.19  | | | | | | | | | | | | |            (47), (49), (53), (55), (56), (64), (65), (71),
% 228.57/40.19  | | | | | | | | | | | | |            (72), (75), (77), (78), (83), (87), (89), (90),
% 228.57/40.19  | | | | | | | | | | | | |            (97), (99), (100), (101), (105), (106), (109),
% 228.57/40.19  | | | | | | | | | | | | |            (111), (112), (113), (114), (118), (119), (120),
% 228.57/40.19  | | | | | | | | | | | | |            (124), (136), (175), (183) are inconsistent by
% 228.57/40.19  | | | | | | | | | | | | |            sub-proof #1022.
% 228.57/40.19  | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | Case 2:
% 228.57/40.19  | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | |   (184)  all_57_3 = e0 & op(e2, e2) = e0
% 228.57/40.19  | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | ALPHA: (184) implies:
% 228.57/40.19  | | | | | | | | | | | | |   (185)  op(e2, e2) = e0
% 228.57/40.19  | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | REF_CLOSE: (14), (23), (75), (185) are inconsistent by
% 228.57/40.19  | | | | | | | | | | | | |            sub-proof #2352.
% 228.57/40.19  | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | End of split
% 228.57/40.19  | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | Case 2:
% 228.57/40.19  | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | |   (186)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 228.57/40.19  | | | | | | | | | | | |            e0 & op(e2, e0) = e0)
% 228.57/40.19  | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | BETA: splitting (186) gives:
% 228.57/40.19  | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | Case 1:
% 228.57/40.19  | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | |   (187)  all_57_5 = e0 & op(e2, e1) = e0
% 228.57/40.19  | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | REF_CLOSE: (44), (124), (187) are inconsistent by sub-proof
% 228.57/40.19  | | | | | | | | | | | | |            #2414.
% 228.57/40.19  | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | Case 2:
% 228.57/40.19  | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | |   (188)  all_57_10 = e0 & op(e2, e0) = e0
% 228.57/40.19  | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | ALPHA: (188) implies:
% 228.57/40.19  | | | | | | | | | | | | |   (189)  all_57_10 = e0
% 228.57/40.19  | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | BETA: splitting (87) gives:
% 228.57/40.19  | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | Case 1:
% 228.57/40.19  | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | |   (190)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 228.57/40.19  | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 228.57/40.19  | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 228.57/40.19  | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | | Case 1:
% 228.57/40.19  | | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | | |   (191)  all_57_12 = e2 & op(e0, e3) = e2
% 228.57/40.19  | | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 228.57/40.19  | | | | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 228.57/40.19  | | | | | | | | | | | | | | |            (19), (20), (21), (22), (23), (24), (25), (26),
% 228.57/40.19  | | | | | | | | | | | | | | |            (27), (28), (29), (30), (31), (32), (33), (34),
% 228.57/40.19  | | | | | | | | | | | | | | |            (35), (36), (37), (38), (39), (40), (41), (42),
% 228.57/40.19  | | | | | | | | | | | | | | |            (43), (44), (45), (46), (47), (48), (49), (50),
% 228.57/40.19  | | | | | | | | | | | | | | |            (51), (52), (53), (54), (55), (56), (57), (59),
% 228.57/40.19  | | | | | | | | | | | | | | |            (60), (61), (62), (63), (64), (65), (66), (67),
% 228.57/40.19  | | | | | | | | | | | | | | |            (68), (69), (70), (71), (72), (73), (74), (75),
% 228.57/40.19  | | | | | | | | | | | | | | |            (76), (77), (78), (79), (80), (81), (82), (83),
% 228.57/40.19  | | | | | | | | | | | | | | |            (84), (85), (87), (88), (89), (90), (91), (92),
% 228.57/40.19  | | | | | | | | | | | | | | |            (93), (94), (95), (96), (97), (98), (99), (100),
% 228.57/40.19  | | | | | | | | | | | | | | |            (101), (102), (103), (104), (105), (106), (107),
% 228.57/40.19  | | | | | | | | | | | | | | |            (108), (109), (110), (111), (112), (113), (114),
% 228.57/40.19  | | | | | | | | | | | | | | |            (115), (116), (117), (118), (119), (120), (136),
% 228.57/40.19  | | | | | | | | | | | | | | |            (180), (191) are inconsistent by sub-proof #575.
% 228.57/40.19  | | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | | Case 2:
% 228.57/40.19  | | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | | |   (192)  all_57_13 = e2 & op(e0, e2) = e2
% 228.57/40.19  | | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | | | ALPHA: (192) implies:
% 228.57/40.19  | | | | | | | | | | | | | | |   (193)  all_57_13 = e2
% 228.57/40.19  | | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | | | BETA: splitting (99) gives:
% 228.57/40.19  | | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | | | Case 1:
% 228.57/40.19  | | | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | | | |   (194)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 228.57/40.19  | | | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 228.57/40.19  | | | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 228.57/40.19  | | | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | | | | Case 1:
% 228.57/40.19  | | | | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | | | | |   (195)  all_57_2 = e2 & op(e2, e3) = e2
% 228.57/40.19  | | | | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | | | | | ALPHA: (195) implies:
% 228.57/40.19  | | | | | | | | | | | | | | | | |   (196)  all_57_2 = e2
% 228.57/40.19  | | | | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (9), (11), (12), (14), (15), (17), (19),
% 228.57/40.19  | | | | | | | | | | | | | | | | |            (23), (24), (32), (35), (37), (44), (45), (47),
% 228.57/40.19  | | | | | | | | | | | | | | | | |            (49), (53), (55), (56), (64), (65), (71), (72),
% 228.57/40.19  | | | | | | | | | | | | | | | | |            (75), (77), (78), (83), (87), (89), (90), (97),
% 228.57/40.19  | | | | | | | | | | | | | | | | |            (99), (100), (101), (105), (106), (109), (111),
% 228.57/40.19  | | | | | | | | | | | | | | | | |            (112), (113), (114), (118), (119), (120), (124),
% 228.57/40.19  | | | | | | | | | | | | | | | | |            (130), (136), (175), (193), (196) are inconsistent
% 228.57/40.19  | | | | | | | | | | | | | | | | |            by sub-proof #574.
% 228.57/40.19  | | | | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | | | | Case 2:
% 228.57/40.19  | | | | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | | | | |   (197)  all_57_3 = e2 & op(e2, e2) = e2
% 228.57/40.19  | | | | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | | | | | ALPHA: (197) implies:
% 228.57/40.19  | | | | | | | | | | | | | | | | |   (198)  op(e2, e2) = e2
% 228.57/40.19  | | | | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (23), (105), (198) are inconsistent by
% 228.57/40.19  | | | | | | | | | | | | | | | | |            sub-proof #2306.
% 228.57/40.19  | | | | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | | | | End of split
% 228.57/40.19  | | | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | | | Case 2:
% 228.57/40.19  | | | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | | | |   (199)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 228.57/40.19  | | | | | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 228.57/40.19  | | | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 228.57/40.19  | | | | | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 228.57/40.19  | | | | | | | | | | | | | | | |            (19), (20), (21), (22), (23), (24), (25), (26),
% 228.57/40.19  | | | | | | | | | | | | | | | |            (27), (28), (29), (30), (31), (32), (33), (34),
% 228.57/40.19  | | | | | | | | | | | | | | | |            (35), (36), (37), (38), (39), (40), (41), (42),
% 228.57/40.19  | | | | | | | | | | | | | | | |            (43), (44), (45), (46), (47), (48), (49), (50),
% 228.57/40.19  | | | | | | | | | | | | | | | |            (51), (52), (53), (54), (55), (56), (57), (58),
% 228.57/40.19  | | | | | | | | | | | | | | | |            (59), (60), (61), (62), (63), (64), (65), (66),
% 228.57/40.19  | | | | | | | | | | | | | | | |            (67), (68), (69), (70), (71), (72), (73), (74),
% 228.57/40.19  | | | | | | | | | | | | | | | |            (75), (76), (77), (78), (79), (80), (81), (82),
% 228.57/40.19  | | | | | | | | | | | | | | | |            (83), (84), (85), (86), (87), (88), (89), (90),
% 228.57/40.19  | | | | | | | | | | | | | | | |            (91), (92), (93), (94), (95), (96), (97), (98),
% 228.57/40.19  | | | | | | | | | | | | | | | |            (99), (100), (101), (102), (103), (104), (105),
% 228.57/40.19  | | | | | | | | | | | | | | | |            (106), (107), (108), (109), (110), (111), (112),
% 228.57/40.19  | | | | | | | | | | | | | | | |            (113), (114), (115), (116), (117), (118), (119),
% 228.57/40.19  | | | | | | | | | | | | | | | |            (120), (124), (136), (180), (189), (199) are
% 228.57/40.19  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #576.
% 228.57/40.19  | | | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | | | End of split
% 228.57/40.19  | | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | | End of split
% 228.57/40.19  | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | Case 2:
% 228.57/40.19  | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | |   (200)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 228.57/40.19  | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 228.57/40.19  | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 228.57/40.19  | | | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 228.57/40.19  | | | | | | | | | | | | | |            (19), (20), (21), (22), (23), (24), (25), (26),
% 228.57/40.19  | | | | | | | | | | | | | |            (27), (28), (29), (30), (31), (32), (33), (34),
% 228.57/40.19  | | | | | | | | | | | | | |            (35), (36), (37), (38), (39), (40), (41), (42),
% 228.57/40.19  | | | | | | | | | | | | | |            (43), (44), (45), (46), (47), (48), (49), (50),
% 228.57/40.19  | | | | | | | | | | | | | |            (51), (52), (53), (54), (55), (56), (57), (59),
% 228.57/40.19  | | | | | | | | | | | | | |            (60), (61), (62), (63), (64), (65), (66), (67),
% 228.57/40.19  | | | | | | | | | | | | | |            (68), (69), (70), (71), (72), (73), (74), (75),
% 228.57/40.19  | | | | | | | | | | | | | |            (76), (77), (78), (79), (80), (81), (82), (83),
% 228.57/40.19  | | | | | | | | | | | | | |            (84), (85), (87), (88), (89), (90), (91), (92),
% 228.57/40.19  | | | | | | | | | | | | | |            (93), (94), (95), (96), (97), (98), (99), (100),
% 228.57/40.19  | | | | | | | | | | | | | |            (101), (102), (103), (104), (105), (106), (107),
% 228.57/40.19  | | | | | | | | | | | | | |            (108), (109), (110), (111), (112), (113), (114),
% 228.57/40.19  | | | | | | | | | | | | | |            (115), (116), (117), (118), (119), (120), (175),
% 228.57/40.19  | | | | | | | | | | | | | |            (180), (200) are inconsistent by sub-proof #573.
% 228.57/40.19  | | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | | End of split
% 228.57/40.19  | | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | | End of split
% 228.57/40.19  | | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | | End of split
% 228.57/40.19  | | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | End of split
% 228.57/40.19  | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | Case 2:
% 228.57/40.19  | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | |   (201)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3
% 228.57/40.19  | | | | | | | | | |            & op(e1, e0) = e3)
% 228.57/40.19  | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | | REF_CLOSE: (11), (14), (17), (19), (37), (44), (53), (65),
% 228.57/40.19  | | | | | | | | | |            (75), (90), (105), (106), (113), (201) are
% 228.57/40.19  | | | | | | | | | |            inconsistent by sub-proof #1786.
% 228.57/40.19  | | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | End of split
% 228.57/40.19  | | | | | | | | | 
% 228.57/40.19  | | | | | | | | Case 2:
% 228.57/40.19  | | | | | | | | | 
% 228.57/40.19  | | | | | | | | |   (202)  all_57_15 = e1 & op(e0, e0) = e1
% 228.57/40.19  | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | ALPHA: (202) implies:
% 228.57/40.19  | | | | | | | | |   (203)  op(e0, e0) = e1
% 228.57/40.19  | | | | | | | | | 
% 228.57/40.19  | | | | | | | | | REF_CLOSE: (11), (14), (83), (203) are inconsistent by
% 228.57/40.19  | | | | | | | | |            sub-proof #2183.
% 228.57/40.19  | | | | | | | | | 
% 228.57/40.19  | | | | | | | | End of split
% 228.57/40.19  | | | | | | | | 
% 228.57/40.19  | | | | | | | End of split
% 228.57/40.19  | | | | | | | 
% 228.57/40.19  | | | | | | End of split
% 228.57/40.19  | | | | | | 
% 228.57/40.19  | | | | | End of split
% 228.57/40.19  | | | | | 
% 228.57/40.19  | | | | Case 2:
% 228.57/40.19  | | | | | 
% 228.57/40.19  | | | | |   (204)  all_57_14 = e0 & op(e0, e1) = e0
% 228.57/40.19  | | | | | 
% 228.57/40.19  | | | | | ALPHA: (204) implies:
% 228.57/40.19  | | | | |   (205)  all_57_14 = e0
% 228.57/40.19  | | | | | 
% 228.57/40.19  | | | | | REF_CLOSE: (11), (14), (37), (44), (53), (55), (56), (58), (65), (75),
% 228.57/40.19  | | | | |            (86), (87), (100), (105), (205) are inconsistent by
% 228.57/40.19  | | | | |            sub-proof #894.
% 228.57/40.19  | | | | | 
% 228.57/40.19  | | | | End of split
% 228.57/40.19  | | | | 
% 228.57/40.19  | | | End of split
% 228.57/40.19  | | | 
% 228.57/40.19  | | Case 2:
% 228.57/40.19  | | | 
% 228.57/40.19  | | |   (206)  all_57_10 = e3 & op(e2, e0) = e3
% 228.57/40.19  | | | 
% 228.57/40.19  | | | ALPHA: (206) implies:
% 228.57/40.19  | | |   (207)  all_57_10 = e3
% 228.57/40.19  | | | 
% 228.57/40.19  | | | REF_CLOSE: (11), (14), (37), (44), (53), (65), (75), (83), (90), (105),
% 228.57/40.19  | | |            (106), (113), (207) are inconsistent by sub-proof #1746.
% 228.57/40.19  | | | 
% 228.57/40.19  | | End of split
% 228.57/40.19  | | 
% 228.57/40.19  | End of split
% 228.57/40.19  | 
% 228.57/40.19  End of proof
% 228.57/40.19  
% 228.57/40.19  Sub-proof #573 shows that the following formulas are inconsistent:
% 228.57/40.19  ----------------------------------------------------------------
% 228.57/40.19    (1)   ~ (all_53_2 = e2)
% 228.57/40.19    (2)  op(e0, e1) = all_53_11
% 228.57/40.19    (3)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.57/40.19    (4)   ~ (all_53_6 = all_53_14)
% 228.57/40.19    (5)   ~ (all_53_6 = e2)
% 228.57/40.19    (6)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.19         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.57/40.19    (7)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.57/40.19         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.57/40.19    (8)   ~ (all_53_8 = all_53_12)
% 228.57/40.19    (9)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.19         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.19    (10)   ~ (all_53_8 = all_53_11)
% 228.57/40.19    (11)   ~ (e3 = e1)
% 228.57/40.19    (12)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.57/40.19          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.57/40.19    (13)   ~ (all_53_13 = e1)
% 228.57/40.19    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.57/40.19            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.57/40.19    (15)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.57/40.19          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.57/40.19    (16)   ~ (all_53_3 = e3)
% 228.57/40.19    (17)   ~ (all_6_2 = e3)
% 228.57/40.19    (18)   ~ (all_53_9 = e1)
% 228.57/40.20    (19)  op(e1, e1) = all_6_2
% 228.57/40.20    (20)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.57/40.20    (21)   ~ (all_53_1 = all_53_9)
% 228.57/40.20    (22)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 228.57/40.20    (23)  op(e2, e2) = e1
% 228.57/40.20    (24)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.57/40.20          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.57/40.20    (25)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 228.57/40.20            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 228.57/40.20              e3) = all_22_1 & $i(all_22_1))
% 228.57/40.20    (26)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 228.57/40.20    (27)  all_55_9 = all_53_6
% 228.57/40.20    (28)   ~ (all_53_4 = all_53_12)
% 228.57/40.20    (29)   ~ (all_53_4 = e1)
% 228.57/40.20    (30)   ~ (all_53_13 = e3)
% 228.57/40.20    (31)   ~ (all_53_8 = all_53_9)
% 228.57/40.20    (32)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.57/40.20          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.57/40.20    (33)   ~ (all_53_9 = all_53_11)
% 228.57/40.20    (34)  all_55_4 = all_53_1
% 228.57/40.20    (35)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.57/40.20    (36)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.57/40.20          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.20    (37)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.57/40.20          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.57/40.20    (38)   ~ (e3 = e2)
% 228.57/40.20    (39)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 228.57/40.20    (40)  all_55_1 = all_53_4
% 228.57/40.20    (41)   ~ (all_53_1 = all_53_3)
% 228.57/40.20    (42)  op(e1, e0) = all_53_14
% 228.57/40.20    (43)   ~ (all_53_6 = all_53_7)
% 228.57/40.20    (44)  all_55_7 = e3 | all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 228.57/40.20    (45)   ~ (e3 = e0)
% 228.57/40.20    (46)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.57/40.20          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.57/40.20    (47)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.57/40.20    (48)  op(e0, e3) = all_53_3
% 228.57/40.20    (49)   ~ (all_53_2 = e0)
% 228.57/40.20    (50)  all_57_0 = e0
% 228.57/40.20    (51)  all_55_2 = all_53_8
% 228.57/40.20    (52)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 228.57/40.20    (53)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.57/40.20    (54)  all_57_15 = e3
% 228.57/40.20    (55)   ~ (all_53_9 = all_53_13)
% 228.57/40.20    (56)  op(e3, e3) = e0
% 228.57/40.20    (57)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.57/40.20          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.57/40.20            e1)
% 228.57/40.20    (58)   ~ (all_53_1 = e1)
% 228.57/40.20    (59)   ~ (all_53_4 = all_53_8)
% 228.57/40.20    (60)   ~ (all_53_14 = e3)
% 228.57/40.20    (61)  all_55_6 = all_53_9
% 228.57/40.20    (62)  op(e3, e2) = all_53_4
% 228.57/40.20    (63)   ~ (all_53_1 = all_53_2)
% 228.57/40.20    (64)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.57/40.20          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 228.57/40.20    (65)   ~ (e2 = e0)
% 228.57/40.20    (66)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.57/40.20            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.57/40.20            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.57/40.20            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.57/40.20              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.57/40.20            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.57/40.20            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.57/40.20              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.57/40.20              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.57/40.20            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.57/40.20            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.57/40.20            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.57/40.20              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.57/40.20              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.57/40.20            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.57/40.20              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.57/40.20            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.57/40.20            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.57/40.20              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.57/40.20              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.57/40.20            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.57/40.20            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.57/40.20    (67)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 228.57/40.20            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 228.57/40.20              e3) = all_12_1 & $i(all_12_1))
% 228.57/40.20    (68)   ~ (all_53_9 = e2)
% 228.57/40.20    (69)   ~ (all_53_6 = e1)
% 228.57/40.20    (70)  all_55_12 = all_53_3
% 228.57/40.20    (71)  all_57_3 = e1
% 228.57/40.20    (72)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.57/40.20          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.57/40.20    (73)   ~ (all_53_1 = e0)
% 228.57/40.20    (74)   ~ (all_53_2 = all_53_14)
% 228.57/40.20    (75)   ~ (e1 = e0)
% 228.57/40.20    (76)   ~ (all_53_4 = e0)
% 228.57/40.20    (77)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.57/40.20          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.57/40.20    (78)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.57/40.20          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.57/40.20    (79)   ~ (all_53_2 = all_53_3)
% 228.57/40.20    (80)  all_57_14 = e1
% 228.57/40.20    (81)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 228.57/40.20    (82)   ~ (all_53_11 = e2)
% 228.57/40.20    (83)  all_55_8 = all_53_2
% 228.57/40.20    (84)  op(e0, e0) = e3
% 228.57/40.20    (85)   ~ (all_53_4 = all_53_6)
% 228.57/40.20    (86)  op(e0, e2) = all_53_7
% 228.57/40.20    (87)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.20          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.57/40.20            e2)
% 228.57/40.20    (88)   ~ (all_53_8 = e2)
% 228.57/40.20    (89)   ~ (all_53_3 = e0)
% 228.57/40.20    (90)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.20              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.57/40.20                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.57/40.20                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.57/40.20    (91)  op(e1, e1) = e2
% 228.57/40.20    (92)   ~ (all_53_1 = all_53_13)
% 228.57/40.20    (93)  op(e2, e0) = all_53_13
% 228.57/40.20    (94)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.57/40.20          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.57/40.20    (95)  all_55_11 = all_53_14
% 228.57/40.20    (96)  all_55_3 = all_53_12
% 228.57/40.20    (97)   ~ (all_53_12 = e3)
% 228.57/40.20    (98)  all_57_7 = e3
% 228.57/40.20    (99)  op(e1, e3) = all_53_2
% 228.57/40.20    (100)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.20           (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.57/40.20    (101)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.57/40.20           (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.57/40.20    (102)   ~ (all_53_12 = e0)
% 228.57/40.20    (103)   ~ (all_53_13 = all_53_14)
% 228.57/40.20    (104)   ~ (all_53_8 = e0)
% 228.57/40.20    (105)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.57/40.20           (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 228.57/40.20    (106)   ~ (e2 = e1)
% 228.57/40.20    (107)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.57/40.20           | (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.57/40.20             e2)
% 228.57/40.20    (108)   ~ (all_53_14 = e2)
% 228.57/40.20    (109)   ~ (all_53_2 = all_53_6)
% 228.57/40.20    (110)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.57/40.20           (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.57/40.20    (111)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 228.57/40.20    (112)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.57/40.20           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.57/40.20    (113)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.57/40.20           (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.57/40.20    (114)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.57/40.20           | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.57/40.20             e1)
% 228.57/40.20    (115)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.57/40.20           (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.57/40.20    (116)  all_55_14 = all_53_11
% 228.57/40.20    (117)  all_55_7 = all_53_13
% 228.57/40.20    (118)   ~ (all_53_11 = e3)
% 228.57/40.20    (119)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.20           (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.57/40.20    (120)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.57/40.20           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.57/40.20    (121)  op(e3, e0) = all_53_12
% 228.57/40.20  
% 228.57/40.20  Begin of proof
% 228.57/40.20  | 
% 228.57/40.20  | BETA: splitting (35) gives:
% 228.57/40.20  | 
% 228.57/40.20  | Case 1:
% 228.57/40.20  | | 
% 228.57/40.20  | |   (122)  all_57_14 = e2 & op(e0, e1) = e2
% 228.57/40.20  | | 
% 228.57/40.20  | | ALPHA: (122) implies:
% 228.57/40.20  | |   (123)  all_57_14 = e2
% 228.57/40.20  | | 
% 228.57/40.20  | | REF_CLOSE: (80), (106), (123) are inconsistent by sub-proof #2178.
% 228.57/40.20  | | 
% 228.57/40.20  | Case 2:
% 228.57/40.20  | | 
% 228.57/40.20  | |   (124)  all_57_15 = e2 & op(e0, e0) = e2
% 228.57/40.20  | | 
% 228.57/40.20  | | ALPHA: (124) implies:
% 228.57/40.20  | |   (125)  all_57_15 = e2
% 228.57/40.20  | | 
% 228.57/40.20  | | COMBINE_EQS: (54), (125) imply:
% 228.57/40.20  | |   (126)  e3 = e2
% 228.57/40.20  | | 
% 228.57/40.20  | | COMBINE_EQS: (98), (126) imply:
% 228.57/40.20  | |   (127)  all_57_7 = e2
% 228.57/40.20  | | 
% 228.57/40.20  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.57/40.20  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 228.57/40.20  | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 228.57/40.20  | |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 228.57/40.20  | |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 228.57/40.20  | |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 228.57/40.20  | |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 228.57/40.20  | |            (81), (82), (83), (84), (85), (86), (87), (88), (89), (90), (91),
% 228.57/40.20  | |            (92), (93), (94), (95), (96), (97), (99), (100), (101), (102),
% 228.57/40.20  | |            (103), (104), (105), (106), (107), (108), (109), (110), (111),
% 228.57/40.20  | |            (112), (113), (114), (115), (116), (117), (118), (119), (120),
% 228.57/40.20  | |            (121), (127) are inconsistent by sub-proof #577.
% 228.57/40.20  | | 
% 228.57/40.20  | End of split
% 228.57/40.20  | 
% 228.57/40.20  End of proof
% 228.57/40.20  
% 228.57/40.20  Sub-proof #574 shows that the following formulas are inconsistent:
% 228.57/40.20  ----------------------------------------------------------------
% 228.57/40.20    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.20         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.57/40.20    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.57/40.20         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.57/40.20    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.20         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.20    (4)   ~ (e3 = e1)
% 228.57/40.20    (5)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.57/40.20         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.57/40.20    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.57/40.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.57/40.20    (7)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.57/40.20         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.57/40.20    (8)   ~ (all_6_2 = e3)
% 228.57/40.20    (9)  op(e1, e1) = all_6_2
% 228.57/40.20    (10)  op(e2, e2) = e1
% 228.57/40.20    (11)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.57/40.20          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.57/40.20    (12)  all_57_2 = e2
% 228.57/40.20    (13)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.57/40.20          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.57/40.20    (14)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.57/40.20          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.20    (15)   ~ (e3 = e2)
% 228.57/40.20    (16)   ~ (e3 = e0)
% 228.57/40.20    (17)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.57/40.20          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.57/40.20    (18)  op(e0, e3) = all_53_3
% 228.57/40.20    (19)  all_57_0 = e0
% 228.57/40.20    (20)  all_57_15 = e3
% 228.57/40.20    (21)  op(e3, e3) = e0
% 228.57/40.20    (22)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.57/40.20          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.57/40.20            e1)
% 228.57/40.20    (23)  all_57_5 = e3
% 228.57/40.20    (24)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.57/40.20          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 228.57/40.20    (25)   ~ (e2 = e0)
% 228.57/40.20    (26)  all_57_13 = e2
% 228.57/40.20    (27)  all_57_3 = e1
% 228.57/40.20    (28)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.57/40.20          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.57/40.20    (29)   ~ (e1 = e0)
% 228.57/40.20    (30)  all_57_12 = e3
% 228.57/40.20    (31)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.57/40.20          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.57/40.20    (32)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.57/40.20          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.57/40.20    (33)  all_57_14 = e1
% 228.57/40.20    (34)  op(e0, e0) = e3
% 228.57/40.20    (35)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.20          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.57/40.20            e2)
% 228.57/40.20    (36)   ~ (all_53_3 = e0)
% 228.57/40.20    (37)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.20              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.57/40.20                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.57/40.20                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.57/40.20    (38)   ~ (all_53_12 = e3)
% 228.57/40.20    (39)  all_57_8 = e0
% 228.57/40.20    (40)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.20          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.57/40.20    (41)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.57/40.20          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.57/40.20    (42)   ~ (all_53_12 = e0)
% 228.57/40.20    (43)   ~ (e2 = e1)
% 228.57/40.20    (44)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.57/40.20          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.57/40.20    (45)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.57/40.20          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.57/40.20    (46)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.57/40.20          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.57/40.20    (47)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.57/40.20          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.57/40.20    (48)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.57/40.20          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.57/40.20    (49)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.57/40.20          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.57/40.20    (50)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.20          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.57/40.20    (51)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.57/40.20          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.57/40.20    (52)  op(e3, e0) = all_53_12
% 228.57/40.20  
% 228.57/40.20  Begin of proof
% 228.57/40.20  | 
% 228.57/40.20  | BETA: splitting (37) gives:
% 228.57/40.20  | 
% 228.57/40.20  | Case 1:
% 228.57/40.20  | | 
% 228.57/40.20  | |   (53)  all_57_15 = e0 & op(e0, e0) = e0
% 228.57/40.20  | | 
% 228.57/40.20  | | ALPHA: (53) implies:
% 228.57/40.20  | |   (54)  op(e0, e0) = e0
% 228.57/40.20  | | 
% 228.57/40.20  | | REF_CLOSE: (6), (16), (34), (54) are inconsistent by sub-proof #2304.
% 228.57/40.20  | | 
% 228.57/40.20  | Case 2:
% 228.57/40.20  | | 
% 228.57/40.20  | |   (55)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 228.57/40.20  | |             e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0 &
% 228.57/40.20  | |             op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 228.57/40.20  | |           (all_57_14 = e0 & op(e0, e1) = e0))
% 228.57/40.20  | | 
% 228.57/40.20  | | ALPHA: (55) implies:
% 228.57/40.20  | |   (56)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 228.57/40.20  | |           e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.57/40.20  | | 
% 228.57/40.20  | | BETA: splitting (56) gives:
% 228.57/40.20  | | 
% 228.57/40.20  | | Case 1:
% 228.57/40.20  | | | 
% 228.57/40.20  | | |   (57)  all_57_12 = e0 & op(e0, e3) = e0
% 228.57/40.20  | | | 
% 228.57/40.20  | | | ALPHA: (57) implies:
% 228.57/40.20  | | |   (58)  op(e0, e3) = e0
% 228.57/40.20  | | | 
% 228.57/40.20  | | | REF_CLOSE: (6), (18), (36), (58) are inconsistent by sub-proof #2366.
% 228.57/40.20  | | | 
% 228.57/40.20  | | Case 2:
% 228.57/40.20  | | | 
% 228.57/40.20  | | |   (59)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1)
% 228.57/40.20  | | |           = e0)
% 228.57/40.20  | | | 
% 228.57/40.20  | | | BETA: splitting (59) gives:
% 228.57/40.20  | | | 
% 228.57/40.20  | | | Case 1:
% 228.57/40.20  | | | | 
% 228.57/40.20  | | | |   (60)  all_57_13 = e0 & op(e0, e2) = e0
% 228.57/40.20  | | | | 
% 228.57/40.20  | | | | ALPHA: (60) implies:
% 228.57/40.20  | | | |   (61)  all_57_13 = e0
% 228.57/40.20  | | | | 
% 228.57/40.20  | | | | COMBINE_EQS: (26), (61) imply:
% 228.57/40.20  | | | |   (62)  e2 = e0
% 228.57/40.20  | | | | 
% 228.57/40.20  | | | | SIMP: (62) implies:
% 228.57/40.20  | | | |   (63)  e2 = e0
% 228.57/40.20  | | | | 
% 228.57/40.20  | | | | COMBINE_EQS: (12), (63) imply:
% 228.57/40.20  | | | |   (64)  all_57_2 = e0
% 228.57/40.20  | | | | 
% 228.57/40.20  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 228.57/40.20  | | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 228.57/40.20  | | | |            (23), (24), (25), (27), (28), (29), (30), (31), (32), (33),
% 228.57/40.20  | | | |            (34), (35), (36), (37), (38), (39), (40), (41), (42), (43),
% 228.57/40.20  | | | |            (44), (45), (46), (47), (48), (49), (50), (51), (52), (61),
% 228.57/40.20  | | | |            (64) are inconsistent by sub-proof #1023.
% 228.57/40.20  | | | | 
% 228.57/40.20  | | | Case 2:
% 228.57/40.20  | | | | 
% 228.57/40.20  | | | |   (65)  all_57_14 = e0 & op(e0, e1) = e0
% 228.57/40.20  | | | | 
% 228.57/40.20  | | | | ALPHA: (65) implies:
% 228.57/40.20  | | | |   (66)  all_57_14 = e0
% 228.57/40.20  | | | | 
% 228.57/40.20  | | | | REF_CLOSE: (4), (15), (20), (22), (25), (29), (30), (35), (43), (66) are
% 228.57/40.20  | | | |            inconsistent by sub-proof #1763.
% 228.57/40.20  | | | | 
% 228.57/40.20  | | | End of split
% 228.57/40.20  | | | 
% 228.57/40.20  | | End of split
% 228.57/40.20  | | 
% 228.57/40.20  | End of split
% 228.57/40.20  | 
% 228.57/40.20  End of proof
% 228.57/40.20  
% 228.57/40.20  Sub-proof #575 shows that the following formulas are inconsistent:
% 228.57/40.20  ----------------------------------------------------------------
% 228.57/40.20    (1)   ~ (all_53_2 = e2)
% 228.57/40.20    (2)  op(e0, e1) = all_53_11
% 228.57/40.20    (3)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.57/40.20    (4)   ~ (all_53_6 = all_53_14)
% 228.57/40.20    (5)   ~ (all_53_6 = e2)
% 228.57/40.20    (6)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.20         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.57/40.20    (7)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.57/40.20         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.57/40.20    (8)   ~ (all_53_8 = all_53_12)
% 228.57/40.20    (9)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.20         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.20    (10)   ~ (all_53_8 = all_53_11)
% 228.57/40.20    (11)   ~ (e3 = e1)
% 228.57/40.20    (12)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.57/40.20          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.57/40.20    (13)   ~ (all_53_13 = e1)
% 228.57/40.20    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.57/40.20            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.57/40.20    (15)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.57/40.20          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.57/40.20    (16)   ~ (all_53_3 = e3)
% 228.57/40.20    (17)   ~ (all_6_2 = e3)
% 228.57/40.20    (18)   ~ (all_53_9 = e1)
% 228.57/40.20    (19)  op(e1, e1) = all_6_2
% 228.57/40.20    (20)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.57/40.20    (21)   ~ (all_53_1 = all_53_9)
% 228.57/40.20    (22)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 228.57/40.20    (23)  op(e2, e2) = e1
% 228.57/40.20    (24)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.57/40.20          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.57/40.20    (25)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 228.57/40.20            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 228.57/40.20              e3) = all_22_1 & $i(all_22_1))
% 228.57/40.20    (26)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 228.57/40.20    (27)  all_55_9 = all_53_6
% 228.57/40.20    (28)   ~ (all_53_4 = all_53_12)
% 228.57/40.20    (29)  all_57_12 = e2 & op(e0, e3) = e2
% 228.57/40.20    (30)   ~ (all_53_4 = e1)
% 228.57/40.20    (31)   ~ (all_53_13 = e3)
% 228.57/40.20    (32)   ~ (all_53_8 = all_53_9)
% 228.57/40.20    (33)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.57/40.20          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.57/40.20    (34)   ~ (all_53_9 = all_53_11)
% 228.57/40.20    (35)  all_55_4 = all_53_1
% 228.57/40.20    (36)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.57/40.20          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.20    (37)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.57/40.20          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.57/40.20    (38)   ~ (e3 = e2)
% 228.57/40.20    (39)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 228.57/40.20    (40)  all_55_1 = all_53_4
% 228.57/40.21    (41)   ~ (all_53_1 = all_53_3)
% 228.57/40.21    (42)  op(e1, e0) = all_53_14
% 228.57/40.21    (43)   ~ (all_53_6 = all_53_7)
% 228.57/40.21    (44)  all_55_7 = e3 | all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 228.57/40.21    (45)   ~ (e3 = e0)
% 228.57/40.21    (46)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.57/40.21          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.57/40.21    (47)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.57/40.21    (48)  op(e0, e3) = all_53_3
% 228.57/40.21    (49)   ~ (all_53_2 = e0)
% 228.57/40.21    (50)  all_57_0 = e0
% 228.57/40.21    (51)  all_55_2 = all_53_8
% 228.57/40.21    (52)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 228.57/40.21    (53)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.57/40.21    (54)  all_57_15 = e3
% 228.57/40.21    (55)   ~ (all_53_9 = all_53_13)
% 228.57/40.21    (56)  op(e3, e3) = e0
% 228.57/40.21    (57)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.57/40.21          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.57/40.21            e1)
% 228.57/40.21    (58)   ~ (all_53_1 = e1)
% 228.57/40.21    (59)   ~ (all_53_4 = all_53_8)
% 228.57/40.21    (60)   ~ (all_53_14 = e3)
% 228.57/40.21    (61)  all_55_6 = all_53_9
% 228.57/40.21    (62)  op(e3, e2) = all_53_4
% 228.57/40.21    (63)   ~ (all_53_1 = all_53_2)
% 228.57/40.21    (64)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.57/40.21          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 228.57/40.21    (65)   ~ (e2 = e0)
% 228.57/40.21    (66)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.57/40.21            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.57/40.21            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.57/40.21            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.57/40.21              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.57/40.21            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.57/40.21            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.57/40.21              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.57/40.21              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.57/40.21            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.57/40.21            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.57/40.21            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.57/40.21              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.57/40.21              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.57/40.21            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.57/40.21              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.57/40.21            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.57/40.21            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.57/40.21              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.57/40.21              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.57/40.21            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.57/40.21            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.57/40.21    (67)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 228.57/40.21            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 228.57/40.21              e3) = all_12_1 & $i(all_12_1))
% 228.57/40.21    (68)   ~ (all_53_9 = e2)
% 228.57/40.21    (69)   ~ (all_53_6 = e1)
% 228.57/40.21    (70)  all_55_12 = all_53_3
% 228.57/40.21    (71)  all_57_3 = e1
% 228.57/40.21    (72)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.57/40.21          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.57/40.21    (73)   ~ (all_53_1 = e0)
% 228.57/40.21    (74)   ~ (all_53_2 = all_53_14)
% 228.57/40.21    (75)   ~ (e1 = e0)
% 228.57/40.21    (76)  all_57_12 = e3
% 228.57/40.21    (77)   ~ (all_53_4 = e0)
% 228.57/40.21    (78)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.57/40.21          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.57/40.21    (79)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.57/40.21          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.57/40.21    (80)   ~ (all_53_2 = all_53_3)
% 228.57/40.21    (81)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 228.57/40.21    (82)   ~ (all_53_11 = e2)
% 228.57/40.21    (83)  all_55_8 = all_53_2
% 228.57/40.21    (84)  op(e0, e0) = e3
% 228.57/40.21    (85)   ~ (all_53_4 = all_53_6)
% 228.57/40.21    (86)  op(e0, e2) = all_53_7
% 228.57/40.21    (87)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.21          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.57/40.21            e2)
% 228.57/40.21    (88)   ~ (all_53_8 = e2)
% 228.57/40.21    (89)   ~ (all_53_3 = e0)
% 228.57/40.21    (90)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.21              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.57/40.21                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.57/40.21                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.57/40.21    (91)  op(e1, e1) = e2
% 228.57/40.21    (92)   ~ (all_53_1 = all_53_13)
% 228.57/40.21    (93)  op(e2, e0) = all_53_13
% 228.57/40.21    (94)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.57/40.21          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.57/40.21    (95)  all_55_11 = all_53_14
% 228.57/40.21    (96)  all_55_3 = all_53_12
% 228.57/40.21    (97)   ~ (all_53_12 = e3)
% 228.57/40.21    (98)  all_57_7 = e3
% 228.57/40.21    (99)  op(e1, e3) = all_53_2
% 228.57/40.21    (100)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.21           (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.57/40.21    (101)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.57/40.21           (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.57/40.21    (102)   ~ (all_53_12 = e0)
% 228.57/40.21    (103)   ~ (all_53_13 = all_53_14)
% 228.57/40.21    (104)   ~ (all_53_8 = e0)
% 228.57/40.21    (105)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.57/40.21           (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 228.57/40.21    (106)   ~ (e2 = e1)
% 228.57/40.21    (107)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.57/40.21           | (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.57/40.21             e2)
% 228.57/40.21    (108)   ~ (all_53_14 = e2)
% 228.57/40.21    (109)   ~ (all_53_2 = all_53_6)
% 228.57/40.21    (110)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.57/40.21           (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.57/40.21    (111)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 228.57/40.21    (112)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.57/40.21           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.57/40.21    (113)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.57/40.21           (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.57/40.21    (114)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.57/40.21           | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.57/40.21             e1)
% 228.57/40.21    (115)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.57/40.21           (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.57/40.21    (116)  all_55_14 = all_53_11
% 228.57/40.21    (117)  all_55_7 = all_53_13
% 228.57/40.21    (118)   ~ (all_53_11 = e3)
% 228.57/40.21    (119)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.21           (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.57/40.21    (120)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.57/40.21           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.57/40.21    (121)  op(e3, e0) = all_53_12
% 228.57/40.21  
% 228.57/40.21  Begin of proof
% 228.57/40.21  | 
% 228.57/40.21  | ALPHA: (29) implies:
% 228.57/40.21  |   (122)  all_57_12 = e2
% 228.57/40.21  | 
% 228.57/40.21  | COMBINE_EQS: (76), (122) imply:
% 228.57/40.21  |   (123)  e3 = e2
% 228.57/40.21  | 
% 228.57/40.21  | COMBINE_EQS: (98), (123) imply:
% 228.57/40.21  |   (124)  all_57_7 = e2
% 228.57/40.21  | 
% 228.57/40.21  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.57/40.21  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 228.57/40.21  |            (24), (25), (26), (27), (28), (30), (31), (32), (33), (34), (35),
% 228.57/40.21  |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 228.57/40.21  |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 228.57/40.21  |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 228.57/40.21  |            (69), (70), (71), (72), (73), (74), (75), (77), (78), (79), (80),
% 228.57/40.21  |            (81), (82), (83), (84), (85), (86), (87), (88), (89), (90), (91),
% 228.57/40.21  |            (92), (93), (94), (95), (96), (97), (99), (100), (101), (102),
% 228.57/40.21  |            (103), (104), (105), (106), (107), (108), (109), (110), (111),
% 228.57/40.21  |            (112), (113), (114), (115), (116), (117), (118), (119), (120),
% 228.57/40.21  |            (121), (124) are inconsistent by sub-proof #577.
% 228.57/40.21  | 
% 228.57/40.21  End of proof
% 228.57/40.21  
% 228.57/40.21  Sub-proof #576 shows that the following formulas are inconsistent:
% 228.57/40.21  ----------------------------------------------------------------
% 228.57/40.21    (1)   ~ (all_53_2 = e2)
% 228.57/40.21    (2)  op(e0, e1) = all_53_11
% 228.57/40.21    (3)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.57/40.21    (4)  all_57_10 = e0
% 228.57/40.21    (5)   ~ (all_53_6 = all_53_14)
% 228.57/40.21    (6)   ~ (all_53_6 = e2)
% 228.57/40.21    (7)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.21         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.57/40.21    (8)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.57/40.21         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.57/40.21    (9)   ~ (all_53_8 = all_53_12)
% 228.57/40.21    (10)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.21          (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.21    (11)   ~ (all_53_8 = all_53_11)
% 228.57/40.21    (12)   ~ (e3 = e1)
% 228.57/40.21    (13)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.57/40.21          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.57/40.21    (14)   ~ (all_53_13 = e1)
% 228.57/40.21    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.57/40.21            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.57/40.21    (16)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.57/40.21          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.57/40.21    (17)   ~ (all_53_3 = e3)
% 228.57/40.21    (18)   ~ (all_6_2 = e3)
% 228.57/40.21    (19)   ~ (all_53_9 = e1)
% 228.57/40.21    (20)  op(e1, e1) = all_6_2
% 228.57/40.21    (21)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.57/40.21    (22)   ~ (all_53_1 = all_53_9)
% 228.57/40.21    (23)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 228.57/40.21    (24)  op(e2, e2) = e1
% 228.57/40.21    (25)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.57/40.21          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.57/40.21    (26)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 228.57/40.21            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 228.57/40.21              e3) = all_22_1 & $i(all_22_1))
% 228.57/40.21    (27)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 228.57/40.21    (28)  all_55_9 = all_53_6
% 228.57/40.21    (29)   ~ (all_53_4 = all_53_12)
% 228.57/40.21    (30)   ~ (all_53_4 = e1)
% 228.57/40.21    (31)   ~ (all_53_13 = e3)
% 228.57/40.21    (32)   ~ (all_53_8 = all_53_9)
% 228.57/40.21    (33)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.57/40.21          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.57/40.21    (34)   ~ (all_53_9 = all_53_11)
% 228.57/40.21    (35)  all_55_4 = all_53_1
% 228.57/40.21    (36)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.57/40.21          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.21    (37)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.57/40.21          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.57/40.21    (38)   ~ (e3 = e2)
% 228.57/40.21    (39)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 228.57/40.21    (40)  all_55_1 = all_53_4
% 228.57/40.21    (41)   ~ (all_53_1 = all_53_3)
% 228.57/40.21    (42)  op(e1, e0) = all_53_14
% 228.57/40.21    (43)   ~ (all_53_6 = all_53_7)
% 228.57/40.21    (44)  all_55_7 = e3 | all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 228.57/40.21    (45)   ~ (e3 = e0)
% 228.57/40.21    (46)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.57/40.21          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.57/40.21    (47)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.57/40.21    (48)  op(e0, e3) = all_53_3
% 228.57/40.21    (49)   ~ (all_53_2 = e0)
% 228.57/40.21    (50)  all_57_0 = e0
% 228.57/40.21    (51)  all_55_2 = all_53_8
% 228.57/40.21    (52)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 228.57/40.21    (53)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.57/40.21    (54)  all_57_15 = e3
% 228.57/40.21    (55)   ~ (all_53_9 = all_53_13)
% 228.57/40.21    (56)  op(e3, e3) = e0
% 228.57/40.21    (57)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.57/40.21          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.57/40.21            e1)
% 228.57/40.21    (58)   ~ (all_53_1 = e1)
% 228.57/40.21    (59)  all_57_5 = e3
% 228.57/40.21    (60)  all_57_6 = e2
% 228.57/40.21    (61)   ~ (all_53_4 = all_53_8)
% 228.57/40.21    (62)   ~ (all_53_14 = e3)
% 228.57/40.21    (63)  all_55_6 = all_53_9
% 228.57/40.21    (64)  op(e3, e2) = all_53_4
% 228.57/40.21    (65)   ~ (all_53_1 = all_53_2)
% 228.57/40.21    (66)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.57/40.21          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 228.57/40.21    (67)   ~ (e2 = e0)
% 228.57/40.21    (68)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.57/40.21            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.57/40.21            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.57/40.21            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.57/40.21              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.57/40.21            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.57/40.21            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.57/40.21              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.57/40.21              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.57/40.21            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.57/40.21            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.57/40.21            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.57/40.21              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.57/40.21              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.57/40.21            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.57/40.21              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.57/40.21            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.57/40.21            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.57/40.21              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.57/40.21              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.57/40.21            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.57/40.21            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.57/40.21    (69)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 228.57/40.21            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 228.57/40.21              e3) = all_12_1 & $i(all_12_1))
% 228.57/40.21    (70)   ~ (all_53_9 = e2)
% 228.57/40.21    (71)   ~ (all_53_6 = e1)
% 228.57/40.21    (72)  all_55_12 = all_53_3
% 228.57/40.21    (73)  all_57_3 = e1
% 228.57/40.21    (74)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.57/40.21          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.57/40.21    (75)   ~ (all_53_1 = e0)
% 228.57/40.21    (76)   ~ (all_53_2 = all_53_14)
% 228.57/40.21    (77)   ~ (e1 = e0)
% 228.57/40.21    (78)  all_57_12 = e3
% 228.57/40.21    (79)   ~ (all_53_4 = e0)
% 228.57/40.21    (80)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.57/40.21          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.57/40.21    (81)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.57/40.21          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.57/40.21    (82)   ~ (all_53_2 = all_53_3)
% 228.57/40.21    (83)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 228.57/40.21    (84)   ~ (all_53_11 = e2)
% 228.57/40.21    (85)  all_55_8 = all_53_2
% 228.57/40.21    (86)  op(e0, e0) = e3
% 228.57/40.21    (87)   ~ (all_53_4 = all_53_6)
% 228.57/40.21    (88)  op(e0, e2) = all_53_7
% 228.57/40.21    (89)  all_57_2 = e1
% 228.57/40.21    (90)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.21          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.57/40.21            e2)
% 228.57/40.21    (91)   ~ (all_53_8 = e2)
% 228.57/40.21    (92)   ~ (all_53_3 = e0)
% 228.57/40.21    (93)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.21              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.57/40.21                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.57/40.21                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.57/40.21    (94)  op(e1, e1) = e2
% 228.57/40.21    (95)   ~ (all_53_1 = all_53_13)
% 228.57/40.21    (96)  op(e2, e0) = all_53_13
% 228.57/40.21    (97)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.57/40.21          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.57/40.21    (98)  all_55_11 = all_53_14
% 228.57/40.21    (99)  all_55_3 = all_53_12
% 228.57/40.21    (100)   ~ (all_53_12 = e3)
% 228.57/40.21    (101)  all_57_7 = e3
% 228.57/40.21    (102)  op(e1, e3) = all_53_2
% 228.57/40.21    (103)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.21           (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.57/40.21    (104)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.57/40.21           (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.57/40.21    (105)   ~ (all_53_12 = e0)
% 228.57/40.21    (106)   ~ (all_53_13 = all_53_14)
% 228.57/40.21    (107)   ~ (all_53_8 = e0)
% 228.57/40.21    (108)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.57/40.21           (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 228.57/40.21    (109)   ~ (e2 = e1)
% 228.57/40.21    (110)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.57/40.21    (111)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.57/40.21           | (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.57/40.21             e2)
% 228.57/40.21    (112)   ~ (all_53_14 = e2)
% 228.57/40.21    (113)   ~ (all_53_2 = all_53_6)
% 228.57/40.21    (114)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.57/40.21           (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.57/40.21    (115)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 228.57/40.21    (116)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.57/40.21           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.57/40.21    (117)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.57/40.21           (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.57/40.21    (118)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.57/40.21           | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.57/40.21             e1)
% 228.57/40.21    (119)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.57/40.21           (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.57/40.21    (120)  all_55_14 = all_53_11
% 228.57/40.21    (121)  all_55_7 = all_53_13
% 228.57/40.21    (122)   ~ (all_53_11 = e3)
% 228.57/40.21    (123)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.21           (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.57/40.21    (124)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.57/40.21           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.57/40.21    (125)  op(e3, e0) = all_53_12
% 228.57/40.21  
% 228.57/40.21  Begin of proof
% 228.57/40.21  | 
% 228.57/40.21  | BETA: splitting (110) gives:
% 228.57/40.21  | 
% 228.57/40.21  | Case 1:
% 228.57/40.21  | | 
% 228.57/40.21  | |   (126)  all_57_5 = e2 & op(e2, e1) = e2
% 228.57/40.21  | | 
% 228.57/40.21  | | ALPHA: (126) implies:
% 228.57/40.21  | |   (127)  all_57_5 = e2
% 228.57/40.21  | | 
% 228.57/40.21  | | COMBINE_EQS: (59), (127) imply:
% 228.57/40.21  | |   (128)  e3 = e2
% 228.57/40.21  | | 
% 228.57/40.21  | | COMBINE_EQS: (101), (128) imply:
% 228.57/40.21  | |   (129)  all_57_7 = e2
% 228.57/40.21  | | 
% 228.57/40.21  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 228.57/40.21  | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 228.57/40.21  | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 228.57/40.21  | |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 228.57/40.21  | |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 228.57/40.21  | |            (58), (61), (62), (63), (64), (65), (66), (67), (68), (69), (70),
% 228.57/40.21  | |            (71), (72), (73), (74), (75), (76), (77), (79), (80), (81), (82),
% 228.57/40.21  | |            (83), (84), (85), (86), (87), (88), (90), (91), (92), (93), (94),
% 228.57/40.21  | |            (95), (96), (97), (98), (99), (100), (102), (103), (104), (105),
% 228.57/40.21  | |            (106), (107), (108), (109), (111), (112), (113), (114), (115),
% 228.57/40.21  | |            (116), (117), (118), (119), (120), (121), (122), (123), (124),
% 228.57/40.21  | |            (125), (129) are inconsistent by sub-proof #577.
% 228.57/40.21  | | 
% 228.57/40.21  | Case 2:
% 228.57/40.21  | | 
% 228.57/40.21  | |   (130)  all_57_10 = e2 & op(e2, e0) = e2
% 228.57/40.21  | | 
% 228.57/40.21  | | ALPHA: (130) implies:
% 228.57/40.21  | |   (131)  all_57_10 = e2
% 228.57/40.21  | | 
% 228.57/40.21  | | COMBINE_EQS: (4), (131) imply:
% 228.57/40.21  | |   (132)  e2 = e0
% 228.57/40.21  | | 
% 228.57/40.21  | | SIMP: (132) implies:
% 228.57/40.21  | |   (133)  e2 = e0
% 228.57/40.21  | | 
% 228.57/40.21  | | COMBINE_EQS: (60), (133) imply:
% 228.57/40.21  | |   (134)  all_57_6 = e0
% 228.57/40.21  | | 
% 228.57/40.21  | | BETA: splitting (114) gives:
% 228.57/40.21  | | 
% 228.57/40.21  | | Case 1:
% 228.57/40.21  | | | 
% 228.57/40.21  | | |   (135)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) =
% 228.57/40.21  | | |            e2)
% 228.57/40.21  | | | 
% 228.57/40.21  | | | REF_CLOSE: (15), (56), (67), (89), (109), (135) are inconsistent by
% 228.57/40.21  | | |            sub-proof #2394.
% 228.57/40.21  | | | 
% 228.57/40.21  | | Case 2:
% 228.57/40.21  | | | 
% 228.57/40.21  | | |   (136)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3)
% 228.57/40.21  | | |            = e2)
% 228.57/40.21  | | | 
% 228.57/40.21  | | | REF_CLOSE: (38), (67), (78), (134), (136) are inconsistent by sub-proof
% 228.57/40.21  | | |            #2391.
% 228.57/40.21  | | | 
% 228.57/40.21  | | End of split
% 228.57/40.21  | | 
% 228.57/40.21  | End of split
% 228.57/40.21  | 
% 228.57/40.21  End of proof
% 228.57/40.21  
% 228.57/40.21  Sub-proof #577 shows that the following formulas are inconsistent:
% 228.57/40.21  ----------------------------------------------------------------
% 228.57/40.21    (1)   ~ (all_53_2 = e2)
% 228.57/40.21    (2)  op(e0, e1) = all_53_11
% 228.57/40.21    (3)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.57/40.21    (4)   ~ (all_53_6 = all_53_14)
% 228.57/40.21    (5)   ~ (all_53_6 = e2)
% 228.57/40.21    (6)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.21         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.57/40.21    (7)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.57/40.21         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.57/40.21    (8)   ~ (all_53_8 = all_53_12)
% 228.57/40.21    (9)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.21         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.21    (10)   ~ (all_53_8 = all_53_11)
% 228.57/40.21    (11)   ~ (e3 = e1)
% 228.57/40.21    (12)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.57/40.21          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.57/40.21    (13)   ~ (all_53_13 = e1)
% 228.57/40.21    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.57/40.21            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.57/40.22    (15)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.57/40.22          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.57/40.22    (16)   ~ (all_53_3 = e3)
% 228.57/40.22    (17)   ~ (all_6_2 = e3)
% 228.57/40.22    (18)   ~ (all_53_9 = e1)
% 228.57/40.22    (19)  op(e1, e1) = all_6_2
% 228.57/40.22    (20)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.57/40.22    (21)   ~ (all_53_1 = all_53_9)
% 228.57/40.22    (22)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 228.57/40.22    (23)  op(e2, e2) = e1
% 228.57/40.22    (24)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.57/40.22          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.57/40.22    (25)  all_57_7 = e2
% 228.57/40.22    (26)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 228.57/40.22            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 228.57/40.22              e3) = all_22_1 & $i(all_22_1))
% 228.57/40.22    (27)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 228.57/40.22    (28)  all_55_9 = all_53_6
% 228.57/40.22    (29)   ~ (all_53_4 = all_53_12)
% 228.57/40.22    (30)   ~ (all_53_4 = e1)
% 228.57/40.22    (31)   ~ (all_53_13 = e3)
% 228.57/40.22    (32)   ~ (all_53_8 = all_53_9)
% 228.57/40.22    (33)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.57/40.22          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.57/40.22    (34)   ~ (all_53_9 = all_53_11)
% 228.57/40.22    (35)  all_55_4 = all_53_1
% 228.57/40.22    (36)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.57/40.22          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.22    (37)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.57/40.22          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.57/40.22    (38)   ~ (e3 = e2)
% 228.57/40.22    (39)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 228.57/40.22    (40)  all_55_1 = all_53_4
% 228.57/40.22    (41)   ~ (all_53_1 = all_53_3)
% 228.57/40.22    (42)  op(e1, e0) = all_53_14
% 228.57/40.22    (43)   ~ (all_53_6 = all_53_7)
% 228.57/40.22    (44)  all_55_7 = e3 | all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 228.57/40.22    (45)   ~ (e3 = e0)
% 228.57/40.22    (46)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.57/40.22          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.57/40.22    (47)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.57/40.22    (48)  op(e0, e3) = all_53_3
% 228.57/40.22    (49)   ~ (all_53_2 = e0)
% 228.57/40.22    (50)  all_57_0 = e0
% 228.57/40.22    (51)  all_55_2 = all_53_8
% 228.57/40.22    (52)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 228.57/40.22    (53)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.57/40.22    (54)  all_57_15 = e3
% 228.57/40.22    (55)   ~ (all_53_9 = all_53_13)
% 228.57/40.22    (56)  op(e3, e3) = e0
% 228.57/40.22    (57)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.57/40.22          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.57/40.22            e1)
% 228.57/40.22    (58)   ~ (all_53_1 = e1)
% 228.57/40.22    (59)   ~ (all_53_4 = all_53_8)
% 228.57/40.22    (60)   ~ (all_53_14 = e3)
% 228.57/40.22    (61)  all_55_6 = all_53_9
% 228.57/40.22    (62)  op(e3, e2) = all_53_4
% 228.57/40.22    (63)   ~ (all_53_1 = all_53_2)
% 228.57/40.22    (64)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.57/40.22          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 228.57/40.22    (65)   ~ (e2 = e0)
% 228.57/40.22    (66)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.57/40.22            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.57/40.22            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.57/40.22            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.57/40.22              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.57/40.22            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.57/40.22            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.57/40.22              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.57/40.22              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.57/40.22            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.57/40.22            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.57/40.22            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.57/40.22              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.57/40.22              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.57/40.22            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.57/40.22              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.57/40.22            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.57/40.22            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.57/40.22              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.57/40.22              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.57/40.22            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.57/40.22            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.57/40.22    (67)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 228.57/40.22            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 228.57/40.22              e3) = all_12_1 & $i(all_12_1))
% 228.57/40.22    (68)   ~ (all_53_9 = e2)
% 228.57/40.22    (69)   ~ (all_53_6 = e1)
% 228.57/40.22    (70)  all_55_12 = all_53_3
% 228.57/40.22    (71)  all_57_3 = e1
% 228.57/40.22    (72)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.57/40.22          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.57/40.22    (73)   ~ (all_53_1 = e0)
% 228.57/40.22    (74)   ~ (all_53_2 = all_53_14)
% 228.57/40.22    (75)   ~ (e1 = e0)
% 228.57/40.22    (76)   ~ (all_53_4 = e0)
% 228.57/40.22    (77)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.57/40.22          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.57/40.22    (78)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.57/40.22          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.57/40.22    (79)   ~ (all_53_2 = all_53_3)
% 228.57/40.22    (80)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 228.57/40.22    (81)   ~ (all_53_11 = e2)
% 228.57/40.22    (82)  all_55_8 = all_53_2
% 228.57/40.22    (83)  op(e0, e0) = e3
% 228.57/40.22    (84)   ~ (all_53_4 = all_53_6)
% 228.57/40.22    (85)  op(e0, e2) = all_53_7
% 228.57/40.22    (86)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.22          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.57/40.22            e2)
% 228.57/40.22    (87)   ~ (all_53_8 = e2)
% 228.57/40.22    (88)   ~ (all_53_3 = e0)
% 228.57/40.22    (89)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.22              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.57/40.22                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.57/40.22                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.57/40.22    (90)  op(e1, e1) = e2
% 228.57/40.22    (91)   ~ (all_53_1 = all_53_13)
% 228.57/40.22    (92)  op(e2, e0) = all_53_13
% 228.57/40.22    (93)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.57/40.22          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.57/40.22    (94)  all_55_11 = all_53_14
% 228.57/40.22    (95)  all_55_3 = all_53_12
% 228.57/40.22    (96)   ~ (all_53_12 = e3)
% 228.57/40.22    (97)  op(e1, e3) = all_53_2
% 228.57/40.22    (98)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.22          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.57/40.22    (99)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.57/40.22          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.57/40.22    (100)   ~ (all_53_12 = e0)
% 228.57/40.22    (101)   ~ (all_53_13 = all_53_14)
% 228.57/40.22    (102)   ~ (all_53_8 = e0)
% 228.57/40.22    (103)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.57/40.22           (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 228.57/40.22    (104)   ~ (e2 = e1)
% 228.57/40.22    (105)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.57/40.22           | (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.57/40.22             e2)
% 228.57/40.22    (106)   ~ (all_53_14 = e2)
% 228.57/40.22    (107)   ~ (all_53_2 = all_53_6)
% 228.57/40.22    (108)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.57/40.22           (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.57/40.22    (109)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 228.57/40.22    (110)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.57/40.22           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.57/40.22    (111)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.57/40.22           (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.57/40.22    (112)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.57/40.22           | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.57/40.22             e1)
% 228.57/40.22    (113)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.57/40.22           (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.57/40.22    (114)  all_55_14 = all_53_11
% 228.57/40.22    (115)  all_55_7 = all_53_13
% 228.57/40.22    (116)   ~ (all_53_11 = e3)
% 228.57/40.22    (117)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.22           (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.57/40.22    (118)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.57/40.22           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.57/40.22    (119)  op(e3, e0) = all_53_12
% 228.57/40.22  
% 228.57/40.22  Begin of proof
% 228.57/40.22  | 
% 228.57/40.22  | BETA: splitting (78) gives:
% 228.57/40.22  | 
% 228.57/40.22  | Case 1:
% 228.57/40.22  | | 
% 228.57/40.22  | |   (120)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 228.57/40.22  | |            e3)
% 228.57/40.22  | | 
% 228.57/40.22  | | BETA: splitting (120) gives:
% 228.57/40.22  | | 
% 228.57/40.22  | | Case 1:
% 228.57/40.22  | | | 
% 228.57/40.22  | | |   (121)  all_57_1 = e3 & op(e3, e2) = e3
% 228.57/40.22  | | | 
% 228.57/40.22  | | | ALPHA: (121) implies:
% 228.57/40.22  | | |   (122)  all_57_1 = e3
% 228.57/40.22  | | | 
% 228.57/40.22  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.57/40.22  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 228.57/40.22  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 228.57/40.22  | | |            (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 228.57/40.22  | | |            (43), (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 228.57/40.22  | | |            (53), (54), (55), (56), (57), (58), (59), (60), (61), (62),
% 228.57/40.22  | | |            (63), (64), (65), (66), (67), (68), (69), (70), (71), (72),
% 228.57/40.22  | | |            (73), (74), (75), (76), (77), (78), (79), (80), (81), (82),
% 228.57/40.22  | | |            (83), (84), (85), (86), (87), (88), (89), (90), (91), (92),
% 228.57/40.22  | | |            (93), (94), (95), (96), (97), (98), (99), (100), (101), (102),
% 228.57/40.22  | | |            (103), (104), (105), (106), (107), (108), (109), (110), (111),
% 228.57/40.22  | | |            (112), (113), (114), (115), (116), (117), (118), (119), (122)
% 228.57/40.22  | | |            are inconsistent by sub-proof #578.
% 228.57/40.22  | | | 
% 228.57/40.22  | | Case 2:
% 228.57/40.22  | | | 
% 228.57/40.22  | | |   (123)  all_57_3 = e3 & op(e2, e2) = e3
% 228.57/40.22  | | | 
% 228.57/40.22  | | | ALPHA: (123) implies:
% 228.57/40.22  | | |   (124)  op(e2, e2) = e3
% 228.57/40.22  | | | 
% 228.57/40.22  | | | REF_CLOSE: (11), (14), (23), (124) are inconsistent by sub-proof #1912.
% 228.57/40.22  | | | 
% 228.57/40.22  | | End of split
% 228.57/40.22  | | 
% 228.57/40.22  | Case 2:
% 228.57/40.22  | | 
% 228.57/40.22  | |   (125)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 228.57/40.22  | |            e3)
% 228.57/40.22  | | 
% 228.57/40.22  | | REF_CLOSE: (11), (14), (25), (38), (45), (54), (57), (65), (75), (83), (86),
% 228.57/40.22  | |            (89), (104), (125) are inconsistent by sub-proof #713.
% 228.57/40.22  | | 
% 228.57/40.22  | End of split
% 228.57/40.22  | 
% 228.57/40.22  End of proof
% 228.57/40.22  
% 228.57/40.22  Sub-proof #578 shows that the following formulas are inconsistent:
% 228.57/40.22  ----------------------------------------------------------------
% 228.57/40.22    (1)   ~ (all_53_2 = e2)
% 228.57/40.22    (2)  op(e0, e1) = all_53_11
% 228.57/40.22    (3)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.57/40.22    (4)   ~ (all_53_6 = all_53_14)
% 228.57/40.22    (5)   ~ (all_53_6 = e2)
% 228.57/40.22    (6)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.22         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.57/40.22    (7)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.57/40.22         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.57/40.22    (8)   ~ (all_53_8 = all_53_12)
% 228.57/40.22    (9)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.22         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.22    (10)   ~ (all_53_8 = all_53_11)
% 228.57/40.22    (11)   ~ (e3 = e1)
% 228.57/40.22    (12)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.57/40.22          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.57/40.22    (13)   ~ (all_53_13 = e1)
% 228.57/40.22    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.57/40.22            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.57/40.22    (15)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.57/40.22          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.57/40.22    (16)   ~ (all_53_3 = e3)
% 228.57/40.22    (17)   ~ (all_6_2 = e3)
% 228.57/40.22    (18)   ~ (all_53_9 = e1)
% 228.57/40.22    (19)  op(e1, e1) = all_6_2
% 228.57/40.22    (20)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.57/40.22    (21)   ~ (all_53_1 = all_53_9)
% 228.57/40.22    (22)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 228.57/40.22    (23)  op(e2, e2) = e1
% 228.57/40.22    (24)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.57/40.22          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.57/40.22    (25)  all_57_7 = e2
% 228.57/40.22    (26)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 228.57/40.22            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 228.57/40.22              e3) = all_22_1 & $i(all_22_1))
% 228.57/40.22    (27)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 228.57/40.22    (28)  all_55_9 = all_53_6
% 228.57/40.22    (29)   ~ (all_53_4 = all_53_12)
% 228.57/40.22    (30)   ~ (all_53_4 = e1)
% 228.57/40.22    (31)   ~ (all_53_13 = e3)
% 228.57/40.22    (32)   ~ (all_53_8 = all_53_9)
% 228.57/40.22    (33)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.57/40.22          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.57/40.22    (34)   ~ (all_53_9 = all_53_11)
% 228.57/40.22    (35)  all_55_4 = all_53_1
% 228.57/40.22    (36)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.57/40.22          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.22    (37)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.57/40.22          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.57/40.22    (38)   ~ (e3 = e2)
% 228.57/40.22    (39)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 228.57/40.22    (40)  all_55_1 = all_53_4
% 228.57/40.22    (41)   ~ (all_53_1 = all_53_3)
% 228.57/40.22    (42)  op(e1, e0) = all_53_14
% 228.57/40.22    (43)   ~ (all_53_6 = all_53_7)
% 228.57/40.22    (44)  all_55_7 = e3 | all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 228.57/40.22    (45)   ~ (e3 = e0)
% 228.57/40.22    (46)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.57/40.22          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.57/40.22    (47)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.57/40.22    (48)  op(e0, e3) = all_53_3
% 228.57/40.22    (49)   ~ (all_53_2 = e0)
% 228.57/40.22    (50)  all_57_0 = e0
% 228.57/40.22    (51)  all_55_2 = all_53_8
% 228.57/40.22    (52)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 228.57/40.22    (53)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.57/40.22    (54)  all_57_15 = e3
% 228.57/40.22    (55)   ~ (all_53_9 = all_53_13)
% 228.57/40.22    (56)  op(e3, e3) = e0
% 228.57/40.22    (57)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.57/40.22          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.57/40.22            e1)
% 228.57/40.22    (58)   ~ (all_53_1 = e1)
% 228.57/40.22    (59)   ~ (all_53_4 = all_53_8)
% 228.57/40.22    (60)   ~ (all_53_14 = e3)
% 228.57/40.22    (61)  all_55_6 = all_53_9
% 228.57/40.22    (62)  op(e3, e2) = all_53_4
% 228.57/40.22    (63)   ~ (all_53_1 = all_53_2)
% 228.57/40.22    (64)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.57/40.22          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 228.57/40.22    (65)   ~ (e2 = e0)
% 228.57/40.22    (66)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.57/40.22            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.57/40.22            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.57/40.22            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.57/40.22              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.57/40.22            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.57/40.22            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.57/40.22              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.57/40.22              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.57/40.22            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.57/40.22            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.57/40.22            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.57/40.22              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.57/40.22              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.57/40.22            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.57/40.22              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.57/40.22            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.57/40.22            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.57/40.22              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.57/40.22              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.57/40.22            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.57/40.22            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.57/40.22    (67)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 228.57/40.22            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 228.57/40.22              e3) = all_12_1 & $i(all_12_1))
% 228.57/40.22    (68)   ~ (all_53_9 = e2)
% 228.57/40.22    (69)   ~ (all_53_6 = e1)
% 228.57/40.22    (70)  all_55_12 = all_53_3
% 228.57/40.22    (71)  all_57_3 = e1
% 228.57/40.22    (72)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.57/40.22          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.57/40.22    (73)   ~ (all_53_1 = e0)
% 228.57/40.22    (74)   ~ (all_53_2 = all_53_14)
% 228.57/40.22    (75)   ~ (e1 = e0)
% 228.57/40.22    (76)   ~ (all_53_4 = e0)
% 228.57/40.22    (77)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.57/40.22          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.57/40.22    (78)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.57/40.22          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.57/40.22    (79)   ~ (all_53_2 = all_53_3)
% 228.57/40.22    (80)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 228.57/40.22    (81)   ~ (all_53_11 = e2)
% 228.57/40.22    (82)  all_55_8 = all_53_2
% 228.57/40.22    (83)  op(e0, e0) = e3
% 228.57/40.22    (84)   ~ (all_53_4 = all_53_6)
% 228.57/40.22    (85)  op(e0, e2) = all_53_7
% 228.57/40.22    (86)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.22          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.57/40.22            e2)
% 228.57/40.22    (87)   ~ (all_53_8 = e2)
% 228.57/40.22    (88)   ~ (all_53_3 = e0)
% 228.57/40.22    (89)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.22              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.57/40.22                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.57/40.22                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.57/40.22    (90)  op(e1, e1) = e2
% 228.57/40.22    (91)   ~ (all_53_1 = all_53_13)
% 228.57/40.22    (92)  op(e2, e0) = all_53_13
% 228.57/40.22    (93)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.57/40.22          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.57/40.22    (94)  all_55_11 = all_53_14
% 228.57/40.22    (95)  all_55_3 = all_53_12
% 228.57/40.22    (96)   ~ (all_53_12 = e3)
% 228.57/40.22    (97)  op(e1, e3) = all_53_2
% 228.57/40.22    (98)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.22          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.57/40.22    (99)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.57/40.22          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.57/40.22    (100)  all_57_1 = e3
% 228.57/40.22    (101)   ~ (all_53_12 = e0)
% 228.57/40.22    (102)   ~ (all_53_13 = all_53_14)
% 228.57/40.22    (103)   ~ (all_53_8 = e0)
% 228.57/40.22    (104)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.57/40.22           (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 228.57/40.22    (105)   ~ (e2 = e1)
% 228.57/40.22    (106)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.57/40.22           | (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.57/40.22             e2)
% 228.57/40.22    (107)   ~ (all_53_14 = e2)
% 228.57/40.22    (108)   ~ (all_53_2 = all_53_6)
% 228.57/40.22    (109)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.57/40.22           (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.57/40.22    (110)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 228.57/40.22    (111)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.57/40.22           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.57/40.22    (112)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.57/40.22           (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.57/40.22    (113)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.57/40.22           | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.57/40.22             e1)
% 228.57/40.22    (114)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.57/40.22           (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.57/40.22    (115)  all_55_14 = all_53_11
% 228.57/40.22    (116)  all_55_7 = all_53_13
% 228.57/40.22    (117)   ~ (all_53_11 = e3)
% 228.57/40.22    (118)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.22           (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.57/40.22    (119)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.57/40.22           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.57/40.22    (120)  op(e3, e0) = all_53_12
% 228.57/40.22  
% 228.57/40.22  Begin of proof
% 228.57/40.22  | 
% 228.57/40.22  | BETA: splitting (15) gives:
% 228.57/40.22  | 
% 228.57/40.22  | Case 1:
% 228.57/40.22  | | 
% 228.57/40.22  | |   (121)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 228.57/40.22  | |            e3)
% 228.57/40.22  | | 
% 228.57/40.22  | | BETA: splitting (121) gives:
% 228.57/40.22  | | 
% 228.57/40.22  | | Case 1:
% 228.57/40.22  | | | 
% 228.57/40.22  | | |   (122)  all_57_6 = e3 & op(e1, e3) = e3
% 228.57/40.22  | | | 
% 228.57/40.22  | | | ALPHA: (122) implies:
% 228.57/40.22  | | |   (123)  all_57_6 = e3
% 228.57/40.22  | | | 
% 228.57/40.22  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.57/40.22  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 228.57/40.22  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 228.57/40.22  | | |            (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 228.57/40.22  | | |            (43), (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 228.57/40.22  | | |            (53), (54), (55), (56), (57), (58), (59), (60), (61), (62),
% 228.57/40.22  | | |            (63), (64), (65), (66), (67), (68), (69), (70), (71), (72),
% 228.57/40.22  | | |            (73), (74), (75), (76), (77), (78), (79), (80), (81), (82),
% 228.57/40.22  | | |            (83), (84), (85), (86), (87), (88), (89), (90), (91), (92),
% 228.57/40.22  | | |            (93), (94), (95), (96), (97), (98), (99), (100), (101), (102),
% 228.57/40.22  | | |            (103), (104), (105), (106), (107), (108), (109), (110), (111),
% 228.57/40.22  | | |            (112), (113), (114), (115), (116), (117), (118), (119), (120),
% 228.57/40.22  | | |            (123) are inconsistent by sub-proof #579.
% 228.57/40.22  | | | 
% 228.57/40.22  | | Case 2:
% 228.57/40.22  | | | 
% 228.57/40.22  | | |   (124)  all_57_7 = e3 & op(e1, e2) = e3
% 228.57/40.22  | | | 
% 228.57/40.22  | | | ALPHA: (124) implies:
% 228.57/40.22  | | |   (125)  all_57_7 = e3
% 228.57/40.22  | | | 
% 228.57/40.22  | | | REF_CLOSE: (25), (38), (125) are inconsistent by sub-proof #2102.
% 228.57/40.22  | | | 
% 228.57/40.22  | | End of split
% 228.57/40.22  | | 
% 228.57/40.22  | Case 2:
% 228.57/40.22  | | 
% 228.57/40.22  | |   (126)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 228.57/40.22  | |            e3)
% 228.57/40.22  | | 
% 228.57/40.23  | | REF_CLOSE: (11), (14), (17), (19), (38), (45), (54), (65), (75), (89),
% 228.57/40.23  | |            (105), (106), (113), (126) are inconsistent by sub-proof #1786.
% 228.57/40.23  | | 
% 228.57/40.23  | End of split
% 228.57/40.23  | 
% 228.57/40.23  End of proof
% 228.57/40.23  
% 228.57/40.23  Sub-proof #579 shows that the following formulas are inconsistent:
% 228.57/40.23  ----------------------------------------------------------------
% 228.57/40.23    (1)   ~ (all_53_2 = e2)
% 228.57/40.23    (2)  op(e0, e1) = all_53_11
% 228.57/40.23    (3)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.57/40.23    (4)   ~ (all_53_6 = all_53_14)
% 228.57/40.23    (5)   ~ (all_53_6 = e2)
% 228.57/40.23    (6)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.23         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.57/40.23    (7)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.57/40.23         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.57/40.23    (8)   ~ (all_53_8 = all_53_12)
% 228.57/40.23    (9)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.23         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.23    (10)   ~ (all_53_8 = all_53_11)
% 228.57/40.23    (11)   ~ (e3 = e1)
% 228.57/40.23    (12)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.57/40.23          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.57/40.23    (13)   ~ (all_53_13 = e1)
% 228.57/40.23    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.57/40.23            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.57/40.23    (15)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.57/40.23          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.57/40.23    (16)   ~ (all_53_3 = e3)
% 228.57/40.23    (17)   ~ (all_6_2 = e3)
% 228.57/40.23    (18)   ~ (all_53_9 = e1)
% 228.57/40.23    (19)  op(e1, e1) = all_6_2
% 228.57/40.23    (20)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.57/40.23    (21)   ~ (all_53_1 = all_53_9)
% 228.57/40.23    (22)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 228.57/40.23    (23)  op(e2, e2) = e1
% 228.57/40.23    (24)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.57/40.23          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.57/40.23    (25)  all_57_7 = e2
% 228.57/40.23    (26)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 228.57/40.23            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 228.57/40.23              e3) = all_22_1 & $i(all_22_1))
% 228.57/40.23    (27)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 228.57/40.23    (28)  all_55_9 = all_53_6
% 228.57/40.23    (29)   ~ (all_53_4 = all_53_12)
% 228.57/40.23    (30)   ~ (all_53_4 = e1)
% 228.57/40.23    (31)   ~ (all_53_13 = e3)
% 228.57/40.23    (32)   ~ (all_53_8 = all_53_9)
% 228.57/40.23    (33)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.57/40.23          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.57/40.23    (34)   ~ (all_53_9 = all_53_11)
% 228.57/40.23    (35)  all_55_4 = all_53_1
% 228.57/40.23    (36)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.57/40.23          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.23    (37)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.57/40.23          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.57/40.23    (38)   ~ (e3 = e2)
% 228.57/40.23    (39)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 228.57/40.23    (40)  all_55_1 = all_53_4
% 228.57/40.23    (41)   ~ (all_53_1 = all_53_3)
% 228.57/40.23    (42)  op(e1, e0) = all_53_14
% 228.57/40.23    (43)   ~ (all_53_6 = all_53_7)
% 228.57/40.23    (44)  all_55_7 = e3 | all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 228.57/40.23    (45)   ~ (e3 = e0)
% 228.57/40.23    (46)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.57/40.23          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.57/40.23    (47)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.57/40.23    (48)  op(e0, e3) = all_53_3
% 228.57/40.23    (49)   ~ (all_53_2 = e0)
% 228.57/40.23    (50)  all_57_0 = e0
% 228.57/40.23    (51)  all_55_2 = all_53_8
% 228.57/40.23    (52)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 228.57/40.23    (53)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.57/40.23    (54)  all_57_15 = e3
% 228.57/40.23    (55)   ~ (all_53_9 = all_53_13)
% 228.57/40.23    (56)  op(e3, e3) = e0
% 228.57/40.23    (57)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.57/40.23          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.57/40.23            e1)
% 228.57/40.23    (58)   ~ (all_53_1 = e1)
% 228.57/40.23    (59)   ~ (all_53_4 = all_53_8)
% 228.57/40.23    (60)   ~ (all_53_14 = e3)
% 228.57/40.23    (61)  all_55_6 = all_53_9
% 228.57/40.23    (62)  op(e3, e2) = all_53_4
% 228.57/40.23    (63)   ~ (all_53_1 = all_53_2)
% 228.57/40.23    (64)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.57/40.23          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 228.57/40.23    (65)   ~ (e2 = e0)
% 228.57/40.23    (66)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.57/40.23            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.57/40.23            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.57/40.23            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.57/40.23              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.57/40.23            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.57/40.23            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.57/40.23              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.57/40.23              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.57/40.23            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.57/40.23            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.57/40.23            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.57/40.23              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.57/40.23              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.57/40.23            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.57/40.23              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.57/40.23            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.57/40.23            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.57/40.23              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.57/40.23              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.57/40.23            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.57/40.23            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.57/40.23    (67)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 228.57/40.23            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 228.57/40.23              e3) = all_12_1 & $i(all_12_1))
% 228.57/40.23    (68)   ~ (all_53_9 = e2)
% 228.57/40.23    (69)   ~ (all_53_6 = e1)
% 228.57/40.23    (70)  all_55_12 = all_53_3
% 228.57/40.23    (71)  all_57_3 = e1
% 228.57/40.23    (72)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.57/40.23          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.57/40.23    (73)   ~ (all_53_1 = e0)
% 228.57/40.23    (74)   ~ (all_53_2 = all_53_14)
% 228.57/40.23    (75)   ~ (e1 = e0)
% 228.57/40.23    (76)   ~ (all_53_4 = e0)
% 228.57/40.23    (77)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.57/40.23          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.57/40.23    (78)  all_57_6 = e3
% 228.57/40.23    (79)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.57/40.23          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.57/40.23    (80)   ~ (all_53_2 = all_53_3)
% 228.57/40.23    (81)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 228.57/40.23    (82)   ~ (all_53_11 = e2)
% 228.57/40.23    (83)  all_55_8 = all_53_2
% 228.57/40.23    (84)  op(e0, e0) = e3
% 228.57/40.23    (85)   ~ (all_53_4 = all_53_6)
% 228.57/40.23    (86)  op(e0, e2) = all_53_7
% 228.57/40.23    (87)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.23          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.57/40.23            e2)
% 228.57/40.23    (88)   ~ (all_53_8 = e2)
% 228.57/40.23    (89)   ~ (all_53_3 = e0)
% 228.57/40.23    (90)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.23              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.57/40.23                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.57/40.23                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.57/40.23    (91)  op(e1, e1) = e2
% 228.57/40.23    (92)   ~ (all_53_1 = all_53_13)
% 228.57/40.23    (93)  op(e2, e0) = all_53_13
% 228.57/40.23    (94)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.57/40.23          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.57/40.23    (95)  all_55_11 = all_53_14
% 228.57/40.23    (96)  all_55_3 = all_53_12
% 228.57/40.23    (97)   ~ (all_53_12 = e3)
% 228.57/40.23    (98)  op(e1, e3) = all_53_2
% 228.57/40.23    (99)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.23          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.57/40.23    (100)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.57/40.23           (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.57/40.23    (101)  all_57_1 = e3
% 228.57/40.23    (102)   ~ (all_53_12 = e0)
% 228.57/40.23    (103)   ~ (all_53_13 = all_53_14)
% 228.57/40.23    (104)   ~ (all_53_8 = e0)
% 228.57/40.23    (105)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.57/40.23           (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 228.57/40.23    (106)   ~ (e2 = e1)
% 228.57/40.23    (107)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.57/40.23           | (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.57/40.23             e2)
% 228.57/40.23    (108)   ~ (all_53_14 = e2)
% 228.57/40.23    (109)   ~ (all_53_2 = all_53_6)
% 228.57/40.23    (110)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.57/40.23           (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.57/40.23    (111)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 228.57/40.23    (112)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.57/40.23           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.57/40.23    (113)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.57/40.23           (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.57/40.23    (114)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.57/40.23           | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.57/40.23             e1)
% 228.57/40.23    (115)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.57/40.23           (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.57/40.23    (116)  all_55_14 = all_53_11
% 228.57/40.23    (117)  all_55_7 = all_53_13
% 228.57/40.23    (118)   ~ (all_53_11 = e3)
% 228.57/40.23    (119)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.23           (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.57/40.23    (120)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.57/40.23           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.57/40.23    (121)  op(e3, e0) = all_53_12
% 228.57/40.23  
% 228.57/40.23  Begin of proof
% 228.57/40.23  | 
% 228.57/40.23  | BETA: splitting (115) gives:
% 228.57/40.23  | 
% 228.57/40.23  | Case 1:
% 228.57/40.23  | | 
% 228.57/40.23  | |   (122)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) =
% 228.57/40.23  | |            e1)
% 228.57/40.23  | | 
% 228.57/40.23  | | BETA: splitting (122) gives:
% 228.57/40.23  | | 
% 228.57/40.23  | | Case 1:
% 228.57/40.23  | | | 
% 228.57/40.23  | | |   (123)  all_57_6 = e1 & op(e1, e3) = e1
% 228.57/40.23  | | | 
% 228.57/40.23  | | | REF_CLOSE: (9), (11), (14), (23), (38), (45), (64), (65), (75), (78),
% 228.57/40.23  | | |            (79), (101), (106), (123) are inconsistent by sub-proof #1771.
% 228.57/40.23  | | | 
% 228.57/40.23  | | Case 2:
% 228.57/40.23  | | | 
% 228.57/40.23  | | |   (124)  all_57_7 = e1 & op(e1, e2) = e1
% 228.57/40.23  | | | 
% 228.57/40.23  | | | REF_CLOSE: (25), (106), (124) are inconsistent by sub-proof #2190.
% 228.57/40.23  | | | 
% 228.57/40.23  | | End of split
% 228.57/40.23  | | 
% 228.57/40.23  | Case 2:
% 228.57/40.23  | | 
% 228.57/40.23  | |   (125)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) =
% 228.57/40.23  | |            e1)
% 228.57/40.23  | | 
% 228.57/40.23  | | BETA: splitting (125) gives:
% 228.57/40.23  | | 
% 228.57/40.23  | | Case 1:
% 228.57/40.23  | | | 
% 228.57/40.23  | | |   (126)  all_57_8 = e1 & op(e1, e1) = e1
% 228.57/40.23  | | | 
% 228.57/40.23  | | | ALPHA: (126) implies:
% 228.57/40.23  | | |   (127)  op(e1, e1) = e1
% 228.57/40.23  | | | 
% 228.57/40.23  | | | REF_CLOSE: (14), (91), (106), (127) are inconsistent by sub-proof #2423.
% 228.57/40.23  | | | 
% 228.57/40.23  | | Case 2:
% 228.57/40.23  | | | 
% 228.57/40.23  | | |   (128)  all_57_11 = e1 & op(e1, e0) = e1
% 228.57/40.23  | | | 
% 228.57/40.23  | | | ALPHA: (128) implies:
% 228.57/40.23  | | |   (129)  all_57_11 = e1
% 228.57/40.23  | | | 
% 228.57/40.23  | | | BETA: splitting (7) gives:
% 228.57/40.23  | | | 
% 228.57/40.23  | | | Case 1:
% 228.57/40.23  | | | | 
% 228.57/40.23  | | | |   (130)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3)
% 228.57/40.23  | | | |            = e1)
% 228.57/40.23  | | | | 
% 228.57/40.23  | | | | REF_CLOSE: (6), (7), (9), (11), (14), (15), (17), (19), (23), (36),
% 228.57/40.23  | | | |            (38), (45), (48), (50), (54), (56), (57), (64), (65), (71),
% 228.57/40.23  | | | |            (72), (75), (78), (79), (84), (89), (90), (94), (97), (99),
% 228.57/40.23  | | | |            (100), (101), (102), (105), (106), (107), (110), (114),
% 228.57/40.23  | | | |            (119), (121), (130) are inconsistent by sub-proof #937.
% 228.57/40.23  | | | | 
% 228.57/40.23  | | | Case 2:
% 228.57/40.23  | | | | 
% 228.57/40.23  | | | |   (131)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0,
% 228.57/40.23  | | | |              e3) = e1)
% 228.57/40.23  | | | | 
% 228.57/40.23  | | | | BETA: splitting (131) gives:
% 228.57/40.23  | | | | 
% 228.57/40.23  | | | | Case 1:
% 228.57/40.23  | | | | | 
% 228.57/40.23  | | | | |   (132)  all_57_6 = e1 & op(e1, e3) = e1
% 228.57/40.23  | | | | | 
% 228.57/40.23  | | | | | REF_CLOSE: (9), (11), (14), (23), (38), (45), (64), (65), (75), (78),
% 228.57/40.23  | | | | |            (79), (101), (106), (132) are inconsistent by sub-proof
% 228.57/40.23  | | | | |            #1771.
% 228.57/40.23  | | | | | 
% 228.57/40.23  | | | | Case 2:
% 228.57/40.23  | | | | | 
% 228.57/40.23  | | | | |   (133)  all_57_12 = e1 & op(e0, e3) = e1
% 228.57/40.23  | | | | | 
% 228.57/40.23  | | | | | ALPHA: (133) implies:
% 228.57/40.23  | | | | |   (134)  all_57_12 = e1
% 228.57/40.23  | | | | | 
% 228.57/40.23  | | | | | BETA: splitting (64) gives:
% 228.57/40.23  | | | | | 
% 228.57/40.23  | | | | | Case 1:
% 228.57/40.23  | | | | | | 
% 228.57/40.23  | | | | | |   (135)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2,
% 228.57/40.23  | | | | | |              e2) = e0)
% 228.57/40.23  | | | | | | 
% 228.57/40.23  | | | | | | REF_CLOSE: (9), (11), (14), (15), (17), (19), (23), (38), (45),
% 228.57/40.23  | | | | | |            (54), (64), (65), (75), (78), (90), (101), (106), (107),
% 228.57/40.23  | | | | | |            (114), (119), (135) are inconsistent by sub-proof #724.
% 228.57/40.23  | | | | | | 
% 228.57/40.23  | | | | | Case 2:
% 228.57/40.23  | | | | | | 
% 228.57/40.23  | | | | | |   (136)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 &
% 228.57/40.23  | | | | | |            op(e0, e2) = e0)
% 228.57/40.23  | | | | | | 
% 228.57/40.23  | | | | | | BETA: splitting (136) gives:
% 228.57/40.23  | | | | | | 
% 228.57/40.23  | | | | | | Case 1:
% 228.57/40.23  | | | | | | | 
% 228.57/40.23  | | | | | | |   (137)  all_57_7 = e0 & op(e1, e2) = e0
% 228.57/40.23  | | | | | | | 
% 228.57/40.23  | | | | | | | REF_CLOSE: (25), (65), (137) are inconsistent by sub-proof #2148.
% 228.57/40.23  | | | | | | | 
% 228.57/40.23  | | | | | | Case 2:
% 228.57/40.23  | | | | | | | 
% 228.57/40.23  | | | | | | |   (138)  all_57_13 = e0 & op(e0, e2) = e0
% 228.57/40.23  | | | | | | | 
% 228.57/40.23  | | | | | | | ALPHA: (138) implies:
% 228.57/40.23  | | | | | | |   (139)  all_57_13 = e0
% 228.57/40.23  | | | | | | | 
% 228.57/40.23  | | | | | | | BETA: splitting (110) gives:
% 228.57/40.23  | | | | | | | 
% 228.57/40.23  | | | | | | | Case 1:
% 228.57/40.23  | | | | | | | | 
% 228.57/40.23  | | | | | | | |   (140)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 &
% 228.57/40.23  | | | | | | | |            op(e2, e3) = e2)
% 228.57/40.23  | | | | | | | | 
% 228.57/40.23  | | | | | | | | BETA: splitting (140) gives:
% 228.57/40.23  | | | | | | | | 
% 228.57/40.23  | | | | | | | | Case 1:
% 228.57/40.23  | | | | | | | | | 
% 228.57/40.23  | | | | | | | | |   (141)  all_57_0 = e2 & op(e3, e3) = e2
% 228.57/40.23  | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | ALPHA: (141) implies:
% 228.57/40.23  | | | | | | | | |   (142)  op(e3, e3) = e2
% 228.57/40.23  | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | REF_CLOSE: (14), (56), (65), (142) are inconsistent by
% 228.57/40.23  | | | | | | | | |            sub-proof #2403.
% 228.57/40.23  | | | | | | | | | 
% 228.57/40.23  | | | | | | | | Case 2:
% 228.57/40.23  | | | | | | | | | 
% 228.57/40.23  | | | | | | | | |   (143)  all_57_2 = e2 & op(e2, e3) = e2
% 228.57/40.23  | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | ALPHA: (143) implies:
% 228.57/40.23  | | | | | | | | |   (144)  all_57_2 = e2
% 228.57/40.23  | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | BETA: splitting (12) gives:
% 228.57/40.23  | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | Case 1:
% 228.57/40.23  | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | |   (145)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 228.57/40.23  | | | | | | | | | |            & op(e1, e2) = e0)
% 228.57/40.23  | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | BETA: splitting (145) gives:
% 228.57/40.23  | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | Case 1:
% 228.57/40.23  | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | |   (146)  all_57_6 = e0 & op(e1, e3) = e0
% 228.57/40.23  | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | ALPHA: (146) implies:
% 228.57/40.23  | | | | | | | | | | |   (147)  all_57_6 = e0
% 228.57/40.23  | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | REF_CLOSE: (9), (11), (14), (15), (17), (19), (23), (38),
% 228.57/40.23  | | | | | | | | | | |            (45), (54), (64), (65), (75), (90), (101), (106),
% 228.57/40.23  | | | | | | | | | | |            (107), (114), (119), (147) are inconsistent by
% 228.57/40.23  | | | | | | | | | | |            sub-proof #1773.
% 228.57/40.23  | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | Case 2:
% 228.57/40.23  | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | |   (148)  all_57_7 = e0 & op(e1, e2) = e0
% 228.57/40.23  | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | ALPHA: (148) implies:
% 228.57/40.23  | | | | | | | | | | |   (149)  all_57_7 = e0
% 228.57/40.23  | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | COMBINE_EQS: (25), (149) imply:
% 228.57/40.23  | | | | | | | | | | |   (150)  e2 = e0
% 228.57/40.23  | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | COMBINE_EQS: (144), (150) imply:
% 228.57/40.23  | | | | | | | | | | |   (151)  all_57_2 = e0
% 228.57/40.23  | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | REF_CLOSE: (6), (7), (9), (11), (12), (14), (15), (17), (19),
% 228.57/40.23  | | | | | | | | | | |            (23), (24), (33), (36), (37), (38), (45), (46),
% 228.57/40.23  | | | | | | | | | | |            (48), (54), (56), (57), (64), (65), (71), (72),
% 228.57/40.23  | | | | | | | | | | |            (75), (77), (79), (84), (87), (89), (90), (94),
% 228.57/40.23  | | | | | | | | | | |            (97), (99), (100), (102), (106), (107), (110),
% 228.57/40.23  | | | | | | | | | | |            (112), (113), (114), (115), (119), (120), (121),
% 228.57/40.23  | | | | | | | | | | |            (151) are inconsistent by sub-proof #1016.
% 228.57/40.23  | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | End of split
% 228.57/40.23  | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | Case 2:
% 228.57/40.23  | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | |   (152)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0
% 228.57/40.23  | | | | | | | | | |            & op(e1, e0) = e0)
% 228.57/40.23  | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | BETA: splitting (152) gives:
% 228.57/40.23  | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | Case 1:
% 228.57/40.23  | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | |   (153)  all_57_8 = e0 & op(e1, e1) = e0
% 228.57/40.23  | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | ALPHA: (153) implies:
% 228.57/40.23  | | | | | | | | | | |   (154)  op(e1, e1) = e0
% 228.57/40.23  | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | BETA: splitting (87) gives:
% 228.57/40.23  | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | Case 1:
% 228.57/40.23  | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | |   (155)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 228.57/40.23  | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 228.57/40.23  | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | BETA: splitting (155) gives:
% 228.57/40.23  | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | Case 1:
% 228.57/40.23  | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | |   (156)  all_57_12 = e2 & op(e0, e3) = e2
% 228.57/40.23  | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | | ALPHA: (156) implies:
% 228.57/40.23  | | | | | | | | | | | | |   (157)  all_57_12 = e2
% 228.57/40.23  | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | | COMBINE_EQS: (134), (157) imply:
% 228.57/40.23  | | | | | | | | | | | | |   (158)  e2 = e1
% 228.57/40.23  | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | | SIMP: (158) implies:
% 228.57/40.23  | | | | | | | | | | | | |   (159)  e2 = e1
% 228.57/40.23  | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | | COMBINE_EQS: (144), (159) imply:
% 228.57/40.23  | | | | | | | | | | | | |   (160)  all_57_2 = e1
% 228.57/40.23  | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | | REF_CLOSE: (6), (7), (9), (11), (14), (15), (17), (19), (23),
% 228.57/40.23  | | | | | | | | | | | | |            (36), (38), (45), (48), (50), (54), (56), (57),
% 228.57/40.23  | | | | | | | | | | | | |            (64), (65), (71), (72), (75), (78), (79), (84),
% 228.57/40.23  | | | | | | | | | | | | |            (89), (90), (94), (97), (99), (100), (101), (102),
% 228.57/40.23  | | | | | | | | | | | | |            (105), (106), (107), (110), (114), (119), (121),
% 228.57/40.23  | | | | | | | | | | | | |            (160) are inconsistent by sub-proof #980.
% 228.57/40.23  | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | Case 2:
% 228.57/40.23  | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | |   (161)  all_57_13 = e2 & op(e0, e2) = e2
% 228.57/40.23  | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | | ALPHA: (161) implies:
% 228.57/40.23  | | | | | | | | | | | | |   (162)  all_57_13 = e2
% 228.57/40.23  | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | | COMBINE_EQS: (139), (162) imply:
% 228.57/40.23  | | | | | | | | | | | | |   (163)  e2 = e0
% 228.57/40.23  | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | | SIMP: (163) implies:
% 228.57/40.23  | | | | | | | | | | | | |   (164)  e2 = e0
% 228.57/40.23  | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | | COMBINE_EQS: (144), (164) imply:
% 228.57/40.23  | | | | | | | | | | | | |   (165)  all_57_2 = e0
% 228.57/40.23  | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | | REF_CLOSE: (6), (7), (9), (11), (12), (14), (15), (17), (19),
% 228.57/40.23  | | | | | | | | | | | | |            (23), (24), (33), (36), (37), (38), (45), (46),
% 228.57/40.23  | | | | | | | | | | | | |            (48), (54), (56), (57), (64), (65), (71), (72),
% 228.57/40.23  | | | | | | | | | | | | |            (75), (77), (79), (84), (87), (89), (90), (94),
% 228.57/40.23  | | | | | | | | | | | | |            (97), (99), (100), (102), (106), (107), (110),
% 228.57/40.23  | | | | | | | | | | | | |            (112), (113), (114), (115), (119), (120), (121),
% 228.57/40.23  | | | | | | | | | | | | |            (165) are inconsistent by sub-proof #1016.
% 228.57/40.23  | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | End of split
% 228.57/40.23  | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | Case 2:
% 228.57/40.23  | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | |   (166)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 228.57/40.23  | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 228.57/40.23  | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | BETA: splitting (166) gives:
% 228.57/40.23  | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | Case 1:
% 228.57/40.23  | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | |   (167)  all_57_14 = e2 & op(e0, e1) = e2
% 228.57/40.23  | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | | ALPHA: (167) implies:
% 228.57/40.23  | | | | | | | | | | | | |   (168)  all_57_14 = e2
% 228.57/40.23  | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | | BETA: splitting (94) gives:
% 228.57/40.23  | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | | Case 1:
% 228.57/40.23  | | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | | |   (169)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 228.57/40.23  | | | | | | | | | | | | | |            & op(e2, e2) = e3)
% 228.57/40.23  | | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | | | BETA: splitting (169) gives:
% 228.57/40.23  | | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | | | Case 1:
% 228.57/40.23  | | | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | | | |   (170)  all_57_2 = e3 & op(e2, e3) = e3
% 228.57/40.23  | | | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | | | | ALPHA: (170) implies:
% 228.57/40.23  | | | | | | | | | | | | | | |   (171)  all_57_2 = e3
% 228.57/40.23  | | | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | | | | REF_CLOSE: (14), (38), (56), (65), (78), (106), (110), (134),
% 228.57/40.23  | | | | | | | | | | | | | | |            (171) are inconsistent by sub-proof #1288.
% 228.57/40.23  | | | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | | | Case 2:
% 228.57/40.23  | | | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | | | |   (172)  all_57_3 = e3 & op(e2, e2) = e3
% 228.57/40.23  | | | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | | | | ALPHA: (172) implies:
% 228.57/40.23  | | | | | | | | | | | | | | |   (173)  op(e2, e2) = e3
% 228.57/40.23  | | | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | | | | REF_CLOSE: (11), (14), (23), (173) are inconsistent by
% 228.57/40.23  | | | | | | | | | | | | | | |            sub-proof #1912.
% 228.57/40.23  | | | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | | | End of split
% 228.57/40.23  | | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | | Case 2:
% 228.57/40.23  | | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | | |   (174)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 228.57/40.23  | | | | | | | | | | | | | |            e3 & op(e2, e0) = e3)
% 228.57/40.23  | | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | | | BETA: splitting (174) gives:
% 228.57/40.23  | | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | | | Case 1:
% 228.57/40.23  | | | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | | | |   (175)  all_57_5 = e3 & op(e2, e1) = e3
% 228.57/40.23  | | | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | | | | ALPHA: (175) implies:
% 228.57/40.23  | | | | | | | | | | | | | | |   (176)  all_57_5 = e3
% 228.57/40.23  | | | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | | | | BETA: splitting (46) gives:
% 228.57/40.23  | | | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | | | | Case 1:
% 228.57/40.23  | | | | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | | | | |   (177)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 228.57/40.23  | | | | | | | | | | | | | | | |            & op(e2, e1) = e1)
% 228.57/40.23  | | | | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | | | | | BETA: splitting (177) gives:
% 228.57/40.23  | | | | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | | | | | Case 1:
% 228.57/40.23  | | | | | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | | | | | |   (178)  all_57_4 = e1 & op(e3, e1) = e1
% 228.57/40.23  | | | | | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | | | | | | ALPHA: (178) implies:
% 228.57/40.23  | | | | | | | | | | | | | | | | |   (179)  all_57_4 = e1
% 228.57/40.23  | | | | | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | | | | | | BETA: splitting (112) gives:
% 228.57/40.23  | | | | | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | | | | | | Case 1:
% 228.57/40.23  | | | | | | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | | | | | | |   (180)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 228.57/40.23  | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e2)
% 228.57/40.23  | | | | | | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | | | | | | | BETA: splitting (180) gives:
% 228.57/40.23  | | | | | | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | | | | | | | Case 1:
% 228.57/40.23  | | | | | | | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | | | | | | | |   (181)  all_57_4 = e2 & op(e3, e1) = e2
% 228.57/40.23  | | | | | | | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | | | | | | | | ALPHA: (181) implies:
% 228.57/40.23  | | | | | | | | | | | | | | | | | | |   (182)  all_57_4 = e2
% 228.57/40.23  | | | | | | | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (179), (182) imply:
% 228.57/40.23  | | | | | | | | | | | | | | | | | | |   (183)  e2 = e1
% 228.57/40.23  | | | | | | | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (144), (183) imply:
% 228.57/40.23  | | | | | | | | | | | | | | | | | | |   (184)  all_57_2 = e1
% 228.57/40.23  | | | | | | | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (9), (11), (14), (15), (17), (19), (23),
% 228.57/40.23  | | | | | | | | | | | | | | | | | | |            (38), (45), (50), (54), (56), (64), (65), (71),
% 228.57/40.23  | | | | | | | | | | | | | | | | | | |            (75), (78), (90), (99), (101), (105), (106),
% 228.57/40.23  | | | | | | | | | | | | | | | | | | |            (107), (110), (114), (119), (176), (184) are
% 228.57/40.23  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1007.
% 228.57/40.23  | | | | | | | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | | | | | | | Case 2:
% 228.57/40.23  | | | | | | | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | | | | | | | |   (185)  all_57_5 = e2 & op(e2, e1) = e2
% 228.57/40.23  | | | | | | | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | | | | | | | | ALPHA: (185) implies:
% 228.57/40.23  | | | | | | | | | | | | | | | | | | |   (186)  all_57_5 = e2
% 228.57/40.23  | | | | | | | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (176), (186) are inconsistent by sub-proof
% 228.57/40.23  | | | | | | | | | | | | | | | | | | |            #2189.
% 228.57/40.23  | | | | | | | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | | | | | | | End of split
% 228.57/40.23  | | | | | | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | | | | | | Case 2:
% 228.57/40.23  | | | | | | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | | | | | | |   (187)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 228.57/40.23  | | | | | | | | | | | | | | | | | |            e2 & op(e0, e1) = e2)
% 228.57/40.23  | | | | | | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 228.57/40.23  | | | | | | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | | | | | | | Case 1:
% 228.57/40.23  | | | | | | | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | | | | | | | |   (188)  all_57_8 = e2 & op(e1, e1) = e2
% 228.57/40.23  | | | | | | | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 228.57/40.23  | | | | | | | | | | | | | | | | | | |            (12), (13), (14), (15), (16), (17), (18), (19),
% 228.57/40.23  | | | | | | | | | | | | | | | | | | |            (20), (21), (22), (23), (24), (26), (27), (28),
% 228.57/40.23  | | | | | | | | | | | | | | | | | | |            (29), (30), (31), (32), (33), (34), (35), (36),
% 228.57/40.23  | | | | | | | | | | | | | | | | | | |            (37), (39), (40), (41), (42), (43), (44), (45),
% 228.57/40.23  | | | | | | | | | | | | | | | | | | |            (46), (47), (48), (49), (50), (51), (52), (53),
% 228.57/40.23  | | | | | | | | | | | | | | | | | | |            (54), (55), (56), (57), (58), (59), (60), (61),
% 228.57/40.23  | | | | | | | | | | | | | | | | | | |            (62), (63), (64), (65), (66), (67), (68), (69),
% 228.57/40.23  | | | | | | | | | | | | | | | | | | |            (70), (71), (72), (73), (74), (75), (76), (77),
% 228.57/40.23  | | | | | | | | | | | | | | | | | | |            (79), (80), (81), (82), (83), (84), (85), (86),
% 228.57/40.23  | | | | | | | | | | | | | | | | | | |            (87), (88), (89), (90), (92), (93), (94), (95),
% 228.57/40.23  | | | | | | | | | | | | | | | | | | |            (96), (97), (98), (99), (100), (102), (103),
% 228.57/40.23  | | | | | | | | | | | | | | | | | | |            (104), (105), (106), (107), (108), (109), (110),
% 228.57/40.23  | | | | | | | | | | | | | | | | | | |            (111), (112), (113), (114), (115), (116), (117),
% 228.57/40.23  | | | | | | | | | | | | | | | | | | |            (118), (119), (120), (121), (188) are inconsistent
% 228.57/40.23  | | | | | | | | | | | | | | | | | | |            by sub-proof #581.
% 228.57/40.23  | | | | | | | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | | | | | | | Case 2:
% 228.57/40.23  | | | | | | | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with e0, e2, e1, e1,
% 228.57/40.23  | | | | | | | | | | | | | | | | | | |              simplifying with (91), (154) gives:
% 228.57/40.23  | | | | | | | | | | | | | | | | | | |   (189)  e2 = e0
% 228.57/40.23  | | | | | | | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (144), (189) imply:
% 228.57/40.23  | | | | | | | | | | | | | | | | | | |   (190)  all_57_2 = e0
% 228.57/40.23  | | | | | | | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (9), (11), (12), (14), (15), (17), (19),
% 228.57/40.23  | | | | | | | | | | | | | | | | | | |            (23), (24), (33), (36), (37), (38), (45), (46),
% 228.57/40.23  | | | | | | | | | | | | | | | | | | |            (48), (54), (56), (57), (64), (65), (71), (72),
% 228.57/40.23  | | | | | | | | | | | | | | | | | | |            (75), (77), (79), (84), (87), (89), (90), (97),
% 228.57/40.23  | | | | | | | | | | | | | | | | | | |            (99), (100), (102), (106), (107), (110), (112),
% 228.57/40.23  | | | | | | | | | | | | | | | | | | |            (113), (114), (115), (119), (120), (121), (176),
% 228.57/40.23  | | | | | | | | | | | | | | | | | | |            (190) are inconsistent by sub-proof #1021.
% 228.57/40.23  | | | | | | | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | | | | | | | End of split
% 228.57/40.23  | | | | | | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | | | | | | End of split
% 228.57/40.23  | | | | | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | | | | | Case 2:
% 228.57/40.23  | | | | | | | | | | | | | | | | | 
% 228.57/40.23  | | | | | | | | | | | | | | | | |   (191)  all_57_5 = e1 & op(e2, e1) = e1
% 228.57/40.23  | | | | | | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11), (14), (23), (38), (45), (64), (65),
% 228.57/40.24  | | | | | | | | | | | | | | | | |            (75), (79), (101), (106), (176), (191) are
% 228.57/40.24  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #580.
% 228.57/40.24  | | | | | | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | | | | | | End of split
% 228.57/40.24  | | | | | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | | | | | Case 2:
% 228.57/40.24  | | | | | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | | | | | |   (192)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 228.57/40.24  | | | | | | | | | | | | | | | |            e1 & op(e0, e1) = e1)
% 228.57/40.24  | | | | | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 228.57/40.24  | | | | | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | | | | | | Case 1:
% 228.57/40.24  | | | | | | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | | | | | | |   (193)  all_57_8 = e1 & op(e1, e1) = e1
% 228.57/40.24  | | | | | | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | | | | | | | ALPHA: (193) implies:
% 228.57/40.24  | | | | | | | | | | | | | | | | |   (194)  op(e1, e1) = e1
% 228.57/40.24  | | | | | | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (91), (106), (194) are inconsistent by
% 228.57/40.24  | | | | | | | | | | | | | | | | |            sub-proof #2423.
% 228.57/40.24  | | | | | | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | | | | | | Case 2:
% 228.57/40.24  | | | | | | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | | | | | | |   (195)  all_57_14 = e1 & op(e0, e1) = e1
% 228.57/40.24  | | | | | | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | | | | | | | ALPHA: (195) implies:
% 228.57/40.24  | | | | | | | | | | | | | | | | |   (196)  all_57_14 = e1
% 228.57/40.24  | | | | | | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | | | | | | | COMBINE_EQS: (168), (196) imply:
% 228.57/40.24  | | | | | | | | | | | | | | | | |   (197)  e2 = e1
% 228.57/40.24  | | | | | | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | | | | | | | COMBINE_EQS: (144), (197) imply:
% 228.57/40.24  | | | | | | | | | | | | | | | | |   (198)  all_57_2 = e1
% 228.57/40.24  | | | | | | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (9), (11), (14), (15), (17), (19), (23),
% 228.57/40.24  | | | | | | | | | | | | | | | | |            (38), (45), (50), (54), (56), (64), (65), (71),
% 228.57/40.24  | | | | | | | | | | | | | | | | |            (75), (78), (90), (99), (101), (105), (106),
% 228.57/40.24  | | | | | | | | | | | | | | | | |            (107), (110), (114), (119), (176), (198) are
% 228.57/40.24  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1007.
% 228.57/40.24  | | | | | | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | | | | | | End of split
% 228.57/40.24  | | | | | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | | | | | End of split
% 228.57/40.24  | | | | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | | | | Case 2:
% 228.57/40.24  | | | | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | | | | |   (199)  all_57_10 = e3 & op(e2, e0) = e3
% 228.57/40.24  | | | | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (11), (14), (15), (17), (19), (23),
% 228.57/40.24  | | | | | | | | | | | | | | |            (36), (38), (45), (48), (54), (56), (57), (64),
% 228.57/40.24  | | | | | | | | | | | | | | |            (65), (71), (72), (75), (78), (79), (84), (89),
% 228.57/40.24  | | | | | | | | | | | | | | |            (90), (97), (100), (102), (106), (107), (110),
% 228.57/40.24  | | | | | | | | | | | | | | |            (114), (119), (121), (199) are inconsistent by
% 228.57/40.24  | | | | | | | | | | | | | | |            sub-proof #981.
% 228.57/40.24  | | | | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | | | | End of split
% 228.57/40.24  | | | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | | | End of split
% 228.57/40.24  | | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | | Case 2:
% 228.57/40.24  | | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | | |   (200)  all_57_15 = e2 & op(e0, e0) = e2
% 228.57/40.24  | | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | | | REF_CLOSE: (38), (54), (200) are inconsistent by sub-proof
% 228.57/40.24  | | | | | | | | | | | | |            #2323.
% 228.57/40.24  | | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | | End of split
% 228.57/40.24  | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | End of split
% 228.57/40.24  | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | Case 2:
% 228.57/40.24  | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | |   (201)  all_57_11 = e0 & op(e1, e0) = e0
% 228.57/40.24  | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | ALPHA: (201) implies:
% 228.57/40.24  | | | | | | | | | | |   (202)  all_57_11 = e0
% 228.57/40.24  | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | COMBINE_EQS: (129), (202) imply:
% 228.57/40.24  | | | | | | | | | | |   (203)  e1 = e0
% 228.57/40.24  | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | COMBINE_EQS: (71), (203) imply:
% 228.57/40.24  | | | | | | | | | | |   (204)  all_57_3 = e0
% 228.57/40.24  | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | REF_CLOSE: (9), (11), (38), (65), (75), (101), (106), (119),
% 228.57/40.24  | | | | | | | | | | |            (139), (204) are inconsistent by sub-proof #1758.
% 228.57/40.24  | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | End of split
% 228.57/40.24  | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | End of split
% 228.57/40.24  | | | | | | | | | 
% 228.57/40.24  | | | | | | | | End of split
% 228.57/40.24  | | | | | | | | 
% 228.57/40.24  | | | | | | | Case 2:
% 228.57/40.24  | | | | | | | | 
% 228.57/40.24  | | | | | | | |   (205)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 &
% 228.57/40.24  | | | | | | | |            op(e0, e3) = e2)
% 228.57/40.24  | | | | | | | | 
% 228.57/40.24  | | | | | | | | BETA: splitting (205) gives:
% 228.57/40.24  | | | | | | | | 
% 228.57/40.24  | | | | | | | | Case 1:
% 228.57/40.24  | | | | | | | | | 
% 228.57/40.24  | | | | | | | | |   (206)  all_57_6 = e2 & op(e1, e3) = e2
% 228.57/40.24  | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | REF_CLOSE: (38), (78), (206) are inconsistent by sub-proof
% 228.57/40.24  | | | | | | | | |            #2012.
% 228.57/40.24  | | | | | | | | | 
% 228.57/40.24  | | | | | | | | Case 2:
% 228.57/40.24  | | | | | | | | | 
% 228.57/40.24  | | | | | | | | |   (207)  all_57_12 = e2 & op(e0, e3) = e2
% 228.57/40.24  | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | REF_CLOSE: (106), (134), (207) are inconsistent by sub-proof
% 228.57/40.24  | | | | | | | | |            #1922.
% 228.57/40.24  | | | | | | | | | 
% 228.57/40.24  | | | | | | | | End of split
% 228.57/40.24  | | | | | | | | 
% 228.57/40.24  | | | | | | | End of split
% 228.57/40.24  | | | | | | | 
% 228.57/40.24  | | | | | | End of split
% 228.57/40.24  | | | | | | 
% 228.57/40.24  | | | | | End of split
% 228.57/40.24  | | | | | 
% 228.57/40.24  | | | | End of split
% 228.57/40.24  | | | | 
% 228.57/40.24  | | | End of split
% 228.57/40.24  | | | 
% 228.57/40.24  | | End of split
% 228.57/40.24  | | 
% 228.57/40.24  | End of split
% 228.57/40.24  | 
% 228.57/40.24  End of proof
% 228.57/40.24  
% 228.57/40.24  Sub-proof #580 shows that the following formulas are inconsistent:
% 228.57/40.24  ----------------------------------------------------------------
% 228.57/40.24    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.24         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.24    (2)   ~ (e3 = e1)
% 228.57/40.24    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.57/40.24           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.57/40.24    (4)  op(e2, e2) = e1
% 228.57/40.24    (5)   ~ (e3 = e2)
% 228.57/40.24    (6)   ~ (e3 = e0)
% 228.57/40.24    (7)  all_57_5 = e1 & op(e2, e1) = e1
% 228.57/40.24    (8)  all_57_5 = e3
% 228.57/40.24    (9)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.57/40.24         (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 228.57/40.24    (10)   ~ (e2 = e0)
% 228.57/40.24    (11)   ~ (e1 = e0)
% 228.57/40.24    (12)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.57/40.24          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.57/40.24    (13)  all_57_1 = e3
% 228.57/40.24    (14)   ~ (e2 = e1)
% 228.57/40.24  
% 228.57/40.24  Begin of proof
% 228.57/40.24  | 
% 228.57/40.24  | ALPHA: (7) implies:
% 228.57/40.24  |   (15)  all_57_5 = e1
% 228.57/40.24  | 
% 228.57/40.24  | COMBINE_EQS: (8), (15) imply:
% 228.57/40.24  |   (16)  e3 = e1
% 228.57/40.24  | 
% 228.57/40.24  | COMBINE_EQS: (13), (16) imply:
% 228.57/40.24  |   (17)  all_57_1 = e1
% 228.57/40.24  | 
% 228.57/40.24  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (9), (10), (11), (12), (14), (17) are
% 228.57/40.24  |            inconsistent by sub-proof #1908.
% 228.57/40.24  | 
% 228.57/40.24  End of proof
% 228.57/40.24  
% 228.57/40.24  Sub-proof #581 shows that the following formulas are inconsistent:
% 228.57/40.24  ----------------------------------------------------------------
% 228.57/40.24    (1)   ~ (all_53_2 = e2)
% 228.57/40.24    (2)  op(e0, e1) = all_53_11
% 228.57/40.24    (3)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.57/40.24    (4)   ~ (all_53_6 = all_53_14)
% 228.57/40.24    (5)   ~ (all_53_6 = e2)
% 228.57/40.24    (6)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.24         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.57/40.24    (7)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.57/40.24         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.57/40.24    (8)   ~ (all_53_8 = all_53_12)
% 228.57/40.24    (9)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.24         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.24    (10)   ~ (all_53_8 = all_53_11)
% 228.57/40.24    (11)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.57/40.24          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.57/40.24    (12)   ~ (all_53_13 = e1)
% 228.57/40.24    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.57/40.24            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.57/40.24    (14)  all_57_8 = e2 & op(e1, e1) = e2
% 228.57/40.24    (15)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.57/40.24          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.57/40.24    (16)   ~ (all_53_3 = e3)
% 228.57/40.24    (17)   ~ (all_6_2 = e3)
% 228.57/40.24    (18)   ~ (all_53_9 = e1)
% 228.57/40.24    (19)  op(e1, e1) = all_6_2
% 228.57/40.24    (20)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.57/40.24    (21)   ~ (all_53_1 = all_53_9)
% 228.57/40.24    (22)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 228.57/40.24    (23)  op(e2, e2) = e1
% 228.57/40.24    (24)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.57/40.24          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.57/40.24    (25)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 228.57/40.24            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 228.57/40.24              e3) = all_22_1 & $i(all_22_1))
% 228.57/40.24    (26)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 228.57/40.24    (27)  all_55_9 = all_53_6
% 228.57/40.24    (28)   ~ (all_53_4 = all_53_12)
% 228.57/40.24    (29)   ~ (all_53_4 = e1)
% 228.57/40.24    (30)   ~ (all_53_13 = e3)
% 228.57/40.24    (31)   ~ (all_53_8 = all_53_9)
% 228.57/40.24    (32)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.57/40.24          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.57/40.24    (33)   ~ (all_53_9 = all_53_11)
% 228.57/40.24    (34)  all_55_4 = all_53_1
% 228.57/40.24    (35)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.57/40.24          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.24    (36)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.57/40.24          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.57/40.24    (37)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 228.57/40.24    (38)  all_55_1 = all_53_4
% 228.57/40.24    (39)   ~ (all_53_1 = all_53_3)
% 228.57/40.24    (40)  op(e1, e0) = all_53_14
% 228.57/40.24    (41)   ~ (all_53_6 = all_53_7)
% 228.57/40.24    (42)  all_55_7 = e3 | all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 228.57/40.24    (43)   ~ (e3 = e0)
% 228.57/40.24    (44)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.57/40.24          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.57/40.24    (45)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.57/40.24    (46)  op(e0, e3) = all_53_3
% 228.57/40.24    (47)   ~ (all_53_2 = e0)
% 228.57/40.24    (48)  all_57_0 = e0
% 228.57/40.24    (49)  all_55_2 = all_53_8
% 228.57/40.24    (50)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 228.57/40.24    (51)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.57/40.24    (52)  all_57_15 = e3
% 228.57/40.24    (53)   ~ (all_53_9 = all_53_13)
% 228.57/40.24    (54)  op(e3, e3) = e0
% 228.57/40.24    (55)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.57/40.24          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.57/40.24            e1)
% 228.57/40.24    (56)   ~ (all_53_1 = e1)
% 228.57/40.24    (57)   ~ (all_53_4 = all_53_8)
% 228.57/40.24    (58)   ~ (all_53_14 = e3)
% 228.57/40.24    (59)  all_55_6 = all_53_9
% 228.57/40.24    (60)  op(e3, e2) = all_53_4
% 228.57/40.24    (61)   ~ (all_53_1 = all_53_2)
% 228.57/40.24    (62)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.57/40.24          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 228.57/40.24    (63)   ~ (e2 = e0)
% 228.57/40.24    (64)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.57/40.24            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.57/40.24            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.57/40.24            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.57/40.24              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.57/40.24            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.57/40.24            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.57/40.24              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.57/40.24              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.57/40.24            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.57/40.24            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.57/40.24            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.57/40.24              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.57/40.24              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.57/40.24            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.57/40.24              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.57/40.24            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.57/40.24            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.57/40.24              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.57/40.24              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.57/40.24            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.57/40.24            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.57/40.24    (65)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 228.57/40.24            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 228.57/40.24              e3) = all_12_1 & $i(all_12_1))
% 228.57/40.24    (66)   ~ (all_53_9 = e2)
% 228.57/40.24    (67)   ~ (all_53_6 = e1)
% 228.57/40.24    (68)  all_55_12 = all_53_3
% 228.57/40.24    (69)  all_57_3 = e1
% 228.57/40.24    (70)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.57/40.24          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.57/40.24    (71)   ~ (all_53_1 = e0)
% 228.57/40.24    (72)   ~ (all_53_2 = all_53_14)
% 228.57/40.24    (73)   ~ (e1 = e0)
% 228.57/40.24    (74)   ~ (all_53_4 = e0)
% 228.57/40.24    (75)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.57/40.24          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.57/40.24    (76)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.57/40.24          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.57/40.24    (77)   ~ (all_53_2 = all_53_3)
% 228.57/40.24    (78)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 228.57/40.24    (79)   ~ (all_53_11 = e2)
% 228.57/40.24    (80)  all_55_8 = all_53_2
% 228.57/40.24    (81)  op(e0, e0) = e3
% 228.57/40.24    (82)   ~ (all_53_4 = all_53_6)
% 228.57/40.24    (83)  op(e0, e2) = all_53_7
% 228.57/40.24    (84)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.24          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.57/40.24            e2)
% 228.57/40.24    (85)   ~ (all_53_8 = e2)
% 228.57/40.24    (86)   ~ (all_53_3 = e0)
% 228.57/40.24    (87)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.24              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.57/40.24                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.57/40.24                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.57/40.24    (88)   ~ (all_53_1 = all_53_13)
% 228.57/40.24    (89)  op(e2, e0) = all_53_13
% 228.57/40.24    (90)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.57/40.24          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.57/40.24    (91)  all_55_11 = all_53_14
% 228.57/40.24    (92)  all_55_3 = all_53_12
% 228.57/40.24    (93)   ~ (all_53_12 = e3)
% 228.57/40.24    (94)  op(e1, e3) = all_53_2
% 228.57/40.24    (95)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.24          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.57/40.24    (96)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.57/40.24          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.57/40.24    (97)   ~ (all_53_12 = e0)
% 228.57/40.24    (98)   ~ (all_53_13 = all_53_14)
% 228.57/40.24    (99)   ~ (all_53_8 = e0)
% 228.57/40.24    (100)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.57/40.24           (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 228.57/40.24    (101)   ~ (e2 = e1)
% 228.57/40.24    (102)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.57/40.24           | (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.57/40.24             e2)
% 228.57/40.24    (103)   ~ (all_53_14 = e2)
% 228.57/40.24    (104)   ~ (all_53_2 = all_53_6)
% 228.57/40.24    (105)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.57/40.24           (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.57/40.24    (106)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 228.57/40.24    (107)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.57/40.24           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.57/40.24    (108)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.57/40.24           (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.57/40.24    (109)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.57/40.24           | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.57/40.24             e1)
% 228.57/40.24    (110)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.57/40.24           (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.57/40.24    (111)  all_55_14 = all_53_11
% 228.57/40.24    (112)  all_55_7 = all_53_13
% 228.57/40.24    (113)   ~ (all_53_11 = e3)
% 228.57/40.24    (114)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.24           (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.57/40.24    (115)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.57/40.24           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.57/40.24    (116)  op(e3, e0) = all_53_12
% 228.57/40.24  
% 228.57/40.24  Begin of proof
% 228.57/40.24  | 
% 228.57/40.24  | ALPHA: (14) implies:
% 228.57/40.24  |   (117)  all_57_8 = e2
% 228.57/40.24  |   (118)  op(e1, e1) = e2
% 228.57/40.24  | 
% 228.57/40.24  | BETA: splitting (42) gives:
% 228.57/40.24  | 
% 228.57/40.24  | Case 1:
% 228.57/40.24  | | 
% 228.57/40.24  | |   (119)  all_55_7 = e3
% 228.57/40.24  | | 
% 228.57/40.24  | | REF_CLOSE: (30), (112), (119) are inconsistent by sub-proof #2109.
% 228.57/40.24  | | 
% 228.57/40.24  | Case 2:
% 228.57/40.24  | | 
% 228.57/40.24  | |   (120)  all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 228.57/40.24  | | 
% 228.57/40.24  | | BETA: splitting (106) gives:
% 228.57/40.24  | | 
% 228.57/40.24  | | Case 1:
% 228.57/40.24  | | | 
% 228.57/40.24  | | |   (121)  all_55_12 = e3
% 228.57/40.24  | | | 
% 228.57/40.24  | | | REF_CLOSE: (16), (68), (121) are inconsistent by sub-proof #2001.
% 228.57/40.24  | | | 
% 228.57/40.24  | | Case 2:
% 228.57/40.24  | | | 
% 228.57/40.24  | | |   (122)   ~ (all_55_12 = e3)
% 228.57/40.24  | | |   (123)  all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 228.57/40.24  | | | 
% 228.57/40.24  | | | BETA: splitting (37) gives:
% 228.57/40.24  | | | 
% 228.57/40.24  | | | Case 1:
% 228.57/40.24  | | | | 
% 228.57/40.24  | | | |   (124)  all_55_6 = e3
% 228.57/40.24  | | | | 
% 228.57/40.24  | | | | COMBINE_EQS: (59), (124) imply:
% 228.57/40.24  | | | |   (125)  all_53_9 = e3
% 228.57/40.24  | | | | 
% 228.57/40.24  | | | | SIMP: (125) implies:
% 228.57/40.24  | | | |   (126)  all_53_9 = e3
% 228.57/40.24  | | | | 
% 228.57/40.24  | | | | REDUCE: (21), (126) imply:
% 228.57/40.24  | | | |   (127)   ~ (all_53_1 = e3)
% 228.57/40.24  | | | | 
% 228.57/40.24  | | | | REDUCE: (31), (126) imply:
% 228.57/40.24  | | | |   (128)   ~ (all_53_8 = e3)
% 228.57/40.24  | | | | 
% 228.57/40.24  | | | | REDUCE: (53), (126) imply:
% 228.57/40.24  | | | |   (129)   ~ (all_53_13 = e3)
% 228.57/40.24  | | | | 
% 228.57/40.24  | | | | REDUCE: (66), (126) imply:
% 228.57/40.24  | | | |   (130)   ~ (e3 = e2)
% 228.57/40.24  | | | | 
% 228.57/40.24  | | | | REDUCE: (18), (126) imply:
% 228.57/40.24  | | | |   (131)   ~ (e3 = e1)
% 228.57/40.24  | | | | 
% 228.57/40.24  | | | | BETA: splitting (51) gives:
% 228.57/40.24  | | | | 
% 228.57/40.24  | | | | Case 1:
% 228.57/40.24  | | | | | 
% 228.57/40.24  | | | | |   (132)  all_55_2 = e3
% 228.57/40.24  | | | | | 
% 228.57/40.24  | | | | | REF_CLOSE: (49), (128), (132) are inconsistent by sub-proof #2028.
% 228.57/40.24  | | | | | 
% 228.57/40.24  | | | | Case 2:
% 228.57/40.24  | | | | | 
% 228.57/40.24  | | | | |   (133)  all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.57/40.24  | | | | | 
% 228.57/40.24  | | | | | BETA: splitting (90) gives:
% 228.57/40.24  | | | | | 
% 228.57/40.24  | | | | | Case 1:
% 228.57/40.24  | | | | | | 
% 228.57/40.24  | | | | | |   (134)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2,
% 228.57/40.24  | | | | | |              e2) = e3)
% 228.57/40.24  | | | | | | 
% 228.57/40.24  | | | | | | BETA: splitting (134) gives:
% 228.57/40.24  | | | | | | 
% 228.57/40.24  | | | | | | Case 1:
% 228.57/40.24  | | | | | | | 
% 228.57/40.24  | | | | | | |   (135)  all_57_2 = e3 & op(e2, e3) = e3
% 228.57/40.24  | | | | | | | 
% 228.57/40.24  | | | | | | | ALPHA: (135) implies:
% 228.57/40.24  | | | | | | |   (136)  all_57_2 = e3
% 228.57/40.24  | | | | | | | 
% 228.57/40.24  | | | | | | | BETA: splitting (50) gives:
% 228.57/40.24  | | | | | | | 
% 228.57/40.24  | | | | | | | Case 1:
% 228.57/40.24  | | | | | | | | 
% 228.57/40.24  | | | | | | | |   (137)  all_55_4 = e3
% 228.57/40.24  | | | | | | | | 
% 228.57/40.24  | | | | | | | | REF_CLOSE: (34), (127), (137) are inconsistent by sub-proof
% 228.57/40.24  | | | | | | | |            #2170.
% 228.57/40.24  | | | | | | | | 
% 228.57/40.24  | | | | | | | Case 2:
% 228.57/40.24  | | | | | | | | 
% 228.57/40.24  | | | | | | | |   (138)   ~ (all_55_4 = e3)
% 228.57/40.24  | | | | | | | |   (139)  all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 228.57/40.24  | | | | | | | | 
% 228.57/40.24  | | | | | | | | BETA: splitting (36) gives:
% 228.57/40.24  | | | | | | | | 
% 228.57/40.24  | | | | | | | | Case 1:
% 228.57/40.24  | | | | | | | | | 
% 228.57/40.24  | | | | | | | | |   (140)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 &
% 228.57/40.24  | | | | | | | | |            op(e2, e1) = e0)
% 228.57/40.24  | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | BETA: splitting (140) gives:
% 228.57/40.24  | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | Case 1:
% 228.57/40.24  | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | |   (141)  all_57_4 = e0 & op(e3, e1) = e0
% 228.57/40.24  | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | ALPHA: (141) implies:
% 228.57/40.24  | | | | | | | | | |   (142)  all_57_4 = e0
% 228.57/40.24  | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | REF_CLOSE: (9), (13), (23), (24), (32), (43), (48), (54),
% 228.57/40.24  | | | | | | | | | |            (62), (63), (70), (73), (76), (93), (101), (116),
% 228.57/40.24  | | | | | | | | | |            (130), (131), (142) are inconsistent by sub-proof
% 228.57/40.24  | | | | | | | | | |            #1012.
% 228.57/40.24  | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | Case 2:
% 228.57/40.24  | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | |   (143)  all_57_5 = e0 & op(e2, e1) = e0
% 228.57/40.24  | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | ALPHA: (143) implies:
% 228.57/40.24  | | | | | | | | | |   (144)  all_57_5 = e0
% 228.57/40.24  | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | BETA: splitting (75) gives:
% 228.57/40.24  | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | Case 1:
% 228.57/40.24  | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | |   (145)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 228.57/40.24  | | | | | | | | | | |            & op(e2, e1) = e3)
% 228.57/40.24  | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | BETA: splitting (145) gives:
% 228.57/40.24  | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | Case 1:
% 228.57/40.24  | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | |   (146)  all_57_4 = e3 & op(e3, e1) = e3
% 228.57/40.24  | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | | ALPHA: (146) implies:
% 228.57/40.24  | | | | | | | | | | | |   (147)  all_57_4 = e3
% 228.57/40.24  | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | | BETA: splitting (133) gives:
% 228.57/40.24  | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | | Case 1:
% 228.57/40.24  | | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | | |   (148)  all_55_2 = e2
% 228.57/40.24  | | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | | | COMBINE_EQS: (49), (148) imply:
% 228.57/40.24  | | | | | | | | | | | | |   (149)  all_53_8 = e2
% 228.57/40.24  | | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | | | REDUCE: (85), (149) imply:
% 228.57/40.24  | | | | | | | | | | | | |   (150)  $false
% 228.57/40.24  | | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | | | CLOSE: (150) is inconsistent.
% 228.57/40.24  | | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | | Case 2:
% 228.57/40.24  | | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | | |   (151)  all_55_2 = e1 | all_55_2 = e0
% 228.57/40.24  | | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | | | BETA: splitting (24) gives:
% 228.57/40.24  | | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | | | Case 1:
% 228.57/40.24  | | | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | | | |   (152)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 228.57/40.24  | | | | | | | | | | | | | |            & op(e3, e2) = e1)
% 228.57/40.24  | | | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | | | | REF_CLOSE: (9), (13), (23), (43), (48), (62), (63), (73),
% 228.57/40.24  | | | | | | | | | | | | | |            (76), (101), (130), (131), (152) are inconsistent
% 228.57/40.24  | | | | | | | | | | | | | |            by sub-proof #1551.
% 228.57/40.24  | | | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | | | Case 2:
% 228.57/40.24  | | | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | | | |   (153)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 228.57/40.24  | | | | | | | | | | | | | |            & op(e3, e0) = e1)
% 228.57/40.24  | | | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | | | | BETA: splitting (153) gives:
% 228.57/40.24  | | | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | | | | Case 1:
% 228.57/40.24  | | | | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | | | | |   (154)  all_57_4 = e1 & op(e3, e1) = e1
% 228.57/40.24  | | | | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | | | | | REF_CLOSE: (131), (147), (154) are inconsistent by sub-proof
% 228.57/40.24  | | | | | | | | | | | | | | |            #2484.
% 228.57/40.24  | | | | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | | | | Case 2:
% 228.57/40.24  | | | | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | | | | |   (155)  all_57_9 = e1 & op(e3, e0) = e1
% 228.57/40.24  | | | | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | | | | | ALPHA: (155) implies:
% 228.57/40.24  | | | | | | | | | | | | | | |   (156)  all_57_9 = e1
% 228.57/40.24  | | | | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | | | | | BETA: splitting (95) gives:
% 228.57/40.24  | | | | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | | | | | Case 1:
% 228.57/40.24  | | | | | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | | | | | |   (157)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 228.57/40.24  | | | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 228.57/40.24  | | | | | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | | | | | | REF_CLOSE: (13), (23), (101), (130), (136), (157) are
% 228.57/40.24  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #969.
% 228.57/40.24  | | | | | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | | | | | Case 2:
% 228.57/40.24  | | | | | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | | | | | |   (158)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 228.57/40.24  | | | | | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 228.57/40.24  | | | | | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | | | | | | BETA: splitting (158) gives:
% 228.57/40.24  | | | | | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | | | | | | Case 1:
% 228.57/40.24  | | | | | | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | | | | | | |   (159)  all_57_5 = e2 & op(e2, e1) = e2
% 228.57/40.24  | | | | | | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | | | | | | | ALPHA: (159) implies:
% 228.57/40.24  | | | | | | | | | | | | | | | | |   (160)  all_57_5 = e2
% 228.57/40.24  | | | | | | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | | | | | | | REF_CLOSE: (63), (144), (160) are inconsistent by sub-proof
% 228.57/40.24  | | | | | | | | | | | | | | | | |            #2363.
% 228.57/40.24  | | | | | | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | | | | | | Case 2:
% 228.57/40.24  | | | | | | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | | | | | | |   (161)  all_57_10 = e2 & op(e2, e0) = e2
% 228.57/40.24  | | | | | | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | | | | | | | ALPHA: (161) implies:
% 228.57/40.24  | | | | | | | | | | | | | | | | |   (162)  all_57_10 = e2
% 228.57/40.24  | | | | | | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (5), (6), (7), (8), (9), (11), (13), (15),
% 228.57/40.24  | | | | | | | | | | | | | | | | |            (17), (19), (20), (23), (24), (26), (27), (28),
% 228.57/40.24  | | | | | | | | | | | | | | | | |            (32), (35), (36), (38), (41), (43), (44), (46),
% 228.57/40.24  | | | | | | | | | | | | | | | | |            (48), (49), (52), (54), (55), (57), (62), (63),
% 228.57/40.24  | | | | | | | | | | | | | | | | |            (67), (69), (70), (73), (74), (75), (76), (81),
% 228.57/40.24  | | | | | | | | | | | | | | | | |            (82), (83), (84), (86), (87), (90), (92), (93),
% 228.57/40.24  | | | | | | | | | | | | | | | | |            (95), (96), (97), (99), (101), (102), (105),
% 228.57/40.24  | | | | | | | | | | | | | | | | |            (107), (108), (109), (110), (114), (115), (116),
% 228.57/40.24  | | | | | | | | | | | | | | | | |            (117), (118), (130), (131), (136), (144), (147),
% 228.57/40.24  | | | | | | | | | | | | | | | | |            (151), (156), (162) are inconsistent by sub-proof
% 228.57/40.24  | | | | | | | | | | | | | | | | |            #590.
% 228.57/40.24  | | | | | | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | | | | | | End of split
% 228.57/40.24  | | | | | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | | | | | End of split
% 228.57/40.24  | | | | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | | | | End of split
% 228.57/40.24  | | | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | | | End of split
% 228.57/40.24  | | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | | End of split
% 228.57/40.24  | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | Case 2:
% 228.57/40.24  | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | |   (163)  all_57_5 = e3 & op(e2, e1) = e3
% 228.57/40.24  | | | | | | | | | | | | 
% 228.57/40.24  | | | | | | | | | | | | ALPHA: (163) implies:
% 228.57/40.24  | | | | | | | | | | | |   (164)  all_57_5 = e3
% 228.57/40.24  | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (11), (12), (13), (15),
% 228.57/40.25  | | | | | | | | | | | |            (16), (17), (19), (22), (23), (24), (25), (26),
% 228.57/40.25  | | | | | | | | | | | |            (27), (30), (32), (34), (35), (36), (39), (43),
% 228.57/40.25  | | | | | | | | | | | |            (44), (45), (46), (47), (48), (52), (54), (55),
% 228.57/40.25  | | | | | | | | | | | |            (56), (61), (62), (63), (64), (65), (67), (68),
% 228.57/40.25  | | | | | | | | | | | |            (69), (70), (71), (72), (73), (75), (76), (77),
% 228.57/40.25  | | | | | | | | | | | |            (80), (81), (84), (86), (87), (88), (89), (91),
% 228.57/40.25  | | | | | | | | | | | |            (93), (94), (95), (96), (97), (100), (101), (102),
% 228.57/40.25  | | | | | | | | | | | |            (103), (104), (105), (107), (108), (109), (110),
% 228.57/40.25  | | | | | | | | | | | |            (112), (114), (115), (116), (117), (118), (120),
% 228.57/40.25  | | | | | | | | | | | |            (123), (127), (130), (131), (139), (164) are
% 228.57/40.25  | | | | | | | | | | | |            inconsistent by sub-proof #583.
% 228.57/40.25  | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | End of split
% 228.57/40.25  | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | Case 2:
% 228.57/40.25  | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | |   (165)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 228.57/40.25  | | | | | | | | | | |            e3 & op(e0, e1) = e3)
% 228.57/40.25  | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | REF_CLOSE: (13), (17), (19), (43), (52), (55), (63), (73),
% 228.57/40.25  | | | | | | | | | | |            (84), (87), (101), (130), (131), (165) are
% 228.57/40.25  | | | | | | | | | | |            inconsistent by sub-proof #1794.
% 228.57/40.25  | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | End of split
% 228.57/40.25  | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | End of split
% 228.57/40.25  | | | | | | | | | 
% 228.57/40.25  | | | | | | | | Case 2:
% 228.57/40.25  | | | | | | | | | 
% 228.57/40.25  | | | | | | | | |   (166)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 &
% 228.57/40.25  | | | | | | | | |            op(e0, e1) = e0)
% 228.57/40.25  | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | BETA: splitting (166) gives:
% 228.57/40.25  | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | Case 1:
% 228.57/40.25  | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | |   (167)  all_57_8 = e0 & op(e1, e1) = e0
% 228.57/40.25  | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | REF_CLOSE: (63), (117), (167) are inconsistent by sub-proof
% 228.57/40.25  | | | | | | | | | |            #917.
% 228.57/40.25  | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | Case 2:
% 228.57/40.25  | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | |   (168)  all_57_14 = e0 & op(e0, e1) = e0
% 228.57/40.25  | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | ALPHA: (168) implies:
% 228.57/40.25  | | | | | | | | | |   (169)  all_57_14 = e0
% 228.57/40.25  | | | | | | | | | |   (170)  op(e0, e1) = e0
% 228.57/40.25  | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | BETA: splitting (75) gives:
% 228.57/40.25  | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | Case 1:
% 228.57/40.25  | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | |   (171)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 228.57/40.25  | | | | | | | | | | |            & op(e2, e1) = e3)
% 228.57/40.25  | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | BETA: splitting (171) gives:
% 228.57/40.25  | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | Case 1:
% 228.57/40.25  | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | |   (172)  all_57_4 = e3 & op(e3, e1) = e3
% 228.57/40.25  | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | ALPHA: (172) implies:
% 228.57/40.25  | | | | | | | | | | | |   (173)  all_57_4 = e3
% 228.57/40.25  | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | BETA: splitting (133) gives:
% 228.57/40.25  | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | Case 1:
% 228.57/40.25  | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | |   (174)  all_55_2 = e2
% 228.57/40.25  | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | COMBINE_EQS: (49), (174) imply:
% 228.57/40.25  | | | | | | | | | | | | |   (175)  all_53_8 = e2
% 228.57/40.25  | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | REDUCE: (85), (175) imply:
% 228.57/40.25  | | | | | | | | | | | | |   (176)  $false
% 228.57/40.25  | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | CLOSE: (176) is inconsistent.
% 228.57/40.25  | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | Case 2:
% 228.57/40.25  | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | |   (177)  all_55_2 = e1 | all_55_2 = e0
% 228.57/40.25  | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | BETA: splitting (24) gives:
% 228.57/40.25  | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | Case 1:
% 228.57/40.25  | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | |   (178)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 228.57/40.25  | | | | | | | | | | | | | |            & op(e3, e2) = e1)
% 228.57/40.25  | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | REF_CLOSE: (9), (13), (23), (43), (48), (62), (63), (73),
% 228.57/40.25  | | | | | | | | | | | | | |            (76), (101), (130), (131), (178) are inconsistent
% 228.57/40.25  | | | | | | | | | | | | | |            by sub-proof #1551.
% 228.57/40.25  | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | Case 2:
% 228.57/40.25  | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | |   (179)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 228.57/40.25  | | | | | | | | | | | | | |            & op(e3, e0) = e1)
% 228.57/40.25  | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | BETA: splitting (179) gives:
% 228.57/40.25  | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | Case 1:
% 228.57/40.25  | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | |   (180)  all_57_4 = e1 & op(e3, e1) = e1
% 228.57/40.25  | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | REF_CLOSE: (131), (173), (180) are inconsistent by sub-proof
% 228.57/40.25  | | | | | | | | | | | | | | |            #2484.
% 228.57/40.25  | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | Case 2:
% 228.57/40.25  | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | |   (181)  all_57_9 = e1 & op(e3, e0) = e1
% 228.57/40.25  | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | ALPHA: (181) implies:
% 228.57/40.25  | | | | | | | | | | | | | | |   (182)  all_57_9 = e1
% 228.57/40.25  | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | BETA: splitting (95) gives:
% 228.57/40.25  | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | Case 1:
% 228.57/40.25  | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | |   (183)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 228.57/40.25  | | | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 228.57/40.25  | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | REF_CLOSE: (13), (23), (101), (130), (136), (183) are
% 228.57/40.25  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #969.
% 228.57/40.25  | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | Case 2:
% 228.57/40.25  | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | |   (184)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 228.57/40.25  | | | | | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 228.57/40.25  | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | BETA: splitting (184) gives:
% 228.57/40.25  | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | Case 1:
% 228.57/40.25  | | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | |   (185)  all_57_5 = e2 & op(e2, e1) = e2
% 228.57/40.25  | | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | | ALPHA: (185) implies:
% 228.57/40.25  | | | | | | | | | | | | | | | | |   (186)  all_57_5 = e2
% 228.57/40.25  | | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | | REF_CLOSE: (44), (73), (101), (117), (131), (169), (173),
% 228.57/40.25  | | | | | | | | | | | | | | | | |            (186) are inconsistent by sub-proof #925.
% 228.57/40.25  | | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | Case 2:
% 228.57/40.25  | | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | |   (187)  all_57_10 = e2 & op(e2, e0) = e2
% 228.57/40.25  | | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | | ALPHA: (187) implies:
% 228.57/40.25  | | | | | | | | | | | | | | | | |   (188)  all_57_10 = e2
% 228.57/40.25  | | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | | BETA: splitting (100) gives:
% 228.57/40.25  | | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | | Case 1:
% 228.57/40.25  | | | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | | |   (189)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 228.57/40.25  | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e0)
% 228.57/40.25  | | | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (9), (11), (13), (15), (17), (19), (23),
% 228.57/40.25  | | | | | | | | | | | | | | | | | |            (24), (32), (35), (36), (43), (44), (46), (52),
% 228.57/40.25  | | | | | | | | | | | | | | | | | |            (54), (55), (62), (63), (69), (70), (73), (75),
% 228.57/40.25  | | | | | | | | | | | | | | | | | |            (76), (81), (84), (86), (87), (90), (93), (95),
% 228.57/40.25  | | | | | | | | | | | | | | | | | |            (96), (97), (101), (102), (105), (107), (108),
% 228.57/40.25  | | | | | | | | | | | | | | | | | |            (109), (110), (114), (115), (116), (130), (131),
% 228.57/40.25  | | | | | | | | | | | | | | | | | |            (189) are inconsistent by sub-proof #916.
% 228.57/40.25  | | | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | | Case 2:
% 228.57/40.25  | | | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | | |   (190)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 228.57/40.25  | | | | | | | | | | | | | | | | | |            e0 & op(e2, e0) = e0)
% 228.57/40.25  | | | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 228.57/40.25  | | | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | | | Case 1:
% 228.57/40.25  | | | | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | | | |   (191)  all_57_5 = e0 & op(e2, e1) = e0
% 228.57/40.25  | | | | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | | | | ALPHA: (191) implies:
% 228.57/40.25  | | | | | | | | | | | | | | | | | | |   (192)  all_57_5 = e0
% 228.57/40.25  | | | | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (5), (6), (7), (8), (9), (11), (13), (15),
% 228.57/40.25  | | | | | | | | | | | | | | | | | | |            (17), (19), (20), (23), (24), (26), (27), (28),
% 228.57/40.25  | | | | | | | | | | | | | | | | | | |            (32), (35), (36), (38), (41), (43), (44), (46),
% 228.57/40.25  | | | | | | | | | | | | | | | | | | |            (48), (49), (52), (54), (55), (57), (62), (63),
% 228.57/40.25  | | | | | | | | | | | | | | | | | | |            (67), (69), (70), (73), (74), (75), (76), (81),
% 228.57/40.25  | | | | | | | | | | | | | | | | | | |            (82), (83), (84), (86), (87), (90), (92), (93),
% 228.57/40.25  | | | | | | | | | | | | | | | | | | |            (95), (96), (97), (99), (101), (102), (105),
% 228.57/40.25  | | | | | | | | | | | | | | | | | | |            (107), (108), (109), (110), (114), (115), (116),
% 228.57/40.25  | | | | | | | | | | | | | | | | | | |            (117), (118), (130), (131), (136), (173), (177),
% 228.57/40.25  | | | | | | | | | | | | | | | | | | |            (182), (188), (192) are inconsistent by sub-proof
% 228.57/40.25  | | | | | | | | | | | | | | | | | | |            #590.
% 228.57/40.25  | | | | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | | | Case 2:
% 228.57/40.25  | | | | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | | | |   (193)  all_57_10 = e0 & op(e2, e0) = e0
% 228.57/40.25  | | | | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | | | | ALPHA: (193) implies:
% 228.57/40.25  | | | | | | | | | | | | | | | | | | |   (194)  all_57_10 = e0
% 228.57/40.25  | | | | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (63), (188), (194) are inconsistent by sub-proof
% 228.57/40.25  | | | | | | | | | | | | | | | | | | |            #2138.
% 228.57/40.25  | | | | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | | | End of split
% 228.57/40.25  | | | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | | End of split
% 228.57/40.25  | | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | End of split
% 228.57/40.25  | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | End of split
% 228.57/40.25  | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | End of split
% 228.57/40.25  | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | End of split
% 228.57/40.25  | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | End of split
% 228.57/40.25  | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | Case 2:
% 228.57/40.25  | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | |   (195)  all_57_5 = e3 & op(e2, e1) = e3
% 228.57/40.25  | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | ALPHA: (195) implies:
% 228.57/40.25  | | | | | | | | | | | |   (196)  all_57_5 = e3
% 228.57/40.25  | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (11), (12), (13), (15),
% 228.57/40.25  | | | | | | | | | | | |            (16), (17), (19), (22), (23), (24), (25), (26),
% 228.57/40.25  | | | | | | | | | | | |            (27), (30), (32), (34), (35), (36), (39), (43),
% 228.57/40.25  | | | | | | | | | | | |            (44), (45), (46), (47), (48), (52), (54), (55),
% 228.57/40.25  | | | | | | | | | | | |            (56), (61), (62), (63), (64), (65), (67), (68),
% 228.57/40.25  | | | | | | | | | | | |            (69), (70), (71), (72), (73), (75), (76), (77),
% 228.57/40.25  | | | | | | | | | | | |            (80), (81), (84), (86), (87), (88), (89), (91),
% 228.57/40.25  | | | | | | | | | | | |            (93), (94), (95), (96), (97), (100), (101), (102),
% 228.57/40.25  | | | | | | | | | | | |            (103), (104), (105), (107), (108), (109), (110),
% 228.57/40.25  | | | | | | | | | | | |            (112), (114), (115), (116), (117), (120), (123),
% 228.57/40.25  | | | | | | | | | | | |            (127), (130), (131), (136), (139), (169), (170),
% 228.57/40.25  | | | | | | | | | | | |            (196) are inconsistent by sub-proof #584.
% 228.57/40.25  | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | End of split
% 228.57/40.25  | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | Case 2:
% 228.57/40.25  | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | |   (197)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 228.57/40.25  | | | | | | | | | | |            e3 & op(e0, e1) = e3)
% 228.57/40.25  | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | REF_CLOSE: (13), (17), (19), (43), (52), (55), (63), (73),
% 228.57/40.25  | | | | | | | | | | |            (84), (87), (101), (130), (131), (197) are
% 228.57/40.25  | | | | | | | | | | |            inconsistent by sub-proof #1794.
% 228.57/40.25  | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | End of split
% 228.57/40.25  | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | End of split
% 228.57/40.25  | | | | | | | | | 
% 228.57/40.25  | | | | | | | | End of split
% 228.57/40.25  | | | | | | | | 
% 228.57/40.25  | | | | | | | End of split
% 228.57/40.25  | | | | | | | 
% 228.57/40.25  | | | | | | Case 2:
% 228.57/40.25  | | | | | | | 
% 228.57/40.25  | | | | | | |   (198)  all_57_3 = e3 & op(e2, e2) = e3
% 228.57/40.25  | | | | | | | 
% 228.57/40.25  | | | | | | | ALPHA: (198) implies:
% 228.57/40.25  | | | | | | |   (199)  op(e2, e2) = e3
% 228.57/40.25  | | | | | | | 
% 228.57/40.25  | | | | | | | REF_CLOSE: (13), (23), (131), (199) are inconsistent by sub-proof
% 228.57/40.25  | | | | | | |            #1912.
% 228.57/40.25  | | | | | | | 
% 228.57/40.25  | | | | | | End of split
% 228.57/40.25  | | | | | | 
% 228.57/40.25  | | | | | Case 2:
% 228.57/40.25  | | | | | | 
% 228.57/40.25  | | | | | |   (200)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 &
% 228.57/40.25  | | | | | |            op(e2, e0) = e3)
% 228.57/40.25  | | | | | | 
% 228.57/40.25  | | | | | | BETA: splitting (200) gives:
% 228.57/40.25  | | | | | | 
% 228.57/40.25  | | | | | | Case 1:
% 228.57/40.25  | | | | | | | 
% 228.57/40.25  | | | | | | |   (201)  all_57_5 = e3 & op(e2, e1) = e3
% 228.57/40.25  | | | | | | | 
% 228.57/40.25  | | | | | | | ALPHA: (201) implies:
% 228.57/40.25  | | | | | | |   (202)  all_57_5 = e3
% 228.57/40.25  | | | | | | | 
% 228.57/40.25  | | | | | | | BETA: splitting (50) gives:
% 228.57/40.25  | | | | | | | 
% 228.57/40.25  | | | | | | | Case 1:
% 228.57/40.25  | | | | | | | | 
% 228.57/40.25  | | | | | | | |   (203)  all_55_4 = e3
% 228.57/40.25  | | | | | | | | 
% 228.57/40.25  | | | | | | | | REF_CLOSE: (34), (127), (203) are inconsistent by sub-proof
% 228.57/40.25  | | | | | | | |            #2170.
% 228.57/40.25  | | | | | | | | 
% 228.57/40.25  | | | | | | | Case 2:
% 228.57/40.25  | | | | | | | | 
% 228.57/40.25  | | | | | | | |   (204)   ~ (all_55_4 = e3)
% 228.57/40.25  | | | | | | | |   (205)  all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 228.57/40.25  | | | | | | | | 
% 228.57/40.25  | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (11), (12), (13), (15),
% 228.57/40.25  | | | | | | | |            (16), (17), (19), (22), (23), (24), (25), (26), (27),
% 228.57/40.25  | | | | | | | |            (30), (32), (34), (35), (36), (39), (43), (44), (45),
% 228.57/40.25  | | | | | | | |            (46), (47), (48), (52), (54), (55), (56), (61), (62),
% 228.57/40.25  | | | | | | | |            (63), (64), (65), (67), (68), (69), (70), (71), (72),
% 228.57/40.25  | | | | | | | |            (73), (75), (76), (77), (80), (81), (84), (86), (87),
% 228.57/40.25  | | | | | | | |            (88), (89), (91), (93), (94), (95), (96), (97),
% 228.57/40.25  | | | | | | | |            (100), (101), (102), (103), (104), (105), (107),
% 228.57/40.25  | | | | | | | |            (108), (109), (110), (112), (114), (115), (116),
% 228.57/40.25  | | | | | | | |            (117), (118), (120), (123), (127), (130), (131),
% 228.57/40.25  | | | | | | | |            (202), (205) are inconsistent by sub-proof #583.
% 228.57/40.25  | | | | | | | | 
% 228.57/40.25  | | | | | | | End of split
% 228.57/40.25  | | | | | | | 
% 228.57/40.25  | | | | | | Case 2:
% 228.57/40.25  | | | | | | | 
% 228.57/40.25  | | | | | | |   (206)  all_57_10 = e3 & op(e2, e0) = e3
% 228.57/40.25  | | | | | | | 
% 228.57/40.25  | | | | | | | ALPHA: (206) implies:
% 228.57/40.25  | | | | | | |   (207)  all_57_10 = e3
% 228.57/40.25  | | | | | | | 
% 228.57/40.25  | | | | | | | REF_CLOSE: (13), (43), (52), (63), (73), (81), (87), (101), (102),
% 228.57/40.25  | | | | | | |            (109), (130), (131), (207) are inconsistent by
% 228.57/40.25  | | | | | | |            sub-proof #1746.
% 228.57/40.25  | | | | | | | 
% 228.57/40.25  | | | | | | End of split
% 228.57/40.25  | | | | | | 
% 228.57/40.25  | | | | | End of split
% 228.57/40.25  | | | | | 
% 228.57/40.25  | | | | End of split
% 228.57/40.25  | | | | 
% 228.57/40.25  | | | Case 2:
% 228.57/40.25  | | | | 
% 228.57/40.25  | | | |   (208)  all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 228.57/40.25  | | | | 
% 228.57/40.25  | | | | BETA: splitting (208) gives:
% 228.57/40.25  | | | | 
% 228.57/40.25  | | | | Case 1:
% 228.57/40.25  | | | | | 
% 228.57/40.25  | | | | |   (209)  all_55_6 = e2
% 228.57/40.25  | | | | | 
% 228.57/40.25  | | | | | REF_CLOSE: (59), (66), (209) are inconsistent by sub-proof #2398.
% 228.57/40.25  | | | | | 
% 228.57/40.25  | | | | Case 2:
% 228.57/40.25  | | | | | 
% 228.57/40.25  | | | | |   (210)  all_55_6 = e1 | all_55_6 = e0
% 228.57/40.25  | | | | | 
% 228.57/40.25  | | | | | BETA: splitting (210) gives:
% 228.57/40.25  | | | | | 
% 228.57/40.25  | | | | | Case 1:
% 228.57/40.25  | | | | | | 
% 228.57/40.25  | | | | | |   (211)  all_55_6 = e1
% 228.57/40.25  | | | | | | 
% 228.57/40.25  | | | | | | REF_CLOSE: (18), (59), (211) are inconsistent by sub-proof #2163.
% 228.57/40.25  | | | | | | 
% 228.57/40.25  | | | | | Case 2:
% 228.57/40.25  | | | | | | 
% 228.57/40.25  | | | | | |   (212)  all_55_6 = e0
% 228.57/40.25  | | | | | | 
% 228.57/40.25  | | | | | | COMBINE_EQS: (59), (212) imply:
% 228.57/40.25  | | | | | |   (213)  all_53_9 = e0
% 228.57/40.25  | | | | | | 
% 228.57/40.25  | | | | | | SIMP: (213) implies:
% 228.57/40.25  | | | | | |   (214)  all_53_9 = e0
% 228.57/40.25  | | | | | | 
% 228.57/40.25  | | | | | | REDUCE: (33), (214) imply:
% 228.57/40.25  | | | | | |   (215)   ~ (all_53_11 = e0)
% 228.57/40.25  | | | | | | 
% 228.57/40.25  | | | | | | SIMP: (215) implies:
% 228.57/40.25  | | | | | |   (216)   ~ (all_53_11 = e0)
% 228.57/40.25  | | | | | | 
% 228.57/40.25  | | | | | | REDUCE: (53), (214) imply:
% 228.57/40.25  | | | | | |   (217)   ~ (all_53_13 = e0)
% 228.57/40.25  | | | | | | 
% 228.57/40.25  | | | | | | SIMP: (217) implies:
% 228.57/40.25  | | | | | |   (218)   ~ (all_53_13 = e0)
% 228.57/40.25  | | | | | | 
% 228.57/40.25  | | | | | | BETA: splitting (78) gives:
% 228.57/40.25  | | | | | | 
% 228.57/40.25  | | | | | | Case 1:
% 228.57/40.25  | | | | | | | 
% 228.57/40.25  | | | | | | |   (219)  all_55_14 = e3
% 228.57/40.25  | | | | | | | 
% 228.57/40.25  | | | | | | | REF_CLOSE: (111), (113), (219) are inconsistent by sub-proof
% 228.57/40.25  | | | | | | |            #2294.
% 228.57/40.25  | | | | | | | 
% 228.57/40.25  | | | | | | Case 2:
% 228.57/40.25  | | | | | | | 
% 228.57/40.25  | | | | | | |   (220)  all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 228.57/40.25  | | | | | | | 
% 228.57/40.25  | | | | | | | BETA: splitting (220) gives:
% 228.57/40.25  | | | | | | | 
% 228.57/40.25  | | | | | | | Case 1:
% 228.57/40.25  | | | | | | | | 
% 228.57/40.25  | | | | | | | |   (221)  all_55_14 = e2
% 228.57/40.25  | | | | | | | | 
% 228.57/40.25  | | | | | | | | REF_CLOSE: (79), (111), (221) are inconsistent by sub-proof
% 228.57/40.25  | | | | | | | |            #2293.
% 228.57/40.25  | | | | | | | | 
% 228.57/40.25  | | | | | | | Case 2:
% 228.57/40.25  | | | | | | | | 
% 228.57/40.25  | | | | | | | |   (222)  all_55_14 = e1 | all_55_14 = e0
% 228.57/40.25  | | | | | | | | 
% 228.57/40.25  | | | | | | | | BETA: splitting (222) gives:
% 228.57/40.25  | | | | | | | | 
% 228.57/40.25  | | | | | | | | Case 1:
% 228.57/40.25  | | | | | | | | | 
% 228.57/40.25  | | | | | | | | |   (223)  all_55_14 = e1
% 228.57/40.25  | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | COMBINE_EQS: (111), (223) imply:
% 228.57/40.25  | | | | | | | | |   (224)  all_53_11 = e1
% 228.57/40.25  | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | SIMP: (224) implies:
% 228.57/40.25  | | | | | | | | |   (225)  all_53_11 = e1
% 228.57/40.25  | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | REDUCE: (10), (225) imply:
% 228.57/40.25  | | | | | | | | |   (226)   ~ (all_53_8 = e1)
% 228.57/40.25  | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | REDUCE: (2), (225) imply:
% 228.57/40.25  | | | | | | | | |   (227)  op(e0, e1) = e1
% 228.57/40.25  | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | BETA: splitting (120) gives:
% 228.57/40.25  | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | Case 1:
% 228.57/40.25  | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | |   (228)  all_55_7 = e2
% 228.57/40.25  | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | COMBINE_EQS: (112), (228) imply:
% 228.57/40.25  | | | | | | | | | |   (229)  all_53_13 = e2
% 228.57/40.25  | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | SIMP: (229) implies:
% 228.57/40.25  | | | | | | | | | |   (230)  all_53_13 = e2
% 228.57/40.25  | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | REDUCE: (88), (230) imply:
% 228.57/40.25  | | | | | | | | | |   (231)   ~ (all_53_1 = e2)
% 228.57/40.25  | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | REDUCE: (98), (230) imply:
% 228.57/40.25  | | | | | | | | | |   (232)   ~ (all_53_14 = e2)
% 228.57/40.25  | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | REDUCE: (89), (230) imply:
% 228.57/40.25  | | | | | | | | | |   (233)  op(e2, e0) = e2
% 228.57/40.25  | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | BETA: splitting (50) gives:
% 228.57/40.25  | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | Case 1:
% 228.57/40.25  | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | |   (234)  all_55_4 = e3
% 228.57/40.25  | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | COMBINE_EQS: (34), (234) imply:
% 228.57/40.25  | | | | | | | | | | |   (235)  all_53_1 = e3
% 228.57/40.25  | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | SIMP: (235) implies:
% 228.57/40.25  | | | | | | | | | | |   (236)  all_53_1 = e3
% 228.57/40.25  | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | REDUCE: (61), (236) imply:
% 228.57/40.25  | | | | | | | | | | |   (237)   ~ (all_53_2 = e3)
% 228.57/40.25  | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | SIMP: (237) implies:
% 228.57/40.25  | | | | | | | | | | |   (238)   ~ (all_53_2 = e3)
% 228.57/40.25  | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | BETA: splitting (45) gives:
% 228.57/40.25  | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | Case 1:
% 228.57/40.25  | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | |   (239)  all_55_8 = e3
% 228.57/40.25  | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | REF_CLOSE: (80), (238), (239) are inconsistent by sub-proof
% 228.57/40.25  | | | | | | | | | | | |            #2496.
% 228.57/40.25  | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | Case 2:
% 228.57/40.25  | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | |   (240)  all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.57/40.25  | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | BETA: splitting (51) gives:
% 228.57/40.25  | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | Case 1:
% 228.57/40.25  | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | |   (241)  all_55_2 = e3
% 228.57/40.25  | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | COMBINE_EQS: (49), (241) imply:
% 228.57/40.25  | | | | | | | | | | | | |   (242)  all_53_8 = e3
% 228.57/40.25  | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | SIMP: (242) implies:
% 228.57/40.25  | | | | | | | | | | | | |   (243)  all_53_8 = e3
% 228.57/40.25  | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | REDUCE: (57), (243) imply:
% 228.57/40.25  | | | | | | | | | | | | |   (244)   ~ (all_53_4 = e3)
% 228.57/40.25  | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | BETA: splitting (64) gives:
% 228.57/40.25  | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | Case 1:
% 228.57/40.25  | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | |   (245)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 228.57/40.25  | | | | | | | | | | | | | |            all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 228.57/40.25  | | | | | | | | | | | | | |            op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 228.57/40.25  | | | | | | | | | | | | | |              all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 228.57/40.25  | | | | | | | | | | | | | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 228.57/40.25  | | | | | | | | | | | | | |            op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 228.57/40.25  | | | | | | | | | | | | | |            $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.57/40.25  | | | | | | | | | | | | | |            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 228.57/40.25  | | | | | | | | | | | | | |            & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 228.57/40.25  | | | | | | | | | | | | | |              all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 228.57/40.25  | | | | | | | | | | | | | |            & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.57/40.25  | | | | | | | | | | | | | |              all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 228.57/40.25  | | | | | | | | | | | | | |            op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 228.57/40.25  | | | | | | | | | | | | | |            & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.57/40.25  | | | | | | | | | | | | | |            $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 228.57/40.25  | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 228.57/40.25  | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | Case 1:
% 228.57/40.25  | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | |   (246)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 228.57/40.25  | | | | | | | | | | | | | | |          all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 228.57/40.25  | | | | | | | | | | | | | | |          op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 228.57/40.25  | | | | | | | | | | | | | | |            all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 228.57/40.25  | | | | | | | | | | | | | | |          op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 228.57/40.25  | | | | | | | | | | | | | | |          op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 228.57/40.25  | | | | | | | | | | | | | | |          $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.57/40.25  | | | | | | | | | | | | | | |          $i(all_52_7)
% 228.57/40.25  | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | ALPHA: (246) implies:
% 228.57/40.25  | | | | | | | | | | | | | | |   (247)  op(e3, e2) = all_52_3
% 228.57/40.25  | | | | | | | | | | | | | | |   (248)  op(all_52_3, all_52_3) = e2
% 228.57/40.25  | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | BETA: splitting (3) gives:
% 228.57/40.25  | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | Case 1:
% 228.57/40.25  | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | |   (249)  all_55_1 = e3
% 228.57/40.25  | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | COMBINE_EQS: (38), (249) imply:
% 228.57/40.25  | | | | | | | | | | | | | | | |   (250)  all_53_4 = e3
% 228.57/40.25  | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | REDUCE: (244), (250) imply:
% 228.57/40.25  | | | | | | | | | | | | | | | |   (251)  $false
% 228.57/40.25  | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | CLOSE: (251) is inconsistent.
% 228.57/40.25  | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | Case 2:
% 228.57/40.25  | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | |   (252)  all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.57/40.25  | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | REF_CLOSE: (13), (23), (29), (38), (60), (74), (247), (248),
% 228.57/40.25  | | | | | | | | | | | | | | | |            (252) are inconsistent by sub-proof #582.
% 228.57/40.25  | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | End of split
% 228.57/40.25  | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | Case 2:
% 228.57/40.25  | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | |   (253)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.57/40.25  | | | | | | | | | | | | | | |          all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 228.57/40.25  | | | | | | | | | | | | | | |          op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 228.57/40.25  | | | | | | | | | | | | | | |            all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 228.57/40.25  | | | | | | | | | | | | | | |          & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.57/40.25  | | | | | | | | | | | | | | |          op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 228.57/40.25  | | | | | | | | | | | | | | |          $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 228.57/40.25  | | | | | | | | | | | | | | |          $i(all_52_15)
% 228.57/40.25  | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | ALPHA: (253) implies:
% 228.57/40.25  | | | | | | | | | | | | | | |   (254)  op(e2, e0) = all_52_15
% 228.57/40.25  | | | | | | | | | | | | | | |   (255)  op(e2, e2) = all_52_11
% 228.57/40.25  | | | | | | | | | | | | | | |   (256)  op(all_52_15, all_52_15) = e0
% 228.57/40.25  | | | | | | | | | | | | | | |   (257)  op(all_52_11, all_52_11) = e2
% 228.57/40.25  | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | BETA: splitting (3) gives:
% 228.57/40.25  | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | Case 1:
% 228.57/40.25  | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | |   (258)  all_55_1 = e3
% 228.57/40.25  | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | COMBINE_EQS: (38), (258) imply:
% 228.57/40.25  | | | | | | | | | | | | | | | |   (259)  all_53_4 = e3
% 228.57/40.25  | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | REDUCE: (244), (259) imply:
% 228.57/40.25  | | | | | | | | | | | | | | | |   (260)  $false
% 228.57/40.25  | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | CLOSE: (260) is inconsistent.
% 228.57/40.25  | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | Case 2:
% 228.57/40.25  | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | |   (261)   ~ (all_55_1 = e3)
% 228.57/40.25  | | | | | | | | | | | | | | | |   (262)  all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.57/40.25  | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | BETA: splitting (262) gives:
% 228.57/40.25  | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | Case 1:
% 228.57/40.25  | | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | |   (263)  all_55_1 = e2
% 228.57/40.25  | | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | | COMBINE_EQS: (38), (263) imply:
% 228.57/40.25  | | | | | | | | | | | | | | | | |   (264)  all_53_4 = e2
% 228.57/40.25  | | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | | REDUCE: (244), (264) imply:
% 228.57/40.25  | | | | | | | | | | | | | | | | |   (265)   ~ (e3 = e2)
% 228.57/40.25  | | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | | SIMP: (265) implies:
% 228.57/40.25  | | | | | | | | | | | | | | | | |   (266)   ~ (e3 = e2)
% 228.57/40.25  | | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with e2, all_52_15, e0, e2,
% 228.57/40.25  | | | | | | | | | | | | | | | | |              simplifying with (233), (254) gives:
% 228.57/40.25  | | | | | | | | | | | | | | | | |   (267)  all_52_15 = e2
% 228.57/40.25  | | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | | REDUCE: (256), (267) imply:
% 228.57/40.25  | | | | | | | | | | | | | | | | |   (268)  op(e2, e2) = e0
% 228.57/40.25  | | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (81), (255), (257), (266), (268) are
% 228.57/40.25  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1229.
% 228.57/40.25  | | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | Case 2:
% 228.57/40.25  | | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | |   (269)  all_55_1 = e1 | all_55_1 = e0
% 228.57/40.25  | | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | | REF_CLOSE: (29), (38), (74), (269) are inconsistent by
% 228.57/40.25  | | | | | | | | | | | | | | | | |            sub-proof #1730.
% 228.57/40.25  | | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | End of split
% 228.57/40.25  | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | End of split
% 228.57/40.25  | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | End of split
% 228.57/40.25  | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | Case 2:
% 228.57/40.25  | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | |   (270)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 228.57/40.25  | | | | | | | | | | | | | |            & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 228.57/40.25  | | | | | | | | | | | | | |            & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.57/40.25  | | | | | | | | | | | | | |              all_52_21) = e1 & op(all_52_23, all_52_23) =
% 228.57/40.25  | | | | | | | | | | | | | |            e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 228.57/40.25  | | | | | | | | | | | | | |            all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 228.57/40.25  | | | | | | | | | | | | | |            = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 228.57/40.25  | | | | | | | | | | | | | |            $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 228.57/40.25  | | | | | | | | | | | | | |            & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 228.57/40.25  | | | | | | | | | | | | | |            e0 & op(all_52_25, all_52_25) = e3 &
% 228.57/40.25  | | | | | | | | | | | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 228.57/40.25  | | | | | | | | | | | | | |              all_52_29) = e1 & op(all_52_31, all_52_31) =
% 228.57/40.25  | | | | | | | | | | | | | |            e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 228.57/40.25  | | | | | | | | | | | | | |            all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 228.57/40.25  | | | | | | | | | | | | | |            = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 228.57/40.25  | | | | | | | | | | | | | |            $i(all_52_29) & $i(all_52_31))
% 228.57/40.25  | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | BETA: splitting (270) gives:
% 228.57/40.25  | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | Case 1:
% 228.57/40.25  | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | |   (271)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 228.57/40.25  | | | | | | | | | | | | | | |          all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 228.57/40.25  | | | | | | | | | | | | | | |          op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.57/40.25  | | | | | | | | | | | | | | |            all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 228.57/40.25  | | | | | | | | | | | | | | |          & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 228.57/40.25  | | | | | | | | | | | | | | |          & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 228.57/40.25  | | | | | | | | | | | | | | |          & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.57/40.25  | | | | | | | | | | | | | | |          $i(all_52_23)
% 228.57/40.25  | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | ALPHA: (271) implies:
% 228.57/40.25  | | | | | | | | | | | | | | |   (272)  op(e1, e0) = all_52_23
% 228.57/40.25  | | | | | | | | | | | | | | |   (273)  op(all_52_23, all_52_23) = e0
% 228.57/40.25  | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | BETA: splitting (240) gives:
% 228.57/40.25  | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | Case 1:
% 228.57/40.25  | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | |   (274)  all_55_8 = e2
% 228.57/40.25  | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | REF_CLOSE: (1), (80), (274) are inconsistent by sub-proof
% 228.57/40.25  | | | | | | | | | | | | | | | |            #2406.
% 228.57/40.25  | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | Case 2:
% 228.57/40.25  | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | |   (275)  all_55_8 = e1 | all_55_8 = e0
% 228.57/40.25  | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | BETA: splitting (275) gives:
% 228.57/40.25  | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | Case 1:
% 228.57/40.25  | | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | |   (276)  all_55_8 = e1
% 228.57/40.25  | | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | | COMBINE_EQS: (80), (276) imply:
% 228.57/40.25  | | | | | | | | | | | | | | | | |   (277)  all_53_2 = e1
% 228.57/40.25  | | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | | SIMP: (277) implies:
% 228.57/40.25  | | | | | | | | | | | | | | | | |   (278)  all_53_2 = e1
% 228.57/40.25  | | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | | REDUCE: (72), (278) imply:
% 228.57/40.25  | | | | | | | | | | | | | | | | |   (279)   ~ (all_53_14 = e1)
% 228.57/40.25  | | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | | SIMP: (279) implies:
% 228.57/40.25  | | | | | | | | | | | | | | | | |   (280)   ~ (all_53_14 = e1)
% 228.57/40.25  | | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | | BETA: splitting (22) gives:
% 228.57/40.25  | | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | | Case 1:
% 228.57/40.25  | | | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | | |   (281)  all_55_11 = e3
% 228.57/40.25  | | | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | | | REF_CLOSE: (58), (91), (281) are inconsistent by sub-proof
% 228.57/40.25  | | | | | | | | | | | | | | | | | |            #2497.
% 228.57/40.25  | | | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | | Case 2:
% 228.57/40.25  | | | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | | |   (282)   ~ (all_55_11 = e3)
% 228.57/40.25  | | | | | | | | | | | | | | | | | |   (283)  all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 228.57/40.25  | | | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | | | BETA: splitting (283) gives:
% 228.57/40.25  | | | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | | | Case 1:
% 228.57/40.25  | | | | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | | | |   (284)  all_55_11 = e2
% 228.57/40.25  | | | | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (91), (103), (284) are inconsistent by sub-proof
% 228.57/40.25  | | | | | | | | | | | | | | | | | | |            #2282.
% 228.57/40.25  | | | | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | | | Case 2:
% 228.57/40.25  | | | | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | | | |   (285)  all_55_11 = e1 | all_55_11 = e0
% 228.57/40.25  | | | | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (40), (58), (81), (91), (272), (273), (280),
% 228.57/40.25  | | | | | | | | | | | | | | | | | | |            (285) are inconsistent by sub-proof #861.
% 228.57/40.25  | | | | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | | | End of split
% 228.57/40.25  | | | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | | End of split
% 228.57/40.25  | | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | Case 2:
% 228.57/40.25  | | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | |   (286)  all_55_8 = e0
% 228.57/40.25  | | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | | REF_CLOSE: (47), (80), (286) are inconsistent by sub-proof
% 228.57/40.25  | | | | | | | | | | | | | | | | |            #1997.
% 228.57/40.25  | | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | | End of split
% 228.57/40.25  | | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | End of split
% 228.57/40.25  | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | Case 2:
% 228.57/40.25  | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | |   (287)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.57/40.25  | | | | | | | | | | | | | | |          all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 228.57/40.25  | | | | | | | | | | | | | | |          op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 228.57/40.25  | | | | | | | | | | | | | | |            all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 228.57/40.25  | | | | | | | | | | | | | | |          & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 228.57/40.25  | | | | | | | | | | | | | | |          & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 228.57/40.25  | | | | | | | | | | | | | | |          & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 228.57/40.25  | | | | | | | | | | | | | | |          $i(all_52_31)
% 228.57/40.25  | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | ALPHA: (287) implies:
% 228.57/40.25  | | | | | | | | | | | | | | |   (288)  op(e0, e1) = all_52_29
% 228.57/40.25  | | | | | | | | | | | | | | |   (289)  op(all_52_29, all_52_29) = e1
% 228.57/40.25  | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | | REF_CLOSE: (3), (13), (29), (38), (74), (118), (227), (244),
% 228.57/40.25  | | | | | | | | | | | | | | |            (288), (289) are inconsistent by sub-proof #1729.
% 228.57/40.25  | | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | | End of split
% 228.57/40.25  | | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | End of split
% 228.57/40.25  | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | Case 2:
% 228.57/40.25  | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | |   (290)  all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 228.57/40.25  | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | | REF_CLOSE: (49), (85), (99), (226), (290) are inconsistent by
% 228.57/40.25  | | | | | | | | | | | | |            sub-proof #1937.
% 228.57/40.25  | | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | | End of split
% 228.57/40.25  | | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | End of split
% 228.57/40.25  | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | Case 2:
% 228.57/40.25  | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | |   (291)  all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 228.57/40.25  | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | | REF_CLOSE: (34), (56), (71), (231), (291) are inconsistent by
% 228.57/40.25  | | | | | | | | | | |            sub-proof #772.
% 228.57/40.25  | | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | End of split
% 228.57/40.25  | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | Case 2:
% 228.57/40.25  | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | |   (292)  all_55_7 = e1 | all_55_7 = e0
% 228.57/40.25  | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | | REF_CLOSE: (12), (112), (218), (292) are inconsistent by
% 228.57/40.25  | | | | | | | | | |            sub-proof #1322.
% 228.57/40.25  | | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | End of split
% 228.57/40.25  | | | | | | | | | 
% 228.57/40.25  | | | | | | | | Case 2:
% 228.57/40.25  | | | | | | | | | 
% 228.57/40.25  | | | | | | | | |   (293)  all_55_14 = e0
% 228.57/40.25  | | | | | | | | | 
% 228.57/40.25  | | | | | | | | | REF_CLOSE: (111), (216), (293) are inconsistent by sub-proof
% 228.57/40.25  | | | | | | | | |            #2288.
% 228.57/40.25  | | | | | | | | | 
% 228.57/40.25  | | | | | | | | End of split
% 228.57/40.25  | | | | | | | | 
% 228.57/40.25  | | | | | | | End of split
% 228.57/40.25  | | | | | | | 
% 228.57/40.25  | | | | | | End of split
% 228.57/40.25  | | | | | | 
% 228.57/40.25  | | | | | End of split
% 228.57/40.25  | | | | | 
% 228.57/40.25  | | | | End of split
% 228.57/40.25  | | | | 
% 228.57/40.25  | | | End of split
% 228.57/40.25  | | | 
% 228.57/40.25  | | End of split
% 228.57/40.25  | | 
% 228.57/40.25  | End of split
% 228.57/40.25  | 
% 228.57/40.25  End of proof
% 228.57/40.25  
% 228.57/40.25  Sub-proof #582 shows that the following formulas are inconsistent:
% 228.57/40.25  ----------------------------------------------------------------
% 228.57/40.25    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.57/40.25           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.57/40.25    (2)  op(e3, e2) = all_52_3
% 228.57/40.25    (3)  op(e2, e2) = e1
% 228.57/40.25    (4)   ~ (all_53_4 = e1)
% 228.57/40.25    (5)  op(all_52_3, all_52_3) = e2
% 228.57/40.25    (6)  all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.57/40.25    (7)  all_55_1 = all_53_4
% 228.57/40.25    (8)  op(e3, e2) = all_53_4
% 228.57/40.25    (9)   ~ (all_53_4 = e0)
% 228.57/40.25  
% 228.57/40.25  Begin of proof
% 228.57/40.25  | 
% 228.57/40.25  | BETA: splitting (6) gives:
% 228.57/40.25  | 
% 228.57/40.25  | Case 1:
% 228.57/40.25  | | 
% 228.57/40.25  | |   (10)  all_55_1 = e2
% 228.57/40.25  | | 
% 228.57/40.25  | | COMBINE_EQS: (7), (10) imply:
% 228.57/40.25  | |   (11)  all_53_4 = e2
% 228.57/40.25  | | 
% 228.57/40.25  | | REDUCE: (4), (11) imply:
% 228.57/40.25  | |   (12)   ~ (e2 = e1)
% 228.57/40.25  | | 
% 228.57/40.25  | | REDUCE: (8), (11) imply:
% 228.57/40.25  | |   (13)  op(e3, e2) = e2
% 228.57/40.25  | | 
% 228.57/40.25  | | GROUND_INST: instantiating (1) with e2, all_52_3, e2, e3, simplifying with
% 228.57/40.25  | |              (2), (13) gives:
% 228.57/40.25  | |   (14)  all_52_3 = e2
% 228.57/40.25  | | 
% 228.57/40.25  | | REDUCE: (5), (14) imply:
% 228.57/40.25  | |   (15)  op(e2, e2) = e2
% 228.57/40.25  | | 
% 228.57/40.26  | | REF_CLOSE: (1), (3), (12), (15) are inconsistent by sub-proof #2306.
% 228.57/40.26  | | 
% 228.57/40.26  | Case 2:
% 228.57/40.26  | | 
% 228.57/40.26  | |   (16)  all_55_1 = e1 | all_55_1 = e0
% 228.57/40.26  | | 
% 228.57/40.26  | | REF_CLOSE: (4), (7), (9), (16) are inconsistent by sub-proof #1730.
% 228.57/40.26  | | 
% 228.57/40.26  | End of split
% 228.57/40.26  | 
% 228.57/40.26  End of proof
% 228.57/40.26  
% 228.57/40.26  Sub-proof #583 shows that the following formulas are inconsistent:
% 228.57/40.26  ----------------------------------------------------------------
% 228.57/40.26    (1)  all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 228.57/40.26    (2)   ~ (all_53_6 = all_53_14)
% 228.57/40.26    (3)   ~ (all_53_6 = e2)
% 228.57/40.26    (4)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.26         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.57/40.26    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.57/40.26         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.57/40.26    (6)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.26         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.26    (7)   ~ (e3 = e1)
% 228.57/40.26    (8)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.57/40.26         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.57/40.26    (9)   ~ (all_53_13 = e1)
% 228.57/40.26    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.57/40.26            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.57/40.26    (11)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.57/40.26          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.57/40.26    (12)   ~ (all_53_3 = e3)
% 228.57/40.26    (13)   ~ (all_6_2 = e3)
% 228.57/40.26    (14)  all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 228.57/40.26    (15)  op(e1, e1) = all_6_2
% 228.57/40.26    (16)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 228.57/40.26    (17)  op(e2, e2) = e1
% 228.57/40.26    (18)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.57/40.26          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.57/40.26    (19)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 228.57/40.26            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 228.57/40.26              e3) = all_22_1 & $i(all_22_1))
% 228.57/40.26    (20)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 228.57/40.26    (21)  all_55_9 = all_53_6
% 228.57/40.26    (22)   ~ (all_53_13 = e3)
% 228.57/40.26    (23)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.57/40.26          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.57/40.26    (24)  all_55_4 = all_53_1
% 228.57/40.26    (25)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.57/40.26          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.26    (26)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.57/40.26          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.57/40.26    (27)   ~ (e3 = e2)
% 228.57/40.26    (28)   ~ (all_53_1 = all_53_3)
% 228.57/40.26    (29)   ~ (e3 = e0)
% 228.57/40.26    (30)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.57/40.26          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.57/40.26    (31)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.57/40.26    (32)  op(e0, e3) = all_53_3
% 228.57/40.26    (33)   ~ (all_53_2 = e0)
% 228.57/40.26    (34)  all_57_0 = e0
% 228.57/40.26    (35)  all_57_15 = e3
% 228.57/40.26    (36)  op(e3, e3) = e0
% 228.57/40.26    (37)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.57/40.26          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.57/40.26            e1)
% 228.57/40.26    (38)   ~ (all_53_1 = e1)
% 228.57/40.26    (39)  all_57_5 = e3
% 228.57/40.26    (40)   ~ (all_53_1 = all_53_2)
% 228.57/40.26    (41)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.57/40.26          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 228.57/40.26    (42)   ~ (e2 = e0)
% 228.57/40.26    (43)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.57/40.26            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.57/40.26            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.57/40.26            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.57/40.26              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.57/40.26            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.57/40.26            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.57/40.26              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.57/40.26              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.57/40.26            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.57/40.26            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.57/40.26            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.57/40.26              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.57/40.26              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.57/40.26            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.57/40.26              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.57/40.26            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.57/40.26            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.57/40.26              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.57/40.26              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.57/40.26            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.57/40.26            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.57/40.26    (44)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 228.57/40.26            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 228.57/40.26              e3) = all_12_1 & $i(all_12_1))
% 228.57/40.26    (45)   ~ (all_53_6 = e1)
% 228.57/40.26    (46)  all_55_12 = all_53_3
% 228.57/40.26    (47)  all_57_3 = e1
% 228.57/40.26    (48)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.57/40.26          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.57/40.26    (49)   ~ (all_53_1 = e0)
% 228.57/40.26    (50)   ~ (all_53_2 = all_53_14)
% 228.57/40.26    (51)   ~ (e1 = e0)
% 228.57/40.26    (52)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.57/40.26          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.57/40.26    (53)  all_57_8 = e2
% 228.57/40.26    (54)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.57/40.26          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.57/40.26    (55)   ~ (all_53_2 = all_53_3)
% 228.57/40.26    (56)  all_55_8 = all_53_2
% 228.57/40.26    (57)  op(e0, e0) = e3
% 228.57/40.26    (58)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.57/40.26          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.57/40.26            e2)
% 228.57/40.26    (59)   ~ (all_53_3 = e0)
% 228.57/40.26    (60)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.57/40.26              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.57/40.26                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.57/40.26                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.57/40.26    (61)  op(e1, e1) = e2
% 228.57/40.26    (62)   ~ (all_53_1 = all_53_13)
% 228.57/40.26    (63)  op(e2, e0) = all_53_13
% 228.57/40.26    (64)  all_55_11 = all_53_14
% 228.57/40.26    (65)   ~ (all_53_12 = e3)
% 228.57/40.26    (66)  op(e1, e3) = all_53_2
% 228.57/40.26    (67)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.57/40.26          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.57/40.26    (68)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.57/40.26          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.57/40.26    (69)   ~ (all_53_12 = e0)
% 228.57/40.26    (70)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.57/40.26          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 228.57/40.26    (71)   ~ (all_53_1 = e3)
% 228.57/40.26    (72)   ~ (e2 = e1)
% 228.57/40.26    (73)  all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 228.57/40.26    (74)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.57/40.26          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.57/40.26    (75)   ~ (all_53_14 = e2)
% 228.57/40.26    (76)   ~ (all_53_2 = all_53_6)
% 228.57/40.26    (77)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.57/40.26          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.57/40.26    (78)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.57/40.26          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.57/40.26    (79)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.57/40.26          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.57/40.26    (80)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.57/40.26          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.57/40.26    (81)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.57/40.26          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.57/40.26    (82)  all_55_7 = all_53_13
% 228.57/40.26    (83)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.57/40.26          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.57/40.26    (84)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.57/40.26          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.57/40.26    (85)  op(e3, e0) = all_53_12
% 228.57/40.26  
% 228.57/40.26  Begin of proof
% 228.57/40.26  | 
% 228.57/40.26  | BETA: splitting (68) gives:
% 228.57/40.26  | 
% 228.57/40.26  | Case 1:
% 228.57/40.26  | | 
% 228.57/40.26  | |   (86)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) =
% 228.57/40.26  | |           e3)
% 228.57/40.26  | | 
% 228.57/40.26  | | BETA: splitting (86) gives:
% 228.57/40.26  | | 
% 228.57/40.26  | | Case 1:
% 228.57/40.26  | | | 
% 228.57/40.26  | | |   (87)  all_57_0 = e3 & op(e3, e3) = e3
% 228.57/40.26  | | | 
% 228.57/40.26  | | | ALPHA: (87) implies:
% 228.57/40.26  | | |   (88)  op(e3, e3) = e3
% 228.57/40.26  | | | 
% 228.57/40.26  | | | REF_CLOSE: (10), (29), (36), (88) are inconsistent by sub-proof #2494.
% 228.57/40.26  | | | 
% 228.57/40.26  | | Case 2:
% 228.57/40.26  | | | 
% 228.57/40.26  | | |   (89)  all_57_2 = e3 & op(e2, e3) = e3
% 228.57/40.26  | | | 
% 228.57/40.26  | | | ALPHA: (89) implies:
% 228.57/40.26  | | |   (90)  all_57_2 = e3
% 228.57/40.26  | | | 
% 228.57/40.26  | | | BETA: splitting (26) gives:
% 228.57/40.26  | | | 
% 228.57/40.26  | | | Case 1:
% 228.57/40.26  | | | | 
% 228.57/40.26  | | | |   (91)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1)
% 228.57/40.26  | | | |           = e0)
% 228.57/40.26  | | | | 
% 228.57/40.26  | | | | BETA: splitting (91) gives:
% 228.57/40.26  | | | | 
% 228.57/40.26  | | | | Case 1:
% 228.57/40.26  | | | | | 
% 228.57/40.26  | | | | |   (92)  all_57_4 = e0 & op(e3, e1) = e0
% 228.57/40.26  | | | | | 
% 228.57/40.26  | | | | | REF_CLOSE: (6), (7), (10), (17), (18), (23), (27), (29), (30), (34),
% 228.57/40.26  | | | | |            (36), (39), (41), (42), (48), (51), (54), (61), (65), (72),
% 228.57/40.26  | | | | |            (85), (92) are inconsistent by sub-proof #927.
% 228.57/40.26  | | | | | 
% 228.57/40.26  | | | | Case 2:
% 228.57/40.26  | | | | | 
% 228.57/40.26  | | | | |   (93)  all_57_5 = e0 & op(e2, e1) = e0
% 228.57/40.26  | | | | | 
% 228.57/40.26  | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (10), (11), (13), (15), (17),
% 228.57/40.26  | | | | |            (18), (23), (25), (26), (27), (29), (30), (32), (35), (36),
% 228.57/40.26  | | | | |            (37), (39), (41), (42), (47), (48), (51), (52), (54), (57),
% 228.57/40.26  | | | | |            (58), (59), (60), (65), (67), (68), (69), (72), (74), (77),
% 228.57/40.26  | | | | |            (78), (79), (80), (81), (83), (84), (85), (90), (93) are
% 228.57/40.26  | | | | |            inconsistent by sub-proof #589.
% 228.57/40.26  | | | | | 
% 228.57/40.26  | | | | End of split
% 228.57/40.26  | | | | 
% 228.57/40.26  | | | Case 2:
% 228.57/40.26  | | | | 
% 228.57/40.26  | | | |   (94)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1)
% 228.57/40.26  | | | |           = e0)
% 228.57/40.26  | | | | 
% 228.57/40.26  | | | | BETA: splitting (94) gives:
% 228.57/40.26  | | | | 
% 228.57/40.26  | | | | Case 1:
% 228.57/40.26  | | | | | 
% 228.57/40.26  | | | | |   (95)  all_57_8 = e0 & op(e1, e1) = e0
% 228.57/40.26  | | | | | 
% 228.57/40.26  | | | | | REF_CLOSE: (42), (53), (95) are inconsistent by sub-proof #917.
% 228.57/40.26  | | | | | 
% 228.57/40.26  | | | | Case 2:
% 228.57/40.26  | | | | | 
% 228.57/40.26  | | | | |   (96)  all_57_14 = e0 & op(e0, e1) = e0
% 228.57/40.26  | | | | | 
% 228.57/40.26  | | | | | ALPHA: (96) implies:
% 228.57/40.26  | | | | |   (97)  all_57_14 = e0
% 228.57/40.26  | | | | |   (98)  op(e0, e1) = e0
% 228.57/40.26  | | | | | 
% 228.57/40.26  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 228.57/40.26  | | | | |            (12), (13), (14), (15), (16), (17), (18), (19), (20), (21),
% 228.57/40.26  | | | | |            (22), (23), (24), (25), (26), (27), (28), (29), (30), (31),
% 228.57/40.26  | | | | |            (32), (33), (34), (35), (36), (37), (38), (39), (40), (41),
% 228.57/40.26  | | | | |            (42), (43), (44), (45), (46), (47), (48), (49), (50), (51),
% 228.57/40.26  | | | | |            (52), (53), (54), (55), (56), (57), (58), (59), (60), (62),
% 228.57/40.26  | | | | |            (63), (64), (65), (66), (67), (68), (69), (70), (71), (72),
% 228.57/40.26  | | | | |            (73), (74), (75), (76), (77), (78), (79), (80), (81), (82),
% 228.57/40.26  | | | | |            (83), (84), (85), (90), (97), (98) are inconsistent by
% 228.57/40.26  | | | | |            sub-proof #584.
% 228.57/40.26  | | | | | 
% 228.57/40.26  | | | | End of split
% 228.57/40.26  | | | | 
% 228.57/40.26  | | | End of split
% 228.57/40.26  | | | 
% 228.57/40.26  | | End of split
% 228.57/40.26  | | 
% 228.57/40.26  | Case 2:
% 228.57/40.26  | | 
% 228.57/40.26  | |   (99)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) =
% 228.57/40.26  | |           e3)
% 228.57/40.26  | | 
% 228.57/40.26  | | BETA: splitting (99) gives:
% 228.57/40.26  | | 
% 228.57/40.26  | | Case 1:
% 228.57/40.26  | | | 
% 228.57/40.26  | | |   (100)  all_57_6 = e3 & op(e1, e3) = e3
% 228.57/40.26  | | | 
% 228.57/40.26  | | | ALPHA: (100) implies:
% 228.57/40.26  | | |   (101)  all_57_6 = e3
% 228.57/40.26  | | | 
% 228.57/40.26  | | | BETA: splitting (5) gives:
% 228.57/40.26  | | | 
% 228.57/40.26  | | | Case 1:
% 228.57/40.26  | | | | 
% 228.57/40.26  | | | |   (102)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3)
% 228.57/40.26  | | | |            = e1)
% 228.57/40.26  | | | | 
% 228.57/40.26  | | | | BETA: splitting (102) gives:
% 228.57/40.26  | | | | 
% 228.57/40.26  | | | | Case 1:
% 228.57/40.26  | | | | | 
% 228.57/40.26  | | | | |   (103)  all_57_0 = e1 & op(e3, e3) = e1
% 228.57/40.26  | | | | | 
% 228.57/40.26  | | | | | REF_CLOSE: (34), (51), (103) are inconsistent by sub-proof #2454.
% 228.57/40.26  | | | | | 
% 228.57/40.26  | | | | Case 2:
% 228.57/40.26  | | | | | 
% 228.57/40.26  | | | | |   (104)  all_57_2 = e1 & op(e2, e3) = e1
% 228.57/40.26  | | | | | 
% 228.57/40.26  | | | | | ALPHA: (104) implies:
% 228.57/40.26  | | | | |   (105)  all_57_2 = e1
% 228.57/40.26  | | | | | 
% 228.57/40.26  | | | | | REF_CLOSE: (4), (5), (6), (7), (10), (11), (13), (15), (17), (18),
% 228.57/40.26  | | | | |            (23), (26), (27), (29), (30), (34), (35), (36), (39), (41),
% 228.57/40.26  | | | | |            (42), (47), (48), (51), (53), (54), (60), (61), (65), (67),
% 228.57/40.26  | | | | |            (68), (70), (72), (74), (77), (78), (79), (80), (83), (85),
% 228.57/40.26  | | | | |            (101), (105) are inconsistent by sub-proof #924.
% 228.57/40.26  | | | | | 
% 228.57/40.26  | | | | End of split
% 228.57/40.26  | | | | 
% 228.57/40.26  | | | Case 2:
% 228.57/40.26  | | | | 
% 228.57/40.26  | | | |   (106)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0,
% 228.57/40.26  | | | |              e3) = e1)
% 228.57/40.26  | | | | 
% 228.57/40.26  | | | | BETA: splitting (106) gives:
% 228.57/40.26  | | | | 
% 228.57/40.26  | | | | Case 1:
% 228.57/40.26  | | | | | 
% 228.57/40.26  | | | | |   (107)  all_57_6 = e1 & op(e1, e3) = e1
% 228.57/40.26  | | | | | 
% 228.57/40.26  | | | | | REF_CLOSE: (7), (101), (107) are inconsistent by sub-proof #2117.
% 228.57/40.26  | | | | | 
% 228.57/40.26  | | | | Case 2:
% 228.57/40.26  | | | | | 
% 228.57/40.26  | | | | |   (108)  all_57_12 = e1 & op(e0, e3) = e1
% 228.57/40.26  | | | | | 
% 228.57/40.26  | | | | | ALPHA: (108) implies:
% 228.57/40.26  | | | | |   (109)  all_57_12 = e1
% 228.57/40.26  | | | | |   (110)  op(e0, e3) = e1
% 228.57/40.26  | | | | | 
% 228.57/40.26  | | | | | BETA: splitting (26) gives:
% 228.57/40.26  | | | | | 
% 228.57/40.26  | | | | | Case 1:
% 228.57/40.26  | | | | | | 
% 228.57/40.26  | | | | | |   (111)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2,
% 228.57/40.26  | | | | | |              e1) = e0)
% 228.57/40.26  | | | | | | 
% 228.57/40.26  | | | | | | BETA: splitting (111) gives:
% 228.57/40.26  | | | | | | 
% 228.57/40.26  | | | | | | Case 1:
% 228.57/40.26  | | | | | | | 
% 228.57/40.26  | | | | | | |   (112)  all_57_4 = e0 & op(e3, e1) = e0
% 228.57/40.26  | | | | | | | 
% 228.57/40.26  | | | | | | | REF_CLOSE: (6), (7), (10), (17), (18), (23), (27), (29), (30),
% 228.57/40.26  | | | | | | |            (34), (36), (39), (41), (42), (48), (51), (54), (61),
% 228.57/40.26  | | | | | | |            (65), (72), (85), (112) are inconsistent by sub-proof
% 228.57/40.26  | | | | | | |            #927.
% 228.57/40.26  | | | | | | | 
% 228.57/40.26  | | | | | | Case 2:
% 228.57/40.26  | | | | | | | 
% 228.57/40.26  | | | | | | |   (113)  all_57_5 = e0 & op(e2, e1) = e0
% 228.57/40.26  | | | | | | | 
% 228.57/40.26  | | | | | | | ALPHA: (113) implies:
% 228.57/40.26  | | | | | | |   (114)  all_57_5 = e0
% 228.57/40.26  | | | | | | | 
% 228.57/40.26  | | | | | | | COMBINE_EQS: (39), (114) imply:
% 228.57/40.26  | | | | | | |   (115)  e3 = e0
% 228.57/40.26  | | | | | | | 
% 228.57/40.26  | | | | | | | SIMP: (115) implies:
% 228.57/40.26  | | | | | | |   (116)  e3 = e0
% 228.57/40.26  | | | | | | | 
% 228.57/40.26  | | | | | | | COMBINE_EQS: (101), (116) imply:
% 228.57/40.26  | | | | | | |   (117)  all_57_6 = e0
% 228.57/40.26  | | | | | | | 
% 228.57/40.26  | | | | | | | REF_CLOSE: (7), (10), (11), (13), (15), (27), (29), (35), (36),
% 228.57/40.26  | | | | | | |            (42), (51), (60), (68), (72), (74), (77), (80), (109),
% 228.57/40.26  | | | | | | |            (117) are inconsistent by sub-proof #1028.
% 228.57/40.26  | | | | | | | 
% 228.57/40.26  | | | | | | End of split
% 228.57/40.26  | | | | | | 
% 228.57/40.26  | | | | | Case 2:
% 228.57/40.26  | | | | | | 
% 228.57/40.26  | | | | | |   (118)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 &
% 228.57/40.26  | | | | | |            op(e0, e1) = e0)
% 228.57/40.26  | | | | | | 
% 228.57/40.26  | | | | | | BETA: splitting (118) gives:
% 228.57/40.26  | | | | | | 
% 228.57/40.26  | | | | | | Case 1:
% 228.57/40.26  | | | | | | | 
% 228.57/40.26  | | | | | | |   (119)  all_57_8 = e0 & op(e1, e1) = e0
% 228.57/40.26  | | | | | | | 
% 228.57/40.26  | | | | | | | REF_CLOSE: (42), (53), (119) are inconsistent by sub-proof #917.
% 228.57/40.26  | | | | | | | 
% 228.57/40.26  | | | | | | Case 2:
% 228.57/40.26  | | | | | | | 
% 228.57/40.26  | | | | | | |   (120)  all_57_14 = e0 & op(e0, e1) = e0
% 228.57/40.26  | | | | | | | 
% 228.57/40.26  | | | | | | | ALPHA: (120) implies:
% 228.57/40.26  | | | | | | |   (121)  all_57_14 = e0
% 228.57/40.26  | | | | | | |   (122)  op(e0, e1) = e0
% 228.57/40.26  | | | | | | | 
% 228.57/40.26  | | | | | | | BETA: splitting (48) gives:
% 228.57/40.26  | | | | | | | 
% 228.57/40.26  | | | | | | | Case 1:
% 228.57/40.26  | | | | | | | | 
% 228.57/40.26  | | | | | | | |   (123)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 &
% 228.57/40.26  | | | | | | | |            op(e3, e2) = e3)
% 228.57/40.26  | | | | | | | | 
% 228.57/40.26  | | | | | | | | BETA: splitting (123) gives:
% 228.57/40.26  | | | | | | | | 
% 228.57/40.26  | | | | | | | | Case 1:
% 228.57/40.26  | | | | | | | | | 
% 228.57/40.26  | | | | | | | | |   (124)  all_57_0 = e3 & op(e3, e3) = e3
% 228.57/40.26  | | | | | | | | | 
% 228.57/40.26  | | | | | | | | | ALPHA: (124) implies:
% 228.57/40.26  | | | | | | | | |   (125)  all_57_0 = e3
% 228.57/40.26  | | | | | | | | | 
% 228.57/40.26  | | | | | | | | | REF_CLOSE: (5), (7), (27), (29), (42), (51), (72), (77), (79),
% 228.57/40.26  | | | | | | | | |            (101), (125) are inconsistent by sub-proof #2010.
% 228.80/40.26  | | | | | | | | | 
% 228.80/40.26  | | | | | | | | Case 2:
% 228.80/40.26  | | | | | | | | | 
% 228.80/40.26  | | | | | | | | |   (126)  all_57_1 = e3 & op(e3, e2) = e3
% 228.80/40.26  | | | | | | | | | 
% 228.80/40.26  | | | | | | | | | REF_CLOSE: (1), (2), (3), (7), (9), (10), (14), (16), (17),
% 228.80/40.26  | | | | | | | | |            (20), (21), (22), (23), (24), (28), (30), (31),
% 228.80/40.26  | | | | | | | | |            (33), (36), (38), (39), (40), (43), (45), (46),
% 228.80/40.26  | | | | | | | | |            (49), (50), (51), (53), (55), (56), (57), (59),
% 228.80/40.26  | | | | | | | | |            (62), (63), (64), (66), (71), (73), (75), (76),
% 228.80/40.26  | | | | | | | | |            (82), (121), (122), (126) are inconsistent by
% 228.80/40.26  | | | | | | | | |            sub-proof #587.
% 228.80/40.26  | | | | | | | | | 
% 228.80/40.26  | | | | | | | | End of split
% 228.80/40.26  | | | | | | | | 
% 228.80/40.26  | | | | | | | Case 2:
% 228.80/40.26  | | | | | | | | 
% 228.80/40.26  | | | | | | | |   (127)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 &
% 228.80/40.26  | | | | | | | |            op(e3, e0) = e3)
% 228.80/40.26  | | | | | | | | 
% 228.80/40.26  | | | | | | | | BETA: splitting (127) gives:
% 228.80/40.26  | | | | | | | | 
% 228.80/40.26  | | | | | | | | Case 1:
% 228.80/40.26  | | | | | | | | | 
% 228.80/40.26  | | | | | | | | |   (128)  all_57_4 = e3 & op(e3, e1) = e3
% 228.80/40.26  | | | | | | | | | 
% 228.80/40.26  | | | | | | | | | ALPHA: (128) implies:
% 228.80/40.26  | | | | | | | | |   (129)  all_57_4 = e3
% 228.80/40.26  | | | | | | | | | 
% 228.80/40.26  | | | | | | | | | BETA: splitting (70) gives:
% 228.80/40.26  | | | | | | | | | 
% 228.80/40.26  | | | | | | | | | Case 1:
% 228.80/40.26  | | | | | | | | | | 
% 228.80/40.26  | | | | | | | | | |   (130)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 228.80/40.26  | | | | | | | | | |            & op(e2, e2) = e0)
% 228.80/40.26  | | | | | | | | | | 
% 228.80/40.26  | | | | | | | | | | REF_CLOSE: (4), (5), (7), (10), (17), (27), (34), (36), (39),
% 228.80/40.26  | | | | | | | | | |            (42), (47), (51), (67), (72), (77), (101), (130)
% 228.80/40.26  | | | | | | | | | |            are inconsistent by sub-proof #1009.
% 228.80/40.26  | | | | | | | | | | 
% 228.80/40.26  | | | | | | | | | Case 2:
% 228.80/40.26  | | | | | | | | | | 
% 228.80/40.26  | | | | | | | | | |   (131)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0
% 228.80/40.26  | | | | | | | | | |            & op(e2, e0) = e0)
% 228.80/40.26  | | | | | | | | | | 
% 228.80/40.26  | | | | | | | | | | BETA: splitting (131) gives:
% 228.80/40.26  | | | | | | | | | | 
% 228.80/40.26  | | | | | | | | | | Case 1:
% 228.80/40.26  | | | | | | | | | | | 
% 228.80/40.26  | | | | | | | | | | |   (132)  all_57_5 = e0 & op(e2, e1) = e0
% 228.80/40.26  | | | | | | | | | | | 
% 228.80/40.26  | | | | | | | | | | | REF_CLOSE: (7), (10), (27), (30), (39), (42), (51), (72),
% 228.80/40.26  | | | | | | | | | | |            (78), (121), (129), (132) are inconsistent by
% 228.80/40.26  | | | | | | | | | | |            sub-proof #926.
% 228.80/40.26  | | | | | | | | | | | 
% 228.80/40.26  | | | | | | | | | | Case 2:
% 228.80/40.26  | | | | | | | | | | | 
% 228.80/40.26  | | | | | | | | | | |   (133)  all_57_10 = e0 & op(e2, e0) = e0
% 228.80/40.26  | | | | | | | | | | | 
% 228.80/40.26  | | | | | | | | | | | ALPHA: (133) implies:
% 228.80/40.26  | | | | | | | | | | |   (134)  all_57_10 = e0
% 228.80/40.26  | | | | | | | | | | | 
% 228.80/40.26  | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (10), (17), (18), (19), (27), (29),
% 228.80/40.26  | | | | | | | | | | |            (30), (34), (35), (39), (41), (42), (44), (47),
% 228.80/40.26  | | | | | | | | | | |            (51), (53), (54), (67), (72), (74), (110), (121),
% 228.80/40.26  | | | | | | | | | | |            (129), (134) are inconsistent by sub-proof #585.
% 228.80/40.26  | | | | | | | | | | | 
% 228.80/40.26  | | | | | | | | | | End of split
% 228.80/40.26  | | | | | | | | | | 
% 228.80/40.26  | | | | | | | | | End of split
% 228.80/40.26  | | | | | | | | | 
% 228.80/40.26  | | | | | | | | Case 2:
% 228.80/40.26  | | | | | | | | | 
% 228.80/40.26  | | | | | | | | |   (135)  all_57_9 = e3 & op(e3, e0) = e3
% 228.80/40.26  | | | | | | | | | 
% 228.80/40.26  | | | | | | | | | ALPHA: (135) implies:
% 228.80/40.26  | | | | | | | | |   (136)  op(e3, e0) = e3
% 228.80/40.26  | | | | | | | | | 
% 228.80/40.26  | | | | | | | | | REF_CLOSE: (10), (65), (85), (136) are inconsistent by
% 228.80/40.26  | | | | | | | | |            sub-proof #2458.
% 228.80/40.26  | | | | | | | | | 
% 228.80/40.26  | | | | | | | | End of split
% 228.80/40.26  | | | | | | | | 
% 228.80/40.26  | | | | | | | End of split
% 228.80/40.26  | | | | | | | 
% 228.80/40.26  | | | | | | End of split
% 228.80/40.26  | | | | | | 
% 228.80/40.26  | | | | | End of split
% 228.80/40.26  | | | | | 
% 228.80/40.26  | | | | End of split
% 228.80/40.26  | | | | 
% 228.80/40.26  | | | End of split
% 228.80/40.26  | | | 
% 228.80/40.26  | | Case 2:
% 228.80/40.26  | | | 
% 228.80/40.26  | | |   (137)  all_57_12 = e3 & op(e0, e3) = e3
% 228.80/40.26  | | | 
% 228.80/40.26  | | | ALPHA: (137) implies:
% 228.80/40.26  | | |   (138)  all_57_12 = e3
% 228.80/40.26  | | | 
% 228.80/40.26  | | | BETA: splitting (26) gives:
% 228.80/40.26  | | | 
% 228.80/40.26  | | | Case 1:
% 228.80/40.26  | | | | 
% 228.80/40.26  | | | |   (139)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1)
% 228.80/40.26  | | | |            = e0)
% 228.80/40.26  | | | | 
% 228.80/40.26  | | | | BETA: splitting (139) gives:
% 228.80/40.26  | | | | 
% 228.80/40.26  | | | | Case 1:
% 228.80/40.26  | | | | | 
% 228.80/40.26  | | | | |   (140)  all_57_4 = e0 & op(e3, e1) = e0
% 228.80/40.26  | | | | | 
% 228.80/40.26  | | | | | REF_CLOSE: (6), (7), (10), (17), (18), (23), (27), (29), (30), (34),
% 228.80/40.26  | | | | |            (36), (39), (41), (42), (48), (51), (54), (61), (65), (72),
% 228.80/40.26  | | | | |            (85), (140) are inconsistent by sub-proof #927.
% 228.80/40.26  | | | | | 
% 228.80/40.26  | | | | Case 2:
% 228.80/40.26  | | | | | 
% 228.80/40.26  | | | | |   (141)  all_57_5 = e0 & op(e2, e1) = e0
% 228.80/40.26  | | | | | 
% 228.80/40.26  | | | | | ALPHA: (141) implies:
% 228.80/40.26  | | | | |   (142)  all_57_5 = e0
% 228.80/40.26  | | | | | 
% 228.80/40.26  | | | | | REF_CLOSE: (29), (39), (142) are inconsistent by sub-proof #2471.
% 228.80/40.26  | | | | | 
% 228.80/40.26  | | | | End of split
% 228.80/40.26  | | | | 
% 228.80/40.26  | | | Case 2:
% 228.80/40.26  | | | | 
% 228.80/40.26  | | | |   (143)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0,
% 228.80/40.26  | | | |              e1) = e0)
% 228.80/40.26  | | | | 
% 228.80/40.26  | | | | BETA: splitting (143) gives:
% 228.80/40.26  | | | | 
% 228.80/40.26  | | | | Case 1:
% 228.80/40.26  | | | | | 
% 228.80/40.26  | | | | |   (144)  all_57_8 = e0 & op(e1, e1) = e0
% 228.80/40.26  | | | | | 
% 228.80/40.26  | | | | | REF_CLOSE: (42), (53), (144) are inconsistent by sub-proof #917.
% 228.80/40.26  | | | | | 
% 228.80/40.26  | | | | Case 2:
% 228.80/40.26  | | | | | 
% 228.80/40.26  | | | | |   (145)  all_57_14 = e0 & op(e0, e1) = e0
% 228.80/40.26  | | | | | 
% 228.80/40.26  | | | | | ALPHA: (145) implies:
% 228.80/40.26  | | | | |   (146)  all_57_14 = e0
% 228.80/40.26  | | | | | 
% 228.80/40.26  | | | | | REF_CLOSE: (7), (27), (35), (37), (42), (51), (58), (72), (138), (146)
% 228.80/40.26  | | | | |            are inconsistent by sub-proof #1763.
% 228.80/40.26  | | | | | 
% 228.80/40.26  | | | | End of split
% 228.80/40.26  | | | | 
% 228.80/40.26  | | | End of split
% 228.80/40.26  | | | 
% 228.80/40.26  | | End of split
% 228.80/40.26  | | 
% 228.80/40.26  | End of split
% 228.80/40.26  | 
% 228.80/40.26  End of proof
% 228.80/40.26  
% 228.80/40.26  Sub-proof #584 shows that the following formulas are inconsistent:
% 228.80/40.26  ----------------------------------------------------------------
% 228.80/40.26    (1)  all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 228.80/40.26    (2)   ~ (all_53_6 = all_53_14)
% 228.80/40.26    (3)   ~ (all_53_6 = e2)
% 228.80/40.26    (4)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.80/40.26         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.80/40.26    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.80/40.26         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.80/40.26    (6)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.80/40.26         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.80/40.26    (7)   ~ (e3 = e1)
% 228.80/40.26    (8)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.80/40.26         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.80/40.26    (9)   ~ (all_53_13 = e1)
% 228.80/40.26    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.80/40.26            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.80/40.26    (11)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.80/40.26          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.80/40.26    (12)   ~ (all_53_3 = e3)
% 228.80/40.26    (13)   ~ (all_6_2 = e3)
% 228.80/40.26    (14)  all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 228.80/40.26    (15)  op(e1, e1) = all_6_2
% 228.80/40.26    (16)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 228.80/40.26    (17)  op(e2, e2) = e1
% 228.80/40.26    (18)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.80/40.26          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.80/40.26    (19)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 228.80/40.26            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 228.80/40.26              e3) = all_22_1 & $i(all_22_1))
% 228.80/40.26    (20)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 228.80/40.26    (21)  all_55_9 = all_53_6
% 228.80/40.26    (22)   ~ (all_53_13 = e3)
% 228.80/40.26    (23)  op(e0, e1) = e0
% 228.80/40.26    (24)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.80/40.26          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.80/40.26    (25)  all_55_4 = all_53_1
% 228.80/40.26    (26)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.80/40.26          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.80/40.27    (27)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.80/40.27          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.80/40.27    (28)   ~ (e3 = e2)
% 228.80/40.27    (29)   ~ (all_53_1 = all_53_3)
% 228.80/40.27    (30)   ~ (e3 = e0)
% 228.80/40.27    (31)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.80/40.27          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.80/40.27    (32)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.80/40.27    (33)  op(e0, e3) = all_53_3
% 228.80/40.27    (34)   ~ (all_53_2 = e0)
% 228.80/40.27    (35)  all_57_0 = e0
% 228.80/40.27    (36)  all_57_15 = e3
% 228.80/40.27    (37)  op(e3, e3) = e0
% 228.80/40.27    (38)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.80/40.27          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.80/40.27            e1)
% 228.80/40.27    (39)   ~ (all_53_1 = e1)
% 228.80/40.27    (40)  all_57_5 = e3
% 228.80/40.27    (41)   ~ (all_53_1 = all_53_2)
% 228.80/40.27    (42)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.80/40.27          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 228.80/40.27    (43)   ~ (e2 = e0)
% 228.80/40.27    (44)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.80/40.27            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.80/40.27            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.80/40.27            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.80/40.27              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.80/40.27            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.80/40.27            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.80/40.27              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.80/40.27              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.80/40.27            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.80/40.27            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.80/40.27            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.80/40.27              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.80/40.27              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.80/40.27            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.80/40.27              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.80/40.27            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.80/40.27            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.80/40.27              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.80/40.27              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.80/40.27            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.80/40.27            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.80/40.27    (45)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 228.80/40.27            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 228.80/40.27              e3) = all_12_1 & $i(all_12_1))
% 228.80/40.27    (46)   ~ (all_53_6 = e1)
% 228.80/40.27    (47)  all_55_12 = all_53_3
% 228.80/40.27    (48)  all_57_2 = e3
% 228.80/40.27    (49)  all_57_3 = e1
% 228.80/40.27    (50)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.80/40.27          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.80/40.27    (51)   ~ (all_53_1 = e0)
% 228.80/40.27    (52)   ~ (all_53_2 = all_53_14)
% 228.80/40.27    (53)   ~ (e1 = e0)
% 228.80/40.27    (54)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.80/40.27          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.80/40.27    (55)  all_57_8 = e2
% 228.80/40.27    (56)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.80/40.27          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.80/40.27    (57)   ~ (all_53_2 = all_53_3)
% 228.80/40.27    (58)  all_55_8 = all_53_2
% 228.80/40.27    (59)  op(e0, e0) = e3
% 228.80/40.27    (60)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.80/40.27          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.80/40.27            e2)
% 228.80/40.27    (61)   ~ (all_53_3 = e0)
% 228.80/40.27    (62)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.80/40.27              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.80/40.27                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.80/40.27                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.80/40.27    (63)   ~ (all_53_1 = all_53_13)
% 228.80/40.27    (64)  op(e2, e0) = all_53_13
% 228.80/40.27    (65)  all_55_11 = all_53_14
% 228.80/40.27    (66)   ~ (all_53_12 = e3)
% 228.80/40.27    (67)  op(e1, e3) = all_53_2
% 228.80/40.27    (68)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.80/40.27          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.80/40.27    (69)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.80/40.27          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.80/40.27    (70)   ~ (all_53_12 = e0)
% 228.80/40.27    (71)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.80/40.27          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 228.80/40.27    (72)   ~ (all_53_1 = e3)
% 228.80/40.27    (73)   ~ (e2 = e1)
% 228.80/40.27    (74)  all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 228.80/40.27    (75)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.80/40.27          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.80/40.27    (76)   ~ (all_53_14 = e2)
% 228.80/40.27    (77)   ~ (all_53_2 = all_53_6)
% 228.80/40.27    (78)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.80/40.27          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.80/40.27    (79)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.80/40.27          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.80/40.27    (80)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.80/40.27          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.80/40.27    (81)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.80/40.27          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.80/40.27    (82)  all_57_14 = e0
% 228.80/40.27    (83)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.80/40.27          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.80/40.27    (84)  all_55_7 = all_53_13
% 228.80/40.27    (85)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.80/40.27          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.80/40.27    (86)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.80/40.27          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.80/40.27    (87)  op(e3, e0) = all_53_12
% 228.80/40.27  
% 228.80/40.27  Begin of proof
% 228.80/40.27  | 
% 228.80/40.27  | BETA: splitting (50) gives:
% 228.80/40.27  | 
% 228.80/40.27  | Case 1:
% 228.80/40.27  | | 
% 228.80/40.27  | |   (88)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) =
% 228.80/40.27  | |           e3)
% 228.80/40.27  | | 
% 228.80/40.27  | | BETA: splitting (88) gives:
% 228.80/40.27  | | 
% 228.80/40.27  | | Case 1:
% 228.80/40.27  | | | 
% 228.80/40.27  | | |   (89)  all_57_0 = e3 & op(e3, e3) = e3
% 228.80/40.27  | | | 
% 228.80/40.27  | | | ALPHA: (89) implies:
% 228.80/40.27  | | |   (90)  op(e3, e3) = e3
% 228.80/40.27  | | | 
% 228.80/40.27  | | | REF_CLOSE: (10), (30), (37), (90) are inconsistent by sub-proof #2494.
% 228.80/40.27  | | | 
% 228.80/40.27  | | Case 2:
% 228.80/40.27  | | | 
% 228.80/40.27  | | |   (91)  all_57_1 = e3 & op(e3, e2) = e3
% 228.80/40.27  | | | 
% 228.80/40.27  | | | REF_CLOSE: (1), (2), (3), (7), (9), (10), (14), (16), (17), (20), (21),
% 228.80/40.27  | | |            (22), (23), (24), (25), (29), (31), (32), (34), (37), (39),
% 228.80/40.27  | | |            (40), (41), (44), (46), (47), (51), (52), (53), (55), (57),
% 228.80/40.27  | | |            (58), (59), (61), (63), (64), (65), (67), (72), (74), (76),
% 228.80/40.27  | | |            (77), (82), (84), (91) are inconsistent by sub-proof #587.
% 228.80/40.27  | | | 
% 228.80/40.27  | | End of split
% 228.80/40.27  | | 
% 228.80/40.27  | Case 2:
% 228.80/40.27  | | 
% 228.80/40.27  | |   (92)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) =
% 228.80/40.27  | |           e3)
% 228.80/40.27  | | 
% 228.80/40.27  | | BETA: splitting (92) gives:
% 228.80/40.27  | | 
% 228.80/40.27  | | Case 1:
% 228.80/40.27  | | | 
% 228.80/40.27  | | |   (93)  all_57_4 = e3 & op(e3, e1) = e3
% 228.80/40.27  | | | 
% 228.80/40.27  | | | ALPHA: (93) implies:
% 228.80/40.27  | | |   (94)  all_57_4 = e3
% 228.80/40.27  | | | 
% 228.80/40.27  | | | BETA: splitting (71) gives:
% 228.80/40.27  | | | 
% 228.80/40.27  | | | Case 1:
% 228.80/40.27  | | | | 
% 228.80/40.27  | | | |   (95)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2)
% 228.80/40.27  | | | |           = e0)
% 228.80/40.27  | | | | 
% 228.80/40.27  | | | | REF_CLOSE: (4), (5), (6), (7), (8), (10), (11), (13), (15), (17), (18),
% 228.80/40.27  | | | |            (24), (26), (27), (28), (30), (31), (33), (36), (37), (38),
% 228.80/40.27  | | | |            (40), (42), (43), (48), (49), (50), (53), (54), (56), (59),
% 228.80/40.27  | | | |            (60), (61), (62), (66), (68), (69), (70), (73), (75), (78),
% 228.80/40.27  | | | |            (79), (80), (81), (83), (85), (86), (87), (95) are
% 228.80/40.27  | | | |            inconsistent by sub-proof #975.
% 228.80/40.27  | | | | 
% 228.80/40.27  | | | Case 2:
% 228.80/40.27  | | | | 
% 228.80/40.27  | | | |   (96)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0)
% 228.80/40.27  | | | |           = e0)
% 228.80/40.27  | | | | 
% 228.80/40.27  | | | | BETA: splitting (96) gives:
% 228.80/40.27  | | | | 
% 228.80/40.27  | | | | Case 1:
% 228.80/40.27  | | | | | 
% 228.80/40.27  | | | | |   (97)  all_57_5 = e0 & op(e2, e1) = e0
% 228.80/40.27  | | | | | 
% 228.80/40.27  | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (10), (11), (13), (15), (17),
% 228.80/40.27  | | | | |            (18), (24), (26), (27), (28), (30), (31), (33), (36), (37),
% 228.80/40.27  | | | | |            (38), (40), (42), (43), (48), (49), (50), (53), (54), (56),
% 228.80/40.27  | | | | |            (59), (60), (61), (62), (66), (68), (69), (70), (73), (75),
% 228.80/40.27  | | | | |            (78), (79), (80), (81), (83), (85), (86), (87), (97) are
% 228.80/40.27  | | | | |            inconsistent by sub-proof #589.
% 228.80/40.27  | | | | | 
% 228.80/40.27  | | | | Case 2:
% 228.80/40.27  | | | | | 
% 228.80/40.27  | | | | |   (98)  all_57_10 = e0 & op(e2, e0) = e0
% 228.80/40.27  | | | | | 
% 228.80/40.27  | | | | | ALPHA: (98) implies:
% 228.80/40.27  | | | | |   (99)  all_57_10 = e0
% 228.80/40.27  | | | | | 
% 228.80/40.27  | | | | | BETA: splitting (1) gives:
% 228.80/40.27  | | | | | 
% 228.80/40.27  | | | | | Case 1:
% 228.80/40.27  | | | | | | 
% 228.80/40.27  | | | | | |   (100)  all_55_4 = e2
% 228.80/40.27  | | | | | | 
% 228.80/40.27  | | | | | | COMBINE_EQS: (25), (100) imply:
% 228.80/40.27  | | | | | |   (101)  all_53_1 = e2
% 228.80/40.27  | | | | | | 
% 228.80/40.27  | | | | | | SIMP: (101) implies:
% 228.80/40.27  | | | | | |   (102)  all_53_1 = e2
% 228.80/40.27  | | | | | | 
% 228.80/40.27  | | | | | | REDUCE: (29), (102) imply:
% 228.80/40.27  | | | | | |   (103)   ~ (all_53_3 = e2)
% 228.80/40.27  | | | | | | 
% 228.80/40.27  | | | | | | SIMP: (103) implies:
% 228.80/40.27  | | | | | |   (104)   ~ (all_53_3 = e2)
% 228.80/40.27  | | | | | | 
% 228.80/40.27  | | | | | | REDUCE: (72), (102) imply:
% 228.80/40.27  | | | | | |   (105)   ~ (e3 = e2)
% 228.80/40.27  | | | | | | 
% 228.80/40.27  | | | | | | BETA: splitting (74) gives:
% 228.80/40.27  | | | | | | 
% 228.80/40.27  | | | | | | Case 1:
% 228.80/40.27  | | | | | | | 
% 228.80/40.27  | | | | | | |   (106)  all_55_12 = e2
% 228.80/40.27  | | | | | | | 
% 228.80/40.27  | | | | | | | REF_CLOSE: (47), (104), (106) are inconsistent by sub-proof #1337.
% 228.80/40.27  | | | | | | | 
% 228.80/40.27  | | | | | | Case 2:
% 228.80/40.27  | | | | | | | 
% 228.80/40.27  | | | | | | |   (107)   ~ (all_55_12 = e2)
% 228.80/40.27  | | | | | | |   (108)  all_55_12 = e1 | all_55_12 = e0
% 228.80/40.27  | | | | | | | 
% 228.80/40.27  | | | | | | | BETA: splitting (108) gives:
% 228.80/40.27  | | | | | | | 
% 228.80/40.27  | | | | | | | Case 1:
% 228.80/40.27  | | | | | | | | 
% 228.80/40.27  | | | | | | | |   (109)  all_55_12 = e1
% 228.80/40.27  | | | | | | | | 
% 228.80/40.27  | | | | | | | | COMBINE_EQS: (47), (109) imply:
% 228.80/40.27  | | | | | | | |   (110)  all_53_3 = e1
% 228.80/40.27  | | | | | | | | 
% 228.80/40.27  | | | | | | | | SIMP: (110) implies:
% 228.80/40.27  | | | | | | | |   (111)  all_53_3 = e1
% 228.80/40.27  | | | | | | | | 
% 228.80/40.27  | | | | | | | | REDUCE: (12), (111) imply:
% 228.80/40.27  | | | | | | | |   (112)   ~ (e3 = e1)
% 228.80/40.27  | | | | | | | | 
% 228.80/40.27  | | | | | | | | REDUCE: (104), (111) imply:
% 228.80/40.27  | | | | | | | |   (113)   ~ (e2 = e1)
% 228.80/40.27  | | | | | | | | 
% 228.80/40.27  | | | | | | | | REDUCE: (33), (111) imply:
% 228.80/40.27  | | | | | | | |   (114)  op(e0, e3) = e1
% 228.80/40.27  | | | | | | | | 
% 228.80/40.27  | | | | | | | | REF_CLOSE: (4), (6), (7), (10), (17), (18), (19), (28), (30),
% 228.80/40.27  | | | | | | | |            (31), (35), (36), (40), (42), (43), (45), (49), (53),
% 228.80/40.27  | | | | | | | |            (55), (56), (68), (73), (75), (82), (94), (99), (114)
% 228.80/40.27  | | | | | | | |            are inconsistent by sub-proof #585.
% 228.80/40.27  | | | | | | | | 
% 228.80/40.27  | | | | | | | Case 2:
% 228.80/40.27  | | | | | | | | 
% 228.80/40.27  | | | | | | | |   (115)  all_55_12 = e0
% 228.80/40.27  | | | | | | | | 
% 228.80/40.27  | | | | | | | | REF_CLOSE: (47), (61), (115) are inconsistent by sub-proof
% 228.80/40.27  | | | | | | | |            #1993.
% 228.80/40.27  | | | | | | | | 
% 228.80/40.27  | | | | | | | End of split
% 228.80/40.27  | | | | | | | 
% 228.80/40.27  | | | | | | End of split
% 228.80/40.27  | | | | | | 
% 228.80/40.27  | | | | | Case 2:
% 228.80/40.27  | | | | | | 
% 228.80/40.27  | | | | | |   (116)  all_55_4 = e1 | all_55_4 = e0
% 228.80/40.27  | | | | | | 
% 228.80/40.27  | | | | | | REF_CLOSE: (25), (39), (51), (116) are inconsistent by sub-proof
% 228.80/40.27  | | | | | |            #773.
% 228.80/40.27  | | | | | | 
% 228.80/40.27  | | | | | End of split
% 228.80/40.27  | | | | | 
% 228.80/40.27  | | | | End of split
% 228.80/40.27  | | | | 
% 228.80/40.27  | | | End of split
% 228.80/40.27  | | | 
% 228.80/40.27  | | Case 2:
% 228.80/40.27  | | | 
% 228.80/40.27  | | |   (117)  all_57_9 = e3 & op(e3, e0) = e3
% 228.80/40.27  | | | 
% 228.80/40.27  | | | ALPHA: (117) implies:
% 228.80/40.27  | | |   (118)  op(e3, e0) = e3
% 228.80/40.27  | | | 
% 228.80/40.27  | | | REF_CLOSE: (10), (66), (87), (118) are inconsistent by sub-proof #2458.
% 228.80/40.27  | | | 
% 228.80/40.27  | | End of split
% 228.80/40.27  | | 
% 228.80/40.27  | End of split
% 228.80/40.27  | 
% 228.80/40.27  End of proof
% 228.80/40.27  
% 228.80/40.27  Sub-proof #585 shows that the following formulas are inconsistent:
% 228.80/40.27  ----------------------------------------------------------------
% 228.80/40.27    (1)  all_57_10 = e0
% 228.80/40.27    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.80/40.27         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.80/40.27    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.80/40.27         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.80/40.27    (4)   ~ (e3 = e1)
% 228.80/40.27    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.80/40.27           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.80/40.27    (6)  op(e2, e2) = e1
% 228.80/40.27    (7)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.80/40.27         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.80/40.27    (8)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) = all_22_1
% 228.80/40.27           & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0, e3) =
% 228.80/40.27           all_22_1 & $i(all_22_1))
% 228.80/40.27    (9)  all_57_4 = e3
% 228.80/40.27    (10)   ~ (e3 = e2)
% 228.80/40.27    (11)   ~ (e3 = e0)
% 228.80/40.27    (12)  op(e0, e3) = e1
% 228.80/40.27    (13)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.80/40.27          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.80/40.27    (14)  all_57_0 = e0
% 228.80/40.27    (15)  all_57_15 = e3
% 228.80/40.27    (16)  all_57_5 = e3
% 228.80/40.27    (17)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.80/40.27          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 228.80/40.27    (18)   ~ (e2 = e0)
% 228.80/40.27    (19)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 228.80/40.27            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 228.80/40.27              e3) = all_12_1 & $i(all_12_1))
% 228.80/40.27    (20)  all_57_3 = e1
% 228.80/40.27    (21)   ~ (e1 = e0)
% 228.80/40.27    (22)  all_57_8 = e2
% 228.80/40.27    (23)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.80/40.27          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.80/40.27    (24)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.80/40.27          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.80/40.27    (25)   ~ (e2 = e1)
% 228.80/40.27    (26)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.80/40.27          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.80/40.27    (27)  all_57_14 = e0
% 228.80/40.27  
% 228.80/40.27  Begin of proof
% 228.80/40.27  | 
% 228.80/40.27  | BETA: splitting (26) gives:
% 228.80/40.27  | 
% 228.80/40.27  | Case 1:
% 228.80/40.27  | | 
% 228.80/40.27  | |   (28)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 228.80/40.27  | |           e2)
% 228.80/40.27  | | 
% 228.80/40.27  | | BETA: splitting (28) gives:
% 228.80/40.27  | | 
% 228.80/40.27  | | Case 1:
% 228.80/40.27  | | | 
% 228.80/40.27  | | |   (29)  all_57_9 = e2 & op(e3, e0) = e2
% 228.80/40.27  | | | 
% 228.80/40.27  | | | ALPHA: (29) implies:
% 228.80/40.27  | | |   (30)  all_57_9 = e2
% 228.80/40.27  | | | 
% 228.80/40.27  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (14), (16),
% 228.80/40.27  | | |            (17), (18), (20), (21), (23), (24), (25), (30) are inconsistent
% 228.80/40.27  | | |            by sub-proof #586.
% 228.80/40.27  | | | 
% 228.80/40.27  | | Case 2:
% 228.80/40.27  | | | 
% 228.80/40.27  | | |   (31)  all_57_10 = e2 & op(e2, e0) = e2
% 228.80/40.27  | | | 
% 228.80/40.27  | | | REF_CLOSE: (1), (18), (31) are inconsistent by sub-proof #1798.
% 228.80/40.27  | | | 
% 228.80/40.27  | | End of split
% 228.80/40.27  | | 
% 228.80/40.27  | Case 2:
% 228.80/40.27  | | 
% 228.80/40.27  | |   (32)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.80/40.27  | |           e2)
% 228.80/40.27  | | 
% 228.80/40.27  | | BETA: splitting (32) gives:
% 228.80/40.27  | | 
% 228.80/40.27  | | Case 1:
% 228.80/40.27  | | | 
% 228.80/40.27  | | |   (33)  all_57_11 = e2 & op(e1, e0) = e2
% 228.80/40.27  | | | 
% 228.80/40.27  | | | ALPHA: (33) implies:
% 228.80/40.27  | | |   (34)  op(e1, e0) = e2
% 228.80/40.27  | | | 
% 228.80/40.27  | | | REF_CLOSE: (5), (8), (12), (19), (34) are inconsistent by sub-proof #1147.
% 228.80/40.27  | | | 
% 228.80/40.27  | | Case 2:
% 228.80/40.27  | | | 
% 228.80/40.27  | | |   (35)  all_57_15 = e2 & op(e0, e0) = e2
% 228.80/40.27  | | | 
% 228.80/40.27  | | | ALPHA: (35) implies:
% 228.80/40.27  | | |   (36)  all_57_15 = e2
% 228.80/40.27  | | | 
% 228.80/40.27  | | | COMBINE_EQS: (15), (36) imply:
% 228.80/40.27  | | |   (37)  e3 = e2
% 228.80/40.27  | | | 
% 228.80/40.27  | | | COMBINE_EQS: (9), (37) imply:
% 228.80/40.27  | | |   (38)  all_57_4 = e2
% 228.80/40.27  | | | 
% 228.80/40.27  | | | REF_CLOSE: (4), (13), (16), (21), (22), (25), (27), (38) are inconsistent
% 228.80/40.27  | | |            by sub-proof #1456.
% 228.80/40.27  | | | 
% 228.80/40.27  | | End of split
% 228.80/40.27  | | 
% 228.80/40.27  | End of split
% 228.80/40.27  | 
% 228.80/40.27  End of proof
% 228.80/40.27  
% 228.80/40.27  Sub-proof #586 shows that the following formulas are inconsistent:
% 228.80/40.27  ----------------------------------------------------------------
% 228.80/40.27    (1)  all_57_9 = e2
% 228.80/40.27    (2)  all_57_10 = e0
% 228.80/40.27    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.80/40.27         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.80/40.27    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.80/40.27         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.80/40.27    (5)   ~ (e3 = e1)
% 228.80/40.27    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.80/40.27           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.80/40.27    (7)  op(e2, e2) = e1
% 228.80/40.27    (8)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.80/40.27         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.80/40.27    (9)  all_57_4 = e3
% 228.80/40.27    (10)   ~ (e3 = e2)
% 228.80/40.27    (11)   ~ (e3 = e0)
% 228.80/40.27    (12)  all_57_0 = e0
% 228.80/40.27    (13)  all_57_5 = e3
% 228.80/40.27    (14)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.80/40.27          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 228.80/40.27    (15)   ~ (e2 = e0)
% 228.80/40.27    (16)  all_57_3 = e1
% 228.80/40.27    (17)   ~ (e1 = e0)
% 228.80/40.27    (18)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.80/40.27          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.80/40.27    (19)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.80/40.27          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.80/40.27    (20)   ~ (e2 = e1)
% 228.80/40.27  
% 228.80/40.27  Begin of proof
% 228.80/40.27  | 
% 228.80/40.27  | BETA: splitting (8) gives:
% 228.80/40.27  | 
% 228.80/40.27  | Case 1:
% 228.80/40.27  | | 
% 228.80/40.27  | |   (21)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) =
% 228.80/40.27  | |           e1)
% 228.80/40.27  | | 
% 228.80/40.27  | | BETA: splitting (21) gives:
% 228.80/40.27  | | 
% 228.80/40.27  | | Case 1:
% 228.80/40.27  | | | 
% 228.80/40.27  | | |   (22)  all_57_0 = e1 & op(e3, e3) = e1
% 228.80/40.27  | | | 
% 228.80/40.27  | | | ALPHA: (22) implies:
% 228.80/40.27  | | |   (23)  all_57_0 = e1
% 228.80/40.27  | | | 
% 228.80/40.27  | | | COMBINE_EQS: (12), (23) imply:
% 228.80/40.27  | | |   (24)  e1 = e0
% 228.80/40.27  | | | 
% 228.80/40.27  | | | REF_CLOSE: (2), (3), (5), (10), (13), (15), (16), (17), (19), (20), (24)
% 228.80/40.27  | | |            are inconsistent by sub-proof #1017.
% 228.80/40.27  | | | 
% 228.80/40.27  | | Case 2:
% 228.80/40.27  | | | 
% 228.80/40.27  | | |   (25)  all_57_1 = e1 & op(e3, e2) = e1
% 228.80/40.27  | | | 
% 228.80/40.27  | | | ALPHA: (25) implies:
% 228.80/40.27  | | |   (26)  all_57_1 = e1
% 228.80/40.27  | | | 
% 228.80/40.27  | | | REF_CLOSE: (4), (5), (6), (7), (10), (11), (14), (15), (17), (18), (20),
% 228.80/40.27  | | |            (26) are inconsistent by sub-proof #1908.
% 228.80/40.27  | | | 
% 228.80/40.27  | | End of split
% 228.80/40.27  | | 
% 228.80/40.27  | Case 2:
% 228.80/40.27  | | 
% 228.80/40.27  | |   (27)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) =
% 228.80/40.27  | |           e1)
% 228.80/40.27  | | 
% 228.80/40.27  | | REF_CLOSE: (1), (5), (9), (20), (27) are inconsistent by sub-proof #1223.
% 228.80/40.27  | | 
% 228.80/40.27  | End of split
% 228.80/40.27  | 
% 228.80/40.27  End of proof
% 228.80/40.27  
% 228.80/40.27  Sub-proof #587 shows that the following formulas are inconsistent:
% 228.80/40.27  ----------------------------------------------------------------
% 228.80/40.27    (1)  all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 228.80/40.27    (2)   ~ (all_53_6 = all_53_14)
% 228.80/40.27    (3)   ~ (all_53_6 = e2)
% 228.80/40.27    (4)   ~ (e3 = e1)
% 228.80/40.27    (5)   ~ (all_53_13 = e1)
% 228.80/40.27    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.80/40.27           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.80/40.27    (7)  all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 228.80/40.27    (8)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 228.80/40.27    (9)  op(e2, e2) = e1
% 228.80/40.27    (10)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 228.80/40.27    (11)  all_55_9 = all_53_6
% 228.80/40.27    (12)   ~ (all_53_13 = e3)
% 228.80/40.27    (13)  op(e0, e1) = e0
% 228.80/40.27    (14)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.80/40.27          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.80/40.27    (15)  all_55_4 = all_53_1
% 228.80/40.27    (16)   ~ (all_53_1 = all_53_3)
% 228.80/40.27    (17)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.80/40.27          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.80/40.27    (18)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.80/40.27    (19)   ~ (all_53_2 = e0)
% 228.80/40.27    (20)  op(e3, e3) = e0
% 228.80/40.27    (21)   ~ (all_53_1 = e1)
% 228.80/40.27    (22)  all_57_5 = e3
% 228.80/40.27    (23)   ~ (all_53_1 = all_53_2)
% 228.80/40.27    (24)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.80/40.27            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.80/40.27            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.80/40.27            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.80/40.27              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.80/40.27            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.80/40.27            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.80/40.27              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.80/40.27              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.80/40.27            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.80/40.27            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.80/40.27            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.80/40.27              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.80/40.27              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.80/40.27            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.80/40.27              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.80/40.27            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.80/40.27            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.80/40.27              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.80/40.27              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.80/40.27            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.80/40.27            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.80/40.27    (25)   ~ (all_53_6 = e1)
% 228.80/40.27    (26)  all_55_12 = all_53_3
% 228.80/40.27    (27)   ~ (all_53_1 = e0)
% 228.80/40.27    (28)   ~ (all_53_2 = all_53_14)
% 228.80/40.27    (29)   ~ (e1 = e0)
% 228.80/40.27    (30)  all_57_8 = e2
% 228.80/40.27    (31)   ~ (all_53_2 = all_53_3)
% 228.80/40.27    (32)  all_55_8 = all_53_2
% 228.80/40.27    (33)  op(e0, e0) = e3
% 228.80/40.27    (34)   ~ (all_53_3 = e0)
% 228.80/40.27    (35)   ~ (all_53_1 = all_53_13)
% 228.80/40.27    (36)  all_57_1 = e3 & op(e3, e2) = e3
% 228.80/40.27    (37)  op(e2, e0) = all_53_13
% 228.80/40.27    (38)  all_55_11 = all_53_14
% 228.80/40.27    (39)  op(e1, e3) = all_53_2
% 228.80/40.27    (40)   ~ (all_53_1 = e3)
% 228.80/40.27    (41)  all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 228.80/40.27    (42)   ~ (all_53_14 = e2)
% 228.80/40.27    (43)   ~ (all_53_2 = all_53_6)
% 228.80/40.27    (44)  all_57_14 = e0
% 228.80/40.27    (45)  all_55_7 = all_53_13
% 228.80/40.27  
% 228.80/40.27  Begin of proof
% 228.80/40.27  | 
% 228.80/40.27  | ALPHA: (36) implies:
% 228.80/40.27  |   (46)  all_57_1 = e3
% 228.80/40.27  | 
% 228.80/40.27  | BETA: splitting (1) gives:
% 228.80/40.27  | 
% 228.80/40.27  | Case 1:
% 228.80/40.27  | | 
% 228.80/40.27  | |   (47)  all_55_4 = e2
% 228.80/40.27  | | 
% 228.80/40.27  | | COMBINE_EQS: (15), (47) imply:
% 228.80/40.27  | |   (48)  all_53_1 = e2
% 228.80/40.27  | | 
% 228.80/40.27  | | SIMP: (48) implies:
% 228.80/40.27  | |   (49)  all_53_1 = e2
% 228.80/40.27  | | 
% 228.80/40.27  | | REDUCE: (23), (49) imply:
% 228.80/40.27  | |   (50)   ~ (all_53_2 = e2)
% 228.80/40.27  | | 
% 228.80/40.27  | | SIMP: (50) implies:
% 228.80/40.27  | |   (51)   ~ (all_53_2 = e2)
% 228.80/40.27  | | 
% 228.80/40.27  | | REDUCE: (16), (49) imply:
% 228.80/40.27  | |   (52)   ~ (all_53_3 = e2)
% 228.80/40.27  | | 
% 228.80/40.27  | | SIMP: (52) implies:
% 228.80/40.27  | |   (53)   ~ (all_53_3 = e2)
% 228.80/40.27  | | 
% 228.80/40.27  | | REDUCE: (35), (49) imply:
% 228.80/40.27  | |   (54)   ~ (all_53_13 = e2)
% 228.80/40.27  | | 
% 228.80/40.27  | | SIMP: (54) implies:
% 228.80/40.27  | |   (55)   ~ (all_53_13 = e2)
% 228.80/40.27  | | 
% 228.80/40.27  | | REDUCE: (40), (49) imply:
% 228.80/40.27  | |   (56)   ~ (e3 = e2)
% 228.80/40.27  | | 
% 228.80/40.27  | | SIMP: (56) implies:
% 228.80/40.27  | |   (57)   ~ (e3 = e2)
% 228.80/40.27  | | 
% 228.80/40.27  | | REDUCE: (21), (49) imply:
% 228.80/40.27  | |   (58)   ~ (e2 = e1)
% 228.80/40.27  | | 
% 228.80/40.27  | | REDUCE: (27), (49) imply:
% 228.80/40.27  | |   (59)   ~ (e2 = e0)
% 228.80/40.27  | | 
% 228.80/40.27  | | BETA: splitting (14) gives:
% 228.80/40.27  | | 
% 228.80/40.27  | | Case 1:
% 228.80/40.27  | | | 
% 228.80/40.27  | | |   (60)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) =
% 228.80/40.27  | | |           e2)
% 228.80/40.27  | | | 
% 228.80/40.27  | | | REF_CLOSE: (6), (20), (46), (57), (59), (60) are inconsistent by sub-proof
% 228.80/40.27  | | |            #1224.
% 228.80/40.27  | | | 
% 228.80/40.27  | | Case 2:
% 228.80/40.27  | | | 
% 228.80/40.27  | | |   (61)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) =
% 228.80/40.27  | | |           e2)
% 228.80/40.27  | | | 
% 228.80/40.27  | | | BETA: splitting (61) gives:
% 228.80/40.27  | | | 
% 228.80/40.27  | | | Case 1:
% 228.80/40.27  | | | | 
% 228.80/40.27  | | | |   (62)  all_57_4 = e2 & op(e3, e1) = e2
% 228.80/40.27  | | | | 
% 228.80/40.27  | | | | ALPHA: (62) implies:
% 228.80/40.27  | | | |   (63)  all_57_4 = e2
% 228.80/40.27  | | | | 
% 228.80/40.27  | | | | REF_CLOSE: (4), (17), (22), (29), (30), (44), (58), (63) are
% 228.80/40.27  | | | |            inconsistent by sub-proof #1456.
% 228.80/40.27  | | | | 
% 228.80/40.27  | | | Case 2:
% 228.80/40.27  | | | | 
% 228.80/40.28  | | | |   (64)  all_57_9 = e2 & op(e3, e0) = e2
% 228.80/40.28  | | | | 
% 228.80/40.28  | | | | ALPHA: (64) implies:
% 228.80/40.28  | | | |   (65)  op(e3, e0) = e2
% 228.80/40.28  | | | | 
% 228.80/40.28  | | | | BETA: splitting (7) gives:
% 228.80/40.28  | | | | 
% 228.80/40.28  | | | | Case 1:
% 228.80/40.28  | | | | | 
% 228.80/40.28  | | | | |   (66)  all_55_7 = e2
% 228.80/40.28  | | | | | 
% 228.80/40.28  | | | | | REF_CLOSE: (45), (55), (66) are inconsistent by sub-proof #2171.
% 228.80/40.28  | | | | | 
% 228.80/40.28  | | | | Case 2:
% 228.80/40.28  | | | | | 
% 228.80/40.28  | | | | |   (67)  all_55_7 = e1 | all_55_7 = e0
% 228.80/40.28  | | | | | 
% 228.80/40.28  | | | | | BETA: splitting (41) gives:
% 228.80/40.28  | | | | | 
% 228.80/40.28  | | | | | Case 1:
% 228.80/40.28  | | | | | | 
% 228.80/40.28  | | | | | |   (68)  all_55_12 = e2
% 228.80/40.28  | | | | | | 
% 228.80/40.28  | | | | | | REF_CLOSE: (26), (53), (68) are inconsistent by sub-proof #1337.
% 228.80/40.28  | | | | | | 
% 228.80/40.28  | | | | | Case 2:
% 228.80/40.28  | | | | | | 
% 228.80/40.28  | | | | | |   (69)  all_55_12 = e1 | all_55_12 = e0
% 228.80/40.28  | | | | | | 
% 228.80/40.28  | | | | | | BETA: splitting (69) gives:
% 228.80/40.28  | | | | | | 
% 228.80/40.28  | | | | | | Case 1:
% 228.80/40.28  | | | | | | | 
% 228.80/40.28  | | | | | | |   (70)  all_55_12 = e1
% 228.80/40.28  | | | | | | | 
% 228.80/40.28  | | | | | | | COMBINE_EQS: (26), (70) imply:
% 228.80/40.28  | | | | | | |   (71)  all_53_3 = e1
% 228.80/40.28  | | | | | | | 
% 228.80/40.28  | | | | | | | SIMP: (71) implies:
% 228.80/40.28  | | | | | | |   (72)  all_53_3 = e1
% 228.80/40.28  | | | | | | | 
% 228.80/40.28  | | | | | | | REDUCE: (31), (72) imply:
% 228.80/40.28  | | | | | | |   (73)   ~ (all_53_2 = e1)
% 228.80/40.28  | | | | | | | 
% 228.80/40.28  | | | | | | | BETA: splitting (18) gives:
% 228.80/40.28  | | | | | | | 
% 228.80/40.28  | | | | | | | Case 1:
% 228.80/40.28  | | | | | | | | 
% 228.80/40.28  | | | | | | | |   (74)  all_55_8 = e3
% 228.80/40.28  | | | | | | | | 
% 228.80/40.28  | | | | | | | | COMBINE_EQS: (32), (74) imply:
% 228.80/40.28  | | | | | | | |   (75)  all_53_2 = e3
% 228.80/40.28  | | | | | | | | 
% 228.80/40.28  | | | | | | | | SIMP: (75) implies:
% 228.80/40.28  | | | | | | | |   (76)  all_53_2 = e3
% 228.80/40.28  | | | | | | | | 
% 228.80/40.28  | | | | | | | | REDUCE: (43), (76) imply:
% 228.80/40.28  | | | | | | | |   (77)   ~ (all_53_6 = e3)
% 228.80/40.28  | | | | | | | | 
% 228.80/40.28  | | | | | | | | SIMP: (77) implies:
% 228.80/40.28  | | | | | | | |   (78)   ~ (all_53_6 = e3)
% 228.80/40.28  | | | | | | | | 
% 228.80/40.28  | | | | | | | | REDUCE: (28), (76) imply:
% 228.80/40.28  | | | | | | | |   (79)   ~ (all_53_14 = e3)
% 228.80/40.28  | | | | | | | | 
% 228.80/40.28  | | | | | | | | SIMP: (79) implies:
% 228.80/40.28  | | | | | | | |   (80)   ~ (all_53_14 = e3)
% 228.80/40.28  | | | | | | | | 
% 228.80/40.28  | | | | | | | | REDUCE: (19), (76) imply:
% 228.80/40.28  | | | | | | | |   (81)   ~ (e3 = e0)
% 228.80/40.28  | | | | | | | | 
% 228.80/40.28  | | | | | | | | REDUCE: (39), (76) imply:
% 228.80/40.28  | | | | | | | |   (82)  op(e1, e3) = e3
% 228.80/40.28  | | | | | | | | 
% 228.80/40.28  | | | | | | | | BETA: splitting (10) gives:
% 228.80/40.28  | | | | | | | | 
% 228.80/40.28  | | | | | | | | Case 1:
% 228.80/40.28  | | | | | | | | | 
% 228.80/40.28  | | | | | | | | |   (83)  all_55_9 = e3
% 228.80/40.28  | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | REF_CLOSE: (11), (78), (83) are inconsistent by sub-proof
% 228.80/40.28  | | | | | | | | |            #2159.
% 228.80/40.28  | | | | | | | | | 
% 228.80/40.28  | | | | | | | | Case 2:
% 228.80/40.28  | | | | | | | | | 
% 228.80/40.28  | | | | | | | | |   (84)  all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 228.80/40.28  | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | BETA: splitting (24) gives:
% 228.80/40.28  | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | Case 1:
% 228.80/40.28  | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | |   (85)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 228.80/40.28  | | | | | | | | | |           all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 228.80/40.28  | | | | | | | | | |           op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 228.80/40.28  | | | | | | | | | |             all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 228.80/40.28  | | | | | | | | | |           op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 228.80/40.28  | | | | | | | | | |           op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 228.80/40.28  | | | | | | | | | |           $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.80/40.28  | | | | | | | | | |           $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 &
% 228.80/40.28  | | | | | | | | | |           all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 228.80/40.28  | | | | | | | | | |             all_52_9) = e3 & op(all_52_11, all_52_11) = e2 &
% 228.80/40.28  | | | | | | | | | |           op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.80/40.28  | | | | | | | | | |             all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2,
% 228.80/40.28  | | | | | | | | | |             e2) = all_52_11 & op(e2, e1) = all_52_13 &
% 228.80/40.28  | | | | | | | | | |           op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.80/40.28  | | | | | | | | | |           $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 228.80/40.28  | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | BETA: splitting (85) gives:
% 228.80/40.28  | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | Case 1:
% 228.80/40.28  | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | |   (86)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 228.80/40.28  | | | | | | | | | | |         all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 228.80/40.28  | | | | | | | | | | |         op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 228.80/40.28  | | | | | | | | | | |           all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 228.80/40.28  | | | | | | | | | | |         op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 228.80/40.28  | | | | | | | | | | |         op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 228.80/40.28  | | | | | | | | | | |         $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.80/40.28  | | | | | | | | | | |         $i(all_52_7)
% 228.80/40.28  | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | ALPHA: (86) implies:
% 228.80/40.28  | | | | | | | | | | |   (87)  op(e3, e0) = all_52_7
% 228.80/40.28  | | | | | | | | | | |   (88)  op(all_52_7, all_52_7) = e0
% 228.80/40.28  | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | BETA: splitting (84) gives:
% 228.80/40.28  | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | Case 1:
% 228.80/40.28  | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | |   (89)  all_55_9 = e2
% 228.80/40.28  | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | | REF_CLOSE: (3), (11), (89) are inconsistent by sub-proof
% 228.80/40.28  | | | | | | | | | | | |            #2274.
% 228.80/40.28  | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | Case 2:
% 228.80/40.28  | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | |   (90)  all_55_9 = e1 | all_55_9 = e0
% 228.80/40.28  | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | | BETA: splitting (90) gives:
% 228.80/40.28  | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | | Case 1:
% 228.80/40.28  | | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | | |   (91)  all_55_9 = e1
% 228.80/40.28  | | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | | | REF_CLOSE: (11), (25), (91) are inconsistent by sub-proof
% 228.80/40.28  | | | | | | | | | | | | |            #2273.
% 228.80/40.28  | | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | | Case 2:
% 228.80/40.28  | | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | | |   (92)  all_55_9 = e0
% 228.80/40.28  | | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | | | COMBINE_EQS: (11), (92) imply:
% 228.80/40.28  | | | | | | | | | | | | |   (93)  all_53_6 = e0
% 228.80/40.28  | | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | | | SIMP: (93) implies:
% 228.80/40.28  | | | | | | | | | | | | |   (94)  all_53_6 = e0
% 228.80/40.28  | | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | | | REDUCE: (2), (94) imply:
% 228.80/40.28  | | | | | | | | | | | | |   (95)   ~ (all_53_14 = e0)
% 228.80/40.28  | | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | | | SIMP: (95) implies:
% 228.80/40.28  | | | | | | | | | | | | |   (96)   ~ (all_53_14 = e0)
% 228.80/40.28  | | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (38), (42), (65), (80), (87), (88),
% 228.80/40.28  | | | | | | | | | | | | |            (96) are inconsistent by sub-proof #588.
% 228.80/40.28  | | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | | End of split
% 228.80/40.28  | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | End of split
% 228.80/40.28  | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | Case 2:
% 228.80/40.28  | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | |   (97)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.80/40.28  | | | | | | | | | | |         all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 228.80/40.28  | | | | | | | | | | |         op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 228.80/40.28  | | | | | | | | | | |           all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 228.80/40.28  | | | | | | | | | | |         & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.80/40.28  | | | | | | | | | | |         op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 228.80/40.28  | | | | | | | | | | |         $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 228.80/40.28  | | | | | | | | | | |         $i(all_52_15)
% 228.80/40.28  | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | REF_CLOSE: (5), (6), (12), (33), (37), (45), (67), (97) are
% 228.80/40.28  | | | | | | | | | | |            inconsistent by sub-proof #888.
% 228.80/40.28  | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | End of split
% 228.80/40.28  | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | Case 2:
% 228.80/40.28  | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | |   (98)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 228.80/40.28  | | | | | | | | | |           all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 228.80/40.28  | | | | | | | | | |           op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.80/40.28  | | | | | | | | | |             all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 228.80/40.28  | | | | | | | | | |           & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 228.80/40.28  | | | | | | | | | |           & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 228.80/40.28  | | | | | | | | | |           & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.80/40.28  | | | | | | | | | |           $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2
% 228.80/40.28  | | | | | | | | | |           & all_52_28 = e1 & all_52_30 = e0 & op(all_52_25,
% 228.80/40.28  | | | | | | | | | |             all_52_25) = e3 & op(all_52_27, all_52_27) = e2
% 228.80/40.28  | | | | | | | | | |           & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.80/40.28  | | | | | | | | | |             all_52_31) = e0 & op(e0, e3) = all_52_25 &
% 228.80/40.28  | | | | | | | | | |           op(e0, e2) = all_52_27 & op(e0, e1) = all_52_29 &
% 228.80/40.28  | | | | | | | | | |           op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.80/40.28  | | | | | | | | | |           $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.80/40.28  | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | BETA: splitting (98) gives:
% 228.80/40.28  | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | Case 1:
% 228.80/40.28  | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | |   (99)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 228.80/40.28  | | | | | | | | | | |         all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 228.80/40.28  | | | | | | | | | | |         op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.80/40.28  | | | | | | | | | | |           all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 228.80/40.28  | | | | | | | | | | |         & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 228.80/40.28  | | | | | | | | | | |         & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 228.80/40.28  | | | | | | | | | | |         & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.80/40.28  | | | | | | | | | | |         $i(all_52_23)
% 228.80/40.28  | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | ALPHA: (99) implies:
% 228.80/40.28  | | | | | | | | | | |   (100)  op(e1, e3) = all_52_17
% 228.80/40.28  | | | | | | | | | | |   (101)  op(all_52_17, all_52_17) = e3
% 228.80/40.28  | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | BETA: splitting (8) gives:
% 228.80/40.28  | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | Case 1:
% 228.80/40.28  | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | |   (102)  all_55_11 = e3
% 228.80/40.28  | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | | REF_CLOSE: (38), (80), (102) are inconsistent by sub-proof
% 228.80/40.28  | | | | | | | | | | | |            #2497.
% 228.80/40.28  | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | Case 2:
% 228.80/40.28  | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | |   (103)  all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 228.80/40.28  | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | | BETA: splitting (103) gives:
% 228.80/40.28  | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | | Case 1:
% 228.80/40.28  | | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | | |   (104)  all_55_11 = e2
% 228.80/40.28  | | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | | | REF_CLOSE: (38), (42), (104) are inconsistent by sub-proof
% 228.80/40.28  | | | | | | | | | | | | |            #2282.
% 228.80/40.28  | | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | | Case 2:
% 228.80/40.28  | | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | | | GROUND_INST: instantiating (6) with e3, all_52_17, e3, e1,
% 228.80/40.28  | | | | | | | | | | | | |              simplifying with (82), (100) gives:
% 228.80/40.28  | | | | | | | | | | | | |   (105)  all_52_17 = e3
% 228.80/40.28  | | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | | | REDUCE: (101), (105) imply:
% 228.80/40.28  | | | | | | | | | | | | |   (106)  op(e3, e3) = e3
% 228.80/40.28  | | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | | | REF_CLOSE: (6), (20), (81), (106) are inconsistent by
% 228.80/40.28  | | | | | | | | | | | | |            sub-proof #2494.
% 228.80/40.28  | | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | | End of split
% 228.80/40.28  | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | End of split
% 228.80/40.28  | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | Case 2:
% 228.80/40.28  | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | |   (107)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.80/40.28  | | | | | | | | | | |          all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 228.80/40.28  | | | | | | | | | | |          op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 228.80/40.28  | | | | | | | | | | |            all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 228.80/40.28  | | | | | | | | | | |          & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 228.80/40.28  | | | | | | | | | | |          & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 228.80/40.28  | | | | | | | | | | |          & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 228.80/40.28  | | | | | | | | | | |          $i(all_52_31)
% 228.80/40.28  | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | ALPHA: (107) implies:
% 228.80/40.28  | | | | | | | | | | |   (108)  op(e0, e0) = all_52_31
% 228.80/40.28  | | | | | | | | | | |   (109)  op(e0, e1) = all_52_29
% 228.80/40.28  | | | | | | | | | | |   (110)  op(all_52_29, all_52_29) = e1
% 228.80/40.28  | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | BETA: splitting (84) gives:
% 228.80/40.28  | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | Case 1:
% 228.80/40.28  | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | |   (111)  all_55_9 = e2
% 228.80/40.28  | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | | REF_CLOSE: (3), (11), (111) are inconsistent by sub-proof
% 228.80/40.28  | | | | | | | | | | | |            #2274.
% 228.80/40.28  | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | Case 2:
% 228.80/40.28  | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | |   (112)  all_55_9 = e1 | all_55_9 = e0
% 228.80/40.28  | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | | BETA: splitting (112) gives:
% 228.80/40.28  | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | | Case 1:
% 228.80/40.28  | | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | | |   (113)  all_55_9 = e1
% 228.80/40.28  | | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | | | REF_CLOSE: (11), (25), (113) are inconsistent by sub-proof
% 228.80/40.28  | | | | | | | | | | | | |            #2273.
% 228.80/40.28  | | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | | Case 2:
% 228.80/40.28  | | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | | |   (114)  all_55_9 = e0
% 228.80/40.28  | | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | | | COMBINE_EQS: (11), (114) imply:
% 228.80/40.28  | | | | | | | | | | | | |   (115)  all_53_6 = e0
% 228.80/40.28  | | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | | | SIMP: (115) implies:
% 228.80/40.28  | | | | | | | | | | | | |   (116)  all_53_6 = e0
% 228.80/40.28  | | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | | | REDUCE: (2), (116) imply:
% 228.80/40.28  | | | | | | | | | | | | |   (117)   ~ (all_53_14 = e0)
% 228.80/40.28  | | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | | | SIMP: (117) implies:
% 228.80/40.28  | | | | | | | | | | | | |   (118)   ~ (all_53_14 = e0)
% 228.80/40.28  | | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | | | BETA: splitting (8) gives:
% 228.80/40.28  | | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | | | Case 1:
% 228.80/40.28  | | | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | | | |   (119)  all_55_11 = e3
% 228.80/40.28  | | | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | | | | REF_CLOSE: (38), (80), (119) are inconsistent by sub-proof
% 228.80/40.28  | | | | | | | | | | | | | |            #2497.
% 228.80/40.28  | | | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | | | Case 2:
% 228.80/40.28  | | | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | | | |   (120)   ~ (all_55_11 = e3)
% 228.80/40.28  | | | | | | | | | | | | | |   (121)  all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 228.80/40.28  | | | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | | | | BETA: splitting (121) gives:
% 228.80/40.28  | | | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | | | | Case 1:
% 228.80/40.28  | | | | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | | | | |   (122)  all_55_11 = e2
% 228.80/40.28  | | | | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | | | | | REF_CLOSE: (38), (42), (122) are inconsistent by sub-proof
% 228.80/40.28  | | | | | | | | | | | | | | |            #2282.
% 228.80/40.28  | | | | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | | | | Case 2:
% 228.80/40.28  | | | | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | | | | |   (123)  all_55_11 = e1 | all_55_11 = e0
% 228.80/40.28  | | | | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | | | | | BETA: splitting (123) gives:
% 228.80/40.28  | | | | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | | | | | Case 1:
% 228.80/40.28  | | | | | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | | | | | |   (124)  all_55_11 = e1
% 228.80/40.28  | | | | | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | | | | | | COMBINE_EQS: (38), (124) imply:
% 228.80/40.28  | | | | | | | | | | | | | | | |   (125)  all_53_14 = e1
% 228.80/40.28  | | | | | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | | | | | | SIMP: (125) implies:
% 228.80/40.28  | | | | | | | | | | | | | | | |   (126)  all_53_14 = e1
% 228.80/40.28  | | | | | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | | | | | | REDUCE: (80), (126) imply:
% 228.80/40.28  | | | | | | | | | | | | | | | |   (127)   ~ (e3 = e1)
% 228.80/40.28  | | | | | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (13), (33), (108), (109), (110) are
% 228.80/40.28  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #887.
% 228.80/40.28  | | | | | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | | | | | Case 2:
% 228.80/40.28  | | | | | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | | | | | |   (128)  all_55_11 = e0
% 228.80/40.28  | | | | | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | | | | | | REF_CLOSE: (38), (118), (128) are inconsistent by sub-proof
% 228.80/40.28  | | | | | | | | | | | | | | | |            #2308.
% 228.80/40.28  | | | | | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | | | | | End of split
% 228.80/40.28  | | | | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | | | | End of split
% 228.80/40.28  | | | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | | | End of split
% 228.80/40.28  | | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | | End of split
% 228.80/40.28  | | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | | End of split
% 228.80/40.28  | | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | | End of split
% 228.80/40.28  | | | | | | | | | | 
% 228.80/40.28  | | | | | | | | | End of split
% 228.80/40.28  | | | | | | | | | 
% 228.80/40.28  | | | | | | | | End of split
% 228.80/40.28  | | | | | | | | 
% 228.80/40.28  | | | | | | | Case 2:
% 228.80/40.28  | | | | | | | | 
% 228.80/40.28  | | | | | | | |   (129)  all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.80/40.28  | | | | | | | | 
% 228.80/40.28  | | | | | | | | REF_CLOSE: (19), (32), (51), (73), (129) are inconsistent by
% 228.80/40.28  | | | | | | | |            sub-proof #886.
% 228.80/40.28  | | | | | | | | 
% 228.80/40.28  | | | | | | | End of split
% 228.80/40.28  | | | | | | | 
% 228.80/40.28  | | | | | | Case 2:
% 228.80/40.28  | | | | | | | 
% 228.80/40.28  | | | | | | |   (130)  all_55_12 = e0
% 228.80/40.28  | | | | | | | 
% 228.80/40.28  | | | | | | | REF_CLOSE: (26), (34), (130) are inconsistent by sub-proof #1993.
% 228.80/40.28  | | | | | | | 
% 228.80/40.28  | | | | | | End of split
% 228.80/40.28  | | | | | | 
% 228.80/40.28  | | | | | End of split
% 228.80/40.28  | | | | | 
% 228.80/40.28  | | | | End of split
% 228.80/40.28  | | | | 
% 228.80/40.28  | | | End of split
% 228.80/40.28  | | | 
% 228.80/40.28  | | End of split
% 228.80/40.28  | | 
% 228.80/40.28  | Case 2:
% 228.80/40.28  | | 
% 228.80/40.28  | |   (131)  all_55_4 = e1 | all_55_4 = e0
% 228.80/40.28  | | 
% 228.80/40.28  | | REF_CLOSE: (15), (21), (27), (131) are inconsistent by sub-proof #773.
% 228.80/40.28  | | 
% 228.80/40.28  | End of split
% 228.80/40.28  | 
% 228.80/40.28  End of proof
% 228.80/40.28  
% 228.80/40.28  Sub-proof #588 shows that the following formulas are inconsistent:
% 228.80/40.28  ----------------------------------------------------------------
% 228.80/40.28    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.80/40.28           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.80/40.28    (2)  op(all_52_7, all_52_7) = e0
% 228.80/40.28    (3)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 228.80/40.28    (4)  op(e2, e2) = e1
% 228.80/40.28    (5)  op(e3, e0) = e2
% 228.80/40.28    (6)   ~ (all_53_14 = e3)
% 228.80/40.28    (7)   ~ (all_53_14 = e0)
% 228.80/40.28    (8)  all_55_11 = all_53_14
% 228.80/40.28    (9)   ~ (all_53_14 = e2)
% 228.80/40.28    (10)  op(e3, e0) = all_52_7
% 228.80/40.28  
% 228.80/40.28  Begin of proof
% 228.80/40.28  | 
% 228.80/40.28  | BETA: splitting (3) gives:
% 228.80/40.28  | 
% 228.80/40.28  | Case 1:
% 228.80/40.28  | | 
% 228.80/40.28  | |   (11)  all_55_11 = e3
% 228.80/40.28  | | 
% 228.80/40.28  | | REF_CLOSE: (6), (8), (11) are inconsistent by sub-proof #2497.
% 228.80/40.28  | | 
% 228.80/40.28  | Case 2:
% 228.80/40.28  | | 
% 228.80/40.28  | |   (12)  all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 228.80/40.28  | | 
% 228.80/40.28  | | BETA: splitting (12) gives:
% 228.80/40.28  | | 
% 228.80/40.28  | | Case 1:
% 228.80/40.28  | | | 
% 228.80/40.28  | | |   (13)  all_55_11 = e2
% 228.80/40.28  | | | 
% 228.80/40.28  | | | REF_CLOSE: (8), (9), (13) are inconsistent by sub-proof #2282.
% 228.80/40.28  | | | 
% 228.80/40.28  | | Case 2:
% 228.80/40.28  | | | 
% 228.80/40.28  | | |   (14)  all_55_11 = e1 | all_55_11 = e0
% 228.80/40.28  | | | 
% 228.80/40.28  | | | BETA: splitting (14) gives:
% 228.80/40.28  | | | 
% 228.80/40.28  | | | Case 1:
% 228.80/40.28  | | | | 
% 228.80/40.28  | | | |   (15)  all_55_11 = e1
% 228.80/40.28  | | | | 
% 228.80/40.28  | | | | COMBINE_EQS: (8), (15) imply:
% 228.80/40.28  | | | |   (16)  all_53_14 = e1
% 228.80/40.28  | | | | 
% 228.80/40.28  | | | | SIMP: (16) implies:
% 228.80/40.28  | | | |   (17)  all_53_14 = e1
% 228.80/40.28  | | | | 
% 228.80/40.28  | | | | REDUCE: (7), (17) imply:
% 228.80/40.28  | | | |   (18)   ~ (e1 = e0)
% 228.80/40.28  | | | | 
% 228.80/40.28  | | | | GROUND_INST: instantiating (1) with e2, all_52_7, e0, e3, simplifying
% 228.80/40.28  | | | |              with (5), (10) gives:
% 228.80/40.28  | | | |   (19)  all_52_7 = e2
% 228.80/40.28  | | | | 
% 228.80/40.28  | | | | REDUCE: (2), (19) imply:
% 228.80/40.28  | | | |   (20)  op(e2, e2) = e0
% 228.80/40.28  | | | | 
% 228.80/40.28  | | | | REF_CLOSE: (1), (4), (18), (20) are inconsistent by sub-proof #2352.
% 228.80/40.28  | | | | 
% 228.80/40.28  | | | Case 2:
% 228.80/40.28  | | | | 
% 228.80/40.28  | | | |   (21)  all_55_11 = e0
% 228.80/40.28  | | | | 
% 228.80/40.28  | | | | REF_CLOSE: (7), (8), (21) are inconsistent by sub-proof #2308.
% 228.80/40.28  | | | | 
% 228.80/40.28  | | | End of split
% 228.80/40.28  | | | 
% 228.80/40.28  | | End of split
% 228.80/40.28  | | 
% 228.80/40.28  | End of split
% 228.80/40.28  | 
% 228.80/40.28  End of proof
% 228.80/40.28  
% 228.80/40.28  Sub-proof #589 shows that the following formulas are inconsistent:
% 228.80/40.28  ----------------------------------------------------------------
% 228.80/40.28    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.80/40.28         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.80/40.28    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.80/40.28         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.80/40.28    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.80/40.28         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.80/40.28    (4)   ~ (e3 = e1)
% 228.80/40.28    (5)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.80/40.28         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.80/40.28    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.80/40.28           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.80/40.28    (7)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.80/40.28         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.80/40.28    (8)   ~ (all_6_2 = e3)
% 228.80/40.28    (9)  op(e1, e1) = all_6_2
% 228.80/40.28    (10)  op(e2, e2) = e1
% 228.80/40.28    (11)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.80/40.28          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.80/40.28    (12)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.80/40.28          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.80/40.28    (13)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.80/40.28          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.80/40.28    (14)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.80/40.28          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.80/40.28    (15)   ~ (e3 = e2)
% 228.80/40.28    (16)   ~ (e3 = e0)
% 228.80/40.28    (17)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.80/40.28          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.80/40.28    (18)  op(e0, e3) = all_53_3
% 228.80/40.28    (19)  all_57_15 = e3
% 228.80/40.28    (20)  op(e3, e3) = e0
% 228.80/40.28    (21)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.80/40.28          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.80/40.28            e1)
% 228.80/40.28    (22)  all_57_5 = e3
% 228.80/40.28    (23)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.80/40.28          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 228.80/40.28    (24)   ~ (e2 = e0)
% 228.80/40.28    (25)  all_57_2 = e3
% 228.80/40.28    (26)  all_57_3 = e1
% 228.80/40.28    (27)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.80/40.28          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.80/40.28    (28)   ~ (e1 = e0)
% 228.80/40.28    (29)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.80/40.28          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.80/40.28    (30)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.80/40.28          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.80/40.28    (31)  op(e0, e0) = e3
% 228.80/40.28    (32)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.80/40.28          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.80/40.28            e2)
% 228.80/40.28    (33)   ~ (all_53_3 = e0)
% 228.80/40.28    (34)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.80/40.28              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.80/40.28                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.80/40.28                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.80/40.28    (35)  all_57_5 = e0 & op(e2, e1) = e0
% 228.80/40.28    (36)   ~ (all_53_12 = e3)
% 228.80/40.28    (37)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.80/40.28          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.80/40.28    (38)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.80/40.28          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.80/40.28    (39)   ~ (all_53_12 = e0)
% 228.80/40.28    (40)   ~ (e2 = e1)
% 228.80/40.28    (41)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.80/40.28          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.80/40.28    (42)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.80/40.28          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.80/40.28    (43)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.80/40.28          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.80/40.28    (44)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.80/40.28          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.80/40.28    (45)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.80/40.28          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.80/40.28    (46)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.80/40.28          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.80/40.28    (47)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.80/40.28          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.80/40.28    (48)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.80/40.28          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.80/40.28    (49)  op(e3, e0) = all_53_12
% 228.80/40.28  
% 228.80/40.28  Begin of proof
% 228.80/40.28  | 
% 228.80/40.28  | ALPHA: (35) implies:
% 228.80/40.28  |   (50)  all_57_5 = e0
% 228.80/40.28  | 
% 228.80/40.28  | COMBINE_EQS: (22), (50) imply:
% 228.80/40.28  |   (51)  e3 = e0
% 228.80/40.28  | 
% 228.80/40.28  | COMBINE_EQS: (25), (51) imply:
% 228.80/40.28  |   (52)  all_57_2 = e0
% 228.80/40.28  | 
% 228.80/40.28  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.80/40.28  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 228.80/40.28  |            (24), (26), (27), (28), (29), (30), (31), (32), (33), (34), (36),
% 228.80/40.28  |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 228.80/40.28  |            (48), (49), (52) are inconsistent by sub-proof #1021.
% 228.80/40.28  | 
% 228.80/40.28  End of proof
% 228.80/40.28  
% 228.80/40.28  Sub-proof #590 shows that the following formulas are inconsistent:
% 228.80/40.28  ----------------------------------------------------------------
% 228.80/40.28    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.80/40.28    (2)   ~ (all_53_6 = e2)
% 228.80/40.28    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.80/40.28         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.80/40.28    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.80/40.28         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.80/40.28    (5)   ~ (all_53_8 = all_53_12)
% 228.80/40.28    (6)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.80/40.28         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.80/40.28    (7)   ~ (e3 = e1)
% 228.80/40.28    (8)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.80/40.28         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.80/40.28    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.80/40.28           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.80/40.28    (10)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.80/40.28          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.80/40.28    (11)   ~ (all_6_2 = e3)
% 228.80/40.28    (12)  op(e1, e1) = all_6_2
% 228.80/40.28    (13)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.80/40.28    (14)  op(e2, e2) = e1
% 228.80/40.28    (15)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.80/40.28          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.80/40.28    (16)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 228.80/40.28    (17)  all_55_9 = all_53_6
% 228.80/40.28    (18)  all_57_9 = e1
% 228.80/40.28    (19)   ~ (all_53_4 = all_53_12)
% 228.80/40.28    (20)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.80/40.28          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.80/40.28    (21)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.80/40.28          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.80/40.28    (22)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.80/40.28          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.80/40.28    (23)  all_57_4 = e3
% 228.80/40.28    (24)   ~ (e3 = e2)
% 228.80/40.28    (25)  all_55_1 = all_53_4
% 228.80/40.28    (26)   ~ (all_53_6 = all_53_7)
% 228.80/40.28    (27)   ~ (e3 = e0)
% 228.80/40.28    (28)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.80/40.28          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.80/40.28    (29)  op(e0, e3) = all_53_3
% 228.80/40.28    (30)  all_57_0 = e0
% 228.80/40.28    (31)  all_55_2 = all_53_8
% 228.80/40.28    (32)  all_57_15 = e3
% 228.80/40.28    (33)  op(e3, e3) = e0
% 228.80/40.28    (34)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.80/40.28          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.80/40.28            e1)
% 228.80/40.28    (35)  all_57_10 = e2
% 228.80/40.28    (36)   ~ (all_53_4 = all_53_8)
% 228.80/40.28    (37)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.80/40.28          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 228.80/40.28    (38)   ~ (e2 = e0)
% 228.80/40.28    (39)   ~ (all_53_6 = e1)
% 228.80/40.28    (40)  all_57_2 = e3
% 228.80/40.28    (41)  all_57_3 = e1
% 228.80/40.28    (42)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.80/40.28          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.80/40.28    (43)   ~ (e1 = e0)
% 228.80/40.28    (44)   ~ (all_53_4 = e0)
% 228.80/40.28    (45)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.80/40.28          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.80/40.28    (46)  all_57_8 = e2
% 228.80/40.28    (47)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.80/40.28          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.80/40.28    (48)  op(e0, e0) = e3
% 228.80/40.28    (49)  all_55_2 = e1 | all_55_2 = e0
% 228.80/40.28    (50)   ~ (all_53_4 = all_53_6)
% 228.80/40.28    (51)  op(e0, e2) = all_53_7
% 228.80/40.28    (52)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.80/40.28          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.80/40.28            e2)
% 228.80/40.28    (53)   ~ (all_53_3 = e0)
% 228.80/40.28    (54)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.80/40.28              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.80/40.28                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.80/40.28                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.80/40.28    (55)  op(e1, e1) = e2
% 228.80/40.28    (56)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.80/40.28          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.80/40.28    (57)  all_55_3 = all_53_12
% 228.80/40.28    (58)   ~ (all_53_12 = e3)
% 228.80/40.28    (59)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.80/40.28          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.80/40.28    (60)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.80/40.28          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.80/40.28    (61)   ~ (all_53_12 = e0)
% 228.80/40.28    (62)   ~ (all_53_8 = e0)
% 228.80/40.28    (63)   ~ (e2 = e1)
% 228.80/40.28    (64)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.80/40.28          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.80/40.28    (65)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.80/40.28          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.80/40.28    (66)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.80/40.28          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.80/40.28    (67)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.80/40.28          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.80/40.28    (68)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.80/40.28          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.80/40.29    (69)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.80/40.29          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.80/40.29    (70)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.80/40.29          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.80/40.29    (71)  all_57_5 = e0
% 228.80/40.29    (72)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.80/40.29          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.80/40.29    (73)  op(e3, e0) = all_53_12
% 228.80/40.29  
% 228.80/40.29  Begin of proof
% 228.80/40.29  | 
% 228.80/40.29  | BETA: splitting (52) gives:
% 228.80/40.29  | 
% 228.80/40.29  | Case 1:
% 228.80/40.29  | | 
% 228.80/40.29  | |   (74)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 228.80/40.29  | |           e2)
% 228.80/40.29  | | 
% 228.80/40.29  | | BETA: splitting (74) gives:
% 228.80/40.29  | | 
% 228.80/40.29  | | Case 1:
% 228.80/40.29  | | | 
% 228.80/40.29  | | |   (75)  all_57_12 = e2 & op(e0, e3) = e2
% 228.80/40.29  | | | 
% 228.80/40.29  | | | ALPHA: (75) implies:
% 228.80/40.29  | | |   (76)  all_57_12 = e2
% 228.80/40.29  | | | 
% 228.80/40.29  | | | BETA: splitting (20) gives:
% 228.80/40.29  | | | 
% 228.80/40.29  | | | Case 1:
% 228.80/40.29  | | | | 
% 228.80/40.29  | | | |   (77)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2)
% 228.80/40.29  | | | |           = e2)
% 228.80/40.29  | | | | 
% 228.80/40.29  | | | | BETA: splitting (77) gives:
% 228.80/40.29  | | | | 
% 228.80/40.29  | | | | Case 1:
% 228.80/40.29  | | | | | 
% 228.80/40.29  | | | | |   (78)  all_57_0 = e2 & op(e3, e3) = e2
% 228.80/40.29  | | | | | 
% 228.80/40.29  | | | | | ALPHA: (78) implies:
% 228.80/40.29  | | | | |   (79)  op(e3, e3) = e2
% 228.80/40.29  | | | | | 
% 228.80/40.29  | | | | | REF_CLOSE: (9), (33), (38), (79) are inconsistent by sub-proof #2403.
% 228.80/40.29  | | | | | 
% 228.80/40.29  | | | | Case 2:
% 228.80/40.29  | | | | | 
% 228.80/40.29  | | | | |   (80)  all_57_1 = e2 & op(e3, e2) = e2
% 228.80/40.29  | | | | | 
% 228.80/40.29  | | | | | ALPHA: (80) implies:
% 228.80/40.29  | | | | |   (81)  all_57_1 = e2
% 228.80/40.29  | | | | | 
% 228.80/40.29  | | | | | BETA: splitting (4) gives:
% 228.80/40.29  | | | | | 
% 228.80/40.29  | | | | | Case 1:
% 228.80/40.29  | | | | | | 
% 228.80/40.29  | | | | | |   (82)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2,
% 228.80/40.29  | | | | | |             e3) = e1)
% 228.80/40.29  | | | | | | 
% 228.80/40.29  | | | | | | BETA: splitting (82) gives:
% 228.80/40.29  | | | | | | 
% 228.80/40.29  | | | | | | Case 1:
% 228.80/40.29  | | | | | | | 
% 228.80/40.29  | | | | | | |   (83)  all_57_0 = e1 & op(e3, e3) = e1
% 228.80/40.29  | | | | | | | 
% 228.80/40.29  | | | | | | | ALPHA: (83) implies:
% 228.80/40.29  | | | | | | |   (84)  all_57_0 = e1
% 228.80/40.29  | | | | | | | 
% 228.80/40.29  | | | | | | | COMBINE_EQS: (30), (84) imply:
% 228.80/40.29  | | | | | | |   (85)  e1 = e0
% 228.80/40.29  | | | | | | | 
% 228.80/40.29  | | | | | | | SIMP: (85) implies:
% 228.80/40.29  | | | | | | |   (86)  e1 = e0
% 228.80/40.29  | | | | | | | 
% 228.80/40.29  | | | | | | | COMBINE_EQS: (41), (86) imply:
% 228.80/40.29  | | | | | | |   (87)  all_57_3 = e0
% 228.80/40.29  | | | | | | | 
% 228.80/40.29  | | | | | | | REF_CLOSE: (3), (7), (18), (24), (27), (32), (35), (38), (43),
% 228.80/40.29  | | | | | | |            (54), (56), (63), (64), (71), (87) are inconsistent by
% 228.80/40.29  | | | | | | |            sub-proof #967.
% 228.80/40.29  | | | | | | | 
% 228.80/40.29  | | | | | | Case 2:
% 228.80/40.29  | | | | | | | 
% 228.80/40.29  | | | | | | |   (88)  all_57_2 = e1 & op(e2, e3) = e1
% 228.80/40.29  | | | | | | | 
% 228.80/40.29  | | | | | | | REF_CLOSE: (7), (40), (88) are inconsistent by sub-proof #1928.
% 228.80/40.29  | | | | | | | 
% 228.80/40.29  | | | | | | End of split
% 228.80/40.29  | | | | | | 
% 228.80/40.29  | | | | | Case 2:
% 228.80/40.29  | | | | | | 
% 228.80/40.29  | | | | | |   (89)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0,
% 228.80/40.29  | | | | | |             e3) = e1)
% 228.80/40.29  | | | | | | 
% 228.80/40.29  | | | | | | BETA: splitting (89) gives:
% 228.80/40.29  | | | | | | 
% 228.80/40.29  | | | | | | Case 1:
% 228.80/40.29  | | | | | | | 
% 228.80/40.29  | | | | | | |   (90)  all_57_6 = e1 & op(e1, e3) = e1
% 228.80/40.29  | | | | | | | 
% 228.80/40.29  | | | | | | | ALPHA: (90) implies:
% 228.80/40.29  | | | | | | |   (91)  all_57_6 = e1
% 228.80/40.29  | | | | | | | 
% 228.80/40.29  | | | | | | | BETA: splitting (37) gives:
% 228.80/40.29  | | | | | | | 
% 228.80/40.29  | | | | | | | Case 1:
% 228.80/40.29  | | | | | | | | 
% 228.80/40.29  | | | | | | | |   (92)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 &
% 228.80/40.29  | | | | | | | |           op(e2, e2) = e0)
% 228.80/40.29  | | | | | | | | 
% 228.80/40.29  | | | | | | | | REF_CLOSE: (3), (7), (9), (18), (20), (23), (24), (27), (32),
% 228.80/40.29  | | | | | | | |            (33), (35), (38), (43), (54), (56), (63), (64), (71),
% 228.80/40.29  | | | | | | | |            (92) are inconsistent by sub-proof #966.
% 228.80/40.29  | | | | | | | | 
% 228.80/40.29  | | | | | | | Case 2:
% 228.80/40.29  | | | | | | | | 
% 228.80/40.29  | | | | | | | |   (93)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 &
% 228.80/40.29  | | | | | | | |           op(e0, e2) = e0)
% 228.80/40.29  | | | | | | | | 
% 228.80/40.29  | | | | | | | | BETA: splitting (93) gives:
% 228.80/40.29  | | | | | | | | 
% 228.80/40.29  | | | | | | | | Case 1:
% 228.80/40.29  | | | | | | | | | 
% 228.80/40.29  | | | | | | | | |   (94)  all_57_7 = e0 & op(e1, e2) = e0
% 228.80/40.29  | | | | | | | | | 
% 228.80/40.29  | | | | | | | | | ALPHA: (94) implies:
% 228.80/40.29  | | | | | | | | |   (95)  all_57_7 = e0
% 228.80/40.29  | | | | | | | | | 
% 228.80/40.29  | | | | | | | | | REF_CLOSE: (7), (9), (10), (11), (12), (24), (27), (32), (38),
% 228.80/40.29  | | | | | | | | |            (43), (54), (63), (64), (68), (91), (95) are
% 228.80/40.29  | | | | | | | | |            inconsistent by sub-proof #1735.
% 228.80/40.29  | | | | | | | | | 
% 228.80/40.29  | | | | | | | | Case 2:
% 228.80/40.29  | | | | | | | | | 
% 228.80/40.29  | | | | | | | | |   (96)  all_57_13 = e0 & op(e0, e2) = e0
% 228.80/40.29  | | | | | | | | | 
% 228.80/40.29  | | | | | | | | | ALPHA: (96) implies:
% 228.80/40.29  | | | | | | | | |   (97)  op(e0, e2) = e0
% 228.80/40.29  | | | | | | | | | 
% 228.80/40.29  | | | | | | | | | BETA: splitting (49) gives:
% 228.80/40.29  | | | | | | | | | 
% 228.80/40.29  | | | | | | | | | Case 1:
% 228.80/40.29  | | | | | | | | | | 
% 228.80/40.29  | | | | | | | | | |   (98)  all_55_2 = e1
% 228.80/40.29  | | | | | | | | | | 
% 228.80/40.29  | | | | | | | | | | COMBINE_EQS: (31), (98) imply:
% 228.80/40.29  | | | | | | | | | |   (99)  all_53_8 = e1
% 228.80/40.29  | | | | | | | | | | 
% 228.80/40.29  | | | | | | | | | | SIMP: (99) implies:
% 228.80/40.29  | | | | | | | | | |   (100)  all_53_8 = e1
% 228.80/40.29  | | | | | | | | | | 
% 228.80/40.29  | | | | | | | | | | REDUCE: (36), (100) imply:
% 228.80/40.29  | | | | | | | | | |   (101)   ~ (all_53_4 = e1)
% 228.80/40.29  | | | | | | | | | | 
% 228.80/40.29  | | | | | | | | | | REDUCE: (5), (100) imply:
% 228.80/40.29  | | | | | | | | | |   (102)   ~ (all_53_12 = e1)
% 228.80/40.29  | | | | | | | | | | 
% 228.80/40.29  | | | | | | | | | | SIMP: (102) implies:
% 228.80/40.29  | | | | | | | | | |   (103)   ~ (all_53_12 = e1)
% 228.80/40.29  | | | | | | | | | | 
% 228.80/40.29  | | | | | | | | | | BETA: splitting (13) gives:
% 228.80/40.29  | | | | | | | | | | 
% 228.80/40.29  | | | | | | | | | | Case 1:
% 228.80/40.29  | | | | | | | | | | | 
% 228.80/40.29  | | | | | | | | | | |   (104)  all_55_3 = e3
% 228.80/40.29  | | | | | | | | | | | 
% 228.80/40.29  | | | | | | | | | | | REF_CLOSE: (57), (58), (104) are inconsistent by sub-proof
% 228.80/40.29  | | | | | | | | | | |            #2169.
% 228.80/40.29  | | | | | | | | | | | 
% 228.80/40.29  | | | | | | | | | | Case 2:
% 228.80/40.29  | | | | | | | | | | | 
% 228.80/40.29  | | | | | | | | | | |   (105)  all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 228.80/40.29  | | | | | | | | | | | 
% 228.80/40.29  | | | | | | | | | | | BETA: splitting (105) gives:
% 228.80/40.29  | | | | | | | | | | | 
% 228.80/40.29  | | | | | | | | | | | Case 1:
% 228.80/40.29  | | | | | | | | | | | | 
% 228.80/40.29  | | | | | | | | | | | |   (106)  all_55_3 = e2
% 228.80/40.29  | | | | | | | | | | | | 
% 228.80/40.29  | | | | | | | | | | | | COMBINE_EQS: (57), (106) imply:
% 228.80/40.29  | | | | | | | | | | | |   (107)  all_53_12 = e2
% 228.80/40.29  | | | | | | | | | | | | 
% 228.80/40.29  | | | | | | | | | | | | SIMP: (107) implies:
% 228.80/40.29  | | | | | | | | | | | |   (108)  all_53_12 = e2
% 228.80/40.29  | | | | | | | | | | | | 
% 228.80/40.29  | | | | | | | | | | | | REDUCE: (19), (108) imply:
% 228.80/40.29  | | | | | | | | | | | |   (109)   ~ (all_53_4 = e2)
% 228.80/40.29  | | | | | | | | | | | | 
% 228.80/40.29  | | | | | | | | | | | | BETA: splitting (1) gives:
% 228.80/40.29  | | | | | | | | | | | | 
% 228.80/40.29  | | | | | | | | | | | | Case 1:
% 228.80/40.29  | | | | | | | | | | | | | 
% 228.80/40.29  | | | | | | | | | | | | |   (110)  all_55_1 = e3
% 228.80/40.29  | | | | | | | | | | | | | 
% 228.80/40.29  | | | | | | | | | | | | | COMBINE_EQS: (25), (110) imply:
% 228.80/40.29  | | | | | | | | | | | | |   (111)  all_53_4 = e3
% 228.80/40.29  | | | | | | | | | | | | | 
% 228.80/40.29  | | | | | | | | | | | | | SIMP: (111) implies:
% 228.80/40.29  | | | | | | | | | | | | |   (112)  all_53_4 = e3
% 228.80/40.29  | | | | | | | | | | | | | 
% 228.80/40.29  | | | | | | | | | | | | | REDUCE: (50), (112) imply:
% 228.80/40.29  | | | | | | | | | | | | |   (113)   ~ (all_53_6 = e3)
% 228.80/40.29  | | | | | | | | | | | | | 
% 228.80/40.29  | | | | | | | | | | | | | SIMP: (113) implies:
% 228.80/40.29  | | | | | | | | | | | | |   (114)   ~ (all_53_6 = e3)
% 228.80/40.29  | | | | | | | | | | | | | 
% 228.80/40.29  | | | | | | | | | | | | | REF_CLOSE: (2), (9), (16), (17), (26), (39), (51), (97),
% 228.80/40.29  | | | | | | | | | | | | |            (114) are inconsistent by sub-proof #883.
% 228.80/40.29  | | | | | | | | | | | | | 
% 228.80/40.29  | | | | | | | | | | | | Case 2:
% 228.80/40.29  | | | | | | | | | | | | | 
% 228.80/40.29  | | | | | | | | | | | | |   (115)  all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.80/40.29  | | | | | | | | | | | | | 
% 228.80/40.29  | | | | | | | | | | | | | REF_CLOSE: (25), (44), (101), (109), (115) are inconsistent
% 228.80/40.29  | | | | | | | | | | | | |            by sub-proof #592.
% 228.80/40.29  | | | | | | | | | | | | | 
% 228.80/40.29  | | | | | | | | | | | | End of split
% 228.80/40.29  | | | | | | | | | | | | 
% 228.80/40.29  | | | | | | | | | | | Case 2:
% 228.80/40.29  | | | | | | | | | | | | 
% 228.80/40.29  | | | | | | | | | | | |   (116)  all_55_3 = e1 | all_55_3 = e0
% 228.80/40.29  | | | | | | | | | | | | 
% 228.80/40.29  | | | | | | | | | | | | REF_CLOSE: (57), (61), (103), (116) are inconsistent by
% 228.80/40.29  | | | | | | | | | | | |            sub-proof #2132.
% 228.80/40.29  | | | | | | | | | | | | 
% 228.80/40.29  | | | | | | | | | | | End of split
% 228.80/40.29  | | | | | | | | | | | 
% 228.80/40.29  | | | | | | | | | | End of split
% 228.80/40.29  | | | | | | | | | | 
% 228.80/40.29  | | | | | | | | | Case 2:
% 228.80/40.29  | | | | | | | | | | 
% 228.80/40.29  | | | | | | | | | |   (117)  all_55_2 = e0
% 228.80/40.29  | | | | | | | | | | 
% 228.80/40.29  | | | | | | | | | | REF_CLOSE: (31), (62), (117) are inconsistent by sub-proof
% 228.80/40.29  | | | | | | | | | |            #2031.
% 228.80/40.29  | | | | | | | | | | 
% 228.80/40.29  | | | | | | | | | End of split
% 228.80/40.29  | | | | | | | | | 
% 228.80/40.29  | | | | | | | | End of split
% 228.80/40.29  | | | | | | | | 
% 228.80/40.29  | | | | | | | End of split
% 228.80/40.29  | | | | | | | 
% 228.80/40.29  | | | | | | Case 2:
% 228.80/40.29  | | | | | | | 
% 228.80/40.29  | | | | | | |   (118)  all_57_12 = e1 & op(e0, e3) = e1
% 228.80/40.29  | | | | | | | 
% 228.80/40.29  | | | | | | | REF_CLOSE: (6), (7), (9), (14), (24), (27), (37), (38), (43),
% 228.80/40.29  | | | | | | |            (47), (63), (76), (81), (118) are inconsistent by
% 228.80/40.29  | | | | | | |            sub-proof #1823.
% 228.80/40.29  | | | | | | | 
% 228.80/40.29  | | | | | | End of split
% 228.80/40.29  | | | | | | 
% 228.80/40.29  | | | | | End of split
% 228.80/40.29  | | | | | 
% 228.80/40.29  | | | | End of split
% 228.80/40.29  | | | | 
% 228.80/40.29  | | | Case 2:
% 228.80/40.29  | | | | 
% 228.80/40.29  | | | |   (119)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0)
% 228.80/40.29  | | | |            = e2)
% 228.80/40.29  | | | | 
% 228.80/40.29  | | | | BETA: splitting (119) gives:
% 228.80/40.29  | | | | 
% 228.80/40.29  | | | | Case 1:
% 228.80/40.29  | | | | | 
% 228.80/40.29  | | | | |   (120)  all_57_4 = e2 & op(e3, e1) = e2
% 228.80/40.29  | | | | | 
% 228.80/40.29  | | | | | REF_CLOSE: (23), (24), (120) are inconsistent by sub-proof #2487.
% 228.80/40.29  | | | | | 
% 228.80/40.29  | | | | Case 2:
% 228.80/40.29  | | | | | 
% 228.80/40.29  | | | | |   (121)  all_57_9 = e2 & op(e3, e0) = e2
% 228.80/40.29  | | | | | 
% 228.80/40.29  | | | | | REF_CLOSE: (18), (63), (121) are inconsistent by sub-proof #2481.
% 228.80/40.29  | | | | | 
% 228.80/40.29  | | | | End of split
% 228.80/40.29  | | | | 
% 228.80/40.29  | | | End of split
% 228.80/40.29  | | | 
% 228.80/40.29  | | Case 2:
% 228.80/40.29  | | | 
% 228.80/40.29  | | |   (122)  all_57_13 = e2 & op(e0, e2) = e2
% 228.80/40.29  | | | 
% 228.80/40.29  | | | REF_CLOSE: (3), (4), (6), (7), (8), (9), (10), (11), (12), (14), (15),
% 228.80/40.29  | | |            (18), (20), (21), (22), (23), (24), (27), (28), (29), (32),
% 228.80/40.29  | | |            (33), (34), (35), (37), (38), (40), (41), (42), (43), (45),
% 228.80/40.29  | | |            (47), (48), (52), (53), (54), (56), (58), (59), (60), (61),
% 228.80/40.29  | | |            (63), (64), (65), (66), (67), (68), (69), (70), (71), (72),
% 228.80/40.29  | | |            (73), (122) are inconsistent by sub-proof #965.
% 228.80/40.29  | | | 
% 228.80/40.29  | | End of split
% 228.80/40.29  | | 
% 228.80/40.29  | Case 2:
% 228.80/40.29  | | 
% 228.80/40.29  | |   (123)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.80/40.29  | |            e2)
% 228.80/40.29  | | 
% 228.80/40.29  | | BETA: splitting (123) gives:
% 228.80/40.29  | | 
% 228.80/40.29  | | Case 1:
% 228.80/40.29  | | | 
% 228.80/40.29  | | |   (124)  all_57_14 = e2 & op(e0, e1) = e2
% 228.80/40.29  | | | 
% 228.80/40.29  | | | ALPHA: (124) implies:
% 228.80/40.29  | | |   (125)  all_57_14 = e2
% 228.80/40.29  | | | 
% 228.80/40.29  | | | BETA: splitting (20) gives:
% 228.80/40.29  | | | 
% 228.80/40.29  | | | Case 1:
% 228.80/40.29  | | | | 
% 228.80/40.29  | | | |   (126)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2)
% 228.80/40.29  | | | |            = e2)
% 228.80/40.29  | | | | 
% 228.80/40.29  | | | | BETA: splitting (126) gives:
% 228.80/40.29  | | | | 
% 228.80/40.29  | | | | Case 1:
% 228.80/40.29  | | | | | 
% 228.80/40.29  | | | | |   (127)  all_57_0 = e2 & op(e3, e3) = e2
% 228.80/40.29  | | | | | 
% 228.80/40.29  | | | | | ALPHA: (127) implies:
% 228.80/40.29  | | | | |   (128)  op(e3, e3) = e2
% 228.80/40.29  | | | | | 
% 228.80/40.29  | | | | | REF_CLOSE: (9), (33), (38), (128) are inconsistent by sub-proof #2403.
% 228.80/40.29  | | | | | 
% 228.80/40.29  | | | | Case 2:
% 228.80/40.29  | | | | | 
% 228.80/40.29  | | | | |   (129)  all_57_1 = e2 & op(e3, e2) = e2
% 228.80/40.29  | | | | | 
% 228.80/40.29  | | | | | ALPHA: (129) implies:
% 228.80/40.29  | | | | |   (130)  all_57_1 = e2
% 228.80/40.29  | | | | | 
% 228.80/40.29  | | | | | BETA: splitting (28) gives:
% 228.80/40.29  | | | | | 
% 228.80/40.29  | | | | | Case 1:
% 228.80/40.29  | | | | | | 
% 228.80/40.29  | | | | | |   (131)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2,
% 228.80/40.29  | | | | | |              e1) = e1)
% 228.80/40.29  | | | | | | 
% 228.80/40.29  | | | | | | BETA: splitting (131) gives:
% 228.80/40.29  | | | | | | 
% 228.80/40.29  | | | | | | Case 1:
% 228.80/40.29  | | | | | | | 
% 228.80/40.29  | | | | | | |   (132)  all_57_4 = e1 & op(e3, e1) = e1
% 228.80/40.29  | | | | | | | 
% 228.80/40.29  | | | | | | | REF_CLOSE: (7), (23), (132) are inconsistent by sub-proof #2484.
% 228.80/40.29  | | | | | | | 
% 228.80/40.29  | | | | | | Case 2:
% 228.80/40.29  | | | | | | | 
% 228.80/40.29  | | | | | | |   (133)  all_57_5 = e1 & op(e2, e1) = e1
% 228.80/40.29  | | | | | | | 
% 228.80/40.29  | | | | | | | ALPHA: (133) implies:
% 228.80/40.29  | | | | | | |   (134)  all_57_5 = e1
% 228.80/40.29  | | | | | | | 
% 228.80/40.29  | | | | | | | COMBINE_EQS: (71), (134) imply:
% 228.80/40.29  | | | | | | |   (135)  e1 = e0
% 228.80/40.29  | | | | | | | 
% 228.80/40.29  | | | | | | | SIMP: (135) implies:
% 228.80/40.29  | | | | | | |   (136)  e1 = e0
% 228.80/40.29  | | | | | | | 
% 228.80/40.29  | | | | | | | COMBINE_EQS: (41), (136) imply:
% 228.80/40.29  | | | | | | |   (137)  all_57_3 = e0
% 228.80/40.29  | | | | | | | 
% 228.80/40.29  | | | | | | | REF_CLOSE: (3), (7), (9), (11), (12), (22), (24), (27), (32),
% 228.80/40.29  | | | | | | |            (34), (35), (38), (40), (43), (45), (46), (52), (54),
% 228.80/40.29  | | | | | | |            (56), (59), (63), (125), (137) are inconsistent by
% 228.80/40.29  | | | | | | |            sub-proof #591.
% 228.80/40.29  | | | | | | | 
% 228.80/40.29  | | | | | | End of split
% 228.80/40.29  | | | | | | 
% 228.80/40.29  | | | | | Case 2:
% 228.80/40.29  | | | | | | 
% 228.80/40.29  | | | | | |   (138)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 &
% 228.80/40.29  | | | | | |            op(e0, e1) = e1)
% 228.80/40.29  | | | | | | 
% 228.80/40.29  | | | | | | BETA: splitting (138) gives:
% 228.80/40.29  | | | | | | 
% 228.80/40.29  | | | | | | Case 1:
% 228.80/40.29  | | | | | | | 
% 228.80/40.29  | | | | | | |   (139)  all_57_8 = e1 & op(e1, e1) = e1
% 228.80/40.29  | | | | | | | 
% 228.80/40.29  | | | | | | | ALPHA: (139) implies:
% 228.80/40.29  | | | | | | |   (140)  op(e1, e1) = e1
% 228.80/40.29  | | | | | | | 
% 228.80/40.29  | | | | | | | REF_CLOSE: (9), (55), (63), (140) are inconsistent by sub-proof
% 228.80/40.29  | | | | | | |            #2423.
% 228.80/40.29  | | | | | | | 
% 228.80/40.29  | | | | | | Case 2:
% 228.80/40.29  | | | | | | | 
% 228.80/40.29  | | | | | | |   (141)  all_57_14 = e1 & op(e0, e1) = e1
% 228.80/40.29  | | | | | | | 
% 228.80/40.29  | | | | | | | ALPHA: (141) implies:
% 228.80/40.29  | | | | | | |   (142)  all_57_14 = e1
% 228.80/40.29  | | | | | | | 
% 228.80/40.29  | | | | | | | COMBINE_EQS: (125), (142) imply:
% 228.80/40.29  | | | | | | |   (143)  e2 = e1
% 228.80/40.29  | | | | | | | 
% 228.80/40.29  | | | | | | | COMBINE_EQS: (130), (143) imply:
% 228.80/40.29  | | | | | | |   (144)  all_57_1 = e1
% 228.80/40.29  | | | | | | | 
% 228.80/40.29  | | | | | | | REF_CLOSE: (6), (7), (9), (14), (24), (27), (37), (38), (43),
% 228.80/40.29  | | | | | | |            (47), (63), (144) are inconsistent by sub-proof #1908.
% 228.80/40.29  | | | | | | | 
% 228.80/40.29  | | | | | | End of split
% 228.80/40.29  | | | | | | 
% 228.80/40.29  | | | | | End of split
% 228.80/40.29  | | | | | 
% 228.80/40.29  | | | | End of split
% 228.80/40.29  | | | | 
% 228.80/40.29  | | | Case 2:
% 228.80/40.29  | | | | 
% 228.80/40.29  | | | |   (145)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0)
% 228.80/40.29  | | | |            = e2)
% 228.80/40.29  | | | | 
% 228.80/40.29  | | | | BETA: splitting (145) gives:
% 228.80/40.29  | | | | 
% 228.80/40.29  | | | | Case 1:
% 228.80/40.29  | | | | | 
% 228.80/40.29  | | | | |   (146)  all_57_4 = e2 & op(e3, e1) = e2
% 228.80/40.29  | | | | | 
% 228.80/40.29  | | | | | REF_CLOSE: (23), (24), (146) are inconsistent by sub-proof #2487.
% 228.80/40.29  | | | | | 
% 228.80/40.29  | | | | Case 2:
% 228.80/40.29  | | | | | 
% 228.80/40.29  | | | | |   (147)  all_57_9 = e2 & op(e3, e0) = e2
% 228.80/40.29  | | | | | 
% 228.80/40.29  | | | | | REF_CLOSE: (18), (63), (147) are inconsistent by sub-proof #2481.
% 228.80/40.29  | | | | | 
% 228.80/40.29  | | | | End of split
% 228.80/40.29  | | | | 
% 228.80/40.29  | | | End of split
% 228.80/40.29  | | | 
% 228.80/40.29  | | Case 2:
% 228.80/40.29  | | | 
% 228.80/40.29  | | |   (148)  all_57_15 = e2 & op(e0, e0) = e2
% 228.80/40.29  | | | 
% 228.80/40.29  | | | REF_CLOSE: (24), (32), (148) are inconsistent by sub-proof #2323.
% 228.80/40.29  | | | 
% 228.80/40.29  | | End of split
% 228.80/40.29  | | 
% 228.80/40.29  | End of split
% 228.80/40.29  | 
% 228.80/40.29  End of proof
% 228.80/40.29  
% 228.80/40.29  Sub-proof #591 shows that the following formulas are inconsistent:
% 228.80/40.29  ----------------------------------------------------------------
% 228.80/40.29    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.80/40.29         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.80/40.29    (2)   ~ (e3 = e1)
% 228.80/40.29    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.80/40.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.80/40.29    (4)   ~ (all_6_2 = e3)
% 228.80/40.29    (5)  op(e1, e1) = all_6_2
% 228.80/40.29    (6)  all_57_3 = e0
% 228.80/40.29    (7)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.80/40.29         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.80/40.29    (8)   ~ (e3 = e2)
% 228.80/40.29    (9)   ~ (e3 = e0)
% 228.80/40.29    (10)  all_57_15 = e3
% 228.80/40.29    (11)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.80/40.29          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.80/40.29            e1)
% 228.80/40.29    (12)  all_57_10 = e2
% 228.80/40.29    (13)   ~ (e2 = e0)
% 228.80/40.29    (14)  all_57_2 = e3
% 228.80/40.29    (15)   ~ (e1 = e0)
% 228.80/40.29    (16)  all_57_14 = e2
% 228.80/40.29    (17)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.80/40.29          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.80/40.29    (18)  all_57_8 = e2
% 228.80/40.29    (19)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.80/40.29          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.80/40.29            e2)
% 228.80/40.29    (20)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.80/40.29              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.80/40.29                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.80/40.29                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.80/40.29    (21)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.80/40.29          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.80/40.29    (22)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.80/40.29          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.80/40.29    (23)   ~ (e2 = e1)
% 228.80/40.29  
% 228.80/40.29  Begin of proof
% 228.80/40.29  | 
% 228.80/40.29  | BETA: splitting (7) gives:
% 228.80/40.29  | 
% 228.80/40.29  | Case 1:
% 228.80/40.29  | | 
% 228.80/40.29  | |   (24)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) =
% 228.80/40.29  | |           e0)
% 228.80/40.29  | | 
% 228.80/40.29  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13),
% 228.80/40.29  | |            (14), (15), (17), (19), (20), (21), (22), (23), (24) are
% 228.80/40.29  | |            inconsistent by sub-proof #746.
% 228.80/40.29  | | 
% 228.80/40.29  | Case 2:
% 228.80/40.29  | | 
% 228.80/40.29  | |   (25)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 228.80/40.29  | |           e0)
% 228.80/40.29  | | 
% 228.80/40.29  | | BETA: splitting (25) gives:
% 228.80/40.29  | | 
% 228.80/40.29  | | Case 1:
% 228.80/40.29  | | | 
% 228.80/40.29  | | |   (26)  all_57_8 = e0 & op(e1, e1) = e0
% 228.80/40.29  | | | 
% 228.80/40.29  | | | REF_CLOSE: (13), (18), (26) are inconsistent by sub-proof #917.
% 228.80/40.29  | | | 
% 228.80/40.29  | | Case 2:
% 228.80/40.29  | | | 
% 228.80/40.29  | | |   (27)  all_57_14 = e0 & op(e0, e1) = e0
% 228.80/40.29  | | | 
% 228.80/40.29  | | | ALPHA: (27) implies:
% 228.80/40.29  | | |   (28)  all_57_14 = e0
% 228.80/40.29  | | | 
% 228.80/40.29  | | | REF_CLOSE: (13), (16), (28) are inconsistent by sub-proof #2422.
% 228.80/40.29  | | | 
% 228.80/40.29  | | End of split
% 228.80/40.29  | | 
% 228.80/40.29  | End of split
% 228.80/40.29  | 
% 228.80/40.29  End of proof
% 228.80/40.29  
% 228.80/40.29  Sub-proof #592 shows that the following formulas are inconsistent:
% 228.80/40.29  ----------------------------------------------------------------
% 228.80/40.29    (1)   ~ (all_53_4 = e1)
% 228.80/40.29    (2)  all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 228.80/40.29    (3)  all_55_1 = all_53_4
% 228.80/40.29    (4)   ~ (all_53_4 = e0)
% 228.80/40.29    (5)   ~ (all_53_4 = e2)
% 228.80/40.29  
% 228.80/40.29  Begin of proof
% 228.80/40.29  | 
% 228.80/40.29  | BETA: splitting (2) gives:
% 228.80/40.29  | 
% 228.80/40.29  | Case 1:
% 228.80/40.29  | | 
% 228.80/40.29  | |   (6)  all_55_1 = e2
% 228.80/40.29  | | 
% 228.80/40.29  | | COMBINE_EQS: (3), (6) imply:
% 228.80/40.29  | |   (7)  all_53_4 = e2
% 228.80/40.29  | | 
% 228.80/40.29  | | REDUCE: (5), (7) imply:
% 228.80/40.29  | |   (8)  $false
% 228.80/40.29  | | 
% 228.80/40.29  | | CLOSE: (8) is inconsistent.
% 228.80/40.29  | | 
% 228.80/40.29  | Case 2:
% 228.80/40.29  | | 
% 228.80/40.29  | |   (9)  all_55_1 = e1 | all_55_1 = e0
% 228.80/40.29  | | 
% 228.80/40.29  | | REF_CLOSE: (1), (3), (4), (9) are inconsistent by sub-proof #1730.
% 228.80/40.29  | | 
% 228.80/40.29  | End of split
% 228.80/40.29  | 
% 228.80/40.29  End of proof
% 228.80/40.29  
% 228.80/40.29  Sub-proof #593 shows that the following formulas are inconsistent:
% 228.80/40.29  ----------------------------------------------------------------
% 228.80/40.29    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.80/40.29         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.80/40.29    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.80/40.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.80/40.29    (3)  e2 = e1
% 228.80/40.29    (4)  op(e2, e2) = e1
% 228.80/40.29    (5)   ~ (e3 = e2)
% 228.80/40.29    (6)   ~ (e3 = e0)
% 228.80/40.29    (7)  all_57_1 = e2
% 228.80/40.29    (8)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.80/40.29         (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 228.80/40.29    (9)   ~ (e2 = e0)
% 228.80/40.29    (10)   ~ (e1 = e0)
% 228.80/40.29    (11)  all_57_7 = e3
% 228.80/40.29    (12)   ~ (e2 = e1)
% 228.80/40.29  
% 228.80/40.29  Begin of proof
% 228.80/40.29  | 
% 228.80/40.29  | SIMP: (3) implies:
% 228.80/40.29  |   (13)  e2 = e1
% 228.80/40.29  | 
% 228.80/40.29  | COMBINE_EQS: (7), (13) imply:
% 228.80/40.29  |   (14)  all_57_1 = e1
% 228.80/40.29  | 
% 228.80/40.29  | REF_CLOSE: (1), (2), (4), (5), (6), (8), (9), (10), (11), (12), (14) are
% 228.80/40.29  |            inconsistent by sub-proof #1909.
% 228.80/40.29  | 
% 228.80/40.29  End of proof
% 228.80/40.29  
% 228.80/40.29  Sub-proof #594 shows that the following formulas are inconsistent:
% 228.80/40.29  ----------------------------------------------------------------
% 228.80/40.29    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.80/40.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.80/40.29    (2)  all_57_4 = e2
% 228.80/40.29    (3)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.80/40.29    (4)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.80/40.29         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.80/40.29    (5)   ~ (e3 = e2)
% 228.80/40.29    (6)   ~ (e3 = e0)
% 228.80/40.29    (7)  op(e3, e3) = e2
% 228.80/40.29    (8)   ~ (e2 = e0)
% 228.80/40.29    (9)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.80/40.29         (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.80/40.29    (10)   ~ (e1 = e0)
% 228.80/40.29    (11)   ~ (all_53_12 = e3)
% 228.80/40.29    (12)   ~ (e2 = e1)
% 228.80/40.29    (13)  op(e3, e0) = all_53_12
% 228.80/40.29  
% 228.80/40.29  Begin of proof
% 228.80/40.29  | 
% 228.80/40.29  | BETA: splitting (3) gives:
% 228.80/40.29  | 
% 228.80/40.29  | Case 1:
% 228.80/40.29  | | 
% 228.80/40.29  | |   (14)  all_57_4 = e1 & op(e3, e1) = e1
% 228.80/40.29  | | 
% 228.80/40.29  | | REF_CLOSE: (2), (12), (14) are inconsistent by sub-proof #2452.
% 228.80/40.29  | | 
% 228.80/40.29  | Case 2:
% 228.80/40.29  | | 
% 228.80/40.29  | |   (15)  all_57_9 = e1 & op(e3, e0) = e1
% 228.80/40.29  | | 
% 228.80/40.29  | | ALPHA: (15) implies:
% 228.80/40.29  | |   (16)  all_57_9 = e1
% 228.80/40.29  | | 
% 228.80/40.29  | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (13), (16)
% 228.80/40.29  | |            are inconsistent by sub-proof #873.
% 228.80/40.29  | | 
% 228.80/40.29  | End of split
% 228.80/40.29  | 
% 228.80/40.29  End of proof
% 228.80/40.29  
% 228.80/40.29  Sub-proof #595 shows that the following formulas are inconsistent:
% 228.80/40.29  ----------------------------------------------------------------
% 228.80/40.29    (1)   ~ (all_53_2 = e2)
% 228.80/40.29    (2)  all_57_0 = e2
% 228.80/40.29    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.80/40.29         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.80/40.29    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.80/40.29         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.80/40.29    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.80/40.29         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.80/40.29    (6)   ~ (e3 = e1)
% 228.80/40.29    (7)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.80/40.29         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.80/40.29    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.80/40.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.80/40.29    (9)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.80/40.29         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.80/40.29    (10)   ~ (all_53_3 = e3)
% 228.80/40.29    (11)   ~ (all_53_3 = all_53_7)
% 228.80/40.29    (12)   ~ (all_6_2 = e3)
% 228.80/40.29    (13)   ~ (all_53_9 = e1)
% 228.80/40.29    (14)  op(e1, e1) = all_6_2
% 228.80/40.29    (15)   ~ (all_53_1 = all_53_9)
% 228.80/40.29    (16)  op(e2, e2) = e1
% 228.80/40.29    (17)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.80/40.29          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.80/40.29    (18)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 228.80/40.29            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 228.80/40.29              e3) = all_22_1 & $i(all_22_1))
% 228.80/40.29    (19)   ~ (all_53_13 = e3)
% 228.80/40.29    (20)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.80/40.29          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.80/40.29    (21)  all_57_6 = e1
% 228.80/40.29    (22)   ~ (all_53_9 = all_53_11)
% 228.80/40.29    (23)  all_55_4 = all_53_1
% 228.80/40.29    (24)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.80/40.29          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.80/40.29    (25)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.80/40.29          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.80/40.29    (26)   ~ (e3 = e2)
% 228.80/40.29    (27)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 228.80/40.29    (28)   ~ (all_53_1 = all_53_3)
% 228.80/40.29    (29)   ~ (e3 = e0)
% 228.80/40.29    (30)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.80/40.29          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.80/40.29    (31)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.80/40.29    (32)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 228.80/40.29    (33)  all_57_15 = e3
% 228.80/40.29    (34)   ~ (all_53_9 = all_53_13)
% 228.80/40.29    (35)  op(e3, e3) = e2
% 228.80/40.29    (36)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.80/40.29          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.80/40.29            e1)
% 228.80/40.29    (37)   ~ (all_53_1 = e1)
% 228.80/40.29    (38)  op(e0, e0) = all_52_31
% 228.80/40.29    (39)  all_57_11 = e0
% 228.80/40.29    (40)  all_55_6 = all_53_9
% 228.80/40.29    (41)   ~ (all_53_1 = all_53_2)
% 228.80/40.29    (42)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.80/40.29          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 228.80/40.29    (43)   ~ (e2 = e0)
% 228.80/40.29    (44)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.80/40.29            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.80/40.29            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.80/40.29            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.80/40.29              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.80/40.29            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.80/40.29            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.80/40.29              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.80/40.29              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.80/40.29            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.80/40.29            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.80/40.29            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.80/40.29              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.80/40.29              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.80/40.29            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.80/40.29              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.80/40.29            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.80/40.29            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.80/40.29              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.80/40.29              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.80/40.29            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.80/40.29            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.80/40.29    (45)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 228.80/40.29            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 228.80/40.29              e3) = all_12_1 & $i(all_12_1))
% 228.80/40.29    (46)  all_55_12 = all_53_3
% 228.80/40.29    (47)  all_57_3 = e1
% 228.80/40.29    (48)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.80/40.29          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.80/40.29    (49)   ~ (e1 = e0)
% 228.80/40.29    (50)   ~ (all_53_3 = all_53_11)
% 228.80/40.29    (51)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.80/40.29          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.80/40.29    (52)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.80/40.29          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.80/40.29    (53)   ~ (all_53_2 = all_53_3)
% 228.80/40.29    (54)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 228.80/40.29    (55)   ~ (all_53_7 = all_53_11)
% 228.80/40.29    (56)  all_55_8 = all_53_2
% 228.80/40.29    (57)  op(e0, e0) = e3
% 228.80/40.29    (58)  op(e0, e2) = all_53_7
% 228.80/40.29    (59)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.80/40.29          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.80/40.29            e2)
% 228.80/40.29    (60)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.80/40.29              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.80/40.29                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.80/40.29                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.80/40.29    (61)   ~ (all_53_1 = all_53_13)
% 228.80/40.29    (62)  op(e2, e0) = all_53_13
% 228.80/40.29    (63)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.80/40.29          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.80/40.29    (64)   ~ (all_53_12 = e3)
% 228.80/40.29    (65)  all_57_7 = e3
% 228.80/40.29    (66)  op(e1, e3) = all_53_2
% 228.80/40.29    (67)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.80/40.29          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.80/40.30    (68)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.80/40.30          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.80/40.30    (69)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.80/40.30          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 228.80/40.30    (70)   ~ (e2 = e1)
% 228.80/40.30    (71)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.80/40.30          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.80/40.30    (72)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.80/40.30          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.80/40.30    (73)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 228.80/40.30    (74)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.80/40.30          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.80/40.30    (75)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.80/40.30          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.80/40.30    (76)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.80/40.30          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.80/40.30    (77)  op(all_52_31, all_52_31) = e0
% 228.80/40.30    (78)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.80/40.30          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.80/40.30    (79)  all_55_14 = all_53_11
% 228.80/40.30    (80)   ~ (all_53_11 = e3)
% 228.80/40.30    (81)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.80/40.30          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.80/40.30    (82)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.80/40.30          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.80/40.30    (83)  op(e3, e0) = all_53_12
% 228.80/40.30  
% 228.80/40.30  Begin of proof
% 228.80/40.30  | 
% 228.80/40.30  | BETA: splitting (68) gives:
% 228.80/40.30  | 
% 228.80/40.30  | Case 1:
% 228.80/40.30  | | 
% 228.80/40.30  | |   (84)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) =
% 228.80/40.30  | |           e3)
% 228.80/40.30  | | 
% 228.80/40.30  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13),
% 228.80/40.30  | |            (14), (15), (16), (17), (19), (20), (21), (22), (23), (24), (26),
% 228.80/40.30  | |            (27), (28), (29), (31), (32), (33), (34), (35), (36), (37), (39),
% 228.80/40.30  | |            (40), (41), (42), (43), (44), (46), (47), (48), (49), (50), (51),
% 228.80/40.30  | |            (52), (53), (54), (55), (56), (57), (58), (59), (60), (61), (62),
% 228.80/40.30  | |            (63), (64), (65), (66), (67), (68), (69), (70), (71), (73), (75),
% 228.80/40.30  | |            (76), (79), (80), (81), (83), (84) are inconsistent by sub-proof
% 228.80/40.30  | |            #600.
% 228.80/40.30  | | 
% 228.80/40.30  | Case 2:
% 228.80/40.30  | | 
% 228.80/40.30  | |   (85)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) =
% 228.80/40.30  | |           e3)
% 228.80/40.30  | | 
% 228.80/40.30  | | BETA: splitting (85) gives:
% 228.80/40.30  | | 
% 228.80/40.30  | | Case 1:
% 228.80/40.30  | | | 
% 228.80/40.30  | | |   (86)  all_57_6 = e3 & op(e1, e3) = e3
% 228.80/40.30  | | | 
% 228.80/40.30  | | | ALPHA: (86) implies:
% 228.80/40.30  | | |   (87)  all_57_6 = e3
% 228.80/40.30  | | | 
% 228.80/40.30  | | | REF_CLOSE: (6), (21), (87) are inconsistent by sub-proof #2017.
% 228.80/40.30  | | | 
% 228.80/40.30  | | Case 2:
% 228.80/40.30  | | | 
% 228.80/40.30  | | |   (88)  all_57_12 = e3 & op(e0, e3) = e3
% 228.80/40.30  | | | 
% 228.80/40.30  | | | ALPHA: (88) implies:
% 228.80/40.30  | | |   (89)  all_57_12 = e3
% 228.80/40.30  | | | 
% 228.80/40.30  | | | BETA: splitting (76) gives:
% 228.80/40.30  | | | 
% 228.80/40.30  | | | Case 1:
% 228.80/40.30  | | | | 
% 228.80/40.30  | | | |   (90)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0)
% 228.80/40.30  | | | |           = e1)
% 228.80/40.30  | | | | 
% 228.80/40.30  | | | | BETA: splitting (90) gives:
% 228.80/40.30  | | | | 
% 228.80/40.30  | | | | Case 1:
% 228.80/40.30  | | | | | 
% 228.80/40.30  | | | | |   (91)  all_57_9 = e1 & op(e3, e0) = e1
% 228.80/40.30  | | | | | 
% 228.80/40.30  | | | | | ALPHA: (91) implies:
% 228.80/40.30  | | | | |   (92)  all_57_9 = e1
% 228.80/40.30  | | | | | 
% 228.80/40.30  | | | | | BETA: splitting (71) gives:
% 228.80/40.30  | | | | | 
% 228.80/40.30  | | | | | Case 1:
% 228.80/40.30  | | | | | | 
% 228.80/40.30  | | | | | |   (93)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2,
% 228.80/40.30  | | | | | |             e0) = e2)
% 228.80/40.30  | | | | | | 
% 228.80/40.30  | | | | | | BETA: splitting (93) gives:
% 228.80/40.30  | | | | | | 
% 228.80/40.30  | | | | | | Case 1:
% 228.80/40.30  | | | | | | | 
% 228.80/40.30  | | | | | | |   (94)  all_57_9 = e2 & op(e3, e0) = e2
% 228.80/40.30  | | | | | | | 
% 228.80/40.30  | | | | | | | REF_CLOSE: (70), (92), (94) are inconsistent by sub-proof #2481.
% 228.80/40.30  | | | | | | | 
% 228.80/40.30  | | | | | | Case 2:
% 228.80/40.30  | | | | | | | 
% 228.80/40.30  | | | | | | |   (95)  all_57_10 = e2 & op(e2, e0) = e2
% 228.80/40.30  | | | | | | | 
% 228.80/40.30  | | | | | | | ALPHA: (95) implies:
% 228.80/40.30  | | | | | | |   (96)  all_57_10 = e2
% 228.80/40.30  | | | | | | |   (97)  op(e2, e0) = e2
% 228.80/40.30  | | | | | | | 
% 228.80/40.30  | | | | | | | BETA: splitting (30) gives:
% 228.80/40.30  | | | | | | | 
% 228.80/40.30  | | | | | | | Case 1:
% 228.80/40.30  | | | | | | | | 
% 228.80/40.30  | | | | | | | |   (98)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 &
% 228.80/40.30  | | | | | | | |           op(e2, e1) = e1)
% 228.80/40.30  | | | | | | | | 
% 228.80/40.30  | | | | | | | | REF_CLOSE: (1), (5), (6), (8), (9), (10), (11), (12), (13),
% 228.80/40.30  | | | | | | | |            (14), (15), (16), (17), (19), (21), (22), (23), (24),
% 228.80/40.30  | | | | | | | |            (26), (27), (28), (29), (31), (32), (33), (34), (35),
% 228.80/40.30  | | | | | | | |            (36), (37), (40), (41), (42), (43), (44), (46), (48),
% 228.80/40.30  | | | | | | | |            (49), (50), (51), (53), (54), (55), (56), (57), (58),
% 228.80/40.30  | | | | | | | |            (59), (60), (61), (62), (64), (65), (66), (70), (71),
% 228.80/40.30  | | | | | | | |            (73), (76), (79), (80), (83), (92), (97), (98) are
% 228.80/40.30  | | | | | | | |            inconsistent by sub-proof #612.
% 228.80/40.30  | | | | | | | | 
% 228.80/40.30  | | | | | | | Case 2:
% 228.80/40.30  | | | | | | | | 
% 228.80/40.30  | | | | | | | |   (99)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 &
% 228.80/40.30  | | | | | | | |           op(e0, e1) = e1)
% 228.80/40.30  | | | | | | | | 
% 228.80/40.30  | | | | | | | | BETA: splitting (99) gives:
% 228.80/40.30  | | | | | | | | 
% 228.80/40.30  | | | | | | | | Case 1:
% 228.80/40.30  | | | | | | | | | 
% 228.80/40.30  | | | | | | | | |   (100)  all_57_8 = e1 & op(e1, e1) = e1
% 228.80/40.30  | | | | | | | | | 
% 228.80/40.30  | | | | | | | | | ALPHA: (100) implies:
% 228.80/40.30  | | | | | | | | |   (101)  op(e1, e1) = e1
% 228.80/40.30  | | | | | | | | | 
% 228.80/40.30  | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 228.80/40.30  | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 228.80/40.30  | | | | | | | | |            (19), (20), (22), (23), (24), (25), (26), (27),
% 228.80/40.30  | | | | | | | | |            (28), (29), (31), (32), (33), (34), (35), (36),
% 228.80/40.30  | | | | | | | | |            (37), (38), (40), (41), (42), (43), (44), (45),
% 228.80/40.30  | | | | | | | | |            (46), (47), (48), (49), (50), (51), (52), (53),
% 228.80/40.30  | | | | | | | | |            (54), (55), (56), (57), (58), (59), (60), (61),
% 228.80/40.30  | | | | | | | | |            (62), (63), (64), (66), (67), (68), (69), (70),
% 228.80/40.30  | | | | | | | | |            (71), (72), (73), (74), (75), (76), (77), (78),
% 228.80/40.30  | | | | | | | | |            (79), (80), (81), (82), (83), (101) are
% 228.80/40.30  | | | | | | | | |            inconsistent by sub-proof #670.
% 228.80/40.30  | | | | | | | | | 
% 228.80/40.30  | | | | | | | | Case 2:
% 228.80/40.30  | | | | | | | | | 
% 228.80/40.30  | | | | | | | | |   (102)  all_57_14 = e1 & op(e0, e1) = e1
% 228.80/40.30  | | | | | | | | | 
% 228.80/40.30  | | | | | | | | | REF_CLOSE: (1), (3), (5), (6), (8), (9), (10), (11), (12),
% 228.80/40.30  | | | | | | | | |            (13), (14), (15), (16), (17), (19), (21), (22),
% 228.80/40.30  | | | | | | | | |            (23), (24), (26), (27), (28), (29), (31), (32),
% 228.80/40.30  | | | | | | | | |            (33), (34), (35), (36), (37), (40), (41), (43),
% 228.80/40.30  | | | | | | | | |            (44), (46), (49), (50), (51), (53), (54), (55),
% 228.80/40.30  | | | | | | | | |            (56), (57), (58), (59), (60), (61), (62), (63),
% 228.80/40.30  | | | | | | | | |            (66), (69), (70), (71), (73), (76), (79), (80),
% 228.80/40.30  | | | | | | | | |            (89), (96), (97), (102) are inconsistent by
% 228.80/40.30  | | | | | | | | |            sub-proof #611.
% 228.80/40.30  | | | | | | | | | 
% 228.80/40.30  | | | | | | | | End of split
% 228.84/40.30  | | | | | | | | 
% 228.84/40.30  | | | | | | | End of split
% 228.84/40.30  | | | | | | | 
% 228.84/40.30  | | | | | | End of split
% 228.84/40.30  | | | | | | 
% 228.84/40.30  | | | | | Case 2:
% 228.84/40.30  | | | | | | 
% 228.84/40.30  | | | | | |   (103)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 &
% 228.84/40.30  | | | | | |            op(e0, e0) = e2)
% 228.84/40.30  | | | | | | 
% 228.84/40.30  | | | | | | REF_CLOSE: (6), (8), (9), (12), (14), (21), (26), (29), (33), (39),
% 228.84/40.30  | | | | | |            (43), (49), (57), (60), (65), (70), (71), (76), (103) are
% 228.84/40.30  | | | | | |            inconsistent by sub-proof #610.
% 228.84/40.30  | | | | | | 
% 228.84/40.30  | | | | | End of split
% 228.84/40.30  | | | | | 
% 228.84/40.30  | | | | Case 2:
% 228.84/40.30  | | | | | 
% 228.84/40.30  | | | | |   (104)  all_57_10 = e1 & op(e2, e0) = e1
% 228.84/40.30  | | | | | 
% 228.84/40.30  | | | | | REF_CLOSE: (3), (4), (5), (6), (8), (9), (12), (14), (16), (17), (20),
% 228.84/40.30  | | | | |            (21), (24), (26), (29), (33), (35), (36), (39), (42), (43),
% 228.84/40.30  | | | | |            (47), (48), (49), (51), (52), (57), (59), (60), (64), (65),
% 228.84/40.30  | | | | |            (67), (68), (69), (70), (71), (75), (76), (81), (83), (104)
% 228.84/40.30  | | | | |            are inconsistent by sub-proof #609.
% 228.84/40.30  | | | | | 
% 228.84/40.30  | | | | End of split
% 228.84/40.30  | | | | 
% 228.84/40.30  | | | Case 2:
% 228.84/40.30  | | | | 
% 228.84/40.30  | | | |   (105)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0,
% 228.84/40.30  | | | |              e0) = e1)
% 228.84/40.30  | | | | 
% 228.84/40.30  | | | | REF_CLOSE: (3), (6), (8), (21), (26), (29), (35), (39), (43), (47),
% 228.84/40.30  | | | |            (49), (57), (63), (67), (70), (75), (89), (105) are
% 228.84/40.30  | | | |            inconsistent by sub-proof #608.
% 228.84/40.30  | | | | 
% 228.84/40.30  | | | End of split
% 228.84/40.30  | | | 
% 228.84/40.30  | | End of split
% 228.84/40.30  | | 
% 228.84/40.30  | End of split
% 228.84/40.30  | 
% 228.84/40.30  End of proof
% 228.84/40.30  
% 228.84/40.30  Sub-proof #596 shows that the following formulas are inconsistent:
% 228.84/40.30  ----------------------------------------------------------------
% 228.84/40.30    (1)   ~ (all_53_2 = e2)
% 228.84/40.30    (2)  all_57_0 = e2
% 228.84/40.30    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.84/40.30         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.84/40.30    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.84/40.30         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.84/40.30    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.84/40.30         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.84/40.30    (6)   ~ (e3 = e1)
% 228.84/40.30    (7)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.84/40.30         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.84/40.30    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.84/40.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.84/40.30    (9)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.84/40.30         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.84/40.30    (10)   ~ (all_53_3 = e3)
% 228.84/40.30    (11)   ~ (all_53_3 = all_53_7)
% 228.84/40.30    (12)   ~ (all_6_2 = e3)
% 228.84/40.30    (13)   ~ (all_53_9 = e1)
% 228.84/40.30    (14)  op(e1, e1) = all_6_2
% 228.84/40.30    (15)   ~ (all_53_1 = all_53_9)
% 228.84/40.30    (16)  op(e2, e2) = e1
% 228.84/40.30    (17)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.84/40.30          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.84/40.30    (18)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 228.84/40.30            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 228.84/40.30              e3) = all_22_1 & $i(all_22_1))
% 228.84/40.30    (19)   ~ (all_53_13 = e3)
% 228.84/40.30    (20)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.84/40.30          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.84/40.30    (21)   ~ (all_53_9 = all_53_11)
% 228.84/40.30    (22)  all_55_4 = all_53_1
% 228.84/40.30    (23)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.84/40.30          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.84/40.30    (24)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.84/40.30          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.84/40.30    (25)   ~ (e3 = e2)
% 228.84/40.30    (26)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 228.84/40.30    (27)   ~ (all_53_1 = all_53_3)
% 228.84/40.30    (28)   ~ (e3 = e0)
% 228.84/40.30    (29)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.84/40.30          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.84/40.30    (30)  all_57_6 = e0
% 228.84/40.30    (31)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.84/40.30    (32)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 228.84/40.30    (33)  all_57_15 = e3
% 228.84/40.30    (34)   ~ (all_53_9 = all_53_13)
% 228.84/40.30    (35)  op(e3, e3) = e2
% 228.84/40.30    (36)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.84/40.30          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.84/40.30            e1)
% 228.84/40.30    (37)  all_57_10 = e2
% 228.84/40.30    (38)   ~ (all_53_1 = e1)
% 228.84/40.30    (39)  op(e0, e0) = all_52_31
% 228.84/40.30    (40)  op(e2, e0) = e2
% 228.84/40.30    (41)  all_55_6 = all_53_9
% 228.84/40.30    (42)   ~ (all_53_1 = all_53_2)
% 228.84/40.30    (43)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.84/40.30          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 228.84/40.30    (44)   ~ (e2 = e0)
% 228.84/40.30    (45)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.84/40.30            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.84/40.30            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.84/40.30            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.84/40.30              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.84/40.30            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.84/40.30            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.84/40.30              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.84/40.30              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.84/40.30            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.84/40.30            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.84/40.30            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.84/40.30              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.84/40.30              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.84/40.30            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.84/40.30              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.84/40.30            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.84/40.30            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.84/40.30              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.84/40.30              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.84/40.30            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.84/40.30            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.84/40.30    (46)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 228.84/40.30            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 228.84/40.30              e3) = all_12_1 & $i(all_12_1))
% 228.84/40.30    (47)  all_55_12 = all_53_3
% 228.84/40.30    (48)  all_57_2 = e3
% 228.84/40.30    (49)  all_57_3 = e1
% 228.84/40.30    (50)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.84/40.30          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.84/40.30    (51)   ~ (e1 = e0)
% 228.84/40.30    (52)   ~ (all_53_3 = all_53_11)
% 228.84/40.30    (53)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.84/40.30          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.84/40.30    (54)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.84/40.30          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.84/40.30    (55)   ~ (all_53_2 = all_53_3)
% 228.84/40.30    (56)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 228.84/40.30    (57)   ~ (all_53_7 = all_53_11)
% 228.84/40.30    (58)  all_55_8 = all_53_2
% 228.84/40.30    (59)  op(e0, e0) = e3
% 228.84/40.30    (60)  op(e0, e2) = all_53_7
% 228.84/40.30    (61)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.84/40.30          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.84/40.30            e2)
% 228.84/40.30    (62)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.84/40.30              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.84/40.30                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.84/40.30                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.84/40.30    (63)   ~ (all_53_1 = all_53_13)
% 228.84/40.30    (64)  op(e2, e0) = all_53_13
% 228.84/40.30    (65)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.84/40.30          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.84/40.30    (66)   ~ (all_53_12 = e3)
% 228.84/40.30    (67)  all_57_7 = e3
% 228.84/40.30    (68)  op(e1, e3) = all_53_2
% 228.84/40.30    (69)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.84/40.30          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.84/40.30    (70)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.84/40.30          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.84/40.30    (71)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.84/40.30          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 228.84/40.30    (72)   ~ (e2 = e1)
% 228.84/40.30    (73)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.84/40.30          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.84/40.30    (74)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.84/40.30          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.84/40.30    (75)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 228.84/40.30    (76)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.84/40.30          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.84/40.30    (77)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.84/40.30          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.84/40.30    (78)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.84/40.30          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.84/40.30    (79)  op(all_52_31, all_52_31) = e0
% 228.84/40.30    (80)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.84/40.30          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.84/40.30    (81)  all_55_14 = all_53_11
% 228.84/40.30    (82)   ~ (all_53_11 = e3)
% 228.84/40.30    (83)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.84/40.30          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.84/40.30    (84)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.84/40.30          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.84/40.30    (85)  op(e3, e0) = all_53_12
% 228.84/40.30  
% 228.84/40.30  Begin of proof
% 228.84/40.30  | 
% 228.84/40.30  | BETA: splitting (71) gives:
% 228.84/40.30  | 
% 228.84/40.30  | Case 1:
% 228.84/40.30  | | 
% 228.84/40.30  | |   (86)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) =
% 228.84/40.30  | |           e0)
% 228.84/40.30  | | 
% 228.84/40.30  | | BETA: splitting (86) gives:
% 228.84/40.30  | | 
% 228.84/40.30  | | Case 1:
% 228.84/40.30  | | | 
% 228.84/40.30  | | |   (87)  all_57_2 = e0 & op(e2, e3) = e0
% 228.84/40.30  | | | 
% 228.84/40.30  | | | ALPHA: (87) implies:
% 228.84/40.30  | | |   (88)  all_57_2 = e0
% 228.84/40.30  | | | 
% 228.84/40.30  | | | COMBINE_EQS: (48), (88) imply:
% 228.84/40.30  | | |   (89)  e3 = e0
% 228.84/40.30  | | | 
% 228.84/40.30  | | | COMBINE_EQS: (67), (89) imply:
% 228.84/40.30  | | |   (90)  all_57_7 = e0
% 228.84/40.30  | | | 
% 228.84/40.30  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.84/40.30  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 228.84/40.30  | | |            (23), (24), (25), (26), (27), (28), (29), (31), (32), (33),
% 228.84/40.30  | | |            (34), (35), (36), (38), (39), (41), (42), (43), (44), (45),
% 228.84/40.30  | | |            (46), (47), (49), (50), (51), (52), (53), (54), (55), (56),
% 228.84/40.30  | | |            (57), (58), (59), (60), (61), (62), (63), (64), (65), (66),
% 228.84/40.30  | | |            (68), (69), (70), (71), (72), (73), (74), (75), (76), (77),
% 228.84/40.30  | | |            (78), (79), (80), (81), (82), (83), (84), (85), (90) are
% 228.84/40.30  | | |            inconsistent by sub-proof #597.
% 228.84/40.30  | | | 
% 228.84/40.30  | | Case 2:
% 228.84/40.30  | | | 
% 228.84/40.30  | | |   (91)  all_57_3 = e0 & op(e2, e2) = e0
% 228.84/40.30  | | | 
% 228.84/40.30  | | | ALPHA: (91) implies:
% 228.84/40.30  | | |   (92)  op(e2, e2) = e0
% 228.84/40.30  | | | 
% 228.84/40.30  | | | REF_CLOSE: (8), (16), (51), (92) are inconsistent by sub-proof #2352.
% 228.84/40.30  | | | 
% 228.84/40.30  | | End of split
% 228.84/40.30  | | 
% 228.84/40.30  | Case 2:
% 228.84/40.30  | | 
% 228.84/40.30  | |   (93)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 228.84/40.30  | |           e0)
% 228.84/40.30  | | 
% 228.84/40.30  | | REF_CLOSE: (1), (5), (6), (8), (9), (10), (11), (12), (13), (14), (15),
% 228.84/40.30  | |            (16), (17), (19), (21), (22), (23), (25), (26), (27), (28), (30),
% 228.84/40.30  | |            (31), (32), (33), (34), (35), (36), (37), (38), (40), (41), (42),
% 228.84/40.30  | |            (44), (45), (47), (51), (52), (53), (55), (56), (57), (58), (59),
% 228.84/40.30  | |            (60), (61), (62), (63), (64), (68), (72), (73), (75), (78), (81),
% 228.84/40.30  | |            (82), (93) are inconsistent by sub-proof #649.
% 228.84/40.30  | | 
% 228.84/40.30  | End of split
% 228.84/40.30  | 
% 228.84/40.30  End of proof
% 228.84/40.30  
% 228.84/40.30  Sub-proof #597 shows that the following formulas are inconsistent:
% 228.84/40.30  ----------------------------------------------------------------
% 228.84/40.30    (1)   ~ (all_53_2 = e2)
% 228.84/40.30    (2)  all_57_0 = e2
% 228.84/40.30    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.84/40.30         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.84/40.30    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.84/40.30         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.84/40.30    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.84/40.30         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.84/40.30    (6)   ~ (e3 = e1)
% 228.84/40.30    (7)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.84/40.30         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.84/40.30    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.84/40.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.84/40.30    (9)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.84/40.30         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.84/40.30    (10)   ~ (all_53_3 = e3)
% 228.84/40.30    (11)   ~ (all_53_3 = all_53_7)
% 228.84/40.30    (12)   ~ (all_6_2 = e3)
% 228.84/40.30    (13)   ~ (all_53_9 = e1)
% 228.84/40.30    (14)  op(e1, e1) = all_6_2
% 228.84/40.30    (15)   ~ (all_53_1 = all_53_9)
% 228.84/40.30    (16)  op(e2, e2) = e1
% 228.84/40.30    (17)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.84/40.30          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.84/40.30    (18)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 228.84/40.30            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 228.84/40.30              e3) = all_22_1 & $i(all_22_1))
% 228.84/40.30    (19)   ~ (all_53_13 = e3)
% 228.84/40.30    (20)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.84/40.30          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.84/40.30    (21)   ~ (all_53_9 = all_53_11)
% 228.84/40.30    (22)  all_55_4 = all_53_1
% 228.84/40.30    (23)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.84/40.30          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.84/40.30    (24)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.84/40.30          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.84/40.30    (25)   ~ (e3 = e2)
% 228.84/40.30    (26)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 228.84/40.30    (27)   ~ (all_53_1 = all_53_3)
% 228.84/40.30    (28)   ~ (e3 = e0)
% 228.84/40.30    (29)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.84/40.30          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.84/40.30    (30)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.84/40.30    (31)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 228.84/40.30    (32)  all_57_15 = e3
% 228.84/40.30    (33)   ~ (all_53_9 = all_53_13)
% 228.84/40.30    (34)  op(e3, e3) = e2
% 228.84/40.30    (35)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.84/40.30          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.84/40.30            e1)
% 228.84/40.30    (36)   ~ (all_53_1 = e1)
% 228.84/40.30    (37)  op(e0, e0) = all_52_31
% 228.84/40.30    (38)  all_55_6 = all_53_9
% 228.84/40.30    (39)   ~ (all_53_1 = all_53_2)
% 228.84/40.30    (40)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.84/40.30          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 228.84/40.30    (41)   ~ (e2 = e0)
% 228.84/40.30    (42)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.84/40.30            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.84/40.30            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.84/40.30            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.84/40.30              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.84/40.30            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.84/40.30            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.84/40.30              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.84/40.30              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.84/40.30            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.84/40.30            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.84/40.30            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.84/40.30              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.84/40.30              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.84/40.30            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.84/40.30              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.84/40.30            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.84/40.30            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.84/40.30              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.84/40.30              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.84/40.30            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.84/40.30            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.84/40.30    (43)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 228.84/40.30            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 228.84/40.30              e3) = all_12_1 & $i(all_12_1))
% 228.84/40.30    (44)  all_55_12 = all_53_3
% 228.84/40.30    (45)  all_57_3 = e1
% 228.84/40.30    (46)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.84/40.30          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.84/40.30    (47)   ~ (e1 = e0)
% 228.84/40.30    (48)   ~ (all_53_3 = all_53_11)
% 228.84/40.30    (49)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.84/40.30          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.84/40.31    (50)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.84/40.31          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.84/40.31    (51)   ~ (all_53_2 = all_53_3)
% 228.84/40.31    (52)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 228.84/40.31    (53)   ~ (all_53_7 = all_53_11)
% 228.84/40.31    (54)  all_55_8 = all_53_2
% 228.84/40.31    (55)  op(e0, e0) = e3
% 228.84/40.31    (56)  op(e0, e2) = all_53_7
% 228.84/40.31    (57)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.84/40.31          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.84/40.31            e2)
% 228.84/40.31    (58)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.84/40.31              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.84/40.31                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.84/40.31                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.84/40.31    (59)   ~ (all_53_1 = all_53_13)
% 228.84/40.31    (60)  op(e2, e0) = all_53_13
% 228.84/40.31    (61)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.84/40.31          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.84/40.31    (62)   ~ (all_53_12 = e3)
% 228.84/40.31    (63)  op(e1, e3) = all_53_2
% 228.84/40.31    (64)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.84/40.31          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.84/40.31    (65)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.84/40.31          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.84/40.31    (66)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.84/40.31          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 228.84/40.31    (67)   ~ (e2 = e1)
% 228.84/40.31    (68)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.84/40.31          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.84/40.31    (69)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.84/40.31          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.84/40.31    (70)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 228.84/40.31    (71)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.84/40.31          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.84/40.31    (72)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.84/40.31          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.84/40.31    (73)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.84/40.31          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.84/40.31    (74)  op(all_52_31, all_52_31) = e0
% 228.84/40.31    (75)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.84/40.31          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.84/40.31    (76)  all_55_14 = all_53_11
% 228.84/40.31    (77)   ~ (all_53_11 = e3)
% 228.84/40.31    (78)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.84/40.31          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.84/40.31    (79)  all_57_7 = e0
% 228.84/40.31    (80)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.84/40.31          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.84/40.31    (81)  op(e3, e0) = all_53_12
% 228.84/40.31  
% 228.84/40.31  Begin of proof
% 228.84/40.31  | 
% 228.84/40.31  | BETA: splitting (50) gives:
% 228.84/40.31  | 
% 228.84/40.31  | Case 1:
% 228.84/40.31  | | 
% 228.84/40.31  | |   (82)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 228.84/40.31  | |           e3)
% 228.84/40.31  | | 
% 228.84/40.31  | | BETA: splitting (82) gives:
% 228.84/40.31  | | 
% 228.84/40.31  | | Case 1:
% 228.84/40.31  | | | 
% 228.84/40.31  | | |   (83)  all_57_1 = e3 & op(e3, e2) = e3
% 228.84/40.31  | | | 
% 228.84/40.31  | | | ALPHA: (83) implies:
% 228.84/40.31  | | |   (84)  all_57_1 = e3
% 228.84/40.31  | | | 
% 228.84/40.31  | | | BETA: splitting (9) gives:
% 228.84/40.31  | | | 
% 228.84/40.31  | | | Case 1:
% 228.84/40.31  | | | | 
% 228.84/40.31  | | | |   (85)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2)
% 228.84/40.31  | | | |           = e3)
% 228.84/40.31  | | | | 
% 228.84/40.31  | | | | BETA: splitting (85) gives:
% 228.84/40.31  | | | | 
% 228.84/40.31  | | | | Case 1:
% 228.84/40.31  | | | | | 
% 228.84/40.31  | | | | |   (86)  all_57_6 = e3 & op(e1, e3) = e3
% 228.84/40.31  | | | | | 
% 228.84/40.31  | | | | | ALPHA: (86) implies:
% 228.84/40.31  | | | | |   (87)  all_57_6 = e3
% 228.84/40.31  | | | | | 
% 228.84/40.31  | | | | | BETA: splitting (75) gives:
% 228.84/40.31  | | | | | 
% 228.84/40.31  | | | | | Case 1:
% 228.84/40.31  | | | | | | 
% 228.84/40.31  | | | | | |   (88)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1,
% 228.84/40.31  | | | | | |             e2) = e1)
% 228.84/40.31  | | | | | | 
% 228.84/40.31  | | | | | | REF_CLOSE: (6), (8), (9), (12), (14), (25), (28), (32), (41), (47),
% 228.84/40.31  | | | | | |            (58), (67), (68), (73), (79), (88) are inconsistent by
% 228.84/40.31  | | | | | |            sub-proof #1155.
% 228.84/40.31  | | | | | | 
% 228.84/40.31  | | | | | Case 2:
% 228.84/40.31  | | | | | | 
% 228.84/40.31  | | | | | |   (89)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1,
% 228.84/40.31  | | | | | |             e0) = e1)
% 228.84/40.31  | | | | | | 
% 228.84/40.31  | | | | | | BETA: splitting (89) gives:
% 228.84/40.31  | | | | | | 
% 228.84/40.31  | | | | | | Case 1:
% 228.84/40.31  | | | | | | | 
% 228.84/40.31  | | | | | | |   (90)  all_57_8 = e1 & op(e1, e1) = e1
% 228.84/40.31  | | | | | | | 
% 228.84/40.31  | | | | | | | ALPHA: (90) implies:
% 228.84/40.31  | | | | | | |   (91)  op(e1, e1) = e1
% 228.84/40.31  | | | | | | | 
% 228.84/40.31  | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 228.84/40.31  | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18), (19),
% 228.84/40.31  | | | | | | |            (20), (21), (22), (23), (24), (25), (26), (27), (28),
% 228.84/40.31  | | | | | | |            (30), (31), (32), (33), (34), (35), (36), (37), (38),
% 228.84/40.31  | | | | | | |            (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 228.84/40.31  | | | | | | |            (48), (49), (50), (51), (52), (53), (54), (55), (56),
% 228.84/40.31  | | | | | | |            (57), (58), (59), (60), (61), (62), (63), (64), (65),
% 228.84/40.31  | | | | | | |            (66), (67), (68), (69), (70), (71), (72), (73), (74),
% 228.84/40.31  | | | | | | |            (75), (76), (77), (78), (80), (81), (91) are
% 228.84/40.31  | | | | | | |            inconsistent by sub-proof #670.
% 228.84/40.31  | | | | | | | 
% 228.84/40.31  | | | | | | Case 2:
% 228.84/40.31  | | | | | | | 
% 228.84/40.31  | | | | | | |   (92)  all_57_11 = e1 & op(e1, e0) = e1
% 228.84/40.31  | | | | | | | 
% 228.84/40.31  | | | | | | | ALPHA: (92) implies:
% 228.84/40.31  | | | | | | |   (93)  all_57_11 = e1
% 228.84/40.31  | | | | | | | 
% 228.84/40.31  | | | | | | | BETA: splitting (68) gives:
% 228.84/40.31  | | | | | | | 
% 228.84/40.31  | | | | | | | Case 1:
% 228.84/40.31  | | | | | | | | 
% 228.84/40.31  | | | | | | | |   (94)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 &
% 228.84/40.31  | | | | | | | |           op(e2, e0) = e2)
% 228.84/40.31  | | | | | | | | 
% 228.84/40.31  | | | | | | | | BETA: splitting (94) gives:
% 228.84/40.31  | | | | | | | | 
% 228.84/40.31  | | | | | | | | Case 1:
% 228.84/40.31  | | | | | | | | | 
% 228.84/40.31  | | | | | | | | |   (95)  all_57_9 = e2 & op(e3, e0) = e2
% 228.84/40.31  | | | | | | | | | 
% 228.84/40.31  | | | | | | | | | REF_CLOSE: (3), (5), (6), (8), (12), (14), (16), (17), (23),
% 228.84/40.31  | | | | | | | | |            (25), (28), (32), (34), (35), (40), (41), (45),
% 228.84/40.31  | | | | | | | | |            (47), (49), (50), (55), (57), (58), (64), (67),
% 228.84/40.31  | | | | | | | | |            (84), (93), (95) are inconsistent by sub-proof
% 228.84/40.31  | | | | | | | | |            #640.
% 228.84/40.31  | | | | | | | | | 
% 228.84/40.31  | | | | | | | | Case 2:
% 228.84/40.31  | | | | | | | | | 
% 228.84/40.31  | | | | | | | | |   (96)  all_57_10 = e2 & op(e2, e0) = e2
% 228.84/40.31  | | | | | | | | | 
% 228.84/40.31  | | | | | | | | | ALPHA: (96) implies:
% 228.84/40.31  | | | | | | | | |   (97)  all_57_10 = e2
% 228.84/40.31  | | | | | | | | |   (98)  op(e2, e0) = e2
% 228.84/40.31  | | | | | | | | | 
% 228.84/40.31  | | | | | | | | | BETA: splitting (61) gives:
% 228.84/40.31  | | | | | | | | | 
% 228.84/40.31  | | | | | | | | | Case 1:
% 228.84/40.31  | | | | | | | | | | 
% 228.84/40.31  | | | | | | | | | |   (99)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 &
% 228.84/40.31  | | | | | | | | | |           op(e2, e2) = e3)
% 228.84/40.31  | | | | | | | | | | 
% 228.84/40.31  | | | | | | | | | | REF_CLOSE: (2), (4), (6), (8), (16), (25), (28), (41), (47),
% 228.84/40.31  | | | | | | | | | |            (67), (69), (72), (87), (99) are inconsistent by
% 228.84/40.31  | | | | | | | | | |            sub-proof #639.
% 228.84/40.31  | | | | | | | | | | 
% 228.84/40.31  | | | | | | | | | Case 2:
% 228.84/40.31  | | | | | | | | | | 
% 228.84/40.31  | | | | | | | | | |   (100)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3
% 228.84/40.31  | | | | | | | | | |            & op(e2, e0) = e3)
% 228.84/40.31  | | | | | | | | | | 
% 228.84/40.31  | | | | | | | | | | BETA: splitting (100) gives:
% 228.84/40.31  | | | | | | | | | | 
% 228.84/40.31  | | | | | | | | | | Case 1:
% 228.84/40.31  | | | | | | | | | | | 
% 228.84/40.31  | | | | | | | | | | |   (101)  all_57_5 = e3 & op(e2, e1) = e3
% 228.84/40.31  | | | | | | | | | | | 
% 228.84/40.31  | | | | | | | | | | | ALPHA: (101) implies:
% 228.84/40.31  | | | | | | | | | | |   (102)  all_57_5 = e3
% 228.84/40.31  | | | | | | | | | | | 
% 228.84/40.31  | | | | | | | | | | | BETA: splitting (17) gives:
% 228.84/40.31  | | | | | | | | | | | 
% 228.84/40.31  | | | | | | | | | | | Case 1:
% 228.84/40.31  | | | | | | | | | | | | 
% 228.84/40.31  | | | | | | | | | | | |   (103)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 228.84/40.31  | | | | | | | | | | | |            & op(e3, e2) = e1)
% 228.84/40.31  | | | | | | | | | | | | 
% 228.84/40.31  | | | | | | | | | | | | REF_CLOSE: (5), (6), (8), (16), (25), (28), (34), (40), (41),
% 228.84/40.31  | | | | | | | | | | | |            (47), (50), (67), (103) are inconsistent by
% 228.84/40.31  | | | | | | | | | | | |            sub-proof #1677.
% 228.84/40.31  | | | | | | | | | | | | 
% 228.84/40.31  | | | | | | | | | | | Case 2:
% 228.84/40.31  | | | | | | | | | | | | 
% 228.84/40.31  | | | | | | | | | | | |   (104)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 228.84/40.31  | | | | | | | | | | | |            & op(e3, e0) = e1)
% 228.84/40.31  | | | | | | | | | | | | 
% 228.84/40.31  | | | | | | | | | | | | BETA: splitting (104) gives:
% 228.84/40.31  | | | | | | | | | | | | 
% 228.84/40.31  | | | | | | | | | | | | Case 1:
% 228.84/40.31  | | | | | | | | | | | | | 
% 228.84/40.31  | | | | | | | | | | | | |   (105)  all_57_4 = e1 & op(e3, e1) = e1
% 228.84/40.31  | | | | | | | | | | | | | 
% 228.84/40.31  | | | | | | | | | | | | | REF_CLOSE: (1), (5), (6), (8), (10), (11), (12), (13), (14),
% 228.84/40.31  | | | | | | | | | | | | |            (15), (16), (19), (21), (22), (25), (26), (27),
% 228.84/40.31  | | | | | | | | | | | | |            (30), (31), (33), (34), (36), (38), (39), (41),
% 228.84/40.31  | | | | | | | | | | | | |            (42), (44), (46), (48), (51), (52), (53), (54),
% 228.84/40.31  | | | | | | | | | | | | |            (55), (56), (59), (60), (62), (63), (67), (70),
% 228.84/40.31  | | | | | | | | | | | | |            (76), (77), (79), (81), (98), (105) are
% 228.84/40.31  | | | | | | | | | | | | |            inconsistent by sub-proof #638.
% 228.84/40.31  | | | | | | | | | | | | | 
% 228.84/40.31  | | | | | | | | | | | | Case 2:
% 228.84/40.31  | | | | | | | | | | | | | 
% 228.84/40.31  | | | | | | | | | | | | |   (106)  all_57_9 = e1 & op(e3, e0) = e1
% 228.84/40.31  | | | | | | | | | | | | | 
% 228.84/40.31  | | | | | | | | | | | | | ALPHA: (106) implies:
% 228.84/40.31  | | | | | | | | | | | | |   (107)  all_57_9 = e1
% 228.84/40.31  | | | | | | | | | | | | | 
% 228.84/40.31  | | | | | | | | | | | | | BETA: splitting (29) gives:
% 228.84/40.31  | | | | | | | | | | | | | 
% 228.84/40.31  | | | | | | | | | | | | | Case 1:
% 228.84/40.31  | | | | | | | | | | | | | | 
% 228.84/40.31  | | | | | | | | | | | | | |   (108)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 228.84/40.31  | | | | | | | | | | | | | |            & op(e2, e1) = e1)
% 228.84/40.31  | | | | | | | | | | | | | | 
% 228.84/40.31  | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (8), (16), (23), (25), (28), (34), (40),
% 228.84/40.31  | | | | | | | | | | | | | |            (41), (46), (47), (50), (62), (67), (81), (84),
% 228.84/40.31  | | | | | | | | | | | | | |            (102), (107), (108) are inconsistent by sub-proof
% 228.84/40.31  | | | | | | | | | | | | | |            #636.
% 228.84/40.31  | | | | | | | | | | | | | | 
% 228.84/40.31  | | | | | | | | | | | | | Case 2:
% 228.84/40.31  | | | | | | | | | | | | | | 
% 228.84/40.31  | | | | | | | | | | | | | |   (109)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 228.84/40.31  | | | | | | | | | | | | | |            e1 & op(e0, e1) = e1)
% 228.84/40.31  | | | | | | | | | | | | | | 
% 228.84/40.31  | | | | | | | | | | | | | | BETA: splitting (109) gives:
% 228.84/40.31  | | | | | | | | | | | | | | 
% 228.84/40.31  | | | | | | | | | | | | | | Case 1:
% 228.84/40.31  | | | | | | | | | | | | | | | 
% 228.84/40.31  | | | | | | | | | | | | | | |   (110)  all_57_8 = e1 & op(e1, e1) = e1
% 228.84/40.31  | | | | | | | | | | | | | | | 
% 228.84/40.31  | | | | | | | | | | | | | | | ALPHA: (110) implies:
% 228.84/40.31  | | | | | | | | | | | | | | |   (111)  op(e1, e1) = e1
% 228.84/40.31  | | | | | | | | | | | | | | | 
% 228.84/40.31  | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 228.84/40.31  | | | | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 228.84/40.31  | | | | | | | | | | | | | | |            (19), (20), (21), (22), (23), (24), (25), (26),
% 228.84/40.31  | | | | | | | | | | | | | | |            (27), (28), (30), (31), (32), (33), (34), (35),
% 228.84/40.31  | | | | | | | | | | | | | | |            (36), (37), (38), (39), (40), (41), (42), (43),
% 228.84/40.31  | | | | | | | | | | | | | | |            (44), (45), (46), (47), (48), (49), (50), (51),
% 228.84/40.31  | | | | | | | | | | | | | | |            (52), (53), (54), (55), (56), (57), (58), (59),
% 228.84/40.31  | | | | | | | | | | | | | | |            (60), (61), (62), (63), (64), (65), (66), (67),
% 228.84/40.31  | | | | | | | | | | | | | | |            (68), (69), (70), (71), (72), (73), (74), (75),
% 228.84/40.31  | | | | | | | | | | | | | | |            (76), (77), (78), (80), (81), (111) are
% 228.84/40.31  | | | | | | | | | | | | | | |            inconsistent by sub-proof #670.
% 228.84/40.31  | | | | | | | | | | | | | | | 
% 228.84/40.31  | | | | | | | | | | | | | | Case 2:
% 228.84/40.31  | | | | | | | | | | | | | | | 
% 228.84/40.31  | | | | | | | | | | | | | | |   (112)  all_57_14 = e1 & op(e0, e1) = e1
% 228.84/40.31  | | | | | | | | | | | | | | | 
% 228.84/40.31  | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10),
% 228.84/40.31  | | | | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (19),
% 228.84/40.31  | | | | | | | | | | | | | | |            (20), (21), (22), (23), (25), (26), (27), (28),
% 228.84/40.31  | | | | | | | | | | | | | | |            (30), (31), (32), (33), (34), (35), (36), (38),
% 228.84/40.31  | | | | | | | | | | | | | | |            (39), (40), (41), (42), (44), (45), (46), (47),
% 228.84/40.31  | | | | | | | | | | | | | | |            (48), (49), (50), (51), (52), (53), (54), (55),
% 228.84/40.31  | | | | | | | | | | | | | | |            (56), (57), (58), (59), (60), (61), (62), (63),
% 228.84/40.31  | | | | | | | | | | | | | | |            (64), (65), (66), (67), (68), (69), (70), (72),
% 228.84/40.31  | | | | | | | | | | | | | | |            (73), (76), (77), (78), (81), (84), (87), (97),
% 228.84/40.31  | | | | | | | | | | | | | | |            (98), (107), (112) are inconsistent by sub-proof
% 228.84/40.31  | | | | | | | | | | | | | | |            #632.
% 228.84/40.31  | | | | | | | | | | | | | | | 
% 228.84/40.31  | | | | | | | | | | | | | | End of split
% 228.84/40.31  | | | | | | | | | | | | | | 
% 228.84/40.31  | | | | | | | | | | | | | End of split
% 228.84/40.31  | | | | | | | | | | | | | 
% 228.84/40.31  | | | | | | | | | | | | End of split
% 228.84/40.31  | | | | | | | | | | | | 
% 228.84/40.31  | | | | | | | | | | | End of split
% 228.84/40.31  | | | | | | | | | | | 
% 228.84/40.31  | | | | | | | | | | Case 2:
% 228.84/40.31  | | | | | | | | | | | 
% 228.84/40.31  | | | | | | | | | | |   (113)  all_57_10 = e3 & op(e2, e0) = e3
% 228.84/40.31  | | | | | | | | | | | 
% 228.84/40.31  | | | | | | | | | | | ALPHA: (113) implies:
% 228.84/40.31  | | | | | | | | | | |   (114)  all_57_10 = e3
% 228.84/40.31  | | | | | | | | | | | 
% 228.84/40.31  | | | | | | | | | | | REF_CLOSE: (6), (8), (25), (28), (32), (41), (47), (55),
% 228.84/40.31  | | | | | | | | | | |            (58), (67), (68), (73), (114) are inconsistent by
% 228.84/40.31  | | | | | | | | | | |            sub-proof #1746.
% 228.84/40.31  | | | | | | | | | | | 
% 228.84/40.31  | | | | | | | | | | End of split
% 228.84/40.31  | | | | | | | | | | 
% 228.84/40.31  | | | | | | | | | End of split
% 228.84/40.31  | | | | | | | | | 
% 228.84/40.31  | | | | | | | | End of split
% 228.84/40.31  | | | | | | | | 
% 228.84/40.31  | | | | | | | Case 2:
% 228.84/40.31  | | | | | | | | 
% 228.84/40.31  | | | | | | | |   (115)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 &
% 228.84/40.31  | | | | | | | |            op(e0, e0) = e2)
% 228.84/40.31  | | | | | | | | 
% 228.84/40.31  | | | | | | | | BETA: splitting (115) gives:
% 228.84/40.31  | | | | | | | | 
% 228.84/40.31  | | | | | | | | Case 1:
% 228.84/40.31  | | | | | | | | | 
% 228.84/40.31  | | | | | | | | |   (116)  all_57_11 = e2 & op(e1, e0) = e2
% 228.84/40.31  | | | | | | | | | 
% 228.84/40.31  | | | | | | | | | REF_CLOSE: (67), (93), (116) are inconsistent by sub-proof
% 228.84/40.31  | | | | | | | | |            #2048.
% 228.84/40.31  | | | | | | | | | 
% 228.84/40.31  | | | | | | | | Case 2:
% 228.84/40.31  | | | | | | | | | 
% 228.84/40.31  | | | | | | | | |   (117)  all_57_15 = e2 & op(e0, e0) = e2
% 228.84/40.31  | | | | | | | | | 
% 228.84/40.31  | | | | | | | | | REF_CLOSE: (6), (8), (17), (23), (25), (28), (32), (34), (41),
% 228.84/40.31  | | | | | | | | |            (46), (47), (62), (67), (81), (84), (117) are
% 228.84/40.31  | | | | | | | | |            inconsistent by sub-proof #633.
% 228.84/40.31  | | | | | | | | | 
% 228.84/40.31  | | | | | | | | End of split
% 228.84/40.31  | | | | | | | | 
% 228.84/40.31  | | | | | | | End of split
% 228.84/40.31  | | | | | | | 
% 228.84/40.31  | | | | | | End of split
% 228.84/40.31  | | | | | | 
% 228.84/40.31  | | | | | End of split
% 228.84/40.31  | | | | | 
% 228.84/40.31  | | | | Case 2:
% 228.84/40.31  | | | | | 
% 228.84/40.31  | | | | |   (118)  all_57_7 = e3 & op(e1, e2) = e3
% 228.84/40.31  | | | | | 
% 228.84/40.31  | | | | | ALPHA: (118) implies:
% 228.84/40.31  | | | | |   (119)  all_57_7 = e3
% 228.84/40.31  | | | | | 
% 228.84/40.31  | | | | | REF_CLOSE: (28), (79), (119) are inconsistent by sub-proof #2269.
% 228.84/40.31  | | | | | 
% 228.84/40.31  | | | | End of split
% 228.84/40.31  | | | | 
% 228.84/40.31  | | | Case 2:
% 228.84/40.31  | | | | 
% 228.84/40.31  | | | |   (120)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1,
% 228.84/40.31  | | | |              e0) = e3)
% 228.84/40.31  | | | | 
% 228.84/40.31  | | | | REF_CLOSE: (6), (8), (12), (14), (25), (28), (32), (41), (47), (58),
% 228.84/40.31  | | | |            (67), (68), (73), (120) are inconsistent by sub-proof #1786.
% 228.84/40.31  | | | | 
% 228.84/40.31  | | | End of split
% 228.84/40.31  | | | 
% 228.84/40.31  | | Case 2:
% 228.84/40.31  | | | 
% 228.84/40.31  | | |   (121)  all_57_3 = e3 & op(e2, e2) = e3
% 228.84/40.31  | | | 
% 228.84/40.31  | | | ALPHA: (121) implies:
% 228.84/40.31  | | |   (122)  op(e2, e2) = e3
% 228.84/40.31  | | | 
% 228.84/40.31  | | | REF_CLOSE: (6), (8), (16), (122) are inconsistent by sub-proof #1912.
% 228.84/40.31  | | | 
% 228.84/40.31  | | End of split
% 228.84/40.31  | | 
% 228.84/40.31  | Case 2:
% 228.84/40.31  | | 
% 228.84/40.31  | |   (123)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 228.84/40.31  | |            e3)
% 228.84/40.31  | | 
% 228.84/40.31  | | REF_CLOSE: (6), (8), (25), (28), (32), (35), (41), (47), (55), (57), (58),
% 228.84/40.31  | |            (67), (79), (123) are inconsistent by sub-proof #993.
% 228.84/40.31  | | 
% 228.84/40.31  | End of split
% 228.84/40.31  | 
% 228.84/40.31  End of proof
% 228.84/40.31  
% 228.84/40.31  Sub-proof #598 shows that the following formulas are inconsistent:
% 228.84/40.31  ----------------------------------------------------------------
% 228.84/40.31    (1)   ~ (all_53_2 = e2)
% 228.84/40.31    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.84/40.31         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.84/40.31    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.84/40.31         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.84/40.31    (4)   ~ (e3 = e1)
% 228.84/40.31    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.84/40.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.84/40.31    (6)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.84/40.31         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.84/40.31    (7)   ~ (all_53_3 = e3)
% 228.84/40.31    (8)   ~ (all_53_3 = all_53_7)
% 228.84/40.31    (9)   ~ (all_6_2 = e3)
% 228.84/40.31    (10)   ~ (all_53_9 = e1)
% 228.84/40.31    (11)  op(e1, e1) = all_6_2
% 228.84/40.31    (12)   ~ (all_53_1 = all_53_9)
% 228.84/40.31    (13)  op(e2, e2) = e1
% 228.84/40.31    (14)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.84/40.31          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.84/40.31    (15)  all_57_4 = e0
% 228.84/40.31    (16)   ~ (all_53_13 = e3)
% 228.84/40.31    (17)   ~ (all_53_9 = all_53_11)
% 228.84/40.31    (18)  all_55_4 = all_53_1
% 228.84/40.31    (19)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.84/40.31          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.84/40.31    (20)   ~ (e3 = e2)
% 228.84/40.31    (21)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 228.84/40.31    (22)   ~ (all_53_1 = all_53_3)
% 228.84/40.31    (23)   ~ (e3 = e0)
% 228.84/40.31    (24)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.84/40.31    (25)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 228.84/40.31    (26)  all_57_15 = e3
% 228.84/40.31    (27)   ~ (all_53_9 = all_53_13)
% 228.84/40.31    (28)  op(e3, e3) = e2
% 228.84/40.31    (29)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.84/40.31          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.84/40.31            e1)
% 228.84/40.31    (30)   ~ (all_53_1 = e1)
% 228.84/40.31    (31)  op(e2, e0) = e2
% 228.84/40.31    (32)  all_57_5 = e3
% 228.84/40.31    (33)  all_55_6 = all_53_9
% 228.84/40.31    (34)   ~ (all_53_1 = all_53_2)
% 228.84/40.31    (35)   ~ (e2 = e0)
% 228.84/40.31    (36)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.84/40.31            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.84/40.31            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.84/40.31            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.84/40.31              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.84/40.31            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.84/40.31            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.84/40.31              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.84/40.31              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.84/40.31            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.84/40.31            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.84/40.31            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.84/40.31              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.84/40.31              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.84/40.31            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.84/40.31              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.84/40.31            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.84/40.31            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.84/40.31              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.84/40.31              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.84/40.31            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.84/40.31            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.84/40.31    (37)  all_55_12 = all_53_3
% 228.84/40.31    (38)   ~ (e1 = e0)
% 228.84/40.31    (39)   ~ (all_53_3 = all_53_11)
% 228.84/40.31    (40)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.84/40.31          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.84/40.31    (41)  all_57_6 = e3
% 228.84/40.31    (42)   ~ (all_53_2 = all_53_3)
% 228.84/40.31    (43)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 228.84/40.31    (44)   ~ (all_53_7 = all_53_11)
% 228.84/40.31    (45)  all_55_8 = all_53_2
% 228.84/40.31    (46)  op(e0, e0) = e3
% 228.84/40.31    (47)  op(e0, e2) = all_53_7
% 228.84/40.31    (48)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0)
% 228.84/40.31    (49)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.84/40.31          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.84/40.31            e2)
% 228.84/40.31    (50)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.84/40.31              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.84/40.31                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.84/40.31                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.84/40.31    (51)   ~ (all_53_1 = all_53_13)
% 228.84/40.31    (52)  op(e2, e0) = all_53_13
% 228.84/40.31    (53)  all_57_2 = e0
% 228.84/40.31    (54)  op(e1, e3) = all_53_2
% 228.84/40.31    (55)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.84/40.31          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.84/40.31    (56)  all_57_1 = e3
% 228.84/40.31    (57)   ~ (e2 = e1)
% 228.84/40.31    (58)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.84/40.31          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.84/40.31    (59)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 228.84/40.31    (60)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.84/40.31          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.84/40.31    (61)  all_55_14 = all_53_11
% 228.84/40.31    (62)   ~ (all_53_11 = e3)
% 228.84/40.31  
% 228.84/40.31  Begin of proof
% 228.84/40.31  | 
% 228.84/40.31  | BETA: splitting (48) gives:
% 228.84/40.31  | 
% 228.84/40.31  | Case 1:
% 228.84/40.31  | | 
% 228.84/40.31  | |   (63)  all_57_1 = e0 & op(e3, e2) = e0
% 228.84/40.31  | | 
% 228.84/40.31  | | ALPHA: (63) implies:
% 228.84/40.31  | |   (64)  all_57_1 = e0
% 228.84/40.31  | | 
% 228.84/40.31  | | COMBINE_EQS: (56), (64) imply:
% 228.84/40.31  | |   (65)  e3 = e0
% 228.84/40.31  | | 
% 228.84/40.31  | | COMBINE_EQS: (32), (65) imply:
% 228.84/40.31  | |   (66)  all_57_5 = e0
% 228.84/40.31  | | 
% 228.84/40.31  | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 228.84/40.31  | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 228.84/40.31  | |            (25), (26), (27), (28), (29), (30), (31), (33), (34), (35), (36),
% 228.84/40.31  | |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 228.84/40.31  | |            (49), (50), (51), (52), (54), (57), (58), (59), (60), (61), (62),
% 228.84/40.31  | |            (66) are inconsistent by sub-proof #617.
% 228.84/40.31  | | 
% 228.84/40.31  | Case 2:
% 228.84/40.31  | | 
% 228.84/40.31  | |   (67)  all_57_3 = e0 & op(e2, e2) = e0
% 228.84/40.31  | | 
% 228.84/40.31  | | ALPHA: (67) implies:
% 228.84/40.31  | |   (68)  all_57_3 = e0
% 228.84/40.31  | | 
% 228.84/40.31  | | REF_CLOSE: (2), (4), (20), (32), (35), (38), (53), (55), (57), (68) are
% 228.84/40.31  | |            inconsistent by sub-proof #2253.
% 228.84/40.31  | | 
% 228.84/40.31  | End of split
% 228.84/40.31  | 
% 228.84/40.31  End of proof
% 228.84/40.31  
% 228.84/40.31  Sub-proof #599 shows that the following formulas are inconsistent:
% 228.84/40.31  ----------------------------------------------------------------
% 228.84/40.31    (1)   ~ (all_53_2 = e2)
% 228.84/40.31    (2)  all_57_0 = e2
% 228.84/40.31    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.84/40.31         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.84/40.31    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.84/40.31         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.84/40.31    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.84/40.31         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.84/40.31    (6)   ~ (e3 = e1)
% 228.84/40.31    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.84/40.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.84/40.31    (8)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.84/40.31         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.84/40.31    (9)   ~ (all_53_3 = e3)
% 228.84/40.31    (10)   ~ (all_53_3 = all_53_7)
% 228.84/40.31    (11)   ~ (all_6_2 = e3)
% 228.84/40.31    (12)   ~ (all_53_9 = e1)
% 228.84/40.31    (13)  op(e1, e1) = all_6_2
% 228.84/40.31    (14)   ~ (all_53_1 = all_53_9)
% 228.84/40.31    (15)  op(e2, e2) = e1
% 228.84/40.31    (16)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.84/40.31          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.84/40.31    (17)   ~ (all_53_13 = e3)
% 228.84/40.31    (18)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.84/40.31          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.84/40.31    (19)  all_57_6 = e1
% 228.84/40.31    (20)   ~ (all_53_9 = all_53_11)
% 228.84/40.31    (21)  all_55_4 = all_53_1
% 228.84/40.31    (22)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.84/40.31          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.84/40.31    (23)   ~ (e3 = e2)
% 228.84/40.31    (24)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 228.84/40.31    (25)   ~ (all_53_1 = all_53_3)
% 228.84/40.31    (26)   ~ (e3 = e0)
% 228.84/40.31    (27)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.84/40.31          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.84/40.31    (28)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.84/40.31    (29)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 228.84/40.31    (30)  all_57_15 = e3
% 228.84/40.31    (31)   ~ (all_53_9 = all_53_13)
% 228.84/40.31    (32)  op(e3, e3) = e2
% 228.84/40.31    (33)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.84/40.31          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.84/40.31            e1)
% 228.84/40.31    (34)   ~ (all_53_1 = e1)
% 228.84/40.31    (35)  all_57_11 = e0
% 228.84/40.31    (36)  all_55_6 = all_53_9
% 228.84/40.31    (37)   ~ (all_53_1 = all_53_2)
% 228.84/40.31    (38)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.84/40.31          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 228.84/40.31    (39)   ~ (e2 = e0)
% 228.84/40.31    (40)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.84/40.31            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.84/40.31            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.84/40.31            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.84/40.31              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.84/40.31            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.84/40.31            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.84/40.31              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.84/40.31              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.84/40.31            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.84/40.31            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.84/40.31            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.84/40.31              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.84/40.31              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.84/40.31            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.84/40.31              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.84/40.31            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.84/40.31            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.84/40.31              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.84/40.31              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.84/40.31            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.84/40.31            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.84/40.31    (41)  all_55_12 = all_53_3
% 228.84/40.31    (42)  all_57_3 = e1
% 228.84/40.31    (43)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.84/40.31          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.84/40.31    (44)   ~ (e1 = e0)
% 228.84/40.31    (45)   ~ (all_53_3 = all_53_11)
% 228.84/40.31    (46)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.84/40.31          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.84/40.31    (47)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.84/40.31          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.84/40.31    (48)   ~ (all_53_2 = all_53_3)
% 228.84/40.31    (49)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 228.84/40.31    (50)   ~ (all_53_7 = all_53_11)
% 228.84/40.31    (51)  all_55_8 = all_53_2
% 228.84/40.31    (52)  op(e0, e0) = e3
% 228.84/40.31    (53)  op(e0, e2) = all_53_7
% 228.84/40.31    (54)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.84/40.31          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.84/40.31            e2)
% 228.84/40.31    (55)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.84/40.31              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.84/40.31                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.84/40.31                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.84/40.31    (56)  op(e1, e1) = e0
% 228.84/40.31    (57)   ~ (all_53_1 = all_53_13)
% 228.84/40.31    (58)  op(e2, e0) = all_53_13
% 228.84/40.31    (59)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.84/40.31          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.84/40.31    (60)   ~ (all_53_12 = e3)
% 228.84/40.32    (61)  all_57_7 = e3
% 228.84/40.32    (62)  op(e1, e3) = all_53_2
% 228.84/40.32    (63)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.84/40.32          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.84/40.32    (64)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.84/40.32          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.84/40.32    (65)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.84/40.32          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 228.84/40.32    (66)   ~ (e2 = e1)
% 228.84/40.32    (67)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.84/40.32          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.84/40.32    (68)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 228.84/40.32    (69)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.84/40.32          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.84/40.32    (70)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.84/40.32          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.84/40.32    (71)  all_55_14 = all_53_11
% 228.84/40.32    (72)   ~ (all_53_11 = e3)
% 228.84/40.32    (73)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.84/40.32          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.84/40.32    (74)  op(e3, e0) = all_53_12
% 228.84/40.32  
% 228.84/40.32  Begin of proof
% 228.84/40.32  | 
% 228.84/40.32  | BETA: splitting (64) gives:
% 228.84/40.32  | 
% 228.84/40.32  | Case 1:
% 228.84/40.32  | | 
% 228.84/40.32  | |   (75)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) =
% 228.84/40.32  | |           e3)
% 228.84/40.32  | | 
% 228.84/40.32  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.84/40.32  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 228.84/40.32  | |            (24), (25), (26), (28), (29), (30), (31), (32), (33), (34), (35),
% 228.84/40.32  | |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 228.84/40.32  | |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (57), (58),
% 228.84/40.32  | |            (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 228.84/40.32  | |            (70), (71), (72), (73), (74), (75) are inconsistent by sub-proof
% 228.84/40.32  | |            #600.
% 228.84/40.32  | | 
% 228.84/40.32  | Case 2:
% 228.84/40.32  | | 
% 228.84/40.32  | |   (76)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) =
% 228.84/40.32  | |           e3)
% 228.84/40.32  | | 
% 228.84/40.32  | | BETA: splitting (76) gives:
% 228.84/40.32  | | 
% 228.84/40.32  | | Case 1:
% 228.84/40.32  | | | 
% 228.84/40.32  | | |   (77)  all_57_6 = e3 & op(e1, e3) = e3
% 228.84/40.32  | | | 
% 228.84/40.32  | | | ALPHA: (77) implies:
% 228.84/40.32  | | |   (78)  all_57_6 = e3
% 228.84/40.32  | | | 
% 228.84/40.32  | | | REF_CLOSE: (6), (19), (78) are inconsistent by sub-proof #2017.
% 228.84/40.32  | | | 
% 228.84/40.32  | | Case 2:
% 228.84/40.32  | | | 
% 228.84/40.32  | | |   (79)  all_57_12 = e3 & op(e0, e3) = e3
% 228.84/40.32  | | | 
% 228.84/40.32  | | | ALPHA: (79) implies:
% 228.84/40.32  | | |   (80)  all_57_12 = e3
% 228.84/40.32  | | | 
% 228.84/40.32  | | | BETA: splitting (70) gives:
% 228.84/40.32  | | | 
% 228.84/40.32  | | | Case 1:
% 228.84/40.32  | | | | 
% 228.84/40.32  | | | |   (81)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0)
% 228.84/40.32  | | | |           = e1)
% 228.84/40.32  | | | | 
% 228.84/40.32  | | | | BETA: splitting (81) gives:
% 228.84/40.32  | | | | 
% 228.84/40.32  | | | | Case 1:
% 228.84/40.32  | | | | | 
% 228.84/40.32  | | | | |   (82)  all_57_9 = e1 & op(e3, e0) = e1
% 228.84/40.32  | | | | | 
% 228.84/40.32  | | | | | ALPHA: (82) implies:
% 228.84/40.32  | | | | |   (83)  all_57_9 = e1
% 228.84/40.32  | | | | | 
% 228.84/40.32  | | | | | BETA: splitting (67) gives:
% 228.84/40.32  | | | | | 
% 228.84/40.32  | | | | | Case 1:
% 228.84/40.32  | | | | | | 
% 228.84/40.32  | | | | | |   (84)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2,
% 228.84/40.32  | | | | | |             e0) = e2)
% 228.84/40.32  | | | | | | 
% 228.84/40.32  | | | | | | BETA: splitting (84) gives:
% 228.84/40.32  | | | | | | 
% 228.84/40.32  | | | | | | Case 1:
% 228.84/40.32  | | | | | | | 
% 228.84/40.32  | | | | | | |   (85)  all_57_9 = e2 & op(e3, e0) = e2
% 228.84/40.32  | | | | | | | 
% 228.84/40.32  | | | | | | | REF_CLOSE: (66), (83), (85) are inconsistent by sub-proof #2481.
% 228.84/40.32  | | | | | | | 
% 228.84/40.32  | | | | | | Case 2:
% 228.84/40.32  | | | | | | | 
% 228.84/40.32  | | | | | | |   (86)  all_57_10 = e2 & op(e2, e0) = e2
% 228.84/40.32  | | | | | | | 
% 228.84/40.32  | | | | | | | ALPHA: (86) implies:
% 228.84/40.32  | | | | | | |   (87)  all_57_10 = e2
% 228.84/40.32  | | | | | | |   (88)  op(e2, e0) = e2
% 228.84/40.32  | | | | | | | 
% 228.84/40.32  | | | | | | | BETA: splitting (27) gives:
% 228.84/40.32  | | | | | | | 
% 228.84/40.32  | | | | | | | Case 1:
% 228.84/40.32  | | | | | | | | 
% 228.84/40.32  | | | | | | | |   (89)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 &
% 228.84/40.32  | | | | | | | |           op(e2, e1) = e1)
% 228.84/40.32  | | | | | | | | 
% 228.84/40.32  | | | | | | | | REF_CLOSE: (1), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 228.84/40.32  | | | | | | | |            (14), (15), (16), (17), (19), (20), (21), (22), (23),
% 228.84/40.32  | | | | | | | |            (24), (25), (26), (28), (29), (30), (31), (32), (33),
% 228.84/40.32  | | | | | | | |            (34), (36), (37), (38), (39), (40), (41), (43), (44),
% 228.84/40.32  | | | | | | | |            (45), (46), (48), (49), (50), (51), (52), (53), (54),
% 228.84/40.32  | | | | | | | |            (55), (57), (58), (60), (61), (62), (66), (67), (68),
% 228.84/40.32  | | | | | | | |            (70), (71), (72), (74), (83), (88), (89) are
% 228.84/40.32  | | | | | | | |            inconsistent by sub-proof #612.
% 228.84/40.32  | | | | | | | | 
% 228.84/40.32  | | | | | | | Case 2:
% 228.84/40.32  | | | | | | | | 
% 228.84/40.32  | | | | | | | |   (90)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 &
% 228.84/40.32  | | | | | | | |           op(e0, e1) = e1)
% 228.84/40.32  | | | | | | | | 
% 228.84/40.32  | | | | | | | | BETA: splitting (90) gives:
% 228.84/40.32  | | | | | | | | 
% 228.84/40.32  | | | | | | | | Case 1:
% 228.84/40.32  | | | | | | | | | 
% 228.84/40.32  | | | | | | | | |   (91)  all_57_8 = e1 & op(e1, e1) = e1
% 228.84/40.32  | | | | | | | | | 
% 228.84/40.32  | | | | | | | | | ALPHA: (91) implies:
% 228.84/40.32  | | | | | | | | |   (92)  op(e1, e1) = e1
% 228.84/40.32  | | | | | | | | | 
% 228.84/40.32  | | | | | | | | | REF_CLOSE: (7), (44), (56), (92) are inconsistent by sub-proof
% 228.84/40.32  | | | | | | | | |            #2427.
% 228.84/40.32  | | | | | | | | | 
% 228.84/40.32  | | | | | | | | Case 2:
% 228.84/40.32  | | | | | | | | | 
% 228.84/40.32  | | | | | | | | |   (93)  all_57_14 = e1 & op(e0, e1) = e1
% 228.84/40.32  | | | | | | | | | 
% 228.84/40.32  | | | | | | | | | REF_CLOSE: (1), (3), (5), (6), (7), (8), (9), (10), (11),
% 228.84/40.32  | | | | | | | | |            (12), (13), (14), (15), (16), (17), (19), (20),
% 228.84/40.32  | | | | | | | | |            (21), (22), (23), (24), (25), (26), (28), (29),
% 228.84/40.32  | | | | | | | | |            (30), (31), (32), (33), (34), (36), (37), (39),
% 228.84/40.32  | | | | | | | | |            (40), (41), (44), (45), (46), (48), (49), (50),
% 228.84/40.32  | | | | | | | | |            (51), (52), (53), (54), (55), (57), (58), (59),
% 228.84/40.32  | | | | | | | | |            (62), (65), (66), (67), (68), (70), (71), (72),
% 228.84/40.32  | | | | | | | | |            (80), (87), (88), (93) are inconsistent by
% 228.84/40.32  | | | | | | | | |            sub-proof #611.
% 228.84/40.32  | | | | | | | | | 
% 228.84/40.32  | | | | | | | | End of split
% 228.84/40.32  | | | | | | | | 
% 228.84/40.32  | | | | | | | End of split
% 228.84/40.32  | | | | | | | 
% 228.84/40.32  | | | | | | End of split
% 228.84/40.32  | | | | | | 
% 228.84/40.32  | | | | | Case 2:
% 228.84/40.32  | | | | | | 
% 228.84/40.32  | | | | | |   (94)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 &
% 228.84/40.32  | | | | | |           op(e0, e0) = e2)
% 228.84/40.32  | | | | | | 
% 228.84/40.32  | | | | | | REF_CLOSE: (6), (7), (8), (11), (13), (19), (23), (26), (30), (35),
% 228.84/40.32  | | | | | |            (39), (44), (52), (55), (61), (66), (67), (70), (94) are
% 228.84/40.32  | | | | | |            inconsistent by sub-proof #610.
% 228.84/40.32  | | | | | | 
% 228.84/40.32  | | | | | End of split
% 228.84/40.32  | | | | | 
% 228.84/40.32  | | | | Case 2:
% 228.84/40.32  | | | | | 
% 228.84/40.32  | | | | |   (95)  all_57_10 = e1 & op(e2, e0) = e1
% 228.84/40.32  | | | | | 
% 228.84/40.32  | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (11), (13), (15), (16), (18),
% 228.84/40.32  | | | | |            (19), (22), (23), (26), (30), (32), (33), (35), (38), (39),
% 228.84/40.32  | | | | |            (42), (43), (44), (46), (47), (52), (54), (55), (60), (61),
% 228.84/40.32  | | | | |            (63), (64), (65), (66), (67), (69), (70), (73), (74), (95)
% 228.84/40.32  | | | | |            are inconsistent by sub-proof #609.
% 228.84/40.32  | | | | | 
% 228.84/40.32  | | | | End of split
% 228.84/40.32  | | | | 
% 228.84/40.32  | | | Case 2:
% 228.84/40.32  | | | | 
% 228.84/40.32  | | | |   (96)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0,
% 228.84/40.32  | | | |             e0) = e1)
% 228.84/40.32  | | | | 
% 228.84/40.32  | | | | REF_CLOSE: (3), (6), (7), (19), (23), (26), (32), (35), (39), (42),
% 228.84/40.32  | | | |            (44), (52), (59), (63), (66), (69), (80), (96) are
% 228.84/40.32  | | | |            inconsistent by sub-proof #608.
% 228.84/40.32  | | | | 
% 228.84/40.32  | | | End of split
% 228.84/40.32  | | | 
% 228.84/40.32  | | End of split
% 228.84/40.32  | | 
% 228.84/40.32  | End of split
% 228.84/40.32  | 
% 228.84/40.32  End of proof
% 228.84/40.32  
% 228.84/40.32  Sub-proof #600 shows that the following formulas are inconsistent:
% 228.84/40.32  ----------------------------------------------------------------
% 228.84/40.32    (1)   ~ (all_53_2 = e2)
% 228.84/40.32    (2)  all_57_0 = e2
% 228.84/40.32    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.84/40.32         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.84/40.32    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.84/40.32         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.84/40.32    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.84/40.32         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.84/40.32    (6)   ~ (e3 = e1)
% 228.84/40.32    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.84/40.32           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.84/40.32    (8)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.84/40.32         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.84/40.32    (9)   ~ (all_53_3 = e3)
% 228.84/40.32    (10)   ~ (all_53_3 = all_53_7)
% 228.84/40.32    (11)   ~ (all_6_2 = e3)
% 228.84/40.32    (12)   ~ (all_53_9 = e1)
% 228.84/40.32    (13)  op(e1, e1) = all_6_2
% 228.84/40.32    (14)   ~ (all_53_1 = all_53_9)
% 228.84/40.32    (15)  op(e2, e2) = e1
% 228.84/40.32    (16)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.84/40.32          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.84/40.32    (17)   ~ (all_53_13 = e3)
% 228.84/40.32    (18)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.84/40.32          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.84/40.32    (19)  all_57_6 = e1
% 228.84/40.32    (20)   ~ (all_53_9 = all_53_11)
% 228.84/40.32    (21)  all_55_4 = all_53_1
% 228.84/40.32    (22)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.84/40.32          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.84/40.32    (23)   ~ (e3 = e2)
% 228.84/40.32    (24)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 228.84/40.32    (25)   ~ (all_53_1 = all_53_3)
% 228.84/40.32    (26)   ~ (e3 = e0)
% 228.84/40.32    (27)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.84/40.32    (28)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 228.84/40.32    (29)  all_57_15 = e3
% 228.84/40.32    (30)   ~ (all_53_9 = all_53_13)
% 228.84/40.32    (31)  op(e3, e3) = e2
% 228.84/40.32    (32)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.84/40.32          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.84/40.32            e1)
% 228.84/40.32    (33)   ~ (all_53_1 = e1)
% 228.84/40.32    (34)  all_57_11 = e0
% 228.84/40.32    (35)  all_55_6 = all_53_9
% 228.84/40.32    (36)   ~ (all_53_1 = all_53_2)
% 228.84/40.32    (37)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.84/40.32          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 228.84/40.32    (38)   ~ (e2 = e0)
% 228.84/40.32    (39)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.84/40.32            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.84/40.32            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.84/40.32            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.84/40.32              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.84/40.32            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.84/40.32            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.84/40.32              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.84/40.32              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.84/40.32            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.84/40.32            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.84/40.32            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.84/40.32              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.84/40.32              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.84/40.32            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.84/40.32              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.84/40.32            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.84/40.32            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.84/40.32              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.84/40.32              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.84/40.32            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.84/40.32            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.84/40.32    (40)  all_55_12 = all_53_3
% 228.84/40.32    (41)  all_57_3 = e1
% 228.84/40.32    (42)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.84/40.32          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.84/40.32    (43)   ~ (e1 = e0)
% 228.84/40.32    (44)   ~ (all_53_3 = all_53_11)
% 228.84/40.32    (45)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.84/40.32          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.84/40.32    (46)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.84/40.32          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.84/40.32    (47)   ~ (all_53_2 = all_53_3)
% 228.84/40.32    (48)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 228.84/40.32    (49)   ~ (all_53_7 = all_53_11)
% 228.84/40.32    (50)  all_55_8 = all_53_2
% 228.84/40.32    (51)  op(e0, e0) = e3
% 228.84/40.32    (52)  op(e0, e2) = all_53_7
% 228.84/40.32    (53)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.84/40.32          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.84/40.32            e2)
% 228.84/40.32    (54)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.84/40.32              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.84/40.32                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.84/40.32                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.84/40.32    (55)   ~ (all_53_1 = all_53_13)
% 228.84/40.32    (56)  op(e2, e0) = all_53_13
% 228.84/40.32    (57)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.84/40.32          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.84/40.32    (58)   ~ (all_53_12 = e3)
% 228.84/40.32    (59)  all_57_7 = e3
% 228.84/40.32    (60)  op(e1, e3) = all_53_2
% 228.84/40.32    (61)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.84/40.32          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.84/40.32    (62)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.84/40.32          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.84/40.32    (63)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.84/40.32          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 228.84/40.32    (64)   ~ (e2 = e1)
% 228.84/40.32    (65)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.84/40.32          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.84/40.32    (66)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 228.84/40.32    (67)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.84/40.32          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.84/40.32    (68)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.84/40.32          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.84/40.32    (69)  all_55_14 = all_53_11
% 228.84/40.32    (70)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3)
% 228.84/40.32    (71)   ~ (all_53_11 = e3)
% 228.84/40.32    (72)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.84/40.32          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.84/40.32    (73)  op(e3, e0) = all_53_12
% 228.84/40.32  
% 228.84/40.32  Begin of proof
% 228.84/40.32  | 
% 228.84/40.32  | BETA: splitting (70) gives:
% 228.84/40.32  | 
% 228.84/40.32  | Case 1:
% 228.84/40.32  | | 
% 228.84/40.32  | |   (74)  all_57_0 = e3 & op(e3, e3) = e3
% 228.84/40.32  | | 
% 228.84/40.32  | | ALPHA: (74) implies:
% 228.84/40.32  | |   (75)  op(e3, e3) = e3
% 228.84/40.32  | | 
% 228.84/40.32  | | REF_CLOSE: (7), (23), (31), (75) are inconsistent by sub-proof #2490.
% 228.84/40.32  | | 
% 228.84/40.32  | Case 2:
% 228.84/40.32  | | 
% 228.84/40.32  | |   (76)  all_57_2 = e3 & op(e2, e3) = e3
% 228.84/40.32  | | 
% 228.84/40.32  | | ALPHA: (76) implies:
% 228.84/40.32  | |   (77)  all_57_2 = e3
% 228.84/40.32  | | 
% 228.84/40.32  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.84/40.32  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 228.84/40.32  | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 228.84/40.32  | |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 228.84/40.32  | |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), (56),
% 228.84/40.32  | |            (57), (58), (59), (60), (61), (62), (63), (64), (65), (66), (67),
% 228.84/40.32  | |            (68), (69), (71), (72), (73), (77) are inconsistent by sub-proof
% 228.84/40.32  | |            #626.
% 228.84/40.32  | | 
% 228.84/40.32  | End of split
% 228.84/40.32  | 
% 228.84/40.32  End of proof
% 228.84/40.32  
% 228.84/40.32  Sub-proof #601 shows that the following formulas are inconsistent:
% 228.84/40.32  ----------------------------------------------------------------
% 228.84/40.32    (1)   ~ (e3 = e1)
% 228.84/40.32    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.84/40.32           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.84/40.32    (3)  all_57_8 = e0 & op(e1, e1) = e0
% 228.84/40.32    (4)  op(e1, e1) = all_52_21
% 228.84/40.32    (5)  op(e0, e0) = e3
% 228.84/40.32    (6)  op(all_52_21, all_52_21) = e1
% 228.84/40.32  
% 228.84/40.32  Begin of proof
% 228.84/40.32  | 
% 228.84/40.32  | ALPHA: (3) implies:
% 228.84/40.32  |   (7)  op(e1, e1) = e0
% 228.84/40.32  | 
% 228.84/40.32  | GROUND_INST: instantiating (2) with e0, all_52_21, e1, e1, simplifying with
% 228.84/40.32  |              (4), (7) gives:
% 228.84/40.32  |   (8)  all_52_21 = e0
% 228.84/40.32  | 
% 228.84/40.32  | REDUCE: (6), (8) imply:
% 228.84/40.32  |   (9)  op(e0, e0) = e1
% 228.84/40.32  | 
% 228.84/40.32  | REF_CLOSE: (1), (2), (5), (9) are inconsistent by sub-proof #2183.
% 228.84/40.32  | 
% 228.84/40.32  End of proof
% 228.84/40.32  
% 228.84/40.32  Sub-proof #602 shows that the following formulas are inconsistent:
% 228.84/40.32  ----------------------------------------------------------------
% 228.84/40.32    (1)   ~ (all_53_2 = e2)
% 228.84/40.32    (2)  all_57_0 = e2
% 228.84/40.32    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.84/40.32         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.84/40.32    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.84/40.32         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.84/40.32    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.84/40.32         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.84/40.32    (6)   ~ (e3 = e1)
% 228.84/40.32    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.84/40.32           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.84/40.32    (8)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.84/40.32         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.84/40.32    (9)   ~ (all_53_3 = e3)
% 228.84/40.32    (10)   ~ (all_53_3 = all_53_7)
% 228.84/40.32    (11)   ~ (all_6_2 = e3)
% 228.84/40.32    (12)   ~ (all_53_9 = e1)
% 228.84/40.32    (13)  op(e1, e1) = all_6_2
% 228.84/40.32    (14)   ~ (all_53_1 = all_53_9)
% 228.84/40.32    (15)  op(e2, e2) = e1
% 228.84/40.32    (16)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.84/40.32          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.84/40.32    (17)   ~ (all_53_13 = e3)
% 228.84/40.32    (18)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.84/40.32          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.84/40.32    (19)   ~ (all_53_9 = all_53_11)
% 228.84/40.32    (20)  all_55_4 = all_53_1
% 228.84/40.32    (21)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.84/40.32          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.84/40.32    (22)   ~ (e3 = e2)
% 228.84/40.32    (23)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 228.84/40.32    (24)   ~ (all_53_1 = all_53_3)
% 228.84/40.32    (25)   ~ (e3 = e0)
% 228.84/40.32    (26)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.84/40.32          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.84/40.32    (27)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.84/40.32    (28)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 228.84/40.32    (29)  all_57_15 = e3
% 228.84/40.32    (30)   ~ (all_53_9 = all_53_13)
% 228.84/40.32    (31)  op(e3, e3) = e2
% 228.84/40.32    (32)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.84/40.32          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.84/40.32            e1)
% 228.84/40.32    (33)   ~ (all_53_1 = e1)
% 228.84/40.32    (34)  all_55_6 = all_53_9
% 228.84/40.32    (35)   ~ (all_53_1 = all_53_2)
% 228.84/40.32    (36)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.84/40.32          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 228.84/40.32    (37)   ~ (e2 = e0)
% 228.84/40.32    (38)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.84/40.32            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.84/40.32            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.84/40.32            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.84/40.32              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.84/40.32            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.84/40.32            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.84/40.32              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.84/40.32              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.84/40.32            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.84/40.32            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.84/40.32            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.84/40.32              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.84/40.32              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.84/40.32            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.84/40.32              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.84/40.32            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.84/40.32            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.84/40.32              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.84/40.32              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.84/40.32            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.84/40.32            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.84/40.32    (39)  all_55_12 = all_53_3
% 228.84/40.32    (40)  all_57_3 = e1
% 228.84/40.32    (41)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.84/40.32          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.84/40.32    (42)   ~ (e1 = e0)
% 228.84/40.32    (43)   ~ (all_53_3 = all_53_11)
% 228.84/40.32    (44)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.84/40.32          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.84/40.32    (45)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.84/40.32          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.84/40.32    (46)   ~ (all_53_2 = all_53_3)
% 228.84/40.32    (47)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 228.84/40.32    (48)   ~ (all_53_7 = all_53_11)
% 228.84/40.32    (49)  all_55_8 = all_53_2
% 228.84/40.32    (50)  op(e0, e0) = e3
% 228.84/40.32    (51)  op(e0, e2) = all_53_7
% 228.84/40.32    (52)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.84/40.32          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.84/40.32            e2)
% 228.84/40.32    (53)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.84/40.32              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.84/40.32                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.84/40.32                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.84/40.32    (54)  op(e1, e1) = e0
% 228.84/40.32    (55)   ~ (all_53_1 = all_53_13)
% 228.84/40.32    (56)  op(e2, e0) = all_53_13
% 228.84/40.32    (57)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.84/40.32          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.84/40.32    (58)   ~ (all_53_12 = e3)
% 228.84/40.32    (59)  op(e1, e3) = all_53_2
% 228.84/40.32    (60)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.84/40.32          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.84/40.32    (61)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.84/40.32          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.84/40.32    (62)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.84/40.32          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 228.84/40.32    (63)   ~ (e2 = e1)
% 228.84/40.32    (64)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.84/40.32          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.84/40.32    (65)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.84/40.32          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.84/40.32    (66)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 228.84/40.32    (67)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.84/40.32          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.84/40.32    (68)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.84/40.32          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.84/40.32    (69)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.84/40.32          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.84/40.32    (70)  all_55_14 = all_53_11
% 228.84/40.32    (71)   ~ (all_53_11 = e3)
% 228.84/40.32    (72)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.84/40.32          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.84/40.32    (73)  all_57_7 = e0
% 228.84/40.32    (74)  op(e3, e0) = all_53_12
% 228.84/40.32  
% 228.84/40.32  Begin of proof
% 228.84/40.32  | 
% 228.84/40.32  | BETA: splitting (45) gives:
% 228.84/40.32  | 
% 228.84/40.32  | Case 1:
% 228.84/40.32  | | 
% 228.84/40.32  | |   (75)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 228.84/40.32  | |           e3)
% 228.84/40.32  | | 
% 228.84/40.32  | | BETA: splitting (75) gives:
% 228.84/40.32  | | 
% 228.84/40.32  | | Case 1:
% 228.84/40.32  | | | 
% 228.84/40.32  | | |   (76)  all_57_1 = e3 & op(e3, e2) = e3
% 228.84/40.32  | | | 
% 228.84/40.32  | | | ALPHA: (76) implies:
% 228.84/40.32  | | |   (77)  all_57_1 = e3
% 228.84/40.32  | | | 
% 228.84/40.32  | | | BETA: splitting (8) gives:
% 228.84/40.32  | | | 
% 228.84/40.32  | | | Case 1:
% 228.84/40.32  | | | | 
% 228.84/40.32  | | | |   (78)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2)
% 228.84/40.32  | | | |           = e3)
% 228.84/40.32  | | | | 
% 228.84/40.32  | | | | BETA: splitting (78) gives:
% 228.84/40.32  | | | | 
% 228.84/40.32  | | | | Case 1:
% 228.84/40.32  | | | | | 
% 228.84/40.32  | | | | |   (79)  all_57_6 = e3 & op(e1, e3) = e3
% 228.84/40.32  | | | | | 
% 228.84/40.32  | | | | | ALPHA: (79) implies:
% 228.84/40.32  | | | | |   (80)  all_57_6 = e3
% 228.84/40.32  | | | | | 
% 228.84/40.32  | | | | | BETA: splitting (69) gives:
% 228.84/40.32  | | | | | 
% 228.84/40.32  | | | | | Case 1:
% 228.84/40.32  | | | | | | 
% 228.84/40.33  | | | | | |   (81)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1,
% 228.84/40.33  | | | | | |             e2) = e1)
% 228.84/40.33  | | | | | | 
% 228.84/40.33  | | | | | | REF_CLOSE: (6), (7), (8), (11), (13), (22), (25), (29), (37), (42),
% 228.84/40.33  | | | | | |            (53), (63), (64), (68), (73), (81) are inconsistent by
% 228.84/40.33  | | | | | |            sub-proof #1155.
% 228.84/40.33  | | | | | | 
% 228.84/40.33  | | | | | Case 2:
% 228.84/40.33  | | | | | | 
% 228.84/40.33  | | | | | |   (82)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1,
% 228.84/40.33  | | | | | |             e0) = e1)
% 228.84/40.33  | | | | | | 
% 228.84/40.33  | | | | | | BETA: splitting (82) gives:
% 228.84/40.33  | | | | | | 
% 228.84/40.33  | | | | | | Case 1:
% 228.84/40.33  | | | | | | | 
% 228.84/40.33  | | | | | | |   (83)  all_57_8 = e1 & op(e1, e1) = e1
% 228.84/40.33  | | | | | | | 
% 228.84/40.33  | | | | | | | ALPHA: (83) implies:
% 228.84/40.33  | | | | | | |   (84)  op(e1, e1) = e1
% 228.84/40.33  | | | | | | | 
% 228.84/40.33  | | | | | | | REF_CLOSE: (7), (42), (54), (84) are inconsistent by sub-proof
% 228.84/40.33  | | | | | | |            #2427.
% 228.84/40.33  | | | | | | | 
% 228.84/40.33  | | | | | | Case 2:
% 228.84/40.33  | | | | | | | 
% 228.84/40.33  | | | | | | |   (85)  all_57_11 = e1 & op(e1, e0) = e1
% 228.84/40.33  | | | | | | | 
% 228.84/40.33  | | | | | | | ALPHA: (85) implies:
% 228.84/40.33  | | | | | | |   (86)  all_57_11 = e1
% 228.84/40.33  | | | | | | | 
% 228.84/40.33  | | | | | | | BETA: splitting (64) gives:
% 228.84/40.33  | | | | | | | 
% 228.84/40.33  | | | | | | | Case 1:
% 228.84/40.33  | | | | | | | | 
% 228.84/40.33  | | | | | | | |   (87)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 &
% 228.84/40.33  | | | | | | | |           op(e2, e0) = e2)
% 228.84/40.33  | | | | | | | | 
% 228.84/40.33  | | | | | | | | BETA: splitting (87) gives:
% 228.84/40.33  | | | | | | | | 
% 228.84/40.33  | | | | | | | | Case 1:
% 228.84/40.33  | | | | | | | | | 
% 228.84/40.33  | | | | | | | | |   (88)  all_57_9 = e2 & op(e3, e0) = e2
% 228.84/40.33  | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | REF_CLOSE: (3), (5), (6), (7), (11), (13), (15), (16), (21),
% 228.84/40.33  | | | | | | | | |            (22), (25), (29), (31), (32), (36), (37), (40),
% 228.84/40.33  | | | | | | | | |            (42), (44), (45), (50), (52), (53), (60), (63),
% 228.84/40.33  | | | | | | | | |            (77), (86), (88) are inconsistent by sub-proof
% 228.84/40.33  | | | | | | | | |            #640.
% 228.84/40.33  | | | | | | | | | 
% 228.84/40.33  | | | | | | | | Case 2:
% 228.84/40.33  | | | | | | | | | 
% 228.84/40.33  | | | | | | | | |   (89)  all_57_10 = e2 & op(e2, e0) = e2
% 228.84/40.33  | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | ALPHA: (89) implies:
% 228.84/40.33  | | | | | | | | |   (90)  all_57_10 = e2
% 228.84/40.33  | | | | | | | | |   (91)  op(e2, e0) = e2
% 228.84/40.33  | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | BETA: splitting (16) gives:
% 228.84/40.33  | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | Case 1:
% 228.84/40.33  | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | |   (92)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 &
% 228.84/40.33  | | | | | | | | | |           op(e3, e2) = e1)
% 228.84/40.33  | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | REF_CLOSE: (5), (6), (7), (15), (22), (25), (31), (36), (37),
% 228.84/40.33  | | | | | | | | | |            (42), (45), (63), (92) are inconsistent by
% 228.84/40.33  | | | | | | | | | |            sub-proof #1677.
% 228.84/40.33  | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | Case 2:
% 228.84/40.33  | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | |   (93)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 &
% 228.84/40.33  | | | | | | | | | |           op(e3, e0) = e1)
% 228.84/40.33  | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | BETA: splitting (93) gives:
% 228.84/40.33  | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | Case 1:
% 228.84/40.33  | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | |   (94)  all_57_4 = e1 & op(e3, e1) = e1
% 228.84/40.33  | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | REF_CLOSE: (1), (5), (6), (7), (9), (10), (11), (12), (13),
% 228.84/40.33  | | | | | | | | | | |            (14), (15), (17), (19), (20), (22), (23), (24),
% 228.84/40.33  | | | | | | | | | | |            (27), (28), (30), (31), (33), (34), (35), (37),
% 228.84/40.33  | | | | | | | | | | |            (38), (39), (41), (43), (46), (47), (48), (49),
% 228.84/40.33  | | | | | | | | | | |            (50), (51), (55), (56), (58), (59), (63), (66),
% 228.84/40.33  | | | | | | | | | | |            (70), (71), (73), (74), (91), (94) are
% 228.84/40.33  | | | | | | | | | | |            inconsistent by sub-proof #638.
% 228.84/40.33  | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | Case 2:
% 228.84/40.33  | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | |   (95)  all_57_9 = e1 & op(e3, e0) = e1
% 228.84/40.33  | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | ALPHA: (95) implies:
% 228.84/40.33  | | | | | | | | | | |   (96)  all_57_9 = e1
% 228.84/40.33  | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | BETA: splitting (26) gives:
% 228.84/40.33  | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | Case 1:
% 228.84/40.33  | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | |   (97)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 228.84/40.33  | | | | | | | | | | | |           & op(e2, e1) = e1)
% 228.84/40.33  | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | BETA: splitting (97) gives:
% 228.84/40.33  | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | Case 1:
% 228.84/40.33  | | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | |   (98)  all_57_4 = e1 & op(e3, e1) = e1
% 228.84/40.33  | | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | | ALPHA: (98) implies:
% 228.84/40.33  | | | | | | | | | | | | |   (99)  all_57_4 = e1
% 228.84/40.33  | | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | | BETA: splitting (41) gives:
% 228.84/40.33  | | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | | Case 1:
% 228.84/40.33  | | | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | | |   (100)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 228.84/40.33  | | | | | | | | | | | | | |            & op(e3, e2) = e3)
% 228.84/40.33  | | | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | | | BETA: splitting (100) gives:
% 228.84/40.33  | | | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | | | Case 1:
% 228.84/40.33  | | | | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | | | |   (101)  all_57_0 = e3 & op(e3, e3) = e3
% 228.84/40.33  | | | | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | | | | ALPHA: (101) implies:
% 228.84/40.33  | | | | | | | | | | | | | | |   (102)  op(e3, e3) = e3
% 228.84/40.33  | | | | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | | | | REF_CLOSE: (7), (22), (31), (102) are inconsistent by
% 228.84/40.33  | | | | | | | | | | | | | | |            sub-proof #2490.
% 228.84/40.33  | | | | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | | | Case 2:
% 228.84/40.33  | | | | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | | | | BETA: splitting (21) gives:
% 228.84/40.33  | | | | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | | | | Case 1:
% 228.84/40.33  | | | | | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | | | | |   (103)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 228.84/40.33  | | | | | | | | | | | | | | | |            & op(e3, e2) = e0)
% 228.84/40.33  | | | | | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | | | | | REF_CLOSE: (7), (25), (31), (37), (77), (103) are
% 228.84/40.33  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1676.
% 228.84/40.33  | | | | | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | | | | Case 2:
% 228.84/40.33  | | | | | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | | | | |   (104)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 228.84/40.33  | | | | | | | | | | | | | | | |            & op(e3, e0) = e0)
% 228.84/40.33  | | | | | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | | | | | BETA: splitting (104) gives:
% 228.84/40.33  | | | | | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | | | | | Case 1:
% 228.84/40.33  | | | | | | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | | | | | |   (105)  all_57_4 = e0 & op(e3, e1) = e0
% 228.84/40.33  | | | | | | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | | | | | | ALPHA: (105) implies:
% 228.84/40.33  | | | | | | | | | | | | | | | | |   (106)  all_57_4 = e0
% 228.84/40.33  | | | | | | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | | | | | | COMBINE_EQS: (99), (106) imply:
% 228.84/40.33  | | | | | | | | | | | | | | | | |   (107)  e1 = e0
% 228.84/40.33  | | | | | | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | | | | | | COMBINE_EQS: (86), (107) imply:
% 228.84/40.33  | | | | | | | | | | | | | | | | |   (108)  all_57_11 = e0
% 228.84/40.33  | | | | | | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | | | | | | COMBINE_EQS: (96), (107) imply:
% 228.84/40.33  | | | | | | | | | | | | | | | | |   (109)  all_57_9 = e0
% 228.84/40.33  | | | | | | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (22), (29), (37), (42), (63), (64), (68),
% 228.84/40.33  | | | | | | | | | | | | | | | | |            (108), (109) are inconsistent by sub-proof #1144.
% 228.84/40.33  | | | | | | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | | | | | Case 2:
% 228.84/40.33  | | | | | | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | | | | | |   (110)  all_57_9 = e0 & op(e3, e0) = e0
% 228.84/40.33  | | | | | | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | | | | | | ALPHA: (110) implies:
% 228.84/40.33  | | | | | | | | | | | | | | | | |   (111)  all_57_9 = e0
% 228.84/40.33  | | | | | | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | | | | | | COMBINE_EQS: (96), (111) imply:
% 228.84/40.33  | | | | | | | | | | | | | | | | |   (112)  e1 = e0
% 228.84/40.33  | | | | | | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | | | | | | COMBINE_EQS: (86), (112) imply:
% 228.84/40.33  | | | | | | | | | | | | | | | | |   (113)  all_57_11 = e0
% 228.84/40.33  | | | | | | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (22), (29), (37), (42), (63), (64), (68),
% 228.84/40.33  | | | | | | | | | | | | | | | | |            (111), (113) are inconsistent by sub-proof #1144.
% 228.84/40.33  | | | | | | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | | | | | End of split
% 228.84/40.33  | | | | | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | | | | End of split
% 228.84/40.33  | | | | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | | | End of split
% 228.84/40.33  | | | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | | Case 2:
% 228.84/40.33  | | | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | | |   (114)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 228.84/40.33  | | | | | | | | | | | | | |            & op(e3, e0) = e3)
% 228.84/40.33  | | | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (58), (74), (99), (114) are inconsistent
% 228.84/40.33  | | | | | | | | | | | | | |            by sub-proof #2281.
% 228.84/40.33  | | | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | | End of split
% 228.84/40.33  | | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | Case 2:
% 228.84/40.33  | | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | |   (115)  all_57_5 = e1 & op(e2, e1) = e1
% 228.84/40.33  | | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | | ALPHA: (115) implies:
% 228.84/40.33  | | | | | | | | | | | | |   (116)  all_57_5 = e1
% 228.84/40.33  | | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | | BETA: splitting (57) gives:
% 228.84/40.33  | | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | | Case 1:
% 228.84/40.33  | | | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | | |   (117)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 228.84/40.33  | | | | | | | | | | | | | |            & op(e2, e2) = e3)
% 228.84/40.33  | | | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (6), (7), (15), (22), (25), (37), (42),
% 228.84/40.33  | | | | | | | | | | | | | |            (63), (65), (67), (80), (117) are inconsistent by
% 228.84/40.33  | | | | | | | | | | | | | |            sub-proof #639.
% 228.84/40.33  | | | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | | Case 2:
% 228.84/40.33  | | | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | | |   (118)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 228.84/40.33  | | | | | | | | | | | | | |            e3 & op(e2, e0) = e3)
% 228.84/40.33  | | | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | | | BETA: splitting (118) gives:
% 228.84/40.33  | | | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | | | Case 1:
% 228.84/40.33  | | | | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | | | |   (119)  all_57_5 = e3 & op(e2, e1) = e3
% 228.84/40.33  | | | | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (15), (22), (25), (36), (37), (42),
% 228.84/40.33  | | | | | | | | | | | | | | |            (45), (63), (77), (116), (119) are inconsistent by
% 228.84/40.33  | | | | | | | | | | | | | | |            sub-proof #621.
% 228.84/40.33  | | | | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | | | Case 2:
% 228.84/40.33  | | | | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | | | |   (120)  all_57_10 = e3 & op(e2, e0) = e3
% 228.84/40.33  | | | | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | | | | ALPHA: (120) implies:
% 228.84/40.33  | | | | | | | | | | | | | | |   (121)  all_57_10 = e3
% 228.84/40.33  | | | | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (22), (25), (29), (37), (42), (50),
% 228.84/40.33  | | | | | | | | | | | | | | |            (53), (63), (64), (68), (121) are inconsistent by
% 228.84/40.33  | | | | | | | | | | | | | | |            sub-proof #1746.
% 228.84/40.33  | | | | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | | | End of split
% 228.84/40.33  | | | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | | End of split
% 228.84/40.33  | | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | End of split
% 228.84/40.33  | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | Case 2:
% 228.84/40.33  | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | |   (122)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 228.84/40.33  | | | | | | | | | | | |            e1 & op(e0, e1) = e1)
% 228.84/40.33  | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | BETA: splitting (122) gives:
% 228.84/40.33  | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | Case 1:
% 228.84/40.33  | | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | |   (123)  all_57_8 = e1 & op(e1, e1) = e1
% 228.84/40.33  | | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | | ALPHA: (123) implies:
% 228.84/40.33  | | | | | | | | | | | | |   (124)  op(e1, e1) = e1
% 228.84/40.33  | | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | | REF_CLOSE: (7), (42), (54), (124) are inconsistent by
% 228.84/40.33  | | | | | | | | | | | | |            sub-proof #2427.
% 228.84/40.33  | | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | Case 2:
% 228.84/40.33  | | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | |   (125)  all_57_14 = e1 & op(e0, e1) = e1
% 228.84/40.33  | | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 228.84/40.33  | | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 228.84/40.33  | | | | | | | | | | | | |            (19), (20), (21), (22), (23), (24), (25), (27),
% 228.84/40.33  | | | | | | | | | | | | |            (28), (29), (30), (31), (32), (33), (34), (35),
% 228.84/40.33  | | | | | | | | | | | | |            (36), (37), (38), (39), (40), (41), (42), (43),
% 228.84/40.33  | | | | | | | | | | | | |            (44), (45), (46), (47), (48), (49), (50), (51),
% 228.84/40.33  | | | | | | | | | | | | |            (52), (53), (55), (56), (57), (58), (59), (60),
% 228.84/40.33  | | | | | | | | | | | | |            (61), (62), (63), (64), (65), (66), (67), (68),
% 228.84/40.33  | | | | | | | | | | | | |            (70), (71), (72), (74), (77), (80), (90), (91),
% 228.84/40.33  | | | | | | | | | | | | |            (96), (125) are inconsistent by sub-proof #632.
% 228.84/40.33  | | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | | End of split
% 228.84/40.33  | | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | | End of split
% 228.84/40.33  | | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | | End of split
% 228.84/40.33  | | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | End of split
% 228.84/40.33  | | | | | | | | | 
% 228.84/40.33  | | | | | | | | End of split
% 228.84/40.33  | | | | | | | | 
% 228.84/40.33  | | | | | | | Case 2:
% 228.84/40.33  | | | | | | | | 
% 228.84/40.33  | | | | | | | |   (126)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 &
% 228.84/40.33  | | | | | | | |            op(e0, e0) = e2)
% 228.84/40.33  | | | | | | | | 
% 228.84/40.33  | | | | | | | | BETA: splitting (126) gives:
% 228.84/40.33  | | | | | | | | 
% 228.84/40.33  | | | | | | | | Case 1:
% 228.84/40.33  | | | | | | | | | 
% 228.84/40.33  | | | | | | | | |   (127)  all_57_11 = e2 & op(e1, e0) = e2
% 228.84/40.33  | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | REF_CLOSE: (63), (86), (127) are inconsistent by sub-proof
% 228.84/40.33  | | | | | | | | |            #2048.
% 228.84/40.33  | | | | | | | | | 
% 228.84/40.33  | | | | | | | | Case 2:
% 228.84/40.33  | | | | | | | | | 
% 228.84/40.33  | | | | | | | | |   (128)  all_57_15 = e2 & op(e0, e0) = e2
% 228.84/40.33  | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | REF_CLOSE: (6), (7), (16), (21), (22), (25), (29), (31), (37),
% 228.84/40.33  | | | | | | | | |            (41), (42), (58), (63), (74), (77), (128) are
% 228.84/40.33  | | | | | | | | |            inconsistent by sub-proof #633.
% 228.84/40.33  | | | | | | | | | 
% 228.84/40.33  | | | | | | | | End of split
% 228.84/40.33  | | | | | | | | 
% 228.84/40.33  | | | | | | | End of split
% 228.84/40.33  | | | | | | | 
% 228.84/40.33  | | | | | | End of split
% 228.84/40.33  | | | | | | 
% 228.84/40.33  | | | | | End of split
% 228.84/40.33  | | | | | 
% 228.84/40.33  | | | | Case 2:
% 228.84/40.33  | | | | | 
% 228.84/40.33  | | | | |   (129)  all_57_7 = e3 & op(e1, e2) = e3
% 228.84/40.33  | | | | | 
% 228.84/40.33  | | | | | ALPHA: (129) implies:
% 228.84/40.33  | | | | |   (130)  all_57_7 = e3
% 228.84/40.33  | | | | | 
% 228.84/40.33  | | | | | REF_CLOSE: (25), (73), (130) are inconsistent by sub-proof #2269.
% 228.84/40.33  | | | | | 
% 228.84/40.33  | | | | End of split
% 228.84/40.33  | | | | 
% 228.84/40.33  | | | Case 2:
% 228.84/40.33  | | | | 
% 228.84/40.33  | | | |   (131)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1,
% 228.84/40.33  | | | |              e0) = e3)
% 228.84/40.33  | | | | 
% 228.84/40.33  | | | | REF_CLOSE: (6), (7), (11), (13), (22), (25), (29), (37), (42), (53),
% 228.84/40.33  | | | |            (63), (64), (68), (131) are inconsistent by sub-proof #1786.
% 228.84/40.33  | | | | 
% 228.84/40.33  | | | End of split
% 228.84/40.33  | | | 
% 228.84/40.33  | | Case 2:
% 228.84/40.33  | | | 
% 228.84/40.33  | | |   (132)  all_57_3 = e3 & op(e2, e2) = e3
% 228.84/40.33  | | | 
% 228.84/40.33  | | | ALPHA: (132) implies:
% 228.84/40.33  | | |   (133)  op(e2, e2) = e3
% 228.84/40.33  | | | 
% 228.84/40.33  | | | REF_CLOSE: (6), (7), (15), (133) are inconsistent by sub-proof #1912.
% 228.84/40.33  | | | 
% 228.84/40.33  | | End of split
% 228.84/40.33  | | 
% 228.84/40.33  | Case 2:
% 228.84/40.33  | | 
% 228.84/40.33  | |   (134)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 228.84/40.33  | |            e3)
% 228.84/40.33  | | 
% 228.84/40.33  | | REF_CLOSE: (6), (7), (22), (25), (29), (32), (37), (42), (50), (52), (53),
% 228.84/40.33  | |            (63), (73), (134) are inconsistent by sub-proof #993.
% 228.84/40.33  | | 
% 228.84/40.33  | End of split
% 228.84/40.33  | 
% 228.84/40.33  End of proof
% 228.84/40.33  
% 228.84/40.33  Sub-proof #603 shows that the following formulas are inconsistent:
% 228.84/40.33  ----------------------------------------------------------------
% 228.84/40.33    (1)   ~ (all_53_2 = e2)
% 228.84/40.33    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.84/40.33         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.84/40.33    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.84/40.33         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.84/40.33    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.84/40.33         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.84/40.33    (5)   ~ (e3 = e1)
% 228.84/40.33    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.84/40.33           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.84/40.33    (7)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.84/40.33         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.84/40.33    (8)   ~ (all_53_3 = e3)
% 228.84/40.33    (9)   ~ (all_53_3 = all_53_7)
% 228.84/40.33    (10)   ~ (all_6_2 = e3)
% 228.84/40.33    (11)   ~ (all_53_9 = e1)
% 228.84/40.33    (12)  op(e1, e1) = all_6_2
% 228.84/40.33    (13)   ~ (all_53_1 = all_53_9)
% 228.84/40.33    (14)  op(e2, e2) = e1
% 228.84/40.33    (15)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.84/40.33          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.84/40.33    (16)   ~ (all_53_13 = e3)
% 228.84/40.33    (17)  all_57_7 = e1
% 228.84/40.33    (18)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.84/40.33          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.84/40.33    (19)   ~ (all_53_9 = all_53_11)
% 228.84/40.33    (20)  all_55_4 = all_53_1
% 228.84/40.33    (21)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.84/40.33          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.84/40.33    (22)   ~ (e3 = e2)
% 228.84/40.33    (23)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 228.84/40.33    (24)   ~ (all_53_1 = all_53_3)
% 228.84/40.33    (25)   ~ (e3 = e0)
% 228.84/40.33    (26)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.84/40.33    (27)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 228.84/40.33    (28)  all_57_15 = e3
% 228.84/40.33    (29)  op(e2, e2) = all_52_11
% 228.84/40.33    (30)   ~ (all_53_9 = all_53_13)
% 228.84/40.33    (31)  op(e3, e3) = e2
% 228.84/40.33    (32)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.84/40.33          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.84/40.33            e1)
% 228.84/40.33    (33)   ~ (all_53_1 = e1)
% 228.84/40.33    (34)  all_57_11 = e0
% 228.84/40.33    (35)  all_55_6 = all_53_9
% 228.84/40.33    (36)   ~ (all_53_1 = all_53_2)
% 228.84/40.33    (37)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.84/40.33          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 228.84/40.33    (38)   ~ (e2 = e0)
% 228.84/40.33    (39)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.84/40.33            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.84/40.33            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.84/40.33            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.84/40.33              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.84/40.33            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.84/40.33            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.84/40.33              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.84/40.33              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.84/40.33            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.84/40.33            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.84/40.33            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.84/40.33              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.84/40.33              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.84/40.33            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.84/40.33              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.84/40.33            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.84/40.33            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.84/40.33              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.84/40.33              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.84/40.33            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.84/40.33            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.84/40.33    (40)  all_55_12 = all_53_3
% 228.84/40.33    (41)  all_57_3 = e1
% 228.84/40.33    (42)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.84/40.33          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.84/40.33    (43)   ~ (e1 = e0)
% 228.84/40.33    (44)   ~ (all_53_3 = all_53_11)
% 228.84/40.33    (45)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.84/40.33          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.84/40.33    (46)  all_57_6 = e3
% 228.84/40.33    (47)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.84/40.33          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.84/40.33    (48)   ~ (all_53_2 = all_53_3)
% 228.84/40.33    (49)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 228.84/40.33    (50)   ~ (all_53_7 = all_53_11)
% 228.84/40.33    (51)  all_55_8 = all_53_2
% 228.84/40.33    (52)  op(e0, e0) = e3
% 228.84/40.33    (53)  op(e0, e2) = all_53_7
% 228.84/40.33    (54)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.84/40.33          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.84/40.33            e2)
% 228.84/40.33    (55)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.84/40.33              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.84/40.33                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.84/40.33                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.84/40.33    (56)   ~ (all_53_1 = all_53_13)
% 228.84/40.33    (57)  op(e2, e0) = all_53_13
% 228.84/40.33    (58)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.84/40.33          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.84/40.33    (59)   ~ (all_53_12 = e3)
% 228.84/40.33    (60)  op(e1, e3) = all_53_2
% 228.84/40.33    (61)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.84/40.33          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.84/40.33    (62)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.84/40.33          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.84/40.33    (63)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.84/40.33          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 228.84/40.33    (64)   ~ (e2 = e1)
% 228.84/40.33    (65)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.84/40.33          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.84/40.33    (66)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 228.84/40.33    (67)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.84/40.33          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.84/40.33    (68)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.84/40.33          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.84/40.33    (69)  all_55_14 = all_53_11
% 228.84/40.33    (70)  op(all_52_11, all_52_11) = e2
% 228.84/40.33    (71)   ~ (all_53_11 = e3)
% 228.84/40.33    (72)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.84/40.33          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.84/40.33    (73)  op(e3, e0) = all_53_12
% 228.84/40.33  
% 228.84/40.33  Begin of proof
% 228.84/40.33  | 
% 228.84/40.33  | BETA: splitting (47) gives:
% 228.84/40.33  | 
% 228.84/40.33  | Case 1:
% 228.84/40.33  | | 
% 228.84/40.33  | |   (74)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 228.84/40.33  | |           e3)
% 228.84/40.33  | | 
% 228.84/40.33  | | BETA: splitting (74) gives:
% 228.84/40.33  | | 
% 228.84/40.33  | | Case 1:
% 228.84/40.33  | | | 
% 228.84/40.33  | | |   (75)  all_57_1 = e3 & op(e3, e2) = e3
% 228.84/40.33  | | | 
% 228.84/40.33  | | | ALPHA: (75) implies:
% 228.84/40.33  | | |   (76)  all_57_1 = e3
% 228.84/40.33  | | | 
% 228.84/40.33  | | | BETA: splitting (21) gives:
% 228.84/40.33  | | | 
% 228.84/40.33  | | | Case 1:
% 228.84/40.33  | | | | 
% 228.84/40.33  | | | |   (77)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2)
% 228.84/40.33  | | | |           = e0)
% 228.84/40.33  | | | | 
% 228.84/40.33  | | | | REF_CLOSE: (4), (5), (6), (7), (10), (12), (14), (22), (25), (28), (31),
% 228.84/40.33  | | | |            (37), (38), (43), (46), (55), (64), (65), (68), (72), (76),
% 228.84/40.33  | | | |            (77) are inconsistent by sub-proof #625.
% 228.84/40.33  | | | | 
% 228.84/40.33  | | | Case 2:
% 228.84/40.33  | | | | 
% 228.84/40.33  | | | |   (78)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0)
% 228.84/40.33  | | | |           = e0)
% 228.84/40.33  | | | | 
% 228.84/40.33  | | | | BETA: splitting (78) gives:
% 228.84/40.33  | | | | 
% 228.84/40.33  | | | | Case 1:
% 228.84/40.33  | | | | | 
% 228.84/40.33  | | | | |   (79)  all_57_4 = e0 & op(e3, e1) = e0
% 228.84/40.33  | | | | | 
% 228.84/40.33  | | | | | ALPHA: (79) implies:
% 228.84/40.33  | | | | |   (80)  all_57_4 = e0
% 228.84/40.33  | | | | | 
% 228.84/40.33  | | | | | BETA: splitting (65) gives:
% 228.84/40.33  | | | | | 
% 228.84/40.33  | | | | | Case 1:
% 228.84/40.33  | | | | | | 
% 228.84/40.33  | | | | | |   (81)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2,
% 228.84/40.33  | | | | | |             e0) = e2)
% 228.84/40.33  | | | | | | 
% 228.84/40.33  | | | | | | BETA: splitting (81) gives:
% 228.84/40.33  | | | | | | 
% 228.84/40.33  | | | | | | Case 1:
% 228.84/40.33  | | | | | | | 
% 228.84/40.33  | | | | | | |   (82)  all_57_9 = e2 & op(e3, e0) = e2
% 228.84/40.33  | | | | | | | 
% 228.84/40.33  | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (10), (12), (14), (15),
% 228.84/40.33  | | | | | | |            (18), (21), (22), (25), (28), (31), (32), (34), (37),
% 228.84/40.33  | | | | | | |            (38), (41), (42), (43), (45), (47), (52), (54), (55),
% 228.84/40.33  | | | | | | |            (59), (61), (62), (63), (64), (65), (67), (68), (72),
% 228.84/40.33  | | | | | | |            (73), (80), (82) are inconsistent by sub-proof #624.
% 228.84/40.33  | | | | | | | 
% 228.84/40.33  | | | | | | Case 2:
% 228.84/40.33  | | | | | | | 
% 228.84/40.33  | | | | | | |   (83)  all_57_10 = e2 & op(e2, e0) = e2
% 228.84/40.33  | | | | | | | 
% 228.84/40.33  | | | | | | | ALPHA: (83) implies:
% 228.84/40.33  | | | | | | |   (84)  all_57_10 = e2
% 228.84/40.33  | | | | | | |   (85)  op(e2, e0) = e2
% 228.84/40.33  | | | | | | | 
% 228.84/40.33  | | | | | | | BETA: splitting (68) gives:
% 228.84/40.33  | | | | | | | 
% 228.84/40.33  | | | | | | | Case 1:
% 228.84/40.33  | | | | | | | | 
% 228.84/40.33  | | | | | | | |   (86)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 &
% 228.84/40.33  | | | | | | | |           op(e2, e0) = e1)
% 228.84/40.33  | | | | | | | | 
% 228.84/40.33  | | | | | | | | BETA: splitting (86) gives:
% 228.84/40.33  | | | | | | | | 
% 228.84/40.33  | | | | | | | | Case 1:
% 228.84/40.33  | | | | | | | | | 
% 228.84/40.33  | | | | | | | | |   (87)  all_57_9 = e1 & op(e3, e0) = e1
% 228.84/40.33  | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | ALPHA: (87) implies:
% 228.84/40.33  | | | | | | | | |   (88)  all_57_9 = e1
% 228.84/40.33  | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 228.84/40.33  | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 228.84/40.33  | | | | | | | | |            (19), (20), (21), (22), (23), (24), (25), (26),
% 228.84/40.33  | | | | | | | | |            (27), (28), (29), (30), (31), (32), (33), (35),
% 228.84/40.33  | | | | | | | | |            (36), (37), (38), (39), (40), (41), (42), (43),
% 228.84/40.33  | | | | | | | | |            (44), (45), (47), (48), (49), (50), (51), (52),
% 228.84/40.33  | | | | | | | | |            (53), (54), (55), (56), (57), (58), (59), (60),
% 228.84/40.33  | | | | | | | | |            (61), (62), (63), (64), (65), (66), (67), (68),
% 228.84/40.33  | | | | | | | | |            (69), (70), (71), (72), (73), (84), (85), (88) are
% 228.84/40.33  | | | | | | | | |            inconsistent by sub-proof #676.
% 228.84/40.33  | | | | | | | | | 
% 228.84/40.33  | | | | | | | | Case 2:
% 228.84/40.33  | | | | | | | | | 
% 228.84/40.33  | | | | | | | | |   (89)  all_57_10 = e1 & op(e2, e0) = e1
% 228.84/40.33  | | | | | | | | | 
% 228.84/40.33  | | | | | | | | | REF_CLOSE: (64), (84), (89) are inconsistent by sub-proof
% 228.84/40.33  | | | | | | | | |            #2360.
% 228.84/40.33  | | | | | | | | | 
% 228.84/40.33  | | | | | | | | End of split
% 228.84/40.33  | | | | | | | | 
% 228.84/40.33  | | | | | | | Case 2:
% 228.84/40.33  | | | | | | | | 
% 228.84/40.33  | | | | | | | |   (90)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 &
% 228.84/40.33  | | | | | | | |           op(e0, e0) = e1)
% 228.84/40.33  | | | | | | | | 
% 228.84/40.33  | | | | | | | | REF_CLOSE: (5), (6), (34), (43), (52), (90) are inconsistent by
% 228.84/40.33  | | | | | | | |            sub-proof #1749.
% 228.84/40.33  | | | | | | | | 
% 228.84/40.33  | | | | | | | End of split
% 228.84/40.33  | | | | | | | 
% 228.84/40.33  | | | | | | End of split
% 228.84/40.33  | | | | | | 
% 228.84/40.33  | | | | | Case 2:
% 228.84/40.33  | | | | | | 
% 228.84/40.33  | | | | | |   (91)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 &
% 228.84/40.33  | | | | | |           op(e0, e0) = e2)
% 228.84/40.33  | | | | | | 
% 228.84/40.33  | | | | | | BETA: splitting (91) gives:
% 228.84/40.33  | | | | | | 
% 228.84/40.33  | | | | | | Case 1:
% 228.84/40.33  | | | | | | | 
% 228.84/40.33  | | | | | | |   (92)  all_57_11 = e2 & op(e1, e0) = e2
% 228.84/40.33  | | | | | | | 
% 228.84/40.33  | | | | | | | REF_CLOSE: (34), (38), (92) are inconsistent by sub-proof #1988.
% 228.84/40.33  | | | | | | | 
% 228.84/40.33  | | | | | | Case 2:
% 228.84/40.33  | | | | | | | 
% 228.84/40.33  | | | | | | |   (93)  all_57_15 = e2 & op(e0, e0) = e2
% 228.84/40.33  | | | | | | | 
% 228.84/40.33  | | | | | | | REF_CLOSE: (5), (6), (15), (21), (22), (25), (28), (31), (38),
% 228.84/40.33  | | | | | | |            (42), (43), (59), (64), (73), (76), (93) are
% 228.84/40.33  | | | | | | |            inconsistent by sub-proof #707.
% 228.84/40.33  | | | | | | | 
% 228.84/40.33  | | | | | | End of split
% 228.84/40.33  | | | | | | 
% 228.84/40.33  | | | | | End of split
% 228.84/40.33  | | | | | 
% 228.84/40.33  | | | | Case 2:
% 228.84/40.33  | | | | | 
% 228.84/40.33  | | | | |   (94)  all_57_9 = e0 & op(e3, e0) = e0
% 228.84/40.33  | | | | | 
% 228.84/40.33  | | | | | ALPHA: (94) implies:
% 228.84/40.33  | | | | |   (95)  all_57_9 = e0
% 228.84/40.33  | | | | | 
% 228.84/40.33  | | | | | REF_CLOSE: (5), (22), (28), (34), (38), (43), (64), (65), (68), (95)
% 228.84/40.33  | | | | |            are inconsistent by sub-proof #1144.
% 228.84/40.33  | | | | | 
% 228.84/40.33  | | | | End of split
% 228.84/40.33  | | | | 
% 228.84/40.33  | | | End of split
% 228.84/40.33  | | | 
% 228.84/40.33  | | Case 2:
% 228.84/40.33  | | | 
% 228.84/40.33  | | |   (96)  all_57_3 = e3 & op(e2, e2) = e3
% 228.84/40.33  | | | 
% 228.84/40.33  | | | ALPHA: (96) implies:
% 228.84/40.33  | | |   (97)  op(e2, e2) = e3
% 228.84/40.33  | | | 
% 228.84/40.33  | | | REF_CLOSE: (5), (6), (14), (97) are inconsistent by sub-proof #1912.
% 228.84/40.33  | | | 
% 228.84/40.33  | | End of split
% 228.84/40.33  | | 
% 228.84/40.33  | Case 2:
% 228.84/40.33  | | 
% 228.84/40.33  | |   (98)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 228.84/40.33  | |           e3)
% 228.84/40.33  | | 
% 228.84/40.33  | | REF_CLOSE: (5), (6), (17), (22), (25), (28), (32), (38), (43), (52), (54),
% 228.84/40.33  | |            (55), (64), (98) are inconsistent by sub-proof #615.
% 228.84/40.33  | | 
% 228.84/40.33  | End of split
% 228.84/40.33  | 
% 228.84/40.33  End of proof
% 228.84/40.33  
% 228.84/40.33  Sub-proof #604 shows that the following formulas are inconsistent:
% 228.84/40.33  ----------------------------------------------------------------
% 228.84/40.33    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.84/40.33         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.84/40.33    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.84/40.33         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.84/40.33    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.84/40.33         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.84/40.33    (4)   ~ (e3 = e1)
% 228.84/40.33    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.84/40.33           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.84/40.33    (6)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.84/40.33         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.84/40.33    (7)   ~ (all_6_2 = e3)
% 228.84/40.33    (8)  op(e1, e1) = all_6_2
% 228.84/40.33    (9)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.84/40.33         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.84/40.33    (10)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.84/40.33          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.84/40.33    (11)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.84/40.33          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.84/40.34    (12)  all_57_3 = e0
% 228.84/40.34    (13)   ~ (e3 = e2)
% 228.84/40.34    (14)   ~ (e3 = e0)
% 228.84/40.34    (15)  all_57_15 = e3
% 228.84/40.34    (16)  op(e3, e3) = e2
% 228.84/40.34    (17)   ~ (e2 = e0)
% 228.84/40.34    (18)  e3 = e2
% 228.84/40.34    (19)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.84/40.34          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.84/40.34    (20)   ~ (e1 = e0)
% 228.84/40.34    (21)  all_57_6 = e3
% 228.84/40.34    (22)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.84/40.34              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.84/40.34                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.84/40.34                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.84/40.34    (23)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.84/40.34          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.84/40.34    (24)   ~ (all_53_12 = e3)
% 228.84/40.34    (25)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.84/40.34          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.84/40.34    (26)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.84/40.34          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.84/40.34    (27)   ~ (e2 = e1)
% 228.84/40.34    (28)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.84/40.34          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.84/40.34    (29)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.84/40.34          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.84/40.34    (30)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.84/40.34          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.84/40.34    (31)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.84/40.34          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.84/40.34    (32)  op(e3, e0) = all_53_12
% 228.84/40.34  
% 228.84/40.34  Begin of proof
% 228.84/40.34  | 
% 228.84/40.34  | SIMP: (18) implies:
% 228.84/40.34  |   (33)  e3 = e2
% 228.84/40.34  | 
% 228.84/40.34  | COMBINE_EQS: (21), (33) imply:
% 228.84/40.34  |   (34)  all_57_6 = e2
% 228.84/40.34  | 
% 228.84/40.34  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.84/40.34  |            (13), (14), (15), (16), (17), (19), (20), (22), (23), (24), (25),
% 228.84/40.34  |            (26), (27), (28), (29), (30), (31), (32), (34) are inconsistent by
% 228.84/40.34  |            sub-proof #728.
% 228.84/40.34  | 
% 228.84/40.34  End of proof
% 228.84/40.34  
% 228.84/40.34  Sub-proof #605 shows that the following formulas are inconsistent:
% 228.84/40.34  ----------------------------------------------------------------
% 228.84/40.34    (1)  all_57_0 = e2
% 228.84/40.34    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.84/40.34         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.84/40.34    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.84/40.34         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.84/40.34    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.84/40.34         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.84/40.34    (5)   ~ (e3 = e1)
% 228.84/40.34    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.84/40.34           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.84/40.34    (7)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.84/40.34         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.84/40.34    (8)   ~ (all_6_2 = e3)
% 228.84/40.34    (9)  op(e1, e1) = all_6_2
% 228.84/40.34    (10)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.84/40.34          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.84/40.34    (11)  op(e2, e2) = e0
% 228.84/40.34    (12)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.84/40.34          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.84/40.34    (13)  all_57_3 = e0
% 228.84/40.34    (14)   ~ (e3 = e2)
% 228.84/40.34    (15)   ~ (e3 = e0)
% 228.84/40.34    (16)  all_57_15 = e3
% 228.84/40.34    (17)  op(e3, e3) = e2
% 228.84/40.34    (18)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.84/40.34          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.84/40.34            e1)
% 228.84/40.34    (19)   ~ (e2 = e0)
% 228.84/40.34    (20)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.84/40.34          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.84/40.34    (21)   ~ (e1 = e0)
% 228.84/40.34    (22)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.84/40.34          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.84/40.34    (23)  op(e0, e0) = e3
% 228.84/40.34    (24)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.84/40.34          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.84/40.34            e2)
% 228.84/40.34    (25)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.84/40.34              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.84/40.34                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.84/40.34                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.84/40.34    (26)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.84/40.34          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.84/40.34    (27)   ~ (all_53_12 = e3)
% 228.84/40.34    (28)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.84/40.34          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.84/40.34    (29)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.84/40.34          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.84/40.34    (30)  all_57_1 = e3
% 228.84/40.34    (31)   ~ (e2 = e1)
% 228.84/40.34    (32)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.84/40.34          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.84/40.34    (33)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.84/40.34          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.84/40.34    (34)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.84/40.34          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.84/40.34    (35)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.84/40.34          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.84/40.34    (36)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.84/40.34          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.84/40.34    (37)  all_57_7 = e0
% 228.84/40.34    (38)  op(e3, e0) = all_53_12
% 228.84/40.34  
% 228.84/40.34  Begin of proof
% 228.84/40.34  | 
% 228.84/40.34  | BETA: splitting (36) gives:
% 228.84/40.34  | 
% 228.84/40.34  | Case 1:
% 228.84/40.34  | | 
% 228.84/40.34  | |   (39)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) =
% 228.84/40.34  | |           e1)
% 228.84/40.34  | | 
% 228.84/40.34  | | REF_CLOSE: (5), (6), (11), (21), (30), (39) are inconsistent by sub-proof
% 228.84/40.34  | |            #2206.
% 228.84/40.34  | | 
% 228.84/40.34  | Case 2:
% 228.84/40.34  | | 
% 228.84/40.34  | |   (40)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 228.84/40.34  | |           e1)
% 228.84/40.34  | | 
% 228.84/40.34  | | BETA: splitting (40) gives:
% 228.84/40.34  | | 
% 228.84/40.34  | | Case 1:
% 228.84/40.34  | | | 
% 228.84/40.34  | | |   (41)  all_57_7 = e1 & op(e1, e2) = e1
% 228.84/40.34  | | | 
% 228.84/40.34  | | | ALPHA: (41) implies:
% 228.84/40.34  | | |   (42)  all_57_7 = e1
% 228.84/40.34  | | | 
% 228.84/40.34  | | | REF_CLOSE: (21), (37), (42) are inconsistent by sub-proof #2211.
% 228.84/40.34  | | | 
% 228.84/40.34  | | Case 2:
% 228.84/40.34  | | | 
% 228.84/40.34  | | |   (43)  all_57_13 = e1 & op(e0, e2) = e1
% 228.84/40.34  | | | 
% 228.84/40.34  | | | ALPHA: (43) implies:
% 228.84/40.34  | | |   (44)  all_57_13 = e1
% 228.84/40.34  | | | 
% 228.84/40.34  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 228.84/40.34  | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 228.84/40.34  | | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 228.84/40.34  | | |            (34), (35), (36), (37), (38), (44) are inconsistent by
% 228.84/40.34  | | |            sub-proof #782.
% 228.84/40.34  | | | 
% 228.84/40.34  | | End of split
% 228.84/40.34  | | 
% 228.84/40.34  | End of split
% 228.84/40.34  | 
% 228.84/40.34  End of proof
% 228.84/40.34  
% 228.84/40.34  Sub-proof #606 shows that the following formulas are inconsistent:
% 228.84/40.34  ----------------------------------------------------------------
% 228.84/40.34    (1)   ~ (all_53_2 = e2)
% 228.84/40.34    (2)  all_57_0 = e2
% 228.84/40.34    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.84/40.34         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.84/40.34    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.84/40.34         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.84/40.34    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.84/40.34         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.84/40.34    (6)   ~ (e3 = e1)
% 228.84/40.34    (7)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.84/40.34         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.84/40.34    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.84/40.34           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.84/40.34    (9)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.84/40.34         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.84/40.34    (10)   ~ (all_53_3 = e3)
% 228.84/40.34    (11)   ~ (all_53_3 = all_53_7)
% 228.84/40.34    (12)   ~ (all_6_2 = e3)
% 228.84/40.34    (13)   ~ (all_53_9 = e1)
% 228.84/40.34    (14)  op(e1, e1) = all_6_2
% 228.84/40.34    (15)   ~ (all_53_1 = all_53_9)
% 228.84/40.34    (16)  op(e2, e2) = e1
% 228.84/40.34    (17)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.84/40.34          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.84/40.34    (18)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 228.84/40.34            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 228.84/40.34              e3) = all_22_1 & $i(all_22_1))
% 228.84/40.34    (19)   ~ (all_53_13 = e3)
% 228.84/40.34    (20)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.84/40.34          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.84/40.34    (21)   ~ (all_53_9 = all_53_11)
% 228.84/40.34    (22)  all_55_4 = all_53_1
% 228.84/40.34    (23)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.84/40.34          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.84/40.34    (24)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 228.84/40.34          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 228.84/40.34    (25)   ~ (e3 = e2)
% 228.84/40.34    (26)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 228.84/40.34    (27)   ~ (all_53_1 = all_53_3)
% 228.84/40.34    (28)   ~ (e3 = e0)
% 228.84/40.34    (29)  all_57_6 = e0
% 228.84/40.34    (30)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.84/40.34    (31)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 228.84/40.34    (32)  all_57_15 = e3
% 228.84/40.34    (33)  op(e2, e2) = all_52_11
% 228.84/40.34    (34)   ~ (all_53_9 = all_53_13)
% 228.84/40.34    (35)  op(e3, e3) = e2
% 228.84/40.34    (36)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.84/40.34          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.84/40.34            e1)
% 228.84/40.34    (37)   ~ (all_53_1 = e1)
% 228.84/40.34    (38)  all_55_6 = all_53_9
% 228.84/40.34    (39)   ~ (all_53_1 = all_53_2)
% 228.84/40.34    (40)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.84/40.34          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 228.84/40.34    (41)   ~ (e2 = e0)
% 228.84/40.34    (42)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.84/40.34            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.84/40.34            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.84/40.34            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.84/40.34              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.84/40.34            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.84/40.34            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.84/40.34              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.84/40.34              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.84/40.34            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.84/40.34            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.84/40.34            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.84/40.34              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.84/40.34              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.84/40.34            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.84/40.34              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.84/40.34            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.84/40.34            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.84/40.34              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.84/40.34              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.84/40.34            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.84/40.34            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.84/40.34    (43)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 228.84/40.34            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 228.84/40.34              e3) = all_12_1 & $i(all_12_1))
% 228.84/40.34    (44)  all_55_12 = all_53_3
% 228.84/40.34    (45)  all_57_2 = e3
% 228.84/40.34    (46)  all_57_3 = e1
% 228.84/40.34    (47)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.84/40.34          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.84/40.34    (48)   ~ (e1 = e0)
% 228.84/40.34    (49)   ~ (all_53_3 = all_53_11)
% 228.84/40.34    (50)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.84/40.34          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.84/40.34    (51)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.84/40.34          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.84/40.34    (52)   ~ (all_53_2 = all_53_3)
% 228.84/40.34    (53)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 228.84/40.34    (54)   ~ (all_53_7 = all_53_11)
% 228.84/40.34    (55)  all_55_8 = all_53_2
% 228.84/40.34    (56)  op(e0, e0) = e3
% 228.84/40.34    (57)  op(e0, e2) = all_53_7
% 228.84/40.34    (58)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.84/40.34          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.84/40.34            e2)
% 228.84/40.34    (59)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.84/40.34              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.84/40.34                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.84/40.34                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.84/40.34    (60)   ~ (all_53_1 = all_53_13)
% 228.84/40.34    (61)  op(e2, e0) = all_53_13
% 228.84/40.34    (62)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.84/40.34          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.84/40.34    (63)   ~ (all_53_12 = e3)
% 228.84/40.34    (64)  op(e1, e3) = all_53_2
% 228.84/40.34    (65)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.84/40.34          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.84/40.34    (66)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.84/40.34          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.84/40.34    (67)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.84/40.34          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 228.84/40.34    (68)   ~ (e2 = e1)
% 228.84/40.34    (69)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.84/40.34          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.84/40.34    (70)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.84/40.34          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.84/40.34    (71)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 228.84/40.34    (72)   ~ (all_53_12 = e2)
% 228.84/40.34    (73)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 228.84/40.34          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 228.84/40.34    (74)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.84/40.34          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.84/40.34    (75)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.84/40.34          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.84/40.34    (76)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.84/40.34          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.84/40.34    (77)  all_55_14 = all_53_11
% 228.84/40.34    (78)  op(all_52_11, all_52_11) = e2
% 228.84/40.34    (79)   ~ (all_53_11 = e3)
% 228.84/40.34    (80)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.84/40.34          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.84/40.34    (81)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.84/40.34          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.84/40.34    (82)  op(e3, e0) = all_53_12
% 228.84/40.34  
% 228.84/40.34  Begin of proof
% 228.84/40.34  | 
% 228.84/40.34  | BETA: splitting (9) gives:
% 228.84/40.34  | 
% 228.84/40.34  | Case 1:
% 228.84/40.34  | | 
% 228.84/40.34  | |   (83)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 228.84/40.34  | |           e3)
% 228.84/40.34  | | 
% 228.84/40.34  | | BETA: splitting (83) gives:
% 228.84/40.34  | | 
% 228.84/40.34  | | Case 1:
% 228.84/40.34  | | | 
% 228.84/40.34  | | |   (84)  all_57_6 = e3 & op(e1, e3) = e3
% 228.84/40.34  | | | 
% 228.84/40.34  | | | ALPHA: (84) implies:
% 228.84/40.34  | | |   (85)  all_57_6 = e3
% 228.84/40.34  | | | 
% 228.84/40.34  | | | REF_CLOSE: (2), (4), (6), (8), (25), (28), (41), (45), (48), (68), (70),
% 228.84/40.34  | | |            (74), (85) are inconsistent by sub-proof #1286.
% 228.84/40.34  | | | 
% 228.84/40.34  | | Case 2:
% 228.84/40.34  | | | 
% 228.84/40.34  | | |   (86)  all_57_7 = e3 & op(e1, e2) = e3
% 228.84/40.34  | | | 
% 228.84/40.34  | | | ALPHA: (86) implies:
% 228.84/40.34  | | |   (87)  all_57_7 = e3
% 228.84/40.34  | | | 
% 228.84/40.34  | | | BETA: splitting (76) gives:
% 228.84/40.34  | | | 
% 228.84/40.34  | | | Case 1:
% 228.84/40.34  | | | | 
% 228.84/40.34  | | | |   (88)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2)
% 228.84/40.34  | | | |           = e1)
% 228.84/40.34  | | | | 
% 228.84/40.34  | | | | REF_CLOSE: (6), (29), (48), (87), (88) are inconsistent by sub-proof
% 228.84/40.34  | | | |            #654.
% 228.84/40.34  | | | | 
% 228.84/40.34  | | | Case 2:
% 228.84/40.34  | | | | 
% 228.84/40.34  | | | |   (89)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0)
% 228.84/40.34  | | | |           = e1)
% 228.84/40.34  | | | | 
% 228.84/40.34  | | | | BETA: splitting (89) gives:
% 228.84/40.34  | | | | 
% 228.84/40.34  | | | | Case 1:
% 228.84/40.34  | | | | | 
% 228.84/40.34  | | | | |   (90)  all_57_8 = e1 & op(e1, e1) = e1
% 228.84/40.34  | | | | | 
% 228.84/40.34  | | | | | ALPHA: (90) implies:
% 228.84/40.34  | | | | |   (91)  op(e1, e1) = e1
% 228.84/40.34  | | | | | 
% 228.84/40.34  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 228.84/40.34  | | | | |            (12), (13), (14), (15), (16), (17), (18), (19), (20), (21),
% 228.84/40.34  | | | | |            (22), (23), (24), (25), (26), (27), (28), (30), (31), (32),
% 228.84/40.34  | | | | |            (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 228.84/40.34  | | | | |            (43), (44), (46), (47), (48), (49), (50), (51), (52), (53),
% 228.84/40.34  | | | | |            (54), (55), (56), (57), (58), (59), (60), (61), (62), (63),
% 228.84/40.34  | | | | |            (64), (65), (66), (67), (68), (69), (70), (71), (72), (73),
% 228.84/40.34  | | | | |            (74), (75), (76), (77), (78), (79), (80), (81), (82), (91)
% 228.84/40.34  | | | | |            are inconsistent by sub-proof #672.
% 228.84/40.34  | | | | | 
% 228.84/40.34  | | | | Case 2:
% 228.84/40.34  | | | | | 
% 228.84/40.34  | | | | |   (92)  all_57_11 = e1 & op(e1, e0) = e1
% 228.84/40.34  | | | | | 
% 228.84/40.34  | | | | | ALPHA: (92) implies:
% 228.84/40.34  | | | | |   (93)  all_57_11 = e1
% 228.84/40.34  | | | | | 
% 228.84/40.34  | | | | | BETA: splitting (69) gives:
% 228.84/40.34  | | | | | 
% 228.84/40.34  | | | | | Case 1:
% 228.84/40.34  | | | | | | 
% 228.84/40.34  | | | | | |   (94)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2,
% 228.84/40.34  | | | | | |             e0) = e2)
% 228.84/40.34  | | | | | | 
% 228.84/40.34  | | | | | | BETA: splitting (94) gives:
% 228.84/40.34  | | | | | | 
% 228.84/40.34  | | | | | | Case 1:
% 228.84/40.34  | | | | | | | 
% 228.84/40.34  | | | | | | |   (95)  all_57_9 = e2 & op(e3, e0) = e2
% 228.84/40.34  | | | | | | | 
% 228.84/40.34  | | | | | | | ALPHA: (95) implies:
% 228.84/40.34  | | | | | | |   (96)  all_57_9 = e2
% 228.84/40.34  | | | | | | | 
% 228.84/40.34  | | | | | | | REF_CLOSE: (3), (5), (6), (8), (12), (14), (16), (17), (23), (25),
% 228.84/40.34  | | | | | | |            (28), (32), (35), (36), (40), (41), (46), (47), (48),
% 228.84/40.34  | | | | | | |            (50), (56), (58), (59), (63), (65), (68), (82), (87),
% 228.84/40.34  | | | | | | |            (93), (96) are inconsistent by sub-proof #653.
% 228.84/40.34  | | | | | | | 
% 228.84/40.34  | | | | | | Case 2:
% 228.84/40.34  | | | | | | | 
% 228.84/40.34  | | | | | | |   (97)  all_57_10 = e2 & op(e2, e0) = e2
% 228.84/40.34  | | | | | | | 
% 228.84/40.34  | | | | | | | ALPHA: (97) implies:
% 228.84/40.34  | | | | | | |   (98)  all_57_10 = e2
% 228.84/40.34  | | | | | | |   (99)  op(e2, e0) = e2
% 228.84/40.34  | | | | | | | 
% 228.84/40.34  | | | | | | | REF_CLOSE: (1), (5), (6), (8), (9), (10), (11), (12), (13), (14),
% 228.84/40.34  | | | | | | |            (15), (16), (17), (19), (21), (22), (23), (25), (26),
% 228.84/40.34  | | | | | | |            (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 228.84/40.34  | | | | | | |            (36), (37), (38), (39), (41), (42), (44), (45), (48),
% 228.84/40.34  | | | | | | |            (49), (50), (52), (53), (54), (55), (56), (57), (58),
% 228.84/40.34  | | | | | | |            (59), (60), (61), (64), (67), (68), (69), (71), (75),
% 228.84/40.34  | | | | | | |            (77), (78), (79), (98), (99) are inconsistent by
% 228.84/40.34  | | | | | | |            sub-proof #607.
% 228.84/40.34  | | | | | | | 
% 228.84/40.34  | | | | | | End of split
% 228.84/40.34  | | | | | | 
% 228.84/40.34  | | | | | Case 2:
% 228.84/40.34  | | | | | | 
% 228.84/40.34  | | | | | |   (100)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 &
% 228.84/40.34  | | | | | |            op(e0, e0) = e2)
% 228.84/40.34  | | | | | | 
% 228.84/40.34  | | | | | | REF_CLOSE: (3), (4), (6), (8), (9), (12), (14), (16), (18), (25),
% 228.84/40.34  | | | | | |            (28), (29), (32), (35), (41), (43), (45), (46), (48),
% 228.84/40.34  | | | | | |            (56), (59), (62), (65), (68), (69), (74), (75), (87),
% 228.84/40.34  | | | | | |            (100) are inconsistent by sub-proof #646.
% 228.84/40.34  | | | | | | 
% 228.84/40.34  | | | | | End of split
% 228.84/40.34  | | | | | 
% 228.84/40.34  | | | | End of split
% 228.84/40.34  | | | | 
% 228.84/40.34  | | | End of split
% 228.84/40.34  | | | 
% 228.84/40.34  | | End of split
% 228.84/40.34  | | 
% 228.84/40.34  | Case 2:
% 228.84/40.34  | | 
% 228.84/40.34  | |   (101)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 228.84/40.34  | |            e3)
% 228.84/40.34  | | 
% 228.84/40.34  | | REF_CLOSE: (6), (8), (12), (14), (25), (28), (32), (41), (48), (59), (68),
% 228.84/40.34  | |            (69), (75), (101) are inconsistent by sub-proof #1786.
% 228.84/40.34  | | 
% 228.84/40.34  | End of split
% 228.84/40.34  | 
% 228.84/40.34  End of proof
% 228.84/40.34  
% 228.84/40.34  Sub-proof #607 shows that the following formulas are inconsistent:
% 228.84/40.34  ----------------------------------------------------------------
% 228.84/40.34    (1)   ~ (all_53_2 = e2)
% 228.84/40.34    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.84/40.34         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.84/40.34    (3)   ~ (e3 = e1)
% 228.84/40.34    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.84/40.34           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.84/40.34    (5)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.84/40.34         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.84/40.34    (6)   ~ (all_53_3 = e3)
% 228.84/40.34    (7)   ~ (all_53_3 = all_53_7)
% 228.84/40.34    (8)   ~ (all_6_2 = e3)
% 228.84/40.34    (9)   ~ (all_53_9 = e1)
% 228.84/40.34    (10)  op(e1, e1) = all_6_2
% 228.84/40.34    (11)   ~ (all_53_1 = all_53_9)
% 228.84/40.34    (12)  op(e2, e2) = e1
% 228.84/40.34    (13)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.84/40.34          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.84/40.34    (14)   ~ (all_53_13 = e3)
% 228.84/40.34    (15)   ~ (all_53_9 = all_53_11)
% 228.84/40.34    (16)  all_55_4 = all_53_1
% 228.84/40.34    (17)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.84/40.34          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.84/40.34    (18)   ~ (e3 = e2)
% 228.84/40.34    (19)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 228.84/40.34    (20)   ~ (all_53_1 = all_53_3)
% 228.84/40.34    (21)   ~ (e3 = e0)
% 228.84/40.34    (22)  all_57_6 = e0
% 228.84/40.34    (23)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.84/40.34    (24)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 228.84/40.34    (25)  all_57_15 = e3
% 228.84/40.34    (26)  op(e2, e2) = all_52_11
% 228.84/40.35    (27)   ~ (all_53_9 = all_53_13)
% 228.84/40.35    (28)  op(e3, e3) = e2
% 228.84/40.35    (29)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.84/40.35          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.84/40.35            e1)
% 228.84/40.35    (30)  all_57_10 = e2
% 228.84/40.35    (31)   ~ (all_53_1 = e1)
% 228.84/40.35    (32)  op(e2, e0) = e2
% 228.84/40.35    (33)  all_55_6 = all_53_9
% 228.84/40.35    (34)   ~ (all_53_1 = all_53_2)
% 228.84/40.35    (35)   ~ (e2 = e0)
% 228.84/40.35    (36)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.84/40.35            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.84/40.35            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.84/40.35            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.84/40.35              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.84/40.35            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.84/40.35            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.84/40.35              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.84/40.35              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.84/40.35            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.84/40.35            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.84/40.35            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.84/40.35              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.84/40.35              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.84/40.35            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.84/40.35              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.84/40.35            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.84/40.35            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.84/40.35              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.84/40.35              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.84/40.35            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.84/40.35            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.84/40.35    (37)  all_55_12 = all_53_3
% 228.84/40.35    (38)  all_57_2 = e3
% 228.84/40.35    (39)   ~ (e1 = e0)
% 228.84/40.35    (40)   ~ (all_53_3 = all_53_11)
% 228.84/40.35    (41)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.84/40.35          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.84/40.35    (42)   ~ (all_53_2 = all_53_3)
% 228.84/40.35    (43)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 228.84/40.35    (44)   ~ (all_53_7 = all_53_11)
% 228.84/40.35    (45)  all_55_8 = all_53_2
% 228.84/40.35    (46)  op(e0, e0) = e3
% 228.84/40.35    (47)  op(e0, e2) = all_53_7
% 228.84/40.35    (48)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.84/40.35          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.84/40.35            e2)
% 228.84/40.35    (49)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.84/40.35              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.84/40.35                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.84/40.35                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.84/40.35    (50)   ~ (all_53_1 = all_53_13)
% 228.84/40.35    (51)  op(e2, e0) = all_53_13
% 228.84/40.35    (52)  op(e1, e3) = all_53_2
% 228.84/40.35    (53)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.84/40.35          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 228.84/40.35    (54)   ~ (e2 = e1)
% 228.84/40.35    (55)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.84/40.35          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.84/40.35    (56)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 228.84/40.35    (57)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.84/40.35          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.84/40.35    (58)  all_55_14 = all_53_11
% 228.84/40.35    (59)  op(all_52_11, all_52_11) = e2
% 228.84/40.35    (60)   ~ (all_53_11 = e3)
% 228.84/40.35  
% 228.84/40.35  Begin of proof
% 228.84/40.35  | 
% 228.84/40.35  | BETA: splitting (53) gives:
% 228.84/40.35  | 
% 228.84/40.35  | Case 1:
% 228.84/40.35  | | 
% 228.84/40.35  | |   (61)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) =
% 228.84/40.35  | |           e0)
% 228.84/40.35  | | 
% 228.84/40.35  | | BETA: splitting (61) gives:
% 228.84/40.35  | | 
% 228.84/40.35  | | Case 1:
% 228.84/40.35  | | | 
% 228.84/40.35  | | |   (62)  all_57_2 = e0 & op(e2, e3) = e0
% 228.84/40.35  | | | 
% 228.84/40.35  | | | REF_CLOSE: (21), (38), (62) are inconsistent by sub-proof #1805.
% 228.84/40.35  | | | 
% 228.84/40.35  | | Case 2:
% 228.84/40.35  | | | 
% 228.84/40.35  | | |   (63)  all_57_3 = e0 & op(e2, e2) = e0
% 228.84/40.35  | | | 
% 228.84/40.35  | | | ALPHA: (63) implies:
% 228.84/40.35  | | |   (64)  op(e2, e2) = e0
% 228.84/40.35  | | | 
% 228.84/40.35  | | | REF_CLOSE: (4), (18), (26), (46), (59), (64) are inconsistent by sub-proof
% 228.84/40.35  | | |            #1229.
% 228.84/40.35  | | | 
% 228.84/40.35  | | End of split
% 228.84/40.35  | | 
% 228.84/40.35  | Case 2:
% 228.84/40.35  | | 
% 228.84/40.35  | |   (65)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 228.84/40.35  | |           e0)
% 228.84/40.35  | | 
% 228.84/40.35  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.84/40.35  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 228.84/40.35  | |            (24), (25), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 228.84/40.35  | |            (36), (37), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 228.84/40.35  | |            (48), (49), (50), (51), (52), (54), (55), (56), (57), (58), (60),
% 228.84/40.35  | |            (65) are inconsistent by sub-proof #649.
% 228.84/40.35  | | 
% 228.84/40.35  | End of split
% 228.84/40.35  | 
% 228.84/40.35  End of proof
% 228.84/40.35  
% 228.84/40.35  Sub-proof #608 shows that the following formulas are inconsistent:
% 228.84/40.35  ----------------------------------------------------------------
% 228.84/40.35    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.84/40.35         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.84/40.35    (2)   ~ (e3 = e1)
% 228.84/40.35    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.84/40.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.84/40.35    (4)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.84/40.35    (5)  all_57_6 = e1
% 228.84/40.35    (6)   ~ (e3 = e2)
% 228.84/40.35    (7)   ~ (e3 = e0)
% 228.84/40.35    (8)  op(e3, e3) = e2
% 228.84/40.35    (9)  all_57_11 = e0
% 228.84/40.35    (10)   ~ (e2 = e0)
% 228.84/40.35    (11)  all_57_3 = e1
% 228.84/40.35    (12)   ~ (e1 = e0)
% 228.84/40.35    (13)  all_57_12 = e3
% 228.84/40.35    (14)  op(e0, e0) = e3
% 228.84/40.35    (15)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.84/40.35          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.84/40.35    (16)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.84/40.35          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.84/40.35    (17)   ~ (e2 = e1)
% 228.84/40.35    (18)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.84/40.35          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.84/40.35  
% 228.84/40.35  Begin of proof
% 228.84/40.35  | 
% 228.84/40.35  | BETA: splitting (4) gives:
% 228.84/40.35  | 
% 228.84/40.35  | Case 1:
% 228.84/40.35  | | 
% 228.84/40.35  | |   (19)  all_57_11 = e1 & op(e1, e0) = e1
% 228.84/40.35  | | 
% 228.84/40.35  | | ALPHA: (19) implies:
% 228.84/40.35  | |   (20)  all_57_11 = e1
% 228.84/40.35  | | 
% 228.84/40.35  | | COMBINE_EQS: (9), (20) imply:
% 228.84/40.35  | |   (21)  e1 = e0
% 228.84/40.35  | | 
% 228.84/40.35  | | COMBINE_EQS: (11), (21) imply:
% 228.84/40.35  | |   (22)  all_57_3 = e0
% 228.84/40.35  | | 
% 228.84/40.35  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (10), (12), (13), (15), (16),
% 228.84/40.35  | |            (17), (18), (22) are inconsistent by sub-proof #1632.
% 228.84/40.35  | | 
% 228.84/40.35  | Case 2:
% 228.84/40.35  | | 
% 228.84/40.35  | |   (23)  all_57_15 = e1 & op(e0, e0) = e1
% 228.84/40.35  | | 
% 228.84/40.35  | | ALPHA: (23) implies:
% 228.84/40.35  | |   (24)  op(e0, e0) = e1
% 228.84/40.35  | | 
% 228.84/40.35  | | REF_CLOSE: (2), (3), (14), (24) are inconsistent by sub-proof #2183.
% 228.84/40.35  | | 
% 228.84/40.35  | End of split
% 228.84/40.35  | 
% 228.84/40.35  End of proof
% 228.84/40.35  
% 228.84/40.35  Sub-proof #609 shows that the following formulas are inconsistent:
% 228.84/40.35  ----------------------------------------------------------------
% 228.84/40.35    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.84/40.35         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.84/40.35    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.84/40.35         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.84/40.35    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.84/40.35         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.84/40.35    (4)   ~ (e3 = e1)
% 228.84/40.35    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.84/40.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.84/40.35    (6)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.84/40.35         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.84/40.35    (7)   ~ (all_6_2 = e3)
% 228.84/40.35    (8)  op(e1, e1) = all_6_2
% 228.84/40.35    (9)  op(e2, e2) = e1
% 228.84/40.35    (10)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.84/40.35          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.84/40.35    (11)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.84/40.35          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.84/40.35    (12)  all_57_6 = e1
% 228.84/40.35    (13)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.84/40.35          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.84/40.35    (14)   ~ (e3 = e2)
% 228.84/40.35    (15)   ~ (e3 = e0)
% 228.84/40.35    (16)  all_57_15 = e3
% 228.84/40.35    (17)  op(e3, e3) = e2
% 228.84/40.35    (18)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.84/40.35          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.84/40.35            e1)
% 228.84/40.35    (19)  all_57_11 = e0
% 228.84/40.35    (20)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.84/40.35          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 228.84/40.35    (21)   ~ (e2 = e0)
% 228.84/40.35    (22)  all_57_3 = e1
% 228.84/40.35    (23)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.84/40.35          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.84/40.35    (24)   ~ (e1 = e0)
% 228.84/40.35    (25)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.84/40.35          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.84/40.35    (26)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.84/40.35          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.84/40.35    (27)  op(e0, e0) = e3
% 228.84/40.35    (28)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.84/40.35          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.84/40.35            e2)
% 228.84/40.35    (29)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.84/40.35              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.84/40.35                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.84/40.35                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.84/40.35    (30)  all_57_10 = e1 & op(e2, e0) = e1
% 228.84/40.35    (31)   ~ (all_53_12 = e3)
% 228.84/40.35    (32)  all_57_7 = e3
% 228.84/40.35    (33)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.84/40.35          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.84/40.35    (34)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.84/40.35          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.84/40.35    (35)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.84/40.35          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 228.84/40.35    (36)   ~ (e2 = e1)
% 228.84/40.35    (37)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.84/40.35          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.84/40.35    (38)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.84/40.35          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.84/40.35    (39)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.84/40.35          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.84/40.35    (40)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.84/40.35          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.84/40.35    (41)  op(e3, e0) = all_53_12
% 228.84/40.35  
% 228.84/40.35  Begin of proof
% 228.84/40.35  | 
% 228.84/40.35  | ALPHA: (30) implies:
% 228.84/40.35  |   (42)  all_57_10 = e1
% 228.84/40.35  | 
% 228.84/40.35  | BETA: splitting (37) gives:
% 228.84/40.35  | 
% 228.84/40.35  | Case 1:
% 228.84/40.35  | | 
% 228.84/40.35  | |   (43)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 228.84/40.35  | |           e2)
% 228.84/40.35  | | 
% 228.84/40.35  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 228.84/40.35  | |            (14), (15), (16), (17), (18), (20), (21), (22), (23), (24), (25),
% 228.84/40.35  | |            (26), (27), (28), (29), (31), (33), (34), (35), (36), (37), (38),
% 228.84/40.35  | |            (39), (40), (41), (42), (43) are inconsistent by sub-proof #627.
% 228.84/40.35  | | 
% 228.84/40.35  | Case 2:
% 228.84/40.35  | | 
% 228.84/40.35  | |   (44)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.84/40.35  | |           e2)
% 228.84/40.35  | | 
% 228.84/40.35  | | REF_CLOSE: (4), (5), (6), (7), (8), (12), (14), (15), (16), (19), (21),
% 228.84/40.35  | |            (24), (27), (29), (32), (36), (37), (39), (44) are inconsistent
% 228.84/40.35  | |            by sub-proof #610.
% 228.84/40.35  | | 
% 228.84/40.35  | End of split
% 228.84/40.35  | 
% 228.84/40.35  End of proof
% 228.84/40.35  
% 228.84/40.35  Sub-proof #610 shows that the following formulas are inconsistent:
% 228.84/40.35  ----------------------------------------------------------------
% 228.84/40.35    (1)   ~ (e3 = e1)
% 228.84/40.35    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.84/40.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.84/40.35    (3)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.84/40.35         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.84/40.35    (4)   ~ (all_6_2 = e3)
% 228.84/40.35    (5)  op(e1, e1) = all_6_2
% 228.84/40.35    (6)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.84/40.35    (7)  all_57_6 = e1
% 228.84/40.35    (8)   ~ (e3 = e2)
% 228.84/40.35    (9)   ~ (e3 = e0)
% 228.84/40.35    (10)  all_57_15 = e3
% 228.84/40.35    (11)  all_57_11 = e0
% 228.84/40.35    (12)   ~ (e2 = e0)
% 228.84/40.35    (13)   ~ (e1 = e0)
% 228.84/40.35    (14)  op(e0, e0) = e3
% 228.84/40.35    (15)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.84/40.35              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.84/40.35                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.84/40.35                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.84/40.35    (16)  all_57_7 = e3
% 228.84/40.35    (17)   ~ (e2 = e1)
% 228.84/40.35    (18)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.84/40.35          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.84/40.35    (19)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.84/40.35          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.84/40.35  
% 228.84/40.35  Begin of proof
% 228.84/40.35  | 
% 228.84/40.35  | BETA: splitting (6) gives:
% 228.84/40.35  | 
% 228.84/40.35  | Case 1:
% 228.84/40.35  | | 
% 228.84/40.35  | |   (20)  all_57_11 = e2 & op(e1, e0) = e2
% 228.84/40.35  | | 
% 228.84/40.35  | | REF_CLOSE: (11), (12), (20) are inconsistent by sub-proof #1988.
% 228.84/40.35  | | 
% 228.84/40.35  | Case 2:
% 228.84/40.35  | | 
% 228.84/40.35  | |   (21)  all_57_15 = e2 & op(e0, e0) = e2
% 228.84/40.35  | | 
% 228.84/40.35  | | ALPHA: (21) implies:
% 228.84/40.35  | |   (22)  all_57_15 = e2
% 228.84/40.35  | | 
% 228.84/40.35  | | COMBINE_EQS: (10), (22) imply:
% 228.84/40.35  | |   (23)  e3 = e2
% 228.84/40.35  | | 
% 228.84/40.35  | | COMBINE_EQS: (16), (23) imply:
% 228.84/40.35  | |   (24)  all_57_7 = e2
% 228.84/40.35  | | 
% 228.84/40.35  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (12), (13), (14),
% 228.84/40.35  | |            (15), (17), (18), (19), (24) are inconsistent by sub-proof #1078.
% 228.84/40.35  | | 
% 228.84/40.35  | End of split
% 228.84/40.35  | 
% 228.84/40.35  End of proof
% 228.84/40.35  
% 228.84/40.35  Sub-proof #611 shows that the following formulas are inconsistent:
% 228.84/40.35  ----------------------------------------------------------------
% 228.84/40.35    (1)   ~ (all_53_2 = e2)
% 228.84/40.35    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.84/40.35         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.84/40.35    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.84/40.35         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.84/40.35    (4)   ~ (e3 = e1)
% 228.84/40.35    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.84/40.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.84/40.35    (6)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.84/40.35         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.84/40.35    (7)   ~ (all_53_3 = e3)
% 228.84/40.35    (8)   ~ (all_53_3 = all_53_7)
% 228.84/40.35    (9)   ~ (all_6_2 = e3)
% 228.84/40.35    (10)   ~ (all_53_9 = e1)
% 228.84/40.35    (11)  op(e1, e1) = all_6_2
% 228.84/40.35    (12)   ~ (all_53_1 = all_53_9)
% 228.84/40.35    (13)  op(e2, e2) = e1
% 228.84/40.35    (14)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.84/40.35          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.84/40.35    (15)   ~ (all_53_13 = e3)
% 228.84/40.35    (16)  all_57_6 = e1
% 228.84/40.35    (17)   ~ (all_53_9 = all_53_11)
% 228.84/40.35    (18)  all_55_4 = all_53_1
% 228.84/40.35    (19)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.84/40.35          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.84/40.35    (20)   ~ (e3 = e2)
% 228.84/40.35    (21)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 228.84/40.35    (22)   ~ (all_53_1 = all_53_3)
% 228.84/40.35    (23)   ~ (e3 = e0)
% 228.84/40.35    (24)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.84/40.35    (25)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 228.84/40.35    (26)  all_57_15 = e3
% 228.84/40.35    (27)   ~ (all_53_9 = all_53_13)
% 228.84/40.35    (28)  op(e3, e3) = e2
% 228.84/40.35    (29)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.84/40.35          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.84/40.35            e1)
% 228.84/40.35    (30)  all_57_10 = e2
% 228.84/40.35    (31)   ~ (all_53_1 = e1)
% 228.84/40.35    (32)  op(e2, e0) = e2
% 228.84/40.35    (33)  all_55_6 = all_53_9
% 228.84/40.35    (34)   ~ (all_53_1 = all_53_2)
% 228.84/40.35    (35)   ~ (e2 = e0)
% 228.84/40.35    (36)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.84/40.35            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.84/40.35            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.84/40.35            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.84/40.35              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.84/40.35            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.84/40.35            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.84/40.35              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.84/40.35              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.84/40.35            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.84/40.35            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.84/40.35            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.84/40.35              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.84/40.35              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.84/40.35            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.84/40.35              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.84/40.35            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.84/40.35            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.84/40.35              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.84/40.35              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.84/40.35            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.84/40.35            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.84/40.35    (37)  all_55_12 = all_53_3
% 228.84/40.35    (38)   ~ (e1 = e0)
% 228.84/40.35    (39)  all_57_12 = e3
% 228.84/40.35    (40)   ~ (all_53_3 = all_53_11)
% 228.84/40.35    (41)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.84/40.35          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.84/40.35    (42)   ~ (all_53_2 = all_53_3)
% 228.84/40.35    (43)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 228.84/40.35    (44)   ~ (all_53_7 = all_53_11)
% 228.84/40.35    (45)  all_55_8 = all_53_2
% 228.84/40.35    (46)  op(e0, e0) = e3
% 228.84/40.35    (47)  op(e0, e2) = all_53_7
% 228.84/40.35    (48)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.84/40.35          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.84/40.35            e2)
% 228.84/40.35    (49)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.84/40.35              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.84/40.35                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.84/40.35                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.84/40.35    (50)   ~ (all_53_1 = all_53_13)
% 228.84/40.35    (51)  op(e2, e0) = all_53_13
% 228.84/40.35    (52)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.84/40.35          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.84/40.35    (53)  op(e1, e3) = all_53_2
% 228.84/40.35    (54)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.84/40.35          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 228.84/40.35    (55)   ~ (e2 = e1)
% 228.84/40.35    (56)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.84/40.35          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.84/40.35    (57)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 228.84/40.35    (58)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.84/40.35          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.84/40.35    (59)  all_55_14 = all_53_11
% 228.84/40.35    (60)  all_57_14 = e1 & op(e0, e1) = e1
% 228.84/40.35    (61)   ~ (all_53_11 = e3)
% 228.84/40.35  
% 228.84/40.35  Begin of proof
% 228.84/40.35  | 
% 228.84/40.35  | ALPHA: (60) implies:
% 228.84/40.35  |   (62)  all_57_14 = e1
% 228.84/40.35  | 
% 228.84/40.35  | BETA: splitting (41) gives:
% 228.84/40.35  | 
% 228.84/40.35  | Case 1:
% 228.84/40.35  | | 
% 228.84/40.35  | |   (63)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) =
% 228.84/40.35  | |           e3)
% 228.84/40.35  | | 
% 228.84/40.35  | | BETA: splitting (63) gives:
% 228.84/40.35  | | 
% 228.84/40.35  | | Case 1:
% 228.84/40.35  | | | 
% 228.84/40.35  | | |   (64)  all_57_4 = e3 & op(e3, e1) = e3
% 228.84/40.35  | | | 
% 228.84/40.35  | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 228.84/40.35  | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 228.84/40.35  | | |            (24), (25), (26), (27), (28), (31), (32), (33), (34), (35),
% 228.84/40.35  | | |            (36), (37), (38), (40), (42), (43), (44), (45), (46), (47),
% 228.84/40.35  | | |            (49), (50), (51), (53), (55), (56), (57), (58), (59), (61),
% 228.84/40.35  | | |            (64) are inconsistent by sub-proof #631.
% 228.84/40.35  | | | 
% 228.84/40.35  | | Case 2:
% 228.84/40.35  | | | 
% 228.84/40.35  | | |   (65)  all_57_5 = e3 & op(e2, e1) = e3
% 228.84/40.35  | | | 
% 228.84/40.35  | | | ALPHA: (65) implies:
% 228.84/40.35  | | |   (66)  all_57_5 = e3
% 228.84/40.35  | | | 
% 228.84/40.35  | | | REF_CLOSE: (2), (4), (5), (9), (11), (13), (20), (23), (26), (29), (30),
% 228.84/40.35  | | |            (35), (38), (39), (41), (46), (48), (49), (52), (54), (55),
% 228.84/40.35  | | |            (56), (58), (62), (66) are inconsistent by sub-proof #1740.
% 228.84/40.35  | | | 
% 228.84/40.35  | | End of split
% 228.84/40.35  | | 
% 228.84/40.35  | Case 2:
% 228.84/40.35  | | 
% 228.84/40.35  | |   (67)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) =
% 228.84/40.35  | |           e3)
% 228.84/40.35  | | 
% 228.84/40.35  | | REF_CLOSE: (4), (5), (9), (11), (20), (23), (26), (29), (35), (38), (48),
% 228.84/40.35  | |            (49), (55), (67) are inconsistent by sub-proof #1794.
% 228.84/40.35  | | 
% 228.84/40.35  | End of split
% 228.84/40.35  | 
% 228.84/40.35  End of proof
% 228.84/40.35  
% 228.84/40.35  Sub-proof #612 shows that the following formulas are inconsistent:
% 228.84/40.35  ----------------------------------------------------------------
% 228.84/40.35    (1)   ~ (all_53_2 = e2)
% 228.84/40.35    (2)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1)
% 228.84/40.35    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.84/40.35         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.84/40.35    (4)   ~ (e3 = e1)
% 228.84/40.35    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.84/40.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.84/40.35    (6)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.84/40.35         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.84/40.35    (7)   ~ (all_53_3 = e3)
% 228.84/40.35    (8)   ~ (all_53_3 = all_53_7)
% 228.84/40.35    (9)   ~ (all_6_2 = e3)
% 228.84/40.35    (10)   ~ (all_53_9 = e1)
% 228.84/40.35    (11)  op(e1, e1) = all_6_2
% 228.84/40.35    (12)   ~ (all_53_1 = all_53_9)
% 228.84/40.35    (13)  op(e2, e2) = e1
% 228.84/40.35    (14)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.84/40.35          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.84/40.35    (15)  all_57_9 = e1
% 228.84/40.35    (16)   ~ (all_53_13 = e3)
% 228.84/40.35    (17)  all_57_6 = e1
% 228.84/40.35    (18)   ~ (all_53_9 = all_53_11)
% 228.84/40.35    (19)  all_55_4 = all_53_1
% 228.84/40.36    (20)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.84/40.36          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.84/40.36    (21)   ~ (e3 = e2)
% 228.84/40.36    (22)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 228.84/40.36    (23)   ~ (all_53_1 = all_53_3)
% 228.84/40.36    (24)   ~ (e3 = e0)
% 228.84/40.36    (25)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.84/40.36    (26)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 228.84/40.36    (27)  all_57_15 = e3
% 228.84/40.36    (28)   ~ (all_53_9 = all_53_13)
% 228.84/40.36    (29)  op(e3, e3) = e2
% 228.84/40.36    (30)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.84/40.36          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.84/40.36            e1)
% 228.84/40.36    (31)   ~ (all_53_1 = e1)
% 228.84/40.36    (32)  op(e2, e0) = e2
% 228.84/40.36    (33)  all_55_6 = all_53_9
% 228.84/40.36    (34)   ~ (all_53_1 = all_53_2)
% 228.84/40.36    (35)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.84/40.36          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 228.84/40.36    (36)   ~ (e2 = e0)
% 228.84/40.36    (37)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.84/40.36            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.84/40.36            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.84/40.36            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.84/40.36              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.84/40.36            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.84/40.36            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.84/40.36              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.84/40.36              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.84/40.36            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.84/40.36            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.84/40.36            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.84/40.36              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.84/40.36              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.84/40.36            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.84/40.36              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.84/40.36            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.84/40.36            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.84/40.36              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.84/40.36              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.84/40.36            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.84/40.36            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.84/40.36    (38)  all_55_12 = all_53_3
% 228.84/40.36    (39)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.84/40.36          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.84/40.36    (40)   ~ (e1 = e0)
% 228.84/40.36    (41)   ~ (all_53_3 = all_53_11)
% 228.84/40.36    (42)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.84/40.36          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.84/40.36    (43)   ~ (all_53_2 = all_53_3)
% 228.84/40.36    (44)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 228.84/40.36    (45)   ~ (all_53_7 = all_53_11)
% 228.84/40.36    (46)  all_55_8 = all_53_2
% 228.84/40.36    (47)  op(e0, e0) = e3
% 228.84/40.36    (48)  op(e0, e2) = all_53_7
% 228.84/40.36    (49)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.84/40.36          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.84/40.36            e2)
% 228.84/40.36    (50)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.84/40.36              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.84/40.36                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.84/40.36                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.84/40.36    (51)   ~ (all_53_1 = all_53_13)
% 228.84/40.36    (52)  op(e2, e0) = all_53_13
% 228.84/40.36    (53)   ~ (all_53_12 = e3)
% 228.84/40.36    (54)  all_57_7 = e3
% 228.84/40.36    (55)  op(e1, e3) = all_53_2
% 228.84/40.36    (56)   ~ (e2 = e1)
% 228.84/40.36    (57)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.84/40.36          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.84/40.36    (58)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 228.84/40.36    (59)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.84/40.36          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.84/40.36    (60)  all_55_14 = all_53_11
% 228.84/40.36    (61)   ~ (all_53_11 = e3)
% 228.84/40.36    (62)  op(e3, e0) = all_53_12
% 228.84/40.36  
% 228.84/40.36  Begin of proof
% 228.84/40.36  | 
% 228.84/40.36  | BETA: splitting (2) gives:
% 228.84/40.36  | 
% 228.84/40.36  | Case 1:
% 228.84/40.36  | | 
% 228.84/40.36  | |   (63)  all_57_4 = e1 & op(e3, e1) = e1
% 228.84/40.36  | | 
% 228.84/40.36  | | ALPHA: (63) implies:
% 228.84/40.36  | |   (64)  all_57_4 = e1
% 228.84/40.36  | | 
% 228.84/40.36  | | REF_CLOSE: (4), (5), (15), (20), (21), (24), (29), (36), (39), (40), (53),
% 228.84/40.36  | |            (62), (64) are inconsistent by sub-proof #813.
% 228.84/40.36  | | 
% 228.84/40.36  | Case 2:
% 228.84/40.36  | | 
% 228.84/40.36  | |   (65)  all_57_5 = e1 & op(e2, e1) = e1
% 228.84/40.36  | | 
% 228.84/40.36  | | ALPHA: (65) implies:
% 228.84/40.36  | |   (66)  all_57_5 = e1
% 228.84/40.36  | | 
% 228.84/40.36  | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 228.84/40.36  | |            (14), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 228.84/40.36  | |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 228.84/40.36  | |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 228.84/40.36  | |            (48), (49), (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 228.84/40.36  | |            (59), (60), (61), (62), (66) are inconsistent by sub-proof #613.
% 228.84/40.36  | | 
% 228.84/40.36  | End of split
% 228.84/40.36  | 
% 228.84/40.36  End of proof
% 228.84/40.36  
% 228.84/40.36  Sub-proof #613 shows that the following formulas are inconsistent:
% 228.84/40.36  ----------------------------------------------------------------
% 228.84/40.36    (1)   ~ (all_53_2 = e2)
% 228.84/40.36    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.84/40.36         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.84/40.36    (3)   ~ (e3 = e1)
% 228.84/40.36    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.84/40.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.84/40.36    (5)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.84/40.36         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.84/40.36    (6)   ~ (all_53_3 = e3)
% 228.84/40.36    (7)   ~ (all_53_3 = all_53_7)
% 228.84/40.36    (8)   ~ (all_6_2 = e3)
% 228.84/40.36    (9)   ~ (all_53_9 = e1)
% 228.84/40.36    (10)  op(e1, e1) = all_6_2
% 228.84/40.36    (11)   ~ (all_53_1 = all_53_9)
% 228.84/40.36    (12)  op(e2, e2) = e1
% 228.84/40.36    (13)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.84/40.36          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.84/40.36    (14)   ~ (all_53_13 = e3)
% 228.84/40.36    (15)  all_57_6 = e1
% 228.84/40.36    (16)   ~ (all_53_9 = all_53_11)
% 228.84/40.36    (17)  all_55_4 = all_53_1
% 228.90/40.36    (18)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.90/40.36          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.90/40.36    (19)   ~ (e3 = e2)
% 228.90/40.36    (20)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 228.90/40.36    (21)   ~ (all_53_1 = all_53_3)
% 228.90/40.36    (22)   ~ (e3 = e0)
% 228.90/40.36    (23)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.90/40.36    (24)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 228.90/40.36    (25)  all_57_15 = e3
% 228.90/40.36    (26)   ~ (all_53_9 = all_53_13)
% 228.90/40.36    (27)  op(e3, e3) = e2
% 228.90/40.36    (28)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.90/40.36          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.90/40.36            e1)
% 228.90/40.36    (29)   ~ (all_53_1 = e1)
% 228.90/40.36    (30)  op(e2, e0) = e2
% 228.90/40.36    (31)  all_55_6 = all_53_9
% 228.90/40.36    (32)   ~ (all_53_1 = all_53_2)
% 228.90/40.36    (33)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.90/40.36          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 228.90/40.36    (34)   ~ (e2 = e0)
% 228.90/40.36    (35)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.90/40.36            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.90/40.36            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.90/40.36            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.90/40.36              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.90/40.36            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.90/40.36            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.90/40.36              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.90/40.36              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.90/40.36            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.90/40.36            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.90/40.36            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.90/40.36              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.90/40.36              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.90/40.36            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.90/40.36              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.90/40.36            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.90/40.36            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.90/40.36              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.90/40.36              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.90/40.36            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.90/40.36            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.90/40.36    (36)  all_55_12 = all_53_3
% 228.90/40.36    (37)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.90/40.36          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.90/40.36    (38)   ~ (e1 = e0)
% 228.90/40.36    (39)   ~ (all_53_3 = all_53_11)
% 228.90/40.36    (40)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.90/40.36          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.90/40.36    (41)   ~ (all_53_2 = all_53_3)
% 228.90/40.36    (42)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 228.90/40.36    (43)   ~ (all_53_7 = all_53_11)
% 228.90/40.36    (44)  all_55_8 = all_53_2
% 228.90/40.36    (45)  op(e0, e0) = e3
% 228.90/40.36    (46)  op(e0, e2) = all_53_7
% 228.90/40.36    (47)  all_57_5 = e1
% 228.90/40.36    (48)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.90/40.36          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.90/40.36            e2)
% 228.90/40.36    (49)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.90/40.36              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.90/40.36                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.90/40.36                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.90/40.36    (50)   ~ (all_53_1 = all_53_13)
% 228.90/40.36    (51)  op(e2, e0) = all_53_13
% 228.90/40.36    (52)   ~ (all_53_12 = e3)
% 228.90/40.36    (53)  all_57_7 = e3
% 228.90/40.36    (54)  op(e1, e3) = all_53_2
% 228.90/40.36    (55)   ~ (e2 = e1)
% 228.90/40.36    (56)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.90/40.36          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.90/40.36    (57)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 228.90/40.36    (58)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.90/40.36          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.90/40.36    (59)  all_55_14 = all_53_11
% 228.90/40.36    (60)   ~ (all_53_11 = e3)
% 228.90/40.36    (61)  op(e3, e0) = all_53_12
% 228.90/40.36  
% 228.90/40.36  Begin of proof
% 228.90/40.36  | 
% 228.90/40.36  | BETA: splitting (37) gives:
% 228.90/40.36  | 
% 228.90/40.36  | Case 1:
% 228.90/40.36  | | 
% 228.90/40.36  | |   (62)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) =
% 228.90/40.36  | |           e3)
% 228.90/40.36  | | 
% 228.90/40.36  | | BETA: splitting (62) gives:
% 228.90/40.36  | | 
% 228.90/40.36  | | Case 1:
% 228.90/40.36  | | | 
% 228.90/40.36  | | |   (63)  all_57_0 = e3 & op(e3, e3) = e3
% 228.90/40.36  | | | 
% 228.90/40.36  | | | ALPHA: (63) implies:
% 228.90/40.36  | | |   (64)  op(e3, e3) = e3
% 228.90/40.36  | | | 
% 228.90/40.36  | | | REF_CLOSE: (4), (19), (27), (64) are inconsistent by sub-proof #2490.
% 228.90/40.36  | | | 
% 228.90/40.36  | | Case 2:
% 228.90/40.36  | | | 
% 228.90/40.36  | | |   (65)  all_57_1 = e3 & op(e3, e2) = e3
% 228.90/40.36  | | | 
% 228.90/40.36  | | | ALPHA: (65) implies:
% 228.90/40.36  | | |   (66)  all_57_1 = e3
% 228.90/40.36  | | | 
% 228.90/40.36  | | | BETA: splitting (40) gives:
% 228.90/40.36  | | | 
% 228.90/40.36  | | | Case 1:
% 228.90/40.36  | | | | 
% 228.90/40.36  | | | |   (67)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1)
% 228.90/40.36  | | | |           = e3)
% 228.90/40.36  | | | | 
% 228.90/40.36  | | | | BETA: splitting (67) gives:
% 228.90/40.36  | | | | 
% 228.90/40.36  | | | | Case 1:
% 228.90/40.36  | | | | | 
% 228.90/40.36  | | | | |   (68)  all_57_4 = e3 & op(e3, e1) = e3
% 228.90/40.36  | | | | | 
% 228.90/40.36  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 228.90/40.36  | | | | |            (12), (13), (14), (15), (16), (17), (18), (19), (20), (21),
% 228.90/40.36  | | | | |            (22), (23), (24), (25), (26), (27), (29), (30), (31), (32),
% 228.90/40.36  | | | | |            (34), (35), (36), (38), (39), (41), (42), (43), (44), (45),
% 228.90/40.36  | | | | |            (46), (49), (50), (51), (54), (55), (56), (57), (58), (59),
% 228.90/40.36  | | | | |            (60), (68) are inconsistent by sub-proof #631.
% 228.90/40.36  | | | | | 
% 228.90/40.36  | | | | Case 2:
% 228.90/40.36  | | | | | 
% 228.90/40.36  | | | | |   (69)  all_57_5 = e3 & op(e2, e1) = e3
% 228.90/40.36  | | | | | 
% 228.90/40.36  | | | | | ALPHA: (69) implies:
% 228.90/40.36  | | | | |   (70)  all_57_5 = e3
% 228.90/40.36  | | | | | 
% 228.90/40.36  | | | | | COMBINE_EQS: (47), (70) imply:
% 228.90/40.36  | | | | |   (71)  e3 = e1
% 228.90/40.36  | | | | | 
% 228.90/40.36  | | | | | COMBINE_EQS: (66), (71) imply:
% 228.90/40.36  | | | | |   (72)  all_57_1 = e1
% 228.90/40.36  | | | | | 
% 228.90/40.36  | | | | | REF_CLOSE: (2), (4), (12), (19), (22), (33), (34), (38), (53), (55),
% 228.90/40.36  | | | | |            (72) are inconsistent by sub-proof #1909.
% 228.90/40.36  | | | | | 
% 228.90/40.36  | | | | End of split
% 228.90/40.36  | | | | 
% 228.90/40.36  | | | Case 2:
% 228.90/40.36  | | | | 
% 228.90/40.36  | | | |   (73)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1)
% 228.90/40.36  | | | |           = e3)
% 228.90/40.36  | | | | 
% 228.90/40.36  | | | | REF_CLOSE: (3), (4), (8), (10), (19), (22), (25), (28), (34), (38),
% 228.90/40.36  | | | |            (48), (49), (55), (73) are inconsistent by sub-proof #1794.
% 228.90/40.36  | | | | 
% 228.90/40.36  | | | End of split
% 228.90/40.36  | | | 
% 228.90/40.36  | | End of split
% 228.90/40.36  | | 
% 228.90/40.36  | Case 2:
% 228.90/40.36  | | 
% 228.90/40.36  | |   (74)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) =
% 228.90/40.36  | |           e3)
% 228.90/40.36  | | 
% 228.90/40.36  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.90/40.36  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 228.90/40.36  | |            (24), (25), (26), (27), (29), (30), (31), (32), (34), (35), (36),
% 228.90/40.36  | |            (38), (39), (41), (42), (43), (44), (45), (46), (49), (50), (51),
% 228.90/40.36  | |            (52), (54), (55), (56), (57), (58), (59), (60), (61), (74) are
% 228.90/40.36  | |            inconsistent by sub-proof #630.
% 228.90/40.36  | | 
% 228.90/40.36  | End of split
% 228.90/40.36  | 
% 228.90/40.36  End of proof
% 228.90/40.36  
% 228.90/40.36  Sub-proof #614 shows that the following formulas are inconsistent:
% 228.90/40.36  ----------------------------------------------------------------
% 228.90/40.36    (1)   ~ (all_53_2 = e2)
% 228.90/40.36    (2)  all_57_0 = e2
% 228.90/40.36    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.90/40.36         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.90/40.36    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.90/40.36         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.90/40.36    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.90/40.36         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.90/40.36    (6)   ~ (e3 = e1)
% 228.90/40.36    (7)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 228.90/40.36         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 228.90/40.36    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.90/40.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.90/40.36    (9)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.90/40.36         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.90/40.36    (10)   ~ (all_53_3 = e3)
% 228.90/40.36    (11)   ~ (all_53_3 = all_53_7)
% 228.90/40.36    (12)   ~ (all_6_2 = e3)
% 228.90/40.36    (13)   ~ (all_53_9 = e1)
% 228.90/40.36    (14)  op(e1, e1) = all_6_2
% 228.90/40.36    (15)  op(all_52_7, all_52_7) = e0
% 228.90/40.36    (16)   ~ (all_53_1 = all_53_9)
% 228.90/40.36    (17)  op(e2, e2) = e1
% 228.90/40.36    (18)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.90/40.36          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.90/40.36    (19)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 228.90/40.36            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 228.90/40.36              e3) = all_22_1 & $i(all_22_1))
% 228.90/40.36    (20)   ~ (all_53_13 = e3)
% 228.90/40.36    (21)  all_57_7 = e1
% 228.90/40.36    (22)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.90/40.36          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.90/40.36    (23)   ~ (all_53_9 = all_53_11)
% 228.90/40.36    (24)  all_55_4 = all_53_1
% 228.90/40.36    (25)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.90/40.36          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.90/40.36    (26)   ~ (e3 = e2)
% 228.90/40.36    (27)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 228.90/40.36    (28)   ~ (all_53_1 = all_53_3)
% 228.90/40.36    (29)   ~ (e3 = e0)
% 228.90/40.36    (30)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 228.90/40.36          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 228.90/40.36    (31)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.90/40.36    (32)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 228.90/40.36    (33)  all_57_15 = e3
% 228.90/40.36    (34)   ~ (all_53_9 = all_53_13)
% 228.90/40.36    (35)  op(e3, e3) = e2
% 228.90/40.36    (36)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.90/40.36          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.90/40.36            e1)
% 228.90/40.36    (37)   ~ (all_53_1 = e1)
% 228.90/40.36    (38)  op(e3, e3) = all_52_1
% 228.90/40.36    (39)  all_57_11 = e0
% 228.90/40.36    (40)  all_55_6 = all_53_9
% 228.90/40.36    (41)   ~ (all_53_1 = all_53_2)
% 228.90/40.36    (42)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.90/40.36          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 228.90/40.36    (43)  op(all_52_1, all_52_1) = e3
% 228.90/40.36    (44)   ~ (e2 = e0)
% 228.90/40.36    (45)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.90/40.36            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.90/40.36            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.90/40.36            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.90/40.36              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.90/40.36            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.90/40.36            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.90/40.36              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.90/40.36              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.90/40.36            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.90/40.36            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.90/40.36            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.90/40.36              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.90/40.36              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.90/40.36            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.90/40.36              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.90/40.36            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.90/40.36            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.90/40.36              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.90/40.36              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.90/40.36            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.90/40.36            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.90/40.36    (46)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 228.90/40.36            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 228.90/40.36              e3) = all_12_1 & $i(all_12_1))
% 228.90/40.36    (47)  all_55_12 = all_53_3
% 228.90/40.36    (48)  all_57_3 = e1
% 228.90/40.36    (49)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.90/40.36          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.90/40.36    (50)   ~ (e1 = e0)
% 228.90/40.36    (51)   ~ (all_53_3 = all_53_11)
% 228.90/40.36    (52)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.90/40.36          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.90/40.36    (53)  all_57_6 = e3
% 228.90/40.36    (54)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.90/40.36          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.90/40.36    (55)   ~ (all_53_2 = all_53_3)
% 228.90/40.36    (56)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 228.90/40.36    (57)   ~ (all_53_7 = all_53_11)
% 228.90/40.36    (58)  all_55_8 = all_53_2
% 228.90/40.36    (59)  op(e0, e0) = e3
% 228.90/40.36    (60)  op(e0, e2) = all_53_7
% 228.90/40.36    (61)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.90/40.36          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.90/40.36            e2)
% 228.90/40.36    (62)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.90/40.36              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.90/40.36                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.90/40.36                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.90/40.36    (63)   ~ (all_53_1 = all_53_13)
% 228.90/40.36    (64)  op(e2, e0) = all_53_13
% 228.90/40.36    (65)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.90/40.36          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.90/40.36    (66)   ~ (all_53_12 = e3)
% 228.90/40.36    (67)  op(e1, e3) = all_53_2
% 228.90/40.36    (68)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.90/40.36          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.90/40.36    (69)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.90/40.36          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.90/40.36    (70)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.90/40.36          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 228.90/40.36    (71)   ~ (e2 = e1)
% 228.90/40.36    (72)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.90/40.36          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.90/40.36    (73)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.90/40.36          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.90/40.36    (74)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 228.90/40.36    (75)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.90/40.36          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.90/40.36    (76)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.90/40.36          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.90/40.36    (77)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 228.90/40.36          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 228.90/40.36    (78)  all_55_14 = all_53_11
% 228.90/40.36    (79)  op(e3, e0) = all_52_7
% 228.90/40.36    (80)   ~ (all_53_11 = e3)
% 228.90/40.36    (81)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.90/40.36          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.90/40.36    (82)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.90/40.36          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.90/40.36    (83)  op(e3, e0) = all_53_12
% 228.90/40.36  
% 228.90/40.36  Begin of proof
% 228.90/40.36  | 
% 228.90/40.36  | BETA: splitting (54) gives:
% 228.90/40.36  | 
% 228.90/40.36  | Case 1:
% 228.90/40.36  | | 
% 228.90/40.36  | |   (84)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 228.90/40.36  | |           e3)
% 228.90/40.36  | | 
% 228.90/40.36  | | BETA: splitting (84) gives:
% 228.90/40.36  | | 
% 228.90/40.36  | | Case 1:
% 228.90/40.36  | | | 
% 228.90/40.36  | | |   (85)  all_57_1 = e3 & op(e3, e2) = e3
% 228.90/40.36  | | | 
% 228.90/40.36  | | | ALPHA: (85) implies:
% 228.90/40.36  | | |   (86)  all_57_1 = e3
% 228.90/40.36  | | | 
% 228.90/40.36  | | | BETA: splitting (25) gives:
% 228.90/40.36  | | | 
% 228.90/40.36  | | | Case 1:
% 228.90/40.36  | | | | 
% 228.90/40.36  | | | |   (87)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2)
% 228.90/40.36  | | | |           = e0)
% 228.90/40.36  | | | | 
% 228.90/40.36  | | | | REF_CLOSE: (5), (6), (8), (9), (12), (14), (17), (26), (29), (33), (35),
% 228.90/40.36  | | | |            (42), (44), (50), (53), (62), (71), (72), (76), (81), (86),
% 228.90/40.36  | | | |            (87) are inconsistent by sub-proof #625.
% 228.90/40.36  | | | | 
% 228.90/40.36  | | | Case 2:
% 228.90/40.36  | | | | 
% 228.90/40.36  | | | |   (88)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0)
% 228.90/40.36  | | | |           = e0)
% 228.90/40.36  | | | | 
% 228.90/40.36  | | | | BETA: splitting (88) gives:
% 228.90/40.36  | | | | 
% 228.90/40.36  | | | | Case 1:
% 228.90/40.36  | | | | | 
% 228.90/40.36  | | | | |   (89)  all_57_4 = e0 & op(e3, e1) = e0
% 228.90/40.36  | | | | | 
% 228.90/40.36  | | | | | ALPHA: (89) implies:
% 228.90/40.36  | | | | |   (90)  all_57_4 = e0
% 228.90/40.36  | | | | | 
% 228.90/40.36  | | | | | BETA: splitting (72) gives:
% 228.90/40.36  | | | | | 
% 228.90/40.36  | | | | | Case 1:
% 228.90/40.36  | | | | | | 
% 228.90/40.37  | | | | | |   (91)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2,
% 228.90/40.37  | | | | | |             e0) = e2)
% 228.90/40.37  | | | | | | 
% 228.90/40.37  | | | | | | BETA: splitting (91) gives:
% 228.90/40.37  | | | | | | 
% 228.90/40.37  | | | | | | Case 1:
% 228.90/40.37  | | | | | | | 
% 228.90/40.37  | | | | | | |   (92)  all_57_9 = e2 & op(e3, e0) = e2
% 228.90/40.37  | | | | | | | 
% 228.90/40.37  | | | | | | | REF_CLOSE: (3), (4), (5), (6), (8), (9), (12), (14), (17), (18),
% 228.90/40.37  | | | | | | |            (22), (25), (26), (29), (33), (35), (36), (39), (42),
% 228.90/40.37  | | | | | | |            (44), (48), (49), (50), (52), (54), (59), (61), (62),
% 228.90/40.37  | | | | | | |            (66), (68), (69), (70), (71), (72), (75), (76), (81),
% 228.90/40.37  | | | | | | |            (83), (90), (92) are inconsistent by sub-proof #624.
% 228.90/40.37  | | | | | | | 
% 228.90/40.37  | | | | | | Case 2:
% 228.90/40.37  | | | | | | | 
% 228.90/40.37  | | | | | | |   (93)  all_57_10 = e2 & op(e2, e0) = e2
% 228.90/40.37  | | | | | | | 
% 228.90/40.37  | | | | | | | ALPHA: (93) implies:
% 228.90/40.37  | | | | | | |   (94)  all_57_10 = e2
% 228.90/40.37  | | | | | | |   (95)  op(e2, e0) = e2
% 228.90/40.37  | | | | | | | 
% 228.90/40.37  | | | | | | | BETA: splitting (70) gives:
% 228.90/40.37  | | | | | | | 
% 228.90/40.37  | | | | | | | Case 1:
% 228.90/40.37  | | | | | | | | 
% 228.90/40.37  | | | | | | | |   (96)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 &
% 228.90/40.37  | | | | | | | |           op(e2, e2) = e0)
% 228.90/40.37  | | | | | | | | 
% 228.90/40.37  | | | | | | | | BETA: splitting (96) gives:
% 228.90/40.37  | | | | | | | | 
% 228.90/40.37  | | | | | | | | Case 1:
% 228.90/40.37  | | | | | | | | | 
% 228.90/40.37  | | | | | | | | |   (97)  all_57_2 = e0 & op(e2, e3) = e0
% 228.90/40.37  | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | ALPHA: (97) implies:
% 228.90/40.37  | | | | | | | | |   (98)  all_57_2 = e0
% 228.90/40.37  | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | BETA: splitting (76) gives:
% 228.90/40.37  | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | Case 1:
% 228.90/40.37  | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | |   (99)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1
% 228.90/40.37  | | | | | | | | | |           & op(e2, e0) = e1)
% 228.90/40.37  | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | BETA: splitting (99) gives:
% 228.90/40.37  | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | Case 1:
% 228.90/40.37  | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | |   (100)  all_57_9 = e1 & op(e3, e0) = e1
% 228.90/40.37  | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | ALPHA: (100) implies:
% 228.90/40.37  | | | | | | | | | | |   (101)  all_57_9 = e1
% 228.90/40.37  | | | | | | | | | | |   (102)  op(e3, e0) = e1
% 228.90/40.37  | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | BETA: splitting (52) gives:
% 228.90/40.37  | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | Case 1:
% 228.90/40.37  | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | |   (103)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 228.90/40.37  | | | | | | | | | | | |            & op(e2, e1) = e3)
% 228.90/40.37  | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | BETA: splitting (103) gives:
% 228.90/40.37  | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | Case 1:
% 228.90/40.37  | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | |   (104)  all_57_4 = e3 & op(e3, e1) = e3
% 228.90/40.37  | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | REF_CLOSE: (1), (5), (6), (8), (9), (10), (11), (12), (13),
% 228.90/40.37  | | | | | | | | | | | | |            (14), (16), (17), (18), (20), (23), (24), (25),
% 228.90/40.37  | | | | | | | | | | | | |            (26), (27), (28), (29), (31), (32), (33), (34),
% 228.90/40.37  | | | | | | | | | | | | |            (35), (37), (40), (41), (44), (45), (47), (50),
% 228.90/40.37  | | | | | | | | | | | | |            (51), (53), (55), (56), (57), (58), (59), (60),
% 228.90/40.37  | | | | | | | | | | | | |            (62), (63), (64), (67), (71), (72), (74), (76),
% 228.90/40.37  | | | | | | | | | | | | |            (78), (80), (90), (95), (104) are inconsistent by
% 228.90/40.37  | | | | | | | | | | | | |            sub-proof #623.
% 228.90/40.37  | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | Case 2:
% 228.90/40.37  | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | |   (105)  all_57_5 = e3 & op(e2, e1) = e3
% 228.90/40.37  | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | ALPHA: (105) implies:
% 228.90/40.37  | | | | | | | | | | | | |   (106)  all_57_5 = e3
% 228.90/40.37  | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | BETA: splitting (42) gives:
% 228.90/40.37  | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | Case 1:
% 228.90/40.37  | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | |   (107)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 228.90/40.37  | | | | | | | | | | | | | |            & op(e2, e2) = e0)
% 228.90/40.37  | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 228.90/40.37  | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | Case 1:
% 228.90/40.37  | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | |   (108)  all_57_1 = e0 & op(e3, e2) = e0
% 228.90/40.37  | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | ALPHA: (108) implies:
% 228.90/40.37  | | | | | | | | | | | | | | |   (109)  all_57_1 = e0
% 228.90/40.37  | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | COMBINE_EQS: (86), (109) imply:
% 228.90/40.37  | | | | | | | | | | | | | | |   (110)  e3 = e0
% 228.90/40.37  | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | COMBINE_EQS: (53), (110) imply:
% 228.90/40.37  | | | | | | | | | | | | | | |   (111)  all_57_6 = e0
% 228.90/40.37  | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | COMBINE_EQS: (106), (110) imply:
% 228.90/40.37  | | | | | | | | | | | | | | |   (112)  all_57_5 = e0
% 228.90/40.37  | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | REF_CLOSE: (1), (5), (6), (8), (9), (10), (11), (12), (13),
% 228.90/40.37  | | | | | | | | | | | | | | |            (14), (16), (17), (18), (20), (23), (24), (25),
% 228.90/40.37  | | | | | | | | | | | | | | |            (26), (27), (28), (29), (31), (32), (33), (34),
% 228.90/40.37  | | | | | | | | | | | | | | |            (35), (36), (37), (40), (41), (44), (45), (47),
% 228.90/40.37  | | | | | | | | | | | | | | |            (50), (51), (52), (55), (56), (57), (58), (59),
% 228.90/40.37  | | | | | | | | | | | | | | |            (60), (61), (62), (63), (64), (67), (71), (72),
% 228.90/40.37  | | | | | | | | | | | | | | |            (74), (76), (78), (80), (95), (111), (112) are
% 228.90/40.37  | | | | | | | | | | | | | | |            inconsistent by sub-proof #650.
% 228.90/40.37  | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | Case 2:
% 228.90/40.37  | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | |   (113)  all_57_3 = e0 & op(e2, e2) = e0
% 228.90/40.37  | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | ALPHA: (113) implies:
% 228.90/40.37  | | | | | | | | | | | | | | |   (114)  all_57_3 = e0
% 228.90/40.37  | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (26), (44), (50), (68), (71), (98),
% 228.90/40.37  | | | | | | | | | | | | | | |            (106), (114) are inconsistent by sub-proof #2253.
% 228.90/40.37  | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | End of split
% 228.90/40.37  | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | Case 2:
% 228.90/40.37  | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | |   (115)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 228.90/40.37  | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0)
% 228.90/40.37  | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | BETA: splitting (115) gives:
% 228.90/40.37  | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | Case 1:
% 228.90/40.37  | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | |   (116)  all_57_7 = e0 & op(e1, e2) = e0
% 228.90/40.37  | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (21), (26), (44), (48), (50), (68),
% 228.90/40.37  | | | | | | | | | | | | | | |            (71), (98), (106), (116) are inconsistent by
% 228.90/40.37  | | | | | | | | | | | | | | |            sub-proof #622.
% 228.90/40.37  | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | Case 2:
% 228.90/40.37  | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | |   (117)  all_57_13 = e0 & op(e0, e2) = e0
% 228.90/40.37  | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | ALPHA: (117) implies:
% 228.90/40.37  | | | | | | | | | | | | | | |   (118)  all_57_13 = e0
% 228.90/40.37  | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | BETA: splitting (61) gives:
% 228.90/40.37  | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | Case 1:
% 228.90/40.37  | | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | |   (119)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 228.90/40.37  | | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 228.90/40.37  | | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10),
% 228.90/40.37  | | | | | | | | | | | | | | | |            (11), (12), (13), (14), (16), (17), (18), (20),
% 228.90/40.37  | | | | | | | | | | | | | | | |            (22), (23), (24), (25), (26), (27), (28), (29),
% 228.90/40.37  | | | | | | | | | | | | | | | |            (31), (32), (33), (34), (35), (36), (37), (40),
% 228.90/40.37  | | | | | | | | | | | | | | | |            (41), (42), (44), (45), (47), (48), (49), (50),
% 228.90/40.37  | | | | | | | | | | | | | | | |            (51), (52), (53), (54), (55), (56), (57), (58),
% 228.90/40.37  | | | | | | | | | | | | | | | |            (59), (60), (61), (62), (63), (64), (65), (66),
% 228.90/40.37  | | | | | | | | | | | | | | | |            (67), (68), (69), (70), (71), (72), (73), (74),
% 228.90/40.37  | | | | | | | | | | | | | | | |            (75), (76), (78), (80), (81), (83), (86), (94),
% 228.90/40.37  | | | | | | | | | | | | | | | |            (95), (101), (119) are inconsistent by sub-proof
% 228.90/40.37  | | | | | | | | | | | | | | | |            #634.
% 228.90/40.37  | | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | Case 2:
% 228.90/40.37  | | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | |   (120)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 228.90/40.37  | | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 228.90/40.37  | | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | | BETA: splitting (120) gives:
% 228.90/40.37  | | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | | Case 1:
% 228.90/40.37  | | | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | | |   (121)  all_57_14 = e2 & op(e0, e1) = e2
% 228.90/40.37  | | | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | | | ALPHA: (121) implies:
% 228.90/40.37  | | | | | | | | | | | | | | | | |   (122)  all_57_14 = e2
% 228.90/40.37  | | | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | | | BETA: splitting (36) gives:
% 228.90/40.37  | | | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | | | Case 1:
% 228.90/40.37  | | | | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | | | |   (123)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 228.90/40.37  | | | | | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 228.90/40.37  | | | | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | | | | BETA: splitting (123) gives:
% 228.90/40.37  | | | | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | | | | Case 1:
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | | | | |   (124)  all_57_12 = e1 & op(e0, e3) = e1
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | ALPHA: (124) implies:
% 228.90/40.37  | | | | | | | | | | | | | | | | | | |   (125)  all_57_12 = e1
% 228.90/40.37  | | | | | | | | | | | | | | | | | | |   (126)  op(e0, e3) = e1
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | BETA: splitting (30) gives:
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | Case 1:
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | |   (127)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e1)
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | | BETA: splitting (127) gives:
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | | Case 1:
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | | |   (128)  all_57_4 = e1 & op(e3, e1) = e1
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | | | ALPHA: (128) implies:
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | | |   (129)  all_57_4 = e1
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (25), (26), (29), (35), (44), (49),
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | | |            (50), (66), (83), (101), (129) are inconsistent by
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | | |            sub-proof #813.
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | | Case 2:
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | | |   (130)  all_57_5 = e1 & op(e2, e1) = e1
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (5), (6), (8), (12), (14), (17), (18),
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | | |            (22), (25), (26), (29), (33), (36), (42), (44),
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | | |            (50), (52), (53), (54), (61), (62), (65), (71),
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | | |            (72), (73), (75), (86), (118), (130) are
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #620.
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | | End of split
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | Case 2:
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | |   (131)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e1) = e1)
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | | BETA: splitting (131) gives:
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | | Case 1:
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | | |   (132)  all_57_8 = e1 & op(e1, e1) = e1
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | | | ALPHA: (132) implies:
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | | |   (133)  op(e1, e1) = e1
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (12), (14),
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | | |            (15), (17), (18), (19), (22), (25), (26), (29),
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | | |            (33), (35), (36), (42), (44), (46), (48), (49),
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | | |            (50), (54), (59), (61), (62), (65), (66), (68),
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | | |            (69), (71), (72), (73), (75), (76), (77), (79),
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | | |            (81), (82), (83), (101), (102), (125), (126),
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | | |            (133) are inconsistent by sub-proof #706.
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | | Case 2:
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | | |   (134)  all_57_14 = e1 & op(e0, e1) = e1
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (5), (6), (8), (9), (12), (14), (17),
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | | |            (18), (22), (25), (26), (29), (33), (35), (36),
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | | |            (42), (44), (48), (49), (50), (52), (54), (59),
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | | |            (61), (62), (65), (66), (68), (69), (70), (71),
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | | |            (72), (75), (76), (81), (83), (94), (101), (122),
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | | |            (134) are inconsistent by sub-proof #619.
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | | End of split
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | End of split
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | | | | Case 2:
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | | | | |   (135)  all_57_13 = e1 & op(e0, e2) = e1
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | ALPHA: (135) implies:
% 228.90/40.37  | | | | | | | | | | | | | | | | | | |   (136)  all_57_13 = e1
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (9), (12), (14),
% 228.90/40.37  | | | | | | | | | | | | | | | | | | |            (17), (18), (25), (26), (29), (33), (35), (36),
% 228.90/40.37  | | | | | | | | | | | | | | | | | | |            (42), (44), (48), (49), (50), (54), (59), (61),
% 228.90/40.37  | | | | | | | | | | | | | | | | | | |            (62), (65), (66), (68), (69), (71), (72), (75),
% 228.90/40.37  | | | | | | | | | | | | | | | | | | |            (76), (81), (83), (86), (122), (136) are
% 228.90/40.37  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #769.
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | | | | End of split
% 228.90/40.37  | | | | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | | | Case 2:
% 228.90/40.37  | | | | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | | | |   (137)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 228.90/40.37  | | | | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 228.90/40.37  | | | | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | | | | BETA: splitting (137) gives:
% 228.90/40.37  | | | | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | | | | Case 1:
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | | | | |   (138)  all_57_14 = e1 & op(e0, e1) = e1
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (5), (6), (8), (9), (12), (14), (17),
% 228.90/40.37  | | | | | | | | | | | | | | | | | | |            (18), (22), (25), (26), (29), (33), (35), (36),
% 228.90/40.37  | | | | | | | | | | | | | | | | | | |            (42), (44), (48), (49), (50), (52), (54), (59),
% 228.90/40.37  | | | | | | | | | | | | | | | | | | |            (61), (62), (65), (66), (68), (69), (70), (71),
% 228.90/40.37  | | | | | | | | | | | | | | | | | | |            (72), (75), (76), (81), (83), (94), (101), (122),
% 228.90/40.37  | | | | | | | | | | | | | | | | | | |            (138) are inconsistent by sub-proof #619.
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | | | | Case 2:
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | | | | |   (139)  all_57_15 = e1 & op(e0, e0) = e1
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | ALPHA: (139) implies:
% 228.90/40.37  | | | | | | | | | | | | | | | | | | |   (140)  op(e0, e0) = e1
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (59), (140) are inconsistent by
% 228.90/40.37  | | | | | | | | | | | | | | | | | | |            sub-proof #2183.
% 228.90/40.37  | | | | | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | | | | End of split
% 228.90/40.37  | | | | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | | | End of split
% 228.90/40.37  | | | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | | Case 2:
% 228.90/40.37  | | | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | | |   (141)  all_57_15 = e2 & op(e0, e0) = e2
% 228.90/40.37  | | | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (18), (25), (26), (29), (33), (35),
% 228.90/40.37  | | | | | | | | | | | | | | | | |            (44), (49), (50), (66), (71), (83), (86), (141)
% 228.90/40.37  | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #633.
% 228.90/40.37  | | | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | | End of split
% 228.90/40.37  | | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | | End of split
% 228.90/40.37  | | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | | End of split
% 228.90/40.37  | | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | | End of split
% 228.90/40.37  | | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | End of split
% 228.90/40.37  | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | Case 2:
% 228.90/40.37  | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | |   (142)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 228.90/40.37  | | | | | | | | | | | |            e3 & op(e0, e1) = e3)
% 228.90/40.37  | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | | REF_CLOSE: (6), (8), (12), (14), (26), (29), (33), (36),
% 228.90/40.37  | | | | | | | | | | | |            (44), (50), (61), (62), (71), (142) are
% 228.90/40.37  | | | | | | | | | | | |            inconsistent by sub-proof #1794.
% 228.90/40.37  | | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | End of split
% 228.90/40.37  | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | Case 2:
% 228.90/40.37  | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | |   (143)  all_57_10 = e1 & op(e2, e0) = e1
% 228.90/40.37  | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | | REF_CLOSE: (71), (94), (143) are inconsistent by sub-proof
% 228.90/40.37  | | | | | | | | | | |            #2360.
% 228.90/40.37  | | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | End of split
% 228.90/40.37  | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | Case 2:
% 228.90/40.37  | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | |   (144)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 228.90/40.37  | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 228.90/40.37  | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | | REF_CLOSE: (3), (6), (8), (26), (29), (39), (44), (48), (50),
% 228.90/40.37  | | | | | | | | | |            (59), (65), (68), (71), (98), (144) are
% 228.90/40.37  | | | | | | | | | |            inconsistent by sub-proof #618.
% 228.90/40.37  | | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | End of split
% 228.90/40.37  | | | | | | | | | 
% 228.90/40.37  | | | | | | | | Case 2:
% 228.90/40.37  | | | | | | | | | 
% 228.90/40.37  | | | | | | | | |   (145)  all_57_3 = e0 & op(e2, e2) = e0
% 228.90/40.37  | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | ALPHA: (145) implies:
% 228.90/40.37  | | | | | | | | |   (146)  op(e2, e2) = e0
% 228.90/40.37  | | | | | | | | | 
% 228.90/40.37  | | | | | | | | | REF_CLOSE: (8), (29), (35), (38), (43), (146) are inconsistent
% 228.90/40.37  | | | | | | | | |            by sub-proof #1653.
% 228.90/40.37  | | | | | | | | | 
% 228.90/40.37  | | | | | | | | End of split
% 228.90/40.37  | | | | | | | | 
% 228.90/40.37  | | | | | | | Case 2:
% 228.90/40.37  | | | | | | | | 
% 228.90/40.37  | | | | | | | |   (147)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 &
% 228.90/40.37  | | | | | | | |            op(e2, e0) = e0)
% 228.90/40.37  | | | | | | | | 
% 228.90/40.37  | | | | | | | | REF_CLOSE: (1), (5), (6), (8), (9), (10), (11), (12), (13),
% 228.90/40.37  | | | | | | | |            (14), (16), (17), (18), (20), (23), (24), (25), (26),
% 228.90/40.37  | | | | | | | |            (27), (28), (29), (31), (32), (33), (34), (35), (36),
% 228.90/40.37  | | | | | | | |            (37), (39), (40), (41), (44), (45), (47), (50), (51),
% 228.90/40.37  | | | | | | | |            (52), (53), (55), (56), (57), (58), (59), (60), (61),
% 228.90/40.37  | | | | | | | |            (62), (63), (64), (67), (71), (72), (74), (76), (78),
% 228.90/40.37  | | | | | | | |            (80), (90), (95), (147) are inconsistent by sub-proof
% 228.90/40.37  | | | | | | | |            #616.
% 228.90/40.37  | | | | | | | | 
% 228.90/40.37  | | | | | | | End of split
% 228.90/40.37  | | | | | | | 
% 228.90/40.37  | | | | | | End of split
% 228.90/40.37  | | | | | | 
% 228.90/40.37  | | | | | Case 2:
% 228.90/40.37  | | | | | | 
% 228.90/40.37  | | | | | |   (148)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 &
% 228.90/40.37  | | | | | |            op(e0, e0) = e2)
% 228.90/40.37  | | | | | | 
% 228.90/40.37  | | | | | | BETA: splitting (148) gives:
% 228.90/40.37  | | | | | | 
% 228.90/40.37  | | | | | | Case 1:
% 228.90/40.37  | | | | | | | 
% 228.90/40.37  | | | | | | |   (149)  all_57_11 = e2 & op(e1, e0) = e2
% 228.90/40.37  | | | | | | | 
% 228.90/40.37  | | | | | | | REF_CLOSE: (39), (44), (149) are inconsistent by sub-proof #1988.
% 228.90/40.37  | | | | | | | 
% 228.90/40.37  | | | | | | Case 2:
% 228.90/40.37  | | | | | | | 
% 228.90/40.37  | | | | | | |   (150)  all_57_15 = e2 & op(e0, e0) = e2
% 228.90/40.37  | | | | | | | 
% 228.90/40.37  | | | | | | | REF_CLOSE: (6), (8), (18), (25), (26), (29), (33), (35), (44),
% 228.90/40.37  | | | | | | |            (49), (50), (66), (71), (83), (86), (150) are
% 228.90/40.37  | | | | | | |            inconsistent by sub-proof #707.
% 228.90/40.37  | | | | | | | 
% 228.90/40.37  | | | | | | End of split
% 228.90/40.37  | | | | | | 
% 228.90/40.37  | | | | | End of split
% 228.90/40.37  | | | | | 
% 228.90/40.37  | | | | Case 2:
% 228.90/40.37  | | | | | 
% 228.90/40.37  | | | | |   (151)  all_57_9 = e0 & op(e3, e0) = e0
% 228.90/40.37  | | | | | 
% 228.90/40.37  | | | | | ALPHA: (151) implies:
% 228.90/40.37  | | | | |   (152)  all_57_9 = e0
% 228.90/40.37  | | | | | 
% 228.90/40.37  | | | | | REF_CLOSE: (6), (26), (33), (39), (44), (50), (71), (72), (76), (152)
% 228.90/40.37  | | | | |            are inconsistent by sub-proof #1144.
% 228.90/40.37  | | | | | 
% 228.90/40.37  | | | | End of split
% 228.90/40.37  | | | | 
% 228.90/40.37  | | | End of split
% 228.90/40.37  | | | 
% 228.90/40.37  | | Case 2:
% 228.90/40.37  | | | 
% 228.90/40.37  | | |   (153)  all_57_3 = e3 & op(e2, e2) = e3
% 228.90/40.37  | | | 
% 228.90/40.37  | | | ALPHA: (153) implies:
% 228.90/40.37  | | |   (154)  op(e2, e2) = e3
% 228.90/40.37  | | | 
% 228.90/40.37  | | | REF_CLOSE: (6), (8), (17), (154) are inconsistent by sub-proof #1912.
% 228.90/40.37  | | | 
% 228.90/40.37  | | End of split
% 228.90/40.37  | | 
% 228.90/40.37  | Case 2:
% 228.90/40.37  | | 
% 228.90/40.37  | |   (155)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 228.90/40.37  | |            e3)
% 228.90/40.37  | | 
% 228.90/40.37  | | REF_CLOSE: (6), (8), (21), (26), (29), (33), (36), (44), (50), (59), (61),
% 228.90/40.37  | |            (62), (71), (155) are inconsistent by sub-proof #615.
% 228.90/40.37  | | 
% 228.90/40.37  | End of split
% 228.90/40.37  | 
% 228.90/40.37  End of proof
% 228.90/40.37  
% 228.90/40.37  Sub-proof #615 shows that the following formulas are inconsistent:
% 228.90/40.37  ----------------------------------------------------------------
% 228.90/40.37    (1)   ~ (e3 = e1)
% 228.90/40.37    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.90/40.37           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.90/40.37    (3)  all_57_7 = e1
% 228.90/40.37    (4)   ~ (e3 = e2)
% 228.90/40.37    (5)   ~ (e3 = e0)
% 228.90/40.37    (6)  all_57_15 = e3
% 228.90/40.37    (7)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 228.90/40.37         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.90/40.37    (8)   ~ (e2 = e0)
% 228.90/40.37    (9)   ~ (e1 = e0)
% 228.90/40.37    (10)  op(e0, e0) = e3
% 228.90/40.37    (11)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.90/40.37          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.90/40.37            e2)
% 228.90/40.37    (12)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.90/40.37              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.90/40.37                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.90/40.37                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.90/40.37    (13)   ~ (e2 = e1)
% 228.90/40.37    (14)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.90/40.37  
% 228.90/40.37  Begin of proof
% 228.90/40.37  | 
% 228.90/40.37  | BETA: splitting (14) gives:
% 228.90/40.37  | 
% 228.90/40.37  | Case 1:
% 228.90/40.37  | | 
% 228.90/40.37  | |   (15)  all_57_7 = e3 & op(e1, e2) = e3
% 228.90/40.37  | | 
% 228.90/40.37  | | ALPHA: (15) implies:
% 228.90/40.37  | |   (16)  all_57_7 = e3
% 228.90/40.37  | | 
% 228.90/40.37  | | REF_CLOSE: (1), (3), (16) are inconsistent by sub-proof #2115.
% 228.90/40.37  | | 
% 228.90/40.37  | Case 2:
% 228.90/40.37  | | 
% 228.90/40.37  | |   (17)  all_57_13 = e3 & op(e0, e2) = e3
% 228.90/40.37  | | 
% 228.90/40.37  | | ALPHA: (17) implies:
% 228.90/40.37  | |   (18)  all_57_13 = e3
% 228.90/40.37  | | 
% 228.90/40.37  | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 228.90/40.37  | |            (18) are inconsistent by sub-proof #1792.
% 228.90/40.37  | | 
% 228.90/40.37  | End of split
% 228.90/40.37  | 
% 228.90/40.37  End of proof
% 228.90/40.37  
% 228.90/40.37  Sub-proof #616 shows that the following formulas are inconsistent:
% 228.90/40.37  ----------------------------------------------------------------
% 228.90/40.37    (1)   ~ (all_53_2 = e2)
% 228.90/40.37    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.90/40.37         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.90/40.37    (3)   ~ (e3 = e1)
% 228.90/40.37    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.90/40.37           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.90/40.37    (5)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.90/40.37         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.90/40.37    (6)   ~ (all_53_3 = e3)
% 228.90/40.37    (7)   ~ (all_53_3 = all_53_7)
% 228.90/40.37    (8)   ~ (all_6_2 = e3)
% 228.90/40.37    (9)   ~ (all_53_9 = e1)
% 228.90/40.37    (10)  op(e1, e1) = all_6_2
% 228.90/40.37    (11)   ~ (all_53_1 = all_53_9)
% 228.90/40.37    (12)  op(e2, e2) = e1
% 228.90/40.38    (13)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.90/40.38          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.90/40.38    (14)  all_57_4 = e0
% 228.90/40.38    (15)   ~ (all_53_13 = e3)
% 228.90/40.38    (16)   ~ (all_53_9 = all_53_11)
% 228.90/40.38    (17)  all_55_4 = all_53_1
% 228.90/40.38    (18)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.90/40.38          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.90/40.38    (19)   ~ (e3 = e2)
% 228.90/40.38    (20)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 228.90/40.38    (21)   ~ (all_53_1 = all_53_3)
% 228.90/40.38    (22)   ~ (e3 = e0)
% 228.90/40.38    (23)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.90/40.38    (24)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 228.90/40.38    (25)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 228.90/40.38    (26)  all_57_15 = e3
% 228.90/40.38    (27)   ~ (all_53_9 = all_53_13)
% 228.90/40.38    (28)  op(e3, e3) = e2
% 228.90/40.38    (29)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.90/40.38          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.90/40.38            e1)
% 228.90/40.38    (30)   ~ (all_53_1 = e1)
% 228.90/40.38    (31)  op(e2, e0) = e2
% 228.90/40.38    (32)  all_57_11 = e0
% 228.90/40.38    (33)  all_55_6 = all_53_9
% 228.90/40.38    (34)   ~ (all_53_1 = all_53_2)
% 228.90/40.38    (35)   ~ (e2 = e0)
% 228.90/40.38    (36)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.90/40.38            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.90/40.38            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.90/40.38            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.90/40.38              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.90/40.38            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.90/40.38            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.90/40.38              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.90/40.38              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.90/40.38            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.90/40.38            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.90/40.38            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.90/40.38              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.90/40.38              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.90/40.38            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.90/40.38              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.90/40.38            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.90/40.38            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.90/40.38              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.90/40.38              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.90/40.38            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.90/40.38            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.90/40.38    (37)  all_55_12 = all_53_3
% 228.90/40.38    (38)   ~ (e1 = e0)
% 228.90/40.38    (39)   ~ (all_53_3 = all_53_11)
% 228.90/40.38    (40)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.90/40.38          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.90/40.38    (41)  all_57_6 = e3
% 228.90/40.38    (42)   ~ (all_53_2 = all_53_3)
% 228.90/40.38    (43)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 228.90/40.38    (44)   ~ (all_53_7 = all_53_11)
% 228.90/40.38    (45)  all_55_8 = all_53_2
% 228.90/40.38    (46)  op(e0, e0) = e3
% 228.90/40.38    (47)  op(e0, e2) = all_53_7
% 228.90/40.38    (48)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.90/40.38          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.90/40.38            e2)
% 228.90/40.38    (49)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.90/40.38              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.90/40.38                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.90/40.38                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.90/40.38    (50)   ~ (all_53_1 = all_53_13)
% 228.90/40.38    (51)  op(e2, e0) = all_53_13
% 228.90/40.38    (52)  op(e1, e3) = all_53_2
% 228.90/40.38    (53)   ~ (e2 = e1)
% 228.90/40.38    (54)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.90/40.38          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.90/40.38    (55)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 228.90/40.38    (56)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.90/40.38          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.90/40.38    (57)  all_55_14 = all_53_11
% 228.90/40.38    (58)   ~ (all_53_11 = e3)
% 228.90/40.38  
% 228.90/40.38  Begin of proof
% 228.90/40.38  | 
% 228.90/40.38  | BETA: splitting (24) gives:
% 228.90/40.38  | 
% 228.90/40.38  | Case 1:
% 228.90/40.38  | | 
% 228.90/40.38  | |   (59)  all_57_5 = e0 & op(e2, e1) = e0
% 228.90/40.38  | | 
% 228.90/40.38  | | ALPHA: (59) implies:
% 228.90/40.38  | |   (60)  all_57_5 = e0
% 228.90/40.38  | | 
% 228.90/40.38  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.90/40.38  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 228.90/40.38  | |            (25), (26), (27), (28), (29), (30), (31), (33), (34), (35), (36),
% 228.90/40.38  | |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 228.90/40.38  | |            (48), (49), (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 228.90/40.38  | |            (60) are inconsistent by sub-proof #617.
% 228.90/40.38  | | 
% 228.90/40.38  | Case 2:
% 228.90/40.38  | | 
% 228.90/40.38  | |   (61)  all_57_10 = e0 & op(e2, e0) = e0
% 228.90/40.38  | | 
% 228.90/40.38  | | ALPHA: (61) implies:
% 228.90/40.38  | |   (62)  all_57_10 = e0
% 228.90/40.38  | | 
% 228.90/40.38  | | REF_CLOSE: (3), (4), (19), (26), (32), (35), (38), (46), (53), (54), (56),
% 228.90/40.38  | |            (62) are inconsistent by sub-proof #1087.
% 228.90/40.38  | | 
% 228.90/40.38  | End of split
% 228.90/40.38  | 
% 228.90/40.38  End of proof
% 228.90/40.38  
% 228.90/40.38  Sub-proof #617 shows that the following formulas are inconsistent:
% 228.90/40.38  ----------------------------------------------------------------
% 228.90/40.38    (1)   ~ (all_53_2 = e2)
% 228.90/40.38    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.90/40.38         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.90/40.38    (3)   ~ (e3 = e1)
% 228.90/40.38    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.90/40.38           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.90/40.38    (5)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.90/40.38         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.90/40.38    (6)   ~ (all_53_3 = e3)
% 228.90/40.38    (7)   ~ (all_53_3 = all_53_7)
% 228.90/40.38    (8)   ~ (all_6_2 = e3)
% 228.90/40.38    (9)   ~ (all_53_9 = e1)
% 228.90/40.38    (10)  op(e1, e1) = all_6_2
% 228.90/40.38    (11)   ~ (all_53_1 = all_53_9)
% 228.90/40.38    (12)  op(e2, e2) = e1
% 228.90/40.38    (13)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.90/40.38          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.90/40.38    (14)  all_57_4 = e0
% 228.90/40.38    (15)   ~ (all_53_13 = e3)
% 228.90/40.38    (16)   ~ (all_53_9 = all_53_11)
% 228.90/40.38    (17)  all_55_4 = all_53_1
% 228.90/40.38    (18)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.90/40.38          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.90/40.38    (19)   ~ (e3 = e2)
% 228.90/40.38    (20)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 228.90/40.38    (21)   ~ (all_53_1 = all_53_3)
% 228.90/40.38    (22)   ~ (e3 = e0)
% 228.90/40.38    (23)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.90/40.38    (24)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 228.90/40.38    (25)  all_57_15 = e3
% 228.90/40.38    (26)   ~ (all_53_9 = all_53_13)
% 228.90/40.38    (27)  op(e3, e3) = e2
% 228.90/40.38    (28)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.90/40.38          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.90/40.38            e1)
% 228.90/40.38    (29)   ~ (all_53_1 = e1)
% 228.90/40.38    (30)  op(e2, e0) = e2
% 228.90/40.38    (31)  all_55_6 = all_53_9
% 228.90/40.38    (32)   ~ (all_53_1 = all_53_2)
% 228.90/40.38    (33)   ~ (e2 = e0)
% 228.90/40.38    (34)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.90/40.38            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.90/40.38            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.90/40.38            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.90/40.38              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.90/40.38            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.90/40.38            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.90/40.38              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.90/40.38              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.90/40.38            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.90/40.38            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.90/40.38            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.90/40.38              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.90/40.38              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.90/40.38            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.90/40.38              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.90/40.38            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.90/40.38            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.90/40.38              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.90/40.38              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.90/40.38            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.90/40.38            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.90/40.38    (35)  all_55_12 = all_53_3
% 228.90/40.38    (36)   ~ (e1 = e0)
% 228.90/40.38    (37)   ~ (all_53_3 = all_53_11)
% 228.90/40.38    (38)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.90/40.38          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.90/40.38    (39)  all_57_6 = e3
% 228.90/40.38    (40)   ~ (all_53_2 = all_53_3)
% 228.90/40.38    (41)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 228.90/40.38    (42)   ~ (all_53_7 = all_53_11)
% 228.90/40.38    (43)  all_55_8 = all_53_2
% 228.90/40.38    (44)  op(e0, e0) = e3
% 228.90/40.38    (45)  op(e0, e2) = all_53_7
% 228.90/40.38    (46)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.90/40.38          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.90/40.38            e2)
% 228.90/40.38    (47)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.90/40.38              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.90/40.38                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.90/40.38                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.90/40.38    (48)   ~ (all_53_1 = all_53_13)
% 228.90/40.38    (49)  op(e2, e0) = all_53_13
% 228.90/40.38    (50)  op(e1, e3) = all_53_2
% 228.90/40.38    (51)   ~ (e2 = e1)
% 228.90/40.38    (52)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.90/40.38          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.90/40.38    (53)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 228.90/40.38    (54)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.90/40.38          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.90/40.38    (55)  all_55_14 = all_53_11
% 228.90/40.38    (56)   ~ (all_53_11 = e3)
% 228.90/40.38    (57)  all_57_5 = e0
% 228.90/40.38  
% 228.90/40.38  Begin of proof
% 228.90/40.38  | 
% 228.90/40.38  | BETA: splitting (38) gives:
% 228.90/40.38  | 
% 228.90/40.38  | Case 1:
% 228.90/40.38  | | 
% 228.90/40.38  | |   (58)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) =
% 228.90/40.38  | |           e3)
% 228.90/40.38  | | 
% 228.90/40.38  | | BETA: splitting (58) gives:
% 228.90/40.38  | | 
% 228.90/40.38  | | Case 1:
% 228.90/40.38  | | | 
% 228.90/40.38  | | |   (59)  all_57_4 = e3 & op(e3, e1) = e3
% 228.90/40.38  | | | 
% 228.90/40.38  | | | ALPHA: (59) implies:
% 228.90/40.38  | | |   (60)  all_57_4 = e3
% 228.90/40.38  | | | 
% 228.90/40.38  | | | COMBINE_EQS: (14), (60) imply:
% 228.90/40.38  | | |   (61)  e3 = e0
% 228.90/40.38  | | | 
% 228.90/40.38  | | | SIMP: (61) implies:
% 228.90/40.38  | | |   (62)  e3 = e0
% 228.90/40.38  | | | 
% 228.90/40.38  | | | COMBINE_EQS: (39), (62) imply:
% 228.90/40.38  | | |   (63)  all_57_6 = e0
% 228.90/40.38  | | | 
% 228.90/40.38  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.90/40.38  | | |            (13), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 228.90/40.38  | | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 228.90/40.38  | | |            (34), (35), (36), (37), (38), (40), (41), (42), (43), (44),
% 228.90/40.38  | | |            (45), (46), (47), (48), (49), (50), (51), (52), (53), (54),
% 228.90/40.38  | | |            (55), (56), (57), (63) are inconsistent by sub-proof #650.
% 228.90/40.38  | | | 
% 228.90/40.38  | | Case 2:
% 228.90/40.38  | | | 
% 228.90/40.38  | | |   (64)  all_57_5 = e3 & op(e2, e1) = e3
% 228.90/40.38  | | | 
% 228.90/40.38  | | | ALPHA: (64) implies:
% 228.90/40.38  | | |   (65)  all_57_5 = e3
% 228.90/40.38  | | | 
% 228.90/40.38  | | | COMBINE_EQS: (57), (65) imply:
% 228.90/40.38  | | |   (66)  e3 = e0
% 228.90/40.38  | | | 
% 228.90/40.38  | | | COMBINE_EQS: (39), (66) imply:
% 228.90/40.38  | | |   (67)  all_57_6 = e0
% 228.90/40.38  | | | 
% 228.90/40.38  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.90/40.38  | | |            (13), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 228.90/40.38  | | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 228.90/40.38  | | |            (34), (35), (36), (37), (38), (40), (41), (42), (43), (44),
% 228.90/40.38  | | |            (45), (46), (47), (48), (49), (50), (51), (52), (53), (54),
% 228.90/40.38  | | |            (55), (56), (57), (67) are inconsistent by sub-proof #650.
% 228.90/40.38  | | | 
% 228.90/40.38  | | End of split
% 228.90/40.38  | | 
% 228.90/40.38  | Case 2:
% 228.90/40.38  | | 
% 228.90/40.38  | |   (68)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) =
% 228.90/40.38  | |           e3)
% 228.90/40.38  | | 
% 228.90/40.38  | | REF_CLOSE: (3), (4), (8), (10), (19), (22), (25), (28), (33), (36), (46),
% 228.90/40.38  | |            (47), (51), (68) are inconsistent by sub-proof #1794.
% 228.90/40.38  | | 
% 228.90/40.38  | End of split
% 228.90/40.38  | 
% 228.90/40.38  End of proof
% 228.90/40.38  
% 228.90/40.38  Sub-proof #618 shows that the following formulas are inconsistent:
% 228.90/40.38  ----------------------------------------------------------------
% 228.90/40.38    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.90/40.38         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.90/40.38    (2)   ~ (e3 = e1)
% 228.90/40.38    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.90/40.38           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.90/40.38    (4)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.90/40.38    (5)   ~ (e3 = e2)
% 228.90/40.38    (6)   ~ (e3 = e0)
% 228.90/40.38    (7)  all_57_11 = e0
% 228.90/40.38    (8)   ~ (e2 = e0)
% 228.90/40.38    (9)  all_57_3 = e1
% 228.90/40.38    (10)   ~ (e1 = e0)
% 228.90/40.38    (11)  op(e0, e0) = e3
% 228.90/40.38    (12)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.90/40.38          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.90/40.38    (13)  all_57_2 = e0
% 228.90/40.38    (14)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.90/40.38          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.90/40.38    (15)   ~ (e2 = e1)
% 228.90/40.38  
% 228.90/40.38  Begin of proof
% 228.90/40.38  | 
% 228.90/40.38  | BETA: splitting (4) gives:
% 228.90/40.38  | 
% 228.90/40.38  | Case 1:
% 228.90/40.38  | | 
% 228.90/40.38  | |   (16)  all_57_11 = e1 & op(e1, e0) = e1
% 228.90/40.38  | | 
% 228.90/40.38  | | ALPHA: (16) implies:
% 228.90/40.38  | |   (17)  all_57_11 = e1
% 228.90/40.38  | | 
% 228.90/40.38  | | COMBINE_EQS: (7), (17) imply:
% 228.90/40.38  | |   (18)  e1 = e0
% 228.90/40.38  | | 
% 228.90/40.38  | | COMBINE_EQS: (9), (18) imply:
% 228.90/40.38  | |   (19)  all_57_3 = e0
% 228.90/40.38  | | 
% 228.90/40.38  | | REF_CLOSE: (1), (2), (5), (6), (8), (10), (12), (13), (14), (15), (19) are
% 228.90/40.38  | |            inconsistent by sub-proof #2246.
% 228.90/40.38  | | 
% 228.90/40.38  | Case 2:
% 228.90/40.38  | | 
% 228.90/40.38  | |   (20)  all_57_15 = e1 & op(e0, e0) = e1
% 228.90/40.38  | | 
% 228.90/40.38  | | ALPHA: (20) implies:
% 228.90/40.38  | |   (21)  op(e0, e0) = e1
% 228.90/40.38  | | 
% 228.90/40.38  | | REF_CLOSE: (2), (3), (11), (21) are inconsistent by sub-proof #2183.
% 228.90/40.38  | | 
% 228.90/40.38  | End of split
% 228.90/40.38  | 
% 228.90/40.38  End of proof
% 228.90/40.38  
% 228.90/40.38  Sub-proof #619 shows that the following formulas are inconsistent:
% 228.90/40.38  ----------------------------------------------------------------
% 228.90/40.38    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.90/40.38         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.90/40.38    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.90/40.38         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.90/40.38    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.90/40.38         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.90/40.38    (4)   ~ (e3 = e1)
% 228.90/40.38    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.90/40.38           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.90/40.38    (6)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.90/40.38         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.90/40.38    (7)   ~ (all_6_2 = e3)
% 228.90/40.38    (8)  op(e1, e1) = all_6_2
% 228.90/40.38    (9)  op(e2, e2) = e1
% 228.90/40.38    (10)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.90/40.38          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.90/40.38    (11)  all_57_9 = e1
% 228.90/40.38    (12)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.90/40.38          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.90/40.38    (13)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.90/40.38          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.90/40.38    (14)   ~ (e3 = e2)
% 228.90/40.38    (15)   ~ (e3 = e0)
% 228.90/40.38    (16)  all_57_15 = e3
% 228.90/40.38    (17)  op(e3, e3) = e2
% 228.90/40.38    (18)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.90/40.38          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.90/40.38            e1)
% 228.90/40.38    (19)  all_57_10 = e2
% 228.90/40.38    (20)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.90/40.38          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 228.90/40.38    (21)   ~ (e2 = e0)
% 228.90/40.38    (22)  all_57_3 = e1
% 228.90/40.38    (23)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.90/40.38          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.90/40.38    (24)   ~ (e1 = e0)
% 228.90/40.38    (25)  all_57_14 = e2
% 228.90/40.38    (26)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.90/40.38          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.90/40.38    (27)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.90/40.38          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.90/40.38    (28)  op(e0, e0) = e3
% 228.90/40.38    (29)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.90/40.38          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.90/40.38            e2)
% 228.90/40.38    (30)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.90/40.38              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.90/40.38                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.90/40.38                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.90/40.38    (31)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.90/40.38          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.90/40.38    (32)   ~ (all_53_12 = e3)
% 228.90/40.38    (33)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.90/40.38          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.90/40.38    (34)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.90/40.38          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.90/40.38    (35)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.90/40.38          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 228.90/40.38    (36)   ~ (e2 = e1)
% 228.90/40.38    (37)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.90/40.38          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.90/40.38    (38)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.90/40.38          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.90/40.38    (39)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.90/40.38          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.90/40.38    (40)  all_57_14 = e1 & op(e0, e1) = e1
% 228.90/40.38    (41)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.90/40.38          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.90/40.38    (42)  op(e3, e0) = all_53_12
% 228.90/40.38  
% 228.90/40.38  Begin of proof
% 228.90/40.38  | 
% 228.90/40.38  | ALPHA: (40) implies:
% 228.90/40.38  |   (43)  all_57_14 = e1
% 228.90/40.38  | 
% 228.90/40.38  | COMBINE_EQS: (25), (43) imply:
% 228.90/40.38  |   (44)  e2 = e1
% 228.90/40.38  | 
% 228.90/40.38  | SIMP: (44) implies:
% 228.90/40.38  |   (45)  e2 = e1
% 228.90/40.38  | 
% 228.90/40.38  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.90/40.38  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 228.90/40.38  |            (24), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 228.90/40.38  |            (36), (37), (38), (39), (41), (42), (45) are inconsistent by
% 228.90/40.38  |            sub-proof #635.
% 228.90/40.38  | 
% 228.90/40.38  End of proof
% 228.90/40.38  
% 228.90/40.38  Sub-proof #620 shows that the following formulas are inconsistent:
% 228.90/40.38  ----------------------------------------------------------------
% 228.90/40.38    (1)  all_57_0 = e2
% 228.90/40.38    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.90/40.38         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.90/40.38    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.90/40.38         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.90/40.38    (4)   ~ (e3 = e1)
% 228.90/40.38    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.90/40.38           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.90/40.38    (6)   ~ (all_6_2 = e3)
% 228.90/40.38    (7)  op(e1, e1) = all_6_2
% 228.90/40.38    (8)  op(e2, e2) = e1
% 228.90/40.38    (9)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.90/40.38         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.90/40.38    (10)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.90/40.38          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.90/40.38    (11)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.90/40.38          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.90/40.38    (12)   ~ (e3 = e2)
% 228.90/40.38    (13)   ~ (e3 = e0)
% 228.90/40.38    (14)  all_57_15 = e3
% 228.90/40.38    (15)  all_57_5 = e1 & op(e2, e1) = e1
% 228.90/40.38    (16)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.90/40.38          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.90/40.38            e1)
% 228.90/40.38    (17)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.90/40.38          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 228.90/40.38    (18)   ~ (e2 = e0)
% 228.90/40.38    (19)   ~ (e1 = e0)
% 228.90/40.38    (20)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.90/40.38          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.90/40.38    (21)  all_57_6 = e3
% 228.90/40.38    (22)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.90/40.38          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.90/40.38    (23)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.90/40.38          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.90/40.38            e2)
% 228.90/40.39    (24)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.90/40.39              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.90/40.39                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.90/40.39                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.90/40.39    (25)  all_57_13 = e0
% 228.90/40.39    (26)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.90/40.39          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.90/40.39    (27)  all_57_1 = e3
% 228.90/40.39    (28)   ~ (e2 = e1)
% 228.90/40.39    (29)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.90/40.39          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.90/40.39    (30)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.90/40.39          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.90/40.39    (31)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.90/40.39          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.90/40.39  
% 228.90/40.39  Begin of proof
% 228.90/40.39  | 
% 228.90/40.39  | ALPHA: (15) implies:
% 228.90/40.39  |   (32)  all_57_5 = e1
% 228.90/40.39  | 
% 228.90/40.39  | BETA: splitting (20) gives:
% 228.90/40.39  | 
% 228.90/40.39  | Case 1:
% 228.90/40.39  | | 
% 228.90/40.39  | |   (33)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) =
% 228.90/40.39  | |           e3)
% 228.90/40.39  | | 
% 228.90/40.39  | | BETA: splitting (33) gives:
% 228.90/40.39  | | 
% 228.90/40.39  | | Case 1:
% 228.90/40.39  | | | 
% 228.90/40.39  | | |   (34)  all_57_4 = e3 & op(e3, e1) = e3
% 228.90/40.39  | | | 
% 228.90/40.39  | | | ALPHA: (34) implies:
% 228.90/40.39  | | |   (35)  all_57_4 = e3
% 228.90/40.39  | | | 
% 228.90/40.39  | | | BETA: splitting (26) gives:
% 228.90/40.39  | | | 
% 228.90/40.39  | | | Case 1:
% 228.90/40.39  | | | | 
% 228.90/40.39  | | | |   (36)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2)
% 228.90/40.39  | | | |           = e3)
% 228.90/40.39  | | | | 
% 228.90/40.39  | | | | REF_CLOSE: (1), (2), (4), (5), (8), (12), (13), (18), (19), (21), (28),
% 228.90/40.39  | | | |            (30), (31), (36) are inconsistent by sub-proof #639.
% 228.90/40.39  | | | | 
% 228.90/40.39  | | | Case 2:
% 228.90/40.39  | | | | 
% 228.90/40.39  | | | |   (37)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0)
% 228.90/40.39  | | | |           = e3)
% 228.90/40.39  | | | | 
% 228.90/40.39  | | | | BETA: splitting (37) gives:
% 228.90/40.39  | | | | 
% 228.90/40.39  | | | | Case 1:
% 228.90/40.39  | | | | | 
% 228.90/40.39  | | | | |   (38)  all_57_5 = e3 & op(e2, e1) = e3
% 228.90/40.39  | | | | | 
% 228.90/40.39  | | | | | REF_CLOSE: (3), (4), (5), (8), (12), (13), (17), (18), (19), (22),
% 228.90/40.39  | | | | |            (27), (28), (32), (38) are inconsistent by sub-proof #621.
% 228.90/40.39  | | | | | 
% 228.90/40.39  | | | | Case 2:
% 228.90/40.39  | | | | | 
% 228.90/40.39  | | | | |   (39)  all_57_10 = e3 & op(e2, e0) = e3
% 228.90/40.39  | | | | | 
% 228.90/40.39  | | | | | ALPHA: (39) implies:
% 228.90/40.39  | | | | |   (40)  all_57_10 = e3
% 228.90/40.39  | | | | | 
% 228.90/40.39  | | | | | REF_CLOSE: (4), (9), (10), (11), (12), (13), (14), (18), (19), (24),
% 228.90/40.39  | | | | |            (27), (28), (29), (35), (40) are inconsistent by sub-proof
% 228.90/40.39  | | | | |            #1436.
% 228.90/40.39  | | | | | 
% 228.90/40.39  | | | | End of split
% 228.90/40.39  | | | | 
% 228.90/40.39  | | | End of split
% 228.90/40.39  | | | 
% 228.90/40.39  | | Case 2:
% 228.90/40.39  | | | 
% 228.90/40.39  | | |   (41)  all_57_5 = e3 & op(e2, e1) = e3
% 228.90/40.39  | | | 
% 228.90/40.39  | | | ALPHA: (41) implies:
% 228.90/40.39  | | |   (42)  all_57_5 = e3
% 228.90/40.39  | | | 
% 228.90/40.39  | | | REF_CLOSE: (3), (4), (5), (8), (12), (13), (17), (18), (19), (22), (27),
% 228.90/40.39  | | |            (28), (32), (42) are inconsistent by sub-proof #637.
% 228.90/40.39  | | | 
% 228.90/40.39  | | End of split
% 228.90/40.39  | | 
% 228.90/40.39  | Case 2:
% 228.90/40.39  | | 
% 228.90/40.39  | |   (43)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) =
% 228.90/40.39  | |           e3)
% 228.90/40.39  | | 
% 228.90/40.39  | | BETA: splitting (43) gives:
% 228.90/40.39  | | 
% 228.90/40.39  | | Case 1:
% 228.90/40.39  | | | 
% 228.90/40.39  | | |   (44)  all_57_8 = e3 & op(e1, e1) = e3
% 228.90/40.39  | | | 
% 228.90/40.39  | | | ALPHA: (44) implies:
% 228.90/40.39  | | |   (45)  op(e1, e1) = e3
% 228.90/40.39  | | | 
% 228.90/40.39  | | | REF_CLOSE: (5), (6), (7), (45) are inconsistent by sub-proof #2468.
% 228.90/40.39  | | | 
% 228.90/40.39  | | Case 2:
% 228.90/40.39  | | | 
% 228.90/40.39  | | |   (46)  all_57_14 = e3 & op(e0, e1) = e3
% 228.90/40.39  | | | 
% 228.90/40.39  | | | ALPHA: (46) implies:
% 228.90/40.39  | | |   (47)  all_57_14 = e3
% 228.90/40.39  | | | 
% 228.90/40.39  | | | REF_CLOSE: (4), (12), (14), (16), (18), (19), (23), (25), (28), (47) are
% 228.90/40.39  | | |            inconsistent by sub-proof #2315.
% 228.90/40.39  | | | 
% 228.90/40.39  | | End of split
% 228.90/40.39  | | 
% 228.90/40.39  | End of split
% 228.90/40.39  | 
% 228.90/40.39  End of proof
% 228.90/40.39  
% 228.90/40.39  Sub-proof #621 shows that the following formulas are inconsistent:
% 228.90/40.39  ----------------------------------------------------------------
% 228.90/40.39    (1)  all_57_5 = e3 & op(e2, e1) = e3
% 228.90/40.39    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.90/40.39         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.90/40.39    (3)   ~ (e3 = e1)
% 228.90/40.39    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.90/40.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.90/40.39    (5)  op(e2, e2) = e1
% 228.90/40.39    (6)   ~ (e3 = e2)
% 228.90/40.39    (7)   ~ (e3 = e0)
% 228.90/40.39    (8)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.90/40.39         (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 228.90/40.39    (9)   ~ (e2 = e0)
% 228.90/40.39    (10)   ~ (e1 = e0)
% 228.90/40.39    (11)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.90/40.39          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.90/40.39    (12)  all_57_5 = e1
% 228.90/40.39    (13)  all_57_1 = e3
% 228.90/40.39    (14)   ~ (e2 = e1)
% 228.90/40.39  
% 228.90/40.39  Begin of proof
% 228.90/40.39  | 
% 228.90/40.39  | ALPHA: (1) implies:
% 228.90/40.39  |   (15)  all_57_5 = e3
% 228.90/40.39  | 
% 228.90/40.39  | COMBINE_EQS: (12), (15) imply:
% 228.90/40.39  |   (16)  e3 = e1
% 228.90/40.39  | 
% 228.90/40.39  | COMBINE_EQS: (13), (16) imply:
% 228.90/40.39  |   (17)  all_57_1 = e1
% 228.90/40.39  | 
% 228.90/40.39  | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (14), (17) are
% 228.90/40.39  |            inconsistent by sub-proof #1908.
% 228.90/40.39  | 
% 228.90/40.39  End of proof
% 228.90/40.39  
% 228.90/40.39  Sub-proof #622 shows that the following formulas are inconsistent:
% 228.90/40.39  ----------------------------------------------------------------
% 228.90/40.39    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.90/40.39         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.90/40.39    (2)   ~ (e3 = e1)
% 228.90/40.39    (3)  all_57_7 = e1
% 228.90/40.39    (4)  all_57_7 = e0 & op(e1, e2) = e0
% 228.90/40.39    (5)   ~ (e3 = e2)
% 228.90/40.39    (6)  all_57_5 = e3
% 228.90/40.39    (7)   ~ (e2 = e0)
% 228.90/40.39    (8)  all_57_3 = e1
% 228.90/40.39    (9)   ~ (e1 = e0)
% 228.90/40.39    (10)  all_57_2 = e0
% 228.90/40.39    (11)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.90/40.39          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.90/40.39    (12)   ~ (e2 = e1)
% 228.90/40.39  
% 228.90/40.39  Begin of proof
% 228.90/40.39  | 
% 228.90/40.39  | ALPHA: (4) implies:
% 228.90/40.39  |   (13)  all_57_7 = e0
% 228.90/40.39  | 
% 228.90/40.39  | COMBINE_EQS: (3), (13) imply:
% 228.90/40.39  |   (14)  e1 = e0
% 228.90/40.39  | 
% 228.90/40.39  | COMBINE_EQS: (8), (14) imply:
% 228.90/40.39  |   (15)  all_57_3 = e0
% 228.90/40.39  | 
% 228.90/40.39  | REF_CLOSE: (1), (2), (5), (6), (7), (9), (10), (11), (12), (15) are
% 228.90/40.39  |            inconsistent by sub-proof #2253.
% 228.90/40.39  | 
% 228.90/40.39  End of proof
% 228.90/40.39  
% 228.90/40.39  Sub-proof #623 shows that the following formulas are inconsistent:
% 228.90/40.39  ----------------------------------------------------------------
% 228.90/40.39    (1)   ~ (all_53_2 = e2)
% 228.90/40.39    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.90/40.39         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.90/40.39    (3)   ~ (e3 = e1)
% 228.90/40.39    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.90/40.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.90/40.39    (5)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.90/40.39         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.90/40.39    (6)   ~ (all_53_3 = e3)
% 228.90/40.39    (7)   ~ (all_53_3 = all_53_7)
% 228.90/40.39    (8)   ~ (all_6_2 = e3)
% 228.90/40.39    (9)   ~ (all_53_9 = e1)
% 228.90/40.39    (10)  op(e1, e1) = all_6_2
% 228.90/40.39    (11)   ~ (all_53_1 = all_53_9)
% 228.90/40.39    (12)  op(e2, e2) = e1
% 228.90/40.39    (13)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.90/40.39          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.90/40.39    (14)  all_57_4 = e0
% 228.90/40.39    (15)   ~ (all_53_13 = e3)
% 228.90/40.39    (16)   ~ (all_53_9 = all_53_11)
% 228.90/40.39    (17)  all_55_4 = all_53_1
% 228.90/40.39    (18)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.90/40.39          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.90/40.39    (19)   ~ (e3 = e2)
% 228.90/40.39    (20)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 228.90/40.39    (21)   ~ (all_53_1 = all_53_3)
% 228.90/40.39    (22)   ~ (e3 = e0)
% 228.90/40.39    (23)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.90/40.39    (24)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 228.90/40.39    (25)  all_57_15 = e3
% 228.90/40.39    (26)   ~ (all_53_9 = all_53_13)
% 228.90/40.39    (27)  op(e3, e3) = e2
% 228.90/40.39    (28)   ~ (all_53_1 = e1)
% 228.90/40.39    (29)  op(e2, e0) = e2
% 228.90/40.39    (30)  all_55_6 = all_53_9
% 228.90/40.39    (31)   ~ (all_53_1 = all_53_2)
% 228.90/40.39    (32)   ~ (e2 = e0)
% 228.90/40.39    (33)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.90/40.39            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.90/40.39            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.90/40.39            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.90/40.39              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.90/40.39            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.90/40.39            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.90/40.39              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.90/40.39              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.90/40.39            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.90/40.39            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.90/40.39            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.90/40.39              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.90/40.39              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.90/40.39            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.90/40.39              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.90/40.39            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.90/40.39            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.90/40.39              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.90/40.39              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.90/40.39            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.90/40.39            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.90/40.39    (34)  all_55_12 = all_53_3
% 228.90/40.39    (35)   ~ (e1 = e0)
% 228.90/40.39    (36)   ~ (all_53_3 = all_53_11)
% 228.90/40.39    (37)  all_57_6 = e3
% 228.90/40.39    (38)   ~ (all_53_2 = all_53_3)
% 228.90/40.39    (39)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 228.90/40.39    (40)   ~ (all_53_7 = all_53_11)
% 228.90/40.39    (41)  all_55_8 = all_53_2
% 228.90/40.39    (42)  op(e0, e0) = e3
% 228.90/40.39    (43)  op(e0, e2) = all_53_7
% 228.90/40.39    (44)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.90/40.39              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.90/40.39                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.90/40.39                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.90/40.39    (45)   ~ (all_53_1 = all_53_13)
% 228.90/40.39    (46)  op(e2, e0) = all_53_13
% 228.90/40.39    (47)  op(e1, e3) = all_53_2
% 228.90/40.39    (48)   ~ (e2 = e1)
% 228.90/40.39    (49)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.90/40.39          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.90/40.39    (50)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 228.90/40.39    (51)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.90/40.39          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.90/40.39    (52)  all_55_14 = all_53_11
% 228.90/40.39    (53)  all_57_4 = e3 & op(e3, e1) = e3
% 228.90/40.39    (54)   ~ (all_53_11 = e3)
% 228.90/40.39  
% 228.90/40.39  Begin of proof
% 228.90/40.39  | 
% 228.90/40.39  | ALPHA: (53) implies:
% 228.90/40.39  |   (55)  all_57_4 = e3
% 228.90/40.39  | 
% 228.90/40.39  | COMBINE_EQS: (14), (55) imply:
% 228.90/40.39  |   (56)  e3 = e0
% 228.90/40.39  | 
% 228.90/40.39  | COMBINE_EQS: (37), (56) imply:
% 228.90/40.39  |   (57)  all_57_6 = e0
% 228.90/40.39  | 
% 228.90/40.39  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.90/40.39  |            (13), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 228.90/40.39  |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 228.90/40.39  |            (36), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 228.90/40.39  |            (48), (49), (50), (51), (52), (54), (55), (57) are inconsistent by
% 228.90/40.39  |            sub-proof #651.
% 228.90/40.39  | 
% 228.90/40.39  End of proof
% 228.90/40.39  
% 228.90/40.39  Sub-proof #624 shows that the following formulas are inconsistent:
% 228.90/40.39  ----------------------------------------------------------------
% 228.90/40.39    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.90/40.39         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.90/40.39    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.90/40.39         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.90/40.39    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.90/40.39         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.90/40.39    (4)   ~ (e3 = e1)
% 228.90/40.39    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.90/40.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.90/40.39    (6)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.90/40.39         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.90/40.39    (7)   ~ (all_6_2 = e3)
% 228.90/40.39    (8)  all_57_9 = e2 & op(e3, e0) = e2
% 228.90/40.39    (9)  op(e1, e1) = all_6_2
% 228.90/40.39    (10)  op(e2, e2) = e1
% 228.90/40.39    (11)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.90/40.39          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.90/40.39    (12)  all_57_4 = e0
% 228.90/40.39    (13)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.90/40.39          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.90/40.39    (14)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.90/40.39          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.90/40.39    (15)   ~ (e3 = e2)
% 228.90/40.39    (16)   ~ (e3 = e0)
% 228.90/40.39    (17)  all_57_15 = e3
% 228.90/40.39    (18)  op(e3, e3) = e2
% 228.90/40.39    (19)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.90/40.39          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.90/40.39            e1)
% 228.90/40.39    (20)  all_57_11 = e0
% 228.90/40.39    (21)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.90/40.39          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 228.90/40.39    (22)   ~ (e2 = e0)
% 228.90/40.39    (23)  all_57_3 = e1
% 228.90/40.39    (24)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.90/40.39          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.90/40.39    (25)   ~ (e1 = e0)
% 228.90/40.39    (26)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.90/40.39          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.90/40.39    (27)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.90/40.39          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.90/40.39    (28)  op(e0, e0) = e3
% 228.90/40.39    (29)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.90/40.39          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.90/40.39            e2)
% 228.90/40.39    (30)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.90/40.39              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.90/40.39                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.90/40.39                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.90/40.39    (31)   ~ (all_53_12 = e3)
% 228.90/40.39    (32)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.90/40.39          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.90/40.39    (33)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.90/40.39          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.90/40.39    (34)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.90/40.39          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 228.90/40.39    (35)   ~ (e2 = e1)
% 228.90/40.39    (36)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.90/40.39          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.90/40.39    (37)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.90/40.39          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.90/40.39    (38)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.90/40.39          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.90/40.39    (39)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.90/40.39          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.90/40.39    (40)  op(e3, e0) = all_53_12
% 228.90/40.39  
% 228.90/40.39  Begin of proof
% 228.90/40.39  | 
% 228.90/40.39  | ALPHA: (8) implies:
% 228.90/40.39  |   (41)  all_57_9 = e2
% 228.90/40.39  | 
% 228.90/40.39  | BETA: splitting (38) gives:
% 228.90/40.39  | 
% 228.90/40.39  | Case 1:
% 228.90/40.39  | | 
% 228.90/40.39  | |   (42)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) =
% 228.90/40.39  | |           e1)
% 228.90/40.39  | | 
% 228.90/40.39  | | BETA: splitting (42) gives:
% 228.90/40.39  | | 
% 228.90/40.39  | | Case 1:
% 228.90/40.39  | | | 
% 228.90/40.39  | | |   (43)  all_57_9 = e1 & op(e3, e0) = e1
% 228.90/40.39  | | | 
% 228.90/40.39  | | | ALPHA: (43) implies:
% 228.90/40.39  | | |   (44)  all_57_9 = e1
% 228.90/40.39  | | | 
% 228.90/40.39  | | | REF_CLOSE: (35), (41), (44) are inconsistent by sub-proof #2444.
% 228.90/40.39  | | | 
% 228.90/40.39  | | Case 2:
% 228.90/40.39  | | | 
% 228.90/40.39  | | |   (45)  all_57_10 = e1 & op(e2, e0) = e1
% 228.90/40.39  | | | 
% 228.90/40.39  | | | ALPHA: (45) implies:
% 228.90/40.39  | | |   (46)  all_57_10 = e1
% 228.90/40.39  | | | 
% 228.90/40.39  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (13), (14),
% 228.90/40.39  | | |            (15), (16), (17), (18), (19), (21), (22), (23), (24), (25),
% 228.90/40.39  | | |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 228.90/40.39  | | |            (36), (37), (38), (39), (40), (41), (46) are inconsistent by
% 228.90/40.39  | | |            sub-proof #805.
% 228.90/40.39  | | | 
% 228.90/40.39  | | End of split
% 228.90/40.39  | | 
% 228.90/40.39  | Case 2:
% 228.90/40.39  | | 
% 228.90/40.39  | |   (47)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.90/40.39  | |           e1)
% 228.90/40.39  | | 
% 228.90/40.39  | | BETA: splitting (47) gives:
% 228.90/40.39  | | 
% 228.90/40.39  | | Case 1:
% 228.90/40.39  | | | 
% 228.90/40.39  | | |   (48)  all_57_11 = e1 & op(e1, e0) = e1
% 228.90/40.39  | | | 
% 228.90/40.39  | | | ALPHA: (48) implies:
% 228.90/40.39  | | |   (49)  all_57_11 = e1
% 228.90/40.39  | | | 
% 228.90/40.39  | | | COMBINE_EQS: (20), (49) imply:
% 228.90/40.39  | | |   (50)  e1 = e0
% 228.90/40.39  | | | 
% 228.90/40.39  | | | REF_CLOSE: (1), (4), (5), (7), (9), (12), (15), (16), (17), (19), (22),
% 228.90/40.39  | | |            (23), (25), (26), (28), (29), (30), (32), (35), (41), (49),
% 228.90/40.39  | | |            (50) are inconsistent by sub-proof #1040.
% 228.90/40.39  | | | 
% 228.90/40.39  | | Case 2:
% 228.90/40.39  | | | 
% 228.90/40.39  | | |   (51)  all_57_15 = e1 & op(e0, e0) = e1
% 228.90/40.39  | | | 
% 228.90/40.39  | | | ALPHA: (51) implies:
% 228.90/40.39  | | |   (52)  op(e0, e0) = e1
% 228.90/40.39  | | | 
% 228.90/40.39  | | | REF_CLOSE: (4), (5), (28), (52) are inconsistent by sub-proof #2183.
% 228.90/40.39  | | | 
% 228.90/40.39  | | End of split
% 228.90/40.39  | | 
% 228.90/40.39  | End of split
% 228.90/40.39  | 
% 228.90/40.39  End of proof
% 228.90/40.39  
% 228.90/40.39  Sub-proof #625 shows that the following formulas are inconsistent:
% 228.90/40.39  ----------------------------------------------------------------
% 228.90/40.39    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.90/40.39         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.90/40.39    (2)   ~ (e3 = e1)
% 228.90/40.39    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.90/40.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.90/40.39    (4)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.90/40.39         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.90/40.39    (5)   ~ (all_6_2 = e3)
% 228.90/40.39    (6)  op(e1, e1) = all_6_2
% 228.90/40.39    (7)  op(e2, e2) = e1
% 228.90/40.39    (8)   ~ (e3 = e2)
% 228.90/40.39    (9)   ~ (e3 = e0)
% 228.90/40.39    (10)  all_57_15 = e3
% 228.90/40.39    (11)  op(e3, e3) = e2
% 228.90/40.39    (12)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.90/40.39          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 228.90/40.39    (13)   ~ (e2 = e0)
% 228.90/40.39    (14)   ~ (e1 = e0)
% 228.90/40.39    (15)  all_57_6 = e3
% 228.90/40.39    (16)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.90/40.39              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.90/40.39                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.90/40.39                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.90/40.39    (17)  all_57_1 = e3
% 228.90/40.39    (18)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0)
% 228.90/40.39    (19)   ~ (e2 = e1)
% 228.90/40.39    (20)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.90/40.39          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.90/40.39    (21)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.90/40.39          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.90/40.39    (22)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.90/40.39          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.90/40.39  
% 228.90/40.39  Begin of proof
% 228.90/40.39  | 
% 228.90/40.39  | BETA: splitting (18) gives:
% 228.90/40.39  | 
% 228.90/40.39  | Case 1:
% 228.90/40.39  | | 
% 228.90/40.39  | |   (23)  all_57_0 = e0 & op(e3, e3) = e0
% 228.90/40.39  | | 
% 228.90/40.39  | | ALPHA: (23) implies:
% 228.90/40.39  | |   (24)  op(e3, e3) = e0
% 228.90/40.39  | | 
% 228.90/40.39  | | REF_CLOSE: (3), (11), (13), (24) are inconsistent by sub-proof #2403.
% 228.90/40.39  | | 
% 228.90/40.39  | Case 2:
% 228.90/40.39  | | 
% 228.90/40.39  | |   (25)  all_57_1 = e0 & op(e3, e2) = e0
% 228.90/40.39  | | 
% 228.90/40.39  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 228.90/40.39  | |            (14), (15), (16), (17), (19), (20), (21), (22), (25) are
% 228.90/40.39  | |            inconsistent by sub-proof #725.
% 228.90/40.39  | | 
% 228.90/40.39  | End of split
% 228.90/40.39  | 
% 228.90/40.39  End of proof
% 228.90/40.39  
% 228.90/40.39  Sub-proof #626 shows that the following formulas are inconsistent:
% 228.90/40.39  ----------------------------------------------------------------
% 228.90/40.39    (1)   ~ (all_53_2 = e2)
% 228.90/40.39    (2)  all_57_0 = e2
% 228.90/40.39    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.90/40.39         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.90/40.39    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.90/40.39         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.90/40.39    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.90/40.39         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.90/40.39    (6)   ~ (e3 = e1)
% 228.90/40.39    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.90/40.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.90/40.39    (8)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.90/40.39         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.90/40.39    (9)   ~ (all_53_3 = e3)
% 228.90/40.39    (10)   ~ (all_53_3 = all_53_7)
% 228.90/40.39    (11)   ~ (all_6_2 = e3)
% 228.90/40.39    (12)   ~ (all_53_9 = e1)
% 228.90/40.39    (13)  op(e1, e1) = all_6_2
% 228.90/40.39    (14)   ~ (all_53_1 = all_53_9)
% 228.90/40.39    (15)  op(e2, e2) = e1
% 228.90/40.39    (16)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.90/40.39          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.90/40.39    (17)   ~ (all_53_13 = e3)
% 228.90/40.39    (18)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.90/40.39          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.90/40.39    (19)  all_57_6 = e1
% 228.90/40.39    (20)   ~ (all_53_9 = all_53_11)
% 228.90/40.39    (21)  all_55_4 = all_53_1
% 228.90/40.40    (22)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.90/40.40          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.90/40.40    (23)   ~ (e3 = e2)
% 228.90/40.40    (24)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 228.90/40.40    (25)   ~ (all_53_1 = all_53_3)
% 228.90/40.40    (26)   ~ (e3 = e0)
% 228.90/40.40    (27)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.90/40.40    (28)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 228.90/40.40    (29)  all_57_15 = e3
% 228.90/40.40    (30)   ~ (all_53_9 = all_53_13)
% 228.90/40.40    (31)  op(e3, e3) = e2
% 228.90/40.40    (32)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.90/40.40          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.90/40.40            e1)
% 228.90/40.40    (33)   ~ (all_53_1 = e1)
% 228.90/40.40    (34)  all_57_11 = e0
% 228.90/40.40    (35)  all_55_6 = all_53_9
% 228.90/40.40    (36)   ~ (all_53_1 = all_53_2)
% 228.90/40.40    (37)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.90/40.40          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 228.90/40.40    (38)   ~ (e2 = e0)
% 228.90/40.40    (39)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.90/40.40            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.90/40.40            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.90/40.40            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.90/40.40              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.90/40.40            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.90/40.40            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.90/40.40              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.90/40.40              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.90/40.40            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.90/40.40            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.90/40.40            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.90/40.40              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.90/40.40              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.90/40.40            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.90/40.40              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.90/40.40            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.90/40.40            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.90/40.40              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.90/40.40              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.90/40.40            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.90/40.40            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.90/40.40    (40)  all_55_12 = all_53_3
% 228.90/40.40    (41)  all_57_2 = e3
% 228.90/40.40    (42)  all_57_3 = e1
% 228.90/40.40    (43)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.90/40.40          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.90/40.40    (44)   ~ (e1 = e0)
% 228.90/40.40    (45)   ~ (all_53_3 = all_53_11)
% 228.90/40.40    (46)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.90/40.40          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.90/40.40    (47)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.90/40.40          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.90/40.40    (48)   ~ (all_53_2 = all_53_3)
% 228.90/40.40    (49)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 228.90/40.40    (50)   ~ (all_53_7 = all_53_11)
% 228.90/40.40    (51)  all_55_8 = all_53_2
% 228.90/40.40    (52)  op(e0, e0) = e3
% 228.90/40.40    (53)  op(e0, e2) = all_53_7
% 228.90/40.40    (54)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.90/40.40          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.90/40.40            e2)
% 228.90/40.40    (55)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.90/40.40              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.90/40.40                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.90/40.40                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.90/40.40    (56)   ~ (all_53_1 = all_53_13)
% 228.90/40.40    (57)  op(e2, e0) = all_53_13
% 228.90/40.40    (58)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.90/40.40          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.90/40.40    (59)   ~ (all_53_12 = e3)
% 228.90/40.40    (60)  all_57_7 = e3
% 228.90/40.40    (61)  op(e1, e3) = all_53_2
% 228.90/40.40    (62)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.90/40.40          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.90/40.40    (63)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.90/40.40          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.90/40.40    (64)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.90/40.40          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 228.90/40.40    (65)   ~ (e2 = e1)
% 228.90/40.40    (66)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.90/40.40          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.90/40.40    (67)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 228.90/40.40    (68)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.90/40.40          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.90/40.40    (69)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.90/40.40          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.90/40.40    (70)  all_55_14 = all_53_11
% 228.90/40.40    (71)   ~ (all_53_11 = e3)
% 228.90/40.40    (72)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.90/40.40          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.90/40.40    (73)  op(e3, e0) = all_53_12
% 228.90/40.40  
% 228.90/40.40  Begin of proof
% 228.90/40.40  | 
% 228.90/40.40  | BETA: splitting (69) gives:
% 228.90/40.40  | 
% 228.90/40.40  | Case 1:
% 228.90/40.40  | | 
% 228.90/40.40  | |   (74)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) =
% 228.90/40.40  | |           e1)
% 228.90/40.40  | | 
% 228.90/40.40  | | BETA: splitting (74) gives:
% 228.90/40.40  | | 
% 228.90/40.40  | | Case 1:
% 228.90/40.40  | | | 
% 228.90/40.40  | | |   (75)  all_57_9 = e1 & op(e3, e0) = e1
% 228.90/40.40  | | | 
% 228.90/40.40  | | | ALPHA: (75) implies:
% 228.90/40.40  | | |   (76)  all_57_9 = e1
% 228.90/40.40  | | | 
% 228.90/40.40  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.90/40.40  | | |            (13), (14), (15), (16), (17), (19), (20), (21), (22), (23),
% 228.90/40.40  | | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 228.90/40.40  | | |            (34), (35), (36), (38), (39), (40), (41), (42), (43), (44),
% 228.90/40.40  | | |            (45), (46), (48), (49), (50), (51), (52), (53), (54), (55),
% 228.90/40.40  | | |            (56), (57), (58), (59), (60), (61), (62), (64), (65), (66),
% 228.90/40.40  | | |            (67), (68), (69), (70), (71), (72), (73), (76) are inconsistent
% 228.90/40.40  | | |            by sub-proof #628.
% 228.90/40.40  | | | 
% 228.90/40.40  | | Case 2:
% 228.90/40.40  | | | 
% 228.90/40.40  | | |   (77)  all_57_10 = e1 & op(e2, e0) = e1
% 228.90/40.40  | | | 
% 228.90/40.40  | | | ALPHA: (77) implies:
% 228.90/40.40  | | |   (78)  all_57_10 = e1
% 228.90/40.40  | | | 
% 228.90/40.40  | | | BETA: splitting (66) gives:
% 228.90/40.40  | | | 
% 228.90/40.40  | | | Case 1:
% 228.90/40.40  | | | | 
% 228.90/40.40  | | | |   (79)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0)
% 228.90/40.40  | | | |           = e2)
% 228.90/40.40  | | | | 
% 228.90/40.40  | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (11), (13), (15), (16), (18),
% 228.90/40.40  | | | |            (22), (23), (26), (29), (31), (32), (37), (38), (42), (43),
% 228.90/40.40  | | | |            (44), (46), (47), (52), (54), (55), (59), (62), (63), (64),
% 228.90/40.40  | | | |            (65), (66), (68), (69), (72), (73), (78), (79) are
% 228.90/40.40  | | | |            inconsistent by sub-proof #627.
% 228.90/40.40  | | | | 
% 228.90/40.40  | | | Case 2:
% 228.90/40.40  | | | | 
% 228.90/40.40  | | | |   (80)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0,
% 228.90/40.40  | | | |             e0) = e2)
% 228.90/40.40  | | | | 
% 228.90/40.40  | | | | REF_CLOSE: (3), (4), (6), (7), (8), (11), (13), (15), (23), (26), (29),
% 228.90/40.40  | | | |            (31), (34), (38), (41), (42), (44), (52), (55), (58), (60),
% 228.90/40.40  | | | |            (62), (65), (66), (68), (69), (80) are inconsistent by
% 228.90/40.40  | | | |            sub-proof #629.
% 228.90/40.40  | | | | 
% 228.90/40.40  | | | End of split
% 228.90/40.40  | | | 
% 228.90/40.40  | | End of split
% 228.90/40.40  | | 
% 228.90/40.40  | Case 2:
% 228.90/40.40  | | 
% 228.90/40.40  | |   (81)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.90/40.40  | |           e1)
% 228.90/40.40  | | 
% 228.90/40.40  | | REF_CLOSE: (6), (7), (34), (44), (52), (81) are inconsistent by sub-proof
% 228.90/40.40  | |            #1749.
% 228.90/40.40  | | 
% 228.90/40.40  | End of split
% 228.90/40.40  | 
% 228.90/40.40  End of proof
% 228.90/40.40  
% 228.90/40.40  Sub-proof #627 shows that the following formulas are inconsistent:
% 228.90/40.40  ----------------------------------------------------------------
% 228.90/40.40    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.90/40.40         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.90/40.40    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.90/40.40         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.90/40.40    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.90/40.40         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.90/40.40    (4)   ~ (e3 = e1)
% 228.90/40.40    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.90/40.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.90/40.40    (6)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.90/40.40         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.90/40.40    (7)   ~ (all_6_2 = e3)
% 228.90/40.40    (8)  all_57_10 = e1
% 228.90/40.40    (9)  op(e1, e1) = all_6_2
% 228.90/40.40    (10)  op(e2, e2) = e1
% 228.90/40.40    (11)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.90/40.40          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.90/40.40    (12)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.90/40.40          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.90/40.40    (13)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.90/40.40          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.90/40.40    (14)   ~ (e3 = e2)
% 228.90/40.40    (15)   ~ (e3 = e0)
% 228.90/40.40    (16)  all_57_15 = e3
% 228.90/40.40    (17)  op(e3, e3) = e2
% 228.90/40.40    (18)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.90/40.40          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.90/40.40            e1)
% 228.90/40.40    (19)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.90/40.40          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 228.90/40.40    (20)   ~ (e2 = e0)
% 228.90/40.40    (21)  all_57_3 = e1
% 228.90/40.40    (22)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.90/40.40          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.90/40.40    (23)   ~ (e1 = e0)
% 228.90/40.40    (24)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.90/40.40          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.90/40.40    (25)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.90/40.40          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.90/40.40    (26)  op(e0, e0) = e3
% 228.90/40.40    (27)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.90/40.40          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.90/40.40            e2)
% 228.90/40.40    (28)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.90/40.40              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.90/40.40                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.90/40.40                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.90/40.40    (29)   ~ (all_53_12 = e3)
% 228.90/40.40    (30)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.90/40.40          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.90/40.40    (31)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.90/40.40          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.90/40.40    (32)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.90/40.40          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 228.90/40.40    (33)   ~ (e2 = e1)
% 228.90/40.40    (34)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.90/40.40          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.90/40.40    (35)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.90/40.40          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.90/40.40    (36)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.90/40.40          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.90/40.40    (37)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.90/40.40    (38)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.90/40.40          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.90/40.40    (39)  op(e3, e0) = all_53_12
% 228.90/40.40  
% 228.90/40.40  Begin of proof
% 228.90/40.40  | 
% 228.90/40.40  | BETA: splitting (37) gives:
% 228.90/40.40  | 
% 228.90/40.40  | Case 1:
% 228.90/40.40  | | 
% 228.90/40.40  | |   (40)  all_57_9 = e2 & op(e3, e0) = e2
% 228.90/40.40  | | 
% 228.90/40.40  | | ALPHA: (40) implies:
% 228.90/40.40  | |   (41)  all_57_9 = e2
% 228.90/40.40  | | 
% 228.90/40.40  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.90/40.40  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 228.90/40.40  | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 228.90/40.40  | |            (35), (36), (38), (39), (41) are inconsistent by sub-proof #805.
% 228.90/40.40  | | 
% 228.90/40.40  | Case 2:
% 228.90/40.40  | | 
% 228.90/40.40  | |   (42)  all_57_10 = e2 & op(e2, e0) = e2
% 228.90/40.40  | | 
% 228.90/40.40  | | REF_CLOSE: (8), (33), (42) are inconsistent by sub-proof #2255.
% 228.90/40.40  | | 
% 228.90/40.40  | End of split
% 228.90/40.40  | 
% 228.90/40.40  End of proof
% 228.90/40.40  
% 228.90/40.40  Sub-proof #628 shows that the following formulas are inconsistent:
% 228.90/40.40  ----------------------------------------------------------------
% 228.90/40.40    (1)   ~ (all_53_2 = e2)
% 228.90/40.40    (2)  all_57_0 = e2
% 228.90/40.40    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.90/40.40         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.90/40.40    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.90/40.40         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.90/40.40    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.90/40.40         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.90/40.40    (6)   ~ (e3 = e1)
% 228.90/40.40    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.90/40.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.90/40.40    (8)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.90/40.40         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.90/40.40    (9)   ~ (all_53_3 = e3)
% 228.90/40.40    (10)   ~ (all_53_3 = all_53_7)
% 228.90/40.40    (11)   ~ (all_6_2 = e3)
% 228.90/40.40    (12)   ~ (all_53_9 = e1)
% 228.90/40.40    (13)  op(e1, e1) = all_6_2
% 228.90/40.40    (14)   ~ (all_53_1 = all_53_9)
% 228.90/40.40    (15)  op(e2, e2) = e1
% 228.90/40.40    (16)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.90/40.40          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.90/40.40    (17)  all_57_9 = e1
% 228.90/40.40    (18)   ~ (all_53_13 = e3)
% 228.90/40.40    (19)  all_57_6 = e1
% 228.90/40.40    (20)   ~ (all_53_9 = all_53_11)
% 228.90/40.40    (21)  all_55_4 = all_53_1
% 228.90/40.40    (22)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.90/40.40          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.90/40.40    (23)   ~ (e3 = e2)
% 228.90/40.40    (24)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 228.90/40.40    (25)   ~ (all_53_1 = all_53_3)
% 228.90/40.40    (26)   ~ (e3 = e0)
% 228.90/40.40    (27)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.90/40.40    (28)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 228.90/40.40    (29)  all_57_15 = e3
% 228.90/40.40    (30)   ~ (all_53_9 = all_53_13)
% 228.90/40.40    (31)  op(e3, e3) = e2
% 228.90/40.40    (32)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.90/40.40          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.90/40.40            e1)
% 228.90/40.40    (33)   ~ (all_53_1 = e1)
% 228.90/40.40    (34)  all_57_11 = e0
% 228.90/40.40    (35)  all_55_6 = all_53_9
% 228.90/40.40    (36)   ~ (all_53_1 = all_53_2)
% 228.90/40.40    (37)   ~ (e2 = e0)
% 228.90/40.40    (38)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.90/40.40            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.90/40.40            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.90/40.40            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.90/40.40              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.90/40.40            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.90/40.40            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.90/40.40              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.90/40.40              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.90/40.40            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.90/40.40            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.90/40.40            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.90/40.40              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.90/40.40              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.90/40.40            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.90/40.40              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.90/40.40            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.90/40.40            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.90/40.40              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.90/40.40              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.90/40.40            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.90/40.40            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.90/40.40    (39)  all_55_12 = all_53_3
% 228.90/40.40    (40)  all_57_2 = e3
% 228.90/40.40    (41)  all_57_3 = e1
% 228.90/40.40    (42)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.90/40.40          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.90/40.40    (43)   ~ (e1 = e0)
% 228.90/40.40    (44)   ~ (all_53_3 = all_53_11)
% 228.90/40.40    (45)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.90/40.40          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.90/40.40    (46)   ~ (all_53_2 = all_53_3)
% 228.90/40.40    (47)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 228.90/40.40    (48)   ~ (all_53_7 = all_53_11)
% 228.90/40.40    (49)  all_55_8 = all_53_2
% 228.90/40.40    (50)  op(e0, e0) = e3
% 228.90/40.40    (51)  op(e0, e2) = all_53_7
% 228.90/40.40    (52)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.90/40.40          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.90/40.40            e2)
% 228.90/40.40    (53)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.90/40.40              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.90/40.40                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.90/40.40                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.90/40.40    (54)   ~ (all_53_1 = all_53_13)
% 228.90/40.40    (55)  op(e2, e0) = all_53_13
% 228.90/40.40    (56)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.90/40.40          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.90/40.40    (57)   ~ (all_53_12 = e3)
% 228.90/40.40    (58)  all_57_7 = e3
% 228.90/40.40    (59)  op(e1, e3) = all_53_2
% 228.90/40.40    (60)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.90/40.40          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.90/40.40    (61)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.90/40.40          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 228.90/40.40    (62)   ~ (e2 = e1)
% 228.90/40.40    (63)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.90/40.40          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.90/40.40    (64)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 228.90/40.40    (65)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.90/40.40          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.90/40.40    (66)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.90/40.40          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.90/40.40    (67)  all_55_14 = all_53_11
% 228.90/40.40    (68)   ~ (all_53_11 = e3)
% 228.90/40.40    (69)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.90/40.40          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.90/40.40    (70)  op(e3, e0) = all_53_12
% 228.90/40.40  
% 228.90/40.40  Begin of proof
% 228.90/40.40  | 
% 228.90/40.40  | BETA: splitting (63) gives:
% 228.90/40.40  | 
% 228.90/40.40  | Case 1:
% 228.90/40.40  | | 
% 228.90/40.40  | |   (71)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 228.90/40.40  | |           e2)
% 228.90/40.40  | | 
% 228.90/40.40  | | BETA: splitting (71) gives:
% 228.90/40.40  | | 
% 228.90/40.40  | | Case 1:
% 228.90/40.40  | | | 
% 228.90/40.40  | | |   (72)  all_57_9 = e2 & op(e3, e0) = e2
% 228.90/40.40  | | | 
% 228.90/40.40  | | | REF_CLOSE: (17), (62), (72) are inconsistent by sub-proof #2481.
% 228.90/40.40  | | | 
% 228.90/40.40  | | Case 2:
% 228.90/40.40  | | | 
% 228.90/40.40  | | |   (73)  all_57_10 = e2 & op(e2, e0) = e2
% 228.90/40.40  | | | 
% 228.90/40.40  | | | ALPHA: (73) implies:
% 228.90/40.40  | | |   (74)  op(e2, e0) = e2
% 228.90/40.40  | | | 
% 228.90/40.40  | | | BETA: splitting (22) gives:
% 228.90/40.40  | | | 
% 228.90/40.40  | | | Case 1:
% 228.90/40.40  | | | | 
% 228.90/40.40  | | | |   (75)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2)
% 228.90/40.40  | | | |           = e0)
% 228.90/40.40  | | | | 
% 228.90/40.40  | | | | BETA: splitting (75) gives:
% 228.90/40.40  | | | | 
% 228.90/40.40  | | | | Case 1:
% 228.90/40.40  | | | | | 
% 228.90/40.40  | | | | |   (76)  all_57_0 = e0 & op(e3, e3) = e0
% 228.90/40.40  | | | | | 
% 228.90/40.40  | | | | | ALPHA: (76) implies:
% 228.90/40.40  | | | | |   (77)  op(e3, e3) = e0
% 228.90/40.40  | | | | | 
% 228.90/40.40  | | | | | REF_CLOSE: (7), (31), (37), (77) are inconsistent by sub-proof #2403.
% 228.90/40.40  | | | | | 
% 228.90/40.40  | | | | Case 2:
% 228.90/40.40  | | | | | 
% 228.90/40.40  | | | | |   (78)  all_57_1 = e0 & op(e3, e2) = e0
% 228.90/40.40  | | | | | 
% 228.90/40.40  | | | | | ALPHA: (78) implies:
% 228.90/40.40  | | | | |   (79)  all_57_1 = e0
% 228.90/40.40  | | | | | 
% 228.90/40.40  | | | | | BETA: splitting (42) gives:
% 228.90/40.40  | | | | | 
% 228.90/40.40  | | | | | Case 1:
% 228.90/40.40  | | | | | | 
% 228.90/40.40  | | | | | |   (80)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3,
% 228.90/40.40  | | | | | |             e2) = e3)
% 228.90/40.40  | | | | | | 
% 228.90/40.40  | | | | | | BETA: splitting (80) gives:
% 228.90/40.40  | | | | | | 
% 228.90/40.40  | | | | | | Case 1:
% 228.90/40.40  | | | | | | | 
% 228.90/40.40  | | | | | | |   (81)  all_57_0 = e3 & op(e3, e3) = e3
% 228.90/40.40  | | | | | | | 
% 228.90/40.40  | | | | | | | ALPHA: (81) implies:
% 228.90/40.40  | | | | | | |   (82)  op(e3, e3) = e3
% 228.90/40.40  | | | | | | | 
% 228.90/40.40  | | | | | | | REF_CLOSE: (7), (23), (31), (82) are inconsistent by sub-proof
% 228.90/40.40  | | | | | | |            #2490.
% 228.90/40.40  | | | | | | | 
% 228.90/40.40  | | | | | | Case 2:
% 228.90/40.40  | | | | | | | 
% 228.90/40.40  | | | | | | |   (83)  all_57_1 = e3 & op(e3, e2) = e3
% 228.90/40.40  | | | | | | | 
% 228.90/40.40  | | | | | | | REF_CLOSE: (6), (7), (8), (11), (13), (19), (23), (26), (29),
% 228.90/40.40  | | | | | | |            (37), (43), (53), (58), (62), (63), (66), (79), (83)
% 228.90/40.40  | | | | | | |            are inconsistent by sub-proof #921.
% 228.90/40.40  | | | | | | | 
% 228.90/40.40  | | | | | | End of split
% 228.90/40.40  | | | | | | 
% 228.90/40.40  | | | | | Case 2:
% 228.90/40.40  | | | | | | 
% 228.90/40.40  | | | | | |   (84)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3,
% 228.90/40.40  | | | | | |             e0) = e3)
% 228.90/40.40  | | | | | | 
% 228.90/40.40  | | | | | | REF_CLOSE: (1), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 228.90/40.40  | | | | | |            (14), (15), (16), (18), (19), (20), (21), (22), (23),
% 228.90/40.40  | | | | | |            (24), (25), (26), (27), (28), (29), (30), (31), (33),
% 228.90/40.40  | | | | | |            (35), (36), (37), (38), (39), (43), (44), (46), (47),
% 228.90/40.40  | | | | | |            (48), (49), (50), (51), (53), (54), (55), (57), (59),
% 228.90/40.40  | | | | | |            (62), (63), (64), (66), (67), (68), (70), (74), (84) are
% 228.90/40.40  | | | | | |            inconsistent by sub-proof #630.
% 228.90/40.40  | | | | | | 
% 228.90/40.40  | | | | | End of split
% 228.90/40.40  | | | | | 
% 228.90/40.40  | | | | End of split
% 228.90/40.40  | | | | 
% 228.90/40.40  | | | Case 2:
% 228.90/40.40  | | | | 
% 228.90/40.40  | | | |   (85)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0)
% 228.90/40.40  | | | |           = e0)
% 228.90/40.40  | | | | 
% 228.90/40.40  | | | | BETA: splitting (85) gives:
% 228.90/40.40  | | | | 
% 228.90/40.40  | | | | Case 1:
% 228.90/40.40  | | | | | 
% 228.90/40.40  | | | | |   (86)  all_57_4 = e0 & op(e3, e1) = e0
% 228.90/40.40  | | | | | 
% 228.90/40.40  | | | | | ALPHA: (86) implies:
% 228.90/40.40  | | | | |   (87)  all_57_4 = e0
% 228.90/40.40  | | | | | 
% 228.90/40.40  | | | | | BETA: splitting (42) gives:
% 228.90/40.40  | | | | | 
% 228.90/40.40  | | | | | Case 1:
% 228.90/40.40  | | | | | | 
% 228.90/40.40  | | | | | |   (88)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3,
% 228.90/40.40  | | | | | |             e2) = e3)
% 228.90/40.40  | | | | | | 
% 228.90/40.40  | | | | | | BETA: splitting (88) gives:
% 228.90/40.40  | | | | | | 
% 228.90/40.40  | | | | | | Case 1:
% 228.90/40.40  | | | | | | | 
% 228.90/40.40  | | | | | | |   (89)  all_57_0 = e3 & op(e3, e3) = e3
% 228.90/40.40  | | | | | | | 
% 228.90/40.40  | | | | | | | ALPHA: (89) implies:
% 228.90/40.41  | | | | | | |   (90)  op(e3, e3) = e3
% 228.90/40.41  | | | | | | | 
% 228.90/40.41  | | | | | | | REF_CLOSE: (7), (23), (31), (90) are inconsistent by sub-proof
% 228.90/40.41  | | | | | | |            #2490.
% 228.90/40.41  | | | | | | | 
% 228.90/40.41  | | | | | | Case 2:
% 228.90/40.41  | | | | | | | 
% 228.90/40.41  | | | | | | |   (91)  all_57_1 = e3 & op(e3, e2) = e3
% 228.90/40.41  | | | | | | | 
% 228.90/40.41  | | | | | | | ALPHA: (91) implies:
% 228.90/40.41  | | | | | | |   (92)  all_57_1 = e3
% 228.90/40.41  | | | | | | | 
% 228.90/40.41  | | | | | | | BETA: splitting (61) gives:
% 228.90/40.41  | | | | | | | 
% 228.90/40.41  | | | | | | | Case 1:
% 228.90/40.41  | | | | | | | | 
% 228.90/40.41  | | | | | | | |   (93)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 &
% 228.90/40.41  | | | | | | | |           op(e2, e2) = e0)
% 228.90/40.41  | | | | | | | | 
% 228.90/40.41  | | | | | | | | BETA: splitting (93) gives:
% 228.90/40.41  | | | | | | | | 
% 228.90/40.41  | | | | | | | | Case 1:
% 228.90/40.41  | | | | | | | | | 
% 228.90/40.41  | | | | | | | | |   (94)  all_57_2 = e0 & op(e2, e3) = e0
% 228.90/40.41  | | | | | | | | | 
% 228.90/40.41  | | | | | | | | | ALPHA: (94) implies:
% 228.90/40.41  | | | | | | | | |   (95)  all_57_2 = e0
% 228.90/40.41  | | | | | | | | | 
% 228.90/40.41  | | | | | | | | | REF_CLOSE: (6), (7), (8), (11), (13), (19), (23), (26), (29),
% 228.90/40.41  | | | | | | | | |            (37), (40), (43), (53), (58), (62), (63), (66),
% 228.90/40.41  | | | | | | | | |            (95) are inconsistent by sub-proof #761.
% 228.90/40.41  | | | | | | | | | 
% 228.90/40.41  | | | | | | | | Case 2:
% 228.90/40.41  | | | | | | | | | 
% 228.90/40.41  | | | | | | | | |   (96)  all_57_3 = e0 & op(e2, e2) = e0
% 228.90/40.41  | | | | | | | | | 
% 228.90/40.41  | | | | | | | | | ALPHA: (96) implies:
% 228.90/40.41  | | | | | | | | |   (97)  all_57_3 = e0
% 228.90/40.41  | | | | | | | | | 
% 228.90/40.41  | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (11), (13),
% 228.90/40.41  | | | | | | | | |            (23), (26), (29), (31), (37), (40), (43), (50),
% 228.90/40.41  | | | | | | | | |            (53), (56), (60), (62), (63), (65), (66), (69),
% 228.90/40.41  | | | | | | | | |            (92), (97) are inconsistent by sub-proof #792.
% 228.90/40.41  | | | | | | | | | 
% 228.90/40.41  | | | | | | | | End of split
% 228.90/40.41  | | | | | | | | 
% 228.90/40.41  | | | | | | | Case 2:
% 228.90/40.41  | | | | | | | | 
% 228.90/40.41  | | | | | | | |   (98)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 &
% 228.90/40.41  | | | | | | | |           op(e2, e0) = e0)
% 228.90/40.41  | | | | | | | | 
% 228.90/40.41  | | | | | | | | BETA: splitting (98) gives:
% 228.90/40.41  | | | | | | | | 
% 228.90/40.41  | | | | | | | | Case 1:
% 228.90/40.41  | | | | | | | | | 
% 228.90/40.41  | | | | | | | | |   (99)  all_57_5 = e0 & op(e2, e1) = e0
% 228.90/40.41  | | | | | | | | | 
% 228.90/40.41  | | | | | | | | | ALPHA: (99) implies:
% 228.90/40.41  | | | | | | | | |   (100)  all_57_5 = e0
% 228.90/40.41  | | | | | | | | | 
% 228.90/40.41  | | | | | | | | | BETA: splitting (45) gives:
% 228.90/40.41  | | | | | | | | | 
% 228.90/40.41  | | | | | | | | | Case 1:
% 228.90/40.41  | | | | | | | | | | 
% 228.90/40.41  | | | | | | | | | |   (101)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 228.90/40.41  | | | | | | | | | |            & op(e2, e1) = e3)
% 228.90/40.41  | | | | | | | | | | 
% 228.90/40.41  | | | | | | | | | | BETA: splitting (101) gives:
% 228.90/40.41  | | | | | | | | | | 
% 228.90/40.41  | | | | | | | | | | Case 1:
% 228.90/40.41  | | | | | | | | | | | 
% 228.90/40.41  | | | | | | | | | | |   (102)  all_57_4 = e3 & op(e3, e1) = e3
% 228.90/40.41  | | | | | | | | | | | 
% 228.90/40.41  | | | | | | | | | | | ALPHA: (102) implies:
% 228.90/40.41  | | | | | | | | | | |   (103)  all_57_4 = e3
% 228.90/40.41  | | | | | | | | | | | 
% 228.90/40.41  | | | | | | | | | | | COMBINE_EQS: (87), (103) imply:
% 228.90/40.41  | | | | | | | | | | |   (104)  e3 = e0
% 228.90/40.41  | | | | | | | | | | | 
% 228.90/40.41  | | | | | | | | | | | COMBINE_EQS: (58), (104) imply:
% 228.90/40.41  | | | | | | | | | | |   (105)  all_57_7 = e0
% 228.90/40.41  | | | | | | | | | | | 
% 228.90/40.41  | | | | | | | | | | | REF_CLOSE: (6), (7), (8), (11), (13), (19), (23), (26), (29),
% 228.90/40.41  | | | | | | | | | | |            (37), (43), (53), (62), (63), (66), (105) are
% 228.90/40.41  | | | | | | | | | | |            inconsistent by sub-proof #1735.
% 228.90/40.41  | | | | | | | | | | | 
% 228.90/40.41  | | | | | | | | | | Case 2:
% 228.90/40.41  | | | | | | | | | | | 
% 228.90/40.41  | | | | | | | | | | |   (106)  all_57_5 = e3 & op(e2, e1) = e3
% 228.90/40.41  | | | | | | | | | | | 
% 228.90/40.41  | | | | | | | | | | | ALPHA: (106) implies:
% 228.90/40.41  | | | | | | | | | | |   (107)  all_57_5 = e3
% 228.90/40.41  | | | | | | | | | | | 
% 228.90/40.41  | | | | | | | | | | | COMBINE_EQS: (100), (107) imply:
% 228.90/40.41  | | | | | | | | | | |   (108)  e3 = e0
% 228.90/40.41  | | | | | | | | | | | 
% 228.90/40.41  | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (15), (23), (26), (37), (40), (43),
% 228.90/40.41  | | | | | | | | | | |            (58), (60), (61), (62), (69), (92), (107), (108)
% 228.90/40.41  | | | | | | | | | | |            are inconsistent by sub-proof #732.
% 228.90/40.41  | | | | | | | | | | | 
% 228.90/40.41  | | | | | | | | | | End of split
% 228.90/40.41  | | | | | | | | | | 
% 228.90/40.41  | | | | | | | | | Case 2:
% 228.90/40.41  | | | | | | | | | | 
% 228.90/40.41  | | | | | | | | | |   (109)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3
% 228.90/40.41  | | | | | | | | | |            & op(e0, e1) = e3)
% 228.90/40.41  | | | | | | | | | | 
% 228.90/40.41  | | | | | | | | | | REF_CLOSE: (6), (7), (11), (13), (23), (26), (29), (32),
% 228.90/40.41  | | | | | | | | | |            (37), (43), (52), (53), (62), (109) are
% 228.90/40.41  | | | | | | | | | |            inconsistent by sub-proof #1794.
% 228.90/40.41  | | | | | | | | | | 
% 228.90/40.41  | | | | | | | | | End of split
% 228.90/40.41  | | | | | | | | | 
% 228.90/40.41  | | | | | | | | Case 2:
% 228.90/40.41  | | | | | | | | | 
% 228.90/40.41  | | | | | | | | |   (110)  all_57_10 = e0 & op(e2, e0) = e0
% 228.90/40.41  | | | | | | | | | 
% 228.90/40.41  | | | | | | | | | ALPHA: (110) implies:
% 228.90/40.41  | | | | | | | | |   (111)  all_57_10 = e0
% 228.90/40.41  | | | | | | | | | 
% 228.90/40.41  | | | | | | | | | REF_CLOSE: (6), (7), (23), (29), (34), (37), (43), (50), (62),
% 228.90/40.41  | | | | | | | | |            (63), (66), (111) are inconsistent by sub-proof
% 228.90/40.41  | | | | | | | | |            #1087.
% 228.90/40.41  | | | | | | | | | 
% 228.90/40.41  | | | | | | | | End of split
% 228.90/40.41  | | | | | | | | 
% 228.90/40.41  | | | | | | | End of split
% 228.90/40.41  | | | | | | | 
% 228.90/40.41  | | | | | | End of split
% 228.90/40.41  | | | | | | 
% 228.90/40.41  | | | | | Case 2:
% 228.90/40.41  | | | | | | 
% 228.90/40.41  | | | | | |   (112)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3,
% 228.90/40.41  | | | | | |              e0) = e3)
% 228.90/40.41  | | | | | | 
% 228.90/40.41  | | | | | | REF_CLOSE: (6), (7), (8), (11), (13), (19), (23), (26), (29), (37),
% 228.90/40.41  | | | | | |            (43), (53), (57), (58), (62), (63), (66), (70), (87),
% 228.90/40.41  | | | | | |            (112) are inconsistent by sub-proof #1026.
% 228.90/40.41  | | | | | | 
% 228.90/40.41  | | | | | End of split
% 228.90/40.41  | | | | | 
% 228.90/40.41  | | | | Case 2:
% 228.90/40.41  | | | | | 
% 228.90/40.41  | | | | |   (113)  all_57_9 = e0 & op(e3, e0) = e0
% 228.90/40.41  | | | | | 
% 228.90/40.41  | | | | | ALPHA: (113) implies:
% 228.90/40.41  | | | | |   (114)  all_57_9 = e0
% 228.90/40.41  | | | | | 
% 228.90/40.41  | | | | | REF_CLOSE: (6), (23), (29), (34), (37), (43), (62), (63), (66), (114)
% 228.90/40.41  | | | | |            are inconsistent by sub-proof #1144.
% 228.90/40.41  | | | | | 
% 228.90/40.41  | | | | End of split
% 228.90/40.41  | | | | 
% 228.90/40.41  | | | End of split
% 228.90/40.41  | | | 
% 228.90/40.41  | | End of split
% 228.90/40.41  | | 
% 228.90/40.41  | Case 2:
% 228.90/40.41  | | 
% 228.90/40.41  | |   (115)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.90/40.41  | |            e2)
% 228.90/40.41  | | 
% 228.90/40.41  | | REF_CLOSE: (3), (4), (6), (7), (8), (11), (13), (15), (23), (26), (29),
% 228.90/40.41  | |            (31), (34), (37), (40), (41), (43), (50), (53), (56), (58), (60),
% 228.90/40.41  | |            (62), (63), (65), (66), (115) are inconsistent by sub-proof #629.
% 228.90/40.41  | | 
% 228.90/40.41  | End of split
% 228.90/40.41  | 
% 228.90/40.41  End of proof
% 228.90/40.41  
% 228.90/40.41  Sub-proof #629 shows that the following formulas are inconsistent:
% 228.90/40.41  ----------------------------------------------------------------
% 228.90/40.41    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.90/40.41         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.90/40.41    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.90/40.41         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.90/40.41    (3)   ~ (e3 = e1)
% 228.90/40.41    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.90/40.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.90/40.41    (5)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.90/40.41         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.90/40.41    (6)   ~ (all_6_2 = e3)
% 228.90/40.41    (7)  op(e1, e1) = all_6_2
% 228.90/40.41    (8)  op(e2, e2) = e1
% 228.90/40.41    (9)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.90/40.41    (10)   ~ (e3 = e2)
% 228.90/40.41    (11)   ~ (e3 = e0)
% 228.90/40.41    (12)  all_57_15 = e3
% 228.90/40.41    (13)  op(e3, e3) = e2
% 228.90/40.41    (14)  all_57_11 = e0
% 228.90/40.41    (15)   ~ (e2 = e0)
% 228.90/40.41    (16)  all_57_2 = e3
% 228.90/40.41    (17)  all_57_3 = e1
% 228.90/40.41    (18)   ~ (e1 = e0)
% 228.90/40.41    (19)  op(e0, e0) = e3
% 228.90/40.41    (20)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.90/40.41              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.90/40.41                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.90/40.41                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.90/40.41    (21)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.90/40.41          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.90/40.41    (22)  all_57_7 = e3
% 228.90/40.41    (23)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.90/40.41          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.90/40.41    (24)   ~ (e2 = e1)
% 228.90/40.41    (25)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.90/40.41          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.90/40.41    (26)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.90/40.41          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.90/40.41    (27)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.90/40.41          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.90/40.41  
% 228.90/40.41  Begin of proof
% 228.90/40.41  | 
% 228.90/40.41  | BETA: splitting (9) gives:
% 228.90/40.41  | 
% 228.90/40.41  | Case 1:
% 228.90/40.41  | | 
% 228.90/40.41  | |   (28)  all_57_11 = e2 & op(e1, e0) = e2
% 228.90/40.41  | | 
% 228.90/40.41  | | REF_CLOSE: (14), (15), (28) are inconsistent by sub-proof #1988.
% 228.90/40.41  | | 
% 228.90/40.41  | Case 2:
% 228.90/40.41  | | 
% 228.90/40.41  | |   (29)  all_57_15 = e2 & op(e0, e0) = e2
% 228.90/40.41  | | 
% 228.90/40.41  | | ALPHA: (29) implies:
% 228.90/40.41  | |   (30)  all_57_15 = e2
% 228.90/40.41  | | 
% 228.90/40.41  | | COMBINE_EQS: (12), (30) imply:
% 228.90/40.41  | |   (31)  e3 = e2
% 228.90/40.41  | | 
% 228.90/40.41  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13),
% 228.90/40.41  | |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 228.90/40.41  | |            (26), (27), (31) are inconsistent by sub-proof #647.
% 228.90/40.41  | | 
% 228.90/40.41  | End of split
% 228.90/40.41  | 
% 228.90/40.41  End of proof
% 228.90/40.41  
% 228.90/40.41  Sub-proof #630 shows that the following formulas are inconsistent:
% 228.90/40.41  ----------------------------------------------------------------
% 228.90/40.41    (1)   ~ (all_53_2 = e2)
% 228.90/40.41    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.90/40.41         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.90/40.41    (3)   ~ (e3 = e1)
% 228.90/40.41    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.90/40.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.90/40.41    (5)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.90/40.41         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.90/40.41    (6)   ~ (all_53_3 = e3)
% 228.90/40.41    (7)   ~ (all_53_3 = all_53_7)
% 228.90/40.41    (8)   ~ (all_6_2 = e3)
% 228.90/40.41    (9)   ~ (all_53_9 = e1)
% 228.90/40.41    (10)  op(e1, e1) = all_6_2
% 228.90/40.41    (11)   ~ (all_53_1 = all_53_9)
% 228.90/40.41    (12)  op(e2, e2) = e1
% 228.90/40.41    (13)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.90/40.41          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.90/40.41    (14)   ~ (all_53_13 = e3)
% 228.90/40.41    (15)  all_57_6 = e1
% 228.90/40.41    (16)   ~ (all_53_9 = all_53_11)
% 228.90/40.41    (17)  all_55_4 = all_53_1
% 228.90/40.41    (18)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.90/40.41          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.90/40.41    (19)   ~ (e3 = e2)
% 228.90/40.41    (20)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 228.90/40.41    (21)   ~ (all_53_1 = all_53_3)
% 228.90/40.41    (22)   ~ (e3 = e0)
% 228.90/40.41    (23)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.90/40.41    (24)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 228.90/40.41    (25)  all_57_15 = e3
% 228.90/40.41    (26)   ~ (all_53_9 = all_53_13)
% 228.90/40.41    (27)  op(e3, e3) = e2
% 228.90/40.41    (28)   ~ (all_53_1 = e1)
% 228.90/40.41    (29)  op(e2, e0) = e2
% 228.90/40.41    (30)  all_55_6 = all_53_9
% 228.90/40.41    (31)   ~ (all_53_1 = all_53_2)
% 228.90/40.41    (32)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.90/40.41    (33)   ~ (e2 = e0)
% 228.90/40.41    (34)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.90/40.41            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.90/40.41            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.90/40.41            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.90/40.41              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.90/40.41            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.90/40.41            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.90/40.41              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.90/40.41              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.90/40.41            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.90/40.41            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.90/40.41            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.90/40.41              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.90/40.41              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.90/40.41            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.90/40.41              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.90/40.41            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.90/40.41            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.90/40.41              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.90/40.41              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.90/40.41            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.90/40.41            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.90/40.41    (35)  all_55_12 = all_53_3
% 228.90/40.41    (36)   ~ (e1 = e0)
% 228.90/40.41    (37)   ~ (all_53_3 = all_53_11)
% 228.90/40.41    (38)   ~ (all_53_2 = all_53_3)
% 228.90/40.41    (39)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 228.90/40.41    (40)   ~ (all_53_7 = all_53_11)
% 228.90/40.41    (41)  all_55_8 = all_53_2
% 228.90/40.41    (42)  op(e0, e0) = e3
% 228.90/40.41    (43)  op(e0, e2) = all_53_7
% 228.90/40.41    (44)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.90/40.41              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.90/40.41                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.90/40.41                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.90/40.41    (45)   ~ (all_53_1 = all_53_13)
% 228.90/40.41    (46)  op(e2, e0) = all_53_13
% 228.90/40.41    (47)   ~ (all_53_12 = e3)
% 228.90/40.41    (48)  op(e1, e3) = all_53_2
% 228.90/40.41    (49)   ~ (e2 = e1)
% 228.90/40.41    (50)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.90/40.41          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.90/40.41    (51)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 228.90/40.41    (52)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.90/40.41          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.90/40.41    (53)  all_55_14 = all_53_11
% 228.90/40.41    (54)   ~ (all_53_11 = e3)
% 228.90/40.41    (55)  op(e3, e0) = all_53_12
% 228.90/40.41  
% 228.90/40.41  Begin of proof
% 228.90/40.41  | 
% 228.90/40.41  | BETA: splitting (32) gives:
% 228.90/40.41  | 
% 228.90/40.41  | Case 1:
% 228.90/40.41  | | 
% 228.90/40.41  | |   (56)  all_57_4 = e3 & op(e3, e1) = e3
% 228.90/40.41  | | 
% 228.90/40.41  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.90/40.41  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 228.90/40.41  | |            (24), (25), (26), (27), (28), (29), (30), (31), (33), (34), (35),
% 228.90/40.41  | |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 228.90/40.41  | |            (48), (49), (50), (51), (52), (53), (54), (56) are inconsistent
% 228.90/40.41  | |            by sub-proof #631.
% 228.90/40.41  | | 
% 228.90/40.41  | Case 2:
% 228.90/40.41  | | 
% 228.90/40.41  | |   (57)  all_57_9 = e3 & op(e3, e0) = e3
% 228.90/40.41  | | 
% 228.90/40.41  | | ALPHA: (57) implies:
% 228.90/40.41  | |   (58)  op(e3, e0) = e3
% 228.90/40.41  | | 
% 228.90/40.41  | | REF_CLOSE: (4), (47), (55), (58) are inconsistent by sub-proof #2458.
% 228.90/40.41  | | 
% 228.90/40.41  | End of split
% 228.90/40.41  | 
% 228.90/40.41  End of proof
% 228.90/40.41  
% 228.90/40.41  Sub-proof #631 shows that the following formulas are inconsistent:
% 228.90/40.41  ----------------------------------------------------------------
% 228.90/40.41    (1)   ~ (all_53_2 = e2)
% 228.90/40.41    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.90/40.41         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.90/40.41    (3)   ~ (e3 = e1)
% 228.90/40.41    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.90/40.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.90/40.41    (5)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.90/40.41         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.90/40.41    (6)   ~ (all_53_3 = e3)
% 228.90/40.41    (7)   ~ (all_53_3 = all_53_7)
% 228.90/40.41    (8)   ~ (all_6_2 = e3)
% 228.90/40.41    (9)   ~ (all_53_9 = e1)
% 228.90/40.41    (10)  op(e1, e1) = all_6_2
% 228.90/40.41    (11)   ~ (all_53_1 = all_53_9)
% 228.90/40.41    (12)  op(e2, e2) = e1
% 228.90/40.41    (13)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.90/40.41          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.90/40.41    (14)   ~ (all_53_13 = e3)
% 228.90/40.41    (15)  all_57_6 = e1
% 228.90/40.41    (16)   ~ (all_53_9 = all_53_11)
% 228.90/40.41    (17)  all_55_4 = all_53_1
% 228.90/40.41    (18)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.90/40.41          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.90/40.41    (19)   ~ (e3 = e2)
% 228.90/40.41    (20)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 228.90/40.41    (21)   ~ (all_53_1 = all_53_3)
% 228.90/40.41    (22)   ~ (e3 = e0)
% 228.90/40.41    (23)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.90/40.41    (24)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 228.90/40.41    (25)  all_57_15 = e3
% 228.90/40.41    (26)   ~ (all_53_9 = all_53_13)
% 228.90/40.41    (27)  op(e3, e3) = e2
% 228.90/40.41    (28)   ~ (all_53_1 = e1)
% 228.90/40.41    (29)  op(e2, e0) = e2
% 228.90/40.41    (30)  all_55_6 = all_53_9
% 228.90/40.41    (31)   ~ (all_53_1 = all_53_2)
% 228.90/40.41    (32)   ~ (e2 = e0)
% 228.90/40.41    (33)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.90/40.41            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.90/40.41            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.90/40.41            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.90/40.41              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.90/40.41            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.90/40.41            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.90/40.41              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.90/40.41              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.90/40.41            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.90/40.41            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.90/40.41            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.90/40.41              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.90/40.41              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.90/40.41            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.90/40.41              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.90/40.41            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.90/40.41            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.90/40.41              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.90/40.41              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.90/40.41            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.90/40.41            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.90/40.41    (34)  all_55_12 = all_53_3
% 228.90/40.41    (35)   ~ (e1 = e0)
% 228.90/40.41    (36)   ~ (all_53_3 = all_53_11)
% 228.90/40.41    (37)   ~ (all_53_2 = all_53_3)
% 228.90/40.41    (38)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 228.90/40.41    (39)   ~ (all_53_7 = all_53_11)
% 228.90/40.41    (40)  all_55_8 = all_53_2
% 228.90/40.41    (41)  op(e0, e0) = e3
% 228.90/40.41    (42)  op(e0, e2) = all_53_7
% 228.90/40.41    (43)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.90/40.41              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.90/40.41                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.90/40.41                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.90/40.41    (44)   ~ (all_53_1 = all_53_13)
% 228.90/40.41    (45)  op(e2, e0) = all_53_13
% 228.90/40.41    (46)  op(e1, e3) = all_53_2
% 228.90/40.41    (47)   ~ (e2 = e1)
% 228.90/40.41    (48)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.90/40.41          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.90/40.41    (49)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 228.90/40.41    (50)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.90/40.41          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.90/40.41    (51)  all_55_14 = all_53_11
% 228.90/40.41    (52)  all_57_4 = e3 & op(e3, e1) = e3
% 228.90/40.41    (53)   ~ (all_53_11 = e3)
% 228.90/40.41  
% 228.90/40.41  Begin of proof
% 228.90/40.41  | 
% 228.90/40.41  | ALPHA: (52) implies:
% 228.90/40.41  |   (54)  all_57_4 = e3
% 228.90/40.41  | 
% 228.90/40.41  | BETA: splitting (2) gives:
% 228.90/40.41  | 
% 228.90/40.41  | Case 1:
% 228.90/40.41  | | 
% 228.90/40.41  | |   (55)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 228.90/40.41  | |           e2)
% 228.90/40.41  | | 
% 228.90/40.41  | | REF_CLOSE: (3), (4), (12), (13), (18), (22), (27), (32), (35), (47), (54),
% 228.90/40.41  | |            (55) are inconsistent by sub-proof #652.
% 228.90/40.41  | | 
% 228.90/40.41  | Case 2:
% 228.90/40.41  | | 
% 228.90/40.41  | |   (56)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 228.90/40.41  | |           e2)
% 228.90/40.41  | | 
% 228.90/40.41  | | BETA: splitting (56) gives:
% 228.90/40.41  | | 
% 228.90/40.41  | | Case 1:
% 228.90/40.41  | | | 
% 228.90/40.41  | | |   (57)  all_57_7 = e2 & op(e1, e2) = e2
% 228.90/40.41  | | | 
% 228.90/40.41  | | | ALPHA: (57) implies:
% 228.90/40.41  | | |   (58)  all_57_7 = e2
% 228.90/40.41  | | | 
% 228.90/40.41  | | | REF_CLOSE: (3), (4), (5), (8), (10), (15), (19), (22), (25), (32), (35),
% 228.90/40.41  | | |            (41), (43), (47), (48), (50), (58) are inconsistent by
% 228.90/40.41  | | |            sub-proof #1078.
% 228.90/40.41  | | | 
% 228.90/40.41  | | Case 2:
% 228.90/40.41  | | | 
% 228.90/40.41  | | |   (59)  all_57_13 = e2 & op(e0, e2) = e2
% 228.90/40.41  | | | 
% 228.90/40.41  | | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (10), (11), (12), (14),
% 228.90/40.41  | | |            (16), (17), (20), (21), (23), (24), (26), (27), (28), (29),
% 228.90/40.41  | | |            (30), (31), (32), (33), (34), (36), (37), (38), (39), (40),
% 228.90/40.41  | | |            (41), (42), (44), (45), (46), (49), (51), (53), (59) are
% 228.90/40.41  | | |            inconsistent by sub-proof #771.
% 228.90/40.41  | | | 
% 228.90/40.41  | | End of split
% 228.90/40.41  | | 
% 228.90/40.41  | End of split
% 228.90/40.41  | 
% 228.90/40.41  End of proof
% 228.90/40.41  
% 228.90/40.41  Sub-proof #632 shows that the following formulas are inconsistent:
% 228.90/40.41  ----------------------------------------------------------------
% 228.90/40.41    (1)   ~ (all_53_2 = e2)
% 228.90/40.41    (2)  all_57_0 = e2
% 228.90/40.41    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.90/40.41         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.90/40.41    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.90/40.41         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.90/40.41    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.90/40.41         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.90/40.41    (6)   ~ (e3 = e1)
% 228.90/40.41    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.90/40.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.90/40.41    (8)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.90/40.41         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.90/40.41    (9)   ~ (all_53_3 = e3)
% 228.90/40.41    (10)   ~ (all_53_3 = all_53_7)
% 228.90/40.41    (11)   ~ (all_6_2 = e3)
% 228.90/40.41    (12)   ~ (all_53_9 = e1)
% 228.90/40.41    (13)  op(e1, e1) = all_6_2
% 228.90/40.41    (14)   ~ (all_53_1 = all_53_9)
% 228.90/40.41    (15)  op(e2, e2) = e1
% 228.90/40.41    (16)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.90/40.41          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.90/40.41    (17)  all_57_9 = e1
% 228.90/40.41    (18)   ~ (all_53_13 = e3)
% 228.90/40.41    (19)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.90/40.41          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.90/40.41    (20)   ~ (all_53_9 = all_53_11)
% 228.90/40.41    (21)  all_55_4 = all_53_1
% 228.90/40.41    (22)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.90/40.41          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.90/40.41    (23)   ~ (e3 = e2)
% 228.90/40.41    (24)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 228.90/40.41    (25)   ~ (all_53_1 = all_53_3)
% 228.90/40.41    (26)   ~ (e3 = e0)
% 228.90/40.41    (27)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.90/40.41    (28)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 228.90/40.41    (29)  all_57_15 = e3
% 228.90/40.41    (30)   ~ (all_53_9 = all_53_13)
% 228.90/40.41    (31)  op(e3, e3) = e2
% 228.90/40.41    (32)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.90/40.41          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.90/40.41            e1)
% 228.90/40.41    (33)  all_57_10 = e2
% 228.90/40.41    (34)   ~ (all_53_1 = e1)
% 228.90/40.41    (35)  op(e2, e0) = e2
% 228.90/40.41    (36)  all_55_6 = all_53_9
% 228.90/40.41    (37)   ~ (all_53_1 = all_53_2)
% 228.90/40.41    (38)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.90/40.41          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 228.90/40.41    (39)   ~ (e2 = e0)
% 228.90/40.42    (40)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.90/40.42            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.90/40.42            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.90/40.42            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.90/40.42              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.90/40.42            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.90/40.42            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.90/40.42              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.90/40.42              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.90/40.42            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.90/40.42            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.90/40.42            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.90/40.42              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.90/40.42              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.90/40.42            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.90/40.42              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.90/40.42            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.90/40.42            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.90/40.42              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.90/40.42              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.90/40.42            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.90/40.42            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.90/40.42    (41)  all_55_12 = all_53_3
% 228.90/40.42    (42)  all_57_3 = e1
% 228.90/40.42    (43)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.90/40.42          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.90/40.42    (44)   ~ (e1 = e0)
% 228.90/40.42    (45)   ~ (all_53_3 = all_53_11)
% 228.90/40.42    (46)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.90/40.42          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.90/40.42    (47)  all_57_6 = e3
% 228.90/40.42    (48)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.90/40.42          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.90/40.42    (49)   ~ (all_53_2 = all_53_3)
% 228.90/40.42    (50)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 228.90/40.42    (51)   ~ (all_53_7 = all_53_11)
% 228.90/40.42    (52)  all_55_8 = all_53_2
% 228.90/40.42    (53)  op(e0, e0) = e3
% 228.90/40.42    (54)  op(e0, e2) = all_53_7
% 228.90/40.42    (55)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.90/40.42          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.90/40.42            e2)
% 228.90/40.42    (56)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.90/40.42              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.90/40.42                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.90/40.42                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.90/40.42    (57)   ~ (all_53_1 = all_53_13)
% 228.90/40.42    (58)  op(e2, e0) = all_53_13
% 228.90/40.42    (59)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.90/40.42          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.90/40.42    (60)   ~ (all_53_12 = e3)
% 228.90/40.42    (61)  op(e1, e3) = all_53_2
% 228.90/40.42    (62)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.90/40.42          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.90/40.42    (63)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.90/40.42          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.90/40.42    (64)  all_57_1 = e3
% 228.90/40.42    (65)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.90/40.42          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 228.90/40.42    (66)   ~ (e2 = e1)
% 228.90/40.42    (67)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.90/40.42          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.90/40.42    (68)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.90/40.42          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.90/40.42    (69)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 228.90/40.42    (70)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.90/40.42          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.90/40.42    (71)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.90/40.42          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.90/40.42    (72)  all_55_14 = all_53_11
% 228.90/40.42    (73)  all_57_14 = e1 & op(e0, e1) = e1
% 228.90/40.42    (74)   ~ (all_53_11 = e3)
% 228.90/40.42    (75)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.90/40.42          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.90/40.42    (76)  op(e3, e0) = all_53_12
% 228.90/40.42  
% 228.90/40.42  Begin of proof
% 228.90/40.42  | 
% 228.90/40.42  | ALPHA: (73) implies:
% 228.90/40.42  |   (77)  all_57_14 = e1
% 228.90/40.42  | 
% 228.90/40.42  | BETA: splitting (55) gives:
% 228.90/40.42  | 
% 228.90/40.42  | Case 1:
% 228.90/40.42  | | 
% 228.90/40.42  | |   (78)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 228.90/40.42  | |           e2)
% 228.90/40.42  | | 
% 228.90/40.42  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.90/40.42  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 228.90/40.42  | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 228.90/40.42  | |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 228.90/40.42  | |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), (56),
% 228.90/40.42  | |            (57), (58), (59), (60), (61), (62), (63), (64), (65), (66), (67),
% 228.90/40.42  | |            (68), (69), (70), (71), (72), (74), (75), (76), (78) are
% 228.90/40.42  | |            inconsistent by sub-proof #634.
% 228.90/40.42  | | 
% 228.90/40.42  | Case 2:
% 228.90/40.42  | | 
% 228.90/40.42  | |   (79)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.90/40.42  | |           e2)
% 228.90/40.42  | | 
% 228.90/40.42  | | BETA: splitting (79) gives:
% 228.90/40.42  | | 
% 228.90/40.42  | | Case 1:
% 228.90/40.42  | | | 
% 228.90/40.42  | | |   (80)  all_57_14 = e2 & op(e0, e1) = e2
% 228.90/40.42  | | | 
% 228.90/40.42  | | | ALPHA: (80) implies:
% 228.90/40.42  | | |   (81)  all_57_14 = e2
% 228.90/40.42  | | | 
% 228.90/40.42  | | | COMBINE_EQS: (77), (81) imply:
% 228.90/40.42  | | |   (82)  e2 = e1
% 228.90/40.42  | | | 
% 228.90/40.42  | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (11), (13), (15), (16), (17),
% 228.90/40.42  | | |            (19), (22), (23), (26), (29), (31), (32), (33), (38), (39),
% 228.90/40.42  | | |            (42), (43), (44), (46), (48), (53), (55), (56), (59), (60),
% 228.90/40.42  | | |            (62), (63), (65), (66), (67), (70), (71), (75), (76), (82) are
% 228.90/40.42  | | |            inconsistent by sub-proof #635.
% 228.90/40.42  | | | 
% 228.90/40.42  | | Case 2:
% 228.90/40.42  | | | 
% 228.90/40.42  | | |   (83)  all_57_15 = e2 & op(e0, e0) = e2
% 228.90/40.42  | | | 
% 228.90/40.42  | | | REF_CLOSE: (6), (7), (16), (22), (23), (26), (29), (31), (39), (43), (44),
% 228.90/40.42  | | |            (60), (64), (66), (76), (83) are inconsistent by sub-proof
% 228.90/40.42  | | |            #633.
% 228.90/40.42  | | | 
% 228.90/40.42  | | End of split
% 228.90/40.42  | | 
% 228.90/40.42  | End of split
% 228.90/40.42  | 
% 228.90/40.42  End of proof
% 228.90/40.42  
% 228.90/40.42  Sub-proof #633 shows that the following formulas are inconsistent:
% 228.90/40.42  ----------------------------------------------------------------
% 228.90/40.42    (1)   ~ (e3 = e1)
% 228.90/40.42    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.90/40.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.90/40.42    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.90/40.42         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.90/40.42    (4)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.90/40.42         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.90/40.42    (5)   ~ (e3 = e2)
% 228.90/40.42    (6)   ~ (e3 = e0)
% 228.90/40.42    (7)  all_57_15 = e3
% 228.90/40.42    (8)  op(e3, e3) = e2
% 228.90/40.42    (9)   ~ (e2 = e0)
% 228.90/40.42    (10)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.90/40.42          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.90/40.42    (11)   ~ (e1 = e0)
% 228.90/40.42    (12)   ~ (all_53_12 = e3)
% 228.90/40.42    (13)  all_57_1 = e3
% 228.90/40.42    (14)   ~ (e2 = e1)
% 228.90/40.42    (15)  all_57_15 = e2 & op(e0, e0) = e2
% 228.90/40.42    (16)  op(e3, e0) = all_53_12
% 228.90/40.42  
% 228.90/40.42  Begin of proof
% 228.90/40.42  | 
% 228.90/40.42  | ALPHA: (15) implies:
% 228.90/40.42  |   (17)  all_57_15 = e2
% 228.90/40.42  | 
% 228.90/40.42  | COMBINE_EQS: (7), (17) imply:
% 228.90/40.42  |   (18)  e3 = e2
% 228.90/40.42  | 
% 228.90/40.42  | SIMP: (18) implies:
% 228.90/40.42  |   (19)  e3 = e2
% 228.90/40.42  | 
% 228.90/40.42  | COMBINE_EQS: (13), (19) imply:
% 228.90/40.42  |   (20)  all_57_1 = e2
% 228.90/40.42  | 
% 228.90/40.42  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (14),
% 228.90/40.42  |            (16), (20) are inconsistent by sub-proof #1650.
% 228.90/40.42  | 
% 228.90/40.42  End of proof
% 228.90/40.42  
% 228.90/40.42  Sub-proof #634 shows that the following formulas are inconsistent:
% 228.90/40.42  ----------------------------------------------------------------
% 228.90/40.42    (1)   ~ (all_53_2 = e2)
% 228.90/40.42    (2)  all_57_0 = e2
% 228.90/40.42    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.90/40.42         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.90/40.42    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.90/40.42         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.90/40.42    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.90/40.42         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.90/40.42    (6)   ~ (e3 = e1)
% 228.90/40.42    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.90/40.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.90/40.42    (8)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.90/40.42         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.90/40.42    (9)   ~ (all_53_3 = e3)
% 228.90/40.42    (10)   ~ (all_53_3 = all_53_7)
% 228.90/40.42    (11)   ~ (all_6_2 = e3)
% 228.90/40.42    (12)   ~ (all_53_9 = e1)
% 228.90/40.42    (13)  op(e1, e1) = all_6_2
% 228.90/40.42    (14)   ~ (all_53_1 = all_53_9)
% 228.90/40.42    (15)  op(e2, e2) = e1
% 228.90/40.42    (16)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.90/40.42          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.90/40.42    (17)  all_57_9 = e1
% 228.90/40.42    (18)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.90/40.42    (19)   ~ (all_53_13 = e3)
% 228.90/40.42    (20)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.90/40.42          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.90/40.42    (21)   ~ (all_53_9 = all_53_11)
% 228.90/40.42    (22)  all_55_4 = all_53_1
% 228.90/40.42    (23)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.90/40.42          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.90/40.42    (24)   ~ (e3 = e2)
% 228.90/40.42    (25)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 228.90/40.42    (26)   ~ (all_53_1 = all_53_3)
% 228.90/40.42    (27)   ~ (e3 = e0)
% 228.90/40.42    (28)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.90/40.42    (29)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 228.90/40.42    (30)  all_57_15 = e3
% 228.90/40.42    (31)   ~ (all_53_9 = all_53_13)
% 228.90/40.42    (32)  op(e3, e3) = e2
% 228.90/40.42    (33)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.90/40.42          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.90/40.42            e1)
% 228.90/40.42    (34)  all_57_10 = e2
% 228.90/40.42    (35)   ~ (all_53_1 = e1)
% 228.90/40.42    (36)  op(e2, e0) = e2
% 228.90/40.42    (37)  all_55_6 = all_53_9
% 228.90/40.42    (38)   ~ (all_53_1 = all_53_2)
% 228.90/40.42    (39)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.90/40.42          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 228.90/40.42    (40)   ~ (e2 = e0)
% 228.90/40.42    (41)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.90/40.42            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.90/40.42            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.90/40.42            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.90/40.42              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.90/40.42            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.90/40.42            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.90/40.42              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.90/40.42              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.90/40.42            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.90/40.42            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.90/40.42            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.90/40.42              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.90/40.42              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.90/40.42            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.90/40.42              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.90/40.42            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.90/40.42            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.90/40.42              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.90/40.42              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.90/40.42            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.90/40.42            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.90/40.42    (42)  all_55_12 = all_53_3
% 228.90/40.42    (43)  all_57_3 = e1
% 228.90/40.42    (44)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.90/40.42          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.90/40.42    (45)   ~ (e1 = e0)
% 228.90/40.42    (46)   ~ (all_53_3 = all_53_11)
% 228.90/40.42    (47)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.90/40.42          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.90/40.42    (48)  all_57_6 = e3
% 228.90/40.42    (49)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.90/40.42          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.90/40.42    (50)   ~ (all_53_2 = all_53_3)
% 228.90/40.42    (51)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 228.90/40.42    (52)   ~ (all_53_7 = all_53_11)
% 228.90/40.42    (53)  all_55_8 = all_53_2
% 228.90/40.42    (54)  op(e0, e0) = e3
% 228.90/40.42    (55)  op(e0, e2) = all_53_7
% 228.90/40.42    (56)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.90/40.42          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.90/40.42            e2)
% 228.90/40.42    (57)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.90/40.42              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.90/40.42                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.90/40.42                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.90/40.42    (58)   ~ (all_53_1 = all_53_13)
% 228.90/40.42    (59)  op(e2, e0) = all_53_13
% 228.90/40.42    (60)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.90/40.42          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.90/40.42    (61)   ~ (all_53_12 = e3)
% 228.90/40.42    (62)  op(e1, e3) = all_53_2
% 228.90/40.42    (63)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.90/40.42          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.90/40.42    (64)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.90/40.42          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.90/40.42    (65)  all_57_1 = e3
% 228.90/40.42    (66)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.90/40.42          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 228.90/40.42    (67)   ~ (e2 = e1)
% 228.90/40.42    (68)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.90/40.42          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.90/40.42    (69)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.90/40.42          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.90/40.42    (70)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 228.90/40.42    (71)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.90/40.42          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.90/40.42    (72)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.90/40.42          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.90/40.42    (73)  all_55_14 = all_53_11
% 228.90/40.42    (74)   ~ (all_53_11 = e3)
% 228.90/40.42    (75)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.90/40.42          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.90/40.42    (76)  op(e3, e0) = all_53_12
% 228.90/40.42  
% 228.90/40.42  Begin of proof
% 228.90/40.42  | 
% 228.90/40.42  | BETA: splitting (18) gives:
% 228.90/40.42  | 
% 228.90/40.42  | Case 1:
% 228.90/40.42  | | 
% 228.90/40.42  | |   (77)  all_57_12 = e2 & op(e0, e3) = e2
% 228.90/40.42  | | 
% 228.90/40.42  | | ALPHA: (77) implies:
% 228.90/40.42  | |   (78)  all_57_12 = e2
% 228.90/40.42  | | 
% 228.90/40.42  | | BETA: splitting (4) gives:
% 228.90/40.42  | | 
% 228.90/40.42  | | Case 1:
% 228.90/40.42  | | | 
% 228.90/40.42  | | |   (79)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) =
% 228.90/40.42  | | |           e1)
% 228.90/40.42  | | | 
% 228.90/40.42  | | | REF_CLOSE: (2), (3), (4), (6), (7), (24), (27), (32), (40), (43), (45),
% 228.90/40.42  | | |            (60), (63), (64), (67), (69), (71), (78), (79) are inconsistent
% 228.90/40.42  | | |            by sub-proof #762.
% 228.90/40.42  | | | 
% 228.90/40.42  | | Case 2:
% 228.90/40.42  | | | 
% 228.90/40.42  | | |   (80)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) =
% 228.90/40.42  | | |           e1)
% 228.90/40.42  | | | 
% 228.90/40.42  | | | BETA: splitting (80) gives:
% 228.90/40.42  | | | 
% 228.90/40.42  | | | Case 1:
% 228.90/40.42  | | | | 
% 228.90/40.42  | | | |   (81)  all_57_6 = e1 & op(e1, e3) = e1
% 228.90/40.42  | | | | 
% 228.90/40.42  | | | | ALPHA: (81) implies:
% 228.90/40.42  | | | |   (82)  all_57_6 = e1
% 228.90/40.42  | | | | 
% 228.90/40.42  | | | | REF_CLOSE: (5), (6), (7), (15), (24), (27), (39), (40), (45), (48),
% 228.90/40.42  | | | |            (49), (65), (67), (82) are inconsistent by sub-proof #1548.
% 228.90/40.42  | | | | 
% 228.90/40.42  | | | Case 2:
% 228.90/40.42  | | | | 
% 228.90/40.42  | | | |   (83)  all_57_12 = e1 & op(e0, e3) = e1
% 228.90/40.42  | | | | 
% 228.90/40.42  | | | | ALPHA: (83) implies:
% 228.90/40.42  | | | |   (84)  all_57_12 = e1
% 228.90/40.42  | | | | 
% 228.90/40.42  | | | | COMBINE_EQS: (78), (84) imply:
% 228.90/40.42  | | | |   (85)  e2 = e1
% 228.90/40.42  | | | | 
% 228.90/40.42  | | | | SIMP: (85) implies:
% 228.90/40.42  | | | |   (86)  e2 = e1
% 228.90/40.42  | | | | 
% 228.90/40.42  | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (11), (13), (15), (16), (17),
% 228.90/40.42  | | | |            (20), (23), (24), (27), (30), (32), (33), (34), (39), (40),
% 228.90/40.42  | | | |            (43), (44), (45), (47), (49), (54), (56), (57), (60), (61),
% 228.90/40.42  | | | |            (63), (64), (66), (67), (68), (71), (72), (75), (76), (86)
% 228.90/40.42  | | | |            are inconsistent by sub-proof #635.
% 228.90/40.42  | | | | 
% 228.90/40.42  | | | End of split
% 228.90/40.42  | | | 
% 228.90/40.42  | | End of split
% 228.90/40.42  | | 
% 228.90/40.42  | Case 2:
% 228.90/40.42  | | 
% 228.90/40.42  | |   (87)  all_57_13 = e2 & op(e0, e2) = e2
% 228.90/40.42  | | 
% 228.90/40.42  | | REF_CLOSE: (1), (6), (7), (9), (10), (11), (12), (13), (14), (15), (19),
% 228.90/40.42  | |            (21), (22), (25), (26), (28), (29), (31), (32), (35), (36), (37),
% 228.90/40.42  | |            (38), (40), (41), (42), (46), (50), (51), (52), (53), (54), (55),
% 228.90/40.42  | |            (58), (59), (62), (70), (73), (74), (87) are inconsistent by
% 228.90/40.42  | |            sub-proof #771.
% 228.90/40.42  | | 
% 228.90/40.42  | End of split
% 228.90/40.42  | 
% 228.90/40.42  End of proof
% 228.90/40.42  
% 228.90/40.42  Sub-proof #635 shows that the following formulas are inconsistent:
% 228.90/40.42  ----------------------------------------------------------------
% 228.90/40.42    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.90/40.42         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.90/40.42    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.90/40.42         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.90/40.42    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.90/40.42         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.90/40.42    (4)   ~ (e3 = e1)
% 228.90/40.42    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.90/40.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.90/40.42    (6)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.90/40.42         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.90/40.42    (7)   ~ (all_6_2 = e3)
% 228.90/40.42    (8)  op(e1, e1) = all_6_2
% 228.90/40.42    (9)  op(e2, e2) = e1
% 228.90/40.42    (10)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.90/40.42          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.90/40.42    (11)  all_57_9 = e1
% 228.90/40.42    (12)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 228.90/40.42          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 228.90/40.42    (13)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.90/40.42          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.90/40.42    (14)   ~ (e3 = e2)
% 228.90/40.42    (15)   ~ (e3 = e0)
% 228.90/40.42    (16)  all_57_15 = e3
% 228.90/40.42    (17)  op(e3, e3) = e2
% 228.90/40.42    (18)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.90/40.42          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.90/40.42            e1)
% 228.90/40.42    (19)  all_57_10 = e2
% 228.90/40.42    (20)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.90/40.42          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 228.90/40.42    (21)   ~ (e2 = e0)
% 228.90/40.42    (22)  all_57_3 = e1
% 228.90/40.42    (23)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.90/40.42          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.90/40.42    (24)   ~ (e1 = e0)
% 228.90/40.42    (25)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.90/40.42          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.90/40.42    (26)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.90/40.42          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.90/40.42    (27)  op(e0, e0) = e3
% 228.90/40.42    (28)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.90/40.42          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.90/40.42            e2)
% 228.90/40.42    (29)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.90/40.42              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.90/40.42                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.90/40.42                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.90/40.42    (30)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.90/40.42          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.90/40.42    (31)   ~ (all_53_12 = e3)
% 228.90/40.42    (32)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.90/40.42          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.90/40.42    (33)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.90/40.42          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.90/40.42    (34)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.90/40.42          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 228.90/40.42    (35)   ~ (e2 = e1)
% 228.90/40.42    (36)  e2 = e1
% 228.90/40.42    (37)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.90/40.42          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.90/40.42    (38)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.90/40.42          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.90/40.42    (39)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.90/40.42          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.90/40.42    (40)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.90/40.42          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.90/40.42    (41)  op(e3, e0) = all_53_12
% 228.90/40.42  
% 228.90/40.42  Begin of proof
% 228.90/40.42  | 
% 228.90/40.42  | COMBINE_EQS: (19), (36) imply:
% 228.90/40.43  |   (42)  all_57_10 = e1
% 228.90/40.43  | 
% 228.90/40.43  | BETA: splitting (37) gives:
% 228.90/40.43  | 
% 228.90/40.43  | Case 1:
% 228.90/40.43  | | 
% 228.90/40.43  | |   (43)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 228.90/40.43  | |           e2)
% 228.90/40.43  | | 
% 228.90/40.43  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 228.90/40.43  | |            (14), (15), (16), (17), (18), (20), (21), (22), (23), (24), (25),
% 228.90/40.43  | |            (26), (27), (28), (29), (31), (32), (33), (34), (35), (37), (38),
% 228.90/40.43  | |            (39), (40), (41), (42), (43) are inconsistent by sub-proof #804.
% 228.90/40.43  | | 
% 228.90/40.43  | Case 2:
% 228.90/40.43  | | 
% 228.90/40.43  | |   (44)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.90/40.43  | |           e2)
% 228.90/40.43  | | 
% 228.90/40.43  | | BETA: splitting (44) gives:
% 228.90/40.43  | | 
% 228.90/40.43  | | Case 1:
% 228.90/40.43  | | | 
% 228.90/40.43  | | |   (45)  all_57_11 = e2 & op(e1, e0) = e2
% 228.90/40.43  | | | 
% 228.90/40.43  | | | ALPHA: (45) implies:
% 228.90/40.43  | | |   (46)  all_57_11 = e2
% 228.90/40.43  | | | 
% 228.90/40.43  | | | BETA: splitting (32) gives:
% 228.90/40.43  | | | 
% 228.90/40.43  | | | Case 1:
% 228.90/40.43  | | | | 
% 228.90/40.43  | | | |   (47)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2)
% 228.90/40.43  | | | |           = e2)
% 228.90/40.43  | | | | 
% 228.90/40.43  | | | | BETA: splitting (47) gives:
% 228.90/40.43  | | | | 
% 228.90/40.43  | | | | Case 1:
% 228.90/40.43  | | | | | 
% 228.90/40.43  | | | | |   (48)  all_57_2 = e2 & op(e2, e3) = e2
% 228.90/40.43  | | | | | 
% 228.90/40.43  | | | | | ALPHA: (48) implies:
% 228.90/40.43  | | | | |   (49)  all_57_2 = e2
% 228.90/40.43  | | | | | 
% 228.90/40.43  | | | | | BETA: splitting (34) gives:
% 228.90/40.43  | | | | | 
% 228.90/40.43  | | | | | Case 1:
% 228.90/40.43  | | | | | | 
% 228.90/40.43  | | | | | |   (50)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2,
% 228.90/40.43  | | | | | |             e2) = e0)
% 228.90/40.43  | | | | | | 
% 228.90/40.43  | | | | | | REF_CLOSE: (5), (9), (21), (24), (49), (50) are inconsistent by
% 228.90/40.43  | | | | | |            sub-proof #661.
% 228.90/40.43  | | | | | | 
% 228.90/40.43  | | | | | Case 2:
% 228.90/40.43  | | | | | | 
% 228.90/40.43  | | | | | |   (51)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2,
% 228.90/40.43  | | | | | |             e0) = e0)
% 228.90/40.43  | | | | | | 
% 228.90/40.43  | | | | | | REF_CLOSE: (4), (5), (9), (14), (15), (16), (21), (24), (29), (30),
% 228.90/40.43  | | | | | |            (35), (37), (39), (42), (46), (49), (51) are inconsistent
% 228.90/40.43  | | | | | |            by sub-proof #682.
% 228.90/40.43  | | | | | | 
% 228.90/40.43  | | | | | End of split
% 228.90/40.43  | | | | | 
% 228.90/40.43  | | | | Case 2:
% 228.90/40.43  | | | | | 
% 228.90/40.43  | | | | |   (52)  all_57_3 = e2 & op(e2, e2) = e2
% 228.90/40.43  | | | | | 
% 228.90/40.43  | | | | | ALPHA: (52) implies:
% 228.90/40.43  | | | | |   (53)  op(e2, e2) = e2
% 228.90/40.43  | | | | | 
% 228.90/40.43  | | | | | REF_CLOSE: (5), (9), (35), (53) are inconsistent by sub-proof #2306.
% 228.90/40.43  | | | | | 
% 228.90/40.43  | | | | End of split
% 228.90/40.43  | | | | 
% 228.90/40.43  | | | Case 2:
% 228.90/40.43  | | | | 
% 228.90/40.43  | | | |   (54)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0)
% 228.90/40.43  | | | |           = e2)
% 228.90/40.43  | | | | 
% 228.90/40.43  | | | | BETA: splitting (54) gives:
% 228.90/40.43  | | | | 
% 228.90/40.43  | | | | Case 1:
% 228.90/40.43  | | | | | 
% 228.90/40.43  | | | | |   (55)  all_57_5 = e2 & op(e2, e1) = e2
% 228.90/40.43  | | | | | 
% 228.90/40.43  | | | | | ALPHA: (55) implies:
% 228.90/40.43  | | | | |   (56)  all_57_5 = e2
% 228.90/40.43  | | | | | 
% 228.90/40.43  | | | | | BETA: splitting (34) gives:
% 228.90/40.43  | | | | | 
% 228.90/40.43  | | | | | Case 1:
% 228.90/40.43  | | | | | | 
% 228.90/40.43  | | | | | |   (57)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2,
% 228.90/40.43  | | | | | |             e2) = e0)
% 228.90/40.43  | | | | | | 
% 228.90/40.43  | | | | | | BETA: splitting (57) gives:
% 228.90/40.43  | | | | | | 
% 228.90/40.43  | | | | | | Case 1:
% 228.90/40.43  | | | | | | | 
% 228.90/40.43  | | | | | | |   (58)  all_57_2 = e0 & op(e2, e3) = e0
% 228.90/40.43  | | | | | | | 
% 228.90/40.43  | | | | | | | REF_CLOSE: (1), (4), (5), (7), (8), (9), (11), (13), (14), (15),
% 228.90/40.43  | | | | | | |            (16), (17), (18), (21), (22), (23), (24), (25), (27),
% 228.90/40.43  | | | | | | |            (28), (29), (30), (31), (32), (35), (37), (41), (56),
% 228.90/40.43  | | | | | | |            (58) are inconsistent by sub-proof #696.
% 228.90/40.43  | | | | | | | 
% 228.90/40.43  | | | | | | Case 2:
% 228.90/40.43  | | | | | | | 
% 228.90/40.43  | | | | | | |   (59)  all_57_3 = e0 & op(e2, e2) = e0
% 228.90/40.43  | | | | | | | 
% 228.90/40.43  | | | | | | | ALPHA: (59) implies:
% 228.90/40.43  | | | | | | |   (60)  op(e2, e2) = e0
% 228.90/40.43  | | | | | | | 
% 228.90/40.43  | | | | | | | REF_CLOSE: (5), (9), (24), (60) are inconsistent by sub-proof
% 228.90/40.43  | | | | | | |            #2352.
% 228.90/40.43  | | | | | | | 
% 228.90/40.43  | | | | | | End of split
% 228.90/40.43  | | | | | | 
% 228.90/40.43  | | | | | Case 2:
% 228.90/40.43  | | | | | | 
% 228.90/40.43  | | | | | |   (61)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2,
% 228.90/40.43  | | | | | |             e0) = e0)
% 228.90/40.43  | | | | | | 
% 228.90/40.43  | | | | | | BETA: splitting (61) gives:
% 228.90/40.43  | | | | | | 
% 228.90/40.43  | | | | | | Case 1:
% 228.90/40.43  | | | | | | | 
% 228.90/40.43  | | | | | | |   (62)  all_57_5 = e0 & op(e2, e1) = e0
% 228.90/40.43  | | | | | | | 
% 228.90/40.43  | | | | | | | REF_CLOSE: (21), (56), (62) are inconsistent by sub-proof #2428.
% 228.90/40.43  | | | | | | | 
% 228.90/40.43  | | | | | | Case 2:
% 228.90/40.43  | | | | | | | 
% 228.90/40.43  | | | | | | |   (63)  all_57_10 = e0 & op(e2, e0) = e0
% 228.90/40.43  | | | | | | | 
% 228.90/40.43  | | | | | | | REF_CLOSE: (24), (42), (63) are inconsistent by sub-proof #1332.
% 228.90/40.43  | | | | | | | 
% 228.90/40.43  | | | | | | End of split
% 228.90/40.43  | | | | | | 
% 228.90/40.43  | | | | | End of split
% 228.90/40.43  | | | | | 
% 228.90/40.43  | | | | Case 2:
% 228.90/40.43  | | | | | 
% 228.90/40.43  | | | | |   (64)  all_57_10 = e2 & op(e2, e0) = e2
% 228.90/40.43  | | | | | 
% 228.90/40.43  | | | | | REF_CLOSE: (19), (35), (42) are inconsistent by sub-proof #2144.
% 228.90/40.43  | | | | | 
% 228.90/40.43  | | | | End of split
% 228.90/40.43  | | | | 
% 228.90/40.43  | | | End of split
% 228.90/40.43  | | | 
% 228.90/40.43  | | Case 2:
% 228.90/40.43  | | | 
% 228.90/40.43  | | |   (65)  all_57_15 = e2 & op(e0, e0) = e2
% 228.90/40.43  | | | 
% 228.90/40.43  | | | REF_CLOSE: (14), (16), (65) are inconsistent by sub-proof #2323.
% 228.90/40.43  | | | 
% 228.90/40.43  | | End of split
% 228.90/40.43  | | 
% 228.90/40.43  | End of split
% 228.90/40.43  | 
% 228.90/40.43  End of proof
% 228.90/40.43  
% 228.90/40.43  Sub-proof #636 shows that the following formulas are inconsistent:
% 228.90/40.43  ----------------------------------------------------------------
% 228.90/40.43    (1)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1)
% 228.90/40.43    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.90/40.43         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.90/40.43    (3)   ~ (e3 = e1)
% 228.90/40.43    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.90/40.43           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.90/40.43    (5)  op(e2, e2) = e1
% 228.90/40.43    (6)  all_57_9 = e1
% 228.90/40.43    (7)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.90/40.43         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.90/40.43    (8)   ~ (e3 = e2)
% 228.90/40.43    (9)   ~ (e3 = e0)
% 228.90/40.43    (10)  op(e3, e3) = e2
% 228.90/40.43    (11)  all_57_5 = e3
% 228.90/40.43    (12)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.90/40.43          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 228.90/40.43    (13)   ~ (e2 = e0)
% 228.90/40.43    (14)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.90/40.43          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.90/40.43    (15)   ~ (e1 = e0)
% 228.90/40.43    (16)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.90/40.43          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.90/40.43    (17)   ~ (all_53_12 = e3)
% 228.90/40.43    (18)  all_57_1 = e3
% 228.90/40.43    (19)   ~ (e2 = e1)
% 228.90/40.43    (20)  op(e3, e0) = all_53_12
% 228.90/40.43  
% 228.90/40.43  Begin of proof
% 228.90/40.43  | 
% 228.90/40.43  | BETA: splitting (1) gives:
% 228.90/40.43  | 
% 228.90/40.43  | Case 1:
% 228.90/40.43  | | 
% 228.90/40.43  | |   (21)  all_57_4 = e1 & op(e3, e1) = e1
% 228.90/40.43  | | 
% 228.90/40.43  | | ALPHA: (21) implies:
% 228.90/40.43  | |   (22)  all_57_4 = e1
% 228.90/40.43  | | 
% 228.90/40.43  | | REF_CLOSE: (3), (4), (6), (7), (8), (9), (10), (13), (14), (15), (17), (20),
% 228.90/40.43  | |            (22) are inconsistent by sub-proof #813.
% 228.90/40.43  | | 
% 228.90/40.43  | Case 2:
% 228.90/40.43  | | 
% 228.90/40.43  | |   (23)  all_57_5 = e1 & op(e2, e1) = e1
% 228.90/40.43  | | 
% 228.90/40.43  | | ALPHA: (23) implies:
% 228.90/40.43  | |   (24)  all_57_5 = e1
% 228.90/40.43  | | 
% 228.90/40.43  | | REF_CLOSE: (2), (3), (4), (5), (8), (9), (11), (12), (13), (15), (16), (18),
% 228.90/40.43  | |            (19), (24) are inconsistent by sub-proof #637.
% 228.90/40.43  | | 
% 228.90/40.43  | End of split
% 228.90/40.43  | 
% 228.90/40.43  End of proof
% 228.90/40.43  
% 228.90/40.43  Sub-proof #637 shows that the following formulas are inconsistent:
% 228.90/40.43  ----------------------------------------------------------------
% 228.90/40.43    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.90/40.43         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.90/40.43    (2)   ~ (e3 = e1)
% 228.90/40.43    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.90/40.43           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.90/40.43    (4)  op(e2, e2) = e1
% 228.90/40.43    (5)   ~ (e3 = e2)
% 228.90/40.43    (6)   ~ (e3 = e0)
% 228.90/40.43    (7)  all_57_5 = e3
% 228.90/40.43    (8)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.90/40.43         (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 228.90/40.43    (9)   ~ (e2 = e0)
% 228.90/40.43    (10)   ~ (e1 = e0)
% 228.90/40.43    (11)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.90/40.43          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.90/40.43    (12)  all_57_5 = e1
% 228.90/40.43    (13)  all_57_1 = e3
% 228.90/40.43    (14)   ~ (e2 = e1)
% 228.90/40.43  
% 228.90/40.43  Begin of proof
% 228.90/40.43  | 
% 228.90/40.43  | COMBINE_EQS: (7), (12) imply:
% 228.90/40.43  |   (15)  e3 = e1
% 228.90/40.43  | 
% 228.90/40.43  | SIMP: (15) implies:
% 228.90/40.43  |   (16)  e3 = e1
% 228.90/40.43  | 
% 228.90/40.43  | COMBINE_EQS: (13), (16) imply:
% 228.90/40.43  |   (17)  all_57_1 = e1
% 228.90/40.43  | 
% 228.90/40.43  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (14), (17) are
% 228.90/40.43  |            inconsistent by sub-proof #1908.
% 228.90/40.43  | 
% 228.90/40.43  End of proof
% 228.90/40.43  
% 228.90/40.43  Sub-proof #638 shows that the following formulas are inconsistent:
% 228.90/40.43  ----------------------------------------------------------------
% 228.90/40.43    (1)   ~ (all_53_2 = e2)
% 228.90/40.43    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.90/40.43         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.90/40.43    (3)   ~ (e3 = e1)
% 228.90/40.43    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.90/40.43           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.90/40.43    (5)   ~ (all_53_3 = e3)
% 228.90/40.43    (6)   ~ (all_53_3 = all_53_7)
% 228.90/40.43    (7)   ~ (all_6_2 = e3)
% 228.90/40.43    (8)   ~ (all_53_9 = e1)
% 228.90/40.43    (9)  op(e1, e1) = all_6_2
% 228.90/40.43    (10)   ~ (all_53_1 = all_53_9)
% 228.90/40.43    (11)  op(e2, e2) = e1
% 228.90/40.43    (12)   ~ (all_53_13 = e3)
% 228.90/40.43    (13)  all_57_4 = e1 & op(e3, e1) = e1
% 228.90/40.43    (14)   ~ (all_53_9 = all_53_11)
% 228.90/40.43    (15)  all_55_4 = all_53_1
% 228.90/40.43    (16)   ~ (e3 = e2)
% 228.90/40.43    (17)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 228.90/40.43    (18)   ~ (all_53_1 = all_53_3)
% 228.90/40.43    (19)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.90/40.43    (20)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 228.90/40.43    (21)   ~ (all_53_9 = all_53_13)
% 228.90/40.43    (22)  op(e3, e3) = e2
% 228.90/40.43    (23)   ~ (all_53_1 = e1)
% 228.90/40.43    (24)  op(e2, e0) = e2
% 228.90/40.43    (25)  all_55_6 = all_53_9
% 228.90/40.43    (26)   ~ (all_53_1 = all_53_2)
% 228.90/40.43    (27)   ~ (e2 = e0)
% 228.90/40.43    (28)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.90/40.43            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.90/40.43            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.90/40.43            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.90/40.43              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.90/40.43            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.90/40.43            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.90/40.43              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.90/40.43              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.90/40.43            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.90/40.43            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.90/40.43            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.90/40.43              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.90/40.43              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.90/40.43            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.90/40.43              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.90/40.43            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.90/40.43            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.90/40.43              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.90/40.43              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.90/40.43            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.90/40.43            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.90/40.43    (29)  all_55_12 = all_53_3
% 228.90/40.43    (30)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.90/40.43          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.90/40.43    (31)   ~ (all_53_3 = all_53_11)
% 228.90/40.43    (32)   ~ (all_53_2 = all_53_3)
% 228.90/40.43    (33)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 228.90/40.43    (34)   ~ (all_53_7 = all_53_11)
% 228.90/40.43    (35)  all_55_8 = all_53_2
% 228.90/40.43    (36)  op(e0, e0) = e3
% 228.90/40.43    (37)  op(e0, e2) = all_53_7
% 228.90/40.43    (38)   ~ (all_53_1 = all_53_13)
% 228.90/40.43    (39)  op(e2, e0) = all_53_13
% 228.90/40.43    (40)   ~ (all_53_12 = e3)
% 228.90/40.43    (41)  op(e1, e3) = all_53_2
% 228.90/40.43    (42)   ~ (e2 = e1)
% 228.90/40.43    (43)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 228.90/40.43    (44)  all_55_14 = all_53_11
% 228.90/40.43    (45)   ~ (all_53_11 = e3)
% 228.90/40.43    (46)  all_57_7 = e0
% 228.90/40.43    (47)  op(e3, e0) = all_53_12
% 228.90/40.43  
% 228.90/40.43  Begin of proof
% 228.90/40.43  | 
% 228.90/40.43  | ALPHA: (13) implies:
% 228.90/40.43  |   (48)  all_57_4 = e1
% 228.90/40.43  | 
% 228.90/40.43  | BETA: splitting (2) gives:
% 228.90/40.43  | 
% 228.90/40.43  | Case 1:
% 228.90/40.43  | | 
% 228.90/40.43  | |   (49)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 228.90/40.43  | |           e2)
% 228.90/40.43  | | 
% 228.90/40.43  | | REF_CLOSE: (3), (4), (11), (16), (22), (30), (40), (42), (47), (48), (49)
% 228.90/40.43  | |            are inconsistent by sub-proof #662.
% 228.90/40.43  | | 
% 228.90/40.43  | Case 2:
% 228.90/40.43  | | 
% 228.90/40.43  | |   (50)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 228.90/40.43  | |           e2)
% 228.90/40.43  | | 
% 228.90/40.43  | | BETA: splitting (50) gives:
% 228.90/40.43  | | 
% 228.90/40.43  | | Case 1:
% 228.90/40.43  | | | 
% 228.90/40.43  | | |   (51)  all_57_7 = e2 & op(e1, e2) = e2
% 228.90/40.43  | | | 
% 228.90/40.43  | | | ALPHA: (51) implies:
% 228.90/40.43  | | |   (52)  all_57_7 = e2
% 228.90/40.43  | | | 
% 228.90/40.43  | | | REF_CLOSE: (27), (46), (52) are inconsistent by sub-proof #2207.
% 228.90/40.43  | | | 
% 228.90/40.43  | | Case 2:
% 228.90/40.43  | | | 
% 228.90/40.43  | | |   (53)  all_57_13 = e2 & op(e0, e2) = e2
% 228.90/40.43  | | | 
% 228.90/40.43  | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (14),
% 228.90/40.43  | | |            (15), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 228.90/40.43  | | |            (26), (27), (28), (29), (31), (32), (33), (34), (35), (36),
% 228.90/40.43  | | |            (37), (38), (39), (41), (43), (44), (45), (53) are inconsistent
% 228.90/40.43  | | |            by sub-proof #771.
% 228.90/40.43  | | | 
% 228.90/40.43  | | End of split
% 228.90/40.43  | | 
% 228.90/40.43  | End of split
% 228.90/40.43  | 
% 228.90/40.43  End of proof
% 228.90/40.43  
% 228.90/40.43  Sub-proof #639 shows that the following formulas are inconsistent:
% 228.90/40.43  ----------------------------------------------------------------
% 228.90/40.43    (1)  all_57_0 = e2
% 228.90/40.43    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.90/40.43         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.90/40.43    (3)   ~ (e3 = e1)
% 228.90/40.43    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.90/40.43           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.90/40.43    (5)  op(e2, e2) = e1
% 228.90/40.43    (6)   ~ (e3 = e2)
% 228.90/40.43    (7)   ~ (e3 = e0)
% 228.90/40.43    (8)   ~ (e2 = e0)
% 228.90/40.43    (9)   ~ (e1 = e0)
% 228.90/40.43    (10)  all_57_6 = e3
% 228.90/40.43    (11)   ~ (e2 = e1)
% 228.90/40.43    (12)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3)
% 228.90/40.43    (13)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.90/40.43          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.90/40.43    (14)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.90/40.43          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.90/40.43  
% 228.90/40.43  Begin of proof
% 228.90/40.43  | 
% 228.90/40.43  | BETA: splitting (12) gives:
% 228.90/40.43  | 
% 228.90/40.43  | Case 1:
% 228.90/40.43  | | 
% 228.90/40.43  | |   (15)  all_57_2 = e3 & op(e2, e3) = e3
% 228.90/40.43  | | 
% 228.90/40.43  | | ALPHA: (15) implies:
% 228.90/40.43  | |   (16)  all_57_2 = e3
% 228.90/40.43  | | 
% 228.90/40.43  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (13), (14),
% 228.90/40.43  | |            (16) are inconsistent by sub-proof #1286.
% 228.90/40.43  | | 
% 228.90/40.43  | Case 2:
% 228.90/40.43  | | 
% 228.90/40.43  | |   (17)  all_57_3 = e3 & op(e2, e2) = e3
% 228.90/40.43  | | 
% 228.90/40.43  | | ALPHA: (17) implies:
% 228.90/40.43  | |   (18)  op(e2, e2) = e3
% 228.90/40.43  | | 
% 228.90/40.43  | | REF_CLOSE: (3), (4), (5), (18) are inconsistent by sub-proof #1912.
% 228.90/40.43  | | 
% 228.90/40.43  | End of split
% 228.90/40.43  | 
% 228.90/40.43  End of proof
% 228.90/40.43  
% 228.90/40.43  Sub-proof #640 shows that the following formulas are inconsistent:
% 228.90/40.43  ----------------------------------------------------------------
% 228.90/40.43    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.90/40.43         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.90/40.43    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.90/40.43         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.90/40.43    (3)   ~ (e3 = e1)
% 228.90/40.43    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.90/40.43           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.90/40.43    (5)   ~ (all_6_2 = e3)
% 228.90/40.43    (6)  all_57_9 = e2 & op(e3, e0) = e2
% 228.90/40.43    (7)  op(e1, e1) = all_6_2
% 228.90/40.43    (8)  op(e2, e2) = e1
% 228.90/40.43    (9)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.90/40.43         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.90/40.43    (10)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.90/40.43          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.90/40.43    (11)   ~ (e3 = e2)
% 228.90/40.43    (12)   ~ (e3 = e0)
% 228.90/40.43    (13)  all_57_15 = e3
% 228.90/40.43    (14)  op(e3, e3) = e2
% 228.90/40.43    (15)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.90/40.43          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.90/40.43            e1)
% 228.90/40.43    (16)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.90/40.43          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 228.90/40.43    (17)   ~ (e2 = e0)
% 228.90/40.43    (18)  all_57_3 = e1
% 228.90/40.43    (19)   ~ (e1 = e0)
% 228.90/40.43    (20)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.90/40.43          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.90/40.43    (21)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.90/40.43          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.90/40.43    (22)  op(e0, e0) = e3
% 228.90/40.43    (23)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.90/40.43          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.90/40.43            e2)
% 228.90/40.43    (24)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.90/40.43              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.90/40.43                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.90/40.43                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.90/40.43    (25)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.90/40.43          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.90/40.43    (26)  all_57_11 = e1
% 228.90/40.43    (27)  all_57_1 = e3
% 228.90/40.43    (28)   ~ (e2 = e1)
% 228.90/40.43  
% 228.90/40.43  Begin of proof
% 228.90/40.43  | 
% 228.90/40.43  | ALPHA: (6) implies:
% 228.90/40.43  |   (29)  all_57_9 = e2
% 228.90/40.43  | 
% 228.90/40.43  | BETA: splitting (9) gives:
% 228.90/40.43  | 
% 228.90/40.43  | Case 1:
% 228.90/40.43  | | 
% 228.90/40.43  | |   (30)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) =
% 228.90/40.43  | |           e1)
% 228.90/40.43  | | 
% 228.90/40.43  | | REF_CLOSE: (2), (3), (4), (8), (11), (12), (14), (16), (17), (19), (21),
% 228.90/40.43  | |            (28), (30) are inconsistent by sub-proof #1677.
% 228.90/40.43  | | 
% 228.90/40.43  | Case 2:
% 228.90/40.43  | | 
% 228.90/40.43  | |   (31)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) =
% 228.90/40.43  | |           e1)
% 228.90/40.43  | | 
% 228.90/40.43  | | BETA: splitting (31) gives:
% 228.90/40.43  | | 
% 228.90/40.43  | | Case 1:
% 228.90/40.43  | | | 
% 228.90/40.43  | | |   (32)  all_57_4 = e1 & op(e3, e1) = e1
% 228.90/40.43  | | | 
% 228.90/40.43  | | | ALPHA: (32) implies:
% 228.90/40.43  | | |   (33)  all_57_4 = e1
% 228.90/40.43  | | | 
% 228.90/40.43  | | | REF_CLOSE: (1), (3), (4), (5), (7), (10), (11), (12), (13), (14), (15),
% 228.90/40.43  | | |            (17), (18), (19), (20), (22), (23), (24), (25), (26), (27),
% 228.90/40.43  | | |            (28), (29), (33) are inconsistent by sub-proof #736.
% 228.90/40.43  | | | 
% 228.90/40.43  | | Case 2:
% 228.90/40.43  | | | 
% 228.90/40.43  | | |   (34)  all_57_9 = e1 & op(e3, e0) = e1
% 228.90/40.43  | | | 
% 228.90/40.43  | | | ALPHA: (34) implies:
% 228.90/40.43  | | |   (35)  all_57_9 = e1
% 228.90/40.43  | | | 
% 228.90/40.43  | | | REF_CLOSE: (28), (29), (35) are inconsistent by sub-proof #2444.
% 228.90/40.43  | | | 
% 228.90/40.43  | | End of split
% 228.90/40.43  | | 
% 228.90/40.43  | End of split
% 228.90/40.43  | 
% 228.90/40.43  End of proof
% 228.90/40.43  
% 228.90/40.43  Sub-proof #641 shows that the following formulas are inconsistent:
% 228.90/40.43  ----------------------------------------------------------------
% 228.90/40.43    (1)   ~ (all_53_2 = e2)
% 228.90/40.43    (2)  all_57_0 = e2
% 228.90/40.43    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.90/40.43         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.90/40.43    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.90/40.43         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.90/40.43    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.90/40.43         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.90/40.43    (6)   ~ (e3 = e1)
% 228.90/40.43    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.90/40.43           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.90/40.43    (8)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.90/40.43         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.90/40.43    (9)   ~ (all_53_3 = e3)
% 228.90/40.43    (10)   ~ (all_53_3 = all_53_7)
% 228.90/40.43    (11)   ~ (all_6_2 = e3)
% 228.90/40.43    (12)   ~ (all_53_9 = e1)
% 228.90/40.43    (13)  op(e1, e1) = all_6_2
% 228.90/40.43    (14)   ~ (all_53_1 = all_53_9)
% 228.90/40.43    (15)  op(e2, e2) = e1
% 228.90/40.43    (16)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.90/40.43          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.90/40.43    (17)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 228.90/40.43            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 228.90/40.43              e3) = all_22_1 & $i(all_22_1))
% 228.90/40.43    (18)   ~ (all_53_13 = e3)
% 228.90/40.43    (19)   ~ (all_53_9 = all_53_11)
% 228.90/40.43    (20)  all_55_4 = all_53_1
% 228.90/40.43    (21)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.90/40.43          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.90/40.43    (22)   ~ (e3 = e2)
% 228.90/40.43    (23)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 228.90/40.43    (24)   ~ (all_53_1 = all_53_3)
% 228.90/40.43    (25)   ~ (e3 = e0)
% 228.90/40.43    (26)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.90/40.43    (27)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 228.90/40.43    (28)  all_57_15 = e3
% 228.90/40.43    (29)   ~ (all_53_9 = all_53_13)
% 228.90/40.43    (30)  op(e3, e3) = e2
% 228.90/40.43    (31)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.90/40.43          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.90/40.43            e1)
% 228.90/40.43    (32)  all_57_10 = e2
% 228.90/40.43    (33)   ~ (all_53_1 = e1)
% 228.90/40.43    (34)  op(e2, e0) = e2
% 228.90/40.43    (35)  all_55_6 = all_53_9
% 228.90/40.43    (36)   ~ (all_53_1 = all_53_2)
% 228.90/40.43    (37)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.90/40.43          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 228.90/40.43    (38)   ~ (e2 = e0)
% 228.90/40.43    (39)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.90/40.43            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.90/40.43            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.90/40.43            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.90/40.43              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.90/40.43            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.90/40.43            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.90/40.43              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.90/40.43              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.90/40.43            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.90/40.43            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.90/40.43            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.90/40.43              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.90/40.43              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.90/40.43            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.90/40.43              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.90/40.43            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.90/40.43            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.90/40.43              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.90/40.43              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.90/40.43            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.90/40.43            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.90/40.43    (40)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 228.90/40.43            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 228.90/40.43              e3) = all_12_1 & $i(all_12_1))
% 228.90/40.43    (41)  all_55_12 = all_53_3
% 228.90/40.43    (42)  all_57_3 = e1
% 228.90/40.43    (43)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.90/40.43          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.90/40.43    (44)   ~ (e1 = e0)
% 228.90/40.43    (45)  all_57_12 = e3
% 228.90/40.44    (46)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.90/40.44    (47)   ~ (all_53_3 = all_53_11)
% 228.90/40.44    (48)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.90/40.44          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.90/40.44    (49)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.90/40.44          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.90/40.44    (50)   ~ (all_53_2 = all_53_3)
% 228.90/40.44    (51)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 228.90/40.44    (52)   ~ (all_53_7 = all_53_11)
% 228.90/40.44    (53)  all_55_8 = all_53_2
% 228.90/40.44    (54)  op(e0, e0) = e3
% 228.90/40.44    (55)  op(e0, e2) = all_53_7
% 228.90/40.44    (56)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.90/40.44          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.90/40.44            e2)
% 228.90/40.44    (57)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.90/40.44              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.90/40.44                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.90/40.44                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.90/40.44    (58)   ~ (all_53_1 = all_53_13)
% 228.90/40.44    (59)  op(e2, e0) = all_53_13
% 228.90/40.44    (60)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.90/40.44          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.90/40.44    (61)   ~ (all_53_12 = e3)
% 228.90/40.44    (62)  all_57_7 = e3
% 228.90/40.44    (63)  op(e1, e3) = all_53_2
% 228.90/40.44    (64)  all_57_8 = e0
% 228.90/40.44    (65)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.90/40.44          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.90/40.44    (66)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.90/40.44          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.90/40.44    (67)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.90/40.44          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 228.90/40.44    (68)   ~ (e2 = e1)
% 228.90/40.44    (69)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.90/40.44          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.90/40.44    (70)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.90/40.44          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.90/40.44    (71)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 228.90/40.44    (72)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.90/40.44          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.90/40.44    (73)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.90/40.44          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.90/40.44    (74)  all_55_14 = all_53_11
% 228.90/40.44    (75)   ~ (all_53_11 = e3)
% 228.90/40.44    (76)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.90/40.44          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.90/40.44    (77)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.90/40.44          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.90/40.44    (78)  op(e3, e0) = all_53_12
% 228.90/40.44  
% 228.90/40.44  Begin of proof
% 228.90/40.44  | 
% 228.90/40.44  | BETA: splitting (46) gives:
% 228.90/40.44  | 
% 228.90/40.44  | Case 1:
% 228.90/40.44  | | 
% 228.90/40.44  | |   (79)  all_57_5 = e3 & op(e2, e1) = e3
% 228.90/40.44  | | 
% 228.90/40.44  | | ALPHA: (79) implies:
% 228.90/40.44  | |   (80)  all_57_5 = e3
% 228.90/40.44  | | 
% 228.90/40.44  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.90/40.44  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 228.90/40.44  | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 228.90/40.44  | |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 228.90/40.44  | |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 228.90/40.44  | |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 228.90/40.44  | |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (80)
% 228.90/40.44  | |            are inconsistent by sub-proof #642.
% 228.90/40.44  | | 
% 228.90/40.44  | Case 2:
% 228.90/40.44  | | 
% 228.90/40.44  | |   (81)  all_57_10 = e3 & op(e2, e0) = e3
% 228.90/40.44  | | 
% 228.90/40.44  | | ALPHA: (81) implies:
% 228.90/40.44  | |   (82)  all_57_10 = e3
% 228.90/40.44  | | 
% 228.90/40.44  | | REF_CLOSE: (6), (7), (22), (25), (28), (38), (44), (54), (57), (68), (69),
% 228.90/40.44  | |            (73), (82) are inconsistent by sub-proof #1746.
% 228.90/40.44  | | 
% 228.90/40.44  | End of split
% 228.90/40.44  | 
% 228.90/40.44  End of proof
% 228.90/40.44  
% 228.90/40.44  Sub-proof #642 shows that the following formulas are inconsistent:
% 228.90/40.44  ----------------------------------------------------------------
% 228.90/40.44    (1)   ~ (all_53_2 = e2)
% 228.90/40.44    (2)  all_57_0 = e2
% 228.90/40.44    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.90/40.44         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.90/40.44    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.90/40.44         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.90/40.44    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.90/40.44         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.90/40.44    (6)   ~ (e3 = e1)
% 228.90/40.44    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.90/40.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.90/40.44    (8)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.90/40.44         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.90/40.44    (9)   ~ (all_53_3 = e3)
% 228.90/40.44    (10)   ~ (all_53_3 = all_53_7)
% 228.90/40.44    (11)   ~ (all_6_2 = e3)
% 228.90/40.44    (12)   ~ (all_53_9 = e1)
% 228.90/40.44    (13)  op(e1, e1) = all_6_2
% 228.90/40.44    (14)   ~ (all_53_1 = all_53_9)
% 228.90/40.44    (15)  op(e2, e2) = e1
% 228.90/40.44    (16)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.90/40.44          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.90/40.44    (17)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 228.90/40.44            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 228.90/40.44              e3) = all_22_1 & $i(all_22_1))
% 228.90/40.44    (18)   ~ (all_53_13 = e3)
% 228.90/40.44    (19)   ~ (all_53_9 = all_53_11)
% 228.90/40.44    (20)  all_55_4 = all_53_1
% 228.90/40.44    (21)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.90/40.44          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.90/40.44    (22)   ~ (e3 = e2)
% 228.90/40.44    (23)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 228.90/40.44    (24)   ~ (all_53_1 = all_53_3)
% 228.90/40.44    (25)   ~ (e3 = e0)
% 228.90/40.44    (26)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.90/40.44    (27)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 228.90/40.44    (28)  all_57_15 = e3
% 228.90/40.44    (29)   ~ (all_53_9 = all_53_13)
% 228.90/40.44    (30)  op(e3, e3) = e2
% 228.90/40.44    (31)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.90/40.44          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.90/40.44            e1)
% 228.90/40.44    (32)  all_57_10 = e2
% 228.90/40.44    (33)   ~ (all_53_1 = e1)
% 228.90/40.44    (34)  op(e2, e0) = e2
% 228.90/40.44    (35)  all_57_5 = e3
% 228.90/40.44    (36)  all_55_6 = all_53_9
% 228.90/40.44    (37)   ~ (all_53_1 = all_53_2)
% 228.90/40.44    (38)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.90/40.44          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 228.90/40.44    (39)   ~ (e2 = e0)
% 228.90/40.44    (40)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.90/40.44            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.90/40.44            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.90/40.44            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.90/40.44              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.90/40.44            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.90/40.44            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.90/40.44              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.90/40.44              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.90/40.44            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.90/40.44            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.90/40.44            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.90/40.44              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.90/40.44              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.90/40.44            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.90/40.44              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.90/40.44            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.90/40.44            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.90/40.44              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.90/40.44              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.90/40.44            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.90/40.44            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.90/40.44    (41)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 228.90/40.44            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 228.90/40.44              e3) = all_12_1 & $i(all_12_1))
% 228.90/40.44    (42)  all_55_12 = all_53_3
% 228.90/40.44    (43)  all_57_3 = e1
% 228.90/40.44    (44)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.90/40.44          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.90/40.44    (45)   ~ (e1 = e0)
% 228.90/40.44    (46)  all_57_12 = e3
% 228.90/40.44    (47)   ~ (all_53_3 = all_53_11)
% 228.90/40.44    (48)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.90/40.44          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.90/40.44    (49)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.90/40.44          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 228.90/40.44    (50)   ~ (all_53_2 = all_53_3)
% 228.90/40.44    (51)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 228.90/40.44    (52)   ~ (all_53_7 = all_53_11)
% 228.90/40.44    (53)  all_55_8 = all_53_2
% 228.90/40.44    (54)  op(e0, e0) = e3
% 228.90/40.44    (55)  op(e0, e2) = all_53_7
% 228.90/40.44    (56)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.90/40.44          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.90/40.44            e2)
% 228.90/40.44    (57)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.90/40.44              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.90/40.44                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.90/40.44                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.90/40.44    (58)   ~ (all_53_1 = all_53_13)
% 228.90/40.44    (59)  op(e2, e0) = all_53_13
% 228.90/40.44    (60)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.90/40.44          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.90/40.44    (61)   ~ (all_53_12 = e3)
% 228.90/40.44    (62)  all_57_7 = e3
% 228.90/40.44    (63)  op(e1, e3) = all_53_2
% 228.90/40.44    (64)  all_57_8 = e0
% 228.90/40.44    (65)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.90/40.44          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.90/40.44    (66)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 228.90/40.44          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 228.90/40.44    (67)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.90/40.44          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 228.90/40.44    (68)   ~ (e2 = e1)
% 228.90/40.44    (69)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.90/40.44          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.90/40.44    (70)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 228.90/40.44          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 228.90/40.44    (71)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 228.90/40.44    (72)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.90/40.44          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.90/40.44    (73)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.90/40.44          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.90/40.44    (74)  all_55_14 = all_53_11
% 228.90/40.44    (75)   ~ (all_53_11 = e3)
% 228.90/40.44    (76)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.90/40.44          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.90/40.44    (77)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.90/40.44          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.90/40.44    (78)  op(e3, e0) = all_53_12
% 228.90/40.44  
% 228.90/40.44  Begin of proof
% 228.90/40.44  | 
% 228.90/40.44  | BETA: splitting (31) gives:
% 228.90/40.44  | 
% 228.90/40.44  | Case 1:
% 228.90/40.44  | | 
% 228.90/40.44  | |   (79)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 228.90/40.44  | |           e1)
% 228.90/40.44  | | 
% 228.90/40.44  | | BETA: splitting (79) gives:
% 228.90/40.44  | | 
% 228.90/40.44  | | Case 1:
% 228.90/40.44  | | | 
% 228.90/40.44  | | |   (80)  all_57_12 = e1 & op(e0, e3) = e1
% 228.90/40.44  | | | 
% 228.90/40.44  | | | ALPHA: (80) implies:
% 228.90/40.44  | | |   (81)  all_57_12 = e1
% 228.90/40.44  | | |   (82)  op(e0, e3) = e1
% 228.90/40.44  | | | 
% 228.90/40.44  | | | COMBINE_EQS: (46), (81) imply:
% 228.90/40.44  | | |   (83)  e3 = e1
% 228.90/40.44  | | | 
% 228.90/40.44  | | | SIMP: (83) implies:
% 228.90/40.44  | | |   (84)  e3 = e1
% 228.90/40.44  | | | 
% 228.90/40.44  | | | COMBINE_EQS: (62), (84) imply:
% 228.90/40.44  | | |   (85)  all_57_7 = e1
% 228.90/40.44  | | | 
% 228.90/40.44  | | | REF_CLOSE: (6), (7), (8), (11), (13), (17), (22), (25), (28), (39), (41),
% 228.90/40.44  | | |            (45), (57), (64), (68), (69), (73), (77), (82), (85) are
% 228.90/40.44  | | |            inconsistent by sub-proof #643.
% 228.90/40.44  | | | 
% 228.90/40.44  | | Case 2:
% 228.90/40.44  | | | 
% 228.90/40.44  | | |   (86)  all_57_13 = e1 & op(e0, e2) = e1
% 228.90/40.44  | | | 
% 228.90/40.44  | | | ALPHA: (86) implies:
% 228.90/40.44  | | |   (87)  all_57_13 = e1
% 228.90/40.44  | | | 
% 228.90/40.44  | | | BETA: splitting (56) gives:
% 228.90/40.44  | | | 
% 228.90/40.44  | | | Case 1:
% 228.90/40.44  | | | | 
% 228.90/40.44  | | | |   (88)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0,
% 228.90/40.44  | | | |             e2) = e2)
% 228.90/40.44  | | | | 
% 228.90/40.44  | | | | BETA: splitting (88) gives:
% 228.90/40.44  | | | | 
% 228.90/40.44  | | | | Case 1:
% 228.90/40.44  | | | | | 
% 228.90/40.44  | | | | |   (89)  all_57_12 = e2 & op(e0, e3) = e2
% 228.90/40.44  | | | | | 
% 228.90/40.44  | | | | | ALPHA: (89) implies:
% 228.90/40.44  | | | | |   (90)  all_57_12 = e2
% 228.90/40.44  | | | | | 
% 228.90/40.44  | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (11), (13), (15), (16),
% 228.90/40.44  | | | | |            (21), (22), (25), (28), (30), (31), (38), (39), (43), (44),
% 228.90/40.44  | | | | |            (45), (49), (54), (56), (57), (60), (61), (65), (66), (68),
% 228.90/40.44  | | | | |            (69), (70), (73), (76), (78), (87), (90) are inconsistent
% 228.90/40.44  | | | | |            by sub-proof #774.
% 228.90/40.44  | | | | | 
% 228.90/40.44  | | | | Case 2:
% 228.90/40.44  | | | | | 
% 228.90/40.44  | | | | |   (91)  all_57_13 = e2 & op(e0, e2) = e2
% 228.90/40.44  | | | | | 
% 228.90/40.44  | | | | | ALPHA: (91) implies:
% 228.90/40.44  | | | | |   (92)  all_57_13 = e2
% 228.90/40.44  | | | | | 
% 228.90/40.44  | | | | | REF_CLOSE: (6), (7), (25), (28), (31), (39), (45), (46), (54), (57),
% 228.90/40.44  | | | | |            (68), (92) are inconsistent by sub-proof #1742.
% 228.90/40.44  | | | | | 
% 228.90/40.44  | | | | End of split
% 228.90/40.44  | | | | 
% 228.90/40.44  | | | Case 2:
% 228.90/40.44  | | | | 
% 228.90/40.44  | | | |   (93)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0,
% 228.90/40.44  | | | |             e0) = e2)
% 228.90/40.44  | | | | 
% 228.90/40.44  | | | | BETA: splitting (93) gives:
% 228.90/40.44  | | | | 
% 228.90/40.44  | | | | Case 1:
% 228.90/40.44  | | | | | 
% 228.90/40.44  | | | | |   (94)  all_57_14 = e2 & op(e0, e1) = e2
% 228.90/40.44  | | | | | 
% 228.90/40.44  | | | | | ALPHA: (94) implies:
% 228.90/40.44  | | | | |   (95)  all_57_14 = e2
% 228.90/40.44  | | | | | 
% 228.90/40.44  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 228.90/40.44  | | | | |            (12), (13), (14), (15), (16), (18), (19), (20), (21), (22),
% 228.90/40.44  | | | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (33),
% 228.90/40.44  | | | | |            (34), (36), (37), (38), (39), (40), (42), (43), (44), (45),
% 228.90/40.44  | | | | |            (47), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 228.90/40.44  | | | | |            (58), (59), (60), (61), (63), (65), (66), (68), (69), (71),
% 228.90/40.44  | | | | |            (72), (73), (74), (75), (76), (78), (87), (95) are
% 228.90/40.44  | | | | |            inconsistent by sub-proof #719.
% 228.90/40.44  | | | | | 
% 228.90/40.44  | | | | Case 2:
% 228.90/40.44  | | | | | 
% 228.90/40.44  | | | | |   (96)  all_57_15 = e2 & op(e0, e0) = e2
% 228.90/40.44  | | | | | 
% 228.90/40.44  | | | | | REF_CLOSE: (3), (6), (7), (11), (13), (15), (22), (25), (28), (31),
% 228.90/40.44  | | | | |            (32), (35), (39), (45), (48), (54), (56), (57), (60), (67),
% 228.90/40.44  | | | | |            (68), (69), (73), (96) are inconsistent by sub-proof #1741.
% 228.90/40.44  | | | | | 
% 228.90/40.44  | | | | End of split
% 228.90/40.44  | | | | 
% 228.90/40.44  | | | End of split
% 228.90/40.44  | | | 
% 228.90/40.44  | | End of split
% 228.90/40.44  | | 
% 228.90/40.44  | Case 2:
% 228.90/40.44  | | 
% 228.90/40.44  | |   (97)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.90/40.44  | |           e1)
% 228.90/40.44  | | 
% 228.90/40.44  | | BETA: splitting (97) gives:
% 228.90/40.44  | | 
% 228.90/40.44  | | Case 1:
% 228.90/40.44  | | | 
% 228.90/40.44  | | |   (98)  all_57_14 = e1 & op(e0, e1) = e1
% 228.90/40.44  | | | 
% 228.90/40.44  | | | ALPHA: (98) implies:
% 228.90/40.44  | | |   (99)  all_57_14 = e1
% 228.90/40.44  | | | 
% 228.90/40.44  | | | REF_CLOSE: (3), (6), (7), (11), (13), (15), (22), (25), (28), (31), (32),
% 228.90/40.44  | | |            (35), (39), (45), (46), (48), (54), (56), (57), (60), (67),
% 228.90/40.44  | | |            (68), (69), (73), (99) are inconsistent by sub-proof #1740.
% 228.90/40.44  | | | 
% 228.90/40.44  | | Case 2:
% 228.90/40.44  | | | 
% 228.90/40.44  | | |   (100)  all_57_15 = e1 & op(e0, e0) = e1
% 228.90/40.44  | | | 
% 228.90/40.44  | | | ALPHA: (100) implies:
% 228.90/40.44  | | |   (101)  op(e0, e0) = e1
% 228.90/40.44  | | | 
% 228.90/40.44  | | | REF_CLOSE: (6), (7), (54), (101) are inconsistent by sub-proof #2183.
% 228.90/40.44  | | | 
% 228.90/40.44  | | End of split
% 228.90/40.44  | | 
% 228.90/40.44  | End of split
% 228.90/40.44  | 
% 228.90/40.44  End of proof
% 228.90/40.44  
% 228.90/40.44  Sub-proof #643 shows that the following formulas are inconsistent:
% 228.90/40.44  ----------------------------------------------------------------
% 228.90/40.44    (1)   ~ (e3 = e1)
% 228.90/40.44    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.90/40.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.90/40.44    (3)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.90/40.44         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.90/40.44    (4)   ~ (all_6_2 = e3)
% 228.90/40.44    (5)  op(e1, e1) = all_6_2
% 228.90/40.44    (6)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) = all_22_1
% 228.90/40.44           & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0, e3) =
% 228.90/40.44           all_22_1 & $i(all_22_1))
% 228.90/40.44    (7)  all_57_7 = e1
% 228.90/40.44    (8)   ~ (e3 = e2)
% 228.90/40.44    (9)   ~ (e3 = e0)
% 228.90/40.44    (10)  op(e0, e3) = e1
% 228.90/40.44    (11)  all_57_15 = e3
% 228.90/40.44    (12)   ~ (e2 = e0)
% 228.90/40.44    (13)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 228.90/40.44            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 228.90/40.44              e3) = all_12_1 & $i(all_12_1))
% 228.90/40.44    (14)   ~ (e1 = e0)
% 228.90/40.44    (15)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.90/40.44              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.90/40.44                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.90/40.44                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.90/40.44    (16)  all_57_8 = e0
% 228.90/40.44    (17)   ~ (e2 = e1)
% 228.90/40.44    (18)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.90/40.44          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.90/40.44    (19)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.90/40.44          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.90/40.44    (20)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 228.90/40.44          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 228.90/40.44  
% 228.90/40.44  Begin of proof
% 228.90/40.44  | 
% 228.90/40.44  | BETA: splitting (20) gives:
% 228.90/40.44  | 
% 228.90/40.44  | Case 1:
% 228.90/40.44  | | 
% 228.90/40.44  | |   (21)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) =
% 228.90/40.44  | |           e2)
% 228.90/40.44  | | 
% 228.90/40.44  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (11), (12), (14), (15),
% 228.90/40.44  | |            (17), (18), (19), (21) are inconsistent by sub-proof #951.
% 228.90/40.44  | | 
% 228.90/40.44  | Case 2:
% 228.90/40.44  | | 
% 228.90/40.44  | |   (22)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) =
% 228.90/40.44  | |           e2)
% 228.90/40.44  | | 
% 228.90/40.44  | | BETA: splitting (22) gives:
% 228.90/40.44  | | 
% 228.90/40.44  | | Case 1:
% 228.90/40.44  | | | 
% 228.90/40.44  | | |   (23)  all_57_8 = e2 & op(e1, e1) = e2
% 228.90/40.44  | | | 
% 228.90/40.44  | | | ALPHA: (23) implies:
% 228.90/40.44  | | |   (24)  all_57_8 = e2
% 228.90/40.44  | | | 
% 228.90/40.44  | | | REF_CLOSE: (12), (16), (24) are inconsistent by sub-proof #1957.
% 228.90/40.44  | | | 
% 228.90/40.44  | | Case 2:
% 228.90/40.44  | | | 
% 228.90/40.44  | | |   (25)  all_57_11 = e2 & op(e1, e0) = e2
% 228.90/40.44  | | | 
% 228.90/40.44  | | | ALPHA: (25) implies:
% 228.90/40.44  | | |   (26)  op(e1, e0) = e2
% 228.90/40.44  | | | 
% 228.90/40.44  | | | REF_CLOSE: (2), (6), (10), (13), (26) are inconsistent by sub-proof #1147.
% 228.90/40.44  | | | 
% 228.90/40.44  | | End of split
% 228.90/40.44  | | 
% 228.90/40.44  | End of split
% 228.90/40.44  | 
% 228.90/40.44  End of proof
% 228.90/40.44  
% 228.90/40.44  Sub-proof #644 shows that the following formulas are inconsistent:
% 228.90/40.44  ----------------------------------------------------------------
% 228.90/40.44    (1)   ~ (all_53_2 = e2)
% 228.90/40.44    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.90/40.44         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.90/40.44    (3)   ~ (e3 = e1)
% 228.90/40.44    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.90/40.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.90/40.44    (5)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.90/40.44         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.90/40.44    (6)   ~ (all_53_3 = e3)
% 228.90/40.44    (7)   ~ (all_53_3 = all_53_7)
% 228.90/40.44    (8)   ~ (all_6_2 = e3)
% 228.90/40.44    (9)   ~ (all_53_9 = e1)
% 228.90/40.44    (10)  op(e1, e1) = all_6_2
% 228.90/40.44    (11)   ~ (all_53_1 = all_53_9)
% 228.90/40.44    (12)  op(e2, e2) = e1
% 228.90/40.44    (13)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.90/40.44          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.90/40.44    (14)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0)
% 228.90/40.44    (15)   ~ (all_53_13 = e3)
% 228.90/40.44    (16)   ~ (all_53_9 = all_53_11)
% 228.90/40.44    (17)  all_55_4 = all_53_1
% 228.90/40.44    (18)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.90/40.44          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.90/40.44    (19)   ~ (e3 = e2)
% 228.90/40.44    (20)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 228.90/40.44    (21)   ~ (all_53_1 = all_53_3)
% 228.90/40.44    (22)   ~ (e3 = e0)
% 228.90/40.44    (23)  all_57_6 = e0
% 228.90/40.44    (24)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.90/40.44    (25)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 228.90/40.44    (26)  all_57_15 = e3
% 228.90/40.44    (27)   ~ (all_53_9 = all_53_13)
% 228.90/40.44    (28)  op(e3, e3) = e2
% 228.90/40.44    (29)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.90/40.44          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.90/40.44            e1)
% 228.90/40.44    (30)   ~ (all_53_1 = e1)
% 228.90/40.44    (31)  op(e2, e0) = e2
% 228.90/40.44    (32)  all_55_6 = all_53_9
% 228.90/40.44    (33)   ~ (all_53_1 = all_53_2)
% 228.90/40.44    (34)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.90/40.44          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 228.90/40.44    (35)   ~ (e2 = e0)
% 228.90/40.45    (36)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.90/40.45            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.90/40.45            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.90/40.45            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.90/40.45              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.90/40.45            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.90/40.45            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.90/40.45              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.90/40.45              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.90/40.45            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.90/40.45            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.90/40.45            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.90/40.45              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.90/40.45              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.90/40.45            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.90/40.45              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.90/40.45            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.90/40.45            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.90/40.45              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.90/40.45              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.90/40.45            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.90/40.45            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.90/40.45    (37)  all_55_12 = all_53_3
% 228.90/40.45    (38)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 228.90/40.45          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 228.90/40.45    (39)   ~ (e1 = e0)
% 228.90/40.45    (40)   ~ (all_53_3 = all_53_11)
% 228.90/40.45    (41)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.90/40.45          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.90/40.45    (42)   ~ (all_53_2 = all_53_3)
% 228.90/40.45    (43)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 228.90/40.45    (44)   ~ (all_53_7 = all_53_11)
% 228.90/40.45    (45)  all_55_8 = all_53_2
% 228.90/40.45    (46)  op(e0, e0) = e3
% 228.90/40.45    (47)  op(e0, e2) = all_53_7
% 228.90/40.45    (48)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.90/40.45          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.90/40.45            e2)
% 228.90/40.45    (49)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.90/40.45              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.90/40.45                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.90/40.45                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.90/40.45    (50)   ~ (all_53_1 = all_53_13)
% 228.90/40.45    (51)  op(e2, e0) = all_53_13
% 228.90/40.45    (52)   ~ (all_53_12 = e3)
% 228.90/40.45    (53)  all_57_7 = e3
% 228.90/40.45    (54)  op(e1, e3) = all_53_2
% 228.90/40.45    (55)   ~ (e2 = e1)
% 228.90/40.45    (56)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.90/40.45          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.90/40.45    (57)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 228.90/40.45    (58)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.90/40.45          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.90/40.45    (59)  all_55_14 = all_53_11
% 228.90/40.45    (60)   ~ (all_53_11 = e3)
% 228.90/40.45    (61)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.90/40.45          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.90/40.45    (62)  op(e3, e0) = all_53_12
% 228.90/40.45  
% 228.90/40.45  Begin of proof
% 228.90/40.45  | 
% 228.90/40.45  | BETA: splitting (14) gives:
% 228.90/40.45  | 
% 228.90/40.45  | Case 1:
% 228.90/40.45  | | 
% 228.90/40.45  | |   (63)  all_57_4 = e0 & op(e3, e1) = e0
% 228.90/40.45  | | 
% 228.90/40.45  | | ALPHA: (63) implies:
% 228.90/40.45  | |   (64)  all_57_4 = e0
% 228.90/40.45  | | 
% 228.90/40.45  | | BETA: splitting (38) gives:
% 228.90/40.45  | | 
% 228.90/40.45  | | Case 1:
% 228.90/40.45  | | | 
% 228.90/40.45  | | |   (65)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) =
% 228.90/40.45  | | |           e3)
% 228.90/40.45  | | | 
% 228.90/40.45  | | | BETA: splitting (65) gives:
% 228.90/40.45  | | | 
% 228.90/40.45  | | | Case 1:
% 228.90/40.45  | | | | 
% 228.90/40.45  | | | |   (66)  all_57_0 = e3 & op(e3, e3) = e3
% 228.90/40.45  | | | | 
% 228.90/40.45  | | | | ALPHA: (66) implies:
% 228.90/40.45  | | | |   (67)  op(e3, e3) = e3
% 228.90/40.45  | | | | 
% 228.90/40.45  | | | | REF_CLOSE: (4), (19), (28), (67) are inconsistent by sub-proof #2490.
% 228.90/40.45  | | | | 
% 228.90/40.45  | | | Case 2:
% 228.90/40.45  | | | | 
% 228.90/40.45  | | | |   (68)  all_57_1 = e3 & op(e3, e2) = e3
% 228.90/40.45  | | | | 
% 228.90/40.45  | | | | ALPHA: (68) implies:
% 228.90/40.45  | | | |   (69)  all_57_1 = e3
% 228.90/40.45  | | | | 
% 228.90/40.45  | | | | REF_CLOSE: (2), (3), (4), (5), (8), (10), (12), (19), (22), (23), (26),
% 228.90/40.45  | | | |            (34), (35), (39), (49), (53), (55), (56), (58), (61), (69)
% 228.90/40.45  | | | |            are inconsistent by sub-proof #1774.
% 228.90/40.45  | | | | 
% 228.90/40.45  | | | End of split
% 228.90/40.45  | | | 
% 228.90/40.45  | | Case 2:
% 228.90/40.45  | | | 
% 228.90/40.45  | | |   (70)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) =
% 228.90/40.45  | | |           e3)
% 228.90/40.45  | | | 
% 228.90/40.45  | | | REF_CLOSE: (4), (22), (52), (62), (64), (70) are inconsistent by sub-proof
% 228.90/40.45  | | |            #1406.
% 228.90/40.45  | | | 
% 228.90/40.45  | | End of split
% 228.90/40.45  | | 
% 228.90/40.45  | Case 2:
% 228.90/40.45  | | 
% 228.90/40.45  | |   (71)  all_57_5 = e0 & op(e2, e1) = e0
% 228.90/40.45  | | 
% 228.90/40.45  | | ALPHA: (71) implies:
% 228.90/40.45  | |   (72)  all_57_5 = e0
% 228.90/40.45  | | 
% 228.90/40.45  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.90/40.45  | |            (13), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 228.90/40.45  | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (35), (36),
% 228.90/40.45  | |            (37), (39), (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 228.90/40.45  | |            (49), (50), (51), (54), (55), (56), (57), (58), (59), (60), (72)
% 228.90/40.45  | |            are inconsistent by sub-proof #650.
% 228.90/40.45  | | 
% 228.90/40.45  | End of split
% 228.90/40.45  | 
% 228.90/40.45  End of proof
% 228.90/40.45  
% 228.90/40.45  Sub-proof #645 shows that the following formulas are inconsistent:
% 228.90/40.45  ----------------------------------------------------------------
% 228.90/40.45    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.90/40.45         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.90/40.45    (2)   ~ (e3 = e1)
% 228.90/40.45    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.90/40.45           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.90/40.45    (4)   ~ (e3 = e2)
% 228.90/40.45    (5)   ~ (e3 = e0)
% 228.90/40.45    (6)  all_57_6 = e0
% 228.90/40.45    (7)  op(e3, e3) = e2
% 228.90/40.45    (8)   ~ (e2 = e0)
% 228.90/40.45    (9)  all_57_3 = e1
% 228.90/40.45    (10)   ~ (e1 = e0)
% 228.90/40.45    (11)  all_57_12 = e3
% 228.90/40.45    (12)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.90/40.45          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.90/40.45    (13)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1)
% 228.90/40.45    (14)  all_57_7 = e3
% 228.90/40.45    (15)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.90/40.45          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.90/40.45    (16)   ~ (e2 = e1)
% 228.90/40.45    (17)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.90/40.45          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.90/40.45  
% 228.90/40.45  Begin of proof
% 228.90/40.45  | 
% 228.90/40.45  | BETA: splitting (13) gives:
% 228.90/40.45  | 
% 228.90/40.45  | Case 1:
% 228.90/40.45  | | 
% 228.90/40.45  | |   (18)  all_57_6 = e1 & op(e1, e3) = e1
% 228.90/40.45  | | 
% 228.90/40.45  | | ALPHA: (18) implies:
% 228.90/40.45  | |   (19)  all_57_6 = e1
% 228.90/40.45  | | 
% 228.90/40.45  | | COMBINE_EQS: (6), (19) imply:
% 228.90/40.45  | |   (20)  e1 = e0
% 228.90/40.45  | | 
% 228.90/40.45  | | SIMP: (20) implies:
% 228.90/40.45  | |   (21)  e1 = e0
% 228.90/40.45  | | 
% 228.90/40.45  | | COMBINE_EQS: (9), (21) imply:
% 228.90/40.45  | |   (22)  all_57_3 = e0
% 228.90/40.45  | | 
% 228.90/40.45  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (10), (11), (12), (15), (16),
% 228.90/40.45  | |            (17), (19), (22) are inconsistent by sub-proof #1632.
% 228.90/40.45  | | 
% 228.90/40.45  | Case 2:
% 228.90/40.45  | | 
% 228.90/40.45  | |   (23)  all_57_7 = e1 & op(e1, e2) = e1
% 228.90/40.45  | | 
% 228.90/40.45  | | REF_CLOSE: (2), (14), (23) are inconsistent by sub-proof #2104.
% 228.90/40.45  | | 
% 228.90/40.45  | End of split
% 228.90/40.45  | 
% 228.90/40.45  End of proof
% 228.90/40.45  
% 228.90/40.45  Sub-proof #646 shows that the following formulas are inconsistent:
% 228.90/40.45  ----------------------------------------------------------------
% 228.90/40.45    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.90/40.45         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.90/40.45    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.90/40.45         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.90/40.45    (3)   ~ (e3 = e1)
% 228.90/40.45    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.90/40.45           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.90/40.45    (5)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.90/40.45         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.90/40.45    (6)   ~ (all_6_2 = e3)
% 228.90/40.45    (7)  op(e1, e1) = all_6_2
% 228.90/40.45    (8)  op(e2, e2) = e1
% 228.90/40.45    (9)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) = all_22_1
% 228.90/40.45           & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0, e3) =
% 228.90/40.45           all_22_1 & $i(all_22_1))
% 228.90/40.45    (10)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.90/40.45    (11)   ~ (e3 = e2)
% 228.90/40.45    (12)   ~ (e3 = e0)
% 228.90/40.45    (13)  all_57_6 = e0
% 228.90/40.45    (14)  all_57_15 = e3
% 228.90/40.45    (15)  op(e3, e3) = e2
% 228.90/40.45    (16)   ~ (e2 = e0)
% 228.90/40.45    (17)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 228.90/40.45            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 228.90/40.45              e3) = all_12_1 & $i(all_12_1))
% 228.90/40.45    (18)  all_57_2 = e3
% 228.90/40.45    (19)  all_57_3 = e1
% 228.90/40.45    (20)   ~ (e1 = e0)
% 228.90/40.45    (21)  op(e0, e0) = e3
% 228.90/40.45    (22)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.90/40.45              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.90/40.45                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.90/40.45                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.90/40.45    (23)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.90/40.45          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.90/40.45    (24)  all_57_7 = e3
% 228.90/40.45    (25)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.90/40.45          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.90/40.45    (26)   ~ (e2 = e1)
% 228.90/40.45    (27)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.90/40.45          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.90/40.45    (28)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.90/40.45          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.90/40.45    (29)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.90/40.45          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.90/40.45  
% 228.90/40.45  Begin of proof
% 228.90/40.45  | 
% 228.90/40.45  | BETA: splitting (10) gives:
% 228.90/40.45  | 
% 228.90/40.45  | Case 1:
% 228.90/40.45  | | 
% 228.90/40.45  | |   (30)  all_57_11 = e2 & op(e1, e0) = e2
% 228.90/40.45  | | 
% 228.90/40.45  | | ALPHA: (30) implies:
% 228.90/40.45  | |   (31)  op(e1, e0) = e2
% 228.90/40.45  | | 
% 228.90/40.45  | | REF_CLOSE: (2), (3), (4), (9), (13), (15), (17), (18), (20), (26), (31) are
% 228.90/40.45  | |            inconsistent by sub-proof #752.
% 228.90/40.45  | | 
% 228.90/40.45  | Case 2:
% 228.90/40.45  | | 
% 228.90/40.45  | |   (32)  all_57_15 = e2 & op(e0, e0) = e2
% 228.90/40.45  | | 
% 228.90/40.45  | | ALPHA: (32) implies:
% 228.90/40.45  | |   (33)  all_57_15 = e2
% 228.90/40.45  | | 
% 228.90/40.45  | | COMBINE_EQS: (14), (33) imply:
% 228.90/40.45  | |   (34)  e3 = e2
% 228.90/40.45  | | 
% 228.90/40.45  | | SIMP: (34) implies:
% 228.90/40.45  | |   (35)  e3 = e2
% 228.90/40.45  | | 
% 228.90/40.45  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (11), (12), (14), (15),
% 228.90/40.45  | |            (16), (18), (19), (20), (21), (22), (23), (24), (25), (26), (27),
% 228.90/40.45  | |            (28), (29), (35) are inconsistent by sub-proof #647.
% 228.90/40.45  | | 
% 228.90/40.45  | End of split
% 228.90/40.45  | 
% 228.90/40.45  End of proof
% 228.90/40.45  
% 228.90/40.45  Sub-proof #647 shows that the following formulas are inconsistent:
% 228.90/40.45  ----------------------------------------------------------------
% 228.90/40.45    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 228.90/40.45         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 228.90/40.45    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 228.90/40.45         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 228.90/40.45    (3)   ~ (e3 = e1)
% 228.90/40.45    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.90/40.45           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.90/40.45    (5)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.90/40.45         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.90/40.45    (6)   ~ (all_6_2 = e3)
% 228.90/40.45    (7)  op(e1, e1) = all_6_2
% 228.90/40.45    (8)  op(e2, e2) = e1
% 228.90/40.45    (9)   ~ (e3 = e2)
% 228.90/40.45    (10)  e3 = e2
% 228.90/40.45    (11)   ~ (e3 = e0)
% 228.90/40.45    (12)  all_57_15 = e3
% 228.90/40.45    (13)  op(e3, e3) = e2
% 228.90/40.45    (14)   ~ (e2 = e0)
% 228.90/40.45    (15)  all_57_2 = e3
% 228.90/40.45    (16)  all_57_3 = e1
% 228.90/40.45    (17)   ~ (e1 = e0)
% 228.90/40.45    (18)  op(e0, e0) = e3
% 228.90/40.45    (19)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.90/40.45              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.90/40.45                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.90/40.45                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.90/40.45    (20)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 228.90/40.45          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 228.90/40.45    (21)  all_57_7 = e3
% 228.90/40.45    (22)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.90/40.45          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 228.90/40.45    (23)   ~ (e2 = e1)
% 228.90/40.45    (24)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.90/40.45          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.90/40.45    (25)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 228.90/40.45          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 228.90/40.45    (26)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.90/40.45          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.90/40.45  
% 228.90/40.45  Begin of proof
% 228.90/40.45  | 
% 228.90/40.45  | COMBINE_EQS: (10), (21) imply:
% 228.90/40.45  |   (27)  all_57_7 = e2
% 228.90/40.45  | 
% 228.90/40.45  | COMBINE_EQS: (10), (15) imply:
% 228.90/40.45  |   (28)  all_57_2 = e2
% 228.90/40.45  | 
% 228.90/40.45  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13),
% 228.90/40.45  |            (14), (16), (17), (18), (19), (20), (22), (23), (24), (25), (26),
% 228.90/40.45  |            (27), (28) are inconsistent by sub-proof #656.
% 228.90/40.45  | 
% 228.90/40.45  End of proof
% 228.90/40.45  
% 228.90/40.45  Sub-proof #648 shows that the following formulas are inconsistent:
% 228.90/40.45  ----------------------------------------------------------------
% 228.90/40.45    (1)   ~ (all_53_2 = e2)
% 228.90/40.45    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.90/40.45         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.90/40.45    (3)   ~ (e3 = e1)
% 228.90/40.45    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.90/40.45           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.90/40.45    (5)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.90/40.45         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.90/40.45    (6)   ~ (all_53_3 = e3)
% 228.90/40.45    (7)   ~ (all_53_3 = all_53_7)
% 228.90/40.45    (8)   ~ (all_6_2 = e3)
% 228.90/40.45    (9)   ~ (all_53_9 = e1)
% 228.90/40.45    (10)  op(e1, e1) = all_6_2
% 228.90/40.45    (11)   ~ (all_53_1 = all_53_9)
% 228.90/40.45    (12)  op(e2, e2) = e1
% 228.90/40.45    (13)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.90/40.45          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.90/40.45    (14)   ~ (all_53_13 = e3)
% 228.90/40.45    (15)   ~ (all_53_9 = all_53_11)
% 228.90/40.45    (16)  all_55_4 = all_53_1
% 228.90/40.45    (17)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.90/40.45          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.90/40.45    (18)   ~ (e3 = e2)
% 228.90/40.45    (19)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 228.90/40.45    (20)   ~ (all_53_1 = all_53_3)
% 228.90/40.45    (21)   ~ (e3 = e0)
% 228.90/40.45    (22)  all_57_6 = e0
% 228.90/40.45    (23)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.90/40.45    (24)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 228.90/40.45    (25)  all_57_15 = e3
% 228.90/40.45    (26)   ~ (all_53_9 = all_53_13)
% 228.90/40.45    (27)  op(e3, e3) = e2
% 228.90/40.45    (28)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.90/40.45          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.90/40.45            e1)
% 228.90/40.45    (29)  all_57_10 = e2
% 228.90/40.45    (30)   ~ (all_53_1 = e1)
% 228.90/40.45    (31)  op(e2, e0) = e2
% 228.90/40.45    (32)  op(e3, e3) = all_52_1
% 228.90/40.45    (33)  all_55_6 = all_53_9
% 228.90/40.45    (34)   ~ (all_53_1 = all_53_2)
% 228.90/40.45    (35)  op(all_52_1, all_52_1) = e3
% 228.90/40.45    (36)   ~ (e2 = e0)
% 228.90/40.45    (37)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.90/40.45            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.90/40.45            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.90/40.45            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.90/40.45              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.90/40.45            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.90/40.45            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.90/40.45              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.90/40.45              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.90/40.45            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.90/40.45            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.90/40.45            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.90/40.45              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.90/40.45              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.90/40.45            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.90/40.45              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.90/40.45            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.90/40.45            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.90/40.45              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.90/40.45              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.90/40.45            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.90/40.45            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.90/40.45    (38)  all_55_12 = all_53_3
% 228.90/40.45    (39)  all_57_2 = e3
% 228.90/40.45    (40)   ~ (e1 = e0)
% 228.90/40.45    (41)   ~ (all_53_3 = all_53_11)
% 228.90/40.45    (42)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.90/40.45          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.90/40.45    (43)   ~ (all_53_2 = all_53_3)
% 228.90/40.45    (44)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 228.90/40.45    (45)   ~ (all_53_7 = all_53_11)
% 228.90/40.45    (46)  all_55_8 = all_53_2
% 228.90/40.45    (47)  op(e0, e0) = e3
% 228.90/40.45    (48)  op(e0, e2) = all_53_7
% 228.90/40.45    (49)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.90/40.45          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.90/40.45            e2)
% 228.90/40.45    (50)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.90/40.45              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.90/40.45                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.90/40.45                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.90/40.45    (51)   ~ (all_53_1 = all_53_13)
% 228.90/40.45    (52)  op(e2, e0) = all_53_13
% 228.90/40.45    (53)  op(e1, e3) = all_53_2
% 228.90/40.45    (54)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 228.90/40.45          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 228.90/40.45    (55)   ~ (e2 = e1)
% 228.90/40.45    (56)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.90/40.45          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.90/40.45    (57)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 228.90/40.45    (58)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.90/40.45          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.90/40.45    (59)  all_55_14 = all_53_11
% 228.90/40.45    (60)   ~ (all_53_11 = e3)
% 228.90/40.45  
% 228.90/40.45  Begin of proof
% 228.90/40.45  | 
% 228.90/40.45  | BETA: splitting (54) gives:
% 228.90/40.45  | 
% 228.90/40.45  | Case 1:
% 228.90/40.45  | | 
% 228.90/40.45  | |   (61)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) =
% 228.90/40.45  | |           e0)
% 228.90/40.45  | | 
% 228.90/40.45  | | BETA: splitting (61) gives:
% 228.90/40.45  | | 
% 228.90/40.45  | | Case 1:
% 228.90/40.45  | | | 
% 228.90/40.45  | | |   (62)  all_57_2 = e0 & op(e2, e3) = e0
% 228.90/40.45  | | | 
% 228.90/40.45  | | | REF_CLOSE: (21), (39), (62) are inconsistent by sub-proof #1805.
% 228.90/40.45  | | | 
% 228.90/40.45  | | Case 2:
% 228.90/40.45  | | | 
% 228.90/40.45  | | |   (63)  all_57_3 = e0 & op(e2, e2) = e0
% 228.90/40.45  | | | 
% 228.90/40.45  | | | ALPHA: (63) implies:
% 228.90/40.45  | | |   (64)  op(e2, e2) = e0
% 228.90/40.45  | | | 
% 228.90/40.45  | | | REF_CLOSE: (4), (21), (27), (32), (35), (64) are inconsistent by sub-proof
% 228.90/40.45  | | |            #1653.
% 228.90/40.45  | | | 
% 228.90/40.45  | | End of split
% 228.90/40.45  | | 
% 228.90/40.45  | Case 2:
% 228.90/40.45  | | 
% 228.90/40.45  | |   (65)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 228.90/40.45  | |           e0)
% 228.90/40.45  | | 
% 228.90/40.45  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.90/40.45  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 228.90/40.45  | |            (24), (25), (26), (27), (28), (29), (30), (31), (33), (34), (36),
% 228.90/40.45  | |            (37), (38), (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 228.90/40.45  | |            (49), (50), (51), (52), (53), (55), (56), (57), (58), (59), (60),
% 228.90/40.45  | |            (65) are inconsistent by sub-proof #649.
% 228.90/40.45  | | 
% 228.90/40.45  | End of split
% 228.90/40.45  | 
% 228.90/40.45  End of proof
% 228.90/40.45  
% 228.90/40.45  Sub-proof #649 shows that the following formulas are inconsistent:
% 228.90/40.45  ----------------------------------------------------------------
% 228.90/40.45    (1)   ~ (all_53_2 = e2)
% 228.90/40.45    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.90/40.45         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.90/40.45    (3)   ~ (e3 = e1)
% 228.90/40.45    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.90/40.45           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.90/40.45    (5)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.90/40.45         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.90/40.45    (6)   ~ (all_53_3 = e3)
% 228.90/40.45    (7)   ~ (all_53_3 = all_53_7)
% 228.90/40.45    (8)   ~ (all_6_2 = e3)
% 228.90/40.45    (9)   ~ (all_53_9 = e1)
% 228.90/40.45    (10)  op(e1, e1) = all_6_2
% 228.90/40.45    (11)   ~ (all_53_1 = all_53_9)
% 228.90/40.45    (12)  op(e2, e2) = e1
% 228.90/40.45    (13)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.90/40.45          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.90/40.45    (14)   ~ (all_53_13 = e3)
% 228.90/40.45    (15)   ~ (all_53_9 = all_53_11)
% 228.90/40.45    (16)  all_55_4 = all_53_1
% 228.90/40.45    (17)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.90/40.45          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.90/40.45    (18)   ~ (e3 = e2)
% 228.90/40.45    (19)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 228.90/40.45    (20)   ~ (all_53_1 = all_53_3)
% 228.90/40.45    (21)   ~ (e3 = e0)
% 228.90/40.45    (22)  all_57_6 = e0
% 228.90/40.45    (23)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 228.90/40.45    (24)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 228.90/40.45    (25)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 228.90/40.45    (26)  all_57_15 = e3
% 228.90/40.45    (27)   ~ (all_53_9 = all_53_13)
% 228.90/40.45    (28)  op(e3, e3) = e2
% 228.90/40.45    (29)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 228.90/40.45          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 228.90/40.45            e1)
% 228.90/40.45    (30)  all_57_10 = e2
% 228.90/40.45    (31)   ~ (all_53_1 = e1)
% 228.90/40.45    (32)  op(e2, e0) = e2
% 228.90/40.45    (33)  all_55_6 = all_53_9
% 228.90/40.46    (34)   ~ (all_53_1 = all_53_2)
% 228.90/40.46    (35)   ~ (e2 = e0)
% 228.90/40.46    (36)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 228.90/40.46            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 228.90/40.46            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 228.90/40.46            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 228.90/40.46              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 228.90/40.46            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 228.90/40.46            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 228.90/40.46              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 228.90/40.46              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 228.90/40.46            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 228.90/40.46            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 228.90/40.46            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 228.90/40.46              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 228.90/40.46              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 228.90/40.46            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 228.90/40.46              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 228.90/40.46            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 228.90/40.46            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 228.90/40.46              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 228.90/40.46              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 228.90/40.46            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 228.90/40.46            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 228.90/40.46    (37)  all_55_12 = all_53_3
% 228.90/40.46    (38)   ~ (e1 = e0)
% 228.90/40.46    (39)   ~ (all_53_3 = all_53_11)
% 228.90/40.46    (40)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 228.90/40.46          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 228.90/40.46    (41)   ~ (all_53_2 = all_53_3)
% 228.90/40.46    (42)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 228.90/40.46    (43)   ~ (all_53_7 = all_53_11)
% 228.90/40.46    (44)  all_55_8 = all_53_2
% 228.90/40.46    (45)  op(e0, e0) = e3
% 228.90/40.46    (46)  op(e0, e2) = all_53_7
% 228.90/40.46    (47)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.90/40.46          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 228.90/40.46            e2)
% 228.90/40.46    (48)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 228.90/40.46              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 228.90/40.46                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 228.90/40.46                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 228.90/40.46    (49)   ~ (all_53_1 = all_53_13)
% 228.90/40.46    (50)  op(e2, e0) = all_53_13
% 228.90/40.46    (51)  op(e1, e3) = all_53_2
% 228.90/40.46    (52)   ~ (e2 = e1)
% 228.90/40.46    (53)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 228.90/40.46          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 228.90/40.46    (54)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 228.90/40.46    (55)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 228.90/40.46          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 228.90/40.46    (56)  all_55_14 = all_53_11
% 228.90/40.46    (57)   ~ (all_53_11 = e3)
% 228.90/40.46  
% 228.90/40.46  Begin of proof
% 228.90/40.46  | 
% 228.90/40.46  | BETA: splitting (24) gives:
% 228.90/40.46  | 
% 228.90/40.46  | Case 1:
% 228.90/40.46  | | 
% 228.90/40.46  | |   (58)  all_57_5 = e0 & op(e2, e1) = e0
% 228.90/40.46  | | 
% 228.90/40.46  | | ALPHA: (58) implies:
% 228.90/40.46  | |   (59)  all_57_5 = e0
% 228.90/40.46  | | 
% 228.90/40.46  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 228.90/40.46  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 228.90/40.46  | |            (25), (26), (27), (28), (29), (31), (32), (33), (34), (35), (36),
% 228.90/40.46  | |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 228.90/40.46  | |            (48), (49), (50), (51), (52), (53), (54), (55), (56), (57), (59)
% 228.90/40.46  | |            are inconsistent by sub-proof #650.
% 228.90/40.46  | | 
% 228.90/40.46  | Case 2:
% 228.90/40.46  | | 
% 228.90/40.46  | |   (60)  all_57_10 = e0 & op(e2, e0) = e0
% 228.90/40.46  | | 
% 228.90/40.46  | | ALPHA: (60) implies:
% 228.90/40.46  | |   (61)  all_57_10 = e0
% 228.90/40.46  | | 
% 228.90/40.46  | | REF_CLOSE: (30), (35), (61) are inconsistent by sub-proof #2138.
% 228.90/40.46  | | 
% 228.90/40.46  | End of split
% 228.90/40.46  | 
% 228.90/40.46  End of proof
% 228.90/40.46  
% 228.90/40.46  Sub-proof #650 shows that the following formulas are inconsistent:
% 228.90/40.46  ----------------------------------------------------------------
% 228.90/40.46    (1)   ~ (all_53_2 = e2)
% 228.90/40.46    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 228.90/40.46         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 228.90/40.46    (3)   ~ (e3 = e1)
% 228.90/40.46    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 228.90/40.46           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 228.90/40.46    (5)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 228.90/40.46         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 228.90/40.46    (6)   ~ (all_53_3 = e3)
% 228.90/40.46    (7)   ~ (all_53_3 = all_53_7)
% 228.90/40.46    (8)   ~ (all_6_2 = e3)
% 228.90/40.46    (9)   ~ (all_53_9 = e1)
% 228.90/40.46    (10)  op(e1, e1) = all_6_2
% 228.90/40.46    (11)   ~ (all_53_1 = all_53_9)
% 228.90/40.46    (12)  op(e2, e2) = e1
% 228.90/40.46    (13)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 228.90/40.46          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 228.90/40.46    (14)   ~ (all_53_13 = e3)
% 228.90/40.46    (15)   ~ (all_53_9 = all_53_11)
% 228.90/40.46    (16)  all_55_4 = all_53_1
% 228.90/40.46    (17)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 228.90/40.46          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 228.90/40.46    (18)   ~ (e3 = e2)
% 228.90/40.46    (19)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 228.90/40.46    (20)   ~ (all_53_1 = all_53_3)
% 229.03/40.46    (21)   ~ (e3 = e0)
% 229.03/40.46    (22)  all_57_6 = e0
% 229.03/40.46    (23)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 229.03/40.46    (24)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 229.03/40.46    (25)  all_57_15 = e3
% 229.03/40.46    (26)   ~ (all_53_9 = all_53_13)
% 229.03/40.46    (27)  op(e3, e3) = e2
% 229.03/40.46    (28)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.03/40.46          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.03/40.46            e1)
% 229.03/40.46    (29)   ~ (all_53_1 = e1)
% 229.03/40.46    (30)  op(e2, e0) = e2
% 229.03/40.46    (31)  all_55_6 = all_53_9
% 229.03/40.46    (32)   ~ (all_53_1 = all_53_2)
% 229.03/40.46    (33)   ~ (e2 = e0)
% 229.03/40.46    (34)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 229.03/40.46            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 229.03/40.46            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 229.03/40.46            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 229.03/40.46              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 229.03/40.46            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 229.03/40.46            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 229.03/40.46              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 229.03/40.46              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 229.03/40.46            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 229.03/40.46            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 229.03/40.46            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 229.03/40.46              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 229.03/40.46              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 229.03/40.46            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 229.03/40.46              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 229.03/40.46            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 229.03/40.46            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 229.03/40.46              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 229.03/40.46              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 229.03/40.46            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 229.03/40.46            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 229.03/40.46    (35)  all_55_12 = all_53_3
% 229.03/40.46    (36)   ~ (e1 = e0)
% 229.03/40.46    (37)   ~ (all_53_3 = all_53_11)
% 229.03/40.46    (38)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.03/40.46          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.03/40.46    (39)   ~ (all_53_2 = all_53_3)
% 229.03/40.46    (40)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 229.03/40.46    (41)   ~ (all_53_7 = all_53_11)
% 229.03/40.46    (42)  all_55_8 = all_53_2
% 229.03/40.46    (43)  op(e0, e0) = e3
% 229.03/40.46    (44)  op(e0, e2) = all_53_7
% 229.03/40.46    (45)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.03/40.46          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.03/40.46            e2)
% 229.03/40.46    (46)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.03/40.46              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.03/40.46                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.03/40.46                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.03/40.46    (47)   ~ (all_53_1 = all_53_13)
% 229.03/40.46    (48)  op(e2, e0) = all_53_13
% 229.03/40.46    (49)  op(e1, e3) = all_53_2
% 229.03/40.46    (50)   ~ (e2 = e1)
% 229.03/40.46    (51)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.03/40.46          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.03/40.46    (52)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 229.03/40.46    (53)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.03/40.46          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.03/40.46    (54)  all_55_14 = all_53_11
% 229.03/40.46    (55)   ~ (all_53_11 = e3)
% 229.03/40.46    (56)  all_57_5 = e0
% 229.03/40.46  
% 229.03/40.46  Begin of proof
% 229.03/40.46  | 
% 229.03/40.46  | BETA: splitting (38) gives:
% 229.03/40.46  | 
% 229.03/40.46  | Case 1:
% 229.03/40.46  | | 
% 229.03/40.46  | |   (57)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) =
% 229.03/40.46  | |           e3)
% 229.03/40.46  | | 
% 229.03/40.46  | | BETA: splitting (57) gives:
% 229.03/40.46  | | 
% 229.03/40.46  | | Case 1:
% 229.03/40.46  | | | 
% 229.03/40.46  | | |   (58)  all_57_4 = e3 & op(e3, e1) = e3
% 229.03/40.46  | | | 
% 229.03/40.46  | | | ALPHA: (58) implies:
% 229.03/40.46  | | |   (59)  all_57_4 = e3
% 229.03/40.46  | | | 
% 229.03/40.46  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 229.03/40.46  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 229.03/40.46  | | |            (23), (24), (25), (26), (27), (29), (30), (31), (32), (33),
% 229.03/40.46  | | |            (34), (35), (36), (37), (39), (40), (41), (42), (43), (44),
% 229.03/40.46  | | |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (55),
% 229.03/40.46  | | |            (59) are inconsistent by sub-proof #651.
% 229.03/40.46  | | | 
% 229.03/40.46  | | Case 2:
% 229.03/40.46  | | | 
% 229.03/40.46  | | |   (60)  all_57_5 = e3 & op(e2, e1) = e3
% 229.03/40.46  | | | 
% 229.03/40.46  | | | ALPHA: (60) implies:
% 229.03/40.46  | | |   (61)  all_57_5 = e3
% 229.03/40.46  | | | 
% 229.03/40.46  | | | REF_CLOSE: (21), (56), (61) are inconsistent by sub-proof #2471.
% 229.03/40.46  | | | 
% 229.03/40.46  | | End of split
% 229.03/40.46  | | 
% 229.03/40.46  | Case 2:
% 229.03/40.46  | | 
% 229.03/40.46  | |   (62)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) =
% 229.03/40.46  | |           e3)
% 229.03/40.46  | | 
% 229.03/40.46  | | REF_CLOSE: (3), (4), (8), (10), (18), (21), (25), (28), (33), (36), (45),
% 229.03/40.46  | |            (46), (50), (62) are inconsistent by sub-proof #1794.
% 229.03/40.46  | | 
% 229.03/40.46  | End of split
% 229.03/40.46  | 
% 229.03/40.46  End of proof
% 229.03/40.46  
% 229.03/40.46  Sub-proof #651 shows that the following formulas are inconsistent:
% 229.03/40.46  ----------------------------------------------------------------
% 229.03/40.46    (1)   ~ (all_53_2 = e2)
% 229.03/40.46    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.03/40.46         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.03/40.46    (3)   ~ (e3 = e1)
% 229.03/40.46    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.03/40.46           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.03/40.46    (5)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.03/40.46         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.03/40.46    (6)   ~ (all_53_3 = e3)
% 229.03/40.46    (7)   ~ (all_53_3 = all_53_7)
% 229.03/40.46    (8)   ~ (all_6_2 = e3)
% 229.03/40.46    (9)   ~ (all_53_9 = e1)
% 229.03/40.46    (10)  op(e1, e1) = all_6_2
% 229.03/40.46    (11)   ~ (all_53_1 = all_53_9)
% 229.03/40.46    (12)  op(e2, e2) = e1
% 229.03/40.46    (13)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.03/40.46          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.03/40.46    (14)   ~ (all_53_13 = e3)
% 229.03/40.46    (15)   ~ (all_53_9 = all_53_11)
% 229.03/40.46    (16)  all_55_4 = all_53_1
% 229.03/40.46    (17)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.03/40.46          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.03/40.46    (18)  all_57_4 = e3
% 229.03/40.46    (19)   ~ (e3 = e2)
% 229.03/40.46    (20)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 229.03/40.46    (21)   ~ (all_53_1 = all_53_3)
% 229.03/40.46    (22)   ~ (e3 = e0)
% 229.03/40.46    (23)  all_57_6 = e0
% 229.03/40.46    (24)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 229.03/40.46    (25)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 229.03/40.46    (26)  all_57_15 = e3
% 229.03/40.46    (27)   ~ (all_53_9 = all_53_13)
% 229.03/40.46    (28)  op(e3, e3) = e2
% 229.03/40.46    (29)   ~ (all_53_1 = e1)
% 229.03/40.46    (30)  op(e2, e0) = e2
% 229.03/40.46    (31)  all_55_6 = all_53_9
% 229.03/40.46    (32)   ~ (all_53_1 = all_53_2)
% 229.03/40.46    (33)   ~ (e2 = e0)
% 229.03/40.46    (34)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 229.03/40.46            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 229.03/40.46            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 229.03/40.46            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 229.03/40.46              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 229.03/40.46            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 229.03/40.46            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 229.03/40.46              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 229.03/40.46              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 229.03/40.46            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 229.03/40.46            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 229.03/40.46            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 229.03/40.46              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 229.03/40.46              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 229.03/40.46            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 229.03/40.46              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 229.03/40.46            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 229.03/40.46            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 229.03/40.46              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 229.03/40.46              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 229.03/40.46            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 229.03/40.46            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 229.03/40.46    (35)  all_55_12 = all_53_3
% 229.03/40.46    (36)   ~ (e1 = e0)
% 229.03/40.46    (37)   ~ (all_53_3 = all_53_11)
% 229.03/40.46    (38)   ~ (all_53_2 = all_53_3)
% 229.03/40.46    (39)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 229.03/40.46    (40)   ~ (all_53_7 = all_53_11)
% 229.03/40.46    (41)  all_55_8 = all_53_2
% 229.03/40.46    (42)  op(e0, e0) = e3
% 229.03/40.46    (43)  op(e0, e2) = all_53_7
% 229.03/40.46    (44)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.03/40.46              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.03/40.46                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.03/40.46                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.03/40.46    (45)   ~ (all_53_1 = all_53_13)
% 229.03/40.46    (46)  op(e2, e0) = all_53_13
% 229.03/40.46    (47)  op(e1, e3) = all_53_2
% 229.03/40.46    (48)   ~ (e2 = e1)
% 229.03/40.46    (49)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.03/40.46          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.03/40.46    (50)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 229.03/40.46    (51)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.03/40.46          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.03/40.46    (52)  all_55_14 = all_53_11
% 229.03/40.46    (53)   ~ (all_53_11 = e3)
% 229.03/40.46  
% 229.03/40.46  Begin of proof
% 229.03/40.46  | 
% 229.03/40.46  | BETA: splitting (2) gives:
% 229.03/40.46  | 
% 229.03/40.46  | Case 1:
% 229.03/40.46  | | 
% 229.03/40.46  | |   (54)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 229.03/40.46  | |           e2)
% 229.03/40.46  | | 
% 229.03/40.46  | | REF_CLOSE: (3), (4), (12), (13), (17), (18), (22), (28), (33), (36), (48),
% 229.03/40.46  | |            (54) are inconsistent by sub-proof #652.
% 229.03/40.46  | | 
% 229.03/40.46  | Case 2:
% 229.03/40.46  | | 
% 229.03/40.46  | |   (55)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 229.03/40.46  | |           e2)
% 229.03/40.46  | | 
% 229.03/40.46  | | BETA: splitting (55) gives:
% 229.03/40.46  | | 
% 229.03/40.46  | | Case 1:
% 229.03/40.46  | | | 
% 229.03/40.46  | | |   (56)  all_57_7 = e2 & op(e1, e2) = e2
% 229.03/40.46  | | | 
% 229.03/40.46  | | | ALPHA: (56) implies:
% 229.03/40.46  | | |   (57)  all_57_7 = e2
% 229.03/40.46  | | | 
% 229.03/40.46  | | | REF_CLOSE: (3), (4), (5), (8), (10), (19), (22), (23), (26), (33), (36),
% 229.03/40.46  | | |            (44), (48), (49), (51), (57) are inconsistent by sub-proof
% 229.03/40.46  | | |            #1775.
% 229.03/40.46  | | | 
% 229.03/40.46  | | Case 2:
% 229.03/40.46  | | | 
% 229.03/40.46  | | |   (58)  all_57_13 = e2 & op(e0, e2) = e2
% 229.03/40.46  | | | 
% 229.03/40.46  | | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (10), (11), (12), (14),
% 229.03/40.46  | | |            (15), (16), (20), (21), (24), (25), (27), (28), (29), (30),
% 229.03/40.46  | | |            (31), (32), (33), (34), (35), (37), (38), (39), (40), (41),
% 229.03/40.46  | | |            (42), (43), (45), (46), (47), (50), (52), (53), (58) are
% 229.03/40.46  | | |            inconsistent by sub-proof #771.
% 229.03/40.46  | | | 
% 229.03/40.46  | | End of split
% 229.03/40.46  | | 
% 229.03/40.46  | End of split
% 229.03/40.46  | 
% 229.03/40.46  End of proof
% 229.03/40.46  
% 229.03/40.46  Sub-proof #652 shows that the following formulas are inconsistent:
% 229.03/40.46  ----------------------------------------------------------------
% 229.03/40.46    (1)   ~ (e3 = e1)
% 229.03/40.46    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.03/40.46           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.03/40.46    (3)  op(e2, e2) = e1
% 229.03/40.46    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.03/40.46         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.03/40.46    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2)
% 229.03/40.46    (6)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.03/40.46         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.03/40.46    (7)  all_57_4 = e3
% 229.03/40.46    (8)   ~ (e3 = e0)
% 229.03/40.46    (9)  op(e3, e3) = e2
% 229.03/40.46    (10)   ~ (e2 = e0)
% 229.03/40.46    (11)   ~ (e1 = e0)
% 229.03/40.46    (12)   ~ (e2 = e1)
% 229.03/40.46  
% 229.03/40.46  Begin of proof
% 229.03/40.46  | 
% 229.03/40.46  | BETA: splitting (5) gives:
% 229.03/40.46  | 
% 229.03/40.46  | Case 1:
% 229.03/40.46  | | 
% 229.03/40.46  | |   (13)  all_57_1 = e2 & op(e3, e2) = e2
% 229.03/40.46  | | 
% 229.03/40.46  | | ALPHA: (13) implies:
% 229.03/40.46  | |   (14)  all_57_1 = e2
% 229.03/40.46  | | 
% 229.03/40.46  | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (9), (10), (11), (12), (14) are
% 229.03/40.46  | |            inconsistent by sub-proof #1659.
% 229.03/40.46  | | 
% 229.03/40.46  | Case 2:
% 229.03/40.46  | | 
% 229.03/40.46  | |   (15)  all_57_3 = e2 & op(e2, e2) = e2
% 229.03/40.46  | | 
% 229.03/40.46  | | ALPHA: (15) implies:
% 229.03/40.46  | |   (16)  op(e2, e2) = e2
% 229.03/40.46  | | 
% 229.03/40.46  | | REF_CLOSE: (2), (3), (12), (16) are inconsistent by sub-proof #2306.
% 229.03/40.46  | | 
% 229.03/40.46  | End of split
% 229.03/40.46  | 
% 229.03/40.46  End of proof
% 229.03/40.46  
% 229.03/40.46  Sub-proof #653 shows that the following formulas are inconsistent:
% 229.03/40.46  ----------------------------------------------------------------
% 229.03/40.46    (1)  all_57_9 = e2
% 229.03/40.46    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.03/40.46         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.03/40.46    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.03/40.46         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.03/40.46    (4)   ~ (e3 = e1)
% 229.03/40.46    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.03/40.46           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.03/40.46    (6)   ~ (all_6_2 = e3)
% 229.03/40.46    (7)  op(e1, e1) = all_6_2
% 229.03/40.46    (8)  op(e2, e2) = e1
% 229.03/40.46    (9)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.03/40.46         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.03/40.46    (10)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.03/40.46          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.03/40.46    (11)   ~ (e3 = e2)
% 229.03/40.46    (12)   ~ (e3 = e0)
% 229.03/40.46    (13)  all_57_15 = e3
% 229.03/40.46    (14)  op(e3, e3) = e2
% 229.03/40.46    (15)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.03/40.46          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.03/40.46            e1)
% 229.03/40.46    (16)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.03/40.46          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.03/40.46    (17)   ~ (e2 = e0)
% 229.03/40.46    (18)  all_57_3 = e1
% 229.03/40.46    (19)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.03/40.46          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.03/40.46    (20)   ~ (e1 = e0)
% 229.03/40.46    (21)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.03/40.46          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.03/40.46    (22)  op(e0, e0) = e3
% 229.03/40.46    (23)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.03/40.46          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.03/40.46            e2)
% 229.03/40.46    (24)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.03/40.46              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.03/40.46                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.03/40.46                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.03/40.46    (25)   ~ (all_53_12 = e3)
% 229.03/40.46    (26)  all_57_7 = e3
% 229.03/40.46    (27)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.03/40.46          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.03/40.46    (28)  all_57_11 = e1
% 229.03/40.46    (29)   ~ (e2 = e1)
% 229.03/40.46    (30)  op(e3, e0) = all_53_12
% 229.03/40.46  
% 229.03/40.46  Begin of proof
% 229.03/40.46  | 
% 229.03/40.46  | BETA: splitting (9) gives:
% 229.03/40.46  | 
% 229.03/40.46  | Case 1:
% 229.03/40.46  | | 
% 229.03/40.46  | |   (31)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) =
% 229.03/40.46  | |           e1)
% 229.03/40.46  | | 
% 229.03/40.46  | | REF_CLOSE: (3), (5), (8), (11), (12), (14), (16), (17), (20), (26), (29),
% 229.03/40.46  | |            (31) are inconsistent by sub-proof #668.
% 229.03/40.46  | | 
% 229.03/40.46  | Case 2:
% 229.03/40.46  | | 
% 229.03/40.46  | |   (32)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) =
% 229.03/40.46  | |           e1)
% 229.03/40.46  | | 
% 229.03/40.46  | | BETA: splitting (32) gives:
% 229.03/40.46  | | 
% 229.03/40.46  | | Case 1:
% 229.03/40.46  | | | 
% 229.03/40.46  | | |   (33)  all_57_4 = e1 & op(e3, e1) = e1
% 229.03/40.46  | | | 
% 229.03/40.46  | | | ALPHA: (33) implies:
% 229.03/40.46  | | |   (34)  all_57_4 = e1
% 229.03/40.46  | | | 
% 229.03/40.46  | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (10), (11), (12), (13), (14),
% 229.03/40.46  | | |            (15), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 229.03/40.46  | | |            (27), (28), (29), (30), (34) are inconsistent by sub-proof
% 229.03/40.46  | | |            #735.
% 229.03/40.46  | | | 
% 229.03/40.46  | | Case 2:
% 229.03/40.46  | | | 
% 229.03/40.46  | | |   (35)  all_57_9 = e1 & op(e3, e0) = e1
% 229.03/40.46  | | | 
% 229.03/40.46  | | | ALPHA: (35) implies:
% 229.03/40.46  | | |   (36)  all_57_9 = e1
% 229.03/40.46  | | | 
% 229.03/40.46  | | | REF_CLOSE: (1), (29), (36) are inconsistent by sub-proof #2444.
% 229.03/40.46  | | | 
% 229.03/40.46  | | End of split
% 229.03/40.46  | | 
% 229.03/40.46  | End of split
% 229.03/40.46  | 
% 229.03/40.46  End of proof
% 229.03/40.46  
% 229.03/40.46  Sub-proof #654 shows that the following formulas are inconsistent:
% 229.03/40.46  ----------------------------------------------------------------
% 229.03/40.46    (1)   ~ (e3 = e1)
% 229.03/40.46    (2)  all_57_6 = e0
% 229.03/40.46    (3)   ~ (e1 = e0)
% 229.03/40.46    (4)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1)
% 229.03/40.46    (5)  all_57_7 = e3
% 229.03/40.46  
% 229.03/40.46  Begin of proof
% 229.03/40.46  | 
% 229.03/40.46  | BETA: splitting (4) gives:
% 229.03/40.46  | 
% 229.03/40.46  | Case 1:
% 229.03/40.46  | | 
% 229.03/40.46  | |   (6)  all_57_6 = e1 & op(e1, e3) = e1
% 229.03/40.46  | | 
% 229.03/40.46  | | ALPHA: (6) implies:
% 229.03/40.46  | |   (7)  all_57_6 = e1
% 229.03/40.46  | | 
% 229.03/40.46  | | REF_CLOSE: (2), (3), (7) are inconsistent by sub-proof #2227.
% 229.03/40.46  | | 
% 229.03/40.46  | Case 2:
% 229.03/40.46  | | 
% 229.03/40.46  | |   (8)  all_57_7 = e1 & op(e1, e2) = e1
% 229.03/40.46  | | 
% 229.03/40.46  | | REF_CLOSE: (1), (5), (8) are inconsistent by sub-proof #2104.
% 229.03/40.46  | | 
% 229.03/40.46  | End of split
% 229.03/40.46  | 
% 229.03/40.46  End of proof
% 229.03/40.46  
% 229.03/40.46  Sub-proof #655 shows that the following formulas are inconsistent:
% 229.03/40.46  ----------------------------------------------------------------
% 229.03/40.46    (1)   ~ (all_53_2 = e2)
% 229.03/40.46    (2)  all_57_0 = e2
% 229.03/40.46    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.03/40.46         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.03/40.46    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.03/40.46         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.03/40.46    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.03/40.46         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.03/40.46    (6)   ~ (e3 = e1)
% 229.03/40.46    (7)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 229.03/40.46         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 229.03/40.47    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.03/40.47           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.03/40.47    (9)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.03/40.47         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.03/40.47    (10)   ~ (all_53_3 = e3)
% 229.03/40.47    (11)   ~ (all_53_3 = all_53_7)
% 229.03/40.47    (12)   ~ (all_6_2 = e3)
% 229.03/40.47    (13)   ~ (all_53_9 = e1)
% 229.03/40.47    (14)  op(e1, e1) = all_6_2
% 229.03/40.47    (15)   ~ (all_53_1 = all_53_9)
% 229.03/40.47    (16)  op(e2, e2) = e1
% 229.03/40.47    (17)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.03/40.47          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.03/40.47    (18)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 229.03/40.47            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 229.03/40.47              e3) = all_22_1 & $i(all_22_1))
% 229.03/40.47    (19)   ~ (all_53_13 = e3)
% 229.03/40.47    (20)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.03/40.47          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.03/40.47    (21)   ~ (all_53_9 = all_53_11)
% 229.03/40.47    (22)  all_55_4 = all_53_1
% 229.03/40.47    (23)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.03/40.47          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.03/40.47    (24)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 229.03/40.47          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.03/40.47    (25)   ~ (e3 = e2)
% 229.03/40.47    (26)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 229.03/40.47    (27)   ~ (all_53_1 = all_53_3)
% 229.03/40.47    (28)   ~ (e3 = e0)
% 229.03/40.47    (29)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 229.03/40.47          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 229.03/40.47    (30)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 229.03/40.47    (31)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 229.03/40.47    (32)  all_57_15 = e3
% 229.03/40.47    (33)   ~ (all_53_9 = all_53_13)
% 229.03/40.47    (34)  op(e3, e3) = e2
% 229.03/40.47    (35)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.03/40.47          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.03/40.47            e1)
% 229.03/40.47    (36)   ~ (all_53_1 = e1)
% 229.03/40.47    (37)  all_55_6 = all_53_9
% 229.03/40.47    (38)   ~ (all_53_1 = all_53_2)
% 229.03/40.47    (39)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.03/40.47          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.03/40.47    (40)   ~ (e2 = e0)
% 229.03/40.47    (41)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 229.03/40.47            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 229.03/40.47            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 229.03/40.47            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 229.03/40.47              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 229.03/40.47            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 229.03/40.47            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 229.03/40.47              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 229.03/40.47              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 229.03/40.47            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 229.03/40.47            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 229.03/40.47            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 229.03/40.47              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 229.03/40.47              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 229.03/40.47            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 229.03/40.47              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 229.03/40.47            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 229.03/40.47            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 229.03/40.47              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 229.03/40.47              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 229.03/40.47            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 229.03/40.47            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 229.03/40.47    (42)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 229.03/40.47            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 229.03/40.47              e3) = all_12_1 & $i(all_12_1))
% 229.03/40.47    (43)  all_55_12 = all_53_3
% 229.03/40.47    (44)  all_57_3 = e1
% 229.03/40.47    (45)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.03/40.47          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.03/40.47    (46)   ~ (e1 = e0)
% 229.03/40.47    (47)   ~ (all_53_3 = all_53_11)
% 229.03/40.47    (48)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.03/40.47          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.03/40.47    (49)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.03/40.47          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.03/40.47    (50)   ~ (all_53_2 = all_53_3)
% 229.03/40.47    (51)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 229.03/40.47    (52)   ~ (all_53_7 = all_53_11)
% 229.03/40.47    (53)  all_55_8 = all_53_2
% 229.03/40.47    (54)  op(e0, e0) = e3
% 229.03/40.47    (55)  op(e0, e2) = all_53_7
% 229.03/40.47    (56)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.03/40.47          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.03/40.47            e2)
% 229.03/40.47    (57)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.03/40.47              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.03/40.47                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.03/40.47                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.03/40.47    (58)  op(e1, e1) = e2
% 229.03/40.47    (59)   ~ (all_53_1 = all_53_13)
% 229.03/40.47    (60)  op(e2, e0) = all_53_13
% 229.03/40.47    (61)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.03/40.47          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.03/40.47    (62)   ~ (all_53_12 = e3)
% 229.03/40.47    (63)  op(e1, e3) = all_53_2
% 229.03/40.47    (64)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.03/40.47          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.03/40.47    (65)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.03/40.47          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.03/40.47    (66)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.03/40.47          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 229.03/40.47    (67)   ~ (e2 = e1)
% 229.03/40.47    (68)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.03/40.47          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.03/40.47    (69)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.03/40.47          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.03/40.47    (70)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 229.03/40.47    (71)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 229.03/40.47          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 229.03/40.47    (72)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.03/40.47          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.03/40.47    (73)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.03/40.47          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.03/40.47    (74)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 229.03/40.47          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 229.03/40.47    (75)  all_55_14 = all_53_11
% 229.03/40.47    (76)   ~ (all_53_11 = e3)
% 229.03/40.47    (77)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.03/40.47          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.03/40.47    (78)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 229.03/40.47          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 229.03/40.47    (79)  op(e3, e0) = all_53_12
% 229.03/40.47  
% 229.03/40.47  Begin of proof
% 229.03/40.47  | 
% 229.03/40.47  | BETA: splitting (68) gives:
% 229.03/40.47  | 
% 229.03/40.47  | Case 1:
% 229.03/40.47  | | 
% 229.03/40.47  | |   (80)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 229.03/40.47  | |           e2)
% 229.03/40.47  | | 
% 229.03/40.47  | | BETA: splitting (80) gives:
% 229.03/40.47  | | 
% 229.03/40.47  | | Case 1:
% 229.03/40.47  | | | 
% 229.03/40.47  | | |   (81)  all_57_9 = e2 & op(e3, e0) = e2
% 229.03/40.47  | | | 
% 229.03/40.47  | | | ALPHA: (81) implies:
% 229.03/40.47  | | |   (82)  all_57_9 = e2
% 229.03/40.47  | | | 
% 229.03/40.47  | | | BETA: splitting (56) gives:
% 229.03/40.47  | | | 
% 229.03/40.47  | | | Case 1:
% 229.03/40.47  | | | | 
% 229.03/40.47  | | | |   (83)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0,
% 229.03/40.47  | | | |             e2) = e2)
% 229.03/40.47  | | | | 
% 229.03/40.47  | | | | BETA: splitting (83) gives:
% 229.03/40.47  | | | | 
% 229.03/40.47  | | | | Case 1:
% 229.03/40.47  | | | | | 
% 229.03/40.47  | | | | |   (84)  all_57_12 = e2 & op(e0, e3) = e2
% 229.03/40.47  | | | | | 
% 229.03/40.47  | | | | | ALPHA: (84) implies:
% 229.03/40.47  | | | | |   (85)  all_57_12 = e2
% 229.03/40.47  | | | | | 
% 229.03/40.47  | | | | | BETA: splitting (4) gives:
% 229.03/40.47  | | | | | 
% 229.03/40.47  | | | | | Case 1:
% 229.03/40.47  | | | | | | 
% 229.03/40.47  | | | | | |   (86)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2,
% 229.03/40.47  | | | | | |             e3) = e1)
% 229.03/40.47  | | | | | | 
% 229.03/40.47  | | | | | | BETA: splitting (86) gives:
% 229.03/40.47  | | | | | | 
% 229.03/40.47  | | | | | | Case 1:
% 229.03/40.47  | | | | | | | 
% 229.03/40.47  | | | | | | |   (87)  all_57_0 = e1 & op(e3, e3) = e1
% 229.03/40.47  | | | | | | | 
% 229.03/40.47  | | | | | | | ALPHA: (87) implies:
% 229.03/40.47  | | | | | | |   (88)  op(e3, e3) = e1
% 229.03/40.47  | | | | | | | 
% 229.03/40.47  | | | | | | | REF_CLOSE: (8), (34), (67), (88) are inconsistent by sub-proof
% 229.03/40.47  | | | | | | |            #1950.
% 229.03/40.47  | | | | | | | 
% 229.03/40.47  | | | | | | Case 2:
% 229.03/40.47  | | | | | | | 
% 229.03/40.47  | | | | | | |   (89)  all_57_2 = e1 & op(e2, e3) = e1
% 229.03/40.47  | | | | | | | 
% 229.03/40.47  | | | | | | | ALPHA: (89) implies:
% 229.03/40.47  | | | | | | |   (90)  all_57_2 = e1
% 229.03/40.47  | | | | | | | 
% 229.03/40.47  | | | | | | | BETA: splitting (61) gives:
% 229.03/40.47  | | | | | | | 
% 229.03/40.47  | | | | | | | Case 1:
% 229.03/40.47  | | | | | | | | 
% 229.03/40.47  | | | | | | | |   (91)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 &
% 229.03/40.47  | | | | | | | |           op(e2, e2) = e3)
% 229.03/40.47  | | | | | | | | 
% 229.03/40.47  | | | | | | | | REF_CLOSE: (6), (8), (16), (90), (91) are inconsistent by
% 229.03/40.47  | | | | | | | |            sub-proof #995.
% 229.03/40.47  | | | | | | | | 
% 229.03/40.47  | | | | | | | Case 2:
% 229.03/40.47  | | | | | | | | 
% 229.03/40.47  | | | | | | | |   (92)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 &
% 229.03/40.47  | | | | | | | |           op(e2, e0) = e3)
% 229.03/40.47  | | | | | | | | 
% 229.03/40.47  | | | | | | | | BETA: splitting (92) gives:
% 229.03/40.47  | | | | | | | | 
% 229.03/40.47  | | | | | | | | Case 1:
% 229.03/40.47  | | | | | | | | | 
% 229.03/40.47  | | | | | | | | |   (93)  all_57_5 = e3 & op(e2, e1) = e3
% 229.03/40.47  | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | ALPHA: (93) implies:
% 229.03/40.47  | | | | | | | | |   (94)  all_57_5 = e3
% 229.03/40.47  | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | BETA: splitting (5) gives:
% 229.03/40.47  | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | Case 1:
% 229.03/40.47  | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | |   (95)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 &
% 229.03/40.47  | | | | | | | | | |           op(e2, e2) = e2)
% 229.03/40.47  | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | BETA: splitting (95) gives:
% 229.03/40.47  | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | Case 1:
% 229.03/40.47  | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | |   (96)  all_57_1 = e2 & op(e3, e2) = e2
% 229.03/40.47  | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | ALPHA: (96) implies:
% 229.03/40.47  | | | | | | | | | | |   (97)  all_57_1 = e2
% 229.03/40.47  | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | BETA: splitting (45) gives:
% 229.03/40.47  | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | Case 1:
% 229.03/40.47  | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | |   (98)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 229.03/40.47  | | | | | | | | | | | |           & op(e3, e2) = e3)
% 229.03/40.47  | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | REF_CLOSE: (8), (25), (34), (97), (98) are inconsistent by
% 229.03/40.47  | | | | | | | | | | | |            sub-proof #1663.
% 229.03/40.47  | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | Case 2:
% 229.03/40.47  | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | |   (99)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 229.03/40.47  | | | | | | | | | | | |           & op(e3, e0) = e3)
% 229.03/40.47  | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | BETA: splitting (99) gives:
% 229.03/40.47  | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | Case 1:
% 229.03/40.47  | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | |   (100)  all_57_4 = e3 & op(e3, e1) = e3
% 229.03/40.47  | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | ALPHA: (100) implies:
% 229.03/40.47  | | | | | | | | | | | | |   (101)  all_57_4 = e3
% 229.03/40.47  | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | BETA: splitting (49) gives:
% 229.03/40.47  | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | Case 1:
% 229.03/40.47  | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | |   (102)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 229.03/40.47  | | | | | | | | | | | | | |            & op(e2, e2) = e3)
% 229.03/40.47  | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (16), (17), (20), (23), (25), (28),
% 229.03/40.47  | | | | | | | | | | | | | |            (40), (46), (67), (82), (101), (102) are
% 229.03/40.47  | | | | | | | | | | | | | |            inconsistent by sub-proof #669.
% 229.03/40.47  | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | Case 2:
% 229.03/40.47  | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | |   (103)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 229.03/40.47  | | | | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 229.03/40.47  | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | BETA: splitting (103) gives:
% 229.03/40.47  | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | Case 1:
% 229.03/40.47  | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | |   (104)  all_57_7 = e3 & op(e1, e2) = e3
% 229.03/40.47  | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | ALPHA: (104) implies:
% 229.03/40.47  | | | | | | | | | | | | | | |   (105)  all_57_7 = e3
% 229.03/40.47  | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | BETA: splitting (17) gives:
% 229.03/40.47  | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | Case 1:
% 229.03/40.47  | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | |   (106)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 229.03/40.47  | | | | | | | | | | | | | | | |            & op(e3, e2) = e1)
% 229.03/40.47  | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (16), (25), (28), (34), (39), (40),
% 229.03/40.47  | | | | | | | | | | | | | | | |            (46), (67), (105), (106) are inconsistent by
% 229.03/40.47  | | | | | | | | | | | | | | | |            sub-proof #668.
% 229.03/40.47  | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | Case 2:
% 229.03/40.47  | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | |   (107)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 229.03/40.47  | | | | | | | | | | | | | | | |            & op(e3, e0) = e1)
% 229.03/40.47  | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 229.03/40.47  | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | Case 1:
% 229.03/40.47  | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | |   (108)  all_57_4 = e1 & op(e3, e1) = e1
% 229.03/40.47  | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | ALPHA: (108) implies:
% 229.03/40.47  | | | | | | | | | | | | | | | | |   (109)  all_57_4 = e1
% 229.03/40.47  | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (25), (34), (45), (62), (79), (97),
% 229.03/40.47  | | | | | | | | | | | | | | | | |            (109) are inconsistent by sub-proof #1308.
% 229.03/40.47  | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | Case 2:
% 229.03/40.47  | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | |   (110)  all_57_9 = e1 & op(e3, e0) = e1
% 229.03/40.47  | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | ALPHA: (110) implies:
% 229.03/40.47  | | | | | | | | | | | | | | | | |   (111)  all_57_9 = e1
% 229.03/40.47  | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (16), (25), (28), (39), (40), (46),
% 229.03/40.47  | | | | | | | | | | | | | | | | |            (67), (82), (97), (105), (111) are inconsistent by
% 229.03/40.47  | | | | | | | | | | | | | | | | |            sub-proof #919.
% 229.03/40.47  | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | End of split
% 229.03/40.47  | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | End of split
% 229.03/40.47  | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | Case 2:
% 229.03/40.47  | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | |   (112)  all_57_13 = e3 & op(e0, e2) = e3
% 229.03/40.47  | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | ALPHA: (112) implies:
% 229.03/40.47  | | | | | | | | | | | | | | |   (113)  all_57_13 = e3
% 229.03/40.47  | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (25), (28), (32), (35), (40), (46),
% 229.03/40.47  | | | | | | | | | | | | | | |            (54), (56), (57), (67), (113) are inconsistent by
% 229.03/40.47  | | | | | | | | | | | | | | |            sub-proof #1792.
% 229.03/40.47  | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | End of split
% 229.03/40.47  | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | End of split
% 229.03/40.47  | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | Case 2:
% 229.03/40.47  | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | |   (114)  all_57_9 = e3 & op(e3, e0) = e3
% 229.03/40.47  | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | ALPHA: (114) implies:
% 229.03/40.47  | | | | | | | | | | | | |   (115)  op(e3, e0) = e3
% 229.03/40.47  | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | REF_CLOSE: (8), (62), (79), (115) are inconsistent by
% 229.03/40.47  | | | | | | | | | | | | |            sub-proof #2458.
% 229.03/40.47  | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | End of split
% 229.03/40.47  | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | End of split
% 229.03/40.47  | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | Case 2:
% 229.03/40.47  | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | |   (116)  all_57_3 = e2 & op(e2, e2) = e2
% 229.03/40.47  | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | ALPHA: (116) implies:
% 229.03/40.47  | | | | | | | | | | |   (117)  op(e2, e2) = e2
% 229.03/40.47  | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | REF_CLOSE: (8), (16), (67), (117) are inconsistent by
% 229.03/40.47  | | | | | | | | | | |            sub-proof #2306.
% 229.03/40.47  | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | End of split
% 229.03/40.47  | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | Case 2:
% 229.03/40.47  | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | |   (118)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2
% 229.03/40.47  | | | | | | | | | |            & op(e0, e2) = e2)
% 229.03/40.47  | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | BETA: splitting (118) gives:
% 229.03/40.47  | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | Case 1:
% 229.03/40.47  | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | |   (119)  all_57_7 = e2 & op(e1, e2) = e2
% 229.03/40.47  | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | ALPHA: (119) implies:
% 229.03/40.47  | | | | | | | | | | |   (120)  all_57_7 = e2
% 229.03/40.47  | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | BETA: splitting (64) gives:
% 229.03/40.47  | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | Case 1:
% 229.03/40.47  | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | |   (121)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 229.03/40.47  | | | | | | | | | | | |            & op(e2, e2) = e2)
% 229.03/40.47  | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | REF_CLOSE: (8), (16), (67), (90), (121) are inconsistent by
% 229.03/40.47  | | | | | | | | | | | |            sub-proof #1828.
% 229.03/40.47  | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | Case 2:
% 229.03/40.47  | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | |   (122)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 229.03/40.47  | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 229.03/40.47  | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | BETA: splitting (122) gives:
% 229.03/40.47  | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | Case 1:
% 229.03/40.47  | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | |   (123)  all_57_5 = e2 & op(e2, e1) = e2
% 229.03/40.47  | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | REF_CLOSE: (25), (94), (123) are inconsistent by sub-proof
% 229.03/40.47  | | | | | | | | | | | | |            #2425.
% 229.03/40.47  | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | Case 2:
% 229.03/40.47  | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | |   (124)  all_57_10 = e2 & op(e2, e0) = e2
% 229.03/40.47  | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | ALPHA: (124) implies:
% 229.03/40.47  | | | | | | | | | | | | |   (125)  all_57_10 = e2
% 229.03/40.47  | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | BETA: splitting (9) gives:
% 229.03/40.47  | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | Case 1:
% 229.03/40.47  | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | |   (126)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 229.03/40.47  | | | | | | | | | | | | | |            & op(e1, e2) = e3)
% 229.03/40.47  | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | BETA: splitting (126) gives:
% 229.03/40.47  | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | Case 1:
% 229.03/40.47  | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | |   (127)  all_57_6 = e3 & op(e1, e3) = e3
% 229.03/40.47  | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | ALPHA: (127) implies:
% 229.03/40.47  | | | | | | | | | | | | | | |   (128)  all_57_6 = e3
% 229.03/40.47  | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | BETA: splitting (17) gives:
% 229.03/40.47  | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | Case 1:
% 229.03/40.47  | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | |   (129)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 229.03/40.47  | | | | | | | | | | | | | | | |            & op(e3, e2) = e1)
% 229.03/40.47  | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (8), (16), (25), (28), (34), (39), (40),
% 229.03/40.47  | | | | | | | | | | | | | | | |            (46), (49), (67), (129) are inconsistent by
% 229.03/40.47  | | | | | | | | | | | | | | | |            sub-proof #1677.
% 229.03/40.47  | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | Case 2:
% 229.03/40.47  | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | |   (130)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 229.03/40.47  | | | | | | | | | | | | | | | |            & op(e3, e0) = e1)
% 229.03/40.47  | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | BETA: splitting (130) gives:
% 229.03/40.47  | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | Case 1:
% 229.03/40.47  | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | |   (131)  all_57_4 = e1 & op(e3, e1) = e1
% 229.03/40.47  | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | ALPHA: (131) implies:
% 229.03/40.47  | | | | | | | | | | | | | | | | |   (132)  all_57_4 = e1
% 229.03/40.47  | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | BETA: splitting (49) gives:
% 229.03/40.47  | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | Case 1:
% 229.03/40.47  | | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | |   (133)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 229.03/40.47  | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e3)
% 229.03/40.47  | | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | | BETA: splitting (133) gives:
% 229.03/40.47  | | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | | |   (134)  all_57_1 = e3 & op(e3, e2) = e3
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | ALPHA: (134) implies:
% 229.03/40.47  | | | | | | | | | | | | | | | | | | |   (135)  all_57_1 = e3
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | BETA: splitting (72) gives:
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | |   (136)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e0)
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | BETA: splitting (136) gives:
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | |   (137)  all_57_0 = e0 & op(e3, e3) = e0
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | ALPHA: (137) implies:
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | |   (138)  all_57_0 = e0
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | |   (139)  op(e3, e3) = e0
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (66) gives:
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | |   (140)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e0)
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (6), (8), (16), (25), (40), (44), (46),
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | |            (64), (67), (69), (94), (128), (138), (139), (140)
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1009.
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | |   (141)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e2, e0) = e0)
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (141) gives:
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | | |   (142)  all_57_5 = e0 & op(e2, e1) = e0
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (142) implies:
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | | |   (143)  all_57_5 = e0
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (94), (143) imply:
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | | |   (144)  e3 = e0
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (144) implies:
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | | |   (145)  e3 = e0
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (128), (145) imply:
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | | |   (146)  all_57_6 = e0
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (8), (9), (12), (14), (16), (25), (28),
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | | |            (32), (39), (40), (46), (57), (67), (68), (73),
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | | |            (77), (135), (146) are inconsistent by sub-proof
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | | |            #1773.
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | | |   (147)  all_57_10 = e0 & op(e2, e0) = e0
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (147) implies:
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | | |   (148)  all_57_10 = e0
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (125), (148) imply:
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | | |   (149)  e2 = e0
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (149) implies:
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | | |   (150)  e2 = e0
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (85), (150) imply:
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | | |   (151)  all_57_12 = e0
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (40), (67), (69), (90), (128), (138), (151)
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1426.
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | End of split
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | |   (152)  all_57_2 = e0 & op(e2, e3) = e0
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | ALPHA: (152) implies:
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | |   (153)  all_57_2 = e0
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (90), (153) imply:
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | |   (154)  e1 = e0
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (44), (154) imply:
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | |   (155)  all_57_3 = e0
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (9), (12), (14),
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | |            (25), (28), (32), (34), (35), (40), (46), (48),
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | |            (56), (57), (64), (65), (67), (68), (69), (72),
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | |            (73), (77), (85), (90), (94), (125), (128), (132),
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | |            (135), (155) are inconsistent by sub-proof #664.
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | End of split
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | |   (156)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e3) = e0)
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | BETA: splitting (156) gives:
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | |   (157)  all_57_6 = e0 & op(e1, e3) = e0
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | ALPHA: (157) implies:
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | |   (158)  all_57_6 = e0
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (8), (9), (12), (14), (16), (25), (28),
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | |            (32), (39), (40), (46), (57), (67), (68), (73),
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | |            (77), (135), (158) are inconsistent by sub-proof
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | |            #1773.
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | |   (159)  all_57_12 = e0 & op(e0, e3) = e0
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | ALPHA: (159) implies:
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | |   (160)  all_57_12 = e0
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (25), (40), (67), (69), (85), (90), (128),
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | |            (160) are inconsistent by sub-proof #1419.
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | End of split
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | End of split
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | | |   (161)  all_57_3 = e3 & op(e2, e2) = e3
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | ALPHA: (161) implies:
% 229.03/40.47  | | | | | | | | | | | | | | | | | | |   (162)  op(e2, e2) = e3
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (16), (162) are inconsistent by
% 229.03/40.47  | | | | | | | | | | | | | | | | | | |            sub-proof #1912.
% 229.03/40.47  | | | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | | End of split
% 229.03/40.47  | | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | Case 2:
% 229.03/40.47  | | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | |   (163)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 229.03/40.47  | | | | | | | | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 229.03/40.47  | | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (25), (28), (32), (35), (40), (46),
% 229.03/40.47  | | | | | | | | | | | | | | | | | |            (54), (56), (57), (67), (120), (163) are
% 229.03/40.47  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #776.
% 229.03/40.47  | | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | End of split
% 229.03/40.47  | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | Case 2:
% 229.03/40.47  | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | |   (164)  all_57_9 = e1 & op(e3, e0) = e1
% 229.03/40.47  | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | ALPHA: (164) implies:
% 229.03/40.47  | | | | | | | | | | | | | | | | |   (165)  all_57_9 = e1
% 229.03/40.47  | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | COMBINE_EQS: (82), (165) imply:
% 229.03/40.47  | | | | | | | | | | | | | | | | |   (166)  e2 = e1
% 229.03/40.47  | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | COMBINE_EQS: (125), (166) imply:
% 229.03/40.47  | | | | | | | | | | | | | | | | |   (167)  all_57_10 = e1
% 229.03/40.47  | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (5), (6), (8), (9), (12), (14), (16),
% 229.03/40.47  | | | | | | | | | | | | | | | | |            (17), (20), (23), (25), (28), (32), (34), (35),
% 229.03/40.47  | | | | | | | | | | | | | | | | |            (39), (40), (44), (45), (46), (48), (49), (54),
% 229.03/40.47  | | | | | | | | | | | | | | | | |            (56), (57), (62), (64), (65), (66), (67), (68),
% 229.03/40.47  | | | | | | | | | | | | | | | | |            (72), (73), (77), (79), (82), (167) are
% 229.03/40.47  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #805.
% 229.03/40.47  | | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | | End of split
% 229.03/40.47  | | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | End of split
% 229.03/40.47  | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | Case 2:
% 229.03/40.47  | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | |   (168)  all_57_7 = e3 & op(e1, e2) = e3
% 229.03/40.47  | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | ALPHA: (168) implies:
% 229.03/40.47  | | | | | | | | | | | | | | |   (169)  all_57_7 = e3
% 229.03/40.47  | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | | REF_CLOSE: (25), (120), (169) are inconsistent by sub-proof
% 229.03/40.47  | | | | | | | | | | | | | | |            #2102.
% 229.03/40.47  | | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | End of split
% 229.03/40.47  | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | Case 2:
% 229.03/40.47  | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | |   (170)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 229.03/40.47  | | | | | | | | | | | | | |            e3 & op(e1, e0) = e3)
% 229.03/40.47  | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (12), (14), (25), (28), (32), (40),
% 229.03/40.47  | | | | | | | | | | | | | |            (46), (57), (67), (68), (73), (170) are
% 229.03/40.47  | | | | | | | | | | | | | |            inconsistent by sub-proof #1786.
% 229.03/40.47  | | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | | End of split
% 229.03/40.47  | | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | | End of split
% 229.03/40.47  | | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | End of split
% 229.03/40.47  | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | Case 2:
% 229.03/40.47  | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | |   (171)  all_57_13 = e2 & op(e0, e2) = e2
% 229.03/40.47  | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | REF_CLOSE: (3), (4), (5), (6), (8), (9), (12), (14), (16),
% 229.03/40.47  | | | | | | | | | | |            (17), (20), (23), (25), (28), (32), (34), (35),
% 229.03/40.47  | | | | | | | | | | |            (39), (40), (44), (45), (46), (48), (49), (54),
% 229.03/40.47  | | | | | | | | | | |            (56), (57), (62), (64), (65), (66), (67), (68),
% 229.03/40.47  | | | | | | | | | | |            (72), (73), (77), (79), (82), (171) are
% 229.03/40.47  | | | | | | | | | | |            inconsistent by sub-proof #663.
% 229.03/40.47  | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | End of split
% 229.03/40.47  | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | End of split
% 229.03/40.47  | | | | | | | | | 
% 229.03/40.47  | | | | | | | | Case 2:
% 229.03/40.47  | | | | | | | | | 
% 229.03/40.47  | | | | | | | | |   (172)  all_57_10 = e3 & op(e2, e0) = e3
% 229.03/40.47  | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | ALPHA: (172) implies:
% 229.03/40.47  | | | | | | | | |   (173)  all_57_10 = e3
% 229.03/40.47  | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | REF_CLOSE: (6), (8), (25), (28), (32), (40), (46), (54), (57),
% 229.03/40.47  | | | | | | | | |            (67), (68), (73), (173) are inconsistent by
% 229.03/40.47  | | | | | | | | |            sub-proof #1746.
% 229.03/40.47  | | | | | | | | | 
% 229.03/40.47  | | | | | | | | End of split
% 229.03/40.47  | | | | | | | | 
% 229.03/40.47  | | | | | | | End of split
% 229.03/40.47  | | | | | | | 
% 229.03/40.47  | | | | | | End of split
% 229.03/40.47  | | | | | | 
% 229.03/40.47  | | | | | Case 2:
% 229.03/40.47  | | | | | | 
% 229.03/40.47  | | | | | |   (174)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 &
% 229.03/40.47  | | | | | |            op(e0, e3) = e1)
% 229.03/40.47  | | | | | | 
% 229.03/40.47  | | | | | | BETA: splitting (174) gives:
% 229.03/40.47  | | | | | | 
% 229.03/40.47  | | | | | | Case 1:
% 229.03/40.47  | | | | | | | 
% 229.03/40.47  | | | | | | |   (175)  all_57_6 = e1 & op(e1, e3) = e1
% 229.03/40.47  | | | | | | | 
% 229.03/40.47  | | | | | | | ALPHA: (175) implies:
% 229.03/40.47  | | | | | | |   (176)  all_57_6 = e1
% 229.03/40.47  | | | | | | | 
% 229.03/40.47  | | | | | | | BETA: splitting (17) gives:
% 229.03/40.47  | | | | | | | 
% 229.03/40.47  | | | | | | | Case 1:
% 229.03/40.47  | | | | | | | | 
% 229.03/40.47  | | | | | | | |   (177)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 &
% 229.03/40.47  | | | | | | | |            op(e3, e2) = e1)
% 229.03/40.47  | | | | | | | | 
% 229.03/40.47  | | | | | | | | REF_CLOSE: (5), (6), (8), (16), (25), (28), (34), (39), (40),
% 229.03/40.47  | | | | | | | |            (46), (49), (67), (177) are inconsistent by sub-proof
% 229.03/40.47  | | | | | | | |            #1677.
% 229.03/40.47  | | | | | | | | 
% 229.03/40.47  | | | | | | | Case 2:
% 229.03/40.47  | | | | | | | | 
% 229.03/40.47  | | | | | | | |   (178)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 &
% 229.03/40.47  | | | | | | | |            op(e3, e0) = e1)
% 229.03/40.47  | | | | | | | | 
% 229.03/40.47  | | | | | | | | BETA: splitting (178) gives:
% 229.03/40.47  | | | | | | | | 
% 229.03/40.47  | | | | | | | | Case 1:
% 229.03/40.47  | | | | | | | | | 
% 229.03/40.47  | | | | | | | | |   (179)  all_57_4 = e1 & op(e3, e1) = e1
% 229.03/40.47  | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | ALPHA: (179) implies:
% 229.03/40.47  | | | | | | | | |   (180)  all_57_4 = e1
% 229.03/40.47  | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | BETA: splitting (5) gives:
% 229.03/40.47  | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | Case 1:
% 229.03/40.47  | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | |   (181)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 229.03/40.47  | | | | | | | | | |            & op(e2, e2) = e2)
% 229.03/40.47  | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | REF_CLOSE: (6), (8), (16), (25), (34), (45), (62), (67),
% 229.03/40.47  | | | | | | | | | |            (79), (180), (181) are inconsistent by sub-proof
% 229.03/40.47  | | | | | | | | | |            #662.
% 229.03/40.47  | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | Case 2:
% 229.03/40.47  | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | |   (182)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2
% 229.03/40.47  | | | | | | | | | |            & op(e0, e2) = e2)
% 229.03/40.47  | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | BETA: splitting (182) gives:
% 229.03/40.47  | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | Case 1:
% 229.03/40.47  | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | |   (183)  all_57_7 = e2 & op(e1, e2) = e2
% 229.03/40.47  | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | ALPHA: (183) implies:
% 229.03/40.47  | | | | | | | | | | |   (184)  all_57_7 = e2
% 229.03/40.47  | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | BETA: splitting (45) gives:
% 229.03/40.47  | | | | | | | | | | | 
% 229.03/40.47  | | | | | | | | | | | Case 1:
% 229.03/40.47  | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | |   (185)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 229.03/40.48  | | | | | | | | | | | |            & op(e3, e2) = e3)
% 229.03/40.48  | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | BETA: splitting (185) gives:
% 229.03/40.48  | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | Case 1:
% 229.03/40.48  | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | |   (186)  all_57_0 = e3 & op(e3, e3) = e3
% 229.03/40.48  | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | ALPHA: (186) implies:
% 229.03/40.48  | | | | | | | | | | | | |   (187)  op(e3, e3) = e3
% 229.03/40.48  | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | REF_CLOSE: (8), (25), (34), (187) are inconsistent by
% 229.03/40.48  | | | | | | | | | | | | |            sub-proof #2490.
% 229.03/40.48  | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | Case 2:
% 229.03/40.48  | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | |   (188)  all_57_1 = e3 & op(e3, e2) = e3
% 229.03/40.48  | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | ALPHA: (188) implies:
% 229.03/40.48  | | | | | | | | | | | | |   (189)  all_57_1 = e3
% 229.03/40.48  | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | REF_CLOSE: (5), (6), (8), (9), (12), (14), (16), (25), (28),
% 229.03/40.48  | | | | | | | | | | | | |            (32), (34), (39), (40), (45), (46), (49), (57),
% 229.03/40.48  | | | | | | | | | | | | |            (62), (65), (67), (68), (72), (73), (77), (79),
% 229.03/40.48  | | | | | | | | | | | | |            (85), (176), (180), (184), (189) are inconsistent
% 229.03/40.48  | | | | | | | | | | | | |            by sub-proof #756.
% 229.03/40.48  | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | End of split
% 229.03/40.48  | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | Case 2:
% 229.03/40.48  | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | |   (190)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 229.03/40.48  | | | | | | | | | | | |            & op(e3, e0) = e3)
% 229.03/40.48  | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | REF_CLOSE: (6), (8), (62), (79), (180), (190) are
% 229.03/40.48  | | | | | | | | | | | |            inconsistent by sub-proof #2281.
% 229.03/40.48  | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | End of split
% 229.03/40.48  | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | Case 2:
% 229.03/40.48  | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | |   (191)  all_57_13 = e2 & op(e0, e2) = e2
% 229.03/40.48  | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | REF_CLOSE: (3), (4), (5), (6), (8), (9), (12), (14), (16),
% 229.03/40.48  | | | | | | | | | | |            (17), (20), (23), (25), (28), (32), (34), (35),
% 229.03/40.48  | | | | | | | | | | |            (39), (40), (44), (45), (46), (48), (49), (54),
% 229.03/40.48  | | | | | | | | | | |            (56), (57), (62), (64), (65), (66), (67), (68),
% 229.03/40.48  | | | | | | | | | | |            (72), (73), (77), (79), (82), (191) are
% 229.03/40.48  | | | | | | | | | | |            inconsistent by sub-proof #663.
% 229.03/40.48  | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | End of split
% 229.03/40.48  | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | End of split
% 229.03/40.48  | | | | | | | | | 
% 229.03/40.48  | | | | | | | | Case 2:
% 229.03/40.48  | | | | | | | | | 
% 229.03/40.48  | | | | | | | | |   (192)  all_57_9 = e1 & op(e3, e0) = e1
% 229.03/40.48  | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | REF_CLOSE: (67), (82), (192) are inconsistent by sub-proof
% 229.03/40.48  | | | | | | | | |            #2451.
% 229.03/40.48  | | | | | | | | | 
% 229.03/40.48  | | | | | | | | End of split
% 229.03/40.48  | | | | | | | | 
% 229.03/40.48  | | | | | | | End of split
% 229.03/40.48  | | | | | | | 
% 229.03/40.48  | | | | | | Case 2:
% 229.03/40.48  | | | | | | | 
% 229.03/40.48  | | | | | | |   (193)  all_57_12 = e1 & op(e0, e3) = e1
% 229.03/40.48  | | | | | | | 
% 229.03/40.48  | | | | | | | REF_CLOSE: (67), (85), (193) are inconsistent by sub-proof #2388.
% 229.03/40.48  | | | | | | | 
% 229.03/40.48  | | | | | | End of split
% 229.03/40.48  | | | | | | 
% 229.03/40.48  | | | | | End of split
% 229.03/40.48  | | | | | 
% 229.03/40.48  | | | | Case 2:
% 229.03/40.48  | | | | | 
% 229.03/40.48  | | | | |   (194)  all_57_13 = e2 & op(e0, e2) = e2
% 229.03/40.48  | | | | | 
% 229.03/40.48  | | | | | REF_CLOSE: (3), (4), (5), (6), (8), (9), (12), (14), (16), (17), (20),
% 229.03/40.48  | | | | |            (23), (25), (28), (32), (34), (35), (39), (40), (44), (45),
% 229.03/40.48  | | | | |            (46), (48), (49), (54), (56), (57), (62), (64), (65), (66),
% 229.03/40.48  | | | | |            (67), (68), (72), (73), (77), (79), (82), (194) are
% 229.03/40.48  | | | | |            inconsistent by sub-proof #663.
% 229.03/40.48  | | | | | 
% 229.03/40.48  | | | | End of split
% 229.03/40.48  | | | | 
% 229.03/40.48  | | | Case 2:
% 229.03/40.48  | | | | 
% 229.03/40.48  | | | |   (195)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0,
% 229.03/40.48  | | | |              e0) = e2)
% 229.03/40.48  | | | | 
% 229.03/40.48  | | | | BETA: splitting (195) gives:
% 229.03/40.48  | | | | 
% 229.03/40.48  | | | | Case 1:
% 229.03/40.48  | | | | | 
% 229.03/40.48  | | | | |   (196)  all_57_14 = e2 & op(e0, e1) = e2
% 229.03/40.48  | | | | | 
% 229.03/40.48  | | | | | ALPHA: (196) implies:
% 229.03/40.48  | | | | |   (197)  all_57_14 = e2
% 229.03/40.48  | | | | | 
% 229.03/40.48  | | | | | BETA: splitting (35) gives:
% 229.03/40.48  | | | | | 
% 229.03/40.48  | | | | | Case 1:
% 229.03/40.48  | | | | | | 
% 229.03/40.48  | | | | | |   (198)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 &
% 229.03/40.48  | | | | | |            op(e0, e2) = e1)
% 229.03/40.48  | | | | | | 
% 229.03/40.48  | | | | | | BETA: splitting (198) gives:
% 229.03/40.48  | | | | | | 
% 229.03/40.48  | | | | | | Case 1:
% 229.03/40.48  | | | | | | | 
% 229.03/40.48  | | | | | | |   (199)  all_57_12 = e1 & op(e0, e3) = e1
% 229.03/40.48  | | | | | | | 
% 229.03/40.48  | | | | | | | ALPHA: (199) implies:
% 229.03/40.48  | | | | | | |   (200)  all_57_12 = e1
% 229.03/40.48  | | | | | | |   (201)  op(e0, e3) = e1
% 229.03/40.48  | | | | | | | 
% 229.03/40.48  | | | | | | | BETA: splitting (64) gives:
% 229.03/40.48  | | | | | | | 
% 229.03/40.48  | | | | | | | Case 1:
% 229.03/40.48  | | | | | | | | 
% 229.03/40.48  | | | | | | | |   (202)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 &
% 229.03/40.48  | | | | | | | |            op(e2, e2) = e2)
% 229.03/40.48  | | | | | | | | 
% 229.03/40.48  | | | | | | | | BETA: splitting (202) gives:
% 229.03/40.48  | | | | | | | | 
% 229.03/40.48  | | | | | | | | Case 1:
% 229.03/40.48  | | | | | | | | | 
% 229.03/40.48  | | | | | | | | |   (203)  all_57_2 = e2 & op(e2, e3) = e2
% 229.03/40.48  | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | ALPHA: (203) implies:
% 229.03/40.48  | | | | | | | | |   (204)  all_57_2 = e2
% 229.03/40.48  | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (9), (12), (14),
% 229.03/40.48  | | | | | | | | |            (16), (17), (18), (23), (25), (28), (29), (32),
% 229.03/40.48  | | | | | | | | |            (34), (35), (39), (40), (42), (44), (45), (46),
% 229.03/40.48  | | | | | | | | |            (48), (49), (54), (56), (57), (58), (61), (62),
% 229.03/40.48  | | | | | | | | |            (64), (65), (66), (67), (68), (69), (72), (73),
% 229.03/40.48  | | | | | | | | |            (77), (79), (82), (197), (200), (201), (204) are
% 229.03/40.48  | | | | | | | | |            inconsistent by sub-proof #659.
% 229.03/40.48  | | | | | | | | | 
% 229.03/40.48  | | | | | | | | Case 2:
% 229.03/40.48  | | | | | | | | | 
% 229.03/40.48  | | | | | | | | |   (205)  all_57_3 = e2 & op(e2, e2) = e2
% 229.03/40.48  | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | ALPHA: (205) implies:
% 229.03/40.48  | | | | | | | | |   (206)  op(e2, e2) = e2
% 229.03/40.48  | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | REF_CLOSE: (8), (16), (67), (206) are inconsistent by
% 229.03/40.48  | | | | | | | | |            sub-proof #2306.
% 229.03/40.48  | | | | | | | | | 
% 229.03/40.48  | | | | | | | | End of split
% 229.03/40.48  | | | | | | | | 
% 229.03/40.48  | | | | | | | Case 2:
% 229.03/40.48  | | | | | | | | 
% 229.03/40.48  | | | | | | | |   (207)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 &
% 229.03/40.48  | | | | | | | |            op(e2, e0) = e2)
% 229.03/40.48  | | | | | | | | 
% 229.03/40.48  | | | | | | | | BETA: splitting (207) gives:
% 229.03/40.48  | | | | | | | | 
% 229.03/40.48  | | | | | | | | Case 1:
% 229.03/40.48  | | | | | | | | | 
% 229.03/40.48  | | | | | | | | |   (208)  all_57_5 = e2 & op(e2, e1) = e2
% 229.03/40.48  | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | ALPHA: (208) implies:
% 229.03/40.48  | | | | | | | | |   (209)  all_57_5 = e2
% 229.03/40.48  | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | BETA: splitting (61) gives:
% 229.03/40.48  | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | Case 1:
% 229.03/40.48  | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | |   (210)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 229.03/40.48  | | | | | | | | | |            & op(e2, e2) = e3)
% 229.03/40.48  | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | BETA: splitting (210) gives:
% 229.03/40.48  | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | Case 1:
% 229.03/40.48  | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | |   (211)  all_57_2 = e3 & op(e2, e3) = e3
% 229.03/40.48  | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | ALPHA: (211) implies:
% 229.03/40.48  | | | | | | | | | | |   (212)  all_57_2 = e3
% 229.03/40.48  | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | BETA: splitting (66) gives:
% 229.03/40.48  | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | Case 1:
% 229.03/40.48  | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | |   (213)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 229.03/40.48  | | | | | | | | | | | |            & op(e2, e2) = e0)
% 229.03/40.48  | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | REF_CLOSE: (8), (16), (28), (46), (212), (213) are
% 229.03/40.48  | | | | | | | | | | | |            inconsistent by sub-proof #658.
% 229.03/40.48  | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | Case 2:
% 229.03/40.48  | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | |   (214)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 229.03/40.48  | | | | | | | | | | | |            e0 & op(e2, e0) = e0)
% 229.03/40.48  | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | BETA: splitting (214) gives:
% 229.03/40.48  | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | Case 1:
% 229.03/40.48  | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | |   (215)  all_57_5 = e0 & op(e2, e1) = e0
% 229.03/40.48  | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | REF_CLOSE: (40), (209), (215) are inconsistent by sub-proof
% 229.03/40.48  | | | | | | | | | | | | |            #2428.
% 229.03/40.48  | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | Case 2:
% 229.03/40.48  | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | |   (216)  all_57_10 = e0 & op(e2, e0) = e0
% 229.03/40.48  | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | ALPHA: (216) implies:
% 229.03/40.48  | | | | | | | | | | | | |   (217)  all_57_10 = e0
% 229.03/40.48  | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | BETA: splitting (5) gives:
% 229.03/40.48  | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | Case 1:
% 229.03/40.48  | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | |   (218)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 229.03/40.48  | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 229.03/40.48  | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 229.03/40.48  | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | Case 1:
% 229.03/40.48  | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | |   (219)  all_57_1 = e2 & op(e3, e2) = e2
% 229.03/40.48  | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | ALPHA: (219) implies:
% 229.03/40.48  | | | | | | | | | | | | | | |   (220)  all_57_1 = e2
% 229.03/40.48  | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | BETA: splitting (48) gives:
% 229.03/40.48  | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | Case 1:
% 229.03/40.48  | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | |   (221)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 229.03/40.48  | | | | | | | | | | | | | | | |            & op(e2, e1) = e3)
% 229.03/40.48  | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 229.03/40.48  | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | Case 1:
% 229.03/40.48  | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | |   (222)  all_57_4 = e3 & op(e3, e1) = e3
% 229.03/40.48  | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | ALPHA: (222) implies:
% 229.03/40.48  | | | | | | | | | | | | | | | | |   (223)  all_57_4 = e3
% 229.03/40.48  | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | BETA: splitting (49) gives:
% 229.03/40.48  | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | Case 1:
% 229.03/40.48  | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | |   (224)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 229.03/40.48  | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e3)
% 229.03/40.48  | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (16), (17), (20), (23), (25), (28),
% 229.03/40.48  | | | | | | | | | | | | | | | | | |            (40), (46), (67), (82), (223), (224) are
% 229.03/40.48  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #669.
% 229.03/40.48  | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | Case 2:
% 229.03/40.48  | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | |   (225)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 229.03/40.48  | | | | | | | | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 229.03/40.48  | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 229.03/40.48  | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | |   (226)  all_57_7 = e3 & op(e1, e2) = e3
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | ALPHA: (226) implies:
% 229.03/40.48  | | | | | | | | | | | | | | | | | | |   (227)  all_57_7 = e3
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | BETA: splitting (72) gives:
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | |   (228)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e0)
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (28), (34), (40), (212), (228) are
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #758.
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | |   (229)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e3) = e0)
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | |   (230)  all_57_6 = e0 & op(e1, e3) = e0
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | ALPHA: (230) implies:
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | |   (231)  all_57_6 = e0
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (23) gives:
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | |   (232)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e0)
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | | |   (233)  all_57_0 = e0 & op(e3, e3) = e0
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (233) implies:
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | | |   (234)  op(e3, e3) = e0
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (12), (14), (25), (28), (32), (40),
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | | |            (46), (57), (65), (67), (68), (69), (73), (200),
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | | |            (227), (231), (234) are inconsistent by sub-proof
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | | |            #1029.
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | | |   (235)  all_57_1 = e0 & op(e3, e2) = e0
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (235) implies:
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | | |   (236)  all_57_1 = e0
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (220), (236) imply:
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | | |   (237)  e2 = e0
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (82), (237) imply:
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | | |   (238)  all_57_9 = e0
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (17), (34), (46), (67), (220), (223),
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | | |            (238) are inconsistent by sub-proof #1661.
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | |   (239)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e0)
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (17), (28), (34), (46), (67), (220),
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | |            (223), (239) are inconsistent by sub-proof #1660.
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | End of split
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | |   (240)  all_57_12 = e0 & op(e0, e3) = e0
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | ALPHA: (240) implies:
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | |   (241)  all_57_12 = e0
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (200), (241) imply:
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | |   (242)  e1 = e0
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (44), (242) imply:
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | |   (243)  all_57_3 = e0
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (8), (17), (23), (25), (28), (34), (40),
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | |            (45), (46), (62), (67), (77), (79), (220), (227),
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | |            (243) are inconsistent by sub-proof #787.
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | End of split
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | End of split
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | |   (244)  all_57_13 = e3 & op(e0, e2) = e3
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | ALPHA: (244) implies:
% 229.03/40.48  | | | | | | | | | | | | | | | | | | |   (245)  all_57_13 = e3
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (28), (32), (35), (40), (46), (54),
% 229.03/40.48  | | | | | | | | | | | | | | | | | | |            (57), (67), (197), (245) are inconsistent by
% 229.03/40.48  | | | | | | | | | | | | | | | | | | |            sub-proof #2212.
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | End of split
% 229.03/40.48  | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | End of split
% 229.03/40.48  | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | Case 2:
% 229.03/40.48  | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | |   (246)  all_57_5 = e3 & op(e2, e1) = e3
% 229.03/40.48  | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | ALPHA: (246) implies:
% 229.03/40.48  | | | | | | | | | | | | | | | | |   (247)  all_57_5 = e3
% 229.03/40.48  | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (16), (25), (40), (64), (67), (212), (217),
% 229.03/40.48  | | | | | | | | | | | | | | | | |            (247) are inconsistent by sub-proof #1797.
% 229.03/40.48  | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | End of split
% 229.03/40.48  | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | Case 2:
% 229.03/40.48  | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | |   (248)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 229.03/40.48  | | | | | | | | | | | | | | | |            e3 & op(e0, e1) = e3)
% 229.03/40.48  | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (12), (14), (25), (28), (32), (35),
% 229.03/40.48  | | | | | | | | | | | | | | | |            (40), (46), (56), (57), (67), (248) are
% 229.03/40.48  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1794.
% 229.03/40.48  | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | End of split
% 229.03/40.48  | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | Case 2:
% 229.03/40.48  | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | |   (249)  all_57_3 = e2 & op(e2, e2) = e2
% 229.03/40.48  | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | ALPHA: (249) implies:
% 229.03/40.48  | | | | | | | | | | | | | | |   (250)  op(e2, e2) = e2
% 229.03/40.48  | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | REF_CLOSE: (8), (16), (67), (250) are inconsistent by
% 229.03/40.48  | | | | | | | | | | | | | | |            sub-proof #2306.
% 229.03/40.48  | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | End of split
% 229.03/40.48  | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | Case 2:
% 229.03/40.48  | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | |   (251)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 229.03/40.48  | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 229.03/40.48  | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | BETA: splitting (251) gives:
% 229.03/40.48  | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | Case 1:
% 229.03/40.48  | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | |   (252)  all_57_7 = e2 & op(e1, e2) = e2
% 229.03/40.48  | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | ALPHA: (252) implies:
% 229.03/40.48  | | | | | | | | | | | | | | |   (253)  all_57_7 = e2
% 229.03/40.48  | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | BETA: splitting (48) gives:
% 229.03/40.48  | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | Case 1:
% 229.03/40.48  | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | |   (254)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 229.03/40.48  | | | | | | | | | | | | | | | |            & op(e2, e1) = e3)
% 229.03/40.48  | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | BETA: splitting (254) gives:
% 229.03/40.48  | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | Case 1:
% 229.03/40.48  | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | |   (255)  all_57_4 = e3 & op(e3, e1) = e3
% 229.03/40.48  | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | ALPHA: (255) implies:
% 229.03/40.48  | | | | | | | | | | | | | | | | |   (256)  all_57_4 = e3
% 229.03/40.48  | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | BETA: splitting (49) gives:
% 229.03/40.48  | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | Case 1:
% 229.03/40.48  | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | |   (257)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 229.03/40.48  | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e3)
% 229.03/40.48  | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (16), (17), (20), (23), (25), (28),
% 229.03/40.48  | | | | | | | | | | | | | | | | | |            (40), (46), (67), (82), (256), (257) are
% 229.03/40.48  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #669.
% 229.03/40.48  | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | Case 2:
% 229.03/40.48  | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | |   (258)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 229.03/40.48  | | | | | | | | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 229.03/40.48  | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | BETA: splitting (258) gives:
% 229.03/40.48  | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | |   (259)  all_57_7 = e3 & op(e1, e2) = e3
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | ALPHA: (259) implies:
% 229.03/40.48  | | | | | | | | | | | | | | | | | | |   (260)  all_57_7 = e3
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (253), (260) imply:
% 229.03/40.48  | | | | | | | | | | | | | | | | | | |   (261)  e3 = e2
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | SIMP: (261) implies:
% 229.03/40.48  | | | | | | | | | | | | | | | | | | |   (262)  e3 = e2
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (212), (262) imply:
% 229.03/40.48  | | | | | | | | | | | | | | | | | | |   (263)  all_57_2 = e2
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (9), (12), (14),
% 229.03/40.48  | | | | | | | | | | | | | | | | | | |            (16), (17), (18), (23), (25), (28), (29), (32),
% 229.03/40.48  | | | | | | | | | | | | | | | | | | |            (34), (35), (39), (40), (42), (44), (45), (46),
% 229.03/40.48  | | | | | | | | | | | | | | | | | | |            (48), (49), (54), (56), (57), (58), (61), (62),
% 229.03/40.48  | | | | | | | | | | | | | | | | | | |            (64), (65), (66), (67), (68), (69), (72), (73),
% 229.03/40.48  | | | | | | | | | | | | | | | | | | |            (77), (79), (82), (197), (200), (201), (263) are
% 229.03/40.48  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #659.
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | |   (264)  all_57_13 = e3 & op(e0, e2) = e3
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | ALPHA: (264) implies:
% 229.03/40.48  | | | | | | | | | | | | | | | | | | |   (265)  all_57_13 = e3
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (28), (32), (35), (40), (46), (54),
% 229.03/40.48  | | | | | | | | | | | | | | | | | | |            (57), (67), (197), (265) are inconsistent by
% 229.03/40.48  | | | | | | | | | | | | | | | | | | |            sub-proof #2212.
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | End of split
% 229.03/40.48  | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | End of split
% 229.03/40.48  | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | Case 2:
% 229.03/40.48  | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | |   (266)  all_57_5 = e3 & op(e2, e1) = e3
% 229.03/40.48  | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | ALPHA: (266) implies:
% 229.03/40.48  | | | | | | | | | | | | | | | | |   (267)  all_57_5 = e3
% 229.03/40.48  | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (16), (25), (40), (64), (67), (212), (217),
% 229.03/40.48  | | | | | | | | | | | | | | | | |            (267) are inconsistent by sub-proof #1797.
% 229.03/40.48  | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | End of split
% 229.03/40.48  | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | Case 2:
% 229.03/40.48  | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | |   (268)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 229.03/40.48  | | | | | | | | | | | | | | | |            e3 & op(e0, e1) = e3)
% 229.03/40.48  | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (12), (14), (25), (28), (32), (35),
% 229.03/40.48  | | | | | | | | | | | | | | | |            (40), (46), (56), (57), (67), (268) are
% 229.03/40.48  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1794.
% 229.03/40.48  | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | End of split
% 229.03/40.48  | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | Case 2:
% 229.03/40.48  | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | |   (269)  all_57_13 = e2 & op(e0, e2) = e2
% 229.03/40.48  | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | ALPHA: (269) implies:
% 229.03/40.48  | | | | | | | | | | | | | | |   (270)  all_57_13 = e2
% 229.03/40.48  | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | REF_CLOSE: (8), (28), (40), (46), (54), (57), (197), (200),
% 229.03/40.48  | | | | | | | | | | | | | | |            (270) are inconsistent by sub-proof #1583.
% 229.03/40.48  | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | End of split
% 229.03/40.48  | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | End of split
% 229.03/40.48  | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | End of split
% 229.03/40.48  | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | End of split
% 229.03/40.48  | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | Case 2:
% 229.03/40.48  | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | |   (271)  all_57_3 = e3 & op(e2, e2) = e3
% 229.03/40.48  | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | ALPHA: (271) implies:
% 229.03/40.48  | | | | | | | | | | |   (272)  op(e2, e2) = e3
% 229.03/40.48  | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | REF_CLOSE: (6), (8), (16), (272) are inconsistent by
% 229.03/40.48  | | | | | | | | | | |            sub-proof #1912.
% 229.03/40.48  | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | End of split
% 229.03/40.48  | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | Case 2:
% 229.03/40.48  | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | |   (273)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3
% 229.03/40.48  | | | | | | | | | |            & op(e2, e0) = e3)
% 229.03/40.48  | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | REF_CLOSE: (6), (8), (25), (28), (32), (40), (46), (54),
% 229.03/40.48  | | | | | | | | | |            (57), (67), (68), (73), (209), (273) are
% 229.03/40.48  | | | | | | | | | |            inconsistent by sub-proof #1745.
% 229.03/40.48  | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | End of split
% 229.03/40.48  | | | | | | | | | 
% 229.03/40.48  | | | | | | | | Case 2:
% 229.03/40.48  | | | | | | | | | 
% 229.03/40.48  | | | | | | | | |   (274)  all_57_10 = e2 & op(e2, e0) = e2
% 229.03/40.48  | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | ALPHA: (274) implies:
% 229.03/40.48  | | | | | | | | |   (275)  all_57_10 = e2
% 229.03/40.48  | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | BETA: splitting (17) gives:
% 229.03/40.48  | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | Case 1:
% 229.03/40.48  | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | |   (276)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 229.03/40.48  | | | | | | | | | |            & op(e3, e2) = e1)
% 229.03/40.48  | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | REF_CLOSE: (5), (6), (8), (16), (25), (28), (34), (39), (40),
% 229.03/40.48  | | | | | | | | | |            (46), (49), (67), (276) are inconsistent by
% 229.03/40.48  | | | | | | | | | |            sub-proof #1677.
% 229.03/40.48  | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | Case 2:
% 229.03/40.48  | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | |   (277)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 229.03/40.48  | | | | | | | | | |            & op(e3, e0) = e1)
% 229.03/40.48  | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | BETA: splitting (277) gives:
% 229.03/40.48  | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | Case 1:
% 229.03/40.48  | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | |   (278)  all_57_4 = e1 & op(e3, e1) = e1
% 229.03/40.48  | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | ALPHA: (278) implies:
% 229.03/40.48  | | | | | | | | | | |   (279)  all_57_4 = e1
% 229.03/40.48  | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | BETA: splitting (45) gives:
% 229.03/40.48  | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | Case 1:
% 229.03/40.48  | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | |   (280)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 229.03/40.48  | | | | | | | | | | | |            & op(e3, e2) = e3)
% 229.03/40.48  | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | BETA: splitting (280) gives:
% 229.03/40.48  | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | Case 1:
% 229.03/40.48  | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | |   (281)  all_57_0 = e3 & op(e3, e3) = e3
% 229.03/40.48  | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | ALPHA: (281) implies:
% 229.03/40.48  | | | | | | | | | | | | |   (282)  op(e3, e3) = e3
% 229.03/40.48  | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | REF_CLOSE: (8), (25), (34), (282) are inconsistent by
% 229.03/40.48  | | | | | | | | | | | | |            sub-proof #2490.
% 229.03/40.48  | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | Case 2:
% 229.03/40.48  | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | |   (283)  all_57_1 = e3 & op(e3, e2) = e3
% 229.03/40.48  | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | ALPHA: (283) implies:
% 229.03/40.48  | | | | | | | | | | | | |   (284)  all_57_1 = e3
% 229.03/40.48  | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | BETA: splitting (5) gives:
% 229.03/40.48  | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | Case 1:
% 229.03/40.48  | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | |   (285)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 229.03/40.48  | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 229.03/40.48  | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | REF_CLOSE: (8), (16), (25), (67), (284), (285) are
% 229.03/40.48  | | | | | | | | | | | | | |            inconsistent by sub-proof #1768.
% 229.03/40.48  | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | Case 2:
% 229.03/40.48  | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | |   (286)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 229.03/40.48  | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 229.03/40.48  | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | BETA: splitting (286) gives:
% 229.03/40.48  | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | Case 1:
% 229.03/40.48  | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | |   (287)  all_57_7 = e2 & op(e1, e2) = e2
% 229.03/40.48  | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | ALPHA: (287) implies:
% 229.03/40.48  | | | | | | | | | | | | | | |   (288)  all_57_7 = e2
% 229.03/40.48  | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | BETA: splitting (57) gives:
% 229.03/40.48  | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | Case 1:
% 229.03/40.48  | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | |   (289)  all_57_15 = e0 & op(e0, e0) = e0
% 229.03/40.48  | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | ALPHA: (289) implies:
% 229.03/40.48  | | | | | | | | | | | | | | | |   (290)  op(e0, e0) = e0
% 229.03/40.48  | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | REF_CLOSE: (8), (28), (54), (290) are inconsistent by
% 229.03/40.48  | | | | | | | | | | | | | | | |            sub-proof #2304.
% 229.03/40.48  | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | Case 2:
% 229.03/40.48  | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | |   (291)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 229.03/40.48  | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 229.03/40.48  | | | | | | | | | | | | | | | |              op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 229.03/40.48  | | | | | | | | | | | | | | | |                e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 229.03/40.48  | | | | | | | | | | | | | | | |              e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 229.03/40.48  | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | ALPHA: (291) implies:
% 229.03/40.48  | | | | | | | | | | | | | | | |   (292)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 229.03/40.48  | | | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 229.03/40.48  | | | | | | | | | | | | | | | |              e1) = e0)
% 229.03/40.48  | | | | | | | | | | | | | | | |   (293)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 229.03/40.48  | | | | | | | | | | | | | | | |            e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 229.03/40.48  | | | | | | | | | | | | | | | |              e0) = e0)
% 229.03/40.48  | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | BETA: splitting (292) gives:
% 229.03/40.48  | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | Case 1:
% 229.03/40.48  | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | |   (294)  all_57_12 = e0 & op(e0, e3) = e0
% 229.03/40.48  | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | REF_CLOSE: (46), (200), (294) are inconsistent by sub-proof
% 229.03/40.48  | | | | | | | | | | | | | | | | |            #1279.
% 229.03/40.48  | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | Case 2:
% 229.03/40.48  | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | |   (295)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 229.03/40.48  | | | | | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 229.03/40.48  | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | BETA: splitting (295) gives:
% 229.03/40.48  | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | Case 1:
% 229.03/40.48  | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | |   (296)  all_57_13 = e0 & op(e0, e2) = e0
% 229.03/40.48  | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | ALPHA: (296) implies:
% 229.03/40.48  | | | | | | | | | | | | | | | | | |   (297)  all_57_13 = e0
% 229.03/40.48  | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | BETA: splitting (293) gives:
% 229.03/40.48  | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | |   (298)  all_57_9 = e0 & op(e3, e0) = e0
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | ALPHA: (298) implies:
% 229.03/40.48  | | | | | | | | | | | | | | | | | | |   (299)  all_57_9 = e0
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (82), (299) imply:
% 229.03/40.48  | | | | | | | | | | | | | | | | | | |   (300)  e2 = e0
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (288), (300) imply:
% 229.03/40.48  | | | | | | | | | | | | | | | | | | |   (301)  all_57_7 = e0
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (8), (16), (25), (28), (32), (35), (40),
% 229.03/40.48  | | | | | | | | | | | | | | | | | | |            (46), (49), (54), (56), (67), (292), (297), (301)
% 229.03/40.48  | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1765.
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | |   (302)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 =
% 229.03/40.48  | | | | | | | | | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | BETA: splitting (302) gives:
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | |   (303)  all_57_10 = e0 & op(e2, e0) = e0
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | ALPHA: (303) implies:
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | |   (304)  all_57_10 = e0
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (275), (304) imply:
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | |   (305)  e2 = e0
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (288), (305) imply:
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | |   (306)  all_57_7 = e0
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (8), (16), (25), (28), (32), (35), (40),
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | |            (46), (49), (54), (56), (67), (292), (297), (306)
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1765.
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | |   (307)  all_57_11 = e0 & op(e1, e0) = e0
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | ALPHA: (307) implies:
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | |   (308)  all_57_11 = e0
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | BETA: splitting (23) gives:
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | |   (309)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e0)
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (28), (34), (40), (284), (309) are
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1676.
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | |   (310)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e0)
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (310) gives:
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | |   (311)  all_57_4 = e0 & op(e3, e1) = e0
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (311) implies:
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | |   (312)  all_57_4 = e0
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (312) imply:
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | |   (313)  e1 = e0
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (44), (313) imply:
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | |   (314)  all_57_3 = e0
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (46), (67), (77), (284), (288), (297), (314)
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1759.
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | |   (315)  all_57_9 = e0 & op(e3, e0) = e0
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (315) implies:
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | |   (316)  all_57_9 = e0
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (25), (32), (40), (46), (67), (68), (73),
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | |            (308), (316) are inconsistent by sub-proof #1144.
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | End of split
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | End of split
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | End of split
% 229.03/40.48  | | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | End of split
% 229.03/40.48  | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | Case 2:
% 229.03/40.48  | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | |   (317)  all_57_14 = e0 & op(e0, e1) = e0
% 229.03/40.48  | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | | REF_CLOSE: (40), (197), (317) are inconsistent by sub-proof
% 229.03/40.48  | | | | | | | | | | | | | | | | | |            #2173.
% 229.03/40.48  | | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | | End of split
% 229.03/40.48  | | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | | End of split
% 229.03/40.48  | | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | End of split
% 229.03/40.48  | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | Case 2:
% 229.03/40.48  | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | |   (318)  all_57_13 = e2 & op(e0, e2) = e2
% 229.03/40.48  | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | ALPHA: (318) implies:
% 229.03/40.48  | | | | | | | | | | | | | | |   (319)  all_57_13 = e2
% 229.03/40.48  | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | | REF_CLOSE: (8), (28), (40), (46), (54), (57), (197), (200),
% 229.03/40.48  | | | | | | | | | | | | | | |            (319) are inconsistent by sub-proof #1583.
% 229.03/40.48  | | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | | End of split
% 229.03/40.48  | | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | | End of split
% 229.03/40.48  | | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | End of split
% 229.03/40.48  | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | Case 2:
% 229.03/40.48  | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | |   (320)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 229.03/40.48  | | | | | | | | | | | |            & op(e3, e0) = e3)
% 229.03/40.48  | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | | REF_CLOSE: (6), (8), (62), (79), (279), (320) are
% 229.03/40.48  | | | | | | | | | | | |            inconsistent by sub-proof #2281.
% 229.03/40.48  | | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | End of split
% 229.03/40.48  | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | Case 2:
% 229.03/40.48  | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | |   (321)  all_57_9 = e1 & op(e3, e0) = e1
% 229.03/40.48  | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | REF_CLOSE: (67), (82), (321) are inconsistent by sub-proof
% 229.03/40.48  | | | | | | | | | | |            #2451.
% 229.03/40.48  | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | End of split
% 229.03/40.48  | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | End of split
% 229.03/40.48  | | | | | | | | | 
% 229.03/40.48  | | | | | | | | End of split
% 229.03/40.48  | | | | | | | | 
% 229.03/40.48  | | | | | | | End of split
% 229.03/40.48  | | | | | | | 
% 229.03/40.48  | | | | | | Case 2:
% 229.03/40.48  | | | | | | | 
% 229.03/40.48  | | | | | | |   (322)  all_57_13 = e1 & op(e0, e2) = e1
% 229.03/40.48  | | | | | | | 
% 229.03/40.48  | | | | | | | ALPHA: (322) implies:
% 229.03/40.48  | | | | | | |   (323)  all_57_13 = e1
% 229.03/40.48  | | | | | | | 
% 229.03/40.48  | | | | | | | BETA: splitting (17) gives:
% 229.03/40.48  | | | | | | | 
% 229.03/40.48  | | | | | | | Case 1:
% 229.03/40.48  | | | | | | | | 
% 229.03/40.48  | | | | | | | |   (324)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 &
% 229.03/40.48  | | | | | | | |            op(e3, e2) = e1)
% 229.03/40.48  | | | | | | | | 
% 229.03/40.48  | | | | | | | | REF_CLOSE: (5), (6), (8), (16), (25), (28), (34), (39), (40),
% 229.03/40.48  | | | | | | | |            (46), (49), (67), (324) are inconsistent by sub-proof
% 229.03/40.48  | | | | | | | |            #1677.
% 229.03/40.48  | | | | | | | | 
% 229.03/40.48  | | | | | | | Case 2:
% 229.03/40.48  | | | | | | | | 
% 229.03/40.48  | | | | | | | |   (325)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 &
% 229.03/40.48  | | | | | | | |            op(e3, e0) = e1)
% 229.03/40.48  | | | | | | | | 
% 229.03/40.48  | | | | | | | | BETA: splitting (325) gives:
% 229.03/40.48  | | | | | | | | 
% 229.03/40.48  | | | | | | | | Case 1:
% 229.03/40.48  | | | | | | | | | 
% 229.03/40.48  | | | | | | | | |   (326)  all_57_4 = e1 & op(e3, e1) = e1
% 229.03/40.48  | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | ALPHA: (326) implies:
% 229.03/40.48  | | | | | | | | |   (327)  all_57_4 = e1
% 229.03/40.48  | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | BETA: splitting (45) gives:
% 229.03/40.48  | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | Case 1:
% 229.03/40.48  | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | |   (328)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 229.03/40.48  | | | | | | | | | |            & op(e3, e2) = e3)
% 229.03/40.48  | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | BETA: splitting (328) gives:
% 229.03/40.48  | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | Case 1:
% 229.03/40.48  | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | |   (329)  all_57_0 = e3 & op(e3, e3) = e3
% 229.03/40.48  | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | ALPHA: (329) implies:
% 229.03/40.48  | | | | | | | | | | |   (330)  op(e3, e3) = e3
% 229.03/40.48  | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | REF_CLOSE: (8), (25), (34), (330) are inconsistent by
% 229.03/40.48  | | | | | | | | | | |            sub-proof #2490.
% 229.03/40.48  | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | Case 2:
% 229.03/40.48  | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | |   (331)  all_57_1 = e3 & op(e3, e2) = e3
% 229.03/40.48  | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | ALPHA: (331) implies:
% 229.03/40.48  | | | | | | | | | | |   (332)  all_57_1 = e3
% 229.03/40.48  | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (9), (12), (14),
% 229.03/40.48  | | | | | | | | | | |            (16), (17), (23), (25), (28), (32), (34), (35),
% 229.03/40.48  | | | | | | | | | | |            (39), (40), (44), (45), (46), (49), (54), (56),
% 229.03/40.48  | | | | | | | | | | |            (57), (61), (62), (64), (65), (67), (68), (72),
% 229.03/40.48  | | | | | | | | | | |            (73), (77), (79), (197), (323), (332) are
% 229.03/40.48  | | | | | | | | | | |            inconsistent by sub-proof #769.
% 229.03/40.48  | | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | End of split
% 229.03/40.48  | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | Case 2:
% 229.03/40.48  | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | |   (333)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 229.03/40.48  | | | | | | | | | |            & op(e3, e0) = e3)
% 229.03/40.48  | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | | REF_CLOSE: (6), (8), (62), (79), (327), (333) are
% 229.03/40.48  | | | | | | | | | |            inconsistent by sub-proof #2281.
% 229.03/40.48  | | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | End of split
% 229.03/40.48  | | | | | | | | | 
% 229.03/40.48  | | | | | | | | Case 2:
% 229.03/40.48  | | | | | | | | | 
% 229.03/40.48  | | | | | | | | |   (334)  all_57_9 = e1 & op(e3, e0) = e1
% 229.03/40.48  | | | | | | | | | 
% 229.03/40.48  | | | | | | | | | REF_CLOSE: (67), (82), (334) are inconsistent by sub-proof
% 229.03/40.48  | | | | | | | | |            #2451.
% 229.03/40.48  | | | | | | | | | 
% 229.03/40.48  | | | | | | | | End of split
% 229.03/40.48  | | | | | | | | 
% 229.03/40.48  | | | | | | | End of split
% 229.03/40.48  | | | | | | | 
% 229.03/40.48  | | | | | | End of split
% 229.03/40.48  | | | | | | 
% 229.03/40.48  | | | | | Case 2:
% 229.03/40.48  | | | | | | 
% 229.03/40.48  | | | | | |   (335)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 &
% 229.03/40.48  | | | | | |            op(e0, e0) = e1)
% 229.03/40.48  | | | | | | 
% 229.03/40.48  | | | | | | REF_CLOSE: (6), (8), (54), (67), (197), (335) are inconsistent by
% 229.03/40.48  | | | | | |            sub-proof #1139.
% 229.03/40.48  | | | | | | 
% 229.03/40.48  | | | | | End of split
% 229.03/40.48  | | | | | 
% 229.03/40.48  | | | | Case 2:
% 229.03/40.48  | | | | | 
% 229.03/40.48  | | | | |   (336)  all_57_15 = e2 & op(e0, e0) = e2
% 229.03/40.48  | | | | | 
% 229.03/40.48  | | | | | REF_CLOSE: (25), (32), (336) are inconsistent by sub-proof #2323.
% 229.03/40.48  | | | | | 
% 229.03/40.48  | | | | End of split
% 229.03/40.48  | | | | 
% 229.03/40.48  | | | End of split
% 229.03/40.48  | | | 
% 229.03/40.48  | | Case 2:
% 229.03/40.48  | | | 
% 229.03/40.48  | | |   (337)  all_57_10 = e2 & op(e2, e0) = e2
% 229.03/40.48  | | | 
% 229.03/40.48  | | | ALPHA: (337) implies:
% 229.03/40.48  | | |   (338)  all_57_10 = e2
% 229.03/40.48  | | |   (339)  op(e2, e0) = e2
% 229.03/40.48  | | | 
% 229.03/40.48  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 229.03/40.48  | | |            (13), (14), (15), (16), (17), (18), (19), (21), (22), (23),
% 229.03/40.48  | | |            (24), (25), (26), (27), (28), (30), (31), (32), (33), (34),
% 229.03/40.48  | | |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44),
% 229.03/40.48  | | |            (45), (46), (47), (48), (49), (50), (51), (52), (53), (54),
% 229.03/40.48  | | |            (55), (56), (57), (58), (59), (60), (61), (62), (63), (64),
% 229.03/40.48  | | |            (65), (67), (68), (69), (70), (71), (72), (73), (74), (75),
% 229.03/40.48  | | |            (76), (77), (78), (79), (338), (339) are inconsistent by
% 229.03/40.48  | | |            sub-proof #718.
% 229.03/40.48  | | | 
% 229.03/40.48  | | End of split
% 229.03/40.48  | | 
% 229.03/40.48  | Case 2:
% 229.03/40.48  | | 
% 229.03/40.49  | |   (340)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.03/40.49  | |            e2)
% 229.03/40.49  | | 
% 229.03/40.49  | | BETA: splitting (340) gives:
% 229.03/40.49  | | 
% 229.03/40.49  | | Case 1:
% 229.03/40.49  | | | 
% 229.03/40.49  | | |   (341)  all_57_11 = e2 & op(e1, e0) = e2
% 229.03/40.49  | | | 
% 229.03/40.49  | | | ALPHA: (341) implies:
% 229.03/40.49  | | |   (342)  all_57_11 = e2
% 229.03/40.49  | | |   (343)  op(e1, e0) = e2
% 229.03/40.49  | | | 
% 229.03/40.49  | | | BETA: splitting (56) gives:
% 229.03/40.49  | | | 
% 229.03/40.49  | | | Case 1:
% 229.03/40.49  | | | | 
% 229.03/40.49  | | | |   (344)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0,
% 229.03/40.49  | | | |              e2) = e2)
% 229.03/40.49  | | | | 
% 229.03/40.49  | | | | BETA: splitting (344) gives:
% 229.03/40.49  | | | | 
% 229.03/40.49  | | | | Case 1:
% 229.03/40.49  | | | | | 
% 229.03/40.49  | | | | |   (345)  all_57_12 = e2 & op(e0, e3) = e2
% 229.03/40.49  | | | | | 
% 229.03/40.49  | | | | | ALPHA: (345) implies:
% 229.03/40.49  | | | | |   (346)  all_57_12 = e2
% 229.03/40.49  | | | | | 
% 229.03/40.49  | | | | | BETA: splitting (4) gives:
% 229.03/40.49  | | | | | 
% 229.03/40.49  | | | | | Case 1:
% 229.03/40.49  | | | | | | 
% 229.03/40.49  | | | | | |   (347)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2,
% 229.03/40.49  | | | | | |              e3) = e1)
% 229.03/40.49  | | | | | | 
% 229.03/40.49  | | | | | | REF_CLOSE: (2), (3), (4), (6), (8), (25), (28), (34), (40), (44),
% 229.03/40.49  | | | | | |            (46), (61), (64), (65), (67), (69), (72), (346), (347)
% 229.03/40.49  | | | | | |            are inconsistent by sub-proof #762.
% 229.03/40.49  | | | | | | 
% 229.03/40.49  | | | | | Case 2:
% 229.03/40.49  | | | | | | 
% 229.03/40.49  | | | | | |   (348)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 &
% 229.03/40.49  | | | | | |            op(e0, e3) = e1)
% 229.03/40.49  | | | | | | 
% 229.03/40.49  | | | | | | BETA: splitting (348) gives:
% 229.03/40.49  | | | | | | 
% 229.03/40.49  | | | | | | Case 1:
% 229.03/40.49  | | | | | | | 
% 229.03/40.49  | | | | | | |   (349)  all_57_6 = e1 & op(e1, e3) = e1
% 229.03/40.49  | | | | | | | 
% 229.03/40.49  | | | | | | | ALPHA: (349) implies:
% 229.03/40.49  | | | | | | |   (350)  all_57_6 = e1
% 229.03/40.49  | | | | | | | 
% 229.03/40.49  | | | | | | | BETA: splitting (5) gives:
% 229.03/40.49  | | | | | | | 
% 229.03/40.49  | | | | | | | Case 1:
% 229.03/40.49  | | | | | | | | 
% 229.03/40.49  | | | | | | | |   (351)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 &
% 229.03/40.49  | | | | | | | |            op(e2, e2) = e2)
% 229.03/40.49  | | | | | | | | 
% 229.03/40.49  | | | | | | | | REF_CLOSE: (6), (8), (16), (17), (23), (25), (28), (34), (40),
% 229.03/40.49  | | | | | | | |            (45), (46), (62), (67), (79), (351) are inconsistent
% 229.03/40.49  | | | | | | | |            by sub-proof #714.
% 229.03/40.49  | | | | | | | | 
% 229.03/40.49  | | | | | | | Case 2:
% 229.03/40.49  | | | | | | | | 
% 229.03/40.49  | | | | | | | |   (352)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 &
% 229.03/40.49  | | | | | | | |            op(e0, e2) = e2)
% 229.03/40.49  | | | | | | | | 
% 229.03/40.49  | | | | | | | | BETA: splitting (352) gives:
% 229.03/40.49  | | | | | | | | 
% 229.03/40.49  | | | | | | | | Case 1:
% 229.03/40.49  | | | | | | | | | 
% 229.03/40.49  | | | | | | | | |   (353)  all_57_7 = e2 & op(e1, e2) = e2
% 229.03/40.49  | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | ALPHA: (353) implies:
% 229.03/40.49  | | | | | | | | |   (354)  all_57_7 = e2
% 229.03/40.49  | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | BETA: splitting (64) gives:
% 229.03/40.49  | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | Case 1:
% 229.03/40.49  | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | |   (355)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 229.03/40.49  | | | | | | | | | |            & op(e2, e2) = e2)
% 229.03/40.49  | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | BETA: splitting (355) gives:
% 229.03/40.49  | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | Case 1:
% 229.03/40.49  | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | |   (356)  all_57_2 = e2 & op(e2, e3) = e2
% 229.03/40.49  | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | ALPHA: (356) implies:
% 229.03/40.49  | | | | | | | | | | |   (357)  all_57_2 = e2
% 229.03/40.49  | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | REF_CLOSE: (3), (4), (6), (8), (9), (12), (14), (16), (25),
% 229.03/40.49  | | | | | | | | | | |            (28), (32), (34), (40), (44), (46), (54), (57),
% 229.03/40.49  | | | | | | | | | | |            (61), (64), (67), (68), (72), (73), (354), (357)
% 229.03/40.49  | | | | | | | | | | |            are inconsistent by sub-proof #656.
% 229.03/40.49  | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | Case 2:
% 229.03/40.49  | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | |   (358)  all_57_3 = e2 & op(e2, e2) = e2
% 229.03/40.49  | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | ALPHA: (358) implies:
% 229.03/40.49  | | | | | | | | | | |   (359)  op(e2, e2) = e2
% 229.03/40.49  | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | REF_CLOSE: (8), (16), (67), (359) are inconsistent by
% 229.03/40.49  | | | | | | | | | | |            sub-proof #2306.
% 229.03/40.49  | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | End of split
% 229.03/40.49  | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | Case 2:
% 229.03/40.49  | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | |   (360)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2
% 229.03/40.49  | | | | | | | | | |            & op(e2, e0) = e2)
% 229.03/40.49  | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | BETA: splitting (360) gives:
% 229.03/40.49  | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | Case 1:
% 229.03/40.49  | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | |   (361)  all_57_5 = e2 & op(e2, e1) = e2
% 229.03/40.49  | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | ALPHA: (361) implies:
% 229.03/40.49  | | | | | | | | | | |   (362)  all_57_5 = e2
% 229.03/40.49  | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | BETA: splitting (48) gives:
% 229.03/40.49  | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | Case 1:
% 229.03/40.49  | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | |   (363)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 229.03/40.49  | | | | | | | | | | | |            & op(e2, e1) = e3)
% 229.03/40.49  | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | BETA: splitting (363) gives:
% 229.03/40.49  | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | Case 1:
% 229.03/40.49  | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | |   (364)  all_57_4 = e3 & op(e3, e1) = e3
% 229.03/40.49  | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | ALPHA: (364) implies:
% 229.03/40.49  | | | | | | | | | | | | |   (365)  all_57_4 = e3
% 229.03/40.49  | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | BETA: splitting (49) gives:
% 229.03/40.49  | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | Case 1:
% 229.03/40.49  | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | |   (366)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 229.03/40.49  | | | | | | | | | | | | | |            & op(e2, e2) = e3)
% 229.03/40.49  | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | BETA: splitting (366) gives:
% 229.03/40.49  | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | Case 1:
% 229.03/40.49  | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | |   (367)  all_57_1 = e3 & op(e3, e2) = e3
% 229.03/40.49  | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | ALPHA: (367) implies:
% 229.03/40.49  | | | | | | | | | | | | | | |   (368)  all_57_1 = e3
% 229.03/40.49  | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | BETA: splitting (65) gives:
% 229.03/40.49  | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | Case 1:
% 229.03/40.49  | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | |   (369)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 229.03/40.49  | | | | | | | | | | | | | | | |            & op(e2, e3) = e3)
% 229.03/40.49  | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | BETA: splitting (369) gives:
% 229.03/40.49  | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | Case 1:
% 229.03/40.49  | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | |   (370)  all_57_0 = e3 & op(e3, e3) = e3
% 229.03/40.49  | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | ALPHA: (370) implies:
% 229.03/40.49  | | | | | | | | | | | | | | | | |   (371)  op(e3, e3) = e3
% 229.03/40.49  | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (17), (20), (23), (25), (28), (40),
% 229.03/40.49  | | | | | | | | | | | | | | | | |            (46), (67), (365), (368), (371) are inconsistent
% 229.03/40.49  | | | | | | | | | | | | | | | | |            by sub-proof #1806.
% 229.03/40.49  | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | Case 2:
% 229.03/40.49  | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | |   (372)  all_57_2 = e3 & op(e2, e3) = e3
% 229.03/40.49  | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | ALPHA: (372) implies:
% 229.03/40.49  | | | | | | | | | | | | | | | | |   (373)  all_57_2 = e3
% 229.03/40.49  | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (8), (9), (12), (14), (16), (25), (28),
% 229.03/40.49  | | | | | | | | | | | | | | | | |            (32), (34), (39), (40), (46), (57), (67), (68),
% 229.03/40.49  | | | | | | | | | | | | | | | | |            (72), (73), (77), (346), (350), (354), (368),
% 229.03/40.49  | | | | | | | | | | | | | | | | |            (373) are inconsistent by sub-proof #757.
% 229.03/40.49  | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | End of split
% 229.03/40.49  | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | Case 2:
% 229.03/40.49  | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | |   (374)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 229.03/40.49  | | | | | | | | | | | | | | | |            e3 & op(e0, e3) = e3)
% 229.03/40.49  | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | BETA: splitting (374) gives:
% 229.03/40.49  | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | Case 1:
% 229.03/40.49  | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | |   (375)  all_57_6 = e3 & op(e1, e3) = e3
% 229.03/40.49  | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | ALPHA: (375) implies:
% 229.03/40.49  | | | | | | | | | | | | | | | | |   (376)  all_57_6 = e3
% 229.03/40.49  | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (8), (16), (25), (28), (39), (40), (46),
% 229.03/40.49  | | | | | | | | | | | | | | | | |            (49), (67), (350), (368), (376) are inconsistent
% 229.03/40.49  | | | | | | | | | | | | | | | | |            by sub-proof #1548.
% 229.03/40.49  | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | Case 2:
% 229.03/40.49  | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | |   (377)  all_57_12 = e3 & op(e0, e3) = e3
% 229.03/40.49  | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | ALPHA: (377) implies:
% 229.03/40.49  | | | | | | | | | | | | | | | | |   (378)  all_57_12 = e3
% 229.03/40.49  | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | COMBINE_EQS: (346), (378) imply:
% 229.03/40.49  | | | | | | | | | | | | | | | | |   (379)  e3 = e2
% 229.03/40.49  | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | SIMP: (379) implies:
% 229.03/40.49  | | | | | | | | | | | | | | | | |   (380)  e3 = e2
% 229.03/40.49  | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | COMBINE_EQS: (368), (380) imply:
% 229.03/40.49  | | | | | | | | | | | | | | | | |   (381)  all_57_1 = e2
% 229.03/40.49  | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (17), (23), (28), (34), (40), (46),
% 229.03/40.49  | | | | | | | | | | | | | | | | |            (67), (365), (381) are inconsistent by sub-proof
% 229.03/40.49  | | | | | | | | | | | | | | | | |            #1659.
% 229.03/40.49  | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | End of split
% 229.03/40.49  | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | End of split
% 229.03/40.49  | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | Case 2:
% 229.03/40.49  | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | |   (382)  all_57_3 = e3 & op(e2, e2) = e3
% 229.03/40.49  | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | ALPHA: (382) implies:
% 229.03/40.49  | | | | | | | | | | | | | | |   (383)  op(e2, e2) = e3
% 229.03/40.49  | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (16), (383) are inconsistent by
% 229.03/40.49  | | | | | | | | | | | | | | |            sub-proof #1912.
% 229.03/40.49  | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | End of split
% 229.03/40.49  | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | Case 2:
% 229.03/40.49  | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | |   (384)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 229.03/40.49  | | | | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 229.03/40.49  | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (25), (28), (32), (35), (40), (46),
% 229.03/40.49  | | | | | | | | | | | | | |            (54), (56), (57), (67), (354), (384) are
% 229.03/40.49  | | | | | | | | | | | | | |            inconsistent by sub-proof #776.
% 229.03/40.49  | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | End of split
% 229.03/40.49  | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | Case 2:
% 229.03/40.49  | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | |   (385)  all_57_5 = e3 & op(e2, e1) = e3
% 229.03/40.49  | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | ALPHA: (385) implies:
% 229.03/40.49  | | | | | | | | | | | | |   (386)  all_57_5 = e3
% 229.03/40.49  | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | REF_CLOSE: (25), (362), (386) are inconsistent by sub-proof
% 229.03/40.49  | | | | | | | | | | | | |            #2189.
% 229.03/40.49  | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | End of split
% 229.03/40.49  | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | Case 2:
% 229.03/40.49  | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | |   (387)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 229.03/40.49  | | | | | | | | | | | |            e3 & op(e0, e1) = e3)
% 229.03/40.49  | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | REF_CLOSE: (6), (8), (12), (14), (25), (28), (32), (35),
% 229.03/40.49  | | | | | | | | | | | |            (40), (46), (56), (57), (67), (387) are
% 229.03/40.49  | | | | | | | | | | | |            inconsistent by sub-proof #1794.
% 229.03/40.49  | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | End of split
% 229.03/40.49  | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | Case 2:
% 229.03/40.49  | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | |   (388)  all_57_10 = e2 & op(e2, e0) = e2
% 229.03/40.49  | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | ALPHA: (388) implies:
% 229.03/40.49  | | | | | | | | | | |   (389)  all_57_10 = e2
% 229.03/40.49  | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (12),
% 229.03/40.49  | | | | | | | | | | |            (14), (16), (17), (18), (23), (24), (25), (28),
% 229.03/40.49  | | | | | | | | | | |            (32), (34), (35), (39), (40), (42), (44), (45),
% 229.03/40.49  | | | | | | | | | | |            (46), (48), (49), (54), (56), (57), (58), (61),
% 229.03/40.49  | | | | | | | | | | |            (62), (64), (65), (67), (68), (69), (71), (72),
% 229.03/40.49  | | | | | | | | | | |            (73), (74), (77), (78), (79), (346), (389) are
% 229.03/40.49  | | | | | | | | | | |            inconsistent by sub-proof #726.
% 229.03/40.49  | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | End of split
% 229.03/40.49  | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | End of split
% 229.03/40.49  | | | | | | | | | 
% 229.03/40.49  | | | | | | | | Case 2:
% 229.03/40.49  | | | | | | | | | 
% 229.03/40.49  | | | | | | | | |   (390)  all_57_13 = e2 & op(e0, e2) = e2
% 229.03/40.49  | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | ALPHA: (390) implies:
% 229.03/40.49  | | | | | | | | |   (391)  all_57_13 = e2
% 229.03/40.49  | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | BETA: splitting (65) gives:
% 229.03/40.49  | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | Case 1:
% 229.03/40.49  | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | |   (392)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 229.03/40.49  | | | | | | | | | |            & op(e2, e3) = e3)
% 229.03/40.49  | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | BETA: splitting (392) gives:
% 229.03/40.49  | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | Case 1:
% 229.03/40.49  | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | |   (393)  all_57_0 = e3 & op(e3, e3) = e3
% 229.03/40.49  | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | ALPHA: (393) implies:
% 229.03/40.49  | | | | | | | | | | |   (394)  op(e3, e3) = e3
% 229.03/40.49  | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | REF_CLOSE: (8), (25), (34), (394) are inconsistent by
% 229.03/40.49  | | | | | | | | | | |            sub-proof #2490.
% 229.03/40.49  | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | Case 2:
% 229.03/40.49  | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | |   (395)  all_57_2 = e3 & op(e2, e3) = e3
% 229.03/40.49  | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | ALPHA: (395) implies:
% 229.03/40.49  | | | | | | | | | | |   (396)  all_57_2 = e3
% 229.03/40.49  | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | BETA: splitting (72) gives:
% 229.03/40.49  | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | Case 1:
% 229.03/40.49  | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | |   (397)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 229.03/40.49  | | | | | | | | | | | |            & op(e2, e3) = e0)
% 229.03/40.49  | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | REF_CLOSE: (8), (28), (34), (40), (396), (397) are
% 229.03/40.49  | | | | | | | | | | | |            inconsistent by sub-proof #758.
% 229.03/40.49  | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | Case 2:
% 229.03/40.49  | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | |   (398)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 229.03/40.49  | | | | | | | | | | | |            e0 & op(e0, e3) = e0)
% 229.03/40.49  | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | BETA: splitting (398) gives:
% 229.03/40.49  | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | Case 1:
% 229.03/40.49  | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | |   (399)  all_57_6 = e0 & op(e1, e3) = e0
% 229.03/40.49  | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | ALPHA: (399) implies:
% 229.03/40.49  | | | | | | | | | | | | |   (400)  all_57_6 = e0
% 229.03/40.49  | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (18), (34), (42), (46), (67),
% 229.03/40.49  | | | | | | | | | | | | |            (343), (396), (400) are inconsistent by sub-proof
% 229.03/40.49  | | | | | | | | | | | | |            #752.
% 229.03/40.49  | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | Case 2:
% 229.03/40.49  | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | |   (401)  all_57_12 = e0 & op(e0, e3) = e0
% 229.03/40.49  | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | REF_CLOSE: (40), (346), (401) are inconsistent by sub-proof
% 229.03/40.49  | | | | | | | | | | | | |            #2185.
% 229.03/40.49  | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | End of split
% 229.03/40.49  | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | End of split
% 229.03/40.49  | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | End of split
% 229.03/40.49  | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | Case 2:
% 229.03/40.49  | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | |   (402)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3
% 229.03/40.49  | | | | | | | | | |            & op(e0, e3) = e3)
% 229.03/40.49  | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | BETA: splitting (402) gives:
% 229.03/40.49  | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | Case 1:
% 229.03/40.49  | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | |   (403)  all_57_6 = e3 & op(e1, e3) = e3
% 229.03/40.49  | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | ALPHA: (403) implies:
% 229.03/40.49  | | | | | | | | | | |   (404)  all_57_6 = e3
% 229.03/40.49  | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | REF_CLOSE: (6), (350), (404) are inconsistent by sub-proof
% 229.03/40.49  | | | | | | | | | | |            #2017.
% 229.03/40.49  | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | Case 2:
% 229.03/40.49  | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | |   (405)  all_57_12 = e3 & op(e0, e3) = e3
% 229.03/40.49  | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | ALPHA: (405) implies:
% 229.03/40.49  | | | | | | | | | | |   (406)  all_57_12 = e3
% 229.03/40.49  | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | REF_CLOSE: (6), (8), (28), (32), (35), (40), (46), (54),
% 229.03/40.49  | | | | | | | | | | |            (57), (67), (391), (406) are inconsistent by
% 229.03/40.49  | | | | | | | | | | |            sub-proof #1742.
% 229.03/40.49  | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | End of split
% 229.03/40.49  | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | End of split
% 229.03/40.49  | | | | | | | | | 
% 229.03/40.49  | | | | | | | | End of split
% 229.03/40.49  | | | | | | | | 
% 229.03/40.49  | | | | | | | End of split
% 229.03/40.49  | | | | | | | 
% 229.03/40.49  | | | | | | Case 2:
% 229.03/40.49  | | | | | | | 
% 229.03/40.49  | | | | | | |   (407)  all_57_12 = e1 & op(e0, e3) = e1
% 229.03/40.49  | | | | | | | 
% 229.03/40.49  | | | | | | | ALPHA: (407) implies:
% 229.03/40.49  | | | | | | |   (408)  op(e0, e3) = e1
% 229.03/40.49  | | | | | | | 
% 229.03/40.49  | | | | | | | REF_CLOSE: (8), (18), (42), (343), (408) are inconsistent by
% 229.03/40.49  | | | | | | |            sub-proof #1147.
% 229.03/40.49  | | | | | | | 
% 229.03/40.49  | | | | | | End of split
% 229.03/40.49  | | | | | | 
% 229.03/40.49  | | | | | End of split
% 229.03/40.49  | | | | | 
% 229.03/40.49  | | | | Case 2:
% 229.03/40.49  | | | | | 
% 229.03/40.49  | | | | |   (409)  all_57_13 = e2 & op(e0, e2) = e2
% 229.03/40.49  | | | | | 
% 229.03/40.49  | | | | | ALPHA: (409) implies:
% 229.03/40.49  | | | | |   (410)  all_57_13 = e2
% 229.03/40.49  | | | | | 
% 229.03/40.49  | | | | | BETA: splitting (57) gives:
% 229.03/40.49  | | | | | 
% 229.03/40.49  | | | | | Case 1:
% 229.03/40.49  | | | | | | 
% 229.03/40.49  | | | | | |   (411)  all_57_15 = e0 & op(e0, e0) = e0
% 229.03/40.49  | | | | | | 
% 229.03/40.49  | | | | | | ALPHA: (411) implies:
% 229.03/40.49  | | | | | |   (412)  op(e0, e0) = e0
% 229.03/40.49  | | | | | | 
% 229.03/40.49  | | | | | | REF_CLOSE: (8), (28), (54), (412) are inconsistent by sub-proof
% 229.03/40.49  | | | | | |            #2304.
% 229.03/40.49  | | | | | | 
% 229.03/40.49  | | | | | Case 2:
% 229.03/40.49  | | | | | | 
% 229.03/40.49  | | | | | |   (413)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 &
% 229.03/40.49  | | | | | |              op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0))
% 229.03/40.49  | | | | | |          & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.03/40.49  | | | | | |              op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 229.03/40.49  | | | | | | 
% 229.03/40.49  | | | | | | ALPHA: (413) implies:
% 229.03/40.49  | | | | | |   (414)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.03/40.49  | | | | | |            op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.03/40.49  | | | | | |   (415)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 &
% 229.03/40.49  | | | | | |            op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 229.03/40.49  | | | | | | 
% 229.03/40.49  | | | | | | BETA: splitting (17) gives:
% 229.03/40.49  | | | | | | 
% 229.03/40.49  | | | | | | Case 1:
% 229.03/40.49  | | | | | | | 
% 229.03/40.49  | | | | | | |   (416)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 &
% 229.03/40.49  | | | | | | |            op(e3, e2) = e1)
% 229.03/40.49  | | | | | | | 
% 229.03/40.49  | | | | | | | REF_CLOSE: (5), (6), (8), (16), (25), (28), (34), (39), (40),
% 229.03/40.49  | | | | | | |            (46), (49), (67), (416) are inconsistent by sub-proof
% 229.03/40.49  | | | | | | |            #1677.
% 229.03/40.49  | | | | | | | 
% 229.03/40.49  | | | | | | Case 2:
% 229.03/40.49  | | | | | | | 
% 229.03/40.49  | | | | | | |   (417)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 &
% 229.03/40.49  | | | | | | |            op(e3, e0) = e1)
% 229.03/40.49  | | | | | | | 
% 229.03/40.49  | | | | | | | BETA: splitting (417) gives:
% 229.03/40.49  | | | | | | | 
% 229.03/40.49  | | | | | | | Case 1:
% 229.03/40.49  | | | | | | | | 
% 229.03/40.49  | | | | | | | |   (418)  all_57_4 = e1 & op(e3, e1) = e1
% 229.03/40.49  | | | | | | | | 
% 229.03/40.49  | | | | | | | | ALPHA: (418) implies:
% 229.03/40.49  | | | | | | | |   (419)  all_57_4 = e1
% 229.03/40.49  | | | | | | | | 
% 229.03/40.49  | | | | | | | | BETA: splitting (45) gives:
% 229.03/40.49  | | | | | | | | 
% 229.03/40.49  | | | | | | | | Case 1:
% 229.03/40.49  | | | | | | | | | 
% 229.03/40.49  | | | | | | | | |   (420)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 &
% 229.03/40.49  | | | | | | | | |            op(e3, e2) = e3)
% 229.03/40.49  | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | BETA: splitting (420) gives:
% 229.03/40.49  | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | Case 1:
% 229.03/40.49  | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | |   (421)  all_57_0 = e3 & op(e3, e3) = e3
% 229.03/40.49  | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | ALPHA: (421) implies:
% 229.03/40.49  | | | | | | | | | |   (422)  op(e3, e3) = e3
% 229.03/40.49  | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | REF_CLOSE: (8), (25), (34), (422) are inconsistent by
% 229.03/40.49  | | | | | | | | | |            sub-proof #2490.
% 229.03/40.49  | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | Case 2:
% 229.03/40.49  | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | |   (423)  all_57_1 = e3 & op(e3, e2) = e3
% 229.03/40.49  | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | ALPHA: (423) implies:
% 229.03/40.49  | | | | | | | | | |   (424)  all_57_1 = e3
% 229.03/40.49  | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | BETA: splitting (48) gives:
% 229.03/40.49  | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | Case 1:
% 229.03/40.49  | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | |   (425)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 229.03/40.49  | | | | | | | | | | |            & op(e2, e1) = e3)
% 229.03/40.49  | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | BETA: splitting (425) gives:
% 229.03/40.49  | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | Case 1:
% 229.03/40.49  | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | |   (426)  all_57_4 = e3 & op(e3, e1) = e3
% 229.03/40.49  | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | REF_CLOSE: (5), (6), (8), (16), (25), (28), (39), (40), (46),
% 229.03/40.49  | | | | | | | | | | | |            (49), (67), (419), (424), (426) are inconsistent
% 229.03/40.49  | | | | | | | | | | | |            by sub-proof #734.
% 229.03/40.49  | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | Case 2:
% 229.03/40.49  | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | |   (427)  all_57_5 = e3 & op(e2, e1) = e3
% 229.03/40.49  | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | ALPHA: (427) implies:
% 229.03/40.49  | | | | | | | | | | | |   (428)  all_57_5 = e3
% 229.03/40.49  | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | BETA: splitting (64) gives:
% 229.03/40.49  | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | Case 1:
% 229.03/40.49  | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | |   (429)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 229.03/40.49  | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 229.03/40.49  | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | BETA: splitting (429) gives:
% 229.03/40.49  | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | Case 1:
% 229.03/40.49  | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | |   (430)  all_57_2 = e2 & op(e2, e3) = e2
% 229.03/40.49  | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | ALPHA: (430) implies:
% 229.03/40.49  | | | | | | | | | | | | | |   (431)  all_57_2 = e2
% 229.03/40.49  | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (5), (6), (8), (9), (12), (14), (16),
% 229.03/40.49  | | | | | | | | | | | | | |            (25), (28), (32), (34), (39), (40), (44), (45),
% 229.03/40.49  | | | | | | | | | | | | | |            (46), (49), (57), (62), (64), (65), (67), (68),
% 229.03/40.49  | | | | | | | | | | | | | |            (72), (73), (77), (79), (419), (424), (428), (431)
% 229.03/40.49  | | | | | | | | | | | | | |            are inconsistent by sub-proof #803.
% 229.03/40.49  | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | Case 2:
% 229.03/40.49  | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | |   (432)  all_57_3 = e2 & op(e2, e2) = e2
% 229.03/40.49  | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | ALPHA: (432) implies:
% 229.03/40.49  | | | | | | | | | | | | | |   (433)  op(e2, e2) = e2
% 229.03/40.49  | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | REF_CLOSE: (8), (16), (67), (433) are inconsistent by
% 229.03/40.49  | | | | | | | | | | | | | |            sub-proof #2306.
% 229.03/40.49  | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | End of split
% 229.03/40.49  | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | Case 2:
% 229.03/40.49  | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | |   (434)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 229.03/40.49  | | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 229.03/40.49  | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | BETA: splitting (434) gives:
% 229.03/40.49  | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | Case 1:
% 229.03/40.49  | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | |   (435)  all_57_5 = e2 & op(e2, e1) = e2
% 229.03/40.49  | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (25), (34), (45), (62), (79), (419),
% 229.03/40.49  | | | | | | | | | | | | | |            (424), (428), (435) are inconsistent by sub-proof
% 229.03/40.49  | | | | | | | | | | | | | |            #806.
% 229.03/40.49  | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | Case 2:
% 229.03/40.49  | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | |   (436)  all_57_10 = e2 & op(e2, e0) = e2
% 229.03/40.49  | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | ALPHA: (436) implies:
% 229.03/40.49  | | | | | | | | | | | | | |   (437)  all_57_10 = e2
% 229.03/40.49  | | | | | | | | | | | | | |   (438)  op(e2, e0) = e2
% 229.03/40.49  | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 229.03/40.49  | | | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 229.03/40.49  | | | | | | | | | | | | | |            (19), (21), (22), (23), (24), (25), (26), (27),
% 229.03/40.49  | | | | | | | | | | | | | |            (28), (30), (31), (32), (33), (34), (35), (36),
% 229.03/40.49  | | | | | | | | | | | | | |            (37), (38), (39), (40), (41), (42), (43), (44),
% 229.03/40.49  | | | | | | | | | | | | | |            (45), (46), (47), (48), (49), (50), (51), (52),
% 229.03/40.49  | | | | | | | | | | | | | |            (53), (54), (55), (56), (57), (58), (59), (60),
% 229.03/40.49  | | | | | | | | | | | | | |            (61), (62), (63), (64), (65), (67), (68), (69),
% 229.03/40.49  | | | | | | | | | | | | | |            (70), (71), (72), (73), (74), (75), (76), (77),
% 229.03/40.49  | | | | | | | | | | | | | |            (78), (79), (437), (438) are inconsistent by
% 229.03/40.49  | | | | | | | | | | | | | |            sub-proof #718.
% 229.03/40.49  | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | End of split
% 229.03/40.49  | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | End of split
% 229.03/40.49  | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | End of split
% 229.03/40.49  | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | Case 2:
% 229.03/40.49  | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | |   (439)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 229.03/40.49  | | | | | | | | | | |            e3 & op(e0, e1) = e3)
% 229.03/40.49  | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | REF_CLOSE: (6), (8), (12), (14), (25), (28), (32), (35),
% 229.03/40.49  | | | | | | | | | | |            (40), (46), (56), (67), (414), (439) are
% 229.03/40.49  | | | | | | | | | | |            inconsistent by sub-proof #1044.
% 229.03/40.49  | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | End of split
% 229.03/40.49  | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | End of split
% 229.03/40.49  | | | | | | | | | 
% 229.03/40.49  | | | | | | | | Case 2:
% 229.03/40.49  | | | | | | | | | 
% 229.03/40.49  | | | | | | | | |   (440)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 &
% 229.03/40.49  | | | | | | | | |            op(e3, e0) = e3)
% 229.03/40.49  | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | REF_CLOSE: (6), (8), (62), (79), (419), (440) are inconsistent
% 229.03/40.49  | | | | | | | | |            by sub-proof #2281.
% 229.03/40.49  | | | | | | | | | 
% 229.03/40.49  | | | | | | | | End of split
% 229.03/40.49  | | | | | | | | 
% 229.03/40.49  | | | | | | | Case 2:
% 229.03/40.49  | | | | | | | | 
% 229.03/40.49  | | | | | | | |   (441)  all_57_9 = e1 & op(e3, e0) = e1
% 229.03/40.49  | | | | | | | | 
% 229.03/40.49  | | | | | | | | ALPHA: (441) implies:
% 229.03/40.49  | | | | | | | |   (442)  all_57_9 = e1
% 229.03/40.49  | | | | | | | | 
% 229.03/40.49  | | | | | | | | BETA: splitting (415) gives:
% 229.03/40.49  | | | | | | | | 
% 229.03/40.49  | | | | | | | | Case 1:
% 229.03/40.49  | | | | | | | | | 
% 229.03/40.49  | | | | | | | | |   (443)  all_57_9 = e0 & op(e3, e0) = e0
% 229.03/40.49  | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | ALPHA: (443) implies:
% 229.03/40.49  | | | | | | | | |   (444)  all_57_9 = e0
% 229.03/40.49  | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | REF_CLOSE: (46), (442), (444) are inconsistent by sub-proof
% 229.03/40.49  | | | | | | | | |            #2479.
% 229.03/40.49  | | | | | | | | | 
% 229.03/40.49  | | | | | | | | Case 2:
% 229.03/40.49  | | | | | | | | | 
% 229.03/40.49  | | | | | | | | |   (445)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0
% 229.03/40.49  | | | | | | | | |            & op(e1, e0) = e0)
% 229.03/40.49  | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | BETA: splitting (445) gives:
% 229.03/40.49  | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | Case 1:
% 229.03/40.49  | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | |   (446)  all_57_10 = e0 & op(e2, e0) = e0
% 229.03/40.49  | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | ALPHA: (446) implies:
% 229.03/40.49  | | | | | | | | | |   (447)  all_57_10 = e0
% 229.03/40.49  | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | BETA: splitting (64) gives:
% 229.03/40.49  | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | Case 1:
% 229.03/40.49  | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | |   (448)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 229.03/40.49  | | | | | | | | | | |            & op(e2, e2) = e2)
% 229.03/40.49  | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | BETA: splitting (448) gives:
% 229.03/40.49  | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | Case 1:
% 229.03/40.49  | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | |   (449)  all_57_2 = e2 & op(e2, e3) = e2
% 229.03/40.49  | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | ALPHA: (449) implies:
% 229.03/40.49  | | | | | | | | | | | |   (450)  all_57_2 = e2
% 229.03/40.49  | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | BETA: splitting (61) gives:
% 229.03/40.49  | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | Case 1:
% 229.03/40.49  | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | |   (451)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 229.03/40.49  | | | | | | | | | | | | |            & op(e2, e2) = e3)
% 229.03/40.49  | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | REF_CLOSE: (6), (8), (16), (25), (450), (451) are
% 229.03/40.49  | | | | | | | | | | | | |            inconsistent by sub-proof #684.
% 229.03/40.49  | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | Case 2:
% 229.03/40.49  | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | |   (452)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 229.03/40.49  | | | | | | | | | | | | |            e3 & op(e2, e0) = e3)
% 229.03/40.49  | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | BETA: splitting (452) gives:
% 229.03/40.49  | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | Case 1:
% 229.03/40.49  | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | |   (453)  all_57_5 = e3 & op(e2, e1) = e3
% 229.03/40.49  | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | ALPHA: (453) implies:
% 229.03/40.49  | | | | | | | | | | | | | |   (454)  all_57_5 = e3
% 229.03/40.49  | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | BETA: splitting (65) gives:
% 229.03/40.49  | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | Case 1:
% 229.03/40.49  | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | |   (455)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 229.03/40.49  | | | | | | | | | | | | | | |            & op(e2, e3) = e3)
% 229.03/40.49  | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | REF_CLOSE: (8), (16), (25), (34), (40), (64), (67), (447),
% 229.03/40.49  | | | | | | | | | | | | | | |            (454), (455) are inconsistent by sub-proof #727.
% 229.03/40.49  | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | Case 2:
% 229.03/40.49  | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | |   (456)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 229.03/40.49  | | | | | | | | | | | | | | |            e3 & op(e0, e3) = e3)
% 229.03/40.49  | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | BETA: splitting (456) gives:
% 229.03/40.49  | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | Case 1:
% 229.03/40.49  | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | |   (457)  all_57_6 = e3 & op(e1, e3) = e3
% 229.03/40.49  | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (6), (8), (16), (25), (28), (32), (34),
% 229.03/40.49  | | | | | | | | | | | | | | | |            (40), (44), (46), (54), (57), (61), (64), (67),
% 229.03/40.49  | | | | | | | | | | | | | | | |            (68), (72), (73), (450), (457) are inconsistent by
% 229.03/40.49  | | | | | | | | | | | | | | | |            sub-proof #657.
% 229.03/40.49  | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | Case 2:
% 229.03/40.49  | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | |   (458)  all_57_12 = e3 & op(e0, e3) = e3
% 229.03/40.49  | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | ALPHA: (458) implies:
% 229.03/40.49  | | | | | | | | | | | | | | | |   (459)  all_57_12 = e3
% 229.03/40.49  | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (6), (8), (25), (28), (34), (40), (44),
% 229.03/40.49  | | | | | | | | | | | | | | | |            (46), (64), (67), (72), (450), (454), (459) are
% 229.03/40.49  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1575.
% 229.03/40.49  | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | End of split
% 229.03/40.49  | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | End of split
% 229.03/40.49  | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | Case 2:
% 229.03/40.49  | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | |   (460)  all_57_10 = e3 & op(e2, e0) = e3
% 229.03/40.49  | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | ALPHA: (460) implies:
% 229.03/40.49  | | | | | | | | | | | | | |   (461)  all_57_10 = e3
% 229.03/40.49  | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | REF_CLOSE: (25), (28), (32), (40), (46), (67), (68), (415),
% 229.03/40.49  | | | | | | | | | | | | | |            (442), (461) are inconsistent by sub-proof #1986.
% 229.03/40.49  | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | End of split
% 229.03/40.49  | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | End of split
% 229.03/40.49  | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | Case 2:
% 229.03/40.49  | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | |   (462)  all_57_3 = e2 & op(e2, e2) = e2
% 229.03/40.49  | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | ALPHA: (462) implies:
% 229.03/40.49  | | | | | | | | | | | |   (463)  op(e2, e2) = e2
% 229.03/40.49  | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | REF_CLOSE: (8), (16), (67), (463) are inconsistent by
% 229.03/40.49  | | | | | | | | | | | |            sub-proof #2306.
% 229.03/40.49  | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | End of split
% 229.03/40.49  | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | Case 2:
% 229.03/40.49  | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | |   (464)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 229.03/40.49  | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 229.03/40.49  | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | BETA: splitting (464) gives:
% 229.03/40.49  | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | Case 1:
% 229.03/40.49  | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | |   (465)  all_57_5 = e2 & op(e2, e1) = e2
% 229.03/40.49  | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | ALPHA: (465) implies:
% 229.03/40.49  | | | | | | | | | | | |   (466)  all_57_5 = e2
% 229.03/40.49  | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | BETA: splitting (61) gives:
% 229.03/40.49  | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | Case 1:
% 229.03/40.49  | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | |   (467)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 229.03/40.49  | | | | | | | | | | | | |            & op(e2, e2) = e3)
% 229.03/40.49  | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | BETA: splitting (467) gives:
% 229.03/40.49  | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | Case 1:
% 229.03/40.49  | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | |   (468)  all_57_2 = e3 & op(e2, e3) = e3
% 229.03/40.49  | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | ALPHA: (468) implies:
% 229.03/40.49  | | | | | | | | | | | | | |   (469)  all_57_2 = e3
% 229.03/40.49  | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | BETA: splitting (48) gives:
% 229.03/40.49  | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | Case 1:
% 229.03/40.49  | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | |   (470)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 229.03/40.49  | | | | | | | | | | | | | | |            & op(e2, e1) = e3)
% 229.03/40.49  | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | BETA: splitting (470) gives:
% 229.03/40.49  | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | Case 1:
% 229.03/40.49  | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | |   (471)  all_57_4 = e3 & op(e3, e1) = e3
% 229.03/40.49  | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | ALPHA: (471) implies:
% 229.03/40.49  | | | | | | | | | | | | | | | |   (472)  all_57_4 = e3
% 229.03/40.49  | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | BETA: splitting (23) gives:
% 229.03/40.49  | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | Case 1:
% 229.03/40.49  | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | |   (473)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 229.03/40.49  | | | | | | | | | | | | | | | | |            & op(e3, e2) = e0)
% 229.03/40.49  | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | BETA: splitting (473) gives:
% 229.03/40.49  | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | Case 1:
% 229.03/40.49  | | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | |   (474)  all_57_0 = e0 & op(e3, e3) = e0
% 229.03/40.49  | | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | | ALPHA: (474) implies:
% 229.03/40.49  | | | | | | | | | | | | | | | | | |   (475)  op(e3, e3) = e0
% 229.03/40.49  | | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (34), (40), (475) are inconsistent by
% 229.03/40.49  | | | | | | | | | | | | | | | | | |            sub-proof #2403.
% 229.03/40.49  | | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | Case 2:
% 229.03/40.49  | | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | |   (476)  all_57_1 = e0 & op(e3, e2) = e0
% 229.03/40.49  | | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | | ALPHA: (476) implies:
% 229.03/40.49  | | | | | | | | | | | | | | | | | |   (477)  all_57_1 = e0
% 229.03/40.49  | | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | | BETA: splitting (29) gives:
% 229.03/40.49  | | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | | |   (478)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 229.03/40.49  | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e1)
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | BETA: splitting (478) gives:
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | |   (479)  all_57_4 = e1 & op(e3, e1) = e1
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (472), (479) are inconsistent by sub-proof
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | |            #2484.
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | |   (480)  all_57_5 = e1 & op(e2, e1) = e1
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (67), (466), (480) are inconsistent by sub-proof
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | |            #1886.
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | End of split
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | | |   (481)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 229.03/40.49  | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e1) = e1)
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | BETA: splitting (481) gives:
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | |   (482)  all_57_8 = e1 & op(e1, e1) = e1
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | ALPHA: (482) implies:
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | |   (483)  op(e1, e1) = e1
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (58), (67), (483) are inconsistent by
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | |            sub-proof #2423.
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | |   (484)  all_57_14 = e1 & op(e0, e1) = e1
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | ALPHA: (484) implies:
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | |   (485)  all_57_14 = e1
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | BETA: splitting (49) gives:
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | |   (486)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e3)
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (16), (28), (477), (486) are
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1737.
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | |   (487)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (487) gives:
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | |   (488)  all_57_7 = e3 & op(e1, e2) = e3
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (488) implies:
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | |   (489)  all_57_7 = e3
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (414) gives:
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | |   (490)  all_57_12 = e0 & op(e0, e3) = e0
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (490) implies:
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | |   (491)  all_57_12 = e0
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4) gives:
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | | |   (492)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e1)
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (34), (67), (469), (492) are
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #753.
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | | |   (493)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e3) = e1)
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (493) gives:
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | | | |   (494)  all_57_6 = e1 & op(e1, e3) = e1
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (494) implies:
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | | | |   (495)  all_57_6 = e1
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24) gives:
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | | | | |   (496)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e0)
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (496) gives:
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (497)  all_57_4 = e0 & op(e3, e1) = e0
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (497) implies:
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (498)  all_57_4 = e0
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (12), (14), (25), (28), (32), (40),
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (46), (57), (67), (68), (73), (472), (489), (495),
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (498) are inconsistent by sub-proof #1027.
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (499)  all_57_5 = e0 & op(e2, e1) = e0
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (499) implies:
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (500)  all_57_5 = e0
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (466), (500) imply:
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (501)  e2 = e0
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (501) implies:
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (502)  e2 = e0
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (342), (502) imply:
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (503)  all_57_11 = e0
% 229.03/40.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (25), (32), (40), (46), (54), (67),
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (68), (73), (447), (503) are inconsistent by
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1087.
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | | |   (504)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (504) gives:
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (505)  all_57_8 = e0 & op(e1, e1) = e0
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (505) implies:
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (506)  op(e1, e1) = e0
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with e0, e2, e1, e1, simplifying
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | | | |              with (58), (506) gives:
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (507)  e2 = e0
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (342), (507) imply:
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (508)  all_57_11 = e0
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (25), (32), (40), (46), (54), (67),
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (68), (73), (447), (508) are inconsistent by
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1087.
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (509)  all_57_14 = e0 & op(e0, e1) = e0
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (509) implies:
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (510)  all_57_14 = e0
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (485), (510) imply:
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (511)  e1 = e0
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (511) implies:
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (512)  e1 = e0
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (44), (512) imply:
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (513)  all_57_3 = e0
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (25), (28), (32), (35), (40), (46),
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (49), (56), (67), (77), (477), (491), (513) are
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #694.
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | |   (514)  all_57_12 = e1 & op(e0, e3) = e1
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (514) implies:
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | |   (515)  op(e0, e3) = e1
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (18), (25), (32), (40), (42), (67), (68),
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | |            (442), (447), (515) are inconsistent by sub-proof
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | |            #1018.
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | |   (516)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (516) gives:
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | |   (517)  all_57_13 = e0 & op(e0, e2) = e0
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (517) implies:
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | |   (518)  all_57_13 = e0
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (410), (518) imply:
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | |   (519)  e2 = e0
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (342), (519) imply:
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | |   (520)  all_57_11 = e0
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (25), (32), (40), (46), (54), (67),
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | |            (68), (73), (447), (520) are inconsistent by
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1087.
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | |   (521)  all_57_14 = e0 & op(e0, e1) = e0
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (521) implies:
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | |   (522)  all_57_14 = e0
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (485), (522) imply:
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | |   (523)  e1 = e0
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (44), (523) imply:
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | |   (524)  all_57_3 = e0
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (9), (12), (14),
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | |            (25), (28), (32), (34), (35), (40), (46), (49),
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | |            (54), (56), (57), (61), (64), (65), (67), (68),
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | |            (69), (72), (73), (77), (477), (524) are
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #689.
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | |   (525)  all_57_13 = e3 & op(e0, e2) = e3
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | 
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (525) implies:
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | |   (526)  all_57_13 = e3
% 229.03/40.50  | | | | | | | | | | | | | | | | | | | | | | 
% 229.06/40.50  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (25), (28), (32), (35), (40), (46),
% 229.06/40.50  | | | | | | | | | | | | | | | | | | | | | |            (54), (56), (67), (414), (526) are inconsistent by
% 229.06/40.50  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2054.
% 229.06/40.50  | | | | | | | | | | | | | | | | | | | | | | 
% 229.06/40.50  | | | | | | | | | | | | | | | | | | | | | End of split
% 229.06/40.50  | | | | | | | | | | | | | | | | | | | | | 
% 229.06/40.50  | | | | | | | | | | | | | | | | | | | | End of split
% 229.06/40.50  | | | | | | | | | | | | | | | | | | | | 
% 229.06/40.50  | | | | | | | | | | | | | | | | | | | End of split
% 229.06/40.50  | | | | | | | | | | | | | | | | | | | 
% 229.06/40.50  | | | | | | | | | | | | | | | | | | End of split
% 229.06/40.50  | | | | | | | | | | | | | | | | | | 
% 229.06/40.50  | | | | | | | | | | | | | | | | | End of split
% 229.06/40.50  | | | | | | | | | | | | | | | | | 
% 229.06/40.50  | | | | | | | | | | | | | | | | Case 2:
% 229.06/40.50  | | | | | | | | | | | | | | | | | 
% 229.06/40.50  | | | | | | | | | | | | | | | | |   (527)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 229.06/40.50  | | | | | | | | | | | | | | | | |            & op(e3, e0) = e0)
% 229.06/40.50  | | | | | | | | | | | | | | | | | 
% 229.06/40.50  | | | | | | | | | | | | | | | | | BETA: splitting (527) gives:
% 229.06/40.50  | | | | | | | | | | | | | | | | | 
% 229.06/40.50  | | | | | | | | | | | | | | | | | Case 1:
% 229.06/40.50  | | | | | | | | | | | | | | | | | | 
% 229.06/40.50  | | | | | | | | | | | | | | | | | |   (528)  all_57_4 = e0 & op(e3, e1) = e0
% 229.06/40.50  | | | | | | | | | | | | | | | | | | 
% 229.06/40.50  | | | | | | | | | | | | | | | | | | REF_CLOSE: (28), (472), (528) are inconsistent by sub-proof
% 229.06/40.50  | | | | | | | | | | | | | | | | | |            #2491.
% 229.06/40.50  | | | | | | | | | | | | | | | | | | 
% 229.06/40.50  | | | | | | | | | | | | | | | | | Case 2:
% 229.06/40.50  | | | | | | | | | | | | | | | | | | 
% 229.06/40.50  | | | | | | | | | | | | | | | | | |   (529)  all_57_9 = e0 & op(e3, e0) = e0
% 229.06/40.50  | | | | | | | | | | | | | | | | | | 
% 229.06/40.50  | | | | | | | | | | | | | | | | | | REF_CLOSE: (46), (442), (529) are inconsistent by sub-proof
% 229.06/40.50  | | | | | | | | | | | | | | | | | |            #1990.
% 229.06/40.50  | | | | | | | | | | | | | | | | | | 
% 229.06/40.50  | | | | | | | | | | | | | | | | | End of split
% 229.06/40.50  | | | | | | | | | | | | | | | | | 
% 229.06/40.50  | | | | | | | | | | | | | | | | End of split
% 229.06/40.50  | | | | | | | | | | | | | | | | 
% 229.06/40.50  | | | | | | | | | | | | | | | Case 2:
% 229.06/40.50  | | | | | | | | | | | | | | | | 
% 229.06/40.50  | | | | | | | | | | | | | | | |   (530)  all_57_5 = e3 & op(e2, e1) = e3
% 229.06/40.50  | | | | | | | | | | | | | | | | 
% 229.06/40.50  | | | | | | | | | | | | | | | | ALPHA: (530) implies:
% 229.06/40.50  | | | | | | | | | | | | | | | |   (531)  all_57_5 = e3
% 229.06/40.50  | | | | | | | | | | | | | | | | 
% 229.06/40.50  | | | | | | | | | | | | | | | | REF_CLOSE: (8), (16), (25), (40), (64), (67), (447), (469),
% 229.06/40.50  | | | | | | | | | | | | | | | |            (531) are inconsistent by sub-proof #1797.
% 229.06/40.50  | | | | | | | | | | | | | | | | 
% 229.06/40.50  | | | | | | | | | | | | | | | End of split
% 229.06/40.50  | | | | | | | | | | | | | | | 
% 229.06/40.50  | | | | | | | | | | | | | | Case 2:
% 229.06/40.50  | | | | | | | | | | | | | | | 
% 229.06/40.50  | | | | | | | | | | | | | | |   (532)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 229.06/40.50  | | | | | | | | | | | | | | |            e3 & op(e0, e1) = e3)
% 229.06/40.50  | | | | | | | | | | | | | | | 
% 229.06/40.50  | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (12), (14), (25), (28), (32), (35),
% 229.06/40.50  | | | | | | | | | | | | | | |            (40), (46), (56), (67), (414), (532) are
% 229.06/40.50  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1044.
% 229.06/40.50  | | | | | | | | | | | | | | | 
% 229.06/40.50  | | | | | | | | | | | | | | End of split
% 229.06/40.50  | | | | | | | | | | | | | | 
% 229.06/40.50  | | | | | | | | | | | | | Case 2:
% 229.06/40.50  | | | | | | | | | | | | | | 
% 229.06/40.50  | | | | | | | | | | | | | |   (533)  all_57_3 = e3 & op(e2, e2) = e3
% 229.06/40.50  | | | | | | | | | | | | | | 
% 229.06/40.50  | | | | | | | | | | | | | | ALPHA: (533) implies:
% 229.06/40.50  | | | | | | | | | | | | | |   (534)  op(e2, e2) = e3
% 229.06/40.50  | | | | | | | | | | | | | | 
% 229.06/40.50  | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (16), (534) are inconsistent by
% 229.06/40.50  | | | | | | | | | | | | | |            sub-proof #1912.
% 229.06/40.50  | | | | | | | | | | | | | | 
% 229.06/40.50  | | | | | | | | | | | | | End of split
% 229.06/40.50  | | | | | | | | | | | | | 
% 229.06/40.50  | | | | | | | | | | | | Case 2:
% 229.06/40.50  | | | | | | | | | | | | | 
% 229.06/40.50  | | | | | | | | | | | | |   (535)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 229.06/40.50  | | | | | | | | | | | | |            e3 & op(e2, e0) = e3)
% 229.06/40.50  | | | | | | | | | | | | | 
% 229.06/40.50  | | | | | | | | | | | | | BETA: splitting (535) gives:
% 229.06/40.50  | | | | | | | | | | | | | 
% 229.06/40.50  | | | | | | | | | | | | | Case 1:
% 229.06/40.50  | | | | | | | | | | | | | | 
% 229.06/40.50  | | | | | | | | | | | | | |   (536)  all_57_5 = e3 & op(e2, e1) = e3
% 229.06/40.50  | | | | | | | | | | | | | | 
% 229.06/40.50  | | | | | | | | | | | | | | ALPHA: (536) implies:
% 229.06/40.50  | | | | | | | | | | | | | |   (537)  all_57_5 = e3
% 229.06/40.50  | | | | | | | | | | | | | | 
% 229.06/40.50  | | | | | | | | | | | | | | REF_CLOSE: (25), (466), (537) are inconsistent by sub-proof
% 229.06/40.50  | | | | | | | | | | | | | |            #2189.
% 229.06/40.50  | | | | | | | | | | | | | | 
% 229.06/40.50  | | | | | | | | | | | | | Case 2:
% 229.06/40.50  | | | | | | | | | | | | | | 
% 229.06/40.50  | | | | | | | | | | | | | |   (538)  all_57_10 = e3 & op(e2, e0) = e3
% 229.06/40.50  | | | | | | | | | | | | | | 
% 229.06/40.50  | | | | | | | | | | | | | | ALPHA: (538) implies:
% 229.06/40.50  | | | | | | | | | | | | | |   (539)  all_57_10 = e3
% 229.06/40.50  | | | | | | | | | | | | | | 
% 229.06/40.50  | | | | | | | | | | | | | | REF_CLOSE: (25), (28), (32), (40), (46), (67), (68), (415),
% 229.06/40.50  | | | | | | | | | | | | | |            (442), (539) are inconsistent by sub-proof #1986.
% 229.06/40.50  | | | | | | | | | | | | | | 
% 229.06/40.50  | | | | | | | | | | | | | End of split
% 229.06/40.50  | | | | | | | | | | | | | 
% 229.06/40.50  | | | | | | | | | | | | End of split
% 229.06/40.50  | | | | | | | | | | | | 
% 229.06/40.50  | | | | | | | | | | | Case 2:
% 229.06/40.50  | | | | | | | | | | | | 
% 229.06/40.50  | | | | | | | | | | | |   (540)  all_57_10 = e2 & op(e2, e0) = e2
% 229.06/40.50  | | | | | | | | | | | | 
% 229.06/40.50  | | | | | | | | | | | | ALPHA: (540) implies:
% 229.06/40.50  | | | | | | | | | | | |   (541)  all_57_10 = e2
% 229.06/40.50  | | | | | | | | | | | |   (542)  op(e2, e0) = e2
% 229.06/40.50  | | | | | | | | | | | | 
% 229.06/40.50  | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 229.06/40.50  | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 229.06/40.50  | | | | | | | | | | | |            (19), (21), (22), (23), (24), (25), (26), (27),
% 229.06/40.50  | | | | | | | | | | | |            (28), (30), (31), (32), (33), (34), (35), (36),
% 229.06/40.50  | | | | | | | | | | | |            (37), (38), (39), (40), (41), (42), (43), (44),
% 229.06/40.50  | | | | | | | | | | | |            (45), (46), (47), (48), (49), (50), (51), (52),
% 229.06/40.50  | | | | | | | | | | | |            (53), (54), (55), (56), (57), (58), (59), (60),
% 229.06/40.50  | | | | | | | | | | | |            (61), (62), (63), (64), (65), (67), (68), (69),
% 229.06/40.50  | | | | | | | | | | | |            (70), (71), (72), (73), (74), (75), (76), (77),
% 229.06/40.50  | | | | | | | | | | | |            (78), (79), (541), (542) are inconsistent by
% 229.06/40.50  | | | | | | | | | | | |            sub-proof #718.
% 229.06/40.50  | | | | | | | | | | | | 
% 229.06/40.50  | | | | | | | | | | | End of split
% 229.06/40.50  | | | | | | | | | | | 
% 229.06/40.50  | | | | | | | | | | End of split
% 229.06/40.50  | | | | | | | | | | 
% 229.06/40.50  | | | | | | | | | Case 2:
% 229.06/40.50  | | | | | | | | | | 
% 229.06/40.50  | | | | | | | | | |   (543)  all_57_11 = e0 & op(e1, e0) = e0
% 229.06/40.50  | | | | | | | | | | 
% 229.06/40.50  | | | | | | | | | | REF_CLOSE: (40), (342), (543) are inconsistent by sub-proof
% 229.06/40.50  | | | | | | | | | |            #2041.
% 229.06/40.50  | | | | | | | | | | 
% 229.06/40.50  | | | | | | | | | End of split
% 229.06/40.50  | | | | | | | | | 
% 229.06/40.50  | | | | | | | | End of split
% 229.06/40.50  | | | | | | | | 
% 229.06/40.50  | | | | | | | End of split
% 229.06/40.50  | | | | | | | 
% 229.06/40.50  | | | | | | End of split
% 229.06/40.50  | | | | | | 
% 229.06/40.50  | | | | | End of split
% 229.06/40.50  | | | | | 
% 229.06/40.50  | | | | End of split
% 229.06/40.50  | | | | 
% 229.06/40.50  | | | Case 2:
% 229.06/40.50  | | | | 
% 229.06/40.50  | | | |   (544)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0,
% 229.06/40.50  | | | |              e0) = e2)
% 229.06/40.50  | | | | 
% 229.06/40.50  | | | | BETA: splitting (544) gives:
% 229.06/40.50  | | | | 
% 229.06/40.50  | | | | Case 1:
% 229.06/40.50  | | | | | 
% 229.06/40.50  | | | | |   (545)  all_57_14 = e2 & op(e0, e1) = e2
% 229.06/40.50  | | | | | 
% 229.06/40.50  | | | | | ALPHA: (545) implies:
% 229.06/40.50  | | | | |   (546)  all_57_14 = e2
% 229.06/40.50  | | | | | 
% 229.06/40.50  | | | | | BETA: splitting (35) gives:
% 229.06/40.50  | | | | | 
% 229.06/40.50  | | | | | Case 1:
% 229.06/40.50  | | | | | | 
% 229.06/40.50  | | | | | |   (547)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 &
% 229.06/40.50  | | | | | |            op(e0, e2) = e1)
% 229.06/40.50  | | | | | | 
% 229.06/40.50  | | | | | | BETA: splitting (547) gives:
% 229.06/40.50  | | | | | | 
% 229.06/40.50  | | | | | | Case 1:
% 229.06/40.50  | | | | | | | 
% 229.06/40.50  | | | | | | |   (548)  all_57_12 = e1 & op(e0, e3) = e1
% 229.06/40.50  | | | | | | | 
% 229.06/40.50  | | | | | | | REF_CLOSE: (3), (5), (6), (7), (8), (9), (12), (14), (16), (17),
% 229.06/40.50  | | | | | | |            (23), (25), (28), (32), (34), (35), (39), (40), (44),
% 229.06/40.50  | | | | | | |            (45), (46), (49), (54), (56), (57), (58), (61), (62),
% 229.06/40.50  | | | | | | |            (64), (67), (68), (72), (73), (74), (77), (79), (546),
% 229.06/40.50  | | | | | | |            (548) are inconsistent by sub-proof #722.
% 229.06/40.50  | | | | | | | 
% 229.06/40.50  | | | | | | Case 2:
% 229.06/40.50  | | | | | | | 
% 229.06/40.50  | | | | | | |   (549)  all_57_13 = e1 & op(e0, e2) = e1
% 229.06/40.50  | | | | | | | 
% 229.06/40.50  | | | | | | | ALPHA: (549) implies:
% 229.06/40.50  | | | | | | |   (550)  all_57_13 = e1
% 229.06/40.50  | | | | | | | 
% 229.06/40.50  | | | | | | | BETA: splitting (5) gives:
% 229.06/40.50  | | | | | | | 
% 229.06/40.50  | | | | | | | Case 1:
% 229.06/40.50  | | | | | | | | 
% 229.06/40.50  | | | | | | | |   (551)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 &
% 229.06/40.50  | | | | | | | |            op(e2, e2) = e2)
% 229.06/40.50  | | | | | | | | 
% 229.06/40.50  | | | | | | | | BETA: splitting (551) gives:
% 229.06/40.50  | | | | | | | | 
% 229.06/40.50  | | | | | | | | Case 1:
% 229.06/40.50  | | | | | | | | | 
% 229.06/40.50  | | | | | | | | |   (552)  all_57_1 = e2 & op(e3, e2) = e2
% 229.06/40.50  | | | | | | | | | 
% 229.06/40.50  | | | | | | | | | ALPHA: (552) implies:
% 229.06/40.50  | | | | | | | | |   (553)  all_57_1 = e2
% 229.06/40.50  | | | | | | | | | 
% 229.06/40.50  | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (9), (12), (14),
% 229.06/40.50  | | | | | | | | |            (16), (17), (23), (25), (28), (32), (34), (35),
% 229.06/40.50  | | | | | | | | |            (39), (40), (44), (45), (46), (49), (54), (56),
% 229.06/40.50  | | | | | | | | |            (57), (61), (62), (64), (65), (67), (68), (72),
% 229.06/40.50  | | | | | | | | |            (73), (77), (79), (546), (550), (553) are
% 229.06/40.50  | | | | | | | | |            inconsistent by sub-proof #721.
% 229.06/40.50  | | | | | | | | | 
% 229.06/40.50  | | | | | | | | Case 2:
% 229.06/40.50  | | | | | | | | | 
% 229.06/40.50  | | | | | | | | |   (554)  all_57_3 = e2 & op(e2, e2) = e2
% 229.06/40.50  | | | | | | | | | 
% 229.06/40.50  | | | | | | | | | ALPHA: (554) implies:
% 229.06/40.50  | | | | | | | | |   (555)  op(e2, e2) = e2
% 229.06/40.50  | | | | | | | | | 
% 229.06/40.50  | | | | | | | | | REF_CLOSE: (8), (16), (67), (555) are inconsistent by
% 229.06/40.50  | | | | | | | | |            sub-proof #2306.
% 229.06/40.50  | | | | | | | | | 
% 229.06/40.50  | | | | | | | | End of split
% 229.06/40.50  | | | | | | | | 
% 229.06/40.50  | | | | | | | Case 2:
% 229.06/40.50  | | | | | | | | 
% 229.06/40.50  | | | | | | | |   (556)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 &
% 229.06/40.50  | | | | | | | |            op(e0, e2) = e2)
% 229.06/40.50  | | | | | | | | 
% 229.06/40.50  | | | | | | | | BETA: splitting (556) gives:
% 229.06/40.50  | | | | | | | | 
% 229.06/40.50  | | | | | | | | Case 1:
% 229.06/40.50  | | | | | | | | | 
% 229.06/40.50  | | | | | | | | |   (557)  all_57_7 = e2 & op(e1, e2) = e2
% 229.06/40.50  | | | | | | | | | 
% 229.06/40.50  | | | | | | | | | ALPHA: (557) implies:
% 229.06/40.50  | | | | | | | | |   (558)  all_57_7 = e2
% 229.06/40.50  | | | | | | | | | 
% 229.06/40.50  | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (9), (12), (14),
% 229.06/40.50  | | | | | | | | |            (16), (17), (23), (25), (28), (32), (34), (35),
% 229.06/40.50  | | | | | | | | |            (39), (40), (44), (45), (46), (49), (54), (56),
% 229.06/40.50  | | | | | | | | |            (57), (61), (62), (64), (65), (67), (68), (72),
% 229.06/40.50  | | | | | | | | |            (73), (77), (79), (546), (550), (558) are
% 229.06/40.50  | | | | | | | | |            inconsistent by sub-proof #720.
% 229.06/40.50  | | | | | | | | | 
% 229.06/40.50  | | | | | | | | Case 2:
% 229.06/40.50  | | | | | | | | | 
% 229.06/40.50  | | | | | | | | |   (559)  all_57_13 = e2 & op(e0, e2) = e2
% 229.06/40.50  | | | | | | | | | 
% 229.06/40.50  | | | | | | | | | REF_CLOSE: (67), (550), (559) are inconsistent by sub-proof
% 229.06/40.50  | | | | | | | | |            #2101.
% 229.06/40.50  | | | | | | | | | 
% 229.06/40.50  | | | | | | | | End of split
% 229.06/40.50  | | | | | | | | 
% 229.06/40.50  | | | | | | | End of split
% 229.06/40.50  | | | | | | | 
% 229.06/40.50  | | | | | | End of split
% 229.06/40.50  | | | | | | 
% 229.06/40.50  | | | | | Case 2:
% 229.06/40.50  | | | | | | 
% 229.06/40.50  | | | | | |   (560)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 &
% 229.06/40.50  | | | | | |            op(e0, e0) = e1)
% 229.06/40.50  | | | | | | 
% 229.06/40.50  | | | | | | REF_CLOSE: (6), (8), (54), (67), (546), (560) are inconsistent by
% 229.06/40.50  | | | | | |            sub-proof #1139.
% 229.06/40.50  | | | | | | 
% 229.06/40.50  | | | | | End of split
% 229.06/40.50  | | | | | 
% 229.06/40.50  | | | | Case 2:
% 229.06/40.50  | | | | | 
% 229.06/40.50  | | | | |   (561)  all_57_15 = e2 & op(e0, e0) = e2
% 229.06/40.50  | | | | | 
% 229.06/40.50  | | | | | REF_CLOSE: (25), (32), (561) are inconsistent by sub-proof #2323.
% 229.06/40.50  | | | | | 
% 229.06/40.50  | | | | End of split
% 229.06/40.50  | | | | 
% 229.06/40.50  | | | End of split
% 229.06/40.50  | | | 
% 229.06/40.50  | | Case 2:
% 229.06/40.50  | | | 
% 229.06/40.50  | | |   (562)  all_57_15 = e2 & op(e0, e0) = e2
% 229.06/40.50  | | | 
% 229.06/40.50  | | | ALPHA: (562) implies:
% 229.06/40.50  | | |   (563)  all_57_15 = e2
% 229.06/40.50  | | | 
% 229.06/40.50  | | | REF_CLOSE: (25), (32), (563) are inconsistent by sub-proof #2058.
% 229.06/40.50  | | | 
% 229.06/40.50  | | End of split
% 229.06/40.50  | | 
% 229.06/40.50  | End of split
% 229.06/40.50  | 
% 229.06/40.50  End of proof
% 229.06/40.50  
% 229.06/40.50  Sub-proof #656 shows that the following formulas are inconsistent:
% 229.06/40.50  ----------------------------------------------------------------
% 229.06/40.50    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.06/40.50         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.06/40.50    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.06/40.50         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.06/40.50    (3)   ~ (e3 = e1)
% 229.06/40.50    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.06/40.50           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.06/40.50    (5)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.06/40.50         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.06/40.50    (6)   ~ (all_6_2 = e3)
% 229.06/40.50    (7)  op(e1, e1) = all_6_2
% 229.06/40.50    (8)  op(e2, e2) = e1
% 229.06/40.50    (9)  all_57_7 = e2
% 229.06/40.50    (10)  all_57_2 = e2
% 229.06/40.50    (11)   ~ (e3 = e2)
% 229.06/40.50    (12)   ~ (e3 = e0)
% 229.06/40.50    (13)  all_57_15 = e3
% 229.06/40.50    (14)  op(e3, e3) = e2
% 229.06/40.50    (15)   ~ (e2 = e0)
% 229.06/40.50    (16)  all_57_3 = e1
% 229.06/40.50    (17)   ~ (e1 = e0)
% 229.06/40.50    (18)  op(e0, e0) = e3
% 229.06/40.50    (19)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.06/40.50              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.06/40.50                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.06/40.50                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.06/40.50    (20)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.06/40.50          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.06/40.50    (21)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.06/40.50          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.06/40.50    (22)   ~ (e2 = e1)
% 229.06/40.50    (23)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.06/40.50          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.06/40.50    (24)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.06/40.50          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.06/40.50    (25)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.06/40.50          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.06/40.50  
% 229.06/40.50  Begin of proof
% 229.06/40.50  | 
% 229.06/40.50  | BETA: splitting (5) gives:
% 229.06/40.50  | 
% 229.06/40.50  | Case 1:
% 229.06/40.50  | | 
% 229.06/40.50  | |   (26)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 229.06/40.50  | |           e3)
% 229.06/40.50  | | 
% 229.06/40.50  | | BETA: splitting (26) gives:
% 229.06/40.50  | | 
% 229.06/40.50  | | Case 1:
% 229.06/40.50  | | | 
% 229.06/40.50  | | |   (27)  all_57_6 = e3 & op(e1, e3) = e3
% 229.06/40.50  | | | 
% 229.06/40.50  | | | REF_CLOSE: (1), (2), (3), (4), (8), (10), (11), (12), (13), (14), (15),
% 229.06/40.50  | | |            (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 229.06/40.50  | | |            (27) are inconsistent by sub-proof #657.
% 229.06/40.50  | | | 
% 229.06/40.50  | | Case 2:
% 229.06/40.50  | | | 
% 229.06/40.50  | | |   (28)  all_57_7 = e3 & op(e1, e2) = e3
% 229.06/40.50  | | | 
% 229.06/40.50  | | | ALPHA: (28) implies:
% 229.06/40.50  | | |   (29)  all_57_7 = e3
% 229.06/40.50  | | | 
% 229.06/40.50  | | | REF_CLOSE: (9), (11), (29) are inconsistent by sub-proof #2102.
% 229.06/40.50  | | | 
% 229.06/40.50  | | End of split
% 229.06/40.50  | | 
% 229.06/40.50  | Case 2:
% 229.06/40.50  | | 
% 229.06/40.50  | |   (30)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 229.06/40.50  | |           e3)
% 229.06/40.50  | | 
% 229.06/40.50  | | REF_CLOSE: (3), (4), (6), (7), (11), (12), (13), (15), (17), (19), (22),
% 229.06/40.50  | |            (23), (25), (30) are inconsistent by sub-proof #1786.
% 229.06/40.50  | | 
% 229.06/40.50  | End of split
% 229.06/40.50  | 
% 229.06/40.50  End of proof
% 229.06/40.50  
% 229.06/40.50  Sub-proof #657 shows that the following formulas are inconsistent:
% 229.06/40.50  ----------------------------------------------------------------
% 229.06/40.50    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.06/40.50         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.06/40.50    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.06/40.50         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.06/40.50    (3)   ~ (e3 = e1)
% 229.06/40.50    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.06/40.50           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.06/40.50    (5)  op(e2, e2) = e1
% 229.06/40.50    (6)  all_57_2 = e2
% 229.06/40.50    (7)   ~ (e3 = e2)
% 229.06/40.50    (8)   ~ (e3 = e0)
% 229.06/40.50    (9)  all_57_15 = e3
% 229.06/40.50    (10)  op(e3, e3) = e2
% 229.06/40.50    (11)   ~ (e2 = e0)
% 229.06/40.50    (12)  all_57_3 = e1
% 229.06/40.50    (13)   ~ (e1 = e0)
% 229.06/40.50    (14)  op(e0, e0) = e3
% 229.06/40.50    (15)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.06/40.50              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.06/40.50                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.06/40.50                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.06/40.50    (16)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.06/40.50          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.06/40.50    (17)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.06/40.50          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.06/40.50    (18)   ~ (e2 = e1)
% 229.06/40.50    (19)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.06/40.50          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.06/40.50    (20)  all_57_6 = e3 & op(e1, e3) = e3
% 229.06/40.50    (21)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.06/40.50          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.06/40.50    (22)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.06/40.50          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.06/40.50  
% 229.06/40.50  Begin of proof
% 229.06/40.50  | 
% 229.06/40.50  | ALPHA: (20) implies:
% 229.06/40.50  |   (23)  all_57_6 = e3
% 229.06/40.50  | 
% 229.06/40.50  | BETA: splitting (16) gives:
% 229.06/40.50  | 
% 229.06/40.50  | Case 1:
% 229.06/40.50  | | 
% 229.06/40.50  | |   (24)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 229.06/40.50  | |           e3)
% 229.06/40.50  | | 
% 229.06/40.50  | | REF_CLOSE: (3), (4), (5), (6), (7), (24) are inconsistent by sub-proof #684.
% 229.06/40.50  | | 
% 229.06/40.50  | Case 2:
% 229.06/40.50  | | 
% 229.06/40.50  | |   (25)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 229.06/40.50  | |           e3)
% 229.06/40.50  | | 
% 229.06/40.50  | | BETA: splitting (25) gives:
% 229.06/40.50  | | 
% 229.06/40.50  | | Case 1:
% 229.06/40.50  | | | 
% 229.06/40.50  | | |   (26)  all_57_5 = e3 & op(e2, e1) = e3
% 229.06/40.50  | | | 
% 229.06/40.50  | | | ALPHA: (26) implies:
% 229.06/40.50  | | |   (27)  all_57_5 = e3
% 229.06/40.50  | | | 
% 229.06/40.50  | | | BETA: splitting (21) gives:
% 229.06/40.50  | | | 
% 229.06/40.50  | | | Case 1:
% 229.06/40.50  | | | | 
% 229.06/40.50  | | | |   (28)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3)
% 229.06/40.50  | | | |           = e0)
% 229.06/40.50  | | | | 
% 229.06/40.50  | | | | REF_CLOSE: (4), (6), (10), (11), (28) are inconsistent by sub-proof
% 229.06/40.50  | | | |            #1577.
% 229.06/40.50  | | | | 
% 229.06/40.50  | | | Case 2:
% 229.06/40.50  | | | | 
% 229.06/40.50  | | | |   (29)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3)
% 229.06/40.50  | | | |           = e0)
% 229.06/40.50  | | | | 
% 229.06/40.50  | | | | BETA: splitting (29) gives:
% 229.06/40.50  | | | | 
% 229.06/40.50  | | | | Case 1:
% 229.06/40.50  | | | | | 
% 229.06/40.50  | | | | |   (30)  all_57_6 = e0 & op(e1, e3) = e0
% 229.06/40.50  | | | | | 
% 229.06/40.50  | | | | | REF_CLOSE: (8), (23), (30) are inconsistent by sub-proof #2465.
% 229.06/40.50  | | | | | 
% 229.06/40.50  | | | | Case 2:
% 229.06/40.50  | | | | | 
% 229.06/40.50  | | | | |   (31)  all_57_12 = e0 & op(e0, e3) = e0
% 229.06/40.50  | | | | | 
% 229.06/40.50  | | | | | ALPHA: (31) implies:
% 229.06/40.50  | | | | |   (32)  all_57_12 = e0
% 229.06/40.50  | | | | | 
% 229.06/40.50  | | | | | BETA: splitting (2) gives:
% 229.06/40.50  | | | | | 
% 229.06/40.50  | | | | | Case 1:
% 229.06/40.50  | | | | | | 
% 229.06/40.50  | | | | | |   (33)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2,
% 229.06/40.50  | | | | | |             e3) = e1)
% 229.06/40.50  | | | | | | 
% 229.06/40.50  | | | | | | REF_CLOSE: (4), (6), (10), (18), (33) are inconsistent by sub-proof
% 229.06/40.50  | | | | | |            #1633.
% 229.06/40.50  | | | | | | 
% 229.06/40.50  | | | | | Case 2:
% 229.06/40.50  | | | | | | 
% 229.06/40.50  | | | | | |   (34)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0,
% 229.06/40.50  | | | | | |             e3) = e1)
% 229.06/40.50  | | | | | | 
% 229.06/40.50  | | | | | | BETA: splitting (34) gives:
% 229.06/40.50  | | | | | | 
% 229.06/40.50  | | | | | | Case 1:
% 229.06/40.50  | | | | | | | 
% 229.06/40.50  | | | | | | |   (35)  all_57_6 = e1 & op(e1, e3) = e1
% 229.06/40.50  | | | | | | | 
% 229.06/40.50  | | | | | | | REF_CLOSE: (3), (23), (35) are inconsistent by sub-proof #2117.
% 229.06/40.50  | | | | | | | 
% 229.06/40.50  | | | | | | Case 2:
% 229.06/40.50  | | | | | | | 
% 229.06/40.50  | | | | | | |   (36)  all_57_12 = e1 & op(e0, e3) = e1
% 229.06/40.50  | | | | | | | 
% 229.06/40.50  | | | | | | | ALPHA: (36) implies:
% 229.06/40.50  | | | | | | |   (37)  all_57_12 = e1
% 229.06/40.50  | | | | | | | 
% 229.06/40.50  | | | | | | | COMBINE_EQS: (32), (37) imply:
% 229.06/40.50  | | | | | | |   (38)  e1 = e0
% 229.06/40.50  | | | | | | | 
% 229.06/40.50  | | | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (10), (11), (12),
% 229.06/40.50  | | | | | | |            (13), (17), (18), (21), (23), (27), (38) are
% 229.06/40.50  | | | | | | |            inconsistent by sub-proof #808.
% 229.06/40.50  | | | | | | | 
% 229.06/40.50  | | | | | | End of split
% 229.06/40.50  | | | | | | 
% 229.06/40.50  | | | | | End of split
% 229.06/40.50  | | | | | 
% 229.06/40.50  | | | | End of split
% 229.06/40.50  | | | | 
% 229.06/40.50  | | | End of split
% 229.06/40.50  | | | 
% 229.06/40.50  | | Case 2:
% 229.06/40.50  | | | 
% 229.06/40.50  | | |   (39)  all_57_10 = e3 & op(e2, e0) = e3
% 229.06/40.50  | | | 
% 229.06/40.50  | | | ALPHA: (39) implies:
% 229.06/40.50  | | |   (40)  all_57_10 = e3
% 229.06/40.50  | | | 
% 229.06/40.50  | | | REF_CLOSE: (3), (4), (7), (8), (9), (11), (13), (14), (15), (18), (19),
% 229.06/40.50  | | |            (22), (40) are inconsistent by sub-proof #1746.
% 229.06/40.50  | | | 
% 229.06/40.50  | | End of split
% 229.06/40.50  | | 
% 229.06/40.50  | End of split
% 229.06/40.50  | 
% 229.06/40.50  End of proof
% 229.06/40.50  
% 229.06/40.50  Sub-proof #658 shows that the following formulas are inconsistent:
% 229.06/40.50  ----------------------------------------------------------------
% 229.06/40.50    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.06/40.50           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.06/40.50    (2)  op(e2, e2) = e1
% 229.06/40.50    (3)   ~ (e3 = e0)
% 229.06/40.50    (4)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0)
% 229.06/40.50    (5)  all_57_2 = e3
% 229.06/40.50    (6)   ~ (e1 = e0)
% 229.06/40.50  
% 229.06/40.50  Begin of proof
% 229.06/40.50  | 
% 229.06/40.50  | BETA: splitting (4) gives:
% 229.06/40.50  | 
% 229.06/40.50  | Case 1:
% 229.06/40.50  | | 
% 229.06/40.50  | |   (7)  all_57_2 = e0 & op(e2, e3) = e0
% 229.06/40.50  | | 
% 229.06/40.50  | | REF_CLOSE: (3), (5), (7) are inconsistent by sub-proof #1805.
% 229.06/40.50  | | 
% 229.06/40.50  | Case 2:
% 229.06/40.50  | | 
% 229.06/40.50  | |   (8)  all_57_3 = e0 & op(e2, e2) = e0
% 229.06/40.50  | | 
% 229.06/40.50  | | ALPHA: (8) implies:
% 229.06/40.50  | |   (9)  op(e2, e2) = e0
% 229.06/40.50  | | 
% 229.06/40.50  | | REF_CLOSE: (1), (2), (6), (9) are inconsistent by sub-proof #2352.
% 229.06/40.50  | | 
% 229.06/40.50  | End of split
% 229.06/40.50  | 
% 229.06/40.50  End of proof
% 229.06/40.50  
% 229.06/40.50  Sub-proof #659 shows that the following formulas are inconsistent:
% 229.06/40.50  ----------------------------------------------------------------
% 229.06/40.50    (1)  all_57_9 = e2
% 229.06/40.50    (2)  all_57_0 = e2
% 229.06/40.50    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.06/40.50         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.06/40.50    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.06/40.50         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.06/40.50    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.06/40.50         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.06/40.50    (6)   ~ (e3 = e1)
% 229.06/40.50    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.06/40.50           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.06/40.50    (8)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.06/40.50         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.06/40.50    (9)   ~ (all_6_2 = e3)
% 229.06/40.50    (10)  op(e1, e1) = all_6_2
% 229.06/40.50    (11)  op(e2, e2) = e1
% 229.06/40.50    (12)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.06/40.50          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.06/40.50    (13)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 229.06/40.50            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 229.06/40.50              e3) = all_22_1 & $i(all_22_1))
% 229.06/40.50    (14)  all_57_2 = e2
% 229.06/40.50    (15)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.06/40.50          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.06/40.50    (16)   ~ (e3 = e2)
% 229.06/40.50    (17)   ~ (e3 = e0)
% 229.06/40.50    (18)  op(e0, e3) = e1
% 229.06/40.50    (19)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 229.06/40.50          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 229.06/40.50    (20)  all_57_15 = e3
% 229.06/40.50    (21)  op(e3, e3) = e2
% 229.06/40.50    (22)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.06/40.50          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.06/40.50            e1)
% 229.06/40.50    (23)  all_57_12 = e1
% 229.06/40.51    (24)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.06/40.51          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.06/40.51    (25)   ~ (e2 = e0)
% 229.06/40.51    (26)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 229.06/40.51            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 229.06/40.51              e3) = all_12_1 & $i(all_12_1))
% 229.06/40.51    (27)  all_57_3 = e1
% 229.06/40.51    (28)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.06/40.51          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.06/40.51    (29)   ~ (e1 = e0)
% 229.06/40.51    (30)  all_57_14 = e2
% 229.06/40.51    (31)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.06/40.51          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.06/40.51    (32)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.06/40.51          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.06/40.51    (33)  op(e0, e0) = e3
% 229.06/40.51    (34)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.06/40.51          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.06/40.51            e2)
% 229.06/40.51    (35)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.06/40.51              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.06/40.51                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.06/40.51                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.06/40.51    (36)  op(e1, e1) = e2
% 229.06/40.51    (37)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.06/40.51          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.06/40.51    (38)   ~ (all_53_12 = e3)
% 229.06/40.51    (39)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.06/40.51          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.06/40.51    (40)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.06/40.51          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.06/40.51    (41)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.06/40.51          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 229.06/40.51    (42)   ~ (e2 = e1)
% 229.06/40.51    (43)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.06/40.51          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.06/40.51    (44)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.06/40.51          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.06/40.51    (45)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.06/40.51          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.06/40.51    (46)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.06/40.51          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.06/40.51    (47)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.06/40.51          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.06/40.51    (48)  op(e3, e0) = all_53_12
% 229.06/40.51  
% 229.06/40.51  Begin of proof
% 229.06/40.51  | 
% 229.06/40.51  | BETA: splitting (37) gives:
% 229.06/40.51  | 
% 229.06/40.51  | Case 1:
% 229.06/40.51  | | 
% 229.06/40.51  | |   (49)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 229.06/40.51  | |           e3)
% 229.06/40.51  | | 
% 229.06/40.51  | | REF_CLOSE: (6), (7), (11), (14), (16), (49) are inconsistent by sub-proof
% 229.06/40.51  | |            #684.
% 229.06/40.51  | | 
% 229.06/40.51  | Case 2:
% 229.06/40.51  | | 
% 229.06/40.51  | |   (50)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 229.06/40.51  | |           e3)
% 229.06/40.51  | | 
% 229.06/40.51  | | BETA: splitting (50) gives:
% 229.06/40.51  | | 
% 229.06/40.51  | | Case 1:
% 229.06/40.51  | | | 
% 229.06/40.51  | | |   (51)  all_57_5 = e3 & op(e2, e1) = e3
% 229.06/40.51  | | | 
% 229.06/40.51  | | | ALPHA: (51) implies:
% 229.06/40.51  | | |   (52)  all_57_5 = e3
% 229.06/40.51  | | | 
% 229.06/40.51  | | | BETA: splitting (41) gives:
% 229.06/40.51  | | | 
% 229.06/40.51  | | | Case 1:
% 229.06/40.51  | | | | 
% 229.06/40.51  | | | |   (53)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2)
% 229.06/40.51  | | | |           = e0)
% 229.06/40.51  | | | | 
% 229.06/40.51  | | | | REF_CLOSE: (7), (11), (14), (25), (29), (53) are inconsistent by
% 229.06/40.51  | | | |            sub-proof #661.
% 229.06/40.51  | | | | 
% 229.06/40.51  | | | Case 2:
% 229.06/40.51  | | | | 
% 229.06/40.51  | | | |   (54)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0)
% 229.06/40.51  | | | |           = e0)
% 229.06/40.51  | | | | 
% 229.06/40.51  | | | | BETA: splitting (54) gives:
% 229.06/40.51  | | | | 
% 229.06/40.51  | | | | Case 1:
% 229.06/40.51  | | | | | 
% 229.06/40.51  | | | | |   (55)  all_57_5 = e0 & op(e2, e1) = e0
% 229.06/40.51  | | | | | 
% 229.06/40.51  | | | | | REF_CLOSE: (17), (52), (55) are inconsistent by sub-proof #2414.
% 229.06/40.51  | | | | | 
% 229.06/40.51  | | | | Case 2:
% 229.06/40.51  | | | | | 
% 229.06/40.51  | | | | |   (56)  all_57_10 = e0 & op(e2, e0) = e0
% 229.06/40.51  | | | | | 
% 229.06/40.51  | | | | | ALPHA: (56) implies:
% 229.06/40.51  | | | | |   (57)  all_57_10 = e0
% 229.06/40.51  | | | | | 
% 229.06/40.51  | | | | | BETA: splitting (5) gives:
% 229.06/40.51  | | | | | 
% 229.06/40.51  | | | | | Case 1:
% 229.06/40.51  | | | | | | 
% 229.06/40.51  | | | | | |   (58)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2,
% 229.06/40.51  | | | | | |             e2) = e2)
% 229.06/40.51  | | | | | | 
% 229.06/40.51  | | | | | | BETA: splitting (58) gives:
% 229.06/40.51  | | | | | | 
% 229.06/40.51  | | | | | | Case 1:
% 229.06/40.51  | | | | | | | 
% 229.06/40.51  | | | | | | |   (59)  all_57_1 = e2 & op(e3, e2) = e2
% 229.06/40.51  | | | | | | | 
% 229.06/40.51  | | | | | | | ALPHA: (59) implies:
% 229.06/40.51  | | | | | | |   (60)  all_57_1 = e2
% 229.06/40.51  | | | | | | | 
% 229.06/40.51  | | | | | | | BETA: splitting (46) gives:
% 229.06/40.51  | | | | | | | 
% 229.06/40.51  | | | | | | | Case 1:
% 229.06/40.51  | | | | | | | | 
% 229.06/40.51  | | | | | | | |   (61)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 &
% 229.06/40.51  | | | | | | | |           op(e2, e0) = e1)
% 229.06/40.51  | | | | | | | | 
% 229.06/40.51  | | | | | | | | BETA: splitting (61) gives:
% 229.06/40.51  | | | | | | | | 
% 229.06/40.51  | | | | | | | | Case 1:
% 229.06/40.51  | | | | | | | | | 
% 229.06/40.51  | | | | | | | | |   (62)  all_57_9 = e1 & op(e3, e0) = e1
% 229.06/40.51  | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | ALPHA: (62) implies:
% 229.06/40.51  | | | | | | | | |   (63)  all_57_9 = e1
% 229.06/40.51  | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | REF_CLOSE: (7), (13), (16), (18), (20), (25), (26), (42),
% 229.06/40.51  | | | | | | | | |            (43), (57), (63) are inconsistent by sub-proof
% 229.06/40.51  | | | | | | | | |            #1018.
% 229.06/40.51  | | | | | | | | | 
% 229.06/40.51  | | | | | | | | Case 2:
% 229.06/40.51  | | | | | | | | | 
% 229.06/40.51  | | | | | | | | |   (64)  all_57_10 = e1 & op(e2, e0) = e1
% 229.06/40.51  | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | ALPHA: (64) implies:
% 229.06/40.51  | | | | | | | | |   (65)  all_57_10 = e1
% 229.06/40.51  | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | COMBINE_EQS: (57), (65) imply:
% 229.06/40.51  | | | | | | | | |   (66)  e1 = e0
% 229.06/40.51  | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | COMBINE_EQS: (27), (66) imply:
% 229.06/40.51  | | | | | | | | |   (67)  all_57_3 = e0
% 229.06/40.51  | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (12),
% 229.06/40.51  | | | | | | | | |            (15), (16), (17), (20), (21), (22), (25), (28),
% 229.06/40.51  | | | | | | | | |            (29), (32), (33), (34), (35), (37), (38), (39),
% 229.06/40.51  | | | | | | | | |            (40), (42), (43), (45), (46), (47), (48), (60),
% 229.06/40.51  | | | | | | | | |            (67) are inconsistent by sub-proof #785.
% 229.06/40.51  | | | | | | | | | 
% 229.06/40.51  | | | | | | | | End of split
% 229.06/40.51  | | | | | | | | 
% 229.06/40.51  | | | | | | | Case 2:
% 229.06/40.51  | | | | | | | | 
% 229.06/40.51  | | | | | | | |   (68)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 &
% 229.06/40.51  | | | | | | | |           op(e0, e0) = e1)
% 229.06/40.51  | | | | | | | | 
% 229.06/40.51  | | | | | | | | BETA: splitting (68) gives:
% 229.06/40.51  | | | | | | | | 
% 229.06/40.51  | | | | | | | | Case 1:
% 229.06/40.51  | | | | | | | | | 
% 229.06/40.51  | | | | | | | | |   (69)  all_57_11 = e1 & op(e1, e0) = e1
% 229.06/40.51  | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | ALPHA: (69) implies:
% 229.06/40.51  | | | | | | | | |   (70)  all_57_11 = e1
% 229.06/40.51  | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | BETA: splitting (32) gives:
% 229.06/40.51  | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | Case 1:
% 229.06/40.51  | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | |   (71)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 &
% 229.06/40.51  | | | | | | | | | |           op(e2, e2) = e3)
% 229.06/40.51  | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | REF_CLOSE: (6), (7), (11), (16), (60), (71) are inconsistent
% 229.06/40.51  | | | | | | | | | |            by sub-proof #1031.
% 229.06/40.51  | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | Case 2:
% 229.06/40.51  | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | |   (72)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3
% 229.06/40.51  | | | | | | | | | |           & op(e0, e2) = e3)
% 229.06/40.51  | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | BETA: splitting (72) gives:
% 229.06/40.51  | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | Case 1:
% 229.06/40.51  | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | |   (73)  all_57_7 = e3 & op(e1, e2) = e3
% 229.06/40.51  | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | ALPHA: (73) implies:
% 229.06/40.51  | | | | | | | | | | |   (74)  all_57_7 = e3
% 229.06/40.51  | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | BETA: splitting (45) gives:
% 229.06/40.51  | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | Case 1:
% 229.06/40.51  | | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | |   (75)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 229.06/40.51  | | | | | | | | | | | |           & op(e2, e3) = e0)
% 229.06/40.51  | | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | | REF_CLOSE: (7), (14), (21), (25), (75) are inconsistent by
% 229.06/40.51  | | | | | | | | | | | |            sub-proof #1577.
% 229.06/40.51  | | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | Case 2:
% 229.06/40.51  | | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | |   (76)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 229.06/40.51  | | | | | | | | | | | |           e0 & op(e0, e3) = e0)
% 229.06/40.51  | | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | | BETA: splitting (76) gives:
% 229.06/40.51  | | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | | Case 1:
% 229.06/40.51  | | | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | | |   (77)  all_57_6 = e0 & op(e1, e3) = e0
% 229.06/40.51  | | | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | | | ALPHA: (77) implies:
% 229.06/40.51  | | | | | | | | | | | | |   (78)  all_57_6 = e0
% 229.06/40.51  | | | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | | | BETA: splitting (15) gives:
% 229.06/40.51  | | | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | | | Case 1:
% 229.06/40.51  | | | | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | | | |   (79)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 229.06/40.51  | | | | | | | | | | | | | |           & op(e3, e2) = e0)
% 229.06/40.51  | | | | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | | | | BETA: splitting (79) gives:
% 229.06/40.51  | | | | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | | | | Case 1:
% 229.06/40.51  | | | | | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | | | | |   (80)  all_57_0 = e0 & op(e3, e3) = e0
% 229.06/40.51  | | | | | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | | | | | ALPHA: (80) implies:
% 229.06/40.51  | | | | | | | | | | | | | | |   (81)  op(e3, e3) = e0
% 229.06/40.51  | | | | | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (8), (9), (10), (16), (17), (20), (23),
% 229.06/40.51  | | | | | | | | | | | | | | |            (25), (29), (35), (40), (42), (43), (44), (46),
% 229.06/40.51  | | | | | | | | | | | | | | |            (74), (78), (81) are inconsistent by sub-proof
% 229.06/40.51  | | | | | | | | | | | | | | |            #1029.
% 229.06/40.51  | | | | | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | | | | Case 2:
% 229.06/40.51  | | | | | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | | | | |   (82)  all_57_1 = e0 & op(e3, e2) = e0
% 229.06/40.51  | | | | | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | | | | | REF_CLOSE: (25), (60), (82) are inconsistent by sub-proof
% 229.06/40.51  | | | | | | | | | | | | | | |            #1723.
% 229.06/40.51  | | | | | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | | | | End of split
% 229.06/40.51  | | | | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | | | Case 2:
% 229.06/40.51  | | | | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | | | |   (83)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 229.06/40.51  | | | | | | | | | | | | | |           & op(e3, e0) = e0)
% 229.06/40.51  | | | | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | | | | BETA: splitting (83) gives:
% 229.06/40.51  | | | | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | | | | Case 1:
% 229.06/40.51  | | | | | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | | | | |   (84)  all_57_4 = e0 & op(e3, e1) = e0
% 229.06/40.51  | | | | | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | | | | | ALPHA: (84) implies:
% 229.06/40.51  | | | | | | | | | | | | | | |   (85)  all_57_4 = e0
% 229.06/40.51  | | | | | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | | | | | BETA: splitting (19) gives:
% 229.06/40.51  | | | | | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | | | | | Case 1:
% 229.06/40.51  | | | | | | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | | | | | |   (86)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 229.06/40.51  | | | | | | | | | | | | | | | |           & op(e2, e1) = e1)
% 229.06/40.51  | | | | | | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | | | | | | BETA: splitting (86) gives:
% 229.06/40.51  | | | | | | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | | | | | | Case 1:
% 229.06/40.51  | | | | | | | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | | | | | | |   (87)  all_57_4 = e1 & op(e3, e1) = e1
% 229.06/40.51  | | | | | | | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | | | | | | | ALPHA: (87) implies:
% 229.06/40.51  | | | | | | | | | | | | | | | | |   (88)  all_57_4 = e1
% 229.06/40.51  | | | | | | | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | | | | | | | COMBINE_EQS: (85), (88) imply:
% 229.06/40.51  | | | | | | | | | | | | | | | | |   (89)  e1 = e0
% 229.06/40.51  | | | | | | | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (6), (7), (9), (10), (16), (17), (20),
% 229.06/40.51  | | | | | | | | | | | | | | | | |            (22), (25), (27), (29), (31), (33), (34), (35),
% 229.06/40.51  | | | | | | | | | | | | | | | | |            (39), (42), (70), (85), (89) are inconsistent by
% 229.06/40.51  | | | | | | | | | | | | | | | | |            sub-proof #1040.
% 229.06/40.51  | | | | | | | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | | | | | | Case 2:
% 229.06/40.51  | | | | | | | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | | | | | | |   (90)  all_57_5 = e1 & op(e2, e1) = e1
% 229.06/40.51  | | | | | | | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (52), (90) are inconsistent by sub-proof
% 229.06/40.51  | | | | | | | | | | | | | | | | |            #2376.
% 229.06/40.51  | | | | | | | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | | | | | | End of split
% 229.06/40.51  | | | | | | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | | | | | Case 2:
% 229.06/40.51  | | | | | | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | | | | | |   (91)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 229.06/40.51  | | | | | | | | | | | | | | | |           e1 & op(e0, e1) = e1)
% 229.06/40.51  | | | | | | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | | | | | | BETA: splitting (91) gives:
% 229.06/40.51  | | | | | | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | | | | | | Case 1:
% 229.06/40.51  | | | | | | | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | | | | | | |   (92)  all_57_8 = e1 & op(e1, e1) = e1
% 229.06/40.51  | | | | | | | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | | | | | | | ALPHA: (92) implies:
% 229.06/40.51  | | | | | | | | | | | | | | | | |   (93)  op(e1, e1) = e1
% 229.06/40.51  | | | | | | | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (36), (42), (93) are inconsistent by
% 229.06/40.51  | | | | | | | | | | | | | | | | |            sub-proof #2423.
% 229.06/40.51  | | | | | | | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | | | | | | Case 2:
% 229.06/40.51  | | | | | | | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | | | | | | |   (94)  all_57_14 = e1 & op(e0, e1) = e1
% 229.06/40.51  | | | | | | | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | | | | | | | ALPHA: (94) implies:
% 229.06/40.51  | | | | | | | | | | | | | | | | |   (95)  all_57_14 = e1
% 229.06/40.51  | | | | | | | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (11), (16), (17), (24), (25), (29),
% 229.06/40.51  | | | | | | | | | | | | | | | | |            (30), (42), (60), (74), (95) are inconsistent by
% 229.06/40.51  | | | | | | | | | | | | | | | | |            sub-proof #660.
% 229.06/40.51  | | | | | | | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | | | | | | End of split
% 229.06/40.51  | | | | | | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | | | | | End of split
% 229.06/40.51  | | | | | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | | | | Case 2:
% 229.06/40.51  | | | | | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | | | | |   (96)  all_57_9 = e0 & op(e3, e0) = e0
% 229.06/40.51  | | | | | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | | | | | REF_CLOSE: (1), (25), (96) are inconsistent by sub-proof
% 229.06/40.51  | | | | | | | | | | | | | | |            #1973.
% 229.06/40.51  | | | | | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | | | | End of split
% 229.06/40.51  | | | | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | | | End of split
% 229.06/40.51  | | | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | | Case 2:
% 229.06/40.51  | | | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | | |   (97)  all_57_12 = e0 & op(e0, e3) = e0
% 229.06/40.51  | | | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | | | ALPHA: (97) implies:
% 229.06/40.51  | | | | | | | | | | | | |   (98)  all_57_12 = e0
% 229.06/40.51  | | | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | | | COMBINE_EQS: (23), (98) imply:
% 229.06/40.51  | | | | | | | | | | | | |   (99)  e1 = e0
% 229.06/40.51  | | | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | | | COMBINE_EQS: (27), (99) imply:
% 229.06/40.51  | | | | | | | | | | | | |   (100)  all_57_3 = e0
% 229.06/40.51  | | | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 229.06/40.51  | | | | | | | | | | | | |            (12), (15), (16), (17), (20), (21), (22), (25),
% 229.06/40.51  | | | | | | | | | | | | |            (28), (29), (32), (33), (34), (35), (37), (38),
% 229.06/40.51  | | | | | | | | | | | | |            (39), (40), (42), (43), (45), (46), (47), (48),
% 229.06/40.51  | | | | | | | | | | | | |            (60), (100) are inconsistent by sub-proof #785.
% 229.06/40.51  | | | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | | End of split
% 229.06/40.51  | | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | End of split
% 229.06/40.51  | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | Case 2:
% 229.06/40.51  | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | |   (101)  all_57_13 = e3 & op(e0, e2) = e3
% 229.06/40.51  | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | ALPHA: (101) implies:
% 229.06/40.51  | | | | | | | | | | |   (102)  all_57_13 = e3
% 229.06/40.51  | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | REF_CLOSE: (6), (7), (17), (20), (22), (25), (29), (30),
% 229.06/40.51  | | | | | | | | | | |            (33), (35), (42), (102) are inconsistent by
% 229.06/40.51  | | | | | | | | | | |            sub-proof #2212.
% 229.06/40.51  | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | End of split
% 229.06/40.51  | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | End of split
% 229.06/40.51  | | | | | | | | | 
% 229.06/40.51  | | | | | | | | Case 2:
% 229.06/40.51  | | | | | | | | | 
% 229.06/40.51  | | | | | | | | |   (103)  all_57_15 = e1 & op(e0, e0) = e1
% 229.06/40.51  | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | ALPHA: (103) implies:
% 229.06/40.51  | | | | | | | | |   (104)  op(e0, e0) = e1
% 229.06/40.51  | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | REF_CLOSE: (6), (7), (33), (104) are inconsistent by sub-proof
% 229.06/40.51  | | | | | | | | |            #2183.
% 229.06/40.51  | | | | | | | | | 
% 229.06/40.51  | | | | | | | | End of split
% 229.06/40.51  | | | | | | | | 
% 229.06/40.51  | | | | | | | End of split
% 229.06/40.51  | | | | | | | 
% 229.06/40.51  | | | | | | Case 2:
% 229.06/40.51  | | | | | | | 
% 229.06/40.51  | | | | | | |   (105)  all_57_3 = e2 & op(e2, e2) = e2
% 229.06/40.51  | | | | | | | 
% 229.06/40.51  | | | | | | | ALPHA: (105) implies:
% 229.06/40.51  | | | | | | |   (106)  op(e2, e2) = e2
% 229.06/40.51  | | | | | | | 
% 229.06/40.51  | | | | | | | REF_CLOSE: (7), (11), (42), (106) are inconsistent by sub-proof
% 229.06/40.51  | | | | | | |            #2306.
% 229.06/40.51  | | | | | | | 
% 229.06/40.51  | | | | | | End of split
% 229.06/40.51  | | | | | | 
% 229.06/40.51  | | | | | Case 2:
% 229.06/40.51  | | | | | | 
% 229.06/40.51  | | | | | |   (107)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 &
% 229.06/40.51  | | | | | |            op(e0, e2) = e2)
% 229.06/40.51  | | | | | | 
% 229.06/40.51  | | | | | | BETA: splitting (107) gives:
% 229.06/40.51  | | | | | | 
% 229.06/40.51  | | | | | | Case 1:
% 229.06/40.51  | | | | | | | 
% 229.06/40.51  | | | | | | |   (108)  all_57_7 = e2 & op(e1, e2) = e2
% 229.06/40.51  | | | | | | | 
% 229.06/40.51  | | | | | | | ALPHA: (108) implies:
% 229.06/40.51  | | | | | | |   (109)  all_57_7 = e2
% 229.06/40.51  | | | | | | | 
% 229.06/40.51  | | | | | | | BETA: splitting (8) gives:
% 229.06/40.51  | | | | | | | 
% 229.06/40.51  | | | | | | | Case 1:
% 229.06/40.51  | | | | | | | | 
% 229.06/40.51  | | | | | | | |   (110)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 &
% 229.06/40.51  | | | | | | | |            op(e1, e2) = e3)
% 229.06/40.51  | | | | | | | | 
% 229.06/40.51  | | | | | | | | BETA: splitting (110) gives:
% 229.06/40.51  | | | | | | | | 
% 229.06/40.51  | | | | | | | | Case 1:
% 229.06/40.51  | | | | | | | | | 
% 229.06/40.51  | | | | | | | | |   (111)  all_57_6 = e3 & op(e1, e3) = e3
% 229.06/40.51  | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | ALPHA: (111) implies:
% 229.06/40.51  | | | | | | | | |   (112)  all_57_6 = e3
% 229.06/40.51  | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | BETA: splitting (32) gives:
% 229.06/40.51  | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | Case 1:
% 229.06/40.51  | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | |   (113)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 229.06/40.51  | | | | | | | | | |            & op(e2, e2) = e3)
% 229.06/40.51  | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | BETA: splitting (113) gives:
% 229.06/40.51  | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | Case 1:
% 229.06/40.51  | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | |   (114)  all_57_1 = e3 & op(e3, e2) = e3
% 229.06/40.51  | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | ALPHA: (114) implies:
% 229.06/40.51  | | | | | | | | | | |   (115)  all_57_1 = e3
% 229.06/40.51  | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 229.06/40.51  | | | | | | | | | | |            (14), (16), (17), (20), (21), (24), (25), (27),
% 229.06/40.51  | | | | | | | | | | |            (29), (32), (35), (39), (42), (43), (45), (46),
% 229.06/40.51  | | | | | | | | | | |            (47), (52), (112), (115) are inconsistent by
% 229.06/40.51  | | | | | | | | | | |            sub-proof #807.
% 229.06/40.51  | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | Case 2:
% 229.06/40.51  | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | |   (116)  all_57_3 = e3 & op(e2, e2) = e3
% 229.06/40.51  | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | ALPHA: (116) implies:
% 229.06/40.51  | | | | | | | | | | |   (117)  op(e2, e2) = e3
% 229.06/40.51  | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | | REF_CLOSE: (6), (7), (11), (117) are inconsistent by
% 229.06/40.51  | | | | | | | | | | |            sub-proof #1912.
% 229.06/40.51  | | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | End of split
% 229.06/40.51  | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | Case 2:
% 229.06/40.51  | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | |   (118)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3
% 229.06/40.51  | | | | | | | | | |            & op(e0, e2) = e3)
% 229.06/40.51  | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | | REF_CLOSE: (6), (7), (16), (17), (20), (22), (25), (29),
% 229.06/40.51  | | | | | | | | | |            (30), (33), (35), (42), (109), (118) are
% 229.06/40.51  | | | | | | | | | |            inconsistent by sub-proof #723.
% 229.06/40.51  | | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | End of split
% 229.06/40.51  | | | | | | | | | 
% 229.06/40.51  | | | | | | | | Case 2:
% 229.06/40.51  | | | | | | | | | 
% 229.06/40.51  | | | | | | | | |   (119)  all_57_7 = e3 & op(e1, e2) = e3
% 229.06/40.51  | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | ALPHA: (119) implies:
% 229.06/40.51  | | | | | | | | |   (120)  all_57_7 = e3
% 229.06/40.51  | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | REF_CLOSE: (16), (109), (120) are inconsistent by sub-proof
% 229.06/40.51  | | | | | | | | |            #2102.
% 229.06/40.51  | | | | | | | | | 
% 229.06/40.51  | | | | | | | | End of split
% 229.06/40.51  | | | | | | | | 
% 229.06/40.51  | | | | | | | Case 2:
% 229.06/40.51  | | | | | | | | 
% 229.06/40.51  | | | | | | | |   (121)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 &
% 229.06/40.51  | | | | | | | |            op(e1, e0) = e3)
% 229.06/40.51  | | | | | | | | 
% 229.06/40.51  | | | | | | | | BETA: splitting (121) gives:
% 229.06/40.51  | | | | | | | | 
% 229.06/40.51  | | | | | | | | Case 1:
% 229.06/40.51  | | | | | | | | | 
% 229.06/40.51  | | | | | | | | |   (122)  all_57_8 = e3 & op(e1, e1) = e3
% 229.06/40.51  | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | ALPHA: (122) implies:
% 229.06/40.51  | | | | | | | | |   (123)  op(e1, e1) = e3
% 229.06/40.51  | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | REF_CLOSE: (7), (9), (10), (123) are inconsistent by sub-proof
% 229.06/40.51  | | | | | | | | |            #2468.
% 229.06/40.51  | | | | | | | | | 
% 229.06/40.51  | | | | | | | | Case 2:
% 229.06/40.51  | | | | | | | | | 
% 229.06/40.51  | | | | | | | | |   (124)  all_57_11 = e3 & op(e1, e0) = e3
% 229.06/40.51  | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | ALPHA: (124) implies:
% 229.06/40.51  | | | | | | | | |   (125)  all_57_11 = e3
% 229.06/40.51  | | | | | | | | | 
% 229.06/40.51  | | | | | | | | | REF_CLOSE: (1), (6), (20), (29), (42), (46), (57), (125) are
% 229.06/40.51  | | | | | | | | |            inconsistent by sub-proof #2139.
% 229.06/40.51  | | | | | | | | | 
% 229.06/40.51  | | | | | | | | End of split
% 229.06/40.51  | | | | | | | | 
% 229.06/40.51  | | | | | | | End of split
% 229.06/40.51  | | | | | | | 
% 229.06/40.51  | | | | | | Case 2:
% 229.06/40.51  | | | | | | | 
% 229.06/40.51  | | | | | | |   (126)  all_57_13 = e2 & op(e0, e2) = e2
% 229.06/40.51  | | | | | | | 
% 229.06/40.51  | | | | | | | ALPHA: (126) implies:
% 229.06/40.51  | | | | | | |   (127)  all_57_13 = e2
% 229.06/40.51  | | | | | | | 
% 229.06/40.51  | | | | | | | REF_CLOSE: (7), (17), (23), (25), (29), (30), (33), (35), (127)
% 229.06/40.51  | | | | | | |            are inconsistent by sub-proof #1583.
% 229.06/40.51  | | | | | | | 
% 229.06/40.51  | | | | | | End of split
% 229.06/40.51  | | | | | | 
% 229.06/40.51  | | | | | End of split
% 229.06/40.51  | | | | | 
% 229.06/40.51  | | | | End of split
% 229.06/40.51  | | | | 
% 229.06/40.51  | | | End of split
% 229.06/40.51  | | | 
% 229.06/40.51  | | Case 2:
% 229.06/40.51  | | | 
% 229.06/40.51  | | |   (128)  all_57_10 = e3 & op(e2, e0) = e3
% 229.06/40.51  | | | 
% 229.06/40.51  | | | ALPHA: (128) implies:
% 229.06/40.51  | | |   (129)  all_57_10 = e3
% 229.06/40.51  | | | 
% 229.06/40.51  | | | REF_CLOSE: (6), (7), (16), (17), (20), (25), (29), (33), (35), (42), (43),
% 229.06/40.51  | | |            (46), (129) are inconsistent by sub-proof #1746.
% 229.06/40.51  | | | 
% 229.06/40.51  | | End of split
% 229.06/40.51  | | 
% 229.06/40.51  | End of split
% 229.06/40.51  | 
% 229.06/40.51  End of proof
% 229.06/40.51  
% 229.06/40.51  Sub-proof #660 shows that the following formulas are inconsistent:
% 229.06/40.51  ----------------------------------------------------------------
% 229.06/40.51    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.06/40.51         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.06/40.51    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.06/40.51           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.06/40.51    (3)  op(e2, e2) = e1
% 229.06/40.51    (4)   ~ (e3 = e2)
% 229.06/40.51    (5)   ~ (e3 = e0)
% 229.06/40.51    (6)  all_57_1 = e2
% 229.06/40.51    (7)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.06/40.51         (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.06/40.51    (8)   ~ (e2 = e0)
% 229.06/40.51    (9)   ~ (e1 = e0)
% 229.06/40.51    (10)  all_57_14 = e2
% 229.06/40.51    (11)  all_57_14 = e1
% 229.06/40.51    (12)  all_57_7 = e3
% 229.06/40.51    (13)   ~ (e2 = e1)
% 229.06/40.51  
% 229.06/40.51  Begin of proof
% 229.06/40.51  | 
% 229.06/40.51  | COMBINE_EQS: (10), (11) imply:
% 229.06/40.51  |   (14)  e2 = e1
% 229.06/40.51  | 
% 229.06/40.51  | COMBINE_EQS: (6), (14) imply:
% 229.06/40.51  |   (15)  all_57_1 = e1
% 229.06/40.51  | 
% 229.06/40.51  | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (12), (13), (15) are
% 229.06/40.51  |            inconsistent by sub-proof #1909.
% 229.06/40.51  | 
% 229.06/40.51  End of proof
% 229.06/40.51  
% 229.06/40.51  Sub-proof #661 shows that the following formulas are inconsistent:
% 229.06/40.51  ----------------------------------------------------------------
% 229.06/40.51    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.06/40.51           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.06/40.51    (2)  op(e2, e2) = e1
% 229.06/40.51    (3)  all_57_2 = e2
% 229.06/40.51    (4)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0)
% 229.06/40.51    (5)   ~ (e2 = e0)
% 229.06/40.51    (6)   ~ (e1 = e0)
% 229.06/40.51  
% 229.06/40.51  Begin of proof
% 229.06/40.51  | 
% 229.06/40.51  | BETA: splitting (4) gives:
% 229.06/40.51  | 
% 229.06/40.51  | Case 1:
% 229.06/40.51  | | 
% 229.06/40.51  | |   (7)  all_57_2 = e0 & op(e2, e3) = e0
% 229.06/40.51  | | 
% 229.06/40.51  | | REF_CLOSE: (3), (5), (7) are inconsistent by sub-proof #1700.
% 229.06/40.51  | | 
% 229.06/40.51  | Case 2:
% 229.06/40.51  | | 
% 229.06/40.51  | |   (8)  all_57_3 = e0 & op(e2, e2) = e0
% 229.06/40.51  | | 
% 229.06/40.51  | | ALPHA: (8) implies:
% 229.06/40.51  | |   (9)  op(e2, e2) = e0
% 229.06/40.51  | | 
% 229.06/40.51  | | REF_CLOSE: (1), (2), (6), (9) are inconsistent by sub-proof #2352.
% 229.06/40.51  | | 
% 229.06/40.51  | End of split
% 229.06/40.51  | 
% 229.06/40.51  End of proof
% 229.06/40.51  
% 229.06/40.51  Sub-proof #662 shows that the following formulas are inconsistent:
% 229.06/40.51  ----------------------------------------------------------------
% 229.06/40.51    (1)   ~ (e3 = e1)
% 229.06/40.51    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.06/40.51           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.06/40.51    (3)  op(e2, e2) = e1
% 229.06/40.51    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2)
% 229.06/40.51    (5)   ~ (e3 = e2)
% 229.06/40.51    (6)  op(e3, e3) = e2
% 229.06/40.51    (7)  all_57_4 = e1
% 229.06/40.51    (8)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.06/40.51         (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.06/40.51    (9)   ~ (all_53_12 = e3)
% 229.06/40.51    (10)   ~ (e2 = e1)
% 229.06/40.51    (11)  op(e3, e0) = all_53_12
% 229.06/40.51  
% 229.06/40.51  Begin of proof
% 229.06/40.51  | 
% 229.06/40.51  | BETA: splitting (4) gives:
% 229.06/40.51  | 
% 229.06/40.51  | Case 1:
% 229.06/40.51  | | 
% 229.06/40.51  | |   (12)  all_57_1 = e2 & op(e3, e2) = e2
% 229.06/40.51  | | 
% 229.06/40.51  | | ALPHA: (12) implies:
% 229.06/40.51  | |   (13)  all_57_1 = e2
% 229.06/40.51  | | 
% 229.06/40.51  | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (9), (11), (13) are inconsistent by
% 229.06/40.51  | |            sub-proof #1308.
% 229.06/40.51  | | 
% 229.06/40.51  | Case 2:
% 229.06/40.51  | | 
% 229.06/40.51  | |   (14)  all_57_3 = e2 & op(e2, e2) = e2
% 229.06/40.51  | | 
% 229.06/40.51  | | ALPHA: (14) implies:
% 229.06/40.51  | |   (15)  op(e2, e2) = e2
% 229.06/40.51  | | 
% 229.06/40.51  | | REF_CLOSE: (2), (3), (10), (15) are inconsistent by sub-proof #2306.
% 229.06/40.51  | | 
% 229.06/40.51  | End of split
% 229.06/40.51  | 
% 229.06/40.51  End of proof
% 229.06/40.51  
% 229.06/40.51  Sub-proof #663 shows that the following formulas are inconsistent:
% 229.06/40.51  ----------------------------------------------------------------
% 229.06/40.51    (1)  all_57_9 = e2
% 229.06/40.51    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.06/40.51         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.06/40.51    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.06/40.51         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.06/40.51    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.06/40.51         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.06/40.51    (5)   ~ (e3 = e1)
% 229.06/40.51    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.06/40.51           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.06/40.51    (7)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.06/40.51         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.06/40.51    (8)   ~ (all_6_2 = e3)
% 229.06/40.51    (9)  op(e1, e1) = all_6_2
% 229.06/40.51    (10)  op(e2, e2) = e1
% 229.06/40.51    (11)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.06/40.51          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.06/40.51    (12)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.06/40.51          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.06/40.51    (13)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.06/40.51          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.06/40.51    (14)   ~ (e3 = e2)
% 229.06/40.51    (15)   ~ (e3 = e0)
% 229.06/40.51    (16)  all_57_15 = e3
% 229.06/40.51    (17)  op(e3, e3) = e2
% 229.06/40.51    (18)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.06/40.51          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.06/40.51            e1)
% 229.06/40.51    (19)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.06/40.51          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.06/40.51    (20)   ~ (e2 = e0)
% 229.06/40.51    (21)  all_57_3 = e1
% 229.06/40.51    (22)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.06/40.51          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.06/40.51    (23)   ~ (e1 = e0)
% 229.06/40.51    (24)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.06/40.51          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.06/40.51    (25)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.06/40.51          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.06/40.51    (26)  op(e0, e0) = e3
% 229.06/40.51    (27)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.06/40.51          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.06/40.51            e2)
% 229.06/40.51    (28)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.06/40.51              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.06/40.51                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.06/40.51                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.06/40.51    (29)   ~ (all_53_12 = e3)
% 229.06/40.51    (30)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.06/40.51          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.06/40.51    (31)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.06/40.51          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.06/40.51    (32)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.06/40.51          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 229.06/40.51    (33)   ~ (e2 = e1)
% 229.06/40.52    (34)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.06/40.52          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.06/40.52    (35)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.06/40.52          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.06/40.52    (36)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.06/40.52          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.06/40.52    (37)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.06/40.52          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.06/40.52    (38)  all_57_13 = e2 & op(e0, e2) = e2
% 229.06/40.52    (39)  op(e3, e0) = all_53_12
% 229.06/40.52  
% 229.06/40.52  Begin of proof
% 229.06/40.52  | 
% 229.06/40.52  | ALPHA: (38) implies:
% 229.06/40.52  |   (40)  all_57_13 = e2
% 229.06/40.52  | 
% 229.06/40.52  | BETA: splitting (36) gives:
% 229.06/40.52  | 
% 229.06/40.52  | Case 1:
% 229.06/40.52  | | 
% 229.06/40.52  | |   (41)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) =
% 229.06/40.52  | |           e1)
% 229.06/40.52  | | 
% 229.06/40.52  | | BETA: splitting (41) gives:
% 229.06/40.52  | | 
% 229.06/40.52  | | Case 1:
% 229.06/40.52  | | | 
% 229.06/40.52  | | |   (42)  all_57_9 = e1 & op(e3, e0) = e1
% 229.06/40.52  | | | 
% 229.06/40.52  | | | ALPHA: (42) implies:
% 229.06/40.52  | | |   (43)  all_57_9 = e1
% 229.06/40.52  | | | 
% 229.06/40.52  | | | REF_CLOSE: (1), (33), (43) are inconsistent by sub-proof #2444.
% 229.06/40.52  | | | 
% 229.06/40.52  | | Case 2:
% 229.06/40.52  | | | 
% 229.06/40.52  | | |   (44)  all_57_10 = e1 & op(e2, e0) = e1
% 229.06/40.52  | | | 
% 229.06/40.52  | | | ALPHA: (44) implies:
% 229.06/40.52  | | |   (45)  all_57_10 = e1
% 229.06/40.52  | | | 
% 229.06/40.52  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 229.06/40.52  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 229.06/40.52  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 229.06/40.52  | | |            (33), (34), (35), (36), (37), (39), (45) are inconsistent by
% 229.06/40.52  | | |            sub-proof #805.
% 229.06/40.52  | | | 
% 229.06/40.52  | | End of split
% 229.06/40.52  | | 
% 229.06/40.52  | Case 2:
% 229.06/40.52  | | 
% 229.06/40.52  | |   (46)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.06/40.52  | |           e1)
% 229.06/40.52  | | 
% 229.06/40.52  | | BETA: splitting (46) gives:
% 229.06/40.52  | | 
% 229.06/40.52  | | Case 1:
% 229.06/40.52  | | | 
% 229.06/40.52  | | |   (47)  all_57_11 = e1 & op(e1, e0) = e1
% 229.06/40.52  | | | 
% 229.06/40.52  | | | ALPHA: (47) implies:
% 229.06/40.52  | | |   (48)  all_57_11 = e1
% 229.06/40.52  | | | 
% 229.06/40.52  | | | BETA: splitting (28) gives:
% 229.06/40.52  | | | 
% 229.06/40.52  | | | Case 1:
% 229.06/40.52  | | | | 
% 229.06/40.52  | | | |   (49)  all_57_15 = e0 & op(e0, e0) = e0
% 229.06/40.52  | | | | 
% 229.06/40.52  | | | | ALPHA: (49) implies:
% 229.06/40.52  | | | |   (50)  op(e0, e0) = e0
% 229.06/40.52  | | | | 
% 229.06/40.52  | | | | REF_CLOSE: (6), (15), (26), (50) are inconsistent by sub-proof #2304.
% 229.06/40.52  | | | | 
% 229.06/40.52  | | | Case 2:
% 229.06/40.52  | | | | 
% 229.06/40.52  | | | |   (51)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2,
% 229.06/40.52  | | | |               e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) &
% 229.06/40.52  | | | |         ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0,
% 229.06/40.52  | | | |               e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 229.06/40.52  | | | | 
% 229.06/40.52  | | | | ALPHA: (51) implies:
% 229.06/40.52  | | | |   (52)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0,
% 229.06/40.52  | | | |             e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.06/40.52  | | | |   (53)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0)
% 229.06/40.52  | | | |           = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 229.06/40.52  | | | | 
% 229.06/40.52  | | | | BETA: splitting (53) gives:
% 229.06/40.52  | | | | 
% 229.06/40.52  | | | | Case 1:
% 229.06/40.52  | | | | | 
% 229.06/40.52  | | | | |   (54)  all_57_9 = e0 & op(e3, e0) = e0
% 229.06/40.52  | | | | | 
% 229.06/40.52  | | | | | ALPHA: (54) implies:
% 229.06/40.52  | | | | |   (55)  all_57_9 = e0
% 229.06/40.52  | | | | | 
% 229.06/40.52  | | | | | REF_CLOSE: (1), (20), (55) are inconsistent by sub-proof #2440.
% 229.06/40.52  | | | | | 
% 229.06/40.52  | | | | Case 2:
% 229.06/40.52  | | | | | 
% 229.06/40.52  | | | | |   (56)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 229.06/40.52  | | | | |             e0) = e0)
% 229.06/40.52  | | | | | 
% 229.06/40.52  | | | | | BETA: splitting (56) gives:
% 229.06/40.52  | | | | | 
% 229.06/40.52  | | | | | Case 1:
% 229.06/40.52  | | | | | | 
% 229.06/40.52  | | | | | |   (57)  all_57_10 = e0 & op(e2, e0) = e0
% 229.06/40.52  | | | | | | 
% 229.06/40.52  | | | | | | ALPHA: (57) implies:
% 229.06/40.52  | | | | | |   (58)  all_57_10 = e0
% 229.06/40.52  | | | | | | 
% 229.06/40.52  | | | | | | BETA: splitting (11) gives:
% 229.06/40.52  | | | | | | 
% 229.06/40.52  | | | | | | Case 1:
% 229.06/40.52  | | | | | | | 
% 229.06/40.52  | | | | | | |   (59)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 &
% 229.06/40.52  | | | | | | |           op(e3, e2) = e1)
% 229.06/40.52  | | | | | | | 
% 229.06/40.52  | | | | | | | REF_CLOSE: (4), (5), (6), (10), (14), (15), (17), (19), (20),
% 229.06/40.52  | | | | | | |            (23), (25), (33), (59) are inconsistent by sub-proof
% 229.06/40.52  | | | | | | |            #1677.
% 229.06/40.52  | | | | | | | 
% 229.06/40.52  | | | | | | Case 2:
% 229.06/40.52  | | | | | | | 
% 229.06/40.52  | | | | | | |   (60)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 &
% 229.06/40.52  | | | | | | |           op(e3, e0) = e1)
% 229.06/40.52  | | | | | | | 
% 229.06/40.52  | | | | | | | BETA: splitting (60) gives:
% 229.06/40.52  | | | | | | | 
% 229.06/40.52  | | | | | | | Case 1:
% 229.06/40.52  | | | | | | | | 
% 229.06/40.52  | | | | | | | |   (61)  all_57_4 = e1 & op(e3, e1) = e1
% 229.06/40.52  | | | | | | | | 
% 229.06/40.52  | | | | | | | | ALPHA: (61) implies:
% 229.06/40.52  | | | | | | | |   (62)  all_57_4 = e1
% 229.06/40.52  | | | | | | | | 
% 229.06/40.52  | | | | | | | | BETA: splitting (22) gives:
% 229.06/40.52  | | | | | | | | 
% 229.06/40.52  | | | | | | | | Case 1:
% 229.06/40.52  | | | | | | | | | 
% 229.06/40.52  | | | | | | | | |   (63)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 &
% 229.06/40.52  | | | | | | | | |           op(e3, e2) = e3)
% 229.06/40.52  | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | BETA: splitting (63) gives:
% 229.06/40.52  | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | Case 1:
% 229.06/40.52  | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | |   (64)  all_57_0 = e3 & op(e3, e3) = e3
% 229.06/40.52  | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | ALPHA: (64) implies:
% 229.06/40.52  | | | | | | | | | |   (65)  op(e3, e3) = e3
% 229.06/40.52  | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | REF_CLOSE: (6), (14), (17), (65) are inconsistent by
% 229.06/40.52  | | | | | | | | | |            sub-proof #2490.
% 229.06/40.52  | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | Case 2:
% 229.06/40.52  | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | |   (66)  all_57_1 = e3 & op(e3, e2) = e3
% 229.06/40.52  | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | ALPHA: (66) implies:
% 229.06/40.52  | | | | | | | | | |   (67)  all_57_1 = e3
% 229.06/40.52  | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | BETA: splitting (24) gives:
% 229.06/40.52  | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | Case 1:
% 229.06/40.52  | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | |   (68)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 229.06/40.52  | | | | | | | | | | |           & op(e2, e1) = e3)
% 229.06/40.52  | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | BETA: splitting (68) gives:
% 229.06/40.52  | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | Case 1:
% 229.06/40.52  | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | |   (69)  all_57_4 = e3 & op(e3, e1) = e3
% 229.06/40.52  | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | ALPHA: (69) implies:
% 229.06/40.52  | | | | | | | | | | | |   (70)  all_57_4 = e3
% 229.06/40.52  | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | REF_CLOSE: (1), (5), (11), (12), (13), (14), (15), (20),
% 229.06/40.52  | | | | | | | | | | | |            (23), (33), (67), (70) are inconsistent by
% 229.06/40.52  | | | | | | | | | | | |            sub-proof #1222.
% 229.06/40.52  | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | Case 2:
% 229.06/40.52  | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | |   (71)  all_57_5 = e3 & op(e2, e1) = e3
% 229.06/40.52  | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | ALPHA: (71) implies:
% 229.06/40.52  | | | | | | | | | | | |   (72)  all_57_5 = e3
% 229.06/40.52  | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | BETA: splitting (30) gives:
% 229.06/40.52  | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | Case 1:
% 229.06/40.52  | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | |   (73)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 229.06/40.52  | | | | | | | | | | | | |           & op(e2, e2) = e2)
% 229.06/40.52  | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | BETA: splitting (73) gives:
% 229.06/40.52  | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | Case 1:
% 229.06/40.52  | | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | |   (74)  all_57_2 = e2 & op(e2, e3) = e2
% 229.06/40.52  | | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | | ALPHA: (74) implies:
% 229.06/40.52  | | | | | | | | | | | | | |   (75)  all_57_2 = e2
% 229.06/40.52  | | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | | BETA: splitting (19) gives:
% 229.06/40.52  | | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | | Case 1:
% 229.06/40.52  | | | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | | |   (76)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 229.06/40.52  | | | | | | | | | | | | | | |           & op(e2, e2) = e0)
% 229.06/40.52  | | | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | | | BETA: splitting (76) gives:
% 229.06/40.52  | | | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | | | Case 1:
% 229.06/40.52  | | | | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | | | |   (77)  all_57_1 = e0 & op(e3, e2) = e0
% 229.06/40.52  | | | | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | | | | REF_CLOSE: (15), (67), (77) are inconsistent by sub-proof
% 229.06/40.52  | | | | | | | | | | | | | | | |            #1811.
% 229.06/40.52  | | | | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | | | Case 2:
% 229.06/40.52  | | | | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | | | |   (78)  all_57_3 = e0 & op(e2, e2) = e0
% 229.06/40.52  | | | | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | | | | ALPHA: (78) implies:
% 229.06/40.52  | | | | | | | | | | | | | | | |   (79)  all_57_3 = e0
% 229.06/40.52  | | | | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | | | | REF_CLOSE: (2), (5), (23), (33), (58), (72), (75), (79) are
% 229.06/40.52  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1530.
% 229.06/40.52  | | | | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | | | End of split
% 229.06/40.52  | | | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | | Case 2:
% 229.06/40.52  | | | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | | |   (80)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 229.06/40.52  | | | | | | | | | | | | | | |           e0 & op(e0, e2) = e0)
% 229.06/40.52  | | | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | | | BETA: splitting (80) gives:
% 229.06/40.52  | | | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | | | Case 1:
% 229.06/40.52  | | | | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | | | |   (81)  all_57_7 = e0 & op(e1, e2) = e0
% 229.06/40.52  | | | | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | | | | ALPHA: (81) implies:
% 229.06/40.52  | | | | | | | | | | | | | | | |   (82)  all_57_7 = e0
% 229.06/40.52  | | | | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | | | | BETA: splitting (31) gives:
% 229.06/40.52  | | | | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | | | | Case 1:
% 229.06/40.52  | | | | | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | | | | |   (83)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 229.06/40.52  | | | | | | | | | | | | | | | | |           & op(e2, e3) = e3)
% 229.06/40.52  | | | | | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10), (14), (17), (20), (30), (33), (58),
% 229.06/40.52  | | | | | | | | | | | | | | | | |            (72), (83) are inconsistent by sub-proof #727.
% 229.06/40.52  | | | | | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | | | | Case 2:
% 229.06/40.52  | | | | | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | | | | |   (84)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 229.06/40.52  | | | | | | | | | | | | | | | | |           e3 & op(e0, e3) = e3)
% 229.06/40.52  | | | | | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | | | | | BETA: splitting (84) gives:
% 229.06/40.52  | | | | | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | | | | | Case 1:
% 229.06/40.52  | | | | | | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | | | | | |   (85)  all_57_6 = e3 & op(e1, e3) = e3
% 229.06/40.52  | | | | | | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | | | | | | ALPHA: (85) implies:
% 229.06/40.52  | | | | | | | | | | | | | | | | | |   (86)  all_57_6 = e3
% 229.06/40.52  | | | | | | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 229.06/40.52  | | | | | | | | | | | | | | | | | |            (14), (15), (16), (17), (19), (20), (21), (23),
% 229.06/40.52  | | | | | | | | | | | | | | | | | |            (25), (28), (30), (33), (34), (35), (36), (37),
% 229.06/40.52  | | | | | | | | | | | | | | | | | |            (67), (72), (75), (86) are inconsistent by
% 229.06/40.52  | | | | | | | | | | | | | | | | | |            sub-proof #807.
% 229.06/40.52  | | | | | | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | | | | | Case 2:
% 229.06/40.52  | | | | | | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | | | | | |   (87)  all_57_12 = e3 & op(e0, e3) = e3
% 229.06/40.52  | | | | | | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | | | | | | ALPHA: (87) implies:
% 229.06/40.52  | | | | | | | | | | | | | | | | | |   (88)  all_57_12 = e3
% 229.06/40.52  | | | | | | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | | | | | | BETA: splitting (3) gives:
% 229.06/40.52  | | | | | | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | | | | | | Case 1:
% 229.06/40.52  | | | | | | | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | | | | | | |   (89)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 229.06/40.52  | | | | | | | | | | | | | | | | | | |           & op(e2, e3) = e1)
% 229.06/40.52  | | | | | | | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (17), (33), (75), (89) are inconsistent by
% 229.06/40.52  | | | | | | | | | | | | | | | | | | |            sub-proof #1633.
% 229.06/40.52  | | | | | | | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | | | | | | Case 2:
% 229.06/40.52  | | | | | | | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | | | | | | |   (90)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 229.06/40.52  | | | | | | | | | | | | | | | | | | |           e1 & op(e0, e3) = e1)
% 229.06/40.52  | | | | | | | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | | | | | | | BETA: splitting (90) gives:
% 229.06/40.52  | | | | | | | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | | | | | | | Case 1:
% 229.06/40.52  | | | | | | | | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | | | | | | | |   (91)  all_57_6 = e1 & op(e1, e3) = e1
% 229.06/40.52  | | | | | | | | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | | | | | | | | ALPHA: (91) implies:
% 229.06/40.52  | | | | | | | | | | | | | | | | | | | |   (92)  all_57_6 = e1
% 229.06/40.52  | | | | | | | | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (14), (15), (16), (20),
% 229.06/40.52  | | | | | | | | | | | | | | | | | | | |            (23), (28), (33), (34), (36), (82), (92) are
% 229.06/40.52  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1735.
% 229.06/40.52  | | | | | | | | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | | | | | | | Case 2:
% 229.06/40.52  | | | | | | | | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | | | | | | | |   (93)  all_57_12 = e1 & op(e0, e3) = e1
% 229.06/40.52  | | | | | | | | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (10), (14), (15), (19), (20), (23),
% 229.06/40.52  | | | | | | | | | | | | | | | | | | | |            (25), (33), (67), (88), (93) are inconsistent by
% 229.06/40.52  | | | | | | | | | | | | | | | | | | | |            sub-proof #1769.
% 229.06/40.52  | | | | | | | | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | | | | | | | End of split
% 229.06/40.52  | | | | | | | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | | | | | | End of split
% 229.06/40.52  | | | | | | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | | | | | End of split
% 229.06/40.52  | | | | | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | | | | End of split
% 229.06/40.52  | | | | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | | | Case 2:
% 229.06/40.52  | | | | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | | | |   (94)  all_57_13 = e0 & op(e0, e2) = e0
% 229.06/40.52  | | | | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | | | | REF_CLOSE: (20), (40), (94) are inconsistent by sub-proof
% 229.06/40.52  | | | | | | | | | | | | | | | |            #1743.
% 229.06/40.52  | | | | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | | | End of split
% 229.06/40.52  | | | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | | End of split
% 229.06/40.52  | | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | Case 2:
% 229.06/40.52  | | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | |   (95)  all_57_3 = e2 & op(e2, e2) = e2
% 229.06/40.52  | | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | | ALPHA: (95) implies:
% 229.06/40.52  | | | | | | | | | | | | | |   (96)  op(e2, e2) = e2
% 229.06/40.52  | | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | | REF_CLOSE: (6), (10), (33), (96) are inconsistent by
% 229.06/40.52  | | | | | | | | | | | | | |            sub-proof #2306.
% 229.06/40.52  | | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | End of split
% 229.06/40.52  | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | Case 2:
% 229.06/40.52  | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | |   (97)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 229.06/40.52  | | | | | | | | | | | | |           e2 & op(e2, e0) = e2)
% 229.06/40.52  | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | BETA: splitting (97) gives:
% 229.06/40.52  | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | Case 1:
% 229.06/40.52  | | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | |   (98)  all_57_5 = e2 & op(e2, e1) = e2
% 229.06/40.52  | | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (14), (17), (22), (29), (39), (62),
% 229.06/40.52  | | | | | | | | | | | | | |            (67), (72), (98) are inconsistent by sub-proof
% 229.06/40.52  | | | | | | | | | | | | | |            #806.
% 229.06/40.52  | | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | Case 2:
% 229.06/40.52  | | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | |   (99)  all_57_10 = e2 & op(e2, e0) = e2
% 229.06/40.52  | | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | | ALPHA: (99) implies:
% 229.06/40.52  | | | | | | | | | | | | | |   (100)  all_57_10 = e2
% 229.06/40.52  | | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | | REF_CLOSE: (20), (58), (100) are inconsistent by sub-proof
% 229.06/40.52  | | | | | | | | | | | | | |            #2138.
% 229.06/40.52  | | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | | End of split
% 229.06/40.52  | | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | | End of split
% 229.06/40.52  | | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | End of split
% 229.06/40.52  | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | Case 2:
% 229.06/40.52  | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | |   (101)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 229.06/40.52  | | | | | | | | | | |            e3 & op(e0, e1) = e3)
% 229.06/40.52  | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | | REF_CLOSE: (5), (6), (8), (9), (14), (15), (16), (18), (20),
% 229.06/40.52  | | | | | | | | | | |            (23), (27), (33), (52), (101) are inconsistent by
% 229.06/40.52  | | | | | | | | | | |            sub-proof #1044.
% 229.06/40.52  | | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | | End of split
% 229.06/40.52  | | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | End of split
% 229.06/40.52  | | | | | | | | | 
% 229.06/40.52  | | | | | | | | Case 2:
% 229.06/40.52  | | | | | | | | | 
% 229.06/40.52  | | | | | | | | |   (102)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 &
% 229.06/40.52  | | | | | | | | |            op(e3, e0) = e3)
% 229.06/40.52  | | | | | | | | | 
% 229.06/40.52  | | | | | | | | | REF_CLOSE: (5), (6), (29), (39), (62), (102) are inconsistent
% 229.06/40.52  | | | | | | | | |            by sub-proof #2281.
% 229.06/40.52  | | | | | | | | | 
% 229.06/40.52  | | | | | | | | End of split
% 229.06/40.52  | | | | | | | | 
% 229.06/40.52  | | | | | | | Case 2:
% 229.06/40.52  | | | | | | | | 
% 229.06/40.52  | | | | | | | |   (103)  all_57_9 = e1 & op(e3, e0) = e1
% 229.06/40.52  | | | | | | | | 
% 229.06/40.52  | | | | | | | | REF_CLOSE: (1), (33), (103) are inconsistent by sub-proof #2451.
% 229.06/40.52  | | | | | | | | 
% 229.06/40.52  | | | | | | | End of split
% 229.06/40.52  | | | | | | | 
% 229.06/40.52  | | | | | | End of split
% 229.06/40.52  | | | | | | 
% 229.06/40.52  | | | | | Case 2:
% 229.06/40.52  | | | | | | 
% 229.06/40.52  | | | | | |   (104)  all_57_11 = e0 & op(e1, e0) = e0
% 229.06/40.52  | | | | | | 
% 229.06/40.52  | | | | | | REF_CLOSE: (23), (48), (104) are inconsistent by sub-proof #1257.
% 229.06/40.52  | | | | | | 
% 229.06/40.52  | | | | | End of split
% 229.06/40.52  | | | | | 
% 229.06/40.52  | | | | End of split
% 229.06/40.52  | | | | 
% 229.06/40.52  | | | End of split
% 229.06/40.52  | | | 
% 229.06/40.52  | | Case 2:
% 229.06/40.52  | | | 
% 229.06/40.52  | | |   (105)  all_57_15 = e1 & op(e0, e0) = e1
% 229.06/40.52  | | | 
% 229.06/40.52  | | | ALPHA: (105) implies:
% 229.06/40.52  | | |   (106)  op(e0, e0) = e1
% 229.06/40.52  | | | 
% 229.06/40.52  | | | REF_CLOSE: (5), (6), (26), (106) are inconsistent by sub-proof #2183.
% 229.06/40.52  | | | 
% 229.06/40.52  | | End of split
% 229.06/40.52  | | 
% 229.06/40.52  | End of split
% 229.06/40.52  | 
% 229.06/40.52  End of proof
% 229.06/40.52  
% 229.06/40.52  Sub-proof #664 shows that the following formulas are inconsistent:
% 229.06/40.52  ----------------------------------------------------------------
% 229.06/40.52    (1)  all_57_0 = e2
% 229.06/40.52    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.06/40.52         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.06/40.52    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.06/40.52         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.06/40.52    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.06/40.52         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.06/40.52    (5)   ~ (e3 = e1)
% 229.06/40.52    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.06/40.52           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.06/40.52    (7)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.06/40.52         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.06/40.52    (8)   ~ (all_6_2 = e3)
% 229.06/40.52    (9)  op(e1, e1) = all_6_2
% 229.06/40.52    (10)  all_57_12 = e2
% 229.06/40.52    (11)  all_57_3 = e0
% 229.06/40.52    (12)   ~ (e3 = e2)
% 229.06/40.52    (13)   ~ (e3 = e0)
% 229.06/40.52    (14)  all_57_15 = e3
% 229.06/40.52    (15)  op(e3, e3) = e2
% 229.06/40.52    (16)  all_57_4 = e1
% 229.06/40.52    (17)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.06/40.52          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.06/40.52            e1)
% 229.06/40.52    (18)  all_57_10 = e2
% 229.06/40.52    (19)  all_57_5 = e3
% 229.06/40.52    (20)   ~ (e2 = e0)
% 229.06/40.52    (21)   ~ (e1 = e0)
% 229.06/40.52    (22)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.06/40.52          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.06/40.52    (23)  all_57_6 = e3
% 229.06/40.52    (24)  all_57_2 = e1
% 229.06/40.52    (25)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.06/40.52          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.06/40.52            e2)
% 229.06/40.52    (26)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.06/40.52              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.06/40.52                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.06/40.52                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.06/40.52    (27)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.06/40.52          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.06/40.52    (28)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.06/40.52          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.06/40.52    (29)  all_57_1 = e3
% 229.06/40.52    (30)   ~ (e2 = e1)
% 229.06/40.52    (31)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.06/40.52          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.06/40.52    (32)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.06/40.52          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.06/40.52    (33)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.06/40.52          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.06/40.52    (34)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.06/40.52          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.06/40.52    (35)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.06/40.52          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.06/40.52  
% 229.06/40.52  Begin of proof
% 229.06/40.52  | 
% 229.06/40.52  | BETA: splitting (33) gives:
% 229.06/40.52  | 
% 229.06/40.52  | Case 1:
% 229.06/40.52  | | 
% 229.06/40.52  | |   (36)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) =
% 229.06/40.52  | |           e0)
% 229.06/40.52  | | 
% 229.06/40.52  | | REF_CLOSE: (2), (5), (6), (11), (12), (15), (19), (20), (21), (27), (30),
% 229.06/40.52  | |            (36) are inconsistent by sub-proof #1644.
% 229.06/40.52  | | 
% 229.06/40.52  | Case 2:
% 229.06/40.52  | | 
% 229.06/40.52  | |   (37)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) =
% 229.06/40.52  | |           e0)
% 229.06/40.52  | | 
% 229.06/40.52  | | BETA: splitting (37) gives:
% 229.06/40.52  | | 
% 229.06/40.52  | | Case 1:
% 229.06/40.52  | | | 
% 229.06/40.52  | | |   (38)  all_57_6 = e0 & op(e1, e3) = e0
% 229.06/40.52  | | | 
% 229.06/40.52  | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13), (14),
% 229.06/40.52  | | |            (16), (17), (18), (20), (21), (22), (25), (26), (28), (29),
% 229.06/40.52  | | |            (30), (31), (32), (33), (34), (35), (38) are inconsistent by
% 229.06/40.52  | | |            sub-proof #666.
% 229.06/40.52  | | | 
% 229.06/40.52  | | Case 2:
% 229.06/40.52  | | | 
% 229.06/40.52  | | |   (39)  all_57_12 = e0 & op(e0, e3) = e0
% 229.06/40.52  | | | 
% 229.06/40.52  | | | ALPHA: (39) implies:
% 229.06/40.52  | | |   (40)  all_57_12 = e0
% 229.06/40.52  | | | 
% 229.06/40.52  | | | REF_CLOSE: (1), (10), (12), (20), (23), (24), (30), (32), (40) are
% 229.06/40.52  | | |            inconsistent by sub-proof #665.
% 229.06/40.52  | | | 
% 229.06/40.52  | | End of split
% 229.06/40.52  | | 
% 229.06/40.52  | End of split
% 229.06/40.52  | 
% 229.06/40.52  End of proof
% 229.06/40.52  
% 229.06/40.52  Sub-proof #665 shows that the following formulas are inconsistent:
% 229.06/40.52  ----------------------------------------------------------------
% 229.06/40.52    (1)  all_57_0 = e2
% 229.06/40.52    (2)  all_57_12 = e0
% 229.06/40.52    (3)  all_57_12 = e2
% 229.06/40.52    (4)   ~ (e3 = e2)
% 229.06/40.52    (5)   ~ (e2 = e0)
% 229.06/40.52    (6)  all_57_6 = e3
% 229.06/40.52    (7)  all_57_2 = e1
% 229.06/40.52    (8)   ~ (e2 = e1)
% 229.06/40.52    (9)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.06/40.52         (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.06/40.52  
% 229.06/40.52  Begin of proof
% 229.06/40.52  | 
% 229.06/40.52  | COMBINE_EQS: (2), (3) imply:
% 229.06/40.52  |   (10)  e2 = e0
% 229.06/40.52  | 
% 229.06/40.52  | SIMP: (10) implies:
% 229.06/40.52  |   (11)  e2 = e0
% 229.06/40.52  | 
% 229.06/40.52  | COMBINE_EQS: (1), (11) imply:
% 229.06/40.52  |   (12)  all_57_0 = e0
% 229.06/40.52  | 
% 229.06/40.52  | REF_CLOSE: (2), (4), (5), (6), (7), (8), (9), (12) are inconsistent by
% 229.06/40.52  |            sub-proof #1426.
% 229.06/40.52  | 
% 229.06/40.52  End of proof
% 229.06/40.52  
% 229.06/40.52  Sub-proof #666 shows that the following formulas are inconsistent:
% 229.06/40.52  ----------------------------------------------------------------
% 229.06/40.52    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.06/40.52         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.06/40.52    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.06/40.52         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.06/40.52    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.06/40.52         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.06/40.52    (4)   ~ (e3 = e1)
% 229.06/40.52    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.06/40.52           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.06/40.52    (6)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.06/40.52         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.06/40.52    (7)   ~ (all_6_2 = e3)
% 229.06/40.52    (8)  op(e1, e1) = all_6_2
% 229.06/40.52    (9)  all_57_3 = e0
% 229.06/40.52    (10)   ~ (e3 = e2)
% 229.06/40.52    (11)   ~ (e3 = e0)
% 229.06/40.52    (12)  all_57_15 = e3
% 229.06/40.52    (13)  all_57_4 = e1
% 229.06/40.52    (14)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.06/40.52          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.06/40.52            e1)
% 229.06/40.52    (15)  all_57_10 = e2
% 229.06/40.52    (16)   ~ (e2 = e0)
% 229.06/40.52    (17)   ~ (e1 = e0)
% 229.06/40.52    (18)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.06/40.52          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.06/40.52    (19)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.06/40.52          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.06/40.52            e2)
% 229.06/40.52    (20)  all_57_6 = e0 & op(e1, e3) = e0
% 229.06/40.52    (21)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.06/40.52              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.06/40.52                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.06/40.52                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.06/40.52    (22)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.06/40.52          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.06/40.52    (23)  all_57_1 = e3
% 229.06/40.52    (24)   ~ (e2 = e1)
% 229.06/40.52    (25)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.06/40.52          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.06/40.52    (26)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.06/40.52          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.06/40.52    (27)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.06/40.52          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.06/40.52    (28)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.06/40.52          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.06/40.52    (29)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.06/40.52          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.06/40.52  
% 229.06/40.52  Begin of proof
% 229.06/40.52  | 
% 229.06/40.52  | ALPHA: (20) implies:
% 229.06/40.52  |   (30)  all_57_6 = e0
% 229.06/40.52  | 
% 229.06/40.52  | BETA: splitting (22) gives:
% 229.06/40.52  | 
% 229.06/40.52  | Case 1:
% 229.06/40.52  | | 
% 229.06/40.52  | |   (31)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) =
% 229.06/40.52  | |           e3)
% 229.06/40.52  | | 
% 229.06/40.52  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 229.06/40.52  | |            (13), (14), (15), (16), (17), (18), (19), (21), (23), (24), (25),
% 229.06/40.52  | |            (26), (27), (28), (29), (31) are inconsistent by sub-proof #667.
% 229.06/40.52  | | 
% 229.06/40.52  | Case 2:
% 229.06/40.52  | | 
% 229.06/40.52  | |   (32)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) =
% 229.06/40.52  | |           e3)
% 229.06/40.52  | | 
% 229.06/40.52  | | REF_CLOSE: (3), (4), (9), (10), (11), (12), (14), (16), (17), (19), (21),
% 229.06/40.52  | |            (23), (24), (29), (30), (32) are inconsistent by sub-proof #790.
% 229.06/40.52  | | 
% 229.06/40.52  | End of split
% 229.06/40.52  | 
% 229.06/40.52  End of proof
% 229.06/40.52  
% 229.06/40.52  Sub-proof #667 shows that the following formulas are inconsistent:
% 229.06/40.52  ----------------------------------------------------------------
% 229.06/40.52    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.06/40.52         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.06/40.52    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.06/40.52         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.06/40.52    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.06/40.52         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.06/40.52    (4)   ~ (e3 = e1)
% 229.06/40.52    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.06/40.52           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.06/40.52    (6)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.06/40.52         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.06/40.52    (7)   ~ (all_6_2 = e3)
% 229.06/40.52    (8)  op(e1, e1) = all_6_2
% 229.06/40.52    (9)  all_57_3 = e0
% 229.06/40.52    (10)   ~ (e3 = e2)
% 229.06/40.52    (11)   ~ (e3 = e0)
% 229.06/40.52    (12)  all_57_15 = e3
% 229.06/40.52    (13)  all_57_4 = e1
% 229.06/40.52    (14)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.06/40.52          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.06/40.52            e1)
% 229.06/40.52    (15)  all_57_10 = e2
% 229.06/40.52    (16)   ~ (e2 = e0)
% 229.06/40.52    (17)   ~ (e1 = e0)
% 229.06/40.52    (18)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.06/40.52          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.06/40.52    (19)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.06/40.52          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.06/40.52            e2)
% 229.06/40.52    (20)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.06/40.52              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.06/40.52                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.06/40.52                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.06/40.52    (21)  all_57_1 = e3
% 229.06/40.52    (22)   ~ (e2 = e1)
% 229.06/40.53    (23)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.06/40.53          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.06/40.53    (24)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.06/40.53          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.06/40.53    (25)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.06/40.53          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.06/40.53    (26)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.06/40.53          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.06/40.53    (27)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3)
% 229.06/40.53    (28)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.06/40.53          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.06/40.53  
% 229.06/40.53  Begin of proof
% 229.06/40.53  | 
% 229.06/40.53  | BETA: splitting (27) gives:
% 229.06/40.53  | 
% 229.06/40.53  | Case 1:
% 229.06/40.53  | | 
% 229.06/40.53  | |   (29)  all_57_0 = e3 & op(e3, e3) = e3
% 229.06/40.53  | | 
% 229.06/40.53  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (16),
% 229.06/40.53  | |            (17), (20), (21), (22), (23), (24), (25), (26), (28), (29) are
% 229.06/40.53  | |            inconsistent by sub-proof #791.
% 229.06/40.53  | | 
% 229.06/40.53  | Case 2:
% 229.06/40.53  | | 
% 229.06/40.53  | |   (30)  all_57_2 = e3 & op(e2, e3) = e3
% 229.06/40.53  | | 
% 229.06/40.53  | | ALPHA: (30) implies:
% 229.06/40.53  | |   (31)  all_57_2 = e3
% 229.06/40.53  | | 
% 229.06/40.53  | | REF_CLOSE: (1), (4), (5), (7), (8), (9), (10), (11), (12), (13), (14), (15),
% 229.06/40.53  | |            (16), (17), (18), (19), (20), (22), (31) are inconsistent by
% 229.06/40.53  | |            sub-proof #1755.
% 229.06/40.53  | | 
% 229.06/40.53  | End of split
% 229.06/40.53  | 
% 229.06/40.53  End of proof
% 229.06/40.53  
% 229.06/40.53  Sub-proof #668 shows that the following formulas are inconsistent:
% 229.06/40.53  ----------------------------------------------------------------
% 229.06/40.53    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.06/40.53         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.06/40.53    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.06/40.53           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.06/40.53    (3)  op(e2, e2) = e1
% 229.06/40.53    (4)   ~ (e3 = e2)
% 229.06/40.53    (5)   ~ (e3 = e0)
% 229.06/40.53    (6)  op(e3, e3) = e2
% 229.06/40.53    (7)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.06/40.53         (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.06/40.53    (8)   ~ (e2 = e0)
% 229.06/40.53    (9)   ~ (e1 = e0)
% 229.06/40.53    (10)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1)
% 229.06/40.53    (11)  all_57_7 = e3
% 229.06/40.53    (12)   ~ (e2 = e1)
% 229.06/40.53  
% 229.06/40.53  Begin of proof
% 229.06/40.53  | 
% 229.06/40.53  | BETA: splitting (10) gives:
% 229.06/40.53  | 
% 229.06/40.53  | Case 1:
% 229.06/40.53  | | 
% 229.06/40.53  | |   (13)  all_57_0 = e1 & op(e3, e3) = e1
% 229.06/40.53  | | 
% 229.06/40.53  | | ALPHA: (13) implies:
% 229.06/40.53  | |   (14)  op(e3, e3) = e1
% 229.06/40.53  | | 
% 229.06/40.53  | | REF_CLOSE: (2), (6), (12), (14) are inconsistent by sub-proof #1950.
% 229.06/40.53  | | 
% 229.06/40.53  | Case 2:
% 229.06/40.53  | | 
% 229.06/40.53  | |   (15)  all_57_1 = e1 & op(e3, e2) = e1
% 229.06/40.53  | | 
% 229.06/40.53  | | ALPHA: (15) implies:
% 229.06/40.53  | |   (16)  all_57_1 = e1
% 229.06/40.53  | | 
% 229.06/40.53  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (11), (12), (16) are
% 229.06/40.53  | |            inconsistent by sub-proof #1909.
% 229.06/40.53  | | 
% 229.06/40.53  | End of split
% 229.06/40.53  | 
% 229.06/40.53  End of proof
% 229.06/40.53  
% 229.06/40.53  Sub-proof #669 shows that the following formulas are inconsistent:
% 229.06/40.53  ----------------------------------------------------------------
% 229.06/40.53    (1)  all_57_9 = e2
% 229.06/40.53    (2)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3)
% 229.06/40.53    (3)   ~ (e3 = e1)
% 229.06/40.53    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.06/40.53           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.06/40.53    (5)  op(e2, e2) = e1
% 229.06/40.53    (6)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.06/40.53         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.06/40.53    (7)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.06/40.53         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.06/40.53    (8)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.06/40.53         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.06/40.53    (9)  all_57_4 = e3
% 229.06/40.53    (10)   ~ (e3 = e2)
% 229.06/40.53    (11)   ~ (e3 = e0)
% 229.06/40.53    (12)   ~ (e2 = e0)
% 229.06/40.53    (13)   ~ (e1 = e0)
% 229.06/40.53    (14)   ~ (e2 = e1)
% 229.06/40.53  
% 229.06/40.53  Begin of proof
% 229.06/40.53  | 
% 229.06/40.53  | BETA: splitting (2) gives:
% 229.06/40.53  | 
% 229.06/40.53  | Case 1:
% 229.06/40.53  | | 
% 229.06/40.53  | |   (15)  all_57_1 = e3 & op(e3, e2) = e3
% 229.06/40.53  | | 
% 229.06/40.53  | | ALPHA: (15) implies:
% 229.06/40.53  | |   (16)  all_57_1 = e3
% 229.06/40.53  | | 
% 229.06/40.53  | | REF_CLOSE: (1), (3), (6), (7), (8), (9), (10), (11), (12), (13), (14), (16)
% 229.06/40.53  | |            are inconsistent by sub-proof #1222.
% 229.06/40.53  | | 
% 229.06/40.53  | Case 2:
% 229.06/40.53  | | 
% 229.06/40.53  | |   (17)  all_57_3 = e3 & op(e2, e2) = e3
% 229.06/40.53  | | 
% 229.06/40.53  | | ALPHA: (17) implies:
% 229.06/40.53  | |   (18)  op(e2, e2) = e3
% 229.06/40.53  | | 
% 229.06/40.53  | | REF_CLOSE: (3), (4), (5), (18) are inconsistent by sub-proof #1912.
% 229.06/40.53  | | 
% 229.06/40.53  | End of split
% 229.06/40.53  | 
% 229.06/40.53  End of proof
% 229.06/40.53  
% 229.06/40.53  Sub-proof #670 shows that the following formulas are inconsistent:
% 229.06/40.53  ----------------------------------------------------------------
% 229.06/40.53    (1)   ~ (all_53_2 = e2)
% 229.06/40.53    (2)  all_57_0 = e2
% 229.06/40.53    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.06/40.53         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.06/40.53    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.06/40.53         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.06/40.53    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.06/40.53         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.06/40.53    (6)   ~ (e3 = e1)
% 229.06/40.53    (7)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 229.06/40.53         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 229.06/40.53    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.06/40.53           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.06/40.53    (9)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.06/40.53         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.06/40.53    (10)   ~ (all_53_3 = e3)
% 229.06/40.53    (11)   ~ (all_53_3 = all_53_7)
% 229.06/40.53    (12)   ~ (all_6_2 = e3)
% 229.06/40.53    (13)   ~ (all_53_9 = e1)
% 229.06/40.53    (14)  op(e1, e1) = all_6_2
% 229.06/40.53    (15)   ~ (all_53_1 = all_53_9)
% 229.06/40.53    (16)  op(e2, e2) = e1
% 229.06/40.53    (17)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.06/40.53          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.06/40.53    (18)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 229.06/40.53            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 229.06/40.53              e3) = all_22_1 & $i(all_22_1))
% 229.06/40.53    (19)   ~ (all_53_13 = e3)
% 229.06/40.53    (20)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.06/40.53          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.06/40.53    (21)   ~ (all_53_9 = all_53_11)
% 229.06/40.53    (22)  all_55_4 = all_53_1
% 229.06/40.53    (23)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.06/40.53          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.06/40.53    (24)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 229.06/40.53          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.06/40.53    (25)   ~ (e3 = e2)
% 229.06/40.53    (26)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 229.06/40.53    (27)   ~ (all_53_1 = all_53_3)
% 229.06/40.53    (28)   ~ (e3 = e0)
% 229.06/40.53    (29)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 229.06/40.53    (30)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 229.06/40.53    (31)  all_57_15 = e3
% 229.06/40.53    (32)   ~ (all_53_9 = all_53_13)
% 229.06/40.53    (33)  op(e3, e3) = e2
% 229.06/40.53    (34)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.06/40.53          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.06/40.53            e1)
% 229.06/40.53    (35)   ~ (all_53_1 = e1)
% 229.06/40.53    (36)  op(e0, e0) = all_52_31
% 229.06/40.53    (37)  all_55_6 = all_53_9
% 229.06/40.53    (38)   ~ (all_53_1 = all_53_2)
% 229.06/40.53    (39)  op(e1, e1) = e1
% 229.06/40.53    (40)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.06/40.53          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.06/40.53    (41)   ~ (e2 = e0)
% 229.06/40.53    (42)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 229.06/40.53            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 229.06/40.53            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 229.06/40.53            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 229.06/40.53              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 229.06/40.53            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 229.06/40.53            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 229.06/40.53              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 229.06/40.53              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 229.06/40.53            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 229.06/40.53            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 229.06/40.53            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 229.06/40.53              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 229.06/40.53              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 229.06/40.53            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 229.06/40.53              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 229.06/40.53            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 229.06/40.53            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 229.06/40.53              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 229.06/40.53              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 229.06/40.53            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 229.06/40.53            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 229.06/40.53    (43)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 229.06/40.53            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 229.06/40.53              e3) = all_12_1 & $i(all_12_1))
% 229.06/40.53    (44)  all_55_12 = all_53_3
% 229.06/40.53    (45)  all_57_3 = e1
% 229.06/40.53    (46)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.06/40.53          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.06/40.53    (47)   ~ (e1 = e0)
% 229.06/40.53    (48)   ~ (all_53_3 = all_53_11)
% 229.06/40.53    (49)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.06/40.53          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.06/40.53    (50)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.06/40.53          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.06/40.53    (51)   ~ (all_53_2 = all_53_3)
% 229.06/40.53    (52)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 229.06/40.53    (53)   ~ (all_53_7 = all_53_11)
% 229.06/40.53    (54)  all_55_8 = all_53_2
% 229.06/40.53    (55)  op(e0, e0) = e3
% 229.06/40.53    (56)  op(e0, e2) = all_53_7
% 229.06/40.53    (57)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.06/40.53          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.06/40.53            e2)
% 229.06/40.53    (58)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.06/40.53              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.06/40.53                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.06/40.53                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.06/40.53    (59)   ~ (all_53_1 = all_53_13)
% 229.06/40.53    (60)  op(e2, e0) = all_53_13
% 229.06/40.53    (61)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.06/40.53          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.06/40.53    (62)   ~ (all_53_12 = e3)
% 229.06/40.53    (63)  op(e1, e3) = all_53_2
% 229.06/40.53    (64)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.06/40.53          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.06/40.53    (65)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.06/40.53          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.06/40.53    (66)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.06/40.53          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 229.06/40.53    (67)   ~ (e2 = e1)
% 229.06/40.53    (68)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.06/40.53          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.06/40.53    (69)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.06/40.53          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.06/40.53    (70)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 229.06/40.53    (71)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 229.06/40.53          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 229.06/40.53    (72)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.06/40.53          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.06/40.53    (73)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.06/40.53          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.06/40.53    (74)  op(all_52_31, all_52_31) = e0
% 229.06/40.53    (75)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 229.06/40.53          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 229.06/40.53    (76)  all_55_14 = all_53_11
% 229.06/40.53    (77)   ~ (all_53_11 = e3)
% 229.06/40.53    (78)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.06/40.53          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.06/40.53    (79)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 229.06/40.53          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 229.06/40.53    (80)  op(e3, e0) = all_53_12
% 229.06/40.53  
% 229.06/40.53  Begin of proof
% 229.06/40.53  | 
% 229.06/40.53  | BETA: splitting (17) gives:
% 229.06/40.53  | 
% 229.06/40.53  | Case 1:
% 229.06/40.53  | | 
% 229.06/40.53  | |   (81)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) =
% 229.06/40.53  | |           e1)
% 229.06/40.53  | | 
% 229.06/40.53  | | REF_CLOSE: (5), (6), (8), (16), (25), (28), (33), (40), (41), (47), (50),
% 229.06/40.53  | |            (67), (81) are inconsistent by sub-proof #1677.
% 229.06/40.53  | | 
% 229.06/40.53  | Case 2:
% 229.06/40.53  | | 
% 229.06/40.53  | |   (82)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) =
% 229.06/40.53  | |           e1)
% 229.06/40.53  | | 
% 229.06/40.53  | | BETA: splitting (82) gives:
% 229.06/40.53  | | 
% 229.06/40.53  | | Case 1:
% 229.06/40.53  | | | 
% 229.06/40.53  | | |   (83)  all_57_4 = e1 & op(e3, e1) = e1
% 229.06/40.53  | | | 
% 229.06/40.53  | | | ALPHA: (83) implies:
% 229.06/40.53  | | |   (84)  all_57_4 = e1
% 229.06/40.53  | | | 
% 229.06/40.53  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 229.06/40.53  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 229.06/40.53  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 229.06/40.53  | | |            (33), (34), (35), (37), (38), (39), (40), (41), (42), (43),
% 229.06/40.53  | | |            (44), (45), (46), (47), (48), (49), (50), (51), (52), (53),
% 229.06/40.53  | | |            (54), (55), (56), (57), (58), (59), (60), (61), (62), (63),
% 229.06/40.53  | | |            (64), (65), (66), (67), (68), (69), (70), (71), (72), (73),
% 229.06/40.53  | | |            (75), (76), (77), (78), (79), (80), (84) are inconsistent by
% 229.06/40.53  | | |            sub-proof #715.
% 229.06/40.53  | | | 
% 229.06/40.53  | | Case 2:
% 229.06/40.53  | | | 
% 229.06/40.53  | | |   (85)  all_57_9 = e1 & op(e3, e0) = e1
% 229.06/40.53  | | | 
% 229.06/40.53  | | | ALPHA: (85) implies:
% 229.06/40.53  | | |   (86)  all_57_9 = e1
% 229.06/40.53  | | | 
% 229.06/40.53  | | | BETA: splitting (34) gives:
% 229.06/40.53  | | | 
% 229.06/40.53  | | | Case 1:
% 229.06/40.53  | | | | 
% 229.06/40.53  | | | |   (87)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0,
% 229.06/40.53  | | | |             e2) = e1)
% 229.06/40.53  | | | | 
% 229.06/40.53  | | | | BETA: splitting (87) gives:
% 229.06/40.53  | | | | 
% 229.06/40.53  | | | | Case 1:
% 229.06/40.53  | | | | | 
% 229.06/40.53  | | | | |   (88)  all_57_12 = e1 & op(e0, e3) = e1
% 229.06/40.53  | | | | | 
% 229.06/40.53  | | | | | REF_CLOSE: (3), (4), (5), (6), (8), (9), (12), (14), (16), (17), (18),
% 229.06/40.53  | | | | |            (23), (25), (28), (31), (33), (34), (36), (39), (40), (41),
% 229.06/40.53  | | | | |            (43), (45), (46), (47), (50), (55), (57), (58), (61), (62),
% 229.06/40.53  | | | | |            (64), (65), (67), (68), (69), (72), (73), (74), (78), (79),
% 229.06/40.53  | | | | |            (80), (88) are inconsistent by sub-proof #671.
% 229.06/40.53  | | | | | 
% 229.06/40.53  | | | | Case 2:
% 229.06/40.53  | | | | | 
% 229.06/40.53  | | | | |   (89)  all_57_13 = e1 & op(e0, e2) = e1
% 229.06/40.53  | | | | | 
% 229.06/40.53  | | | | | ALPHA: (89) implies:
% 229.06/40.53  | | | | |   (90)  all_57_13 = e1
% 229.06/40.53  | | | | | 
% 229.06/40.53  | | | | | BETA: splitting (4) gives:
% 229.06/40.53  | | | | | 
% 229.06/40.53  | | | | | Case 1:
% 229.06/40.53  | | | | | | 
% 229.06/40.53  | | | | | |   (91)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2,
% 229.06/40.53  | | | | | |             e3) = e1)
% 229.06/40.53  | | | | | | 
% 229.06/40.53  | | | | | | REF_CLOSE: (3), (5), (6), (8), (16), (17), (23), (25), (28), (31),
% 229.06/40.53  | | | | | |            (33), (34), (40), (41), (45), (46), (47), (50), (55),
% 229.06/40.53  | | | | | |            (57), (58), (61), (62), (64), (67), (80), (90), (91) are
% 229.06/40.53  | | | | | |            inconsistent by sub-proof #704.
% 229.06/40.53  | | | | | | 
% 229.06/40.53  | | | | | Case 2:
% 229.06/40.53  | | | | | | 
% 229.06/40.53  | | | | | |   (92)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0,
% 229.06/40.53  | | | | | |             e3) = e1)
% 229.06/40.53  | | | | | | 
% 229.06/40.53  | | | | | | BETA: splitting (92) gives:
% 229.06/40.53  | | | | | | 
% 229.06/40.53  | | | | | | Case 1:
% 229.06/40.53  | | | | | | | 
% 229.06/40.53  | | | | | | |   (93)  all_57_6 = e1 & op(e1, e3) = e1
% 229.06/40.53  | | | | | | | 
% 229.06/40.53  | | | | | | | ALPHA: (93) implies:
% 229.06/40.53  | | | | | | |   (94)  all_57_6 = e1
% 229.06/40.53  | | | | | | | 
% 229.06/40.53  | | | | | | | REF_CLOSE: (5), (6), (8), (9), (12), (14), (16), (17), (23), (25),
% 229.06/40.53  | | | | | | |            (28), (31), (33), (40), (41), (45), (46), (47), (58),
% 229.06/40.53  | | | | | | |            (62), (67), (68), (73), (78), (80), (90), (94) are
% 229.06/40.53  | | | | | | |            inconsistent by sub-proof #797.
% 229.06/40.53  | | | | | | | 
% 229.06/40.53  | | | | | | Case 2:
% 229.06/40.53  | | | | | | | 
% 229.06/40.53  | | | | | | |   (95)  all_57_12 = e1 & op(e0, e3) = e1
% 229.06/40.53  | | | | | | | 
% 229.06/40.53  | | | | | | | REF_CLOSE: (3), (4), (5), (6), (8), (9), (12), (14), (16), (17),
% 229.06/40.53  | | | | | | |            (18), (23), (25), (28), (31), (33), (34), (36), (39),
% 229.06/40.53  | | | | | | |            (40), (41), (43), (45), (46), (47), (50), (55), (57),
% 229.06/40.53  | | | | | | |            (58), (61), (62), (64), (65), (67), (68), (69), (72),
% 229.06/40.53  | | | | | | |            (73), (74), (78), (79), (80), (95) are inconsistent by
% 229.06/40.53  | | | | | | |            sub-proof #671.
% 229.06/40.53  | | | | | | | 
% 229.06/40.53  | | | | | | End of split
% 229.06/40.53  | | | | | | 
% 229.06/40.53  | | | | | End of split
% 229.06/40.53  | | | | | 
% 229.06/40.53  | | | | End of split
% 229.06/40.53  | | | | 
% 229.06/40.53  | | | Case 2:
% 229.06/40.53  | | | | 
% 229.06/40.53  | | | |   (96)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0,
% 229.06/40.53  | | | |             e0) = e1)
% 229.06/40.53  | | | | 
% 229.06/40.53  | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (12), (14), (16),
% 229.06/40.53  | | | |            (17), (18), (20), (23), (25), (28), (31), (33), (34), (39),
% 229.06/40.53  | | | |            (40), (41), (43), (45), (46), (47), (49), (50), (55), (57),
% 229.06/40.53  | | | |            (58), (61), (62), (64), (65), (66), (67), (68), (69), (71),
% 229.06/40.53  | | | |            (72), (73), (78), (80), (86), (96) are inconsistent by
% 229.06/40.53  | | | |            sub-proof #688.
% 229.06/40.53  | | | | 
% 229.06/40.53  | | | End of split
% 229.06/40.53  | | | 
% 229.06/40.53  | | End of split
% 229.06/40.53  | | 
% 229.06/40.53  | End of split
% 229.06/40.53  | 
% 229.06/40.53  End of proof
% 229.06/40.53  
% 229.06/40.53  Sub-proof #671 shows that the following formulas are inconsistent:
% 229.06/40.53  ----------------------------------------------------------------
% 229.06/40.53    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.06/40.53         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.06/40.53    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.06/40.53         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.06/40.53    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.06/40.53         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.06/40.53    (4)   ~ (e3 = e1)
% 229.06/40.53    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.06/40.53           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.06/40.53    (6)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.06/40.53         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.06/40.53    (7)   ~ (all_6_2 = e3)
% 229.06/40.53    (8)  op(e1, e1) = all_6_2
% 229.06/40.53    (9)  op(e2, e2) = e1
% 229.06/40.53    (10)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.06/40.53          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.06/40.53    (11)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 229.06/40.53            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 229.06/40.53              e3) = all_22_1 & $i(all_22_1))
% 229.06/40.53    (12)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.06/40.53          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.06/40.53    (13)   ~ (e3 = e2)
% 229.06/40.53    (14)   ~ (e3 = e0)
% 229.06/40.53    (15)  all_57_15 = e3
% 229.06/40.53    (16)  op(e3, e3) = e2
% 229.06/40.53    (17)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.06/40.53          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.06/40.53            e1)
% 229.06/40.53    (18)  op(e0, e0) = all_52_31
% 229.06/40.53    (19)  op(e1, e1) = e1
% 229.06/40.53    (20)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.06/40.53          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.06/40.53    (21)   ~ (e2 = e0)
% 229.06/40.53    (22)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 229.06/40.53            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 229.06/40.53              e3) = all_12_1 & $i(all_12_1))
% 229.06/40.53    (23)  all_57_3 = e1
% 229.06/40.53    (24)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.06/40.53          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.06/40.53    (25)   ~ (e1 = e0)
% 229.06/40.53    (26)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.06/40.53          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.06/40.53    (27)  op(e0, e0) = e3
% 229.06/40.53    (28)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.06/40.53          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.06/40.53            e2)
% 229.06/40.53    (29)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.06/40.53              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.06/40.53                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.06/40.53                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.06/40.53    (30)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.06/40.53          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.06/40.53    (31)   ~ (all_53_12 = e3)
% 229.06/40.53    (32)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.06/40.53          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.06/40.53    (33)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.06/40.53          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.06/40.53    (34)   ~ (e2 = e1)
% 229.06/40.53    (35)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.06/40.53          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.06/40.53    (36)  all_57_12 = e1 & op(e0, e3) = e1
% 229.06/40.53    (37)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.06/40.53          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.06/40.53    (38)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.06/40.53          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.06/40.53    (39)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.06/40.53          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.06/40.53    (40)  op(all_52_31, all_52_31) = e0
% 229.06/40.53    (41)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.06/40.53          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.06/40.53    (42)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 229.06/40.53          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 229.06/40.53    (43)  op(e3, e0) = all_53_12
% 229.06/40.53  
% 229.06/40.53  Begin of proof
% 229.06/40.53  | 
% 229.06/40.53  | ALPHA: (36) implies:
% 229.06/40.54  |   (44)  all_57_12 = e1
% 229.06/40.54  |   (45)  op(e0, e3) = e1
% 229.06/40.54  | 
% 229.06/40.54  | BETA: splitting (2) gives:
% 229.06/40.54  | 
% 229.06/40.54  | Case 1:
% 229.06/40.54  | | 
% 229.06/40.54  | |   (46)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) =
% 229.06/40.54  | |           e1)
% 229.06/40.54  | | 
% 229.06/40.54  | | BETA: splitting (46) gives:
% 229.06/40.54  | | 
% 229.06/40.54  | | Case 1:
% 229.06/40.54  | | | 
% 229.06/40.54  | | |   (47)  all_57_0 = e1 & op(e3, e3) = e1
% 229.06/40.54  | | | 
% 229.06/40.54  | | | ALPHA: (47) implies:
% 229.06/40.54  | | |   (48)  op(e3, e3) = e1
% 229.06/40.54  | | | 
% 229.06/40.54  | | | REF_CLOSE: (5), (16), (34), (48) are inconsistent by sub-proof #1950.
% 229.06/40.54  | | | 
% 229.06/40.54  | | Case 2:
% 229.06/40.54  | | | 
% 229.06/40.54  | | |   (49)  all_57_2 = e1 & op(e2, e3) = e1
% 229.06/40.54  | | | 
% 229.06/40.54  | | | ALPHA: (49) implies:
% 229.06/40.54  | | |   (50)  all_57_2 = e1
% 229.06/40.54  | | | 
% 229.06/40.54  | | | BETA: splitting (38) gives:
% 229.06/40.54  | | | 
% 229.06/40.54  | | | Case 1:
% 229.06/40.54  | | | | 
% 229.06/40.54  | | | |   (51)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3)
% 229.06/40.54  | | | |           = e0)
% 229.06/40.54  | | | | 
% 229.06/40.54  | | | | REF_CLOSE: (1), (4), (5), (13), (14), (16), (21), (23), (25), (30),
% 229.06/40.54  | | | |            (32), (34), (50), (51) are inconsistent by sub-proof #764.
% 229.06/40.54  | | | | 
% 229.06/40.54  | | | Case 2:
% 229.06/40.54  | | | | 
% 229.06/40.54  | | | |   (52)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3)
% 229.06/40.54  | | | |           = e0)
% 229.06/40.54  | | | | 
% 229.06/40.54  | | | | BETA: splitting (52) gives:
% 229.06/40.54  | | | | 
% 229.06/40.54  | | | | Case 1:
% 229.06/40.54  | | | | | 
% 229.06/40.54  | | | | |   (53)  all_57_6 = e0 & op(e1, e3) = e0
% 229.06/40.54  | | | | | 
% 229.06/40.54  | | | | | ALPHA: (53) implies:
% 229.06/40.54  | | | | |   (54)  all_57_6 = e0
% 229.06/40.54  | | | | | 
% 229.06/40.54  | | | | | BETA: splitting (6) gives:
% 229.06/40.54  | | | | | 
% 229.06/40.54  | | | | | Case 1:
% 229.06/40.54  | | | | | | 
% 229.11/40.54  | | | | | |   (55)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1,
% 229.11/40.54  | | | | | |             e2) = e3)
% 229.11/40.54  | | | | | | 
% 229.11/40.54  | | | | | | BETA: splitting (55) gives:
% 229.11/40.54  | | | | | | 
% 229.11/40.54  | | | | | | Case 1:
% 229.11/40.54  | | | | | | | 
% 229.11/40.54  | | | | | | |   (56)  all_57_6 = e3 & op(e1, e3) = e3
% 229.11/40.54  | | | | | | | 
% 229.11/40.54  | | | | | | | ALPHA: (56) implies:
% 229.11/40.54  | | | | | | |   (57)  all_57_6 = e3
% 229.11/40.54  | | | | | | | 
% 229.11/40.54  | | | | | | | REF_CLOSE: (14), (54), (57) are inconsistent by sub-proof #1822.
% 229.11/40.54  | | | | | | | 
% 229.11/40.54  | | | | | | Case 2:
% 229.11/40.54  | | | | | | | 
% 229.11/40.54  | | | | | | |   (58)  all_57_7 = e3 & op(e1, e2) = e3
% 229.11/40.54  | | | | | | | 
% 229.11/40.54  | | | | | | | ALPHA: (58) implies:
% 229.11/40.54  | | | | | | |   (59)  all_57_7 = e3
% 229.11/40.54  | | | | | | | 
% 229.11/40.54  | | | | | | | BETA: splitting (33) gives:
% 229.11/40.54  | | | | | | | 
% 229.11/40.54  | | | | | | | Case 1:
% 229.11/40.54  | | | | | | | | 
% 229.11/40.54  | | | | | | | |   (60)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 &
% 229.11/40.54  | | | | | | | |           op(e2, e3) = e3)
% 229.11/40.54  | | | | | | | | 
% 229.11/40.54  | | | | | | | | BETA: splitting (60) gives:
% 229.11/40.54  | | | | | | | | 
% 229.11/40.54  | | | | | | | | Case 1:
% 229.11/40.54  | | | | | | | | | 
% 229.11/40.54  | | | | | | | | |   (61)  all_57_0 = e3 & op(e3, e3) = e3
% 229.11/40.54  | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | ALPHA: (61) implies:
% 229.11/40.54  | | | | | | | | |   (62)  op(e3, e3) = e3
% 229.11/40.54  | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | REF_CLOSE: (5), (13), (16), (62) are inconsistent by sub-proof
% 229.11/40.54  | | | | | | | | |            #2490.
% 229.11/40.54  | | | | | | | | | 
% 229.11/40.54  | | | | | | | | Case 2:
% 229.11/40.54  | | | | | | | | | 
% 229.11/40.54  | | | | | | | | |   (63)  all_57_2 = e3 & op(e2, e3) = e3
% 229.11/40.54  | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | ALPHA: (63) implies:
% 229.11/40.54  | | | | | | | | |   (64)  all_57_2 = e3
% 229.11/40.54  | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | COMBINE_EQS: (50), (64) imply:
% 229.11/40.54  | | | | | | | | |   (65)  e3 = e1
% 229.11/40.54  | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | SIMP: (65) implies:
% 229.11/40.54  | | | | | | | | |   (66)  e3 = e1
% 229.11/40.54  | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | COMBINE_EQS: (59), (66) imply:
% 229.11/40.54  | | | | | | | | |   (67)  all_57_7 = e1
% 229.11/40.54  | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 229.11/40.54  | | | | | | | | |            (12), (13), (14), (15), (16), (17), (19), (20),
% 229.11/40.54  | | | | | | | | |            (21), (22), (24), (25), (26), (27), (28), (29),
% 229.11/40.54  | | | | | | | | |            (31), (34), (35), (39), (41), (42), (43), (45),
% 229.11/40.54  | | | | | | | | |            (67) are inconsistent by sub-proof #711.
% 229.11/40.54  | | | | | | | | | 
% 229.11/40.54  | | | | | | | | End of split
% 229.11/40.54  | | | | | | | | 
% 229.11/40.54  | | | | | | | Case 2:
% 229.11/40.54  | | | | | | | | 
% 229.11/40.54  | | | | | | | |   (68)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 &
% 229.11/40.54  | | | | | | | |           op(e0, e3) = e3)
% 229.11/40.54  | | | | | | | | 
% 229.11/40.54  | | | | | | | | BETA: splitting (68) gives:
% 229.11/40.54  | | | | | | | | 
% 229.11/40.54  | | | | | | | | Case 1:
% 229.11/40.54  | | | | | | | | | 
% 229.11/40.54  | | | | | | | | |   (69)  all_57_6 = e3 & op(e1, e3) = e3
% 229.11/40.54  | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | ALPHA: (69) implies:
% 229.11/40.54  | | | | | | | | |   (70)  all_57_6 = e3
% 229.11/40.54  | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | REF_CLOSE: (14), (54), (70) are inconsistent by sub-proof
% 229.11/40.54  | | | | | | | | |            #1822.
% 229.11/40.54  | | | | | | | | | 
% 229.11/40.54  | | | | | | | | Case 2:
% 229.11/40.54  | | | | | | | | | 
% 229.11/40.54  | | | | | | | | |   (71)  all_57_12 = e3 & op(e0, e3) = e3
% 229.11/40.54  | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | ALPHA: (71) implies:
% 229.11/40.54  | | | | | | | | |   (72)  all_57_12 = e3
% 229.11/40.54  | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | COMBINE_EQS: (44), (72) imply:
% 229.11/40.54  | | | | | | | | |   (73)  e3 = e1
% 229.11/40.54  | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | SIMP: (73) implies:
% 229.11/40.54  | | | | | | | | |   (74)  e3 = e1
% 229.11/40.54  | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | COMBINE_EQS: (59), (74) imply:
% 229.11/40.54  | | | | | | | | |   (75)  all_57_7 = e1
% 229.11/40.54  | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 229.11/40.54  | | | | | | | | |            (12), (13), (14), (15), (16), (17), (19), (20),
% 229.11/40.54  | | | | | | | | |            (21), (22), (24), (25), (26), (27), (28), (29),
% 229.11/40.54  | | | | | | | | |            (31), (34), (35), (39), (41), (42), (43), (45),
% 229.11/40.54  | | | | | | | | |            (75) are inconsistent by sub-proof #711.
% 229.11/40.54  | | | | | | | | | 
% 229.11/40.54  | | | | | | | | End of split
% 229.11/40.54  | | | | | | | | 
% 229.11/40.54  | | | | | | | End of split
% 229.11/40.54  | | | | | | | 
% 229.11/40.54  | | | | | | End of split
% 229.11/40.54  | | | | | | 
% 229.11/40.54  | | | | | Case 2:
% 229.11/40.54  | | | | | | 
% 229.11/40.54  | | | | | |   (76)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1,
% 229.11/40.54  | | | | | |             e0) = e3)
% 229.11/40.54  | | | | | | 
% 229.11/40.54  | | | | | | REF_CLOSE: (4), (5), (7), (8), (13), (14), (15), (21), (25), (29),
% 229.11/40.54  | | | | | |            (34), (35), (39), (76) are inconsistent by sub-proof
% 229.11/40.54  | | | | | |            #1786.
% 229.11/40.54  | | | | | | 
% 229.11/40.54  | | | | | End of split
% 229.11/40.54  | | | | | 
% 229.11/40.54  | | | | Case 2:
% 229.11/40.54  | | | | | 
% 229.11/40.54  | | | | |   (77)  all_57_12 = e0 & op(e0, e3) = e0
% 229.11/40.54  | | | | | 
% 229.11/40.54  | | | | | ALPHA: (77) implies:
% 229.11/40.54  | | | | |   (78)  all_57_12 = e0
% 229.11/40.54  | | | | | 
% 229.11/40.54  | | | | | COMBINE_EQS: (44), (78) imply:
% 229.11/40.54  | | | | |   (79)  e1 = e0
% 229.11/40.54  | | | | | 
% 229.11/40.54  | | | | | REF_CLOSE: (1), (4), (13), (14), (21), (23), (25), (30), (32), (34),
% 229.11/40.54  | | | | |            (50), (79) are inconsistent by sub-proof #1590.
% 229.11/40.54  | | | | | 
% 229.11/40.54  | | | | End of split
% 229.11/40.54  | | | | 
% 229.11/40.54  | | | End of split
% 229.11/40.54  | | | 
% 229.11/40.54  | | End of split
% 229.11/40.54  | | 
% 229.11/40.54  | Case 2:
% 229.11/40.54  | | 
% 229.11/40.54  | |   (80)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) =
% 229.11/40.54  | |           e1)
% 229.11/40.54  | | 
% 229.11/40.54  | | BETA: splitting (80) gives:
% 229.11/40.54  | | 
% 229.11/40.54  | | Case 1:
% 229.11/40.54  | | | 
% 229.11/40.54  | | |   (81)  all_57_6 = e1 & op(e1, e3) = e1
% 229.11/40.54  | | | 
% 229.11/40.54  | | | ALPHA: (81) implies:
% 229.11/40.54  | | |   (82)  all_57_6 = e1
% 229.11/40.54  | | | 
% 229.11/40.54  | | | REF_CLOSE: (4), (5), (6), (7), (8), (13), (14), (15), (16), (21), (25),
% 229.11/40.54  | | |            (27), (29), (33), (34), (35), (37), (38), (39), (44), (82) are
% 229.11/40.54  | | |            inconsistent by sub-proof #759.
% 229.11/40.54  | | | 
% 229.11/40.54  | | Case 2:
% 229.11/40.54  | | | 
% 229.11/40.54  | | | 
% 229.11/40.54  | | | GROUND_INST: instantiating (5) with e3, all_52_31, e0, e0, simplifying
% 229.11/40.54  | | |              with (18), (27) gives:
% 229.11/40.54  | | |   (83)  all_52_31 = e3
% 229.11/40.54  | | | 
% 229.11/40.54  | | | REDUCE: (40), (83) imply:
% 229.11/40.54  | | |   (84)  op(e3, e3) = e0
% 229.11/40.54  | | | 
% 229.11/40.54  | | | REF_CLOSE: (5), (16), (21), (84) are inconsistent by sub-proof #2403.
% 229.11/40.54  | | | 
% 229.11/40.54  | | End of split
% 229.11/40.54  | | 
% 229.11/40.54  | End of split
% 229.11/40.54  | 
% 229.11/40.54  End of proof
% 229.11/40.54  
% 229.11/40.54  Sub-proof #672 shows that the following formulas are inconsistent:
% 229.11/40.54  ----------------------------------------------------------------
% 229.11/40.54    (1)   ~ (all_53_2 = e2)
% 229.11/40.54    (2)  all_57_0 = e2
% 229.11/40.54    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.11/40.54         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.11/40.54    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.11/40.54         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.11/40.54    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.11/40.54         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.11/40.54    (6)   ~ (e3 = e1)
% 229.11/40.54    (7)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 229.11/40.54         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 229.11/40.54    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.11/40.54           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.11/40.54    (9)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.11/40.54         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.11/40.54    (10)   ~ (all_53_3 = e3)
% 229.11/40.54    (11)   ~ (all_53_3 = all_53_7)
% 229.11/40.54    (12)   ~ (all_6_2 = e3)
% 229.11/40.54    (13)   ~ (all_53_9 = e1)
% 229.11/40.54    (14)  op(e1, e1) = all_6_2
% 229.11/40.54    (15)   ~ (all_53_1 = all_53_9)
% 229.11/40.54    (16)  op(e2, e2) = e1
% 229.11/40.54    (17)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.11/40.54          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.11/40.54    (18)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 229.11/40.54            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 229.11/40.54              e3) = all_22_1 & $i(all_22_1))
% 229.11/40.54    (19)   ~ (all_53_13 = e3)
% 229.11/40.54    (20)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.11/40.54          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.11/40.54    (21)   ~ (all_53_9 = all_53_11)
% 229.11/40.54    (22)  all_55_4 = all_53_1
% 229.11/40.54    (23)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.11/40.54          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.11/40.54    (24)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 229.11/40.54          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.11/40.54    (25)   ~ (e3 = e2)
% 229.11/40.54    (26)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 229.11/40.54    (27)   ~ (all_53_1 = all_53_3)
% 229.11/40.54    (28)   ~ (e3 = e0)
% 229.11/40.54    (29)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 229.11/40.54    (30)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 229.11/40.54    (31)  all_57_15 = e3
% 229.11/40.54    (32)  op(e2, e2) = all_52_11
% 229.11/40.54    (33)   ~ (all_53_9 = all_53_13)
% 229.11/40.54    (34)  op(e3, e3) = e2
% 229.11/40.54    (35)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.11/40.54          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.11/40.54            e1)
% 229.11/40.54    (36)   ~ (all_53_1 = e1)
% 229.11/40.54    (37)  all_55_6 = all_53_9
% 229.11/40.54    (38)   ~ (all_53_1 = all_53_2)
% 229.11/40.54    (39)  op(e1, e1) = e1
% 229.11/40.54    (40)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.11/40.54          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.11/40.54    (41)   ~ (e2 = e0)
% 229.11/40.54    (42)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 229.11/40.54            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 229.11/40.54            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 229.11/40.54            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 229.11/40.54              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 229.11/40.54            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 229.11/40.54            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 229.11/40.54              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 229.11/40.54              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 229.11/40.54            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 229.11/40.54            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 229.11/40.54            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 229.11/40.54              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 229.11/40.54              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 229.11/40.54            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 229.11/40.54              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 229.11/40.54            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 229.11/40.54            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 229.11/40.54              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 229.11/40.54              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 229.11/40.54            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 229.11/40.54            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 229.11/40.54    (43)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 229.11/40.54            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 229.11/40.54              e3) = all_12_1 & $i(all_12_1))
% 229.11/40.54    (44)  all_55_12 = all_53_3
% 229.11/40.54    (45)  all_57_3 = e1
% 229.11/40.54    (46)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.11/40.54          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.11/40.54    (47)   ~ (e1 = e0)
% 229.11/40.54    (48)   ~ (all_53_3 = all_53_11)
% 229.11/40.54    (49)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.11/40.54          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.11/40.54    (50)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.11/40.54          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.11/40.54    (51)   ~ (all_53_2 = all_53_3)
% 229.11/40.54    (52)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 229.11/40.54    (53)   ~ (all_53_7 = all_53_11)
% 229.11/40.54    (54)  all_55_8 = all_53_2
% 229.11/40.54    (55)  op(e0, e0) = e3
% 229.11/40.54    (56)  op(e0, e2) = all_53_7
% 229.11/40.54    (57)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.11/40.54          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.11/40.54            e2)
% 229.11/40.54    (58)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.11/40.54              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.11/40.54                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.11/40.54                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.11/40.54    (59)   ~ (all_53_1 = all_53_13)
% 229.11/40.54    (60)  op(e2, e0) = all_53_13
% 229.11/40.54    (61)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.11/40.54          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.11/40.54    (62)   ~ (all_53_12 = e3)
% 229.11/40.54    (63)  op(e1, e3) = all_53_2
% 229.11/40.54    (64)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.11/40.54          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.11/40.54    (65)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.11/40.54          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.11/40.54    (66)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.11/40.54          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 229.11/40.54    (67)   ~ (e2 = e1)
% 229.11/40.54    (68)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.11/40.54          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.11/40.54    (69)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.11/40.54          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.11/40.54    (70)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 229.11/40.54    (71)   ~ (all_53_12 = e2)
% 229.11/40.54    (72)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 229.11/40.54          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 229.11/40.54    (73)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.11/40.54          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.11/40.54    (74)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.11/40.54          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.11/40.54    (75)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 229.11/40.54          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 229.11/40.54    (76)  all_55_14 = all_53_11
% 229.11/40.54    (77)  op(all_52_11, all_52_11) = e2
% 229.11/40.54    (78)   ~ (all_53_11 = e3)
% 229.11/40.54    (79)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.11/40.54          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.11/40.54    (80)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 229.11/40.54          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 229.11/40.54    (81)  op(e3, e0) = all_53_12
% 229.11/40.54  
% 229.11/40.54  Begin of proof
% 229.11/40.54  | 
% 229.11/40.54  | BETA: splitting (17) gives:
% 229.11/40.54  | 
% 229.11/40.54  | Case 1:
% 229.11/40.54  | | 
% 229.11/40.54  | |   (82)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) =
% 229.11/40.54  | |           e1)
% 229.11/40.54  | | 
% 229.11/40.54  | | REF_CLOSE: (5), (6), (8), (16), (25), (28), (34), (40), (41), (47), (50),
% 229.11/40.54  | |            (67), (82) are inconsistent by sub-proof #1677.
% 229.11/40.54  | | 
% 229.11/40.54  | Case 2:
% 229.11/40.54  | | 
% 229.11/40.54  | |   (83)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) =
% 229.11/40.54  | |           e1)
% 229.11/40.54  | | 
% 229.11/40.54  | | BETA: splitting (83) gives:
% 229.11/40.54  | | 
% 229.11/40.54  | | Case 1:
% 229.11/40.54  | | | 
% 229.11/40.54  | | |   (84)  all_57_4 = e1 & op(e3, e1) = e1
% 229.11/40.54  | | | 
% 229.11/40.54  | | | ALPHA: (84) implies:
% 229.11/40.54  | | |   (85)  all_57_4 = e1
% 229.11/40.54  | | | 
% 229.11/40.54  | | | BETA: splitting (74) gives:
% 229.11/40.54  | | | 
% 229.11/40.54  | | | Case 1:
% 229.11/40.54  | | | | 
% 229.11/40.54  | | | |   (86)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0)
% 229.11/40.54  | | | |           = e1)
% 229.11/40.54  | | | | 
% 229.11/40.54  | | | | BETA: splitting (86) gives:
% 229.11/40.54  | | | | 
% 229.11/40.54  | | | | Case 1:
% 229.11/40.54  | | | | | 
% 229.11/40.54  | | | | |   (87)  all_57_9 = e1 & op(e3, e0) = e1
% 229.11/40.54  | | | | | 
% 229.11/40.54  | | | | | ALPHA: (87) implies:
% 229.11/40.54  | | | | |   (88)  all_57_9 = e1
% 229.11/40.54  | | | | |   (89)  op(e3, e0) = e1
% 229.11/40.54  | | | | | 
% 229.11/40.54  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 229.11/40.54  | | | | |            (12), (13), (14), (15), (16), (17), (18), (19), (20), (21),
% 229.11/40.54  | | | | |            (22), (23), (24), (25), (26), (27), (28), (29), (30), (31),
% 229.11/40.54  | | | | |            (32), (33), (34), (35), (36), (37), (38), (39), (40), (41),
% 229.11/40.54  | | | | |            (42), (43), (44), (45), (46), (47), (48), (49), (50), (51),
% 229.11/40.54  | | | | |            (52), (53), (54), (55), (56), (57), (58), (59), (60), (61),
% 229.11/40.54  | | | | |            (62), (63), (64), (65), (66), (67), (68), (69), (70), (71),
% 229.11/40.54  | | | | |            (72), (73), (74), (75), (76), (77), (78), (79), (80), (81),
% 229.11/40.54  | | | | |            (88), (89) are inconsistent by sub-proof #674.
% 229.11/40.54  | | | | | 
% 229.11/40.54  | | | | Case 2:
% 229.11/40.54  | | | | | 
% 229.11/40.54  | | | | |   (90)  all_57_10 = e1 & op(e2, e0) = e1
% 229.11/40.54  | | | | | 
% 229.11/40.54  | | | | | ALPHA: (90) implies:
% 229.11/40.54  | | | | |   (91)  all_57_10 = e1
% 229.11/40.54  | | | | | 
% 229.11/40.54  | | | | | BETA: splitting (68) gives:
% 229.11/40.54  | | | | | 
% 229.11/40.54  | | | | | Case 1:
% 229.11/40.54  | | | | | | 
% 229.11/40.54  | | | | | |   (92)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2,
% 229.11/40.54  | | | | | |             e0) = e2)
% 229.11/40.54  | | | | | | 
% 229.11/40.54  | | | | | | REF_CLOSE: (3), (4), (5), (6), (8), (9), (12), (14), (16), (17),
% 229.11/40.54  | | | | | |            (20), (23), (25), (28), (31), (34), (35), (40), (41),
% 229.11/40.54  | | | | | |            (45), (46), (47), (49), (50), (55), (57), (58), (62),
% 229.11/40.54  | | | | | |            (64), (65), (66), (67), (68), (73), (74), (79), (81),
% 229.11/40.54  | | | | | |            (91), (92) are inconsistent by sub-proof #804.
% 229.11/40.54  | | | | | | 
% 229.11/40.54  | | | | | Case 2:
% 229.11/40.54  | | | | | | 
% 229.11/40.54  | | | | | |   (93)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 &
% 229.11/40.54  | | | | | |           op(e0, e0) = e2)
% 229.11/40.54  | | | | | | 
% 229.11/40.54  | | | | | | BETA: splitting (93) gives:
% 229.11/40.54  | | | | | | 
% 229.11/40.54  | | | | | | Case 1:
% 229.11/40.54  | | | | | | | 
% 229.11/40.54  | | | | | | |   (94)  all_57_11 = e2 & op(e1, e0) = e2
% 229.11/40.54  | | | | | | | 
% 229.11/40.54  | | | | | | | ALPHA: (94) implies:
% 229.11/40.54  | | | | | | |   (95)  all_57_11 = e2
% 229.11/40.54  | | | | | | |   (96)  op(e1, e0) = e2
% 229.11/40.54  | | | | | | | 
% 229.11/40.54  | | | | | | | BETA: splitting (35) gives:
% 229.11/40.54  | | | | | | | 
% 229.11/40.54  | | | | | | | Case 1:
% 229.11/40.54  | | | | | | | | 
% 229.11/40.54  | | | | | | | |   (97)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 &
% 229.11/40.54  | | | | | | | |           op(e0, e2) = e1)
% 229.11/40.54  | | | | | | | | 
% 229.11/40.54  | | | | | | | | BETA: splitting (97) gives:
% 229.11/40.54  | | | | | | | | 
% 229.11/40.54  | | | | | | | | Case 1:
% 229.11/40.54  | | | | | | | | | 
% 229.11/40.54  | | | | | | | | |   (98)  all_57_12 = e1 & op(e0, e3) = e1
% 229.11/40.54  | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | ALPHA: (98) implies:
% 229.11/40.54  | | | | | | | | |   (99)  op(e0, e3) = e1
% 229.11/40.54  | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | REF_CLOSE: (8), (18), (43), (96), (99) are inconsistent by
% 229.11/40.54  | | | | | | | | |            sub-proof #1147.
% 229.11/40.54  | | | | | | | | | 
% 229.11/40.54  | | | | | | | | Case 2:
% 229.11/40.54  | | | | | | | | | 
% 229.11/40.54  | | | | | | | | |   (100)  all_57_13 = e1 & op(e0, e2) = e1
% 229.11/40.54  | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | ALPHA: (100) implies:
% 229.11/40.54  | | | | | | | | |   (101)  all_57_13 = e1
% 229.11/40.54  | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | BETA: splitting (64) gives:
% 229.11/40.54  | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | Case 1:
% 229.11/40.54  | | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | |   (102)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 229.11/40.54  | | | | | | | | | |            & op(e2, e2) = e2)
% 229.11/40.54  | | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | | BETA: splitting (102) gives:
% 229.11/40.54  | | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | | Case 1:
% 229.11/40.54  | | | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | | |   (103)  all_57_2 = e2 & op(e2, e3) = e2
% 229.11/40.54  | | | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | | | ALPHA: (103) implies:
% 229.11/40.54  | | | | | | | | | | |   (104)  all_57_2 = e2
% 229.11/40.54  | | | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | | | BETA: splitting (66) gives:
% 229.11/40.54  | | | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | | | Case 1:
% 229.11/40.54  | | | | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | | | |   (105)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 229.11/40.54  | | | | | | | | | | | |            & op(e2, e2) = e0)
% 229.11/40.54  | | | | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | | | | REF_CLOSE: (8), (25), (32), (41), (55), (77), (104), (105)
% 229.11/40.54  | | | | | | | | | | | |            are inconsistent by sub-proof #685.
% 229.11/40.54  | | | | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | | | Case 2:
% 229.11/40.54  | | | | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | | | |   (106)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 229.11/40.54  | | | | | | | | | | | |            e0 & op(e2, e0) = e0)
% 229.11/40.54  | | | | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | | | | BETA: splitting (106) gives:
% 229.11/40.54  | | | | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | | | | Case 1:
% 229.11/40.54  | | | | | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | | | | |   (107)  all_57_5 = e0 & op(e2, e1) = e0
% 229.11/40.54  | | | | | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | | | | | ALPHA: (107) implies:
% 229.11/40.54  | | | | | | | | | | | | |   (108)  all_57_5 = e0
% 229.11/40.54  | | | | | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | | | | | REF_CLOSE: (6), (8), (16), (25), (28), (31), (41), (47),
% 229.11/40.54  | | | | | | | | | | | | |            (58), (61), (67), (68), (74), (95), (104), (108)
% 229.11/40.54  | | | | | | | | | | | | |            are inconsistent by sub-proof #683.
% 229.11/40.54  | | | | | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | | | | Case 2:
% 229.11/40.54  | | | | | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | | | | |   (109)  all_57_10 = e0 & op(e2, e0) = e0
% 229.11/40.54  | | | | | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (9), (12), (14),
% 229.11/40.54  | | | | | | | | | | | | |            (17), (23), (25), (28), (31), (34), (35), (41),
% 229.11/40.54  | | | | | | | | | | | | |            (45), (46), (47), (50), (55), (57), (58), (61),
% 229.11/40.54  | | | | | | | | | | | | |            (62), (64), (65), (67), (68), (73), (74), (79),
% 229.11/40.54  | | | | | | | | | | | | |            (81), (91), (101), (109) are inconsistent by
% 229.11/40.54  | | | | | | | | | | | | |            sub-proof #673.
% 229.11/40.54  | | | | | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | | | | End of split
% 229.11/40.54  | | | | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | | | End of split
% 229.11/40.54  | | | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | | Case 2:
% 229.11/40.54  | | | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | | |   (110)  all_57_3 = e2 & op(e2, e2) = e2
% 229.11/40.54  | | | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | | | ALPHA: (110) implies:
% 229.11/40.54  | | | | | | | | | | |   (111)  op(e2, e2) = e2
% 229.11/40.54  | | | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | | | REF_CLOSE: (8), (16), (67), (111) are inconsistent by
% 229.11/40.54  | | | | | | | | | | |            sub-proof #2306.
% 229.11/40.54  | | | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | | End of split
% 229.11/40.54  | | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | Case 2:
% 229.11/40.54  | | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | |   (112)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2
% 229.11/40.54  | | | | | | | | | |            & op(e2, e0) = e2)
% 229.11/40.54  | | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | | BETA: splitting (112) gives:
% 229.11/40.54  | | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | | Case 1:
% 229.11/40.54  | | | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | | |   (113)  all_57_5 = e2 & op(e2, e1) = e2
% 229.11/40.54  | | | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | | | ALPHA: (113) implies:
% 229.11/40.54  | | | | | | | | | | |   (114)  all_57_5 = e2
% 229.11/40.54  | | | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | | | BETA: splitting (66) gives:
% 229.11/40.54  | | | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | | | Case 1:
% 229.11/40.54  | | | | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | | | |   (115)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 229.11/40.54  | | | | | | | | | | | |            & op(e2, e2) = e0)
% 229.11/40.54  | | | | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | | | | BETA: splitting (115) gives:
% 229.11/40.54  | | | | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | | | | Case 1:
% 229.11/40.54  | | | | | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | | | | |   (116)  all_57_2 = e0 & op(e2, e3) = e0
% 229.11/40.54  | | | | | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | | | | | ALPHA: (116) implies:
% 229.11/40.54  | | | | | | | | | | | | |   (117)  all_57_2 = e0
% 229.11/40.54  | | | | | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | | | | | REF_CLOSE: (3), (4), (5), (6), (8), (9), (12), (14), (16),
% 229.11/40.54  | | | | | | | | | | | | |            (17), (18), (23), (25), (28), (31), (34), (40),
% 229.11/40.54  | | | | | | | | | | | | |            (41), (43), (45), (46), (47), (58), (61), (62),
% 229.11/40.54  | | | | | | | | | | | | |            (64), (67), (68), (74), (79), (81), (96), (101),
% 229.11/40.54  | | | | | | | | | | | | |            (117) are inconsistent by sub-proof #796.
% 229.11/40.54  | | | | | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | | | | Case 2:
% 229.11/40.54  | | | | | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | | | | |   (118)  all_57_3 = e0 & op(e2, e2) = e0
% 229.11/40.54  | | | | | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | | | | | ALPHA: (118) implies:
% 229.11/40.54  | | | | | | | | | | | | |   (119)  op(e2, e2) = e0
% 229.11/40.54  | | | | | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | | | | | REF_CLOSE: (8), (25), (32), (55), (77), (119) are
% 229.11/40.54  | | | | | | | | | | | | |            inconsistent by sub-proof #1229.
% 229.11/40.54  | | | | | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | | | | End of split
% 229.11/40.54  | | | | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | | | Case 2:
% 229.11/40.54  | | | | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | | | |   (120)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 229.11/40.54  | | | | | | | | | | | |            e0 & op(e2, e0) = e0)
% 229.11/40.54  | | | | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | | | | BETA: splitting (120) gives:
% 229.11/40.54  | | | | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | | | | Case 1:
% 229.11/40.54  | | | | | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | | | | |   (121)  all_57_5 = e0 & op(e2, e1) = e0
% 229.11/40.54  | | | | | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | | | | | REF_CLOSE: (41), (114), (121) are inconsistent by sub-proof
% 229.11/40.54  | | | | | | | | | | | | |            #2428.
% 229.11/40.54  | | | | | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | | | | Case 2:
% 229.11/40.54  | | | | | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | | | | |   (122)  all_57_10 = e0 & op(e2, e0) = e0
% 229.11/40.54  | | | | | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (9), (12), (14),
% 229.11/40.54  | | | | | | | | | | | | |            (17), (23), (25), (28), (31), (34), (35), (41),
% 229.11/40.54  | | | | | | | | | | | | |            (45), (46), (47), (50), (55), (57), (58), (61),
% 229.11/40.54  | | | | | | | | | | | | |            (62), (64), (65), (67), (68), (73), (74), (79),
% 229.11/40.54  | | | | | | | | | | | | |            (81), (91), (101), (122) are inconsistent by
% 229.11/40.54  | | | | | | | | | | | | |            sub-proof #673.
% 229.11/40.54  | | | | | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | | | | End of split
% 229.11/40.54  | | | | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | | | End of split
% 229.11/40.54  | | | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | | Case 2:
% 229.11/40.54  | | | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | | |   (123)  all_57_10 = e2 & op(e2, e0) = e2
% 229.11/40.54  | | | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | | | ALPHA: (123) implies:
% 229.11/40.54  | | | | | | | | | | |   (124)  all_57_10 = e2
% 229.11/40.54  | | | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | | | REF_CLOSE: (67), (91), (124) are inconsistent by sub-proof
% 229.11/40.54  | | | | | | | | | | |            #2144.
% 229.11/40.54  | | | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | | End of split
% 229.11/40.54  | | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | End of split
% 229.11/40.54  | | | | | | | | | 
% 229.11/40.54  | | | | | | | | End of split
% 229.11/40.54  | | | | | | | | 
% 229.11/40.54  | | | | | | | Case 2:
% 229.11/40.54  | | | | | | | | 
% 229.11/40.54  | | | | | | | |   (125)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 &
% 229.11/40.54  | | | | | | | |            op(e0, e0) = e1)
% 229.11/40.54  | | | | | | | | 
% 229.11/40.54  | | | | | | | | BETA: splitting (125) gives:
% 229.11/40.54  | | | | | | | | 
% 229.11/40.54  | | | | | | | | Case 1:
% 229.11/40.54  | | | | | | | | | 
% 229.11/40.54  | | | | | | | | |   (126)  all_57_14 = e1 & op(e0, e1) = e1
% 229.11/40.54  | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | ALPHA: (126) implies:
% 229.11/40.54  | | | | | | | | |   (127)  all_57_14 = e1
% 229.11/40.54  | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | BETA: splitting (46) gives:
% 229.11/40.54  | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | Case 1:
% 229.11/40.54  | | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | |   (128)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 229.11/40.54  | | | | | | | | | |            & op(e3, e2) = e3)
% 229.11/40.54  | | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | | BETA: splitting (128) gives:
% 229.11/40.54  | | | | | | | | | | 
% 229.11/40.54  | | | | | | | | | | Case 1:
% 229.11/40.54  | | | | | | | | | | | 
% 229.11/40.55  | | | | | | | | | | |   (129)  all_57_0 = e3 & op(e3, e3) = e3
% 229.11/40.55  | | | | | | | | | | | 
% 229.11/40.55  | | | | | | | | | | | ALPHA: (129) implies:
% 229.11/40.55  | | | | | | | | | | |   (130)  op(e3, e3) = e3
% 229.11/40.55  | | | | | | | | | | | 
% 229.11/40.55  | | | | | | | | | | | REF_CLOSE: (8), (25), (34), (130) are inconsistent by
% 229.11/40.55  | | | | | | | | | | |            sub-proof #2490.
% 229.11/40.55  | | | | | | | | | | | 
% 229.11/40.55  | | | | | | | | | | Case 2:
% 229.11/40.55  | | | | | | | | | | | 
% 229.11/40.55  | | | | | | | | | | |   (131)  all_57_1 = e3 & op(e3, e2) = e3
% 229.11/40.55  | | | | | | | | | | | 
% 229.11/40.55  | | | | | | | | | | | ALPHA: (131) implies:
% 229.11/40.55  | | | | | | | | | | |   (132)  all_57_1 = e3
% 229.11/40.55  | | | | | | | | | | | 
% 229.11/40.55  | | | | | | | | | | | BETA: splitting (64) gives:
% 229.11/40.55  | | | | | | | | | | | 
% 229.11/40.55  | | | | | | | | | | | Case 1:
% 229.11/40.55  | | | | | | | | | | | | 
% 229.11/40.55  | | | | | | | | | | | |   (133)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 229.11/40.55  | | | | | | | | | | | |            & op(e2, e2) = e2)
% 229.11/40.55  | | | | | | | | | | | | 
% 229.11/40.55  | | | | | | | | | | | | REF_CLOSE: (6), (8), (16), (25), (28), (31), (32), (41),
% 229.11/40.55  | | | | | | | | | | | |            (47), (55), (58), (61), (66), (67), (68), (74),
% 229.11/40.55  | | | | | | | | | | | |            (77), (91), (95), (133) are inconsistent by
% 229.11/40.55  | | | | | | | | | | | |            sub-proof #681.
% 229.11/40.55  | | | | | | | | | | | | 
% 229.11/40.55  | | | | | | | | | | | Case 2:
% 229.11/40.55  | | | | | | | | | | | | 
% 229.11/40.55  | | | | | | | | | | | |   (134)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 229.11/40.55  | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 229.11/40.55  | | | | | | | | | | | | 
% 229.11/40.55  | | | | | | | | | | | | BETA: splitting (134) gives:
% 229.11/40.55  | | | | | | | | | | | | 
% 229.11/40.55  | | | | | | | | | | | | Case 1:
% 229.11/40.55  | | | | | | | | | | | | | 
% 229.11/40.55  | | | | | | | | | | | | |   (135)  all_57_5 = e2 & op(e2, e1) = e2
% 229.11/40.55  | | | | | | | | | | | | | 
% 229.11/40.55  | | | | | | | | | | | | | ALPHA: (135) implies:
% 229.11/40.55  | | | | | | | | | | | | |   (136)  all_57_5 = e2
% 229.11/40.55  | | | | | | | | | | | | | 
% 229.11/40.55  | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (9), (12), (14),
% 229.11/40.55  | | | | | | | | | | | | |            (16), (17), (20), (23), (24), (25), (28), (31),
% 229.11/40.55  | | | | | | | | | | | | |            (34), (35), (39), (41), (45), (46), (47), (49),
% 229.11/40.55  | | | | | | | | | | | | |            (55), (57), (58), (61), (62), (64), (67), (68),
% 229.11/40.55  | | | | | | | | | | | | |            (73), (74), (79), (81), (85), (127), (132), (136)
% 229.11/40.55  | | | | | | | | | | | | |            are inconsistent by sub-proof #766.
% 229.11/40.55  | | | | | | | | | | | | | 
% 229.11/40.55  | | | | | | | | | | | | Case 2:
% 229.11/40.55  | | | | | | | | | | | | | 
% 229.11/40.55  | | | | | | | | | | | | |   (137)  all_57_10 = e2 & op(e2, e0) = e2
% 229.11/40.55  | | | | | | | | | | | | | 
% 229.11/40.55  | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 229.11/40.55  | | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 229.11/40.55  | | | | | | | | | | | | |            (19), (21), (22), (23), (24), (25), (26), (27),
% 229.11/40.55  | | | | | | | | | | | | |            (28), (29), (30), (31), (33), (34), (35), (36),
% 229.11/40.55  | | | | | | | | | | | | |            (37), (38), (40), (41), (42), (43), (44), (45),
% 229.11/40.55  | | | | | | | | | | | | |            (46), (47), (48), (49), (50), (51), (52), (53),
% 229.11/40.55  | | | | | | | | | | | | |            (54), (55), (56), (57), (58), (59), (60), (61),
% 229.11/40.55  | | | | | | | | | | | | |            (62), (63), (64), (65), (67), (68), (69), (70),
% 229.11/40.55  | | | | | | | | | | | | |            (72), (73), (74), (75), (76), (78), (79), (80),
% 229.11/40.55  | | | | | | | | | | | | |            (81), (85), (91), (95), (127), (137) are
% 229.11/40.55  | | | | | | | | | | | | |            inconsistent by sub-proof #737.
% 229.11/40.55  | | | | | | | | | | | | | 
% 229.11/40.55  | | | | | | | | | | | | End of split
% 229.11/40.55  | | | | | | | | | | | | 
% 229.11/40.55  | | | | | | | | | | | End of split
% 229.11/40.55  | | | | | | | | | | | 
% 229.11/40.55  | | | | | | | | | | End of split
% 229.11/40.55  | | | | | | | | | | 
% 229.11/40.55  | | | | | | | | | Case 2:
% 229.11/40.55  | | | | | | | | | | 
% 229.11/40.55  | | | | | | | | | |   (138)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 229.11/40.55  | | | | | | | | | |            & op(e3, e0) = e3)
% 229.11/40.55  | | | | | | | | | | 
% 229.11/40.55  | | | | | | | | | | REF_CLOSE: (6), (8), (62), (81), (85), (138) are inconsistent
% 229.11/40.55  | | | | | | | | | |            by sub-proof #2281.
% 229.11/40.55  | | | | | | | | | | 
% 229.11/40.55  | | | | | | | | | End of split
% 229.11/40.55  | | | | | | | | | 
% 229.11/40.55  | | | | | | | | Case 2:
% 229.11/40.55  | | | | | | | | | 
% 229.11/40.55  | | | | | | | | |   (139)  all_57_15 = e1 & op(e0, e0) = e1
% 229.11/40.55  | | | | | | | | | 
% 229.11/40.55  | | | | | | | | | ALPHA: (139) implies:
% 229.11/40.55  | | | | | | | | |   (140)  op(e0, e0) = e1
% 229.11/40.55  | | | | | | | | | 
% 229.11/40.55  | | | | | | | | | REF_CLOSE: (6), (8), (55), (140) are inconsistent by sub-proof
% 229.11/40.55  | | | | | | | | |            #2183.
% 229.11/40.55  | | | | | | | | | 
% 229.11/40.55  | | | | | | | | End of split
% 229.11/40.55  | | | | | | | | 
% 229.11/40.55  | | | | | | | End of split
% 229.11/40.55  | | | | | | | 
% 229.11/40.55  | | | | | | Case 2:
% 229.11/40.55  | | | | | | | 
% 229.11/40.55  | | | | | | |   (141)  all_57_15 = e2 & op(e0, e0) = e2
% 229.11/40.55  | | | | | | | 
% 229.11/40.55  | | | | | | | REF_CLOSE: (25), (31), (141) are inconsistent by sub-proof #2323.
% 229.11/40.55  | | | | | | | 
% 229.11/40.55  | | | | | | End of split
% 229.11/40.55  | | | | | | 
% 229.11/40.55  | | | | | End of split
% 229.11/40.55  | | | | | 
% 229.11/40.55  | | | | End of split
% 229.11/40.55  | | | | 
% 229.11/40.55  | | | Case 2:
% 229.11/40.55  | | | | 
% 229.11/40.55  | | | |   (142)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0,
% 229.11/40.55  | | | |              e0) = e1)
% 229.11/40.55  | | | | 
% 229.11/40.55  | | | | BETA: splitting (142) gives:
% 229.11/40.55  | | | | 
% 229.11/40.55  | | | | Case 1:
% 229.11/40.55  | | | | | 
% 229.11/40.55  | | | | |   (143)  all_57_11 = e1 & op(e1, e0) = e1
% 229.11/40.55  | | | | | 
% 229.11/40.55  | | | | | ALPHA: (143) implies:
% 229.11/40.55  | | | | |   (144)  all_57_11 = e1
% 229.11/40.55  | | | | | 
% 229.11/40.55  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 229.11/40.55  | | | | |            (12), (13), (14), (15), (16), (17), (18), (19), (20), (21),
% 229.11/40.55  | | | | |            (22), (23), (24), (25), (26), (27), (28), (29), (30), (31),
% 229.11/40.55  | | | | |            (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 229.11/40.55  | | | | |            (43), (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 229.11/40.55  | | | | |            (53), (54), (55), (56), (57), (58), (59), (60), (61), (62),
% 229.11/40.55  | | | | |            (63), (64), (65), (66), (67), (68), (69), (70), (72), (73),
% 229.11/40.55  | | | | |            (74), (75), (76), (78), (79), (80), (81), (85), (144) are
% 229.11/40.55  | | | | |            inconsistent by sub-proof #716.
% 229.11/40.55  | | | | | 
% 229.11/40.55  | | | | Case 2:
% 229.11/40.55  | | | | | 
% 229.11/40.55  | | | | |   (145)  all_57_15 = e1 & op(e0, e0) = e1
% 229.11/40.55  | | | | | 
% 229.11/40.55  | | | | | ALPHA: (145) implies:
% 229.11/40.55  | | | | |   (146)  op(e0, e0) = e1
% 229.11/40.55  | | | | | 
% 229.11/40.55  | | | | | REF_CLOSE: (6), (8), (55), (146) are inconsistent by sub-proof #2183.
% 229.11/40.55  | | | | | 
% 229.11/40.55  | | | | End of split
% 229.11/40.55  | | | | 
% 229.11/40.55  | | | End of split
% 229.11/40.55  | | | 
% 229.11/40.55  | | Case 2:
% 229.11/40.55  | | | 
% 229.11/40.55  | | |   (147)  all_57_9 = e1 & op(e3, e0) = e1
% 229.11/40.55  | | | 
% 229.11/40.55  | | | ALPHA: (147) implies:
% 229.11/40.55  | | |   (148)  all_57_9 = e1
% 229.11/40.55  | | |   (149)  op(e3, e0) = e1
% 229.11/40.55  | | | 
% 229.11/40.55  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 229.11/40.55  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 229.11/40.55  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 229.11/40.55  | | |            (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 229.11/40.55  | | |            (43), (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 229.11/40.55  | | |            (53), (54), (55), (56), (57), (58), (59), (60), (61), (62),
% 229.11/40.55  | | |            (63), (64), (65), (66), (67), (68), (69), (70), (71), (72),
% 229.11/40.55  | | |            (73), (74), (75), (76), (77), (78), (79), (80), (81), (148),
% 229.11/40.55  | | |            (149) are inconsistent by sub-proof #674.
% 229.11/40.55  | | | 
% 229.11/40.55  | | End of split
% 229.11/40.55  | | 
% 229.11/40.55  | End of split
% 229.11/40.55  | 
% 229.11/40.55  End of proof
% 229.11/40.55  
% 229.11/40.55  Sub-proof #673 shows that the following formulas are inconsistent:
% 229.11/40.55  ----------------------------------------------------------------
% 229.11/40.55    (1)  all_57_0 = e2
% 229.11/40.55    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.11/40.55         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.11/40.55    (3)  all_57_13 = e1
% 229.11/40.55    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.11/40.55         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.11/40.55    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.11/40.55         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.11/40.55    (6)   ~ (e3 = e1)
% 229.11/40.55    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.11/40.55           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.11/40.55    (8)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.11/40.55         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.11/40.55    (9)   ~ (all_6_2 = e3)
% 229.11/40.55    (10)  all_57_10 = e1
% 229.11/40.55    (11)  op(e1, e1) = all_6_2
% 229.11/40.55    (12)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.11/40.55          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.11/40.55    (13)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.11/40.55          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.11/40.55    (14)   ~ (e3 = e2)
% 229.11/40.55    (15)   ~ (e3 = e0)
% 229.11/40.55    (16)  all_57_10 = e0 & op(e2, e0) = e0
% 229.11/40.55    (17)  all_57_15 = e3
% 229.11/40.55    (18)  op(e3, e3) = e2
% 229.11/40.55    (19)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.11/40.55          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.11/40.55            e1)
% 229.11/40.55    (20)   ~ (e2 = e0)
% 229.11/40.55    (21)  all_57_3 = e1
% 229.11/40.55    (22)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.11/40.55          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.11/40.55    (23)   ~ (e1 = e0)
% 229.11/40.55    (24)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.11/40.55          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.11/40.55    (25)  op(e0, e0) = e3
% 229.11/40.55    (26)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.11/40.55          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.11/40.55            e2)
% 229.11/40.55    (27)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.11/40.55              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.11/40.55                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.11/40.55                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.11/40.55    (28)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.11/40.55          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.11/40.55    (29)   ~ (all_53_12 = e3)
% 229.11/40.55    (30)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.11/40.55          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.11/40.55    (31)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.11/40.55          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.11/40.55    (32)   ~ (e2 = e1)
% 229.11/40.55    (33)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.11/40.55          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.11/40.55    (34)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.11/40.55          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.11/40.55    (35)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.11/40.55          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.11/40.55    (36)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.11/40.55          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.11/40.55    (37)  op(e3, e0) = all_53_12
% 229.11/40.55  
% 229.11/40.55  Begin of proof
% 229.11/40.55  | 
% 229.11/40.55  | ALPHA: (16) implies:
% 229.11/40.55  |   (38)  all_57_10 = e0
% 229.11/40.55  | 
% 229.11/40.55  | COMBINE_EQS: (10), (38) imply:
% 229.11/40.55  |   (39)  e1 = e0
% 229.11/40.55  | 
% 229.11/40.55  | COMBINE_EQS: (3), (39) imply:
% 229.11/40.55  |   (40)  all_57_13 = e0
% 229.11/40.55  | 
% 229.11/40.55  | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (11), (12), (13), (14),
% 229.11/40.55  |            (15), (17), (18), (19), (20), (21), (22), (23), (24), (25), (26),
% 229.11/40.55  |            (27), (28), (29), (30), (31), (32), (33), (34), (35), (36), (37),
% 229.11/40.55  |            (39), (40) are inconsistent by sub-proof #778.
% 229.11/40.55  | 
% 229.11/40.55  End of proof
% 229.11/40.55  
% 229.11/40.55  Sub-proof #674 shows that the following formulas are inconsistent:
% 229.11/40.55  ----------------------------------------------------------------
% 229.11/40.55    (1)   ~ (all_53_2 = e2)
% 229.11/40.55    (2)  all_57_0 = e2
% 229.11/40.55    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.11/40.55         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.11/40.55    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.11/40.55         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.11/40.55    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.11/40.55         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.11/40.55    (6)   ~ (e3 = e1)
% 229.11/40.55    (7)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 229.11/40.55         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 229.11/40.55    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.11/40.55           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.11/40.55    (9)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.11/40.55         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.11/40.55    (10)   ~ (all_53_3 = e3)
% 229.11/40.55    (11)   ~ (all_53_3 = all_53_7)
% 229.11/40.55    (12)   ~ (all_6_2 = e3)
% 229.11/40.55    (13)   ~ (all_53_9 = e1)
% 229.11/40.55    (14)  op(e1, e1) = all_6_2
% 229.11/40.55    (15)   ~ (all_53_1 = all_53_9)
% 229.11/40.55    (16)  op(e2, e2) = e1
% 229.11/40.55    (17)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.11/40.55          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.11/40.55    (18)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 229.11/40.55            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 229.11/40.55              e3) = all_22_1 & $i(all_22_1))
% 229.11/40.55    (19)  all_57_9 = e1
% 229.11/40.55    (20)   ~ (all_53_13 = e3)
% 229.11/40.55    (21)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.11/40.55          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.11/40.55    (22)   ~ (all_53_9 = all_53_11)
% 229.11/40.55    (23)  all_55_4 = all_53_1
% 229.11/40.55    (24)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.11/40.55          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.11/40.55    (25)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 229.11/40.55          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.11/40.55    (26)   ~ (e3 = e2)
% 229.11/40.55    (27)  op(e3, e0) = e1
% 229.11/40.55    (28)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 229.11/40.55    (29)   ~ (all_53_1 = all_53_3)
% 229.11/40.55    (30)   ~ (e3 = e0)
% 229.11/40.55    (31)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 229.11/40.55    (32)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 229.11/40.55    (33)  all_57_15 = e3
% 229.11/40.55    (34)  op(e2, e2) = all_52_11
% 229.11/40.55    (35)   ~ (all_53_9 = all_53_13)
% 229.11/40.55    (36)  op(e3, e3) = e2
% 229.11/40.55    (37)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.11/40.55          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.11/40.55            e1)
% 229.11/40.55    (38)   ~ (all_53_1 = e1)
% 229.11/40.55    (39)  all_55_6 = all_53_9
% 229.11/40.55    (40)   ~ (all_53_1 = all_53_2)
% 229.11/40.55    (41)  op(e1, e1) = e1
% 229.11/40.55    (42)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.11/40.55          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.11/40.55    (43)   ~ (e2 = e0)
% 229.11/40.55    (44)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 229.11/40.55            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 229.11/40.55            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 229.11/40.55            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 229.11/40.55              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 229.11/40.55            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 229.11/40.55            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 229.11/40.55              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 229.11/40.55              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 229.11/40.55            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 229.11/40.55            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 229.11/40.55            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 229.11/40.55              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 229.11/40.55              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 229.11/40.55            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 229.11/40.55              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 229.11/40.55            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 229.11/40.55            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 229.11/40.55              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 229.11/40.55              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 229.11/40.55            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 229.11/40.55            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 229.11/40.55    (45)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 229.11/40.55            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 229.11/40.55              e3) = all_12_1 & $i(all_12_1))
% 229.11/40.55    (46)  all_55_12 = all_53_3
% 229.11/40.55    (47)  all_57_3 = e1
% 229.11/40.55    (48)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.11/40.55          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.11/40.55    (49)   ~ (e1 = e0)
% 229.11/40.55    (50)   ~ (all_53_3 = all_53_11)
% 229.11/40.55    (51)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.11/40.55          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.11/40.55    (52)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.11/40.55          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.11/40.55    (53)   ~ (all_53_2 = all_53_3)
% 229.11/40.55    (54)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 229.11/40.55    (55)   ~ (all_53_7 = all_53_11)
% 229.11/40.55    (56)  all_55_8 = all_53_2
% 229.11/40.55    (57)  op(e0, e0) = e3
% 229.11/40.55    (58)  op(e0, e2) = all_53_7
% 229.11/40.55    (59)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.11/40.55          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.11/40.55            e2)
% 229.11/40.55    (60)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.11/40.55              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.11/40.55                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.11/40.55                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.11/40.55    (61)   ~ (all_53_1 = all_53_13)
% 229.11/40.55    (62)  op(e2, e0) = all_53_13
% 229.11/40.55    (63)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.11/40.55          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.11/40.55    (64)   ~ (all_53_12 = e3)
% 229.11/40.55    (65)  op(e1, e3) = all_53_2
% 229.11/40.55    (66)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.11/40.55          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.11/40.55    (67)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.11/40.55          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.11/40.55    (68)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.11/40.55          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 229.11/40.55    (69)   ~ (e2 = e1)
% 229.11/40.55    (70)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.11/40.55          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.11/40.55    (71)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.11/40.55          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.11/40.55    (72)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 229.11/40.55    (73)   ~ (all_53_12 = e2)
% 229.11/40.55    (74)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 229.11/40.55          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 229.11/40.55    (75)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.11/40.55          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.11/40.55    (76)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.11/40.55          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.11/40.55    (77)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 229.11/40.55          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 229.11/40.55    (78)  all_55_14 = all_53_11
% 229.11/40.55    (79)  op(all_52_11, all_52_11) = e2
% 229.11/40.55    (80)   ~ (all_53_11 = e3)
% 229.11/40.55    (81)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.11/40.55          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.11/40.55    (82)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 229.11/40.55          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 229.11/40.55    (83)  op(e3, e0) = all_53_12
% 229.11/40.55  
% 229.11/40.55  Begin of proof
% 229.11/40.55  | 
% 229.11/40.55  | BETA: splitting (37) gives:
% 229.11/40.55  | 
% 229.11/40.55  | Case 1:
% 229.11/40.55  | | 
% 229.11/40.55  | |   (84)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 229.11/40.55  | |           e1)
% 229.11/40.55  | | 
% 229.11/40.55  | | BETA: splitting (84) gives:
% 229.11/40.55  | | 
% 229.11/40.55  | | Case 1:
% 229.11/40.55  | | | 
% 229.11/40.55  | | |   (85)  all_57_12 = e1 & op(e0, e3) = e1
% 229.11/40.55  | | | 
% 229.11/40.55  | | | ALPHA: (85) implies:
% 229.11/40.55  | | |   (86)  all_57_12 = e1
% 229.11/40.55  | | |   (87)  op(e0, e3) = e1
% 229.11/40.55  | | | 
% 229.11/40.55  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 229.11/40.55  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 229.11/40.55  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 229.11/40.55  | | |            (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 229.11/40.55  | | |            (43), (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 229.11/40.55  | | |            (53), (54), (55), (56), (57), (58), (59), (60), (61), (62),
% 229.11/40.55  | | |            (63), (64), (65), (66), (67), (68), (69), (70), (71), (72),
% 229.11/40.55  | | |            (73), (74), (75), (76), (77), (78), (79), (80), (81), (82),
% 229.11/40.55  | | |            (83), (86), (87) are inconsistent by sub-proof #675.
% 229.11/40.55  | | | 
% 229.11/40.55  | | Case 2:
% 229.11/40.55  | | | 
% 229.11/40.55  | | |   (88)  all_57_13 = e1 & op(e0, e2) = e1
% 229.11/40.55  | | | 
% 229.11/40.55  | | | ALPHA: (88) implies:
% 229.11/40.55  | | |   (89)  all_57_13 = e1
% 229.11/40.55  | | | 
% 229.11/40.55  | | | BETA: splitting (4) gives:
% 229.11/40.55  | | | 
% 229.11/40.55  | | | Case 1:
% 229.11/40.55  | | | | 
% 229.11/40.55  | | | |   (90)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3)
% 229.11/40.55  | | | |           = e1)
% 229.11/40.55  | | | | 
% 229.11/40.55  | | | | BETA: splitting (90) gives:
% 229.11/40.55  | | | | 
% 229.11/40.55  | | | | Case 1:
% 229.11/40.55  | | | | | 
% 229.11/40.55  | | | | |   (91)  all_57_0 = e1 & op(e3, e3) = e1
% 229.11/40.55  | | | | | 
% 229.11/40.55  | | | | | ALPHA: (91) implies:
% 229.11/40.55  | | | | |   (92)  op(e3, e3) = e1
% 229.11/40.55  | | | | | 
% 229.11/40.55  | | | | | REF_CLOSE: (8), (36), (69), (92) are inconsistent by sub-proof #1950.
% 229.11/40.55  | | | | | 
% 229.11/40.55  | | | | Case 2:
% 229.11/40.55  | | | | | 
% 229.11/40.55  | | | | |   (93)  all_57_2 = e1 & op(e2, e3) = e1
% 229.11/40.55  | | | | | 
% 229.11/40.55  | | | | | ALPHA: (93) implies:
% 229.11/40.55  | | | | |   (94)  all_57_2 = e1
% 229.11/40.55  | | | | | 
% 229.11/40.55  | | | | | REF_CLOSE: (3), (5), (6), (8), (16), (17), (24), (26), (30), (33),
% 229.11/40.55  | | | | |            (36), (37), (42), (43), (47), (48), (49), (52), (57), (59),
% 229.11/40.55  | | | | |            (60), (63), (64), (66), (69), (83), (89), (94) are
% 229.11/40.55  | | | | |            inconsistent by sub-proof #705.
% 229.11/40.55  | | | | | 
% 229.11/40.55  | | | | End of split
% 229.11/40.55  | | | | 
% 229.11/40.55  | | | Case 2:
% 229.11/40.55  | | | | 
% 229.11/40.55  | | | |   (95)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3)
% 229.11/40.55  | | | |           = e1)
% 229.11/40.55  | | | | 
% 229.11/40.55  | | | | BETA: splitting (95) gives:
% 229.11/40.55  | | | | 
% 229.11/40.55  | | | | Case 1:
% 229.11/40.55  | | | | | 
% 229.11/40.55  | | | | |   (96)  all_57_6 = e1 & op(e1, e3) = e1
% 229.11/40.55  | | | | | 
% 229.11/40.55  | | | | | ALPHA: (96) implies:
% 229.11/40.55  | | | | |   (97)  all_57_6 = e1
% 229.11/40.55  | | | | | 
% 229.11/40.55  | | | | | REF_CLOSE: (5), (6), (8), (9), (12), (14), (16), (17), (24), (26),
% 229.11/40.55  | | | | |            (30), (33), (36), (42), (43), (47), (48), (49), (60), (64),
% 229.11/40.55  | | | | |            (69), (70), (76), (81), (83), (89), (97) are inconsistent
% 229.11/40.55  | | | | |            by sub-proof #797.
% 229.11/40.55  | | | | | 
% 229.11/40.55  | | | | Case 2:
% 229.11/40.55  | | | | | 
% 229.11/40.55  | | | | |   (98)  all_57_12 = e1 & op(e0, e3) = e1
% 229.11/40.55  | | | | | 
% 229.11/40.55  | | | | | ALPHA: (98) implies:
% 229.11/40.55  | | | | |   (99)  all_57_12 = e1
% 229.11/40.55  | | | | |   (100)  op(e0, e3) = e1
% 229.11/40.55  | | | | | 
% 229.11/40.55  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 229.11/40.55  | | | | |            (12), (13), (14), (15), (16), (17), (18), (19), (20), (21),
% 229.11/40.55  | | | | |            (22), (23), (24), (25), (26), (27), (28), (29), (30), (31),
% 229.11/40.55  | | | | |            (32), (33), (34), (35), (36), (37), (38), (39), (40), (41),
% 229.11/40.55  | | | | |            (42), (43), (44), (45), (46), (47), (48), (49), (50), (51),
% 229.11/40.56  | | | | |            (52), (53), (54), (55), (56), (57), (58), (59), (60), (61),
% 229.11/40.56  | | | | |            (62), (63), (64), (65), (66), (67), (68), (69), (70), (71),
% 229.11/40.56  | | | | |            (72), (73), (74), (75), (76), (77), (78), (79), (80), (81),
% 229.11/40.56  | | | | |            (82), (83), (99), (100) are inconsistent by sub-proof #675.
% 229.11/40.56  | | | | | 
% 229.11/40.56  | | | | End of split
% 229.11/40.56  | | | | 
% 229.11/40.56  | | | End of split
% 229.11/40.56  | | | 
% 229.11/40.56  | | End of split
% 229.11/40.56  | | 
% 229.11/40.56  | Case 2:
% 229.11/40.56  | | 
% 229.11/40.56  | |   (101)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.11/40.56  | |            e1)
% 229.11/40.56  | | 
% 229.11/40.56  | | BETA: splitting (101) gives:
% 229.11/40.56  | | 
% 229.11/40.56  | | Case 1:
% 229.11/40.56  | | | 
% 229.11/40.56  | | |   (102)  all_57_14 = e1 & op(e0, e1) = e1
% 229.11/40.56  | | | 
% 229.11/40.56  | | | ALPHA: (102) implies:
% 229.11/40.56  | | |   (103)  all_57_14 = e1
% 229.11/40.56  | | | 
% 229.11/40.56  | | | BETA: splitting (4) gives:
% 229.11/40.56  | | | 
% 229.11/40.56  | | | Case 1:
% 229.11/40.56  | | | | 
% 229.11/40.56  | | | |   (104)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3)
% 229.11/40.56  | | | |            = e1)
% 229.11/40.56  | | | | 
% 229.11/40.56  | | | | BETA: splitting (104) gives:
% 229.11/40.56  | | | | 
% 229.11/40.56  | | | | Case 1:
% 229.11/40.56  | | | | | 
% 229.11/40.56  | | | | |   (105)  all_57_0 = e1 & op(e3, e3) = e1
% 229.11/40.56  | | | | | 
% 229.11/40.56  | | | | | ALPHA: (105) implies:
% 229.11/40.56  | | | | |   (106)  op(e3, e3) = e1
% 229.11/40.56  | | | | | 
% 229.11/40.56  | | | | | REF_CLOSE: (8), (36), (69), (106) are inconsistent by sub-proof #1950.
% 229.11/40.56  | | | | | 
% 229.11/40.56  | | | | Case 2:
% 229.11/40.56  | | | | | 
% 229.11/40.56  | | | | |   (107)  all_57_2 = e1 & op(e2, e3) = e1
% 229.11/40.56  | | | | | 
% 229.11/40.56  | | | | | ALPHA: (107) implies:
% 229.11/40.56  | | | | |   (108)  all_57_2 = e1
% 229.11/40.56  | | | | | 
% 229.11/40.56  | | | | | REF_CLOSE: (3), (6), (8), (12), (14), (16), (19), (24), (26), (30),
% 229.11/40.56  | | | | |            (33), (36), (37), (41), (43), (47), (48), (49), (51), (57),
% 229.11/40.56  | | | | |            (59), (60), (63), (64), (66), (69), (70), (74), (83),
% 229.11/40.56  | | | | |            (103), (108) are inconsistent by sub-proof #699.
% 229.11/40.56  | | | | | 
% 229.11/40.56  | | | | End of split
% 229.11/40.56  | | | | 
% 229.11/40.56  | | | Case 2:
% 229.11/40.56  | | | | 
% 229.11/40.56  | | | |   (109)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0,
% 229.11/40.56  | | | |              e3) = e1)
% 229.11/40.56  | | | | 
% 229.11/40.56  | | | | BETA: splitting (109) gives:
% 229.11/40.56  | | | | 
% 229.11/40.56  | | | | Case 1:
% 229.11/40.56  | | | | | 
% 229.11/40.56  | | | | |   (110)  all_57_6 = e1 & op(e1, e3) = e1
% 229.11/40.56  | | | | | 
% 229.11/40.56  | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (12), (14), (16),
% 229.11/40.56  | | | | |            (17), (19), (21), (24), (26), (30), (33), (36), (37), (41),
% 229.11/40.56  | | | | |            (42), (43), (47), (48), (49), (51), (52), (57), (59), (60),
% 229.11/40.56  | | | | |            (63), (64), (66), (67), (68), (69), (70), (71), (74), (75),
% 229.11/40.56  | | | | |            (76), (81), (83), (103), (110) are inconsistent by
% 229.11/40.56  | | | | |            sub-proof #693.
% 229.11/40.56  | | | | | 
% 229.11/40.56  | | | | Case 2:
% 229.11/40.56  | | | | | 
% 229.11/40.56  | | | | |   (111)  all_57_12 = e1 & op(e0, e3) = e1
% 229.11/40.56  | | | | | 
% 229.11/40.56  | | | | | ALPHA: (111) implies:
% 229.11/40.56  | | | | |   (112)  all_57_12 = e1
% 229.11/40.56  | | | | |   (113)  op(e0, e3) = e1
% 229.11/40.56  | | | | | 
% 229.11/40.56  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 229.11/40.56  | | | | |            (12), (13), (14), (15), (16), (17), (18), (19), (20), (21),
% 229.11/40.56  | | | | |            (22), (23), (24), (25), (26), (27), (28), (29), (30), (31),
% 229.11/40.56  | | | | |            (32), (33), (34), (35), (36), (37), (38), (39), (40), (41),
% 229.11/40.56  | | | | |            (42), (43), (44), (45), (46), (47), (48), (49), (50), (51),
% 229.11/40.56  | | | | |            (52), (53), (54), (55), (56), (57), (58), (59), (60), (61),
% 229.11/40.56  | | | | |            (62), (63), (64), (65), (66), (67), (68), (69), (70), (71),
% 229.11/40.56  | | | | |            (72), (73), (74), (75), (76), (77), (78), (79), (80), (81),
% 229.11/40.56  | | | | |            (82), (83), (112), (113) are inconsistent by sub-proof
% 229.11/40.56  | | | | |            #675.
% 229.11/40.56  | | | | | 
% 229.11/40.56  | | | | End of split
% 229.11/40.56  | | | | 
% 229.11/40.56  | | | End of split
% 229.11/40.56  | | | 
% 229.11/40.56  | | Case 2:
% 229.11/40.56  | | | 
% 229.11/40.56  | | |   (114)  all_57_15 = e1 & op(e0, e0) = e1
% 229.11/40.56  | | | 
% 229.11/40.56  | | | ALPHA: (114) implies:
% 229.11/40.56  | | |   (115)  op(e0, e0) = e1
% 229.11/40.56  | | | 
% 229.11/40.56  | | | REF_CLOSE: (6), (8), (57), (115) are inconsistent by sub-proof #2183.
% 229.11/40.56  | | | 
% 229.11/40.56  | | End of split
% 229.11/40.56  | | 
% 229.11/40.56  | End of split
% 229.11/40.56  | 
% 229.11/40.56  End of proof
% 229.11/40.56  
% 229.11/40.56  Sub-proof #675 shows that the following formulas are inconsistent:
% 229.11/40.56  ----------------------------------------------------------------
% 229.11/40.56    (1)   ~ (all_53_2 = e2)
% 229.11/40.56    (2)  all_57_0 = e2
% 229.11/40.56    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.11/40.56         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.11/40.56    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.11/40.56         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.11/40.56    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.11/40.56         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.11/40.56    (6)   ~ (e3 = e1)
% 229.11/40.56    (7)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 229.11/40.56         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 229.11/40.56    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.11/40.56           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.11/40.56    (9)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.11/40.56         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.11/40.56    (10)   ~ (all_53_3 = e3)
% 229.11/40.56    (11)   ~ (all_53_3 = all_53_7)
% 229.11/40.56    (12)   ~ (all_6_2 = e3)
% 229.11/40.56    (13)   ~ (all_53_9 = e1)
% 229.11/40.56    (14)  op(e1, e1) = all_6_2
% 229.11/40.56    (15)   ~ (all_53_1 = all_53_9)
% 229.11/40.56    (16)  op(e2, e2) = e1
% 229.11/40.56    (17)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.11/40.56          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.11/40.56    (18)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 229.11/40.56            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 229.11/40.56              e3) = all_22_1 & $i(all_22_1))
% 229.11/40.56    (19)  all_57_9 = e1
% 229.11/40.56    (20)   ~ (all_53_13 = e3)
% 229.11/40.56    (21)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.11/40.56          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.11/40.56    (22)   ~ (all_53_9 = all_53_11)
% 229.11/40.56    (23)  all_55_4 = all_53_1
% 229.11/40.56    (24)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.11/40.56          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.11/40.56    (25)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 229.11/40.56          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.11/40.56    (26)   ~ (e3 = e2)
% 229.11/40.56    (27)  op(e3, e0) = e1
% 229.11/40.56    (28)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 229.11/40.56    (29)   ~ (all_53_1 = all_53_3)
% 229.11/40.56    (30)   ~ (e3 = e0)
% 229.11/40.56    (31)  op(e0, e3) = e1
% 229.11/40.56    (32)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 229.11/40.56    (33)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 229.11/40.56    (34)  all_57_15 = e3
% 229.11/40.56    (35)  op(e2, e2) = all_52_11
% 229.11/40.56    (36)   ~ (all_53_9 = all_53_13)
% 229.11/40.56    (37)  op(e3, e3) = e2
% 229.11/40.56    (38)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.11/40.56          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.11/40.56            e1)
% 229.11/40.56    (39)   ~ (all_53_1 = e1)
% 229.11/40.56    (40)  all_57_12 = e1
% 229.11/40.56    (41)  all_55_6 = all_53_9
% 229.11/40.56    (42)   ~ (all_53_1 = all_53_2)
% 229.11/40.56    (43)  op(e1, e1) = e1
% 229.11/40.56    (44)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.11/40.56          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.11/40.56    (45)   ~ (e2 = e0)
% 229.11/40.56    (46)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 229.11/40.56            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 229.11/40.56            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 229.11/40.56            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 229.11/40.56              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 229.11/40.56            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 229.11/40.56            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 229.11/40.56              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 229.11/40.56              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 229.11/40.56            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 229.11/40.56            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 229.11/40.56            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 229.11/40.56              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 229.11/40.56              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 229.11/40.56            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 229.11/40.56              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 229.11/40.56            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 229.11/40.56            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 229.11/40.56              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 229.11/40.56              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 229.11/40.56            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 229.11/40.56            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 229.11/40.56    (47)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 229.11/40.56            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 229.11/40.56              e3) = all_12_1 & $i(all_12_1))
% 229.11/40.56    (48)  all_55_12 = all_53_3
% 229.11/40.56    (49)  all_57_3 = e1
% 229.11/40.56    (50)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.11/40.56          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.11/40.56    (51)   ~ (e1 = e0)
% 229.11/40.56    (52)   ~ (all_53_3 = all_53_11)
% 229.11/40.56    (53)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.11/40.56          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.11/40.56    (54)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.11/40.56          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.11/40.56    (55)   ~ (all_53_2 = all_53_3)
% 229.11/40.56    (56)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 229.11/40.56    (57)   ~ (all_53_7 = all_53_11)
% 229.11/40.56    (58)  all_55_8 = all_53_2
% 229.11/40.56    (59)  op(e0, e0) = e3
% 229.11/40.56    (60)  op(e0, e2) = all_53_7
% 229.11/40.56    (61)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.11/40.56          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.11/40.56            e2)
% 229.11/40.56    (62)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.11/40.56              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.11/40.56                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.11/40.56                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.11/40.56    (63)   ~ (all_53_1 = all_53_13)
% 229.11/40.56    (64)  op(e2, e0) = all_53_13
% 229.11/40.56    (65)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.11/40.56          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.11/40.56    (66)   ~ (all_53_12 = e3)
% 229.11/40.56    (67)  op(e1, e3) = all_53_2
% 229.11/40.56    (68)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.11/40.56          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.11/40.56    (69)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.11/40.56          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.11/40.56    (70)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.11/40.56          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 229.11/40.56    (71)   ~ (e2 = e1)
% 229.11/40.56    (72)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.11/40.56          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.11/40.56    (73)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.11/40.56          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.11/40.56    (74)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 229.11/40.56    (75)   ~ (all_53_12 = e2)
% 229.11/40.56    (76)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 229.11/40.56          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 229.11/40.56    (77)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.11/40.56          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.11/40.56    (78)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.11/40.56          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.11/40.56    (79)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 229.11/40.56          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 229.11/40.56    (80)  all_55_14 = all_53_11
% 229.11/40.56    (81)  op(all_52_11, all_52_11) = e2
% 229.11/40.56    (82)   ~ (all_53_11 = e3)
% 229.11/40.56    (83)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.11/40.56          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.11/40.56    (84)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 229.11/40.56          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 229.11/40.56    (85)  op(e3, e0) = all_53_12
% 229.11/40.56  
% 229.11/40.56  Begin of proof
% 229.11/40.56  | 
% 229.11/40.56  | BETA: splitting (79) gives:
% 229.11/40.56  | 
% 229.11/40.56  | Case 1:
% 229.11/40.56  | | 
% 229.11/40.56  | |   (86)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) =
% 229.11/40.56  | |           e1)
% 229.11/40.56  | | 
% 229.11/40.56  | | REF_CLOSE: (5), (6), (8), (9), (12), (14), (16), (17), (18), (24), (26),
% 229.11/40.56  | |            (30), (31), (34), (37), (38), (40), (43), (44), (45), (47), (50),
% 229.11/40.56  | |            (51), (54), (59), (61), (62), (66), (69), (71), (72), (73), (77),
% 229.11/40.56  | |            (78), (83), (84), (85), (86) are inconsistent by sub-proof #710.
% 229.11/40.56  | | 
% 229.11/40.56  | Case 2:
% 229.11/40.56  | | 
% 229.11/40.56  | |   (87)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) =
% 229.11/40.56  | |           e1)
% 229.11/40.56  | | 
% 229.11/40.56  | | BETA: splitting (87) gives:
% 229.11/40.56  | | 
% 229.11/40.56  | | Case 1:
% 229.11/40.56  | | | 
% 229.11/40.56  | | |   (88)  all_57_8 = e1 & op(e1, e1) = e1
% 229.11/40.56  | | | 
% 229.11/40.56  | | | GROUND_INST: instantiating (8) with e1, all_52_11, e2, e2, simplifying
% 229.11/40.56  | | |              with (16), (35) gives:
% 229.11/40.56  | | |   (89)  all_52_11 = e1
% 229.11/40.56  | | | 
% 229.11/40.56  | | | GROUND_INST: instantiating (8) with all_53_12, e1, e0, e3, simplifying
% 229.11/40.56  | | |              with (27), (85) gives:
% 229.11/40.56  | | |   (90)  all_53_12 = e1
% 229.11/40.56  | | | 
% 229.11/40.56  | | | REDUCE: (75), (90) imply:
% 229.11/40.56  | | |   (91)   ~ (e2 = e1)
% 229.11/40.56  | | | 
% 229.11/40.56  | | | REDUCE: (81), (89) imply:
% 229.11/40.56  | | |   (92)  op(e1, e1) = e2
% 229.11/40.56  | | | 
% 229.11/40.56  | | | REF_CLOSE: (8), (43), (71), (92) are inconsistent by sub-proof #2423.
% 229.11/40.56  | | | 
% 229.11/40.56  | | Case 2:
% 229.11/40.56  | | | 
% 229.11/40.56  | | |   (93)  all_57_11 = e1 & op(e1, e0) = e1
% 229.11/40.56  | | | 
% 229.11/40.56  | | | ALPHA: (93) implies:
% 229.11/40.56  | | |   (94)  all_57_11 = e1
% 229.11/40.56  | | | 
% 229.11/40.56  | | | BETA: splitting (72) gives:
% 229.11/40.56  | | | 
% 229.11/40.56  | | | Case 1:
% 229.11/40.56  | | | | 
% 229.11/40.56  | | | |   (95)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0)
% 229.11/40.56  | | | |           = e2)
% 229.11/40.56  | | | | 
% 229.11/40.56  | | | | BETA: splitting (95) gives:
% 229.11/40.56  | | | | 
% 229.11/40.56  | | | | Case 1:
% 229.11/40.56  | | | | | 
% 229.11/40.56  | | | | |   (96)  all_57_9 = e2 & op(e3, e0) = e2
% 229.11/40.56  | | | | | 
% 229.11/40.56  | | | | | ALPHA: (96) implies:
% 229.11/40.56  | | | | |   (97)  all_57_9 = e2
% 229.11/40.56  | | | | | 
% 229.11/40.56  | | | | | REF_CLOSE: (19), (71), (97) are inconsistent by sub-proof #2444.
% 229.11/40.56  | | | | | 
% 229.11/40.56  | | | | Case 2:
% 229.11/40.56  | | | | | 
% 229.11/40.56  | | | | |   (98)  all_57_10 = e2 & op(e2, e0) = e2
% 229.11/40.56  | | | | | 
% 229.11/40.56  | | | | | ALPHA: (98) implies:
% 229.11/40.56  | | | | |   (99)  all_57_10 = e2
% 229.11/40.56  | | | | |   (100)  op(e2, e0) = e2
% 229.11/40.56  | | | | | 
% 229.11/40.56  | | | | | BETA: splitting (38) gives:
% 229.11/40.56  | | | | | 
% 229.11/40.56  | | | | | Case 1:
% 229.11/40.56  | | | | | | 
% 229.11/40.56  | | | | | |   (101)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 &
% 229.11/40.56  | | | | | |            op(e0, e2) = e1)
% 229.11/40.56  | | | | | | 
% 229.11/40.56  | | | | | | BETA: splitting (101) gives:
% 229.11/40.56  | | | | | | 
% 229.11/40.56  | | | | | | Case 1:
% 229.11/40.56  | | | | | | | 
% 229.11/40.56  | | | | | | |   (102)  all_57_12 = e1 & op(e0, e3) = e1
% 229.11/40.56  | | | | | | | 
% 229.11/40.56  | | | | | | | REF_CLOSE: (1), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 229.11/40.56  | | | | | | |            (14), (15), (16), (17), (18), (19), (20), (22), (23),
% 229.11/40.56  | | | | | | |            (24), (26), (28), (29), (30), (31), (32), (33), (34),
% 229.11/40.56  | | | | | | |            (36), (37), (39), (41), (42), (43), (45), (46), (47),
% 229.11/40.56  | | | | | | |            (48), (50), (51), (52), (55), (56), (57), (58), (59),
% 229.11/40.56  | | | | | | |            (60), (62), (63), (64), (66), (67), (71), (72), (74),
% 229.11/40.56  | | | | | | |            (78), (80), (82), (85), (94), (99), (100) are
% 229.11/40.56  | | | | | | |            inconsistent by sub-proof #686.
% 229.11/40.56  | | | | | | | 
% 229.11/40.56  | | | | | | Case 2:
% 229.11/40.56  | | | | | | | 
% 229.11/40.56  | | | | | | |   (103)  all_57_13 = e1 & op(e0, e2) = e1
% 229.11/40.56  | | | | | | | 
% 229.11/40.56  | | | | | | | ALPHA: (103) implies:
% 229.11/40.56  | | | | | | |   (104)  all_57_13 = e1
% 229.11/40.56  | | | | | | | 
% 229.11/40.56  | | | | | | | BETA: splitting (4) gives:
% 229.11/40.56  | | | | | | | 
% 229.11/40.56  | | | | | | | Case 1:
% 229.11/40.56  | | | | | | | | 
% 229.11/40.56  | | | | | | | |   (105)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 &
% 229.11/40.56  | | | | | | | |            op(e2, e3) = e1)
% 229.11/40.56  | | | | | | | | 
% 229.11/40.56  | | | | | | | | BETA: splitting (105) gives:
% 229.11/40.56  | | | | | | | | 
% 229.11/40.56  | | | | | | | | Case 1:
% 229.11/40.56  | | | | | | | | | 
% 229.11/40.56  | | | | | | | | |   (106)  all_57_0 = e1 & op(e3, e3) = e1
% 229.11/40.56  | | | | | | | | | 
% 229.11/40.56  | | | | | | | | | ALPHA: (106) implies:
% 229.11/40.56  | | | | | | | | |   (107)  op(e3, e3) = e1
% 229.11/40.56  | | | | | | | | | 
% 229.11/40.56  | | | | | | | | | REF_CLOSE: (8), (37), (71), (107) are inconsistent by
% 229.11/40.56  | | | | | | | | |            sub-proof #1950.
% 229.11/40.56  | | | | | | | | | 
% 229.11/40.56  | | | | | | | | Case 2:
% 229.11/40.56  | | | | | | | | | 
% 229.11/40.56  | | | | | | | | |   (108)  all_57_2 = e1 & op(e2, e3) = e1
% 229.11/40.56  | | | | | | | | | 
% 229.11/40.56  | | | | | | | | | ALPHA: (108) implies:
% 229.11/40.56  | | | | | | | | |   (109)  all_57_2 = e1
% 229.11/40.56  | | | | | | | | | 
% 229.11/40.56  | | | | | | | | | BETA: splitting (5) gives:
% 229.11/40.56  | | | | | | | | | 
% 229.11/40.56  | | | | | | | | | Case 1:
% 229.11/40.56  | | | | | | | | | | 
% 229.11/40.56  | | | | | | | | | |   (110)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 229.11/40.56  | | | | | | | | | |            & op(e2, e2) = e2)
% 229.11/40.56  | | | | | | | | | | 
% 229.11/40.56  | | | | | | | | | | REF_CLOSE: (6), (8), (16), (17), (24), (26), (30), (37),
% 229.11/40.56  | | | | | | | | | |            (45), (50), (51), (66), (71), (85), (110) are
% 229.11/40.56  | | | | | | | | | |            inconsistent by sub-proof #714.
% 229.11/40.56  | | | | | | | | | | 
% 229.11/40.56  | | | | | | | | | Case 2:
% 229.11/40.56  | | | | | | | | | | 
% 229.11/40.56  | | | | | | | | | |   (111)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2
% 229.11/40.56  | | | | | | | | | |            & op(e0, e2) = e2)
% 229.11/40.56  | | | | | | | | | | 
% 229.11/40.56  | | | | | | | | | | BETA: splitting (111) gives:
% 229.11/40.56  | | | | | | | | | | 
% 229.11/40.56  | | | | | | | | | | Case 1:
% 229.11/40.56  | | | | | | | | | | | 
% 229.11/40.56  | | | | | | | | | | |   (112)  all_57_7 = e2 & op(e1, e2) = e2
% 229.11/40.56  | | | | | | | | | | | 
% 229.11/40.56  | | | | | | | | | | | ALPHA: (112) implies:
% 229.11/40.56  | | | | | | | | | | |   (113)  all_57_7 = e2
% 229.11/40.56  | | | | | | | | | | | 
% 229.11/40.56  | | | | | | | | | | | REF_CLOSE: (3), (6), (8), (16), (26), (30), (34), (38), (44),
% 229.11/40.56  | | | | | | | | | | |            (45), (49), (51), (54), (59), (61), (62), (65),
% 229.11/40.56  | | | | | | | | | | |            (68), (71), (104), (109), (113) are inconsistent
% 229.11/40.56  | | | | | | | | | | |            by sub-proof #775.
% 229.11/40.56  | | | | | | | | | | | 
% 229.11/40.56  | | | | | | | | | | Case 2:
% 229.11/40.56  | | | | | | | | | | | 
% 229.11/40.56  | | | | | | | | | | |   (114)  all_57_13 = e2 & op(e0, e2) = e2
% 229.11/40.56  | | | | | | | | | | | 
% 229.11/40.56  | | | | | | | | | | | REF_CLOSE: (1), (6), (8), (10), (11), (12), (13), (14), (15),
% 229.11/40.56  | | | | | | | | | | |            (16), (20), (22), (23), (28), (29), (32), (33),
% 229.11/40.56  | | | | | | | | | | |            (36), (37), (39), (41), (42), (45), (46), (48),
% 229.11/40.56  | | | | | | | | | | |            (52), (55), (56), (57), (58), (59), (60), (63),
% 229.11/40.56  | | | | | | | | | | |            (64), (67), (74), (80), (82), (100), (114) are
% 229.11/40.56  | | | | | | | | | | |            inconsistent by sub-proof #771.
% 229.11/40.56  | | | | | | | | | | | 
% 229.11/40.56  | | | | | | | | | | End of split
% 229.11/40.56  | | | | | | | | | | 
% 229.11/40.56  | | | | | | | | | End of split
% 229.11/40.56  | | | | | | | | | 
% 229.11/40.56  | | | | | | | | End of split
% 229.11/40.56  | | | | | | | | 
% 229.11/40.56  | | | | | | | Case 2:
% 229.11/40.56  | | | | | | | | 
% 229.11/40.56  | | | | | | | |   (115)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 &
% 229.11/40.56  | | | | | | | |            op(e0, e3) = e1)
% 229.11/40.56  | | | | | | | | 
% 229.11/40.56  | | | | | | | | BETA: splitting (115) gives:
% 229.11/40.56  | | | | | | | | 
% 229.11/40.56  | | | | | | | | Case 1:
% 229.11/40.56  | | | | | | | | | 
% 229.11/40.56  | | | | | | | | |   (116)  all_57_6 = e1 & op(e1, e3) = e1
% 229.11/40.56  | | | | | | | | | 
% 229.11/40.56  | | | | | | | | | ALPHA: (116) implies:
% 229.11/40.56  | | | | | | | | |   (117)  all_57_6 = e1
% 229.11/40.56  | | | | | | | | | 
% 229.11/40.56  | | | | | | | | | REF_CLOSE: (5), (6), (8), (9), (12), (14), (16), (17), (24),
% 229.11/40.56  | | | | | | | | |            (26), (30), (34), (37), (44), (45), (49), (50),
% 229.11/40.56  | | | | | | | | |            (51), (62), (66), (71), (72), (78), (83), (85),
% 229.11/40.56  | | | | | | | | |            (104), (117) are inconsistent by sub-proof #797.
% 229.11/40.56  | | | | | | | | | 
% 229.11/40.56  | | | | | | | | Case 2:
% 229.11/40.56  | | | | | | | | | 
% 229.11/40.56  | | | | | | | | |   (118)  all_57_12 = e1 & op(e0, e3) = e1
% 229.11/40.56  | | | | | | | | | 
% 229.11/40.56  | | | | | | | | | REF_CLOSE: (1), (5), (6), (7), (8), (9), (10), (11), (12),
% 229.11/40.56  | | | | | | | | |            (13), (14), (15), (16), (17), (18), (19), (20),
% 229.11/40.56  | | | | | | | | |            (22), (23), (24), (26), (28), (29), (30), (31),
% 229.11/40.56  | | | | | | | | |            (32), (33), (34), (36), (37), (39), (41), (42),
% 229.11/40.56  | | | | | | | | |            (43), (45), (46), (47), (48), (50), (51), (52),
% 229.11/40.56  | | | | | | | | |            (55), (56), (57), (58), (59), (60), (62), (63),
% 229.11/40.56  | | | | | | | | |            (64), (66), (67), (71), (72), (74), (78), (80),
% 229.11/40.56  | | | | | | | | |            (82), (85), (94), (99), (100) are inconsistent by
% 229.11/40.56  | | | | | | | | |            sub-proof #686.
% 229.11/40.56  | | | | | | | | | 
% 229.11/40.56  | | | | | | | | End of split
% 229.11/40.56  | | | | | | | | 
% 229.11/40.56  | | | | | | | End of split
% 229.11/40.56  | | | | | | | 
% 229.11/40.56  | | | | | | End of split
% 229.11/40.56  | | | | | | 
% 229.11/40.56  | | | | | Case 2:
% 229.11/40.56  | | | | | | 
% 229.11/40.56  | | | | | |   (119)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 &
% 229.11/40.56  | | | | | |            op(e0, e0) = e1)
% 229.11/40.56  | | | | | | 
% 229.11/40.56  | | | | | | BETA: splitting (119) gives:
% 229.11/40.56  | | | | | | 
% 229.11/40.56  | | | | | | Case 1:
% 229.11/40.56  | | | | | | | 
% 229.11/40.56  | | | | | | |   (120)  all_57_14 = e1 & op(e0, e1) = e1
% 229.11/40.56  | | | | | | | 
% 229.11/40.56  | | | | | | | ALPHA: (120) implies:
% 229.11/40.56  | | | | | | |   (121)  all_57_14 = e1
% 229.11/40.56  | | | | | | | 
% 229.11/40.56  | | | | | | | BETA: splitting (4) gives:
% 229.11/40.56  | | | | | | | 
% 229.11/40.56  | | | | | | | Case 1:
% 229.11/40.56  | | | | | | | | 
% 229.11/40.56  | | | | | | | |   (122)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 &
% 229.11/40.56  | | | | | | | |            op(e2, e3) = e1)
% 229.11/40.56  | | | | | | | | 
% 229.11/40.56  | | | | | | | | BETA: splitting (122) gives:
% 229.11/40.56  | | | | | | | | 
% 229.11/40.56  | | | | | | | | Case 1:
% 229.11/40.56  | | | | | | | | | 
% 229.11/40.56  | | | | | | | | |   (123)  all_57_0 = e1 & op(e3, e3) = e1
% 229.11/40.56  | | | | | | | | | 
% 229.11/40.56  | | | | | | | | | ALPHA: (123) implies:
% 229.11/40.56  | | | | | | | | |   (124)  op(e3, e3) = e1
% 229.11/40.56  | | | | | | | | | 
% 229.11/40.56  | | | | | | | | | REF_CLOSE: (8), (37), (71), (124) are inconsistent by
% 229.11/40.56  | | | | | | | | |            sub-proof #1950.
% 229.11/40.56  | | | | | | | | | 
% 229.11/40.56  | | | | | | | | Case 2:
% 229.11/40.56  | | | | | | | | | 
% 229.11/40.56  | | | | | | | | |   (125)  all_57_2 = e1 & op(e2, e3) = e1
% 229.11/40.56  | | | | | | | | | 
% 229.11/40.56  | | | | | | | | | ALPHA: (125) implies:
% 229.11/40.56  | | | | | | | | |   (126)  all_57_2 = e1
% 229.11/40.56  | | | | | | | | | 
% 229.11/40.56  | | | | | | | | | BETA: splitting (84) gives:
% 229.11/40.56  | | | | | | | | | 
% 229.11/40.56  | | | | | | | | | Case 1:
% 229.11/40.56  | | | | | | | | | | 
% 229.11/40.56  | | | | | | | | | |   (127)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 229.11/40.56  | | | | | | | | | |            & op(e1, e2) = e2)
% 229.11/40.56  | | | | | | | | | | 
% 229.11/40.56  | | | | | | | | | | BETA: splitting (127) gives:
% 229.11/40.56  | | | | | | | | | | 
% 229.11/40.56  | | | | | | | | | | Case 1:
% 229.11/40.56  | | | | | | | | | | | 
% 229.11/40.56  | | | | | | | | | | |   (128)  all_57_6 = e2 & op(e1, e3) = e2
% 229.11/40.56  | | | | | | | | | | | 
% 229.11/40.56  | | | | | | | | | | | ALPHA: (128) implies:
% 229.11/40.56  | | | | | | | | | | |   (129)  all_57_6 = e2
% 229.11/40.56  | | | | | | | | | | | 
% 229.11/40.56  | | | | | | | | | | | BETA: splitting (76) gives:
% 229.11/40.56  | | | | | | | | | | | 
% 229.11/40.56  | | | | | | | | | | | Case 1:
% 229.11/40.56  | | | | | | | | | | | | 
% 229.11/40.56  | | | | | | | | | | | |   (130)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 229.11/40.56  | | | | | | | | | | | |            & op(e2, e1) = e2)
% 229.11/40.56  | | | | | | | | | | | | 
% 229.11/40.56  | | | | | | | | | | | | BETA: splitting (130) gives:
% 229.11/40.56  | | | | | | | | | | | | 
% 229.11/40.56  | | | | | | | | | | | | Case 1:
% 229.11/40.56  | | | | | | | | | | | | | 
% 229.11/40.56  | | | | | | | | | | | | |   (131)  all_57_4 = e2 & op(e3, e1) = e2
% 229.11/40.56  | | | | | | | | | | | | | 
% 229.11/40.56  | | | | | | | | | | | | | ALPHA: (131) implies:
% 229.11/40.56  | | | | | | | | | | | | |   (132)  all_57_4 = e2
% 229.11/40.56  | | | | | | | | | | | | | 
% 229.11/40.56  | | | | | | | | | | | | | REF_CLOSE: (3), (6), (8), (19), (24), (26), (30), (37), (45),
% 229.11/40.56  | | | | | | | | | | | | |            (49), (50), (51), (65), (66), (68), (71), (85),
% 229.11/40.56  | | | | | | | | | | | | |            (126), (132) are inconsistent by sub-proof #702.
% 229.11/40.56  | | | | | | | | | | | | | 
% 229.11/40.56  | | | | | | | | | | | | Case 2:
% 229.11/40.56  | | | | | | | | | | | | | 
% 229.11/40.56  | | | | | | | | | | | | |   (133)  all_57_5 = e2 & op(e2, e1) = e2
% 229.11/40.56  | | | | | | | | | | | | | 
% 229.11/40.56  | | | | | | | | | | | | | ALPHA: (133) implies:
% 229.11/40.56  | | | | | | | | | | | | |   (134)  all_57_5 = e2
% 229.11/40.56  | | | | | | | | | | | | | 
% 229.11/40.56  | | | | | | | | | | | | | REF_CLOSE: (3), (6), (8), (12), (14), (16), (26), (30), (34),
% 229.11/40.56  | | | | | | | | | | | | |            (38), (45), (51), (53), (59), (61), (62), (65),
% 229.11/40.56  | | | | | | | | | | | | |            (70), (71), (72), (78), (99), (134) are
% 229.11/40.56  | | | | | | | | | | | | |            inconsistent by sub-proof #1744.
% 229.11/40.56  | | | | | | | | | | | | | 
% 229.11/40.56  | | | | | | | | | | | | End of split
% 229.11/40.56  | | | | | | | | | | | | 
% 229.11/40.56  | | | | | | | | | | | Case 2:
% 229.11/40.56  | | | | | | | | | | | | 
% 229.11/40.56  | | | | | | | | | | | |   (135)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 229.11/40.56  | | | | | | | | | | | |            e2 & op(e0, e1) = e2)
% 229.11/40.56  | | | | | | | | | | | | 
% 229.11/40.56  | | | | | | | | | | | | BETA: splitting (135) gives:
% 229.11/40.56  | | | | | | | | | | | | 
% 229.11/40.56  | | | | | | | | | | | | Case 1:
% 229.11/40.56  | | | | | | | | | | | | | 
% 229.11/40.56  | | | | | | | | | | | | |   (136)  all_57_8 = e2 & op(e1, e1) = e2
% 229.11/40.56  | | | | | | | | | | | | | 
% 229.11/40.56  | | | | | | | | | | | | | ALPHA: (136) implies:
% 229.11/40.56  | | | | | | | | | | | | |   (137)  op(e1, e1) = e2
% 229.11/40.56  | | | | | | | | | | | | | 
% 229.11/40.56  | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 229.11/40.56  | | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 229.11/40.56  | | | | | | | | | | | | |            (20), (22), (23), (24), (25), (26), (28), (29),
% 229.11/40.56  | | | | | | | | | | | | |            (30), (32), (33), (34), (36), (37), (38), (39),
% 229.11/40.56  | | | | | | | | | | | | |            (41), (42), (44), (45), (46), (47), (48), (49),
% 229.11/40.56  | | | | | | | | | | | | |            (50), (51), (52), (53), (54), (55), (56), (57),
% 229.11/40.56  | | | | | | | | | | | | |            (58), (59), (60), (61), (62), (63), (64), (65),
% 229.11/40.56  | | | | | | | | | | | | |            (66), (67), (68), (69), (71), (72), (73), (74),
% 229.11/40.56  | | | | | | | | | | | | |            (76), (77), (78), (79), (80), (82), (83), (84),
% 229.11/40.56  | | | | | | | | | | | | |            (85), (99), (100), (137) are inconsistent by
% 229.11/40.56  | | | | | | | | | | | | |            sub-proof #718.
% 229.11/40.56  | | | | | | | | | | | | | 
% 229.11/40.56  | | | | | | | | | | | | Case 2:
% 229.11/40.56  | | | | | | | | | | | | | 
% 229.11/40.56  | | | | | | | | | | | | |   (138)  all_57_14 = e2 & op(e0, e1) = e2
% 229.11/40.56  | | | | | | | | | | | | | 
% 229.11/40.56  | | | | | | | | | | | | | ALPHA: (138) implies:
% 229.11/40.56  | | | | | | | | | | | | |   (139)  all_57_14 = e2
% 229.11/40.56  | | | | | | | | | | | | | 
% 229.11/40.56  | | | | | | | | | | | | | COMBINE_EQS: (121), (139) imply:
% 229.11/40.56  | | | | | | | | | | | | |   (140)  e2 = e1
% 229.11/40.56  | | | | | | | | | | | | | 
% 229.11/40.56  | | | | | | | | | | | | | SIMP: (140) implies:
% 229.11/40.56  | | | | | | | | | | | | |   (141)  e2 = e1
% 229.11/40.56  | | | | | | | | | | | | | 
% 229.11/40.56  | | | | | | | | | | | | | COMBINE_EQS: (129), (141) imply:
% 229.11/40.56  | | | | | | | | | | | | |   (142)  all_57_6 = e1
% 229.11/40.56  | | | | | | | | | | | | | 
% 229.11/40.57  | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 229.11/40.57  | | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 229.11/40.57  | | | | | | | | | | | | |            (19), (20), (21), (22), (23), (24), (25), (26),
% 229.11/40.57  | | | | | | | | | | | | |            (28), (29), (30), (32), (33), (34), (35), (36),
% 229.11/40.57  | | | | | | | | | | | | |            (37), (38), (39), (41), (42), (44), (45), (46),
% 229.11/40.57  | | | | | | | | | | | | |            (47), (48), (49), (50), (51), (52), (53), (54),
% 229.11/40.57  | | | | | | | | | | | | |            (55), (56), (57), (58), (59), (60), (61), (62),
% 229.11/40.57  | | | | | | | | | | | | |            (63), (64), (65), (66), (67), (68), (69), (70),
% 229.11/40.57  | | | | | | | | | | | | |            (71), (72), (73), (74), (76), (77), (78), (79),
% 229.11/40.57  | | | | | | | | | | | | |            (80), (81), (82), (83), (84), (85), (94), (99),
% 229.11/40.57  | | | | | | | | | | | | |            (100), (142) are inconsistent by sub-proof #677.
% 229.11/40.57  | | | | | | | | | | | | | 
% 229.11/40.57  | | | | | | | | | | | | End of split
% 229.11/40.57  | | | | | | | | | | | | 
% 229.11/40.57  | | | | | | | | | | | End of split
% 229.11/40.57  | | | | | | | | | | | 
% 229.11/40.57  | | | | | | | | | | Case 2:
% 229.11/40.57  | | | | | | | | | | | 
% 229.11/40.57  | | | | | | | | | | |   (143)  all_57_7 = e2 & op(e1, e2) = e2
% 229.11/40.57  | | | | | | | | | | | 
% 229.11/40.57  | | | | | | | | | | | ALPHA: (143) implies:
% 229.11/40.57  | | | | | | | | | | |   (144)  all_57_7 = e2
% 229.11/40.57  | | | | | | | | | | | 
% 229.11/40.57  | | | | | | | | | | | BETA: splitting (76) gives:
% 229.11/40.57  | | | | | | | | | | | 
% 229.11/40.57  | | | | | | | | | | | Case 1:
% 229.11/40.57  | | | | | | | | | | | | 
% 229.11/40.57  | | | | | | | | | | | |   (145)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 229.11/40.57  | | | | | | | | | | | |            & op(e2, e1) = e2)
% 229.11/40.57  | | | | | | | | | | | | 
% 229.11/40.57  | | | | | | | | | | | | BETA: splitting (145) gives:
% 229.11/40.57  | | | | | | | | | | | | 
% 229.11/40.57  | | | | | | | | | | | | Case 1:
% 229.11/40.57  | | | | | | | | | | | | | 
% 229.11/40.57  | | | | | | | | | | | | |   (146)  all_57_4 = e2 & op(e3, e1) = e2
% 229.11/40.57  | | | | | | | | | | | | | 
% 229.11/40.57  | | | | | | | | | | | | | ALPHA: (146) implies:
% 229.11/40.57  | | | | | | | | | | | | |   (147)  all_57_4 = e2
% 229.11/40.57  | | | | | | | | | | | | | 
% 229.11/40.57  | | | | | | | | | | | | | REF_CLOSE: (3), (6), (8), (19), (24), (26), (30), (37), (45),
% 229.11/40.57  | | | | | | | | | | | | |            (49), (50), (51), (65), (66), (68), (71), (85),
% 229.11/40.57  | | | | | | | | | | | | |            (126), (147) are inconsistent by sub-proof #702.
% 229.11/40.57  | | | | | | | | | | | | | 
% 229.11/40.57  | | | | | | | | | | | | Case 2:
% 229.11/40.57  | | | | | | | | | | | | | 
% 229.11/40.57  | | | | | | | | | | | | |   (148)  all_57_5 = e2 & op(e2, e1) = e2
% 229.11/40.57  | | | | | | | | | | | | | 
% 229.11/40.57  | | | | | | | | | | | | | ALPHA: (148) implies:
% 229.11/40.57  | | | | | | | | | | | | |   (149)  all_57_5 = e2
% 229.11/40.57  | | | | | | | | | | | | | 
% 229.11/40.57  | | | | | | | | | | | | | REF_CLOSE: (3), (6), (8), (12), (14), (16), (26), (30), (34),
% 229.11/40.57  | | | | | | | | | | | | |            (38), (45), (51), (53), (59), (61), (62), (65),
% 229.11/40.57  | | | | | | | | | | | | |            (70), (71), (72), (78), (99), (149) are
% 229.11/40.57  | | | | | | | | | | | | |            inconsistent by sub-proof #1744.
% 229.11/40.57  | | | | | | | | | | | | | 
% 229.11/40.57  | | | | | | | | | | | | End of split
% 229.11/40.57  | | | | | | | | | | | | 
% 229.11/40.57  | | | | | | | | | | | Case 2:
% 229.11/40.57  | | | | | | | | | | | | 
% 229.11/40.57  | | | | | | | | | | | |   (150)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 229.11/40.57  | | | | | | | | | | | |            e2 & op(e0, e1) = e2)
% 229.11/40.57  | | | | | | | | | | | | 
% 229.11/40.57  | | | | | | | | | | | | BETA: splitting (150) gives:
% 229.11/40.57  | | | | | | | | | | | | 
% 229.11/40.57  | | | | | | | | | | | | Case 1:
% 229.11/40.57  | | | | | | | | | | | | | 
% 229.11/40.57  | | | | | | | | | | | | |   (151)  all_57_8 = e2 & op(e1, e1) = e2
% 229.11/40.57  | | | | | | | | | | | | | 
% 229.11/40.57  | | | | | | | | | | | | | ALPHA: (151) implies:
% 229.11/40.57  | | | | | | | | | | | | |   (152)  op(e1, e1) = e2
% 229.11/40.57  | | | | | | | | | | | | | 
% 229.11/40.57  | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 229.11/40.57  | | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 229.11/40.57  | | | | | | | | | | | | |            (20), (22), (23), (24), (25), (26), (28), (29),
% 229.11/40.57  | | | | | | | | | | | | |            (30), (32), (33), (34), (36), (37), (38), (39),
% 229.11/40.57  | | | | | | | | | | | | |            (41), (42), (44), (45), (46), (47), (48), (49),
% 229.11/40.57  | | | | | | | | | | | | |            (50), (51), (52), (53), (54), (55), (56), (57),
% 229.11/40.57  | | | | | | | | | | | | |            (58), (59), (60), (61), (62), (63), (64), (65),
% 229.11/40.57  | | | | | | | | | | | | |            (66), (67), (68), (69), (71), (72), (73), (74),
% 229.11/40.57  | | | | | | | | | | | | |            (76), (77), (78), (79), (80), (82), (83), (84),
% 229.11/40.57  | | | | | | | | | | | | |            (85), (99), (100), (152) are inconsistent by
% 229.11/40.57  | | | | | | | | | | | | |            sub-proof #718.
% 229.11/40.57  | | | | | | | | | | | | | 
% 229.11/40.57  | | | | | | | | | | | | Case 2:
% 229.11/40.57  | | | | | | | | | | | | | 
% 229.11/40.57  | | | | | | | | | | | | |   (153)  all_57_14 = e2 & op(e0, e1) = e2
% 229.11/40.57  | | | | | | | | | | | | | 
% 229.11/40.57  | | | | | | | | | | | | | ALPHA: (153) implies:
% 229.11/40.57  | | | | | | | | | | | | |   (154)  all_57_14 = e2
% 229.11/40.57  | | | | | | | | | | | | | 
% 229.11/40.57  | | | | | | | | | | | | | COMBINE_EQS: (121), (154) imply:
% 229.11/40.57  | | | | | | | | | | | | |   (155)  e2 = e1
% 229.11/40.57  | | | | | | | | | | | | | 
% 229.11/40.57  | | | | | | | | | | | | | SIMP: (155) implies:
% 229.11/40.57  | | | | | | | | | | | | |   (156)  e2 = e1
% 229.11/40.57  | | | | | | | | | | | | | 
% 229.11/40.57  | | | | | | | | | | | | | COMBINE_EQS: (144), (156) imply:
% 229.11/40.57  | | | | | | | | | | | | |   (157)  all_57_7 = e1
% 229.11/40.57  | | | | | | | | | | | | | 
% 229.11/40.57  | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (10), (11),
% 229.11/40.57  | | | | | | | | | | | | |            (12), (13), (14), (15), (16), (17), (19), (20),
% 229.11/40.57  | | | | | | | | | | | | |            (21), (22), (23), (24), (26), (28), (29), (30),
% 229.11/40.57  | | | | | | | | | | | | |            (32), (33), (34), (35), (36), (37), (38), (39),
% 229.11/40.57  | | | | | | | | | | | | |            (41), (42), (44), (45), (46), (48), (49), (50),
% 229.11/40.57  | | | | | | | | | | | | |            (51), (52), (53), (54), (55), (56), (57), (58),
% 229.11/40.57  | | | | | | | | | | | | |            (59), (60), (61), (62), (63), (64), (65), (66),
% 229.11/40.57  | | | | | | | | | | | | |            (67), (68), (69), (70), (71), (72), (74), (77),
% 229.11/40.57  | | | | | | | | | | | | |            (78), (80), (81), (82), (83), (85), (99), (100),
% 229.11/40.57  | | | | | | | | | | | | |            (157) are inconsistent by sub-proof #676.
% 229.11/40.57  | | | | | | | | | | | | | 
% 229.11/40.57  | | | | | | | | | | | | End of split
% 229.11/40.57  | | | | | | | | | | | | 
% 229.11/40.57  | | | | | | | | | | | End of split
% 229.11/40.57  | | | | | | | | | | | 
% 229.11/40.57  | | | | | | | | | | End of split
% 229.11/40.57  | | | | | | | | | | 
% 229.11/40.57  | | | | | | | | | Case 2:
% 229.11/40.57  | | | | | | | | | | 
% 229.11/40.57  | | | | | | | | | |   (158)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2
% 229.11/40.57  | | | | | | | | | |            & op(e1, e0) = e2)
% 229.11/40.57  | | | | | | | | | | 
% 229.11/40.57  | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 229.11/40.57  | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 229.11/40.57  | | | | | | | | | |            (19), (20), (22), (23), (24), (25), (26), (28),
% 229.11/40.57  | | | | | | | | | |            (29), (30), (32), (33), (34), (35), (36), (37),
% 229.11/40.57  | | | | | | | | | |            (38), (39), (41), (42), (44), (45), (46), (47),
% 229.11/40.57  | | | | | | | | | |            (48), (49), (50), (51), (52), (53), (54), (55),
% 229.11/40.57  | | | | | | | | | |            (56), (57), (58), (59), (60), (61), (62), (63),
% 229.11/40.57  | | | | | | | | | |            (64), (65), (66), (67), (68), (69), (70), (71),
% 229.11/40.57  | | | | | | | | | |            (72), (73), (74), (76), (77), (78), (79), (80),
% 229.11/40.57  | | | | | | | | | |            (81), (82), (83), (84), (85), (94), (99), (100),
% 229.11/40.57  | | | | | | | | | |            (158) are inconsistent by sub-proof #678.
% 229.11/40.57  | | | | | | | | | | 
% 229.11/40.57  | | | | | | | | | End of split
% 229.11/40.57  | | | | | | | | | 
% 229.11/40.57  | | | | | | | | End of split
% 229.11/40.57  | | | | | | | | 
% 229.11/40.57  | | | | | | | Case 2:
% 229.11/40.57  | | | | | | | | 
% 229.11/40.57  | | | | | | | |   (159)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 &
% 229.11/40.57  | | | | | | | |            op(e0, e3) = e1)
% 229.11/40.57  | | | | | | | | 
% 229.11/40.57  | | | | | | | | BETA: splitting (159) gives:
% 229.11/40.57  | | | | | | | | 
% 229.11/40.57  | | | | | | | | Case 1:
% 229.11/40.57  | | | | | | | | | 
% 229.11/40.57  | | | | | | | | |   (160)  all_57_6 = e1 & op(e1, e3) = e1
% 229.11/40.57  | | | | | | | | | 
% 229.11/40.57  | | | | | | | | | ALPHA: (160) implies:
% 229.11/40.57  | | | | | | | | |   (161)  all_57_6 = e1
% 229.11/40.57  | | | | | | | | | 
% 229.11/40.57  | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 229.11/40.57  | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 229.11/40.57  | | | | | | | | |            (19), (20), (21), (22), (23), (24), (25), (26),
% 229.11/40.57  | | | | | | | | |            (28), (29), (30), (32), (33), (34), (35), (36),
% 229.11/40.57  | | | | | | | | |            (37), (38), (39), (41), (42), (44), (45), (46),
% 229.11/40.57  | | | | | | | | |            (47), (48), (49), (50), (51), (52), (53), (54),
% 229.11/40.57  | | | | | | | | |            (55), (56), (57), (58), (59), (60), (61), (62),
% 229.11/40.57  | | | | | | | | |            (63), (64), (65), (66), (67), (68), (69), (70),
% 229.11/40.57  | | | | | | | | |            (71), (72), (73), (74), (76), (77), (78), (79),
% 229.11/40.57  | | | | | | | | |            (80), (81), (82), (83), (84), (85), (94), (99),
% 229.11/40.57  | | | | | | | | |            (100), (161) are inconsistent by sub-proof #677.
% 229.11/40.57  | | | | | | | | | 
% 229.11/40.57  | | | | | | | | Case 2:
% 229.11/40.57  | | | | | | | | | 
% 229.11/40.57  | | | | | | | | |   (162)  all_57_12 = e1 & op(e0, e3) = e1
% 229.11/40.57  | | | | | | | | | 
% 229.11/40.57  | | | | | | | | | REF_CLOSE: (1), (5), (6), (7), (8), (9), (10), (11), (12),
% 229.11/40.57  | | | | | | | | |            (13), (14), (15), (16), (17), (18), (19), (20),
% 229.11/40.57  | | | | | | | | |            (22), (23), (24), (26), (28), (29), (30), (31),
% 229.11/40.57  | | | | | | | | |            (32), (33), (34), (36), (37), (39), (41), (42),
% 229.11/40.57  | | | | | | | | |            (43), (45), (46), (47), (48), (50), (51), (52),
% 229.11/40.57  | | | | | | | | |            (55), (56), (57), (58), (59), (60), (62), (63),
% 229.11/40.57  | | | | | | | | |            (64), (66), (67), (71), (72), (74), (78), (80),
% 229.11/40.57  | | | | | | | | |            (82), (85), (94), (99), (100) are inconsistent by
% 229.11/40.57  | | | | | | | | |            sub-proof #686.
% 229.11/40.57  | | | | | | | | | 
% 229.11/40.57  | | | | | | | | End of split
% 229.11/40.57  | | | | | | | | 
% 229.11/40.57  | | | | | | | End of split
% 229.11/40.57  | | | | | | | 
% 229.11/40.57  | | | | | | Case 2:
% 229.11/40.57  | | | | | | | 
% 229.11/40.57  | | | | | | |   (163)  all_57_15 = e1 & op(e0, e0) = e1
% 229.11/40.57  | | | | | | | 
% 229.11/40.57  | | | | | | | ALPHA: (163) implies:
% 229.11/40.57  | | | | | | |   (164)  op(e0, e0) = e1
% 229.11/40.57  | | | | | | | 
% 229.11/40.57  | | | | | | | REF_CLOSE: (6), (8), (59), (164) are inconsistent by sub-proof
% 229.11/40.57  | | | | | | |            #2183.
% 229.11/40.57  | | | | | | | 
% 229.11/40.57  | | | | | | End of split
% 229.11/40.57  | | | | | | 
% 229.11/40.57  | | | | | End of split
% 229.11/40.57  | | | | | 
% 229.11/40.57  | | | | End of split
% 229.11/40.57  | | | | 
% 229.11/40.57  | | | Case 2:
% 229.11/40.57  | | | | 
% 229.11/40.57  | | | |   (165)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0,
% 229.11/40.57  | | | |              e0) = e2)
% 229.11/40.57  | | | | 
% 229.11/40.57  | | | | REF_CLOSE: (26), (34), (71), (94), (165) are inconsistent by sub-proof
% 229.11/40.57  | | | |            #717.
% 229.11/40.57  | | | | 
% 229.11/40.57  | | | End of split
% 229.11/40.57  | | | 
% 229.11/40.57  | | End of split
% 229.11/40.57  | | 
% 229.11/40.57  | End of split
% 229.11/40.57  | 
% 229.11/40.57  End of proof
% 229.11/40.57  
% 229.11/40.57  Sub-proof #676 shows that the following formulas are inconsistent:
% 229.11/40.57  ----------------------------------------------------------------
% 229.11/40.57    (1)   ~ (all_53_2 = e2)
% 229.11/40.57    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.11/40.57         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.11/40.57    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.11/40.57         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.11/40.57    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.11/40.57         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.11/40.57    (5)   ~ (e3 = e1)
% 229.11/40.57    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.11/40.57           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.11/40.57    (7)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.11/40.57         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.11/40.57    (8)   ~ (all_53_3 = e3)
% 229.11/40.57    (9)   ~ (all_53_3 = all_53_7)
% 229.11/40.57    (10)   ~ (all_6_2 = e3)
% 229.11/40.57    (11)   ~ (all_53_9 = e1)
% 229.11/40.57    (12)  op(e1, e1) = all_6_2
% 229.11/40.57    (13)   ~ (all_53_1 = all_53_9)
% 229.11/40.57    (14)  op(e2, e2) = e1
% 229.11/40.57    (15)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.11/40.57          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.11/40.57    (16)  all_57_9 = e1
% 229.11/40.57    (17)   ~ (all_53_13 = e3)
% 229.11/40.57    (18)  all_57_7 = e1
% 229.11/40.57    (19)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.11/40.57          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.11/40.57    (20)   ~ (all_53_9 = all_53_11)
% 229.11/40.57    (21)  all_55_4 = all_53_1
% 229.11/40.57    (22)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.11/40.57          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.11/40.57    (23)   ~ (e3 = e2)
% 229.11/40.57    (24)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 229.11/40.57    (25)   ~ (all_53_1 = all_53_3)
% 229.11/40.57    (26)   ~ (e3 = e0)
% 229.11/40.57    (27)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 229.11/40.57    (28)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 229.11/40.57    (29)  all_57_15 = e3
% 229.11/40.57    (30)  op(e2, e2) = all_52_11
% 229.11/40.57    (31)   ~ (all_53_9 = all_53_13)
% 229.11/40.57    (32)  op(e3, e3) = e2
% 229.11/40.57    (33)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.11/40.57          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.11/40.57            e1)
% 229.11/40.57    (34)  all_57_10 = e2
% 229.11/40.57    (35)   ~ (all_53_1 = e1)
% 229.11/40.57    (36)  op(e2, e0) = e2
% 229.11/40.57    (37)  all_55_6 = all_53_9
% 229.11/40.57    (38)   ~ (all_53_1 = all_53_2)
% 229.11/40.57    (39)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.11/40.57          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.11/40.57    (40)   ~ (e2 = e0)
% 229.11/40.57    (41)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 229.11/40.57            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 229.11/40.57            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 229.11/40.57            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 229.11/40.57              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 229.11/40.57            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 229.11/40.57            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 229.11/40.57              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 229.11/40.57              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 229.11/40.57            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 229.11/40.57            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 229.11/40.57            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 229.11/40.57              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 229.11/40.57              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 229.11/40.57            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 229.11/40.57              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 229.11/40.57            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 229.11/40.57            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 229.11/40.57              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 229.11/40.57              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 229.11/40.57            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 229.11/40.57            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 229.11/40.57    (42)  all_55_12 = all_53_3
% 229.11/40.57    (43)  all_57_3 = e1
% 229.11/40.57    (44)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.11/40.57          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.11/40.57    (45)   ~ (e1 = e0)
% 229.11/40.57    (46)   ~ (all_53_3 = all_53_11)
% 229.11/40.57    (47)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.11/40.57          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.11/40.57    (48)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.11/40.57          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.11/40.57    (49)   ~ (all_53_2 = all_53_3)
% 229.11/40.57    (50)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 229.11/40.57    (51)   ~ (all_53_7 = all_53_11)
% 229.11/40.57    (52)  all_55_8 = all_53_2
% 229.11/40.57    (53)  op(e0, e0) = e3
% 229.11/40.57    (54)  op(e0, e2) = all_53_7
% 229.11/40.57    (55)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.11/40.57          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.11/40.57            e2)
% 229.11/40.57    (56)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.11/40.57              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.11/40.57                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.11/40.57                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.11/40.57    (57)   ~ (all_53_1 = all_53_13)
% 229.11/40.57    (58)  op(e2, e0) = all_53_13
% 229.11/40.57    (59)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.11/40.57          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.11/40.57    (60)   ~ (all_53_12 = e3)
% 229.11/40.57    (61)  op(e1, e3) = all_53_2
% 229.11/40.57    (62)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.11/40.57          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.11/40.57    (63)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.11/40.57          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.11/40.57    (64)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.11/40.57          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 229.11/40.57    (65)   ~ (e2 = e1)
% 229.11/40.57    (66)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.11/40.57          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.11/40.57    (67)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 229.11/40.57    (68)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.11/40.57          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.11/40.57    (69)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.11/40.57          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.11/40.57    (70)  all_55_14 = all_53_11
% 229.11/40.57    (71)  op(all_52_11, all_52_11) = e2
% 229.11/40.57    (72)   ~ (all_53_11 = e3)
% 229.11/40.57    (73)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.11/40.57          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.11/40.57    (74)  op(e3, e0) = all_53_12
% 229.11/40.57  
% 229.11/40.57  Begin of proof
% 229.11/40.57  | 
% 229.11/40.57  | BETA: splitting (4) gives:
% 229.11/40.57  | 
% 229.11/40.57  | Case 1:
% 229.11/40.57  | | 
% 229.11/40.57  | |   (75)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 229.11/40.57  | |           e2)
% 229.11/40.57  | | 
% 229.11/40.57  | | REF_CLOSE: (5), (6), (14), (15), (22), (23), (26), (32), (40), (44), (45),
% 229.11/40.57  | |            (60), (65), (74), (75) are inconsistent by sub-proof #714.
% 229.11/40.57  | | 
% 229.11/40.57  | Case 2:
% 229.11/40.57  | | 
% 229.11/40.57  | |   (76)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 229.11/40.57  | |           e2)
% 229.11/40.57  | | 
% 229.11/40.57  | | BETA: splitting (76) gives:
% 229.11/40.57  | | 
% 229.11/40.57  | | Case 1:
% 229.11/40.57  | | | 
% 229.11/40.57  | | |   (77)  all_57_7 = e2 & op(e1, e2) = e2
% 229.11/40.57  | | | 
% 229.11/40.57  | | | ALPHA: (77) implies:
% 229.11/40.57  | | |   (78)  all_57_7 = e2
% 229.11/40.57  | | | 
% 229.11/40.57  | | | COMBINE_EQS: (18), (78) imply:
% 229.11/40.57  | | |   (79)  e2 = e1
% 229.11/40.57  | | | 
% 229.11/40.57  | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (10), (12), (14), (15), (16),
% 229.11/40.57  | | |            (19), (22), (23), (26), (29), (30), (32), (33), (34), (39),
% 229.11/40.57  | | |            (40), (43), (44), (45), (47), (48), (53), (55), (56), (59),
% 229.11/40.57  | | |            (60), (62), (63), (64), (65), (66), (68), (69), (71), (73),
% 229.11/40.57  | | |            (74), (79) are inconsistent by sub-proof #679.
% 229.11/40.57  | | | 
% 229.11/40.57  | | Case 2:
% 229.11/40.57  | | | 
% 229.11/40.57  | | |   (80)  all_57_13 = e2 & op(e0, e2) = e2
% 229.11/40.57  | | | 
% 229.11/40.57  | | | REF_CLOSE: (1), (5), (6), (8), (9), (10), (11), (12), (13), (14), (17),
% 229.11/40.57  | | |            (20), (21), (24), (25), (27), (28), (31), (32), (35), (36),
% 229.11/40.57  | | |            (37), (38), (40), (41), (42), (46), (49), (50), (51), (52),
% 229.11/40.57  | | |            (53), (54), (57), (58), (61), (67), (70), (72), (80) are
% 229.11/40.57  | | |            inconsistent by sub-proof #771.
% 229.11/40.57  | | | 
% 229.11/40.57  | | End of split
% 229.11/40.57  | | 
% 229.11/40.57  | End of split
% 229.11/40.57  | 
% 229.11/40.57  End of proof
% 229.11/40.57  
% 229.11/40.57  Sub-proof #677 shows that the following formulas are inconsistent:
% 229.11/40.57  ----------------------------------------------------------------
% 229.11/40.57    (1)   ~ (all_53_2 = e2)
% 229.11/40.57    (2)  all_57_0 = e2
% 229.11/40.57    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.11/40.57         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.11/40.57    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.11/40.57         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.11/40.57    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.11/40.57         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.11/40.57    (6)   ~ (e3 = e1)
% 229.11/40.57    (7)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 229.11/40.57         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 229.11/40.57    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.11/40.57           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.11/40.57    (9)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.11/40.57         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.11/40.57    (10)   ~ (all_53_3 = e3)
% 229.11/40.57    (11)   ~ (all_53_3 = all_53_7)
% 229.11/40.57    (12)   ~ (all_6_2 = e3)
% 229.11/40.57    (13)   ~ (all_53_9 = e1)
% 229.11/40.57    (14)  op(e1, e1) = all_6_2
% 229.11/40.57    (15)   ~ (all_53_1 = all_53_9)
% 229.11/40.57    (16)  op(e2, e2) = e1
% 229.11/40.57    (17)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.11/40.57          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.11/40.57    (18)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 229.11/40.57            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 229.11/40.57              e3) = all_22_1 & $i(all_22_1))
% 229.11/40.57    (19)  all_57_9 = e1
% 229.11/40.57    (20)   ~ (all_53_13 = e3)
% 229.11/40.57    (21)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.11/40.57          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.11/40.57    (22)  all_57_6 = e1
% 229.11/40.57    (23)   ~ (all_53_9 = all_53_11)
% 229.11/40.57    (24)  all_55_4 = all_53_1
% 229.11/40.57    (25)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.11/40.57          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.11/40.57    (26)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 229.11/40.57          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.11/40.57    (27)   ~ (e3 = e2)
% 229.11/40.57    (28)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 229.11/40.57    (29)   ~ (all_53_1 = all_53_3)
% 229.11/40.57    (30)   ~ (e3 = e0)
% 229.11/40.57    (31)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 229.11/40.57    (32)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 229.11/40.57    (33)  all_57_15 = e3
% 229.11/40.57    (34)  op(e2, e2) = all_52_11
% 229.11/40.57    (35)   ~ (all_53_9 = all_53_13)
% 229.11/40.57    (36)  op(e3, e3) = e2
% 229.11/40.57    (37)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.11/40.57          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.11/40.57            e1)
% 229.11/40.57    (38)  all_57_10 = e2
% 229.11/40.57    (39)   ~ (all_53_1 = e1)
% 229.11/40.57    (40)  op(e2, e0) = e2
% 229.11/40.57    (41)  all_55_6 = all_53_9
% 229.11/40.57    (42)   ~ (all_53_1 = all_53_2)
% 229.11/40.57    (43)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.11/40.57          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.11/40.57    (44)   ~ (e2 = e0)
% 229.11/40.57    (45)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 229.11/40.57            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 229.11/40.57            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 229.11/40.57            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 229.11/40.57              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 229.11/40.57            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 229.11/40.57            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 229.11/40.57              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 229.11/40.57              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 229.11/40.57            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 229.11/40.57            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 229.11/40.57            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 229.11/40.57              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 229.11/40.57              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 229.11/40.57            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 229.11/40.57              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 229.11/40.57            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 229.11/40.57            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 229.11/40.57              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 229.11/40.57              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 229.11/40.57            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 229.11/40.57            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 229.11/40.57    (46)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 229.11/40.57            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 229.11/40.57              e3) = all_12_1 & $i(all_12_1))
% 229.11/40.57    (47)  all_55_12 = all_53_3
% 229.11/40.57    (48)  all_57_3 = e1
% 229.11/40.57    (49)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.11/40.57          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.11/40.57    (50)   ~ (e1 = e0)
% 229.11/40.57    (51)   ~ (all_53_3 = all_53_11)
% 229.11/40.57    (52)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.11/40.57          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.11/40.57    (53)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.11/40.57          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.11/40.57    (54)   ~ (all_53_2 = all_53_3)
% 229.11/40.57    (55)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 229.11/40.57    (56)   ~ (all_53_7 = all_53_11)
% 229.11/40.57    (57)  all_55_8 = all_53_2
% 229.11/40.57    (58)  op(e0, e0) = e3
% 229.11/40.57    (59)  op(e0, e2) = all_53_7
% 229.11/40.57    (60)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.11/40.57          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.11/40.57            e2)
% 229.11/40.57    (61)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.11/40.57              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.11/40.57                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.11/40.57                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.11/40.57    (62)   ~ (all_53_1 = all_53_13)
% 229.11/40.57    (63)  op(e2, e0) = all_53_13
% 229.11/40.57    (64)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.11/40.57          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.11/40.57    (65)   ~ (all_53_12 = e3)
% 229.11/40.57    (66)  op(e1, e3) = all_53_2
% 229.11/40.57    (67)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.11/40.57          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.11/40.57    (68)  all_57_11 = e1
% 229.11/40.57    (69)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.11/40.57          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.11/40.57    (70)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.11/40.57          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 229.11/40.57    (71)   ~ (e2 = e1)
% 229.11/40.57    (72)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.11/40.57          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.11/40.58    (73)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.11/40.58          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.11/40.58    (74)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 229.11/40.58    (75)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 229.11/40.58          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 229.11/40.58    (76)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.11/40.58          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.11/40.58    (77)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.11/40.58          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.11/40.58    (78)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 229.11/40.58          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 229.11/40.58    (79)  all_55_14 = all_53_11
% 229.11/40.58    (80)  op(all_52_11, all_52_11) = e2
% 229.11/40.58    (81)   ~ (all_53_11 = e3)
% 229.11/40.58    (82)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.11/40.58          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.11/40.58    (83)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 229.11/40.58          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 229.11/40.58    (84)  op(e3, e0) = all_53_12
% 229.11/40.58  
% 229.11/40.58  Begin of proof
% 229.11/40.58  | 
% 229.11/40.58  | BETA: splitting (83) gives:
% 229.11/40.58  | 
% 229.11/40.58  | Case 1:
% 229.11/40.58  | | 
% 229.11/40.58  | |   (85)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) =
% 229.11/40.58  | |           e2)
% 229.11/40.58  | | 
% 229.11/40.58  | | BETA: splitting (85) gives:
% 229.11/40.58  | | 
% 229.11/40.58  | | Case 1:
% 229.11/40.58  | | | 
% 229.11/40.58  | | |   (86)  all_57_6 = e2 & op(e1, e3) = e2
% 229.11/40.58  | | | 
% 229.11/40.58  | | | ALPHA: (86) implies:
% 229.11/40.58  | | |   (87)  all_57_6 = e2
% 229.11/40.58  | | | 
% 229.11/40.58  | | | COMBINE_EQS: (22), (87) imply:
% 229.11/40.58  | | |   (88)  e2 = e1
% 229.11/40.58  | | | 
% 229.11/40.58  | | | REF_CLOSE: (3), (4), (5), (6), (8), (9), (12), (14), (16), (17), (19),
% 229.11/40.58  | | |            (21), (25), (27), (30), (33), (34), (36), (37), (38), (43),
% 229.11/40.58  | | |            (44), (48), (49), (50), (52), (53), (58), (60), (61), (64),
% 229.11/40.58  | | |            (65), (67), (69), (70), (71), (72), (76), (77), (80), (82),
% 229.11/40.58  | | |            (84), (88) are inconsistent by sub-proof #679.
% 229.11/40.58  | | | 
% 229.11/40.58  | | Case 2:
% 229.11/40.58  | | | 
% 229.11/40.58  | | |   (89)  all_57_7 = e2 & op(e1, e2) = e2
% 229.11/40.58  | | | 
% 229.11/40.58  | | | ALPHA: (89) implies:
% 229.11/40.58  | | |   (90)  all_57_7 = e2
% 229.11/40.58  | | | 
% 229.11/40.58  | | | REF_CLOSE: (6), (8), (9), (12), (14), (22), (27), (30), (33), (44), (50),
% 229.11/40.58  | | |            (58), (61), (71), (72), (77), (90) are inconsistent by
% 229.11/40.58  | | |            sub-proof #1078.
% 229.11/40.58  | | | 
% 229.11/40.58  | | End of split
% 229.11/40.58  | | 
% 229.11/40.58  | Case 2:
% 229.11/40.58  | | 
% 229.11/40.58  | |   (91)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) =
% 229.11/40.58  | |           e2)
% 229.11/40.58  | | 
% 229.11/40.58  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 229.11/40.58  | |            (13), (14), (15), (16), (17), (18), (19), (20), (23), (24), (25),
% 229.11/40.58  | |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 229.11/40.58  | |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 229.11/40.58  | |            (48), (49), (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 229.11/40.58  | |            (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 229.11/40.58  | |            (70), (71), (72), (73), (74), (75), (76), (77), (78), (79), (80),
% 229.11/40.58  | |            (81), (82), (83), (84), (91) are inconsistent by sub-proof #678.
% 229.11/40.58  | | 
% 229.11/40.58  | End of split
% 229.11/40.58  | 
% 229.11/40.58  End of proof
% 229.11/40.58  
% 229.11/40.58  Sub-proof #678 shows that the following formulas are inconsistent:
% 229.11/40.58  ----------------------------------------------------------------
% 229.11/40.58    (1)   ~ (all_53_2 = e2)
% 229.11/40.58    (2)  all_57_0 = e2
% 229.11/40.58    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.11/40.58         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.11/40.58    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.11/40.58         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.11/40.58    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.11/40.58         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.11/40.58    (6)   ~ (e3 = e1)
% 229.11/40.58    (7)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 229.11/40.58         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 229.11/40.58    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.11/40.58           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.11/40.58    (9)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.11/40.58         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.11/40.58    (10)   ~ (all_53_3 = e3)
% 229.11/40.58    (11)   ~ (all_53_3 = all_53_7)
% 229.11/40.58    (12)   ~ (all_6_2 = e3)
% 229.11/40.58    (13)   ~ (all_53_9 = e1)
% 229.11/40.58    (14)  op(e1, e1) = all_6_2
% 229.11/40.58    (15)   ~ (all_53_1 = all_53_9)
% 229.11/40.58    (16)  op(e2, e2) = e1
% 229.11/40.58    (17)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.11/40.58          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.11/40.58    (18)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 229.11/40.58            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 229.11/40.58              e3) = all_22_1 & $i(all_22_1))
% 229.11/40.58    (19)  all_57_9 = e1
% 229.11/40.58    (20)   ~ (all_53_13 = e3)
% 229.11/40.58    (21)   ~ (all_53_9 = all_53_11)
% 229.11/40.58    (22)  all_55_4 = all_53_1
% 229.11/40.58    (23)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.11/40.58          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.11/40.58    (24)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 229.11/40.58          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.11/40.58    (25)   ~ (e3 = e2)
% 229.11/40.58    (26)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 229.11/40.58    (27)   ~ (all_53_1 = all_53_3)
% 229.11/40.58    (28)   ~ (e3 = e0)
% 229.11/40.58    (29)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 229.11/40.58    (30)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 229.11/40.58    (31)  all_57_15 = e3
% 229.11/40.58    (32)  op(e2, e2) = all_52_11
% 229.11/40.58    (33)   ~ (all_53_9 = all_53_13)
% 229.11/40.58    (34)  op(e3, e3) = e2
% 229.11/40.58    (35)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.11/40.58          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.11/40.58            e1)
% 229.11/40.58    (36)  all_57_10 = e2
% 229.11/40.58    (37)   ~ (all_53_1 = e1)
% 229.11/40.58    (38)  op(e2, e0) = e2
% 229.11/40.58    (39)  all_55_6 = all_53_9
% 229.11/40.58    (40)   ~ (all_53_1 = all_53_2)
% 229.11/40.58    (41)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.11/40.58          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.11/40.58    (42)   ~ (e2 = e0)
% 229.11/40.58    (43)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 229.11/40.58            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 229.11/40.58            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 229.11/40.58            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 229.11/40.58              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 229.11/40.58            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 229.11/40.58            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 229.11/40.58              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 229.11/40.58              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 229.11/40.58            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 229.11/40.58            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 229.11/40.58            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 229.11/40.58              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 229.11/40.58              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 229.11/40.58            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 229.11/40.58              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 229.11/40.58            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 229.11/40.58            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 229.11/40.58              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 229.11/40.58              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 229.11/40.58            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 229.11/40.58            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 229.11/40.58    (44)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 229.11/40.58            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 229.11/40.58              e3) = all_12_1 & $i(all_12_1))
% 229.11/40.58    (45)  all_55_12 = all_53_3
% 229.11/40.58    (46)  all_57_3 = e1
% 229.11/40.58    (47)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.11/40.58          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.11/40.58    (48)   ~ (e1 = e0)
% 229.11/40.58    (49)   ~ (all_53_3 = all_53_11)
% 229.11/40.58    (50)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.11/40.58          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.11/40.58    (51)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.11/40.58          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.11/40.58    (52)   ~ (all_53_2 = all_53_3)
% 229.11/40.58    (53)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 229.11/40.58    (54)   ~ (all_53_7 = all_53_11)
% 229.11/40.58    (55)  all_55_8 = all_53_2
% 229.11/40.58    (56)  op(e0, e0) = e3
% 229.11/40.58    (57)  op(e0, e2) = all_53_7
% 229.11/40.58    (58)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.11/40.58          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.11/40.58            e2)
% 229.11/40.58    (59)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.11/40.58              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.11/40.58                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.11/40.58                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.11/40.58    (60)   ~ (all_53_1 = all_53_13)
% 229.11/40.58    (61)  op(e2, e0) = all_53_13
% 229.11/40.58    (62)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.11/40.58          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.11/40.58    (63)   ~ (all_53_12 = e3)
% 229.11/40.58    (64)  op(e1, e3) = all_53_2
% 229.11/40.58    (65)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.11/40.58          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.11/40.58    (66)  all_57_11 = e1
% 229.11/40.58    (67)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.11/40.58          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.11/40.58    (68)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.11/40.58          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 229.11/40.58    (69)   ~ (e2 = e1)
% 229.11/40.58    (70)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.11/40.58          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.11/40.58    (71)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.11/40.58          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.11/40.58    (72)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 229.11/40.58    (73)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 229.11/40.58    (74)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 229.11/40.58          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 229.11/40.58    (75)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.11/40.58          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.11/40.58    (76)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.11/40.58          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.11/40.58    (77)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 229.11/40.58          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 229.11/40.58    (78)  all_55_14 = all_53_11
% 229.11/40.58    (79)  op(all_52_11, all_52_11) = e2
% 229.11/40.58    (80)   ~ (all_53_11 = e3)
% 229.11/40.58    (81)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.11/40.58          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.11/40.58    (82)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 229.11/40.58          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 229.11/40.58    (83)  op(e3, e0) = all_53_12
% 229.11/40.58  
% 229.11/40.58  Begin of proof
% 229.11/40.58  | 
% 229.11/40.58  | BETA: splitting (73) gives:
% 229.11/40.58  | 
% 229.11/40.58  | Case 1:
% 229.11/40.58  | | 
% 229.11/40.58  | |   (84)  all_57_8 = e2 & op(e1, e1) = e2
% 229.11/40.58  | | 
% 229.11/40.58  | | ALPHA: (84) implies:
% 229.11/40.58  | |   (85)  op(e1, e1) = e2
% 229.11/40.58  | | 
% 229.11/40.58  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 229.11/40.58  | |            (13), (14), (15), (16), (17), (18), (20), (21), (22), (23), (24),
% 229.11/40.58  | |            (25), (26), (27), (28), (29), (30), (31), (33), (34), (35), (36),
% 229.11/40.58  | |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 229.11/40.58  | |            (48), (49), (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 229.11/40.58  | |            (59), (60), (61), (62), (63), (64), (65), (67), (69), (70), (71),
% 229.11/40.58  | |            (72), (74), (75), (76), (77), (78), (80), (81), (82), (83), (85)
% 229.11/40.58  | |            are inconsistent by sub-proof #718.
% 229.11/40.58  | | 
% 229.11/40.58  | Case 2:
% 229.11/40.58  | | 
% 229.11/40.58  | |   (86)  all_57_11 = e2 & op(e1, e0) = e2
% 229.11/40.58  | | 
% 229.11/40.58  | | ALPHA: (86) implies:
% 229.11/40.58  | |   (87)  all_57_11 = e2
% 229.11/40.58  | | 
% 229.11/40.58  | | COMBINE_EQS: (66), (87) imply:
% 229.11/40.58  | |   (88)  e2 = e1
% 229.11/40.58  | | 
% 229.11/40.58  | | SIMP: (88) implies:
% 229.11/40.58  | |   (89)  e2 = e1
% 229.11/40.58  | | 
% 229.11/40.58  | | COMBINE_EQS: (36), (89) imply:
% 229.11/40.58  | |   (90)  all_57_10 = e1
% 229.11/40.58  | | 
% 229.11/40.58  | | REF_CLOSE: (3), (6), (8), (12), (14), (16), (19), (23), (25), (28), (31),
% 229.11/40.58  | |            (32), (34), (35), (42), (46), (47), (48), (50), (56), (58), (59),
% 229.11/40.58  | |            (62), (63), (65), (68), (69), (70), (76), (79), (83), (87), (90)
% 229.11/40.58  | |            are inconsistent by sub-proof #680.
% 229.11/40.58  | | 
% 229.11/40.58  | End of split
% 229.11/40.58  | 
% 229.11/40.58  End of proof
% 229.11/40.58  
% 229.11/40.58  Sub-proof #679 shows that the following formulas are inconsistent:
% 229.11/40.58  ----------------------------------------------------------------
% 229.11/40.58    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.11/40.58         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.11/40.58    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.11/40.58         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.11/40.58    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.11/40.58         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.11/40.58    (4)   ~ (e3 = e1)
% 229.11/40.58    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.11/40.58           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.11/40.58    (6)  e2 = e1
% 229.11/40.58    (7)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.11/40.58         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.11/40.58    (8)   ~ (all_6_2 = e3)
% 229.11/40.58    (9)  op(e1, e1) = all_6_2
% 229.11/40.58    (10)  op(e2, e2) = e1
% 229.11/40.58    (11)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.11/40.58          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.11/40.58    (12)  all_57_9 = e1
% 229.11/40.58    (13)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.11/40.58          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.11/40.58    (14)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.11/40.58          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.11/40.58    (15)   ~ (e3 = e2)
% 229.11/40.58    (16)   ~ (e3 = e0)
% 229.11/40.58    (17)  all_57_15 = e3
% 229.11/40.58    (18)  op(e2, e2) = all_52_11
% 229.11/40.58    (19)  op(e3, e3) = e2
% 229.11/40.58    (20)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.11/40.58          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.11/40.58            e1)
% 229.11/40.58    (21)  all_57_10 = e2
% 229.11/40.58    (22)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.11/40.58          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.11/40.58    (23)   ~ (e2 = e0)
% 229.11/40.58    (24)  all_57_3 = e1
% 229.11/40.58    (25)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.11/40.58          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.11/40.58    (26)   ~ (e1 = e0)
% 229.11/40.58    (27)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.11/40.58          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.11/40.58    (28)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.11/40.58          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.11/40.58    (29)  op(e0, e0) = e3
% 229.11/40.58    (30)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.11/40.58          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.11/40.58            e2)
% 229.11/40.58    (31)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.11/40.58              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.11/40.58                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.11/40.58                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.11/40.58    (32)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.11/40.58          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.11/40.58    (33)   ~ (all_53_12 = e3)
% 229.11/40.58    (34)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.11/40.58          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.11/40.58    (35)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.11/40.58          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.11/40.58    (36)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.11/40.58          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 229.11/40.58    (37)   ~ (e2 = e1)
% 229.11/40.58    (38)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.11/40.58          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.11/40.58    (39)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.11/40.58          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.11/40.58    (40)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.11/40.58          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.11/40.58    (41)  op(all_52_11, all_52_11) = e2
% 229.11/40.58    (42)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.11/40.58          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.11/40.58    (43)  op(e3, e0) = all_53_12
% 229.11/40.58  
% 229.11/40.58  Begin of proof
% 229.11/40.58  | 
% 229.11/40.58  | SIMP: (6) implies:
% 229.11/40.58  |   (44)  e2 = e1
% 229.11/40.58  | 
% 229.11/40.58  | COMBINE_EQS: (21), (44) imply:
% 229.11/40.58  |   (45)  all_57_10 = e1
% 229.11/40.58  | 
% 229.11/40.58  | BETA: splitting (38) gives:
% 229.11/40.58  | 
% 229.11/40.58  | Case 1:
% 229.11/40.58  | | 
% 229.11/40.58  | |   (46)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 229.11/40.58  | |           e2)
% 229.11/40.58  | | 
% 229.11/40.58  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (13), (14),
% 229.11/40.58  | |            (15), (16), (17), (19), (20), (22), (23), (24), (25), (26), (27),
% 229.11/40.58  | |            (28), (29), (30), (31), (33), (34), (35), (36), (37), (38), (39),
% 229.11/40.58  | |            (40), (42), (43), (45), (46) are inconsistent by sub-proof #804.
% 229.11/40.58  | | 
% 229.11/40.58  | Case 2:
% 229.11/40.58  | | 
% 229.11/40.58  | |   (47)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.11/40.58  | |           e2)
% 229.11/40.58  | | 
% 229.11/40.58  | | BETA: splitting (47) gives:
% 229.11/40.58  | | 
% 229.11/40.58  | | Case 1:
% 229.11/40.58  | | | 
% 229.11/40.58  | | |   (48)  all_57_11 = e2 & op(e1, e0) = e2
% 229.11/40.58  | | | 
% 229.11/40.58  | | | ALPHA: (48) implies:
% 229.11/40.58  | | |   (49)  all_57_11 = e2
% 229.11/40.58  | | | 
% 229.11/40.58  | | | REF_CLOSE: (1), (4), (5), (8), (9), (10), (12), (14), (15), (16), (17),
% 229.11/40.58  | | |            (18), (19), (20), (23), (24), (25), (26), (27), (29), (30),
% 229.11/40.58  | | |            (31), (32), (33), (34), (36), (37), (38), (40), (41), (43),
% 229.11/40.58  | | |            (45), (49) are inconsistent by sub-proof #680.
% 229.11/40.58  | | | 
% 229.11/40.58  | | Case 2:
% 229.11/40.58  | | | 
% 229.11/40.58  | | |   (50)  all_57_15 = e2 & op(e0, e0) = e2
% 229.11/40.58  | | | 
% 229.11/40.58  | | | REF_CLOSE: (15), (17), (50) are inconsistent by sub-proof #2323.
% 229.11/40.58  | | | 
% 229.11/40.58  | | End of split
% 229.11/40.58  | | 
% 229.11/40.58  | End of split
% 229.11/40.58  | 
% 229.11/40.58  End of proof
% 229.11/40.58  
% 229.11/40.58  Sub-proof #680 shows that the following formulas are inconsistent:
% 229.11/40.58  ----------------------------------------------------------------
% 229.11/40.58    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.11/40.58         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.11/40.58    (2)   ~ (e3 = e1)
% 229.11/40.58    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.11/40.58           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.11/40.58    (4)   ~ (all_6_2 = e3)
% 229.11/40.58    (5)  all_57_10 = e1
% 229.11/40.58    (6)  op(e1, e1) = all_6_2
% 229.11/40.58    (7)  op(e2, e2) = e1
% 229.11/40.58    (8)  all_57_9 = e1
% 229.11/40.58    (9)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.11/40.58         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.11/40.58    (10)   ~ (e3 = e2)
% 229.11/40.58    (11)   ~ (e3 = e0)
% 229.11/40.58    (12)  all_57_15 = e3
% 229.11/40.58    (13)  op(e2, e2) = all_52_11
% 229.11/40.58    (14)  op(e3, e3) = e2
% 229.11/40.58    (15)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.11/40.58          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.11/40.58            e1)
% 229.11/40.58    (16)  all_57_11 = e2
% 229.11/40.58    (17)   ~ (e2 = e0)
% 229.11/40.58    (18)  all_57_3 = e1
% 229.11/40.58    (19)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.11/40.58          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.11/40.58    (20)   ~ (e1 = e0)
% 229.11/40.58    (21)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.11/40.58          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.11/40.58    (22)  op(e0, e0) = e3
% 229.11/40.58    (23)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.11/40.58          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.11/40.58            e2)
% 229.11/40.58    (24)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.11/40.58              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.11/40.58                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.11/40.58                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.11/40.59    (25)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.11/40.59          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.11/40.59    (26)   ~ (all_53_12 = e3)
% 229.11/40.59    (27)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.11/40.59          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.11/40.59    (28)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.11/40.59          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 229.11/40.59    (29)   ~ (e2 = e1)
% 229.11/40.59    (30)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.11/40.59          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.11/40.59    (31)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.11/40.59          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.11/40.59    (32)  op(all_52_11, all_52_11) = e2
% 229.11/40.59    (33)  op(e3, e0) = all_53_12
% 229.11/40.59  
% 229.11/40.59  Begin of proof
% 229.11/40.59  | 
% 229.11/40.59  | BETA: splitting (27) gives:
% 229.11/40.59  | 
% 229.11/40.59  | Case 1:
% 229.11/40.59  | | 
% 229.11/40.59  | |   (34)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 229.11/40.59  | |           e2)
% 229.11/40.59  | | 
% 229.11/40.59  | | REF_CLOSE: (2), (3), (5), (7), (10), (11), (12), (13), (16), (17), (20),
% 229.11/40.59  | |            (22), (24), (25), (28), (29), (30), (31), (32), (34) are
% 229.11/40.59  | |            inconsistent by sub-proof #681.
% 229.11/40.59  | | 
% 229.11/40.59  | Case 2:
% 229.11/40.59  | | 
% 229.11/40.59  | |   (35)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 229.11/40.59  | |           e2)
% 229.11/40.59  | | 
% 229.11/40.59  | | BETA: splitting (35) gives:
% 229.11/40.59  | | 
% 229.11/40.59  | | Case 1:
% 229.11/40.59  | | | 
% 229.11/40.59  | | |   (36)  all_57_5 = e2 & op(e2, e1) = e2
% 229.11/40.59  | | | 
% 229.11/40.59  | | | ALPHA: (36) implies:
% 229.11/40.59  | | |   (37)  all_57_5 = e2
% 229.11/40.59  | | | 
% 229.11/40.59  | | | BETA: splitting (28) gives:
% 229.11/40.59  | | | 
% 229.11/40.59  | | | Case 1:
% 229.11/40.59  | | | | 
% 229.11/40.59  | | | |   (38)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2)
% 229.11/40.59  | | | |           = e0)
% 229.11/40.59  | | | | 
% 229.11/40.59  | | | | BETA: splitting (38) gives:
% 229.11/40.59  | | | | 
% 229.11/40.59  | | | | Case 1:
% 229.11/40.59  | | | | | 
% 229.11/40.59  | | | | |   (39)  all_57_2 = e0 & op(e2, e3) = e0
% 229.11/40.59  | | | | | 
% 229.11/40.59  | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12),
% 229.11/40.59  | | | | |            (14), (15), (17), (18), (19), (20), (21), (22), (23), (24),
% 229.11/40.59  | | | | |            (25), (26), (27), (29), (30), (33), (37), (39) are
% 229.11/40.59  | | | | |            inconsistent by sub-proof #696.
% 229.11/40.59  | | | | | 
% 229.11/40.59  | | | | Case 2:
% 229.11/40.59  | | | | | 
% 229.11/40.59  | | | | |   (40)  all_57_3 = e0 & op(e2, e2) = e0
% 229.11/40.59  | | | | | 
% 229.11/40.59  | | | | | ALPHA: (40) implies:
% 229.11/40.59  | | | | |   (41)  op(e2, e2) = e0
% 229.11/40.59  | | | | | 
% 229.11/40.59  | | | | | REF_CLOSE: (3), (10), (13), (22), (32), (41) are inconsistent by
% 229.11/40.59  | | | | |            sub-proof #1229.
% 229.11/40.59  | | | | | 
% 229.11/40.59  | | | | End of split
% 229.11/40.59  | | | | 
% 229.11/40.59  | | | Case 2:
% 229.11/40.59  | | | | 
% 229.11/40.59  | | | |   (42)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0)
% 229.11/40.59  | | | |           = e0)
% 229.11/40.59  | | | | 
% 229.11/40.59  | | | | BETA: splitting (42) gives:
% 229.11/40.59  | | | | 
% 229.11/40.59  | | | | Case 1:
% 229.11/40.59  | | | | | 
% 229.11/40.59  | | | | |   (43)  all_57_5 = e0 & op(e2, e1) = e0
% 229.11/40.59  | | | | | 
% 229.11/40.59  | | | | | REF_CLOSE: (17), (37), (43) are inconsistent by sub-proof #2428.
% 229.11/40.59  | | | | | 
% 229.11/40.59  | | | | Case 2:
% 229.11/40.59  | | | | | 
% 229.11/40.59  | | | | |   (44)  all_57_10 = e0 & op(e2, e0) = e0
% 229.11/40.59  | | | | | 
% 229.11/40.59  | | | | | REF_CLOSE: (5), (20), (44) are inconsistent by sub-proof #1332.
% 229.11/40.59  | | | | | 
% 229.11/40.59  | | | | End of split
% 229.11/40.59  | | | | 
% 229.11/40.59  | | | End of split
% 229.11/40.59  | | | 
% 229.11/40.59  | | Case 2:
% 229.11/40.59  | | | 
% 229.11/40.59  | | |   (45)  all_57_10 = e2 & op(e2, e0) = e2
% 229.11/40.59  | | | 
% 229.11/40.59  | | | ALPHA: (45) implies:
% 229.11/40.59  | | |   (46)  all_57_10 = e2
% 229.11/40.59  | | | 
% 229.11/40.59  | | | REF_CLOSE: (5), (29), (46) are inconsistent by sub-proof #2144.
% 229.11/40.59  | | | 
% 229.11/40.59  | | End of split
% 229.11/40.59  | | 
% 229.11/40.59  | End of split
% 229.11/40.59  | 
% 229.11/40.59  End of proof
% 229.11/40.59  
% 229.11/40.59  Sub-proof #681 shows that the following formulas are inconsistent:
% 229.11/40.59  ----------------------------------------------------------------
% 229.11/40.59    (1)   ~ (e3 = e1)
% 229.11/40.59    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.11/40.59           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.11/40.59    (3)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2)
% 229.11/40.59    (4)  all_57_10 = e1
% 229.11/40.59    (5)  op(e2, e2) = e1
% 229.11/40.59    (6)   ~ (e3 = e2)
% 229.11/40.59    (7)   ~ (e3 = e0)
% 229.11/40.59    (8)  all_57_15 = e3
% 229.11/40.59    (9)  op(e2, e2) = all_52_11
% 229.11/40.59    (10)  all_57_11 = e2
% 229.11/40.59    (11)   ~ (e2 = e0)
% 229.11/40.59    (12)   ~ (e1 = e0)
% 229.11/40.59    (13)  op(e0, e0) = e3
% 229.11/40.59    (14)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.11/40.59              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.11/40.59                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.11/40.59                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.11/40.59    (15)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.11/40.59          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.11/40.59    (16)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.11/40.59          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 229.11/40.59    (17)   ~ (e2 = e1)
% 229.11/40.59    (18)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.11/40.59          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.11/40.59    (19)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.11/40.59          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.11/40.59    (20)  op(all_52_11, all_52_11) = e2
% 229.11/40.59  
% 229.11/40.59  Begin of proof
% 229.11/40.59  | 
% 229.11/40.59  | BETA: splitting (3) gives:
% 229.11/40.59  | 
% 229.11/40.59  | Case 1:
% 229.11/40.59  | | 
% 229.11/40.59  | |   (21)  all_57_2 = e2 & op(e2, e3) = e2
% 229.11/40.59  | | 
% 229.11/40.59  | | ALPHA: (21) implies:
% 229.11/40.59  | |   (22)  all_57_2 = e2
% 229.11/40.59  | | 
% 229.11/40.59  | | BETA: splitting (16) gives:
% 229.11/40.59  | | 
% 229.11/40.59  | | Case 1:
% 229.11/40.59  | | | 
% 229.11/40.59  | | |   (23)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) =
% 229.11/40.59  | | |           e0)
% 229.11/40.59  | | | 
% 229.11/40.59  | | | REF_CLOSE: (2), (6), (9), (11), (13), (20), (22), (23) are inconsistent by
% 229.11/40.59  | | |            sub-proof #685.
% 229.11/40.59  | | | 
% 229.11/40.59  | | Case 2:
% 229.11/40.59  | | | 
% 229.11/40.59  | | |   (24)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 229.11/40.59  | | |           e0)
% 229.11/40.59  | | | 
% 229.11/40.59  | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (10), (11), (12), (14),
% 229.11/40.59  | | |            (15), (17), (18), (19), (22), (24) are inconsistent by
% 229.11/40.59  | | |            sub-proof #682.
% 229.11/40.59  | | | 
% 229.11/40.59  | | End of split
% 229.11/40.59  | | 
% 229.11/40.59  | Case 2:
% 229.11/40.59  | | 
% 229.11/40.59  | |   (25)  all_57_3 = e2 & op(e2, e2) = e2
% 229.11/40.59  | | 
% 229.11/40.59  | | ALPHA: (25) implies:
% 229.11/40.59  | |   (26)  op(e2, e2) = e2
% 229.11/40.59  | | 
% 229.11/40.59  | | REF_CLOSE: (2), (5), (17), (26) are inconsistent by sub-proof #2306.
% 229.11/40.59  | | 
% 229.11/40.59  | End of split
% 229.11/40.59  | 
% 229.11/40.59  End of proof
% 229.11/40.59  
% 229.11/40.59  Sub-proof #682 shows that the following formulas are inconsistent:
% 229.11/40.59  ----------------------------------------------------------------
% 229.11/40.59    (1)   ~ (e3 = e1)
% 229.11/40.59    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.11/40.59           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.11/40.59    (3)  all_57_10 = e1
% 229.11/40.59    (4)  op(e2, e2) = e1
% 229.11/40.59    (5)  all_57_2 = e2
% 229.11/40.59    (6)   ~ (e3 = e2)
% 229.11/40.59    (7)   ~ (e3 = e0)
% 229.11/40.59    (8)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 229.11/40.59    (9)  all_57_15 = e3
% 229.11/40.59    (10)  all_57_11 = e2
% 229.11/40.59    (11)   ~ (e2 = e0)
% 229.11/40.59    (12)   ~ (e1 = e0)
% 229.11/40.59    (13)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.11/40.59              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.11/40.59                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.11/40.59                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.11/40.59    (14)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.11/40.59          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.11/40.59    (15)   ~ (e2 = e1)
% 229.11/40.59    (16)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.11/40.59          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.11/40.59    (17)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.11/40.59          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.11/40.59  
% 229.11/40.59  Begin of proof
% 229.11/40.59  | 
% 229.11/40.59  | BETA: splitting (8) gives:
% 229.11/40.59  | 
% 229.11/40.59  | Case 1:
% 229.11/40.59  | | 
% 229.11/40.59  | |   (18)  all_57_5 = e0 & op(e2, e1) = e0
% 229.11/40.59  | | 
% 229.11/40.59  | | ALPHA: (18) implies:
% 229.11/40.59  | |   (19)  all_57_5 = e0
% 229.11/40.59  | | 
% 229.11/40.59  | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (9), (10), (11), (12), (13), (14),
% 229.11/40.59  | |            (15), (16), (17), (19) are inconsistent by sub-proof #683.
% 229.11/40.59  | | 
% 229.11/40.59  | Case 2:
% 229.11/40.59  | | 
% 229.11/40.59  | |   (20)  all_57_10 = e0 & op(e2, e0) = e0
% 229.11/40.59  | | 
% 229.11/40.59  | | REF_CLOSE: (3), (12), (20) are inconsistent by sub-proof #1332.
% 229.11/40.59  | | 
% 229.11/40.59  | End of split
% 229.11/40.59  | 
% 229.11/40.59  End of proof
% 229.11/40.59  
% 229.11/40.59  Sub-proof #683 shows that the following formulas are inconsistent:
% 229.11/40.59  ----------------------------------------------------------------
% 229.11/40.59    (1)   ~ (e3 = e1)
% 229.11/40.59    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.11/40.59           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.11/40.59    (3)  op(e2, e2) = e1
% 229.11/40.59    (4)  all_57_2 = e2
% 229.11/40.59    (5)   ~ (e3 = e2)
% 229.11/40.59    (6)   ~ (e3 = e0)
% 229.11/40.59    (7)  all_57_15 = e3
% 229.11/40.59    (8)  all_57_11 = e2
% 229.11/40.59    (9)   ~ (e2 = e0)
% 229.11/40.59    (10)   ~ (e1 = e0)
% 229.11/40.59    (11)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.11/40.59              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.11/40.59                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.11/40.59                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.11/40.59    (12)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.11/40.59          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.11/40.59    (13)   ~ (e2 = e1)
% 229.11/40.59    (14)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.11/40.59          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.11/40.59    (15)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.11/40.59          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.11/40.59    (16)  all_57_5 = e0
% 229.11/40.59  
% 229.11/40.59  Begin of proof
% 229.11/40.59  | 
% 229.11/40.59  | BETA: splitting (12) gives:
% 229.11/40.59  | 
% 229.11/40.59  | Case 1:
% 229.11/40.59  | | 
% 229.11/40.59  | |   (17)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 229.11/40.59  | |           e3)
% 229.11/40.59  | | 
% 229.11/40.59  | | REF_CLOSE: (1), (2), (3), (4), (5), (17) are inconsistent by sub-proof #684.
% 229.11/40.59  | | 
% 229.11/40.59  | Case 2:
% 229.11/40.59  | | 
% 229.11/40.59  | |   (18)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 229.11/40.59  | |           e3)
% 229.11/40.59  | | 
% 229.11/40.59  | | BETA: splitting (18) gives:
% 229.11/40.59  | | 
% 229.11/40.59  | | Case 1:
% 229.11/40.59  | | | 
% 229.11/40.59  | | |   (19)  all_57_5 = e3 & op(e2, e1) = e3
% 229.11/40.59  | | | 
% 229.11/40.59  | | | ALPHA: (19) implies:
% 229.11/40.59  | | |   (20)  all_57_5 = e3
% 229.11/40.59  | | | 
% 229.11/40.59  | | | REF_CLOSE: (6), (16), (20) are inconsistent by sub-proof #2471.
% 229.11/40.59  | | | 
% 229.11/40.59  | | Case 2:
% 229.11/40.59  | | | 
% 229.11/40.59  | | |   (21)  all_57_10 = e3 & op(e2, e0) = e3
% 229.11/40.59  | | | 
% 229.11/40.59  | | | ALPHA: (21) implies:
% 229.11/40.59  | | |   (22)  all_57_10 = e3
% 229.11/40.59  | | | 
% 229.11/40.59  | | | REF_CLOSE: (1), (5), (6), (7), (8), (9), (10), (11), (13), (14), (15),
% 229.11/40.59  | | |            (22) are inconsistent by sub-proof #1983.
% 229.11/40.59  | | | 
% 229.11/40.59  | | End of split
% 229.11/40.59  | | 
% 229.11/40.59  | End of split
% 229.11/40.59  | 
% 229.11/40.59  End of proof
% 229.11/40.59  
% 229.11/40.59  Sub-proof #684 shows that the following formulas are inconsistent:
% 229.11/40.59  ----------------------------------------------------------------
% 229.11/40.59    (1)   ~ (e3 = e1)
% 229.11/40.59    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.11/40.59           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.11/40.59    (3)  op(e2, e2) = e1
% 229.11/40.59    (4)  all_57_2 = e2
% 229.11/40.59    (5)   ~ (e3 = e2)
% 229.11/40.59    (6)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3)
% 229.11/40.59  
% 229.11/40.59  Begin of proof
% 229.11/40.59  | 
% 229.11/40.59  | BETA: splitting (6) gives:
% 229.11/40.59  | 
% 229.11/40.59  | Case 1:
% 229.11/40.59  | | 
% 229.11/40.59  | |   (7)  all_57_2 = e3 & op(e2, e3) = e3
% 229.11/40.59  | | 
% 229.11/40.59  | | ALPHA: (7) implies:
% 229.11/40.59  | |   (8)  all_57_2 = e3
% 229.11/40.59  | | 
% 229.11/40.59  | | REF_CLOSE: (4), (5), (8) are inconsistent by sub-proof #1800.
% 229.11/40.59  | | 
% 229.11/40.59  | Case 2:
% 229.11/40.59  | | 
% 229.11/40.59  | |   (9)  all_57_3 = e3 & op(e2, e2) = e3
% 229.11/40.59  | | 
% 229.11/40.59  | | ALPHA: (9) implies:
% 229.11/40.59  | |   (10)  op(e2, e2) = e3
% 229.11/40.59  | | 
% 229.11/40.59  | | REF_CLOSE: (1), (2), (3), (10) are inconsistent by sub-proof #1912.
% 229.11/40.59  | | 
% 229.11/40.59  | End of split
% 229.11/40.59  | 
% 229.11/40.59  End of proof
% 229.11/40.59  
% 229.11/40.59  Sub-proof #685 shows that the following formulas are inconsistent:
% 229.11/40.59  ----------------------------------------------------------------
% 229.11/40.59    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.11/40.59           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.11/40.59    (2)  all_57_2 = e2
% 229.11/40.59    (3)   ~ (e3 = e2)
% 229.11/40.59    (4)  op(e2, e2) = all_52_11
% 229.11/40.59    (5)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0)
% 229.11/40.59    (6)   ~ (e2 = e0)
% 229.11/40.59    (7)  op(e0, e0) = e3
% 229.11/40.59    (8)  op(all_52_11, all_52_11) = e2
% 229.11/40.59  
% 229.11/40.59  Begin of proof
% 229.11/40.59  | 
% 229.11/40.59  | BETA: splitting (5) gives:
% 229.11/40.59  | 
% 229.11/40.59  | Case 1:
% 229.11/40.59  | | 
% 229.11/40.59  | |   (9)  all_57_2 = e0 & op(e2, e3) = e0
% 229.11/40.59  | | 
% 229.11/40.59  | | REF_CLOSE: (2), (6), (9) are inconsistent by sub-proof #1700.
% 229.11/40.59  | | 
% 229.11/40.59  | Case 2:
% 229.11/40.59  | | 
% 229.11/40.59  | |   (10)  all_57_3 = e0 & op(e2, e2) = e0
% 229.11/40.59  | | 
% 229.11/40.59  | | ALPHA: (10) implies:
% 229.11/40.59  | |   (11)  op(e2, e2) = e0
% 229.11/40.59  | | 
% 229.11/40.59  | | REF_CLOSE: (1), (3), (4), (7), (8), (11) are inconsistent by sub-proof
% 229.11/40.59  | |            #1229.
% 229.11/40.59  | | 
% 229.11/40.59  | End of split
% 229.11/40.59  | 
% 229.11/40.59  End of proof
% 229.11/40.59  
% 229.11/40.59  Sub-proof #686 shows that the following formulas are inconsistent:
% 229.11/40.59  ----------------------------------------------------------------
% 229.11/40.59    (1)   ~ (all_53_2 = e2)
% 229.11/40.59    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.11/40.59         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.11/40.59    (3)   ~ (e3 = e1)
% 229.11/40.59    (4)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 229.11/40.59         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 229.11/40.59    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.11/40.59           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.11/40.59    (6)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.11/40.59         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.11/40.59    (7)   ~ (all_53_3 = e3)
% 229.11/40.59    (8)   ~ (all_53_3 = all_53_7)
% 229.11/40.59    (9)   ~ (all_6_2 = e3)
% 229.11/40.59    (10)   ~ (all_53_9 = e1)
% 229.11/40.59    (11)  op(e1, e1) = all_6_2
% 229.11/40.59    (12)   ~ (all_53_1 = all_53_9)
% 229.11/40.59    (13)  op(e2, e2) = e1
% 229.11/40.59    (14)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.11/40.59          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.11/40.59    (15)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 229.11/40.59            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 229.11/40.59              e3) = all_22_1 & $i(all_22_1))
% 229.11/40.59    (16)  all_57_9 = e1
% 229.11/40.59    (17)   ~ (all_53_13 = e3)
% 229.11/40.59    (18)   ~ (all_53_9 = all_53_11)
% 229.11/40.59    (19)  all_55_4 = all_53_1
% 229.11/40.59    (20)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.11/40.59          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.11/40.59    (21)   ~ (e3 = e2)
% 229.11/40.59    (22)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 229.11/40.59    (23)   ~ (all_53_1 = all_53_3)
% 229.11/40.59    (24)   ~ (e3 = e0)
% 229.11/40.59    (25)  op(e0, e3) = e1
% 229.11/40.59    (26)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 229.11/40.59    (27)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 229.11/40.59    (28)  all_57_15 = e3
% 229.11/40.59    (29)   ~ (all_53_9 = all_53_13)
% 229.11/40.59    (30)  op(e3, e3) = e2
% 229.11/40.59    (31)  all_57_10 = e2
% 229.11/40.59    (32)   ~ (all_53_1 = e1)
% 229.11/40.59    (33)  op(e2, e0) = e2
% 229.11/40.59    (34)  all_55_6 = all_53_9
% 229.11/40.59    (35)   ~ (all_53_1 = all_53_2)
% 229.11/40.59    (36)  op(e1, e1) = e1
% 229.11/40.59    (37)   ~ (e2 = e0)
% 229.11/40.59    (38)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 229.11/40.59            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 229.11/40.59            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 229.11/40.59            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 229.11/40.59              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 229.11/40.59            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 229.11/40.59            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 229.11/40.59              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 229.11/40.59              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 229.11/40.59            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 229.11/40.59            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 229.11/40.59            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 229.11/40.59              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 229.11/40.59              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 229.11/40.59            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 229.11/40.59              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 229.11/40.59            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 229.11/40.59            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 229.11/40.59              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 229.11/40.59              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 229.11/40.59            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 229.11/40.59            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 229.11/40.59    (39)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 229.11/40.59            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 229.11/40.59              e3) = all_12_1 & $i(all_12_1))
% 229.11/40.59    (40)  all_55_12 = all_53_3
% 229.11/40.59    (41)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.11/40.59          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.11/40.59    (42)   ~ (e1 = e0)
% 229.11/40.59    (43)   ~ (all_53_3 = all_53_11)
% 229.11/40.59    (44)   ~ (all_53_2 = all_53_3)
% 229.11/40.59    (45)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 229.11/40.59    (46)   ~ (all_53_7 = all_53_11)
% 229.11/40.59    (47)  all_55_8 = all_53_2
% 229.11/40.59    (48)  op(e0, e0) = e3
% 229.11/40.59    (49)  op(e0, e2) = all_53_7
% 229.11/40.59    (50)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.11/40.59              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.11/40.59                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.11/40.59                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.11/40.59    (51)   ~ (all_53_1 = all_53_13)
% 229.11/40.59    (52)  op(e2, e0) = all_53_13
% 229.11/40.59    (53)   ~ (all_53_12 = e3)
% 229.11/40.59    (54)  op(e1, e3) = all_53_2
% 229.11/40.59    (55)  all_57_11 = e1
% 229.11/40.59    (56)   ~ (e2 = e1)
% 229.11/40.59    (57)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.11/40.59          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.11/40.59    (58)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 229.11/40.60    (59)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.11/40.60          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.11/40.60    (60)  all_55_14 = all_53_11
% 229.11/40.60    (61)   ~ (all_53_11 = e3)
% 229.11/40.60    (62)  op(e3, e0) = all_53_12
% 229.11/40.60  
% 229.11/40.60  Begin of proof
% 229.11/40.60  | 
% 229.11/40.60  | BETA: splitting (2) gives:
% 229.11/40.60  | 
% 229.11/40.60  | Case 1:
% 229.11/40.60  | | 
% 229.11/40.60  | |   (63)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 229.11/40.60  | |           e2)
% 229.11/40.60  | | 
% 229.11/40.60  | | REF_CLOSE: (3), (5), (13), (14), (20), (21), (24), (30), (37), (41), (42),
% 229.11/40.60  | |            (53), (56), (62), (63) are inconsistent by sub-proof #714.
% 229.11/40.60  | | 
% 229.11/40.60  | Case 2:
% 229.11/40.60  | | 
% 229.11/40.60  | |   (64)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 229.11/40.60  | |           e2)
% 229.11/40.60  | | 
% 229.11/40.60  | | BETA: splitting (64) gives:
% 229.11/40.60  | | 
% 229.11/40.60  | | Case 1:
% 229.11/40.60  | | | 
% 229.11/40.60  | | |   (65)  all_57_7 = e2 & op(e1, e2) = e2
% 229.11/40.60  | | | 
% 229.11/40.60  | | | ALPHA: (65) implies:
% 229.11/40.60  | | |   (66)  all_57_7 = e2
% 229.11/40.60  | | | 
% 229.11/40.60  | | | REF_CLOSE: (3), (4), (5), (6), (9), (11), (15), (16), (21), (24), (25),
% 229.11/40.60  | | |            (28), (31), (36), (37), (39), (42), (50), (55), (56), (57),
% 229.11/40.60  | | |            (59), (66) are inconsistent by sub-proof #708.
% 229.11/40.60  | | | 
% 229.11/40.60  | | Case 2:
% 229.11/40.60  | | | 
% 229.11/40.60  | | |   (67)  all_57_13 = e2 & op(e0, e2) = e2
% 229.11/40.60  | | | 
% 229.11/40.60  | | | REF_CLOSE: (1), (3), (5), (7), (8), (9), (10), (11), (12), (13), (17),
% 229.11/40.60  | | |            (18), (19), (22), (23), (26), (27), (29), (30), (32), (33),
% 229.11/40.60  | | |            (34), (35), (37), (38), (40), (43), (44), (45), (46), (47),
% 229.11/40.60  | | |            (48), (49), (51), (52), (54), (58), (60), (61), (67) are
% 229.11/40.60  | | |            inconsistent by sub-proof #771.
% 229.11/40.60  | | | 
% 229.11/40.60  | | End of split
% 229.11/40.60  | | 
% 229.11/40.60  | End of split
% 229.11/40.60  | 
% 229.11/40.60  End of proof
% 229.11/40.60  
% 229.11/40.60  Sub-proof #687 shows that the following formulas are inconsistent:
% 229.11/40.60  ----------------------------------------------------------------
% 229.11/40.60    (1)  all_57_0 = e2
% 229.11/40.60    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.11/40.60         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.11/40.60    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.11/40.60         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.11/40.60    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.11/40.60         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.11/40.60    (5)   ~ (e3 = e1)
% 229.11/40.60    (6)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 229.11/40.60         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 229.11/40.60    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.11/40.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.11/40.60    (8)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.11/40.60         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.11/40.60    (9)   ~ (all_6_2 = e3)
% 229.11/40.60    (10)  op(e1, e1) = all_6_2
% 229.11/40.60    (11)  op(all_52_7, all_52_7) = e0
% 229.11/40.60    (12)  op(e2, e2) = e1
% 229.11/40.60    (13)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.11/40.60          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.11/40.60    (14)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 229.11/40.60            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 229.11/40.60              e3) = all_22_1 & $i(all_22_1))
% 229.11/40.60    (15)  all_57_9 = e1
% 229.11/40.60    (16)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.11/40.60          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.11/40.60    (17)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.11/40.60          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.11/40.60    (18)   ~ (e3 = e2)
% 229.11/40.60    (19)  op(e3, e0) = e1
% 229.11/40.60    (20)   ~ (e3 = e0)
% 229.11/40.60    (21)  all_57_15 = e3
% 229.11/40.60    (22)  op(e3, e3) = e2
% 229.11/40.60    (23)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.11/40.60          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.11/40.60            e1)
% 229.11/40.60    (24)  op(e1, e1) = e1
% 229.11/40.60    (25)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.11/40.60          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.11/40.60    (26)   ~ (e2 = e0)
% 229.11/40.60    (27)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 229.11/40.60            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 229.11/40.60              e3) = all_12_1 & $i(all_12_1))
% 229.11/40.60    (28)  all_57_3 = e1
% 229.11/40.60    (29)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.11/40.60          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.11/40.60    (30)   ~ (e1 = e0)
% 229.11/40.60    (31)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.11/40.60          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.11/40.60    (32)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.11/40.60          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.11/40.60    (33)  op(e0, e0) = e3
% 229.11/40.60    (34)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.11/40.60          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.11/40.60            e2)
% 229.11/40.60    (35)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.11/40.60              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.11/40.60                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.11/40.60                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.11/40.60    (36)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.11/40.60          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.11/40.60    (37)   ~ (all_53_12 = e3)
% 229.11/40.60    (38)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.11/40.60          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.11/40.60    (39)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.11/40.60          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.11/40.60    (40)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.11/40.60          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 229.11/40.60    (41)   ~ (e2 = e1)
% 229.11/40.60    (42)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.11/40.60          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.11/40.60    (43)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.11/40.60          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.11/40.60    (44)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 229.11/40.60          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 229.11/40.60    (45)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.11/40.60          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.11/40.60    (46)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.11/40.60          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.11/40.60    (47)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 229.11/40.60          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 229.11/40.60    (48)  op(e3, e0) = all_52_7
% 229.11/40.60    (49)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.11/40.60          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.11/40.60    (50)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 229.11/40.60          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 229.11/40.60    (51)  op(e3, e0) = all_53_12
% 229.11/40.60  
% 229.11/40.60  Begin of proof
% 229.11/40.60  | 
% 229.11/40.60  | BETA: splitting (23) gives:
% 229.11/40.60  | 
% 229.11/40.60  | Case 1:
% 229.11/40.60  | | 
% 229.11/40.60  | |   (52)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 229.11/40.60  | |           e1)
% 229.11/40.60  | | 
% 229.11/40.60  | | BETA: splitting (52) gives:
% 229.11/40.60  | | 
% 229.11/40.60  | | Case 1:
% 229.11/40.60  | | | 
% 229.11/40.60  | | |   (53)  all_57_12 = e1 & op(e0, e3) = e1
% 229.11/40.60  | | | 
% 229.11/40.60  | | | ALPHA: (53) implies:
% 229.11/40.60  | | |   (54)  all_57_12 = e1
% 229.11/40.60  | | |   (55)  op(e0, e3) = e1
% 229.11/40.60  | | | 
% 229.11/40.60  | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 229.11/40.60  | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 229.11/40.60  | | |            (24), (25), (26), (27), (28), (29), (30), (32), (33), (34),
% 229.11/40.60  | | |            (35), (36), (37), (38), (39), (41), (42), (43), (45), (46),
% 229.11/40.60  | | |            (47), (48), (49), (50), (51), (54), (55) are inconsistent by
% 229.11/40.60  | | |            sub-proof #706.
% 229.11/40.60  | | | 
% 229.11/40.60  | | Case 2:
% 229.11/40.60  | | | 
% 229.11/40.60  | | |   (56)  all_57_13 = e1 & op(e0, e2) = e1
% 229.11/40.60  | | | 
% 229.11/40.60  | | | ALPHA: (56) implies:
% 229.11/40.60  | | |   (57)  all_57_13 = e1
% 229.11/40.60  | | | 
% 229.11/40.60  | | | BETA: splitting (3) gives:
% 229.11/40.60  | | | 
% 229.11/40.60  | | | Case 1:
% 229.11/40.60  | | | | 
% 229.11/40.60  | | | |   (58)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3)
% 229.11/40.60  | | | |           = e1)
% 229.11/40.60  | | | | 
% 229.11/40.60  | | | | REF_CLOSE: (2), (4), (5), (7), (12), (13), (17), (18), (20), (21), (22),
% 229.11/40.60  | | | |            (23), (25), (26), (28), (29), (30), (32), (33), (34), (35),
% 229.11/40.60  | | | |            (36), (37), (38), (41), (51), (57), (58) are inconsistent by
% 229.11/40.60  | | | |            sub-proof #704.
% 229.11/40.60  | | | | 
% 229.11/40.60  | | | Case 2:
% 229.11/40.60  | | | | 
% 229.11/40.60  | | | |   (59)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3)
% 229.11/40.60  | | | |           = e1)
% 229.11/40.60  | | | | 
% 229.11/40.60  | | | | BETA: splitting (59) gives:
% 229.11/40.60  | | | | 
% 229.11/40.60  | | | | Case 1:
% 229.11/40.60  | | | | | 
% 229.11/40.60  | | | | |   (60)  all_57_6 = e1 & op(e1, e3) = e1
% 229.11/40.60  | | | | | 
% 229.11/40.60  | | | | | ALPHA: (60) implies:
% 229.11/40.60  | | | | |   (61)  all_57_6 = e1
% 229.11/40.60  | | | | | 
% 229.11/40.60  | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (10), (12), (13), (17), (18),
% 229.11/40.60  | | | | |            (20), (21), (22), (25), (26), (28), (29), (30), (35), (37),
% 229.11/40.60  | | | | |            (41), (42), (46), (49), (51), (57), (61) are inconsistent
% 229.11/40.60  | | | | |            by sub-proof #797.
% 229.11/40.60  | | | | | 
% 229.11/40.60  | | | | Case 2:
% 229.11/40.60  | | | | | 
% 229.11/40.60  | | | | |   (62)  all_57_12 = e1 & op(e0, e3) = e1
% 229.11/40.60  | | | | | 
% 229.11/40.60  | | | | | ALPHA: (62) implies:
% 229.11/40.60  | | | | |   (63)  all_57_12 = e1
% 229.11/40.60  | | | | |   (64)  op(e0, e3) = e1
% 229.11/40.60  | | | | | 
% 229.11/40.60  | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 229.11/40.60  | | | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 229.11/40.60  | | | | |            (23), (24), (25), (26), (27), (28), (29), (30), (32), (33),
% 229.11/40.60  | | | | |            (34), (35), (36), (37), (38), (39), (41), (42), (43), (45),
% 229.11/40.60  | | | | |            (46), (47), (48), (49), (50), (51), (63), (64) are
% 229.11/40.60  | | | | |            inconsistent by sub-proof #706.
% 229.11/40.60  | | | | | 
% 229.11/40.60  | | | | End of split
% 229.11/40.60  | | | | 
% 229.11/40.60  | | | End of split
% 229.11/40.60  | | | 
% 229.11/40.60  | | End of split
% 229.11/40.60  | | 
% 229.11/40.60  | Case 2:
% 229.11/40.60  | | 
% 229.11/40.60  | |   (65)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.11/40.60  | |           e1)
% 229.11/40.60  | | 
% 229.11/40.60  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 229.11/40.60  | |            (14), (15), (16), (17), (18), (20), (21), (22), (23), (24), (25),
% 229.11/40.60  | |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 229.11/40.60  | |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (49),
% 229.11/40.60  | |            (51), (65) are inconsistent by sub-proof #688.
% 229.11/40.60  | | 
% 229.11/40.60  | End of split
% 229.11/40.60  | 
% 229.11/40.60  End of proof
% 229.11/40.60  
% 229.11/40.60  Sub-proof #688 shows that the following formulas are inconsistent:
% 229.11/40.60  ----------------------------------------------------------------
% 229.11/40.60    (1)  all_57_0 = e2
% 229.11/40.60    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.11/40.60         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.11/40.60    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.11/40.60         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.11/40.60    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.11/40.60         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.11/40.60    (5)   ~ (e3 = e1)
% 229.11/40.60    (6)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 229.11/40.60         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 229.11/40.60    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.11/40.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.11/40.60    (8)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.11/40.60         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.11/40.60    (9)   ~ (all_6_2 = e3)
% 229.11/40.60    (10)  op(e1, e1) = all_6_2
% 229.11/40.60    (11)  op(e2, e2) = e1
% 229.11/40.60    (12)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.11/40.60          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.11/40.60    (13)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 229.11/40.60            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 229.11/40.60              e3) = all_22_1 & $i(all_22_1))
% 229.11/40.60    (14)  all_57_9 = e1
% 229.11/40.60    (15)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.11/40.60          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.11/40.60    (16)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.11/40.60          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.11/40.60    (17)   ~ (e3 = e2)
% 229.11/40.60    (18)   ~ (e3 = e0)
% 229.11/40.60    (19)  all_57_15 = e3
% 229.11/40.60    (20)  op(e3, e3) = e2
% 229.11/40.60    (21)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.11/40.60          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.11/40.60            e1)
% 229.11/40.60    (22)  op(e1, e1) = e1
% 229.11/40.60    (23)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.11/40.60          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.11/40.60    (24)   ~ (e2 = e0)
% 229.11/40.60    (25)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 229.11/40.60            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 229.11/40.60              e3) = all_12_1 & $i(all_12_1))
% 229.11/40.60    (26)  all_57_3 = e1
% 229.11/40.60    (27)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.11/40.60          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.11/40.60    (28)   ~ (e1 = e0)
% 229.11/40.60    (29)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.11/40.60          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.11/40.60    (30)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.11/40.60          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.11/40.60    (31)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.11/40.60    (32)  op(e0, e0) = e3
% 229.11/40.60    (33)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.11/40.60          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.11/40.60            e2)
% 229.11/40.60    (34)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.11/40.60              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.11/40.60                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.11/40.60                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.11/40.60    (35)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.11/40.60          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.11/40.60    (36)   ~ (all_53_12 = e3)
% 229.11/40.60    (37)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.11/40.60          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.11/40.60    (38)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.11/40.60          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.11/40.60    (39)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.11/40.60          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 229.11/40.60    (40)   ~ (e2 = e1)
% 229.11/40.60    (41)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.11/40.60          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.11/40.60    (42)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.11/40.60          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.11/40.60    (43)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 229.11/40.60          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 229.11/40.60    (44)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.11/40.60          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.11/40.60    (45)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.11/40.60          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.11/40.60    (46)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.11/40.60          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.11/40.60    (47)  op(e3, e0) = all_53_12
% 229.11/40.60  
% 229.11/40.60  Begin of proof
% 229.11/40.60  | 
% 229.11/40.60  | BETA: splitting (31) gives:
% 229.11/40.60  | 
% 229.11/40.60  | Case 1:
% 229.11/40.60  | | 
% 229.11/40.60  | |   (48)  all_57_14 = e1 & op(e0, e1) = e1
% 229.11/40.60  | | 
% 229.11/40.60  | | ALPHA: (48) implies:
% 229.11/40.60  | |   (49)  all_57_14 = e1
% 229.11/40.60  | | 
% 229.11/40.60  | | BETA: splitting (3) gives:
% 229.11/40.60  | | 
% 229.11/40.60  | | Case 1:
% 229.11/40.60  | | | 
% 229.11/40.60  | | |   (50)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) =
% 229.11/40.60  | | |           e1)
% 229.11/40.60  | | | 
% 229.11/40.60  | | | REF_CLOSE: (2), (5), (7), (9), (10), (11), (14), (16), (17), (18), (19),
% 229.11/40.60  | | |            (20), (21), (22), (24), (26), (27), (28), (29), (32), (33),
% 229.11/40.60  | | |            (34), (35), (36), (37), (40), (41), (43), (47), (49), (50) are
% 229.11/40.60  | | |            inconsistent by sub-proof #698.
% 229.11/40.60  | | | 
% 229.11/40.60  | | Case 2:
% 229.11/40.60  | | | 
% 229.11/40.60  | | |   (51)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) =
% 229.11/40.60  | | |           e1)
% 229.11/40.60  | | | 
% 229.11/40.60  | | | BETA: splitting (51) gives:
% 229.11/40.60  | | | 
% 229.11/40.60  | | | Case 1:
% 229.11/40.60  | | | | 
% 229.11/40.60  | | | |   (52)  all_57_6 = e1 & op(e1, e3) = e1
% 229.11/40.60  | | | | 
% 229.11/40.60  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 229.11/40.60  | | | |            (12), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 229.11/40.60  | | | |            (23), (24), (26), (27), (28), (29), (30), (32), (33), (34),
% 229.11/40.60  | | | |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44),
% 229.11/40.60  | | | |            (45), (46), (47), (49), (52) are inconsistent by sub-proof
% 229.11/40.60  | | | |            #693.
% 229.11/40.60  | | | | 
% 229.11/40.60  | | | Case 2:
% 229.11/40.60  | | | | 
% 229.11/40.60  | | | |   (53)  all_57_12 = e1 & op(e0, e3) = e1
% 229.11/40.60  | | | | 
% 229.11/40.60  | | | | ALPHA: (53) implies:
% 229.11/40.60  | | | |   (54)  op(e0, e3) = e1
% 229.11/40.60  | | | | 
% 229.11/40.60  | | | | BETA: splitting (34) gives:
% 229.11/40.60  | | | | 
% 229.11/40.60  | | | | Case 1:
% 229.11/40.60  | | | | | 
% 229.11/40.60  | | | | |   (55)  all_57_15 = e0 & op(e0, e0) = e0
% 229.11/40.60  | | | | | 
% 229.11/40.60  | | | | | ALPHA: (55) implies:
% 229.11/40.60  | | | | |   (56)  op(e0, e0) = e0
% 229.11/40.60  | | | | | 
% 229.11/40.60  | | | | | REF_CLOSE: (7), (18), (32), (56) are inconsistent by sub-proof #2304.
% 229.11/40.60  | | | | | 
% 229.11/40.60  | | | | Case 2:
% 229.11/40.60  | | | | | 
% 229.11/40.60  | | | | |   (57)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2,
% 229.11/40.60  | | | | |               e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) &
% 229.11/40.60  | | | | |         ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0,
% 229.11/40.60  | | | | |               e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 229.11/40.60  | | | | | 
% 229.11/40.60  | | | | | ALPHA: (57) implies:
% 229.11/40.60  | | | | |   (58)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0,
% 229.11/40.60  | | | | |             e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.11/40.60  | | | | |   (59)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2,
% 229.11/40.60  | | | | |             e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 229.11/40.60  | | | | | 
% 229.11/40.60  | | | | | BETA: splitting (43) gives:
% 229.11/40.60  | | | | | 
% 229.11/40.60  | | | | | Case 1:
% 229.11/40.60  | | | | | | 
% 229.11/40.60  | | | | | |   (60)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2,
% 229.11/40.60  | | | | | |             e1) = e2)
% 229.11/40.60  | | | | | | 
% 229.11/40.60  | | | | | | BETA: splitting (60) gives:
% 229.11/40.60  | | | | | | 
% 229.11/40.60  | | | | | | Case 1:
% 229.11/40.60  | | | | | | | 
% 229.11/40.60  | | | | | | |   (61)  all_57_4 = e2 & op(e3, e1) = e2
% 229.11/40.60  | | | | | | | 
% 229.11/40.60  | | | | | | | ALPHA: (61) implies:
% 229.11/40.60  | | | | | | |   (62)  all_57_4 = e2
% 229.11/40.60  | | | | | | | 
% 229.11/40.60  | | | | | | | REF_CLOSE: (7), (14), (16), (17), (18), (20), (24), (27), (28),
% 229.11/40.60  | | | | | | |            (36), (47), (62) are inconsistent by sub-proof #873.
% 229.11/40.60  | | | | | | | 
% 229.11/40.60  | | | | | | Case 2:
% 229.11/40.60  | | | | | | | 
% 229.11/40.60  | | | | | | |   (63)  all_57_5 = e2 & op(e2, e1) = e2
% 229.11/40.60  | | | | | | | 
% 229.11/40.60  | | | | | | | ALPHA: (63) implies:
% 229.11/40.60  | | | | | | |   (64)  all_57_5 = e2
% 229.11/40.60  | | | | | | | 
% 229.11/40.60  | | | | | | | BETA: splitting (29) gives:
% 229.11/40.60  | | | | | | | 
% 229.11/40.60  | | | | | | | Case 1:
% 229.11/40.60  | | | | | | | | 
% 229.11/40.60  | | | | | | | |   (65)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 &
% 229.11/40.60  | | | | | | | |           op(e2, e1) = e3)
% 229.11/40.60  | | | | | | | | 
% 229.11/40.60  | | | | | | | | BETA: splitting (65) gives:
% 229.11/40.60  | | | | | | | | 
% 229.11/40.60  | | | | | | | | Case 1:
% 229.11/40.60  | | | | | | | | | 
% 229.11/40.60  | | | | | | | | |   (66)  all_57_4 = e3 & op(e3, e1) = e3
% 229.11/40.60  | | | | | | | | | 
% 229.11/40.60  | | | | | | | | | ALPHA: (66) implies:
% 229.11/40.60  | | | | | | | | |   (67)  all_57_4 = e3
% 229.11/40.60  | | | | | | | | | 
% 229.11/40.60  | | | | | | | | | BETA: splitting (16) gives:
% 229.11/40.60  | | | | | | | | | 
% 229.11/40.60  | | | | | | | | | Case 1:
% 229.11/40.60  | | | | | | | | | | 
% 229.11/40.60  | | | | | | | | | |   (68)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 &
% 229.11/40.60  | | | | | | | | | |           op(e3, e2) = e0)
% 229.11/40.60  | | | | | | | | | | 
% 229.11/40.60  | | | | | | | | | | BETA: splitting (68) gives:
% 229.11/40.60  | | | | | | | | | | 
% 229.11/40.60  | | | | | | | | | | Case 1:
% 229.11/40.60  | | | | | | | | | | | 
% 229.11/40.60  | | | | | | | | | | |   (69)  all_57_0 = e0 & op(e3, e3) = e0
% 229.11/40.60  | | | | | | | | | | | 
% 229.11/40.60  | | | | | | | | | | | ALPHA: (69) implies:
% 229.11/40.60  | | | | | | | | | | |   (70)  op(e3, e3) = e0
% 229.11/40.60  | | | | | | | | | | | 
% 229.11/40.60  | | | | | | | | | | | REF_CLOSE: (7), (20), (24), (70) are inconsistent by
% 229.11/40.60  | | | | | | | | | | |            sub-proof #2403.
% 229.11/40.60  | | | | | | | | | | | 
% 229.11/40.60  | | | | | | | | | | Case 2:
% 229.11/40.60  | | | | | | | | | | | 
% 229.11/40.60  | | | | | | | | | | |   (71)  all_57_1 = e0 & op(e3, e2) = e0
% 229.11/40.60  | | | | | | | | | | | 
% 229.11/40.60  | | | | | | | | | | | ALPHA: (71) implies:
% 229.11/40.60  | | | | | | | | | | |   (72)  all_57_1 = e0
% 229.11/40.60  | | | | | | | | | | | 
% 229.11/40.60  | | | | | | | | | | | BETA: splitting (39) gives:
% 229.11/40.60  | | | | | | | | | | | 
% 229.11/40.60  | | | | | | | | | | | Case 1:
% 229.11/40.60  | | | | | | | | | | | | 
% 229.11/40.60  | | | | | | | | | | | |   (73)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 229.11/40.60  | | | | | | | | | | | |           & op(e2, e2) = e0)
% 229.11/40.60  | | | | | | | | | | | | 
% 229.11/40.60  | | | | | | | | | | | | BETA: splitting (73) gives:
% 229.11/40.60  | | | | | | | | | | | | 
% 229.11/40.60  | | | | | | | | | | | | Case 1:
% 229.11/40.60  | | | | | | | | | | | | | 
% 229.11/40.60  | | | | | | | | | | | | |   (74)  all_57_2 = e0 & op(e2, e3) = e0
% 229.11/40.60  | | | | | | | | | | | | | 
% 229.11/40.60  | | | | | | | | | | | | | ALPHA: (74) implies:
% 229.11/40.60  | | | | | | | | | | | | |   (75)  all_57_2 = e0
% 229.11/40.60  | | | | | | | | | | | | | 
% 229.11/40.60  | | | | | | | | | | | | | REF_CLOSE: (5), (7), (11), (14), (17), (18), (19), (20),
% 229.11/40.60  | | | | | | | | | | | | |            (24), (27), (28), (35), (36), (40), (41), (47),
% 229.11/40.60  | | | | | | | | | | | | |            (59), (64), (67), (72), (75) are inconsistent by
% 229.11/40.60  | | | | | | | | | | | | |            sub-proof #697.
% 229.11/40.60  | | | | | | | | | | | | | 
% 229.11/40.60  | | | | | | | | | | | | Case 2:
% 229.11/40.60  | | | | | | | | | | | | | 
% 229.11/40.60  | | | | | | | | | | | | |   (76)  all_57_3 = e0 & op(e2, e2) = e0
% 229.11/40.60  | | | | | | | | | | | | | 
% 229.11/40.60  | | | | | | | | | | | | | ALPHA: (76) implies:
% 229.11/40.60  | | | | | | | | | | | | |   (77)  all_57_3 = e0
% 229.11/40.60  | | | | | | | | | | | | | 
% 229.11/40.60  | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10),
% 229.11/40.60  | | | | | | | | | | | | |            (17), (18), (19), (20), (21), (24), (28), (30),
% 229.11/40.60  | | | | | | | | | | | | |            (32), (33), (34), (35), (37), (38), (40), (41),
% 229.11/40.60  | | | | | | | | | | | | |            (42), (44), (45), (46), (72), (77) are
% 229.11/40.60  | | | | | | | | | | | | |            inconsistent by sub-proof #689.
% 229.11/40.60  | | | | | | | | | | | | | 
% 229.11/40.60  | | | | | | | | | | | | End of split
% 229.11/40.60  | | | | | | | | | | | | 
% 229.11/40.60  | | | | | | | | | | | Case 2:
% 229.11/40.60  | | | | | | | | | | | | 
% 229.11/40.60  | | | | | | | | | | | |   (78)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 229.11/40.60  | | | | | | | | | | | |           e0 & op(e2, e0) = e0)
% 229.11/40.60  | | | | | | | | | | | | 
% 229.11/40.60  | | | | | | | | | | | | BETA: splitting (78) gives:
% 229.11/40.60  | | | | | | | | | | | | 
% 229.11/40.60  | | | | | | | | | | | | Case 1:
% 229.11/40.60  | | | | | | | | | | | | | 
% 229.11/40.60  | | | | | | | | | | | | |   (79)  all_57_5 = e0 & op(e2, e1) = e0
% 229.11/40.60  | | | | | | | | | | | | | 
% 229.11/40.60  | | | | | | | | | | | | | ALPHA: (79) implies:
% 229.11/40.60  | | | | | | | | | | | | |   (80)  all_57_5 = e0
% 229.11/40.60  | | | | | | | | | | | | | 
% 229.11/40.60  | | | | | | | | | | | | | REF_CLOSE: (24), (64), (80) are inconsistent by sub-proof
% 229.11/40.60  | | | | | | | | | | | | |            #2363.
% 229.11/40.60  | | | | | | | | | | | | | 
% 229.11/40.60  | | | | | | | | | | | | Case 2:
% 229.11/40.60  | | | | | | | | | | | | | 
% 229.11/40.60  | | | | | | | | | | | | |   (81)  all_57_10 = e0 & op(e2, e0) = e0
% 229.11/40.60  | | | | | | | | | | | | | 
% 229.11/40.60  | | | | | | | | | | | | | ALPHA: (81) implies:
% 229.11/40.60  | | | | | | | | | | | | |   (82)  all_57_10 = e0
% 229.11/40.60  | | | | | | | | | | | | | 
% 229.11/40.60  | | | | | | | | | | | | | REF_CLOSE: (7), (13), (14), (17), (19), (24), (25), (40),
% 229.11/40.60  | | | | | | | | | | | | |            (41), (54), (82) are inconsistent by sub-proof
% 229.11/40.60  | | | | | | | | | | | | |            #1018.
% 229.11/40.60  | | | | | | | | | | | | | 
% 229.11/40.60  | | | | | | | | | | | | End of split
% 229.11/40.60  | | | | | | | | | | | | 
% 229.11/40.60  | | | | | | | | | | | End of split
% 229.11/40.60  | | | | | | | | | | | 
% 229.11/40.60  | | | | | | | | | | End of split
% 229.11/40.60  | | | | | | | | | | 
% 229.11/40.60  | | | | | | | | | Case 2:
% 229.11/40.60  | | | | | | | | | | 
% 229.11/40.60  | | | | | | | | | |   (83)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 &
% 229.11/40.60  | | | | | | | | | |           op(e3, e0) = e0)
% 229.11/40.60  | | | | | | | | | | 
% 229.11/40.60  | | | | | | | | | | BETA: splitting (83) gives:
% 229.11/40.60  | | | | | | | | | | 
% 229.11/40.60  | | | | | | | | | | Case 1:
% 229.11/40.60  | | | | | | | | | | | 
% 229.11/40.60  | | | | | | | | | | |   (84)  all_57_4 = e0 & op(e3, e1) = e0
% 229.11/40.60  | | | | | | | | | | | 
% 229.11/40.60  | | | | | | | | | | | REF_CLOSE: (18), (67), (84) are inconsistent by sub-proof
% 229.11/40.60  | | | | | | | | | | |            #2491.
% 229.11/40.60  | | | | | | | | | | | 
% 229.11/40.60  | | | | | | | | | | Case 2:
% 229.11/40.60  | | | | | | | | | | | 
% 229.11/40.60  | | | | | | | | | | |   (85)  all_57_9 = e0 & op(e3, e0) = e0
% 229.11/40.60  | | | | | | | | | | | 
% 229.11/40.60  | | | | | | | | | | | REF_CLOSE: (14), (28), (85) are inconsistent by sub-proof
% 229.11/40.60  | | | | | | | | | | |            #1990.
% 229.11/40.60  | | | | | | | | | | | 
% 229.11/40.60  | | | | | | | | | | End of split
% 229.11/40.60  | | | | | | | | | | 
% 229.11/40.60  | | | | | | | | | End of split
% 229.11/40.60  | | | | | | | | | 
% 229.11/40.60  | | | | | | | | Case 2:
% 229.11/40.60  | | | | | | | | | 
% 229.11/40.60  | | | | | | | | |   (86)  all_57_5 = e3 & op(e2, e1) = e3
% 229.11/40.60  | | | | | | | | | 
% 229.11/40.60  | | | | | | | | | ALPHA: (86) implies:
% 229.11/40.60  | | | | | | | | |   (87)  all_57_5 = e3
% 229.11/40.60  | | | | | | | | | 
% 229.11/40.60  | | | | | | | | | REF_CLOSE: (17), (64), (87) are inconsistent by sub-proof
% 229.11/40.60  | | | | | | | | |            #2189.
% 229.11/40.60  | | | | | | | | | 
% 229.11/40.60  | | | | | | | | End of split
% 229.11/40.60  | | | | | | | | 
% 229.11/40.60  | | | | | | | Case 2:
% 229.11/40.60  | | | | | | | | 
% 229.11/40.60  | | | | | | | |   (88)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 &
% 229.11/40.60  | | | | | | | |           op(e0, e1) = e3)
% 229.11/40.60  | | | | | | | | 
% 229.11/40.60  | | | | | | | | REF_CLOSE: (5), (7), (9), (10), (17), (18), (19), (21), (24),
% 229.11/40.60  | | | | | | | |            (28), (33), (40), (58), (88) are inconsistent by
% 229.11/40.60  | | | | | | | |            sub-proof #1044.
% 229.11/40.60  | | | | | | | | 
% 229.11/40.60  | | | | | | | End of split
% 229.11/40.60  | | | | | | | 
% 229.11/40.60  | | | | | | End of split
% 229.11/40.60  | | | | | | 
% 229.11/40.60  | | | | | Case 2:
% 229.11/40.60  | | | | | | 
% 229.11/40.61  | | | | | |   (89)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0,
% 229.11/40.61  | | | | | |             e1) = e2)
% 229.11/40.61  | | | | | | 
% 229.11/40.61  | | | | | | REF_CLOSE: (7), (22), (40), (49), (89) are inconsistent by sub-proof
% 229.11/40.61  | | | | | |            #700.
% 229.11/40.61  | | | | | | 
% 229.11/40.61  | | | | | End of split
% 229.11/40.61  | | | | | 
% 229.11/40.61  | | | | End of split
% 229.11/40.61  | | | | 
% 229.11/40.61  | | | End of split
% 229.11/40.61  | | | 
% 229.11/40.61  | | End of split
% 229.11/40.61  | | 
% 229.11/40.61  | Case 2:
% 229.11/40.61  | | 
% 229.11/40.61  | |   (90)  all_57_15 = e1 & op(e0, e0) = e1
% 229.11/40.61  | | 
% 229.11/40.61  | | ALPHA: (90) implies:
% 229.11/40.61  | |   (91)  op(e0, e0) = e1
% 229.11/40.61  | | 
% 229.11/40.61  | | REF_CLOSE: (5), (7), (32), (91) are inconsistent by sub-proof #2183.
% 229.11/40.61  | | 
% 229.11/40.61  | End of split
% 229.11/40.61  | 
% 229.11/40.61  End of proof
% 229.11/40.61  
% 229.11/40.61  Sub-proof #689 shows that the following formulas are inconsistent:
% 229.11/40.61  ----------------------------------------------------------------
% 229.11/40.61    (1)  all_57_0 = e2
% 229.11/40.61    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.11/40.61         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.11/40.61    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.11/40.61         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.11/40.61    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.11/40.61         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.11/40.61    (5)   ~ (e3 = e1)
% 229.11/40.61    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.11/40.61           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.11/40.61    (7)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.11/40.61         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.11/40.61    (8)   ~ (all_6_2 = e3)
% 229.11/40.61    (9)  op(e1, e1) = all_6_2
% 229.11/40.61    (10)  all_57_3 = e0
% 229.11/40.61    (11)   ~ (e3 = e2)
% 229.11/40.61    (12)   ~ (e3 = e0)
% 229.11/40.61    (13)  all_57_1 = e0
% 229.11/40.61    (14)  all_57_15 = e3
% 229.11/40.61    (15)  op(e3, e3) = e2
% 229.11/40.61    (16)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.11/40.61          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.11/40.61            e1)
% 229.11/40.61    (17)   ~ (e2 = e0)
% 229.11/40.61    (18)   ~ (e1 = e0)
% 229.11/40.61    (19)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.11/40.61          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.11/40.61    (20)  op(e0, e0) = e3
% 229.11/40.61    (21)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.11/40.61          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.11/40.61            e2)
% 229.11/40.61    (22)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.11/40.61              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.11/40.61                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.11/40.61                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.11/40.61    (23)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.11/40.61          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.11/40.61    (24)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.11/40.61          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.11/40.61    (25)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.11/40.61          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.11/40.61    (26)   ~ (e2 = e1)
% 229.11/40.61    (27)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.11/40.61          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.11/40.61    (28)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.11/40.61          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.11/40.61    (29)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.11/40.61          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.11/40.61    (30)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.11/40.61          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.11/40.61    (31)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.11/40.61          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.11/40.61  
% 229.11/40.61  Begin of proof
% 229.11/40.61  | 
% 229.11/40.61  | BETA: splitting (29) gives:
% 229.11/40.61  | 
% 229.11/40.61  | Case 1:
% 229.11/40.61  | | 
% 229.11/40.61  | |   (32)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) =
% 229.11/40.61  | |           e0)
% 229.11/40.61  | | 
% 229.11/40.61  | | REF_CLOSE: (2), (5), (6), (10), (11), (12), (15), (17), (18), (23), (24),
% 229.11/40.61  | |            (26), (32) are inconsistent by sub-proof #1654.
% 229.11/40.61  | | 
% 229.11/40.61  | Case 2:
% 229.11/40.61  | | 
% 229.11/40.61  | |   (33)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) =
% 229.11/40.61  | |           e0)
% 229.11/40.61  | | 
% 229.11/40.61  | | BETA: splitting (33) gives:
% 229.11/40.61  | | 
% 229.11/40.61  | | Case 1:
% 229.11/40.61  | | | 
% 229.11/40.61  | | |   (34)  all_57_6 = e0 & op(e1, e3) = e0
% 229.11/40.61  | | | 
% 229.11/40.61  | | | ALPHA: (34) implies:
% 229.11/40.61  | | |   (35)  all_57_6 = e0
% 229.11/40.61  | | | 
% 229.11/40.61  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 229.11/40.61  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 229.11/40.61  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (35) are
% 229.11/40.61  | | |            inconsistent by sub-proof #690.
% 229.11/40.61  | | | 
% 229.11/40.61  | | Case 2:
% 229.11/40.61  | | | 
% 229.11/40.61  | | |   (36)  all_57_12 = e0 & op(e0, e3) = e0
% 229.11/40.61  | | | 
% 229.11/40.61  | | | ALPHA: (36) implies:
% 229.11/40.61  | | |   (37)  all_57_12 = e0
% 229.11/40.61  | | | 
% 229.11/40.61  | | | REF_CLOSE: (4), (5), (10), (11), (12), (13), (14), (16), (17), (18), (19),
% 229.11/40.61  | | |            (21), (26), (31), (37) are inconsistent by sub-proof #694.
% 229.11/40.61  | | | 
% 229.11/40.61  | | End of split
% 229.11/40.61  | | 
% 229.11/40.61  | End of split
% 229.11/40.61  | 
% 229.11/40.61  End of proof
% 229.11/40.61  
% 229.11/40.61  Sub-proof #690 shows that the following formulas are inconsistent:
% 229.11/40.61  ----------------------------------------------------------------
% 229.11/40.61    (1)  all_57_0 = e2
% 229.11/40.61    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.11/40.61         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.11/40.61    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.11/40.61         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.11/40.61    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.11/40.61         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.11/40.61    (5)   ~ (e3 = e1)
% 229.11/40.61    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.11/40.61           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.11/40.61    (7)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.11/40.61         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.11/40.61    (8)   ~ (all_6_2 = e3)
% 229.11/40.61    (9)  op(e1, e1) = all_6_2
% 229.11/40.61    (10)  all_57_3 = e0
% 229.11/40.61    (11)   ~ (e3 = e2)
% 229.11/40.61    (12)   ~ (e3 = e0)
% 229.11/40.61    (13)  all_57_6 = e0
% 229.11/40.61    (14)  all_57_1 = e0
% 229.11/40.61    (15)  all_57_15 = e3
% 229.11/40.61    (16)  op(e3, e3) = e2
% 229.11/40.61    (17)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.11/40.61          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.11/40.61            e1)
% 229.11/40.61    (18)   ~ (e2 = e0)
% 229.11/40.61    (19)   ~ (e1 = e0)
% 229.11/40.61    (20)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.11/40.61          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.11/40.61    (21)  op(e0, e0) = e3
% 229.11/40.61    (22)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.11/40.61          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.11/40.61            e2)
% 229.11/40.61    (23)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.11/40.61              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.11/40.61                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.11/40.61                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.11/40.61    (24)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.11/40.61          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.11/40.61    (25)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.11/40.61          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.11/40.61    (26)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.11/40.61          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.11/40.61    (27)   ~ (e2 = e1)
% 229.11/40.61    (28)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.11/40.61          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.11/40.61    (29)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.11/40.61          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.11/40.61    (30)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.11/40.61          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.11/40.61    (31)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.11/40.61          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.11/40.61    (32)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.11/40.61          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.11/40.61  
% 229.11/40.61  Begin of proof
% 229.11/40.61  | 
% 229.11/40.61  | BETA: splitting (20) gives:
% 229.11/40.61  | 
% 229.11/40.61  | Case 1:
% 229.11/40.61  | | 
% 229.11/40.61  | |   (33)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 229.11/40.61  | |           e3)
% 229.11/40.61  | | 
% 229.11/40.61  | | BETA: splitting (33) gives:
% 229.11/40.61  | | 
% 229.11/40.61  | | Case 1:
% 229.11/40.61  | | | 
% 229.11/40.61  | | |   (34)  all_57_1 = e3 & op(e3, e2) = e3
% 229.11/40.61  | | | 
% 229.11/40.61  | | | ALPHA: (34) implies:
% 229.11/40.61  | | |   (35)  all_57_1 = e3
% 229.11/40.61  | | | 
% 229.11/40.61  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 229.11/40.61  | | |            (13), (15), (16), (17), (18), (19), (21), (22), (23), (24),
% 229.11/40.61  | | |            (25), (26), (27), (28), (29), (30), (31), (32), (35) are
% 229.11/40.61  | | |            inconsistent by sub-proof #789.
% 229.11/40.61  | | | 
% 229.11/40.61  | | Case 2:
% 229.11/40.61  | | | 
% 229.11/40.61  | | |   (36)  all_57_3 = e3 & op(e2, e2) = e3
% 229.11/40.61  | | | 
% 229.11/40.61  | | | ALPHA: (36) implies:
% 229.11/40.61  | | |   (37)  all_57_3 = e3
% 229.11/40.61  | | | 
% 229.11/40.61  | | | REF_CLOSE: (10), (12), (37) are inconsistent by sub-proof #2358.
% 229.11/40.61  | | | 
% 229.11/40.61  | | End of split
% 229.11/40.61  | | 
% 229.11/40.61  | Case 2:
% 229.11/40.61  | | 
% 229.11/40.61  | |   (38)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 229.11/40.61  | |           e3)
% 229.11/40.61  | | 
% 229.11/40.61  | | BETA: splitting (38) gives:
% 229.11/40.61  | | 
% 229.11/40.61  | | Case 1:
% 229.11/40.61  | | | 
% 229.11/40.61  | | |   (39)  all_57_7 = e3 & op(e1, e2) = e3
% 229.11/40.61  | | | 
% 229.11/40.61  | | | ALPHA: (39) implies:
% 229.11/40.61  | | |   (40)  all_57_7 = e3
% 229.11/40.61  | | | 
% 229.11/40.61  | | | REF_CLOSE: (4), (5), (10), (11), (14), (18), (19), (27), (32), (40) are
% 229.11/40.61  | | |            inconsistent by sub-proof #2098.
% 229.11/40.61  | | | 
% 229.11/40.61  | | Case 2:
% 229.11/40.61  | | | 
% 229.11/40.61  | | |   (41)  all_57_13 = e3 & op(e0, e2) = e3
% 229.11/40.61  | | | 
% 229.11/40.61  | | | ALPHA: (41) implies:
% 229.11/40.61  | | |   (42)  all_57_13 = e3
% 229.11/40.61  | | | 
% 229.11/40.61  | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 229.11/40.61  | | |            (14), (15), (17), (18), (19), (22), (23), (24), (25), (26),
% 229.11/40.61  | | |            (27), (28), (29), (30), (31), (32), (42) are inconsistent by
% 229.11/40.61  | | |            sub-proof #691.
% 229.11/40.61  | | | 
% 229.11/40.61  | | End of split
% 229.11/40.61  | | 
% 229.11/40.61  | End of split
% 229.11/40.61  | 
% 229.11/40.61  End of proof
% 229.11/40.61  
% 229.11/40.61  Sub-proof #691 shows that the following formulas are inconsistent:
% 229.11/40.61  ----------------------------------------------------------------
% 229.11/40.61    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.11/40.61         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.11/40.61    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.11/40.61         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.11/40.61    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.11/40.61         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.11/40.61    (4)   ~ (e3 = e1)
% 229.11/40.61    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.11/40.61           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.11/40.61    (6)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.11/40.61         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.11/40.61    (7)   ~ (all_6_2 = e3)
% 229.11/40.61    (8)  op(e1, e1) = all_6_2
% 229.11/40.61    (9)  all_57_3 = e0
% 229.11/40.61    (10)   ~ (e3 = e2)
% 229.11/40.61    (11)   ~ (e3 = e0)
% 229.11/40.61    (12)  all_57_6 = e0
% 229.11/40.61    (13)  all_57_1 = e0
% 229.11/40.61    (14)  all_57_15 = e3
% 229.11/40.61    (15)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.11/40.61          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.11/40.61            e1)
% 229.11/40.61    (16)   ~ (e2 = e0)
% 229.11/40.61    (17)   ~ (e1 = e0)
% 229.11/40.61    (18)  all_57_13 = e3
% 229.11/40.61    (19)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.11/40.61          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.11/40.61            e2)
% 229.11/40.61    (20)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.11/40.61              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.11/40.61                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.11/40.61                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.11/40.61    (21)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.11/40.61          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.11/40.61    (22)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.11/40.61          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.11/40.61    (23)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.11/40.61          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.11/40.61    (24)   ~ (e2 = e1)
% 229.11/40.61    (25)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.11/40.61          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.11/40.61    (26)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.11/40.61          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.11/40.61    (27)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.11/40.61          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.11/40.61    (28)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.11/40.61          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.11/40.61    (29)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.11/40.61          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.11/40.61  
% 229.11/40.61  Begin of proof
% 229.11/40.61  | 
% 229.11/40.61  | BETA: splitting (23) gives:
% 229.11/40.61  | 
% 229.11/40.61  | Case 1:
% 229.11/40.61  | | 
% 229.11/40.61  | |   (30)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) =
% 229.11/40.61  | |           e3)
% 229.11/40.61  | | 
% 229.11/40.61  | | BETA: splitting (30) gives:
% 229.11/40.61  | | 
% 229.11/40.61  | | Case 1:
% 229.11/40.61  | | | 
% 229.11/40.61  | | |   (31)  all_57_0 = e3 & op(e3, e3) = e3
% 229.11/40.61  | | | 
% 229.11/40.61  | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13), (14),
% 229.11/40.61  | | |            (16), (17), (20), (24), (25), (26), (27), (28), (29), (31) are
% 229.11/40.61  | | |            inconsistent by sub-proof #692.
% 229.11/40.61  | | | 
% 229.11/40.61  | | Case 2:
% 229.11/40.61  | | | 
% 229.11/40.61  | | |   (32)  all_57_2 = e3 & op(e2, e3) = e3
% 229.11/40.61  | | | 
% 229.11/40.61  | | | ALPHA: (32) implies:
% 229.11/40.61  | | |   (33)  all_57_2 = e3
% 229.11/40.61  | | | 
% 229.11/40.61  | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 229.11/40.61  | | |            (14), (16), (17), (20), (21), (22), (24), (25), (28), (29),
% 229.11/40.61  | | |            (33) are inconsistent by sub-proof #826.
% 229.11/40.61  | | | 
% 229.11/40.61  | | End of split
% 229.11/40.61  | | 
% 229.11/40.61  | Case 2:
% 229.11/40.61  | | 
% 229.11/40.61  | |   (34)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) =
% 229.11/40.61  | |           e3)
% 229.11/40.61  | | 
% 229.11/40.61  | | REF_CLOSE: (4), (10), (11), (12), (14), (15), (16), (17), (18), (19), (20),
% 229.11/40.61  | |            (24), (34) are inconsistent by sub-proof #786.
% 229.11/40.61  | | 
% 229.11/40.61  | End of split
% 229.11/40.61  | 
% 229.11/40.61  End of proof
% 229.11/40.61  
% 229.11/40.61  Sub-proof #692 shows that the following formulas are inconsistent:
% 229.11/40.61  ----------------------------------------------------------------
% 229.11/40.61    (1)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.11/40.61         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.11/40.61    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.11/40.61         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.11/40.61    (3)   ~ (e3 = e1)
% 229.11/40.61    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.11/40.61           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.11/40.61    (5)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.11/40.61         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.11/40.61    (6)   ~ (all_6_2 = e3)
% 229.11/40.61    (7)  op(e1, e1) = all_6_2
% 229.11/40.61    (8)  all_57_3 = e0
% 229.11/40.61    (9)   ~ (e3 = e2)
% 229.11/40.61    (10)   ~ (e3 = e0)
% 229.11/40.61    (11)  all_57_1 = e0
% 229.11/40.61    (12)  all_57_15 = e3
% 229.11/40.61    (13)   ~ (e2 = e0)
% 229.11/40.61    (14)   ~ (e1 = e0)
% 229.11/40.61    (15)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.11/40.61              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.11/40.61                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.11/40.61                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.11/40.61    (16)   ~ (e2 = e1)
% 229.11/40.61    (17)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.11/40.61          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.11/40.61    (18)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.11/40.61          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.11/40.61    (19)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.11/40.61          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.11/40.61    (20)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.11/40.61          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.11/40.61    (21)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.11/40.61          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.11/40.61    (22)  all_57_0 = e3 & op(e3, e3) = e3
% 229.11/40.61  
% 229.11/40.61  Begin of proof
% 229.11/40.61  | 
% 229.11/40.61  | ALPHA: (22) implies:
% 229.11/40.61  |   (23)  all_57_0 = e3
% 229.11/40.61  | 
% 229.11/40.61  | BETA: splitting (5) gives:
% 229.11/40.61  | 
% 229.11/40.61  | Case 1:
% 229.11/40.61  | | 
% 229.11/40.61  | |   (24)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 229.11/40.61  | |           e3)
% 229.11/40.61  | | 
% 229.11/40.61  | | BETA: splitting (24) gives:
% 229.11/40.61  | | 
% 229.11/40.61  | | Case 1:
% 229.11/40.61  | | | 
% 229.11/40.61  | | |   (25)  all_57_6 = e3 & op(e1, e3) = e3
% 229.11/40.61  | | | 
% 229.11/40.61  | | | ALPHA: (25) implies:
% 229.11/40.61  | | |   (26)  all_57_6 = e3
% 229.11/40.61  | | | 
% 229.11/40.61  | | | REF_CLOSE: (1), (3), (9), (10), (13), (14), (16), (18), (19), (23), (26)
% 229.11/40.61  | | |            are inconsistent by sub-proof #2010.
% 229.11/40.61  | | | 
% 229.11/40.61  | | Case 2:
% 229.11/40.61  | | | 
% 229.11/40.61  | | |   (27)  all_57_7 = e3 & op(e1, e2) = e3
% 229.11/40.61  | | | 
% 229.11/40.61  | | | ALPHA: (27) implies:
% 229.11/40.61  | | |   (28)  all_57_7 = e3
% 229.11/40.61  | | | 
% 229.11/40.61  | | | REF_CLOSE: (2), (3), (8), (9), (11), (13), (14), (16), (21), (28) are
% 229.11/40.61  | | |            inconsistent by sub-proof #2098.
% 229.11/40.61  | | | 
% 229.11/40.61  | | End of split
% 229.11/40.61  | | 
% 229.11/40.61  | Case 2:
% 229.11/40.61  | | 
% 229.11/40.61  | |   (29)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 229.11/40.61  | |           e3)
% 229.11/40.61  | | 
% 229.11/40.61  | | REF_CLOSE: (3), (4), (6), (7), (9), (10), (12), (13), (14), (15), (16),
% 229.11/40.61  | |            (17), (20), (29) are inconsistent by sub-proof #1786.
% 229.11/40.61  | | 
% 229.11/40.61  | End of split
% 229.11/40.61  | 
% 229.11/40.61  End of proof
% 229.11/40.61  
% 229.11/40.61  Sub-proof #693 shows that the following formulas are inconsistent:
% 229.11/40.61  ----------------------------------------------------------------
% 229.11/40.61    (1)  all_57_0 = e2
% 229.11/40.61    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.11/40.61         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.11/40.61    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.11/40.61         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.11/40.61    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.11/40.61         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.11/40.61    (5)   ~ (e3 = e1)
% 229.11/40.61    (6)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 229.11/40.61         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 229.11/40.61    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.11/40.61           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.11/40.61    (8)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.11/40.61         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.11/40.61    (9)   ~ (all_6_2 = e3)
% 229.11/40.61    (10)  op(e1, e1) = all_6_2
% 229.11/40.61    (11)  op(e2, e2) = e1
% 229.11/40.61    (12)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.11/40.61          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.11/40.61    (13)  all_57_9 = e1
% 229.11/40.61    (14)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.11/40.61          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.11/40.61    (15)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.11/40.61          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.11/40.61    (16)   ~ (e3 = e2)
% 229.11/40.61    (17)   ~ (e3 = e0)
% 229.11/40.61    (18)  all_57_15 = e3
% 229.11/40.61    (19)  all_57_6 = e1 & op(e1, e3) = e1
% 229.11/40.61    (20)  op(e3, e3) = e2
% 229.11/40.61    (21)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.11/40.61          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.11/40.61            e1)
% 229.11/40.61    (22)  op(e1, e1) = e1
% 229.11/40.61    (23)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.11/40.61          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.11/40.61    (24)   ~ (e2 = e0)
% 229.11/40.61    (25)  all_57_3 = e1
% 229.11/40.61    (26)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.11/40.61          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.11/40.61    (27)   ~ (e1 = e0)
% 229.11/40.61    (28)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.11/40.61          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.11/40.61    (29)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.11/40.61          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.11/40.61    (30)  all_57_14 = e1
% 229.11/40.61    (31)  op(e0, e0) = e3
% 229.11/40.61    (32)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.11/40.61          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.11/40.61            e2)
% 229.11/40.61    (33)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.11/40.61              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.11/40.61                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.11/40.61                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.11/40.61    (34)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.11/40.61          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.11/40.61    (35)   ~ (all_53_12 = e3)
% 229.11/40.61    (36)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.11/40.61          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.11/40.61    (37)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.11/40.61          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.11/40.61    (38)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.11/40.61          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 229.11/40.61    (39)   ~ (e2 = e1)
% 229.11/40.61    (40)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.11/40.61          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.11/40.61    (41)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.11/40.61          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.11/40.61    (42)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 229.11/40.61          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 229.11/40.62    (43)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.11/40.62          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.11/40.62    (44)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.11/40.62          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.11/40.62    (45)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.11/40.62          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.11/40.62    (46)  op(e3, e0) = all_53_12
% 229.11/40.62  
% 229.11/40.62  Begin of proof
% 229.11/40.62  | 
% 229.11/40.62  | ALPHA: (19) implies:
% 229.11/40.62  |   (47)  all_57_6 = e1
% 229.11/40.62  | 
% 229.11/40.62  | BETA: splitting (42) gives:
% 229.11/40.62  | 
% 229.11/40.62  | Case 1:
% 229.11/40.62  | | 
% 229.11/40.62  | |   (48)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) =
% 229.11/40.62  | |           e2)
% 229.11/40.62  | | 
% 229.11/40.62  | | BETA: splitting (48) gives:
% 229.11/40.62  | | 
% 229.11/40.62  | | Case 1:
% 229.11/40.62  | | | 
% 229.11/40.62  | | |   (49)  all_57_4 = e2 & op(e3, e1) = e2
% 229.11/40.62  | | | 
% 229.11/40.62  | | | ALPHA: (49) implies:
% 229.11/40.62  | | |   (50)  all_57_4 = e2
% 229.11/40.62  | | | 
% 229.11/40.62  | | | BETA: splitting (26) gives:
% 229.11/40.62  | | | 
% 229.11/40.62  | | | Case 1:
% 229.11/40.62  | | | | 
% 229.11/40.62  | | | |   (51)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2)
% 229.11/40.62  | | | |           = e3)
% 229.11/40.62  | | | | 
% 229.11/40.62  | | | | BETA: splitting (51) gives:
% 229.11/40.62  | | | | 
% 229.11/40.62  | | | | Case 1:
% 229.11/40.62  | | | | | 
% 229.11/40.62  | | | | |   (52)  all_57_0 = e3 & op(e3, e3) = e3
% 229.11/40.62  | | | | | 
% 229.11/40.62  | | | | | ALPHA: (52) implies:
% 229.11/40.62  | | | | |   (53)  op(e3, e3) = e3
% 229.11/40.62  | | | | | 
% 229.11/40.62  | | | | | REF_CLOSE: (7), (16), (20), (53) are inconsistent by sub-proof #2490.
% 229.11/40.62  | | | | | 
% 229.11/40.62  | | | | Case 2:
% 229.11/40.62  | | | | | 
% 229.11/40.62  | | | | |   (54)  all_57_1 = e3 & op(e3, e2) = e3
% 229.11/40.62  | | | | | 
% 229.11/40.62  | | | | | ALPHA: (54) implies:
% 229.11/40.62  | | | | |   (55)  all_57_1 = e3
% 229.11/40.62  | | | | | 
% 229.11/40.62  | | | | | BETA: splitting (15) gives:
% 229.11/40.62  | | | | | 
% 229.11/40.62  | | | | | Case 1:
% 229.11/40.62  | | | | | | 
% 229.11/40.62  | | | | | |   (56)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3,
% 229.11/40.62  | | | | | |             e2) = e0)
% 229.11/40.62  | | | | | | 
% 229.11/40.62  | | | | | | REF_CLOSE: (7), (16), (17), (20), (24), (26), (35), (46), (50), (56)
% 229.11/40.62  | | | | | |            are inconsistent by sub-proof #874.
% 229.11/40.62  | | | | | | 
% 229.11/40.62  | | | | | Case 2:
% 229.11/40.62  | | | | | | 
% 229.11/40.62  | | | | | |   (57)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3,
% 229.11/40.62  | | | | | |             e0) = e0)
% 229.11/40.62  | | | | | | 
% 229.11/40.62  | | | | | | BETA: splitting (57) gives:
% 229.11/40.62  | | | | | | 
% 229.11/40.62  | | | | | | Case 1:
% 229.11/40.62  | | | | | | | 
% 229.11/40.62  | | | | | | |   (58)  all_57_4 = e0 & op(e3, e1) = e0
% 229.11/40.62  | | | | | | | 
% 229.11/40.62  | | | | | | | REF_CLOSE: (24), (50), (58) are inconsistent by sub-proof #2045.
% 229.11/40.62  | | | | | | | 
% 229.11/40.62  | | | | | | Case 2:
% 229.11/40.62  | | | | | | | 
% 229.11/40.62  | | | | | | |   (59)  all_57_9 = e0 & op(e3, e0) = e0
% 229.11/40.62  | | | | | | | 
% 229.11/40.62  | | | | | | | ALPHA: (59) implies:
% 229.11/40.62  | | | | | | |   (60)  all_57_9 = e0
% 229.11/40.62  | | | | | | | 
% 229.11/40.62  | | | | | | | COMBINE_EQS: (13), (60) imply:
% 229.11/40.62  | | | | | | |   (61)  e1 = e0
% 229.11/40.62  | | | | | | | 
% 229.11/40.62  | | | | | | | COMBINE_EQS: (47), (61) imply:
% 229.11/40.62  | | | | | | |   (62)  all_57_6 = e0
% 229.11/40.62  | | | | | | | 
% 229.11/40.62  | | | | | | | COMBINE_EQS: (25), (61) imply:
% 229.11/40.62  | | | | | | |   (63)  all_57_3 = e0
% 229.11/40.62  | | | | | | | 
% 229.11/40.62  | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (16),
% 229.11/40.62  | | | | | | |            (17), (18), (20), (21), (24), (27), (31), (32), (33),
% 229.11/40.62  | | | | | | |            (34), (36), (37), (39), (40), (41), (43), (44), (45),
% 229.11/40.62  | | | | | | |            (55), (62), (63) are inconsistent by sub-proof #789.
% 229.11/40.62  | | | | | | | 
% 229.11/40.62  | | | | | | End of split
% 229.11/40.62  | | | | | | 
% 229.11/40.62  | | | | | End of split
% 229.11/40.62  | | | | | 
% 229.11/40.62  | | | | End of split
% 229.11/40.62  | | | | 
% 229.11/40.62  | | | Case 2:
% 229.11/40.62  | | | | 
% 229.11/40.62  | | | |   (64)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0)
% 229.11/40.62  | | | |           = e3)
% 229.11/40.62  | | | | 
% 229.11/40.62  | | | | REF_CLOSE: (7), (16), (35), (46), (50), (64) are inconsistent by
% 229.11/40.62  | | | |            sub-proof #2448.
% 229.11/40.62  | | | | 
% 229.11/40.62  | | | End of split
% 229.11/40.62  | | | 
% 229.11/40.62  | | Case 2:
% 229.11/40.62  | | | 
% 229.11/40.62  | | |   (65)  all_57_5 = e2 & op(e2, e1) = e2
% 229.11/40.62  | | | 
% 229.11/40.62  | | | ALPHA: (65) implies:
% 229.11/40.62  | | |   (66)  all_57_5 = e2
% 229.11/40.62  | | | 
% 229.11/40.62  | | | BETA: splitting (28) gives:
% 229.11/40.62  | | | 
% 229.11/40.62  | | | Case 1:
% 229.11/40.62  | | | | 
% 229.11/40.62  | | | |   (67)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1)
% 229.11/40.62  | | | |           = e3)
% 229.11/40.62  | | | | 
% 229.11/40.62  | | | | BETA: splitting (67) gives:
% 229.11/40.62  | | | | 
% 229.11/40.62  | | | | Case 1:
% 229.11/40.62  | | | | | 
% 229.11/40.62  | | | | |   (68)  all_57_4 = e3 & op(e3, e1) = e3
% 229.11/40.62  | | | | | 
% 229.11/40.62  | | | | | ALPHA: (68) implies:
% 229.11/40.62  | | | | |   (69)  all_57_4 = e3
% 229.11/40.62  | | | | | 
% 229.11/40.62  | | | | | BETA: splitting (15) gives:
% 229.11/40.62  | | | | | 
% 229.11/40.62  | | | | | Case 1:
% 229.11/40.62  | | | | | | 
% 229.11/40.62  | | | | | |   (70)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3,
% 229.11/40.62  | | | | | |             e2) = e0)
% 229.11/40.62  | | | | | | 
% 229.11/40.62  | | | | | | BETA: splitting (70) gives:
% 229.11/40.62  | | | | | | 
% 229.11/40.62  | | | | | | Case 1:
% 229.11/40.62  | | | | | | | 
% 229.11/40.62  | | | | | | |   (71)  all_57_0 = e0 & op(e3, e3) = e0
% 229.11/40.62  | | | | | | | 
% 229.11/40.62  | | | | | | | ALPHA: (71) implies:
% 229.11/40.62  | | | | | | |   (72)  op(e3, e3) = e0
% 229.11/40.62  | | | | | | | 
% 229.11/40.62  | | | | | | | REF_CLOSE: (7), (20), (24), (72) are inconsistent by sub-proof
% 229.11/40.62  | | | | | | |            #2403.
% 229.11/40.62  | | | | | | | 
% 229.11/40.62  | | | | | | Case 2:
% 229.11/40.62  | | | | | | | 
% 229.11/40.62  | | | | | | |   (73)  all_57_1 = e0 & op(e3, e2) = e0
% 229.11/40.62  | | | | | | | 
% 229.11/40.62  | | | | | | | ALPHA: (73) implies:
% 229.11/40.62  | | | | | | |   (74)  all_57_1 = e0
% 229.11/40.62  | | | | | | | 
% 229.11/40.62  | | | | | | | BETA: splitting (34) gives:
% 229.11/40.62  | | | | | | | 
% 229.11/40.62  | | | | | | | Case 1:
% 229.11/40.62  | | | | | | | | 
% 229.11/40.62  | | | | | | | |   (75)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 &
% 229.11/40.62  | | | | | | | |           op(e2, e2) = e3)
% 229.11/40.62  | | | | | | | | 
% 229.11/40.62  | | | | | | | | BETA: splitting (75) gives:
% 229.11/40.62  | | | | | | | | 
% 229.11/40.62  | | | | | | | | Case 1:
% 229.11/40.62  | | | | | | | | | 
% 229.11/40.62  | | | | | | | | |   (76)  all_57_2 = e3 & op(e2, e3) = e3
% 229.11/40.62  | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | ALPHA: (76) implies:
% 229.11/40.62  | | | | | | | | |   (77)  all_57_2 = e3
% 229.11/40.62  | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | BETA: splitting (43) gives:
% 229.11/40.62  | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | Case 1:
% 229.11/40.62  | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | |   (78)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 &
% 229.11/40.62  | | | | | | | | | |           op(e2, e3) = e0)
% 229.11/40.62  | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | | BETA: splitting (78) gives:
% 229.11/40.62  | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | | Case 1:
% 229.11/40.62  | | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | | |   (79)  all_57_0 = e0 & op(e3, e3) = e0
% 229.11/40.62  | | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | | | ALPHA: (79) implies:
% 229.11/40.62  | | | | | | | | | | |   (80)  all_57_0 = e0
% 229.11/40.62  | | | | | | | | | | |   (81)  op(e3, e3) = e0
% 229.11/40.62  | | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (11), (12), (14), (16), (17), (18),
% 229.11/40.62  | | | | | | | | | | |            (21), (23), (24), (25), (26), (27), (29), (31),
% 229.11/40.62  | | | | | | | | | | |            (32), (33), (35), (39), (45), (46), (74), (80),
% 229.11/40.62  | | | | | | | | | | |            (81) are inconsistent by sub-proof #824.
% 229.11/40.62  | | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | | Case 2:
% 229.11/40.62  | | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | | |   (82)  all_57_2 = e0 & op(e2, e3) = e0
% 229.11/40.62  | | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | | | REF_CLOSE: (2), (5), (7), (9), (10), (11), (13), (15), (16),
% 229.11/40.62  | | | | | | | | | | |            (17), (18), (20), (21), (24), (25), (26), (27),
% 229.11/40.62  | | | | | | | | | | |            (28), (31), (32), (33), (34), (35), (36), (39),
% 229.11/40.62  | | | | | | | | | | |            (40), (46), (66), (82) are inconsistent by
% 229.11/40.62  | | | | | | | | | | |            sub-proof #696.
% 229.11/40.62  | | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | | End of split
% 229.11/40.62  | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | Case 2:
% 229.11/40.62  | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | |   (83)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0
% 229.11/40.62  | | | | | | | | | |           & op(e0, e3) = e0)
% 229.11/40.62  | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | | BETA: splitting (83) gives:
% 229.11/40.62  | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | | Case 1:
% 229.11/40.62  | | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | | |   (84)  all_57_6 = e0 & op(e1, e3) = e0
% 229.11/40.62  | | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | | | REF_CLOSE: (2), (4), (5), (7), (8), (9), (10), (16), (17),
% 229.11/40.62  | | | | | | | | | | |            (18), (24), (25), (27), (33), (34), (36), (39),
% 229.11/40.62  | | | | | | | | | | |            (40), (44), (45), (47), (74), (77), (84) are
% 229.11/40.62  | | | | | | | | | | |            inconsistent by sub-proof #695.
% 229.11/40.62  | | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | | Case 2:
% 229.11/40.62  | | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | | |   (85)  all_57_12 = e0 & op(e0, e3) = e0
% 229.11/40.62  | | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | | | ALPHA: (85) implies:
% 229.11/40.62  | | | | | | | | | | |   (86)  all_57_12 = e0
% 229.11/40.62  | | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | | | BETA: splitting (38) gives:
% 229.11/40.62  | | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | | | Case 1:
% 229.11/40.62  | | | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | | | |   (87)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 229.11/40.62  | | | | | | | | | | | |           & op(e2, e2) = e0)
% 229.11/40.62  | | | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | | | | BETA: splitting (87) gives:
% 229.11/40.62  | | | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | | | | Case 1:
% 229.11/40.62  | | | | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | | | | |   (88)  all_57_2 = e0 & op(e2, e3) = e0
% 229.11/40.62  | | | | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | | | | | REF_CLOSE: (2), (5), (7), (9), (10), (11), (13), (15), (16),
% 229.11/40.62  | | | | | | | | | | | | |            (17), (18), (20), (21), (24), (25), (26), (27),
% 229.11/40.62  | | | | | | | | | | | | |            (28), (31), (32), (33), (34), (35), (36), (39),
% 229.11/40.62  | | | | | | | | | | | | |            (40), (46), (66), (88) are inconsistent by
% 229.11/40.62  | | | | | | | | | | | | |            sub-proof #696.
% 229.11/40.62  | | | | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | | | | Case 2:
% 229.11/40.62  | | | | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | | | | |   (89)  all_57_3 = e0 & op(e2, e2) = e0
% 229.11/40.62  | | | | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | | | | | ALPHA: (89) implies:
% 229.11/40.62  | | | | | | | | | | | | |   (90)  all_57_3 = e0
% 229.11/40.62  | | | | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (16), (17), (18), (21), (24), (27),
% 229.11/40.62  | | | | | | | | | | | | |            (29), (32), (39), (45), (74), (86), (90) are
% 229.11/40.62  | | | | | | | | | | | | |            inconsistent by sub-proof #694.
% 229.11/40.62  | | | | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | | | | End of split
% 229.11/40.62  | | | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | | | Case 2:
% 229.11/40.62  | | | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | | | |   (91)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 229.11/40.62  | | | | | | | | | | | |           e0 & op(e2, e0) = e0)
% 229.11/40.62  | | | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | | | | BETA: splitting (91) gives:
% 229.11/40.62  | | | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | | | | Case 1:
% 229.11/40.62  | | | | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | | | | |   (92)  all_57_5 = e0 & op(e2, e1) = e0
% 229.11/40.62  | | | | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | | | | | ALPHA: (92) implies:
% 229.11/40.62  | | | | | | | | | | | | |   (93)  all_57_5 = e0
% 229.11/40.62  | | | | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | | | | | REF_CLOSE: (24), (66), (93) are inconsistent by sub-proof
% 229.11/40.62  | | | | | | | | | | | | |            #2363.
% 229.11/40.62  | | | | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | | | | Case 2:
% 229.11/40.62  | | | | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | | | | |   (94)  all_57_10 = e0 & op(e2, e0) = e0
% 229.11/40.62  | | | | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | | | | | ALPHA: (94) implies:
% 229.11/40.62  | | | | | | | | | | | | |   (95)  all_57_10 = e0
% 229.11/40.62  | | | | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | | | | | BETA: splitting (6) gives:
% 229.11/40.62  | | | | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | | | | | Case 1:
% 229.11/40.62  | | | | | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | | | | | |   (96)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 229.11/40.62  | | | | | | | | | | | | | |           & op(e1, e2) = e0)
% 229.11/40.62  | | | | | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | | | | | | BETA: splitting (96) gives:
% 229.11/40.62  | | | | | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | | | | | | Case 1:
% 229.11/40.62  | | | | | | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | | | | | | |   (97)  all_57_6 = e0 & op(e1, e3) = e0
% 229.11/40.62  | | | | | | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (5), (7), (8), (9), (10), (16), (17),
% 229.11/40.62  | | | | | | | | | | | | | | |            (18), (24), (25), (27), (33), (34), (36), (39),
% 229.11/40.62  | | | | | | | | | | | | | | |            (40), (44), (45), (47), (74), (77), (97) are
% 229.11/40.62  | | | | | | | | | | | | | | |            inconsistent by sub-proof #695.
% 229.11/40.62  | | | | | | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | | | | | | Case 2:
% 229.11/40.62  | | | | | | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | | | | | | |   (98)  all_57_7 = e0 & op(e1, e2) = e0
% 229.11/40.62  | | | | | | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | | | | | | | ALPHA: (98) implies:
% 229.11/40.62  | | | | | | | | | | | | | | |   (99)  all_57_7 = e0
% 229.11/40.62  | | | | | | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (9), (10), (16), (17), (18), (24),
% 229.11/40.62  | | | | | | | | | | | | | | |            (27), (33), (39), (40), (44), (47), (99) are
% 229.11/40.62  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1735.
% 229.11/40.62  | | | | | | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | | | | | | End of split
% 229.11/40.62  | | | | | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | | | | | Case 2:
% 229.11/40.62  | | | | | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | | | | | |   (100)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 229.11/40.62  | | | | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 229.11/40.62  | | | | | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | | | | | | BETA: splitting (100) gives:
% 229.11/40.62  | | | | | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | | | | | | Case 1:
% 229.11/40.62  | | | | | | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | | | | | | |   (101)  all_57_8 = e0 & op(e1, e1) = e0
% 229.11/40.62  | | | | | | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | | | | | | | ALPHA: (101) implies:
% 229.11/40.62  | | | | | | | | | | | | | | |   (102)  op(e1, e1) = e0
% 229.11/40.62  | | | | | | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | | | | | | | REF_CLOSE: (7), (22), (27), (102) are inconsistent by
% 229.11/40.62  | | | | | | | | | | | | | | |            sub-proof #2427.
% 229.11/40.62  | | | | | | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | | | | | | Case 2:
% 229.11/40.62  | | | | | | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | | | | | | |   (103)  all_57_11 = e0 & op(e1, e0) = e0
% 229.11/40.62  | | | | | | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | | | | | | | ALPHA: (103) implies:
% 229.11/40.62  | | | | | | | | | | | | | | |   (104)  all_57_11 = e0
% 229.11/40.62  | | | | | | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (16), (18), (24), (27), (31), (39),
% 229.11/40.62  | | | | | | | | | | | | | | |            (40), (44), (95), (104) are inconsistent by
% 229.11/40.62  | | | | | | | | | | | | | | |            sub-proof #1087.
% 229.11/40.62  | | | | | | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | | | | | | End of split
% 229.11/40.62  | | | | | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | | | | | End of split
% 229.11/40.62  | | | | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | | | | End of split
% 229.11/40.62  | | | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | | | End of split
% 229.11/40.62  | | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | | End of split
% 229.11/40.62  | | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | End of split
% 229.11/40.62  | | | | | | | | | 
% 229.11/40.62  | | | | | | | | Case 2:
% 229.11/40.62  | | | | | | | | | 
% 229.11/40.62  | | | | | | | | |   (105)  all_57_3 = e3 & op(e2, e2) = e3
% 229.11/40.62  | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | ALPHA: (105) implies:
% 229.11/40.62  | | | | | | | | |   (106)  op(e2, e2) = e3
% 229.11/40.62  | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | REF_CLOSE: (5), (7), (11), (106) are inconsistent by sub-proof
% 229.11/40.62  | | | | | | | | |            #1912.
% 229.11/40.62  | | | | | | | | | 
% 229.11/40.62  | | | | | | | | End of split
% 229.11/40.62  | | | | | | | | 
% 229.11/40.62  | | | | | | | Case 2:
% 229.11/40.62  | | | | | | | | 
% 229.11/40.62  | | | | | | | |   (107)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 &
% 229.11/40.62  | | | | | | | |            op(e2, e0) = e3)
% 229.11/40.62  | | | | | | | | 
% 229.11/40.62  | | | | | | | | BETA: splitting (107) gives:
% 229.11/40.62  | | | | | | | | 
% 229.11/40.62  | | | | | | | | Case 1:
% 229.11/40.62  | | | | | | | | | 
% 229.11/40.62  | | | | | | | | |   (108)  all_57_5 = e3 & op(e2, e1) = e3
% 229.11/40.62  | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | ALPHA: (108) implies:
% 229.11/40.62  | | | | | | | | |   (109)  all_57_5 = e3
% 229.11/40.62  | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | COMBINE_EQS: (66), (109) imply:
% 229.11/40.62  | | | | | | | | |   (110)  e3 = e2
% 229.11/40.62  | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | SIMP: (110) implies:
% 229.11/40.62  | | | | | | | | |   (111)  e3 = e2
% 229.11/40.62  | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | COMBINE_EQS: (69), (111) imply:
% 229.11/40.62  | | | | | | | | |   (112)  all_57_4 = e2
% 229.11/40.62  | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | REF_CLOSE: (7), (16), (17), (20), (26), (35), (46), (74),
% 229.11/40.62  | | | | | | | | |            (112) are inconsistent by sub-proof #875.
% 229.11/40.62  | | | | | | | | | 
% 229.11/40.62  | | | | | | | | Case 2:
% 229.11/40.62  | | | | | | | | | 
% 229.11/40.62  | | | | | | | | |   (113)  all_57_10 = e3 & op(e2, e0) = e3
% 229.11/40.62  | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | ALPHA: (113) implies:
% 229.11/40.62  | | | | | | | | |   (114)  all_57_10 = e3
% 229.11/40.62  | | | | | | | | | 
% 229.11/40.62  | | | | | | | | | REF_CLOSE: (13), (16), (17), (18), (24), (27), (33), (39),
% 229.11/40.62  | | | | | | | | |            (40), (114) are inconsistent by sub-proof #1985.
% 229.11/40.62  | | | | | | | | | 
% 229.11/40.62  | | | | | | | | End of split
% 229.11/40.62  | | | | | | | | 
% 229.11/40.62  | | | | | | | End of split
% 229.11/40.62  | | | | | | | 
% 229.11/40.62  | | | | | | End of split
% 229.11/40.62  | | | | | | 
% 229.11/40.62  | | | | | Case 2:
% 229.11/40.62  | | | | | | 
% 229.11/40.62  | | | | | |   (115)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3,
% 229.11/40.62  | | | | | |              e0) = e0)
% 229.11/40.62  | | | | | | 
% 229.11/40.62  | | | | | | BETA: splitting (115) gives:
% 229.11/40.62  | | | | | | 
% 229.11/40.62  | | | | | | Case 1:
% 229.11/40.62  | | | | | | | 
% 229.11/40.62  | | | | | | |   (116)  all_57_4 = e0 & op(e3, e1) = e0
% 229.11/40.62  | | | | | | | 
% 229.11/40.62  | | | | | | | REF_CLOSE: (17), (69), (116) are inconsistent by sub-proof #2491.
% 229.11/40.62  | | | | | | | 
% 229.11/40.62  | | | | | | Case 2:
% 229.11/40.62  | | | | | | | 
% 229.11/40.62  | | | | | | |   (117)  all_57_9 = e0 & op(e3, e0) = e0
% 229.11/40.62  | | | | | | | 
% 229.11/40.62  | | | | | | | REF_CLOSE: (13), (27), (117) are inconsistent by sub-proof #1990.
% 229.11/40.62  | | | | | | | 
% 229.11/40.62  | | | | | | End of split
% 229.11/40.62  | | | | | | 
% 229.11/40.62  | | | | | End of split
% 229.11/40.62  | | | | | 
% 229.11/40.62  | | | | Case 2:
% 229.11/40.62  | | | | | 
% 229.11/40.62  | | | | |   (118)  all_57_5 = e3 & op(e2, e1) = e3
% 229.11/40.62  | | | | | 
% 229.11/40.62  | | | | | ALPHA: (118) implies:
% 229.11/40.62  | | | | |   (119)  all_57_5 = e3
% 229.11/40.62  | | | | | 
% 229.11/40.62  | | | | | REF_CLOSE: (16), (66), (119) are inconsistent by sub-proof #2189.
% 229.11/40.62  | | | | | 
% 229.11/40.62  | | | | End of split
% 229.11/40.62  | | | | 
% 229.11/40.62  | | | Case 2:
% 229.11/40.62  | | | | 
% 229.11/40.62  | | | |   (120)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0,
% 229.11/40.62  | | | |              e1) = e3)
% 229.11/40.62  | | | | 
% 229.11/40.62  | | | | REF_CLOSE: (5), (7), (9), (10), (16), (17), (18), (21), (24), (27),
% 229.11/40.62  | | | |            (32), (33), (39), (120) are inconsistent by sub-proof #1794.
% 229.11/40.62  | | | | 
% 229.11/40.62  | | | End of split
% 229.11/40.62  | | | 
% 229.11/40.62  | | End of split
% 229.11/40.62  | | 
% 229.11/40.62  | Case 2:
% 229.11/40.62  | | 
% 229.11/40.62  | |   (121)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) =
% 229.11/40.62  | |            e2)
% 229.11/40.62  | | 
% 229.11/40.62  | | REF_CLOSE: (7), (22), (30), (39), (121) are inconsistent by sub-proof #700.
% 229.11/40.62  | | 
% 229.11/40.62  | End of split
% 229.11/40.62  | 
% 229.11/40.62  End of proof
% 229.11/40.62  
% 229.11/40.62  Sub-proof #694 shows that the following formulas are inconsistent:
% 229.11/40.62  ----------------------------------------------------------------
% 229.11/40.62    (1)  all_57_12 = e0
% 229.11/40.62    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.11/40.62         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.11/40.62    (3)   ~ (e3 = e1)
% 229.11/40.62    (4)  all_57_3 = e0
% 229.11/40.62    (5)   ~ (e3 = e2)
% 229.11/40.62    (6)   ~ (e3 = e0)
% 229.11/40.62    (7)  all_57_1 = e0
% 229.11/40.62    (8)  all_57_15 = e3
% 229.11/40.62    (9)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 229.11/40.62         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.11/40.62    (10)   ~ (e2 = e0)
% 229.11/40.62    (11)   ~ (e1 = e0)
% 229.11/40.62    (12)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.11/40.62          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.11/40.62    (13)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.11/40.62          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.11/40.62            e2)
% 229.11/40.62    (14)   ~ (e2 = e1)
% 229.11/40.62    (15)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.11/40.62          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.11/40.62  
% 229.11/40.62  Begin of proof
% 229.11/40.62  | 
% 229.11/40.62  | BETA: splitting (12) gives:
% 229.11/40.62  | 
% 229.11/40.62  | Case 1:
% 229.11/40.62  | | 
% 229.11/40.62  | |   (16)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 229.11/40.62  | |           e3)
% 229.11/40.62  | | 
% 229.11/40.62  | | REF_CLOSE: (4), (6), (7), (16) are inconsistent by sub-proof #1284.
% 229.11/40.62  | | 
% 229.11/40.62  | Case 2:
% 229.11/40.62  | | 
% 229.11/40.62  | |   (17)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 229.11/40.62  | |           e3)
% 229.11/40.62  | | 
% 229.11/40.62  | | BETA: splitting (17) gives:
% 229.11/40.62  | | 
% 229.11/40.62  | | Case 1:
% 229.11/40.62  | | | 
% 229.11/40.62  | | |   (18)  all_57_7 = e3 & op(e1, e2) = e3
% 229.11/40.62  | | | 
% 229.11/40.62  | | | ALPHA: (18) implies:
% 229.11/40.62  | | |   (19)  all_57_7 = e3
% 229.11/40.62  | | | 
% 229.11/40.62  | | | REF_CLOSE: (2), (3), (4), (5), (7), (10), (11), (14), (15), (19) are
% 229.11/40.62  | | |            inconsistent by sub-proof #2098.
% 229.11/40.62  | | | 
% 229.11/40.62  | | Case 2:
% 229.11/40.62  | | | 
% 229.11/40.62  | | |   (20)  all_57_13 = e3 & op(e0, e2) = e3
% 229.11/40.62  | | | 
% 229.11/40.62  | | | ALPHA: (20) implies:
% 229.11/40.62  | | |   (21)  all_57_13 = e3
% 229.11/40.62  | | | 
% 229.11/40.62  | | | REF_CLOSE: (1), (3), (5), (8), (9), (10), (11), (13), (14), (21) are
% 229.11/40.62  | | |            inconsistent by sub-proof #2059.
% 229.11/40.62  | | | 
% 229.11/40.62  | | End of split
% 229.11/40.62  | | 
% 229.11/40.62  | End of split
% 229.11/40.62  | 
% 229.11/40.62  End of proof
% 229.11/40.62  
% 229.11/40.62  Sub-proof #695 shows that the following formulas are inconsistent:
% 229.11/40.62  ----------------------------------------------------------------
% 229.11/40.62    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.11/40.62         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.11/40.62    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.11/40.62         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.11/40.62    (3)   ~ (e3 = e1)
% 229.11/40.62    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.11/40.62           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.11/40.62    (5)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.11/40.62         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.11/40.62    (6)   ~ (all_6_2 = e3)
% 229.11/40.62    (7)  op(e1, e1) = all_6_2
% 229.11/40.62    (8)  all_57_6 = e1
% 229.11/40.62    (9)   ~ (e3 = e2)
% 229.11/40.62    (10)   ~ (e3 = e0)
% 229.11/40.62    (11)  all_57_1 = e0
% 229.11/40.62    (12)  all_57_15 = e3
% 229.11/40.62    (13)   ~ (e2 = e0)
% 229.11/40.62    (14)  all_57_2 = e3
% 229.11/40.62    (15)  all_57_3 = e1
% 229.11/40.62    (16)   ~ (e1 = e0)
% 229.11/40.62    (17)  all_57_6 = e0 & op(e1, e3) = e0
% 229.11/40.62    (18)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.11/40.62              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.11/40.62                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.11/40.62                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.11/40.62    (19)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.11/40.62          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.11/40.62    (20)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.11/40.62          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.11/40.62    (21)   ~ (e2 = e1)
% 229.11/40.62    (22)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.11/40.62          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.11/40.62    (23)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.11/40.62          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.11/40.62    (24)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.11/40.62          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.11/40.62  
% 229.11/40.62  Begin of proof
% 229.11/40.62  | 
% 229.11/40.62  | ALPHA: (17) implies:
% 229.11/40.62  |   (25)  all_57_6 = e0
% 229.11/40.62  | 
% 229.11/40.62  | COMBINE_EQS: (8), (25) imply:
% 229.11/40.62  |   (26)  e1 = e0
% 229.11/40.62  | 
% 229.11/40.62  | SIMP: (26) implies:
% 229.11/40.62  |   (27)  e1 = e0
% 229.11/40.62  | 
% 229.11/40.62  | COMBINE_EQS: (15), (27) imply:
% 229.11/40.62  |   (28)  all_57_3 = e0
% 229.11/40.62  | 
% 229.11/40.62  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13),
% 229.11/40.62  |            (14), (16), (18), (19), (20), (21), (22), (23), (24), (25), (28)
% 229.11/40.62  |            are inconsistent by sub-proof #826.
% 229.11/40.62  | 
% 229.11/40.62  End of proof
% 229.11/40.62  
% 229.11/40.62  Sub-proof #696 shows that the following formulas are inconsistent:
% 229.11/40.62  ----------------------------------------------------------------
% 229.11/40.62    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.11/40.62         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.11/40.62    (2)   ~ (e3 = e1)
% 229.11/40.62    (3)  all_57_2 = e0 & op(e2, e3) = e0
% 229.11/40.62    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.11/40.62           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.11/40.62    (5)   ~ (all_6_2 = e3)
% 229.11/40.62    (6)  op(e1, e1) = all_6_2
% 229.11/40.62    (7)  op(e2, e2) = e1
% 229.11/40.62    (8)  all_57_9 = e1
% 229.11/40.62    (9)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.11/40.62         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.11/40.62    (10)   ~ (e3 = e2)
% 229.11/40.62    (11)   ~ (e3 = e0)
% 229.11/40.62    (12)  all_57_15 = e3
% 229.11/40.62    (13)  op(e3, e3) = e2
% 229.11/40.62    (14)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.11/40.62          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.11/40.62            e1)
% 229.11/40.62    (15)   ~ (e2 = e0)
% 229.11/40.62    (16)  all_57_3 = e1
% 229.11/40.62    (17)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.11/40.62          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.11/40.62    (18)   ~ (e1 = e0)
% 229.11/40.62    (19)  all_57_5 = e2
% 229.11/40.62    (20)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.11/40.62          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.11/40.62    (21)  op(e0, e0) = e3
% 229.11/40.62    (22)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.11/40.62          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.11/40.62            e2)
% 229.11/40.62    (23)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.11/40.62              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.11/40.62                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.11/40.62                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.11/40.62    (24)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.11/40.62          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.11/40.62    (25)   ~ (all_53_12 = e3)
% 229.11/40.62    (26)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.11/40.62          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.11/40.62    (27)   ~ (e2 = e1)
% 229.11/40.62    (28)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.11/40.62          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.11/40.62    (29)  op(e3, e0) = all_53_12
% 229.11/40.62  
% 229.11/40.62  Begin of proof
% 229.11/40.62  | 
% 229.11/40.62  | ALPHA: (3) implies:
% 229.11/40.62  |   (30)  all_57_2 = e0
% 229.11/40.62  | 
% 229.11/40.62  | BETA: splitting (23) gives:
% 229.11/40.62  | 
% 229.11/40.62  | Case 1:
% 229.11/40.62  | | 
% 229.11/40.62  | |   (31)  all_57_15 = e0 & op(e0, e0) = e0
% 229.11/40.62  | | 
% 229.11/40.62  | | ALPHA: (31) implies:
% 229.11/40.62  | |   (32)  op(e0, e0) = e0
% 229.11/40.62  | | 
% 229.11/40.62  | | REF_CLOSE: (4), (11), (21), (32) are inconsistent by sub-proof #2304.
% 229.11/40.62  | | 
% 229.11/40.62  | Case 2:
% 229.11/40.62  | | 
% 229.11/40.62  | |   (33)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 229.11/40.62  | |             e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0 &
% 229.11/40.62  | |             op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 229.11/40.62  | |           (all_57_14 = e0 & op(e0, e1) = e0))
% 229.11/40.62  | | 
% 229.11/40.62  | | ALPHA: (33) implies:
% 229.11/40.62  | |   (34)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 229.11/40.62  | |           e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.11/40.62  | |   (35)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 229.11/40.62  | |           e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 229.11/40.62  | | 
% 229.11/40.62  | | BETA: splitting (20) gives:
% 229.11/40.62  | | 
% 229.11/40.62  | | Case 1:
% 229.11/40.62  | | | 
% 229.11/40.62  | | |   (36)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) =
% 229.11/40.62  | | |           e3)
% 229.11/40.62  | | | 
% 229.11/40.62  | | | BETA: splitting (36) gives:
% 229.11/40.62  | | | 
% 229.11/40.62  | | | Case 1:
% 229.11/40.62  | | | | 
% 229.11/40.62  | | | |   (37)  all_57_4 = e3 & op(e3, e1) = e3
% 229.11/40.62  | | | | 
% 229.11/40.62  | | | | ALPHA: (37) implies:
% 229.11/40.62  | | | |   (38)  all_57_4 = e3
% 229.11/40.62  | | | | 
% 229.11/40.62  | | | | BETA: splitting (9) gives:
% 229.11/40.62  | | | | 
% 229.11/40.62  | | | | Case 1:
% 229.11/40.62  | | | | | 
% 229.11/40.62  | | | | |   (39)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3,
% 229.11/40.62  | | | | |             e2) = e0)
% 229.11/40.62  | | | | | 
% 229.11/40.62  | | | | | BETA: splitting (39) gives:
% 229.11/40.62  | | | | | 
% 229.11/40.62  | | | | | Case 1:
% 229.11/40.62  | | | | | | 
% 229.11/40.62  | | | | | |   (40)  all_57_0 = e0 & op(e3, e3) = e0
% 229.11/40.62  | | | | | | 
% 229.11/40.62  | | | | | | ALPHA: (40) implies:
% 229.11/40.62  | | | | | |   (41)  op(e3, e3) = e0
% 229.11/40.62  | | | | | | 
% 229.11/40.62  | | | | | | REF_CLOSE: (4), (13), (15), (41) are inconsistent by sub-proof
% 229.11/40.62  | | | | | |            #2403.
% 229.11/40.62  | | | | | | 
% 229.11/40.62  | | | | | Case 2:
% 229.11/40.62  | | | | | | 
% 229.11/40.62  | | | | | |   (42)  all_57_1 = e0 & op(e3, e2) = e0
% 229.11/40.62  | | | | | | 
% 229.11/40.62  | | | | | | ALPHA: (42) implies:
% 229.11/40.62  | | | | | |   (43)  all_57_1 = e0
% 229.11/40.62  | | | | | | 
% 229.11/40.62  | | | | | | REF_CLOSE: (2), (4), (7), (8), (10), (11), (12), (13), (15), (17),
% 229.11/40.62  | | | | | |            (18), (19), (24), (25), (27), (28), (29), (30), (35),
% 229.11/40.62  | | | | | |            (38), (43) are inconsistent by sub-proof #697.
% 229.11/40.62  | | | | | | 
% 229.11/40.62  | | | | | End of split
% 229.11/40.62  | | | | | 
% 229.11/40.62  | | | | Case 2:
% 229.11/40.62  | | | | | 
% 229.11/40.62  | | | | |   (44)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3,
% 229.11/40.62  | | | | |             e0) = e0)
% 229.11/40.62  | | | | | 
% 229.11/40.62  | | | | | BETA: splitting (44) gives:
% 229.11/40.62  | | | | | 
% 229.11/40.62  | | | | | Case 1:
% 229.11/40.62  | | | | | | 
% 229.11/40.62  | | | | | |   (45)  all_57_4 = e0 & op(e3, e1) = e0
% 229.11/40.62  | | | | | | 
% 229.11/40.62  | | | | | | REF_CLOSE: (11), (38), (45) are inconsistent by sub-proof #2491.
% 229.11/40.62  | | | | | | 
% 229.11/40.62  | | | | | Case 2:
% 229.11/40.62  | | | | | | 
% 229.11/40.62  | | | | | |   (46)  all_57_9 = e0 & op(e3, e0) = e0
% 229.11/40.62  | | | | | | 
% 229.11/40.62  | | | | | | REF_CLOSE: (1), (2), (8), (10), (11), (15), (16), (18), (24), (26),
% 229.11/40.62  | | | | | |            (27), (30), (46) are inconsistent by sub-proof #703.
% 229.11/40.62  | | | | | | 
% 229.11/40.62  | | | | | End of split
% 229.11/40.62  | | | | | 
% 229.11/40.62  | | | | End of split
% 229.11/40.62  | | | | 
% 229.11/40.62  | | | Case 2:
% 229.11/40.62  | | | | 
% 229.11/40.62  | | | |   (47)  all_57_5 = e3 & op(e2, e1) = e3
% 229.11/40.62  | | | | 
% 229.11/40.62  | | | | ALPHA: (47) implies:
% 229.11/40.62  | | | |   (48)  all_57_5 = e3
% 229.11/40.62  | | | | 
% 229.11/40.62  | | | | REF_CLOSE: (10), (19), (48) are inconsistent by sub-proof #2189.
% 229.11/40.62  | | | | 
% 229.11/40.62  | | | End of split
% 229.11/40.62  | | | 
% 229.11/40.62  | | Case 2:
% 229.11/40.62  | | | 
% 229.11/40.62  | | |   (49)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) =
% 229.11/40.62  | | |           e3)
% 229.11/40.62  | | | 
% 229.11/40.62  | | | REF_CLOSE: (2), (4), (5), (6), (10), (11), (12), (14), (15), (18), (22),
% 229.11/40.62  | | |            (27), (34), (49) are inconsistent by sub-proof #1044.
% 229.11/40.62  | | | 
% 229.11/40.62  | | End of split
% 229.11/40.62  | | 
% 229.11/40.62  | End of split
% 229.11/40.62  | 
% 229.11/40.62  End of proof
% 229.11/40.62  
% 229.11/40.62  Sub-proof #697 shows that the following formulas are inconsistent:
% 229.11/40.62  ----------------------------------------------------------------
% 229.11/40.62    (1)   ~ (e3 = e1)
% 229.11/40.62    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.11/40.62           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.11/40.62    (3)  op(e2, e2) = e1
% 229.11/40.62    (4)  all_57_9 = e1
% 229.11/40.62    (5)  all_57_4 = e3
% 229.11/40.62    (6)   ~ (e3 = e2)
% 229.11/40.62    (7)   ~ (e3 = e0)
% 229.11/40.62    (8)  all_57_1 = e0
% 229.11/40.62    (9)  all_57_15 = e3
% 229.11/40.62    (10)  op(e3, e3) = e2
% 229.11/40.62    (11)   ~ (e2 = e0)
% 229.11/40.63    (12)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.11/40.63          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.11/40.63    (13)   ~ (e1 = e0)
% 229.11/40.63    (14)  all_57_5 = e2
% 229.11/40.63    (15)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.11/40.63          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.11/40.63    (16)  all_57_2 = e0
% 229.11/40.63    (17)   ~ (all_53_12 = e3)
% 229.11/40.63    (18)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) |
% 229.11/40.63          (all_57_11 = e0 & op(e1, e0) = e0)
% 229.11/40.63    (19)   ~ (e2 = e1)
% 229.11/40.63    (20)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.11/40.63          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.11/40.63    (21)  op(e3, e0) = all_53_12
% 229.11/40.63  
% 229.11/40.63  Begin of proof
% 229.11/40.63  | 
% 229.11/40.63  | BETA: splitting (15) gives:
% 229.11/40.63  | 
% 229.11/40.63  | Case 1:
% 229.11/40.63  | | 
% 229.11/40.63  | |   (22)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 229.11/40.63  | |           e3)
% 229.11/40.63  | | 
% 229.11/40.63  | | BETA: splitting (22) gives:
% 229.11/40.63  | | 
% 229.11/40.63  | | Case 1:
% 229.11/40.63  | | | 
% 229.11/40.63  | | |   (23)  all_57_2 = e3 & op(e2, e3) = e3
% 229.11/40.63  | | | 
% 229.11/40.63  | | | ALPHA: (23) implies:
% 229.11/40.63  | | |   (24)  all_57_2 = e3
% 229.11/40.63  | | | 
% 229.11/40.63  | | | COMBINE_EQS: (16), (24) imply:
% 229.11/40.63  | | |   (25)  e3 = e0
% 229.11/40.63  | | | 
% 229.11/40.63  | | | REDUCE: (7), (25) imply:
% 229.11/40.63  | | |   (26)  $false
% 229.11/40.63  | | | 
% 229.11/40.63  | | | CLOSE: (26) is inconsistent.
% 229.11/40.63  | | | 
% 229.11/40.63  | | Case 2:
% 229.11/40.63  | | | 
% 229.11/40.63  | | |   (27)  all_57_3 = e3 & op(e2, e2) = e3
% 229.11/40.63  | | | 
% 229.11/40.63  | | | ALPHA: (27) implies:
% 229.11/40.63  | | |   (28)  op(e2, e2) = e3
% 229.11/40.63  | | | 
% 229.11/40.63  | | | REF_CLOSE: (1), (2), (3), (28) are inconsistent by sub-proof #1912.
% 229.11/40.63  | | | 
% 229.11/40.63  | | End of split
% 229.11/40.63  | | 
% 229.11/40.63  | Case 2:
% 229.11/40.63  | | 
% 229.11/40.63  | |   (29)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 229.11/40.63  | |           e3)
% 229.11/40.63  | | 
% 229.11/40.63  | | BETA: splitting (29) gives:
% 229.11/40.63  | | 
% 229.11/40.63  | | Case 1:
% 229.11/40.63  | | | 
% 229.11/40.63  | | |   (30)  all_57_5 = e3 & op(e2, e1) = e3
% 229.11/40.63  | | | 
% 229.11/40.63  | | | ALPHA: (30) implies:
% 229.11/40.63  | | |   (31)  all_57_5 = e3
% 229.11/40.63  | | | 
% 229.11/40.63  | | | COMBINE_EQS: (14), (31) imply:
% 229.11/40.63  | | |   (32)  e3 = e2
% 229.11/40.63  | | | 
% 229.11/40.63  | | | COMBINE_EQS: (5), (32) imply:
% 229.11/40.63  | | |   (33)  all_57_4 = e2
% 229.11/40.63  | | | 
% 229.11/40.63  | | | REF_CLOSE: (2), (6), (7), (8), (10), (12), (17), (21), (33) are
% 229.11/40.63  | | |            inconsistent by sub-proof #875.
% 229.11/40.63  | | | 
% 229.11/40.63  | | Case 2:
% 229.11/40.63  | | | 
% 229.11/40.63  | | |   (34)  all_57_10 = e3 & op(e2, e0) = e3
% 229.11/40.63  | | | 
% 229.11/40.63  | | | ALPHA: (34) implies:
% 229.11/40.63  | | |   (35)  all_57_10 = e3
% 229.11/40.63  | | | 
% 229.11/40.63  | | | REF_CLOSE: (4), (6), (7), (9), (11), (13), (18), (19), (20), (35) are
% 229.11/40.63  | | |            inconsistent by sub-proof #1986.
% 229.11/40.63  | | | 
% 229.11/40.63  | | End of split
% 229.11/40.63  | | 
% 229.11/40.63  | End of split
% 229.11/40.63  | 
% 229.11/40.63  End of proof
% 229.11/40.63  
% 229.11/40.63  Sub-proof #698 shows that the following formulas are inconsistent:
% 229.11/40.63  ----------------------------------------------------------------
% 229.11/40.63    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.11/40.63         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.11/40.63    (2)   ~ (e3 = e1)
% 229.11/40.63    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.11/40.63           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.11/40.63    (4)   ~ (all_6_2 = e3)
% 229.11/40.63    (5)  op(e1, e1) = all_6_2
% 229.11/40.63    (6)  op(e2, e2) = e1
% 229.11/40.63    (7)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1)
% 229.11/40.63    (8)  all_57_9 = e1
% 229.11/40.63    (9)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.11/40.63         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.11/40.63    (10)   ~ (e3 = e2)
% 229.11/40.63    (11)   ~ (e3 = e0)
% 229.11/40.63    (12)  all_57_15 = e3
% 229.11/40.63    (13)  op(e3, e3) = e2
% 229.11/40.63    (14)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.11/40.63          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.11/40.63            e1)
% 229.11/40.63    (15)  op(e1, e1) = e1
% 229.11/40.63    (16)   ~ (e2 = e0)
% 229.11/40.63    (17)  all_57_3 = e1
% 229.11/40.63    (18)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.11/40.63          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.11/40.63    (19)   ~ (e1 = e0)
% 229.11/40.63    (20)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.11/40.63          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.11/40.63    (21)  all_57_14 = e1
% 229.11/40.63    (22)  op(e0, e0) = e3
% 229.11/40.63    (23)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.11/40.63          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.11/40.63            e2)
% 229.11/40.63    (24)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.11/40.63              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.11/40.63                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.11/40.63                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.11/40.63    (25)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.11/40.63          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.11/40.63    (26)   ~ (all_53_12 = e3)
% 229.11/40.63    (27)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.11/40.63          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.11/40.63    (28)   ~ (e2 = e1)
% 229.11/40.63    (29)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.11/40.63          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.11/40.63    (30)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 229.11/40.63          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 229.11/40.63    (31)  op(e3, e0) = all_53_12
% 229.11/40.63  
% 229.11/40.63  Begin of proof
% 229.11/40.63  | 
% 229.11/40.63  | BETA: splitting (7) gives:
% 229.11/40.63  | 
% 229.11/40.63  | Case 1:
% 229.11/40.63  | | 
% 229.11/40.63  | |   (32)  all_57_0 = e1 & op(e3, e3) = e1
% 229.11/40.63  | | 
% 229.11/40.63  | | ALPHA: (32) implies:
% 229.11/40.63  | |   (33)  op(e3, e3) = e1
% 229.11/40.63  | | 
% 229.11/40.63  | | REF_CLOSE: (3), (13), (28), (33) are inconsistent by sub-proof #1950.
% 229.11/40.63  | | 
% 229.11/40.63  | Case 2:
% 229.11/40.63  | | 
% 229.11/40.63  | |   (34)  all_57_2 = e1 & op(e2, e3) = e1
% 229.11/40.63  | | 
% 229.11/40.63  | | ALPHA: (34) implies:
% 229.11/40.63  | |   (35)  all_57_2 = e1
% 229.11/40.63  | | 
% 229.11/40.63  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13),
% 229.11/40.63  | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 229.11/40.63  | |            (25), (26), (27), (28), (29), (30), (31), (35) are inconsistent
% 229.11/40.63  | |            by sub-proof #699.
% 229.11/40.63  | | 
% 229.11/40.63  | End of split
% 229.11/40.63  | 
% 229.11/40.63  End of proof
% 229.11/40.63  
% 229.11/40.63  Sub-proof #699 shows that the following formulas are inconsistent:
% 229.11/40.63  ----------------------------------------------------------------
% 229.11/40.63    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.11/40.63         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.11/40.63    (2)   ~ (e3 = e1)
% 229.11/40.63    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.11/40.63           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.11/40.63    (4)   ~ (all_6_2 = e3)
% 229.11/40.63    (5)  op(e1, e1) = all_6_2
% 229.11/40.63    (6)  op(e2, e2) = e1
% 229.11/40.63    (7)  all_57_9 = e1
% 229.11/40.63    (8)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.11/40.63         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.11/40.63    (9)   ~ (e3 = e2)
% 229.11/40.63    (10)   ~ (e3 = e0)
% 229.11/40.63    (11)  all_57_15 = e3
% 229.11/40.63    (12)  op(e3, e3) = e2
% 229.11/40.63    (13)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.11/40.63          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.11/40.63            e1)
% 229.11/40.63    (14)  op(e1, e1) = e1
% 229.11/40.63    (15)   ~ (e2 = e0)
% 229.11/40.63    (16)  all_57_3 = e1
% 229.11/40.63    (17)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.11/40.63          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.11/40.63    (18)   ~ (e1 = e0)
% 229.11/40.63    (19)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.11/40.63          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.11/40.63    (20)  all_57_14 = e1
% 229.11/40.63    (21)  op(e0, e0) = e3
% 229.11/40.63    (22)  all_57_2 = e1
% 229.11/40.63    (23)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.11/40.63          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.11/40.63            e2)
% 229.11/40.63    (24)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.11/40.63              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.11/40.63                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.11/40.63                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.11/40.63    (25)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.11/40.63          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.11/40.63    (26)   ~ (all_53_12 = e3)
% 229.11/40.63    (27)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.11/40.63          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.11/40.63    (28)   ~ (e2 = e1)
% 229.11/40.63    (29)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.11/40.63          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.11/40.63    (30)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 229.11/40.63          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 229.11/40.63    (31)  op(e3, e0) = all_53_12
% 229.11/40.63  
% 229.11/40.63  Begin of proof
% 229.11/40.63  | 
% 229.11/40.63  | BETA: splitting (30) gives:
% 229.11/40.63  | 
% 229.11/40.63  | Case 1:
% 229.11/40.63  | | 
% 229.11/40.63  | |   (32)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) =
% 229.11/40.63  | |           e2)
% 229.11/40.63  | | 
% 229.11/40.63  | | BETA: splitting (32) gives:
% 229.11/40.63  | | 
% 229.11/40.63  | | Case 1:
% 229.11/40.63  | | | 
% 229.11/40.63  | | |   (33)  all_57_4 = e2 & op(e3, e1) = e2
% 229.11/40.63  | | | 
% 229.11/40.63  | | | ALPHA: (33) implies:
% 229.11/40.63  | | |   (34)  all_57_4 = e2
% 229.11/40.63  | | | 
% 229.11/40.63  | | | REF_CLOSE: (1), (2), (3), (7), (8), (9), (10), (12), (15), (16), (17),
% 229.11/40.63  | | |            (18), (22), (25), (26), (27), (28), (31), (34) are inconsistent
% 229.11/40.63  | | |            by sub-proof #702.
% 229.11/40.63  | | | 
% 229.11/40.63  | | Case 2:
% 229.11/40.63  | | | 
% 229.11/40.63  | | |   (35)  all_57_5 = e2 & op(e2, e1) = e2
% 229.11/40.63  | | | 
% 229.11/40.63  | | | ALPHA: (35) implies:
% 229.11/40.63  | | |   (36)  all_57_5 = e2
% 229.11/40.63  | | | 
% 229.11/40.63  | | | BETA: splitting (19) gives:
% 229.11/40.63  | | | 
% 229.11/40.63  | | | Case 1:
% 229.11/40.63  | | | | 
% 229.11/40.63  | | | |   (37)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1)
% 229.11/40.63  | | | |           = e3)
% 229.11/40.63  | | | | 
% 229.11/40.63  | | | | BETA: splitting (37) gives:
% 229.11/40.63  | | | | 
% 229.11/40.63  | | | | Case 1:
% 229.11/40.63  | | | | | 
% 229.11/40.63  | | | | |   (38)  all_57_4 = e3 & op(e3, e1) = e3
% 229.11/40.63  | | | | | 
% 229.11/40.63  | | | | | ALPHA: (38) implies:
% 229.11/40.63  | | | | |   (39)  all_57_4 = e3
% 229.11/40.63  | | | | | 
% 229.11/40.63  | | | | | BETA: splitting (24) gives:
% 229.11/40.63  | | | | | 
% 229.11/40.63  | | | | | Case 1:
% 229.11/40.63  | | | | | | 
% 229.11/40.63  | | | | | |   (40)  all_57_15 = e0 & op(e0, e0) = e0
% 229.11/40.63  | | | | | | 
% 229.11/40.63  | | | | | | ALPHA: (40) implies:
% 229.11/40.63  | | | | | |   (41)  op(e0, e0) = e0
% 229.11/40.63  | | | | | | 
% 229.11/40.63  | | | | | | REF_CLOSE: (3), (10), (21), (41) are inconsistent by sub-proof
% 229.11/40.63  | | | | | |            #2304.
% 229.11/40.63  | | | | | | 
% 229.11/40.63  | | | | | Case 2:
% 229.11/40.63  | | | | | | 
% 229.11/40.63  | | | | | |   (42)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 &
% 229.11/40.63  | | | | | |             op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) &
% 229.11/40.63  | | | | | |         ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.11/40.63  | | | | | |             op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 229.11/40.63  | | | | | | 
% 229.11/40.63  | | | | | | ALPHA: (42) implies:
% 229.11/40.63  | | | | | |   (43)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2,
% 229.11/40.63  | | | | | |             e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 229.11/40.63  | | | | | | 
% 229.11/40.63  | | | | | | BETA: splitting (25) gives:
% 229.11/40.63  | | | | | | 
% 229.11/40.63  | | | | | | Case 1:
% 229.11/40.63  | | | | | | | 
% 229.11/40.63  | | | | | | |   (44)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 &
% 229.11/40.63  | | | | | | |           op(e2, e2) = e3)
% 229.11/40.63  | | | | | | | 
% 229.11/40.63  | | | | | | | BETA: splitting (44) gives:
% 229.11/40.63  | | | | | | | 
% 229.11/40.63  | | | | | | | Case 1:
% 229.11/40.63  | | | | | | | | 
% 229.11/40.63  | | | | | | | |   (45)  all_57_2 = e3 & op(e2, e3) = e3
% 229.11/40.63  | | | | | | | | 
% 229.11/40.63  | | | | | | | | REF_CLOSE: (2), (22), (45) are inconsistent by sub-proof #701.
% 229.11/40.63  | | | | | | | | 
% 229.11/40.63  | | | | | | | Case 2:
% 229.11/40.63  | | | | | | | | 
% 229.11/40.63  | | | | | | | |   (46)  all_57_3 = e3 & op(e2, e2) = e3
% 229.11/40.63  | | | | | | | | 
% 229.11/40.63  | | | | | | | | ALPHA: (46) implies:
% 229.11/40.63  | | | | | | | |   (47)  op(e2, e2) = e3
% 229.11/40.63  | | | | | | | | 
% 229.11/40.63  | | | | | | | | REF_CLOSE: (2), (3), (6), (47) are inconsistent by sub-proof
% 229.11/40.63  | | | | | | | |            #1912.
% 229.11/40.63  | | | | | | | | 
% 229.11/40.63  | | | | | | | End of split
% 229.11/40.63  | | | | | | | 
% 229.11/40.63  | | | | | | Case 2:
% 229.11/40.63  | | | | | | | 
% 229.11/40.63  | | | | | | |   (48)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 &
% 229.11/40.63  | | | | | | |           op(e2, e0) = e3)
% 229.11/40.63  | | | | | | | 
% 229.11/40.63  | | | | | | | BETA: splitting (48) gives:
% 229.11/40.63  | | | | | | | 
% 229.11/40.63  | | | | | | | Case 1:
% 229.11/40.63  | | | | | | | | 
% 229.11/40.63  | | | | | | | |   (49)  all_57_5 = e3 & op(e2, e1) = e3
% 229.11/40.63  | | | | | | | | 
% 229.11/40.63  | | | | | | | | ALPHA: (49) implies:
% 229.11/40.63  | | | | | | | |   (50)  all_57_5 = e3
% 229.11/40.63  | | | | | | | | 
% 229.11/40.63  | | | | | | | | COMBINE_EQS: (36), (50) imply:
% 229.11/40.63  | | | | | | | |   (51)  e3 = e2
% 229.11/40.63  | | | | | | | | 
% 229.11/40.63  | | | | | | | | COMBINE_EQS: (39), (51) imply:
% 229.11/40.63  | | | | | | | |   (52)  all_57_4 = e2
% 229.11/40.63  | | | | | | | | 
% 229.11/40.63  | | | | | | | | REF_CLOSE: (1), (2), (3), (7), (8), (9), (10), (12), (15), (16),
% 229.11/40.63  | | | | | | | |            (17), (18), (22), (25), (26), (27), (28), (31), (52)
% 229.11/40.63  | | | | | | | |            are inconsistent by sub-proof #702.
% 229.11/40.63  | | | | | | | | 
% 229.11/40.63  | | | | | | | Case 2:
% 229.11/40.63  | | | | | | | | 
% 229.11/40.63  | | | | | | | |   (53)  all_57_10 = e3 & op(e2, e0) = e3
% 229.11/40.63  | | | | | | | | 
% 229.11/40.63  | | | | | | | | ALPHA: (53) implies:
% 229.11/40.63  | | | | | | | |   (54)  all_57_10 = e3
% 229.11/40.63  | | | | | | | | 
% 229.11/40.63  | | | | | | | | REF_CLOSE: (7), (9), (10), (11), (15), (18), (28), (29), (43),
% 229.11/40.63  | | | | | | | |            (54) are inconsistent by sub-proof #1986.
% 229.11/40.63  | | | | | | | | 
% 229.11/40.63  | | | | | | | End of split
% 229.11/40.63  | | | | | | | 
% 229.11/40.63  | | | | | | End of split
% 229.11/40.63  | | | | | | 
% 229.11/40.63  | | | | | End of split
% 229.11/40.63  | | | | | 
% 229.11/40.63  | | | | Case 2:
% 229.11/40.63  | | | | | 
% 229.11/40.63  | | | | |   (55)  all_57_5 = e3 & op(e2, e1) = e3
% 229.11/40.63  | | | | | 
% 229.11/40.63  | | | | | ALPHA: (55) implies:
% 229.11/40.63  | | | | |   (56)  all_57_5 = e3
% 229.11/40.63  | | | | | 
% 229.11/40.63  | | | | | REF_CLOSE: (9), (36), (56) are inconsistent by sub-proof #2189.
% 229.11/40.63  | | | | | 
% 229.11/40.63  | | | | End of split
% 229.11/40.63  | | | | 
% 229.11/40.63  | | | Case 2:
% 229.11/40.63  | | | | 
% 229.11/40.63  | | | |   (57)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1)
% 229.11/40.63  | | | |           = e3)
% 229.11/40.63  | | | | 
% 229.11/40.63  | | | | REF_CLOSE: (2), (3), (4), (5), (9), (10), (11), (13), (15), (18), (23),
% 229.11/40.63  | | | |            (24), (28), (57) are inconsistent by sub-proof #1794.
% 229.11/40.63  | | | | 
% 229.11/40.63  | | | End of split
% 229.11/40.63  | | | 
% 229.11/40.63  | | End of split
% 229.11/40.63  | | 
% 229.11/40.63  | Case 2:
% 229.11/40.63  | | 
% 229.11/40.63  | |   (58)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) =
% 229.11/40.63  | |           e2)
% 229.11/40.63  | | 
% 229.11/40.63  | | REF_CLOSE: (3), (14), (20), (28), (58) are inconsistent by sub-proof #700.
% 229.11/40.63  | | 
% 229.11/40.63  | End of split
% 229.11/40.63  | 
% 229.11/40.63  End of proof
% 229.11/40.63  
% 229.11/40.63  Sub-proof #700 shows that the following formulas are inconsistent:
% 229.11/40.63  ----------------------------------------------------------------
% 229.11/40.63    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.11/40.63           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.11/40.63    (2)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 229.11/40.63    (3)  op(e1, e1) = e1
% 229.11/40.63    (4)  all_57_14 = e1
% 229.11/40.63    (5)   ~ (e2 = e1)
% 229.11/40.63  
% 229.11/40.63  Begin of proof
% 229.11/40.63  | 
% 229.11/40.63  | BETA: splitting (2) gives:
% 229.11/40.63  | 
% 229.11/40.63  | Case 1:
% 229.11/40.63  | | 
% 229.11/40.63  | |   (6)  all_57_8 = e2 & op(e1, e1) = e2
% 229.11/40.63  | | 
% 229.11/40.63  | | ALPHA: (6) implies:
% 229.11/40.63  | |   (7)  op(e1, e1) = e2
% 229.11/40.63  | | 
% 229.11/40.63  | | REF_CLOSE: (1), (3), (5), (7) are inconsistent by sub-proof #2423.
% 229.11/40.63  | | 
% 229.11/40.63  | Case 2:
% 229.11/40.63  | | 
% 229.11/40.63  | |   (8)  all_57_14 = e2 & op(e0, e1) = e2
% 229.11/40.63  | | 
% 229.11/40.63  | | ALPHA: (8) implies:
% 229.11/40.63  | |   (9)  all_57_14 = e2
% 229.11/40.63  | | 
% 229.11/40.63  | | REF_CLOSE: (4), (5), (9) are inconsistent by sub-proof #2178.
% 229.11/40.63  | | 
% 229.11/40.63  | End of split
% 229.11/40.63  | 
% 229.11/40.63  End of proof
% 229.11/40.63  
% 229.11/40.63  Sub-proof #701 shows that the following formulas are inconsistent:
% 229.11/40.63  ----------------------------------------------------------------
% 229.11/40.63    (1)  all_57_2 = e3 & op(e2, e3) = e3
% 229.11/40.63    (2)  all_57_2 = e1
% 229.11/40.63    (3)   ~ (e3 = e1)
% 229.11/40.63  
% 229.11/40.63  Begin of proof
% 229.11/40.63  | 
% 229.11/40.63  | ALPHA: (1) implies:
% 229.11/40.63  |   (4)  all_57_2 = e3
% 229.11/40.63  | 
% 229.11/40.63  | COMBINE_EQS: (2), (4) imply:
% 229.11/40.63  |   (5)  e3 = e1
% 229.11/40.63  | 
% 229.11/40.63  | REDUCE: (3), (5) imply:
% 229.11/40.63  |   (6)  $false
% 229.11/40.63  | 
% 229.11/40.63  | CLOSE: (6) is inconsistent.
% 229.11/40.63  | 
% 229.11/40.63  End of proof
% 229.11/40.63  
% 229.11/40.63  Sub-proof #702 shows that the following formulas are inconsistent:
% 229.11/40.63  ----------------------------------------------------------------
% 229.11/40.63    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.11/40.63         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.11/40.63    (2)   ~ (e3 = e1)
% 229.11/40.63    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.11/40.63           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.11/40.63    (4)  all_57_4 = e2
% 229.11/40.63    (5)  all_57_9 = e1
% 229.11/40.63    (6)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.11/40.63         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.11/40.63    (7)   ~ (e3 = e2)
% 229.11/40.63    (8)   ~ (e3 = e0)
% 229.11/40.63    (9)  op(e3, e3) = e2
% 229.11/40.63    (10)   ~ (e2 = e0)
% 229.11/40.63    (11)  all_57_3 = e1
% 229.11/40.63    (12)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.11/40.63          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.11/40.63    (13)   ~ (e1 = e0)
% 229.11/40.63    (14)  all_57_2 = e1
% 229.11/40.63    (15)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.11/40.63          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.11/40.63    (16)   ~ (all_53_12 = e3)
% 229.11/40.63    (17)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.11/40.63          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.11/40.63    (18)   ~ (e2 = e1)
% 229.11/40.63    (19)  op(e3, e0) = all_53_12
% 229.11/40.63  
% 229.11/40.63  Begin of proof
% 229.11/40.63  | 
% 229.11/40.63  | BETA: splitting (6) gives:
% 229.11/40.63  | 
% 229.11/40.63  | Case 1:
% 229.11/40.63  | | 
% 229.11/40.63  | |   (20)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) =
% 229.11/40.63  | |           e0)
% 229.11/40.63  | | 
% 229.11/40.63  | | REF_CLOSE: (3), (4), (7), (8), (9), (10), (12), (16), (19), (20) are
% 229.11/40.63  | |            inconsistent by sub-proof #874.
% 229.11/40.63  | | 
% 229.11/40.63  | Case 2:
% 229.11/40.63  | | 
% 229.11/40.63  | |   (21)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) =
% 229.11/40.63  | |           e0)
% 229.11/40.63  | | 
% 229.11/40.63  | | BETA: splitting (21) gives:
% 229.11/40.63  | | 
% 229.11/40.63  | | Case 1:
% 229.11/40.63  | | | 
% 229.11/40.63  | | |   (22)  all_57_4 = e0 & op(e3, e1) = e0
% 229.11/40.63  | | | 
% 229.11/40.63  | | | REF_CLOSE: (4), (10), (22) are inconsistent by sub-proof #2045.
% 229.11/40.63  | | | 
% 229.11/40.63  | | Case 2:
% 229.11/40.63  | | | 
% 229.11/40.63  | | |   (23)  all_57_9 = e0 & op(e3, e0) = e0
% 229.11/40.63  | | | 
% 229.11/40.63  | | | ALPHA: (23) implies:
% 229.11/40.63  | | |   (24)  all_57_9 = e0
% 229.11/40.63  | | | 
% 229.11/40.63  | | | COMBINE_EQS: (5), (24) imply:
% 229.11/40.63  | | |   (25)  e1 = e0
% 229.11/40.63  | | | 
% 229.11/40.63  | | | SIMP: (25) implies:
% 229.11/40.63  | | |   (26)  e1 = e0
% 229.11/40.63  | | | 
% 229.11/40.63  | | | COMBINE_EQS: (14), (26) imply:
% 229.11/40.63  | | |   (27)  all_57_2 = e0
% 229.11/40.63  | | | 
% 229.11/40.63  | | | BETA: splitting (6) gives:
% 229.11/40.63  | | | 
% 229.11/40.63  | | | Case 1:
% 229.11/40.63  | | | | 
% 229.11/40.63  | | | |   (28)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2)
% 229.11/40.63  | | | |           = e0)
% 229.11/40.63  | | | | 
% 229.11/40.63  | | | | BETA: splitting (28) gives:
% 229.11/40.63  | | | | 
% 229.11/40.63  | | | | Case 1:
% 229.11/40.63  | | | | | 
% 229.11/40.63  | | | | |   (29)  all_57_0 = e0 & op(e3, e3) = e0
% 229.11/40.63  | | | | | 
% 229.11/40.63  | | | | | ALPHA: (29) implies:
% 229.11/40.63  | | | | |   (30)  op(e3, e3) = e0
% 229.11/40.63  | | | | | 
% 229.11/40.63  | | | | | REF_CLOSE: (3), (9), (10), (30) are inconsistent by sub-proof #2403.
% 229.11/40.63  | | | | | 
% 229.11/40.63  | | | | Case 2:
% 229.11/40.63  | | | | | 
% 229.11/40.63  | | | | |   (31)  all_57_1 = e0 & op(e3, e2) = e0
% 229.11/40.63  | | | | | 
% 229.11/40.63  | | | | | ALPHA: (31) implies:
% 229.11/40.63  | | | | |   (32)  all_57_1 = e0
% 229.11/40.63  | | | | | 
% 229.11/40.63  | | | | | BETA: splitting (12) gives:
% 229.11/40.63  | | | | | 
% 229.11/40.63  | | | | | Case 1:
% 229.11/40.63  | | | | | | 
% 229.11/40.63  | | | | | |   (33)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3,
% 229.11/40.63  | | | | | |             e2) = e3)
% 229.11/40.63  | | | | | | 
% 229.11/40.63  | | | | | | REF_CLOSE: (3), (7), (8), (9), (32), (33) are inconsistent by
% 229.11/40.63  | | | | | |            sub-proof #1610.
% 229.11/40.63  | | | | | | 
% 229.11/40.63  | | | | | Case 2:
% 229.11/40.63  | | | | | | 
% 229.11/40.63  | | | | | |   (34)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3,
% 229.11/40.63  | | | | | |             e0) = e3)
% 229.11/40.63  | | | | | | 
% 229.11/40.63  | | | | | | REF_CLOSE: (3), (4), (7), (16), (19), (34) are inconsistent by
% 229.11/40.63  | | | | | |            sub-proof #876.
% 229.11/40.63  | | | | | | 
% 229.11/40.63  | | | | | End of split
% 229.11/40.63  | | | | | 
% 229.11/40.63  | | | | End of split
% 229.11/40.63  | | | | 
% 229.11/40.63  | | | Case 2:
% 229.11/40.63  | | | | 
% 229.11/40.63  | | | | 
% 229.11/40.63  | | | | BETA: splitting (21) gives:
% 229.11/40.63  | | | | 
% 229.11/40.63  | | | | Case 1:
% 229.11/40.63  | | | | | 
% 229.11/40.63  | | | | |   (35)  all_57_4 = e0 & op(e3, e1) = e0
% 229.11/40.63  | | | | | 
% 229.11/40.63  | | | | | REF_CLOSE: (4), (10), (35) are inconsistent by sub-proof #2045.
% 229.11/40.63  | | | | | 
% 229.11/40.63  | | | | Case 2:
% 229.11/40.63  | | | | | 
% 229.11/40.63  | | | | | 
% 229.11/40.63  | | | | | REF_CLOSE: (1), (2), (5), (7), (8), (10), (11), (13), (15), (17),
% 229.11/40.63  | | | | |            (18), (23), (27) are inconsistent by sub-proof #703.
% 229.11/40.63  | | | | | 
% 229.11/40.63  | | | | End of split
% 229.11/40.63  | | | | 
% 229.11/40.63  | | | End of split
% 229.11/40.63  | | | 
% 229.11/40.63  | | End of split
% 229.11/40.63  | | 
% 229.11/40.63  | End of split
% 229.11/40.63  | 
% 229.11/40.63  End of proof
% 229.11/40.63  
% 229.11/40.63  Sub-proof #703 shows that the following formulas are inconsistent:
% 229.11/40.63  ----------------------------------------------------------------
% 229.11/40.63    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.11/40.63         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.11/40.63    (2)   ~ (e3 = e1)
% 229.11/40.63    (3)  all_57_9 = e0 & op(e3, e0) = e0
% 229.11/40.63    (4)  all_57_9 = e1
% 229.11/40.63    (5)   ~ (e3 = e2)
% 229.11/40.63    (6)   ~ (e3 = e0)
% 229.11/40.63    (7)   ~ (e2 = e0)
% 229.11/40.63    (8)  all_57_3 = e1
% 229.11/40.63    (9)   ~ (e1 = e0)
% 229.11/40.63    (10)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.11/40.63          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.11/40.63    (11)  all_57_2 = e0
% 229.11/40.63    (12)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.11/40.63          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.11/40.63    (13)   ~ (e2 = e1)
% 229.11/40.63  
% 229.11/40.63  Begin of proof
% 229.11/40.63  | 
% 229.11/40.63  | ALPHA: (3) implies:
% 229.11/40.63  |   (14)  all_57_9 = e0
% 229.11/40.63  | 
% 229.11/40.63  | COMBINE_EQS: (4), (14) imply:
% 229.11/40.63  |   (15)  e1 = e0
% 229.11/40.63  | 
% 229.11/40.63  | COMBINE_EQS: (8), (15) imply:
% 229.11/40.63  |   (16)  all_57_3 = e0
% 229.11/40.63  | 
% 229.11/40.63  | REF_CLOSE: (1), (2), (5), (6), (7), (9), (10), (11), (12), (13), (16) are
% 229.11/40.63  |            inconsistent by sub-proof #2246.
% 229.11/40.63  | 
% 229.11/40.63  End of proof
% 229.11/40.63  
% 229.11/40.63  Sub-proof #704 shows that the following formulas are inconsistent:
% 229.11/40.63  ----------------------------------------------------------------
% 229.11/40.63    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.11/40.63         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.11/40.63    (2)  all_57_13 = e1
% 229.11/40.63    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.11/40.63         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.11/40.63    (4)   ~ (e3 = e1)
% 229.11/40.63    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.11/40.63           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.11/40.63    (6)  op(e2, e2) = e1
% 229.11/40.63    (7)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.11/40.63         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.11/40.63    (8)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1)
% 229.11/40.63    (9)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.11/40.63         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.11/40.63    (10)   ~ (e3 = e2)
% 229.11/40.63    (11)   ~ (e3 = e0)
% 229.11/40.63    (12)  all_57_15 = e3
% 229.11/40.63    (13)  op(e3, e3) = e2
% 229.11/40.63    (14)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.11/40.63          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.11/40.63            e1)
% 229.11/40.63    (15)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.11/40.63          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.11/40.63    (16)   ~ (e2 = e0)
% 229.11/40.63    (17)  all_57_3 = e1
% 229.11/40.63    (18)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.11/40.63          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.11/40.63    (19)   ~ (e1 = e0)
% 229.11/40.63    (20)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.11/40.63          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.11/40.63    (21)  op(e0, e0) = e3
% 229.11/40.63    (22)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.11/40.63          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.11/40.63            e2)
% 229.11/40.63    (23)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.11/40.63              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.11/40.63                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.11/40.63                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.11/40.63    (24)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.11/40.63          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.11/40.63    (25)   ~ (all_53_12 = e3)
% 229.11/40.63    (26)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.11/40.63          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.11/40.63    (27)   ~ (e2 = e1)
% 229.11/40.63    (28)  op(e3, e0) = all_53_12
% 229.11/40.63  
% 229.11/40.63  Begin of proof
% 229.11/40.63  | 
% 229.11/40.63  | BETA: splitting (8) gives:
% 229.11/40.63  | 
% 229.11/40.63  | Case 1:
% 229.11/40.63  | | 
% 229.11/40.63  | |   (29)  all_57_0 = e1 & op(e3, e3) = e1
% 229.11/40.63  | | 
% 229.11/40.63  | | ALPHA: (29) implies:
% 229.11/40.63  | |   (30)  op(e3, e3) = e1
% 229.11/40.63  | | 
% 229.11/40.63  | | REF_CLOSE: (5), (13), (27), (30) are inconsistent by sub-proof #1950.
% 229.11/40.63  | | 
% 229.11/40.63  | Case 2:
% 229.11/40.63  | | 
% 229.11/40.63  | |   (31)  all_57_2 = e1 & op(e2, e3) = e1
% 229.11/40.63  | | 
% 229.11/40.63  | | ALPHA: (31) implies:
% 229.11/40.63  | |   (32)  all_57_2 = e1
% 229.11/40.63  | | 
% 229.11/40.63  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13),
% 229.11/40.63  | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 229.11/40.63  | |            (25), (26), (27), (28), (32) are inconsistent by sub-proof #705.
% 229.11/40.63  | | 
% 229.11/40.63  | End of split
% 229.11/40.63  | 
% 229.11/40.63  End of proof
% 229.11/40.63  
% 229.11/40.63  Sub-proof #705 shows that the following formulas are inconsistent:
% 229.11/40.63  ----------------------------------------------------------------
% 229.11/40.63    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.11/40.63         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.11/40.64    (2)  all_57_13 = e1
% 229.11/40.64    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.11/40.64         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.11/40.64    (4)   ~ (e3 = e1)
% 229.11/40.64    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.11/40.64           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.11/40.64    (6)  op(e2, e2) = e1
% 229.11/40.64    (7)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.11/40.64         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.11/40.64    (8)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.11/40.64         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.11/40.64    (9)   ~ (e3 = e2)
% 229.11/40.64    (10)   ~ (e3 = e0)
% 229.11/40.64    (11)  all_57_15 = e3
% 229.11/40.64    (12)  op(e3, e3) = e2
% 229.11/40.64    (13)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.11/40.64          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.11/40.64            e1)
% 229.11/40.64    (14)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.11/40.64          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.11/40.64    (15)   ~ (e2 = e0)
% 229.11/40.64    (16)  all_57_3 = e1
% 229.11/40.64    (17)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.11/40.64          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.11/40.64    (18)   ~ (e1 = e0)
% 229.11/40.64    (19)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.11/40.64          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.11/40.64    (20)  op(e0, e0) = e3
% 229.21/40.64    (21)  all_57_2 = e1
% 229.21/40.64    (22)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.21/40.64          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.21/40.64            e2)
% 229.21/40.64    (23)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.21/40.64              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.21/40.64                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.21/40.64                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.21/40.64    (24)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.21/40.64          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.21/40.64    (25)   ~ (all_53_12 = e3)
% 229.21/40.64    (26)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.21/40.64          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.21/40.64    (27)   ~ (e2 = e1)
% 229.21/40.64    (28)  op(e3, e0) = all_53_12
% 229.21/40.64  
% 229.21/40.64  Begin of proof
% 229.21/40.64  | 
% 229.21/40.64  | BETA: splitting (3) gives:
% 229.21/40.64  | 
% 229.21/40.64  | Case 1:
% 229.21/40.64  | | 
% 229.21/40.64  | |   (29)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 229.21/40.64  | |           e2)
% 229.21/40.64  | | 
% 229.21/40.64  | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (10), (12), (15), (17), (18), (25),
% 229.21/40.64  | |            (27), (28), (29) are inconsistent by sub-proof #714.
% 229.21/40.64  | | 
% 229.21/40.64  | Case 2:
% 229.21/40.64  | | 
% 229.21/40.64  | |   (30)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 229.21/40.64  | |           e2)
% 229.21/40.64  | | 
% 229.21/40.64  | | BETA: splitting (30) gives:
% 229.21/40.64  | | 
% 229.21/40.64  | | Case 1:
% 229.21/40.64  | | | 
% 229.21/40.64  | | |   (31)  all_57_7 = e2 & op(e1, e2) = e2
% 229.21/40.64  | | | 
% 229.21/40.64  | | | ALPHA: (31) implies:
% 229.21/40.64  | | |   (32)  all_57_7 = e2
% 229.21/40.64  | | | 
% 229.21/40.64  | | | REF_CLOSE: (1), (2), (4), (5), (6), (9), (10), (11), (13), (14), (15),
% 229.21/40.64  | | |            (16), (18), (19), (20), (21), (22), (23), (24), (26), (27),
% 229.21/40.64  | | |            (32) are inconsistent by sub-proof #775.
% 229.21/40.64  | | | 
% 229.21/40.64  | | Case 2:
% 229.21/40.64  | | | 
% 229.21/40.64  | | |   (33)  all_57_13 = e2 & op(e0, e2) = e2
% 229.21/40.64  | | | 
% 229.21/40.64  | | | ALPHA: (33) implies:
% 229.21/40.64  | | |   (34)  all_57_13 = e2
% 229.21/40.64  | | | 
% 229.21/40.64  | | | REF_CLOSE: (2), (27), (34) are inconsistent by sub-proof #2327.
% 229.21/40.64  | | | 
% 229.21/40.64  | | End of split
% 229.21/40.64  | | 
% 229.21/40.64  | End of split
% 229.21/40.64  | 
% 229.21/40.64  End of proof
% 229.21/40.64  
% 229.21/40.64  Sub-proof #706 shows that the following formulas are inconsistent:
% 229.21/40.64  ----------------------------------------------------------------
% 229.21/40.64    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.21/40.64         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.21/40.64    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.21/40.64         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.21/40.64    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.21/40.64         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.21/40.64    (4)   ~ (e3 = e1)
% 229.21/40.64    (5)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 229.21/40.64         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 229.21/40.64    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.21/40.64           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.21/40.64    (7)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.21/40.64         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.21/40.64    (8)   ~ (all_6_2 = e3)
% 229.21/40.64    (9)  op(e1, e1) = all_6_2
% 229.21/40.64    (10)  op(all_52_7, all_52_7) = e0
% 229.21/40.64    (11)  op(e2, e2) = e1
% 229.21/40.64    (12)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.21/40.64          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.21/40.64    (13)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 229.21/40.64            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 229.21/40.64              e3) = all_22_1 & $i(all_22_1))
% 229.21/40.64    (14)  all_57_9 = e1
% 229.21/40.64    (15)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.21/40.64          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.21/40.64    (16)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.21/40.64          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.21/40.64    (17)   ~ (e3 = e2)
% 229.21/40.64    (18)  op(e3, e0) = e1
% 229.21/40.64    (19)   ~ (e3 = e0)
% 229.21/40.64    (20)  op(e0, e3) = e1
% 229.21/40.64    (21)  all_57_15 = e3
% 229.21/40.64    (22)  op(e3, e3) = e2
% 229.21/40.64    (23)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.21/40.64          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.21/40.64            e1)
% 229.21/40.64    (24)  all_57_12 = e1
% 229.21/40.64    (25)  op(e1, e1) = e1
% 229.21/40.64    (26)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.21/40.64          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.21/40.64    (27)   ~ (e2 = e0)
% 229.21/40.64    (28)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 229.21/40.64            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 229.21/40.64              e3) = all_12_1 & $i(all_12_1))
% 229.21/40.64    (29)  all_57_3 = e1
% 229.21/40.64    (30)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.21/40.64          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.21/40.64    (31)   ~ (e1 = e0)
% 229.21/40.64    (32)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.21/40.64          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.21/40.64    (33)  op(e0, e0) = e3
% 229.21/40.64    (34)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.21/40.64          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.21/40.64            e2)
% 229.21/40.64    (35)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.21/40.64              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.21/40.64                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.21/40.64                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.21/40.64    (36)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.21/40.64          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.21/40.64    (37)   ~ (all_53_12 = e3)
% 229.21/40.64    (38)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.21/40.64          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.21/40.64    (39)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.21/40.64          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.21/40.64    (40)   ~ (e2 = e1)
% 229.21/40.64    (41)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.21/40.64          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.21/40.64    (42)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.21/40.64          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.21/40.64    (43)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.21/40.64          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.21/40.64    (44)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.21/40.64          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.21/40.64    (45)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 229.21/40.64          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 229.21/40.64    (46)  op(e3, e0) = all_52_7
% 229.21/40.64    (47)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.21/40.64          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.21/40.64    (48)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 229.21/40.64          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 229.21/40.64    (49)  op(e3, e0) = all_53_12
% 229.21/40.64  
% 229.21/40.64  Begin of proof
% 229.21/40.64  | 
% 229.21/40.64  | BETA: splitting (45) gives:
% 229.21/40.64  | 
% 229.21/40.64  | Case 1:
% 229.21/40.64  | | 
% 229.21/40.64  | |   (50)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) =
% 229.21/40.64  | |           e1)
% 229.21/40.64  | | 
% 229.21/40.64  | | REF_CLOSE: (3), (4), (6), (7), (8), (9), (11), (12), (13), (16), (17), (19),
% 229.21/40.64  | |            (20), (21), (22), (23), (24), (25), (26), (27), (28), (30), (31),
% 229.21/40.64  | |            (32), (33), (34), (35), (37), (39), (40), (41), (42), (43), (44),
% 229.21/40.64  | |            (47), (48), (49), (50) are inconsistent by sub-proof #710.
% 229.21/40.64  | | 
% 229.21/40.64  | Case 2:
% 229.21/40.64  | | 
% 229.21/40.64  | |   (51)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) =
% 229.21/40.64  | |           e1)
% 229.21/40.64  | | 
% 229.21/40.64  | | BETA: splitting (51) gives:
% 229.21/40.64  | | 
% 229.21/40.64  | | Case 1:
% 229.21/40.64  | | | 
% 229.21/40.64  | | |   (52)  all_57_8 = e1 & op(e1, e1) = e1
% 229.21/40.64  | | | 
% 229.21/40.64  | | | GROUND_INST: instantiating (6) with all_53_12, e1, e0, e3, simplifying
% 229.21/40.64  | | |              with (18), (49) gives:
% 229.21/40.64  | | |   (53)  all_53_12 = e1
% 229.21/40.64  | | | 
% 229.21/40.64  | | | GROUND_INST: instantiating (6) with all_53_12, all_52_7, e0, e3,
% 229.21/40.64  | | |              simplifying with (46), (49) gives:
% 229.21/40.64  | | |   (54)  all_53_12 = all_52_7
% 229.21/40.64  | | | 
% 229.21/40.64  | | | COMBINE_EQS: (53), (54) imply:
% 229.21/40.64  | | |   (55)  all_52_7 = e1
% 229.21/40.64  | | | 
% 229.21/40.64  | | | REDUCE: (10), (55) imply:
% 229.21/40.64  | | |   (56)  op(e1, e1) = e0
% 229.21/40.64  | | | 
% 229.21/40.64  | | | REF_CLOSE: (6), (25), (31), (56) are inconsistent by sub-proof #2427.
% 229.21/40.64  | | | 
% 229.21/40.64  | | Case 2:
% 229.21/40.64  | | | 
% 229.21/40.64  | | |   (57)  all_57_11 = e1 & op(e1, e0) = e1
% 229.21/40.64  | | | 
% 229.21/40.64  | | | ALPHA: (57) implies:
% 229.21/40.64  | | |   (58)  all_57_11 = e1
% 229.21/40.64  | | | 
% 229.21/40.64  | | | BETA: splitting (48) gives:
% 229.21/40.64  | | | 
% 229.21/40.64  | | | Case 1:
% 229.21/40.64  | | | | 
% 229.21/40.64  | | | |   (59)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2)
% 229.21/40.64  | | | |           = e2)
% 229.21/40.64  | | | | 
% 229.21/40.64  | | | | BETA: splitting (59) gives:
% 229.21/40.64  | | | | 
% 229.21/40.64  | | | | Case 1:
% 229.21/40.64  | | | | | 
% 229.21/40.64  | | | | |   (60)  all_57_6 = e2 & op(e1, e3) = e2
% 229.21/40.64  | | | | | 
% 229.21/40.64  | | | | | ALPHA: (60) implies:
% 229.21/40.64  | | | | |   (61)  all_57_6 = e2
% 229.21/40.64  | | | | | 
% 229.21/40.64  | | | | | BETA: splitting (43) gives:
% 229.21/40.64  | | | | | 
% 229.21/40.64  | | | | | Case 1:
% 229.21/40.64  | | | | | | 
% 229.21/40.64  | | | | | |   (62)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2,
% 229.21/40.64  | | | | | |             e3) = e0)
% 229.21/40.64  | | | | | | 
% 229.21/40.64  | | | | | | BETA: splitting (62) gives:
% 229.21/40.64  | | | | | | 
% 229.21/40.64  | | | | | | Case 1:
% 229.21/40.64  | | | | | | | 
% 229.21/40.64  | | | | | | |   (63)  all_57_0 = e0 & op(e3, e3) = e0
% 229.21/40.64  | | | | | | | 
% 229.21/40.64  | | | | | | | ALPHA: (63) implies:
% 229.21/40.64  | | | | | | |   (64)  op(e3, e3) = e0
% 229.21/40.64  | | | | | | | 
% 229.21/40.64  | | | | | | | REF_CLOSE: (6), (22), (27), (64) are inconsistent by sub-proof
% 229.21/40.64  | | | | | | |            #2403.
% 229.21/40.64  | | | | | | | 
% 229.21/40.64  | | | | | | Case 2:
% 229.21/40.64  | | | | | | | 
% 229.21/40.64  | | | | | | |   (65)  all_57_2 = e0 & op(e2, e3) = e0
% 229.21/40.64  | | | | | | | 
% 229.21/40.64  | | | | | | | ALPHA: (65) implies:
% 229.21/40.64  | | | | | | |   (66)  all_57_2 = e0
% 229.21/40.64  | | | | | | | 
% 229.21/40.64  | | | | | | | REF_CLOSE: (1), (4), (6), (13), (14), (17), (19), (20), (21),
% 229.21/40.64  | | | | | | |            (27), (28), (29), (31), (33), (35), (36), (38), (40),
% 229.21/40.64  | | | | | | |            (41), (58), (66) are inconsistent by sub-proof #709.
% 229.21/40.64  | | | | | | | 
% 229.21/40.64  | | | | | | End of split
% 229.21/40.64  | | | | | | 
% 229.21/40.64  | | | | | Case 2:
% 229.21/40.64  | | | | | | 
% 229.21/40.64  | | | | | |   (67)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0,
% 229.21/40.64  | | | | | |             e3) = e0)
% 229.21/40.64  | | | | | | 
% 229.21/40.64  | | | | | | BETA: splitting (67) gives:
% 229.21/40.64  | | | | | | 
% 229.21/40.64  | | | | | | Case 1:
% 229.21/40.64  | | | | | | | 
% 229.21/40.64  | | | | | | |   (68)  all_57_6 = e0 & op(e1, e3) = e0
% 229.21/40.64  | | | | | | | 
% 229.21/40.64  | | | | | | | REF_CLOSE: (27), (61), (68) are inconsistent by sub-proof #2386.
% 229.21/40.64  | | | | | | | 
% 229.21/40.64  | | | | | | Case 2:
% 229.21/40.64  | | | | | | | 
% 229.21/40.64  | | | | | | |   (69)  all_57_12 = e0 & op(e0, e3) = e0
% 229.21/40.64  | | | | | | | 
% 229.21/40.64  | | | | | | | ALPHA: (69) implies:
% 229.21/40.64  | | | | | | |   (70)  all_57_12 = e0
% 229.21/40.64  | | | | | | | 
% 229.21/40.64  | | | | | | | COMBINE_EQS: (24), (70) imply:
% 229.21/40.64  | | | | | | |   (71)  e1 = e0
% 229.21/40.64  | | | | | | | 
% 229.21/40.64  | | | | | | | COMBINE_EQS: (29), (71) imply:
% 229.21/40.64  | | | | | | |   (72)  all_57_3 = e0
% 229.21/40.64  | | | | | | | 
% 229.21/40.64  | | | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (12), (15),
% 229.21/40.64  | | | | | | |            (16), (17), (19), (21), (22), (27), (30), (31), (35),
% 229.21/40.64  | | | | | | |            (36), (37), (38), (39), (40), (41), (43), (44), (47),
% 229.21/40.64  | | | | | | |            (49), (61), (72) are inconsistent by sub-proof #728.
% 229.21/40.64  | | | | | | | 
% 229.21/40.64  | | | | | | End of split
% 229.21/40.64  | | | | | | 
% 229.21/40.64  | | | | | End of split
% 229.21/40.64  | | | | | 
% 229.21/40.64  | | | | Case 2:
% 229.21/40.64  | | | | | 
% 229.21/40.64  | | | | |   (73)  all_57_7 = e2 & op(e1, e2) = e2
% 229.21/40.64  | | | | | 
% 229.21/40.64  | | | | | ALPHA: (73) implies:
% 229.21/40.64  | | | | |   (74)  all_57_7 = e2
% 229.21/40.64  | | | | | 
% 229.21/40.64  | | | | | BETA: splitting (35) gives:
% 229.21/40.64  | | | | | 
% 229.21/40.64  | | | | | Case 1:
% 229.21/40.64  | | | | | | 
% 229.21/40.64  | | | | | |   (75)  all_57_15 = e0 & op(e0, e0) = e0
% 229.21/40.64  | | | | | | 
% 229.21/40.64  | | | | | | ALPHA: (75) implies:
% 229.21/40.64  | | | | | |   (76)  op(e0, e0) = e0
% 229.21/40.64  | | | | | | 
% 229.21/40.64  | | | | | | REF_CLOSE: (6), (19), (33), (76) are inconsistent by sub-proof
% 229.21/40.64  | | | | | |            #2304.
% 229.21/40.64  | | | | | | 
% 229.21/40.64  | | | | | Case 2:
% 229.21/40.64  | | | | | | 
% 229.21/40.64  | | | | | |   (77)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 &
% 229.21/40.64  | | | | | |             op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) &
% 229.21/40.64  | | | | | |         ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.21/40.64  | | | | | |             op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 229.21/40.64  | | | | | | 
% 229.21/40.64  | | | | | | ALPHA: (77) implies:
% 229.21/40.64  | | | | | |   (78)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.21/40.64  | | | | | |           op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.21/40.64  | | | | | | 
% 229.21/40.64  | | | | | | BETA: splitting (32) gives:
% 229.21/40.64  | | | | | | 
% 229.21/40.64  | | | | | | Case 1:
% 229.21/40.64  | | | | | | | 
% 229.21/40.64  | | | | | | |   (79)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 &
% 229.21/40.64  | | | | | | |           op(e2, e2) = e3)
% 229.21/40.64  | | | | | | | 
% 229.21/40.64  | | | | | | | BETA: splitting (79) gives:
% 229.21/40.64  | | | | | | | 
% 229.21/40.64  | | | | | | | Case 1:
% 229.21/40.64  | | | | | | | | 
% 229.21/40.64  | | | | | | | |   (80)  all_57_1 = e3 & op(e3, e2) = e3
% 229.21/40.64  | | | | | | | | 
% 229.21/40.64  | | | | | | | | ALPHA: (80) implies:
% 229.21/40.64  | | | | | | | |   (81)  all_57_1 = e3
% 229.21/40.64  | | | | | | | | 
% 229.21/40.64  | | | | | | | | BETA: splitting (41) gives:
% 229.21/40.64  | | | | | | | | 
% 229.21/40.64  | | | | | | | | Case 1:
% 229.21/40.64  | | | | | | | | | 
% 229.21/40.64  | | | | | | | | |   (82)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 &
% 229.21/40.64  | | | | | | | | |           op(e2, e0) = e2)
% 229.21/40.64  | | | | | | | | | 
% 229.21/40.64  | | | | | | | | | BETA: splitting (82) gives:
% 229.21/40.64  | | | | | | | | | 
% 229.21/40.64  | | | | | | | | | Case 1:
% 229.21/40.64  | | | | | | | | | | 
% 229.21/40.64  | | | | | | | | | |   (83)  all_57_9 = e2 & op(e3, e0) = e2
% 229.21/40.64  | | | | | | | | | | 
% 229.21/40.64  | | | | | | | | | | ALPHA: (83) implies:
% 229.21/40.64  | | | | | | | | | |   (84)  all_57_9 = e2
% 229.21/40.64  | | | | | | | | | | 
% 229.21/40.64  | | | | | | | | | | COMBINE_EQS: (14), (84) imply:
% 229.21/40.64  | | | | | | | | | |   (85)  e2 = e1
% 229.21/40.64  | | | | | | | | | | 
% 229.21/40.64  | | | | | | | | | | SIMP: (85) implies:
% 229.21/40.64  | | | | | | | | | |   (86)  e2 = e1
% 229.21/40.64  | | | | | | | | | | 
% 229.21/40.64  | | | | | | | | | | COMBINE_EQS: (74), (86) imply:
% 229.21/40.64  | | | | | | | | | |   (87)  all_57_7 = e1
% 229.21/40.64  | | | | | | | | | | 
% 229.21/40.64  | | | | | | | | | | REF_CLOSE: (3), (4), (6), (7), (8), (9), (11), (12), (13),
% 229.21/40.64  | | | | | | | | | |            (16), (17), (19), (20), (21), (22), (23), (25),
% 229.21/40.64  | | | | | | | | | |            (26), (27), (28), (30), (31), (32), (33), (34),
% 229.21/40.64  | | | | | | | | | |            (35), (37), (40), (41), (44), (47), (48), (49),
% 229.21/40.64  | | | | | | | | | |            (87) are inconsistent by sub-proof #711.
% 229.21/40.64  | | | | | | | | | | 
% 229.21/40.64  | | | | | | | | | Case 2:
% 229.21/40.64  | | | | | | | | | | 
% 229.21/40.64  | | | | | | | | | |   (88)  all_57_10 = e2 & op(e2, e0) = e2
% 229.21/40.64  | | | | | | | | | | 
% 229.21/40.64  | | | | | | | | | | ALPHA: (88) implies:
% 229.21/40.64  | | | | | | | | | |   (89)  all_57_10 = e2
% 229.21/40.64  | | | | | | | | | | 
% 229.21/40.64  | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (13), (14), (17),
% 229.21/40.64  | | | | | | | | | |            (19), (20), (21), (25), (27), (28), (31), (35),
% 229.21/40.64  | | | | | | | | | |            (40), (41), (44), (58), (74), (89) are
% 229.21/40.64  | | | | | | | | | |            inconsistent by sub-proof #708.
% 229.21/40.64  | | | | | | | | | | 
% 229.21/40.64  | | | | | | | | | End of split
% 229.21/40.64  | | | | | | | | | 
% 229.21/40.64  | | | | | | | | Case 2:
% 229.21/40.64  | | | | | | | | | 
% 229.21/40.64  | | | | | | | | |   (90)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 &
% 229.21/40.64  | | | | | | | | |           op(e0, e0) = e2)
% 229.21/40.64  | | | | | | | | | 
% 229.21/40.64  | | | | | | | | | BETA: splitting (90) gives:
% 229.21/40.64  | | | | | | | | | 
% 229.21/40.64  | | | | | | | | | Case 1:
% 229.21/40.64  | | | | | | | | | | 
% 229.21/40.64  | | | | | | | | | |   (91)  all_57_11 = e2 & op(e1, e0) = e2
% 229.21/40.64  | | | | | | | | | | 
% 229.21/40.64  | | | | | | | | | | ALPHA: (91) implies:
% 229.21/40.64  | | | | | | | | | |   (92)  op(e1, e0) = e2
% 229.21/40.64  | | | | | | | | | | 
% 229.21/40.64  | | | | | | | | | | REF_CLOSE: (6), (13), (20), (28), (92) are inconsistent by
% 229.21/40.64  | | | | | | | | | |            sub-proof #1147.
% 229.21/40.64  | | | | | | | | | | 
% 229.21/40.64  | | | | | | | | | Case 2:
% 229.21/40.64  | | | | | | | | | | 
% 229.21/40.64  | | | | | | | | | |   (93)  all_57_15 = e2 & op(e0, e0) = e2
% 229.21/40.64  | | | | | | | | | | 
% 229.21/40.64  | | | | | | | | | | REF_CLOSE: (4), (6), (12), (16), (17), (19), (21), (22),
% 229.21/40.64  | | | | | | | | | |            (27), (30), (31), (37), (40), (49), (81), (93) are
% 229.21/40.64  | | | | | | | | | |            inconsistent by sub-proof #707.
% 229.21/40.64  | | | | | | | | | | 
% 229.21/40.64  | | | | | | | | | End of split
% 229.21/40.64  | | | | | | | | | 
% 229.21/40.64  | | | | | | | | End of split
% 229.21/40.64  | | | | | | | | 
% 229.21/40.64  | | | | | | | Case 2:
% 229.21/40.64  | | | | | | | | 
% 229.21/40.64  | | | | | | | |   (94)  all_57_3 = e3 & op(e2, e2) = e3
% 229.21/40.64  | | | | | | | | 
% 229.21/40.64  | | | | | | | | ALPHA: (94) implies:
% 229.21/40.64  | | | | | | | |   (95)  op(e2, e2) = e3
% 229.21/40.64  | | | | | | | | 
% 229.21/40.64  | | | | | | | | REF_CLOSE: (4), (6), (11), (95) are inconsistent by sub-proof
% 229.21/40.64  | | | | | | | |            #1912.
% 229.21/40.64  | | | | | | | | 
% 229.21/40.64  | | | | | | | End of split
% 229.21/40.64  | | | | | | | 
% 229.21/40.64  | | | | | | Case 2:
% 229.21/40.64  | | | | | | | 
% 229.21/40.64  | | | | | | |   (96)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 &
% 229.21/40.64  | | | | | | |           op(e0, e2) = e3)
% 229.21/40.64  | | | | | | | 
% 229.21/40.64  | | | | | | | BETA: splitting (96) gives:
% 229.21/40.64  | | | | | | | 
% 229.21/40.64  | | | | | | | Case 1:
% 229.21/40.64  | | | | | | | | 
% 229.21/40.64  | | | | | | | |   (97)  all_57_7 = e3 & op(e1, e2) = e3
% 229.21/40.64  | | | | | | | | 
% 229.21/40.64  | | | | | | | | ALPHA: (97) implies:
% 229.21/40.64  | | | | | | | |   (98)  all_57_7 = e3
% 229.21/40.64  | | | | | | | | 
% 229.21/40.64  | | | | | | | | REF_CLOSE: (17), (74), (98) are inconsistent by sub-proof #2102.
% 229.21/40.64  | | | | | | | | 
% 229.21/40.64  | | | | | | | Case 2:
% 229.21/40.64  | | | | | | | | 
% 229.21/40.64  | | | | | | | |   (99)  all_57_13 = e3 & op(e0, e2) = e3
% 229.21/40.64  | | | | | | | | 
% 229.21/40.64  | | | | | | | | ALPHA: (99) implies:
% 229.21/40.64  | | | | | | | |   (100)  all_57_13 = e3
% 229.21/40.64  | | | | | | | | 
% 229.21/40.64  | | | | | | | | REF_CLOSE: (4), (6), (17), (19), (21), (23), (27), (31), (33),
% 229.21/40.64  | | | | | | | |            (34), (40), (78), (100) are inconsistent by sub-proof
% 229.21/40.64  | | | | | | | |            #2054.
% 229.21/40.64  | | | | | | | | 
% 229.21/40.64  | | | | | | | End of split
% 229.21/40.64  | | | | | | | 
% 229.21/40.64  | | | | | | End of split
% 229.21/40.64  | | | | | | 
% 229.21/40.64  | | | | | End of split
% 229.21/40.64  | | | | | 
% 229.21/40.64  | | | | End of split
% 229.21/40.64  | | | | 
% 229.21/40.64  | | | Case 2:
% 229.21/40.64  | | | | 
% 229.21/40.64  | | | |   (101)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1,
% 229.21/40.64  | | | |              e0) = e2)
% 229.21/40.64  | | | | 
% 229.21/40.64  | | | | REF_CLOSE: (6), (13), (20), (25), (28), (40), (101) are inconsistent by
% 229.21/40.64  | | | |            sub-proof #1011.
% 229.21/40.64  | | | | 
% 229.21/40.64  | | | End of split
% 229.21/40.64  | | | 
% 229.21/40.64  | | End of split
% 229.21/40.64  | | 
% 229.21/40.64  | End of split
% 229.21/40.64  | 
% 229.21/40.64  End of proof
% 229.21/40.64  
% 229.21/40.64  Sub-proof #707 shows that the following formulas are inconsistent:
% 229.21/40.64  ----------------------------------------------------------------
% 229.21/40.64    (1)   ~ (e3 = e1)
% 229.21/40.64    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.21/40.64           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.21/40.64    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.21/40.64         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.21/40.64    (4)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.21/40.64         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.21/40.64    (5)   ~ (e3 = e2)
% 229.21/40.64    (6)   ~ (e3 = e0)
% 229.21/40.64    (7)  all_57_15 = e3
% 229.21/40.64    (8)  op(e3, e3) = e2
% 229.21/40.64    (9)   ~ (e2 = e0)
% 229.21/40.64    (10)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.21/40.64          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.21/40.64    (11)   ~ (e1 = e0)
% 229.21/40.64    (12)   ~ (all_53_12 = e3)
% 229.21/40.64    (13)  all_57_1 = e3
% 229.21/40.64    (14)   ~ (e2 = e1)
% 229.21/40.64    (15)  all_57_15 = e2 & op(e0, e0) = e2
% 229.21/40.64    (16)  op(e3, e0) = all_53_12
% 229.21/40.64  
% 229.21/40.64  Begin of proof
% 229.21/40.64  | 
% 229.21/40.64  | ALPHA: (15) implies:
% 229.21/40.64  |   (17)  all_57_15 = e2
% 229.21/40.64  | 
% 229.21/40.64  | COMBINE_EQS: (7), (17) imply:
% 229.21/40.64  |   (18)  e3 = e2
% 229.21/40.64  | 
% 229.21/40.64  | COMBINE_EQS: (13), (18) imply:
% 229.21/40.64  |   (19)  all_57_1 = e2
% 229.21/40.64  | 
% 229.21/40.64  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (14),
% 229.21/40.64  |            (16), (19) are inconsistent by sub-proof #1650.
% 229.21/40.64  | 
% 229.21/40.64  End of proof
% 229.21/40.64  
% 229.21/40.64  Sub-proof #708 shows that the following formulas are inconsistent:
% 229.21/40.64  ----------------------------------------------------------------
% 229.21/40.64    (1)   ~ (e3 = e1)
% 229.21/40.64    (2)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 229.21/40.64         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 229.21/40.64    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.21/40.64           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.21/40.64    (4)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.21/40.64         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.21/40.64    (5)   ~ (all_6_2 = e3)
% 229.21/40.64    (6)  op(e1, e1) = all_6_2
% 229.21/40.64    (7)  all_57_7 = e2
% 229.21/40.64    (8)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) = all_22_1
% 229.21/40.64           & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0, e3) =
% 229.21/40.64           all_22_1 & $i(all_22_1))
% 229.21/40.64    (9)  all_57_9 = e1
% 229.21/40.64    (10)   ~ (e3 = e2)
% 229.21/40.64    (11)   ~ (e3 = e0)
% 229.21/40.64    (12)  op(e0, e3) = e1
% 229.21/40.64    (13)  all_57_15 = e3
% 229.21/40.64    (14)  all_57_10 = e2
% 229.21/40.64    (15)  op(e1, e1) = e1
% 229.21/40.64    (16)   ~ (e2 = e0)
% 229.21/40.64    (17)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 229.21/40.64            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 229.21/40.64              e3) = all_12_1 & $i(all_12_1))
% 229.21/40.64    (18)   ~ (e1 = e0)
% 229.21/40.64    (19)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.21/40.64              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.21/40.64                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.21/40.64                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.21/40.64    (20)  all_57_11 = e1
% 229.21/40.64    (21)   ~ (e2 = e1)
% 229.21/40.64    (22)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.21/40.64          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.21/40.64    (23)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.21/40.64          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.21/40.64  
% 229.21/40.64  Begin of proof
% 229.21/40.64  | 
% 229.21/40.64  | BETA: splitting (2) gives:
% 229.21/40.64  | 
% 229.21/40.64  | Case 1:
% 229.21/40.64  | | 
% 229.21/40.64  | |   (24)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) =
% 229.21/40.64  | |           e0)
% 229.21/40.64  | | 
% 229.21/40.64  | | BETA: splitting (24) gives:
% 229.21/40.64  | | 
% 229.21/40.64  | | Case 1:
% 229.21/40.64  | | | 
% 229.21/40.64  | | |   (25)  all_57_6 = e0 & op(e1, e3) = e0
% 229.21/40.64  | | | 
% 229.21/40.64  | | | ALPHA: (25) implies:
% 229.21/40.64  | | |   (26)  all_57_6 = e0
% 229.21/40.64  | | | 
% 229.21/40.64  | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (10), (11), (13), (16), (18),
% 229.21/40.64  | | |            (19), (21), (22), (23), (26) are inconsistent by sub-proof
% 229.21/40.64  | | |            #1775.
% 229.21/40.64  | | | 
% 229.21/40.64  | | Case 2:
% 229.21/40.64  | | | 
% 229.21/40.64  | | |   (27)  all_57_7 = e0 & op(e1, e2) = e0
% 229.21/40.64  | | | 
% 229.21/40.64  | | | ALPHA: (27) implies:
% 229.21/40.64  | | |   (28)  all_57_7 = e0
% 229.21/40.64  | | | 
% 229.21/40.64  | | | COMBINE_EQS: (7), (28) imply:
% 229.21/40.64  | | |   (29)  e2 = e0
% 229.21/40.64  | | | 
% 229.21/40.64  | | | COMBINE_EQS: (14), (29) imply:
% 229.21/40.64  | | |   (30)  all_57_10 = e0
% 229.21/40.64  | | | 
% 229.21/40.64  | | | REF_CLOSE: (3), (8), (9), (10), (12), (13), (16), (17), (21), (22), (30)
% 229.21/40.64  | | |            are inconsistent by sub-proof #1018.
% 229.21/40.64  | | | 
% 229.21/40.64  | | End of split
% 229.21/40.64  | | 
% 229.21/40.64  | Case 2:
% 229.21/40.64  | | 
% 229.21/40.64  | |   (31)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 229.21/40.64  | |           e0)
% 229.21/40.64  | | 
% 229.21/40.64  | | BETA: splitting (31) gives:
% 229.21/40.64  | | 
% 229.21/40.64  | | Case 1:
% 229.21/40.64  | | | 
% 229.21/40.64  | | |   (32)  all_57_8 = e0 & op(e1, e1) = e0
% 229.21/40.64  | | | 
% 229.21/40.64  | | | ALPHA: (32) implies:
% 229.21/40.64  | | |   (33)  op(e1, e1) = e0
% 229.21/40.64  | | | 
% 229.21/40.64  | | | REF_CLOSE: (3), (15), (18), (33) are inconsistent by sub-proof #2427.
% 229.21/40.64  | | | 
% 229.21/40.64  | | Case 2:
% 229.21/40.64  | | | 
% 229.21/40.64  | | |   (34)  all_57_11 = e0 & op(e1, e0) = e0
% 229.21/40.64  | | | 
% 229.21/40.64  | | | ALPHA: (34) implies:
% 229.21/40.64  | | |   (35)  all_57_11 = e0
% 229.21/40.64  | | | 
% 229.21/40.64  | | | COMBINE_EQS: (20), (35) imply:
% 229.21/40.64  | | |   (36)  e1 = e0
% 229.21/40.64  | | | 
% 229.21/40.64  | | | COMBINE_EQS: (9), (36) imply:
% 229.21/40.64  | | |   (37)  all_57_9 = e0
% 229.21/40.64  | | | 
% 229.21/40.64  | | | REF_CLOSE: (1), (10), (13), (16), (18), (21), (22), (23), (35), (37) are
% 229.21/40.64  | | |            inconsistent by sub-proof #1144.
% 229.21/40.64  | | | 
% 229.21/40.64  | | End of split
% 229.21/40.64  | | 
% 229.21/40.64  | End of split
% 229.21/40.64  | 
% 229.21/40.64  End of proof
% 229.21/40.64  
% 229.21/40.64  Sub-proof #709 shows that the following formulas are inconsistent:
% 229.21/40.64  ----------------------------------------------------------------
% 229.21/40.64    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.21/40.64         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.21/40.64    (2)   ~ (e3 = e1)
% 229.21/40.64    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.21/40.64           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.21/40.65    (4)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) = all_22_1
% 229.21/40.65           & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0, e3) =
% 229.21/40.65           all_22_1 & $i(all_22_1))
% 229.21/40.65    (5)  all_57_9 = e1
% 229.21/40.65    (6)   ~ (e3 = e2)
% 229.21/40.65    (7)   ~ (e3 = e0)
% 229.21/40.65    (8)  op(e0, e3) = e1
% 229.21/40.65    (9)  all_57_15 = e3
% 229.21/40.65    (10)   ~ (e2 = e0)
% 229.21/40.65    (11)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 229.21/40.65            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 229.21/40.65              e3) = all_12_1 & $i(all_12_1))
% 229.21/40.65    (12)  all_57_3 = e1
% 229.21/40.65    (13)   ~ (e1 = e0)
% 229.21/40.65    (14)  op(e0, e0) = e3
% 229.21/40.65    (15)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.21/40.65              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.21/40.65                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.21/40.65                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.21/40.65    (16)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.21/40.65          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.21/40.65    (17)  all_57_2 = e0
% 229.21/40.65    (18)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.21/40.65          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.21/40.65    (19)  all_57_11 = e1
% 229.21/40.65    (20)   ~ (e2 = e1)
% 229.21/40.65    (21)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.21/40.65          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.21/40.65  
% 229.21/40.65  Begin of proof
% 229.21/40.65  | 
% 229.21/40.65  | BETA: splitting (15) gives:
% 229.21/40.65  | 
% 229.21/40.65  | Case 1:
% 229.21/40.65  | | 
% 229.21/40.65  | |   (22)  all_57_15 = e0 & op(e0, e0) = e0
% 229.21/40.65  | | 
% 229.21/40.65  | | ALPHA: (22) implies:
% 229.21/40.65  | |   (23)  op(e0, e0) = e0
% 229.21/40.65  | | 
% 229.21/40.65  | | REF_CLOSE: (3), (7), (14), (23) are inconsistent by sub-proof #2304.
% 229.21/40.65  | | 
% 229.21/40.65  | Case 2:
% 229.21/40.65  | | 
% 229.21/40.65  | |   (24)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 229.21/40.65  | |             e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0 &
% 229.21/40.65  | |             op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 229.21/40.65  | |           (all_57_14 = e0 & op(e0, e1) = e0))
% 229.21/40.65  | | 
% 229.21/40.65  | | ALPHA: (24) implies:
% 229.21/40.65  | |   (25)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 229.21/40.65  | |           e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 229.21/40.65  | | 
% 229.21/40.65  | | BETA: splitting (25) gives:
% 229.21/40.65  | | 
% 229.21/40.65  | | Case 1:
% 229.21/40.65  | | | 
% 229.21/40.65  | | |   (26)  all_57_9 = e0 & op(e3, e0) = e0
% 229.21/40.65  | | | 
% 229.21/40.65  | | | ALPHA: (26) implies:
% 229.21/40.65  | | |   (27)  all_57_9 = e0
% 229.21/40.65  | | | 
% 229.21/40.65  | | | COMBINE_EQS: (5), (27) imply:
% 229.21/40.65  | | |   (28)  e1 = e0
% 229.21/40.65  | | | 
% 229.21/40.65  | | | REF_CLOSE: (1), (2), (6), (7), (10), (12), (13), (16), (17), (18), (20),
% 229.21/40.65  | | |            (28) are inconsistent by sub-proof #1824.
% 229.21/40.65  | | | 
% 229.21/40.65  | | Case 2:
% 229.21/40.65  | | | 
% 229.21/40.65  | | |   (29)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.21/40.65  | | |           = e0)
% 229.21/40.65  | | | 
% 229.21/40.65  | | | BETA: splitting (29) gives:
% 229.21/40.65  | | | 
% 229.21/40.65  | | | Case 1:
% 229.21/40.65  | | | | 
% 229.21/40.65  | | | |   (30)  all_57_10 = e0 & op(e2, e0) = e0
% 229.21/40.65  | | | | 
% 229.21/40.65  | | | | ALPHA: (30) implies:
% 229.21/40.65  | | | |   (31)  all_57_10 = e0
% 229.21/40.65  | | | | 
% 229.21/40.65  | | | | REF_CLOSE: (3), (4), (5), (6), (8), (9), (10), (11), (20), (21), (31)
% 229.21/40.65  | | | |            are inconsistent by sub-proof #1018.
% 229.21/40.65  | | | | 
% 229.21/40.65  | | | Case 2:
% 229.21/40.65  | | | | 
% 229.21/40.65  | | | |   (32)  all_57_11 = e0 & op(e1, e0) = e0
% 229.21/40.65  | | | | 
% 229.21/40.65  | | | | ALPHA: (32) implies:
% 229.21/40.65  | | | |   (33)  all_57_11 = e0
% 229.21/40.65  | | | | 
% 229.21/40.65  | | | | COMBINE_EQS: (19), (33) imply:
% 229.21/40.65  | | | |   (34)  e1 = e0
% 229.21/40.65  | | | | 
% 229.21/40.65  | | | | REF_CLOSE: (1), (2), (6), (7), (10), (12), (13), (16), (17), (18), (20),
% 229.21/40.65  | | | |            (34) are inconsistent by sub-proof #1824.
% 229.21/40.65  | | | | 
% 229.21/40.65  | | | End of split
% 229.21/40.65  | | | 
% 229.21/40.65  | | End of split
% 229.21/40.65  | | 
% 229.21/40.65  | End of split
% 229.21/40.65  | 
% 229.21/40.65  End of proof
% 229.21/40.65  
% 229.21/40.65  Sub-proof #710 shows that the following formulas are inconsistent:
% 229.21/40.65  ----------------------------------------------------------------
% 229.21/40.65    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.21/40.65         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.21/40.65    (2)   ~ (e3 = e1)
% 229.21/40.65    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.21/40.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.21/40.65    (4)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.21/40.65         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.21/40.65    (5)   ~ (all_6_2 = e3)
% 229.21/40.65    (6)  op(e1, e1) = all_6_2
% 229.21/40.65    (7)  op(e2, e2) = e1
% 229.21/40.65    (8)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.21/40.65         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.21/40.65    (9)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) = all_22_1
% 229.21/40.65           & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0, e3) =
% 229.21/40.65           all_22_1 & $i(all_22_1))
% 229.21/40.65    (10)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.21/40.65          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.21/40.65    (11)   ~ (e3 = e2)
% 229.21/40.65    (12)   ~ (e3 = e0)
% 229.21/40.65    (13)  op(e0, e3) = e1
% 229.21/40.65    (14)  all_57_15 = e3
% 229.21/40.65    (15)  op(e3, e3) = e2
% 229.21/40.65    (16)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.21/40.65          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.21/40.65            e1)
% 229.21/40.65    (17)  all_57_12 = e1
% 229.21/40.65    (18)  op(e1, e1) = e1
% 229.21/40.65    (19)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.21/40.65          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.21/40.65    (20)   ~ (e2 = e0)
% 229.21/40.65    (21)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 229.21/40.65            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 229.21/40.65              e3) = all_12_1 & $i(all_12_1))
% 229.21/40.65    (22)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.21/40.65          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.21/40.65    (23)   ~ (e1 = e0)
% 229.21/40.65    (24)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.21/40.65          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.21/40.65    (25)  op(e0, e0) = e3
% 229.21/40.65    (26)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.21/40.65          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.21/40.65            e2)
% 229.21/40.65    (27)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.21/40.65              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.21/40.65                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.21/40.65                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.21/40.65    (28)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1)
% 229.21/40.65    (29)   ~ (all_53_12 = e3)
% 229.21/40.65    (30)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.21/40.65          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.21/40.65    (31)   ~ (e2 = e1)
% 229.21/40.65    (32)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.21/40.65          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.21/40.65    (33)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.21/40.65          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.21/40.65    (34)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.21/40.65          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.21/40.65    (35)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.21/40.65          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.21/40.65    (36)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.21/40.65          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.21/40.65    (37)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 229.21/40.65          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 229.21/40.65    (38)  op(e3, e0) = all_53_12
% 229.21/40.65  
% 229.21/40.65  Begin of proof
% 229.21/40.65  | 
% 229.21/40.65  | BETA: splitting (28) gives:
% 229.21/40.65  | 
% 229.21/40.65  | Case 1:
% 229.21/40.65  | | 
% 229.21/40.65  | |   (39)  all_57_6 = e1 & op(e1, e3) = e1
% 229.21/40.65  | | 
% 229.21/40.65  | | ALPHA: (39) implies:
% 229.21/40.65  | |   (40)  all_57_6 = e1
% 229.21/40.65  | | 
% 229.21/40.65  | | REF_CLOSE: (2), (3), (4), (5), (6), (11), (12), (14), (15), (17), (20),
% 229.21/40.65  | |            (23), (25), (27), (30), (31), (32), (33), (34), (35), (40) are
% 229.21/40.65  | |            inconsistent by sub-proof #759.
% 229.21/40.65  | | 
% 229.21/40.65  | Case 2:
% 229.21/40.65  | | 
% 229.21/40.65  | |   (41)  all_57_7 = e1 & op(e1, e2) = e1
% 229.21/40.65  | | 
% 229.21/40.65  | | ALPHA: (41) implies:
% 229.21/40.65  | |   (42)  all_57_7 = e1
% 229.21/40.65  | | 
% 229.21/40.65  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 229.21/40.65  | |            (13), (14), (15), (16), (18), (19), (20), (21), (22), (23), (24),
% 229.21/40.65  | |            (25), (26), (27), (29), (31), (32), (35), (36), (37), (38), (42)
% 229.21/40.65  | |            are inconsistent by sub-proof #711.
% 229.21/40.65  | | 
% 229.21/40.65  | End of split
% 229.21/40.65  | 
% 229.21/40.65  End of proof
% 229.21/40.65  
% 229.21/40.65  Sub-proof #711 shows that the following formulas are inconsistent:
% 229.21/40.65  ----------------------------------------------------------------
% 229.21/40.65    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.21/40.65         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.21/40.65    (2)   ~ (e3 = e1)
% 229.21/40.65    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.21/40.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.21/40.65    (4)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.21/40.65         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.21/40.65    (5)   ~ (all_6_2 = e3)
% 229.21/40.65    (6)  op(e1, e1) = all_6_2
% 229.21/40.65    (7)  op(e2, e2) = e1
% 229.21/40.65    (8)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.21/40.65         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.21/40.65    (9)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) = all_22_1
% 229.21/40.65           & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0, e3) =
% 229.21/40.65           all_22_1 & $i(all_22_1))
% 229.21/40.65    (10)  all_57_7 = e1
% 229.21/40.65    (11)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.21/40.65          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.21/40.65    (12)   ~ (e3 = e2)
% 229.21/40.65    (13)   ~ (e3 = e0)
% 229.21/40.65    (14)  op(e0, e3) = e1
% 229.21/40.65    (15)  all_57_15 = e3
% 229.21/40.65    (16)  op(e3, e3) = e2
% 229.21/40.65    (17)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.21/40.65          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.21/40.65            e1)
% 229.21/40.65    (18)  op(e1, e1) = e1
% 229.21/40.65    (19)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.21/40.65          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.21/40.65    (20)   ~ (e2 = e0)
% 229.21/40.65    (21)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 229.21/40.65            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 229.21/40.65              e3) = all_12_1 & $i(all_12_1))
% 229.21/40.65    (22)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.21/40.65          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.21/40.65    (23)   ~ (e1 = e0)
% 229.21/40.65    (24)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.21/40.65          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.21/40.65    (25)  op(e0, e0) = e3
% 229.21/40.65    (26)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.21/40.65          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.21/40.65            e2)
% 229.21/40.65    (27)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.21/40.65              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.21/40.65                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.21/40.65                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.21/40.65    (28)   ~ (all_53_12 = e3)
% 229.21/40.65    (29)   ~ (e2 = e1)
% 229.21/40.65    (30)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.21/40.65          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.21/40.65    (31)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.21/40.65          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.21/40.65    (32)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.21/40.65          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.21/40.65    (33)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 229.21/40.65          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 229.21/40.65    (34)  op(e3, e0) = all_53_12
% 229.21/40.65  
% 229.21/40.65  Begin of proof
% 229.21/40.65  | 
% 229.21/40.65  | BETA: splitting (1) gives:
% 229.21/40.65  | 
% 229.21/40.65  | Case 1:
% 229.21/40.65  | | 
% 229.21/40.65  | |   (35)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 229.21/40.65  | |           e2)
% 229.21/40.65  | | 
% 229.21/40.65  | | REF_CLOSE: (2), (3), (7), (8), (11), (12), (13), (16), (20), (22), (23),
% 229.21/40.65  | |            (28), (29), (34), (35) are inconsistent by sub-proof #714.
% 229.21/40.65  | | 
% 229.21/40.65  | Case 2:
% 229.21/40.65  | | 
% 229.21/40.65  | |   (36)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 229.21/40.65  | |           e2)
% 229.21/40.65  | | 
% 229.21/40.65  | | BETA: splitting (36) gives:
% 229.21/40.65  | | 
% 229.21/40.65  | | Case 1:
% 229.21/40.65  | | | 
% 229.21/40.65  | | |   (37)  all_57_7 = e2 & op(e1, e2) = e2
% 229.21/40.65  | | | 
% 229.21/40.65  | | | ALPHA: (37) implies:
% 229.21/40.65  | | |   (38)  all_57_7 = e2
% 229.21/40.65  | | | 
% 229.21/40.65  | | | REF_CLOSE: (10), (29), (38) are inconsistent by sub-proof #1761.
% 229.21/40.65  | | | 
% 229.21/40.65  | | Case 2:
% 229.21/40.65  | | | 
% 229.21/40.65  | | |   (39)  all_57_13 = e2 & op(e0, e2) = e2
% 229.21/40.65  | | | 
% 229.21/40.65  | | | ALPHA: (39) implies:
% 229.21/40.65  | | |   (40)  all_57_13 = e2
% 229.21/40.65  | | | 
% 229.21/40.65  | | | BETA: splitting (33) gives:
% 229.21/40.65  | | | 
% 229.21/40.65  | | | Case 1:
% 229.21/40.65  | | | | 
% 229.21/40.65  | | | |   (41)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2)
% 229.21/40.65  | | | |           = e2)
% 229.21/40.65  | | | | 
% 229.21/40.65  | | | | BETA: splitting (41) gives:
% 229.21/40.65  | | | | 
% 229.21/40.65  | | | | Case 1:
% 229.21/40.65  | | | | | 
% 229.21/40.65  | | | | |   (42)  all_57_6 = e2 & op(e1, e3) = e2
% 229.21/40.65  | | | | | 
% 229.21/40.65  | | | | | ALPHA: (42) implies:
% 229.21/40.65  | | | | |   (43)  all_57_6 = e2
% 229.21/40.65  | | | | | 
% 229.21/40.65  | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (10), (12), (13), (15), (20),
% 229.21/40.65  | | | | |            (23), (27), (29), (30), (31), (43) are inconsistent by
% 229.21/40.65  | | | | |            sub-proof #1245.
% 229.21/40.65  | | | | | 
% 229.21/40.65  | | | | Case 2:
% 229.21/40.65  | | | | | 
% 229.21/40.65  | | | | |   (44)  all_57_7 = e2 & op(e1, e2) = e2
% 229.21/40.65  | | | | | 
% 229.21/40.65  | | | | | ALPHA: (44) implies:
% 229.21/40.65  | | | | |   (45)  all_57_7 = e2
% 229.21/40.65  | | | | | 
% 229.21/40.65  | | | | | REF_CLOSE: (1), (2), (3), (7), (12), (13), (15), (17), (19), (20),
% 229.21/40.65  | | | | |            (23), (24), (25), (26), (27), (29), (32), (40), (45) are
% 229.21/40.65  | | | | |            inconsistent by sub-proof #712.
% 229.21/40.65  | | | | | 
% 229.21/40.65  | | | | End of split
% 229.21/40.65  | | | | 
% 229.21/40.65  | | | Case 2:
% 229.21/40.65  | | | | 
% 229.21/40.65  | | | |   (46)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0)
% 229.21/40.65  | | | |           = e2)
% 229.21/40.65  | | | | 
% 229.21/40.65  | | | | REF_CLOSE: (3), (9), (14), (18), (21), (29), (46) are inconsistent by
% 229.21/40.65  | | | |            sub-proof #1011.
% 229.21/40.65  | | | | 
% 229.21/40.65  | | | End of split
% 229.21/40.65  | | | 
% 229.21/40.65  | | End of split
% 229.21/40.65  | | 
% 229.21/40.65  | End of split
% 229.21/40.65  | 
% 229.21/40.65  End of proof
% 229.21/40.65  
% 229.21/40.65  Sub-proof #712 shows that the following formulas are inconsistent:
% 229.21/40.65  ----------------------------------------------------------------
% 229.21/40.65    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.21/40.65         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.21/40.65    (2)   ~ (e3 = e1)
% 229.21/40.65    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.21/40.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.21/40.65    (4)  op(e2, e2) = e1
% 229.21/40.65    (5)  all_57_7 = e2
% 229.21/40.65    (6)   ~ (e3 = e2)
% 229.21/40.65    (7)   ~ (e3 = e0)
% 229.21/40.65    (8)  all_57_15 = e3
% 229.21/40.65    (9)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 229.21/40.65         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.21/40.65    (10)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.21/40.65          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.21/40.65    (11)   ~ (e2 = e0)
% 229.21/40.65    (12)  all_57_13 = e2
% 229.21/40.65    (13)   ~ (e1 = e0)
% 229.21/40.65    (14)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.21/40.65          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.21/40.65    (15)  op(e0, e0) = e3
% 229.21/40.65    (16)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.21/40.65          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.21/40.65            e2)
% 229.21/40.65    (17)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.21/40.65              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.21/40.65                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.21/40.65                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.21/40.65    (18)   ~ (e2 = e1)
% 229.21/40.65    (19)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.21/40.65          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.21/40.65  
% 229.21/40.65  Begin of proof
% 229.21/40.65  | 
% 229.21/40.65  | BETA: splitting (14) gives:
% 229.21/40.65  | 
% 229.21/40.65  | Case 1:
% 229.21/40.65  | | 
% 229.21/40.65  | |   (20)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 229.21/40.65  | |           e3)
% 229.21/40.65  | | 
% 229.21/40.65  | | BETA: splitting (20) gives:
% 229.21/40.65  | | 
% 229.21/40.65  | | Case 1:
% 229.21/40.65  | | | 
% 229.21/40.65  | | |   (21)  all_57_1 = e3 & op(e3, e2) = e3
% 229.21/40.65  | | | 
% 229.21/40.65  | | | ALPHA: (21) implies:
% 229.21/40.65  | | |   (22)  all_57_1 = e3
% 229.21/40.65  | | | 
% 229.21/40.65  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (10), (11), (12), (13),
% 229.21/40.65  | | |            (18), (19), (22) are inconsistent by sub-proof #1697.
% 229.21/40.65  | | | 
% 229.21/40.65  | | Case 2:
% 229.21/40.65  | | | 
% 229.21/40.65  | | |   (23)  all_57_3 = e3 & op(e2, e2) = e3
% 229.21/40.65  | | | 
% 229.21/40.65  | | | ALPHA: (23) implies:
% 229.21/40.65  | | |   (24)  op(e2, e2) = e3
% 229.21/40.65  | | | 
% 229.21/40.65  | | | REF_CLOSE: (2), (3), (4), (24) are inconsistent by sub-proof #1912.
% 229.21/40.65  | | | 
% 229.21/40.65  | | End of split
% 229.21/40.65  | | 
% 229.21/40.65  | Case 2:
% 229.21/40.65  | | 
% 229.21/40.65  | |   (25)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 229.21/40.65  | |           e3)
% 229.21/40.65  | | 
% 229.21/40.65  | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (9), (11), (13), (15), (16), (17),
% 229.21/40.65  | |            (18), (25) are inconsistent by sub-proof #713.
% 229.21/40.65  | | 
% 229.21/40.65  | End of split
% 229.21/40.65  | 
% 229.21/40.65  End of proof
% 229.21/40.65  
% 229.21/40.65  Sub-proof #713 shows that the following formulas are inconsistent:
% 229.21/40.65  ----------------------------------------------------------------
% 229.21/40.65    (1)   ~ (e3 = e1)
% 229.21/40.65    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.21/40.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.21/40.65    (3)  all_57_7 = e2
% 229.21/40.65    (4)   ~ (e3 = e2)
% 229.21/40.65    (5)   ~ (e3 = e0)
% 229.21/40.65    (6)  all_57_15 = e3
% 229.21/40.65    (7)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 229.21/40.65         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.21/40.65    (8)   ~ (e2 = e0)
% 229.21/40.65    (9)   ~ (e1 = e0)
% 229.21/40.65    (10)  op(e0, e0) = e3
% 229.21/40.65    (11)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.21/40.65          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.21/40.65            e2)
% 229.21/40.65    (12)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.21/40.65              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.21/40.65                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.21/40.65                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.21/40.65    (13)   ~ (e2 = e1)
% 229.21/40.65    (14)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.21/40.65  
% 229.21/40.65  Begin of proof
% 229.21/40.65  | 
% 229.21/40.65  | BETA: splitting (14) gives:
% 229.21/40.65  | 
% 229.21/40.65  | Case 1:
% 229.21/40.65  | | 
% 229.21/40.65  | |   (15)  all_57_7 = e3 & op(e1, e2) = e3
% 229.21/40.65  | | 
% 229.21/40.65  | | REF_CLOSE: (3), (4), (15) are inconsistent by sub-proof #2194.
% 229.21/40.65  | | 
% 229.21/40.65  | Case 2:
% 229.21/40.65  | | 
% 229.21/40.65  | |   (16)  all_57_13 = e3 & op(e0, e2) = e3
% 229.21/40.65  | | 
% 229.21/40.65  | | ALPHA: (16) implies:
% 229.21/40.65  | |   (17)  all_57_13 = e3
% 229.21/40.65  | | 
% 229.21/40.65  | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 229.21/40.65  | |            (17) are inconsistent by sub-proof #1792.
% 229.21/40.65  | | 
% 229.21/40.65  | End of split
% 229.21/40.65  | 
% 229.21/40.65  End of proof
% 229.21/40.65  
% 229.21/40.65  Sub-proof #714 shows that the following formulas are inconsistent:
% 229.21/40.65  ----------------------------------------------------------------
% 229.21/40.65    (1)   ~ (e3 = e1)
% 229.21/40.65    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.21/40.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.21/40.65    (3)  op(e2, e2) = e1
% 229.21/40.65    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.21/40.65         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.21/40.65    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2)
% 229.21/40.65    (6)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.21/40.65         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.21/40.65    (7)   ~ (e3 = e2)
% 229.21/40.65    (8)   ~ (e3 = e0)
% 229.21/40.65    (9)  op(e3, e3) = e2
% 229.21/40.65    (10)   ~ (e2 = e0)
% 229.21/40.65    (11)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.21/40.65          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.21/40.65    (12)   ~ (e1 = e0)
% 229.21/40.65    (13)   ~ (all_53_12 = e3)
% 229.21/40.65    (14)   ~ (e2 = e1)
% 229.21/40.65    (15)  op(e3, e0) = all_53_12
% 229.21/40.65  
% 229.21/40.65  Begin of proof
% 229.21/40.65  | 
% 229.21/40.65  | BETA: splitting (5) gives:
% 229.21/40.65  | 
% 229.21/40.65  | Case 1:
% 229.21/40.65  | | 
% 229.21/40.65  | |   (16)  all_57_1 = e2 & op(e3, e2) = e2
% 229.21/40.65  | | 
% 229.21/40.65  | | ALPHA: (16) implies:
% 229.21/40.65  | |   (17)  all_57_1 = e2
% 229.21/40.65  | | 
% 229.21/40.65  | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (9), (10), (11), (12), (13), (14),
% 229.21/40.65  | |            (15), (17) are inconsistent by sub-proof #1650.
% 229.21/40.65  | | 
% 229.21/40.65  | Case 2:
% 229.21/40.65  | | 
% 229.21/40.65  | |   (18)  all_57_3 = e2 & op(e2, e2) = e2
% 229.21/40.65  | | 
% 229.21/40.65  | | ALPHA: (18) implies:
% 229.21/40.65  | |   (19)  op(e2, e2) = e2
% 229.21/40.65  | | 
% 229.21/40.65  | | REF_CLOSE: (2), (3), (14), (19) are inconsistent by sub-proof #2306.
% 229.21/40.65  | | 
% 229.21/40.65  | End of split
% 229.21/40.65  | 
% 229.21/40.65  End of proof
% 229.21/40.65  
% 229.21/40.65  Sub-proof #715 shows that the following formulas are inconsistent:
% 229.21/40.65  ----------------------------------------------------------------
% 229.21/40.65    (1)   ~ (all_53_2 = e2)
% 229.21/40.65    (2)  all_57_0 = e2
% 229.21/40.65    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.21/40.65         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.21/40.65    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.21/40.65         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.21/40.65    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.21/40.65         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.21/40.65    (6)   ~ (e3 = e1)
% 229.21/40.65    (7)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 229.21/40.65         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 229.21/40.65    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.21/40.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.21/40.65    (9)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.21/40.65         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.21/40.65    (10)   ~ (all_53_3 = e3)
% 229.21/40.65    (11)   ~ (all_53_3 = all_53_7)
% 229.21/40.65    (12)   ~ (all_6_2 = e3)
% 229.21/40.65    (13)   ~ (all_53_9 = e1)
% 229.21/40.65    (14)  op(e1, e1) = all_6_2
% 229.21/40.65    (15)   ~ (all_53_1 = all_53_9)
% 229.21/40.65    (16)  op(e2, e2) = e1
% 229.21/40.66    (17)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.21/40.66          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.21/40.66    (18)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 229.21/40.66            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 229.21/40.66              e3) = all_22_1 & $i(all_22_1))
% 229.21/40.66    (19)   ~ (all_53_13 = e3)
% 229.21/40.66    (20)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.21/40.66          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.21/40.66    (21)   ~ (all_53_9 = all_53_11)
% 229.21/40.66    (22)  all_55_4 = all_53_1
% 229.21/40.66    (23)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.21/40.66          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.21/40.66    (24)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 229.21/40.66          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.21/40.66    (25)   ~ (e3 = e2)
% 229.21/40.66    (26)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 229.21/40.66    (27)   ~ (all_53_1 = all_53_3)
% 229.21/40.66    (28)   ~ (e3 = e0)
% 229.21/40.66    (29)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 229.21/40.66    (30)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 229.21/40.66    (31)  all_57_15 = e3
% 229.21/40.66    (32)   ~ (all_53_9 = all_53_13)
% 229.21/40.66    (33)  op(e3, e3) = e2
% 229.21/40.66    (34)  all_57_4 = e1
% 229.21/40.66    (35)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.21/40.66          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.21/40.66            e1)
% 229.21/40.66    (36)   ~ (all_53_1 = e1)
% 229.21/40.66    (37)  all_55_6 = all_53_9
% 229.21/40.66    (38)   ~ (all_53_1 = all_53_2)
% 229.21/40.66    (39)  op(e1, e1) = e1
% 229.21/40.66    (40)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.21/40.66          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.21/40.66    (41)   ~ (e2 = e0)
% 229.21/40.66    (42)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 229.21/40.66            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 229.21/40.66            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 229.21/40.66            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 229.21/40.66              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 229.21/40.66            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 229.21/40.66            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 229.21/40.66              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 229.21/40.66              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 229.21/40.66            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 229.21/40.66            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 229.21/40.66            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 229.21/40.66              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 229.21/40.66              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 229.21/40.66            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 229.21/40.66              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 229.21/40.66            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 229.21/40.66            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 229.21/40.66              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 229.21/40.66              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 229.21/40.66            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 229.21/40.66            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 229.21/40.66    (43)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 229.21/40.66            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 229.21/40.66              e3) = all_12_1 & $i(all_12_1))
% 229.21/40.66    (44)  all_55_12 = all_53_3
% 229.21/40.66    (45)  all_57_3 = e1
% 229.21/40.66    (46)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.21/40.66          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.21/40.66    (47)   ~ (e1 = e0)
% 229.21/40.66    (48)   ~ (all_53_3 = all_53_11)
% 229.21/40.66    (49)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.21/40.66          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.21/40.66    (50)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.21/40.66          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.21/40.66    (51)   ~ (all_53_2 = all_53_3)
% 229.21/40.66    (52)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 229.21/40.66    (53)   ~ (all_53_7 = all_53_11)
% 229.21/40.66    (54)  all_55_8 = all_53_2
% 229.21/40.66    (55)  op(e0, e0) = e3
% 229.21/40.66    (56)  op(e0, e2) = all_53_7
% 229.21/40.66    (57)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.21/40.66          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.21/40.66            e2)
% 229.21/40.66    (58)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.21/40.66              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.21/40.66                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.21/40.66                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.21/40.66    (59)   ~ (all_53_1 = all_53_13)
% 229.21/40.66    (60)  op(e2, e0) = all_53_13
% 229.21/40.66    (61)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.21/40.66          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.21/40.66    (62)   ~ (all_53_12 = e3)
% 229.21/40.66    (63)  op(e1, e3) = all_53_2
% 229.21/40.66    (64)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.21/40.66          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.21/40.66    (65)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.21/40.66          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.21/40.66    (66)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.21/40.66          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 229.21/40.66    (67)   ~ (e2 = e1)
% 229.21/40.66    (68)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.21/40.66          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.21/40.66    (69)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.21/40.66          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.21/40.66    (70)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 229.21/40.66    (71)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 229.21/40.66          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 229.21/40.66    (72)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.21/40.66          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.21/40.66    (73)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.21/40.66          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.21/40.66    (74)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 229.21/40.66          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 229.21/40.66    (75)  all_55_14 = all_53_11
% 229.21/40.66    (76)   ~ (all_53_11 = e3)
% 229.21/40.66    (77)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.21/40.66          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.21/40.66    (78)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 229.21/40.66          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 229.21/40.66    (79)  op(e3, e0) = all_53_12
% 229.21/40.66  
% 229.21/40.66  Begin of proof
% 229.21/40.66  | 
% 229.21/40.66  | BETA: splitting (73) gives:
% 229.21/40.66  | 
% 229.21/40.66  | Case 1:
% 229.21/40.66  | | 
% 229.21/40.66  | |   (80)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) =
% 229.21/40.66  | |           e1)
% 229.21/40.66  | | 
% 229.21/40.66  | | BETA: splitting (80) gives:
% 229.21/40.66  | | 
% 229.21/40.66  | | Case 1:
% 229.21/40.66  | | | 
% 229.21/40.66  | | |   (81)  all_57_9 = e1 & op(e3, e0) = e1
% 229.21/40.66  | | | 
% 229.21/40.66  | | | ALPHA: (81) implies:
% 229.21/40.66  | | |   (82)  all_57_9 = e1
% 229.21/40.66  | | | 
% 229.21/40.66  | | | REF_CLOSE: (6), (8), (23), (25), (28), (33), (34), (41), (46), (47), (62),
% 229.21/40.66  | | |            (79), (82) are inconsistent by sub-proof #813.
% 229.21/40.66  | | | 
% 229.21/40.66  | | Case 2:
% 229.21/40.66  | | | 
% 229.21/40.66  | | |   (83)  all_57_10 = e1 & op(e2, e0) = e1
% 229.21/40.66  | | | 
% 229.21/40.66  | | | ALPHA: (83) implies:
% 229.21/40.66  | | |   (84)  all_57_10 = e1
% 229.21/40.66  | | | 
% 229.21/40.66  | | | BETA: splitting (68) gives:
% 229.21/40.66  | | | 
% 229.21/40.66  | | | Case 1:
% 229.21/40.66  | | | | 
% 229.21/40.66  | | | |   (85)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0)
% 229.21/40.66  | | | |           = e2)
% 229.21/40.66  | | | | 
% 229.21/40.66  | | | | REF_CLOSE: (3), (4), (5), (6), (8), (9), (12), (14), (16), (17), (20),
% 229.21/40.66  | | | |            (23), (25), (28), (31), (33), (35), (40), (41), (45), (46),
% 229.21/40.66  | | | |            (47), (49), (50), (55), (57), (58), (62), (64), (65), (66),
% 229.21/40.66  | | | |            (67), (68), (72), (73), (77), (79), (84), (85) are
% 229.21/40.66  | | | |            inconsistent by sub-proof #804.
% 229.21/40.66  | | | | 
% 229.21/40.66  | | | Case 2:
% 229.21/40.66  | | | | 
% 229.21/40.66  | | | |   (86)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0,
% 229.21/40.66  | | | |             e0) = e2)
% 229.21/40.66  | | | | 
% 229.21/40.66  | | | | BETA: splitting (86) gives:
% 229.21/40.66  | | | | 
% 229.21/40.66  | | | | Case 1:
% 229.21/40.66  | | | | | 
% 229.21/40.66  | | | | |   (87)  all_57_11 = e2 & op(e1, e0) = e2
% 229.21/40.66  | | | | | 
% 229.21/40.66  | | | | | ALPHA: (87) implies:
% 229.21/40.66  | | | | |   (88)  all_57_11 = e2
% 229.21/40.66  | | | | |   (89)  op(e1, e0) = e2
% 229.21/40.66  | | | | | 
% 229.21/40.66  | | | | | BETA: splitting (35) gives:
% 229.21/40.66  | | | | | 
% 229.21/40.66  | | | | | Case 1:
% 229.21/40.66  | | | | | | 
% 229.21/40.66  | | | | | |   (90)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 &
% 229.21/40.66  | | | | | |           op(e0, e2) = e1)
% 229.21/40.66  | | | | | | 
% 229.21/40.66  | | | | | | BETA: splitting (90) gives:
% 229.21/40.66  | | | | | | 
% 229.21/40.66  | | | | | | Case 1:
% 229.21/40.66  | | | | | | | 
% 229.21/40.66  | | | | | | |   (91)  all_57_12 = e1 & op(e0, e3) = e1
% 229.21/40.66  | | | | | | | 
% 229.21/40.66  | | | | | | | ALPHA: (91) implies:
% 229.21/40.66  | | | | | | |   (92)  op(e0, e3) = e1
% 229.21/40.66  | | | | | | | 
% 229.21/40.66  | | | | | | | REF_CLOSE: (8), (18), (43), (89), (92) are inconsistent by
% 229.21/40.66  | | | | | | |            sub-proof #1147.
% 229.21/40.66  | | | | | | | 
% 229.21/40.66  | | | | | | Case 2:
% 229.21/40.66  | | | | | | | 
% 229.21/40.66  | | | | | | |   (93)  all_57_13 = e1 & op(e0, e2) = e1
% 229.21/40.66  | | | | | | | 
% 229.21/40.66  | | | | | | | ALPHA: (93) implies:
% 229.21/40.66  | | | | | | |   (94)  all_57_13 = e1
% 229.21/40.66  | | | | | | | 
% 229.21/40.66  | | | | | | | BETA: splitting (46) gives:
% 229.21/40.66  | | | | | | | 
% 229.21/40.66  | | | | | | | Case 1:
% 229.21/40.66  | | | | | | | | 
% 229.21/40.66  | | | | | | | |   (95)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 &
% 229.21/40.66  | | | | | | | |           op(e3, e2) = e3)
% 229.21/40.66  | | | | | | | | 
% 229.21/40.66  | | | | | | | | BETA: splitting (95) gives:
% 229.21/40.66  | | | | | | | | 
% 229.21/40.66  | | | | | | | | Case 1:
% 229.21/40.66  | | | | | | | | | 
% 229.21/40.66  | | | | | | | | |   (96)  all_57_0 = e3 & op(e3, e3) = e3
% 229.21/40.66  | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | ALPHA: (96) implies:
% 229.21/40.66  | | | | | | | | |   (97)  op(e3, e3) = e3
% 229.21/40.66  | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | REF_CLOSE: (8), (25), (33), (97) are inconsistent by sub-proof
% 229.21/40.66  | | | | | | | | |            #2490.
% 229.21/40.66  | | | | | | | | | 
% 229.21/40.66  | | | | | | | | Case 2:
% 229.21/40.66  | | | | | | | | | 
% 229.21/40.66  | | | | | | | | |   (98)  all_57_1 = e3 & op(e3, e2) = e3
% 229.21/40.66  | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | ALPHA: (98) implies:
% 229.21/40.66  | | | | | | | | |   (99)  all_57_1 = e3
% 229.21/40.66  | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | BETA: splitting (64) gives:
% 229.21/40.66  | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | Case 1:
% 229.21/40.66  | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | |   (100)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 229.21/40.66  | | | | | | | | | |            & op(e2, e2) = e2)
% 229.21/40.66  | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | REF_CLOSE: (3), (4), (5), (6), (8), (9), (12), (14), (16),
% 229.21/40.66  | | | | | | | | | |            (25), (28), (31), (33), (34), (40), (41), (45),
% 229.21/40.66  | | | | | | | | | |            (46), (47), (50), (58), (61), (62), (64), (65),
% 229.21/40.66  | | | | | | | | | |            (67), (68), (72), (73), (77), (79), (88), (99),
% 229.21/40.66  | | | | | | | | | |            (100) are inconsistent by sub-proof #802.
% 229.21/40.66  | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | Case 2:
% 229.21/40.66  | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | |   (101)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2
% 229.21/40.66  | | | | | | | | | |            & op(e2, e0) = e2)
% 229.21/40.66  | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | BETA: splitting (101) gives:
% 229.21/40.66  | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | Case 1:
% 229.21/40.66  | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | |   (102)  all_57_5 = e2 & op(e2, e1) = e2
% 229.21/40.66  | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | ALPHA: (102) implies:
% 229.21/40.66  | | | | | | | | | | |   (103)  all_57_5 = e2
% 229.21/40.66  | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | BETA: splitting (61) gives:
% 229.21/40.66  | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | Case 1:
% 229.21/40.66  | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | |   (104)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 229.21/40.66  | | | | | | | | | | | |            & op(e2, e2) = e3)
% 229.21/40.66  | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | BETA: splitting (104) gives:
% 229.21/40.66  | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | Case 1:
% 229.21/40.66  | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | |   (105)  all_57_2 = e3 & op(e2, e3) = e3
% 229.21/40.66  | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | ALPHA: (105) implies:
% 229.21/40.66  | | | | | | | | | | | | |   (106)  all_57_2 = e3
% 229.21/40.66  | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | BETA: splitting (40) gives:
% 229.21/40.66  | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | Case 1:
% 229.21/40.66  | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | |   (107)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 229.21/40.66  | | | | | | | | | | | | | |            & op(e2, e2) = e0)
% 229.21/40.66  | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 229.21/40.66  | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | | Case 1:
% 229.21/40.66  | | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | | |   (108)  all_57_1 = e0 & op(e3, e2) = e0
% 229.21/40.66  | | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (5), (6), (8), (9), (12), (14), (16),
% 229.21/40.66  | | | | | | | | | | | | | | |            (17), (18), (23), (25), (28), (31), (33), (40),
% 229.21/40.66  | | | | | | | | | | | | | | |            (41), (43), (45), (46), (47), (58), (61), (62),
% 229.21/40.66  | | | | | | | | | | | | | | |            (64), (67), (68), (73), (77), (79), (89), (94),
% 229.21/40.66  | | | | | | | | | | | | | | |            (99), (106), (108) are inconsistent by sub-proof
% 229.21/40.66  | | | | | | | | | | | | | | |            #795.
% 229.21/40.66  | | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | | Case 2:
% 229.21/40.66  | | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | | |   (109)  all_57_3 = e0 & op(e2, e2) = e0
% 229.21/40.66  | | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | | | ALPHA: (109) implies:
% 229.21/40.66  | | | | | | | | | | | | | | |   (110)  all_57_3 = e0
% 229.21/40.66  | | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (9), (12), (14),
% 229.21/40.66  | | | | | | | | | | | | | | |            (25), (28), (31), (33), (41), (47), (55), (58),
% 229.21/40.66  | | | | | | | | | | | | | | |            (61), (64), (67), (68), (72), (73), (77), (99),
% 229.21/40.66  | | | | | | | | | | | | | | |            (106), (110) are inconsistent by sub-proof #792.
% 229.21/40.66  | | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | | End of split
% 229.21/40.66  | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | Case 2:
% 229.21/40.66  | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | |   (111)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 229.21/40.66  | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0)
% 229.21/40.66  | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | | BETA: splitting (111) gives:
% 229.21/40.66  | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | | Case 1:
% 229.21/40.66  | | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | | |   (112)  all_57_7 = e0 & op(e1, e2) = e0
% 229.21/40.66  | | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | | | ALPHA: (112) implies:
% 229.21/40.66  | | | | | | | | | | | | | | |   (113)  all_57_7 = e0
% 229.21/40.66  | | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | | | BETA: splitting (23) gives:
% 229.21/40.66  | | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | | | Case 1:
% 229.21/40.66  | | | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | | | |   (114)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 229.21/40.66  | | | | | | | | | | | | | | | |            & op(e3, e2) = e0)
% 229.21/40.66  | | | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | | | | BETA: splitting (114) gives:
% 229.21/40.66  | | | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | | | | Case 1:
% 229.21/40.66  | | | | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | | | | |   (115)  all_57_0 = e0 & op(e3, e3) = e0
% 229.21/40.66  | | | | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | | | | | ALPHA: (115) implies:
% 229.21/40.66  | | | | | | | | | | | | | | | | |   (116)  op(e3, e3) = e0
% 229.21/40.66  | | | | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (33), (41), (116) are inconsistent by
% 229.21/40.66  | | | | | | | | | | | | | | | | |            sub-proof #2403.
% 229.21/40.66  | | | | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | | | | Case 2:
% 229.21/40.66  | | | | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | | | | |   (117)  all_57_1 = e0 & op(e3, e2) = e0
% 229.21/40.66  | | | | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (5), (6), (8), (9), (12), (14), (16),
% 229.21/40.66  | | | | | | | | | | | | | | | | |            (17), (18), (23), (25), (28), (31), (33), (40),
% 229.21/40.66  | | | | | | | | | | | | | | | | |            (41), (43), (45), (46), (47), (58), (61), (62),
% 229.21/40.66  | | | | | | | | | | | | | | | | |            (64), (67), (68), (73), (77), (79), (89), (94),
% 229.21/40.66  | | | | | | | | | | | | | | | | |            (99), (106), (117) are inconsistent by sub-proof
% 229.21/40.66  | | | | | | | | | | | | | | | | |            #795.
% 229.21/40.66  | | | | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | | | | End of split
% 229.21/40.66  | | | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | | | Case 2:
% 229.21/40.66  | | | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | | | |   (118)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 229.21/40.66  | | | | | | | | | | | | | | | |            & op(e3, e0) = e0)
% 229.21/40.66  | | | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | | | | BETA: splitting (118) gives:
% 229.21/40.66  | | | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | | | | Case 1:
% 229.21/40.66  | | | | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | | | | |   (119)  all_57_4 = e0 & op(e3, e1) = e0
% 229.21/40.66  | | | | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | | | | | ALPHA: (119) implies:
% 229.21/40.66  | | | | | | | | | | | | | | | | |   (120)  all_57_4 = e0
% 229.21/40.66  | | | | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | | | | | COMBINE_EQS: (34), (120) imply:
% 229.21/40.66  | | | | | | | | | | | | | | | | |   (121)  e1 = e0
% 229.21/40.66  | | | | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | | | | | SIMP: (121) implies:
% 229.21/40.66  | | | | | | | | | | | | | | | | |   (122)  e1 = e0
% 229.21/40.66  | | | | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | | | | | COMBINE_EQS: (45), (122) imply:
% 229.21/40.66  | | | | | | | | | | | | | | | | |   (123)  all_57_3 = e0
% 229.21/40.66  | | | | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (9), (12), (14),
% 229.21/40.66  | | | | | | | | | | | | | | | | |            (17), (23), (25), (28), (31), (33), (35), (41),
% 229.21/40.66  | | | | | | | | | | | | | | | | |            (46), (47), (50), (55), (57), (58), (61), (62),
% 229.21/40.66  | | | | | | | | | | | | | | | | |            (64), (65), (67), (68), (69), (72), (73), (77),
% 229.21/40.66  | | | | | | | | | | | | | | | | |            (79), (94), (99), (113), (123) are inconsistent by
% 229.21/40.66  | | | | | | | | | | | | | | | | |            sub-proof #782.
% 229.21/40.66  | | | | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | | | | Case 2:
% 229.21/40.66  | | | | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | | | | |   (124)  all_57_9 = e0 & op(e3, e0) = e0
% 229.21/40.66  | | | | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | | | | | ALPHA: (124) implies:
% 229.21/40.66  | | | | | | | | | | | | | | | | |   (125)  all_57_9 = e0
% 229.21/40.66  | | | | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | | | | | BETA: splitting (9) gives:
% 229.21/40.66  | | | | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | | | | | Case 1:
% 229.21/40.66  | | | | | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | | | | | |   (126)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 229.21/40.66  | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e3)
% 229.21/40.66  | | | | | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | | | | | | BETA: splitting (126) gives:
% 229.21/40.66  | | | | | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | | | | | | Case 1:
% 229.21/40.66  | | | | | | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | | | | | | |   (127)  all_57_6 = e3 & op(e1, e3) = e3
% 229.21/40.66  | | | | | | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | | | | | | | ALPHA: (127) implies:
% 229.21/40.66  | | | | | | | | | | | | | | | | | | |   (128)  all_57_6 = e3
% 229.21/40.66  | | | | | | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (6), (8), (25), (28), (41), (47), (67),
% 229.21/40.66  | | | | | | | | | | | | | | | | | | |            (69), (72), (106), (128) are inconsistent by
% 229.21/40.66  | | | | | | | | | | | | | | | | | | |            sub-proof #1286.
% 229.21/40.66  | | | | | | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | | | | | | Case 2:
% 229.21/40.66  | | | | | | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | | | | | | |   (129)  all_57_7 = e3 & op(e1, e2) = e3
% 229.21/40.66  | | | | | | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | | | | | | | ALPHA: (129) implies:
% 229.21/40.66  | | | | | | | | | | | | | | | | | | |   (130)  all_57_7 = e3
% 229.21/40.66  | | | | | | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (113), (130) imply:
% 229.21/40.66  | | | | | | | | | | | | | | | | | | |   (131)  e3 = e0
% 229.21/40.66  | | | | | | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (106), (131) imply:
% 229.21/40.66  | | | | | | | | | | | | | | | | | | |   (132)  all_57_2 = e0
% 229.21/40.66  | | | | | | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (5), (6), (8), (9), (12), (14), (16),
% 229.21/40.66  | | | | | | | | | | | | | | | | | | |            (17), (18), (23), (25), (28), (31), (33), (40),
% 229.21/40.66  | | | | | | | | | | | | | | | | | | |            (41), (43), (45), (46), (47), (58), (61), (62),
% 229.21/40.66  | | | | | | | | | | | | | | | | | | |            (64), (67), (68), (73), (77), (79), (89), (94),
% 229.21/40.66  | | | | | | | | | | | | | | | | | | |            (132) are inconsistent by sub-proof #796.
% 229.21/40.66  | | | | | | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | | | | | | End of split
% 229.21/40.66  | | | | | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | | | | | Case 2:
% 229.21/40.66  | | | | | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | | | | | |   (133)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 229.21/40.66  | | | | | | | | | | | | | | | | | |            e3 & op(e1, e0) = e3)
% 229.21/40.66  | | | | | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (12), (14), (25), (31), (41), (47),
% 229.21/40.66  | | | | | | | | | | | | | | | | | |            (67), (68), (73), (125), (133) are inconsistent by
% 229.21/40.66  | | | | | | | | | | | | | | | | | |            sub-proof #781.
% 229.21/40.66  | | | | | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | | | | | End of split
% 229.21/40.66  | | | | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | | | | End of split
% 229.21/40.66  | | | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | | | End of split
% 229.21/40.66  | | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | | Case 2:
% 229.21/40.66  | | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | | |   (134)  all_57_13 = e0 & op(e0, e2) = e0
% 229.21/40.66  | | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | | | ALPHA: (134) implies:
% 229.21/40.66  | | | | | | | | | | | | | | |   (135)  all_57_13 = e0
% 229.21/40.66  | | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | | | COMBINE_EQS: (94), (135) imply:
% 229.21/40.66  | | | | | | | | | | | | | | |   (136)  e1 = e0
% 229.21/40.66  | | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | | | SIMP: (136) implies:
% 229.21/40.66  | | | | | | | | | | | | | | |   (137)  e1 = e0
% 229.21/40.66  | | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (9), (12), (14),
% 229.21/40.66  | | | | | | | | | | | | | | |            (17), (23), (25), (28), (31), (33), (35), (41),
% 229.21/40.66  | | | | | | | | | | | | | | |            (45), (46), (47), (50), (55), (57), (58), (61),
% 229.21/40.66  | | | | | | | | | | | | | | |            (62), (64), (65), (67), (68), (72), (73), (77),
% 229.21/40.66  | | | | | | | | | | | | | | |            (79), (135), (137) are inconsistent by sub-proof
% 229.21/40.66  | | | | | | | | | | | | | | |            #778.
% 229.21/40.66  | | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | | End of split
% 229.21/40.66  | | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | End of split
% 229.21/40.66  | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | Case 2:
% 229.21/40.66  | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | |   (138)  all_57_3 = e3 & op(e2, e2) = e3
% 229.21/40.66  | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | ALPHA: (138) implies:
% 229.21/40.66  | | | | | | | | | | | | |   (139)  op(e2, e2) = e3
% 229.21/40.66  | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | | REF_CLOSE: (6), (8), (16), (139) are inconsistent by
% 229.21/40.66  | | | | | | | | | | | | |            sub-proof #1912.
% 229.21/40.66  | | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | End of split
% 229.21/40.66  | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | Case 2:
% 229.21/40.66  | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | |   (140)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 229.21/40.66  | | | | | | | | | | | |            e3 & op(e2, e0) = e3)
% 229.21/40.66  | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | | REF_CLOSE: (6), (8), (12), (14), (17), (20), (23), (25),
% 229.21/40.66  | | | | | | | | | | | |            (28), (31), (33), (34), (35), (41), (46), (47),
% 229.21/40.66  | | | | | | | | | | | |            (49), (57), (58), (62), (67), (68), (79), (99),
% 229.21/40.66  | | | | | | | | | | | |            (103), (140) are inconsistent by sub-proof #777.
% 229.21/40.66  | | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | End of split
% 229.21/40.66  | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | Case 2:
% 229.21/40.66  | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | |   (141)  all_57_10 = e2 & op(e2, e0) = e2
% 229.21/40.66  | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | ALPHA: (141) implies:
% 229.21/40.66  | | | | | | | | | | |   (142)  op(e2, e0) = e2
% 229.21/40.66  | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10),
% 229.21/40.66  | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (19),
% 229.21/40.66  | | | | | | | | | | |            (21), (22), (23), (25), (26), (27), (28), (29),
% 229.21/40.66  | | | | | | | | | | |            (30), (31), (32), (33), (34), (35), (36), (37),
% 229.21/40.66  | | | | | | | | | | |            (38), (40), (41), (42), (44), (45), (46), (47),
% 229.21/40.66  | | | | | | | | | | |            (48), (50), (51), (52), (53), (54), (55), (56),
% 229.21/40.66  | | | | | | | | | | |            (57), (58), (59), (60), (61), (62), (63), (64),
% 229.21/40.66  | | | | | | | | | | |            (65), (67), (68), (69), (70), (72), (73), (75),
% 229.21/40.66  | | | | | | | | | | |            (76), (77), (79), (94), (99), (142) are
% 229.21/40.66  | | | | | | | | | | |            inconsistent by sub-proof #767.
% 229.21/40.66  | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | End of split
% 229.21/40.66  | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | End of split
% 229.21/40.66  | | | | | | | | | 
% 229.21/40.66  | | | | | | | | End of split
% 229.21/40.66  | | | | | | | | 
% 229.21/40.66  | | | | | | | Case 2:
% 229.21/40.66  | | | | | | | | 
% 229.21/40.66  | | | | | | | |   (143)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 &
% 229.21/40.66  | | | | | | | |            op(e3, e0) = e3)
% 229.21/40.66  | | | | | | | | 
% 229.21/40.66  | | | | | | | | REF_CLOSE: (6), (8), (34), (62), (79), (143) are inconsistent by
% 229.21/40.66  | | | | | | | |            sub-proof #2281.
% 229.21/40.66  | | | | | | | | 
% 229.21/40.66  | | | | | | | End of split
% 229.21/40.66  | | | | | | | 
% 229.21/40.66  | | | | | | End of split
% 229.21/40.66  | | | | | | 
% 229.21/40.66  | | | | | Case 2:
% 229.21/40.66  | | | | | | 
% 229.21/40.66  | | | | | |   (144)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 &
% 229.21/40.66  | | | | | |            op(e0, e0) = e1)
% 229.21/40.66  | | | | | | 
% 229.21/40.66  | | | | | | BETA: splitting (144) gives:
% 229.21/40.66  | | | | | | 
% 229.21/40.66  | | | | | | Case 1:
% 229.21/40.66  | | | | | | | 
% 229.21/40.66  | | | | | | |   (145)  all_57_14 = e1 & op(e0, e1) = e1
% 229.21/40.66  | | | | | | | 
% 229.21/40.66  | | | | | | | ALPHA: (145) implies:
% 229.21/40.66  | | | | | | |   (146)  all_57_14 = e1
% 229.21/40.66  | | | | | | | 
% 229.21/40.66  | | | | | | | BETA: splitting (46) gives:
% 229.21/40.66  | | | | | | | 
% 229.21/40.66  | | | | | | | Case 1:
% 229.21/40.66  | | | | | | | | 
% 229.21/40.66  | | | | | | | |   (147)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 &
% 229.21/40.66  | | | | | | | |            op(e3, e2) = e3)
% 229.21/40.66  | | | | | | | | 
% 229.21/40.66  | | | | | | | | BETA: splitting (147) gives:
% 229.21/40.66  | | | | | | | | 
% 229.21/40.66  | | | | | | | | Case 1:
% 229.21/40.66  | | | | | | | | | 
% 229.21/40.66  | | | | | | | | |   (148)  all_57_0 = e3 & op(e3, e3) = e3
% 229.21/40.66  | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | ALPHA: (148) implies:
% 229.21/40.66  | | | | | | | | |   (149)  op(e3, e3) = e3
% 229.21/40.66  | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | REF_CLOSE: (8), (25), (33), (149) are inconsistent by
% 229.21/40.66  | | | | | | | | |            sub-proof #2490.
% 229.21/40.66  | | | | | | | | | 
% 229.21/40.66  | | | | | | | | Case 2:
% 229.21/40.66  | | | | | | | | | 
% 229.21/40.66  | | | | | | | | |   (150)  all_57_1 = e3 & op(e3, e2) = e3
% 229.21/40.66  | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | ALPHA: (150) implies:
% 229.21/40.66  | | | | | | | | |   (151)  all_57_1 = e3
% 229.21/40.66  | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | BETA: splitting (64) gives:
% 229.21/40.66  | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | Case 1:
% 229.21/40.66  | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | |   (152)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 229.21/40.66  | | | | | | | | | |            & op(e2, e2) = e2)
% 229.21/40.66  | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | REF_CLOSE: (3), (4), (5), (6), (8), (9), (12), (14), (16),
% 229.21/40.66  | | | | | | | | | |            (25), (28), (31), (33), (34), (40), (41), (45),
% 229.21/40.66  | | | | | | | | | |            (46), (47), (50), (58), (61), (62), (64), (65),
% 229.21/40.66  | | | | | | | | | |            (67), (68), (72), (73), (77), (79), (88), (151),
% 229.21/40.66  | | | | | | | | | |            (152) are inconsistent by sub-proof #802.
% 229.21/40.66  | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | Case 2:
% 229.21/40.66  | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | |   (153)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2
% 229.21/40.66  | | | | | | | | | |            & op(e2, e0) = e2)
% 229.21/40.66  | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | BETA: splitting (153) gives:
% 229.21/40.66  | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | Case 1:
% 229.21/40.66  | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | |   (154)  all_57_5 = e2 & op(e2, e1) = e2
% 229.21/40.66  | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | ALPHA: (154) implies:
% 229.21/40.66  | | | | | | | | | | |   (155)  all_57_5 = e2
% 229.21/40.66  | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (9), (12), (14),
% 229.21/40.66  | | | | | | | | | | |            (16), (17), (20), (23), (24), (25), (28), (31),
% 229.21/40.66  | | | | | | | | | | |            (33), (34), (35), (39), (41), (45), (46), (47),
% 229.21/40.66  | | | | | | | | | | |            (49), (55), (57), (58), (61), (62), (64), (67),
% 229.21/40.66  | | | | | | | | | | |            (68), (72), (73), (77), (79), (146), (151), (155)
% 229.21/40.66  | | | | | | | | | | |            are inconsistent by sub-proof #766.
% 229.21/40.66  | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | Case 2:
% 229.21/40.66  | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | |   (156)  all_57_10 = e2 & op(e2, e0) = e2
% 229.21/40.66  | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 229.21/40.66  | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 229.21/40.66  | | | | | | | | | | |            (19), (21), (22), (23), (24), (25), (26), (27),
% 229.21/40.66  | | | | | | | | | | |            (28), (29), (30), (31), (32), (33), (34), (35),
% 229.21/40.66  | | | | | | | | | | |            (36), (37), (38), (40), (41), (42), (43), (44),
% 229.21/40.66  | | | | | | | | | | |            (45), (46), (47), (48), (49), (50), (51), (52),
% 229.21/40.66  | | | | | | | | | | |            (53), (54), (55), (56), (57), (58), (59), (60),
% 229.21/40.66  | | | | | | | | | | |            (61), (62), (63), (64), (65), (67), (68), (69),
% 229.21/40.66  | | | | | | | | | | |            (70), (71), (72), (73), (74), (75), (76), (77),
% 229.21/40.66  | | | | | | | | | | |            (78), (79), (84), (88), (146), (156) are
% 229.21/40.66  | | | | | | | | | | |            inconsistent by sub-proof #737.
% 229.21/40.66  | | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | | End of split
% 229.21/40.66  | | | | | | | | | | 
% 229.21/40.66  | | | | | | | | | End of split
% 229.21/40.66  | | | | | | | | | 
% 229.21/40.66  | | | | | | | | End of split
% 229.21/40.66  | | | | | | | | 
% 229.21/40.66  | | | | | | | Case 2:
% 229.21/40.66  | | | | | | | | 
% 229.21/40.66  | | | | | | | |   (157)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 &
% 229.21/40.66  | | | | | | | |            op(e3, e0) = e3)
% 229.21/40.66  | | | | | | | | 
% 229.21/40.66  | | | | | | | | REF_CLOSE: (6), (8), (34), (62), (79), (157) are inconsistent by
% 229.21/40.66  | | | | | | | |            sub-proof #2281.
% 229.21/40.66  | | | | | | | | 
% 229.21/40.66  | | | | | | | End of split
% 229.21/40.66  | | | | | | | 
% 229.21/40.66  | | | | | | Case 2:
% 229.21/40.66  | | | | | | | 
% 229.21/40.66  | | | | | | |   (158)  all_57_15 = e1 & op(e0, e0) = e1
% 229.21/40.66  | | | | | | | 
% 229.21/40.66  | | | | | | | ALPHA: (158) implies:
% 229.21/40.66  | | | | | | |   (159)  op(e0, e0) = e1
% 229.21/40.66  | | | | | | | 
% 229.21/40.66  | | | | | | | REF_CLOSE: (6), (8), (55), (159) are inconsistent by sub-proof
% 229.21/40.66  | | | | | | |            #2183.
% 229.21/40.66  | | | | | | | 
% 229.21/40.66  | | | | | | End of split
% 229.21/40.66  | | | | | | 
% 229.21/40.66  | | | | | End of split
% 229.21/40.66  | | | | | 
% 229.21/40.66  | | | | Case 2:
% 229.21/40.66  | | | | | 
% 229.21/40.66  | | | | |   (160)  all_57_15 = e2 & op(e0, e0) = e2
% 229.21/40.66  | | | | | 
% 229.21/40.66  | | | | | REF_CLOSE: (25), (31), (160) are inconsistent by sub-proof #2323.
% 229.21/40.66  | | | | | 
% 229.21/40.66  | | | | End of split
% 229.21/40.66  | | | | 
% 229.21/40.66  | | | End of split
% 229.21/40.66  | | | 
% 229.21/40.66  | | End of split
% 229.21/40.66  | | 
% 229.21/40.66  | Case 2:
% 229.21/40.66  | | 
% 229.21/40.67  | |   (161)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.21/40.67  | |            e1)
% 229.21/40.67  | | 
% 229.21/40.67  | | BETA: splitting (161) gives:
% 229.21/40.67  | | 
% 229.21/40.67  | | Case 1:
% 229.21/40.67  | | | 
% 229.21/40.67  | | |   (162)  all_57_11 = e1 & op(e1, e0) = e1
% 229.21/40.67  | | | 
% 229.21/40.67  | | | ALPHA: (162) implies:
% 229.21/40.67  | | |   (163)  all_57_11 = e1
% 229.21/40.67  | | | 
% 229.21/40.67  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 229.21/40.67  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 229.21/40.67  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 229.21/40.67  | | |            (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 229.21/40.67  | | |            (43), (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 229.21/40.67  | | |            (53), (54), (55), (56), (57), (58), (59), (60), (61), (62),
% 229.21/40.67  | | |            (63), (64), (65), (66), (67), (68), (69), (70), (71), (72),
% 229.21/40.67  | | |            (73), (74), (75), (76), (77), (78), (79), (163) are
% 229.21/40.67  | | |            inconsistent by sub-proof #716.
% 229.21/40.67  | | | 
% 229.21/40.67  | | Case 2:
% 229.21/40.67  | | | 
% 229.21/40.67  | | |   (164)  all_57_15 = e1 & op(e0, e0) = e1
% 229.21/40.67  | | | 
% 229.21/40.67  | | | ALPHA: (164) implies:
% 229.21/40.67  | | |   (165)  op(e0, e0) = e1
% 229.21/40.67  | | | 
% 229.21/40.67  | | | REF_CLOSE: (6), (8), (55), (165) are inconsistent by sub-proof #2183.
% 229.21/40.67  | | | 
% 229.21/40.67  | | End of split
% 229.21/40.67  | | 
% 229.21/40.67  | End of split
% 229.21/40.67  | 
% 229.21/40.67  End of proof
% 229.21/40.67  
% 229.21/40.67  Sub-proof #716 shows that the following formulas are inconsistent:
% 229.21/40.67  ----------------------------------------------------------------
% 229.21/40.67    (1)   ~ (all_53_2 = e2)
% 229.21/40.67    (2)  all_57_0 = e2
% 229.21/40.67    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.21/40.67         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.21/40.67    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.21/40.67         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.21/40.67    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.21/40.67         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.21/40.67    (6)   ~ (e3 = e1)
% 229.21/40.67    (7)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 229.21/40.67         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 229.21/40.67    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.21/40.67           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.21/40.67    (9)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.21/40.67         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.21/40.67    (10)   ~ (all_53_3 = e3)
% 229.21/40.67    (11)   ~ (all_53_3 = all_53_7)
% 229.21/40.67    (12)   ~ (all_6_2 = e3)
% 229.21/40.67    (13)   ~ (all_53_9 = e1)
% 229.21/40.67    (14)  op(e1, e1) = all_6_2
% 229.21/40.67    (15)   ~ (all_53_1 = all_53_9)
% 229.21/40.67    (16)  op(e2, e2) = e1
% 229.21/40.67    (17)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.21/40.67          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.21/40.67    (18)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 229.21/40.67            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 229.21/40.67              e3) = all_22_1 & $i(all_22_1))
% 229.21/40.67    (19)   ~ (all_53_13 = e3)
% 229.21/40.67    (20)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.21/40.67          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.21/40.67    (21)   ~ (all_53_9 = all_53_11)
% 229.21/40.67    (22)  all_55_4 = all_53_1
% 229.21/40.67    (23)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.21/40.67          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.21/40.67    (24)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 229.21/40.67          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.21/40.67    (25)   ~ (e3 = e2)
% 229.21/40.67    (26)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 229.21/40.67    (27)   ~ (all_53_1 = all_53_3)
% 229.21/40.67    (28)   ~ (e3 = e0)
% 229.21/40.67    (29)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 229.21/40.67    (30)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 229.21/40.67    (31)  all_57_15 = e3
% 229.21/40.67    (32)   ~ (all_53_9 = all_53_13)
% 229.21/40.67    (33)  op(e3, e3) = e2
% 229.21/40.67    (34)  all_57_4 = e1
% 229.21/40.67    (35)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.21/40.67          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.21/40.67            e1)
% 229.21/40.67    (36)   ~ (all_53_1 = e1)
% 229.21/40.67    (37)  all_55_6 = all_53_9
% 229.21/40.67    (38)   ~ (all_53_1 = all_53_2)
% 229.21/40.67    (39)  op(e1, e1) = e1
% 229.21/40.67    (40)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.21/40.67          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.21/40.67    (41)   ~ (e2 = e0)
% 229.21/40.67    (42)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 229.21/40.67            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 229.21/40.67            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 229.21/40.67            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 229.21/40.67              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 229.21/40.67            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 229.21/40.67            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 229.21/40.67              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 229.21/40.67              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 229.21/40.67            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 229.21/40.67            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 229.21/40.67            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 229.21/40.67              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 229.21/40.67              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 229.21/40.67            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 229.21/40.67              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 229.21/40.67            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 229.21/40.67            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 229.21/40.67              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 229.21/40.67              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 229.21/40.67            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 229.21/40.67            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 229.21/40.67    (43)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 229.21/40.67            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 229.21/40.67              e3) = all_12_1 & $i(all_12_1))
% 229.21/40.67    (44)  all_55_12 = all_53_3
% 229.21/40.67    (45)  all_57_3 = e1
% 229.21/40.67    (46)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.21/40.67          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.21/40.67    (47)   ~ (e1 = e0)
% 229.21/40.67    (48)   ~ (all_53_3 = all_53_11)
% 229.21/40.67    (49)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.21/40.67          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.21/40.67    (50)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.21/40.67          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.21/40.67    (51)   ~ (all_53_2 = all_53_3)
% 229.21/40.67    (52)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 229.21/40.67    (53)   ~ (all_53_7 = all_53_11)
% 229.21/40.67    (54)  all_55_8 = all_53_2
% 229.21/40.67    (55)  op(e0, e0) = e3
% 229.21/40.67    (56)  op(e0, e2) = all_53_7
% 229.21/40.67    (57)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.21/40.67          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.21/40.67            e2)
% 229.21/40.67    (58)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.21/40.67              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.21/40.67                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.21/40.67                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.21/40.67    (59)   ~ (all_53_1 = all_53_13)
% 229.21/40.67    (60)  op(e2, e0) = all_53_13
% 229.21/40.67    (61)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.21/40.67          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.21/40.67    (62)   ~ (all_53_12 = e3)
% 229.21/40.67    (63)  op(e1, e3) = all_53_2
% 229.21/40.67    (64)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.21/40.67          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.21/40.67    (65)  all_57_11 = e1
% 229.21/40.67    (66)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.21/40.67          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.21/40.67    (67)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.21/40.67          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 229.21/40.67    (68)   ~ (e2 = e1)
% 229.21/40.67    (69)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.21/40.67          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.21/40.67    (70)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.21/40.67          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.21/40.67    (71)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 229.21/40.67    (72)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 229.21/40.67          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 229.21/40.67    (73)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.21/40.67          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.21/40.67    (74)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.21/40.67          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.21/40.67    (75)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 229.21/40.67          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 229.21/40.67    (76)  all_55_14 = all_53_11
% 229.21/40.67    (77)   ~ (all_53_11 = e3)
% 229.21/40.67    (78)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.21/40.67          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.21/40.67    (79)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 229.21/40.67          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 229.21/40.67    (80)  op(e3, e0) = all_53_12
% 229.21/40.67  
% 229.21/40.67  Begin of proof
% 229.21/40.67  | 
% 229.21/40.67  | BETA: splitting (69) gives:
% 229.21/40.67  | 
% 229.21/40.67  | Case 1:
% 229.21/40.67  | | 
% 229.21/40.67  | |   (81)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 229.21/40.67  | |           e2)
% 229.21/40.67  | | 
% 229.21/40.67  | | BETA: splitting (81) gives:
% 229.21/40.67  | | 
% 229.21/40.67  | | Case 1:
% 229.21/40.67  | | | 
% 229.21/40.67  | | |   (82)  all_57_9 = e2 & op(e3, e0) = e2
% 229.21/40.67  | | | 
% 229.21/40.67  | | | ALPHA: (82) implies:
% 229.21/40.67  | | |   (83)  all_57_9 = e2
% 229.21/40.67  | | | 
% 229.21/40.67  | | | REF_CLOSE: (3), (6), (8), (12), (14), (23), (25), (28), (31), (33), (34),
% 229.21/40.67  | | |            (35), (41), (45), (46), (47), (49), (55), (57), (58), (62),
% 229.21/40.67  | | |            (64), (65), (68), (80), (83) are inconsistent by sub-proof
% 229.21/40.67  | | |            #735.
% 229.21/40.67  | | | 
% 229.21/40.67  | | Case 2:
% 229.21/40.67  | | | 
% 229.21/40.67  | | |   (84)  all_57_10 = e2 & op(e2, e0) = e2
% 229.21/40.67  | | | 
% 229.21/40.67  | | | ALPHA: (84) implies:
% 229.21/40.67  | | |   (85)  all_57_10 = e2
% 229.21/40.67  | | |   (86)  op(e2, e0) = e2
% 229.21/40.67  | | | 
% 229.21/40.67  | | | BETA: splitting (35) gives:
% 229.21/40.67  | | | 
% 229.21/40.67  | | | Case 1:
% 229.21/40.67  | | | | 
% 229.21/40.67  | | | |   (87)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0,
% 229.21/40.67  | | | |             e2) = e1)
% 229.21/40.67  | | | | 
% 229.21/40.67  | | | | BETA: splitting (87) gives:
% 229.21/40.67  | | | | 
% 229.21/40.67  | | | | Case 1:
% 229.21/40.67  | | | | | 
% 229.21/40.67  | | | | |   (88)  all_57_12 = e1 & op(e0, e3) = e1
% 229.21/40.67  | | | | | 
% 229.21/40.67  | | | | | ALPHA: (88) implies:
% 229.21/40.67  | | | | |   (89)  all_57_12 = e1
% 229.21/40.67  | | | | |   (90)  op(e0, e3) = e1
% 229.21/40.67  | | | | | 
% 229.21/40.67  | | | | | BETA: splitting (46) gives:
% 229.21/40.67  | | | | | 
% 229.21/40.67  | | | | | Case 1:
% 229.21/40.67  | | | | | | 
% 229.21/40.67  | | | | | |   (91)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3,
% 229.21/40.67  | | | | | |             e2) = e3)
% 229.21/40.67  | | | | | | 
% 229.21/40.67  | | | | | | BETA: splitting (91) gives:
% 229.21/40.67  | | | | | | 
% 229.21/40.67  | | | | | | Case 1:
% 229.21/40.67  | | | | | | | 
% 229.21/40.67  | | | | | | |   (92)  all_57_0 = e3 & op(e3, e3) = e3
% 229.21/40.67  | | | | | | | 
% 229.21/40.67  | | | | | | | ALPHA: (92) implies:
% 229.21/40.67  | | | | | | |   (93)  op(e3, e3) = e3
% 229.21/40.67  | | | | | | | 
% 229.21/40.67  | | | | | | | REF_CLOSE: (8), (25), (33), (93) are inconsistent by sub-proof
% 229.21/40.67  | | | | | | |            #2490.
% 229.21/40.67  | | | | | | | 
% 229.21/40.67  | | | | | | Case 2:
% 229.21/40.67  | | | | | | | 
% 229.21/40.67  | | | | | | |   (94)  all_57_1 = e3 & op(e3, e2) = e3
% 229.21/40.67  | | | | | | | 
% 229.21/40.67  | | | | | | | ALPHA: (94) implies:
% 229.21/40.67  | | | | | | |   (95)  all_57_1 = e3
% 229.21/40.67  | | | | | | | 
% 229.21/40.67  | | | | | | | BETA: splitting (23) gives:
% 229.21/40.67  | | | | | | | 
% 229.21/40.67  | | | | | | | Case 1:
% 229.21/40.67  | | | | | | | | 
% 229.21/40.67  | | | | | | | |   (96)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 &
% 229.21/40.67  | | | | | | | |           op(e3, e2) = e0)
% 229.21/40.67  | | | | | | | | 
% 229.21/40.67  | | | | | | | | REF_CLOSE: (8), (28), (33), (41), (95), (96) are inconsistent by
% 229.21/40.67  | | | | | | | |            sub-proof #1676.
% 229.21/40.67  | | | | | | | | 
% 229.21/40.67  | | | | | | | Case 2:
% 229.21/40.67  | | | | | | | | 
% 229.21/40.67  | | | | | | | |   (97)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 &
% 229.21/40.67  | | | | | | | |           op(e3, e0) = e0)
% 229.21/40.67  | | | | | | | | 
% 229.21/40.67  | | | | | | | | BETA: splitting (97) gives:
% 229.21/40.67  | | | | | | | | 
% 229.21/40.67  | | | | | | | | Case 1:
% 229.21/40.67  | | | | | | | | | 
% 229.21/40.67  | | | | | | | | |   (98)  all_57_4 = e0 & op(e3, e1) = e0
% 229.21/40.67  | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | REF_CLOSE: (34), (47), (98) are inconsistent by sub-proof
% 229.21/40.67  | | | | | | | | |            #2429.
% 229.21/40.67  | | | | | | | | | 
% 229.21/40.67  | | | | | | | | Case 2:
% 229.21/40.67  | | | | | | | | | 
% 229.21/40.67  | | | | | | | | |   (99)  all_57_9 = e0 & op(e3, e0) = e0
% 229.21/40.67  | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | ALPHA: (99) implies:
% 229.21/40.67  | | | | | | | | |   (100)  all_57_9 = e0
% 229.21/40.67  | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | BETA: splitting (79) gives:
% 229.21/40.67  | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | Case 1:
% 229.21/40.67  | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | |   (101)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 229.21/40.67  | | | | | | | | | |            & op(e1, e2) = e2)
% 229.21/40.67  | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | BETA: splitting (101) gives:
% 229.21/40.67  | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | Case 1:
% 229.21/40.67  | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | |   (102)  all_57_6 = e2 & op(e1, e3) = e2
% 229.21/40.67  | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | ALPHA: (102) implies:
% 229.21/40.67  | | | | | | | | | | |   (103)  all_57_6 = e2
% 229.21/40.67  | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | BETA: splitting (49) gives:
% 229.21/40.67  | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | Case 1:
% 229.21/40.67  | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | |   (104)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 229.21/40.67  | | | | | | | | | | | |            & op(e2, e1) = e3)
% 229.21/40.67  | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | BETA: splitting (104) gives:
% 229.21/40.67  | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | Case 1:
% 229.21/40.67  | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | |   (105)  all_57_4 = e3 & op(e3, e1) = e3
% 229.21/40.67  | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | REF_CLOSE: (5), (6), (8), (16), (25), (28), (34), (40), (41),
% 229.21/40.67  | | | | | | | | | | | | |            (47), (50), (68), (95), (105) are inconsistent by
% 229.21/40.67  | | | | | | | | | | | | |            sub-proof #734.
% 229.21/40.67  | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | Case 2:
% 229.21/40.67  | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | |   (106)  all_57_5 = e3 & op(e2, e1) = e3
% 229.21/40.67  | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | ALPHA: (106) implies:
% 229.21/40.67  | | | | | | | | | | | | |   (107)  all_57_5 = e3
% 229.21/40.67  | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | BETA: splitting (67) gives:
% 229.21/40.67  | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | Case 1:
% 229.21/40.67  | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | |   (108)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 229.21/40.67  | | | | | | | | | | | | | |            & op(e2, e2) = e0)
% 229.21/40.67  | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | BETA: splitting (108) gives:
% 229.21/40.67  | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | Case 1:
% 229.21/40.67  | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | |   (109)  all_57_2 = e0 & op(e2, e3) = e0
% 229.21/40.67  | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | ALPHA: (109) implies:
% 229.21/40.67  | | | | | | | | | | | | | | |   (110)  all_57_2 = e0
% 229.21/40.67  | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | BETA: splitting (9) gives:
% 229.21/40.67  | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | Case 1:
% 229.21/40.67  | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | |   (111)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 229.21/40.67  | | | | | | | | | | | | | | | |            & op(e1, e2) = e3)
% 229.21/40.67  | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | BETA: splitting (111) gives:
% 229.21/40.67  | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | Case 1:
% 229.21/40.67  | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | |   (112)  all_57_6 = e3 & op(e1, e3) = e3
% 229.21/40.67  | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (25), (33), (34), (46), (62), (80),
% 229.21/40.67  | | | | | | | | | | | | | | | | |            (95), (103), (112) are inconsistent by sub-proof
% 229.21/40.67  | | | | | | | | | | | | | | | | |            #733.
% 229.21/40.67  | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | Case 2:
% 229.21/40.67  | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | |   (113)  all_57_7 = e3 & op(e1, e2) = e3
% 229.21/40.67  | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | | ALPHA: (113) implies:
% 229.21/40.67  | | | | | | | | | | | | | | | | |   (114)  all_57_7 = e3
% 229.21/40.67  | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | | BETA: splitting (66) gives:
% 229.21/40.67  | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | | Case 1:
% 229.21/40.67  | | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | | |   (115)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 229.21/40.67  | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e3)
% 229.21/40.67  | | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | | | BETA: splitting (115) gives:
% 229.21/40.67  | | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | | | Case 1:
% 229.21/40.67  | | | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | | | |   (116)  all_57_0 = e3 & op(e3, e3) = e3
% 229.21/40.67  | | | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | | | | ALPHA: (116) implies:
% 229.21/40.67  | | | | | | | | | | | | | | | | | | |   (117)  op(e3, e3) = e3
% 229.21/40.67  | | | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (25), (33), (117) are inconsistent by
% 229.21/40.67  | | | | | | | | | | | | | | | | | | |            sub-proof #2490.
% 229.21/40.67  | | | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | | | Case 2:
% 229.21/40.67  | | | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | | | |   (118)  all_57_2 = e3 & op(e2, e3) = e3
% 229.21/40.67  | | | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | | | | ALPHA: (118) implies:
% 229.21/40.67  | | | | | | | | | | | | | | | | | | |   (119)  all_57_2 = e3
% 229.21/40.67  | | | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (110), (119) imply:
% 229.21/40.67  | | | | | | | | | | | | | | | | | | |   (120)  e3 = e0
% 229.21/40.67  | | | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (8), (16), (25), (28), (41), (47), (64),
% 229.21/40.67  | | | | | | | | | | | | | | | | | | |            (67), (68), (78), (95), (107), (114), (119), (120)
% 229.21/40.67  | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #732.
% 229.21/40.67  | | | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | | | End of split
% 229.21/40.67  | | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | | Case 2:
% 229.21/40.67  | | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | | |   (121)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 229.21/40.67  | | | | | | | | | | | | | | | | | |            e3 & op(e0, e3) = e3)
% 229.21/40.67  | | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | | | BETA: splitting (121) gives:
% 229.21/40.67  | | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | | | Case 1:
% 229.21/40.67  | | | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | | | |   (122)  all_57_6 = e3 & op(e1, e3) = e3
% 229.21/40.67  | | | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (25), (33), (34), (46), (62), (80),
% 229.21/40.67  | | | | | | | | | | | | | | | | | | |            (95), (103), (122) are inconsistent by sub-proof
% 229.21/40.67  | | | | | | | | | | | | | | | | | | |            #733.
% 229.21/40.67  | | | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | | | Case 2:
% 229.21/40.67  | | | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | | | |   (123)  all_57_12 = e3 & op(e0, e3) = e3
% 229.21/40.67  | | | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | | | | ALPHA: (123) implies:
% 229.21/40.67  | | | | | | | | | | | | | | | | | | |   (124)  all_57_12 = e3
% 229.21/40.67  | | | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (16), (25), (28), (40), (41), (47),
% 229.21/40.67  | | | | | | | | | | | | | | | | | | |            (68), (89), (95), (114), (124) are inconsistent by
% 229.21/40.67  | | | | | | | | | | | | | | | | | | |            sub-proof #1039.
% 229.21/40.67  | | | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | | | End of split
% 229.21/40.67  | | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | | End of split
% 229.21/40.67  | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | End of split
% 229.21/40.67  | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | Case 2:
% 229.21/40.67  | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | |   (125)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 229.21/40.67  | | | | | | | | | | | | | | | |            e3 & op(e1, e0) = e3)
% 229.21/40.67  | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (12), (14), (31), (47), (68), (74),
% 229.21/40.67  | | | | | | | | | | | | | | | |            (85), (100), (125) are inconsistent by sub-proof
% 229.21/40.67  | | | | | | | | | | | | | | | |            #731.
% 229.21/40.67  | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | End of split
% 229.21/40.67  | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | Case 2:
% 229.21/40.67  | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | |   (126)  all_57_3 = e0 & op(e2, e2) = e0
% 229.21/40.67  | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | ALPHA: (126) implies:
% 229.21/40.67  | | | | | | | | | | | | | | |   (127)  all_57_3 = e0
% 229.21/40.67  | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (5), (6), (8), (9), (12), (14), (17),
% 229.21/40.67  | | | | | | | | | | | | | | |            (20), (23), (25), (28), (31), (33), (41), (46),
% 229.21/40.67  | | | | | | | | | | | | | | |            (47), (58), (61), (62), (64), (66), (68), (69),
% 229.21/40.67  | | | | | | | | | | | | | | |            (73), (74), (78), (80), (103), (127) are
% 229.21/40.67  | | | | | | | | | | | | | | |            inconsistent by sub-proof #728.
% 229.21/40.67  | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | End of split
% 229.21/40.67  | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | Case 2:
% 229.21/40.67  | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | |   (128)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 229.21/40.67  | | | | | | | | | | | | | |            e0 & op(e2, e0) = e0)
% 229.21/40.67  | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | BETA: splitting (128) gives:
% 229.21/40.67  | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | Case 1:
% 229.21/40.67  | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | |   (129)  all_57_5 = e0 & op(e2, e1) = e0
% 229.21/40.67  | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | ALPHA: (129) implies:
% 229.21/40.67  | | | | | | | | | | | | | | |   (130)  all_57_5 = e0
% 229.21/40.67  | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | REF_CLOSE: (28), (107), (130) are inconsistent by sub-proof
% 229.21/40.67  | | | | | | | | | | | | | | |            #2471.
% 229.21/40.67  | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | Case 2:
% 229.21/40.67  | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | |   (131)  all_57_10 = e0 & op(e2, e0) = e0
% 229.21/40.67  | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | ALPHA: (131) implies:
% 229.21/40.67  | | | | | | | | | | | | | | |   (132)  all_57_10 = e0
% 229.21/40.67  | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | BETA: splitting (64) gives:
% 229.21/40.67  | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | Case 1:
% 229.21/40.67  | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | |   (133)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 229.21/40.67  | | | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 229.21/40.67  | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | BETA: splitting (133) gives:
% 229.21/40.67  | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | Case 1:
% 229.21/40.67  | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | |   (134)  all_57_2 = e2 & op(e2, e3) = e2
% 229.21/40.67  | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | | ALPHA: (134) implies:
% 229.21/40.67  | | | | | | | | | | | | | | | | |   (135)  all_57_2 = e2
% 229.21/40.67  | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | | BETA: splitting (66) gives:
% 229.21/40.67  | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | | Case 1:
% 229.21/40.67  | | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | | |   (136)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 229.21/40.67  | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e3)
% 229.21/40.67  | | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (16), (25), (33), (41), (64), (68), (107),
% 229.21/40.67  | | | | | | | | | | | | | | | | | |            (132), (136) are inconsistent by sub-proof #727.
% 229.21/40.67  | | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | | Case 2:
% 229.21/40.67  | | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | | |   (137)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 229.21/40.67  | | | | | | | | | | | | | | | | | |            e3 & op(e0, e3) = e3)
% 229.21/40.67  | | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | | | BETA: splitting (137) gives:
% 229.21/40.67  | | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | | | Case 1:
% 229.21/40.67  | | | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | | | |   (138)  all_57_6 = e3 & op(e1, e3) = e3
% 229.21/40.67  | | | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | | | | ALPHA: (138) implies:
% 229.21/40.67  | | | | | | | | | | | | | | | | | | |   (139)  all_57_6 = e3
% 229.21/40.67  | | | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (5), (6), (8), (9), (12), (14), (16),
% 229.21/40.67  | | | | | | | | | | | | | | | | | | |            (25), (28), (31), (33), (40), (41), (45), (47),
% 229.21/40.67  | | | | | | | | | | | | | | | | | | |            (50), (58), (64), (68), (69), (73), (74), (78),
% 229.21/40.67  | | | | | | | | | | | | | | | | | | |            (95), (107), (135), (139) are inconsistent by
% 229.21/40.67  | | | | | | | | | | | | | | | | | | |            sub-proof #807.
% 229.21/40.67  | | | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | | | Case 2:
% 229.21/40.67  | | | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | | | |   (140)  all_57_12 = e3 & op(e0, e3) = e3
% 229.21/40.67  | | | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | | | | ALPHA: (140) implies:
% 229.21/40.67  | | | | | | | | | | | | | | | | | | |   (141)  all_57_12 = e3
% 229.21/40.67  | | | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | | | | BETA: splitting (4) gives:
% 229.21/40.67  | | | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | | | | Case 1:
% 229.21/40.67  | | | | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | | | | |   (142)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 229.21/40.67  | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e1)
% 229.21/40.67  | | | | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (33), (68), (135), (142) are inconsistent by
% 229.21/40.67  | | | | | | | | | | | | | | | | | | | |            sub-proof #1633.
% 229.21/40.67  | | | | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | | | | Case 2:
% 229.21/40.67  | | | | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | | | | |   (143)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 229.21/40.67  | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e3) = e1)
% 229.21/40.67  | | | | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | | | | | BETA: splitting (143) gives:
% 229.21/40.67  | | | | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.21/40.67  | | | | | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | | | | | |   (144)  all_57_6 = e1 & op(e1, e3) = e1
% 229.21/40.67  | | | | | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (68), (103), (144) are inconsistent by sub-proof
% 229.21/40.67  | | | | | | | | | | | | | | | | | | | | |            #2389.
% 229.21/40.67  | | | | | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.21/40.67  | | | | | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (8), (16), (25), (28), (40), (41), (47),
% 229.21/40.67  | | | | | | | | | | | | | | | | | | | | |            (50), (68), (88), (95), (141) are inconsistent by
% 229.21/40.67  | | | | | | | | | | | | | | | | | | | | |            sub-proof #1769.
% 229.21/40.67  | | | | | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | | | | | End of split
% 229.21/40.67  | | | | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | | | | End of split
% 229.21/40.67  | | | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | | | End of split
% 229.21/40.67  | | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | | End of split
% 229.21/40.67  | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | Case 2:
% 229.21/40.67  | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | |   (145)  all_57_3 = e2 & op(e2, e2) = e2
% 229.21/40.67  | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | | ALPHA: (145) implies:
% 229.21/40.67  | | | | | | | | | | | | | | | | |   (146)  op(e2, e2) = e2
% 229.21/40.67  | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (16), (68), (146) are inconsistent by
% 229.21/40.67  | | | | | | | | | | | | | | | | |            sub-proof #2306.
% 229.21/40.67  | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | End of split
% 229.21/40.67  | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | Case 2:
% 229.21/40.67  | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | |   (147)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 229.21/40.67  | | | | | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 229.21/40.67  | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | BETA: splitting (147) gives:
% 229.21/40.67  | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | Case 1:
% 229.21/40.67  | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | |   (148)  all_57_5 = e2 & op(e2, e1) = e2
% 229.21/40.67  | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (25), (33), (34), (46), (62), (80),
% 229.21/40.67  | | | | | | | | | | | | | | | | |            (95), (107), (148) are inconsistent by sub-proof
% 229.21/40.67  | | | | | | | | | | | | | | | | |            #806.
% 229.21/40.67  | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | Case 2:
% 229.21/40.67  | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | | COMBINE_EQS: (85), (132) imply:
% 229.21/40.67  | | | | | | | | | | | | | | | | |   (149)  e2 = e0
% 229.21/40.67  | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | | SIMP: (149) implies:
% 229.21/40.67  | | | | | | | | | | | | | | | | |   (150)  e2 = e0
% 229.21/40.67  | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | | COMBINE_EQS: (103), (150) imply:
% 229.21/40.67  | | | | | | | | | | | | | | | | |   (151)  all_57_6 = e0
% 229.21/40.67  | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (8), (9), (12), (14), (16), (25), (28),
% 229.21/40.67  | | | | | | | | | | | | | | | | |            (31), (40), (41), (47), (58), (68), (69), (74),
% 229.21/40.67  | | | | | | | | | | | | | | | | |            (78), (95), (151) are inconsistent by sub-proof
% 229.21/40.67  | | | | | | | | | | | | | | | | |            #1773.
% 229.21/40.67  | | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | | End of split
% 229.21/40.67  | | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | | End of split
% 229.21/40.67  | | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | | End of split
% 229.21/40.67  | | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | | End of split
% 229.21/40.67  | | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | End of split
% 229.21/40.67  | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | Case 2:
% 229.21/40.67  | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | |   (152)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 229.21/40.67  | | | | | | | | | | | |            e3 & op(e0, e1) = e3)
% 229.21/40.67  | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | | REF_CLOSE: (6), (8), (12), (14), (25), (28), (31), (35),
% 229.21/40.67  | | | | | | | | | | | |            (41), (47), (57), (58), (68), (152) are
% 229.21/40.67  | | | | | | | | | | | |            inconsistent by sub-proof #1794.
% 229.21/40.67  | | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | End of split
% 229.21/40.67  | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | Case 2:
% 229.21/40.67  | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | |   (153)  all_57_7 = e2 & op(e1, e2) = e2
% 229.21/40.67  | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | ALPHA: (153) implies:
% 229.21/40.67  | | | | | | | | | | |   (154)  all_57_7 = e2
% 229.21/40.67  | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | REF_CLOSE: (6), (7), (8), (9), (12), (14), (25), (28), (31),
% 229.21/40.67  | | | | | | | | | | |            (39), (41), (47), (58), (68), (69), (74), (100),
% 229.21/40.67  | | | | | | | | | | |            (154) are inconsistent by sub-proof #959.
% 229.21/40.67  | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | End of split
% 229.21/40.67  | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | Case 2:
% 229.21/40.67  | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | |   (155)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2
% 229.21/40.67  | | | | | | | | | |            & op(e1, e0) = e2)
% 229.21/40.67  | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | BETA: splitting (155) gives:
% 229.21/40.67  | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | Case 1:
% 229.21/40.67  | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | |   (156)  all_57_8 = e2 & op(e1, e1) = e2
% 229.21/40.67  | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | ALPHA: (156) implies:
% 229.21/40.67  | | | | | | | | | | |   (157)  op(e1, e1) = e2
% 229.21/40.67  | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 229.21/40.67  | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 229.21/40.67  | | | | | | | | | | |            (19), (21), (22), (23), (24), (25), (26), (27),
% 229.21/40.67  | | | | | | | | | | |            (28), (29), (30), (31), (32), (33), (35), (36),
% 229.21/40.67  | | | | | | | | | | |            (37), (38), (40), (41), (42), (43), (44), (45),
% 229.21/40.67  | | | | | | | | | | |            (46), (47), (48), (49), (50), (51), (52), (53),
% 229.21/40.67  | | | | | | | | | | |            (54), (55), (56), (57), (58), (59), (60), (61),
% 229.21/40.67  | | | | | | | | | | |            (62), (63), (64), (66), (68), (69), (70), (71),
% 229.21/40.67  | | | | | | | | | | |            (72), (73), (74), (75), (76), (77), (78), (79),
% 229.21/40.67  | | | | | | | | | | |            (80), (85), (86), (157) are inconsistent by
% 229.21/40.67  | | | | | | | | | | |            sub-proof #718.
% 229.21/40.67  | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | Case 2:
% 229.21/40.67  | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | |   (158)  all_57_11 = e2 & op(e1, e0) = e2
% 229.21/40.67  | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | ALPHA: (158) implies:
% 229.21/40.67  | | | | | | | | | | |   (159)  op(e1, e0) = e2
% 229.21/40.67  | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | | REF_CLOSE: (8), (18), (43), (90), (159) are inconsistent by
% 229.21/40.67  | | | | | | | | | | |            sub-proof #1147.
% 229.21/40.67  | | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | | End of split
% 229.21/40.67  | | | | | | | | | | 
% 229.21/40.67  | | | | | | | | | End of split
% 229.21/40.67  | | | | | | | | | 
% 229.21/40.67  | | | | | | | | End of split
% 229.21/40.67  | | | | | | | | 
% 229.21/40.67  | | | | | | | End of split
% 229.21/40.67  | | | | | | | 
% 229.21/40.67  | | | | | | End of split
% 229.21/40.67  | | | | | | 
% 229.21/40.67  | | | | | Case 2:
% 229.21/40.67  | | | | | | 
% 229.21/40.67  | | | | | |   (160)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3,
% 229.21/40.67  | | | | | |              e0) = e3)
% 229.21/40.67  | | | | | | 
% 229.21/40.67  | | | | | | REF_CLOSE: (6), (8), (34), (62), (80), (160) are inconsistent by
% 229.21/40.67  | | | | | |            sub-proof #2281.
% 229.21/40.67  | | | | | | 
% 229.21/40.67  | | | | | End of split
% 229.21/40.67  | | | | | 
% 229.21/40.67  | | | | Case 2:
% 229.21/40.67  | | | | | 
% 229.21/40.67  | | | | |   (161)  all_57_13 = e1 & op(e0, e2) = e1
% 229.21/40.67  | | | | | 
% 229.21/40.67  | | | | | ALPHA: (161) implies:
% 229.21/40.67  | | | | |   (162)  all_57_13 = e1
% 229.21/40.67  | | | | | 
% 229.21/40.67  | | | | | BETA: splitting (46) gives:
% 229.21/40.67  | | | | | 
% 229.21/40.67  | | | | | Case 1:
% 229.21/40.67  | | | | | | 
% 229.21/40.67  | | | | | |   (163)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3,
% 229.21/40.67  | | | | | |              e2) = e3)
% 229.21/40.67  | | | | | | 
% 229.21/40.67  | | | | | | BETA: splitting (163) gives:
% 229.21/40.67  | | | | | | 
% 229.21/40.67  | | | | | | Case 1:
% 229.21/40.67  | | | | | | | 
% 229.21/40.67  | | | | | | |   (164)  all_57_0 = e3 & op(e3, e3) = e3
% 229.21/40.67  | | | | | | | 
% 229.21/40.67  | | | | | | | ALPHA: (164) implies:
% 229.21/40.67  | | | | | | |   (165)  op(e3, e3) = e3
% 229.21/40.67  | | | | | | | 
% 229.21/40.67  | | | | | | | REF_CLOSE: (8), (25), (33), (165) are inconsistent by sub-proof
% 229.21/40.67  | | | | | | |            #2490.
% 229.21/40.67  | | | | | | | 
% 229.21/40.67  | | | | | | Case 2:
% 229.21/40.67  | | | | | | | 
% 229.21/40.67  | | | | | | |   (166)  all_57_1 = e3 & op(e3, e2) = e3
% 229.21/40.67  | | | | | | | 
% 229.21/40.67  | | | | | | | ALPHA: (166) implies:
% 229.21/40.68  | | | | | | |   (167)  all_57_1 = e3
% 229.21/40.68  | | | | | | | 
% 229.21/40.68  | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11),
% 229.21/40.68  | | | | | | |            (12), (13), (14), (15), (16), (17), (19), (21), (22),
% 229.21/40.68  | | | | | | |            (23), (25), (26), (27), (28), (29), (30), (31), (32),
% 229.21/40.68  | | | | | | |            (33), (34), (35), (36), (37), (38), (40), (41), (42),
% 229.21/40.68  | | | | | | |            (44), (45), (46), (47), (48), (50), (51), (52), (53),
% 229.21/40.68  | | | | | | |            (54), (55), (56), (57), (58), (59), (60), (61), (62),
% 229.21/40.68  | | | | | | |            (63), (64), (66), (68), (69), (70), (71), (73), (74),
% 229.21/40.68  | | | | | | |            (76), (77), (78), (80), (86), (162), (167) are
% 229.21/40.68  | | | | | | |            inconsistent by sub-proof #767.
% 229.21/40.68  | | | | | | | 
% 229.21/40.68  | | | | | | End of split
% 229.21/40.68  | | | | | | 
% 229.21/40.68  | | | | | Case 2:
% 229.21/40.68  | | | | | | 
% 229.21/40.68  | | | | | |   (168)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3,
% 229.21/40.68  | | | | | |              e0) = e3)
% 229.21/40.68  | | | | | | 
% 229.21/40.68  | | | | | | REF_CLOSE: (6), (8), (34), (62), (80), (168) are inconsistent by
% 229.21/40.68  | | | | | |            sub-proof #2281.
% 229.21/40.68  | | | | | | 
% 229.21/40.68  | | | | | End of split
% 229.21/40.68  | | | | | 
% 229.21/40.68  | | | | End of split
% 229.21/40.68  | | | | 
% 229.21/40.68  | | | Case 2:
% 229.21/40.68  | | | | 
% 229.21/40.68  | | | |   (169)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0,
% 229.21/40.68  | | | |              e0) = e1)
% 229.21/40.68  | | | | 
% 229.21/40.68  | | | | BETA: splitting (169) gives:
% 229.21/40.68  | | | | 
% 229.21/40.68  | | | | Case 1:
% 229.21/40.68  | | | | | 
% 229.21/40.68  | | | | |   (170)  all_57_14 = e1 & op(e0, e1) = e1
% 229.21/40.68  | | | | | 
% 229.21/40.68  | | | | | ALPHA: (170) implies:
% 229.21/40.68  | | | | |   (171)  all_57_14 = e1
% 229.21/40.68  | | | | | 
% 229.21/40.68  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 229.21/40.68  | | | | |            (12), (13), (14), (15), (16), (17), (18), (19), (21), (22),
% 229.21/40.68  | | | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 229.21/40.68  | | | | |            (33), (34), (35), (36), (37), (38), (40), (41), (42), (43),
% 229.21/40.68  | | | | |            (44), (45), (46), (47), (48), (49), (50), (51), (52), (53),
% 229.21/40.68  | | | | |            (54), (55), (56), (57), (58), (59), (60), (61), (62), (63),
% 229.21/40.68  | | | | |            (64), (65), (66), (68), (69), (70), (71), (72), (73), (74),
% 229.21/40.68  | | | | |            (75), (76), (77), (78), (79), (80), (85), (86), (171) are
% 229.21/40.68  | | | | |            inconsistent by sub-proof #738.
% 229.21/40.68  | | | | | 
% 229.21/40.68  | | | | Case 2:
% 229.21/40.68  | | | | | 
% 229.21/40.68  | | | | |   (172)  all_57_15 = e1 & op(e0, e0) = e1
% 229.21/40.68  | | | | | 
% 229.21/40.68  | | | | | ALPHA: (172) implies:
% 229.21/40.68  | | | | |   (173)  op(e0, e0) = e1
% 229.21/40.68  | | | | | 
% 229.21/40.68  | | | | | REF_CLOSE: (6), (8), (55), (173) are inconsistent by sub-proof #2183.
% 229.21/40.68  | | | | | 
% 229.21/40.68  | | | | End of split
% 229.21/40.68  | | | | 
% 229.21/40.68  | | | End of split
% 229.21/40.68  | | | 
% 229.21/40.68  | | End of split
% 229.21/40.68  | | 
% 229.21/40.68  | Case 2:
% 229.21/40.68  | | 
% 229.21/40.68  | |   (174)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.21/40.68  | |            e2)
% 229.21/40.68  | | 
% 229.21/40.68  | | REF_CLOSE: (25), (31), (65), (68), (174) are inconsistent by sub-proof #717.
% 229.21/40.68  | | 
% 229.21/40.68  | End of split
% 229.21/40.68  | 
% 229.21/40.68  End of proof
% 229.21/40.68  
% 229.21/40.68  Sub-proof #717 shows that the following formulas are inconsistent:
% 229.21/40.68  ----------------------------------------------------------------
% 229.21/40.68    (1)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.21/40.68    (2)   ~ (e3 = e2)
% 229.21/40.68    (3)  all_57_15 = e3
% 229.21/40.68    (4)  all_57_11 = e1
% 229.21/40.68    (5)   ~ (e2 = e1)
% 229.21/40.68  
% 229.21/40.68  Begin of proof
% 229.21/40.68  | 
% 229.21/40.68  | BETA: splitting (1) gives:
% 229.21/40.68  | 
% 229.21/40.68  | Case 1:
% 229.21/40.68  | | 
% 229.21/40.68  | |   (6)  all_57_11 = e2 & op(e1, e0) = e2
% 229.21/40.68  | | 
% 229.21/40.68  | | ALPHA: (6) implies:
% 229.21/40.68  | |   (7)  all_57_11 = e2
% 229.21/40.68  | | 
% 229.21/40.68  | | REF_CLOSE: (4), (5), (7) are inconsistent by sub-proof #2113.
% 229.21/40.68  | | 
% 229.21/40.68  | Case 2:
% 229.21/40.68  | | 
% 229.21/40.68  | |   (8)  all_57_15 = e2 & op(e0, e0) = e2
% 229.21/40.68  | | 
% 229.21/40.68  | | REF_CLOSE: (2), (3), (8) are inconsistent by sub-proof #2323.
% 229.21/40.68  | | 
% 229.21/40.68  | End of split
% 229.21/40.68  | 
% 229.21/40.68  End of proof
% 229.21/40.68  
% 229.21/40.68  Sub-proof #718 shows that the following formulas are inconsistent:
% 229.21/40.68  ----------------------------------------------------------------
% 229.21/40.68    (1)   ~ (all_53_2 = e2)
% 229.21/40.68    (2)  all_57_0 = e2
% 229.21/40.68    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.21/40.68         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.21/40.68    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.21/40.68         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.21/40.68    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.21/40.68         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.21/40.68    (6)   ~ (e3 = e1)
% 229.21/40.68    (7)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 229.21/40.68         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 229.21/40.68    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.21/40.68           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.21/40.68    (9)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.21/40.68         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.21/40.68    (10)   ~ (all_53_3 = e3)
% 229.21/40.68    (11)   ~ (all_53_3 = all_53_7)
% 229.21/40.68    (12)   ~ (all_6_2 = e3)
% 229.21/40.68    (13)   ~ (all_53_9 = e1)
% 229.21/40.68    (14)  op(e1, e1) = all_6_2
% 229.21/40.68    (15)   ~ (all_53_1 = all_53_9)
% 229.21/40.68    (16)  op(e2, e2) = e1
% 229.21/40.68    (17)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.21/40.68          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.21/40.68    (18)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 229.21/40.68            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 229.21/40.68              e3) = all_22_1 & $i(all_22_1))
% 229.21/40.68    (19)   ~ (all_53_13 = e3)
% 229.21/40.68    (20)   ~ (all_53_9 = all_53_11)
% 229.21/40.68    (21)  all_55_4 = all_53_1
% 229.21/40.68    (22)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.21/40.68          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.21/40.68    (23)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 229.21/40.68          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.21/40.68    (24)   ~ (e3 = e2)
% 229.21/40.68    (25)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 229.21/40.68    (26)   ~ (all_53_1 = all_53_3)
% 229.21/40.68    (27)   ~ (e3 = e0)
% 229.21/40.68    (28)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 229.21/40.68    (29)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 229.21/40.68    (30)  all_57_15 = e3
% 229.21/40.68    (31)   ~ (all_53_9 = all_53_13)
% 229.21/40.68    (32)  op(e3, e3) = e2
% 229.21/40.68    (33)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.21/40.68          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.21/40.68            e1)
% 229.21/40.68    (34)  all_57_10 = e2
% 229.21/40.68    (35)   ~ (all_53_1 = e1)
% 229.21/40.68    (36)  op(e2, e0) = e2
% 229.21/40.68    (37)  all_55_6 = all_53_9
% 229.21/40.68    (38)   ~ (all_53_1 = all_53_2)
% 229.21/40.68    (39)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.21/40.68          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.21/40.68    (40)   ~ (e2 = e0)
% 229.21/40.68    (41)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 229.21/40.68            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 229.21/40.68            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 229.21/40.68            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 229.21/40.68              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 229.21/40.68            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 229.21/40.68            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 229.21/40.68              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 229.21/40.68              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 229.21/40.68            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 229.21/40.68            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 229.21/40.68            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 229.21/40.68              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 229.21/40.68              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 229.21/40.68            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 229.21/40.68              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 229.21/40.68            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 229.21/40.68            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 229.21/40.68              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 229.21/40.68              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 229.21/40.68            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 229.21/40.68            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 229.21/40.68    (42)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 229.21/40.68            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 229.21/40.68              e3) = all_12_1 & $i(all_12_1))
% 229.21/40.68    (43)  all_55_12 = all_53_3
% 229.21/40.68    (44)  all_57_3 = e1
% 229.21/40.68    (45)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.21/40.68          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.21/40.68    (46)   ~ (e1 = e0)
% 229.21/40.68    (47)   ~ (all_53_3 = all_53_11)
% 229.21/40.68    (48)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.21/40.68          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.21/40.68    (49)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.21/40.68          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.21/40.68    (50)   ~ (all_53_2 = all_53_3)
% 229.21/40.68    (51)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 229.21/40.68    (52)   ~ (all_53_7 = all_53_11)
% 229.21/40.68    (53)  all_55_8 = all_53_2
% 229.21/40.68    (54)  op(e0, e0) = e3
% 229.21/40.68    (55)  op(e0, e2) = all_53_7
% 229.21/40.68    (56)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.21/40.68          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.21/40.68            e2)
% 229.21/40.68    (57)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.21/40.68              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.21/40.68                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.21/40.68                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.21/40.68    (58)  op(e1, e1) = e2
% 229.21/40.68    (59)   ~ (all_53_1 = all_53_13)
% 229.21/40.68    (60)  op(e2, e0) = all_53_13
% 229.21/40.68    (61)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.21/40.68          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.21/40.68    (62)   ~ (all_53_12 = e3)
% 229.21/40.68    (63)  op(e1, e3) = all_53_2
% 229.21/40.68    (64)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.21/40.68          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.21/40.68    (65)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.21/40.68          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.21/40.68    (66)   ~ (e2 = e1)
% 229.21/40.68    (67)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.21/40.68          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.21/40.68    (68)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.21/40.68          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.21/40.68    (69)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 229.21/40.68    (70)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 229.21/40.68          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 229.21/40.68    (71)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.21/40.68          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.21/40.68    (72)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.21/40.68          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.21/40.68    (73)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 229.21/40.68          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 229.21/40.68    (74)  all_55_14 = all_53_11
% 229.21/40.68    (75)   ~ (all_53_11 = e3)
% 229.21/40.68    (76)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.21/40.68          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.21/40.68    (77)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 229.21/40.68          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 229.21/40.68    (78)  op(e3, e0) = all_53_12
% 229.21/40.68  
% 229.21/40.68  Begin of proof
% 229.21/40.68  | 
% 229.21/40.68  | BETA: splitting (56) gives:
% 229.21/40.68  | 
% 229.21/40.68  | Case 1:
% 229.21/40.68  | | 
% 229.21/40.68  | |   (79)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 229.21/40.68  | |           e2)
% 229.21/40.68  | | 
% 229.21/40.68  | | BETA: splitting (79) gives:
% 229.21/40.68  | | 
% 229.21/40.68  | | Case 1:
% 229.21/40.68  | | | 
% 229.21/40.68  | | |   (80)  all_57_12 = e2 & op(e0, e3) = e2
% 229.21/40.68  | | | 
% 229.21/40.68  | | | ALPHA: (80) implies:
% 229.21/40.68  | | |   (81)  all_57_12 = e2
% 229.21/40.68  | | | 
% 229.21/40.68  | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (12), (14), (16), (17),
% 229.21/40.68  | | |            (18), (22), (23), (24), (27), (30), (32), (33), (34), (39),
% 229.21/40.68  | | |            (40), (42), (44), (45), (46), (48), (49), (54), (56), (57),
% 229.21/40.68  | | |            (58), (61), (62), (64), (65), (66), (67), (68), (70), (71),
% 229.21/40.68  | | |            (72), (73), (76), (77), (78), (81) are inconsistent by
% 229.21/40.68  | | |            sub-proof #726.
% 229.21/40.68  | | | 
% 229.21/40.68  | | Case 2:
% 229.21/40.68  | | | 
% 229.21/40.68  | | |   (82)  all_57_13 = e2 & op(e0, e2) = e2
% 229.21/40.68  | | | 
% 229.21/40.68  | | | REF_CLOSE: (1), (6), (8), (10), (11), (12), (13), (14), (15), (16), (19),
% 229.21/40.68  | | |            (20), (21), (25), (26), (28), (29), (31), (32), (35), (36),
% 229.21/40.68  | | |            (37), (38), (40), (41), (43), (47), (50), (51), (52), (53),
% 229.21/40.68  | | |            (54), (55), (59), (60), (63), (69), (74), (75), (82) are
% 229.21/40.68  | | |            inconsistent by sub-proof #771.
% 229.21/40.68  | | | 
% 229.21/40.68  | | End of split
% 229.21/40.68  | | 
% 229.21/40.68  | Case 2:
% 229.21/40.68  | | 
% 229.21/40.68  | |   (83)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.21/40.68  | |           e2)
% 229.21/40.68  | | 
% 229.21/40.68  | | BETA: splitting (83) gives:
% 229.21/40.68  | | 
% 229.21/40.68  | | Case 1:
% 229.21/40.68  | | | 
% 229.21/40.68  | | |   (84)  all_57_14 = e2 & op(e0, e1) = e2
% 229.21/40.68  | | | 
% 229.21/40.68  | | | ALPHA: (84) implies:
% 229.21/40.68  | | |   (85)  all_57_14 = e2
% 229.21/40.68  | | | 
% 229.21/40.68  | | | BETA: splitting (33) gives:
% 229.21/40.68  | | | 
% 229.21/40.68  | | | Case 1:
% 229.21/40.68  | | | | 
% 229.21/40.68  | | | |   (86)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0,
% 229.21/40.68  | | | |             e2) = e1)
% 229.21/40.68  | | | | 
% 229.21/40.68  | | | | BETA: splitting (86) gives:
% 229.21/40.68  | | | | 
% 229.21/40.68  | | | | Case 1:
% 229.21/40.68  | | | | | 
% 229.21/40.68  | | | | |   (87)  all_57_12 = e1 & op(e0, e3) = e1
% 229.21/40.68  | | | | | 
% 229.21/40.68  | | | | | REF_CLOSE: (3), (5), (6), (7), (8), (9), (12), (14), (16), (17), (22),
% 229.21/40.68  | | | | |            (24), (27), (30), (32), (33), (39), (40), (44), (45), (46),
% 229.21/40.68  | | | | |            (49), (54), (56), (57), (58), (61), (62), (64), (66), (67),
% 229.21/40.68  | | | | |            (71), (72), (73), (76), (78), (85), (87) are inconsistent
% 229.21/40.68  | | | | |            by sub-proof #722.
% 229.21/40.68  | | | | | 
% 229.21/40.68  | | | | Case 2:
% 229.21/40.68  | | | | | 
% 229.21/40.68  | | | | |   (88)  all_57_13 = e1 & op(e0, e2) = e1
% 229.21/40.68  | | | | | 
% 229.21/40.68  | | | | | ALPHA: (88) implies:
% 229.21/40.68  | | | | |   (89)  all_57_13 = e1
% 229.21/40.68  | | | | | 
% 229.21/40.68  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12),
% 229.21/40.68  | | | | |            (13), (14), (15), (16), (17), (19), (20), (21), (22), (24),
% 229.21/40.68  | | | | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (35),
% 229.21/40.68  | | | | |            (36), (37), (38), (39), (40), (41), (43), (44), (45), (46),
% 229.21/40.68  | | | | |            (47), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 229.21/40.68  | | | | |            (59), (60), (61), (62), (63), (64), (65), (66), (67), (69),
% 229.21/40.68  | | | | |            (71), (72), (74), (75), (76), (78), (85), (89) are
% 229.21/40.68  | | | | |            inconsistent by sub-proof #719.
% 229.21/40.68  | | | | | 
% 229.21/40.68  | | | | End of split
% 229.21/40.68  | | | | 
% 229.21/40.68  | | | Case 2:
% 229.21/40.68  | | | | 
% 229.21/40.68  | | | |   (90)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0,
% 229.21/40.68  | | | |             e0) = e1)
% 229.21/40.68  | | | | 
% 229.21/40.68  | | | | REF_CLOSE: (6), (8), (54), (66), (85), (90) are inconsistent by
% 229.21/40.68  | | | |            sub-proof #1139.
% 229.21/40.68  | | | | 
% 229.21/40.68  | | | End of split
% 229.21/40.68  | | | 
% 229.21/40.68  | | Case 2:
% 229.21/40.68  | | | 
% 229.21/40.68  | | |   (91)  all_57_15 = e2 & op(e0, e0) = e2
% 229.21/40.68  | | | 
% 229.21/40.68  | | | REF_CLOSE: (24), (30), (91) are inconsistent by sub-proof #2323.
% 229.21/40.68  | | | 
% 229.21/40.68  | | End of split
% 229.21/40.68  | | 
% 229.21/40.68  | End of split
% 229.21/40.68  | 
% 229.21/40.68  End of proof
% 229.21/40.68  
% 229.21/40.68  Sub-proof #719 shows that the following formulas are inconsistent:
% 229.21/40.68  ----------------------------------------------------------------
% 229.21/40.68    (1)   ~ (all_53_2 = e2)
% 229.21/40.68    (2)  all_57_0 = e2
% 229.21/40.68    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.21/40.68         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.21/40.68    (4)  all_57_13 = e1
% 229.21/40.68    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.21/40.68         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.21/40.68    (6)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.21/40.68         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.21/40.68    (7)   ~ (e3 = e1)
% 229.21/40.68    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.21/40.68           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.21/40.68    (9)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.21/40.68         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.21/40.68    (10)   ~ (all_53_3 = e3)
% 229.21/40.68    (11)   ~ (all_53_3 = all_53_7)
% 229.21/40.68    (12)   ~ (all_6_2 = e3)
% 229.21/40.68    (13)   ~ (all_53_9 = e1)
% 229.21/40.68    (14)  op(e1, e1) = all_6_2
% 229.21/40.68    (15)   ~ (all_53_1 = all_53_9)
% 229.21/40.68    (16)  op(e2, e2) = e1
% 229.21/40.68    (17)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.21/40.68          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.21/40.68    (18)   ~ (all_53_13 = e3)
% 229.21/40.68    (19)   ~ (all_53_9 = all_53_11)
% 229.21/40.68    (20)  all_55_4 = all_53_1
% 229.21/40.68    (21)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.21/40.68          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.21/40.68    (22)   ~ (e3 = e2)
% 229.21/40.68    (23)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 229.21/40.68    (24)   ~ (all_53_1 = all_53_3)
% 229.21/40.68    (25)   ~ (e3 = e0)
% 229.21/40.68    (26)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 229.21/40.68    (27)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 229.21/40.68    (28)  all_57_15 = e3
% 229.21/40.68    (29)   ~ (all_53_9 = all_53_13)
% 229.21/40.68    (30)  op(e3, e3) = e2
% 229.21/40.68    (31)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.21/40.68          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.21/40.68            e1)
% 229.21/40.68    (32)   ~ (all_53_1 = e1)
% 229.21/40.68    (33)  op(e2, e0) = e2
% 229.21/40.68    (34)  all_55_6 = all_53_9
% 229.21/40.68    (35)   ~ (all_53_1 = all_53_2)
% 229.21/40.68    (36)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.21/40.68          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.21/40.68    (37)   ~ (e2 = e0)
% 229.21/40.68    (38)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 229.21/40.68            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 229.21/40.68            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 229.21/40.68            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 229.21/40.68              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 229.21/40.68            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 229.21/40.68            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 229.21/40.68              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 229.21/40.68              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 229.21/40.68            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 229.21/40.68            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 229.21/40.68            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 229.21/40.68              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 229.21/40.68              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 229.21/40.68            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 229.21/40.68              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 229.21/40.68            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 229.21/40.68            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 229.21/40.68              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 229.21/40.68              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 229.21/40.68            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 229.21/40.68            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 229.21/40.68    (39)  all_55_12 = all_53_3
% 229.21/40.68    (40)  all_57_3 = e1
% 229.21/40.68    (41)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.21/40.68          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.21/40.68    (42)   ~ (e1 = e0)
% 229.21/40.68    (43)  all_57_14 = e2
% 229.21/40.68    (44)   ~ (all_53_3 = all_53_11)
% 229.21/40.68    (45)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.21/40.68          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.21/40.68    (46)   ~ (all_53_2 = all_53_3)
% 229.21/40.68    (47)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 229.21/40.68    (48)   ~ (all_53_7 = all_53_11)
% 229.21/40.68    (49)  all_55_8 = all_53_2
% 229.21/40.68    (50)  op(e0, e0) = e3
% 229.21/40.68    (51)  op(e0, e2) = all_53_7
% 229.21/40.68    (52)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.21/40.68          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.21/40.68            e2)
% 229.21/40.68    (53)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.21/40.68              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.21/40.68                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.21/40.68                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.21/40.68    (54)   ~ (all_53_1 = all_53_13)
% 229.21/40.68    (55)  op(e2, e0) = all_53_13
% 229.21/40.68    (56)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.21/40.68          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.21/40.68    (57)   ~ (all_53_12 = e3)
% 229.21/40.68    (58)  op(e1, e3) = all_53_2
% 229.21/40.68    (59)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.21/40.68          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.21/40.68    (60)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.21/40.68          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.21/40.68    (61)   ~ (e2 = e1)
% 229.21/40.68    (62)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.21/40.68          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.21/40.68    (63)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 229.21/40.68    (64)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.21/40.68          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.21/40.68    (65)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.21/40.68          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.21/40.68    (66)  all_55_14 = all_53_11
% 229.21/40.68    (67)   ~ (all_53_11 = e3)
% 229.21/40.68    (68)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.21/40.68          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.21/40.68    (69)  op(e3, e0) = all_53_12
% 229.21/40.68  
% 229.21/40.68  Begin of proof
% 229.21/40.68  | 
% 229.21/40.68  | BETA: splitting (6) gives:
% 229.21/40.68  | 
% 229.21/40.68  | Case 1:
% 229.21/40.68  | | 
% 229.21/40.68  | |   (70)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 229.21/40.68  | |           e2)
% 229.21/40.68  | | 
% 229.21/40.68  | | BETA: splitting (70) gives:
% 229.21/40.68  | | 
% 229.21/40.68  | | Case 1:
% 229.21/40.68  | | | 
% 229.21/40.68  | | |   (71)  all_57_1 = e2 & op(e3, e2) = e2
% 229.21/40.68  | | | 
% 229.21/40.68  | | | ALPHA: (71) implies:
% 229.21/40.68  | | |   (72)  all_57_1 = e2
% 229.21/40.68  | | | 
% 229.21/40.68  | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (12), (14), (16), (17),
% 229.21/40.68  | | |            (21), (22), (25), (28), (30), (31), (36), (37), (40), (41),
% 229.21/40.68  | | |            (42), (43), (45), (50), (52), (53), (56), (57), (59), (60),
% 229.21/40.68  | | |            (61), (62), (64), (65), (68), (69), (72) are inconsistent by
% 229.21/40.68  | | |            sub-proof #721.
% 229.21/40.68  | | | 
% 229.21/40.68  | | Case 2:
% 229.21/40.68  | | | 
% 229.21/40.68  | | |   (73)  all_57_3 = e2 & op(e2, e2) = e2
% 229.21/40.68  | | | 
% 229.21/40.68  | | | ALPHA: (73) implies:
% 229.21/40.68  | | |   (74)  op(e2, e2) = e2
% 229.21/40.68  | | | 
% 229.21/40.68  | | | REF_CLOSE: (8), (16), (61), (74) are inconsistent by sub-proof #2306.
% 229.21/40.68  | | | 
% 229.21/40.68  | | End of split
% 229.21/40.68  | | 
% 229.21/40.68  | Case 2:
% 229.21/40.68  | | 
% 229.21/40.68  | |   (75)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 229.21/40.68  | |           e2)
% 229.21/40.68  | | 
% 229.21/40.68  | | BETA: splitting (75) gives:
% 229.21/40.68  | | 
% 229.21/40.68  | | Case 1:
% 229.21/40.68  | | | 
% 229.21/40.68  | | |   (76)  all_57_7 = e2 & op(e1, e2) = e2
% 229.21/40.68  | | | 
% 229.21/40.68  | | | ALPHA: (76) implies:
% 229.21/40.68  | | |   (77)  all_57_7 = e2
% 229.21/40.68  | | | 
% 229.21/40.68  | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (12), (14), (16), (17),
% 229.21/40.68  | | |            (21), (22), (25), (28), (30), (31), (36), (37), (40), (41),
% 229.21/40.68  | | |            (42), (43), (45), (50), (52), (53), (56), (57), (59), (60),
% 229.21/40.68  | | |            (61), (62), (64), (65), (68), (69), (77) are inconsistent by
% 229.21/40.68  | | |            sub-proof #720.
% 229.21/40.68  | | | 
% 229.21/40.68  | | Case 2:
% 229.21/40.68  | | | 
% 229.21/40.68  | | |   (78)  all_57_13 = e2 & op(e0, e2) = e2
% 229.21/40.68  | | | 
% 229.21/40.68  | | | REF_CLOSE: (1), (7), (8), (10), (11), (12), (13), (14), (15), (16), (18),
% 229.21/40.68  | | |            (19), (20), (23), (24), (26), (27), (29), (30), (32), (33),
% 229.21/40.68  | | |            (34), (35), (37), (38), (39), (44), (46), (47), (48), (49),
% 229.21/40.68  | | |            (50), (51), (54), (55), (58), (63), (66), (67), (78) are
% 229.21/40.68  | | |            inconsistent by sub-proof #771.
% 229.21/40.68  | | | 
% 229.21/40.68  | | End of split
% 229.21/40.68  | | 
% 229.21/40.68  | End of split
% 229.21/40.68  | 
% 229.21/40.68  End of proof
% 229.21/40.68  
% 229.21/40.68  Sub-proof #720 shows that the following formulas are inconsistent:
% 229.21/40.68  ----------------------------------------------------------------
% 229.21/40.68    (1)  all_57_0 = e2
% 229.21/40.68    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.21/40.68         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.21/40.68    (3)  all_57_13 = e1
% 229.21/40.68    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.21/40.68         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.21/40.68    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.21/40.68         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.21/40.68    (6)   ~ (e3 = e1)
% 229.21/40.69    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.21/40.69           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.21/40.69    (8)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.21/40.69         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.21/40.69    (9)   ~ (all_6_2 = e3)
% 229.21/40.69    (10)  op(e1, e1) = all_6_2
% 229.21/40.69    (11)  op(e2, e2) = e1
% 229.21/40.69    (12)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.21/40.69          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.21/40.69    (13)  all_57_7 = e2
% 229.21/40.69    (14)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.21/40.69          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.21/40.69    (15)   ~ (e3 = e2)
% 229.21/40.69    (16)   ~ (e3 = e0)
% 229.21/40.69    (17)  all_57_15 = e3
% 229.21/40.69    (18)  op(e3, e3) = e2
% 229.21/40.69    (19)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.21/40.69          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.21/40.69            e1)
% 229.21/40.69    (20)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.21/40.69          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.21/40.69    (21)   ~ (e2 = e0)
% 229.21/40.69    (22)  all_57_3 = e1
% 229.21/40.69    (23)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.21/40.69          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.21/40.69    (24)   ~ (e1 = e0)
% 229.21/40.69    (25)  all_57_14 = e2
% 229.21/40.69    (26)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.21/40.69          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.21/40.69    (27)  op(e0, e0) = e3
% 229.21/40.69    (28)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.21/40.69          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.21/40.69            e2)
% 229.21/40.69    (29)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.21/40.69              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.21/40.69                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.21/40.69                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.21/40.69    (30)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.21/40.69          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.21/40.69    (31)   ~ (all_53_12 = e3)
% 229.21/40.69    (32)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.21/40.69          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.21/40.69    (33)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.21/40.69          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.21/40.69    (34)   ~ (e2 = e1)
% 229.21/40.69    (35)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.21/40.69          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.21/40.69    (36)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.21/40.69          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.21/40.69    (37)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.21/40.69          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.21/40.69    (38)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.21/40.69          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.21/40.69    (39)  op(e3, e0) = all_53_12
% 229.21/40.69  
% 229.21/40.69  Begin of proof
% 229.21/40.69  | 
% 229.21/40.69  | BETA: splitting (26) gives:
% 229.21/40.69  | 
% 229.21/40.69  | Case 1:
% 229.21/40.69  | | 
% 229.21/40.69  | |   (40)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 229.21/40.69  | |           e3)
% 229.21/40.69  | | 
% 229.21/40.69  | | BETA: splitting (40) gives:
% 229.21/40.69  | | 
% 229.21/40.69  | | Case 1:
% 229.21/40.69  | | | 
% 229.21/40.69  | | |   (41)  all_57_1 = e3 & op(e3, e2) = e3
% 229.21/40.69  | | | 
% 229.21/40.69  | | | ALPHA: (41) implies:
% 229.21/40.69  | | |   (42)  all_57_1 = e3
% 229.21/40.69  | | | 
% 229.21/40.69  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 229.21/40.69  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 229.21/40.69  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 229.21/40.69  | | |            (33), (34), (35), (36), (37), (38), (39), (42) are inconsistent
% 229.21/40.69  | | |            by sub-proof #770.
% 229.21/40.69  | | | 
% 229.21/40.69  | | Case 2:
% 229.21/40.69  | | | 
% 229.21/40.69  | | |   (43)  all_57_3 = e3 & op(e2, e2) = e3
% 229.21/40.69  | | | 
% 229.21/40.69  | | | ALPHA: (43) implies:
% 229.21/40.69  | | |   (44)  op(e2, e2) = e3
% 229.21/40.69  | | | 
% 229.21/40.69  | | | REF_CLOSE: (6), (7), (11), (44) are inconsistent by sub-proof #1912.
% 229.21/40.69  | | | 
% 229.21/40.69  | | End of split
% 229.21/40.69  | | 
% 229.21/40.69  | Case 2:
% 229.21/40.69  | | 
% 229.21/40.69  | |   (45)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 229.21/40.69  | |           e3)
% 229.21/40.69  | | 
% 229.21/40.69  | | REF_CLOSE: (6), (7), (13), (15), (16), (17), (19), (21), (24), (25), (27),
% 229.21/40.69  | |            (29), (34), (45) are inconsistent by sub-proof #723.
% 229.21/40.69  | | 
% 229.21/40.69  | End of split
% 229.21/40.69  | 
% 229.21/40.69  End of proof
% 229.21/40.69  
% 229.21/40.69  Sub-proof #721 shows that the following formulas are inconsistent:
% 229.21/40.69  ----------------------------------------------------------------
% 229.21/40.69    (1)  all_57_0 = e2
% 229.21/40.69    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.21/40.69         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.21/40.69    (3)  all_57_13 = e1
% 229.21/40.69    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.21/40.69         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.21/40.69    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.21/40.69         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.21/40.69    (6)   ~ (e3 = e1)
% 229.21/40.69    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.21/40.69           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.21/40.69    (8)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.21/40.69         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.21/40.69    (9)   ~ (all_6_2 = e3)
% 229.21/40.69    (10)  op(e1, e1) = all_6_2
% 229.21/40.69    (11)  op(e2, e2) = e1
% 229.21/40.69    (12)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.21/40.69          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.21/40.69    (13)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.21/40.69          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.21/40.69    (14)   ~ (e3 = e2)
% 229.21/40.69    (15)   ~ (e3 = e0)
% 229.21/40.69    (16)  all_57_1 = e2
% 229.21/40.69    (17)  all_57_15 = e3
% 229.21/40.69    (18)  op(e3, e3) = e2
% 229.21/40.69    (19)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.21/40.69          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.21/40.69            e1)
% 229.21/40.69    (20)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.21/40.69          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.21/40.69    (21)   ~ (e2 = e0)
% 229.21/40.69    (22)  all_57_3 = e1
% 229.21/40.69    (23)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.21/40.69          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.21/40.69    (24)   ~ (e1 = e0)
% 229.21/40.69    (25)  all_57_14 = e2
% 229.21/40.69    (26)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.21/40.69          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.21/40.69    (27)  op(e0, e0) = e3
% 229.21/40.69    (28)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.21/40.69          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.21/40.69            e2)
% 229.21/40.69    (29)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.21/40.69              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.21/40.69                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.21/40.69                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.21/40.69    (30)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.21/40.69          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.21/40.69    (31)   ~ (all_53_12 = e3)
% 229.21/40.69    (32)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.21/40.69          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.21/40.69    (33)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.21/40.69          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.21/40.69    (34)   ~ (e2 = e1)
% 229.21/40.69    (35)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.21/40.69          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.21/40.69    (36)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.21/40.69          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.21/40.69    (37)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.21/40.69          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.21/40.69    (38)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.21/40.69          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.21/40.69    (39)  op(e3, e0) = all_53_12
% 229.21/40.69  
% 229.21/40.69  Begin of proof
% 229.21/40.69  | 
% 229.21/40.69  | BETA: splitting (23) gives:
% 229.21/40.69  | 
% 229.21/40.69  | Case 1:
% 229.21/40.69  | | 
% 229.21/40.69  | |   (40)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) =
% 229.21/40.69  | |           e3)
% 229.21/40.69  | | 
% 229.21/40.69  | | BETA: splitting (40) gives:
% 229.21/40.69  | | 
% 229.21/40.69  | | Case 1:
% 229.21/40.69  | | | 
% 229.21/40.69  | | |   (41)  all_57_0 = e3 & op(e3, e3) = e3
% 229.21/40.69  | | | 
% 229.21/40.69  | | | ALPHA: (41) implies:
% 229.21/40.69  | | |   (42)  op(e3, e3) = e3
% 229.21/40.69  | | | 
% 229.21/40.69  | | | REF_CLOSE: (7), (14), (18), (42) are inconsistent by sub-proof #2490.
% 229.21/40.69  | | | 
% 229.21/40.69  | | Case 2:
% 229.21/40.69  | | | 
% 229.21/40.69  | | |   (43)  all_57_1 = e3 & op(e3, e2) = e3
% 229.21/40.69  | | | 
% 229.21/40.69  | | | ALPHA: (43) implies:
% 229.21/40.69  | | |   (44)  all_57_1 = e3
% 229.21/40.69  | | | 
% 229.21/40.69  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 229.21/40.69  | | |            (13), (14), (15), (17), (18), (19), (20), (21), (22), (23),
% 229.21/40.69  | | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 229.21/40.69  | | |            (34), (35), (36), (37), (38), (39), (44) are inconsistent by
% 229.21/40.69  | | |            sub-proof #769.
% 229.21/40.69  | | | 
% 229.21/40.69  | | End of split
% 229.21/40.69  | | 
% 229.21/40.69  | Case 2:
% 229.21/40.69  | | 
% 229.21/40.69  | |   (45)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) =
% 229.21/40.69  | |           e3)
% 229.21/40.69  | | 
% 229.21/40.69  | | REF_CLOSE: (6), (7), (12), (13), (15), (16), (18), (21), (24), (31), (34),
% 229.21/40.69  | |            (39), (45) are inconsistent by sub-proof #1651.
% 229.21/40.69  | | 
% 229.21/40.69  | End of split
% 229.21/40.69  | 
% 229.21/40.69  End of proof
% 229.21/40.69  
% 229.21/40.69  Sub-proof #722 shows that the following formulas are inconsistent:
% 229.21/40.69  ----------------------------------------------------------------
% 229.21/40.69    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.21/40.69         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.21/40.69    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.21/40.69         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.21/40.69    (3)   ~ (e3 = e1)
% 229.21/40.69    (4)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 229.21/40.69         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 229.21/40.69    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.21/40.69           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.21/40.69    (6)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.21/40.69         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.21/40.69    (7)   ~ (all_6_2 = e3)
% 229.21/40.69    (8)  op(e1, e1) = all_6_2
% 229.21/40.69    (9)  op(e2, e2) = e1
% 229.21/40.69    (10)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.21/40.69          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.21/40.69    (11)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.21/40.69          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.21/40.69    (12)   ~ (e3 = e2)
% 229.21/40.69    (13)   ~ (e3 = e0)
% 229.21/40.69    (14)  all_57_15 = e3
% 229.21/40.69    (15)  op(e3, e3) = e2
% 229.21/40.69    (16)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.21/40.69          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.21/40.69            e1)
% 229.21/40.69    (17)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.21/40.69          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.21/40.69    (18)   ~ (e2 = e0)
% 229.21/40.69    (19)  all_57_3 = e1
% 229.21/40.69    (20)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.21/40.69          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.21/40.69    (21)   ~ (e1 = e0)
% 229.21/40.69    (22)  all_57_14 = e2
% 229.21/40.69    (23)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.21/40.69          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.21/40.69    (24)  op(e0, e0) = e3
% 229.21/40.69    (25)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.21/40.69          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.21/40.69            e2)
% 229.21/40.69    (26)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.21/40.69              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.21/40.69                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.21/40.69                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.21/40.69    (27)  op(e1, e1) = e2
% 229.21/40.69    (28)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.21/40.69          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.21/40.69    (29)   ~ (all_53_12 = e3)
% 229.21/40.69    (30)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.21/40.69          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.21/40.69    (31)   ~ (e2 = e1)
% 229.21/40.69    (32)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.21/40.69          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.21/40.69    (33)  all_57_12 = e1 & op(e0, e3) = e1
% 229.21/40.69    (34)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.21/40.69          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.21/40.69    (35)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.21/40.69          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.21/40.69    (36)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 229.21/40.69          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 229.21/40.69    (37)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.21/40.69          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.21/40.69    (38)  op(e3, e0) = all_53_12
% 229.21/40.69  
% 229.21/40.69  Begin of proof
% 229.21/40.69  | 
% 229.21/40.69  | ALPHA: (33) implies:
% 229.21/40.69  |   (39)  all_57_12 = e1
% 229.21/40.69  | 
% 229.21/40.69  | BETA: splitting (2) gives:
% 229.21/40.69  | 
% 229.21/40.69  | Case 1:
% 229.21/40.69  | | 
% 229.21/40.69  | |   (40)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 229.21/40.69  | |           e2)
% 229.21/40.69  | | 
% 229.21/40.69  | | BETA: splitting (40) gives:
% 229.21/40.69  | | 
% 229.21/40.69  | | Case 1:
% 229.21/40.69  | | | 
% 229.21/40.69  | | |   (41)  all_57_1 = e2 & op(e3, e2) = e2
% 229.21/40.69  | | | 
% 229.21/40.69  | | | ALPHA: (41) implies:
% 229.21/40.69  | | |   (42)  all_57_1 = e2
% 229.21/40.69  | | | 
% 229.21/40.69  | | | BETA: splitting (20) gives:
% 229.21/40.69  | | | 
% 229.21/40.69  | | | Case 1:
% 229.21/40.69  | | | | 
% 229.21/40.69  | | | |   (43)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2)
% 229.21/40.69  | | | |           = e3)
% 229.21/40.69  | | | | 
% 229.21/40.69  | | | | REF_CLOSE: (5), (12), (15), (42), (43) are inconsistent by sub-proof
% 229.21/40.69  | | | |            #1663.
% 229.21/40.69  | | | | 
% 229.21/40.69  | | | Case 2:
% 229.21/40.69  | | | | 
% 229.21/40.69  | | | |   (44)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0)
% 229.21/40.69  | | | |           = e3)
% 229.21/40.69  | | | | 
% 229.21/40.69  | | | | REF_CLOSE: (3), (5), (10), (11), (13), (15), (18), (21), (29), (31),
% 229.21/40.69  | | | |            (38), (42), (44) are inconsistent by sub-proof #1651.
% 229.21/40.69  | | | | 
% 229.21/40.69  | | | End of split
% 229.21/40.69  | | | 
% 229.21/40.69  | | Case 2:
% 229.21/40.69  | | | 
% 229.21/40.69  | | |   (45)  all_57_3 = e2 & op(e2, e2) = e2
% 229.21/40.69  | | | 
% 229.21/40.69  | | | ALPHA: (45) implies:
% 229.21/40.69  | | |   (46)  op(e2, e2) = e2
% 229.21/40.69  | | | 
% 229.21/40.69  | | | REF_CLOSE: (5), (9), (31), (46) are inconsistent by sub-proof #2306.
% 229.21/40.69  | | | 
% 229.21/40.69  | | End of split
% 229.21/40.69  | | 
% 229.21/40.69  | Case 2:
% 229.21/40.69  | | 
% 229.21/40.69  | |   (47)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 229.21/40.69  | |           e2)
% 229.21/40.69  | | 
% 229.21/40.69  | | BETA: splitting (47) gives:
% 229.21/40.69  | | 
% 229.21/40.69  | | Case 1:
% 229.21/40.69  | | | 
% 229.21/40.69  | | |   (48)  all_57_7 = e2 & op(e1, e2) = e2
% 229.21/40.69  | | | 
% 229.21/40.69  | | | ALPHA: (48) implies:
% 229.21/40.69  | | |   (49)  all_57_7 = e2
% 229.21/40.69  | | | 
% 229.21/40.69  | | | BETA: splitting (23) gives:
% 229.21/40.69  | | | 
% 229.21/40.69  | | | Case 1:
% 229.21/40.69  | | | | 
% 229.21/40.69  | | | |   (50)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2)
% 229.21/40.69  | | | |           = e3)
% 229.21/40.69  | | | | 
% 229.21/40.69  | | | | BETA: splitting (50) gives:
% 229.21/40.69  | | | | 
% 229.21/40.69  | | | | Case 1:
% 229.21/40.69  | | | | | 
% 229.21/40.69  | | | | |   (51)  all_57_1 = e3 & op(e3, e2) = e3
% 229.21/40.69  | | | | | 
% 229.21/40.69  | | | | | ALPHA: (51) implies:
% 229.21/40.69  | | | | |   (52)  all_57_1 = e3
% 229.21/40.69  | | | | | 
% 229.21/40.69  | | | | | BETA: splitting (6) gives:
% 229.21/40.69  | | | | | 
% 229.21/40.69  | | | | | Case 1:
% 229.21/40.69  | | | | | | 
% 229.21/40.69  | | | | | |   (53)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1,
% 229.21/40.69  | | | | | |             e2) = e3)
% 229.21/40.69  | | | | | | 
% 229.21/40.69  | | | | | | BETA: splitting (53) gives:
% 229.21/40.69  | | | | | | 
% 229.21/40.69  | | | | | | Case 1:
% 229.21/40.69  | | | | | | | 
% 229.21/40.69  | | | | | | |   (54)  all_57_6 = e3 & op(e1, e3) = e3
% 229.21/40.69  | | | | | | | 
% 229.21/40.69  | | | | | | | ALPHA: (54) implies:
% 229.21/40.69  | | | | | | |   (55)  all_57_6 = e3
% 229.21/40.69  | | | | | | | 
% 229.21/40.69  | | | | | | | BETA: splitting (17) gives:
% 229.21/40.69  | | | | | | | 
% 229.21/40.69  | | | | | | | Case 1:
% 229.21/40.69  | | | | | | | | 
% 229.21/40.69  | | | | | | | |   (56)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 &
% 229.21/40.69  | | | | | | | |           op(e2, e2) = e0)
% 229.21/40.69  | | | | | | | | 
% 229.21/40.69  | | | | | | | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (9), (12), (13), (14),
% 229.21/40.69  | | | | | | | |            (17), (18), (21), (26), (31), (32), (35), (37), (52),
% 229.21/40.69  | | | | | | | |            (55), (56) are inconsistent by sub-proof #724.
% 229.21/40.69  | | | | | | | | 
% 229.21/40.69  | | | | | | | Case 2:
% 229.21/40.69  | | | | | | | | 
% 229.21/40.69  | | | | | | | |   (57)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 &
% 229.21/40.69  | | | | | | | |           op(e0, e2) = e0)
% 229.21/40.69  | | | | | | | | 
% 229.21/40.69  | | | | | | | | BETA: splitting (57) gives:
% 229.21/40.69  | | | | | | | | 
% 229.21/40.69  | | | | | | | | Case 1:
% 229.21/40.69  | | | | | | | | | 
% 229.21/40.69  | | | | | | | | |   (58)  all_57_7 = e0 & op(e1, e2) = e0
% 229.21/40.69  | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | REF_CLOSE: (18), (49), (58) are inconsistent by sub-proof
% 229.21/40.69  | | | | | | | | |            #2148.
% 229.21/40.69  | | | | | | | | | 
% 229.21/40.69  | | | | | | | | Case 2:
% 229.21/40.69  | | | | | | | | | 
% 229.21/40.69  | | | | | | | | |   (59)  all_57_13 = e0 & op(e0, e2) = e0
% 229.21/40.69  | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | ALPHA: (59) implies:
% 229.21/40.69  | | | | | | | | |   (60)  all_57_13 = e0
% 229.21/40.69  | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | BETA: splitting (4) gives:
% 229.21/40.69  | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | Case 1:
% 229.21/40.69  | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | |   (61)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 &
% 229.21/40.69  | | | | | | | | | |           op(e1, e2) = e0)
% 229.21/40.69  | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | BETA: splitting (61) gives:
% 229.21/40.69  | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | Case 1:
% 229.21/40.69  | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | |   (62)  all_57_6 = e0 & op(e1, e3) = e0
% 229.21/40.69  | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | ALPHA: (62) implies:
% 229.21/40.69  | | | | | | | | | | |   (63)  all_57_6 = e0
% 229.21/40.69  | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (9), (12), (13),
% 229.21/40.69  | | | | | | | | | | |            (14), (17), (18), (21), (26), (31), (32), (35),
% 229.21/40.69  | | | | | | | | | | |            (37), (52), (63) are inconsistent by sub-proof
% 229.21/40.69  | | | | | | | | | | |            #1773.
% 229.21/40.69  | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | Case 2:
% 229.21/40.69  | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | |   (64)  all_57_7 = e0 & op(e1, e2) = e0
% 229.21/40.69  | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | ALPHA: (64) implies:
% 229.21/40.69  | | | | | | | | | | |   (65)  all_57_7 = e0
% 229.21/40.69  | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | REF_CLOSE: (2), (5), (9), (12), (18), (31), (52), (60), (65)
% 229.21/40.69  | | | | | | | | | | |            are inconsistent by sub-proof #1767.
% 229.21/40.69  | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | End of split
% 229.21/40.69  | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | Case 2:
% 229.21/40.69  | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | |   (66)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0
% 229.21/40.69  | | | | | | | | | |           & op(e1, e0) = e0)
% 229.21/40.69  | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | BETA: splitting (66) gives:
% 229.21/40.69  | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | Case 1:
% 229.21/40.69  | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | |   (67)  all_57_8 = e0 & op(e1, e1) = e0
% 229.21/40.69  | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | ALPHA: (67) implies:
% 229.21/40.69  | | | | | | | | | | |   (68)  op(e1, e1) = e0
% 229.21/40.69  | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | BETA: splitting (26) gives:
% 229.21/40.69  | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | Case 1:
% 229.21/40.69  | | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | |   (69)  all_57_15 = e0 & op(e0, e0) = e0
% 229.21/40.69  | | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | | ALPHA: (69) implies:
% 229.21/40.69  | | | | | | | | | | | |   (70)  op(e0, e0) = e0
% 229.21/40.69  | | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | | REF_CLOSE: (5), (13), (24), (70) are inconsistent by
% 229.21/40.69  | | | | | | | | | | | |            sub-proof #2304.
% 229.21/40.69  | | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | Case 2:
% 229.21/40.69  | | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | |   (71)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 229.21/40.69  | | | | | | | | | | | |             e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 229.21/40.69  | | | | | | | | | | | |             op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 229.21/40.69  | | | | | | | | | | | |               e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 229.21/40.69  | | | | | | | | | | | |             e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 229.21/40.69  | | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | | ALPHA: (71) implies:
% 229.21/40.69  | | | | | | | | | | | |   (72)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 229.21/40.69  | | | | | | | | | | | |           e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 229.21/40.69  | | | | | | | | | | | |             e1) = e0)
% 229.21/40.69  | | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | | GROUND_INST: instantiating (5) with e0, e2, e1, e1, simplifying
% 229.21/40.69  | | | | | | | | | | | |              with (27), (68) gives:
% 229.21/40.69  | | | | | | | | | | | |   (73)  e2 = e0
% 229.21/40.69  | | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | | COMBINE_EQS: (49), (73) imply:
% 229.21/40.69  | | | | | | | | | | | |   (74)  all_57_7 = e0
% 229.21/40.69  | | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | | REF_CLOSE: (2), (3), (5), (9), (12), (13), (14), (16), (18),
% 229.21/40.69  | | | | | | | | | | | |            (21), (23), (24), (25), (31), (60), (72), (74) are
% 229.21/40.69  | | | | | | | | | | | |            inconsistent by sub-proof #1765.
% 229.21/40.69  | | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | End of split
% 229.21/40.69  | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | Case 2:
% 229.21/40.69  | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | |   (75)  all_57_11 = e0 & op(e1, e0) = e0
% 229.21/40.69  | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | ALPHA: (75) implies:
% 229.21/40.69  | | | | | | | | | | |   (76)  all_57_11 = e0
% 229.21/40.69  | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | BETA: splitting (34) gives:
% 229.21/40.69  | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | Case 1:
% 229.21/40.69  | | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | |   (77)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 229.21/40.69  | | | | | | | | | | | |           & op(e2, e3) = e0)
% 229.21/40.69  | | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | | BETA: splitting (77) gives:
% 229.21/40.69  | | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | | Case 1:
% 229.21/40.69  | | | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | | |   (78)  all_57_0 = e0 & op(e3, e3) = e0
% 229.21/40.69  | | | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | | | ALPHA: (78) implies:
% 229.21/40.69  | | | | | | | | | | | | |   (79)  op(e3, e3) = e0
% 229.21/40.69  | | | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | | | REF_CLOSE: (5), (15), (18), (79) are inconsistent by
% 229.21/40.69  | | | | | | | | | | | | |            sub-proof #2403.
% 229.21/40.69  | | | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | | Case 2:
% 229.21/40.69  | | | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | | |   (80)  all_57_2 = e0 & op(e2, e3) = e0
% 229.21/40.69  | | | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | | | ALPHA: (80) implies:
% 229.21/40.69  | | | | | | | | | | | | |   (81)  all_57_2 = e0
% 229.21/40.69  | | | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | | | BETA: splitting (36) gives:
% 229.21/40.69  | | | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | | | Case 1:
% 229.21/40.69  | | | | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | | | |   (82)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 229.21/40.69  | | | | | | | | | | | | | |           & op(e1, e2) = e1)
% 229.21/40.69  | | | | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | | | | BETA: splitting (82) gives:
% 229.21/40.69  | | | | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | | | | Case 1:
% 229.21/40.69  | | | | | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | | | | |   (83)  all_57_6 = e1 & op(e1, e3) = e1
% 229.21/40.69  | | | | | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (5), (9), (12), (13), (17), (18), (21),
% 229.21/40.69  | | | | | | | | | | | | | | |            (23), (31), (52), (55), (83) are inconsistent by
% 229.21/40.69  | | | | | | | | | | | | | | |            sub-proof #1771.
% 229.21/40.69  | | | | | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | | | | Case 2:
% 229.21/40.69  | | | | | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | | | | |   (84)  all_57_7 = e1 & op(e1, e2) = e1
% 229.21/40.69  | | | | | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | | | | | REF_CLOSE: (31), (49), (84) are inconsistent by sub-proof
% 229.21/40.69  | | | | | | | | | | | | | | |            #2190.
% 229.21/40.69  | | | | | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | | | | End of split
% 229.21/40.69  | | | | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | | | Case 2:
% 229.21/40.69  | | | | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | | | |   (85)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 229.21/40.69  | | | | | | | | | | | | | |           e1 & op(e1, e0) = e1)
% 229.21/40.69  | | | | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | | | | BETA: splitting (85) gives:
% 229.21/40.69  | | | | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | | | | Case 1:
% 229.21/40.69  | | | | | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | | | | |   (86)  all_57_8 = e1 & op(e1, e1) = e1
% 229.21/40.69  | | | | | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | | | | | ALPHA: (86) implies:
% 229.21/40.69  | | | | | | | | | | | | | | |   (87)  op(e1, e1) = e1
% 229.21/40.69  | | | | | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | | | | | REF_CLOSE: (5), (27), (31), (87) are inconsistent by
% 229.21/40.69  | | | | | | | | | | | | | | |            sub-proof #2423.
% 229.21/40.69  | | | | | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | | | | Case 2:
% 229.21/40.69  | | | | | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | | | | |   (88)  all_57_11 = e1 & op(e1, e0) = e1
% 229.21/40.69  | | | | | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | | | | | ALPHA: (88) implies:
% 229.21/40.69  | | | | | | | | | | | | | | |   (89)  all_57_11 = e1
% 229.21/40.69  | | | | | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | | | | | COMBINE_EQS: (76), (89) imply:
% 229.21/40.69  | | | | | | | | | | | | | | |   (90)  e1 = e0
% 229.21/40.69  | | | | | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (12), (13), (18), (19), (21), (28),
% 229.21/40.69  | | | | | | | | | | | | | | |            (30), (31), (81), (90) are inconsistent by
% 229.21/40.69  | | | | | | | | | | | | | | |            sub-proof #1824.
% 229.21/40.69  | | | | | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | | | | End of split
% 229.21/40.69  | | | | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | | | End of split
% 229.21/40.69  | | | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | | End of split
% 229.21/40.69  | | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | Case 2:
% 229.21/40.69  | | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | |   (91)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 229.21/40.69  | | | | | | | | | | | |           e0 & op(e0, e3) = e0)
% 229.21/40.69  | | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | | BETA: splitting (91) gives:
% 229.21/40.69  | | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | | Case 1:
% 229.21/40.69  | | | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | | |   (92)  all_57_6 = e0 & op(e1, e3) = e0
% 229.21/40.69  | | | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | | | ALPHA: (92) implies:
% 229.21/40.69  | | | | | | | | | | | | |   (93)  all_57_6 = e0
% 229.21/40.69  | | | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (9), (12), (13),
% 229.21/40.69  | | | | | | | | | | | | |            (14), (17), (18), (21), (26), (31), (32), (35),
% 229.21/40.69  | | | | | | | | | | | | |            (37), (52), (93) are inconsistent by sub-proof
% 229.21/40.69  | | | | | | | | | | | | |            #1773.
% 229.21/40.69  | | | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | | Case 2:
% 229.21/40.69  | | | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | | |   (94)  all_57_12 = e0 & op(e0, e3) = e0
% 229.21/40.69  | | | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | | | ALPHA: (94) implies:
% 229.21/40.69  | | | | | | | | | | | | |   (95)  all_57_12 = e0
% 229.21/40.69  | | | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | | | COMBINE_EQS: (39), (95) imply:
% 229.21/40.69  | | | | | | | | | | | | |   (96)  e1 = e0
% 229.21/40.69  | | | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | | | COMBINE_EQS: (19), (96) imply:
% 229.21/40.69  | | | | | | | | | | | | |   (97)  all_57_3 = e0
% 229.21/40.69  | | | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | | | REF_CLOSE: (3), (12), (13), (14), (16), (18), (21), (23),
% 229.21/40.69  | | | | | | | | | | | | |            (25), (31), (37), (49), (60), (95), (97) are
% 229.21/40.69  | | | | | | | | | | | | |            inconsistent by sub-proof #779.
% 229.21/40.69  | | | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | | End of split
% 229.21/40.69  | | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | | End of split
% 229.21/40.69  | | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | | End of split
% 229.21/40.69  | | | | | | | | | | 
% 229.21/40.69  | | | | | | | | | End of split
% 229.21/40.69  | | | | | | | | | 
% 229.21/40.69  | | | | | | | | End of split
% 229.21/40.69  | | | | | | | | 
% 229.21/40.69  | | | | | | | End of split
% 229.21/40.69  | | | | | | | 
% 229.21/40.69  | | | | | | Case 2:
% 229.21/40.69  | | | | | | | 
% 229.21/40.69  | | | | | | |   (98)  all_57_7 = e3 & op(e1, e2) = e3
% 229.21/40.69  | | | | | | | 
% 229.21/40.69  | | | | | | | ALPHA: (98) implies:
% 229.21/40.69  | | | | | | |   (99)  all_57_7 = e3
% 229.21/40.69  | | | | | | | 
% 229.21/40.69  | | | | | | | COMBINE_EQS: (49), (99) imply:
% 229.21/40.69  | | | | | | |   (100)  e3 = e2
% 229.21/40.69  | | | | | | | 
% 229.21/40.69  | | | | | | | SIMP: (100) implies:
% 229.21/40.69  | | | | | | |   (101)  e3 = e2
% 229.21/40.69  | | | | | | | 
% 229.21/40.69  | | | | | | | COMBINE_EQS: (52), (101) imply:
% 229.21/40.69  | | | | | | |   (102)  all_57_1 = e2
% 229.21/40.69  | | | | | | | 
% 229.21/40.69  | | | | | | | REF_CLOSE: (3), (5), (10), (11), (12), (13), (15), (18), (20),
% 229.21/40.69  | | | | | | |            (21), (29), (31), (38), (102) are inconsistent by
% 229.21/40.69  | | | | | | |            sub-proof #1650.
% 229.21/40.69  | | | | | | | 
% 229.21/40.69  | | | | | | End of split
% 229.21/40.69  | | | | | | 
% 229.21/40.69  | | | | | Case 2:
% 229.21/40.69  | | | | | | 
% 229.21/40.70  | | | | | |   (103)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 &
% 229.21/40.70  | | | | | |            op(e1, e0) = e3)
% 229.21/40.70  | | | | | | 
% 229.21/40.70  | | | | | | REF_CLOSE: (3), (5), (7), (8), (12), (13), (14), (18), (21), (26),
% 229.21/40.70  | | | | | |            (31), (32), (35), (103) are inconsistent by sub-proof
% 229.21/40.70  | | | | | |            #1786.
% 229.21/40.70  | | | | | | 
% 229.21/40.70  | | | | | End of split
% 229.21/40.70  | | | | | 
% 229.21/40.70  | | | | Case 2:
% 229.21/40.70  | | | | | 
% 229.21/40.70  | | | | |   (104)  all_57_3 = e3 & op(e2, e2) = e3
% 229.21/40.70  | | | | | 
% 229.21/40.70  | | | | | ALPHA: (104) implies:
% 229.21/40.70  | | | | |   (105)  op(e2, e2) = e3
% 229.21/40.70  | | | | | 
% 229.21/40.70  | | | | | REF_CLOSE: (3), (5), (9), (105) are inconsistent by sub-proof #1912.
% 229.21/40.70  | | | | | 
% 229.21/40.70  | | | | End of split
% 229.21/40.70  | | | | 
% 229.21/40.70  | | | Case 2:
% 229.21/40.70  | | | | 
% 229.21/40.70  | | | |   (106)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0,
% 229.21/40.70  | | | |              e2) = e3)
% 229.21/40.70  | | | | 
% 229.21/40.70  | | | | REF_CLOSE: (3), (5), (12), (13), (14), (16), (18), (21), (22), (24),
% 229.21/40.70  | | | |            (26), (31), (49), (106) are inconsistent by sub-proof #723.
% 229.21/40.70  | | | | 
% 229.21/40.70  | | | End of split
% 229.21/40.70  | | | 
% 229.21/40.70  | | Case 2:
% 229.21/40.70  | | | 
% 229.21/40.70  | | |   (107)  all_57_13 = e2 & op(e0, e2) = e2
% 229.21/40.70  | | | 
% 229.21/40.70  | | | ALPHA: (107) implies:
% 229.21/40.70  | | |   (108)  all_57_13 = e2
% 229.21/40.70  | | | 
% 229.21/40.70  | | | REF_CLOSE: (5), (13), (18), (21), (22), (24), (26), (39), (108) are
% 229.21/40.70  | | |            inconsistent by sub-proof #1583.
% 229.21/40.70  | | | 
% 229.21/40.70  | | End of split
% 229.21/40.70  | | 
% 229.21/40.70  | End of split
% 229.21/40.70  | 
% 229.21/40.70  End of proof
% 229.21/40.70  
% 229.21/40.70  Sub-proof #723 shows that the following formulas are inconsistent:
% 229.21/40.70  ----------------------------------------------------------------
% 229.21/40.70    (1)   ~ (e3 = e1)
% 229.21/40.70    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.21/40.70           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.21/40.70    (3)  all_57_7 = e2
% 229.21/40.70    (4)   ~ (e3 = e2)
% 229.21/40.70    (5)   ~ (e3 = e0)
% 229.21/40.70    (6)  all_57_15 = e3
% 229.21/40.70    (7)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 229.21/40.70         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.21/40.70    (8)   ~ (e2 = e0)
% 229.21/40.70    (9)   ~ (e1 = e0)
% 229.21/40.70    (10)  all_57_14 = e2
% 229.21/40.70    (11)  op(e0, e0) = e3
% 229.21/40.70    (12)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.21/40.70              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.21/40.70                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.21/40.70                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.21/40.70    (13)   ~ (e2 = e1)
% 229.21/40.70    (14)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.21/40.70  
% 229.21/40.70  Begin of proof
% 229.21/40.70  | 
% 229.21/40.70  | BETA: splitting (14) gives:
% 229.21/40.70  | 
% 229.21/40.70  | Case 1:
% 229.21/40.70  | | 
% 229.21/40.70  | |   (15)  all_57_7 = e3 & op(e1, e2) = e3
% 229.21/40.70  | | 
% 229.21/40.70  | | ALPHA: (15) implies:
% 229.21/40.70  | |   (16)  all_57_7 = e3
% 229.21/40.70  | | 
% 229.21/40.70  | | REF_CLOSE: (3), (4), (16) are inconsistent by sub-proof #2102.
% 229.21/40.70  | | 
% 229.21/40.70  | Case 2:
% 229.21/40.70  | | 
% 229.21/40.70  | |   (17)  all_57_13 = e3 & op(e0, e2) = e3
% 229.21/40.70  | | 
% 229.21/40.70  | | ALPHA: (17) implies:
% 229.21/40.70  | |   (18)  all_57_13 = e3
% 229.21/40.70  | | 
% 229.21/40.70  | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (9), (10), (11), (12), (13), (18)
% 229.21/40.70  | |            are inconsistent by sub-proof #2212.
% 229.21/40.70  | | 
% 229.21/40.70  | End of split
% 229.21/40.70  | 
% 229.21/40.70  End of proof
% 229.21/40.70  
% 229.21/40.70  Sub-proof #724 shows that the following formulas are inconsistent:
% 229.21/40.70  ----------------------------------------------------------------
% 229.21/40.70    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.21/40.70         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.21/40.70    (2)   ~ (e3 = e1)
% 229.21/40.70    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.21/40.70           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.21/40.70    (4)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.21/40.70         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.21/40.70    (5)   ~ (all_6_2 = e3)
% 229.21/40.70    (6)  op(e1, e1) = all_6_2
% 229.21/40.70    (7)  op(e2, e2) = e1
% 229.21/40.70    (8)   ~ (e3 = e2)
% 229.21/40.70    (9)   ~ (e3 = e0)
% 229.21/40.70    (10)  all_57_15 = e3
% 229.21/40.70    (11)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.21/40.70          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.21/40.70    (12)   ~ (e2 = e0)
% 229.21/40.70    (13)   ~ (e1 = e0)
% 229.21/40.70    (14)  all_57_6 = e3
% 229.21/40.70    (15)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0)
% 229.21/40.70    (16)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.21/40.70              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.21/40.70                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.21/40.70                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.21/40.70    (17)  all_57_1 = e3
% 229.21/40.70    (18)   ~ (e2 = e1)
% 229.21/40.70    (19)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.21/40.70          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.21/40.70    (20)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.21/40.70          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.21/40.70    (21)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.21/40.70          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.21/40.70  
% 229.21/40.70  Begin of proof
% 229.21/40.70  | 
% 229.21/40.70  | BETA: splitting (15) gives:
% 229.21/40.70  | 
% 229.21/40.70  | Case 1:
% 229.21/40.70  | | 
% 229.21/40.70  | |   (22)  all_57_1 = e0 & op(e3, e2) = e0
% 229.21/40.70  | | 
% 229.21/40.70  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 229.21/40.70  | |            (13), (14), (16), (17), (18), (19), (20), (21), (22) are
% 229.21/40.70  | |            inconsistent by sub-proof #725.
% 229.21/40.70  | | 
% 229.21/40.70  | Case 2:
% 229.21/40.70  | | 
% 229.21/40.70  | |   (23)  all_57_3 = e0 & op(e2, e2) = e0
% 229.21/40.70  | | 
% 229.21/40.70  | | ALPHA: (23) implies:
% 229.26/40.70  | |   (24)  op(e2, e2) = e0
% 229.26/40.70  | | 
% 229.26/40.70  | | REF_CLOSE: (3), (7), (13), (24) are inconsistent by sub-proof #2352.
% 229.26/40.70  | | 
% 229.26/40.70  | End of split
% 229.26/40.70  | 
% 229.26/40.70  End of proof
% 229.26/40.70  
% 229.26/40.70  Sub-proof #725 shows that the following formulas are inconsistent:
% 229.26/40.70  ----------------------------------------------------------------
% 229.26/40.70    (1)  all_57_1 = e0 & op(e3, e2) = e0
% 229.26/40.70    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.26/40.70         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.26/40.70    (3)   ~ (e3 = e1)
% 229.26/40.70    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.26/40.70           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.26/40.70    (5)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.26/40.70         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.26/40.70    (6)   ~ (all_6_2 = e3)
% 229.26/40.70    (7)  op(e1, e1) = all_6_2
% 229.26/40.70    (8)  op(e2, e2) = e1
% 229.26/40.70    (9)   ~ (e3 = e2)
% 229.26/40.70    (10)   ~ (e3 = e0)
% 229.26/40.70    (11)  all_57_15 = e3
% 229.26/40.70    (12)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.26/40.70          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.26/40.70    (13)   ~ (e2 = e0)
% 229.26/40.70    (14)   ~ (e1 = e0)
% 229.26/40.70    (15)  all_57_6 = e3
% 229.26/40.70    (16)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.26/40.70              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.26/40.70                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.26/40.70                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.26/40.70    (17)  all_57_1 = e3
% 229.26/40.70    (18)   ~ (e2 = e1)
% 229.26/40.70    (19)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.26/40.70          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.26/40.70    (20)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.26/40.70          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.26/40.70    (21)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.26/40.70          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.26/40.70  
% 229.26/40.70  Begin of proof
% 229.26/40.70  | 
% 229.26/40.70  | ALPHA: (1) implies:
% 229.26/40.70  |   (22)  all_57_1 = e0
% 229.26/40.70  | 
% 229.26/40.70  | COMBINE_EQS: (17), (22) imply:
% 229.26/40.70  |   (23)  e3 = e0
% 229.26/40.70  | 
% 229.26/40.70  | COMBINE_EQS: (15), (23) imply:
% 229.26/40.70  |   (24)  all_57_6 = e0
% 229.26/40.70  | 
% 229.26/40.70  | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 229.26/40.70  |            (14), (16), (17), (18), (19), (20), (21), (24) are inconsistent by
% 229.26/40.70  |            sub-proof #1773.
% 229.26/40.70  | 
% 229.26/40.70  End of proof
% 229.26/40.70  
% 229.26/40.70  Sub-proof #726 shows that the following formulas are inconsistent:
% 229.26/40.70  ----------------------------------------------------------------
% 229.26/40.70    (1)  all_57_0 = e2
% 229.26/40.70    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.26/40.70         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.26/40.70    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.26/40.70         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.26/40.70    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.26/40.70         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.26/40.70    (5)   ~ (e3 = e1)
% 229.26/40.70    (6)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 229.26/40.70         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 229.26/40.70    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.26/40.70           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.26/40.70    (8)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.26/40.70         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.26/40.70    (9)   ~ (all_6_2 = e3)
% 229.26/40.70    (10)  op(e1, e1) = all_6_2
% 229.26/40.70    (11)  op(e2, e2) = e1
% 229.26/40.70    (12)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.26/40.70          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.26/40.70    (13)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 229.26/40.70            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 229.26/40.70              e3) = all_22_1 & $i(all_22_1))
% 229.26/40.70    (14)  all_57_12 = e2
% 229.26/40.70    (15)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.26/40.70          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.26/40.70    (16)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 229.26/40.70          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.26/40.70    (17)   ~ (e3 = e2)
% 229.26/40.70    (18)   ~ (e3 = e0)
% 229.26/40.70    (19)  all_57_15 = e3
% 229.26/40.70    (20)  op(e3, e3) = e2
% 229.26/40.70    (21)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.26/40.70          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.26/40.70            e1)
% 229.26/40.70    (22)  all_57_10 = e2
% 229.26/40.70    (23)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.26/40.70          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.26/40.70    (24)   ~ (e2 = e0)
% 229.26/40.70    (25)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 229.26/40.70            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 229.26/40.70              e3) = all_12_1 & $i(all_12_1))
% 229.26/40.70    (26)  all_57_3 = e1
% 229.26/40.70    (27)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.26/40.70          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.26/40.70    (28)   ~ (e1 = e0)
% 229.26/40.70    (29)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.26/40.70          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.26/40.70    (30)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.26/40.70          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.26/40.70    (31)  op(e0, e0) = e3
% 229.26/40.70    (32)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.26/40.70          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.26/40.70            e2)
% 229.26/40.70    (33)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.26/40.70              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.26/40.70                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.26/40.70                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.26/40.70    (34)  op(e1, e1) = e2
% 229.26/40.70    (35)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.26/40.70          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.26/40.70    (36)   ~ (all_53_12 = e3)
% 229.26/40.70    (37)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.26/40.70          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.26/40.70    (38)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.26/40.70          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.26/40.70    (39)   ~ (e2 = e1)
% 229.26/40.70    (40)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.26/40.70          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.26/40.70    (41)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.26/40.70          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.26/40.70    (42)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 229.26/40.70          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 229.26/40.70    (43)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.26/40.70          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.26/40.70    (44)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.26/40.70          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.26/40.70    (45)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 229.26/40.70          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 229.26/40.70    (46)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.26/40.70          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.26/40.70    (47)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 229.26/40.70          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 229.26/40.70    (48)  op(e3, e0) = all_53_12
% 229.26/40.70  
% 229.26/40.70  Begin of proof
% 229.26/40.70  | 
% 229.26/40.70  | BETA: splitting (21) gives:
% 229.26/40.70  | 
% 229.26/40.70  | Case 1:
% 229.26/40.70  | | 
% 229.26/40.70  | |   (49)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 229.26/40.70  | |           e1)
% 229.26/40.70  | | 
% 229.26/40.70  | | BETA: splitting (49) gives:
% 229.26/40.70  | | 
% 229.26/40.70  | | Case 1:
% 229.26/40.70  | | | 
% 229.26/40.70  | | |   (50)  all_57_12 = e1 & op(e0, e3) = e1
% 229.26/40.70  | | | 
% 229.26/40.70  | | | REF_CLOSE: (14), (39), (50) are inconsistent by sub-proof #2388.
% 229.26/40.70  | | | 
% 229.26/40.70  | | Case 2:
% 229.26/40.70  | | | 
% 229.26/40.70  | | |   (51)  all_57_13 = e1 & op(e0, e2) = e1
% 229.26/40.70  | | | 
% 229.26/40.70  | | | ALPHA: (51) implies:
% 229.26/40.70  | | |   (52)  all_57_13 = e1
% 229.26/40.70  | | | 
% 229.26/40.70  | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (14),
% 229.26/40.70  | | |            (15), (17), (18), (19), (20), (21), (23), (24), (26), (27),
% 229.26/40.70  | | |            (28), (30), (31), (32), (33), (35), (36), (37), (38), (39),
% 229.26/40.70  | | |            (40), (41), (44), (46), (48), (52) are inconsistent by
% 229.26/40.70  | | |            sub-proof #774.
% 229.26/40.70  | | | 
% 229.26/40.70  | | End of split
% 229.26/40.70  | | 
% 229.26/40.70  | Case 2:
% 229.26/40.70  | | 
% 229.26/40.70  | |   (53)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.26/40.70  | |           e1)
% 229.26/40.70  | | 
% 229.26/40.70  | | BETA: splitting (53) gives:
% 229.26/40.70  | | 
% 229.26/40.70  | | Case 1:
% 229.26/40.70  | | | 
% 229.26/40.70  | | |   (54)  all_57_14 = e1 & op(e0, e1) = e1
% 229.26/40.70  | | | 
% 229.26/40.70  | | | ALPHA: (54) implies:
% 229.26/40.70  | | |   (55)  all_57_14 = e1
% 229.26/40.70  | | | 
% 229.26/40.70  | | | BETA: splitting (3) gives:
% 229.26/40.70  | | | 
% 229.26/40.70  | | | Case 1:
% 229.26/40.70  | | | | 
% 229.26/40.70  | | | |   (56)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3)
% 229.26/40.70  | | | |           = e1)
% 229.26/40.70  | | | | 
% 229.26/40.70  | | | | REF_CLOSE: (1), (2), (3), (5), (7), (14), (17), (18), (20), (24), (26),
% 229.26/40.70  | | | |            (28), (35), (37), (38), (39), (41), (43), (56) are
% 229.26/40.70  | | | |            inconsistent by sub-proof #762.
% 229.26/40.70  | | | | 
% 229.26/40.70  | | | Case 2:
% 229.26/40.70  | | | | 
% 229.26/40.70  | | | |   (57)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3)
% 229.26/40.70  | | | |           = e1)
% 229.26/40.70  | | | | 
% 229.26/40.70  | | | | BETA: splitting (57) gives:
% 229.26/40.70  | | | | 
% 229.26/40.70  | | | | Case 1:
% 229.26/40.70  | | | | | 
% 229.26/40.70  | | | | |   (58)  all_57_6 = e1 & op(e1, e3) = e1
% 229.26/40.70  | | | | | 
% 229.26/40.70  | | | | | ALPHA: (58) implies:
% 229.26/40.70  | | | | |   (59)  all_57_6 = e1
% 229.26/40.70  | | | | | 
% 229.26/40.70  | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 229.26/40.70  | | | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 229.26/40.70  | | | | |            (23), (24), (25), (26), (27), (28), (29), (31), (32), (33),
% 229.26/40.70  | | | | |            (34), (35), (36), (37), (38), (39), (40), (42), (43), (44),
% 229.26/40.70  | | | | |            (45), (46), (47), (48), (55), (59) are inconsistent by
% 229.26/40.70  | | | | |            sub-proof #739.
% 229.26/40.70  | | | | | 
% 229.26/40.70  | | | | Case 2:
% 229.26/40.70  | | | | | 
% 229.26/40.70  | | | | |   (60)  all_57_12 = e1 & op(e0, e3) = e1
% 229.26/40.70  | | | | | 
% 229.26/40.70  | | | | | REF_CLOSE: (14), (39), (60) are inconsistent by sub-proof #2388.
% 229.26/40.70  | | | | | 
% 229.26/40.70  | | | | End of split
% 229.26/40.70  | | | | 
% 229.26/40.70  | | | End of split
% 229.26/40.70  | | | 
% 229.26/40.70  | | Case 2:
% 229.26/40.70  | | | 
% 229.26/40.70  | | |   (61)  all_57_15 = e1 & op(e0, e0) = e1
% 229.26/40.70  | | | 
% 229.26/40.70  | | | ALPHA: (61) implies:
% 229.26/40.70  | | |   (62)  op(e0, e0) = e1
% 229.26/40.70  | | | 
% 229.26/40.70  | | | REF_CLOSE: (5), (7), (31), (62) are inconsistent by sub-proof #2183.
% 229.26/40.70  | | | 
% 229.26/40.70  | | End of split
% 229.26/40.70  | | 
% 229.26/40.70  | End of split
% 229.26/40.70  | 
% 229.26/40.70  End of proof
% 229.26/40.70  
% 229.26/40.70  Sub-proof #727 shows that the following formulas are inconsistent:
% 229.26/40.70  ----------------------------------------------------------------
% 229.26/40.70    (1)  all_57_10 = e0
% 229.26/40.70    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.26/40.70           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.26/40.70    (3)  op(e2, e2) = e1
% 229.26/40.70    (4)   ~ (e3 = e2)
% 229.26/40.70    (5)  op(e3, e3) = e2
% 229.26/40.70    (6)  all_57_5 = e3
% 229.26/40.70    (7)   ~ (e2 = e0)
% 229.26/40.70    (8)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.26/40.70         (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.26/40.70    (9)   ~ (e2 = e1)
% 229.26/40.70    (10)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3)
% 229.26/40.70  
% 229.26/40.70  Begin of proof
% 229.26/40.70  | 
% 229.26/40.70  | BETA: splitting (10) gives:
% 229.26/40.70  | 
% 229.26/40.70  | Case 1:
% 229.26/40.70  | | 
% 229.26/40.70  | |   (11)  all_57_0 = e3 & op(e3, e3) = e3
% 229.26/40.70  | | 
% 229.26/40.70  | | ALPHA: (11) implies:
% 229.26/40.70  | |   (12)  op(e3, e3) = e3
% 229.26/40.70  | | 
% 229.26/40.70  | | REF_CLOSE: (2), (4), (5), (12) are inconsistent by sub-proof #2490.
% 229.26/40.70  | | 
% 229.26/40.70  | Case 2:
% 229.26/40.70  | | 
% 229.26/40.70  | |   (13)  all_57_2 = e3 & op(e2, e3) = e3
% 229.26/40.70  | | 
% 229.26/40.70  | | ALPHA: (13) implies:
% 229.26/40.70  | |   (14)  all_57_2 = e3
% 229.26/40.70  | | 
% 229.26/40.70  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (14) are inconsistent by
% 229.26/40.70  | |            sub-proof #1797.
% 229.26/40.70  | | 
% 229.26/40.70  | End of split
% 229.26/40.70  | 
% 229.26/40.70  End of proof
% 229.26/40.70  
% 229.26/40.70  Sub-proof #728 shows that the following formulas are inconsistent:
% 229.26/40.70  ----------------------------------------------------------------
% 229.26/40.70    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.26/40.70         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.26/40.70    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.26/40.70         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.26/40.70    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.26/40.70         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.26/40.70    (4)   ~ (e3 = e1)
% 229.26/40.70    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.26/40.70           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.26/40.70    (6)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.26/40.70         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.26/40.70    (7)   ~ (all_6_2 = e3)
% 229.26/40.70    (8)  op(e1, e1) = all_6_2
% 229.26/40.70    (9)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.26/40.70         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.26/40.70    (10)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.26/40.70          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.26/40.70    (11)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.26/40.70          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.26/40.70    (12)  all_57_3 = e0
% 229.26/40.70    (13)   ~ (e3 = e2)
% 229.26/40.70    (14)   ~ (e3 = e0)
% 229.26/40.70    (15)  all_57_15 = e3
% 229.26/40.70    (16)  op(e3, e3) = e2
% 229.26/40.70    (17)  all_57_6 = e2
% 229.26/40.70    (18)   ~ (e2 = e0)
% 229.26/40.70    (19)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.26/40.70          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.26/40.70    (20)   ~ (e1 = e0)
% 229.26/40.70    (21)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.26/40.70              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.26/40.70                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.26/40.70                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.26/40.70    (22)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.26/40.70          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.26/40.70    (23)   ~ (all_53_12 = e3)
% 229.26/40.70    (24)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.26/40.70          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.26/40.70    (25)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.26/40.70          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.26/40.70    (26)   ~ (e2 = e1)
% 229.26/40.70    (27)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.26/40.70          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.26/40.70    (28)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.26/40.70          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.26/40.70    (29)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.26/40.70          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.26/40.70    (30)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.26/40.70          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.26/40.70    (31)  op(e3, e0) = all_53_12
% 229.26/40.70  
% 229.26/40.70  Begin of proof
% 229.26/40.70  | 
% 229.26/40.70  | BETA: splitting (6) gives:
% 229.26/40.70  | 
% 229.26/40.70  | Case 1:
% 229.26/40.70  | | 
% 229.26/40.70  | |   (32)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 229.26/40.70  | |           e3)
% 229.26/40.70  | | 
% 229.26/40.70  | | BETA: splitting (32) gives:
% 229.26/40.70  | | 
% 229.26/40.70  | | Case 1:
% 229.26/40.70  | | | 
% 229.26/40.70  | | |   (33)  all_57_6 = e3 & op(e1, e3) = e3
% 229.26/40.70  | | | 
% 229.26/40.70  | | | ALPHA: (33) implies:
% 229.26/40.70  | | |   (34)  all_57_6 = e3
% 229.26/40.70  | | | 
% 229.26/40.70  | | | REF_CLOSE: (13), (17), (34) are inconsistent by sub-proof #2463.
% 229.26/40.70  | | | 
% 229.26/40.70  | | Case 2:
% 229.26/40.70  | | | 
% 229.26/40.70  | | |   (35)  all_57_7 = e3 & op(e1, e2) = e3
% 229.26/40.70  | | | 
% 229.26/40.70  | | | ALPHA: (35) implies:
% 229.26/40.70  | | |   (36)  all_57_7 = e3
% 229.26/40.70  | | | 
% 229.26/40.70  | | | REF_CLOSE: (1), (2), (3), (4), (5), (9), (10), (11), (12), (13), (14),
% 229.26/40.70  | | |            (16), (17), (18), (19), (20), (22), (23), (24), (25), (26),
% 229.26/40.70  | | |            (28), (30), (31), (36) are inconsistent by sub-proof #729.
% 229.26/40.70  | | | 
% 229.26/40.70  | | End of split
% 229.26/40.70  | | 
% 229.26/40.70  | Case 2:
% 229.26/40.70  | | 
% 229.26/40.70  | |   (37)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 229.26/40.70  | |           e3)
% 229.26/40.70  | | 
% 229.26/40.70  | | REF_CLOSE: (4), (5), (7), (8), (13), (14), (15), (18), (20), (21), (26),
% 229.26/40.70  | |            (27), (29), (37) are inconsistent by sub-proof #1786.
% 229.26/40.70  | | 
% 229.26/40.70  | End of split
% 229.26/40.70  | 
% 229.26/40.70  End of proof
% 229.26/40.70  
% 229.26/40.70  Sub-proof #729 shows that the following formulas are inconsistent:
% 229.26/40.70  ----------------------------------------------------------------
% 229.26/40.70    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.26/40.70         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.26/40.70    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.26/40.70         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.26/40.70    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.26/40.70         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.26/40.70    (4)   ~ (e3 = e1)
% 229.26/40.70    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.26/40.70           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.26/40.70    (6)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.26/40.70         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.26/40.70    (7)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.26/40.70         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.26/40.71    (8)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.26/40.71         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.26/40.71    (9)  all_57_3 = e0
% 229.26/40.71    (10)   ~ (e3 = e2)
% 229.26/40.71    (11)   ~ (e3 = e0)
% 229.26/40.71    (12)  op(e3, e3) = e2
% 229.26/40.71    (13)  all_57_6 = e2
% 229.26/40.71    (14)   ~ (e2 = e0)
% 229.26/40.71    (15)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.26/40.71          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.26/40.71    (16)   ~ (e1 = e0)
% 229.26/40.71    (17)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.26/40.71          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.26/40.71    (18)   ~ (all_53_12 = e3)
% 229.26/40.71    (19)  all_57_7 = e3
% 229.26/40.71    (20)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.26/40.71          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.26/40.71    (21)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.26/40.71          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.26/40.71    (22)   ~ (e2 = e1)
% 229.26/40.71    (23)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.26/40.71          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.26/40.71    (24)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.26/40.71          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.26/40.71    (25)  op(e3, e0) = all_53_12
% 229.26/40.71  
% 229.26/40.71  Begin of proof
% 229.26/40.71  | 
% 229.26/40.71  | BETA: splitting (23) gives:
% 229.26/40.71  | 
% 229.26/40.71  | Case 1:
% 229.26/40.71  | | 
% 229.26/40.71  | |   (26)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) =
% 229.26/40.71  | |           e0)
% 229.26/40.71  | | 
% 229.26/40.71  | | BETA: splitting (26) gives:
% 229.26/40.71  | | 
% 229.26/40.71  | | Case 1:
% 229.26/40.71  | | | 
% 229.26/40.71  | | |   (27)  all_57_0 = e0 & op(e3, e3) = e0
% 229.26/40.71  | | | 
% 229.26/40.71  | | | ALPHA: (27) implies:
% 229.26/40.71  | | |   (28)  op(e3, e3) = e0
% 229.26/40.71  | | | 
% 229.26/40.71  | | | REF_CLOSE: (5), (12), (14), (28) are inconsistent by sub-proof #2403.
% 229.26/40.71  | | | 
% 229.26/40.71  | | Case 2:
% 229.26/40.71  | | | 
% 229.26/40.71  | | |   (29)  all_57_2 = e0 & op(e2, e3) = e0
% 229.26/40.71  | | | 
% 229.26/40.71  | | | ALPHA: (29) implies:
% 229.26/40.71  | | |   (30)  all_57_2 = e0
% 229.26/40.71  | | | 
% 229.26/40.71  | | | REF_CLOSE: (1), (4), (9), (10), (11), (14), (16), (17), (20), (22), (30)
% 229.26/40.71  | | |            are inconsistent by sub-proof #2246.
% 229.26/40.71  | | | 
% 229.26/40.71  | | End of split
% 229.26/40.71  | | 
% 229.26/40.71  | Case 2:
% 229.26/40.71  | | 
% 229.26/40.71  | |   (31)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) =
% 229.26/40.71  | |           e0)
% 229.26/40.71  | | 
% 229.26/40.71  | | BETA: splitting (31) gives:
% 229.26/40.71  | | 
% 229.26/40.71  | | Case 1:
% 229.26/40.71  | | | 
% 229.26/40.71  | | |   (32)  all_57_6 = e0 & op(e1, e3) = e0
% 229.26/40.71  | | | 
% 229.26/40.71  | | | REF_CLOSE: (13), (14), (32) are inconsistent by sub-proof #2386.
% 229.26/40.71  | | | 
% 229.26/40.71  | | Case 2:
% 229.26/40.71  | | | 
% 229.26/40.71  | | |   (33)  all_57_12 = e0 & op(e0, e3) = e0
% 229.26/40.71  | | | 
% 229.26/40.71  | | | ALPHA: (33) implies:
% 229.26/40.71  | | |   (34)  all_57_12 = e0
% 229.26/40.71  | | | 
% 229.26/40.71  | | | BETA: splitting (15) gives:
% 229.26/40.71  | | | 
% 229.26/40.71  | | | Case 1:
% 229.26/40.71  | | | | 
% 229.26/40.71  | | | |   (35)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2)
% 229.26/40.71  | | | |           = e3)
% 229.26/40.71  | | | | 
% 229.26/40.71  | | | | REF_CLOSE: (3), (4), (5), (9), (10), (12), (14), (16), (19), (22), (24),
% 229.26/40.71  | | | |            (35) are inconsistent by sub-proof #1620.
% 229.26/40.71  | | | | 
% 229.26/40.71  | | | Case 2:
% 229.26/40.71  | | | | 
% 229.26/40.71  | | | |   (36)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0)
% 229.26/40.71  | | | |           = e3)
% 229.26/40.71  | | | | 
% 229.26/40.71  | | | | BETA: splitting (36) gives:
% 229.26/40.71  | | | | 
% 229.26/40.71  | | | | Case 1:
% 229.26/40.71  | | | | | 
% 229.26/40.71  | | | | |   (37)  all_57_4 = e3 & op(e3, e1) = e3
% 229.26/40.71  | | | | | 
% 229.26/40.71  | | | | | ALPHA: (37) implies:
% 229.26/40.71  | | | | |   (38)  all_57_4 = e3
% 229.26/40.71  | | | | | 
% 229.26/40.71  | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 229.26/40.71  | | | | |            (13), (14), (16), (19), (21), (22), (24), (34), (38) are
% 229.26/40.71  | | | | |            inconsistent by sub-proof #730.
% 229.26/40.71  | | | | | 
% 229.26/40.71  | | | | Case 2:
% 229.26/40.71  | | | | | 
% 229.26/40.71  | | | | |   (39)  all_57_9 = e3 & op(e3, e0) = e3
% 229.26/40.71  | | | | | 
% 229.26/40.71  | | | | | ALPHA: (39) implies:
% 229.26/40.71  | | | | |   (40)  op(e3, e0) = e3
% 229.26/40.71  | | | | | 
% 229.26/40.71  | | | | | REF_CLOSE: (5), (18), (25), (40) are inconsistent by sub-proof #2458.
% 229.26/40.71  | | | | | 
% 229.26/40.71  | | | | End of split
% 229.26/40.71  | | | | 
% 229.26/40.71  | | | End of split
% 229.26/40.71  | | | 
% 229.26/40.71  | | End of split
% 229.26/40.71  | | 
% 229.26/40.71  | End of split
% 229.26/40.71  | 
% 229.26/40.71  End of proof
% 229.26/40.71  
% 229.26/40.71  Sub-proof #730 shows that the following formulas are inconsistent:
% 229.26/40.71  ----------------------------------------------------------------
% 229.26/40.71    (1)  all_57_12 = e0
% 229.26/40.71    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.26/40.71         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.26/40.71    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.26/40.71         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.26/40.71    (4)   ~ (e3 = e1)
% 229.26/40.71    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.26/40.71           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.26/40.71    (6)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.26/40.71         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.26/40.71    (7)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.26/40.71         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.26/40.71    (8)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.26/40.71         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.26/40.71    (9)  all_57_3 = e0
% 229.26/40.71    (10)  all_57_4 = e3
% 229.26/40.71    (11)   ~ (e3 = e2)
% 229.26/40.71    (12)   ~ (e3 = e0)
% 229.26/40.71    (13)  op(e3, e3) = e2
% 229.26/40.71    (14)  all_57_6 = e2
% 229.26/40.71    (15)   ~ (e2 = e0)
% 229.26/40.71    (16)   ~ (e1 = e0)
% 229.26/40.71    (17)  all_57_7 = e3
% 229.26/40.71    (18)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.26/40.71          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.26/40.71    (19)   ~ (e2 = e1)
% 229.26/40.71    (20)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.26/40.71          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.26/40.71  
% 229.26/40.71  Begin of proof
% 229.26/40.71  | 
% 229.26/40.71  | BETA: splitting (2) gives:
% 229.26/40.71  | 
% 229.26/40.71  | Case 1:
% 229.26/40.71  | | 
% 229.26/40.71  | |   (21)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) =
% 229.26/40.71  | |           e1)
% 229.26/40.71  | | 
% 229.26/40.71  | | BETA: splitting (21) gives:
% 229.26/40.71  | | 
% 229.26/40.71  | | Case 1:
% 229.26/40.71  | | | 
% 229.26/40.71  | | |   (22)  all_57_0 = e1 & op(e3, e3) = e1
% 229.26/40.71  | | | 
% 229.26/40.71  | | | ALPHA: (22) implies:
% 229.26/40.71  | | |   (23)  op(e3, e3) = e1
% 229.26/40.71  | | | 
% 229.26/40.71  | | | REF_CLOSE: (5), (13), (19), (23) are inconsistent by sub-proof #1950.
% 229.26/40.71  | | | 
% 229.26/40.71  | | Case 2:
% 229.26/40.71  | | | 
% 229.26/40.71  | | |   (24)  all_57_2 = e1 & op(e2, e3) = e1
% 229.26/40.71  | | | 
% 229.26/40.71  | | | ALPHA: (24) implies:
% 229.26/40.71  | | |   (25)  all_57_2 = e1
% 229.26/40.71  | | | 
% 229.26/40.71  | | | BETA: splitting (18) gives:
% 229.26/40.71  | | | 
% 229.26/40.71  | | | Case 1:
% 229.26/40.71  | | | | 
% 229.26/40.71  | | | |   (26)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3)
% 229.26/40.71  | | | |           = e3)
% 229.26/40.71  | | | | 
% 229.26/40.71  | | | | BETA: splitting (26) gives:
% 229.26/40.71  | | | | 
% 229.26/40.71  | | | | Case 1:
% 229.26/40.71  | | | | | 
% 229.26/40.71  | | | | |   (27)  all_57_0 = e3 & op(e3, e3) = e3
% 229.26/40.71  | | | | | 
% 229.26/40.71  | | | | | ALPHA: (27) implies:
% 229.26/40.71  | | | | |   (28)  op(e3, e3) = e3
% 229.26/40.71  | | | | | 
% 229.26/40.71  | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (15),
% 229.26/40.71  | | | | |            (16), (17), (19), (20), (28) are inconsistent by sub-proof
% 229.26/40.71  | | | | |            #1539.
% 229.26/40.71  | | | | | 
% 229.26/40.71  | | | | Case 2:
% 229.26/40.71  | | | | | 
% 229.26/40.71  | | | | |   (29)  all_57_2 = e3 & op(e2, e3) = e3
% 229.26/40.71  | | | | | 
% 229.26/40.71  | | | | | ALPHA: (29) implies:
% 229.26/40.71  | | | | |   (30)  all_57_2 = e3
% 229.26/40.71  | | | | | 
% 229.26/40.71  | | | | | REF_CLOSE: (4), (25), (30) are inconsistent by sub-proof #2397.
% 229.26/40.71  | | | | | 
% 229.26/40.71  | | | | End of split
% 229.26/40.71  | | | | 
% 229.26/40.71  | | | Case 2:
% 229.26/40.71  | | | | 
% 229.26/40.71  | | | |   (31)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3)
% 229.26/40.71  | | | |           = e3)
% 229.26/40.71  | | | | 
% 229.26/40.71  | | | | BETA: splitting (31) gives:
% 229.26/40.71  | | | | 
% 229.26/40.71  | | | | Case 1:
% 229.26/40.71  | | | | | 
% 229.26/40.71  | | | | |   (32)  all_57_6 = e3 & op(e1, e3) = e3
% 229.26/40.71  | | | | | 
% 229.26/40.71  | | | | | ALPHA: (32) implies:
% 229.26/40.71  | | | | |   (33)  all_57_6 = e3
% 229.26/40.71  | | | | | 
% 229.26/40.71  | | | | | REF_CLOSE: (11), (14), (33) are inconsistent by sub-proof #2463.
% 229.26/40.71  | | | | | 
% 229.26/40.71  | | | | Case 2:
% 229.26/40.71  | | | | | 
% 229.26/40.71  | | | | |   (34)  all_57_12 = e3 & op(e0, e3) = e3
% 229.26/40.71  | | | | | 
% 229.26/40.71  | | | | | ALPHA: (34) implies:
% 229.26/40.71  | | | | |   (35)  all_57_12 = e3
% 229.26/40.71  | | | | | 
% 229.26/40.71  | | | | | REF_CLOSE: (1), (12), (35) are inconsistent by sub-proof #2153.
% 229.26/40.71  | | | | | 
% 229.26/40.71  | | | | End of split
% 229.26/40.71  | | | | 
% 229.26/40.71  | | | End of split
% 229.26/40.71  | | | 
% 229.26/40.71  | | End of split
% 229.26/40.71  | | 
% 229.26/40.71  | Case 2:
% 229.26/40.71  | | 
% 229.26/40.71  | |   (36)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) =
% 229.26/40.71  | |           e1)
% 229.26/40.71  | | 
% 229.26/40.71  | | REF_CLOSE: (1), (14), (16), (19), (36) are inconsistent by sub-proof #1513.
% 229.26/40.71  | | 
% 229.26/40.71  | End of split
% 229.26/40.71  | 
% 229.26/40.71  End of proof
% 229.26/40.71  
% 229.26/40.71  Sub-proof #731 shows that the following formulas are inconsistent:
% 229.26/40.71  ----------------------------------------------------------------
% 229.26/40.71    (1)   ~ (e3 = e1)
% 229.26/40.71    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.26/40.71           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.26/40.71    (3)   ~ (all_6_2 = e3)
% 229.26/40.71    (4)  op(e1, e1) = all_6_2
% 229.26/40.71    (5)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.26/40.71    (6)  all_57_15 = e3
% 229.26/40.71    (7)  all_57_10 = e2
% 229.26/40.71    (8)  all_57_9 = e0
% 229.26/40.71    (9)   ~ (e1 = e0)
% 229.26/40.71    (10)   ~ (e2 = e1)
% 229.26/40.71    (11)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.26/40.71          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.26/40.71  
% 229.26/40.71  Begin of proof
% 229.26/40.71  | 
% 229.26/40.71  | BETA: splitting (5) gives:
% 229.26/40.71  | 
% 229.26/40.71  | Case 1:
% 229.26/40.71  | | 
% 229.26/40.71  | |   (12)  all_57_8 = e3 & op(e1, e1) = e3
% 229.26/40.71  | | 
% 229.26/40.71  | | ALPHA: (12) implies:
% 229.26/40.71  | |   (13)  op(e1, e1) = e3
% 229.26/40.71  | | 
% 229.26/40.71  | | REF_CLOSE: (2), (3), (4), (13) are inconsistent by sub-proof #2468.
% 229.26/40.71  | | 
% 229.26/40.71  | Case 2:
% 229.26/40.71  | | 
% 229.26/40.71  | |   (14)  all_57_11 = e3 & op(e1, e0) = e3
% 229.26/40.71  | | 
% 229.26/40.71  | | ALPHA: (14) implies:
% 229.26/40.71  | |   (15)  all_57_11 = e3
% 229.26/40.71  | | 
% 229.26/40.71  | | REF_CLOSE: (1), (6), (7), (8), (9), (10), (11), (15) are inconsistent by
% 229.26/40.71  | |            sub-proof #2142.
% 229.26/40.71  | | 
% 229.26/40.71  | End of split
% 229.26/40.71  | 
% 229.26/40.71  End of proof
% 229.26/40.71  
% 229.26/40.71  Sub-proof #732 shows that the following formulas are inconsistent:
% 229.26/40.71  ----------------------------------------------------------------
% 229.26/40.71    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.26/40.71         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.26/40.71    (2)   ~ (e3 = e1)
% 229.26/40.71    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.26/40.71           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.26/40.71    (4)  op(e2, e2) = e1
% 229.26/40.71    (5)   ~ (e3 = e2)
% 229.26/40.71    (6)   ~ (e3 = e0)
% 229.26/40.71    (7)  e3 = e0
% 229.26/40.71    (8)  all_57_5 = e3
% 229.26/40.71    (9)   ~ (e2 = e0)
% 229.26/40.71    (10)  all_57_2 = e3
% 229.26/40.71    (11)   ~ (e1 = e0)
% 229.26/40.71    (12)  all_57_7 = e3
% 229.26/40.71    (13)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.26/40.71          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.26/40.71    (14)  all_57_1 = e3
% 229.26/40.71    (15)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.26/40.71          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 229.26/40.71    (16)   ~ (e2 = e1)
% 229.26/40.71    (17)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.26/40.71          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.26/40.71  
% 229.26/40.71  Begin of proof
% 229.26/40.71  | 
% 229.26/40.71  | COMBINE_EQS: (7), (14) imply:
% 229.26/40.71  |   (18)  all_57_1 = e0
% 229.26/40.71  | 
% 229.26/40.71  | BETA: splitting (15) gives:
% 229.26/40.71  | 
% 229.26/40.71  | Case 1:
% 229.26/40.71  | | 
% 229.26/40.71  | |   (19)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) =
% 229.26/40.71  | |           e0)
% 229.26/40.71  | | 
% 229.26/40.71  | | BETA: splitting (19) gives:
% 229.26/40.71  | | 
% 229.26/40.71  | | Case 1:
% 229.26/40.71  | | | 
% 229.26/40.71  | | |   (20)  all_57_2 = e0 & op(e2, e3) = e0
% 229.26/40.71  | | | 
% 229.26/40.71  | | | REF_CLOSE: (6), (10), (20) are inconsistent by sub-proof #1805.
% 229.26/40.71  | | | 
% 229.26/40.71  | | Case 2:
% 229.26/40.71  | | | 
% 229.26/40.71  | | |   (21)  all_57_3 = e0 & op(e2, e2) = e0
% 229.26/40.71  | | | 
% 229.26/40.71  | | | ALPHA: (21) implies:
% 229.26/40.71  | | |   (22)  all_57_3 = e0
% 229.26/40.71  | | | 
% 229.26/40.71  | | | REF_CLOSE: (1), (2), (5), (9), (11), (12), (16), (17), (18), (22) are
% 229.26/40.71  | | |            inconsistent by sub-proof #2098.
% 229.26/40.71  | | | 
% 229.26/40.71  | | End of split
% 229.26/40.71  | | 
% 229.26/40.71  | Case 2:
% 229.26/40.71  | | 
% 229.26/40.71  | |   (23)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 229.26/40.71  | |           e0)
% 229.26/40.71  | | 
% 229.26/40.71  | | REF_CLOSE: (3), (4), (5), (6), (8), (9), (10), (13), (16), (23) are
% 229.26/40.71  | |            inconsistent by sub-proof #1796.
% 229.26/40.71  | | 
% 229.26/40.71  | End of split
% 229.26/40.71  | 
% 229.26/40.71  End of proof
% 229.26/40.71  
% 229.26/40.71  Sub-proof #733 shows that the following formulas are inconsistent:
% 229.26/40.71  ----------------------------------------------------------------
% 229.26/40.71    (1)   ~ (e3 = e1)
% 229.26/40.71    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.26/40.71           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.26/40.71    (3)   ~ (e3 = e2)
% 229.26/40.71    (4)  op(e3, e3) = e2
% 229.26/40.71    (5)  all_57_4 = e1
% 229.26/40.71    (6)  all_57_6 = e2
% 229.26/40.71    (7)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.26/40.71         (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.26/40.71    (8)   ~ (all_53_12 = e3)
% 229.26/40.71    (9)  all_57_1 = e3
% 229.26/40.71    (10)  all_57_6 = e3 & op(e1, e3) = e3
% 229.26/40.71    (11)  op(e3, e0) = all_53_12
% 229.26/40.71  
% 229.26/40.71  Begin of proof
% 229.26/40.71  | 
% 229.26/40.71  | ALPHA: (10) implies:
% 229.26/40.71  |   (12)  all_57_6 = e3
% 229.26/40.71  | 
% 229.26/40.71  | COMBINE_EQS: (6), (12) imply:
% 229.26/40.71  |   (13)  e3 = e2
% 229.26/40.71  | 
% 229.26/40.71  | COMBINE_EQS: (9), (13) imply:
% 229.26/40.71  |   (14)  all_57_1 = e2
% 229.26/40.71  | 
% 229.26/40.71  | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (11), (14) are inconsistent by
% 229.26/40.71  |            sub-proof #1308.
% 229.26/40.71  | 
% 229.26/40.71  End of proof
% 229.26/40.71  
% 229.26/40.71  Sub-proof #734 shows that the following formulas are inconsistent:
% 229.26/40.71  ----------------------------------------------------------------
% 229.26/40.71    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.26/40.71         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.26/40.71    (2)   ~ (e3 = e1)
% 229.26/40.71    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.26/40.71           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.26/40.71    (4)  op(e2, e2) = e1
% 229.26/40.71    (5)   ~ (e3 = e2)
% 229.26/40.71    (6)   ~ (e3 = e0)
% 229.26/40.71    (7)  all_57_4 = e1
% 229.26/40.71    (8)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.26/40.71         (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.26/40.71    (9)   ~ (e2 = e0)
% 229.26/40.71    (10)   ~ (e1 = e0)
% 229.26/40.71    (11)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.26/40.71          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.26/40.71    (12)  all_57_1 = e3
% 229.26/40.71    (13)   ~ (e2 = e1)
% 229.26/40.71    (14)  all_57_4 = e3 & op(e3, e1) = e3
% 229.26/40.71  
% 229.26/40.71  Begin of proof
% 229.26/40.71  | 
% 229.26/40.71  | ALPHA: (14) implies:
% 229.26/40.71  |   (15)  all_57_4 = e3
% 229.26/40.71  | 
% 229.26/40.71  | COMBINE_EQS: (7), (15) imply:
% 229.26/40.71  |   (16)  e3 = e1
% 229.26/40.71  | 
% 229.26/40.71  | SIMP: (16) implies:
% 229.26/40.71  |   (17)  e3 = e1
% 229.26/40.71  | 
% 229.26/40.71  | COMBINE_EQS: (12), (17) imply:
% 229.26/40.71  |   (18)  all_57_1 = e1
% 229.26/40.71  | 
% 229.26/40.71  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (13), (18) are
% 229.26/40.71  |            inconsistent by sub-proof #1908.
% 229.26/40.71  | 
% 229.26/40.71  End of proof
% 229.26/40.71  
% 229.26/40.71  Sub-proof #735 shows that the following formulas are inconsistent:
% 229.26/40.71  ----------------------------------------------------------------
% 229.26/40.71    (1)  all_57_9 = e2
% 229.26/40.71    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.26/40.71         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.26/40.71    (3)   ~ (e3 = e1)
% 229.26/40.71    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.26/40.71           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.26/40.71    (5)   ~ (all_6_2 = e3)
% 229.26/40.71    (6)  op(e1, e1) = all_6_2
% 229.26/40.71    (7)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.26/40.71         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.26/40.71    (8)   ~ (e3 = e2)
% 229.26/40.71    (9)   ~ (e3 = e0)
% 229.26/40.71    (10)  all_57_15 = e3
% 229.26/40.71    (11)  op(e3, e3) = e2
% 229.26/40.71    (12)  all_57_4 = e1
% 229.26/40.71    (13)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.26/40.71          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.26/40.71            e1)
% 229.26/40.71    (14)   ~ (e2 = e0)
% 229.26/40.71    (15)  all_57_3 = e1
% 229.26/40.71    (16)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.26/40.71          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.26/40.71    (17)   ~ (e1 = e0)
% 229.26/40.71    (18)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.26/40.71          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.26/40.71    (19)  op(e0, e0) = e3
% 229.26/40.71    (20)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.26/40.71          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.26/40.71            e2)
% 229.26/40.71    (21)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.26/40.71              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.26/40.71                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.26/40.71                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.26/40.71    (22)   ~ (all_53_12 = e3)
% 229.26/40.71    (23)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.26/40.71          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.26/40.71    (24)  all_57_11 = e1
% 229.26/40.71    (25)   ~ (e2 = e1)
% 229.26/40.71    (26)  op(e3, e0) = all_53_12
% 229.26/40.71  
% 229.26/40.71  Begin of proof
% 229.26/40.71  | 
% 229.26/40.71  | BETA: splitting (16) gives:
% 229.26/40.71  | 
% 229.26/40.71  | Case 1:
% 229.26/40.71  | | 
% 229.26/40.71  | |   (27)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) =
% 229.26/40.71  | |           e3)
% 229.26/40.71  | | 
% 229.26/40.71  | | BETA: splitting (27) gives:
% 229.26/40.71  | | 
% 229.26/40.71  | | Case 1:
% 229.26/40.71  | | | 
% 229.26/40.71  | | |   (28)  all_57_0 = e3 & op(e3, e3) = e3
% 229.26/40.71  | | | 
% 229.26/40.71  | | | ALPHA: (28) implies:
% 229.26/40.71  | | |   (29)  op(e3, e3) = e3
% 229.26/40.71  | | | 
% 229.26/40.71  | | | REF_CLOSE: (4), (8), (11), (29) are inconsistent by sub-proof #2490.
% 229.26/40.71  | | | 
% 229.26/40.71  | | Case 2:
% 229.26/40.71  | | | 
% 229.26/40.71  | | |   (30)  all_57_1 = e3 & op(e3, e2) = e3
% 229.26/40.71  | | | 
% 229.26/40.71  | | | ALPHA: (30) implies:
% 229.26/40.71  | | |   (31)  all_57_1 = e3
% 229.26/40.71  | | | 
% 229.26/40.71  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 229.26/40.71  | | |            (13), (14), (15), (17), (18), (19), (20), (21), (23), (24),
% 229.26/40.71  | | |            (25), (31) are inconsistent by sub-proof #736.
% 229.26/40.71  | | | 
% 229.26/40.71  | | End of split
% 229.26/40.71  | | 
% 229.26/40.71  | Case 2:
% 229.26/40.71  | | 
% 229.26/40.71  | |   (32)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) =
% 229.26/40.71  | |           e3)
% 229.26/40.71  | | 
% 229.26/40.71  | | REF_CLOSE: (3), (4), (12), (22), (26), (32) are inconsistent by sub-proof
% 229.26/40.71  | |            #2281.
% 229.26/40.71  | | 
% 229.26/40.71  | End of split
% 229.26/40.71  | 
% 229.26/40.71  End of proof
% 229.26/40.71  
% 229.26/40.71  Sub-proof #736 shows that the following formulas are inconsistent:
% 229.26/40.71  ----------------------------------------------------------------
% 229.26/40.71    (1)  all_57_9 = e2
% 229.26/40.71    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.26/40.71         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.26/40.71    (3)   ~ (e3 = e1)
% 229.26/40.71    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.26/40.71           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.26/40.71    (5)   ~ (all_6_2 = e3)
% 229.26/40.71    (6)  op(e1, e1) = all_6_2
% 229.26/40.71    (7)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.26/40.71         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.26/40.71    (8)   ~ (e3 = e2)
% 229.26/40.71    (9)   ~ (e3 = e0)
% 229.26/40.71    (10)  all_57_15 = e3
% 229.26/40.71    (11)  op(e3, e3) = e2
% 229.26/40.71    (12)  all_57_4 = e1
% 229.26/40.71    (13)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.26/40.71          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.26/40.71            e1)
% 229.26/40.71    (14)   ~ (e2 = e0)
% 229.26/40.71    (15)  all_57_3 = e1
% 229.26/40.71    (16)   ~ (e1 = e0)
% 229.26/40.71    (17)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.26/40.71          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.26/40.71    (18)  op(e0, e0) = e3
% 229.26/40.71    (19)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.26/40.71          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.26/40.71            e2)
% 229.26/40.71    (20)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.26/40.71              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.26/40.71                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.26/40.71                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.26/40.71    (21)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.26/40.71          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.26/40.71    (22)  all_57_11 = e1
% 229.26/40.71    (23)  all_57_1 = e3
% 229.26/40.71    (24)   ~ (e2 = e1)
% 229.26/40.71  
% 229.26/40.71  Begin of proof
% 229.26/40.71  | 
% 229.26/40.71  | BETA: splitting (7) gives:
% 229.26/40.71  | 
% 229.26/40.71  | Case 1:
% 229.26/40.71  | | 
% 229.26/40.71  | |   (25)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) =
% 229.26/40.71  | |           e0)
% 229.26/40.71  | | 
% 229.26/40.71  | | REF_CLOSE: (4), (9), (11), (14), (23), (25) are inconsistent by sub-proof
% 229.26/40.71  | |            #1676.
% 229.26/40.71  | | 
% 229.26/40.71  | Case 2:
% 229.26/40.71  | | 
% 229.26/40.71  | |   (26)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) =
% 229.26/40.71  | |           e0)
% 229.26/40.71  | | 
% 229.26/40.71  | | BETA: splitting (26) gives:
% 229.26/40.71  | | 
% 229.26/40.71  | | Case 1:
% 229.26/40.71  | | | 
% 229.26/40.71  | | |   (27)  all_57_4 = e0 & op(e3, e1) = e0
% 229.26/40.71  | | | 
% 229.26/40.71  | | | ALPHA: (27) implies:
% 229.26/40.71  | | |   (28)  all_57_4 = e0
% 229.26/40.71  | | | 
% 229.26/40.71  | | | COMBINE_EQS: (12), (28) imply:
% 229.26/40.71  | | |   (29)  e1 = e0
% 229.26/40.71  | | | 
% 229.26/40.71  | | | COMBINE_EQS: (15), (29) imply:
% 229.26/40.71  | | |   (30)  all_57_3 = e0
% 229.26/40.71  | | | 
% 229.26/40.71  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (13), (14), (16),
% 229.26/40.71  | | |            (17), (18), (19), (20), (21), (22), (24), (28), (30) are
% 229.26/40.71  | | |            inconsistent by sub-proof #1041.
% 229.26/40.71  | | | 
% 229.26/40.71  | | Case 2:
% 229.26/40.71  | | | 
% 229.26/40.71  | | |   (31)  all_57_9 = e0 & op(e3, e0) = e0
% 229.26/40.71  | | | 
% 229.26/40.71  | | | REF_CLOSE: (1), (14), (31) are inconsistent by sub-proof #1973.
% 229.26/40.71  | | | 
% 229.26/40.71  | | End of split
% 229.26/40.71  | | 
% 229.26/40.71  | End of split
% 229.26/40.71  | 
% 229.26/40.71  End of proof
% 229.26/40.71  
% 229.26/40.71  Sub-proof #737 shows that the following formulas are inconsistent:
% 229.26/40.71  ----------------------------------------------------------------
% 229.26/40.71    (1)   ~ (all_53_2 = e2)
% 229.26/40.71    (2)  all_57_0 = e2
% 229.26/40.71    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.26/40.71         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.26/40.71    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.26/40.71         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.26/40.71    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.26/40.71         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.26/40.71    (6)   ~ (e3 = e1)
% 229.26/40.71    (7)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 229.26/40.71         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 229.26/40.71    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.26/40.71           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.26/40.71    (9)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.26/40.71         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.26/40.71    (10)   ~ (all_53_3 = e3)
% 229.26/40.71    (11)   ~ (all_53_3 = all_53_7)
% 229.26/40.71    (12)   ~ (all_6_2 = e3)
% 229.26/40.71    (13)   ~ (all_53_9 = e1)
% 229.26/40.71    (14)  all_57_10 = e1
% 229.26/40.71    (15)  op(e1, e1) = all_6_2
% 229.26/40.71    (16)   ~ (all_53_1 = all_53_9)
% 229.26/40.71    (17)  op(e2, e2) = e1
% 229.26/40.71    (18)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.26/40.71          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.26/40.71    (19)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 229.26/40.71            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 229.26/40.71              e3) = all_22_1 & $i(all_22_1))
% 229.26/40.71    (20)   ~ (all_53_13 = e3)
% 229.26/40.71    (21)   ~ (all_53_9 = all_53_11)
% 229.26/40.71    (22)  all_55_4 = all_53_1
% 229.26/40.71    (23)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.26/40.71          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.26/40.71    (24)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 229.26/40.71          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.26/40.71    (25)   ~ (e3 = e2)
% 229.26/40.71    (26)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 229.26/40.71    (27)   ~ (all_53_1 = all_53_3)
% 229.26/40.71    (28)   ~ (e3 = e0)
% 229.26/40.72    (29)  all_57_10 = e2 & op(e2, e0) = e2
% 229.26/40.72    (30)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 229.26/40.72    (31)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 229.26/40.72    (32)  all_57_15 = e3
% 229.26/40.72    (33)   ~ (all_53_9 = all_53_13)
% 229.26/40.72    (34)  op(e3, e3) = e2
% 229.26/40.72    (35)  all_57_4 = e1
% 229.26/40.72    (36)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.26/40.72          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.26/40.72            e1)
% 229.26/40.72    (37)   ~ (all_53_1 = e1)
% 229.26/40.72    (38)  all_57_11 = e2
% 229.26/40.72    (39)  all_55_6 = all_53_9
% 229.26/40.72    (40)   ~ (all_53_1 = all_53_2)
% 229.26/40.72    (41)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.26/40.72          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.26/40.72    (42)   ~ (e2 = e0)
% 229.26/40.72    (43)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 229.26/40.72            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 229.26/40.72            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 229.26/40.72            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 229.26/40.72              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 229.26/40.72            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 229.26/40.72            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 229.26/40.72              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 229.26/40.72              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 229.26/40.72            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 229.26/40.72            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 229.26/40.72            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 229.26/40.72              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 229.26/40.72              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 229.26/40.72            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 229.26/40.72              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 229.26/40.72            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 229.26/40.72            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 229.26/40.72              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 229.26/40.72              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 229.26/40.72            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 229.26/40.72            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 229.26/40.72    (44)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 229.26/40.72            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 229.26/40.72              e3) = all_12_1 & $i(all_12_1))
% 229.26/40.72    (45)  all_55_12 = all_53_3
% 229.26/40.72    (46)  all_57_3 = e1
% 229.26/40.72    (47)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.26/40.72          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.26/40.72    (48)   ~ (e1 = e0)
% 229.26/40.72    (49)   ~ (all_53_3 = all_53_11)
% 229.26/40.72    (50)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.26/40.72          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.26/40.72    (51)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.26/40.72          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.26/40.72    (52)   ~ (all_53_2 = all_53_3)
% 229.26/40.72    (53)  all_57_14 = e1
% 229.26/40.72    (54)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 229.26/40.72    (55)   ~ (all_53_7 = all_53_11)
% 229.26/40.72    (56)  all_55_8 = all_53_2
% 229.26/40.72    (57)  op(e0, e0) = e3
% 229.26/40.72    (58)  op(e0, e2) = all_53_7
% 229.26/40.72    (59)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.26/40.72          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.26/40.72            e2)
% 229.26/40.72    (60)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.26/40.72              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.26/40.72                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.26/40.72                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.26/40.72    (61)   ~ (all_53_1 = all_53_13)
% 229.26/40.72    (62)  op(e2, e0) = all_53_13
% 229.26/40.72    (63)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.26/40.72          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.26/40.72    (64)   ~ (all_53_12 = e3)
% 229.26/40.72    (65)  op(e1, e3) = all_53_2
% 229.26/40.72    (66)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.26/40.72          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.26/40.72    (67)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.26/40.72          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.26/40.72    (68)   ~ (e2 = e1)
% 229.26/40.72    (69)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.26/40.72          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.26/40.72    (70)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.26/40.72          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.26/40.72    (71)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 229.26/40.72    (72)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 229.26/40.72          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 229.26/40.72    (73)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.26/40.72          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.26/40.72    (74)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.26/40.72          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.26/40.72    (75)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 229.26/40.72          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 229.26/40.72    (76)  all_55_14 = all_53_11
% 229.26/40.72    (77)   ~ (all_53_11 = e3)
% 229.26/40.72    (78)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.26/40.72          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.26/40.72    (79)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 229.26/40.72          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 229.26/40.72    (80)  op(e3, e0) = all_53_12
% 229.26/40.72  
% 229.26/40.72  Begin of proof
% 229.26/40.72  | 
% 229.26/40.72  | ALPHA: (29) implies:
% 229.26/40.72  |   (81)  all_57_10 = e2
% 229.26/40.72  |   (82)  op(e2, e0) = e2
% 229.26/40.72  | 
% 229.26/40.72  | COMBINE_EQS: (14), (81) imply:
% 229.26/40.72  |   (83)  e2 = e1
% 229.26/40.72  | 
% 229.26/40.72  | SIMP: (83) implies:
% 229.26/40.72  |   (84)  e2 = e1
% 229.26/40.72  | 
% 229.26/40.72  | COMBINE_EQS: (38), (84) imply:
% 229.26/40.72  |   (85)  all_57_11 = e1
% 229.26/40.72  | 
% 229.26/40.72  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 229.26/40.72  |            (13), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 229.26/40.72  |            (25), (26), (27), (28), (30), (31), (32), (33), (34), (35), (36),
% 229.26/40.72  |            (37), (39), (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 229.26/40.72  |            (49), (50), (51), (52), (53), (54), (55), (56), (57), (58), (59),
% 229.26/40.72  |            (60), (61), (62), (63), (64), (65), (66), (67), (68), (69), (70),
% 229.26/40.72  |            (71), (72), (73), (74), (75), (76), (77), (78), (79), (80), (81),
% 229.26/40.72  |            (82), (85) are inconsistent by sub-proof #738.
% 229.26/40.72  | 
% 229.26/40.72  End of proof
% 229.26/40.72  
% 229.26/40.72  Sub-proof #738 shows that the following formulas are inconsistent:
% 229.26/40.72  ----------------------------------------------------------------
% 229.26/40.72    (1)   ~ (all_53_2 = e2)
% 229.26/40.72    (2)  all_57_0 = e2
% 229.26/40.72    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.26/40.72         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.26/40.72    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.26/40.72         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.26/40.72    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.26/40.72         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.26/40.72    (6)   ~ (e3 = e1)
% 229.26/40.72    (7)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 229.26/40.72         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 229.26/40.72    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.26/40.72           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.26/40.72    (9)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.26/40.72         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.26/40.72    (10)   ~ (all_53_3 = e3)
% 229.26/40.72    (11)   ~ (all_53_3 = all_53_7)
% 229.26/40.72    (12)   ~ (all_6_2 = e3)
% 229.26/40.72    (13)   ~ (all_53_9 = e1)
% 229.26/40.72    (14)  op(e1, e1) = all_6_2
% 229.26/40.72    (15)   ~ (all_53_1 = all_53_9)
% 229.26/40.72    (16)  op(e2, e2) = e1
% 229.26/40.72    (17)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.26/40.72          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.26/40.72    (18)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 229.26/40.72            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 229.26/40.72              e3) = all_22_1 & $i(all_22_1))
% 229.26/40.72    (19)   ~ (all_53_13 = e3)
% 229.26/40.72    (20)   ~ (all_53_9 = all_53_11)
% 229.26/40.72    (21)  all_55_4 = all_53_1
% 229.26/40.72    (22)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.26/40.72          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.26/40.72    (23)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 229.26/40.72          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.26/40.72    (24)   ~ (e3 = e2)
% 229.26/40.72    (25)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 229.26/40.72    (26)   ~ (all_53_1 = all_53_3)
% 229.26/40.72    (27)   ~ (e3 = e0)
% 229.26/40.72    (28)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 229.26/40.72    (29)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 229.26/40.72    (30)  all_57_15 = e3
% 229.26/40.72    (31)   ~ (all_53_9 = all_53_13)
% 229.26/40.72    (32)  op(e3, e3) = e2
% 229.26/40.72    (33)  all_57_4 = e1
% 229.26/40.72    (34)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.26/40.72          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.26/40.72            e1)
% 229.26/40.72    (35)  all_57_10 = e2
% 229.26/40.72    (36)   ~ (all_53_1 = e1)
% 229.26/40.72    (37)  op(e2, e0) = e2
% 229.26/40.72    (38)  all_55_6 = all_53_9
% 229.26/40.72    (39)   ~ (all_53_1 = all_53_2)
% 229.26/40.72    (40)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.26/40.72          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.26/40.72    (41)   ~ (e2 = e0)
% 229.26/40.72    (42)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 229.26/40.72            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 229.26/40.72            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 229.26/40.72            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 229.26/40.72              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 229.26/40.72            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 229.26/40.72            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 229.26/40.72              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 229.26/40.72              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 229.26/40.72            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 229.26/40.72            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 229.26/40.72            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 229.26/40.72              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 229.26/40.72              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 229.26/40.72            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 229.26/40.72              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 229.26/40.72            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 229.26/40.72            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 229.26/40.72              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 229.26/40.72              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 229.26/40.72            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 229.26/40.72            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 229.26/40.72    (43)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 229.26/40.72            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 229.26/40.72              e3) = all_12_1 & $i(all_12_1))
% 229.26/40.72    (44)  all_55_12 = all_53_3
% 229.26/40.72    (45)  all_57_3 = e1
% 229.26/40.72    (46)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.26/40.72          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.26/40.72    (47)   ~ (e1 = e0)
% 229.26/40.72    (48)   ~ (all_53_3 = all_53_11)
% 229.26/40.72    (49)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.26/40.72          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.26/40.72    (50)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.26/40.72          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.26/40.72    (51)   ~ (all_53_2 = all_53_3)
% 229.26/40.72    (52)  all_57_14 = e1
% 229.26/40.72    (53)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 229.26/40.72    (54)   ~ (all_53_7 = all_53_11)
% 229.26/40.72    (55)  all_55_8 = all_53_2
% 229.26/40.72    (56)  op(e0, e0) = e3
% 229.26/40.72    (57)  op(e0, e2) = all_53_7
% 229.26/40.72    (58)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.26/40.72          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.26/40.72            e2)
% 229.26/40.72    (59)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.26/40.72              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.26/40.72                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.26/40.72                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.26/40.72    (60)   ~ (all_53_1 = all_53_13)
% 229.26/40.72    (61)  op(e2, e0) = all_53_13
% 229.26/40.72    (62)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.26/40.72          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.26/40.72    (63)   ~ (all_53_12 = e3)
% 229.26/40.72    (64)  op(e1, e3) = all_53_2
% 229.26/40.72    (65)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.26/40.72          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.26/40.72    (66)  all_57_11 = e1
% 229.26/40.72    (67)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.26/40.72          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.26/40.72    (68)   ~ (e2 = e1)
% 229.26/40.72    (69)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.26/40.72          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.26/40.72    (70)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.26/40.72          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.26/40.72    (71)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 229.26/40.72    (72)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 229.26/40.72          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 229.26/40.72    (73)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.26/40.72          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.26/40.72    (74)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.26/40.72          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.26/40.72    (75)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 229.26/40.72          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 229.26/40.72    (76)  all_55_14 = all_53_11
% 229.26/40.72    (77)   ~ (all_53_11 = e3)
% 229.26/40.72    (78)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.26/40.72          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.26/40.72    (79)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 229.26/40.72          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 229.26/40.72    (80)  op(e3, e0) = all_53_12
% 229.26/40.72  
% 229.26/40.72  Begin of proof
% 229.26/40.72  | 
% 229.26/40.72  | BETA: splitting (46) gives:
% 229.26/40.72  | 
% 229.26/40.72  | Case 1:
% 229.26/40.72  | | 
% 229.26/40.72  | |   (81)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) =
% 229.26/40.72  | |           e3)
% 229.26/40.72  | | 
% 229.26/40.72  | | BETA: splitting (81) gives:
% 229.26/40.72  | | 
% 229.26/40.72  | | Case 1:
% 229.26/40.72  | | | 
% 229.26/40.72  | | |   (82)  all_57_0 = e3 & op(e3, e3) = e3
% 229.26/40.72  | | | 
% 229.26/40.72  | | | ALPHA: (82) implies:
% 229.26/40.72  | | |   (83)  op(e3, e3) = e3
% 229.26/40.72  | | | 
% 229.26/40.72  | | | REF_CLOSE: (8), (24), (32), (83) are inconsistent by sub-proof #2490.
% 229.26/40.72  | | | 
% 229.26/40.72  | | Case 2:
% 229.26/40.72  | | | 
% 229.26/40.72  | | |   (84)  all_57_1 = e3 & op(e3, e2) = e3
% 229.26/40.72  | | | 
% 229.26/40.72  | | | ALPHA: (84) implies:
% 229.26/40.72  | | |   (85)  all_57_1 = e3
% 229.26/40.72  | | | 
% 229.26/40.72  | | | BETA: splitting (58) gives:
% 229.26/40.72  | | | 
% 229.26/40.72  | | | Case 1:
% 229.26/40.72  | | | | 
% 229.26/40.72  | | | |   (86)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0,
% 229.26/40.72  | | | |             e2) = e2)
% 229.26/40.72  | | | | 
% 229.26/40.72  | | | | BETA: splitting (86) gives:
% 229.26/40.72  | | | | 
% 229.26/40.72  | | | | Case 1:
% 229.26/40.72  | | | | | 
% 229.26/40.72  | | | | |   (87)  all_57_12 = e2 & op(e0, e3) = e2
% 229.26/40.72  | | | | | 
% 229.26/40.72  | | | | | ALPHA: (87) implies:
% 229.26/40.72  | | | | |   (88)  all_57_12 = e2
% 229.26/40.72  | | | | | 
% 229.26/40.72  | | | | | BETA: splitting (4) gives:
% 229.26/40.72  | | | | | 
% 229.26/40.72  | | | | | Case 1:
% 229.26/40.72  | | | | | | 
% 229.26/40.72  | | | | | |   (89)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2,
% 229.26/40.72  | | | | | |             e3) = e1)
% 229.26/40.72  | | | | | | 
% 229.26/40.72  | | | | | | REF_CLOSE: (2), (3), (4), (6), (8), (24), (27), (32), (41), (45),
% 229.26/40.72  | | | | | |            (47), (62), (65), (67), (68), (70), (73), (88), (89) are
% 229.26/40.72  | | | | | |            inconsistent by sub-proof #762.
% 229.26/40.72  | | | | | | 
% 229.26/40.72  | | | | | Case 2:
% 229.26/40.72  | | | | | | 
% 229.26/40.72  | | | | | |   (90)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0,
% 229.26/40.72  | | | | | |             e3) = e1)
% 229.26/40.72  | | | | | | 
% 229.26/40.72  | | | | | | BETA: splitting (90) gives:
% 229.26/40.72  | | | | | | 
% 229.26/40.72  | | | | | | Case 1:
% 229.26/40.72  | | | | | | | 
% 229.26/40.72  | | | | | | |   (91)  all_57_6 = e1 & op(e1, e3) = e1
% 229.26/40.72  | | | | | | | 
% 229.26/40.72  | | | | | | | ALPHA: (91) implies:
% 229.26/40.72  | | | | | | |   (92)  all_57_6 = e1
% 229.26/40.72  | | | | | | | 
% 229.26/40.72  | | | | | | | BETA: splitting (79) gives:
% 229.26/40.72  | | | | | | | 
% 229.26/40.72  | | | | | | | Case 1:
% 229.26/40.72  | | | | | | | | 
% 229.26/40.72  | | | | | | | |   (93)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 &
% 229.26/40.72  | | | | | | | |           op(e1, e2) = e2)
% 229.26/40.72  | | | | | | | | 
% 229.26/40.72  | | | | | | | | BETA: splitting (93) gives:
% 229.26/40.72  | | | | | | | | 
% 229.26/40.72  | | | | | | | | Case 1:
% 229.26/40.72  | | | | | | | | | 
% 229.26/40.72  | | | | | | | | |   (94)  all_57_6 = e2 & op(e1, e3) = e2
% 229.26/40.72  | | | | | | | | | 
% 229.26/40.72  | | | | | | | | | ALPHA: (94) implies:
% 229.26/40.72  | | | | | | | | |   (95)  all_57_6 = e2
% 229.26/40.72  | | | | | | | | | 
% 229.26/40.72  | | | | | | | | | COMBINE_EQS: (92), (95) imply:
% 229.26/40.72  | | | | | | | | |   (96)  e2 = e1
% 229.26/40.72  | | | | | | | | | 
% 229.26/40.72  | | | | | | | | | COMBINE_EQS: (88), (96) imply:
% 229.26/40.72  | | | | | | | | |   (97)  all_57_12 = e1
% 229.26/40.72  | | | | | | | | | 
% 229.26/40.72  | | | | | | | | | REF_CLOSE: (6), (8), (9), (12), (14), (24), (27), (30), (32),
% 229.26/40.72  | | | | | | | | |            (41), (47), (56), (59), (67), (68), (69), (70),
% 229.26/40.72  | | | | | | | | |            (73), (74), (92), (97) are inconsistent by
% 229.26/40.72  | | | | | | | | |            sub-proof #759.
% 229.26/40.72  | | | | | | | | | 
% 229.26/40.72  | | | | | | | | Case 2:
% 229.26/40.72  | | | | | | | | | 
% 229.26/40.72  | | | | | | | | |   (98)  all_57_7 = e2 & op(e1, e2) = e2
% 229.26/40.72  | | | | | | | | | 
% 229.26/40.72  | | | | | | | | | ALPHA: (98) implies:
% 229.26/40.72  | | | | | | | | |   (99)  all_57_7 = e2
% 229.26/40.72  | | | | | | | | | 
% 229.26/40.72  | | | | | | | | | REF_CLOSE: (5), (6), (8), (9), (12), (14), (16), (24), (27),
% 229.26/40.72  | | | | | | | | |            (30), (32), (33), (40), (41), (46), (47), (50),
% 229.26/40.72  | | | | | | | | |            (59), (63), (67), (68), (69), (73), (74), (78),
% 229.26/40.72  | | | | | | | | |            (80), (85), (88), (92), (99) are inconsistent by
% 229.26/40.72  | | | | | | | | |            sub-proof #756.
% 229.26/40.72  | | | | | | | | | 
% 229.26/40.72  | | | | | | | | End of split
% 229.26/40.72  | | | | | | | | 
% 229.26/40.72  | | | | | | | Case 2:
% 229.26/40.72  | | | | | | | | 
% 229.26/40.72  | | | | | | | |   (100)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 &
% 229.26/40.72  | | | | | | | |            op(e1, e0) = e2)
% 229.26/40.72  | | | | | | | | 
% 229.26/40.72  | | | | | | | | BETA: splitting (100) gives:
% 229.26/40.72  | | | | | | | | 
% 229.26/40.72  | | | | | | | | Case 1:
% 229.26/40.72  | | | | | | | | | 
% 229.26/40.72  | | | | | | | | |   (101)  all_57_8 = e2 & op(e1, e1) = e2
% 229.26/40.72  | | | | | | | | | 
% 229.26/40.72  | | | | | | | | | ALPHA: (101) implies:
% 229.26/40.72  | | | | | | | | |   (102)  op(e1, e1) = e2
% 229.26/40.72  | | | | | | | | | 
% 229.26/40.72  | | | | | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (12), (14),
% 229.26/40.72  | | | | | | | | |            (16), (17), (18), (22), (23), (24), (27), (30),
% 229.26/40.72  | | | | | | | | |            (32), (34), (35), (40), (41), (43), (45), (46),
% 229.26/40.72  | | | | | | | | |            (47), (49), (52), (56), (58), (59), (62), (63),
% 229.26/40.72  | | | | | | | | |            (65), (67), (68), (69), (72), (73), (74), (75),
% 229.26/40.72  | | | | | | | | |            (78), (79), (80), (88), (92), (102) are
% 229.26/40.72  | | | | | | | | |            inconsistent by sub-proof #739.
% 229.26/40.72  | | | | | | | | | 
% 229.26/40.72  | | | | | | | | Case 2:
% 229.26/40.72  | | | | | | | | | 
% 229.26/40.72  | | | | | | | | |   (103)  all_57_11 = e2 & op(e1, e0) = e2
% 229.26/40.72  | | | | | | | | | 
% 229.26/40.72  | | | | | | | | | ALPHA: (103) implies:
% 229.26/40.72  | | | | | | | | |   (104)  all_57_11 = e2
% 229.26/40.72  | | | | | | | | | 
% 229.26/40.72  | | | | | | | | | COMBINE_EQS: (66), (104) imply:
% 229.26/40.72  | | | | | | | | |   (105)  e2 = e1
% 229.26/40.72  | | | | | | | | | 
% 229.26/40.72  | | | | | | | | | COMBINE_EQS: (88), (105) imply:
% 229.26/40.72  | | | | | | | | |   (106)  all_57_12 = e1
% 229.26/40.72  | | | | | | | | | 
% 229.26/40.72  | | | | | | | | | REF_CLOSE: (6), (8), (9), (12), (14), (24), (27), (30), (32),
% 229.26/40.72  | | | | | | | | |            (41), (47), (56), (59), (67), (68), (69), (70),
% 229.26/40.72  | | | | | | | | |            (73), (74), (92), (106) are inconsistent by
% 229.26/40.72  | | | | | | | | |            sub-proof #759.
% 229.26/40.72  | | | | | | | | | 
% 229.26/40.72  | | | | | | | | End of split
% 229.26/40.72  | | | | | | | | 
% 229.26/40.72  | | | | | | | End of split
% 229.26/40.72  | | | | | | | 
% 229.26/40.72  | | | | | | Case 2:
% 229.26/40.72  | | | | | | | 
% 229.26/40.72  | | | | | | |   (107)  all_57_12 = e1 & op(e0, e3) = e1
% 229.26/40.72  | | | | | | | 
% 229.26/40.72  | | | | | | | ALPHA: (107) implies:
% 229.26/40.72  | | | | | | |   (108)  all_57_12 = e1
% 229.26/40.72  | | | | | | | 
% 229.26/40.72  | | | | | | | REF_CLOSE: (68), (88), (108) are inconsistent by sub-proof #2321.
% 229.26/40.72  | | | | | | | 
% 229.26/40.72  | | | | | | End of split
% 229.26/40.72  | | | | | | 
% 229.26/40.72  | | | | | End of split
% 229.26/40.72  | | | | | 
% 229.26/40.72  | | | | Case 2:
% 229.26/40.72  | | | | | 
% 229.26/40.72  | | | | |   (109)  all_57_13 = e2 & op(e0, e2) = e2
% 229.26/40.72  | | | | | 
% 229.26/40.72  | | | | | REF_CLOSE: (1), (6), (8), (10), (11), (12), (13), (14), (15), (16),
% 229.26/40.72  | | | | |            (19), (20), (21), (25), (26), (28), (29), (31), (32), (36),
% 229.26/40.72  | | | | |            (37), (38), (39), (41), (42), (44), (48), (51), (53), (54),
% 229.26/40.72  | | | | |            (55), (56), (57), (60), (61), (64), (71), (76), (77), (109)
% 229.26/40.72  | | | | |            are inconsistent by sub-proof #771.
% 229.26/40.72  | | | | | 
% 229.26/40.72  | | | | End of split
% 229.26/40.72  | | | | 
% 229.26/40.72  | | | Case 2:
% 229.26/40.72  | | | | 
% 229.26/40.72  | | | |   (110)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0,
% 229.26/40.72  | | | |              e0) = e2)
% 229.26/40.72  | | | | 
% 229.26/40.72  | | | | BETA: splitting (110) gives:
% 229.26/40.72  | | | | 
% 229.26/40.72  | | | | Case 1:
% 229.26/40.72  | | | | | 
% 229.26/40.72  | | | | |   (111)  all_57_14 = e2 & op(e0, e1) = e2
% 229.26/40.72  | | | | | 
% 229.26/40.72  | | | | | REF_CLOSE: (52), (68), (111) are inconsistent by sub-proof #1968.
% 229.26/40.72  | | | | | 
% 229.26/40.72  | | | | Case 2:
% 229.26/40.72  | | | | | 
% 229.26/40.72  | | | | |   (112)  all_57_15 = e2 & op(e0, e0) = e2
% 229.26/40.72  | | | | | 
% 229.26/40.72  | | | | | REF_CLOSE: (6), (8), (24), (30), (32), (33), (46), (63), (80), (85),
% 229.26/40.72  | | | | |            (112) are inconsistent by sub-proof #768.
% 229.26/40.72  | | | | | 
% 229.26/40.72  | | | | End of split
% 229.26/40.72  | | | | 
% 229.26/40.72  | | | End of split
% 229.26/40.72  | | | 
% 229.26/40.72  | | End of split
% 229.26/40.72  | | 
% 229.26/40.72  | Case 2:
% 229.26/40.72  | | 
% 229.26/40.72  | |   (113)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) =
% 229.26/40.72  | |            e3)
% 229.26/40.72  | | 
% 229.26/40.72  | | REF_CLOSE: (6), (8), (33), (63), (80), (113) are inconsistent by sub-proof
% 229.26/40.72  | |            #2281.
% 229.26/40.72  | | 
% 229.26/40.72  | End of split
% 229.26/40.72  | 
% 229.26/40.72  End of proof
% 229.26/40.72  
% 229.26/40.72  Sub-proof #739 shows that the following formulas are inconsistent:
% 229.26/40.72  ----------------------------------------------------------------
% 229.26/40.72    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.26/40.72         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.26/40.72    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.26/40.72         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.26/40.72    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.26/40.72         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.26/40.72    (4)   ~ (e3 = e1)
% 229.26/40.72    (5)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 229.26/40.72         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 229.26/40.72    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.26/40.72           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.26/40.72    (7)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.26/40.72         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.26/40.72    (8)   ~ (all_6_2 = e3)
% 229.26/40.72    (9)  op(e1, e1) = all_6_2
% 229.26/40.72    (10)  op(e2, e2) = e1
% 229.26/40.72    (11)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.26/40.72          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.26/40.72    (12)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 229.26/40.72            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 229.26/40.72              e3) = all_22_1 & $i(all_22_1))
% 229.26/40.72    (13)  all_57_12 = e2
% 229.26/40.72    (14)  all_57_6 = e1
% 229.26/40.72    (15)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.26/40.72          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.26/40.72    (16)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 229.26/40.72          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.26/40.72    (17)   ~ (e3 = e2)
% 229.26/40.72    (18)   ~ (e3 = e0)
% 229.26/40.72    (19)  all_57_15 = e3
% 229.26/40.72    (20)  op(e3, e3) = e2
% 229.26/40.72    (21)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.26/40.72          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.26/40.72            e1)
% 229.26/40.72    (22)  all_57_10 = e2
% 229.26/40.72    (23)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.26/40.72          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.26/40.73    (24)   ~ (e2 = e0)
% 229.26/40.73    (25)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 229.26/40.73            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 229.26/40.73              e3) = all_12_1 & $i(all_12_1))
% 229.26/40.73    (26)  all_57_3 = e1
% 229.26/40.73    (27)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.26/40.73          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.26/40.73    (28)   ~ (e1 = e0)
% 229.26/40.73    (29)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.26/40.73          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.26/40.73    (30)  all_57_14 = e1
% 229.26/40.73    (31)  op(e0, e0) = e3
% 229.26/40.73    (32)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.26/40.73          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.26/40.73            e2)
% 229.26/40.73    (33)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.26/40.73              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.26/40.73                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.26/40.73                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.26/40.73    (34)  op(e1, e1) = e2
% 229.26/40.73    (35)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.26/40.73          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.26/40.73    (36)   ~ (all_53_12 = e3)
% 229.26/40.73    (37)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.26/40.73          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.26/40.73    (38)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.26/40.73          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.26/40.73    (39)   ~ (e2 = e1)
% 229.26/40.73    (40)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.26/40.73          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.26/40.73    (41)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 229.26/40.73          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 229.26/40.73    (42)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.26/40.73          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.26/40.73    (43)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.26/40.73          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.26/40.73    (44)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 229.26/40.73          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 229.26/40.73    (45)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.26/40.73          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.26/40.73    (46)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 229.26/40.73          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 229.26/40.73    (47)  op(e3, e0) = all_53_12
% 229.26/40.73  
% 229.26/40.73  Begin of proof
% 229.26/40.73  | 
% 229.26/40.73  | BETA: splitting (7) gives:
% 229.26/40.73  | 
% 229.26/40.73  | Case 1:
% 229.26/40.73  | | 
% 229.26/40.73  | |   (48)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 229.26/40.73  | |           e3)
% 229.26/40.73  | | 
% 229.26/40.73  | | BETA: splitting (48) gives:
% 229.26/40.73  | | 
% 229.26/40.73  | | Case 1:
% 229.26/40.73  | | | 
% 229.26/40.73  | | |   (49)  all_57_6 = e3 & op(e1, e3) = e3
% 229.26/40.73  | | | 
% 229.26/40.73  | | | ALPHA: (49) implies:
% 229.26/40.73  | | |   (50)  all_57_6 = e3
% 229.26/40.73  | | | 
% 229.26/40.73  | | | REF_CLOSE: (4), (14), (50) are inconsistent by sub-proof #2017.
% 229.26/40.73  | | | 
% 229.26/40.73  | | Case 2:
% 229.26/40.73  | | | 
% 229.26/40.73  | | |   (51)  all_57_7 = e3 & op(e1, e2) = e3
% 229.26/40.73  | | | 
% 229.26/40.73  | | | ALPHA: (51) implies:
% 229.26/40.73  | | |   (52)  all_57_7 = e3
% 229.26/40.73  | | | 
% 229.26/40.73  | | | BETA: splitting (3) gives:
% 229.26/40.73  | | | 
% 229.26/40.73  | | | Case 1:
% 229.26/40.73  | | | | 
% 229.26/40.73  | | | |   (53)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2)
% 229.26/40.73  | | | |           = e2)
% 229.26/40.73  | | | | 
% 229.26/40.73  | | | | BETA: splitting (53) gives:
% 229.26/40.73  | | | | 
% 229.26/40.73  | | | | Case 1:
% 229.26/40.73  | | | | | 
% 229.26/40.73  | | | | |   (54)  all_57_1 = e2 & op(e3, e2) = e2
% 229.26/40.73  | | | | | 
% 229.26/40.73  | | | | | ALPHA: (54) implies:
% 229.26/40.73  | | | | |   (55)  all_57_1 = e2
% 229.26/40.73  | | | | | 
% 229.26/40.73  | | | | | BETA: splitting (27) gives:
% 229.26/40.73  | | | | | 
% 229.26/40.73  | | | | | Case 1:
% 229.26/40.73  | | | | | | 
% 229.26/40.73  | | | | | |   (56)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3,
% 229.26/40.73  | | | | | |             e2) = e3)
% 229.26/40.73  | | | | | | 
% 229.26/40.73  | | | | | | REF_CLOSE: (6), (17), (20), (55), (56) are inconsistent by sub-proof
% 229.26/40.73  | | | | | |            #1663.
% 229.26/40.73  | | | | | | 
% 229.26/40.73  | | | | | Case 2:
% 229.26/40.73  | | | | | | 
% 229.26/40.73  | | | | | |   (57)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3,
% 229.26/40.73  | | | | | |             e0) = e3)
% 229.26/40.73  | | | | | | 
% 229.26/40.73  | | | | | | BETA: splitting (57) gives:
% 229.26/40.73  | | | | | | 
% 229.26/40.73  | | | | | | Case 1:
% 229.26/40.73  | | | | | | | 
% 229.26/40.73  | | | | | | |   (58)  all_57_4 = e3 & op(e3, e1) = e3
% 229.26/40.73  | | | | | | | 
% 229.26/40.73  | | | | | | | ALPHA: (58) implies:
% 229.26/40.73  | | | | | | |   (59)  all_57_4 = e3
% 229.26/40.73  | | | | | | | 
% 229.26/40.73  | | | | | | | BETA: splitting (15) gives:
% 229.26/40.73  | | | | | | | 
% 229.26/40.73  | | | | | | | Case 1:
% 229.26/40.73  | | | | | | | | 
% 229.26/40.73  | | | | | | | |   (60)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 &
% 229.26/40.73  | | | | | | | |           op(e3, e2) = e0)
% 229.26/40.73  | | | | | | | | 
% 229.26/40.73  | | | | | | | | REF_CLOSE: (6), (20), (24), (55), (60) are inconsistent by
% 229.26/40.73  | | | | | | | |            sub-proof #1665.
% 229.26/40.73  | | | | | | | | 
% 229.26/40.73  | | | | | | | Case 2:
% 229.26/40.73  | | | | | | | | 
% 229.26/40.73  | | | | | | | |   (61)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 &
% 229.26/40.73  | | | | | | | |           op(e3, e0) = e0)
% 229.26/40.73  | | | | | | | | 
% 229.26/40.73  | | | | | | | | BETA: splitting (61) gives:
% 229.26/40.73  | | | | | | | | 
% 229.26/40.73  | | | | | | | | Case 1:
% 229.26/40.73  | | | | | | | | | 
% 229.26/40.73  | | | | | | | | |   (62)  all_57_4 = e0 & op(e3, e1) = e0
% 229.26/40.73  | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | ALPHA: (62) implies:
% 229.26/40.73  | | | | | | | | |   (63)  all_57_4 = e0
% 229.26/40.73  | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | COMBINE_EQS: (59), (63) imply:
% 229.26/40.73  | | | | | | | | |   (64)  e3 = e0
% 229.26/40.73  | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | COMBINE_EQS: (52), (64) imply:
% 229.26/40.73  | | | | | | | | |   (65)  all_57_7 = e0
% 229.26/40.73  | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (14), (17), (18), (19),
% 229.26/40.73  | | | | | | | | |            (24), (28), (33), (39), (40), (43), (65) are
% 229.26/40.73  | | | | | | | | |            inconsistent by sub-proof #1735.
% 229.26/40.73  | | | | | | | | | 
% 229.26/40.73  | | | | | | | | Case 2:
% 229.26/40.73  | | | | | | | | | 
% 229.26/40.73  | | | | | | | | |   (66)  all_57_9 = e0 & op(e3, e0) = e0
% 229.26/40.73  | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | ALPHA: (66) implies:
% 229.26/40.73  | | | | | | | | |   (67)  all_57_9 = e0
% 229.26/40.73  | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | REF_CLOSE: (4), (6), (11), (20), (28), (39), (55), (59), (67)
% 229.26/40.73  | | | | | | | | |            are inconsistent by sub-proof #1661.
% 229.26/40.73  | | | | | | | | | 
% 229.26/40.73  | | | | | | | | End of split
% 229.26/40.73  | | | | | | | | 
% 229.26/40.73  | | | | | | | End of split
% 229.26/40.73  | | | | | | | 
% 229.26/40.73  | | | | | | Case 2:
% 229.26/40.73  | | | | | | | 
% 229.26/40.73  | | | | | | |   (68)  all_57_9 = e3 & op(e3, e0) = e3
% 229.26/40.73  | | | | | | | 
% 229.26/40.73  | | | | | | | ALPHA: (68) implies:
% 229.26/40.73  | | | | | | |   (69)  op(e3, e0) = e3
% 229.26/40.73  | | | | | | | 
% 229.26/40.73  | | | | | | | REF_CLOSE: (6), (36), (47), (69) are inconsistent by sub-proof
% 229.26/40.73  | | | | | | |            #2458.
% 229.26/40.73  | | | | | | | 
% 229.26/40.73  | | | | | | End of split
% 229.26/40.73  | | | | | | 
% 229.26/40.73  | | | | | End of split
% 229.26/40.73  | | | | | 
% 229.26/40.73  | | | | Case 2:
% 229.26/40.73  | | | | | 
% 229.26/40.73  | | | | |   (70)  all_57_3 = e2 & op(e2, e2) = e2
% 229.26/40.73  | | | | | 
% 229.26/40.73  | | | | | ALPHA: (70) implies:
% 229.26/40.73  | | | | |   (71)  op(e2, e2) = e2
% 229.26/40.73  | | | | | 
% 229.26/40.73  | | | | | REF_CLOSE: (6), (10), (39), (71) are inconsistent by sub-proof #2306.
% 229.26/40.73  | | | | | 
% 229.26/40.73  | | | | End of split
% 229.26/40.73  | | | | 
% 229.26/40.73  | | | Case 2:
% 229.26/40.73  | | | | 
% 229.26/40.73  | | | |   (72)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2)
% 229.26/40.73  | | | |           = e2)
% 229.26/40.73  | | | | 
% 229.26/40.73  | | | | BETA: splitting (72) gives:
% 229.26/40.73  | | | | 
% 229.26/40.73  | | | | Case 1:
% 229.26/40.73  | | | | | 
% 229.26/40.73  | | | | |   (73)  all_57_7 = e2 & op(e1, e2) = e2
% 229.26/40.73  | | | | | 
% 229.26/40.73  | | | | | REF_CLOSE: (17), (52), (73) are inconsistent by sub-proof #2092.
% 229.26/40.73  | | | | | 
% 229.26/40.73  | | | | Case 2:
% 229.26/40.73  | | | | | 
% 229.26/40.73  | | | | |   (74)  all_57_13 = e2 & op(e0, e2) = e2
% 229.26/40.73  | | | | | 
% 229.26/40.73  | | | | | ALPHA: (74) implies:
% 229.26/40.73  | | | | |   (75)  all_57_13 = e2
% 229.26/40.73  | | | | | 
% 229.26/40.73  | | | | | BETA: splitting (5) gives:
% 229.26/40.73  | | | | | 
% 229.26/40.73  | | | | | Case 1:
% 229.26/40.73  | | | | | | 
% 229.26/40.73  | | | | | |   (76)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1,
% 229.26/40.73  | | | | | |             e2) = e0)
% 229.26/40.73  | | | | | | 
% 229.26/40.73  | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (14), (17), (18), (19), (24),
% 229.26/40.73  | | | | | |            (28), (33), (39), (40), (43), (76) are inconsistent by
% 229.26/40.73  | | | | | |            sub-proof #755.
% 229.26/40.73  | | | | | | 
% 229.26/40.73  | | | | | Case 2:
% 229.26/40.73  | | | | | | 
% 229.26/40.73  | | | | | |   (77)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1,
% 229.26/40.73  | | | | | |             e0) = e0)
% 229.26/40.73  | | | | | | 
% 229.26/40.73  | | | | | | BETA: splitting (77) gives:
% 229.26/40.73  | | | | | | 
% 229.26/40.73  | | | | | | Case 1:
% 229.26/40.73  | | | | | | | 
% 229.26/40.73  | | | | | | |   (78)  all_57_8 = e0 & op(e1, e1) = e0
% 229.26/40.73  | | | | | | | 
% 229.26/40.73  | | | | | | | ALPHA: (78) implies:
% 229.26/40.73  | | | | | | |   (79)  all_57_8 = e0
% 229.26/40.73  | | | | | | | 
% 229.26/40.73  | | | | | | | BETA: splitting (46) gives:
% 229.26/40.73  | | | | | | | 
% 229.26/40.73  | | | | | | | Case 1:
% 229.26/40.73  | | | | | | | | 
% 229.26/40.73  | | | | | | | |   (80)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 &
% 229.26/40.73  | | | | | | | |           op(e1, e2) = e2)
% 229.26/40.73  | | | | | | | | 
% 229.26/40.73  | | | | | | | | REF_CLOSE: (3), (4), (6), (7), (8), (9), (10), (11), (14), (15),
% 229.26/40.73  | | | | | | | |            (17), (18), (19), (20), (23), (24), (26), (27), (28),
% 229.26/40.73  | | | | | | | |            (33), (36), (39), (40), (43), (45), (47), (52), (75),
% 229.26/40.73  | | | | | | | |            (80) are inconsistent by sub-proof #754.
% 229.26/40.73  | | | | | | | | 
% 229.26/40.73  | | | | | | | Case 2:
% 229.26/40.73  | | | | | | | | 
% 229.26/40.73  | | | | | | | |   (81)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 &
% 229.26/40.73  | | | | | | | |           op(e1, e0) = e2)
% 229.26/40.73  | | | | | | | | 
% 229.26/40.73  | | | | | | | | BETA: splitting (81) gives:
% 229.26/40.73  | | | | | | | | 
% 229.26/40.73  | | | | | | | | Case 1:
% 229.26/40.73  | | | | | | | | | 
% 229.26/40.73  | | | | | | | | |   (82)  all_57_8 = e2 & op(e1, e1) = e2
% 229.26/40.73  | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | ALPHA: (82) implies:
% 229.26/40.73  | | | | | | | | |   (83)  all_57_8 = e2
% 229.26/40.73  | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | REF_CLOSE: (24), (79), (83) are inconsistent by sub-proof
% 229.26/40.73  | | | | | | | | |            #1957.
% 229.26/40.73  | | | | | | | | | 
% 229.26/40.73  | | | | | | | | Case 2:
% 229.26/40.73  | | | | | | | | | 
% 229.26/40.73  | | | | | | | | |   (84)  all_57_11 = e2 & op(e1, e0) = e2
% 229.26/40.73  | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | ALPHA: (84) implies:
% 229.26/40.73  | | | | | | | | |   (85)  all_57_11 = e2
% 229.26/40.73  | | | | | | | | |   (86)  op(e1, e0) = e2
% 229.26/40.73  | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11),
% 229.26/40.73  | | | | | | | | |            (12), (13), (14), (15), (16), (17), (18), (19),
% 229.26/40.73  | | | | | | | | |            (20), (21), (22), (23), (24), (25), (26), (27),
% 229.26/40.73  | | | | | | | | |            (28), (29), (30), (31), (32), (33), (34), (35),
% 229.26/40.73  | | | | | | | | |            (36), (37), (38), (39), (40), (41), (42), (43),
% 229.26/40.73  | | | | | | | | |            (44), (45), (46), (47), (52), (75), (85), (86) are
% 229.26/40.73  | | | | | | | | |            inconsistent by sub-proof #740.
% 229.26/40.73  | | | | | | | | | 
% 229.26/40.73  | | | | | | | | End of split
% 229.26/40.73  | | | | | | | | 
% 229.26/40.73  | | | | | | | End of split
% 229.26/40.73  | | | | | | | 
% 229.26/40.73  | | | | | | Case 2:
% 229.26/40.73  | | | | | | | 
% 229.26/40.73  | | | | | | |   (87)  all_57_11 = e0 & op(e1, e0) = e0
% 229.26/40.73  | | | | | | | 
% 229.26/40.73  | | | | | | | ALPHA: (87) implies:
% 229.26/40.73  | | | | | | |   (88)  all_57_11 = e0
% 229.26/40.73  | | | | | | | 
% 229.26/40.73  | | | | | | | BETA: splitting (46) gives:
% 229.26/40.73  | | | | | | | 
% 229.26/40.73  | | | | | | | Case 1:
% 229.26/40.73  | | | | | | | | 
% 229.26/40.73  | | | | | | | |   (89)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 &
% 229.26/40.73  | | | | | | | |           op(e1, e2) = e2)
% 229.26/40.73  | | | | | | | | 
% 229.26/40.73  | | | | | | | | REF_CLOSE: (3), (4), (6), (7), (8), (9), (10), (11), (14), (15),
% 229.26/40.73  | | | | | | | |            (17), (18), (19), (20), (23), (24), (26), (27), (28),
% 229.26/40.73  | | | | | | | |            (33), (36), (39), (40), (43), (45), (47), (52), (75),
% 229.26/40.73  | | | | | | | |            (89) are inconsistent by sub-proof #754.
% 229.26/40.73  | | | | | | | | 
% 229.26/40.73  | | | | | | | Case 2:
% 229.26/40.73  | | | | | | | | 
% 229.26/40.73  | | | | | | | |   (90)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 &
% 229.26/40.73  | | | | | | | |           op(e1, e0) = e2)
% 229.26/40.73  | | | | | | | | 
% 229.26/40.73  | | | | | | | | BETA: splitting (90) gives:
% 229.26/40.73  | | | | | | | | 
% 229.26/40.73  | | | | | | | | Case 1:
% 229.26/40.73  | | | | | | | | | 
% 229.26/40.73  | | | | | | | | |   (91)  all_57_8 = e2 & op(e1, e1) = e2
% 229.26/40.73  | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | ALPHA: (91) implies:
% 229.26/40.73  | | | | | | | | |   (92)  all_57_8 = e2
% 229.26/40.73  | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | BETA: splitting (43) gives:
% 229.26/40.73  | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | Case 1:
% 229.26/40.73  | | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | |   (93)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1
% 229.26/40.73  | | | | | | | | | |           & op(e2, e0) = e1)
% 229.26/40.73  | | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | | BETA: splitting (93) gives:
% 229.26/40.73  | | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | | Case 1:
% 229.26/40.73  | | | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | | |   (94)  all_57_9 = e1 & op(e3, e0) = e1
% 229.26/40.73  | | | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | | | ALPHA: (94) implies:
% 229.26/40.73  | | | | | | | | | | |   (95)  all_57_9 = e1
% 229.26/40.73  | | | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | | | BETA: splitting (35) gives:
% 229.26/40.73  | | | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | | | Case 1:
% 229.26/40.73  | | | | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | | | |   (96)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 229.26/40.73  | | | | | | | | | | | |           & op(e2, e2) = e3)
% 229.26/40.73  | | | | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | | | | BETA: splitting (96) gives:
% 229.26/40.73  | | | | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | | | | Case 1:
% 229.26/40.73  | | | | | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | | | | |   (97)  all_57_2 = e3 & op(e2, e3) = e3
% 229.26/40.73  | | | | | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | | | | | ALPHA: (97) implies:
% 229.26/40.73  | | | | | | | | | | | | |   (98)  all_57_2 = e3
% 229.26/40.73  | | | | | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | | | | | REF_CLOSE: (1), (4), (6), (7), (8), (9), (13), (14), (16),
% 229.26/40.73  | | | | | | | | | | | | |            (17), (18), (19), (20), (21), (22), (24), (26),
% 229.26/40.73  | | | | | | | | | | | | |            (28), (29), (30), (32), (33), (35), (37), (39),
% 229.26/40.73  | | | | | | | | | | | | |            (40), (42), (43), (52), (92), (98) are
% 229.26/40.73  | | | | | | | | | | | | |            inconsistent by sub-proof #744.
% 229.26/40.73  | | | | | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | | | | Case 2:
% 229.26/40.73  | | | | | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | | | | |   (99)  all_57_3 = e3 & op(e2, e2) = e3
% 229.26/40.73  | | | | | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | | | | | ALPHA: (99) implies:
% 229.26/40.73  | | | | | | | | | | | | |   (100)  op(e2, e2) = e3
% 229.26/40.73  | | | | | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | | | | | REF_CLOSE: (4), (6), (10), (100) are inconsistent by
% 229.26/40.73  | | | | | | | | | | | | |            sub-proof #1912.
% 229.26/40.73  | | | | | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | | | | End of split
% 229.26/40.73  | | | | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | | | Case 2:
% 229.26/40.73  | | | | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | | | |   (101)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 229.26/40.73  | | | | | | | | | | | |            e3 & op(e2, e0) = e3)
% 229.26/40.73  | | | | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | | | | BETA: splitting (101) gives:
% 229.26/40.73  | | | | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | | | | Case 1:
% 229.26/40.73  | | | | | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | | | | |   (102)  all_57_5 = e3 & op(e2, e1) = e3
% 229.26/40.73  | | | | | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | | | | | ALPHA: (102) implies:
% 229.26/40.73  | | | | | | | | | | | | |   (103)  all_57_5 = e3
% 229.26/40.73  | | | | | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | | | | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (9), (10), (12),
% 229.26/40.73  | | | | | | | | | | | | |            (13), (14), (16), (17), (18), (19), (20), (21),
% 229.26/40.73  | | | | | | | | | | | | |            (22), (24), (25), (26), (28), (29), (30), (31),
% 229.26/40.73  | | | | | | | | | | | | |            (32), (33), (34), (35), (37), (38), (39), (40),
% 229.26/40.73  | | | | | | | | | | | | |            (42), (43), (44), (46), (52), (92), (103) are
% 229.26/40.73  | | | | | | | | | | | | |            inconsistent by sub-proof #742.
% 229.26/40.73  | | | | | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | | | | Case 2:
% 229.26/40.73  | | | | | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | | | | |   (104)  all_57_10 = e3 & op(e2, e0) = e3
% 229.26/40.73  | | | | | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | | | | | ALPHA: (104) implies:
% 229.26/40.73  | | | | | | | | | | | | |   (105)  all_57_10 = e3
% 229.26/40.73  | | | | | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | | | | | REF_CLOSE: (17), (19), (24), (39), (40), (88), (95), (105)
% 229.26/40.73  | | | | | | | | | | | | |            are inconsistent by sub-proof #1987.
% 229.26/40.73  | | | | | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | | | | End of split
% 229.26/40.73  | | | | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | | | End of split
% 229.26/40.73  | | | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | | Case 2:
% 229.26/40.73  | | | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | | |   (106)  all_57_10 = e1 & op(e2, e0) = e1
% 229.26/40.73  | | | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | | | REF_CLOSE: (3), (4), (6), (7), (8), (9), (10), (11), (14),
% 229.26/40.73  | | | | | | | | | | |            (15), (17), (18), (19), (20), (22), (23), (24),
% 229.26/40.73  | | | | | | | | | | |            (26), (27), (28), (33), (36), (39), (40), (43),
% 229.26/40.73  | | | | | | | | | | |            (45), (47), (52), (75), (106) are inconsistent by
% 229.26/40.73  | | | | | | | | | | |            sub-proof #741.
% 229.26/40.73  | | | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | | End of split
% 229.26/40.73  | | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | Case 2:
% 229.26/40.73  | | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | |   (107)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 229.26/40.73  | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 229.26/40.73  | | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | | REF_CLOSE: (4), (6), (28), (31), (88), (107) are inconsistent
% 229.26/40.73  | | | | | | | | | |            by sub-proof #1105.
% 229.26/40.73  | | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | End of split
% 229.26/40.73  | | | | | | | | | 
% 229.26/40.73  | | | | | | | | Case 2:
% 229.26/40.73  | | | | | | | | | 
% 229.26/40.73  | | | | | | | | |   (108)  all_57_11 = e2 & op(e1, e0) = e2
% 229.26/40.73  | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | ALPHA: (108) implies:
% 229.26/40.73  | | | | | | | | |   (109)  all_57_11 = e2
% 229.26/40.73  | | | | | | | | |   (110)  op(e1, e0) = e2
% 229.26/40.73  | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11),
% 229.26/40.73  | | | | | | | | |            (12), (13), (14), (15), (16), (17), (18), (19),
% 229.26/40.73  | | | | | | | | |            (20), (21), (22), (23), (24), (25), (26), (27),
% 229.26/40.73  | | | | | | | | |            (28), (29), (30), (31), (32), (33), (34), (35),
% 229.26/40.73  | | | | | | | | |            (36), (37), (38), (39), (40), (41), (42), (43),
% 229.26/40.73  | | | | | | | | |            (44), (45), (46), (47), (52), (75), (109), (110)
% 229.26/40.73  | | | | | | | | |            are inconsistent by sub-proof #740.
% 229.26/40.73  | | | | | | | | | 
% 229.26/40.73  | | | | | | | | End of split
% 229.26/40.73  | | | | | | | | 
% 229.26/40.73  | | | | | | | End of split
% 229.26/40.73  | | | | | | | 
% 229.26/40.73  | | | | | | End of split
% 229.26/40.73  | | | | | | 
% 229.26/40.73  | | | | | End of split
% 229.26/40.73  | | | | | 
% 229.26/40.73  | | | | End of split
% 229.26/40.73  | | | | 
% 229.26/40.73  | | | End of split
% 229.26/40.73  | | | 
% 229.26/40.73  | | End of split
% 229.26/40.73  | | 
% 229.26/40.73  | Case 2:
% 229.26/40.73  | | 
% 229.26/40.73  | |   (111)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 229.26/40.73  | |            e3)
% 229.26/40.73  | | 
% 229.26/40.73  | | REF_CLOSE: (4), (6), (8), (9), (17), (18), (19), (24), (28), (33), (39),
% 229.26/40.73  | |            (40), (43), (111) are inconsistent by sub-proof #1786.
% 229.26/40.73  | | 
% 229.26/40.73  | End of split
% 229.26/40.73  | 
% 229.26/40.73  End of proof
% 229.26/40.73  
% 229.26/40.73  Sub-proof #740 shows that the following formulas are inconsistent:
% 229.26/40.73  ----------------------------------------------------------------
% 229.26/40.73    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.26/40.73         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.26/40.73    (2)  op(e1, e0) = e2
% 229.26/40.73    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.26/40.73         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.26/40.73    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.26/40.73         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.26/40.73    (5)   ~ (e3 = e1)
% 229.26/40.73    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.26/40.73           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.26/40.73    (7)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.26/40.73         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.26/40.73    (8)   ~ (all_6_2 = e3)
% 229.26/40.73    (9)  op(e1, e1) = all_6_2
% 229.26/40.73    (10)  op(e2, e2) = e1
% 229.26/40.73    (11)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.26/40.73          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.26/40.73    (12)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 229.26/40.73            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 229.26/40.73              e3) = all_22_1 & $i(all_22_1))
% 229.26/40.73    (13)  all_57_12 = e2
% 229.26/40.73    (14)  all_57_6 = e1
% 229.26/40.73    (15)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.26/40.73          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.26/40.73    (16)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 229.26/40.73          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.26/40.73    (17)   ~ (e3 = e2)
% 229.26/40.73    (18)   ~ (e3 = e0)
% 229.26/40.73    (19)  all_57_15 = e3
% 229.26/40.73    (20)  op(e3, e3) = e2
% 229.26/40.73    (21)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.26/40.73          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.26/40.73            e1)
% 229.26/40.73    (22)  all_57_10 = e2
% 229.26/40.73    (23)  all_57_11 = e2
% 229.26/40.73    (24)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.26/40.73          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.26/40.73    (25)   ~ (e2 = e0)
% 229.26/40.73    (26)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 229.26/40.73            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 229.26/40.73              e3) = all_12_1 & $i(all_12_1))
% 229.26/40.73    (27)  all_57_13 = e2
% 229.26/40.73    (28)  all_57_3 = e1
% 229.26/40.73    (29)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.26/40.73          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.26/40.73    (30)   ~ (e1 = e0)
% 229.26/40.73    (31)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.26/40.73          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.26/40.73    (32)  all_57_14 = e1
% 229.26/40.73    (33)  op(e0, e0) = e3
% 229.26/40.73    (34)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.26/40.73          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.26/40.73            e2)
% 229.26/40.73    (35)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.26/40.73              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.26/40.73                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.26/40.73                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.26/40.73    (36)  op(e1, e1) = e2
% 229.26/40.73    (37)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.26/40.73          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.26/40.73    (38)   ~ (all_53_12 = e3)
% 229.26/40.73    (39)  all_57_7 = e3
% 229.26/40.73    (40)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.26/40.73          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.26/40.73    (41)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.26/40.73          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.26/40.73    (42)   ~ (e2 = e1)
% 229.26/40.73    (43)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.26/40.73          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.26/40.73    (44)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 229.26/40.73          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 229.26/40.73    (45)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.26/40.73          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.26/40.73    (46)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.26/40.73          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.26/40.73    (47)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 229.26/40.73          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 229.26/40.73    (48)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.26/40.73          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.26/40.73    (49)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 229.26/40.73          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 229.26/40.73    (50)  op(e3, e0) = all_53_12
% 229.26/40.73  
% 229.26/40.73  Begin of proof
% 229.26/40.73  | 
% 229.26/40.73  | BETA: splitting (46) gives:
% 229.26/40.73  | 
% 229.26/40.73  | Case 1:
% 229.26/40.73  | | 
% 229.26/40.73  | |   (51)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) =
% 229.26/40.73  | |           e1)
% 229.26/40.73  | | 
% 229.26/40.73  | | BETA: splitting (51) gives:
% 229.26/40.73  | | 
% 229.26/40.73  | | Case 1:
% 229.26/40.73  | | | 
% 229.26/40.73  | | |   (52)  all_57_9 = e1 & op(e3, e0) = e1
% 229.26/40.73  | | | 
% 229.26/40.73  | | | ALPHA: (52) implies:
% 229.26/40.73  | | |   (53)  all_57_9 = e1
% 229.26/40.73  | | | 
% 229.26/40.73  | | | BETA: splitting (37) gives:
% 229.26/40.73  | | | 
% 229.26/40.73  | | | Case 1:
% 229.26/40.73  | | | | 
% 229.26/40.73  | | | |   (54)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2)
% 229.26/40.73  | | | |           = e3)
% 229.26/40.73  | | | | 
% 229.26/40.73  | | | | BETA: splitting (54) gives:
% 229.26/40.73  | | | | 
% 229.26/40.73  | | | | Case 1:
% 229.26/40.73  | | | | | 
% 229.26/40.73  | | | | |   (55)  all_57_2 = e3 & op(e2, e3) = e3
% 229.26/40.73  | | | | | 
% 229.26/40.73  | | | | | ALPHA: (55) implies:
% 229.26/40.73  | | | | |   (56)  all_57_2 = e3
% 229.26/40.73  | | | | | 
% 229.26/40.73  | | | | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (9), (12), (13), (17), (18),
% 229.26/40.73  | | | | |            (19), (20), (22), (23), (25), (26), (30), (33), (35), (36),
% 229.26/40.73  | | | | |            (39), (42), (43), (45), (46), (47), (56) are inconsistent
% 229.26/40.73  | | | | |            by sub-proof #750.
% 229.26/40.73  | | | | | 
% 229.26/40.73  | | | | Case 2:
% 229.26/40.73  | | | | | 
% 229.26/40.73  | | | | |   (57)  all_57_3 = e3 & op(e2, e2) = e3
% 229.26/40.73  | | | | | 
% 229.26/40.73  | | | | | ALPHA: (57) implies:
% 229.26/40.73  | | | | |   (58)  op(e2, e2) = e3
% 229.26/40.73  | | | | | 
% 229.26/40.73  | | | | | REF_CLOSE: (5), (6), (10), (58) are inconsistent by sub-proof #1912.
% 229.26/40.73  | | | | | 
% 229.26/40.73  | | | | End of split
% 229.26/40.73  | | | | 
% 229.26/40.73  | | | Case 2:
% 229.26/40.73  | | | | 
% 229.26/40.73  | | | |   (59)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0)
% 229.26/40.73  | | | |           = e3)
% 229.26/40.73  | | | | 
% 229.26/40.73  | | | | BETA: splitting (59) gives:
% 229.26/40.73  | | | | 
% 229.26/40.73  | | | | Case 1:
% 229.26/40.73  | | | | | 
% 229.26/40.73  | | | | |   (60)  all_57_5 = e3 & op(e2, e1) = e3
% 229.26/40.73  | | | | | 
% 229.26/40.73  | | | | | ALPHA: (60) implies:
% 229.26/40.73  | | | | |   (61)  all_57_5 = e3
% 229.26/40.73  | | | | | 
% 229.26/40.73  | | | | | BETA: splitting (44) gives:
% 229.26/40.73  | | | | | 
% 229.26/40.73  | | | | | Case 1:
% 229.26/40.73  | | | | | | 
% 229.26/40.73  | | | | | |   (62)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2,
% 229.26/40.73  | | | | | |             e1) = e2)
% 229.26/40.73  | | | | | | 
% 229.26/40.73  | | | | | | BETA: splitting (62) gives:
% 229.26/40.73  | | | | | | 
% 229.26/40.73  | | | | | | Case 1:
% 229.26/40.73  | | | | | | | 
% 229.26/40.73  | | | | | | |   (63)  all_57_4 = e2 & op(e3, e1) = e2
% 229.26/40.73  | | | | | | | 
% 229.26/40.73  | | | | | | | ALPHA: (63) implies:
% 229.26/40.73  | | | | | | |   (64)  all_57_4 = e2
% 229.26/40.73  | | | | | | | 
% 229.26/40.73  | | | | | | | BETA: splitting (29) gives:
% 229.26/40.73  | | | | | | | 
% 229.26/40.73  | | | | | | | Case 1:
% 229.26/40.73  | | | | | | | | 
% 229.26/40.73  | | | | | | | |   (65)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 &
% 229.26/40.73  | | | | | | | |           op(e3, e2) = e3)
% 229.26/40.73  | | | | | | | | 
% 229.26/40.73  | | | | | | | | BETA: splitting (65) gives:
% 229.26/40.73  | | | | | | | | 
% 229.26/40.73  | | | | | | | | Case 1:
% 229.26/40.73  | | | | | | | | | 
% 229.26/40.73  | | | | | | | | |   (66)  all_57_0 = e3 & op(e3, e3) = e3
% 229.26/40.73  | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | ALPHA: (66) implies:
% 229.26/40.73  | | | | | | | | |   (67)  op(e3, e3) = e3
% 229.26/40.73  | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | REF_CLOSE: (6), (17), (20), (67) are inconsistent by sub-proof
% 229.26/40.73  | | | | | | | | |            #2490.
% 229.26/40.73  | | | | | | | | | 
% 229.26/40.73  | | | | | | | | Case 2:
% 229.26/40.73  | | | | | | | | | 
% 229.26/40.73  | | | | | | | | |   (68)  all_57_1 = e3 & op(e3, e2) = e3
% 229.26/40.73  | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | ALPHA: (68) implies:
% 229.26/40.73  | | | | | | | | |   (69)  all_57_1 = e3
% 229.26/40.73  | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | BETA: splitting (24) gives:
% 229.26/40.73  | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | Case 1:
% 229.26/40.73  | | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | |   (70)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 &
% 229.26/40.73  | | | | | | | | | |           op(e2, e2) = e0)
% 229.26/40.73  | | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | | BETA: splitting (70) gives:
% 229.26/40.73  | | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | | Case 1:
% 229.26/40.73  | | | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | | |   (71)  all_57_1 = e0 & op(e3, e2) = e0
% 229.26/40.73  | | | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | | | ALPHA: (71) implies:
% 229.26/40.73  | | | | | | | | | | |   (72)  all_57_1 = e0
% 229.26/40.73  | | | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | | | COMBINE_EQS: (69), (72) imply:
% 229.26/40.73  | | | | | | | | | | |   (73)  e3 = e0
% 229.26/40.73  | | | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | | | COMBINE_EQS: (39), (73) imply:
% 229.26/40.73  | | | | | | | | | | |   (74)  all_57_7 = e0
% 229.26/40.73  | | | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (17), (18), (19), (23),
% 229.26/40.73  | | | | | | | | | | |            (25), (30), (35), (36), (42), (43), (46), (47),
% 229.26/40.73  | | | | | | | | | | |            (74) are inconsistent by sub-proof #1154.
% 229.26/40.73  | | | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | | Case 2:
% 229.26/40.73  | | | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | | |   (75)  all_57_3 = e0 & op(e2, e2) = e0
% 229.26/40.73  | | | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | | | ALPHA: (75) implies:
% 229.26/40.73  | | | | | | | | | | |   (76)  all_57_3 = e0
% 229.26/40.73  | | | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | | | REF_CLOSE: (5), (27), (30), (39), (42), (48), (69), (76) are
% 229.26/40.73  | | | | | | | | | | |            inconsistent by sub-proof #1779.
% 229.26/40.73  | | | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | | End of split
% 229.26/40.73  | | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | Case 2:
% 229.26/40.73  | | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | |   (77)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0
% 229.26/40.73  | | | | | | | | | |           & op(e0, e2) = e0)
% 229.26/40.73  | | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | | BETA: splitting (77) gives:
% 229.26/40.73  | | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | | Case 1:
% 229.26/40.73  | | | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | | |   (78)  all_57_7 = e0 & op(e1, e2) = e0
% 229.26/40.73  | | | | | | | | | | | 
% 229.26/40.73  | | | | | | | | | | | ALPHA: (78) implies:
% 229.26/40.73  | | | | | | | | | | |   (79)  all_57_7 = e0
% 229.26/40.73  | | | | | | | | | | | 
% 229.26/40.74  | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (17), (18), (19), (23),
% 229.26/40.74  | | | | | | | | | | |            (25), (30), (35), (36), (42), (43), (46), (47),
% 229.26/40.74  | | | | | | | | | | |            (79) are inconsistent by sub-proof #1154.
% 229.26/40.74  | | | | | | | | | | | 
% 229.26/40.74  | | | | | | | | | | Case 2:
% 229.26/40.74  | | | | | | | | | | | 
% 229.26/40.74  | | | | | | | | | | |   (80)  all_57_13 = e0 & op(e0, e2) = e0
% 229.26/40.74  | | | | | | | | | | | 
% 229.26/40.74  | | | | | | | | | | | ALPHA: (80) implies:
% 229.26/40.74  | | | | | | | | | | |   (81)  all_57_13 = e0
% 229.26/40.74  | | | | | | | | | | | 
% 229.26/40.74  | | | | | | | | | | | COMBINE_EQS: (27), (81) imply:
% 229.26/40.74  | | | | | | | | | | |   (82)  e2 = e0
% 229.26/40.74  | | | | | | | | | | | 
% 229.26/40.74  | | | | | | | | | | | SIMP: (82) implies:
% 229.26/40.74  | | | | | | | | | | |   (83)  e2 = e0
% 229.26/40.74  | | | | | | | | | | | 
% 229.26/40.74  | | | | | | | | | | | REF_CLOSE: (5), (6), (17), (19), (22), (23), (25), (30),
% 229.26/40.74  | | | | | | | | | | |            (33), (42), (43), (46), (83) are inconsistent by
% 229.26/40.74  | | | | | | | | | | |            sub-proof #751.
% 229.26/40.74  | | | | | | | | | | | 
% 229.26/40.74  | | | | | | | | | | End of split
% 229.26/40.74  | | | | | | | | | | 
% 229.26/40.74  | | | | | | | | | End of split
% 229.26/40.74  | | | | | | | | | 
% 229.26/40.74  | | | | | | | | End of split
% 229.26/40.74  | | | | | | | | 
% 229.26/40.74  | | | | | | | Case 2:
% 229.26/40.74  | | | | | | | | 
% 229.26/40.74  | | | | | | | |   (84)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 &
% 229.26/40.74  | | | | | | | |           op(e3, e0) = e3)
% 229.26/40.74  | | | | | | | | 
% 229.26/40.74  | | | | | | | | BETA: splitting (84) gives:
% 229.26/40.74  | | | | | | | | 
% 229.26/40.74  | | | | | | | | Case 1:
% 229.26/40.74  | | | | | | | | | 
% 229.26/40.74  | | | | | | | | |   (85)  all_57_4 = e3 & op(e3, e1) = e3
% 229.26/40.74  | | | | | | | | | 
% 229.26/40.74  | | | | | | | | | ALPHA: (85) implies:
% 229.26/40.74  | | | | | | | | |   (86)  all_57_4 = e3
% 229.26/40.74  | | | | | | | | | 
% 229.26/40.74  | | | | | | | | | COMBINE_EQS: (64), (86) imply:
% 229.26/40.74  | | | | | | | | |   (87)  e3 = e2
% 229.26/40.74  | | | | | | | | | 
% 229.26/40.74  | | | | | | | | | SIMP: (87) implies:
% 229.26/40.74  | | | | | | | | |   (88)  e3 = e2
% 229.26/40.74  | | | | | | | | | 
% 229.26/40.74  | | | | | | | | | COMBINE_EQS: (61), (88) imply:
% 229.26/40.74  | | | | | | | | |   (89)  all_57_5 = e2
% 229.26/40.74  | | | | | | | | | 
% 229.26/40.74  | | | | | | | | | REF_CLOSE: (1), (3), (5), (6), (7), (8), (9), (10), (12),
% 229.26/40.74  | | | | | | | | |            (13), (14), (16), (17), (18), (19), (20), (21),
% 229.26/40.74  | | | | | | | | |            (22), (25), (26), (28), (30), (31), (32), (33),
% 229.26/40.74  | | | | | | | | |            (34), (35), (36), (37), (39), (40), (42), (43),
% 229.26/40.74  | | | | | | | | |            (45), (46), (47), (49), (89) are inconsistent by
% 229.26/40.74  | | | | | | | | |            sub-proof #743.
% 229.26/40.74  | | | | | | | | | 
% 229.26/40.74  | | | | | | | | Case 2:
% 229.26/40.74  | | | | | | | | | 
% 229.26/40.74  | | | | | | | | |   (90)  all_57_9 = e3 & op(e3, e0) = e3
% 229.26/40.74  | | | | | | | | | 
% 229.26/40.74  | | | | | | | | | ALPHA: (90) implies:
% 229.26/40.74  | | | | | | | | |   (91)  op(e3, e0) = e3
% 229.26/40.74  | | | | | | | | | 
% 229.26/40.74  | | | | | | | | | REF_CLOSE: (6), (38), (50), (91) are inconsistent by sub-proof
% 229.26/40.74  | | | | | | | | |            #2458.
% 229.26/40.74  | | | | | | | | | 
% 229.26/40.74  | | | | | | | | End of split
% 229.26/40.74  | | | | | | | | 
% 229.26/40.74  | | | | | | | End of split
% 229.26/40.74  | | | | | | | 
% 229.26/40.74  | | | | | | Case 2:
% 229.26/40.74  | | | | | | | 
% 229.26/40.74  | | | | | | |   (92)  all_57_5 = e2 & op(e2, e1) = e2
% 229.26/40.74  | | | | | | | 
% 229.26/40.74  | | | | | | | ALPHA: (92) implies:
% 229.26/40.74  | | | | | | |   (93)  all_57_5 = e2
% 229.26/40.74  | | | | | | | 
% 229.26/40.74  | | | | | | | REF_CLOSE: (1), (3), (5), (6), (7), (8), (9), (10), (12), (13),
% 229.26/40.74  | | | | | | |            (14), (16), (17), (18), (19), (20), (21), (22), (25),
% 229.26/40.74  | | | | | | |            (26), (28), (30), (31), (32), (33), (34), (35), (36),
% 229.26/40.74  | | | | | | |            (37), (39), (40), (42), (43), (45), (46), (47), (49),
% 229.26/40.74  | | | | | | |            (93) are inconsistent by sub-proof #743.
% 229.26/40.74  | | | | | | | 
% 229.26/40.74  | | | | | | End of split
% 229.26/40.74  | | | | | | 
% 229.26/40.74  | | | | | Case 2:
% 229.26/40.74  | | | | | | 
% 229.26/40.74  | | | | | |   (94)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0,
% 229.26/40.74  | | | | | |             e1) = e2)
% 229.26/40.74  | | | | | | 
% 229.26/40.74  | | | | | | BETA: splitting (94) gives:
% 229.26/40.74  | | | | | | 
% 229.26/40.74  | | | | | | Case 1:
% 229.26/40.74  | | | | | | | 
% 229.26/40.74  | | | | | | |   (95)  all_57_8 = e2 & op(e1, e1) = e2
% 229.26/40.74  | | | | | | | 
% 229.26/40.74  | | | | | | | ALPHA: (95) implies:
% 229.26/40.74  | | | | | | |   (96)  all_57_8 = e2
% 229.26/40.74  | | | | | | | 
% 229.26/40.74  | | | | | | | REF_CLOSE: (1), (3), (5), (6), (7), (8), (9), (10), (12), (13),
% 229.26/40.74  | | | | | | |            (14), (16), (17), (18), (19), (20), (21), (22), (25),
% 229.26/40.74  | | | | | | |            (26), (28), (30), (31), (32), (33), (34), (35), (36),
% 229.26/40.74  | | | | | | |            (37), (39), (40), (41), (42), (43), (45), (46), (47),
% 229.26/40.74  | | | | | | |            (49), (61), (96) are inconsistent by sub-proof #742.
% 229.26/40.74  | | | | | | | 
% 229.26/40.74  | | | | | | Case 2:
% 229.26/40.74  | | | | | | | 
% 229.26/40.74  | | | | | | |   (97)  all_57_14 = e2 & op(e0, e1) = e2
% 229.26/40.74  | | | | | | | 
% 229.26/40.74  | | | | | | | ALPHA: (97) implies:
% 229.26/40.74  | | | | | | |   (98)  all_57_14 = e2
% 229.26/40.74  | | | | | | | 
% 229.26/40.74  | | | | | | | COMBINE_EQS: (32), (98) imply:
% 229.26/40.74  | | | | | | |   (99)  e2 = e1
% 229.26/40.74  | | | | | | | 
% 229.26/40.74  | | | | | | | SIMP: (99) implies:
% 229.26/40.74  | | | | | | |   (100)  e2 = e1
% 229.26/40.74  | | | | | | | 
% 229.26/40.74  | | | | | | | COMBINE_EQS: (13), (100) imply:
% 229.26/40.74  | | | | | | |   (101)  all_57_12 = e1
% 229.26/40.74  | | | | | | | 
% 229.26/40.74  | | | | | | | REF_CLOSE: (6), (18), (25), (27), (30), (33), (35), (98), (101)
% 229.26/40.74  | | | | | | |            are inconsistent by sub-proof #1583.
% 229.26/40.74  | | | | | | | 
% 229.26/40.74  | | | | | | End of split
% 229.26/40.74  | | | | | | 
% 229.26/40.74  | | | | | End of split
% 229.26/40.74  | | | | | 
% 229.26/40.74  | | | | Case 2:
% 229.26/40.74  | | | | | 
% 229.26/40.74  | | | | |   (102)  all_57_10 = e3 & op(e2, e0) = e3
% 229.26/40.74  | | | | | 
% 229.26/40.74  | | | | | ALPHA: (102) implies:
% 229.26/40.74  | | | | |   (103)  all_57_10 = e3
% 229.26/40.74  | | | | | 
% 229.26/40.74  | | | | | REF_CLOSE: (17), (18), (19), (25), (30), (35), (42), (43), (53), (103)
% 229.26/40.74  | | | | |            are inconsistent by sub-proof #1985.
% 229.26/40.74  | | | | | 
% 229.26/40.74  | | | | End of split
% 229.26/40.74  | | | | 
% 229.26/40.74  | | | End of split
% 229.26/40.74  | | | 
% 229.26/40.74  | | Case 2:
% 229.26/40.74  | | | 
% 229.26/40.74  | | |   (104)  all_57_10 = e1 & op(e2, e0) = e1
% 229.26/40.74  | | | 
% 229.26/40.74  | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (10), (11), (14), (15), (17),
% 229.26/40.74  | | |            (18), (19), (20), (22), (24), (25), (27), (28), (29), (30),
% 229.26/40.74  | | |            (35), (38), (39), (42), (43), (46), (48), (50), (104) are
% 229.26/40.74  | | |            inconsistent by sub-proof #741.
% 229.26/40.74  | | | 
% 229.26/40.74  | | End of split
% 229.26/40.74  | | 
% 229.26/40.74  | Case 2:
% 229.26/40.74  | | 
% 229.26/40.74  | |   (105)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.26/40.74  | |            e1)
% 229.26/40.74  | | 
% 229.26/40.74  | | BETA: splitting (105) gives:
% 229.26/40.74  | | 
% 229.26/40.74  | | Case 1:
% 229.26/40.74  | | | 
% 229.26/40.74  | | |   (106)  all_57_11 = e1 & op(e1, e0) = e1
% 229.26/40.74  | | | 
% 229.26/40.74  | | | ALPHA: (106) implies:
% 229.26/40.74  | | |   (107)  all_57_11 = e1
% 229.26/40.74  | | | 
% 229.26/40.74  | | | COMBINE_EQS: (23), (107) imply:
% 229.26/40.74  | | |   (108)  e2 = e1
% 229.26/40.74  | | | 
% 229.26/40.74  | | | COMBINE_EQS: (27), (108) imply:
% 229.26/40.74  | | |   (109)  all_57_13 = e1
% 229.26/40.74  | | | 
% 229.26/40.74  | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (10), (11), (14), (15), (17),
% 229.26/40.74  | | |            (18), (19), (20), (24), (25), (28), (29), (30), (35), (38),
% 229.26/40.74  | | |            (39), (42), (43), (46), (48), (50), (109) are inconsistent by
% 229.26/40.74  | | |            sub-proof #798.
% 229.26/40.74  | | | 
% 229.26/40.74  | | Case 2:
% 229.26/40.74  | | | 
% 229.26/40.74  | | |   (110)  all_57_15 = e1 & op(e0, e0) = e1
% 229.26/40.74  | | | 
% 229.26/40.74  | | | ALPHA: (110) implies:
% 229.26/40.74  | | |   (111)  op(e0, e0) = e1
% 229.26/40.74  | | | 
% 229.26/40.74  | | | REF_CLOSE: (5), (6), (33), (111) are inconsistent by sub-proof #2183.
% 229.26/40.74  | | | 
% 229.26/40.74  | | End of split
% 229.26/40.74  | | 
% 229.26/40.74  | End of split
% 229.26/40.74  | 
% 229.26/40.74  End of proof
% 229.26/40.74  
% 229.26/40.74  Sub-proof #741 shows that the following formulas are inconsistent:
% 229.26/40.74  ----------------------------------------------------------------
% 229.26/40.74    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.26/40.74         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.26/40.74    (2)   ~ (e3 = e1)
% 229.26/40.74    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.26/40.74           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.26/40.74    (4)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.26/40.74         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.26/40.74    (5)   ~ (all_6_2 = e3)
% 229.26/40.74    (6)  op(e1, e1) = all_6_2
% 229.26/40.74    (7)  op(e2, e2) = e1
% 229.26/40.74    (8)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.26/40.74         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.26/40.74    (9)  all_57_6 = e1
% 229.26/40.74    (10)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.26/40.74          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.26/40.74    (11)   ~ (e3 = e2)
% 229.26/40.74    (12)   ~ (e3 = e0)
% 229.26/40.74    (13)  all_57_15 = e3
% 229.26/40.74    (14)  op(e3, e3) = e2
% 229.26/40.74    (15)  all_57_10 = e2
% 229.26/40.74    (16)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.26/40.74          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.26/40.74    (17)   ~ (e2 = e0)
% 229.26/40.74    (18)  all_57_13 = e2
% 229.26/40.74    (19)  all_57_3 = e1
% 229.26/40.74    (20)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.26/40.74          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.26/40.74    (21)   ~ (e1 = e0)
% 229.26/40.74    (22)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.26/40.74              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.26/40.74                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.26/40.74                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.26/40.74    (23)  all_57_10 = e1 & op(e2, e0) = e1
% 229.26/40.74    (24)   ~ (all_53_12 = e3)
% 229.26/40.74    (25)  all_57_7 = e3
% 229.26/40.74    (26)   ~ (e2 = e1)
% 229.26/40.74    (27)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.26/40.74          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.26/40.74    (28)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.26/40.74          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.26/40.74    (29)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.26/40.74          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.26/40.74    (30)  op(e3, e0) = all_53_12
% 229.26/40.74  
% 229.26/40.74  Begin of proof
% 229.26/40.74  | 
% 229.26/40.74  | ALPHA: (23) implies:
% 229.26/40.74  |   (31)  all_57_10 = e1
% 229.26/40.74  | 
% 229.26/40.74  | COMBINE_EQS: (15), (31) imply:
% 229.26/40.74  |   (32)  e2 = e1
% 229.26/40.74  | 
% 229.26/40.74  | COMBINE_EQS: (18), (32) imply:
% 229.26/40.74  |   (33)  all_57_13 = e1
% 229.26/40.74  | 
% 229.26/40.74  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 229.26/40.74  |            (13), (14), (16), (17), (19), (20), (21), (22), (24), (25), (26),
% 229.26/40.74  |            (27), (28), (29), (30), (33) are inconsistent by sub-proof #798.
% 229.26/40.74  | 
% 229.26/40.74  End of proof
% 229.26/40.74  
% 229.26/40.74  Sub-proof #742 shows that the following formulas are inconsistent:
% 229.26/40.74  ----------------------------------------------------------------
% 229.26/40.74    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.26/40.74         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.26/40.74    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.26/40.74         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.26/40.74    (3)   ~ (e3 = e1)
% 229.26/40.74    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.26/40.74           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.26/40.74    (5)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.26/40.74         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.26/40.74    (6)   ~ (all_6_2 = e3)
% 229.26/40.74    (7)  op(e1, e1) = all_6_2
% 229.26/40.74    (8)  op(e2, e2) = e1
% 229.26/40.74    (9)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) = all_22_1
% 229.26/40.74           & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0, e3) =
% 229.26/40.74           all_22_1 & $i(all_22_1))
% 229.26/40.74    (10)  all_57_12 = e2
% 229.26/40.74    (11)  all_57_6 = e1
% 229.26/40.74    (12)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 229.26/40.74          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.26/40.74    (13)   ~ (e3 = e2)
% 229.26/40.74    (14)   ~ (e3 = e0)
% 229.26/40.74    (15)  all_57_15 = e3
% 229.26/40.74    (16)  op(e3, e3) = e2
% 229.26/40.74    (17)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.26/40.74          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.26/40.74            e1)
% 229.26/40.74    (18)  all_57_10 = e2
% 229.26/40.74    (19)  all_57_5 = e3
% 229.26/40.74    (20)   ~ (e2 = e0)
% 229.26/40.74    (21)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 229.26/40.74            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 229.26/40.74              e3) = all_12_1 & $i(all_12_1))
% 229.26/40.74    (22)  all_57_3 = e1
% 229.26/40.74    (23)   ~ (e1 = e0)
% 229.26/40.74    (24)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.26/40.74          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.26/40.74    (25)  all_57_8 = e2
% 229.26/40.74    (26)  all_57_14 = e1
% 229.26/40.74    (27)  op(e0, e0) = e3
% 229.26/40.74    (28)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.26/40.74          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.26/40.74            e2)
% 229.26/40.74    (29)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.26/40.74              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.26/40.74                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.26/40.74                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.26/40.74    (30)  op(e1, e1) = e2
% 229.26/40.74    (31)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.26/40.74          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.26/40.74    (32)  all_57_7 = e3
% 229.26/40.74    (33)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.26/40.74          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.26/40.74    (34)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.26/40.74          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.26/40.74    (35)   ~ (e2 = e1)
% 229.26/40.74    (36)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.26/40.74          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.26/40.74    (37)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.26/40.74          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.26/40.74    (38)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.26/40.74          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.26/40.74    (39)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 229.26/40.74          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 229.26/40.74    (40)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 229.26/40.74          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 229.26/40.74  
% 229.26/40.74  Begin of proof
% 229.26/40.74  | 
% 229.26/40.74  | BETA: splitting (34) gives:
% 229.26/40.74  | 
% 229.26/40.74  | Case 1:
% 229.26/40.74  | | 
% 229.26/40.74  | |   (41)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) =
% 229.26/40.74  | |           e3)
% 229.26/40.74  | | 
% 229.26/40.74  | | BETA: splitting (41) gives:
% 229.26/40.74  | | 
% 229.26/40.74  | | Case 1:
% 229.26/40.74  | | | 
% 229.26/40.74  | | |   (42)  all_57_0 = e3 & op(e3, e3) = e3
% 229.26/40.74  | | | 
% 229.26/40.74  | | | ALPHA: (42) implies:
% 229.26/40.74  | | |   (43)  op(e3, e3) = e3
% 229.26/40.74  | | | 
% 229.26/40.74  | | | REF_CLOSE: (4), (13), (16), (43) are inconsistent by sub-proof #2490.
% 229.26/40.74  | | | 
% 229.26/40.74  | | Case 2:
% 229.26/40.74  | | | 
% 229.26/40.74  | | |   (44)  all_57_2 = e3 & op(e2, e3) = e3
% 229.26/40.74  | | | 
% 229.26/40.74  | | | ALPHA: (44) implies:
% 229.26/40.74  | | |   (45)  all_57_2 = e3
% 229.26/40.74  | | | 
% 229.26/40.74  | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (10), (11), (12), (13), (14),
% 229.26/40.74  | | |            (15), (16), (17), (18), (20), (22), (23), (24), (25), (26),
% 229.26/40.74  | | |            (28), (29), (31), (32), (33), (35), (36), (37), (38), (45) are
% 229.26/40.74  | | |            inconsistent by sub-proof #744.
% 229.26/40.74  | | | 
% 229.26/40.74  | | End of split
% 229.26/40.74  | | 
% 229.26/40.74  | Case 2:
% 229.26/40.74  | | 
% 229.26/40.74  | |   (46)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) =
% 229.26/40.74  | |           e3)
% 229.26/40.74  | | 
% 229.26/40.74  | | BETA: splitting (46) gives:
% 229.26/40.74  | | 
% 229.26/40.74  | | Case 1:
% 229.26/40.74  | | | 
% 229.26/40.74  | | |   (47)  all_57_6 = e3 & op(e1, e3) = e3
% 229.26/40.74  | | | 
% 229.26/40.74  | | | ALPHA: (47) implies:
% 229.26/40.74  | | |   (48)  all_57_6 = e3
% 229.26/40.74  | | | 
% 229.26/40.74  | | | REF_CLOSE: (3), (11), (48) are inconsistent by sub-proof #2017.
% 229.26/40.74  | | | 
% 229.26/40.74  | | Case 2:
% 229.26/40.74  | | | 
% 229.26/40.74  | | |   (49)  all_57_12 = e3 & op(e0, e3) = e3
% 229.26/40.74  | | | 
% 229.26/40.74  | | | ALPHA: (49) implies:
% 229.26/40.74  | | |   (50)  all_57_12 = e3
% 229.26/40.74  | | | 
% 229.26/40.74  | | | COMBINE_EQS: (10), (50) imply:
% 229.26/40.74  | | |   (51)  e3 = e2
% 229.26/40.74  | | | 
% 229.26/40.74  | | | SIMP: (51) implies:
% 229.26/40.74  | | |   (52)  e3 = e2
% 229.26/40.74  | | | 
% 229.26/40.74  | | | COMBINE_EQS: (19), (52) imply:
% 229.26/40.74  | | |   (53)  all_57_5 = e2
% 229.26/40.74  | | | 
% 229.26/40.74  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 229.26/40.74  | | |            (13), (14), (15), (16), (17), (18), (20), (21), (22), (23),
% 229.26/40.74  | | |            (24), (26), (27), (28), (29), (30), (31), (32), (33), (35),
% 229.26/40.74  | | |            (36), (37), (38), (39), (40), (53) are inconsistent by
% 229.26/40.74  | | |            sub-proof #743.
% 229.26/40.74  | | | 
% 229.26/40.74  | | End of split
% 229.26/40.74  | | 
% 229.26/40.74  | End of split
% 229.26/40.74  | 
% 229.26/40.74  End of proof
% 229.26/40.74  
% 229.26/40.74  Sub-proof #743 shows that the following formulas are inconsistent:
% 229.26/40.74  ----------------------------------------------------------------
% 229.26/40.74    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.26/40.74         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.26/40.74    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.26/40.74         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.26/40.74    (3)   ~ (e3 = e1)
% 229.26/40.74    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.26/40.74           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.26/40.74    (5)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.26/40.74         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.26/40.74    (6)   ~ (all_6_2 = e3)
% 229.26/40.74    (7)  op(e1, e1) = all_6_2
% 229.26/40.74    (8)  op(e2, e2) = e1
% 229.26/40.74    (9)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) = all_22_1
% 229.26/40.74           & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0, e3) =
% 229.26/40.74           all_22_1 & $i(all_22_1))
% 229.26/40.74    (10)  all_57_12 = e2
% 229.26/40.74    (11)  all_57_6 = e1
% 229.26/40.74    (12)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 229.26/40.74          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.26/40.74    (13)   ~ (e3 = e2)
% 229.26/40.74    (14)   ~ (e3 = e0)
% 229.26/40.74    (15)  all_57_15 = e3
% 229.26/40.74    (16)  op(e3, e3) = e2
% 229.26/40.74    (17)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.26/40.74          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.26/40.74            e1)
% 229.26/40.74    (18)  all_57_10 = e2
% 229.26/40.74    (19)   ~ (e2 = e0)
% 229.26/40.74    (20)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 229.26/40.74            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 229.26/40.74              e3) = all_12_1 & $i(all_12_1))
% 229.26/40.74    (21)  all_57_3 = e1
% 229.26/40.74    (22)   ~ (e1 = e0)
% 229.26/40.74    (23)  all_57_5 = e2
% 229.26/40.74    (24)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.26/40.74          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.26/40.74    (25)  all_57_14 = e1
% 229.26/40.74    (26)  op(e0, e0) = e3
% 229.26/40.74    (27)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.26/40.74          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.26/40.74            e2)
% 229.26/40.74    (28)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.26/40.74              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.26/40.74                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.26/40.74                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.26/40.74    (29)  op(e1, e1) = e2
% 229.26/40.74    (30)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.26/40.74          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.26/40.74    (31)  all_57_7 = e3
% 229.26/40.74    (32)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.26/40.74          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.26/40.74    (33)   ~ (e2 = e1)
% 229.26/40.74    (34)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.26/40.74          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.26/40.74    (35)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.26/40.74          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.26/40.74    (36)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.26/40.74          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.26/40.74    (37)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 229.26/40.74          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 229.26/40.74    (38)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 229.26/40.74          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 229.26/40.74  
% 229.26/40.74  Begin of proof
% 229.26/40.74  | 
% 229.26/40.74  | BETA: splitting (30) gives:
% 229.26/40.74  | 
% 229.26/40.74  | Case 1:
% 229.26/40.74  | | 
% 229.26/40.74  | |   (39)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 229.26/40.74  | |           e3)
% 229.26/40.74  | | 
% 229.26/40.74  | | BETA: splitting (39) gives:
% 229.26/40.74  | | 
% 229.26/40.74  | | Case 1:
% 229.26/40.74  | | | 
% 229.26/40.74  | | |   (40)  all_57_2 = e3 & op(e2, e3) = e3
% 229.26/40.74  | | | 
% 229.26/40.74  | | | ALPHA: (40) implies:
% 229.26/40.74  | | |   (41)  all_57_2 = e3
% 229.26/40.74  | | | 
% 229.26/40.74  | | | BETA: splitting (38) gives:
% 229.26/40.74  | | | 
% 229.26/40.74  | | | Case 1:
% 229.26/40.74  | | | | 
% 229.26/40.74  | | | |   (42)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2)
% 229.26/40.74  | | | |           = e2)
% 229.26/40.74  | | | | 
% 229.26/40.74  | | | | BETA: splitting (42) gives:
% 229.26/40.74  | | | | 
% 229.26/40.74  | | | | Case 1:
% 229.26/40.74  | | | | | 
% 229.26/40.74  | | | | |   (43)  all_57_6 = e2 & op(e1, e3) = e2
% 229.26/40.74  | | | | | 
% 229.26/40.74  | | | | | ALPHA: (43) implies:
% 229.26/40.74  | | | | |   (44)  all_57_6 = e2
% 229.26/40.74  | | | | | 
% 229.26/40.74  | | | | | BETA: splitting (2) gives:
% 229.26/40.74  | | | | | 
% 229.26/40.74  | | | | | Case 1:
% 229.26/40.74  | | | | | | 
% 229.26/40.74  | | | | | |   (45)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2,
% 229.26/40.74  | | | | | |             e3) = e1)
% 229.26/40.74  | | | | | | 
% 229.26/40.74  | | | | | | REF_CLOSE: (3), (4), (16), (33), (41), (45) are inconsistent by
% 229.26/40.74  | | | | | |            sub-proof #749.
% 229.26/40.74  | | | | | | 
% 229.26/40.74  | | | | | Case 2:
% 229.26/40.74  | | | | | | 
% 229.26/40.74  | | | | | |   (46)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0,
% 229.26/40.74  | | | | | |             e3) = e1)
% 229.26/40.74  | | | | | | 
% 229.26/40.74  | | | | | | BETA: splitting (46) gives:
% 229.26/40.74  | | | | | | 
% 229.26/40.74  | | | | | | Case 1:
% 229.26/40.74  | | | | | | | 
% 229.26/40.74  | | | | | | |   (47)  all_57_6 = e1 & op(e1, e3) = e1
% 229.26/40.74  | | | | | | | 
% 229.26/40.74  | | | | | | | REF_CLOSE: (11), (33), (44) are inconsistent by sub-proof #2233.
% 229.26/40.74  | | | | | | | 
% 229.26/40.74  | | | | | | Case 2:
% 229.26/40.74  | | | | | | | 
% 229.26/40.74  | | | | | | |   (48)  all_57_12 = e1 & op(e0, e3) = e1
% 229.26/40.74  | | | | | | | 
% 229.26/40.74  | | | | | | | REF_CLOSE: (10), (33), (48) are inconsistent by sub-proof #2388.
% 229.26/40.74  | | | | | | | 
% 229.26/40.74  | | | | | | End of split
% 229.26/40.74  | | | | | | 
% 229.26/40.74  | | | | | End of split
% 229.26/40.74  | | | | | 
% 229.26/40.74  | | | | Case 2:
% 229.26/40.74  | | | | | 
% 229.26/40.74  | | | | |   (49)  all_57_7 = e2 & op(e1, e2) = e2
% 229.26/40.74  | | | | | 
% 229.26/40.74  | | | | | REF_CLOSE: (13), (31), (49) are inconsistent by sub-proof #2092.
% 229.26/40.74  | | | | | 
% 229.26/40.74  | | | | End of split
% 229.26/40.74  | | | | 
% 229.26/40.74  | | | Case 2:
% 229.26/40.74  | | | | 
% 229.26/40.74  | | | |   (50)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0)
% 229.26/40.74  | | | |           = e2)
% 229.26/40.74  | | | | 
% 229.26/40.74  | | | | BETA: splitting (50) gives:
% 229.26/40.74  | | | | 
% 229.26/40.74  | | | | Case 1:
% 229.26/40.74  | | | | | 
% 229.26/40.74  | | | | |   (51)  all_57_8 = e2 & op(e1, e1) = e2
% 229.26/40.74  | | | | | 
% 229.26/40.74  | | | | | ALPHA: (51) implies:
% 229.26/40.74  | | | | |   (52)  all_57_8 = e2
% 229.26/40.74  | | | | | 
% 229.26/40.74  | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (10), (11), (12), (13), (14),
% 229.26/40.74  | | | | |            (15), (16), (17), (18), (19), (21), (22), (24), (25), (27),
% 229.26/40.74  | | | | |            (28), (30), (31), (32), (33), (34), (35), (36), (41), (52)
% 229.26/40.74  | | | | |            are inconsistent by sub-proof #744.
% 229.26/40.74  | | | | | 
% 229.26/40.74  | | | | Case 2:
% 229.26/40.74  | | | | | 
% 229.26/40.74  | | | | |   (53)  all_57_11 = e2 & op(e1, e0) = e2
% 229.26/40.74  | | | | | 
% 229.26/40.74  | | | | | ALPHA: (53) implies:
% 229.26/40.74  | | | | |   (54)  all_57_11 = e2
% 229.26/40.74  | | | | |   (55)  op(e1, e0) = e2
% 229.26/40.74  | | | | | 
% 229.26/40.74  | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (9), (10), (13), (14), (15),
% 229.26/40.74  | | | | |            (16), (18), (19), (20), (22), (26), (28), (29), (31), (33),
% 229.26/40.74  | | | | |            (34), (35), (36), (37), (41), (54), (55) are inconsistent
% 229.26/40.74  | | | | |            by sub-proof #750.
% 229.26/40.74  | | | | | 
% 229.26/40.74  | | | | End of split
% 229.26/40.74  | | | | 
% 229.26/40.74  | | | End of split
% 229.26/40.74  | | | 
% 229.26/40.74  | | Case 2:
% 229.26/40.74  | | | 
% 229.26/40.74  | | |   (56)  all_57_3 = e3 & op(e2, e2) = e3
% 229.26/40.74  | | | 
% 229.26/40.74  | | | ALPHA: (56) implies:
% 229.26/40.74  | | |   (57)  op(e2, e2) = e3
% 229.26/40.74  | | | 
% 229.26/40.74  | | | REF_CLOSE: (3), (4), (8), (57) are inconsistent by sub-proof #1912.
% 229.26/40.74  | | | 
% 229.26/40.74  | | End of split
% 229.26/40.74  | | 
% 229.26/40.74  | Case 2:
% 229.26/40.74  | | 
% 229.26/40.74  | |   (58)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 229.26/40.74  | |           e3)
% 229.26/40.74  | | 
% 229.26/40.74  | | REF_CLOSE: (3), (4), (13), (14), (15), (19), (22), (23), (26), (28), (33),
% 229.26/40.74  | |            (34), (36), (58) are inconsistent by sub-proof #1745.
% 229.26/40.74  | | 
% 229.26/40.74  | End of split
% 229.26/40.74  | 
% 229.26/40.74  End of proof
% 229.26/40.74  
% 229.26/40.74  Sub-proof #744 shows that the following formulas are inconsistent:
% 229.26/40.74  ----------------------------------------------------------------
% 229.26/40.74    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.26/40.74         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.26/40.74    (2)   ~ (e3 = e1)
% 229.26/40.74    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.26/40.74           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.26/40.75    (4)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.26/40.75         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.26/40.75    (5)   ~ (all_6_2 = e3)
% 229.26/40.75    (6)  op(e1, e1) = all_6_2
% 229.26/40.75    (7)  all_57_12 = e2
% 229.26/40.75    (8)  all_57_6 = e1
% 229.26/40.75    (9)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 229.26/40.75         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.26/40.75    (10)   ~ (e3 = e2)
% 229.26/40.75    (11)   ~ (e3 = e0)
% 229.26/40.75    (12)  all_57_15 = e3
% 229.26/40.75    (13)  op(e3, e3) = e2
% 229.26/40.75    (14)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.26/40.75          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.26/40.75            e1)
% 229.26/40.75    (15)  all_57_10 = e2
% 229.26/40.75    (16)   ~ (e2 = e0)
% 229.26/40.75    (17)  all_57_2 = e3
% 229.26/40.75    (18)  all_57_3 = e1
% 229.26/40.75    (19)   ~ (e1 = e0)
% 229.26/40.75    (20)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.26/40.75          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.26/40.75    (21)  all_57_8 = e2
% 229.26/40.75    (22)  all_57_14 = e1
% 229.26/40.75    (23)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.26/40.75          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.26/40.75            e2)
% 229.26/40.75    (24)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.26/40.75              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.26/40.75                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.26/40.75                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.26/40.75    (25)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.26/40.75          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.26/40.75    (26)  all_57_7 = e3
% 229.26/40.75    (27)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.26/40.75          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.26/40.75    (28)   ~ (e2 = e1)
% 229.26/40.75    (29)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.26/40.75          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.26/40.75    (30)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.26/40.75          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.26/40.75    (31)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.26/40.75          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.26/40.75  
% 229.26/40.75  Begin of proof
% 229.26/40.75  | 
% 229.26/40.75  | BETA: splitting (30) gives:
% 229.26/40.75  | 
% 229.26/40.75  | Case 1:
% 229.26/40.75  | | 
% 229.26/40.75  | |   (32)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) =
% 229.26/40.75  | |           e0)
% 229.26/40.75  | | 
% 229.26/40.75  | | BETA: splitting (32) gives:
% 229.26/40.75  | | 
% 229.26/40.75  | | Case 1:
% 229.26/40.75  | | | 
% 229.26/40.75  | | |   (33)  all_57_0 = e0 & op(e3, e3) = e0
% 229.26/40.75  | | | 
% 229.26/40.75  | | | ALPHA: (33) implies:
% 229.26/40.75  | | |   (34)  op(e3, e3) = e0
% 229.26/40.75  | | | 
% 229.26/40.75  | | | REF_CLOSE: (3), (13), (16), (34) are inconsistent by sub-proof #2403.
% 229.26/40.75  | | | 
% 229.26/40.75  | | Case 2:
% 229.26/40.75  | | | 
% 229.26/40.75  | | |   (35)  all_57_2 = e0 & op(e2, e3) = e0
% 229.26/40.75  | | | 
% 229.26/40.75  | | | ALPHA: (35) implies:
% 229.26/40.75  | | |   (36)  all_57_2 = e0
% 229.26/40.75  | | | 
% 229.26/40.75  | | | COMBINE_EQS: (17), (36) imply:
% 229.26/40.75  | | |   (37)  e3 = e0
% 229.26/40.75  | | | 
% 229.26/40.75  | | | COMBINE_EQS: (26), (37) imply:
% 229.26/40.75  | | |   (38)  all_57_7 = e0
% 229.26/40.75  | | | 
% 229.26/40.75  | | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (10), (11), (12), (16), (19),
% 229.26/40.75  | | |            (24), (28), (29), (31), (38) are inconsistent by sub-proof
% 229.26/40.75  | | |            #1735.
% 229.26/40.75  | | | 
% 229.26/40.75  | | End of split
% 229.26/40.75  | | 
% 229.26/40.75  | Case 2:
% 229.26/40.75  | | 
% 229.26/40.75  | |   (39)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) =
% 229.26/40.75  | |           e0)
% 229.26/40.75  | | 
% 229.26/40.75  | | BETA: splitting (39) gives:
% 229.26/40.75  | | 
% 229.26/40.75  | | Case 1:
% 229.26/40.75  | | | 
% 229.26/40.75  | | |   (40)  all_57_6 = e0 & op(e1, e3) = e0
% 229.26/40.75  | | | 
% 229.26/40.75  | | | ALPHA: (40) implies:
% 229.26/40.75  | | |   (41)  all_57_6 = e0
% 229.26/40.75  | | | 
% 229.26/40.75  | | | COMBINE_EQS: (8), (41) imply:
% 229.26/40.75  | | |   (42)  e1 = e0
% 229.26/40.75  | | | 
% 229.26/40.75  | | | COMBINE_EQS: (18), (42) imply:
% 229.26/40.75  | | |   (43)  all_57_3 = e0
% 229.26/40.75  | | | 
% 229.26/40.75  | | | REF_CLOSE: (1), (2), (3), (5), (6), (9), (10), (11), (12), (14), (15),
% 229.26/40.75  | | |            (16), (17), (19), (20), (21), (22), (23), (24), (25), (27),
% 229.26/40.75  | | |            (28), (43) are inconsistent by sub-proof #745.
% 229.26/40.75  | | | 
% 229.26/40.75  | | Case 2:
% 229.26/40.75  | | | 
% 229.26/40.75  | | |   (44)  all_57_12 = e0 & op(e0, e3) = e0
% 229.26/40.75  | | | 
% 229.26/40.75  | | | REF_CLOSE: (7), (16), (44) are inconsistent by sub-proof #2185.
% 229.26/40.75  | | | 
% 229.26/40.75  | | End of split
% 229.26/40.75  | | 
% 229.26/40.75  | End of split
% 229.26/40.75  | 
% 229.26/40.75  End of proof
% 229.26/40.75  
% 229.26/40.75  Sub-proof #745 shows that the following formulas are inconsistent:
% 229.26/40.75  ----------------------------------------------------------------
% 229.26/40.75    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.26/40.75         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.26/40.75    (2)   ~ (e3 = e1)
% 229.26/40.75    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.26/40.75           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.26/40.75    (4)   ~ (all_6_2 = e3)
% 229.26/40.75    (5)  op(e1, e1) = all_6_2
% 229.26/40.75    (6)  all_57_3 = e0
% 229.26/40.75    (7)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 229.26/40.75         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.26/40.75    (8)   ~ (e3 = e2)
% 229.26/40.75    (9)   ~ (e3 = e0)
% 229.26/40.75    (10)  all_57_15 = e3
% 229.26/40.75    (11)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.26/40.75          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.26/40.75            e1)
% 229.26/40.75    (12)  all_57_10 = e2
% 229.26/40.75    (13)   ~ (e2 = e0)
% 229.26/40.75    (14)  all_57_2 = e3
% 229.26/40.75    (15)   ~ (e1 = e0)
% 229.26/40.75    (16)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.26/40.75          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.26/40.75    (17)  all_57_8 = e2
% 229.26/40.75    (18)  all_57_14 = e1
% 229.26/40.75    (19)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.26/40.75          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.26/40.75            e2)
% 229.26/40.75    (20)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.26/40.75              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.26/40.75                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.26/40.75                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.26/40.75    (21)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.26/40.75          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.26/40.75    (22)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.26/40.75          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.26/40.75    (23)   ~ (e2 = e1)
% 229.26/40.75  
% 229.26/40.75  Begin of proof
% 229.26/40.75  | 
% 229.26/40.75  | BETA: splitting (7) gives:
% 229.26/40.75  | 
% 229.26/40.75  | Case 1:
% 229.26/40.75  | | 
% 229.26/40.75  | |   (24)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) =
% 229.26/40.75  | |           e0)
% 229.26/40.75  | | 
% 229.26/40.75  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13),
% 229.26/40.75  | |            (14), (15), (16), (19), (20), (21), (22), (23), (24) are
% 229.26/40.75  | |            inconsistent by sub-proof #746.
% 229.26/40.75  | | 
% 229.26/40.75  | Case 2:
% 229.26/40.75  | | 
% 229.26/40.75  | |   (25)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 229.26/40.75  | |           e0)
% 229.26/40.75  | | 
% 229.26/40.75  | | BETA: splitting (25) gives:
% 229.26/40.75  | | 
% 229.26/40.75  | | Case 1:
% 229.26/40.75  | | | 
% 229.26/40.75  | | |   (26)  all_57_8 = e0 & op(e1, e1) = e0
% 229.26/40.75  | | | 
% 229.26/40.75  | | | REF_CLOSE: (13), (17), (26) are inconsistent by sub-proof #917.
% 229.26/40.75  | | | 
% 229.26/40.75  | | Case 2:
% 229.26/40.75  | | | 
% 229.26/40.75  | | |   (27)  all_57_14 = e0 & op(e0, e1) = e0
% 229.26/40.75  | | | 
% 229.26/40.75  | | | REF_CLOSE: (15), (18), (27) are inconsistent by sub-proof #2181.
% 229.26/40.75  | | | 
% 229.26/40.75  | | End of split
% 229.26/40.75  | | 
% 229.26/40.75  | End of split
% 229.26/40.75  | 
% 229.26/40.75  End of proof
% 229.26/40.75  
% 229.26/40.75  Sub-proof #746 shows that the following formulas are inconsistent:
% 229.26/40.75  ----------------------------------------------------------------
% 229.26/40.75    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.26/40.75         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.26/40.75    (2)   ~ (e3 = e1)
% 229.26/40.75    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.26/40.75           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.26/40.75    (4)   ~ (all_6_2 = e3)
% 229.26/40.75    (5)  op(e1, e1) = all_6_2
% 229.26/40.75    (6)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0)
% 229.26/40.75    (7)  all_57_3 = e0
% 229.26/40.75    (8)   ~ (e3 = e2)
% 229.26/40.75    (9)   ~ (e3 = e0)
% 229.26/40.75    (10)  all_57_15 = e3
% 229.26/40.75    (11)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.26/40.75          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.26/40.75            e1)
% 229.26/40.75    (12)  all_57_10 = e2
% 229.26/40.75    (13)   ~ (e2 = e0)
% 229.26/40.75    (14)  all_57_2 = e3
% 229.26/40.75    (15)   ~ (e1 = e0)
% 229.26/40.75    (16)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.26/40.75          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.26/40.75    (17)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.26/40.75          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.26/40.75            e2)
% 229.26/40.75    (18)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.26/40.75              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.26/40.75                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.26/40.75                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.26/40.75    (19)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.26/40.75          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.26/40.75    (20)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.26/40.75          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.26/40.75    (21)   ~ (e2 = e1)
% 229.26/40.75  
% 229.26/40.75  Begin of proof
% 229.26/40.75  | 
% 229.26/40.75  | BETA: splitting (6) gives:
% 229.26/40.75  | 
% 229.26/40.75  | Case 1:
% 229.26/40.75  | | 
% 229.26/40.75  | |   (22)  all_57_4 = e0 & op(e3, e1) = e0
% 229.26/40.75  | | 
% 229.26/40.75  | | ALPHA: (22) implies:
% 229.26/40.75  | |   (23)  all_57_4 = e0
% 229.26/40.75  | | 
% 229.26/40.75  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 229.26/40.75  | |            (14), (15), (16), (17), (18), (19), (20), (21), (23) are
% 229.26/40.75  | |            inconsistent by sub-proof #747.
% 229.26/40.75  | | 
% 229.26/40.75  | Case 2:
% 229.26/40.75  | | 
% 229.26/40.75  | |   (24)  all_57_5 = e0 & op(e2, e1) = e0
% 229.26/40.75  | | 
% 229.26/40.75  | | ALPHA: (24) implies:
% 229.26/40.75  | |   (25)  all_57_5 = e0
% 229.26/40.75  | | 
% 229.26/40.75  | | REF_CLOSE: (1), (2), (7), (12), (14), (15), (21), (25) are inconsistent by
% 229.26/40.75  | |            sub-proof #2359.
% 229.26/40.75  | | 
% 229.26/40.75  | End of split
% 229.26/40.75  | 
% 229.26/40.75  End of proof
% 229.26/40.75  
% 229.26/40.75  Sub-proof #747 shows that the following formulas are inconsistent:
% 229.26/40.75  ----------------------------------------------------------------
% 229.26/40.75    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.26/40.75         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.26/40.75    (2)   ~ (e3 = e1)
% 229.26/40.75    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.26/40.75           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.26/40.75    (4)   ~ (all_6_2 = e3)
% 229.26/40.75    (5)  op(e1, e1) = all_6_2
% 229.26/40.75    (6)  all_57_4 = e0
% 229.26/40.75    (7)  all_57_3 = e0
% 229.26/40.75    (8)   ~ (e3 = e2)
% 229.26/40.75    (9)   ~ (e3 = e0)
% 229.26/40.75    (10)  all_57_15 = e3
% 229.26/40.75    (11)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.26/40.75          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.26/40.75            e1)
% 229.26/40.75    (12)  all_57_10 = e2
% 229.26/40.75    (13)   ~ (e2 = e0)
% 229.26/40.75    (14)  all_57_2 = e3
% 229.26/40.75    (15)   ~ (e1 = e0)
% 229.26/40.75    (16)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.26/40.75          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.26/40.75    (17)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.26/40.75          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.26/40.75            e2)
% 229.26/40.75    (18)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.26/40.75              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.26/40.75                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.26/40.75                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.26/40.75    (19)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.26/40.75          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.26/40.75    (20)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.26/40.75          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.26/40.75    (21)   ~ (e2 = e1)
% 229.26/40.75  
% 229.26/40.75  Begin of proof
% 229.26/40.75  | 
% 229.26/40.75  | BETA: splitting (16) gives:
% 229.26/40.75  | 
% 229.26/40.75  | Case 1:
% 229.26/40.75  | | 
% 229.26/40.75  | |   (22)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) =
% 229.26/40.75  | |           e3)
% 229.26/40.75  | | 
% 229.26/40.75  | | REF_CLOSE: (1), (2), (6), (7), (8), (9), (12), (13), (14), (15), (19), (20),
% 229.26/40.75  | |            (21), (22) are inconsistent by sub-proof #748.
% 229.26/40.75  | | 
% 229.26/40.75  | Case 2:
% 229.26/40.75  | | 
% 229.26/40.75  | |   (23)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) =
% 229.26/40.75  | |           e3)
% 229.26/40.75  | | 
% 229.26/40.75  | | REF_CLOSE: (2), (3), (4), (5), (8), (9), (10), (11), (13), (15), (17), (18),
% 229.26/40.75  | |            (21), (23) are inconsistent by sub-proof #1794.
% 229.26/40.75  | | 
% 229.26/40.75  | End of split
% 229.26/40.75  | 
% 229.26/40.75  End of proof
% 229.26/40.75  
% 229.26/40.75  Sub-proof #748 shows that the following formulas are inconsistent:
% 229.26/40.75  ----------------------------------------------------------------
% 229.26/40.75    (1)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3)
% 229.26/40.75    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.26/40.75         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.26/40.75    (3)   ~ (e3 = e1)
% 229.26/40.75    (4)  all_57_4 = e0
% 229.26/40.75    (5)  all_57_3 = e0
% 229.26/40.75    (6)   ~ (e3 = e2)
% 229.26/40.75    (7)   ~ (e3 = e0)
% 229.26/40.75    (8)  all_57_10 = e2
% 229.26/40.75    (9)   ~ (e2 = e0)
% 229.26/40.75    (10)  all_57_2 = e3
% 229.26/40.75    (11)   ~ (e1 = e0)
% 229.26/40.75    (12)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.26/40.75          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.26/40.75    (13)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.26/40.75          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.26/40.75    (14)   ~ (e2 = e1)
% 229.26/40.75  
% 229.26/40.75  Begin of proof
% 229.26/40.75  | 
% 229.26/40.75  | BETA: splitting (1) gives:
% 229.26/40.75  | 
% 229.26/40.75  | Case 1:
% 229.26/40.75  | | 
% 229.26/40.75  | |   (15)  all_57_4 = e3 & op(e3, e1) = e3
% 229.26/40.75  | | 
% 229.26/40.75  | | ALPHA: (15) implies:
% 229.26/40.75  | |   (16)  all_57_4 = e3
% 229.26/40.75  | | 
% 229.26/40.75  | | COMBINE_EQS: (4), (16) imply:
% 229.26/40.75  | |   (17)  e3 = e0
% 229.26/40.75  | | 
% 229.26/40.75  | | REF_CLOSE: (2), (3), (5), (6), (7), (9), (10), (11), (12), (13), (14), (17)
% 229.26/40.75  | |            are inconsistent by sub-proof #1333.
% 229.26/40.75  | | 
% 229.26/40.75  | Case 2:
% 229.26/40.75  | | 
% 229.26/40.75  | |   (18)  all_57_5 = e3 & op(e2, e1) = e3
% 229.26/40.75  | | 
% 229.26/40.75  | | ALPHA: (18) implies:
% 229.26/40.75  | |   (19)  all_57_5 = e3
% 229.26/40.75  | | 
% 229.26/40.75  | | REF_CLOSE: (2), (3), (5), (8), (10), (11), (14), (19) are inconsistent by
% 229.26/40.75  | |            sub-proof #1804.
% 229.26/40.75  | | 
% 229.26/40.75  | End of split
% 229.26/40.75  | 
% 229.26/40.75  End of proof
% 229.26/40.75  
% 229.26/40.75  Sub-proof #749 shows that the following formulas are inconsistent:
% 229.26/40.75  ----------------------------------------------------------------
% 229.26/40.75    (1)   ~ (e3 = e1)
% 229.26/40.75    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.26/40.75           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.26/40.75    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1)
% 229.26/40.75    (4)  op(e3, e3) = e2
% 229.26/40.75    (5)  all_57_2 = e3
% 229.26/40.75    (6)   ~ (e2 = e1)
% 229.26/40.75  
% 229.26/40.75  Begin of proof
% 229.26/40.75  | 
% 229.26/40.75  | BETA: splitting (3) gives:
% 229.26/40.75  | 
% 229.26/40.75  | Case 1:
% 229.26/40.75  | | 
% 229.26/40.75  | |   (7)  all_57_0 = e1 & op(e3, e3) = e1
% 229.26/40.75  | | 
% 229.26/40.75  | | ALPHA: (7) implies:
% 229.26/40.75  | |   (8)  op(e3, e3) = e1
% 229.26/40.75  | | 
% 229.26/40.75  | | REF_CLOSE: (2), (4), (6), (8) are inconsistent by sub-proof #1950.
% 229.26/40.75  | | 
% 229.26/40.75  | Case 2:
% 229.26/40.75  | | 
% 229.26/40.75  | |   (9)  all_57_2 = e1 & op(e2, e3) = e1
% 229.26/40.75  | | 
% 229.26/40.75  | | ALPHA: (9) implies:
% 229.26/40.75  | |   (10)  all_57_2 = e1
% 229.26/40.75  | | 
% 229.26/40.75  | | REF_CLOSE: (1), (5), (10) are inconsistent by sub-proof #2397.
% 229.26/40.75  | | 
% 229.26/40.75  | End of split
% 229.26/40.75  | 
% 229.26/40.75  End of proof
% 229.26/40.75  
% 229.26/40.75  Sub-proof #750 shows that the following formulas are inconsistent:
% 229.26/40.75  ----------------------------------------------------------------
% 229.26/40.75    (1)  op(e1, e0) = e2
% 229.26/40.75    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.26/40.75         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.26/40.75    (3)   ~ (e3 = e1)
% 229.26/40.75    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.26/40.75           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.26/40.75    (5)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.26/40.75         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.26/40.75    (6)   ~ (all_6_2 = e3)
% 229.26/40.75    (7)  op(e1, e1) = all_6_2
% 229.26/40.75    (8)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) = all_22_1
% 229.26/40.75           & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0, e3) =
% 229.26/40.75           all_22_1 & $i(all_22_1))
% 229.26/40.75    (9)  all_57_12 = e2
% 229.26/40.75    (10)   ~ (e3 = e2)
% 229.26/40.75    (11)   ~ (e3 = e0)
% 229.26/40.75    (12)  all_57_15 = e3
% 229.26/40.75    (13)  op(e3, e3) = e2
% 229.26/40.75    (14)  all_57_10 = e2
% 229.26/40.75    (15)  all_57_11 = e2
% 229.26/40.75    (16)   ~ (e2 = e0)
% 229.26/40.75    (17)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 229.26/40.75            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 229.26/40.75              e3) = all_12_1 & $i(all_12_1))
% 229.26/40.75    (18)  all_57_2 = e3
% 229.26/40.75    (19)   ~ (e1 = e0)
% 229.26/40.75    (20)  op(e0, e0) = e3
% 229.26/40.75    (21)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.26/40.75              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.26/40.75                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.26/40.75                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.26/40.75    (22)  op(e1, e1) = e2
% 229.26/40.75    (23)  all_57_7 = e3
% 229.26/40.75    (24)   ~ (e2 = e1)
% 229.26/40.75    (25)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.26/40.75          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.26/40.75    (26)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.26/40.75          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.26/40.75    (27)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.26/40.75          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.26/40.75    (28)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 229.26/40.75          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 229.26/40.75  
% 229.26/40.75  Begin of proof
% 229.26/40.75  | 
% 229.26/40.75  | BETA: splitting (26) gives:
% 229.26/40.75  | 
% 229.26/40.75  | Case 1:
% 229.26/40.75  | | 
% 229.26/40.75  | |   (29)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) =
% 229.26/40.75  | |           e0)
% 229.26/40.75  | | 
% 229.26/40.75  | | BETA: splitting (29) gives:
% 229.26/40.75  | | 
% 229.26/40.75  | | Case 1:
% 229.26/40.75  | | | 
% 229.26/40.75  | | |   (30)  all_57_0 = e0 & op(e3, e3) = e0
% 229.26/40.75  | | | 
% 229.26/40.75  | | | ALPHA: (30) implies:
% 229.26/40.75  | | |   (31)  op(e3, e3) = e0
% 229.26/40.75  | | | 
% 229.26/40.75  | | | REF_CLOSE: (4), (13), (16), (31) are inconsistent by sub-proof #2403.
% 229.26/40.75  | | | 
% 229.26/40.75  | | Case 2:
% 229.26/40.75  | | | 
% 229.26/40.75  | | |   (32)  all_57_2 = e0 & op(e2, e3) = e0
% 229.26/40.75  | | | 
% 229.26/40.75  | | | ALPHA: (32) implies:
% 229.26/40.75  | | |   (33)  all_57_2 = e0
% 229.26/40.75  | | | 
% 229.26/40.75  | | | COMBINE_EQS: (18), (33) imply:
% 229.26/40.75  | | |   (34)  e3 = e0
% 229.26/40.75  | | | 
% 229.26/40.75  | | | COMBINE_EQS: (23), (34) imply:
% 229.26/40.75  | | |   (35)  all_57_7 = e0
% 229.26/40.75  | | | 
% 229.26/40.75  | | | REF_CLOSE: (3), (4), (5), (6), (7), (10), (11), (12), (15), (16), (19),
% 229.26/40.75  | | |            (21), (22), (24), (25), (27), (28), (35) are inconsistent by
% 229.26/40.75  | | |            sub-proof #1154.
% 229.26/40.75  | | | 
% 229.26/40.75  | | End of split
% 229.26/40.75  | | 
% 229.26/40.75  | Case 2:
% 229.26/40.75  | | 
% 229.26/40.75  | |   (36)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) =
% 229.26/40.75  | |           e0)
% 229.26/40.75  | | 
% 229.26/40.75  | | BETA: splitting (36) gives:
% 229.26/40.75  | | 
% 229.26/40.75  | | Case 1:
% 229.26/40.75  | | | 
% 229.26/40.75  | | |   (37)  all_57_6 = e0 & op(e1, e3) = e0
% 229.26/40.75  | | | 
% 229.26/40.75  | | | ALPHA: (37) implies:
% 229.26/40.75  | | |   (38)  all_57_6 = e0
% 229.26/40.75  | | | 
% 229.26/40.75  | | | REF_CLOSE: (1), (2), (3), (4), (8), (13), (17), (18), (19), (24), (38) are
% 229.26/40.75  | | |            inconsistent by sub-proof #752.
% 229.26/40.75  | | | 
% 229.26/40.75  | | Case 2:
% 229.26/40.75  | | | 
% 229.26/40.75  | | |   (39)  all_57_12 = e0 & op(e0, e3) = e0
% 229.26/40.75  | | | 
% 229.26/40.75  | | | ALPHA: (39) implies:
% 229.26/40.75  | | |   (40)  all_57_12 = e0
% 229.26/40.75  | | | 
% 229.26/40.75  | | | COMBINE_EQS: (9), (40) imply:
% 229.26/40.75  | | |   (41)  e2 = e0
% 229.26/40.75  | | | 
% 229.26/40.75  | | | REF_CLOSE: (3), (4), (10), (12), (14), (15), (16), (19), (20), (24), (25),
% 229.26/40.75  | | |            (27), (41) are inconsistent by sub-proof #751.
% 229.26/40.75  | | | 
% 229.26/40.75  | | End of split
% 229.26/40.75  | | 
% 229.26/40.75  | End of split
% 229.26/40.75  | 
% 229.26/40.75  End of proof
% 229.26/40.75  
% 229.26/40.75  Sub-proof #751 shows that the following formulas are inconsistent:
% 229.26/40.75  ----------------------------------------------------------------
% 229.26/40.75    (1)   ~ (e3 = e1)
% 229.26/40.75    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.26/40.75           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.26/40.75    (3)   ~ (e3 = e2)
% 229.26/40.75    (4)  all_57_15 = e3
% 229.26/40.75    (5)  all_57_10 = e2
% 229.26/40.75    (6)  all_57_11 = e2
% 229.26/40.75    (7)   ~ (e2 = e0)
% 229.26/40.75    (8)  e2 = e0
% 229.26/40.75    (9)   ~ (e1 = e0)
% 229.26/40.75    (10)  op(e0, e0) = e3
% 229.26/40.75    (11)   ~ (e2 = e1)
% 229.26/40.75    (12)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.26/40.75          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.26/40.75    (13)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.26/40.75          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.26/40.75  
% 229.26/40.75  Begin of proof
% 229.26/40.75  | 
% 229.26/40.75  | COMBINE_EQS: (6), (8) imply:
% 229.26/40.75  |   (14)  all_57_11 = e0
% 229.26/40.75  | 
% 229.26/40.75  | COMBINE_EQS: (5), (8) imply:
% 229.26/40.75  |   (15)  all_57_10 = e0
% 229.26/40.75  | 
% 229.26/40.75  | REF_CLOSE: (1), (2), (3), (4), (7), (9), (10), (11), (12), (13), (14), (15)
% 229.26/40.75  |            are inconsistent by sub-proof #1087.
% 229.26/40.75  | 
% 229.26/40.75  End of proof
% 229.26/40.75  
% 229.26/40.75  Sub-proof #752 shows that the following formulas are inconsistent:
% 229.26/40.75  ----------------------------------------------------------------
% 229.26/40.75    (1)  op(e1, e0) = e2
% 229.26/40.75    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.26/40.75         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.26/40.75    (3)   ~ (e3 = e1)
% 229.26/40.75    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.26/40.75           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.26/40.75    (5)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) = all_22_1
% 229.26/40.75           & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0, e3) =
% 229.26/40.75           all_22_1 & $i(all_22_1))
% 229.26/40.75    (6)  all_57_6 = e0
% 229.26/40.75    (7)  op(e3, e3) = e2
% 229.26/40.75    (8)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) = all_12_1
% 229.26/40.75           & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0, e3) =
% 229.26/40.75           all_12_1 & $i(all_12_1))
% 229.26/40.75    (9)  all_57_2 = e3
% 229.26/40.75    (10)   ~ (e1 = e0)
% 229.26/40.75    (11)   ~ (e2 = e1)
% 229.26/40.75  
% 229.26/40.75  Begin of proof
% 229.26/40.75  | 
% 229.26/40.75  | BETA: splitting (2) gives:
% 229.26/40.75  | 
% 229.26/40.75  | Case 1:
% 229.26/40.75  | | 
% 229.26/40.75  | |   (12)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) =
% 229.26/40.75  | |           e1)
% 229.26/40.75  | | 
% 229.26/40.75  | | REF_CLOSE: (3), (4), (7), (9), (11), (12) are inconsistent by sub-proof
% 229.26/40.75  | |            #753.
% 229.26/40.75  | | 
% 229.26/40.75  | Case 2:
% 229.26/40.75  | | 
% 229.26/40.75  | |   (13)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) =
% 229.26/40.75  | |           e1)
% 229.26/40.75  | | 
% 229.26/40.75  | | REF_CLOSE: (1), (4), (5), (6), (8), (10), (13) are inconsistent by sub-proof
% 229.26/40.75  | |            #1118.
% 229.26/40.75  | | 
% 229.26/40.75  | End of split
% 229.26/40.75  | 
% 229.26/40.75  End of proof
% 229.26/40.75  
% 229.26/40.75  Sub-proof #753 shows that the following formulas are inconsistent:
% 229.26/40.75  ----------------------------------------------------------------
% 229.26/40.75    (1)   ~ (e3 = e1)
% 229.26/40.76    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.26/40.76           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.26/40.76    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1)
% 229.26/40.76    (4)  op(e3, e3) = e2
% 229.26/40.76    (5)  all_57_2 = e3
% 229.26/40.76    (6)   ~ (e2 = e1)
% 229.26/40.76  
% 229.26/40.76  Begin of proof
% 229.26/40.76  | 
% 229.26/40.76  | BETA: splitting (3) gives:
% 229.26/40.76  | 
% 229.26/40.76  | Case 1:
% 229.26/40.76  | | 
% 229.26/40.76  | |   (7)  all_57_0 = e1 & op(e3, e3) = e1
% 229.26/40.76  | | 
% 229.26/40.76  | | ALPHA: (7) implies:
% 229.26/40.76  | |   (8)  op(e3, e3) = e1
% 229.26/40.76  | | 
% 229.26/40.76  | | REF_CLOSE: (2), (4), (6), (8) are inconsistent by sub-proof #1950.
% 229.26/40.76  | | 
% 229.26/40.76  | Case 2:
% 229.26/40.76  | | 
% 229.26/40.76  | |   (9)  all_57_2 = e1 & op(e2, e3) = e1
% 229.26/40.76  | | 
% 229.26/40.76  | | REF_CLOSE: (1), (5), (9) are inconsistent by sub-proof #1928.
% 229.26/40.76  | | 
% 229.26/40.76  | End of split
% 229.26/40.76  | 
% 229.26/40.76  End of proof
% 229.26/40.76  
% 229.26/40.76  Sub-proof #754 shows that the following formulas are inconsistent:
% 229.26/40.76  ----------------------------------------------------------------
% 229.26/40.76    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.26/40.76         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.26/40.76    (2)   ~ (e3 = e1)
% 229.26/40.76    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.26/40.76           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.26/40.76    (4)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.26/40.76         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.26/40.76    (5)   ~ (all_6_2 = e3)
% 229.26/40.76    (6)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2)
% 229.26/40.76    (7)  op(e1, e1) = all_6_2
% 229.26/40.76    (8)  op(e2, e2) = e1
% 229.26/40.76    (9)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.26/40.76         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.26/40.76    (10)  all_57_6 = e1
% 229.26/40.76    (11)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.26/40.76          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.26/40.76    (12)   ~ (e3 = e2)
% 229.26/40.76    (13)   ~ (e3 = e0)
% 229.26/40.76    (14)  all_57_15 = e3
% 229.26/40.76    (15)  op(e3, e3) = e2
% 229.26/40.76    (16)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.26/40.76          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.26/40.76    (17)   ~ (e2 = e0)
% 229.26/40.76    (18)  all_57_13 = e2
% 229.26/40.76    (19)  all_57_3 = e1
% 229.26/40.76    (20)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.26/40.76          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.26/40.76    (21)   ~ (e1 = e0)
% 229.26/40.76    (22)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.26/40.76              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.26/40.76                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.26/40.76                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.26/40.76    (23)   ~ (all_53_12 = e3)
% 229.26/40.76    (24)  all_57_7 = e3
% 229.26/40.76    (25)   ~ (e2 = e1)
% 229.26/40.76    (26)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.26/40.76          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.26/40.76    (27)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.26/40.76          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.26/40.76    (28)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.26/40.76          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.26/40.76    (29)  op(e3, e0) = all_53_12
% 229.26/40.76  
% 229.26/40.76  Begin of proof
% 229.26/40.76  | 
% 229.26/40.76  | BETA: splitting (6) gives:
% 229.26/40.76  | 
% 229.26/40.76  | Case 1:
% 229.26/40.76  | | 
% 229.26/40.76  | |   (30)  all_57_6 = e2 & op(e1, e3) = e2
% 229.26/40.76  | | 
% 229.26/40.76  | | ALPHA: (30) implies:
% 229.26/40.76  | |   (31)  all_57_6 = e2
% 229.26/40.76  | | 
% 229.26/40.76  | | COMBINE_EQS: (10), (31) imply:
% 229.26/40.76  | |   (32)  e2 = e1
% 229.26/40.76  | | 
% 229.26/40.76  | | SIMP: (32) implies:
% 229.26/40.76  | |   (33)  e2 = e1
% 229.26/40.76  | | 
% 229.26/40.76  | | COMBINE_EQS: (18), (33) imply:
% 229.26/40.76  | |   (34)  all_57_13 = e1
% 229.26/40.76  | | 
% 229.26/40.76  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 229.26/40.76  | |            (14), (15), (16), (17), (19), (20), (21), (22), (23), (24), (25),
% 229.26/40.76  | |            (26), (27), (28), (29), (34) are inconsistent by sub-proof #798.
% 229.26/40.76  | | 
% 229.26/40.76  | Case 2:
% 229.26/40.76  | | 
% 229.26/40.76  | |   (35)  all_57_7 = e2 & op(e1, e2) = e2
% 229.26/40.76  | | 
% 229.26/40.76  | | REF_CLOSE: (12), (24), (35) are inconsistent by sub-proof #2092.
% 229.26/40.76  | | 
% 229.26/40.76  | End of split
% 229.26/40.76  | 
% 229.26/40.76  End of proof
% 229.26/40.76  
% 229.26/40.76  Sub-proof #755 shows that the following formulas are inconsistent:
% 229.26/40.76  ----------------------------------------------------------------
% 229.26/40.76    (1)   ~ (e3 = e1)
% 229.26/40.76    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.26/40.76           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.26/40.76    (3)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.26/40.76         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.26/40.76    (4)   ~ (all_6_2 = e3)
% 229.26/40.76    (5)  op(e1, e1) = all_6_2
% 229.26/40.76    (6)  all_57_6 = e1
% 229.26/40.76    (7)   ~ (e3 = e2)
% 229.26/40.76    (8)   ~ (e3 = e0)
% 229.26/40.76    (9)  all_57_15 = e3
% 229.26/40.76    (10)   ~ (e2 = e0)
% 229.26/40.76    (11)   ~ (e1 = e0)
% 229.26/40.76    (12)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.26/40.76              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.26/40.76                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.26/40.76                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.26/40.76    (13)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0)
% 229.26/40.76    (14)   ~ (e2 = e1)
% 229.26/40.76    (15)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.26/40.76          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.26/40.76    (16)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.26/40.76          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.26/40.76  
% 229.26/40.76  Begin of proof
% 229.26/40.76  | 
% 229.26/40.76  | BETA: splitting (13) gives:
% 229.26/40.76  | 
% 229.26/40.76  | Case 1:
% 229.26/40.76  | | 
% 229.26/40.76  | |   (17)  all_57_6 = e0 & op(e1, e3) = e0
% 229.26/40.76  | | 
% 229.26/40.76  | | REF_CLOSE: (6), (11), (17) are inconsistent by sub-proof #2347.
% 229.26/40.76  | | 
% 229.26/40.76  | Case 2:
% 229.26/40.76  | | 
% 229.26/40.76  | |   (18)  all_57_7 = e0 & op(e1, e2) = e0
% 229.26/40.76  | | 
% 229.26/40.76  | | ALPHA: (18) implies:
% 229.26/40.76  | |   (19)  all_57_7 = e0
% 229.26/40.76  | | 
% 229.26/40.76  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 229.26/40.76  | |            (14), (15), (16), (19) are inconsistent by sub-proof #1735.
% 229.26/40.76  | | 
% 229.26/40.76  | End of split
% 229.26/40.76  | 
% 229.26/40.76  End of proof
% 229.26/40.76  
% 229.26/40.76  Sub-proof #756 shows that the following formulas are inconsistent:
% 229.26/40.76  ----------------------------------------------------------------
% 229.26/40.76    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.26/40.76         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.26/40.76    (2)   ~ (e3 = e1)
% 229.26/40.76    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.26/40.76           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.26/40.76    (4)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.26/40.76         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.26/40.76    (5)   ~ (all_6_2 = e3)
% 229.26/40.76    (6)  op(e1, e1) = all_6_2
% 229.26/40.76    (7)  op(e2, e2) = e1
% 229.26/40.76    (8)  all_57_7 = e2
% 229.26/40.76    (9)  all_57_12 = e2
% 229.26/40.76    (10)  all_57_6 = e1
% 229.26/40.76    (11)   ~ (e3 = e2)
% 229.26/40.76    (12)   ~ (e3 = e0)
% 229.26/40.76    (13)  all_57_15 = e3
% 229.26/40.76    (14)  op(e3, e3) = e2
% 229.26/40.76    (15)  all_57_4 = e1
% 229.26/40.76    (16)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.26/40.76          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.26/40.76    (17)   ~ (e2 = e0)
% 229.33/40.76    (18)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.33/40.76          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.33/40.76    (19)   ~ (e1 = e0)
% 229.33/40.76    (20)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.33/40.76          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.33/40.76    (21)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.33/40.76              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.33/40.76                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.33/40.76                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.33/40.76    (22)   ~ (all_53_12 = e3)
% 229.33/40.76    (23)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.33/40.76          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.33/40.76    (24)  all_57_1 = e3
% 229.33/40.76    (25)   ~ (e2 = e1)
% 229.33/40.76    (26)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.33/40.76          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.33/40.76    (27)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.33/40.76          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.33/40.76    (28)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.33/40.76          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.33/40.76    (29)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.33/40.76          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.33/40.76    (30)  op(e3, e0) = all_53_12
% 229.33/40.76  
% 229.33/40.76  Begin of proof
% 229.33/40.76  | 
% 229.33/40.76  | BETA: splitting (23) gives:
% 229.33/40.76  | 
% 229.33/40.76  | Case 1:
% 229.33/40.76  | | 
% 229.33/40.76  | |   (31)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) =
% 229.33/40.76  | |           e3)
% 229.33/40.76  | | 
% 229.33/40.76  | | BETA: splitting (31) gives:
% 229.33/40.76  | | 
% 229.33/40.76  | | Case 1:
% 229.33/40.76  | | | 
% 229.33/40.76  | | |   (32)  all_57_0 = e3 & op(e3, e3) = e3
% 229.33/40.76  | | | 
% 229.33/40.76  | | | ALPHA: (32) implies:
% 229.33/40.76  | | |   (33)  op(e3, e3) = e3
% 229.33/40.76  | | | 
% 229.33/40.76  | | | REF_CLOSE: (3), (11), (14), (33) are inconsistent by sub-proof #2490.
% 229.33/40.76  | | | 
% 229.33/40.76  | | Case 2:
% 229.33/40.76  | | | 
% 229.33/40.76  | | |   (34)  all_57_2 = e3 & op(e2, e3) = e3
% 229.33/40.76  | | | 
% 229.33/40.76  | | | ALPHA: (34) implies:
% 229.33/40.76  | | |   (35)  all_57_2 = e3
% 229.33/40.76  | | | 
% 229.33/40.76  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 229.33/40.76  | | |            (13), (14), (16), (17), (19), (21), (24), (25), (26), (27),
% 229.33/40.76  | | |            (28), (29), (35) are inconsistent by sub-proof #757.
% 229.33/40.76  | | | 
% 229.33/40.76  | | End of split
% 229.33/40.76  | | 
% 229.33/40.76  | Case 2:
% 229.33/40.76  | | 
% 229.33/40.76  | |   (36)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) =
% 229.33/40.76  | |           e3)
% 229.33/40.76  | | 
% 229.33/40.76  | | BETA: splitting (36) gives:
% 229.33/40.76  | | 
% 229.33/40.76  | | Case 1:
% 229.33/40.76  | | | 
% 229.33/40.76  | | |   (37)  all_57_6 = e3 & op(e1, e3) = e3
% 229.33/40.76  | | | 
% 229.33/40.76  | | | ALPHA: (37) implies:
% 229.33/40.76  | | |   (38)  all_57_6 = e3
% 229.33/40.76  | | | 
% 229.33/40.76  | | | REF_CLOSE: (1), (2), (3), (7), (10), (11), (12), (16), (17), (19), (20),
% 229.33/40.76  | | |            (24), (25), (38) are inconsistent by sub-proof #1548.
% 229.33/40.76  | | | 
% 229.33/40.76  | | Case 2:
% 229.33/40.76  | | | 
% 229.33/40.76  | | |   (39)  all_57_12 = e3 & op(e0, e3) = e3
% 229.33/40.76  | | | 
% 229.33/40.76  | | | ALPHA: (39) implies:
% 229.33/40.76  | | |   (40)  all_57_12 = e3
% 229.33/40.76  | | | 
% 229.33/40.76  | | | COMBINE_EQS: (9), (40) imply:
% 229.33/40.76  | | |   (41)  e3 = e2
% 229.33/40.76  | | | 
% 229.33/40.76  | | | SIMP: (41) implies:
% 229.33/40.76  | | |   (42)  e3 = e2
% 229.33/40.76  | | | 
% 229.33/40.76  | | | COMBINE_EQS: (24), (42) imply:
% 229.33/40.76  | | |   (43)  all_57_1 = e2
% 229.33/40.76  | | | 
% 229.33/40.76  | | | REF_CLOSE: (2), (3), (11), (14), (15), (18), (22), (30), (43) are
% 229.33/40.76  | | |            inconsistent by sub-proof #1308.
% 229.33/40.76  | | | 
% 229.33/40.76  | | End of split
% 229.33/40.76  | | 
% 229.33/40.76  | End of split
% 229.33/40.76  | 
% 229.33/40.76  End of proof
% 229.33/40.76  
% 229.33/40.76  Sub-proof #757 shows that the following formulas are inconsistent:
% 229.33/40.76  ----------------------------------------------------------------
% 229.33/40.76    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.33/40.76         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.33/40.76    (2)   ~ (e3 = e1)
% 229.33/40.76    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.33/40.76           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.33/40.76    (4)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.33/40.76         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.33/40.76    (5)   ~ (all_6_2 = e3)
% 229.33/40.76    (6)  op(e1, e1) = all_6_2
% 229.33/40.76    (7)  op(e2, e2) = e1
% 229.33/40.76    (8)  all_57_7 = e2
% 229.33/40.76    (9)  all_57_12 = e2
% 229.33/40.76    (10)  all_57_6 = e1
% 229.33/40.76    (11)   ~ (e3 = e2)
% 229.33/40.76    (12)   ~ (e3 = e0)
% 229.33/40.76    (13)  all_57_15 = e3
% 229.33/40.76    (14)  op(e3, e3) = e2
% 229.33/40.76    (15)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.33/40.76          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.33/40.76    (16)   ~ (e2 = e0)
% 229.33/40.76    (17)  all_57_2 = e3
% 229.33/40.76    (18)   ~ (e1 = e0)
% 229.33/40.76    (19)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.33/40.76              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.33/40.76                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.33/40.76                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.33/40.76    (20)  all_57_1 = e3
% 229.33/40.76    (21)   ~ (e2 = e1)
% 229.33/40.76    (22)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.33/40.76          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.33/40.76    (23)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.33/40.76          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.33/40.76    (24)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.33/40.76          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.33/40.76    (25)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.33/40.76          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.33/40.76  
% 229.33/40.76  Begin of proof
% 229.33/40.76  | 
% 229.33/40.76  | BETA: splitting (23) gives:
% 229.33/40.76  | 
% 229.33/40.76  | Case 1:
% 229.33/40.76  | | 
% 229.33/40.76  | |   (26)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) =
% 229.33/40.76  | |           e0)
% 229.33/40.76  | | 
% 229.33/40.76  | | REF_CLOSE: (3), (12), (14), (16), (17), (26) are inconsistent by sub-proof
% 229.33/40.76  | |            #758.
% 229.33/40.76  | | 
% 229.33/40.76  | Case 2:
% 229.33/40.76  | | 
% 229.33/40.76  | |   (27)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) =
% 229.33/40.76  | |           e0)
% 229.33/40.76  | | 
% 229.33/40.76  | | BETA: splitting (27) gives:
% 229.33/40.76  | | 
% 229.33/40.76  | | Case 1:
% 229.33/40.76  | | | 
% 229.33/40.76  | | |   (28)  all_57_6 = e0 & op(e1, e3) = e0
% 229.33/40.76  | | | 
% 229.33/40.76  | | | ALPHA: (28) implies:
% 229.33/40.76  | | |   (29)  all_57_6 = e0
% 229.33/40.76  | | | 
% 229.33/40.76  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (11), (12), (13), (15),
% 229.33/40.76  | | |            (16), (18), (19), (20), (21), (22), (24), (25), (29) are
% 229.33/40.76  | | |            inconsistent by sub-proof #1773.
% 229.33/40.76  | | | 
% 229.33/40.76  | | Case 2:
% 229.33/40.76  | | | 
% 229.33/40.76  | | |   (30)  all_57_12 = e0 & op(e0, e3) = e0
% 229.33/40.76  | | | 
% 229.33/40.76  | | | ALPHA: (30) implies:
% 229.33/40.76  | | |   (31)  all_57_12 = e0
% 229.33/40.76  | | | 
% 229.33/40.76  | | | COMBINE_EQS: (9), (31) imply:
% 229.33/40.76  | | |   (32)  e2 = e0
% 229.33/40.76  | | | 
% 229.33/40.76  | | | COMBINE_EQS: (8), (32) imply:
% 229.33/40.76  | | |   (33)  all_57_7 = e0
% 229.33/40.76  | | | 
% 229.33/40.76  | | | REF_CLOSE: (2), (3), (4), (5), (6), (10), (11), (12), (13), (16), (18),
% 229.33/40.76  | | |            (19), (21), (22), (24), (33) are inconsistent by sub-proof
% 229.33/40.76  | | |            #1735.
% 229.33/40.76  | | | 
% 229.33/40.76  | | End of split
% 229.33/40.76  | | 
% 229.33/40.76  | End of split
% 229.33/40.76  | 
% 229.33/40.76  End of proof
% 229.33/40.76  
% 229.33/40.76  Sub-proof #758 shows that the following formulas are inconsistent:
% 229.33/40.76  ----------------------------------------------------------------
% 229.33/40.76    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.33/40.76           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.33/40.76    (2)   ~ (e3 = e0)
% 229.33/40.76    (3)  op(e3, e3) = e2
% 229.33/40.76    (4)   ~ (e2 = e0)
% 229.33/40.76    (5)  all_57_2 = e3
% 229.33/40.76    (6)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0)
% 229.33/40.76  
% 229.33/40.76  Begin of proof
% 229.33/40.76  | 
% 229.33/40.76  | BETA: splitting (6) gives:
% 229.33/40.76  | 
% 229.33/40.76  | Case 1:
% 229.33/40.76  | | 
% 229.33/40.76  | |   (7)  all_57_0 = e0 & op(e3, e3) = e0
% 229.33/40.76  | | 
% 229.33/40.76  | | ALPHA: (7) implies:
% 229.33/40.76  | |   (8)  op(e3, e3) = e0
% 229.33/40.76  | | 
% 229.33/40.76  | | REF_CLOSE: (1), (3), (4), (8) are inconsistent by sub-proof #2403.
% 229.33/40.76  | | 
% 229.33/40.76  | Case 2:
% 229.33/40.76  | | 
% 229.33/40.76  | |   (9)  all_57_2 = e0 & op(e2, e3) = e0
% 229.33/40.76  | | 
% 229.33/40.76  | | REF_CLOSE: (2), (5), (9) are inconsistent by sub-proof #1805.
% 229.33/40.76  | | 
% 229.33/40.76  | End of split
% 229.33/40.76  | 
% 229.33/40.76  End of proof
% 229.33/40.76  
% 229.33/40.76  Sub-proof #759 shows that the following formulas are inconsistent:
% 229.33/40.76  ----------------------------------------------------------------
% 229.33/40.76    (1)   ~ (e3 = e1)
% 229.33/40.76    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.33/40.76           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.33/40.76    (3)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.33/40.76         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.33/40.76    (4)   ~ (all_6_2 = e3)
% 229.33/40.76    (5)  op(e1, e1) = all_6_2
% 229.33/40.76    (6)  all_57_6 = e1
% 229.33/40.76    (7)   ~ (e3 = e2)
% 229.33/40.76    (8)   ~ (e3 = e0)
% 229.33/40.76    (9)  all_57_15 = e3
% 229.33/40.76    (10)  op(e3, e3) = e2
% 229.33/40.76    (11)  all_57_12 = e1
% 229.33/40.76    (12)   ~ (e2 = e0)
% 229.33/40.76    (13)   ~ (e1 = e0)
% 229.33/40.76    (14)  op(e0, e0) = e3
% 229.33/40.76    (15)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.33/40.76              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.33/40.76                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.33/40.76                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.33/40.76    (16)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.33/40.76          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.33/40.76    (17)   ~ (e2 = e1)
% 229.33/40.76    (18)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.33/40.76          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.33/40.76    (19)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.33/40.76          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.33/40.76    (20)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.33/40.76          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.33/40.76    (21)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.33/40.76          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.33/40.76  
% 229.33/40.76  Begin of proof
% 229.33/40.76  | 
% 229.33/40.76  | BETA: splitting (20) gives:
% 229.33/40.76  | 
% 229.33/40.76  | Case 1:
% 229.33/40.76  | | 
% 229.33/40.76  | |   (22)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) =
% 229.33/40.76  | |           e0)
% 229.33/40.76  | | 
% 229.33/40.76  | | BETA: splitting (22) gives:
% 229.33/40.76  | | 
% 229.33/40.76  | | Case 1:
% 229.33/40.76  | | | 
% 229.33/40.76  | | |   (23)  all_57_0 = e0 & op(e3, e3) = e0
% 229.33/40.76  | | | 
% 229.33/40.76  | | | ALPHA: (23) implies:
% 229.33/40.76  | | |   (24)  op(e3, e3) = e0
% 229.33/40.76  | | | 
% 229.33/40.76  | | | REF_CLOSE: (1), (2), (6), (7), (8), (11), (12), (16), (17), (19), (24) are
% 229.33/40.76  | | |            inconsistent by sub-proof #1205.
% 229.33/40.76  | | | 
% 229.33/40.76  | | Case 2:
% 229.33/40.76  | | | 
% 229.33/40.76  | | |   (25)  all_57_2 = e0 & op(e2, e3) = e0
% 229.33/40.76  | | | 
% 229.33/40.76  | | | ALPHA: (25) implies:
% 229.33/40.76  | | |   (26)  all_57_2 = e0
% 229.33/40.76  | | | 
% 229.33/40.76  | | | BETA: splitting (15) gives:
% 229.33/40.76  | | | 
% 229.33/40.76  | | | Case 1:
% 229.33/40.76  | | | | 
% 229.33/40.76  | | | |   (27)  all_57_15 = e0 & op(e0, e0) = e0
% 229.33/40.76  | | | | 
% 229.33/40.76  | | | | ALPHA: (27) implies:
% 229.33/40.76  | | | |   (28)  op(e0, e0) = e0
% 229.33/40.76  | | | | 
% 229.33/40.76  | | | | REF_CLOSE: (2), (8), (14), (28) are inconsistent by sub-proof #2304.
% 229.33/40.76  | | | | 
% 229.33/40.76  | | | Case 2:
% 229.33/40.76  | | | | 
% 229.33/40.76  | | | |   (29)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2,
% 229.33/40.76  | | | |               e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) &
% 229.33/40.76  | | | |         ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0,
% 229.33/40.76  | | | |               e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 229.33/40.76  | | | | 
% 229.33/40.76  | | | | ALPHA: (29) implies:
% 229.33/40.76  | | | |   (30)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0)
% 229.33/40.76  | | | |           = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 229.33/40.76  | | | | 
% 229.33/40.76  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 229.33/40.76  | | | |            (12), (13), (15), (16), (17), (18), (21), (26), (30) are
% 229.33/40.76  | | | |            inconsistent by sub-proof #760.
% 229.33/40.76  | | | | 
% 229.33/40.76  | | | End of split
% 229.33/40.76  | | | 
% 229.33/40.76  | | End of split
% 229.33/40.76  | | 
% 229.33/40.76  | Case 2:
% 229.33/40.76  | | 
% 229.33/40.76  | |   (31)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) =
% 229.33/40.76  | |           e0)
% 229.33/40.76  | | 
% 229.33/40.76  | | BETA: splitting (31) gives:
% 229.33/40.76  | | 
% 229.33/40.76  | | Case 1:
% 229.33/40.76  | | | 
% 229.33/40.76  | | |   (32)  all_57_6 = e0 & op(e1, e3) = e0
% 229.33/40.76  | | | 
% 229.33/40.76  | | | REF_CLOSE: (6), (13), (32) are inconsistent by sub-proof #2347.
% 229.33/40.76  | | | 
% 229.33/40.76  | | Case 2:
% 229.33/40.76  | | | 
% 229.33/40.76  | | |   (33)  all_57_12 = e0 & op(e0, e3) = e0
% 229.33/40.76  | | | 
% 229.33/40.76  | | | REF_CLOSE: (11), (13), (33) are inconsistent by sub-proof #1279.
% 229.33/40.76  | | | 
% 229.33/40.76  | | End of split
% 229.33/40.76  | | 
% 229.33/40.76  | End of split
% 229.33/40.76  | 
% 229.33/40.76  End of proof
% 229.33/40.76  
% 229.33/40.76  Sub-proof #760 shows that the following formulas are inconsistent:
% 229.33/40.76  ----------------------------------------------------------------
% 229.33/40.76    (1)   ~ (e3 = e1)
% 229.33/40.76    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.33/40.76           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.33/40.76    (3)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.33/40.76         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.33/40.76    (4)   ~ (all_6_2 = e3)
% 229.33/40.76    (5)  op(e1, e1) = all_6_2
% 229.33/40.76    (6)  all_57_6 = e1
% 229.33/40.76    (7)   ~ (e3 = e2)
% 229.33/40.76    (8)   ~ (e3 = e0)
% 229.33/40.76    (9)  all_57_15 = e3
% 229.33/40.76    (10)  op(e3, e3) = e2
% 229.33/40.76    (11)  all_57_12 = e1
% 229.33/40.76    (12)   ~ (e2 = e0)
% 229.33/40.76    (13)   ~ (e1 = e0)
% 229.33/40.76    (14)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.33/40.76              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.33/40.76                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.33/40.76                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.33/40.76    (15)  all_57_2 = e0
% 229.33/40.76    (16)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.33/40.76          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.33/40.76    (17)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) |
% 229.33/40.76          (all_57_11 = e0 & op(e1, e0) = e0)
% 229.33/40.76    (18)   ~ (e2 = e1)
% 229.33/40.76    (19)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.33/40.76          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.33/40.76    (20)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.33/40.76          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.33/40.76  
% 229.33/40.76  Begin of proof
% 229.33/40.76  | 
% 229.33/40.76  | BETA: splitting (3) gives:
% 229.33/40.76  | 
% 229.33/40.76  | Case 1:
% 229.33/40.76  | | 
% 229.33/40.76  | |   (21)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 229.33/40.76  | |           e3)
% 229.33/40.76  | | 
% 229.33/40.76  | | BETA: splitting (21) gives:
% 229.33/40.76  | | 
% 229.33/40.76  | | Case 1:
% 229.33/40.76  | | | 
% 229.33/40.76  | | |   (22)  all_57_6 = e3 & op(e1, e3) = e3
% 229.33/40.76  | | | 
% 229.33/40.76  | | | ALPHA: (22) implies:
% 229.33/40.76  | | |   (23)  all_57_6 = e3
% 229.33/40.76  | | | 
% 229.33/40.76  | | | REF_CLOSE: (1), (6), (23) are inconsistent by sub-proof #2017.
% 229.33/40.76  | | | 
% 229.33/40.76  | | Case 2:
% 229.33/40.76  | | | 
% 229.33/40.76  | | |   (24)  all_57_7 = e3 & op(e1, e2) = e3
% 229.33/40.76  | | | 
% 229.33/40.76  | | | ALPHA: (24) implies:
% 229.33/40.76  | | |   (25)  all_57_7 = e3
% 229.33/40.76  | | | 
% 229.33/40.76  | | | BETA: splitting (16) gives:
% 229.33/40.76  | | | 
% 229.33/40.76  | | | Case 1:
% 229.33/40.76  | | | | 
% 229.33/40.76  | | | |   (26)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3)
% 229.33/40.76  | | | |           = e3)
% 229.33/40.76  | | | | 
% 229.33/40.76  | | | | BETA: splitting (26) gives:
% 229.33/40.76  | | | | 
% 229.33/40.76  | | | | Case 1:
% 229.33/40.76  | | | | | 
% 229.33/40.76  | | | | |   (27)  all_57_0 = e3 & op(e3, e3) = e3
% 229.33/40.76  | | | | | 
% 229.33/40.76  | | | | | ALPHA: (27) implies:
% 229.33/40.76  | | | | |   (28)  op(e3, e3) = e3
% 229.33/40.76  | | | | | 
% 229.33/40.77  | | | | | REF_CLOSE: (2), (7), (10), (28) are inconsistent by sub-proof #2490.
% 229.33/40.77  | | | | | 
% 229.33/40.77  | | | | Case 2:
% 229.33/40.77  | | | | | 
% 229.33/40.77  | | | | |   (29)  all_57_2 = e3 & op(e2, e3) = e3
% 229.33/40.77  | | | | | 
% 229.33/40.77  | | | | | ALPHA: (29) implies:
% 229.33/40.77  | | | | |   (30)  all_57_2 = e3
% 229.33/40.77  | | | | | 
% 229.33/40.77  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (12), (13),
% 229.33/40.77  | | | | |            (14), (15), (18), (19), (20), (25), (30) are inconsistent
% 229.33/40.77  | | | | |            by sub-proof #761.
% 229.33/40.77  | | | | | 
% 229.33/40.77  | | | | End of split
% 229.33/40.77  | | | | 
% 229.33/40.77  | | | Case 2:
% 229.33/40.77  | | | | 
% 229.33/40.77  | | | |   (31)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3)
% 229.33/40.77  | | | |           = e3)
% 229.33/40.77  | | | | 
% 229.33/40.77  | | | | REF_CLOSE: (1), (6), (11), (31) are inconsistent by sub-proof #1206.
% 229.33/40.77  | | | | 
% 229.33/40.77  | | | End of split
% 229.33/40.77  | | | 
% 229.33/40.77  | | End of split
% 229.33/40.77  | | 
% 229.33/40.77  | Case 2:
% 229.33/40.77  | | 
% 229.33/40.77  | |   (32)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 229.33/40.77  | |           e3)
% 229.33/40.77  | | 
% 229.33/40.77  | | REF_CLOSE: (1), (2), (4), (5), (7), (8), (9), (12), (13), (17), (18), (19),
% 229.33/40.77  | |            (20), (32) are inconsistent by sub-proof #1080.
% 229.33/40.77  | | 
% 229.33/40.77  | End of split
% 229.33/40.77  | 
% 229.33/40.77  End of proof
% 229.33/40.77  
% 229.33/40.77  Sub-proof #761 shows that the following formulas are inconsistent:
% 229.33/40.77  ----------------------------------------------------------------
% 229.33/40.77    (1)   ~ (e3 = e1)
% 229.33/40.77    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.33/40.77           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.33/40.77    (3)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.33/40.77         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.33/40.77    (4)   ~ (all_6_2 = e3)
% 229.33/40.77    (5)  op(e1, e1) = all_6_2
% 229.33/40.77    (6)  all_57_6 = e1
% 229.33/40.77    (7)   ~ (e3 = e2)
% 229.33/40.77    (8)   ~ (e3 = e0)
% 229.33/40.77    (9)  all_57_15 = e3
% 229.33/40.77    (10)   ~ (e2 = e0)
% 229.33/40.77    (11)  all_57_2 = e3
% 229.33/40.77    (12)   ~ (e1 = e0)
% 229.33/40.77    (13)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.33/40.77              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.33/40.77                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.33/40.77                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.33/40.77    (14)  all_57_2 = e0
% 229.33/40.77    (15)  all_57_7 = e3
% 229.33/40.77    (16)   ~ (e2 = e1)
% 229.33/40.77    (17)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.33/40.77          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.33/40.77    (18)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.33/40.77          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.33/40.77  
% 229.33/40.77  Begin of proof
% 229.33/40.77  | 
% 229.33/40.77  | COMBINE_EQS: (11), (14) imply:
% 229.33/40.77  |   (19)  e3 = e0
% 229.33/40.77  | 
% 229.33/40.77  | SIMP: (19) implies:
% 229.33/40.77  |   (20)  e3 = e0
% 229.33/40.77  | 
% 229.33/40.77  | COMBINE_EQS: (15), (20) imply:
% 229.33/40.77  |   (21)  all_57_7 = e0
% 229.33/40.77  | 
% 229.33/40.77  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 229.33/40.77  |            (16), (17), (18), (21) are inconsistent by sub-proof #1735.
% 229.33/40.77  | 
% 229.33/40.77  End of proof
% 229.33/40.77  
% 229.33/40.77  Sub-proof #762 shows that the following formulas are inconsistent:
% 229.33/40.77  ----------------------------------------------------------------
% 229.33/40.77    (1)  all_57_0 = e2
% 229.33/40.77    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.33/40.77         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.33/40.77    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.33/40.77         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.33/40.77    (4)   ~ (e3 = e1)
% 229.33/40.77    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.33/40.77           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.33/40.77    (6)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1)
% 229.33/40.77    (7)  all_57_12 = e2
% 229.33/40.77    (8)   ~ (e3 = e2)
% 229.33/40.77    (9)   ~ (e3 = e0)
% 229.33/40.77    (10)  op(e3, e3) = e2
% 229.33/40.77    (11)   ~ (e2 = e0)
% 229.33/40.77    (12)  all_57_3 = e1
% 229.33/40.77    (13)   ~ (e1 = e0)
% 229.33/40.77    (14)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.33/40.77          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.33/40.77    (15)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.33/40.77          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.33/40.77    (16)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.33/40.77          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.33/40.77    (17)   ~ (e2 = e1)
% 229.33/40.77    (18)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.33/40.77          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.33/40.77    (19)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.33/40.77          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.33/40.77  
% 229.33/40.77  Begin of proof
% 229.33/40.77  | 
% 229.33/40.77  | BETA: splitting (6) gives:
% 229.33/40.77  | 
% 229.33/40.77  | Case 1:
% 229.33/40.77  | | 
% 229.33/40.77  | |   (20)  all_57_0 = e1 & op(e3, e3) = e1
% 229.33/40.77  | | 
% 229.33/40.77  | | ALPHA: (20) implies:
% 229.33/40.77  | |   (21)  op(e3, e3) = e1
% 229.33/40.77  | | 
% 229.33/40.77  | | REF_CLOSE: (5), (10), (17), (21) are inconsistent by sub-proof #1950.
% 229.33/40.77  | | 
% 229.33/40.77  | Case 2:
% 229.33/40.77  | | 
% 229.33/40.77  | |   (22)  all_57_2 = e1 & op(e2, e3) = e1
% 229.33/40.77  | | 
% 229.33/40.77  | | ALPHA: (22) implies:
% 229.33/40.77  | |   (23)  all_57_2 = e1
% 229.33/40.77  | | 
% 229.33/40.77  | | BETA: splitting (16) gives:
% 229.33/40.77  | | 
% 229.33/40.77  | | Case 1:
% 229.33/40.77  | | | 
% 229.33/40.77  | | |   (24)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) =
% 229.33/40.77  | | |           e3)
% 229.33/40.77  | | | 
% 229.33/40.77  | | | REF_CLOSE: (4), (5), (8), (10), (23), (24) are inconsistent by sub-proof
% 229.33/40.77  | | |            #765.
% 229.33/40.77  | | | 
% 229.33/40.77  | | Case 2:
% 229.33/40.77  | | | 
% 229.33/40.77  | | |   (25)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) =
% 229.33/40.77  | | |           e3)
% 229.33/40.77  | | | 
% 229.33/40.77  | | | BETA: splitting (25) gives:
% 229.33/40.77  | | | 
% 229.33/40.77  | | | Case 1:
% 229.33/40.77  | | | | 
% 229.33/40.77  | | | |   (26)  all_57_6 = e3 & op(e1, e3) = e3
% 229.33/40.77  | | | | 
% 229.33/40.77  | | | | ALPHA: (26) implies:
% 229.33/40.77  | | | |   (27)  all_57_6 = e3
% 229.33/40.77  | | | | 
% 229.33/40.77  | | | | BETA: splitting (19) gives:
% 229.33/40.77  | | | | 
% 229.33/40.77  | | | | Case 1:
% 229.33/40.77  | | | | | 
% 229.33/40.77  | | | | |   (28)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2,
% 229.33/40.77  | | | | |             e3) = e0)
% 229.33/40.77  | | | | | 
% 229.33/40.77  | | | | | REF_CLOSE: (2), (4), (5), (8), (9), (10), (11), (12), (13), (14),
% 229.33/40.77  | | | | |            (15), (17), (23), (28) are inconsistent by sub-proof #764.
% 229.33/40.77  | | | | | 
% 229.33/40.77  | | | | Case 2:
% 229.33/40.77  | | | | | 
% 229.33/40.77  | | | | |   (29)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0,
% 229.33/40.77  | | | | |             e3) = e0)
% 229.33/40.77  | | | | | 
% 229.33/40.77  | | | | | BETA: splitting (29) gives:
% 229.33/40.77  | | | | | 
% 229.33/40.77  | | | | | Case 1:
% 229.33/40.77  | | | | | | 
% 229.33/40.77  | | | | | |   (30)  all_57_6 = e0 & op(e1, e3) = e0
% 229.33/40.77  | | | | | | 
% 229.33/40.77  | | | | | | REF_CLOSE: (9), (27), (30) are inconsistent by sub-proof #2465.
% 229.33/40.77  | | | | | | 
% 229.33/40.77  | | | | | Case 2:
% 229.33/40.77  | | | | | | 
% 229.33/40.77  | | | | | |   (31)  all_57_12 = e0 & op(e0, e3) = e0
% 229.33/40.77  | | | | | | 
% 229.33/40.77  | | | | | | ALPHA: (31) implies:
% 229.33/40.77  | | | | | |   (32)  all_57_12 = e0
% 229.33/40.77  | | | | | | 
% 229.33/40.77  | | | | | | REF_CLOSE: (1), (3), (4), (7), (8), (11), (13), (17), (18), (27),
% 229.33/40.77  | | | | | |            (32) are inconsistent by sub-proof #763.
% 229.33/40.77  | | | | | | 
% 229.33/40.77  | | | | | End of split
% 229.33/40.77  | | | | | 
% 229.33/40.77  | | | | End of split
% 229.33/40.77  | | | | 
% 229.33/40.77  | | | Case 2:
% 229.33/40.77  | | | | 
% 229.33/40.77  | | | |   (33)  all_57_12 = e3 & op(e0, e3) = e3
% 229.33/40.77  | | | | 
% 229.33/40.77  | | | | ALPHA: (33) implies:
% 229.33/40.77  | | | |   (34)  all_57_12 = e3
% 229.33/40.77  | | | | 
% 229.33/40.77  | | | | REF_CLOSE: (7), (8), (34) are inconsistent by sub-proof #2392.
% 229.33/40.77  | | | | 
% 229.33/40.77  | | | End of split
% 229.33/40.77  | | | 
% 229.33/40.77  | | End of split
% 229.33/40.77  | | 
% 229.33/40.77  | End of split
% 229.33/40.77  | 
% 229.33/40.77  End of proof
% 229.33/40.77  
% 229.33/40.77  Sub-proof #763 shows that the following formulas are inconsistent:
% 229.33/40.77  ----------------------------------------------------------------
% 229.33/40.77    (1)  all_57_0 = e2
% 229.33/40.77    (2)  all_57_12 = e0
% 229.33/40.77    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.33/40.77         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.33/40.77    (4)   ~ (e3 = e1)
% 229.33/40.77    (5)  all_57_12 = e2
% 229.33/40.77    (6)   ~ (e3 = e2)
% 229.33/40.77    (7)   ~ (e2 = e0)
% 229.33/40.77    (8)   ~ (e1 = e0)
% 229.33/40.77    (9)  all_57_6 = e3
% 229.33/40.77    (10)   ~ (e2 = e1)
% 229.33/40.77    (11)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.33/40.77          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.33/40.77  
% 229.33/40.77  Begin of proof
% 229.33/40.77  | 
% 229.33/40.77  | COMBINE_EQS: (2), (5) imply:
% 229.33/40.77  |   (12)  e2 = e0
% 229.33/40.77  | 
% 229.33/40.77  | COMBINE_EQS: (1), (12) imply:
% 229.33/40.77  |   (13)  all_57_0 = e0
% 229.33/40.77  | 
% 229.33/40.77  | REF_CLOSE: (2), (3), (4), (6), (7), (8), (9), (10), (11), (13) are
% 229.33/40.77  |            inconsistent by sub-proof #1425.
% 229.33/40.77  | 
% 229.33/40.77  End of proof
% 229.33/40.77  
% 229.33/40.77  Sub-proof #764 shows that the following formulas are inconsistent:
% 229.33/40.77  ----------------------------------------------------------------
% 229.33/40.77    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.33/40.77         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.33/40.77    (2)   ~ (e3 = e1)
% 229.33/40.77    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.33/40.77           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.33/40.77    (4)   ~ (e3 = e2)
% 229.33/40.77    (5)   ~ (e3 = e0)
% 229.33/40.77    (6)  op(e3, e3) = e2
% 229.33/40.77    (7)   ~ (e2 = e0)
% 229.33/40.77    (8)  all_57_3 = e1
% 229.33/40.77    (9)   ~ (e1 = e0)
% 229.33/40.77    (10)  all_57_2 = e1
% 229.33/40.77    (11)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.33/40.77          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.33/40.77    (12)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.33/40.77          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.33/40.77    (13)   ~ (e2 = e1)
% 229.33/40.77    (14)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0)
% 229.33/40.77  
% 229.33/40.77  Begin of proof
% 229.33/40.77  | 
% 229.33/40.77  | BETA: splitting (14) gives:
% 229.33/40.77  | 
% 229.33/40.77  | Case 1:
% 229.33/40.77  | | 
% 229.33/40.77  | |   (15)  all_57_0 = e0 & op(e3, e3) = e0
% 229.33/40.77  | | 
% 229.33/40.77  | | ALPHA: (15) implies:
% 229.33/40.77  | |   (16)  op(e3, e3) = e0
% 229.33/40.77  | | 
% 229.33/40.77  | | REF_CLOSE: (3), (6), (7), (16) are inconsistent by sub-proof #2403.
% 229.33/40.77  | | 
% 229.33/40.77  | Case 2:
% 229.33/40.77  | | 
% 229.33/40.77  | |   (17)  all_57_2 = e0 & op(e2, e3) = e0
% 229.33/40.77  | | 
% 229.33/40.77  | | ALPHA: (17) implies:
% 229.33/40.77  | |   (18)  all_57_2 = e0
% 229.33/40.77  | | 
% 229.33/40.77  | | COMBINE_EQS: (10), (18) imply:
% 229.33/40.77  | |   (19)  e1 = e0
% 229.33/40.77  | | 
% 229.33/40.77  | | REF_CLOSE: (1), (2), (4), (5), (7), (8), (9), (10), (11), (12), (13), (19)
% 229.33/40.77  | |            are inconsistent by sub-proof #1590.
% 229.33/40.77  | | 
% 229.33/40.77  | End of split
% 229.33/40.77  | 
% 229.33/40.77  End of proof
% 229.33/40.77  
% 229.33/40.77  Sub-proof #765 shows that the following formulas are inconsistent:
% 229.33/40.77  ----------------------------------------------------------------
% 229.33/40.77    (1)   ~ (e3 = e1)
% 229.33/40.77    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.33/40.77           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.33/40.77    (3)   ~ (e3 = e2)
% 229.33/40.77    (4)  op(e3, e3) = e2
% 229.33/40.77    (5)  all_57_2 = e1
% 229.33/40.77    (6)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3)
% 229.33/40.77  
% 229.33/40.77  Begin of proof
% 229.33/40.77  | 
% 229.33/40.77  | BETA: splitting (6) gives:
% 229.33/40.77  | 
% 229.33/40.77  | Case 1:
% 229.33/40.77  | | 
% 229.33/40.77  | |   (7)  all_57_0 = e3 & op(e3, e3) = e3
% 229.33/40.77  | | 
% 229.33/40.77  | | ALPHA: (7) implies:
% 229.33/40.77  | |   (8)  op(e3, e3) = e3
% 229.33/40.77  | | 
% 229.33/40.77  | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #2490.
% 229.33/40.77  | | 
% 229.33/40.77  | Case 2:
% 229.33/40.77  | | 
% 229.33/40.77  | |   (9)  all_57_2 = e3 & op(e2, e3) = e3
% 229.33/40.77  | | 
% 229.33/40.77  | | ALPHA: (9) implies:
% 229.33/40.77  | |   (10)  all_57_2 = e3
% 229.33/40.77  | | 
% 229.33/40.77  | | REF_CLOSE: (1), (5), (10) are inconsistent by sub-proof #2397.
% 229.33/40.77  | | 
% 229.33/40.77  | End of split
% 229.33/40.77  | 
% 229.33/40.77  End of proof
% 229.33/40.77  
% 229.33/40.77  Sub-proof #766 shows that the following formulas are inconsistent:
% 229.33/40.77  ----------------------------------------------------------------
% 229.33/40.77    (1)  all_57_0 = e2
% 229.33/40.77    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.33/40.77         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.33/40.77    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.33/40.77         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.33/40.77    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.33/40.77         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.33/40.77    (5)   ~ (e3 = e1)
% 229.33/40.77    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.33/40.77           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.33/40.77    (7)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.33/40.77         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.33/40.77    (8)   ~ (all_6_2 = e3)
% 229.33/40.77    (9)  op(e1, e1) = all_6_2
% 229.33/40.77    (10)  op(e2, e2) = e1
% 229.33/40.77    (11)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.33/40.77          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.33/40.77    (12)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.33/40.77          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.33/40.77    (13)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.33/40.77          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.33/40.77    (14)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 229.33/40.77          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.33/40.77    (15)   ~ (e3 = e2)
% 229.33/40.77    (16)   ~ (e3 = e0)
% 229.33/40.77    (17)  all_57_15 = e3
% 229.33/40.77    (18)  op(e3, e3) = e2
% 229.33/40.77    (19)  all_57_4 = e1
% 229.33/40.77    (20)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.33/40.77          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.33/40.77            e1)
% 229.33/40.77    (21)  op(e1, e1) = e1
% 229.33/40.77    (22)   ~ (e2 = e0)
% 229.33/40.77    (23)  all_57_3 = e1
% 229.33/40.77    (24)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.33/40.77          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.33/40.77    (25)   ~ (e1 = e0)
% 229.33/40.77    (26)  all_57_5 = e2
% 229.33/40.77    (27)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.33/40.77          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.33/40.77    (28)  all_57_14 = e1
% 229.33/40.77    (29)  op(e0, e0) = e3
% 229.33/40.77    (30)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.33/40.77          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.33/40.77            e2)
% 229.33/40.77    (31)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.33/40.77              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.33/40.77                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.33/40.77                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.33/40.77    (32)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.33/40.77          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.33/40.77    (33)   ~ (all_53_12 = e3)
% 229.33/40.77    (34)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.33/40.77          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.33/40.77    (35)  all_57_1 = e3
% 229.33/40.77    (36)   ~ (e2 = e1)
% 229.33/40.77    (37)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.33/40.77          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.33/40.77    (38)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.33/40.77          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.33/40.77    (39)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.33/40.77          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.33/40.77    (40)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.33/40.77          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.33/40.77    (41)  op(e3, e0) = all_53_12
% 229.33/40.77  
% 229.33/40.77  Begin of proof
% 229.33/40.77  | 
% 229.33/40.77  | BETA: splitting (32) gives:
% 229.33/40.77  | 
% 229.33/40.77  | Case 1:
% 229.33/40.77  | | 
% 229.33/40.77  | |   (42)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 229.33/40.77  | |           e3)
% 229.33/40.77  | | 
% 229.33/40.77  | | BETA: splitting (42) gives:
% 229.33/40.77  | | 
% 229.33/40.77  | | Case 1:
% 229.33/40.77  | | | 
% 229.33/40.77  | | |   (43)  all_57_2 = e3 & op(e2, e3) = e3
% 229.33/40.77  | | | 
% 229.33/40.77  | | | ALPHA: (43) implies:
% 229.33/40.77  | | |   (44)  all_57_2 = e3
% 229.33/40.77  | | | 
% 229.33/40.77  | | | BETA: splitting (14) gives:
% 229.33/40.77  | | | 
% 229.33/40.77  | | | Case 1:
% 229.33/40.77  | | | | 
% 229.33/40.77  | | | |   (45)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1)
% 229.33/40.77  | | | |           = e0)
% 229.33/40.77  | | | | 
% 229.33/40.77  | | | | BETA: splitting (45) gives:
% 229.33/40.77  | | | | 
% 229.33/40.77  | | | | Case 1:
% 229.33/40.77  | | | | | 
% 229.33/40.77  | | | | |   (46)  all_57_4 = e0 & op(e3, e1) = e0
% 229.33/40.77  | | | | | 
% 229.33/40.77  | | | | | ALPHA: (46) implies:
% 229.33/40.77  | | | | |   (47)  all_57_4 = e0
% 229.33/40.77  | | | | | 
% 229.33/40.77  | | | | | COMBINE_EQS: (19), (47) imply:
% 229.33/40.77  | | | | |   (48)  e1 = e0
% 229.33/40.77  | | | | | 
% 229.33/40.77  | | | | | COMBINE_EQS: (23), (48) imply:
% 229.33/40.77  | | | | |   (49)  all_57_3 = e0
% 229.33/40.77  | | | | | 
% 229.33/40.77  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (15), (16),
% 229.33/40.77  | | | | |            (17), (18), (22), (25), (29), (31), (32), (34), (35), (36),
% 229.33/40.77  | | | | |            (37), (38), (39), (40), (44), (49) are inconsistent by
% 229.33/40.77  | | | | |            sub-proof #792.
% 229.33/40.77  | | | | | 
% 229.33/40.77  | | | | Case 2:
% 229.33/40.77  | | | | | 
% 229.33/40.77  | | | | |   (50)  all_57_5 = e0 & op(e2, e1) = e0
% 229.33/40.77  | | | | | 
% 229.33/40.77  | | | | | REF_CLOSE: (22), (26), (50) are inconsistent by sub-proof #2428.
% 229.33/40.77  | | | | | 
% 229.33/40.77  | | | | End of split
% 229.33/40.77  | | | | 
% 229.33/40.77  | | | Case 2:
% 229.33/40.77  | | | | 
% 229.33/40.77  | | | |   (51)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1)
% 229.33/40.77  | | | |           = e0)
% 229.33/40.77  | | | | 
% 229.33/40.77  | | | | BETA: splitting (51) gives:
% 229.33/40.77  | | | | 
% 229.33/40.77  | | | | Case 1:
% 229.33/40.77  | | | | | 
% 229.33/40.77  | | | | |   (52)  all_57_8 = e0 & op(e1, e1) = e0
% 229.33/40.77  | | | | | 
% 229.33/40.77  | | | | | ALPHA: (52) implies:
% 229.33/40.77  | | | | |   (53)  op(e1, e1) = e0
% 229.33/40.77  | | | | | 
% 229.33/40.77  | | | | | REF_CLOSE: (6), (21), (25), (53) are inconsistent by sub-proof #2427.
% 229.33/40.77  | | | | | 
% 229.33/40.77  | | | | Case 2:
% 229.33/40.77  | | | | | 
% 229.33/40.77  | | | | |   (54)  all_57_14 = e0 & op(e0, e1) = e0
% 229.33/40.77  | | | | | 
% 229.33/40.77  | | | | | ALPHA: (54) implies:
% 229.33/40.77  | | | | |   (55)  all_57_14 = e0
% 229.33/40.77  | | | | | 
% 229.33/40.77  | | | | | COMBINE_EQS: (28), (55) imply:
% 229.33/40.77  | | | | |   (56)  e1 = e0
% 229.33/40.77  | | | | | 
% 229.33/40.77  | | | | | COMBINE_EQS: (23), (56) imply:
% 229.33/40.77  | | | | |   (57)  all_57_3 = e0
% 229.33/40.77  | | | | | 
% 229.33/40.77  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (15), (16),
% 229.33/40.77  | | | | |            (17), (18), (22), (25), (29), (31), (32), (34), (35), (36),
% 229.33/40.77  | | | | |            (37), (38), (39), (40), (44), (57) are inconsistent by
% 229.33/40.77  | | | | |            sub-proof #792.
% 229.33/40.77  | | | | | 
% 229.33/40.77  | | | | End of split
% 229.33/40.77  | | | | 
% 229.33/40.77  | | | End of split
% 229.33/40.77  | | | 
% 229.33/40.77  | | Case 2:
% 229.33/40.77  | | | 
% 229.33/40.77  | | |   (58)  all_57_3 = e3 & op(e2, e2) = e3
% 229.33/40.77  | | | 
% 229.33/40.77  | | | ALPHA: (58) implies:
% 229.33/40.77  | | |   (59)  op(e2, e2) = e3
% 229.33/40.77  | | | 
% 229.33/40.77  | | | REF_CLOSE: (5), (6), (10), (59) are inconsistent by sub-proof #1912.
% 229.33/40.77  | | | 
% 229.33/40.77  | | End of split
% 229.33/40.77  | | 
% 229.33/40.77  | Case 2:
% 229.33/40.77  | | 
% 229.33/40.77  | |   (60)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 229.33/40.77  | |           e3)
% 229.33/40.77  | | 
% 229.33/40.77  | | REF_CLOSE: (5), (6), (8), (9), (11), (12), (13), (15), (16), (17), (18),
% 229.33/40.77  | |            (19), (20), (22), (24), (25), (26), (27), (30), (31), (33), (35),
% 229.33/40.77  | |            (36), (37), (41), (60) are inconsistent by sub-proof #777.
% 229.33/40.77  | | 
% 229.33/40.77  | End of split
% 229.33/40.77  | 
% 229.33/40.77  End of proof
% 229.33/40.77  
% 229.33/40.77  Sub-proof #767 shows that the following formulas are inconsistent:
% 229.33/40.77  ----------------------------------------------------------------
% 229.33/40.77    (1)   ~ (all_53_2 = e2)
% 229.33/40.77    (2)  all_57_0 = e2
% 229.33/40.77    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.33/40.77         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.33/40.77    (4)  all_57_13 = e1
% 229.33/40.77    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.33/40.77         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.33/40.77    (6)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.33/40.77         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.33/40.77    (7)   ~ (e3 = e1)
% 229.33/40.77    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.33/40.77           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.33/40.77    (9)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.33/40.77         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.33/40.77    (10)   ~ (all_53_3 = e3)
% 229.33/40.77    (11)   ~ (all_53_3 = all_53_7)
% 229.33/40.77    (12)   ~ (all_6_2 = e3)
% 229.33/40.77    (13)   ~ (all_53_9 = e1)
% 229.33/40.77    (14)  op(e1, e1) = all_6_2
% 229.33/40.77    (15)   ~ (all_53_1 = all_53_9)
% 229.33/40.77    (16)  op(e2, e2) = e1
% 229.33/40.77    (17)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.33/40.77          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.33/40.77    (18)   ~ (all_53_13 = e3)
% 229.33/40.77    (19)   ~ (all_53_9 = all_53_11)
% 229.33/40.77    (20)  all_55_4 = all_53_1
% 229.33/40.77    (21)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.33/40.77          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.33/40.77    (22)   ~ (e3 = e2)
% 229.33/40.77    (23)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 229.33/40.77    (24)   ~ (all_53_1 = all_53_3)
% 229.33/40.77    (25)   ~ (e3 = e0)
% 229.33/40.77    (26)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 229.33/40.77    (27)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 229.33/40.77    (28)  all_57_15 = e3
% 229.33/40.77    (29)   ~ (all_53_9 = all_53_13)
% 229.33/40.77    (30)  op(e3, e3) = e2
% 229.33/40.77    (31)  all_57_4 = e1
% 229.33/40.77    (32)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.33/40.77          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.33/40.77            e1)
% 229.33/40.77    (33)   ~ (all_53_1 = e1)
% 229.33/40.77    (34)  op(e2, e0) = e2
% 229.33/40.77    (35)  all_55_6 = all_53_9
% 229.33/40.77    (36)   ~ (all_53_1 = all_53_2)
% 229.33/40.77    (37)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.33/40.77          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.33/40.77    (38)   ~ (e2 = e0)
% 229.33/40.77    (39)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 229.33/40.77            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 229.33/40.77            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 229.33/40.77            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 229.33/40.77              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 229.33/40.77            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 229.33/40.78            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 229.33/40.78              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 229.33/40.78              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 229.33/40.78            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 229.33/40.78            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 229.33/40.78            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 229.33/40.78              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 229.33/40.78              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 229.33/40.78            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 229.33/40.78              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 229.33/40.78            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 229.33/40.78            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 229.33/40.78              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 229.33/40.78              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 229.33/40.78            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 229.33/40.78            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 229.33/40.78    (40)  all_55_12 = all_53_3
% 229.33/40.78    (41)  all_57_3 = e1
% 229.33/40.78    (42)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.33/40.78          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.33/40.78    (43)   ~ (e1 = e0)
% 229.33/40.78    (44)   ~ (all_53_3 = all_53_11)
% 229.33/40.78    (45)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.33/40.78          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.33/40.78    (46)   ~ (all_53_2 = all_53_3)
% 229.33/40.78    (47)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 229.33/40.78    (48)   ~ (all_53_7 = all_53_11)
% 229.33/40.78    (49)  all_55_8 = all_53_2
% 229.33/40.78    (50)  op(e0, e0) = e3
% 229.33/40.78    (51)  op(e0, e2) = all_53_7
% 229.33/40.78    (52)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.33/40.78          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.33/40.78            e2)
% 229.33/40.78    (53)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.33/40.78              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.33/40.78                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.33/40.78                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.33/40.78    (54)   ~ (all_53_1 = all_53_13)
% 229.33/40.78    (55)  op(e2, e0) = all_53_13
% 229.33/40.78    (56)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.33/40.78          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.33/40.78    (57)   ~ (all_53_12 = e3)
% 229.33/40.78    (58)  op(e1, e3) = all_53_2
% 229.33/40.78    (59)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.33/40.78          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.33/40.78    (60)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.33/40.78          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.33/40.78    (61)  all_57_1 = e3
% 229.33/40.78    (62)   ~ (e2 = e1)
% 229.33/40.78    (63)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.33/40.78          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.33/40.78    (64)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.33/40.78          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.33/40.78    (65)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 229.33/40.78    (66)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.33/40.78          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.33/40.78    (67)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.33/40.78          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.33/40.78    (68)  all_55_14 = all_53_11
% 229.33/40.78    (69)   ~ (all_53_11 = e3)
% 229.33/40.78    (70)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.33/40.78          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.33/40.78    (71)  op(e3, e0) = all_53_12
% 229.33/40.78  
% 229.33/40.78  Begin of proof
% 229.33/40.78  | 
% 229.33/40.78  | BETA: splitting (52) gives:
% 229.33/40.78  | 
% 229.33/40.78  | Case 1:
% 229.33/40.78  | | 
% 229.33/40.78  | |   (72)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 229.33/40.78  | |           e2)
% 229.33/40.78  | | 
% 229.33/40.78  | | BETA: splitting (72) gives:
% 229.33/40.78  | | 
% 229.33/40.78  | | Case 1:
% 229.33/40.78  | | | 
% 229.33/40.78  | | |   (73)  all_57_12 = e2 & op(e0, e3) = e2
% 229.33/40.78  | | | 
% 229.33/40.78  | | | ALPHA: (73) implies:
% 229.33/40.78  | | |   (74)  all_57_12 = e2
% 229.33/40.78  | | | 
% 229.33/40.78  | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (12), (14), (16), (17),
% 229.33/40.78  | | |            (21), (22), (25), (28), (30), (32), (37), (38), (41), (42),
% 229.33/40.78  | | |            (43), (45), (50), (52), (53), (56), (57), (59), (60), (62),
% 229.33/40.78  | | |            (63), (64), (67), (70), (71), (74) are inconsistent by
% 229.33/40.78  | | |            sub-proof #774.
% 229.33/40.78  | | | 
% 229.33/40.78  | | Case 2:
% 229.33/40.78  | | | 
% 229.33/40.78  | | |   (75)  all_57_13 = e2 & op(e0, e2) = e2
% 229.33/40.78  | | | 
% 229.33/40.78  | | | REF_CLOSE: (1), (7), (8), (10), (11), (12), (13), (14), (15), (16), (18),
% 229.33/40.78  | | |            (19), (20), (23), (24), (26), (27), (29), (30), (33), (34),
% 229.33/40.78  | | |            (35), (36), (38), (39), (40), (44), (46), (47), (48), (49),
% 229.33/40.78  | | |            (50), (51), (54), (55), (58), (65), (68), (69), (75) are
% 229.33/40.78  | | |            inconsistent by sub-proof #771.
% 229.33/40.78  | | | 
% 229.33/40.78  | | End of split
% 229.33/40.78  | | 
% 229.33/40.78  | Case 2:
% 229.33/40.78  | | 
% 229.33/40.78  | |   (76)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.33/40.78  | |           e2)
% 229.33/40.78  | | 
% 229.33/40.78  | | BETA: splitting (76) gives:
% 229.33/40.78  | | 
% 229.33/40.78  | | Case 1:
% 229.33/40.78  | | | 
% 229.33/40.78  | | |   (77)  all_57_14 = e2 & op(e0, e1) = e2
% 229.33/40.78  | | | 
% 229.33/40.78  | | | ALPHA: (77) implies:
% 229.33/40.78  | | |   (78)  all_57_14 = e2
% 229.33/40.78  | | | 
% 229.33/40.78  | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (12), (14), (16), (17),
% 229.33/40.78  | | |            (21), (22), (25), (28), (30), (32), (37), (38), (41), (42),
% 229.33/40.78  | | |            (43), (45), (50), (52), (53), (56), (57), (59), (60), (61),
% 229.33/40.78  | | |            (62), (63), (66), (67), (70), (71), (78) are inconsistent by
% 229.33/40.78  | | |            sub-proof #769.
% 229.33/40.78  | | | 
% 229.33/40.78  | | Case 2:
% 229.33/40.78  | | | 
% 229.33/40.78  | | |   (79)  all_57_15 = e2 & op(e0, e0) = e2
% 229.33/40.78  | | | 
% 229.33/40.78  | | | REF_CLOSE: (7), (8), (22), (28), (30), (31), (42), (57), (61), (71), (79)
% 229.33/40.78  | | |            are inconsistent by sub-proof #768.
% 229.33/40.78  | | | 
% 229.33/40.78  | | End of split
% 229.33/40.78  | | 
% 229.33/40.78  | End of split
% 229.33/40.78  | 
% 229.33/40.78  End of proof
% 229.33/40.78  
% 229.33/40.78  Sub-proof #768 shows that the following formulas are inconsistent:
% 229.33/40.78  ----------------------------------------------------------------
% 229.33/40.78    (1)   ~ (e3 = e1)
% 229.33/40.78    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.33/40.78           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.33/40.78    (3)   ~ (e3 = e2)
% 229.33/40.78    (4)  all_57_15 = e3
% 229.33/40.78    (5)  op(e3, e3) = e2
% 229.33/40.78    (6)  all_57_4 = e1
% 229.33/40.78    (7)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.33/40.78         (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.33/40.78    (8)   ~ (all_53_12 = e3)
% 229.33/40.78    (9)  all_57_1 = e3
% 229.33/40.78    (10)  all_57_15 = e2 & op(e0, e0) = e2
% 229.33/40.78    (11)  op(e3, e0) = all_53_12
% 229.33/40.78  
% 229.33/40.78  Begin of proof
% 229.33/40.78  | 
% 229.33/40.78  | ALPHA: (10) implies:
% 229.33/40.78  |   (12)  all_57_15 = e2
% 229.33/40.78  | 
% 229.33/40.78  | COMBINE_EQS: (4), (12) imply:
% 229.33/40.78  |   (13)  e3 = e2
% 229.33/40.78  | 
% 229.33/40.78  | SIMP: (13) implies:
% 229.33/40.78  |   (14)  e3 = e2
% 229.33/40.78  | 
% 229.33/40.78  | COMBINE_EQS: (9), (14) imply:
% 229.33/40.78  |   (15)  all_57_1 = e2
% 229.33/40.78  | 
% 229.33/40.78  | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (11), (15) are inconsistent by
% 229.33/40.78  |            sub-proof #1308.
% 229.33/40.78  | 
% 229.33/40.78  End of proof
% 229.33/40.78  
% 229.33/40.78  Sub-proof #769 shows that the following formulas are inconsistent:
% 229.33/40.78  ----------------------------------------------------------------
% 229.33/40.78    (1)  all_57_0 = e2
% 229.33/40.78    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.33/40.78         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.33/40.78    (3)  all_57_13 = e1
% 229.33/40.78    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.33/40.78         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.33/40.78    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.33/40.78         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.33/40.78    (6)   ~ (e3 = e1)
% 229.33/40.78    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.33/40.78           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.33/40.78    (8)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.33/40.78         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.33/40.78    (9)   ~ (all_6_2 = e3)
% 229.33/40.78    (10)  op(e1, e1) = all_6_2
% 229.33/40.78    (11)  op(e2, e2) = e1
% 229.33/40.78    (12)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.33/40.78          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.33/40.78    (13)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.33/40.78          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.33/40.78    (14)   ~ (e3 = e2)
% 229.33/40.78    (15)   ~ (e3 = e0)
% 229.33/40.78    (16)  all_57_15 = e3
% 229.33/40.78    (17)  op(e3, e3) = e2
% 229.33/40.78    (18)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.33/40.78          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.33/40.78            e1)
% 229.33/40.78    (19)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.33/40.78          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.33/40.78    (20)   ~ (e2 = e0)
% 229.33/40.78    (21)  all_57_3 = e1
% 229.33/40.78    (22)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.33/40.78          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.33/40.78    (23)   ~ (e1 = e0)
% 229.33/40.78    (24)  all_57_14 = e2
% 229.33/40.78    (25)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.33/40.78          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.33/40.78    (26)  op(e0, e0) = e3
% 229.33/40.78    (27)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.33/40.78          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.33/40.78            e2)
% 229.33/40.78    (28)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.33/40.78              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.33/40.78                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.33/40.78                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.33/40.78    (29)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.33/40.78          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.33/40.78    (30)   ~ (all_53_12 = e3)
% 229.33/40.78    (31)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.33/40.78          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.33/40.78    (32)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.33/40.78          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.33/40.78    (33)  all_57_1 = e3
% 229.33/40.78    (34)   ~ (e2 = e1)
% 229.33/40.78    (35)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.33/40.78          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.33/40.78    (36)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.33/40.78          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.33/40.78    (37)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.33/40.78          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.33/40.78    (38)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.33/40.78          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.33/40.78    (39)  op(e3, e0) = all_53_12
% 229.33/40.78  
% 229.33/40.78  Begin of proof
% 229.33/40.78  | 
% 229.33/40.78  | BETA: splitting (5) gives:
% 229.33/40.78  | 
% 229.33/40.78  | Case 1:
% 229.33/40.78  | | 
% 229.33/40.78  | |   (40)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 229.33/40.78  | |           e2)
% 229.33/40.78  | | 
% 229.33/40.78  | | REF_CLOSE: (7), (11), (14), (33), (34), (40) are inconsistent by sub-proof
% 229.33/40.78  | |            #1768.
% 229.33/40.78  | | 
% 229.33/40.78  | Case 2:
% 229.33/40.78  | | 
% 229.33/40.78  | |   (41)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 229.33/40.78  | |           e2)
% 229.33/40.78  | | 
% 229.33/40.78  | | BETA: splitting (41) gives:
% 229.33/40.78  | | 
% 229.33/40.78  | | Case 1:
% 229.33/40.78  | | | 
% 229.33/40.78  | | |   (42)  all_57_7 = e2 & op(e1, e2) = e2
% 229.33/40.78  | | | 
% 229.33/40.78  | | | ALPHA: (42) implies:
% 229.33/40.78  | | |   (43)  all_57_7 = e2
% 229.33/40.78  | | | 
% 229.33/40.78  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 229.33/40.78  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 229.33/40.78  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 229.33/40.78  | | |            (33), (34), (35), (36), (37), (38), (39), (43) are inconsistent
% 229.33/40.78  | | |            by sub-proof #770.
% 229.33/40.78  | | | 
% 229.33/40.78  | | Case 2:
% 229.33/40.78  | | | 
% 229.33/40.78  | | |   (44)  all_57_13 = e2 & op(e0, e2) = e2
% 229.33/40.78  | | | 
% 229.33/40.78  | | | REF_CLOSE: (3), (34), (44) are inconsistent by sub-proof #2101.
% 229.33/40.78  | | | 
% 229.33/40.78  | | End of split
% 229.33/40.78  | | 
% 229.33/40.78  | End of split
% 229.33/40.78  | 
% 229.33/40.78  End of proof
% 229.33/40.78  
% 229.33/40.78  Sub-proof #770 shows that the following formulas are inconsistent:
% 229.33/40.78  ----------------------------------------------------------------
% 229.33/40.78    (1)  all_57_0 = e2
% 229.33/40.78    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.33/40.78         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.33/40.78    (3)  all_57_13 = e1
% 229.33/40.78    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.33/40.78         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.33/40.78    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.33/40.78         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.33/40.78    (6)   ~ (e3 = e1)
% 229.33/40.78    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.33/40.78           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.33/40.78    (8)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.33/40.78         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.33/40.78    (9)   ~ (all_6_2 = e3)
% 229.33/40.78    (10)  op(e1, e1) = all_6_2
% 229.33/40.78    (11)  op(e2, e2) = e1
% 229.33/40.78    (12)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.33/40.78          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.33/40.78    (13)  all_57_7 = e2
% 229.33/40.78    (14)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.33/40.78          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.33/40.78    (15)   ~ (e3 = e2)
% 229.33/40.78    (16)   ~ (e3 = e0)
% 229.33/40.78    (17)  all_57_15 = e3
% 229.33/40.78    (18)  op(e3, e3) = e2
% 229.33/40.78    (19)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.33/40.78          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.33/40.78            e1)
% 229.33/40.78    (20)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.33/40.78          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.33/40.78    (21)   ~ (e2 = e0)
% 229.33/40.78    (22)  all_57_3 = e1
% 229.33/40.78    (23)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.33/40.78          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.33/40.78    (24)   ~ (e1 = e0)
% 229.33/40.78    (25)  all_57_14 = e2
% 229.33/40.78    (26)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.33/40.78          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.33/40.78    (27)  op(e0, e0) = e3
% 229.33/40.78    (28)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.33/40.78          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.33/40.78            e2)
% 229.33/40.78    (29)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.33/40.78              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.33/40.78                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.33/40.78                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.33/40.78    (30)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.33/40.78          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.33/40.78    (31)   ~ (all_53_12 = e3)
% 229.33/40.78    (32)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.33/40.78          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.33/40.78    (33)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.33/40.78          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.33/40.78    (34)  all_57_1 = e3
% 229.33/40.78    (35)   ~ (e2 = e1)
% 229.33/40.78    (36)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.33/40.78          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.33/40.78    (37)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.33/40.78          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.33/40.78    (38)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.33/40.78          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.33/40.78    (39)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.33/40.78          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.33/40.78    (40)  op(e3, e0) = all_53_12
% 229.33/40.78  
% 229.33/40.78  Begin of proof
% 229.33/40.78  | 
% 229.33/40.78  | BETA: splitting (29) gives:
% 229.33/40.78  | 
% 229.33/40.78  | Case 1:
% 229.33/40.78  | | 
% 229.33/40.78  | |   (41)  all_57_15 = e0 & op(e0, e0) = e0
% 229.33/40.78  | | 
% 229.33/40.78  | | ALPHA: (41) implies:
% 229.33/40.78  | |   (42)  op(e0, e0) = e0
% 229.33/40.78  | | 
% 229.33/40.78  | | REF_CLOSE: (7), (16), (27), (42) are inconsistent by sub-proof #2304.
% 229.33/40.78  | | 
% 229.33/40.78  | Case 2:
% 229.33/40.78  | | 
% 229.33/40.78  | |   (43)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 229.33/40.78  | |             e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0 &
% 229.33/40.78  | |             op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 229.33/40.78  | |           (all_57_14 = e0 & op(e0, e1) = e0))
% 229.33/40.78  | | 
% 229.33/40.78  | | ALPHA: (43) implies:
% 229.33/40.78  | |   (44)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 229.33/40.78  | |           e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.33/40.78  | |   (45)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 229.33/40.78  | |           e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 229.33/40.78  | | 
% 229.33/40.78  | | BETA: splitting (44) gives:
% 229.33/40.78  | | 
% 229.33/40.78  | | Case 1:
% 229.33/40.78  | | | 
% 229.33/40.78  | | |   (46)  all_57_12 = e0 & op(e0, e3) = e0
% 229.33/40.78  | | | 
% 229.33/40.78  | | | ALPHA: (46) implies:
% 229.33/40.78  | | |   (47)  all_57_12 = e0
% 229.33/40.78  | | | 
% 229.33/40.78  | | | BETA: splitting (4) gives:
% 229.33/40.78  | | | 
% 229.33/40.78  | | | Case 1:
% 229.33/40.78  | | | | 
% 229.33/40.78  | | | |   (48)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3)
% 229.33/40.78  | | | |           = e1)
% 229.33/40.78  | | | | 
% 229.33/40.78  | | | | REF_CLOSE: (2), (3), (6), (7), (11), (13), (15), (16), (18), (20), (21),
% 229.33/40.78  | | | |            (22), (24), (30), (32), (34), (35), (48) are inconsistent by
% 229.33/40.78  | | | |            sub-proof #1588.
% 229.33/40.78  | | | | 
% 229.33/40.78  | | | Case 2:
% 229.33/40.78  | | | | 
% 229.33/40.78  | | | |   (49)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3)
% 229.33/40.78  | | | |           = e1)
% 229.33/40.78  | | | | 
% 229.33/40.78  | | | | BETA: splitting (49) gives:
% 229.33/40.78  | | | | 
% 229.33/40.78  | | | | Case 1:
% 229.33/40.78  | | | | | 
% 229.33/40.78  | | | | |   (50)  all_57_6 = e1 & op(e1, e3) = e1
% 229.33/40.78  | | | | | 
% 229.33/40.78  | | | | | ALPHA: (50) implies:
% 229.33/40.78  | | | | |   (51)  all_57_6 = e1
% 229.33/40.78  | | | | | 
% 229.33/40.78  | | | | | REF_CLOSE: (6), (7), (8), (9), (10), (13), (15), (16), (17), (21),
% 229.33/40.78  | | | | |            (24), (35), (36), (38), (45), (51) are inconsistent by
% 229.33/40.78  | | | | |            sub-proof #1079.
% 229.33/40.78  | | | | | 
% 229.33/40.78  | | | | Case 2:
% 229.33/40.78  | | | | | 
% 229.33/40.78  | | | | |   (52)  all_57_12 = e1 & op(e0, e3) = e1
% 229.33/40.78  | | | | | 
% 229.33/40.78  | | | | | ALPHA: (52) implies:
% 229.33/40.78  | | | | |   (53)  all_57_12 = e1
% 229.33/40.78  | | | | | 
% 229.33/40.78  | | | | | COMBINE_EQS: (47), (53) imply:
% 229.33/40.78  | | | | |   (54)  e1 = e0
% 229.33/40.78  | | | | | 
% 229.33/40.78  | | | | | SIMP: (54) implies:
% 229.33/40.78  | | | | |   (55)  e1 = e0
% 229.33/40.78  | | | | | 
% 229.33/40.78  | | | | | COMBINE_EQS: (3), (55) imply:
% 229.33/40.78  | | | | |   (56)  all_57_13 = e0
% 229.33/40.78  | | | | | 
% 229.33/40.78  | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (12), (14),
% 229.33/40.78  | | | | |            (15), (16), (17), (18), (19), (21), (22), (23), (24), (26),
% 229.33/40.78  | | | | |            (27), (28), (29), (30), (31), (32), (33), (35), (36), (37),
% 229.33/40.78  | | | | |            (38), (39), (40), (55), (56) are inconsistent by sub-proof
% 229.33/40.78  | | | | |            #778.
% 229.33/40.78  | | | | | 
% 229.33/40.78  | | | | End of split
% 229.33/40.78  | | | | 
% 229.33/40.78  | | | End of split
% 229.33/40.78  | | | 
% 229.33/40.78  | | Case 2:
% 229.33/40.78  | | | 
% 229.33/40.78  | | |   (57)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1)
% 229.33/40.78  | | |           = e0)
% 229.33/40.78  | | | 
% 229.33/40.78  | | | BETA: splitting (57) gives:
% 229.33/40.78  | | | 
% 229.33/40.78  | | | Case 1:
% 229.33/40.78  | | | | 
% 229.33/40.78  | | | |   (58)  all_57_13 = e0 & op(e0, e2) = e0
% 229.33/40.78  | | | | 
% 229.33/40.78  | | | | ALPHA: (58) implies:
% 229.33/40.78  | | | |   (59)  all_57_13 = e0
% 229.33/40.78  | | | | 
% 229.33/40.78  | | | | COMBINE_EQS: (3), (59) imply:
% 229.33/40.78  | | | |   (60)  e1 = e0
% 229.33/40.78  | | | | 
% 229.33/40.78  | | | | REF_CLOSE: (3), (6), (13), (22), (24), (34), (35), (39), (60) are
% 229.33/40.78  | | | |            inconsistent by sub-proof #1587.
% 229.33/40.78  | | | | 
% 229.33/40.78  | | | Case 2:
% 229.33/40.78  | | | | 
% 229.33/40.78  | | | |   (61)  all_57_14 = e0 & op(e0, e1) = e0
% 229.33/40.78  | | | | 
% 229.33/40.78  | | | | REF_CLOSE: (21), (25), (61) are inconsistent by sub-proof #2173.
% 229.33/40.78  | | | | 
% 229.33/40.78  | | | End of split
% 229.33/40.78  | | | 
% 229.33/40.78  | | End of split
% 229.33/40.78  | | 
% 229.33/40.78  | End of split
% 229.33/40.78  | 
% 229.33/40.78  End of proof
% 229.33/40.78  
% 229.33/40.78  Sub-proof #771 shows that the following formulas are inconsistent:
% 229.33/40.78  ----------------------------------------------------------------
% 229.33/40.78    (1)   ~ (all_53_2 = e2)
% 229.33/40.78    (2)   ~ (e3 = e1)
% 229.33/40.78    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.33/40.78           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.33/40.78    (4)   ~ (all_53_3 = e3)
% 229.33/40.78    (5)   ~ (all_53_3 = all_53_7)
% 229.33/40.78    (6)   ~ (all_6_2 = e3)
% 229.33/40.78    (7)   ~ (all_53_9 = e1)
% 229.33/40.78    (8)  op(e1, e1) = all_6_2
% 229.33/40.78    (9)   ~ (all_53_1 = all_53_9)
% 229.33/40.78    (10)  op(e2, e2) = e1
% 229.33/40.78    (11)   ~ (all_53_13 = e3)
% 229.33/40.78    (12)   ~ (all_53_9 = all_53_11)
% 229.33/40.78    (13)  all_55_4 = all_53_1
% 229.33/40.78    (14)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 229.33/40.78    (15)   ~ (all_53_1 = all_53_3)
% 229.33/40.78    (16)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 229.33/40.78    (17)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 229.33/40.78    (18)   ~ (all_53_9 = all_53_13)
% 229.33/40.78    (19)  op(e3, e3) = e2
% 229.33/40.78    (20)   ~ (all_53_1 = e1)
% 229.33/40.78    (21)  op(e2, e0) = e2
% 229.33/40.78    (22)  all_55_6 = all_53_9
% 229.33/40.78    (23)   ~ (all_53_1 = all_53_2)
% 229.33/40.78    (24)   ~ (e2 = e0)
% 229.33/40.78    (25)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 229.33/40.78            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 229.33/40.78            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 229.33/40.78            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 229.33/40.78              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 229.33/40.78            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 229.33/40.78            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 229.33/40.79              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 229.33/40.79              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 229.33/40.79            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 229.33/40.79            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 229.33/40.79            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 229.33/40.79              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 229.33/40.79              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 229.33/40.79            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 229.33/40.79              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 229.33/40.79            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 229.33/40.79            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 229.33/40.79              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 229.33/40.79              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 229.33/40.79            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 229.33/40.79            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 229.33/40.79    (26)  all_55_12 = all_53_3
% 229.33/40.79    (27)   ~ (all_53_3 = all_53_11)
% 229.33/40.79    (28)   ~ (all_53_2 = all_53_3)
% 229.33/40.79    (29)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 229.33/40.79    (30)   ~ (all_53_7 = all_53_11)
% 229.33/40.79    (31)  all_55_8 = all_53_2
% 229.33/40.79    (32)  op(e0, e0) = e3
% 229.33/40.79    (33)  op(e0, e2) = all_53_7
% 229.33/40.79    (34)   ~ (all_53_1 = all_53_13)
% 229.33/40.79    (35)  op(e2, e0) = all_53_13
% 229.33/40.79    (36)  op(e1, e3) = all_53_2
% 229.33/40.79    (37)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 229.33/40.79    (38)  all_55_14 = all_53_11
% 229.33/40.79    (39)   ~ (all_53_11 = e3)
% 229.33/40.79    (40)  all_57_13 = e2 & op(e0, e2) = e2
% 229.33/40.79  
% 229.33/40.79  Begin of proof
% 229.33/40.79  | 
% 229.33/40.79  | ALPHA: (40) implies:
% 229.33/40.79  |   (41)  op(e0, e2) = e2
% 229.33/40.79  | 
% 229.33/40.79  | GROUND_INST: instantiating (3) with all_53_7, e2, e2, e0, simplifying with
% 229.33/40.79  |              (33), (41) gives:
% 229.33/40.79  |   (42)  all_53_7 = e2
% 229.33/40.79  | 
% 229.33/40.79  | GROUND_INST: instantiating (3) with all_53_13, e2, e0, e2, simplifying with
% 229.33/40.79  |              (21), (35) gives:
% 229.33/40.79  |   (43)  all_53_13 = e2
% 229.33/40.79  | 
% 229.33/40.79  | REDUCE: (34), (43) imply:
% 229.33/40.79  |   (44)   ~ (all_53_1 = e2)
% 229.33/40.79  | 
% 229.33/40.79  | REDUCE: (5), (42) imply:
% 229.33/40.79  |   (45)   ~ (all_53_3 = e2)
% 229.33/40.79  | 
% 229.33/40.79  | REDUCE: (30), (42) imply:
% 229.33/40.79  |   (46)   ~ (all_53_11 = e2)
% 229.33/40.79  | 
% 229.33/40.79  | SIMP: (46) implies:
% 229.33/40.79  |   (47)   ~ (all_53_11 = e2)
% 229.33/40.79  | 
% 229.33/40.79  | REDUCE: (18), (43) imply:
% 229.33/40.79  |   (48)   ~ (all_53_9 = e2)
% 229.33/40.79  | 
% 229.33/40.79  | REDUCE: (11), (43) imply:
% 229.33/40.79  |   (49)   ~ (e3 = e2)
% 229.33/40.79  | 
% 229.33/40.79  | SIMP: (49) implies:
% 229.33/40.79  |   (50)   ~ (e3 = e2)
% 229.33/40.79  | 
% 229.33/40.79  | BETA: splitting (25) gives:
% 229.33/40.79  | 
% 229.33/40.79  | Case 1:
% 229.33/40.79  | | 
% 229.33/40.79  | |   (51)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 229.33/40.79  | |           op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 229.33/40.79  | |           op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3,
% 229.33/40.79  | |             e3) = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 &
% 229.33/40.79  | |           op(e3, e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5)
% 229.33/40.79  | |           & $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1
% 229.33/40.79  | |           & all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 229.33/40.79  | |             all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 229.33/40.79  | |             all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11
% 229.33/40.79  | |           & op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 229.33/40.79  | |           $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 229.33/40.79  | | 
% 229.33/40.79  | | BETA: splitting (51) gives:
% 229.33/40.79  | | 
% 229.33/40.79  | | Case 1:
% 229.33/40.79  | | | 
% 229.33/40.79  | | |   (52)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 229.33/40.79  | | |         op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 229.33/40.79  | | |         op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3,
% 229.33/40.79  | | |           e3) = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 &
% 229.33/40.79  | | |         op(e3, e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5)
% 229.33/40.79  | | |         & $i(all_52_7)
% 229.33/40.79  | | | 
% 229.33/40.79  | | | REF_CLOSE: (2), (3), (10), (19), (52) are inconsistent by sub-proof #1597.
% 229.33/40.79  | | | 
% 229.33/40.79  | | Case 2:
% 229.33/40.79  | | | 
% 229.33/40.79  | | |   (53)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0 &
% 229.33/40.79  | | |         op(all_52_9, all_52_9) = e3 & op(all_52_11, all_52_11) = e2 &
% 229.33/40.79  | | |         op(all_52_13, all_52_13) = e1 & op(all_52_15, all_52_15) = e0 &
% 229.33/40.79  | | |         op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 & op(e2, e1) =
% 229.33/40.79  | | |         all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) & $i(all_52_11)
% 229.33/40.79  | | |         & $i(all_52_13) & $i(all_52_15)
% 229.33/40.79  | | | 
% 229.33/40.79  | | | ALPHA: (53) implies:
% 229.33/40.79  | | |   (54)  op(e2, e0) = all_52_15
% 229.33/40.79  | | |   (55)  op(e2, e2) = all_52_11
% 229.33/40.79  | | |   (56)  op(all_52_15, all_52_15) = e0
% 229.33/40.79  | | |   (57)  op(all_52_11, all_52_11) = e2
% 229.33/40.79  | | | 
% 229.33/40.79  | | | GROUND_INST: instantiating (3) with e2, all_52_15, e0, e2, simplifying
% 229.33/40.79  | | |              with (21), (54) gives:
% 229.33/40.79  | | |   (58)  all_52_15 = e2
% 229.33/40.79  | | | 
% 229.33/40.79  | | | REDUCE: (56), (58) imply:
% 229.33/40.79  | | |   (59)  op(e2, e2) = e0
% 229.33/40.79  | | | 
% 229.33/40.79  | | | REF_CLOSE: (3), (32), (50), (55), (57), (59) are inconsistent by sub-proof
% 229.33/40.79  | | |            #1229.
% 229.33/40.79  | | | 
% 229.33/40.79  | | End of split
% 229.33/40.79  | | 
% 229.33/40.79  | Case 2:
% 229.33/40.79  | | 
% 229.33/40.79  | |   (60)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 &
% 229.33/40.79  | |           op(all_52_17, all_52_17) = e3 & op(all_52_19, all_52_19) = e2 &
% 229.33/40.79  | |           op(all_52_21, all_52_21) = e1 & op(all_52_23, all_52_23) = e0 &
% 229.33/40.79  | |           op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) =
% 229.33/40.79  | |           all_52_21 & op(e1, e0) = all_52_23 & $i(all_52_17) & $i(all_52_19)
% 229.33/40.79  | |           & $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3 & all_52_26 =
% 229.33/40.79  | |           e2 & all_52_28 = e1 & all_52_30 = e0 & op(all_52_25, all_52_25) =
% 229.33/40.79  | |           e3 & op(all_52_27, all_52_27) = e2 & op(all_52_29, all_52_29) = e1
% 229.33/40.79  | |           & op(all_52_31, all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0,
% 229.33/40.79  | |             e2) = all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0) =
% 229.33/40.79  | |           all_52_31 & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 229.33/40.79  | |           $i(all_52_31))
% 229.33/40.79  | | 
% 229.33/40.79  | | BETA: splitting (60) gives:
% 229.33/40.79  | | 
% 229.33/40.79  | | Case 1:
% 229.33/40.79  | | | 
% 229.33/40.79  | | |   (61)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 229.33/40.79  | | |         & op(all_52_17, all_52_17) = e3 & op(all_52_19, all_52_19) = e2 &
% 229.33/40.79  | | |         op(all_52_21, all_52_21) = e1 & op(all_52_23, all_52_23) = e0 &
% 229.33/40.79  | | |         op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) =
% 229.33/40.79  | | |         all_52_21 & op(e1, e0) = all_52_23 & $i(all_52_17) & $i(all_52_19)
% 229.33/40.79  | | |         & $i(all_52_21) & $i(all_52_23)
% 229.33/40.79  | | | 
% 229.33/40.79  | | | ALPHA: (61) implies:
% 229.33/40.79  | | |   (62)  op(e1, e3) = all_52_17
% 229.33/40.79  | | |   (63)  op(all_52_17, all_52_17) = e3
% 229.33/40.79  | | | 
% 229.33/40.79  | | | GROUND_INST: instantiating (3) with all_53_2, all_52_17, e3, e1,
% 229.33/40.79  | | |              simplifying with (36), (62) gives:
% 229.33/40.79  | | |   (64)  all_53_2 = all_52_17
% 229.33/40.79  | | | 
% 229.33/40.79  | | | COMBINE_EQS: (31), (64) imply:
% 229.33/40.79  | | |   (65)  all_55_8 = all_52_17
% 229.33/40.79  | | | 
% 229.33/40.79  | | | REDUCE: (23), (64) imply:
% 229.33/40.79  | | |   (66)   ~ (all_53_1 = all_52_17)
% 229.33/40.79  | | | 
% 229.33/40.79  | | | REDUCE: (28), (64) imply:
% 229.33/40.79  | | |   (67)   ~ (all_53_3 = all_52_17)
% 229.33/40.79  | | | 
% 229.33/40.79  | | | SIMP: (67) implies:
% 229.33/40.79  | | |   (68)   ~ (all_53_3 = all_52_17)
% 229.33/40.79  | | | 
% 229.33/40.79  | | | REDUCE: (1), (64) imply:
% 229.33/40.79  | | |   (69)   ~ (all_52_17 = e2)
% 229.33/40.79  | | | 
% 229.33/40.79  | | | BETA: splitting (29) gives:
% 229.33/40.79  | | | 
% 229.33/40.79  | | | Case 1:
% 229.33/40.79  | | | | 
% 229.33/40.79  | | | |   (70)  all_55_14 = e3
% 229.33/40.79  | | | | 
% 229.33/40.79  | | | | COMBINE_EQS: (38), (70) imply:
% 229.33/40.79  | | | |   (71)  all_53_11 = e3
% 229.33/40.79  | | | | 
% 229.33/40.79  | | | | REDUCE: (39), (71) imply:
% 229.33/40.79  | | | |   (72)  $false
% 229.33/40.79  | | | | 
% 229.33/40.79  | | | | CLOSE: (72) is inconsistent.
% 229.33/40.79  | | | | 
% 229.33/40.79  | | | Case 2:
% 229.33/40.79  | | | | 
% 229.33/40.79  | | | |   (73)  all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 229.33/40.79  | | | | 
% 229.33/40.79  | | | | BETA: splitting (14) gives:
% 229.33/40.79  | | | | 
% 229.33/40.79  | | | | Case 1:
% 229.33/40.79  | | | | | 
% 229.33/40.79  | | | | |   (74)  all_55_6 = e3
% 229.33/40.79  | | | | | 
% 229.33/40.79  | | | | | COMBINE_EQS: (22), (74) imply:
% 229.33/40.79  | | | | |   (75)  all_53_9 = e3
% 229.33/40.79  | | | | | 
% 229.33/40.79  | | | | | REDUCE: (9), (75) imply:
% 229.33/40.79  | | | | |   (76)   ~ (all_53_1 = e3)
% 229.33/40.79  | | | | | 
% 229.33/40.79  | | | | | BETA: splitting (17) gives:
% 229.33/40.79  | | | | | 
% 229.33/40.79  | | | | | Case 1:
% 229.33/40.79  | | | | | | 
% 229.33/40.79  | | | | | |   (77)  all_55_4 = e3
% 229.33/40.79  | | | | | | 
% 229.33/40.79  | | | | | | REF_CLOSE: (13), (76), (77) are inconsistent by sub-proof #2170.
% 229.33/40.79  | | | | | | 
% 229.33/40.79  | | | | | Case 2:
% 229.33/40.79  | | | | | | 
% 229.33/40.79  | | | | | |   (78)  all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 229.33/40.79  | | | | | | 
% 229.33/40.79  | | | | | | BETA: splitting (78) gives:
% 229.33/40.79  | | | | | | 
% 229.33/40.79  | | | | | | Case 1:
% 229.33/40.79  | | | | | | | 
% 229.33/40.79  | | | | | | |   (79)  all_55_4 = e2
% 229.33/40.79  | | | | | | | 
% 229.33/40.79  | | | | | | | REF_CLOSE: (13), (44), (79) are inconsistent by sub-proof #2168.
% 229.33/40.79  | | | | | | | 
% 229.33/40.79  | | | | | | Case 2:
% 229.33/40.79  | | | | | | | 
% 229.33/40.79  | | | | | | |   (80)  all_55_4 = e1 | all_55_4 = e0
% 229.33/40.79  | | | | | | | 
% 229.33/40.79  | | | | | | | BETA: splitting (80) gives:
% 229.33/40.79  | | | | | | | 
% 229.33/40.79  | | | | | | | Case 1:
% 229.33/40.79  | | | | | | | | 
% 229.33/40.79  | | | | | | | |   (81)  all_55_4 = e1
% 229.33/40.79  | | | | | | | | 
% 229.33/40.79  | | | | | | | | REF_CLOSE: (13), (20), (81) are inconsistent by sub-proof #2166.
% 229.33/40.79  | | | | | | | | 
% 229.33/40.79  | | | | | | | Case 2:
% 229.33/40.79  | | | | | | | | 
% 229.33/40.79  | | | | | | | |   (82)  all_55_4 = e0
% 229.33/40.79  | | | | | | | | 
% 229.33/40.79  | | | | | | | | COMBINE_EQS: (13), (82) imply:
% 229.33/40.79  | | | | | | | |   (83)  all_53_1 = e0
% 229.33/40.79  | | | | | | | | 
% 229.33/40.79  | | | | | | | | SIMP: (83) implies:
% 229.33/40.79  | | | | | | | |   (84)  all_53_1 = e0
% 229.33/40.79  | | | | | | | | 
% 229.33/40.79  | | | | | | | | REDUCE: (15), (84) imply:
% 229.33/40.79  | | | | | | | |   (85)   ~ (all_53_3 = e0)
% 229.33/40.79  | | | | | | | | 
% 229.33/40.79  | | | | | | | | SIMP: (85) implies:
% 229.33/40.79  | | | | | | | |   (86)   ~ (all_53_3 = e0)
% 229.33/40.79  | | | | | | | | 
% 229.33/40.79  | | | | | | | | REDUCE: (66), (84) imply:
% 229.33/40.79  | | | | | | | |   (87)   ~ (all_52_17 = e0)
% 229.33/40.79  | | | | | | | | 
% 229.33/40.79  | | | | | | | | SIMP: (87) implies:
% 229.33/40.79  | | | | | | | |   (88)   ~ (all_52_17 = e0)
% 229.33/40.79  | | | | | | | | 
% 229.33/40.79  | | | | | | | | BETA: splitting (37) gives:
% 229.33/40.79  | | | | | | | | 
% 229.33/40.79  | | | | | | | | Case 1:
% 229.33/40.79  | | | | | | | | | 
% 229.33/40.79  | | | | | | | | |   (89)  all_55_12 = e3
% 229.33/40.79  | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | REF_CLOSE: (4), (26), (89) are inconsistent by sub-proof
% 229.33/40.79  | | | | | | | | |            #2001.
% 229.33/40.79  | | | | | | | | | 
% 229.33/40.79  | | | | | | | | Case 2:
% 229.33/40.79  | | | | | | | | | 
% 229.33/40.79  | | | | | | | | |   (90)  all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 229.33/40.79  | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | BETA: splitting (90) gives:
% 229.33/40.79  | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | Case 1:
% 229.33/40.79  | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | |   (91)  all_55_12 = e2
% 229.33/40.79  | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | REF_CLOSE: (26), (45), (91) are inconsistent by sub-proof
% 229.33/40.79  | | | | | | | | | |            #1337.
% 229.33/40.79  | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | Case 2:
% 229.33/40.79  | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | |   (92)  all_55_12 = e1 | all_55_12 = e0
% 229.33/40.79  | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | BETA: splitting (92) gives:
% 229.33/40.79  | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | Case 1:
% 229.33/40.79  | | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | |   (93)  all_55_12 = e1
% 229.33/40.79  | | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | | COMBINE_EQS: (26), (93) imply:
% 229.33/40.79  | | | | | | | | | | |   (94)  all_53_3 = e1
% 229.33/40.79  | | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | | SIMP: (94) implies:
% 229.33/40.79  | | | | | | | | | | |   (95)  all_53_3 = e1
% 229.33/40.79  | | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | | REDUCE: (68), (95) imply:
% 229.33/40.79  | | | | | | | | | | |   (96)   ~ (all_52_17 = e1)
% 229.33/40.79  | | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | | SIMP: (96) implies:
% 229.33/40.79  | | | | | | | | | | |   (97)   ~ (all_52_17 = e1)
% 229.33/40.79  | | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | | REF_CLOSE: (3), (16), (19), (63), (65), (69), (88), (97) are
% 229.33/40.79  | | | | | | | | | | |            inconsistent by sub-proof #1866.
% 229.33/40.79  | | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | Case 2:
% 229.33/40.79  | | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | |   (98)  all_55_12 = e0
% 229.33/40.79  | | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | | REF_CLOSE: (26), (86), (98) are inconsistent by sub-proof
% 229.33/40.79  | | | | | | | | | | |            #1993.
% 229.33/40.79  | | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | End of split
% 229.33/40.79  | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | End of split
% 229.33/40.79  | | | | | | | | | 
% 229.33/40.79  | | | | | | | | End of split
% 229.33/40.79  | | | | | | | | 
% 229.33/40.79  | | | | | | | End of split
% 229.33/40.79  | | | | | | | 
% 229.33/40.79  | | | | | | End of split
% 229.33/40.79  | | | | | | 
% 229.33/40.79  | | | | | End of split
% 229.33/40.79  | | | | | 
% 229.33/40.79  | | | | Case 2:
% 229.33/40.79  | | | | | 
% 229.33/40.79  | | | | |   (99)  all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 229.33/40.79  | | | | | 
% 229.33/40.79  | | | | | BETA: splitting (99) gives:
% 229.33/40.79  | | | | | 
% 229.33/40.79  | | | | | Case 1:
% 229.33/40.79  | | | | | | 
% 229.33/40.79  | | | | | |   (100)  all_55_6 = e2
% 229.33/40.79  | | | | | | 
% 229.33/40.79  | | | | | | REF_CLOSE: (22), (48), (100) are inconsistent by sub-proof #2398.
% 229.33/40.79  | | | | | | 
% 229.33/40.79  | | | | | Case 2:
% 229.33/40.79  | | | | | | 
% 229.33/40.79  | | | | | |   (101)  all_55_6 = e1 | all_55_6 = e0
% 229.33/40.79  | | | | | | 
% 229.33/40.79  | | | | | | BETA: splitting (101) gives:
% 229.33/40.79  | | | | | | 
% 229.33/40.79  | | | | | | Case 1:
% 229.33/40.79  | | | | | | | 
% 229.33/40.79  | | | | | | |   (102)  all_55_6 = e1
% 229.33/40.79  | | | | | | | 
% 229.33/40.79  | | | | | | | REF_CLOSE: (7), (22), (102) are inconsistent by sub-proof #2163.
% 229.33/40.79  | | | | | | | 
% 229.33/40.79  | | | | | | Case 2:
% 229.33/40.79  | | | | | | | 
% 229.33/40.79  | | | | | | |   (103)  all_55_6 = e0
% 229.33/40.79  | | | | | | | 
% 229.33/40.79  | | | | | | | COMBINE_EQS: (22), (103) imply:
% 229.33/40.79  | | | | | | |   (104)  all_53_9 = e0
% 229.33/40.79  | | | | | | | 
% 229.33/40.79  | | | | | | | SIMP: (104) implies:
% 229.33/40.79  | | | | | | |   (105)  all_53_9 = e0
% 229.33/40.79  | | | | | | | 
% 229.33/40.79  | | | | | | | REDUCE: (9), (105) imply:
% 229.33/40.79  | | | | | | |   (106)   ~ (all_53_1 = e0)
% 229.33/40.79  | | | | | | | 
% 229.33/40.79  | | | | | | | REDUCE: (12), (105) imply:
% 229.33/40.79  | | | | | | |   (107)   ~ (all_53_11 = e0)
% 229.33/40.79  | | | | | | | 
% 229.33/40.79  | | | | | | | SIMP: (107) implies:
% 229.33/40.79  | | | | | | |   (108)   ~ (all_53_11 = e0)
% 229.33/40.79  | | | | | | | 
% 229.33/40.79  | | | | | | | BETA: splitting (17) gives:
% 229.33/40.79  | | | | | | | 
% 229.33/40.79  | | | | | | | Case 1:
% 229.33/40.79  | | | | | | | | 
% 229.33/40.79  | | | | | | | |   (109)  all_55_4 = e3
% 229.33/40.79  | | | | | | | | 
% 229.33/40.79  | | | | | | | | COMBINE_EQS: (13), (109) imply:
% 229.33/40.79  | | | | | | | |   (110)  all_53_1 = e3
% 229.33/40.79  | | | | | | | | 
% 229.33/40.79  | | | | | | | | SIMP: (110) implies:
% 229.33/40.79  | | | | | | | |   (111)  all_53_1 = e3
% 229.33/40.79  | | | | | | | | 
% 229.33/40.79  | | | | | | | | REDUCE: (15), (111) imply:
% 229.33/40.79  | | | | | | | |   (112)   ~ (all_53_3 = e3)
% 229.33/40.79  | | | | | | | | 
% 229.33/40.79  | | | | | | | | REDUCE: (66), (111) imply:
% 229.33/40.79  | | | | | | | |   (113)   ~ (all_52_17 = e3)
% 229.33/40.79  | | | | | | | | 
% 229.33/40.79  | | | | | | | | SIMP: (113) implies:
% 229.33/40.79  | | | | | | | |   (114)   ~ (all_52_17 = e3)
% 229.33/40.79  | | | | | | | | 
% 229.33/40.79  | | | | | | | | BETA: splitting (73) gives:
% 229.33/40.79  | | | | | | | | 
% 229.33/40.79  | | | | | | | | Case 1:
% 229.33/40.79  | | | | | | | | | 
% 229.33/40.79  | | | | | | | | |   (115)  all_55_14 = e2
% 229.33/40.79  | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | COMBINE_EQS: (38), (115) imply:
% 229.33/40.79  | | | | | | | | |   (116)  all_53_11 = e2
% 229.33/40.79  | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | REDUCE: (47), (116) imply:
% 229.33/40.79  | | | | | | | | |   (117)  $false
% 229.33/40.79  | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | CLOSE: (117) is inconsistent.
% 229.33/40.79  | | | | | | | | | 
% 229.33/40.79  | | | | | | | | Case 2:
% 229.33/40.79  | | | | | | | | | 
% 229.33/40.79  | | | | | | | | |   (118)  all_55_14 = e1 | all_55_14 = e0
% 229.33/40.79  | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | BETA: splitting (118) gives:
% 229.33/40.79  | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | Case 1:
% 229.33/40.79  | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | |   (119)  all_55_14 = e1
% 229.33/40.79  | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | COMBINE_EQS: (38), (119) imply:
% 229.33/40.79  | | | | | | | | | |   (120)  all_53_11 = e1
% 229.33/40.79  | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | REDUCE: (27), (120) imply:
% 229.33/40.79  | | | | | | | | | |   (121)   ~ (all_53_3 = e1)
% 229.33/40.79  | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | BETA: splitting (37) gives:
% 229.33/40.79  | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | Case 1:
% 229.33/40.79  | | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | |   (122)  all_55_12 = e3
% 229.33/40.79  | | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | | REF_CLOSE: (4), (26), (122) are inconsistent by sub-proof
% 229.33/40.79  | | | | | | | | | | |            #2001.
% 229.33/40.79  | | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | Case 2:
% 229.33/40.79  | | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | |   (123)  all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 229.33/40.79  | | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | | BETA: splitting (123) gives:
% 229.33/40.79  | | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | | Case 1:
% 229.33/40.79  | | | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | | |   (124)  all_55_12 = e2
% 229.33/40.79  | | | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | | | REF_CLOSE: (26), (45), (124) are inconsistent by sub-proof
% 229.33/40.79  | | | | | | | | | | | |            #1337.
% 229.33/40.79  | | | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | | Case 2:
% 229.33/40.79  | | | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | | |   (125)  all_55_12 = e1 | all_55_12 = e0
% 229.33/40.79  | | | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | | | BETA: splitting (125) gives:
% 229.33/40.79  | | | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | | | Case 1:
% 229.33/40.79  | | | | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | | | |   (126)  all_55_12 = e1
% 229.33/40.79  | | | | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | | | | COMBINE_EQS: (26), (126) imply:
% 229.33/40.79  | | | | | | | | | | | | |   (127)  all_53_3 = e1
% 229.33/40.79  | | | | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | | | | REDUCE: (121), (127) imply:
% 229.33/40.79  | | | | | | | | | | | | |   (128)  $false
% 229.33/40.79  | | | | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | | | | CLOSE: (128) is inconsistent.
% 229.33/40.79  | | | | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | | | Case 2:
% 229.33/40.79  | | | | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | | | |   (129)  all_55_12 = e0
% 229.33/40.79  | | | | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | | | | COMBINE_EQS: (26), (129) imply:
% 229.33/40.79  | | | | | | | | | | | | |   (130)  all_53_3 = e0
% 229.33/40.79  | | | | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | | | | REDUCE: (68), (130) imply:
% 229.33/40.79  | | | | | | | | | | | | |   (131)   ~ (all_52_17 = e0)
% 229.33/40.79  | | | | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | | | | SIMP: (131) implies:
% 229.33/40.79  | | | | | | | | | | | | |   (132)   ~ (all_52_17 = e0)
% 229.33/40.79  | | | | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | | | | REF_CLOSE: (3), (6), (8), (16), (63), (65), (69), (114),
% 229.33/40.79  | | | | | | | | | | | | |            (132) are inconsistent by sub-proof #1868.
% 229.33/40.79  | | | | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | | | End of split
% 229.33/40.79  | | | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | | End of split
% 229.33/40.79  | | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | End of split
% 229.33/40.79  | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | Case 2:
% 229.33/40.79  | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | |   (133)  all_55_14 = e0
% 229.33/40.79  | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | COMBINE_EQS: (38), (133) imply:
% 229.33/40.79  | | | | | | | | | |   (134)  all_53_11 = e0
% 229.33/40.79  | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | REDUCE: (108), (134) imply:
% 229.33/40.79  | | | | | | | | | |   (135)  $false
% 229.33/40.79  | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | CLOSE: (135) is inconsistent.
% 229.33/40.79  | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | End of split
% 229.33/40.79  | | | | | | | | | 
% 229.33/40.79  | | | | | | | | End of split
% 229.33/40.79  | | | | | | | | 
% 229.33/40.79  | | | | | | | Case 2:
% 229.33/40.79  | | | | | | | | 
% 229.33/40.79  | | | | | | | |   (136)  all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 229.33/40.79  | | | | | | | | 
% 229.33/40.79  | | | | | | | | REF_CLOSE: (13), (20), (44), (106), (136) are inconsistent by
% 229.33/40.79  | | | | | | | |            sub-proof #772.
% 229.33/40.79  | | | | | | | | 
% 229.33/40.79  | | | | | | | End of split
% 229.33/40.79  | | | | | | | 
% 229.33/40.79  | | | | | | End of split
% 229.33/40.79  | | | | | | 
% 229.33/40.79  | | | | | End of split
% 229.33/40.79  | | | | | 
% 229.33/40.79  | | | | End of split
% 229.33/40.79  | | | | 
% 229.33/40.79  | | | End of split
% 229.33/40.79  | | | 
% 229.33/40.79  | | Case 2:
% 229.33/40.79  | | | 
% 229.33/40.79  | | |   (137)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 229.33/40.79  | | |          & op(all_52_25, all_52_25) = e3 & op(all_52_27, all_52_27) = e2 &
% 229.33/40.79  | | |          op(all_52_29, all_52_29) = e1 & op(all_52_31, all_52_31) = e0 &
% 229.33/40.79  | | |          op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 & op(e0, e1) =
% 229.33/40.79  | | |          all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 229.33/40.79  | | |          $i(all_52_27) & $i(all_52_29) & $i(all_52_31)
% 229.33/40.79  | | | 
% 229.33/40.79  | | | REF_CLOSE: (3), (19), (24), (32), (137) are inconsistent by sub-proof
% 229.33/40.79  | | |            #1115.
% 229.33/40.79  | | | 
% 229.33/40.79  | | End of split
% 229.33/40.79  | | 
% 229.33/40.79  | End of split
% 229.33/40.79  | 
% 229.33/40.79  End of proof
% 229.33/40.79  
% 229.33/40.79  Sub-proof #772 shows that the following formulas are inconsistent:
% 229.33/40.79  ----------------------------------------------------------------
% 229.33/40.79    (1)  all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 229.33/40.79    (2)  all_55_4 = all_53_1
% 229.33/40.79    (3)   ~ (all_53_1 = e1)
% 229.33/40.79    (4)   ~ (all_53_1 = e0)
% 229.33/40.79    (5)   ~ (all_53_1 = e2)
% 229.33/40.79  
% 229.33/40.79  Begin of proof
% 229.33/40.79  | 
% 229.33/40.79  | BETA: splitting (1) gives:
% 229.33/40.79  | 
% 229.33/40.79  | Case 1:
% 229.33/40.79  | | 
% 229.33/40.79  | |   (6)  all_55_4 = e2
% 229.33/40.79  | | 
% 229.33/40.79  | | REF_CLOSE: (2), (5), (6) are inconsistent by sub-proof #2168.
% 229.33/40.79  | | 
% 229.33/40.79  | Case 2:
% 229.33/40.79  | | 
% 229.33/40.79  | |   (7)  all_55_4 = e1 | all_55_4 = e0
% 229.33/40.79  | | 
% 229.33/40.79  | | REF_CLOSE: (2), (3), (4), (7) are inconsistent by sub-proof #773.
% 229.33/40.79  | | 
% 229.33/40.79  | End of split
% 229.33/40.79  | 
% 229.33/40.79  End of proof
% 229.33/40.79  
% 229.33/40.79  Sub-proof #773 shows that the following formulas are inconsistent:
% 229.33/40.79  ----------------------------------------------------------------
% 229.33/40.79    (1)  all_55_4 = e1 | all_55_4 = e0
% 229.33/40.79    (2)  all_55_4 = all_53_1
% 229.33/40.79    (3)   ~ (all_53_1 = e1)
% 229.33/40.79    (4)   ~ (all_53_1 = e0)
% 229.33/40.79  
% 229.33/40.79  Begin of proof
% 229.33/40.79  | 
% 229.33/40.79  | BETA: splitting (1) gives:
% 229.33/40.79  | 
% 229.33/40.79  | Case 1:
% 229.33/40.79  | | 
% 229.33/40.79  | |   (5)  all_55_4 = e1
% 229.33/40.79  | | 
% 229.33/40.79  | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #2166.
% 229.33/40.79  | | 
% 229.33/40.79  | Case 2:
% 229.33/40.79  | | 
% 229.33/40.79  | |   (6)  all_55_4 = e0
% 229.33/40.79  | | 
% 229.33/40.79  | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #1865.
% 229.33/40.79  | | 
% 229.33/40.79  | End of split
% 229.33/40.79  | 
% 229.33/40.79  End of proof
% 229.33/40.79  
% 229.33/40.79  Sub-proof #774 shows that the following formulas are inconsistent:
% 229.33/40.79  ----------------------------------------------------------------
% 229.33/40.79    (1)  all_57_0 = e2
% 229.33/40.79    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.33/40.79         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.33/40.79    (3)  all_57_13 = e1
% 229.33/40.79    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.33/40.79         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.33/40.79    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.33/40.79         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.33/40.79    (6)   ~ (e3 = e1)
% 229.33/40.79    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.33/40.79           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.33/40.79    (8)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.33/40.79         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.33/40.79    (9)   ~ (all_6_2 = e3)
% 229.33/40.79    (10)  op(e1, e1) = all_6_2
% 229.33/40.79    (11)  op(e2, e2) = e1
% 229.33/40.79    (12)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.33/40.79          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.33/40.79    (13)  all_57_12 = e2
% 229.33/40.79    (14)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.33/40.79          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.33/40.79    (15)   ~ (e3 = e2)
% 229.33/40.79    (16)   ~ (e3 = e0)
% 229.33/40.79    (17)  all_57_15 = e3
% 229.33/40.79    (18)  op(e3, e3) = e2
% 229.33/40.79    (19)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.33/40.79          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.33/40.79            e1)
% 229.33/40.79    (20)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.33/40.79          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.33/40.79    (21)   ~ (e2 = e0)
% 229.33/40.79    (22)  all_57_3 = e1
% 229.33/40.79    (23)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.33/40.79          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.33/40.79    (24)   ~ (e1 = e0)
% 229.33/40.79    (25)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.33/40.79          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.33/40.79    (26)  op(e0, e0) = e3
% 229.33/40.79    (27)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.33/40.79          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.33/40.79            e2)
% 229.33/40.79    (28)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.33/40.79              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.33/40.79                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.33/40.79                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.33/40.79    (29)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.33/40.79          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.33/40.79    (30)   ~ (all_53_12 = e3)
% 229.33/40.79    (31)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.33/40.79          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.33/40.79    (32)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.33/40.79          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.33/40.79    (33)   ~ (e2 = e1)
% 229.33/40.79    (34)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.33/40.79          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.33/40.79    (35)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.33/40.79          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.33/40.79    (36)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.33/40.79          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.33/40.79    (37)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.33/40.79          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.33/40.79    (38)  op(e3, e0) = all_53_12
% 229.33/40.79  
% 229.33/40.79  Begin of proof
% 229.33/40.79  | 
% 229.33/40.79  | BETA: splitting (4) gives:
% 229.33/40.79  | 
% 229.33/40.79  | Case 1:
% 229.33/40.79  | | 
% 229.33/40.79  | |   (39)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) =
% 229.33/40.79  | |           e1)
% 229.33/40.79  | | 
% 229.33/40.79  | | BETA: splitting (39) gives:
% 229.33/40.79  | | 
% 229.33/40.79  | | Case 1:
% 229.33/40.79  | | | 
% 229.33/40.79  | | |   (40)  all_57_0 = e1 & op(e3, e3) = e1
% 229.33/40.79  | | | 
% 229.33/40.79  | | | ALPHA: (40) implies:
% 229.33/40.79  | | |   (41)  op(e3, e3) = e1
% 229.33/40.79  | | | 
% 229.33/40.79  | | | REF_CLOSE: (7), (18), (33), (41) are inconsistent by sub-proof #1950.
% 229.33/40.79  | | | 
% 229.33/40.79  | | Case 2:
% 229.33/40.79  | | | 
% 229.33/40.79  | | |   (42)  all_57_2 = e1 & op(e2, e3) = e1
% 229.33/40.79  | | | 
% 229.33/40.79  | | | ALPHA: (42) implies:
% 229.33/40.79  | | |   (43)  all_57_2 = e1
% 229.33/40.79  | | | 
% 229.33/40.79  | | | BETA: splitting (5) gives:
% 229.33/40.79  | | | 
% 229.33/40.79  | | | Case 1:
% 229.33/40.79  | | | | 
% 229.33/40.79  | | | |   (44)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2)
% 229.33/40.79  | | | |           = e2)
% 229.33/40.79  | | | | 
% 229.33/40.79  | | | | BETA: splitting (44) gives:
% 229.33/40.79  | | | | 
% 229.33/40.79  | | | | Case 1:
% 229.33/40.79  | | | | | 
% 229.33/40.79  | | | | |   (45)  all_57_1 = e2 & op(e3, e2) = e2
% 229.33/40.79  | | | | | 
% 229.33/40.79  | | | | | ALPHA: (45) implies:
% 229.33/40.79  | | | | |   (46)  all_57_1 = e2
% 229.33/40.79  | | | | | 
% 229.33/40.79  | | | | | BETA: splitting (23) gives:
% 229.33/40.79  | | | | | 
% 229.33/40.79  | | | | | Case 1:
% 229.33/40.79  | | | | | | 
% 229.33/40.79  | | | | | |   (47)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3,
% 229.33/40.79  | | | | | |             e2) = e3)
% 229.33/40.79  | | | | | | 
% 229.33/40.79  | | | | | | REF_CLOSE: (7), (15), (18), (46), (47) are inconsistent by sub-proof
% 229.33/40.79  | | | | | |            #1663.
% 229.33/40.79  | | | | | | 
% 229.33/40.79  | | | | | Case 2:
% 229.33/40.79  | | | | | | 
% 229.33/40.79  | | | | | |   (48)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3,
% 229.33/40.79  | | | | | |             e0) = e3)
% 229.33/40.79  | | | | | | 
% 229.33/40.79  | | | | | | BETA: splitting (48) gives:
% 229.33/40.79  | | | | | | 
% 229.33/40.79  | | | | | | Case 1:
% 229.33/40.79  | | | | | | | 
% 229.33/40.79  | | | | | | |   (49)  all_57_4 = e3 & op(e3, e1) = e3
% 229.33/40.79  | | | | | | | 
% 229.33/40.79  | | | | | | | ALPHA: (49) implies:
% 229.33/40.79  | | | | | | |   (50)  all_57_4 = e3
% 229.33/40.79  | | | | | | | 
% 229.33/40.79  | | | | | | | BETA: splitting (25) gives:
% 229.33/40.79  | | | | | | | 
% 229.33/40.79  | | | | | | | Case 1:
% 229.33/40.79  | | | | | | | | 
% 229.33/40.79  | | | | | | | |   (51)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 &
% 229.33/40.79  | | | | | | | |           op(e2, e2) = e3)
% 229.33/40.79  | | | | | | | | 
% 229.33/40.79  | | | | | | | | REF_CLOSE: (6), (7), (11), (15), (46), (51) are inconsistent by
% 229.33/40.79  | | | | | | | |            sub-proof #1031.
% 229.33/40.79  | | | | | | | | 
% 229.33/40.79  | | | | | | | Case 2:
% 229.33/40.79  | | | | | | | | 
% 229.33/40.79  | | | | | | | |   (52)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 &
% 229.33/40.79  | | | | | | | |           op(e0, e2) = e3)
% 229.33/40.79  | | | | | | | | 
% 229.33/40.79  | | | | | | | | BETA: splitting (52) gives:
% 229.33/40.79  | | | | | | | | 
% 229.33/40.79  | | | | | | | | Case 1:
% 229.33/40.79  | | | | | | | | | 
% 229.33/40.79  | | | | | | | | |   (53)  all_57_7 = e3 & op(e1, e2) = e3
% 229.33/40.79  | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | ALPHA: (53) implies:
% 229.33/40.79  | | | | | | | | |   (54)  all_57_7 = e3
% 229.33/40.79  | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | BETA: splitting (32) gives:
% 229.33/40.79  | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | Case 1:
% 229.33/40.79  | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | |   (55)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 &
% 229.33/40.79  | | | | | | | | | |           op(e2, e3) = e3)
% 229.33/40.79  | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | BETA: splitting (55) gives:
% 229.33/40.79  | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | Case 1:
% 229.33/40.79  | | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | |   (56)  all_57_0 = e3 & op(e3, e3) = e3
% 229.33/40.79  | | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | | ALPHA: (56) implies:
% 229.33/40.79  | | | | | | | | | | |   (57)  op(e3, e3) = e3
% 229.33/40.79  | | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | | REF_CLOSE: (7), (15), (18), (57) are inconsistent by
% 229.33/40.79  | | | | | | | | | | |            sub-proof #2490.
% 229.33/40.79  | | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | Case 2:
% 229.33/40.79  | | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | |   (58)  all_57_2 = e3 & op(e2, e3) = e3
% 229.33/40.79  | | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | | ALPHA: (58) implies:
% 229.33/40.79  | | | | | | | | | | |   (59)  all_57_2 = e3
% 229.33/40.79  | | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | | COMBINE_EQS: (43), (59) imply:
% 229.33/40.79  | | | | | | | | | | |   (60)  e3 = e1
% 229.33/40.79  | | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | | SIMP: (60) implies:
% 229.33/40.79  | | | | | | | | | | |   (61)  e3 = e1
% 229.33/40.79  | | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | | COMBINE_EQS: (50), (61) imply:
% 229.33/40.79  | | | | | | | | | | |   (62)  all_57_4 = e1
% 229.33/40.79  | | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | | REF_CLOSE: (6), (7), (15), (18), (23), (30), (38), (46), (62)
% 229.33/40.79  | | | | | | | | | | |            are inconsistent by sub-proof #1308.
% 229.33/40.79  | | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | End of split
% 229.33/40.79  | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | Case 2:
% 229.33/40.79  | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | |   (63)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3
% 229.33/40.79  | | | | | | | | | |           & op(e0, e3) = e3)
% 229.33/40.79  | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | BETA: splitting (63) gives:
% 229.33/40.79  | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | Case 1:
% 229.33/40.79  | | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | |   (64)  all_57_6 = e3 & op(e1, e3) = e3
% 229.33/40.79  | | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | | ALPHA: (64) implies:
% 229.33/40.79  | | | | | | | | | | |   (65)  all_57_6 = e3
% 229.33/40.79  | | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | | BETA: splitting (20) gives:
% 229.33/40.79  | | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | | Case 1:
% 229.33/40.79  | | | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | | |   (66)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 229.33/40.79  | | | | | | | | | | | |           & op(e2, e2) = e0)
% 229.33/40.79  | | | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | | | BETA: splitting (66) gives:
% 229.33/40.79  | | | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | | | Case 1:
% 229.33/40.79  | | | | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | | | |   (67)  all_57_1 = e0 & op(e3, e2) = e0
% 229.33/40.79  | | | | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | | | | ALPHA: (67) implies:
% 229.33/40.79  | | | | | | | | | | | | |   (68)  all_57_1 = e0
% 229.33/40.79  | | | | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | | | | COMBINE_EQS: (46), (68) imply:
% 229.33/40.79  | | | | | | | | | | | | |   (69)  e2 = e0
% 229.33/40.79  | | | | | | | | | | | | | 
% 229.33/40.79  | | | | | | | | | | | | | COMBINE_EQS: (13), (69) imply:
% 229.33/40.80  | | | | | | | | | | | | |   (70)  all_57_12 = e0
% 229.33/40.80  | | | | | | | | | | | | | 
% 229.33/40.80  | | | | | | | | | | | | | COMBINE_EQS: (1), (69) imply:
% 229.33/40.80  | | | | | | | | | | | | |   (71)  all_57_0 = e0
% 229.33/40.80  | | | | | | | | | | | | | 
% 229.33/40.80  | | | | | | | | | | | | | REF_CLOSE: (4), (6), (15), (21), (24), (33), (35), (65),
% 229.33/40.80  | | | | | | | | | | | | |            (70), (71) are inconsistent by sub-proof #1425.
% 229.33/40.80  | | | | | | | | | | | | | 
% 229.33/40.80  | | | | | | | | | | | | Case 2:
% 229.33/40.80  | | | | | | | | | | | | | 
% 229.33/40.80  | | | | | | | | | | | | |   (72)  all_57_3 = e0 & op(e2, e2) = e0
% 229.33/40.80  | | | | | | | | | | | | | 
% 229.33/40.80  | | | | | | | | | | | | | ALPHA: (72) implies:
% 229.33/40.80  | | | | | | | | | | | | |   (73)  all_57_3 = e0
% 229.33/40.80  | | | | | | | | | | | | | 
% 229.33/40.80  | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (12), (14), (15), (16), (18), (21),
% 229.33/40.80  | | | | | | | | | | | | |            (24), (33), (37), (46), (50), (54), (73) are
% 229.33/40.80  | | | | | | | | | | | | |            inconsistent by sub-proof #800.
% 229.33/40.80  | | | | | | | | | | | | | 
% 229.33/40.80  | | | | | | | | | | | | End of split
% 229.33/40.80  | | | | | | | | | | | | 
% 229.33/40.80  | | | | | | | | | | | Case 2:
% 229.33/40.80  | | | | | | | | | | | | 
% 229.33/40.80  | | | | | | | | | | | |   (74)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 229.33/40.80  | | | | | | | | | | | |           e0 & op(e0, e2) = e0)
% 229.33/40.80  | | | | | | | | | | | | 
% 229.33/40.80  | | | | | | | | | | | | BETA: splitting (74) gives:
% 229.33/40.80  | | | | | | | | | | | | 
% 229.33/40.80  | | | | | | | | | | | | Case 1:
% 229.33/40.80  | | | | | | | | | | | | | 
% 229.33/40.80  | | | | | | | | | | | | |   (75)  all_57_7 = e0 & op(e1, e2) = e0
% 229.33/40.80  | | | | | | | | | | | | | 
% 229.33/40.80  | | | | | | | | | | | | | REF_CLOSE: (16), (54), (75) are inconsistent by sub-proof
% 229.33/40.80  | | | | | | | | | | | | |            #2042.
% 229.33/40.80  | | | | | | | | | | | | | 
% 229.33/40.80  | | | | | | | | | | | | Case 2:
% 229.33/40.80  | | | | | | | | | | | | | 
% 229.33/40.80  | | | | | | | | | | | | |   (76)  all_57_13 = e0 & op(e0, e2) = e0
% 229.33/40.80  | | | | | | | | | | | | | 
% 229.33/40.80  | | | | | | | | | | | | | REF_CLOSE: (3), (5), (6), (7), (12), (14), (15), (16), (18),
% 229.33/40.80  | | | | | | | | | | | | |            (21), (22), (24), (33), (37), (46), (50), (54),
% 229.33/40.80  | | | | | | | | | | | | |            (76) are inconsistent by sub-proof #799.
% 229.33/40.80  | | | | | | | | | | | | | 
% 229.33/40.80  | | | | | | | | | | | | End of split
% 229.33/40.80  | | | | | | | | | | | | 
% 229.33/40.80  | | | | | | | | | | | End of split
% 229.33/40.80  | | | | | | | | | | | 
% 229.33/40.80  | | | | | | | | | | Case 2:
% 229.33/40.80  | | | | | | | | | | | 
% 229.33/40.80  | | | | | | | | | | |   (77)  all_57_12 = e3 & op(e0, e3) = e3
% 229.33/40.80  | | | | | | | | | | | 
% 229.33/40.80  | | | | | | | | | | | ALPHA: (77) implies:
% 229.33/40.80  | | | | | | | | | | |   (78)  all_57_12 = e3
% 229.33/40.80  | | | | | | | | | | | 
% 229.33/40.80  | | | | | | | | | | | COMBINE_EQS: (13), (78) imply:
% 229.33/40.80  | | | | | | | | | | |   (79)  e3 = e2
% 229.33/40.80  | | | | | | | | | | | 
% 229.33/40.80  | | | | | | | | | | | SIMP: (79) implies:
% 229.33/40.80  | | | | | | | | | | |   (80)  e3 = e2
% 229.33/40.80  | | | | | | | | | | | 
% 229.33/40.80  | | | | | | | | | | | COMBINE_EQS: (54), (80) imply:
% 229.33/40.80  | | | | | | | | | | |   (81)  all_57_7 = e2
% 229.33/40.80  | | | | | | | | | | | 
% 229.33/40.80  | | | | | | | | | | | REF_CLOSE: (2), (3), (6), (7), (11), (15), (16), (17), (19),
% 229.33/40.80  | | | | | | | | | | |            (20), (21), (22), (24), (25), (26), (27), (28),
% 229.33/40.80  | | | | | | | | | | |            (29), (31), (33), (43), (81) are inconsistent by
% 229.33/40.80  | | | | | | | | | | |            sub-proof #775.
% 229.33/40.80  | | | | | | | | | | | 
% 229.33/40.80  | | | | | | | | | | End of split
% 229.33/40.80  | | | | | | | | | | 
% 229.33/40.80  | | | | | | | | | End of split
% 229.33/40.80  | | | | | | | | | 
% 229.33/40.80  | | | | | | | | Case 2:
% 229.33/40.80  | | | | | | | | | 
% 229.33/40.80  | | | | | | | | |   (82)  all_57_13 = e3 & op(e0, e2) = e3
% 229.33/40.80  | | | | | | | | | 
% 229.33/40.80  | | | | | | | | | ALPHA: (82) implies:
% 229.33/40.80  | | | | | | | | |   (83)  all_57_13 = e3
% 229.33/40.80  | | | | | | | | | 
% 229.33/40.80  | | | | | | | | | REF_CLOSE: (6), (7), (15), (16), (17), (19), (21), (24), (26),
% 229.33/40.80  | | | | | | | | |            (27), (28), (33), (83) are inconsistent by
% 229.33/40.80  | | | | | | | | |            sub-proof #1792.
% 229.33/40.80  | | | | | | | | | 
% 229.33/40.80  | | | | | | | | End of split
% 229.33/40.80  | | | | | | | | 
% 229.33/40.80  | | | | | | | End of split
% 229.33/40.80  | | | | | | | 
% 229.33/40.80  | | | | | | Case 2:
% 229.33/40.80  | | | | | | | 
% 229.33/40.80  | | | | | | |   (84)  all_57_9 = e3 & op(e3, e0) = e3
% 229.33/40.80  | | | | | | | 
% 229.33/40.80  | | | | | | | ALPHA: (84) implies:
% 229.33/40.80  | | | | | | |   (85)  op(e3, e0) = e3
% 229.33/40.80  | | | | | | | 
% 229.33/40.80  | | | | | | | REF_CLOSE: (7), (30), (38), (85) are inconsistent by sub-proof
% 229.33/40.80  | | | | | | |            #2458.
% 229.33/40.80  | | | | | | | 
% 229.33/40.80  | | | | | | End of split
% 229.33/40.80  | | | | | | 
% 229.33/40.80  | | | | | End of split
% 229.33/40.80  | | | | | 
% 229.33/40.80  | | | | Case 2:
% 229.33/40.80  | | | | | 
% 229.33/40.80  | | | | |   (86)  all_57_3 = e2 & op(e2, e2) = e2
% 229.33/40.80  | | | | | 
% 229.33/40.80  | | | | | ALPHA: (86) implies:
% 229.33/40.80  | | | | |   (87)  op(e2, e2) = e2
% 229.33/40.80  | | | | | 
% 229.33/40.80  | | | | | REF_CLOSE: (7), (11), (33), (87) are inconsistent by sub-proof #2306.
% 229.33/40.80  | | | | | 
% 229.33/40.80  | | | | End of split
% 229.33/40.80  | | | | 
% 229.33/40.80  | | | Case 2:
% 229.33/40.80  | | | | 
% 229.33/40.80  | | | |   (88)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2)
% 229.33/40.80  | | | |           = e2)
% 229.33/40.80  | | | | 
% 229.33/40.80  | | | | BETA: splitting (88) gives:
% 229.33/40.80  | | | | 
% 229.33/40.80  | | | | Case 1:
% 229.33/40.80  | | | | | 
% 229.33/40.80  | | | | |   (89)  all_57_7 = e2 & op(e1, e2) = e2
% 229.33/40.80  | | | | | 
% 229.33/40.80  | | | | | ALPHA: (89) implies:
% 229.33/40.80  | | | | |   (90)  all_57_7 = e2
% 229.33/40.80  | | | | | 
% 229.33/40.80  | | | | | REF_CLOSE: (2), (3), (6), (7), (11), (15), (16), (17), (19), (20),
% 229.33/40.80  | | | | |            (21), (22), (24), (25), (26), (27), (28), (29), (31), (33),
% 229.33/40.80  | | | | |            (43), (90) are inconsistent by sub-proof #775.
% 229.33/40.80  | | | | | 
% 229.33/40.80  | | | | Case 2:
% 229.33/40.80  | | | | | 
% 229.33/40.80  | | | | |   (91)  all_57_13 = e2 & op(e0, e2) = e2
% 229.33/40.80  | | | | | 
% 229.33/40.80  | | | | | REF_CLOSE: (3), (33), (91) are inconsistent by sub-proof #2101.
% 229.33/40.80  | | | | | 
% 229.33/40.80  | | | | End of split
% 229.33/40.80  | | | | 
% 229.33/40.80  | | | End of split
% 229.33/40.80  | | | 
% 229.33/40.80  | | End of split
% 229.33/40.80  | | 
% 229.33/40.80  | Case 2:
% 229.33/40.80  | | 
% 229.33/40.80  | |   (92)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) =
% 229.33/40.80  | |           e1)
% 229.33/40.80  | | 
% 229.33/40.80  | | BETA: splitting (92) gives:
% 229.33/40.80  | | 
% 229.33/40.80  | | Case 1:
% 229.33/40.80  | | | 
% 229.33/40.80  | | |   (93)  all_57_6 = e1 & op(e1, e3) = e1
% 229.33/40.80  | | | 
% 229.33/40.80  | | | ALPHA: (93) implies:
% 229.33/40.80  | | |   (94)  all_57_6 = e1
% 229.33/40.80  | | | 
% 229.33/40.80  | | | REF_CLOSE: (3), (5), (6), (7), (8), (9), (10), (11), (12), (14), (15),
% 229.33/40.80  | | |            (16), (17), (18), (20), (21), (22), (23), (24), (28), (30),
% 229.33/40.80  | | |            (33), (34), (36), (37), (38), (94) are inconsistent by
% 229.33/40.80  | | |            sub-proof #797.
% 229.33/40.80  | | | 
% 229.33/40.80  | | Case 2:
% 229.33/40.80  | | | 
% 229.33/40.80  | | |   (95)  all_57_12 = e1 & op(e0, e3) = e1
% 229.33/40.80  | | | 
% 229.33/40.80  | | | REF_CLOSE: (13), (33), (95) are inconsistent by sub-proof #2388.
% 229.33/40.80  | | | 
% 229.33/40.80  | | End of split
% 229.33/40.80  | | 
% 229.33/40.80  | End of split
% 229.33/40.80  | 
% 229.33/40.80  End of proof
% 229.33/40.80  
% 229.33/40.80  Sub-proof #775 shows that the following formulas are inconsistent:
% 229.33/40.80  ----------------------------------------------------------------
% 229.33/40.80    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.33/40.80         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.33/40.80    (2)  all_57_13 = e1
% 229.33/40.80    (3)   ~ (e3 = e1)
% 229.33/40.80    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.33/40.80           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.33/40.80    (5)  op(e2, e2) = e1
% 229.33/40.80    (6)  all_57_7 = e2
% 229.33/40.80    (7)   ~ (e3 = e2)
% 229.33/40.80    (8)   ~ (e3 = e0)
% 229.33/40.80    (9)  all_57_15 = e3
% 229.33/40.80    (10)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.33/40.80          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.33/40.80            e1)
% 229.33/40.80    (11)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.33/40.80          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.33/40.80    (12)   ~ (e2 = e0)
% 229.33/40.80    (13)  all_57_3 = e1
% 229.33/40.80    (14)   ~ (e1 = e0)
% 229.33/40.80    (15)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.33/40.80          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.33/40.80    (16)  op(e0, e0) = e3
% 229.33/40.80    (17)  all_57_2 = e1
% 229.33/40.80    (18)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.33/40.80          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.33/40.80            e2)
% 229.33/40.80    (19)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.33/40.80              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.33/40.80                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.33/40.80                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.33/40.80    (20)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.33/40.80          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.33/40.80    (21)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.33/40.80          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.33/40.80    (22)   ~ (e2 = e1)
% 229.33/40.80  
% 229.33/40.80  Begin of proof
% 229.33/40.80  | 
% 229.33/40.80  | BETA: splitting (15) gives:
% 229.33/40.80  | 
% 229.33/40.80  | Case 1:
% 229.33/40.80  | | 
% 229.33/40.80  | |   (23)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 229.33/40.80  | |           e3)
% 229.33/40.80  | | 
% 229.33/40.80  | | BETA: splitting (23) gives:
% 229.33/40.80  | | 
% 229.33/40.80  | | Case 1:
% 229.33/40.80  | | | 
% 229.33/40.80  | | |   (24)  all_57_1 = e3 & op(e3, e2) = e3
% 229.33/40.80  | | | 
% 229.33/40.80  | | | ALPHA: (24) implies:
% 229.33/40.80  | | |   (25)  all_57_1 = e3
% 229.33/40.80  | | | 
% 229.33/40.80  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (11), (12), (13), (14),
% 229.33/40.80  | | |            (17), (20), (21), (22), (25) are inconsistent by sub-proof
% 229.33/40.80  | | |            #1589.
% 229.33/40.80  | | | 
% 229.33/40.80  | | Case 2:
% 229.33/40.80  | | | 
% 229.33/40.80  | | |   (26)  all_57_3 = e3 & op(e2, e2) = e3
% 229.33/40.80  | | | 
% 229.33/40.80  | | | ALPHA: (26) implies:
% 229.33/40.80  | | |   (27)  op(e2, e2) = e3
% 229.33/40.80  | | | 
% 229.33/40.80  | | | REF_CLOSE: (3), (4), (5), (27) are inconsistent by sub-proof #1912.
% 229.33/40.80  | | | 
% 229.33/40.80  | | End of split
% 229.33/40.80  | | 
% 229.33/40.80  | Case 2:
% 229.33/40.80  | | 
% 229.33/40.80  | |   (28)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 229.33/40.80  | |           e3)
% 229.33/40.80  | | 
% 229.33/40.80  | | REF_CLOSE: (3), (4), (6), (7), (8), (9), (10), (12), (14), (16), (18), (19),
% 229.33/40.80  | |            (22), (28) are inconsistent by sub-proof #776.
% 229.33/40.80  | | 
% 229.33/40.80  | End of split
% 229.33/40.80  | 
% 229.33/40.80  End of proof
% 229.33/40.80  
% 229.33/40.80  Sub-proof #776 shows that the following formulas are inconsistent:
% 229.33/40.80  ----------------------------------------------------------------
% 229.33/40.80    (1)   ~ (e3 = e1)
% 229.33/40.80    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.33/40.80           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.33/40.80    (3)  all_57_7 = e2
% 229.33/40.80    (4)   ~ (e3 = e2)
% 229.33/40.80    (5)   ~ (e3 = e0)
% 229.33/40.80    (6)  all_57_15 = e3
% 229.33/40.80    (7)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 229.33/40.80         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.33/40.80    (8)   ~ (e2 = e0)
% 229.33/40.80    (9)   ~ (e1 = e0)
% 229.33/40.80    (10)  op(e0, e0) = e3
% 229.33/40.80    (11)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.33/40.80          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.33/40.80            e2)
% 229.33/40.80    (12)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.33/40.80              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.33/40.80                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.33/40.80                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.33/40.80    (13)   ~ (e2 = e1)
% 229.33/40.80    (14)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.33/40.80  
% 229.33/40.80  Begin of proof
% 229.33/40.80  | 
% 229.33/40.80  | BETA: splitting (14) gives:
% 229.33/40.80  | 
% 229.33/40.80  | Case 1:
% 229.33/40.80  | | 
% 229.33/40.80  | |   (15)  all_57_7 = e3 & op(e1, e2) = e3
% 229.33/40.80  | | 
% 229.33/40.80  | | ALPHA: (15) implies:
% 229.33/40.80  | |   (16)  all_57_7 = e3
% 229.33/40.80  | | 
% 229.33/40.80  | | REF_CLOSE: (3), (4), (16) are inconsistent by sub-proof #2102.
% 229.33/40.80  | | 
% 229.33/40.80  | Case 2:
% 229.33/40.80  | | 
% 229.33/40.80  | |   (17)  all_57_13 = e3 & op(e0, e2) = e3
% 229.33/40.80  | | 
% 229.33/40.80  | | ALPHA: (17) implies:
% 229.33/40.80  | |   (18)  all_57_13 = e3
% 229.33/40.80  | | 
% 229.33/40.80  | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 229.33/40.80  | |            (18) are inconsistent by sub-proof #1792.
% 229.33/40.80  | | 
% 229.33/40.80  | End of split
% 229.33/40.80  | 
% 229.33/40.80  End of proof
% 229.33/40.80  
% 229.33/40.80  Sub-proof #777 shows that the following formulas are inconsistent:
% 229.33/40.80  ----------------------------------------------------------------
% 229.33/40.80    (1)   ~ (e3 = e1)
% 229.33/40.80    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.33/40.80           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.33/40.80    (3)   ~ (all_6_2 = e3)
% 229.33/40.80    (4)  op(e1, e1) = all_6_2
% 229.33/40.80    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.33/40.80         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.33/40.80    (6)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.33/40.80         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.33/40.80    (7)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.33/40.80         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.33/40.80    (8)   ~ (e3 = e2)
% 229.33/40.80    (9)   ~ (e3 = e0)
% 229.33/40.80    (10)  all_57_15 = e3
% 229.33/40.80    (11)  op(e3, e3) = e2
% 229.33/40.80    (12)  all_57_4 = e1
% 229.33/40.80    (13)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.33/40.80          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.33/40.80            e1)
% 229.33/40.80    (14)   ~ (e2 = e0)
% 229.33/40.80    (15)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.33/40.80          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.33/40.80    (16)   ~ (e1 = e0)
% 229.33/40.80    (17)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.33/40.80    (18)  all_57_5 = e2
% 229.33/40.80    (19)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.33/40.80          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.33/40.80    (20)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.33/40.80          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.33/40.80            e2)
% 229.33/40.80    (21)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.33/40.80              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.33/40.80                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.33/40.80                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.33/40.80    (22)   ~ (all_53_12 = e3)
% 229.33/40.80    (23)  all_57_1 = e3
% 229.33/40.80    (24)   ~ (e2 = e1)
% 229.33/40.80    (25)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.33/40.80          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.33/40.80    (26)  op(e3, e0) = all_53_12
% 229.33/40.80  
% 229.33/40.80  Begin of proof
% 229.33/40.80  | 
% 229.33/40.80  | BETA: splitting (17) gives:
% 229.33/40.80  | 
% 229.33/40.80  | Case 1:
% 229.33/40.80  | | 
% 229.33/40.80  | |   (27)  all_57_5 = e3 & op(e2, e1) = e3
% 229.33/40.80  | | 
% 229.33/40.80  | | ALPHA: (27) implies:
% 229.33/40.80  | |   (28)  all_57_5 = e3
% 229.33/40.80  | | 
% 229.33/40.80  | | COMBINE_EQS: (18), (28) imply:
% 229.33/40.80  | |   (29)  e3 = e2
% 229.33/40.80  | | 
% 229.33/40.80  | | SIMP: (29) implies:
% 229.33/40.80  | |   (30)  e3 = e2
% 229.33/40.80  | | 
% 229.33/40.80  | | COMBINE_EQS: (23), (30) imply:
% 229.33/40.80  | |   (31)  all_57_1 = e2
% 229.33/40.80  | | 
% 229.33/40.80  | | REF_CLOSE: (1), (2), (8), (11), (12), (15), (22), (26), (31) are
% 229.33/40.80  | |            inconsistent by sub-proof #1308.
% 229.33/40.80  | | 
% 229.33/40.80  | Case 2:
% 229.33/40.80  | | 
% 229.33/40.80  | |   (32)  all_57_10 = e3 & op(e2, e0) = e3
% 229.33/40.80  | | 
% 229.33/40.80  | | ALPHA: (32) implies:
% 229.33/40.80  | |   (33)  all_57_10 = e3
% 229.33/40.80  | | 
% 229.33/40.80  | | BETA: splitting (19) gives:
% 229.33/40.80  | | 
% 229.33/40.80  | | Case 1:
% 229.33/40.80  | | | 
% 229.33/40.80  | | |   (34)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) =
% 229.33/40.80  | | |           e3)
% 229.33/40.80  | | | 
% 229.33/40.80  | | | BETA: splitting (34) gives:
% 229.33/40.80  | | | 
% 229.33/40.80  | | | Case 1:
% 229.33/40.80  | | | | 
% 229.33/40.80  | | | |   (35)  all_57_4 = e3 & op(e3, e1) = e3
% 229.33/40.80  | | | | 
% 229.33/40.80  | | | | ALPHA: (35) implies:
% 229.33/40.80  | | | |   (36)  all_57_4 = e3
% 229.33/40.80  | | | | 
% 229.33/40.80  | | | | REF_CLOSE: (1), (5), (6), (7), (8), (9), (10), (14), (16), (21), (23),
% 229.33/40.80  | | | |            (24), (25), (33), (36) are inconsistent by sub-proof #1436.
% 229.33/40.80  | | | | 
% 229.33/40.80  | | | Case 2:
% 229.33/40.80  | | | | 
% 229.33/40.80  | | | |   (37)  all_57_5 = e3 & op(e2, e1) = e3
% 229.33/40.80  | | | | 
% 229.33/40.80  | | | | ALPHA: (37) implies:
% 229.33/40.80  | | | |   (38)  all_57_5 = e3
% 229.33/40.80  | | | | 
% 229.33/40.80  | | | | REF_CLOSE: (8), (18), (38) are inconsistent by sub-proof #2189.
% 229.33/40.80  | | | | 
% 229.33/40.80  | | | End of split
% 229.33/40.80  | | | 
% 229.33/40.80  | | Case 2:
% 229.33/40.80  | | | 
% 229.33/40.80  | | |   (39)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) =
% 229.33/40.80  | | |           e3)
% 229.33/40.80  | | | 
% 229.33/40.80  | | | REF_CLOSE: (1), (2), (3), (4), (8), (9), (10), (13), (14), (16), (20),
% 229.33/40.80  | | |            (21), (24), (39) are inconsistent by sub-proof #1794.
% 229.33/40.80  | | | 
% 229.33/40.80  | | End of split
% 229.33/40.80  | | 
% 229.33/40.80  | End of split
% 229.33/40.80  | 
% 229.33/40.80  End of proof
% 229.33/40.80  
% 229.33/40.80  Sub-proof #778 shows that the following formulas are inconsistent:
% 229.33/40.80  ----------------------------------------------------------------
% 229.33/40.80    (1)  all_57_0 = e2
% 229.33/40.80    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.33/40.80         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.33/40.80    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.33/40.80         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.33/40.80    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.33/40.80         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.33/40.80    (5)   ~ (e3 = e1)
% 229.33/40.80    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.33/40.80           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.33/40.80    (7)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.33/40.80         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.33/40.80    (8)   ~ (all_6_2 = e3)
% 229.33/40.80    (9)  op(e1, e1) = all_6_2
% 229.33/40.80    (10)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.33/40.80          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.33/40.80    (11)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.33/40.80          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.33/40.80    (12)   ~ (e3 = e2)
% 229.33/40.80    (13)   ~ (e3 = e0)
% 229.33/40.80    (14)  all_57_15 = e3
% 229.33/40.80    (15)  op(e3, e3) = e2
% 229.33/40.80    (16)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.33/40.80          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.33/40.80            e1)
% 229.33/40.80    (17)   ~ (e2 = e0)
% 229.33/40.80    (18)  all_57_3 = e1
% 229.33/40.80    (19)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.33/40.80          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.33/40.80    (20)   ~ (e1 = e0)
% 229.33/40.80    (21)  e1 = e0
% 229.33/40.80    (22)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.33/40.80          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.33/40.80    (23)  op(e0, e0) = e3
% 229.33/40.80    (24)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.33/40.80          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.33/40.80            e2)
% 229.33/40.80    (25)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.33/40.80              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.33/40.80                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.33/40.80                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.33/40.80    (26)  all_57_13 = e0
% 229.33/40.80    (27)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.33/40.80          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.33/40.80    (28)   ~ (all_53_12 = e3)
% 229.33/40.80    (29)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.33/40.80          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.33/40.80    (30)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.33/40.80          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.33/40.80    (31)   ~ (e2 = e1)
% 229.33/40.80    (32)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.33/40.80          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.33/40.80    (33)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.33/40.80          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.33/40.80    (34)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.33/40.80          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.33/40.80    (35)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.33/40.80          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.33/40.80    (36)  op(e3, e0) = all_53_12
% 229.33/40.80  
% 229.33/40.80  Begin of proof
% 229.33/40.80  | 
% 229.33/40.80  | COMBINE_EQS: (18), (21) imply:
% 229.33/40.80  |   (37)  all_57_3 = e0
% 229.33/40.80  | 
% 229.33/40.80  | BETA: splitting (33) gives:
% 229.33/40.80  | 
% 229.33/40.80  | Case 1:
% 229.33/40.80  | | 
% 229.33/40.80  | |   (38)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) =
% 229.33/40.80  | |           e0)
% 229.33/40.80  | | 
% 229.33/40.80  | | REF_CLOSE: (2), (5), (6), (12), (13), (15), (17), (20), (27), (29), (31),
% 229.33/40.80  | |            (37), (38) are inconsistent by sub-proof #1654.
% 229.33/40.80  | | 
% 229.33/40.80  | Case 2:
% 229.33/40.80  | | 
% 229.33/40.80  | |   (39)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) =
% 229.33/40.80  | |           e0)
% 229.33/40.80  | | 
% 229.33/40.80  | | BETA: splitting (39) gives:
% 229.33/40.80  | | 
% 229.33/40.80  | | Case 1:
% 229.33/40.80  | | | 
% 229.33/40.80  | | |   (40)  all_57_6 = e0 & op(e1, e3) = e0
% 229.33/40.80  | | | 
% 229.33/40.80  | | | ALPHA: (40) implies:
% 229.33/40.80  | | |   (41)  all_57_6 = e0
% 229.33/40.80  | | | 
% 229.33/40.80  | | | BETA: splitting (4) gives:
% 229.33/40.80  | | | 
% 229.33/40.80  | | | Case 1:
% 229.33/40.80  | | | | 
% 229.33/40.80  | | | |   (42)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2)
% 229.33/40.80  | | | |           = e2)
% 229.33/40.80  | | | | 
% 229.33/40.80  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 229.33/40.80  | | | |            (12), (13), (14), (15), (16), (17), (19), (20), (22), (23),
% 229.33/40.80  | | | |            (24), (25), (27), (28), (29), (30), (31), (32), (33), (34),
% 229.33/40.80  | | | |            (35), (36), (37), (42) are inconsistent by sub-proof #780.
% 229.33/40.80  | | | | 
% 229.33/40.80  | | | Case 2:
% 229.33/40.80  | | | | 
% 229.33/40.80  | | | |   (43)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2)
% 229.33/40.80  | | | |           = e2)
% 229.33/40.80  | | | | 
% 229.33/40.80  | | | | BETA: splitting (43) gives:
% 229.33/40.80  | | | | 
% 229.33/40.80  | | | | Case 1:
% 229.33/40.80  | | | | | 
% 229.33/40.80  | | | | |   (44)  all_57_7 = e2 & op(e1, e2) = e2
% 229.33/40.80  | | | | | 
% 229.33/40.80  | | | | | ALPHA: (44) implies:
% 229.33/40.80  | | | | |   (45)  all_57_7 = e2
% 229.33/40.80  | | | | | 
% 229.33/40.80  | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (12), (13), (14), (17), (20),
% 229.33/40.80  | | | | |            (25), (31), (32), (34), (41), (45) are inconsistent by
% 229.33/40.80  | | | | |            sub-proof #1775.
% 229.33/40.80  | | | | | 
% 229.33/40.80  | | | | Case 2:
% 229.33/40.80  | | | | | 
% 229.33/40.80  | | | | |   (46)  all_57_13 = e2 & op(e0, e2) = e2
% 229.33/40.80  | | | | | 
% 229.33/40.80  | | | | | ALPHA: (46) implies:
% 229.33/40.80  | | | | |   (47)  all_57_13 = e2
% 229.33/40.80  | | | | | 
% 229.33/40.80  | | | | | REF_CLOSE: (17), (26), (47) are inconsistent by sub-proof #1911.
% 229.33/40.80  | | | | | 
% 229.33/40.80  | | | | End of split
% 229.33/40.80  | | | | 
% 229.33/40.80  | | | End of split
% 229.33/40.80  | | | 
% 229.33/40.80  | | Case 2:
% 229.33/40.80  | | | 
% 229.33/40.80  | | |   (48)  all_57_12 = e0 & op(e0, e3) = e0
% 229.33/40.80  | | | 
% 229.33/40.80  | | | ALPHA: (48) implies:
% 229.33/40.80  | | |   (49)  all_57_12 = e0
% 229.33/40.80  | | | 
% 229.33/40.80  | | | BETA: splitting (4) gives:
% 229.33/40.80  | | | 
% 229.33/40.80  | | | Case 1:
% 229.33/40.80  | | | | 
% 229.33/40.80  | | | |   (50)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2)
% 229.33/40.80  | | | |           = e2)
% 229.33/40.80  | | | | 
% 229.33/40.80  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 229.33/40.80  | | | |            (12), (13), (14), (15), (16), (17), (19), (20), (22), (23),
% 229.33/40.80  | | | |            (24), (25), (27), (28), (29), (30), (31), (32), (33), (34),
% 229.33/40.80  | | | |            (35), (36), (37), (50) are inconsistent by sub-proof #780.
% 229.33/40.80  | | | | 
% 229.33/40.80  | | | Case 2:
% 229.33/40.80  | | | | 
% 229.33/40.80  | | | |   (51)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2)
% 229.33/40.80  | | | |           = e2)
% 229.33/40.80  | | | | 
% 229.33/40.80  | | | | BETA: splitting (51) gives:
% 229.33/40.80  | | | | 
% 229.33/40.80  | | | | Case 1:
% 229.33/40.80  | | | | | 
% 229.33/40.80  | | | | |   (52)  all_57_7 = e2 & op(e1, e2) = e2
% 229.33/40.80  | | | | | 
% 229.33/40.80  | | | | | ALPHA: (52) implies:
% 229.33/40.80  | | | | |   (53)  all_57_7 = e2
% 229.33/40.80  | | | | | 
% 229.33/40.80  | | | | | REF_CLOSE: (5), (12), (13), (14), (16), (17), (20), (22), (24), (26),
% 229.33/40.80  | | | | |            (31), (35), (37), (49), (53) are inconsistent by sub-proof
% 229.33/40.80  | | | | |            #779.
% 229.33/40.80  | | | | | 
% 229.33/40.80  | | | | Case 2:
% 229.33/40.80  | | | | | 
% 229.33/40.80  | | | | |   (54)  all_57_13 = e2 & op(e0, e2) = e2
% 229.33/40.80  | | | | | 
% 229.33/40.80  | | | | | ALPHA: (54) implies:
% 229.33/40.80  | | | | |   (55)  all_57_13 = e2
% 229.33/40.80  | | | | | 
% 229.33/40.80  | | | | | REF_CLOSE: (17), (26), (55) are inconsistent by sub-proof #1911.
% 229.33/40.80  | | | | | 
% 229.33/40.80  | | | | End of split
% 229.33/40.80  | | | | 
% 229.33/40.80  | | | End of split
% 229.33/40.80  | | | 
% 229.33/40.80  | | End of split
% 229.33/40.80  | | 
% 229.33/40.80  | End of split
% 229.33/40.80  | 
% 229.33/40.80  End of proof
% 229.33/40.80  
% 229.33/40.80  Sub-proof #779 shows that the following formulas are inconsistent:
% 229.33/40.80  ----------------------------------------------------------------
% 229.33/40.80    (1)  all_57_12 = e0
% 229.33/40.80    (2)   ~ (e3 = e1)
% 229.33/40.80    (3)  all_57_7 = e2
% 229.33/40.80    (4)  all_57_3 = e0
% 229.33/40.80    (5)   ~ (e3 = e2)
% 229.33/40.80    (6)   ~ (e3 = e0)
% 229.33/40.80    (7)  all_57_15 = e3
% 229.33/40.80    (8)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 229.33/40.80         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.33/40.80    (9)   ~ (e2 = e0)
% 229.33/40.80    (10)   ~ (e1 = e0)
% 229.33/40.81    (11)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.33/40.81          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.33/40.81    (12)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.33/40.81          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.33/40.81            e2)
% 229.33/40.81    (13)  all_57_13 = e0
% 229.33/40.81    (14)   ~ (e2 = e1)
% 229.33/40.81    (15)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.33/40.81          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.33/40.81  
% 229.33/40.81  Begin of proof
% 229.33/40.81  | 
% 229.33/40.81  | BETA: splitting (11) gives:
% 229.33/40.81  | 
% 229.33/40.81  | Case 1:
% 229.33/40.81  | | 
% 229.33/40.81  | |   (16)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 229.33/40.81  | |           e3)
% 229.33/40.81  | | 
% 229.33/40.81  | | BETA: splitting (16) gives:
% 229.33/40.81  | | 
% 229.33/40.81  | | Case 1:
% 229.33/40.81  | | | 
% 229.33/40.81  | | |   (17)  all_57_1 = e3 & op(e3, e2) = e3
% 229.33/40.81  | | | 
% 229.33/40.81  | | | ALPHA: (17) implies:
% 229.33/40.81  | | |   (18)  all_57_1 = e3
% 229.33/40.81  | | | 
% 229.33/40.81  | | | REF_CLOSE: (2), (3), (4), (10), (13), (14), (15), (18) are inconsistent by
% 229.33/40.81  | | |            sub-proof #1759.
% 229.33/40.81  | | | 
% 229.33/40.81  | | Case 2:
% 229.33/40.81  | | | 
% 229.33/40.81  | | |   (19)  all_57_3 = e3 & op(e2, e2) = e3
% 229.33/40.81  | | | 
% 229.33/40.81  | | | ALPHA: (19) implies:
% 229.33/40.81  | | |   (20)  all_57_3 = e3
% 229.33/40.81  | | | 
% 229.33/40.81  | | | REF_CLOSE: (4), (6), (20) are inconsistent by sub-proof #2358.
% 229.33/40.81  | | | 
% 229.33/40.81  | | End of split
% 229.33/40.81  | | 
% 229.33/40.81  | Case 2:
% 229.33/40.81  | | 
% 229.33/40.81  | |   (21)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 229.33/40.81  | |           e3)
% 229.33/40.81  | | 
% 229.33/40.81  | | BETA: splitting (21) gives:
% 229.33/40.81  | | 
% 229.33/40.81  | | Case 1:
% 229.33/40.81  | | | 
% 229.33/40.81  | | |   (22)  all_57_7 = e3 & op(e1, e2) = e3
% 229.33/40.81  | | | 
% 229.33/40.81  | | | ALPHA: (22) implies:
% 229.33/40.81  | | |   (23)  all_57_7 = e3
% 229.33/40.81  | | | 
% 229.33/40.81  | | | REF_CLOSE: (3), (5), (23) are inconsistent by sub-proof #2102.
% 229.33/40.81  | | | 
% 229.33/40.81  | | Case 2:
% 229.33/40.81  | | | 
% 229.33/40.81  | | |   (24)  all_57_13 = e3 & op(e0, e2) = e3
% 229.33/40.81  | | | 
% 229.33/40.81  | | | ALPHA: (24) implies:
% 229.33/40.81  | | |   (25)  all_57_13 = e3
% 229.33/40.81  | | | 
% 229.33/40.81  | | | REF_CLOSE: (1), (2), (5), (7), (8), (9), (10), (12), (14), (25) are
% 229.33/40.81  | | |            inconsistent by sub-proof #2059.
% 229.33/40.81  | | | 
% 229.33/40.81  | | End of split
% 229.33/40.81  | | 
% 229.33/40.81  | End of split
% 229.33/40.81  | 
% 229.33/40.81  End of proof
% 229.33/40.81  
% 229.33/40.81  Sub-proof #780 shows that the following formulas are inconsistent:
% 229.33/40.81  ----------------------------------------------------------------
% 229.33/40.81    (1)  all_57_0 = e2
% 229.33/40.81    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.33/40.81         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.33/40.81    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.33/40.81         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.33/40.81    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.33/40.81         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.33/40.81    (5)   ~ (e3 = e1)
% 229.33/40.81    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.33/40.81           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.33/40.81    (7)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.33/40.81         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.33/40.81    (8)   ~ (all_6_2 = e3)
% 229.33/40.81    (9)  op(e1, e1) = all_6_2
% 229.33/40.81    (10)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.33/40.81          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.33/40.81    (11)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2)
% 229.33/40.81    (12)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.33/40.81          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.33/40.81    (13)  all_57_3 = e0
% 229.33/40.81    (14)   ~ (e3 = e2)
% 229.33/40.81    (15)   ~ (e3 = e0)
% 229.33/40.81    (16)  all_57_15 = e3
% 229.33/40.81    (17)  op(e3, e3) = e2
% 229.33/40.81    (18)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.33/40.81          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.33/40.81            e1)
% 229.33/40.81    (19)   ~ (e2 = e0)
% 229.33/40.81    (20)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.33/40.81          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.33/40.81    (21)   ~ (e1 = e0)
% 229.33/40.81    (22)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.33/40.81          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.33/40.81    (23)  op(e0, e0) = e3
% 229.33/40.81    (24)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.33/40.81          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.33/40.81            e2)
% 229.33/40.81    (25)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.33/40.81              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.33/40.81                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.33/40.81                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.33/40.81    (26)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.33/40.81          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.33/40.81    (27)   ~ (all_53_12 = e3)
% 229.33/40.81    (28)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.33/40.81          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.33/40.81    (29)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.33/40.81          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.33/40.81    (30)   ~ (e2 = e1)
% 229.33/40.81    (31)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.33/40.81          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.33/40.81    (32)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.33/40.81          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.33/40.81    (33)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.33/40.81          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.33/40.81    (34)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.33/40.81          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.33/40.81    (35)  op(e3, e0) = all_53_12
% 229.33/40.81  
% 229.33/40.81  Begin of proof
% 229.33/40.81  | 
% 229.33/40.81  | BETA: splitting (11) gives:
% 229.33/40.81  | 
% 229.33/40.81  | Case 1:
% 229.33/40.81  | | 
% 229.33/40.81  | |   (36)  all_57_1 = e2 & op(e3, e2) = e2
% 229.33/40.81  | | 
% 229.33/40.81  | | ALPHA: (36) implies:
% 229.33/40.81  | |   (37)  all_57_1 = e2
% 229.33/40.81  | | 
% 229.33/40.81  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 229.33/40.81  | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 229.33/40.81  | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 229.33/40.81  | |            (37) are inconsistent by sub-proof #785.
% 229.33/40.81  | | 
% 229.33/40.81  | Case 2:
% 229.33/40.81  | | 
% 229.33/40.81  | |   (38)  all_57_3 = e2 & op(e2, e2) = e2
% 229.33/40.81  | | 
% 229.33/40.81  | | REF_CLOSE: (13), (19), (38) are inconsistent by sub-proof #2103.
% 229.33/40.81  | | 
% 229.33/40.81  | End of split
% 229.33/40.81  | 
% 229.33/40.81  End of proof
% 229.33/40.81  
% 229.33/40.81  Sub-proof #781 shows that the following formulas are inconsistent:
% 229.33/40.81  ----------------------------------------------------------------
% 229.33/40.81    (1)   ~ (e3 = e1)
% 229.33/40.81    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.33/40.81           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.33/40.81    (3)   ~ (all_6_2 = e3)
% 229.33/40.81    (4)  op(e1, e1) = all_6_2
% 229.33/40.81    (5)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.33/40.81    (6)   ~ (e3 = e2)
% 229.33/40.81    (7)  all_57_15 = e3
% 229.33/40.81    (8)  all_57_9 = e0
% 229.33/40.81    (9)   ~ (e2 = e0)
% 229.33/40.81    (10)   ~ (e1 = e0)
% 229.33/40.81    (11)   ~ (e2 = e1)
% 229.33/40.81    (12)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.33/40.81          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.33/40.81    (13)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.33/40.81          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.33/40.81  
% 229.33/40.81  Begin of proof
% 229.33/40.81  | 
% 229.33/40.81  | BETA: splitting (5) gives:
% 229.33/40.81  | 
% 229.33/40.81  | Case 1:
% 229.33/40.81  | | 
% 229.33/40.81  | |   (14)  all_57_8 = e3 & op(e1, e1) = e3
% 229.33/40.81  | | 
% 229.33/40.81  | | ALPHA: (14) implies:
% 229.33/40.81  | |   (15)  op(e1, e1) = e3
% 229.33/40.81  | | 
% 229.33/40.81  | | REF_CLOSE: (2), (3), (4), (15) are inconsistent by sub-proof #2468.
% 229.33/40.81  | | 
% 229.33/40.81  | Case 2:
% 229.33/40.81  | | 
% 229.33/40.81  | |   (16)  all_57_11 = e3 & op(e1, e0) = e3
% 229.33/40.81  | | 
% 229.33/40.81  | | ALPHA: (16) implies:
% 229.33/40.81  | |   (17)  all_57_11 = e3
% 229.33/40.81  | | 
% 229.33/40.81  | | REF_CLOSE: (1), (6), (7), (8), (9), (10), (11), (12), (13), (17) are
% 229.33/40.81  | |            inconsistent by sub-proof #2140.
% 229.33/40.81  | | 
% 229.33/40.81  | End of split
% 229.33/40.81  | 
% 229.33/40.81  End of proof
% 229.33/40.81  
% 229.33/40.81  Sub-proof #782 shows that the following formulas are inconsistent:
% 229.33/40.81  ----------------------------------------------------------------
% 229.33/40.81    (1)  all_57_0 = e2
% 229.33/40.81    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.33/40.81         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.33/40.81    (3)  all_57_13 = e1
% 229.33/40.81    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.33/40.81         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.33/40.81    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.33/40.81         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.33/40.81    (6)   ~ (e3 = e1)
% 229.33/40.81    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.33/40.81           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.33/40.81    (8)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.33/40.81         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.33/40.81    (9)   ~ (all_6_2 = e3)
% 229.33/40.81    (10)  op(e1, e1) = all_6_2
% 229.33/40.81    (11)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.33/40.81          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.33/40.81    (12)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.33/40.81          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.33/40.81    (13)  all_57_3 = e0
% 229.33/40.81    (14)   ~ (e3 = e2)
% 229.33/40.81    (15)   ~ (e3 = e0)
% 229.33/40.81    (16)  all_57_15 = e3
% 229.33/40.81    (17)  op(e3, e3) = e2
% 229.33/40.81    (18)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.33/40.81          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.33/40.81            e1)
% 229.33/40.81    (19)   ~ (e2 = e0)
% 229.33/40.81    (20)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.33/40.81          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.33/40.81    (21)   ~ (e1 = e0)
% 229.33/40.81    (22)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.33/40.81          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.33/40.81    (23)  op(e0, e0) = e3
% 229.33/40.81    (24)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.33/40.81          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.33/40.81            e2)
% 229.33/40.81    (25)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.33/40.81              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.33/40.81                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.33/40.81                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.33/40.81    (26)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.33/40.81          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.33/40.81    (27)   ~ (all_53_12 = e3)
% 229.33/40.81    (28)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.33/40.81          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.33/40.81    (29)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.33/40.81          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.33/40.81    (30)  all_57_1 = e3
% 229.33/40.81    (31)   ~ (e2 = e1)
% 229.33/40.81    (32)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.33/40.81          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.33/40.81    (33)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.33/40.81          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.33/40.81    (34)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.33/40.81          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.33/40.81    (35)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.33/40.81          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.33/40.81    (36)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.33/40.81          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.33/40.81    (37)  all_57_7 = e0
% 229.33/40.81    (38)  op(e3, e0) = all_53_12
% 229.33/40.81  
% 229.33/40.81  Begin of proof
% 229.33/40.81  | 
% 229.33/40.81  | BETA: splitting (8) gives:
% 229.33/40.81  | 
% 229.33/40.81  | Case 1:
% 229.33/40.81  | | 
% 229.33/40.81  | |   (39)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 229.33/40.81  | |           e3)
% 229.33/40.81  | | 
% 229.33/40.81  | | BETA: splitting (39) gives:
% 229.33/40.81  | | 
% 229.33/40.81  | | Case 1:
% 229.33/40.81  | | | 
% 229.33/40.81  | | |   (40)  all_57_6 = e3 & op(e1, e3) = e3
% 229.33/40.81  | | | 
% 229.33/40.81  | | | ALPHA: (40) implies:
% 229.33/40.81  | | |   (41)  all_57_6 = e3
% 229.33/40.81  | | | 
% 229.33/40.81  | | | BETA: splitting (34) gives:
% 229.33/40.81  | | | 
% 229.33/40.81  | | | Case 1:
% 229.33/40.81  | | | | 
% 229.33/40.81  | | | |   (42)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3)
% 229.33/40.81  | | | |           = e0)
% 229.33/40.81  | | | | 
% 229.33/40.81  | | | | REF_CLOSE: (2), (6), (7), (13), (14), (15), (17), (19), (21), (26),
% 229.33/40.81  | | | |            (28), (31), (42) are inconsistent by sub-proof #1654.
% 229.33/40.81  | | | | 
% 229.33/40.81  | | | Case 2:
% 229.33/40.81  | | | | 
% 229.33/40.81  | | | |   (43)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3)
% 229.33/40.81  | | | |           = e0)
% 229.33/40.81  | | | | 
% 229.33/40.81  | | | | BETA: splitting (43) gives:
% 229.33/40.81  | | | | 
% 229.33/40.81  | | | | Case 1:
% 229.33/40.81  | | | | | 
% 229.33/40.81  | | | | |   (44)  all_57_6 = e0 & op(e1, e3) = e0
% 229.33/40.81  | | | | | 
% 229.33/40.81  | | | | | ALPHA: (44) implies:
% 229.33/40.81  | | | | |   (45)  all_57_6 = e0
% 229.33/40.81  | | | | | 
% 229.33/40.81  | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (13), (14),
% 229.33/40.81  | | | | |            (15), (16), (17), (18), (19), (21), (23), (24), (25), (26),
% 229.33/40.81  | | | | |            (28), (29), (30), (31), (32), (33), (34), (35), (36), (45)
% 229.33/40.81  | | | | |            are inconsistent by sub-proof #789.
% 229.33/40.81  | | | | | 
% 229.33/40.81  | | | | Case 2:
% 229.33/40.81  | | | | | 
% 229.33/40.81  | | | | |   (46)  all_57_12 = e0 & op(e0, e3) = e0
% 229.33/40.81  | | | | | 
% 229.33/40.81  | | | | | ALPHA: (46) implies:
% 229.33/40.81  | | | | |   (47)  all_57_12 = e0
% 229.33/40.81  | | | | | 
% 229.33/40.81  | | | | | BETA: splitting (5) gives:
% 229.33/40.81  | | | | | 
% 229.33/40.81  | | | | | Case 1:
% 229.33/40.81  | | | | | | 
% 229.33/40.82  | | | | | |   (48)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2,
% 229.33/40.82  | | | | | |             e2) = e2)
% 229.33/40.82  | | | | | | 
% 229.33/40.82  | | | | | | BETA: splitting (48) gives:
% 229.33/40.82  | | | | | | 
% 229.33/40.82  | | | | | | Case 1:
% 229.33/40.82  | | | | | | | 
% 229.33/40.82  | | | | | | |   (49)  all_57_1 = e2 & op(e3, e2) = e2
% 229.33/40.82  | | | | | | | 
% 229.33/40.82  | | | | | | | ALPHA: (49) implies:
% 229.33/40.82  | | | | | | |   (50)  all_57_1 = e2
% 229.33/40.82  | | | | | | | 
% 229.33/40.82  | | | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11),
% 229.33/40.82  | | | | | | |            (12), (13), (14), (15), (16), (17), (18), (19), (20),
% 229.33/40.82  | | | | | | |            (21), (22), (23), (24), (25), (26), (27), (28), (29),
% 229.33/40.82  | | | | | | |            (31), (32), (34), (35), (36), (38), (50) are
% 229.33/40.82  | | | | | | |            inconsistent by sub-proof #785.
% 229.33/40.82  | | | | | | | 
% 229.33/40.82  | | | | | | Case 2:
% 229.33/40.82  | | | | | | | 
% 229.33/40.82  | | | | | | |   (51)  all_57_3 = e2 & op(e2, e2) = e2
% 229.33/40.82  | | | | | | | 
% 229.33/40.82  | | | | | | | REF_CLOSE: (1), (4), (6), (13), (14), (19), (21), (31), (33),
% 229.33/40.82  | | | | | | |            (41), (47), (51) are inconsistent by sub-proof #784.
% 229.33/40.82  | | | | | | | 
% 229.33/40.82  | | | | | | End of split
% 229.33/40.82  | | | | | | 
% 229.33/40.82  | | | | | Case 2:
% 229.33/40.82  | | | | | | 
% 229.33/40.82  | | | | | |   (52)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0,
% 229.33/40.82  | | | | | |             e2) = e2)
% 229.33/40.82  | | | | | | 
% 229.33/40.82  | | | | | | BETA: splitting (52) gives:
% 229.33/40.82  | | | | | | 
% 229.33/40.82  | | | | | | Case 1:
% 229.33/40.82  | | | | | | | 
% 229.33/40.82  | | | | | | |   (53)  all_57_7 = e2 & op(e1, e2) = e2
% 229.33/40.82  | | | | | | | 
% 229.33/40.82  | | | | | | | REF_CLOSE: (1), (4), (6), (14), (19), (21), (31), (33), (37),
% 229.33/40.82  | | | | | | |            (41), (47), (53) are inconsistent by sub-proof #783.
% 229.33/40.82  | | | | | | | 
% 229.33/40.82  | | | | | | Case 2:
% 229.33/40.82  | | | | | | | 
% 229.33/40.82  | | | | | | |   (54)  all_57_13 = e2 & op(e0, e2) = e2
% 229.33/40.82  | | | | | | | 
% 229.33/40.82  | | | | | | | ALPHA: (54) implies:
% 229.33/40.82  | | | | | | |   (55)  all_57_13 = e2
% 229.33/40.82  | | | | | | | 
% 229.33/40.82  | | | | | | | REF_CLOSE: (3), (31), (55) are inconsistent by sub-proof #2327.
% 229.33/40.82  | | | | | | | 
% 229.33/40.82  | | | | | | End of split
% 229.33/40.82  | | | | | | 
% 229.33/40.82  | | | | | End of split
% 229.33/40.82  | | | | | 
% 229.33/40.82  | | | | End of split
% 229.33/40.82  | | | | 
% 229.33/40.82  | | | End of split
% 229.33/40.82  | | | 
% 229.33/40.82  | | Case 2:
% 229.33/40.82  | | | 
% 229.33/40.82  | | |   (56)  all_57_7 = e3 & op(e1, e2) = e3
% 229.33/40.82  | | | 
% 229.33/40.82  | | | ALPHA: (56) implies:
% 229.33/40.82  | | |   (57)  all_57_7 = e3
% 229.33/40.82  | | | 
% 229.33/40.82  | | | REF_CLOSE: (5), (6), (13), (14), (19), (21), (30), (31), (36), (57) are
% 229.33/40.82  | | |            inconsistent by sub-proof #1778.
% 229.33/40.82  | | | 
% 229.33/40.82  | | End of split
% 229.33/40.82  | | 
% 229.33/40.82  | Case 2:
% 229.33/40.82  | | 
% 229.33/40.82  | |   (58)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 229.33/40.82  | |           e3)
% 229.33/40.82  | | 
% 229.33/40.82  | | REF_CLOSE: (6), (7), (9), (10), (14), (15), (16), (19), (21), (25), (31),
% 229.33/40.82  | |            (32), (35), (58) are inconsistent by sub-proof #1786.
% 229.33/40.82  | | 
% 229.33/40.82  | End of split
% 229.33/40.82  | 
% 229.33/40.82  End of proof
% 229.33/40.82  
% 229.33/40.82  Sub-proof #783 shows that the following formulas are inconsistent:
% 229.33/40.82  ----------------------------------------------------------------
% 229.33/40.82    (1)  all_57_0 = e2
% 229.33/40.82    (2)  all_57_12 = e0
% 229.33/40.82    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.33/40.82         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.33/40.82    (4)   ~ (e3 = e1)
% 229.33/40.82    (5)   ~ (e3 = e2)
% 229.33/40.82    (6)   ~ (e2 = e0)
% 229.33/40.82    (7)   ~ (e1 = e0)
% 229.33/40.82    (8)  all_57_6 = e3
% 229.33/40.82    (9)  all_57_7 = e2 & op(e1, e2) = e2
% 229.33/40.82    (10)   ~ (e2 = e1)
% 229.33/40.82    (11)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.33/40.82          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.33/40.82    (12)  all_57_7 = e0
% 229.33/40.82  
% 229.33/40.82  Begin of proof
% 229.33/40.82  | 
% 229.33/40.82  | ALPHA: (9) implies:
% 229.33/40.82  |   (13)  all_57_7 = e2
% 229.33/40.82  | 
% 229.33/40.82  | COMBINE_EQS: (12), (13) imply:
% 229.33/40.82  |   (14)  e2 = e0
% 229.33/40.82  | 
% 229.33/40.82  | SIMP: (14) implies:
% 229.33/40.82  |   (15)  e2 = e0
% 229.33/40.82  | 
% 229.33/40.82  | COMBINE_EQS: (1), (15) imply:
% 229.33/40.82  |   (16)  all_57_0 = e0
% 229.33/40.82  | 
% 229.33/40.82  | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (10), (11), (16) are
% 229.33/40.82  |            inconsistent by sub-proof #1425.
% 229.33/40.82  | 
% 229.33/40.82  End of proof
% 229.33/40.82  
% 229.33/40.82  Sub-proof #784 shows that the following formulas are inconsistent:
% 229.33/40.82  ----------------------------------------------------------------
% 229.33/40.82    (1)  all_57_0 = e2
% 229.33/40.82    (2)  all_57_3 = e2 & op(e2, e2) = e2
% 229.33/40.82    (3)  all_57_12 = e0
% 229.33/40.82    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.33/40.82         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.33/40.82    (5)   ~ (e3 = e1)
% 229.33/40.82    (6)  all_57_3 = e0
% 229.33/40.82    (7)   ~ (e3 = e2)
% 229.33/40.82    (8)   ~ (e2 = e0)
% 229.33/40.82    (9)   ~ (e1 = e0)
% 229.33/40.82    (10)  all_57_6 = e3
% 229.33/40.82    (11)   ~ (e2 = e1)
% 229.33/40.82    (12)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.33/40.82          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.33/40.82  
% 229.33/40.82  Begin of proof
% 229.33/40.82  | 
% 229.33/40.82  | ALPHA: (2) implies:
% 229.33/40.82  |   (13)  all_57_3 = e2
% 229.33/40.82  | 
% 229.33/40.82  | COMBINE_EQS: (6), (13) imply:
% 229.33/40.82  |   (14)  e2 = e0
% 229.33/40.82  | 
% 229.33/40.82  | SIMP: (14) implies:
% 229.33/40.82  |   (15)  e2 = e0
% 229.33/40.82  | 
% 229.33/40.82  | COMBINE_EQS: (1), (15) imply:
% 229.33/40.82  |   (16)  all_57_0 = e0
% 229.33/40.82  | 
% 229.33/40.82  | REF_CLOSE: (3), (4), (5), (7), (8), (9), (10), (11), (12), (16) are
% 229.33/40.82  |            inconsistent by sub-proof #1425.
% 229.33/40.82  | 
% 229.33/40.82  End of proof
% 229.33/40.82  
% 229.33/40.82  Sub-proof #785 shows that the following formulas are inconsistent:
% 229.33/40.82  ----------------------------------------------------------------
% 229.33/40.82    (1)  all_57_0 = e2
% 229.33/40.82    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.33/40.82         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.33/40.82    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.33/40.82         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.33/40.82    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.33/40.82         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.33/40.82    (5)   ~ (e3 = e1)
% 229.33/40.82    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.33/40.82           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.33/40.82    (7)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.33/40.82         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.33/40.82    (8)   ~ (all_6_2 = e3)
% 229.33/40.82    (9)  op(e1, e1) = all_6_2
% 229.33/40.82    (10)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.33/40.82          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.33/40.82    (11)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.33/40.82          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.33/40.82    (12)  all_57_3 = e0
% 229.33/40.82    (13)   ~ (e3 = e2)
% 229.33/40.82    (14)   ~ (e3 = e0)
% 229.33/40.82    (15)  all_57_1 = e2
% 229.33/40.82    (16)  all_57_15 = e3
% 229.33/40.82    (17)  op(e3, e3) = e2
% 229.33/40.82    (18)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.33/40.82          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.33/40.82            e1)
% 229.33/40.82    (19)   ~ (e2 = e0)
% 229.33/40.82    (20)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.33/40.82          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.33/40.82    (21)   ~ (e1 = e0)
% 229.33/40.82    (22)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.33/40.82          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.33/40.82    (23)  op(e0, e0) = e3
% 229.33/40.82    (24)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.33/40.82          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.33/40.82            e2)
% 229.33/40.82    (25)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.33/40.82              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.33/40.82                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.33/40.82                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.33/40.82    (26)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.33/40.82          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.33/40.82    (27)   ~ (all_53_12 = e3)
% 229.33/40.82    (28)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.33/40.82          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.33/40.82    (29)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.33/40.82          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.33/40.82    (30)   ~ (e2 = e1)
% 229.33/40.82    (31)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.33/40.82          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.33/40.82    (32)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.33/40.82          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.33/40.82    (33)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.33/40.82          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.33/40.82    (34)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.33/40.82          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.33/40.82    (35)  op(e3, e0) = all_53_12
% 229.33/40.82  
% 229.33/40.82  Begin of proof
% 229.33/40.82  | 
% 229.33/40.82  | BETA: splitting (22) gives:
% 229.33/40.82  | 
% 229.33/40.82  | Case 1:
% 229.33/40.82  | | 
% 229.33/40.82  | |   (36)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 229.33/40.82  | |           e3)
% 229.33/40.82  | | 
% 229.33/40.82  | | REF_CLOSE: (12), (13), (14), (15), (36) are inconsistent by sub-proof #788.
% 229.33/40.82  | | 
% 229.33/40.82  | Case 2:
% 229.33/40.82  | | 
% 229.33/40.82  | |   (37)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 229.33/40.82  | |           e3)
% 229.33/40.82  | | 
% 229.33/40.82  | | BETA: splitting (37) gives:
% 229.33/40.82  | | 
% 229.33/40.82  | | Case 1:
% 229.33/40.82  | | | 
% 229.33/40.82  | | |   (38)  all_57_7 = e3 & op(e1, e2) = e3
% 229.33/40.82  | | | 
% 229.33/40.82  | | | ALPHA: (38) implies:
% 229.33/40.82  | | |   (39)  all_57_7 = e3
% 229.33/40.82  | | | 
% 229.33/40.82  | | | REF_CLOSE: (4), (5), (6), (10), (11), (12), (13), (14), (15), (17), (19),
% 229.33/40.82  | | |            (20), (21), (27), (30), (34), (35), (39) are inconsistent by
% 229.33/40.82  | | |            sub-proof #787.
% 229.33/40.82  | | | 
% 229.33/40.82  | | Case 2:
% 229.33/40.82  | | | 
% 229.33/40.82  | | |   (40)  all_57_13 = e3 & op(e0, e2) = e3
% 229.33/40.82  | | | 
% 229.33/40.82  | | | ALPHA: (40) implies:
% 229.33/40.82  | | |   (41)  all_57_13 = e3
% 229.33/40.82  | | | 
% 229.33/40.82  | | | BETA: splitting (24) gives:
% 229.33/40.82  | | | 
% 229.33/40.82  | | | Case 1:
% 229.33/40.82  | | | | 
% 229.33/40.82  | | | |   (42)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0,
% 229.33/40.82  | | | |             e2) = e2)
% 229.33/40.82  | | | | 
% 229.33/40.82  | | | | BETA: splitting (42) gives:
% 229.33/40.82  | | | | 
% 229.33/40.82  | | | | Case 1:
% 229.33/40.82  | | | | | 
% 229.33/40.82  | | | | |   (43)  all_57_12 = e2 & op(e0, e3) = e2
% 229.33/40.82  | | | | | 
% 229.33/40.82  | | | | | ALPHA: (43) implies:
% 229.33/40.82  | | | | |   (44)  all_57_12 = e2
% 229.33/40.82  | | | | | 
% 229.33/40.82  | | | | | BETA: splitting (32) gives:
% 229.33/40.82  | | | | | 
% 229.33/40.82  | | | | | Case 1:
% 229.33/40.82  | | | | | | 
% 229.33/40.82  | | | | | |   (45)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2,
% 229.33/40.82  | | | | | |             e3) = e0)
% 229.33/40.82  | | | | | | 
% 229.33/40.82  | | | | | | REF_CLOSE: (2), (5), (6), (12), (13), (14), (17), (19), (21), (26),
% 229.33/40.82  | | | | | |            (28), (30), (45) are inconsistent by sub-proof #1654.
% 229.33/40.82  | | | | | | 
% 229.33/40.82  | | | | | Case 2:
% 229.33/40.82  | | | | | | 
% 229.33/40.82  | | | | | |   (46)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0,
% 229.33/40.82  | | | | | |             e3) = e0)
% 229.33/40.82  | | | | | | 
% 229.33/40.82  | | | | | | BETA: splitting (46) gives:
% 229.33/40.82  | | | | | | 
% 229.33/40.82  | | | | | | Case 1:
% 229.33/40.82  | | | | | | | 
% 229.33/40.82  | | | | | | |   (47)  all_57_6 = e0 & op(e1, e3) = e0
% 229.33/40.82  | | | | | | | 
% 229.33/40.82  | | | | | | | ALPHA: (47) implies:
% 229.33/40.82  | | | | | | |   (48)  all_57_6 = e0
% 229.33/40.82  | | | | | | | 
% 229.33/40.82  | | | | | | | BETA: splitting (29) gives:
% 229.33/40.82  | | | | | | | 
% 229.33/40.82  | | | | | | | Case 1:
% 229.33/40.82  | | | | | | | | 
% 229.33/40.82  | | | | | | | |   (49)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 &
% 229.33/40.82  | | | | | | | |           op(e2, e3) = e3)
% 229.33/40.82  | | | | | | | | 
% 229.33/40.82  | | | | | | | | BETA: splitting (49) gives:
% 229.33/40.82  | | | | | | | | 
% 229.33/40.82  | | | | | | | | Case 1:
% 229.33/40.82  | | | | | | | | | 
% 229.33/40.82  | | | | | | | | |   (50)  all_57_0 = e3 & op(e3, e3) = e3
% 229.33/40.82  | | | | | | | | | 
% 229.33/40.82  | | | | | | | | | ALPHA: (50) implies:
% 229.33/40.82  | | | | | | | | |   (51)  op(e3, e3) = e3
% 229.33/40.82  | | | | | | | | | 
% 229.33/40.82  | | | | | | | | | REF_CLOSE: (6), (13), (17), (51) are inconsistent by sub-proof
% 229.33/40.82  | | | | | | | | |            #2490.
% 229.33/40.82  | | | | | | | | | 
% 229.33/40.82  | | | | | | | | Case 2:
% 229.33/40.82  | | | | | | | | | 
% 229.33/40.82  | | | | | | | | |   (52)  all_57_2 = e3 & op(e2, e3) = e3
% 229.33/40.82  | | | | | | | | | 
% 229.33/40.82  | | | | | | | | | ALPHA: (52) implies:
% 229.33/40.82  | | | | | | | | |   (53)  all_57_2 = e3
% 229.33/40.82  | | | | | | | | | 
% 229.33/40.82  | | | | | | | | | BETA: splitting (25) gives:
% 229.33/40.82  | | | | | | | | | 
% 229.33/40.82  | | | | | | | | | Case 1:
% 229.33/40.82  | | | | | | | | | | 
% 229.33/40.82  | | | | | | | | | |   (54)  all_57_15 = e0 & op(e0, e0) = e0
% 229.33/40.82  | | | | | | | | | | 
% 229.33/40.82  | | | | | | | | | | ALPHA: (54) implies:
% 229.33/40.82  | | | | | | | | | |   (55)  op(e0, e0) = e0
% 229.33/40.82  | | | | | | | | | | 
% 229.33/40.82  | | | | | | | | | | REF_CLOSE: (6), (14), (23), (55) are inconsistent by
% 229.33/40.82  | | | | | | | | | |            sub-proof #2304.
% 229.33/40.82  | | | | | | | | | | 
% 229.33/40.82  | | | | | | | | | Case 2:
% 229.33/40.82  | | | | | | | | | | 
% 229.33/40.82  | | | | | | | | | |   (56)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0
% 229.33/40.82  | | | | | | | | | |             & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 229.33/40.82  | | | | | | | | | |               e0) = e0)) & ((all_57_12 = e0 & op(e0, e3) =
% 229.33/40.82  | | | | | | | | | |             e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 229.33/40.82  | | | | | | | | | |           (all_57_14 = e0 & op(e0, e1) = e0))
% 229.33/40.82  | | | | | | | | | | 
% 229.33/40.82  | | | | | | | | | | ALPHA: (56) implies:
% 229.33/40.82  | | | | | | | | | |   (57)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0
% 229.33/40.82  | | | | | | | | | |           & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.33/40.82  | | | | | | | | | |           = e0)
% 229.33/40.82  | | | | | | | | | | 
% 229.33/40.82  | | | | | | | | | | BETA: splitting (7) gives:
% 229.33/40.82  | | | | | | | | | | 
% 229.33/40.82  | | | | | | | | | | Case 1:
% 229.33/40.82  | | | | | | | | | | | 
% 229.33/40.82  | | | | | | | | | | |   (58)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 229.33/40.82  | | | | | | | | | | |           & op(e1, e2) = e3)
% 229.33/40.82  | | | | | | | | | | | 
% 229.33/40.82  | | | | | | | | | | | BETA: splitting (58) gives:
% 229.33/40.82  | | | | | | | | | | | 
% 229.33/40.82  | | | | | | | | | | | Case 1:
% 229.33/40.82  | | | | | | | | | | | | 
% 229.33/40.82  | | | | | | | | | | | |   (59)  all_57_6 = e3 & op(e1, e3) = e3
% 229.33/40.82  | | | | | | | | | | | | 
% 229.33/40.82  | | | | | | | | | | | | ALPHA: (59) implies:
% 229.33/40.82  | | | | | | | | | | | |   (60)  all_57_6 = e3
% 229.33/40.82  | | | | | | | | | | | | 
% 229.33/40.82  | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (5), (6), (12), (13), (14), (17),
% 229.33/40.82  | | | | | | | | | | | |            (19), (21), (26), (28), (30), (32), (53), (60) are
% 229.33/40.82  | | | | | | | | | | | |            inconsistent by sub-proof #794.
% 229.33/40.82  | | | | | | | | | | | | 
% 229.33/40.82  | | | | | | | | | | | Case 2:
% 229.33/40.82  | | | | | | | | | | | | 
% 229.33/40.83  | | | | | | | | | | | |   (61)  all_57_7 = e3 & op(e1, e2) = e3
% 229.33/40.83  | | | | | | | | | | | | 
% 229.33/40.83  | | | | | | | | | | | | ALPHA: (61) implies:
% 229.33/40.83  | | | | | | | | | | | |   (62)  all_57_7 = e3
% 229.33/40.83  | | | | | | | | | | | | 
% 229.33/40.83  | | | | | | | | | | | | REF_CLOSE: (5), (12), (15), (21), (30), (34), (41), (62) are
% 229.33/40.83  | | | | | | | | | | | |            inconsistent by sub-proof #2008.
% 229.33/40.83  | | | | | | | | | | | | 
% 229.33/40.83  | | | | | | | | | | | End of split
% 229.33/40.83  | | | | | | | | | | | 
% 229.33/40.83  | | | | | | | | | | Case 2:
% 229.33/40.83  | | | | | | | | | | | 
% 229.33/40.83  | | | | | | | | | | |   (63)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 229.33/40.83  | | | | | | | | | | |           e3 & op(e1, e0) = e3)
% 229.33/40.83  | | | | | | | | | | | 
% 229.33/40.83  | | | | | | | | | | | REF_CLOSE: (5), (6), (8), (9), (13), (14), (16), (19), (21),
% 229.33/40.83  | | | | | | | | | | |            (30), (31), (33), (57), (63) are inconsistent by
% 229.33/40.83  | | | | | | | | | | |            sub-proof #1080.
% 229.33/40.83  | | | | | | | | | | | 
% 229.33/40.83  | | | | | | | | | | End of split
% 229.33/40.83  | | | | | | | | | | 
% 229.33/40.83  | | | | | | | | | End of split
% 229.33/40.83  | | | | | | | | | 
% 229.33/40.83  | | | | | | | | End of split
% 229.33/40.83  | | | | | | | | 
% 229.33/40.83  | | | | | | | Case 2:
% 229.33/40.83  | | | | | | | | 
% 229.33/40.83  | | | | | | | |   (64)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 &
% 229.33/40.83  | | | | | | | |           op(e0, e3) = e3)
% 229.33/40.83  | | | | | | | | 
% 229.33/40.83  | | | | | | | | REF_CLOSE: (5), (13), (14), (16), (18), (19), (21), (24), (25),
% 229.33/40.83  | | | | | | | |            (30), (41), (48), (64) are inconsistent by sub-proof
% 229.33/40.83  | | | | | | | |            #786.
% 229.33/40.83  | | | | | | | | 
% 229.33/40.83  | | | | | | | End of split
% 229.33/40.83  | | | | | | | 
% 229.33/40.83  | | | | | | Case 2:
% 229.33/40.83  | | | | | | | 
% 229.33/40.83  | | | | | | |   (65)  all_57_12 = e0 & op(e0, e3) = e0
% 229.33/40.83  | | | | | | | 
% 229.33/40.83  | | | | | | | REF_CLOSE: (19), (44), (65) are inconsistent by sub-proof #2185.
% 229.33/40.83  | | | | | | | 
% 229.33/40.83  | | | | | | End of split
% 229.33/40.83  | | | | | | 
% 229.33/40.83  | | | | | End of split
% 229.33/40.83  | | | | | 
% 229.33/40.83  | | | | Case 2:
% 229.33/40.83  | | | | | 
% 229.33/40.83  | | | | |   (66)  all_57_13 = e2 & op(e0, e2) = e2
% 229.33/40.83  | | | | | 
% 229.33/40.83  | | | | | REF_CLOSE: (13), (41), (66) are inconsistent by sub-proof #2146.
% 229.33/40.83  | | | | | 
% 229.33/40.83  | | | | End of split
% 229.33/40.83  | | | | 
% 229.33/40.83  | | | Case 2:
% 229.33/40.83  | | | | 
% 229.33/40.83  | | | |   (67)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0,
% 229.33/40.83  | | | |             e0) = e2)
% 229.33/40.83  | | | | 
% 229.33/40.83  | | | | BETA: splitting (67) gives:
% 229.33/40.83  | | | | 
% 229.33/40.83  | | | | Case 1:
% 229.33/40.83  | | | | | 
% 229.33/40.83  | | | | |   (68)  all_57_14 = e2 & op(e0, e1) = e2
% 229.33/40.83  | | | | | 
% 229.33/40.83  | | | | | ALPHA: (68) implies:
% 229.33/40.83  | | | | |   (69)  all_57_14 = e2
% 229.33/40.83  | | | | | 
% 229.33/40.83  | | | | | REF_CLOSE: (5), (6), (14), (16), (18), (19), (21), (23), (25), (30),
% 229.33/40.83  | | | | |            (41), (69) are inconsistent by sub-proof #2212.
% 229.33/40.83  | | | | | 
% 229.33/40.83  | | | | Case 2:
% 229.33/40.83  | | | | | 
% 229.33/40.83  | | | | |   (70)  all_57_15 = e2 & op(e0, e0) = e2
% 229.33/40.83  | | | | | 
% 229.33/40.83  | | | | | ALPHA: (70) implies:
% 229.33/40.83  | | | | |   (71)  all_57_15 = e2
% 229.33/40.83  | | | | | 
% 229.33/40.83  | | | | | REF_CLOSE: (13), (16), (71) are inconsistent by sub-proof #2058.
% 229.33/40.83  | | | | | 
% 229.33/40.83  | | | | End of split
% 229.33/40.83  | | | | 
% 229.33/40.83  | | | End of split
% 229.33/40.83  | | | 
% 229.33/40.83  | | End of split
% 229.33/40.83  | | 
% 229.33/40.83  | End of split
% 229.33/40.83  | 
% 229.33/40.83  End of proof
% 229.33/40.83  
% 229.33/40.83  Sub-proof #786 shows that the following formulas are inconsistent:
% 229.33/40.83  ----------------------------------------------------------------
% 229.33/40.83    (1)   ~ (e3 = e1)
% 229.33/40.83    (2)   ~ (e3 = e2)
% 229.33/40.83    (3)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.33/40.83    (4)   ~ (e3 = e0)
% 229.33/40.83    (5)  all_57_6 = e0
% 229.33/40.83    (6)  all_57_15 = e3
% 229.33/40.83    (7)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 229.33/40.83         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.33/40.83    (8)   ~ (e2 = e0)
% 229.33/40.83    (9)   ~ (e1 = e0)
% 229.33/40.83    (10)  all_57_13 = e3
% 229.33/40.83    (11)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.33/40.83          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.33/40.83            e2)
% 229.33/40.83    (12)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.33/40.83              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.33/40.83                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.33/40.83                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.33/40.83    (13)   ~ (e2 = e1)
% 229.33/40.83  
% 229.33/40.83  Begin of proof
% 229.33/40.83  | 
% 229.33/40.83  | BETA: splitting (3) gives:
% 229.33/40.83  | 
% 229.33/40.83  | Case 1:
% 229.33/40.83  | | 
% 229.33/40.83  | |   (14)  all_57_6 = e3 & op(e1, e3) = e3
% 229.33/40.83  | | 
% 229.33/40.83  | | ALPHA: (14) implies:
% 229.33/40.83  | |   (15)  all_57_6 = e3
% 229.33/40.83  | | 
% 229.33/40.83  | | REF_CLOSE: (4), (5), (15) are inconsistent by sub-proof #1822.
% 229.33/40.83  | | 
% 229.33/40.83  | Case 2:
% 229.33/40.83  | | 
% 229.33/40.83  | |   (16)  all_57_12 = e3 & op(e0, e3) = e3
% 229.33/40.83  | | 
% 229.33/40.83  | | ALPHA: (16) implies:
% 229.33/40.83  | |   (17)  all_57_12 = e3
% 229.33/40.83  | | 
% 229.33/40.83  | | REF_CLOSE: (1), (2), (6), (7), (8), (9), (10), (11), (12), (13), (17) are
% 229.33/40.83  | |            inconsistent by sub-proof #1733.
% 229.33/40.83  | | 
% 229.33/40.83  | End of split
% 229.33/40.83  | 
% 229.33/40.83  End of proof
% 229.33/40.83  
% 229.33/40.83  Sub-proof #787 shows that the following formulas are inconsistent:
% 229.33/40.83  ----------------------------------------------------------------
% 229.33/40.83    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.33/40.83         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.33/40.83    (2)   ~ (e3 = e1)
% 229.33/40.83    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.33/40.83           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.33/40.83    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.33/40.83         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.33/40.83    (5)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.33/40.83         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.33/40.83    (6)  all_57_3 = e0
% 229.33/40.83    (7)   ~ (e3 = e2)
% 229.33/40.83    (8)   ~ (e3 = e0)
% 229.33/40.83    (9)  all_57_1 = e2
% 229.33/40.83    (10)  op(e3, e3) = e2
% 229.33/40.83    (11)   ~ (e2 = e0)
% 229.33/40.83    (12)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.33/40.83          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.33/40.83    (13)   ~ (e1 = e0)
% 229.33/40.83    (14)   ~ (all_53_12 = e3)
% 229.33/40.83    (15)  all_57_7 = e3
% 229.33/40.83    (16)   ~ (e2 = e1)
% 229.33/40.83    (17)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.33/40.83          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.33/40.83    (18)  op(e3, e0) = all_53_12
% 229.33/40.83  
% 229.33/40.83  Begin of proof
% 229.33/40.83  | 
% 229.33/40.83  | BETA: splitting (12) gives:
% 229.33/40.83  | 
% 229.33/40.83  | Case 1:
% 229.33/40.83  | | 
% 229.33/40.83  | |   (19)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) =
% 229.33/40.83  | |           e3)
% 229.33/40.83  | | 
% 229.33/40.83  | | REF_CLOSE: (1), (2), (3), (6), (7), (10), (11), (13), (15), (16), (17), (19)
% 229.33/40.83  | |            are inconsistent by sub-proof #1620.
% 229.33/40.83  | | 
% 229.33/40.83  | Case 2:
% 229.33/40.83  | | 
% 229.33/40.83  | |   (20)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) =
% 229.33/40.83  | |           e3)
% 229.33/40.83  | | 
% 229.33/40.83  | | BETA: splitting (20) gives:
% 229.33/40.83  | | 
% 229.33/40.83  | | Case 1:
% 229.33/40.83  | | | 
% 229.33/40.83  | | |   (21)  all_57_4 = e3 & op(e3, e1) = e3
% 229.33/40.83  | | | 
% 229.33/40.83  | | | ALPHA: (21) implies:
% 229.33/40.83  | | |   (22)  all_57_4 = e3
% 229.33/40.83  | | | 
% 229.33/40.83  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 229.33/40.83  | | |            (15), (16), (17), (22) are inconsistent by sub-proof #800.
% 229.33/40.83  | | | 
% 229.33/40.83  | | Case 2:
% 229.33/40.83  | | | 
% 229.33/40.83  | | |   (23)  all_57_9 = e3 & op(e3, e0) = e3
% 229.33/40.83  | | | 
% 229.33/40.83  | | | ALPHA: (23) implies:
% 229.33/40.83  | | |   (24)  op(e3, e0) = e3
% 229.33/40.83  | | | 
% 229.33/40.83  | | | REF_CLOSE: (3), (14), (18), (24) are inconsistent by sub-proof #2458.
% 229.33/40.83  | | | 
% 229.33/40.83  | | End of split
% 229.33/40.83  | | 
% 229.33/40.83  | End of split
% 229.33/40.83  | 
% 229.33/40.83  End of proof
% 229.33/40.83  
% 229.33/40.83  Sub-proof #788 shows that the following formulas are inconsistent:
% 229.33/40.83  ----------------------------------------------------------------
% 229.33/40.83    (1)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3)
% 229.33/40.83    (2)  all_57_3 = e0
% 229.33/40.83    (3)   ~ (e3 = e2)
% 229.33/40.83    (4)   ~ (e3 = e0)
% 229.33/40.83    (5)  all_57_1 = e2
% 229.33/40.83  
% 229.33/40.83  Begin of proof
% 229.33/40.83  | 
% 229.33/40.83  | BETA: splitting (1) gives:
% 229.33/40.83  | 
% 229.33/40.83  | Case 1:
% 229.33/40.83  | | 
% 229.33/40.83  | |   (6)  all_57_1 = e3 & op(e3, e2) = e3
% 229.33/40.83  | | 
% 229.33/40.83  | | REF_CLOSE: (3), (5), (6) are inconsistent by sub-proof #1664.
% 229.33/40.83  | | 
% 229.33/40.83  | Case 2:
% 229.33/40.83  | | 
% 229.33/40.83  | |   (7)  all_57_3 = e3 & op(e2, e2) = e3
% 229.33/40.83  | | 
% 229.33/40.83  | | ALPHA: (7) implies:
% 229.33/40.83  | |   (8)  all_57_3 = e3
% 229.33/40.83  | | 
% 229.33/40.83  | | REF_CLOSE: (2), (4), (8) are inconsistent by sub-proof #2358.
% 229.33/40.83  | | 
% 229.33/40.83  | End of split
% 229.33/40.83  | 
% 229.33/40.83  End of proof
% 229.33/40.83  
% 229.33/40.83  Sub-proof #789 shows that the following formulas are inconsistent:
% 229.33/40.83  ----------------------------------------------------------------
% 229.33/40.83    (1)  all_57_0 = e2
% 229.33/40.83    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.33/40.83         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.33/40.83    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.33/40.83         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.33/40.83    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.33/40.83         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.33/40.83    (5)   ~ (e3 = e1)
% 229.33/40.83    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.33/40.83           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.33/40.83    (7)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.33/40.83         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.33/40.83    (8)   ~ (all_6_2 = e3)
% 229.33/40.83    (9)  op(e1, e1) = all_6_2
% 229.33/40.83    (10)  all_57_3 = e0
% 229.33/40.83    (11)   ~ (e3 = e2)
% 229.33/40.83    (12)   ~ (e3 = e0)
% 229.33/40.83    (13)  all_57_6 = e0
% 229.33/40.83    (14)  all_57_15 = e3
% 229.33/40.83    (15)  op(e3, e3) = e2
% 229.33/40.83    (16)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.33/40.83          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.33/40.83            e1)
% 229.33/40.83    (17)   ~ (e2 = e0)
% 229.33/40.83    (18)   ~ (e1 = e0)
% 229.33/40.83    (19)  op(e0, e0) = e3
% 229.33/40.83    (20)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.33/40.83          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.33/40.83            e2)
% 229.33/40.83    (21)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.33/40.83              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.33/40.83                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.33/40.83                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.33/40.83    (22)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.33/40.83          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.33/40.83    (23)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.33/40.83          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.33/40.83    (24)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.33/40.83          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.33/40.83    (25)  all_57_1 = e3
% 229.33/40.83    (26)   ~ (e2 = e1)
% 229.33/40.83    (27)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.33/40.83          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.33/40.83    (28)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.33/40.83          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.33/40.83    (29)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.33/40.83          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.33/40.83    (30)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.33/40.83          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.33/40.83    (31)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.33/40.83          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.33/40.83  
% 229.33/40.83  Begin of proof
% 229.33/40.83  | 
% 229.33/40.83  | BETA: splitting (24) gives:
% 229.33/40.83  | 
% 229.33/40.83  | Case 1:
% 229.33/40.83  | | 
% 229.33/40.83  | |   (32)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) =
% 229.33/40.83  | |           e3)
% 229.33/40.83  | | 
% 229.33/40.83  | | BETA: splitting (32) gives:
% 229.33/40.83  | | 
% 229.33/40.83  | | Case 1:
% 229.33/40.83  | | | 
% 229.33/40.83  | | |   (33)  all_57_0 = e3 & op(e3, e3) = e3
% 229.33/40.83  | | | 
% 229.33/40.83  | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (14),
% 229.33/40.83  | | |            (17), (18), (21), (25), (26), (27), (28), (29), (30), (31),
% 229.33/40.83  | | |            (33) are inconsistent by sub-proof #791.
% 229.33/40.83  | | | 
% 229.33/40.83  | | Case 2:
% 229.33/40.83  | | | 
% 229.33/40.83  | | |   (34)  all_57_2 = e3 & op(e2, e3) = e3
% 229.33/40.83  | | | 
% 229.33/40.83  | | | ALPHA: (34) implies:
% 229.33/40.83  | | |   (35)  all_57_2 = e3
% 229.33/40.83  | | | 
% 229.33/40.83  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 229.33/40.83  | | |            (14), (15), (17), (18), (19), (21), (22), (23), (25), (26),
% 229.33/40.83  | | |            (27), (29), (30), (31), (35) are inconsistent by sub-proof
% 229.33/40.83  | | |            #792.
% 229.33/40.83  | | | 
% 229.33/40.83  | | End of split
% 229.33/40.83  | | 
% 229.33/40.83  | Case 2:
% 229.33/40.83  | | 
% 229.33/40.83  | |   (36)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) =
% 229.33/40.83  | |           e3)
% 229.33/40.83  | | 
% 229.33/40.83  | | REF_CLOSE: (4), (5), (10), (11), (12), (13), (14), (16), (17), (18), (20),
% 229.33/40.83  | |            (21), (25), (26), (31), (36) are inconsistent by sub-proof #790.
% 229.33/40.83  | | 
% 229.33/40.83  | End of split
% 229.33/40.83  | 
% 229.33/40.83  End of proof
% 229.33/40.83  
% 229.33/40.83  Sub-proof #790 shows that the following formulas are inconsistent:
% 229.33/40.83  ----------------------------------------------------------------
% 229.33/40.83    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.33/40.83         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.33/40.83    (2)   ~ (e3 = e1)
% 229.33/40.83    (3)  all_57_3 = e0
% 229.33/40.83    (4)   ~ (e3 = e2)
% 229.33/40.83    (5)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.33/40.84    (6)   ~ (e3 = e0)
% 229.33/40.84    (7)  all_57_6 = e0
% 229.33/40.84    (8)  all_57_15 = e3
% 229.33/40.84    (9)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 229.33/40.84         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.33/40.84    (10)   ~ (e2 = e0)
% 229.33/40.84    (11)   ~ (e1 = e0)
% 229.33/40.84    (12)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.33/40.84          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.33/40.84            e2)
% 229.33/40.84    (13)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.33/40.84              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.33/40.84                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.33/40.84                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.33/40.84    (14)  all_57_1 = e3
% 229.33/40.84    (15)   ~ (e2 = e1)
% 229.33/40.84    (16)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.33/40.84          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.33/40.84  
% 229.33/40.84  Begin of proof
% 229.33/40.84  | 
% 229.33/40.84  | BETA: splitting (5) gives:
% 229.33/40.84  | 
% 229.33/40.84  | Case 1:
% 229.33/40.84  | | 
% 229.33/40.84  | |   (17)  all_57_6 = e3 & op(e1, e3) = e3
% 229.33/40.84  | | 
% 229.33/40.84  | | ALPHA: (17) implies:
% 229.33/40.84  | |   (18)  all_57_6 = e3
% 229.33/40.84  | | 
% 229.33/40.84  | | REF_CLOSE: (6), (7), (18) are inconsistent by sub-proof #1822.
% 229.33/40.84  | | 
% 229.33/40.84  | Case 2:
% 229.33/40.84  | | 
% 229.33/40.84  | |   (19)  all_57_12 = e3 & op(e0, e3) = e3
% 229.33/40.84  | | 
% 229.33/40.84  | | ALPHA: (19) implies:
% 229.33/40.84  | |   (20)  all_57_12 = e3
% 229.33/40.84  | | 
% 229.33/40.84  | | REF_CLOSE: (1), (2), (3), (4), (6), (8), (9), (10), (11), (12), (13), (14),
% 229.33/40.84  | |            (15), (16), (20) are inconsistent by sub-proof #1037.
% 229.33/40.84  | | 
% 229.33/40.84  | End of split
% 229.33/40.84  | 
% 229.33/40.84  End of proof
% 229.33/40.84  
% 229.33/40.84  Sub-proof #791 shows that the following formulas are inconsistent:
% 229.33/40.84  ----------------------------------------------------------------
% 229.33/40.84    (1)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.33/40.84         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.33/40.84    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.33/40.84         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.33/40.84    (3)   ~ (e3 = e1)
% 229.33/40.84    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.33/40.84           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.33/40.84    (5)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.33/40.84         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.33/40.84    (6)   ~ (all_6_2 = e3)
% 229.33/40.84    (7)  op(e1, e1) = all_6_2
% 229.33/40.84    (8)  all_57_3 = e0
% 229.33/40.84    (9)   ~ (e3 = e2)
% 229.33/40.84    (10)   ~ (e3 = e0)
% 229.33/40.84    (11)  all_57_15 = e3
% 229.33/40.84    (12)   ~ (e2 = e0)
% 229.33/40.84    (13)   ~ (e1 = e0)
% 229.33/40.84    (14)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.33/40.84              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.33/40.84                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.33/40.84                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.33/40.84    (15)  all_57_1 = e3
% 229.33/40.84    (16)   ~ (e2 = e1)
% 229.33/40.84    (17)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.33/40.84          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.33/40.84    (18)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.33/40.84          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.33/40.84    (19)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.33/40.84          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.33/40.84    (20)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.33/40.84          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.33/40.84    (21)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.33/40.84          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.33/40.84    (22)  all_57_0 = e3 & op(e3, e3) = e3
% 229.33/40.84  
% 229.33/40.84  Begin of proof
% 229.33/40.84  | 
% 229.33/40.84  | ALPHA: (22) implies:
% 229.33/40.84  |   (23)  all_57_0 = e3
% 229.33/40.84  | 
% 229.33/40.84  | BETA: splitting (5) gives:
% 229.33/40.84  | 
% 229.33/40.84  | Case 1:
% 229.33/40.84  | | 
% 229.33/40.84  | |   (24)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 229.33/40.84  | |           e3)
% 229.33/40.84  | | 
% 229.33/40.84  | | BETA: splitting (24) gives:
% 229.33/40.84  | | 
% 229.33/40.84  | | Case 1:
% 229.33/40.84  | | | 
% 229.33/40.84  | | |   (25)  all_57_6 = e3 & op(e1, e3) = e3
% 229.33/40.84  | | | 
% 229.33/40.84  | | | ALPHA: (25) implies:
% 229.33/40.84  | | |   (26)  all_57_6 = e3
% 229.33/40.84  | | | 
% 229.33/40.84  | | | REF_CLOSE: (1), (3), (9), (10), (12), (13), (16), (18), (19), (23), (26)
% 229.33/40.84  | | |            are inconsistent by sub-proof #2010.
% 229.33/40.84  | | | 
% 229.33/40.84  | | Case 2:
% 229.33/40.84  | | | 
% 229.33/40.84  | | |   (27)  all_57_7 = e3 & op(e1, e2) = e3
% 229.33/40.84  | | | 
% 229.33/40.84  | | | ALPHA: (27) implies:
% 229.33/40.84  | | |   (28)  all_57_7 = e3
% 229.33/40.84  | | | 
% 229.33/40.84  | | | REF_CLOSE: (2), (3), (8), (9), (12), (13), (15), (16), (21), (28) are
% 229.33/40.84  | | |            inconsistent by sub-proof #1778.
% 229.33/40.84  | | | 
% 229.33/40.84  | | End of split
% 229.33/40.84  | | 
% 229.33/40.84  | Case 2:
% 229.33/40.84  | | 
% 229.33/40.84  | |   (29)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 229.33/40.84  | |           e3)
% 229.33/40.84  | | 
% 229.33/40.84  | | BETA: splitting (29) gives:
% 229.33/40.84  | | 
% 229.33/40.84  | | Case 1:
% 229.33/40.84  | | | 
% 229.33/40.84  | | |   (30)  all_57_8 = e3 & op(e1, e1) = e3
% 229.33/40.84  | | | 
% 229.33/40.84  | | | ALPHA: (30) implies:
% 229.33/40.84  | | |   (31)  op(e1, e1) = e3
% 229.33/40.84  | | | 
% 229.33/40.84  | | | REF_CLOSE: (4), (6), (7), (31) are inconsistent by sub-proof #2468.
% 229.33/40.84  | | | 
% 229.33/40.84  | | Case 2:
% 229.33/40.84  | | | 
% 229.33/40.84  | | |   (32)  all_57_11 = e3 & op(e1, e0) = e3
% 229.33/40.84  | | | 
% 229.33/40.84  | | | ALPHA: (32) implies:
% 229.33/40.84  | | |   (33)  all_57_11 = e3
% 229.33/40.84  | | | 
% 229.33/40.84  | | | REF_CLOSE: (3), (9), (10), (11), (12), (13), (14), (16), (17), (20), (33)
% 229.33/40.84  | | |            are inconsistent by sub-proof #2134.
% 229.33/40.84  | | | 
% 229.33/40.84  | | End of split
% 229.33/40.84  | | 
% 229.33/40.84  | End of split
% 229.33/40.84  | 
% 229.33/40.84  End of proof
% 229.33/40.84  
% 229.33/40.84  Sub-proof #792 shows that the following formulas are inconsistent:
% 229.33/40.84  ----------------------------------------------------------------
% 229.33/40.84    (1)  all_57_0 = e2
% 229.33/40.84    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.33/40.84         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.33/40.84    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.33/40.84         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.33/40.84    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.33/40.84         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.33/40.84    (5)   ~ (e3 = e1)
% 229.33/40.84    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.33/40.84           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.33/40.84    (7)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.33/40.84         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.33/40.84    (8)   ~ (all_6_2 = e3)
% 229.33/40.84    (9)  op(e1, e1) = all_6_2
% 229.33/40.84    (10)  all_57_3 = e0
% 229.33/40.84    (11)   ~ (e3 = e2)
% 229.33/40.84    (12)   ~ (e3 = e0)
% 229.33/40.84    (13)  all_57_15 = e3
% 229.33/40.84    (14)  op(e3, e3) = e2
% 229.33/40.84    (15)   ~ (e2 = e0)
% 229.33/40.84    (16)  all_57_2 = e3
% 229.33/40.84    (17)   ~ (e1 = e0)
% 229.33/40.84    (18)  op(e0, e0) = e3
% 229.33/40.84    (19)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.33/40.84              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.33/40.84                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.33/40.84                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.33/40.84    (20)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.33/40.84          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.33/40.84    (21)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.33/40.84          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.33/40.84    (22)  all_57_1 = e3
% 229.33/40.84    (23)   ~ (e2 = e1)
% 229.33/40.84    (24)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.33/40.84          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.33/40.84    (25)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.33/40.84          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.33/40.84    (26)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.33/40.84          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.33/40.84    (27)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.33/40.84          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.33/40.84  
% 229.33/40.84  Begin of proof
% 229.33/40.84  | 
% 229.33/40.84  | BETA: splitting (19) gives:
% 229.33/40.84  | 
% 229.33/40.84  | Case 1:
% 229.33/40.84  | | 
% 229.33/40.84  | |   (28)  all_57_15 = e0 & op(e0, e0) = e0
% 229.33/40.84  | | 
% 229.33/40.84  | | ALPHA: (28) implies:
% 229.33/40.84  | |   (29)  op(e0, e0) = e0
% 229.33/40.84  | | 
% 229.33/40.84  | | REF_CLOSE: (6), (12), (18), (29) are inconsistent by sub-proof #2304.
% 229.33/40.84  | | 
% 229.33/40.84  | Case 2:
% 229.33/40.84  | | 
% 229.33/40.84  | |   (30)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 229.33/40.84  | |             e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0 &
% 229.33/40.84  | |             op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 229.33/40.84  | |           (all_57_14 = e0 & op(e0, e1) = e0))
% 229.33/40.84  | | 
% 229.33/40.84  | | ALPHA: (30) implies:
% 229.33/40.84  | |   (31)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 229.33/40.84  | |           e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 229.33/40.84  | | 
% 229.33/40.84  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 229.33/40.84  | |            (13), (14), (15), (16), (17), (20), (21), (22), (23), (24), (25),
% 229.33/40.84  | |            (26), (27), (31) are inconsistent by sub-proof #793.
% 229.33/40.84  | | 
% 229.33/40.84  | End of split
% 229.33/40.84  | 
% 229.33/40.84  End of proof
% 229.33/40.84  
% 229.33/40.84  Sub-proof #793 shows that the following formulas are inconsistent:
% 229.33/40.84  ----------------------------------------------------------------
% 229.33/40.84    (1)  all_57_0 = e2
% 229.33/40.84    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.33/40.84         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.33/40.84    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.33/40.84         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.33/40.84    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.33/40.84         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.33/40.84    (5)   ~ (e3 = e1)
% 229.33/40.84    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.33/40.84           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.33/40.84    (7)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.33/40.84         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.33/40.84    (8)   ~ (all_6_2 = e3)
% 229.33/40.84    (9)  op(e1, e1) = all_6_2
% 229.33/40.84    (10)  all_57_3 = e0
% 229.33/40.84    (11)   ~ (e3 = e2)
% 229.33/40.84    (12)   ~ (e3 = e0)
% 229.33/40.84    (13)  all_57_15 = e3
% 229.33/40.84    (14)  op(e3, e3) = e2
% 229.33/40.84    (15)   ~ (e2 = e0)
% 229.33/40.84    (16)  all_57_2 = e3
% 229.33/40.84    (17)   ~ (e1 = e0)
% 229.33/40.84    (18)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.33/40.84          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.33/40.84    (19)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.33/40.84          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.33/40.84    (20)  all_57_1 = e3
% 229.33/40.84    (21)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) |
% 229.33/40.84          (all_57_11 = e0 & op(e1, e0) = e0)
% 229.33/40.84    (22)   ~ (e2 = e1)
% 229.33/40.84    (23)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.33/40.84          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.33/40.84    (24)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.33/40.84          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.33/40.84    (25)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.33/40.84          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.33/40.84    (26)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.33/40.84          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.33/40.84  
% 229.33/40.84  Begin of proof
% 229.33/40.84  | 
% 229.33/40.84  | BETA: splitting (7) gives:
% 229.33/40.84  | 
% 229.33/40.84  | Case 1:
% 229.33/40.84  | | 
% 229.33/40.85  | |   (27)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 229.33/40.85  | |           e3)
% 229.33/40.85  | | 
% 229.33/40.85  | | BETA: splitting (27) gives:
% 229.33/40.85  | | 
% 229.33/40.85  | | Case 1:
% 229.33/40.85  | | | 
% 229.33/40.85  | | |   (28)  all_57_6 = e3 & op(e1, e3) = e3
% 229.33/40.85  | | | 
% 229.33/40.85  | | | ALPHA: (28) implies:
% 229.33/40.85  | | |   (29)  all_57_6 = e3
% 229.33/40.85  | | | 
% 229.33/40.85  | | | REF_CLOSE: (1), (2), (3), (5), (6), (10), (11), (12), (14), (15), (16),
% 229.33/40.85  | | |            (17), (18), (19), (22), (24), (29) are inconsistent by
% 229.33/40.85  | | |            sub-proof #794.
% 229.33/40.85  | | | 
% 229.33/40.85  | | Case 2:
% 229.33/40.85  | | | 
% 229.33/40.85  | | |   (30)  all_57_7 = e3 & op(e1, e2) = e3
% 229.33/40.85  | | | 
% 229.33/40.85  | | | ALPHA: (30) implies:
% 229.33/40.85  | | |   (31)  all_57_7 = e3
% 229.33/40.85  | | | 
% 229.33/40.85  | | | REF_CLOSE: (4), (5), (10), (11), (15), (17), (20), (22), (26), (31) are
% 229.33/40.85  | | |            inconsistent by sub-proof #1778.
% 229.33/40.85  | | | 
% 229.33/40.85  | | End of split
% 229.33/40.85  | | 
% 229.33/40.85  | Case 2:
% 229.33/40.85  | | 
% 229.33/40.85  | |   (32)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 229.33/40.85  | |           e3)
% 229.33/40.85  | | 
% 229.33/40.85  | | REF_CLOSE: (5), (6), (8), (9), (11), (12), (13), (15), (17), (21), (22),
% 229.33/40.85  | |            (23), (25), (32) are inconsistent by sub-proof #1080.
% 229.33/40.85  | | 
% 229.33/40.85  | End of split
% 229.33/40.85  | 
% 229.33/40.85  End of proof
% 229.33/40.85  
% 229.33/40.85  Sub-proof #794 shows that the following formulas are inconsistent:
% 229.33/40.85  ----------------------------------------------------------------
% 229.33/40.85    (1)  all_57_0 = e2
% 229.33/40.85    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.33/40.85         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.33/40.85    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.33/40.85         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.33/40.85    (4)   ~ (e3 = e1)
% 229.33/40.85    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.33/40.85           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.33/40.85    (6)  all_57_3 = e0
% 229.33/40.85    (7)   ~ (e3 = e2)
% 229.33/40.85    (8)   ~ (e3 = e0)
% 229.33/40.85    (9)  op(e3, e3) = e2
% 229.33/40.85    (10)   ~ (e2 = e0)
% 229.33/40.85    (11)  all_57_2 = e3
% 229.33/40.85    (12)   ~ (e1 = e0)
% 229.33/40.85    (13)  all_57_6 = e3
% 229.33/40.85    (14)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.33/40.85          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.33/40.85    (15)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.33/40.85          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.33/40.85    (16)   ~ (e2 = e1)
% 229.33/40.85    (17)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.33/40.85          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.33/40.85  
% 229.33/40.85  Begin of proof
% 229.33/40.85  | 
% 229.33/40.85  | BETA: splitting (17) gives:
% 229.33/40.85  | 
% 229.33/40.85  | Case 1:
% 229.33/40.85  | | 
% 229.33/40.85  | |   (18)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) =
% 229.33/40.85  | |           e0)
% 229.33/40.85  | | 
% 229.33/40.85  | | REF_CLOSE: (2), (4), (5), (6), (7), (8), (9), (10), (12), (14), (15), (16),
% 229.33/40.85  | |            (18) are inconsistent by sub-proof #1654.
% 229.33/40.85  | | 
% 229.33/40.85  | Case 2:
% 229.33/40.85  | | 
% 229.33/40.85  | |   (19)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) =
% 229.33/40.85  | |           e0)
% 229.33/40.85  | | 
% 229.33/40.85  | | BETA: splitting (19) gives:
% 229.33/40.85  | | 
% 229.33/40.85  | | Case 1:
% 229.33/40.85  | | | 
% 229.33/40.85  | | |   (20)  all_57_6 = e0 & op(e1, e3) = e0
% 229.33/40.85  | | | 
% 229.33/40.85  | | | ALPHA: (20) implies:
% 229.33/40.85  | | |   (21)  all_57_6 = e0
% 229.33/40.85  | | | 
% 229.33/40.85  | | | COMBINE_EQS: (13), (21) imply:
% 229.33/40.85  | | |   (22)  e3 = e0
% 229.33/40.85  | | | 
% 229.33/40.85  | | | REF_CLOSE: (2), (4), (6), (7), (8), (10), (11), (12), (14), (15), (16),
% 229.33/40.85  | | |            (22) are inconsistent by sub-proof #1333.
% 229.33/40.85  | | | 
% 229.33/40.85  | | Case 2:
% 229.33/40.85  | | | 
% 229.33/40.85  | | |   (23)  all_57_12 = e0 & op(e0, e3) = e0
% 229.33/40.85  | | | 
% 229.33/40.85  | | | ALPHA: (23) implies:
% 229.33/40.85  | | |   (24)  all_57_12 = e0
% 229.33/40.85  | | | 
% 229.33/40.85  | | | REF_CLOSE: (1), (3), (4), (11), (12), (13), (16), (24) are inconsistent by
% 229.33/40.85  | | |            sub-proof #1535.
% 229.33/40.85  | | | 
% 229.33/40.85  | | End of split
% 229.33/40.85  | | 
% 229.33/40.85  | End of split
% 229.33/40.85  | 
% 229.33/40.85  End of proof
% 229.33/40.85  
% 229.33/40.85  Sub-proof #795 shows that the following formulas are inconsistent:
% 229.33/40.85  ----------------------------------------------------------------
% 229.33/40.85    (1)  all_57_1 = e0 & op(e3, e2) = e0
% 229.33/40.85    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.33/40.85         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.33/40.85    (3)  op(e1, e0) = e2
% 229.33/40.85    (4)  all_57_13 = e1
% 229.33/40.85    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.33/40.85         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.33/40.85    (6)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.33/40.85         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.33/40.85    (7)   ~ (e3 = e1)
% 229.33/40.85    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.33/40.85           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.33/40.85    (9)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.33/40.85         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.33/40.85    (10)   ~ (all_6_2 = e3)
% 229.33/40.85    (11)  op(e1, e1) = all_6_2
% 229.33/40.85    (12)  op(e2, e2) = e1
% 229.33/40.85    (13)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.33/40.85          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.33/40.85    (14)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 229.33/40.85            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 229.33/40.85              e3) = all_22_1 & $i(all_22_1))
% 229.33/40.85    (15)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.33/40.85          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.33/40.85    (16)   ~ (e3 = e2)
% 229.33/40.85    (17)   ~ (e3 = e0)
% 229.33/40.85    (18)  all_57_15 = e3
% 229.33/40.85    (19)  op(e3, e3) = e2
% 229.33/40.85    (20)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.33/40.85          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.33/40.85    (21)   ~ (e2 = e0)
% 229.33/40.85    (22)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 229.33/40.85            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 229.33/40.85              e3) = all_12_1 & $i(all_12_1))
% 229.33/40.85    (23)  all_57_2 = e3
% 229.33/40.85    (24)  all_57_3 = e1
% 229.33/40.85    (25)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.33/40.85          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.33/40.85    (26)   ~ (e1 = e0)
% 229.33/40.85    (27)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.33/40.85              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.33/40.85                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.33/40.85                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.33/40.85    (28)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.33/40.85          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.33/40.85    (29)   ~ (all_53_12 = e3)
% 229.33/40.85    (30)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.33/40.85          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.33/40.85    (31)  all_57_1 = e3
% 229.33/40.85    (32)   ~ (e2 = e1)
% 229.33/40.85    (33)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.33/40.85          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.33/40.85    (34)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.33/40.85          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.33/40.85    (35)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.33/40.85          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.33/40.85    (36)  op(e3, e0) = all_53_12
% 229.33/40.85  
% 229.33/40.85  Begin of proof
% 229.33/40.85  | 
% 229.33/40.85  | ALPHA: (1) implies:
% 229.33/40.85  |   (37)  all_57_1 = e0
% 229.33/40.85  | 
% 229.33/40.85  | COMBINE_EQS: (31), (37) imply:
% 229.33/40.85  |   (38)  e3 = e0
% 229.33/40.85  | 
% 229.33/40.85  | COMBINE_EQS: (23), (38) imply:
% 229.33/40.85  |   (39)  all_57_2 = e0
% 229.33/40.85  | 
% 229.33/40.85  | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 229.33/40.85  |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (24), (25),
% 229.33/40.85  |            (26), (27), (28), (29), (30), (32), (33), (34), (35), (36), (39)
% 229.33/40.85  |            are inconsistent by sub-proof #796.
% 229.33/40.85  | 
% 229.33/40.85  End of proof
% 229.33/40.85  
% 229.33/40.85  Sub-proof #796 shows that the following formulas are inconsistent:
% 229.33/40.85  ----------------------------------------------------------------
% 229.33/40.85    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.33/40.85         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.33/40.85    (2)  op(e1, e0) = e2
% 229.33/40.85    (3)  all_57_13 = e1
% 229.33/40.85    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.33/40.85         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.33/40.85    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.33/40.85         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.33/40.85    (6)   ~ (e3 = e1)
% 229.33/40.85    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.33/40.85           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.33/40.85    (8)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.33/40.85         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.33/40.85    (9)   ~ (all_6_2 = e3)
% 229.33/40.85    (10)  op(e1, e1) = all_6_2
% 229.33/40.85    (11)  op(e2, e2) = e1
% 229.33/40.85    (12)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.33/40.85          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.33/40.85    (13)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 229.33/40.85            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 229.33/40.85              e3) = all_22_1 & $i(all_22_1))
% 229.33/40.85    (14)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.33/40.85          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.33/40.85    (15)   ~ (e3 = e2)
% 229.33/40.85    (16)   ~ (e3 = e0)
% 229.33/40.85    (17)  all_57_15 = e3
% 229.33/40.85    (18)  op(e3, e3) = e2
% 229.33/40.85    (19)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.33/40.85          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.33/40.85    (20)   ~ (e2 = e0)
% 229.33/40.85    (21)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 229.33/40.85            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 229.33/40.85              e3) = all_12_1 & $i(all_12_1))
% 229.33/40.85    (22)  all_57_3 = e1
% 229.33/40.85    (23)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.33/40.85          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.33/40.85    (24)   ~ (e1 = e0)
% 229.33/40.85    (25)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.33/40.85              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.33/40.85                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.33/40.85                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.33/40.85    (26)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.33/40.85          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.33/40.85    (27)  all_57_2 = e0
% 229.33/40.85    (28)   ~ (all_53_12 = e3)
% 229.33/40.85    (29)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.33/40.85          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.33/40.85    (30)   ~ (e2 = e1)
% 229.33/40.85    (31)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.33/40.85          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.33/40.85    (32)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.33/40.85          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.33/40.85    (33)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.33/40.85          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.33/40.85    (34)  op(e3, e0) = all_53_12
% 229.33/40.85  
% 229.33/40.85  Begin of proof
% 229.33/40.85  | 
% 229.33/40.85  | BETA: splitting (4) gives:
% 229.33/40.85  | 
% 229.33/40.85  | Case 1:
% 229.33/40.85  | | 
% 229.33/40.85  | |   (35)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) =
% 229.33/40.85  | |           e1)
% 229.33/40.85  | | 
% 229.33/40.86  | | REF_CLOSE: (1), (6), (7), (15), (16), (18), (20), (22), (24), (26), (27),
% 229.33/40.86  | |            (29), (30), (35) are inconsistent by sub-proof #801.
% 229.33/40.86  | | 
% 229.33/40.86  | Case 2:
% 229.33/40.86  | | 
% 229.33/40.86  | |   (36)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) =
% 229.33/40.86  | |           e1)
% 229.33/40.86  | | 
% 229.33/40.86  | | BETA: splitting (36) gives:
% 229.33/40.86  | | 
% 229.33/40.86  | | Case 1:
% 229.33/40.86  | | | 
% 229.33/40.86  | | |   (37)  all_57_6 = e1 & op(e1, e3) = e1
% 229.33/40.86  | | | 
% 229.33/40.86  | | | ALPHA: (37) implies:
% 229.33/40.86  | | |   (38)  all_57_6 = e1
% 229.33/40.86  | | | 
% 229.33/40.86  | | | REF_CLOSE: (3), (5), (6), (7), (8), (9), (10), (11), (12), (14), (15),
% 229.33/40.86  | | |            (16), (17), (18), (19), (20), (22), (23), (24), (25), (28),
% 229.33/40.86  | | |            (30), (31), (32), (33), (34), (38) are inconsistent by
% 229.33/40.86  | | |            sub-proof #797.
% 229.33/40.86  | | | 
% 229.33/40.86  | | Case 2:
% 229.33/40.86  | | | 
% 229.33/40.86  | | |   (39)  all_57_12 = e1 & op(e0, e3) = e1
% 229.33/40.86  | | | 
% 229.33/40.86  | | | ALPHA: (39) implies:
% 229.33/40.86  | | |   (40)  op(e0, e3) = e1
% 229.33/40.86  | | | 
% 229.33/40.86  | | | REF_CLOSE: (2), (7), (13), (21), (40) are inconsistent by sub-proof #1147.
% 229.33/40.86  | | | 
% 229.33/40.86  | | End of split
% 229.33/40.86  | | 
% 229.33/40.86  | End of split
% 229.33/40.86  | 
% 229.33/40.86  End of proof
% 229.33/40.86  
% 229.33/40.86  Sub-proof #797 shows that the following formulas are inconsistent:
% 229.33/40.86  ----------------------------------------------------------------
% 229.33/40.86    (1)  all_57_13 = e1
% 229.33/40.86    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.33/40.86         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.33/40.86    (3)   ~ (e3 = e1)
% 229.33/40.86    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.33/40.86           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.33/40.86    (5)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.33/40.86         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.33/40.86    (6)   ~ (all_6_2 = e3)
% 229.33/40.86    (7)  op(e1, e1) = all_6_2
% 229.33/40.86    (8)  op(e2, e2) = e1
% 229.33/40.86    (9)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.33/40.86         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.33/40.86    (10)  all_57_6 = e1
% 229.33/40.86    (11)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.33/40.86          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.33/40.86    (12)   ~ (e3 = e2)
% 229.33/40.86    (13)   ~ (e3 = e0)
% 229.33/40.86    (14)  all_57_15 = e3
% 229.33/40.86    (15)  op(e3, e3) = e2
% 229.33/40.86    (16)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.33/40.86          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.33/40.86    (17)   ~ (e2 = e0)
% 229.33/40.86    (18)  all_57_3 = e1
% 229.33/40.86    (19)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.33/40.86          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.33/40.86    (20)   ~ (e1 = e0)
% 229.33/40.86    (21)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.33/40.86              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.33/40.86                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.33/40.86                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.33/40.86    (22)   ~ (all_53_12 = e3)
% 229.33/40.86    (23)   ~ (e2 = e1)
% 229.33/40.86    (24)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.33/40.86          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.53/40.86    (25)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.53/40.86          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.53/40.86    (26)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.53/40.86          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.53/40.86    (27)  op(e3, e0) = all_53_12
% 229.53/40.86  
% 229.53/40.86  Begin of proof
% 229.53/40.86  | 
% 229.53/40.86  | BETA: splitting (5) gives:
% 229.53/40.86  | 
% 229.53/40.86  | Case 1:
% 229.53/40.86  | | 
% 229.53/40.86  | |   (28)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 229.53/40.86  | |           e3)
% 229.53/40.86  | | 
% 229.53/40.86  | | BETA: splitting (28) gives:
% 229.53/40.86  | | 
% 229.53/40.86  | | Case 1:
% 229.53/40.86  | | | 
% 229.53/40.86  | | |   (29)  all_57_6 = e3 & op(e1, e3) = e3
% 229.53/40.86  | | | 
% 229.53/40.86  | | | ALPHA: (29) implies:
% 229.53/40.86  | | |   (30)  all_57_6 = e3
% 229.53/40.86  | | | 
% 229.53/40.86  | | | REF_CLOSE: (3), (10), (30) are inconsistent by sub-proof #2017.
% 229.53/40.86  | | | 
% 229.53/40.86  | | Case 2:
% 229.53/40.86  | | | 
% 229.53/40.86  | | |   (31)  all_57_7 = e3 & op(e1, e2) = e3
% 229.53/40.86  | | | 
% 229.53/40.86  | | | ALPHA: (31) implies:
% 229.53/40.86  | | |   (32)  all_57_7 = e3
% 229.53/40.86  | | | 
% 229.53/40.86  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 229.53/40.86  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 229.53/40.86  | | |            (23), (24), (25), (26), (27), (32) are inconsistent by
% 229.53/40.86  | | |            sub-proof #798.
% 229.53/40.86  | | | 
% 229.53/40.86  | | End of split
% 229.53/40.86  | | 
% 229.53/40.86  | Case 2:
% 229.53/40.86  | | 
% 229.53/40.86  | |   (33)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 229.53/40.86  | |           e3)
% 229.53/40.86  | | 
% 229.53/40.86  | | REF_CLOSE: (3), (4), (6), (7), (12), (13), (14), (17), (20), (21), (23),
% 229.53/40.86  | |            (24), (25), (33) are inconsistent by sub-proof #1786.
% 229.53/40.86  | | 
% 229.53/40.86  | End of split
% 229.53/40.86  | 
% 229.53/40.86  End of proof
% 229.53/40.86  
% 229.53/40.86  Sub-proof #798 shows that the following formulas are inconsistent:
% 229.53/40.86  ----------------------------------------------------------------
% 229.53/40.86    (1)  all_57_13 = e1
% 229.53/40.86    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.53/40.86         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.53/40.86    (3)   ~ (e3 = e1)
% 229.53/40.86    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.53/40.86           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.53/40.86    (5)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.53/40.86         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.53/40.86    (6)   ~ (all_6_2 = e3)
% 229.53/40.86    (7)  op(e1, e1) = all_6_2
% 229.53/40.86    (8)  op(e2, e2) = e1
% 229.53/40.86    (9)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.53/40.86         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.53/40.86    (10)  all_57_6 = e1
% 229.53/40.86    (11)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.53/40.86          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.53/40.86    (12)   ~ (e3 = e2)
% 229.53/40.86    (13)   ~ (e3 = e0)
% 229.53/40.86    (14)  all_57_15 = e3
% 229.53/40.86    (15)  op(e3, e3) = e2
% 229.53/40.86    (16)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.53/40.86          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.53/40.86    (17)   ~ (e2 = e0)
% 229.53/40.86    (18)  all_57_3 = e1
% 229.53/40.86    (19)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.53/40.86          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.53/40.86    (20)   ~ (e1 = e0)
% 229.53/40.86    (21)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.53/40.86              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.53/40.86                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.53/40.86                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.53/40.86    (22)   ~ (all_53_12 = e3)
% 229.53/40.86    (23)  all_57_7 = e3
% 229.53/40.86    (24)   ~ (e2 = e1)
% 229.53/40.86    (25)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.53/40.86          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.53/40.86    (26)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.53/40.86          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.53/40.86    (27)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.53/40.86          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.53/40.86    (28)  op(e3, e0) = all_53_12
% 229.53/40.86  
% 229.53/40.86  Begin of proof
% 229.53/40.86  | 
% 229.53/40.86  | BETA: splitting (2) gives:
% 229.53/40.86  | 
% 229.53/40.86  | Case 1:
% 229.53/40.86  | | 
% 229.53/40.86  | |   (29)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 229.53/40.86  | |           e2)
% 229.53/40.86  | | 
% 229.53/40.86  | | BETA: splitting (29) gives:
% 229.53/40.86  | | 
% 229.53/40.86  | | Case 1:
% 229.53/40.86  | | | 
% 229.53/40.86  | | |   (30)  all_57_1 = e2 & op(e3, e2) = e2
% 229.53/40.86  | | | 
% 229.53/40.86  | | | ALPHA: (30) implies:
% 229.53/40.86  | | |   (31)  all_57_1 = e2
% 229.53/40.86  | | | 
% 229.53/40.86  | | | BETA: splitting (19) gives:
% 229.53/40.86  | | | 
% 229.53/40.86  | | | Case 1:
% 229.53/40.86  | | | | 
% 229.53/40.86  | | | |   (32)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2)
% 229.53/40.86  | | | |           = e3)
% 229.53/40.86  | | | | 
% 229.53/40.86  | | | | REF_CLOSE: (4), (12), (15), (31), (32) are inconsistent by sub-proof
% 229.53/40.86  | | | |            #1663.
% 229.53/40.86  | | | | 
% 229.53/40.86  | | | Case 2:
% 229.53/40.86  | | | | 
% 229.53/40.86  | | | |   (33)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0)
% 229.53/40.86  | | | |           = e3)
% 229.53/40.86  | | | | 
% 229.53/40.86  | | | | BETA: splitting (33) gives:
% 229.53/40.86  | | | | 
% 229.53/40.86  | | | | Case 1:
% 229.53/40.86  | | | | | 
% 229.53/40.86  | | | | |   (34)  all_57_4 = e3 & op(e3, e1) = e3
% 229.53/40.86  | | | | | 
% 229.53/40.86  | | | | | ALPHA: (34) implies:
% 229.53/40.86  | | | | |   (35)  all_57_4 = e3
% 229.53/40.86  | | | | | 
% 229.53/40.86  | | | | | BETA: splitting (16) gives:
% 229.53/40.86  | | | | | 
% 229.53/40.86  | | | | | Case 1:
% 229.53/40.86  | | | | | | 
% 229.53/40.86  | | | | | |   (36)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2,
% 229.53/40.86  | | | | | |             e2) = e0)
% 229.53/40.86  | | | | | | 
% 229.53/40.86  | | | | | | BETA: splitting (36) gives:
% 229.53/40.86  | | | | | | 
% 229.53/40.86  | | | | | | Case 1:
% 229.53/40.86  | | | | | | | 
% 229.53/40.86  | | | | | | |   (37)  all_57_1 = e0 & op(e3, e2) = e0
% 229.53/40.86  | | | | | | | 
% 229.53/40.86  | | | | | | | REF_CLOSE: (17), (31), (37) are inconsistent by sub-proof #1723.
% 229.53/40.86  | | | | | | | 
% 229.53/40.86  | | | | | | Case 2:
% 229.53/40.86  | | | | | | | 
% 229.53/40.86  | | | | | | |   (38)  all_57_3 = e0 & op(e2, e2) = e0
% 229.53/40.86  | | | | | | | 
% 229.53/40.86  | | | | | | | ALPHA: (38) implies:
% 229.53/40.86  | | | | | | |   (39)  all_57_3 = e0
% 229.53/40.86  | | | | | | | 
% 229.53/40.86  | | | | | | | REF_CLOSE: (2), (3), (4), (9), (11), (12), (13), (15), (17), (20),
% 229.53/40.86  | | | | | | |            (23), (24), (27), (31), (35), (39) are inconsistent by
% 229.53/40.86  | | | | | | |            sub-proof #800.
% 229.53/40.86  | | | | | | | 
% 229.53/40.86  | | | | | | End of split
% 229.53/40.86  | | | | | | 
% 229.53/40.86  | | | | | Case 2:
% 229.53/40.86  | | | | | | 
% 229.53/40.86  | | | | | |   (40)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0,
% 229.53/40.86  | | | | | |             e2) = e0)
% 229.53/40.86  | | | | | | 
% 229.53/40.86  | | | | | | BETA: splitting (40) gives:
% 229.53/40.86  | | | | | | 
% 229.53/40.86  | | | | | | Case 1:
% 229.53/40.86  | | | | | | | 
% 229.53/40.86  | | | | | | |   (41)  all_57_7 = e0 & op(e1, e2) = e0
% 229.53/40.86  | | | | | | | 
% 229.53/40.86  | | | | | | | ALPHA: (41) implies:
% 229.53/40.86  | | | | | | |   (42)  all_57_7 = e0
% 229.53/40.86  | | | | | | | 
% 229.53/40.86  | | | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (10), (12), (13), (14), (17),
% 229.53/40.86  | | | | | | |            (20), (21), (24), (25), (26), (42) are inconsistent by
% 229.53/40.86  | | | | | | |            sub-proof #1735.
% 229.53/40.86  | | | | | | | 
% 229.53/40.86  | | | | | | Case 2:
% 229.53/40.86  | | | | | | | 
% 229.53/40.86  | | | | | | |   (43)  all_57_13 = e0 & op(e0, e2) = e0
% 229.53/40.86  | | | | | | | 
% 229.53/40.86  | | | | | | | REF_CLOSE: (1), (2), (3), (4), (9), (11), (12), (13), (15), (17),
% 229.53/40.86  | | | | | | |            (18), (20), (23), (24), (27), (31), (35), (43) are
% 229.53/40.86  | | | | | | |            inconsistent by sub-proof #799.
% 229.53/40.86  | | | | | | | 
% 229.53/40.86  | | | | | | End of split
% 229.53/40.86  | | | | | | 
% 229.53/40.86  | | | | | End of split
% 229.53/40.86  | | | | | 
% 229.53/40.86  | | | | Case 2:
% 229.53/40.86  | | | | | 
% 229.53/40.86  | | | | |   (44)  all_57_9 = e3 & op(e3, e0) = e3
% 229.53/40.86  | | | | | 
% 229.53/40.86  | | | | | ALPHA: (44) implies:
% 229.53/40.86  | | | | |   (45)  op(e3, e0) = e3
% 229.53/40.86  | | | | | 
% 229.53/40.86  | | | | | REF_CLOSE: (4), (22), (28), (45) are inconsistent by sub-proof #2458.
% 229.53/40.86  | | | | | 
% 229.53/40.86  | | | | End of split
% 229.53/40.86  | | | | 
% 229.53/40.86  | | | End of split
% 229.53/40.86  | | | 
% 229.53/40.86  | | Case 2:
% 229.53/40.86  | | | 
% 229.53/40.86  | | |   (46)  all_57_3 = e2 & op(e2, e2) = e2
% 229.53/40.86  | | | 
% 229.53/40.86  | | | ALPHA: (46) implies:
% 229.53/40.86  | | |   (47)  op(e2, e2) = e2
% 229.53/40.86  | | | 
% 229.53/40.86  | | | REF_CLOSE: (4), (8), (24), (47) are inconsistent by sub-proof #2306.
% 229.53/40.86  | | | 
% 229.53/40.86  | | End of split
% 229.53/40.86  | | 
% 229.53/40.86  | Case 2:
% 229.53/40.86  | | 
% 229.53/40.86  | |   (48)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 229.53/40.86  | |           e2)
% 229.53/40.86  | | 
% 229.53/40.86  | | BETA: splitting (48) gives:
% 229.53/40.86  | | 
% 229.53/40.86  | | Case 1:
% 229.53/40.86  | | | 
% 229.53/40.86  | | |   (49)  all_57_7 = e2 & op(e1, e2) = e2
% 229.53/40.86  | | | 
% 229.53/40.86  | | | REF_CLOSE: (12), (23), (49) are inconsistent by sub-proof #2092.
% 229.53/40.86  | | | 
% 229.53/40.86  | | Case 2:
% 229.53/40.86  | | | 
% 229.53/40.86  | | |   (50)  all_57_13 = e2 & op(e0, e2) = e2
% 229.53/40.86  | | | 
% 229.53/40.86  | | | REF_CLOSE: (1), (24), (50) are inconsistent by sub-proof #2101.
% 229.53/40.86  | | | 
% 229.53/40.86  | | End of split
% 229.53/40.86  | | 
% 229.53/40.86  | End of split
% 229.53/40.86  | 
% 229.53/40.86  End of proof
% 229.53/40.86  
% 229.53/40.86  Sub-proof #799 shows that the following formulas are inconsistent:
% 229.53/40.86  ----------------------------------------------------------------
% 229.53/40.86    (1)  all_57_13 = e1
% 229.53/40.86    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.53/40.86         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.53/40.86    (3)   ~ (e3 = e1)
% 229.53/40.86    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.53/40.86           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.53/40.86    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.53/40.86         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.53/40.86    (6)  all_57_13 = e0 & op(e0, e2) = e0
% 229.53/40.86    (7)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.53/40.86         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.53/40.86    (8)  all_57_4 = e3
% 229.53/40.86    (9)   ~ (e3 = e2)
% 229.53/40.86    (10)   ~ (e3 = e0)
% 229.53/40.86    (11)  all_57_1 = e2
% 229.53/40.87    (12)  op(e3, e3) = e2
% 229.53/40.87    (13)   ~ (e2 = e0)
% 229.53/40.87    (14)  all_57_3 = e1
% 229.53/40.87    (15)   ~ (e1 = e0)
% 229.53/40.87    (16)  all_57_7 = e3
% 229.53/40.87    (17)   ~ (e2 = e1)
% 229.53/40.87    (18)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.53/40.87          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.53/40.87  
% 229.53/40.87  Begin of proof
% 229.53/40.87  | 
% 229.53/40.87  | ALPHA: (6) implies:
% 229.53/40.87  |   (19)  all_57_13 = e0
% 229.53/40.87  | 
% 229.53/40.87  | COMBINE_EQS: (1), (19) imply:
% 229.53/40.87  |   (20)  e1 = e0
% 229.53/40.87  | 
% 229.53/40.87  | COMBINE_EQS: (14), (20) imply:
% 229.53/40.87  |   (21)  all_57_3 = e0
% 229.53/40.87  | 
% 229.53/40.87  | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13), (15),
% 229.53/40.87  |            (16), (17), (18), (21) are inconsistent by sub-proof #800.
% 229.53/40.87  | 
% 229.53/40.87  End of proof
% 229.53/40.87  
% 229.53/40.87  Sub-proof #800 shows that the following formulas are inconsistent:
% 229.53/40.87  ----------------------------------------------------------------
% 229.53/40.87    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.53/40.87         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.53/40.87    (2)   ~ (e3 = e1)
% 229.53/40.87    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.53/40.87           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.53/40.87    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.53/40.87         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.53/40.87    (5)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.53/40.87         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.53/40.87    (6)  all_57_3 = e0
% 229.53/40.87    (7)  all_57_4 = e3
% 229.53/40.87    (8)   ~ (e3 = e2)
% 229.53/40.87    (9)   ~ (e3 = e0)
% 229.53/40.87    (10)  all_57_1 = e2
% 229.53/40.87    (11)  op(e3, e3) = e2
% 229.53/40.87    (12)   ~ (e2 = e0)
% 229.53/40.87    (13)   ~ (e1 = e0)
% 229.53/40.87    (14)  all_57_7 = e3
% 229.53/40.87    (15)   ~ (e2 = e1)
% 229.53/40.87    (16)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.53/40.87          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.53/40.87  
% 229.53/40.87  Begin of proof
% 229.53/40.87  | 
% 229.53/40.87  | BETA: splitting (5) gives:
% 229.53/40.87  | 
% 229.53/40.87  | Case 1:
% 229.53/40.87  | | 
% 229.53/40.87  | |   (17)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) =
% 229.53/40.87  | |           e0)
% 229.53/40.87  | | 
% 229.53/40.87  | | BETA: splitting (17) gives:
% 229.53/40.87  | | 
% 229.53/40.87  | | Case 1:
% 229.53/40.87  | | | 
% 229.53/40.87  | | |   (18)  all_57_0 = e0 & op(e3, e3) = e0
% 229.53/40.87  | | | 
% 229.53/40.87  | | | ALPHA: (18) implies:
% 229.53/40.87  | | |   (19)  op(e3, e3) = e0
% 229.53/40.87  | | | 
% 229.53/40.87  | | | REF_CLOSE: (3), (11), (12), (19) are inconsistent by sub-proof #2403.
% 229.53/40.87  | | | 
% 229.53/40.87  | | Case 2:
% 229.53/40.87  | | | 
% 229.53/40.87  | | |   (20)  all_57_1 = e0 & op(e3, e2) = e0
% 229.53/40.87  | | | 
% 229.53/40.87  | | | ALPHA: (20) implies:
% 229.53/40.87  | | |   (21)  all_57_1 = e0
% 229.53/40.87  | | | 
% 229.53/40.87  | | | REF_CLOSE: (1), (2), (6), (8), (12), (13), (14), (15), (16), (21) are
% 229.53/40.87  | | |            inconsistent by sub-proof #2098.
% 229.53/40.87  | | | 
% 229.53/40.87  | | End of split
% 229.53/40.87  | | 
% 229.53/40.87  | Case 2:
% 229.53/40.87  | | 
% 229.53/40.87  | |   (22)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) =
% 229.53/40.87  | |           e0)
% 229.53/40.87  | | 
% 229.53/40.87  | | REF_CLOSE: (2), (3), (4), (7), (9), (10), (11), (13), (15), (22) are
% 229.53/40.87  | |            inconsistent by sub-proof #1660.
% 229.53/40.87  | | 
% 229.53/40.87  | End of split
% 229.53/40.87  | 
% 229.53/40.87  End of proof
% 229.53/40.87  
% 229.53/40.87  Sub-proof #801 shows that the following formulas are inconsistent:
% 229.53/40.87  ----------------------------------------------------------------
% 229.53/40.87    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.53/40.87         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.53/40.87    (2)   ~ (e3 = e1)
% 229.53/40.87    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.53/40.87           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.53/40.87    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1)
% 229.53/40.87    (5)   ~ (e3 = e2)
% 229.53/40.87    (6)   ~ (e3 = e0)
% 229.53/40.87    (7)  op(e3, e3) = e2
% 229.53/40.87    (8)   ~ (e2 = e0)
% 229.53/40.87    (9)  all_57_3 = e1
% 229.53/40.87    (10)   ~ (e1 = e0)
% 229.53/40.87    (11)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.53/40.87          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.53/40.87    (12)  all_57_2 = e0
% 229.53/40.87    (13)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.53/40.87          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.53/40.87    (14)   ~ (e2 = e1)
% 229.53/40.87  
% 229.53/40.87  Begin of proof
% 229.53/40.87  | 
% 229.53/40.87  | BETA: splitting (4) gives:
% 229.53/40.87  | 
% 229.53/40.87  | Case 1:
% 229.53/40.87  | | 
% 229.53/40.87  | |   (15)  all_57_0 = e1 & op(e3, e3) = e1
% 229.53/40.87  | | 
% 229.53/40.87  | | ALPHA: (15) implies:
% 229.53/40.87  | |   (16)  op(e3, e3) = e1
% 229.53/40.87  | | 
% 229.53/40.87  | | REF_CLOSE: (3), (7), (14), (16) are inconsistent by sub-proof #1950.
% 229.53/40.87  | | 
% 229.53/40.87  | Case 2:
% 229.53/40.87  | | 
% 229.53/40.87  | |   (17)  all_57_2 = e1 & op(e2, e3) = e1
% 229.53/40.87  | | 
% 229.53/40.87  | | ALPHA: (17) implies:
% 229.53/40.87  | |   (18)  all_57_2 = e1
% 229.53/40.87  | | 
% 229.53/40.87  | | COMBINE_EQS: (12), (18) imply:
% 229.53/40.87  | |   (19)  e1 = e0
% 229.53/40.87  | | 
% 229.53/40.87  | | REF_CLOSE: (1), (2), (5), (6), (8), (9), (10), (11), (12), (13), (14), (19)
% 229.53/40.87  | |            are inconsistent by sub-proof #1824.
% 229.53/40.87  | | 
% 229.53/40.87  | End of split
% 229.53/40.87  | 
% 229.53/40.87  End of proof
% 229.53/40.87  
% 229.53/40.87  Sub-proof #802 shows that the following formulas are inconsistent:
% 229.53/40.87  ----------------------------------------------------------------
% 229.53/40.87    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.53/40.87         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.53/40.87    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.53/40.87         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.53/40.87    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.53/40.87         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.53/40.87    (4)   ~ (e3 = e1)
% 229.53/40.87    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.53/40.87           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.53/40.87    (6)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.53/40.87         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.53/40.87    (7)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2)
% 229.53/40.87    (8)   ~ (all_6_2 = e3)
% 229.53/40.87    (9)  op(e1, e1) = all_6_2
% 229.53/40.87    (10)  op(e2, e2) = e1
% 229.53/40.87    (11)   ~ (e3 = e2)
% 229.53/40.87    (12)   ~ (e3 = e0)
% 229.53/40.87    (13)  all_57_15 = e3
% 229.53/40.87    (14)  op(e3, e3) = e2
% 229.53/40.87    (15)  all_57_4 = e1
% 229.53/40.87    (16)  all_57_11 = e2
% 229.53/40.87    (17)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.53/40.87          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.53/40.87    (18)   ~ (e2 = e0)
% 229.53/40.87    (19)  all_57_3 = e1
% 229.53/40.87    (20)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.53/40.87          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.53/40.87    (21)   ~ (e1 = e0)
% 229.53/40.87    (22)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.53/40.87          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.53/40.87    (23)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.53/40.87              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.53/40.87                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.53/40.87                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.53/40.87    (24)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.53/40.87          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.53/40.87    (25)   ~ (all_53_12 = e3)
% 229.53/40.87    (26)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.53/40.87          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.53/40.87    (27)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.53/40.87          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.53/40.87    (28)  all_57_1 = e3
% 229.53/40.87    (29)   ~ (e2 = e1)
% 229.53/40.87    (30)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.53/40.87          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.53/40.87    (31)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.53/40.87          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.53/40.87    (32)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.53/40.87          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.53/40.87    (33)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.53/40.87          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.53/40.87    (34)  op(e3, e0) = all_53_12
% 229.53/40.87  
% 229.53/40.87  Begin of proof
% 229.53/40.87  | 
% 229.53/40.87  | BETA: splitting (7) gives:
% 229.53/40.87  | 
% 229.53/40.87  | Case 1:
% 229.53/40.87  | | 
% 229.53/40.87  | |   (35)  all_57_2 = e2 & op(e2, e3) = e2
% 229.53/40.87  | | 
% 229.53/40.87  | | ALPHA: (35) implies:
% 229.53/40.87  | |   (36)  all_57_2 = e2
% 229.53/40.87  | | 
% 229.53/40.87  | | BETA: splitting (24) gives:
% 229.53/40.87  | | 
% 229.53/40.87  | | Case 1:
% 229.53/40.87  | | | 
% 229.53/40.87  | | |   (37)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 229.53/40.87  | | |           e3)
% 229.53/40.87  | | | 
% 229.53/40.87  | | | BETA: splitting (37) gives:
% 229.53/40.87  | | | 
% 229.53/40.87  | | | Case 1:
% 229.53/40.87  | | | | 
% 229.53/40.87  | | | |   (38)  all_57_2 = e3 & op(e2, e3) = e3
% 229.53/40.87  | | | | 
% 229.53/40.87  | | | | REF_CLOSE: (4), (5), (11), (14), (15), (20), (25), (28), (34), (36),
% 229.53/40.87  | | | |            (38) are inconsistent by sub-proof #812.
% 229.53/40.87  | | | | 
% 229.53/40.87  | | | Case 2:
% 229.53/40.87  | | | | 
% 229.53/40.87  | | | |   (39)  all_57_3 = e3 & op(e2, e2) = e3
% 229.53/40.87  | | | | 
% 229.53/40.87  | | | | ALPHA: (39) implies:
% 229.53/40.87  | | | |   (40)  op(e2, e2) = e3
% 229.53/40.87  | | | | 
% 229.53/40.87  | | | | REF_CLOSE: (4), (5), (10), (40) are inconsistent by sub-proof #1912.
% 229.53/40.87  | | | | 
% 229.53/40.87  | | | End of split
% 229.53/40.87  | | | 
% 229.53/40.87  | | Case 2:
% 229.53/40.87  | | | 
% 229.53/40.87  | | |   (41)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 229.53/40.87  | | |           e3)
% 229.53/40.87  | | | 
% 229.53/40.87  | | | BETA: splitting (41) gives:
% 229.53/40.87  | | | 
% 229.53/40.87  | | | Case 1:
% 229.53/40.87  | | | | 
% 229.53/40.87  | | | |   (42)  all_57_5 = e3 & op(e2, e1) = e3
% 229.53/40.87  | | | | 
% 229.53/40.87  | | | | ALPHA: (42) implies:
% 229.53/40.87  | | | |   (43)  all_57_5 = e3
% 229.53/40.87  | | | | 
% 229.53/40.87  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12),
% 229.53/40.87  | | | |            (13), (14), (15), (17), (18), (19), (20), (21), (22), (23),
% 229.53/40.87  | | | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 229.53/40.87  | | | |            (36), (43) are inconsistent by sub-proof #803.
% 229.53/40.87  | | | | 
% 229.53/40.87  | | | Case 2:
% 229.53/40.87  | | | | 
% 229.53/40.87  | | | |   (44)  all_57_10 = e3 & op(e2, e0) = e3
% 229.53/40.87  | | | | 
% 229.53/40.87  | | | | ALPHA: (44) implies:
% 229.53/40.87  | | | |   (45)  all_57_10 = e3
% 229.53/40.87  | | | | 
% 229.53/40.87  | | | | REF_CLOSE: (4), (11), (12), (13), (16), (18), (21), (23), (29), (30),
% 229.53/40.87  | | | |            (32), (45) are inconsistent by sub-proof #1983.
% 229.53/40.87  | | | | 
% 229.53/40.87  | | | End of split
% 229.53/40.87  | | | 
% 229.53/40.87  | | End of split
% 229.53/40.87  | | 
% 229.53/40.87  | Case 2:
% 229.53/40.87  | | 
% 229.53/40.87  | |   (46)  all_57_3 = e2 & op(e2, e2) = e2
% 229.53/40.87  | | 
% 229.53/40.87  | | ALPHA: (46) implies:
% 229.53/40.87  | |   (47)  op(e2, e2) = e2
% 229.53/40.87  | | 
% 229.53/40.87  | | REF_CLOSE: (5), (10), (29), (47) are inconsistent by sub-proof #2306.
% 229.53/40.87  | | 
% 229.53/40.87  | End of split
% 229.53/40.87  | 
% 229.53/40.87  End of proof
% 229.53/40.87  
% 229.53/40.87  Sub-proof #803 shows that the following formulas are inconsistent:
% 229.53/40.87  ----------------------------------------------------------------
% 229.53/40.87    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.53/40.87         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.53/40.87    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.53/40.87         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.53/40.87    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.53/40.87         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.53/40.87    (4)   ~ (e3 = e1)
% 229.53/40.87    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.53/40.87           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.53/40.87    (6)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.53/40.87         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.53/40.87    (7)   ~ (all_6_2 = e3)
% 229.53/40.87    (8)  op(e1, e1) = all_6_2
% 229.53/40.87    (9)  op(e2, e2) = e1
% 229.53/40.87    (10)  all_57_2 = e2
% 229.53/40.87    (11)   ~ (e3 = e2)
% 229.53/40.87    (12)   ~ (e3 = e0)
% 229.53/40.88    (13)  all_57_15 = e3
% 229.53/40.88    (14)  op(e3, e3) = e2
% 229.53/40.88    (15)  all_57_4 = e1
% 229.53/40.88    (16)  all_57_5 = e3
% 229.53/40.88    (17)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.53/40.88          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.53/40.88    (18)   ~ (e2 = e0)
% 229.53/40.88    (19)  all_57_3 = e1
% 229.53/40.88    (20)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.53/40.88          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.53/40.88    (21)   ~ (e1 = e0)
% 229.53/40.88    (22)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.53/40.88          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.53/40.88    (23)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.53/40.88              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.53/40.88                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.53/40.88                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.53/40.88    (24)   ~ (all_53_12 = e3)
% 229.53/40.88    (25)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.53/40.88          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.53/40.88    (26)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.53/40.88          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.53/40.88    (27)  all_57_1 = e3
% 229.53/40.88    (28)   ~ (e2 = e1)
% 229.53/40.88    (29)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.53/40.88          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.53/40.88    (30)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.53/40.88          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.53/40.88    (31)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.53/40.88          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.53/40.88    (32)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.53/40.88          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.53/40.88    (33)  op(e3, e0) = all_53_12
% 229.53/40.88  
% 229.53/40.88  Begin of proof
% 229.53/40.88  | 
% 229.53/40.88  | BETA: splitting (26) gives:
% 229.53/40.88  | 
% 229.53/40.88  | Case 1:
% 229.53/40.88  | | 
% 229.53/40.88  | |   (34)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) =
% 229.53/40.88  | |           e3)
% 229.53/40.88  | | 
% 229.53/40.88  | | REF_CLOSE: (4), (5), (10), (11), (14), (15), (20), (24), (27), (33), (34)
% 229.53/40.88  | |            are inconsistent by sub-proof #811.
% 229.53/40.88  | | 
% 229.53/40.88  | Case 2:
% 229.53/40.88  | | 
% 229.53/40.88  | |   (35)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) =
% 229.53/40.88  | |           e3)
% 229.53/40.88  | | 
% 229.53/40.88  | | BETA: splitting (35) gives:
% 229.53/40.88  | | 
% 229.53/40.88  | | Case 1:
% 229.53/40.88  | | | 
% 229.53/40.88  | | |   (36)  all_57_6 = e3 & op(e1, e3) = e3
% 229.53/40.88  | | | 
% 229.53/40.88  | | | ALPHA: (36) implies:
% 229.53/40.88  | | |   (37)  all_57_6 = e3
% 229.53/40.88  | | | 
% 229.53/40.88  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 229.53/40.88  | | |            (13), (14), (16), (17), (18), (19), (21), (22), (23), (25),
% 229.53/40.88  | | |            (27), (28), (29), (30), (31), (32), (37) are inconsistent by
% 229.53/40.88  | | |            sub-proof #807.
% 229.53/40.88  | | | 
% 229.53/40.88  | | Case 2:
% 229.53/40.88  | | | 
% 229.53/40.88  | | |   (38)  all_57_12 = e3 & op(e0, e3) = e3
% 229.53/40.88  | | | 
% 229.53/40.88  | | | ALPHA: (38) implies:
% 229.53/40.88  | | |   (39)  all_57_12 = e3
% 229.53/40.88  | | | 
% 229.53/40.88  | | | REF_CLOSE: (1), (2), (4), (5), (10), (11), (12), (14), (16), (18), (19),
% 229.53/40.88  | | |            (21), (25), (28), (30), (39) are inconsistent by sub-proof
% 229.53/40.88  | | |            #1575.
% 229.53/40.88  | | | 
% 229.53/40.88  | | End of split
% 229.53/40.88  | | 
% 229.53/40.88  | End of split
% 229.53/40.88  | 
% 229.53/40.88  End of proof
% 229.53/40.88  
% 229.53/40.88  Sub-proof #804 shows that the following formulas are inconsistent:
% 229.53/40.88  ----------------------------------------------------------------
% 229.53/40.88    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.53/40.88         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.53/40.88    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.53/40.88         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.53/40.88    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.53/40.88         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.53/40.88    (4)   ~ (e3 = e1)
% 229.53/40.88    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.53/40.88           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.53/40.88    (6)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.53/40.88         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.53/40.88    (7)   ~ (all_6_2 = e3)
% 229.53/40.88    (8)  all_57_10 = e1
% 229.53/40.88    (9)  op(e1, e1) = all_6_2
% 229.53/40.88    (10)  op(e2, e2) = e1
% 229.53/40.88    (11)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.53/40.88          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.53/40.88    (12)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.53/40.88          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.53/40.88    (13)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.53/40.88          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.53/40.88    (14)   ~ (e3 = e2)
% 229.53/40.88    (15)   ~ (e3 = e0)
% 229.53/40.88    (16)  all_57_15 = e3
% 229.53/40.88    (17)  op(e3, e3) = e2
% 229.53/40.88    (18)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.53/40.88          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.53/40.88            e1)
% 229.53/40.88    (19)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.53/40.88          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.53/40.88    (20)   ~ (e2 = e0)
% 229.53/40.88    (21)  all_57_3 = e1
% 229.53/40.88    (22)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.53/40.88          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.53/40.88    (23)   ~ (e1 = e0)
% 229.53/40.88    (24)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.53/40.88          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.53/40.88    (25)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.53/40.88          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.53/40.88    (26)  op(e0, e0) = e3
% 229.53/40.88    (27)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.53/40.88          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.53/40.88            e2)
% 229.53/40.88    (28)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.53/40.88              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.53/40.88                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.53/40.88                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.53/40.88    (29)   ~ (all_53_12 = e3)
% 229.53/40.88    (30)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.53/40.88          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.53/40.88    (31)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.53/40.88          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.53/40.88    (32)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.53/40.88          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 229.53/40.88    (33)   ~ (e2 = e1)
% 229.53/40.88    (34)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.53/40.88          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.53/40.88    (35)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.53/40.88          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.53/40.88    (36)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.53/40.88          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.53/40.88    (37)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.53/40.88    (38)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.53/40.88          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.53/40.88    (39)  op(e3, e0) = all_53_12
% 229.53/40.88  
% 229.53/40.88  Begin of proof
% 229.53/40.88  | 
% 229.53/40.88  | BETA: splitting (37) gives:
% 229.53/40.88  | 
% 229.53/40.88  | Case 1:
% 229.53/40.88  | | 
% 229.53/40.88  | |   (40)  all_57_9 = e2 & op(e3, e0) = e2
% 229.53/40.88  | | 
% 229.53/40.88  | | ALPHA: (40) implies:
% 229.53/40.88  | |   (41)  all_57_9 = e2
% 229.53/40.88  | | 
% 229.53/40.88  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 229.53/40.88  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 229.53/40.88  | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 229.53/40.88  | |            (35), (36), (38), (39), (41) are inconsistent by sub-proof #805.
% 229.53/40.88  | | 
% 229.53/40.88  | Case 2:
% 229.53/40.88  | | 
% 229.53/40.88  | |   (42)  all_57_10 = e2 & op(e2, e0) = e2
% 229.53/40.88  | | 
% 229.53/40.88  | | ALPHA: (42) implies:
% 229.53/40.88  | |   (43)  all_57_10 = e2
% 229.53/40.88  | | 
% 229.53/40.88  | | REF_CLOSE: (8), (33), (43) are inconsistent by sub-proof #2144.
% 229.53/40.88  | | 
% 229.53/40.88  | End of split
% 229.53/40.88  | 
% 229.53/40.88  End of proof
% 229.53/40.88  
% 229.53/40.88  Sub-proof #805 shows that the following formulas are inconsistent:
% 229.53/40.88  ----------------------------------------------------------------
% 229.53/40.88    (1)  all_57_9 = e2
% 229.53/40.88    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.53/40.88         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.53/40.88    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.53/40.88         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.53/40.88    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.53/40.88         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.53/40.88    (5)   ~ (e3 = e1)
% 229.53/40.88    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.53/40.88           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.53/40.88    (7)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.53/40.88         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.53/40.88    (8)   ~ (all_6_2 = e3)
% 229.53/40.88    (9)  all_57_10 = e1
% 229.53/40.88    (10)  op(e1, e1) = all_6_2
% 229.53/40.88    (11)  op(e2, e2) = e1
% 229.53/40.88    (12)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.53/40.88          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.53/40.88    (13)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.53/40.88          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.53/40.88    (14)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.53/40.88          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.53/40.88    (15)   ~ (e3 = e2)
% 229.53/40.88    (16)   ~ (e3 = e0)
% 229.53/40.88    (17)  all_57_15 = e3
% 229.53/40.88    (18)  op(e3, e3) = e2
% 229.53/40.88    (19)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.53/40.88          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.53/40.88            e1)
% 229.53/40.88    (20)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.53/40.88          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.53/40.88    (21)   ~ (e2 = e0)
% 229.53/40.88    (22)  all_57_3 = e1
% 229.53/40.88    (23)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.53/40.88          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.53/40.88    (24)   ~ (e1 = e0)
% 229.53/40.88    (25)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.53/40.88          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.53/40.88    (26)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.53/40.88          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.53/40.88    (27)  op(e0, e0) = e3
% 229.53/40.88    (28)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.53/40.88          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.53/40.88            e2)
% 229.53/40.89    (29)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.53/40.89              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.53/40.89                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.53/40.89                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.53/40.89    (30)   ~ (all_53_12 = e3)
% 229.53/40.89    (31)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.53/40.89          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.53/40.89    (32)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.53/40.89          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.53/40.89    (33)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.53/40.89          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 229.53/40.89    (34)   ~ (e2 = e1)
% 229.53/40.89    (35)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.53/40.89          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.53/40.89    (36)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.53/40.89          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.53/40.89    (37)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.53/40.89          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.53/40.89    (38)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.53/40.89          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.53/40.89    (39)  op(e3, e0) = all_53_12
% 229.53/40.89  
% 229.53/40.89  Begin of proof
% 229.53/40.89  | 
% 229.53/40.89  | BETA: splitting (29) gives:
% 229.53/40.89  | 
% 229.53/40.89  | Case 1:
% 229.53/40.89  | | 
% 229.53/40.89  | |   (40)  all_57_15 = e0 & op(e0, e0) = e0
% 229.53/40.89  | | 
% 229.53/40.89  | | ALPHA: (40) implies:
% 229.53/40.89  | |   (41)  op(e0, e0) = e0
% 229.53/40.89  | | 
% 229.53/40.89  | | REF_CLOSE: (6), (16), (27), (41) are inconsistent by sub-proof #2304.
% 229.53/40.89  | | 
% 229.53/40.89  | Case 2:
% 229.53/40.89  | | 
% 229.53/40.89  | |   (42)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 229.53/40.89  | |             e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0 &
% 229.53/40.89  | |             op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 229.53/40.89  | |           (all_57_14 = e0 & op(e0, e1) = e0))
% 229.53/40.89  | | 
% 229.53/40.89  | | ALPHA: (42) implies:
% 229.53/40.89  | |   (43)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 229.53/40.89  | |           e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.53/40.89  | |   (44)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 229.53/40.89  | |           e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 229.53/40.89  | | 
% 229.53/40.89  | | BETA: splitting (44) gives:
% 229.53/40.89  | | 
% 229.53/40.89  | | Case 1:
% 229.53/40.89  | | | 
% 229.53/40.89  | | |   (45)  all_57_9 = e0 & op(e3, e0) = e0
% 229.53/40.89  | | | 
% 229.53/40.89  | | | ALPHA: (45) implies:
% 229.53/40.89  | | |   (46)  all_57_9 = e0
% 229.53/40.89  | | | 
% 229.53/40.89  | | | REF_CLOSE: (1), (21), (46) are inconsistent by sub-proof #2440.
% 229.53/40.89  | | | 
% 229.53/40.89  | | Case 2:
% 229.53/40.89  | | | 
% 229.53/40.89  | | |   (47)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.53/40.89  | | |           = e0)
% 229.53/40.89  | | | 
% 229.53/40.89  | | | BETA: splitting (47) gives:
% 229.53/40.89  | | | 
% 229.53/40.89  | | | Case 1:
% 229.53/40.89  | | | | 
% 229.53/40.89  | | | |   (48)  all_57_10 = e0 & op(e2, e0) = e0
% 229.53/40.89  | | | | 
% 229.53/40.89  | | | | REF_CLOSE: (9), (24), (48) are inconsistent by sub-proof #1332.
% 229.53/40.89  | | | | 
% 229.53/40.89  | | | Case 2:
% 229.53/40.89  | | | | 
% 229.53/40.89  | | | |   (49)  all_57_11 = e0 & op(e1, e0) = e0
% 229.53/40.89  | | | | 
% 229.53/40.89  | | | | ALPHA: (49) implies:
% 229.53/40.89  | | | |   (50)  all_57_11 = e0
% 229.53/40.89  | | | | 
% 229.53/40.89  | | | | BETA: splitting (12) gives:
% 229.53/40.89  | | | | 
% 229.53/40.89  | | | | Case 1:
% 229.53/40.89  | | | | | 
% 229.53/40.89  | | | | |   (51)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3,
% 229.53/40.89  | | | | |             e2) = e1)
% 229.53/40.89  | | | | | 
% 229.53/40.89  | | | | | REF_CLOSE: (4), (5), (6), (11), (15), (16), (18), (20), (21), (24),
% 229.53/40.89  | | | | |            (26), (34), (51) are inconsistent by sub-proof #1677.
% 229.53/40.89  | | | | | 
% 229.53/40.89  | | | | Case 2:
% 229.53/40.89  | | | | | 
% 229.53/40.89  | | | | |   (52)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3,
% 229.53/40.89  | | | | |             e0) = e1)
% 229.53/40.89  | | | | | 
% 229.53/40.89  | | | | | BETA: splitting (52) gives:
% 229.53/40.89  | | | | | 
% 229.53/40.89  | | | | | Case 1:
% 229.53/40.89  | | | | | | 
% 229.53/40.89  | | | | | |   (53)  all_57_4 = e1 & op(e3, e1) = e1
% 229.53/40.89  | | | | | | 
% 229.53/40.89  | | | | | | ALPHA: (53) implies:
% 229.53/40.89  | | | | | |   (54)  all_57_4 = e1
% 229.53/40.89  | | | | | | 
% 229.53/40.89  | | | | | | BETA: splitting (23) gives:
% 229.53/40.89  | | | | | | 
% 229.53/40.89  | | | | | | Case 1:
% 229.53/40.89  | | | | | | | 
% 229.53/40.89  | | | | | | |   (55)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 &
% 229.53/40.89  | | | | | | |           op(e3, e2) = e3)
% 229.53/40.89  | | | | | | | 
% 229.53/40.89  | | | | | | | BETA: splitting (55) gives:
% 229.53/40.89  | | | | | | | 
% 229.53/40.89  | | | | | | | Case 1:
% 229.53/40.89  | | | | | | | | 
% 229.53/40.89  | | | | | | | |   (56)  all_57_0 = e3 & op(e3, e3) = e3
% 229.53/40.89  | | | | | | | | 
% 229.53/40.89  | | | | | | | | ALPHA: (56) implies:
% 229.53/40.89  | | | | | | | |   (57)  op(e3, e3) = e3
% 229.53/40.89  | | | | | | | | 
% 229.53/40.89  | | | | | | | | REF_CLOSE: (6), (15), (18), (57) are inconsistent by sub-proof
% 229.53/40.89  | | | | | | | |            #2490.
% 229.53/40.89  | | | | | | | | 
% 229.53/40.89  | | | | | | | Case 2:
% 229.53/40.89  | | | | | | | | 
% 229.53/40.89  | | | | | | | |   (58)  all_57_1 = e3 & op(e3, e2) = e3
% 229.53/40.89  | | | | | | | | 
% 229.53/40.89  | | | | | | | | ALPHA: (58) implies:
% 229.53/40.89  | | | | | | | |   (59)  all_57_1 = e3
% 229.53/40.89  | | | | | | | | 
% 229.53/40.89  | | | | | | | | BETA: splitting (25) gives:
% 229.53/40.89  | | | | | | | | 
% 229.53/40.89  | | | | | | | | Case 1:
% 229.53/40.89  | | | | | | | | | 
% 229.53/40.89  | | | | | | | | |   (60)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 &
% 229.53/40.89  | | | | | | | | |           op(e2, e1) = e3)
% 229.53/40.89  | | | | | | | | | 
% 229.53/40.89  | | | | | | | | | BETA: splitting (60) gives:
% 229.53/40.89  | | | | | | | | | 
% 229.53/40.89  | | | | | | | | | Case 1:
% 229.53/40.89  | | | | | | | | | | 
% 229.53/40.89  | | | | | | | | | |   (61)  all_57_4 = e3 & op(e3, e1) = e3
% 229.53/40.89  | | | | | | | | | | 
% 229.53/40.89  | | | | | | | | | | ALPHA: (61) implies:
% 229.53/40.89  | | | | | | | | | |   (62)  all_57_4 = e3
% 229.53/40.89  | | | | | | | | | | 
% 229.53/40.89  | | | | | | | | | | REF_CLOSE: (1), (5), (12), (13), (14), (15), (16), (21),
% 229.53/40.89  | | | | | | | | | |            (24), (34), (59), (62) are inconsistent by
% 229.53/40.89  | | | | | | | | | |            sub-proof #1222.
% 229.53/40.89  | | | | | | | | | | 
% 229.53/40.89  | | | | | | | | | Case 2:
% 229.53/40.89  | | | | | | | | | | 
% 229.53/40.89  | | | | | | | | | |   (63)  all_57_5 = e3 & op(e2, e1) = e3
% 229.53/40.89  | | | | | | | | | | 
% 229.53/40.89  | | | | | | | | | | ALPHA: (63) implies:
% 229.53/40.89  | | | | | | | | | |   (64)  all_57_5 = e3
% 229.53/40.89  | | | | | | | | | | 
% 229.53/40.89  | | | | | | | | | | BETA: splitting (31) gives:
% 229.53/40.89  | | | | | | | | | | 
% 229.53/40.89  | | | | | | | | | | Case 1:
% 229.53/40.89  | | | | | | | | | | | 
% 229.53/40.89  | | | | | | | | | | |   (65)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 229.53/40.89  | | | | | | | | | | |           & op(e2, e2) = e2)
% 229.53/40.89  | | | | | | | | | | | 
% 229.53/40.89  | | | | | | | | | | | BETA: splitting (65) gives:
% 229.53/40.89  | | | | | | | | | | | 
% 229.53/40.89  | | | | | | | | | | | Case 1:
% 229.53/40.89  | | | | | | | | | | | | 
% 229.53/40.89  | | | | | | | | | | | |   (66)  all_57_2 = e2 & op(e2, e3) = e2
% 229.53/40.89  | | | | | | | | | | | | 
% 229.53/40.89  | | | | | | | | | | | | ALPHA: (66) implies:
% 229.53/40.89  | | | | | | | | | | | |   (67)  all_57_2 = e2
% 229.53/40.89  | | | | | | | | | | | | 
% 229.53/40.89  | | | | | | | | | | | | BETA: splitting (32) gives:
% 229.53/40.89  | | | | | | | | | | | | 
% 229.53/40.89  | | | | | | | | | | | | Case 1:
% 229.53/40.89  | | | | | | | | | | | | | 
% 229.53/40.89  | | | | | | | | | | | | |   (68)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 229.53/40.89  | | | | | | | | | | | | |           & op(e2, e3) = e3)
% 229.53/40.89  | | | | | | | | | | | | | 
% 229.53/40.89  | | | | | | | | | | | | | REF_CLOSE: (5), (6), (15), (18), (23), (30), (39), (54),
% 229.53/40.89  | | | | | | | | | | | | |            (59), (67), (68) are inconsistent by sub-proof
% 229.53/40.89  | | | | | | | | | | | | |            #811.
% 229.53/40.89  | | | | | | | | | | | | | 
% 229.53/40.89  | | | | | | | | | | | | Case 2:
% 229.53/40.89  | | | | | | | | | | | | | 
% 229.53/40.89  | | | | | | | | | | | | |   (69)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 229.53/40.89  | | | | | | | | | | | | |           e3 & op(e0, e3) = e3)
% 229.53/40.89  | | | | | | | | | | | | | 
% 229.53/40.89  | | | | | | | | | | | | | BETA: splitting (69) gives:
% 229.53/40.89  | | | | | | | | | | | | | 
% 229.53/40.89  | | | | | | | | | | | | | Case 1:
% 229.53/40.89  | | | | | | | | | | | | | | 
% 229.53/40.89  | | | | | | | | | | | | | |   (70)  all_57_6 = e3 & op(e1, e3) = e3
% 229.53/40.89  | | | | | | | | | | | | | | 
% 229.53/40.89  | | | | | | | | | | | | | | ALPHA: (70) implies:
% 229.53/40.89  | | | | | | | | | | | | | |   (71)  all_57_6 = e3
% 229.53/40.89  | | | | | | | | | | | | | | 
% 229.53/40.89  | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (10), (11),
% 229.53/40.89  | | | | | | | | | | | | | |            (15), (16), (17), (18), (20), (21), (22), (24),
% 229.53/40.89  | | | | | | | | | | | | | |            (26), (29), (31), (34), (35), (36), (37), (38),
% 229.53/40.89  | | | | | | | | | | | | | |            (59), (64), (67), (71) are inconsistent by
% 229.53/40.89  | | | | | | | | | | | | | |            sub-proof #807.
% 229.53/40.89  | | | | | | | | | | | | | | 
% 229.53/40.89  | | | | | | | | | | | | | Case 2:
% 229.53/40.89  | | | | | | | | | | | | | | 
% 229.53/40.89  | | | | | | | | | | | | | |   (72)  all_57_12 = e3 & op(e0, e3) = e3
% 229.53/40.89  | | | | | | | | | | | | | | 
% 229.53/40.89  | | | | | | | | | | | | | | ALPHA: (72) implies:
% 229.53/40.89  | | | | | | | | | | | | | |   (73)  all_57_12 = e3
% 229.53/40.89  | | | | | | | | | | | | | | 
% 229.53/40.89  | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (5), (6), (15), (16), (17), (19), (21),
% 229.53/40.89  | | | | | | | | | | | | | |            (24), (27), (28), (33), (34), (35), (37), (38),
% 229.53/40.89  | | | | | | | | | | | | | |            (43), (50), (59), (64), (67), (73) are
% 229.53/40.89  | | | | | | | | | | | | | |            inconsistent by sub-proof #841.
% 229.53/40.89  | | | | | | | | | | | | | | 
% 229.53/40.89  | | | | | | | | | | | | | End of split
% 229.53/40.89  | | | | | | | | | | | | | 
% 229.53/40.89  | | | | | | | | | | | | End of split
% 229.53/40.89  | | | | | | | | | | | | 
% 229.53/40.89  | | | | | | | | | | | Case 2:
% 229.53/40.89  | | | | | | | | | | | | 
% 229.53/40.89  | | | | | | | | | | | |   (74)  all_57_3 = e2 & op(e2, e2) = e2
% 229.53/40.89  | | | | | | | | | | | | 
% 229.53/40.89  | | | | | | | | | | | | ALPHA: (74) implies:
% 229.53/40.89  | | | | | | | | | | | |   (75)  op(e2, e2) = e2
% 229.53/40.89  | | | | | | | | | | | | 
% 229.53/40.89  | | | | | | | | | | | | REF_CLOSE: (6), (11), (34), (75) are inconsistent by
% 229.53/40.89  | | | | | | | | | | | |            sub-proof #2306.
% 229.53/40.89  | | | | | | | | | | | | 
% 229.53/40.89  | | | | | | | | | | | End of split
% 229.53/40.89  | | | | | | | | | | | 
% 229.53/40.89  | | | | | | | | | | Case 2:
% 229.53/40.89  | | | | | | | | | | | 
% 229.53/40.89  | | | | | | | | | | |   (76)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 229.53/40.89  | | | | | | | | | | |           e2 & op(e2, e0) = e2)
% 229.53/40.89  | | | | | | | | | | | 
% 229.53/40.89  | | | | | | | | | | | BETA: splitting (76) gives:
% 229.53/40.89  | | | | | | | | | | | 
% 229.53/40.89  | | | | | | | | | | | Case 1:
% 229.53/40.89  | | | | | | | | | | | | 
% 229.53/40.89  | | | | | | | | | | | |   (77)  all_57_5 = e2 & op(e2, e1) = e2
% 229.53/40.89  | | | | | | | | | | | | 
% 229.53/40.89  | | | | | | | | | | | | REF_CLOSE: (5), (6), (15), (18), (23), (30), (39), (54),
% 229.53/40.89  | | | | | | | | | | | |            (59), (64), (77) are inconsistent by sub-proof
% 229.53/40.89  | | | | | | | | | | | |            #806.
% 229.53/40.89  | | | | | | | | | | | | 
% 229.53/40.89  | | | | | | | | | | | Case 2:
% 229.53/40.89  | | | | | | | | | | | | 
% 229.53/40.89  | | | | | | | | | | | |   (78)  all_57_10 = e2 & op(e2, e0) = e2
% 229.53/40.89  | | | | | | | | | | | | 
% 229.53/40.89  | | | | | | | | | | | | ALPHA: (78) implies:
% 229.53/40.89  | | | | | | | | | | | |   (79)  all_57_10 = e2
% 229.53/40.89  | | | | | | | | | | | | 
% 229.53/40.89  | | | | | | | | | | | | REF_CLOSE: (9), (34), (79) are inconsistent by sub-proof
% 229.53/40.89  | | | | | | | | | | | |            #2144.
% 229.53/40.89  | | | | | | | | | | | | 
% 229.53/40.89  | | | | | | | | | | | End of split
% 229.53/40.89  | | | | | | | | | | | 
% 229.53/40.89  | | | | | | | | | | End of split
% 229.53/40.89  | | | | | | | | | | 
% 229.53/40.89  | | | | | | | | | End of split
% 229.53/40.89  | | | | | | | | | 
% 229.53/40.89  | | | | | | | | Case 2:
% 229.53/40.89  | | | | | | | | | 
% 229.53/40.89  | | | | | | | | |   (80)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 &
% 229.53/40.89  | | | | | | | | |           op(e0, e1) = e3)
% 229.53/40.89  | | | | | | | | | 
% 229.53/40.89  | | | | | | | | | REF_CLOSE: (5), (6), (8), (10), (15), (16), (17), (19), (21),
% 229.53/40.89  | | | | | | | | |            (24), (28), (34), (43), (80) are inconsistent by
% 229.53/40.89  | | | | | | | | |            sub-proof #1044.
% 229.53/40.89  | | | | | | | | | 
% 229.53/40.89  | | | | | | | | End of split
% 229.53/40.89  | | | | | | | | 
% 229.53/40.89  | | | | | | | End of split
% 229.53/40.89  | | | | | | | 
% 229.53/40.89  | | | | | | Case 2:
% 229.53/40.89  | | | | | | | 
% 229.53/40.89  | | | | | | |   (81)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 &
% 229.53/40.89  | | | | | | |           op(e3, e0) = e3)
% 229.53/40.89  | | | | | | | 
% 229.53/40.89  | | | | | | | REF_CLOSE: (5), (6), (30), (39), (54), (81) are inconsistent by
% 229.53/40.89  | | | | | | |            sub-proof #2281.
% 229.53/40.89  | | | | | | | 
% 229.53/40.89  | | | | | | End of split
% 229.53/40.89  | | | | | | 
% 229.53/40.89  | | | | | Case 2:
% 229.53/40.89  | | | | | | 
% 229.53/40.89  | | | | | |   (82)  all_57_9 = e1 & op(e3, e0) = e1
% 229.53/40.89  | | | | | | 
% 229.53/40.89  | | | | | | REF_CLOSE: (1), (34), (82) are inconsistent by sub-proof #2451.
% 229.53/40.89  | | | | | | 
% 229.53/40.89  | | | | | End of split
% 229.53/40.89  | | | | | 
% 229.53/40.89  | | | | End of split
% 229.53/40.89  | | | | 
% 229.53/40.89  | | | End of split
% 229.53/40.89  | | | 
% 229.53/40.89  | | End of split
% 229.53/40.89  | | 
% 229.53/40.89  | End of split
% 229.53/40.89  | 
% 229.53/40.89  End of proof
% 229.53/40.89  
% 229.53/40.89  Sub-proof #806 shows that the following formulas are inconsistent:
% 229.53/40.89  ----------------------------------------------------------------
% 229.53/40.89    (1)   ~ (e3 = e1)
% 229.53/40.89    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.53/40.89           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.53/40.89    (3)   ~ (e3 = e2)
% 229.53/40.89    (4)  op(e3, e3) = e2
% 229.53/40.89    (5)  all_57_4 = e1
% 229.53/40.89    (6)  all_57_5 = e3
% 229.53/40.89    (7)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.53/40.89         (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.53/40.89    (8)   ~ (all_53_12 = e3)
% 229.53/40.89    (9)  all_57_5 = e2 & op(e2, e1) = e2
% 229.53/40.89    (10)  all_57_1 = e3
% 229.53/40.89    (11)  op(e3, e0) = all_53_12
% 229.53/40.89  
% 229.53/40.89  Begin of proof
% 229.53/40.89  | 
% 229.53/40.89  | ALPHA: (9) implies:
% 229.53/40.89  |   (12)  all_57_5 = e2
% 229.53/40.89  | 
% 229.53/40.89  | COMBINE_EQS: (6), (12) imply:
% 229.53/40.89  |   (13)  e3 = e2
% 229.53/40.89  | 
% 229.53/40.89  | COMBINE_EQS: (10), (13) imply:
% 229.53/40.89  |   (14)  all_57_1 = e2
% 229.53/40.89  | 
% 229.53/40.89  | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (11), (14) are inconsistent by
% 229.53/40.89  |            sub-proof #1308.
% 229.53/40.89  | 
% 229.53/40.89  End of proof
% 229.53/40.89  
% 229.53/40.89  Sub-proof #807 shows that the following formulas are inconsistent:
% 229.53/40.89  ----------------------------------------------------------------
% 229.53/40.89    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.53/40.89         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.53/40.89    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.53/40.89         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.53/40.89    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.53/40.89         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.53/40.89    (4)   ~ (e3 = e1)
% 229.53/40.89    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.53/40.89           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.53/40.89    (6)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.53/40.89         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.53/40.89    (7)   ~ (all_6_2 = e3)
% 229.53/40.89    (8)  op(e1, e1) = all_6_2
% 229.53/40.89    (9)  op(e2, e2) = e1
% 229.53/40.89    (10)  all_57_2 = e2
% 229.53/40.89    (11)   ~ (e3 = e2)
% 229.53/40.89    (12)   ~ (e3 = e0)
% 229.53/40.89    (13)  all_57_15 = e3
% 229.53/40.89    (14)  op(e3, e3) = e2
% 229.53/40.89    (15)  all_57_5 = e3
% 229.53/40.89    (16)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.53/40.89          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.53/40.89    (17)   ~ (e2 = e0)
% 229.53/40.89    (18)  all_57_3 = e1
% 229.53/40.89    (19)   ~ (e1 = e0)
% 229.53/40.89    (20)  all_57_6 = e3
% 229.53/40.89    (21)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.53/40.89          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.53/40.89    (22)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.53/40.89              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.53/40.89                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.53/40.89                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.53/40.89    (23)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.53/40.89          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.53/40.89    (24)  all_57_1 = e3
% 229.53/40.89    (25)   ~ (e2 = e1)
% 229.53/40.89    (26)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.53/40.89          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.53/40.89    (27)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.53/40.89          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.53/40.90    (28)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.53/40.90          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.53/40.90    (29)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.53/40.90          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.53/40.90  
% 229.53/40.90  Begin of proof
% 229.53/40.90  | 
% 229.53/40.90  | BETA: splitting (27) gives:
% 229.53/40.90  | 
% 229.53/40.90  | Case 1:
% 229.53/40.90  | | 
% 229.53/40.90  | |   (30)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) =
% 229.53/40.90  | |           e0)
% 229.53/40.90  | | 
% 229.53/40.90  | | REF_CLOSE: (5), (10), (14), (17), (30) are inconsistent by sub-proof #1577.
% 229.53/40.90  | | 
% 229.53/40.90  | Case 2:
% 229.53/40.90  | | 
% 229.53/40.90  | |   (31)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) =
% 229.53/40.90  | |           e0)
% 229.53/40.90  | | 
% 229.53/40.90  | | BETA: splitting (31) gives:
% 229.53/40.90  | | 
% 229.53/40.90  | | Case 1:
% 229.53/40.90  | | | 
% 229.53/40.90  | | |   (32)  all_57_6 = e0 & op(e1, e3) = e0
% 229.53/40.90  | | | 
% 229.53/40.90  | | | ALPHA: (32) implies:
% 229.53/40.90  | | |   (33)  all_57_6 = e0
% 229.53/40.90  | | | 
% 229.53/40.90  | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (11), (12), (13), (16),
% 229.53/40.90  | | |            (17), (19), (22), (24), (25), (26), (28), (29), (33) are
% 229.53/40.90  | | |            inconsistent by sub-proof #1773.
% 229.53/40.90  | | | 
% 229.53/40.90  | | Case 2:
% 229.53/40.90  | | | 
% 229.53/40.90  | | |   (34)  all_57_12 = e0 & op(e0, e3) = e0
% 229.53/40.90  | | | 
% 229.53/40.90  | | | ALPHA: (34) implies:
% 229.53/40.90  | | |   (35)  all_57_12 = e0
% 229.53/40.90  | | | 
% 229.53/40.90  | | | BETA: splitting (2) gives:
% 229.53/40.90  | | | 
% 229.53/40.90  | | | Case 1:
% 229.53/40.90  | | | | 
% 229.53/40.90  | | | |   (36)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3)
% 229.53/40.90  | | | |           = e1)
% 229.57/40.90  | | | | 
% 229.57/40.90  | | | | REF_CLOSE: (5), (10), (14), (25), (36) are inconsistent by sub-proof
% 229.57/40.90  | | | |            #1633.
% 229.57/40.90  | | | | 
% 229.57/40.90  | | | Case 2:
% 229.57/40.90  | | | | 
% 229.57/40.90  | | | |   (37)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3)
% 229.57/40.90  | | | |           = e1)
% 229.57/40.90  | | | | 
% 229.57/40.90  | | | | BETA: splitting (37) gives:
% 229.57/40.90  | | | | 
% 229.57/40.90  | | | | Case 1:
% 229.57/40.90  | | | | | 
% 229.57/40.90  | | | | |   (38)  all_57_6 = e1 & op(e1, e3) = e1
% 229.57/40.90  | | | | | 
% 229.57/40.90  | | | | | REF_CLOSE: (3), (4), (5), (9), (11), (12), (16), (17), (19), (20),
% 229.57/40.90  | | | | |            (21), (24), (25), (38) are inconsistent by sub-proof #1771.
% 229.57/40.90  | | | | | 
% 229.57/40.90  | | | | Case 2:
% 229.57/40.90  | | | | | 
% 229.57/40.90  | | | | |   (39)  all_57_12 = e1 & op(e0, e3) = e1
% 229.57/40.90  | | | | | 
% 229.57/40.90  | | | | | ALPHA: (39) implies:
% 229.57/40.90  | | | | |   (40)  all_57_12 = e1
% 229.57/40.90  | | | | | 
% 229.57/40.90  | | | | | COMBINE_EQS: (35), (40) imply:
% 229.57/40.90  | | | | |   (41)  e1 = e0
% 229.57/40.90  | | | | | 
% 229.57/40.90  | | | | | SIMP: (41) implies:
% 229.57/40.90  | | | | |   (42)  e1 = e0
% 229.57/40.90  | | | | | 
% 229.57/40.90  | | | | | REF_CLOSE: (1), (2), (4), (5), (10), (11), (12), (14), (15), (17),
% 229.57/40.90  | | | | |            (18), (19), (20), (23), (25), (27), (42) are inconsistent
% 229.57/40.90  | | | | |            by sub-proof #808.
% 229.57/40.90  | | | | | 
% 229.57/40.90  | | | | End of split
% 229.57/40.90  | | | | 
% 229.57/40.90  | | | End of split
% 229.57/40.90  | | | 
% 229.57/40.90  | | End of split
% 229.57/40.90  | | 
% 229.57/40.90  | End of split
% 229.57/40.90  | 
% 229.57/40.90  End of proof
% 229.57/40.90  
% 229.57/40.90  Sub-proof #808 shows that the following formulas are inconsistent:
% 229.57/40.90  ----------------------------------------------------------------
% 229.57/40.90    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.57/40.90         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.57/40.90    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.57/40.90         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.57/40.90    (3)   ~ (e3 = e1)
% 229.57/40.90    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.57/40.90           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.57/40.90    (5)  all_57_2 = e2
% 229.57/40.90    (6)   ~ (e3 = e2)
% 229.57/40.90    (7)   ~ (e3 = e0)
% 229.57/40.90    (8)  op(e3, e3) = e2
% 229.57/40.90    (9)  all_57_5 = e3
% 229.57/40.90    (10)   ~ (e2 = e0)
% 229.57/40.90    (11)  all_57_3 = e1
% 229.57/40.90    (12)   ~ (e1 = e0)
% 229.57/40.90    (13)  e1 = e0
% 229.57/40.90    (14)  all_57_6 = e3
% 229.57/40.90    (15)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.57/40.90          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.57/40.90    (16)   ~ (e2 = e1)
% 229.57/40.90    (17)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.57/40.90          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.57/40.90  
% 229.57/40.90  Begin of proof
% 229.57/40.90  | 
% 229.57/40.90  | COMBINE_EQS: (11), (13) imply:
% 229.57/40.90  |   (18)  all_57_3 = e0
% 229.57/40.90  | 
% 229.57/40.90  | BETA: splitting (2) gives:
% 229.57/40.90  | 
% 229.57/40.90  | Case 1:
% 229.57/40.90  | | 
% 229.57/40.90  | |   (19)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) =
% 229.57/40.90  | |           e1)
% 229.57/40.90  | | 
% 229.57/40.90  | | REF_CLOSE: (4), (5), (8), (16), (19) are inconsistent by sub-proof #1633.
% 229.57/40.90  | | 
% 229.57/40.90  | Case 2:
% 229.57/40.90  | | 
% 229.57/40.90  | |   (20)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) =
% 229.57/40.90  | |           e1)
% 229.57/40.90  | | 
% 229.57/40.90  | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (10), (12), (14), (15), (16),
% 229.57/40.90  | |            (17), (18), (20) are inconsistent by sub-proof #809.
% 229.57/40.90  | | 
% 229.57/40.90  | End of split
% 229.57/40.90  | 
% 229.57/40.90  End of proof
% 229.57/40.90  
% 229.57/40.90  Sub-proof #809 shows that the following formulas are inconsistent:
% 229.57/40.90  ----------------------------------------------------------------
% 229.57/40.90    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.57/40.90         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.57/40.90    (2)   ~ (e3 = e1)
% 229.57/40.90    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.57/40.90           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.57/40.90    (4)  all_57_3 = e0
% 229.57/40.90    (5)   ~ (e3 = e2)
% 229.57/40.90    (6)   ~ (e3 = e0)
% 229.57/40.90    (7)  op(e3, e3) = e2
% 229.57/40.90    (8)  all_57_5 = e3
% 229.57/40.90    (9)   ~ (e2 = e0)
% 229.57/40.90    (10)   ~ (e1 = e0)
% 229.57/40.90    (11)  all_57_6 = e3
% 229.57/40.90    (12)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.57/40.90    (13)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.57/40.90          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.57/40.90    (14)   ~ (e2 = e1)
% 229.57/40.90    (15)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.57/40.90          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.57/40.90  
% 229.57/40.90  Begin of proof
% 229.57/40.90  | 
% 229.57/40.90  | BETA: splitting (12) gives:
% 229.57/40.90  | 
% 229.57/40.90  | Case 1:
% 229.57/40.90  | | 
% 229.57/40.90  | |   (16)  all_57_6 = e1 & op(e1, e3) = e1
% 229.57/40.90  | | 
% 229.57/40.90  | | REF_CLOSE: (2), (11), (16) are inconsistent by sub-proof #2117.
% 229.57/40.90  | | 
% 229.57/40.90  | Case 2:
% 229.57/40.90  | | 
% 229.57/40.90  | |   (17)  all_57_12 = e1 & op(e0, e3) = e1
% 229.57/40.90  | | 
% 229.57/40.90  | | ALPHA: (17) implies:
% 229.57/40.90  | |   (18)  all_57_12 = e1
% 229.57/40.90  | | 
% 229.57/40.90  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 229.57/40.90  | |            (14), (15), (18) are inconsistent by sub-proof #810.
% 229.57/40.90  | | 
% 229.57/40.90  | End of split
% 229.57/40.90  | 
% 229.57/40.90  End of proof
% 229.57/40.90  
% 229.57/40.90  Sub-proof #810 shows that the following formulas are inconsistent:
% 229.57/40.90  ----------------------------------------------------------------
% 229.57/40.90    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.57/40.90         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.57/40.90    (2)   ~ (e3 = e1)
% 229.57/40.90    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.57/40.90           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.57/40.90    (4)  all_57_3 = e0
% 229.57/40.90    (5)   ~ (e3 = e2)
% 229.57/40.90    (6)   ~ (e3 = e0)
% 229.57/40.90    (7)  op(e3, e3) = e2
% 229.57/40.90    (8)  all_57_5 = e3
% 229.57/40.90    (9)  all_57_12 = e1
% 229.57/40.90    (10)   ~ (e2 = e0)
% 229.57/40.90    (11)   ~ (e1 = e0)
% 229.57/40.90    (12)  all_57_6 = e3
% 229.57/40.90    (13)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.57/40.90          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.57/40.90    (14)   ~ (e2 = e1)
% 229.57/40.90    (15)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.57/40.90          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.57/40.90  
% 229.57/40.90  Begin of proof
% 229.57/40.90  | 
% 229.57/40.90  | BETA: splitting (15) gives:
% 229.57/40.90  | 
% 229.57/40.90  | Case 1:
% 229.57/40.90  | | 
% 229.57/40.90  | |   (16)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) =
% 229.57/40.90  | |           e0)
% 229.57/40.90  | | 
% 229.57/40.90  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (10), (11), (13), (14), (16)
% 229.57/40.90  | |            are inconsistent by sub-proof #1644.
% 229.57/40.90  | | 
% 229.57/40.90  | Case 2:
% 229.57/40.90  | | 
% 229.57/40.90  | |   (17)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) =
% 229.57/40.90  | |           e0)
% 229.57/40.90  | | 
% 229.57/40.90  | | BETA: splitting (17) gives:
% 229.57/40.90  | | 
% 229.57/40.90  | | Case 1:
% 229.57/40.90  | | | 
% 229.57/40.90  | | |   (18)  all_57_6 = e0 & op(e1, e3) = e0
% 229.57/40.90  | | | 
% 229.57/40.90  | | | ALPHA: (18) implies:
% 229.57/40.90  | | |   (19)  all_57_6 = e0
% 229.57/40.90  | | | 
% 229.57/40.90  | | | REF_CLOSE: (6), (12), (19) are inconsistent by sub-proof #1822.
% 229.57/40.90  | | | 
% 229.57/40.90  | | Case 2:
% 229.57/40.90  | | | 
% 229.57/40.90  | | |   (20)  all_57_12 = e0 & op(e0, e3) = e0
% 229.57/40.90  | | | 
% 229.57/40.90  | | | ALPHA: (20) implies:
% 229.57/40.90  | | |   (21)  all_57_12 = e0
% 229.57/40.90  | | | 
% 229.57/40.90  | | | REF_CLOSE: (9), (11), (21) are inconsistent by sub-proof #2014.
% 229.57/40.90  | | | 
% 229.57/40.90  | | End of split
% 229.57/40.90  | | 
% 229.57/40.90  | End of split
% 229.57/40.90  | 
% 229.57/40.90  End of proof
% 229.57/40.90  
% 229.57/40.90  Sub-proof #811 shows that the following formulas are inconsistent:
% 229.57/40.90  ----------------------------------------------------------------
% 229.57/40.90    (1)   ~ (e3 = e1)
% 229.57/40.90    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.57/40.90           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.57/40.90    (3)  all_57_2 = e2
% 229.57/40.90    (4)   ~ (e3 = e2)
% 229.57/40.90    (5)  op(e3, e3) = e2
% 229.57/40.90    (6)  all_57_4 = e1
% 229.57/40.90    (7)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.57/40.90         (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.57/40.90    (8)   ~ (all_53_12 = e3)
% 229.57/40.90    (9)  all_57_1 = e3
% 229.57/40.90    (10)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3)
% 229.57/40.90    (11)  op(e3, e0) = all_53_12
% 229.57/40.90  
% 229.57/40.90  Begin of proof
% 229.57/40.90  | 
% 229.57/40.90  | BETA: splitting (10) gives:
% 229.57/40.90  | 
% 229.57/40.90  | Case 1:
% 229.57/40.90  | | 
% 229.57/40.90  | |   (12)  all_57_0 = e3 & op(e3, e3) = e3
% 229.57/40.90  | | 
% 229.57/40.90  | | ALPHA: (12) implies:
% 229.57/40.90  | |   (13)  op(e3, e3) = e3
% 229.57/40.90  | | 
% 229.57/40.90  | | REF_CLOSE: (2), (4), (5), (13) are inconsistent by sub-proof #2490.
% 229.57/40.90  | | 
% 229.57/40.90  | Case 2:
% 229.57/40.90  | | 
% 229.57/40.90  | |   (14)  all_57_2 = e3 & op(e2, e3) = e3
% 229.57/40.90  | | 
% 229.57/40.90  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (14) are
% 229.57/40.90  | |            inconsistent by sub-proof #812.
% 229.57/40.90  | | 
% 229.57/40.90  | End of split
% 229.57/40.90  | 
% 229.57/40.90  End of proof
% 229.57/40.90  
% 229.57/40.90  Sub-proof #812 shows that the following formulas are inconsistent:
% 229.57/40.90  ----------------------------------------------------------------
% 229.57/40.90    (1)   ~ (e3 = e1)
% 229.57/40.90    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.57/40.90           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.57/40.90    (3)  all_57_2 = e3 & op(e2, e3) = e3
% 229.57/40.90    (4)  all_57_2 = e2
% 229.57/40.90    (5)   ~ (e3 = e2)
% 229.57/40.90    (6)  op(e3, e3) = e2
% 229.57/40.90    (7)  all_57_4 = e1
% 229.57/40.90    (8)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.57/40.90         (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.57/40.90    (9)   ~ (all_53_12 = e3)
% 229.57/40.90    (10)  all_57_1 = e3
% 229.57/40.90    (11)  op(e3, e0) = all_53_12
% 229.57/40.90  
% 229.57/40.90  Begin of proof
% 229.57/40.90  | 
% 229.57/40.90  | ALPHA: (3) implies:
% 229.57/40.90  |   (12)  all_57_2 = e3
% 229.57/40.90  | 
% 229.57/40.90  | COMBINE_EQS: (4), (12) imply:
% 229.57/40.90  |   (13)  e3 = e2
% 229.57/40.90  | 
% 229.57/40.90  | SIMP: (13) implies:
% 229.57/40.90  |   (14)  e3 = e2
% 229.57/40.90  | 
% 229.57/40.90  | COMBINE_EQS: (10), (14) imply:
% 229.57/40.90  |   (15)  all_57_1 = e2
% 229.57/40.90  | 
% 229.57/40.90  | REF_CLOSE: (1), (2), (5), (6), (7), (8), (9), (11), (15) are inconsistent by
% 229.57/40.90  |            sub-proof #1308.
% 229.57/40.90  | 
% 229.57/40.90  End of proof
% 229.57/40.90  
% 229.57/40.90  Sub-proof #813 shows that the following formulas are inconsistent:
% 229.57/40.90  ----------------------------------------------------------------
% 229.57/40.90    (1)   ~ (e3 = e1)
% 229.57/40.90    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.57/40.90           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.57/40.90    (3)  all_57_9 = e1
% 229.57/40.90    (4)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.57/40.90         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.57/40.90    (5)   ~ (e3 = e2)
% 229.57/40.90    (6)   ~ (e3 = e0)
% 229.57/40.90    (7)  op(e3, e3) = e2
% 229.57/40.90    (8)  all_57_4 = e1
% 229.57/40.90    (9)   ~ (e2 = e0)
% 229.57/40.90    (10)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.57/40.90          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.57/40.90    (11)   ~ (e1 = e0)
% 229.57/40.90    (12)   ~ (all_53_12 = e3)
% 229.57/40.90    (13)  op(e3, e0) = all_53_12
% 229.57/40.90  
% 229.57/40.90  Begin of proof
% 229.57/40.90  | 
% 229.57/40.90  | BETA: splitting (10) gives:
% 229.57/40.90  | 
% 229.57/40.90  | Case 1:
% 229.57/40.90  | | 
% 229.57/40.90  | |   (14)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) =
% 229.57/40.90  | |           e3)
% 229.57/40.90  | | 
% 229.57/40.90  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (11), (14) are
% 229.57/40.90  | |            inconsistent by sub-proof #1674.
% 229.57/40.90  | | 
% 229.57/40.90  | Case 2:
% 229.57/40.90  | | 
% 229.57/40.90  | |   (15)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) =
% 229.57/40.91  | |           e3)
% 229.57/40.91  | | 
% 229.57/40.91  | | REF_CLOSE: (1), (2), (8), (12), (13), (15) are inconsistent by sub-proof
% 229.57/40.91  | |            #2281.
% 229.57/40.91  | | 
% 229.57/40.91  | End of split
% 229.57/40.91  | 
% 229.57/40.91  End of proof
% 229.57/40.91  
% 229.57/40.91  Sub-proof #814 shows that the following formulas are inconsistent:
% 229.57/40.91  ----------------------------------------------------------------
% 229.57/40.91    (1)   ~ (e3 = e1)
% 229.57/40.91    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.57/40.91           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.57/40.91    (3)  op(e2, e2) = e1
% 229.57/40.91    (4)   ~ (e3 = e2)
% 229.57/40.91    (5)   ~ (e3 = e0)
% 229.57/40.91    (6)  all_57_15 = e3
% 229.57/40.91    (7)   ~ (e2 = e0)
% 229.57/40.91    (8)   ~ (e1 = e0)
% 229.57/40.91    (9)  op(e0, e0) = e3
% 229.57/40.91    (10)  all_57_2 = e1
% 229.57/40.91    (11)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.57/40.91              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.57/40.91                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.57/40.91                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.57/40.91    (12)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.57/40.91          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.57/40.91    (13)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.57/40.91          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.57/40.91    (14)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.57/40.91          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 229.57/40.91    (15)   ~ (e2 = e1)
% 229.57/40.91    (16)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.57/40.91          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.57/40.91    (17)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.57/40.91          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.57/40.91  
% 229.57/40.91  Begin of proof
% 229.57/40.91  | 
% 229.57/40.91  | BETA: splitting (12) gives:
% 229.57/40.91  | 
% 229.57/40.91  | Case 1:
% 229.57/40.91  | | 
% 229.57/40.91  | |   (18)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 229.57/40.91  | |           e3)
% 229.57/40.91  | | 
% 229.57/40.91  | | REF_CLOSE: (1), (2), (3), (10), (18) are inconsistent by sub-proof #995.
% 229.57/40.91  | | 
% 229.57/40.91  | Case 2:
% 229.57/40.91  | | 
% 229.57/40.91  | |   (19)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 229.57/40.91  | |           e3)
% 229.57/40.91  | | 
% 229.57/40.91  | | BETA: splitting (19) gives:
% 229.57/40.91  | | 
% 229.57/40.91  | | Case 1:
% 229.57/40.91  | | | 
% 229.57/40.91  | | |   (20)  all_57_5 = e3 & op(e2, e1) = e3
% 229.57/40.91  | | | 
% 229.57/40.91  | | | ALPHA: (20) implies:
% 229.57/40.91  | | |   (21)  all_57_5 = e3
% 229.57/40.91  | | | 
% 229.57/40.91  | | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (10), (13), (14), (15), (21) are
% 229.57/40.91  | | |            inconsistent by sub-proof #1825.
% 229.57/40.91  | | | 
% 229.57/40.91  | | Case 2:
% 229.57/40.91  | | | 
% 229.57/40.91  | | |   (22)  all_57_10 = e3 & op(e2, e0) = e3
% 229.57/40.91  | | | 
% 229.57/40.91  | | | ALPHA: (22) implies:
% 229.57/40.91  | | |   (23)  all_57_10 = e3
% 229.57/40.91  | | | 
% 229.57/40.91  | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (11), (15), (16), (17),
% 229.57/40.91  | | |            (23) are inconsistent by sub-proof #1746.
% 229.57/40.91  | | | 
% 229.57/40.91  | | End of split
% 229.57/40.91  | | 
% 229.57/40.91  | End of split
% 229.57/40.91  | 
% 229.57/40.91  End of proof
% 229.57/40.91  
% 229.57/40.91  Sub-proof #815 shows that the following formulas are inconsistent:
% 229.57/40.91  ----------------------------------------------------------------
% 229.57/40.91    (1)  all_57_10 = e0
% 229.57/40.91    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.57/40.91         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.57/40.91    (3)   ~ (e3 = e1)
% 229.57/40.91    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.57/40.91           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.57/40.91    (5)  op(e2, e2) = e0
% 229.57/40.91    (6)  all_57_2 = e3
% 229.57/40.91    (7)   ~ (e1 = e0)
% 229.57/40.91    (8)  all_57_5 = e2
% 229.57/40.91    (9)   ~ (e2 = e1)
% 229.57/40.91  
% 229.57/40.91  Begin of proof
% 229.57/40.91  | 
% 229.57/40.91  | BETA: splitting (2) gives:
% 229.57/40.91  | 
% 229.57/40.91  | Case 1:
% 229.57/40.91  | | 
% 229.57/40.91  | |   (10)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) =
% 229.57/40.91  | |           e1)
% 229.57/40.91  | | 
% 229.57/40.91  | | BETA: splitting (10) gives:
% 229.57/40.91  | | 
% 229.57/40.91  | | Case 1:
% 229.57/40.91  | | | 
% 229.57/40.91  | | |   (11)  all_57_2 = e1 & op(e2, e3) = e1
% 229.57/40.91  | | | 
% 229.57/40.91  | | | REF_CLOSE: (3), (6), (11) are inconsistent by sub-proof #1928.
% 229.57/40.91  | | | 
% 229.57/40.91  | | Case 2:
% 229.57/40.91  | | | 
% 229.57/40.91  | | |   (12)  all_57_3 = e1 & op(e2, e2) = e1
% 229.57/40.91  | | | 
% 229.57/40.91  | | | ALPHA: (12) implies:
% 229.57/40.91  | | |   (13)  op(e2, e2) = e1
% 229.57/40.91  | | | 
% 229.57/40.91  | | | REF_CLOSE: (4), (5), (7), (13) are inconsistent by sub-proof #2352.
% 229.57/40.91  | | | 
% 229.57/40.91  | | End of split
% 229.57/40.91  | | 
% 229.57/40.91  | Case 2:
% 229.57/40.91  | | 
% 229.57/40.91  | |   (14)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) =
% 229.57/40.91  | |           e1)
% 229.57/40.91  | | 
% 229.57/40.91  | | BETA: splitting (14) gives:
% 229.57/40.91  | | 
% 229.57/40.91  | | Case 1:
% 229.57/40.91  | | | 
% 229.57/40.91  | | |   (15)  all_57_5 = e1 & op(e2, e1) = e1
% 229.57/40.91  | | | 
% 229.57/40.91  | | | REF_CLOSE: (8), (9), (15) are inconsistent by sub-proof #1886.
% 229.57/40.91  | | | 
% 229.57/40.91  | | Case 2:
% 229.57/40.91  | | | 
% 229.57/40.91  | | |   (16)  all_57_10 = e1 & op(e2, e0) = e1
% 229.57/40.91  | | | 
% 229.57/40.91  | | | ALPHA: (16) implies:
% 229.57/40.91  | | |   (17)  all_57_10 = e1
% 229.57/40.91  | | | 
% 229.57/40.91  | | | REF_CLOSE: (1), (7), (17) are inconsistent by sub-proof #1531.
% 229.57/40.91  | | | 
% 229.57/40.91  | | End of split
% 229.57/40.91  | | 
% 229.57/40.91  | End of split
% 229.57/40.91  | 
% 229.57/40.91  End of proof
% 229.57/40.91  
% 229.57/40.91  Sub-proof #816 shows that the following formulas are inconsistent:
% 229.57/40.91  ----------------------------------------------------------------
% 229.57/40.91    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.57/40.91         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.57/40.91    (2)   ~ (e3 = e1)
% 229.57/40.91    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.57/40.91           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.57/40.91    (4)   ~ (e3 = e2)
% 229.57/40.91    (5)   ~ (e3 = e0)
% 229.57/40.91    (6)  all_57_15 = e3
% 229.57/40.91    (7)   ~ (e2 = e0)
% 229.57/40.91    (8)  all_57_2 = e3
% 229.57/40.91    (9)  e3 = e2
% 229.57/40.91    (10)  op(e2, e2) = e2
% 229.57/40.91    (11)   ~ (e1 = e0)
% 229.57/40.91    (12)  op(e0, e0) = e3
% 229.57/40.91    (13)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.57/40.91              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.57/40.91                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.57/40.91                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.57/40.91    (14)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.57/40.91          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.57/40.91    (15)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.57/40.91          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 229.57/40.91    (16)   ~ (e2 = e1)
% 229.57/40.91    (17)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.57/40.91          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.57/40.91    (18)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.57/40.91          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.57/40.91  
% 229.57/40.91  Begin of proof
% 229.57/40.91  | 
% 229.57/40.91  | SIMP: (9) implies:
% 229.57/40.91  |   (19)  e3 = e2
% 229.57/40.91  | 
% 229.57/40.91  | COMBINE_EQS: (8), (19) imply:
% 229.57/40.91  |   (20)  all_57_2 = e2
% 229.57/40.91  | 
% 229.57/40.91  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (10), (11), (12), (13), (14),
% 229.57/40.91  |            (15), (16), (17), (18), (20) are inconsistent by sub-proof #1169.
% 229.57/40.91  | 
% 229.57/40.91  End of proof
% 229.57/40.91  
% 229.57/40.91  Sub-proof #817 shows that the following formulas are inconsistent:
% 229.57/40.91  ----------------------------------------------------------------
% 229.57/40.91    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.57/40.91           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.57/40.91    (2)   ~ (e3 = e0)
% 229.57/40.92    (3)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0)
% 229.57/40.92    (4)   ~ (e2 = e0)
% 229.57/40.92    (5)  all_57_2 = e3
% 229.57/40.92    (6)  op(e2, e2) = e2
% 229.57/40.92  
% 229.57/40.92  Begin of proof
% 229.57/40.92  | 
% 229.57/40.92  | BETA: splitting (3) gives:
% 229.57/40.92  | 
% 229.57/40.92  | Case 1:
% 229.57/40.92  | | 
% 229.57/40.92  | |   (7)  all_57_2 = e0 & op(e2, e3) = e0
% 229.57/40.92  | | 
% 229.57/40.92  | | REF_CLOSE: (2), (5), (7) are inconsistent by sub-proof #1805.
% 229.57/40.92  | | 
% 229.57/40.92  | Case 2:
% 229.57/40.92  | | 
% 229.57/40.92  | |   (8)  all_57_3 = e0 & op(e2, e2) = e0
% 229.57/40.92  | | 
% 229.57/40.92  | | ALPHA: (8) implies:
% 229.57/40.92  | |   (9)  op(e2, e2) = e0
% 229.57/40.92  | | 
% 229.57/40.92  | | REF_CLOSE: (1), (4), (6), (9) are inconsistent by sub-proof #2472.
% 229.57/40.92  | | 
% 229.57/40.92  | End of split
% 229.57/40.92  | 
% 229.57/40.92  End of proof
% 229.57/40.92  
% 229.57/40.92  Sub-proof #818 shows that the following formulas are inconsistent:
% 229.57/40.92  ----------------------------------------------------------------
% 229.57/40.92    (1)  all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 229.57/40.92    (2)  op(e3, e3) = all_10_2
% 229.57/40.92    (3)   ~ (all_53_7 = e3)
% 229.57/40.92    (4)   ~ (all_48_2 = e0) | ( ~ (all_48_0 = e2) & op(all_48_1, e3) = all_48_0 &
% 229.57/40.92           op(e3, e0) = all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 =
% 229.57/40.92             e1) & op(e3, e0) = all_48_1 & $i(all_48_1))
% 229.57/40.92    (5)  op(e0, e1) = all_53_11
% 229.57/40.92    (6)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 229.57/40.92    (7)   ~ (all_20_2 = e2) | ( ~ (all_20_0 = e1) & op(all_20_1, e3) = all_20_0 &
% 229.57/40.92           op(e3, e2) = all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 =
% 229.57/40.92             e0) & op(e3, e2) = all_20_1 & $i(all_20_1))
% 229.57/40.92    (8)   ~ (all_53_3 = all_10_2)
% 229.57/40.92    (9)   ~ (all_53_6 = all_53_14)
% 229.57/40.92    (10)   ~ (all_53_1 = all_10_2)
% 229.57/40.92    (11)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 229.57/40.92    (12)   ~ (all_53_6 = e2)
% 229.57/40.92    (13)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.57/40.92          (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.57/40.92    (14)  all_48_2 = all_10_2
% 229.57/40.92    (15)  op(e2, e3) = all_53_1
% 229.57/40.92    (16)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.57/40.92          (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.57/40.92    (17)   ~ (all_53_8 = all_53_12)
% 229.57/40.92    (18)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.57/40.92          (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.57/40.92    (19)   ~ (e3 = e1)
% 229.57/40.92    (20)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 229.57/40.92          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 229.57/40.92    (21)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.57/40.92            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.57/40.92    (22)  all_55_0 = all_10_2
% 229.57/40.92    (23)  all_22_2 = e3
% 229.57/40.92    (24)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.57/40.92          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.57/40.92    (25)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 229.57/40.92            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 229.57/40.92              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 229.57/40.92    (26)   ~ (all_53_8 = all_10_2)
% 229.57/40.92    (27)   ~ (all_53_3 = all_53_7)
% 229.57/40.92    (28)   ~ (all_6_2 = e3)
% 229.57/40.92    (29)  op(e1, e1) = all_6_2
% 229.57/40.92    (30)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 229.57/40.92    (31)  all_34_2 = all_6_2
% 229.57/40.92    (32)  all_55_0 = e3 | all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 229.57/40.92    (33)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 229.57/40.92    (34)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.57/40.92          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.57/40.92    (35)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 229.57/40.92    (36)  all_55_9 = all_53_6
% 229.57/40.92    (37)   ~ (all_53_11 = all_6_2)
% 229.57/40.92    (38)   ~ (all_53_13 = e2)
% 229.57/40.92    (39)   ~ (all_18_2 = e0) | ( ~ (all_18_0 = e1) & op(all_18_1, e3) = all_18_0 &
% 229.57/40.92            op(e3, e0) = all_18_1 & $i(all_18_0) & $i(all_18_1)) | ( ~ (all_18_1 =
% 229.57/40.92              e2) & op(e3, e0) = all_18_1 & $i(all_18_1))
% 229.57/40.92    (40)   ~ (all_53_4 = all_53_12)
% 229.57/40.92    (41)   ~ (all_53_7 = e2)
% 229.57/40.92    (42)   ~ (all_53_2 = all_6_2)
% 229.57/40.92    (43)   ~ (all_53_13 = e3)
% 229.57/40.92    (44)   ~ (all_53_8 = all_53_9)
% 229.57/40.92    (45)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.57/40.92          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.57/40.92    (46)   ~ (all_53_9 = all_53_11)
% 229.57/40.92    (47)  all_55_4 = all_53_1
% 229.57/40.92    (48)   ~ (all_53_9 = all_6_2)
% 229.57/40.92    (49)   ~ (all_53_12 = all_53_13)
% 229.57/40.92    (50)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.57/40.92          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.57/40.92    (51)   ~ (all_53_14 = all_6_2)
% 229.57/40.92    (52)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 229.57/40.92          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.57/40.92    (53)   ~ (e3 = e2)
% 229.57/40.92    (54)   ~ (all_53_4 = all_10_2)
% 229.57/40.92    (55)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 229.57/40.92    (56)  all_55_1 = all_53_4
% 229.57/40.92    (57)   ~ (all_53_1 = all_53_3)
% 229.57/40.92    (58)  op(e1, e0) = all_53_14
% 229.57/40.92    (59)   ~ (all_53_6 = all_53_7)
% 229.57/40.92    (60)  all_55_7 = e3 | all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 229.57/40.92    (61)   ~ (e3 = e0)
% 229.57/40.92    (62)  all_20_2 = all_10_2
% 229.57/40.92    (63)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 229.57/40.92          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 229.57/40.92    (64)   ~ (all_53_8 = all_6_2)
% 229.57/40.92    (65)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 229.57/40.92    (66)  op(e0, e3) = all_53_3
% 229.57/40.92    (67)  all_55_2 = all_53_8
% 229.57/40.92    (68)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 229.57/40.92    (69)   ~ (all_53_4 = all_53_7)
% 229.57/40.92    (70)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 229.57/40.92    (71)  all_57_15 = e3
% 229.57/40.92    (72)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.57/40.92          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.57/40.92            e1)
% 229.57/40.92    (73)   ~ (all_53_4 = all_53_8)
% 229.57/40.92    (74)   ~ (all_53_14 = e3)
% 229.57/40.92    (75)  all_55_6 = all_53_9
% 229.57/40.92    (76)  op(e3, e2) = all_53_4
% 229.57/40.92    (77)   ~ (all_53_1 = all_53_2)
% 229.57/40.92    (78)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.57/40.92          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.57/40.92    (79)   ~ (all_53_2 = all_10_2)
% 229.57/40.92    (80)   ~ (e2 = e0)
% 229.57/40.92    (81)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 229.57/40.92            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 229.57/40.92            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 229.57/40.92            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 229.57/40.92              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 229.57/40.92            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 229.57/40.92            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 229.57/40.92              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 229.57/40.92              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 229.57/40.92            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 229.57/40.92            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 229.57/40.92            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 229.57/40.92              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 229.57/40.92              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 229.57/40.92            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 229.57/40.92              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 229.57/40.92            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 229.57/40.92            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 229.57/40.92              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 229.57/40.92              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 229.57/40.92            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 229.57/40.92            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 229.57/40.92    (82)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 229.57/40.92            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 229.57/40.92              e3) = all_12_1 & $i(all_12_1))
% 229.57/40.92    (83)   ~ (all_53_9 = e2)
% 229.57/40.92    (84)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.57/40.92          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.57/40.92    (85)   ~ (all_53_2 = all_53_14)
% 229.57/40.92    (86)  op(e2, e2) = e2
% 229.57/40.92    (87)   ~ (e1 = e0)
% 229.57/40.92    (88)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 229.57/40.92            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 229.57/40.92              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 229.57/40.92    (89)   ~ (all_53_3 = all_53_11)
% 229.57/40.92    (90)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.57/40.92          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.57/40.92    (91)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.57/40.92          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.57/40.92    (92)   ~ (all_53_2 = all_53_3)
% 229.57/40.92    (93)   ~ (all_10_2 = e1)
% 229.57/40.92    (94)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 229.57/40.92    (95)   ~ (all_53_7 = all_53_11)
% 229.57/40.92    (96)  all_55_8 = all_53_2
% 229.57/40.92    (97)  op(e0, e0) = e3
% 229.57/40.92    (98)   ~ (all_53_4 = all_53_6)
% 229.57/40.92    (99)  op(e0, e2) = all_53_7
% 229.57/40.92    (100)  all_18_2 = all_10_2
% 229.57/40.92    (101)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.57/40.92           | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.57/40.92             e2)
% 229.57/40.92    (102)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) =
% 229.57/40.92                 e0) | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 229.57/40.92                 op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) |
% 229.57/40.92               (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 229.57/40.92                 e0)))
% 229.57/40.92    (103)  all_55_10 = all_6_2
% 229.57/40.92    (104)   ~ (all_53_6 = all_6_2)
% 229.57/40.92    (105)  all_55_13 = all_53_7
% 229.57/40.92    (106)  op(e2, e0) = all_53_13
% 229.57/40.92    (107)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.57/40.92           (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.57/40.92    (108)  all_38_2 = all_6_2
% 229.57/40.92    (109)  all_55_11 = all_53_14
% 229.57/40.92    (110)  all_55_3 = all_53_12
% 229.57/40.92    (111)   ~ (all_53_12 = e3)
% 229.57/40.92    (112)   ~ (all_53_4 = e2)
% 229.57/40.92    (113)  op(e1, e3) = all_53_2
% 229.57/40.92    (114)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.57/40.92           (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.57/40.92    (115)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.57/40.92           (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.57/40.92    (116)   ~ (all_53_12 = all_10_2)
% 229.57/40.92    (117)   ~ (all_53_13 = all_53_14)
% 229.57/40.92    (118)   ~ (all_53_1 = e2)
% 229.57/40.92    (119)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.57/40.92           (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 229.57/40.92    (120)   ~ (e2 = e1)
% 229.57/40.92    (121)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.57/40.92           | (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.57/40.92             e2)
% 229.57/40.92    (122)  op(e2, e1) = all_53_9
% 229.57/40.92    (123)  op(e1, e2) = all_53_6
% 229.57/40.92    (124)   ~ (all_53_2 = all_53_6)
% 229.57/40.92    (125)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.57/40.92           (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.57/40.92    (126)  all_24_2 = all_6_2
% 229.57/40.92    (127)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 229.57/40.92           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 229.57/40.92    (128)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.57/40.92           (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.57/40.93    (129)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.57/40.93           | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.57/40.93             e1)
% 229.57/40.93    (130)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 229.57/40.93           (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 229.57/40.93    (131)   ~ (all_53_12 = all_53_14)
% 229.57/40.93    (132)  all_55_14 = all_53_11
% 229.57/40.93    (133)   ~ (all_22_2 = e3) | ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0
% 229.57/40.93             & op(e0, e3) = all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~
% 229.57/40.93             (all_22_1 = e2) & op(e0, e3) = all_22_1 & $i(all_22_1))
% 229.57/40.93    (134)  all_57_3 = e2
% 229.57/40.93    (135)  op(e3, e1) = all_53_8
% 229.57/40.93    (136)  all_55_7 = all_53_13
% 229.57/40.93    (137)   ~ (all_53_11 = e3)
% 229.57/40.93    (138)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.57/40.93           (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.57/40.93    (139)   ~ (all_34_2 = e0) | ( ~ (all_34_0 = e3) & op(all_34_1, e1) = all_34_0
% 229.57/40.93             & op(e1, e0) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~
% 229.57/40.93             (all_34_1 = e2) & op(e1, e0) = all_34_1 & $i(all_34_1))
% 229.57/40.93    (140)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 229.57/40.93           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 229.57/40.93    (141)  op(e3, e0) = all_53_12
% 229.57/40.93  
% 229.57/40.93  Begin of proof
% 229.57/40.93  | 
% 229.57/40.93  | BETA: splitting (39) gives:
% 229.57/40.93  | 
% 229.57/40.93  | Case 1:
% 229.57/40.93  | | 
% 229.57/40.93  | |   (142)   ~ (all_18_2 = e0)
% 229.57/40.93  | | 
% 229.57/40.93  | | REDUCE: (100), (142) imply:
% 229.57/40.93  | |   (143)   ~ (all_10_2 = e0)
% 229.57/40.93  | | 
% 229.57/40.93  | | BETA: splitting (7) gives:
% 229.57/40.93  | | 
% 229.57/40.93  | | Case 1:
% 229.57/40.93  | | | 
% 229.57/40.93  | | |   (144)   ~ (all_20_2 = e2)
% 229.57/40.93  | | | 
% 229.57/40.93  | | | REDUCE: (62), (144) imply:
% 229.57/40.93  | | |   (145)   ~ (all_10_2 = e2)
% 229.57/40.93  | | | 
% 229.57/40.93  | | | BETA: splitting (32) gives:
% 229.57/40.93  | | | 
% 229.57/40.93  | | | Case 1:
% 229.57/40.93  | | | | 
% 229.57/40.93  | | | |   (146)  all_55_0 = e3
% 229.57/40.93  | | | | 
% 229.57/40.93  | | | | COMBINE_EQS: (22), (146) imply:
% 229.57/40.93  | | | |   (147)  all_10_2 = e3
% 229.57/40.93  | | | | 
% 229.57/40.93  | | | | REDUCE: (2), (147) imply:
% 229.57/40.93  | | | |   (148)  op(e3, e3) = e3
% 229.57/40.93  | | | | 
% 229.57/40.93  | | | | REF_CLOSE: (5), (9), (11), (13), (16), (17), (18), (19), (20), (21),
% 229.57/40.93  | | | |            (23), (24), (25), (28), (29), (31), (34), (38), (40), (41),
% 229.57/40.93  | | | |            (44), (45), (46), (48), (50), (51), (52), (53), (55), (58),
% 229.57/40.93  | | | |            (61), (63), (64), (71), (72), (75), (76), (78), (80), (81),
% 229.57/40.93  | | | |            (82), (83), (84), (86), (87), (88), (90), (91), (97), (99),
% 229.57/40.93  | | | |            (101), (102), (103), (106), (107), (108), (111), (112),
% 229.57/40.93  | | | |            (114), (115), (119), (120), (121), (122), (123), (125),
% 229.57/40.93  | | | |            (126), (127), (128), (129), (130), (133), (134), (135),
% 229.57/40.93  | | | |            (138), (139), (140), (141), (148) are inconsistent by
% 229.57/40.93  | | | |            sub-proof #1073.
% 229.57/40.93  | | | | 
% 229.57/40.93  | | | Case 2:
% 229.57/40.93  | | | | 
% 229.57/40.93  | | | |   (149)  all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 229.57/40.93  | | | | 
% 229.57/40.93  | | | | REF_CLOSE: (22), (93), (143), (145), (149) are inconsistent by sub-proof
% 229.57/40.93  | | | |            #1953.
% 229.57/40.93  | | | | 
% 229.57/40.93  | | | End of split
% 229.57/40.93  | | | 
% 229.57/40.93  | | Case 2:
% 229.57/40.93  | | | 
% 229.57/40.93  | | |   (150)  all_20_2 = e2
% 229.57/40.93  | | | 
% 229.57/40.93  | | | COMBINE_EQS: (62), (150) imply:
% 229.57/40.93  | | |   (151)  all_10_2 = e2
% 229.57/40.93  | | | 
% 229.57/40.93  | | | REDUCE: (8), (151) imply:
% 229.57/40.93  | | |   (152)   ~ (all_53_3 = e2)
% 229.57/40.93  | | | 
% 229.57/40.93  | | | REDUCE: (116), (151) imply:
% 229.57/40.93  | | |   (153)   ~ (all_53_12 = e2)
% 229.57/40.93  | | | 
% 229.57/40.93  | | | REDUCE: (2), (151) imply:
% 229.57/40.93  | | |   (154)  op(e3, e3) = e2
% 229.57/40.93  | | | 
% 229.57/40.93  | | | REF_CLOSE: (5), (11), (21), (25), (28), (29), (31), (38), (41), (46),
% 229.57/40.93  | | |            (48), (51), (53), (55), (58), (66), (71), (74), (75), (80),
% 229.57/40.93  | | |            (81), (86), (97), (99), (101), (103), (106), (121), (122),
% 229.57/40.93  | | |            (126), (139), (141), (152), (153), (154) are inconsistent by
% 229.57/40.93  | | |            sub-proof #1072.
% 229.57/40.93  | | | 
% 229.57/40.93  | | End of split
% 229.57/40.93  | | 
% 229.57/40.93  | Case 2:
% 229.57/40.93  | | 
% 229.57/40.93  | |   (155)  all_18_2 = e0
% 229.57/40.93  | |   (156)  ( ~ (all_18_0 = e1) & op(all_18_1, e3) = all_18_0 & op(e3, e0) =
% 229.57/40.93  | |            all_18_1 & $i(all_18_0) & $i(all_18_1)) | ( ~ (all_18_1 = e2) &
% 229.57/40.93  | |            op(e3, e0) = all_18_1 & $i(all_18_1))
% 229.57/40.93  | | 
% 229.57/40.93  | | COMBINE_EQS: (100), (155) imply:
% 229.57/40.93  | |   (157)  all_10_2 = e0
% 229.57/40.93  | | 
% 229.57/40.93  | | COMBINE_EQS: (14), (157) imply:
% 229.57/40.93  | |   (158)  all_48_2 = e0
% 229.57/40.93  | | 
% 229.57/40.93  | | REDUCE: (10), (157) imply:
% 229.57/40.93  | |   (159)   ~ (all_53_1 = e0)
% 229.57/40.93  | | 
% 229.57/40.93  | | REDUCE: (79), (157) imply:
% 229.57/40.93  | |   (160)   ~ (all_53_2 = e0)
% 229.57/40.93  | | 
% 229.57/40.93  | | REDUCE: (8), (157) imply:
% 229.57/40.93  | |   (161)   ~ (all_53_3 = e0)
% 229.57/40.93  | | 
% 229.57/40.93  | | REDUCE: (54), (157) imply:
% 229.57/40.93  | |   (162)   ~ (all_53_4 = e0)
% 229.57/40.93  | | 
% 229.57/40.93  | | REDUCE: (26), (157) imply:
% 229.57/40.93  | |   (163)   ~ (all_53_8 = e0)
% 229.57/40.93  | | 
% 229.57/40.93  | | REDUCE: (116), (157) imply:
% 229.57/40.93  | |   (164)   ~ (all_53_12 = e0)
% 229.57/40.93  | | 
% 229.57/40.93  | | REDUCE: (93), (157) imply:
% 229.57/40.93  | |   (165)   ~ (e1 = e0)
% 229.57/40.93  | | 
% 229.57/40.93  | | REDUCE: (2), (157) imply:
% 229.57/40.93  | |   (166)  op(e3, e3) = e0
% 229.57/40.93  | | 
% 229.57/40.93  | | BETA: splitting (128) gives:
% 229.57/40.93  | | 
% 229.57/40.93  | | Case 1:
% 229.57/40.93  | | | 
% 229.57/40.93  | | |   (167)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) =
% 229.57/40.93  | | |            e0)
% 229.57/40.93  | | | 
% 229.57/40.93  | | | BETA: splitting (167) gives:
% 229.57/40.93  | | | 
% 229.57/40.93  | | | Case 1:
% 229.57/40.93  | | | | 
% 229.57/40.93  | | | |   (168)  all_57_0 = e0 & op(e3, e3) = e0
% 229.57/40.93  | | | | 
% 229.57/40.93  | | | | ALPHA: (168) implies:
% 229.57/40.93  | | | |   (169)  all_57_0 = e0
% 229.57/40.93  | | | | 
% 229.57/40.93  | | | | REF_CLOSE: (1), (3), (4), (6), (9), (11), (12), (13), (15), (16), (17),
% 229.57/40.93  | | | |            (18), (19), (20), (21), (23), (24), (25), (27), (28), (29),
% 229.57/40.93  | | | |            (30), (33), (34), (35), (36), (37), (38), (40), (41), (42),
% 229.57/40.93  | | | |            (43), (45), (47), (49), (50), (51), (52), (53), (56), (57),
% 229.57/40.93  | | | |            (58), (59), (60), (61), (63), (64), (65), (66), (67), (68),
% 229.57/40.93  | | | |            (69), (70), (71), (72), (73), (74), (76), (77), (78), (80),
% 229.57/40.93  | | | |            (81), (82), (84), (85), (86), (87), (88), (89), (90), (91),
% 229.57/40.93  | | | |            (92), (94), (95), (96), (97), (98), (99), (101), (102),
% 229.57/40.93  | | | |            (103), (104), (105), (106), (107), (108), (109), (110),
% 229.57/40.93  | | | |            (111), (112), (113), (114), (115), (117), (118), (119),
% 229.57/40.93  | | | |            (120), (121), (124), (125), (126), (127), (128), (129),
% 229.57/40.93  | | | |            (130), (131), (132), (133), (134), (136), (137), (138),
% 229.57/40.93  | | | |            (140), (141), (156), (158), (159), (160), (161), (162),
% 229.57/40.93  | | | |            (163), (164), (166), (169) are inconsistent by sub-proof
% 229.57/40.93  | | | |            #832.
% 229.57/40.93  | | | | 
% 229.57/40.93  | | | Case 2:
% 229.57/40.93  | | | | 
% 229.57/40.93  | | | |   (170)  all_57_2 = e0 & op(e2, e3) = e0
% 229.57/40.93  | | | | 
% 229.57/40.93  | | | | ALPHA: (170) implies:
% 229.57/40.93  | | | |   (171)  all_57_2 = e0
% 229.57/40.93  | | | | 
% 229.57/40.93  | | | | BETA: splitting (50) gives:
% 229.57/40.93  | | | | 
% 229.57/40.93  | | | | Case 1:
% 229.57/40.93  | | | | | 
% 229.57/40.93  | | | | |   (172)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3,
% 229.57/40.93  | | | | |              e2) = e0)
% 229.57/40.93  | | | | | 
% 229.57/40.93  | | | | | BETA: splitting (172) gives:
% 229.57/40.93  | | | | | 
% 229.57/40.93  | | | | | Case 1:
% 229.57/40.93  | | | | | | 
% 229.57/40.93  | | | | | |   (173)  all_57_0 = e0 & op(e3, e3) = e0
% 229.57/40.93  | | | | | | 
% 229.57/40.93  | | | | | | ALPHA: (173) implies:
% 229.57/40.93  | | | | | |   (174)  all_57_0 = e0
% 229.57/40.93  | | | | | | 
% 229.57/40.93  | | | | | | REF_CLOSE: (1), (3), (4), (6), (9), (11), (12), (13), (15), (16),
% 229.57/40.93  | | | | | |            (17), (18), (19), (20), (21), (23), (24), (25), (27),
% 229.57/40.93  | | | | | |            (28), (29), (30), (33), (34), (35), (36), (37), (38),
% 229.57/40.93  | | | | | |            (40), (41), (42), (43), (45), (47), (49), (50), (51),
% 229.57/40.93  | | | | | |            (52), (53), (56), (57), (58), (59), (60), (61), (63),
% 229.57/40.93  | | | | | |            (64), (65), (66), (67), (68), (69), (70), (71), (72),
% 229.57/40.93  | | | | | |            (73), (74), (76), (77), (78), (80), (81), (82), (84),
% 229.57/40.93  | | | | | |            (85), (86), (87), (88), (89), (90), (91), (92), (94),
% 229.57/40.93  | | | | | |            (95), (96), (97), (98), (99), (101), (102), (103), (104),
% 229.57/40.93  | | | | | |            (105), (106), (107), (108), (109), (110), (111), (112),
% 229.57/40.93  | | | | | |            (113), (114), (115), (117), (118), (119), (120), (121),
% 229.57/40.93  | | | | | |            (124), (125), (126), (127), (128), (129), (130), (131),
% 229.57/40.93  | | | | | |            (132), (133), (134), (136), (137), (138), (140), (141),
% 229.57/40.93  | | | | | |            (156), (158), (159), (160), (161), (162), (163), (164),
% 229.57/40.93  | | | | | |            (166), (174) are inconsistent by sub-proof #832.
% 229.57/40.93  | | | | | | 
% 229.57/40.93  | | | | | Case 2:
% 229.57/40.93  | | | | | | 
% 229.57/40.93  | | | | | |   (175)  all_57_1 = e0 & op(e3, e2) = e0
% 229.57/40.93  | | | | | | 
% 229.57/40.93  | | | | | | ALPHA: (175) implies:
% 229.57/40.93  | | | | | |   (176)  all_57_1 = e0
% 229.57/40.93  | | | | | | 
% 229.57/40.93  | | | | | | BETA: splitting (107) gives:
% 229.57/40.93  | | | | | | 
% 229.57/40.93  | | | | | | Case 1:
% 229.57/40.93  | | | | | | | 
% 229.57/40.93  | | | | | | |   (177)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 &
% 229.57/40.93  | | | | | | |            op(e2, e2) = e3)
% 229.57/40.93  | | | | | | | 
% 229.57/40.93  | | | | | | | REF_CLOSE: (21), (53), (61), (86), (171), (177) are inconsistent
% 229.57/40.93  | | | | | | |            by sub-proof #831.
% 229.57/40.93  | | | | | | | 
% 229.57/40.93  | | | | | | Case 2:
% 229.57/40.93  | | | | | | | 
% 229.57/40.93  | | | | | | |   (178)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 &
% 229.57/40.93  | | | | | | |            op(e2, e0) = e3)
% 229.57/40.93  | | | | | | | 
% 229.57/40.93  | | | | | | | BETA: splitting (178) gives:
% 229.57/40.93  | | | | | | | 
% 229.57/40.93  | | | | | | | Case 1:
% 229.57/40.93  | | | | | | | | 
% 229.57/40.93  | | | | | | | |   (179)  all_57_5 = e3 & op(e2, e1) = e3
% 229.57/40.93  | | | | | | | | 
% 229.57/40.93  | | | | | | | | ALPHA: (179) implies:
% 229.57/40.93  | | | | | | | |   (180)  all_57_5 = e3
% 229.57/40.93  | | | | | | | |   (181)  op(e2, e1) = e3
% 229.57/40.93  | | | | | | | | 
% 229.57/40.93  | | | | | | | | BETA: splitting (13) gives:
% 229.57/40.93  | | | | | | | | 
% 229.57/40.93  | | | | | | | | Case 1:
% 229.57/40.93  | | | | | | | | | 
% 229.57/40.93  | | | | | | | | |   (182)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 &
% 229.57/40.93  | | | | | | | | |            op(e2, e2) = e1)
% 229.57/40.93  | | | | | | | | | 
% 229.57/40.93  | | | | | | | | | BETA: splitting (182) gives:
% 229.57/40.93  | | | | | | | | | 
% 229.57/40.93  | | | | | | | | | Case 1:
% 229.57/40.93  | | | | | | | | | | 
% 229.57/40.93  | | | | | | | | | |   (183)  all_57_2 = e1 & op(e2, e3) = e1
% 229.57/40.93  | | | | | | | | | | 
% 229.57/40.93  | | | | | | | | | | ALPHA: (183) implies:
% 229.57/40.93  | | | | | | | | | |   (184)  all_57_2 = e1
% 229.57/40.93  | | | | | | | | | | 
% 229.57/40.93  | | | | | | | | | | REF_CLOSE: (87), (171), (184) are inconsistent by sub-proof
% 229.57/40.93  | | | | | | | | | |            #2473.
% 229.57/40.93  | | | | | | | | | | 
% 229.57/40.93  | | | | | | | | | Case 2:
% 229.57/40.93  | | | | | | | | | | 
% 229.57/40.93  | | | | | | | | | |   (185)  all_57_3 = e1 & op(e2, e2) = e1
% 229.57/40.93  | | | | | | | | | | 
% 229.57/40.93  | | | | | | | | | | ALPHA: (185) implies:
% 229.57/40.93  | | | | | | | | | |   (186)  all_57_3 = e1
% 229.57/40.93  | | | | | | | | | |   (187)  op(e2, e2) = e1
% 229.57/40.93  | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | REF_CLOSE: (18), (19), (21), (53), (61), (66), (71), (72),
% 229.57/40.94  | | | | | | | | | |            (80), (87), (91), (97), (101), (102), (115),
% 229.57/40.94  | | | | | | | | | |            (120), (125), (138), (161), (166), (171), (176),
% 229.57/40.94  | | | | | | | | | |            (186), (187) are inconsistent by sub-proof #1059.
% 229.57/40.94  | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | End of split
% 229.57/40.94  | | | | | | | | | 
% 229.57/40.94  | | | | | | | | Case 2:
% 229.57/40.94  | | | | | | | | | 
% 229.57/40.94  | | | | | | | | |   (188)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 &
% 229.57/40.94  | | | | | | | | |            op(e2, e0) = e1)
% 229.57/40.94  | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | BETA: splitting (188) gives:
% 229.57/40.94  | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | Case 1:
% 229.57/40.94  | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | |   (189)  all_57_5 = e1 & op(e2, e1) = e1
% 229.57/40.94  | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | REF_CLOSE: (19), (180), (189) are inconsistent by sub-proof
% 229.57/40.94  | | | | | | | | | |            #2376.
% 229.57/40.94  | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | Case 2:
% 229.57/40.94  | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | |   (190)  all_57_10 = e1 & op(e2, e0) = e1
% 229.57/40.94  | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | ALPHA: (190) implies:
% 229.57/40.94  | | | | | | | | | |   (191)  all_57_10 = e1
% 229.57/40.94  | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | BETA: splitting (84) gives:
% 229.57/40.94  | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | Case 1:
% 229.57/40.94  | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | |   (192)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 229.57/40.94  | | | | | | | | | | |            & op(e3, e2) = e3)
% 229.57/40.94  | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | REF_CLOSE: (21), (61), (166), (176), (192) are inconsistent
% 229.57/40.94  | | | | | | | | | | |            by sub-proof #2404.
% 229.57/40.94  | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | Case 2:
% 229.57/40.94  | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | |   (193)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 229.57/40.94  | | | | | | | | | | |            & op(e3, e0) = e3)
% 229.57/40.94  | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | BETA: splitting (193) gives:
% 229.57/40.94  | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | Case 1:
% 229.57/40.94  | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | |   (194)  all_57_4 = e3 & op(e3, e1) = e3
% 229.57/40.94  | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | ALPHA: (194) implies:
% 229.57/40.94  | | | | | | | | | | | |   (195)  all_57_4 = e3
% 229.57/40.94  | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | BETA: splitting (45) gives:
% 229.57/40.94  | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | Case 1:
% 229.57/40.94  | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | |   (196)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 229.57/40.94  | | | | | | | | | | | | |            & op(e3, e2) = e2)
% 229.57/40.94  | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | BETA: splitting (196) gives:
% 229.57/40.94  | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | Case 1:
% 229.57/40.94  | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | |   (197)  all_57_0 = e2 & op(e3, e3) = e2
% 229.57/40.94  | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | ALPHA: (197) implies:
% 229.57/40.94  | | | | | | | | | | | | | |   (198)  op(e3, e3) = e2
% 229.57/40.94  | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | REF_CLOSE: (21), (80), (166), (198) are inconsistent by
% 229.57/40.94  | | | | | | | | | | | | | |            sub-proof #2403.
% 229.57/40.94  | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | Case 2:
% 229.57/40.94  | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | |   (199)  all_57_1 = e2 & op(e3, e2) = e2
% 229.57/40.94  | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | ALPHA: (199) implies:
% 229.57/40.94  | | | | | | | | | | | | | |   (200)  all_57_1 = e2
% 229.57/40.94  | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | COMBINE_EQS: (176), (200) imply:
% 229.57/40.94  | | | | | | | | | | | | | |   (201)  e2 = e0
% 229.57/40.94  | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | REF_CLOSE: (53), (80), (114), (120), (134), (171), (180),
% 229.57/40.94  | | | | | | | | | | | | | |            (191), (201) are inconsistent by sub-proof #1077.
% 229.57/40.94  | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | End of split
% 229.57/40.94  | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | Case 2:
% 229.57/40.94  | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | |   (202)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 229.57/40.94  | | | | | | | | | | | | |            & op(e3, e0) = e2)
% 229.57/40.94  | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | BETA: splitting (202) gives:
% 229.57/40.94  | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | Case 1:
% 229.57/40.94  | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | |   (203)  all_57_4 = e2 & op(e3, e1) = e2
% 229.57/40.94  | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | REF_CLOSE: (53), (195), (203) are inconsistent by sub-proof
% 229.57/40.94  | | | | | | | | | | | | | |            #2487.
% 229.57/40.94  | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | Case 2:
% 229.57/40.94  | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | |   (204)  all_57_9 = e2 & op(e3, e0) = e2
% 229.57/40.94  | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | ALPHA: (204) implies:
% 229.57/40.94  | | | | | | | | | | | | | |   (205)  all_57_9 = e2
% 229.57/40.94  | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | BETA: splitting (91) gives:
% 229.57/40.94  | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | Case 1:
% 229.57/40.94  | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | |   (206)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 229.57/40.94  | | | | | | | | | | | | | | |            & op(e2, e2) = e3)
% 229.57/40.94  | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 229.57/40.94  | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | Case 1:
% 229.57/40.94  | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | |   (207)  all_57_1 = e3 & op(e3, e2) = e3
% 229.57/40.94  | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | ALPHA: (207) implies:
% 229.57/40.94  | | | | | | | | | | | | | | | |   (208)  all_57_1 = e3
% 229.57/40.94  | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | REF_CLOSE: (19), (34), (45), (50), (53), (61), (80), (87),
% 229.57/40.94  | | | | | | | | | | | | | | | |            (120), (195), (205), (208) are inconsistent by
% 229.57/40.94  | | | | | | | | | | | | | | | |            sub-proof #1222.
% 229.57/40.94  | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | Case 2:
% 229.57/40.94  | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | |   (209)  all_57_3 = e3 & op(e2, e2) = e3
% 229.57/40.94  | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | ALPHA: (209) implies:
% 229.57/40.94  | | | | | | | | | | | | | | | |   (210)  op(e2, e2) = e3
% 229.57/40.94  | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | REF_CLOSE: (21), (53), (86), (210) are inconsistent by
% 229.57/40.94  | | | | | | | | | | | | | | | |            sub-proof #2298.
% 229.57/40.94  | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | End of split
% 229.57/40.94  | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | Case 2:
% 229.57/40.94  | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | |   (211)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 229.57/40.94  | | | | | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 229.57/40.94  | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 229.57/40.94  | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | Case 1:
% 229.57/40.94  | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | |   (212)  all_57_7 = e3 & op(e1, e2) = e3
% 229.57/40.94  | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | ALPHA: (212) implies:
% 229.57/40.94  | | | | | | | | | | | | | | | |   (213)  all_57_7 = e3
% 229.57/40.94  | | | | | | | | | | | | | | | |   (214)  op(e1, e2) = e3
% 229.57/40.94  | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | BETA: splitting (138) gives:
% 229.57/40.94  | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | Case 1:
% 229.57/40.94  | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | |   (215)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 229.57/40.94  | | | | | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 229.57/40.94  | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 229.57/40.94  | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | Case 1:
% 229.57/40.94  | | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | |   (216)  all_57_1 = e1 & op(e3, e2) = e1
% 229.57/40.94  | | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | | REF_CLOSE: (87), (176), (216) are inconsistent by sub-proof
% 229.57/40.94  | | | | | | | | | | | | | | | | | |            #2446.
% 229.57/40.94  | | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | Case 2:
% 229.57/40.94  | | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | |   (217)  all_57_3 = e1 & op(e2, e2) = e1
% 229.57/40.94  | | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | | ALPHA: (217) implies:
% 229.57/40.94  | | | | | | | | | | | | | | | | | |   (218)  all_57_3 = e1
% 229.57/40.94  | | | | | | | | | | | | | | | | | |   (219)  op(e2, e2) = e1
% 229.57/40.94  | | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (19), (21), (53), (61), (66), (71), (72),
% 229.57/40.94  | | | | | | | | | | | | | | | | | |            (80), (87), (97), (101), (102), (115), (120),
% 229.57/40.94  | | | | | | | | | | | | | | | | | |            (125), (138), (161), (166), (171), (176), (213),
% 229.57/40.94  | | | | | | | | | | | | | | | | | |            (218), (219) are inconsistent by sub-proof #1060.
% 229.57/40.94  | | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | End of split
% 229.57/40.94  | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | Case 2:
% 229.57/40.94  | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | |   (220)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 229.57/40.94  | | | | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 229.57/40.94  | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 229.57/40.94  | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | Case 1:
% 229.57/40.94  | | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | |   (221)  all_57_7 = e1 & op(e1, e2) = e1
% 229.57/40.94  | | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | | ALPHA: (221) implies:
% 229.57/40.94  | | | | | | | | | | | | | | | | | |   (222)  all_57_7 = e1
% 229.57/40.94  | | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (21), (61), (84), (111), (141), (166),
% 229.57/40.94  | | | | | | | | | | | | | | | | | |            (176), (195), (213), (222) are inconsistent by
% 229.57/40.94  | | | | | | | | | | | | | | | | | |            sub-proof #830.
% 229.57/40.94  | | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | Case 2:
% 229.57/40.94  | | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | |   (223)  all_57_13 = e1 & op(e0, e2) = e1
% 229.57/40.94  | | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | | ALPHA: (223) implies:
% 229.57/40.94  | | | | | | | | | | | | | | | | | |   (224)  all_57_13 = e1
% 229.57/40.94  | | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | | BETA: splitting (115) gives:
% 229.57/40.94  | | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | | |   (225)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 229.57/40.94  | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e3)
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | |   (226)  all_57_0 = e3 & op(e3, e3) = e3
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | ALPHA: (226) implies:
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | |   (227)  op(e3, e3) = e3
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (11), (13), (16), (17), (18), (19),
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | |            (20), (21), (23), (24), (25), (29), (31), (34),
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | |            (38), (40), (41), (44), (45), (46), (48), (50),
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | |            (51), (52), (55), (58), (61), (63), (64), (71),
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | |            (72), (75), (76), (78), (80), (81), (82), (83),
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | |            (84), (86), (87), (88), (97), (99), (101), (102),
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | |            (103), (106), (107), (108), (111), (112), (114),
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | |            (115), (119), (120), (121), (122), (123), (125),
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | |            (126), (127), (128), (129), (130), (133), (134),
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | |            (135), (138), (139), (140), (141), (180), (181),
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | |            (213), (214), (227) are inconsistent by sub-proof
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | |            #1075.
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | |   (228)  all_57_2 = e3 & op(e2, e3) = e3
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | ALPHA: (228) implies:
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | |   (229)  all_57_2 = e3
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (19), (53), (61), (80), (87), (114), (119),
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | |            (120), (180), (191), (229) are inconsistent by
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | |            sub-proof #1331.
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | End of split
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | | |   (230)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 229.57/40.94  | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e3) = e3)
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | |   (231)  all_57_6 = e3 & op(e1, e3) = e3
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | ALPHA: (231) implies:
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | |   (232)  all_57_6 = e3
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | BETA: splitting (125) gives:
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | |   (233)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e2)
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | |   (234)  all_57_0 = e2 & op(e3, e3) = e2
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (234) implies:
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | |   (235)  op(e3, e3) = e2
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (80), (166), (235) are inconsistent by
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2403.
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | |   (236)  all_57_2 = e2 & op(e2, e3) = e2
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (236) implies:
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | |   (237)  all_57_2 = e2
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (19), (21), (53), (61), (80), (86), (87),
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | |            (107), (114), (119), (120), (134), (180), (237)
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2239.
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | |   (238)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e3) = e2)
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | |   (239)  all_57_6 = e2 & op(e1, e3) = e2
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (239) implies:
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | |   (240)  all_57_6 = e2
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (53), (232), (240) are inconsistent by sub-proof
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | |            #2463.
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | |   (241)  all_57_12 = e2 & op(e0, e3) = e2
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (241) implies:
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | |   (242)  all_57_12 = e2
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16) gives:
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | | |   (243)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e1)
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | | | |   (244)  all_57_0 = e1 & op(e3, e3) = e1
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (244) implies:
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | | | |   (245)  all_57_0 = e1
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (102) gives:
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | | | | |   (246)  all_57_15 = e0 & op(e0, e0) = e0
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (246) implies:
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | | | | |   (247)  op(e0, e0) = e0
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (61), (97), (247) are inconsistent by
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2304.
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | | | | |   (248)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 229.57/40.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (248) implies:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | |   (249)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e0)
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | |   (250)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e0)
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | |   (251)  all_57_12 = e0 & op(e0, e3) = e0
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (251) implies:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | |   (252)  op(e0, e3) = e0
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (66), (161), (252) are inconsistent by
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2366.
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | |   (253)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (253) gives:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (254)  all_57_13 = e0 & op(e0, e2) = e0
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (19), (21), (34), (45), (50), (53), (61),
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (71), (72), (80), (84), (87), (91), (97), (101),
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (111), (120), (121), (129), (134), (138), (141),
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (166), (176), (195), (224), (245), (249),
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (250), (254) are inconsistent by sub-proof #829.
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (255)  all_57_14 = e0 & op(e0, e1) = e0
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (255) implies:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (256)  all_57_14 = e0
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (250) gives:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (257)  all_57_9 = e0 & op(e3, e0) = e0
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (141), (164), (257) are inconsistent by
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2434.
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (258)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 =
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (258) gives:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (259)  all_57_10 = e0 & op(e2, e0) = e0
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (259) implies:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (260)  all_57_10 = e0
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (191), (260) imply:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (261)  e1 = e0
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (261) implies:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (262)  e1 = e0
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (262) imply:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (263)  all_57_0 = e0
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (19), (21), (34), (45), (50), (53), (61),
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (71), (72), (80), (84), (87), (91), (97), (101),
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (111), (120), (121), (129), (134), (138), (141),
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (166), (176), (195), (249), (250), (263)
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #891.
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (264)  all_57_11 = e0 & op(e1, e0) = e0
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (264) implies:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (265)  all_57_11 = e0
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (140) gives:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (266)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e2)
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (266) gives:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (267)  all_57_6 = e2 & op(e1, e3) = e2
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (267) implies:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (268)  all_57_6 = e2
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (21), (53), (61), (71), (72), (80), (87),
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (101), (115), (120), (166), (171), (256), (268)
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1556.
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (269)  all_57_7 = e2 & op(e1, e2) = e2
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (21), (34), (45), (50), (53), (61), (71),
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (72), (80), (87), (91), (97), (101), (120), (134),
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (195), (205), (249), (269) are inconsistent by
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #898.
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (270)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e1, e0) = e2)
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (270) gives:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (271)  all_57_8 = e2 & op(e1, e1) = e2
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (271) implies:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (272)  op(e1, e1) = e2
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (130) gives:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (273)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e1)
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (273) gives:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (274)  all_57_6 = e1 & op(e1, e3) = e1
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (21), (61), (84), (111), (141), (166),
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (176), (195), (232), (274) are inconsistent by
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #828.
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (275)  all_57_7 = e1 & op(e1, e2) = e1
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (275) implies:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (276)  all_57_7 = e1
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (21), (34), (45), (50), (53), (61), (71),
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (72), (80), (84), (87), (91), (97), (101), (111),
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (120), (134), (141), (166), (176), (195), (249),
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (276) are inconsistent by sub-proof #827.
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (277)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e1, e0) = e1)
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (277) gives:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (278)  all_57_8 = e1 & op(e1, e1) = e1
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (278) implies:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (279)  op(e1, e1) = e1
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (120), (272), (279) are inconsistent by
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2423.
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (280)  all_57_11 = e1 & op(e1, e0) = e1
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (280) implies:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (281)  all_57_11 = e1
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (265), (281) imply:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (282)  e1 = e0
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (282) imply:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (283)  all_57_0 = e0
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (21), (34), (45), (53), (61), (80), (84),
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (87), (97), (111), (120), (129), (141), (166),
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (176), (191), (195), (205), (265), (283) are
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #903.
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (284)  all_57_11 = e2 & op(e1, e0) = e2
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (284) implies:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (285)  all_57_11 = e2
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (53), (80), (114), (120), (134), (171), (180),
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (191), (265), (285) are inconsistent by sub-proof
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #837.
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | |   (286)  all_57_2 = e1 & op(e2, e3) = e1
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (286) implies:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | |   (287)  all_57_2 = e1
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (87), (171), (287) are inconsistent by sub-proof
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | |            #2473.
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | |   (288)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e3) = e1)
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (288) gives:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | |   (289)  all_57_6 = e1 & op(e1, e3) = e1
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (21), (61), (84), (111), (141), (166),
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | |            (176), (195), (232), (289) are inconsistent by
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #828.
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | |   (290)  all_57_12 = e1 & op(e0, e3) = e1
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (290) implies:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | |   (291)  all_57_12 = e1
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (242), (291) imply:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | |   (292)  e2 = e1
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (292) implies:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | |   (293)  e2 = e1
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (205), (293) imply:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | |   (294)  all_57_9 = e1
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (45), (53), (80), (120), (166), (176),
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | |            (195), (294) are inconsistent by sub-proof #2402.
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | |   (295)  all_57_12 = e3 & op(e0, e3) = e3
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | ALPHA: (295) implies:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | |   (296)  all_57_12 = e3
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | BETA: splitting (16) gives:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | |   (297)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e1)
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (297) gives:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | |   (298)  all_57_0 = e1 & op(e3, e3) = e1
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (298) implies:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | |   (299)  all_57_0 = e1
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | |   (300)  op(e3, e3) = e1
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (125) gives:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | |   (301)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e2)
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (301) gives:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | |   (302)  all_57_0 = e2 & op(e3, e3) = e2
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (302) implies:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | |   (303)  op(e3, e3) = e2
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (120), (300), (303) are inconsistent by
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1950.
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | |   (304)  all_57_2 = e2 & op(e2, e3) = e2
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (304) implies:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | |   (305)  all_57_2 = e2
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (19), (21), (53), (61), (80), (86), (87),
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | |            (107), (114), (119), (120), (134), (180), (305)
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2239.
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | |   (306)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e3) = e2)
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (306) gives:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | |   (307)  all_57_6 = e2 & op(e1, e3) = e2
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (307) implies:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | |   (308)  all_57_6 = e2
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (102) gives:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | |   (309)  all_57_15 = e0 & op(e0, e0) = e0
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (309) implies:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | |   (310)  op(e0, e0) = e0
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (61), (97), (310) are inconsistent by
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2304.
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | |   (311)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (311) implies:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | |   (312)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e0)
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | |   (313)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e0)
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (312) gives:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | |   (314)  all_57_12 = e0 & op(e0, e3) = e0
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (314) implies:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | |   (315)  op(e0, e3) = e0
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (66), (161), (315) are inconsistent by
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2366.
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | |   (316)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (316) gives:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (317)  all_57_13 = e0 & op(e0, e2) = e0
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (19), (21), (34), (45), (50), (53), (61),
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (71), (72), (80), (84), (87), (91), (97), (101),
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (111), (120), (121), (129), (134), (138), (141),
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (166), (176), (195), (224), (299), (312),
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (313), (317) are inconsistent by sub-proof #829.
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (318)  all_57_14 = e0 & op(e0, e1) = e0
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (318) implies:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (319)  all_57_14 = e0
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (21), (53), (61), (71), (72), (80), (87),
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (101), (115), (120), (166), (171), (308), (319)
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1556.
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | |   (320)  all_57_12 = e2 & op(e0, e3) = e2
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (320) implies:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | |   (321)  all_57_12 = e2
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (53), (296), (321) are inconsistent by sub-proof
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | |            #2392.
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | |   (322)  all_57_2 = e1 & op(e2, e3) = e1
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (322) implies:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | |   (323)  all_57_2 = e1
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (87), (171), (323) are inconsistent by sub-proof
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | |            #2473.
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | |   (324)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e3) = e1)
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (324) gives:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | |   (325)  all_57_6 = e1 & op(e1, e3) = e1
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (325) implies:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | |   (326)  all_57_6 = e1
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (125) gives:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | |   (327)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e2)
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (327) gives:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | |   (328)  all_57_0 = e2 & op(e3, e3) = e2
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (328) implies:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | |   (329)  op(e3, e3) = e2
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (80), (166), (329) are inconsistent by
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2403.
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | |   (330)  all_57_2 = e2 & op(e2, e3) = e2
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (330) implies:
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | |   (331)  all_57_2 = e2
% 229.57/40.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (19), (21), (24), (28), (29), (53), (61),
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | | |            (71), (80), (87), (102), (107), (114), (119),
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | | |            (120), (121), (129), (134), (180), (191), (213),
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | | |            (326), (331) are inconsistent by sub-proof #1106.
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | |   (332)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e3) = e2)
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (332) gives:
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | | |   (333)  all_57_6 = e2 & op(e1, e3) = e2
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (333) implies:
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | | |   (334)  all_57_6 = e2
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (326), (334) imply:
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | | |   (335)  e2 = e1
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (134), (335) imply:
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | | |   (336)  all_57_3 = e1
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (19), (21), (53), (61), (66), (71), (72),
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | | |            (80), (87), (97), (101), (102), (114), (120),
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | | |            (161), (171), (180), (224), (296), (336) are
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1065.
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | | |   (337)  all_57_12 = e2 & op(e0, e3) = e2
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (337) implies:
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | | |   (338)  all_57_12 = e2
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (296), (338) imply:
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | | |   (339)  e3 = e2
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (339) implies:
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | | |   (340)  e3 = e2
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (213), (340) imply:
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | | |   (341)  all_57_7 = e2
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (21), (24), (28), (29), (53), (61), (71),
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | | |            (80), (87), (97), (102), (120), (121), (129),
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | | |            (326), (341) are inconsistent by sub-proof #1078.
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | |   (342)  all_57_12 = e1 & op(e0, e3) = e1
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (342) implies:
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | |   (343)  all_57_12 = e1
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (296), (343) imply:
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | |   (344)  e3 = e1
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | SIMP: (344) implies:
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | |   (345)  e3 = e1
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (195), (345) imply:
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | |   (346)  all_57_4 = e1
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (21), (61), (84), (111), (141), (166),
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | |            (176), (346) are inconsistent by sub-proof #2280.
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | End of split
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | | End of split
% 229.57/40.96  | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | End of split
% 229.57/40.96  | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | End of split
% 229.57/40.96  | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | Case 2:
% 229.57/40.96  | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | |   (347)  all_57_13 = e3 & op(e0, e2) = e3
% 229.57/40.96  | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | ALPHA: (347) implies:
% 229.57/40.96  | | | | | | | | | | | | | | | |   (348)  all_57_13 = e3
% 229.57/40.96  | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | REF_CLOSE: (19), (21), (53), (61), (71), (72), (80), (87),
% 229.57/40.96  | | | | | | | | | | | | | | | |            (97), (101), (102), (120), (348) are inconsistent
% 229.57/40.96  | | | | | | | | | | | | | | | |            by sub-proof #1792.
% 229.57/40.96  | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | End of split
% 229.57/40.96  | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | End of split
% 229.57/40.96  | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | End of split
% 229.57/40.96  | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | End of split
% 229.57/40.96  | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | Case 2:
% 229.57/40.96  | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | |   (349)  all_57_9 = e3 & op(e3, e0) = e3
% 229.57/40.96  | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | ALPHA: (349) implies:
% 229.57/40.96  | | | | | | | | | | | |   (350)  op(e3, e0) = e3
% 229.57/40.96  | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | REF_CLOSE: (21), (111), (141), (350) are inconsistent by
% 229.57/40.96  | | | | | | | | | | | |            sub-proof #2458.
% 229.57/40.96  | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | End of split
% 229.57/40.96  | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | End of split
% 229.57/40.96  | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | End of split
% 229.57/40.96  | | | | | | | | | 
% 229.57/40.96  | | | | | | | | End of split
% 229.57/40.96  | | | | | | | | 
% 229.57/40.96  | | | | | | | Case 2:
% 229.57/40.96  | | | | | | | | 
% 229.57/40.96  | | | | | | | |   (351)  all_57_10 = e3 & op(e2, e0) = e3
% 229.57/40.96  | | | | | | | | 
% 229.57/40.96  | | | | | | | | ALPHA: (351) implies:
% 229.57/40.96  | | | | | | | |   (352)  all_57_10 = e3
% 229.57/40.96  | | | | | | | | 
% 229.57/40.96  | | | | | | | | REF_CLOSE: (19), (21), (53), (61), (71), (80), (87), (97),
% 229.57/40.96  | | | | | | | |            (102), (120), (121), (129), (352) are inconsistent by
% 229.57/40.96  | | | | | | | |            sub-proof #1746.
% 229.57/40.96  | | | | | | | | 
% 229.57/40.96  | | | | | | | End of split
% 229.57/40.96  | | | | | | | 
% 229.57/40.96  | | | | | | End of split
% 229.57/40.96  | | | | | | 
% 229.57/40.96  | | | | | End of split
% 229.57/40.96  | | | | | 
% 229.57/40.96  | | | | Case 2:
% 229.57/40.96  | | | | | 
% 229.57/40.96  | | | | |   (353)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3,
% 229.57/40.96  | | | | |              e0) = e0)
% 229.57/40.96  | | | | | 
% 229.57/40.96  | | | | | BETA: splitting (353) gives:
% 229.57/40.96  | | | | | 
% 229.57/40.96  | | | | | Case 1:
% 229.57/40.96  | | | | | | 
% 229.57/40.96  | | | | | |   (354)  all_57_4 = e0 & op(e3, e1) = e0
% 229.57/40.96  | | | | | | 
% 229.57/40.96  | | | | | | ALPHA: (354) implies:
% 229.57/40.96  | | | | | |   (355)  all_57_4 = e0
% 229.57/40.96  | | | | | | 
% 229.57/40.96  | | | | | | BETA: splitting (107) gives:
% 229.57/40.96  | | | | | | 
% 229.57/40.96  | | | | | | Case 1:
% 229.57/40.96  | | | | | | | 
% 229.57/40.96  | | | | | | |   (356)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 &
% 229.57/40.96  | | | | | | |            op(e2, e2) = e3)
% 229.57/40.96  | | | | | | | 
% 229.57/40.96  | | | | | | | REF_CLOSE: (21), (53), (61), (86), (171), (356) are inconsistent
% 229.57/40.96  | | | | | | |            by sub-proof #831.
% 229.57/40.96  | | | | | | | 
% 229.57/40.96  | | | | | | Case 2:
% 229.57/40.96  | | | | | | | 
% 229.57/40.96  | | | | | | |   (357)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 &
% 229.57/40.96  | | | | | | |            op(e2, e0) = e3)
% 229.57/40.96  | | | | | | | 
% 229.57/40.96  | | | | | | | BETA: splitting (357) gives:
% 229.57/40.96  | | | | | | | 
% 229.57/40.96  | | | | | | | Case 1:
% 229.57/40.96  | | | | | | | | 
% 229.57/40.96  | | | | | | | |   (358)  all_57_5 = e3 & op(e2, e1) = e3
% 229.57/40.96  | | | | | | | | 
% 229.57/40.96  | | | | | | | | ALPHA: (358) implies:
% 229.57/40.96  | | | | | | | |   (359)  all_57_5 = e3
% 229.57/40.96  | | | | | | | | 
% 229.57/40.96  | | | | | | | | BETA: splitting (115) gives:
% 229.57/40.96  | | | | | | | | 
% 229.57/40.96  | | | | | | | | Case 1:
% 229.57/40.96  | | | | | | | | | 
% 229.57/40.96  | | | | | | | | |   (360)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 &
% 229.57/40.96  | | | | | | | | |            op(e2, e3) = e3)
% 229.57/40.96  | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | REF_CLOSE: (21), (61), (166), (171), (360) are inconsistent by
% 229.57/40.96  | | | | | | | | |            sub-proof #1559.
% 229.57/40.96  | | | | | | | | | 
% 229.57/40.96  | | | | | | | | Case 2:
% 229.57/40.96  | | | | | | | | | 
% 229.57/40.96  | | | | | | | | |   (361)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 &
% 229.57/40.96  | | | | | | | | |            op(e0, e3) = e3)
% 229.57/40.96  | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | BETA: splitting (361) gives:
% 229.57/40.96  | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | Case 1:
% 229.57/40.96  | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | |   (362)  all_57_6 = e3 & op(e1, e3) = e3
% 229.57/40.96  | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | ALPHA: (362) implies:
% 229.57/40.96  | | | | | | | | | |   (363)  all_57_6 = e3
% 229.57/40.96  | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | BETA: splitting (84) gives:
% 229.57/40.96  | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | Case 1:
% 229.57/40.96  | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | |   (364)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 229.57/40.96  | | | | | | | | | | |            & op(e3, e2) = e3)
% 229.57/40.96  | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | BETA: splitting (364) gives:
% 229.57/40.96  | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | Case 1:
% 229.57/40.96  | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | |   (365)  all_57_0 = e3 & op(e3, e3) = e3
% 229.57/40.96  | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | ALPHA: (365) implies:
% 229.57/40.96  | | | | | | | | | | | |   (366)  all_57_0 = e3
% 229.57/40.96  | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | REF_CLOSE: (16), (19), (53), (61), (80), (87), (120), (125),
% 229.57/40.96  | | | | | | | | | | | |            (128), (363), (366) are inconsistent by sub-proof
% 229.57/40.96  | | | | | | | | | | | |            #2010.
% 229.57/40.96  | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | Case 2:
% 229.57/40.96  | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | |   (367)  all_57_1 = e3 & op(e3, e2) = e3
% 229.57/40.96  | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | ALPHA: (367) implies:
% 229.57/40.96  | | | | | | | | | | | |   (368)  all_57_1 = e3
% 229.57/40.96  | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | BETA: splitting (34) gives:
% 229.57/40.96  | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | Case 1:
% 229.57/40.96  | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | |   (369)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 229.57/40.96  | | | | | | | | | | | | |            & op(e3, e2) = e1)
% 229.57/40.96  | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | BETA: splitting (369) gives:
% 229.57/40.96  | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | Case 1:
% 229.57/40.96  | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | |   (370)  all_57_0 = e1 & op(e3, e3) = e1
% 229.57/40.96  | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | ALPHA: (370) implies:
% 229.57/40.96  | | | | | | | | | | | | | |   (371)  all_57_0 = e1
% 229.57/40.96  | | | | | | | | | | | | | |   (372)  op(e3, e3) = e1
% 229.57/40.96  | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | BETA: splitting (102) gives:
% 229.57/40.96  | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | Case 1:
% 229.57/40.96  | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | |   (373)  all_57_15 = e0 & op(e0, e0) = e0
% 229.57/40.96  | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | ALPHA: (373) implies:
% 229.57/40.96  | | | | | | | | | | | | | | |   (374)  op(e0, e0) = e0
% 229.57/40.96  | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | REF_CLOSE: (21), (61), (97), (374) are inconsistent by
% 229.57/40.96  | | | | | | | | | | | | | | |            sub-proof #2304.
% 229.57/40.96  | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | Case 2:
% 229.57/40.96  | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | |   (375)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 229.57/40.96  | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 229.57/40.96  | | | | | | | | | | | | | | |              op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 229.57/40.96  | | | | | | | | | | | | | | |                e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 229.57/40.96  | | | | | | | | | | | | | | |              e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 229.57/40.96  | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | ALPHA: (375) implies:
% 229.57/40.96  | | | | | | | | | | | | | | |   (376)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 229.57/40.96  | | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 229.57/40.96  | | | | | | | | | | | | | | |              e1) = e0)
% 229.57/40.96  | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | BETA: splitting (91) gives:
% 229.57/40.96  | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | Case 1:
% 229.57/40.96  | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | |   (377)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 229.57/40.96  | | | | | | | | | | | | | | | |            & op(e2, e2) = e3)
% 229.57/40.96  | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | BETA: splitting (377) gives:
% 229.57/40.96  | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | Case 1:
% 229.57/40.96  | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (21) with e0, e1, e3, e3,
% 229.57/40.96  | | | | | | | | | | | | | | | | |              simplifying with (166), (372) gives:
% 229.57/40.96  | | | | | | | | | | | | | | | | |   (378)  e1 = e0
% 229.57/40.96  | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | COMBINE_EQS: (371), (378) imply:
% 229.57/40.96  | | | | | | | | | | | | | | | | |   (379)  all_57_0 = e0
% 229.57/40.96  | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (6), (9), (11), (12), (13), (15),
% 229.57/40.96  | | | | | | | | | | | | | | | | |            (16), (17), (18), (19), (20), (21), (23), (24),
% 229.57/40.96  | | | | | | | | | | | | | | | | |            (25), (27), (28), (29), (30), (33), (34), (35),
% 229.57/40.96  | | | | | | | | | | | | | | | | |            (36), (37), (38), (40), (41), (42), (43), (45),
% 229.57/40.96  | | | | | | | | | | | | | | | | |            (47), (49), (50), (51), (52), (53), (56), (57),
% 229.57/40.96  | | | | | | | | | | | | | | | | |            (58), (59), (60), (61), (63), (64), (65), (66),
% 229.57/40.96  | | | | | | | | | | | | | | | | |            (67), (68), (69), (70), (71), (72), (73), (74),
% 229.57/40.96  | | | | | | | | | | | | | | | | |            (76), (77), (78), (80), (81), (82), (84), (85),
% 229.57/40.96  | | | | | | | | | | | | | | | | |            (86), (87), (88), (89), (90), (91), (92), (94),
% 229.57/40.96  | | | | | | | | | | | | | | | | |            (95), (96), (97), (98), (99), (101), (102), (103),
% 229.57/40.96  | | | | | | | | | | | | | | | | |            (104), (105), (106), (107), (108), (109), (110),
% 229.57/40.96  | | | | | | | | | | | | | | | | |            (111), (112), (113), (114), (115), (117), (118),
% 229.57/40.96  | | | | | | | | | | | | | | | | |            (119), (120), (121), (124), (125), (126), (127),
% 229.57/40.96  | | | | | | | | | | | | | | | | |            (128), (129), (130), (131), (132), (133), (134),
% 229.57/40.96  | | | | | | | | | | | | | | | | |            (136), (137), (138), (140), (141), (156), (158),
% 229.57/40.96  | | | | | | | | | | | | | | | | |            (159), (160), (161), (162), (163), (164), (166),
% 229.57/40.96  | | | | | | | | | | | | | | | | |            (379) are inconsistent by sub-proof #832.
% 229.57/40.96  | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | Case 2:
% 229.57/40.96  | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | |   (380)  all_57_3 = e3 & op(e2, e2) = e3
% 229.57/40.96  | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | ALPHA: (380) implies:
% 229.57/40.96  | | | | | | | | | | | | | | | | |   (381)  op(e2, e2) = e3
% 229.57/40.96  | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (53), (86), (381) are inconsistent by
% 229.57/40.96  | | | | | | | | | | | | | | | | |            sub-proof #2298.
% 229.57/40.96  | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | End of split
% 229.57/40.96  | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | Case 2:
% 229.57/40.96  | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | |   (382)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 229.57/40.96  | | | | | | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 229.57/40.96  | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | BETA: splitting (382) gives:
% 229.57/40.96  | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | Case 1:
% 229.57/40.96  | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | |   (383)  all_57_7 = e3 & op(e1, e2) = e3
% 229.57/40.96  | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | ALPHA: (383) implies:
% 229.57/40.96  | | | | | | | | | | | | | | | | |   (384)  all_57_7 = e3
% 229.57/40.96  | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (19), (21), (53), (61), (78), (80), (86),
% 229.57/40.96  | | | | | | | | | | | | | | | | |            (87), (120), (138), (368), (384) are inconsistent
% 229.57/40.96  | | | | | | | | | | | | | | | | |            by sub-proof #1167.
% 229.57/40.96  | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | Case 2:
% 229.57/40.96  | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | |   (385)  all_57_13 = e3 & op(e0, e2) = e3
% 229.57/40.96  | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | ALPHA: (385) implies:
% 229.57/40.96  | | | | | | | | | | | | | | | | |   (386)  all_57_13 = e3
% 229.57/40.96  | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (21), (53), (61), (71), (72), (80), (87),
% 229.57/40.96  | | | | | | | | | | | | | | | | |            (97), (101), (120), (376), (386) are inconsistent
% 229.57/40.96  | | | | | | | | | | | | | | | | |            by sub-proof #2054.
% 229.57/40.96  | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | End of split
% 229.57/40.96  | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | End of split
% 229.57/40.96  | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | End of split
% 229.57/40.96  | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | Case 2:
% 229.57/40.96  | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | |   (387)  all_57_1 = e1 & op(e3, e2) = e1
% 229.57/40.96  | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | ALPHA: (387) implies:
% 229.57/40.96  | | | | | | | | | | | | | |   (388)  all_57_1 = e1
% 229.57/40.96  | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | COMBINE_EQS: (368), (388) imply:
% 229.57/40.96  | | | | | | | | | | | | | |   (389)  e3 = e1
% 229.57/40.96  | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | COMBINE_EQS: (359), (389) imply:
% 229.57/40.96  | | | | | | | | | | | | | |   (390)  all_57_5 = e1
% 229.57/40.96  | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | REF_CLOSE: (19), (21), (28), (29), (53), (61), (71), (72),
% 229.57/40.96  | | | | | | | | | | | | | |            (80), (87), (90), (101), (102), (120), (355),
% 229.57/40.96  | | | | | | | | | | | | | |            (390) are inconsistent by sub-proof #943.
% 229.57/40.96  | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | End of split
% 229.57/40.96  | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | Case 2:
% 229.57/40.96  | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | |   (391)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 229.57/40.96  | | | | | | | | | | | | |            & op(e3, e0) = e1)
% 229.57/40.96  | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | REF_CLOSE: (21), (45), (53), (61), (80), (84), (87), (111),
% 229.57/40.96  | | | | | | | | | | | | |            (120), (141), (166), (355), (391) are inconsistent
% 229.57/40.96  | | | | | | | | | | | | |            by sub-proof #1013.
% 229.57/40.96  | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | End of split
% 229.57/40.96  | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | End of split
% 229.57/40.96  | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | Case 2:
% 229.57/40.96  | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | |   (392)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 229.57/40.96  | | | | | | | | | | |            & op(e3, e0) = e3)
% 229.57/40.96  | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | BETA: splitting (392) gives:
% 229.57/40.96  | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | Case 1:
% 229.57/40.96  | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | |   (393)  all_57_4 = e3 & op(e3, e1) = e3
% 229.57/40.96  | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | ALPHA: (393) implies:
% 229.57/40.96  | | | | | | | | | | | |   (394)  all_57_4 = e3
% 229.57/40.96  | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | COMBINE_EQS: (355), (394) imply:
% 229.57/40.96  | | | | | | | | | | | |   (395)  e3 = e0
% 229.57/40.96  | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | SIMP: (395) implies:
% 229.57/40.96  | | | | | | | | | | | |   (396)  e3 = e0
% 229.57/40.96  | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | COMBINE_EQS: (363), (396) imply:
% 229.57/40.96  | | | | | | | | | | | |   (397)  all_57_6 = e0
% 229.57/40.96  | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | REF_CLOSE: (13), (16), (18), (19), (21), (24), (28), (29),
% 229.57/40.96  | | | | | | | | | | | |            (34), (41), (45), (50), (53), (61), (66), (71),
% 229.57/40.96  | | | | | | | | | | | |            (72), (78), (80), (84), (86), (87), (90), (91),
% 229.57/40.96  | | | | | | | | | | | |            (97), (99), (101), (102), (107), (111), (114),
% 229.57/40.96  | | | | | | | | | | | |            (115), (119), (120), (121), (125), (127), (129),
% 229.57/40.96  | | | | | | | | | | | |            (130), (134), (138), (141), (161), (164), (166),
% 229.57/40.96  | | | | | | | | | | | |            (355), (397) are inconsistent by sub-proof #821.
% 229.57/40.96  | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | Case 2:
% 229.57/40.96  | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | |   (398)  all_57_9 = e3 & op(e3, e0) = e3
% 229.57/40.96  | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | ALPHA: (398) implies:
% 229.57/40.96  | | | | | | | | | | | |   (399)  op(e3, e0) = e3
% 229.57/40.96  | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | REF_CLOSE: (21), (111), (141), (399) are inconsistent by
% 229.57/40.96  | | | | | | | | | | | |            sub-proof #2458.
% 229.57/40.96  | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | End of split
% 229.57/40.96  | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | End of split
% 229.57/40.96  | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | Case 2:
% 229.57/40.96  | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | |   (400)  all_57_12 = e3 & op(e0, e3) = e3
% 229.57/40.96  | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | ALPHA: (400) implies:
% 229.57/40.96  | | | | | | | | | |   (401)  all_57_12 = e3
% 229.57/40.96  | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | BETA: splitting (84) gives:
% 229.57/40.96  | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | Case 1:
% 229.57/40.96  | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | |   (402)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 229.57/40.96  | | | | | | | | | | |            & op(e3, e2) = e3)
% 229.57/40.96  | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | BETA: splitting (402) gives:
% 229.57/40.96  | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | Case 1:
% 229.57/40.96  | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | |   (403)  all_57_0 = e3 & op(e3, e3) = e3
% 229.57/40.96  | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | ALPHA: (403) implies:
% 229.57/40.96  | | | | | | | | | | | |   (404)  op(e3, e3) = e3
% 229.57/40.96  | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | REF_CLOSE: (21), (61), (166), (404) are inconsistent by
% 229.57/40.96  | | | | | | | | | | | |            sub-proof #2494.
% 229.57/40.96  | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | Case 2:
% 229.57/40.96  | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | |   (405)  all_57_1 = e3 & op(e3, e2) = e3
% 229.57/40.96  | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | ALPHA: (405) implies:
% 229.57/40.96  | | | | | | | | | | | |   (406)  all_57_1 = e3
% 229.57/40.96  | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | BETA: splitting (16) gives:
% 229.57/40.96  | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | Case 1:
% 229.57/40.96  | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | |   (407)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 229.57/40.96  | | | | | | | | | | | | |            & op(e2, e3) = e1)
% 229.57/40.96  | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | BETA: splitting (407) gives:
% 229.57/40.96  | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | Case 1:
% 229.57/40.96  | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | |   (408)  all_57_0 = e1 & op(e3, e3) = e1
% 229.57/40.96  | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | ALPHA: (408) implies:
% 229.57/40.96  | | | | | | | | | | | | | |   (409)  op(e3, e3) = e1
% 229.57/40.96  | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | BETA: splitting (101) gives:
% 229.57/40.96  | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | Case 1:
% 229.57/40.96  | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | |   (410)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 229.57/40.96  | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 229.57/40.96  | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | BETA: splitting (410) gives:
% 229.57/40.96  | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | Case 1:
% 229.57/40.96  | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | |   (411)  all_57_12 = e2 & op(e0, e3) = e2
% 229.57/40.96  | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | ALPHA: (411) implies:
% 229.57/40.96  | | | | | | | | | | | | | | | |   (412)  all_57_12 = e2
% 229.57/40.96  | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | COMBINE_EQS: (401), (412) imply:
% 229.57/40.96  | | | | | | | | | | | | | | | |   (413)  e3 = e2
% 229.57/40.96  | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | SIMP: (413) implies:
% 229.57/40.96  | | | | | | | | | | | | | | | |   (414)  e3 = e2
% 229.57/40.96  | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | COMBINE_EQS: (406), (414) imply:
% 229.57/40.96  | | | | | | | | | | | | | | | |   (415)  all_57_1 = e2
% 229.57/40.96  | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | REF_CLOSE: (21), (53), (61), (84), (111), (141), (166),
% 229.57/40.96  | | | | | | | | | | | | | | | |            (355), (415) are inconsistent by sub-proof #1405.
% 229.57/40.96  | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | Case 2:
% 229.57/40.96  | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | |   (416)  all_57_13 = e2 & op(e0, e2) = e2
% 229.57/40.96  | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | ALPHA: (416) implies:
% 229.57/40.96  | | | | | | | | | | | | | | | |   (417)  all_57_13 = e2
% 229.57/40.96  | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | REF_CLOSE: (19), (21), (61), (71), (72), (80), (87), (97),
% 229.57/40.96  | | | | | | | | | | | | | | | |            (102), (120), (401), (417) are inconsistent by
% 229.57/40.96  | | | | | | | | | | | | | | | |            sub-proof #1742.
% 229.57/40.96  | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | End of split
% 229.57/40.96  | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | Case 2:
% 229.57/40.96  | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | |   (418)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 229.57/40.96  | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 229.57/40.96  | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | BETA: splitting (418) gives:
% 229.57/40.96  | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | Case 1:
% 229.57/40.96  | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | |   (419)  all_57_14 = e2 & op(e0, e1) = e2
% 229.57/40.96  | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | ALPHA: (419) implies:
% 229.57/40.96  | | | | | | | | | | | | | | | |   (420)  all_57_14 = e2
% 229.57/40.96  | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | BETA: splitting (72) gives:
% 229.57/40.96  | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | Case 1:
% 229.57/40.96  | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | |   (421)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 229.57/40.96  | | | | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 229.57/40.96  | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | BETA: splitting (421) gives:
% 229.57/40.96  | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | Case 1:
% 229.57/40.96  | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | |   (422)  all_57_12 = e1 & op(e0, e3) = e1
% 229.57/40.96  | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (21), (28), (29), (53), (61), (71), (72),
% 229.57/40.96  | | | | | | | | | | | | | | | | | |            (80), (87), (90), (101), (102), (120), (355),
% 229.57/40.96  | | | | | | | | | | | | | | | | | |            (359), (401), (422) are inconsistent by sub-proof
% 229.57/40.96  | | | | | | | | | | | | | | | | | |            #820.
% 229.57/40.96  | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | Case 2:
% 229.57/40.96  | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | |   (423)  all_57_13 = e1 & op(e0, e2) = e1
% 229.57/40.96  | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | | ALPHA: (423) implies:
% 229.57/40.96  | | | | | | | | | | | | | | | | | |   (424)  all_57_13 = e1
% 229.57/40.96  | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | | BETA: splitting (24) gives:
% 229.57/40.96  | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | | |   (425)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 229.57/40.96  | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e3)
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | BETA: splitting (425) gives:
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | |   (426)  all_57_6 = e3 & op(e1, e3) = e3
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | ALPHA: (426) implies:
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | |   (427)  all_57_6 = e3
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | BETA: splitting (125) gives:
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | |   (428)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e2)
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (19), (21), (53), (80), (87), (114), (120),
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | |            (134), (171), (359), (409), (428) are inconsistent
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | |            by sub-proof #819.
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | |   (429)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e3) = e2)
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (429) gives:
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | |   (430)  all_57_6 = e2 & op(e1, e3) = e2
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (430) implies:
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | |   (431)  all_57_6 = e2
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (53), (427), (431) are inconsistent by sub-proof
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | |            #2463.
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | |   (432)  all_57_12 = e2 & op(e0, e3) = e2
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (53), (401), (432) are inconsistent by sub-proof
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | |            #2232.
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | |   (433)  all_57_7 = e3 & op(e1, e2) = e3
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | ALPHA: (433) implies:
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | |   (434)  all_57_7 = e3
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (19), (53), (61), (78), (80), (87), (120),
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | |            (138), (406), (424), (434) are inconsistent by
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | |            sub-proof #1214.
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | End of split
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | | |   (435)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 229.57/40.96  | | | | | | | | | | | | | | | | | | |            e3 & op(e1, e0) = e3)
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (21), (28), (29), (53), (61), (71), (80),
% 229.57/40.96  | | | | | | | | | | | | | | | | | | |            (87), (102), (120), (121), (129), (435) are
% 229.57/40.96  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1786.
% 229.57/40.96  | | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | | End of split
% 229.57/40.96  | | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | | End of split
% 229.57/40.96  | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | Case 2:
% 229.57/40.96  | | | | | | | | | | | | | | | | | 
% 229.57/40.96  | | | | | | | | | | | | | | | | |   (436)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 229.57/40.97  | | | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 229.57/40.97  | | | | | | | | | | | | | | | | | 
% 229.57/40.97  | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (21), (97), (120), (420), (436) are
% 229.57/40.97  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1139.
% 229.57/40.97  | | | | | | | | | | | | | | | | | 
% 229.57/40.97  | | | | | | | | | | | | | | | | End of split
% 229.57/40.97  | | | | | | | | | | | | | | | | 
% 229.57/40.97  | | | | | | | | | | | | | | | Case 2:
% 229.57/40.97  | | | | | | | | | | | | | | | | 
% 229.57/40.97  | | | | | | | | | | | | | | | |   (437)  all_57_15 = e2 & op(e0, e0) = e2
% 229.57/40.97  | | | | | | | | | | | | | | | | 
% 229.57/40.97  | | | | | | | | | | | | | | | | ALPHA: (437) implies:
% 229.57/40.97  | | | | | | | | | | | | | | | |   (438)  all_57_15 = e2
% 229.57/40.97  | | | | | | | | | | | | | | | | 
% 229.57/40.97  | | | | | | | | | | | | | | | | COMBINE_EQS: (71), (438) imply:
% 229.57/40.97  | | | | | | | | | | | | | | | |   (439)  e3 = e2
% 229.57/40.97  | | | | | | | | | | | | | | | | 
% 229.57/40.97  | | | | | | | | | | | | | | | | COMBINE_EQS: (406), (439) imply:
% 229.57/40.97  | | | | | | | | | | | | | | | |   (440)  all_57_1 = e2
% 229.57/40.97  | | | | | | | | | | | | | | | | 
% 229.57/40.97  | | | | | | | | | | | | | | | | REF_CLOSE: (21), (53), (61), (84), (111), (141), (166),
% 229.57/40.97  | | | | | | | | | | | | | | | |            (355), (440) are inconsistent by sub-proof #1405.
% 229.57/40.97  | | | | | | | | | | | | | | | | 
% 229.57/40.97  | | | | | | | | | | | | | | | End of split
% 229.57/40.97  | | | | | | | | | | | | | | | 
% 229.57/40.97  | | | | | | | | | | | | | | End of split
% 229.57/40.97  | | | | | | | | | | | | | | 
% 229.57/40.97  | | | | | | | | | | | | | Case 2:
% 229.57/40.97  | | | | | | | | | | | | | | 
% 229.57/40.97  | | | | | | | | | | | | | |   (441)  all_57_2 = e1 & op(e2, e3) = e1
% 229.57/40.97  | | | | | | | | | | | | | | 
% 229.57/40.97  | | | | | | | | | | | | | | ALPHA: (441) implies:
% 229.57/40.97  | | | | | | | | | | | | | |   (442)  all_57_2 = e1
% 229.57/40.97  | | | | | | | | | | | | | | 
% 229.57/40.97  | | | | | | | | | | | | | | REF_CLOSE: (87), (171), (442) are inconsistent by sub-proof
% 229.57/40.97  | | | | | | | | | | | | | |            #2473.
% 229.57/40.97  | | | | | | | | | | | | | | 
% 229.57/40.97  | | | | | | | | | | | | | End of split
% 229.57/40.97  | | | | | | | | | | | | | 
% 229.57/40.97  | | | | | | | | | | | | Case 2:
% 229.57/40.97  | | | | | | | | | | | | | 
% 229.57/40.97  | | | | | | | | | | | | |   (443)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 229.57/40.97  | | | | | | | | | | | | |            e1 & op(e0, e3) = e1)
% 229.57/40.97  | | | | | | | | | | | | | 
% 229.57/40.97  | | | | | | | | | | | | | BETA: splitting (443) gives:
% 229.57/40.97  | | | | | | | | | | | | | 
% 229.57/40.97  | | | | | | | | | | | | | Case 1:
% 229.57/40.97  | | | | | | | | | | | | | | 
% 229.57/40.97  | | | | | | | | | | | | | |   (444)  all_57_6 = e1 & op(e1, e3) = e1
% 229.57/40.97  | | | | | | | | | | | | | | 
% 229.57/40.97  | | | | | | | | | | | | | | ALPHA: (444) implies:
% 229.57/40.97  | | | | | | | | | | | | | |   (445)  all_57_6 = e1
% 229.57/40.97  | | | | | | | | | | | | | | 
% 229.57/40.97  | | | | | | | | | | | | | | REF_CLOSE: (18), (19), (21), (24), (28), (29), (53), (61),
% 229.57/40.97  | | | | | | | | | | | | | |            (71), (78), (80), (86), (87), (102), (120), (121),
% 229.57/40.97  | | | | | | | | | | | | | |            (129), (138), (406), (445) are inconsistent by
% 229.57/40.97  | | | | | | | | | | | | | |            sub-proof #1071.
% 229.57/40.97  | | | | | | | | | | | | | | 
% 229.57/40.97  | | | | | | | | | | | | | Case 2:
% 229.57/40.97  | | | | | | | | | | | | | | 
% 229.57/40.97  | | | | | | | | | | | | | |   (446)  all_57_12 = e1 & op(e0, e3) = e1
% 229.57/40.97  | | | | | | | | | | | | | | 
% 229.57/40.97  | | | | | | | | | | | | | | REF_CLOSE: (19), (21), (28), (29), (53), (61), (71), (72),
% 229.57/40.97  | | | | | | | | | | | | | |            (80), (87), (90), (101), (102), (120), (355),
% 229.57/40.97  | | | | | | | | | | | | | |            (359), (401), (446) are inconsistent by sub-proof
% 229.57/40.97  | | | | | | | | | | | | | |            #820.
% 229.57/40.97  | | | | | | | | | | | | | | 
% 229.57/40.97  | | | | | | | | | | | | | End of split
% 229.57/40.97  | | | | | | | | | | | | | 
% 229.57/40.97  | | | | | | | | | | | | End of split
% 229.57/40.97  | | | | | | | | | | | | 
% 229.57/40.97  | | | | | | | | | | | End of split
% 229.57/40.97  | | | | | | | | | | | 
% 229.57/40.97  | | | | | | | | | | Case 2:
% 229.57/40.97  | | | | | | | | | | | 
% 229.57/40.97  | | | | | | | | | | |   (447)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 229.57/40.97  | | | | | | | | | | |            & op(e3, e0) = e3)
% 229.57/40.97  | | | | | | | | | | | 
% 229.57/40.97  | | | | | | | | | | | REF_CLOSE: (21), (61), (111), (141), (355), (447) are
% 229.57/40.97  | | | | | | | | | | |            inconsistent by sub-proof #1406.
% 229.57/40.97  | | | | | | | | | | | 
% 229.57/40.97  | | | | | | | | | | End of split
% 229.57/40.97  | | | | | | | | | | 
% 229.57/40.97  | | | | | | | | | End of split
% 229.57/40.97  | | | | | | | | | 
% 229.57/40.97  | | | | | | | | End of split
% 229.57/40.97  | | | | | | | | 
% 229.57/40.97  | | | | | | | Case 2:
% 229.57/40.97  | | | | | | | | 
% 229.57/40.97  | | | | | | | |   (448)  all_57_10 = e3 & op(e2, e0) = e3
% 229.57/40.97  | | | | | | | | 
% 229.57/40.97  | | | | | | | | ALPHA: (448) implies:
% 229.57/40.97  | | | | | | | |   (449)  all_57_10 = e3
% 229.57/40.97  | | | | | | | | 
% 229.57/40.97  | | | | | | | | REF_CLOSE: (19), (21), (53), (61), (71), (80), (87), (97),
% 229.57/40.97  | | | | | | | |            (102), (120), (121), (129), (449) are inconsistent by
% 229.57/40.97  | | | | | | | |            sub-proof #1746.
% 229.57/40.97  | | | | | | | | 
% 229.57/40.97  | | | | | | | End of split
% 229.57/40.97  | | | | | | | 
% 229.57/40.97  | | | | | | End of split
% 229.57/40.97  | | | | | | 
% 229.57/40.97  | | | | | Case 2:
% 229.57/40.97  | | | | | | 
% 229.57/40.97  | | | | | |   (450)  all_57_9 = e0 & op(e3, e0) = e0
% 229.57/40.97  | | | | | | 
% 229.57/40.97  | | | | | | REF_CLOSE: (21), (141), (164), (450) are inconsistent by sub-proof
% 229.57/40.97  | | | | | |            #2434.
% 229.57/40.97  | | | | | | 
% 229.57/40.97  | | | | | End of split
% 229.57/40.97  | | | | | 
% 229.57/40.97  | | | | End of split
% 229.57/40.97  | | | | 
% 229.57/40.97  | | | End of split
% 229.57/40.97  | | | 
% 229.57/40.97  | | Case 2:
% 229.57/40.97  | | | 
% 229.57/40.97  | | |   (451)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3)
% 229.57/40.97  | | |            = e0)
% 229.57/40.97  | | | 
% 229.57/40.97  | | | BETA: splitting (451) gives:
% 229.57/40.97  | | | 
% 229.57/40.97  | | | Case 1:
% 229.57/40.97  | | | | 
% 229.57/40.97  | | | |   (452)  all_57_6 = e0 & op(e1, e3) = e0
% 229.57/40.97  | | | | 
% 229.57/40.97  | | | | ALPHA: (452) implies:
% 229.57/40.97  | | | |   (453)  all_57_6 = e0
% 229.57/40.97  | | | | 
% 229.57/40.97  | | | | BETA: splitting (50) gives:
% 229.57/40.97  | | | | 
% 229.57/40.97  | | | | Case 1:
% 229.57/40.97  | | | | | 
% 229.57/40.97  | | | | |   (454)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3,
% 229.57/40.97  | | | | |              e2) = e0)
% 229.57/40.97  | | | | | 
% 229.57/40.97  | | | | | BETA: splitting (454) gives:
% 229.57/40.97  | | | | | 
% 229.57/40.97  | | | | | Case 1:
% 229.57/40.97  | | | | | | 
% 229.57/40.97  | | | | | |   (455)  all_57_0 = e0 & op(e3, e3) = e0
% 229.57/40.97  | | | | | | 
% 229.57/40.97  | | | | | | ALPHA: (455) implies:
% 229.57/40.97  | | | | | |   (456)  all_57_0 = e0
% 229.57/40.97  | | | | | | 
% 229.57/40.97  | | | | | | REF_CLOSE: (16), (19), (21), (24), (28), (29), (53), (61), (71),
% 229.57/40.97  | | | | | |            (80), (87), (102), (115), (120), (121), (125), (129),
% 229.57/40.97  | | | | | |            (166), (453), (456) are inconsistent by sub-proof #869.
% 229.57/40.97  | | | | | | 
% 229.57/40.97  | | | | | Case 2:
% 229.57/40.97  | | | | | | 
% 229.57/40.97  | | | | | |   (457)  all_57_1 = e0 & op(e3, e2) = e0
% 229.57/40.97  | | | | | | 
% 229.57/40.97  | | | | | | ALPHA: (457) implies:
% 229.57/40.97  | | | | | |   (458)  all_57_1 = e0
% 229.57/40.97  | | | | | | 
% 229.57/40.97  | | | | | | REF_CLOSE: (13), (16), (18), (19), (21), (24), (28), (29), (34),
% 229.57/40.97  | | | | | |            (41), (45), (50), (53), (61), (66), (71), (72), (78),
% 229.57/40.97  | | | | | |            (80), (84), (86), (87), (90), (91), (97), (99), (101),
% 229.57/40.97  | | | | | |            (102), (107), (111), (114), (115), (119), (120), (121),
% 229.57/40.97  | | | | | |            (125), (127), (129), (130), (134), (138), (141), (161),
% 229.57/40.97  | | | | | |            (164), (166), (453), (458) are inconsistent by sub-proof
% 229.57/40.97  | | | | | |            #822.
% 229.57/40.97  | | | | | | 
% 229.57/40.97  | | | | | End of split
% 229.57/40.97  | | | | | 
% 229.57/40.97  | | | | Case 2:
% 229.57/40.97  | | | | | 
% 229.57/40.97  | | | | |   (459)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3,
% 229.57/40.97  | | | | |              e0) = e0)
% 229.57/40.97  | | | | | 
% 229.57/40.97  | | | | | BETA: splitting (459) gives:
% 229.57/40.97  | | | | | 
% 229.57/40.97  | | | | | Case 1:
% 229.57/40.97  | | | | | | 
% 229.57/40.97  | | | | | |   (460)  all_57_4 = e0 & op(e3, e1) = e0
% 229.57/40.97  | | | | | | 
% 229.57/40.97  | | | | | | ALPHA: (460) implies:
% 229.57/40.97  | | | | | |   (461)  all_57_4 = e0
% 229.57/40.97  | | | | | | 
% 229.57/40.97  | | | | | | REF_CLOSE: (13), (16), (18), (19), (21), (24), (28), (29), (34),
% 229.57/40.97  | | | | | |            (41), (45), (50), (53), (61), (66), (71), (72), (78),
% 229.57/40.97  | | | | | |            (80), (84), (86), (87), (90), (91), (97), (99), (101),
% 229.57/40.97  | | | | | |            (102), (107), (111), (114), (115), (119), (120), (121),
% 229.57/40.97  | | | | | |            (125), (127), (129), (130), (134), (138), (141), (161),
% 229.57/40.97  | | | | | |            (164), (166), (453), (461) are inconsistent by sub-proof
% 229.57/40.97  | | | | | |            #821.
% 229.57/40.97  | | | | | | 
% 229.57/40.97  | | | | | Case 2:
% 229.57/40.97  | | | | | | 
% 229.57/40.97  | | | | | |   (462)  all_57_9 = e0 & op(e3, e0) = e0
% 229.57/40.97  | | | | | | 
% 229.57/40.97  | | | | | | REF_CLOSE: (21), (141), (164), (462) are inconsistent by sub-proof
% 229.57/40.97  | | | | | |            #2434.
% 229.57/40.97  | | | | | | 
% 229.57/40.97  | | | | | End of split
% 229.57/40.97  | | | | | 
% 229.57/40.97  | | | | End of split
% 229.57/40.97  | | | | 
% 229.57/40.97  | | | Case 2:
% 229.57/40.97  | | | | 
% 229.57/40.97  | | | |   (463)  all_57_12 = e0 & op(e0, e3) = e0
% 229.57/40.97  | | | | 
% 229.57/40.97  | | | | ALPHA: (463) implies:
% 229.57/40.97  | | | |   (464)  op(e0, e3) = e0
% 229.57/40.97  | | | | 
% 229.57/40.97  | | | | REF_CLOSE: (21), (66), (161), (464) are inconsistent by sub-proof #2366.
% 229.57/40.97  | | | | 
% 229.57/40.97  | | | End of split
% 229.57/40.97  | | | 
% 229.57/40.97  | | End of split
% 229.57/40.97  | | 
% 229.57/40.97  | End of split
% 229.57/40.97  | 
% 229.57/40.97  End of proof
% 229.57/40.97  
% 229.57/40.97  Sub-proof #819 shows that the following formulas are inconsistent:
% 229.57/40.97  ----------------------------------------------------------------
% 229.57/40.97    (1)  op(e3, e3) = e1
% 229.57/40.97    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.57/40.97         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.57/40.97    (3)   ~ (e3 = e1)
% 229.57/40.97    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.57/40.97           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.57/40.97    (5)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2)
% 229.57/40.97    (6)   ~ (e3 = e2)
% 229.57/40.97    (7)  all_57_5 = e3
% 229.57/40.97    (8)   ~ (e2 = e0)
% 229.57/40.97    (9)   ~ (e1 = e0)
% 229.57/40.97    (10)  all_57_2 = e0
% 229.57/40.97    (11)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.57/40.97          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.57/40.97    (12)   ~ (e2 = e1)
% 229.57/40.97    (13)  all_57_3 = e2
% 229.57/40.97  
% 229.57/40.97  Begin of proof
% 229.57/40.97  | 
% 229.57/40.97  | BETA: splitting (5) gives:
% 229.57/40.97  | 
% 229.57/40.97  | Case 1:
% 229.57/40.97  | | 
% 229.57/40.97  | |   (14)  all_57_0 = e2 & op(e3, e3) = e2
% 229.57/40.97  | | 
% 229.57/40.97  | | ALPHA: (14) implies:
% 229.57/40.97  | |   (15)  op(e3, e3) = e2
% 229.57/40.97  | | 
% 229.57/40.97  | | REF_CLOSE: (1), (4), (12), (15) are inconsistent by sub-proof #1950.
% 229.57/40.97  | | 
% 229.57/40.97  | Case 2:
% 229.57/40.97  | | 
% 229.57/40.97  | |   (16)  all_57_2 = e2 & op(e2, e3) = e2
% 229.57/40.97  | | 
% 229.57/40.97  | | ALPHA: (16) implies:
% 229.57/40.97  | |   (17)  all_57_2 = e2
% 229.57/40.97  | | 
% 229.57/40.97  | | COMBINE_EQS: (10), (17) imply:
% 229.57/40.97  | |   (18)  e2 = e0
% 229.57/40.97  | | 
% 229.57/40.97  | | COMBINE_EQS: (13), (18) imply:
% 229.57/40.97  | |   (19)  all_57_3 = e0
% 229.57/40.97  | | 
% 229.57/40.97  | | REF_CLOSE: (2), (3), (6), (7), (8), (9), (10), (11), (12), (19) are
% 229.57/40.97  | |            inconsistent by sub-proof #2253.
% 229.57/40.97  | | 
% 229.57/40.97  | End of split
% 229.57/40.97  | 
% 229.57/40.97  End of proof
% 229.57/40.97  
% 229.57/40.97  Sub-proof #820 shows that the following formulas are inconsistent:
% 229.57/40.97  ----------------------------------------------------------------
% 229.57/40.97    (1)   ~ (e3 = e1)
% 229.57/40.97    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.57/40.97           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.57/40.97    (3)   ~ (all_6_2 = e3)
% 229.57/40.97    (4)  op(e1, e1) = all_6_2
% 229.57/40.97    (5)  all_57_4 = e0
% 229.57/40.97    (6)   ~ (e3 = e2)
% 229.57/40.97    (7)   ~ (e3 = e0)
% 229.57/40.97    (8)  all_57_15 = e3
% 229.57/40.97    (9)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 229.57/40.97         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.57/40.97    (10)  all_57_5 = e3
% 229.57/40.97    (11)   ~ (e2 = e0)
% 229.57/40.97    (12)   ~ (e1 = e0)
% 229.57/40.97    (13)  all_57_12 = e3
% 229.57/40.97    (14)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.57/40.97          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.57/40.97    (15)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.57/40.97          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.57/40.97            e2)
% 229.57/40.97    (16)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.57/40.97              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.57/40.97                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.57/40.97                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.57/40.97    (17)   ~ (e2 = e1)
% 229.57/40.97    (18)  all_57_12 = e1 & op(e0, e3) = e1
% 229.57/40.97  
% 229.57/40.97  Begin of proof
% 229.57/40.97  | 
% 229.57/40.97  | ALPHA: (18) implies:
% 229.57/40.97  |   (19)  all_57_12 = e1
% 229.57/40.97  | 
% 229.57/40.97  | COMBINE_EQS: (13), (19) imply:
% 229.57/40.97  |   (20)  e3 = e1
% 229.57/40.97  | 
% 229.57/40.97  | SIMP: (20) implies:
% 229.57/40.97  |   (21)  e3 = e1
% 229.57/40.97  | 
% 229.57/40.97  | COMBINE_EQS: (10), (21) imply:
% 229.57/40.97  |   (22)  all_57_5 = e1
% 229.57/40.97  | 
% 229.57/40.97  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (14),
% 229.57/40.97  |            (15), (16), (17), (22) are inconsistent by sub-proof #943.
% 229.57/40.97  | 
% 229.57/40.97  End of proof
% 229.57/40.97  
% 229.57/40.97  Sub-proof #821 shows that the following formulas are inconsistent:
% 229.57/40.97  ----------------------------------------------------------------
% 229.57/40.97    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.57/40.97         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.57/40.97    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.57/40.97         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.57/40.97    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.57/40.97         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.57/40.97    (4)   ~ (e3 = e1)
% 229.57/40.97    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.57/40.97           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.57/40.97    (6)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.57/40.97         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.57/40.97    (7)   ~ (all_6_2 = e3)
% 229.57/40.97    (8)  op(e1, e1) = all_6_2
% 229.57/40.97    (9)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.57/40.97         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.57/40.97    (10)   ~ (all_53_7 = e2)
% 229.57/40.97    (11)  all_57_4 = e0
% 229.57/40.97    (12)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.57/40.97          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.57/40.97    (13)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.57/40.97          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.57/40.97    (14)   ~ (e3 = e2)
% 229.57/40.97    (15)   ~ (e3 = e0)
% 229.57/40.97    (16)  all_57_6 = e0
% 229.57/40.97    (17)  op(e0, e3) = all_53_3
% 229.57/40.97    (18)  all_57_15 = e3
% 229.57/40.97    (19)  op(e3, e3) = e0
% 229.57/40.97    (20)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.57/40.97          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.57/40.97            e1)
% 229.57/40.97    (21)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.57/40.97          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.57/40.97    (22)   ~ (e2 = e0)
% 229.57/40.97    (23)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.57/40.97          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.57/40.97    (24)  op(e2, e2) = e2
% 229.57/40.97    (25)   ~ (e1 = e0)
% 229.57/40.97    (26)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.57/40.97          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.57/40.97    (27)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.57/40.97          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.57/40.97    (28)  op(e0, e0) = e3
% 229.57/40.97    (29)  op(e0, e2) = all_53_7
% 229.57/40.97    (30)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.57/40.97          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.57/40.97            e2)
% 229.57/40.97    (31)   ~ (all_53_3 = e0)
% 229.57/40.97    (32)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.57/40.97              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.57/40.97                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.57/40.97                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.57/40.97    (33)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.57/40.97          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.57/40.97    (34)   ~ (all_53_12 = e3)
% 229.57/40.97    (35)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.57/40.97          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.57/40.97    (36)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.57/40.97          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.57/40.97    (37)   ~ (all_53_12 = e0)
% 229.57/40.97    (38)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.57/40.97          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 229.57/40.97    (39)   ~ (e2 = e1)
% 229.57/40.97    (40)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.57/40.97          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.57/40.97    (41)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.57/40.97          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.57/40.97    (42)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 229.57/40.97          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 229.57/40.97    (43)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.57/40.97          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.57/40.97    (44)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 229.57/40.97          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 229.57/40.97    (45)  all_57_3 = e2
% 229.57/40.97    (46)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.57/40.97          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.57/40.97    (47)  op(e3, e0) = all_53_12
% 229.57/40.97  
% 229.57/40.97  Begin of proof
% 229.57/40.97  | 
% 229.57/40.97  | BETA: splitting (23) gives:
% 229.57/40.97  | 
% 229.57/40.97  | Case 1:
% 229.57/40.97  | | 
% 229.57/40.97  | |   (48)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) =
% 229.57/40.97  | |           e3)
% 229.57/40.97  | | 
% 229.57/40.97  | | BETA: splitting (48) gives:
% 229.57/40.97  | | 
% 229.57/40.97  | | Case 1:
% 229.57/40.97  | | | 
% 229.57/40.97  | | |   (49)  all_57_0 = e3 & op(e3, e3) = e3
% 229.57/40.97  | | | 
% 229.57/40.97  | | | ALPHA: (49) implies:
% 229.57/40.97  | | |   (50)  op(e3, e3) = e3
% 229.57/40.97  | | | 
% 229.57/40.97  | | | REF_CLOSE: (5), (15), (19), (50) are inconsistent by sub-proof #2494.
% 229.57/40.97  | | | 
% 229.57/40.97  | | Case 2:
% 229.57/40.97  | | | 
% 229.57/40.97  | | |   (51)  all_57_1 = e3 & op(e3, e2) = e3
% 229.57/40.97  | | | 
% 229.57/40.97  | | | ALPHA: (51) implies:
% 229.57/40.97  | | |   (52)  all_57_1 = e3
% 229.57/40.97  | | | 
% 229.57/40.97  | | | BETA: splitting (6) gives:
% 229.57/40.97  | | | 
% 229.57/40.97  | | | Case 1:
% 229.57/40.97  | | | | 
% 229.57/40.97  | | | |   (53)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2)
% 229.57/40.97  | | | |           = e3)
% 229.57/40.97  | | | | 
% 229.57/40.97  | | | | BETA: splitting (53) gives:
% 229.57/40.97  | | | | 
% 229.57/40.97  | | | | Case 1:
% 229.57/40.97  | | | | | 
% 229.57/40.97  | | | | |   (54)  all_57_6 = e3 & op(e1, e3) = e3
% 229.57/40.97  | | | | | 
% 229.57/40.97  | | | | | ALPHA: (54) implies:
% 229.57/40.97  | | | | |   (55)  all_57_6 = e3
% 229.57/40.97  | | | | | 
% 229.57/40.97  | | | | | COMBINE_EQS: (16), (55) imply:
% 229.57/40.97  | | | | |   (56)  e3 = e0
% 229.57/40.97  | | | | | 
% 229.57/40.97  | | | | | COMBINE_EQS: (52), (56) imply:
% 229.57/40.97  | | | | |   (57)  all_57_1 = e0
% 229.57/40.97  | | | | | 
% 229.57/40.97  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12),
% 229.57/40.97  | | | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 229.57/40.97  | | | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 229.57/40.97  | | | | |            (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 229.57/40.97  | | | | |            (43), (44), (45), (46), (47), (57) are inconsistent by
% 229.57/40.97  | | | | |            sub-proof #822.
% 229.57/40.97  | | | | | 
% 229.57/40.97  | | | | Case 2:
% 229.57/40.97  | | | | | 
% 229.57/40.97  | | | | |   (58)  all_57_7 = e3 & op(e1, e2) = e3
% 229.57/40.97  | | | | | 
% 229.57/40.97  | | | | | ALPHA: (58) implies:
% 229.57/40.97  | | | | |   (59)  all_57_7 = e3
% 229.57/40.97  | | | | | 
% 229.57/40.97  | | | | | REF_CLOSE: (3), (4), (5), (14), (15), (21), (22), (24), (25), (39),
% 229.57/40.97  | | | | |            (46), (52), (59) are inconsistent by sub-proof #1167.
% 229.57/40.97  | | | | | 
% 229.57/40.97  | | | | End of split
% 229.57/40.97  | | | | 
% 229.57/40.97  | | | Case 2:
% 229.57/40.97  | | | | 
% 229.57/40.97  | | | |   (60)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0)
% 229.57/40.97  | | | |           = e3)
% 229.57/40.97  | | | | 
% 229.57/40.97  | | | | REF_CLOSE: (4), (5), (7), (8), (14), (15), (18), (22), (25), (32), (39),
% 229.57/40.97  | | | |            (40), (43), (60) are inconsistent by sub-proof #1786.
% 229.57/40.97  | | | | 
% 229.57/40.97  | | | End of split
% 229.57/40.97  | | | 
% 229.57/40.97  | | End of split
% 229.57/40.97  | | 
% 229.57/40.97  | Case 2:
% 229.57/40.97  | | 
% 229.57/40.97  | |   (61)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) =
% 229.57/40.97  | |           e3)
% 229.57/40.97  | | 
% 229.57/40.97  | | REF_CLOSE: (5), (11), (15), (34), (47), (61) are inconsistent by sub-proof
% 229.57/40.97  | |            #1406.
% 229.57/40.97  | | 
% 229.57/40.97  | End of split
% 229.57/40.97  | 
% 229.57/40.97  End of proof
% 229.57/40.97  
% 229.57/40.97  Sub-proof #822 shows that the following formulas are inconsistent:
% 229.57/40.97  ----------------------------------------------------------------
% 229.57/40.97    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.57/40.97         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.57/40.97    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.57/40.97         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.57/40.97    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.57/40.97         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.57/40.97    (4)   ~ (e3 = e1)
% 229.57/40.97    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.57/40.97           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.57/40.97    (6)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.57/40.97         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.57/40.97    (7)   ~ (all_6_2 = e3)
% 229.57/40.97    (8)  op(e1, e1) = all_6_2
% 229.57/40.97    (9)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.57/40.97         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.57/40.97    (10)   ~ (all_53_7 = e2)
% 229.57/40.97    (11)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.57/40.97          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.57/40.97    (12)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.57/40.97          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.57/40.97    (13)   ~ (e3 = e2)
% 229.57/40.97    (14)   ~ (e3 = e0)
% 229.57/40.97    (15)  all_57_6 = e0
% 229.57/40.97    (16)  all_57_1 = e0
% 229.57/40.97    (17)  op(e0, e3) = all_53_3
% 229.57/40.97    (18)  all_57_15 = e3
% 229.57/40.97    (19)  op(e3, e3) = e0
% 229.57/40.97    (20)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.57/40.97          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.57/40.97            e1)
% 229.57/40.97    (21)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.57/40.97          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.57/40.97    (22)   ~ (e2 = e0)
% 229.57/40.97    (23)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.57/40.97          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.57/40.97    (24)  op(e2, e2) = e2
% 229.57/40.97    (25)   ~ (e1 = e0)
% 229.57/40.97    (26)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.57/40.97          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.57/40.98    (27)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.57/40.98          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.57/40.98    (28)  op(e0, e0) = e3
% 229.57/40.98    (29)  op(e0, e2) = all_53_7
% 229.57/40.98    (30)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.57/40.98          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.57/40.98            e2)
% 229.57/40.98    (31)   ~ (all_53_3 = e0)
% 229.57/40.98    (32)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.57/40.98              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.57/40.98                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.57/40.98                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.57/40.98    (33)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.57/40.98          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.57/40.98    (34)   ~ (all_53_12 = e3)
% 229.57/40.98    (35)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.57/40.98          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.57/40.98    (36)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.57/40.98          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.57/40.98    (37)   ~ (all_53_12 = e0)
% 229.57/40.98    (38)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.57/40.98          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 229.57/40.98    (39)   ~ (e2 = e1)
% 229.57/40.98    (40)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.57/40.98          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.57/40.98    (41)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.57/40.98          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.57/40.98    (42)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 229.57/40.98          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 229.57/40.98    (43)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.57/40.98          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.57/40.98    (44)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 229.57/40.98          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 229.57/40.98    (45)  all_57_3 = e2
% 229.57/40.98    (46)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.57/40.98          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.57/40.98    (47)  op(e3, e0) = all_53_12
% 229.57/40.98  
% 229.57/40.98  Begin of proof
% 229.57/40.98  | 
% 229.57/40.98  | BETA: splitting (23) gives:
% 229.57/40.98  | 
% 229.57/40.98  | Case 1:
% 229.57/40.98  | | 
% 229.57/40.98  | |   (48)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) =
% 229.57/40.98  | |           e3)
% 229.57/40.98  | | 
% 229.57/40.98  | | REF_CLOSE: (5), (14), (16), (19), (48) are inconsistent by sub-proof #2404.
% 229.57/40.98  | | 
% 229.57/40.98  | Case 2:
% 229.57/40.98  | | 
% 229.57/40.98  | |   (49)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) =
% 229.57/40.98  | |           e3)
% 229.57/40.98  | | 
% 229.57/40.98  | | BETA: splitting (49) gives:
% 229.57/40.98  | | 
% 229.57/40.98  | | Case 1:
% 229.57/40.98  | | | 
% 229.57/40.98  | | |   (50)  all_57_4 = e3 & op(e3, e1) = e3
% 229.57/40.98  | | | 
% 229.57/40.98  | | | ALPHA: (50) implies:
% 229.57/40.98  | | |   (51)  all_57_4 = e3
% 229.57/40.98  | | | 
% 229.57/40.98  | | | BETA: splitting (6) gives:
% 229.57/40.98  | | | 
% 229.57/40.98  | | | Case 1:
% 229.57/40.98  | | | | 
% 229.57/40.98  | | | |   (52)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2)
% 229.57/40.98  | | | |           = e3)
% 229.57/40.98  | | | | 
% 229.57/40.98  | | | | BETA: splitting (52) gives:
% 229.57/40.98  | | | | 
% 229.57/40.98  | | | | Case 1:
% 229.57/40.98  | | | | | 
% 229.57/40.98  | | | | |   (53)  all_57_6 = e3 & op(e1, e3) = e3
% 229.57/40.98  | | | | | 
% 229.57/40.98  | | | | | ALPHA: (53) implies:
% 229.57/40.98  | | | | |   (54)  all_57_6 = e3
% 229.57/40.98  | | | | | 
% 229.57/40.98  | | | | | REF_CLOSE: (14), (15), (54) are inconsistent by sub-proof #1822.
% 229.57/40.98  | | | | | 
% 229.57/40.98  | | | | Case 2:
% 229.57/40.98  | | | | | 
% 229.57/40.98  | | | | |   (55)  all_57_7 = e3 & op(e1, e2) = e3
% 229.57/40.98  | | | | | 
% 229.57/40.98  | | | | | ALPHA: (55) implies:
% 229.57/40.98  | | | | |   (56)  all_57_7 = e3
% 229.57/40.98  | | | | | 
% 229.57/40.98  | | | | | BETA: splitting (41) gives:
% 229.57/40.98  | | | | | 
% 229.57/40.98  | | | | | Case 1:
% 229.57/40.98  | | | | | | 
% 229.57/40.98  | | | | | |   (57)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2,
% 229.57/40.98  | | | | | |             e3) = e2)
% 229.57/40.98  | | | | | | 
% 229.57/40.98  | | | | | | BETA: splitting (57) gives:
% 229.57/40.98  | | | | | | 
% 229.57/40.98  | | | | | | Case 1:
% 229.57/40.98  | | | | | | | 
% 229.57/40.98  | | | | | | |   (58)  all_57_0 = e2 & op(e3, e3) = e2
% 229.57/40.98  | | | | | | | 
% 229.57/40.98  | | | | | | | ALPHA: (58) implies:
% 229.57/40.98  | | | | | | |   (59)  op(e3, e3) = e2
% 229.57/40.98  | | | | | | | 
% 229.57/40.98  | | | | | | | REF_CLOSE: (5), (19), (22), (59) are inconsistent by sub-proof
% 229.57/40.98  | | | | | | |            #2403.
% 229.57/40.98  | | | | | | | 
% 229.57/40.98  | | | | | | Case 2:
% 229.57/40.98  | | | | | | | 
% 229.57/40.98  | | | | | | |   (60)  all_57_2 = e2 & op(e2, e3) = e2
% 229.57/40.98  | | | | | | | 
% 229.57/40.98  | | | | | | | ALPHA: (60) implies:
% 229.57/40.98  | | | | | | |   (61)  all_57_2 = e2
% 229.57/40.98  | | | | | | | 
% 229.57/40.98  | | | | | | | REF_CLOSE: (1), (4), (5), (13), (14), (18), (22), (24), (25),
% 229.57/40.98  | | | | | | |            (28), (32), (33), (35), (38), (39), (40), (43), (45),
% 229.57/40.98  | | | | | | |            (61) are inconsistent by sub-proof #844.
% 229.57/40.98  | | | | | | | 
% 229.57/40.98  | | | | | | End of split
% 229.57/40.98  | | | | | | 
% 229.57/40.98  | | | | | Case 2:
% 229.57/40.98  | | | | | | 
% 229.57/40.98  | | | | | |   (62)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0,
% 229.57/40.98  | | | | | |             e3) = e2)
% 229.57/40.98  | | | | | | 
% 229.57/40.98  | | | | | | BETA: splitting (62) gives:
% 229.57/40.98  | | | | | | 
% 229.57/40.98  | | | | | | Case 1:
% 229.57/40.98  | | | | | | | 
% 229.57/40.98  | | | | | | |   (63)  all_57_6 = e2 & op(e1, e3) = e2
% 229.57/40.98  | | | | | | | 
% 229.57/40.98  | | | | | | | ALPHA: (63) implies:
% 229.57/40.98  | | | | | | |   (64)  all_57_6 = e2
% 229.57/40.98  | | | | | | | 
% 229.57/40.98  | | | | | | | COMBINE_EQS: (15), (64) imply:
% 229.57/40.98  | | | | | | |   (65)  e2 = e0
% 229.57/40.98  | | | | | | | 
% 229.57/40.98  | | | | | | | REF_CLOSE: (3), (4), (13), (16), (22), (25), (39), (45), (46),
% 229.57/40.98  | | | | | | |            (56), (65) are inconsistent by sub-proof #904.
% 229.57/40.98  | | | | | | | 
% 229.57/40.98  | | | | | | Case 2:
% 229.57/40.98  | | | | | | | 
% 229.57/40.98  | | | | | | |   (66)  all_57_12 = e2 & op(e0, e3) = e2
% 229.57/40.98  | | | | | | | 
% 229.57/40.98  | | | | | | | ALPHA: (66) implies:
% 229.57/40.98  | | | | | | |   (67)  all_57_12 = e2
% 229.57/40.98  | | | | | | | 
% 229.57/40.98  | | | | | | | BETA: splitting (2) gives:
% 229.57/40.98  | | | | | | | 
% 229.57/40.98  | | | | | | | Case 1:
% 229.57/40.98  | | | | | | | | 
% 229.57/40.98  | | | | | | | |   (68)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 &
% 229.57/40.98  | | | | | | | |           op(e2, e3) = e1)
% 229.57/40.98  | | | | | | | | 
% 229.57/40.98  | | | | | | | | BETA: splitting (68) gives:
% 229.57/40.98  | | | | | | | | 
% 229.57/40.98  | | | | | | | | Case 1:
% 229.57/40.98  | | | | | | | | | 
% 229.57/40.98  | | | | | | | | |   (69)  all_57_0 = e1 & op(e3, e3) = e1
% 229.57/40.98  | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | ALPHA: (69) implies:
% 229.57/40.98  | | | | | | | | |   (70)  all_57_0 = e1
% 229.57/40.98  | | | | | | | | |   (71)  op(e3, e3) = e1
% 229.57/40.98  | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | BETA: splitting (36) gives:
% 229.57/40.98  | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | Case 1:
% 229.57/40.98  | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | |   (72)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 &
% 229.57/40.98  | | | | | | | | | |           op(e2, e3) = e3)
% 229.57/40.98  | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | BETA: splitting (72) gives:
% 229.57/40.98  | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | Case 1:
% 229.57/40.98  | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | |   (73)  all_57_0 = e3 & op(e3, e3) = e3
% 229.57/40.98  | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | ALPHA: (73) implies:
% 229.57/40.98  | | | | | | | | | | |   (74)  op(e3, e3) = e3
% 229.57/40.98  | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | REF_CLOSE: (4), (5), (71), (74) are inconsistent by sub-proof
% 229.57/40.98  | | | | | | | | | | |            #2495.
% 229.57/40.98  | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | Case 2:
% 229.57/40.98  | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | |   (75)  all_57_2 = e3 & op(e2, e3) = e3
% 229.57/40.98  | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | ALPHA: (75) implies:
% 229.57/40.98  | | | | | | | | | | |   (76)  all_57_2 = e3
% 229.57/40.98  | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | BETA: splitting (11) gives:
% 229.57/40.98  | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | Case 1:
% 229.57/40.98  | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | |   (77)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 229.57/40.98  | | | | | | | | | | | |           & op(e3, e2) = e2)
% 229.57/40.98  | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | BETA: splitting (77) gives:
% 229.57/40.98  | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | Case 1:
% 229.57/40.98  | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | |   (78)  all_57_0 = e2 & op(e3, e3) = e2
% 229.57/40.98  | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | ALPHA: (78) implies:
% 229.57/40.98  | | | | | | | | | | | | |   (79)  op(e3, e3) = e2
% 229.57/40.98  | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | REF_CLOSE: (5), (39), (71), (79) are inconsistent by
% 229.57/40.98  | | | | | | | | | | | | |            sub-proof #1950.
% 229.57/40.98  | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | Case 2:
% 229.57/40.98  | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | |   (80)  all_57_1 = e2 & op(e3, e2) = e2
% 229.57/40.98  | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | ALPHA: (80) implies:
% 229.57/40.98  | | | | | | | | | | | | |   (81)  all_57_1 = e2
% 229.57/40.98  | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | COMBINE_EQS: (16), (81) imply:
% 229.57/40.98  | | | | | | | | | | | | |   (82)  e2 = e0
% 229.57/40.98  | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | SIMP: (82) implies:
% 229.57/40.98  | | | | | | | | | | | | |   (83)  e2 = e0
% 229.57/40.98  | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | COMBINE_EQS: (45), (83) imply:
% 229.57/40.98  | | | | | | | | | | | | |   (84)  all_57_3 = e0
% 229.57/40.98  | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (13), (14),
% 229.57/40.98  | | | | | | | | | | | | |            (15), (16), (18), (22), (25), (32), (33), (35),
% 229.57/40.98  | | | | | | | | | | | | |            (39), (40), (43), (46), (76), (84) are
% 229.57/40.98  | | | | | | | | | | | | |            inconsistent by sub-proof #826.
% 229.57/40.98  | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | End of split
% 229.57/40.98  | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | Case 2:
% 229.57/40.98  | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | |   (85)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 229.57/40.98  | | | | | | | | | | | |           & op(e3, e0) = e2)
% 229.57/40.98  | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | BETA: splitting (85) gives:
% 229.57/40.98  | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | Case 1:
% 229.57/40.98  | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | |   (86)  all_57_4 = e2 & op(e3, e1) = e2
% 229.57/40.98  | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | ALPHA: (86) implies:
% 229.57/40.98  | | | | | | | | | | | | |   (87)  all_57_4 = e2
% 229.57/40.98  | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | COMBINE_EQS: (51), (87) imply:
% 229.57/40.98  | | | | | | | | | | | | |   (88)  e3 = e2
% 229.57/40.98  | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | REF_CLOSE: (1), (4), (5), (13), (14), (18), (22), (24), (25),
% 229.57/40.98  | | | | | | | | | | | | |            (28), (32), (33), (35), (38), (39), (40), (43),
% 229.57/40.98  | | | | | | | | | | | | |            (45), (76), (88) are inconsistent by sub-proof
% 229.57/40.98  | | | | | | | | | | | | |            #825.
% 229.57/40.98  | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | Case 2:
% 229.57/40.98  | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | |   (89)  all_57_9 = e2 & op(e3, e0) = e2
% 229.57/40.98  | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | ALPHA: (89) implies:
% 229.57/40.98  | | | | | | | | | | | | |   (90)  all_57_9 = e2
% 229.57/40.98  | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | BETA: splitting (46) gives:
% 229.57/40.98  | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | Case 1:
% 229.57/40.98  | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | |   (91)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 229.57/40.98  | | | | | | | | | | | | | |           & op(e2, e2) = e1)
% 229.57/40.98  | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | BETA: splitting (91) gives:
% 229.57/40.98  | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | Case 1:
% 229.57/40.98  | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | |   (92)  all_57_1 = e1 & op(e3, e2) = e1
% 229.57/40.98  | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | ALPHA: (92) implies:
% 229.57/40.98  | | | | | | | | | | | | | | |   (93)  all_57_1 = e1
% 229.57/40.98  | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | COMBINE_EQS: (16), (93) imply:
% 229.57/40.98  | | | | | | | | | | | | | | |   (94)  e1 = e0
% 229.57/40.98  | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | SIMP: (94) implies:
% 229.57/40.98  | | | | | | | | | | | | | | |   (95)  e1 = e0
% 229.57/40.98  | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | COMBINE_EQS: (70), (95) imply:
% 229.57/40.98  | | | | | | | | | | | | | | |   (96)  all_57_0 = e0
% 229.57/40.98  | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (5), (9), (11), (12), (13), (14), (16),
% 229.57/40.98  | | | | | | | | | | | | | | |            (18), (19), (20), (22), (23), (25), (27), (28),
% 229.57/40.98  | | | | | | | | | | | | | | |            (30), (32), (34), (37), (39), (40), (43), (45),
% 229.57/40.98  | | | | | | | | | | | | | | |            (46), (47), (96) are inconsistent by sub-proof
% 229.57/40.98  | | | | | | | | | | | | | | |            #882.
% 229.57/40.98  | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | Case 2:
% 229.57/40.98  | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | |   (97)  all_57_3 = e1 & op(e2, e2) = e1
% 229.57/40.98  | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | ALPHA: (97) implies:
% 229.57/40.98  | | | | | | | | | | | | | | |   (98)  all_57_3 = e1
% 229.57/40.98  | | | | | | | | | | | | | | |   (99)  op(e2, e2) = e1
% 229.57/40.98  | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (13), (14), (15),
% 229.57/40.98  | | | | | | | | | | | | | | |            (16), (17), (18), (20), (21), (22), (25), (27),
% 229.57/40.98  | | | | | | | | | | | | | | |            (28), (31), (32), (36), (39), (40), (41), (43),
% 229.57/40.98  | | | | | | | | | | | | | | |            (46), (71), (98), (99) are inconsistent by
% 229.57/40.98  | | | | | | | | | | | | | | |            sub-proof #1054.
% 229.57/40.98  | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | End of split
% 229.57/40.98  | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | Case 2:
% 229.57/40.98  | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | |   (100)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 229.57/40.98  | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 229.57/40.98  | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | BETA: splitting (100) gives:
% 229.57/40.98  | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | Case 1:
% 229.57/40.98  | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | |   (101)  all_57_7 = e1 & op(e1, e2) = e1
% 229.57/40.98  | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | ALPHA: (101) implies:
% 229.57/40.98  | | | | | | | | | | | | | | |   (102)  all_57_7 = e1
% 229.57/40.98  | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (13), (14), (15), (18),
% 229.57/40.98  | | | | | | | | | | | | | | |            (22), (25), (32), (39), (40), (43), (102) are
% 229.57/40.98  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1157.
% 229.57/40.98  | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | Case 2:
% 229.57/40.98  | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | |   (103)  all_57_13 = e1 & op(e0, e2) = e1
% 229.57/40.98  | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | ALPHA: (103) implies:
% 229.57/40.98  | | | | | | | | | | | | | | |   (104)  all_57_13 = e1
% 229.57/40.98  | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | BETA: splitting (32) gives:
% 229.57/40.98  | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | Case 1:
% 229.57/40.98  | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | |   (105)  all_57_15 = e0 & op(e0, e0) = e0
% 229.57/40.98  | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | ALPHA: (105) implies:
% 229.57/40.98  | | | | | | | | | | | | | | | |   (106)  op(e0, e0) = e0
% 229.57/40.98  | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | REF_CLOSE: (5), (14), (28), (106) are inconsistent by
% 229.57/40.98  | | | | | | | | | | | | | | | |            sub-proof #2304.
% 229.57/40.98  | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | Case 2:
% 229.57/40.98  | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | |   (107)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 229.57/40.98  | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 229.57/40.98  | | | | | | | | | | | | | | | |              op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 229.57/40.98  | | | | | | | | | | | | | | | |                e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 229.57/40.98  | | | | | | | | | | | | | | | |              e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 229.57/40.98  | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | ALPHA: (107) implies:
% 229.57/40.98  | | | | | | | | | | | | | | | |   (108)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 229.57/40.98  | | | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 229.57/40.98  | | | | | | | | | | | | | | | |              e1) = e0)
% 229.57/40.98  | | | | | | | | | | | | | | | |   (109)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 229.57/40.98  | | | | | | | | | | | | | | | |            e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 229.57/40.98  | | | | | | | | | | | | | | | |              e0) = e0)
% 229.57/40.98  | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | BETA: splitting (108) gives:
% 229.57/40.98  | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | Case 1:
% 229.57/40.98  | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | |   (110)  all_57_12 = e0 & op(e0, e3) = e0
% 229.57/40.98  | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | ALPHA: (110) implies:
% 229.57/40.98  | | | | | | | | | | | | | | | | |   (111)  op(e0, e3) = e0
% 229.57/40.98  | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (17), (31), (111) are inconsistent by
% 229.57/40.98  | | | | | | | | | | | | | | | | |            sub-proof #2366.
% 229.57/40.98  | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | Case 2:
% 229.57/40.98  | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | |   (112)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 229.57/40.98  | | | | | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 229.57/40.98  | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | BETA: splitting (112) gives:
% 229.57/40.98  | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | Case 1:
% 229.57/40.98  | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | |   (113)  all_57_13 = e0 & op(e0, e2) = e0
% 229.57/40.98  | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | ALPHA: (113) implies:
% 229.57/40.98  | | | | | | | | | | | | | | | | | |   (114)  all_57_13 = e0
% 229.57/40.98  | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (104), (114) imply:
% 229.57/40.98  | | | | | | | | | | | | | | | | | |   (115)  e1 = e0
% 229.57/40.98  | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | SIMP: (115) implies:
% 229.57/40.98  | | | | | | | | | | | | | | | | | |   (116)  e1 = e0
% 229.57/40.98  | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (70), (116) imply:
% 229.57/40.98  | | | | | | | | | | | | | | | | | |   (117)  all_57_0 = e0
% 229.57/40.98  | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | BETA: splitting (46) gives:
% 229.57/40.98  | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | |   (118)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 229.57/40.98  | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | BETA: splitting (118) gives:
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | |   (119)  all_57_1 = e1 & op(e3, e2) = e1
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (25), (119) are inconsistent by sub-proof
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | |            #2446.
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | |   (120)  all_57_3 = e1 & op(e2, e2) = e1
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | ALPHA: (120) implies:
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | |   (121)  all_57_3 = e1
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | |   (122)  op(e2, e2) = e1
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (5), (9), (11), (13), (14), (16), (18),
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | |            (19), (20), (21), (22), (23), (25), (27), (28),
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | |            (30), (32), (34), (39), (46), (47), (117), (121),
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | |            (122) are inconsistent by sub-proof #824.
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | End of split
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | BETA: splitting (100) gives:
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | |   (123)  all_57_7 = e1 & op(e1, e2) = e1
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | ALPHA: (123) implies:
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | |   (124)  all_57_7 = e1
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (9), (11), (12), (13), (14), (16), (18),
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | |            (19), (20), (22), (23), (25), (27), (28), (30),
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | |            (34), (39), (45), (47), (51), (108), (124) are
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #827.
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (104), (114) are inconsistent by sub-proof
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | |            #1760.
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | End of split
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | End of split
% 229.57/40.98  | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | Case 2:
% 229.57/40.98  | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | |   (125)  all_57_14 = e0 & op(e0, e1) = e0
% 229.57/40.98  | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | ALPHA: (125) implies:
% 229.57/40.98  | | | | | | | | | | | | | | | | | |   (126)  all_57_14 = e0
% 229.57/40.98  | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | BETA: splitting (42) gives:
% 229.57/40.98  | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | |   (127)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 229.57/40.98  | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e2)
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | BETA: splitting (127) gives:
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | |   (128)  all_57_4 = e2 & op(e3, e1) = e2
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | ALPHA: (128) implies:
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | |   (129)  all_57_4 = e2
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (51), (129) imply:
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | |   (130)  e3 = e2
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (5), (13), (14), (18), (22), (24), (25),
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | |            (28), (32), (33), (35), (38), (39), (40), (43),
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | |            (45), (76), (130) are inconsistent by sub-proof
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | |            #825.
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | |   (131)  all_57_5 = e2 & op(e2, e1) = e2
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | ALPHA: (131) implies:
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | |   (132)  all_57_5 = e2
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | BETA: splitting (1) gives:
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | |   (133)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (133) gives:
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | |   (134)  all_57_2 = e1 & op(e2, e3) = e1
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (134) implies:
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | |   (135)  all_57_2 = e1
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (13), (14), (15), (19), (22), (36),
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | |            (39), (41), (135) are inconsistent by sub-proof
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | |            #2390.
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | |   (136)  all_57_3 = e1 & op(e2, e2) = e1
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (136) implies:
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | |   (137)  op(e2, e2) = e1
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (5), (13), (14), (16), (18), (20), (22),
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | |            (25), (27), (28), (30), (39), (104), (108), (126),
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | |            (137) are inconsistent by sub-proof #1736.
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | |   (138)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (138) gives:
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | |   (139)  all_57_5 = e1 & op(e2, e1) = e1
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (139) implies:
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | |   (140)  all_57_5 = e1
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (132), (140) imply:
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | |   (141)  e2 = e1
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | SIMP: (141) implies:
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | |   (142)  e2 = e1
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (90), (142) imply:
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | |   (143)  all_57_9 = e1
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (11), (13), (16), (19), (22), (39), (51),
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | |            (143) are inconsistent by sub-proof #2402.
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | |   (144)  all_57_10 = e1 & op(e2, e0) = e1
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (144) implies:
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | |   (145)  all_57_10 = e1
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (109) gives:
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | |   (146)  all_57_9 = e0 & op(e3, e0) = e0
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (37), (47), (146) are inconsistent by
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2434.
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | |   (147)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 =
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (147) gives:
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | | |   (148)  all_57_10 = e0 & op(e2, e0) = e0
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (148) implies:
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | | |   (149)  all_57_10 = e0
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (145), (149) imply:
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | | |   (150)  e1 = e0
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (150) implies:
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | | |   (151)  e1 = e0
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (70), (151) imply:
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | | |   (152)  all_57_0 = e0
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (9), (11), (13), (14), (16), (18), (19),
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | | |            (22), (23), (25), (28), (34), (39), (40), (43),
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | | |            (47), (51), (149), (152) are inconsistent by
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #905.
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | | |   (153)  all_57_11 = e0 & op(e1, e0) = e0
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (153) implies:
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | | |   (154)  all_57_11 = e0
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (5), (7), (8), (13), (14), (18), (20),
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | | |            (22), (24), (25), (26), (28), (30), (32), (33),
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | | |            (35), (38), (39), (40), (43), (45), (51), (90),
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | | |            (132), (145), (154) are inconsistent by sub-proof
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | | |            #865.
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | End of split
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | |   (155)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 229.57/40.98  | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e1) = e2)
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | BETA: splitting (155) gives:
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | |   (156)  all_57_8 = e2 & op(e1, e1) = e2
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | ALPHA: (156) implies:
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | |   (157)  op(e1, e1) = e2
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | BETA: splitting (44) gives:
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | |   (158)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e1)
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (158) gives:
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | |   (159)  all_57_6 = e1 & op(e1, e3) = e1
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (159) implies:
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | |   (160)  all_57_6 = e1
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (15), (160) imply:
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | |   (161)  e1 = e0
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (70), (161) imply:
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | |   (162)  all_57_0 = e0
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (5), (9), (11), (12), (13), (14), (16),
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | |            (18), (19), (20), (22), (23), (25), (27), (28),
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | |            (30), (34), (37), (39), (40), (43), (45), (46),
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | |            (47), (51), (108), (109), (162) are inconsistent
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #891.
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | |   (163)  all_57_7 = e1 & op(e1, e2) = e1
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (163) implies:
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | |   (164)  all_57_7 = e1
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (9), (11), (12), (13), (14), (16), (18),
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | |            (19), (20), (22), (23), (25), (27), (28), (30),
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | |            (34), (39), (45), (47), (51), (108), (164) are
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #827.
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | |   (165)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | |            e1 & op(e1, e0) = e1)
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (165) gives:
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | |   (166)  all_57_8 = e1 & op(e1, e1) = e1
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.98  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (166) implies:
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | |   (167)  op(e1, e1) = e1
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (39), (157), (167) are inconsistent by
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2423.
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | |   (168)  all_57_11 = e1 & op(e1, e0) = e1
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (168) implies:
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | |   (169)  all_57_11 = e1
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (109) gives:
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | |   (170)  all_57_9 = e0 & op(e3, e0) = e0
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (37), (47), (170) are inconsistent by
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2434.
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | |   (171)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 =
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (171) gives:
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | |   (172)  all_57_10 = e0 & op(e2, e0) = e0
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (30) gives:
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | |   (173)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (173) gives:
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (172) implies:
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | | |   (174)  all_57_10 = e0
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with e0, e1, e3, e3, simplifying
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | | |              with (19), (71) gives:
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | | |   (175)  e1 = e0
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (70), (175) imply:
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | | |   (176)  all_57_0 = e0
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (9), (11), (13), (14), (16), (18), (19),
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | | |            (22), (23), (25), (28), (34), (39), (40), (43),
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | | |            (47), (51), (169), (174), (176) are inconsistent
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #906.
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | | |   (177)  all_57_13 = e2 & op(e0, e2) = e2
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (177) implies:
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | | |   (178)  op(e0, e2) = e2
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10), (29), (178) are inconsistent by
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2335.
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | |   (179)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (179) gives:
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | | |   (180)  all_57_14 = e2 & op(e0, e1) = e2
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (13), (14),
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | | |            (15), (16), (18), (22), (25), (32), (33), (35),
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | | |            (39), (40), (43), (45), (46), (76), (126), (180)
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #823.
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | | |   (181)  all_57_15 = e2 & op(e0, e0) = e2
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (181) implies:
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | | |   (182)  all_57_15 = e2
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (18), (182) imply:
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | | |   (183)  e3 = e2
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (5), (13), (14), (18), (22), (24), (25),
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | | |            (28), (32), (33), (35), (38), (39), (40), (43),
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | | |            (45), (76), (183) are inconsistent by sub-proof
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | | |            #825.
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | |   (184)  all_57_11 = e0 & op(e1, e0) = e0
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (184) implies:
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | |   (185)  all_57_11 = e0
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (169), (185) imply:
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | |   (186)  e1 = e0
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (186) implies:
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | |   (187)  e1 = e0
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (70), (187) imply:
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | |   (188)  all_57_0 = e0
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (9), (11), (13), (14), (16), (19), (22),
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | |            (23), (25), (28), (34), (39), (43), (47), (51),
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | |            (90), (185), (188) are inconsistent by sub-proof
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | |            #902.
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | |   (189)  all_57_14 = e2 & op(e0, e1) = e2
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (13), (14),
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | |            (15), (16), (18), (22), (25), (32), (33), (35),
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | |            (39), (40), (43), (45), (46), (76), (126), (189)
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #823.
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | End of split
% 229.57/40.99  | | | | | | | | | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | | | | | | | | | End of split
% 229.57/40.99  | | | | | | | | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | | | | | | | | End of split
% 229.57/40.99  | | | | | | | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | | | | | | | End of split
% 229.57/40.99  | | | | | | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | | | | | | End of split
% 229.57/40.99  | | | | | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | | | | | End of split
% 229.57/40.99  | | | | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | | | | End of split
% 229.57/40.99  | | | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | | | End of split
% 229.57/40.99  | | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | | End of split
% 229.57/40.99  | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | End of split
% 229.57/40.99  | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | Case 2:
% 229.57/40.99  | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | |   (190)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3
% 229.57/40.99  | | | | | | | | | |            & op(e0, e3) = e3)
% 229.57/40.99  | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | BETA: splitting (190) gives:
% 229.57/40.99  | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | Case 1:
% 229.57/40.99  | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | |   (191)  all_57_6 = e3 & op(e1, e3) = e3
% 229.57/40.99  | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | | REF_CLOSE: (14), (15), (191) are inconsistent by sub-proof
% 229.57/40.99  | | | | | | | | | | |            #2395.
% 229.57/40.99  | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | Case 2:
% 229.57/40.99  | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | |   (192)  all_57_12 = e3 & op(e0, e3) = e3
% 229.57/40.99  | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | | ALPHA: (192) implies:
% 229.57/40.99  | | | | | | | | | | |   (193)  all_57_12 = e3
% 229.57/40.99  | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | | COMBINE_EQS: (67), (193) imply:
% 229.57/40.99  | | | | | | | | | | |   (194)  e3 = e2
% 229.57/40.99  | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | | COMBINE_EQS: (56), (194) imply:
% 229.57/40.99  | | | | | | | | | | |   (195)  all_57_7 = e2
% 229.57/40.99  | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (13), (14), (15), (18),
% 229.57/40.99  | | | | | | | | | | |            (22), (25), (32), (39), (40), (43), (195) are
% 229.57/40.99  | | | | | | | | | | |            inconsistent by sub-proof #1775.
% 229.57/40.99  | | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | | End of split
% 229.57/40.99  | | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | End of split
% 229.57/40.99  | | | | | | | | | 
% 229.57/40.99  | | | | | | | | Case 2:
% 229.57/40.99  | | | | | | | | | 
% 229.57/40.99  | | | | | | | | |   (196)  all_57_2 = e1 & op(e2, e3) = e1
% 229.57/40.99  | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | ALPHA: (196) implies:
% 229.57/40.99  | | | | | | | | |   (197)  all_57_2 = e1
% 229.57/40.99  | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | REF_CLOSE: (4), (5), (13), (14), (15), (19), (22), (36), (39),
% 229.57/40.99  | | | | | | | | |            (41), (197) are inconsistent by sub-proof #2390.
% 229.57/40.99  | | | | | | | | | 
% 229.57/40.99  | | | | | | | | End of split
% 229.57/40.99  | | | | | | | | 
% 229.57/40.99  | | | | | | | Case 2:
% 229.57/40.99  | | | | | | | | 
% 229.57/40.99  | | | | | | | |   (198)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 &
% 229.57/40.99  | | | | | | | |            op(e0, e3) = e1)
% 229.57/40.99  | | | | | | | | 
% 229.57/40.99  | | | | | | | | BETA: splitting (198) gives:
% 229.57/40.99  | | | | | | | | 
% 229.57/40.99  | | | | | | | | Case 1:
% 229.57/40.99  | | | | | | | | | 
% 229.57/40.99  | | | | | | | | |   (199)  all_57_6 = e1 & op(e1, e3) = e1
% 229.57/40.99  | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | ALPHA: (199) implies:
% 229.57/40.99  | | | | | | | | |   (200)  all_57_6 = e1
% 229.57/40.99  | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | REF_CLOSE: (15), (25), (200) are inconsistent by sub-proof
% 229.57/40.99  | | | | | | | | |            #2227.
% 229.57/40.99  | | | | | | | | | 
% 229.57/40.99  | | | | | | | | Case 2:
% 229.57/40.99  | | | | | | | | | 
% 229.57/40.99  | | | | | | | | |   (201)  all_57_12 = e1 & op(e0, e3) = e1
% 229.57/40.99  | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | ALPHA: (201) implies:
% 229.57/40.99  | | | | | | | | |   (202)  all_57_12 = e1
% 229.57/40.99  | | | | | | | | | 
% 229.57/40.99  | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (13), (14), (15), (18),
% 229.57/40.99  | | | | | | | | |            (19), (22), (25), (32), (36), (39), (40), (41),
% 229.57/40.99  | | | | | | | | |            (43), (56), (202) are inconsistent by sub-proof
% 229.57/40.99  | | | | | | | | |            #1029.
% 229.57/40.99  | | | | | | | | | 
% 229.57/40.99  | | | | | | | | End of split
% 229.57/40.99  | | | | | | | | 
% 229.57/40.99  | | | | | | | End of split
% 229.57/40.99  | | | | | | | 
% 229.57/40.99  | | | | | | End of split
% 229.57/40.99  | | | | | | 
% 229.57/40.99  | | | | | End of split
% 229.57/40.99  | | | | | 
% 229.57/40.99  | | | | End of split
% 229.57/40.99  | | | | 
% 229.57/40.99  | | | Case 2:
% 229.57/40.99  | | | | 
% 229.57/40.99  | | | |   (203)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1,
% 229.57/40.99  | | | |              e0) = e3)
% 229.57/40.99  | | | | 
% 229.57/40.99  | | | | REF_CLOSE: (4), (5), (7), (8), (13), (14), (18), (22), (25), (32), (39),
% 229.57/40.99  | | | |            (40), (43), (203) are inconsistent by sub-proof #1786.
% 229.57/40.99  | | | | 
% 229.57/40.99  | | | End of split
% 229.57/40.99  | | | 
% 229.57/40.99  | | Case 2:
% 229.57/40.99  | | | 
% 229.57/40.99  | | |   (204)  all_57_9 = e3 & op(e3, e0) = e3
% 229.57/40.99  | | | 
% 229.57/40.99  | | | ALPHA: (204) implies:
% 229.57/40.99  | | |   (205)  op(e3, e0) = e3
% 229.57/40.99  | | | 
% 229.57/40.99  | | | REF_CLOSE: (5), (34), (47), (205) are inconsistent by sub-proof #2458.
% 229.57/40.99  | | | 
% 229.57/40.99  | | End of split
% 229.57/40.99  | | 
% 229.57/40.99  | End of split
% 229.57/40.99  | 
% 229.57/40.99  End of proof
% 229.57/40.99  
% 229.57/40.99  Sub-proof #823 shows that the following formulas are inconsistent:
% 229.57/40.99  ----------------------------------------------------------------
% 229.57/40.99    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.57/40.99         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.57/40.99    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.57/40.99         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.57/40.99    (3)   ~ (e3 = e1)
% 229.57/40.99    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.57/40.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.57/40.99    (5)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.57/40.99         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.57/40.99    (6)   ~ (all_6_2 = e3)
% 229.57/40.99    (7)  op(e1, e1) = all_6_2
% 229.57/40.99    (8)   ~ (e3 = e2)
% 229.57/40.99    (9)   ~ (e3 = e0)
% 229.57/40.99    (10)  all_57_6 = e0
% 229.57/40.99    (11)  all_57_1 = e0
% 229.57/40.99    (12)  all_57_15 = e3
% 229.57/40.99    (13)   ~ (e2 = e0)
% 229.57/40.99    (14)  all_57_2 = e3
% 229.57/40.99    (15)   ~ (e1 = e0)
% 229.57/40.99    (16)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.57/40.99              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.57/40.99                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.57/40.99                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.57/40.99    (17)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.57/40.99          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.57/40.99    (18)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.57/40.99          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.57/40.99    (19)   ~ (e2 = e1)
% 229.57/40.99    (20)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.57/40.99          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.57/40.99    (21)  all_57_14 = e2 & op(e0, e1) = e2
% 229.57/40.99    (22)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.57/40.99          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.57/40.99    (23)  all_57_14 = e0
% 229.57/40.99    (24)  all_57_3 = e2
% 229.57/40.99    (25)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.57/40.99          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.57/40.99  
% 229.57/40.99  Begin of proof
% 229.57/40.99  | 
% 229.57/40.99  | ALPHA: (21) implies:
% 229.57/40.99  |   (26)  all_57_14 = e2
% 229.57/40.99  | 
% 229.57/40.99  | COMBINE_EQS: (23), (26) imply:
% 229.57/40.99  |   (27)  e2 = e0
% 229.57/40.99  | 
% 229.57/40.99  | COMBINE_EQS: (24), (27) imply:
% 229.57/40.99  |   (28)  all_57_3 = e0
% 229.57/40.99  | 
% 229.57/40.99  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 229.57/40.99  |            (13), (14), (15), (16), (17), (18), (19), (20), (22), (25), (28)
% 229.57/40.99  |            are inconsistent by sub-proof #826.
% 229.57/40.99  | 
% 229.57/40.99  End of proof
% 229.57/40.99  
% 229.57/40.99  Sub-proof #824 shows that the following formulas are inconsistent:
% 229.57/40.99  ----------------------------------------------------------------
% 229.57/40.99    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.57/40.99         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.57/40.99    (2)   ~ (e3 = e1)
% 229.57/40.99    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.57/40.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.57/40.99    (4)  op(e2, e2) = e1
% 229.57/40.99    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.57/40.99         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.57/40.99    (6)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.57/40.99         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.57/40.99    (7)   ~ (e3 = e2)
% 229.57/40.99    (8)   ~ (e3 = e0)
% 229.57/40.99    (9)  all_57_1 = e0
% 229.57/40.99    (10)  all_57_0 = e0
% 229.57/40.99    (11)  all_57_15 = e3
% 229.57/40.99    (12)  op(e3, e3) = e0
% 229.57/40.99    (13)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.57/40.99          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.57/40.99            e1)
% 229.57/40.99    (14)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.57/40.99          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.57/40.99    (15)   ~ (e2 = e0)
% 229.57/40.99    (16)  all_57_3 = e1
% 229.57/40.99    (17)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.57/40.99          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.57/40.99    (18)   ~ (e1 = e0)
% 229.57/40.99    (19)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.57/40.99          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.57/40.99    (20)  op(e0, e0) = e3
% 229.57/40.99    (21)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.57/40.99          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.57/40.99            e2)
% 229.57/40.99    (22)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.57/40.99              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.57/40.99                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.57/40.99                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.57/40.99    (23)   ~ (all_53_12 = e3)
% 229.57/40.99    (24)   ~ (e2 = e1)
% 229.57/40.99    (25)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.57/40.99          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.57/40.99    (26)  op(e3, e0) = all_53_12
% 229.57/40.99  
% 229.57/40.99  Begin of proof
% 229.57/40.99  | 
% 229.57/40.99  | BETA: splitting (19) gives:
% 229.57/40.99  | 
% 229.57/40.99  | Case 1:
% 229.57/40.99  | | 
% 229.57/40.99  | |   (27)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 229.57/40.99  | |           e3)
% 229.57/40.99  | | 
% 229.57/40.99  | | REF_CLOSE: (2), (3), (4), (8), (9), (27) are inconsistent by sub-proof
% 229.57/40.99  | |            #1737.
% 229.57/40.99  | | 
% 229.57/40.99  | Case 2:
% 229.57/40.99  | | 
% 229.57/40.99  | |   (28)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 229.57/40.99  | |           e3)
% 229.57/40.99  | | 
% 229.57/40.99  | | BETA: splitting (28) gives:
% 229.57/40.99  | | 
% 229.57/40.99  | | Case 1:
% 229.57/40.99  | | | 
% 229.57/40.99  | | |   (29)  all_57_7 = e3 & op(e1, e2) = e3
% 229.57/40.99  | | | 
% 229.57/40.99  | | | ALPHA: (29) implies:
% 229.57/40.99  | | |   (30)  all_57_7 = e3
% 229.57/40.99  | | | 
% 229.57/40.99  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (14),
% 229.57/40.99  | | |            (15), (16), (17), (18), (23), (24), (25), (26), (30) are
% 229.57/40.99  | | |            inconsistent by sub-proof #1706.
% 229.57/40.99  | | | 
% 229.57/40.99  | | Case 2:
% 229.57/40.99  | | | 
% 229.57/40.99  | | |   (31)  all_57_13 = e3 & op(e0, e2) = e3
% 229.57/40.99  | | | 
% 229.57/40.99  | | | ALPHA: (31) implies:
% 229.57/40.99  | | |   (32)  all_57_13 = e3
% 229.57/40.99  | | | 
% 229.57/40.99  | | | REF_CLOSE: (2), (3), (7), (8), (11), (13), (15), (18), (20), (21), (22),
% 229.57/40.99  | | |            (24), (32) are inconsistent by sub-proof #1792.
% 229.57/40.99  | | | 
% 229.57/40.99  | | End of split
% 229.57/40.99  | | 
% 229.57/40.99  | End of split
% 229.57/40.99  | 
% 229.57/40.99  End of proof
% 229.57/40.99  
% 229.57/40.99  Sub-proof #825 shows that the following formulas are inconsistent:
% 229.57/40.99  ----------------------------------------------------------------
% 229.57/40.99    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.57/40.99         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.57/40.99    (2)   ~ (e3 = e1)
% 229.57/40.99    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.57/40.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.57/40.99    (4)   ~ (e3 = e2)
% 229.57/40.99    (5)   ~ (e3 = e0)
% 229.57/40.99    (6)  all_57_15 = e3
% 229.57/40.99    (7)   ~ (e2 = e0)
% 229.57/40.99    (8)  all_57_2 = e3
% 229.57/40.99    (9)  e3 = e2
% 229.57/40.99    (10)  op(e2, e2) = e2
% 229.57/40.99    (11)   ~ (e1 = e0)
% 229.57/40.99    (12)  op(e0, e0) = e3
% 229.57/40.99    (13)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.57/40.99              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.57/40.99                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.57/40.99                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.57/40.99    (14)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.57/40.99          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.57/40.99    (15)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.57/40.99          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.57/40.99    (16)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.57/40.99          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 229.57/40.99    (17)   ~ (e2 = e1)
% 229.57/40.99    (18)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.57/40.99          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.57/40.99    (19)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.57/40.99          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.57/40.99    (20)  all_57_3 = e2
% 229.57/40.99  
% 229.57/40.99  Begin of proof
% 229.57/40.99  | 
% 229.57/40.99  | SIMP: (9) implies:
% 229.57/40.99  |   (21)  e3 = e2
% 229.57/40.99  | 
% 229.57/40.99  | COMBINE_EQS: (8), (21) imply:
% 229.57/40.99  |   (22)  all_57_2 = e2
% 229.57/40.99  | 
% 229.57/40.99  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (10), (11), (12), (13), (14),
% 229.57/40.99  |            (15), (16), (17), (18), (19), (20), (22) are inconsistent by
% 229.57/40.99  |            sub-proof #844.
% 229.57/40.99  | 
% 229.57/40.99  End of proof
% 229.57/40.99  
% 229.57/40.99  Sub-proof #826 shows that the following formulas are inconsistent:
% 229.57/40.99  ----------------------------------------------------------------
% 229.57/40.99    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.57/40.99         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.57/40.99    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.57/40.99         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.57/40.99    (3)   ~ (e3 = e1)
% 229.57/40.99    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.57/40.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.57/40.99    (5)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.57/40.99         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.57/40.99    (6)   ~ (all_6_2 = e3)
% 229.57/40.99    (7)  op(e1, e1) = all_6_2
% 229.57/40.99    (8)  all_57_3 = e0
% 229.57/40.99    (9)   ~ (e3 = e2)
% 229.57/40.99    (10)   ~ (e3 = e0)
% 229.57/40.99    (11)  all_57_6 = e0
% 229.57/40.99    (12)  all_57_1 = e0
% 229.57/40.99    (13)  all_57_15 = e3
% 229.57/40.99    (14)   ~ (e2 = e0)
% 229.57/40.99    (15)  all_57_2 = e3
% 229.57/40.99    (16)   ~ (e1 = e0)
% 229.57/40.99    (17)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.57/40.99              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.57/40.99                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.57/40.99                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.57/40.99    (18)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.57/40.99          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.57/40.99    (19)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.57/40.99          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.57/40.99    (20)   ~ (e2 = e1)
% 229.57/40.99    (21)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.57/40.99          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.57/40.99    (22)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.57/40.99          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.57/40.99    (23)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.57/40.99          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.57/40.99  
% 229.57/40.99  Begin of proof
% 229.57/40.99  | 
% 229.57/40.99  | BETA: splitting (5) gives:
% 229.57/40.99  | 
% 229.57/40.99  | Case 1:
% 229.57/40.99  | | 
% 229.57/40.99  | |   (24)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 229.57/40.99  | |           e3)
% 229.57/40.99  | | 
% 229.57/40.99  | | BETA: splitting (24) gives:
% 229.57/40.99  | | 
% 229.57/40.99  | | Case 1:
% 229.57/40.99  | | | 
% 229.57/40.99  | | |   (25)  all_57_6 = e3 & op(e1, e3) = e3
% 229.57/40.99  | | | 
% 229.57/40.99  | | | ALPHA: (25) implies:
% 229.57/40.99  | | |   (26)  all_57_6 = e3
% 229.57/40.99  | | | 
% 229.57/40.99  | | | COMBINE_EQS: (11), (26) imply:
% 229.57/40.99  | | |   (27)  e3 = e0
% 229.57/40.99  | | | 
% 229.57/40.99  | | | COMBINE_EQS: (15), (27) imply:
% 229.57/40.99  | | |   (28)  all_57_2 = e0
% 229.57/40.99  | | | 
% 229.57/40.99  | | | REF_CLOSE: (1), (3), (8), (9), (10), (14), (16), (18), (19), (20), (28)
% 229.57/40.99  | | |            are inconsistent by sub-proof #2246.
% 229.57/40.99  | | | 
% 229.57/40.99  | | Case 2:
% 229.57/40.99  | | | 
% 229.57/40.99  | | |   (29)  all_57_7 = e3 & op(e1, e2) = e3
% 229.57/40.99  | | | 
% 229.57/40.99  | | | ALPHA: (29) implies:
% 229.57/40.99  | | |   (30)  all_57_7 = e3
% 229.57/40.99  | | | 
% 229.57/40.99  | | | REF_CLOSE: (2), (3), (8), (9), (12), (14), (16), (20), (23), (30) are
% 229.57/40.99  | | |            inconsistent by sub-proof #2098.
% 229.57/40.99  | | | 
% 229.57/40.99  | | End of split
% 229.57/40.99  | | 
% 229.57/40.99  | Case 2:
% 229.57/40.99  | | 
% 229.57/40.99  | |   (31)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 229.57/40.99  | |           e3)
% 229.57/40.99  | | 
% 229.57/40.99  | | REF_CLOSE: (3), (4), (6), (7), (9), (10), (13), (14), (16), (17), (20),
% 229.57/40.99  | |            (21), (22), (31) are inconsistent by sub-proof #1786.
% 229.57/40.99  | | 
% 229.57/40.99  | End of split
% 229.57/40.99  | 
% 229.57/40.99  End of proof
% 229.57/40.99  
% 229.57/40.99  Sub-proof #827 shows that the following formulas are inconsistent:
% 229.57/40.99  ----------------------------------------------------------------
% 229.57/40.99    (1)   ~ (e3 = e1)
% 229.57/40.99    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.57/40.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.57/40.99    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.57/40.99         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.57/40.99    (4)  all_57_7 = e1
% 229.57/40.99    (5)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.57/40.99         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.57/40.99    (6)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.57/40.99         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.57/40.99    (7)  all_57_4 = e3
% 229.57/41.00    (8)   ~ (e3 = e2)
% 229.57/41.00    (9)   ~ (e3 = e0)
% 229.57/41.00    (10)  all_57_1 = e0
% 229.57/41.00    (11)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.57/41.00          | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.57/41.00    (12)  all_57_15 = e3
% 229.57/41.00    (13)  op(e3, e3) = e0
% 229.57/41.00    (14)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.57/41.00          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.57/41.00            e1)
% 229.57/41.00    (15)   ~ (e2 = e0)
% 229.57/41.00    (16)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.57/41.00          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.57/41.00    (17)   ~ (e1 = e0)
% 229.57/41.00    (18)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.57/41.00          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.57/41.00    (19)  op(e0, e0) = e3
% 229.57/41.00    (20)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.57/41.00          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.57/41.00            e2)
% 229.57/41.00    (21)   ~ (all_53_12 = e3)
% 229.57/41.00    (22)   ~ (e2 = e1)
% 229.57/41.00    (23)  all_57_3 = e2
% 229.57/41.00    (24)  op(e3, e0) = all_53_12
% 229.57/41.00  
% 229.57/41.00  Begin of proof
% 229.57/41.00  | 
% 229.57/41.00  | BETA: splitting (18) gives:
% 229.57/41.00  | 
% 229.57/41.00  | Case 1:
% 229.57/41.00  | | 
% 229.57/41.00  | |   (25)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 229.57/41.00  | |           e3)
% 229.57/41.00  | | 
% 229.57/41.00  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (13), (15), (17), (22),
% 229.57/41.00  | |            (23), (25) are inconsistent by sub-proof #892.
% 229.57/41.00  | | 
% 229.57/41.00  | Case 2:
% 229.57/41.00  | | 
% 229.57/41.00  | |   (26)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 229.57/41.00  | |           e3)
% 229.57/41.00  | | 
% 229.57/41.00  | | BETA: splitting (26) gives:
% 229.57/41.00  | | 
% 229.57/41.00  | | Case 1:
% 229.57/41.00  | | | 
% 229.57/41.00  | | |   (27)  all_57_7 = e3 & op(e1, e2) = e3
% 229.57/41.00  | | | 
% 229.57/41.00  | | | ALPHA: (27) implies:
% 229.57/41.00  | | |   (28)  all_57_7 = e3
% 229.57/41.00  | | | 
% 229.57/41.00  | | | REF_CLOSE: (1), (2), (4), (7), (9), (10), (13), (16), (21), (24), (28) are
% 229.57/41.00  | | |            inconsistent by sub-proof #830.
% 229.57/41.00  | | | 
% 229.57/41.00  | | Case 2:
% 229.57/41.00  | | | 
% 229.57/41.00  | | |   (29)  all_57_13 = e3 & op(e0, e2) = e3
% 229.57/41.00  | | | 
% 229.57/41.00  | | | ALPHA: (29) implies:
% 229.57/41.00  | | |   (30)  all_57_13 = e3
% 229.57/41.00  | | | 
% 229.57/41.00  | | | REF_CLOSE: (1), (2), (8), (9), (11), (12), (14), (15), (17), (19), (20),
% 229.57/41.00  | | |            (22), (30) are inconsistent by sub-proof #2054.
% 229.57/41.00  | | | 
% 229.57/41.00  | | End of split
% 229.57/41.00  | | 
% 229.57/41.00  | End of split
% 229.57/41.00  | 
% 229.57/41.00  End of proof
% 229.57/41.00  
% 229.57/41.00  Sub-proof #828 shows that the following formulas are inconsistent:
% 229.57/41.00  ----------------------------------------------------------------
% 229.57/41.00    (1)   ~ (e3 = e1)
% 229.57/41.00    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.57/41.00           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.57/41.00    (3)  all_57_4 = e3
% 229.57/41.00    (4)   ~ (e3 = e0)
% 229.57/41.00    (5)  all_57_1 = e0
% 229.57/41.00    (6)  all_57_6 = e1 & op(e1, e3) = e1
% 229.57/41.00    (7)  op(e3, e3) = e0
% 229.57/41.00    (8)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.57/41.00         (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.57/41.00    (9)  all_57_6 = e3
% 229.57/41.00    (10)   ~ (all_53_12 = e3)
% 229.57/41.00    (11)  op(e3, e0) = all_53_12
% 229.57/41.00  
% 229.57/41.00  Begin of proof
% 229.57/41.00  | 
% 229.57/41.00  | ALPHA: (6) implies:
% 229.57/41.00  |   (12)  all_57_6 = e1
% 229.57/41.00  | 
% 229.57/41.00  | COMBINE_EQS: (9), (12) imply:
% 229.57/41.00  |   (13)  e3 = e1
% 229.57/41.00  | 
% 229.57/41.00  | SIMP: (13) implies:
% 229.57/41.00  |   (14)  e3 = e1
% 229.57/41.00  | 
% 229.57/41.00  | COMBINE_EQS: (3), (14) imply:
% 229.57/41.00  |   (15)  all_57_4 = e1
% 229.57/41.00  | 
% 229.57/41.00  | REF_CLOSE: (1), (2), (4), (5), (7), (8), (10), (11), (15) are inconsistent by
% 229.57/41.00  |            sub-proof #2280.
% 229.57/41.00  | 
% 229.57/41.00  End of proof
% 229.57/41.00  
% 229.57/41.00  Sub-proof #829 shows that the following formulas are inconsistent:
% 229.57/41.00  ----------------------------------------------------------------
% 229.57/41.00    (1)  all_57_13 = e1
% 229.57/41.00    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.57/41.00         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.57/41.00    (3)   ~ (e3 = e1)
% 229.57/41.00    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.57/41.00           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.57/41.00    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.57/41.00         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.57/41.00    (6)  all_57_13 = e0 & op(e0, e2) = e0
% 229.57/41.00    (7)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.57/41.00         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.57/41.00    (8)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.57/41.00         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.57/41.00    (9)  all_57_4 = e3
% 229.57/41.00    (10)   ~ (e3 = e2)
% 229.57/41.00    (11)   ~ (e3 = e0)
% 229.57/41.00    (12)  all_57_1 = e0
% 229.57/41.00    (13)  all_57_0 = e1
% 229.57/41.00    (14)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.57/41.00          | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.57/41.00    (15)  all_57_15 = e3
% 229.57/41.00    (16)  op(e3, e3) = e0
% 229.57/41.00    (17)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.57/41.00          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.57/41.00            e1)
% 229.57/41.00    (18)   ~ (e2 = e0)
% 229.57/41.00    (19)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.57/41.00          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.57/41.00    (20)   ~ (e1 = e0)
% 229.57/41.00    (21)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.57/41.00          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.57/41.00    (22)  op(e0, e0) = e3
% 229.57/41.00    (23)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.57/41.00          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.57/41.00            e2)
% 229.57/41.00    (24)   ~ (all_53_12 = e3)
% 229.57/41.00    (25)   ~ (all_53_12 = e0)
% 229.57/41.00    (26)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) |
% 229.57/41.00          (all_57_11 = e0 & op(e1, e0) = e0)
% 229.57/41.00    (27)   ~ (e2 = e1)
% 229.57/41.00    (28)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.57/41.00          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.57/41.00    (29)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.57/41.00          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.57/41.00    (30)  all_57_3 = e2
% 229.57/41.00    (31)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.57/41.00          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.57/41.00    (32)  op(e3, e0) = all_53_12
% 229.57/41.00  
% 229.57/41.00  Begin of proof
% 229.57/41.00  | 
% 229.57/41.00  | ALPHA: (6) implies:
% 229.57/41.00  |   (33)  all_57_13 = e0
% 229.57/41.00  | 
% 229.57/41.00  | COMBINE_EQS: (1), (33) imply:
% 229.57/41.00  |   (34)  e1 = e0
% 229.57/41.00  | 
% 229.57/41.00  | SIMP: (34) implies:
% 229.57/41.00  |   (35)  e1 = e0
% 229.57/41.00  | 
% 229.57/41.00  | COMBINE_EQS: (13), (35) imply:
% 229.57/41.00  |   (36)  all_57_0 = e0
% 229.57/41.00  | 
% 229.57/41.00  | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (14), (15),
% 229.57/41.00  |            (16), (17), (18), (19), (20), (21), (22), (23), (24), (25), (26),
% 229.57/41.00  |            (27), (28), (29), (30), (31), (32), (36) are inconsistent by
% 229.57/41.00  |            sub-proof #891.
% 229.57/41.00  | 
% 229.57/41.00  End of proof
% 229.57/41.00  
% 229.57/41.00  Sub-proof #830 shows that the following formulas are inconsistent:
% 229.57/41.00  ----------------------------------------------------------------
% 229.57/41.00    (1)   ~ (e3 = e1)
% 229.57/41.00    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.57/41.00           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.57/41.00    (3)  all_57_7 = e1
% 229.57/41.00    (4)  all_57_4 = e3
% 229.57/41.00    (5)   ~ (e3 = e0)
% 229.57/41.00    (6)  all_57_1 = e0
% 229.57/41.00    (7)  op(e3, e3) = e0
% 229.57/41.00    (8)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.57/41.00         (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.57/41.00    (9)   ~ (all_53_12 = e3)
% 229.57/41.00    (10)  all_57_7 = e3
% 229.57/41.00    (11)  op(e3, e0) = all_53_12
% 229.57/41.00  
% 229.57/41.00  Begin of proof
% 229.57/41.00  | 
% 229.57/41.00  | COMBINE_EQS: (3), (10) imply:
% 229.57/41.00  |   (12)  e3 = e1
% 229.57/41.00  | 
% 229.57/41.00  | SIMP: (12) implies:
% 229.57/41.00  |   (13)  e3 = e1
% 229.57/41.00  | 
% 229.57/41.00  | COMBINE_EQS: (4), (13) imply:
% 229.57/41.00  |   (14)  all_57_4 = e1
% 229.57/41.00  | 
% 229.57/41.00  | REF_CLOSE: (1), (2), (5), (6), (7), (8), (9), (11), (14) are inconsistent by
% 229.57/41.00  |            sub-proof #2280.
% 229.57/41.00  | 
% 229.57/41.00  End of proof
% 229.57/41.00  
% 229.57/41.00  Sub-proof #831 shows that the following formulas are inconsistent:
% 229.57/41.00  ----------------------------------------------------------------
% 229.57/41.00    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.57/41.00           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.57/41.00    (2)   ~ (e3 = e2)
% 229.57/41.00    (3)   ~ (e3 = e0)
% 229.57/41.00    (4)  op(e2, e2) = e2
% 229.57/41.00    (5)  all_57_2 = e0
% 229.57/41.00    (6)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3)
% 229.57/41.00  
% 229.57/41.00  Begin of proof
% 229.57/41.00  | 
% 229.57/41.00  | BETA: splitting (6) gives:
% 229.57/41.00  | 
% 229.57/41.00  | Case 1:
% 229.57/41.00  | | 
% 229.57/41.00  | |   (7)  all_57_2 = e3 & op(e2, e3) = e3
% 229.57/41.00  | | 
% 229.57/41.00  | | ALPHA: (7) implies:
% 229.57/41.00  | |   (8)  all_57_2 = e3
% 229.57/41.00  | | 
% 229.57/41.00  | | REF_CLOSE: (3), (5), (8) are inconsistent by sub-proof #2258.
% 229.57/41.00  | | 
% 229.57/41.00  | Case 2:
% 229.57/41.00  | | 
% 229.57/41.00  | |   (9)  all_57_3 = e3 & op(e2, e2) = e3
% 229.57/41.00  | | 
% 229.57/41.00  | | ALPHA: (9) implies:
% 229.57/41.00  | |   (10)  op(e2, e2) = e3
% 229.57/41.00  | | 
% 229.57/41.00  | | REF_CLOSE: (1), (2), (4), (10) are inconsistent by sub-proof #2298.
% 229.57/41.00  | | 
% 229.57/41.00  | End of split
% 229.57/41.00  | 
% 229.57/41.00  End of proof
% 229.57/41.00  
% 229.57/41.00  Sub-proof #832 shows that the following formulas are inconsistent:
% 229.57/41.00  ----------------------------------------------------------------
% 229.57/41.00    (1)  all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 229.57/41.00    (2)   ~ (all_53_7 = e3)
% 229.57/41.00    (3)   ~ (all_48_2 = e0) | ( ~ (all_48_0 = e2) & op(all_48_1, e3) = all_48_0 &
% 229.57/41.00           op(e3, e0) = all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 =
% 229.57/41.00             e1) & op(e3, e0) = all_48_1 & $i(all_48_1))
% 229.57/41.00    (4)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 229.57/41.00    (5)  all_48_2 = e0
% 229.57/41.00    (6)   ~ (all_53_6 = all_53_14)
% 229.57/41.00    (7)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 229.57/41.00    (8)   ~ (all_53_6 = e2)
% 229.57/41.00    (9)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.57/41.00         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.57/41.00    (10)  op(e2, e3) = all_53_1
% 229.57/41.00    (11)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.57/41.00          (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.57/41.00    (12)   ~ (all_53_8 = all_53_12)
% 229.57/41.00    (13)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.57/41.00          (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.57/41.00    (14)   ~ (e3 = e1)
% 229.57/41.00    (15)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 229.57/41.00          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 229.57/41.00    (16)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.57/41.00            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.57/41.00    (17)  all_22_2 = e3
% 229.57/41.00    (18)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.57/41.00          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.57/41.00    (19)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 229.57/41.00            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 229.57/41.00              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 229.57/41.00    (20)   ~ (all_53_3 = all_53_7)
% 229.57/41.00    (21)   ~ (all_6_2 = e3)
% 229.57/41.00    (22)  ( ~ (all_18_0 = e1) & op(all_18_1, e3) = all_18_0 & op(e3, e0) =
% 229.57/41.00            all_18_1 & $i(all_18_0) & $i(all_18_1)) | ( ~ (all_18_1 = e2) & op(e3,
% 229.57/41.00              e0) = all_18_1 & $i(all_18_1))
% 229.57/41.00    (23)  op(e1, e1) = all_6_2
% 229.57/41.00    (24)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 229.57/41.00    (25)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 229.57/41.00    (26)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.57/41.00          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.57/41.00    (27)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 229.57/41.00    (28)  all_55_9 = all_53_6
% 229.57/41.00    (29)   ~ (all_53_11 = all_6_2)
% 229.57/41.00    (30)   ~ (all_53_13 = e2)
% 229.57/41.00    (31)   ~ (all_53_4 = all_53_12)
% 229.57/41.00    (32)   ~ (all_53_7 = e2)
% 229.57/41.00    (33)   ~ (all_53_2 = all_6_2)
% 229.57/41.00    (34)   ~ (all_53_13 = e3)
% 229.57/41.00    (35)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.57/41.00          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.57/41.00    (36)  all_55_4 = all_53_1
% 229.57/41.00    (37)   ~ (all_53_12 = all_53_13)
% 229.57/41.00    (38)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.57/41.00          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.57/41.00    (39)   ~ (all_53_14 = all_6_2)
% 229.57/41.00    (40)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 229.57/41.00          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.57/41.00    (41)   ~ (e3 = e2)
% 229.57/41.00    (42)  all_55_1 = all_53_4
% 229.57/41.00    (43)   ~ (all_53_1 = all_53_3)
% 229.57/41.00    (44)  op(e1, e0) = all_53_14
% 229.57/41.00    (45)   ~ (all_53_6 = all_53_7)
% 229.57/41.00    (46)  all_55_7 = e3 | all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 229.57/41.00    (47)   ~ (e3 = e0)
% 229.57/41.00    (48)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 229.57/41.00          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 229.57/41.00    (49)   ~ (all_53_8 = all_6_2)
% 229.57/41.00    (50)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 229.57/41.00    (51)  op(e0, e3) = all_53_3
% 229.57/41.00    (52)   ~ (all_53_2 = e0)
% 229.57/41.00    (53)  all_57_0 = e0
% 229.57/41.00    (54)  all_55_2 = all_53_8
% 229.57/41.00    (55)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 229.57/41.00    (56)   ~ (all_53_4 = all_53_7)
% 229.57/41.00    (57)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 229.57/41.00    (58)  all_57_15 = e3
% 229.57/41.00    (59)  op(e3, e3) = e0
% 229.57/41.00    (60)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.57/41.00          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.57/41.00            e1)
% 229.57/41.00    (61)   ~ (all_53_4 = all_53_8)
% 229.57/41.00    (62)   ~ (all_53_14 = e3)
% 229.57/41.00    (63)  op(e3, e2) = all_53_4
% 229.57/41.00    (64)   ~ (all_53_1 = all_53_2)
% 229.57/41.00    (65)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.57/41.00          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.57/41.00    (66)   ~ (e2 = e0)
% 229.57/41.00    (67)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 229.57/41.00            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 229.57/41.00            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 229.57/41.00            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 229.57/41.00              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 229.57/41.00            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 229.57/41.00            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 229.57/41.00              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 229.57/41.00              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 229.57/41.00            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 229.57/41.00            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 229.57/41.00            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 229.57/41.00              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 229.57/41.00              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 229.57/41.00            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 229.57/41.00              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 229.57/41.00            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 229.57/41.00            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 229.57/41.00              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 229.57/41.00              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 229.57/41.00            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 229.57/41.00            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 229.57/41.00    (68)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 229.57/41.00            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 229.57/41.00              e3) = all_12_1 & $i(all_12_1))
% 229.57/41.00    (69)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.57/41.00          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.57/41.00    (70)   ~ (all_53_1 = e0)
% 229.57/41.00    (71)   ~ (all_53_2 = all_53_14)
% 229.57/41.00    (72)  op(e2, e2) = e2
% 229.57/41.00    (73)   ~ (e1 = e0)
% 229.57/41.00    (74)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 229.57/41.00            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 229.57/41.00              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 229.57/41.00    (75)   ~ (all_53_3 = all_53_11)
% 229.57/41.00    (76)   ~ (all_53_4 = e0)
% 229.57/41.00    (77)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.57/41.00          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.57/41.00    (78)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.57/41.00          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.57/41.00    (79)   ~ (all_53_2 = all_53_3)
% 229.57/41.00    (80)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 229.57/41.00    (81)   ~ (all_53_7 = all_53_11)
% 229.57/41.00    (82)  all_55_8 = all_53_2
% 229.57/41.00    (83)  op(e0, e0) = e3
% 229.57/41.00    (84)   ~ (all_53_4 = all_53_6)
% 229.57/41.00    (85)  op(e0, e2) = all_53_7
% 229.57/41.00    (86)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.57/41.00          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.57/41.00            e2)
% 229.57/41.00    (87)   ~ (all_53_3 = e0)
% 229.57/41.00    (88)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.57/41.00              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.57/41.00                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.57/41.00                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.57/41.00    (89)  all_55_10 = all_6_2
% 229.57/41.00    (90)   ~ (all_53_6 = all_6_2)
% 229.57/41.00    (91)  all_55_13 = all_53_7
% 229.57/41.00    (92)  op(e2, e0) = all_53_13
% 229.57/41.00    (93)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.57/41.00          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.57/41.00    (94)  all_38_2 = all_6_2
% 229.57/41.00    (95)  all_55_11 = all_53_14
% 229.57/41.00    (96)  all_55_3 = all_53_12
% 229.57/41.00    (97)   ~ (all_53_12 = e3)
% 229.57/41.00    (98)   ~ (all_53_4 = e2)
% 229.57/41.00    (99)  op(e1, e3) = all_53_2
% 229.57/41.00    (100)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.57/41.00           (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.57/41.00    (101)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.57/41.00           (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.57/41.00    (102)   ~ (all_53_12 = e0)
% 229.57/41.00    (103)   ~ (all_53_13 = all_53_14)
% 229.57/41.00    (104)   ~ (all_53_8 = e0)
% 229.57/41.00    (105)   ~ (all_53_1 = e2)
% 229.57/41.00    (106)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.57/41.00           (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 229.57/41.00    (107)   ~ (e2 = e1)
% 229.57/41.00    (108)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.57/41.00           | (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.57/41.00             e2)
% 229.57/41.00    (109)   ~ (all_53_2 = all_53_6)
% 229.57/41.00    (110)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.57/41.00           (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.57/41.00    (111)  all_24_2 = all_6_2
% 229.57/41.00    (112)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 229.57/41.00           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 229.57/41.00    (113)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.57/41.01           (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.57/41.01    (114)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.57/41.01           | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.57/41.01             e1)
% 229.57/41.01    (115)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 229.57/41.01           (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 229.57/41.01    (116)   ~ (all_53_12 = all_53_14)
% 229.57/41.01    (117)  all_55_14 = all_53_11
% 229.57/41.01    (118)   ~ (all_22_2 = e3) | ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0
% 229.57/41.01             & op(e0, e3) = all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~
% 229.57/41.01             (all_22_1 = e2) & op(e0, e3) = all_22_1 & $i(all_22_1))
% 229.57/41.01    (119)  all_57_3 = e2
% 229.57/41.01    (120)  all_55_7 = all_53_13
% 229.57/41.01    (121)   ~ (all_53_11 = e3)
% 229.57/41.01    (122)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.57/41.01           (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.57/41.01    (123)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 229.57/41.01           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 229.57/41.01    (124)  op(e3, e0) = all_53_12
% 229.57/41.01  
% 229.57/41.01  Begin of proof
% 229.57/41.01  | 
% 229.57/41.01  | BETA: splitting (118) gives:
% 229.57/41.01  | 
% 229.57/41.01  | Case 1:
% 229.57/41.01  | | 
% 229.57/41.01  | |   (125)   ~ (all_22_2 = e3)
% 229.57/41.01  | | 
% 229.57/41.01  | | REDUCE: (17), (125) imply:
% 229.57/41.01  | |   (126)  $false
% 229.57/41.01  | | 
% 229.57/41.01  | | CLOSE: (126) is inconsistent.
% 229.57/41.01  | | 
% 229.57/41.01  | Case 2:
% 229.57/41.01  | | 
% 229.57/41.01  | |   (127)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 229.57/41.01  | |            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) &
% 229.57/41.01  | |            op(e0, e3) = all_22_1 & $i(all_22_1))
% 229.57/41.01  | | 
% 229.57/41.01  | | BETA: splitting (19) gives:
% 229.57/41.01  | | 
% 229.57/41.01  | | Case 1:
% 229.57/41.01  | | | 
% 229.57/41.01  | | |   (128)   ~ (all_24_2 = e0)
% 229.57/41.01  | | | 
% 229.57/41.01  | | | REDUCE: (111), (128) imply:
% 229.57/41.01  | | |   (129)   ~ (all_6_2 = e0)
% 229.57/41.01  | | | 
% 229.57/41.01  | | | BETA: splitting (74) gives:
% 229.57/41.01  | | | 
% 229.57/41.01  | | | Case 1:
% 229.57/41.01  | | | | 
% 229.57/41.01  | | | |   (130)   ~ (all_38_2 = e2)
% 229.57/41.01  | | | | 
% 229.57/41.01  | | | | REDUCE: (94), (130) imply:
% 229.57/41.01  | | | |   (131)   ~ (all_6_2 = e2)
% 229.57/41.01  | | | | 
% 229.57/41.01  | | | | BETA: splitting (7) gives:
% 229.57/41.01  | | | | 
% 229.57/41.01  | | | | Case 1:
% 229.57/41.01  | | | | | 
% 229.57/41.01  | | | | |   (132)  all_55_10 = e3
% 229.57/41.01  | | | | | 
% 229.57/41.01  | | | | | REF_CLOSE: (21), (89), (132) are inconsistent by sub-proof #2500.
% 229.57/41.01  | | | | | 
% 229.57/41.01  | | | | Case 2:
% 229.57/41.01  | | | | | 
% 229.57/41.01  | | | | |   (133)   ~ (all_55_10 = e3)
% 229.57/41.01  | | | | |   (134)  all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 229.57/41.01  | | | | | 
% 229.57/41.01  | | | | | BETA: splitting (134) gives:
% 229.57/41.01  | | | | | 
% 229.57/41.01  | | | | | Case 1:
% 229.57/41.01  | | | | | | 
% 229.57/41.01  | | | | | |   (135)  all_55_10 = e2
% 229.57/41.01  | | | | | | 
% 229.57/41.01  | | | | | | REF_CLOSE: (89), (131), (135) are inconsistent by sub-proof #2499.
% 229.57/41.01  | | | | | | 
% 229.57/41.01  | | | | | Case 2:
% 229.57/41.01  | | | | | | 
% 229.57/41.01  | | | | | |   (136)   ~ (all_55_10 = e2)
% 229.57/41.01  | | | | | |   (137)  all_55_10 = e1 | all_55_10 = e0
% 229.57/41.01  | | | | | | 
% 229.57/41.01  | | | | | | BETA: splitting (137) gives:
% 229.57/41.01  | | | | | | 
% 229.57/41.01  | | | | | | Case 1:
% 229.57/41.01  | | | | | | | 
% 229.57/41.01  | | | | | | |   (138)  all_55_10 = e1
% 229.57/41.01  | | | | | | | 
% 229.57/41.01  | | | | | | | COMBINE_EQS: (89), (138) imply:
% 229.57/41.01  | | | | | | |   (139)  all_6_2 = e1
% 229.57/41.01  | | | | | | | 
% 229.57/41.01  | | | | | | | SIMP: (139) implies:
% 229.57/41.01  | | | | | | |   (140)  all_6_2 = e1
% 229.57/41.01  | | | | | | | 
% 229.57/41.01  | | | | | | | REDUCE: (33), (140) imply:
% 229.57/41.01  | | | | | | |   (141)   ~ (all_53_2 = e1)
% 229.57/41.01  | | | | | | | 
% 229.57/41.01  | | | | | | | REDUCE: (90), (140) imply:
% 229.57/41.01  | | | | | | |   (142)   ~ (all_53_6 = e1)
% 229.57/41.01  | | | | | | | 
% 229.57/41.01  | | | | | | | REDUCE: (49), (140) imply:
% 229.57/41.01  | | | | | | |   (143)   ~ (all_53_8 = e1)
% 229.57/41.01  | | | | | | | 
% 229.57/41.01  | | | | | | | REDUCE: (29), (140) imply:
% 229.57/41.01  | | | | | | |   (144)   ~ (all_53_11 = e1)
% 229.57/41.01  | | | | | | | 
% 229.57/41.01  | | | | | | | REDUCE: (39), (140) imply:
% 229.57/41.01  | | | | | | |   (145)   ~ (all_53_14 = e1)
% 229.57/41.01  | | | | | | | 
% 229.57/41.01  | | | | | | | REDUCE: (21), (140) imply:
% 229.57/41.01  | | | | | | |   (146)   ~ (e3 = e1)
% 229.57/41.01  | | | | | | | 
% 229.57/41.01  | | | | | | | REDUCE: (131), (140) imply:
% 229.57/41.01  | | | | | | |   (147)   ~ (e2 = e1)
% 229.57/41.01  | | | | | | | 
% 229.57/41.01  | | | | | | | REDUCE: (23), (140) imply:
% 229.57/41.01  | | | | | | |   (148)  op(e1, e1) = e1
% 229.57/41.01  | | | | | | | 
% 229.57/41.01  | | | | | | | BETA: splitting (48) gives:
% 229.57/41.01  | | | | | | | 
% 229.57/41.01  | | | | | | | Case 1:
% 229.57/41.01  | | | | | | | | 
% 229.57/41.01  | | | | | | | |   (149)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 &
% 229.57/41.01  | | | | | | | |            op(e2, e1) = e1)
% 229.57/41.01  | | | | | | | | 
% 229.57/41.01  | | | | | | | | BETA: splitting (149) gives:
% 229.57/41.01  | | | | | | | | 
% 229.57/41.01  | | | | | | | | Case 1:
% 229.57/41.01  | | | | | | | | | 
% 229.57/41.01  | | | | | | | | |   (150)  all_57_4 = e1 & op(e3, e1) = e1
% 229.57/41.01  | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | ALPHA: (150) implies:
% 229.57/41.01  | | | | | | | | |   (151)  all_57_4 = e1
% 229.57/41.01  | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | REF_CLOSE: (3), (5), (9), (11), (13), (14), (15), (16), (18),
% 229.57/41.01  | | | | | | | | |            (21), (22), (23), (26), (35), (38), (40), (41),
% 229.57/41.01  | | | | | | | | |            (47), (48), (50), (51), (52), (53), (58), (59),
% 229.57/41.01  | | | | | | | | |            (60), (65), (66), (67), (68), (69), (72), (73),
% 229.57/41.01  | | | | | | | | |            (77), (78), (79), (82), (83), (86), (87), (88),
% 229.57/41.01  | | | | | | | | |            (89), (93), (97), (99), (100), (101), (102), (106),
% 229.57/41.01  | | | | | | | | |            (107), (108), (110), (112), (113), (114), (115),
% 229.57/41.01  | | | | | | | | |            (119), (122), (123), (124), (127), (129), (131),
% 229.57/41.01  | | | | | | | | |            (137), (148), (151) are inconsistent by sub-proof
% 229.57/41.01  | | | | | | | | |            #944.
% 229.57/41.01  | | | | | | | | | 
% 229.57/41.01  | | | | | | | | Case 2:
% 229.57/41.01  | | | | | | | | | 
% 229.57/41.01  | | | | | | | | |   (152)  all_57_5 = e1 & op(e2, e1) = e1
% 229.57/41.01  | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | ALPHA: (152) implies:
% 229.57/41.01  | | | | | | | | |   (153)  all_57_5 = e1
% 229.57/41.01  | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | REF_CLOSE: (14), (16), (21), (23), (40), (41), (47), (58),
% 229.57/41.01  | | | | | | | | |            (60), (66), (73), (77), (86), (88), (107), (112),
% 229.57/41.01  | | | | | | | | |            (148), (153) are inconsistent by sub-proof #941.
% 229.57/41.01  | | | | | | | | | 
% 229.57/41.01  | | | | | | | | End of split
% 229.57/41.01  | | | | | | | | 
% 229.57/41.01  | | | | | | | Case 2:
% 229.57/41.01  | | | | | | | | 
% 229.57/41.01  | | | | | | | |   (154)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 &
% 229.57/41.01  | | | | | | | |            op(e0, e1) = e1)
% 229.57/41.01  | | | | | | | | 
% 229.57/41.01  | | | | | | | | BETA: splitting (154) gives:
% 229.57/41.01  | | | | | | | | 
% 229.57/41.01  | | | | | | | | Case 1:
% 229.57/41.01  | | | | | | | | | 
% 229.57/41.01  | | | | | | | | |   (155)  all_57_8 = e1 & op(e1, e1) = e1
% 229.57/41.01  | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | ALPHA: (155) implies:
% 229.57/41.01  | | | | | | | | |   (156)  all_57_8 = e1
% 229.57/41.01  | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | BETA: splitting (3) gives:
% 229.57/41.01  | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | Case 1:
% 229.57/41.01  | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | |   (157)   ~ (all_48_2 = e0)
% 229.57/41.01  | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | REDUCE: (5), (157) imply:
% 229.57/41.01  | | | | | | | | | |   (158)  $false
% 229.57/41.01  | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | CLOSE: (158) is inconsistent.
% 229.57/41.01  | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | Case 2:
% 229.57/41.01  | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | |   (159)  ( ~ (all_48_0 = e2) & op(all_48_1, e3) = all_48_0 &
% 229.57/41.01  | | | | | | | | | |            op(e3, e0) = all_48_1 & $i(all_48_0) &
% 229.57/41.01  | | | | | | | | | |            $i(all_48_1)) | ( ~ (all_48_1 = e1) & op(e3, e0)
% 229.57/41.01  | | | | | | | | | |            = all_48_1 & $i(all_48_1))
% 229.57/41.01  | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | BETA: splitting (1) gives:
% 229.57/41.01  | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | Case 1:
% 229.57/41.01  | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | |   (160)  all_55_13 = e3
% 229.57/41.01  | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | REF_CLOSE: (2), (91), (160) are inconsistent by sub-proof
% 229.57/41.01  | | | | | | | | | | |            #2080.
% 229.57/41.01  | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | Case 2:
% 229.57/41.01  | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | |   (161)   ~ (all_55_13 = e3)
% 229.57/41.01  | | | | | | | | | | |   (162)  all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 229.57/41.01  | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | BETA: splitting (24) gives:
% 229.57/41.01  | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | Case 1:
% 229.57/41.01  | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | |   (163)  all_55_3 = e3
% 229.57/41.01  | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | REF_CLOSE: (96), (97), (163) are inconsistent by sub-proof
% 229.57/41.01  | | | | | | | | | | | |            #2169.
% 229.57/41.01  | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | Case 2:
% 229.57/41.01  | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | |   (164)   ~ (all_55_3 = e3)
% 229.57/41.01  | | | | | | | | | | | |   (165)  all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 229.57/41.01  | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | BETA: splitting (4) gives:
% 229.57/41.01  | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | Case 1:
% 229.57/41.01  | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | |   (166)  all_55_1 = e3
% 229.57/41.01  | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | COMBINE_EQS: (42), (166) imply:
% 229.57/41.01  | | | | | | | | | | | | |   (167)  all_53_4 = e3
% 229.57/41.01  | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | SIMP: (167) implies:
% 229.57/41.01  | | | | | | | | | | | | |   (168)  all_53_4 = e3
% 229.57/41.01  | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | REDUCE: (84), (168) imply:
% 229.57/41.01  | | | | | | | | | | | | |   (169)   ~ (all_53_6 = e3)
% 229.57/41.01  | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | SIMP: (169) implies:
% 229.57/41.01  | | | | | | | | | | | | |   (170)   ~ (all_53_6 = e3)
% 229.57/41.01  | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | REDUCE: (61), (168) imply:
% 229.57/41.01  | | | | | | | | | | | | |   (171)   ~ (all_53_8 = e3)
% 229.57/41.01  | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | SIMP: (171) implies:
% 229.57/41.01  | | | | | | | | | | | | |   (172)   ~ (all_53_8 = e3)
% 229.57/41.01  | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | REDUCE: (31), (168) imply:
% 229.57/41.01  | | | | | | | | | | | | |   (173)   ~ (all_53_12 = e3)
% 229.57/41.01  | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | BETA: splitting (69) gives:
% 229.57/41.01  | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | Case 1:
% 229.57/41.01  | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | |   (174)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 229.57/41.01  | | | | | | | | | | | | | |            & op(e3, e2) = e3)
% 229.57/41.01  | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | BETA: splitting (174) gives:
% 229.57/41.01  | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | Case 1:
% 229.57/41.01  | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | |   (175)  all_57_0 = e3 & op(e3, e3) = e3
% 229.57/41.01  | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | ALPHA: (175) implies:
% 229.57/41.01  | | | | | | | | | | | | | | |   (176)  op(e3, e3) = e3
% 229.57/41.01  | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | REF_CLOSE: (16), (47), (59), (176) are inconsistent by
% 229.57/41.01  | | | | | | | | | | | | | | |            sub-proof #2494.
% 229.57/41.01  | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | Case 2:
% 229.57/41.01  | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | |   (177)  all_57_1 = e3 & op(e3, e2) = e3
% 229.57/41.01  | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | ALPHA: (177) implies:
% 229.57/41.01  | | | | | | | | | | | | | | |   (178)  all_57_1 = e3
% 229.57/41.01  | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | BETA: splitting (122) gives:
% 229.57/41.01  | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | Case 1:
% 229.57/41.01  | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | |   (179)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 229.57/41.01  | | | | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 229.57/41.01  | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | REF_CLOSE: (3), (5), (9), (11), (13), (14), (15), (16), (18),
% 229.57/41.01  | | | | | | | | | | | | | | | |            (21), (22), (23), (26), (35), (38), (40), (41),
% 229.57/41.01  | | | | | | | | | | | | | | | |            (47), (48), (50), (51), (52), (53), (58), (59),
% 229.57/41.01  | | | | | | | | | | | | | | | |            (60), (65), (66), (67), (68), (69), (77), (78),
% 229.57/41.01  | | | | | | | | | | | | | | | |            (79), (82), (83), (86), (87), (88), (89), (93),
% 229.57/41.01  | | | | | | | | | | | | | | | |            (97), (99), (100), (101), (102), (106), (108),
% 229.57/41.01  | | | | | | | | | | | | | | | |            (110), (112), (113), (114), (115), (122), (123),
% 229.57/41.01  | | | | | | | | | | | | | | | |            (124), (127), (129), (131), (137), (178), (179)
% 229.57/41.01  | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #962.
% 229.57/41.01  | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | Case 2:
% 229.57/41.01  | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | |   (180)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 229.57/41.01  | | | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 229.57/41.01  | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | BETA: splitting (180) gives:
% 229.57/41.01  | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.01  | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | |   (181)  all_57_7 = e1 & op(e1, e2) = e1
% 229.57/41.01  | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | ALPHA: (181) implies:
% 229.57/41.01  | | | | | | | | | | | | | | | | |   (182)  all_57_7 = e1
% 229.57/41.01  | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (15), (16), (18), (21), (23), (41), (47),
% 229.57/41.01  | | | | | | | | | | | | | | | | |            (58), (66), (73), (88), (107), (108), (114),
% 229.57/41.01  | | | | | | | | | | | | | | | | |            (123), (148), (182) are inconsistent by sub-proof
% 229.57/41.01  | | | | | | | | | | | | | | | | |            #1069.
% 229.57/41.01  | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.01  | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | |   (183)  all_57_13 = e1 & op(e0, e2) = e1
% 229.57/41.01  | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | ALPHA: (183) implies:
% 229.57/41.01  | | | | | | | | | | | | | | | | |   (184)  all_57_13 = e1
% 229.57/41.01  | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | BETA: splitting (26) gives:
% 229.57/41.01  | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | |   (185)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 229.57/41.01  | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e1)
% 229.57/41.01  | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | |   (186)  all_57_0 = e1 & op(e3, e3) = e1
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (53), (73), (186) are inconsistent by sub-proof
% 229.57/41.01  | | | | | | | | | | | | | | | | | | |            #2454.
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | |   (187)  all_57_1 = e1 & op(e3, e2) = e1
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (178), (187) are inconsistent by sub-proof
% 229.57/41.01  | | | | | | | | | | | | | | | | | | |            #2453.
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.01  | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | |   (188)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 229.57/41.01  | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e1)
% 229.57/41.01  | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | BETA: splitting (188) gives:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | |   (189)  all_57_4 = e1 & op(e3, e1) = e1
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | ALPHA: (189) implies:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | |   (190)  all_57_4 = e1
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (13), (14), (15), (16), (18), (21), (23),
% 229.57/41.01  | | | | | | | | | | | | | | | | | | |            (26), (35), (38), (40), (41), (47), (58), (59),
% 229.57/41.01  | | | | | | | | | | | | | | | | | | |            (60), (65), (66), (68), (69), (72), (73), (77),
% 229.57/41.01  | | | | | | | | | | | | | | | | | | |            (83), (86), (88), (93), (97), (107), (108), (110),
% 229.57/41.01  | | | | | | | | | | | | | | | | | | |            (112), (113), (114), (115), (119), (122), (123),
% 229.57/41.01  | | | | | | | | | | | | | | | | | | |            (124), (127), (148), (156), (178), (184), (190)
% 229.57/41.01  | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #946.
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | |   (191)  all_57_9 = e1 & op(e3, e0) = e1
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | ALPHA: (191) implies:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | |   (192)  all_57_9 = e1
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | BETA: splitting (77) gives:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | |   (193)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e3)
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | |   (194)  all_57_4 = e3 & op(e3, e1) = e3
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | ALPHA: (194) implies:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | |   (195)  all_57_4 = e3
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (16), (26), (35), (38), (41), (47), (59),
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | |            (66), (73), (107), (178), (195) are inconsistent
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1220.
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | |   (196)  all_57_5 = e3 & op(e2, e1) = e3
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | ALPHA: (196) implies:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | |   (197)  all_57_5 = e3
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (106) gives:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | |   (198)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e0)
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | |   (199)  all_57_2 = e0 & op(e2, e3) = e0
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (199) implies:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | |   (200)  all_57_2 = e0
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (65) gives:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | |   (201)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e0)
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (202)  all_57_1 = e0 & op(e3, e2) = e0
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (202) implies:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (203)  all_57_1 = e0
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (35), (41), (47), (59), (66), (69), (97),
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | |            (107), (124), (192), (203) are inconsistent by
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2400.
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (204)  all_57_3 = e0 & op(e2, e2) = e0
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (204) implies:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (205)  all_57_3 = e0
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (14), (41), (47), (66), (73), (93), (100),
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | |            (107), (200), (205) are inconsistent by sub-proof
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | |            #2246.
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | |   (206)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0)
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (207)  all_57_7 = e0 & op(e1, e2) = e0
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (207) implies:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (208)  all_57_7 = e0
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18) gives:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | |   (209)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e3)
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (210)  all_57_6 = e3 & op(e1, e3) = e3
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (210) implies:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (211)  all_57_6 = e3
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (11), (12), (13), (14), (15), (16),
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18), (21), (22), (23), (25), (26), (27), (28),
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (30), (34), (35), (36), (37), (38), (40), (46),
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (47), (48), (50), (51), (53), (54), (55), (57),
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (58), (59), (60), (62), (64), (65), (67), (69),
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (70), (71), (72), (73), (77), (78), (82), (83),
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (86), (87), (88), (92), (93), (95), (96), (97),
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (99), (100), (101), (102), (104), (105), (106),
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (108), (109), (110), (112), (113), (114), (115),
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (116), (119), (120), (122), (123), (124), (141),
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (142), (143), (148), (159), (165), (170), (172),
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (178), (192), (208), (211) are inconsistent by
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #884.
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (212)  all_57_7 = e3 & op(e1, e2) = e3
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (212) implies:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (213)  all_57_7 = e3
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (14), (16), (41), (47), (65), (66), (72),
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (73), (107), (122), (178), (213) are inconsistent
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1167.
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | |   (214)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e1, e0) = e3)
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (16), (21), (23), (41), (47), (58), (66),
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | |            (73), (88), (107), (108), (114), (214) are
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1786.
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (215)  all_57_13 = e0 & op(e0, e2) = e0
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (215) implies:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (216)  op(e0, e2) = e0
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (16), (27), (28), (45), (85), (142), (170),
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | |            (216) are inconsistent by sub-proof #883.
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | |   (217)  all_57_3 = e0 & op(e2, e2) = e0
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (217) implies:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | |   (218)  op(e2, e2) = e0
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (66), (72), (218) are inconsistent by
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2472.
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | |   (219)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e2, e0) = e0)
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | |   (220)  all_57_5 = e0 & op(e2, e1) = e0
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (220) implies:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | |   (221)  all_57_5 = e0
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (14), (16), (21), (23), (26), (35), (38),
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | |            (41), (47), (53), (58), (59), (60), (66), (69),
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | |            (73), (77), (78), (83), (86), (88), (97), (102),
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | |            (107), (108), (114), (119), (122), (124), (178),
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | |            (221) are inconsistent by sub-proof #880.
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | |   (222)  all_57_10 = e0 & op(e2, e0) = e0
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (222) implies:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | |   (223)  all_57_10 = e0
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (65) gives:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | |   (224)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e0)
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (225)  all_57_1 = e0 & op(e3, e2) = e0
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (225) implies:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (226)  all_57_1 = e0
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (35), (41), (47), (59), (66), (69), (97),
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | |            (107), (124), (192), (226) are inconsistent by
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2400.
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (227)  all_57_3 = e0 & op(e2, e2) = e0
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (227) implies:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (228)  all_57_3 = e0
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (14), (41), (66), (73), (100), (107), (197),
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | |            (223), (228) are inconsistent by sub-proof #1518.
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | |   (229)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0)
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (230)  all_57_7 = e0 & op(e1, e2) = e0
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (230) implies:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (231)  all_57_7 = e0
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18) gives:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | |   (232)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e3)
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (233)  all_57_6 = e3 & op(e1, e3) = e3
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (233) implies:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (234)  all_57_6 = e3
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (11), (12), (13), (14), (15), (16),
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (18), (21), (22), (23), (25), (26), (27), (28),
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (30), (34), (35), (36), (37), (38), (40), (46),
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (47), (48), (50), (51), (53), (54), (55), (57),
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (58), (59), (60), (62), (64), (65), (67), (69),
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (70), (71), (72), (73), (77), (78), (82), (83),
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (86), (87), (88), (92), (93), (95), (96), (97),
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (99), (100), (101), (102), (104), (105), (106),
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (108), (109), (110), (112), (113), (114), (115),
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (116), (119), (120), (122), (123), (124), (141),
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (142), (143), (148), (159), (165), (170), (172),
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (178), (192), (231), (234) are inconsistent by
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #884.
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (235)  all_57_7 = e3 & op(e1, e2) = e3
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (235) implies:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (236)  all_57_7 = e3
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (14), (16), (41), (47), (65), (66), (72),
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (73), (107), (122), (178), (236) are inconsistent
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1167.
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | |   (237)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e1, e0) = e3)
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (16), (21), (23), (41), (58), (66), (73),
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | |            (107), (108), (114), (223), (237) are inconsistent
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #978.
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (238)  all_57_13 = e0 & op(e0, e2) = e0
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (238) implies:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (239)  op(e0, e2) = e0
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (16), (27), (28), (45), (85), (142), (170),
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | |            (239) are inconsistent by sub-proof #883.
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | |   (240)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e1) = e3)
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (16), (21), (23), (41), (47), (58), (60),
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | |            (66), (73), (86), (88), (107), (240) are
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1794.
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.01  | | | | | | | | | | | | | | | | | | | 
% 229.57/41.01  | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.01  | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | End of split
% 229.57/41.02  | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | End of split
% 229.57/41.02  | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | End of split
% 229.57/41.02  | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | End of split
% 229.57/41.02  | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | Case 2:
% 229.57/41.02  | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | |   (241)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 229.57/41.02  | | | | | | | | | | | | | |            & op(e3, e0) = e3)
% 229.57/41.02  | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 229.57/41.02  | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | Case 1:
% 229.57/41.02  | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | |   (242)  all_57_4 = e3 & op(e3, e1) = e3
% 229.57/41.02  | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | ALPHA: (242) implies:
% 229.57/41.02  | | | | | | | | | | | | | | |   (243)  all_57_4 = e3
% 229.57/41.02  | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | BETA: splitting (78) gives:
% 229.57/41.02  | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | Case 1:
% 229.57/41.02  | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | |   (244)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 229.57/41.02  | | | | | | | | | | | | | | | |            & op(e2, e2) = e3)
% 229.57/41.02  | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | REF_CLOSE: (14), (16), (26), (35), (38), (41), (47), (59),
% 229.57/41.02  | | | | | | | | | | | | | | | |            (66), (73), (107), (119), (243), (244) are
% 229.57/41.02  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #892.
% 229.57/41.02  | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | Case 2:
% 229.57/41.02  | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | |   (245)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 229.57/41.02  | | | | | | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 229.57/41.02  | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 229.57/41.02  | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.02  | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | |   (246)  all_57_7 = e3 & op(e1, e2) = e3
% 229.57/41.02  | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | ALPHA: (246) implies:
% 229.57/41.02  | | | | | | | | | | | | | | | | |   (247)  all_57_7 = e3
% 229.57/41.02  | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | BETA: splitting (65) gives:
% 229.57/41.02  | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | |   (248)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 229.57/41.02  | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e0)
% 229.57/41.02  | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (14), (16), (26), (35), (38), (41), (47),
% 229.57/41.02  | | | | | | | | | | | | | | | | | |            (53), (58), (59), (60), (66), (69), (72), (73),
% 229.57/41.02  | | | | | | | | | | | | | | | | | |            (78), (83), (86), (88), (97), (102), (107), (108),
% 229.57/41.02  | | | | | | | | | | | | | | | | | |            (114), (119), (122), (124), (248) are inconsistent
% 229.57/41.02  | | | | | | | | | | | | | | | | | |            by sub-proof #879.
% 229.57/41.02  | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | |   (249)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 229.57/41.02  | | | | | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0)
% 229.57/41.02  | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | |   (250)  all_57_7 = e0 & op(e1, e2) = e0
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (47), (247), (250) are inconsistent by sub-proof
% 229.57/41.02  | | | | | | | | | | | | | | | | | | |            #2042.
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | |   (251)  all_57_13 = e0 & op(e0, e2) = e0
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | ALPHA: (251) implies:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | |   (252)  op(e0, e2) = e0
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (16), (27), (28), (45), (85), (142), (170),
% 229.57/41.02  | | | | | | | | | | | | | | | | | | |            (252) are inconsistent by sub-proof #883.
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.02  | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | End of split
% 229.57/41.02  | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.02  | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | |   (253)  all_57_13 = e3 & op(e0, e2) = e3
% 229.57/41.02  | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | ALPHA: (253) implies:
% 229.57/41.02  | | | | | | | | | | | | | | | | |   (254)  all_57_13 = e3
% 229.57/41.02  | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (16), (41), (47), (58), (60), (66), (73),
% 229.57/41.02  | | | | | | | | | | | | | | | | |            (83), (86), (88), (107), (254) are inconsistent by
% 229.57/41.02  | | | | | | | | | | | | | | | | |            sub-proof #1792.
% 229.57/41.02  | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | End of split
% 229.57/41.02  | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | End of split
% 229.57/41.02  | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | Case 2:
% 229.57/41.02  | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | |   (255)  all_57_9 = e3 & op(e3, e0) = e3
% 229.57/41.02  | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | ALPHA: (255) implies:
% 229.57/41.02  | | | | | | | | | | | | | | |   (256)  op(e3, e0) = e3
% 229.57/41.02  | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | REF_CLOSE: (16), (97), (124), (256) are inconsistent by
% 229.57/41.02  | | | | | | | | | | | | | | |            sub-proof #2458.
% 229.57/41.02  | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | End of split
% 229.57/41.02  | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | End of split
% 229.57/41.02  | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | Case 2:
% 229.57/41.02  | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | |   (257)   ~ (all_55_1 = e3)
% 229.57/41.02  | | | | | | | | | | | | |   (258)  all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 229.57/41.02  | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | REDUCE: (42), (257) imply:
% 229.57/41.02  | | | | | | | | | | | | |   (259)   ~ (all_53_4 = e3)
% 229.57/41.02  | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | BETA: splitting (258) gives:
% 229.57/41.02  | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | Case 1:
% 229.57/41.02  | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | |   (260)  all_55_1 = e2
% 229.57/41.02  | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | REF_CLOSE: (42), (98), (260) are inconsistent by sub-proof
% 229.57/41.02  | | | | | | | | | | | | | |            #2284.
% 229.57/41.02  | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | Case 2:
% 229.57/41.02  | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | |   (261)   ~ (all_55_1 = e2)
% 229.57/41.02  | | | | | | | | | | | | | |   (262)  all_55_1 = e1 | all_55_1 = e0
% 229.57/41.02  | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | BETA: splitting (69) gives:
% 229.57/41.02  | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | Case 1:
% 229.57/41.02  | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | |   (263)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 229.57/41.02  | | | | | | | | | | | | | | |            & op(e3, e2) = e3)
% 229.57/41.02  | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | BETA: splitting (263) gives:
% 229.57/41.02  | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | Case 1:
% 229.57/41.02  | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | |   (264)  all_57_0 = e3 & op(e3, e3) = e3
% 229.57/41.02  | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | ALPHA: (264) implies:
% 229.57/41.02  | | | | | | | | | | | | | | | |   (265)  op(e3, e3) = e3
% 229.57/41.02  | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | REF_CLOSE: (16), (47), (59), (265) are inconsistent by
% 229.57/41.02  | | | | | | | | | | | | | | | |            sub-proof #2494.
% 229.57/41.02  | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | Case 2:
% 229.57/41.02  | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | |   (266)  all_57_1 = e3 & op(e3, e2) = e3
% 229.57/41.02  | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | ALPHA: (266) implies:
% 229.57/41.02  | | | | | | | | | | | | | | | |   (267)  all_57_1 = e3
% 229.57/41.02  | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | BETA: splitting (122) gives:
% 229.57/41.02  | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.02  | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | |   (268)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 229.57/41.02  | | | | | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 229.57/41.02  | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (5), (9), (11), (13), (14), (15), (16), (18),
% 229.57/41.02  | | | | | | | | | | | | | | | | |            (21), (22), (23), (26), (35), (38), (40), (41),
% 229.57/41.02  | | | | | | | | | | | | | | | | |            (47), (48), (50), (51), (52), (53), (58), (59),
% 229.57/41.02  | | | | | | | | | | | | | | | | |            (60), (65), (66), (67), (68), (69), (77), (78),
% 229.57/41.02  | | | | | | | | | | | | | | | | |            (79), (82), (83), (86), (87), (88), (89), (93),
% 229.57/41.02  | | | | | | | | | | | | | | | | |            (97), (99), (100), (101), (102), (106), (108),
% 229.57/41.02  | | | | | | | | | | | | | | | | |            (110), (112), (113), (114), (115), (122), (123),
% 229.57/41.02  | | | | | | | | | | | | | | | | |            (124), (127), (129), (131), (137), (267), (268)
% 229.57/41.02  | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #962.
% 229.57/41.02  | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.02  | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | |   (269)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 229.57/41.02  | | | | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 229.57/41.02  | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | BETA: splitting (269) gives:
% 229.57/41.02  | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | |   (270)  all_57_7 = e1 & op(e1, e2) = e1
% 229.57/41.02  | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | ALPHA: (270) implies:
% 229.57/41.02  | | | | | | | | | | | | | | | | | |   (271)  all_57_7 = e1
% 229.57/41.02  | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (15), (16), (18), (21), (23), (41), (47),
% 229.57/41.02  | | | | | | | | | | | | | | | | | |            (58), (66), (73), (88), (107), (108), (114),
% 229.57/41.02  | | | | | | | | | | | | | | | | | |            (123), (148), (271) are inconsistent by sub-proof
% 229.57/41.02  | | | | | | | | | | | | | | | | | |            #1069.
% 229.57/41.02  | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | |   (272)  all_57_13 = e1 & op(e0, e2) = e1
% 229.57/41.02  | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | ALPHA: (272) implies:
% 229.57/41.02  | | | | | | | | | | | | | | | | | |   (273)  all_57_13 = e1
% 229.57/41.02  | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | BETA: splitting (26) gives:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | |   (274)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 229.57/41.02  | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e1)
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | BETA: splitting (274) gives:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | |   (275)  all_57_0 = e1 & op(e3, e3) = e1
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (53), (73), (275) are inconsistent by sub-proof
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | |            #2454.
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | |   (276)  all_57_1 = e1 & op(e3, e2) = e1
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (267), (276) are inconsistent by sub-proof
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | |            #2453.
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | |   (277)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 229.57/41.02  | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e1)
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | BETA: splitting (277) gives:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | |   (278)  all_57_4 = e1 & op(e3, e1) = e1
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | ALPHA: (278) implies:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | |   (279)  all_57_4 = e1
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (5), (9), (11), (13), (14), (15), (16), (18),
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | |            (21), (22), (23), (26), (35), (38), (40), (41),
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | |            (47), (48), (50), (51), (52), (53), (58), (59),
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | |            (60), (65), (66), (67), (68), (69), (72), (73),
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | |            (77), (78), (79), (82), (83), (86), (87), (88),
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | |            (89), (93), (97), (99), (100), (101), (102),
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | |            (106), (107), (108), (110), (112), (113), (114),
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | |            (115), (119), (122), (123), (124), (127), (129),
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | |            (131), (137), (148), (267), (279) are inconsistent
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | |            by sub-proof #945.
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | |   (280)  all_57_9 = e1 & op(e3, e0) = e1
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | ALPHA: (280) implies:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | |   (281)  all_57_9 = e1
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | BETA: splitting (262) gives:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | |   (282)  all_55_1 = e1
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (42), (282) imply:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | |   (283)  all_53_4 = e1
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | REDUCE: (56), (283) imply:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | |   (284)   ~ (all_53_7 = e1)
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | SIMP: (284) implies:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | |   (285)   ~ (all_53_7 = e1)
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (108) gives:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | |   (286)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (286) gives:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | |   (287)  all_57_9 = e2 & op(e3, e0) = e2
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (287) implies:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | |   (288)  all_57_9 = e2
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (107), (281), (288) are inconsistent by sub-proof
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | |            #2444.
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | |   (289)  all_57_10 = e2 & op(e2, e0) = e2
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (30), (92), (289) are inconsistent by
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2432.
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | |   (290)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (290) gives:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | |   (291)  all_57_11 = e2 & op(e1, e0) = e2
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (291) implies:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | |   (292)  all_57_11 = e2
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (162) gives:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | |   (293)  all_55_13 = e2
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (32), (91), (293) are inconsistent by sub-proof
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | |            #2287.
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | |   (294)   ~ (all_55_13 = e2)
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | |   (295)  all_55_13 = e1 | all_55_13 = e0
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (295) gives:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | |   (296)  all_55_13 = e1
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (91), (285), (296) are inconsistent by sub-proof
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | |            #2002.
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | |   (297)  all_55_13 = e0
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (91), (297) imply:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | |   (298)  all_53_7 = e0
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (298) implies:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | |   (299)  all_53_7 = e0
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (81), (299) imply:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | |   (300)   ~ (all_53_11 = e0)
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (300) implies:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | |   (301)   ~ (all_53_11 = e0)
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2), (299) imply:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | |   (302)   ~ (e3 = e0)
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (32), (299) imply:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | |   (303)   ~ (e2 = e0)
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (285), (299) imply:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | |   (304)   ~ (e1 = e0)
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (80) gives:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | |   (305)  all_55_14 = e3
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (117), (305) imply:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | |   (306)  all_53_11 = e3
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (306) imply:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | |   (307)  $false
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (307) is inconsistent.
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | |   (308)  all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (35) gives:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (309)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e2)
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (41), (59), (66), (267), (309) are
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1224.
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (310)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e2)
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (310) gives:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (311)  all_57_4 = e2 & op(e3, e1) = e2
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (311) implies:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (312)  all_57_4 = e2
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (88) gives:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (313)  all_57_15 = e0 & op(e0, e0) = e0
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (313) implies:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (314)  op(e0, e0) = e0
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (47), (83), (314) are inconsistent by
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2304.
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (315)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (315) implies:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (316)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e0)
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (317)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e0)
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (316) gives:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (318)  all_57_12 = e0 & op(e0, e3) = e0
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (318) implies:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (319)  op(e0, e3) = e0
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (51), (87), (319) are inconsistent by
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2366.
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (320)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (320) gives:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (321)  all_57_13 = e0 & op(e0, e2) = e0
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (73), (273), (321) are inconsistent by sub-proof
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1920.
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (322)  all_57_14 = e0 & op(e0, e1) = e0
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (322) implies:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (323)  all_57_14 = e0
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (101) gives:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (324)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e3)
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (324) gives:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (325)  all_57_0 = e3 & op(e3, e3) = e3
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (13), (14), (16), (18), (21), (23), (41),
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (47), (58), (65), (66), (72), (73), (88), (107),
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (108), (110), (113), (114), (122), (267), (325)
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #878.
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (326)  all_57_2 = e3 & op(e2, e3) = e3
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (326) implies:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (327)  all_57_2 = e3
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (18) gives:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (328)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e3)
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (328) gives:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (329)  all_57_6 = e3 & op(e1, e3) = e3
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (329) implies:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (330)  all_57_6 = e3
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (14), (16), (41), (53), (59), (66), (73),
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (107), (110), (327), (330) are inconsistent by
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1287.
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (331)  all_57_7 = e3 & op(e1, e2) = e3
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (331) implies:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (332)  all_57_7 = e3
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (14), (41), (47), (65), (66), (73), (107),
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (122), (267), (273), (332) are inconsistent by
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1214.
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (333)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e1, e0) = e3)
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (16), (21), (23), (41), (47), (58), (66),
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (73), (107), (108), (114), (317), (333) are
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1080.
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (334)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e3) = e3)
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (334) gives:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (335)  all_57_6 = e3 & op(e1, e3) = e3
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (335) implies:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (336)  all_57_6 = e3
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (110) gives:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (337)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e2)
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (337) gives:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (338)  all_57_0 = e2 & op(e3, e3) = e2
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (338) implies:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (339)  op(e3, e3) = e2
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (38), (41), (47), (66), (69), (73), (97),
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (124), (281), (312), (339) are inconsistent by
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #873.
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (340)  all_57_2 = e2 & op(e2, e3) = e2
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (340) implies:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (341)  all_57_2 = e2
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (86) gives:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (342)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (342) gives:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (343)  all_57_12 = e2 & op(e0, e3) = e2
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (51), (75), (117), (144), (301), (308),
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (343) are inconsistent by sub-proof #872.
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (344)  all_57_13 = e2 & op(e0, e2) = e2
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (344) implies:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (345)  op(e0, e2) = e2
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (32), (85), (345) are inconsistent by
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2335.
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (346)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (346) gives:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (347)  all_57_14 = e2 & op(e0, e1) = e2
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (347) implies:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (348)  all_57_14 = e2
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (323), (348) imply:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (349)  e2 = e0
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (14), (41), (47), (66), (73), (93), (100),
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (107), (119), (341), (349) are inconsistent by
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2245.
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (350)  all_57_15 = e2 & op(e0, e0) = e2
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (350) implies:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (351)  all_57_15 = e2
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (58), (351) imply:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (352)  e3 = e2
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (14), (16), (18), (21), (23), (41), (47),
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (58), (65), (66), (73), (88), (107), (108), (114),
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (122), (267), (273), (336), (352) are inconsistent
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #953.
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (353)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e3) = e2)
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (353) gives:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (354)  all_57_6 = e2 & op(e1, e3) = e2
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (354) implies:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (355)  all_57_6 = e2
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (14), (16), (18), (21), (23), (41), (47),
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (58), (65), (66), (73), (88), (107), (108), (114),
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (122), (267), (273), (355) are inconsistent by
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #961.
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (356)  all_57_12 = e2 & op(e0, e3) = e2
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (51), (75), (117), (144), (301), (308),
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (356) are inconsistent by sub-proof #872.
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (357)  all_57_12 = e3 & op(e0, e3) = e3
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (357) implies:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (358)  all_57_12 = e3
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (41), (58), (60), (66), (73), (86), (107),
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (323), (358) are inconsistent by sub-proof #1763.
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (359)  all_57_9 = e2 & op(e3, e0) = e2
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (359) implies:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (360)  all_57_9 = e2
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (281), (360) imply:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (361)  e2 = e1
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (361) implies:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (362)  e2 = e1
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (292), (362) imply:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (363)  all_57_11 = e1
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (14), (15), (16), (18), (21), (23), (41),
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (47), (58), (65), (66), (73), (88), (107), (108),
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (114), (122), (123), (148), (267), (273), (360),
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (363) are inconsistent by sub-proof #955.
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | |   (364)  all_57_15 = e2 & op(e0, e0) = e2
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (364) implies:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | |   (365)  all_57_15 = e2
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (58), (365) are inconsistent by sub-proof
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | |            #2058.
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | |   (366)  all_55_1 = e0
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (42), (366) imply:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | |   (367)  all_53_4 = e0
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | REDUCE: (76), (367) imply:
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | |   (368)  $false
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | CLOSE: (368) is inconsistent.
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.02  | | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.02  | | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | | End of split
% 229.57/41.02  | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | End of split
% 229.57/41.02  | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | End of split
% 229.57/41.02  | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | Case 2:
% 229.57/41.02  | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | |   (369)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 229.57/41.02  | | | | | | | | | | | | | | |            & op(e3, e0) = e3)
% 229.57/41.02  | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | BETA: splitting (369) gives:
% 229.57/41.02  | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | Case 1:
% 229.57/41.02  | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | |   (370)  all_57_4 = e3 & op(e3, e1) = e3
% 229.57/41.02  | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | ALPHA: (370) implies:
% 229.57/41.02  | | | | | | | | | | | | | | | |   (371)  all_57_4 = e3
% 229.57/41.02  | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | BETA: splitting (78) gives:
% 229.57/41.02  | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.02  | | | | | | | | | | | | | | | | | 
% 229.57/41.02  | | | | | | | | | | | | | | | | |   (372)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 229.57/41.02  | | | | | | | | | | | | | | | | |            & op(e2, e2) = e3)
% 229.57/41.02  | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (16), (26), (35), (38), (41), (47), (59),
% 229.57/41.03  | | | | | | | | | | | | | | | | |            (66), (73), (107), (119), (371), (372) are
% 229.57/41.03  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #892.
% 229.57/41.03  | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.03  | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | |   (373)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 229.57/41.03  | | | | | | | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 229.57/41.03  | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | BETA: splitting (373) gives:
% 229.57/41.03  | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | |   (374)  all_57_7 = e3 & op(e1, e2) = e3
% 229.57/41.03  | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | ALPHA: (374) implies:
% 229.57/41.03  | | | | | | | | | | | | | | | | | |   (375)  all_57_7 = e3
% 229.57/41.03  | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | BETA: splitting (35) gives:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | |   (376)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 229.57/41.03  | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e2)
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | BETA: splitting (376) gives:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | |   (377)  all_57_0 = e2 & op(e3, e3) = e2
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | ALPHA: (377) implies:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | |   (378)  op(e3, e3) = e2
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (59), (66), (378) are inconsistent by
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | |            sub-proof #2403.
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | |   (379)  all_57_1 = e2 & op(e3, e2) = e2
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | ALPHA: (379) implies:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | |   (380)  all_57_1 = e2
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (14), (16), (26), (35), (38), (41), (47),
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | |            (53), (58), (59), (60), (65), (66), (69), (72),
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | |            (73), (78), (83), (86), (88), (97), (102), (107),
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | |            (108), (114), (119), (122), (124), (371), (375),
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | |            (380) are inconsistent by sub-proof #870.
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | |   (381)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 229.57/41.03  | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e2)
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | BETA: splitting (381) gives:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | |   (382)  all_57_4 = e2 & op(e3, e1) = e2
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | ALPHA: (382) implies:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | |   (383)  all_57_4 = e2
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (371), (383) are inconsistent by sub-proof
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | |            #2482.
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | |   (384)  all_57_9 = e2 & op(e3, e0) = e2
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | ALPHA: (384) implies:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | |   (385)  all_57_9 = e2
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | BETA: splitting (262) gives:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | |   (386)  all_55_1 = e1
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (42), (386) imply:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | |   (387)  all_53_4 = e1
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | REDUCE: (56), (387) imply:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | |   (388)   ~ (all_53_7 = e1)
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | SIMP: (388) implies:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | |   (389)   ~ (all_53_7 = e1)
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | REDUCE: (31), (387) imply:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | |   (390)   ~ (all_53_12 = e1)
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | SIMP: (390) implies:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | |   (391)   ~ (all_53_12 = e1)
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (122) gives:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | |   (392)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (392) gives:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | |   (393)  all_57_1 = e1 & op(e3, e2) = e1
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (393) implies:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | |   (394)  all_57_1 = e1
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (114) gives:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | |   (395)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (395) gives:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | |   (396)  all_57_9 = e1 & op(e3, e0) = e1
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (396) implies:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | |   (397)  all_57_9 = e1
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (107), (385), (397) are inconsistent by sub-proof
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | |            #2444.
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | |   (398)  all_57_10 = e1 & op(e2, e0) = e1
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (398) implies:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | |   (399)  all_57_10 = e1
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (112) gives:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | |   (400)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e2)
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11), (14), (15), (16), (18), (21), (23),
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | |            (41), (47), (53), (58), (59), (60), (66), (72),
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | |            (73), (77), (83), (86), (88), (93), (100), (101),
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | |            (106), (107), (108), (110), (114), (119), (148),
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | |            (371), (375), (385), (399), (400) are inconsistent
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #864.
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | |   (401)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e1) = e2)
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (401) gives:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (402)  all_57_8 = e2 & op(e1, e1) = e2
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (402) implies:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (403)  op(e1, e1) = e2
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (107), (148), (403) are inconsistent by
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2423.
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (404)  all_57_14 = e2 & op(e0, e1) = e2
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (404) implies:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (405)  all_57_14 = e2
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15) gives:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (406)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e0)
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (14), (16), (18), (21), (23), (41), (47),
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (53), (58), (59), (66), (73), (88), (101), (107),
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (108), (110), (114), (375), (406) are inconsistent
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #868.
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (407)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (407) gives:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (408)  all_57_8 = e0 & op(e1, e1) = e0
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (408) implies:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (409)  op(e1, e1) = e0
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (73), (148), (409) are inconsistent by
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2427.
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (410)  all_57_11 = e0 & op(e1, e0) = e0
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (410) implies:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (411)  all_57_11 = e0
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (60) gives:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (412)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (412) gives:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (413)  all_57_12 = e1 & op(e0, e3) = e1
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (413) implies:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (414)  op(e0, e3) = e1
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (40) gives:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (415)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e0)
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (415) gives:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (416)  all_57_4 = e0 & op(e3, e1) = e0
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (47), (371), (416) are inconsistent by sub-proof
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2491.
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (417)  all_57_5 = e0 & op(e2, e1) = e0
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (417) implies:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (418)  all_57_5 = e0
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (93) gives:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (419)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e3)
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (419) gives:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (420)  all_57_2 = e3 & op(e2, e3) = e3
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (420) implies:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (421)  all_57_2 = e3
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (65) gives:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (422)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e0)
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (422) gives:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (423)  all_57_1 = e0 & op(e3, e2) = e0
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (423) implies:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (424)  all_57_1 = e0
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (14), (16), (26), (35), (41), (47), (53),
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (59), (66), (69), (73), (83), (97), (107), (114),
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (122), (124), (371), (375), (411), (424)
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #901.
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (425)  all_57_3 = e0 & op(e2, e2) = e0
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (425) implies:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (426)  op(e2, e2) = e0
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (66), (72), (426) are inconsistent by
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2472.
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (427)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0)
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (427) gives:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (428)  all_57_7 = e0 & op(e1, e2) = e0
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (428) implies:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (429)  all_57_7 = e0
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (375), (429) imply:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (430)  e3 = e0
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (371), (430) imply:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (431)  all_57_4 = e0
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (14), (16), (21), (23), (41), (47), (58),
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (60), (66), (73), (77), (86), (88), (100), (106),
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (107), (399), (421), (431) are inconsistent by
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #867.
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (432)  all_57_13 = e0 & op(e0, e2) = e0
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (432) implies:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (433)  all_57_13 = e0
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (434)  op(e0, e2) = e0
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (88) gives:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (435)  all_57_15 = e0 & op(e0, e0) = e0
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (435) implies:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (436)  op(e0, e0) = e0
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (47), (83), (436) are inconsistent by
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2304.
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (437)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (437) implies:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (438)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e0)
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (439)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e0)
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (440)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (440) gives:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (441)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_52_7)
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (441) implies:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (442)  op(e3, e0) = all_52_7
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (443)  op(all_52_7, all_52_7) = e0
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (165) gives:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (444)  all_55_3 = e2
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (96), (444) imply:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (445)  all_53_12 = e2
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (445) implies:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (446)  all_53_12 = e2
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (37), (446) imply:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (447)   ~ (all_53_13 = e2)
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (116), (446) imply:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (448)   ~ (all_53_14 = e2)
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (448) implies:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (449)   ~ (all_53_14 = e2)
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (124), (446) imply:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (450)  op(e3, e0) = e2
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (25) gives:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (451)  all_55_11 = e3
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (62), (95), (451) are inconsistent by sub-proof
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2497.
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (452)  all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (452) gives:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (453)  all_55_11 = e2
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (95), (449), (453) are inconsistent by sub-proof
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2282.
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (454)   ~ (all_55_11 = e2)
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (455)  all_55_11 = e1 | all_55_11 = e0
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (455) gives:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (456)  all_55_11 = e1
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (95), (145), (456) are inconsistent by sub-proof
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2309.
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (457)  all_55_11 = e0
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (95), (457) imply:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (458)  all_53_14 = e0
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (458) implies:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (459)  all_53_14 = e0
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (103), (459) imply:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (460)   ~ (all_53_13 = e0)
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (449), (459) imply:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (461)   ~ (e2 = e0)
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (46) gives:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (462)  all_55_7 = e3
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (120), (462) are inconsistent by sub-proof
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2109.
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (463)  all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22) gives:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (464)   ~ (all_18_0 = e1) & op(all_18_1, e3) = all_18_0 &
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e3, e0) = all_18_1 & $i(all_18_0) &
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_18_1)
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (464) implies:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (465)  op(e3, e0) = all_18_1
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (159) gives:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (466)   ~ (all_48_0 = e2) & op(all_48_1, e3) = all_48_0 &
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e3, e0) = all_48_1 & $i(all_48_0) &
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_48_1)
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (466) implies:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (467)  op(e3, e0) = all_48_1
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (30), (66), (72), (120), (442), (443),
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (450), (460), (463), (465), (467) are inconsistent
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #863.
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (468)   ~ (all_48_1 = e1) & op(e3, e0) = all_48_1 &
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_48_1)
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (468) implies:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (469)  op(e3, e0) = all_48_1
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (30), (66), (72), (120), (442), (443),
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (450), (460), (463), (465), (469) are inconsistent
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #863.
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (470)   ~ (all_18_1 = e2) & op(e3, e0) = all_18_1 &
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_18_1)
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (470) implies:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (471)   ~ (all_18_1 = e2)
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (472)  op(e3, e0) = all_18_1
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (159), (450), (471), (472) are inconsistent
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1899.
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (473)  all_55_3 = e1 | all_55_3 = e0
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (96), (102), (391), (473) are inconsistent by
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2132.
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (474)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_52_15)
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (474) implies:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (475)  op(e2, e0) = all_52_15
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (476)  op(all_52_15, all_52_15) = e0
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (165) gives:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (477)  all_55_3 = e2
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (96), (477) imply:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (478)  all_53_12 = e2
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (478) implies:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (479)  all_53_12 = e2
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (37), (479) imply:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (480)   ~ (all_53_13 = e2)
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (116), (479) imply:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (481)   ~ (all_53_14 = e2)
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (481) implies:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (482)   ~ (all_53_14 = e2)
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (97), (479) imply:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (483)   ~ (e3 = e2)
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (25) gives:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (484)  all_55_11 = e3
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (62), (95), (484) are inconsistent by sub-proof
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2497.
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (485)   ~ (all_55_11 = e3)
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (486)  all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (486) gives:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (487)  all_55_11 = e2
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (95), (482), (487) are inconsistent by sub-proof
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2282.
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (488)   ~ (all_55_11 = e2)
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (489)  all_55_11 = e1 | all_55_11 = e0
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (489) gives:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (490)  all_55_11 = e1
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (95), (145), (490) are inconsistent by sub-proof
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2309.
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (491)  all_55_11 = e0
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (95), (491) imply:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (492)  all_53_14 = e0
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (492) implies:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (493)  all_53_14 = e0
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (103), (493) imply:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (494)   ~ (all_53_13 = e0)
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (62), (493) imply:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (495)   ~ (e3 = e0)
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (482), (493) imply:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (496)   ~ (e2 = e0)
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (46) gives:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (497)  all_55_7 = e3
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (120), (497) are inconsistent by sub-proof
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2109.
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (498)   ~ (all_55_7 = e3)
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (499)  all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (499) gives:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (500)  all_55_7 = e2
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (120), (500) are inconsistent by sub-proof
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2171.
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (501)   ~ (all_55_7 = e2)
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (502)  all_55_7 = e1 | all_55_7 = e0
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (502) gives:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (503)  all_55_7 = e1
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (120), (503) imply:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (504)  all_53_13 = e1
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (504) implies:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (505)  all_53_13 = e1
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (92), (505) imply:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (506)  op(e2, e0) = e1
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with e1, all_52_15, e0, e2,
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (475), (506) gives:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (507)  all_52_15 = e1
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (476), (507) imply:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (508)  op(e1, e1) = e0
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (93) gives:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (419) gives:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11), (13), (14), (15), (16), (18), (21),
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (23), (26), (30), (35), (38), (40), (41), (47),
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (48), (51), (53), (58), (59), (60), (65), (66),
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (69), (73), (77), (78), (83), (86), (87), (88),
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (92), (93), (97), (100), (101), (102), (106),
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (107), (108), (110), (112), (113), (114), (115),
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (119), (122), (123), (124), (411), (418), (421),
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (433), (438), (439), (508) are inconsistent by
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #896.
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (509)  all_57_3 = e3 & op(e2, e2) = e3
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (509) implies:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (510)  all_57_3 = e3
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (119), (510) are inconsistent by sub-proof
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1166.
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (511)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e2, e0) = e3)
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (16), (41), (47), (58), (66), (73), (83),
% 229.57/41.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (107), (108), (114), (411), (418), (511) are
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #862.
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (512)  all_55_7 = e0
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (120), (494), (512) are inconsistent by sub-proof
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2130.
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (513)  all_55_3 = e1 | all_55_3 = e0
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (96), (102), (391), (513) are inconsistent by
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2132.
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (514)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_21) = e1 & op(all_52_23, all_52_23) =
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(all_52_25, all_52_25) = e3 &
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_52_29) = e1 & op(all_52_31, all_52_31) =
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_52_29) & $i(all_52_31))
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (514) gives:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (515)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_52_23)
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (515) implies:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (516)  op(e1, e0) = all_52_23
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (517)  op(all_52_23, all_52_23) = e0
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (25), (44), (51), (62), (68), (83), (95),
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (127), (145), (414), (516), (517) are inconsistent
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #859.
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (518)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_52_31)
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (518) implies:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (519)  op(e0, e0) = all_52_31
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (520)  op(e0, e2) = all_52_27
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (521)  op(all_52_27, all_52_27) = e2
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (41), (83), (434), (519), (520), (521) are
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #858.
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (522)  all_57_3 = e3 & op(e2, e2) = e3
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (522) implies:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (523)  all_57_3 = e3
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (119), (523) are inconsistent by sub-proof
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1166.
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (524)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e2, e0) = e3)
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (16), (41), (47), (58), (66), (73), (83),
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (107), (108), (114), (411), (418), (524) are
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #862.
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (525)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (525) gives:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (526)  all_57_8 = e0 & op(e1, e1) = e0
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (526) implies:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (527)  op(e1, e1) = e0
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (73), (148), (527) are inconsistent by
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2427.
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (528)  all_57_14 = e0 & op(e0, e1) = e0
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (41), (58), (66), (73), (107), (108), (114),
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (385), (405), (411), (528) are inconsistent by
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #857.
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (529)  all_57_13 = e1 & op(e0, e2) = e1
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (529) implies:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (530)  all_57_13 = e1
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (5), (9), (11), (13), (14), (15), (16), (18),
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (21), (22), (23), (26), (30), (32), (35), (38),
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (40), (41), (47), (48), (50), (51), (52), (53),
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (58), (59), (60), (65), (66), (67), (68), (69),
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (72), (73), (77), (78), (79), (82), (83), (85),
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (86), (87), (88), (89), (92), (93), (97), (99),
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (100), (101), (102), (106), (107), (108), (110),
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (112), (113), (114), (115), (119), (122), (123),
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (124), (127), (129), (131), (137), (148), (371),
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (385), (399), (405), (411), (530) are inconsistent
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #853.
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (531)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (531) gives:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (532)  all_57_14 = e1 & op(e0, e1) = e1
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (532) implies:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (533)  all_57_14 = e1
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (5), (9), (11), (13), (14), (15), (16), (18),
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (21), (22), (23), (26), (30), (32), (35), (38),
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (40), (41), (47), (48), (50), (51), (52), (53),
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (58), (59), (60), (65), (66), (67), (68), (69),
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (72), (73), (77), (78), (79), (82), (83), (85),
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (86), (87), (88), (89), (92), (93), (97), (99),
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (100), (101), (102), (106), (107), (108), (110),
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (112), (113), (114), (115), (119), (122), (123),
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (124), (127), (129), (131), (137), (148), (533)
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #855.
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (534)  all_57_15 = e1 & op(e0, e0) = e1
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (534) implies:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (535)  op(e0, e0) = e1
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (16), (83), (535) are inconsistent by
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2183.
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | |   (536)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (536) gives:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | |   (537)  all_57_11 = e1 & op(e1, e0) = e1
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (537) implies:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | |   (538)  all_57_11 = e1
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (13), (14), (15), (16), (18), (21), (23),
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | |            (26), (35), (41), (47), (53), (58), (59), (66),
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | |            (69), (73), (83), (88), (97), (101), (107), (108),
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | |            (110), (114), (119), (122), (124), (148), (371),
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | |            (375), (394), (538) are inconsistent by sub-proof
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | |            #852.
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | |   (539)  all_57_15 = e1 & op(e0, e0) = e1
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (539) implies:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | |   (540)  op(e0, e0) = e1
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (16), (83), (540) are inconsistent by
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2183.
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | |   (541)  all_57_3 = e1 & op(e2, e2) = e1
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (541) implies:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | |   (542)  all_57_3 = e1
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | |   (543)  op(e2, e2) = e1
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (5), (9), (11), (13), (15), (16), (18), (21),
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | |            (22), (23), (26), (35), (38), (40), (41), (47),
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | |            (48), (50), (51), (52), (53), (58), (59), (60),
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | |            (65), (66), (67), (68), (69), (77), (78), (79),
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | |            (82), (83), (86), (87), (88), (89), (93), (97),
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | |            (99), (100), (101), (102), (106), (108), (110),
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | |            (112), (113), (114), (115), (122), (123), (124),
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | |            (127), (129), (131), (137), (542), (543) are
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #963.
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | |   (544)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (544) gives:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | |   (545)  all_57_7 = e1 & op(e1, e2) = e1
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (545) implies:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | |   (546)  all_57_7 = e1
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (15), (16), (18), (21), (23), (41), (47),
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | |            (58), (66), (73), (88), (107), (108), (114),
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | |            (123), (148), (546) are inconsistent by sub-proof
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | |            #1069.
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | |   (547)  all_57_13 = e1 & op(e0, e2) = e1
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (547) implies:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | |   (548)  all_57_13 = e1
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (114) gives:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | |   (549)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (549) gives:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | |   (550)  all_57_9 = e1 & op(e3, e0) = e1
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (550) implies:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | |   (551)  all_57_9 = e1
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (107), (385), (551) are inconsistent by sub-proof
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | |            #2444.
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | |   (552)  all_57_10 = e1 & op(e2, e0) = e1
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (552) implies:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | |   (553)  all_57_10 = e1
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (112) gives:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | |   (554)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e2)
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11), (14), (15), (16), (18), (21), (23),
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | |            (41), (47), (53), (58), (59), (60), (66), (72),
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | |            (73), (77), (83), (86), (88), (93), (100), (101),
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | |            (106), (107), (108), (110), (114), (119), (148),
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | |            (371), (375), (385), (553), (554) are inconsistent
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #864.
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | |   (555)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e1) = e2)
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (555) gives:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (556)  all_57_8 = e2 & op(e1, e1) = e2
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (556) implies:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (557)  op(e1, e1) = e2
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (107), (148), (557) are inconsistent by
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2423.
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (558)  all_57_14 = e2 & op(e0, e1) = e2
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (558) implies:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (559)  all_57_14 = e2
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15) gives:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (560)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e0)
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (14), (16), (18), (21), (23), (41), (47),
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (53), (58), (59), (66), (73), (88), (101), (107),
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (108), (110), (114), (375), (560) are inconsistent
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #868.
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (561)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (561) gives:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (562)  all_57_8 = e0 & op(e1, e1) = e0
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (562) implies:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (563)  op(e1, e1) = e0
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (73), (148), (563) are inconsistent by
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2427.
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (564)  all_57_11 = e0 & op(e1, e0) = e0
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (564) implies:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (565)  all_57_11 = e0
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (5), (9), (11), (13), (14), (15), (16), (18),
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (21), (22), (23), (26), (30), (32), (35), (38),
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (40), (41), (47), (48), (50), (51), (52), (53),
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (58), (59), (60), (65), (66), (67), (68), (69),
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (72), (73), (77), (78), (79), (82), (83), (85),
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (86), (87), (88), (89), (92), (93), (97), (99),
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (100), (101), (102), (106), (107), (108), (110),
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (112), (113), (114), (115), (119), (122), (123),
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (124), (127), (129), (131), (137), (148), (371),
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (385), (548), (553), (559), (565) are inconsistent
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #853.
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | |   (566)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (566) gives:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | |   (567)  all_57_11 = e1 & op(e1, e0) = e1
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (567) implies:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | |   (568)  all_57_11 = e1
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (162) gives:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | |   (569)  all_55_13 = e2
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (91), (569) imply:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | |   (570)  all_53_7 = e2
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (32), (570) imply:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | |   (571)  $false
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (571) is inconsistent.
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | |   (572)   ~ (all_55_13 = e2)
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | |   (573)  all_55_13 = e1 | all_55_13 = e0
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (573) gives:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (574)  all_55_13 = e1
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (91), (574) imply:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (575)  all_53_7 = e1
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (389), (575) imply:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (576)  $false
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (576) is inconsistent.
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (577)  all_55_13 = e0
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (91), (577) imply:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (578)  all_53_7 = e0
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2), (578) imply:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (579)   ~ (e3 = e0)
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (32), (578) imply:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (580)   ~ (e2 = e0)
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (389), (578) imply:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (581)   ~ (e1 = e0)
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (85), (578) imply:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (582)  op(e0, e2) = e0
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (112) gives:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (583)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e2)
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (583) gives:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (584)  all_57_4 = e2 & op(e3, e1) = e2
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (584) implies:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (585)  all_57_4 = e2
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (371), (585) imply:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (586)  e3 = e2
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (375), (586) imply:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (587)  all_57_7 = e2
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (15), (16), (18), (21), (23), (41), (47),
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (58), (66), (73), (88), (107), (108), (114),
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (148), (385), (568), (587) are inconsistent by
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #957.
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (588)  all_57_5 = e2 & op(e2, e1) = e2
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (588) implies:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (589)  all_57_5 = e2
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (106) gives:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (590)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e0)
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (590) gives:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (591)  all_57_2 = e0 & op(e2, e3) = e0
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (591) implies:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (592)  all_57_2 = e0
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (93) gives:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (593)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e3)
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (593) gives:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (594)  all_57_2 = e3 & op(e2, e3) = e3
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (594) implies:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (595)  all_57_2 = e3
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (47), (592), (595) are inconsistent by sub-proof
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2258.
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (596)  all_57_3 = e3 & op(e2, e2) = e3
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (596) implies:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (597)  all_57_3 = e3
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (119), (597) imply:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (598)  e3 = e2
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (598) implies:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (599)  e3 = e2
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (375), (599) imply:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (600)  all_57_7 = e2
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (15), (16), (18), (21), (23), (41), (47),
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (58), (66), (73), (88), (107), (108), (114),
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (148), (385), (568), (600) are inconsistent by
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #957.
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (601)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e2, e0) = e3)
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (601) gives:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (602)  all_57_5 = e3 & op(e2, e1) = e3
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (602) implies:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (603)  all_57_5 = e3
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (589), (603) imply:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (604)  e3 = e2
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (604) implies:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (605)  e3 = e2
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (375), (605) imply:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (606)  all_57_7 = e2
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (15), (16), (18), (21), (23), (41), (47),
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (58), (66), (73), (88), (107), (108), (114),
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (148), (385), (568), (606) are inconsistent by
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #957.
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (607)  all_57_10 = e3 & op(e2, e0) = e3
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (607) implies:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (608)  all_57_10 = e3
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (16), (41), (47), (58), (66), (73), (83),
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (88), (107), (108), (114), (608) are inconsistent
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1746.
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (609)  all_57_3 = e0 & op(e2, e2) = e0
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (609) implies:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (610)  op(e2, e2) = e0
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (66), (72), (610) are inconsistent by
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2472.
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (611)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e2, e0) = e0)
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (611) gives:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (612)  all_57_5 = e0 & op(e2, e1) = e0
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (66), (589), (612) are inconsistent by sub-proof
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2428.
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (613)  all_57_10 = e0 & op(e2, e0) = e0
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (613) implies:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (614)  all_57_10 = e0
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (615)  op(e2, e0) = e0
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15) gives:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (616)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e0)
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (616) gives:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (617)  all_57_6 = e0 & op(e1, e3) = e0
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (617) implies:
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (618)  all_57_6 = e0
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11) gives:
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (619)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e1)
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (16), (41), (47), (53), (58), (59), (66),
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (73), (83), (101), (107), (108), (110), (114),
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (568), (614), (618), (619) are inconsistent by
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #930.
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (620)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e3) = e1)
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (620) gives:
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (621)  all_57_6 = e1 & op(e1, e3) = e1
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (621) implies:
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (622)  all_57_6 = e1
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (618), (622) imply:
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (623)  e1 = e0
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (16), (41), (58), (66), (73), (83), (107),
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (108), (114), (568), (614), (623) are inconsistent
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #932.
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (624)  all_57_12 = e1 & op(e0, e3) = e1
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (624) implies:
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (625)  all_57_12 = e1
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (16), (18), (21), (23), (41), (47), (58),
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (59), (66), (73), (88), (101), (107), (108),
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (110), (114), (618), (625) are inconsistent by
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1028.
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (626)  all_57_7 = e0 & op(e1, e2) = e0
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (626) implies:
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (627)  all_57_7 = e0
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (47), (375), (627) are inconsistent by sub-proof
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2269.
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (628)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (628) gives:
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (629)  all_57_8 = e0 & op(e1, e1) = e0
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (629) implies:
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (630)  op(e1, e1) = e0
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (14), (16), (24), (30), (31), (34), (37),
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (41), (42), (56), (59), (63), (67), (72), (83),
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (85), (92), (96), (97), (98), (124), (582), (615),
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (630) are inconsistent by sub-proof #846.
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (631)  all_57_11 = e0 & op(e1, e0) = e0
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (631) implies:
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (632)  all_57_11 = e0
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (16), (73), (83), (107), (114), (385),
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (614), (632) are inconsistent by sub-proof #1104.
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (633)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e1) = e2)
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (633) gives:
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (634)  all_57_8 = e2 & op(e1, e1) = e2
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (634) implies:
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (635)  op(e1, e1) = e2
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (107), (148), (635) are inconsistent by
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2423.
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (636)  all_57_14 = e2 & op(e0, e1) = e2
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (636) implies:
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (637)  all_57_14 = e2
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (26) gives:
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (638)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e1)
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (638) gives:
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (639)  all_57_0 = e1 & op(e3, e3) = e1
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (53), (73), (639) are inconsistent by sub-proof
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2454.
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (640)  all_57_1 = e1 & op(e3, e2) = e1
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (640) implies:
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (641)  all_57_1 = e1
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (13), (14), (15), (16), (18), (21), (23),
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (26), (35), (41), (47), (53), (58), (59), (66),
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (69), (73), (83), (88), (97), (101), (107), (108),
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (110), (114), (119), (122), (124), (148), (371),
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (375), (568), (641) are inconsistent by sub-proof
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #852.
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (642)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e1)
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (5), (9), (11), (13), (14), (15), (16), (18),
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (21), (22), (23), (26), (30), (32), (35), (38),
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (40), (41), (47), (48), (50), (51), (52), (53),
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (58), (59), (60), (65), (66), (67), (68), (69),
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (72), (73), (77), (78), (79), (82), (83), (85),
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (86), (87), (88), (89), (92), (93), (97), (99),
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (100), (101), (102), (106), (107), (108), (110),
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (112), (113), (114), (115), (119), (122), (123),
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (124), (127), (129), (131), (137), (148), (385),
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (637), (642) are inconsistent by sub-proof #854.
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | |   (643)  all_57_15 = e1 & op(e0, e0) = e1
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (643) implies:
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | |   (644)  op(e0, e0) = e1
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (16), (83), (644) are inconsistent by
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2183.
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | |   (645)  all_55_1 = e0
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (42), (645) imply:
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | |   (646)  all_53_4 = e0
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | REDUCE: (76), (646) imply:
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | |   (647)  $false
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | CLOSE: (647) is inconsistent.
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.05  | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.05  | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | |   (648)  all_57_13 = e3 & op(e0, e2) = e3
% 229.57/41.05  | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | ALPHA: (648) implies:
% 229.57/41.05  | | | | | | | | | | | | | | | | | |   (649)  all_57_13 = e3
% 229.57/41.05  | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (16), (41), (47), (58), (60), (66), (73),
% 229.57/41.05  | | | | | | | | | | | | | | | | | |            (83), (86), (88), (107), (649) are inconsistent by
% 229.57/41.05  | | | | | | | | | | | | | | | | | |            sub-proof #1792.
% 229.57/41.05  | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | End of split
% 229.57/41.05  | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | End of split
% 229.57/41.05  | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | Case 2:
% 229.57/41.05  | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | |   (650)  all_57_9 = e3 & op(e3, e0) = e3
% 229.57/41.05  | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | ALPHA: (650) implies:
% 229.57/41.05  | | | | | | | | | | | | | | | |   (651)  op(e3, e0) = e3
% 229.57/41.05  | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | REF_CLOSE: (16), (97), (124), (651) are inconsistent by
% 229.57/41.05  | | | | | | | | | | | | | | | |            sub-proof #2458.
% 229.57/41.05  | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | End of split
% 229.57/41.05  | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | End of split
% 229.57/41.05  | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | End of split
% 229.57/41.05  | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | End of split
% 229.57/41.05  | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | End of split
% 229.57/41.05  | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | End of split
% 229.57/41.05  | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | End of split
% 229.57/41.05  | | | | | | | | | 
% 229.57/41.05  | | | | | | | | Case 2:
% 229.57/41.05  | | | | | | | | | 
% 229.57/41.05  | | | | | | | | |   (652)  all_57_14 = e1 & op(e0, e1) = e1
% 229.57/41.05  | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | ALPHA: (652) implies:
% 229.57/41.05  | | | | | | | | |   (653)  all_57_14 = e1
% 229.57/41.05  | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | REF_CLOSE: (3), (5), (9), (11), (13), (14), (15), (16), (18),
% 229.57/41.05  | | | | | | | | |            (21), (22), (23), (26), (30), (32), (35), (38),
% 229.57/41.05  | | | | | | | | |            (40), (41), (47), (48), (50), (51), (52), (53),
% 229.57/41.05  | | | | | | | | |            (58), (59), (60), (65), (66), (67), (68), (69),
% 229.57/41.05  | | | | | | | | |            (72), (73), (77), (78), (79), (82), (83), (85),
% 229.57/41.05  | | | | | | | | |            (86), (87), (88), (89), (92), (93), (97), (99),
% 229.57/41.05  | | | | | | | | |            (100), (101), (102), (106), (107), (108), (110),
% 229.57/41.05  | | | | | | | | |            (112), (113), (114), (115), (119), (122), (123),
% 229.57/41.05  | | | | | | | | |            (124), (127), (129), (131), (137), (148), (653) are
% 229.57/41.05  | | | | | | | | |            inconsistent by sub-proof #855.
% 229.57/41.05  | | | | | | | | | 
% 229.57/41.05  | | | | | | | | End of split
% 229.57/41.05  | | | | | | | | 
% 229.57/41.05  | | | | | | | End of split
% 229.57/41.05  | | | | | | | 
% 229.57/41.05  | | | | | | Case 2:
% 229.57/41.05  | | | | | | | 
% 229.57/41.05  | | | | | | |   (654)  all_55_10 = e0
% 229.57/41.05  | | | | | | | 
% 229.57/41.05  | | | | | | | REF_CLOSE: (89), (129), (654) are inconsistent by sub-proof #2118.
% 229.57/41.05  | | | | | | | 
% 229.57/41.05  | | | | | | End of split
% 229.57/41.05  | | | | | | 
% 229.57/41.05  | | | | | End of split
% 229.57/41.05  | | | | | 
% 229.57/41.05  | | | | End of split
% 229.57/41.05  | | | | 
% 229.57/41.05  | | | Case 2:
% 229.57/41.05  | | | | 
% 229.57/41.05  | | | |   (655)  all_38_2 = e2
% 229.57/41.05  | | | | 
% 229.57/41.05  | | | | COMBINE_EQS: (94), (655) imply:
% 229.57/41.05  | | | |   (656)  all_6_2 = e2
% 229.57/41.05  | | | | 
% 229.57/41.05  | | | | REDUCE: (21), (656) imply:
% 229.57/41.05  | | | |   (657)   ~ (e3 = e2)
% 229.57/41.05  | | | | 
% 229.57/41.05  | | | | REDUCE: (23), (656) imply:
% 229.57/41.05  | | | |   (658)  op(e1, e1) = e2
% 229.57/41.05  | | | | 
% 229.57/41.05  | | | | BETA: splitting (110) gives:
% 229.57/41.05  | | | | 
% 229.57/41.05  | | | | Case 1:
% 229.57/41.05  | | | | | 
% 229.57/41.05  | | | | |   (659)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2,
% 229.57/41.05  | | | | |              e3) = e2)
% 229.57/41.05  | | | | | 
% 229.57/41.05  | | | | | BETA: splitting (659) gives:
% 229.57/41.05  | | | | | 
% 229.57/41.05  | | | | | Case 1:
% 229.57/41.05  | | | | | | 
% 229.57/41.05  | | | | | |   (660)  all_57_0 = e2 & op(e3, e3) = e2
% 229.57/41.05  | | | | | | 
% 229.57/41.05  | | | | | | ALPHA: (660) implies:
% 229.57/41.05  | | | | | |   (661)  op(e3, e3) = e2
% 229.57/41.05  | | | | | | 
% 229.57/41.05  | | | | | | REF_CLOSE: (16), (59), (66), (661) are inconsistent by sub-proof
% 229.57/41.05  | | | | | |            #2403.
% 229.57/41.05  | | | | | | 
% 229.57/41.05  | | | | | Case 2:
% 229.57/41.05  | | | | | | 
% 229.57/41.05  | | | | | |   (662)  all_57_2 = e2 & op(e2, e3) = e2
% 229.57/41.05  | | | | | | 
% 229.57/41.05  | | | | | | ALPHA: (662) implies:
% 229.57/41.05  | | | | | |   (663)  all_57_2 = e2
% 229.57/41.05  | | | | | | 
% 229.57/41.05  | | | | | | REF_CLOSE: (9), (14), (16), (41), (47), (58), (66), (72), (73),
% 229.57/41.05  | | | | | |            (83), (88), (93), (100), (106), (107), (108), (114),
% 229.57/41.05  | | | | | |            (119), (663) are inconsistent by sub-proof #844.
% 229.57/41.05  | | | | | | 
% 229.57/41.05  | | | | | End of split
% 229.57/41.05  | | | | | 
% 229.57/41.05  | | | | Case 2:
% 229.57/41.05  | | | | | 
% 229.57/41.05  | | | | |   (664)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0,
% 229.57/41.05  | | | | |              e3) = e2)
% 229.57/41.05  | | | | | 
% 229.57/41.05  | | | | | BETA: splitting (664) gives:
% 229.57/41.05  | | | | | 
% 229.57/41.05  | | | | | Case 1:
% 229.57/41.05  | | | | | | 
% 229.57/41.05  | | | | | |   (665)  all_57_6 = e2 & op(e1, e3) = e2
% 229.57/41.05  | | | | | | 
% 229.57/41.05  | | | | | | ALPHA: (665) implies:
% 229.57/41.05  | | | | | |   (666)  all_57_6 = e2
% 229.57/41.05  | | | | | | 
% 229.57/41.05  | | | | | | BETA: splitting (18) gives:
% 229.57/41.05  | | | | | | 
% 229.57/41.05  | | | | | | Case 1:
% 229.57/41.05  | | | | | | | 
% 229.57/41.05  | | | | | | |   (667)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 &
% 229.57/41.05  | | | | | | |            op(e1, e2) = e3)
% 229.57/41.05  | | | | | | | 
% 229.57/41.05  | | | | | | | BETA: splitting (667) gives:
% 229.57/41.05  | | | | | | | 
% 229.57/41.05  | | | | | | | Case 1:
% 229.57/41.05  | | | | | | | | 
% 229.57/41.05  | | | | | | | |   (668)  all_57_6 = e3 & op(e1, e3) = e3
% 229.57/41.05  | | | | | | | | 
% 229.57/41.05  | | | | | | | | ALPHA: (668) implies:
% 229.57/41.05  | | | | | | | |   (669)  all_57_6 = e3
% 229.57/41.05  | | | | | | | | 
% 229.57/41.05  | | | | | | | | REF_CLOSE: (41), (666), (669) are inconsistent by sub-proof
% 229.57/41.05  | | | | | | | |            #2463.
% 229.57/41.05  | | | | | | | | 
% 229.57/41.05  | | | | | | | Case 2:
% 229.57/41.05  | | | | | | | | 
% 229.57/41.05  | | | | | | | |   (670)  all_57_7 = e3 & op(e1, e2) = e3
% 229.57/41.05  | | | | | | | | 
% 229.57/41.05  | | | | | | | | ALPHA: (670) implies:
% 229.57/41.05  | | | | | | | |   (671)  all_57_7 = e3
% 229.57/41.05  | | | | | | | | 
% 229.57/41.05  | | | | | | | | BETA: splitting (65) gives:
% 229.57/41.05  | | | | | | | | 
% 229.57/41.05  | | | | | | | | Case 1:
% 229.57/41.05  | | | | | | | | | 
% 229.57/41.05  | | | | | | | | |   (672)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 &
% 229.57/41.05  | | | | | | | | |            op(e2, e2) = e0)
% 229.57/41.05  | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | REF_CLOSE: (13), (14), (16), (26), (35), (38), (41), (47),
% 229.57/41.05  | | | | | | | | |            (53), (58), (59), (60), (66), (69), (72), (73),
% 229.57/41.05  | | | | | | | | |            (78), (83), (86), (88), (97), (102), (107), (108),
% 229.57/41.05  | | | | | | | | |            (114), (119), (122), (124), (672) are inconsistent
% 229.57/41.05  | | | | | | | | |            by sub-proof #879.
% 229.57/41.05  | | | | | | | | | 
% 229.57/41.05  | | | | | | | | Case 2:
% 229.57/41.05  | | | | | | | | | 
% 229.57/41.05  | | | | | | | | |   (673)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 &
% 229.57/41.05  | | | | | | | | |            op(e0, e2) = e0)
% 229.57/41.05  | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | BETA: splitting (673) gives:
% 229.57/41.05  | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | Case 1:
% 229.57/41.05  | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | |   (674)  all_57_7 = e0 & op(e1, e2) = e0
% 229.57/41.05  | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | REF_CLOSE: (47), (671), (674) are inconsistent by sub-proof
% 229.57/41.05  | | | | | | | | | |            #2042.
% 229.57/41.05  | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | Case 2:
% 229.57/41.05  | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | |   (675)  all_57_13 = e0 & op(e0, e2) = e0
% 229.57/41.05  | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | ALPHA: (675) implies:
% 229.57/41.05  | | | | | | | | | |   (676)  all_57_13 = e0
% 229.57/41.05  | | | | | | | | | |   (677)  op(e0, e2) = e0
% 229.57/41.05  | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | BETA: splitting (15) gives:
% 229.57/41.05  | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | Case 1:
% 229.57/41.05  | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | |   (678)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 229.57/41.05  | | | | | | | | | | |            & op(e1, e2) = e0)
% 229.57/41.05  | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | REF_CLOSE: (11), (14), (16), (18), (21), (23), (41), (47),
% 229.57/41.05  | | | | | | | | | | |            (53), (58), (59), (66), (73), (88), (101), (107),
% 229.57/41.05  | | | | | | | | | | |            (108), (110), (114), (671), (678) are inconsistent
% 229.57/41.05  | | | | | | | | | | |            by sub-proof #868.
% 229.57/41.05  | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | Case 2:
% 229.57/41.05  | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | |   (679)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 229.57/41.05  | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 229.57/41.05  | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | BETA: splitting (679) gives:
% 229.57/41.05  | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | Case 1:
% 229.57/41.05  | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | |   (680)  all_57_8 = e0 & op(e1, e1) = e0
% 229.57/41.05  | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | ALPHA: (680) implies:
% 229.57/41.05  | | | | | | | | | | | |   (681)  op(e1, e1) = e0
% 229.57/41.05  | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | REF_CLOSE: (4), (9), (11), (13), (14), (15), (16), (18),
% 229.57/41.05  | | | | | | | | | | | |            (21), (23), (24), (26), (30), (31), (32), (34),
% 229.57/41.05  | | | | | | | | | | | |            (35), (37), (38), (40), (41), (42), (47), (48),
% 229.57/41.05  | | | | | | | | | | | |            (51), (53), (56), (58), (59), (60), (63), (65),
% 229.57/41.05  | | | | | | | | | | | |            (66), (67), (68), (69), (72), (73), (77), (78),
% 229.57/41.05  | | | | | | | | | | | |            (83), (85), (86), (87), (88), (92), (93), (96),
% 229.57/41.05  | | | | | | | | | | | |            (97), (98), (100), (101), (102), (106), (107),
% 229.57/41.05  | | | | | | | | | | | |            (108), (110), (112), (113), (114), (115), (119),
% 229.57/41.05  | | | | | | | | | | | |            (122), (123), (124), (127), (676), (677), (681)
% 229.57/41.05  | | | | | | | | | | | |            are inconsistent by sub-proof #840.
% 229.57/41.05  | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | Case 2:
% 229.57/41.05  | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | |   (682)  all_57_11 = e0 & op(e1, e0) = e0
% 229.57/41.05  | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | ALPHA: (682) implies:
% 229.57/41.05  | | | | | | | | | | | |   (683)  all_57_11 = e0
% 229.57/41.05  | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | REF_CLOSE: (14), (16), (18), (21), (23), (41), (47), (58),
% 229.57/41.05  | | | | | | | | | | | |            (66), (73), (88), (107), (108), (114), (115),
% 229.57/41.05  | | | | | | | | | | | |            (658), (666), (683) are inconsistent by sub-proof
% 229.57/41.05  | | | | | | | | | | | |            #1122.
% 229.57/41.05  | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | End of split
% 229.57/41.05  | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | End of split
% 229.57/41.05  | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | End of split
% 229.57/41.05  | | | | | | | | | 
% 229.57/41.05  | | | | | | | | End of split
% 229.57/41.05  | | | | | | | | 
% 229.57/41.05  | | | | | | | End of split
% 229.57/41.05  | | | | | | | 
% 229.57/41.05  | | | | | | Case 2:
% 229.57/41.05  | | | | | | | 
% 229.57/41.05  | | | | | | |   (684)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 &
% 229.57/41.05  | | | | | | |            op(e1, e0) = e3)
% 229.57/41.05  | | | | | | | 
% 229.57/41.05  | | | | | | | REF_CLOSE: (14), (16), (21), (23), (41), (47), (58), (66), (73),
% 229.57/41.05  | | | | | | |            (88), (107), (108), (114), (684) are inconsistent by
% 229.57/41.05  | | | | | | |            sub-proof #1786.
% 229.57/41.05  | | | | | | | 
% 229.57/41.05  | | | | | | End of split
% 229.57/41.05  | | | | | | 
% 229.57/41.05  | | | | | Case 2:
% 229.57/41.05  | | | | | | 
% 229.57/41.05  | | | | | |   (685)  all_57_12 = e2 & op(e0, e3) = e2
% 229.57/41.05  | | | | | | 
% 229.57/41.05  | | | | | | ALPHA: (685) implies:
% 229.57/41.05  | | | | | |   (686)  all_57_12 = e2
% 229.57/41.05  | | | | | |   (687)  op(e0, e3) = e2
% 229.57/41.05  | | | | | | 
% 229.57/41.05  | | | | | | BETA: splitting (35) gives:
% 229.57/41.05  | | | | | | 
% 229.57/41.05  | | | | | | Case 1:
% 229.57/41.05  | | | | | | | 
% 229.57/41.05  | | | | | | |   (688)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 &
% 229.57/41.05  | | | | | | |            op(e3, e2) = e2)
% 229.57/41.05  | | | | | | | 
% 229.57/41.05  | | | | | | | BETA: splitting (688) gives:
% 229.57/41.05  | | | | | | | 
% 229.57/41.05  | | | | | | | Case 1:
% 229.57/41.05  | | | | | | | | 
% 229.57/41.05  | | | | | | | |   (689)  all_57_0 = e2 & op(e3, e3) = e2
% 229.57/41.05  | | | | | | | | 
% 229.57/41.05  | | | | | | | | ALPHA: (689) implies:
% 229.57/41.05  | | | | | | | |   (690)  op(e3, e3) = e2
% 229.57/41.05  | | | | | | | | 
% 229.57/41.05  | | | | | | | | REF_CLOSE: (16), (59), (66), (690) are inconsistent by sub-proof
% 229.57/41.05  | | | | | | | |            #2403.
% 229.57/41.05  | | | | | | | | 
% 229.57/41.05  | | | | | | | Case 2:
% 229.57/41.05  | | | | | | | | 
% 229.57/41.05  | | | | | | | |   (691)  all_57_1 = e2 & op(e3, e2) = e2
% 229.57/41.05  | | | | | | | | 
% 229.57/41.05  | | | | | | | | ALPHA: (691) implies:
% 229.57/41.05  | | | | | | | |   (692)  all_57_1 = e2
% 229.57/41.05  | | | | | | | | 
% 229.57/41.05  | | | | | | | | REF_CLOSE: (13), (14), (16), (26), (35), (38), (41), (47), (53),
% 229.57/41.05  | | | | | | | |            (58), (59), (60), (65), (66), (69), (72), (73), (78),
% 229.57/41.05  | | | | | | | |            (83), (86), (88), (97), (102), (107), (108), (114),
% 229.57/41.05  | | | | | | | |            (119), (122), (124), (692) are inconsistent by
% 229.57/41.05  | | | | | | | |            sub-proof #839.
% 229.57/41.05  | | | | | | | | 
% 229.57/41.05  | | | | | | | End of split
% 229.57/41.05  | | | | | | | 
% 229.57/41.05  | | | | | | Case 2:
% 229.57/41.05  | | | | | | | 
% 229.57/41.05  | | | | | | |   (693)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 &
% 229.57/41.05  | | | | | | |            op(e3, e0) = e2)
% 229.57/41.05  | | | | | | | 
% 229.57/41.05  | | | | | | | BETA: splitting (693) gives:
% 229.57/41.05  | | | | | | | 
% 229.57/41.05  | | | | | | | Case 1:
% 229.57/41.05  | | | | | | | | 
% 229.57/41.05  | | | | | | | |   (694)  all_57_4 = e2 & op(e3, e1) = e2
% 229.57/41.05  | | | | | | | | 
% 229.57/41.05  | | | | | | | | ALPHA: (694) implies:
% 229.57/41.05  | | | | | | | |   (695)  all_57_4 = e2
% 229.57/41.05  | | | | | | | | 
% 229.57/41.05  | | | | | | | | BETA: splitting (77) gives:
% 229.57/41.05  | | | | | | | | 
% 229.57/41.05  | | | | | | | | Case 1:
% 229.57/41.05  | | | | | | | | | 
% 229.57/41.05  | | | | | | | | |   (696)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 &
% 229.57/41.05  | | | | | | | | |            op(e2, e1) = e3)
% 229.57/41.05  | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | BETA: splitting (696) gives:
% 229.57/41.05  | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | Case 1:
% 229.57/41.05  | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | |   (697)  all_57_4 = e3 & op(e3, e1) = e3
% 229.57/41.05  | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | REF_CLOSE: (41), (695), (697) are inconsistent by sub-proof
% 229.57/41.05  | | | | | | | | | |            #877.
% 229.57/41.05  | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | Case 2:
% 229.57/41.05  | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | |   (698)  all_57_5 = e3 & op(e2, e1) = e3
% 229.57/41.05  | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | ALPHA: (698) implies:
% 229.57/41.05  | | | | | | | | | |   (699)  all_57_5 = e3
% 229.57/41.05  | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | BETA: splitting (108) gives:
% 229.57/41.05  | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | Case 1:
% 229.57/41.05  | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | |   (700)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 229.57/41.05  | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 229.57/41.05  | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | BETA: splitting (700) gives:
% 229.57/41.05  | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | Case 1:
% 229.57/41.05  | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | |   (701)  all_57_9 = e2 & op(e3, e0) = e2
% 229.57/41.05  | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | ALPHA: (701) implies:
% 229.57/41.05  | | | | | | | | | | | |   (702)  all_57_9 = e2
% 229.57/41.05  | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | BETA: splitting (69) gives:
% 229.57/41.05  | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | Case 1:
% 229.57/41.05  | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | |   (703)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 229.57/41.05  | | | | | | | | | | | | |            & op(e3, e2) = e3)
% 229.57/41.05  | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | REF_CLOSE: (14), (16), (26), (47), (53), (59), (73), (107),
% 229.57/41.05  | | | | | | | | | | | | |            (695), (702), (703) are inconsistent by sub-proof
% 229.57/41.05  | | | | | | | | | | | | |            #2449.
% 229.57/41.05  | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | Case 2:
% 229.57/41.05  | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | |   (704)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 229.57/41.05  | | | | | | | | | | | | |            & op(e3, e0) = e3)
% 229.57/41.05  | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | REF_CLOSE: (16), (41), (97), (124), (695), (704) are
% 229.57/41.05  | | | | | | | | | | | | |            inconsistent by sub-proof #2448.
% 229.57/41.05  | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | End of split
% 229.57/41.05  | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | Case 2:
% 229.57/41.05  | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | |   (705)  all_57_10 = e2 & op(e2, e0) = e2
% 229.57/41.05  | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | REF_CLOSE: (16), (30), (92), (705) are inconsistent by
% 229.57/41.05  | | | | | | | | | | | |            sub-proof #2432.
% 229.57/41.05  | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | End of split
% 229.57/41.05  | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | Case 2:
% 229.57/41.05  | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | |   (706)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 229.57/41.05  | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 229.57/41.05  | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | BETA: splitting (706) gives:
% 229.57/41.05  | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | Case 1:
% 229.57/41.05  | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | |   (707)  all_57_11 = e2 & op(e1, e0) = e2
% 229.57/41.05  | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | ALPHA: (707) implies:
% 229.57/41.05  | | | | | | | | | | | |   (708)  all_57_11 = e2
% 229.57/41.05  | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | BETA: splitting (69) gives:
% 229.57/41.05  | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | Case 1:
% 229.57/41.05  | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | |   (709)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 229.57/41.05  | | | | | | | | | | | | |            & op(e3, e2) = e3)
% 229.57/41.05  | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | BETA: splitting (709) gives:
% 229.57/41.05  | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | Case 1:
% 229.57/41.05  | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | |   (710)  all_57_0 = e3 & op(e3, e3) = e3
% 229.57/41.05  | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | ALPHA: (710) implies:
% 229.57/41.05  | | | | | | | | | | | | | |   (711)  op(e3, e3) = e3
% 229.57/41.05  | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | REF_CLOSE: (16), (47), (59), (711) are inconsistent by
% 229.57/41.05  | | | | | | | | | | | | | |            sub-proof #2494.
% 229.57/41.05  | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | Case 2:
% 229.57/41.05  | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | |   (712)  all_57_1 = e3 & op(e3, e2) = e3
% 229.57/41.05  | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | ALPHA: (712) implies:
% 229.57/41.05  | | | | | | | | | | | | | |   (713)  all_57_1 = e3
% 229.57/41.05  | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | BETA: splitting (106) gives:
% 229.57/41.05  | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | Case 1:
% 229.57/41.05  | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | |   (714)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 229.57/41.05  | | | | | | | | | | | | | | |            & op(e2, e2) = e0)
% 229.57/41.05  | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | BETA: splitting (714) gives:
% 229.57/41.05  | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | Case 1:
% 229.57/41.05  | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | |   (715)  all_57_2 = e0 & op(e2, e3) = e0
% 229.57/41.05  | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | ALPHA: (715) implies:
% 229.57/41.05  | | | | | | | | | | | | | | | |   (716)  all_57_2 = e0
% 229.57/41.05  | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | BETA: splitting (101) gives:
% 229.57/41.05  | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.05  | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | |   (717)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 229.57/41.05  | | | | | | | | | | | | | | | | |            & op(e2, e3) = e3)
% 229.57/41.05  | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | BETA: splitting (717) gives:
% 229.57/41.05  | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.05  | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | |   (718)  all_57_0 = e3 & op(e3, e3) = e3
% 229.57/41.05  | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (13), (14), (16), (18), (21), (23), (41),
% 229.57/41.05  | | | | | | | | | | | | | | | | | |            (47), (58), (65), (66), (72), (73), (88), (107),
% 229.57/41.05  | | | | | | | | | | | | | | | | | |            (108), (110), (113), (114), (122), (713), (718)
% 229.57/41.05  | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #878.
% 229.57/41.05  | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.05  | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | |   (719)  all_57_2 = e3 & op(e2, e3) = e3
% 229.57/41.05  | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | ALPHA: (719) implies:
% 229.57/41.05  | | | | | | | | | | | | | | | | | |   (720)  all_57_2 = e3
% 229.57/41.05  | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (716), (720) imply:
% 229.57/41.05  | | | | | | | | | | | | | | | | | |   (721)  e3 = e0
% 229.57/41.05  | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (14), (16), (26), (35), (38), (41), (47),
% 229.57/41.05  | | | | | | | | | | | | | | | | | |            (53), (58), (59), (60), (66), (69), (73), (78),
% 229.57/41.05  | | | | | | | | | | | | | | | | | |            (83), (86), (88), (97), (102), (107), (108),
% 229.57/41.05  | | | | | | | | | | | | | | | | | |            (114), (119), (122), (124), (713), (721) are
% 229.57/41.05  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #881.
% 229.57/41.05  | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | End of split
% 229.57/41.05  | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.05  | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | |   (722)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 229.57/41.05  | | | | | | | | | | | | | | | | |            e3 & op(e0, e3) = e3)
% 229.57/41.05  | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | BETA: splitting (722) gives:
% 229.57/41.05  | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.05  | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | |   (723)  all_57_6 = e3 & op(e1, e3) = e3
% 229.57/41.05  | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | ALPHA: (723) implies:
% 229.57/41.05  | | | | | | | | | | | | | | | | | |   (724)  all_57_6 = e3
% 229.57/41.05  | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | BETA: splitting (9) gives:
% 229.57/41.05  | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | |   (725)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 229.57/41.05  | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | BETA: splitting (725) gives:
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | |   (726)  all_57_2 = e1 & op(e2, e3) = e1
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | ALPHA: (726) implies:
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | |   (727)  all_57_2 = e1
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (73), (716), (727) are inconsistent by sub-proof
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | |            #2473.
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | |   (728)  all_57_3 = e1 & op(e2, e2) = e1
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.05  | | | | | | | | | | | | | | | | | | | | ALPHA: (728) implies:
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | |   (729)  all_57_3 = e1
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11), (14), (16), (41), (53), (59), (66),
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | |            (73), (100), (107), (110), (699), (716), (724),
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | |            (729) are inconsistent by sub-proof #1066.
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | |   (730)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 229.57/41.06  | | | | | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | BETA: splitting (730) gives:
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | |   (731)  all_57_5 = e1 & op(e2, e1) = e1
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | ALPHA: (731) implies:
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | |   (732)  all_57_5 = e1
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (699), (732) imply:
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | |   (733)  e3 = e1
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (724), (733) imply:
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | |   (734)  all_57_6 = e1
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (14), (16), (18), (21), (23), (41), (47),
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | |            (58), (65), (66), (72), (73), (88), (107), (108),
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | |            (114), (122), (713), (734) are inconsistent by
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | |            sub-proof #1071.
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | |   (735)  all_57_10 = e1 & op(e2, e0) = e1
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | ALPHA: (735) implies:
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | |   (736)  all_57_10 = e1
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | BETA: splitting (115) gives:
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | |   (737)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e1)
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (737) gives:
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | |   (738)  all_57_6 = e1 & op(e1, e3) = e1
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (738) implies:
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | |   (739)  all_57_6 = e1
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (14), (16), (18), (21), (23), (41), (47),
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | |            (58), (65), (66), (72), (73), (88), (107), (108),
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | |            (114), (122), (713), (739) are inconsistent by
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1071.
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | |   (740)  all_57_7 = e1 & op(e1, e2) = e1
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (740) implies:
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | |   (741)  all_57_7 = e1
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15) gives:
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | |   (742)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e0)
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (742) gives:
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | | |   (743)  all_57_6 = e0 & op(e1, e3) = e0
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (743) implies:
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | | |   (744)  all_57_6 = e0
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (16), (18), (21), (23), (41), (47), (58),
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | | |            (66), (73), (88), (107), (108), (114), (741),
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | | |            (744) are inconsistent by sub-proof #1157.
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | | |   (745)  all_57_7 = e0 & op(e1, e2) = e0
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (745) implies:
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | | |   (746)  all_57_7 = e0
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (16), (18), (21), (23), (41), (47), (58),
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | | |            (66), (73), (88), (107), (108), (114), (115),
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | | |            (658), (708), (746) are inconsistent by sub-proof
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | | |            #1154.
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | |   (747)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (747) gives:
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | | |   (748)  all_57_8 = e0 & op(e1, e1) = e0
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (748) implies:
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | | |   (749)  op(e1, e1) = e0
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9), (11), (13), (14), (15), (16), (18),
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | | |            (21), (23), (24), (26), (30), (31), (32), (34),
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | | |            (35), (37), (38), (40), (41), (42), (47), (48),
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | | |            (51), (53), (56), (58), (59), (60), (63), (65),
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | | |            (66), (67), (68), (69), (72), (73), (77), (78),
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | | |            (83), (85), (86), (87), (88), (92), (93), (96),
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | | |            (97), (98), (100), (101), (102), (106), (107),
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | | |            (108), (110), (112), (113), (114), (115), (119),
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | | |            (122), (123), (124), (127), (749) are inconsistent
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #838.
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | | |   (750)  all_57_11 = e0 & op(e1, e0) = e0
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (750) implies:
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | | |   (751)  all_57_11 = e0
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (66), (100), (107), (119), (699), (708),
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | | |            (716), (736), (751) are inconsistent by sub-proof
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | | |            #837.
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | |   (752)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | |            e1 & op(e1, e0) = e1)
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (752) gives:
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | |   (753)  all_57_8 = e1 & op(e1, e1) = e1
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (753) implies:
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | |   (754)  op(e1, e1) = e1
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (107), (658), (754) are inconsistent by
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2423.
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | |   (755)  all_57_11 = e1 & op(e1, e0) = e1
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (755) implies:
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | |   (756)  all_57_11 = e1
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (708), (756) imply:
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | |   (757)  e2 = e1
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (119), (757) imply:
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | |   (758)  all_57_3 = e1
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11), (14), (16), (41), (53), (59), (66),
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | |            (73), (100), (107), (110), (699), (716), (724),
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | |            (758) are inconsistent by sub-proof #1066.
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.06  | | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.06  | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.06  | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | |   (759)  all_57_12 = e3 & op(e0, e3) = e3
% 229.57/41.06  | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | ALPHA: (759) implies:
% 229.57/41.06  | | | | | | | | | | | | | | | | | |   (760)  all_57_12 = e3
% 229.57/41.06  | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (686), (760) imply:
% 229.57/41.06  | | | | | | | | | | | | | | | | | |   (761)  e3 = e2
% 229.57/41.06  | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | SIMP: (761) implies:
% 229.57/41.06  | | | | | | | | | | | | | | | | | |   (762)  e3 = e2
% 229.57/41.06  | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (713), (762) imply:
% 229.57/41.06  | | | | | | | | | | | | | | | | | |   (763)  all_57_1 = e2
% 229.57/41.06  | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (14), (16), (26), (35), (38), (41), (47),
% 229.57/41.06  | | | | | | | | | | | | | | | | | |            (53), (58), (59), (60), (65), (66), (69), (72),
% 229.57/41.06  | | | | | | | | | | | | | | | | | |            (73), (78), (83), (86), (88), (97), (102), (107),
% 229.57/41.06  | | | | | | | | | | | | | | | | | |            (108), (114), (119), (122), (124), (763) are
% 229.57/41.06  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #839.
% 229.57/41.06  | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | End of split
% 229.57/41.06  | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | End of split
% 229.57/41.06  | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | Case 2:
% 229.57/41.06  | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | |   (764)  all_57_3 = e0 & op(e2, e2) = e0
% 229.57/41.06  | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | ALPHA: (764) implies:
% 229.57/41.06  | | | | | | | | | | | | | | | |   (765)  op(e2, e2) = e0
% 229.57/41.06  | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | REF_CLOSE: (16), (66), (72), (765) are inconsistent by
% 229.57/41.06  | | | | | | | | | | | | | | | |            sub-proof #2472.
% 229.57/41.06  | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | End of split
% 229.57/41.06  | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | Case 2:
% 229.57/41.06  | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | |   (766)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 229.57/41.06  | | | | | | | | | | | | | | |            e0 & op(e2, e0) = e0)
% 229.57/41.06  | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | BETA: splitting (766) gives:
% 229.57/41.06  | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | Case 1:
% 229.57/41.06  | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | |   (767)  all_57_5 = e0 & op(e2, e1) = e0
% 229.57/41.06  | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | ALPHA: (767) implies:
% 229.57/41.06  | | | | | | | | | | | | | | | |   (768)  all_57_5 = e0
% 229.57/41.06  | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | REF_CLOSE: (13), (14), (16), (21), (23), (26), (35), (38),
% 229.57/41.06  | | | | | | | | | | | | | | | |            (41), (47), (53), (58), (59), (60), (66), (69),
% 229.57/41.06  | | | | | | | | | | | | | | | |            (73), (77), (78), (83), (86), (88), (97), (102),
% 229.57/41.06  | | | | | | | | | | | | | | | |            (107), (108), (114), (119), (122), (124), (713),
% 229.57/41.06  | | | | | | | | | | | | | | | |            (768) are inconsistent by sub-proof #880.
% 229.57/41.06  | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | Case 2:
% 229.57/41.06  | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | |   (769)  all_57_10 = e0 & op(e2, e0) = e0
% 229.57/41.06  | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | ALPHA: (769) implies:
% 229.57/41.06  | | | | | | | | | | | | | | | |   (770)  all_57_10 = e0
% 229.57/41.06  | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | BETA: splitting (15) gives:
% 229.57/41.06  | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.06  | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | |   (771)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 229.57/41.06  | | | | | | | | | | | | | | | | |            & op(e1, e2) = e0)
% 229.57/41.06  | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (16), (18), (21), (23), (41), (47), (58),
% 229.57/41.06  | | | | | | | | | | | | | | | | |            (66), (73), (88), (107), (108), (114), (115),
% 229.57/41.06  | | | | | | | | | | | | | | | | |            (658), (708), (771) are inconsistent by sub-proof
% 229.57/41.06  | | | | | | | | | | | | | | | | |            #1153.
% 229.57/41.06  | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.06  | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | |   (772)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 229.57/41.06  | | | | | | | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 229.57/41.06  | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | BETA: splitting (772) gives:
% 229.57/41.06  | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.06  | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | |   (773)  all_57_8 = e0 & op(e1, e1) = e0
% 229.57/41.06  | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | ALPHA: (773) implies:
% 229.57/41.06  | | | | | | | | | | | | | | | | | |   (774)  op(e1, e1) = e0
% 229.57/41.06  | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9), (11), (13), (14), (15), (16), (18),
% 229.57/41.06  | | | | | | | | | | | | | | | | | |            (21), (23), (24), (26), (30), (31), (32), (34),
% 229.57/41.06  | | | | | | | | | | | | | | | | | |            (35), (37), (38), (40), (41), (42), (47), (48),
% 229.57/41.06  | | | | | | | | | | | | | | | | | |            (51), (53), (56), (58), (59), (60), (63), (65),
% 229.57/41.06  | | | | | | | | | | | | | | | | | |            (66), (67), (68), (69), (72), (73), (77), (78),
% 229.57/41.06  | | | | | | | | | | | | | | | | | |            (83), (85), (86), (87), (88), (92), (93), (96),
% 229.57/41.06  | | | | | | | | | | | | | | | | | |            (97), (98), (100), (101), (102), (106), (107),
% 229.57/41.06  | | | | | | | | | | | | | | | | | |            (108), (110), (112), (113), (114), (115), (119),
% 229.57/41.06  | | | | | | | | | | | | | | | | | |            (122), (123), (124), (127), (774) are inconsistent
% 229.57/41.06  | | | | | | | | | | | | | | | | | |            by sub-proof #838.
% 229.57/41.06  | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.06  | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | |   (775)  all_57_11 = e0 & op(e1, e0) = e0
% 229.57/41.06  | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | ALPHA: (775) implies:
% 229.57/41.06  | | | | | | | | | | | | | | | | | |   (776)  all_57_11 = e0
% 229.57/41.06  | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (16), (41), (58), (66), (73), (83), (107),
% 229.57/41.06  | | | | | | | | | | | | | | | | | |            (108), (114), (770), (776) are inconsistent by
% 229.57/41.06  | | | | | | | | | | | | | | | | | |            sub-proof #1087.
% 229.57/41.06  | | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | | End of split
% 229.57/41.06  | | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | | End of split
% 229.57/41.06  | | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | | End of split
% 229.57/41.06  | | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | | End of split
% 229.57/41.06  | | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | End of split
% 229.57/41.06  | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | Case 2:
% 229.57/41.06  | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | |   (777)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 229.57/41.06  | | | | | | | | | | | | |            & op(e3, e0) = e3)
% 229.57/41.06  | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | | REF_CLOSE: (16), (41), (97), (124), (695), (777) are
% 229.57/41.06  | | | | | | | | | | | | |            inconsistent by sub-proof #2448.
% 229.57/41.06  | | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | End of split
% 229.57/41.06  | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | Case 2:
% 229.57/41.06  | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | |   (778)  all_57_15 = e2 & op(e0, e0) = e2
% 229.57/41.06  | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | REF_CLOSE: (41), (58), (778) are inconsistent by sub-proof
% 229.57/41.06  | | | | | | | | | | | |            #2323.
% 229.57/41.06  | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | End of split
% 229.57/41.06  | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | End of split
% 229.57/41.06  | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | End of split
% 229.57/41.06  | | | | | | | | | 
% 229.57/41.06  | | | | | | | | Case 2:
% 229.57/41.06  | | | | | | | | | 
% 229.57/41.06  | | | | | | | | |   (779)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 &
% 229.57/41.06  | | | | | | | | |            op(e0, e1) = e3)
% 229.57/41.06  | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | REF_CLOSE: (14), (16), (21), (23), (41), (47), (58), (60),
% 229.57/41.06  | | | | | | | | |            (66), (73), (86), (88), (107), (779) are
% 229.57/41.06  | | | | | | | | |            inconsistent by sub-proof #1794.
% 229.57/41.06  | | | | | | | | | 
% 229.57/41.06  | | | | | | | | End of split
% 229.57/41.06  | | | | | | | | 
% 229.57/41.06  | | | | | | | Case 2:
% 229.57/41.06  | | | | | | | | 
% 229.57/41.06  | | | | | | | |   (780)  all_57_9 = e2 & op(e3, e0) = e2
% 229.57/41.06  | | | | | | | | 
% 229.57/41.06  | | | | | | | | ALPHA: (780) implies:
% 229.57/41.06  | | | | | | | |   (781)  op(e3, e0) = e2
% 229.57/41.06  | | | | | | | | 
% 229.57/41.06  | | | | | | | | GROUND_INST: instantiating (16) with all_53_3, e2, e3, e0,
% 229.57/41.06  | | | | | | | |              simplifying with (51), (687) gives:
% 229.57/41.06  | | | | | | | |   (782)  all_53_3 = e2
% 229.57/41.06  | | | | | | | | 
% 229.57/41.06  | | | | | | | | GROUND_INST: instantiating (16) with all_53_12, e2, e0, e3,
% 229.57/41.06  | | | | | | | |              simplifying with (124), (781) gives:
% 229.57/41.06  | | | | | | | |   (783)  all_53_12 = e2
% 229.57/41.06  | | | | | | | | 
% 229.57/41.06  | | | | | | | | BETA: splitting (3) gives:
% 229.57/41.06  | | | | | | | | 
% 229.57/41.06  | | | | | | | | Case 1:
% 229.57/41.06  | | | | | | | | | 
% 229.57/41.06  | | | | | | | | |   (784)   ~ (all_48_2 = e0)
% 229.57/41.06  | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | REDUCE: (5), (784) imply:
% 229.57/41.06  | | | | | | | | |   (785)  $false
% 229.57/41.06  | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | CLOSE: (785) is inconsistent.
% 229.57/41.06  | | | | | | | | | 
% 229.57/41.06  | | | | | | | | Case 2:
% 229.57/41.06  | | | | | | | | | 
% 229.57/41.06  | | | | | | | | |   (786)  ( ~ (all_48_0 = e2) & op(all_48_1, e3) = all_48_0 &
% 229.57/41.06  | | | | | | | | |            op(e3, e0) = all_48_1 & $i(all_48_0) &
% 229.57/41.06  | | | | | | | | |            $i(all_48_1)) | ( ~ (all_48_1 = e1) & op(e3, e0) =
% 229.57/41.06  | | | | | | | | |            all_48_1 & $i(all_48_1))
% 229.57/41.06  | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | BETA: splitting (67) gives:
% 229.57/41.06  | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | Case 1:
% 229.57/41.06  | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | |   (787)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 229.57/41.06  | | | | | | | | | |            all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 229.57/41.06  | | | | | | | | | |            op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 229.57/41.06  | | | | | | | | | |              all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 229.57/41.06  | | | | | | | | | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 229.57/41.06  | | | | | | | | | |            op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 229.57/41.06  | | | | | | | | | |            $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 229.57/41.06  | | | | | | | | | |            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 &
% 229.57/41.06  | | | | | | | | | |            all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 229.57/41.06  | | | | | | | | | |              all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 229.57/41.06  | | | | | | | | | |            & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 229.57/41.06  | | | | | | | | | |              all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 229.57/41.06  | | | | | | | | | |            op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13 &
% 229.57/41.06  | | | | | | | | | |            op(e2, e0) = all_52_15 & $i(all_52_9) &
% 229.57/41.06  | | | | | | | | | |            $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 229.57/41.06  | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | BETA: splitting (787) gives:
% 229.57/41.06  | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | Case 1:
% 229.57/41.06  | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | |   (788)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 229.57/41.06  | | | | | | | | | | |          all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 229.57/41.06  | | | | | | | | | | |          op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 229.57/41.06  | | | | | | | | | | |            all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 229.57/41.06  | | | | | | | | | | |          op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 229.57/41.06  | | | | | | | | | | |          op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 229.57/41.06  | | | | | | | | | | |          $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 229.57/41.06  | | | | | | | | | | |          $i(all_52_7)
% 229.57/41.06  | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | ALPHA: (788) implies:
% 229.57/41.06  | | | | | | | | | | |   (789)  op(e3, e0) = all_52_7
% 229.57/41.06  | | | | | | | | | | |   (790)  op(all_52_7, all_52_7) = e0
% 229.57/41.06  | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | BETA: splitting (22) gives:
% 229.57/41.06  | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | Case 1:
% 229.57/41.06  | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | |   (791)   ~ (all_18_0 = e1) & op(all_18_1, e3) = all_18_0 &
% 229.57/41.06  | | | | | | | | | | | |          op(e3, e0) = all_18_1 & $i(all_18_0) &
% 229.57/41.06  | | | | | | | | | | | |          $i(all_18_1)
% 229.57/41.06  | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | ALPHA: (791) implies:
% 229.57/41.06  | | | | | | | | | | | |   (792)  op(e3, e0) = all_18_1
% 229.57/41.06  | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | GROUND_INST: instantiating (16) with e2, all_52_7, e0, e3,
% 229.57/41.06  | | | | | | | | | | | |              simplifying with (781), (789) gives:
% 229.57/41.06  | | | | | | | | | | | |   (793)  all_52_7 = e2
% 229.57/41.06  | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_18_1, all_52_7, e0,
% 229.57/41.06  | | | | | | | | | | | |              e3, simplifying with (789), (792) gives:
% 229.57/41.06  | | | | | | | | | | | |   (794)  all_52_7 = all_18_1
% 229.57/41.06  | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | COMBINE_EQS: (793), (794) imply:
% 229.57/41.06  | | | | | | | | | | | |   (795)  all_18_1 = e2
% 229.57/41.06  | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | REDUCE: (790), (793) imply:
% 229.57/41.06  | | | | | | | | | | | |   (796)  op(e2, e2) = e0
% 229.57/41.06  | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | REF_CLOSE: (16), (66), (72), (796) are inconsistent by
% 229.57/41.06  | | | | | | | | | | | |            sub-proof #2472.
% 229.57/41.06  | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | Case 2:
% 229.57/41.06  | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | |   (797)   ~ (all_18_1 = e2) & op(e3, e0) = all_18_1 &
% 229.57/41.06  | | | | | | | | | | | |          $i(all_18_1)
% 229.57/41.06  | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | ALPHA: (797) implies:
% 229.57/41.06  | | | | | | | | | | | |   (798)   ~ (all_18_1 = e2)
% 229.57/41.06  | | | | | | | | | | | |   (799)  op(e3, e0) = all_18_1
% 229.57/41.06  | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | | REF_CLOSE: (16), (781), (786), (798), (799) are inconsistent
% 229.57/41.06  | | | | | | | | | | | |            by sub-proof #1899.
% 229.57/41.06  | | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | End of split
% 229.57/41.06  | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | Case 2:
% 229.57/41.06  | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | |   (800)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 229.57/41.06  | | | | | | | | | | |          all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 229.57/41.06  | | | | | | | | | | |          op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 229.57/41.06  | | | | | | | | | | |            all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 229.57/41.06  | | | | | | | | | | |          & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 229.57/41.06  | | | | | | | | | | |          op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 229.57/41.06  | | | | | | | | | | |          $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 229.57/41.06  | | | | | | | | | | |          $i(all_52_15)
% 229.57/41.06  | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | ALPHA: (800) implies:
% 229.57/41.06  | | | | | | | | | | |   (801)  op(e2, e3) = all_52_9
% 229.57/41.06  | | | | | | | | | | |   (802)  op(all_52_9, all_52_9) = e3
% 229.57/41.06  | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | REF_CLOSE: (10), (16), (22), (36), (55), (59), (70), (105),
% 229.57/41.06  | | | | | | | | | | |            (781), (786), (801), (802) are inconsistent by
% 229.57/41.06  | | | | | | | | | | |            sub-proof #1898.
% 229.57/41.06  | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | End of split
% 229.57/41.06  | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | Case 2:
% 229.57/41.06  | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | |   (803)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 229.57/41.06  | | | | | | | | | |            all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 229.57/41.06  | | | | | | | | | |            op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 229.57/41.06  | | | | | | | | | |              all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 229.57/41.06  | | | | | | | | | |            & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 229.57/41.06  | | | | | | | | | |            & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 229.57/41.06  | | | | | | | | | |            & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 229.57/41.06  | | | | | | | | | |            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2
% 229.57/41.06  | | | | | | | | | |            & all_52_28 = e1 & all_52_30 = e0 & op(all_52_25,
% 229.57/41.06  | | | | | | | | | |              all_52_25) = e3 & op(all_52_27, all_52_27) = e2
% 229.57/41.06  | | | | | | | | | |            & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 229.57/41.06  | | | | | | | | | |              all_52_31) = e0 & op(e0, e3) = all_52_25 &
% 229.57/41.06  | | | | | | | | | |            op(e0, e2) = all_52_27 & op(e0, e1) = all_52_29 &
% 229.57/41.06  | | | | | | | | | |            op(e0, e0) = all_52_31 & $i(all_52_25) &
% 229.57/41.06  | | | | | | | | | |            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 229.57/41.06  | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | BETA: splitting (803) gives:
% 229.57/41.06  | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | Case 1:
% 229.57/41.06  | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | |   (804)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 229.57/41.06  | | | | | | | | | | |          all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 229.57/41.06  | | | | | | | | | | |          op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 229.57/41.06  | | | | | | | | | | |            all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 229.57/41.06  | | | | | | | | | | |          & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 229.57/41.06  | | | | | | | | | | |          & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 229.57/41.06  | | | | | | | | | | |          & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 229.57/41.06  | | | | | | | | | | |          $i(all_52_23)
% 229.57/41.06  | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | ALPHA: (804) implies:
% 229.57/41.06  | | | | | | | | | | |   (805)  op(e1, e1) = all_52_21
% 229.57/41.06  | | | | | | | | | | |   (806)  op(all_52_21, all_52_21) = e1
% 229.57/41.06  | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | REF_CLOSE: (16), (68), (72), (107), (127), (658), (687),
% 229.57/41.06  | | | | | | | | | | |            (805), (806) are inconsistent by sub-proof #835.
% 229.57/41.06  | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | Case 2:
% 229.57/41.06  | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | |   (807)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 229.57/41.06  | | | | | | | | | | |          all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 229.57/41.06  | | | | | | | | | | |          op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 229.57/41.06  | | | | | | | | | | |            all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 229.57/41.06  | | | | | | | | | | |          & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 229.57/41.06  | | | | | | | | | | |          & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 229.57/41.06  | | | | | | | | | | |          & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 229.57/41.06  | | | | | | | | | | |          $i(all_52_31)
% 229.57/41.06  | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | ALPHA: (807) implies:
% 229.57/41.06  | | | | | | | | | | |   (808)  op(e0, e3) = all_52_25
% 229.57/41.06  | | | | | | | | | | |   (809)  op(all_52_25, all_52_25) = e3
% 229.57/41.06  | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | | REF_CLOSE: (16), (41), (68), (72), (127), (687), (808), (809)
% 229.57/41.06  | | | | | | | | | | |            are inconsistent by sub-proof #833.
% 229.57/41.06  | | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | | End of split
% 229.57/41.06  | | | | | | | | | | 
% 229.57/41.06  | | | | | | | | | End of split
% 229.57/41.06  | | | | | | | | | 
% 229.57/41.06  | | | | | | | | End of split
% 229.57/41.06  | | | | | | | | 
% 229.57/41.06  | | | | | | | End of split
% 229.57/41.06  | | | | | | | 
% 229.57/41.06  | | | | | | End of split
% 229.57/41.06  | | | | | | 
% 229.57/41.06  | | | | | End of split
% 229.57/41.06  | | | | | 
% 229.57/41.06  | | | | End of split
% 229.57/41.06  | | | | 
% 229.57/41.06  | | | End of split
% 229.57/41.06  | | | 
% 229.57/41.06  | | Case 2:
% 229.57/41.06  | | | 
% 229.57/41.06  | | |   (810)  all_24_2 = e0
% 229.57/41.06  | | | 
% 229.57/41.06  | | | COMBINE_EQS: (111), (810) imply:
% 229.57/41.06  | | |   (811)  all_6_2 = e0
% 229.57/41.06  | | | 
% 229.57/41.06  | | | SIMP: (811) implies:
% 229.57/41.06  | | |   (812)  all_6_2 = e0
% 229.57/41.06  | | | 
% 229.57/41.06  | | | REDUCE: (21), (812) imply:
% 229.57/41.06  | | |   (813)   ~ (e3 = e0)
% 229.57/41.06  | | | 
% 229.57/41.06  | | | REDUCE: (23), (812) imply:
% 229.57/41.06  | | |   (814)  op(e1, e1) = e0
% 229.57/41.06  | | | 
% 229.57/41.06  | | | REF_CLOSE: (4), (9), (11), (13), (14), (15), (16), (18), (21), (23), (24),
% 229.57/41.06  | | |            (26), (30), (31), (32), (34), (35), (37), (38), (40), (41),
% 229.57/41.06  | | |            (42), (47), (48), (51), (53), (56), (58), (59), (60), (63),
% 229.57/41.06  | | |            (65), (66), (67), (68), (69), (72), (73), (77), (78), (83),
% 229.57/41.06  | | |            (85), (86), (87), (88), (92), (93), (96), (97), (98), (100),
% 229.57/41.06  | | |            (101), (102), (106), (107), (108), (110), (112), (113), (114),
% 229.57/41.06  | | |            (115), (119), (122), (123), (124), (127), (814) are
% 229.57/41.06  | | |            inconsistent by sub-proof #838.
% 229.57/41.06  | | | 
% 229.57/41.06  | | End of split
% 229.57/41.06  | | 
% 229.57/41.06  | End of split
% 229.57/41.06  | 
% 229.57/41.06  End of proof
% 229.57/41.06  
% 229.57/41.06  Sub-proof #833 shows that the following formulas are inconsistent:
% 229.57/41.06  ----------------------------------------------------------------
% 229.57/41.06    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.57/41.06           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.57/41.06    (2)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) = all_22_1
% 229.57/41.06           & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0, e3) =
% 229.57/41.06           all_22_1 & $i(all_22_1))
% 229.57/41.06    (3)  op(e0, e3) = all_52_25
% 229.57/41.06    (4)   ~ (e3 = e2)
% 229.57/41.06    (5)  op(all_52_25, all_52_25) = e3
% 229.57/41.06    (6)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) = all_12_1
% 229.57/41.06           & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0, e3) =
% 229.57/41.06           all_12_1 & $i(all_12_1))
% 229.57/41.06    (7)  op(e2, e2) = e2
% 229.57/41.06    (8)  op(e0, e3) = e2
% 229.57/41.06  
% 229.57/41.06  Begin of proof
% 229.57/41.06  | 
% 229.57/41.06  | BETA: splitting (2) gives:
% 229.57/41.06  | 
% 229.57/41.06  | Case 1:
% 229.57/41.06  | | 
% 229.57/41.06  | |   (9)   ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 229.57/41.06  | |        all_22_1 & $i(all_22_0) & $i(all_22_1)
% 229.57/41.06  | | 
% 229.57/41.06  | | ALPHA: (9) implies:
% 229.57/41.06  | |   (10)  op(e0, e3) = all_22_1
% 229.57/41.06  | | 
% 229.57/41.06  | | BETA: splitting (6) gives:
% 229.57/41.06  | | 
% 229.57/41.06  | | Case 1:
% 229.57/41.06  | | | 
% 229.57/41.06  | | |   (11)   ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 229.57/41.06  | | |         all_12_1 & $i(all_12_0) & $i(all_12_1)
% 229.57/41.06  | | | 
% 229.57/41.06  | | | ALPHA: (11) implies:
% 229.57/41.06  | | |   (12)  op(e0, e3) = all_12_1
% 229.57/41.06  | | | 
% 229.57/41.06  | | | REF_CLOSE: (1), (3), (4), (5), (7), (8), (10), (12) are inconsistent by
% 229.57/41.06  | | |            sub-proof #834.
% 229.57/41.06  | | | 
% 229.57/41.06  | | Case 2:
% 229.57/41.06  | | | 
% 229.57/41.06  | | |   (13)   ~ (all_12_1 = e1) & op(e0, e3) = all_12_1 & $i(all_12_1)
% 229.57/41.06  | | | 
% 229.57/41.06  | | | ALPHA: (13) implies:
% 229.57/41.06  | | |   (14)  op(e0, e3) = all_12_1
% 229.57/41.06  | | | 
% 229.57/41.06  | | | REF_CLOSE: (1), (3), (4), (5), (7), (8), (10), (14) are inconsistent by
% 229.57/41.06  | | |            sub-proof #834.
% 229.57/41.06  | | | 
% 229.57/41.06  | | End of split
% 229.57/41.06  | | 
% 229.57/41.06  | Case 2:
% 229.57/41.06  | | 
% 229.57/41.06  | |   (15)   ~ (all_22_1 = e2) & op(e0, e3) = all_22_1 & $i(all_22_1)
% 229.57/41.06  | | 
% 229.57/41.06  | | REF_CLOSE: (1), (8), (15) are inconsistent by sub-proof #836.
% 229.57/41.06  | | 
% 229.57/41.06  | End of split
% 229.57/41.06  | 
% 229.57/41.06  End of proof
% 229.57/41.06  
% 229.57/41.06  Sub-proof #834 shows that the following formulas are inconsistent:
% 229.57/41.06  ----------------------------------------------------------------
% 229.57/41.06    (1)  op(e0, e3) = all_12_1
% 229.57/41.06    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.57/41.06           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.57/41.06    (3)  op(e0, e3) = all_52_25
% 229.57/41.06    (4)   ~ (e3 = e2)
% 229.57/41.06    (5)  op(e0, e3) = all_22_1
% 229.57/41.06    (6)  op(all_52_25, all_52_25) = e3
% 229.57/41.06    (7)  op(e2, e2) = e2
% 229.57/41.06    (8)  op(e0, e3) = e2
% 229.57/41.06  
% 229.57/41.06  Begin of proof
% 229.57/41.06  | 
% 229.57/41.06  | GROUND_INST: instantiating (2) with e2, all_52_25, e3, e0, simplifying with
% 229.57/41.06  |              (3), (8) gives:
% 229.57/41.06  |   (9)  all_52_25 = e2
% 229.57/41.06  | 
% 229.57/41.06  | GROUND_INST: instantiating (2) with all_22_1, all_52_25, e3, e0, simplifying
% 229.57/41.06  |              with (3), (5) gives:
% 229.57/41.06  |   (10)  all_52_25 = all_22_1
% 229.57/41.06  | 
% 229.57/41.06  | GROUND_INST: instantiating (2) with all_12_1, all_52_25, e3, e0, simplifying
% 229.57/41.06  |              with (1), (3) gives:
% 229.57/41.06  |   (11)  all_52_25 = all_12_1
% 229.57/41.07  | 
% 229.57/41.07  | COMBINE_EQS: (10), (11) imply:
% 229.57/41.07  |   (12)  all_22_1 = all_12_1
% 229.57/41.07  | 
% 229.57/41.07  | COMBINE_EQS: (9), (10) imply:
% 229.57/41.07  |   (13)  all_22_1 = e2
% 229.57/41.07  | 
% 229.57/41.07  | COMBINE_EQS: (12), (13) imply:
% 229.57/41.07  |   (14)  all_12_1 = e2
% 229.57/41.07  | 
% 229.57/41.07  | REDUCE: (6), (9) imply:
% 229.57/41.07  |   (15)  op(e2, e2) = e3
% 229.57/41.07  | 
% 229.57/41.07  | REF_CLOSE: (2), (4), (7), (15) are inconsistent by sub-proof #2298.
% 229.57/41.07  | 
% 229.57/41.07  End of proof
% 229.57/41.07  
% 229.57/41.07  Sub-proof #835 shows that the following formulas are inconsistent:
% 229.57/41.07  ----------------------------------------------------------------
% 229.57/41.07    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.57/41.07           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.57/41.07    (2)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) = all_22_1
% 229.57/41.07           & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0, e3) =
% 229.57/41.07           all_22_1 & $i(all_22_1))
% 229.57/41.07    (3)  op(e1, e1) = all_52_21
% 229.57/41.07    (4)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) = all_12_1
% 229.57/41.07           & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0, e3) =
% 229.57/41.07           all_12_1 & $i(all_12_1))
% 229.57/41.07    (5)  op(e2, e2) = e2
% 229.57/41.07    (6)  op(e1, e1) = e2
% 229.57/41.07    (7)   ~ (e2 = e1)
% 229.57/41.07    (8)  op(e0, e3) = e2
% 229.57/41.07    (9)  op(all_52_21, all_52_21) = e1
% 229.57/41.07  
% 229.57/41.07  Begin of proof
% 229.57/41.07  | 
% 229.57/41.07  | BETA: splitting (2) gives:
% 229.57/41.07  | 
% 229.57/41.07  | Case 1:
% 229.57/41.07  | | 
% 229.57/41.07  | |   (10)   ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 229.57/41.07  | |         all_22_1 & $i(all_22_0) & $i(all_22_1)
% 229.57/41.07  | | 
% 229.57/41.07  | | ALPHA: (10) implies:
% 229.57/41.07  | |   (11)  op(e0, e3) = all_22_1
% 229.57/41.07  | | 
% 229.57/41.07  | | BETA: splitting (4) gives:
% 229.57/41.07  | | 
% 229.57/41.07  | | Case 1:
% 229.57/41.07  | | | 
% 229.57/41.07  | | | 
% 229.57/41.07  | | | GROUND_INST: instantiating (1) with e2, all_52_21, e1, e1, simplifying
% 229.57/41.07  | | |              with (3), (6) gives:
% 229.57/41.07  | | |   (12)  all_52_21 = e2
% 229.57/41.07  | | | 
% 229.57/41.07  | | | REDUCE: (9), (12) imply:
% 229.57/41.07  | | |   (13)  op(e2, e2) = e1
% 229.57/41.07  | | | 
% 229.57/41.07  | | | REF_CLOSE: (1), (5), (7), (13) are inconsistent by sub-proof #2306.
% 229.57/41.07  | | | 
% 229.57/41.07  | | Case 2:
% 229.57/41.07  | | | 
% 229.57/41.07  | | |   (14)   ~ (all_12_1 = e1) & op(e0, e3) = all_12_1 & $i(all_12_1)
% 229.57/41.07  | | | 
% 229.57/41.07  | | | ALPHA: (14) implies:
% 229.57/41.07  | | |   (15)   ~ (all_12_1 = e1)
% 229.57/41.07  | | |   (16)  op(e0, e3) = all_12_1
% 229.57/41.07  | | | 
% 229.57/41.07  | | | GROUND_INST: instantiating (1) with e2, all_22_1, e3, e0, simplifying with
% 229.57/41.07  | | |              (8), (11) gives:
% 229.57/41.07  | | |   (17)  all_22_1 = e2
% 229.57/41.07  | | | 
% 229.57/41.07  | | | GROUND_INST: instantiating (1) with all_12_1, all_22_1, e3, e0,
% 229.57/41.07  | | |              simplifying with (11), (16) gives:
% 229.57/41.07  | | |   (18)  all_22_1 = all_12_1
% 229.57/41.07  | | | 
% 229.57/41.07  | | | GROUND_INST: instantiating (1) with e2, all_52_21, e1, e1, simplifying
% 229.57/41.07  | | |              with (3), (6) gives:
% 229.57/41.07  | | |   (19)  all_52_21 = e2
% 229.57/41.07  | | | 
% 229.57/41.07  | | | COMBINE_EQS: (17), (18) imply:
% 229.57/41.07  | | |   (20)  all_12_1 = e2
% 229.57/41.07  | | | 
% 229.57/41.07  | | | REDUCE: (9), (19) imply:
% 229.57/41.07  | | |   (21)  op(e2, e2) = e1
% 229.57/41.07  | | | 
% 229.57/41.07  | | | REF_CLOSE: (1), (5), (7), (21) are inconsistent by sub-proof #2306.
% 229.57/41.07  | | | 
% 229.57/41.07  | | End of split
% 229.57/41.07  | | 
% 229.57/41.07  | Case 2:
% 229.57/41.07  | | 
% 229.57/41.07  | |   (22)   ~ (all_22_1 = e2) & op(e0, e3) = all_22_1 & $i(all_22_1)
% 229.57/41.07  | | 
% 229.57/41.07  | | REF_CLOSE: (1), (8), (22) are inconsistent by sub-proof #836.
% 229.57/41.07  | | 
% 229.57/41.07  | End of split
% 229.57/41.07  | 
% 229.57/41.07  End of proof
% 229.57/41.07  
% 229.57/41.07  Sub-proof #836 shows that the following formulas are inconsistent:
% 229.57/41.07  ----------------------------------------------------------------
% 229.57/41.07    (1)   ~ (all_22_1 = e2) & op(e0, e3) = all_22_1 & $i(all_22_1)
% 229.57/41.07    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.57/41.07           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.57/41.07    (3)  op(e0, e3) = e2
% 229.57/41.07  
% 229.57/41.07  Begin of proof
% 229.57/41.07  | 
% 229.57/41.07  | ALPHA: (1) implies:
% 229.57/41.07  |   (4)   ~ (all_22_1 = e2)
% 229.57/41.07  |   (5)  op(e0, e3) = all_22_1
% 229.57/41.07  | 
% 229.57/41.07  | GROUND_INST: instantiating (2) with e2, all_22_1, e3, e0, simplifying with
% 229.57/41.07  |              (3), (5) gives:
% 229.57/41.07  |   (6)  all_22_1 = e2
% 229.57/41.07  | 
% 229.57/41.07  | REDUCE: (4), (6) imply:
% 229.57/41.07  |   (7)  $false
% 229.57/41.07  | 
% 229.57/41.07  | CLOSE: (7) is inconsistent.
% 229.57/41.07  | 
% 229.57/41.07  End of proof
% 229.57/41.07  
% 229.57/41.07  Sub-proof #837 shows that the following formulas are inconsistent:
% 229.57/41.07  ----------------------------------------------------------------
% 229.57/41.07    (1)  all_57_10 = e1
% 229.57/41.07    (2)   ~ (e3 = e2)
% 229.57/41.07    (3)  all_57_5 = e3
% 229.57/41.07    (4)  all_57_11 = e0
% 229.57/41.07    (5)  all_57_11 = e2
% 229.57/41.07    (6)   ~ (e2 = e0)
% 229.57/41.07    (7)  all_57_2 = e0
% 229.57/41.07    (8)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.57/41.07         (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.57/41.07    (9)   ~ (e2 = e1)
% 229.57/41.07    (10)  all_57_3 = e2
% 229.57/41.07  
% 229.57/41.07  Begin of proof
% 229.57/41.07  | 
% 229.57/41.07  | COMBINE_EQS: (4), (5) imply:
% 229.57/41.07  |   (11)  e2 = e0
% 229.57/41.07  | 
% 229.57/41.07  | COMBINE_EQS: (10), (11) imply:
% 229.57/41.07  |   (12)  all_57_3 = e0
% 229.57/41.07  | 
% 229.57/41.07  | REF_CLOSE: (1), (2), (3), (6), (7), (8), (9), (12) are inconsistent by
% 229.57/41.07  |            sub-proof #2254.
% 229.57/41.07  | 
% 229.57/41.07  End of proof
% 229.57/41.07  
% 229.57/41.07  Sub-proof #838 shows that the following formulas are inconsistent:
% 229.57/41.07  ----------------------------------------------------------------
% 229.57/41.07    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 229.57/41.07    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.57/41.07         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.57/41.07    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.57/41.07         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.57/41.07    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.57/41.07         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.57/41.07    (5)   ~ (e3 = e1)
% 229.57/41.07    (6)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 229.57/41.07         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 229.57/41.07    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.57/41.07           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.57/41.07    (8)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.57/41.07         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.57/41.07    (9)   ~ (all_6_2 = e3)
% 229.57/41.07    (10)  op(e1, e1) = all_6_2
% 229.57/41.07    (11)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 229.57/41.07    (12)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.57/41.07          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.57/41.07    (13)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 229.57/41.07            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 229.57/41.07              e3) = all_22_1 & $i(all_22_1))
% 229.57/41.07    (14)   ~ (all_53_13 = e2)
% 229.57/41.07    (15)   ~ (all_53_4 = all_53_12)
% 229.57/41.07    (16)   ~ (all_53_7 = e2)
% 229.57/41.07    (17)   ~ (all_53_13 = e3)
% 229.57/41.07    (18)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.57/41.07          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.57/41.07    (19)   ~ (all_53_12 = all_53_13)
% 229.57/41.07    (20)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.57/41.07          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.57/41.07    (21)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 229.57/41.07          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.57/41.07    (22)   ~ (e3 = e2)
% 229.57/41.07    (23)  all_55_1 = all_53_4
% 229.57/41.07    (24)   ~ (e3 = e0)
% 229.57/41.07    (25)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 229.57/41.07          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 229.57/41.07    (26)  op(e0, e3) = all_53_3
% 229.57/41.07    (27)  all_57_0 = e0
% 229.57/41.07    (28)   ~ (all_53_4 = all_53_7)
% 229.57/41.07    (29)  all_57_15 = e3
% 229.57/41.07    (30)  op(e3, e3) = e0
% 229.57/41.07    (31)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.57/41.07          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.57/41.07            e1)
% 229.57/41.07    (32)  op(e3, e2) = all_53_4
% 229.57/41.07    (33)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.57/41.07          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.57/41.07    (34)   ~ (e2 = e0)
% 229.57/41.07    (35)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 229.57/41.07            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 229.57/41.07            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 229.57/41.07            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 229.57/41.07              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 229.57/41.07            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 229.57/41.07            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 229.57/41.07              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 229.57/41.07              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 229.57/41.07            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 229.57/41.07            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 229.57/41.07            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 229.57/41.07              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 229.57/41.07              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 229.57/41.07            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 229.57/41.07              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 229.57/41.07            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 229.57/41.07            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 229.57/41.07              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 229.57/41.07              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 229.57/41.07            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 229.57/41.07            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 229.57/41.07    (36)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 229.57/41.07            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 229.57/41.07              e3) = all_12_1 & $i(all_12_1))
% 229.57/41.07    (37)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.57/41.07          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.57/41.07    (38)  op(e2, e2) = e2
% 229.57/41.07    (39)   ~ (e1 = e0)
% 229.57/41.07    (40)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.57/41.07          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.57/41.07    (41)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.57/41.07          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.57/41.07    (42)  op(e0, e0) = e3
% 229.57/41.07    (43)  op(e0, e2) = all_53_7
% 229.57/41.07    (44)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.57/41.07          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.57/41.07            e2)
% 229.57/41.07    (45)   ~ (all_53_3 = e0)
% 229.57/41.07    (46)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.57/41.07              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.57/41.07                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.57/41.07                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.57/41.07    (47)  op(e1, e1) = e0
% 229.57/41.07    (48)  op(e2, e0) = all_53_13
% 229.57/41.07    (49)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.57/41.07          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.57/41.07    (50)  all_55_3 = all_53_12
% 229.57/41.07    (51)   ~ (all_53_12 = e3)
% 229.57/41.07    (52)   ~ (all_53_4 = e2)
% 229.57/41.07    (53)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.57/41.07          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.57/41.07    (54)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.57/41.07          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.57/41.07    (55)   ~ (all_53_12 = e0)
% 229.57/41.07    (56)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.57/41.07          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 229.57/41.07    (57)   ~ (e2 = e1)
% 229.57/41.07    (58)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.57/41.07          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.57/41.07    (59)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.57/41.07          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.57/41.07    (60)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 229.57/41.07          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 229.57/41.07    (61)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.57/41.07          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.57/41.07    (62)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.57/41.07          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.57/41.07    (63)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 229.57/41.07          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 229.57/41.07    (64)  all_57_3 = e2
% 229.57/41.07    (65)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.57/41.07          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.57/41.07    (66)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 229.57/41.07          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 229.57/41.07    (67)  op(e3, e0) = all_53_12
% 229.57/41.07  
% 229.57/41.07  Begin of proof
% 229.57/41.07  | 
% 229.57/41.07  | BETA: splitting (33) gives:
% 229.57/41.07  | 
% 229.57/41.07  | Case 1:
% 229.57/41.07  | | 
% 229.57/41.07  | |   (68)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) =
% 229.57/41.07  | |           e0)
% 229.57/41.07  | | 
% 229.57/41.07  | | BETA: splitting (68) gives:
% 229.57/41.07  | | 
% 229.57/41.07  | | Case 1:
% 229.57/41.07  | | | 
% 229.57/41.07  | | |   (69)  all_57_1 = e0 & op(e3, e2) = e0
% 229.57/41.07  | | | 
% 229.57/41.07  | | | ALPHA: (69) implies:
% 229.57/41.07  | | |   (70)  all_57_1 = e0
% 229.57/41.07  | | | 
% 229.57/41.07  | | | REF_CLOSE: (4), (5), (7), (12), (18), (20), (22), (24), (27), (29), (30),
% 229.57/41.07  | | |            (31), (34), (37), (39), (41), (42), (44), (46), (51), (55),
% 229.57/41.07  | | |            (57), (58), (62), (64), (65), (67), (70) are inconsistent by
% 229.57/41.07  | | |            sub-proof #882.
% 229.57/41.07  | | | 
% 229.57/41.07  | | Case 2:
% 229.57/41.07  | | | 
% 229.57/41.07  | | |   (71)  all_57_3 = e0 & op(e2, e2) = e0
% 229.57/41.07  | | | 
% 229.57/41.07  | | | ALPHA: (71) implies:
% 229.57/41.07  | | |   (72)  op(e2, e2) = e0
% 229.57/41.07  | | | 
% 229.57/41.07  | | | REF_CLOSE: (7), (34), (38), (72) are inconsistent by sub-proof #2472.
% 229.57/41.07  | | | 
% 229.57/41.07  | | End of split
% 229.57/41.07  | | 
% 229.57/41.07  | Case 2:
% 229.57/41.07  | | 
% 229.57/41.07  | |   (73)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 229.57/41.07  | |           e0)
% 229.57/41.07  | | 
% 229.57/41.07  | | BETA: splitting (73) gives:
% 229.57/41.07  | | 
% 229.57/41.07  | | Case 1:
% 229.57/41.07  | | | 
% 229.57/41.07  | | |   (74)  all_57_7 = e0 & op(e1, e2) = e0
% 229.57/41.07  | | | 
% 229.57/41.07  | | | ALPHA: (74) implies:
% 229.57/41.07  | | |   (75)  all_57_7 = e0
% 229.57/41.07  | | | 
% 229.57/41.07  | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (14), (18),
% 229.57/41.07  | | |            (20), (21), (22), (24), (25), (26), (27), (29), (30), (31),
% 229.57/41.07  | | |            (33), (34), (37), (38), (39), (40), (41), (42), (44), (45),
% 229.57/41.07  | | |            (46), (47), (48), (49), (51), (53), (54), (55), (56), (57),
% 229.57/41.07  | | |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67),
% 229.57/41.07  | | |            (75) are inconsistent by sub-proof #889.
% 229.57/41.07  | | | 
% 229.57/41.07  | | Case 2:
% 229.57/41.07  | | | 
% 229.57/41.07  | | |   (76)  all_57_13 = e0 & op(e0, e2) = e0
% 229.57/41.07  | | | 
% 229.57/41.07  | | | ALPHA: (76) implies:
% 229.57/41.07  | | |   (77)  all_57_13 = e0
% 229.57/41.07  | | |   (78)  op(e0, e2) = e0
% 229.57/41.07  | | | 
% 229.57/41.07  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 229.57/41.07  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 229.57/41.07  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 229.57/41.07  | | |            (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 229.57/41.07  | | |            (43), (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 229.57/41.07  | | |            (53), (54), (55), (56), (57), (58), (59), (60), (61), (62),
% 229.57/41.07  | | |            (63), (64), (65), (66), (67), (77), (78) are inconsistent by
% 229.57/41.07  | | |            sub-proof #840.
% 229.57/41.07  | | | 
% 229.57/41.07  | | End of split
% 229.57/41.07  | | 
% 229.57/41.07  | End of split
% 229.57/41.07  | 
% 229.57/41.07  End of proof
% 229.57/41.07  
% 229.57/41.07  Sub-proof #839 shows that the following formulas are inconsistent:
% 229.57/41.07  ----------------------------------------------------------------
% 229.57/41.07    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.57/41.07         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.57/41.07    (2)   ~ (e3 = e1)
% 229.57/41.07    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.57/41.07           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.57/41.07    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.57/41.07         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.57/41.07    (5)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.57/41.07         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.57/41.07    (6)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.57/41.07         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.57/41.07    (7)   ~ (e3 = e2)
% 229.57/41.07    (8)   ~ (e3 = e0)
% 229.57/41.07    (9)  all_57_1 = e2
% 229.57/41.07    (10)  all_57_0 = e0
% 229.57/41.07    (11)  all_57_15 = e3
% 229.57/41.07    (12)  op(e3, e3) = e0
% 229.57/41.07    (13)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.57/41.07          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.57/41.07            e1)
% 229.57/41.07    (14)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.57/41.07          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.57/41.07    (15)   ~ (e2 = e0)
% 229.57/41.07    (16)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.57/41.07          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.57/41.07    (17)  op(e2, e2) = e2
% 229.57/41.07    (18)   ~ (e1 = e0)
% 229.57/41.07    (19)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.57/41.07          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.57/41.07    (20)  op(e0, e0) = e3
% 229.57/41.07    (21)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.57/41.07          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.57/41.07            e2)
% 229.57/41.07    (22)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.57/41.07              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.57/41.07                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.57/41.07                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.57/41.07    (23)   ~ (all_53_12 = e3)
% 229.57/41.07    (24)   ~ (all_53_12 = e0)
% 229.57/41.07    (25)   ~ (e2 = e1)
% 229.57/41.07    (26)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.57/41.07          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.57/41.07    (27)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.57/41.07          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.57/41.07    (28)  all_57_3 = e2
% 229.57/41.07    (29)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.57/41.07          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.57/41.07    (30)  op(e3, e0) = all_53_12
% 229.57/41.07  
% 229.57/41.07  Begin of proof
% 229.57/41.07  | 
% 229.57/41.07  | BETA: splitting (16) gives:
% 229.57/41.07  | 
% 229.57/41.07  | Case 1:
% 229.57/41.07  | | 
% 229.57/41.07  | |   (31)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) =
% 229.57/41.07  | |           e3)
% 229.57/41.07  | | 
% 229.57/41.07  | | REF_CLOSE: (3), (7), (8), (9), (12), (31) are inconsistent by sub-proof
% 229.57/41.07  | |            #1407.
% 229.57/41.07  | | 
% 229.57/41.07  | Case 2:
% 229.57/41.07  | | 
% 229.57/41.07  | |   (32)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) =
% 229.57/41.07  | |           e3)
% 229.57/41.07  | | 
% 229.57/41.07  | | BETA: splitting (32) gives:
% 229.57/41.07  | | 
% 229.57/41.07  | | Case 1:
% 229.57/41.07  | | | 
% 229.57/41.07  | | |   (33)  all_57_4 = e3 & op(e3, e1) = e3
% 229.57/41.07  | | | 
% 229.57/41.07  | | | ALPHA: (33) implies:
% 229.57/41.07  | | |   (34)  all_57_4 = e3
% 229.57/41.07  | | | 
% 229.57/41.08  | | | BETA: splitting (19) gives:
% 229.57/41.08  | | | 
% 229.57/41.08  | | | Case 1:
% 229.57/41.08  | | | | 
% 229.57/41.08  | | | |   (35)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2)
% 229.57/41.08  | | | |           = e3)
% 229.57/41.08  | | | | 
% 229.57/41.08  | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (12), (15), (18), (25),
% 229.57/41.08  | | | |            (28), (34), (35) are inconsistent by sub-proof #892.
% 229.57/41.08  | | | | 
% 229.57/41.08  | | | Case 2:
% 229.57/41.08  | | | | 
% 229.57/41.08  | | | |   (36)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2)
% 229.57/41.08  | | | |           = e3)
% 229.57/41.08  | | | | 
% 229.57/41.08  | | | | BETA: splitting (36) gives:
% 229.57/41.08  | | | | 
% 229.57/41.08  | | | | Case 1:
% 229.57/41.08  | | | | | 
% 229.57/41.08  | | | | |   (37)  all_57_7 = e3 & op(e1, e2) = e3
% 229.57/41.08  | | | | | 
% 229.57/41.08  | | | | | ALPHA: (37) implies:
% 229.57/41.08  | | | | |   (38)  all_57_7 = e3
% 229.57/41.08  | | | | | 
% 229.57/41.08  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 229.57/41.08  | | | | |            (12), (13), (14), (15), (16), (17), (18), (19), (20), (21),
% 229.57/41.08  | | | | |            (22), (23), (24), (25), (26), (27), (28), (29), (30), (34),
% 229.57/41.08  | | | | |            (38) are inconsistent by sub-proof #870.
% 229.57/41.08  | | | | | 
% 229.57/41.08  | | | | Case 2:
% 229.57/41.08  | | | | | 
% 229.57/41.08  | | | | |   (39)  all_57_13 = e3 & op(e0, e2) = e3
% 229.57/41.08  | | | | | 
% 229.57/41.08  | | | | | ALPHA: (39) implies:
% 229.57/41.08  | | | | |   (40)  all_57_13 = e3
% 229.57/41.08  | | | | | 
% 229.57/41.08  | | | | | REF_CLOSE: (2), (3), (7), (8), (11), (13), (15), (18), (20), (21),
% 229.57/41.08  | | | | |            (22), (25), (40) are inconsistent by sub-proof #1792.
% 229.57/41.08  | | | | | 
% 229.57/41.08  | | | | End of split
% 229.57/41.08  | | | | 
% 229.57/41.08  | | | End of split
% 229.57/41.08  | | | 
% 229.57/41.08  | | Case 2:
% 229.57/41.08  | | | 
% 229.57/41.08  | | |   (41)  all_57_9 = e3 & op(e3, e0) = e3
% 229.57/41.08  | | | 
% 229.57/41.08  | | | ALPHA: (41) implies:
% 229.57/41.08  | | |   (42)  op(e3, e0) = e3
% 229.57/41.08  | | | 
% 229.57/41.08  | | | REF_CLOSE: (3), (23), (30), (42) are inconsistent by sub-proof #2458.
% 229.57/41.08  | | | 
% 229.57/41.08  | | End of split
% 229.57/41.08  | | 
% 229.57/41.08  | End of split
% 229.57/41.08  | 
% 229.57/41.08  End of proof
% 229.57/41.08  
% 229.57/41.08  Sub-proof #840 shows that the following formulas are inconsistent:
% 229.57/41.08  ----------------------------------------------------------------
% 229.57/41.08    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 229.57/41.08    (2)  op(e0, e2) = e0
% 229.57/41.08    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.57/41.08         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.57/41.08    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.57/41.08         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.57/41.08    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.57/41.08         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.57/41.08    (6)   ~ (e3 = e1)
% 229.57/41.08    (7)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 229.57/41.08         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 229.57/41.08    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.57/41.08           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.57/41.08    (9)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.57/41.08         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.57/41.08    (10)   ~ (all_6_2 = e3)
% 229.57/41.08    (11)  op(e1, e1) = all_6_2
% 229.57/41.08    (12)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 229.57/41.08    (13)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.57/41.08          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.57/41.08    (14)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 229.57/41.08            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 229.57/41.08              e3) = all_22_1 & $i(all_22_1))
% 229.57/41.08    (15)   ~ (all_53_13 = e2)
% 229.57/41.08    (16)   ~ (all_53_4 = all_53_12)
% 229.57/41.08    (17)   ~ (all_53_7 = e2)
% 229.57/41.08    (18)   ~ (all_53_13 = e3)
% 229.57/41.08    (19)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.57/41.08          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.57/41.08    (20)   ~ (all_53_12 = all_53_13)
% 229.57/41.08    (21)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.57/41.08          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.57/41.08    (22)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 229.57/41.08          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.57/41.08    (23)   ~ (e3 = e2)
% 229.57/41.08    (24)  all_55_1 = all_53_4
% 229.57/41.08    (25)   ~ (e3 = e0)
% 229.57/41.08    (26)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 229.57/41.08          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 229.57/41.08    (27)  op(e0, e3) = all_53_3
% 229.57/41.08    (28)  all_57_0 = e0
% 229.57/41.08    (29)   ~ (all_53_4 = all_53_7)
% 229.57/41.08    (30)  all_57_15 = e3
% 229.57/41.08    (31)  op(e3, e3) = e0
% 229.57/41.08    (32)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.57/41.08          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.57/41.08            e1)
% 229.57/41.08    (33)  op(e3, e2) = all_53_4
% 229.57/41.08    (34)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.57/41.08          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.57/41.08    (35)   ~ (e2 = e0)
% 229.57/41.08    (36)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 229.57/41.08            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 229.57/41.08            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 229.57/41.08            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 229.57/41.08              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 229.57/41.08            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 229.57/41.08            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 229.57/41.08              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 229.57/41.08              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 229.57/41.08            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 229.57/41.08            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 229.57/41.08            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 229.57/41.08              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 229.57/41.08              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 229.57/41.08            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 229.57/41.08              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 229.57/41.08            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 229.57/41.08            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 229.57/41.08              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 229.57/41.08              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 229.57/41.08            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 229.57/41.08            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 229.57/41.08    (37)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 229.57/41.08            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 229.57/41.08              e3) = all_12_1 & $i(all_12_1))
% 229.57/41.08    (38)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.57/41.08          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.57/41.08    (39)  op(e2, e2) = e2
% 229.57/41.08    (40)   ~ (e1 = e0)
% 229.57/41.08    (41)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.57/41.08          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.57/41.08    (42)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.57/41.08          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.57/41.08    (43)  op(e0, e0) = e3
% 229.57/41.08    (44)  op(e0, e2) = all_53_7
% 229.57/41.08    (45)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.57/41.08          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.57/41.08            e2)
% 229.57/41.08    (46)   ~ (all_53_3 = e0)
% 229.57/41.08    (47)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.57/41.08              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.57/41.08                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.57/41.08                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.57/41.08    (48)  op(e1, e1) = e0
% 229.57/41.08    (49)  op(e2, e0) = all_53_13
% 229.57/41.08    (50)  all_57_13 = e0
% 229.57/41.08    (51)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.57/41.08          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.57/41.08    (52)  all_55_3 = all_53_12
% 229.57/41.08    (53)   ~ (all_53_12 = e3)
% 229.57/41.08    (54)   ~ (all_53_4 = e2)
% 229.57/41.08    (55)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.57/41.08          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.57/41.08    (56)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.57/41.08          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.57/41.08    (57)   ~ (all_53_12 = e0)
% 229.57/41.08    (58)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.57/41.08          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 229.57/41.08    (59)   ~ (e2 = e1)
% 229.57/41.08    (60)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.57/41.08          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.57/41.08    (61)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.57/41.08          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.57/41.08    (62)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 229.57/41.08          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 229.57/41.08    (63)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.57/41.08          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.57/41.08    (64)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.57/41.08          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.57/41.08    (65)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 229.57/41.08          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 229.57/41.08    (66)  all_57_3 = e2
% 229.57/41.08    (67)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.57/41.08          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.57/41.08    (68)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 229.57/41.08          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 229.57/41.08    (69)  op(e3, e0) = all_53_12
% 229.57/41.08  
% 229.57/41.08  Begin of proof
% 229.57/41.08  | 
% 229.57/41.08  | BETA: splitting (47) gives:
% 229.57/41.08  | 
% 229.57/41.08  | Case 1:
% 229.57/41.08  | | 
% 229.57/41.08  | |   (70)  all_57_15 = e0 & op(e0, e0) = e0
% 229.57/41.08  | | 
% 229.57/41.08  | | ALPHA: (70) implies:
% 229.57/41.08  | |   (71)  op(e0, e0) = e0
% 229.57/41.08  | | 
% 229.57/41.08  | | REF_CLOSE: (8), (25), (43), (71) are inconsistent by sub-proof #2304.
% 229.57/41.08  | | 
% 229.57/41.08  | Case 2:
% 229.57/41.08  | | 
% 229.57/41.08  | |   (72)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 229.57/41.08  | |             e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0 &
% 229.57/41.08  | |             op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 229.57/41.08  | |           (all_57_14 = e0 & op(e0, e1) = e0))
% 229.57/41.08  | | 
% 229.57/41.08  | | ALPHA: (72) implies:
% 229.57/41.08  | |   (73)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 229.57/41.08  | |           e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.57/41.08  | |   (74)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 229.57/41.08  | |           e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 229.57/41.08  | | 
% 229.57/41.08  | | BETA: splitting (58) gives:
% 229.57/41.08  | | 
% 229.57/41.08  | | Case 1:
% 229.57/41.08  | | | 
% 229.57/41.08  | | |   (75)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) =
% 229.57/41.08  | | |           e0)
% 229.57/41.08  | | | 
% 229.57/41.08  | | | BETA: splitting (75) gives:
% 229.57/41.08  | | | 
% 229.57/41.08  | | | Case 1:
% 229.57/41.08  | | | | 
% 229.57/41.08  | | | |   (76)  all_57_2 = e0 & op(e2, e3) = e0
% 229.57/41.08  | | | | 
% 229.57/41.08  | | | | ALPHA: (76) implies:
% 229.57/41.08  | | | |   (77)  all_57_2 = e0
% 229.57/41.08  | | | | 
% 229.57/41.08  | | | | BETA: splitting (51) gives:
% 229.57/41.08  | | | | 
% 229.57/41.08  | | | | Case 1:
% 229.57/41.08  | | | | | 
% 229.57/41.08  | | | | |   (78)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2,
% 229.57/41.08  | | | | |             e2) = e3)
% 229.57/41.08  | | | | | 
% 229.57/41.08  | | | | | BETA: splitting (78) gives:
% 229.57/41.08  | | | | | 
% 229.57/41.08  | | | | | Case 1:
% 229.57/41.08  | | | | | | 
% 229.57/41.08  | | | | | |   (79)  all_57_2 = e3 & op(e2, e3) = e3
% 229.57/41.08  | | | | | | 
% 229.57/41.08  | | | | | | ALPHA: (79) implies:
% 229.57/41.08  | | | | | |   (80)  all_57_2 = e3
% 229.57/41.08  | | | | | | 
% 229.57/41.08  | | | | | | REF_CLOSE: (25), (77), (80) are inconsistent by sub-proof #2258.
% 229.57/41.08  | | | | | | 
% 229.57/41.08  | | | | | Case 2:
% 229.57/41.08  | | | | | | 
% 229.57/41.08  | | | | | |   (81)  all_57_3 = e3 & op(e2, e2) = e3
% 229.57/41.08  | | | | | | 
% 229.57/41.08  | | | | | | ALPHA: (81) implies:
% 229.57/41.08  | | | | | |   (82)  all_57_3 = e3
% 229.57/41.08  | | | | | | 
% 229.57/41.08  | | | | | | REF_CLOSE: (23), (66), (82) are inconsistent by sub-proof #1166.
% 229.57/41.08  | | | | | | 
% 229.57/41.08  | | | | | End of split
% 229.57/41.08  | | | | | 
% 229.57/41.08  | | | | Case 2:
% 229.57/41.08  | | | | | 
% 229.57/41.08  | | | | |   (83)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2,
% 229.57/41.08  | | | | |             e0) = e3)
% 229.57/41.08  | | | | | 
% 229.57/41.08  | | | | | BETA: splitting (83) gives:
% 229.57/41.08  | | | | | 
% 229.57/41.08  | | | | | Case 1:
% 229.57/41.08  | | | | | | 
% 229.57/41.08  | | | | | |   (84)  all_57_5 = e3 & op(e2, e1) = e3
% 229.57/41.08  | | | | | | 
% 229.57/41.08  | | | | | | ALPHA: (84) implies:
% 229.57/41.08  | | | | | |   (85)  all_57_5 = e3
% 229.57/41.08  | | | | | | 
% 229.57/41.08  | | | | | | BETA: splitting (74) gives:
% 229.57/41.08  | | | | | | 
% 229.57/41.08  | | | | | | Case 1:
% 229.57/41.08  | | | | | | | 
% 229.57/41.08  | | | | | | |   (86)  all_57_9 = e0 & op(e3, e0) = e0
% 229.57/41.08  | | | | | | | 
% 229.57/41.08  | | | | | | | REF_CLOSE: (8), (57), (69), (86) are inconsistent by sub-proof
% 229.57/41.08  | | | | | | |            #2434.
% 229.57/41.08  | | | | | | | 
% 229.57/41.08  | | | | | | Case 2:
% 229.57/41.08  | | | | | | | 
% 229.57/41.08  | | | | | | |   (87)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 229.57/41.08  | | | | | | |           op(e1, e0) = e0)
% 229.57/41.08  | | | | | | | 
% 229.57/41.08  | | | | | | | BETA: splitting (87) gives:
% 229.57/41.08  | | | | | | | 
% 229.57/41.08  | | | | | | | Case 1:
% 229.57/41.08  | | | | | | | | 
% 229.57/41.08  | | | | | | | |   (88)  all_57_10 = e0 & op(e2, e0) = e0
% 229.57/41.08  | | | | | | | | 
% 229.57/41.08  | | | | | | | | ALPHA: (88) implies:
% 229.57/41.08  | | | | | | | |   (89)  op(e2, e0) = e0
% 229.57/41.08  | | | | | | | | 
% 229.57/41.08  | | | | | | | | REF_CLOSE: (1), (2), (6), (8), (12), (15), (16), (18), (20),
% 229.57/41.08  | | | | | | | |            (23), (24), (29), (31), (33), (36), (39), (43), (44),
% 229.57/41.08  | | | | | | | |            (48), (49), (52), (53), (54), (69), (89) are
% 229.57/41.08  | | | | | | | |            inconsistent by sub-proof #846.
% 229.57/41.08  | | | | | | | | 
% 229.57/41.08  | | | | | | | Case 2:
% 229.57/41.08  | | | | | | | | 
% 229.57/41.08  | | | | | | | |   (90)  all_57_11 = e0 & op(e1, e0) = e0
% 229.57/41.08  | | | | | | | | 
% 229.57/41.08  | | | | | | | | ALPHA: (90) implies:
% 229.57/41.08  | | | | | | | |   (91)  all_57_11 = e0
% 229.57/41.08  | | | | | | | | 
% 229.57/41.08  | | | | | | | | BETA: splitting (60) gives:
% 229.57/41.08  | | | | | | | | 
% 229.57/41.08  | | | | | | | | Case 1:
% 229.57/41.08  | | | | | | | | | 
% 229.57/41.08  | | | | | | | | |   (92)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 &
% 229.57/41.08  | | | | | | | | |           op(e2, e0) = e2)
% 229.57/41.08  | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | BETA: splitting (92) gives:
% 229.57/41.08  | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | Case 1:
% 229.57/41.08  | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | |   (93)  all_57_9 = e2 & op(e3, e0) = e2
% 229.57/41.08  | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | ALPHA: (93) implies:
% 229.57/41.08  | | | | | | | | | |   (94)  all_57_9 = e2
% 229.57/41.08  | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | BETA: splitting (3) gives:
% 229.57/41.08  | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | Case 1:
% 229.57/41.08  | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | |   (95)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 229.57/41.08  | | | | | | | | | | |           & op(e2, e2) = e1)
% 229.57/41.08  | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | BETA: splitting (95) gives:
% 229.57/41.08  | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | Case 1:
% 229.57/41.08  | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | |   (96)  all_57_2 = e1 & op(e2, e3) = e1
% 229.57/41.08  | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | ALPHA: (96) implies:
% 229.57/41.08  | | | | | | | | | | | |   (97)  all_57_2 = e1
% 229.57/41.08  | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | REF_CLOSE: (40), (77), (97) are inconsistent by sub-proof
% 229.57/41.08  | | | | | | | | | | | |            #2473.
% 229.57/41.08  | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | Case 2:
% 229.57/41.08  | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | |   (98)  all_57_3 = e1 & op(e2, e2) = e1
% 229.57/41.08  | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | ALPHA: (98) implies:
% 229.57/41.08  | | | | | | | | | | | |   (99)  all_57_3 = e1
% 229.57/41.08  | | | | | | | | | | | |   (100)  op(e2, e2) = e1
% 229.57/41.08  | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 229.57/41.08  | | | | | | | | | | | |            (13), (19), (21), (22), (23), (25), (26), (27),
% 229.57/41.08  | | | | | | | | | | | |            (30), (31), (32), (34), (35), (38), (40), (41),
% 229.57/41.08  | | | | | | | | | | | |            (42), (43), (45), (46), (47), (51), (53), (55),
% 229.57/41.08  | | | | | | | | | | | |            (56), (57), (59), (60), (61), (62), (63), (64),
% 229.57/41.08  | | | | | | | | | | | |            (65), (67), (68), (69), (77), (99), (100) are
% 229.57/41.08  | | | | | | | | | | | |            inconsistent by sub-proof #1016.
% 229.57/41.08  | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | End of split
% 229.57/41.08  | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | Case 2:
% 229.57/41.08  | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | |   (101)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 229.57/41.08  | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 229.57/41.08  | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | BETA: splitting (101) gives:
% 229.57/41.08  | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | Case 1:
% 229.57/41.08  | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | |   (102)  all_57_5 = e1 & op(e2, e1) = e1
% 229.57/41.08  | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | REF_CLOSE: (6), (85), (102) are inconsistent by sub-proof
% 229.57/41.08  | | | | | | | | | | | |            #2376.
% 229.57/41.08  | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | Case 2:
% 229.57/41.08  | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | |   (103)  all_57_10 = e1 & op(e2, e0) = e1
% 229.57/41.08  | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | ALPHA: (103) implies:
% 229.57/41.08  | | | | | | | | | | | |   (104)  all_57_10 = e1
% 229.57/41.08  | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | BETA: splitting (56) gives:
% 229.57/41.08  | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | Case 1:
% 229.57/41.08  | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | |   (105)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 229.57/41.08  | | | | | | | | | | | | |            & op(e2, e3) = e3)
% 229.57/41.08  | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | BETA: splitting (105) gives:
% 229.57/41.08  | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | Case 1:
% 229.57/41.08  | | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | |   (106)  all_57_0 = e3 & op(e3, e3) = e3
% 229.57/41.08  | | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | | ALPHA: (106) implies:
% 229.57/41.08  | | | | | | | | | | | | | |   (107)  op(e3, e3) = e3
% 229.57/41.08  | | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | | REF_CLOSE: (8), (25), (31), (107) are inconsistent by
% 229.57/41.08  | | | | | | | | | | | | | |            sub-proof #2494.
% 229.57/41.08  | | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | Case 2:
% 229.57/41.08  | | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | |   (108)  all_57_2 = e3 & op(e2, e3) = e3
% 229.57/41.08  | | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | | ALPHA: (108) implies:
% 229.57/41.08  | | | | | | | | | | | | | |   (109)  all_57_2 = e3
% 229.57/41.08  | | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (23), (25), (35), (40), (55), (58),
% 229.57/41.08  | | | | | | | | | | | | | |            (59), (85), (104), (109) are inconsistent by
% 229.57/41.08  | | | | | | | | | | | | | |            sub-proof #1331.
% 229.57/41.08  | | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | End of split
% 229.57/41.08  | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | Case 2:
% 229.57/41.08  | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | |   (110)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 229.57/41.08  | | | | | | | | | | | | |            e3 & op(e0, e3) = e3)
% 229.57/41.08  | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | BETA: splitting (110) gives:
% 229.57/41.08  | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | Case 1:
% 229.57/41.08  | | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | |   (111)  all_57_6 = e3 & op(e1, e3) = e3
% 229.57/41.08  | | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | | ALPHA: (111) implies:
% 229.57/41.08  | | | | | | | | | | | | | |   (112)  all_57_6 = e3
% 229.57/41.08  | | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | | BETA: splitting (4) gives:
% 229.57/41.08  | | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | | Case 1:
% 229.57/41.08  | | | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | | |   (113)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 229.57/41.08  | | | | | | | | | | | | | | |            & op(e2, e3) = e1)
% 229.57/41.08  | | | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (28), (40), (43), (59), (64), (77),
% 229.57/41.08  | | | | | | | | | | | | | | |            (91), (94), (104), (113) are inconsistent by
% 229.57/41.08  | | | | | | | | | | | | | | |            sub-proof #843.
% 229.57/41.08  | | | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | | Case 2:
% 229.57/41.08  | | | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | | |   (114)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 229.57/41.08  | | | | | | | | | | | | | | |            e1 & op(e0, e3) = e1)
% 229.57/41.08  | | | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | | | BETA: splitting (114) gives:
% 229.57/41.08  | | | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | | | Case 1:
% 229.57/41.08  | | | | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | | | |   (115)  all_57_6 = e1 & op(e1, e3) = e1
% 229.57/41.08  | | | | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (112), (115) are inconsistent by sub-proof
% 229.57/41.08  | | | | | | | | | | | | | | | |            #2117.
% 229.57/41.08  | | | | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | | | Case 2:
% 229.57/41.08  | | | | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | | | |   (116)  all_57_12 = e1 & op(e0, e3) = e1
% 229.57/41.08  | | | | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | | | | ALPHA: (116) implies:
% 229.57/41.08  | | | | | | | | | | | | | | | |   (117)  all_57_12 = e1
% 229.57/41.08  | | | | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | | | | BETA: splitting (45) gives:
% 229.57/41.08  | | | | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.08  | | | | | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | | | | |   (118)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 229.57/41.08  | | | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 229.57/41.08  | | | | | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | | | | | BETA: splitting (118) gives:
% 229.57/41.08  | | | | | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.08  | | | | | | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | | | | | |   (119)  all_57_12 = e2 & op(e0, e3) = e2
% 229.57/41.08  | | | | | | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | | | | | | ALPHA: (119) implies:
% 229.57/41.08  | | | | | | | | | | | | | | | | | |   (120)  all_57_12 = e2
% 229.57/41.08  | | | | | | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (117), (120) imply:
% 229.57/41.08  | | | | | | | | | | | | | | | | | |   (121)  e2 = e1
% 229.57/41.08  | | | | | | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | | | | | | SIMP: (121) implies:
% 229.57/41.08  | | | | | | | | | | | | | | | | | |   (122)  e2 = e1
% 229.57/41.08  | | | | | | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (66), (122) imply:
% 229.57/41.08  | | | | | | | | | | | | | | | | | |   (123)  all_57_3 = e1
% 229.57/41.08  | | | | | | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (6), (8), (23), (28), (31), (35), (40),
% 229.57/41.08  | | | | | | | | | | | | | | | | | |            (55), (59), (61), (77), (85), (112), (123) are
% 229.57/41.08  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1066.
% 229.57/41.08  | | | | | | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.08  | | | | | | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | | | | | |   (124)  all_57_13 = e2 & op(e0, e2) = e2
% 229.57/41.08  | | | | | | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | | | | | | ALPHA: (124) implies:
% 229.57/41.08  | | | | | | | | | | | | | | | | | |   (125)  op(e0, e2) = e2
% 229.57/41.08  | | | | | | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (17), (44), (125) are inconsistent by
% 229.57/41.08  | | | | | | | | | | | | | | | | | |            sub-proof #2335.
% 229.57/41.08  | | | | | | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | | | | | End of split
% 229.57/41.08  | | | | | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.08  | | | | | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | | | | |   (126)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 229.57/41.08  | | | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 229.57/41.08  | | | | | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | | | | | BETA: splitting (126) gives:
% 229.57/41.08  | | | | | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.08  | | | | | | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | | | | | |   (127)  all_57_14 = e2 & op(e0, e1) = e2
% 229.57/41.08  | | | | | | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | | | | | | ALPHA: (127) implies:
% 229.57/41.08  | | | | | | | | | | | | | | | | | |   (128)  all_57_14 = e2
% 229.57/41.08  | | | | | | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | | | | | | BETA: splitting (65) gives:
% 229.57/41.08  | | | | | | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.08  | | | | | | | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | | | | | | |   (129)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 229.57/41.08  | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e1)
% 229.57/41.08  | | | | | | | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | | | | | | | BETA: splitting (129) gives:
% 229.57/41.08  | | | | | | | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.08  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | | | | | | | |   (130)  all_57_6 = e1 & op(e1, e3) = e1
% 229.57/41.08  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | | | | | | | | ALPHA: (130) implies:
% 229.57/41.08  | | | | | | | | | | | | | | | | | | | |   (131)  all_57_6 = e1
% 229.57/41.08  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (23), (25), (31), (35), (56), (59),
% 229.57/41.08  | | | | | | | | | | | | | | | | | | | |            (61), (117), (131) are inconsistent by sub-proof
% 229.57/41.08  | | | | | | | | | | | | | | | | | | | |            #1205.
% 229.57/41.08  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.08  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | | | | | | | |   (132)  all_57_7 = e1 & op(e1, e2) = e1
% 229.57/41.08  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | | | | | | | | ALPHA: (132) implies:
% 229.57/41.08  | | | | | | | | | | | | | | | | | | | |   (133)  all_57_7 = e1
% 229.57/41.08  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | | | | | | | | BETA: splitting (68) gives:
% 229.57/41.08  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.08  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | | | | | | | | |   (134)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 229.57/41.08  | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e2)
% 229.57/41.08  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (134) gives:
% 229.57/41.08  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.08  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | | | | | | | | | |   (135)  all_57_6 = e2 & op(e1, e3) = e2
% 229.57/41.08  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (135) implies:
% 229.57/41.08  | | | | | | | | | | | | | | | | | | | | | |   (136)  all_57_6 = e2
% 229.57/41.08  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (10), (11), (23), (25), (30), (35),
% 229.57/41.08  | | | | | | | | | | | | | | | | | | | | | |            (40), (47), (59), (60), (64), (133), (136) are
% 229.57/41.08  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1245.
% 229.57/41.08  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.08  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | | | | | | | | | |   (137)  all_57_7 = e2 & op(e1, e2) = e2
% 229.57/41.08  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.08  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (137) implies:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | |   (138)  all_57_7 = e2
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (133), (138) imply:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | |   (139)  e2 = e1
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (66), (139) imply:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | |   (140)  all_57_3 = e1
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (6), (8), (23), (28), (31), (35), (40),
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | |            (55), (59), (61), (77), (85), (112), (140) are
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1066.
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | |   (141)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | |            e2 & op(e1, e0) = e2)
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (141) gives:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | |   (142)  all_57_8 = e2 & op(e1, e1) = e2
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (142) implies:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | |   (143)  op(e1, e1) = e2
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (61) gives:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | |   (144)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e2)
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (144) gives:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | |   (145)  all_57_0 = e2 & op(e3, e3) = e2
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (145) implies:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | |   (146)  op(e3, e3) = e2
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (31), (35), (146) are inconsistent by
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2403.
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | |   (147)  all_57_2 = e2 & op(e2, e3) = e2
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (147) implies:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | |   (148)  all_57_2 = e2
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (77), (148) imply:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | |   (149)  e2 = e0
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (149) implies:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | |   (150)  e2 = e0
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (66), (150) imply:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | |   (151)  all_57_3 = e0
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (23), (35), (40), (55), (59), (77),
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | |            (85), (151) are inconsistent by sub-proof #2253.
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | |   (152)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e3) = e2)
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (152) gives:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | |   (153)  all_57_6 = e2 & op(e1, e3) = e2
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (153) implies:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | |   (154)  all_57_6 = e2
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (10), (11), (23), (25), (30), (35),
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | |            (40), (47), (59), (60), (64), (65), (91), (143),
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | |            (154) are inconsistent by sub-proof #1122.
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | |   (155)  all_57_12 = e2 & op(e0, e3) = e2
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (155) implies:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | |   (156)  all_57_12 = e2
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (117), (156) imply:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | |   (157)  e2 = e1
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (66), (157) imply:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | |   (158)  all_57_3 = e1
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (6), (8), (23), (28), (31), (35), (40),
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | |            (55), (59), (61), (77), (85), (112), (158) are
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1066.
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | |   (159)  all_57_11 = e2 & op(e1, e0) = e2
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (159) implies:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | |   (160)  op(e1, e0) = e2
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (14), (32), (37), (40), (43), (50),
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | |            (59), (128), (160) are inconsistent by sub-proof
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | |            #1100.
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | |   (161)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 229.57/41.09  | | | | | | | | | | | | | | | | | | |            e1 & op(e1, e0) = e1)
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (40), (43), (48), (59), (64), (91),
% 229.57/41.09  | | | | | | | | | | | | | | | | | | |            (94), (104), (161) are inconsistent by sub-proof
% 229.57/41.09  | | | | | | | | | | | | | | | | | | |            #1102.
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.09  | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | |   (162)  all_57_15 = e2 & op(e0, e0) = e2
% 229.57/41.09  | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | REF_CLOSE: (23), (30), (162) are inconsistent by sub-proof
% 229.57/41.09  | | | | | | | | | | | | | | | | | |            #2323.
% 229.57/41.09  | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | End of split
% 229.57/41.09  | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | End of split
% 229.57/41.09  | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | End of split
% 229.57/41.09  | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | End of split
% 229.57/41.09  | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | Case 2:
% 229.57/41.09  | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | |   (163)  all_57_12 = e3 & op(e0, e3) = e3
% 229.57/41.09  | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | ALPHA: (163) implies:
% 229.57/41.09  | | | | | | | | | | | | | |   (164)  all_57_12 = e3
% 229.57/41.09  | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | BETA: splitting (4) gives:
% 229.57/41.09  | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | Case 1:
% 229.57/41.09  | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | |   (165)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 229.57/41.09  | | | | | | | | | | | | | | |            & op(e2, e3) = e1)
% 229.57/41.09  | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (28), (40), (43), (59), (64), (77),
% 229.57/41.09  | | | | | | | | | | | | | | |            (91), (94), (104), (165) are inconsistent by
% 229.57/41.09  | | | | | | | | | | | | | | |            sub-proof #843.
% 229.57/41.09  | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | Case 2:
% 229.57/41.09  | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | |   (166)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 229.57/41.09  | | | | | | | | | | | | | | |            e1 & op(e0, e3) = e1)
% 229.57/41.09  | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | BETA: splitting (166) gives:
% 229.57/41.09  | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | Case 1:
% 229.57/41.09  | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | |   (167)  all_57_6 = e1 & op(e1, e3) = e1
% 229.57/41.09  | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | ALPHA: (167) implies:
% 229.57/41.09  | | | | | | | | | | | | | | | |   (168)  all_57_6 = e1
% 229.57/41.09  | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | BETA: splitting (45) gives:
% 229.57/41.09  | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.09  | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | |   (169)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 229.57/41.09  | | | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 229.57/41.09  | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | BETA: splitting (169) gives:
% 229.57/41.09  | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | |   (170)  all_57_12 = e2 & op(e0, e3) = e2
% 229.57/41.09  | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | REF_CLOSE: (23), (164), (170) are inconsistent by sub-proof
% 229.57/41.09  | | | | | | | | | | | | | | | | | |            #2232.
% 229.57/41.09  | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | |   (171)  all_57_13 = e2 & op(e0, e2) = e2
% 229.57/41.09  | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | ALPHA: (171) implies:
% 229.57/41.09  | | | | | | | | | | | | | | | | | |   (172)  all_57_13 = e2
% 229.57/41.09  | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (25), (30), (32), (35), (40), (43),
% 229.57/41.09  | | | | | | | | | | | | | | | | | |            (47), (59), (164), (172) are inconsistent by
% 229.57/41.09  | | | | | | | | | | | | | | | | | |            sub-proof #1742.
% 229.57/41.09  | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | End of split
% 229.57/41.09  | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.09  | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | |   (173)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 229.57/41.09  | | | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 229.57/41.09  | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | BETA: splitting (173) gives:
% 229.57/41.09  | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | |   (174)  all_57_14 = e2 & op(e0, e1) = e2
% 229.57/41.09  | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | ALPHA: (174) implies:
% 229.57/41.09  | | | | | | | | | | | | | | | | | |   (175)  all_57_14 = e2
% 229.57/41.09  | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | BETA: splitting (26) gives:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | |   (176)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 229.57/41.09  | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e1)
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | BETA: splitting (176) gives:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | |   (177)  all_57_4 = e1 & op(e3, e1) = e1
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | ALPHA: (177) implies:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | |   (178)  all_57_4 = e1
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | BETA: splitting (38) gives:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | |   (179)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e3)
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (179) gives:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | |   (180)  all_57_0 = e3 & op(e3, e3) = e3
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (180) implies:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | |   (181)  op(e3, e3) = e3
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (25), (31), (181) are inconsistent by
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2494.
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | |   (182)  all_57_1 = e3 & op(e3, e2) = e3
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (182) implies:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | |   (183)  all_57_1 = e3
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | |   (184)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (184) gives:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | |   (185)  all_57_1 = e1 & op(e3, e2) = e1
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (23), (25), (31), (35), (56), (59),
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | |            (61), (164), (168), (183), (185) are inconsistent
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1182.
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | |   (186)  all_57_3 = e1 & op(e2, e2) = e1
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (186) implies:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | |   (187)  all_57_3 = e1
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | |   (188)  op(e2, e2) = e1
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | |            (13), (19), (21), (22), (23), (25), (26), (27),
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | |            (28), (30), (31), (32), (34), (35), (38), (40),
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | |            (41), (42), (43), (45), (46), (47), (51), (53),
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | |            (55), (56), (57), (58), (59), (60), (61), (62),
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | |            (63), (64), (65), (67), (68), (69), (164), (175),
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | |            (187), (188) are inconsistent by sub-proof #913.
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | |   (189)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | |   (190)  all_57_7 = e1 & op(e1, e2) = e1
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (190) implies:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | |   (191)  all_57_7 = e1
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (61) gives:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | |   (192)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e2)
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | | |   (193)  all_57_0 = e2 & op(e3, e3) = e2
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (193) implies:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | | |   (194)  op(e3, e3) = e2
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (21), (25), (35), (40), (94), (178), (183),
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | | |            (194) are inconsistent by sub-proof #842.
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | | |   (195)  all_57_2 = e2 & op(e2, e3) = e2
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (195) implies:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | | |   (196)  all_57_2 = e2
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (8), (23), (25), (30), (32), (35), (40),
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | | |            (43), (45), (58), (59), (60), (64), (67), (73),
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | | |            (85), (91), (94), (164), (183), (196) are
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #841.
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | |   (197)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e3) = e2)
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | | |   (198)  all_57_6 = e2 & op(e1, e3) = e2
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (198) implies:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | | |   (199)  all_57_6 = e2
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (10), (11), (23), (25), (30), (35),
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | | |            (40), (47), (59), (60), (64), (191), (199) are
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1245.
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | | |   (200)  all_57_12 = e2 & op(e0, e3) = e2
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (200) implies:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | | |   (201)  all_57_12 = e2
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23), (164), (201) are inconsistent by sub-proof
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | | |            #2392.
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | |   (202)  all_57_13 = e1 & op(e0, e2) = e1
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (202) implies:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | |   (203)  all_57_13 = e1
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (50), (203) imply:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | |   (204)  e1 = e0
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (168), (204) imply:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | |   (205)  all_57_6 = e0
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (9), (10), (11), (23), (25), (28),
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | |            (30), (31), (35), (40), (47), (56), (59), (60),
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | |            (61), (64), (205) are inconsistent by sub-proof
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | |            #869.
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | |   (206)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e3)
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | |   (207)  all_57_4 = e3 & op(e3, e1) = e3
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (207) implies:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | |   (208)  all_57_4 = e3
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (178), (208) imply:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | |   (209)  e3 = e1
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | SIMP: (209) implies:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | |   (210)  e3 = e1
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (164), (210) imply:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | |   (211)  all_57_12 = e1
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (23), (25), (31), (35), (56), (59),
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | |            (61), (168), (211) are inconsistent by sub-proof
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | |            #1205.
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | |   (212)  all_57_9 = e3 & op(e3, e0) = e3
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (212) implies:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | |   (213)  op(e3, e0) = e3
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (53), (69), (213) are inconsistent by
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2458.
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | |   (214)  all_57_5 = e1 & op(e2, e1) = e1
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | ALPHA: (214) implies:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | |   (215)  all_57_5 = e1
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (85), (215) imply:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | |   (216)  e3 = e1
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (164), (216) imply:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | |   (217)  all_57_12 = e1
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (23), (25), (31), (35), (56), (59),
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | |            (61), (168), (217) are inconsistent by sub-proof
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | |            #1205.
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | |   (218)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 229.57/41.09  | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e1) = e1)
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (40), (48), (59), (175), (218) are
% 229.57/41.09  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1905.
% 229.57/41.09  | | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | End of split
% 229.57/41.09  | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | Case 2:
% 229.57/41.09  | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | |   (219)  all_57_15 = e2 & op(e0, e0) = e2
% 229.57/41.09  | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | | REF_CLOSE: (23), (30), (219) are inconsistent by sub-proof
% 229.57/41.09  | | | | | | | | | | | | | | | | | |            #2323.
% 229.57/41.09  | | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | | End of split
% 229.57/41.09  | | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | End of split
% 229.57/41.09  | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | Case 2:
% 229.57/41.09  | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | |   (220)  all_57_12 = e1 & op(e0, e3) = e1
% 229.57/41.09  | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (164), (220) are inconsistent by sub-proof
% 229.57/41.09  | | | | | | | | | | | | | | | |            #2230.
% 229.57/41.09  | | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | | End of split
% 229.57/41.09  | | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | | End of split
% 229.57/41.09  | | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | | End of split
% 229.57/41.09  | | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | | End of split
% 229.57/41.09  | | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | | End of split
% 229.57/41.09  | | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | End of split
% 229.57/41.09  | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | Case 2:
% 229.57/41.09  | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | |   (221)  all_57_10 = e2 & op(e2, e0) = e2
% 229.57/41.09  | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | REF_CLOSE: (8), (15), (49), (221) are inconsistent by
% 229.57/41.09  | | | | | | | | | |            sub-proof #2432.
% 229.57/41.09  | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | End of split
% 229.57/41.09  | | | | | | | | | 
% 229.57/41.09  | | | | | | | | Case 2:
% 229.57/41.09  | | | | | | | | | 
% 229.57/41.09  | | | | | | | | |   (222)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2
% 229.57/41.09  | | | | | | | | |            & op(e0, e0) = e2)
% 229.57/41.09  | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | BETA: splitting (222) gives:
% 229.57/41.09  | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | Case 1:
% 229.57/41.09  | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | |   (223)  all_57_11 = e2 & op(e1, e0) = e2
% 229.57/41.09  | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | ALPHA: (223) implies:
% 229.57/41.09  | | | | | | | | | |   (224)  all_57_11 = e2
% 229.57/41.09  | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | COMBINE_EQS: (91), (224) imply:
% 229.57/41.09  | | | | | | | | | |   (225)  e2 = e0
% 229.57/41.09  | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | SIMP: (225) implies:
% 229.57/41.09  | | | | | | | | | |   (226)  e2 = e0
% 229.57/41.09  | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | COMBINE_EQS: (66), (226) imply:
% 229.57/41.09  | | | | | | | | | |   (227)  all_57_3 = e0
% 229.57/41.09  | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | REF_CLOSE: (3), (6), (23), (35), (40), (55), (59), (77),
% 229.57/41.09  | | | | | | | | | |            (85), (227) are inconsistent by sub-proof #2253.
% 229.57/41.09  | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | Case 2:
% 229.57/41.09  | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | |   (228)  all_57_15 = e2 & op(e0, e0) = e2
% 229.57/41.09  | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | ALPHA: (228) implies:
% 229.57/41.09  | | | | | | | | | |   (229)  all_57_15 = e2
% 229.57/41.09  | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | | REF_CLOSE: (23), (30), (229) are inconsistent by sub-proof
% 229.57/41.09  | | | | | | | | | |            #2058.
% 229.57/41.09  | | | | | | | | | | 
% 229.57/41.09  | | | | | | | | | End of split
% 229.57/41.09  | | | | | | | | | 
% 229.57/41.09  | | | | | | | | End of split
% 229.57/41.09  | | | | | | | | 
% 229.57/41.09  | | | | | | | End of split
% 229.57/41.09  | | | | | | | 
% 229.57/41.09  | | | | | | End of split
% 229.57/41.09  | | | | | | 
% 229.57/41.09  | | | | | Case 2:
% 229.57/41.09  | | | | | | 
% 229.57/41.09  | | | | | |   (230)  all_57_10 = e3 & op(e2, e0) = e3
% 229.57/41.09  | | | | | | 
% 229.57/41.09  | | | | | | ALPHA: (230) implies:
% 229.57/41.09  | | | | | |   (231)  all_57_10 = e3
% 229.57/41.09  | | | | | | 
% 229.57/41.09  | | | | | | REF_CLOSE: (6), (8), (23), (25), (30), (35), (40), (43), (47), (59),
% 229.57/41.09  | | | | | |            (60), (64), (74), (231) are inconsistent by sub-proof
% 229.57/41.09  | | | | | |            #1747.
% 229.57/41.09  | | | | | | 
% 229.57/41.09  | | | | | End of split
% 229.57/41.09  | | | | | 
% 229.57/41.09  | | | | End of split
% 229.57/41.09  | | | | 
% 229.57/41.09  | | | Case 2:
% 229.57/41.09  | | | | 
% 229.57/41.09  | | | |   (232)  all_57_3 = e0 & op(e2, e2) = e0
% 229.57/41.09  | | | | 
% 229.57/41.09  | | | | ALPHA: (232) implies:
% 229.57/41.09  | | | |   (233)  op(e2, e2) = e0
% 229.57/41.09  | | | | 
% 229.57/41.09  | | | | REF_CLOSE: (8), (35), (39), (233) are inconsistent by sub-proof #2472.
% 229.57/41.09  | | | | 
% 229.57/41.09  | | | End of split
% 229.57/41.09  | | | 
% 229.57/41.09  | | Case 2:
% 229.57/41.09  | | | 
% 229.57/41.09  | | |   (234)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0)
% 229.57/41.09  | | |            = e0)
% 229.57/41.09  | | | 
% 229.57/41.09  | | | BETA: splitting (234) gives:
% 229.57/41.09  | | | 
% 229.57/41.09  | | | Case 1:
% 229.57/41.09  | | | | 
% 229.57/41.09  | | | |   (235)  all_57_5 = e0 & op(e2, e1) = e0
% 229.57/41.09  | | | | 
% 229.57/41.09  | | | | ALPHA: (235) implies:
% 229.57/41.09  | | | |   (236)  all_57_5 = e0
% 229.57/41.09  | | | | 
% 229.57/41.09  | | | | BETA: splitting (51) gives:
% 229.57/41.09  | | | | 
% 229.57/41.09  | | | | Case 1:
% 229.57/41.09  | | | | | 
% 229.57/41.09  | | | | |   (237)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2,
% 229.57/41.09  | | | | |              e2) = e3)
% 229.57/41.09  | | | | | 
% 229.57/41.09  | | | | | BETA: splitting (237) gives:
% 229.57/41.09  | | | | | 
% 229.57/41.09  | | | | | Case 1:
% 229.57/41.09  | | | | | | 
% 229.57/41.09  | | | | | |   (238)  all_57_2 = e3 & op(e2, e3) = e3
% 229.57/41.09  | | | | | | 
% 229.57/41.09  | | | | | | ALPHA: (238) implies:
% 229.57/41.09  | | | | | |   (239)  all_57_2 = e3
% 229.57/41.09  | | | | | | 
% 229.57/41.09  | | | | | | BETA: splitting (74) gives:
% 229.57/41.09  | | | | | | 
% 229.57/41.09  | | | | | | Case 1:
% 229.57/41.09  | | | | | | | 
% 229.57/41.09  | | | | | | |   (240)  all_57_9 = e0 & op(e3, e0) = e0
% 229.57/41.09  | | | | | | | 
% 229.57/41.09  | | | | | | | REF_CLOSE: (8), (57), (69), (240) are inconsistent by sub-proof
% 229.57/41.09  | | | | | | |            #2434.
% 229.57/41.09  | | | | | | | 
% 229.57/41.09  | | | | | | Case 2:
% 229.57/41.09  | | | | | | | 
% 229.57/41.09  | | | | | | |   (241)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 229.57/41.09  | | | | | | |            op(e1, e0) = e0)
% 229.57/41.09  | | | | | | | 
% 229.57/41.09  | | | | | | | BETA: splitting (241) gives:
% 229.57/41.09  | | | | | | | 
% 229.57/41.09  | | | | | | | Case 1:
% 229.57/41.09  | | | | | | | | 
% 229.57/41.09  | | | | | | | |   (242)  all_57_10 = e0 & op(e2, e0) = e0
% 229.57/41.09  | | | | | | | | 
% 229.57/41.09  | | | | | | | | ALPHA: (242) implies:
% 229.57/41.09  | | | | | | | |   (243)  op(e2, e0) = e0
% 229.57/41.09  | | | | | | | | 
% 229.57/41.09  | | | | | | | | REF_CLOSE: (1), (2), (6), (8), (12), (15), (16), (18), (20),
% 229.57/41.09  | | | | | | | |            (23), (24), (29), (31), (33), (36), (39), (43), (44),
% 229.57/41.09  | | | | | | | |            (48), (49), (52), (53), (54), (69), (243) are
% 229.57/41.09  | | | | | | | |            inconsistent by sub-proof #846.
% 229.57/41.09  | | | | | | | | 
% 229.57/41.09  | | | | | | | Case 2:
% 229.57/41.09  | | | | | | | | 
% 229.57/41.09  | | | | | | | |   (244)  all_57_11 = e0 & op(e1, e0) = e0
% 229.57/41.09  | | | | | | | | 
% 229.57/41.09  | | | | | | | | ALPHA: (244) implies:
% 229.57/41.09  | | | | | | | |   (245)  all_57_11 = e0
% 229.57/41.09  | | | | | | | | 
% 229.57/41.09  | | | | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 229.57/41.09  | | | | | | | |            (15), (19), (21), (22), (23), (25), (26), (27), (28),
% 229.57/41.09  | | | | | | | |            (30), (31), (32), (34), (35), (38), (40), (41), (42),
% 229.57/41.09  | | | | | | | |            (43), (45), (46), (47), (48), (49), (50), (51), (53),
% 229.57/41.09  | | | | | | | |            (55), (56), (57), (58), (59), (60), (61), (62), (63),
% 229.57/41.09  | | | | | | | |            (64), (65), (66), (67), (68), (69), (73), (74),
% 229.57/41.09  | | | | | | | |            (236), (239), (245) are inconsistent by sub-proof
% 229.57/41.09  | | | | | | | |            #896.
% 229.57/41.09  | | | | | | | | 
% 229.57/41.09  | | | | | | | End of split
% 229.57/41.09  | | | | | | | 
% 229.57/41.09  | | | | | | End of split
% 229.57/41.09  | | | | | | 
% 229.57/41.09  | | | | | Case 2:
% 229.57/41.09  | | | | | | 
% 229.57/41.09  | | | | | |   (246)  all_57_3 = e3 & op(e2, e2) = e3
% 229.57/41.09  | | | | | | 
% 229.57/41.09  | | | | | | ALPHA: (246) implies:
% 229.57/41.09  | | | | | |   (247)  all_57_3 = e3
% 229.57/41.09  | | | | | | 
% 229.57/41.09  | | | | | | REF_CLOSE: (23), (66), (247) are inconsistent by sub-proof #1166.
% 229.57/41.09  | | | | | | 
% 229.57/41.09  | | | | | End of split
% 229.57/41.09  | | | | | 
% 229.57/41.09  | | | | Case 2:
% 229.57/41.09  | | | | | 
% 229.57/41.09  | | | | |   (248)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2,
% 229.57/41.09  | | | | |              e0) = e3)
% 229.57/41.09  | | | | | 
% 229.57/41.09  | | | | | REF_CLOSE: (6), (8), (23), (25), (30), (35), (40), (43), (47), (59),
% 229.57/41.09  | | | | |            (60), (64), (74), (236), (248) are inconsistent by
% 229.57/41.09  | | | | |            sub-proof #895.
% 229.57/41.09  | | | | | 
% 229.57/41.09  | | | | End of split
% 229.57/41.09  | | | | 
% 229.57/41.09  | | | Case 2:
% 229.57/41.09  | | | | 
% 229.57/41.09  | | | |   (249)  all_57_10 = e0 & op(e2, e0) = e0
% 229.57/41.09  | | | | 
% 229.57/41.09  | | | | ALPHA: (249) implies:
% 229.57/41.09  | | | |   (250)  op(e2, e0) = e0
% 229.57/41.09  | | | | 
% 229.57/41.09  | | | | REF_CLOSE: (1), (2), (6), (8), (12), (15), (16), (18), (20), (23), (24),
% 229.57/41.09  | | | |            (29), (31), (33), (36), (39), (43), (44), (48), (49), (52),
% 229.57/41.09  | | | |            (53), (54), (69), (250) are inconsistent by sub-proof #846.
% 229.57/41.09  | | | | 
% 229.57/41.09  | | | End of split
% 229.57/41.09  | | | 
% 229.57/41.09  | | End of split
% 229.57/41.09  | | 
% 229.57/41.09  | End of split
% 229.57/41.09  | 
% 229.57/41.09  End of proof
% 229.57/41.09  
% 229.57/41.09  Sub-proof #841 shows that the following formulas are inconsistent:
% 229.57/41.09  ----------------------------------------------------------------
% 229.57/41.09    (1)  all_57_9 = e2
% 229.57/41.09    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.57/41.09         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.57/41.09    (3)   ~ (e3 = e1)
% 229.57/41.09    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.57/41.09           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.57/41.09    (5)  all_57_2 = e2
% 229.57/41.09    (6)   ~ (e3 = e2)
% 229.57/41.09    (7)   ~ (e3 = e0)
% 229.57/41.09    (8)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 229.57/41.09         (all_57_14 = e0 & op(e0, e1) = e0)
% 229.57/41.09    (9)  all_57_15 = e3
% 229.57/41.09    (10)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.57/41.09          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.57/41.09            e1)
% 229.57/41.09    (11)  all_57_5 = e3
% 229.57/41.09    (12)  all_57_11 = e0
% 229.57/41.09    (13)   ~ (e2 = e0)
% 229.57/41.09    (14)   ~ (e1 = e0)
% 229.57/41.09    (15)  all_57_12 = e3
% 229.57/41.09    (16)  op(e0, e0) = e3
% 229.57/41.09    (17)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.57/41.09          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.57/41.09            e2)
% 229.57/41.09    (18)  all_57_1 = e3
% 229.57/41.09    (19)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.57/41.09          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 229.57/41.09    (20)   ~ (e2 = e1)
% 229.57/41.09    (21)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.57/41.09          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.57/41.09    (22)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.57/41.09          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.57/41.09    (23)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.57/41.09          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.57/41.09  
% 229.57/41.09  Begin of proof
% 229.57/41.09  | 
% 229.57/41.09  | BETA: splitting (19) gives:
% 229.57/41.09  | 
% 229.57/41.09  | Case 1:
% 229.57/41.09  | | 
% 229.57/41.09  | |   (24)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) =
% 229.57/41.09  | |           e0)
% 229.57/41.09  | | 
% 229.57/41.09  | | BETA: splitting (24) gives:
% 229.57/41.09  | | 
% 229.57/41.09  | | Case 1:
% 229.57/41.09  | | | 
% 229.57/41.10  | | |   (25)  all_57_2 = e0 & op(e2, e3) = e0
% 229.57/41.10  | | | 
% 229.57/41.10  | | | ALPHA: (25) implies:
% 229.57/41.10  | | |   (26)  all_57_2 = e0
% 229.57/41.10  | | | 
% 229.57/41.10  | | | COMBINE_EQS: (5), (26) imply:
% 229.57/41.10  | | |   (27)  e2 = e0
% 229.57/41.10  | | | 
% 229.57/41.10  | | | COMBINE_EQS: (1), (27) imply:
% 229.57/41.10  | | |   (28)  all_57_9 = e0
% 229.57/41.10  | | | 
% 229.57/41.10  | | | REF_CLOSE: (3), (6), (9), (12), (13), (14), (20), (21), (22), (28) are
% 229.57/41.10  | | |            inconsistent by sub-proof #1144.
% 229.57/41.10  | | | 
% 229.57/41.10  | | Case 2:
% 229.57/41.10  | | | 
% 229.57/41.10  | | |   (29)  all_57_3 = e0 & op(e2, e2) = e0
% 229.57/41.10  | | | 
% 229.57/41.10  | | | ALPHA: (29) implies:
% 229.57/41.10  | | |   (30)  all_57_3 = e0
% 229.57/41.10  | | | 
% 229.57/41.10  | | | REF_CLOSE: (2), (3), (6), (7), (8), (9), (10), (13), (14), (15), (17),
% 229.57/41.10  | | |            (18), (20), (23), (30) are inconsistent by sub-proof #1038.
% 229.57/41.10  | | | 
% 229.57/41.10  | | End of split
% 229.57/41.10  | | 
% 229.57/41.10  | Case 2:
% 229.57/41.10  | | 
% 229.57/41.10  | |   (31)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 229.57/41.10  | |           e0)
% 229.57/41.10  | | 
% 229.57/41.10  | | BETA: splitting (31) gives:
% 229.57/41.10  | | 
% 229.57/41.10  | | Case 1:
% 229.57/41.10  | | | 
% 229.57/41.10  | | |   (32)  all_57_5 = e0 & op(e2, e1) = e0
% 229.57/41.10  | | | 
% 229.57/41.10  | | | REF_CLOSE: (7), (11), (32) are inconsistent by sub-proof #2414.
% 229.57/41.10  | | | 
% 229.57/41.10  | | Case 2:
% 229.57/41.10  | | | 
% 229.57/41.10  | | |   (33)  all_57_10 = e0 & op(e2, e0) = e0
% 229.57/41.10  | | | 
% 229.57/41.10  | | | ALPHA: (33) implies:
% 229.57/41.10  | | |   (34)  all_57_10 = e0
% 229.57/41.10  | | | 
% 229.57/41.10  | | | REF_CLOSE: (3), (4), (6), (9), (12), (13), (14), (16), (20), (21), (22),
% 229.57/41.10  | | |            (34) are inconsistent by sub-proof #1087.
% 229.57/41.10  | | | 
% 229.57/41.10  | | End of split
% 229.57/41.10  | | 
% 229.57/41.10  | End of split
% 229.57/41.10  | 
% 229.57/41.10  End of proof
% 229.57/41.10  
% 229.57/41.10  Sub-proof #842 shows that the following formulas are inconsistent:
% 229.57/41.10  ----------------------------------------------------------------
% 229.57/41.10    (1)  all_57_9 = e2
% 229.57/41.10    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.57/41.10           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.57/41.10    (3)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.57/41.10         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.57/41.10    (4)   ~ (e3 = e0)
% 229.57/41.10    (5)  op(e3, e3) = e2
% 229.57/41.10    (6)  all_57_4 = e1
% 229.57/41.10    (7)   ~ (e2 = e0)
% 229.57/41.10    (8)   ~ (e1 = e0)
% 229.57/41.10    (9)  all_57_1 = e3
% 229.57/41.10  
% 229.57/41.10  Begin of proof
% 229.57/41.10  | 
% 229.57/41.10  | BETA: splitting (3) gives:
% 229.57/41.10  | 
% 229.57/41.10  | Case 1:
% 229.57/41.10  | | 
% 229.57/41.10  | |   (10)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) =
% 229.57/41.10  | |           e0)
% 229.57/41.10  | | 
% 229.57/41.10  | | REF_CLOSE: (2), (4), (5), (7), (9), (10) are inconsistent by sub-proof
% 229.57/41.10  | |            #1676.
% 229.57/41.10  | | 
% 229.57/41.10  | Case 2:
% 229.57/41.10  | | 
% 229.57/41.10  | |   (11)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) =
% 229.57/41.10  | |           e0)
% 229.57/41.10  | | 
% 229.57/41.10  | | BETA: splitting (11) gives:
% 229.57/41.10  | | 
% 229.57/41.10  | | Case 1:
% 229.57/41.10  | | | 
% 229.57/41.10  | | |   (12)  all_57_4 = e0 & op(e3, e1) = e0
% 229.57/41.10  | | | 
% 229.57/41.10  | | | REF_CLOSE: (6), (8), (12) are inconsistent by sub-proof #2429.
% 229.57/41.10  | | | 
% 229.57/41.10  | | Case 2:
% 229.57/41.10  | | | 
% 229.57/41.10  | | |   (13)  all_57_9 = e0 & op(e3, e0) = e0
% 229.57/41.10  | | | 
% 229.57/41.10  | | | REF_CLOSE: (1), (7), (13) are inconsistent by sub-proof #1973.
% 229.57/41.10  | | | 
% 229.57/41.10  | | End of split
% 229.57/41.10  | | 
% 229.57/41.10  | End of split
% 229.57/41.10  | 
% 229.57/41.10  End of proof
% 229.57/41.10  
% 229.57/41.10  Sub-proof #843 shows that the following formulas are inconsistent:
% 229.57/41.10  ----------------------------------------------------------------
% 229.57/41.10    (1)  all_57_9 = e2
% 229.57/41.10    (2)   ~ (e3 = e1)
% 229.57/41.10    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.57/41.10           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.57/41.10    (4)  all_57_10 = e1
% 229.57/41.10    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1)
% 229.57/41.10    (6)  all_57_0 = e0
% 229.57/41.10    (7)  all_57_11 = e0
% 229.57/41.10    (8)   ~ (e1 = e0)
% 229.57/41.10    (9)  op(e0, e0) = e3
% 229.57/41.10    (10)  all_57_2 = e0
% 229.78/41.10    (11)   ~ (e2 = e1)
% 229.78/41.10    (12)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.78/41.10          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.78/41.10  
% 229.78/41.10  Begin of proof
% 229.78/41.10  | 
% 229.78/41.10  | BETA: splitting (5) gives:
% 229.78/41.10  | 
% 229.78/41.10  | Case 1:
% 229.78/41.10  | | 
% 229.78/41.10  | |   (13)  all_57_0 = e1 & op(e3, e3) = e1
% 229.78/41.10  | | 
% 229.78/41.10  | | ALPHA: (13) implies:
% 229.78/41.10  | |   (14)  all_57_0 = e1
% 229.78/41.10  | | 
% 229.78/41.10  | | COMBINE_EQS: (6), (14) imply:
% 229.78/41.10  | |   (15)  e1 = e0
% 229.78/41.10  | | 
% 229.78/41.10  | | REF_CLOSE: (1), (2), (3), (4), (7), (8), (9), (11), (12), (15) are
% 229.78/41.10  | |            inconsistent by sub-proof #1103.
% 229.78/41.10  | | 
% 229.78/41.10  | Case 2:
% 229.78/41.10  | | 
% 229.78/41.10  | |   (16)  all_57_2 = e1 & op(e2, e3) = e1
% 229.78/41.10  | | 
% 229.78/41.10  | | ALPHA: (16) implies:
% 229.78/41.10  | |   (17)  all_57_2 = e1
% 229.78/41.10  | | 
% 229.78/41.10  | | COMBINE_EQS: (10), (17) imply:
% 229.78/41.10  | |   (18)  e1 = e0
% 229.78/41.10  | | 
% 229.78/41.10  | | REF_CLOSE: (1), (2), (3), (4), (7), (8), (9), (11), (12), (18) are
% 229.78/41.10  | |            inconsistent by sub-proof #1103.
% 229.78/41.10  | | 
% 229.78/41.10  | End of split
% 229.78/41.10  | 
% 229.78/41.10  End of proof
% 229.78/41.10  
% 229.78/41.10  Sub-proof #844 shows that the following formulas are inconsistent:
% 229.78/41.10  ----------------------------------------------------------------
% 229.78/41.10    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.78/41.10         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.78/41.10    (2)   ~ (e3 = e1)
% 229.78/41.10    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.78/41.10           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.78/41.10    (4)  all_57_2 = e2
% 229.78/41.10    (5)   ~ (e3 = e2)
% 229.78/41.10    (6)   ~ (e3 = e0)
% 229.78/41.10    (7)  all_57_15 = e3
% 229.78/41.10    (8)   ~ (e2 = e0)
% 229.78/41.10    (9)  op(e2, e2) = e2
% 229.78/41.10    (10)   ~ (e1 = e0)
% 229.78/41.10    (11)  op(e0, e0) = e3
% 229.78/41.10    (12)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.78/41.10              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.78/41.10                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.78/41.10                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.78/41.10    (13)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.78/41.10          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.78/41.10    (14)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.78/41.10          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.78/41.10    (15)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.78/41.10          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 229.78/41.10    (16)   ~ (e2 = e1)
% 229.78/41.10    (17)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.78/41.10          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.78/41.10    (18)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.78/41.10          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.78/41.10    (19)  all_57_3 = e2
% 229.78/41.10  
% 229.78/41.10  Begin of proof
% 229.78/41.10  | 
% 229.78/41.10  | BETA: splitting (13) gives:
% 229.78/41.10  | 
% 229.78/41.10  | Case 1:
% 229.78/41.10  | | 
% 229.78/41.10  | |   (20)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 229.78/41.10  | |           e3)
% 229.78/41.10  | | 
% 229.78/41.10  | | BETA: splitting (20) gives:
% 229.78/41.10  | | 
% 229.78/41.10  | | Case 1:
% 229.78/41.10  | | | 
% 229.78/41.10  | | |   (21)  all_57_2 = e3 & op(e2, e3) = e3
% 229.78/41.10  | | | 
% 229.78/41.10  | | | ALPHA: (21) implies:
% 229.78/41.10  | | |   (22)  all_57_2 = e3
% 229.78/41.10  | | | 
% 229.78/41.10  | | | REF_CLOSE: (4), (5), (22) are inconsistent by sub-proof #1800.
% 229.78/41.10  | | | 
% 229.78/41.10  | | Case 2:
% 229.78/41.10  | | | 
% 229.78/41.10  | | |   (23)  all_57_3 = e3 & op(e2, e2) = e3
% 229.78/41.10  | | | 
% 229.78/41.10  | | | REF_CLOSE: (5), (19), (23) are inconsistent by sub-proof #845.
% 229.78/41.10  | | | 
% 229.78/41.10  | | End of split
% 229.78/41.10  | | 
% 229.78/41.10  | Case 2:
% 229.78/41.10  | | 
% 229.78/41.10  | |   (24)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 229.78/41.10  | |           e3)
% 229.78/41.10  | | 
% 229.78/41.10  | | BETA: splitting (24) gives:
% 229.78/41.10  | | 
% 229.78/41.10  | | Case 1:
% 229.78/41.10  | | | 
% 229.78/41.10  | | |   (25)  all_57_5 = e3 & op(e2, e1) = e3
% 229.78/41.10  | | | 
% 229.78/41.10  | | | ALPHA: (25) implies:
% 229.78/41.10  | | |   (26)  all_57_5 = e3
% 229.78/41.10  | | | 
% 229.78/41.10  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (13), (14), (15),
% 229.78/41.10  | | |            (16), (19), (26) are inconsistent by sub-proof #2239.
% 229.78/41.10  | | | 
% 229.78/41.10  | | Case 2:
% 229.78/41.10  | | | 
% 229.78/41.10  | | |   (27)  all_57_10 = e3 & op(e2, e0) = e3
% 229.78/41.10  | | | 
% 229.78/41.10  | | | ALPHA: (27) implies:
% 229.78/41.10  | | |   (28)  all_57_10 = e3
% 229.78/41.10  | | | 
% 229.78/41.10  | | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (10), (11), (12), (16), (17),
% 229.78/41.10  | | |            (18), (28) are inconsistent by sub-proof #1746.
% 229.78/41.10  | | | 
% 229.78/41.10  | | End of split
% 229.78/41.10  | | 
% 229.78/41.10  | End of split
% 229.78/41.10  | 
% 229.78/41.10  End of proof
% 229.78/41.10  
% 229.78/41.10  Sub-proof #845 shows that the following formulas are inconsistent:
% 229.78/41.10  ----------------------------------------------------------------
% 229.78/41.10    (1)  all_57_3 = e3 & op(e2, e2) = e3
% 229.78/41.10    (2)  all_57_3 = e2
% 229.78/41.10    (3)   ~ (e3 = e2)
% 229.78/41.10  
% 229.78/41.10  Begin of proof
% 229.78/41.10  | 
% 229.78/41.10  | ALPHA: (1) implies:
% 229.78/41.10  |   (4)  all_57_3 = e3
% 229.78/41.10  | 
% 229.78/41.10  | COMBINE_EQS: (2), (4) imply:
% 229.78/41.10  |   (5)  e3 = e2
% 229.78/41.10  | 
% 229.78/41.10  | REDUCE: (3), (5) imply:
% 229.78/41.10  |   (6)  $false
% 229.78/41.10  | 
% 229.78/41.10  | CLOSE: (6) is inconsistent.
% 229.78/41.10  | 
% 229.78/41.10  End of proof
% 229.78/41.10  
% 229.78/41.10  Sub-proof #846 shows that the following formulas are inconsistent:
% 229.78/41.10  ----------------------------------------------------------------
% 229.78/41.10    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 229.78/41.10    (2)  op(e0, e2) = e0
% 229.78/41.10    (3)  op(e2, e0) = e0
% 229.78/41.10    (4)   ~ (e3 = e1)
% 229.78/41.10    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.78/41.10           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.78/41.10    (6)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 229.78/41.10    (7)   ~ (all_53_13 = e2)
% 229.78/41.10    (8)   ~ (all_53_4 = all_53_12)
% 229.78/41.10    (9)   ~ (all_53_13 = e3)
% 229.78/41.10    (10)   ~ (all_53_12 = all_53_13)
% 229.78/41.10    (11)   ~ (e3 = e2)
% 229.78/41.10    (12)  all_55_1 = all_53_4
% 229.78/41.10    (13)   ~ (all_53_4 = all_53_7)
% 229.78/41.10    (14)  op(e3, e3) = e0
% 229.78/41.10    (15)  op(e3, e2) = all_53_4
% 229.78/41.10    (16)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 229.78/41.10            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 229.78/41.10            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 229.78/41.10            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 229.78/41.10              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 229.78/41.10            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 229.78/41.10            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 229.78/41.10              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 229.78/41.10              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 229.78/41.10            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 229.78/41.10            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 229.78/41.10            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 229.78/41.10              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 229.78/41.10              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 229.78/41.10            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 229.78/41.10              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 229.78/41.10            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 229.78/41.10            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 229.78/41.10              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 229.78/41.10              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 229.78/41.10            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 229.78/41.10            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 229.78/41.10    (17)  op(e2, e2) = e2
% 229.78/41.10    (18)  op(e0, e0) = e3
% 229.78/41.10    (19)  op(e0, e2) = all_53_7
% 229.78/41.10    (20)  op(e1, e1) = e0
% 229.78/41.10    (21)  op(e2, e0) = all_53_13
% 229.78/41.10    (22)  all_55_3 = all_53_12
% 229.78/41.10    (23)   ~ (all_53_12 = e3)
% 229.78/41.10    (24)   ~ (all_53_4 = e2)
% 229.78/41.10    (25)  op(e3, e0) = all_53_12
% 229.78/41.10  
% 229.78/41.10  Begin of proof
% 229.78/41.10  | 
% 229.78/41.10  | GROUND_INST: instantiating (5) with all_53_7, e0, e2, e0, simplifying with
% 229.78/41.10  |              (2), (19) gives:
% 229.78/41.10  |   (26)  all_53_7 = e0
% 229.78/41.10  | 
% 229.78/41.10  | GROUND_INST: instantiating (5) with all_53_13, e0, e0, e2, simplifying with
% 229.78/41.10  |              (3), (21) gives:
% 229.78/41.10  |   (27)  all_53_13 = e0
% 229.78/41.10  | 
% 229.78/41.10  | REDUCE: (13), (26) imply:
% 229.78/41.10  |   (28)   ~ (all_53_4 = e0)
% 229.78/41.10  | 
% 229.78/41.10  | REDUCE: (10), (27) imply:
% 229.78/41.10  |   (29)   ~ (all_53_12 = e0)
% 229.78/41.10  | 
% 229.78/41.10  | REDUCE: (9), (27) imply:
% 229.78/41.10  |   (30)   ~ (e3 = e0)
% 229.78/41.10  | 
% 229.78/41.10  | SIMP: (30) implies:
% 229.78/41.10  |   (31)   ~ (e3 = e0)
% 229.78/41.10  | 
% 229.78/41.10  | REDUCE: (7), (27) imply:
% 229.78/41.10  |   (32)   ~ (e2 = e0)
% 229.78/41.10  | 
% 229.78/41.10  | SIMP: (32) implies:
% 229.78/41.10  |   (33)   ~ (e2 = e0)
% 229.78/41.10  | 
% 229.78/41.10  | BETA: splitting (16) gives:
% 229.78/41.10  | 
% 229.78/41.10  | Case 1:
% 229.78/41.10  | | 
% 229.78/41.10  | |   (34)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 229.78/41.10  | |           op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 229.78/41.10  | |           op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3,
% 229.78/41.10  | |             e3) = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 &
% 229.78/41.10  | |           op(e3, e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5)
% 229.78/41.10  | |           & $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1
% 229.78/41.10  | |           & all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 229.78/41.10  | |             all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 229.78/41.10  | |             all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11
% 229.78/41.10  | |           & op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 229.78/41.10  | |           $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 229.78/41.10  | | 
% 229.78/41.10  | | BETA: splitting (34) gives:
% 229.78/41.10  | | 
% 229.78/41.10  | | Case 1:
% 229.78/41.10  | | | 
% 229.78/41.10  | | |   (35)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 229.78/41.10  | | |         op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 229.78/41.10  | | |         op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3,
% 229.78/41.10  | | |           e3) = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 &
% 229.78/41.10  | | |         op(e3, e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5)
% 229.78/41.10  | | |         & $i(all_52_7)
% 229.78/41.10  | | | 
% 229.78/41.10  | | | ALPHA: (35) implies:
% 229.78/41.10  | | |   (36)  op(e3, e0) = all_52_7
% 229.78/41.10  | | |   (37)  op(e3, e2) = all_52_3
% 229.78/41.10  | | |   (38)  op(e3, e3) = all_52_1
% 229.78/41.10  | | |   (39)  op(all_52_7, all_52_7) = e0
% 229.78/41.10  | | |   (40)  op(all_52_3, all_52_3) = e2
% 229.78/41.10  | | |   (41)  op(all_52_1, all_52_1) = e3
% 229.78/41.10  | | | 
% 229.78/41.10  | | | GROUND_INST: instantiating (5) with all_53_12, all_52_7, e0, e3,
% 229.78/41.10  | | |              simplifying with (25), (36) gives:
% 229.78/41.10  | | |   (42)  all_53_12 = all_52_7
% 229.78/41.10  | | | 
% 229.78/41.10  | | | GROUND_INST: instantiating (5) with all_53_4, all_52_3, e2, e3,
% 229.78/41.10  | | |              simplifying with (15), (37) gives:
% 229.78/41.10  | | |   (43)  all_53_4 = all_52_3
% 229.78/41.10  | | | 
% 229.78/41.10  | | | GROUND_INST: instantiating (5) with e0, all_52_1, e3, e3, simplifying with
% 229.78/41.10  | | |              (14), (38) gives:
% 229.78/41.10  | | |   (44)  all_52_1 = e0
% 229.78/41.10  | | | 
% 229.78/41.10  | | | COMBINE_EQS: (22), (42) imply:
% 229.78/41.10  | | |   (45)  all_55_3 = all_52_7
% 229.78/41.10  | | | 
% 229.78/41.10  | | | COMBINE_EQS: (12), (43) imply:
% 229.78/41.10  | | |   (46)  all_55_1 = all_52_3
% 229.78/41.10  | | | 
% 229.78/41.10  | | | REDUCE: (8), (42), (43) imply:
% 229.78/41.10  | | |   (47)   ~ (all_52_3 = all_52_7)
% 229.78/41.10  | | | 
% 229.78/41.10  | | | REDUCE: (24), (43) imply:
% 229.78/41.10  | | |   (48)   ~ (all_52_3 = e2)
% 229.78/41.10  | | | 
% 229.78/41.10  | | | REDUCE: (28), (43) imply:
% 229.78/41.10  | | |   (49)   ~ (all_52_3 = e0)
% 229.78/41.10  | | | 
% 229.78/41.10  | | | REDUCE: (23), (42) imply:
% 229.78/41.10  | | |   (50)   ~ (all_52_7 = e3)
% 229.78/41.10  | | | 
% 229.78/41.10  | | | REDUCE: (29), (42) imply:
% 229.78/41.10  | | |   (51)   ~ (all_52_7 = e0)
% 229.78/41.10  | | | 
% 229.78/41.10  | | | BETA: splitting (1) gives:
% 229.78/41.10  | | | 
% 229.78/41.10  | | | Case 1:
% 229.78/41.10  | | | | 
% 229.78/41.10  | | | |   (52)  all_55_1 = e3
% 229.78/41.10  | | | | 
% 229.78/41.10  | | | | COMBINE_EQS: (46), (52) imply:
% 229.78/41.10  | | | |   (53)  all_52_3 = e3
% 229.78/41.10  | | | | 
% 229.78/41.10  | | | | SIMP: (53) implies:
% 229.78/41.10  | | | |   (54)  all_52_3 = e3
% 229.78/41.10  | | | | 
% 229.78/41.10  | | | | REDUCE: (40), (54) imply:
% 229.78/41.10  | | | |   (55)  op(e3, e3) = e2
% 229.78/41.10  | | | | 
% 229.78/41.10  | | | | REF_CLOSE: (5), (14), (33), (55) are inconsistent by sub-proof #2403.
% 229.78/41.10  | | | | 
% 229.78/41.10  | | | Case 2:
% 229.78/41.10  | | | | 
% 229.78/41.10  | | | |   (56)  all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 229.78/41.10  | | | | 
% 229.78/41.10  | | | | BETA: splitting (56) gives:
% 229.78/41.10  | | | | 
% 229.78/41.10  | | | | Case 1:
% 229.78/41.10  | | | | | 
% 229.78/41.10  | | | | |   (57)  all_55_1 = e2
% 229.78/41.10  | | | | | 
% 229.78/41.10  | | | | | REF_CLOSE: (46), (48), (57) are inconsistent by sub-proof #851.
% 229.78/41.10  | | | | | 
% 229.78/41.10  | | | | Case 2:
% 229.78/41.10  | | | | | 
% 229.78/41.10  | | | | |   (58)  all_55_1 = e1 | all_55_1 = e0
% 229.78/41.10  | | | | | 
% 229.78/41.10  | | | | | BETA: splitting (58) gives:
% 229.78/41.10  | | | | | 
% 229.78/41.10  | | | | | Case 1:
% 229.78/41.10  | | | | | | 
% 229.78/41.10  | | | | | |   (59)  all_55_1 = e1
% 229.78/41.10  | | | | | | 
% 229.78/41.10  | | | | | | COMBINE_EQS: (46), (59) imply:
% 229.78/41.10  | | | | | |   (60)  all_52_3 = e1
% 229.78/41.10  | | | | | | 
% 229.78/41.10  | | | | | | SIMP: (60) implies:
% 229.78/41.10  | | | | | |   (61)  all_52_3 = e1
% 229.78/41.10  | | | | | | 
% 229.78/41.10  | | | | | | REDUCE: (47), (61) imply:
% 229.78/41.10  | | | | | |   (62)   ~ (all_52_7 = e1)
% 229.78/41.10  | | | | | | 
% 229.78/41.10  | | | | | | SIMP: (62) implies:
% 229.78/41.10  | | | | | |   (63)   ~ (all_52_7 = e1)
% 229.78/41.10  | | | | | | 
% 229.78/41.10  | | | | | | BETA: splitting (6) gives:
% 229.78/41.10  | | | | | | 
% 229.78/41.10  | | | | | | Case 1:
% 229.78/41.10  | | | | | | | 
% 229.78/41.10  | | | | | | |   (64)  all_55_3 = e3
% 229.78/41.10  | | | | | | | 
% 229.78/41.10  | | | | | | | REF_CLOSE: (45), (50), (64) are inconsistent by sub-proof #1451.
% 229.78/41.10  | | | | | | | 
% 229.78/41.10  | | | | | | Case 2:
% 229.78/41.10  | | | | | | | 
% 229.78/41.10  | | | | | | |   (65)   ~ (all_55_3 = e3)
% 229.78/41.10  | | | | | | |   (66)  all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 229.78/41.10  | | | | | | | 
% 229.78/41.10  | | | | | | | BETA: splitting (66) gives:
% 229.78/41.10  | | | | | | | 
% 229.78/41.10  | | | | | | | Case 1:
% 229.78/41.10  | | | | | | | | 
% 229.78/41.10  | | | | | | | |   (67)  all_55_3 = e2
% 229.78/41.10  | | | | | | | | 
% 229.78/41.10  | | | | | | | | REF_CLOSE: (5), (17), (39), (45), (51), (67) are inconsistent by
% 229.78/41.10  | | | | | | | |            sub-proof #850.
% 229.78/41.10  | | | | | | | | 
% 229.78/41.10  | | | | | | | Case 2:
% 229.78/41.10  | | | | | | | | 
% 229.78/41.10  | | | | | | | |   (68)  all_55_3 = e1 | all_55_3 = e0
% 229.78/41.10  | | | | | | | | 
% 229.78/41.10  | | | | | | | | REF_CLOSE: (5), (18), (39), (45), (50), (63), (68) are
% 229.78/41.10  | | | | | | | |            inconsistent by sub-proof #1448.
% 229.78/41.10  | | | | | | | | 
% 229.78/41.10  | | | | | | | End of split
% 229.78/41.10  | | | | | | | 
% 229.78/41.10  | | | | | | End of split
% 229.78/41.10  | | | | | | 
% 229.78/41.10  | | | | | Case 2:
% 229.78/41.10  | | | | | | 
% 229.78/41.10  | | | | | |   (69)  all_55_1 = e0
% 229.78/41.10  | | | | | | 
% 229.78/41.10  | | | | | | REF_CLOSE: (46), (49), (69) are inconsistent by sub-proof #849.
% 229.78/41.10  | | | | | | 
% 229.78/41.10  | | | | | End of split
% 229.78/41.10  | | | | | 
% 229.78/41.10  | | | | End of split
% 229.78/41.10  | | | | 
% 229.78/41.10  | | | End of split
% 229.78/41.10  | | | 
% 229.78/41.10  | | Case 2:
% 229.78/41.10  | | | 
% 229.78/41.10  | | |   (70)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0 &
% 229.78/41.10  | | |         op(all_52_9, all_52_9) = e3 & op(all_52_11, all_52_11) = e2 &
% 229.78/41.10  | | |         op(all_52_13, all_52_13) = e1 & op(all_52_15, all_52_15) = e0 &
% 229.78/41.10  | | |         op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 & op(e2, e1) =
% 229.78/41.10  | | |         all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) & $i(all_52_11)
% 229.78/41.10  | | |         & $i(all_52_13) & $i(all_52_15)
% 229.78/41.10  | | | 
% 229.78/41.10  | | | REF_CLOSE: (3), (5), (18), (31), (70) are inconsistent by sub-proof #848.
% 229.78/41.10  | | | 
% 229.78/41.10  | | End of split
% 229.78/41.10  | | 
% 229.78/41.10  | Case 2:
% 229.78/41.10  | | 
% 229.78/41.10  | |   (71)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 &
% 229.78/41.10  | |           op(all_52_17, all_52_17) = e3 & op(all_52_19, all_52_19) = e2 &
% 229.78/41.10  | |           op(all_52_21, all_52_21) = e1 & op(all_52_23, all_52_23) = e0 &
% 229.78/41.10  | |           op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) =
% 229.78/41.10  | |           all_52_21 & op(e1, e0) = all_52_23 & $i(all_52_17) & $i(all_52_19)
% 229.78/41.10  | |           & $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3 & all_52_26 =
% 229.78/41.10  | |           e2 & all_52_28 = e1 & all_52_30 = e0 & op(all_52_25, all_52_25) =
% 229.78/41.10  | |           e3 & op(all_52_27, all_52_27) = e2 & op(all_52_29, all_52_29) = e1
% 229.78/41.10  | |           & op(all_52_31, all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0,
% 229.78/41.10  | |             e2) = all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0) =
% 229.78/41.10  | |           all_52_31 & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 229.78/41.10  | |           $i(all_52_31))
% 229.78/41.10  | | 
% 229.78/41.10  | | BETA: splitting (71) gives:
% 229.78/41.10  | | 
% 229.78/41.10  | | Case 1:
% 229.78/41.10  | | | 
% 229.78/41.10  | | |   (72)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 229.78/41.10  | | |         & op(all_52_17, all_52_17) = e3 & op(all_52_19, all_52_19) = e2 &
% 229.78/41.10  | | |         op(all_52_21, all_52_21) = e1 & op(all_52_23, all_52_23) = e0 &
% 229.78/41.10  | | |         op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) =
% 229.78/41.10  | | |         all_52_21 & op(e1, e0) = all_52_23 & $i(all_52_17) & $i(all_52_19)
% 229.78/41.10  | | |         & $i(all_52_21) & $i(all_52_23)
% 229.78/41.10  | | | 
% 229.78/41.10  | | | REF_CLOSE: (4), (5), (18), (20), (72) are inconsistent by sub-proof #847.
% 229.78/41.10  | | | 
% 229.78/41.10  | | Case 2:
% 229.78/41.10  | | | 
% 229.78/41.10  | | |   (73)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 229.78/41.10  | | |         & op(all_52_25, all_52_25) = e3 & op(all_52_27, all_52_27) = e2 &
% 229.78/41.10  | | |         op(all_52_29, all_52_29) = e1 & op(all_52_31, all_52_31) = e0 &
% 229.78/41.10  | | |         op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 & op(e0, e1) =
% 229.78/41.10  | | |         all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) & $i(all_52_27)
% 229.78/41.10  | | |         & $i(all_52_29) & $i(all_52_31)
% 229.78/41.10  | | | 
% 229.78/41.10  | | | ALPHA: (73) implies:
% 229.78/41.10  | | |   (74)  op(e0, e0) = all_52_31
% 229.78/41.10  | | |   (75)  op(e0, e2) = all_52_27
% 229.78/41.10  | | |   (76)  op(all_52_27, all_52_27) = e2
% 229.78/41.10  | | | 
% 229.78/41.10  | | | REF_CLOSE: (2), (5), (11), (18), (74), (75), (76) are inconsistent by
% 229.78/41.10  | | |            sub-proof #858.
% 229.78/41.10  | | | 
% 229.78/41.10  | | End of split
% 229.78/41.10  | | 
% 229.78/41.10  | End of split
% 229.78/41.10  | 
% 229.78/41.10  End of proof
% 229.78/41.10  
% 229.78/41.10  Sub-proof #847 shows that the following formulas are inconsistent:
% 229.78/41.10  ----------------------------------------------------------------
% 229.78/41.10    (1)   ~ (e3 = e1)
% 229.78/41.10    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.78/41.10           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.78/41.10    (3)  op(e0, e0) = e3
% 229.78/41.10    (4)  op(e1, e1) = e0
% 229.78/41.10    (5)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 &
% 229.78/41.10         op(all_52_17, all_52_17) = e3 & op(all_52_19, all_52_19) = e2 &
% 229.78/41.10         op(all_52_21, all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1,
% 229.78/41.10           e3) = all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 &
% 229.78/41.10         op(e1, e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 229.78/41.10         $i(all_52_23)
% 229.78/41.10  
% 229.78/41.10  Begin of proof
% 229.78/41.10  | 
% 229.78/41.10  | ALPHA: (5) implies:
% 229.78/41.10  |   (6)  op(e1, e1) = all_52_21
% 229.78/41.10  |   (7)  op(all_52_21, all_52_21) = e1
% 229.78/41.10  | 
% 229.78/41.10  | GROUND_INST: instantiating (2) with e0, all_52_21, e1, e1, simplifying with
% 229.78/41.10  |              (4), (6) gives:
% 229.78/41.10  |   (8)  all_52_21 = e0
% 229.78/41.10  | 
% 229.78/41.10  | REDUCE: (7), (8) imply:
% 229.78/41.10  |   (9)  op(e0, e0) = e1
% 229.78/41.10  | 
% 229.78/41.10  | REF_CLOSE: (1), (2), (3), (9) are inconsistent by sub-proof #2183.
% 229.78/41.10  | 
% 229.78/41.10  End of proof
% 229.78/41.10  
% 229.78/41.10  Sub-proof #848 shows that the following formulas are inconsistent:
% 229.78/41.10  ----------------------------------------------------------------
% 229.78/41.10    (1)  op(e2, e0) = e0
% 229.78/41.10    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.78/41.10           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.78/41.11    (3)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0 &
% 229.78/41.11         op(all_52_9, all_52_9) = e3 & op(all_52_11, all_52_11) = e2 &
% 229.78/41.11         op(all_52_13, all_52_13) = e1 & op(all_52_15, all_52_15) = e0 & op(e2,
% 229.78/41.11           e3) = all_52_9 & op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13 &
% 229.78/41.11         op(e2, e0) = all_52_15 & $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 229.78/41.11         $i(all_52_15)
% 229.78/41.11    (4)   ~ (e3 = e0)
% 229.78/41.11    (5)  op(e0, e0) = e3
% 229.78/41.11  
% 229.78/41.11  Begin of proof
% 229.78/41.11  | 
% 229.78/41.11  | ALPHA: (3) implies:
% 229.78/41.11  |   (6)  op(e2, e0) = all_52_15
% 229.78/41.11  |   (7)  op(all_52_15, all_52_15) = e0
% 229.78/41.11  | 
% 229.78/41.11  | GROUND_INST: instantiating (2) with e0, all_52_15, e0, e2, simplifying with
% 229.78/41.11  |              (1), (6) gives:
% 229.78/41.11  |   (8)  all_52_15 = e0
% 229.78/41.11  | 
% 229.78/41.11  | REDUCE: (7), (8) imply:
% 229.78/41.11  |   (9)  op(e0, e0) = e0
% 229.78/41.11  | 
% 229.78/41.11  | REF_CLOSE: (2), (4), (5), (9) are inconsistent by sub-proof #2304.
% 229.78/41.11  | 
% 229.78/41.11  End of proof
% 229.78/41.11  
% 229.78/41.11  Sub-proof #849 shows that the following formulas are inconsistent:
% 229.78/41.11  ----------------------------------------------------------------
% 229.78/41.11    (1)  all_55_1 = all_52_3
% 229.78/41.11    (2)  all_55_1 = e0
% 229.78/41.11    (3)   ~ (all_52_3 = e0)
% 229.78/41.11  
% 229.78/41.11  Begin of proof
% 229.78/41.11  | 
% 229.78/41.11  | COMBINE_EQS: (1), (2) imply:
% 229.78/41.11  |   (4)  all_52_3 = e0
% 229.78/41.11  | 
% 229.78/41.11  | SIMP: (4) implies:
% 229.78/41.11  |   (5)  all_52_3 = e0
% 229.78/41.11  | 
% 229.78/41.11  | REDUCE: (3), (5) imply:
% 229.78/41.11  |   (6)  $false
% 229.78/41.11  | 
% 229.78/41.11  | CLOSE: (6) is inconsistent.
% 229.78/41.11  | 
% 229.78/41.11  End of proof
% 229.78/41.11  
% 229.78/41.11  Sub-proof #850 shows that the following formulas are inconsistent:
% 229.78/41.11  ----------------------------------------------------------------
% 229.78/41.11    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.78/41.11           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.78/41.11    (2)  op(all_52_7, all_52_7) = e0
% 229.78/41.11    (3)  all_55_3 = all_52_7
% 229.78/41.11    (4)  all_55_3 = e2
% 229.78/41.11    (5)  op(e2, e2) = e2
% 229.78/41.11    (6)   ~ (all_52_7 = e0)
% 229.78/41.11  
% 229.78/41.11  Begin of proof
% 229.78/41.11  | 
% 229.78/41.11  | COMBINE_EQS: (3), (4) imply:
% 229.78/41.11  |   (7)  all_52_7 = e2
% 229.78/41.11  | 
% 229.78/41.11  | SIMP: (7) implies:
% 229.78/41.11  |   (8)  all_52_7 = e2
% 229.78/41.11  | 
% 229.78/41.11  | REDUCE: (6), (8) imply:
% 229.78/41.11  |   (9)   ~ (e2 = e0)
% 229.78/41.11  | 
% 229.78/41.11  | REDUCE: (2), (8) imply:
% 229.78/41.11  |   (10)  op(e2, e2) = e0
% 229.78/41.11  | 
% 229.78/41.11  | REF_CLOSE: (1), (5), (9), (10) are inconsistent by sub-proof #2472.
% 229.78/41.11  | 
% 229.78/41.11  End of proof
% 229.78/41.11  
% 229.78/41.11  Sub-proof #851 shows that the following formulas are inconsistent:
% 229.78/41.11  ----------------------------------------------------------------
% 229.78/41.11    (1)  all_55_1 = all_52_3
% 229.78/41.11    (2)  all_55_1 = e2
% 229.78/41.11    (3)   ~ (all_52_3 = e2)
% 229.78/41.11  
% 229.78/41.11  Begin of proof
% 229.78/41.11  | 
% 229.78/41.11  | COMBINE_EQS: (1), (2) imply:
% 229.78/41.11  |   (4)  all_52_3 = e2
% 229.78/41.11  | 
% 229.78/41.11  | SIMP: (4) implies:
% 229.78/41.11  |   (5)  all_52_3 = e2
% 229.78/41.11  | 
% 229.78/41.11  | REDUCE: (3), (5) imply:
% 229.78/41.11  |   (6)  $false
% 229.78/41.11  | 
% 229.78/41.11  | CLOSE: (6) is inconsistent.
% 229.78/41.11  | 
% 229.78/41.11  End of proof
% 229.78/41.11  
% 229.78/41.11  Sub-proof #852 shows that the following formulas are inconsistent:
% 229.78/41.11  ----------------------------------------------------------------
% 229.78/41.11    (1)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.78/41.11         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.78/41.11    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.78/41.11         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.78/41.11    (3)   ~ (e3 = e1)
% 229.78/41.11    (4)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 229.78/41.11         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 229.78/41.11    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.78/41.11           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.78/41.11    (6)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.78/41.11         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.78/41.11    (7)   ~ (all_6_2 = e3)
% 229.78/41.11    (8)  op(e1, e1) = all_6_2
% 229.78/41.11    (9)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.78/41.11         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.78/41.11    (10)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.78/41.11          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.78/41.11    (11)  all_57_4 = e3
% 229.78/41.11    (12)   ~ (e3 = e2)
% 229.78/41.11    (13)   ~ (e3 = e0)
% 229.78/41.11    (14)  all_57_0 = e0
% 229.78/41.11    (15)  all_57_15 = e3
% 229.78/41.11    (16)  all_57_1 = e1
% 229.78/41.11    (17)  op(e3, e3) = e0
% 229.78/41.11    (18)  op(e1, e1) = e1
% 229.78/41.11    (19)   ~ (e2 = e0)
% 229.78/41.11    (20)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.78/41.11          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.78/41.11    (21)   ~ (e1 = e0)
% 229.78/41.11    (22)  op(e0, e0) = e3
% 229.78/41.11    (23)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.78/41.11              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.78/41.11                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.78/41.11                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.78/41.11    (24)   ~ (all_53_12 = e3)
% 229.78/41.11    (25)  all_57_7 = e3
% 229.78/41.11    (26)  all_57_11 = e1
% 229.78/41.11    (27)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.78/41.11          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.78/41.11    (28)   ~ (e2 = e1)
% 229.78/41.11    (29)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.78/41.11          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.78/41.11    (30)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.78/41.11          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.78/41.11    (31)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.78/41.11          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.78/41.11    (32)  all_57_3 = e2
% 229.78/41.11    (33)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.78/41.11          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.78/41.11    (34)  op(e3, e0) = all_53_12
% 229.78/41.11  
% 229.78/41.11  Begin of proof
% 229.78/41.11  | 
% 229.78/41.11  | BETA: splitting (4) gives:
% 229.78/41.11  | 
% 229.78/41.11  | Case 1:
% 229.78/41.11  | | 
% 229.78/41.11  | |   (35)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) =
% 229.78/41.11  | |           e0)
% 229.78/41.11  | | 
% 229.78/41.11  | | REF_CLOSE: (1), (3), (5), (6), (7), (8), (12), (13), (14), (15), (17), (19),
% 229.78/41.11  | |            (21), (23), (25), (27), (28), (29), (30), (31), (35) are
% 229.78/41.11  | |            inconsistent by sub-proof #868.
% 229.78/41.11  | | 
% 229.78/41.11  | Case 2:
% 229.78/41.11  | | 
% 229.78/41.11  | |   (36)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 229.78/41.11  | |           e0)
% 229.78/41.11  | | 
% 229.78/41.11  | | BETA: splitting (36) gives:
% 229.78/41.11  | | 
% 229.78/41.11  | | Case 1:
% 229.78/41.11  | | | 
% 229.78/41.11  | | |   (37)  all_57_8 = e0 & op(e1, e1) = e0
% 229.78/41.11  | | | 
% 229.78/41.11  | | | ALPHA: (37) implies:
% 229.78/41.11  | | |   (38)  op(e1, e1) = e0
% 229.78/41.11  | | | 
% 229.78/41.11  | | | REF_CLOSE: (5), (18), (21), (38) are inconsistent by sub-proof #2427.
% 229.78/41.11  | | | 
% 229.78/41.11  | | Case 2:
% 229.78/41.11  | | | 
% 229.78/41.11  | | |   (39)  all_57_11 = e0 & op(e1, e0) = e0
% 229.78/41.11  | | | 
% 229.78/41.11  | | | ALPHA: (39) implies:
% 229.78/41.11  | | |   (40)  all_57_11 = e0
% 229.78/41.11  | | | 
% 229.78/41.11  | | | COMBINE_EQS: (26), (40) imply:
% 229.78/41.11  | | |   (41)  e1 = e0
% 229.78/41.11  | | | 
% 229.78/41.11  | | | COMBINE_EQS: (16), (41) imply:
% 229.78/41.11  | | |   (42)  all_57_1 = e0
% 229.78/41.11  | | | 
% 229.78/41.11  | | | REF_CLOSE: (2), (3), (5), (9), (10), (11), (12), (13), (14), (17), (19),
% 229.78/41.11  | | |            (20), (21), (22), (24), (25), (28), (31), (32), (33), (34),
% 229.78/41.11  | | |            (40), (42) are inconsistent by sub-proof #901.
% 229.78/41.11  | | | 
% 229.78/41.11  | | End of split
% 229.78/41.11  | | 
% 229.78/41.11  | End of split
% 229.78/41.11  | 
% 229.78/41.11  End of proof
% 229.78/41.11  
% 229.78/41.11  Sub-proof #853 shows that the following formulas are inconsistent:
% 229.78/41.11  ----------------------------------------------------------------
% 229.78/41.11    (1)   ~ (all_48_2 = e0) | ( ~ (all_48_0 = e2) & op(all_48_1, e3) = all_48_0 &
% 229.78/41.11           op(e3, e0) = all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 =
% 229.78/41.11             e1) & op(e3, e0) = all_48_1 & $i(all_48_1))
% 229.78/41.11    (2)  all_57_9 = e2
% 229.78/41.11    (3)  all_48_2 = e0
% 229.78/41.11    (4)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.78/41.11         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.78/41.11    (5)  all_57_13 = e1
% 229.78/41.11    (6)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.78/41.11         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.78/41.11    (7)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.78/41.11         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.78/41.11    (8)   ~ (e3 = e1)
% 229.78/41.11    (9)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 229.78/41.11         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 229.78/41.11    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.78/41.11            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.78/41.11    (11)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.78/41.11          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.78/41.11    (12)   ~ (all_6_2 = e3)
% 229.78/41.11    (13)  ( ~ (all_18_0 = e1) & op(all_18_1, e3) = all_18_0 & op(e3, e0) =
% 229.78/41.11            all_18_1 & $i(all_18_0) & $i(all_18_1)) | ( ~ (all_18_1 = e2) & op(e3,
% 229.78/41.11              e0) = all_18_1 & $i(all_18_1))
% 229.78/41.11    (14)  all_57_10 = e1
% 229.78/41.11    (15)  op(e1, e1) = all_6_2
% 229.78/41.11    (16)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.78/41.11          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.78/41.11    (17)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 229.78/41.11            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 229.78/41.11              e3) = all_22_1 & $i(all_22_1))
% 229.78/41.11    (18)   ~ (all_53_13 = e2)
% 229.78/41.11    (19)   ~ (all_53_7 = e2)
% 229.78/41.11    (20)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.78/41.11          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.78/41.11    (21)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.78/41.11          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.78/41.11    (22)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 229.78/41.11          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.78/41.11    (23)  all_57_4 = e3
% 229.78/41.11    (24)   ~ (e3 = e2)
% 229.78/41.11    (25)  all_55_10 = e1 | all_55_10 = e0
% 229.78/41.11    (26)   ~ (e3 = e0)
% 229.78/41.11    (27)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 229.78/41.11          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 229.78/41.11    (28)   ~ (all_6_2 = e2)
% 229.78/41.11    (29)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 229.78/41.11    (30)  op(e0, e3) = all_53_3
% 229.78/41.11    (31)   ~ (all_53_2 = e0)
% 229.78/41.11    (32)  all_57_0 = e0
% 229.78/41.11    (33)  all_57_15 = e3
% 229.78/41.11    (34)  op(e3, e3) = e0
% 229.78/41.11    (35)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.78/41.11          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.78/41.11            e1)
% 229.78/41.11    (36)  all_57_11 = e0
% 229.78/41.11    (37)  op(e1, e1) = e1
% 229.78/41.11    (38)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.78/41.11          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.78/41.11    (39)   ~ (e2 = e0)
% 229.78/41.11    (40)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 229.78/41.11            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 229.78/41.11            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 229.78/41.11            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 229.78/41.11              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 229.78/41.11            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 229.78/41.11            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 229.78/41.11              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 229.78/41.11              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 229.78/41.11            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 229.78/41.11            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 229.78/41.11            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 229.78/41.11              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 229.78/41.11              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 229.78/41.11            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 229.78/41.11              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 229.78/41.11            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 229.78/41.11            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 229.78/41.11              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 229.78/41.11              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 229.78/41.11            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 229.78/41.11            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 229.78/41.11    (41)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 229.78/41.11            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 229.78/41.11              e3) = all_12_1 & $i(all_12_1))
% 229.78/41.11    (42)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.78/41.11          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.78/41.11    (43)  op(e2, e2) = e2
% 229.78/41.11    (44)   ~ (e1 = e0)
% 229.78/41.11    (45)  all_57_14 = e2
% 229.78/41.11    (46)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.78/41.11          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.78/41.11    (47)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.78/41.11          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.78/41.11    (48)   ~ (all_53_2 = all_53_3)
% 229.78/41.11    (49)  all_55_8 = all_53_2
% 229.78/41.11    (50)  op(e0, e0) = e3
% 229.78/41.11    (51)  op(e0, e2) = all_53_7
% 229.78/41.11    (52)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.78/41.11          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.78/41.11            e2)
% 229.78/41.11    (53)   ~ (all_53_3 = e0)
% 229.78/41.11    (54)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.78/41.11              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.78/41.11                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.78/41.11                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.78/41.11    (55)  all_55_10 = all_6_2
% 229.78/41.11    (56)  op(e2, e0) = all_53_13
% 229.78/41.11    (57)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.78/41.11          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.78/41.11    (58)   ~ (all_53_12 = e3)
% 229.78/41.11    (59)  op(e1, e3) = all_53_2
% 229.78/41.11    (60)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.78/41.11          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.78/41.11    (61)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.78/41.11          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.78/41.11    (62)   ~ (all_53_12 = e0)
% 229.78/41.11    (63)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.78/41.11          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 229.78/41.11    (64)   ~ (e2 = e1)
% 229.78/41.11    (65)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.78/41.11          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.78/41.11    (66)   ~ (all_6_2 = e0)
% 229.78/41.11    (67)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.78/41.11          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.78/41.11    (68)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 229.78/41.11          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 229.78/41.11    (69)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.78/41.11          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.78/41.11    (70)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.78/41.11          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.78/41.11    (71)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 229.78/41.11          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 229.78/41.11    (72)  all_57_3 = e2
% 229.78/41.11    (73)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.78/41.11          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.78/41.11    (74)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 229.78/41.11          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 229.78/41.11    (75)  op(e3, e0) = all_53_12
% 229.78/41.11  
% 229.78/41.11  Begin of proof
% 229.78/41.11  | 
% 229.78/41.11  | BETA: splitting (16) gives:
% 229.78/41.11  | 
% 229.78/41.11  | Case 1:
% 229.78/41.11  | | 
% 229.78/41.11  | |   (76)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) =
% 229.78/41.11  | |           e1)
% 229.78/41.11  | | 
% 229.78/41.11  | | BETA: splitting (76) gives:
% 229.78/41.11  | | 
% 229.78/41.11  | | Case 1:
% 229.78/41.11  | | | 
% 229.78/41.11  | | |   (77)  all_57_0 = e1 & op(e3, e3) = e1
% 229.78/41.11  | | | 
% 229.78/41.11  | | | ALPHA: (77) implies:
% 229.78/41.11  | | |   (78)  all_57_0 = e1
% 229.78/41.11  | | | 
% 229.78/41.11  | | | COMBINE_EQS: (32), (78) imply:
% 229.78/41.11  | | |   (79)  e1 = e0
% 229.78/41.11  | | | 
% 229.78/41.11  | | | REF_CLOSE: (8), (10), (14), (24), (33), (36), (39), (44), (50), (64),
% 229.78/41.11  | | |            (65), (70), (79) are inconsistent by sub-proof #1086.
% 229.78/41.11  | | | 
% 229.78/41.11  | | Case 2:
% 229.78/41.11  | | | 
% 229.78/41.11  | | |   (80)  all_57_1 = e1 & op(e3, e2) = e1
% 229.78/41.11  | | | 
% 229.78/41.11  | | | ALPHA: (80) implies:
% 229.78/41.11  | | |   (81)  all_57_1 = e1
% 229.78/41.11  | | | 
% 229.78/41.11  | | | BETA: splitting (54) gives:
% 229.78/41.11  | | | 
% 229.78/41.11  | | | Case 1:
% 229.78/41.11  | | | | 
% 229.78/41.11  | | | |   (82)  all_57_15 = e0 & op(e0, e0) = e0
% 229.78/41.11  | | | | 
% 229.78/41.11  | | | | ALPHA: (82) implies:
% 229.78/41.11  | | | |   (83)  op(e0, e0) = e0
% 229.78/41.11  | | | | 
% 229.78/41.11  | | | | REF_CLOSE: (10), (26), (50), (83) are inconsistent by sub-proof #2304.
% 229.78/41.11  | | | | 
% 229.78/41.11  | | | Case 2:
% 229.78/41.11  | | | | 
% 229.78/41.11  | | | |   (84)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2,
% 229.78/41.11  | | | |               e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) &
% 229.78/41.11  | | | |         ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0,
% 229.78/41.11  | | | |               e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 229.78/41.11  | | | | 
% 229.78/41.11  | | | | ALPHA: (84) implies:
% 229.78/41.11  | | | |   (85)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0,
% 229.78/41.11  | | | |             e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.78/41.11  | | | |   (86)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0)
% 229.78/41.11  | | | |           = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 229.78/41.11  | | | | 
% 229.78/41.11  | | | | BETA: splitting (85) gives:
% 229.78/41.11  | | | | 
% 229.78/41.11  | | | | Case 1:
% 229.78/41.11  | | | | | 
% 229.78/41.11  | | | | |   (87)  all_57_12 = e0 & op(e0, e3) = e0
% 229.78/41.11  | | | | | 
% 229.78/41.11  | | | | | ALPHA: (87) implies:
% 229.78/41.11  | | | | |   (88)  op(e0, e3) = e0
% 229.78/41.11  | | | | | 
% 229.78/41.11  | | | | | REF_CLOSE: (10), (30), (53), (88) are inconsistent by sub-proof #2366.
% 229.78/41.11  | | | | | 
% 229.78/41.11  | | | | Case 2:
% 229.78/41.11  | | | | | 
% 229.78/41.11  | | | | |   (89)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 229.78/41.11  | | | | |             e1) = e0)
% 229.78/41.11  | | | | | 
% 229.78/41.11  | | | | | BETA: splitting (89) gives:
% 229.78/41.11  | | | | | 
% 229.78/41.11  | | | | | Case 1:
% 229.78/41.11  | | | | | | 
% 229.78/41.11  | | | | | |   (90)  all_57_13 = e0 & op(e0, e2) = e0
% 229.78/41.11  | | | | | | 
% 229.78/41.11  | | | | | | ALPHA: (90) implies:
% 229.78/41.11  | | | | | |   (91)  all_57_13 = e0
% 229.78/41.11  | | | | | | 
% 229.78/41.11  | | | | | | COMBINE_EQS: (5), (91) imply:
% 229.78/41.11  | | | | | |   (92)  e1 = e0
% 229.78/41.11  | | | | | | 
% 229.78/41.11  | | | | | | COMBINE_EQS: (81), (92) imply:
% 229.78/41.11  | | | | | |   (93)  all_57_1 = e0
% 229.78/41.11  | | | | | | 
% 229.78/41.11  | | | | | | REF_CLOSE: (7), (8), (10), (16), (20), (21), (23), (24), (26), (32),
% 229.78/41.11  | | | | | |            (33), (34), (35), (39), (42), (44), (47), (50), (52),
% 229.78/41.11  | | | | | |            (58), (62), (64), (65), (70), (72), (73), (75), (85),
% 229.78/41.11  | | | | | |            (86), (93) are inconsistent by sub-proof #891.
% 229.78/41.11  | | | | | | 
% 229.78/41.11  | | | | | Case 2:
% 229.78/41.11  | | | | | | 
% 229.78/41.11  | | | | | |   (94)  all_57_14 = e0 & op(e0, e1) = e0
% 229.78/41.11  | | | | | | 
% 229.78/41.11  | | | | | | REF_CLOSE: (2), (8), (24), (33), (36), (39), (44), (45), (64), (65),
% 229.78/41.11  | | | | | |            (70), (94) are inconsistent by sub-proof #857.
% 229.78/41.11  | | | | | | 
% 229.78/41.11  | | | | | End of split
% 229.78/41.11  | | | | | 
% 229.78/41.11  | | | | End of split
% 229.78/41.11  | | | | 
% 229.78/41.11  | | | End of split
% 229.78/41.11  | | | 
% 229.78/41.11  | | End of split
% 229.78/41.11  | | 
% 229.78/41.11  | Case 2:
% 229.78/41.11  | | 
% 229.78/41.11  | |   (95)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) =
% 229.78/41.11  | |           e1)
% 229.78/41.11  | | 
% 229.78/41.12  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13),
% 229.78/41.12  | |            (15), (16), (17), (18), (19), (20), (21), (22), (24), (25), (26),
% 229.78/41.12  | |            (27), (28), (29), (30), (31), (32), (33), (34), (35), (37), (38),
% 229.78/41.12  | |            (39), (40), (41), (42), (43), (44), (45), (46), (47), (48), (49),
% 229.78/41.12  | |            (50), (51), (52), (53), (54), (55), (56), (57), (58), (59), (60),
% 229.78/41.12  | |            (61), (62), (63), (64), (65), (66), (67), (68), (69), (70), (71),
% 229.78/41.12  | |            (72), (73), (74), (75), (95) are inconsistent by sub-proof #854.
% 229.78/41.12  | | 
% 229.78/41.12  | End of split
% 229.78/41.12  | 
% 229.78/41.12  End of proof
% 229.78/41.12  
% 229.78/41.12  Sub-proof #854 shows that the following formulas are inconsistent:
% 229.78/41.12  ----------------------------------------------------------------
% 229.78/41.12    (1)   ~ (all_48_2 = e0) | ( ~ (all_48_0 = e2) & op(all_48_1, e3) = all_48_0 &
% 229.78/41.12           op(e3, e0) = all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 =
% 229.78/41.12             e1) & op(e3, e0) = all_48_1 & $i(all_48_1))
% 229.78/41.12    (2)  all_57_9 = e2
% 229.78/41.12    (3)  all_48_2 = e0
% 229.78/41.12    (4)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.78/41.12         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.78/41.12    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.78/41.12         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.78/41.12    (6)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.78/41.12         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.78/41.12    (7)   ~ (e3 = e1)
% 229.78/41.12    (8)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 229.78/41.12         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 229.78/41.12    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.78/41.12           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.78/41.12    (10)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.78/41.12          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.78/41.12    (11)   ~ (all_6_2 = e3)
% 229.78/41.12    (12)  ( ~ (all_18_0 = e1) & op(all_18_1, e3) = all_18_0 & op(e3, e0) =
% 229.78/41.12            all_18_1 & $i(all_18_0) & $i(all_18_1)) | ( ~ (all_18_1 = e2) & op(e3,
% 229.78/41.12              e0) = all_18_1 & $i(all_18_1))
% 229.78/41.12    (13)  op(e1, e1) = all_6_2
% 229.78/41.12    (14)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.78/41.12          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.78/41.12    (15)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 229.78/41.12            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 229.78/41.12              e3) = all_22_1 & $i(all_22_1))
% 229.78/41.12    (16)   ~ (all_53_13 = e2)
% 229.78/41.12    (17)   ~ (all_53_7 = e2)
% 229.78/41.12    (18)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.78/41.12          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.78/41.12    (19)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.78/41.12    (20)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.78/41.12          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.78/41.12    (21)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 229.78/41.12          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.78/41.12    (22)   ~ (e3 = e2)
% 229.78/41.12    (23)  all_55_10 = e1 | all_55_10 = e0
% 229.78/41.12    (24)   ~ (e3 = e0)
% 229.78/41.12    (25)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 229.78/41.12          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 229.78/41.12    (26)   ~ (all_6_2 = e2)
% 229.78/41.12    (27)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 229.78/41.12    (28)  op(e0, e3) = all_53_3
% 229.78/41.12    (29)   ~ (all_53_2 = e0)
% 229.78/41.12    (30)  all_57_0 = e0
% 229.78/41.12    (31)  all_57_15 = e3
% 229.78/41.12    (32)  op(e3, e3) = e0
% 229.78/41.12    (33)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.78/41.12          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.78/41.12            e1)
% 229.78/41.12    (34)  op(e1, e1) = e1
% 229.78/41.12    (35)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.78/41.12          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.78/41.12    (36)   ~ (e2 = e0)
% 229.78/41.12    (37)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 229.78/41.12            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 229.78/41.12            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 229.78/41.12            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 229.78/41.12              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 229.78/41.12            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 229.78/41.12            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 229.78/41.12              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 229.78/41.12              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 229.78/41.12            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 229.78/41.12            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 229.78/41.12            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 229.78/41.12              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 229.78/41.12              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 229.78/41.12            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 229.78/41.12              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 229.78/41.12            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 229.78/41.12            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 229.78/41.12              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 229.78/41.12              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 229.78/41.12            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 229.78/41.12            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 229.78/41.12    (38)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 229.78/41.12            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 229.78/41.12              e3) = all_12_1 & $i(all_12_1))
% 229.78/41.12    (39)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.78/41.12          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.78/41.12    (40)  op(e2, e2) = e2
% 229.78/41.12    (41)   ~ (e1 = e0)
% 229.78/41.12    (42)  all_57_14 = e2
% 229.78/41.12    (43)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.78/41.12          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.78/41.12    (44)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.78/41.12          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.78/41.12    (45)   ~ (all_53_2 = all_53_3)
% 229.78/41.12    (46)  all_55_8 = all_53_2
% 229.78/41.12    (47)  op(e0, e0) = e3
% 229.78/41.12    (48)  op(e0, e2) = all_53_7
% 229.78/41.12    (49)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.78/41.12          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.78/41.12            e2)
% 229.78/41.12    (50)   ~ (all_53_3 = e0)
% 229.78/41.12    (51)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.78/41.12              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.78/41.12                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.78/41.12                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.78/41.12    (52)  all_55_10 = all_6_2
% 229.78/41.12    (53)  op(e2, e0) = all_53_13
% 229.78/41.12    (54)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.78/41.12          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.78/41.12    (55)   ~ (all_53_12 = e3)
% 229.78/41.12    (56)  op(e1, e3) = all_53_2
% 229.78/41.12    (57)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.78/41.12          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.78/41.12    (58)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.78/41.12          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.78/41.12    (59)   ~ (all_53_12 = e0)
% 229.78/41.12    (60)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.78/41.12          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 229.78/41.12    (61)   ~ (e2 = e1)
% 229.78/41.12    (62)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.78/41.12          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.78/41.12    (63)   ~ (all_6_2 = e0)
% 229.78/41.12    (64)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.78/41.12          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.78/41.12    (65)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 229.78/41.12          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 229.78/41.12    (66)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.78/41.12          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.78/41.12    (67)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.78/41.12          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.78/41.12    (68)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 229.78/41.12          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 229.78/41.12    (69)  all_57_3 = e2
% 229.78/41.12    (70)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.78/41.12          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.78/41.12    (71)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 229.78/41.12          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 229.78/41.12    (72)  op(e3, e0) = all_53_12
% 229.78/41.12  
% 229.78/41.12  Begin of proof
% 229.78/41.12  | 
% 229.78/41.12  | BETA: splitting (19) gives:
% 229.78/41.12  | 
% 229.78/41.12  | Case 1:
% 229.78/41.12  | | 
% 229.78/41.12  | |   (73)  all_57_4 = e1 & op(e3, e1) = e1
% 229.78/41.12  | | 
% 229.78/41.12  | | ALPHA: (73) implies:
% 229.78/41.12  | |   (74)  all_57_4 = e1
% 229.78/41.12  | | 
% 229.78/41.12  | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 229.78/41.12  | |            (14), (15), (18), (20), (21), (22), (23), (24), (25), (26), (27),
% 229.78/41.12  | |            (28), (29), (30), (31), (32), (33), (34), (35), (36), (37), (38),
% 229.78/41.12  | |            (39), (40), (41), (43), (44), (45), (46), (47), (49), (50), (51),
% 229.78/41.12  | |            (52), (54), (55), (56), (57), (58), (59), (60), (61), (62), (63),
% 229.78/41.12  | |            (64), (65), (66), (67), (68), (69), (70), (71), (72), (74) are
% 229.78/41.12  | |            inconsistent by sub-proof #944.
% 229.78/41.12  | | 
% 229.78/41.12  | Case 2:
% 229.78/41.12  | | 
% 229.78/41.12  | |   (75)  all_57_9 = e1 & op(e3, e0) = e1
% 229.78/41.12  | | 
% 229.78/41.12  | | ALPHA: (75) implies:
% 229.78/41.12  | |   (76)  all_57_9 = e1
% 229.78/41.12  | | 
% 229.78/41.12  | | COMBINE_EQS: (2), (76) imply:
% 229.78/41.12  | |   (77)  e2 = e1
% 229.78/41.12  | | 
% 229.78/41.12  | | COMBINE_EQS: (42), (77) imply:
% 229.78/41.12  | |   (78)  all_57_14 = e1
% 229.78/41.12  | | 
% 229.78/41.12  | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 229.78/41.12  | |            (14), (15), (16), (17), (18), (20), (21), (22), (23), (24), (25),
% 229.78/41.12  | |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 229.78/41.12  | |            (37), (38), (39), (40), (41), (43), (44), (45), (46), (47), (48),
% 229.78/41.12  | |            (49), (50), (51), (52), (53), (54), (55), (56), (57), (58), (59),
% 229.78/41.12  | |            (60), (61), (62), (63), (64), (65), (66), (67), (68), (69), (70),
% 229.78/41.12  | |            (71), (72), (78) are inconsistent by sub-proof #855.
% 229.78/41.12  | | 
% 229.78/41.12  | End of split
% 229.78/41.12  | 
% 229.78/41.12  End of proof
% 229.78/41.12  
% 229.78/41.12  Sub-proof #855 shows that the following formulas are inconsistent:
% 229.78/41.12  ----------------------------------------------------------------
% 229.78/41.12    (1)   ~ (all_48_2 = e0) | ( ~ (all_48_0 = e2) & op(all_48_1, e3) = all_48_0 &
% 229.78/41.12           op(e3, e0) = all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 =
% 229.78/41.12             e1) & op(e3, e0) = all_48_1 & $i(all_48_1))
% 229.78/41.12    (2)  all_48_2 = e0
% 229.78/41.12    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.78/41.12         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.78/41.12    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.78/41.12         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.78/41.12    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.78/41.12         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.78/41.12    (6)   ~ (e3 = e1)
% 229.78/41.12    (7)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 229.78/41.12         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 229.78/41.12    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.78/41.12           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.78/41.12    (9)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.78/41.12         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.78/41.12    (10)   ~ (all_6_2 = e3)
% 229.78/41.12    (11)  ( ~ (all_18_0 = e1) & op(all_18_1, e3) = all_18_0 & op(e3, e0) =
% 229.78/41.12            all_18_1 & $i(all_18_0) & $i(all_18_1)) | ( ~ (all_18_1 = e2) & op(e3,
% 229.78/41.12              e0) = all_18_1 & $i(all_18_1))
% 229.78/41.12    (12)  op(e1, e1) = all_6_2
% 229.78/41.12    (13)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.78/41.12          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.78/41.12    (14)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 229.78/41.12            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 229.78/41.12              e3) = all_22_1 & $i(all_22_1))
% 229.78/41.12    (15)   ~ (all_53_13 = e2)
% 229.78/41.12    (16)   ~ (all_53_7 = e2)
% 229.78/41.12    (17)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.78/41.12          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.78/41.12    (18)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.78/41.12          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.78/41.12    (19)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 229.78/41.12          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.78/41.12    (20)   ~ (e3 = e2)
% 229.78/41.12    (21)  all_55_10 = e1 | all_55_10 = e0
% 229.78/41.12    (22)   ~ (e3 = e0)
% 229.78/41.12    (23)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 229.78/41.12          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 229.78/41.12    (24)   ~ (all_6_2 = e2)
% 229.78/41.12    (25)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 229.78/41.12    (26)  op(e0, e3) = all_53_3
% 229.78/41.12    (27)   ~ (all_53_2 = e0)
% 229.78/41.12    (28)  all_57_0 = e0
% 229.78/41.12    (29)  all_57_15 = e3
% 229.78/41.12    (30)  op(e3, e3) = e0
% 229.78/41.12    (31)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.78/41.12          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.78/41.12            e1)
% 229.78/41.12    (32)  op(e1, e1) = e1
% 229.78/41.12    (33)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.78/41.12          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.78/41.12    (34)   ~ (e2 = e0)
% 229.78/41.12    (35)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 229.78/41.12            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 229.78/41.12            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 229.78/41.12            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 229.78/41.12              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 229.78/41.12            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 229.78/41.12            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 229.78/41.12              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 229.78/41.12              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 229.78/41.12            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 229.78/41.12            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 229.78/41.12            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 229.78/41.12              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 229.78/41.12              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 229.78/41.12            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 229.78/41.12              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 229.78/41.12            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 229.78/41.12            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 229.78/41.12              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 229.78/41.12              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 229.78/41.12            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 229.78/41.12            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 229.78/41.12    (36)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 229.78/41.12            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 229.78/41.12              e3) = all_12_1 & $i(all_12_1))
% 229.78/41.12    (37)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.78/41.12          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.78/41.12    (38)  op(e2, e2) = e2
% 229.78/41.12    (39)   ~ (e1 = e0)
% 229.78/41.12    (40)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.78/41.12          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.78/41.12    (41)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.78/41.12          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.78/41.12    (42)   ~ (all_53_2 = all_53_3)
% 229.78/41.12    (43)  all_57_14 = e1
% 229.78/41.12    (44)  all_55_8 = all_53_2
% 229.78/41.12    (45)  op(e0, e0) = e3
% 229.78/41.12    (46)  op(e0, e2) = all_53_7
% 229.78/41.12    (47)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.78/41.12          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.78/41.12            e2)
% 229.78/41.12    (48)   ~ (all_53_3 = e0)
% 229.78/41.12    (49)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.78/41.12              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.78/41.12                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.78/41.12                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.78/41.12    (50)  all_55_10 = all_6_2
% 229.78/41.12    (51)  op(e2, e0) = all_53_13
% 229.78/41.12    (52)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.78/41.12          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.78/41.12    (53)   ~ (all_53_12 = e3)
% 229.78/41.12    (54)  op(e1, e3) = all_53_2
% 229.78/41.12    (55)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.78/41.12          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.78/41.12    (56)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.78/41.12          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.78/41.12    (57)   ~ (all_53_12 = e0)
% 229.78/41.12    (58)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.78/41.12          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 229.78/41.12    (59)   ~ (e2 = e1)
% 229.78/41.12    (60)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.78/41.12          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.78/41.12    (61)   ~ (all_6_2 = e0)
% 229.78/41.12    (62)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.78/41.12          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.78/41.12    (63)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 229.78/41.12          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 229.78/41.12    (64)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.78/41.12          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.78/41.12    (65)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.78/41.12          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.78/41.13    (66)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 229.78/41.13          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 229.78/41.13    (67)  all_57_3 = e2
% 229.78/41.13    (68)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.78/41.13          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.78/41.13    (69)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 229.78/41.13          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 229.78/41.13    (70)  op(e3, e0) = all_53_12
% 229.78/41.13  
% 229.78/41.13  Begin of proof
% 229.78/41.13  | 
% 229.78/41.13  | BETA: splitting (63) gives:
% 229.78/41.13  | 
% 229.78/41.13  | Case 1:
% 229.78/41.13  | | 
% 229.78/41.13  | |   (71)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) =
% 229.78/41.13  | |           e2)
% 229.78/41.13  | | 
% 229.78/41.13  | | BETA: splitting (71) gives:
% 229.78/41.13  | | 
% 229.78/41.13  | | Case 1:
% 229.78/41.13  | | | 
% 229.78/41.13  | | |   (72)  all_57_4 = e2 & op(e3, e1) = e2
% 229.78/41.13  | | | 
% 229.78/41.13  | | | ALPHA: (72) implies:
% 229.78/41.13  | | |   (73)  all_57_4 = e2
% 229.78/41.13  | | | 
% 229.78/41.13  | | | BETA: splitting (47) gives:
% 229.78/41.13  | | | 
% 229.78/41.13  | | | Case 1:
% 229.78/41.13  | | | | 
% 229.78/41.13  | | | |   (74)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0,
% 229.78/41.13  | | | |             e2) = e2)
% 229.78/41.13  | | | | 
% 229.78/41.13  | | | | BETA: splitting (74) gives:
% 229.78/41.13  | | | | 
% 229.78/41.13  | | | | Case 1:
% 229.78/41.13  | | | | | 
% 229.78/41.13  | | | | |   (75)  all_57_12 = e2 & op(e0, e3) = e2
% 229.78/41.13  | | | | | 
% 229.78/41.13  | | | | | ALPHA: (75) implies:
% 229.78/41.13  | | | | |   (76)  all_57_12 = e2
% 229.78/41.13  | | | | | 
% 229.78/41.13  | | | | | BETA: splitting (37) gives:
% 229.78/41.13  | | | | | 
% 229.78/41.13  | | | | | Case 1:
% 229.78/41.13  | | | | | | 
% 229.78/41.13  | | | | | |   (77)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3,
% 229.78/41.13  | | | | | |             e2) = e3)
% 229.78/41.13  | | | | | | 
% 229.78/41.13  | | | | | | BETA: splitting (77) gives:
% 229.78/41.13  | | | | | | 
% 229.78/41.13  | | | | | | Case 1:
% 229.78/41.13  | | | | | | | 
% 229.78/41.13  | | | | | | |   (78)  all_57_0 = e3 & op(e3, e3) = e3
% 229.78/41.13  | | | | | | | 
% 229.78/41.13  | | | | | | | ALPHA: (78) implies:
% 229.78/41.13  | | | | | | |   (79)  op(e3, e3) = e3
% 229.78/41.13  | | | | | | | 
% 229.78/41.13  | | | | | | | REF_CLOSE: (8), (22), (30), (79) are inconsistent by sub-proof
% 229.78/41.13  | | | | | | |            #2494.
% 229.78/41.13  | | | | | | | 
% 229.78/41.13  | | | | | | Case 2:
% 229.78/41.13  | | | | | | | 
% 229.78/41.13  | | | | | | |   (80)  all_57_1 = e3 & op(e3, e2) = e3
% 229.78/41.13  | | | | | | | 
% 229.78/41.13  | | | | | | | ALPHA: (80) implies:
% 229.78/41.13  | | | | | | |   (81)  all_57_1 = e3
% 229.78/41.13  | | | | | | | 
% 229.78/41.13  | | | | | | | BETA: splitting (68) gives:
% 229.78/41.13  | | | | | | | 
% 229.78/41.13  | | | | | | | Case 1:
% 229.78/41.13  | | | | | | | | 
% 229.78/41.13  | | | | | | | |   (82)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 &
% 229.78/41.13  | | | | | | | |           op(e2, e2) = e1)
% 229.78/41.13  | | | | | | | | 
% 229.78/41.13  | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 229.78/41.13  | | | | | | | |            (11), (12), (13), (14), (17), (18), (19), (20), (21),
% 229.78/41.13  | | | | | | | |            (22), (23), (24), (25), (26), (27), (28), (29), (30),
% 229.78/41.13  | | | | | | | |            (31), (33), (34), (35), (36), (37), (40), (41), (42),
% 229.78/41.13  | | | | | | | |            (44), (45), (47), (48), (49), (50), (52), (53), (54),
% 229.78/41.13  | | | | | | | |            (55), (56), (57), (58), (60), (61), (62), (63), (64),
% 229.78/41.13  | | | | | | | |            (65), (66), (68), (69), (70), (81), (82) are
% 229.78/41.13  | | | | | | | |            inconsistent by sub-proof #962.
% 229.78/41.13  | | | | | | | | 
% 229.78/41.13  | | | | | | | Case 2:
% 229.78/41.13  | | | | | | | | 
% 229.78/41.13  | | | | | | | |   (83)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 &
% 229.78/41.13  | | | | | | | |           op(e0, e2) = e1)
% 229.78/41.13  | | | | | | | | 
% 229.78/41.13  | | | | | | | | BETA: splitting (83) gives:
% 229.78/41.13  | | | | | | | | 
% 229.78/41.13  | | | | | | | | Case 1:
% 229.78/41.13  | | | | | | | | | 
% 229.78/41.13  | | | | | | | | |   (84)  all_57_7 = e1 & op(e1, e2) = e1
% 229.78/41.13  | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | ALPHA: (84) implies:
% 229.78/41.13  | | | | | | | | |   (85)  all_57_7 = e1
% 229.78/41.13  | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | BETA: splitting (9) gives:
% 229.78/41.13  | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | Case 1:
% 229.78/41.13  | | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | |   (86)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 &
% 229.78/41.13  | | | | | | | | | |           op(e1, e2) = e3)
% 229.78/41.13  | | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | | BETA: splitting (86) gives:
% 229.78/41.13  | | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | | Case 1:
% 229.78/41.13  | | | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | | |   (87)  all_57_6 = e3 & op(e1, e3) = e3
% 229.78/41.13  | | | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | | | ALPHA: (87) implies:
% 229.78/41.13  | | | | | | | | | | |   (88)  all_57_6 = e3
% 229.78/41.13  | | | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | | | BETA: splitting (19) gives:
% 229.78/41.13  | | | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | | | Case 1:
% 229.78/41.13  | | | | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | | | |   (89)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 229.78/41.13  | | | | | | | | | | | |           & op(e2, e1) = e0)
% 229.78/41.13  | | | | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | | | | BETA: splitting (89) gives:
% 229.78/41.13  | | | | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | | | | Case 1:
% 229.78/41.13  | | | | | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | | | | |   (90)  all_57_4 = e0 & op(e3, e1) = e0
% 229.78/41.13  | | | | | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | | | | | ALPHA: (90) implies:
% 229.78/41.13  | | | | | | | | | | | | |   (91)  all_57_4 = e0
% 229.78/41.13  | | | | | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | | | | | COMBINE_EQS: (73), (91) imply:
% 229.78/41.13  | | | | | | | | | | | | |   (92)  e2 = e0
% 229.78/41.13  | | | | | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | | | | | COMBINE_EQS: (76), (92) imply:
% 229.78/41.13  | | | | | | | | | | | | |   (93)  all_57_12 = e0
% 229.78/41.13  | | | | | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | | | | | REF_CLOSE: (4), (6), (20), (28), (34), (39), (59), (62),
% 229.78/41.13  | | | | | | | | | | | | |            (88), (93) are inconsistent by sub-proof #1425.
% 229.78/41.13  | | | | | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | | | | Case 2:
% 229.78/41.13  | | | | | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | | | | |   (94)  all_57_5 = e0 & op(e2, e1) = e0
% 229.78/41.13  | | | | | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | | | | | ALPHA: (94) implies:
% 229.78/41.13  | | | | | | | | | | | | |   (95)  all_57_5 = e0
% 229.78/41.13  | | | | | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | | | | | REF_CLOSE: (5), (6), (8), (10), (12), (13), (17), (18), (20),
% 229.78/41.13  | | | | | | | | | | | | |            (22), (28), (29), (30), (31), (34), (37), (39),
% 229.78/41.13  | | | | | | | | | | | | |            (40), (41), (45), (47), (49), (53), (57), (59),
% 229.78/41.13  | | | | | | | | | | | | |            (60), (65), (67), (68), (70), (81), (95) are
% 229.78/41.13  | | | | | | | | | | | | |            inconsistent by sub-proof #880.
% 229.78/41.13  | | | | | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | | | | End of split
% 229.78/41.13  | | | | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | | | Case 2:
% 229.78/41.13  | | | | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | | | |   (96)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 229.78/41.13  | | | | | | | | | | | |           e0 & op(e0, e1) = e0)
% 229.78/41.13  | | | | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | | | | BETA: splitting (96) gives:
% 229.78/41.13  | | | | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | | | | Case 1:
% 229.78/41.13  | | | | | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | | | | |   (97)  all_57_8 = e0 & op(e1, e1) = e0
% 229.78/41.13  | | | | | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | | | | | ALPHA: (97) implies:
% 229.78/41.13  | | | | | | | | | | | | |   (98)  op(e1, e1) = e0
% 229.78/41.13  | | | | | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | | | | | REF_CLOSE: (8), (32), (39), (98) are inconsistent by
% 229.78/41.13  | | | | | | | | | | | | |            sub-proof #2427.
% 229.78/41.13  | | | | | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | | | | Case 2:
% 229.78/41.13  | | | | | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | | | | |   (99)  all_57_14 = e0 & op(e0, e1) = e0
% 229.78/41.13  | | | | | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | | | | | ALPHA: (99) implies:
% 229.78/41.13  | | | | | | | | | | | | |   (100)  all_57_14 = e0
% 229.78/41.13  | | | | | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | | | | | COMBINE_EQS: (43), (100) imply:
% 229.78/41.13  | | | | | | | | | | | | |   (101)  e1 = e0
% 229.78/41.13  | | | | | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | | | | | COMBINE_EQS: (85), (101) imply:
% 229.78/41.13  | | | | | | | | | | | | |   (102)  all_57_7 = e0
% 229.78/41.13  | | | | | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (10), (12),
% 229.78/41.13  | | | | | | | | | | | | |            (13), (15), (17), (18), (19), (20), (22), (23),
% 229.78/41.13  | | | | | | | | | | | | |            (26), (28), (29), (30), (31), (33), (34), (37),
% 229.78/41.13  | | | | | | | | | | | | |            (38), (39), (40), (41), (43), (45), (47), (48),
% 229.78/41.13  | | | | | | | | | | | | |            (49), (51), (52), (53), (55), (56), (57), (58),
% 229.78/41.13  | | | | | | | | | | | | |            (59), (60), (62), (63), (64), (65), (66), (67),
% 229.78/41.13  | | | | | | | | | | | | |            (68), (69), (70), (73), (81), (102) are
% 229.78/41.13  | | | | | | | | | | | | |            inconsistent by sub-proof #856.
% 229.78/41.13  | | | | | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | | | | End of split
% 229.78/41.13  | | | | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | | | End of split
% 229.78/41.13  | | | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | | Case 2:
% 229.78/41.13  | | | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | | |   (103)  all_57_7 = e3 & op(e1, e2) = e3
% 229.78/41.13  | | | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | | | ALPHA: (103) implies:
% 229.78/41.13  | | | | | | | | | | |   (104)  all_57_7 = e3
% 229.78/41.13  | | | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | | | REF_CLOSE: (5), (6), (8), (20), (22), (33), (34), (38), (39),
% 229.78/41.13  | | | | | | | | | | |            (59), (68), (81), (104) are inconsistent by
% 229.78/41.13  | | | | | | | | | | |            sub-proof #1167.
% 229.78/41.13  | | | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | | End of split
% 229.78/41.13  | | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | Case 2:
% 229.78/41.13  | | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | |   (105)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3
% 229.78/41.13  | | | | | | | | | |            & op(e1, e0) = e3)
% 229.78/41.13  | | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | | REF_CLOSE: (6), (8), (10), (12), (20), (22), (29), (34),
% 229.78/41.13  | | | | | | | | | |            (39), (49), (59), (60), (65), (105) are
% 229.78/41.13  | | | | | | | | | |            inconsistent by sub-proof #1786.
% 229.78/41.13  | | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | End of split
% 229.78/41.13  | | | | | | | | | 
% 229.78/41.13  | | | | | | | | Case 2:
% 229.78/41.13  | | | | | | | | | 
% 229.78/41.13  | | | | | | | | |   (106)  all_57_13 = e1 & op(e0, e2) = e1
% 229.78/41.13  | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | ALPHA: (106) implies:
% 229.78/41.13  | | | | | | | | |   (107)  all_57_13 = e1
% 229.78/41.13  | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | BETA: splitting (33) gives:
% 229.78/41.13  | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | Case 1:
% 229.78/41.13  | | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | |   (108)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 229.78/41.13  | | | | | | | | | |            & op(e2, e2) = e0)
% 229.78/41.13  | | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | | REF_CLOSE: (5), (6), (8), (13), (17), (18), (20), (22), (28),
% 229.78/41.13  | | | | | | | | | |            (29), (30), (31), (34), (37), (38), (39), (41),
% 229.78/41.13  | | | | | | | | | |            (45), (47), (49), (53), (57), (59), (60), (65),
% 229.78/41.13  | | | | | | | | | |            (67), (68), (70), (108) are inconsistent by
% 229.78/41.13  | | | | | | | | | |            sub-proof #879.
% 229.78/41.13  | | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | Case 2:
% 229.78/41.13  | | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | |   (109)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0
% 229.78/41.13  | | | | | | | | | |            & op(e0, e2) = e0)
% 229.78/41.13  | | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | | BETA: splitting (109) gives:
% 229.78/41.13  | | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | | Case 1:
% 229.78/41.13  | | | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | | |   (110)  all_57_7 = e0 & op(e1, e2) = e0
% 229.78/41.13  | | | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | | | ALPHA: (110) implies:
% 229.78/41.13  | | | | | | | | | | |   (111)  all_57_7 = e0
% 229.78/41.13  | | | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (10), (12),
% 229.78/41.13  | | | | | | | | | | |            (13), (15), (17), (18), (19), (20), (22), (23),
% 229.78/41.13  | | | | | | | | | | |            (26), (28), (29), (30), (31), (33), (34), (37),
% 229.78/41.13  | | | | | | | | | | |            (38), (39), (40), (41), (43), (45), (47), (48),
% 229.78/41.13  | | | | | | | | | | |            (49), (51), (52), (53), (55), (56), (57), (58),
% 229.78/41.13  | | | | | | | | | | |            (59), (60), (62), (63), (64), (65), (66), (67),
% 229.78/41.13  | | | | | | | | | | |            (68), (69), (70), (73), (81), (111) are
% 229.78/41.13  | | | | | | | | | | |            inconsistent by sub-proof #856.
% 229.78/41.13  | | | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | | Case 2:
% 229.78/41.13  | | | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | | |   (112)  all_57_13 = e0 & op(e0, e2) = e0
% 229.78/41.13  | | | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | | | REF_CLOSE: (39), (107), (112) are inconsistent by sub-proof
% 229.78/41.13  | | | | | | | | | | |            #1920.
% 229.78/41.13  | | | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | | End of split
% 229.78/41.13  | | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | End of split
% 229.78/41.13  | | | | | | | | | 
% 229.78/41.13  | | | | | | | | End of split
% 229.78/41.13  | | | | | | | | 
% 229.78/41.13  | | | | | | | End of split
% 229.78/41.13  | | | | | | | 
% 229.78/41.13  | | | | | | End of split
% 229.78/41.13  | | | | | | 
% 229.78/41.13  | | | | | Case 2:
% 229.78/41.13  | | | | | | 
% 229.78/41.13  | | | | | |   (113)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3,
% 229.78/41.13  | | | | | |              e0) = e3)
% 229.78/41.13  | | | | | | 
% 229.78/41.13  | | | | | | REF_CLOSE: (8), (20), (53), (70), (73), (113) are inconsistent by
% 229.78/41.13  | | | | | |            sub-proof #2448.
% 229.78/41.13  | | | | | | 
% 229.78/41.13  | | | | | End of split
% 229.78/41.13  | | | | | 
% 229.78/41.13  | | | | Case 2:
% 229.78/41.13  | | | | | 
% 229.78/41.13  | | | | |   (114)  all_57_13 = e2 & op(e0, e2) = e2
% 229.78/41.13  | | | | | 
% 229.78/41.13  | | | | | ALPHA: (114) implies:
% 229.78/41.13  | | | | |   (115)  op(e0, e2) = e2
% 229.78/41.13  | | | | | 
% 229.78/41.13  | | | | | REF_CLOSE: (8), (16), (46), (115) are inconsistent by sub-proof #2335.
% 229.78/41.13  | | | | | 
% 229.78/41.13  | | | | End of split
% 229.78/41.13  | | | | 
% 229.78/41.13  | | | Case 2:
% 229.78/41.13  | | | | 
% 229.78/41.13  | | | |   (116)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0,
% 229.78/41.13  | | | |              e0) = e2)
% 229.78/41.13  | | | | 
% 229.78/41.13  | | | | REF_CLOSE: (20), (29), (43), (59), (116) are inconsistent by sub-proof
% 229.78/41.13  | | | |            #1529.
% 229.78/41.13  | | | | 
% 229.78/41.13  | | | End of split
% 229.78/41.13  | | | 
% 229.78/41.13  | | Case 2:
% 229.78/41.13  | | | 
% 229.78/41.13  | | |   (117)  all_57_5 = e2 & op(e2, e1) = e2
% 229.78/41.13  | | | 
% 229.78/41.13  | | | ALPHA: (117) implies:
% 229.78/41.13  | | |   (118)  all_57_5 = e2
% 229.78/41.13  | | | 
% 229.78/41.13  | | | BETA: splitting (52) gives:
% 229.78/41.13  | | | 
% 229.78/41.13  | | | Case 1:
% 229.78/41.13  | | | | 
% 229.78/41.13  | | | |   (119)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2)
% 229.78/41.13  | | | |            = e3)
% 229.78/41.13  | | | | 
% 229.78/41.13  | | | | BETA: splitting (119) gives:
% 229.78/41.13  | | | | 
% 229.78/41.13  | | | | Case 1:
% 229.78/41.13  | | | | | 
% 229.78/41.13  | | | | |   (120)  all_57_2 = e3 & op(e2, e3) = e3
% 229.78/41.13  | | | | | 
% 229.78/41.13  | | | | | ALPHA: (120) implies:
% 229.78/41.13  | | | | |   (121)  all_57_2 = e3
% 229.78/41.13  | | | | | 
% 229.78/41.13  | | | | | BETA: splitting (3) gives:
% 229.78/41.13  | | | | | 
% 229.78/41.13  | | | | | Case 1:
% 229.78/41.13  | | | | | | 
% 229.78/41.13  | | | | | |   (122)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2,
% 229.78/41.13  | | | | | |              e2) = e1)
% 229.78/41.13  | | | | | | 
% 229.78/41.13  | | | | | | BETA: splitting (122) gives:
% 229.78/41.13  | | | | | | 
% 229.78/41.13  | | | | | | Case 1:
% 229.78/41.13  | | | | | | | 
% 229.78/41.13  | | | | | | |   (123)  all_57_2 = e1 & op(e2, e3) = e1
% 229.78/41.13  | | | | | | | 
% 229.78/41.13  | | | | | | | REF_CLOSE: (6), (121), (123) are inconsistent by sub-proof #1928.
% 229.78/41.13  | | | | | | | 
% 229.78/41.13  | | | | | | Case 2:
% 229.78/41.13  | | | | | | | 
% 229.78/41.13  | | | | | | |   (124)  all_57_3 = e1 & op(e2, e2) = e1
% 229.78/41.13  | | | | | | | 
% 229.78/41.13  | | | | | | | ALPHA: (124) implies:
% 229.78/41.13  | | | | | | |   (125)  all_57_3 = e1
% 229.78/41.13  | | | | | | |   (126)  op(e2, e2) = e1
% 229.78/41.13  | | | | | | | 
% 229.78/41.13  | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11),
% 229.78/41.13  | | | | | | |            (12), (13), (14), (17), (18), (19), (20), (21), (22),
% 229.78/41.13  | | | | | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31),
% 229.78/41.13  | | | | | | |            (33), (34), (35), (36), (37), (40), (41), (42), (44),
% 229.78/41.13  | | | | | | |            (45), (47), (48), (49), (50), (52), (53), (54), (55),
% 229.78/41.13  | | | | | | |            (56), (57), (58), (60), (61), (62), (63), (64), (65),
% 229.78/41.13  | | | | | | |            (66), (68), (69), (70), (125), (126) are inconsistent
% 229.78/41.13  | | | | | | |            by sub-proof #963.
% 229.78/41.13  | | | | | | | 
% 229.78/41.13  | | | | | | End of split
% 229.78/41.13  | | | | | | 
% 229.78/41.13  | | | | | Case 2:
% 229.78/41.13  | | | | | | 
% 229.78/41.13  | | | | | |   (127)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 &
% 229.78/41.13  | | | | | |            op(e2, e0) = e1)
% 229.78/41.13  | | | | | | 
% 229.78/41.13  | | | | | | BETA: splitting (127) gives:
% 229.78/41.13  | | | | | | 
% 229.78/41.13  | | | | | | Case 1:
% 229.78/41.13  | | | | | | | 
% 229.78/41.13  | | | | | | |   (128)  all_57_5 = e1 & op(e2, e1) = e1
% 229.78/41.13  | | | | | | | 
% 229.78/41.13  | | | | | | | REF_CLOSE: (59), (118), (128) are inconsistent by sub-proof #1886.
% 229.78/41.13  | | | | | | | 
% 229.78/41.13  | | | | | | Case 2:
% 229.78/41.13  | | | | | | | 
% 229.78/41.13  | | | | | | |   (129)  all_57_10 = e1 & op(e2, e0) = e1
% 229.78/41.13  | | | | | | | 
% 229.78/41.13  | | | | | | | ALPHA: (129) implies:
% 229.78/41.13  | | | | | | |   (130)  all_57_10 = e1
% 229.78/41.13  | | | | | | | 
% 229.78/41.13  | | | | | | | BETA: splitting (19) gives:
% 229.78/41.13  | | | | | | | 
% 229.78/41.13  | | | | | | | Case 1:
% 229.78/41.13  | | | | | | | | 
% 229.78/41.13  | | | | | | | |   (131)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 &
% 229.78/41.13  | | | | | | | |            op(e2, e1) = e0)
% 229.78/41.13  | | | | | | | | 
% 229.78/41.13  | | | | | | | | BETA: splitting (131) gives:
% 229.78/41.13  | | | | | | | | 
% 229.78/41.13  | | | | | | | | Case 1:
% 229.78/41.13  | | | | | | | | | 
% 229.78/41.13  | | | | | | | | |   (132)  all_57_4 = e0 & op(e3, e1) = e0
% 229.78/41.13  | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | ALPHA: (132) implies:
% 229.78/41.13  | | | | | | | | |   (133)  all_57_4 = e0
% 229.78/41.13  | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | REF_CLOSE: (3), (6), (8), (10), (12), (20), (22), (29), (31),
% 229.78/41.13  | | | | | | | | |            (34), (39), (40), (47), (49), (55), (58), (59),
% 229.78/41.13  | | | | | | | | |            (121), (130), (133) are inconsistent by sub-proof
% 229.78/41.13  | | | | | | | | |            #867.
% 229.78/41.13  | | | | | | | | | 
% 229.78/41.13  | | | | | | | | Case 2:
% 229.78/41.13  | | | | | | | | | 
% 229.78/41.13  | | | | | | | | |   (134)  all_57_5 = e0 & op(e2, e1) = e0
% 229.78/41.13  | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | REF_CLOSE: (34), (118), (134) are inconsistent by sub-proof
% 229.78/41.13  | | | | | | | | |            #2428.
% 229.78/41.13  | | | | | | | | | 
% 229.78/41.13  | | | | | | | | End of split
% 229.78/41.13  | | | | | | | | 
% 229.78/41.13  | | | | | | | Case 2:
% 229.78/41.13  | | | | | | | | 
% 229.78/41.13  | | | | | | | |   (135)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 &
% 229.78/41.13  | | | | | | | |            op(e0, e1) = e0)
% 229.78/41.13  | | | | | | | | 
% 229.78/41.13  | | | | | | | | BETA: splitting (135) gives:
% 229.78/41.13  | | | | | | | | 
% 229.78/41.13  | | | | | | | | Case 1:
% 229.78/41.13  | | | | | | | | | 
% 229.78/41.13  | | | | | | | | |   (136)  all_57_8 = e0 & op(e1, e1) = e0
% 229.78/41.13  | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | ALPHA: (136) implies:
% 229.78/41.13  | | | | | | | | |   (137)  op(e1, e1) = e0
% 229.78/41.13  | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | REF_CLOSE: (8), (32), (39), (137) are inconsistent by
% 229.78/41.13  | | | | | | | | |            sub-proof #2427.
% 229.78/41.13  | | | | | | | | | 
% 229.78/41.13  | | | | | | | | Case 2:
% 229.78/41.13  | | | | | | | | | 
% 229.78/41.13  | | | | | | | | |   (138)  all_57_14 = e0 & op(e0, e1) = e0
% 229.78/41.13  | | | | | | | | | 
% 229.78/41.13  | | | | | | | | | REF_CLOSE: (39), (43), (138) are inconsistent by sub-proof
% 229.78/41.13  | | | | | | | | |            #2181.
% 229.78/41.13  | | | | | | | | | 
% 229.78/41.13  | | | | | | | | End of split
% 229.78/41.13  | | | | | | | | 
% 229.78/41.13  | | | | | | | End of split
% 229.78/41.13  | | | | | | | 
% 229.78/41.13  | | | | | | End of split
% 229.78/41.13  | | | | | | 
% 229.78/41.13  | | | | | End of split
% 229.78/41.13  | | | | | 
% 229.78/41.13  | | | | Case 2:
% 229.78/41.13  | | | | | 
% 229.78/41.13  | | | | |   (139)  all_57_3 = e3 & op(e2, e2) = e3
% 229.78/41.13  | | | | | 
% 229.78/41.13  | | | | | ALPHA: (139) implies:
% 229.78/41.13  | | | | |   (140)  all_57_3 = e3
% 229.78/41.13  | | | | | 
% 229.78/41.13  | | | | | REF_CLOSE: (20), (67), (140) are inconsistent by sub-proof #1166.
% 229.78/41.13  | | | | | 
% 229.78/41.13  | | | | End of split
% 229.78/41.13  | | | | 
% 229.78/41.13  | | | Case 2:
% 229.78/41.13  | | | | 
% 229.78/41.13  | | | |   (141)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2,
% 229.78/41.13  | | | |              e0) = e3)
% 229.78/41.13  | | | | 
% 229.78/41.13  | | | | REF_CLOSE: (6), (8), (20), (22), (29), (34), (39), (45), (49), (59),
% 229.78/41.13  | | | |            (60), (65), (118), (141) are inconsistent by sub-proof #1745.
% 229.78/41.13  | | | | 
% 229.78/41.13  | | | End of split
% 229.78/41.13  | | | 
% 229.78/41.13  | | End of split
% 229.78/41.13  | | 
% 229.78/41.13  | Case 2:
% 229.78/41.13  | | 
% 229.78/41.13  | |   (142)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) =
% 229.78/41.13  | |            e2)
% 229.78/41.13  | | 
% 229.78/41.13  | | BETA: splitting (142) gives:
% 229.78/41.13  | | 
% 229.78/41.13  | | Case 1:
% 229.78/41.13  | | | 
% 229.78/41.13  | | |   (143)  all_57_8 = e2 & op(e1, e1) = e2
% 229.78/41.13  | | | 
% 229.78/41.13  | | | ALPHA: (143) implies:
% 229.78/41.13  | | |   (144)  op(e1, e1) = e2
% 229.78/41.13  | | | 
% 229.78/41.13  | | | REF_CLOSE: (8), (32), (59), (144) are inconsistent by sub-proof #2423.
% 229.78/41.13  | | | 
% 229.78/41.13  | | Case 2:
% 229.78/41.13  | | | 
% 229.78/41.13  | | |   (145)  all_57_14 = e2 & op(e0, e1) = e2
% 229.78/41.13  | | | 
% 229.78/41.13  | | | REF_CLOSE: (43), (59), (145) are inconsistent by sub-proof #1968.
% 229.78/41.13  | | | 
% 229.78/41.13  | | End of split
% 229.78/41.13  | | 
% 229.78/41.13  | End of split
% 229.78/41.13  | 
% 229.78/41.13  End of proof
% 229.78/41.13  
% 229.78/41.13  Sub-proof #856 shows that the following formulas are inconsistent:
% 229.78/41.13  ----------------------------------------------------------------
% 229.78/41.13    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.78/41.13         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.78/41.13    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.78/41.13         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.78/41.13    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.78/41.13         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.78/41.13    (4)   ~ (e3 = e1)
% 229.78/41.13    (5)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 229.78/41.13         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 229.78/41.13    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.78/41.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.78/41.13    (7)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.78/41.13         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.78/41.13    (8)   ~ (all_6_2 = e3)
% 229.78/41.13    (9)  op(e1, e1) = all_6_2
% 229.78/41.13    (10)  all_57_4 = e2
% 229.78/41.13    (11)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.78/41.13          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.78/41.13    (12)   ~ (all_53_13 = e2)
% 229.78/41.13    (13)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.78/41.13          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.78/41.13    (14)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.78/41.13          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.78/41.13    (15)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 229.78/41.13          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.78/41.13    (16)   ~ (e3 = e2)
% 229.78/41.13    (17)   ~ (e3 = e0)
% 229.78/41.13    (18)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 229.78/41.13          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 229.78/41.13    (19)  op(e0, e3) = all_53_3
% 229.78/41.13    (20)  all_57_0 = e0
% 229.78/41.13    (21)  all_57_15 = e3
% 229.78/41.13    (22)  op(e3, e3) = e0
% 229.78/41.13    (23)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.78/41.13          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.78/41.13            e1)
% 229.78/41.13    (24)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.78/41.13          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.78/41.13    (25)   ~ (e2 = e0)
% 229.78/41.13    (26)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.78/41.13          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.78/41.13    (27)  op(e2, e2) = e2
% 229.78/41.13    (28)   ~ (e1 = e0)
% 229.78/41.13    (29)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.78/41.13          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.78/41.13    (30)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.78/41.13          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.78/41.13    (31)  all_57_14 = e1
% 229.78/41.13    (32)  op(e0, e0) = e3
% 229.78/41.13    (33)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.78/41.13          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.78/41.13            e2)
% 229.78/41.13    (34)   ~ (all_53_3 = e0)
% 229.78/41.13    (35)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.78/41.13              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.78/41.13                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.78/41.13                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.78/41.13    (36)  op(e2, e0) = all_53_13
% 229.78/41.13    (37)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.78/41.13          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.78/41.13    (38)   ~ (all_53_12 = e3)
% 229.78/41.13    (39)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.78/41.13          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.78/41.13    (40)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.78/41.13          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.78/41.13    (41)  all_57_1 = e3
% 229.78/41.13    (42)   ~ (all_53_12 = e0)
% 229.78/41.13    (43)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.78/41.13          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 229.78/41.13    (44)   ~ (e2 = e1)
% 229.78/41.13    (45)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.78/41.13          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.78/41.13    (46)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.78/41.13          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.78/41.13    (47)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 229.78/41.13          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 229.78/41.13    (48)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.78/41.13          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.78/41.13    (49)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.78/41.13          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.78/41.13    (50)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 229.78/41.13          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 229.78/41.13    (51)  all_57_3 = e2
% 229.78/41.13    (52)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.78/41.13          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.78/41.13    (53)  all_57_7 = e0
% 229.78/41.14    (54)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 229.78/41.14          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 229.78/41.14    (55)  op(e3, e0) = all_53_12
% 229.78/41.14  
% 229.78/41.14  Begin of proof
% 229.78/41.14  | 
% 229.78/41.14  | BETA: splitting (15) gives:
% 229.78/41.14  | 
% 229.78/41.14  | Case 1:
% 229.78/41.14  | | 
% 229.78/41.14  | |   (56)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) =
% 229.78/41.14  | |           e0)
% 229.78/41.14  | | 
% 229.78/41.14  | | BETA: splitting (56) gives:
% 229.78/41.14  | | 
% 229.78/41.14  | | Case 1:
% 229.78/41.14  | | | 
% 229.78/41.14  | | |   (57)  all_57_4 = e0 & op(e3, e1) = e0
% 229.78/41.14  | | | 
% 229.78/41.14  | | | REF_CLOSE: (10), (25), (57) are inconsistent by sub-proof #2045.
% 229.78/41.14  | | | 
% 229.78/41.14  | | Case 2:
% 229.78/41.14  | | | 
% 229.78/41.14  | | |   (58)  all_57_5 = e0 & op(e2, e1) = e0
% 229.78/41.14  | | | 
% 229.78/41.14  | | | ALPHA: (58) implies:
% 229.78/41.14  | | |   (59)  all_57_5 = e0
% 229.78/41.14  | | | 
% 229.78/41.14  | | | REF_CLOSE: (3), (4), (6), (8), (9), (11), (13), (14), (16), (17), (20),
% 229.78/41.14  | | |            (21), (22), (23), (25), (26), (28), (29), (30), (32), (33),
% 229.78/41.14  | | |            (35), (38), (41), (42), (44), (45), (49), (51), (52), (55),
% 229.78/41.14  | | |            (59) are inconsistent by sub-proof #880.
% 229.78/41.14  | | | 
% 229.78/41.14  | | End of split
% 229.78/41.14  | | 
% 229.78/41.14  | Case 2:
% 229.78/41.14  | | 
% 229.78/41.14  | |   (60)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 229.78/41.14  | |           e0)
% 229.78/41.14  | | 
% 229.78/41.14  | | BETA: splitting (60) gives:
% 229.78/41.14  | | 
% 229.78/41.14  | | Case 1:
% 229.78/41.14  | | | 
% 229.78/41.14  | | |   (61)  all_57_8 = e0 & op(e1, e1) = e0
% 229.78/41.14  | | | 
% 229.78/41.14  | | | ALPHA: (61) implies:
% 229.78/41.14  | | |   (62)  op(e1, e1) = e0
% 229.78/41.14  | | | 
% 229.78/41.14  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13),
% 229.78/41.14  | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 229.78/41.14  | | |            (24), (25), (26), (27), (28), (29), (30), (32), (33), (34),
% 229.78/41.14  | | |            (35), (36), (37), (38), (39), (40), (42), (43), (44), (45),
% 229.78/41.14  | | |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (55),
% 229.78/41.14  | | |            (62) are inconsistent by sub-proof #889.
% 229.78/41.14  | | | 
% 229.78/41.14  | | Case 2:
% 229.78/41.14  | | | 
% 229.78/41.14  | | |   (63)  all_57_14 = e0 & op(e0, e1) = e0
% 229.78/41.14  | | | 
% 229.78/41.14  | | | REF_CLOSE: (28), (31), (63) are inconsistent by sub-proof #2181.
% 229.78/41.14  | | | 
% 229.78/41.14  | | End of split
% 229.78/41.14  | | 
% 229.78/41.14  | End of split
% 229.78/41.14  | 
% 229.78/41.14  End of proof
% 229.78/41.14  
% 229.78/41.14  Sub-proof #857 shows that the following formulas are inconsistent:
% 229.78/41.14  ----------------------------------------------------------------
% 229.78/41.14    (1)  all_57_9 = e2
% 229.78/41.14    (2)   ~ (e3 = e1)
% 229.78/41.14    (3)   ~ (e3 = e2)
% 229.78/41.14    (4)  all_57_15 = e3
% 229.78/41.14    (5)  all_57_11 = e0
% 229.78/41.14    (6)   ~ (e2 = e0)
% 229.78/41.14    (7)   ~ (e1 = e0)
% 229.78/41.14    (8)  all_57_14 = e2
% 229.78/41.14    (9)   ~ (e2 = e1)
% 229.78/41.14    (10)  all_57_14 = e0 & op(e0, e1) = e0
% 229.78/41.14    (11)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.78/41.14          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.78/41.14    (12)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.78/41.14          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.78/41.14  
% 229.78/41.14  Begin of proof
% 229.78/41.14  | 
% 229.78/41.14  | ALPHA: (10) implies:
% 229.78/41.14  |   (13)  all_57_14 = e0
% 229.78/41.14  | 
% 229.78/41.14  | COMBINE_EQS: (8), (13) imply:
% 229.78/41.14  |   (14)  e2 = e0
% 229.78/41.14  | 
% 229.78/41.14  | COMBINE_EQS: (1), (14) imply:
% 229.78/41.14  |   (15)  all_57_9 = e0
% 229.78/41.14  | 
% 229.78/41.14  | REF_CLOSE: (2), (3), (4), (5), (6), (7), (9), (11), (12), (15) are
% 229.78/41.14  |            inconsistent by sub-proof #1144.
% 229.78/41.14  | 
% 229.78/41.14  End of proof
% 229.78/41.14  
% 229.78/41.14  Sub-proof #858 shows that the following formulas are inconsistent:
% 229.78/41.14  ----------------------------------------------------------------
% 229.78/41.14    (1)  op(e0, e2) = e0
% 229.78/41.14    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.78/41.14           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.78/41.14    (3)   ~ (e3 = e2)
% 229.78/41.14    (4)  op(e0, e0) = all_52_31
% 229.78/41.14    (5)  op(e0, e0) = e3
% 229.78/41.14    (6)  op(e0, e2) = all_52_27
% 229.78/41.14    (7)  op(all_52_27, all_52_27) = e2
% 229.78/41.14  
% 229.78/41.14  Begin of proof
% 229.78/41.14  | 
% 229.78/41.14  | GROUND_INST: instantiating (2) with e3, all_52_31, e0, e0, simplifying with
% 229.78/41.14  |              (4), (5) gives:
% 229.78/41.14  |   (8)  all_52_31 = e3
% 229.78/41.14  | 
% 229.78/41.14  | GROUND_INST: instantiating (2) with e0, all_52_27, e2, e0, simplifying with
% 229.78/41.14  |              (1), (6) gives:
% 229.78/41.14  |   (9)  all_52_27 = e0
% 229.78/41.14  | 
% 229.78/41.14  | REDUCE: (7), (9) imply:
% 229.78/41.14  |   (10)  op(e0, e0) = e2
% 229.78/41.14  | 
% 229.78/41.14  | GROUND_INST: instantiating (2) with e3, e2, e0, e0, simplifying with (5), (10)
% 229.78/41.14  |              gives:
% 229.78/41.14  |   (11)  e3 = e2
% 229.78/41.14  | 
% 229.78/41.14  | REDUCE: (3), (11) imply:
% 229.78/41.14  |   (12)  $false
% 229.78/41.14  | 
% 229.78/41.14  | CLOSE: (12) is inconsistent.
% 229.78/41.14  | 
% 229.78/41.14  End of proof
% 229.78/41.14  
% 229.78/41.14  Sub-proof #859 shows that the following formulas are inconsistent:
% 229.78/41.14  ----------------------------------------------------------------
% 229.78/41.14    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.78/41.14           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.78/41.14    (2)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 229.78/41.14    (3)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) = all_22_1
% 229.78/41.14           & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0, e3) =
% 229.78/41.14           all_22_1 & $i(all_22_1))
% 229.78/41.14    (4)  op(e1, e0) = all_53_14
% 229.78/41.14    (5)  op(e0, e3) = e1
% 229.78/41.14    (6)  op(e0, e3) = all_53_3
% 229.78/41.14    (7)  op(e1, e0) = all_52_23
% 229.78/41.14    (8)   ~ (all_53_14 = e3)
% 229.78/41.14    (9)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) = all_12_1
% 229.78/41.14           & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0, e3) =
% 229.78/41.14           all_12_1 & $i(all_12_1))
% 229.78/41.14    (10)  op(all_52_23, all_52_23) = e0
% 229.78/41.14    (11)   ~ (all_53_14 = e1)
% 229.78/41.14    (12)  op(e0, e0) = e3
% 229.78/41.14    (13)  all_55_11 = all_53_14
% 229.78/41.14  
% 229.78/41.14  Begin of proof
% 229.78/41.14  | 
% 229.78/41.14  | GROUND_INST: instantiating (1) with all_53_3, e1, e3, e0, simplifying with
% 229.78/41.14  |              (5), (6) gives:
% 229.78/41.14  |   (14)  all_53_3 = e1
% 229.78/41.14  | 
% 229.78/41.14  | GROUND_INST: instantiating (1) with all_53_14, all_52_23, e0, e1, simplifying
% 229.78/41.14  |              with (4), (7) gives:
% 229.78/41.14  |   (15)  all_53_14 = all_52_23
% 229.78/41.14  | 
% 229.78/41.14  | COMBINE_EQS: (13), (15) imply:
% 229.78/41.14  |   (16)  all_55_11 = all_52_23
% 229.78/41.14  | 
% 229.78/41.14  | REDUCE: (8), (15) imply:
% 229.78/41.14  |   (17)   ~ (all_52_23 = e3)
% 229.78/41.14  | 
% 229.78/41.14  | BETA: splitting (3) gives:
% 229.78/41.14  | 
% 229.78/41.14  | Case 1:
% 229.78/41.14  | | 
% 229.78/41.14  | |   (18)   ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 229.78/41.14  | |         all_22_1 & $i(all_22_0) & $i(all_22_1)
% 229.78/41.14  | | 
% 229.78/41.14  | | ALPHA: (18) implies:
% 229.78/41.14  | |   (19)  op(e0, e3) = all_22_1
% 229.78/41.14  | | 
% 229.78/41.14  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 229.78/41.14  | |            (16), (17), (19) are inconsistent by sub-proof #860.
% 229.78/41.14  | | 
% 229.78/41.14  | Case 2:
% 229.78/41.14  | | 
% 229.78/41.14  | |   (20)   ~ (all_22_1 = e2) & op(e0, e3) = all_22_1 & $i(all_22_1)
% 229.78/41.14  | | 
% 229.78/41.14  | | ALPHA: (20) implies:
% 229.78/41.14  | |   (21)  op(e0, e3) = all_22_1
% 229.78/41.14  | | 
% 229.78/41.14  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 229.78/41.14  | |            (16), (17), (21) are inconsistent by sub-proof #860.
% 229.78/41.14  | | 
% 229.78/41.14  | End of split
% 229.78/41.14  | 
% 229.78/41.14  End of proof
% 229.78/41.14  
% 229.78/41.14  Sub-proof #860 shows that the following formulas are inconsistent:
% 229.78/41.14  ----------------------------------------------------------------
% 229.78/41.14    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.78/41.14           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.78/41.14    (2)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 229.78/41.14    (3)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) = all_22_1
% 229.78/41.14           & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0, e3) =
% 229.78/41.14           all_22_1 & $i(all_22_1))
% 229.78/41.14    (4)  op(e1, e0) = all_53_14
% 229.78/41.14    (5)  op(e0, e3) = e1
% 229.78/41.14    (6)  op(e0, e3) = all_22_1
% 229.78/41.14    (7)  all_55_11 = all_52_23
% 229.78/41.14    (8)   ~ (all_52_23 = e3)
% 229.78/41.14    (9)  op(e1, e0) = all_52_23
% 229.78/41.14    (10)   ~ (all_53_14 = e3)
% 229.78/41.14    (11)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 229.78/41.14            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 229.78/41.14              e3) = all_12_1 & $i(all_12_1))
% 229.78/41.14    (12)  op(all_52_23, all_52_23) = e0
% 229.78/41.14    (13)   ~ (all_53_14 = e1)
% 229.78/41.14    (14)  op(e0, e0) = e3
% 229.78/41.14    (15)  all_55_11 = all_53_14
% 229.78/41.14  
% 229.78/41.14  Begin of proof
% 229.78/41.14  | 
% 229.78/41.14  | BETA: splitting (11) gives:
% 229.78/41.14  | 
% 229.78/41.14  | Case 1:
% 229.78/41.14  | | 
% 229.78/41.14  | |   (16)   ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 229.78/41.14  | |         all_12_1 & $i(all_12_0) & $i(all_12_1)
% 229.78/41.14  | | 
% 229.78/41.14  | | ALPHA: (16) implies:
% 229.78/41.14  | |   (17)   ~ (all_12_0 = e2)
% 229.78/41.14  | |   (18)  op(e0, e3) = all_12_1
% 229.78/41.14  | |   (19)  op(all_12_1, e0) = all_12_0
% 229.78/41.14  | | 
% 229.78/41.14  | | GROUND_INST: instantiating (1) with e1, all_22_1, e3, e0, simplifying with
% 229.78/41.14  | |              (5), (6) gives:
% 229.78/41.14  | |   (20)  all_22_1 = e1
% 229.78/41.14  | | 
% 229.78/41.14  | | GROUND_INST: instantiating (1) with all_12_1, all_22_1, e3, e0, simplifying
% 229.78/41.14  | |              with (6), (18) gives:
% 229.78/41.14  | |   (21)  all_22_1 = all_12_1
% 229.78/41.14  | | 
% 229.78/41.14  | | COMBINE_EQS: (20), (21) imply:
% 229.78/41.14  | |   (22)  all_12_1 = e1
% 229.78/41.14  | | 
% 229.78/41.14  | | REDUCE: (19), (22) imply:
% 229.78/41.14  | |   (23)  op(e1, e0) = all_12_0
% 229.78/41.14  | | 
% 229.78/41.14  | | GROUND_INST: instantiating (1) with all_52_23, all_12_0, e0, e1, simplifying
% 229.78/41.14  | |              with (9), (23) gives:
% 229.78/41.14  | |   (24)  all_52_23 = all_12_0
% 229.78/41.14  | | 
% 229.78/41.14  | | COMBINE_EQS: (7), (24) imply:
% 229.78/41.14  | |   (25)  all_55_11 = all_12_0
% 229.78/41.14  | | 
% 229.78/41.14  | | REDUCE: (8), (24) imply:
% 229.78/41.14  | |   (26)   ~ (all_12_0 = e3)
% 229.78/41.14  | | 
% 229.78/41.14  | | BETA: splitting (2) gives:
% 229.78/41.14  | | 
% 229.78/41.14  | | Case 1:
% 229.78/41.14  | | | 
% 229.78/41.14  | | |   (27)  all_55_11 = e3
% 229.78/41.14  | | | 
% 229.78/41.14  | | | COMBINE_EQS: (25), (27) imply:
% 229.78/41.14  | | |   (28)  all_12_0 = e3
% 229.78/41.14  | | | 
% 229.78/41.14  | | | REDUCE: (26), (28) imply:
% 229.78/41.14  | | |   (29)  $false
% 229.78/41.14  | | | 
% 229.78/41.14  | | | CLOSE: (29) is inconsistent.
% 229.78/41.14  | | | 
% 229.78/41.14  | | Case 2:
% 229.78/41.14  | | | 
% 229.78/41.14  | | |   (30)  all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 229.78/41.14  | | | 
% 229.78/41.14  | | | BETA: splitting (30) gives:
% 229.78/41.14  | | | 
% 229.78/41.14  | | | Case 1:
% 229.78/41.14  | | | | 
% 229.78/41.14  | | | |   (31)  all_55_11 = e2
% 229.78/41.14  | | | | 
% 229.78/41.14  | | | | COMBINE_EQS: (25), (31) imply:
% 229.78/41.14  | | | |   (32)  all_12_0 = e2
% 229.78/41.14  | | | | 
% 229.78/41.14  | | | | REDUCE: (17), (32) imply:
% 229.78/41.14  | | | |   (33)  $false
% 229.78/41.14  | | | | 
% 229.78/41.14  | | | | CLOSE: (33) is inconsistent.
% 229.78/41.14  | | | | 
% 229.78/41.14  | | | Case 2:
% 229.78/41.14  | | | | 
% 229.78/41.14  | | | |   (34)  all_55_11 = e1 | all_55_11 = e0
% 229.78/41.14  | | | | 
% 229.78/41.14  | | | | REF_CLOSE: (1), (4), (9), (10), (12), (13), (14), (15), (34) are
% 229.78/41.14  | | | |            inconsistent by sub-proof #861.
% 229.78/41.14  | | | | 
% 229.78/41.14  | | | End of split
% 229.78/41.14  | | | 
% 229.78/41.14  | | End of split
% 229.78/41.14  | | 
% 229.78/41.14  | Case 2:
% 229.78/41.14  | | 
% 229.78/41.14  | |   (35)   ~ (all_12_1 = e1) & op(e0, e3) = all_12_1 & $i(all_12_1)
% 229.78/41.14  | | 
% 229.78/41.14  | | REF_CLOSE: (1), (3), (5), (35) are inconsistent by sub-proof #1148.
% 229.78/41.14  | | 
% 229.78/41.14  | End of split
% 229.78/41.14  | 
% 229.78/41.14  End of proof
% 229.78/41.14  
% 229.78/41.14  Sub-proof #861 shows that the following formulas are inconsistent:
% 229.78/41.14  ----------------------------------------------------------------
% 229.78/41.14    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.78/41.14           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.78/41.14    (2)  op(e1, e0) = all_53_14
% 229.78/41.14    (3)  op(e1, e0) = all_52_23
% 229.78/41.14    (4)   ~ (all_53_14 = e3)
% 229.78/41.14    (5)  op(all_52_23, all_52_23) = e0
% 229.78/41.14    (6)   ~ (all_53_14 = e1)
% 229.78/41.14    (7)  op(e0, e0) = e3
% 229.78/41.14    (8)  all_55_11 = all_53_14
% 229.78/41.14    (9)  all_55_11 = e1 | all_55_11 = e0
% 229.78/41.14  
% 229.78/41.14  Begin of proof
% 229.78/41.14  | 
% 229.78/41.14  | BETA: splitting (9) gives:
% 229.78/41.14  | 
% 229.78/41.14  | Case 1:
% 229.78/41.14  | | 
% 229.78/41.14  | |   (10)  all_55_11 = e1
% 229.78/41.14  | | 
% 229.78/41.14  | | REF_CLOSE: (6), (8), (10) are inconsistent by sub-proof #2309.
% 229.78/41.14  | | 
% 229.78/41.14  | Case 2:
% 229.78/41.14  | | 
% 229.78/41.14  | |   (11)  all_55_11 = e0
% 229.78/41.14  | | 
% 229.78/41.14  | | COMBINE_EQS: (8), (11) imply:
% 229.78/41.14  | |   (12)  all_53_14 = e0
% 229.78/41.14  | | 
% 229.78/41.14  | | SIMP: (12) implies:
% 229.78/41.14  | |   (13)  all_53_14 = e0
% 229.78/41.14  | | 
% 229.78/41.14  | | REDUCE: (4), (13) imply:
% 229.78/41.14  | |   (14)   ~ (e3 = e0)
% 229.78/41.14  | | 
% 229.78/41.14  | | SIMP: (14) implies:
% 229.78/41.14  | |   (15)   ~ (e3 = e0)
% 229.78/41.14  | | 
% 229.78/41.14  | | REDUCE: (2), (13) imply:
% 229.78/41.14  | |   (16)  op(e1, e0) = e0
% 229.78/41.14  | | 
% 229.78/41.14  | | GROUND_INST: instantiating (1) with e0, all_52_23, e0, e1, simplifying with
% 229.78/41.14  | |              (3), (16) gives:
% 229.78/41.14  | |   (17)  all_52_23 = e0
% 229.78/41.14  | | 
% 229.78/41.14  | | REDUCE: (5), (17) imply:
% 229.78/41.14  | |   (18)  op(e0, e0) = e0
% 229.78/41.14  | | 
% 229.78/41.14  | | REF_CLOSE: (1), (7), (15), (18) are inconsistent by sub-proof #2304.
% 229.78/41.14  | | 
% 229.78/41.14  | End of split
% 229.78/41.14  | 
% 229.78/41.14  End of proof
% 229.78/41.14  
% 229.78/41.14  Sub-proof #862 shows that the following formulas are inconsistent:
% 229.78/41.14  ----------------------------------------------------------------
% 229.78/41.14    (1)   ~ (e3 = e1)
% 229.78/41.14    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.78/41.14           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.78/41.14    (3)   ~ (e3 = e2)
% 229.78/41.14    (4)   ~ (e3 = e0)
% 229.78/41.14    (5)  all_57_15 = e3
% 229.78/41.14    (6)  all_57_11 = e0
% 229.78/41.14    (7)   ~ (e2 = e0)
% 229.78/41.14    (8)   ~ (e1 = e0)
% 229.78/41.14    (9)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.78/41.14    (10)  op(e0, e0) = e3
% 229.78/41.14    (11)   ~ (e2 = e1)
% 229.78/41.14    (12)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.78/41.14          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.78/41.14    (13)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.78/41.14          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.78/41.14    (14)  all_57_5 = e0
% 229.78/41.14  
% 229.78/41.14  Begin of proof
% 229.78/41.14  | 
% 229.78/41.14  | BETA: splitting (9) gives:
% 229.78/41.14  | 
% 229.78/41.14  | Case 1:
% 229.78/41.14  | | 
% 229.78/41.14  | |   (15)  all_57_5 = e3 & op(e2, e1) = e3
% 229.78/41.14  | | 
% 229.78/41.14  | | ALPHA: (15) implies:
% 229.78/41.14  | |   (16)  all_57_5 = e3
% 229.78/41.14  | | 
% 229.78/41.14  | | REF_CLOSE: (4), (14), (16) are inconsistent by sub-proof #2471.
% 229.78/41.14  | | 
% 229.78/41.14  | Case 2:
% 229.78/41.14  | | 
% 229.78/41.14  | |   (17)  all_57_10 = e3 & op(e2, e0) = e3
% 229.78/41.14  | | 
% 229.78/41.14  | | ALPHA: (17) implies:
% 229.78/41.14  | |   (18)  all_57_10 = e3
% 229.78/41.14  | | 
% 229.78/41.14  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (10), (11), (12), (13), (18)
% 229.78/41.14  | |            are inconsistent by sub-proof #1748.
% 229.78/41.14  | | 
% 229.78/41.14  | End of split
% 229.78/41.14  | 
% 229.78/41.14  End of proof
% 229.78/41.14  
% 229.78/41.14  Sub-proof #863 shows that the following formulas are inconsistent:
% 229.78/41.14  ----------------------------------------------------------------
% 229.78/41.14    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.78/41.14           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.78/41.14    (2)  all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 229.78/41.14    (3)  op(all_52_7, all_52_7) = e0
% 229.78/41.14    (4)   ~ (all_53_13 = e2)
% 229.78/41.14    (5)  op(e3, e0) = e2
% 229.78/41.14    (6)   ~ (e2 = e0)
% 229.78/41.14    (7)  op(e2, e2) = e2
% 229.78/41.14    (8)  op(e3, e0) = all_18_1
% 229.78/41.14    (9)   ~ (all_53_13 = e0)
% 229.78/41.14    (10)  op(e3, e0) = all_48_1
% 229.78/41.14    (11)  op(e3, e0) = all_52_7
% 229.78/41.14    (12)  all_55_7 = all_53_13
% 229.78/41.14  
% 229.78/41.14  Begin of proof
% 229.78/41.14  | 
% 229.78/41.14  | BETA: splitting (2) gives:
% 229.78/41.14  | 
% 229.78/41.14  | Case 1:
% 229.78/41.14  | | 
% 229.78/41.14  | |   (13)  all_55_7 = e2
% 229.78/41.14  | | 
% 229.78/41.14  | | REF_CLOSE: (4), (12), (13) are inconsistent by sub-proof #2171.
% 229.78/41.14  | | 
% 229.78/41.14  | Case 2:
% 229.78/41.14  | | 
% 229.78/41.14  | |   (14)  all_55_7 = e1 | all_55_7 = e0
% 229.78/41.14  | | 
% 229.78/41.14  | | BETA: splitting (14) gives:
% 229.78/41.14  | | 
% 229.78/41.14  | | Case 1:
% 229.78/41.14  | | | 
% 229.78/41.14  | | | 
% 229.78/41.14  | | | GROUND_INST: instantiating (1) with e2, all_48_1, e0, e3, simplifying with
% 229.78/41.14  | | |              (5), (10) gives:
% 229.78/41.14  | | |   (15)  all_48_1 = e2
% 229.78/41.14  | | | 
% 229.78/41.14  | | | GROUND_INST: instantiating (1) with all_48_1, all_52_7, e0, e3,
% 229.78/41.14  | | |              simplifying with (10), (11) gives:
% 229.78/41.14  | | |   (16)  all_52_7 = all_48_1
% 229.78/41.14  | | | 
% 229.78/41.14  | | | GROUND_INST: instantiating (1) with all_18_1, all_52_7, e0, e3,
% 229.78/41.14  | | |              simplifying with (8), (11) gives:
% 229.78/41.14  | | |   (17)  all_52_7 = all_18_1
% 229.78/41.14  | | | 
% 229.78/41.14  | | | COMBINE_EQS: (16), (17) imply:
% 229.78/41.14  | | |   (18)  all_48_1 = all_18_1
% 229.78/41.14  | | | 
% 229.78/41.14  | | | SIMP: (18) implies:
% 229.78/41.14  | | |   (19)  all_48_1 = all_18_1
% 229.78/41.14  | | | 
% 229.78/41.14  | | | COMBINE_EQS: (15), (19) imply:
% 229.78/41.14  | | |   (20)  all_18_1 = e2
% 229.78/41.14  | | | 
% 229.78/41.14  | | | COMBINE_EQS: (17), (20) imply:
% 229.78/41.14  | | |   (21)  all_52_7 = e2
% 229.78/41.14  | | | 
% 229.78/41.14  | | | REDUCE: (3), (21) imply:
% 229.78/41.14  | | |   (22)  op(e2, e2) = e0
% 229.78/41.14  | | | 
% 229.78/41.14  | | | REF_CLOSE: (1), (6), (7), (22) are inconsistent by sub-proof #2472.
% 229.78/41.14  | | | 
% 229.78/41.14  | | Case 2:
% 229.78/41.14  | | | 
% 229.78/41.14  | | |   (23)  all_55_7 = e0
% 229.78/41.14  | | | 
% 229.78/41.14  | | | REF_CLOSE: (9), (12), (23) are inconsistent by sub-proof #2130.
% 229.78/41.14  | | | 
% 229.78/41.14  | | End of split
% 229.78/41.14  | | 
% 229.78/41.14  | End of split
% 229.78/41.14  | 
% 229.78/41.14  End of proof
% 229.78/41.14  
% 229.78/41.14  Sub-proof #864 shows that the following formulas are inconsistent:
% 229.78/41.14  ----------------------------------------------------------------
% 229.78/41.14    (1)  all_57_9 = e2
% 229.78/41.14    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.78/41.14         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.78/41.14    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.78/41.14         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.78/41.14    (4)   ~ (e3 = e1)
% 229.78/41.14    (5)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 229.78/41.14         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 229.78/41.14    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.78/41.14           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.78/41.14    (7)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.78/41.14         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.78/41.14    (8)   ~ (all_6_2 = e3)
% 229.78/41.14    (9)  all_57_10 = e1
% 229.78/41.14    (10)  op(e1, e1) = all_6_2
% 229.78/41.14    (11)  all_57_4 = e3
% 229.78/41.14    (12)   ~ (e3 = e2)
% 229.78/41.14    (13)   ~ (e3 = e0)
% 229.78/41.14    (14)  all_57_0 = e0
% 229.78/41.14    (15)  all_57_15 = e3
% 229.78/41.14    (16)  op(e3, e3) = e0
% 229.78/41.14    (17)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.78/41.14          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.78/41.14            e1)
% 229.78/41.14    (18)  op(e1, e1) = e1
% 229.78/41.14    (19)   ~ (e2 = e0)
% 229.78/41.14    (20)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2)
% 229.78/41.14    (21)  op(e2, e2) = e2
% 229.78/41.14    (22)   ~ (e1 = e0)
% 229.78/41.14    (23)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.78/41.14          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.78/41.14    (24)  op(e0, e0) = e3
% 229.78/41.14    (25)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.78/41.14          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.78/41.14            e2)
% 229.78/41.14    (26)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.78/41.14              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.78/41.14                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.78/41.14                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.78/41.14    (27)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.78/41.14          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.78/41.14    (28)  all_57_7 = e3
% 229.78/41.14    (29)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.78/41.14          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.78/41.14    (30)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.78/41.14          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.78/41.14    (31)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.78/41.14          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 229.78/41.14    (32)   ~ (e2 = e1)
% 229.78/41.14    (33)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.78/41.14          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.78/41.14    (34)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.78/41.14          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.78/41.14    (35)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.78/41.14          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.78/41.14    (36)  all_57_3 = e2
% 229.78/41.14  
% 229.78/41.14  Begin of proof
% 229.78/41.14  | 
% 229.78/41.14  | BETA: splitting (20) gives:
% 229.78/41.14  | 
% 229.78/41.14  | Case 1:
% 229.78/41.14  | | 
% 229.78/41.15  | |   (37)  all_57_4 = e2 & op(e3, e1) = e2
% 229.78/41.15  | | 
% 229.78/41.15  | | REF_CLOSE: (11), (12), (37) are inconsistent by sub-proof #2487.
% 229.78/41.15  | | 
% 229.78/41.15  | Case 2:
% 229.78/41.15  | | 
% 229.78/41.15  | |   (38)  all_57_5 = e2 & op(e2, e1) = e2
% 229.78/41.15  | | 
% 229.78/41.15  | | ALPHA: (38) implies:
% 229.78/41.15  | |   (39)  all_57_5 = e2
% 229.78/41.15  | | 
% 229.78/41.15  | | BETA: splitting (5) gives:
% 229.78/41.15  | | 
% 229.78/41.15  | | Case 1:
% 229.78/41.15  | | | 
% 229.78/41.15  | | |   (40)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) =
% 229.78/41.15  | | |           e0)
% 229.78/41.15  | | | 
% 229.78/41.15  | | | REF_CLOSE: (3), (4), (6), (7), (8), (10), (12), (13), (14), (15), (16),
% 229.78/41.15  | | |            (19), (22), (26), (28), (30), (32), (33), (34), (35), (40) are
% 229.78/41.15  | | |            inconsistent by sub-proof #868.
% 229.78/41.15  | | | 
% 229.78/41.15  | | Case 2:
% 229.78/41.15  | | | 
% 229.78/41.15  | | |   (41)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 229.78/41.15  | | |           e0)
% 229.78/41.15  | | | 
% 229.78/41.15  | | | BETA: splitting (41) gives:
% 229.78/41.15  | | | 
% 229.78/41.15  | | | Case 1:
% 229.78/41.15  | | | | 
% 229.78/41.15  | | | |   (42)  all_57_8 = e0 & op(e1, e1) = e0
% 229.78/41.15  | | | | 
% 229.78/41.15  | | | | ALPHA: (42) implies:
% 229.78/41.15  | | | |   (43)  op(e1, e1) = e0
% 229.78/41.15  | | | | 
% 229.78/41.15  | | | | REF_CLOSE: (6), (18), (22), (43) are inconsistent by sub-proof #2427.
% 229.78/41.15  | | | | 
% 229.78/41.15  | | | Case 2:
% 229.78/41.15  | | | | 
% 229.78/41.15  | | | |   (44)  all_57_11 = e0 & op(e1, e0) = e0
% 229.78/41.15  | | | | 
% 229.78/41.15  | | | | ALPHA: (44) implies:
% 229.78/41.15  | | | |   (45)  all_57_11 = e0
% 229.78/41.15  | | | | 
% 229.78/41.15  | | | | REF_CLOSE: (1), (2), (4), (6), (8), (9), (10), (11), (12), (13), (15),
% 229.78/41.15  | | | |            (17), (19), (21), (22), (23), (24), (25), (26), (27), (29),
% 229.78/41.15  | | | |            (31), (32), (33), (35), (36), (39), (45) are inconsistent by
% 229.78/41.15  | | | |            sub-proof #865.
% 229.78/41.15  | | | | 
% 229.78/41.15  | | | End of split
% 229.78/41.15  | | | 
% 229.78/41.15  | | End of split
% 229.78/41.15  | | 
% 229.78/41.15  | End of split
% 229.78/41.15  | 
% 229.78/41.15  End of proof
% 229.78/41.15  
% 229.78/41.15  Sub-proof #865 shows that the following formulas are inconsistent:
% 229.78/41.15  ----------------------------------------------------------------
% 229.78/41.15    (1)  all_57_9 = e2
% 229.78/41.15    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.78/41.15         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.78/41.15    (3)   ~ (e3 = e1)
% 229.78/41.15    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.78/41.15           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.78/41.15    (5)   ~ (all_6_2 = e3)
% 229.78/41.15    (6)  all_57_10 = e1
% 229.78/41.15    (7)  op(e1, e1) = all_6_2
% 229.78/41.15    (8)  all_57_4 = e3
% 229.78/41.15    (9)   ~ (e3 = e2)
% 229.78/41.15    (10)   ~ (e3 = e0)
% 229.78/41.15    (11)  all_57_15 = e3
% 229.78/41.15    (12)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.78/41.15          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.78/41.15            e1)
% 229.78/41.15    (13)  all_57_11 = e0
% 229.78/41.15    (14)   ~ (e2 = e0)
% 229.78/41.15    (15)  op(e2, e2) = e2
% 229.78/41.15    (16)   ~ (e1 = e0)
% 229.78/41.15    (17)  all_57_5 = e2
% 229.78/41.15    (18)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.78/41.15          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.78/41.15    (19)  op(e0, e0) = e3
% 229.78/41.15    (20)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.78/41.15          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.78/41.15            e2)
% 229.78/41.15    (21)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.78/41.15              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.78/41.15                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.78/41.15                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.78/41.15    (22)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.78/41.15          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.78/41.15    (23)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.78/41.15          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.78/41.15    (24)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.78/41.15          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 229.78/41.15    (25)   ~ (e2 = e1)
% 229.78/41.15    (26)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.78/41.15          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.78/41.15    (27)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.78/41.15          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.78/41.15    (28)  all_57_3 = e2
% 229.78/41.15  
% 229.78/41.15  Begin of proof
% 229.78/41.15  | 
% 229.78/41.15  | BETA: splitting (24) gives:
% 229.78/41.15  | 
% 229.78/41.15  | Case 1:
% 229.78/41.15  | | 
% 229.78/41.15  | |   (29)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) =
% 229.78/41.15  | |           e0)
% 229.78/41.15  | | 
% 229.78/41.15  | | BETA: splitting (29) gives:
% 229.78/41.15  | | 
% 229.78/41.15  | | Case 1:
% 229.78/41.15  | | | 
% 229.78/41.15  | | |   (30)  all_57_2 = e0 & op(e2, e3) = e0
% 229.78/41.15  | | | 
% 229.78/41.15  | | | ALPHA: (30) implies:
% 229.78/41.15  | | |   (31)  all_57_2 = e0
% 229.78/41.15  | | | 
% 229.78/41.15  | | | BETA: splitting (22) gives:
% 229.78/41.15  | | | 
% 229.78/41.15  | | | Case 1:
% 229.78/41.15  | | | | 
% 229.78/41.15  | | | |   (32)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2)
% 229.78/41.15  | | | |           = e3)
% 229.78/41.15  | | | | 
% 229.78/41.15  | | | | BETA: splitting (32) gives:
% 229.78/41.15  | | | | 
% 229.78/41.15  | | | | Case 1:
% 229.78/41.15  | | | | | 
% 229.78/41.15  | | | | |   (33)  all_57_2 = e3 & op(e2, e3) = e3
% 229.78/41.15  | | | | | 
% 229.78/41.15  | | | | | ALPHA: (33) implies:
% 229.78/41.15  | | | | |   (34)  all_57_2 = e3
% 229.78/41.15  | | | | | 
% 229.78/41.15  | | | | | COMBINE_EQS: (31), (34) imply:
% 229.78/41.15  | | | | |   (35)  e3 = e0
% 229.78/41.15  | | | | | 
% 229.78/41.15  | | | | | SIMP: (35) implies:
% 229.78/41.15  | | | | |   (36)  e3 = e0
% 229.78/41.15  | | | | | 
% 229.78/41.15  | | | | | COMBINE_EQS: (8), (36) imply:
% 229.78/41.15  | | | | |   (37)  all_57_4 = e0
% 229.78/41.15  | | | | | 
% 229.78/41.15  | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (14),
% 229.78/41.15  | | | | |            (16), (18), (20), (21), (23), (24), (25), (34), (37) are
% 229.78/41.15  | | | | |            inconsistent by sub-proof #867.
% 229.78/41.15  | | | | | 
% 229.78/41.15  | | | | Case 2:
% 229.78/41.15  | | | | | 
% 229.78/41.15  | | | | |   (38)  all_57_3 = e3 & op(e2, e2) = e3
% 229.78/41.15  | | | | | 
% 229.78/41.15  | | | | | ALPHA: (38) implies:
% 229.78/41.15  | | | | |   (39)  all_57_3 = e3
% 229.78/41.15  | | | | | 
% 229.78/41.15  | | | | | REF_CLOSE: (9), (28), (39) are inconsistent by sub-proof #1166.
% 229.78/41.15  | | | | | 
% 229.78/41.15  | | | | End of split
% 229.78/41.15  | | | | 
% 229.78/41.15  | | | Case 2:
% 229.78/41.15  | | | | 
% 229.78/41.15  | | | |   (40)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0)
% 229.78/41.15  | | | |           = e3)
% 229.78/41.15  | | | | 
% 229.78/41.15  | | | | REF_CLOSE: (3), (4), (9), (11), (13), (14), (16), (17), (19), (25),
% 229.78/41.15  | | | |            (26), (27), (40) are inconsistent by sub-proof #866.
% 229.78/41.15  | | | | 
% 229.78/41.15  | | | End of split
% 229.78/41.15  | | | 
% 229.78/41.15  | | Case 2:
% 229.78/41.15  | | | 
% 229.78/41.15  | | |   (41)  all_57_3 = e0 & op(e2, e2) = e0
% 229.78/41.15  | | | 
% 229.78/41.15  | | | ALPHA: (41) implies:
% 229.78/41.15  | | |   (42)  op(e2, e2) = e0
% 229.78/41.15  | | | 
% 229.78/41.15  | | | REF_CLOSE: (4), (14), (15), (42) are inconsistent by sub-proof #2472.
% 229.78/41.15  | | | 
% 229.78/41.15  | | End of split
% 229.78/41.15  | | 
% 229.78/41.15  | Case 2:
% 229.78/41.15  | | 
% 229.78/41.15  | |   (43)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 229.78/41.15  | |           e0)
% 229.78/41.15  | | 
% 229.78/41.15  | | BETA: splitting (43) gives:
% 229.78/41.15  | | 
% 229.78/41.15  | | Case 1:
% 229.78/41.15  | | | 
% 229.78/41.15  | | |   (44)  all_57_5 = e0 & op(e2, e1) = e0
% 229.78/41.15  | | | 
% 229.78/41.15  | | | ALPHA: (44) implies:
% 229.78/41.15  | | |   (45)  all_57_5 = e0
% 229.78/41.15  | | | 
% 229.78/41.15  | | | COMBINE_EQS: (17), (45) imply:
% 229.78/41.15  | | |   (46)  e2 = e0
% 229.78/41.15  | | | 
% 229.78/41.15  | | | COMBINE_EQS: (1), (46) imply:
% 229.78/41.15  | | |   (47)  all_57_9 = e0
% 229.78/41.15  | | | 
% 229.78/41.15  | | | REF_CLOSE: (3), (9), (11), (13), (14), (16), (25), (26), (27), (47) are
% 229.78/41.15  | | |            inconsistent by sub-proof #1144.
% 229.78/41.15  | | | 
% 229.78/41.15  | | Case 2:
% 229.78/41.15  | | | 
% 229.78/41.15  | | |   (48)  all_57_10 = e0 & op(e2, e0) = e0
% 229.78/41.15  | | | 
% 229.78/41.15  | | | ALPHA: (48) implies:
% 229.78/41.15  | | |   (49)  all_57_10 = e0
% 229.78/41.15  | | | 
% 229.78/41.15  | | | REF_CLOSE: (3), (4), (9), (11), (13), (14), (16), (19), (25), (26), (27),
% 229.78/41.15  | | |            (49) are inconsistent by sub-proof #1087.
% 229.78/41.15  | | | 
% 229.78/41.15  | | End of split
% 229.78/41.15  | | 
% 229.78/41.15  | End of split
% 229.78/41.15  | 
% 229.78/41.15  End of proof
% 229.78/41.15  
% 229.78/41.15  Sub-proof #866 shows that the following formulas are inconsistent:
% 229.78/41.15  ----------------------------------------------------------------
% 229.78/41.15    (1)   ~ (e3 = e1)
% 229.78/41.15    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.78/41.15           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.78/41.15    (3)   ~ (e3 = e2)
% 229.78/41.15    (4)  all_57_15 = e3
% 229.78/41.15    (5)  all_57_11 = e0
% 229.78/41.15    (6)   ~ (e2 = e0)
% 229.78/41.15    (7)   ~ (e1 = e0)
% 229.78/41.15    (8)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.78/41.15    (9)  all_57_5 = e2
% 229.78/41.15    (10)  op(e0, e0) = e3
% 229.78/41.15    (11)   ~ (e2 = e1)
% 229.78/41.15    (12)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.78/41.15          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.78/41.15    (13)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.78/41.15          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.78/41.15  
% 229.78/41.15  Begin of proof
% 229.78/41.15  | 
% 229.78/41.15  | BETA: splitting (8) gives:
% 229.78/41.15  | 
% 229.78/41.15  | Case 1:
% 229.78/41.15  | | 
% 229.78/41.15  | |   (14)  all_57_5 = e3 & op(e2, e1) = e3
% 229.78/41.15  | | 
% 229.78/41.15  | | ALPHA: (14) implies:
% 229.78/41.15  | |   (15)  all_57_5 = e3
% 229.78/41.15  | | 
% 229.78/41.15  | | REF_CLOSE: (3), (9), (15) are inconsistent by sub-proof #2189.
% 229.78/41.15  | | 
% 229.78/41.15  | Case 2:
% 229.78/41.15  | | 
% 229.78/41.15  | |   (16)  all_57_10 = e3 & op(e2, e0) = e3
% 229.78/41.15  | | 
% 229.78/41.15  | | ALPHA: (16) implies:
% 229.78/41.15  | |   (17)  all_57_10 = e3
% 229.78/41.15  | | 
% 229.78/41.15  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (10), (11), (12), (13), (17)
% 229.78/41.15  | |            are inconsistent by sub-proof #1748.
% 229.78/41.15  | | 
% 229.78/41.15  | End of split
% 229.78/41.15  | 
% 229.78/41.15  End of proof
% 229.78/41.15  
% 229.78/41.15  Sub-proof #867 shows that the following formulas are inconsistent:
% 229.78/41.15  ----------------------------------------------------------------
% 229.78/41.15    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.78/41.15         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.78/41.15    (2)   ~ (e3 = e1)
% 229.78/41.15    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.78/41.15           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.78/41.15    (4)   ~ (all_6_2 = e3)
% 229.78/41.15    (5)  all_57_10 = e1
% 229.78/41.15    (6)  op(e1, e1) = all_6_2
% 229.78/41.15    (7)  all_57_4 = e0
% 229.78/41.15    (8)   ~ (e3 = e2)
% 229.78/41.15    (9)   ~ (e3 = e0)
% 229.78/41.15    (10)  all_57_15 = e3
% 229.78/41.15    (11)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.78/41.15          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.78/41.15            e1)
% 229.78/41.15    (12)   ~ (e2 = e0)
% 229.78/41.15    (13)  all_57_2 = e3
% 229.78/41.15    (14)   ~ (e1 = e0)
% 229.78/41.15    (15)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.78/41.15          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.78/41.15    (16)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.78/41.15          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.78/41.15            e2)
% 229.78/41.15    (17)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.78/41.15              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.78/41.15                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.78/41.15                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.78/41.15    (18)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.78/41.15          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.78/41.15    (19)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.78/41.15          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 229.78/41.15    (20)   ~ (e2 = e1)
% 229.78/41.15  
% 229.78/41.15  Begin of proof
% 229.78/41.15  | 
% 229.78/41.15  | BETA: splitting (15) gives:
% 229.78/41.15  | 
% 229.78/41.15  | Case 1:
% 229.78/41.15  | | 
% 229.78/41.15  | |   (21)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) =
% 229.78/41.15  | |           e3)
% 229.78/41.15  | | 
% 229.78/41.15  | | BETA: splitting (21) gives:
% 229.78/41.15  | | 
% 229.78/41.15  | | Case 1:
% 229.78/41.15  | | | 
% 229.78/41.15  | | |   (22)  all_57_4 = e3 & op(e3, e1) = e3
% 229.78/41.15  | | | 
% 229.78/41.15  | | | ALPHA: (22) implies:
% 229.78/41.15  | | |   (23)  all_57_4 = e3
% 229.78/41.15  | | | 
% 229.78/41.15  | | | REF_CLOSE: (7), (9), (23) are inconsistent by sub-proof #2372.
% 229.78/41.15  | | | 
% 229.78/41.15  | | Case 2:
% 229.78/41.15  | | | 
% 229.78/41.15  | | |   (24)  all_57_5 = e3 & op(e2, e1) = e3
% 229.78/41.15  | | | 
% 229.78/41.15  | | | ALPHA: (24) implies:
% 229.78/41.15  | | |   (25)  all_57_5 = e3
% 229.78/41.15  | | | 
% 229.78/41.15  | | | REF_CLOSE: (1), (2), (5), (8), (9), (12), (13), (14), (18), (19), (20),
% 229.78/41.15  | | |            (25) are inconsistent by sub-proof #1331.
% 229.78/41.15  | | | 
% 229.78/41.15  | | End of split
% 229.78/41.15  | | 
% 229.78/41.15  | Case 2:
% 229.78/41.15  | | 
% 229.78/41.15  | |   (26)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) =
% 229.78/41.15  | |           e3)
% 229.78/41.15  | | 
% 229.78/41.15  | | REF_CLOSE: (2), (3), (4), (6), (8), (9), (10), (11), (12), (14), (16), (17),
% 229.78/41.15  | |            (20), (26) are inconsistent by sub-proof #1794.
% 229.78/41.15  | | 
% 229.78/41.15  | End of split
% 229.78/41.15  | 
% 229.78/41.15  End of proof
% 229.78/41.15  
% 229.78/41.15  Sub-proof #868 shows that the following formulas are inconsistent:
% 229.78/41.15  ----------------------------------------------------------------
% 229.78/41.15    (1)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.78/41.15         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.78/41.15    (2)   ~ (e3 = e1)
% 229.78/41.15    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.78/41.15           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.78/41.15    (4)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.78/41.15         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.78/41.15    (5)   ~ (all_6_2 = e3)
% 229.78/41.15    (6)  op(e1, e1) = all_6_2
% 229.78/41.15    (7)   ~ (e3 = e2)
% 229.78/41.15    (8)   ~ (e3 = e0)
% 229.78/41.15    (9)  all_57_0 = e0
% 229.78/41.15    (10)  all_57_15 = e3
% 229.78/41.15    (11)  op(e3, e3) = e0
% 229.78/41.15    (12)   ~ (e2 = e0)
% 229.78/41.15    (13)   ~ (e1 = e0)
% 229.78/41.15    (14)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.78/41.15              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.78/41.15                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.78/41.15                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.78/41.15    (15)  all_57_7 = e3
% 229.78/41.15    (16)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0)
% 229.78/41.15    (17)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.78/41.15          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.78/41.15    (18)   ~ (e2 = e1)
% 229.78/41.15    (19)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.78/41.15          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.78/41.15    (20)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.78/41.15          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.78/41.15    (21)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.78/41.15          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.78/41.15  
% 229.78/41.15  Begin of proof
% 229.78/41.15  | 
% 229.78/41.15  | BETA: splitting (16) gives:
% 229.78/41.15  | 
% 229.78/41.15  | Case 1:
% 229.78/41.15  | | 
% 229.78/41.15  | |   (22)  all_57_6 = e0 & op(e1, e3) = e0
% 229.78/41.15  | | 
% 229.78/41.15  | | ALPHA: (22) implies:
% 229.78/41.15  | |   (23)  all_57_6 = e0
% 229.78/41.15  | | 
% 229.78/41.15  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 229.78/41.15  | |            (13), (14), (17), (18), (19), (20), (21), (23) are inconsistent
% 229.78/41.15  | |            by sub-proof #869.
% 229.78/41.15  | | 
% 229.78/41.15  | Case 2:
% 229.78/41.15  | | 
% 229.78/41.15  | |   (24)  all_57_7 = e0 & op(e1, e2) = e0
% 229.78/41.15  | | 
% 229.78/41.15  | | REF_CLOSE: (8), (15), (24) are inconsistent by sub-proof #2042.
% 229.78/41.15  | | 
% 229.78/41.15  | End of split
% 229.78/41.15  | 
% 229.78/41.15  End of proof
% 229.78/41.15  
% 229.78/41.15  Sub-proof #869 shows that the following formulas are inconsistent:
% 229.78/41.15  ----------------------------------------------------------------
% 229.78/41.15    (1)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.78/41.15         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.78/41.15    (2)   ~ (e3 = e1)
% 229.78/41.15    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.78/41.15           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.78/41.15    (4)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.78/41.15         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.78/41.15    (5)   ~ (all_6_2 = e3)
% 229.78/41.15    (6)  op(e1, e1) = all_6_2
% 229.78/41.15    (7)   ~ (e3 = e2)
% 229.78/41.15    (8)   ~ (e3 = e0)
% 229.78/41.15    (9)  all_57_6 = e0
% 229.78/41.15    (10)  all_57_0 = e0
% 229.78/41.15    (11)  all_57_15 = e3
% 229.78/41.15    (12)  op(e3, e3) = e0
% 229.78/41.15    (13)   ~ (e2 = e0)
% 229.78/41.15    (14)   ~ (e1 = e0)
% 229.78/41.15    (15)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.78/41.15              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.78/41.15                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.78/41.15                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.78/41.15    (16)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.78/41.15          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.78/41.15    (17)   ~ (e2 = e1)
% 229.78/41.15    (18)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.78/41.15          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.78/41.15    (19)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.78/41.15          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.78/41.15    (20)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.78/41.15          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.78/41.15  
% 229.78/41.15  Begin of proof
% 229.78/41.15  | 
% 229.78/41.15  | BETA: splitting (1) gives:
% 229.78/41.15  | 
% 229.78/41.15  | Case 1:
% 229.78/41.15  | | 
% 229.78/41.15  | |   (21)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) =
% 229.78/41.15  | |           e1)
% 229.78/41.15  | | 
% 229.78/41.15  | | BETA: splitting (21) gives:
% 229.78/41.15  | | 
% 229.78/41.15  | | Case 1:
% 229.78/41.15  | | | 
% 229.78/41.15  | | |   (22)  all_57_0 = e1 & op(e3, e3) = e1
% 229.78/41.15  | | | 
% 229.78/41.15  | | | REF_CLOSE: (10), (14), (22) are inconsistent by sub-proof #2454.
% 229.78/41.15  | | | 
% 229.78/41.15  | | Case 2:
% 229.78/41.15  | | | 
% 229.78/41.15  | | |   (23)  all_57_2 = e1 & op(e2, e3) = e1
% 229.78/41.15  | | | 
% 229.78/41.15  | | | ALPHA: (23) implies:
% 229.78/41.15  | | |   (24)  all_57_2 = e1
% 229.78/41.15  | | | 
% 229.78/41.15  | | | REF_CLOSE: (2), (3), (7), (8), (9), (12), (13), (16), (17), (19), (24) are
% 229.78/41.15  | | |            inconsistent by sub-proof #2390.
% 229.78/41.15  | | | 
% 229.78/41.15  | | End of split
% 229.78/41.15  | | 
% 229.78/41.15  | Case 2:
% 229.78/41.15  | | 
% 229.78/41.15  | |   (25)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) =
% 229.78/41.15  | |           e1)
% 229.78/41.15  | | 
% 229.78/41.15  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13), (14),
% 229.78/41.15  | |            (15), (16), (17), (18), (19), (20), (25) are inconsistent by
% 229.78/41.15  | |            sub-proof #984.
% 229.78/41.15  | | 
% 229.78/41.15  | End of split
% 229.78/41.15  | 
% 229.78/41.15  End of proof
% 229.78/41.15  
% 229.78/41.15  Sub-proof #870 shows that the following formulas are inconsistent:
% 229.78/41.15  ----------------------------------------------------------------
% 229.78/41.15    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.78/41.15         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.78/41.15    (2)   ~ (e3 = e1)
% 229.78/41.15    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.78/41.15           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.78/41.15    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.78/41.15         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.78/41.15    (5)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.78/41.15         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.78/41.15    (6)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.78/41.15         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.78/41.15    (7)  all_57_4 = e3
% 229.78/41.15    (8)   ~ (e3 = e2)
% 229.78/41.15    (9)   ~ (e3 = e0)
% 229.78/41.15    (10)  all_57_1 = e2
% 229.78/41.15    (11)  all_57_0 = e0
% 229.78/41.15    (12)  all_57_15 = e3
% 229.78/41.15    (13)  op(e3, e3) = e0
% 229.78/41.15    (14)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.78/41.15          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.78/41.15            e1)
% 229.78/41.15    (15)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.78/41.15          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.78/41.15    (16)   ~ (e2 = e0)
% 229.78/41.15    (17)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.78/41.15          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.78/41.15    (18)  op(e2, e2) = e2
% 229.78/41.15    (19)   ~ (e1 = e0)
% 229.78/41.15    (20)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.78/41.15          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.78/41.15    (21)  op(e0, e0) = e3
% 229.78/41.15    (22)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.78/41.15          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.78/41.15            e2)
% 229.78/41.16    (23)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.78/41.16              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.78/41.16                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.78/41.16                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.78/41.16    (24)   ~ (all_53_12 = e3)
% 229.78/41.16    (25)  all_57_7 = e3
% 229.78/41.16    (26)   ~ (all_53_12 = e0)
% 229.78/41.16    (27)   ~ (e2 = e1)
% 229.78/41.16    (28)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.78/41.16          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.78/41.16    (29)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.78/41.16          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.78/41.16    (30)  all_57_3 = e2
% 229.78/41.16    (31)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.78/41.16          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.78/41.16    (32)  op(e3, e0) = all_53_12
% 229.78/41.16  
% 229.78/41.16  Begin of proof
% 229.78/41.16  | 
% 229.78/41.16  | BETA: splitting (15) gives:
% 229.78/41.16  | 
% 229.78/41.16  | Case 1:
% 229.78/41.16  | | 
% 229.78/41.16  | |   (33)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) =
% 229.78/41.16  | |           e0)
% 229.78/41.16  | | 
% 229.78/41.16  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (11), (12), (13), (14),
% 229.78/41.16  | |            (16), (17), (18), (19), (20), (21), (22), (23), (24), (26), (27),
% 229.78/41.16  | |            (28), (29), (30), (31), (32), (33) are inconsistent by sub-proof
% 229.78/41.16  | |            #879.
% 229.78/41.16  | | 
% 229.78/41.16  | Case 2:
% 229.78/41.16  | | 
% 229.78/41.16  | |   (34)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 229.78/41.16  | |           e0)
% 229.78/41.16  | | 
% 229.78/41.16  | | BETA: splitting (34) gives:
% 229.78/41.16  | | 
% 229.78/41.16  | | Case 1:
% 229.78/41.16  | | | 
% 229.78/41.16  | | |   (35)  all_57_7 = e0 & op(e1, e2) = e0
% 229.78/41.16  | | | 
% 229.78/41.16  | | | ALPHA: (35) implies:
% 229.78/41.16  | | |   (36)  all_57_7 = e0
% 229.78/41.16  | | | 
% 229.78/41.16  | | | COMBINE_EQS: (25), (36) imply:
% 229.78/41.16  | | |   (37)  e3 = e0
% 229.78/41.16  | | | 
% 229.78/41.16  | | | COMBINE_EQS: (7), (37) imply:
% 229.78/41.16  | | |   (38)  all_57_4 = e0
% 229.78/41.16  | | | 
% 229.78/41.16  | | | REF_CLOSE: (3), (8), (9), (10), (13), (17), (24), (32), (38) are
% 229.78/41.16  | | |            inconsistent by sub-proof #1405.
% 229.78/41.16  | | | 
% 229.78/41.16  | | Case 2:
% 229.78/41.16  | | | 
% 229.78/41.16  | | |   (39)  all_57_13 = e0 & op(e0, e2) = e0
% 229.78/41.16  | | | 
% 229.78/41.16  | | | ALPHA: (39) implies:
% 229.78/41.16  | | |   (40)  all_57_13 = e0
% 229.78/41.16  | | | 
% 229.78/41.16  | | | REF_CLOSE: (2), (3), (10), (18), (19), (25), (27), (31), (40) are
% 229.78/41.16  | | |            inconsistent by sub-proof #871.
% 229.78/41.16  | | | 
% 229.78/41.16  | | End of split
% 229.78/41.16  | | 
% 229.78/41.16  | End of split
% 229.78/41.16  | 
% 229.78/41.16  End of proof
% 229.78/41.16  
% 229.78/41.16  Sub-proof #871 shows that the following formulas are inconsistent:
% 229.78/41.16  ----------------------------------------------------------------
% 229.78/41.16    (1)   ~ (e3 = e1)
% 229.78/41.16    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.78/41.16           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.78/41.16    (3)  all_57_1 = e2
% 229.78/41.16    (4)  op(e2, e2) = e2
% 229.78/41.16    (5)   ~ (e1 = e0)
% 229.78/41.16    (6)  all_57_13 = e0
% 229.78/41.16    (7)  all_57_7 = e3
% 229.78/41.16    (8)   ~ (e2 = e1)
% 229.78/41.16    (9)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.78/41.16         (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.78/41.16  
% 229.78/41.16  Begin of proof
% 229.78/41.16  | 
% 229.78/41.16  | BETA: splitting (9) gives:
% 229.78/41.16  | 
% 229.78/41.16  | Case 1:
% 229.78/41.16  | | 
% 229.78/41.16  | |   (10)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) =
% 229.78/41.16  | |           e1)
% 229.78/41.16  | | 
% 229.78/41.16  | | REF_CLOSE: (2), (3), (4), (8), (10) are inconsistent by sub-proof #1133.
% 229.78/41.16  | | 
% 229.78/41.16  | Case 2:
% 229.78/41.16  | | 
% 229.78/41.16  | |   (11)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 229.78/41.16  | |           e1)
% 229.78/41.16  | | 
% 229.78/41.16  | | REF_CLOSE: (1), (5), (6), (7), (11) are inconsistent by sub-proof #1142.
% 229.78/41.16  | | 
% 229.78/41.16  | End of split
% 229.78/41.16  | 
% 229.78/41.16  End of proof
% 229.78/41.16  
% 229.78/41.16  Sub-proof #872 shows that the following formulas are inconsistent:
% 229.78/41.16  ----------------------------------------------------------------
% 229.78/41.16    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.78/41.16           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.78/41.16    (2)  all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 229.78/41.16    (3)  all_57_12 = e2 & op(e0, e3) = e2
% 229.78/41.16    (4)  op(e0, e3) = all_53_3
% 229.78/41.16    (5)   ~ (all_53_11 = e0)
% 229.78/41.16    (6)   ~ (all_53_3 = all_53_11)
% 229.78/41.16    (7)   ~ (all_53_11 = e1)
% 229.78/41.16    (8)  all_55_14 = all_53_11
% 229.78/41.16  
% 229.78/41.16  Begin of proof
% 229.78/41.16  | 
% 229.78/41.16  | ALPHA: (3) implies:
% 229.78/41.16  |   (9)  op(e0, e3) = e2
% 229.78/41.16  | 
% 229.78/41.16  | BETA: splitting (2) gives:
% 229.78/41.16  | 
% 229.78/41.16  | Case 1:
% 229.78/41.16  | | 
% 229.78/41.16  | |   (10)  all_55_14 = e2
% 229.78/41.16  | | 
% 229.78/41.16  | | COMBINE_EQS: (8), (10) imply:
% 229.78/41.16  | |   (11)  all_53_11 = e2
% 229.78/41.16  | | 
% 229.78/41.16  | | REDUCE: (6), (11) imply:
% 229.78/41.16  | |   (12)   ~ (all_53_3 = e2)
% 229.78/41.16  | | 
% 229.78/41.16  | | REF_CLOSE: (1), (4), (9), (12) are inconsistent by sub-proof #1980.
% 229.78/41.16  | | 
% 229.78/41.16  | Case 2:
% 229.78/41.16  | | 
% 229.78/41.16  | |   (13)  all_55_14 = e1 | all_55_14 = e0
% 229.78/41.16  | | 
% 229.78/41.16  | | REF_CLOSE: (5), (7), (8), (13) are inconsistent by sub-proof #1720.
% 229.78/41.16  | | 
% 229.78/41.16  | End of split
% 229.78/41.16  | 
% 229.78/41.16  End of proof
% 229.78/41.16  
% 229.78/41.16  Sub-proof #873 shows that the following formulas are inconsistent:
% 229.78/41.16  ----------------------------------------------------------------
% 229.78/41.16    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.78/41.16           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.78/41.16    (2)  all_57_4 = e2
% 229.78/41.16    (3)  all_57_9 = e1
% 229.78/41.16    (4)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.78/41.16         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.78/41.16    (5)   ~ (e3 = e2)
% 229.78/41.16    (6)   ~ (e3 = e0)
% 229.78/41.16    (7)  op(e3, e3) = e2
% 229.78/41.16    (8)   ~ (e2 = e0)
% 229.78/41.16    (9)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.78/41.16         (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.78/41.16    (10)   ~ (e1 = e0)
% 229.78/41.16    (11)   ~ (all_53_12 = e3)
% 229.78/41.16    (12)  op(e3, e0) = all_53_12
% 229.78/41.16  
% 229.78/41.16  Begin of proof
% 229.78/41.16  | 
% 229.78/41.16  | BETA: splitting (4) gives:
% 229.78/41.16  | 
% 229.78/41.16  | Case 1:
% 229.78/41.16  | | 
% 229.78/41.16  | |   (13)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) =
% 229.78/41.16  | |           e0)
% 229.78/41.16  | | 
% 229.78/41.16  | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (9), (11), (12), (13) are
% 229.78/41.16  | |            inconsistent by sub-proof #874.
% 229.78/41.16  | | 
% 229.78/41.16  | Case 2:
% 229.78/41.16  | | 
% 229.78/41.16  | |   (14)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) =
% 229.78/41.16  | |           e0)
% 229.78/41.16  | | 
% 229.78/41.16  | | BETA: splitting (14) gives:
% 229.78/41.16  | | 
% 229.78/41.16  | | Case 1:
% 229.78/41.16  | | | 
% 229.78/41.16  | | |   (15)  all_57_4 = e0 & op(e3, e1) = e0
% 229.78/41.16  | | | 
% 229.78/41.16  | | | REF_CLOSE: (2), (8), (15) are inconsistent by sub-proof #2045.
% 229.78/41.16  | | | 
% 229.78/41.16  | | Case 2:
% 229.78/41.16  | | | 
% 229.78/41.16  | | |   (16)  all_57_9 = e0 & op(e3, e0) = e0
% 229.78/41.16  | | | 
% 229.78/41.16  | | | REF_CLOSE: (3), (10), (16) are inconsistent by sub-proof #1990.
% 229.78/41.16  | | | 
% 229.78/41.16  | | End of split
% 229.78/41.16  | | 
% 229.78/41.16  | End of split
% 229.78/41.16  | 
% 229.78/41.16  End of proof
% 229.78/41.16  
% 229.78/41.16  Sub-proof #874 shows that the following formulas are inconsistent:
% 229.78/41.16  ----------------------------------------------------------------
% 229.78/41.16    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.78/41.16           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.78/41.16    (2)  all_57_4 = e2
% 229.78/41.16    (3)   ~ (e3 = e2)
% 229.78/41.16    (4)   ~ (e3 = e0)
% 229.78/41.16    (5)  op(e3, e3) = e2
% 229.78/41.16    (6)   ~ (e2 = e0)
% 229.78/41.16    (7)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.78/41.16         (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.78/41.16    (8)   ~ (all_53_12 = e3)
% 229.78/41.16    (9)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0)
% 229.78/41.16    (10)  op(e3, e0) = all_53_12
% 229.78/41.16  
% 229.78/41.16  Begin of proof
% 229.78/41.16  | 
% 229.78/41.16  | BETA: splitting (9) gives:
% 229.78/41.16  | 
% 229.78/41.16  | Case 1:
% 229.78/41.16  | | 
% 229.78/41.16  | |   (11)  all_57_0 = e0 & op(e3, e3) = e0
% 229.78/41.16  | | 
% 229.78/41.16  | | ALPHA: (11) implies:
% 229.78/41.16  | |   (12)  op(e3, e3) = e0
% 229.78/41.16  | | 
% 229.78/41.16  | | REF_CLOSE: (1), (5), (6), (12) are inconsistent by sub-proof #2403.
% 229.78/41.16  | | 
% 229.78/41.16  | Case 2:
% 229.78/41.16  | | 
% 229.78/41.16  | |   (13)  all_57_1 = e0 & op(e3, e2) = e0
% 229.78/41.16  | | 
% 229.78/41.16  | | ALPHA: (13) implies:
% 229.78/41.16  | |   (14)  all_57_1 = e0
% 229.78/41.16  | | 
% 229.78/41.16  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (10), (14) are inconsistent by
% 229.78/41.16  | |            sub-proof #875.
% 229.78/41.16  | | 
% 229.78/41.16  | End of split
% 229.78/41.16  | 
% 229.78/41.16  End of proof
% 229.78/41.16  
% 229.78/41.16  Sub-proof #875 shows that the following formulas are inconsistent:
% 229.78/41.16  ----------------------------------------------------------------
% 229.78/41.16    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.78/41.16           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.78/41.16    (2)  all_57_4 = e2
% 229.78/41.16    (3)   ~ (e3 = e2)
% 229.78/41.16    (4)   ~ (e3 = e0)
% 229.78/41.16    (5)  all_57_1 = e0
% 229.78/41.16    (6)  op(e3, e3) = e2
% 229.78/41.16    (7)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.78/41.16         (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.78/41.16    (8)   ~ (all_53_12 = e3)
% 229.78/41.16    (9)  op(e3, e0) = all_53_12
% 229.78/41.16  
% 229.78/41.16  Begin of proof
% 229.78/41.16  | 
% 229.78/41.16  | BETA: splitting (7) gives:
% 229.78/41.16  | 
% 229.78/41.16  | Case 1:
% 229.78/41.16  | | 
% 229.78/41.16  | |   (10)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) =
% 229.78/41.16  | |           e3)
% 229.78/41.16  | | 
% 229.78/41.16  | | REF_CLOSE: (1), (3), (4), (5), (6), (10) are inconsistent by sub-proof
% 229.78/41.16  | |            #1610.
% 229.78/41.16  | | 
% 229.78/41.16  | Case 2:
% 229.78/41.16  | | 
% 229.78/41.16  | |   (11)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) =
% 229.78/41.16  | |           e3)
% 229.78/41.16  | | 
% 229.78/41.16  | | REF_CLOSE: (1), (2), (3), (8), (9), (11) are inconsistent by sub-proof #876.
% 229.78/41.16  | | 
% 229.78/41.16  | End of split
% 229.78/41.16  | 
% 229.78/41.16  End of proof
% 229.78/41.16  
% 229.78/41.16  Sub-proof #876 shows that the following formulas are inconsistent:
% 229.78/41.16  ----------------------------------------------------------------
% 229.78/41.16    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.78/41.16           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.78/41.16    (2)  all_57_4 = e2
% 229.78/41.16    (3)   ~ (e3 = e2)
% 229.78/41.16    (4)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.78/41.16    (5)   ~ (all_53_12 = e3)
% 229.78/41.16    (6)  op(e3, e0) = all_53_12
% 229.78/41.16  
% 229.78/41.16  Begin of proof
% 229.78/41.16  | 
% 229.78/41.16  | BETA: splitting (4) gives:
% 229.78/41.16  | 
% 229.78/41.16  | Case 1:
% 229.78/41.16  | | 
% 229.78/41.16  | |   (7)  all_57_4 = e3 & op(e3, e1) = e3
% 229.78/41.16  | | 
% 229.78/41.16  | | REF_CLOSE: (2), (3), (7) are inconsistent by sub-proof #877.
% 229.78/41.16  | | 
% 229.78/41.16  | Case 2:
% 229.78/41.16  | | 
% 229.78/41.16  | |   (8)  all_57_9 = e3 & op(e3, e0) = e3
% 229.78/41.16  | | 
% 229.78/41.16  | | ALPHA: (8) implies:
% 229.78/41.16  | |   (9)  op(e3, e0) = e3
% 229.78/41.16  | | 
% 229.78/41.16  | | REF_CLOSE: (1), (5), (6), (9) are inconsistent by sub-proof #2458.
% 229.78/41.16  | | 
% 229.78/41.16  | End of split
% 229.78/41.16  | 
% 229.78/41.16  End of proof
% 229.78/41.16  
% 229.78/41.16  Sub-proof #877 shows that the following formulas are inconsistent:
% 229.78/41.16  ----------------------------------------------------------------
% 229.78/41.16    (1)  all_57_4 = e3 & op(e3, e1) = e3
% 229.78/41.16    (2)  all_57_4 = e2
% 229.78/41.16    (3)   ~ (e3 = e2)
% 229.78/41.16  
% 229.78/41.16  Begin of proof
% 229.78/41.16  | 
% 229.78/41.16  | ALPHA: (1) implies:
% 229.78/41.16  |   (4)  all_57_4 = e3
% 229.78/41.16  | 
% 229.78/41.16  | COMBINE_EQS: (2), (4) imply:
% 229.78/41.16  |   (5)  e3 = e2
% 229.78/41.16  | 
% 229.78/41.16  | REDUCE: (3), (5) imply:
% 229.78/41.16  |   (6)  $false
% 229.78/41.16  | 
% 229.78/41.16  | CLOSE: (6) is inconsistent.
% 229.78/41.16  | 
% 229.78/41.16  End of proof
% 229.78/41.16  
% 229.78/41.16  Sub-proof #878 shows that the following formulas are inconsistent:
% 229.78/41.16  ----------------------------------------------------------------
% 229.78/41.16    (1)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.78/41.16         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.78/41.16    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.78/41.16         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.78/41.16    (3)   ~ (e3 = e1)
% 229.78/41.16    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.78/41.16           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.78/41.16    (5)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.78/41.16         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.78/41.16    (6)   ~ (all_6_2 = e3)
% 229.78/41.16    (7)  op(e1, e1) = all_6_2
% 229.78/41.16    (8)   ~ (e3 = e2)
% 229.78/41.16    (9)   ~ (e3 = e0)
% 229.78/41.16    (10)  all_57_15 = e3
% 229.78/41.16    (11)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.78/41.16          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.78/41.16    (12)   ~ (e2 = e0)
% 229.78/41.16    (13)  op(e2, e2) = e2
% 229.78/41.16    (14)   ~ (e1 = e0)
% 229.78/41.16    (15)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.78/41.16              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.78/41.16                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.78/41.16                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.78/41.16    (16)  all_57_1 = e3
% 229.78/41.16    (17)   ~ (e2 = e1)
% 229.78/41.16    (18)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.78/41.16          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.78/41.16    (19)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.78/41.16          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.78/41.16    (20)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.78/41.16          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.78/41.16    (21)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.78/41.16          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.78/41.16    (22)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.78/41.16          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.78/41.16    (23)  all_57_0 = e3 & op(e3, e3) = e3
% 229.78/41.16  
% 229.78/41.16  Begin of proof
% 229.78/41.16  | 
% 229.78/41.16  | ALPHA: (23) implies:
% 229.78/41.16  |   (24)  all_57_0 = e3
% 229.78/41.16  | 
% 229.78/41.16  | BETA: splitting (5) gives:
% 229.78/41.16  | 
% 229.78/41.16  | Case 1:
% 229.78/41.16  | | 
% 229.78/41.16  | |   (25)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 229.78/41.16  | |           e3)
% 229.78/41.16  | | 
% 229.78/41.16  | | BETA: splitting (25) gives:
% 229.78/41.16  | | 
% 229.78/41.16  | | Case 1:
% 229.78/41.16  | | | 
% 229.78/41.16  | | |   (26)  all_57_6 = e3 & op(e1, e3) = e3
% 229.78/41.16  | | | 
% 229.78/41.16  | | | ALPHA: (26) implies:
% 229.78/41.16  | | |   (27)  all_57_6 = e3
% 229.78/41.16  | | | 
% 229.78/41.16  | | | REF_CLOSE: (1), (3), (8), (9), (12), (14), (17), (19), (20), (24), (27)
% 229.78/41.16  | | |            are inconsistent by sub-proof #2010.
% 229.78/41.16  | | | 
% 229.78/41.16  | | Case 2:
% 229.78/41.16  | | | 
% 229.78/41.16  | | |   (28)  all_57_7 = e3 & op(e1, e2) = e3
% 229.78/41.16  | | | 
% 229.78/41.16  | | | ALPHA: (28) implies:
% 229.78/41.16  | | |   (29)  all_57_7 = e3
% 229.78/41.16  | | | 
% 229.78/41.16  | | | REF_CLOSE: (2), (3), (4), (8), (9), (11), (12), (13), (14), (16), (17),
% 229.78/41.16  | | |            (22), (29) are inconsistent by sub-proof #1167.
% 229.78/41.16  | | | 
% 229.78/41.16  | | End of split
% 229.78/41.16  | | 
% 229.78/41.16  | Case 2:
% 229.78/41.16  | | 
% 229.78/41.16  | |   (30)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 229.78/41.16  | |           e3)
% 229.78/41.16  | | 
% 229.78/41.16  | | REF_CLOSE: (3), (4), (6), (7), (8), (9), (10), (12), (14), (15), (17), (18),
% 229.78/41.16  | |            (21), (30) are inconsistent by sub-proof #1786.
% 229.78/41.16  | | 
% 229.78/41.16  | End of split
% 229.78/41.16  | 
% 229.78/41.16  End of proof
% 229.78/41.16  
% 229.78/41.16  Sub-proof #879 shows that the following formulas are inconsistent:
% 229.78/41.16  ----------------------------------------------------------------
% 229.78/41.16    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.78/41.16         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.78/41.16    (2)   ~ (e3 = e1)
% 229.78/41.16    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.78/41.16           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.78/41.16    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.78/41.16         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.78/41.16    (5)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.78/41.16         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.78/41.16    (6)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.78/41.16         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.78/41.16    (7)   ~ (e3 = e2)
% 229.78/41.16    (8)   ~ (e3 = e0)
% 229.78/41.16    (9)  all_57_0 = e0
% 229.78/41.16    (10)  all_57_15 = e3
% 229.78/41.16    (11)  op(e3, e3) = e0
% 229.78/41.16    (12)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.78/41.16          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.78/41.16            e1)
% 229.78/41.16    (13)   ~ (e2 = e0)
% 229.78/41.16    (14)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.78/41.16          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.78/41.16    (15)  op(e2, e2) = e2
% 229.78/41.16    (16)   ~ (e1 = e0)
% 229.78/41.16    (17)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.78/41.16          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.78/41.16    (18)  op(e0, e0) = e3
% 229.78/41.16    (19)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0)
% 229.78/41.16    (20)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.78/41.16          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.78/41.16            e2)
% 229.78/41.16    (21)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.78/41.16              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.78/41.16                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.78/41.16                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.78/41.16    (22)   ~ (all_53_12 = e3)
% 229.78/41.16    (23)   ~ (all_53_12 = e0)
% 229.78/41.16    (24)   ~ (e2 = e1)
% 229.78/41.16    (25)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.78/41.16          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.78/41.16    (26)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.78/41.16          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.78/41.16    (27)  all_57_3 = e2
% 229.78/41.16    (28)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.78/41.16          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.78/41.16    (29)  op(e3, e0) = all_53_12
% 229.78/41.16  
% 229.78/41.16  Begin of proof
% 229.78/41.16  | 
% 229.78/41.16  | BETA: splitting (19) gives:
% 229.78/41.16  | 
% 229.78/41.16  | Case 1:
% 229.78/41.16  | | 
% 229.78/41.16  | |   (30)  all_57_1 = e0 & op(e3, e2) = e0
% 229.78/41.16  | | 
% 229.78/41.16  | | ALPHA: (30) implies:
% 229.78/41.16  | |   (31)  all_57_1 = e0
% 229.78/41.16  | | 
% 229.78/41.16  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 229.78/41.16  | |            (13), (14), (16), (17), (18), (20), (21), (22), (23), (24), (25),
% 229.78/41.16  | |            (26), (27), (28), (29), (31) are inconsistent by sub-proof #882.
% 229.78/41.16  | | 
% 229.78/41.16  | Case 2:
% 229.78/41.16  | | 
% 229.78/41.16  | |   (32)  all_57_3 = e0 & op(e2, e2) = e0
% 229.78/41.16  | | 
% 229.78/41.16  | | ALPHA: (32) implies:
% 229.78/41.16  | |   (33)  op(e2, e2) = e0
% 229.78/41.16  | | 
% 229.78/41.16  | | REF_CLOSE: (3), (13), (15), (33) are inconsistent by sub-proof #2472.
% 229.78/41.16  | | 
% 229.78/41.16  | End of split
% 229.78/41.16  | 
% 229.78/41.16  End of proof
% 229.78/41.16  
% 229.78/41.16  Sub-proof #880 shows that the following formulas are inconsistent:
% 229.78/41.16  ----------------------------------------------------------------
% 229.78/41.16    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.78/41.16         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.78/41.16    (2)   ~ (e3 = e1)
% 229.78/41.16    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.78/41.16           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.78/41.16    (4)   ~ (all_6_2 = e3)
% 229.78/41.16    (5)  op(e1, e1) = all_6_2
% 229.78/41.16    (6)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.78/41.16         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.78/41.16    (7)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.78/41.16         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.78/41.16    (8)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.78/41.16         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.78/41.16    (9)   ~ (e3 = e2)
% 229.78/41.16    (10)   ~ (e3 = e0)
% 229.78/41.16    (11)  all_57_0 = e0
% 229.78/41.16    (12)  all_57_15 = e3
% 229.78/41.16    (13)  op(e3, e3) = e0
% 229.78/41.16    (14)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.78/41.16          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.78/41.16            e1)
% 229.78/41.16    (15)   ~ (e2 = e0)
% 229.78/41.17    (16)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.78/41.17          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.78/41.17    (17)   ~ (e1 = e0)
% 229.78/41.17    (18)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.78/41.17          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.78/41.17    (19)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.78/41.17          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.78/41.17    (20)  op(e0, e0) = e3
% 229.78/41.17    (21)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.78/41.17          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.78/41.17            e2)
% 229.78/41.17    (22)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.78/41.17              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.78/41.17                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.78/41.17                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.78/41.17    (23)   ~ (all_53_12 = e3)
% 229.78/41.17    (24)  all_57_1 = e3
% 229.78/41.17    (25)   ~ (all_53_12 = e0)
% 229.78/41.17    (26)   ~ (e2 = e1)
% 229.78/41.17    (27)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.78/41.17          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.78/41.17    (28)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.78/41.17          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.78/41.17    (29)  all_57_3 = e2
% 229.78/41.17    (30)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.78/41.17          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.78/41.17    (31)  all_57_5 = e0
% 229.78/41.17    (32)  op(e3, e0) = all_53_12
% 229.78/41.17  
% 229.78/41.17  Begin of proof
% 229.78/41.17  | 
% 229.78/41.17  | BETA: splitting (18) gives:
% 229.78/41.17  | 
% 229.78/41.17  | Case 1:
% 229.78/41.17  | | 
% 229.78/41.17  | |   (33)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) =
% 229.78/41.17  | |           e3)
% 229.78/41.17  | | 
% 229.78/41.17  | | BETA: splitting (33) gives:
% 229.78/41.17  | | 
% 229.78/41.17  | | Case 1:
% 229.78/41.17  | | | 
% 229.78/41.17  | | |   (34)  all_57_4 = e3 & op(e3, e1) = e3
% 229.78/41.17  | | | 
% 229.78/41.17  | | | ALPHA: (34) implies:
% 229.78/41.17  | | |   (35)  all_57_4 = e3
% 229.78/41.17  | | | 
% 229.78/41.17  | | | REF_CLOSE: (2), (3), (6), (7), (8), (9), (10), (13), (15), (17), (24),
% 229.78/41.17  | | |            (26), (35) are inconsistent by sub-proof #1220.
% 229.78/41.17  | | | 
% 229.78/41.17  | | Case 2:
% 229.78/41.17  | | | 
% 229.78/41.17  | | |   (36)  all_57_5 = e3 & op(e2, e1) = e3
% 229.78/41.17  | | | 
% 229.78/41.17  | | | ALPHA: (36) implies:
% 229.78/41.17  | | |   (37)  all_57_5 = e3
% 229.78/41.17  | | | 
% 229.78/41.17  | | | COMBINE_EQS: (31), (37) imply:
% 229.78/41.17  | | |   (38)  e3 = e0
% 229.78/41.17  | | | 
% 229.78/41.17  | | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (9), (10), (11), (12), (13),
% 229.78/41.17  | | |            (14), (15), (16), (17), (19), (20), (21), (22), (23), (24),
% 229.78/41.17  | | |            (25), (26), (27), (28), (29), (30), (32), (38) are inconsistent
% 229.78/41.17  | | |            by sub-proof #881.
% 229.78/41.17  | | | 
% 229.78/41.17  | | End of split
% 229.78/41.17  | | 
% 229.78/41.17  | Case 2:
% 229.78/41.17  | | 
% 229.78/41.17  | |   (39)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) =
% 229.78/41.17  | |           e3)
% 229.78/41.17  | | 
% 229.78/41.17  | | REF_CLOSE: (2), (3), (4), (5), (9), (10), (12), (14), (15), (17), (21),
% 229.78/41.17  | |            (22), (26), (39) are inconsistent by sub-proof #1794.
% 229.78/41.17  | | 
% 229.78/41.17  | End of split
% 229.78/41.17  | 
% 229.78/41.17  End of proof
% 229.78/41.17  
% 229.78/41.17  Sub-proof #881 shows that the following formulas are inconsistent:
% 229.78/41.17  ----------------------------------------------------------------
% 229.78/41.17    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.78/41.17         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.78/41.17    (2)   ~ (e3 = e1)
% 229.78/41.17    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.78/41.17           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.78/41.17    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.78/41.17         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.78/41.17    (5)  e3 = e0
% 229.78/41.17    (6)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.78/41.17         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.78/41.17    (7)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.78/41.17         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.78/41.17    (8)   ~ (e3 = e2)
% 229.78/41.17    (9)   ~ (e3 = e0)
% 229.78/41.17    (10)  all_57_0 = e0
% 229.78/41.17    (11)  all_57_15 = e3
% 229.78/41.17    (12)  op(e3, e3) = e0
% 229.78/41.17    (13)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.78/41.17          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.78/41.17            e1)
% 229.78/41.17    (14)   ~ (e2 = e0)
% 229.78/41.17    (15)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.78/41.17          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.78/41.17    (16)   ~ (e1 = e0)
% 229.78/41.17    (17)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.78/41.17          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.78/41.17    (18)  op(e0, e0) = e3
% 229.78/41.17    (19)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.78/41.17          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.78/41.17            e2)
% 229.78/41.17    (20)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.78/41.17              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.78/41.17                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.78/41.17                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.78/41.17    (21)   ~ (all_53_12 = e3)
% 229.78/41.17    (22)  all_57_1 = e3
% 229.78/41.17    (23)   ~ (all_53_12 = e0)
% 229.78/41.17    (24)   ~ (e2 = e1)
% 229.78/41.17    (25)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.78/41.17          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.78/41.17    (26)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.78/41.17          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.78/41.17    (27)  all_57_3 = e2
% 229.78/41.17    (28)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.78/41.17          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.78/41.17    (29)  op(e3, e0) = all_53_12
% 229.78/41.17  
% 229.78/41.17  Begin of proof
% 229.78/41.17  | 
% 229.78/41.17  | SIMP: (5) implies:
% 229.78/41.17  |   (30)  e3 = e0
% 229.78/41.17  | 
% 229.78/41.17  | COMBINE_EQS: (22), (30) imply:
% 229.78/41.17  |   (31)  all_57_1 = e0
% 229.78/41.17  | 
% 229.78/41.17  | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13),
% 229.78/41.17  |            (14), (15), (16), (17), (18), (19), (20), (21), (23), (24), (25),
% 229.78/41.17  |            (26), (27), (28), (29), (31) are inconsistent by sub-proof #882.
% 229.78/41.17  | 
% 229.78/41.17  End of proof
% 229.78/41.17  
% 229.78/41.17  Sub-proof #882 shows that the following formulas are inconsistent:
% 229.78/41.17  ----------------------------------------------------------------
% 229.78/41.17    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.78/41.17         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.78/41.17    (2)   ~ (e3 = e1)
% 229.78/41.17    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.78/41.17           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.78/41.17    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.78/41.17         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.78/41.17    (5)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.78/41.17         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.78/41.17    (6)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.78/41.17         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.78/41.17    (7)   ~ (e3 = e2)
% 229.78/41.17    (8)   ~ (e3 = e0)
% 229.78/41.17    (9)  all_57_1 = e0
% 229.78/41.17    (10)  all_57_0 = e0
% 229.78/41.17    (11)  all_57_15 = e3
% 229.78/41.17    (12)  op(e3, e3) = e0
% 229.78/41.17    (13)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.78/41.17          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.78/41.17            e1)
% 229.78/41.17    (14)   ~ (e2 = e0)
% 229.78/41.17    (15)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.78/41.17          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.78/41.17    (16)   ~ (e1 = e0)
% 229.78/41.17    (17)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.78/41.17          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.78/41.17    (18)  op(e0, e0) = e3
% 229.78/41.17    (19)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.78/41.17          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.78/41.17            e2)
% 229.78/41.17    (20)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.78/41.17              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.78/41.17                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.78/41.17                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.78/41.17    (21)   ~ (all_53_12 = e3)
% 229.78/41.17    (22)   ~ (all_53_12 = e0)
% 229.78/41.17    (23)   ~ (e2 = e1)
% 229.78/41.17    (24)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.78/41.17          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.78/41.17    (25)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.78/41.17          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.78/41.17    (26)  all_57_3 = e2
% 229.78/41.17    (27)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.78/41.17          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.78/41.17    (28)  op(e3, e0) = all_53_12
% 229.78/41.17  
% 229.78/41.17  Begin of proof
% 229.78/41.17  | 
% 229.78/41.17  | BETA: splitting (20) gives:
% 229.78/41.17  | 
% 229.78/41.17  | Case 1:
% 229.78/41.17  | | 
% 229.78/41.17  | |   (29)  all_57_15 = e0 & op(e0, e0) = e0
% 229.78/41.17  | | 
% 229.78/41.17  | | ALPHA: (29) implies:
% 229.78/41.17  | |   (30)  op(e0, e0) = e0
% 229.78/41.17  | | 
% 229.78/41.17  | | REF_CLOSE: (3), (8), (18), (30) are inconsistent by sub-proof #2304.
% 229.78/41.17  | | 
% 229.78/41.17  | Case 2:
% 229.78/41.17  | | 
% 229.78/41.17  | |   (31)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 229.78/41.17  | |             e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0 &
% 229.78/41.17  | |             op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 229.78/41.17  | |           (all_57_14 = e0 & op(e0, e1) = e0))
% 229.78/41.17  | | 
% 229.78/41.17  | | ALPHA: (31) implies:
% 229.78/41.17  | |   (32)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 229.78/41.17  | |           e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.78/41.17  | |   (33)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 229.78/41.17  | |           e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 229.78/41.17  | | 
% 229.78/41.17  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 229.78/41.17  | |            (13), (14), (15), (16), (17), (18), (19), (21), (22), (23), (24),
% 229.78/41.17  | |            (25), (26), (27), (28), (32), (33) are inconsistent by sub-proof
% 229.78/41.17  | |            #890.
% 229.78/41.17  | | 
% 229.78/41.17  | End of split
% 229.78/41.17  | 
% 229.78/41.17  End of proof
% 229.78/41.17  
% 229.78/41.17  Sub-proof #883 shows that the following formulas are inconsistent:
% 229.78/41.17  ----------------------------------------------------------------
% 229.78/41.17    (1)  op(e0, e2) = e0
% 229.78/41.17    (2)   ~ (all_53_6 = e2)
% 229.78/41.17    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.78/41.17           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.78/41.17    (4)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 229.78/41.17    (5)  all_55_9 = all_53_6
% 229.78/41.17    (6)   ~ (all_53_6 = all_53_7)
% 229.78/41.17    (7)   ~ (all_53_6 = e1)
% 229.78/41.17    (8)  op(e0, e2) = all_53_7
% 229.78/41.17    (9)   ~ (all_53_6 = e3)
% 229.78/41.17  
% 229.78/41.17  Begin of proof
% 229.78/41.17  | 
% 229.78/41.17  | BETA: splitting (4) gives:
% 229.78/41.17  | 
% 229.78/41.17  | Case 1:
% 229.78/41.17  | | 
% 229.78/41.17  | |   (10)  all_55_9 = e3
% 229.78/41.17  | | 
% 229.78/41.17  | | REF_CLOSE: (5), (9), (10) are inconsistent by sub-proof #2159.
% 229.78/41.17  | | 
% 229.78/41.17  | Case 2:
% 229.78/41.17  | | 
% 229.78/41.17  | |   (11)  all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 229.78/41.17  | | 
% 229.78/41.17  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (11) are inconsistent by
% 229.78/41.17  | |            sub-proof #2077.
% 229.78/41.17  | | 
% 229.78/41.17  | End of split
% 229.78/41.17  | 
% 229.78/41.17  End of proof
% 229.78/41.17  
% 229.78/41.17  Sub-proof #884 shows that the following formulas are inconsistent:
% 229.78/41.17  ----------------------------------------------------------------
% 229.78/41.17    (1)  ( ~ (all_48_0 = e2) & op(all_48_1, e3) = all_48_0 & op(e3, e0) = all_48_1
% 229.78/41.17           & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 = e1) & op(e3, e0) =
% 229.78/41.17           all_48_1 & $i(all_48_1))
% 229.78/41.17    (2)   ~ (all_53_2 = e1)
% 229.78/41.17    (3)   ~ (all_53_6 = all_53_14)
% 229.78/41.17    (4)   ~ (all_53_6 = e2)
% 229.78/41.17    (5)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.78/41.17         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.78/41.17    (6)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.78/41.17         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.78/41.17    (7)   ~ (all_53_8 = all_53_12)
% 229.78/41.17    (8)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.78/41.17         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.78/41.17    (9)   ~ (e3 = e1)
% 229.78/41.17    (10)  all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 229.78/41.17    (11)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 229.78/41.17          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 229.78/41.17    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.78/41.17            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.78/41.17    (13)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.78/41.17          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.78/41.17    (14)   ~ (all_6_2 = e3)
% 229.78/41.17    (15)  ( ~ (all_18_0 = e1) & op(all_18_1, e3) = all_18_0 & op(e3, e0) =
% 229.78/41.17            all_18_1 & $i(all_18_0) & $i(all_18_1)) | ( ~ (all_18_1 = e2) & op(e3,
% 229.78/41.17              e0) = all_18_1 & $i(all_18_1))
% 229.78/41.17    (16)  op(e1, e1) = all_6_2
% 229.78/41.17    (17)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 229.78/41.17    (18)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.78/41.17          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.78/41.17    (19)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 229.78/41.17    (20)  all_55_9 = all_53_6
% 229.78/41.17    (21)   ~ (all_53_8 = e1)
% 229.78/41.17    (22)   ~ (all_53_13 = e2)
% 229.78/41.17    (23)  all_57_9 = e1
% 229.78/41.17    (24)   ~ (all_53_8 = e3)
% 229.78/41.17    (25)   ~ (all_53_13 = e3)
% 229.78/41.17    (26)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.78/41.17          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.78/41.17    (27)  all_55_4 = all_53_1
% 229.78/41.17    (28)   ~ (all_53_12 = all_53_13)
% 229.78/41.17    (29)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.78/41.17          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.78/41.17    (30)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 229.78/41.17          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.78/41.17    (31)  all_55_7 = e3 | all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 229.78/41.17    (32)   ~ (e3 = e0)
% 229.78/41.17    (33)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 229.78/41.17          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 229.78/41.17    (34)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 229.78/41.17    (35)  op(e0, e3) = all_53_3
% 229.78/41.17    (36)  all_57_0 = e0
% 229.78/41.17    (37)  all_55_2 = all_53_8
% 229.78/41.17    (38)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 229.78/41.17    (39)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 229.78/41.17    (40)  all_57_15 = e3
% 229.78/41.17    (41)  op(e3, e3) = e0
% 229.78/41.17    (42)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.78/41.17          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.78/41.17            e1)
% 229.78/41.17    (43)   ~ (all_53_14 = e3)
% 229.78/41.17    (44)   ~ (all_53_1 = all_53_2)
% 229.78/41.17    (45)  op(e1, e1) = e1
% 229.78/41.17    (46)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.78/41.17          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.78/41.17    (47)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 229.78/41.17            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 229.78/41.17            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 229.78/41.17            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 229.78/41.17              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 229.78/41.17            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 229.78/41.17            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 229.78/41.17              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 229.78/41.17              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 229.78/41.17            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 229.78/41.17            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 229.78/41.17            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 229.78/41.17              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 229.78/41.17              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 229.78/41.17            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 229.78/41.17              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 229.78/41.17            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 229.78/41.17            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 229.78/41.17              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 229.78/41.17              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 229.78/41.17            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 229.78/41.17            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 229.78/41.17    (48)   ~ (all_53_6 = e1)
% 229.78/41.17    (49)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.78/41.17          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.78/41.17    (50)   ~ (all_53_1 = e0)
% 229.78/41.17    (51)   ~ (all_53_2 = all_53_14)
% 229.78/41.17    (52)  op(e2, e2) = e2
% 229.78/41.17    (53)   ~ (e1 = e0)
% 229.78/41.17    (54)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.78/41.17          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.78/41.17    (55)  all_57_6 = e3
% 229.78/41.17    (56)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.78/41.17          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.78/41.17    (57)  all_55_8 = all_53_2
% 229.78/41.17    (58)  op(e0, e0) = e3
% 229.78/41.17    (59)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.78/41.17          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.78/41.17            e2)
% 229.78/41.17    (60)   ~ (all_53_3 = e0)
% 229.78/41.17    (61)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.78/41.17              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.78/41.17                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.78/41.17                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.78/41.17    (62)  op(e2, e0) = all_53_13
% 229.78/41.17    (63)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.78/41.17          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.78/41.17    (64)  all_55_11 = all_53_14
% 229.78/41.17    (65)  all_55_3 = all_53_12
% 229.78/41.17    (66)   ~ (all_53_12 = e3)
% 229.78/41.17    (67)  op(e1, e3) = all_53_2
% 229.78/41.18    (68)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.78/41.18          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.78/41.18    (69)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.78/41.18          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.78/41.18    (70)  all_57_1 = e3
% 229.78/41.18    (71)   ~ (all_53_12 = e0)
% 229.78/41.18    (72)   ~ (all_53_8 = e0)
% 229.78/41.18    (73)   ~ (all_53_1 = e2)
% 229.78/41.18    (74)   ~ (all_53_6 = e3)
% 229.78/41.18    (75)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.78/41.18          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 229.78/41.18    (76)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.78/41.18          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.78/41.18    (77)   ~ (all_53_2 = all_53_6)
% 229.78/41.18    (78)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.78/41.18          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.78/41.18    (79)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 229.78/41.18          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 229.78/41.18    (80)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.78/41.18          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.78/41.18    (81)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.78/41.18          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.78/41.18    (82)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 229.78/41.18          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 229.78/41.18    (83)   ~ (all_53_12 = all_53_14)
% 229.78/41.18    (84)  all_57_3 = e2
% 229.78/41.18    (85)  all_55_7 = all_53_13
% 229.78/41.18    (86)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.78/41.18          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.78/41.18    (87)  all_57_7 = e0
% 229.78/41.18    (88)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 229.78/41.18          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 229.78/41.18    (89)  op(e3, e0) = all_53_12
% 229.78/41.18  
% 229.78/41.18  Begin of proof
% 229.78/41.18  | 
% 229.78/41.18  | BETA: splitting (39) gives:
% 229.78/41.18  | 
% 229.78/41.18  | Case 1:
% 229.78/41.18  | | 
% 229.78/41.18  | |   (90)  all_55_2 = e3
% 229.78/41.18  | | 
% 229.78/41.18  | | REF_CLOSE: (24), (37), (90) are inconsistent by sub-proof #2028.
% 229.78/41.18  | | 
% 229.78/41.18  | Case 2:
% 229.78/41.18  | | 
% 229.78/41.18  | |   (91)   ~ (all_55_2 = e3)
% 229.78/41.18  | |   (92)  all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 229.78/41.18  | | 
% 229.78/41.18  | | BETA: splitting (92) gives:
% 229.78/41.18  | | 
% 229.78/41.18  | | Case 1:
% 229.78/41.18  | | | 
% 229.78/41.18  | | |   (93)  all_55_2 = e2
% 229.78/41.18  | | | 
% 229.78/41.18  | | | COMBINE_EQS: (37), (93) imply:
% 229.78/41.18  | | |   (94)  all_53_8 = e2
% 229.78/41.18  | | | 
% 229.78/41.18  | | | SIMP: (94) implies:
% 229.78/41.18  | | |   (95)  all_53_8 = e2
% 229.78/41.18  | | | 
% 229.78/41.18  | | | REDUCE: (7), (95) imply:
% 229.78/41.18  | | |   (96)   ~ (all_53_12 = e2)
% 229.78/41.18  | | | 
% 229.78/41.18  | | | SIMP: (96) implies:
% 229.78/41.18  | | |   (97)   ~ (all_53_12 = e2)
% 229.78/41.18  | | | 
% 229.78/41.18  | | | REDUCE: (24), (95) imply:
% 229.78/41.18  | | |   (98)   ~ (e3 = e2)
% 229.78/41.18  | | | 
% 229.78/41.18  | | | SIMP: (98) implies:
% 229.78/41.18  | | |   (99)   ~ (e3 = e2)
% 229.78/41.18  | | | 
% 229.78/41.18  | | | REDUCE: (21), (95) imply:
% 229.78/41.18  | | |   (100)   ~ (e2 = e1)
% 229.78/41.18  | | | 
% 229.78/41.18  | | | REDUCE: (72), (95) imply:
% 229.78/41.18  | | |   (101)   ~ (e2 = e0)
% 229.78/41.18  | | | 
% 229.78/41.18  | | | BETA: splitting (19) gives:
% 229.78/41.18  | | | 
% 229.78/41.18  | | | Case 1:
% 229.78/41.18  | | | | 
% 229.78/41.18  | | | |   (102)  all_55_9 = e3
% 229.78/41.18  | | | | 
% 229.78/41.18  | | | | REF_CLOSE: (20), (74), (102) are inconsistent by sub-proof #2159.
% 229.78/41.18  | | | | 
% 229.78/41.18  | | | Case 2:
% 229.78/41.18  | | | | 
% 229.78/41.18  | | | |   (103)  all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 229.78/41.18  | | | | 
% 229.78/41.18  | | | | BETA: splitting (10) gives:
% 229.78/41.18  | | | | 
% 229.78/41.18  | | | | Case 1:
% 229.78/41.18  | | | | | 
% 229.78/41.18  | | | | |   (104)  all_55_3 = e2
% 229.78/41.18  | | | | | 
% 229.78/41.18  | | | | | REF_CLOSE: (65), (97), (104) are inconsistent by sub-proof #1612.
% 229.78/41.18  | | | | | 
% 229.78/41.18  | | | | Case 2:
% 229.78/41.18  | | | | | 
% 229.78/41.18  | | | | |   (105)  all_55_3 = e1 | all_55_3 = e0
% 229.78/41.18  | | | | | 
% 229.78/41.18  | | | | | BETA: splitting (30) gives:
% 229.78/41.18  | | | | | 
% 229.78/41.18  | | | | | Case 1:
% 229.78/41.18  | | | | | | 
% 229.78/41.18  | | | | | |   (106)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2,
% 229.78/41.18  | | | | | |              e1) = e0)
% 229.78/41.18  | | | | | | 
% 229.78/41.18  | | | | | | BETA: splitting (106) gives:
% 229.78/41.18  | | | | | | 
% 229.78/41.18  | | | | | | Case 1:
% 229.78/41.18  | | | | | | | 
% 229.78/41.18  | | | | | | |   (107)  all_57_4 = e0 & op(e3, e1) = e0
% 229.78/41.18  | | | | | | | 
% 229.78/41.18  | | | | | | | ALPHA: (107) implies:
% 229.78/41.18  | | | | | | |   (108)  all_57_4 = e0
% 229.78/41.18  | | | | | | | 
% 229.78/41.18  | | | | | | | REF_CLOSE: (12), (23), (26), (32), (41), (49), (66), (89), (99),
% 229.78/41.18  | | | | | | |            (100), (101), (108) are inconsistent by sub-proof
% 229.78/41.18  | | | | | | |            #1403.
% 229.78/41.18  | | | | | | | 
% 229.78/41.18  | | | | | | Case 2:
% 229.78/41.18  | | | | | | | 
% 229.78/41.18  | | | | | | |   (109)  all_57_5 = e0 & op(e2, e1) = e0
% 229.78/41.18  | | | | | | | 
% 229.78/41.18  | | | | | | | ALPHA: (109) implies:
% 229.78/41.18  | | | | | | |   (110)  all_57_5 = e0
% 229.78/41.18  | | | | | | | 
% 229.78/41.18  | | | | | | | REF_CLOSE: (6), (9), (12), (13), (14), (16), (18), (26), (29),
% 229.78/41.18  | | | | | | |            (32), (40), (42), (53), (54), (55), (59), (61), (63),
% 229.78/41.18  | | | | | | |            (70), (76), (78), (80), (81), (84), (87), (99), (100),
% 229.78/41.18  | | | | | | |            (101), (110) are inconsistent by sub-proof #948.
% 229.78/41.18  | | | | | | | 
% 229.78/41.18  | | | | | | End of split
% 229.78/41.18  | | | | | | 
% 229.78/41.18  | | | | | Case 2:
% 229.78/41.18  | | | | | | 
% 229.78/41.18  | | | | | |   (111)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 &
% 229.78/41.18  | | | | | |            op(e0, e1) = e0)
% 229.78/41.18  | | | | | | 
% 229.78/41.18  | | | | | | BETA: splitting (111) gives:
% 229.78/41.18  | | | | | | 
% 229.78/41.18  | | | | | | Case 1:
% 229.78/41.18  | | | | | | | 
% 229.78/41.18  | | | | | | |   (112)  all_57_8 = e0 & op(e1, e1) = e0
% 229.78/41.18  | | | | | | | 
% 229.78/41.18  | | | | | | | ALPHA: (112) implies:
% 229.78/41.18  | | | | | | |   (113)  op(e1, e1) = e0
% 229.78/41.18  | | | | | | | 
% 229.78/41.18  | | | | | | | REF_CLOSE: (5), (6), (8), (9), (11), (12), (13), (14), (16), (18),
% 229.78/41.18  | | | | | | |            (22), (26), (29), (30), (32), (33), (35), (36), (40),
% 229.78/41.18  | | | | | | |            (41), (42), (46), (49), (52), (53), (54), (56), (58),
% 229.78/41.18  | | | | | | |            (59), (60), (61), (62), (63), (66), (68), (69), (71),
% 229.78/41.18  | | | | | | |            (75), (76), (78), (79), (80), (81), (82), (84), (86),
% 229.78/41.18  | | | | | | |            (87), (88), (89), (99), (100), (101), (113) are
% 229.78/41.18  | | | | | | |            inconsistent by sub-proof #889.
% 229.78/41.18  | | | | | | | 
% 229.78/41.18  | | | | | | Case 2:
% 229.78/41.18  | | | | | | | 
% 229.78/41.18  | | | | | | |   (114)  all_57_14 = e0 & op(e0, e1) = e0
% 229.78/41.18  | | | | | | | 
% 229.78/41.18  | | | | | | | ALPHA: (114) implies:
% 229.78/41.18  | | | | | | |   (115)  op(e0, e1) = e0
% 229.78/41.18  | | | | | | | 
% 229.78/41.18  | | | | | | | BETA: splitting (105) gives:
% 229.78/41.18  | | | | | | | 
% 229.78/41.18  | | | | | | | Case 1:
% 229.78/41.18  | | | | | | | | 
% 229.78/41.18  | | | | | | | |   (116)  all_55_3 = e1
% 229.78/41.18  | | | | | | | | 
% 229.78/41.18  | | | | | | | | COMBINE_EQS: (65), (116) imply:
% 229.78/41.18  | | | | | | | |   (117)  all_53_12 = e1
% 229.78/41.18  | | | | | | | | 
% 229.78/41.18  | | | | | | | | SIMP: (117) implies:
% 229.78/41.18  | | | | | | | |   (118)  all_53_12 = e1
% 229.78/41.18  | | | | | | | | 
% 229.78/41.18  | | | | | | | | REDUCE: (28), (118) imply:
% 229.78/41.18  | | | | | | | |   (119)   ~ (all_53_13 = e1)
% 229.78/41.18  | | | | | | | | 
% 229.78/41.18  | | | | | | | | SIMP: (119) implies:
% 229.78/41.18  | | | | | | | |   (120)   ~ (all_53_13 = e1)
% 229.78/41.18  | | | | | | | | 
% 229.78/41.18  | | | | | | | | REDUCE: (83), (118) imply:
% 229.78/41.18  | | | | | | | |   (121)   ~ (all_53_14 = e1)
% 229.78/41.18  | | | | | | | | 
% 229.78/41.18  | | | | | | | | SIMP: (121) implies:
% 229.78/41.18  | | | | | | | |   (122)   ~ (all_53_14 = e1)
% 229.78/41.18  | | | | | | | | 
% 229.78/41.18  | | | | | | | | REDUCE: (89), (118) imply:
% 229.78/41.18  | | | | | | | |   (123)  op(e3, e0) = e1
% 229.78/41.18  | | | | | | | | 
% 229.78/41.18  | | | | | | | | BETA: splitting (31) gives:
% 229.78/41.18  | | | | | | | | 
% 229.78/41.18  | | | | | | | | Case 1:
% 229.78/41.18  | | | | | | | | | 
% 229.78/41.18  | | | | | | | | |   (124)  all_55_7 = e3
% 229.78/41.18  | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | REF_CLOSE: (25), (85), (124) are inconsistent by sub-proof
% 229.78/41.18  | | | | | | | | |            #2109.
% 229.78/41.18  | | | | | | | | | 
% 229.78/41.18  | | | | | | | | Case 2:
% 229.78/41.18  | | | | | | | | | 
% 229.78/41.18  | | | | | | | | |   (125)   ~ (all_55_7 = e3)
% 229.78/41.18  | | | | | | | | |   (126)  all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 229.78/41.18  | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | BETA: splitting (103) gives:
% 229.78/41.18  | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | Case 1:
% 229.78/41.18  | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | |   (127)  all_55_9 = e2
% 229.78/41.18  | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | REF_CLOSE: (4), (20), (127) are inconsistent by sub-proof
% 229.78/41.18  | | | | | | | | | |            #2274.
% 229.78/41.18  | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | Case 2:
% 229.78/41.18  | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | |   (128)  all_55_9 = e1 | all_55_9 = e0
% 229.78/41.18  | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | BETA: splitting (128) gives:
% 229.78/41.18  | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | Case 1:
% 229.78/41.18  | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | |   (129)  all_55_9 = e1
% 229.78/41.18  | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | REF_CLOSE: (20), (48), (129) are inconsistent by sub-proof
% 229.78/41.18  | | | | | | | | | | |            #2273.
% 229.78/41.18  | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | Case 2:
% 229.78/41.18  | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | |   (130)  all_55_9 = e0
% 229.78/41.18  | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | COMBINE_EQS: (20), (130) imply:
% 229.78/41.18  | | | | | | | | | | |   (131)  all_53_6 = e0
% 229.78/41.18  | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | SIMP: (131) implies:
% 229.78/41.18  | | | | | | | | | | |   (132)  all_53_6 = e0
% 229.78/41.18  | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | REDUCE: (77), (132) imply:
% 229.78/41.18  | | | | | | | | | | |   (133)   ~ (all_53_2 = e0)
% 229.78/41.18  | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | REDUCE: (3), (132) imply:
% 229.78/41.18  | | | | | | | | | | |   (134)   ~ (all_53_14 = e0)
% 229.78/41.18  | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | SIMP: (134) implies:
% 229.78/41.18  | | | | | | | | | | |   (135)   ~ (all_53_14 = e0)
% 229.78/41.18  | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | REDUCE: (48), (132) imply:
% 229.78/41.18  | | | | | | | | | | |   (136)   ~ (e1 = e0)
% 229.78/41.18  | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | BETA: splitting (17) gives:
% 229.78/41.18  | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | Case 1:
% 229.78/41.18  | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | |   (137)  all_55_11 = e3
% 229.78/41.18  | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | REF_CLOSE: (43), (64), (137) are inconsistent by sub-proof
% 229.78/41.18  | | | | | | | | | | | |            #2497.
% 229.78/41.18  | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | Case 2:
% 229.78/41.18  | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | |   (138)  all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 229.78/41.18  | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | BETA: splitting (126) gives:
% 229.78/41.18  | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | Case 1:
% 229.78/41.18  | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | |   (139)  all_55_7 = e2
% 229.78/41.18  | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | REF_CLOSE: (22), (85), (139) are inconsistent by sub-proof
% 229.78/41.18  | | | | | | | | | | | | |            #2171.
% 229.78/41.18  | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | Case 2:
% 229.78/41.18  | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | |   (140)  all_55_7 = e1 | all_55_7 = e0
% 229.78/41.18  | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | BETA: splitting (138) gives:
% 229.78/41.18  | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | Case 1:
% 229.78/41.18  | | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | |   (141)  all_55_11 = e2
% 229.78/41.18  | | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | | COMBINE_EQS: (64), (141) imply:
% 229.78/41.18  | | | | | | | | | | | | | |   (142)  all_53_14 = e2
% 229.78/41.18  | | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | | SIMP: (142) implies:
% 229.78/41.18  | | | | | | | | | | | | | |   (143)  all_53_14 = e2
% 229.78/41.18  | | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | | REDUCE: (51), (143) imply:
% 229.78/41.18  | | | | | | | | | | | | | |   (144)   ~ (all_53_2 = e2)
% 229.78/41.18  | | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | | BETA: splitting (34) gives:
% 229.78/41.18  | | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | | Case 1:
% 229.78/41.18  | | | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | | |   (145)  all_55_8 = e3
% 229.78/41.18  | | | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | | | COMBINE_EQS: (57), (145) imply:
% 229.78/41.18  | | | | | | | | | | | | | | |   (146)  all_53_2 = e3
% 229.78/41.18  | | | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | | | SIMP: (146) implies:
% 229.78/41.18  | | | | | | | | | | | | | | |   (147)  all_53_2 = e3
% 229.78/41.18  | | | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | | | REDUCE: (44), (147) imply:
% 229.78/41.18  | | | | | | | | | | | | | | |   (148)   ~ (all_53_1 = e3)
% 229.78/41.18  | | | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | | | BETA: splitting (38) gives:
% 229.78/41.18  | | | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | | | Case 1:
% 229.78/41.18  | | | | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | | | |   (149)  all_55_4 = e3
% 229.78/41.18  | | | | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | | | | REF_CLOSE: (27), (148), (149) are inconsistent by sub-proof
% 229.78/41.18  | | | | | | | | | | | | | | | |            #2170.
% 229.78/41.18  | | | | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | | | Case 2:
% 229.78/41.18  | | | | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | | | |   (150)   ~ (all_55_4 = e3)
% 229.78/41.18  | | | | | | | | | | | | | | | |   (151)  all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 229.78/41.18  | | | | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | | | | BETA: splitting (151) gives:
% 229.78/41.18  | | | | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | | | | Case 1:
% 229.78/41.18  | | | | | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | | | | |   (152)  all_55_4 = e2
% 229.78/41.18  | | | | | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (73), (152) are inconsistent by sub-proof
% 229.78/41.18  | | | | | | | | | | | | | | | | |            #2168.
% 229.78/41.18  | | | | | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | | | | Case 2:
% 229.78/41.18  | | | | | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | | | | |   (153)  all_55_4 = e1 | all_55_4 = e0
% 229.78/41.18  | | | | | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | | | | | BETA: splitting (47) gives:
% 229.78/41.18  | | | | | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | | | | | Case 1:
% 229.78/41.18  | | | | | | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | | | | | |   (154)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 229.78/41.18  | | | | | | | | | | | | | | | | | |            all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 229.78/41.18  | | | | | | | | | | | | | | | | | |            op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 229.78/41.18  | | | | | | | | | | | | | | | | | |              all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 229.78/41.18  | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 229.78/41.18  | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 229.78/41.18  | | | | | | | | | | | | | | | | | |            $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 229.78/41.18  | | | | | | | | | | | | | | | | | |            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2
% 229.78/41.18  | | | | | | | | | | | | | | | | | |            & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9,
% 229.78/41.18  | | | | | | | | | | | | | | | | | |              all_52_9) = e3 & op(all_52_11, all_52_11) = e2
% 229.78/41.18  | | | | | | | | | | | | | | | | | |            & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 229.78/41.18  | | | | | | | | | | | | | | | | | |              all_52_15) = e0 & op(e2, e3) = all_52_9 &
% 229.78/41.18  | | | | | | | | | | | | | | | | | |            op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13
% 229.78/41.18  | | | | | | | | | | | | | | | | | |            & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 229.78/41.18  | | | | | | | | | | | | | | | | | |            $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 229.78/41.18  | | | | | | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | | | | | | BETA: splitting (154) gives:
% 229.78/41.18  | | | | | | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | | | | | | Case 1:
% 229.78/41.18  | | | | | | | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | | | | | | |   (155)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 &
% 229.78/41.18  | | | | | | | | | | | | | | | | | | |          all_52_6 = e0 & op(all_52_1, all_52_1) = e3 &
% 229.78/41.18  | | | | | | | | | | | | | | | | | | |          op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 229.78/41.18  | | | | | | | | | | | | | | | | | | |            all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 229.78/41.18  | | | | | | | | | | | | | | | | | | |          op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 &
% 229.78/41.18  | | | | | | | | | | | | | | | | | | |          op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 229.78/41.18  | | | | | | | | | | | | | | | | | | |          $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 229.78/41.18  | | | | | | | | | | | | | | | | | | |          $i(all_52_7)
% 229.78/41.18  | | | | | | | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | | | | | | | ALPHA: (155) implies:
% 229.78/41.18  | | | | | | | | | | | | | | | | | | |   (156)  op(e3, e0) = all_52_7
% 229.78/41.18  | | | | | | | | | | | | | | | | | | |   (157)  op(all_52_7, all_52_7) = e0
% 229.78/41.18  | | | | | | | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (15), (45), (53), (123), (156), (157) are
% 229.78/41.18  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1001.
% 229.78/41.18  | | | | | | | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | | | | | | Case 2:
% 229.78/41.18  | | | | | | | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | | | | | | |   (158)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 229.78/41.18  | | | | | | | | | | | | | | | | | | |          all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 229.78/41.18  | | | | | | | | | | | | | | | | | | |          op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 229.78/41.18  | | | | | | | | | | | | | | | | | | |            all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 229.78/41.18  | | | | | | | | | | | | | | | | | | |          & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 229.78/41.18  | | | | | | | | | | | | | | | | | | |          op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 229.78/41.18  | | | | | | | | | | | | | | | | | | |          $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 229.78/41.18  | | | | | | | | | | | | | | | | | | |          $i(all_52_15)
% 229.78/41.18  | | | | | | | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (25), (58), (62), (85), (120), (140), (158)
% 229.78/41.18  | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #888.
% 229.78/41.18  | | | | | | | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | | | | | | End of split
% 229.78/41.18  | | | | | | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | | | | | Case 2:
% 229.78/41.18  | | | | | | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | | | | | |   (159)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1
% 229.78/41.18  | | | | | | | | | | | | | | | | | |            & all_52_22 = e0 & op(all_52_17, all_52_17) = e3
% 229.78/41.18  | | | | | | | | | | | | | | | | | |            & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 229.78/41.18  | | | | | | | | | | | | | | | | | |              all_52_21) = e1 & op(all_52_23, all_52_23) =
% 229.78/41.18  | | | | | | | | | | | | | | | | | |            e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 229.78/41.18  | | | | | | | | | | | | | | | | | |            all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 229.78/41.18  | | | | | | | | | | | | | | | | | |            = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 229.78/41.18  | | | | | | | | | | | | | | | | | |            $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 229.78/41.18  | | | | | | | | | | | | | | | | | |            & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 229.78/41.18  | | | | | | | | | | | | | | | | | |            e0 & op(all_52_25, all_52_25) = e3 &
% 229.78/41.18  | | | | | | | | | | | | | | | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 229.78/41.18  | | | | | | | | | | | | | | | | | |              all_52_29) = e1 & op(all_52_31, all_52_31) =
% 229.78/41.18  | | | | | | | | | | | | | | | | | |            e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 229.78/41.18  | | | | | | | | | | | | | | | | | |            all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 229.78/41.18  | | | | | | | | | | | | | | | | | |            = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 229.78/41.18  | | | | | | | | | | | | | | | | | |            $i(all_52_29) & $i(all_52_31))
% 229.78/41.18  | | | | | | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | | | | | | BETA: splitting (159) gives:
% 229.78/41.18  | | | | | | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | | | | | | Case 1:
% 229.78/41.18  | | | | | | | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | | | | | | |   (160)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 229.78/41.18  | | | | | | | | | | | | | | | | | | |          all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 229.78/41.18  | | | | | | | | | | | | | | | | | | |          op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 229.78/41.18  | | | | | | | | | | | | | | | | | | |            all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 229.78/41.18  | | | | | | | | | | | | | | | | | | |          & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19
% 229.78/41.18  | | | | | | | | | | | | | | | | | | |          & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23
% 229.78/41.18  | | | | | | | | | | | | | | | | | | |          & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 229.78/41.18  | | | | | | | | | | | | | | | | | | |          $i(all_52_23)
% 229.78/41.18  | | | | | | | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | | | | | | | ALPHA: (160) implies:
% 229.78/41.18  | | | | | | | | | | | | | | | | | | |   (161)  op(e1, e3) = all_52_17
% 229.78/41.18  | | | | | | | | | | | | | | | | | | |   (162)  op(all_52_17, all_52_17) = e3
% 229.78/41.18  | | | | | | | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (12), (15), (34), (41), (57), (67),
% 229.78/41.18  | | | | | | | | | | | | | | | | | | |            (123), (133), (161), (162) are inconsistent by
% 229.78/41.18  | | | | | | | | | | | | | | | | | | |            sub-proof #999.
% 229.78/41.18  | | | | | | | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | | | | | | Case 2:
% 229.78/41.18  | | | | | | | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | | | | | | |   (163)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 229.78/41.18  | | | | | | | | | | | | | | | | | | |          all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 229.78/41.18  | | | | | | | | | | | | | | | | | | |          op(all_52_27, all_52_27) = e2 & op(all_52_29,
% 229.78/41.18  | | | | | | | | | | | | | | | | | | |            all_52_29) = e1 & op(all_52_31, all_52_31) = e0
% 229.78/41.18  | | | | | | | | | | | | | | | | | | |          & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27
% 229.78/41.18  | | | | | | | | | | | | | | | | | | |          & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31
% 229.78/41.18  | | | | | | | | | | | | | | | | | | |          & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 229.78/41.18  | | | | | | | | | | | | | | | | | | |          $i(all_52_31)
% 229.78/41.18  | | | | | | | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | | | | | | | ALPHA: (163) implies:
% 229.78/41.18  | | | | | | | | | | | | | | | | | | |   (164)  op(e0, e0) = all_52_31
% 229.78/41.18  | | | | | | | | | | | | | | | | | | |   (165)  op(e0, e1) = all_52_29
% 229.78/41.18  | | | | | | | | | | | | | | | | | | |   (166)  op(all_52_29, all_52_29) = e1
% 229.78/41.18  | | | | | | | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | | | | | | | BETA: splitting (153) gives:
% 229.78/41.18  | | | | | | | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | | | | | | | Case 1:
% 229.78/41.18  | | | | | | | | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | | | | | | | |   (167)  all_55_4 = e1
% 229.78/41.18  | | | | | | | | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (27), (167) imply:
% 229.78/41.18  | | | | | | | | | | | | | | | | | | | |   (168)  all_53_1 = e1
% 229.78/41.18  | | | | | | | | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (168) imply:
% 229.78/41.18  | | | | | | | | | | | | | | | | | | | |   (169)   ~ (e3 = e1)
% 229.78/41.18  | | | | | | | | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (12), (58), (115), (164), (165), (166) are
% 229.78/41.18  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #887.
% 229.78/41.18  | | | | | | | | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | | | | | | | Case 2:
% 229.78/41.18  | | | | | | | | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | | | | | | | |   (170)  all_55_4 = e0
% 229.78/41.18  | | | | | | | | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (27), (170) imply:
% 229.78/41.18  | | | | | | | | | | | | | | | | | | | |   (171)  all_53_1 = e0
% 229.78/41.18  | | | | | | | | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | | | | | | | | REDUCE: (50), (171) imply:
% 229.78/41.18  | | | | | | | | | | | | | | | | | | | |   (172)  $false
% 229.78/41.18  | | | | | | | | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | | | | | | | | CLOSE: (172) is inconsistent.
% 229.78/41.18  | | | | | | | | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | | | | | | | End of split
% 229.78/41.18  | | | | | | | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | | | | | | End of split
% 229.78/41.18  | | | | | | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | | | | | End of split
% 229.78/41.18  | | | | | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | | | | End of split
% 229.78/41.18  | | | | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | | | End of split
% 229.78/41.18  | | | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | | Case 2:
% 229.78/41.18  | | | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | | |   (173)  all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 229.78/41.18  | | | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | | | REF_CLOSE: (2), (57), (133), (144), (173) are inconsistent by
% 229.78/41.18  | | | | | | | | | | | | | | |            sub-proof #886.
% 229.78/41.18  | | | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | | End of split
% 229.78/41.18  | | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | Case 2:
% 229.78/41.18  | | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | |   (174)  all_55_11 = e1 | all_55_11 = e0
% 229.78/41.18  | | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | | REF_CLOSE: (64), (122), (135), (174) are inconsistent by
% 229.78/41.18  | | | | | | | | | | | | | |            sub-proof #2307.
% 229.78/41.18  | | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | | End of split
% 229.78/41.18  | | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | | End of split
% 229.78/41.18  | | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | | End of split
% 229.78/41.18  | | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | | End of split
% 229.78/41.18  | | | | | | | | | | 
% 229.78/41.18  | | | | | | | | | End of split
% 229.78/41.18  | | | | | | | | | 
% 229.78/41.18  | | | | | | | | End of split
% 229.78/41.18  | | | | | | | | 
% 229.78/41.18  | | | | | | | Case 2:
% 229.78/41.18  | | | | | | | | 
% 229.78/41.18  | | | | | | | |   (175)  all_55_3 = e0
% 229.78/41.18  | | | | | | | | 
% 229.78/41.18  | | | | | | | | REF_CLOSE: (65), (71), (175) are inconsistent by sub-proof #885.
% 229.78/41.18  | | | | | | | | 
% 229.78/41.18  | | | | | | | End of split
% 229.78/41.18  | | | | | | | 
% 229.78/41.18  | | | | | | End of split
% 229.78/41.18  | | | | | | 
% 229.78/41.18  | | | | | End of split
% 229.78/41.18  | | | | | 
% 229.78/41.18  | | | | End of split
% 229.78/41.18  | | | | 
% 229.78/41.18  | | | End of split
% 229.78/41.18  | | | 
% 229.78/41.18  | | Case 2:
% 229.78/41.18  | | | 
% 229.78/41.18  | | |   (176)  all_55_2 = e1 | all_55_2 = e0
% 229.78/41.18  | | | 
% 229.78/41.18  | | | REF_CLOSE: (21), (37), (72), (176) are inconsistent by sub-proof #2030.
% 229.78/41.18  | | | 
% 229.78/41.18  | | End of split
% 229.78/41.18  | | 
% 229.78/41.18  | End of split
% 229.78/41.18  | 
% 229.78/41.18  End of proof
% 229.78/41.18  
% 229.78/41.18  Sub-proof #885 shows that the following formulas are inconsistent:
% 229.78/41.18  ----------------------------------------------------------------
% 229.78/41.18    (1)  all_55_3 = all_53_12
% 229.78/41.18    (2)  all_55_3 = e0
% 229.78/41.18    (3)   ~ (all_53_12 = e0)
% 229.78/41.18  
% 229.78/41.18  Begin of proof
% 229.78/41.18  | 
% 229.78/41.18  | COMBINE_EQS: (1), (2) imply:
% 229.78/41.18  |   (4)  all_53_12 = e0
% 229.78/41.18  | 
% 229.78/41.18  | SIMP: (4) implies:
% 229.78/41.18  |   (5)  all_53_12 = e0
% 229.78/41.18  | 
% 229.78/41.18  | REDUCE: (3), (5) imply:
% 229.78/41.18  |   (6)  $false
% 229.78/41.18  | 
% 229.78/41.18  | CLOSE: (6) is inconsistent.
% 229.78/41.18  | 
% 229.78/41.18  End of proof
% 229.78/41.18  
% 229.78/41.18  Sub-proof #886 shows that the following formulas are inconsistent:
% 229.78/41.18  ----------------------------------------------------------------
% 229.78/41.18    (1)   ~ (all_53_2 = e2)
% 229.78/41.18    (2)  all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 229.78/41.18    (3)   ~ (all_53_2 = e1)
% 229.78/41.18    (4)   ~ (all_53_2 = e0)
% 229.78/41.18    (5)  all_55_8 = all_53_2
% 229.78/41.18  
% 229.78/41.18  Begin of proof
% 229.78/41.18  | 
% 229.78/41.18  | BETA: splitting (2) gives:
% 229.78/41.18  | 
% 229.78/41.18  | Case 1:
% 229.78/41.18  | | 
% 229.78/41.18  | |   (6)  all_55_8 = e2
% 229.78/41.18  | | 
% 229.78/41.18  | | REF_CLOSE: (1), (5), (6) are inconsistent by sub-proof #2406.
% 229.78/41.18  | | 
% 229.78/41.18  | Case 2:
% 229.78/41.18  | | 
% 229.78/41.18  | |   (7)  all_55_8 = e1 | all_55_8 = e0
% 229.78/41.18  | | 
% 229.78/41.18  | | REF_CLOSE: (3), (4), (5), (7) are inconsistent by sub-proof #1974.
% 229.78/41.18  | | 
% 229.78/41.18  | End of split
% 229.78/41.18  | 
% 229.78/41.18  End of proof
% 229.78/41.18  
% 229.78/41.18  Sub-proof #887 shows that the following formulas are inconsistent:
% 229.78/41.18  ----------------------------------------------------------------
% 229.78/41.18    (1)   ~ (e3 = e1)
% 229.78/41.18    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.78/41.18           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.78/41.18    (3)  op(e0, e1) = e0
% 229.78/41.18    (4)  op(e0, e0) = all_52_31
% 229.78/41.18    (5)  op(e0, e1) = all_52_29
% 229.78/41.18    (6)  op(e0, e0) = e3
% 229.78/41.18    (7)  op(all_52_29, all_52_29) = e1
% 229.78/41.18  
% 229.78/41.18  Begin of proof
% 229.78/41.18  | 
% 229.78/41.18  | GROUND_INST: instantiating (2) with e3, all_52_31, e0, e0, simplifying with
% 229.78/41.18  |              (4), (6) gives:
% 229.78/41.18  |   (8)  all_52_31 = e3
% 229.78/41.18  | 
% 229.78/41.18  | GROUND_INST: instantiating (2) with e0, all_52_29, e1, e0, simplifying with
% 229.78/41.18  |              (3), (5) gives:
% 229.78/41.18  |   (9)  all_52_29 = e0
% 229.78/41.18  | 
% 229.78/41.18  | REDUCE: (7), (9) imply:
% 229.78/41.18  |   (10)  op(e0, e0) = e1
% 229.78/41.18  | 
% 229.78/41.18  | REF_CLOSE: (1), (2), (6), (10) are inconsistent by sub-proof #2183.
% 229.78/41.18  | 
% 229.78/41.18  End of proof
% 229.78/41.18  
% 229.78/41.18  Sub-proof #888 shows that the following formulas are inconsistent:
% 229.78/41.18  ----------------------------------------------------------------
% 229.78/41.18    (1)   ~ (all_53_13 = e1)
% 229.78/41.18    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.78/41.18           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.78/41.18    (3)   ~ (all_53_13 = e3)
% 229.78/41.18    (4)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0 &
% 229.78/41.18         op(all_52_9, all_52_9) = e3 & op(all_52_11, all_52_11) = e2 &
% 229.78/41.18         op(all_52_13, all_52_13) = e1 & op(all_52_15, all_52_15) = e0 & op(e2,
% 229.78/41.18           e3) = all_52_9 & op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13 &
% 229.78/41.18         op(e2, e0) = all_52_15 & $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 229.78/41.18         $i(all_52_15)
% 229.78/41.18    (5)  all_55_7 = e1 | all_55_7 = e0
% 229.78/41.18    (6)  op(e0, e0) = e3
% 229.78/41.18    (7)  op(e2, e0) = all_53_13
% 229.78/41.18    (8)  all_55_7 = all_53_13
% 229.78/41.18  
% 229.78/41.18  Begin of proof
% 229.78/41.18  | 
% 229.78/41.18  | ALPHA: (4) implies:
% 229.78/41.18  |   (9)  op(e2, e0) = all_52_15
% 229.78/41.18  |   (10)  op(all_52_15, all_52_15) = e0
% 229.78/41.18  | 
% 229.78/41.18  | BETA: splitting (5) gives:
% 229.78/41.18  | 
% 229.78/41.18  | Case 1:
% 229.78/41.18  | | 
% 229.78/41.18  | |   (11)  all_55_7 = e1
% 229.78/41.18  | | 
% 229.78/41.18  | | REF_CLOSE: (1), (8), (11) are inconsistent by sub-proof #1970.
% 229.78/41.18  | | 
% 229.78/41.18  | Case 2:
% 229.78/41.18  | | 
% 229.78/41.18  | |   (12)  all_55_7 = e0
% 229.78/41.18  | | 
% 229.78/41.18  | | COMBINE_EQS: (8), (12) imply:
% 229.78/41.18  | |   (13)  all_53_13 = e0
% 229.78/41.18  | | 
% 229.78/41.18  | | SIMP: (13) implies:
% 229.78/41.18  | |   (14)  all_53_13 = e0
% 229.78/41.18  | | 
% 229.78/41.18  | | REDUCE: (3), (14) imply:
% 229.78/41.18  | |   (15)   ~ (e3 = e0)
% 229.78/41.18  | | 
% 229.78/41.18  | | SIMP: (15) implies:
% 229.78/41.18  | |   (16)   ~ (e3 = e0)
% 229.78/41.18  | | 
% 229.78/41.18  | | REDUCE: (7), (14) imply:
% 229.78/41.18  | |   (17)  op(e2, e0) = e0
% 229.78/41.18  | | 
% 229.78/41.18  | | GROUND_INST: instantiating (2) with e0, all_52_15, e0, e2, simplifying with
% 229.78/41.18  | |              (9), (17) gives:
% 229.78/41.18  | |   (18)  all_52_15 = e0
% 229.78/41.18  | | 
% 229.78/41.18  | | REDUCE: (10), (18) imply:
% 229.78/41.18  | |   (19)  op(e0, e0) = e0
% 229.78/41.18  | | 
% 229.78/41.18  | | REF_CLOSE: (2), (6), (16), (19) are inconsistent by sub-proof #2304.
% 229.78/41.18  | | 
% 229.78/41.18  | End of split
% 229.78/41.18  | 
% 229.78/41.18  End of proof
% 229.78/41.18  
% 229.78/41.18  Sub-proof #889 shows that the following formulas are inconsistent:
% 229.78/41.18  ----------------------------------------------------------------
% 229.78/41.18    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.78/41.18         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.78/41.18    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.78/41.18         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.78/41.18    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.78/41.18         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.78/41.18    (4)   ~ (e3 = e1)
% 229.78/41.18    (5)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 229.78/41.18         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 229.78/41.18    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.78/41.18           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.78/41.18    (7)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.78/41.18         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.78/41.19    (8)   ~ (all_6_2 = e3)
% 229.78/41.19    (9)  op(e1, e1) = all_6_2
% 229.78/41.19    (10)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.78/41.19          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.78/41.19    (11)   ~ (all_53_13 = e2)
% 229.78/41.19    (12)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.78/41.19          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.78/41.19    (13)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.78/41.19          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.78/41.19    (14)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 229.78/41.19          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.78/41.19    (15)   ~ (e3 = e2)
% 229.78/41.19    (16)   ~ (e3 = e0)
% 229.78/41.19    (17)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 229.78/41.19          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 229.78/41.19    (18)  op(e0, e3) = all_53_3
% 229.78/41.19    (19)  all_57_0 = e0
% 229.78/41.19    (20)  all_57_15 = e3
% 229.78/41.19    (21)  op(e3, e3) = e0
% 229.78/41.19    (22)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.78/41.19          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.78/41.19            e1)
% 229.78/41.19    (23)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.78/41.19          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.78/41.19    (24)   ~ (e2 = e0)
% 229.78/41.19    (25)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.78/41.19          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.78/41.19    (26)  op(e2, e2) = e2
% 229.78/41.19    (27)   ~ (e1 = e0)
% 229.78/41.19    (28)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.78/41.19          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.78/41.19    (29)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.78/41.19          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.78/41.19    (30)  op(e0, e0) = e3
% 229.78/41.19    (31)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.78/41.19          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.78/41.19            e2)
% 229.78/41.19    (32)   ~ (all_53_3 = e0)
% 229.78/41.19    (33)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.78/41.19              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.78/41.19                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.78/41.19                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.78/41.19    (34)  op(e1, e1) = e0
% 229.78/41.19    (35)  op(e2, e0) = all_53_13
% 229.78/41.19    (36)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.78/41.19          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.78/41.19    (37)   ~ (all_53_12 = e3)
% 229.78/41.19    (38)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.78/41.19          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.78/41.19    (39)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.78/41.19          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.78/41.19    (40)   ~ (all_53_12 = e0)
% 229.78/41.19    (41)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.78/41.19          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 229.78/41.19    (42)   ~ (e2 = e1)
% 229.78/41.19    (43)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.78/41.19          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.78/41.19    (44)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.78/41.19          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.78/41.19    (45)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 229.78/41.19          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 229.78/41.19    (46)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.78/41.19          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.78/41.19    (47)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.78/41.19          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.78/41.19    (48)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 229.78/41.19          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 229.78/41.19    (49)  all_57_3 = e2
% 229.78/41.19    (50)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.78/41.19          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.78/41.19    (51)  all_57_7 = e0
% 229.78/41.19    (52)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 229.78/41.19          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 229.78/41.19    (53)  op(e3, e0) = all_53_12
% 229.78/41.19  
% 229.78/41.19  Begin of proof
% 229.78/41.19  | 
% 229.78/41.19  | BETA: splitting (33) gives:
% 229.78/41.19  | 
% 229.78/41.19  | Case 1:
% 229.78/41.19  | | 
% 229.78/41.19  | |   (54)  all_57_15 = e0 & op(e0, e0) = e0
% 229.78/41.19  | | 
% 229.78/41.19  | | ALPHA: (54) implies:
% 229.78/41.19  | |   (55)  op(e0, e0) = e0
% 229.78/41.19  | | 
% 229.78/41.19  | | REF_CLOSE: (6), (16), (30), (55) are inconsistent by sub-proof #2304.
% 229.78/41.19  | | 
% 229.78/41.19  | Case 2:
% 229.78/41.19  | | 
% 229.78/41.19  | |   (56)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 229.78/41.19  | |             e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0 &
% 229.78/41.19  | |             op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 229.78/41.19  | |           (all_57_14 = e0 & op(e0, e1) = e0))
% 229.78/41.19  | | 
% 229.78/41.19  | | ALPHA: (56) implies:
% 229.78/41.19  | |   (57)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 229.78/41.19  | |           e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.78/41.19  | |   (58)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 229.78/41.19  | |           e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 229.78/41.19  | | 
% 229.78/41.19  | | BETA: splitting (41) gives:
% 229.78/41.19  | | 
% 229.78/41.19  | | Case 1:
% 229.78/41.19  | | | 
% 229.78/41.19  | | |   (59)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) =
% 229.78/41.19  | | |           e0)
% 229.78/41.19  | | | 
% 229.78/41.19  | | | BETA: splitting (59) gives:
% 229.78/41.19  | | | 
% 229.78/41.19  | | | Case 1:
% 229.78/41.19  | | | | 
% 229.78/41.19  | | | |   (60)  all_57_2 = e0 & op(e2, e3) = e0
% 229.78/41.19  | | | | 
% 229.78/41.19  | | | | ALPHA: (60) implies:
% 229.78/41.19  | | | |   (61)  all_57_2 = e0
% 229.78/41.19  | | | | 
% 229.78/41.19  | | | | BETA: splitting (57) gives:
% 229.78/41.19  | | | | 
% 229.78/41.19  | | | | Case 1:
% 229.78/41.19  | | | | | 
% 229.78/41.19  | | | | |   (62)  all_57_12 = e0 & op(e0, e3) = e0
% 229.78/41.19  | | | | | 
% 229.78/41.19  | | | | | ALPHA: (62) implies:
% 229.78/41.19  | | | | |   (63)  op(e0, e3) = e0
% 229.78/41.19  | | | | | 
% 229.78/41.19  | | | | | REF_CLOSE: (6), (18), (32), (63) are inconsistent by sub-proof #2366.
% 229.78/41.19  | | | | | 
% 229.78/41.19  | | | | Case 2:
% 229.78/41.19  | | | | | 
% 229.78/41.19  | | | | |   (64)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 229.78/41.19  | | | | |             e1) = e0)
% 229.78/41.19  | | | | | 
% 229.78/41.19  | | | | | BETA: splitting (64) gives:
% 229.78/41.19  | | | | | 
% 229.78/41.19  | | | | | Case 1:
% 229.78/41.19  | | | | | | 
% 229.78/41.19  | | | | | |   (65)  all_57_13 = e0 & op(e0, e2) = e0
% 229.78/41.19  | | | | | | 
% 229.78/41.19  | | | | | | ALPHA: (65) implies:
% 229.78/41.19  | | | | | |   (66)  all_57_13 = e0
% 229.78/41.19  | | | | | | 
% 229.78/41.19  | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12),
% 229.78/41.19  | | | | | |            (13), (14), (15), (16), (17), (18), (20), (21), (22),
% 229.78/41.19  | | | | | |            (23), (24), (25), (27), (28), (29), (30), (31), (32),
% 229.78/41.19  | | | | | |            (33), (36), (37), (38), (39), (40), (42), (43), (44),
% 229.78/41.19  | | | | | |            (45), (46), (47), (48), (49), (50), (51), (52), (53),
% 229.78/41.19  | | | | | |            (57), (61), (66) are inconsistent by sub-proof #938.
% 229.78/41.19  | | | | | | 
% 229.78/41.19  | | | | | Case 2:
% 229.78/41.19  | | | | | | 
% 229.78/41.19  | | | | | |   (67)  all_57_14 = e0 & op(e0, e1) = e0
% 229.78/41.19  | | | | | | 
% 229.78/41.19  | | | | | | ALPHA: (67) implies:
% 229.78/41.19  | | | | | |   (68)  all_57_14 = e0
% 229.78/41.19  | | | | | | 
% 229.78/41.19  | | | | | | BETA: splitting (50) gives:
% 229.78/41.19  | | | | | | 
% 229.78/41.19  | | | | | | Case 1:
% 229.78/41.19  | | | | | | | 
% 229.78/41.19  | | | | | | |   (69)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 &
% 229.78/41.19  | | | | | | |           op(e2, e2) = e1)
% 229.78/41.19  | | | | | | | 
% 229.78/41.19  | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 229.78/41.19  | | | | | | |            (12), (13), (14), (15), (16), (17), (18), (20), (21),
% 229.78/41.19  | | | | | | |            (22), (23), (24), (25), (27), (28), (29), (30), (31),
% 229.78/41.19  | | | | | | |            (32), (33), (36), (37), (38), (39), (40), (42), (43),
% 229.78/41.19  | | | | | | |            (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 229.78/41.19  | | | | | | |            (53), (57), (61), (69) are inconsistent by sub-proof
% 229.78/41.19  | | | | | | |            #939.
% 229.78/41.19  | | | | | | | 
% 229.78/41.19  | | | | | | Case 2:
% 229.78/41.19  | | | | | | | 
% 229.78/41.19  | | | | | | |   (70)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 &
% 229.78/41.19  | | | | | | |           op(e0, e2) = e1)
% 229.78/41.19  | | | | | | | 
% 229.78/41.19  | | | | | | | BETA: splitting (70) gives:
% 229.78/41.19  | | | | | | | 
% 229.78/41.19  | | | | | | | Case 1:
% 229.78/41.19  | | | | | | | | 
% 229.78/41.19  | | | | | | | |   (71)  all_57_7 = e1 & op(e1, e2) = e1
% 229.78/41.19  | | | | | | | | 
% 229.78/41.19  | | | | | | | | ALPHA: (71) implies:
% 229.78/41.19  | | | | | | | |   (72)  all_57_7 = e1
% 229.78/41.19  | | | | | | | | 
% 229.78/41.19  | | | | | | | | REF_CLOSE: (27), (51), (72) are inconsistent by sub-proof #2211.
% 229.78/41.19  | | | | | | | | 
% 229.78/41.19  | | | | | | | Case 2:
% 229.78/41.19  | | | | | | | | 
% 229.78/41.19  | | | | | | | |   (73)  all_57_13 = e1 & op(e0, e2) = e1
% 229.78/41.19  | | | | | | | | 
% 229.78/41.19  | | | | | | | | ALPHA: (73) implies:
% 229.78/41.19  | | | | | | | |   (74)  all_57_13 = e1
% 229.78/41.19  | | | | | | | | 
% 229.78/41.19  | | | | | | | | BETA: splitting (2) gives:
% 229.78/41.19  | | | | | | | | 
% 229.78/41.19  | | | | | | | | Case 1:
% 229.78/41.19  | | | | | | | | | 
% 229.78/41.19  | | | | | | | | |   (75)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 &
% 229.78/41.19  | | | | | | | | |           op(e2, e3) = e1)
% 229.78/41.19  | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | BETA: splitting (75) gives:
% 229.78/41.19  | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | Case 1:
% 229.78/41.19  | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | |   (76)  all_57_0 = e1 & op(e3, e3) = e1
% 229.78/41.19  | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | ALPHA: (76) implies:
% 229.78/41.19  | | | | | | | | | |   (77)  all_57_0 = e1
% 229.78/41.19  | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | COMBINE_EQS: (19), (77) imply:
% 229.78/41.19  | | | | | | | | | |   (78)  e1 = e0
% 229.78/41.19  | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | SIMP: (78) implies:
% 229.78/41.19  | | | | | | | | | |   (79)  e1 = e0
% 229.78/41.19  | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | COMBINE_EQS: (74), (79) imply:
% 229.78/41.19  | | | | | | | | | |   (80)  all_57_13 = e0
% 229.78/41.19  | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 229.78/41.19  | | | | | | | | | |            (12), (13), (14), (15), (16), (17), (18), (20),
% 229.78/41.19  | | | | | | | | | |            (21), (22), (23), (24), (25), (27), (28), (29),
% 229.78/41.19  | | | | | | | | | |            (30), (31), (32), (33), (36), (37), (38), (39),
% 229.78/41.19  | | | | | | | | | |            (40), (42), (43), (44), (45), (46), (47), (48),
% 229.78/41.19  | | | | | | | | | |            (49), (50), (51), (52), (53), (57), (61), (80) are
% 229.78/41.19  | | | | | | | | | |            inconsistent by sub-proof #938.
% 229.78/41.19  | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | Case 2:
% 229.78/41.19  | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | |   (81)  all_57_2 = e1 & op(e2, e3) = e1
% 229.78/41.19  | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | ALPHA: (81) implies:
% 229.78/41.19  | | | | | | | | | |   (82)  all_57_2 = e1
% 229.78/41.19  | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | COMBINE_EQS: (61), (82) imply:
% 229.78/41.19  | | | | | | | | | |   (83)  e1 = e0
% 229.78/41.19  | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | SIMP: (83) implies:
% 229.78/41.19  | | | | | | | | | |   (84)  e1 = e0
% 229.78/41.19  | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | COMBINE_EQS: (74), (84) imply:
% 229.78/41.19  | | | | | | | | | |   (85)  all_57_13 = e0
% 229.78/41.19  | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 229.78/41.19  | | | | | | | | | |            (12), (13), (14), (15), (16), (17), (18), (20),
% 229.78/41.19  | | | | | | | | | |            (21), (22), (23), (24), (25), (27), (28), (29),
% 229.78/41.19  | | | | | | | | | |            (30), (31), (32), (33), (36), (37), (38), (39),
% 229.78/41.19  | | | | | | | | | |            (40), (42), (43), (44), (45), (46), (47), (48),
% 229.78/41.19  | | | | | | | | | |            (49), (50), (51), (52), (53), (57), (61), (85) are
% 229.78/41.19  | | | | | | | | | |            inconsistent by sub-proof #938.
% 229.78/41.19  | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | End of split
% 229.78/41.19  | | | | | | | | | 
% 229.78/41.19  | | | | | | | | Case 2:
% 229.78/41.19  | | | | | | | | | 
% 229.78/41.19  | | | | | | | | |   (86)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 &
% 229.78/41.19  | | | | | | | | |           op(e0, e3) = e1)
% 229.78/41.19  | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | BETA: splitting (86) gives:
% 229.78/41.19  | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | Case 1:
% 229.78/41.19  | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | |   (87)  all_57_6 = e1 & op(e1, e3) = e1
% 229.78/41.19  | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | ALPHA: (87) implies:
% 229.78/41.19  | | | | | | | | | |   (88)  all_57_6 = e1
% 229.78/41.19  | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (15), (16), (20), (24),
% 229.78/41.19  | | | | | | | | | |            (27), (33), (42), (43), (47), (51), (88) are
% 229.78/41.19  | | | | | | | | | |            inconsistent by sub-proof #1735.
% 229.78/41.19  | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | Case 2:
% 229.78/41.19  | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | |   (89)  all_57_12 = e1 & op(e0, e3) = e1
% 229.78/41.19  | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | ALPHA: (89) implies:
% 229.78/41.19  | | | | | | | | | |   (90)  all_57_12 = e1
% 229.78/41.19  | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | REF_CLOSE: (4), (6), (15), (16), (20), (21), (22), (24),
% 229.78/41.19  | | | | | | | | | |            (27), (31), (39), (42), (44), (61), (68), (90) are
% 229.78/41.19  | | | | | | | | | |            inconsistent by sub-proof #1555.
% 229.78/41.19  | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | End of split
% 229.78/41.19  | | | | | | | | | 
% 229.78/41.19  | | | | | | | | End of split
% 229.78/41.19  | | | | | | | | 
% 229.78/41.19  | | | | | | | End of split
% 229.78/41.19  | | | | | | | 
% 229.78/41.19  | | | | | | End of split
% 229.78/41.19  | | | | | | 
% 229.78/41.19  | | | | | End of split
% 229.78/41.19  | | | | | 
% 229.78/41.19  | | | | End of split
% 229.78/41.19  | | | | 
% 229.78/41.19  | | | Case 2:
% 229.78/41.19  | | | | 
% 229.78/41.19  | | | |   (91)  all_57_3 = e0 & op(e2, e2) = e0
% 229.78/41.19  | | | | 
% 229.78/41.19  | | | | ALPHA: (91) implies:
% 229.78/41.19  | | | |   (92)  op(e2, e2) = e0
% 229.78/41.19  | | | | 
% 229.78/41.19  | | | | REF_CLOSE: (6), (24), (26), (92) are inconsistent by sub-proof #2472.
% 229.78/41.19  | | | | 
% 229.78/41.19  | | | End of split
% 229.78/41.19  | | | 
% 229.78/41.19  | | Case 2:
% 229.78/41.19  | | | 
% 229.78/41.19  | | |   (93)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 229.78/41.19  | | |           e0)
% 229.78/41.19  | | | 
% 229.78/41.19  | | | BETA: splitting (93) gives:
% 229.78/41.19  | | | 
% 229.78/41.19  | | | Case 1:
% 229.78/41.19  | | | | 
% 229.78/41.19  | | | |   (94)  all_57_5 = e0 & op(e2, e1) = e0
% 229.78/41.19  | | | | 
% 229.78/41.19  | | | | ALPHA: (94) implies:
% 229.78/41.19  | | | |   (95)  all_57_5 = e0
% 229.78/41.19  | | | | 
% 229.78/41.19  | | | | BETA: splitting (29) gives:
% 229.78/41.19  | | | | 
% 229.78/41.19  | | | | Case 1:
% 229.78/41.19  | | | | | 
% 229.78/41.19  | | | | |   (96)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2,
% 229.78/41.19  | | | | |             e2) = e3)
% 229.78/41.19  | | | | | 
% 229.78/41.19  | | | | | BETA: splitting (96) gives:
% 229.78/41.19  | | | | | 
% 229.78/41.19  | | | | | Case 1:
% 229.78/41.19  | | | | | | 
% 229.78/41.19  | | | | | |   (97)  all_57_1 = e3 & op(e3, e2) = e3
% 229.78/41.19  | | | | | | 
% 229.78/41.19  | | | | | | ALPHA: (97) implies:
% 229.78/41.19  | | | | | |   (98)  all_57_1 = e3
% 229.78/41.19  | | | | | | 
% 229.78/41.19  | | | | | | BETA: splitting (36) gives:
% 229.78/41.19  | | | | | | 
% 229.78/41.19  | | | | | | Case 1:
% 229.78/41.19  | | | | | | | 
% 229.78/41.19  | | | | | | |   (99)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 &
% 229.78/41.19  | | | | | | |           op(e2, e2) = e3)
% 229.78/41.19  | | | | | | | 
% 229.78/41.19  | | | | | | | BETA: splitting (99) gives:
% 229.78/41.19  | | | | | | | 
% 229.78/41.19  | | | | | | | Case 1:
% 229.78/41.19  | | | | | | | | 
% 229.78/41.19  | | | | | | | |   (100)  all_57_2 = e3 & op(e2, e3) = e3
% 229.78/41.19  | | | | | | | | 
% 229.78/41.19  | | | | | | | | ALPHA: (100) implies:
% 229.78/41.19  | | | | | | | |   (101)  all_57_2 = e3
% 229.78/41.19  | | | | | | | | 
% 229.78/41.19  | | | | | | | | BETA: splitting (50) gives:
% 229.78/41.19  | | | | | | | | 
% 229.78/41.19  | | | | | | | | Case 1:
% 229.78/41.19  | | | | | | | | | 
% 229.78/41.19  | | | | | | | | |   (102)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 &
% 229.78/41.19  | | | | | | | | |            op(e2, e2) = e1)
% 229.78/41.19  | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | BETA: splitting (102) gives:
% 229.78/41.19  | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | Case 1:
% 229.78/41.19  | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | |   (103)  all_57_1 = e1 & op(e3, e2) = e1
% 229.78/41.19  | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | ALPHA: (103) implies:
% 229.78/41.19  | | | | | | | | | |   (104)  all_57_1 = e1
% 229.78/41.19  | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | REF_CLOSE: (4), (6), (15), (16), (20), (22), (24), (27),
% 229.78/41.19  | | | | | | | | | |            (29), (30), (31), (42), (49), (51), (57), (104)
% 229.78/41.19  | | | | | | | | | |            are inconsistent by sub-proof #940.
% 229.78/41.19  | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | Case 2:
% 229.78/41.19  | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | |   (105)  all_57_3 = e1 & op(e2, e2) = e1
% 229.78/41.19  | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | ALPHA: (105) implies:
% 229.78/41.19  | | | | | | | | | |   (106)  all_57_3 = e1
% 229.78/41.19  | | | | | | | | | |   (107)  op(e2, e2) = e1
% 229.78/41.19  | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 229.78/41.19  | | | | | | | | | |            (12), (13), (14), (15), (16), (17), (18), (19),
% 229.78/41.19  | | | | | | | | | |            (20), (21), (22), (23), (24), (25), (27), (28),
% 229.78/41.19  | | | | | | | | | |            (29), (30), (31), (32), (33), (34), (36), (37),
% 229.78/41.19  | | | | | | | | | |            (38), (39), (40), (41), (42), (43), (44), (45),
% 229.78/41.19  | | | | | | | | | |            (46), (47), (48), (50), (51), (52), (53), (106),
% 229.78/41.19  | | | | | | | | | |            (107) are inconsistent by sub-proof #933.
% 229.78/41.19  | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | End of split
% 229.78/41.19  | | | | | | | | | 
% 229.78/41.19  | | | | | | | | Case 2:
% 229.78/41.19  | | | | | | | | | 
% 229.78/41.19  | | | | | | | | |   (108)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 &
% 229.78/41.19  | | | | | | | | |            op(e0, e2) = e1)
% 229.78/41.19  | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | BETA: splitting (108) gives:
% 229.78/41.19  | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | Case 1:
% 229.78/41.19  | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | |   (109)  all_57_7 = e1 & op(e1, e2) = e1
% 229.78/41.19  | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | ALPHA: (109) implies:
% 229.78/41.19  | | | | | | | | | |   (110)  all_57_7 = e1
% 229.78/41.19  | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | REF_CLOSE: (27), (51), (110) are inconsistent by sub-proof
% 229.78/41.19  | | | | | | | | | |            #2211.
% 229.78/41.19  | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | Case 2:
% 229.78/41.19  | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | |   (111)  all_57_13 = e1 & op(e0, e2) = e1
% 229.78/41.19  | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | ALPHA: (111) implies:
% 229.78/41.19  | | | | | | | | | |   (112)  all_57_13 = e1
% 229.78/41.19  | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | BETA: splitting (1) gives:
% 229.78/41.19  | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | Case 1:
% 229.78/41.19  | | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | |   (113)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 229.78/41.19  | | | | | | | | | | |            & op(e2, e2) = e1)
% 229.78/41.19  | | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | | BETA: splitting (113) gives:
% 229.78/41.19  | | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | | Case 1:
% 229.78/41.19  | | | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | | |   (114)  all_57_2 = e1 & op(e2, e3) = e1
% 229.78/41.19  | | | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | | | ALPHA: (114) implies:
% 229.78/41.19  | | | | | | | | | | | |   (115)  all_57_2 = e1
% 229.78/41.19  | | | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | | | COMBINE_EQS: (101), (115) imply:
% 229.78/41.19  | | | | | | | | | | | |   (116)  e3 = e1
% 229.78/41.19  | | | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | | | COMBINE_EQS: (98), (116) imply:
% 229.78/41.19  | | | | | | | | | | | |   (117)  all_57_1 = e1
% 229.78/41.19  | | | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | | | REF_CLOSE: (4), (6), (15), (16), (20), (22), (24), (27),
% 229.78/41.19  | | | | | | | | | | | |            (29), (30), (31), (42), (49), (51), (57), (117)
% 229.78/41.19  | | | | | | | | | | | |            are inconsistent by sub-proof #940.
% 229.78/41.19  | | | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | | Case 2:
% 229.78/41.19  | | | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | | |   (118)  all_57_3 = e1 & op(e2, e2) = e1
% 229.78/41.19  | | | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | | | ALPHA: (118) implies:
% 229.78/41.19  | | | | | | | | | | | |   (119)  all_57_3 = e1
% 229.78/41.19  | | | | | | | | | | | |   (120)  op(e2, e2) = e1
% 229.78/41.19  | | | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 229.78/41.19  | | | | | | | | | | | |            (12), (13), (14), (15), (16), (17), (18), (19),
% 229.78/41.19  | | | | | | | | | | | |            (20), (21), (22), (23), (24), (25), (27), (28),
% 229.78/41.19  | | | | | | | | | | | |            (29), (30), (31), (32), (33), (34), (36), (37),
% 229.78/41.19  | | | | | | | | | | | |            (38), (39), (40), (41), (42), (43), (44), (45),
% 229.78/41.19  | | | | | | | | | | | |            (46), (47), (48), (50), (51), (52), (53), (119),
% 229.78/41.19  | | | | | | | | | | | |            (120) are inconsistent by sub-proof #933.
% 229.78/41.19  | | | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | | End of split
% 229.78/41.19  | | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | Case 2:
% 229.78/41.19  | | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | |   (121)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 229.78/41.19  | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 229.78/41.19  | | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | | BETA: splitting (121) gives:
% 229.78/41.19  | | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | | Case 1:
% 229.78/41.19  | | | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | | |   (122)  all_57_5 = e1 & op(e2, e1) = e1
% 229.78/41.19  | | | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | | | ALPHA: (122) implies:
% 229.78/41.19  | | | | | | | | | | | |   (123)  all_57_5 = e1
% 229.78/41.19  | | | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | | | COMBINE_EQS: (95), (123) imply:
% 229.78/41.19  | | | | | | | | | | | |   (124)  e1 = e0
% 229.78/41.19  | | | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | | | SIMP: (124) implies:
% 229.78/41.19  | | | | | | | | | | | |   (125)  e1 = e0
% 229.78/41.19  | | | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | | | COMBINE_EQS: (112), (125) imply:
% 229.78/41.19  | | | | | | | | | | | |   (126)  all_57_13 = e0
% 229.78/41.19  | | | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | | | BETA: splitting (36) gives:
% 229.78/41.19  | | | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | | | Case 1:
% 229.78/41.19  | | | | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | | | | BETA: splitting (99) gives:
% 229.78/41.19  | | | | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | | | | Case 1:
% 229.78/41.19  | | | | | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | | | | | BETA: splitting (58) gives:
% 229.78/41.19  | | | | | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | | | | | Case 1:
% 229.78/41.19  | | | | | | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | | | | | |   (127)  all_57_9 = e0 & op(e3, e0) = e0
% 229.78/41.19  | | | | | | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | | | | | | REF_CLOSE: (6), (40), (53), (127) are inconsistent by
% 229.78/41.19  | | | | | | | | | | | | | | |            sub-proof #2434.
% 229.78/41.19  | | | | | | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | | | | | Case 2:
% 229.78/41.19  | | | | | | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | | | | | |   (128)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 =
% 229.78/41.19  | | | | | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 229.78/41.19  | | | | | | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | | | | | | BETA: splitting (128) gives:
% 229.78/41.19  | | | | | | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | | | | | | Case 1:
% 229.78/41.19  | | | | | | | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | | | | | | |   (129)  all_57_10 = e0 & op(e2, e0) = e0
% 229.78/41.19  | | | | | | | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | | | | | | | ALPHA: (129) implies:
% 229.78/41.19  | | | | | | | | | | | | | | | |   (130)  all_57_10 = e0
% 229.78/41.19  | | | | | | | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | | | | | | | BETA: splitting (7) gives:
% 229.78/41.19  | | | | | | | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | | | | | | | Case 1:
% 229.78/41.19  | | | | | | | | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | | | | | | | |   (131)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 229.78/41.19  | | | | | | | | | | | | | | | | |            & op(e1, e2) = e3)
% 229.78/41.19  | | | | | | | | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | | | | | | | | BETA: splitting (131) gives:
% 229.78/41.19  | | | | | | | | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | | | | | | | | Case 1:
% 229.78/41.19  | | | | | | | | | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | | | | | | | | |   (132)  all_57_6 = e3 & op(e1, e3) = e3
% 229.78/41.19  | | | | | | | | | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | | | | | | | | | ALPHA: (132) implies:
% 229.78/41.19  | | | | | | | | | | | | | | | | | |   (133)  all_57_6 = e3
% 229.78/41.19  | | | | | | | | | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 229.78/41.19  | | | | | | | | | | | | | | | | | |            (12), (13), (14), (15), (16), (17), (18), (19),
% 229.78/41.19  | | | | | | | | | | | | | | | | | |            (20), (21), (22), (23), (24), (25), (26), (27),
% 229.78/41.19  | | | | | | | | | | | | | | | | | |            (28), (29), (30), (31), (32), (33), (34), (36),
% 229.78/41.19  | | | | | | | | | | | | | | | | | |            (37), (38), (39), (40), (41), (42), (43), (44),
% 229.78/41.19  | | | | | | | | | | | | | | | | | |            (45), (46), (47), (48), (49), (50), (51), (52),
% 229.78/41.19  | | | | | | | | | | | | | | | | | |            (53), (57), (58), (126), (130), (133) are
% 229.78/41.19  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #922.
% 229.78/41.19  | | | | | | | | | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | | | | | | | | Case 2:
% 229.78/41.19  | | | | | | | | | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | | | | | | | | |   (134)  all_57_7 = e3 & op(e1, e2) = e3
% 229.78/41.19  | | | | | | | | | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | | | | | | | | | ALPHA: (134) implies:
% 229.78/41.19  | | | | | | | | | | | | | | | | | |   (135)  all_57_7 = e3
% 229.78/41.19  | | | | | | | | | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (51), (135) are inconsistent by sub-proof
% 229.78/41.19  | | | | | | | | | | | | | | | | | |            #2269.
% 229.78/41.19  | | | | | | | | | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | | | | | | | | End of split
% 229.78/41.19  | | | | | | | | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | | | | | | | Case 2:
% 229.78/41.19  | | | | | | | | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | | | | | | | |   (136)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 229.78/41.19  | | | | | | | | | | | | | | | | |            e3 & op(e1, e0) = e3)
% 229.78/41.19  | | | | | | | | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (9), (15), (16), (20), (24), (27),
% 229.78/41.19  | | | | | | | | | | | | | | | | |            (42), (43), (47), (58), (136) are inconsistent by
% 229.78/41.19  | | | | | | | | | | | | | | | | |            sub-proof #1080.
% 229.78/41.19  | | | | | | | | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | | | | | | | End of split
% 229.78/41.19  | | | | | | | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | | | | | | Case 2:
% 229.78/41.19  | | | | | | | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | | | | | | |   (137)  all_57_11 = e0 & op(e1, e0) = e0
% 229.78/41.19  | | | | | | | | | | | | | | | | 
% 229.78/41.19  | | | | | | | | | | | | | | | | ALPHA: (137) implies:
% 229.78/41.19  | | | | | | | | | | | | | | | |   (138)  all_57_11 = e0
% 229.78/41.19  | | | | | | | | | | | | | | | | 
% 229.78/41.20  | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 229.78/41.20  | | | | | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 229.78/41.20  | | | | | | | | | | | | | | | |            (19), (20), (21), (22), (23), (24), (25), (27),
% 229.78/41.20  | | | | | | | | | | | | | | | |            (28), (29), (30), (31), (32), (33), (34), (35),
% 229.78/41.20  | | | | | | | | | | | | | | | |            (36), (37), (38), (39), (40), (41), (42), (43),
% 229.78/41.20  | | | | | | | | | | | | | | | |            (44), (45), (46), (47), (48), (49), (50), (52),
% 229.78/41.20  | | | | | | | | | | | | | | | |            (53), (57), (58), (95), (101), (126), (138) are
% 229.78/41.20  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #896.
% 229.78/41.20  | | | | | | | | | | | | | | | | 
% 229.78/41.20  | | | | | | | | | | | | | | | End of split
% 229.78/41.20  | | | | | | | | | | | | | | | 
% 229.78/41.20  | | | | | | | | | | | | | | End of split
% 229.78/41.20  | | | | | | | | | | | | | | 
% 229.78/41.20  | | | | | | | | | | | | | Case 2:
% 229.78/41.20  | | | | | | | | | | | | | | 
% 229.78/41.20  | | | | | | | | | | | | | |   (139)  all_57_3 = e3 & op(e2, e2) = e3
% 229.78/41.20  | | | | | | | | | | | | | | 
% 229.78/41.20  | | | | | | | | | | | | | | ALPHA: (139) implies:
% 229.78/41.20  | | | | | | | | | | | | | |   (140)  all_57_3 = e3
% 229.78/41.20  | | | | | | | | | | | | | | 
% 229.78/41.20  | | | | | | | | | | | | | | REF_CLOSE: (15), (49), (140) are inconsistent by sub-proof
% 229.78/41.20  | | | | | | | | | | | | | |            #1166.
% 229.78/41.20  | | | | | | | | | | | | | | 
% 229.78/41.20  | | | | | | | | | | | | | End of split
% 229.78/41.20  | | | | | | | | | | | | | 
% 229.78/41.20  | | | | | | | | | | | | Case 2:
% 229.78/41.20  | | | | | | | | | | | | | 
% 229.78/41.20  | | | | | | | | | | | | |   (141)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 229.78/41.20  | | | | | | | | | | | | |            e3 & op(e2, e0) = e3)
% 229.78/41.20  | | | | | | | | | | | | | 
% 229.78/41.20  | | | | | | | | | | | | | REF_CLOSE: (4), (6), (15), (16), (20), (24), (27), (30),
% 229.78/41.20  | | | | | | | | | | | | |            (33), (42), (43), (47), (58), (95), (141) are
% 229.78/41.20  | | | | | | | | | | | | |            inconsistent by sub-proof #895.
% 229.78/41.20  | | | | | | | | | | | | | 
% 229.78/41.20  | | | | | | | | | | | | End of split
% 229.78/41.20  | | | | | | | | | | | | 
% 229.78/41.20  | | | | | | | | | | | Case 2:
% 229.78/41.20  | | | | | | | | | | | | 
% 229.78/41.20  | | | | | | | | | | | |   (142)  all_57_10 = e1 & op(e2, e0) = e1
% 229.78/41.20  | | | | | | | | | | | | 
% 229.78/41.20  | | | | | | | | | | | | ALPHA: (142) implies:
% 229.78/41.20  | | | | | | | | | | | |   (143)  all_57_10 = e1
% 229.78/41.20  | | | | | | | | | | | | 
% 229.78/41.20  | | | | | | | | | | | | BETA: splitting (58) gives:
% 229.78/41.20  | | | | | | | | | | | | 
% 229.78/41.20  | | | | | | | | | | | | Case 1:
% 229.78/41.20  | | | | | | | | | | | | | 
% 229.78/41.20  | | | | | | | | | | | | |   (144)  all_57_9 = e0 & op(e3, e0) = e0
% 229.78/41.20  | | | | | | | | | | | | | 
% 229.78/41.20  | | | | | | | | | | | | | REF_CLOSE: (6), (40), (53), (144) are inconsistent by
% 229.78/41.20  | | | | | | | | | | | | |            sub-proof #2434.
% 229.78/41.20  | | | | | | | | | | | | | 
% 229.78/41.20  | | | | | | | | | | | | Case 2:
% 229.78/41.20  | | | | | | | | | | | | | 
% 229.78/41.20  | | | | | | | | | | | | |   (145)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 =
% 229.78/41.20  | | | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 229.78/41.20  | | | | | | | | | | | | | 
% 229.78/41.20  | | | | | | | | | | | | | BETA: splitting (145) gives:
% 229.78/41.20  | | | | | | | | | | | | | 
% 229.78/41.20  | | | | | | | | | | | | | Case 1:
% 229.78/41.20  | | | | | | | | | | | | | | 
% 229.78/41.20  | | | | | | | | | | | | | |   (146)  all_57_10 = e0 & op(e2, e0) = e0
% 229.78/41.20  | | | | | | | | | | | | | | 
% 229.78/41.20  | | | | | | | | | | | | | | ALPHA: (146) implies:
% 229.78/41.20  | | | | | | | | | | | | | |   (147)  all_57_10 = e0
% 229.78/41.20  | | | | | | | | | | | | | | 
% 229.78/41.20  | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 229.78/41.20  | | | | | | | | | | | | | |            (12), (13), (14), (15), (16), (17), (18), (19),
% 229.78/41.20  | | | | | | | | | | | | | |            (20), (21), (22), (23), (24), (25), (26), (27),
% 229.78/41.20  | | | | | | | | | | | | | |            (28), (29), (30), (31), (32), (33), (34), (36),
% 229.78/41.20  | | | | | | | | | | | | | |            (37), (38), (39), (40), (41), (42), (43), (44),
% 229.78/41.20  | | | | | | | | | | | | | |            (45), (46), (47), (48), (49), (50), (51), (52),
% 229.78/41.20  | | | | | | | | | | | | | |            (53), (57), (58), (98), (147) are inconsistent by
% 229.78/41.20  | | | | | | | | | | | | | |            sub-proof #893.
% 229.78/41.20  | | | | | | | | | | | | | | 
% 229.78/41.20  | | | | | | | | | | | | | Case 2:
% 229.78/41.20  | | | | | | | | | | | | | | 
% 229.78/41.20  | | | | | | | | | | | | | |   (148)  all_57_11 = e0 & op(e1, e0) = e0
% 229.78/41.20  | | | | | | | | | | | | | | 
% 229.78/41.20  | | | | | | | | | | | | | | ALPHA: (148) implies:
% 229.78/41.20  | | | | | | | | | | | | | |   (149)  all_57_11 = e0
% 229.78/41.20  | | | | | | | | | | | | | | 
% 229.78/41.20  | | | | | | | | | | | | | | BETA: splitting (43) gives:
% 229.78/41.20  | | | | | | | | | | | | | | 
% 229.78/41.20  | | | | | | | | | | | | | | Case 1:
% 229.78/41.20  | | | | | | | | | | | | | | | 
% 229.78/41.20  | | | | | | | | | | | | | | |   (150)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 229.78/41.20  | | | | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 229.78/41.20  | | | | | | | | | | | | | | | 
% 229.78/41.20  | | | | | | | | | | | | | | | BETA: splitting (150) gives:
% 229.78/41.20  | | | | | | | | | | | | | | | 
% 229.78/41.20  | | | | | | | | | | | | | | | Case 1:
% 229.78/41.20  | | | | | | | | | | | | | | | | 
% 229.78/41.20  | | | | | | | | | | | | | | | |   (151)  all_57_9 = e2 & op(e3, e0) = e2
% 229.78/41.20  | | | | | | | | | | | | | | | | 
% 229.78/41.20  | | | | | | | | | | | | | | | | ALPHA: (151) implies:
% 229.78/41.20  | | | | | | | | | | | | | | | |   (152)  all_57_9 = e2
% 229.78/41.20  | | | | | | | | | | | | | | | | 
% 229.78/41.20  | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10),
% 229.78/41.20  | | | | | | | | | | | | | | | |            (12), (13), (15), (16), (17), (19), (20), (21),
% 229.78/41.20  | | | | | | | | | | | | | | | |            (22), (24), (25), (27), (28), (29), (30), (31),
% 229.78/41.20  | | | | | | | | | | | | | | | |            (33), (34), (37), (38), (39), (40), (41), (42),
% 229.78/41.20  | | | | | | | | | | | | | | | |            (43), (44), (45), (47), (48), (49), (50), (52),
% 229.78/41.20  | | | | | | | | | | | | | | | |            (53), (57), (58), (95), (101), (143), (149), (152)
% 229.78/41.20  | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #897.
% 229.78/41.20  | | | | | | | | | | | | | | | | 
% 229.78/41.20  | | | | | | | | | | | | | | | Case 2:
% 229.78/41.20  | | | | | | | | | | | | | | | | 
% 229.78/41.20  | | | | | | | | | | | | | | | |   (153)  all_57_10 = e2 & op(e2, e0) = e2
% 229.78/41.20  | | | | | | | | | | | | | | | | 
% 229.78/41.20  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (35), (153) are inconsistent by
% 229.78/41.20  | | | | | | | | | | | | | | | |            sub-proof #2432.
% 229.78/41.20  | | | | | | | | | | | | | | | | 
% 229.78/41.20  | | | | | | | | | | | | | | | End of split
% 229.78/41.20  | | | | | | | | | | | | | | | 
% 229.78/41.20  | | | | | | | | | | | | | | Case 2:
% 229.78/41.20  | | | | | | | | | | | | | | | 
% 229.78/41.20  | | | | | | | | | | | | | | |   (154)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 229.78/41.20  | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 229.78/41.20  | | | | | | | | | | | | | | | 
% 229.78/41.20  | | | | | | | | | | | | | | | BETA: splitting (154) gives:
% 229.78/41.20  | | | | | | | | | | | | | | | 
% 229.78/41.20  | | | | | | | | | | | | | | | Case 1:
% 229.78/41.20  | | | | | | | | | | | | | | | | 
% 229.78/41.20  | | | | | | | | | | | | | | | |   (155)  all_57_11 = e2 & op(e1, e0) = e2
% 229.78/41.20  | | | | | | | | | | | | | | | | 
% 229.78/41.20  | | | | | | | | | | | | | | | | ALPHA: (155) implies:
% 229.78/41.20  | | | | | | | | | | | | | | | |   (156)  all_57_11 = e2
% 229.78/41.20  | | | | | | | | | | | | | | | | 
% 229.78/41.20  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (15), (16), (20), (24),
% 229.78/41.20  | | | | | | | | | | | | | | | |            (27), (33), (34), (42), (43), (47), (48), (51),
% 229.78/41.20  | | | | | | | | | | | | | | | |            (156) are inconsistent by sub-proof #947.
% 229.78/41.20  | | | | | | | | | | | | | | | | 
% 229.78/41.20  | | | | | | | | | | | | | | | Case 2:
% 229.78/41.20  | | | | | | | | | | | | | | | | 
% 229.78/41.20  | | | | | | | | | | | | | | | |   (157)  all_57_15 = e2 & op(e0, e0) = e2
% 229.78/41.20  | | | | | | | | | | | | | | | | 
% 229.78/41.20  | | | | | | | | | | | | | | | | REF_CLOSE: (15), (20), (157) are inconsistent by sub-proof
% 229.78/41.20  | | | | | | | | | | | | | | | |            #2323.
% 229.78/41.20  | | | | | | | | | | | | | | | | 
% 229.78/41.20  | | | | | | | | | | | | | | | End of split
% 229.78/41.20  | | | | | | | | | | | | | | | 
% 229.78/41.20  | | | | | | | | | | | | | | End of split
% 229.78/41.20  | | | | | | | | | | | | | | 
% 229.78/41.20  | | | | | | | | | | | | | End of split
% 229.78/41.20  | | | | | | | | | | | | | 
% 229.78/41.20  | | | | | | | | | | | | End of split
% 229.78/41.20  | | | | | | | | | | | | 
% 229.78/41.20  | | | | | | | | | | | End of split
% 229.78/41.20  | | | | | | | | | | | 
% 229.78/41.20  | | | | | | | | | | End of split
% 229.78/41.20  | | | | | | | | | | 
% 229.78/41.20  | | | | | | | | | End of split
% 229.78/41.20  | | | | | | | | | 
% 229.78/41.20  | | | | | | | | End of split
% 229.78/41.20  | | | | | | | | 
% 229.78/41.20  | | | | | | | Case 2:
% 229.78/41.20  | | | | | | | | 
% 229.78/41.20  | | | | | | | |   (158)  all_57_3 = e3 & op(e2, e2) = e3
% 229.78/41.20  | | | | | | | | 
% 229.78/41.20  | | | | | | | | ALPHA: (158) implies:
% 229.78/41.20  | | | | | | | |   (159)  all_57_3 = e3
% 229.78/41.20  | | | | | | | | 
% 229.78/41.20  | | | | | | | | REF_CLOSE: (15), (49), (159) are inconsistent by sub-proof
% 229.78/41.20  | | | | | | | |            #1166.
% 229.78/41.20  | | | | | | | | 
% 229.78/41.20  | | | | | | | End of split
% 229.78/41.20  | | | | | | | 
% 229.78/41.20  | | | | | | Case 2:
% 229.78/41.20  | | | | | | | 
% 229.78/41.20  | | | | | | |   (160)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 &
% 229.78/41.20  | | | | | | |            op(e2, e0) = e3)
% 229.78/41.20  | | | | | | | 
% 229.78/41.20  | | | | | | | BETA: splitting (160) gives:
% 229.78/41.20  | | | | | | | 
% 229.78/41.20  | | | | | | | Case 1:
% 229.78/41.20  | | | | | | | | 
% 229.78/41.20  | | | | | | | |   (161)  all_57_5 = e3 & op(e2, e1) = e3
% 229.78/41.20  | | | | | | | | 
% 229.78/41.20  | | | | | | | | ALPHA: (161) implies:
% 229.78/41.20  | | | | | | | |   (162)  all_57_5 = e3
% 229.78/41.20  | | | | | | | | 
% 229.78/41.20  | | | | | | | | COMBINE_EQS: (95), (162) imply:
% 229.78/41.20  | | | | | | | |   (163)  e3 = e0
% 229.78/41.20  | | | | | | | | 
% 229.78/41.20  | | | | | | | | SIMP: (163) implies:
% 229.78/41.20  | | | | | | | |   (164)  e3 = e0
% 229.78/41.20  | | | | | | | | 
% 229.78/41.20  | | | | | | | | COMBINE_EQS: (98), (164) imply:
% 229.78/41.20  | | | | | | | |   (165)  all_57_1 = e0
% 229.78/41.20  | | | | | | | | 
% 229.78/41.20  | | | | | | | | REF_CLOSE: (3), (4), (6), (10), (12), (13), (15), (16), (19),
% 229.78/41.20  | | | | | | | |            (20), (21), (22), (24), (25), (27), (29), (30), (31),
% 229.78/41.20  | | | | | | | |            (37), (40), (42), (43), (47), (49), (50), (53), (57),
% 229.78/41.20  | | | | | | | |            (58), (165) are inconsistent by sub-proof #890.
% 229.78/41.20  | | | | | | | | 
% 229.78/41.20  | | | | | | | Case 2:
% 229.78/41.20  | | | | | | | | 
% 229.78/41.20  | | | | | | | |   (166)  all_57_10 = e3 & op(e2, e0) = e3
% 229.78/41.20  | | | | | | | | 
% 229.78/41.20  | | | | | | | | ALPHA: (166) implies:
% 229.78/41.20  | | | | | | | |   (167)  all_57_10 = e3
% 229.78/41.20  | | | | | | | | 
% 229.78/41.20  | | | | | | | | REF_CLOSE: (4), (6), (8), (9), (10), (12), (13), (15), (16),
% 229.78/41.20  | | | | | | | |            (20), (22), (24), (27), (28), (31), (33), (42), (43),
% 229.78/41.20  | | | | | | | |            (95), (98), (167) are inconsistent by sub-proof #949.
% 229.78/41.20  | | | | | | | | 
% 229.78/41.20  | | | | | | | End of split
% 229.78/41.20  | | | | | | | 
% 229.78/41.20  | | | | | | End of split
% 229.78/41.20  | | | | | | 
% 229.78/41.20  | | | | | Case 2:
% 229.78/41.20  | | | | | | 
% 229.78/41.20  | | | | | |   (168)  all_57_3 = e3 & op(e2, e2) = e3
% 229.78/41.20  | | | | | | 
% 229.78/41.20  | | | | | | ALPHA: (168) implies:
% 229.78/41.20  | | | | | |   (169)  all_57_3 = e3
% 229.78/41.20  | | | | | | 
% 229.78/41.20  | | | | | | REF_CLOSE: (15), (49), (169) are inconsistent by sub-proof #1166.
% 229.78/41.20  | | | | | | 
% 229.78/41.20  | | | | | End of split
% 229.78/41.20  | | | | | 
% 229.78/41.20  | | | | Case 2:
% 229.78/41.20  | | | | | 
% 229.88/41.20  | | | | |   (170)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0,
% 229.88/41.20  | | | | |              e2) = e3)
% 229.88/41.20  | | | | | 
% 229.88/41.20  | | | | | REF_CLOSE: (4), (6), (15), (16), (20), (22), (24), (27), (30), (31),
% 229.88/41.20  | | | | |            (42), (51), (57), (170) are inconsistent by sub-proof
% 229.88/41.20  | | | | |            #1766.
% 229.88/41.20  | | | | | 
% 229.88/41.20  | | | | End of split
% 229.88/41.20  | | | | 
% 229.88/41.20  | | | Case 2:
% 229.88/41.20  | | | | 
% 229.88/41.20  | | | |   (171)  all_57_10 = e0 & op(e2, e0) = e0
% 229.88/41.20  | | | | 
% 229.88/41.20  | | | | ALPHA: (171) implies:
% 229.88/41.20  | | | |   (172)  all_57_10 = e0
% 229.88/41.20  | | | | 
% 229.88/41.20  | | | | BETA: splitting (29) gives:
% 229.88/41.20  | | | | 
% 229.88/41.20  | | | | Case 1:
% 229.88/41.20  | | | | | 
% 229.88/41.20  | | | | |   (173)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2,
% 229.88/41.20  | | | | |              e2) = e3)
% 229.88/41.20  | | | | | 
% 229.88/41.20  | | | | | BETA: splitting (173) gives:
% 229.88/41.20  | | | | | 
% 229.88/41.20  | | | | | Case 1:
% 229.88/41.20  | | | | | | 
% 229.88/41.20  | | | | | |   (174)  all_57_1 = e3 & op(e3, e2) = e3
% 229.88/41.20  | | | | | | 
% 229.88/41.20  | | | | | | ALPHA: (174) implies:
% 229.88/41.20  | | | | | |   (175)  all_57_1 = e3
% 229.88/41.20  | | | | | | 
% 229.88/41.20  | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12),
% 229.88/41.20  | | | | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21),
% 229.88/41.20  | | | | | |            (22), (23), (24), (25), (26), (27), (28), (29), (30),
% 229.88/41.20  | | | | | |            (31), (32), (33), (34), (36), (37), (38), (39), (40),
% 229.88/41.20  | | | | | |            (41), (42), (43), (44), (45), (46), (47), (48), (49),
% 229.88/41.20  | | | | | |            (50), (51), (52), (53), (57), (58), (172), (175) are
% 229.88/41.20  | | | | | |            inconsistent by sub-proof #893.
% 229.88/41.20  | | | | | | 
% 229.88/41.20  | | | | | Case 2:
% 229.88/41.20  | | | | | | 
% 229.88/41.20  | | | | | |   (176)  all_57_3 = e3 & op(e2, e2) = e3
% 229.88/41.20  | | | | | | 
% 229.88/41.20  | | | | | | ALPHA: (176) implies:
% 229.88/41.20  | | | | | |   (177)  all_57_3 = e3
% 229.88/41.20  | | | | | | 
% 229.88/41.20  | | | | | | REF_CLOSE: (15), (49), (177) are inconsistent by sub-proof #1166.
% 229.88/41.20  | | | | | | 
% 229.88/41.20  | | | | | End of split
% 229.88/41.20  | | | | | 
% 229.88/41.20  | | | | Case 2:
% 229.88/41.20  | | | | | 
% 229.88/41.20  | | | | |   (178)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0,
% 229.88/41.20  | | | | |              e2) = e3)
% 229.88/41.20  | | | | | 
% 229.88/41.20  | | | | | REF_CLOSE: (4), (6), (15), (16), (20), (22), (24), (27), (30), (31),
% 229.88/41.20  | | | | |            (42), (51), (57), (178) are inconsistent by sub-proof
% 229.88/41.20  | | | | |            #1766.
% 229.88/41.20  | | | | | 
% 229.88/41.20  | | | | End of split
% 229.88/41.20  | | | | 
% 229.88/41.20  | | | End of split
% 229.88/41.20  | | | 
% 229.88/41.20  | | End of split
% 229.88/41.20  | | 
% 229.88/41.20  | End of split
% 229.88/41.20  | 
% 229.88/41.20  End of proof
% 229.88/41.20  
% 229.88/41.20  Sub-proof #890 shows that the following formulas are inconsistent:
% 229.88/41.20  ----------------------------------------------------------------
% 229.88/41.20    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.88/41.20         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.88/41.20    (2)   ~ (e3 = e1)
% 229.88/41.20    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.88/41.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.88/41.20    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.88/41.20         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.88/41.20    (5)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.88/41.20         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.88/41.20    (6)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.88/41.20         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.88/41.20    (7)   ~ (e3 = e2)
% 229.88/41.20    (8)   ~ (e3 = e0)
% 229.88/41.20    (9)  all_57_1 = e0
% 229.88/41.20    (10)  all_57_0 = e0
% 229.88/41.20    (11)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.88/41.20          | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.88/41.20    (12)  all_57_15 = e3
% 229.88/41.20    (13)  op(e3, e3) = e0
% 229.88/41.20    (14)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.88/41.20          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.88/41.20            e1)
% 229.88/41.20    (15)   ~ (e2 = e0)
% 229.88/41.20    (16)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.88/41.20          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.88/41.20    (17)   ~ (e1 = e0)
% 229.88/41.20    (18)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.88/41.20          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.88/41.20    (19)  op(e0, e0) = e3
% 229.88/41.20    (20)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.88/41.20          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.88/41.20            e2)
% 229.88/41.20    (21)   ~ (all_53_12 = e3)
% 229.88/41.20    (22)   ~ (all_53_12 = e0)
% 229.88/41.20    (23)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) |
% 229.88/41.20          (all_57_11 = e0 & op(e1, e0) = e0)
% 229.88/41.20    (24)   ~ (e2 = e1)
% 229.88/41.20    (25)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.88/41.20          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.88/41.20    (26)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.88/41.20          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.88/41.20    (27)  all_57_3 = e2
% 229.88/41.20    (28)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.88/41.20          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.88/41.20    (29)  op(e3, e0) = all_53_12
% 229.88/41.20  
% 229.88/41.20  Begin of proof
% 229.88/41.20  | 
% 229.88/41.20  | BETA: splitting (16) gives:
% 229.88/41.20  | 
% 229.88/41.20  | Case 1:
% 229.88/41.20  | | 
% 229.88/41.20  | |   (30)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) =
% 229.88/41.20  | |           e3)
% 229.88/41.20  | | 
% 229.88/41.20  | | REF_CLOSE: (3), (8), (9), (13), (30) are inconsistent by sub-proof #2404.
% 229.88/41.20  | | 
% 229.88/41.20  | Case 2:
% 229.88/41.20  | | 
% 229.88/41.20  | |   (31)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) =
% 229.88/41.20  | |           e3)
% 229.88/41.20  | | 
% 229.88/41.20  | | BETA: splitting (31) gives:
% 229.88/41.20  | | 
% 229.88/41.20  | | Case 1:
% 229.88/41.20  | | | 
% 229.88/41.20  | | |   (32)  all_57_4 = e3 & op(e3, e1) = e3
% 229.88/41.20  | | | 
% 229.88/41.20  | | | ALPHA: (32) implies:
% 229.88/41.20  | | |   (33)  all_57_4 = e3
% 229.88/41.20  | | | 
% 229.88/41.20  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 229.88/41.20  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 229.88/41.20  | | |            (23), (24), (25), (26), (27), (28), (29), (33) are inconsistent
% 229.88/41.20  | | |            by sub-proof #891.
% 229.88/41.20  | | | 
% 229.88/41.20  | | Case 2:
% 229.88/41.20  | | | 
% 229.88/41.20  | | |   (34)  all_57_9 = e3 & op(e3, e0) = e3
% 229.88/41.20  | | | 
% 229.88/41.20  | | | ALPHA: (34) implies:
% 229.88/41.20  | | |   (35)  op(e3, e0) = e3
% 229.88/41.20  | | | 
% 229.88/41.20  | | | REF_CLOSE: (3), (21), (29), (35) are inconsistent by sub-proof #2458.
% 229.88/41.20  | | | 
% 229.88/41.20  | | End of split
% 229.88/41.20  | | 
% 229.88/41.20  | End of split
% 229.88/41.20  | 
% 229.88/41.20  End of proof
% 229.88/41.20  
% 229.88/41.20  Sub-proof #891 shows that the following formulas are inconsistent:
% 229.88/41.20  ----------------------------------------------------------------
% 229.88/41.20    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.88/41.20         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.88/41.20    (2)   ~ (e3 = e1)
% 229.88/41.20    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.88/41.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.88/41.20    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.88/41.20         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.88/41.20    (5)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.88/41.20         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.88/41.20    (6)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.88/41.20         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.88/41.20    (7)  all_57_4 = e3
% 229.88/41.20    (8)   ~ (e3 = e2)
% 229.88/41.20    (9)   ~ (e3 = e0)
% 229.88/41.20    (10)  all_57_1 = e0
% 229.88/41.20    (11)  all_57_0 = e0
% 229.88/41.20    (12)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.88/41.20          | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.88/41.20    (13)  all_57_15 = e3
% 229.88/41.20    (14)  op(e3, e3) = e0
% 229.88/41.20    (15)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.88/41.20          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.88/41.20            e1)
% 229.88/41.20    (16)   ~ (e2 = e0)
% 229.88/41.20    (17)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.88/41.20          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.88/41.20    (18)   ~ (e1 = e0)
% 229.88/41.20    (19)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.88/41.20          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.88/41.20    (20)  op(e0, e0) = e3
% 229.88/41.20    (21)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.88/41.20          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.88/41.20            e2)
% 229.88/41.20    (22)   ~ (all_53_12 = e3)
% 229.88/41.20    (23)   ~ (all_53_12 = e0)
% 229.88/41.20    (24)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) |
% 229.88/41.20          (all_57_11 = e0 & op(e1, e0) = e0)
% 229.88/41.20    (25)   ~ (e2 = e1)
% 229.88/41.20    (26)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.88/41.20          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.88/41.20    (27)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.88/41.20          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.88/41.20    (28)  all_57_3 = e2
% 229.88/41.20    (29)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.88/41.20          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.88/41.20    (30)  op(e3, e0) = all_53_12
% 229.88/41.20  
% 229.88/41.20  Begin of proof
% 229.88/41.20  | 
% 229.88/41.20  | BETA: splitting (19) gives:
% 229.88/41.20  | 
% 229.88/41.20  | Case 1:
% 229.88/41.20  | | 
% 229.88/41.20  | |   (31)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 229.88/41.20  | |           e3)
% 229.88/41.20  | | 
% 229.88/41.20  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (14), (16), (18), (25),
% 229.88/41.20  | |            (28), (31) are inconsistent by sub-proof #892.
% 229.88/41.20  | | 
% 229.88/41.20  | Case 2:
% 229.88/41.20  | | 
% 229.88/41.20  | |   (32)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 229.88/41.20  | |           e3)
% 229.88/41.20  | | 
% 229.88/41.20  | | BETA: splitting (32) gives:
% 229.88/41.20  | | 
% 229.88/41.20  | | Case 1:
% 229.88/41.20  | | | 
% 229.88/41.20  | | |   (33)  all_57_7 = e3 & op(e1, e2) = e3
% 229.88/41.20  | | | 
% 229.88/41.20  | | | ALPHA: (33) implies:
% 229.88/41.20  | | |   (34)  all_57_7 = e3
% 229.88/41.20  | | | 
% 229.88/41.20  | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (13), (14),
% 229.88/41.20  | | |            (16), (17), (18), (20), (22), (23), (24), (25), (26), (27),
% 229.88/41.20  | | |            (28), (29), (30), (34) are inconsistent by sub-proof #900.
% 229.88/41.20  | | | 
% 229.88/41.20  | | Case 2:
% 229.88/41.20  | | | 
% 229.88/41.20  | | |   (35)  all_57_13 = e3 & op(e0, e2) = e3
% 229.88/41.20  | | | 
% 229.88/41.20  | | | ALPHA: (35) implies:
% 229.88/41.20  | | |   (36)  all_57_13 = e3
% 229.88/41.20  | | | 
% 229.88/41.20  | | | REF_CLOSE: (2), (3), (8), (9), (12), (13), (15), (16), (18), (20), (21),
% 229.88/41.20  | | |            (25), (36) are inconsistent by sub-proof #2054.
% 229.88/41.20  | | | 
% 229.88/41.20  | | End of split
% 229.88/41.20  | | 
% 229.88/41.20  | End of split
% 229.88/41.20  | 
% 229.88/41.20  End of proof
% 229.88/41.20  
% 229.88/41.20  Sub-proof #892 shows that the following formulas are inconsistent:
% 229.88/41.20  ----------------------------------------------------------------
% 229.88/41.20    (1)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3)
% 229.88/41.20    (2)   ~ (e3 = e1)
% 229.88/41.20    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.88/41.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.88/41.20    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.88/41.20         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.88/41.20    (5)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.88/41.20         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.88/41.20    (6)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.88/41.20         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.88/41.20    (7)  all_57_4 = e3
% 229.88/41.20    (8)   ~ (e3 = e2)
% 229.88/41.20    (9)   ~ (e3 = e0)
% 229.88/41.20    (10)  op(e3, e3) = e0
% 229.88/41.20    (11)   ~ (e2 = e0)
% 229.88/41.20    (12)   ~ (e1 = e0)
% 229.88/41.20    (13)   ~ (e2 = e1)
% 229.88/41.20    (14)  all_57_3 = e2
% 229.88/41.20  
% 229.88/41.20  Begin of proof
% 229.88/41.20  | 
% 229.88/41.20  | BETA: splitting (1) gives:
% 229.88/41.20  | 
% 229.88/41.20  | Case 1:
% 229.88/41.20  | | 
% 229.88/41.20  | |   (15)  all_57_1 = e3 & op(e3, e2) = e3
% 229.88/41.20  | | 
% 229.88/41.20  | | ALPHA: (15) implies:
% 229.88/41.20  | |   (16)  all_57_1 = e3
% 229.88/41.20  | | 
% 229.88/41.20  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 229.88/41.20  | |            (16) are inconsistent by sub-proof #1220.
% 229.88/41.20  | | 
% 229.88/41.20  | Case 2:
% 229.88/41.20  | | 
% 229.88/41.20  | |   (17)  all_57_3 = e3 & op(e2, e2) = e3
% 229.88/41.20  | | 
% 229.88/41.20  | | ALPHA: (17) implies:
% 229.88/41.20  | |   (18)  all_57_3 = e3
% 229.88/41.20  | | 
% 229.88/41.20  | | REF_CLOSE: (8), (14), (18) are inconsistent by sub-proof #1166.
% 229.88/41.20  | | 
% 229.88/41.20  | End of split
% 229.88/41.20  | 
% 229.88/41.20  End of proof
% 229.88/41.20  
% 229.88/41.20  Sub-proof #893 shows that the following formulas are inconsistent:
% 229.88/41.20  ----------------------------------------------------------------
% 229.88/41.20    (1)  all_57_10 = e0
% 229.88/41.20    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.88/41.20         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.88/41.20    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.88/41.20         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.88/41.20    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.88/41.20         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.88/41.20    (5)   ~ (e3 = e1)
% 229.88/41.20    (6)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 229.88/41.20         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 229.88/41.20    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.88/41.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.88/41.20    (8)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.88/41.20         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.88/41.20    (9)   ~ (all_6_2 = e3)
% 229.88/41.20    (10)  op(e1, e1) = all_6_2
% 229.88/41.20    (11)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.88/41.20          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.88/41.21    (12)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.88/41.21          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.88/41.21    (13)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.88/41.21          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.88/41.21    (14)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 229.88/41.21          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.88/41.21    (15)   ~ (e3 = e2)
% 229.88/41.21    (16)   ~ (e3 = e0)
% 229.88/41.21    (17)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 229.88/41.21          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 229.88/41.21    (18)  op(e0, e3) = all_53_3
% 229.88/41.21    (19)  all_57_0 = e0
% 229.88/41.21    (20)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.88/41.21          | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.88/41.21    (21)  all_57_15 = e3
% 229.88/41.21    (22)  op(e3, e3) = e0
% 229.88/41.21    (23)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.88/41.21          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.88/41.21            e1)
% 229.88/41.21    (24)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.88/41.21          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.88/41.21    (25)   ~ (e2 = e0)
% 229.88/41.21    (26)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.88/41.21          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.88/41.21    (27)  op(e2, e2) = e2
% 229.88/41.21    (28)   ~ (e1 = e0)
% 229.88/41.21    (29)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.88/41.21          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.88/41.21    (30)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.88/41.21          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.88/41.21    (31)  op(e0, e0) = e3
% 229.88/41.21    (32)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.88/41.21          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.88/41.21            e2)
% 229.88/41.21    (33)   ~ (all_53_3 = e0)
% 229.88/41.21    (34)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.88/41.21              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.88/41.21                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.88/41.21                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.88/41.21    (35)  op(e1, e1) = e0
% 229.88/41.21    (36)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.88/41.21          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.88/41.21    (37)   ~ (all_53_12 = e3)
% 229.88/41.21    (38)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.88/41.21          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.88/41.21    (39)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.88/41.21          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.88/41.21    (40)  all_57_1 = e3
% 229.88/41.21    (41)   ~ (all_53_12 = e0)
% 229.88/41.21    (42)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) |
% 229.88/41.21          (all_57_11 = e0 & op(e1, e0) = e0)
% 229.88/41.21    (43)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.88/41.21          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 229.88/41.21    (44)   ~ (e2 = e1)
% 229.88/41.21    (45)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.88/41.21          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.88/41.21    (46)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.88/41.21          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.88/41.21    (47)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 229.88/41.21          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 229.88/41.21    (48)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.88/41.21          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.88/41.21    (49)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.88/41.21          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.88/41.21    (50)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 229.88/41.21          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 229.88/41.21    (51)  all_57_3 = e2
% 229.88/41.21    (52)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.88/41.21          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.88/41.21    (53)  all_57_7 = e0
% 229.88/41.21    (54)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 229.88/41.21          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 229.88/41.21    (55)  op(e3, e0) = all_53_12
% 229.88/41.21  
% 229.88/41.21  Begin of proof
% 229.88/41.21  | 
% 229.88/41.21  | BETA: splitting (8) gives:
% 229.88/41.21  | 
% 229.88/41.21  | Case 1:
% 229.88/41.21  | | 
% 229.88/41.21  | |   (56)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 229.88/41.21  | |           e3)
% 229.88/41.21  | | 
% 229.88/41.21  | | BETA: splitting (56) gives:
% 229.88/41.21  | | 
% 229.88/41.21  | | Case 1:
% 229.88/41.21  | | | 
% 229.88/41.21  | | |   (57)  all_57_6 = e3 & op(e1, e3) = e3
% 229.88/41.21  | | | 
% 229.88/41.21  | | | ALPHA: (57) implies:
% 229.88/41.21  | | |   (58)  all_57_6 = e3
% 229.88/41.21  | | | 
% 229.88/41.21  | | | BETA: splitting (20) gives:
% 229.88/41.21  | | | 
% 229.88/41.21  | | | Case 1:
% 229.88/41.21  | | | | 
% 229.88/41.21  | | | |   (59)  all_57_12 = e0 & op(e0, e3) = e0
% 229.88/41.21  | | | | 
% 229.88/41.21  | | | | ALPHA: (59) implies:
% 229.88/41.21  | | | |   (60)  all_57_12 = e0
% 229.88/41.21  | | | | 
% 229.88/41.21  | | | | REF_CLOSE: (3), (5), (15), (19), (25), (28), (44), (46), (58), (60) are
% 229.88/41.21  | | | |            inconsistent by sub-proof #1425.
% 229.88/41.21  | | | | 
% 229.88/41.21  | | | Case 2:
% 229.88/41.21  | | | | 
% 229.88/41.21  | | | |   (61)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 229.88/41.21  | | | |             e1) = e0)
% 229.88/41.21  | | | | 
% 229.88/41.21  | | | | BETA: splitting (61) gives:
% 229.88/41.21  | | | | 
% 229.88/41.21  | | | | Case 1:
% 229.88/41.21  | | | | | 
% 229.88/41.21  | | | | |   (62)  all_57_13 = e0 & op(e0, e2) = e0
% 229.88/41.21  | | | | | 
% 229.88/41.21  | | | | | ALPHA: (62) implies:
% 229.88/41.21  | | | | |   (63)  all_57_13 = e0
% 229.88/41.21  | | | | | 
% 229.88/41.21  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 229.88/41.21  | | | | |            (12), (13), (14), (15), (16), (17), (18), (19), (20), (21),
% 229.88/41.21  | | | | |            (22), (23), (24), (25), (26), (27), (28), (29), (30), (31),
% 229.88/41.21  | | | | |            (32), (33), (34), (35), (36), (37), (38), (39), (41), (42),
% 229.88/41.21  | | | | |            (43), (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 229.88/41.21  | | | | |            (53), (54), (55), (58), (63) are inconsistent by sub-proof
% 229.88/41.21  | | | | |            #922.
% 229.88/41.21  | | | | | 
% 229.88/41.21  | | | | Case 2:
% 229.88/41.21  | | | | | 
% 229.88/41.21  | | | | |   (64)  all_57_14 = e0 & op(e0, e1) = e0
% 229.88/41.21  | | | | | 
% 229.88/41.21  | | | | | ALPHA: (64) implies:
% 229.88/41.21  | | | | |   (65)  all_57_14 = e0
% 229.88/41.21  | | | | | 
% 229.88/41.21  | | | | | BETA: splitting (46) gives:
% 229.88/41.21  | | | | | 
% 229.88/41.21  | | | | | Case 1:
% 229.88/41.21  | | | | | | 
% 229.88/41.21  | | | | | |   (66)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2,
% 229.88/41.21  | | | | | |             e3) = e2)
% 229.88/41.21  | | | | | | 
% 229.88/41.21  | | | | | | BETA: splitting (66) gives:
% 229.88/41.21  | | | | | | 
% 229.88/41.21  | | | | | | Case 1:
% 229.88/41.21  | | | | | | | 
% 229.88/41.21  | | | | | | |   (67)  all_57_0 = e2 & op(e3, e3) = e2
% 229.88/41.21  | | | | | | | 
% 229.88/41.21  | | | | | | | ALPHA: (67) implies:
% 229.88/41.21  | | | | | | |   (68)  op(e3, e3) = e2
% 229.88/41.21  | | | | | | | 
% 229.88/41.21  | | | | | | | REF_CLOSE: (7), (22), (25), (68) are inconsistent by sub-proof
% 229.88/41.21  | | | | | | |            #2403.
% 229.88/41.21  | | | | | | | 
% 229.88/41.21  | | | | | | Case 2:
% 229.88/41.21  | | | | | | | 
% 229.88/41.21  | | | | | | |   (69)  all_57_2 = e2 & op(e2, e3) = e2
% 229.88/41.21  | | | | | | | 
% 229.88/41.21  | | | | | | | ALPHA: (69) implies:
% 229.88/41.21  | | | | | | |   (70)  all_57_2 = e2
% 229.88/41.21  | | | | | | | 
% 229.88/41.21  | | | | | | | BETA: splitting (36) gives:
% 229.88/41.21  | | | | | | | 
% 229.88/41.21  | | | | | | | Case 1:
% 229.88/41.21  | | | | | | | | 
% 229.88/41.21  | | | | | | | |   (71)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 &
% 229.88/41.21  | | | | | | | |           op(e2, e2) = e3)
% 229.88/41.21  | | | | | | | | 
% 229.88/41.21  | | | | | | | | BETA: splitting (71) gives:
% 229.88/41.21  | | | | | | | | 
% 229.88/41.21  | | | | | | | | Case 1:
% 229.88/41.21  | | | | | | | | | 
% 229.88/41.21  | | | | | | | | |   (72)  all_57_2 = e3 & op(e2, e3) = e3
% 229.88/41.21  | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | ALPHA: (72) implies:
% 229.88/41.21  | | | | | | | | |   (73)  all_57_2 = e3
% 229.88/41.21  | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | REF_CLOSE: (3), (5), (7), (15), (19), (22), (25), (28), (44),
% 229.88/41.21  | | | | | | | | |            (46), (58), (73) are inconsistent by sub-proof
% 229.88/41.21  | | | | | | | | |            #1287.
% 229.88/41.21  | | | | | | | | | 
% 229.88/41.21  | | | | | | | | Case 2:
% 229.88/41.21  | | | | | | | | | 
% 229.88/41.21  | | | | | | | | |   (74)  all_57_3 = e3 & op(e2, e2) = e3
% 229.88/41.21  | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | ALPHA: (74) implies:
% 229.88/41.21  | | | | | | | | |   (75)  all_57_3 = e3
% 229.88/41.21  | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | REF_CLOSE: (15), (51), (75) are inconsistent by sub-proof
% 229.88/41.21  | | | | | | | | |            #1166.
% 229.88/41.21  | | | | | | | | | 
% 229.88/41.21  | | | | | | | | End of split
% 229.88/41.21  | | | | | | | | 
% 229.88/41.21  | | | | | | | Case 2:
% 229.88/41.21  | | | | | | | | 
% 229.88/41.21  | | | | | | | |   (76)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 &
% 229.88/41.21  | | | | | | | |           op(e2, e0) = e3)
% 229.88/41.21  | | | | | | | | 
% 229.88/41.21  | | | | | | | | BETA: splitting (76) gives:
% 229.88/41.21  | | | | | | | | 
% 229.88/41.21  | | | | | | | | Case 1:
% 229.88/41.21  | | | | | | | | | 
% 229.88/41.21  | | | | | | | | |   (77)  all_57_5 = e3 & op(e2, e1) = e3
% 229.88/41.21  | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | ALPHA: (77) implies:
% 229.88/41.21  | | | | | | | | |   (78)  all_57_5 = e3
% 229.88/41.21  | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | REF_CLOSE: (1), (2), (5), (7), (27), (28), (44), (70), (78)
% 229.88/41.21  | | | | | | | | |            are inconsistent by sub-proof #2241.
% 229.88/41.21  | | | | | | | | | 
% 229.88/41.21  | | | | | | | | Case 2:
% 229.88/41.21  | | | | | | | | | 
% 229.88/41.21  | | | | | | | | |   (79)  all_57_10 = e3 & op(e2, e0) = e3
% 229.88/41.21  | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | ALPHA: (79) implies:
% 229.88/41.21  | | | | | | | | |   (80)  all_57_10 = e3
% 229.88/41.21  | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | REF_CLOSE: (5), (7), (15), (16), (21), (25), (28), (31), (34),
% 229.88/41.21  | | | | | | | | |            (42), (44), (45), (49), (80) are inconsistent by
% 229.88/41.21  | | | | | | | | |            sub-proof #1747.
% 229.88/41.21  | | | | | | | | | 
% 229.88/41.21  | | | | | | | | End of split
% 229.88/41.21  | | | | | | | | 
% 229.88/41.21  | | | | | | | End of split
% 229.88/41.21  | | | | | | | 
% 229.88/41.21  | | | | | | End of split
% 229.88/41.21  | | | | | | 
% 229.88/41.21  | | | | | Case 2:
% 229.88/41.21  | | | | | | 
% 229.88/41.21  | | | | | |   (81)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0,
% 229.88/41.21  | | | | | |             e3) = e2)
% 229.88/41.21  | | | | | | 
% 229.88/41.21  | | | | | | BETA: splitting (81) gives:
% 229.88/41.21  | | | | | | 
% 229.88/41.21  | | | | | | Case 1:
% 229.88/41.21  | | | | | | | 
% 229.88/41.21  | | | | | | |   (82)  all_57_6 = e2 & op(e1, e3) = e2
% 229.88/41.21  | | | | | | | 
% 229.88/41.21  | | | | | | | REF_CLOSE: (15), (58), (82) are inconsistent by sub-proof #2012.
% 229.88/41.21  | | | | | | | 
% 229.88/41.21  | | | | | | Case 2:
% 229.88/41.21  | | | | | | | 
% 229.88/41.21  | | | | | | |   (83)  all_57_12 = e2 & op(e0, e3) = e2
% 229.88/41.21  | | | | | | | 
% 229.88/41.21  | | | | | | | ALPHA: (83) implies:
% 229.88/41.21  | | | | | | |   (84)  all_57_12 = e2
% 229.88/41.21  | | | | | | | 
% 229.88/41.21  | | | | | | | BETA: splitting (23) gives:
% 229.88/41.21  | | | | | | | 
% 229.88/41.21  | | | | | | | Case 1:
% 229.88/41.21  | | | | | | | | 
% 229.88/41.21  | | | | | | | |   (85)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 &
% 229.88/41.21  | | | | | | | |           op(e0, e2) = e1)
% 229.88/41.21  | | | | | | | | 
% 229.88/41.21  | | | | | | | | BETA: splitting (85) gives:
% 229.88/41.21  | | | | | | | | 
% 229.88/41.21  | | | | | | | | Case 1:
% 229.88/41.21  | | | | | | | | | 
% 229.88/41.21  | | | | | | | | |   (86)  all_57_12 = e1 & op(e0, e3) = e1
% 229.88/41.21  | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | REF_CLOSE: (44), (84), (86) are inconsistent by sub-proof
% 229.88/41.21  | | | | | | | | |            #2388.
% 229.88/41.21  | | | | | | | | | 
% 229.88/41.21  | | | | | | | | Case 2:
% 229.88/41.21  | | | | | | | | | 
% 229.88/41.21  | | | | | | | | |   (87)  all_57_13 = e1 & op(e0, e2) = e1
% 229.88/41.21  | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | ALPHA: (87) implies:
% 229.88/41.21  | | | | | | | | |   (88)  all_57_13 = e1
% 229.88/41.21  | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | BETA: splitting (3) gives:
% 229.88/41.21  | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | Case 1:
% 229.88/41.21  | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | |   (89)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 &
% 229.88/41.21  | | | | | | | | | |           op(e2, e3) = e1)
% 229.88/41.21  | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | BETA: splitting (89) gives:
% 229.88/41.21  | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | Case 1:
% 229.88/41.21  | | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | |   (90)  all_57_0 = e1 & op(e3, e3) = e1
% 229.88/41.21  | | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | | ALPHA: (90) implies:
% 229.88/41.21  | | | | | | | | | | |   (91)  all_57_0 = e1
% 229.88/41.21  | | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | | COMBINE_EQS: (19), (91) imply:
% 229.88/41.21  | | | | | | | | | | |   (92)  e1 = e0
% 229.88/41.21  | | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | | SIMP: (92) implies:
% 229.88/41.21  | | | | | | | | | | |   (93)  e1 = e0
% 229.88/41.21  | | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | | COMBINE_EQS: (88), (93) imply:
% 229.88/41.21  | | | | | | | | | | |   (94)  all_57_13 = e0
% 229.88/41.21  | | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 229.88/41.21  | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 229.88/41.21  | | | | | | | | | | |            (19), (20), (21), (22), (23), (24), (25), (26),
% 229.88/41.21  | | | | | | | | | | |            (27), (28), (29), (30), (31), (32), (33), (34),
% 229.88/41.21  | | | | | | | | | | |            (35), (36), (37), (38), (39), (41), (42), (43),
% 229.88/41.21  | | | | | | | | | | |            (44), (45), (46), (47), (48), (49), (50), (51),
% 229.88/41.21  | | | | | | | | | | |            (52), (53), (54), (55), (58), (94) are
% 229.88/41.21  | | | | | | | | | | |            inconsistent by sub-proof #922.
% 229.88/41.21  | | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | Case 2:
% 229.88/41.21  | | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | |   (95)  all_57_2 = e1 & op(e2, e3) = e1
% 229.88/41.21  | | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | | ALPHA: (95) implies:
% 229.88/41.21  | | | | | | | | | | |   (96)  all_57_2 = e1
% 229.88/41.21  | | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | | BETA: splitting (36) gives:
% 229.88/41.21  | | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | | Case 1:
% 229.88/41.21  | | | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | | |   (97)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 229.88/41.21  | | | | | | | | | | | |           & op(e2, e2) = e3)
% 229.88/41.21  | | | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | | | BETA: splitting (97) gives:
% 229.88/41.21  | | | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | | | Case 1:
% 229.88/41.21  | | | | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | | | |   (98)  all_57_2 = e3 & op(e2, e3) = e3
% 229.88/41.21  | | | | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | | | | ALPHA: (98) implies:
% 229.88/41.21  | | | | | | | | | | | | |   (99)  all_57_2 = e3
% 229.88/41.21  | | | | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | | | | REF_CLOSE: (3), (5), (7), (15), (19), (22), (25), (28), (44),
% 229.88/41.21  | | | | | | | | | | | | |            (46), (58), (99) are inconsistent by sub-proof
% 229.88/41.21  | | | | | | | | | | | | |            #1287.
% 229.88/41.21  | | | | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | | | Case 2:
% 229.88/41.21  | | | | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | | | |   (100)  all_57_3 = e3 & op(e2, e2) = e3
% 229.88/41.21  | | | | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | | | | ALPHA: (100) implies:
% 229.88/41.21  | | | | | | | | | | | | |   (101)  all_57_3 = e3
% 229.88/41.21  | | | | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | | | | COMBINE_EQS: (51), (101) imply:
% 229.88/41.21  | | | | | | | | | | | | |   (102)  e3 = e2
% 229.88/41.21  | | | | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | | | | SIMP: (102) implies:
% 229.88/41.21  | | | | | | | | | | | | |   (103)  e3 = e2
% 229.88/41.21  | | | | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | | | | COMBINE_EQS: (58), (103) imply:
% 229.88/41.21  | | | | | | | | | | | | |   (104)  all_57_6 = e2
% 229.88/41.21  | | | | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | | | | REF_CLOSE: (5), (7), (15), (16), (21), (22), (23), (25),
% 229.88/41.21  | | | | | | | | | | | | |            (28), (32), (39), (44), (65), (96), (104) are
% 229.88/41.21  | | | | | | | | | | | | |            inconsistent by sub-proof #894.
% 229.88/41.21  | | | | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | | | End of split
% 229.88/41.21  | | | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | | Case 2:
% 229.88/41.21  | | | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | | |   (105)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 229.88/41.21  | | | | | | | | | | | |            e3 & op(e2, e0) = e3)
% 229.88/41.21  | | | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | | | BETA: splitting (105) gives:
% 229.88/41.21  | | | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | | | Case 1:
% 229.88/41.21  | | | | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | | | |   (106)  all_57_5 = e3 & op(e2, e1) = e3
% 229.88/41.21  | | | | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | | | | ALPHA: (106) implies:
% 229.88/41.21  | | | | | | | | | | | | |   (107)  all_57_5 = e3
% 229.88/41.21  | | | | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | | | | BETA: splitting (54) gives:
% 229.88/41.21  | | | | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | | | | Case 1:
% 229.88/41.21  | | | | | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | | | | |   (108)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 229.88/41.21  | | | | | | | | | | | | | |            & op(e1, e2) = e2)
% 229.88/41.21  | | | | | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | | | | | BETA: splitting (108) gives:
% 229.88/41.21  | | | | | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | | | | | Case 1:
% 229.88/41.21  | | | | | | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | | | | | |   (109)  all_57_6 = e2 & op(e1, e3) = e2
% 229.88/41.21  | | | | | | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | | | | | | ALPHA: (109) implies:
% 229.88/41.21  | | | | | | | | | | | | | | |   (110)  all_57_6 = e2
% 229.88/41.21  | | | | | | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (15), (16), (21), (22), (23), (25),
% 229.88/41.21  | | | | | | | | | | | | | | |            (28), (32), (39), (44), (65), (96), (110) are
% 229.88/41.21  | | | | | | | | | | | | | | |            inconsistent by sub-proof #894.
% 229.88/41.21  | | | | | | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | | | | | Case 2:
% 229.88/41.21  | | | | | | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | | | | | |   (111)  all_57_7 = e2 & op(e1, e2) = e2
% 229.88/41.21  | | | | | | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | | | | | | ALPHA: (111) implies:
% 229.88/41.21  | | | | | | | | | | | | | | |   (112)  all_57_7 = e2
% 229.88/41.21  | | | | | | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | | | | | | COMBINE_EQS: (53), (112) imply:
% 229.88/41.21  | | | | | | | | | | | | | | |   (113)  e2 = e0
% 229.88/41.21  | | | | | | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | | | | | | COMBINE_EQS: (51), (113) imply:
% 229.88/41.21  | | | | | | | | | | | | | | |   (114)  all_57_3 = e0
% 229.88/41.21  | | | | | | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (5), (15), (25), (28), (38), (44),
% 229.88/41.21  | | | | | | | | | | | | | | |            (107), (114) are inconsistent by sub-proof #1518.
% 229.88/41.21  | | | | | | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | | | | | End of split
% 229.88/41.21  | | | | | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | | | | Case 2:
% 229.88/41.21  | | | | | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | | | | |   (115)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 229.88/41.21  | | | | | | | | | | | | | |            e2 & op(e1, e0) = e2)
% 229.88/41.21  | | | | | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | | | | | BETA: splitting (115) gives:
% 229.88/41.21  | | | | | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | | | | | Case 1:
% 229.88/41.21  | | | | | | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | | | | | |   (116)  all_57_8 = e2 & op(e1, e1) = e2
% 229.88/41.21  | | | | | | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | | | | | | ALPHA: (116) implies:
% 229.88/41.21  | | | | | | | | | | | | | | |   (117)  op(e1, e1) = e2
% 229.88/41.21  | | | | | | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with e0, e2, e1, e1, simplifying
% 229.88/41.21  | | | | | | | | | | | | | | |              with (35), (117) gives:
% 229.88/41.21  | | | | | | | | | | | | | | |   (118)  e2 = e0
% 229.88/41.21  | | | | | | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | | | | | | COMBINE_EQS: (51), (118) imply:
% 229.88/41.21  | | | | | | | | | | | | | | |   (119)  all_57_3 = e0
% 229.88/41.21  | | | | | | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (5), (15), (25), (28), (38), (44),
% 229.88/41.21  | | | | | | | | | | | | | | |            (107), (119) are inconsistent by sub-proof #1518.
% 229.88/41.21  | | | | | | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | | | | | Case 2:
% 229.88/41.21  | | | | | | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | | | | | |   (120)  all_57_11 = e2 & op(e1, e0) = e2
% 229.88/41.21  | | | | | | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | | | | | | ALPHA: (120) implies:
% 229.88/41.21  | | | | | | | | | | | | | | |   (121)  all_57_11 = e2
% 229.88/41.21  | | | | | | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (9), (10), (15), (16), (21), (25),
% 229.88/41.21  | | | | | | | | | | | | | | |            (28), (34), (35), (44), (45), (49), (50), (53),
% 229.88/41.21  | | | | | | | | | | | | | | |            (121) are inconsistent by sub-proof #947.
% 229.88/41.21  | | | | | | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | | | | | End of split
% 229.88/41.21  | | | | | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | | | | End of split
% 229.88/41.21  | | | | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | | | Case 2:
% 229.88/41.21  | | | | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | | | |   (122)  all_57_10 = e3 & op(e2, e0) = e3
% 229.88/41.21  | | | | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | | | | ALPHA: (122) implies:
% 229.88/41.21  | | | | | | | | | | | | |   (123)  all_57_10 = e3
% 229.88/41.21  | | | | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | | | | REF_CLOSE: (5), (7), (15), (16), (21), (25), (28), (31),
% 229.88/41.21  | | | | | | | | | | | | |            (34), (42), (44), (45), (49), (123) are
% 229.88/41.21  | | | | | | | | | | | | |            inconsistent by sub-proof #1747.
% 229.88/41.21  | | | | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | | | End of split
% 229.88/41.21  | | | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | | End of split
% 229.88/41.21  | | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | End of split
% 229.88/41.21  | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | Case 2:
% 229.88/41.21  | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | |   (124)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1
% 229.88/41.21  | | | | | | | | | |            & op(e0, e3) = e1)
% 229.88/41.21  | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | | REF_CLOSE: (5), (7), (8), (9), (10), (15), (16), (21), (25),
% 229.88/41.21  | | | | | | | | | |            (28), (34), (44), (45), (49), (53), (84), (124)
% 229.88/41.21  | | | | | | | | | |            are inconsistent by sub-proof #923.
% 229.88/41.21  | | | | | | | | | | 
% 229.88/41.21  | | | | | | | | | End of split
% 229.88/41.21  | | | | | | | | | 
% 229.88/41.21  | | | | | | | | End of split
% 229.88/41.21  | | | | | | | | 
% 229.88/41.21  | | | | | | | Case 2:
% 229.88/41.21  | | | | | | | | 
% 229.88/41.21  | | | | | | | |   (125)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 &
% 229.88/41.21  | | | | | | | |            op(e0, e0) = e1)
% 229.88/41.21  | | | | | | | | 
% 229.88/41.21  | | | | | | | | REF_CLOSE: (5), (7), (28), (31), (65), (125) are inconsistent by
% 229.88/41.21  | | | | | | | |            sub-proof #2056.
% 229.88/41.21  | | | | | | | | 
% 229.88/41.21  | | | | | | | End of split
% 229.88/41.21  | | | | | | | 
% 229.88/41.21  | | | | | | End of split
% 229.88/41.21  | | | | | | 
% 229.88/41.21  | | | | | End of split
% 229.88/41.21  | | | | | 
% 229.88/41.21  | | | | End of split
% 229.88/41.21  | | | | 
% 229.88/41.21  | | | End of split
% 229.88/41.21  | | | 
% 229.88/41.21  | | Case 2:
% 229.88/41.21  | | | 
% 229.88/41.21  | | |   (126)  all_57_7 = e3 & op(e1, e2) = e3
% 229.88/41.21  | | | 
% 229.88/41.21  | | | ALPHA: (126) implies:
% 229.88/41.21  | | |   (127)  all_57_7 = e3
% 229.88/41.21  | | | 
% 229.88/41.21  | | | REF_CLOSE: (4), (5), (7), (15), (16), (24), (25), (27), (28), (40), (44),
% 229.88/41.21  | | |            (52), (127) are inconsistent by sub-proof #1167.
% 229.88/41.21  | | | 
% 229.88/41.21  | | End of split
% 229.88/41.21  | | 
% 229.88/41.21  | Case 2:
% 229.88/41.21  | | 
% 229.88/41.21  | |   (128)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 229.88/41.21  | |            e3)
% 229.88/41.21  | | 
% 229.88/41.21  | | REF_CLOSE: (5), (7), (9), (10), (15), (16), (21), (25), (28), (42), (44),
% 229.88/41.21  | |            (45), (49), (128) are inconsistent by sub-proof #1080.
% 229.88/41.21  | | 
% 229.88/41.21  | End of split
% 229.88/41.21  | 
% 229.88/41.21  End of proof
% 229.88/41.21  
% 229.88/41.21  Sub-proof #894 shows that the following formulas are inconsistent:
% 229.88/41.21  ----------------------------------------------------------------
% 229.88/41.21    (1)   ~ (e3 = e1)
% 229.88/41.21    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.88/41.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.88/41.21    (3)   ~ (e3 = e2)
% 229.88/41.21    (4)   ~ (e3 = e0)
% 229.88/41.21    (5)  all_57_15 = e3
% 229.88/41.21    (6)  op(e3, e3) = e0
% 229.88/41.21    (7)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 229.88/41.21         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.88/41.21    (8)  all_57_6 = e2
% 229.88/41.21    (9)   ~ (e2 = e0)
% 229.88/41.21    (10)   ~ (e1 = e0)
% 229.88/41.21    (11)  all_57_2 = e1
% 229.88/41.21    (12)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.88/41.21          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.88/41.21            e2)
% 229.88/41.21    (13)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.88/41.21          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.88/41.21    (14)   ~ (e2 = e1)
% 229.88/41.21    (15)  all_57_14 = e0
% 229.88/41.21  
% 229.88/41.21  Begin of proof
% 229.88/41.21  | 
% 229.88/41.21  | BETA: splitting (13) gives:
% 229.88/41.21  | 
% 229.88/41.21  | Case 1:
% 229.88/41.21  | | 
% 229.88/41.21  | |   (16)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) =
% 229.88/41.21  | |           e3)
% 229.88/41.21  | | 
% 229.88/41.21  | | REF_CLOSE: (1), (2), (4), (6), (11), (16) are inconsistent by sub-proof
% 229.88/41.21  | |            #2396.
% 229.88/41.21  | | 
% 229.88/41.21  | Case 2:
% 229.88/41.21  | | 
% 229.88/41.21  | |   (17)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) =
% 229.88/41.21  | |           e3)
% 229.88/41.21  | | 
% 229.88/41.21  | | BETA: splitting (17) gives:
% 229.88/41.21  | | 
% 229.88/41.21  | | Case 1:
% 229.88/41.21  | | | 
% 229.88/41.21  | | |   (18)  all_57_6 = e3 & op(e1, e3) = e3
% 229.88/41.21  | | | 
% 229.88/41.21  | | | ALPHA: (18) implies:
% 229.88/41.21  | | |   (19)  all_57_6 = e3
% 229.88/41.21  | | | 
% 229.88/41.21  | | | REF_CLOSE: (3), (8), (19) are inconsistent by sub-proof #2463.
% 229.88/41.21  | | | 
% 229.88/41.21  | | Case 2:
% 229.88/41.21  | | | 
% 229.88/41.21  | | |   (20)  all_57_12 = e3 & op(e0, e3) = e3
% 229.88/41.21  | | | 
% 229.88/41.21  | | | ALPHA: (20) implies:
% 229.88/41.21  | | |   (21)  all_57_12 = e3
% 229.88/41.21  | | | 
% 229.88/41.21  | | | REF_CLOSE: (1), (3), (5), (7), (9), (10), (12), (14), (15), (21) are
% 229.88/41.21  | | |            inconsistent by sub-proof #1763.
% 229.88/41.21  | | | 
% 229.88/41.21  | | End of split
% 229.88/41.21  | | 
% 229.88/41.21  | End of split
% 229.88/41.21  | 
% 229.88/41.21  End of proof
% 229.88/41.21  
% 229.88/41.21  Sub-proof #895 shows that the following formulas are inconsistent:
% 229.88/41.21  ----------------------------------------------------------------
% 229.88/41.21    (1)   ~ (e3 = e1)
% 229.88/41.21    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.88/41.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.88/41.21    (3)   ~ (e3 = e2)
% 229.88/41.21    (4)   ~ (e3 = e0)
% 229.88/41.21    (5)  all_57_15 = e3
% 229.88/41.21    (6)   ~ (e2 = e0)
% 229.88/41.21    (7)   ~ (e1 = e0)
% 229.88/41.21    (8)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.88/41.21    (9)  op(e0, e0) = e3
% 229.88/41.21    (10)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.88/41.21              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.88/41.21                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.88/41.21                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.88/41.21    (11)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) |
% 229.88/41.21          (all_57_11 = e0 & op(e1, e0) = e0)
% 229.88/41.21    (12)   ~ (e2 = e1)
% 229.88/41.21    (13)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.88/41.21          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.88/41.22    (14)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.88/41.22          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.88/41.22    (15)  all_57_5 = e0
% 229.88/41.22  
% 229.88/41.22  Begin of proof
% 229.88/41.22  | 
% 229.88/41.22  | BETA: splitting (8) gives:
% 229.88/41.22  | 
% 229.88/41.22  | Case 1:
% 229.88/41.22  | | 
% 229.88/41.22  | |   (16)  all_57_5 = e3 & op(e2, e1) = e3
% 229.88/41.22  | | 
% 229.88/41.22  | | ALPHA: (16) implies:
% 229.88/41.22  | |   (17)  all_57_5 = e3
% 229.88/41.22  | | 
% 229.88/41.22  | | REF_CLOSE: (4), (15), (17) are inconsistent by sub-proof #2471.
% 229.88/41.22  | | 
% 229.88/41.22  | Case 2:
% 229.88/41.22  | | 
% 229.88/41.22  | |   (18)  all_57_10 = e3 & op(e2, e0) = e3
% 229.88/41.22  | | 
% 229.88/41.22  | | ALPHA: (18) implies:
% 229.88/41.22  | |   (19)  all_57_10 = e3
% 229.88/41.22  | | 
% 229.88/41.22  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13),
% 229.88/41.22  | |            (14), (19) are inconsistent by sub-proof #1747.
% 229.88/41.22  | | 
% 229.88/41.22  | End of split
% 229.88/41.22  | 
% 229.88/41.22  End of proof
% 229.88/41.22  
% 229.88/41.22  Sub-proof #896 shows that the following formulas are inconsistent:
% 229.88/41.22  ----------------------------------------------------------------
% 229.88/41.22    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.88/41.22         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.88/41.22    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.88/41.22         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.88/41.22    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.88/41.22         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.88/41.22    (4)   ~ (e3 = e1)
% 229.88/41.22    (5)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 229.88/41.22         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 229.88/41.22    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.88/41.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.88/41.22    (7)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.88/41.22         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.88/41.22    (8)   ~ (all_6_2 = e3)
% 229.88/41.22    (9)  op(e1, e1) = all_6_2
% 229.88/41.22    (10)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.88/41.22          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.88/41.22    (11)   ~ (all_53_13 = e2)
% 229.88/41.22    (12)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.88/41.22          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.88/41.22    (13)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.88/41.22          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.88/41.22    (14)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 229.88/41.22          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.88/41.22    (15)   ~ (e3 = e2)
% 229.88/41.22    (16)   ~ (e3 = e0)
% 229.88/41.22    (17)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 229.88/41.22          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 229.88/41.22    (18)  op(e0, e3) = all_53_3
% 229.88/41.22    (19)  all_57_0 = e0
% 229.88/41.22    (20)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.88/41.22          | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.88/41.22    (21)  all_57_15 = e3
% 229.88/41.22    (22)  op(e3, e3) = e0
% 229.88/41.22    (23)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.88/41.22          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.88/41.22            e1)
% 229.88/41.22    (24)  all_57_11 = e0
% 229.88/41.22    (25)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.88/41.22          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.88/41.22    (26)   ~ (e2 = e0)
% 229.88/41.22    (27)  all_57_2 = e3
% 229.88/41.22    (28)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.88/41.22          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.88/41.22    (29)   ~ (e1 = e0)
% 229.88/41.22    (30)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.88/41.22          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.88/41.22    (31)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.88/41.22          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.88/41.22    (32)  op(e0, e0) = e3
% 229.88/41.22    (33)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.88/41.22          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.88/41.22            e2)
% 229.88/41.22    (34)   ~ (all_53_3 = e0)
% 229.88/41.22    (35)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.88/41.22              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.88/41.22                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.88/41.22                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.88/41.22    (36)  op(e1, e1) = e0
% 229.88/41.22    (37)  op(e2, e0) = all_53_13
% 229.88/41.22    (38)  all_57_13 = e0
% 229.88/41.22    (39)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.88/41.22          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.88/41.22    (40)   ~ (all_53_12 = e3)
% 229.88/41.22    (41)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.88/41.22          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.88/41.22    (42)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.88/41.22          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.88/41.22    (43)   ~ (all_53_12 = e0)
% 229.88/41.22    (44)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) |
% 229.88/41.22          (all_57_11 = e0 & op(e1, e0) = e0)
% 229.88/41.22    (45)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.88/41.22          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 229.88/41.22    (46)   ~ (e2 = e1)
% 229.88/41.22    (47)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.88/41.22          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.88/41.22    (48)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.88/41.22          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.88/41.22    (49)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 229.88/41.22          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 229.88/41.22    (50)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.88/41.22          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.88/41.22    (51)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.88/41.22          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.88/41.22    (52)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 229.88/41.22          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 229.88/41.22    (53)  all_57_3 = e2
% 229.88/41.22    (54)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.88/41.22          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.88/41.22    (55)  all_57_5 = e0
% 229.88/41.22    (56)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 229.88/41.22          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 229.88/41.22    (57)  op(e3, e0) = all_53_12
% 229.88/41.22  
% 229.88/41.22  Begin of proof
% 229.88/41.22  | 
% 229.88/41.22  | BETA: splitting (47) gives:
% 229.88/41.22  | 
% 229.88/41.22  | Case 1:
% 229.88/41.22  | | 
% 229.88/41.22  | |   (58)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 229.88/41.22  | |           e2)
% 229.88/41.22  | | 
% 229.88/41.22  | | BETA: splitting (58) gives:
% 229.88/41.22  | | 
% 229.88/41.22  | | Case 1:
% 229.88/41.22  | | | 
% 229.88/41.22  | | |   (59)  all_57_9 = e2 & op(e3, e0) = e2
% 229.88/41.22  | | | 
% 229.88/41.22  | | | ALPHA: (59) implies:
% 229.88/41.22  | | |   (60)  all_57_9 = e2
% 229.88/41.22  | | | 
% 229.88/41.22  | | | BETA: splitting (1) gives:
% 229.88/41.22  | | | 
% 229.88/41.22  | | | Case 1:
% 229.88/41.22  | | | | 
% 229.88/41.22  | | | |   (61)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2)
% 229.88/41.22  | | | |           = e1)
% 229.88/41.22  | | | | 
% 229.88/41.22  | | | | BETA: splitting (61) gives:
% 229.88/41.22  | | | | 
% 229.88/41.22  | | | | Case 1:
% 229.88/41.22  | | | | | 
% 229.88/41.22  | | | | |   (62)  all_57_2 = e1 & op(e2, e3) = e1
% 229.88/41.22  | | | | | 
% 229.88/41.22  | | | | | REF_CLOSE: (4), (27), (62) are inconsistent by sub-proof #1928.
% 229.88/41.22  | | | | | 
% 229.88/41.22  | | | | Case 2:
% 229.88/41.22  | | | | | 
% 229.88/41.22  | | | | |   (63)  all_57_3 = e1 & op(e2, e2) = e1
% 229.88/41.22  | | | | | 
% 229.88/41.22  | | | | | ALPHA: (63) implies:
% 229.88/41.22  | | | | |   (64)  all_57_3 = e1
% 229.88/41.22  | | | | |   (65)  op(e2, e2) = e1
% 229.88/41.22  | | | | | 
% 229.88/41.22  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12),
% 229.88/41.22  | | | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 229.88/41.22  | | | | |            (23), (24), (25), (26), (28), (29), (30), (31), (32), (33),
% 229.88/41.22  | | | | |            (34), (35), (36), (38), (39), (40), (41), (42), (43), (44),
% 229.88/41.22  | | | | |            (45), (46), (47), (48), (49), (50), (51), (52), (54), (56),
% 229.88/41.22  | | | | |            (57), (64), (65) are inconsistent by sub-proof #909.
% 229.88/41.22  | | | | | 
% 229.88/41.22  | | | | End of split
% 229.88/41.22  | | | | 
% 229.88/41.22  | | | Case 2:
% 229.88/41.22  | | | | 
% 229.88/41.22  | | | |   (66)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0)
% 229.88/41.22  | | | |           = e1)
% 229.88/41.22  | | | | 
% 229.88/41.22  | | | | BETA: splitting (66) gives:
% 229.88/41.22  | | | | 
% 229.88/41.22  | | | | Case 1:
% 229.88/41.22  | | | | | 
% 229.88/41.22  | | | | |   (67)  all_57_5 = e1 & op(e2, e1) = e1
% 229.88/41.22  | | | | | 
% 229.88/41.22  | | | | | ALPHA: (67) implies:
% 229.88/41.22  | | | | |   (68)  all_57_5 = e1
% 229.88/41.22  | | | | | 
% 229.88/41.22  | | | | | REF_CLOSE: (29), (55), (68) are inconsistent by sub-proof #2350.
% 229.88/41.22  | | | | | 
% 229.88/41.22  | | | | Case 2:
% 229.88/41.22  | | | | | 
% 229.88/41.22  | | | | |   (69)  all_57_10 = e1 & op(e2, e0) = e1
% 229.88/41.22  | | | | | 
% 229.88/41.22  | | | | | ALPHA: (69) implies:
% 229.88/41.22  | | | | |   (70)  all_57_10 = e1
% 229.88/41.22  | | | | | 
% 229.88/41.22  | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (12), (13),
% 229.88/41.22  | | | | |            (15), (16), (17), (19), (20), (21), (22), (23), (24), (26),
% 229.88/41.22  | | | | |            (27), (28), (29), (30), (31), (32), (33), (35), (36), (40),
% 229.88/41.22  | | | | |            (41), (42), (43), (44), (45), (46), (47), (48), (49), (51),
% 229.88/41.22  | | | | |            (52), (53), (54), (55), (56), (57), (60), (70) are
% 229.88/41.22  | | | | |            inconsistent by sub-proof #897.
% 229.88/41.22  | | | | | 
% 229.88/41.22  | | | | End of split
% 229.88/41.22  | | | | 
% 229.88/41.22  | | | End of split
% 229.88/41.22  | | | 
% 229.88/41.22  | | Case 2:
% 229.88/41.22  | | | 
% 229.88/41.22  | | |   (71)  all_57_10 = e2 & op(e2, e0) = e2
% 229.88/41.22  | | | 
% 229.88/41.22  | | | REF_CLOSE: (6), (11), (37), (71) are inconsistent by sub-proof #2432.
% 229.88/41.22  | | | 
% 229.88/41.22  | | End of split
% 229.88/41.22  | | 
% 229.88/41.22  | Case 2:
% 229.88/41.22  | | 
% 229.88/41.22  | |   (72)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.88/41.22  | |           e2)
% 229.88/41.22  | | 
% 229.88/41.22  | | BETA: splitting (72) gives:
% 229.88/41.22  | | 
% 229.88/41.22  | | Case 1:
% 229.88/41.22  | | | 
% 229.88/41.22  | | |   (73)  all_57_11 = e2 & op(e1, e0) = e2
% 229.88/41.22  | | | 
% 229.88/41.22  | | | ALPHA: (73) implies:
% 229.88/41.22  | | |   (74)  all_57_11 = e2
% 229.88/41.22  | | | 
% 229.88/41.22  | | | REF_CLOSE: (24), (26), (74) are inconsistent by sub-proof #1949.
% 229.88/41.22  | | | 
% 229.88/41.22  | | Case 2:
% 229.88/41.22  | | | 
% 229.88/41.22  | | |   (75)  all_57_15 = e2 & op(e0, e0) = e2
% 229.88/41.22  | | | 
% 229.88/41.22  | | | ALPHA: (75) implies:
% 229.88/41.22  | | |   (76)  all_57_15 = e2
% 229.88/41.22  | | | 
% 229.88/41.22  | | | REF_CLOSE: (15), (21), (76) are inconsistent by sub-proof #2058.
% 229.88/41.22  | | | 
% 229.88/41.22  | | End of split
% 229.88/41.22  | | 
% 229.88/41.22  | End of split
% 229.88/41.22  | 
% 229.88/41.22  End of proof
% 229.88/41.22  
% 229.88/41.22  Sub-proof #897 shows that the following formulas are inconsistent:
% 229.88/41.22  ----------------------------------------------------------------
% 229.88/41.22    (1)  all_57_9 = e2
% 229.88/41.22    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.88/41.22         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.88/41.22    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.88/41.22         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.88/41.22    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.88/41.22         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.88/41.22    (5)   ~ (e3 = e1)
% 229.88/41.22    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.88/41.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.88/41.22    (7)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.88/41.22         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.88/41.22    (8)   ~ (all_6_2 = e3)
% 229.88/41.22    (9)  all_57_10 = e1
% 229.88/41.22    (10)  op(e1, e1) = all_6_2
% 229.88/41.22    (11)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.88/41.22          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.88/41.22    (12)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.88/41.22          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.88/41.22    (13)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.88/41.22          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.88/41.22    (14)   ~ (e3 = e2)
% 229.88/41.22    (15)   ~ (e3 = e0)
% 229.88/41.22    (16)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 229.88/41.22          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 229.88/41.22    (17)  all_57_0 = e0
% 229.88/41.22    (18)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.88/41.22          | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.88/41.22    (19)  all_57_15 = e3
% 229.88/41.22    (20)  op(e3, e3) = e0
% 229.88/41.22    (21)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.88/41.22          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.88/41.22            e1)
% 229.88/41.22    (22)  all_57_11 = e0
% 229.88/41.22    (23)   ~ (e2 = e0)
% 229.88/41.22    (24)  all_57_2 = e3
% 229.88/41.22    (25)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.88/41.22          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.88/41.22    (26)   ~ (e1 = e0)
% 229.88/41.22    (27)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.88/41.22          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.88/41.22    (28)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.88/41.22          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.88/41.22    (29)  op(e0, e0) = e3
% 229.88/41.22    (30)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.88/41.22          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.88/41.22            e2)
% 229.88/41.22    (31)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.88/41.22              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.88/41.22                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.88/41.22                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.88/41.22    (32)  op(e1, e1) = e0
% 229.88/41.22    (33)   ~ (all_53_12 = e3)
% 229.88/41.22    (34)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.88/41.22          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.88/41.22    (35)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.88/41.22          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.88/41.22    (36)   ~ (all_53_12 = e0)
% 229.88/41.22    (37)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) |
% 229.88/41.22          (all_57_11 = e0 & op(e1, e0) = e0)
% 229.88/41.22    (38)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.88/41.22          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 229.88/41.22    (39)   ~ (e2 = e1)
% 229.88/41.22    (40)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.88/41.22          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.88/41.22    (41)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.88/41.22          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.88/41.22    (42)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 229.88/41.22          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 229.88/41.22    (43)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.88/41.22          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.88/41.22    (44)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 229.88/41.22          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 229.88/41.22    (45)  all_57_3 = e2
% 229.88/41.22    (46)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.88/41.22          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.88/41.22    (47)  all_57_5 = e0
% 229.88/41.22    (48)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 229.88/41.22          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 229.88/41.22    (49)  op(e3, e0) = all_53_12
% 229.88/41.22  
% 229.88/41.22  Begin of proof
% 229.88/41.22  | 
% 229.88/41.22  | BETA: splitting (27) gives:
% 229.88/41.22  | 
% 229.88/41.22  | Case 1:
% 229.88/41.22  | | 
% 229.88/41.22  | |   (50)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) =
% 229.88/41.22  | |           e3)
% 229.88/41.22  | | 
% 229.88/41.22  | | BETA: splitting (50) gives:
% 229.88/41.22  | | 
% 229.88/41.22  | | Case 1:
% 229.88/41.22  | | | 
% 229.88/41.22  | | |   (51)  all_57_4 = e3 & op(e3, e1) = e3
% 229.88/41.22  | | | 
% 229.88/41.22  | | | ALPHA: (51) implies:
% 229.88/41.22  | | |   (52)  all_57_4 = e3
% 229.88/41.22  | | | 
% 229.88/41.22  | | | BETA: splitting (48) gives:
% 229.88/41.22  | | | 
% 229.88/41.22  | | | Case 1:
% 229.88/41.22  | | | | 
% 229.88/41.22  | | | |   (53)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2)
% 229.88/41.22  | | | |           = e2)
% 229.88/41.22  | | | | 
% 229.88/41.22  | | | | BETA: splitting (53) gives:
% 229.88/41.22  | | | | 
% 229.88/41.22  | | | | Case 1:
% 229.88/41.22  | | | | | 
% 229.88/41.22  | | | | |   (54)  all_57_6 = e2 & op(e1, e3) = e2
% 229.88/41.22  | | | | | 
% 229.88/41.22  | | | | | ALPHA: (54) implies:
% 229.88/41.22  | | | | |   (55)  all_57_6 = e2
% 229.88/41.22  | | | | | 
% 229.88/41.22  | | | | | BETA: splitting (11) gives:
% 229.88/41.22  | | | | | 
% 229.88/41.22  | | | | | Case 1:
% 229.88/41.22  | | | | | | 
% 229.88/41.22  | | | | | |   (56)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3,
% 229.88/41.22  | | | | | |             e2) = e1)
% 229.88/41.22  | | | | | | 
% 229.88/41.22  | | | | | | BETA: splitting (56) gives:
% 229.88/41.22  | | | | | | 
% 229.88/41.22  | | | | | | Case 1:
% 229.88/41.22  | | | | | | | 
% 229.88/41.22  | | | | | | |   (57)  all_57_0 = e1 & op(e3, e3) = e1
% 229.88/41.22  | | | | | | | 
% 229.88/41.22  | | | | | | | ALPHA: (57) implies:
% 229.88/41.22  | | | | | | |   (58)  all_57_0 = e1
% 229.88/41.22  | | | | | | | 
% 229.88/41.22  | | | | | | | COMBINE_EQS: (17), (58) imply:
% 229.88/41.22  | | | | | | |   (59)  e1 = e0
% 229.88/41.22  | | | | | | | 
% 229.88/41.22  | | | | | | | REF_CLOSE: (1), (5), (6), (9), (22), (26), (29), (39), (43), (59)
% 229.88/41.22  | | | | | | |            are inconsistent by sub-proof #1103.
% 229.88/41.22  | | | | | | | 
% 229.88/41.22  | | | | | | Case 2:
% 229.88/41.22  | | | | | | | 
% 229.88/41.22  | | | | | | |   (60)  all_57_1 = e1 & op(e3, e2) = e1
% 229.88/41.22  | | | | | | | 
% 229.88/41.22  | | | | | | | ALPHA: (60) implies:
% 229.88/41.22  | | | | | | |   (61)  all_57_1 = e1
% 229.88/41.22  | | | | | | | 
% 229.88/41.22  | | | | | | | BETA: splitting (28) gives:
% 229.88/41.22  | | | | | | | 
% 229.88/41.22  | | | | | | | Case 1:
% 229.88/41.22  | | | | | | | | 
% 229.88/41.22  | | | | | | | |   (62)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 &
% 229.88/41.22  | | | | | | | |           op(e2, e2) = e3)
% 229.88/41.22  | | | | | | | | 
% 229.88/41.22  | | | | | | | | REF_CLOSE: (1), (5), (11), (12), (13), (14), (15), (23), (26),
% 229.88/41.22  | | | | | | | |            (39), (45), (52), (62) are inconsistent by sub-proof
% 229.88/41.22  | | | | | | | |            #908.
% 229.88/41.22  | | | | | | | | 
% 229.88/41.22  | | | | | | | Case 2:
% 229.88/41.22  | | | | | | | | 
% 229.88/41.22  | | | | | | | |   (63)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 &
% 229.88/41.22  | | | | | | | |           op(e0, e2) = e3)
% 229.88/41.22  | | | | | | | | 
% 229.88/41.22  | | | | | | | | BETA: splitting (63) gives:
% 229.88/41.22  | | | | | | | | 
% 229.88/41.22  | | | | | | | | Case 1:
% 229.88/41.22  | | | | | | | | | 
% 229.88/41.22  | | | | | | | | |   (64)  all_57_7 = e3 & op(e1, e2) = e3
% 229.88/41.22  | | | | | | | | | 
% 229.88/41.22  | | | | | | | | | ALPHA: (64) implies:
% 229.88/41.22  | | | | | | | | |   (65)  all_57_7 = e3
% 229.88/41.22  | | | | | | | | | 
% 229.88/41.22  | | | | | | | | | BETA: splitting (3) gives:
% 229.88/41.22  | | | | | | | | | 
% 229.88/41.22  | | | | | | | | | Case 1:
% 229.88/41.22  | | | | | | | | | | 
% 229.88/41.22  | | | | | | | | | |   (66)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 &
% 229.88/41.22  | | | | | | | | | |           op(e2, e3) = e1)
% 229.88/41.22  | | | | | | | | | | 
% 229.88/41.22  | | | | | | | | | | BETA: splitting (66) gives:
% 229.88/41.22  | | | | | | | | | | 
% 229.88/41.22  | | | | | | | | | | Case 1:
% 229.88/41.22  | | | | | | | | | | | 
% 229.88/41.22  | | | | | | | | | | |   (67)  all_57_0 = e1 & op(e3, e3) = e1
% 229.88/41.22  | | | | | | | | | | | 
% 229.88/41.22  | | | | | | | | | | | ALPHA: (67) implies:
% 229.88/41.22  | | | | | | | | | | |   (68)  all_57_0 = e1
% 229.88/41.22  | | | | | | | | | | | 
% 229.88/41.22  | | | | | | | | | | | COMBINE_EQS: (17), (68) imply:
% 229.88/41.22  | | | | | | | | | | |   (69)  e1 = e0
% 229.88/41.22  | | | | | | | | | | | 
% 229.88/41.22  | | | | | | | | | | | SIMP: (69) implies:
% 229.88/41.22  | | | | | | | | | | |   (70)  e1 = e0
% 229.88/41.22  | | | | | | | | | | | 
% 229.88/41.22  | | | | | | | | | | | COMBINE_EQS: (61), (70) imply:
% 229.88/41.22  | | | | | | | | | | |   (71)  all_57_1 = e0
% 229.88/41.22  | | | | | | | | | | | 
% 229.88/41.22  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (11), (12), (14), (15), (17), (19),
% 229.88/41.22  | | | | | | | | | | |            (20), (23), (25), (26), (29), (33), (36), (37),
% 229.88/41.22  | | | | | | | | | | |            (39), (40), (43), (45), (46), (49), (52), (65),
% 229.88/41.22  | | | | | | | | | | |            (71) are inconsistent by sub-proof #900.
% 229.88/41.22  | | | | | | | | | | | 
% 229.88/41.22  | | | | | | | | | | Case 2:
% 229.88/41.22  | | | | | | | | | | | 
% 229.88/41.22  | | | | | | | | | | |   (72)  all_57_2 = e1 & op(e2, e3) = e1
% 229.88/41.22  | | | | | | | | | | | 
% 229.88/41.22  | | | | | | | | | | | ALPHA: (72) implies:
% 229.88/41.22  | | | | | | | | | | |   (73)  all_57_2 = e1
% 229.88/41.22  | | | | | | | | | | | 
% 229.88/41.22  | | | | | | | | | | | COMBINE_EQS: (24), (73) imply:
% 229.88/41.22  | | | | | | | | | | |   (74)  e3 = e1
% 229.88/41.22  | | | | | | | | | | | 
% 229.88/41.22  | | | | | | | | | | | SIMP: (74) implies:
% 229.88/41.22  | | | | | | | | | | |   (75)  e3 = e1
% 229.88/41.22  | | | | | | | | | | | 
% 229.88/41.22  | | | | | | | | | | | COMBINE_EQS: (65), (75) imply:
% 229.88/41.22  | | | | | | | | | | |   (76)  all_57_7 = e1
% 229.88/41.22  | | | | | | | | | | | 
% 229.88/41.22  | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (10), (14), (15), (19), (23),
% 229.88/41.23  | | | | | | | | | | |            (26), (31), (39), (40), (43), (55), (76) are
% 229.88/41.23  | | | | | | | | | | |            inconsistent by sub-proof #1245.
% 229.88/41.23  | | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | End of split
% 229.88/41.23  | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | Case 2:
% 229.88/41.23  | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | |   (77)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1
% 229.88/41.23  | | | | | | | | | |           & op(e0, e3) = e1)
% 229.88/41.23  | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | BETA: splitting (77) gives:
% 229.88/41.23  | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | Case 1:
% 229.88/41.23  | | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | |   (78)  all_57_6 = e1 & op(e1, e3) = e1
% 229.88/41.23  | | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | | ALPHA: (78) implies:
% 229.88/41.23  | | | | | | | | | | |   (79)  all_57_6 = e1
% 229.88/41.23  | | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | | REF_CLOSE: (39), (55), (79) are inconsistent by sub-proof
% 229.88/41.23  | | | | | | | | | | |            #2233.
% 229.88/41.23  | | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | Case 2:
% 229.88/41.23  | | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | |   (80)  all_57_12 = e1 & op(e0, e3) = e1
% 229.88/41.23  | | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | | ALPHA: (80) implies:
% 229.88/41.23  | | | | | | | | | | |   (81)  all_57_12 = e1
% 229.88/41.23  | | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | | BETA: splitting (42) gives:
% 229.88/41.23  | | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | | Case 1:
% 229.88/41.23  | | | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | | |   (82)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 229.88/41.23  | | | | | | | | | | | |           & op(e2, e1) = e2)
% 229.88/41.23  | | | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | | | BETA: splitting (82) gives:
% 229.88/41.23  | | | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | | | Case 1:
% 229.88/41.23  | | | | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | | | |   (83)  all_57_4 = e2 & op(e3, e1) = e2
% 229.88/41.23  | | | | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | | | | REF_CLOSE: (5), (6), (14), (15), (20), (24), (35), (52),
% 229.88/41.23  | | | | | | | | | | | | |            (55), (81), (83) are inconsistent by sub-proof
% 229.88/41.23  | | | | | | | | | | | | |            #899.
% 229.88/41.23  | | | | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | | | Case 2:
% 229.88/41.23  | | | | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | | | |   (84)  all_57_5 = e2 & op(e2, e1) = e2
% 229.88/41.23  | | | | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | | | | ALPHA: (84) implies:
% 229.88/41.23  | | | | | | | | | | | | |   (85)  all_57_5 = e2
% 229.88/41.23  | | | | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | | | | COMBINE_EQS: (47), (85) imply:
% 229.88/41.23  | | | | | | | | | | | | |   (86)  e2 = e0
% 229.88/41.23  | | | | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | | | | COMBINE_EQS: (55), (86) imply:
% 229.88/41.23  | | | | | | | | | | | | |   (87)  all_57_6 = e0
% 229.88/41.23  | | | | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (10), (14), (15), (19), (20),
% 229.88/41.23  | | | | | | | | | | | | |            (23), (24), (26), (31), (39), (40), (41), (43),
% 229.88/41.23  | | | | | | | | | | | | |            (65), (81), (87) are inconsistent by sub-proof
% 229.88/41.23  | | | | | | | | | | | | |            #1030.
% 229.88/41.23  | | | | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | | | End of split
% 229.88/41.23  | | | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | | Case 2:
% 229.88/41.23  | | | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | | |   (88)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 229.88/41.23  | | | | | | | | | | | |           e2 & op(e0, e1) = e2)
% 229.88/41.23  | | | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | | | BETA: splitting (88) gives:
% 229.88/41.23  | | | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | | | Case 1:
% 229.88/41.23  | | | | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | | | |   (89)  all_57_8 = e2 & op(e1, e1) = e2
% 229.88/41.23  | | | | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | | | | ALPHA: (89) implies:
% 229.88/41.23  | | | | | | | | | | | | |   (90)  op(e1, e1) = e2
% 229.88/41.23  | | | | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (10), (14), (15), (19), (22),
% 229.88/41.23  | | | | | | | | | | | | |            (23), (26), (31), (39), (40), (43), (44), (55),
% 229.88/41.23  | | | | | | | | | | | | |            (90) are inconsistent by sub-proof #1122.
% 229.88/41.23  | | | | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | | | Case 2:
% 229.88/41.23  | | | | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | | | |   (91)  all_57_14 = e2 & op(e0, e1) = e2
% 229.88/41.23  | | | | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | | | | ALPHA: (91) implies:
% 229.88/41.23  | | | | | | | | | | | | |   (92)  all_57_14 = e2
% 229.88/41.23  | | | | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | | | | BETA: splitting (16) gives:
% 229.88/41.23  | | | | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | | | | Case 1:
% 229.88/41.23  | | | | | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | | | | |   (93)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 229.88/41.23  | | | | | | | | | | | | | |           & op(e2, e1) = e1)
% 229.88/41.23  | | | | | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | | | | | BETA: splitting (93) gives:
% 229.88/41.23  | | | | | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | | | | | Case 1:
% 229.88/41.23  | | | | | | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | | | | | |   (94)  all_57_4 = e1 & op(e3, e1) = e1
% 229.88/41.23  | | | | | | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | | | | | | ALPHA: (94) implies:
% 229.88/41.23  | | | | | | | | | | | | | | |   (95)  all_57_4 = e1
% 229.88/41.23  | | | | | | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | | | | | | COMBINE_EQS: (52), (95) imply:
% 229.88/41.23  | | | | | | | | | | | | | | |   (96)  e3 = e1
% 229.88/41.23  | | | | | | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | | | | | | SIMP: (96) implies:
% 229.88/41.23  | | | | | | | | | | | | | | |   (97)  e3 = e1
% 229.88/41.23  | | | | | | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | | | | | | COMBINE_EQS: (65), (97) imply:
% 229.88/41.23  | | | | | | | | | | | | | | |   (98)  all_57_7 = e1
% 229.88/41.23  | | | | | | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (10), (14), (15), (19), (23),
% 229.88/41.23  | | | | | | | | | | | | | | |            (26), (31), (39), (40), (43), (55), (98) are
% 229.88/41.23  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1245.
% 229.88/41.23  | | | | | | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | | | | | Case 2:
% 229.88/41.23  | | | | | | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | | | | | |   (99)  all_57_5 = e1 & op(e2, e1) = e1
% 229.88/41.23  | | | | | | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | | | | | | ALPHA: (99) implies:
% 229.88/41.23  | | | | | | | | | | | | | | |   (100)  all_57_5 = e1
% 229.88/41.23  | | | | | | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | | | | | | COMBINE_EQS: (47), (100) imply:
% 229.88/41.23  | | | | | | | | | | | | | | |   (101)  e1 = e0
% 229.88/41.23  | | | | | | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | | | | | | COMBINE_EQS: (61), (101) imply:
% 229.88/41.23  | | | | | | | | | | | | | | |   (102)  all_57_1 = e0
% 229.88/41.23  | | | | | | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (11), (12), (14), (15), (17), (19),
% 229.88/41.23  | | | | | | | | | | | | | | |            (20), (23), (25), (26), (29), (33), (36), (37),
% 229.88/41.23  | | | | | | | | | | | | | | |            (39), (40), (43), (45), (46), (49), (52), (65),
% 229.88/41.23  | | | | | | | | | | | | | | |            (102) are inconsistent by sub-proof #900.
% 229.88/41.23  | | | | | | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | | | | | End of split
% 229.88/41.23  | | | | | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | | | | Case 2:
% 229.88/41.23  | | | | | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | | | | |   (103)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 229.88/41.23  | | | | | | | | | | | | | |            e1 & op(e0, e1) = e1)
% 229.88/41.23  | | | | | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | | | | | BETA: splitting (103) gives:
% 229.88/41.23  | | | | | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | | | | | Case 1:
% 229.88/41.23  | | | | | | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | | | | | |   (104)  all_57_8 = e1 & op(e1, e1) = e1
% 229.88/41.23  | | | | | | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | | | | | | ALPHA: (104) implies:
% 229.88/41.23  | | | | | | | | | | | | | | |   (105)  op(e1, e1) = e1
% 229.88/41.23  | | | | | | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | | | | | | REF_CLOSE: (6), (26), (32), (105) are inconsistent by
% 229.88/41.23  | | | | | | | | | | | | | | |            sub-proof #2427.
% 229.88/41.23  | | | | | | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | | | | | Case 2:
% 229.88/41.23  | | | | | | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | | | | | |   (106)  all_57_14 = e1 & op(e0, e1) = e1
% 229.88/41.23  | | | | | | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | | | | | | ALPHA: (106) implies:
% 229.88/41.23  | | | | | | | | | | | | | | |   (107)  all_57_14 = e1
% 229.88/41.23  | | | | | | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | | | | | | COMBINE_EQS: (92), (107) imply:
% 229.88/41.23  | | | | | | | | | | | | | | |   (108)  e2 = e1
% 229.88/41.23  | | | | | | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | | | | | | SIMP: (108) implies:
% 229.88/41.23  | | | | | | | | | | | | | | |   (109)  e2 = e1
% 229.88/41.23  | | | | | | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | | | | | | COMBINE_EQS: (55), (109) imply:
% 229.88/41.23  | | | | | | | | | | | | | | |   (110)  all_57_6 = e1
% 229.88/41.23  | | | | | | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (14), (15), (20), (23), (35), (39),
% 229.88/41.23  | | | | | | | | | | | | | | |            (41), (81), (110) are inconsistent by sub-proof
% 229.88/41.23  | | | | | | | | | | | | | | |            #1205.
% 229.88/41.23  | | | | | | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | | | | | End of split
% 229.88/41.23  | | | | | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | | | | End of split
% 229.88/41.23  | | | | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | | | End of split
% 229.88/41.23  | | | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | | End of split
% 229.88/41.23  | | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | | End of split
% 229.88/41.23  | | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | End of split
% 229.88/41.23  | | | | | | | | | 
% 229.88/41.23  | | | | | | | | Case 2:
% 229.88/41.23  | | | | | | | | | 
% 229.88/41.23  | | | | | | | | |   (111)  all_57_13 = e3 & op(e0, e2) = e3
% 229.88/41.23  | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | ALPHA: (111) implies:
% 229.88/41.23  | | | | | | | | |   (112)  all_57_13 = e3
% 229.88/41.23  | | | | | | | | | 
% 229.88/41.23  | | | | | | | | | REF_CLOSE: (5), (6), (14), (15), (18), (19), (21), (23), (26),
% 229.88/41.23  | | | | | | | | |            (29), (30), (39), (112) are inconsistent by
% 229.88/41.23  | | | | | | | | |            sub-proof #2054.
% 229.88/41.23  | | | | | | | | | 
% 229.88/41.23  | | | | | | | | End of split
% 229.88/41.23  | | | | | | | | 
% 229.88/41.23  | | | | | | | End of split
% 229.88/41.23  | | | | | | | 
% 229.88/41.23  | | | | | | End of split
% 229.88/41.23  | | | | | | 
% 229.88/41.23  | | | | | Case 2:
% 229.88/41.23  | | | | | | 
% 229.88/41.23  | | | | | |   (113)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3,
% 229.88/41.23  | | | | | |              e0) = e1)
% 229.88/41.23  | | | | | | 
% 229.88/41.23  | | | | | | BETA: splitting (113) gives:
% 229.88/41.23  | | | | | | 
% 229.88/41.23  | | | | | | Case 1:
% 229.88/41.23  | | | | | | | 
% 229.88/41.23  | | | | | | |   (114)  all_57_4 = e1 & op(e3, e1) = e1
% 229.88/41.23  | | | | | | | 
% 229.88/41.23  | | | | | | | REF_CLOSE: (5), (52), (114) are inconsistent by sub-proof #2484.
% 229.88/41.23  | | | | | | | 
% 229.88/41.23  | | | | | | Case 2:
% 229.88/41.23  | | | | | | | 
% 229.88/41.23  | | | | | | |   (115)  all_57_9 = e1 & op(e3, e0) = e1
% 229.88/41.23  | | | | | | | 
% 229.88/41.23  | | | | | | | REF_CLOSE: (1), (39), (115) are inconsistent by sub-proof #2451.
% 229.88/41.23  | | | | | | | 
% 229.88/41.23  | | | | | | End of split
% 229.88/41.23  | | | | | | 
% 229.88/41.23  | | | | | End of split
% 229.88/41.23  | | | | | 
% 229.88/41.23  | | | | Case 2:
% 229.88/41.23  | | | | | 
% 229.88/41.23  | | | | |   (116)  all_57_7 = e2 & op(e1, e2) = e2
% 229.88/41.23  | | | | | 
% 229.88/41.23  | | | | | REF_CLOSE: (1), (5), (6), (11), (12), (13), (14), (15), (18), (19),
% 229.88/41.23  | | | | |            (21), (23), (26), (28), (29), (30), (39), (45), (52), (116)
% 229.88/41.23  | | | | |            are inconsistent by sub-proof #898.
% 229.88/41.23  | | | | | 
% 229.88/41.23  | | | | End of split
% 229.88/41.23  | | | | 
% 229.88/41.23  | | | Case 2:
% 229.88/41.23  | | | | 
% 229.88/41.23  | | | |   (117)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1,
% 229.88/41.23  | | | |              e0) = e2)
% 229.88/41.23  | | | | 
% 229.88/41.23  | | | | BETA: splitting (117) gives:
% 229.88/41.23  | | | | 
% 229.88/41.23  | | | | Case 1:
% 229.88/41.23  | | | | | 
% 229.88/41.23  | | | | |   (118)  all_57_8 = e2 & op(e1, e1) = e2
% 229.88/41.23  | | | | | 
% 229.88/41.23  | | | | | ALPHA: (118) implies:
% 229.88/41.23  | | | | |   (119)  op(e1, e1) = e2
% 229.88/41.23  | | | | | 
% 229.88/41.23  | | | | | BETA: splitting (7) gives:
% 229.88/41.23  | | | | | 
% 229.88/41.23  | | | | | Case 1:
% 229.88/41.23  | | | | | | 
% 229.88/41.23  | | | | | |   (120)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1,
% 229.88/41.23  | | | | | |              e2) = e3)
% 229.88/41.23  | | | | | | 
% 229.88/41.23  | | | | | | BETA: splitting (120) gives:
% 229.88/41.23  | | | | | | 
% 229.88/41.23  | | | | | | Case 1:
% 229.88/41.23  | | | | | | | 
% 229.88/41.23  | | | | | | |   (121)  all_57_6 = e3 & op(e1, e3) = e3
% 229.88/41.23  | | | | | | | 
% 229.88/41.23  | | | | | | | ALPHA: (121) implies:
% 229.88/41.23  | | | | | | |   (122)  all_57_6 = e3
% 229.88/41.23  | | | | | | | 
% 229.88/41.23  | | | | | | | REF_CLOSE: (3), (5), (6), (14), (17), (20), (23), (24), (26),
% 229.88/41.23  | | | | | | |            (39), (41), (122) are inconsistent by sub-proof #1287.
% 229.88/41.23  | | | | | | | 
% 229.88/41.23  | | | | | | Case 2:
% 229.88/41.23  | | | | | | | 
% 229.88/41.23  | | | | | | | 
% 229.88/41.23  | | | | | | | GROUND_INST: instantiating (6) with e0, e2, e1, e1, simplifying
% 229.88/41.23  | | | | | | |              with (32), (119) gives:
% 229.88/41.23  | | | | | | |   (123)  e2 = e0
% 229.88/41.23  | | | | | | | 
% 229.88/41.23  | | | | | | | COMBINE_EQS: (1), (123) imply:
% 229.88/41.23  | | | | | | |   (124)  all_57_9 = e0
% 229.88/41.23  | | | | | | | 
% 229.88/41.23  | | | | | | | REF_CLOSE: (9), (14), (19), (22), (23), (39), (40), (124) are
% 229.88/41.23  | | | | | | |            inconsistent by sub-proof #1145.
% 229.88/41.23  | | | | | | | 
% 229.88/41.23  | | | | | | End of split
% 229.88/41.23  | | | | | | 
% 229.88/41.23  | | | | | Case 2:
% 229.88/41.23  | | | | | | 
% 229.88/41.23  | | | | | |   (125)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 &
% 229.88/41.23  | | | | | |            op(e1, e0) = e3)
% 229.88/41.23  | | | | | | 
% 229.88/41.23  | | | | | | REF_CLOSE: (5), (6), (8), (10), (14), (15), (19), (23), (26), (37),
% 229.88/41.23  | | | | | |            (39), (40), (43), (125) are inconsistent by sub-proof
% 229.88/41.23  | | | | | |            #1080.
% 229.88/41.23  | | | | | | 
% 229.88/41.23  | | | | | End of split
% 229.88/41.23  | | | | | 
% 229.88/41.23  | | | | Case 2:
% 229.88/41.23  | | | | | 
% 229.88/41.23  | | | | |   (126)  all_57_11 = e2 & op(e1, e0) = e2
% 229.88/41.23  | | | | | 
% 229.88/41.23  | | | | | ALPHA: (126) implies:
% 229.88/41.23  | | | | |   (127)  all_57_11 = e2
% 229.88/41.23  | | | | | 
% 229.88/41.23  | | | | | COMBINE_EQS: (22), (127) imply:
% 229.88/41.23  | | | | |   (128)  e2 = e0
% 229.88/41.23  | | | | | 
% 229.88/41.23  | | | | | SIMP: (128) implies:
% 229.88/41.23  | | | | |   (129)  e2 = e0
% 229.88/41.23  | | | | | 
% 229.88/41.23  | | | | | COMBINE_EQS: (1), (129) imply:
% 229.88/41.23  | | | | |   (130)  all_57_9 = e0
% 229.88/41.23  | | | | | 
% 229.88/41.23  | | | | | REF_CLOSE: (9), (14), (19), (22), (23), (39), (40), (130) are
% 229.88/41.23  | | | | |            inconsistent by sub-proof #1145.
% 229.88/41.23  | | | | | 
% 229.88/41.23  | | | | End of split
% 229.88/41.23  | | | | 
% 229.88/41.23  | | | End of split
% 229.88/41.23  | | | 
% 229.88/41.23  | | Case 2:
% 229.88/41.23  | | | 
% 229.88/41.23  | | |   (131)  all_57_5 = e3 & op(e2, e1) = e3
% 229.88/41.23  | | | 
% 229.88/41.23  | | | ALPHA: (131) implies:
% 229.88/41.23  | | |   (132)  all_57_5 = e3
% 229.88/41.23  | | | 
% 229.88/41.23  | | | REF_CLOSE: (2), (5), (9), (14), (15), (23), (24), (26), (34), (38), (39),
% 229.88/41.23  | | |            (132) are inconsistent by sub-proof #1331.
% 229.88/41.23  | | | 
% 229.88/41.23  | | End of split
% 229.88/41.23  | | 
% 229.88/41.23  | Case 2:
% 229.88/41.23  | | 
% 229.88/41.23  | |   (133)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) =
% 229.88/41.23  | |            e3)
% 229.88/41.23  | | 
% 229.88/41.23  | | REF_CLOSE: (5), (6), (8), (10), (14), (15), (18), (19), (21), (23), (26),
% 229.88/41.23  | |            (30), (39), (133) are inconsistent by sub-proof #1044.
% 229.88/41.23  | | 
% 229.88/41.23  | End of split
% 229.88/41.23  | 
% 229.88/41.23  End of proof
% 229.88/41.23  
% 229.88/41.23  Sub-proof #898 shows that the following formulas are inconsistent:
% 229.88/41.23  ----------------------------------------------------------------
% 229.88/41.23    (1)  all_57_9 = e2
% 229.88/41.23    (2)   ~ (e3 = e1)
% 229.88/41.23    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.88/41.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.88/41.23    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.88/41.23         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.88/41.23    (5)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.88/41.23         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.88/41.23    (6)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.88/41.23         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.88/41.23    (7)  all_57_4 = e3
% 229.88/41.23    (8)   ~ (e3 = e2)
% 229.88/41.23    (9)   ~ (e3 = e0)
% 229.88/41.23    (10)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.88/41.23          | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.88/41.23    (11)  all_57_15 = e3
% 229.88/41.23    (12)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.88/41.23          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.88/41.23            e1)
% 229.88/41.23    (13)   ~ (e2 = e0)
% 229.88/41.23    (14)   ~ (e1 = e0)
% 229.88/41.23    (15)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.88/41.23          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.88/41.23    (16)  op(e0, e0) = e3
% 229.88/41.23    (17)  all_57_7 = e2 & op(e1, e2) = e2
% 229.88/41.23    (18)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.88/41.23          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.88/41.23            e2)
% 229.88/41.23    (19)   ~ (e2 = e1)
% 229.88/41.23    (20)  all_57_3 = e2
% 229.88/41.23  
% 229.88/41.23  Begin of proof
% 229.88/41.23  | 
% 229.88/41.23  | ALPHA: (17) implies:
% 229.88/41.23  |   (21)  all_57_7 = e2
% 229.88/41.23  | 
% 229.88/41.23  | BETA: splitting (15) gives:
% 229.88/41.23  | 
% 229.88/41.23  | Case 1:
% 229.88/41.23  | | 
% 229.88/41.23  | |   (22)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 229.88/41.23  | |           e3)
% 229.88/41.23  | | 
% 229.88/41.23  | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (13), (14), (19), (20),
% 229.88/41.23  | |            (22) are inconsistent by sub-proof #908.
% 229.88/41.23  | | 
% 229.88/41.23  | Case 2:
% 229.88/41.23  | | 
% 229.88/41.23  | |   (23)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 229.88/41.23  | |           e3)
% 229.88/41.23  | | 
% 229.88/41.23  | | BETA: splitting (23) gives:
% 229.88/41.23  | | 
% 229.88/41.23  | | Case 1:
% 229.88/41.23  | | | 
% 229.88/41.23  | | |   (24)  all_57_7 = e3 & op(e1, e2) = e3
% 229.88/41.23  | | | 
% 229.88/41.23  | | | REF_CLOSE: (8), (21), (24) are inconsistent by sub-proof #2194.
% 229.88/41.23  | | | 
% 229.88/41.23  | | Case 2:
% 229.88/41.23  | | | 
% 229.88/41.23  | | |   (25)  all_57_13 = e3 & op(e0, e2) = e3
% 229.88/41.23  | | | 
% 229.88/41.23  | | | ALPHA: (25) implies:
% 229.88/41.23  | | |   (26)  all_57_13 = e3
% 229.88/41.23  | | | 
% 229.88/41.23  | | | REF_CLOSE: (2), (3), (8), (9), (10), (11), (12), (13), (14), (16), (18),
% 229.88/41.23  | | |            (19), (26) are inconsistent by sub-proof #2054.
% 229.88/41.23  | | | 
% 229.88/41.23  | | End of split
% 229.88/41.23  | | 
% 229.88/41.23  | End of split
% 229.88/41.23  | 
% 229.88/41.23  End of proof
% 229.88/41.23  
% 229.88/41.23  Sub-proof #899 shows that the following formulas are inconsistent:
% 229.88/41.23  ----------------------------------------------------------------
% 229.88/41.23    (1)   ~ (e3 = e1)
% 229.88/41.23    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.88/41.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.88/41.23    (3)  all_57_4 = e3
% 229.88/41.23    (4)   ~ (e3 = e2)
% 229.88/41.23    (5)   ~ (e3 = e0)
% 229.88/41.23    (6)  op(e3, e3) = e0
% 229.88/41.23    (7)  all_57_6 = e2
% 229.88/41.23    (8)  all_57_12 = e1
% 229.88/41.23    (9)  all_57_2 = e3
% 229.88/41.23    (10)  all_57_4 = e2 & op(e3, e1) = e2
% 229.88/41.23    (11)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.88/41.23          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.88/41.23  
% 229.88/41.23  Begin of proof
% 229.88/41.23  | 
% 229.88/41.23  | ALPHA: (10) implies:
% 229.88/41.23  |   (12)  all_57_4 = e2
% 229.88/41.23  | 
% 229.88/41.23  | COMBINE_EQS: (3), (12) imply:
% 229.88/41.23  |   (13)  e3 = e2
% 229.88/41.23  | 
% 229.88/41.23  | SIMP: (13) implies:
% 229.88/41.23  |   (14)  e3 = e2
% 229.88/41.23  | 
% 229.88/41.23  | COMBINE_EQS: (9), (14) imply:
% 229.88/41.23  |   (15)  all_57_2 = e2
% 229.88/41.23  | 
% 229.88/41.23  | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (11), (15) are inconsistent by
% 229.88/41.23  |            sub-proof #1212.
% 229.88/41.23  | 
% 229.88/41.23  End of proof
% 229.88/41.23  
% 229.88/41.23  Sub-proof #900 shows that the following formulas are inconsistent:
% 229.88/41.23  ----------------------------------------------------------------
% 229.88/41.23    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.88/41.23         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.88/41.23    (2)   ~ (e3 = e1)
% 229.88/41.23    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.88/41.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.88/41.23    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.88/41.23         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.88/41.23    (5)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.88/41.23         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.88/41.23    (6)  all_57_4 = e3
% 229.88/41.23    (7)   ~ (e3 = e2)
% 229.88/41.23    (8)   ~ (e3 = e0)
% 229.88/41.23    (9)  all_57_1 = e0
% 229.88/41.23    (10)  all_57_0 = e0
% 229.88/41.23    (11)  all_57_15 = e3
% 229.88/41.23    (12)  op(e3, e3) = e0
% 229.88/41.23    (13)   ~ (e2 = e0)
% 229.88/41.23    (14)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.88/41.23          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.88/41.23    (15)   ~ (e1 = e0)
% 229.88/41.23    (16)  op(e0, e0) = e3
% 229.88/41.23    (17)   ~ (all_53_12 = e3)
% 229.88/41.23    (18)  all_57_7 = e3
% 229.88/41.23    (19)   ~ (all_53_12 = e0)
% 229.88/41.23    (20)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) |
% 229.88/41.23          (all_57_11 = e0 & op(e1, e0) = e0)
% 229.88/41.23    (21)   ~ (e2 = e1)
% 229.88/41.23    (22)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.88/41.23          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.88/41.23    (23)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.88/41.23          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.88/41.23    (24)  all_57_3 = e2
% 229.88/41.23    (25)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.88/41.23          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.88/41.23    (26)  op(e3, e0) = all_53_12
% 229.88/41.23  
% 229.88/41.23  Begin of proof
% 229.88/41.23  | 
% 229.88/41.23  | BETA: splitting (20) gives:
% 229.88/41.23  | 
% 229.88/41.23  | Case 1:
% 229.88/41.23  | | 
% 229.88/41.23  | |   (27)  all_57_9 = e0 & op(e3, e0) = e0
% 229.88/41.23  | | 
% 229.88/41.23  | | REF_CLOSE: (3), (19), (26), (27) are inconsistent by sub-proof #2434.
% 229.88/41.23  | | 
% 229.88/41.23  | Case 2:
% 229.88/41.23  | | 
% 229.88/41.23  | |   (28)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 229.88/41.23  | |           e0)
% 229.88/41.23  | | 
% 229.88/41.23  | | BETA: splitting (28) gives:
% 229.88/41.23  | | 
% 229.88/41.23  | | Case 1:
% 229.88/41.23  | | | 
% 229.88/41.23  | | |   (29)  all_57_10 = e0 & op(e2, e0) = e0
% 229.88/41.23  | | | 
% 229.88/41.23  | | | ALPHA: (29) implies:
% 229.88/41.23  | | |   (30)  all_57_10 = e0
% 229.88/41.23  | | | 
% 229.88/41.23  | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 229.88/41.23  | | |            (14), (15), (16), (17), (21), (22), (23), (26), (30) are
% 229.88/41.23  | | |            inconsistent by sub-proof #905.
% 229.88/41.23  | | | 
% 229.88/41.23  | | Case 2:
% 229.88/41.23  | | | 
% 229.88/41.23  | | |   (31)  all_57_11 = e0 & op(e1, e0) = e0
% 229.88/41.23  | | | 
% 229.88/41.23  | | | ALPHA: (31) implies:
% 229.88/41.23  | | |   (32)  all_57_11 = e0
% 229.88/41.23  | | | 
% 229.88/41.23  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 229.88/41.23  | | |            (14), (15), (16), (17), (18), (21), (23), (24), (25), (26),
% 229.88/41.23  | | |            (32) are inconsistent by sub-proof #901.
% 229.88/41.23  | | | 
% 229.88/41.23  | | End of split
% 229.88/41.23  | | 
% 229.88/41.23  | End of split
% 229.88/41.23  | 
% 229.88/41.23  End of proof
% 229.88/41.23  
% 229.88/41.23  Sub-proof #901 shows that the following formulas are inconsistent:
% 229.88/41.23  ----------------------------------------------------------------
% 229.88/41.23    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.88/41.23         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.88/41.23    (2)   ~ (e3 = e1)
% 229.88/41.23    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.88/41.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.88/41.23    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.88/41.23         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.88/41.23    (5)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.88/41.23         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.88/41.23    (6)  all_57_4 = e3
% 229.88/41.23    (7)   ~ (e3 = e2)
% 229.88/41.23    (8)   ~ (e3 = e0)
% 229.88/41.23    (9)  all_57_1 = e0
% 229.88/41.23    (10)  all_57_0 = e0
% 229.88/41.23    (11)  op(e3, e3) = e0
% 229.88/41.23    (12)  all_57_11 = e0
% 229.88/41.23    (13)   ~ (e2 = e0)
% 229.88/41.23    (14)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.88/41.23          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.88/41.23    (15)   ~ (e1 = e0)
% 229.88/41.23    (16)  op(e0, e0) = e3
% 229.88/41.23    (17)   ~ (all_53_12 = e3)
% 229.88/41.23    (18)  all_57_7 = e3
% 229.88/41.23    (19)   ~ (e2 = e1)
% 229.88/41.23    (20)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.88/41.23          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.88/41.23    (21)  all_57_3 = e2
% 229.88/41.23    (22)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.88/41.23          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.88/41.23    (23)  op(e3, e0) = all_53_12
% 229.88/41.23  
% 229.88/41.23  Begin of proof
% 229.88/41.23  | 
% 229.88/41.23  | BETA: splitting (5) gives:
% 229.88/41.23  | 
% 229.88/41.23  | Case 1:
% 229.88/41.23  | | 
% 229.88/41.23  | |   (24)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) =
% 229.88/41.23  | |           e2)
% 229.88/41.23  | | 
% 229.88/41.23  | | BETA: splitting (24) gives:
% 229.88/41.23  | | 
% 229.88/41.23  | | Case 1:
% 229.88/41.23  | | | 
% 229.88/41.23  | | |   (25)  all_57_0 = e2 & op(e3, e3) = e2
% 229.88/41.23  | | | 
% 229.88/41.23  | | | ALPHA: (25) implies:
% 229.88/41.23  | | |   (26)  op(e3, e3) = e2
% 229.88/41.23  | | | 
% 229.88/41.23  | | | REF_CLOSE: (3), (11), (13), (26) are inconsistent by sub-proof #2403.
% 229.88/41.23  | | | 
% 229.88/41.23  | | Case 2:
% 229.88/41.23  | | | 
% 229.88/41.23  | | |   (27)  all_57_1 = e2 & op(e3, e2) = e2
% 229.88/41.23  | | | 
% 229.88/41.23  | | | ALPHA: (27) implies:
% 229.88/41.23  | | |   (28)  all_57_1 = e2
% 229.88/41.23  | | | 
% 229.88/41.23  | | | COMBINE_EQS: (9), (28) imply:
% 229.88/41.23  | | |   (29)  e2 = e0
% 229.88/41.23  | | | 
% 229.88/41.23  | | | REF_CLOSE: (1), (2), (7), (9), (13), (15), (18), (19), (21), (22), (29)
% 229.88/41.23  | | |            are inconsistent by sub-proof #904.
% 229.88/41.23  | | | 
% 229.88/41.23  | | End of split
% 229.88/41.23  | | 
% 229.88/41.23  | Case 2:
% 229.88/41.23  | | 
% 229.88/41.23  | |   (30)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) =
% 229.88/41.23  | |           e2)
% 229.88/41.23  | | 
% 229.88/41.23  | | BETA: splitting (30) gives:
% 229.88/41.23  | | 
% 229.88/41.23  | | Case 1:
% 229.88/41.23  | | | 
% 229.88/41.23  | | |   (31)  all_57_4 = e2 & op(e3, e1) = e2
% 229.88/41.23  | | | 
% 229.88/41.23  | | | REF_CLOSE: (6), (7), (31) are inconsistent by sub-proof #2487.
% 229.88/41.23  | | | 
% 229.88/41.23  | | Case 2:
% 229.88/41.23  | | | 
% 229.88/41.23  | | |   (32)  all_57_9 = e2 & op(e3, e0) = e2
% 229.88/41.23  | | | 
% 229.88/41.23  | | | ALPHA: (32) implies:
% 229.88/41.23  | | |   (33)  all_57_9 = e2
% 229.88/41.23  | | | 
% 229.88/41.23  | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 229.88/41.23  | | |            (14), (15), (16), (17), (19), (20), (23), (33) are inconsistent
% 229.88/41.23  | | |            by sub-proof #902.
% 229.88/41.23  | | | 
% 229.88/41.23  | | End of split
% 229.88/41.23  | | 
% 229.88/41.23  | End of split
% 229.88/41.23  | 
% 229.88/41.23  End of proof
% 229.88/41.23  
% 229.88/41.23  Sub-proof #902 shows that the following formulas are inconsistent:
% 229.88/41.23  ----------------------------------------------------------------
% 229.88/41.23    (1)  all_57_9 = e2
% 229.88/41.23    (2)   ~ (e3 = e1)
% 229.88/41.23    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.88/41.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.88/41.24    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.88/41.24         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.88/41.24    (5)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.88/41.24         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.88/41.24    (6)  all_57_4 = e3
% 229.88/41.24    (7)   ~ (e3 = e2)
% 229.88/41.24    (8)   ~ (e3 = e0)
% 229.88/41.24    (9)  all_57_1 = e0
% 229.88/41.24    (10)  all_57_0 = e0
% 229.88/41.24    (11)  op(e3, e3) = e0
% 229.88/41.24    (12)  all_57_11 = e0
% 229.88/41.24    (13)   ~ (e2 = e0)
% 229.88/41.24    (14)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.88/41.24          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.88/41.24    (15)   ~ (e1 = e0)
% 229.88/41.24    (16)  op(e0, e0) = e3
% 229.88/41.24    (17)   ~ (all_53_12 = e3)
% 229.88/41.24    (18)   ~ (e2 = e1)
% 229.88/41.24    (19)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.88/41.24          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.88/41.24    (20)  op(e3, e0) = all_53_12
% 229.88/41.24  
% 229.88/41.24  Begin of proof
% 229.88/41.24  | 
% 229.88/41.24  | BETA: splitting (19) gives:
% 229.88/41.24  | 
% 229.88/41.24  | Case 1:
% 229.88/41.24  | | 
% 229.88/41.24  | |   (21)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) =
% 229.88/41.24  | |           e1)
% 229.88/41.24  | | 
% 229.88/41.24  | | BETA: splitting (21) gives:
% 229.88/41.24  | | 
% 229.88/41.24  | | Case 1:
% 229.88/41.24  | | | 
% 229.88/41.24  | | |   (22)  all_57_9 = e1 & op(e3, e0) = e1
% 229.88/41.24  | | | 
% 229.88/41.24  | | | ALPHA: (22) implies:
% 229.88/41.24  | | |   (23)  all_57_9 = e1
% 229.88/41.24  | | | 
% 229.88/41.24  | | | REF_CLOSE: (3), (5), (6), (7), (9), (11), (13), (18), (23) are
% 229.88/41.24  | | |            inconsistent by sub-proof #2402.
% 229.88/41.24  | | | 
% 229.88/41.24  | | Case 2:
% 229.88/41.24  | | | 
% 229.88/41.24  | | |   (24)  all_57_10 = e1 & op(e2, e0) = e1
% 229.88/41.24  | | | 
% 229.88/41.24  | | | ALPHA: (24) implies:
% 229.88/41.24  | | |   (25)  all_57_10 = e1
% 229.88/41.24  | | | 
% 229.88/41.24  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 229.88/41.24  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (25) are
% 229.88/41.24  | | |            inconsistent by sub-proof #903.
% 229.88/41.24  | | | 
% 229.88/41.24  | | End of split
% 229.88/41.24  | | 
% 229.88/41.24  | Case 2:
% 229.88/41.24  | | 
% 229.88/41.24  | |   (26)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.88/41.24  | |           e1)
% 229.88/41.24  | | 
% 229.88/41.24  | | REF_CLOSE: (2), (3), (12), (15), (16), (26) are inconsistent by sub-proof
% 229.88/41.24  | |            #1105.
% 229.88/41.24  | | 
% 229.88/41.24  | End of split
% 229.88/41.24  | 
% 229.88/41.24  End of proof
% 229.88/41.24  
% 229.88/41.24  Sub-proof #903 shows that the following formulas are inconsistent:
% 229.88/41.24  ----------------------------------------------------------------
% 229.88/41.24    (1)  all_57_9 = e2
% 229.88/41.24    (2)   ~ (e3 = e1)
% 229.88/41.24    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.88/41.24           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.88/41.24    (4)  all_57_10 = e1
% 229.88/41.24    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.88/41.24         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.88/41.24    (6)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.88/41.24         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.88/41.24    (7)  all_57_4 = e3
% 229.88/41.24    (8)   ~ (e3 = e2)
% 229.88/41.24    (9)   ~ (e3 = e0)
% 229.88/41.24    (10)  all_57_1 = e0
% 229.88/41.24    (11)  all_57_0 = e0
% 229.88/41.24    (12)  op(e3, e3) = e0
% 229.88/41.24    (13)  all_57_11 = e0
% 229.88/41.24    (14)   ~ (e2 = e0)
% 229.88/41.24    (15)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.88/41.24          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.88/41.24    (16)   ~ (e1 = e0)
% 229.88/41.24    (17)  op(e0, e0) = e3
% 229.88/41.24    (18)   ~ (all_53_12 = e3)
% 229.88/41.24    (19)   ~ (e2 = e1)
% 229.88/41.24    (20)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.88/41.24          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.88/41.24    (21)  op(e3, e0) = all_53_12
% 229.88/41.24  
% 229.88/41.24  Begin of proof
% 229.88/41.24  | 
% 229.88/41.24  | BETA: splitting (5) gives:
% 229.88/41.24  | 
% 229.88/41.24  | Case 1:
% 229.88/41.24  | | 
% 229.88/41.24  | |   (22)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) =
% 229.88/41.24  | |           e1)
% 229.88/41.24  | | 
% 229.88/41.24  | | BETA: splitting (22) gives:
% 229.88/41.24  | | 
% 229.88/41.24  | | Case 1:
% 229.88/41.24  | | | 
% 229.88/41.24  | | |   (23)  all_57_0 = e1 & op(e3, e3) = e1
% 229.88/41.24  | | | 
% 229.88/41.24  | | | ALPHA: (23) implies:
% 229.88/41.24  | | |   (24)  all_57_0 = e1
% 229.88/41.24  | | | 
% 229.88/41.24  | | | COMBINE_EQS: (11), (24) imply:
% 229.88/41.24  | | |   (25)  e1 = e0
% 229.88/41.24  | | | 
% 229.88/41.24  | | | REF_CLOSE: (1), (2), (3), (4), (13), (16), (17), (19), (20), (25) are
% 229.88/41.24  | | |            inconsistent by sub-proof #1103.
% 229.88/41.24  | | | 
% 229.88/41.24  | | Case 2:
% 229.88/41.24  | | | 
% 229.88/41.24  | | |   (26)  all_57_1 = e1 & op(e3, e2) = e1
% 229.88/41.24  | | | 
% 229.88/41.24  | | | ALPHA: (26) implies:
% 229.88/41.24  | | |   (27)  all_57_1 = e1
% 229.88/41.24  | | | 
% 229.88/41.24  | | | COMBINE_EQS: (10), (27) imply:
% 229.88/41.24  | | |   (28)  e1 = e0
% 229.88/41.24  | | | 
% 229.88/41.24  | | | REF_CLOSE: (1), (2), (3), (4), (13), (16), (17), (19), (20), (28) are
% 229.88/41.24  | | |            inconsistent by sub-proof #1103.
% 229.88/41.24  | | | 
% 229.88/41.24  | | End of split
% 229.88/41.24  | | 
% 229.88/41.24  | Case 2:
% 229.88/41.24  | | 
% 229.88/41.24  | |   (29)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) =
% 229.88/41.24  | |           e1)
% 229.88/41.24  | | 
% 229.88/41.24  | | REF_CLOSE: (2), (3), (6), (7), (8), (9), (10), (12), (14), (15), (18), (19),
% 229.88/41.24  | |            (21), (29) are inconsistent by sub-proof #907.
% 229.88/41.24  | | 
% 229.88/41.24  | End of split
% 229.88/41.24  | 
% 229.88/41.24  End of proof
% 229.88/41.24  
% 229.88/41.24  Sub-proof #904 shows that the following formulas are inconsistent:
% 229.88/41.24  ----------------------------------------------------------------
% 229.88/41.24    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.88/41.24         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.88/41.24    (2)   ~ (e3 = e1)
% 229.88/41.24    (3)   ~ (e3 = e2)
% 229.88/41.24    (4)  all_57_1 = e0
% 229.88/41.24    (5)  e2 = e0
% 229.88/41.24    (6)   ~ (e2 = e0)
% 229.88/41.24    (7)   ~ (e1 = e0)
% 229.88/41.24    (8)  all_57_7 = e3
% 229.88/41.24    (9)   ~ (e2 = e1)
% 229.88/41.24    (10)  all_57_3 = e2
% 229.88/41.24    (11)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.88/41.24          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.88/41.24  
% 229.88/41.24  Begin of proof
% 229.88/41.24  | 
% 229.88/41.24  | SIMP: (5) implies:
% 229.88/41.24  |   (12)  e2 = e0
% 229.88/41.24  | 
% 229.88/41.24  | COMBINE_EQS: (10), (12) imply:
% 229.88/41.24  |   (13)  all_57_3 = e0
% 229.88/41.24  | 
% 229.88/41.24  | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (11), (13) are inconsistent
% 229.88/41.24  |            by sub-proof #2098.
% 229.88/41.24  | 
% 229.88/41.24  End of proof
% 229.88/41.24  
% 229.88/41.24  Sub-proof #905 shows that the following formulas are inconsistent:
% 229.88/41.24  ----------------------------------------------------------------
% 229.88/41.24    (1)  all_57_10 = e0
% 229.88/41.24    (2)   ~ (e3 = e1)
% 229.88/41.24    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.88/41.24           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.88/41.24    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.88/41.24         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.88/41.24    (5)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.88/41.24         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.88/41.24    (6)  all_57_4 = e3
% 229.88/41.24    (7)   ~ (e3 = e2)
% 229.88/41.24    (8)   ~ (e3 = e0)
% 229.88/41.24    (9)  all_57_1 = e0
% 229.88/41.24    (10)  all_57_0 = e0
% 229.88/41.24    (11)  all_57_15 = e3
% 229.88/41.24    (12)  op(e3, e3) = e0
% 229.88/41.24    (13)   ~ (e2 = e0)
% 229.88/41.24    (14)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.88/41.24          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.88/41.24    (15)   ~ (e1 = e0)
% 229.88/41.24    (16)  op(e0, e0) = e3
% 229.88/41.24    (17)   ~ (all_53_12 = e3)
% 229.88/41.24    (18)   ~ (e2 = e1)
% 229.88/41.24    (19)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.88/41.24          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.88/41.24    (20)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.88/41.24          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.88/41.24    (21)  op(e3, e0) = all_53_12
% 229.88/41.24  
% 229.88/41.24  Begin of proof
% 229.88/41.24  | 
% 229.88/41.24  | BETA: splitting (20) gives:
% 229.88/41.24  | 
% 229.88/41.24  | Case 1:
% 229.88/41.24  | | 
% 229.88/41.24  | |   (22)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) =
% 229.88/41.24  | |           e1)
% 229.88/41.24  | | 
% 229.88/41.24  | | BETA: splitting (22) gives:
% 229.88/41.24  | | 
% 229.88/41.24  | | Case 1:
% 229.88/41.24  | | | 
% 229.88/41.24  | | |   (23)  all_57_9 = e1 & op(e3, e0) = e1
% 229.88/41.24  | | | 
% 229.88/41.24  | | | ALPHA: (23) implies:
% 229.88/41.24  | | |   (24)  all_57_9 = e1
% 229.88/41.24  | | | 
% 229.88/41.24  | | | REF_CLOSE: (3), (5), (6), (7), (9), (12), (13), (18), (24) are
% 229.88/41.24  | | |            inconsistent by sub-proof #2402.
% 229.88/41.24  | | | 
% 229.88/41.24  | | Case 2:
% 229.88/41.24  | | | 
% 229.88/41.24  | | |   (25)  all_57_10 = e1 & op(e2, e0) = e1
% 229.88/41.24  | | | 
% 229.88/41.24  | | | ALPHA: (25) implies:
% 229.88/41.24  | | |   (26)  all_57_10 = e1
% 229.88/41.24  | | | 
% 229.88/41.24  | | | REF_CLOSE: (1), (15), (26) are inconsistent by sub-proof #1531.
% 229.88/41.24  | | | 
% 229.88/41.24  | | End of split
% 229.88/41.24  | | 
% 229.88/41.24  | Case 2:
% 229.88/41.24  | | 
% 229.88/41.24  | |   (27)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.88/41.24  | |           e1)
% 229.88/41.24  | | 
% 229.88/41.24  | | BETA: splitting (27) gives:
% 229.88/41.24  | | 
% 229.88/41.24  | | Case 1:
% 229.88/41.24  | | | 
% 229.88/41.24  | | |   (28)  all_57_11 = e1 & op(e1, e0) = e1
% 229.88/41.24  | | | 
% 229.88/41.24  | | | ALPHA: (28) implies:
% 229.88/41.24  | | |   (29)  all_57_11 = e1
% 229.88/41.24  | | | 
% 229.88/41.24  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 229.88/41.24  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (29) are
% 229.88/41.24  | | |            inconsistent by sub-proof #906.
% 229.88/41.24  | | | 
% 229.88/41.24  | | Case 2:
% 229.88/41.24  | | | 
% 229.88/41.24  | | |   (30)  all_57_15 = e1 & op(e0, e0) = e1
% 229.88/41.24  | | | 
% 229.88/41.24  | | | ALPHA: (30) implies:
% 229.88/41.24  | | |   (31)  op(e0, e0) = e1
% 229.88/41.24  | | | 
% 229.88/41.24  | | | REF_CLOSE: (2), (3), (16), (31) are inconsistent by sub-proof #2183.
% 229.88/41.24  | | | 
% 229.88/41.24  | | End of split
% 229.88/41.24  | | 
% 229.88/41.24  | End of split
% 229.88/41.24  | 
% 229.88/41.24  End of proof
% 229.88/41.24  
% 229.88/41.24  Sub-proof #906 shows that the following formulas are inconsistent:
% 229.88/41.24  ----------------------------------------------------------------
% 229.88/41.24    (1)  all_57_10 = e0
% 229.88/41.24    (2)   ~ (e3 = e1)
% 229.88/41.24    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.88/41.24           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.88/41.24    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.88/41.24         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.88/41.24    (5)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.88/41.24         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.88/41.24    (6)  all_57_4 = e3
% 229.88/41.24    (7)   ~ (e3 = e2)
% 229.88/41.24    (8)   ~ (e3 = e0)
% 229.88/41.24    (9)  all_57_1 = e0
% 229.88/41.24    (10)  all_57_0 = e0
% 229.88/41.24    (11)  all_57_15 = e3
% 229.88/41.24    (12)  op(e3, e3) = e0
% 229.88/41.24    (13)   ~ (e2 = e0)
% 229.88/41.24    (14)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.88/41.24          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.88/41.24    (15)   ~ (e1 = e0)
% 229.88/41.24    (16)  op(e0, e0) = e3
% 229.88/41.24    (17)   ~ (all_53_12 = e3)
% 229.88/41.24    (18)  all_57_11 = e1
% 229.88/41.24    (19)   ~ (e2 = e1)
% 229.88/41.24    (20)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.88/41.24          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.88/41.24    (21)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.88/41.24          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.88/41.24    (22)  op(e3, e0) = all_53_12
% 229.88/41.24  
% 229.88/41.24  Begin of proof
% 229.88/41.24  | 
% 229.88/41.24  | BETA: splitting (4) gives:
% 229.88/41.24  | 
% 229.88/41.24  | Case 1:
% 229.88/41.24  | | 
% 229.88/41.24  | |   (23)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) =
% 229.88/41.24  | |           e1)
% 229.88/41.24  | | 
% 229.88/41.24  | | BETA: splitting (23) gives:
% 229.88/41.24  | | 
% 229.88/41.24  | | Case 1:
% 229.88/41.24  | | | 
% 229.88/41.24  | | |   (24)  all_57_0 = e1 & op(e3, e3) = e1
% 229.88/41.24  | | | 
% 229.88/41.24  | | | ALPHA: (24) implies:
% 229.88/41.24  | | |   (25)  all_57_0 = e1
% 229.88/41.24  | | | 
% 229.88/41.24  | | | COMBINE_EQS: (10), (25) imply:
% 229.88/41.24  | | |   (26)  e1 = e0
% 229.88/41.24  | | | 
% 229.88/41.24  | | | REF_CLOSE: (1), (2), (3), (7), (11), (13), (15), (16), (18), (19), (20),
% 229.88/41.24  | | |            (21), (26) are inconsistent by sub-proof #932.
% 229.88/41.24  | | | 
% 229.88/41.24  | | Case 2:
% 229.88/41.24  | | | 
% 229.88/41.24  | | |   (27)  all_57_1 = e1 & op(e3, e2) = e1
% 229.88/41.24  | | | 
% 229.88/41.24  | | | ALPHA: (27) implies:
% 229.88/41.24  | | |   (28)  all_57_1 = e1
% 229.88/41.24  | | | 
% 229.88/41.24  | | | COMBINE_EQS: (9), (28) imply:
% 229.88/41.24  | | |   (29)  e1 = e0
% 229.88/41.24  | | | 
% 229.88/41.24  | | | REF_CLOSE: (1), (2), (3), (7), (11), (13), (15), (16), (18), (19), (20),
% 229.88/41.24  | | |            (21), (29) are inconsistent by sub-proof #932.
% 229.88/41.24  | | | 
% 229.88/41.24  | | End of split
% 229.88/41.24  | | 
% 229.88/41.24  | Case 2:
% 229.88/41.24  | | 
% 229.88/41.24  | |   (30)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) =
% 229.88/41.24  | |           e1)
% 229.88/41.24  | | 
% 229.88/41.24  | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (9), (12), (13), (14), (17), (19),
% 229.88/41.24  | |            (22), (30) are inconsistent by sub-proof #907.
% 229.88/41.24  | | 
% 229.88/41.24  | End of split
% 229.88/41.24  | 
% 229.88/41.24  End of proof
% 229.88/41.24  
% 229.88/41.24  Sub-proof #907 shows that the following formulas are inconsistent:
% 229.88/41.24  ----------------------------------------------------------------
% 229.88/41.24    (1)   ~ (e3 = e1)
% 229.88/41.24    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.88/41.24           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.88/41.24    (3)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.88/41.24         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.88/41.24    (4)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.88/41.24    (5)  all_57_4 = e3
% 229.88/41.24    (6)   ~ (e3 = e2)
% 229.88/41.24    (7)   ~ (e3 = e0)
% 229.88/41.24    (8)  all_57_1 = e0
% 229.88/41.24    (9)  op(e3, e3) = e0
% 229.88/41.24    (10)   ~ (e2 = e0)
% 229.88/41.24    (11)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.88/41.24          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.88/41.24    (12)   ~ (all_53_12 = e3)
% 229.88/41.24    (13)   ~ (e2 = e1)
% 229.88/41.24    (14)  op(e3, e0) = all_53_12
% 229.88/41.24  
% 229.88/41.24  Begin of proof
% 229.88/41.24  | 
% 229.88/41.24  | BETA: splitting (4) gives:
% 229.88/41.24  | 
% 229.88/41.24  | Case 1:
% 229.88/41.24  | | 
% 229.88/41.24  | |   (15)  all_57_4 = e1 & op(e3, e1) = e1
% 229.88/41.24  | | 
% 229.88/41.24  | | ALPHA: (15) implies:
% 229.88/41.24  | |   (16)  all_57_4 = e1
% 229.88/41.24  | | 
% 229.88/41.24  | | REF_CLOSE: (1), (2), (7), (8), (9), (11), (12), (14), (16) are inconsistent
% 229.88/41.24  | |            by sub-proof #2280.
% 229.88/41.24  | | 
% 229.88/41.24  | Case 2:
% 229.88/41.24  | | 
% 229.88/41.24  | |   (17)  all_57_9 = e1 & op(e3, e0) = e1
% 229.88/41.24  | | 
% 229.88/41.24  | | ALPHA: (17) implies:
% 229.88/41.24  | |   (18)  all_57_9 = e1
% 229.88/41.24  | | 
% 229.88/41.24  | | REF_CLOSE: (2), (3), (5), (6), (8), (9), (10), (13), (18) are inconsistent
% 229.88/41.24  | |            by sub-proof #2402.
% 229.88/41.24  | | 
% 229.88/41.24  | End of split
% 229.88/41.24  | 
% 229.88/41.24  End of proof
% 229.88/41.24  
% 229.88/41.24  Sub-proof #908 shows that the following formulas are inconsistent:
% 229.88/41.24  ----------------------------------------------------------------
% 229.88/41.24    (1)  all_57_9 = e2
% 229.88/41.24    (2)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3)
% 229.88/41.24    (3)   ~ (e3 = e1)
% 229.88/41.24    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.88/41.24         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.88/41.24    (5)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.88/41.24         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.88/41.24    (6)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.88/41.24         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.88/41.24    (7)  all_57_4 = e3
% 229.88/41.24    (8)   ~ (e3 = e2)
% 229.88/41.24    (9)   ~ (e3 = e0)
% 229.88/41.24    (10)   ~ (e2 = e0)
% 229.88/41.24    (11)   ~ (e1 = e0)
% 229.88/41.24    (12)   ~ (e2 = e1)
% 229.88/41.24    (13)  all_57_3 = e2
% 229.88/41.24  
% 229.88/41.24  Begin of proof
% 229.88/41.24  | 
% 229.88/41.24  | BETA: splitting (2) gives:
% 229.88/41.24  | 
% 229.88/41.24  | Case 1:
% 229.88/41.24  | | 
% 229.88/41.24  | |   (14)  all_57_1 = e3 & op(e3, e2) = e3
% 229.88/41.24  | | 
% 229.88/41.24  | | ALPHA: (14) implies:
% 229.88/41.24  | |   (15)  all_57_1 = e3
% 229.88/41.24  | | 
% 229.88/41.24  | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (15)
% 229.88/41.24  | |            are inconsistent by sub-proof #1222.
% 229.88/41.24  | | 
% 229.88/41.24  | Case 2:
% 229.88/41.24  | | 
% 229.88/41.24  | |   (16)  all_57_3 = e3 & op(e2, e2) = e3
% 229.88/41.24  | | 
% 229.88/41.24  | | ALPHA: (16) implies:
% 229.88/41.24  | |   (17)  all_57_3 = e3
% 229.88/41.24  | | 
% 229.88/41.24  | | REF_CLOSE: (8), (13), (17) are inconsistent by sub-proof #1166.
% 229.88/41.24  | | 
% 229.88/41.24  | End of split
% 229.88/41.24  | 
% 229.88/41.24  End of proof
% 229.88/41.24  
% 229.88/41.24  Sub-proof #909 shows that the following formulas are inconsistent:
% 229.88/41.24  ----------------------------------------------------------------
% 229.88/41.24    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.88/41.24         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.88/41.24    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.88/41.24         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.88/41.24    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.88/41.24         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.88/41.24    (4)   ~ (e3 = e1)
% 229.88/41.24    (5)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 229.88/41.24         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 229.88/41.24    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.88/41.24           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.88/41.24    (7)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.88/41.24         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.88/41.24    (8)   ~ (all_6_2 = e3)
% 229.88/41.24    (9)  op(e1, e1) = all_6_2
% 229.88/41.24    (10)  op(e2, e2) = e1
% 229.88/41.24    (11)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.88/41.24          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.88/41.24    (12)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.88/41.24          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.88/41.24    (13)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.88/41.24          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.88/41.24    (14)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 229.88/41.24          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.88/41.24    (15)   ~ (e3 = e2)
% 229.88/41.24    (16)   ~ (e3 = e0)
% 229.88/41.24    (17)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 229.88/41.24          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 229.88/41.24    (18)  op(e0, e3) = all_53_3
% 229.88/41.24    (19)  all_57_0 = e0
% 229.88/41.24    (20)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.88/41.24          | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.88/41.24    (21)  all_57_15 = e3
% 229.88/41.24    (22)  op(e3, e3) = e0
% 229.88/41.24    (23)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.88/41.24          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.88/41.24            e1)
% 229.88/41.24    (24)  all_57_11 = e0
% 229.88/41.24    (25)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.88/41.24          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.88/41.24    (26)   ~ (e2 = e0)
% 229.88/41.24    (27)  all_57_3 = e1
% 229.88/41.24    (28)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.88/41.24          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.88/41.24    (29)   ~ (e1 = e0)
% 229.88/41.24    (30)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.88/41.24          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.88/41.24    (31)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.88/41.24          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.88/41.24    (32)  op(e0, e0) = e3
% 229.88/41.24    (33)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.88/41.24          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.88/41.24            e2)
% 229.88/41.24    (34)   ~ (all_53_3 = e0)
% 229.88/41.24    (35)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.88/41.25              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.88/41.25                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.88/41.25                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.88/41.25    (36)  op(e1, e1) = e0
% 229.88/41.25    (37)  all_57_13 = e0
% 229.88/41.25    (38)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.88/41.25          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.88/41.25    (39)   ~ (all_53_12 = e3)
% 229.88/41.25    (40)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.88/41.25          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.88/41.25    (41)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.88/41.25          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.88/41.25    (42)   ~ (all_53_12 = e0)
% 229.88/41.25    (43)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) |
% 229.88/41.25          (all_57_11 = e0 & op(e1, e0) = e0)
% 229.88/41.25    (44)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.88/41.25          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 229.88/41.25    (45)   ~ (e2 = e1)
% 229.88/41.25    (46)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.88/41.25          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.88/41.25    (47)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.88/41.25          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.88/41.25    (48)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 229.88/41.25          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 229.88/41.25    (49)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.88/41.25          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.88/41.25    (50)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.88/41.25          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.88/41.25    (51)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 229.88/41.25          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 229.88/41.25    (52)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.88/41.25          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.88/41.25    (53)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 229.88/41.25          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 229.88/41.25    (54)  op(e3, e0) = all_53_12
% 229.88/41.25  
% 229.88/41.25  Begin of proof
% 229.88/41.25  | 
% 229.88/41.25  | BETA: splitting (51) gives:
% 229.88/41.25  | 
% 229.88/41.25  | Case 1:
% 229.88/41.25  | | 
% 229.88/41.25  | |   (55)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) =
% 229.88/41.25  | |           e1)
% 229.88/41.25  | | 
% 229.88/41.25  | | BETA: splitting (55) gives:
% 229.88/41.25  | | 
% 229.88/41.25  | | Case 1:
% 229.88/41.25  | | | 
% 229.88/41.25  | | |   (56)  all_57_6 = e1 & op(e1, e3) = e1
% 229.88/41.25  | | | 
% 229.88/41.25  | | | ALPHA: (56) implies:
% 229.88/41.25  | | |   (57)  all_57_6 = e1
% 229.88/41.25  | | | 
% 229.88/41.25  | | | BETA: splitting (53) gives:
% 229.88/41.25  | | | 
% 229.88/41.25  | | | Case 1:
% 229.88/41.25  | | | | 
% 229.88/41.25  | | | |   (58)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2)
% 229.88/41.25  | | | |           = e2)
% 229.88/41.25  | | | | 
% 229.88/41.25  | | | | BETA: splitting (58) gives:
% 229.88/41.25  | | | | 
% 229.88/41.25  | | | | Case 1:
% 229.88/41.25  | | | | | 
% 229.88/41.25  | | | | |   (59)  all_57_6 = e2 & op(e1, e3) = e2
% 229.88/41.25  | | | | | 
% 229.88/41.25  | | | | | ALPHA: (59) implies:
% 229.88/41.25  | | | | |   (60)  all_57_6 = e2
% 229.88/41.25  | | | | | 
% 229.88/41.25  | | | | | REF_CLOSE: (45), (57), (60) are inconsistent by sub-proof #2233.
% 229.88/41.25  | | | | | 
% 229.88/41.25  | | | | Case 2:
% 229.88/41.25  | | | | | 
% 229.88/41.25  | | | | |   (61)  all_57_7 = e2 & op(e1, e2) = e2
% 229.88/41.25  | | | | | 
% 229.88/41.25  | | | | | ALPHA: (61) implies:
% 229.88/41.25  | | | | |   (62)  all_57_7 = e2
% 229.88/41.25  | | | | | 
% 229.88/41.25  | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (15), (16), (21), (26), (29),
% 229.88/41.25  | | | | |            (43), (45), (46), (50), (57), (62) are inconsistent by
% 229.88/41.25  | | | | |            sub-proof #1079.
% 229.88/41.25  | | | | | 
% 229.88/41.25  | | | | End of split
% 229.88/41.25  | | | | 
% 229.88/41.25  | | | Case 2:
% 229.88/41.25  | | | | 
% 229.88/41.25  | | | |   (63)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0)
% 229.88/41.25  | | | |           = e2)
% 229.88/41.25  | | | | 
% 229.88/41.25  | | | | BETA: splitting (63) gives:
% 229.88/41.25  | | | | 
% 229.88/41.25  | | | | Case 1:
% 229.88/41.25  | | | | | 
% 229.88/41.25  | | | | |   (64)  all_57_8 = e2 & op(e1, e1) = e2
% 229.88/41.25  | | | | | 
% 229.88/41.25  | | | | | ALPHA: (64) implies:
% 229.88/41.25  | | | | |   (65)  all_57_8 = e2
% 229.88/41.25  | | | | | 
% 229.88/41.25  | | | | | BETA: splitting (7) gives:
% 229.88/41.25  | | | | | 
% 229.88/41.25  | | | | | Case 1:
% 229.88/41.25  | | | | | | 
% 229.88/41.25  | | | | | |   (66)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1,
% 229.88/41.25  | | | | | |             e2) = e3)
% 229.88/41.25  | | | | | | 
% 229.88/41.25  | | | | | | BETA: splitting (66) gives:
% 229.88/41.25  | | | | | | 
% 229.88/41.25  | | | | | | Case 1:
% 229.88/41.25  | | | | | | | 
% 229.88/41.25  | | | | | | |   (67)  all_57_6 = e3 & op(e1, e3) = e3
% 229.88/41.25  | | | | | | | 
% 229.88/41.25  | | | | | | | ALPHA: (67) implies:
% 229.88/41.25  | | | | | | |   (68)  all_57_6 = e3
% 229.88/41.25  | | | | | | | 
% 229.88/41.25  | | | | | | | REF_CLOSE: (4), (57), (68) are inconsistent by sub-proof #2017.
% 229.88/41.25  | | | | | | | 
% 229.88/41.25  | | | | | | Case 2:
% 229.88/41.25  | | | | | | | 
% 229.88/41.25  | | | | | | |   (69)  all_57_7 = e3 & op(e1, e2) = e3
% 229.88/41.25  | | | | | | | 
% 229.88/41.25  | | | | | | | ALPHA: (69) implies:
% 229.88/41.25  | | | | | | |   (70)  all_57_7 = e3
% 229.88/41.25  | | | | | | | 
% 229.88/41.25  | | | | | | | BETA: splitting (41) gives:
% 229.88/41.25  | | | | | | | 
% 229.88/41.25  | | | | | | | Case 1:
% 229.88/41.25  | | | | | | | | 
% 229.88/41.25  | | | | | | | |   (71)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 &
% 229.88/41.25  | | | | | | | |           op(e2, e3) = e3)
% 229.88/41.25  | | | | | | | | 
% 229.88/41.25  | | | | | | | | BETA: splitting (71) gives:
% 229.88/41.25  | | | | | | | | 
% 229.88/41.25  | | | | | | | | Case 1:
% 229.88/41.25  | | | | | | | | | 
% 229.88/41.25  | | | | | | | | |   (72)  all_57_0 = e3 & op(e3, e3) = e3
% 229.88/41.25  | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | ALPHA: (72) implies:
% 229.88/41.25  | | | | | | | | |   (73)  op(e3, e3) = e3
% 229.88/41.25  | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | REF_CLOSE: (6), (16), (22), (73) are inconsistent by sub-proof
% 229.88/41.25  | | | | | | | | |            #2494.
% 229.88/41.25  | | | | | | | | | 
% 229.88/41.25  | | | | | | | | Case 2:
% 229.88/41.25  | | | | | | | | | 
% 229.88/41.25  | | | | | | | | |   (74)  all_57_2 = e3 & op(e2, e3) = e3
% 229.88/41.25  | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | ALPHA: (74) implies:
% 229.88/41.25  | | | | | | | | |   (75)  all_57_2 = e3
% 229.88/41.25  | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | BETA: splitting (50) gives:
% 229.88/41.25  | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | Case 1:
% 229.88/41.25  | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | |   (76)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1
% 229.88/41.25  | | | | | | | | | |           & op(e2, e0) = e1)
% 229.88/41.25  | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | BETA: splitting (76) gives:
% 229.88/41.25  | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | Case 1:
% 229.88/41.25  | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | |   (77)  all_57_9 = e1 & op(e3, e0) = e1
% 229.88/41.25  | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | ALPHA: (77) implies:
% 229.88/41.25  | | | | | | | | | | |   (78)  all_57_9 = e1
% 229.88/41.25  | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | BETA: splitting (46) gives:
% 229.88/41.25  | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | Case 1:
% 229.88/41.25  | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | |   (79)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 229.88/41.25  | | | | | | | | | | | |           e2 & op(e2, e0) = e2)
% 229.88/41.25  | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | BETA: splitting (79) gives:
% 229.88/41.25  | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | Case 1:
% 229.88/41.25  | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | |   (80)  all_57_9 = e2 & op(e3, e0) = e2
% 229.88/41.25  | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | ALPHA: (80) implies:
% 229.88/41.25  | | | | | | | | | | | | |   (81)  all_57_9 = e2
% 229.88/41.25  | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | REF_CLOSE: (45), (78), (81) are inconsistent by sub-proof
% 229.88/41.25  | | | | | | | | | | | | |            #2444.
% 229.88/41.25  | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | Case 2:
% 229.88/41.25  | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | |   (82)  all_57_10 = e2 & op(e2, e0) = e2
% 229.88/41.25  | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | ALPHA: (82) implies:
% 229.88/41.25  | | | | | | | | | | | | |   (83)  all_57_10 = e2
% 229.88/41.25  | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | BETA: splitting (3) gives:
% 229.88/41.25  | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | Case 1:
% 229.88/41.25  | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | |   (84)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 229.88/41.25  | | | | | | | | | | | | | |           & op(e2, e2) = e2)
% 229.88/41.25  | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | BETA: splitting (84) gives:
% 229.88/41.25  | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | Case 1:
% 229.88/41.25  | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | |   (85)  all_57_1 = e2 & op(e3, e2) = e2
% 229.88/41.25  | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | ALPHA: (85) implies:
% 229.88/41.25  | | | | | | | | | | | | | | |   (86)  all_57_1 = e2
% 229.88/41.25  | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | BETA: splitting (28) gives:
% 229.88/41.25  | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | Case 1:
% 229.88/41.25  | | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | |   (87)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 229.88/41.25  | | | | | | | | | | | | | | | |           & op(e3, e2) = e3)
% 229.88/41.25  | | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | | BETA: splitting (87) gives:
% 229.88/41.25  | | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | | Case 1:
% 229.88/41.25  | | | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | | |   (88)  all_57_0 = e3 & op(e3, e3) = e3
% 229.88/41.25  | | | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | | | ALPHA: (88) implies:
% 229.88/41.25  | | | | | | | | | | | | | | | | |   (89)  op(e3, e3) = e3
% 229.88/41.25  | | | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (16), (22), (89) are inconsistent by
% 229.88/41.25  | | | | | | | | | | | | | | | | |            sub-proof #2494.
% 229.88/41.25  | | | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | | Case 2:
% 229.88/41.25  | | | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | | |   (90)  all_57_1 = e3 & op(e3, e2) = e3
% 229.88/41.25  | | | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | | | ALPHA: (90) implies:
% 229.88/41.25  | | | | | | | | | | | | | | | | |   (91)  all_57_1 = e3
% 229.88/41.25  | | | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | | | COMBINE_EQS: (86), (91) imply:
% 229.88/41.25  | | | | | | | | | | | | | | | | |   (92)  e3 = e2
% 229.88/41.25  | | | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | | | SIMP: (92) implies:
% 229.88/41.25  | | | | | | | | | | | | | | | | |   (93)  e3 = e2
% 229.88/41.25  | | | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | | | COMBINE_EQS: (70), (93) imply:
% 229.88/41.25  | | | | | | | | | | | | | | | | |   (94)  all_57_7 = e2
% 229.88/41.25  | | | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (15), (16), (21), (26),
% 229.88/41.25  | | | | | | | | | | | | | | | | |            (29), (43), (45), (46), (50), (57), (94) are
% 229.88/41.25  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1079.
% 229.88/41.25  | | | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | | End of split
% 229.88/41.25  | | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | Case 2:
% 229.88/41.25  | | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | |   (95)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 229.88/41.25  | | | | | | | | | | | | | | | |           & op(e3, e0) = e3)
% 229.88/41.25  | | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | | BETA: splitting (95) gives:
% 229.88/41.25  | | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | | Case 1:
% 229.88/41.25  | | | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | | |   (96)  all_57_4 = e3 & op(e3, e1) = e3
% 229.88/41.25  | | | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | | | ALPHA: (96) implies:
% 229.88/41.25  | | | | | | | | | | | | | | | | |   (97)  all_57_4 = e3
% 229.88/41.25  | | | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | | | BETA: splitting (12) gives:
% 229.88/41.25  | | | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | | | Case 1:
% 229.88/41.25  | | | | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | | | |   (98)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 229.88/41.25  | | | | | | | | | | | | | | | | | |           & op(e3, e2) = e2)
% 229.88/41.25  | | | | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | | | | BETA: splitting (98) gives:
% 229.88/41.25  | | | | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | | | | Case 1:
% 229.88/41.25  | | | | | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | | | | |   (99)  all_57_0 = e2 & op(e3, e3) = e2
% 229.88/41.25  | | | | | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | | | | | ALPHA: (99) implies:
% 229.88/41.25  | | | | | | | | | | | | | | | | | | |   (100)  op(e3, e3) = e2
% 229.88/41.25  | | | | | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (22), (26), (100) are inconsistent by
% 229.88/41.25  | | | | | | | | | | | | | | | | | | |            sub-proof #2403.
% 229.88/41.25  | | | | | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | | | | Case 2:
% 229.88/41.25  | | | | | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | | | | | ALPHA: (64) implies:
% 229.88/41.25  | | | | | | | | | | | | | | | | | | |   (101)  op(e1, e1) = e2
% 229.88/41.25  | | | | | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with e0, e2, e1, e1, simplifying
% 229.88/41.25  | | | | | | | | | | | | | | | | | | |              with (36), (101) gives:
% 229.88/41.25  | | | | | | | | | | | | | | | | | | |   (102)  e2 = e0
% 229.88/41.25  | | | | | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (86), (102) imply:
% 229.88/41.25  | | | | | | | | | | | | | | | | | | |   (103)  all_57_1 = e0
% 229.88/41.25  | | | | | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (12), (15), (16), (21),
% 229.88/41.25  | | | | | | | | | | | | | | | | | | |            (22), (26), (28), (29), (35), (39), (45), (46),
% 229.88/41.25  | | | | | | | | | | | | | | | | | | |            (50), (54), (57), (70), (78), (103) are
% 229.88/41.25  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #920.
% 229.88/41.25  | | | | | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | | | | End of split
% 229.88/41.25  | | | | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | | | Case 2:
% 229.88/41.25  | | | | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | | | |   (104)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 229.88/41.25  | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e2)
% 229.88/41.25  | | | | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | | | | BETA: splitting (104) gives:
% 229.88/41.25  | | | | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | | | | Case 1:
% 229.88/41.25  | | | | | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | | | | |   (105)  all_57_4 = e2 & op(e3, e1) = e2
% 229.88/41.25  | | | | | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | | | | | ALPHA: (105) implies:
% 229.88/41.25  | | | | | | | | | | | | | | | | | | |   (106)  all_57_4 = e2
% 229.88/41.25  | | | | | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (97), (106) imply:
% 229.88/41.25  | | | | | | | | | | | | | | | | | | |   (107)  e3 = e2
% 229.88/41.25  | | | | | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | | | | | SIMP: (107) implies:
% 229.88/41.25  | | | | | | | | | | | | | | | | | | |   (108)  e3 = e2
% 229.88/41.25  | | | | | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (70), (108) imply:
% 229.88/41.25  | | | | | | | | | | | | | | | | | | |   (109)  all_57_7 = e2
% 229.88/41.25  | | | | | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (15), (16), (21), (26),
% 229.88/41.25  | | | | | | | | | | | | | | | | | | |            (29), (43), (45), (46), (50), (57), (109) are
% 229.88/41.25  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1079.
% 229.88/41.25  | | | | | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | | | | Case 2:
% 229.88/41.25  | | | | | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | | | | |   (110)  all_57_9 = e2 & op(e3, e0) = e2
% 229.88/41.25  | | | | | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | | | | | ALPHA: (110) implies:
% 229.88/41.25  | | | | | | | | | | | | | | | | | | |   (111)  all_57_9 = e2
% 229.88/41.25  | | | | | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (10), (15), (16), (25), (26), (29),
% 229.88/41.25  | | | | | | | | | | | | | | | | | | |            (45), (70), (78), (86), (111) are inconsistent by
% 229.88/41.25  | | | | | | | | | | | | | | | | | | |            sub-proof #919.
% 229.88/41.25  | | | | | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | | | | End of split
% 229.88/41.25  | | | | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | | | End of split
% 229.88/41.25  | | | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | | Case 2:
% 229.88/41.25  | | | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | | |   (112)  all_57_9 = e3 & op(e3, e0) = e3
% 229.88/41.25  | | | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | | | ALPHA: (112) implies:
% 229.88/41.25  | | | | | | | | | | | | | | | | |   (113)  op(e3, e0) = e3
% 229.88/41.25  | | | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (39), (54), (113) are inconsistent by
% 229.88/41.25  | | | | | | | | | | | | | | | | |            sub-proof #2458.
% 229.88/41.25  | | | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | | End of split
% 229.88/41.25  | | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | End of split
% 229.88/41.25  | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | Case 2:
% 229.88/41.25  | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | |   (114)  all_57_3 = e2 & op(e2, e2) = e2
% 229.88/41.25  | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | ALPHA: (114) implies:
% 229.88/41.25  | | | | | | | | | | | | | | |   (115)  op(e2, e2) = e2
% 229.88/41.25  | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | REF_CLOSE: (6), (10), (45), (115) are inconsistent by
% 229.88/41.25  | | | | | | | | | | | | | | |            sub-proof #2306.
% 229.88/41.25  | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | End of split
% 229.88/41.25  | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | Case 2:
% 229.88/41.25  | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | |   (116)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 229.88/41.25  | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 229.88/41.25  | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | BETA: splitting (116) gives:
% 229.88/41.25  | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | Case 1:
% 229.88/41.25  | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | |   (117)  all_57_7 = e2 & op(e1, e2) = e2
% 229.88/41.25  | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | ALPHA: (117) implies:
% 229.88/41.25  | | | | | | | | | | | | | | |   (118)  all_57_7 = e2
% 229.88/41.25  | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (15), (16), (21), (26),
% 229.88/41.25  | | | | | | | | | | | | | | |            (29), (43), (45), (46), (50), (57), (118) are
% 229.88/41.25  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1079.
% 229.88/41.25  | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | Case 2:
% 229.88/41.25  | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | |   (119)  all_57_13 = e2 & op(e0, e2) = e2
% 229.88/41.25  | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | ALPHA: (119) implies:
% 229.88/41.25  | | | | | | | | | | | | | | |   (120)  all_57_13 = e2
% 229.88/41.25  | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (15), (21), (24), (26), (29), (32),
% 229.88/41.25  | | | | | | | | | | | | | | |            (37), (45), (46), (50), (83), (120) are
% 229.88/41.25  | | | | | | | | | | | | | | |            inconsistent by sub-proof #918.
% 229.88/41.25  | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | End of split
% 229.88/41.25  | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | End of split
% 229.88/41.25  | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | End of split
% 229.88/41.25  | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | Case 2:
% 229.88/41.25  | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | |   (121)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 229.88/41.25  | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 229.88/41.25  | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | BETA: splitting (121) gives:
% 229.88/41.25  | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | Case 1:
% 229.88/41.25  | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | |   (122)  all_57_11 = e2 & op(e1, e0) = e2
% 229.88/41.25  | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | ALPHA: (122) implies:
% 229.88/41.25  | | | | | | | | | | | | |   (123)  all_57_11 = e2
% 229.88/41.25  | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | BETA: splitting (5) gives:
% 229.88/41.25  | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | Case 1:
% 229.88/41.25  | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | |   (124)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 229.88/41.25  | | | | | | | | | | | | | |            & op(e1, e2) = e0)
% 229.88/41.25  | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | BETA: splitting (124) gives:
% 229.88/41.25  | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | Case 1:
% 229.88/41.25  | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | |   (125)  all_57_6 = e0 & op(e1, e3) = e0
% 229.88/41.25  | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | ALPHA: (125) implies:
% 229.88/41.25  | | | | | | | | | | | | | | |   (126)  all_57_6 = e0
% 229.88/41.25  | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (6), (7), (8), (9), (10), (13),
% 229.88/41.25  | | | | | | | | | | | | | | |            (15), (16), (18), (21), (22), (23), (25), (26),
% 229.88/41.25  | | | | | | | | | | | | | | |            (27), (28), (29), (31), (32), (34), (35), (39),
% 229.88/41.25  | | | | | | | | | | | | | | |            (41), (42), (45), (46), (47), (50), (52), (54),
% 229.88/41.25  | | | | | | | | | | | | | | |            (126) are inconsistent by sub-proof #983.
% 229.88/41.25  | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | Case 2:
% 229.88/41.25  | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | |   (127)  all_57_7 = e0 & op(e1, e2) = e0
% 229.88/41.25  | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | ALPHA: (127) implies:
% 229.88/41.25  | | | | | | | | | | | | | | |   (128)  all_57_7 = e0
% 229.88/41.25  | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (15), (16), (21), (26),
% 229.88/41.25  | | | | | | | | | | | | | | |            (29), (35), (45), (46), (50), (51), (65), (123),
% 229.88/41.25  | | | | | | | | | | | | | | |            (128) are inconsistent by sub-proof #952.
% 229.88/41.25  | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | End of split
% 229.88/41.25  | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | Case 2:
% 229.88/41.25  | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | |   (129)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 229.88/41.25  | | | | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 229.88/41.25  | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | BETA: splitting (129) gives:
% 229.88/41.25  | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | Case 1:
% 229.88/41.25  | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | |   (130)  all_57_8 = e0 & op(e1, e1) = e0
% 229.88/41.25  | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | REF_CLOSE: (26), (65), (130) are inconsistent by sub-proof
% 229.88/41.25  | | | | | | | | | | | | | | |            #917.
% 229.88/41.25  | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | Case 2:
% 229.88/41.25  | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | |   (131)  all_57_11 = e0 & op(e1, e0) = e0
% 229.88/41.25  | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | | REF_CLOSE: (26), (123), (131) are inconsistent by sub-proof
% 229.88/41.25  | | | | | | | | | | | | | | |            #2041.
% 229.88/41.25  | | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | | End of split
% 229.88/41.25  | | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | End of split
% 229.88/41.25  | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | Case 2:
% 229.88/41.25  | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | |   (132)  all_57_15 = e2 & op(e0, e0) = e2
% 229.88/41.25  | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | ALPHA: (132) implies:
% 229.88/41.25  | | | | | | | | | | | | |   (133)  all_57_15 = e2
% 229.88/41.25  | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | COMBINE_EQS: (21), (133) imply:
% 229.88/41.25  | | | | | | | | | | | | |   (134)  e3 = e2
% 229.88/41.25  | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | COMBINE_EQS: (70), (134) imply:
% 229.88/41.25  | | | | | | | | | | | | |   (135)  all_57_7 = e2
% 229.88/41.25  | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (15), (16), (21), (26),
% 229.88/41.25  | | | | | | | | | | | | |            (29), (43), (45), (46), (50), (57), (135) are
% 229.88/41.25  | | | | | | | | | | | | |            inconsistent by sub-proof #1079.
% 229.88/41.25  | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | End of split
% 229.88/41.25  | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | End of split
% 229.88/41.25  | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | Case 2:
% 229.88/41.25  | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | |   (136)  all_57_10 = e1 & op(e2, e0) = e1
% 229.88/41.25  | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | ALPHA: (136) implies:
% 229.88/41.25  | | | | | | | | | | |   (137)  all_57_10 = e1
% 229.88/41.25  | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | BETA: splitting (40) gives:
% 229.88/41.25  | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | Case 1:
% 229.88/41.25  | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | |   (138)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 229.88/41.25  | | | | | | | | | | | |            & op(e2, e2) = e2)
% 229.88/41.25  | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | BETA: splitting (138) gives:
% 229.88/41.25  | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | Case 1:
% 229.88/41.25  | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | |   (139)  all_57_2 = e2 & op(e2, e3) = e2
% 229.88/41.25  | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | ALPHA: (139) implies:
% 229.88/41.25  | | | | | | | | | | | | |   (140)  all_57_2 = e2
% 229.88/41.25  | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | COMBINE_EQS: (75), (140) imply:
% 229.88/41.25  | | | | | | | | | | | | |   (141)  e3 = e2
% 229.88/41.25  | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | COMBINE_EQS: (70), (141) imply:
% 229.88/41.25  | | | | | | | | | | | | |   (142)  all_57_7 = e2
% 229.88/41.25  | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (15), (16), (21), (26),
% 229.88/41.25  | | | | | | | | | | | | |            (29), (43), (45), (46), (50), (57), (142) are
% 229.88/41.25  | | | | | | | | | | | | |            inconsistent by sub-proof #1079.
% 229.88/41.25  | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | Case 2:
% 229.88/41.25  | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | |   (143)  all_57_3 = e2 & op(e2, e2) = e2
% 229.88/41.25  | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | ALPHA: (143) implies:
% 229.88/41.25  | | | | | | | | | | | | |   (144)  op(e2, e2) = e2
% 229.88/41.25  | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | | REF_CLOSE: (6), (10), (45), (144) are inconsistent by
% 229.88/41.25  | | | | | | | | | | | | |            sub-proof #2306.
% 229.88/41.25  | | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | End of split
% 229.88/41.25  | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | Case 2:
% 229.88/41.25  | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | |   (145)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 229.88/41.25  | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 229.88/41.25  | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 229.88/41.25  | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 229.88/41.25  | | | | | | | | | | | |            (21), (22), (23), (25), (26), (27), (28), (29),
% 229.88/41.25  | | | | | | | | | | | |            (30), (31), (32), (33), (34), (35), (38), (39),
% 229.88/41.25  | | | | | | | | | | | |            (40), (41), (42), (44), (45), (46), (47), (48),
% 229.88/41.25  | | | | | | | | | | | |            (49), (50), (51), (52), (53), (54), (57), (137),
% 229.88/41.25  | | | | | | | | | | | |            (145) are inconsistent by sub-proof #914.
% 229.88/41.25  | | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | End of split
% 229.88/41.25  | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | End of split
% 229.88/41.25  | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | Case 2:
% 229.88/41.25  | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | |   (146)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 229.88/41.25  | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 229.88/41.25  | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | BETA: splitting (146) gives:
% 229.88/41.25  | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | Case 1:
% 229.88/41.25  | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | |   (147)  all_57_11 = e1 & op(e1, e0) = e1
% 229.88/41.25  | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | ALPHA: (147) implies:
% 229.88/41.25  | | | | | | | | | | |   (148)  all_57_11 = e1
% 229.88/41.25  | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | COMBINE_EQS: (24), (148) imply:
% 229.88/41.25  | | | | | | | | | | |   (149)  e1 = e0
% 229.88/41.25  | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (6), (7), (8), (9), (10), (13),
% 229.88/41.25  | | | | | | | | | | |            (15), (16), (18), (21), (22), (23), (25), (26),
% 229.88/41.25  | | | | | | | | | | |            (27), (28), (29), (31), (32), (34), (35), (39),
% 229.88/41.25  | | | | | | | | | | |            (41), (42), (45), (46), (47), (50), (52), (54),
% 229.88/41.25  | | | | | | | | | | |            (57), (149) are inconsistent by sub-proof #915.
% 229.88/41.25  | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | Case 2:
% 229.88/41.25  | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | |   (150)  all_57_15 = e1 & op(e0, e0) = e1
% 229.88/41.25  | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | ALPHA: (150) implies:
% 229.88/41.25  | | | | | | | | | | |   (151)  op(e0, e0) = e1
% 229.88/41.25  | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | | REF_CLOSE: (4), (6), (32), (151) are inconsistent by
% 229.88/41.25  | | | | | | | | | | |            sub-proof #2183.
% 229.88/41.25  | | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | | End of split
% 229.88/41.25  | | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | End of split
% 229.88/41.25  | | | | | | | | | 
% 229.88/41.25  | | | | | | | | End of split
% 229.88/41.25  | | | | | | | | 
% 229.88/41.25  | | | | | | | Case 2:
% 229.88/41.25  | | | | | | | | 
% 229.88/41.25  | | | | | | | |   (152)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 &
% 229.88/41.25  | | | | | | | |            op(e0, e3) = e3)
% 229.88/41.25  | | | | | | | | 
% 229.88/41.25  | | | | | | | | BETA: splitting (152) gives:
% 229.88/41.25  | | | | | | | | 
% 229.88/41.25  | | | | | | | | Case 1:
% 229.88/41.25  | | | | | | | | | 
% 229.88/41.25  | | | | | | | | |   (153)  all_57_6 = e3 & op(e1, e3) = e3
% 229.88/41.25  | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | ALPHA: (153) implies:
% 229.88/41.25  | | | | | | | | |   (154)  all_57_6 = e3
% 229.88/41.25  | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | REF_CLOSE: (4), (57), (154) are inconsistent by sub-proof
% 229.88/41.25  | | | | | | | | |            #2017.
% 229.88/41.25  | | | | | | | | | 
% 229.88/41.25  | | | | | | | | Case 2:
% 229.88/41.25  | | | | | | | | | 
% 229.88/41.25  | | | | | | | | |   (155)  all_57_12 = e3 & op(e0, e3) = e3
% 229.88/41.25  | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | ALPHA: (155) implies:
% 229.88/41.25  | | | | | | | | |   (156)  all_57_12 = e3
% 229.88/41.25  | | | | | | | | | 
% 229.88/41.25  | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 229.88/41.25  | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 229.88/41.25  | | | | | | | | |            (19), (21), (22), (23), (25), (26), (27), (28),
% 229.88/41.25  | | | | | | | | |            (29), (30), (31), (32), (33), (34), (35), (37),
% 229.88/41.25  | | | | | | | | |            (38), (39), (40), (41), (42), (44), (45), (46),
% 229.88/41.25  | | | | | | | | |            (47), (48), (49), (50), (51), (52), (53), (54),
% 229.88/41.25  | | | | | | | | |            (156) are inconsistent by sub-proof #912.
% 229.88/41.25  | | | | | | | | | 
% 229.88/41.25  | | | | | | | | End of split
% 229.88/41.25  | | | | | | | | 
% 229.88/41.25  | | | | | | | End of split
% 229.88/41.25  | | | | | | | 
% 229.88/41.25  | | | | | | End of split
% 229.88/41.25  | | | | | | 
% 229.88/41.25  | | | | | Case 2:
% 229.88/41.25  | | | | | | 
% 229.88/41.25  | | | | | |   (157)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 &
% 229.88/41.25  | | | | | |            op(e1, e0) = e3)
% 229.88/41.25  | | | | | | 
% 229.88/41.25  | | | | | | REF_CLOSE: (4), (6), (8), (9), (15), (16), (21), (26), (29), (43),
% 229.88/41.25  | | | | | |            (45), (46), (50), (157) are inconsistent by sub-proof
% 229.88/41.25  | | | | | |            #1080.
% 229.88/41.25  | | | | | | 
% 229.88/41.25  | | | | | End of split
% 229.88/41.25  | | | | | 
% 229.88/41.25  | | | | Case 2:
% 229.88/41.25  | | | | | 
% 229.88/41.25  | | | | |   (158)  all_57_11 = e2 & op(e1, e0) = e2
% 229.88/41.25  | | | | | 
% 229.88/41.25  | | | | | ALPHA: (158) implies:
% 229.88/41.25  | | | | |   (159)  all_57_11 = e2
% 229.88/41.25  | | | | | 
% 229.88/41.25  | | | | | REF_CLOSE: (24), (26), (159) are inconsistent by sub-proof #1949.
% 229.88/41.25  | | | | | 
% 229.88/41.25  | | | | End of split
% 229.88/41.25  | | | | 
% 229.88/41.25  | | | End of split
% 229.88/41.25  | | | 
% 229.88/41.25  | | Case 2:
% 229.88/41.25  | | | 
% 229.88/41.25  | | |   (160)  all_57_7 = e1 & op(e1, e2) = e1
% 229.88/41.25  | | | 
% 229.88/41.25  | | | ALPHA: (160) implies:
% 229.88/41.25  | | |   (161)  all_57_7 = e1
% 229.88/41.25  | | | 
% 229.88/41.25  | | | BETA: splitting (3) gives:
% 229.88/41.25  | | | 
% 229.88/41.25  | | | Case 1:
% 229.88/41.25  | | | | 
% 229.88/41.25  | | | |   (162)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2)
% 229.88/41.25  | | | |            = e2)
% 229.88/41.25  | | | | 
% 229.88/41.25  | | | | BETA: splitting (162) gives:
% 229.88/41.25  | | | | 
% 229.88/41.25  | | | | Case 1:
% 229.88/41.25  | | | | | 
% 229.88/41.25  | | | | |   (163)  all_57_1 = e2 & op(e3, e2) = e2
% 229.88/41.25  | | | | | 
% 229.88/41.25  | | | | | ALPHA: (163) implies:
% 229.88/41.25  | | | | |   (164)  all_57_1 = e2
% 229.88/41.25  | | | | | 
% 229.88/41.25  | | | | | BETA: splitting (31) gives:
% 229.88/41.25  | | | | | 
% 229.88/41.25  | | | | | Case 1:
% 229.88/41.25  | | | | | | 
% 229.88/41.25  | | | | | |   (165)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2,
% 229.88/41.25  | | | | | |              e2) = e3)
% 229.88/41.25  | | | | | | 
% 229.88/41.25  | | | | | | REF_CLOSE: (4), (6), (10), (15), (164), (165) are inconsistent by
% 229.88/41.25  | | | | | |            sub-proof #1031.
% 229.88/41.25  | | | | | | 
% 229.88/41.25  | | | | | Case 2:
% 229.88/41.25  | | | | | | 
% 229.88/41.25  | | | | | |   (166)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 &
% 229.88/41.25  | | | | | |            op(e0, e2) = e3)
% 229.88/41.25  | | | | | | 
% 229.88/41.25  | | | | | | REF_CLOSE: (4), (6), (15), (16), (20), (21), (23), (26), (29), (32),
% 229.88/41.25  | | | | | |            (33), (45), (161), (166) are inconsistent by sub-proof
% 229.88/41.25  | | | | | |            #911.
% 229.88/41.25  | | | | | | 
% 229.88/41.25  | | | | | End of split
% 229.88/41.25  | | | | | 
% 229.88/41.25  | | | | Case 2:
% 229.88/41.25  | | | | | 
% 229.88/41.25  | | | | |   (167)  all_57_3 = e2 & op(e2, e2) = e2
% 229.88/41.25  | | | | | 
% 229.88/41.25  | | | | | ALPHA: (167) implies:
% 229.88/41.25  | | | | |   (168)  op(e2, e2) = e2
% 229.88/41.25  | | | | | 
% 229.88/41.25  | | | | | REF_CLOSE: (6), (10), (45), (168) are inconsistent by sub-proof #2306.
% 229.88/41.25  | | | | | 
% 229.88/41.25  | | | | End of split
% 229.88/41.25  | | | | 
% 229.88/41.25  | | | Case 2:
% 229.88/41.25  | | | | 
% 229.88/41.25  | | | |   (169)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0,
% 229.88/41.25  | | | |              e2) = e2)
% 229.88/41.25  | | | | 
% 229.88/41.25  | | | | BETA: splitting (169) gives:
% 229.88/41.25  | | | | 
% 229.88/41.25  | | | | Case 1:
% 229.88/41.25  | | | | | 
% 229.88/41.25  | | | | |   (170)  all_57_7 = e2 & op(e1, e2) = e2
% 229.88/41.25  | | | | | 
% 229.88/41.25  | | | | | ALPHA: (170) implies:
% 229.88/41.25  | | | | |   (171)  all_57_7 = e2
% 229.88/41.25  | | | | | 
% 229.88/41.25  | | | | | REF_CLOSE: (45), (161), (171) are inconsistent by sub-proof #1761.
% 229.88/41.25  | | | | | 
% 229.88/41.25  | | | | Case 2:
% 229.88/41.25  | | | | | 
% 229.88/41.25  | | | | |   (172)  all_57_13 = e2 & op(e0, e2) = e2
% 229.88/41.25  | | | | | 
% 229.88/41.25  | | | | | ALPHA: (172) implies:
% 229.88/41.25  | | | | |   (173)  all_57_13 = e2
% 229.88/41.25  | | | | | 
% 229.88/41.25  | | | | | REF_CLOSE: (26), (37), (173) are inconsistent by sub-proof #1911.
% 229.88/41.25  | | | | | 
% 229.88/41.25  | | | | End of split
% 229.88/41.25  | | | | 
% 229.88/41.25  | | | End of split
% 229.88/41.25  | | | 
% 229.88/41.25  | | End of split
% 229.88/41.25  | | 
% 229.88/41.25  | Case 2:
% 229.88/41.25  | | 
% 229.88/41.25  | |   (174)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) =
% 229.88/41.25  | |            e1)
% 229.88/41.25  | | 
% 229.88/41.26  | | REF_CLOSE: (6), (24), (29), (36), (174) are inconsistent by sub-proof #910.
% 229.88/41.26  | | 
% 229.88/41.26  | End of split
% 229.88/41.26  | 
% 229.88/41.26  End of proof
% 229.88/41.26  
% 229.88/41.26  Sub-proof #910 shows that the following formulas are inconsistent:
% 229.88/41.26  ----------------------------------------------------------------
% 229.88/41.26    (1)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 229.88/41.26    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.88/41.26           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.88/41.26    (3)  all_57_11 = e0
% 229.88/41.26    (4)   ~ (e1 = e0)
% 229.88/41.26    (5)  op(e1, e1) = e0
% 229.88/41.26  
% 229.88/41.26  Begin of proof
% 229.88/41.26  | 
% 229.88/41.26  | BETA: splitting (1) gives:
% 229.88/41.26  | 
% 229.88/41.26  | Case 1:
% 229.88/41.26  | | 
% 229.88/41.26  | |   (6)  all_57_8 = e1 & op(e1, e1) = e1
% 229.88/41.26  | | 
% 229.88/41.26  | | ALPHA: (6) implies:
% 229.88/41.26  | |   (7)  op(e1, e1) = e1
% 229.88/41.26  | | 
% 229.88/41.26  | | REF_CLOSE: (2), (4), (5), (7) are inconsistent by sub-proof #2427.
% 229.88/41.26  | | 
% 229.88/41.26  | Case 2:
% 229.88/41.26  | | 
% 229.88/41.26  | |   (8)  all_57_11 = e1 & op(e1, e0) = e1
% 229.88/41.26  | | 
% 229.88/41.26  | | ALPHA: (8) implies:
% 229.88/41.26  | |   (9)  all_57_11 = e1
% 229.88/41.26  | | 
% 229.88/41.26  | | REF_CLOSE: (3), (4), (9) are inconsistent by sub-proof #1862.
% 229.88/41.26  | | 
% 229.88/41.26  | End of split
% 229.88/41.26  | 
% 229.88/41.26  End of proof
% 229.88/41.26  
% 229.88/41.26  Sub-proof #911 shows that the following formulas are inconsistent:
% 229.88/41.26  ----------------------------------------------------------------
% 229.88/41.26    (1)   ~ (e3 = e1)
% 229.88/41.26    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.88/41.26           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.88/41.26    (3)  all_57_7 = e1
% 229.88/41.26    (4)   ~ (e3 = e2)
% 229.88/41.26    (5)   ~ (e3 = e0)
% 229.88/41.26    (6)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 229.88/41.26         (all_57_14 = e0 & op(e0, e1) = e0)
% 229.88/41.26    (7)  all_57_15 = e3
% 229.88/41.26    (8)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 229.88/41.26         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.88/41.26    (9)   ~ (e2 = e0)
% 229.88/41.26    (10)   ~ (e1 = e0)
% 229.88/41.26    (11)  op(e0, e0) = e3
% 229.88/41.26    (12)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.88/41.26          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.88/41.26            e2)
% 229.88/41.26    (13)   ~ (e2 = e1)
% 229.88/41.26    (14)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.88/41.26  
% 229.88/41.26  Begin of proof
% 229.88/41.26  | 
% 229.88/41.26  | BETA: splitting (14) gives:
% 229.88/41.26  | 
% 229.88/41.26  | Case 1:
% 229.88/41.26  | | 
% 229.88/41.26  | |   (15)  all_57_7 = e3 & op(e1, e2) = e3
% 229.88/41.26  | | 
% 229.88/41.26  | | ALPHA: (15) implies:
% 229.88/41.26  | |   (16)  all_57_7 = e3
% 229.88/41.26  | | 
% 229.88/41.26  | | REF_CLOSE: (1), (3), (16) are inconsistent by sub-proof #2115.
% 229.88/41.26  | | 
% 229.88/41.26  | Case 2:
% 229.88/41.26  | | 
% 229.88/41.26  | |   (17)  all_57_13 = e3 & op(e0, e2) = e3
% 229.88/41.26  | | 
% 229.88/41.26  | | ALPHA: (17) implies:
% 229.88/41.26  | |   (18)  all_57_13 = e3
% 229.88/41.26  | | 
% 229.88/41.26  | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 229.88/41.26  | |            (18) are inconsistent by sub-proof #2054.
% 229.88/41.26  | | 
% 229.88/41.26  | End of split
% 229.88/41.26  | 
% 229.88/41.26  End of proof
% 229.88/41.26  
% 229.88/41.26  Sub-proof #912 shows that the following formulas are inconsistent:
% 229.88/41.26  ----------------------------------------------------------------
% 229.88/41.26    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.88/41.26         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.88/41.26    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.88/41.26         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.88/41.26    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.88/41.26         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.88/41.26    (4)   ~ (e3 = e1)
% 229.88/41.26    (5)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 229.88/41.26         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 229.88/41.26    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.88/41.26           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.88/41.26    (7)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.88/41.26         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.88/41.26    (8)   ~ (all_6_2 = e3)
% 229.88/41.26    (9)  op(e1, e1) = all_6_2
% 229.88/41.26    (10)  op(e2, e2) = e1
% 229.88/41.26    (11)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.88/41.26          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.88/41.26    (12)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.88/41.26          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.88/41.26    (13)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.88/41.26          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.88/41.26    (14)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 229.88/41.26          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.88/41.26    (15)   ~ (e3 = e2)
% 229.88/41.26    (16)   ~ (e3 = e0)
% 229.88/41.26    (17)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 229.88/41.26          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 229.88/41.26    (18)  op(e0, e3) = all_53_3
% 229.88/41.26    (19)  all_57_0 = e0
% 229.88/41.26    (20)  all_57_15 = e3
% 229.88/41.26    (21)  op(e3, e3) = e0
% 229.88/41.26    (22)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.88/41.26          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.88/41.26            e1)
% 229.88/41.26    (23)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.88/41.26          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.88/41.26    (24)   ~ (e2 = e0)
% 229.88/41.26    (25)  all_57_3 = e1
% 229.88/41.26    (26)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.88/41.26          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.88/41.26    (27)   ~ (e1 = e0)
% 229.88/41.26    (28)  all_57_12 = e3
% 229.88/41.26    (29)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.88/41.26          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.88/41.26    (30)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.88/41.26          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.88/41.26    (31)  op(e0, e0) = e3
% 229.88/41.26    (32)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.88/41.26          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.88/41.26            e2)
% 229.88/41.26    (33)   ~ (all_53_3 = e0)
% 229.88/41.26    (34)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.88/41.26              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.88/41.26                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.88/41.26                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.88/41.26    (35)  all_57_13 = e0
% 229.88/41.26    (36)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.88/41.26          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.88/41.26    (37)   ~ (all_53_12 = e3)
% 229.88/41.26    (38)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.88/41.26          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.88/41.26    (39)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.88/41.26          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.88/41.26    (40)   ~ (all_53_12 = e0)
% 229.88/41.26    (41)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.88/41.26          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 229.88/41.26    (42)   ~ (e2 = e1)
% 229.88/41.26    (43)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.88/41.26          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.88/41.26    (44)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.88/41.26          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.88/41.26    (45)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 229.88/41.26          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 229.88/41.26    (46)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.88/41.26          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.88/41.26    (47)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.88/41.26          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.88/41.26    (48)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 229.88/41.26          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 229.88/41.26    (49)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.88/41.26          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.88/41.26    (50)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 229.88/41.26          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 229.88/41.26    (51)  op(e3, e0) = all_53_12
% 229.88/41.26  
% 229.88/41.26  Begin of proof
% 229.88/41.26  | 
% 229.88/41.26  | BETA: splitting (32) gives:
% 229.88/41.26  | 
% 229.88/41.26  | Case 1:
% 229.88/41.26  | | 
% 229.88/41.26  | |   (52)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 229.88/41.26  | |           e2)
% 229.88/41.26  | | 
% 229.88/41.26  | | BETA: splitting (52) gives:
% 229.88/41.26  | | 
% 229.88/41.26  | | Case 1:
% 229.88/41.26  | | | 
% 229.88/41.26  | | |   (53)  all_57_12 = e2 & op(e0, e3) = e2
% 229.88/41.26  | | | 
% 229.88/41.26  | | | ALPHA: (53) implies:
% 229.88/41.26  | | |   (54)  all_57_12 = e2
% 229.88/41.26  | | | 
% 229.88/41.26  | | | REF_CLOSE: (15), (28), (54) are inconsistent by sub-proof #2392.
% 229.88/41.26  | | | 
% 229.88/41.26  | | Case 2:
% 229.88/41.26  | | | 
% 229.88/41.26  | | |   (55)  all_57_13 = e2 & op(e0, e2) = e2
% 229.88/41.26  | | | 
% 229.88/41.26  | | | REF_CLOSE: (24), (35), (55) are inconsistent by sub-proof #2316.
% 229.88/41.26  | | | 
% 229.88/41.26  | | End of split
% 229.88/41.26  | | 
% 229.88/41.26  | Case 2:
% 229.88/41.26  | | 
% 229.88/41.26  | |   (56)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.88/41.26  | |           e2)
% 229.88/41.26  | | 
% 229.88/41.26  | | BETA: splitting (56) gives:
% 229.88/41.26  | | 
% 229.88/41.26  | | Case 1:
% 229.88/41.26  | | | 
% 229.88/41.26  | | |   (57)  all_57_14 = e2 & op(e0, e1) = e2
% 229.88/41.26  | | | 
% 229.88/41.26  | | | ALPHA: (57) implies:
% 229.88/41.26  | | |   (58)  all_57_14 = e2
% 229.88/41.26  | | | 
% 229.95/41.26  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 229.95/41.26  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 229.95/41.26  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 229.95/41.26  | | |            (33), (34), (36), (37), (38), (39), (40), (41), (42), (43),
% 229.95/41.26  | | |            (44), (45), (46), (47), (48), (49), (50), (51), (58) are
% 229.95/41.26  | | |            inconsistent by sub-proof #913.
% 229.95/41.26  | | | 
% 229.95/41.26  | | Case 2:
% 229.95/41.26  | | | 
% 229.95/41.26  | | |   (59)  all_57_15 = e2 & op(e0, e0) = e2
% 229.95/41.26  | | | 
% 229.95/41.26  | | | ALPHA: (59) implies:
% 229.95/41.26  | | |   (60)  all_57_15 = e2
% 229.95/41.26  | | | 
% 229.95/41.26  | | | REF_CLOSE: (15), (20), (60) are inconsistent by sub-proof #2058.
% 229.95/41.26  | | | 
% 229.95/41.26  | | End of split
% 229.95/41.26  | | 
% 229.95/41.26  | End of split
% 229.95/41.26  | 
% 229.95/41.26  End of proof
% 229.95/41.26  
% 229.95/41.26  Sub-proof #913 shows that the following formulas are inconsistent:
% 229.95/41.26  ----------------------------------------------------------------
% 229.95/41.26    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.95/41.26         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.95/41.26    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.95/41.26         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.95/41.26    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.95/41.26         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.95/41.26    (4)   ~ (e3 = e1)
% 229.95/41.26    (5)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 229.95/41.26         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 229.95/41.26    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.95/41.26           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.95/41.26    (7)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.95/41.26         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.95/41.26    (8)   ~ (all_6_2 = e3)
% 229.95/41.26    (9)  op(e1, e1) = all_6_2
% 229.95/41.26    (10)  op(e2, e2) = e1
% 229.95/41.26    (11)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.95/41.26          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.95/41.26    (12)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.95/41.26          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.95/41.26    (13)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.95/41.26          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.95/41.26    (14)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 229.95/41.26          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.95/41.26    (15)   ~ (e3 = e2)
% 229.95/41.26    (16)   ~ (e3 = e0)
% 229.95/41.26    (17)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 229.95/41.26          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 229.95/41.26    (18)  op(e0, e3) = all_53_3
% 229.95/41.26    (19)  all_57_0 = e0
% 229.95/41.26    (20)  all_57_15 = e3
% 229.95/41.26    (21)  op(e3, e3) = e0
% 229.95/41.26    (22)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.95/41.26          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.95/41.26            e1)
% 229.95/41.26    (23)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.95/41.26          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.95/41.26    (24)   ~ (e2 = e0)
% 229.95/41.26    (25)  all_57_3 = e1
% 229.95/41.26    (26)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.95/41.26          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.95/41.26    (27)   ~ (e1 = e0)
% 229.95/41.26    (28)  all_57_12 = e3
% 229.95/41.26    (29)  all_57_14 = e2
% 229.95/41.26    (30)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.95/41.26          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.95/41.26    (31)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.95/41.26          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.95/41.26    (32)  op(e0, e0) = e3
% 229.95/41.26    (33)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.95/41.26          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.95/41.26            e2)
% 229.95/41.26    (34)   ~ (all_53_3 = e0)
% 229.95/41.26    (35)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.95/41.26              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.95/41.26                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.95/41.26                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.95/41.26    (36)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.95/41.26          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.95/41.26    (37)   ~ (all_53_12 = e3)
% 229.95/41.26    (38)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.95/41.26          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.95/41.26    (39)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.95/41.26          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.95/41.26    (40)   ~ (all_53_12 = e0)
% 229.95/41.26    (41)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.95/41.26          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 229.95/41.26    (42)   ~ (e2 = e1)
% 229.95/41.26    (43)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.95/41.26          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.95/41.26    (44)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.95/41.26          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.95/41.26    (45)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 229.95/41.26          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 229.95/41.26    (46)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.95/41.26          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.95/41.26    (47)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.95/41.26          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.95/41.26    (48)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 229.95/41.26          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 229.95/41.26    (49)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.95/41.26          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.95/41.26    (50)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 229.95/41.26          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 229.95/41.26    (51)  op(e3, e0) = all_53_12
% 229.95/41.26  
% 229.95/41.26  Begin of proof
% 229.95/41.26  | 
% 229.95/41.26  | BETA: splitting (22) gives:
% 229.95/41.26  | 
% 229.95/41.26  | Case 1:
% 229.95/41.26  | | 
% 229.95/41.26  | |   (52)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 229.95/41.26  | |           e1)
% 229.95/41.26  | | 
% 229.95/41.26  | | BETA: splitting (52) gives:
% 229.95/41.26  | | 
% 229.95/41.26  | | Case 1:
% 229.95/41.26  | | | 
% 229.95/41.26  | | |   (53)  all_57_12 = e1 & op(e0, e3) = e1
% 229.95/41.26  | | | 
% 229.95/41.26  | | | ALPHA: (53) implies:
% 229.95/41.26  | | |   (54)  all_57_12 = e1
% 229.95/41.26  | | | 
% 229.95/41.26  | | | REF_CLOSE: (4), (28), (54) are inconsistent by sub-proof #2151.
% 229.95/41.26  | | | 
% 229.95/41.26  | | Case 2:
% 229.95/41.26  | | | 
% 229.95/41.26  | | |   (55)  all_57_13 = e1 & op(e0, e2) = e1
% 229.95/41.26  | | | 
% 229.95/41.26  | | | ALPHA: (55) implies:
% 229.95/41.26  | | |   (56)  all_57_13 = e1
% 229.95/41.26  | | | 
% 229.95/41.26  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 229.95/41.26  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 229.95/41.26  | | |            (23), (24), (25), (26), (27), (30), (31), (32), (33), (34),
% 229.95/41.26  | | |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44),
% 229.95/41.26  | | |            (45), (46), (47), (48), (49), (50), (51), (56) are inconsistent
% 229.95/41.26  | | |            by sub-proof #976.
% 229.95/41.26  | | | 
% 229.95/41.26  | | End of split
% 229.95/41.26  | | 
% 229.95/41.26  | Case 2:
% 229.95/41.26  | | 
% 229.95/41.26  | |   (57)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.95/41.26  | |           e1)
% 229.95/41.26  | | 
% 229.95/41.26  | | REF_CLOSE: (4), (6), (29), (32), (42), (57) are inconsistent by sub-proof
% 229.95/41.26  | |            #1139.
% 229.95/41.26  | | 
% 229.95/41.26  | End of split
% 229.95/41.26  | 
% 229.95/41.26  End of proof
% 229.95/41.26  
% 229.95/41.26  Sub-proof #914 shows that the following formulas are inconsistent:
% 229.95/41.26  ----------------------------------------------------------------
% 229.95/41.26    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.95/41.26         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.95/41.26    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.95/41.26         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.95/41.26    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.95/41.26         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.95/41.26    (4)   ~ (e3 = e1)
% 229.95/41.26    (5)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 229.95/41.26         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 229.95/41.26    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.95/41.26           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.95/41.26    (7)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.95/41.26         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.95/41.26    (8)   ~ (all_6_2 = e3)
% 229.95/41.26    (9)  all_57_10 = e1
% 229.95/41.26    (10)  op(e1, e1) = all_6_2
% 229.95/41.26    (11)  op(e2, e2) = e1
% 229.95/41.26    (12)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.95/41.26          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.95/41.26    (13)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.95/41.26          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.95/41.26    (14)  all_57_6 = e1
% 229.95/41.26    (15)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.95/41.26          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.95/41.26    (16)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 229.95/41.26          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.95/41.27    (17)   ~ (e3 = e2)
% 229.95/41.27    (18)   ~ (e3 = e0)
% 229.95/41.27    (19)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 229.95/41.27          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 229.95/41.27    (20)  op(e0, e3) = all_53_3
% 229.95/41.27    (21)  all_57_15 = e3
% 229.95/41.27    (22)  op(e3, e3) = e0
% 229.95/41.27    (23)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.95/41.27          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.95/41.27            e1)
% 229.95/41.27    (24)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.95/41.27          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.95/41.27    (25)   ~ (e2 = e0)
% 229.95/41.27    (26)  all_57_3 = e1
% 229.95/41.27    (27)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.95/41.27          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.95/41.27    (28)   ~ (e1 = e0)
% 229.95/41.27    (29)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.95/41.27          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.95/41.27    (30)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.95/41.27          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.95/41.27    (31)  op(e0, e0) = e3
% 229.95/41.27    (32)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.95/41.27          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.95/41.27            e2)
% 229.95/41.27    (33)   ~ (all_53_3 = e0)
% 229.95/41.27    (34)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.95/41.27              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.95/41.27                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.95/41.27                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.95/41.27    (35)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.95/41.27          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.95/41.27    (36)   ~ (all_53_12 = e3)
% 229.95/41.27    (37)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.95/41.27          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.95/41.27    (38)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.95/41.27          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.95/41.27    (39)   ~ (all_53_12 = e0)
% 229.95/41.27    (40)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.95/41.27          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 229.95/41.27    (41)   ~ (e2 = e1)
% 229.95/41.27    (42)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.95/41.27    (43)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.95/41.27          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.95/41.27    (44)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.95/41.27          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.95/41.27    (45)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 229.95/41.27          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 229.95/41.27    (46)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.95/41.27          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.95/41.27    (47)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.95/41.27          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.95/41.27    (48)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 229.95/41.27          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 229.95/41.27    (49)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.95/41.27          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.95/41.27    (50)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 229.95/41.27          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 229.95/41.27    (51)  op(e3, e0) = all_53_12
% 229.95/41.27  
% 229.95/41.27  Begin of proof
% 229.95/41.27  | 
% 229.95/41.27  | BETA: splitting (42) gives:
% 229.95/41.27  | 
% 229.95/41.27  | Case 1:
% 229.95/41.27  | | 
% 229.95/41.27  | |   (52)  all_57_5 = e2 & op(e2, e1) = e2
% 229.95/41.27  | | 
% 229.95/41.27  | | ALPHA: (52) implies:
% 229.95/41.27  | |   (53)  all_57_5 = e2
% 229.95/41.27  | | 
% 229.95/41.27  | | BETA: splitting (40) gives:
% 229.95/41.27  | | 
% 229.95/41.27  | | Case 1:
% 229.95/41.27  | | | 
% 229.95/41.27  | | |   (54)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) =
% 229.95/41.27  | | |           e0)
% 229.95/41.27  | | | 
% 229.95/41.27  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13),
% 229.95/41.27  | | |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 229.95/41.27  | | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 229.95/41.27  | | |            (35), (36), (37), (38), (39), (41), (43), (44), (45), (46),
% 229.95/41.27  | | |            (47), (48), (49), (50), (51), (54) are inconsistent by
% 229.95/41.27  | | |            sub-proof #916.
% 229.95/41.27  | | | 
% 229.95/41.27  | | Case 2:
% 229.95/41.27  | | | 
% 229.95/41.27  | | |   (55)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 229.95/41.27  | | |           e0)
% 229.95/41.27  | | | 
% 229.95/41.27  | | | BETA: splitting (55) gives:
% 229.95/41.27  | | | 
% 229.95/41.27  | | | Case 1:
% 229.95/41.27  | | | | 
% 229.95/41.27  | | | |   (56)  all_57_5 = e0 & op(e2, e1) = e0
% 229.95/41.27  | | | | 
% 229.95/41.27  | | | | REF_CLOSE: (25), (53), (56) are inconsistent by sub-proof #2428.
% 229.95/41.27  | | | | 
% 229.95/41.27  | | | Case 2:
% 229.95/41.27  | | | | 
% 229.95/41.27  | | | |   (57)  all_57_10 = e0 & op(e2, e0) = e0
% 229.95/41.27  | | | | 
% 229.95/41.27  | | | | ALPHA: (57) implies:
% 229.95/41.27  | | | |   (58)  all_57_10 = e0
% 229.95/41.27  | | | | 
% 229.95/41.27  | | | | COMBINE_EQS: (9), (58) imply:
% 229.95/41.27  | | | |   (59)  e1 = e0
% 229.95/41.27  | | | | 
% 229.95/41.27  | | | | REF_CLOSE: (2), (3), (4), (6), (7), (8), (10), (11), (14), (15), (17),
% 229.95/41.27  | | | |            (18), (20), (21), (22), (23), (24), (25), (26), (27), (28),
% 229.95/41.27  | | | |            (30), (31), (33), (34), (36), (38), (39), (41), (43), (44),
% 229.95/41.27  | | | |            (47), (49), (51), (59) are inconsistent by sub-proof #915.
% 229.95/41.27  | | | | 
% 229.95/41.27  | | | End of split
% 229.95/41.27  | | | 
% 229.95/41.27  | | End of split
% 229.95/41.27  | | 
% 229.95/41.27  | Case 2:
% 229.95/41.27  | | 
% 229.95/41.27  | |   (60)  all_57_10 = e2 & op(e2, e0) = e2
% 229.95/41.27  | | 
% 229.95/41.27  | | ALPHA: (60) implies:
% 229.95/41.27  | |   (61)  all_57_10 = e2
% 229.95/41.27  | | 
% 229.95/41.27  | | REF_CLOSE: (9), (41), (61) are inconsistent by sub-proof #2144.
% 229.95/41.27  | | 
% 229.95/41.27  | End of split
% 229.95/41.27  | 
% 229.95/41.27  End of proof
% 229.95/41.27  
% 229.95/41.27  Sub-proof #915 shows that the following formulas are inconsistent:
% 229.95/41.27  ----------------------------------------------------------------
% 229.95/41.27    (1)  e1 = e0
% 229.95/41.27    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.95/41.27         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.95/41.27    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.95/41.27         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.95/41.27    (4)   ~ (e3 = e1)
% 229.95/41.27    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.95/41.27           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.95/41.27    (6)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.95/41.27         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.95/41.27    (7)   ~ (all_6_2 = e3)
% 229.95/41.27    (8)  op(e1, e1) = all_6_2
% 229.95/41.27    (9)  op(e2, e2) = e1
% 229.95/41.27    (10)  all_57_6 = e1
% 229.95/41.27    (11)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.95/41.27          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.95/41.27    (12)   ~ (e3 = e2)
% 229.95/41.27    (13)   ~ (e3 = e0)
% 229.95/41.27    (14)  op(e0, e3) = all_53_3
% 229.95/41.27    (15)  all_57_15 = e3
% 229.95/41.27    (16)  op(e3, e3) = e0
% 229.95/41.27    (17)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.95/41.27          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.95/41.27            e1)
% 229.95/41.27    (18)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.95/41.27          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.95/41.27    (19)   ~ (e2 = e0)
% 229.95/41.27    (20)  all_57_3 = e1
% 229.95/41.27    (21)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.95/41.27          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.95/41.27    (22)   ~ (e1 = e0)
% 229.95/41.27    (23)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.95/41.27          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.95/41.27    (24)  op(e0, e0) = e3
% 229.95/41.27    (25)   ~ (all_53_3 = e0)
% 229.95/41.27    (26)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.95/41.27              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.95/41.27                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.95/41.27                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.95/41.27    (27)   ~ (all_53_12 = e3)
% 229.95/41.27    (28)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.95/41.27          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.95/41.27    (29)   ~ (all_53_12 = e0)
% 229.95/41.27    (30)   ~ (e2 = e1)
% 229.95/41.27    (31)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.95/41.27          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.95/41.27    (32)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.95/41.27          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.95/41.27    (33)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.95/41.27          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.95/41.27    (34)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.95/41.27          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.95/41.27    (35)  op(e3, e0) = all_53_12
% 229.95/41.27  
% 229.95/41.27  Begin of proof
% 229.95/41.27  | 
% 229.95/41.27  | SIMP: (1) implies:
% 229.95/41.27  |   (36)  e1 = e0
% 229.95/41.27  | 
% 229.95/41.27  | COMBINE_EQS: (10), (36) imply:
% 229.95/41.27  |   (37)  all_57_6 = e0
% 229.95/41.27  | 
% 229.95/41.27  | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13), (14),
% 229.95/41.27  |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 229.95/41.27  |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (37)
% 229.95/41.27  |            are inconsistent by sub-proof #983.
% 229.95/41.27  | 
% 229.95/41.27  End of proof
% 229.95/41.27  
% 229.95/41.27  Sub-proof #916 shows that the following formulas are inconsistent:
% 229.95/41.27  ----------------------------------------------------------------
% 229.95/41.27    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.95/41.27         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.95/41.27    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.95/41.27         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.95/41.27    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.95/41.27         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.95/41.27    (4)   ~ (e3 = e1)
% 229.95/41.27    (5)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 229.95/41.27         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 229.95/41.27    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.95/41.27           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.95/41.27    (7)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.95/41.27         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.95/41.27    (8)   ~ (all_6_2 = e3)
% 229.95/41.27    (9)  op(e1, e1) = all_6_2
% 229.95/41.27    (10)  op(e2, e2) = e1
% 229.95/41.27    (11)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.95/41.27          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.95/41.27    (12)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.95/41.27          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.95/41.27    (13)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.95/41.27          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.95/41.27    (14)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 229.95/41.27          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.95/41.27    (15)   ~ (e3 = e2)
% 229.95/41.27    (16)   ~ (e3 = e0)
% 229.95/41.27    (17)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 229.95/41.27          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 229.95/41.27    (18)  op(e0, e3) = all_53_3
% 229.95/41.27    (19)  all_57_15 = e3
% 229.95/41.27    (20)  op(e3, e3) = e0
% 229.95/41.27    (21)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.95/41.27          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.95/41.27            e1)
% 229.95/41.27    (22)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0)
% 229.95/41.27    (23)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.95/41.27          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.95/41.27    (24)   ~ (e2 = e0)
% 229.95/41.27    (25)  all_57_3 = e1
% 229.95/41.27    (26)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.95/41.27          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.95/41.27    (27)   ~ (e1 = e0)
% 229.95/41.27    (28)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.95/41.27          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.95/41.27    (29)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.95/41.27          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.95/41.27    (30)  op(e0, e0) = e3
% 229.95/41.27    (31)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.95/41.27          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.95/41.27            e2)
% 229.95/41.27    (32)   ~ (all_53_3 = e0)
% 229.95/41.27    (33)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.95/41.27              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.95/41.27                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.95/41.27                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.95/41.27    (34)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.95/41.27          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.95/41.27    (35)   ~ (all_53_12 = e3)
% 229.95/41.27    (36)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.95/41.27          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.95/41.27    (37)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.95/41.27          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.95/41.27    (38)   ~ (all_53_12 = e0)
% 229.95/41.27    (39)   ~ (e2 = e1)
% 229.95/41.27    (40)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.95/41.27          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.95/41.27    (41)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.95/41.27          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.95/41.27    (42)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 229.95/41.27          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 229.95/41.27    (43)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.95/41.27          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.95/41.27    (44)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.95/41.27          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.95/41.27    (45)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 229.95/41.27          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 229.95/41.27    (46)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.95/41.27          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.95/41.27    (47)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 229.95/41.27          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 229.95/41.27    (48)  op(e3, e0) = all_53_12
% 229.95/41.27  
% 229.95/41.27  Begin of proof
% 229.95/41.27  | 
% 229.95/41.27  | BETA: splitting (22) gives:
% 229.95/41.27  | 
% 229.95/41.27  | Case 1:
% 229.95/41.27  | | 
% 229.95/41.27  | |   (49)  all_57_2 = e0 & op(e2, e3) = e0
% 229.95/41.27  | | 
% 229.95/41.27  | | ALPHA: (49) implies:
% 229.95/41.27  | |   (50)  all_57_2 = e0
% 229.95/41.27  | | 
% 229.95/41.27  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 229.95/41.27  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (23), (24),
% 229.95/41.27  | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 229.95/41.27  | |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 229.95/41.27  | |            (47), (48), (50) are inconsistent by sub-proof #1016.
% 229.95/41.27  | | 
% 229.95/41.27  | Case 2:
% 229.95/41.27  | | 
% 229.95/41.27  | |   (51)  all_57_3 = e0 & op(e2, e2) = e0
% 229.95/41.27  | | 
% 229.95/41.27  | | ALPHA: (51) implies:
% 229.95/41.27  | |   (52)  op(e2, e2) = e0
% 229.95/41.27  | | 
% 229.95/41.27  | | REF_CLOSE: (6), (10), (27), (52) are inconsistent by sub-proof #2352.
% 229.95/41.27  | | 
% 229.95/41.27  | End of split
% 229.95/41.27  | 
% 229.95/41.27  End of proof
% 229.95/41.27  
% 229.95/41.27  Sub-proof #917 shows that the following formulas are inconsistent:
% 229.95/41.27  ----------------------------------------------------------------
% 229.95/41.27    (1)  all_57_8 = e0 & op(e1, e1) = e0
% 229.95/41.27    (2)  all_57_8 = e2
% 229.95/41.27    (3)   ~ (e2 = e0)
% 229.95/41.27  
% 229.95/41.27  Begin of proof
% 229.95/41.27  | 
% 229.95/41.27  | ALPHA: (1) implies:
% 229.95/41.27  |   (4)  all_57_8 = e0
% 229.95/41.27  | 
% 229.95/41.27  | COMBINE_EQS: (2), (4) imply:
% 229.95/41.27  |   (5)  e2 = e0
% 229.95/41.27  | 
% 229.95/41.27  | REDUCE: (3), (5) imply:
% 229.95/41.27  |   (6)  $false
% 229.95/41.27  | 
% 229.95/41.27  | CLOSE: (6) is inconsistent.
% 229.95/41.27  | 
% 229.95/41.27  End of proof
% 229.95/41.27  
% 229.95/41.27  Sub-proof #918 shows that the following formulas are inconsistent:
% 229.95/41.27  ----------------------------------------------------------------
% 229.95/41.27    (1)   ~ (e3 = e1)
% 229.95/41.27    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.95/41.27           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.95/41.27    (3)   ~ (e3 = e2)
% 229.95/41.27    (4)  all_57_15 = e3
% 229.95/41.27    (5)  all_57_10 = e2
% 229.95/41.27    (6)  all_57_11 = e0
% 229.95/41.27    (7)   ~ (e2 = e0)
% 229.95/41.27    (8)  all_57_13 = e2
% 229.95/41.27    (9)   ~ (e1 = e0)
% 229.95/41.27    (10)  op(e0, e0) = e3
% 229.95/41.27    (11)  all_57_13 = e0
% 229.95/41.27    (12)   ~ (e2 = e1)
% 229.95/41.27    (13)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.95/41.27          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.95/41.27    (14)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.95/41.27          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.95/41.27  
% 229.95/41.27  Begin of proof
% 229.95/41.27  | 
% 229.95/41.27  | COMBINE_EQS: (8), (11) imply:
% 229.95/41.27  |   (15)  e2 = e0
% 229.95/41.27  | 
% 229.95/41.27  | COMBINE_EQS: (5), (15) imply:
% 229.95/41.27  |   (16)  all_57_10 = e0
% 229.95/41.27  | 
% 229.95/41.27  | REF_CLOSE: (1), (2), (3), (4), (6), (7), (9), (10), (12), (13), (14), (16) are
% 229.95/41.27  |            inconsistent by sub-proof #1087.
% 229.95/41.27  | 
% 229.95/41.27  End of proof
% 229.95/41.27  
% 229.95/41.27  Sub-proof #919 shows that the following formulas are inconsistent:
% 229.95/41.27  ----------------------------------------------------------------
% 229.95/41.27    (1)  all_57_9 = e2
% 229.95/41.27    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.95/41.27         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.95/41.27    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.95/41.27           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.95/41.27    (4)  op(e2, e2) = e1
% 229.95/41.27    (5)  all_57_9 = e1
% 229.95/41.27    (6)   ~ (e3 = e2)
% 229.95/41.27    (7)   ~ (e3 = e0)
% 229.95/41.27    (8)  all_57_1 = e2
% 229.95/41.27    (9)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.95/41.27         (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.95/41.27    (10)   ~ (e2 = e0)
% 229.95/41.27    (11)   ~ (e1 = e0)
% 229.95/41.27    (12)  all_57_7 = e3
% 229.95/41.27    (13)   ~ (e2 = e1)
% 229.95/41.27  
% 229.95/41.27  Begin of proof
% 229.95/41.27  | 
% 229.95/41.27  | COMBINE_EQS: (1), (5) imply:
% 229.95/41.27  |   (14)  e2 = e1
% 229.95/41.27  | 
% 229.95/41.27  | COMBINE_EQS: (8), (14) imply:
% 229.95/41.27  |   (15)  all_57_1 = e1
% 229.95/41.27  | 
% 229.95/41.27  | REF_CLOSE: (2), (3), (4), (6), (7), (9), (10), (11), (12), (13), (15) are
% 229.95/41.27  |            inconsistent by sub-proof #1909.
% 229.95/41.27  | 
% 229.95/41.27  End of proof
% 229.95/41.27  
% 229.95/41.27  Sub-proof #920 shows that the following formulas are inconsistent:
% 229.95/41.27  ----------------------------------------------------------------
% 229.95/41.27    (1)   ~ (e3 = e1)
% 229.95/41.27    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.95/41.28           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.95/41.28    (3)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.95/41.28         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.95/41.28    (4)   ~ (all_6_2 = e3)
% 229.95/41.28    (5)  op(e1, e1) = all_6_2
% 229.95/41.28    (6)  all_57_9 = e1
% 229.95/41.28    (7)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.95/41.28         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.95/41.28    (8)  all_57_6 = e1
% 229.95/41.28    (9)   ~ (e3 = e2)
% 229.95/41.28    (10)   ~ (e3 = e0)
% 229.95/41.28    (11)  all_57_1 = e0
% 229.95/41.28    (12)  all_57_15 = e3
% 229.95/41.28    (13)  op(e3, e3) = e0
% 229.95/41.28    (14)   ~ (e2 = e0)
% 229.95/41.28    (15)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.95/41.28          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.95/41.28    (16)   ~ (e1 = e0)
% 229.95/41.28    (17)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.95/41.28              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.95/41.28                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.95/41.28                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.95/41.28    (18)   ~ (all_53_12 = e3)
% 229.95/41.28    (19)  all_57_7 = e3
% 229.95/41.28    (20)   ~ (e2 = e1)
% 229.95/41.28    (21)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.95/41.28          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.95/41.28    (22)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.95/41.28          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.95/41.28    (23)  op(e3, e0) = all_53_12
% 229.95/41.28  
% 229.95/41.28  Begin of proof
% 229.95/41.28  | 
% 229.95/41.28  | BETA: splitting (15) gives:
% 229.95/41.28  | 
% 229.95/41.28  | Case 1:
% 229.95/41.28  | | 
% 229.95/41.28  | |   (24)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) =
% 229.95/41.28  | |           e3)
% 229.95/41.28  | | 
% 229.95/41.28  | | BETA: splitting (24) gives:
% 229.95/41.28  | | 
% 229.95/41.28  | | Case 1:
% 229.95/41.28  | | | 
% 229.95/41.28  | | |   (25)  all_57_0 = e3 & op(e3, e3) = e3
% 229.95/41.28  | | | 
% 229.95/41.28  | | | ALPHA: (25) implies:
% 229.95/41.28  | | |   (26)  op(e3, e3) = e3
% 229.95/41.28  | | | 
% 229.95/41.28  | | | REF_CLOSE: (2), (10), (13), (26) are inconsistent by sub-proof #2494.
% 229.95/41.28  | | | 
% 229.95/41.28  | | Case 2:
% 229.95/41.28  | | | 
% 229.95/41.28  | | |   (27)  all_57_1 = e3 & op(e3, e2) = e3
% 229.95/41.28  | | | 
% 229.95/41.28  | | | REF_CLOSE: (1), (2), (3), (4), (5), (8), (9), (10), (11), (12), (14),
% 229.95/41.28  | | |            (16), (17), (19), (20), (21), (22), (27) are inconsistent by
% 229.95/41.28  | | |            sub-proof #921.
% 229.95/41.28  | | | 
% 229.95/41.28  | | End of split
% 229.95/41.28  | | 
% 229.95/41.28  | Case 2:
% 229.95/41.28  | | 
% 229.95/41.28  | |   (28)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) =
% 229.95/41.28  | |           e3)
% 229.95/41.28  | | 
% 229.95/41.28  | | REF_CLOSE: (2), (6), (7), (9), (11), (13), (14), (18), (20), (23), (28) are
% 229.95/41.28  | |            inconsistent by sub-proof #2401.
% 229.95/41.28  | | 
% 229.95/41.28  | End of split
% 229.95/41.28  | 
% 229.95/41.28  End of proof
% 229.95/41.28  
% 229.95/41.28  Sub-proof #921 shows that the following formulas are inconsistent:
% 229.95/41.28  ----------------------------------------------------------------
% 229.95/41.28    (1)   ~ (e3 = e1)
% 229.95/41.28    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.95/41.28           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.95/41.28    (3)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.95/41.28         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.95/41.28    (4)   ~ (all_6_2 = e3)
% 229.95/41.28    (5)  op(e1, e1) = all_6_2
% 229.95/41.28    (6)  all_57_6 = e1
% 229.95/41.28    (7)   ~ (e3 = e2)
% 229.95/41.28    (8)   ~ (e3 = e0)
% 229.95/41.28    (9)  all_57_1 = e0
% 229.95/41.28    (10)  all_57_15 = e3
% 229.95/41.28    (11)   ~ (e2 = e0)
% 229.95/41.28    (12)   ~ (e1 = e0)
% 229.95/41.28    (13)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.95/41.28              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.95/41.28                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.95/41.28                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.95/41.28    (14)  all_57_1 = e3 & op(e3, e2) = e3
% 229.95/41.28    (15)  all_57_7 = e3
% 229.95/41.28    (16)   ~ (e2 = e1)
% 229.95/41.28    (17)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.95/41.28          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.95/41.28    (18)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.95/41.28          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.95/41.28  
% 229.95/41.28  Begin of proof
% 229.95/41.28  | 
% 229.95/41.28  | ALPHA: (14) implies:
% 229.95/41.28  |   (19)  all_57_1 = e3
% 229.95/41.28  | 
% 229.95/41.28  | COMBINE_EQS: (9), (19) imply:
% 229.95/41.28  |   (20)  e3 = e0
% 229.95/41.28  | 
% 229.95/41.28  | SIMP: (20) implies:
% 229.95/41.28  |   (21)  e3 = e0
% 229.95/41.28  | 
% 229.95/41.28  | COMBINE_EQS: (15), (21) imply:
% 229.95/41.28  |   (22)  all_57_7 = e0
% 229.95/41.28  | 
% 229.95/41.28  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13),
% 229.95/41.28  |            (16), (17), (18), (22) are inconsistent by sub-proof #1735.
% 229.95/41.28  | 
% 229.95/41.28  End of proof
% 229.95/41.28  
% 229.95/41.28  Sub-proof #922 shows that the following formulas are inconsistent:
% 229.95/41.28  ----------------------------------------------------------------
% 229.95/41.28    (1)  all_57_10 = e0
% 229.95/41.28    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.95/41.28         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.95/41.28    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.95/41.28         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.95/41.28    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.95/41.28         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.95/41.28    (5)   ~ (e3 = e1)
% 229.95/41.28    (6)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 229.95/41.28         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 229.95/41.28    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.95/41.28           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.95/41.28    (8)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.95/41.28         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.95/41.28    (9)   ~ (all_6_2 = e3)
% 229.95/41.28    (10)  op(e1, e1) = all_6_2
% 229.95/41.28    (11)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.95/41.28          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.95/41.28    (12)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.95/41.28          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.95/41.28    (13)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.95/41.28          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.95/41.28    (14)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 229.95/41.28          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.95/41.28    (15)   ~ (e3 = e2)
% 229.95/41.28    (16)   ~ (e3 = e0)
% 229.95/41.28    (17)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 229.95/41.28          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 229.95/41.28    (18)  op(e0, e3) = all_53_3
% 229.95/41.28    (19)  all_57_0 = e0
% 229.95/41.28    (20)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.95/41.28          | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.95/41.28    (21)  all_57_15 = e3
% 229.95/41.28    (22)  op(e3, e3) = e0
% 229.95/41.28    (23)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.95/41.28          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.95/41.28            e1)
% 229.95/41.28    (24)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.95/41.28          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.95/41.28    (25)   ~ (e2 = e0)
% 229.95/41.28    (26)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.95/41.28          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.95/41.28    (27)  op(e2, e2) = e2
% 229.95/41.28    (28)   ~ (e1 = e0)
% 229.95/41.28    (29)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.95/41.28          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.95/41.28    (30)  all_57_6 = e3
% 229.95/41.28    (31)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.95/41.28          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.95/41.28    (32)  op(e0, e0) = e3
% 229.95/41.28    (33)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.95/41.28          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.95/41.28            e2)
% 229.95/41.28    (34)   ~ (all_53_3 = e0)
% 229.95/41.28    (35)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.95/41.28              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.95/41.28                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.95/41.28                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.95/41.28    (36)  op(e1, e1) = e0
% 229.95/41.28    (37)  all_57_13 = e0
% 229.95/41.28    (38)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.95/41.28          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.95/41.28    (39)   ~ (all_53_12 = e3)
% 229.95/41.28    (40)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.95/41.28          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.95/41.28    (41)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.95/41.28          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.95/41.28    (42)   ~ (all_53_12 = e0)
% 229.95/41.28    (43)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) |
% 229.95/41.28          (all_57_11 = e0 & op(e1, e0) = e0)
% 229.95/41.28    (44)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.95/41.28          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 229.95/41.28    (45)   ~ (e2 = e1)
% 229.95/41.28    (46)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.95/41.28          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.95/41.28    (47)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.95/41.28          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.95/41.28    (48)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 229.95/41.28          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 229.95/41.28    (49)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.95/41.28          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.95/41.28    (50)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.95/41.28          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.95/41.28    (51)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 229.95/41.28          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 229.95/41.28    (52)  all_57_3 = e2
% 229.95/41.28    (53)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.95/41.28          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.95/41.28    (54)  all_57_7 = e0
% 229.95/41.28    (55)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 229.95/41.28          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 229.95/41.28    (56)  op(e3, e0) = all_53_12
% 229.95/41.28  
% 229.95/41.28  Begin of proof
% 229.95/41.28  | 
% 229.95/41.28  | BETA: splitting (51) gives:
% 229.95/41.28  | 
% 229.95/41.28  | Case 1:
% 229.95/41.28  | | 
% 229.95/41.28  | |   (57)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) =
% 229.95/41.28  | |           e1)
% 229.95/41.28  | | 
% 229.95/41.28  | | REF_CLOSE: (5), (7), (8), (9), (10), (15), (16), (21), (25), (28), (35),
% 229.95/41.28  | |            (45), (46), (50), (54), (57) are inconsistent by sub-proof #1155.
% 229.95/41.28  | | 
% 229.95/41.28  | Case 2:
% 229.95/41.28  | | 
% 229.95/41.28  | |   (58)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) =
% 229.95/41.28  | |           e1)
% 229.95/41.28  | | 
% 229.95/41.28  | | BETA: splitting (58) gives:
% 229.95/41.28  | | 
% 229.95/41.28  | | Case 1:
% 229.95/41.28  | | | 
% 229.95/41.28  | | |   (59)  all_57_8 = e1 & op(e1, e1) = e1
% 229.95/41.28  | | | 
% 229.95/41.28  | | | ALPHA: (59) implies:
% 229.95/41.28  | | |   (60)  op(e1, e1) = e1
% 229.95/41.28  | | | 
% 229.95/41.28  | | | REF_CLOSE: (7), (28), (36), (60) are inconsistent by sub-proof #2427.
% 229.95/41.28  | | | 
% 229.95/41.28  | | Case 2:
% 229.95/41.28  | | | 
% 229.95/41.28  | | |   (61)  all_57_11 = e1 & op(e1, e0) = e1
% 229.95/41.28  | | | 
% 229.95/41.28  | | | ALPHA: (61) implies:
% 229.95/41.28  | | |   (62)  all_57_11 = e1
% 229.95/41.28  | | | 
% 229.95/41.28  | | | BETA: splitting (47) gives:
% 229.95/41.28  | | | 
% 229.95/41.28  | | | Case 1:
% 229.95/41.28  | | | | 
% 229.95/41.28  | | | |   (63)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3)
% 229.95/41.28  | | | |           = e2)
% 229.95/41.28  | | | | 
% 229.95/41.28  | | | | BETA: splitting (63) gives:
% 229.95/41.28  | | | | 
% 229.95/41.28  | | | | Case 1:
% 229.95/41.28  | | | | | 
% 229.95/41.28  | | | | |   (64)  all_57_0 = e2 & op(e3, e3) = e2
% 229.95/41.28  | | | | | 
% 229.95/41.28  | | | | | ALPHA: (64) implies:
% 229.95/41.28  | | | | |   (65)  op(e3, e3) = e2
% 229.95/41.28  | | | | | 
% 229.95/41.28  | | | | | REF_CLOSE: (7), (22), (25), (65) are inconsistent by sub-proof #2403.
% 229.95/41.28  | | | | | 
% 229.95/41.28  | | | | Case 2:
% 229.95/41.28  | | | | | 
% 229.95/41.28  | | | | |   (66)  all_57_2 = e2 & op(e2, e3) = e2
% 229.95/41.28  | | | | | 
% 229.95/41.28  | | | | | ALPHA: (66) implies:
% 229.95/41.28  | | | | |   (67)  all_57_2 = e2
% 229.95/41.28  | | | | | 
% 229.95/41.28  | | | | | BETA: splitting (3) gives:
% 229.95/41.28  | | | | | 
% 229.95/41.28  | | | | | Case 1:
% 229.95/41.28  | | | | | | 
% 229.95/41.28  | | | | | |   (68)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2,
% 229.95/41.28  | | | | | |             e3) = e1)
% 229.95/41.28  | | | | | | 
% 229.95/41.28  | | | | | | BETA: splitting (68) gives:
% 229.95/41.28  | | | | | | 
% 229.95/41.28  | | | | | | Case 1:
% 229.95/41.28  | | | | | | | 
% 229.95/41.28  | | | | | | |   (69)  all_57_0 = e1 & op(e3, e3) = e1
% 229.95/41.28  | | | | | | | 
% 229.95/41.28  | | | | | | | ALPHA: (69) implies:
% 229.95/41.28  | | | | | | |   (70)  all_57_0 = e1
% 229.95/41.28  | | | | | | | 
% 229.95/41.28  | | | | | | | COMBINE_EQS: (19), (70) imply:
% 229.95/41.28  | | | | | | |   (71)  e1 = e0
% 229.95/41.28  | | | | | | | 
% 229.95/41.28  | | | | | | | REF_CLOSE: (1), (5), (7), (15), (21), (25), (28), (32), (45),
% 229.95/41.28  | | | | | | |            (46), (50), (62), (71) are inconsistent by sub-proof
% 229.95/41.28  | | | | | | |            #932.
% 229.95/41.28  | | | | | | | 
% 229.95/41.28  | | | | | | Case 2:
% 229.95/41.28  | | | | | | | 
% 229.95/41.28  | | | | | | |   (72)  all_57_2 = e1 & op(e2, e3) = e1
% 229.95/41.28  | | | | | | | 
% 229.95/41.28  | | | | | | | REF_CLOSE: (45), (67), (72) are inconsistent by sub-proof #2244.
% 229.95/41.28  | | | | | | | 
% 229.95/41.28  | | | | | | End of split
% 229.95/41.28  | | | | | | 
% 229.95/41.28  | | | | | Case 2:
% 229.95/41.28  | | | | | | 
% 229.95/41.28  | | | | | |   (73)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0,
% 229.95/41.28  | | | | | |             e3) = e1)
% 229.95/41.28  | | | | | | 
% 229.95/41.28  | | | | | | BETA: splitting (73) gives:
% 229.95/41.28  | | | | | | 
% 229.95/41.28  | | | | | | Case 1:
% 229.95/41.28  | | | | | | | 
% 229.95/41.28  | | | | | | |   (74)  all_57_6 = e1 & op(e1, e3) = e1
% 229.95/41.28  | | | | | | | 
% 229.95/41.28  | | | | | | | ALPHA: (74) implies:
% 229.95/41.28  | | | | | | |   (75)  all_57_6 = e1
% 229.95/41.28  | | | | | | | 
% 229.95/41.28  | | | | | | | REF_CLOSE: (5), (7), (8), (9), (10), (15), (16), (21), (25), (28),
% 229.95/41.28  | | | | | | |            (35), (45), (46), (50), (54), (75) are inconsistent by
% 229.95/41.28  | | | | | | |            sub-proof #1735.
% 229.95/41.28  | | | | | | | 
% 229.95/41.28  | | | | | | Case 2:
% 229.95/41.28  | | | | | | | 
% 229.95/41.28  | | | | | | |   (76)  all_57_12 = e1 & op(e0, e3) = e1
% 229.95/41.28  | | | | | | | 
% 229.95/41.28  | | | | | | | ALPHA: (76) implies:
% 229.95/41.28  | | | | | | |   (77)  all_57_12 = e1
% 229.95/41.28  | | | | | | | 
% 229.95/41.28  | | | | | | | BETA: splitting (31) gives:
% 229.95/41.28  | | | | | | | 
% 229.95/41.28  | | | | | | | Case 1:
% 229.95/41.28  | | | | | | | | 
% 229.95/41.28  | | | | | | | |   (78)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 &
% 229.95/41.28  | | | | | | | |           op(e2, e2) = e3)
% 229.95/41.28  | | | | | | | | 
% 229.95/41.28  | | | | | | | | BETA: splitting (78) gives:
% 229.95/41.28  | | | | | | | | 
% 229.95/41.28  | | | | | | | | Case 1:
% 229.95/41.28  | | | | | | | | | 
% 229.95/41.28  | | | | | | | | |   (79)  all_57_1 = e3 & op(e3, e2) = e3
% 229.95/41.28  | | | | | | | | | 
% 229.95/41.28  | | | | | | | | | ALPHA: (79) implies:
% 229.95/41.28  | | | | | | | | |   (80)  all_57_1 = e3
% 229.95/41.28  | | | | | | | | | 
% 229.95/41.28  | | | | | | | | | BETA: splitting (53) gives:
% 229.95/41.28  | | | | | | | | | 
% 229.95/41.28  | | | | | | | | | Case 1:
% 229.95/41.28  | | | | | | | | | | 
% 229.95/41.28  | | | | | | | | | |   (81)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 &
% 229.95/41.28  | | | | | | | | | |           op(e2, e2) = e1)
% 229.95/41.28  | | | | | | | | | | 
% 229.95/41.28  | | | | | | | | | | BETA: splitting (81) gives:
% 229.95/41.28  | | | | | | | | | | 
% 229.95/41.28  | | | | | | | | | | Case 1:
% 229.95/41.28  | | | | | | | | | | | 
% 229.95/41.28  | | | | | | | | | | |   (82)  all_57_1 = e1 & op(e3, e2) = e1
% 229.95/41.28  | | | | | | | | | | | 
% 229.95/41.28  | | | | | | | | | | | ALPHA: (82) implies:
% 229.95/41.28  | | | | | | | | | | |   (83)  all_57_1 = e1
% 229.95/41.28  | | | | | | | | | | | 
% 229.95/41.28  | | | | | | | | | | | COMBINE_EQS: (80), (83) imply:
% 229.95/41.28  | | | | | | | | | | |   (84)  e3 = e1
% 229.95/41.28  | | | | | | | | | | | 
% 229.95/41.28  | | | | | | | | | | | COMBINE_EQS: (30), (84) imply:
% 229.95/41.28  | | | | | | | | | | |   (85)  all_57_6 = e1
% 229.95/41.28  | | | | | | | | | | | 
% 229.95/41.28  | | | | | | | | | | | REF_CLOSE: (5), (7), (15), (16), (22), (25), (41), (45),
% 229.95/41.28  | | | | | | | | | | |            (47), (77), (85) are inconsistent by sub-proof
% 229.95/41.28  | | | | | | | | | | |            #1205.
% 229.95/41.28  | | | | | | | | | | | 
% 229.95/41.28  | | | | | | | | | | Case 2:
% 229.95/41.28  | | | | | | | | | | | 
% 229.95/41.28  | | | | | | | | | | |   (86)  all_57_3 = e1 & op(e2, e2) = e1
% 229.95/41.28  | | | | | | | | | | | 
% 229.95/41.28  | | | | | | | | | | | ALPHA: (86) implies:
% 229.95/41.28  | | | | | | | | | | |   (87)  all_57_3 = e1
% 229.95/41.28  | | | | | | | | | | |   (88)  op(e2, e2) = e1
% 229.95/41.28  | | | | | | | | | | | 
% 229.95/41.28  | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 229.95/41.28  | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 229.95/41.28  | | | | | | | | | | |            (19), (21), (22), (23), (24), (25), (26), (28),
% 229.95/41.28  | | | | | | | | | | |            (29), (31), (32), (33), (34), (35), (36), (38),
% 229.95/41.28  | | | | | | | | | | |            (39), (40), (41), (42), (44), (45), (46), (47),
% 229.95/41.28  | | | | | | | | | | |            (48), (49), (50), (51), (53), (54), (55), (56),
% 229.95/41.28  | | | | | | | | | | |            (80), (87), (88) are inconsistent by sub-proof
% 229.95/41.28  | | | | | | | | | | |            #934.
% 229.95/41.28  | | | | | | | | | | | 
% 229.95/41.28  | | | | | | | | | | End of split
% 229.95/41.28  | | | | | | | | | | 
% 229.95/41.28  | | | | | | | | | Case 2:
% 229.95/41.28  | | | | | | | | | | 
% 229.95/41.28  | | | | | | | | | |   (89)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1
% 229.95/41.28  | | | | | | | | | |           & op(e0, e2) = e1)
% 229.95/41.28  | | | | | | | | | | 
% 229.95/41.28  | | | | | | | | | | REF_CLOSE: (1), (5), (7), (15), (21), (25), (28), (32), (37),
% 229.95/41.28  | | | | | | | | | |            (45), (46), (50), (54), (62), (89) are
% 229.95/41.28  | | | | | | | | | |            inconsistent by sub-proof #931.
% 229.95/41.28  | | | | | | | | | | 
% 229.95/41.28  | | | | | | | | | End of split
% 229.95/41.28  | | | | | | | | | 
% 229.95/41.28  | | | | | | | | Case 2:
% 229.95/41.28  | | | | | | | | | 
% 229.95/41.28  | | | | | | | | |   (90)  all_57_3 = e3 & op(e2, e2) = e3
% 229.95/41.28  | | | | | | | | | 
% 229.95/41.28  | | | | | | | | | ALPHA: (90) implies:
% 229.95/41.28  | | | | | | | | |   (91)  all_57_3 = e3
% 229.95/41.28  | | | | | | | | | 
% 229.95/41.28  | | | | | | | | | COMBINE_EQS: (52), (91) imply:
% 229.95/41.28  | | | | | | | | |   (92)  e3 = e2
% 229.95/41.28  | | | | | | | | | 
% 229.95/41.28  | | | | | | | | | SIMP: (92) implies:
% 229.95/41.28  | | | | | | | | |   (93)  e3 = e2
% 229.95/41.28  | | | | | | | | | 
% 229.95/41.28  | | | | | | | | | COMBINE_EQS: (30), (93) imply:
% 229.95/41.28  | | | | | | | | |   (94)  all_57_6 = e2
% 229.95/41.28  | | | | | | | | | 
% 229.95/41.28  | | | | | | | | | REF_CLOSE: (5), (7), (15), (16), (22), (41), (67), (77), (94)
% 229.95/41.28  | | | | | | | | |            are inconsistent by sub-proof #1212.
% 229.95/41.28  | | | | | | | | | 
% 229.95/41.28  | | | | | | | | End of split
% 229.95/41.28  | | | | | | | | 
% 229.95/41.28  | | | | | | | Case 2:
% 229.95/41.28  | | | | | | | | 
% 229.95/41.28  | | | | | | | |   (95)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 &
% 229.95/41.28  | | | | | | | |           op(e0, e2) = e3)
% 229.95/41.28  | | | | | | | | 
% 229.95/41.28  | | | | | | | | BETA: splitting (95) gives:
% 229.95/41.28  | | | | | | | | 
% 229.95/41.28  | | | | | | | | Case 1:
% 229.95/41.28  | | | | | | | | | 
% 229.95/41.28  | | | | | | | | |   (96)  all_57_7 = e3 & op(e1, e2) = e3
% 229.95/41.28  | | | | | | | | | 
% 229.95/41.28  | | | | | | | | | ALPHA: (96) implies:
% 229.95/41.28  | | | | | | | | |   (97)  all_57_7 = e3
% 229.95/41.28  | | | | | | | | | 
% 229.95/41.28  | | | | | | | | | COMBINE_EQS: (54), (97) imply:
% 229.95/41.28  | | | | | | | | |   (98)  e3 = e0
% 229.95/41.28  | | | | | | | | | 
% 229.95/41.28  | | | | | | | | | SIMP: (98) implies:
% 229.95/41.28  | | | | | | | | |   (99)  e3 = e0
% 229.95/41.28  | | | | | | | | | 
% 229.95/41.28  | | | | | | | | | COMBINE_EQS: (30), (99) imply:
% 229.95/41.28  | | | | | | | | |   (100)  all_57_6 = e0
% 229.95/41.28  | | | | | | | | | 
% 229.95/41.28  | | | | | | | | | BETA: splitting (38) gives:
% 229.95/41.28  | | | | | | | | | 
% 229.95/41.28  | | | | | | | | | Case 1:
% 229.95/41.28  | | | | | | | | | | 
% 229.95/41.28  | | | | | | | | | |   (101)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 229.95/41.28  | | | | | | | | | |            & op(e2, e2) = e3)
% 229.95/41.28  | | | | | | | | | | 
% 229.95/41.28  | | | | | | | | | | BETA: splitting (101) gives:
% 229.95/41.28  | | | | | | | | | | 
% 229.95/41.28  | | | | | | | | | | Case 1:
% 229.95/41.28  | | | | | | | | | | | 
% 229.95/41.28  | | | | | | | | | | |   (102)  all_57_2 = e3 & op(e2, e3) = e3
% 229.95/41.28  | | | | | | | | | | | 
% 229.95/41.28  | | | | | | | | | | | ALPHA: (102) implies:
% 229.95/41.28  | | | | | | | | | | |   (103)  all_57_2 = e3
% 229.95/41.28  | | | | | | | | | | | 
% 229.95/41.28  | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (9), (10), (15), (16), (21), (25),
% 229.95/41.28  | | | | | | | | | | |            (28), (35), (45), (46), (50), (67), (97), (100),
% 229.95/41.28  | | | | | | | | | | |            (103) are inconsistent by sub-proof #1055.
% 229.95/41.28  | | | | | | | | | | | 
% 229.95/41.28  | | | | | | | | | | Case 2:
% 229.95/41.28  | | | | | | | | | | | 
% 229.95/41.28  | | | | | | | | | | |   (104)  all_57_3 = e3 & op(e2, e2) = e3
% 229.95/41.28  | | | | | | | | | | | 
% 229.95/41.28  | | | | | | | | | | | ALPHA: (104) implies:
% 229.95/41.28  | | | | | | | | | | |   (105)  all_57_3 = e3
% 229.95/41.28  | | | | | | | | | | | 
% 229.95/41.28  | | | | | | | | | | | COMBINE_EQS: (52), (105) imply:
% 229.95/41.28  | | | | | | | | | | |   (106)  e3 = e2
% 229.95/41.28  | | | | | | | | | | | 
% 229.95/41.28  | | | | | | | | | | | SIMP: (106) implies:
% 229.95/41.28  | | | | | | | | | | |   (107)  e3 = e2
% 229.95/41.28  | | | | | | | | | | | 
% 229.95/41.28  | | | | | | | | | | | COMBINE_EQS: (97), (107) imply:
% 229.95/41.28  | | | | | | | | | | |   (108)  all_57_7 = e2
% 229.95/41.28  | | | | | | | | | | | 
% 229.95/41.28  | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (9), (10), (15), (16), (21), (25),
% 229.95/41.28  | | | | | | | | | | |            (28), (35), (45), (46), (50), (100), (108) are
% 229.95/41.28  | | | | | | | | | | |            inconsistent by sub-proof #1775.
% 229.95/41.28  | | | | | | | | | | | 
% 229.95/41.28  | | | | | | | | | | End of split
% 229.95/41.28  | | | | | | | | | | 
% 229.95/41.28  | | | | | | | | | Case 2:
% 229.95/41.28  | | | | | | | | | | 
% 229.95/41.28  | | | | | | | | | |   (109)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3
% 229.95/41.28  | | | | | | | | | |            & op(e2, e0) = e3)
% 229.95/41.28  | | | | | | | | | | 
% 229.95/41.28  | | | | | | | | | | BETA: splitting (109) gives:
% 229.95/41.28  | | | | | | | | | | 
% 229.95/41.28  | | | | | | | | | | Case 1:
% 229.95/41.28  | | | | | | | | | | | 
% 229.95/41.28  | | | | | | | | | | |   (110)  all_57_5 = e3 & op(e2, e1) = e3
% 229.95/41.28  | | | | | | | | | | | 
% 229.95/41.28  | | | | | | | | | | | ALPHA: (110) implies:
% 229.95/41.28  | | | | | | | | | | |   (111)  all_57_5 = e3
% 229.95/41.28  | | | | | | | | | | | 
% 229.95/41.28  | | | | | | | | | | | BETA: splitting (3) gives:
% 229.95/41.28  | | | | | | | | | | | 
% 229.95/41.28  | | | | | | | | | | | Case 1:
% 229.95/41.28  | | | | | | | | | | | | 
% 229.95/41.28  | | | | | | | | | | | |   (112)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 229.95/41.28  | | | | | | | | | | | |            & op(e2, e3) = e1)
% 229.95/41.28  | | | | | | | | | | | | 
% 229.95/41.28  | | | | | | | | | | | | REF_CLOSE: (1), (5), (7), (15), (16), (19), (21), (22), (25),
% 229.95/41.28  | | | | | | | | | | | |            (28), (32), (41), (45), (46), (47), (50), (62),
% 229.95/41.28  | | | | | | | | | | | |            (100), (112) are inconsistent by sub-proof #930.
% 229.95/41.28  | | | | | | | | | | | | 
% 229.95/41.28  | | | | | | | | | | | Case 2:
% 229.95/41.28  | | | | | | | | | | | | 
% 229.95/41.28  | | | | | | | | | | | | 
% 229.95/41.28  | | | | | | | | | | | | BETA: splitting (73) gives:
% 229.95/41.28  | | | | | | | | | | | | 
% 229.95/41.28  | | | | | | | | | | | | Case 1:
% 229.95/41.28  | | | | | | | | | | | | | 
% 229.95/41.28  | | | | | | | | | | | | |   (113)  all_57_6 = e1 & op(e1, e3) = e1
% 229.95/41.28  | | | | | | | | | | | | | 
% 229.95/41.28  | | | | | | | | | | | | | ALPHA: (113) implies:
% 229.95/41.28  | | | | | | | | | | | | |   (114)  all_57_6 = e1
% 229.95/41.28  | | | | | | | | | | | | | 
% 229.95/41.28  | | | | | | | | | | | | | REF_CLOSE: (2), (5), (7), (8), (9), (10), (15), (16), (21),
% 229.95/41.28  | | | | | | | | | | | | |            (25), (27), (28), (35), (38), (40), (44), (45),
% 229.95/41.28  | | | | | | | | | | | | |            (46), (50), (52), (67), (97), (111), (114) are
% 229.95/41.28  | | | | | | | | | | | | |            inconsistent by sub-proof #1082.
% 229.95/41.28  | | | | | | | | | | | | | 
% 229.95/41.28  | | | | | | | | | | | | Case 2:
% 229.95/41.28  | | | | | | | | | | | | | 
% 229.95/41.28  | | | | | | | | | | | | | 
% 229.95/41.28  | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (9), (10), (15), (16), (21), (22),
% 229.95/41.28  | | | | | | | | | | | | |            (25), (28), (35), (41), (45), (46), (47), (50),
% 229.95/41.28  | | | | | | | | | | | | |            (77), (100) are inconsistent by sub-proof #1028.
% 229.95/41.28  | | | | | | | | | | | | | 
% 229.95/41.28  | | | | | | | | | | | | End of split
% 229.95/41.28  | | | | | | | | | | | | 
% 229.95/41.28  | | | | | | | | | | | End of split
% 229.95/41.28  | | | | | | | | | | | 
% 229.95/41.28  | | | | | | | | | | Case 2:
% 229.95/41.28  | | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | |   (115)  all_57_10 = e3 & op(e2, e0) = e3
% 229.95/41.29  | | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | | ALPHA: (115) implies:
% 229.95/41.29  | | | | | | | | | | |   (116)  all_57_10 = e3
% 229.95/41.29  | | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | | REF_CLOSE: (5), (7), (15), (16), (21), (25), (28), (32),
% 229.95/41.29  | | | | | | | | | | |            (35), (43), (45), (46), (50), (116) are
% 229.95/41.29  | | | | | | | | | | |            inconsistent by sub-proof #1747.
% 229.95/41.29  | | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | End of split
% 229.95/41.29  | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | End of split
% 229.95/41.29  | | | | | | | | | 
% 229.95/41.29  | | | | | | | | Case 2:
% 229.95/41.29  | | | | | | | | | 
% 229.95/41.29  | | | | | | | | |   (117)  all_57_13 = e3 & op(e0, e2) = e3
% 229.95/41.29  | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | ALPHA: (117) implies:
% 229.95/41.29  | | | | | | | | |   (118)  all_57_13 = e3
% 229.95/41.29  | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | REF_CLOSE: (5), (15), (16), (20), (21), (23), (25), (28),
% 229.95/41.29  | | | | | | | | |            (33), (45), (77), (118) are inconsistent by
% 229.95/41.29  | | | | | | | | |            sub-proof #2057.
% 229.95/41.29  | | | | | | | | | 
% 229.95/41.29  | | | | | | | | End of split
% 229.95/41.29  | | | | | | | | 
% 229.95/41.29  | | | | | | | End of split
% 229.95/41.29  | | | | | | | 
% 229.95/41.29  | | | | | | End of split
% 229.95/41.29  | | | | | | 
% 229.95/41.29  | | | | | End of split
% 229.95/41.29  | | | | | 
% 229.95/41.29  | | | | End of split
% 229.95/41.29  | | | | 
% 229.95/41.29  | | | Case 2:
% 229.95/41.29  | | | | 
% 229.95/41.29  | | | |   (119)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0,
% 229.95/41.29  | | | |              e3) = e2)
% 229.95/41.29  | | | | 
% 229.95/41.29  | | | | BETA: splitting (119) gives:
% 229.95/41.29  | | | | 
% 229.95/41.29  | | | | Case 1:
% 229.95/41.29  | | | | | 
% 229.95/41.29  | | | | |   (120)  all_57_6 = e2 & op(e1, e3) = e2
% 229.95/41.29  | | | | | 
% 229.95/41.29  | | | | | REF_CLOSE: (15), (30), (120) are inconsistent by sub-proof #2012.
% 229.95/41.29  | | | | | 
% 229.95/41.29  | | | | Case 2:
% 229.95/41.29  | | | | | 
% 229.95/41.29  | | | | |   (121)  all_57_12 = e2 & op(e0, e3) = e2
% 229.95/41.29  | | | | | 
% 229.95/41.29  | | | | | ALPHA: (121) implies:
% 229.95/41.29  | | | | |   (122)  all_57_12 = e2
% 229.95/41.29  | | | | | 
% 229.95/41.29  | | | | | BETA: splitting (3) gives:
% 229.95/41.29  | | | | | 
% 229.95/41.29  | | | | | Case 1:
% 229.95/41.29  | | | | | | 
% 229.95/41.29  | | | | | |   (123)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2,
% 229.95/41.29  | | | | | |              e3) = e1)
% 229.95/41.29  | | | | | | 
% 229.95/41.29  | | | | | | BETA: splitting (123) gives:
% 229.95/41.29  | | | | | | 
% 229.95/41.29  | | | | | | Case 1:
% 229.95/41.29  | | | | | | | 
% 229.95/41.29  | | | | | | |   (124)  all_57_0 = e1 & op(e3, e3) = e1
% 229.95/41.29  | | | | | | | 
% 229.95/41.29  | | | | | | | ALPHA: (124) implies:
% 229.95/41.29  | | | | | | |   (125)  all_57_0 = e1
% 229.95/41.29  | | | | | | | 
% 229.95/41.29  | | | | | | | COMBINE_EQS: (19), (125) imply:
% 229.95/41.29  | | | | | | |   (126)  e1 = e0
% 229.95/41.29  | | | | | | | 
% 229.95/41.29  | | | | | | | REF_CLOSE: (1), (5), (7), (15), (21), (25), (28), (32), (45),
% 229.95/41.29  | | | | | | |            (46), (50), (62), (126) are inconsistent by sub-proof
% 229.95/41.29  | | | | | | |            #932.
% 229.95/41.29  | | | | | | | 
% 229.95/41.29  | | | | | | Case 2:
% 229.95/41.29  | | | | | | | 
% 229.95/41.29  | | | | | | |   (127)  all_57_2 = e1 & op(e2, e3) = e1
% 229.95/41.29  | | | | | | | 
% 229.95/41.29  | | | | | | | ALPHA: (127) implies:
% 229.95/41.29  | | | | | | |   (128)  all_57_2 = e1
% 229.95/41.29  | | | | | | | 
% 229.95/41.29  | | | | | | | BETA: splitting (31) gives:
% 229.95/41.29  | | | | | | | 
% 229.95/41.29  | | | | | | | Case 1:
% 229.95/41.29  | | | | | | | | 
% 229.95/41.29  | | | | | | | |   (129)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 &
% 229.95/41.29  | | | | | | | |            op(e2, e2) = e3)
% 229.95/41.29  | | | | | | | | 
% 229.95/41.29  | | | | | | | | BETA: splitting (129) gives:
% 229.95/41.29  | | | | | | | | 
% 229.95/41.29  | | | | | | | | Case 1:
% 229.95/41.29  | | | | | | | | | 
% 229.95/41.29  | | | | | | | | |   (130)  all_57_1 = e3 & op(e3, e2) = e3
% 229.95/41.29  | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | ALPHA: (130) implies:
% 229.95/41.29  | | | | | | | | |   (131)  all_57_1 = e3
% 229.95/41.29  | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | BETA: splitting (38) gives:
% 229.95/41.29  | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | Case 1:
% 229.95/41.29  | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | |   (132)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 229.95/41.29  | | | | | | | | | |            & op(e2, e2) = e3)
% 229.95/41.29  | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | BETA: splitting (132) gives:
% 229.95/41.29  | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | Case 1:
% 229.95/41.29  | | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | |   (133)  all_57_2 = e3 & op(e2, e3) = e3
% 229.95/41.29  | | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | | ALPHA: (133) implies:
% 229.95/41.29  | | | | | | | | | | |   (134)  all_57_2 = e3
% 229.95/41.29  | | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | | REF_CLOSE: (3), (5), (7), (15), (19), (22), (25), (28), (30),
% 229.95/41.29  | | | | | | | | | | |            (45), (47), (134) are inconsistent by sub-proof
% 229.95/41.29  | | | | | | | | | | |            #1287.
% 229.95/41.29  | | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | Case 2:
% 229.95/41.29  | | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | |   (135)  all_57_3 = e3 & op(e2, e2) = e3
% 229.95/41.29  | | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | | ALPHA: (135) implies:
% 229.95/41.29  | | | | | | | | | | |   (136)  all_57_3 = e3
% 229.95/41.29  | | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | | COMBINE_EQS: (52), (136) imply:
% 229.95/41.29  | | | | | | | | | | |   (137)  e3 = e2
% 229.95/41.29  | | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | | SIMP: (137) implies:
% 229.95/41.29  | | | | | | | | | | |   (138)  e3 = e2
% 229.95/41.29  | | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | | COMBINE_EQS: (30), (138) imply:
% 229.95/41.29  | | | | | | | | | | |   (139)  all_57_6 = e2
% 229.95/41.29  | | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | | COMBINE_EQS: (131), (138) imply:
% 229.95/41.29  | | | | | | | | | | |   (140)  all_57_1 = e2
% 229.95/41.29  | | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (9), (10), (15), (16), (21), (25),
% 229.95/41.29  | | | | | | | | | | |            (27), (28), (35), (37), (45), (46), (50), (53),
% 229.95/41.29  | | | | | | | | | | |            (139), (140) are inconsistent by sub-proof #1099.
% 229.95/41.29  | | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | End of split
% 229.95/41.29  | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | Case 2:
% 229.95/41.29  | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | |   (141)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3
% 229.95/41.29  | | | | | | | | | |            & op(e2, e0) = e3)
% 229.95/41.29  | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | BETA: splitting (141) gives:
% 229.95/41.29  | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | Case 1:
% 229.95/41.29  | | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | |   (142)  all_57_5 = e3 & op(e2, e1) = e3
% 229.95/41.29  | | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | | ALPHA: (142) implies:
% 229.95/41.29  | | | | | | | | | | |   (143)  all_57_5 = e3
% 229.95/41.29  | | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | | BETA: splitting (55) gives:
% 229.95/41.29  | | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | | Case 1:
% 229.95/41.29  | | | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | | |   (144)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 229.95/41.29  | | | | | | | | | | | |            & op(e1, e2) = e2)
% 229.95/41.29  | | | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | | | BETA: splitting (144) gives:
% 229.95/41.29  | | | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | | | Case 1:
% 229.95/41.29  | | | | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | | | |   (145)  all_57_6 = e2 & op(e1, e3) = e2
% 229.95/41.29  | | | | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | | | | ALPHA: (145) implies:
% 229.95/41.29  | | | | | | | | | | | | |   (146)  all_57_6 = e2
% 229.95/41.29  | | | | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | | | | COMBINE_EQS: (30), (146) imply:
% 229.95/41.29  | | | | | | | | | | | | |   (147)  e3 = e2
% 229.95/41.29  | | | | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | | | | SIMP: (147) implies:
% 229.95/41.29  | | | | | | | | | | | | |   (148)  e3 = e2
% 229.95/41.29  | | | | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | | | | COMBINE_EQS: (131), (148) imply:
% 229.95/41.29  | | | | | | | | | | | | |   (149)  all_57_1 = e2
% 229.95/41.29  | | | | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (9), (10), (15), (16), (21), (25),
% 229.95/41.29  | | | | | | | | | | | | |            (27), (28), (35), (37), (45), (46), (50), (53),
% 229.95/41.29  | | | | | | | | | | | | |            (146), (149) are inconsistent by sub-proof #1099.
% 229.95/41.29  | | | | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | | | Case 2:
% 229.95/41.29  | | | | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | | | |   (150)  all_57_7 = e2 & op(e1, e2) = e2
% 229.95/41.29  | | | | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | | | | ALPHA: (150) implies:
% 229.95/41.29  | | | | | | | | | | | | |   (151)  all_57_7 = e2
% 229.95/41.29  | | | | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | | | | COMBINE_EQS: (54), (151) imply:
% 229.95/41.29  | | | | | | | | | | | | |   (152)  e2 = e0
% 229.95/41.29  | | | | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | | | | COMBINE_EQS: (52), (152) imply:
% 229.95/41.29  | | | | | | | | | | | | |   (153)  all_57_3 = e0
% 229.95/41.29  | | | | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | | | | REF_CLOSE: (5), (28), (37), (45), (53), (131), (151), (153)
% 229.95/41.29  | | | | | | | | | | | | |            are inconsistent by sub-proof #1759.
% 229.95/41.29  | | | | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | | | End of split
% 229.95/41.29  | | | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | | Case 2:
% 229.95/41.29  | | | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | | |   (154)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 229.95/41.29  | | | | | | | | | | | |            e2 & op(e1, e0) = e2)
% 229.95/41.29  | | | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | | | BETA: splitting (154) gives:
% 229.95/41.29  | | | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | | | Case 1:
% 229.95/41.29  | | | | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | | | |   (155)  all_57_8 = e2 & op(e1, e1) = e2
% 229.95/41.29  | | | | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | | | | ALPHA: (155) implies:
% 229.95/41.29  | | | | | | | | | | | | |   (156)  all_57_8 = e2
% 229.95/41.29  | | | | | | | | | | | | |   (157)  op(e1, e1) = e2
% 229.95/41.29  | | | | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | | | | BETA: splitting (53) gives:
% 229.95/41.29  | | | | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | | | | Case 1:
% 229.95/41.29  | | | | | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | | | | |   (158)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 229.95/41.29  | | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 229.95/41.29  | | | | | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | | | | | BETA: splitting (158) gives:
% 229.95/41.29  | | | | | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | | | | | Case 1:
% 229.95/41.29  | | | | | | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | | | | | |   (159)  all_57_1 = e1 & op(e3, e2) = e1
% 229.95/41.29  | | | | | | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (9), (10), (15), (16), (21), (25),
% 229.95/41.29  | | | | | | | | | | | | | | |            (28), (30), (35), (45), (46), (50), (54), (131),
% 229.95/41.29  | | | | | | | | | | | | | | |            (159) are inconsistent by sub-proof #929.
% 229.95/41.29  | | | | | | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | | | | | Case 2:
% 229.95/41.29  | | | | | | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | | | | | |   (160)  all_57_3 = e1 & op(e2, e2) = e1
% 229.95/41.29  | | | | | | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | | | | | | ALPHA: (160) implies:
% 229.95/41.29  | | | | | | | | | | | | | | |   (161)  all_57_3 = e1
% 229.95/41.29  | | | | | | | | | | | | | | |   (162)  op(e2, e2) = e1
% 229.95/41.29  | | | | | | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (10), (11),
% 229.95/41.29  | | | | | | | | | | | | | | |            (12), (14), (15), (16), (17), (19), (21), (22),
% 229.95/41.29  | | | | | | | | | | | | | | |            (24), (25), (26), (28), (30), (31), (35), (39),
% 229.95/41.29  | | | | | | | | | | | | | | |            (40), (41), (44), (45), (46), (47), (48), (49),
% 229.95/41.29  | | | | | | | | | | | | | | |            (50), (53), (56), (128), (143), (156), (157),
% 229.95/41.29  | | | | | | | | | | | | | | |            (161), (162) are inconsistent by sub-proof #924.
% 229.95/41.29  | | | | | | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | | | | | End of split
% 229.95/41.29  | | | | | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | | | | Case 2:
% 229.95/41.29  | | | | | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | | | | |   (163)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 229.95/41.29  | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 229.95/41.29  | | | | | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | | | | | REF_CLOSE: (1), (5), (7), (15), (21), (25), (28), (32), (37),
% 229.95/41.29  | | | | | | | | | | | | | |            (45), (46), (50), (54), (62), (163) are
% 229.95/41.29  | | | | | | | | | | | | | |            inconsistent by sub-proof #931.
% 229.95/41.29  | | | | | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | | | | End of split
% 229.95/41.29  | | | | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | | | Case 2:
% 229.95/41.29  | | | | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | | | |   (164)  all_57_11 = e2 & op(e1, e0) = e2
% 229.95/41.29  | | | | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | | | | ALPHA: (164) implies:
% 229.95/41.29  | | | | | | | | | | | | |   (165)  all_57_11 = e2
% 229.95/41.29  | | | | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (9), (10), (15), (16), (21), (25),
% 229.95/41.29  | | | | | | | | | | | | |            (28), (35), (36), (45), (46), (50), (51), (54),
% 229.95/41.29  | | | | | | | | | | | | |            (165) are inconsistent by sub-proof #947.
% 229.95/41.29  | | | | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | | | End of split
% 229.95/41.29  | | | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | | End of split
% 229.95/41.29  | | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | Case 2:
% 229.95/41.29  | | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | |   (166)  all_57_10 = e3 & op(e2, e0) = e3
% 229.95/41.29  | | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | | ALPHA: (166) implies:
% 229.95/41.29  | | | | | | | | | | |   (167)  all_57_10 = e3
% 229.95/41.29  | | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | | REF_CLOSE: (5), (7), (15), (16), (21), (25), (28), (32),
% 229.95/41.29  | | | | | | | | | | |            (35), (43), (45), (46), (50), (167) are
% 229.95/41.29  | | | | | | | | | | |            inconsistent by sub-proof #1747.
% 229.95/41.29  | | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | | End of split
% 229.95/41.29  | | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | End of split
% 229.95/41.29  | | | | | | | | | 
% 229.95/41.29  | | | | | | | | Case 2:
% 229.95/41.29  | | | | | | | | | 
% 229.95/41.29  | | | | | | | | |   (168)  all_57_3 = e3 & op(e2, e2) = e3
% 229.95/41.29  | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | ALPHA: (168) implies:
% 229.95/41.29  | | | | | | | | |   (169)  all_57_3 = e3
% 229.95/41.29  | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | REF_CLOSE: (15), (52), (169) are inconsistent by sub-proof
% 229.95/41.29  | | | | | | | | |            #1166.
% 229.95/41.29  | | | | | | | | | 
% 229.95/41.29  | | | | | | | | End of split
% 229.95/41.29  | | | | | | | | 
% 229.95/41.29  | | | | | | | Case 2:
% 229.95/41.29  | | | | | | | | 
% 229.95/41.29  | | | | | | | |   (170)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 &
% 229.95/41.29  | | | | | | | |            op(e0, e2) = e3)
% 229.95/41.29  | | | | | | | | 
% 229.95/41.29  | | | | | | | | BETA: splitting (170) gives:
% 229.95/41.29  | | | | | | | | 
% 229.95/41.29  | | | | | | | | Case 1:
% 229.95/41.29  | | | | | | | | | 
% 229.95/41.29  | | | | | | | | |   (171)  all_57_7 = e3 & op(e1, e2) = e3
% 229.95/41.29  | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | ALPHA: (171) implies:
% 229.95/41.29  | | | | | | | | |   (172)  all_57_7 = e3
% 229.95/41.29  | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | COMBINE_EQS: (54), (172) imply:
% 229.95/41.29  | | | | | | | | |   (173)  e3 = e0
% 229.95/41.29  | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | SIMP: (173) implies:
% 229.95/41.29  | | | | | | | | |   (174)  e3 = e0
% 229.95/41.29  | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | COMBINE_EQS: (30), (174) imply:
% 229.95/41.29  | | | | | | | | |   (175)  all_57_6 = e0
% 229.95/41.29  | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | REF_CLOSE: (5), (7), (15), (16), (22), (25), (41), (45), (47),
% 229.95/41.29  | | | | | | | | |            (128), (175) are inconsistent by sub-proof #2390.
% 229.95/41.29  | | | | | | | | | 
% 229.95/41.29  | | | | | | | | Case 2:
% 229.95/41.29  | | | | | | | | | 
% 229.95/41.29  | | | | | | | | |   (176)  all_57_13 = e3 & op(e0, e2) = e3
% 229.95/41.29  | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | ALPHA: (176) implies:
% 229.95/41.29  | | | | | | | | |   (177)  all_57_13 = e3
% 229.95/41.29  | | | | | | | | | 
% 229.95/41.29  | | | | | | | | | REF_CLOSE: (5), (7), (15), (16), (20), (21), (23), (25), (28),
% 229.95/41.29  | | | | | | | | |            (32), (33), (45), (177) are inconsistent by
% 229.95/41.29  | | | | | | | | |            sub-proof #2054.
% 229.95/41.29  | | | | | | | | | 
% 229.95/41.29  | | | | | | | | End of split
% 229.95/41.29  | | | | | | | | 
% 229.95/41.29  | | | | | | | End of split
% 229.95/41.29  | | | | | | | 
% 229.95/41.29  | | | | | | End of split
% 229.95/41.29  | | | | | | 
% 229.95/41.29  | | | | | Case 2:
% 229.95/41.29  | | | | | | 
% 229.95/41.29  | | | | | |   (178)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 &
% 229.95/41.29  | | | | | |            op(e0, e3) = e1)
% 229.95/41.29  | | | | | | 
% 229.95/41.29  | | | | | | REF_CLOSE: (5), (7), (8), (9), (10), (15), (16), (21), (25), (28),
% 229.95/41.29  | | | | | |            (35), (45), (46), (50), (54), (122), (178) are
% 229.95/41.29  | | | | | |            inconsistent by sub-proof #923.
% 229.95/41.29  | | | | | | 
% 229.95/41.29  | | | | | End of split
% 229.95/41.29  | | | | | 
% 229.95/41.29  | | | | End of split
% 229.95/41.29  | | | | 
% 229.95/41.29  | | | End of split
% 229.95/41.29  | | | 
% 229.95/41.29  | | End of split
% 229.95/41.29  | | 
% 229.95/41.29  | End of split
% 229.95/41.29  | 
% 229.95/41.29  End of proof
% 229.95/41.29  
% 229.95/41.29  Sub-proof #923 shows that the following formulas are inconsistent:
% 229.95/41.29  ----------------------------------------------------------------
% 229.95/41.29    (1)   ~ (e3 = e1)
% 229.95/41.29    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.95/41.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.95/41.29    (3)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.95/41.29         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.95/41.29    (4)   ~ (all_6_2 = e3)
% 229.95/41.29    (5)  op(e1, e1) = all_6_2
% 229.95/41.29    (6)  all_57_12 = e2
% 229.95/41.29    (7)   ~ (e3 = e2)
% 229.95/41.29    (8)   ~ (e3 = e0)
% 229.95/41.29    (9)  all_57_15 = e3
% 229.95/41.29    (10)   ~ (e2 = e0)
% 229.95/41.29    (11)   ~ (e1 = e0)
% 229.95/41.29    (12)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.95/41.29    (13)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.95/41.29              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.95/41.29                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.95/41.29                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.95/41.29    (14)   ~ (e2 = e1)
% 229.95/41.29    (15)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.95/41.29          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.95/41.29    (16)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.95/41.29          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.95/41.29    (17)  all_57_7 = e0
% 229.95/41.29  
% 229.95/41.29  Begin of proof
% 229.95/41.29  | 
% 229.95/41.29  | BETA: splitting (12) gives:
% 229.95/41.29  | 
% 229.95/41.29  | Case 1:
% 229.95/41.29  | | 
% 229.95/41.29  | |   (18)  all_57_6 = e1 & op(e1, e3) = e1
% 229.95/41.29  | | 
% 229.95/41.29  | | ALPHA: (18) implies:
% 229.95/41.29  | |   (19)  all_57_6 = e1
% 229.95/41.29  | | 
% 229.95/41.29  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (13), (14),
% 229.95/41.29  | |            (15), (16), (17), (19) are inconsistent by sub-proof #1735.
% 229.95/41.29  | | 
% 229.95/41.29  | Case 2:
% 229.95/41.29  | | 
% 229.95/41.29  | |   (20)  all_57_12 = e1 & op(e0, e3) = e1
% 229.95/41.29  | | 
% 229.95/41.29  | | REF_CLOSE: (6), (14), (20) are inconsistent by sub-proof #2388.
% 229.95/41.29  | | 
% 229.95/41.29  | End of split
% 229.95/41.29  | 
% 229.95/41.29  End of proof
% 229.95/41.29  
% 229.95/41.29  Sub-proof #924 shows that the following formulas are inconsistent:
% 229.95/41.29  ----------------------------------------------------------------
% 229.95/41.29    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.95/41.29         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.95/41.29    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.95/41.29         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.95/41.29    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.95/41.29         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.95/41.29    (4)   ~ (e3 = e1)
% 229.95/41.29    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.95/41.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.95/41.29    (6)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.95/41.29         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.95/41.29    (7)   ~ (all_6_2 = e3)
% 229.95/41.29    (8)  op(e1, e1) = all_6_2
% 229.95/41.29    (9)  op(e2, e2) = e1
% 229.95/41.29    (10)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.95/41.29          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.95/41.29    (11)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.95/41.29          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.95/41.29    (12)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 229.95/41.29          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.95/41.29    (13)   ~ (e3 = e2)
% 229.95/41.29    (14)   ~ (e3 = e0)
% 229.95/41.29    (15)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 229.95/41.29          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 229.95/41.29    (16)  all_57_0 = e0
% 229.95/41.29    (17)  all_57_15 = e3
% 229.95/41.29    (18)  op(e3, e3) = e0
% 229.95/41.29    (19)  all_57_5 = e3
% 229.95/41.29    (20)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.95/41.29          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.95/41.29    (21)   ~ (e2 = e0)
% 229.95/41.29    (22)  all_57_3 = e1
% 229.95/41.29    (23)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.95/41.29          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.95/41.29    (24)   ~ (e1 = e0)
% 229.95/41.29    (25)  all_57_8 = e2
% 229.95/41.29    (26)  all_57_6 = e3
% 229.95/41.29    (27)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.95/41.29          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.95/41.29    (28)  all_57_2 = e1
% 229.95/41.29    (29)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.95/41.29              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.95/41.29                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.95/41.29                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.95/41.29    (30)  op(e1, e1) = e2
% 229.95/41.29    (31)   ~ (all_53_12 = e3)
% 229.95/41.29    (32)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.95/41.29          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.95/41.29    (33)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.95/41.29          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.95/41.29    (34)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.95/41.29          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 229.95/41.29    (35)   ~ (e2 = e1)
% 229.95/41.29    (36)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.95/41.29          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.95/41.29    (37)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.95/41.29          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.95/41.29    (38)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 229.95/41.29          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 229.95/41.29    (39)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.95/41.29          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.95/41.29    (40)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.95/41.29          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.95/41.29    (41)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.95/41.29          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.95/41.29    (42)  op(e3, e0) = all_53_12
% 229.95/41.29  
% 229.95/41.29  Begin of proof
% 229.95/41.29  | 
% 229.95/41.29  | BETA: splitting (12) gives:
% 229.95/41.29  | 
% 229.95/41.29  | Case 1:
% 229.95/41.29  | | 
% 229.95/41.29  | |   (43)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) =
% 229.95/41.29  | |           e0)
% 229.95/41.29  | | 
% 229.95/41.29  | | BETA: splitting (43) gives:
% 229.95/41.29  | | 
% 229.95/41.29  | | Case 1:
% 229.95/41.29  | | | 
% 229.95/41.29  | | |   (44)  all_57_4 = e0 & op(e3, e1) = e0
% 229.95/41.29  | | | 
% 229.95/41.29  | | | REF_CLOSE: (3), (4), (5), (9), (10), (11), (13), (14), (15), (16), (18),
% 229.95/41.29  | | |            (19), (20), (21), (23), (24), (27), (30), (31), (35), (42),
% 229.95/41.29  | | |            (44) are inconsistent by sub-proof #927.
% 229.95/41.29  | | | 
% 229.95/41.29  | | Case 2:
% 229.95/41.29  | | | 
% 229.95/41.29  | | |   (45)  all_57_5 = e0 & op(e2, e1) = e0
% 229.95/41.29  | | | 
% 229.95/41.29  | | | ALPHA: (45) implies:
% 229.95/41.29  | | |   (46)  all_57_5 = e0
% 229.95/41.29  | | | 
% 229.95/41.29  | | | COMBINE_EQS: (19), (46) imply:
% 229.95/41.29  | | |   (47)  e3 = e0
% 229.95/41.29  | | | 
% 229.95/41.29  | | | COMBINE_EQS: (26), (47) imply:
% 229.95/41.29  | | |   (48)  all_57_6 = e0
% 229.95/41.29  | | | 
% 229.95/41.29  | | | REF_CLOSE: (4), (5), (13), (14), (18), (21), (28), (33), (35), (37), (48)
% 229.95/41.29  | | |            are inconsistent by sub-proof #2390.
% 229.95/41.29  | | | 
% 229.95/41.29  | | End of split
% 229.95/41.29  | | 
% 229.95/41.29  | Case 2:
% 229.95/41.29  | | 
% 229.95/41.29  | |   (49)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 229.95/41.29  | |           e0)
% 229.95/41.29  | | 
% 229.95/41.29  | | BETA: splitting (49) gives:
% 229.95/41.29  | | 
% 229.95/41.29  | | Case 1:
% 229.95/41.29  | | | 
% 229.95/41.29  | | |   (50)  all_57_8 = e0 & op(e1, e1) = e0
% 229.95/41.29  | | | 
% 229.95/41.29  | | | ALPHA: (50) implies:
% 229.95/41.29  | | |   (51)  all_57_8 = e0
% 229.95/41.29  | | | 
% 229.95/41.29  | | | REF_CLOSE: (21), (25), (51) are inconsistent by sub-proof #1957.
% 229.95/41.29  | | | 
% 229.95/41.29  | | Case 2:
% 229.95/41.29  | | | 
% 229.95/41.29  | | |   (52)  all_57_14 = e0 & op(e0, e1) = e0
% 229.95/41.29  | | | 
% 229.95/41.29  | | | ALPHA: (52) implies:
% 229.95/41.29  | | |   (53)  all_57_14 = e0
% 229.95/41.29  | | | 
% 229.95/41.29  | | | BETA: splitting (23) gives:
% 229.95/41.29  | | | 
% 229.95/41.29  | | | Case 1:
% 229.95/41.29  | | | | 
% 229.95/41.29  | | | |   (54)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2)
% 229.95/41.29  | | | |           = e3)
% 229.95/41.29  | | | | 
% 229.95/41.29  | | | | BETA: splitting (54) gives:
% 229.95/41.29  | | | | 
% 229.95/41.29  | | | | Case 1:
% 229.95/41.29  | | | | | 
% 229.95/41.29  | | | | |   (55)  all_57_0 = e3 & op(e3, e3) = e3
% 229.95/41.29  | | | | | 
% 229.95/41.29  | | | | | ALPHA: (55) implies:
% 229.95/41.29  | | | | |   (56)  all_57_0 = e3
% 229.95/41.29  | | | | | 
% 229.95/41.29  | | | | | REF_CLOSE: (2), (4), (13), (14), (21), (24), (26), (35), (37), (39),
% 229.95/41.29  | | | | |            (56) are inconsistent by sub-proof #2010.
% 229.95/41.29  | | | | | 
% 229.95/41.29  | | | | Case 2:
% 229.95/41.29  | | | | | 
% 229.95/41.29  | | | | |   (57)  all_57_1 = e3 & op(e3, e2) = e3
% 229.95/41.29  | | | | | 
% 229.95/41.29  | | | | | ALPHA: (57) implies:
% 229.95/41.29  | | | | |   (58)  all_57_1 = e3
% 229.95/41.29  | | | | | 
% 229.95/41.29  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (13), (14),
% 229.95/41.29  | | | | |            (16), (17), (18), (19), (20), (21), (22), (24), (26), (28),
% 229.95/41.29  | | | | |            (29), (32), (34), (35), (36), (37), (40), (41), (58) are
% 229.95/41.29  | | | | |            inconsistent by sub-proof #1007.
% 229.95/41.29  | | | | | 
% 229.95/41.29  | | | | End of split
% 229.95/41.29  | | | | 
% 229.95/41.29  | | | Case 2:
% 229.95/41.29  | | | | 
% 229.95/41.29  | | | |   (59)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0)
% 229.95/41.29  | | | |           = e3)
% 229.95/41.29  | | | | 
% 229.95/41.29  | | | | BETA: splitting (59) gives:
% 229.95/41.29  | | | | 
% 229.95/41.29  | | | | Case 1:
% 229.95/41.29  | | | | | 
% 229.95/41.29  | | | | |   (60)  all_57_4 = e3 & op(e3, e1) = e3
% 229.95/41.29  | | | | | 
% 229.95/41.29  | | | | | ALPHA: (60) implies:
% 229.95/41.29  | | | | |   (61)  all_57_4 = e3
% 229.95/41.29  | | | | | 
% 229.95/41.29  | | | | | BETA: splitting (34) gives:
% 229.95/41.29  | | | | | 
% 229.95/41.29  | | | | | Case 1:
% 229.95/41.29  | | | | | | 
% 229.95/41.29  | | | | | |   (62)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2,
% 229.95/41.29  | | | | | |             e2) = e0)
% 229.95/41.29  | | | | | | 
% 229.95/41.29  | | | | | | REF_CLOSE: (1), (2), (4), (5), (9), (13), (16), (18), (19), (21),
% 229.95/41.29  | | | | | |            (22), (24), (26), (32), (35), (37), (62) are inconsistent
% 229.95/41.29  | | | | | |            by sub-proof #1009.
% 229.95/41.29  | | | | | | 
% 229.95/41.29  | | | | | Case 2:
% 229.95/41.29  | | | | | | 
% 229.95/41.29  | | | | | |   (63)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2,
% 229.95/41.29  | | | | | |             e0) = e0)
% 229.95/41.29  | | | | | | 
% 229.95/41.29  | | | | | | BETA: splitting (63) gives:
% 229.95/41.29  | | | | | | 
% 229.95/41.29  | | | | | | Case 1:
% 229.95/41.29  | | | | | | | 
% 229.95/41.29  | | | | | | |   (64)  all_57_5 = e0 & op(e2, e1) = e0
% 229.95/41.29  | | | | | | | 
% 229.95/41.29  | | | | | | | REF_CLOSE: (4), (5), (13), (15), (19), (21), (24), (35), (38),
% 229.95/41.29  | | | | | | |            (53), (61), (64) are inconsistent by sub-proof #926.
% 229.95/41.29  | | | | | | | 
% 229.95/41.29  | | | | | | Case 2:
% 229.95/41.29  | | | | | | | 
% 229.95/41.29  | | | | | | |   (65)  all_57_10 = e0 & op(e2, e0) = e0
% 229.95/41.29  | | | | | | | 
% 229.95/41.29  | | | | | | | ALPHA: (65) implies:
% 229.95/41.29  | | | | | | |   (66)  all_57_10 = e0
% 229.95/41.29  | | | | | | | 
% 229.95/41.29  | | | | | | | BETA: splitting (32) gives:
% 229.95/41.29  | | | | | | | 
% 229.95/41.29  | | | | | | | Case 1:
% 229.95/41.29  | | | | | | | | 
% 229.95/41.29  | | | | | | | |   (67)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 &
% 229.95/41.29  | | | | | | | |           op(e2, e2) = e2)
% 229.95/41.29  | | | | | | | | 
% 229.95/41.29  | | | | | | | | REF_CLOSE: (5), (9), (28), (35), (67) are inconsistent by
% 229.95/41.29  | | | | | | | |            sub-proof #1828.
% 229.95/41.29  | | | | | | | | 
% 229.95/41.29  | | | | | | | Case 2:
% 229.95/41.29  | | | | | | | | 
% 229.95/41.29  | | | | | | | |   (68)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 &
% 229.95/41.29  | | | | | | | |           op(e2, e0) = e2)
% 229.95/41.30  | | | | | | | | 
% 229.95/41.30  | | | | | | | | BETA: splitting (68) gives:
% 229.95/41.30  | | | | | | | | 
% 229.95/41.30  | | | | | | | | Case 1:
% 229.95/41.30  | | | | | | | | | 
% 229.95/41.30  | | | | | | | | |   (69)  all_57_5 = e2 & op(e2, e1) = e2
% 229.95/41.30  | | | | | | | | | 
% 229.95/41.30  | | | | | | | | | ALPHA: (69) implies:
% 229.95/41.30  | | | | | | | | |   (70)  all_57_5 = e2
% 229.95/41.30  | | | | | | | | | 
% 229.95/41.30  | | | | | | | | | REF_CLOSE: (4), (15), (24), (25), (35), (53), (61), (70) are
% 229.95/41.30  | | | | | | | | |            inconsistent by sub-proof #925.
% 229.95/41.30  | | | | | | | | | 
% 229.95/41.30  | | | | | | | | Case 2:
% 229.95/41.30  | | | | | | | | | 
% 229.95/41.30  | | | | | | | | |   (71)  all_57_10 = e2 & op(e2, e0) = e2
% 229.95/41.30  | | | | | | | | | 
% 229.95/41.30  | | | | | | | | | ALPHA: (71) implies:
% 229.95/41.30  | | | | | | | | |   (72)  all_57_10 = e2
% 229.95/41.30  | | | | | | | | | 
% 229.95/41.30  | | | | | | | | | REF_CLOSE: (21), (66), (72) are inconsistent by sub-proof
% 229.95/41.30  | | | | | | | | |            #2138.
% 229.95/41.30  | | | | | | | | | 
% 229.95/41.30  | | | | | | | | End of split
% 229.95/41.30  | | | | | | | | 
% 229.95/41.30  | | | | | | | End of split
% 229.95/41.30  | | | | | | | 
% 229.95/41.30  | | | | | | End of split
% 229.95/41.30  | | | | | | 
% 229.95/41.30  | | | | | End of split
% 229.95/41.30  | | | | | 
% 229.95/41.30  | | | | Case 2:
% 229.95/41.30  | | | | | 
% 229.95/41.30  | | | | |   (73)  all_57_9 = e3 & op(e3, e0) = e3
% 229.95/41.30  | | | | | 
% 229.95/41.30  | | | | | ALPHA: (73) implies:
% 229.95/41.30  | | | | |   (74)  op(e3, e0) = e3
% 229.95/41.30  | | | | | 
% 229.95/41.30  | | | | | REF_CLOSE: (5), (31), (42), (74) are inconsistent by sub-proof #2458.
% 229.95/41.30  | | | | | 
% 229.95/41.30  | | | | End of split
% 229.95/41.30  | | | | 
% 229.95/41.30  | | | End of split
% 229.95/41.30  | | | 
% 229.95/41.30  | | End of split
% 229.95/41.30  | | 
% 229.95/41.30  | End of split
% 229.95/41.30  | 
% 229.95/41.30  End of proof
% 229.95/41.30  
% 229.95/41.30  Sub-proof #925 shows that the following formulas are inconsistent:
% 229.95/41.30  ----------------------------------------------------------------
% 229.95/41.30    (1)   ~ (e3 = e1)
% 229.95/41.30    (2)  all_57_4 = e3
% 229.95/41.30    (3)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 229.95/41.30         (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 229.95/41.30    (4)   ~ (e1 = e0)
% 229.95/41.30    (5)  all_57_5 = e2
% 229.95/41.30    (6)  all_57_8 = e2
% 229.95/41.30    (7)   ~ (e2 = e1)
% 229.95/41.30    (8)  all_57_14 = e0
% 229.95/41.30  
% 229.95/41.30  Begin of proof
% 229.95/41.30  | 
% 229.95/41.30  | BETA: splitting (3) gives:
% 229.95/41.30  | 
% 229.95/41.30  | Case 1:
% 229.95/41.30  | | 
% 229.95/41.30  | |   (9)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1)
% 229.95/41.30  | | 
% 229.95/41.30  | | BETA: splitting (9) gives:
% 229.95/41.30  | | 
% 229.95/41.30  | | Case 1:
% 229.95/41.30  | | | 
% 229.95/41.30  | | |   (10)  all_57_4 = e1 & op(e3, e1) = e1
% 229.95/41.30  | | | 
% 229.95/41.30  | | | REF_CLOSE: (1), (2), (10) are inconsistent by sub-proof #2484.
% 229.95/41.30  | | | 
% 229.95/41.30  | | Case 2:
% 229.95/41.30  | | | 
% 229.95/41.30  | | |   (11)  all_57_5 = e1 & op(e2, e1) = e1
% 229.95/41.30  | | | 
% 229.95/41.30  | | | REF_CLOSE: (5), (7), (11) are inconsistent by sub-proof #1886.
% 229.95/41.30  | | | 
% 229.95/41.30  | | End of split
% 229.95/41.30  | | 
% 229.95/41.30  | Case 2:
% 229.95/41.30  | | 
% 229.95/41.30  | |   (12)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) =
% 229.95/41.30  | |           e1)
% 229.95/41.30  | | 
% 229.95/41.30  | | BETA: splitting (12) gives:
% 229.95/41.30  | | 
% 229.95/41.30  | | Case 1:
% 229.95/41.30  | | | 
% 229.95/41.30  | | |   (13)  all_57_8 = e1 & op(e1, e1) = e1
% 229.95/41.30  | | | 
% 229.95/41.30  | | | ALPHA: (13) implies:
% 229.95/41.30  | | |   (14)  all_57_8 = e1
% 229.95/41.30  | | | 
% 229.95/41.30  | | | REF_CLOSE: (6), (7), (14) are inconsistent by sub-proof #1485.
% 229.95/41.30  | | | 
% 229.95/41.30  | | Case 2:
% 229.95/41.30  | | | 
% 229.95/41.30  | | |   (15)  all_57_14 = e1 & op(e0, e1) = e1
% 229.95/41.30  | | | 
% 229.95/41.30  | | | ALPHA: (15) implies:
% 229.95/41.30  | | |   (16)  all_57_14 = e1
% 229.95/41.30  | | | 
% 229.95/41.30  | | | REF_CLOSE: (4), (8), (16) are inconsistent by sub-proof #2122.
% 229.95/41.30  | | | 
% 229.95/41.30  | | End of split
% 229.95/41.30  | | 
% 229.95/41.30  | End of split
% 229.95/41.30  | 
% 229.95/41.30  End of proof
% 229.95/41.30  
% 229.95/41.30  Sub-proof #926 shows that the following formulas are inconsistent:
% 229.95/41.30  ----------------------------------------------------------------
% 229.95/41.30    (1)   ~ (e3 = e1)
% 229.95/41.30    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.95/41.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.95/41.30    (3)  all_57_4 = e3
% 229.95/41.30    (4)   ~ (e3 = e2)
% 229.95/41.30    (5)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 229.95/41.30         (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 229.95/41.30    (6)  all_57_5 = e3
% 229.95/41.30    (7)   ~ (e2 = e0)
% 229.95/41.30    (8)   ~ (e1 = e0)
% 229.95/41.30    (9)  all_57_5 = e0 & op(e2, e1) = e0
% 229.95/41.30    (10)   ~ (e2 = e1)
% 229.95/41.30    (11)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 229.95/41.30          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 229.95/41.30    (12)  all_57_14 = e0
% 229.95/41.30  
% 229.95/41.30  Begin of proof
% 229.95/41.30  | 
% 229.95/41.30  | ALPHA: (9) implies:
% 229.95/41.30  |   (13)  all_57_5 = e0
% 229.95/41.30  | 
% 229.95/41.30  | COMBINE_EQS: (6), (13) imply:
% 229.95/41.30  |   (14)  e3 = e0
% 229.95/41.30  | 
% 229.95/41.30  | COMBINE_EQS: (3), (14) imply:
% 229.95/41.30  |   (15)  all_57_4 = e0
% 229.95/41.30  | 
% 229.95/41.30  | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (10), (11), (12), (15) are
% 229.95/41.30  |            inconsistent by sub-proof #2378.
% 229.95/41.30  | 
% 229.95/41.30  End of proof
% 229.95/41.30  
% 229.95/41.30  Sub-proof #927 shows that the following formulas are inconsistent:
% 229.95/41.30  ----------------------------------------------------------------
% 229.95/41.30    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.95/41.30         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.95/41.30    (2)   ~ (e3 = e1)
% 229.95/41.30    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.95/41.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.95/41.30    (4)  op(e2, e2) = e1
% 229.95/41.30    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.95/41.30         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.95/41.30    (6)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.95/41.30         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.95/41.30    (7)   ~ (e3 = e2)
% 229.95/41.30    (8)   ~ (e3 = e0)
% 229.95/41.30    (9)  all_57_4 = e0 & op(e3, e1) = e0
% 229.95/41.30    (10)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 229.95/41.30          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 229.95/41.30    (11)  all_57_0 = e0
% 229.95/41.30    (12)  op(e3, e3) = e0
% 229.95/41.30    (13)  all_57_5 = e3
% 229.95/41.30    (14)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.95/41.30          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.95/41.30    (15)   ~ (e2 = e0)
% 229.95/41.30    (16)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.95/41.30          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.95/41.30    (17)   ~ (e1 = e0)
% 229.95/41.30    (18)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.95/41.30          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.95/41.30    (19)  op(e1, e1) = e2
% 229.95/41.30    (20)   ~ (all_53_12 = e3)
% 229.95/41.30    (21)   ~ (e2 = e1)
% 229.95/41.30    (22)  op(e3, e0) = all_53_12
% 229.95/41.30  
% 229.95/41.30  Begin of proof
% 229.95/41.30  | 
% 229.95/41.30  | ALPHA: (9) implies:
% 229.95/41.30  |   (23)  all_57_4 = e0
% 229.95/41.30  | 
% 229.95/41.30  | BETA: splitting (10) gives:
% 229.95/41.30  | 
% 229.95/41.30  | Case 1:
% 229.95/41.30  | | 
% 229.95/41.30  | |   (24)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) =
% 229.95/41.30  | |           e1)
% 229.95/41.30  | | 
% 229.95/41.30  | | BETA: splitting (24) gives:
% 229.95/41.30  | | 
% 229.95/41.30  | | Case 1:
% 229.95/41.30  | | | 
% 229.95/41.30  | | |   (25)  all_57_4 = e1 & op(e3, e1) = e1
% 229.95/41.30  | | | 
% 229.95/41.30  | | | REF_CLOSE: (17), (23), (25) are inconsistent by sub-proof #1411.
% 229.95/41.30  | | | 
% 229.95/41.30  | | Case 2:
% 229.95/41.30  | | | 
% 229.95/41.30  | | |   (26)  all_57_5 = e1 & op(e2, e1) = e1
% 229.95/41.30  | | | 
% 229.95/41.30  | | | REF_CLOSE: (2), (13), (26) are inconsistent by sub-proof #2376.
% 229.95/41.30  | | | 
% 229.95/41.30  | | End of split
% 229.95/41.30  | | 
% 229.95/41.30  | Case 2:
% 229.95/41.30  | | 
% 229.95/41.30  | |   (27)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) =
% 229.95/41.30  | |           e1)
% 229.95/41.30  | | 
% 229.95/41.30  | | BETA: splitting (27) gives:
% 229.95/41.30  | | 
% 229.95/41.30  | | Case 1:
% 229.95/41.30  | | | 
% 229.95/41.30  | | |   (28)  all_57_8 = e1 & op(e1, e1) = e1
% 229.95/41.30  | | | 
% 229.95/41.30  | | | ALPHA: (28) implies:
% 229.95/41.30  | | |   (29)  op(e1, e1) = e1
% 229.95/41.30  | | | 
% 229.95/41.30  | | | REF_CLOSE: (3), (19), (21), (29) are inconsistent by sub-proof #2423.
% 229.95/41.30  | | | 
% 229.95/41.30  | | Case 2:
% 229.95/41.30  | | | 
% 229.95/41.30  | | |   (30)  all_57_14 = e1 & op(e0, e1) = e1
% 229.95/41.30  | | | 
% 229.95/41.30  | | | ALPHA: (30) implies:
% 229.95/41.30  | | |   (31)  all_57_14 = e1
% 229.95/41.30  | | | 
% 229.95/41.30  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13),
% 229.95/41.30  | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 229.95/41.30  | | |            (31) are inconsistent by sub-proof #928.
% 229.95/41.30  | | | 
% 229.95/41.30  | | End of split
% 229.95/41.30  | | 
% 229.95/41.30  | End of split
% 229.95/41.30  | 
% 229.95/41.30  End of proof
% 229.95/41.30  
% 229.95/41.30  Sub-proof #928 shows that the following formulas are inconsistent:
% 229.95/41.30  ----------------------------------------------------------------
% 229.95/41.30    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.95/41.30         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.95/41.30    (2)   ~ (e3 = e1)
% 229.95/41.30    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.95/41.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.95/41.30    (4)  op(e2, e2) = e1
% 229.95/41.30    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.95/41.30         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.95/41.30    (6)  all_57_4 = e0
% 229.95/41.30    (7)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.95/41.30         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.95/41.30    (8)   ~ (e3 = e2)
% 229.95/41.30    (9)   ~ (e3 = e0)
% 229.95/41.30    (10)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 229.95/41.30          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 229.95/41.30    (11)  all_57_0 = e0
% 229.95/41.30    (12)  op(e3, e3) = e0
% 229.95/41.30    (13)  all_57_5 = e3
% 229.95/41.30    (14)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.95/41.30          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.95/41.30    (15)   ~ (e2 = e0)
% 229.95/41.30    (16)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.95/41.30          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.95/41.30    (17)   ~ (e1 = e0)
% 229.95/41.30    (18)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.95/41.30          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.95/41.30    (19)  all_57_14 = e1
% 229.95/41.30    (20)  op(e1, e1) = e2
% 229.95/41.30    (21)   ~ (all_53_12 = e3)
% 229.95/41.30    (22)   ~ (e2 = e1)
% 229.95/41.30    (23)  op(e3, e0) = all_53_12
% 229.95/41.30  
% 229.95/41.30  Begin of proof
% 229.95/41.30  | 
% 229.95/41.30  | BETA: splitting (5) gives:
% 229.95/41.30  | 
% 229.95/41.30  | Case 1:
% 229.95/41.30  | | 
% 229.95/41.30  | |   (24)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) =
% 229.95/41.30  | |           e1)
% 229.95/41.30  | | 
% 229.95/41.30  | | BETA: splitting (24) gives:
% 229.95/41.30  | | 
% 229.95/41.30  | | Case 1:
% 229.95/41.30  | | | 
% 229.95/41.30  | | |   (25)  all_57_0 = e1 & op(e3, e3) = e1
% 229.95/41.30  | | | 
% 229.95/41.30  | | | ALPHA: (25) implies:
% 229.95/41.30  | | |   (26)  all_57_0 = e1
% 229.95/41.30  | | | 
% 229.95/41.30  | | | COMBINE_EQS: (11), (26) imply:
% 229.95/41.30  | | |   (27)  e1 = e0
% 229.95/41.30  | | | 
% 229.95/41.30  | | | SIMP: (27) implies:
% 229.95/41.30  | | |   (28)  e1 = e0
% 229.95/41.30  | | | 
% 229.95/41.30  | | | COMBINE_EQS: (19), (28) imply:
% 229.95/41.30  | | |   (29)  all_57_14 = e0
% 229.95/41.30  | | | 
% 229.95/41.30  | | | REF_CLOSE: (2), (3), (6), (10), (13), (17), (20), (22), (29) are
% 229.95/41.30  | | |            inconsistent by sub-proof #2379.
% 229.95/41.30  | | | 
% 229.95/41.30  | | Case 2:
% 229.95/41.30  | | | 
% 229.95/41.30  | | |   (30)  all_57_1 = e1 & op(e3, e2) = e1
% 229.95/41.30  | | | 
% 229.95/41.30  | | | ALPHA: (30) implies:
% 229.95/41.30  | | |   (31)  all_57_1 = e1
% 229.95/41.30  | | | 
% 229.95/41.30  | | | REF_CLOSE: (1), (2), (3), (4), (8), (9), (14), (15), (17), (18), (22),
% 229.95/41.30  | | |            (31) are inconsistent by sub-proof #1908.
% 229.95/41.30  | | | 
% 229.95/41.30  | | End of split
% 229.95/41.30  | | 
% 229.95/41.30  | Case 2:
% 229.95/41.30  | | 
% 229.95/41.30  | |   (32)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) =
% 229.95/41.30  | |           e1)
% 229.95/41.30  | | 
% 229.95/41.30  | | BETA: splitting (32) gives:
% 229.95/41.30  | | 
% 229.95/41.30  | | Case 1:
% 229.95/41.30  | | | 
% 229.95/41.30  | | |   (33)  all_57_4 = e1 & op(e3, e1) = e1
% 229.95/41.30  | | | 
% 229.95/41.30  | | | ALPHA: (33) implies:
% 229.95/41.30  | | |   (34)  all_57_4 = e1
% 229.95/41.30  | | | 
% 229.95/41.30  | | | COMBINE_EQS: (6), (34) imply:
% 229.95/41.30  | | |   (35)  e1 = e0
% 229.95/41.30  | | | 
% 229.95/41.30  | | | COMBINE_EQS: (19), (35) imply:
% 229.95/41.30  | | |   (36)  all_57_14 = e0
% 229.95/41.30  | | | 
% 229.95/41.30  | | | REF_CLOSE: (2), (3), (6), (10), (13), (17), (20), (22), (36) are
% 229.95/41.30  | | |            inconsistent by sub-proof #2379.
% 229.95/41.30  | | | 
% 229.95/41.30  | | Case 2:
% 229.95/41.30  | | | 
% 229.95/41.30  | | |   (37)  all_57_9 = e1 & op(e3, e0) = e1
% 229.95/41.30  | | | 
% 229.95/41.30  | | | ALPHA: (37) implies:
% 229.95/41.30  | | |   (38)  all_57_9 = e1
% 229.95/41.30  | | | 
% 229.95/41.30  | | | REF_CLOSE: (3), (6), (7), (8), (9), (12), (15), (16), (21), (22), (23),
% 229.95/41.30  | | |            (38) are inconsistent by sub-proof #1403.
% 229.95/41.30  | | | 
% 229.95/41.30  | | End of split
% 229.95/41.30  | | 
% 229.95/41.30  | End of split
% 229.95/41.30  | 
% 229.95/41.30  End of proof
% 229.95/41.30  
% 229.95/41.30  Sub-proof #929 shows that the following formulas are inconsistent:
% 229.95/41.30  ----------------------------------------------------------------
% 229.95/41.30    (1)   ~ (e3 = e1)
% 229.95/41.30    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.95/41.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.95/41.30    (3)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.95/41.30         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.95/41.30    (4)   ~ (all_6_2 = e3)
% 229.95/41.30    (5)  op(e1, e1) = all_6_2
% 229.95/41.30    (6)  all_57_1 = e1 & op(e3, e2) = e1
% 229.95/41.30    (7)   ~ (e3 = e2)
% 229.95/41.30    (8)   ~ (e3 = e0)
% 229.95/41.30    (9)  all_57_15 = e3
% 229.95/41.30    (10)   ~ (e2 = e0)
% 229.95/41.30    (11)   ~ (e1 = e0)
% 229.95/41.30    (12)  all_57_6 = e3
% 229.95/41.30    (13)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.95/41.30              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.95/41.30                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.95/41.30                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.95/41.30    (14)  all_57_1 = e3
% 229.95/41.30    (15)   ~ (e2 = e1)
% 229.95/41.30    (16)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.95/41.30          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.95/41.30    (17)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.95/41.30          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.95/41.30    (18)  all_57_7 = e0
% 229.95/41.30  
% 229.95/41.30  Begin of proof
% 229.95/41.30  | 
% 229.95/41.30  | ALPHA: (6) implies:
% 229.95/41.30  |   (19)  all_57_1 = e1
% 229.95/41.30  | 
% 229.95/41.30  | COMBINE_EQS: (14), (19) imply:
% 229.95/41.30  |   (20)  e3 = e1
% 229.95/41.30  | 
% 229.95/41.30  | COMBINE_EQS: (12), (20) imply:
% 229.95/41.30  |   (21)  all_57_6 = e1
% 229.95/41.30  | 
% 229.95/41.30  | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (13), (15),
% 229.95/41.30  |            (16), (17), (18), (21) are inconsistent by sub-proof #1735.
% 229.95/41.30  | 
% 229.95/41.30  End of proof
% 229.95/41.30  
% 229.95/41.30  Sub-proof #930 shows that the following formulas are inconsistent:
% 229.95/41.30  ----------------------------------------------------------------
% 229.95/41.30    (1)  all_57_10 = e0
% 229.95/41.30    (2)   ~ (e3 = e1)
% 229.95/41.30    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.95/41.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.95/41.30    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1)
% 229.95/41.30    (5)   ~ (e3 = e2)
% 229.95/41.30    (6)   ~ (e3 = e0)
% 229.95/41.30    (7)  all_57_6 = e0
% 229.95/41.30    (8)  all_57_0 = e0
% 229.95/41.30    (9)  all_57_15 = e3
% 229.95/41.30    (10)  op(e3, e3) = e0
% 229.95/41.30    (11)   ~ (e2 = e0)
% 229.95/41.30    (12)   ~ (e1 = e0)
% 229.95/41.30    (13)  op(e0, e0) = e3
% 229.95/41.30    (14)  all_57_11 = e1
% 229.95/41.30    (15)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.95/41.30          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.95/41.30    (16)   ~ (e2 = e1)
% 229.95/41.30    (17)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.95/41.30          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.95/41.30    (18)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.95/41.30          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.95/41.30    (19)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.95/41.30          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.95/41.30  
% 229.95/41.30  Begin of proof
% 229.95/41.30  | 
% 229.95/41.30  | BETA: splitting (4) gives:
% 229.95/41.30  | 
% 229.95/41.30  | Case 1:
% 229.95/41.30  | | 
% 229.95/41.30  | |   (20)  all_57_0 = e1 & op(e3, e3) = e1
% 229.95/41.30  | | 
% 229.95/41.30  | | ALPHA: (20) implies:
% 229.95/41.30  | |   (21)  all_57_0 = e1
% 229.95/41.30  | | 
% 229.95/41.30  | | COMBINE_EQS: (8), (21) imply:
% 229.95/41.30  | |   (22)  e1 = e0
% 229.95/41.30  | | 
% 229.95/41.30  | | REF_CLOSE: (1), (2), (3), (5), (9), (11), (12), (13), (14), (16), (17),
% 229.95/41.30  | |            (19), (22) are inconsistent by sub-proof #932.
% 229.95/41.30  | | 
% 229.95/41.30  | Case 2:
% 229.95/41.30  | | 
% 229.95/41.30  | |   (23)  all_57_2 = e1 & op(e2, e3) = e1
% 229.95/41.30  | | 
% 229.95/41.30  | | ALPHA: (23) implies:
% 229.95/41.30  | |   (24)  all_57_2 = e1
% 229.95/41.30  | | 
% 229.95/41.30  | | REF_CLOSE: (2), (3), (5), (6), (7), (10), (11), (15), (16), (18), (24) are
% 229.95/41.30  | |            inconsistent by sub-proof #2390.
% 229.95/41.30  | | 
% 229.95/41.30  | End of split
% 229.95/41.30  | 
% 229.95/41.30  End of proof
% 229.95/41.30  
% 229.95/41.30  Sub-proof #931 shows that the following formulas are inconsistent:
% 229.95/41.30  ----------------------------------------------------------------
% 229.95/41.30    (1)  all_57_10 = e0
% 229.95/41.30    (2)   ~ (e3 = e1)
% 229.95/41.30    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.95/41.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.95/41.30    (4)   ~ (e3 = e2)
% 229.95/41.30    (5)  all_57_15 = e3
% 229.95/41.30    (6)   ~ (e2 = e0)
% 229.95/41.30    (7)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.95/41.30    (8)   ~ (e1 = e0)
% 229.95/41.30    (9)  op(e0, e0) = e3
% 229.95/41.30    (10)  all_57_13 = e0
% 229.95/41.30    (11)  all_57_11 = e1
% 229.95/41.30    (12)   ~ (e2 = e1)
% 229.95/41.30    (13)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.95/41.30          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.95/41.30    (14)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.95/41.30          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.95/41.30    (15)  all_57_7 = e0
% 229.95/41.30  
% 229.95/41.30  Begin of proof
% 229.95/41.30  | 
% 229.95/41.30  | BETA: splitting (7) gives:
% 229.95/41.30  | 
% 229.95/41.30  | Case 1:
% 229.95/41.30  | | 
% 229.95/41.30  | |   (16)  all_57_7 = e1 & op(e1, e2) = e1
% 229.95/41.30  | | 
% 229.95/41.30  | | ALPHA: (16) implies:
% 229.95/41.30  | |   (17)  all_57_7 = e1
% 229.95/41.30  | | 
% 229.95/41.30  | | COMBINE_EQS: (15), (17) imply:
% 229.95/41.30  | |   (18)  e1 = e0
% 229.95/41.30  | | 
% 229.95/41.30  | | COMBINE_EQS: (11), (18) imply:
% 229.95/41.30  | |   (19)  all_57_11 = e0
% 229.95/41.30  | | 
% 229.95/41.30  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (12), (13), (14), (19)
% 229.95/41.30  | |            are inconsistent by sub-proof #1087.
% 229.95/41.30  | | 
% 229.95/41.30  | Case 2:
% 229.95/41.30  | | 
% 229.95/41.30  | |   (20)  all_57_13 = e1 & op(e0, e2) = e1
% 229.95/41.30  | | 
% 229.95/41.30  | | ALPHA: (20) implies:
% 229.95/41.30  | |   (21)  all_57_13 = e1
% 229.95/41.30  | | 
% 229.95/41.30  | | COMBINE_EQS: (10), (21) imply:
% 229.95/41.30  | |   (22)  e1 = e0
% 229.95/41.30  | | 
% 229.95/41.30  | | COMBINE_EQS: (11), (22) imply:
% 229.95/41.30  | |   (23)  all_57_11 = e0
% 229.95/41.30  | | 
% 229.95/41.30  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (12), (13), (14), (23)
% 229.95/41.30  | |            are inconsistent by sub-proof #1087.
% 229.95/41.30  | | 
% 229.95/41.30  | End of split
% 229.95/41.30  | 
% 229.95/41.30  End of proof
% 229.95/41.30  
% 229.95/41.30  Sub-proof #932 shows that the following formulas are inconsistent:
% 229.95/41.30  ----------------------------------------------------------------
% 229.95/41.30    (1)  e1 = e0
% 229.95/41.30    (2)  all_57_10 = e0
% 229.95/41.30    (3)   ~ (e3 = e1)
% 229.95/41.30    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.95/41.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.95/41.30    (5)   ~ (e3 = e2)
% 229.95/41.30    (6)  all_57_15 = e3
% 229.95/41.30    (7)   ~ (e2 = e0)
% 229.95/41.30    (8)   ~ (e1 = e0)
% 229.95/41.30    (9)  op(e0, e0) = e3
% 229.95/41.30    (10)  all_57_11 = e1
% 229.95/41.30    (11)   ~ (e2 = e1)
% 229.95/41.30    (12)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.95/41.30          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.95/41.30    (13)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.95/41.30          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.95/41.30  
% 229.95/41.30  Begin of proof
% 229.95/41.30  | 
% 229.95/41.30  | SIMP: (1) implies:
% 229.95/41.30  |   (14)  e1 = e0
% 229.95/41.30  | 
% 229.95/41.30  | COMBINE_EQS: (10), (14) imply:
% 229.95/41.30  |   (15)  all_57_11 = e0
% 229.95/41.30  | 
% 229.95/41.30  | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13), (15) are
% 229.95/41.30  |            inconsistent by sub-proof #1087.
% 229.95/41.30  | 
% 229.95/41.30  End of proof
% 229.95/41.30  
% 229.95/41.30  Sub-proof #933 shows that the following formulas are inconsistent:
% 229.95/41.30  ----------------------------------------------------------------
% 229.95/41.30    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.95/41.30         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.95/41.30    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.95/41.30         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.95/41.30    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.95/41.30         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.95/41.30    (4)   ~ (e3 = e1)
% 229.95/41.30    (5)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 229.95/41.30         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 229.95/41.30    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.95/41.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.95/41.30    (7)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.95/41.30         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.95/41.30    (8)   ~ (all_6_2 = e3)
% 229.95/41.30    (9)  op(e1, e1) = all_6_2
% 229.95/41.30    (10)  op(e2, e2) = e1
% 229.95/41.30    (11)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.95/41.30          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.95/41.31    (12)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.95/41.31          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.95/41.31    (13)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.95/41.31          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.95/41.31    (14)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 229.95/41.31          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.95/41.31    (15)   ~ (e3 = e2)
% 229.95/41.31    (16)   ~ (e3 = e0)
% 229.95/41.31    (17)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 229.95/41.31          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 229.95/41.31    (18)  op(e0, e3) = all_53_3
% 229.95/41.31    (19)  all_57_0 = e0
% 229.95/41.31    (20)  all_57_15 = e3
% 229.95/41.31    (21)  op(e3, e3) = e0
% 229.95/41.31    (22)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.95/41.31          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.95/41.31            e1)
% 229.95/41.31    (23)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.95/41.31          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.95/41.31    (24)   ~ (e2 = e0)
% 229.95/41.31    (25)  all_57_3 = e1
% 229.95/41.31    (26)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.95/41.31          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.95/41.31    (27)   ~ (e1 = e0)
% 229.95/41.31    (28)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.95/41.31          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.95/41.31    (29)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.95/41.31          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.95/41.31    (30)  op(e0, e0) = e3
% 229.95/41.31    (31)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.95/41.31          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.95/41.31            e2)
% 229.95/41.31    (32)   ~ (all_53_3 = e0)
% 229.95/41.31    (33)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.95/41.31              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.95/41.31                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.95/41.31                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.95/41.31    (34)  op(e1, e1) = e0
% 229.95/41.31    (35)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.95/41.31          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.95/41.31    (36)   ~ (all_53_12 = e3)
% 229.95/41.31    (37)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.95/41.31          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.95/41.31    (38)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.95/41.31          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.95/41.31    (39)   ~ (all_53_12 = e0)
% 229.95/41.31    (40)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.95/41.31          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 229.95/41.31    (41)   ~ (e2 = e1)
% 229.95/41.31    (42)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.95/41.31          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.95/41.31    (43)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.95/41.31          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.95/41.31    (44)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 229.95/41.31          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 229.95/41.31    (45)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.95/41.31          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.95/41.31    (46)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.95/41.31          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.95/41.31    (47)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 229.95/41.31          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 229.95/41.31    (48)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.95/41.31          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.95/41.31    (49)  all_57_7 = e0
% 229.95/41.31    (50)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 229.95/41.31          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 229.95/41.31    (51)  op(e3, e0) = all_53_12
% 229.95/41.31  
% 229.95/41.31  Begin of proof
% 229.95/41.31  | 
% 229.95/41.31  | BETA: splitting (29) gives:
% 229.95/41.31  | 
% 229.95/41.31  | Case 1:
% 229.95/41.31  | | 
% 229.95/41.31  | |   (52)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 229.95/41.31  | |           e3)
% 229.95/41.31  | | 
% 229.95/41.31  | | BETA: splitting (52) gives:
% 229.95/41.31  | | 
% 229.95/41.31  | | Case 1:
% 229.95/41.31  | | | 
% 229.95/41.31  | | |   (53)  all_57_1 = e3 & op(e3, e2) = e3
% 229.95/41.31  | | | 
% 229.95/41.31  | | | ALPHA: (53) implies:
% 229.95/41.31  | | |   (54)  all_57_1 = e3
% 229.95/41.31  | | | 
% 229.95/41.31  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 229.95/41.31  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 229.95/41.31  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 229.95/41.31  | | |            (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 229.95/41.31  | | |            (43), (44), (45), (46), (47), (48), (49), (50), (51), (54) are
% 229.95/41.31  | | |            inconsistent by sub-proof #934.
% 229.95/41.31  | | | 
% 229.95/41.31  | | Case 2:
% 229.95/41.31  | | | 
% 229.95/41.31  | | |   (55)  all_57_3 = e3 & op(e2, e2) = e3
% 229.95/41.31  | | | 
% 229.95/41.31  | | | ALPHA: (55) implies:
% 229.95/41.31  | | |   (56)  op(e2, e2) = e3
% 229.95/41.31  | | | 
% 229.95/41.31  | | | REF_CLOSE: (4), (6), (10), (56) are inconsistent by sub-proof #1912.
% 229.95/41.31  | | | 
% 229.95/41.31  | | End of split
% 229.95/41.31  | | 
% 229.95/41.31  | Case 2:
% 229.95/41.31  | | 
% 229.95/41.31  | |   (57)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 229.95/41.31  | |           e3)
% 229.95/41.31  | | 
% 229.95/41.31  | | REF_CLOSE: (4), (6), (15), (16), (20), (22), (24), (27), (30), (31), (33),
% 229.95/41.31  | |            (41), (49), (57) are inconsistent by sub-proof #993.
% 229.95/41.31  | | 
% 229.95/41.31  | End of split
% 229.95/41.31  | 
% 229.95/41.31  End of proof
% 229.95/41.31  
% 229.95/41.31  Sub-proof #934 shows that the following formulas are inconsistent:
% 229.95/41.31  ----------------------------------------------------------------
% 229.95/41.31    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.95/41.31         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.95/41.31    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.95/41.31         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.95/41.31    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.95/41.31         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.95/41.31    (4)   ~ (e3 = e1)
% 229.95/41.31    (5)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 229.95/41.31         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 229.95/41.31    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.95/41.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.95/41.31    (7)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.95/41.31         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.95/41.31    (8)   ~ (all_6_2 = e3)
% 229.95/41.31    (9)  op(e1, e1) = all_6_2
% 229.95/41.31    (10)  op(e2, e2) = e1
% 229.95/41.31    (11)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.95/41.31          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.95/41.31    (12)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.95/41.31          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.95/41.31    (13)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.95/41.31          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.95/41.31    (14)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 229.95/41.31          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.95/41.31    (15)   ~ (e3 = e2)
% 229.95/41.31    (16)   ~ (e3 = e0)
% 229.95/41.31    (17)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 229.95/41.31          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 229.95/41.31    (18)  op(e0, e3) = all_53_3
% 229.95/41.31    (19)  all_57_0 = e0
% 229.95/41.31    (20)  all_57_15 = e3
% 229.95/41.31    (21)  op(e3, e3) = e0
% 229.95/41.31    (22)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.95/41.31          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.95/41.31            e1)
% 229.95/41.31    (23)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.95/41.31          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.95/41.31    (24)   ~ (e2 = e0)
% 229.95/41.31    (25)  all_57_3 = e1
% 229.95/41.31    (26)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.95/41.31          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.95/41.31    (27)   ~ (e1 = e0)
% 229.95/41.31    (28)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.95/41.31          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.95/41.31    (29)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.95/41.31          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.95/41.31    (30)  op(e0, e0) = e3
% 229.95/41.31    (31)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.95/41.31          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.95/41.31            e2)
% 229.95/41.31    (32)   ~ (all_53_3 = e0)
% 229.95/41.31    (33)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.95/41.31              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.95/41.31                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.95/41.31                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.95/41.31    (34)  op(e1, e1) = e0
% 229.95/41.31    (35)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.95/41.31          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.95/41.31    (36)   ~ (all_53_12 = e3)
% 229.95/41.31    (37)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.95/41.31          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.95/41.31    (38)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.95/41.31          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.95/41.31    (39)  all_57_1 = e3
% 229.95/41.31    (40)   ~ (all_53_12 = e0)
% 229.95/41.31    (41)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.95/41.31          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 229.95/41.31    (42)   ~ (e2 = e1)
% 229.95/41.31    (43)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.95/41.31          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.95/41.31    (44)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.95/41.31          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.95/41.31    (45)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 229.95/41.31          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 229.95/41.31    (46)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.95/41.31          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.95/41.31    (47)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.95/41.31          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.95/41.31    (48)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 229.95/41.31          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 229.95/41.31    (49)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.95/41.31          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.95/41.31    (50)  all_57_7 = e0
% 229.95/41.31    (51)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 229.95/41.31          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 229.95/41.31    (52)  op(e3, e0) = all_53_12
% 229.95/41.31  
% 229.95/41.31  Begin of proof
% 229.95/41.31  | 
% 229.95/41.31  | BETA: splitting (3) gives:
% 229.95/41.31  | 
% 229.95/41.31  | Case 1:
% 229.95/41.31  | | 
% 229.95/41.31  | |   (53)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 229.95/41.31  | |           e2)
% 229.95/41.31  | | 
% 229.95/41.31  | | REF_CLOSE: (6), (10), (15), (39), (42), (53) are inconsistent by sub-proof
% 229.95/41.31  | |            #1768.
% 229.95/41.31  | | 
% 229.95/41.31  | Case 2:
% 229.95/41.31  | | 
% 229.95/41.31  | |   (54)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 229.95/41.31  | |           e2)
% 229.95/41.31  | | 
% 229.95/41.31  | | BETA: splitting (54) gives:
% 229.95/41.31  | | 
% 229.95/41.31  | | Case 1:
% 229.95/41.31  | | | 
% 229.95/41.31  | | |   (55)  all_57_7 = e2 & op(e1, e2) = e2
% 229.95/41.31  | | | 
% 229.95/41.31  | | | ALPHA: (55) implies:
% 229.95/41.31  | | |   (56)  all_57_7 = e2
% 229.95/41.31  | | | 
% 229.95/41.31  | | | REF_CLOSE: (24), (50), (56) are inconsistent by sub-proof #2207.
% 229.95/41.31  | | | 
% 229.95/41.31  | | Case 2:
% 229.95/41.31  | | | 
% 229.95/41.31  | | |   (57)  all_57_13 = e2 & op(e0, e2) = e2
% 229.95/41.31  | | | 
% 229.95/41.31  | | | ALPHA: (57) implies:
% 229.95/41.31  | | |   (58)  all_57_13 = e2
% 229.95/41.31  | | | 
% 229.95/41.31  | | | BETA: splitting (7) gives:
% 229.95/41.31  | | | 
% 229.95/41.31  | | | Case 1:
% 229.95/41.31  | | | | 
% 229.95/41.31  | | | |   (59)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2)
% 229.95/41.31  | | | |           = e3)
% 229.95/41.31  | | | | 
% 229.95/41.31  | | | | BETA: splitting (59) gives:
% 229.95/41.31  | | | | 
% 229.95/41.31  | | | | Case 1:
% 229.95/41.31  | | | | | 
% 229.95/41.31  | | | | |   (60)  all_57_6 = e3 & op(e1, e3) = e3
% 229.95/41.31  | | | | | 
% 229.95/41.31  | | | | | ALPHA: (60) implies:
% 229.95/41.31  | | | | |   (61)  all_57_6 = e3
% 229.95/41.31  | | | | | 
% 229.95/41.31  | | | | | BETA: splitting (48) gives:
% 229.95/41.31  | | | | | 
% 229.95/41.31  | | | | | Case 1:
% 229.95/41.31  | | | | | | 
% 229.95/41.31  | | | | | |   (62)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1,
% 229.95/41.31  | | | | | |             e2) = e1)
% 229.95/41.31  | | | | | | 
% 229.95/41.31  | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (15), (16), (20), (24), (27),
% 229.95/41.31  | | | | | |            (33), (42), (43), (47), (50), (62) are inconsistent by
% 229.95/41.31  | | | | | |            sub-proof #1155.
% 229.95/41.31  | | | | | | 
% 229.95/41.31  | | | | | Case 2:
% 229.95/41.31  | | | | | | 
% 229.95/41.31  | | | | | |   (63)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1,
% 229.95/41.31  | | | | | |             e0) = e1)
% 229.95/41.31  | | | | | | 
% 229.95/41.31  | | | | | | BETA: splitting (63) gives:
% 229.95/41.31  | | | | | | 
% 229.95/41.31  | | | | | | Case 1:
% 229.95/41.31  | | | | | | | 
% 229.95/41.31  | | | | | | |   (64)  all_57_8 = e1 & op(e1, e1) = e1
% 229.95/41.31  | | | | | | | 
% 229.95/41.31  | | | | | | | ALPHA: (64) implies:
% 229.95/41.31  | | | | | | |   (65)  op(e1, e1) = e1
% 229.95/41.31  | | | | | | | 
% 229.95/41.31  | | | | | | | REF_CLOSE: (6), (27), (34), (65) are inconsistent by sub-proof
% 229.95/41.31  | | | | | | |            #2427.
% 229.95/41.31  | | | | | | | 
% 229.95/41.31  | | | | | | Case 2:
% 229.95/41.31  | | | | | | | 
% 229.95/41.31  | | | | | | |   (66)  all_57_11 = e1 & op(e1, e0) = e1
% 229.95/41.31  | | | | | | | 
% 229.95/41.31  | | | | | | | ALPHA: (66) implies:
% 229.95/41.31  | | | | | | |   (67)  all_57_11 = e1
% 229.95/41.31  | | | | | | | 
% 229.95/41.31  | | | | | | | BETA: splitting (51) gives:
% 229.95/41.31  | | | | | | | 
% 229.95/41.31  | | | | | | | Case 1:
% 229.95/41.31  | | | | | | | | 
% 229.95/41.31  | | | | | | | |   (68)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 &
% 229.95/41.31  | | | | | | | |           op(e1, e2) = e2)
% 229.95/41.31  | | | | | | | | 
% 229.95/41.31  | | | | | | | | BETA: splitting (68) gives:
% 229.95/41.31  | | | | | | | | 
% 229.95/41.31  | | | | | | | | Case 1:
% 229.95/41.31  | | | | | | | | | 
% 229.95/41.31  | | | | | | | | |   (69)  all_57_6 = e2 & op(e1, e3) = e2
% 229.95/41.31  | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | REF_CLOSE: (15), (61), (69) are inconsistent by sub-proof
% 229.95/41.31  | | | | | | | | |            #2012.
% 229.95/41.31  | | | | | | | | | 
% 229.95/41.31  | | | | | | | | Case 2:
% 229.95/41.31  | | | | | | | | | 
% 229.95/41.31  | | | | | | | | |   (70)  all_57_7 = e2 & op(e1, e2) = e2
% 229.95/41.31  | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | ALPHA: (70) implies:
% 229.95/41.31  | | | | | | | | |   (71)  all_57_7 = e2
% 229.95/41.31  | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | COMBINE_EQS: (50), (71) imply:
% 229.95/41.31  | | | | | | | | |   (72)  e2 = e0
% 229.95/41.31  | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | SIMP: (72) implies:
% 229.95/41.31  | | | | | | | | |   (73)  e2 = e0
% 229.95/41.31  | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | COMBINE_EQS: (58), (73) imply:
% 229.95/41.31  | | | | | | | | |   (74)  all_57_13 = e0
% 229.95/41.31  | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | REF_CLOSE: (3), (6), (10), (15), (24), (39), (42), (50), (74)
% 229.95/41.31  | | | | | | | | |            are inconsistent by sub-proof #1767.
% 229.95/41.31  | | | | | | | | | 
% 229.95/41.31  | | | | | | | | End of split
% 229.95/41.31  | | | | | | | | 
% 229.95/41.31  | | | | | | | Case 2:
% 229.95/41.31  | | | | | | | | 
% 229.95/41.31  | | | | | | | |   (75)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 &
% 229.95/41.31  | | | | | | | |           op(e1, e0) = e2)
% 229.95/41.31  | | | | | | | | 
% 229.95/41.31  | | | | | | | | BETA: splitting (75) gives:
% 229.95/41.31  | | | | | | | | 
% 229.95/41.31  | | | | | | | | Case 1:
% 229.95/41.31  | | | | | | | | | 
% 229.95/41.31  | | | | | | | | |   (76)  all_57_8 = e2 & op(e1, e1) = e2
% 229.95/41.31  | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | ALPHA: (76) implies:
% 229.95/41.31  | | | | | | | | |   (77)  all_57_8 = e2
% 229.95/41.31  | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | BETA: splitting (33) gives:
% 229.95/41.31  | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | Case 1:
% 229.95/41.31  | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | |   (78)  all_57_15 = e0 & op(e0, e0) = e0
% 229.95/41.31  | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | ALPHA: (78) implies:
% 229.95/41.31  | | | | | | | | | |   (79)  op(e0, e0) = e0
% 229.95/41.31  | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | REF_CLOSE: (6), (16), (30), (79) are inconsistent by
% 229.95/41.31  | | | | | | | | | |            sub-proof #2304.
% 229.95/41.31  | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | Case 2:
% 229.95/41.31  | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | |   (80)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0
% 229.95/41.31  | | | | | | | | | |             & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 229.95/41.31  | | | | | | | | | |               e0) = e0)) & ((all_57_12 = e0 & op(e0, e3) =
% 229.95/41.31  | | | | | | | | | |             e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 229.95/41.31  | | | | | | | | | |           (all_57_14 = e0 & op(e0, e1) = e0))
% 229.95/41.31  | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | ALPHA: (80) implies:
% 229.95/41.31  | | | | | | | | | |   (81)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0
% 229.95/41.31  | | | | | | | | | |           & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1)
% 229.95/41.31  | | | | | | | | | |           = e0)
% 229.95/41.31  | | | | | | | | | |   (82)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0
% 229.95/41.31  | | | | | | | | | |           & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.95/41.31  | | | | | | | | | |           = e0)
% 229.95/41.31  | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | BETA: splitting (2) gives:
% 229.95/41.31  | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | Case 1:
% 229.95/41.31  | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | |   (83)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 229.95/41.31  | | | | | | | | | | |           & op(e2, e3) = e1)
% 229.95/41.31  | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10),
% 229.95/41.31  | | | | | | | | | | |            (13), (15), (16), (18), (19), (20), (21), (22),
% 229.95/41.31  | | | | | | | | | | |            (23), (24), (25), (26), (27), (29), (30), (32),
% 229.95/41.31  | | | | | | | | | | |            (33), (35), (36), (37), (38), (39), (40), (41),
% 229.95/41.31  | | | | | | | | | | |            (42), (43), (44), (47), (49), (52), (61), (83) are
% 229.95/41.31  | | | | | | | | | | |            inconsistent by sub-proof #937.
% 229.95/41.31  | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | Case 2:
% 229.95/41.31  | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | |   (84)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 229.95/41.31  | | | | | | | | | | |           e1 & op(e0, e3) = e1)
% 229.95/41.31  | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | BETA: splitting (84) gives:
% 229.95/41.31  | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | Case 1:
% 229.95/41.31  | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | |   (85)  all_57_6 = e1 & op(e1, e3) = e1
% 229.95/41.31  | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | ALPHA: (85) implies:
% 229.95/41.31  | | | | | | | | | | | |   (86)  all_57_6 = e1
% 229.95/41.31  | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (15), (16), (20), (24),
% 229.95/41.31  | | | | | | | | | | | |            (27), (33), (42), (43), (47), (50), (86) are
% 229.95/41.31  | | | | | | | | | | | |            inconsistent by sub-proof #1735.
% 229.95/41.31  | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | Case 2:
% 229.95/41.31  | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | |   (87)  all_57_12 = e1 & op(e0, e3) = e1
% 229.95/41.31  | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | ALPHA: (87) implies:
% 229.95/41.31  | | | | | | | | | | | |   (88)  all_57_12 = e1
% 229.95/41.31  | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | BETA: splitting (44) gives:
% 229.95/41.31  | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | Case 1:
% 229.95/41.31  | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | |   (89)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 229.95/41.31  | | | | | | | | | | | | |           & op(e2, e3) = e2)
% 229.95/41.31  | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | BETA: splitting (89) gives:
% 229.95/41.31  | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | Case 1:
% 229.95/41.31  | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | |   (90)  all_57_0 = e2 & op(e3, e3) = e2
% 229.95/41.31  | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | ALPHA: (90) implies:
% 229.95/41.31  | | | | | | | | | | | | | |   (91)  op(e3, e3) = e2
% 229.95/41.31  | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | REF_CLOSE: (6), (21), (24), (91) are inconsistent by
% 229.95/41.31  | | | | | | | | | | | | | |            sub-proof #2403.
% 229.95/41.31  | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | Case 2:
% 229.95/41.31  | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | |   (92)  all_57_2 = e2 & op(e2, e3) = e2
% 229.95/41.31  | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | ALPHA: (92) implies:
% 229.95/41.31  | | | | | | | | | | | | | |   (93)  all_57_2 = e2
% 229.95/41.31  | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | BETA: splitting (35) gives:
% 229.95/41.31  | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | Case 1:
% 229.95/41.31  | | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | |   (94)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 229.95/41.31  | | | | | | | | | | | | | | |           & op(e2, e2) = e3)
% 229.95/41.31  | | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | | BETA: splitting (94) gives:
% 229.95/41.31  | | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | | Case 1:
% 229.95/41.31  | | | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | | |   (95)  all_57_2 = e3 & op(e2, e3) = e3
% 229.95/41.31  | | | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | | | ALPHA: (95) implies:
% 229.95/41.31  | | | | | | | | | | | | | | | |   (96)  all_57_2 = e3
% 229.95/41.31  | | | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 229.95/41.31  | | | | | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 229.95/41.31  | | | | | | | | | | | | | | | |            (20), (21), (22), (23), (24), (25), (26), (27),
% 229.95/41.31  | | | | | | | | | | | | | | | |            (28), (29), (30), (31), (32), (33), (35), (36),
% 229.95/41.31  | | | | | | | | | | | | | | | |            (37), (38), (40), (42), (43), (44), (45), (46),
% 229.95/41.31  | | | | | | | | | | | | | | | |            (47), (48), (49), (50), (51), (52), (88), (96) are
% 229.95/41.31  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1014.
% 229.95/41.31  | | | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | | Case 2:
% 229.95/41.31  | | | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | | |   (97)  all_57_3 = e3 & op(e2, e2) = e3
% 229.95/41.31  | | | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | | | ALPHA: (97) implies:
% 229.95/41.31  | | | | | | | | | | | | | | | |   (98)  op(e2, e2) = e3
% 229.95/41.31  | | | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (10), (98) are inconsistent by sub-proof
% 229.95/41.31  | | | | | | | | | | | | | | | |            #1912.
% 229.95/41.31  | | | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | | End of split
% 229.95/41.31  | | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | Case 2:
% 229.95/41.31  | | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | |   (99)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 229.95/41.31  | | | | | | | | | | | | | | |           e3 & op(e2, e0) = e3)
% 229.95/41.31  | | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | | BETA: splitting (99) gives:
% 229.95/41.31  | | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | | Case 1:
% 229.95/41.31  | | | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | | |   (100)  all_57_5 = e3 & op(e2, e1) = e3
% 229.95/41.31  | | | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | | | ALPHA: (100) implies:
% 229.95/41.31  | | | | | | | | | | | | | | | |   (101)  all_57_5 = e3
% 229.95/41.31  | | | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | | | BETA: splitting (81) gives:
% 229.95/41.31  | | | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | | | Case 1:
% 229.95/41.31  | | | | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | | | |   (102)  all_57_12 = e0 & op(e0, e3) = e0
% 229.95/41.31  | | | | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | | | | ALPHA: (102) implies:
% 229.95/41.31  | | | | | | | | | | | | | | | | |   (103)  all_57_12 = e0
% 229.95/41.31  | | | | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (15), (19), (24), (27), (42), (44),
% 229.95/41.31  | | | | | | | | | | | | | | | | |            (61), (103) are inconsistent by sub-proof #1425.
% 229.95/41.31  | | | | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | | | Case 2:
% 229.95/41.31  | | | | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | | | |   (104)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 229.95/41.31  | | | | | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 229.95/41.31  | | | | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | | | | BETA: splitting (104) gives:
% 229.95/41.31  | | | | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | | | | Case 1:
% 229.95/41.31  | | | | | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | | | | |   (105)  all_57_13 = e0 & op(e0, e2) = e0
% 229.95/41.31  | | | | | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | | | | | ALPHA: (105) implies:
% 229.95/41.31  | | | | | | | | | | | | | | | | | |   (106)  all_57_13 = e0
% 229.95/41.31  | | | | | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (10), (15), (24), (39), (42), (50),
% 229.95/41.31  | | | | | | | | | | | | | | | | | |            (106) are inconsistent by sub-proof #1767.
% 229.95/41.31  | | | | | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | | | | Case 2:
% 229.95/41.31  | | | | | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | | | | |   (107)  all_57_14 = e0 & op(e0, e1) = e0
% 229.95/41.31  | | | | | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | | | | | ALPHA: (107) implies:
% 229.95/41.31  | | | | | | | | | | | | | | | | | |   (108)  all_57_14 = e0
% 229.95/41.31  | | | | | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | | | | | BETA: splitting (45) gives:
% 229.95/41.31  | | | | | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | | | | | Case 1:
% 229.95/41.31  | | | | | | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | | | | | |   (109)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 229.95/41.31  | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e2)
% 229.95/41.31  | | | | | | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | | | | | | BETA: splitting (109) gives:
% 229.95/41.31  | | | | | | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | | | | | | Case 1:
% 229.95/41.31  | | | | | | | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | | | | | | |   (110)  all_57_4 = e2 & op(e3, e1) = e2
% 229.95/41.31  | | | | | | | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | | | | | | | ALPHA: (110) implies:
% 229.95/41.31  | | | | | | | | | | | | | | | | | | | |   (111)  all_57_4 = e2
% 229.95/41.31  | | | | | | | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (17), (27), (42), (77), (101), (108), (111)
% 229.95/41.31  | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1456.
% 229.95/41.31  | | | | | | | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | | | | | | Case 2:
% 229.95/41.31  | | | | | | | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | | | | | | |   (112)  all_57_5 = e2 & op(e2, e1) = e2
% 229.95/41.31  | | | | | | | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (15), (16), (21), (38), (61), (88),
% 229.95/41.31  | | | | | | | | | | | | | | | | | | | |            (93), (101), (112) are inconsistent by sub-proof
% 229.95/41.31  | | | | | | | | | | | | | | | | | | | |            #1005.
% 229.95/41.31  | | | | | | | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | | | | | | End of split
% 229.95/41.31  | | | | | | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | | | | | Case 2:
% 229.95/41.31  | | | | | | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | | | | | |   (113)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 229.95/41.31  | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e1) = e2)
% 229.95/41.31  | | | | | | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | | | | | | BETA: splitting (113) gives:
% 229.95/41.31  | | | | | | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | | | | | | Case 1:
% 229.95/41.31  | | | | | | | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | | | | | | | ALPHA: (76) implies:
% 229.95/41.31  | | | | | | | | | | | | | | | | | | | |   (114)  op(e1, e1) = e2
% 229.95/41.31  | | | | | | | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with e0, e2, e1, e1, simplifying
% 229.95/41.31  | | | | | | | | | | | | | | | | | | | |              with (34), (114) gives:
% 229.95/41.31  | | | | | | | | | | | | | | | | | | | |   (115)  e2 = e0
% 229.95/41.31  | | | | | | | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (93), (115) imply:
% 229.95/41.31  | | | | | | | | | | | | | | | | | | | |   (116)  all_57_2 = e0
% 229.95/41.31  | | | | | | | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (15), (16), (20), (21), (22), (24),
% 229.95/41.31  | | | | | | | | | | | | | | | | | | | |            (27), (31), (38), (42), (44), (88), (108), (116)
% 229.95/41.31  | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1555.
% 229.95/41.31  | | | | | | | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | | | | | | Case 2:
% 229.95/41.31  | | | | | | | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | | | | | | |   (117)  all_57_14 = e2 & op(e0, e1) = e2
% 229.95/41.31  | | | | | | | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | | | | | | | ALPHA: (117) implies:
% 229.95/41.31  | | | | | | | | | | | | | | | | | | | |   (118)  all_57_14 = e2
% 229.95/41.31  | | | | | | | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (15), (16), (20), (21), (22), (24),
% 229.95/41.31  | | | | | | | | | | | | | | | | | | | |            (27), (31), (38), (42), (44), (88), (93), (108),
% 229.95/41.31  | | | | | | | | | | | | | | | | | | | |            (118) are inconsistent by sub-proof #936.
% 229.95/41.31  | | | | | | | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | | | | | | End of split
% 229.95/41.31  | | | | | | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | | | | | End of split
% 229.95/41.31  | | | | | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | | | | End of split
% 229.95/41.31  | | | | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | | | End of split
% 229.95/41.31  | | | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | | Case 2:
% 229.95/41.31  | | | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | | |   (119)  all_57_10 = e3 & op(e2, e0) = e3
% 229.95/41.31  | | | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | | | ALPHA: (119) implies:
% 229.95/41.31  | | | | | | | | | | | | | | | |   (120)  all_57_10 = e3
% 229.95/41.31  | | | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (6), (7), (8), (9), (10), (13),
% 229.95/41.31  | | | | | | | | | | | | | | | |            (15), (16), (18), (20), (21), (22), (23), (24),
% 229.95/41.31  | | | | | | | | | | | | | | | |            (25), (26), (27), (29), (30), (32), (33), (36),
% 229.95/41.31  | | | | | | | | | | | | | | | |            (38), (40), (42), (43), (44), (47), (49), (52),
% 229.95/41.31  | | | | | | | | | | | | | | | |            (61), (82), (120) are inconsistent by sub-proof
% 229.95/41.31  | | | | | | | | | | | | | | | |            #982.
% 229.95/41.31  | | | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | | End of split
% 229.95/41.31  | | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | End of split
% 229.95/41.31  | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | End of split
% 229.95/41.31  | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | Case 2:
% 229.95/41.31  | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | |   (121)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 229.95/41.31  | | | | | | | | | | | | |            e2 & op(e0, e3) = e2)
% 229.95/41.31  | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | BETA: splitting (121) gives:
% 229.95/41.31  | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | Case 1:
% 229.95/41.31  | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | |   (122)  all_57_6 = e2 & op(e1, e3) = e2
% 229.95/41.31  | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | ALPHA: (122) implies:
% 229.95/41.31  | | | | | | | | | | | | | |   (123)  all_57_6 = e2
% 229.95/41.31  | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 229.95/41.31  | | | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 229.95/41.31  | | | | | | | | | | | | | |            (20), (21), (22), (23), (24), (25), (26), (27),
% 229.95/41.31  | | | | | | | | | | | | | |            (28), (29), (30), (31), (32), (33), (35), (36),
% 229.95/41.31  | | | | | | | | | | | | | |            (37), (38), (40), (42), (43), (44), (45), (46),
% 229.95/41.31  | | | | | | | | | | | | | |            (47), (48), (49), (50), (51), (52), (88), (123)
% 229.95/41.31  | | | | | | | | | | | | | |            are inconsistent by sub-proof #989.
% 229.95/41.31  | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | Case 2:
% 229.95/41.31  | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | |   (124)  all_57_12 = e2 & op(e0, e3) = e2
% 229.95/41.31  | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | ALPHA: (124) implies:
% 229.95/41.31  | | | | | | | | | | | | | |   (125)  all_57_12 = e2
% 229.95/41.31  | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | COMBINE_EQS: (88), (125) imply:
% 229.95/41.31  | | | | | | | | | | | | | |   (126)  e2 = e1
% 229.95/41.31  | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 229.95/41.31  | | | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 229.95/41.31  | | | | | | | | | | | | | |            (19), (20), (21), (22), (23), (24), (25), (26),
% 229.95/41.31  | | | | | | | | | | | | | |            (27), (28), (29), (30), (31), (32), (33), (35),
% 229.95/41.31  | | | | | | | | | | | | | |            (36), (37), (38), (40), (41), (42), (43), (44),
% 229.95/41.31  | | | | | | | | | | | | | |            (45), (46), (47), (48), (49), (51), (52), (58),
% 229.95/41.31  | | | | | | | | | | | | | |            (126) are inconsistent by sub-proof #935.
% 229.95/41.31  | | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | | End of split
% 229.95/41.31  | | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | | End of split
% 229.95/41.31  | | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | | End of split
% 229.95/41.31  | | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | | End of split
% 229.95/41.31  | | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | End of split
% 229.95/41.31  | | | | | | | | | 
% 229.95/41.31  | | | | | | | | Case 2:
% 229.95/41.31  | | | | | | | | | 
% 229.95/41.31  | | | | | | | | |   (127)  all_57_11 = e2 & op(e1, e0) = e2
% 229.95/41.31  | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | ALPHA: (127) implies:
% 229.95/41.31  | | | | | | | | |   (128)  all_57_11 = e2
% 229.95/41.31  | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | COMBINE_EQS: (67), (128) imply:
% 229.95/41.31  | | | | | | | | |   (129)  e2 = e1
% 229.95/41.31  | | | | | | | | | 
% 229.95/41.31  | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 229.95/41.31  | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 229.95/41.31  | | | | | | | | |            (19), (20), (21), (22), (23), (24), (25), (26),
% 229.95/41.31  | | | | | | | | |            (27), (28), (29), (30), (31), (32), (33), (35),
% 229.95/41.31  | | | | | | | | |            (36), (37), (38), (40), (41), (42), (43), (44),
% 229.95/41.31  | | | | | | | | |            (45), (46), (47), (48), (49), (51), (52), (58),
% 229.95/41.31  | | | | | | | | |            (129) are inconsistent by sub-proof #935.
% 229.95/41.31  | | | | | | | | | 
% 229.95/41.31  | | | | | | | | End of split
% 229.95/41.31  | | | | | | | | 
% 229.95/41.31  | | | | | | | End of split
% 229.95/41.31  | | | | | | | 
% 229.95/41.31  | | | | | | End of split
% 229.95/41.31  | | | | | | 
% 229.95/41.31  | | | | | End of split
% 229.95/41.31  | | | | | 
% 229.95/41.31  | | | | Case 2:
% 229.95/41.32  | | | | | 
% 229.95/41.32  | | | | |   (130)  all_57_7 = e3 & op(e1, e2) = e3
% 229.95/41.32  | | | | | 
% 229.95/41.32  | | | | | ALPHA: (130) implies:
% 229.95/41.32  | | | | |   (131)  all_57_7 = e3
% 229.95/41.32  | | | | | 
% 229.95/41.32  | | | | | REF_CLOSE: (3), (4), (6), (10), (11), (12), (15), (16), (19), (21),
% 229.95/41.32  | | | | |            (23), (24), (25), (26), (27), (36), (39), (42), (49), (50),
% 229.95/41.32  | | | | |            (52), (58), (131) are inconsistent by sub-proof #1547.
% 229.95/41.32  | | | | | 
% 229.95/41.32  | | | | End of split
% 229.95/41.32  | | | | 
% 229.95/41.32  | | | Case 2:
% 229.95/41.32  | | | | 
% 229.95/41.32  | | | |   (132)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1,
% 229.95/41.32  | | | |              e0) = e3)
% 229.95/41.32  | | | | 
% 229.95/41.32  | | | | REF_CLOSE: (4), (6), (8), (9), (15), (16), (20), (24), (27), (33), (42),
% 229.95/41.32  | | | |            (43), (47), (132) are inconsistent by sub-proof #1786.
% 229.95/41.32  | | | | 
% 229.95/41.32  | | | End of split
% 229.95/41.32  | | | 
% 229.95/41.32  | | End of split
% 229.95/41.32  | | 
% 229.95/41.32  | End of split
% 229.95/41.32  | 
% 229.95/41.32  End of proof
% 229.95/41.32  
% 229.95/41.32  Sub-proof #935 shows that the following formulas are inconsistent:
% 229.95/41.32  ----------------------------------------------------------------
% 229.95/41.32    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.95/41.32         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.95/41.32    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.95/41.32         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.95/41.32    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.95/41.32         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.95/41.32    (4)   ~ (e3 = e1)
% 229.95/41.32    (5)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 229.95/41.32         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 229.95/41.32    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.95/41.32           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.95/41.32    (7)  e2 = e1
% 229.95/41.32    (8)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.95/41.32         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.95/41.32    (9)   ~ (all_6_2 = e3)
% 229.95/41.32    (10)  op(e1, e1) = all_6_2
% 229.95/41.32    (11)  op(e2, e2) = e1
% 229.95/41.32    (12)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.95/41.32          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.95/41.32    (13)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.95/41.32          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.95/41.32    (14)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.95/41.32          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.95/41.32    (15)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 229.95/41.32          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.95/41.32    (16)   ~ (e3 = e2)
% 229.95/41.32    (17)   ~ (e3 = e0)
% 229.95/41.32    (18)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 229.95/41.32          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 229.95/41.32    (19)  op(e0, e3) = all_53_3
% 229.95/41.32    (20)  all_57_0 = e0
% 229.95/41.32    (21)  all_57_15 = e3
% 229.95/41.32    (22)  op(e3, e3) = e0
% 229.95/41.32    (23)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.95/41.32          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.95/41.32            e1)
% 229.95/41.32    (24)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.95/41.32          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.95/41.32    (25)   ~ (e2 = e0)
% 229.95/41.32    (26)  all_57_13 = e2
% 229.95/41.32    (27)  all_57_3 = e1
% 229.95/41.32    (28)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.95/41.32          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.95/41.32    (29)   ~ (e1 = e0)
% 229.95/41.32    (30)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.95/41.32          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.95/41.32    (31)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.95/41.32          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.95/41.32    (32)  op(e0, e0) = e3
% 229.95/41.32    (33)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.95/41.32          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.95/41.32            e2)
% 229.95/41.32    (34)   ~ (all_53_3 = e0)
% 229.95/41.32    (35)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.95/41.32              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.95/41.32                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.95/41.32                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.95/41.32    (36)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.95/41.32          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.95/41.32    (37)   ~ (all_53_12 = e3)
% 229.95/41.32    (38)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.95/41.32          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.95/41.32    (39)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.95/41.32          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.95/41.32    (40)   ~ (all_53_12 = e0)
% 229.95/41.32    (41)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.95/41.32          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 229.95/41.32    (42)   ~ (e2 = e1)
% 229.95/41.32    (43)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.95/41.32          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.95/41.32    (44)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.95/41.32          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.95/41.32    (45)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 229.95/41.32          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 229.95/41.32    (46)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.95/41.32          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.95/41.32    (47)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.95/41.32          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.95/41.32    (48)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 229.95/41.32          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 229.95/41.32    (49)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.95/41.32          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.95/41.32    (50)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 229.95/41.32          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 229.95/41.32    (51)  op(e3, e0) = all_53_12
% 229.95/41.32  
% 229.95/41.32  Begin of proof
% 229.95/41.32  | 
% 229.95/41.32  | SIMP: (7) implies:
% 229.95/41.32  |   (52)  e2 = e1
% 229.95/41.32  | 
% 229.95/41.32  | COMBINE_EQS: (26), (52) imply:
% 229.95/41.32  |   (53)  all_57_13 = e1
% 229.95/41.32  | 
% 229.95/41.32  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13),
% 229.95/41.32  |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 229.95/41.32  |            (25), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 229.95/41.32  |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 229.95/41.32  |            (48), (49), (50), (51), (53) are inconsistent by sub-proof #976.
% 229.95/41.32  | 
% 229.95/41.32  End of proof
% 229.95/41.32  
% 229.95/41.32  Sub-proof #936 shows that the following formulas are inconsistent:
% 229.95/41.32  ----------------------------------------------------------------
% 229.95/41.32    (1)   ~ (e3 = e1)
% 229.95/41.32    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.95/41.32           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.95/41.32    (3)  all_57_2 = e2
% 229.95/41.32    (4)   ~ (e3 = e2)
% 229.95/41.32    (5)   ~ (e3 = e0)
% 229.95/41.32    (6)  all_57_15 = e3
% 229.95/41.32    (7)  op(e3, e3) = e0
% 229.95/41.32    (8)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 229.95/41.32         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.95/41.32    (9)  all_57_12 = e1
% 229.95/41.32    (10)   ~ (e2 = e0)
% 229.95/41.32    (11)   ~ (e1 = e0)
% 229.95/41.32    (12)  all_57_14 = e2
% 229.95/41.32    (13)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.95/41.32          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.95/41.32            e2)
% 229.95/41.32    (14)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.95/41.32          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.95/41.32    (15)   ~ (e2 = e1)
% 229.95/41.32    (16)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.95/41.32          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.95/41.32    (17)  all_57_14 = e0
% 229.95/41.32  
% 229.95/41.32  Begin of proof
% 229.95/41.32  | 
% 229.95/41.32  | COMBINE_EQS: (12), (17) imply:
% 229.95/41.32  |   (18)  e2 = e0
% 229.95/41.32  | 
% 229.95/41.32  | COMBINE_EQS: (3), (18) imply:
% 229.95/41.32  |   (19)  all_57_2 = e0
% 229.95/41.32  | 
% 229.95/41.32  | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (13), (14),
% 229.95/41.32  |            (15), (16), (17), (19) are inconsistent by sub-proof #1555.
% 229.95/41.32  | 
% 229.95/41.32  End of proof
% 229.95/41.32  
% 229.95/41.32  Sub-proof #937 shows that the following formulas are inconsistent:
% 229.95/41.32  ----------------------------------------------------------------
% 229.95/41.32    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.95/41.32         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.95/41.32    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.95/41.32         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.95/41.32    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.95/41.32         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.95/41.32    (4)   ~ (e3 = e1)
% 229.95/41.32    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.95/41.32           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.95/41.32    (6)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.95/41.32         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.95/41.32    (7)   ~ (all_6_2 = e3)
% 229.95/41.32    (8)  op(e1, e1) = all_6_2
% 229.95/41.32    (9)  op(e2, e2) = e1
% 229.95/41.32    (10)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1)
% 229.95/41.32    (11)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.95/41.32          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.95/41.32    (12)   ~ (e3 = e2)
% 229.95/41.32    (13)   ~ (e3 = e0)
% 229.95/41.32    (14)  op(e0, e3) = all_53_3
% 229.95/41.32    (15)  all_57_0 = e0
% 229.95/41.32    (16)  all_57_15 = e3
% 229.95/41.32    (17)  op(e3, e3) = e0
% 229.95/41.32    (18)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.95/41.32          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.95/41.32            e1)
% 229.95/41.32    (19)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.95/41.32          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.95/41.32    (20)   ~ (e2 = e0)
% 229.95/41.32    (21)  all_57_3 = e1
% 229.95/41.32    (22)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.95/41.32          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.95/41.32    (23)   ~ (e1 = e0)
% 229.95/41.32    (24)  all_57_6 = e3
% 229.95/41.32    (25)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.95/41.32          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.95/41.32    (26)  op(e0, e0) = e3
% 229.95/41.32    (27)   ~ (all_53_3 = e0)
% 229.95/41.32    (28)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.95/41.32              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.95/41.32                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.95/41.32                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.95/41.32    (29)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.95/41.32          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.95/41.32    (30)   ~ (all_53_12 = e3)
% 229.95/41.32    (31)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.95/41.32          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.95/41.32    (32)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.95/41.32          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.95/41.32    (33)  all_57_1 = e3
% 229.95/41.32    (34)   ~ (all_53_12 = e0)
% 229.95/41.32    (35)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.95/41.32          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 229.95/41.32    (36)   ~ (e2 = e1)
% 229.95/41.32    (37)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.95/41.32          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.95/41.32    (38)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.95/41.32          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.95/41.32    (39)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.95/41.32          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.95/41.32    (40)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.95/41.32          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.95/41.32    (41)  op(e3, e0) = all_53_12
% 229.95/41.32  
% 229.95/41.32  Begin of proof
% 229.95/41.32  | 
% 229.95/41.32  | BETA: splitting (10) gives:
% 229.95/41.32  | 
% 229.95/41.32  | Case 1:
% 229.95/41.32  | | 
% 229.95/41.32  | |   (42)  all_57_0 = e1 & op(e3, e3) = e1
% 229.95/41.32  | | 
% 229.95/41.32  | | REF_CLOSE: (15), (23), (42) are inconsistent by sub-proof #2454.
% 229.95/41.32  | | 
% 229.95/41.32  | Case 2:
% 229.95/41.32  | | 
% 229.95/41.32  | |   (43)  all_57_2 = e1 & op(e2, e3) = e1
% 229.95/41.32  | | 
% 229.95/41.32  | | ALPHA: (43) implies:
% 229.95/41.32  | |   (44)  all_57_2 = e1
% 229.95/41.32  | | 
% 229.95/41.32  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13),
% 229.95/41.32  | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 229.95/41.32  | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 229.95/41.32  | |            (36), (37), (38), (39), (40), (41), (44) are inconsistent by
% 229.95/41.32  | |            sub-proof #980.
% 229.95/41.32  | | 
% 229.95/41.32  | End of split
% 229.95/41.32  | 
% 229.95/41.32  End of proof
% 229.95/41.32  
% 229.95/41.32  Sub-proof #938 shows that the following formulas are inconsistent:
% 229.95/41.32  ----------------------------------------------------------------
% 229.95/41.32    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.95/41.32         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.95/41.32    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.95/41.32         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.95/41.32    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.95/41.32         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.95/41.32    (4)   ~ (e3 = e1)
% 229.95/41.32    (5)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 229.95/41.32         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 229.95/41.32    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.95/41.32           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.95/41.32    (7)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.95/41.32         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.95/41.32    (8)   ~ (all_6_2 = e3)
% 229.95/41.32    (9)  op(e1, e1) = all_6_2
% 229.95/41.32    (10)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.95/41.32          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.95/41.32    (11)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.95/41.32          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.95/41.32    (12)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.95/41.32          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.95/41.32    (13)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 229.95/41.32          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.95/41.32    (14)   ~ (e3 = e2)
% 229.95/41.32    (15)   ~ (e3 = e0)
% 229.95/41.32    (16)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 229.95/41.32          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 229.95/41.32    (17)  op(e0, e3) = all_53_3
% 229.95/41.32    (18)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.95/41.32          | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.95/41.32    (19)  all_57_15 = e3
% 229.95/41.32    (20)  op(e3, e3) = e0
% 229.95/41.32    (21)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.95/41.32          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.95/41.32            e1)
% 229.95/41.32    (22)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.95/41.32          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.95/41.32    (23)   ~ (e2 = e0)
% 229.95/41.32    (24)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.95/41.32          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.95/41.32    (25)   ~ (e1 = e0)
% 229.95/41.32    (26)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.95/41.32          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.95/41.32    (27)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.95/41.32          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.95/41.32    (28)  op(e0, e0) = e3
% 229.95/41.32    (29)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.95/41.32          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.95/41.32            e2)
% 229.95/41.32    (30)   ~ (all_53_3 = e0)
% 229.95/41.32    (31)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.95/41.32              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.95/41.32                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.95/41.32                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.95/41.32    (32)  all_57_13 = e0
% 229.95/41.32    (33)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.95/41.32          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.95/41.32    (34)  all_57_2 = e0
% 229.95/41.32    (35)   ~ (all_53_12 = e3)
% 229.95/41.32    (36)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.95/41.32          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.95/41.32    (37)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.95/41.32          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.95/41.32    (38)   ~ (all_53_12 = e0)
% 229.95/41.32    (39)   ~ (e2 = e1)
% 229.95/41.32    (40)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.95/41.32          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.95/41.32    (41)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.95/41.32          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.95/41.32    (42)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 229.95/41.32          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 229.95/41.32    (43)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.95/41.32          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.95/41.32    (44)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.95/41.32          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.95/41.32    (45)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 229.95/41.32          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 229.95/41.32    (46)  all_57_3 = e2
% 229.95/41.32    (47)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.95/41.32          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.95/41.32    (48)  all_57_7 = e0
% 229.95/41.32    (49)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 229.95/41.32          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 229.95/41.32    (50)  op(e3, e0) = all_53_12
% 229.95/41.32  
% 229.95/41.32  Begin of proof
% 229.95/41.32  | 
% 229.95/41.32  | BETA: splitting (47) gives:
% 229.95/41.32  | 
% 229.95/41.32  | Case 1:
% 229.95/41.32  | | 
% 229.95/41.32  | |   (51)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) =
% 229.95/41.32  | |           e1)
% 229.95/41.32  | | 
% 229.95/41.32  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 229.95/41.32  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 229.95/41.32  | |            (24), (25), (26), (27), (28), (29), (30), (31), (33), (34), (35),
% 229.95/41.32  | |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 229.95/41.32  | |            (47), (48), (49), (50), (51) are inconsistent by sub-proof #939.
% 229.95/41.32  | | 
% 229.95/41.32  | Case 2:
% 229.95/41.32  | | 
% 229.95/41.32  | |   (52)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 229.95/41.32  | |           e1)
% 229.95/41.32  | | 
% 229.95/41.32  | | BETA: splitting (52) gives:
% 229.95/41.32  | | 
% 229.95/41.32  | | Case 1:
% 229.95/41.32  | | | 
% 229.95/41.32  | | |   (53)  all_57_7 = e1 & op(e1, e2) = e1
% 229.95/41.32  | | | 
% 229.95/41.32  | | | ALPHA: (53) implies:
% 229.95/41.32  | | |   (54)  all_57_7 = e1
% 229.95/41.32  | | | 
% 229.95/41.32  | | | REF_CLOSE: (25), (48), (54) are inconsistent by sub-proof #2211.
% 229.95/41.32  | | | 
% 229.95/41.32  | | Case 2:
% 229.95/41.32  | | | 
% 229.95/41.32  | | |   (55)  all_57_13 = e1 & op(e0, e2) = e1
% 229.95/41.32  | | | 
% 229.95/41.32  | | | ALPHA: (55) implies:
% 229.95/41.32  | | |   (56)  all_57_13 = e1
% 229.95/41.32  | | | 
% 229.95/41.32  | | | REF_CLOSE: (25), (32), (56) are inconsistent by sub-proof #1760.
% 229.95/41.32  | | | 
% 229.95/41.32  | | End of split
% 229.95/41.32  | | 
% 229.95/41.32  | End of split
% 229.95/41.32  | 
% 229.95/41.32  End of proof
% 229.95/41.32  
% 229.95/41.32  Sub-proof #939 shows that the following formulas are inconsistent:
% 229.95/41.32  ----------------------------------------------------------------
% 229.95/41.32    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.95/41.32         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.95/41.32    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.95/41.32         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.95/41.32    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.95/41.32         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.95/41.32    (4)   ~ (e3 = e1)
% 229.95/41.32    (5)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 229.95/41.32         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 229.95/41.32    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.95/41.32           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.95/41.32    (7)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.95/41.32         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.95/41.32    (8)   ~ (all_6_2 = e3)
% 229.95/41.32    (9)  op(e1, e1) = all_6_2
% 229.95/41.32    (10)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.95/41.32          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.95/41.32    (11)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1)
% 229.95/41.32    (12)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.95/41.32          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.95/41.32    (13)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.95/41.32          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.95/41.32    (14)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 229.95/41.32          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.95/41.32    (15)   ~ (e3 = e2)
% 229.95/41.32    (16)   ~ (e3 = e0)
% 229.95/41.32    (17)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 229.95/41.32          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 229.95/41.32    (18)  op(e0, e3) = all_53_3
% 229.95/41.32    (19)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.95/41.32          | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.95/41.32    (20)  all_57_15 = e3
% 229.95/41.32    (21)  op(e3, e3) = e0
% 229.95/41.32    (22)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.95/41.32          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.95/41.32            e1)
% 229.95/41.32    (23)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.95/41.32          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.95/41.32    (24)   ~ (e2 = e0)
% 229.95/41.32    (25)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.95/41.32          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.95/41.32    (26)   ~ (e1 = e0)
% 229.95/41.32    (27)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.95/41.32          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.95/41.33    (28)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.95/41.33          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.95/41.33    (29)  op(e0, e0) = e3
% 229.95/41.33    (30)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.95/41.33          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.95/41.33            e2)
% 229.95/41.33    (31)   ~ (all_53_3 = e0)
% 229.95/41.33    (32)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.95/41.33              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.95/41.33                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.95/41.33                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.95/41.33    (33)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.95/41.33          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.95/41.33    (34)  all_57_2 = e0
% 229.95/41.33    (35)   ~ (all_53_12 = e3)
% 229.95/41.33    (36)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.95/41.33          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.95/41.33    (37)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.95/41.33          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.95/41.33    (38)   ~ (all_53_12 = e0)
% 229.95/41.33    (39)   ~ (e2 = e1)
% 229.95/41.33    (40)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.95/41.33          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.95/41.33    (41)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.95/41.33          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.95/41.33    (42)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 229.95/41.33          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 229.95/41.33    (43)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.95/41.33          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.95/41.33    (44)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.95/41.33          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.95/41.33    (45)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 229.95/41.33          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 229.95/41.33    (46)  all_57_3 = e2
% 229.95/41.33    (47)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.95/41.33          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.95/41.33    (48)  all_57_7 = e0
% 229.95/41.33    (49)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 229.95/41.33          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 229.95/41.33    (50)  op(e3, e0) = all_53_12
% 229.95/41.33  
% 229.95/41.33  Begin of proof
% 229.95/41.33  | 
% 229.95/41.33  | BETA: splitting (11) gives:
% 229.95/41.33  | 
% 229.95/41.33  | Case 1:
% 229.95/41.33  | | 
% 229.95/41.33  | |   (51)  all_57_1 = e1 & op(e3, e2) = e1
% 229.95/41.33  | | 
% 229.95/41.33  | | ALPHA: (51) implies:
% 229.95/41.33  | |   (52)  all_57_1 = e1
% 229.95/41.33  | | 
% 229.95/41.33  | | REF_CLOSE: (4), (6), (15), (16), (19), (20), (22), (24), (26), (28), (29),
% 229.95/41.33  | |            (30), (39), (46), (48), (52) are inconsistent by sub-proof #940.
% 229.95/41.33  | | 
% 229.95/41.33  | Case 2:
% 229.95/41.33  | | 
% 229.95/41.33  | |   (53)  all_57_3 = e1 & op(e2, e2) = e1
% 229.95/41.33  | | 
% 229.95/41.33  | | ALPHA: (53) implies:
% 229.95/41.33  | |   (54)  all_57_3 = e1
% 229.95/41.33  | |   (55)  op(e2, e2) = e1
% 229.95/41.33  | | 
% 229.95/41.33  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 229.95/41.33  | |            (14), (15), (16), (17), (18), (20), (21), (22), (23), (24), (25),
% 229.95/41.33  | |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 229.95/41.33  | |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (47), (49),
% 229.95/41.33  | |            (50), (54), (55) are inconsistent by sub-proof #1016.
% 229.95/41.33  | | 
% 229.95/41.33  | End of split
% 229.95/41.33  | 
% 229.95/41.33  End of proof
% 229.95/41.33  
% 229.95/41.33  Sub-proof #940 shows that the following formulas are inconsistent:
% 229.95/41.33  ----------------------------------------------------------------
% 229.95/41.33    (1)   ~ (e3 = e1)
% 229.95/41.33    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.95/41.33           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.95/41.33    (3)   ~ (e3 = e2)
% 229.95/41.33    (4)   ~ (e3 = e0)
% 229.95/41.33    (5)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 229.95/41.33         (all_57_14 = e0 & op(e0, e1) = e0)
% 229.95/41.33    (6)  all_57_15 = e3
% 229.95/41.33    (7)  all_57_1 = e1
% 229.95/41.33    (8)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 229.95/41.33         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.95/41.33    (9)   ~ (e2 = e0)
% 229.95/41.33    (10)   ~ (e1 = e0)
% 229.95/41.33    (11)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.95/41.33          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.95/41.33    (12)  op(e0, e0) = e3
% 229.95/41.33    (13)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.95/41.33          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.95/41.33            e2)
% 229.95/41.33    (14)   ~ (e2 = e1)
% 229.95/41.33    (15)  all_57_3 = e2
% 229.95/41.33    (16)  all_57_7 = e0
% 229.95/41.33  
% 229.95/41.33  Begin of proof
% 229.95/41.33  | 
% 229.95/41.33  | BETA: splitting (11) gives:
% 229.95/41.33  | 
% 229.95/41.33  | Case 1:
% 229.95/41.33  | | 
% 229.95/41.33  | |   (17)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 229.95/41.33  | |           e3)
% 229.95/41.33  | | 
% 229.95/41.33  | | BETA: splitting (17) gives:
% 229.95/41.33  | | 
% 229.95/41.33  | | Case 1:
% 229.95/41.33  | | | 
% 229.95/41.33  | | |   (18)  all_57_1 = e3 & op(e3, e2) = e3
% 229.95/41.33  | | | 
% 229.95/41.33  | | | REF_CLOSE: (1), (7), (18) are inconsistent by sub-proof #2196.
% 229.95/41.33  | | | 
% 229.95/41.33  | | Case 2:
% 229.95/41.33  | | | 
% 229.95/41.33  | | |   (19)  all_57_3 = e3 & op(e2, e2) = e3
% 229.95/41.33  | | | 
% 229.95/41.33  | | | ALPHA: (19) implies:
% 229.95/41.33  | | |   (20)  all_57_3 = e3
% 229.95/41.33  | | | 
% 229.95/41.33  | | | REF_CLOSE: (3), (15), (20) are inconsistent by sub-proof #1166.
% 229.95/41.33  | | | 
% 229.95/41.33  | | End of split
% 229.95/41.33  | | 
% 229.95/41.33  | Case 2:
% 229.95/41.33  | | 
% 229.95/41.33  | |   (21)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 229.95/41.33  | |           e3)
% 229.95/41.33  | | 
% 229.95/41.33  | | BETA: splitting (21) gives:
% 229.95/41.33  | | 
% 229.95/41.33  | | Case 1:
% 229.95/41.33  | | | 
% 229.95/41.33  | | |   (22)  all_57_7 = e3 & op(e1, e2) = e3
% 229.95/41.33  | | | 
% 229.95/41.33  | | | REF_CLOSE: (4), (16), (22) are inconsistent by sub-proof #2345.
% 229.95/41.33  | | | 
% 229.95/41.33  | | Case 2:
% 229.95/41.33  | | | 
% 229.95/41.33  | | |   (23)  all_57_13 = e3 & op(e0, e2) = e3
% 229.95/41.33  | | | 
% 229.95/41.33  | | | ALPHA: (23) implies:
% 229.95/41.33  | | |   (24)  all_57_13 = e3
% 229.95/41.33  | | | 
% 229.95/41.33  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (12), (13), (14),
% 229.95/41.33  | | |            (24) are inconsistent by sub-proof #2054.
% 229.95/41.33  | | | 
% 229.95/41.33  | | End of split
% 229.95/41.33  | | 
% 229.95/41.33  | End of split
% 229.95/41.33  | 
% 229.95/41.33  End of proof
% 229.95/41.33  
% 229.95/41.33  Sub-proof #941 shows that the following formulas are inconsistent:
% 229.95/41.33  ----------------------------------------------------------------
% 229.95/41.33    (1)   ~ (e3 = e1)
% 229.95/41.33    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.95/41.33           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.95/41.33    (3)   ~ (all_6_2 = e3)
% 229.95/41.33    (4)  op(e1, e1) = all_6_2
% 229.95/41.33    (5)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 229.95/41.33         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.95/41.33    (6)   ~ (e3 = e2)
% 229.95/41.33    (7)   ~ (e3 = e0)
% 229.95/41.33    (8)  all_57_15 = e3
% 229.95/41.33    (9)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 229.95/41.33         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.95/41.33    (10)  op(e1, e1) = e1
% 229.95/41.33    (11)   ~ (e2 = e0)
% 229.95/41.33    (12)   ~ (e1 = e0)
% 229.95/41.33    (13)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.95/41.33          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.95/41.33    (14)  all_57_5 = e1
% 229.95/41.33    (15)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.95/41.33          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.95/41.33            e2)
% 229.95/41.33    (16)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.95/41.33              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.95/41.33                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.95/41.33                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.95/41.33    (17)   ~ (e2 = e1)
% 229.95/41.33    (18)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 229.95/41.33          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 229.95/41.33  
% 229.95/41.33  Begin of proof
% 229.95/41.33  | 
% 229.95/41.33  | BETA: splitting (5) gives:
% 229.95/41.33  | 
% 229.95/41.33  | Case 1:
% 229.95/41.33  | | 
% 229.95/41.33  | |   (19)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) =
% 229.95/41.33  | |           e0)
% 229.95/41.33  | | 
% 229.95/41.33  | | BETA: splitting (19) gives:
% 229.95/41.33  | | 
% 229.95/41.33  | | Case 1:
% 229.95/41.33  | | | 
% 229.95/41.33  | | |   (20)  all_57_4 = e0 & op(e3, e1) = e0
% 229.95/41.33  | | | 
% 229.95/41.33  | | | ALPHA: (20) implies:
% 229.95/41.33  | | |   (21)  all_57_4 = e0
% 229.95/41.33  | | | 
% 229.95/41.33  | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (11), (12), (13), (14),
% 229.95/41.33  | | |            (15), (16), (17), (21) are inconsistent by sub-proof #943.
% 229.95/41.33  | | | 
% 229.95/41.33  | | Case 2:
% 229.95/41.33  | | | 
% 229.95/41.33  | | |   (22)  all_57_5 = e0 & op(e2, e1) = e0
% 229.95/41.33  | | | 
% 229.95/41.33  | | | REF_CLOSE: (12), (14), (22) are inconsistent by sub-proof #942.
% 229.95/41.33  | | | 
% 229.95/41.33  | | End of split
% 229.95/41.33  | | 
% 229.95/41.33  | Case 2:
% 229.95/41.33  | | 
% 229.95/41.33  | |   (23)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 229.95/41.33  | |           e0)
% 229.95/41.33  | | 
% 229.95/41.33  | | BETA: splitting (23) gives:
% 229.95/41.33  | | 
% 229.95/41.33  | | Case 1:
% 229.95/41.33  | | | 
% 229.95/41.33  | | |   (24)  all_57_8 = e0 & op(e1, e1) = e0
% 229.95/41.33  | | | 
% 229.95/41.33  | | | ALPHA: (24) implies:
% 229.95/41.33  | | |   (25)  op(e1, e1) = e0
% 229.95/41.33  | | | 
% 229.95/41.33  | | | REF_CLOSE: (2), (10), (12), (25) are inconsistent by sub-proof #2427.
% 229.95/41.33  | | | 
% 229.95/41.33  | | Case 2:
% 229.95/41.33  | | | 
% 229.95/41.33  | | |   (26)  all_57_14 = e0 & op(e0, e1) = e0
% 229.95/41.33  | | | 
% 229.95/41.33  | | | ALPHA: (26) implies:
% 229.95/41.33  | | |   (27)  all_57_14 = e0
% 229.95/41.33  | | | 
% 229.95/41.33  | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13),
% 229.95/41.33  | | |            (14), (15), (16), (17), (18), (27) are inconsistent by
% 229.95/41.33  | | |            sub-proof #1230.
% 229.95/41.33  | | | 
% 229.95/41.33  | | End of split
% 229.95/41.33  | | 
% 229.95/41.33  | End of split
% 229.95/41.33  | 
% 229.95/41.33  End of proof
% 229.95/41.33  
% 229.95/41.33  Sub-proof #942 shows that the following formulas are inconsistent:
% 229.95/41.33  ----------------------------------------------------------------
% 229.95/41.33    (1)  all_57_5 = e0 & op(e2, e1) = e0
% 229.95/41.33    (2)  all_57_5 = e1
% 229.95/41.33    (3)   ~ (e1 = e0)
% 229.95/41.33  
% 229.95/41.33  Begin of proof
% 229.95/41.33  | 
% 229.95/41.33  | ALPHA: (1) implies:
% 229.95/41.33  |   (4)  all_57_5 = e0
% 229.95/41.33  | 
% 229.95/41.33  | COMBINE_EQS: (2), (4) imply:
% 229.95/41.33  |   (5)  e1 = e0
% 229.95/41.33  | 
% 229.95/41.33  | REDUCE: (3), (5) imply:
% 229.95/41.33  |   (6)  $false
% 229.95/41.33  | 
% 229.95/41.33  | CLOSE: (6) is inconsistent.
% 229.95/41.33  | 
% 229.95/41.33  End of proof
% 229.95/41.33  
% 229.95/41.33  Sub-proof #943 shows that the following formulas are inconsistent:
% 229.95/41.33  ----------------------------------------------------------------
% 229.95/41.33    (1)   ~ (e3 = e1)
% 229.95/41.33    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.95/41.33           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.95/41.33    (3)   ~ (all_6_2 = e3)
% 229.95/41.33    (4)  op(e1, e1) = all_6_2
% 229.95/41.33    (5)  all_57_4 = e0
% 229.95/41.33    (6)   ~ (e3 = e2)
% 229.95/41.33    (7)   ~ (e3 = e0)
% 229.95/41.33    (8)  all_57_15 = e3
% 229.95/41.33    (9)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 229.95/41.33         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.95/41.33    (10)   ~ (e2 = e0)
% 229.95/41.33    (11)   ~ (e1 = e0)
% 229.95/41.33    (12)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.95/41.33          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.95/41.33    (13)  all_57_5 = e1
% 229.95/41.33    (14)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.95/41.33          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.95/41.33            e2)
% 229.95/41.33    (15)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.95/41.33              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.95/41.33                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.95/41.33                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.95/41.33    (16)   ~ (e2 = e1)
% 229.95/41.33  
% 229.95/41.33  Begin of proof
% 229.95/41.33  | 
% 229.95/41.33  | BETA: splitting (12) gives:
% 229.95/41.33  | 
% 229.95/41.33  | Case 1:
% 229.95/41.33  | | 
% 229.95/41.33  | |   (17)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) =
% 229.95/41.33  | |           e3)
% 229.95/41.33  | | 
% 229.95/41.33  | | BETA: splitting (17) gives:
% 229.95/41.33  | | 
% 229.95/41.33  | | Case 1:
% 229.95/41.33  | | | 
% 229.95/41.33  | | |   (18)  all_57_4 = e3 & op(e3, e1) = e3
% 229.95/41.33  | | | 
% 229.95/41.33  | | | ALPHA: (18) implies:
% 229.95/41.33  | | |   (19)  all_57_4 = e3
% 229.95/41.33  | | | 
% 229.95/41.33  | | | REF_CLOSE: (5), (7), (19) are inconsistent by sub-proof #2372.
% 229.95/41.33  | | | 
% 229.95/41.33  | | Case 2:
% 229.95/41.33  | | | 
% 229.95/41.33  | | |   (20)  all_57_5 = e3 & op(e2, e1) = e3
% 229.95/41.33  | | | 
% 229.95/41.33  | | | ALPHA: (20) implies:
% 229.95/41.33  | | |   (21)  all_57_5 = e3
% 229.95/41.33  | | | 
% 229.95/41.33  | | | REF_CLOSE: (1), (13), (21) are inconsistent by sub-proof #2382.
% 229.95/41.33  | | | 
% 229.95/41.33  | | End of split
% 229.95/41.33  | | 
% 229.95/41.33  | Case 2:
% 229.95/41.33  | | 
% 229.95/41.33  | |   (22)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) =
% 229.95/41.33  | |           e3)
% 229.95/41.33  | | 
% 229.95/41.33  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (14), (15),
% 229.95/41.33  | |            (16), (22) are inconsistent by sub-proof #1794.
% 229.95/41.33  | | 
% 229.95/41.33  | End of split
% 229.95/41.33  | 
% 229.95/41.33  End of proof
% 229.95/41.33  
% 229.95/41.33  Sub-proof #944 shows that the following formulas are inconsistent:
% 229.95/41.33  ----------------------------------------------------------------
% 229.95/41.33    (1)   ~ (all_48_2 = e0) | ( ~ (all_48_0 = e2) & op(all_48_1, e3) = all_48_0 &
% 229.95/41.33           op(e3, e0) = all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 =
% 229.95/41.33             e1) & op(e3, e0) = all_48_1 & $i(all_48_1))
% 229.95/41.33    (2)  all_48_2 = e0
% 229.95/41.33    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.95/41.33         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.95/41.33    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.95/41.33         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.95/41.33    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.95/41.33         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.95/41.33    (6)   ~ (e3 = e1)
% 229.95/41.33    (7)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 229.95/41.33         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 229.95/41.33    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.95/41.33           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.95/41.33    (9)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.95/41.33         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.95/41.33    (10)   ~ (all_6_2 = e3)
% 229.95/41.33    (11)  ( ~ (all_18_0 = e1) & op(all_18_1, e3) = all_18_0 & op(e3, e0) =
% 229.95/41.33            all_18_1 & $i(all_18_0) & $i(all_18_1)) | ( ~ (all_18_1 = e2) & op(e3,
% 229.95/41.33              e0) = all_18_1 & $i(all_18_1))
% 229.95/41.33    (12)  op(e1, e1) = all_6_2
% 229.95/41.33    (13)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.95/41.33          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.95/41.33    (14)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 229.95/41.33            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 229.95/41.33              e3) = all_22_1 & $i(all_22_1))
% 229.95/41.33    (15)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.95/41.33          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.95/41.33    (16)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.95/41.33          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.95/41.33    (17)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 229.95/41.33          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.95/41.33    (18)   ~ (e3 = e2)
% 229.95/41.33    (19)  all_55_10 = e1 | all_55_10 = e0
% 229.95/41.33    (20)   ~ (e3 = e0)
% 229.95/41.33    (21)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 229.95/41.33          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 229.95/41.33    (22)   ~ (all_6_2 = e2)
% 229.95/41.33    (23)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 229.95/41.33    (24)  op(e0, e3) = all_53_3
% 229.95/41.33    (25)   ~ (all_53_2 = e0)
% 229.95/41.33    (26)  all_57_0 = e0
% 229.95/41.33    (27)  all_57_15 = e3
% 229.95/41.33    (28)  all_57_4 = e1
% 229.95/41.33    (29)  op(e3, e3) = e0
% 229.95/41.33    (30)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.95/41.33          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.95/41.33            e1)
% 229.95/41.33    (31)  op(e1, e1) = e1
% 229.95/41.33    (32)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.95/41.33          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.95/41.33    (33)   ~ (e2 = e0)
% 229.95/41.33    (34)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 229.95/41.33            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 229.95/41.33            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 229.95/41.33            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 229.95/41.33              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 229.95/41.33            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 229.95/41.33            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 229.95/41.33              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 229.95/41.33              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 229.95/41.33            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 229.95/41.33            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 229.95/41.33            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 229.95/41.33              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 229.95/41.33              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 229.95/41.33            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 229.95/41.33              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 229.95/41.33            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 229.95/41.33            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 229.95/41.33              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 229.95/41.33              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 229.95/41.33            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 229.95/41.33            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 229.95/41.33    (35)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 229.95/41.33            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 229.95/41.33              e3) = all_12_1 & $i(all_12_1))
% 229.95/41.33    (36)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.95/41.33          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.95/41.33    (37)  op(e2, e2) = e2
% 229.95/41.33    (38)   ~ (e1 = e0)
% 229.95/41.33    (39)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.95/41.33          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.95/41.33    (40)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.95/41.33          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.95/41.33    (41)   ~ (all_53_2 = all_53_3)
% 229.95/41.33    (42)  all_55_8 = all_53_2
% 229.95/41.33    (43)  op(e0, e0) = e3
% 229.95/41.33    (44)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.95/41.33          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.95/41.33            e2)
% 229.95/41.33    (45)   ~ (all_53_3 = e0)
% 229.95/41.33    (46)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.95/41.33              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.95/41.33                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.95/41.33                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.95/41.33    (47)  all_55_10 = all_6_2
% 229.95/41.33    (48)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.95/41.33          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.95/41.33    (49)   ~ (all_53_12 = e3)
% 229.95/41.33    (50)  op(e1, e3) = all_53_2
% 229.95/41.33    (51)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.95/41.33          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.95/41.33    (52)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.95/41.33          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.95/41.33    (53)   ~ (all_53_12 = e0)
% 229.95/41.33    (54)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.95/41.33          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 229.95/41.33    (55)   ~ (e2 = e1)
% 229.95/41.33    (56)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.95/41.33          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.95/41.33    (57)   ~ (all_6_2 = e0)
% 229.95/41.33    (58)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.95/41.33          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.95/41.33    (59)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 229.95/41.33          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 229.95/41.33    (60)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.95/41.33          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.95/41.33    (61)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.95/41.33          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.95/41.33    (62)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 229.95/41.33          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 229.95/41.33    (63)  all_57_3 = e2
% 229.95/41.33    (64)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.95/41.33          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.95/41.33    (65)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 229.95/41.33          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 229.95/41.33    (66)  op(e3, e0) = all_53_12
% 229.95/41.33  
% 229.95/41.33  Begin of proof
% 229.95/41.33  | 
% 229.95/41.33  | BETA: splitting (36) gives:
% 229.95/41.33  | 
% 229.95/41.33  | Case 1:
% 229.95/41.33  | | 
% 229.95/41.33  | |   (67)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) =
% 229.95/41.33  | |           e3)
% 229.95/41.33  | | 
% 229.95/41.33  | | BETA: splitting (67) gives:
% 229.95/41.33  | | 
% 229.95/41.33  | | Case 1:
% 229.95/41.33  | | | 
% 229.95/41.33  | | |   (68)  all_57_0 = e3 & op(e3, e3) = e3
% 229.95/41.33  | | | 
% 229.95/41.33  | | | ALPHA: (68) implies:
% 229.95/41.33  | | |   (69)  op(e3, e3) = e3
% 229.95/41.33  | | | 
% 229.95/41.33  | | | REF_CLOSE: (8), (20), (29), (69) are inconsistent by sub-proof #2494.
% 229.95/41.33  | | | 
% 229.95/41.33  | | Case 2:
% 229.95/41.33  | | | 
% 229.95/41.33  | | |   (70)  all_57_1 = e3 & op(e3, e2) = e3
% 229.95/41.33  | | | 
% 229.95/41.33  | | | ALPHA: (70) implies:
% 229.95/41.33  | | |   (71)  all_57_1 = e3
% 229.95/41.33  | | | 
% 229.95/41.33  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 229.95/41.33  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 229.95/41.33  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 229.95/41.33  | | |            (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 229.95/41.33  | | |            (43), (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 229.95/41.33  | | |            (53), (54), (55), (56), (57), (58), (59), (60), (61), (62),
% 229.95/41.33  | | |            (63), (64), (65), (66), (71) are inconsistent by sub-proof
% 229.95/41.33  | | |            #945.
% 229.95/41.33  | | | 
% 229.95/41.33  | | End of split
% 229.95/41.33  | | 
% 229.95/41.33  | Case 2:
% 229.95/41.33  | | 
% 229.95/41.33  | |   (72)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) =
% 229.95/41.33  | |           e3)
% 229.95/41.33  | | 
% 229.95/41.33  | | REF_CLOSE: (6), (8), (28), (49), (66), (72) are inconsistent by sub-proof
% 229.95/41.33  | |            #1004.
% 229.95/41.33  | | 
% 229.95/41.33  | End of split
% 229.95/41.33  | 
% 229.95/41.33  End of proof
% 229.95/41.33  
% 229.95/41.33  Sub-proof #945 shows that the following formulas are inconsistent:
% 229.95/41.33  ----------------------------------------------------------------
% 229.95/41.33    (1)   ~ (all_48_2 = e0) | ( ~ (all_48_0 = e2) & op(all_48_1, e3) = all_48_0 &
% 229.95/41.33           op(e3, e0) = all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 =
% 229.95/41.33             e1) & op(e3, e0) = all_48_1 & $i(all_48_1))
% 229.95/41.33    (2)  all_48_2 = e0
% 229.95/41.33    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.95/41.33         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 229.95/41.33    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.95/41.33         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.95/41.33    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.95/41.33         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.95/41.33    (6)   ~ (e3 = e1)
% 229.95/41.33    (7)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 229.95/41.33         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 229.95/41.33    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.95/41.33           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.95/41.33    (9)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.95/41.33         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.95/41.33    (10)   ~ (all_6_2 = e3)
% 229.95/41.33    (11)  ( ~ (all_18_0 = e1) & op(all_18_1, e3) = all_18_0 & op(e3, e0) =
% 229.95/41.33            all_18_1 & $i(all_18_0) & $i(all_18_1)) | ( ~ (all_18_1 = e2) & op(e3,
% 229.95/41.33              e0) = all_18_1 & $i(all_18_1))
% 229.95/41.33    (12)  op(e1, e1) = all_6_2
% 229.95/41.33    (13)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.95/41.33          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.95/41.33    (14)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 229.95/41.33            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 229.95/41.33              e3) = all_22_1 & $i(all_22_1))
% 229.95/41.33    (15)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.95/41.33          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.95/41.33    (16)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.95/41.33          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.95/41.33    (17)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 229.95/41.33          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.95/41.33    (18)   ~ (e3 = e2)
% 229.95/41.33    (19)  all_55_10 = e1 | all_55_10 = e0
% 229.95/41.33    (20)   ~ (e3 = e0)
% 229.95/41.33    (21)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 229.95/41.33          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 229.95/41.34    (22)   ~ (all_6_2 = e2)
% 229.95/41.34    (23)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 229.95/41.34    (24)  op(e0, e3) = all_53_3
% 229.95/41.34    (25)   ~ (all_53_2 = e0)
% 229.95/41.34    (26)  all_57_0 = e0
% 229.95/41.34    (27)  all_57_15 = e3
% 229.95/41.34    (28)  all_57_4 = e1
% 229.95/41.34    (29)  op(e3, e3) = e0
% 229.95/41.34    (30)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.95/41.34          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.95/41.34            e1)
% 229.95/41.34    (31)  op(e1, e1) = e1
% 229.95/41.34    (32)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.95/41.34          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.95/41.34    (33)   ~ (e2 = e0)
% 229.95/41.34    (34)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 229.95/41.34            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 229.95/41.34            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 229.95/41.34            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 229.95/41.34              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 229.95/41.34            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 229.95/41.34            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 229.95/41.34              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 229.95/41.34              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 229.95/41.34            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 229.95/41.34            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 229.95/41.34            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 229.95/41.34              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 229.95/41.34              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 229.95/41.34            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 229.95/41.34              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 229.95/41.34            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 229.95/41.34            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 229.95/41.34              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 229.95/41.34              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 229.95/41.34            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 229.95/41.34            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 229.95/41.34    (35)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 229.95/41.34            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 229.95/41.34              e3) = all_12_1 & $i(all_12_1))
% 229.95/41.34    (36)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.95/41.34          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.95/41.34    (37)  op(e2, e2) = e2
% 229.95/41.34    (38)   ~ (e1 = e0)
% 229.95/41.34    (39)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.95/41.34          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.95/41.34    (40)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.95/41.34          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 229.95/41.34    (41)   ~ (all_53_2 = all_53_3)
% 229.95/41.34    (42)  all_55_8 = all_53_2
% 229.95/41.34    (43)  op(e0, e0) = e3
% 229.95/41.34    (44)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.95/41.34          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.95/41.34            e2)
% 229.95/41.34    (45)   ~ (all_53_3 = e0)
% 229.95/41.34    (46)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.95/41.34              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.95/41.34                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.95/41.34                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.95/41.34    (47)  all_55_10 = all_6_2
% 229.95/41.34    (48)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.95/41.34          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.95/41.34    (49)   ~ (all_53_12 = e3)
% 229.95/41.34    (50)  op(e1, e3) = all_53_2
% 229.95/41.34    (51)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.95/41.34          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 229.95/41.34    (52)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 229.95/41.34          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 229.95/41.34    (53)  all_57_1 = e3
% 229.95/41.34    (54)   ~ (all_53_12 = e0)
% 229.95/41.34    (55)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.95/41.34          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 229.95/41.34    (56)   ~ (e2 = e1)
% 229.95/41.34    (57)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.95/41.34          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.95/41.34    (58)   ~ (all_6_2 = e0)
% 229.95/41.34    (59)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.95/41.34          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.95/41.34    (60)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 229.95/41.34          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 229.95/41.34    (61)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.95/41.34          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.95/41.34    (62)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.95/41.34          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.95/41.34    (63)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 229.95/41.34          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 229.95/41.34    (64)  all_57_3 = e2
% 229.95/41.34    (65)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.95/41.34          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.95/41.34    (66)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 229.95/41.34          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 229.95/41.34    (67)  op(e3, e0) = all_53_12
% 229.95/41.34  
% 229.95/41.34  Begin of proof
% 229.95/41.34  | 
% 229.95/41.34  | BETA: splitting (63) gives:
% 229.95/41.34  | 
% 229.95/41.34  | Case 1:
% 229.95/41.34  | | 
% 229.95/41.34  | |   (68)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) =
% 229.95/41.34  | |           e1)
% 229.95/41.34  | | 
% 229.95/41.34  | | BETA: splitting (68) gives:
% 229.95/41.34  | | 
% 229.95/41.34  | | Case 1:
% 229.95/41.34  | | | 
% 229.95/41.34  | | |   (69)  all_57_6 = e1 & op(e1, e3) = e1
% 229.95/41.34  | | | 
% 229.95/41.34  | | | ALPHA: (69) implies:
% 229.95/41.34  | | |   (70)  all_57_6 = e1
% 229.95/41.34  | | | 
% 229.95/41.34  | | | REF_CLOSE: (5), (6), (8), (9), (10), (12), (18), (20), (27), (32), (33),
% 229.95/41.34  | | |            (37), (38), (46), (53), (56), (57), (62), (65), (70) are
% 229.95/41.34  | | |            inconsistent by sub-proof #1071.
% 229.95/41.34  | | | 
% 229.95/41.34  | | Case 2:
% 229.95/41.34  | | | 
% 229.95/41.34  | | |   (71)  all_57_7 = e1 & op(e1, e2) = e1
% 229.95/41.34  | | | 
% 229.95/41.34  | | | ALPHA: (71) implies:
% 229.95/41.34  | | |   (72)  all_57_7 = e1
% 229.95/41.34  | | | 
% 229.95/41.34  | | | REF_CLOSE: (6), (7), (8), (9), (10), (12), (18), (20), (27), (31), (33),
% 229.95/41.34  | | |            (38), (46), (56), (57), (62), (66), (72) are inconsistent by
% 229.95/41.34  | | |            sub-proof #1069.
% 229.95/41.34  | | | 
% 229.95/41.34  | | End of split
% 229.95/41.34  | | 
% 229.95/41.34  | Case 2:
% 229.95/41.34  | | 
% 229.95/41.34  | |   (73)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) =
% 229.95/41.34  | |           e1)
% 229.95/41.34  | | 
% 229.95/41.34  | | BETA: splitting (73) gives:
% 229.95/41.34  | | 
% 229.95/41.34  | | Case 1:
% 229.95/41.34  | | | 
% 229.95/41.34  | | |   (74)  all_57_8 = e1 & op(e1, e1) = e1
% 229.95/41.34  | | | 
% 229.95/41.34  | | | ALPHA: (74) implies:
% 229.95/41.34  | | |   (75)  all_57_8 = e1
% 229.95/41.34  | | | 
% 229.95/41.34  | | | BETA: splitting (65) gives:
% 229.95/41.34  | | | 
% 229.95/41.34  | | | Case 1:
% 229.95/41.34  | | | | 
% 229.95/41.34  | | | |   (76)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2)
% 229.95/41.34  | | | |           = e1)
% 229.95/41.34  | | | | 
% 229.95/41.34  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 229.95/41.34  | | | |            (12), (13), (14), (15), (16), (17), (18), (19), (20), (21),
% 229.95/41.34  | | | |            (22), (23), (24), (25), (26), (27), (29), (30), (32), (33),
% 229.95/41.34  | | | |            (34), (35), (36), (39), (40), (41), (42), (43), (44), (45),
% 229.95/41.34  | | | |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (55),
% 229.95/41.34  | | | |            (57), (58), (59), (60), (61), (62), (63), (65), (66), (67),
% 229.95/41.34  | | | |            (76) are inconsistent by sub-proof #962.
% 229.95/41.34  | | | | 
% 229.95/41.34  | | | Case 2:
% 229.95/41.34  | | | | 
% 229.95/41.34  | | | |   (77)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2)
% 229.95/41.34  | | | |           = e1)
% 229.95/41.34  | | | | 
% 229.95/41.34  | | | | BETA: splitting (77) gives:
% 229.95/41.34  | | | | 
% 229.95/41.34  | | | | Case 1:
% 229.95/41.34  | | | | | 
% 229.95/41.34  | | | | |   (78)  all_57_7 = e1 & op(e1, e2) = e1
% 229.95/41.34  | | | | | 
% 229.95/41.34  | | | | | ALPHA: (78) implies:
% 229.95/41.34  | | | | |   (79)  all_57_7 = e1
% 229.95/41.34  | | | | | 
% 229.95/41.34  | | | | | REF_CLOSE: (6), (7), (8), (9), (10), (12), (18), (20), (27), (31),
% 229.95/41.34  | | | | |            (33), (38), (46), (56), (57), (62), (66), (79) are
% 229.95/41.34  | | | | |            inconsistent by sub-proof #1069.
% 229.95/41.34  | | | | | 
% 229.95/41.34  | | | | Case 2:
% 229.95/41.34  | | | | | 
% 229.95/41.34  | | | | |   (80)  all_57_13 = e1 & op(e0, e2) = e1
% 229.95/41.34  | | | | | 
% 229.95/41.34  | | | | | ALPHA: (80) implies:
% 229.95/41.34  | | | | |   (81)  all_57_13 = e1
% 229.95/41.34  | | | | | 
% 229.95/41.34  | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (10), (12), (13), (14), (15),
% 229.95/41.34  | | | | |            (16), (17), (18), (20), (27), (28), (29), (30), (31), (32),
% 229.95/41.34  | | | | |            (33), (35), (36), (37), (38), (39), (43), (44), (46), (48),
% 229.95/41.34  | | | | |            (49), (53), (56), (57), (59), (60), (61), (62), (63), (64),
% 229.95/41.34  | | | | |            (65), (66), (67), (75), (81) are inconsistent by sub-proof
% 229.95/41.34  | | | | |            #946.
% 229.95/41.34  | | | | | 
% 229.95/41.34  | | | | End of split
% 229.95/41.34  | | | | 
% 229.95/41.34  | | | End of split
% 229.95/41.34  | | | 
% 229.95/41.34  | | Case 2:
% 229.95/41.34  | | | 
% 229.95/41.34  | | |   (82)  all_57_11 = e1 & op(e1, e0) = e1
% 229.95/41.34  | | | 
% 229.95/41.34  | | | ALPHA: (82) implies:
% 229.95/41.34  | | |   (83)  all_57_11 = e1
% 229.95/41.34  | | | 
% 229.95/41.34  | | | BETA: splitting (65) gives:
% 229.95/41.34  | | | 
% 229.95/41.34  | | | Case 1:
% 229.95/41.34  | | | | 
% 229.95/41.34  | | | |   (84)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2)
% 229.95/41.34  | | | |           = e1)
% 229.95/41.34  | | | | 
% 229.95/41.34  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 229.95/41.34  | | | |            (12), (13), (14), (15), (16), (17), (18), (19), (20), (21),
% 229.95/41.34  | | | |            (22), (23), (24), (25), (26), (27), (29), (30), (32), (33),
% 229.95/41.34  | | | |            (34), (35), (36), (39), (40), (41), (42), (43), (44), (45),
% 229.95/41.34  | | | |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (55),
% 229.95/41.34  | | | |            (57), (58), (59), (60), (61), (62), (63), (65), (66), (67),
% 229.95/41.34  | | | |            (84) are inconsistent by sub-proof #962.
% 229.95/41.34  | | | | 
% 229.95/41.34  | | | Case 2:
% 229.95/41.34  | | | | 
% 229.95/41.34  | | | |   (85)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2)
% 229.95/41.34  | | | |           = e1)
% 229.95/41.34  | | | | 
% 229.95/41.34  | | | | BETA: splitting (85) gives:
% 229.95/41.34  | | | | 
% 229.95/41.34  | | | | Case 1:
% 229.95/41.34  | | | | | 
% 229.95/41.34  | | | | |   (86)  all_57_7 = e1 & op(e1, e2) = e1
% 229.95/41.34  | | | | | 
% 229.95/41.34  | | | | | ALPHA: (86) implies:
% 229.95/41.34  | | | | |   (87)  all_57_7 = e1
% 229.95/41.34  | | | | | 
% 229.95/41.34  | | | | | BETA: splitting (15) gives:
% 229.95/41.34  | | | | | 
% 229.95/41.34  | | | | | Case 1:
% 229.95/41.34  | | | | | | 
% 229.95/41.34  | | | | | |   (88)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3,
% 229.95/41.34  | | | | | |             e2) = e2)
% 229.95/41.34  | | | | | | 
% 229.95/41.34  | | | | | | REF_CLOSE: (8), (18), (29), (33), (53), (88) are inconsistent by
% 229.95/41.34  | | | | | |            sub-proof #1224.
% 229.95/41.34  | | | | | | 
% 229.95/41.34  | | | | | Case 2:
% 229.95/41.34  | | | | | | 
% 229.95/41.34  | | | | | |   (89)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3,
% 229.95/41.34  | | | | | |             e0) = e2)
% 229.95/41.34  | | | | | | 
% 229.95/41.34  | | | | | | BETA: splitting (89) gives:
% 229.95/41.34  | | | | | | 
% 229.95/41.34  | | | | | | Case 1:
% 229.95/41.34  | | | | | | | 
% 229.95/41.34  | | | | | | |   (90)  all_57_4 = e2 & op(e3, e1) = e2
% 229.95/41.34  | | | | | | | 
% 229.95/41.34  | | | | | | | ALPHA: (90) implies:
% 229.95/41.34  | | | | | | |   (91)  all_57_4 = e2
% 229.95/41.34  | | | | | | | 
% 229.95/41.34  | | | | | | | REF_CLOSE: (28), (56), (91) are inconsistent by sub-proof #2430.
% 229.95/41.34  | | | | | | | 
% 229.95/41.34  | | | | | | Case 2:
% 229.95/41.34  | | | | | | | 
% 229.95/41.34  | | | | | | |   (92)  all_57_9 = e2 & op(e3, e0) = e2
% 229.95/41.34  | | | | | | | 
% 229.95/41.34  | | | | | | | ALPHA: (92) implies:
% 229.95/41.34  | | | | | | |   (93)  all_57_9 = e2
% 229.95/41.34  | | | | | | | 
% 229.95/41.34  | | | | | | | BETA: splitting (66) gives:
% 229.95/41.34  | | | | | | | 
% 229.95/41.34  | | | | | | | Case 1:
% 229.95/41.34  | | | | | | | | 
% 229.95/41.34  | | | | | | | |   (94)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 &
% 229.95/41.34  | | | | | | | |           op(e1, e2) = e2)
% 229.95/41.34  | | | | | | | | 
% 229.95/41.34  | | | | | | | | BETA: splitting (94) gives:
% 229.95/41.34  | | | | | | | | 
% 229.95/41.34  | | | | | | | | Case 1:
% 229.95/41.34  | | | | | | | | | 
% 229.95/41.34  | | | | | | | | |   (95)  all_57_6 = e2 & op(e1, e3) = e2
% 229.95/41.34  | | | | | | | | | 
% 229.95/41.34  | | | | | | | | | ALPHA: (95) implies:
% 229.95/41.34  | | | | | | | | |   (96)  all_57_6 = e2
% 229.95/41.34  | | | | | | | | | 
% 229.95/41.34  | | | | | | | | | REF_CLOSE: (6), (8), (9), (10), (12), (18), (20), (27), (33),
% 229.95/41.34  | | | | | | | | |            (38), (46), (56), (57), (62), (87), (96) are
% 229.95/41.34  | | | | | | | | |            inconsistent by sub-proof #1245.
% 229.95/41.34  | | | | | | | | | 
% 229.95/41.34  | | | | | | | | Case 2:
% 229.95/41.34  | | | | | | | | | 
% 229.95/41.34  | | | | | | | | |   (97)  all_57_7 = e2 & op(e1, e2) = e2
% 229.95/41.34  | | | | | | | | | 
% 229.95/41.34  | | | | | | | | | ALPHA: (97) implies:
% 229.95/41.34  | | | | | | | | |   (98)  all_57_7 = e2
% 229.95/41.34  | | | | | | | | | 
% 229.95/41.34  | | | | | | | | | REF_CLOSE: (6), (7), (8), (9), (10), (12), (18), (20), (27),
% 229.95/41.34  | | | | | | | | |            (31), (33), (38), (46), (56), (57), (62), (83),
% 229.95/41.34  | | | | | | | | |            (93), (98) are inconsistent by sub-proof #957.
% 229.95/41.34  | | | | | | | | | 
% 229.95/41.34  | | | | | | | | End of split
% 229.95/41.34  | | | | | | | | 
% 229.95/41.34  | | | | | | | Case 2:
% 229.95/41.34  | | | | | | | | 
% 229.95/41.34  | | | | | | | |   (99)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 &
% 229.95/41.34  | | | | | | | |           op(e1, e0) = e2)
% 229.95/41.34  | | | | | | | | 
% 229.95/41.34  | | | | | | | | REF_CLOSE: (6), (7), (8), (9), (10), (12), (18), (20), (27),
% 229.95/41.34  | | | | | | | |            (31), (33), (38), (46), (56), (57), (62), (87), (99)
% 229.95/41.34  | | | | | | | |            are inconsistent by sub-proof #1070.
% 229.95/41.34  | | | | | | | | 
% 229.95/41.34  | | | | | | | End of split
% 229.95/41.34  | | | | | | | 
% 229.95/41.34  | | | | | | End of split
% 229.95/41.34  | | | | | | 
% 229.95/41.34  | | | | | End of split
% 229.95/41.34  | | | | | 
% 229.95/41.34  | | | | Case 2:
% 229.95/41.34  | | | | | 
% 229.95/41.34  | | | | |   (100)  all_57_13 = e1 & op(e0, e2) = e1
% 229.95/41.34  | | | | | 
% 229.95/41.34  | | | | | ALPHA: (100) implies:
% 229.95/41.34  | | | | |   (101)  all_57_13 = e1
% 229.95/41.34  | | | | | 
% 229.95/41.34  | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (10), (12), (15), (18), (20),
% 229.95/41.34  | | | | |            (27), (28), (29), (31), (32), (33), (38), (46), (53), (56),
% 229.95/41.34  | | | | |            (57), (62), (65), (66), (83), (101) are inconsistent by
% 229.95/41.34  | | | | |            sub-proof #954.
% 229.95/41.34  | | | | | 
% 229.95/41.34  | | | | End of split
% 229.95/41.34  | | | | 
% 229.95/41.34  | | | End of split
% 229.95/41.34  | | | 
% 229.95/41.34  | | End of split
% 229.95/41.34  | | 
% 229.95/41.34  | End of split
% 229.95/41.34  | 
% 229.95/41.34  End of proof
% 229.95/41.34  
% 229.95/41.34  Sub-proof #946 shows that the following formulas are inconsistent:
% 229.95/41.34  ----------------------------------------------------------------
% 229.95/41.34    (1)  all_57_13 = e1
% 229.95/41.34    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.95/41.34         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.95/41.34    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.95/41.34         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.95/41.34    (4)   ~ (e3 = e1)
% 229.95/41.34    (5)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 229.95/41.34         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 229.95/41.34    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.95/41.34           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.95/41.34    (7)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.95/41.34         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.95/41.34    (8)   ~ (all_6_2 = e3)
% 229.95/41.34    (9)  op(e1, e1) = all_6_2
% 229.95/41.34    (10)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.95/41.34          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.95/41.34    (11)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 229.95/41.34            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 229.95/41.34              e3) = all_22_1 & $i(all_22_1))
% 229.95/41.34    (12)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.95/41.34          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.95/41.34    (13)  all_57_8 = e1
% 229.95/41.34    (14)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.95/41.34          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.95/41.34    (15)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 229.95/41.34          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 229.95/41.34    (16)   ~ (e3 = e2)
% 229.95/41.34    (17)   ~ (e3 = e0)
% 229.95/41.34    (18)  all_57_15 = e3
% 229.95/41.34    (19)  all_57_4 = e1
% 229.95/41.34    (20)  op(e3, e3) = e0
% 229.95/41.34    (21)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.95/41.34          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.95/41.34            e1)
% 229.95/41.34    (22)  op(e1, e1) = e1
% 229.95/41.34    (23)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.95/41.34          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.95/41.34    (24)   ~ (e2 = e0)
% 229.95/41.34    (25)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 229.95/41.34            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 229.95/41.34              e3) = all_12_1 & $i(all_12_1))
% 229.95/41.34    (26)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 229.95/41.34          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 229.95/41.34    (27)  op(e2, e2) = e2
% 229.95/41.34    (28)   ~ (e1 = e0)
% 229.95/41.34    (29)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.95/41.34          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.95/41.34    (30)  op(e0, e0) = e3
% 229.95/41.34    (31)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.95/41.34          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.95/41.34            e2)
% 229.95/41.34    (32)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.95/41.34              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.95/41.34                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.95/41.34                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.95/41.34    (33)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.95/41.34          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.95/41.34    (34)   ~ (all_53_12 = e3)
% 229.95/41.34    (35)  all_57_1 = e3
% 229.95/41.34    (36)   ~ (e2 = e1)
% 229.95/41.34    (37)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.95/41.34          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.95/41.34    (38)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.95/41.34          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.95/41.34    (39)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 229.95/41.34          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 229.95/41.34    (40)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.95/41.34          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.95/41.34    (41)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.95/41.34          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.95/41.34    (42)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 229.95/41.34          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 229.95/41.34    (43)  all_57_3 = e2
% 229.95/41.34    (44)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.95/41.34          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.95/41.34    (45)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 229.95/41.34          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 229.95/41.34    (46)  op(e3, e0) = all_53_12
% 229.95/41.34  
% 229.95/41.34  Begin of proof
% 229.95/41.34  | 
% 229.95/41.34  | BETA: splitting (12) gives:
% 229.95/41.34  | 
% 229.95/41.34  | Case 1:
% 229.95/41.34  | | 
% 229.95/41.34  | |   (47)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) =
% 229.95/41.34  | |           e2)
% 229.95/41.34  | | 
% 229.95/41.34  | | REF_CLOSE: (6), (16), (20), (24), (35), (47) are inconsistent by sub-proof
% 229.95/41.34  | |            #1224.
% 229.95/41.34  | | 
% 229.95/41.34  | Case 2:
% 229.95/41.34  | | 
% 229.95/41.34  | |   (48)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) =
% 229.95/41.34  | |           e2)
% 229.95/41.34  | | 
% 229.95/41.34  | | BETA: splitting (48) gives:
% 229.95/41.34  | | 
% 229.95/41.34  | | Case 1:
% 229.95/41.34  | | | 
% 229.95/41.34  | | |   (49)  all_57_4 = e2 & op(e3, e1) = e2
% 229.95/41.34  | | | 
% 229.95/41.34  | | | ALPHA: (49) implies:
% 229.95/41.34  | | |   (50)  all_57_4 = e2
% 229.95/41.34  | | | 
% 229.95/41.34  | | | REF_CLOSE: (19), (36), (50) are inconsistent by sub-proof #2430.
% 229.95/41.34  | | | 
% 229.95/41.34  | | Case 2:
% 229.95/41.34  | | | 
% 229.95/41.34  | | |   (51)  all_57_9 = e2 & op(e3, e0) = e2
% 229.95/41.34  | | | 
% 229.95/41.34  | | | ALPHA: (51) implies:
% 229.95/41.34  | | |   (52)  all_57_9 = e2
% 229.95/41.34  | | | 
% 229.95/41.34  | | | BETA: splitting (23) gives:
% 229.95/41.34  | | | 
% 229.95/41.34  | | | Case 1:
% 229.95/41.34  | | | | 
% 229.95/41.34  | | | |   (53)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2)
% 229.95/41.34  | | | |           = e0)
% 229.95/41.34  | | | | 
% 229.95/41.34  | | | | BETA: splitting (53) gives:
% 229.95/41.34  | | | | 
% 229.95/41.34  | | | | Case 1:
% 229.95/41.34  | | | | | 
% 229.95/41.34  | | | | |   (54)  all_57_1 = e0 & op(e3, e2) = e0
% 229.95/41.34  | | | | | 
% 229.95/41.34  | | | | | ALPHA: (54) implies:
% 229.95/41.34  | | | | |   (55)  all_57_1 = e0
% 229.95/41.34  | | | | | 
% 229.95/41.34  | | | | | REF_CLOSE: (4), (6), (17), (19), (20), (26), (34), (46), (55) are
% 229.95/41.34  | | | | |            inconsistent by sub-proof #2280.
% 229.95/41.34  | | | | | 
% 229.95/41.34  | | | | Case 2:
% 229.95/41.34  | | | | | 
% 229.95/41.34  | | | | |   (56)  all_57_3 = e0 & op(e2, e2) = e0
% 229.95/41.34  | | | | | 
% 229.95/41.34  | | | | | ALPHA: (56) implies:
% 229.95/41.34  | | | | |   (57)  op(e2, e2) = e0
% 229.95/41.34  | | | | | 
% 229.95/41.34  | | | | | REF_CLOSE: (6), (24), (27), (57) are inconsistent by sub-proof #2472.
% 229.95/41.34  | | | | | 
% 229.95/41.34  | | | | End of split
% 229.95/41.34  | | | | 
% 229.95/41.34  | | | Case 2:
% 229.95/41.34  | | | | 
% 229.95/41.34  | | | |   (58)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2)
% 229.95/41.34  | | | |           = e0)
% 229.95/41.34  | | | | 
% 229.95/41.34  | | | | BETA: splitting (58) gives:
% 229.95/41.34  | | | | 
% 229.95/41.34  | | | | Case 1:
% 229.95/41.34  | | | | | 
% 229.95/41.34  | | | | |   (59)  all_57_7 = e0 & op(e1, e2) = e0
% 229.95/41.34  | | | | | 
% 229.95/41.34  | | | | | ALPHA: (59) implies:
% 229.95/41.34  | | | | |   (60)  all_57_7 = e0
% 229.95/41.34  | | | | | 
% 229.95/41.34  | | | | | BETA: splitting (7) gives:
% 229.95/41.34  | | | | | 
% 229.95/41.34  | | | | | Case 1:
% 229.95/41.34  | | | | | | 
% 229.95/41.34  | | | | | |   (61)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1,
% 229.95/41.34  | | | | | |             e2) = e3)
% 229.95/41.34  | | | | | | 
% 229.95/41.34  | | | | | | BETA: splitting (61) gives:
% 229.95/41.34  | | | | | | 
% 229.95/41.34  | | | | | | Case 1:
% 229.95/41.34  | | | | | | | 
% 229.95/41.34  | | | | | | |   (62)  all_57_6 = e3 & op(e1, e3) = e3
% 229.95/41.34  | | | | | | | 
% 229.95/41.34  | | | | | | | ALPHA: (62) implies:
% 229.95/41.34  | | | | | | |   (63)  all_57_6 = e3
% 229.95/41.34  | | | | | | | 
% 229.95/41.34  | | | | | | | BETA: splitting (29) gives:
% 229.95/41.34  | | | | | | | 
% 229.95/41.34  | | | | | | | Case 1:
% 229.95/41.34  | | | | | | | | 
% 229.95/41.34  | | | | | | | |   (64)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 &
% 229.95/41.34  | | | | | | | |           op(e2, e1) = e3)
% 229.95/41.34  | | | | | | | | 
% 229.95/41.34  | | | | | | | | BETA: splitting (64) gives:
% 229.95/41.34  | | | | | | | | 
% 229.95/41.34  | | | | | | | | Case 1:
% 229.95/41.34  | | | | | | | | | 
% 229.95/41.34  | | | | | | | | |   (65)  all_57_4 = e3 & op(e3, e1) = e3
% 229.95/41.34  | | | | | | | | | 
% 229.95/41.34  | | | | | | | | | ALPHA: (65) implies:
% 229.95/41.34  | | | | | | | | |   (66)  all_57_4 = e3
% 229.95/41.34  | | | | | | | | | 
% 229.95/41.34  | | | | | | | | | REF_CLOSE: (4), (10), (12), (14), (16), (17), (24), (28),
% 229.95/41.34  | | | | | | | | |            (35), (36), (52), (66) are inconsistent by
% 229.95/41.34  | | | | | | | | |            sub-proof #1222.
% 229.95/41.34  | | | | | | | | | 
% 229.95/41.34  | | | | | | | | Case 2:
% 229.95/41.34  | | | | | | | | | 
% 229.95/41.34  | | | | | | | | |   (67)  all_57_5 = e3 & op(e2, e1) = e3
% 229.95/41.34  | | | | | | | | | 
% 229.95/41.34  | | | | | | | | | ALPHA: (67) implies:
% 229.95/41.34  | | | | | | | | |   (68)  all_57_5 = e3
% 229.95/41.34  | | | | | | | | | 
% 229.95/41.34  | | | | | | | | | BETA: splitting (45) gives:
% 229.95/41.34  | | | | | | | | | 
% 229.95/41.34  | | | | | | | | | Case 1:
% 229.95/41.34  | | | | | | | | | | 
% 229.95/41.34  | | | | | | | | | |   (69)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 &
% 229.95/41.34  | | | | | | | | | |           op(e1, e2) = e2)
% 229.95/41.34  | | | | | | | | | | 
% 229.95/41.34  | | | | | | | | | | BETA: splitting (69) gives:
% 229.95/41.34  | | | | | | | | | | 
% 229.95/41.34  | | | | | | | | | | Case 1:
% 229.95/41.34  | | | | | | | | | | | 
% 229.95/41.34  | | | | | | | | | | |   (70)  all_57_6 = e2 & op(e1, e3) = e2
% 229.95/41.34  | | | | | | | | | | | 
% 229.95/41.34  | | | | | | | | | | | ALPHA: (70) implies:
% 229.95/41.34  | | | | | | | | | | |   (71)  all_57_6 = e2
% 229.95/41.34  | | | | | | | | | | | 
% 229.95/41.34  | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (16), (17),
% 229.95/41.34  | | | | | | | | | | |            (18), (23), (24), (28), (32), (35), (36), (37),
% 229.95/41.34  | | | | | | | | | | |            (41), (44), (71) are inconsistent by sub-proof
% 229.95/41.34  | | | | | | | | | | |            #961.
% 229.95/41.34  | | | | | | | | | | | 
% 229.95/41.34  | | | | | | | | | | Case 2:
% 229.95/41.34  | | | | | | | | | | | 
% 229.95/41.34  | | | | | | | | | | |   (72)  all_57_7 = e2 & op(e1, e2) = e2
% 229.95/41.34  | | | | | | | | | | | 
% 229.95/41.34  | | | | | | | | | | | ALPHA: (72) implies:
% 229.95/41.34  | | | | | | | | | | |   (73)  all_57_7 = e2
% 229.95/41.34  | | | | | | | | | | | 
% 229.95/41.34  | | | | | | | | | | | COMBINE_EQS: (60), (73) imply:
% 229.95/41.34  | | | | | | | | | | |   (74)  e2 = e0
% 229.95/41.34  | | | | | | | | | | | 
% 229.95/41.34  | | | | | | | | | | | SIMP: (74) implies:
% 229.95/41.34  | | | | | | | | | | |   (75)  e2 = e0
% 229.95/41.34  | | | | | | | | | | | 
% 229.95/41.34  | | | | | | | | | | | COMBINE_EQS: (52), (75) imply:
% 229.95/41.34  | | | | | | | | | | |   (76)  all_57_9 = e0
% 229.95/41.34  | | | | | | | | | | | 
% 229.95/41.34  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (16), (17), (18),
% 229.95/41.34  | | | | | | | | | | |            (22), (24), (28), (32), (36), (37), (41), (73),
% 229.95/41.34  | | | | | | | | | | |            (76) are inconsistent by sub-proof #959.
% 229.95/41.34  | | | | | | | | | | | 
% 229.95/41.34  | | | | | | | | | | End of split
% 229.95/41.34  | | | | | | | | | | 
% 229.95/41.34  | | | | | | | | | Case 2:
% 229.95/41.34  | | | | | | | | | | 
% 229.95/41.34  | | | | | | | | | |   (77)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2
% 229.95/41.34  | | | | | | | | | |           & op(e1, e0) = e2)
% 229.95/41.34  | | | | | | | | | | 
% 229.95/41.34  | | | | | | | | | | BETA: splitting (77) gives:
% 229.95/41.34  | | | | | | | | | | 
% 229.95/41.34  | | | | | | | | | | Case 1:
% 229.95/41.34  | | | | | | | | | | | 
% 229.95/41.34  | | | | | | | | | | |   (78)  all_57_8 = e2 & op(e1, e1) = e2
% 229.95/41.34  | | | | | | | | | | | 
% 229.95/41.34  | | | | | | | | | | | ALPHA: (78) implies:
% 229.95/41.34  | | | | | | | | | | |   (79)  op(e1, e1) = e2
% 229.95/41.34  | | | | | | | | | | | 
% 229.95/41.34  | | | | | | | | | | | REF_CLOSE: (6), (22), (36), (79) are inconsistent by
% 229.95/41.34  | | | | | | | | | | |            sub-proof #2423.
% 229.95/41.34  | | | | | | | | | | | 
% 229.95/41.34  | | | | | | | | | | Case 2:
% 229.95/41.34  | | | | | | | | | | | 
% 229.95/41.34  | | | | | | | | | | |   (80)  all_57_11 = e2 & op(e1, e0) = e2
% 229.95/41.34  | | | | | | | | | | | 
% 229.95/41.34  | | | | | | | | | | | ALPHA: (80) implies:
% 229.95/41.34  | | | | | | | | | | |   (81)  all_57_11 = e2
% 229.95/41.34  | | | | | | | | | | | 
% 229.95/41.34  | | | | | | | | | | | BETA: splitting (39) gives:
% 229.95/41.34  | | | | | | | | | | | 
% 229.95/41.34  | | | | | | | | | | | Case 1:
% 229.95/41.34  | | | | | | | | | | | | 
% 229.95/41.34  | | | | | | | | | | | |   (82)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 229.95/41.34  | | | | | | | | | | | |           & op(e2, e1) = e2)
% 229.95/41.34  | | | | | | | | | | | | 
% 229.95/41.34  | | | | | | | | | | | | BETA: splitting (82) gives:
% 229.95/41.34  | | | | | | | | | | | | 
% 229.95/41.34  | | | | | | | | | | | | Case 1:
% 229.95/41.34  | | | | | | | | | | | | | 
% 229.95/41.34  | | | | | | | | | | | | |   (83)  all_57_4 = e2 & op(e3, e1) = e2
% 229.95/41.34  | | | | | | | | | | | | | 
% 229.95/41.34  | | | | | | | | | | | | | ALPHA: (83) implies:
% 229.95/41.34  | | | | | | | | | | | | |   (84)  all_57_4 = e2
% 229.95/41.34  | | | | | | | | | | | | | 
% 229.95/41.34  | | | | | | | | | | | | | COMBINE_EQS: (19), (84) imply:
% 229.95/41.34  | | | | | | | | | | | | |   (85)  e2 = e1
% 229.95/41.34  | | | | | | | | | | | | | 
% 229.95/41.34  | | | | | | | | | | | | | SIMP: (85) implies:
% 229.95/41.34  | | | | | | | | | | | | |   (86)  e2 = e1
% 229.95/41.34  | | | | | | | | | | | | | 
% 229.95/41.34  | | | | | | | | | | | | | COMBINE_EQS: (81), (86) imply:
% 229.95/41.34  | | | | | | | | | | | | |   (87)  all_57_11 = e1
% 229.95/41.34  | | | | | | | | | | | | | 
% 229.95/41.34  | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (12),
% 229.95/41.34  | | | | | | | | | | | | |            (16), (17), (18), (19), (20), (22), (23), (24),
% 229.95/41.34  | | | | | | | | | | | | |            (28), (32), (35), (36), (37), (41), (44), (45),
% 229.95/41.34  | | | | | | | | | | | | |            (87) are inconsistent by sub-proof #954.
% 229.95/41.34  | | | | | | | | | | | | | 
% 229.95/41.34  | | | | | | | | | | | | Case 2:
% 229.95/41.34  | | | | | | | | | | | | | 
% 229.95/41.34  | | | | | | | | | | | | |   (88)  all_57_5 = e2 & op(e2, e1) = e2
% 229.95/41.34  | | | | | | | | | | | | | 
% 229.95/41.34  | | | | | | | | | | | | | ALPHA: (88) implies:
% 229.95/41.34  | | | | | | | | | | | | |   (89)  all_57_5 = e2
% 229.95/41.34  | | | | | | | | | | | | | 
% 229.95/41.34  | | | | | | | | | | | | | COMBINE_EQS: (68), (89) imply:
% 229.95/41.34  | | | | | | | | | | | | |   (90)  e3 = e2
% 229.95/41.34  | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (16), (17),
% 229.95/41.35  | | | | | | | | | | | | |            (18), (23), (24), (28), (32), (35), (36), (37),
% 229.95/41.35  | | | | | | | | | | | | |            (41), (44), (63), (90) are inconsistent by
% 229.95/41.35  | | | | | | | | | | | | |            sub-proof #953.
% 229.95/41.35  | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | End of split
% 229.95/41.35  | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | Case 2:
% 229.95/41.35  | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | |   (91)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 229.95/41.35  | | | | | | | | | | | |           e2 & op(e0, e1) = e2)
% 229.95/41.35  | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | BETA: splitting (91) gives:
% 229.95/41.35  | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | Case 1:
% 229.95/41.35  | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | |   (92)  all_57_8 = e2 & op(e1, e1) = e2
% 229.95/41.35  | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | | ALPHA: (92) implies:
% 229.95/41.35  | | | | | | | | | | | | |   (93)  all_57_8 = e2
% 229.95/41.35  | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (16), (17), (18), (24),
% 229.95/41.35  | | | | | | | | | | | | |            (28), (32), (36), (37), (41), (42), (60), (81),
% 229.95/41.35  | | | | | | | | | | | | |            (93) are inconsistent by sub-proof #952.
% 229.95/41.35  | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | Case 2:
% 229.95/41.35  | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | |   (94)  all_57_14 = e2 & op(e0, e1) = e2
% 229.95/41.35  | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | | ALPHA: (94) implies:
% 229.95/41.35  | | | | | | | | | | | | |   (95)  all_57_14 = e2
% 229.95/41.35  | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | | BETA: splitting (15) gives:
% 229.95/41.35  | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | | Case 1:
% 229.95/41.35  | | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | | |   (96)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 229.95/41.35  | | | | | | | | | | | | | |           & op(e2, e1) = e0)
% 229.95/41.35  | | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | | | BETA: splitting (96) gives:
% 229.95/41.35  | | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | | | Case 1:
% 229.95/41.35  | | | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | | | |   (97)  all_57_4 = e0 & op(e3, e1) = e0
% 229.95/41.35  | | | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | | | | ALPHA: (97) implies:
% 229.95/41.35  | | | | | | | | | | | | | | |   (98)  all_57_4 = e0
% 229.95/41.35  | | | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | | | | COMBINE_EQS: (19), (98) imply:
% 229.95/41.35  | | | | | | | | | | | | | | |   (99)  e1 = e0
% 229.95/41.35  | | | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | | | | COMBINE_EQS: (1), (99) imply:
% 229.95/41.35  | | | | | | | | | | | | | | |   (100)  all_57_13 = e0
% 229.95/41.35  | | | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | | | | COMBINE_EQS: (13), (99) imply:
% 229.95/41.35  | | | | | | | | | | | | | | |   (101)  all_57_8 = e0
% 229.95/41.35  | | | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | | | | BETA: splitting (44) gives:
% 229.95/41.35  | | | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | | | | Case 1:
% 229.95/41.35  | | | | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | | | | |   (102)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 229.95/41.35  | | | | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 229.95/41.35  | | | | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (27), (35), (36), (102) are inconsistent
% 229.95/41.35  | | | | | | | | | | | | | | | |            by sub-proof #1168.
% 229.95/41.35  | | | | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | | | | Case 2:
% 229.95/41.35  | | | | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | | | | |   (103)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 229.95/41.35  | | | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 229.95/41.35  | | | | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | | | | | BETA: splitting (103) gives:
% 229.95/41.35  | | | | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | | | | | Case 1:
% 229.95/41.35  | | | | | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | | | | | |   (104)  all_57_7 = e1 & op(e1, e2) = e1
% 229.95/41.35  | | | | | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | | | | | | ALPHA: (104) implies:
% 229.95/41.35  | | | | | | | | | | | | | | | | |   (105)  all_57_7 = e1
% 229.95/41.35  | | | | | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | | | | | | BETA: splitting (45) gives:
% 229.95/41.35  | | | | | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | | | | | | Case 1:
% 229.95/41.35  | | | | | | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | | | | | | |   (106)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 229.95/41.35  | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e2)
% 229.95/41.35  | | | | | | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (16), (17), (18), (24),
% 229.95/41.35  | | | | | | | | | | | | | | | | | |            (28), (32), (36), (37), (41), (105), (106) are
% 229.95/41.35  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #951.
% 229.95/41.35  | | | | | | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | | | | | | Case 2:
% 229.95/41.35  | | | | | | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | | | | | | | BETA: splitting (77) gives:
% 229.95/41.35  | | | | | | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | | | | | | | Case 1:
% 229.95/41.35  | | | | | | | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | | | | | | | |   (107)  all_57_8 = e2 & op(e1, e1) = e2
% 229.95/41.35  | | | | | | | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | | | | | | | | ALPHA: (107) implies:
% 229.95/41.35  | | | | | | | | | | | | | | | | | | |   (108)  all_57_8 = e2
% 229.95/41.35  | | | | | | | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (101), (108) imply:
% 229.95/41.35  | | | | | | | | | | | | | | | | | | |   (109)  e2 = e0
% 229.95/41.35  | | | | | | | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | | | | | | | | SIMP: (109) implies:
% 229.95/41.35  | | | | | | | | | | | | | | | | | | |   (110)  e2 = e0
% 229.95/41.35  | | | | | | | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (43), (110) imply:
% 229.95/41.35  | | | | | | | | | | | | | | | | | | |   (111)  all_57_3 = e0
% 229.95/41.35  | | | | | | | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (16), (24), (28), (35), (36), (44),
% 229.95/41.35  | | | | | | | | | | | | | | | | | | |            (100), (111) are inconsistent by sub-proof #1758.
% 229.95/41.35  | | | | | | | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | | | | | | | Case 2:
% 229.95/41.35  | | | | | | | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | | | | | | | | ALPHA: (80) implies:
% 229.95/41.35  | | | | | | | | | | | | | | | | | | |   (112)  op(e1, e0) = e2
% 229.95/41.35  | | | | | | | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (11), (21), (25), (28), (30), (36),
% 229.95/41.35  | | | | | | | | | | | | | | | | | | |            (95), (100), (112) are inconsistent by sub-proof
% 229.95/41.35  | | | | | | | | | | | | | | | | | | |            #1100.
% 229.95/41.35  | | | | | | | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | | | | | | | End of split
% 229.95/41.35  | | | | | | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | | | | | | End of split
% 229.95/41.35  | | | | | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | | | | | Case 2:
% 229.95/41.35  | | | | | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | | | | | |   (113)  all_57_13 = e1 & op(e0, e2) = e1
% 229.95/41.35  | | | | | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (28), (100) are inconsistent by sub-proof
% 229.95/41.35  | | | | | | | | | | | | | | | | |            #1760.
% 229.95/41.35  | | | | | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | | | | | End of split
% 229.95/41.35  | | | | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | | | | End of split
% 229.95/41.35  | | | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | | | Case 2:
% 229.95/41.35  | | | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | | | |   (114)  all_57_5 = e0 & op(e2, e1) = e0
% 229.95/41.35  | | | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | | | | ALPHA: (114) implies:
% 229.95/41.35  | | | | | | | | | | | | | | |   (115)  all_57_5 = e0
% 229.95/41.35  | | | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (6), (7), (8), (9), (10), (12), (14),
% 229.95/41.35  | | | | | | | | | | | | | | |            (16), (17), (18), (21), (24), (28), (29), (31),
% 229.95/41.35  | | | | | | | | | | | | | | |            (32), (33), (35), (36), (37), (38), (40), (41),
% 229.95/41.35  | | | | | | | | | | | | | | |            (43), (60), (63), (115) are inconsistent by
% 229.95/41.35  | | | | | | | | | | | | | | |            sub-proof #948.
% 229.95/41.35  | | | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | | | End of split
% 229.95/41.35  | | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | | Case 2:
% 229.95/41.35  | | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | | |   (116)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 229.95/41.35  | | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 229.95/41.35  | | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | | | BETA: splitting (116) gives:
% 229.95/41.35  | | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | | | Case 1:
% 229.95/41.35  | | | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | | | |   (117)  all_57_8 = e0 & op(e1, e1) = e0
% 229.95/41.35  | | | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | | | | ALPHA: (117) implies:
% 229.95/41.35  | | | | | | | | | | | | | | |   (118)  op(e1, e1) = e0
% 229.95/41.35  | | | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (16), (17), (18), (24),
% 229.95/41.35  | | | | | | | | | | | | | | |            (28), (32), (36), (37), (41), (42), (60), (81),
% 229.95/41.35  | | | | | | | | | | | | | | |            (118) are inconsistent by sub-proof #947.
% 229.95/41.35  | | | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | | | Case 2:
% 229.95/41.35  | | | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | | | |   (119)  all_57_14 = e0 & op(e0, e1) = e0
% 229.95/41.35  | | | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | | | | ALPHA: (119) implies:
% 229.95/41.35  | | | | | | | | | | | | | | |   (120)  all_57_14 = e0
% 229.95/41.35  | | | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | | | | COMBINE_EQS: (95), (120) imply:
% 229.95/41.35  | | | | | | | | | | | | | | |   (121)  e2 = e0
% 229.95/41.35  | | | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | | | | REF_CLOSE: (4), (16), (18), (24), (28), (36), (37), (41),
% 229.95/41.35  | | | | | | | | | | | | | | |            (52), (81), (121) are inconsistent by sub-proof
% 229.95/41.35  | | | | | | | | | | | | | | |            #1049.
% 229.95/41.35  | | | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | | | End of split
% 229.95/41.35  | | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | | End of split
% 229.95/41.35  | | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | | End of split
% 229.95/41.35  | | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | | End of split
% 229.95/41.35  | | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | | End of split
% 229.95/41.35  | | | | | | | | | | 
% 229.95/41.35  | | | | | | | | | End of split
% 229.95/41.35  | | | | | | | | | 
% 229.95/41.35  | | | | | | | | End of split
% 229.95/41.35  | | | | | | | | 
% 229.95/41.35  | | | | | | | Case 2:
% 229.95/41.35  | | | | | | | | 
% 229.95/41.35  | | | | | | | |   (122)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 &
% 229.95/41.35  | | | | | | | |            op(e0, e1) = e3)
% 229.95/41.35  | | | | | | | | 
% 229.95/41.35  | | | | | | | | REF_CLOSE: (4), (6), (8), (9), (16), (17), (18), (21), (24),
% 229.95/41.35  | | | | | | | |            (28), (31), (32), (36), (122) are inconsistent by
% 229.95/41.35  | | | | | | | |            sub-proof #1794.
% 229.95/41.35  | | | | | | | | 
% 229.95/41.35  | | | | | | | End of split
% 229.95/41.35  | | | | | | | 
% 229.95/41.35  | | | | | | Case 2:
% 229.95/41.35  | | | | | | | 
% 229.95/41.35  | | | | | | |   (123)  all_57_7 = e3 & op(e1, e2) = e3
% 229.95/41.35  | | | | | | | 
% 229.95/41.35  | | | | | | | ALPHA: (123) implies:
% 229.95/41.35  | | | | | | |   (124)  all_57_7 = e3
% 229.95/41.35  | | | | | | | 
% 229.95/41.35  | | | | | | | REF_CLOSE: (1), (3), (4), (16), (17), (23), (24), (28), (35),
% 229.95/41.35  | | | | | | |            (36), (44), (124) are inconsistent by sub-proof #1214.
% 229.95/41.35  | | | | | | | 
% 229.95/41.35  | | | | | | End of split
% 229.95/41.35  | | | | | | 
% 229.95/41.35  | | | | | Case 2:
% 229.95/41.35  | | | | | | 
% 229.95/41.35  | | | | | |   (125)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 &
% 229.95/41.35  | | | | | |            op(e1, e0) = e3)
% 229.95/41.35  | | | | | | 
% 229.95/41.35  | | | | | | REF_CLOSE: (4), (6), (8), (9), (16), (17), (18), (24), (28), (32),
% 229.95/41.35  | | | | | |            (36), (37), (41), (125) are inconsistent by sub-proof
% 229.95/41.35  | | | | | |            #1786.
% 229.95/41.35  | | | | | | 
% 229.95/41.35  | | | | | End of split
% 229.95/41.35  | | | | | 
% 229.95/41.35  | | | | Case 2:
% 229.95/41.35  | | | | | 
% 229.95/41.35  | | | | |   (126)  all_57_13 = e0 & op(e0, e2) = e0
% 229.95/41.35  | | | | | 
% 229.95/41.35  | | | | | ALPHA: (126) implies:
% 229.95/41.35  | | | | |   (127)  all_57_13 = e0
% 229.95/41.35  | | | | | 
% 229.95/41.35  | | | | | REF_CLOSE: (1), (28), (127) are inconsistent by sub-proof #1760.
% 229.95/41.35  | | | | | 
% 229.95/41.35  | | | | End of split
% 229.95/41.35  | | | | 
% 229.95/41.35  | | | End of split
% 229.95/41.35  | | | 
% 229.95/41.35  | | End of split
% 229.95/41.35  | | 
% 229.95/41.35  | End of split
% 229.95/41.35  | 
% 229.95/41.35  End of proof
% 229.95/41.35  
% 229.95/41.35  Sub-proof #947 shows that the following formulas are inconsistent:
% 229.95/41.35  ----------------------------------------------------------------
% 229.95/41.35    (1)   ~ (e3 = e1)
% 229.95/41.35    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.95/41.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.95/41.35    (3)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.95/41.35         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.95/41.35    (4)   ~ (all_6_2 = e3)
% 229.95/41.35    (5)  op(e1, e1) = all_6_2
% 229.95/41.35    (6)   ~ (e3 = e2)
% 229.95/41.35    (7)   ~ (e3 = e0)
% 229.95/41.35    (8)  all_57_15 = e3
% 229.95/41.35    (9)  all_57_11 = e2
% 229.95/41.35    (10)   ~ (e2 = e0)
% 229.95/41.35    (11)   ~ (e1 = e0)
% 229.95/41.35    (12)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.95/41.35              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.95/41.35                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.95/41.35                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.95/41.35    (13)  op(e1, e1) = e0
% 229.95/41.35    (14)   ~ (e2 = e1)
% 229.95/41.35    (15)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.95/41.35          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.95/41.35    (16)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.95/41.35          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.95/41.35    (17)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 229.95/41.35          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 229.95/41.35    (18)  all_57_7 = e0
% 229.95/41.35  
% 229.95/41.35  Begin of proof
% 229.95/41.35  | 
% 229.95/41.35  | BETA: splitting (17) gives:
% 229.95/41.35  | 
% 229.95/41.35  | Case 1:
% 229.95/41.35  | | 
% 229.95/41.35  | |   (19)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) =
% 229.95/41.35  | |           e1)
% 229.95/41.35  | | 
% 229.95/41.35  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (14),
% 229.95/41.35  | |            (15), (16), (18), (19) are inconsistent by sub-proof #1155.
% 229.95/41.35  | | 
% 229.95/41.35  | Case 2:
% 229.95/41.35  | | 
% 229.95/41.35  | |   (20)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) =
% 229.95/41.35  | |           e1)
% 229.95/41.35  | | 
% 229.95/41.35  | | REF_CLOSE: (2), (9), (11), (13), (14), (20) are inconsistent by sub-proof
% 229.95/41.35  | |            #1201.
% 229.95/41.35  | | 
% 229.95/41.35  | End of split
% 229.95/41.35  | 
% 229.95/41.35  End of proof
% 229.95/41.35  
% 229.95/41.35  Sub-proof #948 shows that the following formulas are inconsistent:
% 229.95/41.35  ----------------------------------------------------------------
% 229.95/41.35    (1)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.95/41.35         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.95/41.35    (2)   ~ (e3 = e1)
% 229.95/41.35    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.95/41.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.95/41.35    (4)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.95/41.35         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.95/41.35    (5)   ~ (all_6_2 = e3)
% 229.95/41.35    (6)  op(e1, e1) = all_6_2
% 229.95/41.35    (7)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.95/41.35         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.95/41.35    (8)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.95/41.35         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.95/41.35    (9)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.95/41.35         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.95/41.35    (10)   ~ (e3 = e2)
% 229.95/41.35    (11)   ~ (e3 = e0)
% 229.95/41.35    (12)  all_57_15 = e3
% 229.95/41.35    (13)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.95/41.35          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.95/41.35            e1)
% 229.95/41.35    (14)   ~ (e2 = e0)
% 229.95/41.35    (15)   ~ (e1 = e0)
% 229.95/41.35    (16)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.95/41.35          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.95/41.35    (17)  all_57_6 = e3
% 229.95/41.35    (18)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.95/41.35          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.95/41.35            e2)
% 229.95/41.35    (19)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.95/41.35              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.95/41.35                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.95/41.35                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.95/41.35    (20)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 229.95/41.35          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 229.95/41.35    (21)  all_57_1 = e3
% 229.95/41.35    (22)   ~ (e2 = e1)
% 229.95/41.35    (23)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.95/41.35          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.95/41.35    (24)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.95/41.35          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.95/41.35    (25)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.95/41.35          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.95/41.35    (26)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.95/41.35          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.95/41.35    (27)  all_57_3 = e2
% 229.95/41.35    (28)  all_57_7 = e0
% 229.95/41.35    (29)  all_57_5 = e0
% 229.95/41.35  
% 229.95/41.35  Begin of proof
% 229.95/41.35  | 
% 229.95/41.35  | BETA: splitting (20) gives:
% 229.95/41.35  | 
% 229.95/41.35  | Case 1:
% 229.95/41.35  | | 
% 229.95/41.35  | |   (30)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 229.95/41.35  | |           e3)
% 229.95/41.35  | | 
% 229.95/41.35  | | BETA: splitting (30) gives:
% 229.95/41.35  | | 
% 229.95/41.35  | | Case 1:
% 229.95/41.35  | | | 
% 229.95/41.35  | | |   (31)  all_57_2 = e3 & op(e2, e3) = e3
% 229.95/41.35  | | | 
% 229.95/41.35  | | | ALPHA: (31) implies:
% 229.95/41.35  | | |   (32)  all_57_2 = e3
% 229.95/41.35  | | | 
% 229.95/41.35  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13),
% 229.95/41.35  | | |            (14), (15), (16), (17), (18), (19), (21), (22), (23), (24),
% 229.95/41.35  | | |            (25), (26), (28), (29), (32) are inconsistent by sub-proof
% 229.95/41.35  | | |            #950.
% 229.95/41.35  | | | 
% 229.95/41.35  | | Case 2:
% 229.95/41.35  | | | 
% 229.95/41.35  | | |   (33)  all_57_3 = e3 & op(e2, e2) = e3
% 229.95/41.35  | | | 
% 229.95/41.35  | | | ALPHA: (33) implies:
% 229.95/41.35  | | |   (34)  all_57_3 = e3
% 229.95/41.35  | | | 
% 229.95/41.35  | | | REF_CLOSE: (10), (27), (34) are inconsistent by sub-proof #1166.
% 229.95/41.35  | | | 
% 229.95/41.35  | | End of split
% 229.95/41.35  | | 
% 229.95/41.35  | Case 2:
% 229.95/41.35  | | 
% 229.95/41.35  | |   (35)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 229.95/41.35  | |           e3)
% 229.95/41.35  | | 
% 229.95/41.35  | | BETA: splitting (35) gives:
% 229.95/41.35  | | 
% 229.95/41.35  | | Case 1:
% 229.95/41.35  | | | 
% 229.95/41.35  | | |   (36)  all_57_5 = e3 & op(e2, e1) = e3
% 229.95/41.35  | | | 
% 229.95/41.35  | | | REF_CLOSE: (11), (29), (36) are inconsistent by sub-proof #1936.
% 229.95/41.35  | | | 
% 229.95/41.35  | | Case 2:
% 229.95/41.35  | | | 
% 229.95/41.35  | | |   (37)  all_57_10 = e3 & op(e2, e0) = e3
% 229.95/41.35  | | | 
% 229.95/41.35  | | | ALPHA: (37) implies:
% 229.95/41.35  | | |   (38)  all_57_10 = e3
% 229.95/41.35  | | | 
% 229.95/41.35  | | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 229.95/41.35  | | |            (14), (15), (16), (18), (19), (21), (22), (23), (29), (38) are
% 229.95/41.35  | | |            inconsistent by sub-proof #949.
% 229.95/41.35  | | | 
% 229.95/41.35  | | End of split
% 229.95/41.35  | | 
% 229.95/41.35  | End of split
% 229.95/41.35  | 
% 229.95/41.35  End of proof
% 229.95/41.35  
% 229.95/41.35  Sub-proof #949 shows that the following formulas are inconsistent:
% 229.95/41.35  ----------------------------------------------------------------
% 229.95/41.35    (1)   ~ (e3 = e1)
% 229.95/41.35    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.95/41.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.95/41.35    (3)   ~ (all_6_2 = e3)
% 229.95/41.35    (4)  op(e1, e1) = all_6_2
% 229.95/41.35    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 229.95/41.35         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 229.95/41.35    (6)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.95/41.35         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.95/41.35    (7)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.95/41.35         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.95/41.35    (8)   ~ (e3 = e2)
% 229.95/41.35    (9)   ~ (e3 = e0)
% 229.95/41.35    (10)  all_57_15 = e3
% 229.95/41.35    (11)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.95/41.35          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.95/41.35            e1)
% 229.95/41.35    (12)   ~ (e2 = e0)
% 229.95/41.35    (13)   ~ (e1 = e0)
% 229.95/41.35    (14)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.95/41.35          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.95/41.35    (15)  all_57_10 = e3
% 229.95/41.35    (16)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.95/41.35          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.95/41.35            e2)
% 229.95/41.35    (17)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.95/41.35              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.95/41.35                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.95/41.35                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.95/41.35    (18)  all_57_1 = e3
% 229.95/41.35    (19)   ~ (e2 = e1)
% 229.95/41.35    (20)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.95/41.35          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.95/41.35    (21)  all_57_5 = e0
% 229.95/41.35  
% 229.95/41.35  Begin of proof
% 229.95/41.35  | 
% 229.95/41.35  | BETA: splitting (14) gives:
% 229.95/41.35  | 
% 229.95/41.35  | Case 1:
% 229.95/41.35  | | 
% 229.95/41.35  | |   (22)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) =
% 229.95/41.35  | |           e3)
% 229.95/41.35  | | 
% 229.95/41.35  | | BETA: splitting (22) gives:
% 229.95/41.35  | | 
% 229.95/41.35  | | Case 1:
% 229.95/41.35  | | | 
% 229.95/41.35  | | |   (23)  all_57_4 = e3 & op(e3, e1) = e3
% 229.95/41.35  | | | 
% 229.95/41.35  | | | ALPHA: (23) implies:
% 229.95/41.35  | | |   (24)  all_57_4 = e3
% 229.95/41.35  | | | 
% 229.95/41.35  | | | REF_CLOSE: (1), (5), (6), (7), (8), (9), (10), (12), (13), (15), (17),
% 229.95/41.35  | | |            (18), (19), (20), (24) are inconsistent by sub-proof #1436.
% 229.95/41.35  | | | 
% 229.95/41.35  | | Case 2:
% 229.95/41.35  | | | 
% 229.95/41.35  | | |   (25)  all_57_5 = e3 & op(e2, e1) = e3
% 229.95/41.35  | | | 
% 229.95/41.35  | | | REF_CLOSE: (9), (21), (25) are inconsistent by sub-proof #1936.
% 229.95/41.35  | | | 
% 229.95/41.35  | | End of split
% 229.95/41.35  | | 
% 229.95/41.35  | Case 2:
% 229.95/41.35  | | 
% 229.95/41.35  | |   (26)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) =
% 229.95/41.35  | |           e3)
% 229.95/41.35  | | 
% 229.95/41.35  | | REF_CLOSE: (1), (2), (3), (4), (8), (9), (10), (11), (12), (13), (16), (17),
% 229.95/41.35  | |            (19), (26) are inconsistent by sub-proof #1794.
% 229.95/41.35  | | 
% 229.95/41.35  | End of split
% 229.95/41.35  | 
% 229.95/41.35  End of proof
% 229.95/41.35  
% 229.95/41.35  Sub-proof #950 shows that the following formulas are inconsistent:
% 229.95/41.35  ----------------------------------------------------------------
% 229.95/41.35    (1)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 229.95/41.35         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 229.95/41.35    (2)   ~ (e3 = e1)
% 229.95/41.35    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.95/41.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.95/41.35    (4)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.95/41.35         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.95/41.35    (5)   ~ (all_6_2 = e3)
% 229.95/41.35    (6)  op(e1, e1) = all_6_2
% 229.95/41.35    (7)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.95/41.35         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.95/41.35    (8)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 229.95/41.35         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 229.95/41.35    (9)   ~ (e3 = e2)
% 229.95/41.35    (10)   ~ (e3 = e0)
% 229.95/41.35    (11)  all_57_15 = e3
% 229.95/41.35    (12)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.95/41.35          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 229.95/41.35            e1)
% 229.95/41.35    (13)   ~ (e2 = e0)
% 229.95/41.35    (14)  all_57_2 = e3
% 229.95/41.35    (15)   ~ (e1 = e0)
% 229.95/41.35    (16)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 229.95/41.35          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 229.95/41.35    (17)  all_57_6 = e3
% 229.95/41.35    (18)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.95/41.35          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 229.95/41.35            e2)
% 229.95/41.35    (19)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.95/41.35              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.95/41.35                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.95/41.35                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.95/41.35    (20)  all_57_1 = e3
% 229.95/41.35    (21)   ~ (e2 = e1)
% 229.95/41.35    (22)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.95/41.35          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.95/41.35    (23)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 229.95/41.35          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 229.95/41.35    (24)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 229.95/41.35          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 229.95/41.35    (25)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.95/41.35          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.95/41.35    (26)  all_57_7 = e0
% 229.95/41.35    (27)  all_57_5 = e0
% 229.95/41.35  
% 229.95/41.35  Begin of proof
% 229.95/41.35  | 
% 229.95/41.35  | BETA: splitting (16) gives:
% 229.95/41.35  | 
% 229.95/41.35  | Case 1:
% 229.95/41.35  | | 
% 229.95/41.35  | |   (28)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) =
% 229.95/41.35  | |           e3)
% 229.95/41.35  | | 
% 229.95/41.35  | | BETA: splitting (28) gives:
% 229.95/41.35  | | 
% 229.95/41.35  | | Case 1:
% 229.95/41.35  | | | 
% 229.95/41.35  | | |   (29)  all_57_4 = e3 & op(e3, e1) = e3
% 229.95/41.35  | | | 
% 229.95/41.35  | | | ALPHA: (29) implies:
% 229.95/41.35  | | |   (30)  all_57_4 = e3
% 229.95/41.35  | | | 
% 229.95/41.35  | | | BETA: splitting (1) gives:
% 229.95/41.35  | | | 
% 229.95/41.35  | | | Case 1:
% 229.95/41.35  | | | | 
% 229.95/41.35  | | | |   (31)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3)
% 229.95/41.35  | | | |           = e1)
% 229.95/41.35  | | | | 
% 229.95/41.35  | | | | BETA: splitting (31) gives:
% 229.95/41.35  | | | | 
% 229.95/41.35  | | | | Case 1:
% 229.95/41.35  | | | | | 
% 229.95/41.35  | | | | |   (32)  all_57_0 = e1 & op(e3, e3) = e1
% 229.95/41.35  | | | | | 
% 229.95/41.35  | | | | | ALPHA: (32) implies:
% 229.95/41.35  | | | | |   (33)  all_57_0 = e1
% 229.95/41.35  | | | | | 
% 229.95/41.35  | | | | | REF_CLOSE: (7), (8), (9), (10), (13), (15), (20), (21), (30), (33) are
% 229.95/41.35  | | | | |            inconsistent by sub-proof #1808.
% 229.95/41.35  | | | | | 
% 229.95/41.35  | | | | Case 2:
% 229.95/41.35  | | | | | 
% 229.95/41.35  | | | | |   (34)  all_57_2 = e1 & op(e2, e3) = e1
% 229.95/41.35  | | | | | 
% 229.95/41.35  | | | | | ALPHA: (34) implies:
% 229.95/41.35  | | | | |   (35)  all_57_2 = e1
% 229.95/41.35  | | | | | 
% 229.95/41.35  | | | | | COMBINE_EQS: (14), (35) imply:
% 229.95/41.35  | | | | |   (36)  e3 = e1
% 229.95/41.35  | | | | | 
% 229.95/41.35  | | | | | COMBINE_EQS: (17), (36) imply:
% 229.95/41.35  | | | | |   (37)  all_57_6 = e1
% 229.95/41.35  | | | | | 
% 229.95/41.35  | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (9), (10), (11), (13), (15), (19),
% 229.95/41.35  | | | | |            (21), (22), (25), (26), (37) are inconsistent by sub-proof
% 229.95/41.35  | | | | |            #1735.
% 229.95/41.35  | | | | | 
% 229.95/41.35  | | | | End of split
% 229.95/41.35  | | | | 
% 229.95/41.35  | | | Case 2:
% 229.95/41.35  | | | | 
% 229.95/41.35  | | | |   (38)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3)
% 229.95/41.35  | | | |           = e1)
% 229.95/41.35  | | | | 
% 229.95/41.35  | | | | BETA: splitting (38) gives:
% 229.95/41.35  | | | | 
% 229.95/41.35  | | | | Case 1:
% 229.95/41.35  | | | | | 
% 229.95/41.35  | | | | |   (39)  all_57_6 = e1 & op(e1, e3) = e1
% 229.95/41.35  | | | | | 
% 229.95/41.35  | | | | | ALPHA: (39) implies:
% 229.95/41.35  | | | | |   (40)  all_57_6 = e1
% 229.95/41.35  | | | | | 
% 229.95/41.35  | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (9), (10), (11), (13), (15), (19),
% 229.95/41.35  | | | | |            (21), (22), (25), (26), (40) are inconsistent by sub-proof
% 229.95/41.35  | | | | |            #1735.
% 229.95/41.35  | | | | | 
% 229.95/41.35  | | | | Case 2:
% 229.95/41.35  | | | | | 
% 229.95/41.35  | | | | |   (41)  all_57_12 = e1 & op(e0, e3) = e1
% 229.95/41.35  | | | | | 
% 229.95/41.35  | | | | | ALPHA: (41) implies:
% 229.95/41.35  | | | | |   (42)  all_57_12 = e1
% 229.95/41.35  | | | | | 
% 229.95/41.35  | | | | | BETA: splitting (24) gives:
% 229.95/41.35  | | | | | 
% 229.95/41.35  | | | | | Case 1:
% 229.95/41.35  | | | | | | 
% 229.95/41.35  | | | | | |   (43)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2,
% 229.95/41.35  | | | | | |             e3) = e0)
% 229.95/41.35  | | | | | | 
% 229.95/41.35  | | | | | | BETA: splitting (43) gives:
% 229.95/41.35  | | | | | | 
% 229.95/41.35  | | | | | | Case 1:
% 229.95/41.35  | | | | | | | 
% 229.95/41.35  | | | | | | |   (44)  all_57_0 = e0 & op(e3, e3) = e0
% 229.95/41.35  | | | | | | | 
% 229.95/41.35  | | | | | | | ALPHA: (44) implies:
% 229.95/41.35  | | | | | | |   (45)  op(e3, e3) = e0
% 229.95/41.35  | | | | | | | 
% 229.95/41.35  | | | | | | | REF_CLOSE: (3), (9), (13), (14), (17), (21), (23), (42), (45) are
% 229.95/41.35  | | | | | | |            inconsistent by sub-proof #1288.
% 229.95/41.35  | | | | | | | 
% 229.95/41.35  | | | | | | Case 2:
% 229.95/41.35  | | | | | | | 
% 229.95/41.35  | | | | | | |   (46)  all_57_2 = e0 & op(e2, e3) = e0
% 229.95/41.35  | | | | | | | 
% 229.95/41.35  | | | | | | | REF_CLOSE: (10), (14), (46) are inconsistent by sub-proof #1805.
% 229.95/41.35  | | | | | | | 
% 229.95/41.35  | | | | | | End of split
% 229.95/41.35  | | | | | | 
% 229.95/41.35  | | | | | Case 2:
% 229.95/41.35  | | | | | | 
% 229.95/41.35  | | | | | |   (47)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0,
% 229.95/41.35  | | | | | |             e3) = e0)
% 229.95/41.35  | | | | | | 
% 229.95/41.35  | | | | | | BETA: splitting (47) gives:
% 229.95/41.35  | | | | | | 
% 229.95/41.35  | | | | | | Case 1:
% 229.95/41.35  | | | | | | | 
% 229.95/41.35  | | | | | | |   (48)  all_57_6 = e0 & op(e1, e3) = e0
% 229.95/41.35  | | | | | | | 
% 229.95/41.35  | | | | | | | ALPHA: (48) implies:
% 229.95/41.35  | | | | | | |   (49)  all_57_6 = e0
% 229.95/41.35  | | | | | | | 
% 229.95/41.35  | | | | | | | REF_CLOSE: (10), (17), (49) are inconsistent by sub-proof #1822.
% 229.95/41.35  | | | | | | | 
% 229.95/41.35  | | | | | | Case 2:
% 229.95/41.35  | | | | | | | 
% 229.95/41.35  | | | | | | |   (50)  all_57_12 = e0 & op(e0, e3) = e0
% 229.95/41.35  | | | | | | | 
% 229.95/41.35  | | | | | | | REF_CLOSE: (15), (42), (50) are inconsistent by sub-proof #1279.
% 229.95/41.35  | | | | | | | 
% 229.95/41.35  | | | | | | End of split
% 229.95/41.35  | | | | | | 
% 229.95/41.35  | | | | | End of split
% 229.95/41.35  | | | | | 
% 229.95/41.35  | | | | End of split
% 229.95/41.35  | | | | 
% 229.95/41.35  | | | End of split
% 229.95/41.35  | | | 
% 229.95/41.35  | | Case 2:
% 229.95/41.35  | | | 
% 229.95/41.35  | | |   (51)  all_57_5 = e3 & op(e2, e1) = e3
% 229.95/41.35  | | | 
% 229.95/41.35  | | | ALPHA: (51) implies:
% 229.95/41.35  | | |   (52)  all_57_5 = e3
% 229.95/41.35  | | | 
% 229.95/41.35  | | | REF_CLOSE: (10), (27), (52) are inconsistent by sub-proof #2471.
% 229.95/41.35  | | | 
% 229.95/41.35  | | End of split
% 229.95/41.35  | | 
% 229.95/41.35  | Case 2:
% 229.95/41.35  | | 
% 229.95/41.35  | |   (53)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) =
% 229.95/41.35  | |           e3)
% 229.95/41.35  | | 
% 229.95/41.35  | | REF_CLOSE: (2), (3), (5), (6), (9), (10), (11), (12), (13), (15), (18),
% 229.95/41.35  | |            (19), (21), (53) are inconsistent by sub-proof #1794.
% 229.95/41.35  | | 
% 229.95/41.35  | End of split
% 229.95/41.35  | 
% 229.95/41.35  End of proof
% 229.95/41.35  
% 229.95/41.35  Sub-proof #951 shows that the following formulas are inconsistent:
% 229.95/41.35  ----------------------------------------------------------------
% 229.95/41.35    (1)   ~ (e3 = e1)
% 229.95/41.35    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.95/41.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.95/41.36    (3)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.95/41.36         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.95/41.36    (4)   ~ (all_6_2 = e3)
% 229.95/41.36    (5)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2)
% 229.95/41.36    (6)  op(e1, e1) = all_6_2
% 229.95/41.36    (7)  all_57_7 = e1
% 229.95/41.36    (8)   ~ (e3 = e2)
% 229.95/41.36    (9)   ~ (e3 = e0)
% 229.95/41.36    (10)  all_57_15 = e3
% 229.95/41.36    (11)   ~ (e2 = e0)
% 229.95/41.36    (12)   ~ (e1 = e0)
% 229.95/41.36    (13)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.95/41.36              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.95/41.36                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.95/41.36                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.95/41.36    (14)   ~ (e2 = e1)
% 229.95/41.36    (15)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.95/41.36          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.95/41.36    (16)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.95/41.36          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.95/41.36  
% 229.95/41.36  Begin of proof
% 229.95/41.36  | 
% 229.95/41.36  | BETA: splitting (5) gives:
% 229.95/41.36  | 
% 229.95/41.36  | Case 1:
% 229.95/41.36  | | 
% 229.95/41.36  | |   (17)  all_57_6 = e2 & op(e1, e3) = e2
% 229.95/41.36  | | 
% 229.95/41.36  | | ALPHA: (17) implies:
% 229.95/41.36  | |   (18)  all_57_6 = e2
% 229.95/41.36  | | 
% 229.95/41.36  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13),
% 229.95/41.36  | |            (14), (15), (16), (18) are inconsistent by sub-proof #1245.
% 229.95/41.36  | | 
% 229.95/41.36  | Case 2:
% 229.95/41.36  | | 
% 229.95/41.36  | |   (19)  all_57_7 = e2 & op(e1, e2) = e2
% 229.95/41.36  | | 
% 229.95/41.36  | | ALPHA: (19) implies:
% 229.95/41.36  | |   (20)  all_57_7 = e2
% 229.95/41.36  | | 
% 229.95/41.36  | | REF_CLOSE: (7), (14), (20) are inconsistent by sub-proof #1761.
% 229.95/41.36  | | 
% 229.95/41.36  | End of split
% 229.95/41.36  | 
% 229.95/41.36  End of proof
% 229.95/41.36  
% 229.95/41.36  Sub-proof #952 shows that the following formulas are inconsistent:
% 229.95/41.36  ----------------------------------------------------------------
% 229.95/41.36    (1)   ~ (e3 = e1)
% 229.95/41.36    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.95/41.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.95/41.36    (3)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.95/41.36         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.95/41.36    (4)   ~ (all_6_2 = e3)
% 229.95/41.36    (5)  op(e1, e1) = all_6_2
% 229.95/41.36    (6)   ~ (e3 = e2)
% 229.95/41.36    (7)   ~ (e3 = e0)
% 229.95/41.36    (8)  all_57_15 = e3
% 229.95/41.36    (9)  all_57_11 = e2
% 229.95/41.36    (10)   ~ (e2 = e0)
% 229.95/41.36    (11)   ~ (e1 = e0)
% 229.95/41.36    (12)  all_57_8 = e2
% 229.95/41.36    (13)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.95/41.36              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.95/41.36                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.95/41.36                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.95/41.36    (14)   ~ (e2 = e1)
% 229.95/41.36    (15)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.95/41.36          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.95/41.36    (16)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.95/41.36          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.95/41.36    (17)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 229.95/41.36          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 229.95/41.36    (18)  all_57_7 = e0
% 229.95/41.36  
% 229.95/41.36  Begin of proof
% 229.95/41.36  | 
% 229.95/41.36  | BETA: splitting (17) gives:
% 229.95/41.36  | 
% 229.95/41.36  | Case 1:
% 229.95/41.36  | | 
% 229.95/41.36  | |   (19)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) =
% 229.95/41.36  | |           e1)
% 229.95/41.36  | | 
% 229.95/41.36  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (13), (14),
% 229.95/41.36  | |            (15), (16), (18), (19) are inconsistent by sub-proof #1155.
% 229.95/41.36  | | 
% 229.95/41.36  | Case 2:
% 229.95/41.36  | | 
% 229.95/41.36  | |   (20)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) =
% 229.95/41.36  | |           e1)
% 229.95/41.36  | | 
% 229.95/41.36  | | BETA: splitting (20) gives:
% 229.95/41.36  | | 
% 229.95/41.36  | | Case 1:
% 229.95/41.36  | | | 
% 229.95/41.36  | | |   (21)  all_57_8 = e1 & op(e1, e1) = e1
% 229.95/41.36  | | | 
% 229.95/41.36  | | | REF_CLOSE: (12), (14), (21) are inconsistent by sub-proof #1533.
% 229.95/41.36  | | | 
% 229.95/41.36  | | Case 2:
% 229.95/41.36  | | | 
% 229.95/41.36  | | |   (22)  all_57_11 = e1 & op(e1, e0) = e1
% 229.95/41.36  | | | 
% 229.95/41.36  | | | REF_CLOSE: (9), (14), (22) are inconsistent by sub-proof #1726.
% 229.95/41.36  | | | 
% 229.95/41.36  | | End of split
% 229.95/41.36  | | 
% 229.95/41.36  | End of split
% 229.95/41.36  | 
% 229.95/41.36  End of proof
% 229.95/41.36  
% 229.95/41.36  Sub-proof #953 shows that the following formulas are inconsistent:
% 229.95/41.36  ----------------------------------------------------------------
% 229.95/41.36    (1)  all_57_13 = e1
% 229.95/41.36    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.95/41.36         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.95/41.36    (3)   ~ (e3 = e1)
% 229.95/41.36    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.95/41.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.95/41.36    (5)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.95/41.36         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.95/41.36    (6)   ~ (all_6_2 = e3)
% 229.95/41.36    (7)  op(e1, e1) = all_6_2
% 229.95/41.36    (8)   ~ (e3 = e2)
% 229.95/41.36    (9)   ~ (e3 = e0)
% 229.95/41.36    (10)  all_57_15 = e3
% 229.95/41.36    (11)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.95/41.36          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.95/41.36    (12)   ~ (e2 = e0)
% 229.95/41.36    (13)  e3 = e2
% 229.95/41.36    (14)   ~ (e1 = e0)
% 229.95/41.36    (15)  all_57_6 = e3
% 229.95/41.36    (16)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.95/41.36              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.95/41.36                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.95/41.36                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.95/41.36    (17)  all_57_1 = e3
% 229.95/41.36    (18)   ~ (e2 = e1)
% 229.95/41.36    (19)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.95/41.36          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.95/41.36    (20)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.95/41.36          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.95/41.36    (21)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.95/41.36          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.95/41.36  
% 229.95/41.36  Begin of proof
% 229.95/41.36  | 
% 229.95/41.36  | SIMP: (13) implies:
% 229.95/41.36  |   (22)  e3 = e2
% 229.95/41.36  | 
% 229.95/41.36  | COMBINE_EQS: (15), (22) imply:
% 229.95/41.36  |   (23)  all_57_6 = e2
% 229.95/41.36  | 
% 229.95/41.36  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 229.95/41.36  |            (14), (16), (17), (18), (19), (20), (21), (23) are inconsistent by
% 229.95/41.36  |            sub-proof #961.
% 229.95/41.36  | 
% 229.95/41.36  End of proof
% 229.95/41.36  
% 229.95/41.36  Sub-proof #954 shows that the following formulas are inconsistent:
% 229.95/41.36  ----------------------------------------------------------------
% 229.95/41.36    (1)  all_57_13 = e1
% 229.95/41.36    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.95/41.36         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.95/41.36    (3)   ~ (e3 = e1)
% 229.95/41.36    (4)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 229.95/41.36         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 229.95/41.36    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 229.95/41.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 229.95/41.36    (6)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 229.95/41.36         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 229.95/41.36    (7)   ~ (all_6_2 = e3)
% 229.95/41.36    (8)  op(e1, e1) = all_6_2
% 229.95/41.36    (9)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 229.95/41.36         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 229.95/41.36    (10)   ~ (e3 = e2)
% 229.95/41.36    (11)   ~ (e3 = e0)
% 229.95/41.36    (12)  all_57_15 = e3
% 229.95/41.36    (13)  all_57_4 = e1
% 229.95/41.36    (14)  op(e3, e3) = e0
% 229.95/41.36    (15)  op(e1, e1) = e1
% 229.95/41.36    (16)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 229.95/41.36          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 229.95/41.36    (17)   ~ (e2 = e0)
% 229.95/41.36    (18)   ~ (e1 = e0)
% 229.95/41.36    (19)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 229.95/41.36              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 229.95/41.36                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 229.95/41.36                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 229.95/41.36    (20)  all_57_11 = e1
% 229.95/41.36    (21)  all_57_1 = e3
% 229.95/41.36    (22)   ~ (e2 = e1)
% 229.95/41.36    (23)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 229.95/41.36          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 229.95/41.36    (24)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 229.95/41.36          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 229.95/41.36    (25)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 229.95/41.36          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 229.95/41.36    (26)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 229.95/41.36          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 229.95/41.36  
% 229.95/41.36  Begin of proof
% 229.95/41.36  | 
% 229.95/41.36  | BETA: splitting (9) gives:
% 229.95/41.36  | 
% 229.95/41.36  | Case 1:
% 229.95/41.36  | | 
% 229.95/41.36  | |   (27)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) =
% 229.95/41.36  | |           e2)
% 229.95/41.36  | | 
% 229.95/41.36  | | REF_CLOSE: (5), (10), (14), (17), (21), (27) are inconsistent by sub-proof
% 229.95/41.36  | |            #1224.
% 229.95/41.36  | | 
% 229.95/41.36  | Case 2:
% 229.95/41.36  | | 
% 229.95/41.36  | |   (28)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) =
% 229.95/41.36  | |           e2)
% 229.95/41.36  | | 
% 229.95/41.36  | | BETA: splitting (28) gives:
% 229.95/41.36  | | 
% 229.95/41.36  | | Case 1:
% 229.95/41.36  | | | 
% 229.95/41.36  | | |   (29)  all_57_4 = e2 & op(e3, e1) = e2
% 229.95/41.36  | | | 
% 229.95/41.36  | | | ALPHA: (29) implies:
% 229.95/41.36  | | |   (30)  all_57_4 = e2
% 229.95/41.36  | | | 
% 229.95/41.36  | | | REF_CLOSE: (13), (22), (30) are inconsistent by sub-proof #2430.
% 229.95/41.36  | | | 
% 229.95/41.36  | | Case 2:
% 229.95/41.36  | | | 
% 229.95/41.36  | | |   (31)  all_57_9 = e2 & op(e3, e0) = e2
% 229.95/41.36  | | | 
% 229.95/41.36  | | | ALPHA: (31) implies:
% 229.95/41.36  | | |   (32)  all_57_9 = e2
% 229.95/41.36  | | | 
% 229.95/41.36  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (15),
% 229.95/41.36  | | |            (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 229.95/41.36  | | |            (26), (32) are inconsistent by sub-proof #955.
% 229.95/41.36  | | | 
% 229.95/41.36  | | End of split
% 229.95/41.36  | | 
% 229.95/41.36  | End of split
% 229.95/41.36  | 
% 229.95/41.36  End of proof
% 229.95/41.36  
% 229.95/41.36  Sub-proof #955 shows that the following formulas are inconsistent:
% 229.95/41.36  ----------------------------------------------------------------
% 229.95/41.36    (1)  all_57_9 = e2
% 229.95/41.36    (2)  all_57_13 = e1
% 229.95/41.36    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 229.95/41.36         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 229.95/41.36    (4)   ~ (e3 = e1)
% 230.05/41.36    (5)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.05/41.36         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.05/41.36    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.05/41.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.05/41.36    (7)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.05/41.36         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.05/41.36    (8)   ~ (all_6_2 = e3)
% 230.05/41.36    (9)  op(e1, e1) = all_6_2
% 230.05/41.36    (10)   ~ (e3 = e2)
% 230.05/41.36    (11)   ~ (e3 = e0)
% 230.05/41.36    (12)  all_57_15 = e3
% 230.05/41.36    (13)  op(e1, e1) = e1
% 230.05/41.36    (14)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.05/41.36          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.05/41.36    (15)   ~ (e2 = e0)
% 230.05/41.36    (16)   ~ (e1 = e0)
% 230.05/41.36    (17)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.05/41.36              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.05/41.36                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.05/41.36                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.05/41.36    (18)  all_57_11 = e1
% 230.05/41.36    (19)  all_57_1 = e3
% 230.05/41.36    (20)   ~ (e2 = e1)
% 230.05/41.36    (21)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.05/41.36          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.05/41.36    (22)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.05/41.36          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.05/41.36    (23)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.05/41.36          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.05/41.36    (24)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.05/41.36          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.05/41.36  
% 230.05/41.36  Begin of proof
% 230.05/41.36  | 
% 230.05/41.36  | BETA: splitting (24) gives:
% 230.05/41.36  | 
% 230.05/41.36  | Case 1:
% 230.05/41.36  | | 
% 230.05/41.36  | |   (25)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) =
% 230.05/41.36  | |           e2)
% 230.05/41.36  | | 
% 230.05/41.36  | | BETA: splitting (25) gives:
% 230.05/41.36  | | 
% 230.05/41.36  | | Case 1:
% 230.05/41.36  | | | 
% 230.05/41.36  | | |   (26)  all_57_6 = e2 & op(e1, e3) = e2
% 230.05/41.36  | | | 
% 230.05/41.36  | | | ALPHA: (26) implies:
% 230.05/41.36  | | |   (27)  all_57_6 = e2
% 230.05/41.36  | | | 
% 230.05/41.36  | | | REF_CLOSE: (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (14),
% 230.05/41.36  | | |            (15), (16), (17), (19), (20), (21), (22), (23), (27) are
% 230.05/41.36  | | |            inconsistent by sub-proof #961.
% 230.05/41.36  | | | 
% 230.05/41.36  | | Case 2:
% 230.05/41.36  | | | 
% 230.05/41.36  | | |   (28)  all_57_7 = e2 & op(e1, e2) = e2
% 230.05/41.36  | | | 
% 230.05/41.36  | | | ALPHA: (28) implies:
% 230.05/41.36  | | |   (29)  all_57_7 = e2
% 230.05/41.36  | | | 
% 230.05/41.36  | | | REF_CLOSE: (1), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 230.05/41.36  | | |            (15), (16), (17), (18), (20), (21), (22), (29) are inconsistent
% 230.05/41.36  | | |            by sub-proof #957.
% 230.05/41.36  | | | 
% 230.05/41.36  | | End of split
% 230.05/41.36  | | 
% 230.05/41.36  | Case 2:
% 230.05/41.36  | | 
% 230.05/41.36  | |   (30)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) =
% 230.05/41.36  | |           e2)
% 230.05/41.36  | | 
% 230.05/41.36  | | REF_CLOSE: (6), (13), (18), (20), (30) are inconsistent by sub-proof #956.
% 230.05/41.36  | | 
% 230.05/41.36  | End of split
% 230.05/41.36  | 
% 230.05/41.36  End of proof
% 230.05/41.36  
% 230.05/41.36  Sub-proof #956 shows that the following formulas are inconsistent:
% 230.05/41.36  ----------------------------------------------------------------
% 230.05/41.36    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.05/41.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.05/41.36    (2)  op(e1, e1) = e1
% 230.05/41.36    (3)  all_57_11 = e1
% 230.05/41.36    (4)   ~ (e2 = e1)
% 230.05/41.36    (5)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.05/41.36  
% 230.05/41.36  Begin of proof
% 230.05/41.36  | 
% 230.05/41.36  | BETA: splitting (5) gives:
% 230.05/41.36  | 
% 230.05/41.36  | Case 1:
% 230.05/41.36  | | 
% 230.05/41.36  | |   (6)  all_57_8 = e2 & op(e1, e1) = e2
% 230.05/41.36  | | 
% 230.05/41.36  | | ALPHA: (6) implies:
% 230.05/41.36  | |   (7)  op(e1, e1) = e2
% 230.05/41.36  | | 
% 230.05/41.36  | | REF_CLOSE: (1), (2), (4), (7) are inconsistent by sub-proof #2423.
% 230.05/41.36  | | 
% 230.05/41.36  | Case 2:
% 230.05/41.36  | | 
% 230.05/41.36  | |   (8)  all_57_11 = e2 & op(e1, e0) = e2
% 230.05/41.36  | | 
% 230.05/41.36  | | ALPHA: (8) implies:
% 230.05/41.36  | |   (9)  all_57_11 = e2
% 230.05/41.36  | | 
% 230.05/41.36  | | REF_CLOSE: (3), (4), (9) are inconsistent by sub-proof #2113.
% 230.05/41.36  | | 
% 230.05/41.36  | End of split
% 230.05/41.36  | 
% 230.05/41.36  End of proof
% 230.05/41.36  
% 230.05/41.36  Sub-proof #957 shows that the following formulas are inconsistent:
% 230.05/41.36  ----------------------------------------------------------------
% 230.05/41.36    (1)  all_57_9 = e2
% 230.05/41.36    (2)   ~ (e3 = e1)
% 230.05/41.36    (3)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.05/41.36         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.05/41.36    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.05/41.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.05/41.36    (5)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.05/41.36         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.05/41.36    (6)   ~ (all_6_2 = e3)
% 230.05/41.36    (7)  op(e1, e1) = all_6_2
% 230.05/41.36    (8)  all_57_7 = e2
% 230.05/41.36    (9)   ~ (e3 = e2)
% 230.05/41.36    (10)   ~ (e3 = e0)
% 230.05/41.36    (11)  all_57_15 = e3
% 230.05/41.36    (12)  op(e1, e1) = e1
% 230.05/41.36    (13)   ~ (e2 = e0)
% 230.05/41.36    (14)   ~ (e1 = e0)
% 230.05/41.36    (15)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.05/41.36              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.05/41.36                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.05/41.36                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.05/41.36    (16)  all_57_11 = e1
% 230.05/41.36    (17)   ~ (e2 = e1)
% 230.05/41.36    (18)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.05/41.36          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.05/41.36    (19)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.05/41.36          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.05/41.36  
% 230.05/41.36  Begin of proof
% 230.05/41.36  | 
% 230.05/41.36  | BETA: splitting (3) gives:
% 230.05/41.36  | 
% 230.05/41.36  | Case 1:
% 230.05/41.36  | | 
% 230.05/41.36  | |   (20)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) =
% 230.05/41.36  | |           e0)
% 230.05/41.36  | | 
% 230.05/41.36  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 230.05/41.36  | |            (13), (14), (15), (17), (18), (19), (20) are inconsistent by
% 230.05/41.36  | |            sub-proof #958.
% 230.05/41.36  | | 
% 230.05/41.36  | Case 2:
% 230.05/41.36  | | 
% 230.05/41.36  | |   (21)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 230.05/41.36  | |           e0)
% 230.05/41.36  | | 
% 230.05/41.36  | | BETA: splitting (21) gives:
% 230.05/41.36  | | 
% 230.05/41.36  | | Case 1:
% 230.05/41.36  | | | 
% 230.05/41.36  | | |   (22)  all_57_8 = e0 & op(e1, e1) = e0
% 230.05/41.36  | | | 
% 230.05/41.36  | | | ALPHA: (22) implies:
% 230.05/41.36  | | |   (23)  op(e1, e1) = e0
% 230.05/41.36  | | | 
% 230.05/41.36  | | | REF_CLOSE: (4), (12), (14), (23) are inconsistent by sub-proof #2427.
% 230.05/41.36  | | | 
% 230.05/41.36  | | Case 2:
% 230.05/41.36  | | | 
% 230.05/41.36  | | |   (24)  all_57_11 = e0 & op(e1, e0) = e0
% 230.05/41.36  | | | 
% 230.05/41.36  | | | REF_CLOSE: (14), (16), (24) are inconsistent by sub-proof #1257.
% 230.05/41.36  | | | 
% 230.05/41.36  | | End of split
% 230.05/41.36  | | 
% 230.05/41.36  | End of split
% 230.05/41.36  | 
% 230.05/41.36  End of proof
% 230.05/41.36  
% 230.05/41.36  Sub-proof #958 shows that the following formulas are inconsistent:
% 230.05/41.36  ----------------------------------------------------------------
% 230.05/41.36    (1)  all_57_9 = e2
% 230.05/41.36    (2)   ~ (e3 = e1)
% 230.05/41.36    (3)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.05/41.36         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.05/41.36    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.05/41.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.05/41.36    (5)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.05/41.36         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.05/41.36    (6)   ~ (all_6_2 = e3)
% 230.05/41.36    (7)  op(e1, e1) = all_6_2
% 230.05/41.36    (8)  all_57_7 = e2
% 230.05/41.36    (9)   ~ (e3 = e2)
% 230.05/41.36    (10)   ~ (e3 = e0)
% 230.05/41.36    (11)  all_57_15 = e3
% 230.05/41.36    (12)  op(e1, e1) = e1
% 230.05/41.36    (13)   ~ (e2 = e0)
% 230.05/41.36    (14)   ~ (e1 = e0)
% 230.05/41.36    (15)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.05/41.36              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.05/41.36                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.05/41.36                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.05/41.36    (16)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0)
% 230.05/41.36    (17)   ~ (e2 = e1)
% 230.05/41.36    (18)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.05/41.36          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.05/41.36    (19)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.05/41.36          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.05/41.36  
% 230.05/41.36  Begin of proof
% 230.05/41.36  | 
% 230.05/41.36  | BETA: splitting (16) gives:
% 230.05/41.36  | 
% 230.05/41.36  | Case 1:
% 230.05/41.36  | | 
% 230.05/41.36  | |   (20)  all_57_6 = e0 & op(e1, e3) = e0
% 230.05/41.36  | | 
% 230.05/41.36  | | ALPHA: (20) implies:
% 230.05/41.36  | |   (21)  all_57_6 = e0
% 230.05/41.36  | | 
% 230.05/41.36  | | REF_CLOSE: (2), (4), (5), (6), (7), (8), (9), (10), (11), (13), (14), (15),
% 230.05/41.36  | |            (17), (18), (19), (21) are inconsistent by sub-proof #1775.
% 230.05/41.36  | | 
% 230.05/41.36  | Case 2:
% 230.05/41.36  | | 
% 230.05/41.36  | |   (22)  all_57_7 = e0 & op(e1, e2) = e0
% 230.05/41.36  | | 
% 230.05/41.36  | | ALPHA: (22) implies:
% 230.05/41.36  | |   (23)  all_57_7 = e0
% 230.05/41.36  | | 
% 230.05/41.36  | | COMBINE_EQS: (8), (23) imply:
% 230.05/41.36  | |   (24)  e2 = e0
% 230.05/41.36  | | 
% 230.05/41.36  | | COMBINE_EQS: (1), (24) imply:
% 230.05/41.36  | |   (25)  all_57_9 = e0
% 230.05/41.36  | | 
% 230.05/41.36  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 230.05/41.36  | |            (14), (15), (17), (18), (19), (25) are inconsistent by sub-proof
% 230.05/41.36  | |            #959.
% 230.05/41.36  | | 
% 230.05/41.36  | End of split
% 230.05/41.36  | 
% 230.05/41.36  End of proof
% 230.05/41.36  
% 230.05/41.36  Sub-proof #959 shows that the following formulas are inconsistent:
% 230.05/41.36  ----------------------------------------------------------------
% 230.05/41.36    (1)   ~ (e3 = e1)
% 230.05/41.36    (2)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.05/41.36         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.05/41.36    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.05/41.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.05/41.36    (4)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.05/41.36         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.05/41.36    (5)   ~ (all_6_2 = e3)
% 230.05/41.36    (6)  op(e1, e1) = all_6_2
% 230.05/41.36    (7)  all_57_7 = e2
% 230.05/41.36    (8)   ~ (e3 = e2)
% 230.05/41.36    (9)   ~ (e3 = e0)
% 230.05/41.36    (10)  all_57_15 = e3
% 230.05/41.36    (11)  all_57_9 = e0
% 230.05/41.36    (12)  op(e1, e1) = e1
% 230.05/41.36    (13)   ~ (e2 = e0)
% 230.05/41.36    (14)   ~ (e1 = e0)
% 230.05/41.36    (15)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.05/41.36              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.05/41.36                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.05/41.36                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.05/41.36    (16)   ~ (e2 = e1)
% 230.05/41.36    (17)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.05/41.36          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.05/41.36    (18)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.05/41.36          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.05/41.36  
% 230.05/41.36  Begin of proof
% 230.05/41.36  | 
% 230.05/41.36  | BETA: splitting (2) gives:
% 230.05/41.36  | 
% 230.05/41.36  | Case 1:
% 230.05/41.36  | | 
% 230.05/41.36  | |   (19)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) =
% 230.05/41.36  | |           e0)
% 230.05/41.37  | | 
% 230.05/41.37  | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (13), (14), (15),
% 230.05/41.37  | |            (16), (17), (18), (19) are inconsistent by sub-proof #960.
% 230.05/41.37  | | 
% 230.05/41.37  | Case 2:
% 230.05/41.37  | | 
% 230.05/41.37  | |   (20)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 230.05/41.37  | |           e0)
% 230.05/41.37  | | 
% 230.05/41.37  | | BETA: splitting (20) gives:
% 230.05/41.37  | | 
% 230.05/41.37  | | Case 1:
% 230.05/41.37  | | | 
% 230.05/41.37  | | |   (21)  all_57_8 = e0 & op(e1, e1) = e0
% 230.05/41.37  | | | 
% 230.05/41.37  | | | ALPHA: (21) implies:
% 230.05/41.37  | | |   (22)  op(e1, e1) = e0
% 230.05/41.37  | | | 
% 230.05/41.37  | | | REF_CLOSE: (3), (12), (14), (22) are inconsistent by sub-proof #2427.
% 230.05/41.37  | | | 
% 230.05/41.37  | | Case 2:
% 230.05/41.37  | | | 
% 230.05/41.37  | | |   (23)  all_57_11 = e0 & op(e1, e0) = e0
% 230.05/41.37  | | | 
% 230.05/41.37  | | | ALPHA: (23) implies:
% 230.05/41.37  | | |   (24)  all_57_11 = e0
% 230.05/41.37  | | | 
% 230.05/41.37  | | | REF_CLOSE: (1), (8), (10), (11), (13), (14), (16), (17), (18), (24) are
% 230.05/41.37  | | |            inconsistent by sub-proof #1144.
% 230.05/41.37  | | | 
% 230.05/41.37  | | End of split
% 230.05/41.37  | | 
% 230.05/41.37  | End of split
% 230.05/41.37  | 
% 230.05/41.37  End of proof
% 230.05/41.37  
% 230.05/41.37  Sub-proof #960 shows that the following formulas are inconsistent:
% 230.05/41.37  ----------------------------------------------------------------
% 230.05/41.37    (1)   ~ (e3 = e1)
% 230.05/41.37    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.05/41.37           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.05/41.37    (3)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.05/41.37         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.05/41.37    (4)   ~ (all_6_2 = e3)
% 230.05/41.37    (5)  op(e1, e1) = all_6_2
% 230.05/41.37    (6)  all_57_7 = e2
% 230.05/41.37    (7)   ~ (e3 = e2)
% 230.05/41.37    (8)   ~ (e3 = e0)
% 230.05/41.37    (9)  all_57_15 = e3
% 230.05/41.37    (10)   ~ (e2 = e0)
% 230.05/41.37    (11)   ~ (e1 = e0)
% 230.05/41.37    (12)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.05/41.37              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.05/41.37                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.05/41.37                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.05/41.37    (13)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0)
% 230.05/41.37    (14)   ~ (e2 = e1)
% 230.05/41.37    (15)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.05/41.37          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.05/41.37    (16)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.05/41.37          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.05/41.37  
% 230.05/41.37  Begin of proof
% 230.05/41.37  | 
% 230.05/41.37  | BETA: splitting (13) gives:
% 230.05/41.37  | 
% 230.05/41.37  | Case 1:
% 230.05/41.37  | | 
% 230.05/41.37  | |   (17)  all_57_6 = e0 & op(e1, e3) = e0
% 230.05/41.37  | | 
% 230.05/41.37  | | ALPHA: (17) implies:
% 230.05/41.37  | |   (18)  all_57_6 = e0
% 230.05/41.37  | | 
% 230.05/41.37  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 230.05/41.37  | |            (14), (15), (16), (18) are inconsistent by sub-proof #1775.
% 230.05/41.37  | | 
% 230.05/41.37  | Case 2:
% 230.05/41.37  | | 
% 230.05/41.37  | |   (19)  all_57_7 = e0 & op(e1, e2) = e0
% 230.05/41.37  | | 
% 230.05/41.37  | | REF_CLOSE: (6), (10), (19) are inconsistent by sub-proof #2148.
% 230.05/41.37  | | 
% 230.05/41.37  | End of split
% 230.05/41.37  | 
% 230.05/41.37  End of proof
% 230.05/41.37  
% 230.05/41.37  Sub-proof #961 shows that the following formulas are inconsistent:
% 230.05/41.37  ----------------------------------------------------------------
% 230.05/41.37    (1)  all_57_13 = e1
% 230.05/41.37    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.05/41.37         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.05/41.37    (3)   ~ (e3 = e1)
% 230.05/41.37    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.05/41.37           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.05/41.37    (5)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.05/41.37         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.05/41.37    (6)   ~ (all_6_2 = e3)
% 230.05/41.37    (7)  op(e1, e1) = all_6_2
% 230.05/41.37    (8)   ~ (e3 = e2)
% 230.05/41.37    (9)   ~ (e3 = e0)
% 230.05/41.37    (10)  all_57_15 = e3
% 230.05/41.37    (11)  all_57_6 = e2
% 230.05/41.37    (12)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.05/41.37          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.05/41.37    (13)   ~ (e2 = e0)
% 230.05/41.37    (14)   ~ (e1 = e0)
% 230.05/41.37    (15)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.05/41.37              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.05/41.37                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.05/41.37                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.05/41.37    (16)  all_57_1 = e3
% 230.05/41.37    (17)   ~ (e2 = e1)
% 230.05/41.37    (18)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.05/41.37          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.05/41.37    (19)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.05/41.37          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.05/41.37    (20)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.05/41.37          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.05/41.37  
% 230.05/41.37  Begin of proof
% 230.05/41.37  | 
% 230.05/41.37  | BETA: splitting (5) gives:
% 230.05/41.37  | 
% 230.05/41.37  | Case 1:
% 230.05/41.37  | | 
% 230.05/41.37  | |   (21)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 230.05/41.37  | |           e3)
% 230.05/41.37  | | 
% 230.05/41.37  | | BETA: splitting (21) gives:
% 230.05/41.37  | | 
% 230.05/41.37  | | Case 1:
% 230.05/41.37  | | | 
% 230.05/41.37  | | |   (22)  all_57_6 = e3 & op(e1, e3) = e3
% 230.05/41.37  | | | 
% 230.05/41.37  | | | ALPHA: (22) implies:
% 230.05/41.37  | | |   (23)  all_57_6 = e3
% 230.05/41.37  | | | 
% 230.05/41.37  | | | REF_CLOSE: (8), (11), (23) are inconsistent by sub-proof #2463.
% 230.05/41.37  | | | 
% 230.05/41.37  | | Case 2:
% 230.05/41.37  | | | 
% 230.05/41.37  | | |   (24)  all_57_7 = e3 & op(e1, e2) = e3
% 230.05/41.37  | | | 
% 230.05/41.37  | | | ALPHA: (24) implies:
% 230.05/41.37  | | |   (25)  all_57_7 = e3
% 230.05/41.37  | | | 
% 230.05/41.37  | | | REF_CLOSE: (1), (2), (3), (8), (9), (12), (13), (14), (16), (17), (20),
% 230.05/41.37  | | |            (25) are inconsistent by sub-proof #1214.
% 230.05/41.37  | | | 
% 230.05/41.37  | | End of split
% 230.05/41.37  | | 
% 230.05/41.37  | Case 2:
% 230.05/41.37  | | 
% 230.05/41.37  | |   (26)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 230.05/41.37  | |           e3)
% 230.05/41.37  | | 
% 230.05/41.37  | | REF_CLOSE: (3), (4), (6), (7), (8), (9), (10), (13), (14), (15), (17), (18),
% 230.05/41.37  | |            (19), (26) are inconsistent by sub-proof #1786.
% 230.05/41.37  | | 
% 230.05/41.37  | End of split
% 230.05/41.37  | 
% 230.05/41.37  End of proof
% 230.05/41.37  
% 230.05/41.37  Sub-proof #962 shows that the following formulas are inconsistent:
% 230.05/41.37  ----------------------------------------------------------------
% 230.05/41.37    (1)   ~ (all_48_2 = e0) | ( ~ (all_48_0 = e2) & op(all_48_1, e3) = all_48_0 &
% 230.05/41.37           op(e3, e0) = all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 =
% 230.05/41.37             e1) & op(e3, e0) = all_48_1 & $i(all_48_1))
% 230.05/41.37    (2)  all_48_2 = e0
% 230.05/41.37    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.05/41.37         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.05/41.37    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.05/41.37         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.05/41.37    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.05/41.37         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.05/41.37    (6)   ~ (e3 = e1)
% 230.05/41.37    (7)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.05/41.37         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.05/41.37    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.05/41.37           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.05/41.37    (9)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.05/41.37         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.05/41.37    (10)   ~ (all_6_2 = e3)
% 230.05/41.37    (11)  ( ~ (all_18_0 = e1) & op(all_18_1, e3) = all_18_0 & op(e3, e0) =
% 230.05/41.37            all_18_1 & $i(all_18_0) & $i(all_18_1)) | ( ~ (all_18_1 = e2) & op(e3,
% 230.05/41.37              e0) = all_18_1 & $i(all_18_1))
% 230.05/41.37    (12)  op(e1, e1) = all_6_2
% 230.05/41.37    (13)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.05/41.37          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.05/41.37    (14)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 230.05/41.37            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 230.05/41.37              e3) = all_22_1 & $i(all_22_1))
% 230.05/41.37    (15)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1)
% 230.05/41.37    (16)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.05/41.37          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.05/41.37    (17)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.05/41.37          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.05/41.37    (18)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 230.05/41.37          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.05/41.37    (19)   ~ (e3 = e2)
% 230.05/41.37    (20)  all_55_10 = e1 | all_55_10 = e0
% 230.05/41.37    (21)   ~ (e3 = e0)
% 230.05/41.37    (22)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.05/41.37          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.05/41.37    (23)   ~ (all_6_2 = e2)
% 230.05/41.37    (24)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 230.05/41.37    (25)  op(e0, e3) = all_53_3
% 230.05/41.37    (26)   ~ (all_53_2 = e0)
% 230.05/41.37    (27)  all_57_0 = e0
% 230.05/41.37    (28)  all_57_15 = e3
% 230.05/41.37    (29)  op(e3, e3) = e0
% 230.05/41.37    (30)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.05/41.37          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.05/41.37            e1)
% 230.05/41.37    (31)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.05/41.37          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.05/41.37    (32)   ~ (e2 = e0)
% 230.05/41.37    (33)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 230.05/41.37            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 230.05/41.37            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 230.05/41.37            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 230.05/41.37              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 230.05/41.37            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 230.05/41.37            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 230.05/41.37              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 230.05/41.37              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 230.05/41.37            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 230.05/41.37            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 230.05/41.37            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 230.05/41.37              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 230.05/41.37              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 230.05/41.37            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 230.05/41.37              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 230.05/41.37            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 230.05/41.37            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 230.05/41.37              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 230.05/41.37              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 230.05/41.37            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 230.05/41.37            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 230.05/41.37    (34)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 230.05/41.37            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 230.05/41.37              e3) = all_12_1 & $i(all_12_1))
% 230.05/41.37    (35)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.05/41.37          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.05/41.37    (36)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 230.05/41.37          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 230.05/41.37    (37)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.05/41.37          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.05/41.37    (38)   ~ (all_53_2 = all_53_3)
% 230.05/41.37    (39)  all_55_8 = all_53_2
% 230.05/41.37    (40)  op(e0, e0) = e3
% 230.05/41.37    (41)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.05/41.37          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.05/41.37            e2)
% 230.05/41.37    (42)   ~ (all_53_3 = e0)
% 230.05/41.37    (43)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.05/41.37              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.05/41.37                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.05/41.37                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.05/41.37    (44)  all_55_10 = all_6_2
% 230.05/41.37    (45)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.05/41.37          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.05/41.37    (46)   ~ (all_53_12 = e3)
% 230.05/41.37    (47)  op(e1, e3) = all_53_2
% 230.05/41.37    (48)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.05/41.37          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.05/41.37    (49)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.05/41.37          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.05/41.37    (50)  all_57_1 = e3
% 230.05/41.37    (51)   ~ (all_53_12 = e0)
% 230.05/41.37    (52)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.05/41.37          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 230.05/41.37    (53)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.05/41.37          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.05/41.37    (54)   ~ (all_6_2 = e0)
% 230.05/41.37    (55)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.05/41.37          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.05/41.37    (56)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.05/41.37          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.05/41.37    (57)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.05/41.37          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.05/41.37    (58)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.05/41.37          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.05/41.37    (59)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.05/41.37          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.05/41.37    (60)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.05/41.37          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.05/41.37    (61)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.05/41.37          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.05/41.37    (62)  op(e3, e0) = all_53_12
% 230.05/41.37  
% 230.05/41.37  Begin of proof
% 230.05/41.37  | 
% 230.05/41.37  | BETA: splitting (15) gives:
% 230.05/41.37  | 
% 230.05/41.37  | Case 1:
% 230.05/41.37  | | 
% 230.05/41.37  | |   (63)  all_57_1 = e1 & op(e3, e2) = e1
% 230.05/41.37  | | 
% 230.05/41.37  | | REF_CLOSE: (6), (50), (63) are inconsistent by sub-proof #2453.
% 230.05/41.37  | | 
% 230.05/41.37  | Case 2:
% 230.05/41.37  | | 
% 230.05/41.37  | |   (64)  all_57_3 = e1 & op(e2, e2) = e1
% 230.05/41.37  | | 
% 230.05/41.37  | | ALPHA: (64) implies:
% 230.05/41.37  | |   (65)  all_57_3 = e1
% 230.05/41.37  | |   (66)  op(e2, e2) = e1
% 230.05/41.37  | | 
% 230.05/41.37  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 230.05/41.37  | |            (14), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 230.05/41.37  | |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 230.05/41.37  | |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 230.05/41.37  | |            (48), (49), (51), (52), (53), (54), (55), (56), (57), (58), (59),
% 230.05/41.37  | |            (60), (61), (62), (65), (66) are inconsistent by sub-proof #963.
% 230.05/41.37  | | 
% 230.05/41.37  | End of split
% 230.05/41.37  | 
% 230.05/41.37  End of proof
% 230.05/41.37  
% 230.05/41.37  Sub-proof #963 shows that the following formulas are inconsistent:
% 230.05/41.37  ----------------------------------------------------------------
% 230.05/41.37    (1)   ~ (all_48_2 = e0) | ( ~ (all_48_0 = e2) & op(all_48_1, e3) = all_48_0 &
% 230.05/41.37           op(e3, e0) = all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 =
% 230.05/41.37             e1) & op(e3, e0) = all_48_1 & $i(all_48_1))
% 230.05/41.37    (2)  all_48_2 = e0
% 230.05/41.37    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.05/41.37         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.05/41.37    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.05/41.37         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.05/41.37    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.05/41.37         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.05/41.37    (6)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.05/41.37         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.05/41.37    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.05/41.37           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.05/41.37    (8)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.05/41.37         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.05/41.37    (9)   ~ (all_6_2 = e3)
% 230.05/41.37    (10)  ( ~ (all_18_0 = e1) & op(all_18_1, e3) = all_18_0 & op(e3, e0) =
% 230.05/41.37            all_18_1 & $i(all_18_0) & $i(all_18_1)) | ( ~ (all_18_1 = e2) & op(e3,
% 230.05/41.37              e0) = all_18_1 & $i(all_18_1))
% 230.05/41.37    (11)  op(e1, e1) = all_6_2
% 230.05/41.37    (12)  op(e2, e2) = e1
% 230.05/41.37    (13)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.05/41.37          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.05/41.37    (14)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 230.05/41.37            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 230.05/41.37              e3) = all_22_1 & $i(all_22_1))
% 230.05/41.37    (15)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.05/41.37          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.05/41.37    (16)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.05/41.37          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.05/41.37    (17)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 230.05/41.37          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.05/41.37    (18)   ~ (e3 = e2)
% 230.05/41.37    (19)  all_55_10 = e1 | all_55_10 = e0
% 230.05/41.37    (20)   ~ (e3 = e0)
% 230.05/41.37    (21)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.05/41.37          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.05/41.37    (22)   ~ (all_6_2 = e2)
% 230.05/41.37    (23)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 230.05/41.37    (24)  op(e0, e3) = all_53_3
% 230.05/41.37    (25)   ~ (all_53_2 = e0)
% 230.05/41.37    (26)  all_57_0 = e0
% 230.05/41.37    (27)  all_57_15 = e3
% 230.05/41.37    (28)  op(e3, e3) = e0
% 230.05/41.37    (29)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.05/41.37          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.05/41.37            e1)
% 230.05/41.37    (30)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.05/41.37          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.05/41.37    (31)   ~ (e2 = e0)
% 230.05/41.37    (32)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 230.05/41.37            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 230.05/41.37            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 230.05/41.37            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 230.05/41.37              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 230.05/41.37            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 230.05/41.37            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 230.05/41.37              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 230.05/41.37              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 230.05/41.37            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 230.05/41.37            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 230.05/41.37            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 230.05/41.37              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 230.05/41.37              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 230.05/41.37            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 230.05/41.37              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 230.05/41.37            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 230.05/41.37            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 230.05/41.37              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 230.05/41.37              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 230.05/41.37            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 230.05/41.37            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 230.05/41.37    (33)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 230.05/41.37            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 230.05/41.37              e3) = all_12_1 & $i(all_12_1))
% 230.05/41.37    (34)  all_57_3 = e1
% 230.05/41.37    (35)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.05/41.37          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.05/41.37    (36)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 230.05/41.37          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 230.05/41.37    (37)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.05/41.37          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.05/41.37    (38)   ~ (all_53_2 = all_53_3)
% 230.05/41.37    (39)  all_55_8 = all_53_2
% 230.05/41.37    (40)  op(e0, e0) = e3
% 230.05/41.37    (41)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.05/41.37          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.05/41.37            e2)
% 230.05/41.37    (42)   ~ (all_53_3 = e0)
% 230.05/41.37    (43)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.05/41.37              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.05/41.37                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.05/41.37                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.05/41.37    (44)  all_55_10 = all_6_2
% 230.05/41.37    (45)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.05/41.37          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.05/41.37    (46)   ~ (all_53_12 = e3)
% 230.05/41.37    (47)  op(e1, e3) = all_53_2
% 230.05/41.37    (48)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.05/41.37          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.05/41.37    (49)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.05/41.37          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.05/41.37    (50)   ~ (all_53_12 = e0)
% 230.05/41.38    (51)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.05/41.38          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 230.05/41.38    (52)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.05/41.38          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.05/41.38    (53)   ~ (all_6_2 = e0)
% 230.05/41.38    (54)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.05/41.38          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.05/41.38    (55)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.05/41.38          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.05/41.38    (56)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.05/41.38          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.05/41.38    (57)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.05/41.38          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.05/41.38    (58)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.05/41.38          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.05/41.38    (59)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.05/41.38          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.05/41.38    (60)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.05/41.38          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.05/41.38    (61)  op(e3, e0) = all_53_12
% 230.05/41.38  
% 230.05/41.38  Begin of proof
% 230.05/41.38  | 
% 230.05/41.38  | BETA: splitting (19) gives:
% 230.05/41.38  | 
% 230.05/41.38  | Case 1:
% 230.05/41.38  | | 
% 230.05/41.38  | |   (62)  all_55_10 = e1
% 230.05/41.38  | | 
% 230.05/41.38  | | COMBINE_EQS: (44), (62) imply:
% 230.05/41.38  | |   (63)  all_6_2 = e1
% 230.05/41.38  | | 
% 230.05/41.38  | | SIMP: (63) implies:
% 230.05/41.38  | |   (64)  all_6_2 = e1
% 230.05/41.38  | | 
% 230.05/41.38  | | REDUCE: (9), (64) imply:
% 230.05/41.38  | |   (65)   ~ (e3 = e1)
% 230.05/41.38  | | 
% 230.05/41.38  | | SIMP: (65) implies:
% 230.05/41.38  | |   (66)   ~ (e3 = e1)
% 230.05/41.38  | | 
% 230.05/41.38  | | REDUCE: (22), (64) imply:
% 230.05/41.38  | |   (67)   ~ (e2 = e1)
% 230.05/41.38  | | 
% 230.05/41.38  | | SIMP: (67) implies:
% 230.05/41.38  | |   (68)   ~ (e2 = e1)
% 230.05/41.38  | | 
% 230.05/41.38  | | REDUCE: (53), (64) imply:
% 230.05/41.38  | |   (69)   ~ (e1 = e0)
% 230.05/41.38  | | 
% 230.05/41.38  | | REDUCE: (11), (64) imply:
% 230.05/41.38  | |   (70)  op(e1, e1) = e1
% 230.05/41.38  | | 
% 230.05/41.38  | | BETA: splitting (29) gives:
% 230.05/41.38  | | 
% 230.05/41.38  | | Case 1:
% 230.05/41.38  | | | 
% 230.05/41.38  | | |   (71)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2)
% 230.05/41.38  | | |           = e1)
% 230.05/41.38  | | | 
% 230.05/41.38  | | | BETA: splitting (71) gives:
% 230.05/41.38  | | | 
% 230.05/41.38  | | | Case 1:
% 230.05/41.38  | | | | 
% 230.05/41.38  | | | |   (72)  all_57_12 = e1 & op(e0, e3) = e1
% 230.05/41.38  | | | | 
% 230.05/41.38  | | | | ALPHA: (72) implies:
% 230.05/41.38  | | | |   (73)  all_57_12 = e1
% 230.05/41.38  | | | |   (74)  op(e0, e3) = e1
% 230.05/41.38  | | | | 
% 230.05/41.38  | | | | BETA: splitting (13) gives:
% 230.05/41.38  | | | | 
% 230.05/41.38  | | | | Case 1:
% 230.05/41.38  | | | | | 
% 230.05/41.38  | | | | |   (75)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3,
% 230.05/41.38  | | | | |             e2) = e1)
% 230.05/41.38  | | | | | 
% 230.05/41.38  | | | | | REF_CLOSE: (5), (7), (12), (18), (20), (26), (30), (31), (37), (66),
% 230.05/41.38  | | | | |            (68), (69), (75) are inconsistent by sub-proof #1551.
% 230.05/41.38  | | | | | 
% 230.05/41.38  | | | | Case 2:
% 230.05/41.38  | | | | | 
% 230.05/41.38  | | | | |   (76)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3,
% 230.05/41.38  | | | | |             e0) = e1)
% 230.05/41.38  | | | | | 
% 230.05/41.38  | | | | | BETA: splitting (76) gives:
% 230.05/41.38  | | | | | 
% 230.05/41.38  | | | | | Case 1:
% 230.05/41.38  | | | | | | 
% 230.05/41.38  | | | | | |   (77)  all_57_4 = e1 & op(e3, e1) = e1
% 230.05/41.38  | | | | | | 
% 230.05/41.38  | | | | | | ALPHA: (77) implies:
% 230.05/41.38  | | | | | |   (78)  all_57_4 = e1
% 230.05/41.38  | | | | | | 
% 230.05/41.38  | | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (11), (12), (13),
% 230.05/41.38  | | | | | |            (14), (15), (16), (17), (18), (20), (21), (24), (26),
% 230.05/41.38  | | | | | |            (27), (28), (29), (30), (31), (33), (34), (35), (36),
% 230.05/41.38  | | | | | |            (37), (40), (41), (42), (43), (45), (46), (48), (49),
% 230.05/41.38  | | | | | |            (50), (51), (52), (54), (55), (56), (57), (58), (59),
% 230.05/41.38  | | | | | |            (60), (61), (66), (68), (69), (70), (73), (74), (78) are
% 230.05/41.38  | | | | | |            inconsistent by sub-proof #1003.
% 230.05/41.38  | | | | | | 
% 230.05/41.38  | | | | | Case 2:
% 230.05/41.38  | | | | | | 
% 230.05/41.38  | | | | | |   (79)  all_57_9 = e1 & op(e3, e0) = e1
% 230.05/41.38  | | | | | | 
% 230.05/41.38  | | | | | | ALPHA: (79) implies:
% 230.05/41.38  | | | | | |   (80)  op(e3, e0) = e1
% 230.05/41.38  | | | | | | 
% 230.05/41.38  | | | | | | REF_CLOSE: (1), (2), (7), (9), (10), (11), (12), (14), (23), (24),
% 230.05/41.38  | | | | | |            (25), (28), (32), (33), (38), (39), (47), (50), (61),
% 230.05/41.38  | | | | | |            (68), (70), (74), (80) are inconsistent by sub-proof
% 230.05/41.38  | | | | | |            #997.
% 230.05/41.38  | | | | | | 
% 230.05/41.38  | | | | | End of split
% 230.05/41.38  | | | | | 
% 230.05/41.38  | | | | End of split
% 230.05/41.38  | | | | 
% 230.05/41.38  | | | Case 2:
% 230.05/41.38  | | | | 
% 230.05/41.38  | | | |   (81)  all_57_13 = e1 & op(e0, e2) = e1
% 230.05/41.38  | | | | 
% 230.05/41.38  | | | | ALPHA: (81) implies:
% 230.05/41.38  | | | |   (82)  all_57_13 = e1
% 230.05/41.38  | | | | 
% 230.05/41.38  | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (11), (12), (13), (15),
% 230.05/41.38  | | | |            (16), (17), (18), (20), (21), (24), (26), (27), (28), (29),
% 230.05/41.38  | | | |            (30), (31), (34), (35), (36), (37), (40), (41), (42), (43),
% 230.05/41.38  | | | |            (45), (46), (48), (49), (50), (51), (52), (54), (55), (56),
% 230.05/41.38  | | | |            (57), (58), (59), (60), (61), (66), (68), (69), (82) are
% 230.05/41.38  | | | |            inconsistent by sub-proof #976.
% 230.05/41.38  | | | | 
% 230.05/41.38  | | | End of split
% 230.05/41.38  | | | 
% 230.05/41.38  | | Case 2:
% 230.05/41.38  | | | 
% 230.05/41.38  | | |   (83)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0)
% 230.05/41.38  | | |           = e1)
% 230.05/41.38  | | | 
% 230.05/41.38  | | | BETA: splitting (83) gives:
% 230.05/41.38  | | | 
% 230.05/41.38  | | | Case 1:
% 230.05/41.38  | | | | 
% 230.05/41.38  | | | |   (84)  all_57_14 = e1 & op(e0, e1) = e1
% 230.05/41.38  | | | | 
% 230.05/41.38  | | | | ALPHA: (84) implies:
% 230.05/41.38  | | | |   (85)  all_57_14 = e1
% 230.05/41.38  | | | | 
% 230.05/41.38  | | | | BETA: splitting (13) gives:
% 230.05/41.38  | | | | 
% 230.05/41.38  | | | | Case 1:
% 230.05/41.38  | | | | | 
% 230.05/41.38  | | | | |   (86)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3,
% 230.05/41.38  | | | | |             e2) = e1)
% 230.05/41.38  | | | | | 
% 230.05/41.38  | | | | | REF_CLOSE: (5), (7), (12), (18), (20), (26), (30), (31), (37), (66),
% 230.05/41.38  | | | | |            (68), (69), (86) are inconsistent by sub-proof #1551.
% 230.05/41.38  | | | | | 
% 230.05/41.38  | | | | Case 2:
% 230.05/41.38  | | | | | 
% 230.05/41.38  | | | | |   (87)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3,
% 230.05/41.38  | | | | |             e0) = e1)
% 230.05/41.38  | | | | | 
% 230.05/41.38  | | | | | BETA: splitting (87) gives:
% 230.05/41.38  | | | | | 
% 230.05/41.38  | | | | | Case 1:
% 230.05/41.38  | | | | | | 
% 230.05/41.38  | | | | | |   (88)  all_57_4 = e1 & op(e3, e1) = e1
% 230.05/41.38  | | | | | | 
% 230.05/41.38  | | | | | | ALPHA: (88) implies:
% 230.05/41.38  | | | | | |   (89)  all_57_4 = e1
% 230.05/41.38  | | | | | | 
% 230.05/41.38  | | | | | | BETA: splitting (4) gives:
% 230.05/41.38  | | | | | | 
% 230.05/41.38  | | | | | | Case 1:
% 230.05/41.38  | | | | | | | 
% 230.05/41.38  | | | | | | |   (90)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 &
% 230.05/41.38  | | | | | | |           op(e2, e3) = e1)
% 230.05/41.38  | | | | | | | 
% 230.05/41.38  | | | | | | | BETA: splitting (90) gives:
% 230.05/41.38  | | | | | | | 
% 230.05/41.38  | | | | | | | Case 1:
% 230.05/41.38  | | | | | | | | 
% 230.05/41.38  | | | | | | | |   (91)  all_57_0 = e1 & op(e3, e3) = e1
% 230.05/41.38  | | | | | | | | 
% 230.05/41.38  | | | | | | | | REF_CLOSE: (5), (7), (12), (13), (15), (18), (20), (26), (28),
% 230.05/41.38  | | | | | | | |            (30), (31), (35), (37), (46), (61), (66), (68), (69),
% 230.05/41.38  | | | | | | | |            (89), (91) are inconsistent by sub-proof #996.
% 230.05/41.38  | | | | | | | | 
% 230.05/41.38  | | | | | | | Case 2:
% 230.05/41.38  | | | | | | | | 
% 230.05/41.38  | | | | | | | |   (92)  all_57_2 = e1 & op(e2, e3) = e1
% 230.05/41.38  | | | | | | | | 
% 230.05/41.38  | | | | | | | | ALPHA: (92) implies:
% 230.05/41.38  | | | | | | | |   (93)  all_57_2 = e1
% 230.05/41.38  | | | | | | | | 
% 230.05/41.38  | | | | | | | | BETA: splitting (45) gives:
% 230.05/41.38  | | | | | | | | 
% 230.05/41.38  | | | | | | | | Case 1:
% 230.05/41.38  | | | | | | | | | 
% 230.05/41.38  | | | | | | | | |   (94)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 &
% 230.05/41.38  | | | | | | | | |           op(e2, e2) = e3)
% 230.05/41.38  | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (11), (12),
% 230.05/41.38  | | | | | | | | |            (13), (15), (16), (17), (18), (20), (21), (24),
% 230.05/41.38  | | | | | | | | |            (27), (28), (29), (30), (31), (34), (35), (36),
% 230.05/41.38  | | | | | | | | |            (37), (40), (41), (42), (43), (46), (48), (49),
% 230.05/41.38  | | | | | | | | |            (50), (51), (52), (54), (55), (56), (57), (58),
% 230.05/41.38  | | | | | | | | |            (59), (60), (61), (66), (68), (69), (89), (94) are
% 230.05/41.38  | | | | | | | | |            inconsistent by sub-proof #973.
% 230.05/41.38  | | | | | | | | | 
% 230.05/41.38  | | | | | | | | Case 2:
% 230.05/41.38  | | | | | | | | | 
% 230.05/41.38  | | | | | | | | |   (95)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 &
% 230.05/41.38  | | | | | | | | |           op(e2, e0) = e3)
% 230.05/41.38  | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | BETA: splitting (95) gives:
% 230.05/41.38  | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | Case 1:
% 230.05/41.38  | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | |   (96)  all_57_5 = e3 & op(e2, e1) = e3
% 230.05/41.38  | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | ALPHA: (96) implies:
% 230.05/41.38  | | | | | | | | | |   (97)  all_57_5 = e3
% 230.05/41.38  | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | BETA: splitting (17) gives:
% 230.05/41.38  | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | Case 1:
% 230.05/41.38  | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | |   (98)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 230.05/41.38  | | | | | | | | | | |           & op(e2, e1) = e0)
% 230.05/41.38  | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | BETA: splitting (98) gives:
% 230.05/41.38  | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | Case 1:
% 230.05/41.38  | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | |   (99)  all_57_4 = e0 & op(e3, e1) = e0
% 230.05/41.38  | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | | ALPHA: (99) implies:
% 230.05/41.38  | | | | | | | | | | | |   (100)  all_57_4 = e0
% 230.05/41.38  | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | | REF_CLOSE: (5), (7), (12), (13), (15), (18), (20), (26),
% 230.05/41.38  | | | | | | | | | | | |            (28), (30), (31), (35), (37), (46), (61), (66),
% 230.05/41.38  | | | | | | | | | | | |            (68), (69), (100) are inconsistent by sub-proof
% 230.05/41.38  | | | | | | | | | | | |            #1012.
% 230.05/41.38  | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | Case 2:
% 230.05/41.38  | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | |   (101)  all_57_5 = e0 & op(e2, e1) = e0
% 230.05/41.38  | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | | ALPHA: (101) implies:
% 230.05/41.38  | | | | | | | | | | | |   (102)  all_57_5 = e0
% 230.05/41.38  | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (11), (12),
% 230.05/41.38  | | | | | | | | | | | |            (13), (15), (16), (17), (18), (20), (21), (24),
% 230.05/41.38  | | | | | | | | | | | |            (27), (28), (29), (30), (31), (34), (35), (36),
% 230.05/41.38  | | | | | | | | | | | |            (37), (40), (41), (42), (43), (45), (46), (48),
% 230.05/41.38  | | | | | | | | | | | |            (49), (50), (51), (52), (54), (55), (56), (57),
% 230.05/41.38  | | | | | | | | | | | |            (58), (59), (60), (61), (66), (68), (69), (89),
% 230.05/41.38  | | | | | | | | | | | |            (102) are inconsistent by sub-proof #972.
% 230.05/41.38  | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | End of split
% 230.05/41.38  | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | Case 2:
% 230.05/41.38  | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | |   (103)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 230.05/41.38  | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 230.05/41.38  | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (11), (12),
% 230.05/41.38  | | | | | | | | | | |            (13), (15), (16), (17), (18), (20), (21), (24),
% 230.05/41.38  | | | | | | | | | | |            (27), (28), (29), (30), (31), (34), (35), (36),
% 230.05/41.38  | | | | | | | | | | |            (37), (40), (41), (42), (43), (46), (48), (49),
% 230.05/41.38  | | | | | | | | | | |            (50), (52), (54), (55), (56), (57), (58), (59),
% 230.05/41.38  | | | | | | | | | | |            (60), (61), (66), (68), (69), (70), (85), (93),
% 230.05/41.38  | | | | | | | | | | |            (97), (103) are inconsistent by sub-proof #971.
% 230.05/41.38  | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | End of split
% 230.05/41.38  | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | Case 2:
% 230.05/41.38  | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | |   (104)  all_57_10 = e3 & op(e2, e0) = e3
% 230.05/41.38  | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | ALPHA: (104) implies:
% 230.05/41.38  | | | | | | | | | |   (105)  all_57_10 = e3
% 230.05/41.38  | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | REF_CLOSE: (7), (18), (20), (27), (31), (40), (43), (52),
% 230.05/41.38  | | | | | | | | | |            (57), (66), (68), (69), (105) are inconsistent by
% 230.05/41.38  | | | | | | | | | |            sub-proof #1746.
% 230.05/41.38  | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | End of split
% 230.05/41.38  | | | | | | | | | 
% 230.05/41.38  | | | | | | | | End of split
% 230.05/41.38  | | | | | | | | 
% 230.05/41.38  | | | | | | | End of split
% 230.05/41.38  | | | | | | | 
% 230.05/41.38  | | | | | | Case 2:
% 230.05/41.38  | | | | | | | 
% 230.05/41.38  | | | | | | |   (106)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 &
% 230.05/41.38  | | | | | | |            op(e0, e3) = e1)
% 230.05/41.38  | | | | | | | 
% 230.05/41.38  | | | | | | | BETA: splitting (106) gives:
% 230.05/41.38  | | | | | | | 
% 230.05/41.38  | | | | | | | Case 1:
% 230.05/41.38  | | | | | | | | 
% 230.05/41.38  | | | | | | | |   (107)  all_57_6 = e1 & op(e1, e3) = e1
% 230.05/41.38  | | | | | | | | 
% 230.05/41.38  | | | | | | | | ALPHA: (107) implies:
% 230.05/41.38  | | | | | | | |   (108)  all_57_6 = e1
% 230.05/41.38  | | | | | | | | 
% 230.05/41.38  | | | | | | | | BETA: splitting (49) gives:
% 230.05/41.38  | | | | | | | | 
% 230.05/41.38  | | | | | | | | Case 1:
% 230.05/41.38  | | | | | | | | | 
% 230.05/41.38  | | | | | | | | |   (109)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 &
% 230.05/41.38  | | | | | | | | |            op(e2, e3) = e3)
% 230.05/41.38  | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | BETA: splitting (109) gives:
% 230.05/41.38  | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | Case 1:
% 230.05/41.38  | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | |   (110)  all_57_0 = e3 & op(e3, e3) = e3
% 230.05/41.38  | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | ALPHA: (110) implies:
% 230.05/41.38  | | | | | | | | | |   (111)  op(e3, e3) = e3
% 230.05/41.38  | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | REF_CLOSE: (7), (20), (28), (111) are inconsistent by
% 230.05/41.38  | | | | | | | | | |            sub-proof #2494.
% 230.05/41.38  | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | Case 2:
% 230.05/41.38  | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | |   (112)  all_57_2 = e3 & op(e2, e3) = e3
% 230.05/41.38  | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | ALPHA: (112) implies:
% 230.05/41.38  | | | | | | | | | |   (113)  all_57_2 = e3
% 230.05/41.38  | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (11), (12),
% 230.05/41.38  | | | | | | | | | |            (13), (15), (16), (17), (18), (20), (21), (24),
% 230.05/41.38  | | | | | | | | | |            (27), (28), (29), (30), (31), (34), (35), (36),
% 230.05/41.38  | | | | | | | | | |            (37), (40), (41), (42), (43), (46), (48), (49),
% 230.05/41.38  | | | | | | | | | |            (50), (51), (52), (54), (55), (56), (57), (58),
% 230.05/41.38  | | | | | | | | | |            (59), (60), (61), (66), (68), (69), (89), (113)
% 230.05/41.38  | | | | | | | | | |            are inconsistent by sub-proof #974.
% 230.05/41.38  | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | End of split
% 230.05/41.38  | | | | | | | | | 
% 230.05/41.38  | | | | | | | | Case 2:
% 230.05/41.38  | | | | | | | | | 
% 230.05/41.38  | | | | | | | | |   (114)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 &
% 230.05/41.38  | | | | | | | | |            op(e0, e3) = e3)
% 230.05/41.38  | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | BETA: splitting (114) gives:
% 230.05/41.38  | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | Case 1:
% 230.05/41.38  | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | |   (115)  all_57_6 = e3 & op(e1, e3) = e3
% 230.05/41.38  | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | ALPHA: (115) implies:
% 230.05/41.38  | | | | | | | | | |   (116)  all_57_6 = e3
% 230.05/41.38  | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | REF_CLOSE: (66), (108), (116) are inconsistent by sub-proof
% 230.05/41.38  | | | | | | | | | |            #2017.
% 230.05/41.38  | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | Case 2:
% 230.05/41.38  | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | |   (117)  all_57_12 = e3 & op(e0, e3) = e3
% 230.05/41.38  | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | ALPHA: (117) implies:
% 230.05/41.38  | | | | | | | | | |   (118)  all_57_12 = e3
% 230.05/41.38  | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | BETA: splitting (17) gives:
% 230.05/41.38  | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | Case 1:
% 230.05/41.38  | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | |   (119)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 230.05/41.38  | | | | | | | | | | |            & op(e2, e1) = e0)
% 230.05/41.38  | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | BETA: splitting (119) gives:
% 230.05/41.38  | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | Case 1:
% 230.05/41.38  | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | |   (120)  all_57_4 = e0 & op(e3, e1) = e0
% 230.05/41.38  | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | | ALPHA: (120) implies:
% 230.05/41.38  | | | | | | | | | | | |   (121)  all_57_4 = e0
% 230.05/41.38  | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | | REF_CLOSE: (5), (7), (12), (13), (15), (18), (20), (26),
% 230.05/41.38  | | | | | | | | | | | |            (28), (30), (31), (35), (37), (46), (61), (66),
% 230.05/41.38  | | | | | | | | | | | |            (68), (69), (121) are inconsistent by sub-proof
% 230.05/41.38  | | | | | | | | | | | |            #1012.
% 230.05/41.38  | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | Case 2:
% 230.05/41.38  | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | |   (122)  all_57_5 = e0 & op(e2, e1) = e0
% 230.05/41.38  | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | | ALPHA: (122) implies:
% 230.05/41.38  | | | | | | | | | | | |   (123)  all_57_5 = e0
% 230.05/41.38  | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (11), (12),
% 230.05/41.38  | | | | | | | | | | | |            (13), (15), (16), (17), (18), (20), (21), (24),
% 230.05/41.38  | | | | | | | | | | | |            (27), (28), (29), (30), (31), (34), (35), (36),
% 230.05/41.38  | | | | | | | | | | | |            (37), (40), (41), (42), (43), (45), (46), (48),
% 230.05/41.38  | | | | | | | | | | | |            (49), (50), (51), (52), (54), (55), (56), (57),
% 230.05/41.38  | | | | | | | | | | | |            (58), (59), (60), (61), (66), (68), (69), (89),
% 230.05/41.38  | | | | | | | | | | | |            (123) are inconsistent by sub-proof #972.
% 230.05/41.38  | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | End of split
% 230.05/41.38  | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | Case 2:
% 230.05/41.38  | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | |   (124)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 230.05/41.38  | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 230.05/41.38  | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | REF_CLOSE: (7), (18), (27), (29), (31), (41), (66), (68),
% 230.05/41.38  | | | | | | | | | | |            (69), (70), (118), (124) are inconsistent by
% 230.05/41.38  | | | | | | | | | | |            sub-proof #970.
% 230.05/41.38  | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | End of split
% 230.05/41.38  | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | End of split
% 230.05/41.38  | | | | | | | | | 
% 230.05/41.38  | | | | | | | | End of split
% 230.05/41.38  | | | | | | | | 
% 230.05/41.38  | | | | | | | Case 2:
% 230.05/41.38  | | | | | | | | 
% 230.05/41.38  | | | | | | | |   (125)  all_57_12 = e1 & op(e0, e3) = e1
% 230.05/41.38  | | | | | | | | 
% 230.05/41.38  | | | | | | | | ALPHA: (125) implies:
% 230.05/41.38  | | | | | | | |   (126)  all_57_12 = e1
% 230.05/41.38  | | | | | | | |   (127)  op(e0, e3) = e1
% 230.05/41.38  | | | | | | | | 
% 230.05/41.38  | | | | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (11), (12), (13),
% 230.05/41.38  | | | | | | | |            (14), (15), (16), (17), (18), (20), (21), (24), (26),
% 230.05/41.38  | | | | | | | |            (27), (28), (29), (30), (31), (33), (34), (35), (36),
% 230.05/41.38  | | | | | | | |            (37), (40), (41), (42), (43), (45), (46), (48), (49),
% 230.05/41.38  | | | | | | | |            (50), (51), (52), (54), (55), (56), (57), (58), (59),
% 230.05/41.38  | | | | | | | |            (60), (61), (66), (68), (69), (70), (89), (126),
% 230.05/41.38  | | | | | | | |            (127) are inconsistent by sub-proof #1003.
% 230.05/41.38  | | | | | | | | 
% 230.05/41.38  | | | | | | | End of split
% 230.05/41.38  | | | | | | | 
% 230.05/41.38  | | | | | | End of split
% 230.05/41.38  | | | | | | 
% 230.05/41.38  | | | | | Case 2:
% 230.05/41.38  | | | | | | 
% 230.05/41.38  | | | | | |   (128)  all_57_9 = e1 & op(e3, e0) = e1
% 230.05/41.38  | | | | | | 
% 230.05/41.38  | | | | | | ALPHA: (128) implies:
% 230.05/41.38  | | | | | |   (129)  all_57_9 = e1
% 230.05/41.38  | | | | | |   (130)  op(e3, e0) = e1
% 230.05/41.38  | | | | | | 
% 230.05/41.38  | | | | | | BETA: splitting (4) gives:
% 230.05/41.38  | | | | | | 
% 230.05/41.38  | | | | | | Case 1:
% 230.05/41.38  | | | | | | | 
% 230.05/41.38  | | | | | | |   (131)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 &
% 230.05/41.38  | | | | | | |            op(e2, e3) = e1)
% 230.05/41.38  | | | | | | | 
% 230.05/41.38  | | | | | | | BETA: splitting (131) gives:
% 230.05/41.38  | | | | | | | 
% 230.05/41.38  | | | | | | | Case 1:
% 230.05/41.38  | | | | | | | | 
% 230.05/41.38  | | | | | | | |   (132)  all_57_0 = e1 & op(e3, e3) = e1
% 230.05/41.38  | | | | | | | | 
% 230.05/41.38  | | | | | | | | REF_CLOSE: (26), (69), (132) are inconsistent by sub-proof
% 230.05/41.38  | | | | | | | |            #2454.
% 230.05/41.38  | | | | | | | | 
% 230.05/41.38  | | | | | | | Case 2:
% 230.05/41.38  | | | | | | | | 
% 230.05/41.38  | | | | | | | |   (133)  all_57_2 = e1 & op(e2, e3) = e1
% 230.05/41.38  | | | | | | | | 
% 230.05/41.38  | | | | | | | | ALPHA: (133) implies:
% 230.05/41.38  | | | | | | | |   (134)  all_57_2 = e1
% 230.05/41.38  | | | | | | | | 
% 230.05/41.38  | | | | | | | | BETA: splitting (45) gives:
% 230.05/41.38  | | | | | | | | 
% 230.05/41.38  | | | | | | | | Case 1:
% 230.05/41.38  | | | | | | | | | 
% 230.05/41.38  | | | | | | | | |   (135)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 &
% 230.05/41.38  | | | | | | | | |            op(e2, e2) = e3)
% 230.05/41.38  | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | REF_CLOSE: (7), (12), (66), (134), (135) are inconsistent by
% 230.05/41.38  | | | | | | | | |            sub-proof #995.
% 230.05/41.38  | | | | | | | | | 
% 230.05/41.38  | | | | | | | | Case 2:
% 230.05/41.38  | | | | | | | | | 
% 230.05/41.38  | | | | | | | | |   (136)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 &
% 230.05/41.38  | | | | | | | | |            op(e2, e0) = e3)
% 230.05/41.38  | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | BETA: splitting (136) gives:
% 230.05/41.38  | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | Case 1:
% 230.05/41.38  | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | |   (137)  all_57_5 = e3 & op(e2, e1) = e3
% 230.05/41.38  | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | ALPHA: (137) implies:
% 230.05/41.38  | | | | | | | | | |   (138)  all_57_5 = e3
% 230.05/41.38  | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | BETA: splitting (17) gives:
% 230.05/41.38  | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | Case 1:
% 230.05/41.38  | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | |   (139)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 230.05/41.38  | | | | | | | | | | |            & op(e2, e1) = e0)
% 230.05/41.38  | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | BETA: splitting (139) gives:
% 230.05/41.38  | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | Case 1:
% 230.05/41.38  | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | |   (140)  all_57_4 = e0 & op(e3, e1) = e0
% 230.05/41.38  | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | | ALPHA: (140) implies:
% 230.05/41.38  | | | | | | | | | | | |   (141)  all_57_4 = e0
% 230.05/41.38  | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | | REF_CLOSE: (7), (15), (18), (20), (28), (31), (35), (46),
% 230.05/41.38  | | | | | | | | | | | |            (61), (68), (129), (141) are inconsistent by
% 230.05/41.38  | | | | | | | | | | | |            sub-proof #1403.
% 230.05/41.38  | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | Case 2:
% 230.05/41.38  | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | |   (142)  all_57_5 = e0 & op(e2, e1) = e0
% 230.05/41.38  | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | | REF_CLOSE: (20), (138), (142) are inconsistent by sub-proof
% 230.05/41.38  | | | | | | | | | | | |            #2414.
% 230.05/41.38  | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | End of split
% 230.05/41.38  | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | Case 2:
% 230.05/41.38  | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | |   (143)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 230.05/41.38  | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 230.05/41.38  | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (11), (12),
% 230.05/41.38  | | | | | | | | | | |            (13), (15), (16), (17), (18), (20), (21), (24),
% 230.05/41.38  | | | | | | | | | | |            (27), (28), (29), (30), (31), (34), (35), (36),
% 230.05/41.38  | | | | | | | | | | |            (37), (40), (41), (42), (43), (46), (48), (49),
% 230.05/41.38  | | | | | | | | | | |            (50), (52), (54), (55), (56), (57), (58), (59),
% 230.05/41.38  | | | | | | | | | | |            (60), (61), (66), (68), (69), (70), (85), (134),
% 230.05/41.38  | | | | | | | | | | |            (138), (143) are inconsistent by sub-proof #971.
% 230.05/41.38  | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | End of split
% 230.05/41.38  | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | Case 2:
% 230.05/41.38  | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | |   (144)  all_57_10 = e3 & op(e2, e0) = e3
% 230.05/41.38  | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | ALPHA: (144) implies:
% 230.05/41.38  | | | | | | | | | |   (145)  all_57_10 = e3
% 230.05/41.38  | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | REF_CLOSE: (18), (20), (27), (31), (43), (52), (68), (69),
% 230.05/41.38  | | | | | | | | | |            (129), (145) are inconsistent by sub-proof #1985.
% 230.05/41.38  | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | End of split
% 230.05/41.38  | | | | | | | | | 
% 230.05/41.38  | | | | | | | | End of split
% 230.05/41.38  | | | | | | | | 
% 230.05/41.38  | | | | | | | End of split
% 230.05/41.38  | | | | | | | 
% 230.05/41.38  | | | | | | Case 2:
% 230.05/41.38  | | | | | | | 
% 230.05/41.38  | | | | | | |   (146)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 &
% 230.05/41.38  | | | | | | |            op(e0, e3) = e1)
% 230.05/41.38  | | | | | | | 
% 230.05/41.38  | | | | | | | BETA: splitting (146) gives:
% 230.05/41.38  | | | | | | | 
% 230.05/41.38  | | | | | | | Case 1:
% 230.05/41.38  | | | | | | | | 
% 230.05/41.38  | | | | | | | |   (147)  all_57_6 = e1 & op(e1, e3) = e1
% 230.05/41.38  | | | | | | | | 
% 230.05/41.38  | | | | | | | | ALPHA: (147) implies:
% 230.05/41.38  | | | | | | | |   (148)  all_57_6 = e1
% 230.05/41.38  | | | | | | | | 
% 230.05/41.38  | | | | | | | | BETA: splitting (49) gives:
% 230.05/41.38  | | | | | | | | 
% 230.05/41.38  | | | | | | | | Case 1:
% 230.05/41.38  | | | | | | | | | 
% 230.05/41.38  | | | | | | | | |   (149)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 &
% 230.05/41.38  | | | | | | | | |            op(e2, e3) = e3)
% 230.05/41.38  | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | BETA: splitting (149) gives:
% 230.05/41.38  | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | Case 1:
% 230.05/41.38  | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | |   (150)  all_57_0 = e3 & op(e3, e3) = e3
% 230.05/41.38  | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | ALPHA: (150) implies:
% 230.05/41.38  | | | | | | | | | |   (151)  op(e3, e3) = e3
% 230.05/41.38  | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | REF_CLOSE: (7), (20), (28), (151) are inconsistent by
% 230.05/41.38  | | | | | | | | | |            sub-proof #2494.
% 230.05/41.38  | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | Case 2:
% 230.05/41.38  | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | |   (152)  all_57_2 = e3 & op(e2, e3) = e3
% 230.05/41.38  | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | ALPHA: (152) implies:
% 230.05/41.38  | | | | | | | | | |   (153)  all_57_2 = e3
% 230.05/41.38  | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | BETA: splitting (17) gives:
% 230.05/41.38  | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | Case 1:
% 230.05/41.38  | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | |   (154)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 230.05/41.38  | | | | | | | | | | |            & op(e2, e1) = e0)
% 230.05/41.38  | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | BETA: splitting (154) gives:
% 230.05/41.38  | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | Case 1:
% 230.05/41.38  | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | |   (155)  all_57_4 = e0 & op(e3, e1) = e0
% 230.05/41.38  | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | | ALPHA: (155) implies:
% 230.05/41.38  | | | | | | | | | | | |   (156)  all_57_4 = e0
% 230.05/41.38  | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | | REF_CLOSE: (7), (15), (18), (20), (28), (31), (35), (46),
% 230.05/41.38  | | | | | | | | | | | |            (61), (68), (129), (156) are inconsistent by
% 230.05/41.38  | | | | | | | | | | | |            sub-proof #1403.
% 230.05/41.38  | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | Case 2:
% 230.05/41.38  | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | |   (157)  all_57_5 = e0 & op(e2, e1) = e0
% 230.05/41.38  | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | | ALPHA: (157) implies:
% 230.05/41.38  | | | | | | | | | | | |   (158)  all_57_5 = e0
% 230.05/41.38  | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | | BETA: splitting (48) gives:
% 230.05/41.38  | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | | Case 1:
% 230.05/41.38  | | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | | |   (159)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 230.05/41.38  | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 230.05/41.38  | | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | | | REF_CLOSE: (7), (12), (18), (68), (153), (159) are
% 230.05/41.38  | | | | | | | | | | | | |            inconsistent by sub-proof #969.
% 230.05/41.38  | | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | | Case 2:
% 230.05/41.38  | | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | | |   (160)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 230.05/41.38  | | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 230.05/41.38  | | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | | | BETA: splitting (160) gives:
% 230.05/41.38  | | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | | | Case 1:
% 230.05/41.38  | | | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | | | |   (161)  all_57_5 = e2 & op(e2, e1) = e2
% 230.05/41.38  | | | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | | | | ALPHA: (161) implies:
% 230.05/41.38  | | | | | | | | | | | | | |   (162)  all_57_5 = e2
% 230.05/41.38  | | | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | | | | REF_CLOSE: (31), (158), (162) are inconsistent by sub-proof
% 230.05/41.38  | | | | | | | | | | | | | |            #2363.
% 230.05/41.38  | | | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | | | Case 2:
% 230.05/41.38  | | | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | | | |   (163)  all_57_10 = e2 & op(e2, e0) = e2
% 230.05/41.38  | | | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | | | | ALPHA: (163) implies:
% 230.05/41.38  | | | | | | | | | | | | | |   (164)  all_57_10 = e2
% 230.05/41.38  | | | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | | | | BETA: splitting (36) gives:
% 230.05/41.38  | | | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | | | | Case 1:
% 230.05/41.38  | | | | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | | | | |   (165)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 230.05/41.38  | | | | | | | | | | | | | | |            & op(e2, e1) = e3)
% 230.05/41.38  | | | | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | | | | | BETA: splitting (165) gives:
% 230.05/41.38  | | | | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | | | | | Case 1:
% 230.05/41.38  | | | | | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | | | | | |   (166)  all_57_4 = e3 & op(e3, e1) = e3
% 230.05/41.38  | | | | | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | | | | | | ALPHA: (166) implies:
% 230.05/41.38  | | | | | | | | | | | | | | | |   (167)  all_57_4 = e3
% 230.05/41.38  | | | | | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | | | | | | BETA: splitting (8) gives:
% 230.05/41.38  | | | | | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | | | | | | Case 1:
% 230.05/41.38  | | | | | | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | | | | | | |   (168)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 230.05/41.38  | | | | | | | | | | | | | | | | |            & op(e1, e2) = e3)
% 230.05/41.38  | | | | | | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | | | | | | | BETA: splitting (168) gives:
% 230.05/41.38  | | | | | | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | | | | | | | Case 1:
% 230.05/41.38  | | | | | | | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | | | | | | | |   (169)  all_57_6 = e3 & op(e1, e3) = e3
% 230.05/41.38  | | | | | | | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | | | | | | | | ALPHA: (169) implies:
% 230.05/41.38  | | | | | | | | | | | | | | | | | |   (170)  all_57_6 = e3
% 230.05/41.38  | | | | | | | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (18), (26), (28), (31), (54), (66),
% 230.05/41.38  | | | | | | | | | | | | | | | | | |            (68), (69), (153), (170) are inconsistent by
% 230.05/41.38  | | | | | | | | | | | | | | | | | |            sub-proof #1287.
% 230.05/41.38  | | | | | | | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | | | | | | | Case 2:
% 230.05/41.38  | | | | | | | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | | | | | | | |   (171)  all_57_7 = e3 & op(e1, e2) = e3
% 230.05/41.38  | | | | | | | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | | | | | | | | ALPHA: (171) implies:
% 230.05/41.38  | | | | | | | | | | | | | | | | | |   (172)  all_57_7 = e3
% 230.05/41.38  | | | | | | | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | | | | | | | | BETA: splitting (41) gives:
% 230.05/41.38  | | | | | | | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | | | | | | | | Case 1:
% 230.05/41.38  | | | | | | | | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | | | | | | | | |   (173)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 230.05/41.38  | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 230.05/41.38  | | | | | | | | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | | | | | | | | | BETA: splitting (173) gives:
% 230.05/41.38  | | | | | | | | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | | | | | | | | | Case 1:
% 230.05/41.38  | | | | | | | | | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | | | | | | | | | |   (174)  all_57_12 = e2 & op(e0, e3) = e2
% 230.05/41.38  | | | | | | | | | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | | | | | | | | | | ALPHA: (174) implies:
% 230.05/41.38  | | | | | | | | | | | | | | | | | | | |   (175)  all_57_12 = e2
% 230.05/41.38  | | | | | | | | | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | | | | | | | | | | BETA: splitting (5) gives:
% 230.05/41.38  | | | | | | | | | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.05/41.38  | | | | | | | | | | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | | | | | | | | | | |   (176)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 230.05/41.38  | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 230.05/41.38  | | | | | | | | | | | | | | | | | | | | | 
% 230.05/41.38  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (176) gives:
% 230.05/41.38  | | | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | |   (177)  all_57_1 = e2 & op(e3, e2) = e2
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (177) implies:
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | |   (178)  all_57_1 = e2
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (60) gives:
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | |   (179)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e2)
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (179) gives:
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | |   (180)  all_57_6 = e2 & op(e1, e3) = e2
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (180) implies:
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | |   (181)  all_57_6 = e2
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (26), (66), (68), (69), (153), (175), (181)
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1927.
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | |   (182)  all_57_7 = e2 & op(e1, e2) = e2
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (172), (182) are inconsistent by sub-proof
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | |            #2092.
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | |   (183)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e1, e0) = e2)
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (183) gives:
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | |   (184)  all_57_8 = e2 & op(e1, e1) = e2
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (184) implies:
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | |   (185)  op(e1, e1) = e2
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (68), (70), (185) are inconsistent by
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2423.
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | |   (186)  all_57_11 = e2 & op(e1, e0) = e2
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (186) implies:
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | |   (187)  all_57_11 = e2
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (43) gives:
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | | |   (188)  all_57_15 = e0 & op(e0, e0) = e0
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (188) implies:
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | | |   (189)  op(e0, e0) = e0
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (20), (40), (189) are inconsistent by
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2304.
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | | |   (190)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (190) implies:
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | | |   (191)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e0)
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (15), (18), (28), (31), (50), (61), (68),
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | | |            (129), (164), (167), (178), (187), (191) are
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #968.
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | |   (192)  all_57_3 = e2 & op(e2, e2) = e2
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (192) implies:
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | |   (193)  op(e2, e2) = e2
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12), (68), (193) are inconsistent by
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2306.
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | End of split
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | |   (194)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | |   (195)  all_57_7 = e2 & op(e1, e2) = e2
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (172), (195) are inconsistent by sub-proof
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | |            #2092.
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | |   (196)  all_57_13 = e2 & op(e0, e2) = e2
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (11), (12),
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | |            (13), (15), (16), (17), (18), (20), (21), (24),
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | |            (27), (28), (29), (30), (31), (34), (35), (36),
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | |            (37), (40), (41), (42), (43), (45), (46), (48),
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | |            (49), (50), (52), (54), (55), (56), (57), (58),
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | |            (59), (60), (61), (66), (68), (69), (129), (153),
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | |            (158), (164), (167), (196) are inconsistent by
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #965.
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | End of split
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | End of split
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | Case 2:
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | |   (197)  all_57_13 = e2 & op(e0, e2) = e2
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (11), (12),
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | |            (13), (15), (16), (17), (18), (20), (21), (24),
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | |            (27), (28), (29), (30), (31), (34), (35), (36),
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | |            (37), (40), (41), (42), (43), (45), (46), (48),
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | |            (49), (50), (52), (54), (55), (56), (57), (58),
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | |            (59), (60), (61), (66), (68), (69), (129), (153),
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | |            (158), (164), (167), (197) are inconsistent by
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | |            sub-proof #965.
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | End of split
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | Case 2:
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | |   (198)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 230.05/41.39  | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (27), (68), (85), (198) are inconsistent by
% 230.05/41.39  | | | | | | | | | | | | | | | | | | |            sub-proof #1529.
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | End of split
% 230.05/41.39  | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | End of split
% 230.05/41.39  | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | Case 2:
% 230.05/41.39  | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | |   (199)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 230.05/41.39  | | | | | | | | | | | | | | | | |            e3 & op(e1, e0) = e3)
% 230.05/41.39  | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (11), (18), (20), (27), (31), (43),
% 230.05/41.39  | | | | | | | | | | | | | | | | |            (52), (57), (66), (68), (69), (199) are
% 230.05/41.39  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1786.
% 230.05/41.39  | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | End of split
% 230.05/41.39  | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | Case 2:
% 230.05/41.39  | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | |   (200)  all_57_5 = e3 & op(e2, e1) = e3
% 230.05/41.39  | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | ALPHA: (200) implies:
% 230.05/41.39  | | | | | | | | | | | | | | | |   (201)  all_57_5 = e3
% 230.05/41.39  | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | COMBINE_EQS: (158), (201) imply:
% 230.05/41.39  | | | | | | | | | | | | | | | |   (202)  e3 = e0
% 230.05/41.39  | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | SIMP: (202) implies:
% 230.05/41.39  | | | | | | | | | | | | | | | |   (203)  e3 = e0
% 230.05/41.39  | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | COMBINE_EQS: (153), (203) imply:
% 230.05/41.39  | | | | | | | | | | | | | | | |   (204)  all_57_2 = e0
% 230.05/41.39  | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (11), (12),
% 230.05/41.39  | | | | | | | | | | | | | | | |            (13), (15), (16), (17), (18), (20), (21), (24),
% 230.05/41.39  | | | | | | | | | | | | | | | |            (27), (28), (29), (30), (31), (34), (35), (36),
% 230.05/41.39  | | | | | | | | | | | | | | | |            (37), (40), (41), (42), (43), (46), (48), (49),
% 230.05/41.39  | | | | | | | | | | | | | | | |            (50), (52), (54), (55), (56), (57), (58), (59),
% 230.05/41.39  | | | | | | | | | | | | | | | |            (60), (61), (66), (68), (69), (201), (204) are
% 230.05/41.39  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1021.
% 230.05/41.39  | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | End of split
% 230.05/41.39  | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | Case 2:
% 230.05/41.39  | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | |   (205)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 230.05/41.39  | | | | | | | | | | | | | | |            e3 & op(e0, e1) = e3)
% 230.05/41.39  | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (11), (18), (20), (27), (29), (31),
% 230.05/41.39  | | | | | | | | | | | | | | |            (41), (43), (66), (68), (69), (205) are
% 230.05/41.39  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1794.
% 230.05/41.39  | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | End of split
% 230.05/41.39  | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | End of split
% 230.05/41.39  | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | End of split
% 230.05/41.39  | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | End of split
% 230.05/41.39  | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | Case 2:
% 230.05/41.39  | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | |   (206)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 230.05/41.39  | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 230.05/41.39  | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | BETA: splitting (206) gives:
% 230.05/41.39  | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | Case 1:
% 230.05/41.39  | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | |   (207)  all_57_8 = e0 & op(e1, e1) = e0
% 230.05/41.39  | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | ALPHA: (207) implies:
% 230.05/41.39  | | | | | | | | | | | |   (208)  op(e1, e1) = e0
% 230.05/41.39  | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | REF_CLOSE: (7), (69), (70), (208) are inconsistent by
% 230.05/41.39  | | | | | | | | | | | |            sub-proof #2427.
% 230.05/41.39  | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | Case 2:
% 230.05/41.39  | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | |   (209)  all_57_14 = e0 & op(e0, e1) = e0
% 230.05/41.39  | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (11), (12), (16), (18),
% 230.05/41.39  | | | | | | | | | | | |            (20), (24), (27), (28), (29), (30), (31), (34),
% 230.05/41.39  | | | | | | | | | | | |            (35), (37), (40), (42), (43), (46), (49), (50),
% 230.05/41.39  | | | | | | | | | | | |            (52), (54), (57), (59), (61), (66), (68), (69),
% 230.05/41.39  | | | | | | | | | | | |            (85), (148), (209) are inconsistent by sub-proof
% 230.05/41.39  | | | | | | | | | | | |            #964.
% 230.05/41.39  | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | End of split
% 230.05/41.39  | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | End of split
% 230.05/41.39  | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | End of split
% 230.05/41.39  | | | | | | | | | 
% 230.05/41.39  | | | | | | | | Case 2:
% 230.05/41.39  | | | | | | | | | 
% 230.05/41.39  | | | | | | | | |   (210)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 &
% 230.05/41.39  | | | | | | | | |            op(e0, e3) = e3)
% 230.05/41.39  | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | BETA: splitting (210) gives:
% 230.05/41.39  | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | Case 1:
% 230.05/41.39  | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | |   (211)  all_57_6 = e3 & op(e1, e3) = e3
% 230.05/41.39  | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | ALPHA: (211) implies:
% 230.05/41.39  | | | | | | | | | |   (212)  all_57_6 = e3
% 230.05/41.39  | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | REF_CLOSE: (66), (148), (212) are inconsistent by sub-proof
% 230.05/41.39  | | | | | | | | | |            #2017.
% 230.05/41.39  | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | Case 2:
% 230.05/41.39  | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | |   (213)  all_57_12 = e3 & op(e0, e3) = e3
% 230.05/41.39  | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | ALPHA: (213) implies:
% 230.05/41.39  | | | | | | | | | |   (214)  all_57_12 = e3
% 230.05/41.39  | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | BETA: splitting (17) gives:
% 230.05/41.39  | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | Case 1:
% 230.05/41.39  | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | |   (215)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 230.05/41.39  | | | | | | | | | | |            & op(e2, e1) = e0)
% 230.05/41.39  | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | BETA: splitting (215) gives:
% 230.05/41.39  | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | Case 1:
% 230.05/41.39  | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | |   (216)  all_57_4 = e0 & op(e3, e1) = e0
% 230.05/41.39  | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | ALPHA: (216) implies:
% 230.05/41.39  | | | | | | | | | | | |   (217)  all_57_4 = e0
% 230.05/41.39  | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | REF_CLOSE: (7), (15), (18), (20), (28), (31), (35), (46),
% 230.05/41.39  | | | | | | | | | | | |            (61), (68), (129), (217) are inconsistent by
% 230.05/41.39  | | | | | | | | | | | |            sub-proof #1403.
% 230.05/41.39  | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | Case 2:
% 230.05/41.39  | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | |   (218)  all_57_5 = e0 & op(e2, e1) = e0
% 230.05/41.39  | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | ALPHA: (218) implies:
% 230.05/41.39  | | | | | | | | | | | |   (219)  all_57_5 = e0
% 230.05/41.39  | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | BETA: splitting (45) gives:
% 230.05/41.39  | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | Case 1:
% 230.05/41.39  | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | |   (220)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 230.05/41.39  | | | | | | | | | | | | |            & op(e2, e2) = e3)
% 230.05/41.39  | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | BETA: splitting (220) gives:
% 230.05/41.39  | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | Case 1:
% 230.05/41.39  | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | |   (221)  all_57_2 = e3 & op(e2, e3) = e3
% 230.05/41.39  | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | ALPHA: (221) implies:
% 230.05/41.39  | | | | | | | | | | | | | |   (222)  all_57_2 = e3
% 230.05/41.39  | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | BETA: splitting (48) gives:
% 230.05/41.39  | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | Case 1:
% 230.05/41.39  | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | |   (223)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 230.05/41.39  | | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 230.05/41.39  | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | REF_CLOSE: (7), (12), (18), (68), (222), (223) are
% 230.05/41.39  | | | | | | | | | | | | | | |            inconsistent by sub-proof #969.
% 230.05/41.39  | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | Case 2:
% 230.05/41.39  | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | |   (224)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 230.05/41.39  | | | | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 230.05/41.39  | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 230.05/41.39  | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | Case 1:
% 230.05/41.39  | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | |   (225)  all_57_5 = e2 & op(e2, e1) = e2
% 230.05/41.39  | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | ALPHA: (225) implies:
% 230.05/41.39  | | | | | | | | | | | | | | | |   (226)  all_57_5 = e2
% 230.05/41.39  | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | REF_CLOSE: (31), (219), (226) are inconsistent by sub-proof
% 230.05/41.39  | | | | | | | | | | | | | | | |            #2363.
% 230.05/41.39  | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | Case 2:
% 230.05/41.39  | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | |   (227)  all_57_10 = e2 & op(e2, e0) = e2
% 230.05/41.39  | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | ALPHA: (227) implies:
% 230.05/41.39  | | | | | | | | | | | | | | | |   (228)  all_57_10 = e2
% 230.05/41.39  | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | BETA: splitting (36) gives:
% 230.05/41.39  | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | Case 1:
% 230.05/41.39  | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | |   (229)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 230.05/41.39  | | | | | | | | | | | | | | | | |            & op(e2, e1) = e3)
% 230.05/41.39  | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 230.05/41.39  | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | Case 1:
% 230.05/41.39  | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | |   (230)  all_57_4 = e3 & op(e3, e1) = e3
% 230.05/41.39  | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | ALPHA: (230) implies:
% 230.05/41.39  | | | | | | | | | | | | | | | | | |   (231)  all_57_4 = e3
% 230.05/41.39  | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | BETA: splitting (41) gives:
% 230.05/41.39  | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | Case 1:
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | |   (232)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 230.05/41.39  | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | Case 1:
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | |   (233)  all_57_12 = e2 & op(e0, e3) = e2
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (214), (233) are inconsistent by sub-proof
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | |            #2232.
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | Case 2:
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | |   (234)  all_57_13 = e2 & op(e0, e2) = e2
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (11), (12),
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | |            (13), (15), (16), (17), (18), (20), (21), (24),
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | |            (27), (28), (29), (30), (31), (34), (35), (36),
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | |            (37), (40), (41), (42), (43), (45), (46), (48),
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | |            (49), (50), (52), (54), (55), (56), (57), (58),
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | |            (59), (60), (61), (66), (68), (69), (129), (219),
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | |            (222), (228), (231), (234) are inconsistent by
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | |            sub-proof #965.
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | End of split
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | Case 2:
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | |   (235)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 230.05/41.39  | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (27), (68), (85), (235) are inconsistent by
% 230.05/41.39  | | | | | | | | | | | | | | | | | | |            sub-proof #1529.
% 230.05/41.39  | | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | End of split
% 230.05/41.39  | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | Case 2:
% 230.05/41.39  | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | |   (236)  all_57_5 = e3 & op(e2, e1) = e3
% 230.05/41.39  | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | ALPHA: (236) implies:
% 230.05/41.39  | | | | | | | | | | | | | | | | | |   (237)  all_57_5 = e3
% 230.05/41.39  | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (219), (237) imply:
% 230.05/41.39  | | | | | | | | | | | | | | | | | |   (238)  e3 = e0
% 230.05/41.39  | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | SIMP: (238) implies:
% 230.05/41.39  | | | | | | | | | | | | | | | | | |   (239)  e3 = e0
% 230.05/41.39  | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (222), (239) imply:
% 230.05/41.39  | | | | | | | | | | | | | | | | | |   (240)  all_57_2 = e0
% 230.05/41.39  | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (11), (12),
% 230.05/41.39  | | | | | | | | | | | | | | | | | |            (13), (15), (16), (17), (18), (20), (21), (24),
% 230.05/41.39  | | | | | | | | | | | | | | | | | |            (26), (27), (28), (29), (30), (31), (34), (35),
% 230.05/41.39  | | | | | | | | | | | | | | | | | |            (36), (37), (40), (41), (42), (43), (46), (48),
% 230.05/41.39  | | | | | | | | | | | | | | | | | |            (49), (50), (52), (54), (55), (56), (57), (58),
% 230.05/41.39  | | | | | | | | | | | | | | | | | |            (59), (60), (61), (66), (68), (69), (85), (214),
% 230.05/41.39  | | | | | | | | | | | | | | | | | |            (237), (240) are inconsistent by sub-proof #1022.
% 230.05/41.39  | | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | End of split
% 230.05/41.39  | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | Case 2:
% 230.05/41.39  | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | |   (241)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 230.05/41.39  | | | | | | | | | | | | | | | | |            e3 & op(e0, e1) = e3)
% 230.05/41.39  | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (11), (18), (20), (27), (29), (31),
% 230.05/41.39  | | | | | | | | | | | | | | | | |            (41), (43), (66), (68), (69), (241) are
% 230.05/41.39  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1794.
% 230.05/41.39  | | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | | End of split
% 230.05/41.39  | | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | | End of split
% 230.05/41.39  | | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | End of split
% 230.05/41.39  | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | Case 2:
% 230.05/41.39  | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | |   (242)  all_57_3 = e3 & op(e2, e2) = e3
% 230.05/41.39  | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | ALPHA: (242) implies:
% 230.05/41.39  | | | | | | | | | | | | | |   (243)  op(e2, e2) = e3
% 230.05/41.39  | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | REF_CLOSE: (7), (12), (66), (243) are inconsistent by
% 230.05/41.39  | | | | | | | | | | | | | |            sub-proof #1912.
% 230.05/41.39  | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | End of split
% 230.05/41.39  | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | Case 2:
% 230.05/41.39  | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | |   (244)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 230.05/41.39  | | | | | | | | | | | | |            e3 & op(e2, e0) = e3)
% 230.05/41.39  | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | BETA: splitting (244) gives:
% 230.05/41.39  | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | Case 1:
% 230.05/41.39  | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | |   (245)  all_57_5 = e3 & op(e2, e1) = e3
% 230.05/41.39  | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | ALPHA: (245) implies:
% 230.05/41.39  | | | | | | | | | | | | | |   (246)  all_57_5 = e3
% 230.05/41.39  | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | REF_CLOSE: (20), (219), (246) are inconsistent by sub-proof
% 230.05/41.39  | | | | | | | | | | | | | |            #2471.
% 230.05/41.39  | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | Case 2:
% 230.05/41.39  | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | |   (247)  all_57_10 = e3 & op(e2, e0) = e3
% 230.05/41.39  | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | ALPHA: (247) implies:
% 230.05/41.39  | | | | | | | | | | | | | |   (248)  all_57_10 = e3
% 230.05/41.39  | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | | REF_CLOSE: (18), (20), (27), (31), (43), (52), (68), (69),
% 230.05/41.39  | | | | | | | | | | | | | |            (129), (248) are inconsistent by sub-proof #1985.
% 230.05/41.39  | | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | | End of split
% 230.05/41.39  | | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | | End of split
% 230.05/41.39  | | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | End of split
% 230.05/41.39  | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | Case 2:
% 230.05/41.39  | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | |   (249)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 230.05/41.39  | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 230.05/41.39  | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | | REF_CLOSE: (7), (18), (27), (29), (31), (41), (66), (68),
% 230.05/41.39  | | | | | | | | | | |            (69), (70), (214), (249) are inconsistent by
% 230.05/41.39  | | | | | | | | | | |            sub-proof #970.
% 230.05/41.39  | | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | | End of split
% 230.05/41.39  | | | | | | | | | | 
% 230.05/41.39  | | | | | | | | | End of split
% 230.05/41.39  | | | | | | | | | 
% 230.05/41.39  | | | | | | | | End of split
% 230.05/41.39  | | | | | | | | 
% 230.05/41.39  | | | | | | | Case 2:
% 230.05/41.39  | | | | | | | | 
% 230.05/41.39  | | | | | | | |   (250)  all_57_12 = e1 & op(e0, e3) = e1
% 230.05/41.39  | | | | | | | | 
% 230.05/41.39  | | | | | | | | ALPHA: (250) implies:
% 230.05/41.39  | | | | | | | |   (251)  op(e0, e3) = e1
% 230.05/41.39  | | | | | | | | 
% 230.05/41.39  | | | | | | | | REF_CLOSE: (1), (2), (7), (9), (10), (11), (12), (14), (23),
% 230.05/41.39  | | | | | | | |            (24), (25), (28), (32), (33), (38), (39), (47), (50),
% 230.05/41.39  | | | | | | | |            (61), (68), (70), (130), (251) are inconsistent by
% 230.05/41.39  | | | | | | | |            sub-proof #997.
% 230.05/41.39  | | | | | | | | 
% 230.05/41.39  | | | | | | | End of split
% 230.05/41.39  | | | | | | | 
% 230.05/41.39  | | | | | | End of split
% 230.05/41.39  | | | | | | 
% 230.05/41.39  | | | | | End of split
% 230.05/41.39  | | | | | 
% 230.05/41.39  | | | | End of split
% 230.05/41.39  | | | | 
% 230.05/41.39  | | | Case 2:
% 230.05/41.39  | | | | 
% 230.05/41.39  | | | |   (252)  all_57_15 = e1 & op(e0, e0) = e1
% 230.05/41.39  | | | | 
% 230.05/41.39  | | | | ALPHA: (252) implies:
% 230.05/41.39  | | | |   (253)  op(e0, e0) = e1
% 230.05/41.39  | | | | 
% 230.05/41.39  | | | | REF_CLOSE: (7), (40), (66), (253) are inconsistent by sub-proof #2183.
% 230.05/41.39  | | | | 
% 230.05/41.39  | | | End of split
% 230.05/41.39  | | | 
% 230.05/41.39  | | End of split
% 230.05/41.39  | | 
% 230.05/41.39  | Case 2:
% 230.05/41.39  | | 
% 230.05/41.39  | |   (254)  all_55_10 = e0
% 230.05/41.39  | | 
% 230.05/41.39  | | REF_CLOSE: (44), (53), (254) are inconsistent by sub-proof #2118.
% 230.05/41.39  | | 
% 230.05/41.39  | End of split
% 230.05/41.39  | 
% 230.05/41.39  End of proof
% 230.05/41.39  
% 230.05/41.39  Sub-proof #964 shows that the following formulas are inconsistent:
% 230.05/41.39  ----------------------------------------------------------------
% 230.05/41.39    (1)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.05/41.39         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.05/41.39    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.05/41.39         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.05/41.39    (3)   ~ (e3 = e1)
% 230.05/41.39    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.05/41.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.05/41.39    (5)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.05/41.39         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.05/41.39    (6)   ~ (all_6_2 = e3)
% 230.05/41.39    (7)  op(e1, e1) = all_6_2
% 230.05/41.39    (8)  op(e2, e2) = e1
% 230.05/41.39    (9)  all_57_6 = e1
% 230.05/41.39    (10)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.05/41.39          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.05/41.39    (11)   ~ (e3 = e2)
% 230.05/41.39    (12)   ~ (e3 = e0)
% 230.05/41.39    (13)  op(e0, e3) = all_53_3
% 230.05/41.39    (14)  all_57_15 = e3
% 230.05/41.39    (15)  op(e3, e3) = e0
% 230.05/41.39    (16)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.05/41.39          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.05/41.39            e1)
% 230.05/41.39    (17)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.05/41.39          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.05/41.39    (18)   ~ (e2 = e0)
% 230.05/41.39    (19)  all_57_3 = e1
% 230.05/41.39    (20)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.05/41.39          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.05/41.39    (21)   ~ (e1 = e0)
% 230.05/41.39    (22)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.05/41.39          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.05/41.39    (23)  all_57_14 = e1
% 230.05/41.39    (24)  op(e0, e0) = e3
% 230.05/41.39    (25)   ~ (all_53_3 = e0)
% 230.05/41.39    (26)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.05/41.39              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.05/41.39                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.05/41.39                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.05/41.39    (27)   ~ (all_53_12 = e3)
% 230.05/41.39    (28)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.05/41.39          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.05/41.39    (29)   ~ (all_53_12 = e0)
% 230.05/41.39    (30)   ~ (e2 = e1)
% 230.05/41.39    (31)  all_57_14 = e0 & op(e0, e1) = e0
% 230.05/41.39    (32)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.05/41.39          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.05/41.39    (33)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.05/41.39          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.05/41.39    (34)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.05/41.39          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.05/41.39    (35)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.05/41.39          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.05/41.39    (36)  op(e3, e0) = all_53_12
% 230.05/41.39  
% 230.05/41.39  Begin of proof
% 230.05/41.39  | 
% 230.05/41.39  | ALPHA: (31) implies:
% 230.05/41.39  |   (37)  all_57_14 = e0
% 230.05/41.39  | 
% 230.05/41.39  | COMBINE_EQS: (23), (37) imply:
% 230.05/41.39  |   (38)  e1 = e0
% 230.05/41.39  | 
% 230.05/41.39  | COMBINE_EQS: (9), (38) imply:
% 230.05/41.39  |   (39)  all_57_6 = e0
% 230.05/41.39  | 
% 230.05/41.39  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13),
% 230.05/41.39  |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (24), (25),
% 230.05/41.39  |            (26), (27), (28), (29), (30), (32), (33), (34), (35), (36), (39)
% 230.05/41.39  |            are inconsistent by sub-proof #983.
% 230.05/41.39  | 
% 230.05/41.39  End of proof
% 230.05/41.39  
% 230.05/41.39  Sub-proof #965 shows that the following formulas are inconsistent:
% 230.05/41.39  ----------------------------------------------------------------
% 230.05/41.39    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.05/41.39         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.05/41.39    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.05/41.39         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.05/41.39    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.05/41.39         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.05/41.39    (4)   ~ (e3 = e1)
% 230.05/41.39    (5)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.05/41.39         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.05/41.39    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.05/41.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.05/41.39    (7)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.05/41.39         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.05/41.39    (8)   ~ (all_6_2 = e3)
% 230.05/41.39    (9)  op(e1, e1) = all_6_2
% 230.05/41.39    (10)  op(e2, e2) = e1
% 230.05/41.39    (11)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.05/41.39          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.05/41.39    (12)  all_57_9 = e1
% 230.05/41.39    (13)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.05/41.39          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.05/41.39    (14)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.05/41.39          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.05/41.39    (15)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 230.05/41.39          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.05/41.39    (16)  all_57_4 = e3
% 230.05/41.39    (17)   ~ (e3 = e2)
% 230.05/41.39    (18)   ~ (e3 = e0)
% 230.05/41.40    (19)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.05/41.40          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.05/41.40    (20)  op(e0, e3) = all_53_3
% 230.05/41.40    (21)  all_57_15 = e3
% 230.05/41.40    (22)  op(e3, e3) = e0
% 230.05/41.40    (23)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.05/41.40          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.05/41.40            e1)
% 230.05/41.40    (24)  all_57_10 = e2
% 230.05/41.40    (25)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.05/41.40          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.05/41.40    (26)   ~ (e2 = e0)
% 230.05/41.40    (27)  all_57_2 = e3
% 230.05/41.40    (28)  all_57_3 = e1
% 230.05/41.40    (29)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.05/41.40          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.05/41.40    (30)   ~ (e1 = e0)
% 230.05/41.40    (31)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 230.05/41.40          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 230.05/41.40    (32)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.05/41.40          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.05/41.40    (33)  op(e0, e0) = e3
% 230.05/41.40    (34)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.05/41.40          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.05/41.40            e2)
% 230.05/41.40    (35)   ~ (all_53_3 = e0)
% 230.05/41.40    (36)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.05/41.40              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.05/41.40                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.05/41.40                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.05/41.40    (37)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.05/41.40          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.05/41.40    (38)   ~ (all_53_12 = e3)
% 230.05/41.40    (39)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.05/41.40          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.05/41.40    (40)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.05/41.40          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.05/41.40    (41)   ~ (all_53_12 = e0)
% 230.05/41.40    (42)   ~ (e2 = e1)
% 230.05/41.40    (43)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.05/41.40          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.05/41.40    (44)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.05/41.40          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.05/41.40    (45)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.05/41.40          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.05/41.40    (46)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.05/41.40          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.05/41.40    (47)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.05/41.40          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.05/41.40    (48)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.05/41.40          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.05/41.40    (49)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.05/41.40          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.05/41.40    (50)  all_57_13 = e2 & op(e0, e2) = e2
% 230.05/41.40    (51)  all_57_5 = e0
% 230.05/41.40    (52)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.05/41.40          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.05/41.40    (53)  op(e3, e0) = all_53_12
% 230.05/41.40  
% 230.05/41.40  Begin of proof
% 230.05/41.40  | 
% 230.05/41.40  | ALPHA: (50) implies:
% 230.05/41.40  |   (54)  all_57_13 = e2
% 230.05/41.40  | 
% 230.05/41.40  | BETA: splitting (25) gives:
% 230.05/41.40  | 
% 230.05/41.40  | Case 1:
% 230.05/41.40  | | 
% 230.05/41.40  | |   (55)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) =
% 230.05/41.40  | |           e0)
% 230.05/41.40  | | 
% 230.05/41.40  | | REF_CLOSE: (1), (4), (6), (12), (13), (16), (17), (18), (21), (22), (24),
% 230.05/41.40  | |            (26), (30), (36), (37), (42), (43), (51), (55) are inconsistent
% 230.05/41.40  | |            by sub-proof #966.
% 230.05/41.40  | | 
% 230.05/41.40  | Case 2:
% 230.05/41.40  | | 
% 230.05/41.40  | |   (56)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 230.05/41.40  | |           e0)
% 230.05/41.40  | | 
% 230.05/41.40  | | BETA: splitting (56) gives:
% 230.05/41.40  | | 
% 230.05/41.40  | | Case 1:
% 230.05/41.40  | | | 
% 230.05/41.40  | | |   (57)  all_57_7 = e0 & op(e1, e2) = e0
% 230.05/41.40  | | | 
% 230.05/41.40  | | | ALPHA: (57) implies:
% 230.05/41.40  | | |   (58)  all_57_7 = e0
% 230.05/41.40  | | | 
% 230.05/41.40  | | | BETA: splitting (32) gives:
% 230.05/41.40  | | | 
% 230.05/41.40  | | | Case 1:
% 230.05/41.40  | | | | 
% 230.05/41.40  | | | |   (59)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2)
% 230.05/41.40  | | | |           = e3)
% 230.05/41.40  | | | | 
% 230.05/41.40  | | | | BETA: splitting (59) gives:
% 230.05/41.40  | | | | 
% 230.05/41.40  | | | | Case 1:
% 230.05/41.40  | | | | | 
% 230.05/41.40  | | | | |   (60)  all_57_1 = e3 & op(e3, e2) = e3
% 230.05/41.40  | | | | | 
% 230.05/41.40  | | | | | ALPHA: (60) implies:
% 230.05/41.40  | | | | |   (61)  all_57_1 = e3
% 230.05/41.40  | | | | | 
% 230.05/41.40  | | | | | BETA: splitting (13) gives:
% 230.05/41.40  | | | | | 
% 230.05/41.40  | | | | | Case 1:
% 230.05/41.40  | | | | | | 
% 230.05/41.40  | | | | | |   (62)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3,
% 230.05/41.40  | | | | | |             e2) = e2)
% 230.05/41.40  | | | | | | 
% 230.05/41.40  | | | | | | REF_CLOSE: (6), (17), (22), (26), (61), (62) are inconsistent by
% 230.05/41.40  | | | | | |            sub-proof #1224.
% 230.05/41.40  | | | | | | 
% 230.05/41.40  | | | | | Case 2:
% 230.05/41.40  | | | | | | 
% 230.05/41.40  | | | | | |   (63)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3,
% 230.05/41.40  | | | | | |             e0) = e2)
% 230.05/41.40  | | | | | | 
% 230.05/41.40  | | | | | | REF_CLOSE: (4), (11), (13), (14), (16), (17), (18), (26), (30),
% 230.05/41.40  | | | | | |            (42), (61), (63) are inconsistent by sub-proof #1221.
% 230.05/41.40  | | | | | | 
% 230.05/41.40  | | | | | End of split
% 230.05/41.40  | | | | | 
% 230.05/41.40  | | | | Case 2:
% 230.05/41.40  | | | | | 
% 230.05/41.40  | | | | |   (64)  all_57_3 = e3 & op(e2, e2) = e3
% 230.05/41.40  | | | | | 
% 230.05/41.40  | | | | | ALPHA: (64) implies:
% 230.05/41.40  | | | | |   (65)  op(e2, e2) = e3
% 230.05/41.40  | | | | | 
% 230.05/41.40  | | | | | REF_CLOSE: (4), (6), (10), (65) are inconsistent by sub-proof #1912.
% 230.05/41.40  | | | | | 
% 230.05/41.40  | | | | End of split
% 230.05/41.40  | | | | 
% 230.05/41.40  | | | Case 2:
% 230.05/41.40  | | | | 
% 230.05/41.40  | | | |   (66)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2)
% 230.05/41.40  | | | |           = e3)
% 230.05/41.40  | | | | 
% 230.05/41.40  | | | | BETA: splitting (66) gives:
% 230.05/41.40  | | | | 
% 230.05/41.40  | | | | Case 1:
% 230.05/41.40  | | | | | 
% 230.05/41.40  | | | | |   (67)  all_57_7 = e3 & op(e1, e2) = e3
% 230.05/41.40  | | | | | 
% 230.05/41.40  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 230.05/41.40  | | | | |            (13), (14), (15), (17), (18), (19), (20), (21), (22), (23),
% 230.05/41.40  | | | | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 230.05/41.40  | | | | |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44),
% 230.05/41.40  | | | | |            (45), (46), (47), (48), (49), (52), (53), (58), (67) are
% 230.05/41.40  | | | | |            inconsistent by sub-proof #1015.
% 230.05/41.40  | | | | | 
% 230.05/41.40  | | | | Case 2:
% 230.05/41.40  | | | | | 
% 230.05/41.40  | | | | |   (68)  all_57_13 = e3 & op(e0, e2) = e3
% 230.05/41.40  | | | | | 
% 230.05/41.40  | | | | | ALPHA: (68) implies:
% 230.05/41.40  | | | | |   (69)  all_57_13 = e3
% 230.05/41.40  | | | | | 
% 230.05/41.40  | | | | | REF_CLOSE: (4), (6), (17), (18), (21), (23), (26), (30), (33), (34),
% 230.05/41.40  | | | | |            (36), (42), (69) are inconsistent by sub-proof #1792.
% 230.05/41.40  | | | | | 
% 230.05/41.40  | | | | End of split
% 230.05/41.40  | | | | 
% 230.05/41.40  | | | End of split
% 230.05/41.40  | | | 
% 230.05/41.40  | | Case 2:
% 230.05/41.40  | | | 
% 230.05/41.40  | | |   (70)  all_57_13 = e0 & op(e0, e2) = e0
% 230.05/41.40  | | | 
% 230.05/41.40  | | | REF_CLOSE: (26), (54), (70) are inconsistent by sub-proof #1743.
% 230.05/41.40  | | | 
% 230.05/41.40  | | End of split
% 230.05/41.40  | | 
% 230.05/41.40  | End of split
% 230.05/41.40  | 
% 230.05/41.40  End of proof
% 230.05/41.40  
% 230.05/41.40  Sub-proof #966 shows that the following formulas are inconsistent:
% 230.05/41.40  ----------------------------------------------------------------
% 230.05/41.40    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.05/41.40         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.05/41.40    (2)   ~ (e3 = e1)
% 230.05/41.40    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.05/41.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.05/41.40    (4)  all_57_9 = e1
% 230.05/41.40    (5)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.05/41.40         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.05/41.40    (6)  all_57_4 = e3
% 230.05/41.40    (7)   ~ (e3 = e2)
% 230.05/41.40    (8)   ~ (e3 = e0)
% 230.05/41.40    (9)  all_57_15 = e3
% 230.05/41.40    (10)  op(e3, e3) = e0
% 230.05/41.40    (11)  all_57_10 = e2
% 230.05/41.40    (12)   ~ (e2 = e0)
% 230.05/41.40    (13)   ~ (e1 = e0)
% 230.05/41.40    (14)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0)
% 230.05/41.40    (15)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.05/41.40              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.05/41.40                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.05/41.40                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.05/41.40    (16)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.05/41.40          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.05/41.40    (17)   ~ (e2 = e1)
% 230.05/41.40    (18)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.05/41.40          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.05/41.40    (19)  all_57_5 = e0
% 230.05/41.40  
% 230.05/41.40  Begin of proof
% 230.05/41.40  | 
% 230.05/41.40  | BETA: splitting (14) gives:
% 230.05/41.40  | 
% 230.05/41.40  | Case 1:
% 230.05/41.40  | | 
% 230.05/41.40  | |   (20)  all_57_1 = e0 & op(e3, e2) = e0
% 230.05/41.40  | | 
% 230.05/41.40  | | ALPHA: (20) implies:
% 230.05/41.40  | |   (21)  all_57_1 = e0
% 230.05/41.40  | | 
% 230.05/41.40  | | REF_CLOSE: (3), (4), (5), (6), (7), (10), (12), (17), (21) are inconsistent
% 230.05/41.40  | |            by sub-proof #2402.
% 230.05/41.40  | | 
% 230.05/41.40  | Case 2:
% 230.05/41.40  | | 
% 230.05/41.40  | |   (22)  all_57_3 = e0 & op(e2, e2) = e0
% 230.05/41.40  | | 
% 230.05/41.40  | | ALPHA: (22) implies:
% 230.05/41.40  | |   (23)  all_57_3 = e0
% 230.05/41.40  | | 
% 230.05/41.40  | | REF_CLOSE: (1), (2), (4), (7), (8), (9), (11), (12), (13), (15), (16), (17),
% 230.05/41.40  | |            (18), (19), (23) are inconsistent by sub-proof #967.
% 230.05/41.40  | | 
% 230.05/41.40  | End of split
% 230.05/41.40  | 
% 230.05/41.40  End of proof
% 230.05/41.40  
% 230.05/41.40  Sub-proof #967 shows that the following formulas are inconsistent:
% 230.05/41.40  ----------------------------------------------------------------
% 230.08/41.40    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.08/41.40         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.08/41.40    (2)   ~ (e3 = e1)
% 230.08/41.40    (3)  all_57_9 = e1
% 230.08/41.40    (4)  all_57_3 = e0
% 230.08/41.40    (5)   ~ (e3 = e2)
% 230.08/41.40    (6)   ~ (e3 = e0)
% 230.08/41.40    (7)  all_57_15 = e3
% 230.08/41.40    (8)  all_57_10 = e2
% 230.08/41.40    (9)   ~ (e2 = e0)
% 230.08/41.40    (10)   ~ (e1 = e0)
% 230.08/41.40    (11)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.08/41.40              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.08/41.40                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.08/41.40                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.08/41.40    (12)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.08/41.40          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.08/41.40    (13)   ~ (e2 = e1)
% 230.08/41.40    (14)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.08/41.40          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.08/41.40    (15)  all_57_5 = e0
% 230.08/41.40  
% 230.08/41.40  Begin of proof
% 230.08/41.40  | 
% 230.08/41.40  | BETA: splitting (12) gives:
% 230.08/41.40  | 
% 230.08/41.40  | Case 1:
% 230.08/41.40  | | 
% 230.08/41.40  | |   (16)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 230.08/41.40  | |           e3)
% 230.08/41.40  | | 
% 230.08/41.40  | | REF_CLOSE: (1), (2), (4), (6), (8), (10), (13), (15), (16) are inconsistent
% 230.08/41.40  | |            by sub-proof #2357.
% 230.08/41.40  | | 
% 230.08/41.40  | Case 2:
% 230.08/41.40  | | 
% 230.08/41.40  | |   (17)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 230.08/41.40  | |           e3)
% 230.08/41.40  | | 
% 230.08/41.40  | | BETA: splitting (17) gives:
% 230.08/41.40  | | 
% 230.08/41.40  | | Case 1:
% 230.08/41.40  | | | 
% 230.08/41.40  | | |   (18)  all_57_5 = e3 & op(e2, e1) = e3
% 230.08/41.40  | | | 
% 230.08/41.40  | | | REF_CLOSE: (6), (15), (18) are inconsistent by sub-proof #1936.
% 230.08/41.40  | | | 
% 230.08/41.40  | | Case 2:
% 230.08/41.40  | | | 
% 230.08/41.40  | | |   (19)  all_57_10 = e3 & op(e2, e0) = e3
% 230.08/41.40  | | | 
% 230.08/41.40  | | | ALPHA: (19) implies:
% 230.08/41.40  | | |   (20)  all_57_10 = e3
% 230.08/41.40  | | | 
% 230.08/41.40  | | | REF_CLOSE: (3), (5), (6), (7), (9), (10), (11), (13), (14), (20) are
% 230.08/41.40  | | |            inconsistent by sub-proof #1985.
% 230.08/41.40  | | | 
% 230.08/41.40  | | End of split
% 230.08/41.40  | | 
% 230.08/41.40  | End of split
% 230.08/41.40  | 
% 230.08/41.40  End of proof
% 230.08/41.40  
% 230.08/41.40  Sub-proof #968 shows that the following formulas are inconsistent:
% 230.08/41.40  ----------------------------------------------------------------
% 230.08/41.40    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.08/41.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.08/41.40    (2)  all_57_9 = e1
% 230.08/41.40    (3)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.08/41.40         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.08/41.40    (4)  all_57_4 = e3
% 230.08/41.40    (5)   ~ (e3 = e2)
% 230.08/41.40    (6)  all_57_1 = e2
% 230.08/41.40    (7)  op(e3, e3) = e0
% 230.08/41.40    (8)  all_57_10 = e2
% 230.08/41.40    (9)  all_57_11 = e2
% 230.08/41.40    (10)   ~ (e2 = e0)
% 230.08/41.40    (11)   ~ (all_53_12 = e0)
% 230.08/41.40    (12)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) |
% 230.08/41.40          (all_57_11 = e0 & op(e1, e0) = e0)
% 230.08/41.40    (13)   ~ (e2 = e1)
% 230.08/41.40    (14)  op(e3, e0) = all_53_12
% 230.08/41.40  
% 230.08/41.40  Begin of proof
% 230.08/41.40  | 
% 230.08/41.40  | BETA: splitting (12) gives:
% 230.08/41.40  | 
% 230.08/41.40  | Case 1:
% 230.08/41.40  | | 
% 230.08/41.40  | |   (15)  all_57_9 = e0 & op(e3, e0) = e0
% 230.08/41.40  | | 
% 230.08/41.40  | | REF_CLOSE: (1), (11), (14), (15) are inconsistent by sub-proof #2434.
% 230.08/41.40  | | 
% 230.08/41.40  | Case 2:
% 230.08/41.40  | | 
% 230.08/41.40  | |   (16)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 230.08/41.40  | |           e0)
% 230.08/41.40  | | 
% 230.08/41.40  | | BETA: splitting (16) gives:
% 230.08/41.40  | | 
% 230.08/41.40  | | Case 1:
% 230.08/41.40  | | | 
% 230.08/41.40  | | |   (17)  all_57_10 = e0 & op(e2, e0) = e0
% 230.08/41.40  | | | 
% 230.08/41.40  | | | ALPHA: (17) implies:
% 230.08/41.40  | | |   (18)  all_57_10 = e0
% 230.08/41.40  | | | 
% 230.08/41.40  | | | COMBINE_EQS: (8), (18) imply:
% 230.08/41.40  | | |   (19)  e2 = e0
% 230.08/41.40  | | | 
% 230.08/41.40  | | | SIMP: (19) implies:
% 230.08/41.40  | | |   (20)  e2 = e0
% 230.08/41.40  | | | 
% 230.08/41.40  | | | COMBINE_EQS: (6), (20) imply:
% 230.08/41.40  | | |   (21)  all_57_1 = e0
% 230.08/41.40  | | | 
% 230.08/41.40  | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (10), (13), (21) are inconsistent
% 230.08/41.40  | | |            by sub-proof #2402.
% 230.08/41.40  | | | 
% 230.08/41.40  | | Case 2:
% 230.08/41.40  | | | 
% 230.08/41.40  | | |   (22)  all_57_11 = e0 & op(e1, e0) = e0
% 230.08/41.40  | | | 
% 230.08/41.40  | | | ALPHA: (22) implies:
% 230.08/41.40  | | |   (23)  all_57_11 = e0
% 230.08/41.40  | | | 
% 230.08/41.40  | | | COMBINE_EQS: (9), (23) imply:
% 230.08/41.40  | | |   (24)  e2 = e0
% 230.08/41.40  | | | 
% 230.08/41.40  | | | SIMP: (24) implies:
% 230.08/41.40  | | |   (25)  e2 = e0
% 230.08/41.40  | | | 
% 230.08/41.40  | | | COMBINE_EQS: (6), (25) imply:
% 230.08/41.40  | | |   (26)  all_57_1 = e0
% 230.08/41.40  | | | 
% 230.08/41.40  | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (10), (13), (26) are inconsistent
% 230.08/41.40  | | |            by sub-proof #2402.
% 230.08/41.40  | | | 
% 230.08/41.40  | | End of split
% 230.08/41.40  | | 
% 230.08/41.40  | End of split
% 230.08/41.40  | 
% 230.08/41.40  End of proof
% 230.08/41.40  
% 230.08/41.40  Sub-proof #969 shows that the following formulas are inconsistent:
% 230.08/41.40  ----------------------------------------------------------------
% 230.08/41.40    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.08/41.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.08/41.40    (2)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2)
% 230.08/41.40    (3)  op(e2, e2) = e1
% 230.08/41.40    (4)   ~ (e3 = e2)
% 230.08/41.40    (5)  all_57_2 = e3
% 230.08/41.40    (6)   ~ (e2 = e1)
% 230.08/41.40  
% 230.08/41.40  Begin of proof
% 230.08/41.40  | 
% 230.08/41.40  | BETA: splitting (2) gives:
% 230.08/41.40  | 
% 230.08/41.40  | Case 1:
% 230.08/41.40  | | 
% 230.08/41.40  | |   (7)  all_57_2 = e2 & op(e2, e3) = e2
% 230.08/41.40  | | 
% 230.08/41.40  | | REF_CLOSE: (4), (5), (7) are inconsistent by sub-proof #1925.
% 230.08/41.40  | | 
% 230.08/41.40  | Case 2:
% 230.08/41.40  | | 
% 230.08/41.40  | |   (8)  all_57_3 = e2 & op(e2, e2) = e2
% 230.08/41.40  | | 
% 230.08/41.40  | | ALPHA: (8) implies:
% 230.08/41.40  | |   (9)  op(e2, e2) = e2
% 230.08/41.40  | | 
% 230.08/41.40  | | REF_CLOSE: (1), (3), (6), (9) are inconsistent by sub-proof #2306.
% 230.08/41.40  | | 
% 230.08/41.40  | End of split
% 230.08/41.40  | 
% 230.08/41.40  End of proof
% 230.08/41.40  
% 230.08/41.40  Sub-proof #970 shows that the following formulas are inconsistent:
% 230.08/41.40  ----------------------------------------------------------------
% 230.08/41.40    (1)   ~ (e3 = e1)
% 230.08/41.40    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.08/41.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.08/41.40    (3)   ~ (e3 = e2)
% 230.08/41.40    (4)  all_57_15 = e3
% 230.08/41.40    (5)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 230.08/41.40         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.08/41.40    (6)  op(e1, e1) = e1
% 230.08/41.40    (7)   ~ (e2 = e0)
% 230.08/41.40    (8)   ~ (e1 = e0)
% 230.08/41.40    (9)  all_57_12 = e3
% 230.08/41.40    (10)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.08/41.40    (11)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.08/41.40          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.08/41.40            e2)
% 230.08/41.40    (12)   ~ (e2 = e1)
% 230.08/41.40  
% 230.08/41.40  Begin of proof
% 230.08/41.40  | 
% 230.08/41.40  | BETA: splitting (10) gives:
% 230.08/41.40  | 
% 230.08/41.40  | Case 1:
% 230.08/41.40  | | 
% 230.08/41.40  | |   (13)  all_57_8 = e0 & op(e1, e1) = e0
% 230.08/41.40  | | 
% 230.08/41.40  | | ALPHA: (13) implies:
% 230.08/41.40  | |   (14)  op(e1, e1) = e0
% 230.08/41.40  | | 
% 230.08/41.40  | | REF_CLOSE: (2), (6), (8), (14) are inconsistent by sub-proof #2427.
% 230.08/41.40  | | 
% 230.08/41.40  | Case 2:
% 230.08/41.40  | | 
% 230.08/41.40  | |   (15)  all_57_14 = e0 & op(e0, e1) = e0
% 230.08/41.40  | | 
% 230.08/41.40  | | ALPHA: (15) implies:
% 230.08/41.40  | |   (16)  all_57_14 = e0
% 230.08/41.40  | | 
% 230.08/41.40  | | REF_CLOSE: (1), (3), (4), (5), (7), (8), (9), (11), (12), (16) are
% 230.08/41.40  | |            inconsistent by sub-proof #1763.
% 230.08/41.40  | | 
% 230.08/41.40  | End of split
% 230.08/41.40  | 
% 230.08/41.40  End of proof
% 230.08/41.40  
% 230.08/41.40  Sub-proof #971 shows that the following formulas are inconsistent:
% 230.08/41.40  ----------------------------------------------------------------
% 230.08/41.40    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.08/41.40         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.08/41.40    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.08/41.40         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.08/41.40    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.08/41.40         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.08/41.40    (4)   ~ (e3 = e1)
% 230.08/41.40    (5)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.08/41.40         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.08/41.40    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.08/41.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.08/41.40    (7)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.08/41.40         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.08/41.40    (8)   ~ (all_6_2 = e3)
% 230.08/41.40    (9)  op(e1, e1) = all_6_2
% 230.08/41.40    (10)  op(e2, e2) = e1
% 230.08/41.40    (11)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.08/41.40          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.08/41.40    (12)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.08/41.40          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.08/41.40    (13)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.08/41.40          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.08/41.40    (14)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 230.08/41.40          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.08/41.40    (15)   ~ (e3 = e2)
% 230.08/41.40    (16)   ~ (e3 = e0)
% 230.08/41.40    (17)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.08/41.40          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.08/41.40    (18)  op(e0, e3) = all_53_3
% 230.08/41.40    (19)  all_57_15 = e3
% 230.08/41.40    (20)  op(e3, e3) = e0
% 230.08/41.40    (21)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.08/41.40          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.08/41.40            e1)
% 230.08/41.40    (22)  all_57_5 = e3
% 230.08/41.40    (23)  op(e1, e1) = e1
% 230.08/41.40    (24)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.08/41.40          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.08/41.40    (25)   ~ (e2 = e0)
% 230.08/41.40    (26)  all_57_3 = e1
% 230.08/41.40    (27)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.08/41.40          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.08/41.40    (28)   ~ (e1 = e0)
% 230.08/41.40    (29)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 230.08/41.40          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 230.08/41.40    (30)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.08/41.40          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.08/41.40    (31)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.08/41.40    (32)  all_57_14 = e1
% 230.08/41.40    (33)  op(e0, e0) = e3
% 230.08/41.40    (34)  all_57_2 = e1
% 230.08/41.40    (35)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.08/41.40          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.08/41.40            e2)
% 230.08/41.40    (36)   ~ (all_53_3 = e0)
% 230.08/41.40    (37)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.08/41.40              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.08/41.40                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.08/41.40                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.08/41.40    (38)   ~ (all_53_12 = e3)
% 230.08/41.40    (39)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.08/41.40          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.08/41.40    (40)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.08/41.40          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.08/41.40    (41)   ~ (all_53_12 = e0)
% 230.08/41.40    (42)   ~ (e2 = e1)
% 230.08/41.40    (43)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.08/41.40          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.08/41.40    (44)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.08/41.40          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.08/41.41    (45)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.08/41.41          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.08/41.41    (46)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.08/41.41          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.08/41.41    (47)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.08/41.41          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.08/41.41    (48)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.08/41.41          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.08/41.41    (49)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.08/41.41          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.08/41.41    (50)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.08/41.41          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.08/41.41    (51)  op(e3, e0) = all_53_12
% 230.08/41.41  
% 230.08/41.41  Begin of proof
% 230.08/41.41  | 
% 230.08/41.41  | BETA: splitting (31) gives:
% 230.08/41.41  | 
% 230.08/41.41  | Case 1:
% 230.08/41.41  | | 
% 230.08/41.41  | |   (52)  all_57_8 = e0 & op(e1, e1) = e0
% 230.08/41.41  | | 
% 230.08/41.41  | | ALPHA: (52) implies:
% 230.08/41.41  | |   (53)  op(e1, e1) = e0
% 230.08/41.41  | | 
% 230.08/41.41  | | REF_CLOSE: (6), (23), (28), (53) are inconsistent by sub-proof #2427.
% 230.08/41.41  | | 
% 230.08/41.41  | Case 2:
% 230.08/41.41  | | 
% 230.08/41.41  | |   (54)  all_57_14 = e0 & op(e0, e1) = e0
% 230.08/41.41  | | 
% 230.08/41.41  | | ALPHA: (54) implies:
% 230.08/41.41  | |   (55)  all_57_14 = e0
% 230.08/41.41  | | 
% 230.08/41.41  | | COMBINE_EQS: (32), (55) imply:
% 230.08/41.41  | |   (56)  e1 = e0
% 230.08/41.41  | | 
% 230.08/41.41  | | COMBINE_EQS: (34), (56) imply:
% 230.08/41.41  | |   (57)  all_57_2 = e0
% 230.08/41.41  | | 
% 230.08/41.41  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 230.08/41.41  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (24),
% 230.08/41.41  | |            (25), (26), (27), (28), (29), (30), (33), (35), (36), (37), (38),
% 230.08/41.41  | |            (39), (40), (41), (42), (43), (44), (45), (46), (47), (48), (49),
% 230.08/41.41  | |            (50), (51), (57) are inconsistent by sub-proof #1021.
% 230.08/41.41  | | 
% 230.08/41.41  | End of split
% 230.08/41.41  | 
% 230.08/41.41  End of proof
% 230.08/41.41  
% 230.08/41.41  Sub-proof #972 shows that the following formulas are inconsistent:
% 230.08/41.41  ----------------------------------------------------------------
% 230.08/41.41    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.08/41.41         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.08/41.41    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.08/41.41         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.08/41.41    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.08/41.41         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.08/41.41    (4)   ~ (e3 = e1)
% 230.08/41.41    (5)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.08/41.41         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.08/41.41    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.08/41.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.08/41.41    (7)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.08/41.41         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.08/41.41    (8)   ~ (all_6_2 = e3)
% 230.08/41.41    (9)  op(e1, e1) = all_6_2
% 230.08/41.41    (10)  op(e2, e2) = e1
% 230.08/41.41    (11)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.08/41.41          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.08/41.41    (12)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.08/41.41          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.08/41.41    (13)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.08/41.41          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.08/41.41    (14)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 230.08/41.41          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.08/41.41    (15)   ~ (e3 = e2)
% 230.08/41.41    (16)   ~ (e3 = e0)
% 230.08/41.41    (17)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.08/41.41          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.08/41.41    (18)  op(e0, e3) = all_53_3
% 230.08/41.41    (19)  all_57_15 = e3
% 230.08/41.41    (20)  all_57_4 = e1
% 230.08/41.41    (21)  op(e3, e3) = e0
% 230.08/41.41    (22)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.08/41.41          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.08/41.41            e1)
% 230.08/41.41    (23)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.08/41.41          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.08/41.41    (24)   ~ (e2 = e0)
% 230.08/41.41    (25)  all_57_3 = e1
% 230.08/41.41    (26)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.08/41.41          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.08/41.41    (27)   ~ (e1 = e0)
% 230.08/41.41    (28)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 230.08/41.41          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 230.08/41.41    (29)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.08/41.41          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.08/41.41    (30)  op(e0, e0) = e3
% 230.08/41.41    (31)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.08/41.41          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.08/41.41            e2)
% 230.08/41.41    (32)   ~ (all_53_3 = e0)
% 230.08/41.41    (33)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.08/41.41              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.08/41.41                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.08/41.41                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.08/41.41    (34)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.08/41.41          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.08/41.41    (35)   ~ (all_53_12 = e3)
% 230.08/41.41    (36)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.08/41.41          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.08/41.41    (37)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.08/41.41          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.08/41.41    (38)   ~ (all_53_12 = e0)
% 230.08/41.41    (39)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.08/41.41          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 230.08/41.41    (40)   ~ (e2 = e1)
% 230.08/41.41    (41)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.08/41.41          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.08/41.41    (42)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.08/41.41          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.08/41.41    (43)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.08/41.41          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.08/41.41    (44)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.08/41.41          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.08/41.41    (45)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.08/41.41          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.08/41.41    (46)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.08/41.41          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.08/41.41    (47)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.08/41.41          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.08/41.41    (48)  all_57_5 = e0
% 230.08/41.41    (49)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.08/41.41          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.08/41.41    (50)  op(e3, e0) = all_53_12
% 230.08/41.41  
% 230.08/41.41  Begin of proof
% 230.08/41.41  | 
% 230.08/41.41  | BETA: splitting (34) gives:
% 230.08/41.41  | 
% 230.08/41.41  | Case 1:
% 230.08/41.41  | | 
% 230.08/41.41  | |   (51)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 230.08/41.41  | |           e3)
% 230.08/41.41  | | 
% 230.08/41.41  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 230.08/41.41  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 230.08/41.41  | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (35),
% 230.08/41.41  | |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 230.08/41.41  | |            (47), (49), (50), (51) are inconsistent by sub-proof #973.
% 230.08/41.41  | | 
% 230.08/41.41  | Case 2:
% 230.08/41.41  | | 
% 230.08/41.41  | |   (52)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 230.08/41.41  | |           e3)
% 230.08/41.41  | | 
% 230.08/41.41  | | BETA: splitting (52) gives:
% 230.08/41.41  | | 
% 230.08/41.41  | | Case 1:
% 230.08/41.41  | | | 
% 230.08/41.41  | | |   (53)  all_57_5 = e3 & op(e2, e1) = e3
% 230.08/41.41  | | | 
% 230.08/41.41  | | | ALPHA: (53) implies:
% 230.08/41.41  | | |   (54)  all_57_5 = e3
% 230.08/41.41  | | | 
% 230.08/41.41  | | | REF_CLOSE: (16), (48), (54) are inconsistent by sub-proof #2471.
% 230.08/41.41  | | | 
% 230.08/41.41  | | Case 2:
% 230.08/41.41  | | | 
% 230.08/41.41  | | |   (55)  all_57_10 = e3 & op(e2, e0) = e3
% 230.08/41.41  | | | 
% 230.08/41.41  | | | ALPHA: (55) implies:
% 230.08/41.41  | | |   (56)  all_57_10 = e3
% 230.08/41.41  | | | 
% 230.08/41.41  | | | REF_CLOSE: (4), (6), (15), (16), (19), (24), (27), (30), (33), (40), (41),
% 230.08/41.41  | | |            (45), (56) are inconsistent by sub-proof #1746.
% 230.08/41.41  | | | 
% 230.08/41.41  | | End of split
% 230.08/41.41  | | 
% 230.08/41.41  | End of split
% 230.08/41.41  | 
% 230.08/41.41  End of proof
% 230.08/41.41  
% 230.08/41.41  Sub-proof #973 shows that the following formulas are inconsistent:
% 230.08/41.41  ----------------------------------------------------------------
% 230.08/41.41    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.08/41.41         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.08/41.41    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.08/41.41         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.08/41.41    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.08/41.41         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.08/41.41    (4)   ~ (e3 = e1)
% 230.08/41.41    (5)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.08/41.41         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.08/41.41    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.08/41.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.08/41.41    (7)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.08/41.41         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.08/41.41    (8)   ~ (all_6_2 = e3)
% 230.08/41.41    (9)  op(e1, e1) = all_6_2
% 230.08/41.41    (10)  op(e2, e2) = e1
% 230.08/41.41    (11)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.08/41.41          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.08/41.41    (12)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.08/41.41          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.08/41.41    (13)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.08/41.41          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.08/41.41    (14)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 230.08/41.41          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.08/41.41    (15)   ~ (e3 = e2)
% 230.08/41.41    (16)   ~ (e3 = e0)
% 230.08/41.41    (17)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.08/41.41          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.08/41.41    (18)  op(e0, e3) = all_53_3
% 230.08/41.41    (19)  all_57_15 = e3
% 230.08/41.41    (20)  all_57_4 = e1
% 230.08/41.41    (21)  op(e3, e3) = e0
% 230.08/41.41    (22)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.08/41.41          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.08/41.41            e1)
% 230.08/41.41    (23)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.08/41.41          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.08/41.41    (24)   ~ (e2 = e0)
% 230.08/41.41    (25)  all_57_3 = e1
% 230.08/41.41    (26)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.08/41.41          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.08/41.41    (27)   ~ (e1 = e0)
% 230.08/41.41    (28)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 230.08/41.41          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 230.08/41.41    (29)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.08/41.41          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.08/41.41    (30)  op(e0, e0) = e3
% 230.08/41.41    (31)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.08/41.41          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.08/41.41            e2)
% 230.08/41.41    (32)   ~ (all_53_3 = e0)
% 230.08/41.41    (33)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.08/41.41              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.08/41.41                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.08/41.41                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.08/41.41    (34)   ~ (all_53_12 = e3)
% 230.08/41.41    (35)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.08/41.41          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.08/41.41    (36)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.08/41.41          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.08/41.41    (37)   ~ (all_53_12 = e0)
% 230.08/41.41    (38)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.08/41.41          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 230.08/41.41    (39)   ~ (e2 = e1)
% 230.08/41.41    (40)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3)
% 230.08/41.41    (41)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.08/41.41          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.08/41.41    (42)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.08/41.41          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.08/41.41    (43)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.08/41.41          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.08/41.41    (44)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.08/41.41          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.08/41.41    (45)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.08/41.41          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.08/41.41    (46)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.08/41.41          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.08/41.41    (47)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.08/41.41          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.08/41.41    (48)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.08/41.41          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.08/41.41    (49)  op(e3, e0) = all_53_12
% 230.08/41.41  
% 230.08/41.41  Begin of proof
% 230.08/41.41  | 
% 230.08/41.41  | BETA: splitting (40) gives:
% 230.08/41.41  | 
% 230.08/41.41  | Case 1:
% 230.08/41.41  | | 
% 230.08/41.41  | |   (50)  all_57_2 = e3 & op(e2, e3) = e3
% 230.08/41.41  | | 
% 230.08/41.41  | | ALPHA: (50) implies:
% 230.08/41.41  | |   (51)  all_57_2 = e3
% 230.08/41.41  | | 
% 230.08/41.41  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 230.08/41.41  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 230.08/41.41  | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 230.08/41.41  | |            (35), (36), (37), (38), (39), (41), (42), (43), (44), (45), (46),
% 230.08/41.41  | |            (47), (48), (49), (51) are inconsistent by sub-proof #974.
% 230.08/41.41  | | 
% 230.08/41.41  | Case 2:
% 230.08/41.41  | | 
% 230.08/41.41  | |   (52)  all_57_3 = e3 & op(e2, e2) = e3
% 230.08/41.41  | | 
% 230.08/41.41  | | ALPHA: (52) implies:
% 230.08/41.41  | |   (53)  op(e2, e2) = e3
% 230.08/41.41  | | 
% 230.08/41.41  | | REF_CLOSE: (4), (6), (10), (53) are inconsistent by sub-proof #1912.
% 230.08/41.41  | | 
% 230.08/41.41  | End of split
% 230.08/41.41  | 
% 230.08/41.41  End of proof
% 230.08/41.41  
% 230.08/41.41  Sub-proof #974 shows that the following formulas are inconsistent:
% 230.08/41.41  ----------------------------------------------------------------
% 230.08/41.41    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.08/41.41         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.08/41.41    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.08/41.41         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.08/41.41    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.08/41.41         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.08/41.41    (4)   ~ (e3 = e1)
% 230.08/41.41    (5)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.08/41.41         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.08/41.41    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.08/41.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.08/41.41    (7)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.08/41.41         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.08/41.41    (8)   ~ (all_6_2 = e3)
% 230.08/41.41    (9)  op(e1, e1) = all_6_2
% 230.08/41.41    (10)  op(e2, e2) = e1
% 230.08/41.41    (11)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.08/41.41          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.08/41.41    (12)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.08/41.41          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.08/41.41    (13)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.08/41.41          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.08/41.41    (14)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 230.08/41.41          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.08/41.41    (15)   ~ (e3 = e2)
% 230.08/41.41    (16)   ~ (e3 = e0)
% 230.08/41.41    (17)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.08/41.41          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.08/41.41    (18)  op(e0, e3) = all_53_3
% 230.08/41.41    (19)  all_57_15 = e3
% 230.08/41.41    (20)  all_57_4 = e1
% 230.08/41.41    (21)  op(e3, e3) = e0
% 230.08/41.41    (22)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.08/41.41          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.08/41.41            e1)
% 230.08/41.41    (23)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.08/41.41          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.08/41.41    (24)   ~ (e2 = e0)
% 230.08/41.41    (25)  all_57_2 = e3
% 230.08/41.41    (26)  all_57_3 = e1
% 230.08/41.41    (27)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.08/41.41          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.08/41.41    (28)   ~ (e1 = e0)
% 230.08/41.41    (29)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 230.08/41.41          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 230.08/41.41    (30)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.08/41.41          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.08/41.41    (31)  op(e0, e0) = e3
% 230.08/41.41    (32)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.08/41.41          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.08/41.41            e2)
% 230.08/41.41    (33)   ~ (all_53_3 = e0)
% 230.08/41.41    (34)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.08/41.41              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.08/41.41                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.08/41.41                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.08/41.41    (35)   ~ (all_53_12 = e3)
% 230.08/41.41    (36)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.08/41.41          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.08/41.41    (37)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.08/41.41          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.08/41.41    (38)   ~ (all_53_12 = e0)
% 230.08/41.41    (39)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.08/41.41          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 230.08/41.41    (40)   ~ (e2 = e1)
% 230.08/41.41    (41)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.08/41.41          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.08/41.41    (42)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.08/41.41          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.08/41.41    (43)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.08/41.41          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.08/41.41    (44)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.08/41.41          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.08/41.41    (45)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.08/41.41          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.08/41.41    (46)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.08/41.41          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.08/41.41    (47)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.08/41.41          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.08/41.41    (48)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.08/41.41          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.08/41.41    (49)  op(e3, e0) = all_53_12
% 230.08/41.41  
% 230.08/41.41  Begin of proof
% 230.08/41.41  | 
% 230.08/41.41  | BETA: splitting (29) gives:
% 230.08/41.41  | 
% 230.08/41.41  | Case 1:
% 230.08/41.41  | | 
% 230.08/41.41  | |   (50)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) =
% 230.08/41.41  | |           e3)
% 230.08/41.41  | | 
% 230.08/41.41  | | BETA: splitting (50) gives:
% 230.08/41.41  | | 
% 230.08/41.41  | | Case 1:
% 230.08/41.41  | | | 
% 230.08/41.41  | | |   (51)  all_57_4 = e3 & op(e3, e1) = e3
% 230.08/41.41  | | | 
% 230.08/41.41  | | | ALPHA: (51) implies:
% 230.08/41.41  | | |   (52)  all_57_4 = e3
% 230.08/41.41  | | | 
% 230.08/41.41  | | | REF_CLOSE: (4), (20), (52) are inconsistent by sub-proof #2426.
% 230.08/41.41  | | | 
% 230.08/41.41  | | Case 2:
% 230.08/41.41  | | | 
% 230.08/41.41  | | |   (53)  all_57_5 = e3 & op(e2, e1) = e3
% 230.08/41.41  | | | 
% 230.08/41.41  | | | ALPHA: (53) implies:
% 230.08/41.42  | | |   (54)  all_57_5 = e3
% 230.08/41.42  | | | 
% 230.08/41.42  | | | BETA: splitting (27) gives:
% 230.08/41.42  | | | 
% 230.08/41.42  | | | Case 1:
% 230.08/41.42  | | | | 
% 230.08/41.42  | | | |   (55)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2)
% 230.08/41.42  | | | |           = e3)
% 230.08/41.42  | | | | 
% 230.08/41.42  | | | | BETA: splitting (55) gives:
% 230.08/41.42  | | | | 
% 230.08/41.42  | | | | Case 1:
% 230.08/41.42  | | | | | 
% 230.08/41.42  | | | | |   (56)  all_57_0 = e3 & op(e3, e3) = e3
% 230.08/41.42  | | | | | 
% 230.08/41.42  | | | | | ALPHA: (56) implies:
% 230.08/41.42  | | | | |   (57)  op(e3, e3) = e3
% 230.08/41.42  | | | | | 
% 230.08/41.42  | | | | | REF_CLOSE: (6), (16), (21), (57) are inconsistent by sub-proof #2494.
% 230.08/41.42  | | | | | 
% 230.08/41.42  | | | | Case 2:
% 230.08/41.42  | | | | | 
% 230.08/41.42  | | | | |   (58)  all_57_1 = e3 & op(e3, e2) = e3
% 230.08/41.42  | | | | | 
% 230.08/41.42  | | | | | ALPHA: (58) implies:
% 230.08/41.42  | | | | |   (59)  all_57_1 = e3
% 230.08/41.42  | | | | | 
% 230.08/41.42  | | | | | BETA: splitting (39) gives:
% 230.08/41.42  | | | | | 
% 230.08/41.42  | | | | | Case 1:
% 230.08/41.42  | | | | | | 
% 230.08/41.42  | | | | | |   (60)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2,
% 230.08/41.42  | | | | | |             e2) = e0)
% 230.08/41.42  | | | | | | 
% 230.08/41.42  | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 230.08/41.42  | | | | | |            (12), (13), (14), (15), (16), (17), (18), (19), (21),
% 230.08/41.42  | | | | | |            (22), (23), (24), (25), (26), (27), (28), (29), (30),
% 230.08/41.42  | | | | | |            (31), (32), (33), (34), (35), (36), (37), (38), (40),
% 230.08/41.42  | | | | | |            (41), (42), (43), (44), (45), (46), (47), (48), (49),
% 230.08/41.42  | | | | | |            (54), (60) are inconsistent by sub-proof #975.
% 230.08/41.42  | | | | | | 
% 230.08/41.42  | | | | | Case 2:
% 230.08/41.42  | | | | | | 
% 230.08/41.42  | | | | | |   (61)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2,
% 230.08/41.42  | | | | | |             e0) = e0)
% 230.08/41.42  | | | | | | 
% 230.08/41.42  | | | | | | BETA: splitting (61) gives:
% 230.08/41.42  | | | | | | 
% 230.08/41.42  | | | | | | Case 1:
% 230.08/41.42  | | | | | | | 
% 230.08/41.42  | | | | | | |   (62)  all_57_5 = e0 & op(e2, e1) = e0
% 230.08/41.42  | | | | | | | 
% 230.08/41.42  | | | | | | | REF_CLOSE: (4), (6), (16), (20), (21), (27), (35), (49), (54),
% 230.08/41.42  | | | | | | |            (59), (62) are inconsistent by sub-proof #1020.
% 230.08/41.42  | | | | | | | 
% 230.08/41.42  | | | | | | Case 2:
% 230.08/41.42  | | | | | | | 
% 230.08/41.42  | | | | | | |   (63)  all_57_10 = e0 & op(e2, e0) = e0
% 230.08/41.42  | | | | | | | 
% 230.08/41.42  | | | | | | | ALPHA: (63) implies:
% 230.08/41.42  | | | | | | |   (64)  all_57_10 = e0
% 230.08/41.42  | | | | | | | 
% 230.08/41.42  | | | | | | | REF_CLOSE: (6), (10), (15), (24), (25), (36), (40), (54), (64) are
% 230.08/41.42  | | | | | | |            inconsistent by sub-proof #1797.
% 230.08/41.42  | | | | | | | 
% 230.08/41.42  | | | | | | End of split
% 230.08/41.42  | | | | | | 
% 230.08/41.42  | | | | | End of split
% 230.08/41.42  | | | | | 
% 230.08/41.42  | | | | End of split
% 230.08/41.42  | | | | 
% 230.08/41.42  | | | Case 2:
% 230.08/41.42  | | | | 
% 230.08/41.42  | | | |   (65)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0)
% 230.08/41.42  | | | |           = e3)
% 230.08/41.42  | | | | 
% 230.08/41.42  | | | | REF_CLOSE: (4), (6), (20), (35), (49), (65) are inconsistent by
% 230.08/41.42  | | | |            sub-proof #2281.
% 230.08/41.42  | | | | 
% 230.08/41.42  | | | End of split
% 230.08/41.42  | | | 
% 230.08/41.42  | | End of split
% 230.08/41.42  | | 
% 230.08/41.42  | Case 2:
% 230.08/41.42  | | 
% 230.08/41.42  | |   (66)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) =
% 230.08/41.42  | |           e3)
% 230.08/41.42  | | 
% 230.08/41.42  | | REF_CLOSE: (4), (6), (8), (9), (15), (16), (19), (22), (24), (28), (32),
% 230.08/41.42  | |            (34), (40), (66) are inconsistent by sub-proof #1794.
% 230.08/41.42  | | 
% 230.08/41.42  | End of split
% 230.08/41.42  | 
% 230.08/41.42  End of proof
% 230.08/41.42  
% 230.08/41.42  Sub-proof #975 shows that the following formulas are inconsistent:
% 230.08/41.42  ----------------------------------------------------------------
% 230.08/41.42    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.08/41.42         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.08/41.42    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.08/41.42         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.08/41.42    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.08/41.42         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.08/41.42    (4)   ~ (e3 = e1)
% 230.08/41.42    (5)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.08/41.42         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.08/41.42    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.08/41.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.08/41.42    (7)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.08/41.42         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.08/41.42    (8)   ~ (all_6_2 = e3)
% 230.08/41.42    (9)  op(e1, e1) = all_6_2
% 230.08/41.42    (10)  op(e2, e2) = e1
% 230.08/41.42    (11)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.08/41.42          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.08/41.42    (12)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.08/41.42          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.08/41.42    (13)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.08/41.42          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.08/41.42    (14)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 230.08/41.42          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.08/41.42    (15)   ~ (e3 = e2)
% 230.08/41.42    (16)   ~ (e3 = e0)
% 230.08/41.42    (17)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.08/41.42          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.08/41.42    (18)  op(e0, e3) = all_53_3
% 230.08/41.42    (19)  all_57_15 = e3
% 230.08/41.42    (20)  op(e3, e3) = e0
% 230.08/41.42    (21)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.08/41.42          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.08/41.42            e1)
% 230.08/41.42    (22)  all_57_5 = e3
% 230.08/41.42    (23)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0)
% 230.08/41.42    (24)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.08/41.42          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.08/41.42    (25)   ~ (e2 = e0)
% 230.08/41.42    (26)  all_57_2 = e3
% 230.08/41.42    (27)  all_57_3 = e1
% 230.08/41.42    (28)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.08/41.42          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.08/41.42    (29)   ~ (e1 = e0)
% 230.08/41.42    (30)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 230.08/41.42          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 230.08/41.42    (31)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.08/41.42          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.08/41.42    (32)  op(e0, e0) = e3
% 230.08/41.42    (33)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.08/41.42          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.08/41.42            e2)
% 230.08/41.42    (34)   ~ (all_53_3 = e0)
% 230.08/41.42    (35)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.08/41.42              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.08/41.42                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.08/41.42                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.08/41.42    (36)   ~ (all_53_12 = e3)
% 230.08/41.42    (37)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.08/41.42          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.08/41.42    (38)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.08/41.42          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.08/41.42    (39)   ~ (all_53_12 = e0)
% 230.08/41.42    (40)   ~ (e2 = e1)
% 230.08/41.42    (41)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.08/41.42          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.08/41.42    (42)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.08/41.42          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.08/41.42    (43)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.08/41.42          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.08/41.42    (44)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.08/41.42          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.08/41.42    (45)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.08/41.42          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.08/41.42    (46)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.08/41.42          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.08/41.42    (47)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.08/41.42          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.08/41.42    (48)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.08/41.42          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.08/41.42    (49)  op(e3, e0) = all_53_12
% 230.08/41.42  
% 230.08/41.42  Begin of proof
% 230.08/41.42  | 
% 230.08/41.42  | BETA: splitting (23) gives:
% 230.08/41.42  | 
% 230.08/41.42  | Case 1:
% 230.08/41.42  | | 
% 230.08/41.42  | |   (50)  all_57_2 = e0 & op(e2, e3) = e0
% 230.08/41.42  | | 
% 230.08/41.42  | | ALPHA: (50) implies:
% 230.08/41.42  | |   (51)  all_57_2 = e0
% 230.08/41.42  | | 
% 230.08/41.42  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 230.08/41.42  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (24),
% 230.08/41.42  | |            (25), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 230.08/41.42  | |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 230.08/41.42  | |            (48), (49), (51) are inconsistent by sub-proof #1021.
% 230.08/41.42  | | 
% 230.08/41.42  | Case 2:
% 230.08/41.42  | | 
% 230.08/41.42  | |   (52)  all_57_3 = e0 & op(e2, e2) = e0
% 230.08/41.42  | | 
% 230.08/41.42  | | ALPHA: (52) implies:
% 230.08/41.42  | |   (53)  all_57_3 = e0
% 230.08/41.42  | | 
% 230.08/41.42  | | REF_CLOSE: (1), (4), (15), (22), (25), (26), (29), (37), (40), (53) are
% 230.08/41.42  | |            inconsistent by sub-proof #1802.
% 230.08/41.42  | | 
% 230.08/41.42  | End of split
% 230.08/41.42  | 
% 230.08/41.42  End of proof
% 230.08/41.42  
% 230.08/41.42  Sub-proof #976 shows that the following formulas are inconsistent:
% 230.08/41.42  ----------------------------------------------------------------
% 230.08/41.42    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.08/41.42         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.08/41.42    (2)  all_57_13 = e1
% 230.08/41.42    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.08/41.42         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.08/41.42    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.08/41.42         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.08/41.42    (5)   ~ (e3 = e1)
% 230.08/41.42    (6)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.08/41.42         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.08/41.42    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.08/41.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.08/41.42    (8)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.08/41.42         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.08/41.42    (9)   ~ (all_6_2 = e3)
% 230.08/41.42    (10)  op(e1, e1) = all_6_2
% 230.08/41.42    (11)  op(e2, e2) = e1
% 230.08/41.42    (12)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.08/41.42          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.08/41.42    (13)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.08/41.42          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.08/41.42    (14)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.08/41.42          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.08/41.42    (15)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 230.08/41.42          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.08/41.42    (16)   ~ (e3 = e2)
% 230.08/41.42    (17)   ~ (e3 = e0)
% 230.08/41.42    (18)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.08/41.42          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.08/41.42    (19)  op(e0, e3) = all_53_3
% 230.08/41.42    (20)  all_57_0 = e0
% 230.08/41.42    (21)  all_57_15 = e3
% 230.08/41.42    (22)  op(e3, e3) = e0
% 230.08/41.42    (23)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.08/41.42          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.08/41.42            e1)
% 230.08/41.42    (24)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.08/41.42          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.08/41.42    (25)   ~ (e2 = e0)
% 230.08/41.42    (26)  all_57_3 = e1
% 230.08/41.42    (27)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.08/41.42          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.08/41.42    (28)   ~ (e1 = e0)
% 230.08/41.42    (29)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 230.08/41.42          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 230.08/41.42    (30)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.08/41.42          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.08/41.42    (31)  op(e0, e0) = e3
% 230.08/41.42    (32)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.08/41.42          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.08/41.42            e2)
% 230.08/41.42    (33)   ~ (all_53_3 = e0)
% 230.08/41.42    (34)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.08/41.42              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.08/41.42                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.08/41.42                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.08/41.42    (35)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.08/41.42          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.08/41.42    (36)   ~ (all_53_12 = e3)
% 230.08/41.42    (37)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.08/41.42          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.08/41.42    (38)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.08/41.42          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.08/41.42    (39)   ~ (all_53_12 = e0)
% 230.08/41.42    (40)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.08/41.42          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 230.08/41.42    (41)   ~ (e2 = e1)
% 230.08/41.42    (42)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.08/41.42          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.08/41.42    (43)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.08/41.42          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.08/41.42    (44)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.08/41.42          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.08/41.42    (45)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.08/41.42          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.08/41.42    (46)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.08/41.42          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.08/41.42    (47)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.08/41.42          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.08/41.42    (48)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.08/41.42          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.08/41.42    (49)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.08/41.42          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.08/41.42    (50)  op(e3, e0) = all_53_12
% 230.08/41.42  
% 230.08/41.42  Begin of proof
% 230.08/41.42  | 
% 230.08/41.42  | BETA: splitting (12) gives:
% 230.08/41.42  | 
% 230.08/41.42  | Case 1:
% 230.08/41.42  | | 
% 230.08/41.42  | |   (51)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) =
% 230.08/41.42  | |           e1)
% 230.08/41.42  | | 
% 230.08/41.42  | | REF_CLOSE: (4), (5), (7), (11), (16), (17), (20), (24), (25), (28), (30),
% 230.08/41.42  | |            (41), (51) are inconsistent by sub-proof #1551.
% 230.08/41.42  | | 
% 230.08/41.42  | Case 2:
% 230.08/41.42  | | 
% 230.08/41.42  | |   (52)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) =
% 230.08/41.42  | |           e1)
% 230.08/41.42  | | 
% 230.08/41.42  | | BETA: splitting (52) gives:
% 230.08/41.42  | | 
% 230.08/41.42  | | Case 1:
% 230.08/41.42  | | | 
% 230.08/41.42  | | |   (53)  all_57_4 = e1 & op(e3, e1) = e1
% 230.08/41.42  | | | 
% 230.08/41.42  | | | ALPHA: (53) implies:
% 230.08/41.42  | | |   (54)  all_57_4 = e1
% 230.08/41.42  | | | 
% 230.08/41.42  | | | BETA: splitting (3) gives:
% 230.08/41.42  | | | 
% 230.08/41.42  | | | Case 1:
% 230.08/41.42  | | | | 
% 230.08/41.42  | | | |   (55)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3)
% 230.08/41.42  | | | |           = e1)
% 230.08/41.42  | | | | 
% 230.08/41.42  | | | | BETA: splitting (55) gives:
% 230.08/41.42  | | | | 
% 230.08/41.42  | | | | Case 1:
% 230.08/41.42  | | | | | 
% 230.08/41.42  | | | | |   (56)  all_57_0 = e1 & op(e3, e3) = e1
% 230.08/41.42  | | | | | 
% 230.08/41.42  | | | | | REF_CLOSE: (4), (5), (7), (11), (12), (13), (16), (17), (20), (22),
% 230.08/41.42  | | | | |            (24), (25), (27), (28), (30), (36), (41), (50), (54), (56)
% 230.08/41.42  | | | | |            are inconsistent by sub-proof #996.
% 230.08/41.42  | | | | | 
% 230.08/41.42  | | | | Case 2:
% 230.08/41.42  | | | | | 
% 230.08/41.42  | | | | |   (57)  all_57_2 = e1 & op(e2, e3) = e1
% 230.08/41.42  | | | | | 
% 230.08/41.42  | | | | | ALPHA: (57) implies:
% 230.08/41.42  | | | | |   (58)  all_57_2 = e1
% 230.08/41.42  | | | | | 
% 230.08/41.42  | | | | | BETA: splitting (35) gives:
% 230.08/41.42  | | | | | 
% 230.08/41.42  | | | | | Case 1:
% 230.08/41.42  | | | | | | 
% 230.08/41.42  | | | | | |   (59)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2,
% 230.08/41.42  | | | | | |             e2) = e3)
% 230.08/41.42  | | | | | | 
% 230.08/41.42  | | | | | | REF_CLOSE: (5), (7), (11), (58), (59) are inconsistent by sub-proof
% 230.08/41.42  | | | | | |            #995.
% 230.08/41.42  | | | | | | 
% 230.08/41.42  | | | | | Case 2:
% 230.08/41.42  | | | | | | 
% 230.08/41.42  | | | | | |   (60)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2,
% 230.08/41.42  | | | | | |             e0) = e3)
% 230.08/41.42  | | | | | | 
% 230.08/41.42  | | | | | | BETA: splitting (60) gives:
% 230.08/41.42  | | | | | | 
% 230.08/41.42  | | | | | | Case 1:
% 230.08/41.42  | | | | | | | 
% 230.08/41.42  | | | | | | |   (61)  all_57_5 = e3 & op(e2, e1) = e3
% 230.08/41.42  | | | | | | | 
% 230.08/41.42  | | | | | | | ALPHA: (61) implies:
% 230.08/41.42  | | | | | | |   (62)  all_57_5 = e3
% 230.08/41.42  | | | | | | | 
% 230.08/41.42  | | | | | | | BETA: splitting (24) gives:
% 230.08/41.42  | | | | | | | 
% 230.08/41.42  | | | | | | | Case 1:
% 230.08/41.42  | | | | | | | | 
% 230.08/41.42  | | | | | | | |   (63)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 &
% 230.08/41.42  | | | | | | | |           op(e2, e2) = e0)
% 230.08/41.42  | | | | | | | | 
% 230.08/41.42  | | | | | | | | REF_CLOSE: (5), (7), (11), (17), (22), (27), (28), (36), (50),
% 230.08/41.42  | | | | | | | |            (54), (63) are inconsistent by sub-proof #994.
% 230.08/41.42  | | | | | | | | 
% 230.08/41.42  | | | | | | | Case 2:
% 230.08/41.42  | | | | | | | | 
% 230.08/41.42  | | | | | | | |   (64)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 &
% 230.08/41.42  | | | | | | | |           op(e0, e2) = e0)
% 230.08/41.42  | | | | | | | | 
% 230.08/41.42  | | | | | | | | BETA: splitting (64) gives:
% 230.08/41.42  | | | | | | | | 
% 230.08/41.42  | | | | | | | | Case 1:
% 230.08/41.42  | | | | | | | | | 
% 230.08/41.42  | | | | | | | | |   (65)  all_57_7 = e0 & op(e1, e2) = e0
% 230.08/41.42  | | | | | | | | | 
% 230.08/41.42  | | | | | | | | | ALPHA: (65) implies:
% 230.08/41.42  | | | | | | | | |   (66)  all_57_7 = e0
% 230.08/41.42  | | | | | | | | | 
% 230.08/41.42  | | | | | | | | | BETA: splitting (30) gives:
% 230.08/41.42  | | | | | | | | | 
% 230.08/41.42  | | | | | | | | | Case 1:
% 230.08/41.42  | | | | | | | | | | 
% 230.08/41.42  | | | | | | | | | |   (67)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 &
% 230.08/41.42  | | | | | | | | | |           op(e2, e2) = e3)
% 230.08/41.42  | | | | | | | | | | 
% 230.08/41.42  | | | | | | | | | | BETA: splitting (67) gives:
% 230.08/41.42  | | | | | | | | | | 
% 230.08/41.42  | | | | | | | | | | Case 1:
% 230.08/41.42  | | | | | | | | | | | 
% 230.08/41.42  | | | | | | | | | | |   (68)  all_57_1 = e3 & op(e3, e2) = e3
% 230.08/41.42  | | | | | | | | | | | 
% 230.08/41.42  | | | | | | | | | | | ALPHA: (68) implies:
% 230.08/41.42  | | | | | | | | | | |   (69)  all_57_1 = e3
% 230.08/41.42  | | | | | | | | | | | 
% 230.08/41.42  | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (7), (8), (9), (10), (11),
% 230.08/41.42  | | | | | | | | | | |            (16), (17), (20), (21), (22), (24), (25), (26),
% 230.08/41.42  | | | | | | | | | | |            (27), (28), (34), (36), (37), (40), (41), (42),
% 230.08/41.42  | | | | | | | | | | |            (43), (46), (48), (50), (54), (58), (62), (66),
% 230.08/41.42  | | | | | | | | | | |            (69) are inconsistent by sub-proof #1006.
% 230.08/41.42  | | | | | | | | | | | 
% 230.08/41.42  | | | | | | | | | | Case 2:
% 230.08/41.42  | | | | | | | | | | | 
% 230.08/41.42  | | | | | | | | | | |   (70)  all_57_3 = e3 & op(e2, e2) = e3
% 230.08/41.42  | | | | | | | | | | | 
% 230.08/41.42  | | | | | | | | | | | ALPHA: (70) implies:
% 230.08/41.42  | | | | | | | | | | |   (71)  op(e2, e2) = e3
% 230.08/41.42  | | | | | | | | | | | 
% 230.08/41.42  | | | | | | | | | | | REF_CLOSE: (5), (7), (11), (71) are inconsistent by sub-proof
% 230.08/41.42  | | | | | | | | | | |            #1912.
% 230.08/41.42  | | | | | | | | | | | 
% 230.08/41.42  | | | | | | | | | | End of split
% 230.08/41.42  | | | | | | | | | | 
% 230.08/41.42  | | | | | | | | | Case 2:
% 230.08/41.42  | | | | | | | | | | 
% 230.08/41.42  | | | | | | | | | |   (72)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3
% 230.08/41.42  | | | | | | | | | |           & op(e0, e2) = e3)
% 230.08/41.42  | | | | | | | | | | 
% 230.08/41.42  | | | | | | | | | | REF_CLOSE: (5), (7), (16), (17), (21), (23), (25), (28),
% 230.08/41.42  | | | | | | | | | |            (31), (32), (34), (41), (66), (72) are
% 230.08/41.42  | | | | | | | | | |            inconsistent by sub-proof #993.
% 230.08/41.42  | | | | | | | | | | 
% 230.08/41.42  | | | | | | | | | End of split
% 230.08/41.42  | | | | | | | | | 
% 230.08/41.42  | | | | | | | | Case 2:
% 230.08/41.42  | | | | | | | | | 
% 230.08/41.42  | | | | | | | | |   (73)  all_57_13 = e0 & op(e0, e2) = e0
% 230.08/41.42  | | | | | | | | | 
% 230.08/41.42  | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 230.08/41.42  | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 230.08/41.42  | | | | | | | | |            (19), (21), (22), (23), (24), (25), (26), (27),
% 230.08/41.42  | | | | | | | | |            (28), (29), (30), (31), (32), (33), (34), (36),
% 230.08/41.42  | | | | | | | | |            (37), (38), (39), (41), (42), (43), (44), (45),
% 230.08/41.42  | | | | | | | | |            (46), (47), (48), (49), (50), (58), (62), (73) are
% 230.08/41.42  | | | | | | | | |            inconsistent by sub-proof #992.
% 230.08/41.42  | | | | | | | | | 
% 230.08/41.42  | | | | | | | | End of split
% 230.08/41.42  | | | | | | | | 
% 230.08/41.42  | | | | | | | End of split
% 230.08/41.42  | | | | | | | 
% 230.08/41.42  | | | | | | Case 2:
% 230.08/41.42  | | | | | | | 
% 230.08/41.42  | | | | | | |   (74)  all_57_10 = e3 & op(e2, e0) = e3
% 230.08/41.42  | | | | | | | 
% 230.08/41.42  | | | | | | | ALPHA: (74) implies:
% 230.08/41.42  | | | | | | |   (75)  all_57_10 = e3
% 230.08/41.42  | | | | | | | 
% 230.08/41.42  | | | | | | | REF_CLOSE: (5), (7), (16), (17), (21), (25), (28), (31), (34),
% 230.08/41.42  | | | | | | |            (41), (42), (46), (75) are inconsistent by sub-proof
% 230.08/41.42  | | | | | | |            #1746.
% 230.08/41.42  | | | | | | | 
% 230.08/41.42  | | | | | | End of split
% 230.08/41.42  | | | | | | 
% 230.08/41.42  | | | | | End of split
% 230.08/41.42  | | | | | 
% 230.08/41.42  | | | | End of split
% 230.08/41.42  | | | | 
% 230.08/41.42  | | | Case 2:
% 230.08/41.42  | | | | 
% 230.08/41.42  | | | |   (76)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3)
% 230.08/41.42  | | | |           = e1)
% 230.08/41.42  | | | | 
% 230.08/41.42  | | | | BETA: splitting (76) gives:
% 230.08/41.42  | | | | 
% 230.08/41.42  | | | | Case 1:
% 230.08/41.42  | | | | | 
% 230.08/41.42  | | | | |   (77)  all_57_6 = e1 & op(e1, e3) = e1
% 230.08/41.42  | | | | | 
% 230.08/41.42  | | | | | ALPHA: (77) implies:
% 230.08/41.42  | | | | |   (78)  all_57_6 = e1
% 230.08/41.42  | | | | | 
% 230.08/41.42  | | | | | BETA: splitting (24) gives:
% 230.08/41.42  | | | | | 
% 230.08/41.42  | | | | | Case 1:
% 230.08/41.42  | | | | | | 
% 230.08/41.42  | | | | | |   (79)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2,
% 230.08/41.42  | | | | | |             e2) = e0)
% 230.08/41.42  | | | | | | 
% 230.08/41.42  | | | | | | REF_CLOSE: (5), (7), (11), (17), (22), (27), (28), (36), (50), (54),
% 230.08/41.42  | | | | | |            (79) are inconsistent by sub-proof #994.
% 230.08/41.42  | | | | | | 
% 230.08/41.42  | | | | | Case 2:
% 230.08/41.42  | | | | | | 
% 230.08/41.42  | | | | | |   (80)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0,
% 230.08/41.42  | | | | | |             e2) = e0)
% 230.08/41.42  | | | | | | 
% 230.08/41.42  | | | | | | BETA: splitting (80) gives:
% 230.08/41.42  | | | | | | 
% 230.08/41.42  | | | | | | Case 1:
% 230.08/41.42  | | | | | | | 
% 230.08/41.42  | | | | | | |   (81)  all_57_7 = e0 & op(e1, e2) = e0
% 230.08/41.42  | | | | | | | 
% 230.08/41.42  | | | | | | | ALPHA: (81) implies:
% 230.08/41.42  | | | | | | |   (82)  all_57_7 = e0
% 230.08/41.42  | | | | | | | 
% 230.08/41.42  | | | | | | | REF_CLOSE: (5), (7), (8), (9), (10), (16), (17), (21), (25), (28),
% 230.08/41.42  | | | | | | |            (34), (41), (42), (46), (78), (82) are inconsistent by
% 230.08/41.42  | | | | | | |            sub-proof #1735.
% 230.08/41.42  | | | | | | | 
% 230.08/41.42  | | | | | | Case 2:
% 230.08/41.42  | | | | | | | 
% 230.08/41.42  | | | | | | |   (83)  all_57_13 = e0 & op(e0, e2) = e0
% 230.08/41.42  | | | | | | | 
% 230.08/41.42  | | | | | | | ALPHA: (83) implies:
% 230.08/41.42  | | | | | | |   (84)  all_57_13 = e0
% 230.08/41.42  | | | | | | | 
% 230.08/41.42  | | | | | | | COMBINE_EQS: (2), (84) imply:
% 230.08/41.42  | | | | | | |   (85)  e1 = e0
% 230.08/41.42  | | | | | | | 
% 230.08/41.42  | | | | | | | COMBINE_EQS: (54), (85) imply:
% 230.08/41.42  | | | | | | |   (86)  all_57_4 = e0
% 230.08/41.42  | | | | | | | 
% 230.08/41.42  | | | | | | | REF_CLOSE: (4), (5), (7), (11), (12), (13), (16), (17), (20),
% 230.08/41.42  | | | | | | |            (22), (24), (25), (27), (28), (30), (36), (41), (50),
% 230.08/41.42  | | | | | | |            (86) are inconsistent by sub-proof #1012.
% 230.08/41.42  | | | | | | | 
% 230.08/41.42  | | | | | | End of split
% 230.08/41.42  | | | | | | 
% 230.08/41.42  | | | | | End of split
% 230.08/41.42  | | | | | 
% 230.08/41.42  | | | | Case 2:
% 230.08/41.42  | | | | | 
% 230.08/41.42  | | | | |   (87)  all_57_12 = e1 & op(e0, e3) = e1
% 230.08/41.42  | | | | | 
% 230.08/41.42  | | | | | ALPHA: (87) implies:
% 230.08/41.42  | | | | |   (88)  all_57_12 = e1
% 230.08/41.42  | | | | | 
% 230.08/41.42  | | | | | BETA: splitting (27) gives:
% 230.08/41.42  | | | | | 
% 230.08/41.42  | | | | | Case 1:
% 230.08/41.42  | | | | | | 
% 230.08/41.42  | | | | | |   (89)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3,
% 230.08/41.42  | | | | | |             e2) = e3)
% 230.08/41.42  | | | | | | 
% 230.08/41.42  | | | | | | BETA: splitting (89) gives:
% 230.08/41.42  | | | | | | 
% 230.08/41.42  | | | | | | Case 1:
% 230.08/41.42  | | | | | | | 
% 230.08/41.42  | | | | | | |   (90)  all_57_0 = e3 & op(e3, e3) = e3
% 230.08/41.42  | | | | | | | 
% 230.08/41.42  | | | | | | | ALPHA: (90) implies:
% 230.08/41.42  | | | | | | |   (91)  op(e3, e3) = e3
% 230.08/41.42  | | | | | | | 
% 230.08/41.42  | | | | | | | REF_CLOSE: (7), (17), (22), (91) are inconsistent by sub-proof
% 230.08/41.42  | | | | | | |            #2494.
% 230.08/41.42  | | | | | | | 
% 230.08/41.42  | | | | | | Case 2:
% 230.08/41.42  | | | | | | | 
% 230.08/41.42  | | | | | | |   (92)  all_57_1 = e3 & op(e3, e2) = e3
% 230.08/41.42  | | | | | | | 
% 230.08/41.42  | | | | | | | ALPHA: (92) implies:
% 230.08/41.42  | | | | | | |   (93)  all_57_1 = e3
% 230.08/41.42  | | | | | | | 
% 230.08/41.42  | | | | | | | BETA: splitting (24) gives:
% 230.08/41.42  | | | | | | | 
% 230.08/41.42  | | | | | | | Case 1:
% 230.08/41.42  | | | | | | | | 
% 230.08/41.42  | | | | | | | |   (94)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 &
% 230.08/41.42  | | | | | | | |           op(e2, e2) = e0)
% 230.08/41.42  | | | | | | | | 
% 230.08/41.42  | | | | | | | | REF_CLOSE: (5), (7), (11), (17), (22), (27), (28), (36), (50),
% 230.08/41.42  | | | | | | | |            (54), (94) are inconsistent by sub-proof #994.
% 230.08/41.42  | | | | | | | | 
% 230.08/41.42  | | | | | | | Case 2:
% 230.08/41.42  | | | | | | | | 
% 230.08/41.43  | | | | | | | |   (95)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 &
% 230.08/41.43  | | | | | | | |           op(e0, e2) = e0)
% 230.08/41.43  | | | | | | | | 
% 230.08/41.43  | | | | | | | | BETA: splitting (95) gives:
% 230.08/41.43  | | | | | | | | 
% 230.08/41.43  | | | | | | | | Case 1:
% 230.08/41.43  | | | | | | | | | 
% 230.08/41.43  | | | | | | | | |   (96)  all_57_7 = e0 & op(e1, e2) = e0
% 230.08/41.43  | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | ALPHA: (96) implies:
% 230.08/41.43  | | | | | | | | |   (97)  all_57_7 = e0
% 230.08/41.43  | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | BETA: splitting (29) gives:
% 230.08/41.43  | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | Case 1:
% 230.08/41.43  | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | |   (98)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 &
% 230.08/41.43  | | | | | | | | | |           op(e2, e1) = e3)
% 230.08/41.43  | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | BETA: splitting (98) gives:
% 230.08/41.43  | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | Case 1:
% 230.08/41.43  | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | |   (99)  all_57_4 = e3 & op(e3, e1) = e3
% 230.08/41.43  | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | ALPHA: (99) implies:
% 230.08/41.43  | | | | | | | | | | |   (100)  all_57_4 = e3
% 230.08/41.43  | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | REF_CLOSE: (5), (7), (12), (13), (14), (16), (17), (22),
% 230.08/41.43  | | | | | | | | | | |            (25), (28), (41), (93), (100) are inconsistent by
% 230.08/41.43  | | | | | | | | | | |            sub-proof #1220.
% 230.08/41.43  | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | Case 2:
% 230.08/41.43  | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | |   (101)  all_57_5 = e3 & op(e2, e1) = e3
% 230.08/41.43  | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | ALPHA: (101) implies:
% 230.08/41.43  | | | | | | | | | | |   (102)  all_57_5 = e3
% 230.08/41.43  | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | BETA: splitting (8) gives:
% 230.08/41.43  | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | Case 1:
% 230.08/41.43  | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | |   (103)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 230.08/41.43  | | | | | | | | | | | |            & op(e1, e2) = e3)
% 230.08/41.43  | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | BETA: splitting (103) gives:
% 230.08/41.43  | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | Case 1:
% 230.08/41.43  | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | |   (104)  all_57_6 = e3 & op(e1, e3) = e3
% 230.08/41.43  | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | ALPHA: (104) implies:
% 230.08/41.43  | | | | | | | | | | | | |   (105)  all_57_6 = e3
% 230.08/41.43  | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | BETA: splitting (32) gives:
% 230.08/41.43  | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | Case 1:
% 230.08/41.43  | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | |   (106)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 230.08/41.43  | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 230.08/41.43  | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | | REF_CLOSE: (2), (41), (88), (106) are inconsistent by
% 230.08/41.43  | | | | | | | | | | | | | |            sub-proof #991.
% 230.08/41.43  | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | Case 2:
% 230.08/41.43  | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | |   (107)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 230.08/41.43  | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 230.08/41.43  | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 230.08/41.43  | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | | Case 1:
% 230.08/41.43  | | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | | |   (108)  all_57_14 = e2 & op(e0, e1) = e2
% 230.08/41.43  | | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | | | ALPHA: (108) implies:
% 230.08/41.43  | | | | | | | | | | | | | | |   (109)  all_57_14 = e2
% 230.08/41.43  | | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 230.08/41.43  | | | | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 230.08/41.43  | | | | | | | | | | | | | | |            (19), (20), (21), (22), (23), (24), (25), (26),
% 230.08/41.43  | | | | | | | | | | | | | | |            (27), (28), (29), (30), (31), (32), (33), (34),
% 230.08/41.43  | | | | | | | | | | | | | | |            (35), (36), (37), (38), (39), (40), (41), (42),
% 230.08/41.43  | | | | | | | | | | | | | | |            (43), (44), (45), (46), (47), (48), (49), (50),
% 230.08/41.43  | | | | | | | | | | | | | | |            (88), (93), (97), (102), (105), (109) are
% 230.08/41.43  | | | | | | | | | | | | | | |            inconsistent by sub-proof #988.
% 230.08/41.43  | | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | | Case 2:
% 230.08/41.43  | | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | | |   (110)  all_57_15 = e2 & op(e0, e0) = e2
% 230.08/41.43  | | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10),
% 230.08/41.43  | | | | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 230.08/41.43  | | | | | | | | | | | | | | |            (19), (21), (22), (23), (24), (25), (26), (27),
% 230.08/41.43  | | | | | | | | | | | | | | |            (28), (29), (30), (31), (32), (33), (34), (35),
% 230.08/41.43  | | | | | | | | | | | | | | |            (36), (37), (38), (39), (41), (42), (43), (44),
% 230.08/41.43  | | | | | | | | | | | | | | |            (45), (46), (47), (48), (49), (50), (88), (97),
% 230.08/41.43  | | | | | | | | | | | | | | |            (105), (110) are inconsistent by sub-proof #987.
% 230.08/41.43  | | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | | End of split
% 230.08/41.43  | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | End of split
% 230.08/41.43  | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | Case 2:
% 230.08/41.43  | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | |   (111)  all_57_7 = e3 & op(e1, e2) = e3
% 230.08/41.43  | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | ALPHA: (111) implies:
% 230.08/41.43  | | | | | | | | | | | | |   (112)  all_57_7 = e3
% 230.08/41.43  | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | COMBINE_EQS: (97), (112) imply:
% 230.08/41.43  | | | | | | | | | | | | |   (113)  e3 = e0
% 230.08/41.43  | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | SIMP: (113) implies:
% 230.08/41.43  | | | | | | | | | | | | |   (114)  e3 = e0
% 230.08/41.43  | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | COMBINE_EQS: (93), (114) imply:
% 230.08/41.43  | | | | | | | | | | | | |   (115)  all_57_1 = e0
% 230.08/41.43  | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | REF_CLOSE: (5), (7), (17), (22), (27), (36), (50), (54),
% 230.08/41.43  | | | | | | | | | | | | |            (115) are inconsistent by sub-proof #2280.
% 230.08/41.43  | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | End of split
% 230.08/41.43  | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | Case 2:
% 230.08/41.43  | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | |   (116)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 230.08/41.43  | | | | | | | | | | | |            e3 & op(e1, e0) = e3)
% 230.08/41.43  | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | REF_CLOSE: (5), (7), (9), (10), (16), (17), (21), (25), (28),
% 230.08/41.43  | | | | | | | | | | | |            (34), (41), (42), (46), (116) are inconsistent by
% 230.08/41.43  | | | | | | | | | | | |            sub-proof #1786.
% 230.08/41.43  | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | End of split
% 230.08/41.43  | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | End of split
% 230.08/41.43  | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | Case 2:
% 230.08/41.43  | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | |   (117)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3
% 230.08/41.43  | | | | | | | | | |            & op(e0, e1) = e3)
% 230.08/41.43  | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | REF_CLOSE: (5), (7), (9), (10), (16), (17), (21), (23), (25),
% 230.08/41.43  | | | | | | | | | |            (28), (32), (34), (41), (117) are inconsistent by
% 230.08/41.43  | | | | | | | | | |            sub-proof #1794.
% 230.08/41.43  | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | End of split
% 230.08/41.43  | | | | | | | | | 
% 230.08/41.43  | | | | | | | | Case 2:
% 230.08/41.43  | | | | | | | | | 
% 230.08/41.43  | | | | | | | | |   (118)  all_57_13 = e0 & op(e0, e2) = e0
% 230.08/41.43  | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | REF_CLOSE: (2), (4), (5), (16), (25), (26), (28), (41), (48),
% 230.08/41.43  | | | | | | | | |            (93), (118) are inconsistent by sub-proof #1757.
% 230.08/41.43  | | | | | | | | | 
% 230.08/41.43  | | | | | | | | End of split
% 230.08/41.43  | | | | | | | | 
% 230.08/41.43  | | | | | | | End of split
% 230.08/41.43  | | | | | | | 
% 230.08/41.43  | | | | | | End of split
% 230.08/41.43  | | | | | | 
% 230.08/41.43  | | | | | Case 2:
% 230.08/41.43  | | | | | | 
% 230.08/41.43  | | | | | |   (119)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3,
% 230.08/41.43  | | | | | |              e0) = e3)
% 230.08/41.43  | | | | | | 
% 230.08/41.43  | | | | | | REF_CLOSE: (5), (7), (36), (50), (54), (119) are inconsistent by
% 230.08/41.43  | | | | | |            sub-proof #2281.
% 230.08/41.43  | | | | | | 
% 230.08/41.43  | | | | | End of split
% 230.08/41.43  | | | | | 
% 230.08/41.43  | | | | End of split
% 230.08/41.43  | | | | 
% 230.08/41.43  | | | End of split
% 230.08/41.43  | | | 
% 230.08/41.43  | | Case 2:
% 230.08/41.43  | | | 
% 230.08/41.43  | | |   (120)  all_57_9 = e1 & op(e3, e0) = e1
% 230.08/41.43  | | | 
% 230.08/41.43  | | | ALPHA: (120) implies:
% 230.08/41.43  | | |   (121)  all_57_9 = e1
% 230.08/41.43  | | | 
% 230.08/41.43  | | | BETA: splitting (3) gives:
% 230.08/41.43  | | | 
% 230.08/41.43  | | | Case 1:
% 230.08/41.43  | | | | 
% 230.08/41.43  | | | |   (122)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3)
% 230.08/41.43  | | | |            = e1)
% 230.08/41.43  | | | | 
% 230.08/41.43  | | | | BETA: splitting (122) gives:
% 230.08/41.43  | | | | 
% 230.08/41.43  | | | | Case 1:
% 230.08/41.43  | | | | | 
% 230.08/41.43  | | | | |   (123)  all_57_0 = e1 & op(e3, e3) = e1
% 230.08/41.43  | | | | | 
% 230.08/41.43  | | | | | REF_CLOSE: (20), (28), (123) are inconsistent by sub-proof #2454.
% 230.08/41.43  | | | | | 
% 230.08/41.43  | | | | Case 2:
% 230.08/41.43  | | | | | 
% 230.08/41.43  | | | | |   (124)  all_57_2 = e1 & op(e2, e3) = e1
% 230.08/41.43  | | | | | 
% 230.08/41.43  | | | | | ALPHA: (124) implies:
% 230.08/41.43  | | | | |   (125)  all_57_2 = e1
% 230.08/41.43  | | | | | 
% 230.08/41.43  | | | | | BETA: splitting (35) gives:
% 230.08/41.43  | | | | | 
% 230.08/41.43  | | | | | Case 1:
% 230.08/41.43  | | | | | | 
% 230.08/41.43  | | | | | |   (126)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2,
% 230.08/41.43  | | | | | |              e2) = e3)
% 230.08/41.43  | | | | | | 
% 230.08/41.43  | | | | | | REF_CLOSE: (5), (7), (11), (125), (126) are inconsistent by
% 230.08/41.43  | | | | | |            sub-proof #995.
% 230.08/41.43  | | | | | | 
% 230.08/41.43  | | | | | Case 2:
% 230.08/41.43  | | | | | | 
% 230.08/41.43  | | | | | |   (127)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 &
% 230.08/41.43  | | | | | |            op(e2, e0) = e3)
% 230.08/41.43  | | | | | | 
% 230.08/41.43  | | | | | | BETA: splitting (127) gives:
% 230.08/41.43  | | | | | | 
% 230.08/41.43  | | | | | | Case 1:
% 230.08/41.43  | | | | | | | 
% 230.08/41.43  | | | | | | |   (128)  all_57_5 = e3 & op(e2, e1) = e3
% 230.08/41.43  | | | | | | | 
% 230.08/41.43  | | | | | | | ALPHA: (128) implies:
% 230.08/41.43  | | | | | | |   (129)  all_57_5 = e3
% 230.08/41.43  | | | | | | | 
% 230.08/41.43  | | | | | | | BETA: splitting (24) gives:
% 230.08/41.43  | | | | | | | 
% 230.08/41.43  | | | | | | | Case 1:
% 230.08/41.43  | | | | | | | | 
% 230.08/41.43  | | | | | | | |   (130)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 &
% 230.08/41.43  | | | | | | | |            op(e2, e2) = e0)
% 230.08/41.43  | | | | | | | | 
% 230.08/41.43  | | | | | | | | REF_CLOSE: (7), (11), (13), (16), (17), (22), (25), (27), (28),
% 230.08/41.43  | | | | | | | |            (36), (41), (50), (121), (130) are inconsistent by
% 230.08/41.43  | | | | | | | |            sub-proof #986.
% 230.08/41.43  | | | | | | | | 
% 230.08/41.43  | | | | | | | Case 2:
% 230.08/41.43  | | | | | | | | 
% 230.08/41.43  | | | | | | | |   (131)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 &
% 230.08/41.43  | | | | | | | |            op(e0, e2) = e0)
% 230.08/41.43  | | | | | | | | 
% 230.08/41.43  | | | | | | | | BETA: splitting (131) gives:
% 230.08/41.43  | | | | | | | | 
% 230.08/41.43  | | | | | | | | Case 1:
% 230.08/41.43  | | | | | | | | | 
% 230.08/41.43  | | | | | | | | |   (132)  all_57_7 = e0 & op(e1, e2) = e0
% 230.08/41.43  | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | ALPHA: (132) implies:
% 230.08/41.43  | | | | | | | | |   (133)  all_57_7 = e0
% 230.08/41.43  | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | BETA: splitting (30) gives:
% 230.08/41.43  | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | Case 1:
% 230.08/41.43  | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | |   (134)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 230.08/41.43  | | | | | | | | | |            & op(e2, e2) = e3)
% 230.08/41.43  | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | BETA: splitting (134) gives:
% 230.08/41.43  | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | Case 1:
% 230.08/41.43  | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | |   (135)  all_57_1 = e3 & op(e3, e2) = e3
% 230.08/41.43  | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | ALPHA: (135) implies:
% 230.08/41.43  | | | | | | | | | | |   (136)  all_57_1 = e3
% 230.08/41.43  | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | BETA: splitting (38) gives:
% 230.08/41.43  | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | Case 1:
% 230.08/41.43  | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | |   (137)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 230.08/41.43  | | | | | | | | | | | |            & op(e2, e3) = e3)
% 230.08/41.43  | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | BETA: splitting (137) gives:
% 230.08/41.43  | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | Case 1:
% 230.08/41.43  | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | |   (138)  all_57_0 = e3 & op(e3, e3) = e3
% 230.08/41.43  | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | ALPHA: (138) implies:
% 230.08/41.43  | | | | | | | | | | | | |   (139)  op(e3, e3) = e3
% 230.08/41.43  | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | REF_CLOSE: (7), (17), (22), (139) are inconsistent by
% 230.08/41.43  | | | | | | | | | | | | |            sub-proof #2494.
% 230.08/41.43  | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | Case 2:
% 230.08/41.43  | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | |   (140)  all_57_2 = e3 & op(e2, e3) = e3
% 230.08/41.43  | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | ALPHA: (140) implies:
% 230.08/41.43  | | | | | | | | | | | | |   (141)  all_57_2 = e3
% 230.08/41.43  | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | COMBINE_EQS: (125), (141) imply:
% 230.08/41.43  | | | | | | | | | | | | |   (142)  e3 = e1
% 230.08/41.43  | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | SIMP: (142) implies:
% 230.08/41.43  | | | | | | | | | | | | |   (143)  e3 = e1
% 230.08/41.43  | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | COMBINE_EQS: (136), (143) imply:
% 230.08/41.43  | | | | | | | | | | | | |   (144)  all_57_1 = e1
% 230.08/41.43  | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (11), (16), (17), (24), (25), (28),
% 230.08/41.43  | | | | | | | | | | | | |            (30), (41), (144) are inconsistent by sub-proof
% 230.08/41.43  | | | | | | | | | | | | |            #1908.
% 230.08/41.43  | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | End of split
% 230.08/41.43  | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | Case 2:
% 230.08/41.43  | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | |   (145)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 230.08/41.43  | | | | | | | | | | | |            e3 & op(e0, e3) = e3)
% 230.08/41.43  | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | BETA: splitting (145) gives:
% 230.08/41.43  | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | Case 1:
% 230.08/41.43  | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | |   (146)  all_57_6 = e3 & op(e1, e3) = e3
% 230.08/41.43  | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | ALPHA: (146) implies:
% 230.08/41.43  | | | | | | | | | | | | |   (147)  all_57_6 = e3
% 230.08/41.43  | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (7), (8), (9), (10), (11),
% 230.08/41.43  | | | | | | | | | | | | |            (14), (16), (17), (19), (20), (21), (22), (23),
% 230.08/41.43  | | | | | | | | | | | | |            (24), (25), (26), (27), (28), (30), (31), (33),
% 230.08/41.43  | | | | | | | | | | | | |            (34), (35), (36), (37), (38), (39), (40), (41),
% 230.08/41.43  | | | | | | | | | | | | |            (42), (43), (46), (48), (50), (125), (136), (147)
% 230.08/41.43  | | | | | | | | | | | | |            are inconsistent by sub-proof #980.
% 230.08/41.43  | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | Case 2:
% 230.08/41.43  | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | |   (148)  all_57_12 = e3 & op(e0, e3) = e3
% 230.08/41.43  | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | ALPHA: (148) implies:
% 230.08/41.43  | | | | | | | | | | | | |   (149)  all_57_12 = e3
% 230.08/41.43  | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | BETA: splitting (40) gives:
% 230.08/41.43  | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | Case 1:
% 230.08/41.43  | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | |   (150)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 230.08/41.43  | | | | | | | | | | | | | |            & op(e2, e2) = e0)
% 230.08/41.43  | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | | BETA: splitting (150) gives:
% 230.08/41.43  | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | | Case 1:
% 230.08/41.43  | | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | | |   (151)  all_57_2 = e0 & op(e2, e3) = e0
% 230.08/41.43  | | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | | | ALPHA: (151) implies:
% 230.08/41.43  | | | | | | | | | | | | | | |   (152)  all_57_2 = e0
% 230.08/41.43  | | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (5), (7), (16), (17), (19), (21), (23),
% 230.08/41.43  | | | | | | | | | | | | | | |            (25), (26), (28), (31), (32), (33), (34), (37),
% 230.08/41.43  | | | | | | | | | | | | | | |            (41), (129), (149), (152) are inconsistent by
% 230.08/41.43  | | | | | | | | | | | | | | |            sub-proof #1065.
% 230.08/41.43  | | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | | Case 2:
% 230.08/41.43  | | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | | |   (153)  all_57_3 = e0 & op(e2, e2) = e0
% 230.08/41.43  | | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | | | ALPHA: (153) implies:
% 230.08/41.43  | | | | | | | | | | | | | | |   (154)  all_57_3 = e0
% 230.08/41.43  | | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (16), (17), (21), (23), (25), (28),
% 230.08/41.43  | | | | | | | | | | | | | | |            (32), (34), (41), (48), (136), (149), (154) are
% 230.08/41.43  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1037.
% 230.08/41.43  | | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | | End of split
% 230.08/41.43  | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | Case 2:
% 230.08/41.43  | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | |   (155)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 230.08/41.43  | | | | | | | | | | | | | |            e0 & op(e2, e0) = e0)
% 230.08/41.43  | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | | BETA: splitting (155) gives:
% 230.08/41.43  | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | | Case 1:
% 230.08/41.43  | | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | | |   (156)  all_57_5 = e0 & op(e2, e1) = e0
% 230.08/41.43  | | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | | | ALPHA: (156) implies:
% 230.08/41.43  | | | | | | | | | | | | | | |   (157)  all_57_5 = e0
% 230.08/41.43  | | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | | | COMBINE_EQS: (129), (157) imply:
% 230.08/41.43  | | | | | | | | | | | | | | |   (158)  e3 = e0
% 230.08/41.43  | | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | | | COMBINE_EQS: (136), (158) imply:
% 230.08/41.43  | | | | | | | | | | | | | | |   (159)  all_57_1 = e0
% 230.08/41.43  | | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | | | REF_CLOSE: (7), (13), (16), (17), (22), (25), (27), (36),
% 230.08/41.43  | | | | | | | | | | | | | | |            (41), (50), (121), (159) are inconsistent by
% 230.08/41.43  | | | | | | | | | | | | | | |            sub-proof #2400.
% 230.08/41.43  | | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | | Case 2:
% 230.08/41.43  | | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | | |   (160)  all_57_10 = e0 & op(e2, e0) = e0
% 230.08/41.43  | | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | | | ALPHA: (160) implies:
% 230.08/41.43  | | | | | | | | | | | | | | |   (161)  all_57_10 = e0
% 230.08/41.43  | | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | | | BETA: splitting (8) gives:
% 230.08/41.43  | | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | | | Case 1:
% 230.08/41.43  | | | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | | | |   (162)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 230.08/41.43  | | | | | | | | | | | | | | | |            & op(e1, e2) = e3)
% 230.08/41.43  | | | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | | | | BETA: splitting (162) gives:
% 230.08/41.43  | | | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | | | | Case 1:
% 230.08/41.43  | | | | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | | | | |   (163)  all_57_6 = e3 & op(e1, e3) = e3
% 230.08/41.43  | | | | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | | | | | ALPHA: (163) implies:
% 230.08/41.43  | | | | | | | | | | | | | | | | |   (164)  all_57_6 = e3
% 230.08/41.43  | | | | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (7), (8), (9), (10), (11),
% 230.08/41.43  | | | | | | | | | | | | | | | | |            (14), (16), (17), (19), (20), (21), (22), (23),
% 230.08/41.43  | | | | | | | | | | | | | | | | |            (24), (25), (26), (27), (28), (30), (31), (33),
% 230.08/41.43  | | | | | | | | | | | | | | | | |            (34), (35), (36), (37), (38), (39), (40), (41),
% 230.08/41.43  | | | | | | | | | | | | | | | | |            (42), (43), (46), (48), (50), (125), (136), (164)
% 230.08/41.43  | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #980.
% 230.08/41.43  | | | | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | | | | Case 2:
% 230.08/41.43  | | | | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | | | | |   (165)  all_57_7 = e3 & op(e1, e2) = e3
% 230.08/41.43  | | | | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (13), (16), (17), (22), (25), (27), (36),
% 230.08/41.43  | | | | | | | | | | | | | | | | |            (41), (50), (121), (133), (136), (165) are
% 230.08/41.43  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #979.
% 230.08/41.43  | | | | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | | | | End of split
% 230.08/41.43  | | | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | | | Case 2:
% 230.08/41.43  | | | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | | | |   (166)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 230.08/41.43  | | | | | | | | | | | | | | | |            e3 & op(e1, e0) = e3)
% 230.08/41.43  | | | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (9), (10), (16), (21), (25), (28), (41),
% 230.08/41.43  | | | | | | | | | | | | | | | |            (42), (46), (161), (166) are inconsistent by
% 230.08/41.43  | | | | | | | | | | | | | | | |            sub-proof #978.
% 230.08/41.43  | | | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | | | End of split
% 230.08/41.43  | | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | | End of split
% 230.08/41.43  | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | End of split
% 230.08/41.43  | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | End of split
% 230.08/41.43  | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | End of split
% 230.08/41.43  | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | Case 2:
% 230.08/41.43  | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | |   (167)  all_57_3 = e3 & op(e2, e2) = e3
% 230.08/41.43  | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | ALPHA: (167) implies:
% 230.08/41.43  | | | | | | | | | | |   (168)  op(e2, e2) = e3
% 230.08/41.43  | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | REF_CLOSE: (5), (7), (11), (168) are inconsistent by
% 230.08/41.43  | | | | | | | | | | |            sub-proof #1912.
% 230.08/41.43  | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | End of split
% 230.08/41.43  | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | Case 2:
% 230.08/41.43  | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | |   (169)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3
% 230.08/41.43  | | | | | | | | | |            & op(e0, e2) = e3)
% 230.08/41.43  | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | REF_CLOSE: (5), (7), (16), (17), (21), (23), (25), (28),
% 230.08/41.43  | | | | | | | | | |            (31), (32), (34), (41), (133), (169) are
% 230.08/41.43  | | | | | | | | | |            inconsistent by sub-proof #993.
% 230.08/41.43  | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | End of split
% 230.08/41.43  | | | | | | | | | 
% 230.08/41.43  | | | | | | | | Case 2:
% 230.08/41.43  | | | | | | | | | 
% 230.08/41.43  | | | | | | | | |   (170)  all_57_13 = e0 & op(e0, e2) = e0
% 230.08/41.43  | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 230.08/41.43  | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 230.08/41.43  | | | | | | | | |            (19), (21), (22), (23), (24), (25), (26), (27),
% 230.08/41.43  | | | | | | | | |            (28), (29), (30), (31), (32), (33), (34), (36),
% 230.08/41.43  | | | | | | | | |            (37), (38), (39), (41), (42), (43), (44), (45),
% 230.08/41.43  | | | | | | | | |            (46), (47), (48), (49), (50), (125), (129), (170)
% 230.08/41.43  | | | | | | | | |            are inconsistent by sub-proof #992.
% 230.08/41.43  | | | | | | | | | 
% 230.08/41.43  | | | | | | | | End of split
% 230.08/41.43  | | | | | | | | 
% 230.08/41.43  | | | | | | | End of split
% 230.08/41.43  | | | | | | | 
% 230.08/41.43  | | | | | | Case 2:
% 230.08/41.43  | | | | | | | 
% 230.08/41.43  | | | | | | |   (171)  all_57_10 = e3 & op(e2, e0) = e3
% 230.08/41.43  | | | | | | | 
% 230.08/41.43  | | | | | | | ALPHA: (171) implies:
% 230.08/41.43  | | | | | | |   (172)  all_57_10 = e3
% 230.08/41.43  | | | | | | | 
% 230.08/41.43  | | | | | | | REF_CLOSE: (16), (17), (21), (25), (28), (34), (41), (42), (121),
% 230.08/41.43  | | | | | | |            (172) are inconsistent by sub-proof #1985.
% 230.08/41.43  | | | | | | | 
% 230.08/41.43  | | | | | | End of split
% 230.08/41.43  | | | | | | 
% 230.08/41.43  | | | | | End of split
% 230.08/41.43  | | | | | 
% 230.08/41.43  | | | | End of split
% 230.08/41.43  | | | | 
% 230.08/41.43  | | | Case 2:
% 230.08/41.43  | | | | 
% 230.08/41.43  | | | |   (173)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0,
% 230.08/41.43  | | | |              e3) = e1)
% 230.08/41.43  | | | | 
% 230.08/41.43  | | | | BETA: splitting (173) gives:
% 230.08/41.43  | | | | 
% 230.08/41.43  | | | | Case 1:
% 230.08/41.43  | | | | | 
% 230.08/41.43  | | | | |   (174)  all_57_6 = e1 & op(e1, e3) = e1
% 230.08/41.43  | | | | | 
% 230.08/41.43  | | | | | ALPHA: (174) implies:
% 230.08/41.43  | | | | |   (175)  all_57_6 = e1
% 230.08/41.43  | | | | | 
% 230.08/41.43  | | | | | BETA: splitting (24) gives:
% 230.08/41.43  | | | | | 
% 230.08/41.43  | | | | | Case 1:
% 230.08/41.43  | | | | | | 
% 230.08/41.43  | | | | | |   (176)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2,
% 230.08/41.43  | | | | | |              e2) = e0)
% 230.08/41.43  | | | | | | 
% 230.08/41.43  | | | | | | REF_CLOSE: (7), (11), (13), (16), (17), (22), (25), (27), (28),
% 230.08/41.43  | | | | | |            (36), (41), (50), (121), (176) are inconsistent by
% 230.08/41.43  | | | | | |            sub-proof #986.
% 230.08/41.43  | | | | | | 
% 230.08/41.43  | | | | | Case 2:
% 230.08/41.43  | | | | | | 
% 230.08/41.43  | | | | | |   (177)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 &
% 230.08/41.43  | | | | | |            op(e0, e2) = e0)
% 230.08/41.43  | | | | | | 
% 230.08/41.43  | | | | | | BETA: splitting (177) gives:
% 230.08/41.43  | | | | | | 
% 230.08/41.43  | | | | | | Case 1:
% 230.08/41.43  | | | | | | | 
% 230.08/41.43  | | | | | | |   (178)  all_57_7 = e0 & op(e1, e2) = e0
% 230.08/41.43  | | | | | | | 
% 230.08/41.43  | | | | | | | ALPHA: (178) implies:
% 230.08/41.43  | | | | | | |   (179)  all_57_7 = e0
% 230.08/41.43  | | | | | | | 
% 230.08/41.43  | | | | | | | REF_CLOSE: (5), (7), (8), (9), (10), (16), (17), (21), (25), (28),
% 230.08/41.43  | | | | | | |            (34), (41), (42), (46), (175), (179) are inconsistent
% 230.08/41.43  | | | | | | |            by sub-proof #1735.
% 230.08/41.43  | | | | | | | 
% 230.08/41.43  | | | | | | Case 2:
% 230.08/41.43  | | | | | | | 
% 230.08/41.43  | | | | | | |   (180)  all_57_13 = e0 & op(e0, e2) = e0
% 230.08/41.43  | | | | | | | 
% 230.08/41.43  | | | | | | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (10), (11), (14),
% 230.08/41.43  | | | | | | |            (16), (17), (19), (21), (22), (23), (24), (25), (26),
% 230.08/41.43  | | | | | | |            (27), (28), (30), (31), (33), (34), (36), (38), (39),
% 230.08/41.43  | | | | | | |            (41), (42), (43), (46), (48), (50), (175), (180) are
% 230.08/41.43  | | | | | | |            inconsistent by sub-proof #977.
% 230.08/41.43  | | | | | | | 
% 230.08/41.43  | | | | | | End of split
% 230.08/41.43  | | | | | | 
% 230.08/41.43  | | | | | End of split
% 230.08/41.43  | | | | | 
% 230.08/41.43  | | | | Case 2:
% 230.08/41.43  | | | | | 
% 230.08/41.43  | | | | |   (181)  all_57_12 = e1 & op(e0, e3) = e1
% 230.08/41.43  | | | | | 
% 230.08/41.43  | | | | | ALPHA: (181) implies:
% 230.08/41.43  | | | | |   (182)  all_57_12 = e1
% 230.08/41.43  | | | | | 
% 230.08/41.43  | | | | | BETA: splitting (24) gives:
% 230.08/41.43  | | | | | 
% 230.08/41.43  | | | | | Case 1:
% 230.08/41.43  | | | | | | 
% 230.08/41.43  | | | | | |   (183)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2,
% 230.08/41.43  | | | | | |              e2) = e0)
% 230.08/41.43  | | | | | | 
% 230.08/41.43  | | | | | | REF_CLOSE: (7), (11), (13), (16), (17), (22), (25), (27), (28),
% 230.08/41.43  | | | | | |            (36), (41), (50), (121), (183) are inconsistent by
% 230.08/41.43  | | | | | |            sub-proof #986.
% 230.08/41.43  | | | | | | 
% 230.08/41.43  | | | | | Case 2:
% 230.08/41.43  | | | | | | 
% 230.08/41.43  | | | | | |   (184)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 &
% 230.08/41.43  | | | | | |            op(e0, e2) = e0)
% 230.08/41.43  | | | | | | 
% 230.08/41.43  | | | | | | BETA: splitting (184) gives:
% 230.08/41.43  | | | | | | 
% 230.08/41.43  | | | | | | Case 1:
% 230.08/41.43  | | | | | | | 
% 230.08/41.43  | | | | | | |   (185)  all_57_7 = e0 & op(e1, e2) = e0
% 230.08/41.43  | | | | | | | 
% 230.08/41.43  | | | | | | | ALPHA: (185) implies:
% 230.08/41.43  | | | | | | |   (186)  all_57_7 = e0
% 230.08/41.43  | | | | | | | 
% 230.08/41.43  | | | | | | | BETA: splitting (30) gives:
% 230.08/41.43  | | | | | | | 
% 230.08/41.43  | | | | | | | Case 1:
% 230.08/41.43  | | | | | | | | 
% 230.08/41.43  | | | | | | | |   (187)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 &
% 230.08/41.43  | | | | | | | |            op(e2, e2) = e3)
% 230.08/41.43  | | | | | | | | 
% 230.08/41.43  | | | | | | | | BETA: splitting (187) gives:
% 230.08/41.43  | | | | | | | | 
% 230.08/41.43  | | | | | | | | Case 1:
% 230.08/41.43  | | | | | | | | | 
% 230.08/41.43  | | | | | | | | |   (188)  all_57_1 = e3 & op(e3, e2) = e3
% 230.08/41.43  | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | ALPHA: (188) implies:
% 230.08/41.43  | | | | | | | | |   (189)  all_57_1 = e3
% 230.08/41.43  | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | BETA: splitting (8) gives:
% 230.08/41.43  | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | Case 1:
% 230.08/41.43  | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | |   (190)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 230.08/41.43  | | | | | | | | | |            & op(e1, e2) = e3)
% 230.08/41.43  | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | BETA: splitting (190) gives:
% 230.08/41.43  | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | Case 1:
% 230.08/41.43  | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | |   (191)  all_57_6 = e3 & op(e1, e3) = e3
% 230.08/41.43  | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | ALPHA: (191) implies:
% 230.08/41.43  | | | | | | | | | | |   (192)  all_57_6 = e3
% 230.08/41.43  | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | BETA: splitting (32) gives:
% 230.08/41.43  | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | Case 1:
% 230.08/41.43  | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | |   (193)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 230.08/41.43  | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 230.08/41.43  | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | REF_CLOSE: (2), (41), (182), (193) are inconsistent by
% 230.08/41.43  | | | | | | | | | | | |            sub-proof #991.
% 230.08/41.43  | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | Case 2:
% 230.08/41.43  | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | |   (194)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 230.08/41.43  | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 230.08/41.43  | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | BETA: splitting (194) gives:
% 230.08/41.43  | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | Case 1:
% 230.08/41.43  | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | |   (195)  all_57_14 = e2 & op(e0, e1) = e2
% 230.08/41.43  | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | ALPHA: (195) implies:
% 230.08/41.43  | | | | | | | | | | | | |   (196)  all_57_14 = e2
% 230.08/41.43  | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | BETA: splitting (35) gives:
% 230.08/41.43  | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | Case 1:
% 230.08/41.43  | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | |   (197)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 230.08/41.43  | | | | | | | | | | | | | |            & op(e2, e2) = e3)
% 230.08/41.43  | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | | REF_CLOSE: (3), (5), (7), (11), (16), (20), (22), (25), (28),
% 230.08/41.43  | | | | | | | | | | | | | |            (41), (43), (192), (197) are inconsistent by
% 230.08/41.43  | | | | | | | | | | | | | |            sub-proof #985.
% 230.08/41.43  | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | Case 2:
% 230.08/41.43  | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | |   (198)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 230.08/41.43  | | | | | | | | | | | | | |            e3 & op(e2, e0) = e3)
% 230.08/41.43  | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 230.08/41.43  | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | | Case 1:
% 230.08/41.43  | | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | | |   (199)  all_57_5 = e3 & op(e2, e1) = e3
% 230.08/41.43  | | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | | | ALPHA: (199) implies:
% 230.08/41.43  | | | | | | | | | | | | | | |   (200)  all_57_5 = e3
% 230.08/41.43  | | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 230.08/41.43  | | | | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 230.08/41.43  | | | | | | | | | | | | | | |            (19), (20), (21), (22), (23), (24), (25), (26),
% 230.08/41.43  | | | | | | | | | | | | | | |            (27), (28), (29), (30), (31), (32), (33), (34),
% 230.08/41.43  | | | | | | | | | | | | | | |            (35), (36), (37), (38), (39), (40), (41), (42),
% 230.08/41.43  | | | | | | | | | | | | | | |            (43), (44), (45), (46), (47), (48), (49), (50),
% 230.08/41.43  | | | | | | | | | | | | | | |            (182), (186), (189), (192), (196), (200) are
% 230.08/41.43  | | | | | | | | | | | | | | |            inconsistent by sub-proof #988.
% 230.08/41.43  | | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | | Case 2:
% 230.08/41.43  | | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | | |   (201)  all_57_10 = e3 & op(e2, e0) = e3
% 230.08/41.43  | | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | | | ALPHA: (201) implies:
% 230.08/41.43  | | | | | | | | | | | | | | |   (202)  all_57_10 = e3
% 230.08/41.43  | | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (21), (25), (28), (34), (41), (42),
% 230.08/41.43  | | | | | | | | | | | | | | |            (121), (202) are inconsistent by sub-proof #1985.
% 230.08/41.43  | | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | | End of split
% 230.08/41.43  | | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | End of split
% 230.08/41.43  | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | Case 2:
% 230.08/41.43  | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | |   (203)  all_57_15 = e2 & op(e0, e0) = e2
% 230.08/41.43  | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10),
% 230.08/41.43  | | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 230.08/41.43  | | | | | | | | | | | | |            (19), (21), (22), (23), (24), (25), (26), (27),
% 230.08/41.43  | | | | | | | | | | | | |            (28), (29), (30), (31), (32), (33), (34), (35),
% 230.08/41.43  | | | | | | | | | | | | |            (36), (37), (38), (39), (41), (42), (43), (44),
% 230.08/41.43  | | | | | | | | | | | | |            (45), (46), (47), (48), (49), (50), (182), (186),
% 230.08/41.43  | | | | | | | | | | | | |            (192), (203) are inconsistent by sub-proof #987.
% 230.08/41.43  | | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | | End of split
% 230.08/41.43  | | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | End of split
% 230.08/41.43  | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | Case 2:
% 230.08/41.43  | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | |   (204)  all_57_7 = e3 & op(e1, e2) = e3
% 230.08/41.43  | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | | REF_CLOSE: (7), (13), (16), (17), (22), (25), (27), (36),
% 230.08/41.43  | | | | | | | | | | |            (41), (50), (121), (186), (189), (204) are
% 230.08/41.43  | | | | | | | | | | |            inconsistent by sub-proof #979.
% 230.08/41.43  | | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | End of split
% 230.08/41.43  | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | Case 2:
% 230.08/41.43  | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | |   (205)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3
% 230.08/41.43  | | | | | | | | | |            & op(e1, e0) = e3)
% 230.08/41.43  | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | | REF_CLOSE: (5), (7), (9), (10), (16), (17), (21), (25), (28),
% 230.08/41.43  | | | | | | | | | |            (34), (41), (42), (46), (205) are inconsistent by
% 230.08/41.43  | | | | | | | | | |            sub-proof #1786.
% 230.08/41.43  | | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | End of split
% 230.08/41.43  | | | | | | | | | 
% 230.08/41.43  | | | | | | | | Case 2:
% 230.08/41.43  | | | | | | | | | 
% 230.08/41.43  | | | | | | | | |   (206)  all_57_3 = e3 & op(e2, e2) = e3
% 230.08/41.43  | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | ALPHA: (206) implies:
% 230.08/41.43  | | | | | | | | |   (207)  op(e2, e2) = e3
% 230.08/41.43  | | | | | | | | | 
% 230.08/41.43  | | | | | | | | | REF_CLOSE: (5), (7), (11), (207) are inconsistent by sub-proof
% 230.08/41.43  | | | | | | | | |            #1912.
% 230.08/41.43  | | | | | | | | | 
% 230.08/41.43  | | | | | | | | End of split
% 230.08/41.43  | | | | | | | | 
% 230.08/41.43  | | | | | | | Case 2:
% 230.08/41.43  | | | | | | | | 
% 230.08/41.43  | | | | | | | |   (208)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 &
% 230.08/41.43  | | | | | | | |            op(e0, e2) = e3)
% 230.08/41.43  | | | | | | | | 
% 230.08/41.43  | | | | | | | | REF_CLOSE: (5), (7), (16), (17), (21), (23), (25), (28), (31),
% 230.08/41.43  | | | | | | | |            (32), (34), (41), (186), (208) are inconsistent by
% 230.08/41.43  | | | | | | | |            sub-proof #993.
% 230.08/41.43  | | | | | | | | 
% 230.08/41.43  | | | | | | | End of split
% 230.08/41.43  | | | | | | | 
% 230.08/41.43  | | | | | | Case 2:
% 230.08/41.43  | | | | | | | 
% 230.08/41.43  | | | | | | |   (209)  all_57_13 = e0 & op(e0, e2) = e0
% 230.08/41.43  | | | | | | | 
% 230.08/41.43  | | | | | | | REF_CLOSE: (2), (28), (209) are inconsistent by sub-proof #1920.
% 230.08/41.43  | | | | | | | 
% 230.08/41.43  | | | | | | End of split
% 230.08/41.43  | | | | | | 
% 230.08/41.43  | | | | | End of split
% 230.08/41.43  | | | | | 
% 230.08/41.43  | | | | End of split
% 230.08/41.43  | | | | 
% 230.08/41.43  | | | End of split
% 230.08/41.43  | | | 
% 230.08/41.43  | | End of split
% 230.08/41.43  | | 
% 230.08/41.43  | End of split
% 230.08/41.43  | 
% 230.08/41.43  End of proof
% 230.08/41.43  
% 230.08/41.43  Sub-proof #977 shows that the following formulas are inconsistent:
% 230.08/41.43  ----------------------------------------------------------------
% 230.08/41.43    (1)  all_57_13 = e1
% 230.08/41.43    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.08/41.43         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.08/41.43    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.08/41.43         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.08/41.43    (4)   ~ (e3 = e1)
% 230.08/41.43    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.08/41.43           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.08/41.43    (6)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.08/41.43         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.08/41.43    (7)   ~ (all_6_2 = e3)
% 230.08/41.43    (8)  op(e1, e1) = all_6_2
% 230.08/41.43    (9)  op(e2, e2) = e1
% 230.08/41.43    (10)  all_57_13 = e0 & op(e0, e2) = e0
% 230.08/41.43    (11)  all_57_6 = e1
% 230.08/41.43    (12)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.08/41.43          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.08/41.43    (13)   ~ (e3 = e2)
% 230.08/41.43    (14)   ~ (e3 = e0)
% 230.08/41.43    (15)  op(e0, e3) = all_53_3
% 230.08/41.43    (16)  all_57_15 = e3
% 230.08/41.43    (17)  op(e3, e3) = e0
% 230.08/41.43    (18)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.08/41.43          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.08/41.43            e1)
% 230.08/41.43    (19)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.08/41.43          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.08/41.43    (20)   ~ (e2 = e0)
% 230.08/41.43    (21)  all_57_3 = e1
% 230.08/41.43    (22)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.08/41.43          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.08/41.43    (23)   ~ (e1 = e0)
% 230.08/41.43    (24)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.08/41.43          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.08/41.43    (25)  op(e0, e0) = e3
% 230.08/41.43    (26)   ~ (all_53_3 = e0)
% 230.08/41.43    (27)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.08/41.43              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.08/41.43                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.08/41.43                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.08/41.43    (28)   ~ (all_53_12 = e3)
% 230.08/41.43    (29)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.08/41.43          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.08/41.43    (30)   ~ (all_53_12 = e0)
% 230.08/41.43    (31)   ~ (e2 = e1)
% 230.08/41.44    (32)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.08/41.44          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.08/41.44    (33)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.08/41.44          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.08/41.44    (34)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.08/41.44          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.08/41.44    (35)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.08/41.44          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.08/41.44    (36)  op(e3, e0) = all_53_12
% 230.08/41.44  
% 230.08/41.44  Begin of proof
% 230.08/41.44  | 
% 230.08/41.44  | ALPHA: (10) implies:
% 230.08/41.44  |   (37)  all_57_13 = e0
% 230.08/41.44  | 
% 230.08/41.44  | COMBINE_EQS: (1), (37) imply:
% 230.08/41.44  |   (38)  e1 = e0
% 230.08/41.44  | 
% 230.08/41.44  | COMBINE_EQS: (11), (38) imply:
% 230.08/41.44  |   (39)  all_57_6 = e0
% 230.08/41.44  | 
% 230.08/41.44  | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (12), (13), (14), (15),
% 230.08/41.44  |            (16), (17), (18), (19), (20), (21), (22), (23), (24), (25), (26),
% 230.08/41.44  |            (27), (28), (29), (30), (31), (32), (33), (34), (35), (36), (39)
% 230.08/41.44  |            are inconsistent by sub-proof #983.
% 230.08/41.44  | 
% 230.08/41.44  End of proof
% 230.08/41.44  
% 230.08/41.44  Sub-proof #978 shows that the following formulas are inconsistent:
% 230.08/41.44  ----------------------------------------------------------------
% 230.08/41.44    (1)  all_57_10 = e0
% 230.08/41.44    (2)   ~ (e3 = e1)
% 230.08/41.44    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.08/41.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.08/41.44    (4)   ~ (all_6_2 = e3)
% 230.08/41.44    (5)  op(e1, e1) = all_6_2
% 230.08/41.44    (6)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.08/41.44    (7)   ~ (e3 = e2)
% 230.08/41.44    (8)  all_57_15 = e3
% 230.08/41.44    (9)   ~ (e2 = e0)
% 230.08/41.44    (10)   ~ (e1 = e0)
% 230.08/41.44    (11)   ~ (e2 = e1)
% 230.08/41.44    (12)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.08/41.44          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.08/41.44    (13)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.08/41.44          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.08/41.44  
% 230.08/41.44  Begin of proof
% 230.08/41.44  | 
% 230.08/41.44  | BETA: splitting (6) gives:
% 230.08/41.44  | 
% 230.08/41.44  | Case 1:
% 230.08/41.44  | | 
% 230.08/41.44  | |   (14)  all_57_8 = e3 & op(e1, e1) = e3
% 230.08/41.44  | | 
% 230.08/41.44  | | ALPHA: (14) implies:
% 230.08/41.44  | |   (15)  op(e1, e1) = e3
% 230.08/41.44  | | 
% 230.08/41.44  | | REF_CLOSE: (3), (4), (5), (15) are inconsistent by sub-proof #2468.
% 230.08/41.44  | | 
% 230.08/41.44  | Case 2:
% 230.08/41.44  | | 
% 230.08/41.44  | |   (16)  all_57_11 = e3 & op(e1, e0) = e3
% 230.08/41.44  | | 
% 230.08/41.44  | | ALPHA: (16) implies:
% 230.08/41.44  | |   (17)  all_57_11 = e3
% 230.08/41.44  | | 
% 230.08/41.44  | | REF_CLOSE: (1), (2), (7), (8), (9), (10), (11), (12), (13), (17) are
% 230.08/41.44  | |            inconsistent by sub-proof #2137.
% 230.08/41.44  | | 
% 230.08/41.44  | End of split
% 230.08/41.44  | 
% 230.08/41.44  End of proof
% 230.08/41.44  
% 230.08/41.44  Sub-proof #979 shows that the following formulas are inconsistent:
% 230.08/41.44  ----------------------------------------------------------------
% 230.08/41.44    (1)  all_57_7 = e3 & op(e1, e2) = e3
% 230.08/41.44    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.08/41.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.08/41.44    (3)  all_57_9 = e1
% 230.08/41.44    (4)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.08/41.44         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.08/41.44    (5)   ~ (e3 = e2)
% 230.08/41.44    (6)   ~ (e3 = e0)
% 230.08/41.44    (7)  op(e3, e3) = e0
% 230.08/41.44    (8)   ~ (e2 = e0)
% 230.08/41.44    (9)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.08/41.44         (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.08/41.44    (10)   ~ (all_53_12 = e3)
% 230.08/41.44    (11)  all_57_1 = e3
% 230.08/41.44    (12)   ~ (e2 = e1)
% 230.08/41.44    (13)  all_57_7 = e0
% 230.08/41.44    (14)  op(e3, e0) = all_53_12
% 230.08/41.44  
% 230.08/41.44  Begin of proof
% 230.08/41.44  | 
% 230.08/41.44  | ALPHA: (1) implies:
% 230.08/41.44  |   (15)  all_57_7 = e3
% 230.08/41.44  | 
% 230.08/41.44  | COMBINE_EQS: (13), (15) imply:
% 230.08/41.44  |   (16)  e3 = e0
% 230.08/41.44  | 
% 230.08/41.44  | SIMP: (16) implies:
% 230.08/41.44  |   (17)  e3 = e0
% 230.08/41.44  | 
% 230.08/41.44  | COMBINE_EQS: (11), (17) imply:
% 230.08/41.44  |   (18)  all_57_1 = e0
% 230.08/41.44  | 
% 230.08/41.44  | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (14), (18) are
% 230.08/41.44  |            inconsistent by sub-proof #2400.
% 230.08/41.44  | 
% 230.08/41.44  End of proof
% 230.08/41.44  
% 230.08/41.44  Sub-proof #980 shows that the following formulas are inconsistent:
% 230.08/41.44  ----------------------------------------------------------------
% 230.08/41.44    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.08/41.44         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.08/41.44    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.08/41.44         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.08/41.44    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.08/41.44         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.15/41.44    (4)   ~ (e3 = e1)
% 230.15/41.44    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.15/41.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.15/41.44    (6)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.15/41.44         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.15/41.44    (7)   ~ (all_6_2 = e3)
% 230.15/41.44    (8)  op(e1, e1) = all_6_2
% 230.15/41.44    (9)  op(e2, e2) = e1
% 230.15/41.44    (10)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.15/41.44          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.15/41.44    (11)   ~ (e3 = e2)
% 230.15/41.44    (12)   ~ (e3 = e0)
% 230.15/41.44    (13)  op(e0, e3) = all_53_3
% 230.15/41.44    (14)  all_57_0 = e0
% 230.15/41.44    (15)  all_57_15 = e3
% 230.15/41.44    (16)  op(e3, e3) = e0
% 230.15/41.44    (17)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.15/41.44          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.15/41.44            e1)
% 230.15/41.44    (18)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.15/41.44          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.15/41.44    (19)   ~ (e2 = e0)
% 230.15/41.44    (20)  all_57_3 = e1
% 230.15/41.44    (21)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.15/41.44          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.15/41.44    (22)   ~ (e1 = e0)
% 230.15/41.44    (23)  all_57_6 = e3
% 230.15/41.44    (24)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.15/41.44          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.15/41.44    (25)  op(e0, e0) = e3
% 230.15/41.44    (26)  all_57_2 = e1
% 230.15/41.44    (27)   ~ (all_53_3 = e0)
% 230.15/41.44    (28)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.15/41.44              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.15/41.44                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.15/41.44                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.15/41.44    (29)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.15/41.44          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.15/41.44    (30)   ~ (all_53_12 = e3)
% 230.15/41.44    (31)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.15/41.44          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.15/41.44    (32)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.15/41.44          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.15/41.44    (33)  all_57_1 = e3
% 230.15/41.44    (34)   ~ (all_53_12 = e0)
% 230.15/41.44    (35)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.15/41.44          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 230.15/41.44    (36)   ~ (e2 = e1)
% 230.15/41.44    (37)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.15/41.44          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.15/41.44    (38)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.15/41.44          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.15/41.44    (39)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.15/41.44          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.15/41.44    (40)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.15/41.44          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.15/41.44    (41)  op(e3, e0) = all_53_12
% 230.15/41.44  
% 230.15/41.44  Begin of proof
% 230.15/41.44  | 
% 230.15/41.44  | BETA: splitting (29) gives:
% 230.15/41.44  | 
% 230.15/41.44  | Case 1:
% 230.15/41.44  | | 
% 230.15/41.44  | |   (42)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 230.15/41.44  | |           e3)
% 230.15/41.44  | | 
% 230.15/41.44  | | REF_CLOSE: (2), (4), (5), (9), (11), (14), (16), (19), (22), (23), (36),
% 230.15/41.44  | |            (38), (42) are inconsistent by sub-proof #985.
% 230.15/41.44  | | 
% 230.15/41.44  | Case 2:
% 230.15/41.44  | | 
% 230.15/41.44  | |   (43)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 230.15/41.44  | |           e3)
% 230.15/41.44  | | 
% 230.15/41.44  | | BETA: splitting (43) gives:
% 230.15/41.44  | | 
% 230.15/41.44  | | Case 1:
% 230.15/41.44  | | | 
% 230.15/41.44  | | |   (44)  all_57_5 = e3 & op(e2, e1) = e3
% 230.15/41.44  | | | 
% 230.15/41.44  | | | ALPHA: (44) implies:
% 230.15/41.44  | | |   (45)  all_57_5 = e3
% 230.15/41.44  | | | 
% 230.15/41.44  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (14),
% 230.15/41.44  | | |            (15), (16), (18), (19), (20), (22), (23), (26), (28), (31),
% 230.15/41.44  | | |            (33), (35), (36), (37), (38), (39), (40), (45) are inconsistent
% 230.15/41.44  | | |            by sub-proof #1007.
% 230.15/41.44  | | | 
% 230.15/41.44  | | Case 2:
% 230.15/41.44  | | | 
% 230.15/41.44  | | |   (46)  all_57_10 = e3 & op(e2, e0) = e3
% 230.15/41.44  | | | 
% 230.15/41.44  | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 230.15/41.44  | | |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 230.15/41.44  | | |            (25), (27), (28), (30), (32), (34), (36), (37), (38), (39),
% 230.15/41.44  | | |            (40), (41), (46) are inconsistent by sub-proof #981.
% 230.15/41.44  | | | 
% 230.15/41.44  | | End of split
% 230.15/41.44  | | 
% 230.15/41.44  | End of split
% 230.15/41.44  | 
% 230.15/41.44  End of proof
% 230.15/41.44  
% 230.15/41.44  Sub-proof #981 shows that the following formulas are inconsistent:
% 230.15/41.44  ----------------------------------------------------------------
% 230.15/41.44    (1)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.15/41.44         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.15/41.44    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.15/41.44         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.15/41.44    (3)   ~ (e3 = e1)
% 230.15/41.44    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.15/41.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.15/41.44    (5)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.15/41.44         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.15/41.44    (6)   ~ (all_6_2 = e3)
% 230.15/41.44    (7)  op(e1, e1) = all_6_2
% 230.15/41.44    (8)  op(e2, e2) = e1
% 230.15/41.44    (9)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.15/41.44         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.15/41.44    (10)   ~ (e3 = e2)
% 230.15/41.44    (11)   ~ (e3 = e0)
% 230.15/41.44    (12)  op(e0, e3) = all_53_3
% 230.15/41.44    (13)  all_57_15 = e3
% 230.15/41.44    (14)  op(e3, e3) = e0
% 230.15/41.44    (15)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.15/41.44          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.15/41.44            e1)
% 230.15/41.44    (16)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.15/41.44          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.15/41.44    (17)   ~ (e2 = e0)
% 230.15/41.44    (18)  all_57_3 = e1
% 230.15/41.44    (19)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.15/41.44          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.15/41.44    (20)   ~ (e1 = e0)
% 230.15/41.44    (21)  all_57_6 = e3
% 230.15/41.44    (22)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.15/41.44          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.15/41.44    (23)  op(e0, e0) = e3
% 230.15/41.44    (24)   ~ (all_53_3 = e0)
% 230.15/41.44    (25)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.15/41.44              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.15/41.44                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.15/41.44                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.15/41.44    (26)   ~ (all_53_12 = e3)
% 230.15/41.44    (27)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.15/41.44          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.15/41.44    (28)   ~ (all_53_12 = e0)
% 230.15/41.44    (29)   ~ (e2 = e1)
% 230.15/41.44    (30)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.15/41.44          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.15/41.44    (31)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.15/41.44          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.15/41.44    (32)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.15/41.44          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.15/41.44    (33)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.15/41.44          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.15/41.44    (34)  all_57_10 = e3 & op(e2, e0) = e3
% 230.15/41.44    (35)  op(e3, e0) = all_53_12
% 230.15/41.44  
% 230.15/41.44  Begin of proof
% 230.15/41.44  | 
% 230.15/41.44  | ALPHA: (34) implies:
% 230.15/41.44  |   (36)  all_57_10 = e3
% 230.15/41.44  | 
% 230.15/41.44  | BETA: splitting (25) gives:
% 230.15/41.44  | 
% 230.15/41.44  | Case 1:
% 230.15/41.44  | | 
% 230.15/41.44  | |   (37)  all_57_15 = e0 & op(e0, e0) = e0
% 230.15/41.44  | | 
% 230.15/41.44  | | ALPHA: (37) implies:
% 230.15/41.44  | |   (38)  op(e0, e0) = e0
% 230.15/41.44  | | 
% 230.15/41.44  | | REF_CLOSE: (4), (11), (23), (38) are inconsistent by sub-proof #2304.
% 230.15/41.44  | | 
% 230.15/41.44  | Case 2:
% 230.15/41.44  | | 
% 230.15/41.44  | |   (39)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 230.15/41.44  | |             e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0 &
% 230.15/41.44  | |             op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 230.15/41.44  | |           (all_57_14 = e0 & op(e0, e1) = e0))
% 230.15/41.44  | | 
% 230.15/41.44  | | ALPHA: (39) implies:
% 230.15/41.44  | |   (40)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 230.15/41.44  | |           e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.15/41.44  | | 
% 230.15/41.44  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 230.15/41.44  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 230.15/41.44  | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (35),
% 230.15/41.44  | |            (36), (40) are inconsistent by sub-proof #982.
% 230.15/41.44  | | 
% 230.15/41.44  | End of split
% 230.15/41.44  | 
% 230.15/41.44  End of proof
% 230.15/41.44  
% 230.15/41.44  Sub-proof #982 shows that the following formulas are inconsistent:
% 230.15/41.44  ----------------------------------------------------------------
% 230.15/41.44    (1)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.15/41.44         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.15/41.44    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.15/41.44         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.15/41.44    (3)   ~ (e3 = e1)
% 230.15/41.44    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.15/41.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.15/41.44    (5)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.15/41.44         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.15/41.44    (6)   ~ (all_6_2 = e3)
% 230.15/41.44    (7)  op(e1, e1) = all_6_2
% 230.15/41.44    (8)  op(e2, e2) = e1
% 230.15/41.44    (9)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.15/41.44         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.15/41.44    (10)   ~ (e3 = e2)
% 230.15/41.44    (11)   ~ (e3 = e0)
% 230.15/41.44    (12)  op(e0, e3) = all_53_3
% 230.15/41.44    (13)  all_57_15 = e3
% 230.15/41.44    (14)  op(e3, e3) = e0
% 230.15/41.44    (15)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.15/41.44          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.15/41.44            e1)
% 230.15/41.44    (16)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.15/41.44          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.15/41.44    (17)   ~ (e2 = e0)
% 230.15/41.44    (18)  all_57_3 = e1
% 230.15/41.44    (19)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.15/41.44          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.15/41.44    (20)   ~ (e1 = e0)
% 230.15/41.44    (21)  all_57_6 = e3
% 230.15/41.44    (22)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.15/41.44          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.15/41.44    (23)  all_57_10 = e3
% 230.15/41.44    (24)  op(e0, e0) = e3
% 230.15/41.44    (25)   ~ (all_53_3 = e0)
% 230.15/41.44    (26)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.15/41.44              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.15/41.44                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.15/41.44                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.15/41.44    (27)   ~ (all_53_12 = e3)
% 230.15/41.44    (28)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.15/41.44          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.15/41.44    (29)   ~ (all_53_12 = e0)
% 230.15/41.44    (30)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) |
% 230.15/41.44          (all_57_11 = e0 & op(e1, e0) = e0)
% 230.15/41.44    (31)   ~ (e2 = e1)
% 230.15/41.44    (32)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.15/41.44          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.15/41.44    (33)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.15/41.44          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.15/41.44    (34)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.15/41.44          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.15/41.44    (35)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.15/41.44          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.15/41.44    (36)  op(e3, e0) = all_53_12
% 230.15/41.44  
% 230.15/41.44  Begin of proof
% 230.15/41.44  | 
% 230.15/41.44  | BETA: splitting (30) gives:
% 230.15/41.44  | 
% 230.15/41.44  | Case 1:
% 230.15/41.44  | | 
% 230.15/41.44  | |   (37)  all_57_9 = e0 & op(e3, e0) = e0
% 230.15/41.44  | | 
% 230.15/41.44  | | ALPHA: (37) implies:
% 230.15/41.44  | |   (38)  all_57_9 = e0
% 230.15/41.44  | | 
% 230.15/41.44  | | REF_CLOSE: (3), (10), (11), (13), (17), (20), (23), (26), (31), (32), (34),
% 230.15/41.44  | |            (38) are inconsistent by sub-proof #1982.
% 230.15/41.44  | | 
% 230.15/41.44  | Case 2:
% 230.15/41.44  | | 
% 230.15/41.44  | |   (39)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 230.15/41.44  | |           e0)
% 230.15/41.44  | | 
% 230.15/41.44  | | BETA: splitting (39) gives:
% 230.15/41.44  | | 
% 230.15/41.44  | | Case 1:
% 230.15/41.44  | | | 
% 230.15/41.44  | | |   (40)  all_57_10 = e0 & op(e2, e0) = e0
% 230.15/41.44  | | | 
% 230.15/41.44  | | | ALPHA: (40) implies:
% 230.15/41.44  | | |   (41)  all_57_10 = e0
% 230.15/41.44  | | | 
% 230.15/41.44  | | | COMBINE_EQS: (23), (41) imply:
% 230.15/41.44  | | |   (42)  e3 = e0
% 230.15/41.44  | | | 
% 230.15/41.44  | | | SIMP: (42) implies:
% 230.15/41.44  | | |   (43)  e3 = e0
% 230.15/41.44  | | | 
% 230.15/41.44  | | | COMBINE_EQS: (21), (43) imply:
% 230.15/41.44  | | |   (44)  all_57_6 = e0
% 230.15/41.44  | | | 
% 230.15/41.44  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 230.15/41.44  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (22), (24),
% 230.15/41.44  | | |            (25), (26), (27), (28), (29), (31), (32), (33), (34), (35),
% 230.15/41.44  | | |            (36), (44) are inconsistent by sub-proof #983.
% 230.15/41.44  | | | 
% 230.15/41.44  | | Case 2:
% 230.15/41.44  | | | 
% 230.15/41.44  | | |   (45)  all_57_11 = e0 & op(e1, e0) = e0
% 230.15/41.44  | | | 
% 230.15/41.44  | | | ALPHA: (45) implies:
% 230.15/41.44  | | |   (46)  all_57_11 = e0
% 230.15/41.44  | | | 
% 230.15/41.44  | | | REF_CLOSE: (3), (4), (10), (13), (17), (20), (23), (24), (31), (32), (34),
% 230.15/41.44  | | |            (46) are inconsistent by sub-proof #1748.
% 230.15/41.44  | | | 
% 230.15/41.44  | | End of split
% 230.15/41.44  | | 
% 230.15/41.44  | End of split
% 230.15/41.44  | 
% 230.15/41.44  End of proof
% 230.15/41.44  
% 230.15/41.44  Sub-proof #983 shows that the following formulas are inconsistent:
% 230.15/41.44  ----------------------------------------------------------------
% 230.15/41.44    (1)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.15/41.44         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.15/41.44    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.15/41.44         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.15/41.44    (3)   ~ (e3 = e1)
% 230.15/41.44    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.15/41.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.15/41.44    (5)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.15/41.44         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.15/41.44    (6)   ~ (all_6_2 = e3)
% 230.15/41.44    (7)  op(e1, e1) = all_6_2
% 230.15/41.44    (8)  op(e2, e2) = e1
% 230.15/41.44    (9)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.15/41.44         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.15/41.44    (10)   ~ (e3 = e2)
% 230.15/41.44    (11)   ~ (e3 = e0)
% 230.15/41.44    (12)  all_57_6 = e0
% 230.15/41.44    (13)  op(e0, e3) = all_53_3
% 230.15/41.44    (14)  all_57_15 = e3
% 230.15/41.44    (15)  op(e3, e3) = e0
% 230.15/41.44    (16)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.15/41.44          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.15/41.44            e1)
% 230.15/41.44    (17)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.15/41.44          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.15/41.44    (18)   ~ (e2 = e0)
% 230.15/41.44    (19)  all_57_3 = e1
% 230.15/41.44    (20)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.15/41.44          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.15/41.44    (21)   ~ (e1 = e0)
% 230.15/41.44    (22)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.15/41.44          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.15/41.44    (23)  op(e0, e0) = e3
% 230.15/41.44    (24)   ~ (all_53_3 = e0)
% 230.15/41.44    (25)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.15/41.44              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.15/41.44                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.15/41.44                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.15/41.44    (26)   ~ (all_53_12 = e3)
% 230.15/41.44    (27)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.15/41.44          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.15/41.44    (28)   ~ (all_53_12 = e0)
% 230.15/41.44    (29)   ~ (e2 = e1)
% 230.15/41.44    (30)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.15/41.44          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.15/41.44    (31)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.15/41.44          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.15/41.44    (32)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.15/41.44          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.15/41.44    (33)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.15/41.44          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.15/41.44    (34)  op(e3, e0) = all_53_12
% 230.15/41.44  
% 230.15/41.44  Begin of proof
% 230.15/41.44  | 
% 230.15/41.44  | BETA: splitting (1) gives:
% 230.15/41.44  | 
% 230.15/41.44  | Case 1:
% 230.15/41.44  | | 
% 230.15/41.45  | |   (35)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) =
% 230.15/41.45  | |           e1)
% 230.15/41.45  | | 
% 230.15/41.45  | | BETA: splitting (35) gives:
% 230.15/41.45  | | 
% 230.15/41.45  | | Case 1:
% 230.15/41.45  | | | 
% 230.15/41.45  | | |   (36)  all_57_0 = e1 & op(e3, e3) = e1
% 230.15/41.45  | | | 
% 230.15/41.45  | | | ALPHA: (36) implies:
% 230.15/41.45  | | |   (37)  all_57_0 = e1
% 230.15/41.45  | | |   (38)  op(e3, e3) = e1
% 230.15/41.45  | | | 
% 230.15/41.45  | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 230.15/41.45  | | |            (14), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 230.15/41.45  | | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 230.15/41.45  | | |            (37), (38) are inconsistent by sub-proof #1053.
% 230.15/41.45  | | | 
% 230.15/41.45  | | Case 2:
% 230.15/41.45  | | | 
% 230.15/41.45  | | |   (39)  all_57_2 = e1 & op(e2, e3) = e1
% 230.15/41.45  | | | 
% 230.15/41.45  | | | ALPHA: (39) implies:
% 230.15/41.45  | | |   (40)  all_57_2 = e1
% 230.15/41.45  | | | 
% 230.15/41.45  | | | REF_CLOSE: (3), (4), (10), (11), (12), (15), (18), (27), (29), (31), (40)
% 230.15/41.45  | | |            are inconsistent by sub-proof #2390.
% 230.15/41.45  | | | 
% 230.15/41.45  | | End of split
% 230.15/41.45  | | 
% 230.15/41.45  | Case 2:
% 230.15/41.45  | | 
% 230.15/41.45  | |   (41)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) =
% 230.15/41.45  | |           e1)
% 230.15/41.45  | | 
% 230.15/41.45  | | REF_CLOSE: (3), (4), (5), (6), (7), (10), (11), (12), (14), (15), (18),
% 230.15/41.45  | |            (21), (25), (27), (29), (30), (31), (32), (41) are inconsistent
% 230.15/41.45  | |            by sub-proof #984.
% 230.15/41.45  | | 
% 230.15/41.45  | End of split
% 230.15/41.45  | 
% 230.15/41.45  End of proof
% 230.15/41.45  
% 230.15/41.45  Sub-proof #984 shows that the following formulas are inconsistent:
% 230.15/41.45  ----------------------------------------------------------------
% 230.15/41.45    (1)   ~ (e3 = e1)
% 230.15/41.45    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.15/41.45           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.15/41.45    (3)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.15/41.45         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.15/41.45    (4)   ~ (all_6_2 = e3)
% 230.15/41.45    (5)  op(e1, e1) = all_6_2
% 230.15/41.45    (6)   ~ (e3 = e2)
% 230.15/41.45    (7)   ~ (e3 = e0)
% 230.15/41.45    (8)  all_57_6 = e0
% 230.15/41.45    (9)  all_57_15 = e3
% 230.15/41.45    (10)  op(e3, e3) = e0
% 230.15/41.45    (11)   ~ (e2 = e0)
% 230.15/41.45    (12)   ~ (e1 = e0)
% 230.15/41.45    (13)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.15/41.45    (14)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.15/41.45              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.15/41.45                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.15/41.45                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.15/41.45    (15)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.15/41.45          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.15/41.45    (16)   ~ (e2 = e1)
% 230.15/41.45    (17)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.15/41.45          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.15/41.45    (18)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.15/41.45          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.15/41.45    (19)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.15/41.45          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.15/41.45  
% 230.15/41.45  Begin of proof
% 230.15/41.45  | 
% 230.15/41.45  | BETA: splitting (13) gives:
% 230.15/41.45  | 
% 230.15/41.45  | Case 1:
% 230.15/41.45  | | 
% 230.15/41.45  | |   (20)  all_57_6 = e1 & op(e1, e3) = e1
% 230.15/41.45  | | 
% 230.15/41.45  | | ALPHA: (20) implies:
% 230.15/41.45  | |   (21)  all_57_6 = e1
% 230.15/41.45  | | 
% 230.15/41.45  | | REF_CLOSE: (8), (12), (21) are inconsistent by sub-proof #2227.
% 230.15/41.45  | | 
% 230.15/41.45  | Case 2:
% 230.15/41.45  | | 
% 230.15/41.45  | |   (22)  all_57_12 = e1 & op(e0, e3) = e1
% 230.15/41.45  | | 
% 230.15/41.45  | | ALPHA: (22) implies:
% 230.15/41.45  | |   (23)  all_57_12 = e1
% 230.15/41.45  | | 
% 230.15/41.45  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 230.15/41.45  | |            (14), (15), (16), (17), (18), (19), (23) are inconsistent by
% 230.15/41.45  | |            sub-proof #1028.
% 230.15/41.45  | | 
% 230.15/41.45  | End of split
% 230.15/41.45  | 
% 230.15/41.45  End of proof
% 230.15/41.45  
% 230.15/41.45  Sub-proof #985 shows that the following formulas are inconsistent:
% 230.15/41.45  ----------------------------------------------------------------
% 230.15/41.45    (1)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.15/41.45         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.15/41.45    (2)   ~ (e3 = e1)
% 230.15/41.45    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.15/41.45           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.15/41.45    (4)  op(e2, e2) = e1
% 230.15/41.45    (5)   ~ (e3 = e2)
% 230.15/41.45    (6)  all_57_0 = e0
% 230.15/41.45    (7)  op(e3, e3) = e0
% 230.15/41.45    (8)   ~ (e2 = e0)
% 230.15/41.45    (9)   ~ (e1 = e0)
% 230.15/41.45    (10)  all_57_6 = e3
% 230.15/41.45    (11)   ~ (e2 = e1)
% 230.15/41.45    (12)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3)
% 230.15/41.45    (13)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.15/41.45          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.15/41.45  
% 230.15/41.45  Begin of proof
% 230.15/41.45  | 
% 230.15/41.45  | BETA: splitting (12) gives:
% 230.15/41.45  | 
% 230.15/41.45  | Case 1:
% 230.15/41.45  | | 
% 230.15/41.45  | |   (14)  all_57_2 = e3 & op(e2, e3) = e3
% 230.15/41.45  | | 
% 230.15/41.45  | | ALPHA: (14) implies:
% 230.15/41.45  | |   (15)  all_57_2 = e3
% 230.15/41.45  | | 
% 230.15/41.45  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (13), (15)
% 230.15/41.45  | |            are inconsistent by sub-proof #1287.
% 230.15/41.45  | | 
% 230.15/41.45  | Case 2:
% 230.15/41.45  | | 
% 230.15/41.45  | |   (16)  all_57_3 = e3 & op(e2, e2) = e3
% 230.15/41.45  | | 
% 230.15/41.45  | | ALPHA: (16) implies:
% 230.15/41.45  | |   (17)  op(e2, e2) = e3
% 230.15/41.45  | | 
% 230.15/41.45  | | REF_CLOSE: (2), (3), (4), (17) are inconsistent by sub-proof #1912.
% 230.15/41.45  | | 
% 230.15/41.45  | End of split
% 230.15/41.45  | 
% 230.15/41.45  End of proof
% 230.15/41.45  
% 230.15/41.45  Sub-proof #986 shows that the following formulas are inconsistent:
% 230.15/41.45  ----------------------------------------------------------------
% 230.15/41.45    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.15/41.45           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.15/41.45    (2)  op(e2, e2) = e1
% 230.15/41.45    (3)  all_57_9 = e1
% 230.15/41.45    (4)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.15/41.45         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.15/41.45    (5)   ~ (e3 = e2)
% 230.15/41.45    (6)   ~ (e3 = e0)
% 230.15/41.45    (7)  op(e3, e3) = e0
% 230.15/41.45    (8)   ~ (e2 = e0)
% 230.15/41.45    (9)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.15/41.45         (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.15/41.45    (10)   ~ (e1 = e0)
% 230.15/41.45    (11)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0)
% 230.15/41.45    (12)   ~ (all_53_12 = e3)
% 230.15/41.45    (13)   ~ (e2 = e1)
% 230.15/41.45    (14)  op(e3, e0) = all_53_12
% 230.15/41.45  
% 230.15/41.45  Begin of proof
% 230.15/41.45  | 
% 230.15/41.45  | BETA: splitting (11) gives:
% 230.15/41.45  | 
% 230.15/41.45  | Case 1:
% 230.15/41.45  | | 
% 230.15/41.45  | |   (15)  all_57_1 = e0 & op(e3, e2) = e0
% 230.15/41.45  | | 
% 230.15/41.45  | | ALPHA: (15) implies:
% 230.15/41.45  | |   (16)  all_57_1 = e0
% 230.15/41.45  | | 
% 230.15/41.45  | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (12), (13), (14), (16)
% 230.15/41.45  | |            are inconsistent by sub-proof #2400.
% 230.15/41.45  | | 
% 230.15/41.45  | Case 2:
% 230.15/41.45  | | 
% 230.15/41.45  | |   (17)  all_57_3 = e0 & op(e2, e2) = e0
% 230.15/41.45  | | 
% 230.15/41.45  | | ALPHA: (17) implies:
% 230.15/41.45  | |   (18)  op(e2, e2) = e0
% 230.15/41.45  | | 
% 230.15/41.45  | | REF_CLOSE: (1), (2), (10), (18) are inconsistent by sub-proof #2352.
% 230.15/41.45  | | 
% 230.15/41.45  | End of split
% 230.15/41.45  | 
% 230.15/41.45  End of proof
% 230.15/41.45  
% 230.15/41.45  Sub-proof #987 shows that the following formulas are inconsistent:
% 230.15/41.45  ----------------------------------------------------------------
% 230.15/41.45    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.15/41.45         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.15/41.45    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.15/41.45         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.15/41.45    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.15/41.45         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.15/41.45    (4)   ~ (e3 = e1)
% 230.15/41.45    (5)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.15/41.45         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.15/41.45    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.15/41.45           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.15/41.45    (7)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.15/41.45         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.15/41.45    (8)   ~ (all_6_2 = e3)
% 230.15/41.45    (9)  op(e1, e1) = all_6_2
% 230.15/41.45    (10)  op(e2, e2) = e1
% 230.15/41.45    (11)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.15/41.45          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.15/41.45    (12)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.15/41.45          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.15/41.45    (13)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.15/41.45          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.15/41.45    (14)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 230.15/41.45          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.15/41.45    (15)   ~ (e3 = e2)
% 230.15/41.45    (16)   ~ (e3 = e0)
% 230.15/41.45    (17)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.15/41.45          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.15/41.45    (18)  op(e0, e3) = all_53_3
% 230.15/41.45    (19)  all_57_15 = e3
% 230.15/41.45    (20)  op(e3, e3) = e0
% 230.15/41.45    (21)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.15/41.45          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.15/41.45            e1)
% 230.15/41.45    (22)  all_57_12 = e1
% 230.15/41.45    (23)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.15/41.45          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.15/41.45    (24)   ~ (e2 = e0)
% 230.15/41.45    (25)  all_57_3 = e1
% 230.15/41.45    (26)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.15/41.45          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.15/41.45    (27)   ~ (e1 = e0)
% 230.15/41.45    (28)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 230.15/41.45          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 230.15/41.45    (29)  all_57_6 = e3
% 230.15/41.45    (30)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.15/41.45          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.15/41.45    (31)  op(e0, e0) = e3
% 230.15/41.45    (32)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.15/41.45          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.15/41.45            e2)
% 230.15/41.45    (33)   ~ (all_53_3 = e0)
% 230.15/41.45    (34)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.15/41.45              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.15/41.45                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.15/41.45                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.15/41.45    (35)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.15/41.45          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.15/41.45    (36)   ~ (all_53_12 = e3)
% 230.15/41.45    (37)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.15/41.45          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.15/41.45    (38)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.15/41.45          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.15/41.45    (39)   ~ (all_53_12 = e0)
% 230.15/41.45    (40)   ~ (e2 = e1)
% 230.15/41.45    (41)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.15/41.45          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.15/41.45    (42)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.15/41.45          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.15/41.45    (43)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.15/41.45          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.15/41.45    (44)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.15/41.45          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.15/41.45    (45)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.15/41.45          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.15/41.45    (46)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.15/41.45          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.15/41.45    (47)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.15/41.45          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.15/41.45    (48)  all_57_15 = e2 & op(e0, e0) = e2
% 230.15/41.45    (49)  all_57_7 = e0
% 230.15/41.45    (50)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.15/41.45          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.15/41.45    (51)  op(e3, e0) = all_53_12
% 230.15/41.45  
% 230.15/41.45  Begin of proof
% 230.15/41.45  | 
% 230.15/41.45  | ALPHA: (48) implies:
% 230.15/41.45  |   (52)  all_57_15 = e2
% 230.15/41.45  | 
% 230.15/41.45  | COMBINE_EQS: (19), (52) imply:
% 230.15/41.45  |   (53)  e3 = e2
% 230.15/41.45  | 
% 230.15/41.45  | COMBINE_EQS: (29), (53) imply:
% 230.15/41.45  |   (54)  all_57_6 = e2
% 230.15/41.45  | 
% 230.15/41.45  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 230.15/41.45  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 230.15/41.45  |            (24), (25), (26), (27), (28), (30), (31), (32), (33), (34), (35),
% 230.15/41.45  |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 230.15/41.45  |            (47), (49), (50), (51), (54) are inconsistent by sub-proof #989.
% 230.15/41.45  | 
% 230.15/41.45  End of proof
% 230.15/41.45  
% 230.15/41.45  Sub-proof #988 shows that the following formulas are inconsistent:
% 230.15/41.45  ----------------------------------------------------------------
% 230.15/41.45    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.15/41.45         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.15/41.45    (2)  all_57_13 = e1
% 230.15/41.45    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.15/41.45         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.15/41.45    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.15/41.45         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.15/41.45    (5)   ~ (e3 = e1)
% 230.15/41.45    (6)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.15/41.45         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.15/41.45    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.15/41.45           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.15/41.45    (8)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.15/41.45         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.15/41.45    (9)   ~ (all_6_2 = e3)
% 230.15/41.45    (10)  op(e1, e1) = all_6_2
% 230.15/41.45    (11)  op(e2, e2) = e1
% 230.15/41.45    (12)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.15/41.45          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.15/41.45    (13)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.15/41.45          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.15/41.45    (14)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.15/41.45          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.15/41.45    (15)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 230.15/41.45          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.15/41.45    (16)   ~ (e3 = e2)
% 230.15/41.45    (17)   ~ (e3 = e0)
% 230.15/41.45    (18)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.15/41.45          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.15/41.45    (19)  op(e0, e3) = all_53_3
% 230.15/41.45    (20)  all_57_0 = e0
% 230.15/41.45    (21)  all_57_15 = e3
% 230.15/41.45    (22)  op(e3, e3) = e0
% 230.15/41.45    (23)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.15/41.45          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.15/41.45            e1)
% 230.15/41.45    (24)  all_57_5 = e3
% 230.15/41.45    (25)  all_57_12 = e1
% 230.15/41.45    (26)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.15/41.45          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.15/41.45    (27)   ~ (e2 = e0)
% 230.15/41.45    (28)  all_57_3 = e1
% 230.15/41.45    (29)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.15/41.45          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.15/41.45    (30)   ~ (e1 = e0)
% 230.15/41.45    (31)  all_57_14 = e2
% 230.15/41.45    (32)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 230.15/41.45          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 230.15/41.45    (33)  all_57_6 = e3
% 230.15/41.45    (34)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.15/41.45          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.15/41.45    (35)  op(e0, e0) = e3
% 230.15/41.45    (36)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.15/41.45          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.15/41.45            e2)
% 230.15/41.45    (37)   ~ (all_53_3 = e0)
% 230.15/41.45    (38)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.15/41.45              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.15/41.45                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.15/41.45                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.15/41.45    (39)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.15/41.45          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.15/41.45    (40)   ~ (all_53_12 = e3)
% 230.15/41.45    (41)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.15/41.45          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.15/41.45    (42)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.15/41.45          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.15/41.45    (43)  all_57_1 = e3
% 230.15/41.45    (44)   ~ (all_53_12 = e0)
% 230.15/41.45    (45)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.15/41.45          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 230.15/41.45    (46)   ~ (e2 = e1)
% 230.15/41.45    (47)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.15/41.45          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.15/41.45    (48)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.15/41.45          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.15/41.45    (49)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.15/41.45          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.15/41.45    (50)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.15/41.45          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.15/41.45    (51)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.15/41.45          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.15/41.45    (52)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.15/41.45          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.15/41.45    (53)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.15/41.45          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.15/41.45    (54)  all_57_7 = e0
% 230.15/41.45    (55)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.15/41.45          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.15/41.45    (56)  op(e3, e0) = all_53_12
% 230.15/41.45  
% 230.15/41.45  Begin of proof
% 230.15/41.45  | 
% 230.15/41.45  | BETA: splitting (4) gives:
% 230.15/41.45  | 
% 230.15/41.45  | Case 1:
% 230.15/41.45  | | 
% 230.15/41.45  | |   (57)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 230.15/41.45  | |           e2)
% 230.15/41.45  | | 
% 230.15/41.45  | | BETA: splitting (57) gives:
% 230.15/41.45  | | 
% 230.15/41.45  | | Case 1:
% 230.15/41.45  | | | 
% 230.15/41.45  | | |   (58)  all_57_1 = e2 & op(e3, e2) = e2
% 230.15/41.45  | | | 
% 230.15/41.45  | | | ALPHA: (58) implies:
% 230.15/41.45  | | |   (59)  all_57_1 = e2
% 230.15/41.45  | | | 
% 230.15/41.45  | | | COMBINE_EQS: (43), (59) imply:
% 230.15/41.45  | | |   (60)  e3 = e2
% 230.15/41.45  | | | 
% 230.15/41.45  | | | COMBINE_EQS: (33), (60) imply:
% 230.15/41.45  | | |   (61)  all_57_6 = e2
% 230.15/41.45  | | | 
% 230.15/41.45  | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 230.15/41.45  | | |            (14), (15), (16), (17), (18), (19), (21), (22), (23), (25),
% 230.15/41.45  | | |            (26), (27), (28), (29), (30), (32), (34), (35), (36), (37),
% 230.15/41.45  | | |            (38), (39), (40), (41), (42), (44), (46), (47), (48), (49),
% 230.15/41.45  | | |            (50), (51), (52), (53), (54), (55), (56), (61) are inconsistent
% 230.15/41.45  | | |            by sub-proof #989.
% 230.15/41.45  | | | 
% 230.15/41.45  | | Case 2:
% 230.15/41.45  | | | 
% 230.15/41.45  | | |   (62)  all_57_3 = e2 & op(e2, e2) = e2
% 230.15/41.45  | | | 
% 230.15/41.45  | | | ALPHA: (62) implies:
% 230.15/41.45  | | |   (63)  op(e2, e2) = e2
% 230.15/41.45  | | | 
% 230.15/41.45  | | | REF_CLOSE: (7), (11), (46), (63) are inconsistent by sub-proof #2306.
% 230.15/41.45  | | | 
% 230.15/41.45  | | End of split
% 230.15/41.45  | | 
% 230.15/41.45  | Case 2:
% 230.15/41.45  | | 
% 230.15/41.45  | |   (64)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 230.15/41.45  | |           e2)
% 230.15/41.45  | | 
% 230.15/41.45  | | BETA: splitting (64) gives:
% 230.15/41.45  | | 
% 230.15/41.45  | | Case 1:
% 230.15/41.45  | | | 
% 230.15/41.45  | | |   (65)  all_57_7 = e2 & op(e1, e2) = e2
% 230.15/41.45  | | | 
% 230.15/41.45  | | | ALPHA: (65) implies:
% 230.15/41.45  | | |   (66)  all_57_7 = e2
% 230.15/41.45  | | | 
% 230.15/41.45  | | | COMBINE_EQS: (54), (66) imply:
% 230.15/41.45  | | |   (67)  e2 = e0
% 230.15/41.45  | | | 
% 230.15/41.45  | | | COMBINE_EQS: (31), (67) imply:
% 230.15/41.45  | | |   (68)  all_57_14 = e0
% 230.15/41.45  | | | 
% 230.15/41.45  | | | BETA: splitting (45) gives:
% 230.15/41.45  | | | 
% 230.15/41.45  | | | Case 1:
% 230.15/41.45  | | | | 
% 230.15/41.45  | | | |   (69)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2)
% 230.15/41.45  | | | |           = e0)
% 230.15/41.45  | | | | 
% 230.15/41.45  | | | | REF_CLOSE: (1), (3), (5), (7), (11), (16), (20), (22), (24), (27), (28),
% 230.15/41.45  | | | |            (30), (33), (41), (46), (48), (69) are inconsistent by
% 230.15/41.45  | | | |            sub-proof #1009.
% 230.15/41.45  | | | | 
% 230.15/41.45  | | | Case 2:
% 230.15/41.45  | | | | 
% 230.15/41.45  | | | |   (70)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0)
% 230.15/41.45  | | | |           = e0)
% 230.15/41.45  | | | | 
% 230.15/41.45  | | | | BETA: splitting (70) gives:
% 230.15/41.45  | | | | 
% 230.15/41.45  | | | | Case 1:
% 230.15/41.45  | | | | | 
% 230.15/41.45  | | | | |   (71)  all_57_5 = e0 & op(e2, e1) = e0
% 230.15/41.45  | | | | | 
% 230.15/41.45  | | | | | ALPHA: (71) implies:
% 230.15/41.45  | | | | |   (72)  all_57_5 = e0
% 230.15/41.45  | | | | | 
% 230.15/41.45  | | | | | COMBINE_EQS: (24), (72) imply:
% 230.15/41.45  | | | | |   (73)  e3 = e0
% 230.15/41.45  | | | | | 
% 230.15/41.45  | | | | | COMBINE_EQS: (33), (73) imply:
% 230.15/41.45  | | | | |   (74)  all_57_6 = e0
% 230.15/41.45  | | | | | 
% 230.15/41.45  | | | | | REF_CLOSE: (5), (7), (8), (9), (10), (16), (17), (21), (22), (25),
% 230.15/41.45  | | | | |            (27), (30), (38), (42), (46), (47), (48), (51), (74) are
% 230.15/41.45  | | | | |            inconsistent by sub-proof #1028.
% 230.15/41.45  | | | | | 
% 230.15/41.45  | | | | Case 2:
% 230.15/41.45  | | | | | 
% 230.15/41.45  | | | | |   (75)  all_57_10 = e0 & op(e2, e0) = e0
% 230.15/41.45  | | | | | 
% 230.15/41.45  | | | | | ALPHA: (75) implies:
% 230.15/41.45  | | | | |   (76)  all_57_10 = e0
% 230.15/41.45  | | | | | 
% 230.15/41.45  | | | | | BETA: splitting (26) gives:
% 230.15/41.45  | | | | | 
% 230.15/41.45  | | | | | Case 1:
% 230.15/41.45  | | | | | | 
% 230.15/41.45  | | | | | |   (77)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2,
% 230.15/41.45  | | | | | |             e2) = e0)
% 230.15/41.45  | | | | | | 
% 230.15/41.45  | | | | | | BETA: splitting (77) gives:
% 230.15/41.45  | | | | | | 
% 230.15/41.45  | | | | | | Case 1:
% 230.15/41.45  | | | | | | | 
% 230.15/41.45  | | | | | | |   (78)  all_57_1 = e0 & op(e3, e2) = e0
% 230.15/41.45  | | | | | | | 
% 230.15/41.45  | | | | | | | ALPHA: (78) implies:
% 230.15/41.45  | | | | | | |   (79)  all_57_1 = e0
% 230.15/41.45  | | | | | | | 
% 230.15/41.45  | | | | | | | COMBINE_EQS: (43), (79) imply:
% 230.15/41.45  | | | | | | |   (80)  e3 = e0
% 230.15/41.45  | | | | | | | 
% 230.15/41.45  | | | | | | | COMBINE_EQS: (33), (80) imply:
% 230.15/41.45  | | | | | | |   (81)  all_57_6 = e0
% 230.15/41.45  | | | | | | | 
% 230.15/41.45  | | | | | | | REF_CLOSE: (5), (7), (8), (9), (10), (16), (17), (21), (22), (25),
% 230.15/41.46  | | | | | | |            (27), (30), (38), (42), (46), (47), (48), (51), (81)
% 230.15/41.46  | | | | | | |            are inconsistent by sub-proof #1028.
% 230.15/41.46  | | | | | | | 
% 230.15/41.46  | | | | | | Case 2:
% 230.15/41.46  | | | | | | | 
% 230.15/41.46  | | | | | | |   (82)  all_57_3 = e0 & op(e2, e2) = e0
% 230.15/41.46  | | | | | | | 
% 230.15/41.46  | | | | | | | ALPHA: (82) implies:
% 230.15/41.46  | | | | | | |   (83)  all_57_3 = e0
% 230.15/41.46  | | | | | | | 
% 230.15/41.46  | | | | | | | REF_CLOSE: (1), (5), (16), (24), (27), (30), (41), (46), (76),
% 230.15/41.46  | | | | | | |            (83) are inconsistent by sub-proof #1518.
% 230.15/41.46  | | | | | | | 
% 230.15/41.46  | | | | | | End of split
% 230.15/41.46  | | | | | | 
% 230.15/41.46  | | | | | Case 2:
% 230.15/41.46  | | | | | | 
% 230.15/41.46  | | | | | |   (84)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0,
% 230.15/41.46  | | | | | |             e2) = e0)
% 230.15/41.46  | | | | | | 
% 230.15/41.46  | | | | | | BETA: splitting (84) gives:
% 230.15/41.46  | | | | | | 
% 230.15/41.46  | | | | | | Case 1:
% 230.15/41.46  | | | | | | | 
% 230.15/41.46  | | | | | | |   (85)  all_57_7 = e0 & op(e1, e2) = e0
% 230.15/41.46  | | | | | | | 
% 230.15/41.46  | | | | | | | REF_CLOSE: (27), (66), (85) are inconsistent by sub-proof #2148.
% 230.15/41.46  | | | | | | | 
% 230.15/41.46  | | | | | | Case 2:
% 230.15/41.46  | | | | | | | 
% 230.15/41.46  | | | | | | |   (86)  all_57_13 = e0 & op(e0, e2) = e0
% 230.15/41.46  | | | | | | | 
% 230.15/41.46  | | | | | | | ALPHA: (86) implies:
% 230.15/41.46  | | | | | | |   (87)  all_57_13 = e0
% 230.15/41.46  | | | | | | | 
% 230.15/41.46  | | | | | | | BETA: splitting (41) gives:
% 230.15/41.46  | | | | | | | 
% 230.15/41.46  | | | | | | | Case 1:
% 230.15/41.46  | | | | | | | | 
% 230.15/41.46  | | | | | | | |   (88)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 &
% 230.15/41.46  | | | | | | | |           op(e2, e2) = e2)
% 230.15/41.46  | | | | | | | | 
% 230.15/41.46  | | | | | | | | BETA: splitting (88) gives:
% 230.15/41.46  | | | | | | | | 
% 230.15/41.46  | | | | | | | | Case 1:
% 230.15/41.46  | | | | | | | | | 
% 230.15/41.46  | | | | | | | | |   (89)  all_57_2 = e2 & op(e2, e3) = e2
% 230.15/41.46  | | | | | | | | | 
% 230.15/41.46  | | | | | | | | | ALPHA: (89) implies:
% 230.15/41.46  | | | | | | | | |   (90)  all_57_2 = e2
% 230.15/41.46  | | | | | | | | | 
% 230.15/41.46  | | | | | | | | | BETA: splitting (36) gives:
% 230.15/41.46  | | | | | | | | | 
% 230.15/41.46  | | | | | | | | | Case 1:
% 230.15/41.46  | | | | | | | | | | 
% 230.15/41.46  | | | | | | | | | |   (91)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2
% 230.15/41.46  | | | | | | | | | |           & op(e0, e2) = e2)
% 230.15/41.46  | | | | | | | | | | 
% 230.15/41.46  | | | | | | | | | | BETA: splitting (91) gives:
% 230.15/41.46  | | | | | | | | | | 
% 230.15/41.46  | | | | | | | | | | Case 1:
% 230.15/41.46  | | | | | | | | | | | 
% 230.15/41.46  | | | | | | | | | | |   (92)  all_57_12 = e2 & op(e0, e3) = e2
% 230.15/41.46  | | | | | | | | | | | 
% 230.15/41.46  | | | | | | | | | | | ALPHA: (92) implies:
% 230.15/41.46  | | | | | | | | | | |   (93)  all_57_12 = e2
% 230.15/41.46  | | | | | | | | | | | 
% 230.15/41.46  | | | | | | | | | | | COMBINE_EQS: (25), (93) imply:
% 230.15/41.46  | | | | | | | | | | |   (94)  e2 = e1
% 230.15/41.46  | | | | | | | | | | | 
% 230.15/41.46  | | | | | | | | | | | SIMP: (94) implies:
% 230.15/41.46  | | | | | | | | | | |   (95)  e2 = e1
% 230.15/41.46  | | | | | | | | | | | 
% 230.15/41.46  | | | | | | | | | | | COMBINE_EQS: (90), (95) imply:
% 230.15/41.46  | | | | | | | | | | |   (96)  all_57_2 = e1
% 230.15/41.46  | | | | | | | | | | | 
% 230.15/41.46  | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (7), (8), (9), (10), (11),
% 230.15/41.46  | | | | | | | | | | |            (16), (17), (20), (21), (22), (24), (26), (27),
% 230.15/41.46  | | | | | | | | | | |            (28), (30), (33), (38), (41), (43), (45), (46),
% 230.15/41.46  | | | | | | | | | | |            (47), (48), (51), (53), (96) are inconsistent by
% 230.15/41.46  | | | | | | | | | | |            sub-proof #1007.
% 230.15/41.46  | | | | | | | | | | | 
% 230.15/41.46  | | | | | | | | | | Case 2:
% 230.15/41.46  | | | | | | | | | | | 
% 230.15/41.46  | | | | | | | | | | |   (97)  all_57_13 = e2 & op(e0, e2) = e2
% 230.15/41.46  | | | | | | | | | | | 
% 230.15/41.46  | | | | | | | | | | | ALPHA: (97) implies:
% 230.15/41.46  | | | | | | | | | | |   (98)  all_57_13 = e2
% 230.15/41.46  | | | | | | | | | | | 
% 230.15/41.46  | | | | | | | | | | | COMBINE_EQS: (87), (98) imply:
% 230.15/41.46  | | | | | | | | | | |   (99)  e2 = e0
% 230.15/41.46  | | | | | | | | | | | 
% 230.15/41.46  | | | | | | | | | | | COMBINE_EQS: (67), (90) imply:
% 230.15/41.46  | | | | | | | | | | |   (100)  all_57_2 = e0
% 230.15/41.46  | | | | | | | | | | | 
% 230.15/41.46  | | | | | | | | | | | REF_CLOSE: (1), (3), (5), (7), (16), (20), (22), (24), (27),
% 230.15/41.46  | | | | | | | | | | |            (28), (30), (33), (41), (46), (48), (100) are
% 230.15/41.46  | | | | | | | | | | |            inconsistent by sub-proof #1066.
% 230.15/41.46  | | | | | | | | | | | 
% 230.15/41.46  | | | | | | | | | | End of split
% 230.15/41.46  | | | | | | | | | | 
% 230.15/41.46  | | | | | | | | | Case 2:
% 230.15/41.46  | | | | | | | | | | 
% 230.15/41.46  | | | | | | | | | |   (101)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 230.15/41.46  | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 230.15/41.46  | | | | | | | | | | 
% 230.15/41.46  | | | | | | | | | | BETA: splitting (101) gives:
% 230.15/41.46  | | | | | | | | | | 
% 230.15/41.46  | | | | | | | | | | Case 1:
% 230.15/41.46  | | | | | | | | | | | 
% 230.15/41.46  | | | | | | | | | | |   (102)  all_57_14 = e2 & op(e0, e1) = e2
% 230.15/41.46  | | | | | | | | | | | 
% 230.15/41.46  | | | | | | | | | | | COMBINE_EQS: (67), (90) imply:
% 230.15/41.46  | | | | | | | | | | |   (103)  all_57_2 = e0
% 230.15/41.46  | | | | | | | | | | | 
% 230.15/41.46  | | | | | | | | | | | REF_CLOSE: (1), (3), (5), (7), (16), (20), (22), (24), (27),
% 230.15/41.46  | | | | | | | | | | |            (28), (30), (33), (41), (46), (48), (103) are
% 230.15/41.46  | | | | | | | | | | |            inconsistent by sub-proof #1066.
% 230.15/41.46  | | | | | | | | | | | 
% 230.15/41.46  | | | | | | | | | | Case 2:
% 230.15/41.46  | | | | | | | | | | | 
% 230.15/41.46  | | | | | | | | | | |   (104)  all_57_15 = e2 & op(e0, e0) = e2
% 230.15/41.46  | | | | | | | | | | | 
% 230.15/41.46  | | | | | | | | | | | ALPHA: (104) implies:
% 230.15/41.46  | | | | | | | | | | |   (105)  all_57_15 = e2
% 230.15/41.46  | | | | | | | | | | | 
% 230.15/41.46  | | | | | | | | | | | REF_CLOSE: (16), (21), (105) are inconsistent by sub-proof
% 230.15/41.46  | | | | | | | | | | |            #2058.
% 230.15/41.46  | | | | | | | | | | | 
% 230.15/41.46  | | | | | | | | | | End of split
% 230.15/41.46  | | | | | | | | | | 
% 230.15/41.46  | | | | | | | | | End of split
% 230.15/41.46  | | | | | | | | | 
% 230.15/41.46  | | | | | | | | Case 2:
% 230.15/41.46  | | | | | | | | | 
% 230.15/41.46  | | | | | | | | |   (106)  all_57_3 = e2 & op(e2, e2) = e2
% 230.15/41.46  | | | | | | | | | 
% 230.15/41.46  | | | | | | | | | ALPHA: (106) implies:
% 230.15/41.46  | | | | | | | | |   (107)  op(e2, e2) = e2
% 230.15/41.46  | | | | | | | | | 
% 230.15/41.46  | | | | | | | | | REF_CLOSE: (7), (11), (46), (107) are inconsistent by
% 230.15/41.46  | | | | | | | | |            sub-proof #2306.
% 230.15/41.46  | | | | | | | | | 
% 230.15/41.46  | | | | | | | | End of split
% 230.15/41.46  | | | | | | | | 
% 230.15/41.46  | | | | | | | Case 2:
% 230.15/41.46  | | | | | | | | 
% 230.15/41.46  | | | | | | | |   (108)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 &
% 230.15/41.46  | | | | | | | |            op(e2, e0) = e2)
% 230.15/41.46  | | | | | | | | 
% 230.15/41.46  | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (7), (8), (9), (10), (11), (16),
% 230.15/41.46  | | | | | | | |            (17), (20), (21), (22), (24), (26), (27), (28), (30),
% 230.15/41.46  | | | | | | | |            (33), (38), (41), (43), (45), (46), (47), (48), (51),
% 230.15/41.46  | | | | | | | |            (53), (108) are inconsistent by sub-proof #1008.
% 230.15/41.46  | | | | | | | | 
% 230.15/41.46  | | | | | | | End of split
% 230.15/41.46  | | | | | | | 
% 230.15/41.46  | | | | | | End of split
% 230.15/41.46  | | | | | | 
% 230.15/41.46  | | | | | End of split
% 230.15/41.46  | | | | | 
% 230.15/41.46  | | | | End of split
% 230.15/41.46  | | | | 
% 230.15/41.46  | | | End of split
% 230.15/41.46  | | | 
% 230.15/41.46  | | Case 2:
% 230.15/41.46  | | | 
% 230.15/41.46  | | |   (109)  all_57_13 = e2 & op(e0, e2) = e2
% 230.15/41.46  | | | 
% 230.15/41.46  | | | REF_CLOSE: (2), (46), (109) are inconsistent by sub-proof #2101.
% 230.15/41.46  | | | 
% 230.15/41.46  | | End of split
% 230.15/41.46  | | 
% 230.15/41.46  | End of split
% 230.15/41.46  | 
% 230.15/41.46  End of proof
% 230.15/41.46  
% 230.15/41.46  Sub-proof #989 shows that the following formulas are inconsistent:
% 230.15/41.46  ----------------------------------------------------------------
% 230.15/41.46    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.15/41.46         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.15/41.46    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.15/41.46         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.15/41.46    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.15/41.46         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.15/41.46    (4)   ~ (e3 = e1)
% 230.15/41.46    (5)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.15/41.46         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.15/41.46    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.15/41.46           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.15/41.46    (7)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.15/41.46         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.15/41.46    (8)   ~ (all_6_2 = e3)
% 230.15/41.46    (9)  op(e1, e1) = all_6_2
% 230.15/41.46    (10)  op(e2, e2) = e1
% 230.15/41.46    (11)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.15/41.46          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.15/41.46    (12)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.15/41.46          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.15/41.46    (13)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.15/41.46          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.15/41.46    (14)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 230.15/41.46          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.15/41.46    (15)   ~ (e3 = e2)
% 230.15/41.46    (16)   ~ (e3 = e0)
% 230.15/41.46    (17)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.15/41.46          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.15/41.46    (18)  op(e0, e3) = all_53_3
% 230.15/41.46    (19)  all_57_15 = e3
% 230.15/41.46    (20)  op(e3, e3) = e0
% 230.15/41.46    (21)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.15/41.46          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.15/41.46            e1)
% 230.15/41.46    (22)  all_57_6 = e2
% 230.15/41.46    (23)  all_57_12 = e1
% 230.15/41.46    (24)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.15/41.46          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.15/41.46    (25)   ~ (e2 = e0)
% 230.15/41.46    (26)  all_57_3 = e1
% 230.15/41.46    (27)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.15/41.46          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.15/41.46    (28)   ~ (e1 = e0)
% 230.15/41.46    (29)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 230.15/41.46          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 230.15/41.46    (30)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.15/41.46          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.15/41.46    (31)  op(e0, e0) = e3
% 230.15/41.46    (32)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.15/41.46          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.15/41.46            e2)
% 230.15/41.46    (33)   ~ (all_53_3 = e0)
% 230.15/41.46    (34)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.15/41.46              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.15/41.46                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.15/41.46                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.15/41.46    (35)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.15/41.46          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.15/41.46    (36)   ~ (all_53_12 = e3)
% 230.15/41.46    (37)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.15/41.46          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.15/41.46    (38)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.15/41.46          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.15/41.46    (39)   ~ (all_53_12 = e0)
% 230.15/41.46    (40)   ~ (e2 = e1)
% 230.15/41.46    (41)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.15/41.46          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.15/41.46    (42)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.15/41.46          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.15/41.46    (43)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.15/41.46          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.15/41.46    (44)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.15/41.46          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.15/41.46    (45)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.15/41.46          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.15/41.46    (46)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.15/41.46          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.15/41.46    (47)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.15/41.46          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.15/41.46    (48)  all_57_7 = e0
% 230.15/41.46    (49)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.15/41.46          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.15/41.46    (50)  op(e3, e0) = all_53_12
% 230.15/41.46  
% 230.15/41.46  Begin of proof
% 230.15/41.46  | 
% 230.15/41.46  | BETA: splitting (38) gives:
% 230.15/41.46  | 
% 230.15/41.46  | Case 1:
% 230.15/41.46  | | 
% 230.15/41.46  | |   (51)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) =
% 230.15/41.46  | |           e3)
% 230.15/41.46  | | 
% 230.15/41.46  | | BETA: splitting (51) gives:
% 230.15/41.46  | | 
% 230.15/41.46  | | Case 1:
% 230.15/41.46  | | | 
% 230.15/41.46  | | |   (52)  all_57_0 = e3 & op(e3, e3) = e3
% 230.15/41.46  | | | 
% 230.15/41.46  | | | ALPHA: (52) implies:
% 230.15/41.46  | | |   (53)  op(e3, e3) = e3
% 230.15/41.46  | | | 
% 230.15/41.46  | | | REF_CLOSE: (6), (16), (20), (53) are inconsistent by sub-proof #2494.
% 230.15/41.46  | | | 
% 230.15/41.46  | | Case 2:
% 230.15/41.46  | | | 
% 230.15/41.46  | | |   (54)  all_57_2 = e3 & op(e2, e3) = e3
% 230.15/41.46  | | | 
% 230.15/41.46  | | | ALPHA: (54) implies:
% 230.15/41.46  | | |   (55)  all_57_2 = e3
% 230.15/41.46  | | | 
% 230.15/41.46  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 230.15/41.46  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (23),
% 230.15/41.46  | | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 230.15/41.46  | | |            (34), (35), (36), (37), (38), (39), (40), (41), (42), (43),
% 230.15/41.46  | | |            (44), (45), (46), (47), (48), (49), (50), (55) are inconsistent
% 230.15/41.46  | | |            by sub-proof #1014.
% 230.15/41.46  | | | 
% 230.15/41.46  | | End of split
% 230.15/41.46  | | 
% 230.15/41.46  | Case 2:
% 230.15/41.46  | | 
% 230.15/41.46  | |   (56)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) =
% 230.15/41.46  | |           e3)
% 230.15/41.46  | | 
% 230.15/41.46  | | REF_CLOSE: (4), (15), (22), (23), (56) are inconsistent by sub-proof #990.
% 230.15/41.46  | | 
% 230.15/41.46  | End of split
% 230.15/41.46  | 
% 230.15/41.46  End of proof
% 230.15/41.46  
% 230.15/41.46  Sub-proof #990 shows that the following formulas are inconsistent:
% 230.15/41.46  ----------------------------------------------------------------
% 230.15/41.46    (1)   ~ (e3 = e1)
% 230.15/41.46    (2)   ~ (e3 = e2)
% 230.15/41.46    (3)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.15/41.46    (4)  all_57_6 = e2
% 230.15/41.46    (5)  all_57_12 = e1
% 230.15/41.46  
% 230.15/41.46  Begin of proof
% 230.15/41.46  | 
% 230.15/41.46  | BETA: splitting (3) gives:
% 230.15/41.46  | 
% 230.15/41.46  | Case 1:
% 230.15/41.46  | | 
% 230.15/41.46  | |   (6)  all_57_6 = e3 & op(e1, e3) = e3
% 230.15/41.46  | | 
% 230.15/41.46  | | ALPHA: (6) implies:
% 230.15/41.46  | |   (7)  all_57_6 = e3
% 230.15/41.46  | | 
% 230.15/41.46  | | REF_CLOSE: (2), (4), (7) are inconsistent by sub-proof #2463.
% 230.15/41.46  | | 
% 230.15/41.46  | Case 2:
% 230.15/41.46  | | 
% 230.15/41.46  | |   (8)  all_57_12 = e3 & op(e0, e3) = e3
% 230.15/41.46  | | 
% 230.15/41.46  | | ALPHA: (8) implies:
% 230.15/41.46  | |   (9)  all_57_12 = e3
% 230.15/41.46  | | 
% 230.15/41.46  | | REF_CLOSE: (1), (5), (9) are inconsistent by sub-proof #2151.
% 230.15/41.46  | | 
% 230.15/41.46  | End of split
% 230.15/41.46  | 
% 230.15/41.46  End of proof
% 230.15/41.46  
% 230.15/41.46  Sub-proof #991 shows that the following formulas are inconsistent:
% 230.15/41.46  ----------------------------------------------------------------
% 230.15/41.46    (1)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.15/41.46    (2)  all_57_12 = e1
% 230.15/41.46    (3)   ~ (e2 = e1)
% 230.15/41.46    (4)  all_57_13 = e1
% 230.15/41.46  
% 230.15/41.46  Begin of proof
% 230.15/41.46  | 
% 230.15/41.46  | BETA: splitting (1) gives:
% 230.15/41.46  | 
% 230.15/41.46  | Case 1:
% 230.15/41.46  | | 
% 230.15/41.46  | |   (5)  all_57_12 = e2 & op(e0, e3) = e2
% 230.15/41.46  | | 
% 230.15/41.46  | | ALPHA: (5) implies:
% 230.15/41.46  | |   (6)  all_57_12 = e2
% 230.15/41.46  | | 
% 230.15/41.46  | | REF_CLOSE: (2), (3), (6) are inconsistent by sub-proof #2321.
% 230.15/41.46  | | 
% 230.15/41.46  | Case 2:
% 230.15/41.46  | | 
% 230.15/41.46  | |   (7)  all_57_13 = e2 & op(e0, e2) = e2
% 230.15/41.46  | | 
% 230.15/41.46  | | ALPHA: (7) implies:
% 230.15/41.46  | |   (8)  all_57_13 = e2
% 230.15/41.46  | | 
% 230.15/41.46  | | REF_CLOSE: (3), (4), (8) are inconsistent by sub-proof #2327.
% 230.15/41.46  | | 
% 230.15/41.46  | End of split
% 230.15/41.46  | 
% 230.15/41.46  End of proof
% 230.15/41.46  
% 230.15/41.46  Sub-proof #992 shows that the following formulas are inconsistent:
% 230.15/41.46  ----------------------------------------------------------------
% 230.15/41.46    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.15/41.46         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.15/41.46    (2)  all_57_13 = e1
% 230.15/41.46    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.15/41.46         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.15/41.46    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.15/41.46         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.15/41.46    (5)   ~ (e3 = e1)
% 230.15/41.46    (6)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.15/41.46         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.15/41.46    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.15/41.46           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.15/41.46    (8)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.15/41.46         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.15/41.46    (9)   ~ (all_6_2 = e3)
% 230.15/41.46    (10)  op(e1, e1) = all_6_2
% 230.15/41.46    (11)  op(e2, e2) = e1
% 230.15/41.46    (12)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.15/41.46          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.15/41.46    (13)  all_57_13 = e0 & op(e0, e2) = e0
% 230.15/41.46    (14)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.15/41.46          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.15/41.46    (15)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.15/41.46          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.15/41.46    (16)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 230.15/41.46          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.15/41.46    (17)   ~ (e3 = e2)
% 230.15/41.46    (18)   ~ (e3 = e0)
% 230.15/41.46    (19)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.15/41.46          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.15/41.46    (20)  op(e0, e3) = all_53_3
% 230.15/41.46    (21)  all_57_15 = e3
% 230.15/41.46    (22)  op(e3, e3) = e0
% 230.15/41.46    (23)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.15/41.46          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.15/41.46            e1)
% 230.15/41.46    (24)  all_57_5 = e3
% 230.15/41.46    (25)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.15/41.46          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.15/41.46    (26)   ~ (e2 = e0)
% 230.15/41.46    (27)  all_57_3 = e1
% 230.15/41.46    (28)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.15/41.46          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.15/41.46    (29)   ~ (e1 = e0)
% 230.15/41.46    (30)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 230.15/41.46          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 230.15/41.46    (31)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.15/41.46          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.15/41.46    (32)  op(e0, e0) = e3
% 230.15/41.46    (33)  all_57_2 = e1
% 230.15/41.46    (34)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.15/41.46          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.15/41.46            e2)
% 230.15/41.46    (35)   ~ (all_53_3 = e0)
% 230.15/41.46    (36)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.15/41.46              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.15/41.46                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.15/41.46                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.15/41.46    (37)   ~ (all_53_12 = e3)
% 230.15/41.46    (38)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.15/41.46          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.15/41.46    (39)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.15/41.46          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.15/41.46    (40)   ~ (all_53_12 = e0)
% 230.15/41.46    (41)   ~ (e2 = e1)
% 230.15/41.46    (42)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.15/41.46          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.15/41.46    (43)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.15/41.46          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.15/41.46    (44)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.15/41.46          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.15/41.46    (45)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.15/41.46          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.15/41.46    (46)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.15/41.46          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.15/41.46    (47)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.15/41.46          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.15/41.46    (48)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.15/41.46          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.15/41.46    (49)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.15/41.46          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.15/41.46    (50)  op(e3, e0) = all_53_12
% 230.15/41.46  
% 230.15/41.46  Begin of proof
% 230.15/41.46  | 
% 230.15/41.46  | ALPHA: (13) implies:
% 230.15/41.46  |   (51)  all_57_13 = e0
% 230.15/41.46  | 
% 230.15/41.46  | COMBINE_EQS: (2), (51) imply:
% 230.15/41.46  |   (52)  e1 = e0
% 230.15/41.46  | 
% 230.15/41.46  | COMBINE_EQS: (33), (52) imply:
% 230.15/41.46  |   (53)  all_57_2 = e0
% 230.15/41.46  | 
% 230.15/41.46  | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (14),
% 230.15/41.46  |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 230.15/41.46  |            (26), (27), (28), (29), (30), (31), (32), (34), (35), (36), (37),
% 230.15/41.46  |            (38), (39), (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 230.15/41.46  |            (49), (50), (53) are inconsistent by sub-proof #1021.
% 230.15/41.46  | 
% 230.15/41.46  End of proof
% 230.15/41.46  
% 230.15/41.46  Sub-proof #993 shows that the following formulas are inconsistent:
% 230.15/41.46  ----------------------------------------------------------------
% 230.15/41.46    (1)   ~ (e3 = e1)
% 230.15/41.46    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.15/41.46           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.15/41.46    (3)   ~ (e3 = e2)
% 230.15/41.46    (4)   ~ (e3 = e0)
% 230.15/41.46    (5)  all_57_15 = e3
% 230.15/41.46    (6)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 230.15/41.46         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.15/41.46    (7)   ~ (e2 = e0)
% 230.15/41.46    (8)   ~ (e1 = e0)
% 230.15/41.46    (9)  op(e0, e0) = e3
% 230.15/41.46    (10)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.15/41.46          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.15/41.46            e2)
% 230.15/41.46    (11)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.15/41.46              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.15/41.46                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.15/41.46                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.15/41.46    (12)   ~ (e2 = e1)
% 230.15/41.46    (13)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.15/41.46    (14)  all_57_7 = e0
% 230.15/41.46  
% 230.15/41.46  Begin of proof
% 230.15/41.46  | 
% 230.15/41.46  | BETA: splitting (13) gives:
% 230.15/41.46  | 
% 230.15/41.46  | Case 1:
% 230.15/41.46  | | 
% 230.15/41.46  | |   (15)  all_57_7 = e3 & op(e1, e2) = e3
% 230.15/41.46  | | 
% 230.15/41.46  | | ALPHA: (15) implies:
% 230.15/41.46  | |   (16)  all_57_7 = e3
% 230.15/41.46  | | 
% 230.15/41.46  | | REF_CLOSE: (4), (14), (16) are inconsistent by sub-proof #2269.
% 230.15/41.46  | | 
% 230.15/41.46  | Case 2:
% 230.15/41.46  | | 
% 230.15/41.46  | |   (17)  all_57_13 = e3 & op(e0, e2) = e3
% 230.15/41.46  | | 
% 230.15/41.46  | | ALPHA: (17) implies:
% 230.15/41.46  | |   (18)  all_57_13 = e3
% 230.15/41.46  | | 
% 230.15/41.46  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 230.15/41.46  | |            (18) are inconsistent by sub-proof #1792.
% 230.15/41.46  | | 
% 230.15/41.46  | End of split
% 230.15/41.46  | 
% 230.15/41.46  End of proof
% 230.15/41.46  
% 230.15/41.46  Sub-proof #994 shows that the following formulas are inconsistent:
% 230.15/41.46  ----------------------------------------------------------------
% 230.15/41.46    (1)   ~ (e3 = e1)
% 230.15/41.46    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.15/41.46           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.15/41.46    (3)  op(e2, e2) = e1
% 230.15/41.46    (4)   ~ (e3 = e0)
% 230.15/41.46    (5)  all_57_4 = e1
% 230.15/41.46    (6)  op(e3, e3) = e0
% 230.15/41.46    (7)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.15/41.46         (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.15/41.46    (8)   ~ (e1 = e0)
% 230.15/41.46    (9)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0)
% 230.15/41.46    (10)   ~ (all_53_12 = e3)
% 230.15/41.46    (11)  op(e3, e0) = all_53_12
% 230.15/41.46  
% 230.15/41.46  Begin of proof
% 230.15/41.46  | 
% 230.15/41.46  | BETA: splitting (9) gives:
% 230.15/41.46  | 
% 230.15/41.46  | Case 1:
% 230.15/41.46  | | 
% 230.15/41.46  | |   (12)  all_57_1 = e0 & op(e3, e2) = e0
% 230.15/41.46  | | 
% 230.15/41.46  | | ALPHA: (12) implies:
% 230.15/41.46  | |   (13)  all_57_1 = e0
% 230.15/41.46  | | 
% 230.15/41.46  | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (10), (11), (13) are inconsistent
% 230.15/41.46  | |            by sub-proof #2280.
% 230.15/41.46  | | 
% 230.15/41.46  | Case 2:
% 230.15/41.46  | | 
% 230.15/41.46  | |   (14)  all_57_3 = e0 & op(e2, e2) = e0
% 230.15/41.46  | | 
% 230.15/41.46  | | ALPHA: (14) implies:
% 230.15/41.46  | |   (15)  op(e2, e2) = e0
% 230.15/41.46  | | 
% 230.15/41.46  | | REF_CLOSE: (2), (3), (8), (15) are inconsistent by sub-proof #2352.
% 230.15/41.46  | | 
% 230.15/41.46  | End of split
% 230.15/41.46  | 
% 230.15/41.46  End of proof
% 230.15/41.46  
% 230.15/41.46  Sub-proof #995 shows that the following formulas are inconsistent:
% 230.15/41.46  ----------------------------------------------------------------
% 230.15/41.46    (1)   ~ (e3 = e1)
% 230.15/41.46    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.15/41.46           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.15/41.46    (3)  op(e2, e2) = e1
% 230.15/41.46    (4)  all_57_2 = e1
% 230.15/41.46    (5)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3)
% 230.15/41.46  
% 230.15/41.46  Begin of proof
% 230.15/41.46  | 
% 230.15/41.46  | BETA: splitting (5) gives:
% 230.15/41.46  | 
% 230.15/41.46  | Case 1:
% 230.15/41.46  | | 
% 230.15/41.46  | |   (6)  all_57_2 = e3 & op(e2, e3) = e3
% 230.15/41.46  | | 
% 230.15/41.46  | | ALPHA: (6) implies:
% 230.15/41.46  | |   (7)  all_57_2 = e3
% 230.15/41.46  | | 
% 230.15/41.46  | | REF_CLOSE: (1), (4), (7) are inconsistent by sub-proof #2397.
% 230.15/41.46  | | 
% 230.15/41.46  | Case 2:
% 230.15/41.46  | | 
% 230.15/41.46  | |   (8)  all_57_3 = e3 & op(e2, e2) = e3
% 230.15/41.46  | | 
% 230.15/41.46  | | ALPHA: (8) implies:
% 230.15/41.46  | |   (9)  op(e2, e2) = e3
% 230.15/41.46  | | 
% 230.15/41.46  | | REF_CLOSE: (1), (2), (3), (9) are inconsistent by sub-proof #1912.
% 230.15/41.46  | | 
% 230.15/41.46  | End of split
% 230.15/41.46  | 
% 230.15/41.46  End of proof
% 230.15/41.46  
% 230.15/41.46  Sub-proof #996 shows that the following formulas are inconsistent:
% 230.15/41.46  ----------------------------------------------------------------
% 230.15/41.46    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.15/41.46         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.15/41.46    (2)   ~ (e3 = e1)
% 230.15/41.47    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.15/41.47           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.15/41.47    (4)  op(e2, e2) = e1
% 230.15/41.47    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.15/41.47         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.15/41.47    (6)  all_57_0 = e1 & op(e3, e3) = e1
% 230.15/41.47    (7)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.15/41.47         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.15/41.47    (8)   ~ (e3 = e2)
% 230.15/41.47    (9)   ~ (e3 = e0)
% 230.15/41.47    (10)  all_57_0 = e0
% 230.15/41.47    (11)  all_57_4 = e1
% 230.15/41.47    (12)  op(e3, e3) = e0
% 230.15/41.47    (13)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.15/41.47          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.15/41.47    (14)   ~ (e2 = e0)
% 230.15/41.47    (15)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.15/41.47          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.15/41.47    (16)   ~ (e1 = e0)
% 230.15/41.47    (17)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.15/41.47          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.15/41.47    (18)   ~ (all_53_12 = e3)
% 230.15/41.47    (19)   ~ (e2 = e1)
% 230.15/41.47    (20)  op(e3, e0) = all_53_12
% 230.15/41.47  
% 230.15/41.47  Begin of proof
% 230.15/41.47  | 
% 230.15/41.47  | ALPHA: (6) implies:
% 230.15/41.47  |   (21)  all_57_0 = e1
% 230.15/41.47  | 
% 230.15/41.47  | COMBINE_EQS: (10), (21) imply:
% 230.15/41.47  |   (22)  e1 = e0
% 230.15/41.47  | 
% 230.15/41.47  | SIMP: (22) implies:
% 230.15/41.47  |   (23)  e1 = e0
% 230.15/41.47  | 
% 230.15/41.47  | COMBINE_EQS: (11), (23) imply:
% 230.15/41.47  |   (24)  all_57_4 = e0
% 230.15/41.47  | 
% 230.15/41.47  | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (12), (13), (14),
% 230.15/41.47  |            (15), (16), (17), (18), (19), (20), (24) are inconsistent by
% 230.15/41.47  |            sub-proof #1012.
% 230.15/41.47  | 
% 230.15/41.47  End of proof
% 230.15/41.47  
% 230.15/41.47  Sub-proof #997 shows that the following formulas are inconsistent:
% 230.15/41.47  ----------------------------------------------------------------
% 230.15/41.47    (1)   ~ (all_48_2 = e0) | ( ~ (all_48_0 = e2) & op(all_48_1, e3) = all_48_0 &
% 230.15/41.47           op(e3, e0) = all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 =
% 230.15/41.47             e1) & op(e3, e0) = all_48_1 & $i(all_48_1))
% 230.15/41.47    (2)  all_48_2 = e0
% 230.15/41.47    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.15/41.47           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.15/41.47    (4)   ~ (all_6_2 = e3)
% 230.15/41.47    (5)  ( ~ (all_18_0 = e1) & op(all_18_1, e3) = all_18_0 & op(e3, e0) = all_18_1
% 230.15/41.47           & $i(all_18_0) & $i(all_18_1)) | ( ~ (all_18_1 = e2) & op(e3, e0) =
% 230.15/41.47           all_18_1 & $i(all_18_1))
% 230.15/41.47    (6)  op(e1, e1) = all_6_2
% 230.15/41.47    (7)  op(e2, e2) = e1
% 230.15/41.47    (8)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) = all_22_1
% 230.15/41.47           & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0, e3) =
% 230.15/41.47           all_22_1 & $i(all_22_1))
% 230.15/41.47    (9)  op(e3, e0) = e1
% 230.15/41.47    (10)  op(e0, e3) = e1
% 230.15/41.47    (11)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 230.15/41.47    (12)  op(e0, e3) = all_53_3
% 230.15/41.47    (13)   ~ (all_53_2 = e0)
% 230.15/41.47    (14)  op(e3, e3) = e0
% 230.15/41.47    (15)  op(e1, e1) = e1
% 230.15/41.47    (16)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 230.15/41.47            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 230.15/41.47            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 230.15/41.47            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 230.15/41.47              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 230.15/41.47            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 230.15/41.47            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 230.15/41.47              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 230.15/41.47              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 230.15/41.47            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 230.15/41.47            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 230.15/41.47            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 230.15/41.47              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 230.15/41.47              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 230.15/41.47            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 230.15/41.47              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 230.15/41.47            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 230.15/41.47            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 230.15/41.47              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 230.15/41.47              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 230.15/41.47            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 230.15/41.47            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 230.15/41.47    (17)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 230.15/41.47            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 230.15/41.47              e3) = all_12_1 & $i(all_12_1))
% 230.15/41.47    (18)   ~ (all_53_2 = all_53_3)
% 230.15/41.47    (19)  all_55_8 = all_53_2
% 230.15/41.47    (20)  op(e1, e3) = all_53_2
% 230.15/41.47    (21)   ~ (all_53_12 = e0)
% 230.15/41.47    (22)   ~ (e2 = e1)
% 230.15/41.47    (23)  op(e3, e0) = all_53_12
% 230.15/41.47  
% 230.15/41.47  Begin of proof
% 230.15/41.47  | 
% 230.15/41.47  | GROUND_INST: instantiating (3) with all_53_3, e1, e3, e0, simplifying with
% 230.15/41.47  |              (10), (12) gives:
% 230.15/41.47  |   (24)  all_53_3 = e1
% 230.15/41.47  | 
% 230.15/41.47  | GROUND_INST: instantiating (3) with all_53_12, e1, e0, e3, simplifying with
% 230.15/41.47  |              (9), (23) gives:
% 230.15/41.47  |   (25)  all_53_12 = e1
% 230.15/41.47  | 
% 230.15/41.47  | REDUCE: (18), (24) imply:
% 230.15/41.47  |   (26)   ~ (all_53_2 = e1)
% 230.15/41.47  | 
% 230.15/41.47  | REDUCE: (21), (25) imply:
% 230.15/41.47  |   (27)   ~ (e1 = e0)
% 230.15/41.47  | 
% 230.15/41.47  | BETA: splitting (1) gives:
% 230.15/41.47  | 
% 230.15/41.47  | Case 1:
% 230.15/41.47  | | 
% 230.15/41.47  | |   (28)   ~ (all_48_2 = e0)
% 230.15/41.47  | | 
% 230.15/41.47  | | REDUCE: (2), (28) imply:
% 230.15/41.47  | |   (29)  $false
% 230.15/41.47  | | 
% 230.15/41.47  | | CLOSE: (29) is inconsistent.
% 230.15/41.47  | | 
% 230.15/41.47  | Case 2:
% 230.15/41.47  | | 
% 230.15/41.47  | |   (30)  ( ~ (all_48_0 = e2) & op(all_48_1, e3) = all_48_0 & op(e3, e0) =
% 230.15/41.47  | |           all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 = e1) &
% 230.15/41.47  | |           op(e3, e0) = all_48_1 & $i(all_48_1))
% 230.15/41.47  | | 
% 230.15/41.47  | | BETA: splitting (17) gives:
% 230.15/41.47  | | 
% 230.15/41.47  | | Case 1:
% 230.15/41.47  | | | 
% 230.15/41.47  | | |   (31)   ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 230.15/41.47  | | |         all_12_1 & $i(all_12_0) & $i(all_12_1)
% 230.15/41.47  | | | 
% 230.15/41.47  | | | ALPHA: (31) implies:
% 230.15/41.47  | | |   (32)  op(e0, e3) = all_12_1
% 230.15/41.47  | | | 
% 230.15/41.47  | | | BETA: splitting (16) gives:
% 230.15/41.47  | | | 
% 230.15/41.47  | | | Case 1:
% 230.15/41.47  | | | | 
% 230.15/41.47  | | | |   (33)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 230.15/41.47  | | | |           op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 230.15/41.47  | | | |           op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 230.15/41.47  | | | |           op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) =
% 230.15/41.47  | | | |           all_52_5 & op(e3, e0) = all_52_7 & $i(all_52_1) & $i(all_52_3)
% 230.15/41.47  | | | |           & $i(all_52_5) & $i(all_52_7)) | (all_52_8 = e3 & all_52_10 =
% 230.15/41.47  | | | |           e2 & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9, all_52_9)
% 230.15/41.47  | | | |           = e3 & op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 230.15/41.47  | | | |             all_52_13) = e1 & op(all_52_15, all_52_15) = e0 & op(e2, e3)
% 230.15/41.47  | | | |           = all_52_9 & op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13 &
% 230.15/41.47  | | | |           op(e2, e0) = all_52_15 & $i(all_52_9) & $i(all_52_11) &
% 230.15/41.47  | | | |           $i(all_52_13) & $i(all_52_15))
% 230.15/41.47  | | | | 
% 230.15/41.47  | | | | BETA: splitting (33) gives:
% 230.15/41.47  | | | | 
% 230.15/41.47  | | | | Case 1:
% 230.15/41.47  | | | | | 
% 230.15/41.47  | | | | |   (34)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 230.15/41.47  | | | | |         & op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 230.15/41.47  | | | | |         op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 230.15/41.47  | | | | |         op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) =
% 230.15/41.47  | | | | |         all_52_5 & op(e3, e0) = all_52_7 & $i(all_52_1) & $i(all_52_3)
% 230.15/41.47  | | | | |         & $i(all_52_5) & $i(all_52_7)
% 230.15/41.47  | | | | | 
% 230.15/41.47  | | | | | ALPHA: (34) implies:
% 230.15/41.47  | | | | |   (35)  op(e3, e0) = all_52_7
% 230.15/41.47  | | | | |   (36)  op(all_52_7, all_52_7) = e0
% 230.15/41.47  | | | | | 
% 230.15/41.47  | | | | | REF_CLOSE: (3), (5), (9), (15), (27), (35), (36) are inconsistent by
% 230.15/41.47  | | | | |            sub-proof #1001.
% 230.15/41.47  | | | | | 
% 230.15/41.47  | | | | Case 2:
% 230.15/41.47  | | | | | 
% 230.15/41.47  | | | | |   (37)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 230.15/41.47  | | | | |         e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11, all_52_11) =
% 230.15/41.47  | | | | |         e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15, all_52_15)
% 230.15/41.47  | | | | |         = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 & op(e2,
% 230.15/41.47  | | | | |           e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 230.15/41.47  | | | | |         $i(all_52_11) & $i(all_52_13) & $i(all_52_15)
% 230.15/41.47  | | | | | 
% 230.15/41.47  | | | | | ALPHA: (37) implies:
% 230.15/41.47  | | | | |   (38)  op(e2, e2) = all_52_11
% 230.15/41.47  | | | | |   (39)  op(all_52_11, all_52_11) = e2
% 230.15/41.47  | | | | | 
% 230.15/41.47  | | | | | BETA: splitting (30) gives:
% 230.15/41.47  | | | | | 
% 230.15/41.47  | | | | | Case 1:
% 230.15/41.47  | | | | | | 
% 230.15/41.47  | | | | | |   (40)   ~ (all_48_0 = e2) & op(all_48_1, e3) = all_48_0 & op(e3,
% 230.15/41.47  | | | | | |           e0) = all_48_1 & $i(all_48_0) & $i(all_48_1)
% 230.15/41.47  | | | | | | 
% 230.15/41.47  | | | | | | ALPHA: (40) implies:
% 230.15/41.47  | | | | | |   (41)  op(e3, e0) = all_48_1
% 230.15/41.47  | | | | | | 
% 230.15/41.47  | | | | | | BETA: splitting (5) gives:
% 230.15/41.47  | | | | | | 
% 230.15/41.47  | | | | | | Case 1:
% 230.15/41.47  | | | | | | | 
% 230.15/41.47  | | | | | | | 
% 230.15/41.47  | | | | | | | GROUND_INST: instantiating (3) with e1, all_52_11, e2, e2,
% 230.15/41.47  | | | | | | |              simplifying with (7), (38) gives:
% 230.15/41.47  | | | | | | |   (42)  all_52_11 = e1
% 230.15/41.47  | | | | | | | 
% 230.15/41.47  | | | | | | | REDUCE: (39), (42) imply:
% 230.15/41.47  | | | | | | |   (43)  op(e1, e1) = e2
% 230.15/41.47  | | | | | | | 
% 230.15/41.47  | | | | | | | REF_CLOSE: (3), (15), (22), (43) are inconsistent by sub-proof
% 230.15/41.47  | | | | | | |            #2423.
% 230.15/41.47  | | | | | | | 
% 230.15/41.47  | | | | | | Case 2:
% 230.15/41.47  | | | | | | | 
% 230.15/41.47  | | | | | | |   (44)   ~ (all_18_1 = e2) & op(e3, e0) = all_18_1 & $i(all_18_1)
% 230.15/41.47  | | | | | | | 
% 230.15/41.47  | | | | | | | ALPHA: (44) implies:
% 230.15/41.47  | | | | | | |   (45)   ~ (all_18_1 = e2)
% 230.15/41.47  | | | | | | |   (46)  op(e3, e0) = all_18_1
% 230.15/41.47  | | | | | | | 
% 230.15/41.47  | | | | | | | GROUND_INST: instantiating (3) with e1, all_52_11, e2, e2,
% 230.15/41.47  | | | | | | |              simplifying with (7), (38) gives:
% 230.15/41.47  | | | | | | |   (47)  all_52_11 = e1
% 230.15/41.47  | | | | | | | 
% 230.15/41.47  | | | | | | | GROUND_INST: instantiating (3) with e1, all_48_1, e0, e3,
% 230.15/41.47  | | | | | | |              simplifying with (9), (41) gives:
% 230.15/41.47  | | | | | | |   (48)  all_48_1 = e1
% 230.15/41.47  | | | | | | | 
% 230.15/41.47  | | | | | | | GROUND_INST: instantiating (3) with all_18_1, all_48_1, e0, e3,
% 230.15/41.47  | | | | | | |              simplifying with (41), (46) gives:
% 230.15/41.47  | | | | | | |   (49)  all_48_1 = all_18_1
% 230.15/41.47  | | | | | | | 
% 230.15/41.47  | | | | | | | COMBINE_EQS: (48), (49) imply:
% 230.15/41.47  | | | | | | |   (50)  all_18_1 = e1
% 230.15/41.47  | | | | | | | 
% 230.15/41.47  | | | | | | | REDUCE: (45), (50) imply:
% 230.15/41.47  | | | | | | |   (51)   ~ (e2 = e1)
% 230.15/41.47  | | | | | | | 
% 230.15/41.47  | | | | | | | REDUCE: (39), (47) imply:
% 230.15/41.47  | | | | | | |   (52)  op(e1, e1) = e2
% 230.15/41.47  | | | | | | | 
% 230.15/41.47  | | | | | | | REF_CLOSE: (3), (15), (22), (52) are inconsistent by sub-proof
% 230.15/41.47  | | | | | | |            #2423.
% 230.15/41.47  | | | | | | | 
% 230.15/41.47  | | | | | | End of split
% 230.15/41.47  | | | | | | 
% 230.15/41.47  | | | | | Case 2:
% 230.15/41.47  | | | | | | 
% 230.15/41.47  | | | | | |   (53)   ~ (all_48_1 = e1) & op(e3, e0) = all_48_1 & $i(all_48_1)
% 230.15/41.47  | | | | | | 
% 230.15/41.47  | | | | | | REF_CLOSE: (3), (5), (9), (53) are inconsistent by sub-proof #1000.
% 230.15/41.47  | | | | | | 
% 230.15/41.47  | | | | | End of split
% 230.15/41.47  | | | | | 
% 230.15/41.47  | | | | End of split
% 230.15/41.47  | | | | 
% 230.15/41.47  | | | Case 2:
% 230.15/41.47  | | | | 
% 230.15/41.47  | | | |   (54)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 230.15/41.47  | | | |           e0 & op(all_52_17, all_52_17) = e3 & op(all_52_19, all_52_19)
% 230.15/41.47  | | | |           = e2 & op(all_52_21, all_52_21) = e1 & op(all_52_23,
% 230.15/41.47  | | | |             all_52_23) = e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 230.15/41.47  | | | |           all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23 &
% 230.15/41.47  | | | |           $i(all_52_17) & $i(all_52_19) & $i(all_52_21) & $i(all_52_23))
% 230.15/41.47  | | | |         | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30
% 230.15/41.47  | | | |           = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 230.15/41.47  | | | |             all_52_27) = e2 & op(all_52_29, all_52_29) = e1 &
% 230.15/41.47  | | | |           op(all_52_31, all_52_31) = e0 & op(e0, e3) = all_52_25 &
% 230.15/41.47  | | | |           op(e0, e2) = all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0) =
% 230.15/41.47  | | | |           all_52_31 & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 230.15/41.47  | | | |           $i(all_52_31))
% 230.15/41.47  | | | | 
% 230.15/41.47  | | | | BETA: splitting (54) gives:
% 230.15/41.47  | | | | 
% 230.15/41.47  | | | | Case 1:
% 230.15/41.47  | | | | | 
% 230.15/41.47  | | | | |   (55)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 230.15/41.47  | | | | |         e0 & op(all_52_17, all_52_17) = e3 & op(all_52_19, all_52_19)
% 230.15/41.47  | | | | |         = e2 & op(all_52_21, all_52_21) = e1 & op(all_52_23,
% 230.15/41.47  | | | | |           all_52_23) = e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 230.15/41.47  | | | | |         all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23 &
% 230.15/41.47  | | | | |         $i(all_52_17) & $i(all_52_19) & $i(all_52_21) & $i(all_52_23)
% 230.15/41.47  | | | | | 
% 230.15/41.47  | | | | | ALPHA: (55) implies:
% 230.15/41.47  | | | | |   (56)  op(e1, e3) = all_52_17
% 230.15/41.47  | | | | |   (57)  op(all_52_17, all_52_17) = e3
% 230.15/41.47  | | | | | 
% 230.15/41.47  | | | | | REF_CLOSE: (3), (5), (9), (11), (13), (14), (19), (20), (26), (30),
% 230.15/41.47  | | | | |            (56), (57) are inconsistent by sub-proof #999.
% 230.15/41.47  | | | | | 
% 230.15/41.47  | | | | Case 2:
% 230.15/41.47  | | | | | 
% 230.15/41.47  | | | | |   (58)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 230.15/41.47  | | | | |         e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27, all_52_27)
% 230.15/41.47  | | | | |         = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 230.15/41.47  | | | | |           all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) =
% 230.15/41.47  | | | | |         all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 &
% 230.15/41.47  | | | | |         $i(all_52_25) & $i(all_52_27) & $i(all_52_29) & $i(all_52_31)
% 230.15/41.47  | | | | | 
% 230.15/41.47  | | | | | ALPHA: (58) implies:
% 230.15/41.47  | | | | |   (59)  op(e0, e3) = all_52_25
% 230.15/41.47  | | | | |   (60)  op(all_52_25, all_52_25) = e3
% 230.15/41.47  | | | | | 
% 230.15/41.47  | | | | | BETA: splitting (8) gives:
% 230.15/41.47  | | | | | 
% 230.15/41.47  | | | | | Case 1:
% 230.15/41.47  | | | | | | 
% 230.15/41.47  | | | | | |   (61)   ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0,
% 230.15/41.47  | | | | | |           e3) = all_22_1 & $i(all_22_0) & $i(all_22_1)
% 230.15/41.47  | | | | | | 
% 230.15/41.47  | | | | | | ALPHA: (61) implies:
% 230.15/41.47  | | | | | |   (62)  op(e0, e3) = all_22_1
% 230.15/41.47  | | | | | | 
% 230.15/41.47  | | | | | | REF_CLOSE: (3), (4), (6), (10), (32), (59), (60), (62) are
% 230.15/41.47  | | | | | |            inconsistent by sub-proof #998.
% 230.15/41.47  | | | | | | 
% 230.15/41.47  | | | | | Case 2:
% 230.15/41.47  | | | | | | 
% 230.15/41.47  | | | | | |   (63)   ~ (all_22_1 = e2) & op(e0, e3) = all_22_1 & $i(all_22_1)
% 230.15/41.47  | | | | | | 
% 230.15/41.47  | | | | | | ALPHA: (63) implies:
% 230.15/41.47  | | | | | |   (64)  op(e0, e3) = all_22_1
% 230.15/41.47  | | | | | | 
% 230.15/41.47  | | | | | | REF_CLOSE: (3), (4), (6), (10), (32), (59), (60), (64) are
% 230.15/41.47  | | | | | |            inconsistent by sub-proof #998.
% 230.15/41.47  | | | | | | 
% 230.15/41.47  | | | | | End of split
% 230.15/41.47  | | | | | 
% 230.15/41.47  | | | | End of split
% 230.15/41.47  | | | | 
% 230.15/41.47  | | | End of split
% 230.15/41.47  | | | 
% 230.15/41.47  | | Case 2:
% 230.15/41.47  | | | 
% 230.15/41.47  | | |   (65)   ~ (all_12_1 = e1) & op(e0, e3) = all_12_1 & $i(all_12_1)
% 230.15/41.47  | | | 
% 230.15/41.47  | | | REF_CLOSE: (3), (8), (10), (65) are inconsistent by sub-proof #1148.
% 230.15/41.47  | | | 
% 230.15/41.47  | | End of split
% 230.15/41.47  | | 
% 230.15/41.47  | End of split
% 230.15/41.47  | 
% 230.15/41.47  End of proof
% 230.15/41.47  
% 230.15/41.47  Sub-proof #998 shows that the following formulas are inconsistent:
% 230.15/41.47  ----------------------------------------------------------------
% 230.15/41.47    (1)  op(e0, e3) = all_12_1
% 230.15/41.47    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.15/41.47           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.15/41.47    (3)   ~ (all_6_2 = e3)
% 230.15/41.47    (4)  op(e1, e1) = all_6_2
% 230.15/41.47    (5)  op(e0, e3) = all_52_25
% 230.15/41.47    (6)  op(e0, e3) = e1
% 230.15/41.47    (7)  op(e0, e3) = all_22_1
% 230.15/41.47    (8)  op(all_52_25, all_52_25) = e3
% 230.15/41.47  
% 230.15/41.47  Begin of proof
% 230.15/41.47  | 
% 230.15/41.47  | GROUND_INST: instantiating (2) with e1, all_22_1, e3, e0, simplifying with
% 230.15/41.47  |              (6), (7) gives:
% 230.15/41.47  |   (9)  all_22_1 = e1
% 230.15/41.47  | 
% 230.15/41.47  | GROUND_INST: instantiating (2) with all_22_1, all_52_25, e3, e0, simplifying
% 230.15/41.47  |              with (5), (7) gives:
% 230.15/41.47  |   (10)  all_52_25 = all_22_1
% 230.15/41.47  | 
% 230.15/41.47  | GROUND_INST: instantiating (2) with all_12_1, all_52_25, e3, e0, simplifying
% 230.15/41.47  |              with (1), (5) gives:
% 230.15/41.47  |   (11)  all_52_25 = all_12_1
% 230.15/41.47  | 
% 230.15/41.47  | COMBINE_EQS: (10), (11) imply:
% 230.15/41.47  |   (12)  all_22_1 = all_12_1
% 230.15/41.47  | 
% 230.15/41.47  | SIMP: (12) implies:
% 230.15/41.47  |   (13)  all_22_1 = all_12_1
% 230.15/41.47  | 
% 230.15/41.47  | COMBINE_EQS: (9), (13) imply:
% 230.15/41.47  |   (14)  all_12_1 = e1
% 230.15/41.47  | 
% 230.15/41.47  | SIMP: (14) implies:
% 230.15/41.47  |   (15)  all_12_1 = e1
% 230.15/41.47  | 
% 230.15/41.47  | COMBINE_EQS: (11), (15) imply:
% 230.15/41.47  |   (16)  all_52_25 = e1
% 230.15/41.47  | 
% 230.15/41.47  | REDUCE: (8), (16) imply:
% 230.15/41.47  |   (17)  op(e1, e1) = e3
% 230.15/41.47  | 
% 230.15/41.47  | REF_CLOSE: (2), (3), (4), (17) are inconsistent by sub-proof #2468.
% 230.15/41.47  | 
% 230.15/41.47  End of proof
% 230.15/41.47  
% 230.15/41.47  Sub-proof #999 shows that the following formulas are inconsistent:
% 230.15/41.47  ----------------------------------------------------------------
% 230.15/41.47    (1)  ( ~ (all_48_0 = e2) & op(all_48_1, e3) = all_48_0 & op(e3, e0) = all_48_1
% 230.15/41.47           & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 = e1) & op(e3, e0) =
% 230.15/41.47           all_48_1 & $i(all_48_1))
% 230.15/41.47    (2)   ~ (all_53_2 = e1)
% 230.15/41.47    (3)  op(e1, e3) = all_52_17
% 230.15/41.47    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.15/41.47           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.15/41.47    (5)  ( ~ (all_18_0 = e1) & op(all_18_1, e3) = all_18_0 & op(e3, e0) = all_18_1
% 230.15/41.47           & $i(all_18_0) & $i(all_18_1)) | ( ~ (all_18_1 = e2) & op(e3, e0) =
% 230.15/41.47           all_18_1 & $i(all_18_1))
% 230.15/41.47    (6)  op(all_52_17, all_52_17) = e3
% 230.15/41.47    (7)  op(e3, e0) = e1
% 230.15/41.47    (8)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 230.15/41.47    (9)   ~ (all_53_2 = e0)
% 230.15/41.47    (10)  op(e3, e3) = e0
% 230.15/41.47    (11)  all_55_8 = all_53_2
% 230.15/41.47    (12)  op(e1, e3) = all_53_2
% 230.15/41.47  
% 230.15/41.47  Begin of proof
% 230.15/41.47  | 
% 230.15/41.47  | BETA: splitting (1) gives:
% 230.15/41.47  | 
% 230.15/41.47  | Case 1:
% 230.15/41.47  | | 
% 230.15/41.47  | |   (13)   ~ (all_48_0 = e2) & op(all_48_1, e3) = all_48_0 & op(e3, e0) =
% 230.15/41.47  | |         all_48_1 & $i(all_48_0) & $i(all_48_1)
% 230.15/41.47  | | 
% 230.15/41.47  | | ALPHA: (13) implies:
% 230.15/41.47  | |   (14)   ~ (all_48_0 = e2)
% 230.15/41.47  | |   (15)  op(e3, e0) = all_48_1
% 230.15/41.47  | |   (16)  op(all_48_1, e3) = all_48_0
% 230.15/41.47  | | 
% 230.15/41.47  | | BETA: splitting (5) gives:
% 230.15/41.47  | | 
% 230.15/41.47  | | Case 1:
% 230.15/41.47  | | | 
% 230.15/41.47  | | |   (17)   ~ (all_18_0 = e1) & op(all_18_1, e3) = all_18_0 & op(e3, e0) =
% 230.15/41.47  | | |         all_18_1 & $i(all_18_0) & $i(all_18_1)
% 230.15/41.47  | | | 
% 230.15/41.47  | | | ALPHA: (17) implies:
% 230.15/41.47  | | |   (18)  op(e3, e0) = all_18_1
% 230.15/41.47  | | |   (19)  op(all_18_1, e3) = all_18_0
% 230.15/41.47  | | | 
% 230.15/41.47  | | | GROUND_INST: instantiating (4) with all_53_2, all_52_17, e3, e1,
% 230.15/41.47  | | |              simplifying with (3), (12) gives:
% 230.15/41.47  | | |   (20)  all_53_2 = all_52_17
% 230.15/41.47  | | | 
% 230.15/41.47  | | | GROUND_INST: instantiating (4) with e1, all_48_1, e0, e3, simplifying with
% 230.15/41.47  | | |              (7), (15) gives:
% 230.15/41.47  | | |   (21)  all_48_1 = e1
% 230.15/41.47  | | | 
% 230.15/41.47  | | | GROUND_INST: instantiating (4) with all_18_1, all_48_1, e0, e3,
% 230.15/41.47  | | |              simplifying with (15), (18) gives:
% 230.15/41.47  | | |   (22)  all_48_1 = all_18_1
% 230.15/41.47  | | | 
% 230.15/41.47  | | | COMBINE_EQS: (21), (22) imply:
% 230.15/41.47  | | |   (23)  all_18_1 = e1
% 230.15/41.47  | | | 
% 230.15/41.47  | | | COMBINE_EQS: (11), (20) imply:
% 230.15/41.47  | | |   (24)  all_55_8 = all_52_17
% 230.15/41.47  | | | 
% 230.15/41.47  | | | REDUCE: (2), (20) imply:
% 230.15/41.47  | | |   (25)   ~ (all_52_17 = e1)
% 230.15/41.47  | | | 
% 230.15/41.47  | | | REDUCE: (9), (20) imply:
% 230.15/41.47  | | |   (26)   ~ (all_52_17 = e0)
% 230.15/41.47  | | | 
% 230.15/41.47  | | | REDUCE: (16), (21) imply:
% 230.15/41.47  | | |   (27)  op(e1, e3) = all_48_0
% 230.15/41.47  | | | 
% 230.15/41.47  | | | REDUCE: (19), (23) imply:
% 230.15/41.47  | | |   (28)  op(e1, e3) = all_18_0
% 230.15/41.47  | | | 
% 230.15/41.47  | | | GROUND_INST: instantiating (4) with all_52_17, all_18_0, e3, e1,
% 230.15/41.47  | | |              simplifying with (3), (28) gives:
% 230.15/41.47  | | |   (29)  all_52_17 = all_18_0
% 230.15/41.47  | | | 
% 230.15/41.47  | | | GROUND_INST: instantiating (4) with all_52_17, all_48_0, e3, e1,
% 230.15/41.47  | | |              simplifying with (3), (27) gives:
% 230.15/41.47  | | |   (30)  all_52_17 = all_48_0
% 230.15/41.47  | | | 
% 230.15/41.47  | | | COMBINE_EQS: (29), (30) imply:
% 230.15/41.47  | | |   (31)  all_48_0 = all_18_0
% 230.15/41.47  | | | 
% 230.15/41.47  | | | COMBINE_EQS: (24), (29) imply:
% 230.15/41.47  | | |   (32)  all_55_8 = all_18_0
% 230.15/41.47  | | | 
% 230.15/41.47  | | | REDUCE: (26), (29) imply:
% 230.15/41.47  | | |   (33)   ~ (all_18_0 = e0)
% 230.15/41.47  | | | 
% 230.15/41.47  | | | REDUCE: (14), (31) imply:
% 230.15/41.47  | | |   (34)   ~ (all_18_0 = e2)
% 230.15/41.47  | | | 
% 230.15/41.47  | | | REDUCE: (6), (29) imply:
% 230.15/41.47  | | |   (35)  op(all_18_0, all_18_0) = e3
% 230.15/41.47  | | | 
% 230.15/41.47  | | | BETA: splitting (8) gives:
% 230.15/41.47  | | | 
% 230.15/41.47  | | | Case 1:
% 230.15/41.47  | | | | 
% 230.15/41.47  | | | |   (36)  all_55_8 = e3
% 230.15/41.47  | | | | 
% 230.15/41.47  | | | | COMBINE_EQS: (32), (36) imply:
% 230.15/41.47  | | | |   (37)  all_18_0 = e3
% 230.15/41.47  | | | | 
% 230.15/41.47  | | | | SIMP: (37) implies:
% 230.15/41.47  | | | |   (38)  all_18_0 = e3
% 230.15/41.47  | | | | 
% 230.15/41.47  | | | | REDUCE: (33), (38) imply:
% 230.15/41.47  | | | |   (39)   ~ (e3 = e0)
% 230.15/41.47  | | | | 
% 230.15/41.47  | | | | REDUCE: (35), (38) imply:
% 230.15/41.47  | | | |   (40)  op(e3, e3) = e3
% 230.15/41.47  | | | | 
% 230.15/41.47  | | | | REF_CLOSE: (4), (10), (39), (40) are inconsistent by sub-proof #2494.
% 230.15/41.47  | | | | 
% 230.15/41.47  | | | Case 2:
% 230.15/41.47  | | | | 
% 230.15/41.47  | | | |   (41)  all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 230.15/41.47  | | | | 
% 230.15/41.47  | | | | BETA: splitting (41) gives:
% 230.15/41.47  | | | | 
% 230.15/41.47  | | | | Case 1:
% 230.15/41.47  | | | | | 
% 230.15/41.47  | | | | |   (42)  all_55_8 = e2
% 230.15/41.47  | | | | | 
% 230.15/41.47  | | | | | REF_CLOSE: (32), (34), (42) are inconsistent by sub-proof #1209.
% 230.15/41.47  | | | | | 
% 230.15/41.47  | | | | Case 2:
% 230.15/41.47  | | | | | 
% 230.15/41.47  | | | | |   (43)  all_55_8 = e1 | all_55_8 = e0
% 230.15/41.47  | | | | | 
% 230.15/41.47  | | | | | REF_CLOSE: (24), (25), (26), (43) are inconsistent by sub-proof #1878.
% 230.15/41.47  | | | | | 
% 230.15/41.47  | | | | End of split
% 230.15/41.47  | | | | 
% 230.15/41.47  | | | End of split
% 230.15/41.47  | | | 
% 230.15/41.47  | | Case 2:
% 230.15/41.47  | | | 
% 230.15/41.47  | | |   (44)   ~ (all_18_1 = e2) & op(e3, e0) = all_18_1 & $i(all_18_1)
% 230.15/41.47  | | | 
% 230.15/41.47  | | | ALPHA: (44) implies:
% 230.15/41.47  | | |   (45)  op(e3, e0) = all_18_1
% 230.15/41.47  | | | 
% 230.15/41.47  | | | GROUND_INST: instantiating (4) with all_53_2, all_52_17, e3, e1,
% 230.15/41.47  | | |              simplifying with (3), (12) gives:
% 230.15/41.47  | | |   (46)  all_53_2 = all_52_17
% 230.15/41.47  | | | 
% 230.15/41.47  | | | GROUND_INST: instantiating (4) with e1, all_48_1, e0, e3, simplifying with
% 230.15/41.47  | | |              (7), (15) gives:
% 230.15/41.47  | | |   (47)  all_48_1 = e1
% 230.15/41.47  | | | 
% 230.15/41.47  | | | GROUND_INST: instantiating (4) with all_18_1, all_48_1, e0, e3,
% 230.15/41.47  | | |              simplifying with (15), (45) gives:
% 230.15/41.47  | | |   (48)  all_48_1 = all_18_1
% 230.15/41.47  | | | 
% 230.15/41.47  | | | COMBINE_EQS: (47), (48) imply:
% 230.15/41.47  | | |   (49)  all_18_1 = e1
% 230.15/41.47  | | | 
% 230.15/41.47  | | | COMBINE_EQS: (11), (46) imply:
% 230.15/41.47  | | |   (50)  all_55_8 = all_52_17
% 230.15/41.47  | | | 
% 230.15/41.47  | | | REDUCE: (2), (46) imply:
% 230.15/41.47  | | |   (51)   ~ (all_52_17 = e1)
% 230.15/41.47  | | | 
% 230.15/41.47  | | | REDUCE: (9), (46) imply:
% 230.15/41.47  | | |   (52)   ~ (all_52_17 = e0)
% 230.15/41.47  | | | 
% 230.15/41.47  | | | REDUCE: (16), (47) imply:
% 230.15/41.47  | | |   (53)  op(e1, e3) = all_48_0
% 230.15/41.47  | | | 
% 230.15/41.47  | | | GROUND_INST: instantiating (4) with all_52_17, all_48_0, e3, e1,
% 230.15/41.47  | | |              simplifying with (3), (53) gives:
% 230.15/41.47  | | |   (54)  all_52_17 = all_48_0
% 230.15/41.47  | | | 
% 230.15/41.47  | | | COMBINE_EQS: (50), (54) imply:
% 230.15/41.47  | | |   (55)  all_55_8 = all_48_0
% 230.15/41.47  | | | 
% 230.15/41.47  | | | REDUCE: (52), (54) imply:
% 230.15/41.47  | | |   (56)   ~ (all_48_0 = e0)
% 230.15/41.47  | | | 
% 230.15/41.47  | | | REDUCE: (6), (54) imply:
% 230.15/41.47  | | |   (57)  op(all_48_0, all_48_0) = e3
% 230.15/41.47  | | | 
% 230.15/41.47  | | | BETA: splitting (8) gives:
% 230.15/41.47  | | | 
% 230.15/41.47  | | | Case 1:
% 230.15/41.47  | | | | 
% 230.15/41.47  | | | |   (58)  all_55_8 = e3
% 230.15/41.47  | | | | 
% 230.15/41.47  | | | | COMBINE_EQS: (55), (58) imply:
% 230.15/41.47  | | | |   (59)  all_48_0 = e3
% 230.15/41.47  | | | | 
% 230.15/41.47  | | | | SIMP: (59) implies:
% 230.15/41.47  | | | |   (60)  all_48_0 = e3
% 230.15/41.47  | | | | 
% 230.15/41.47  | | | | REDUCE: (56), (60) imply:
% 230.15/41.47  | | | |   (61)   ~ (e3 = e0)
% 230.15/41.47  | | | | 
% 230.15/41.47  | | | | REDUCE: (57), (60) imply:
% 230.15/41.47  | | | |   (62)  op(e3, e3) = e3
% 230.15/41.47  | | | | 
% 230.15/41.47  | | | | REF_CLOSE: (4), (10), (61), (62) are inconsistent by sub-proof #2494.
% 230.15/41.47  | | | | 
% 230.15/41.47  | | | Case 2:
% 230.15/41.47  | | | | 
% 230.15/41.47  | | | |   (63)  all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 230.15/41.47  | | | | 
% 230.15/41.47  | | | | BETA: splitting (63) gives:
% 230.15/41.47  | | | | 
% 230.15/41.47  | | | | Case 1:
% 230.15/41.47  | | | | | 
% 230.15/41.47  | | | | |   (64)  all_55_8 = e2
% 230.15/41.47  | | | | | 
% 230.15/41.47  | | | | | COMBINE_EQS: (55), (64) imply:
% 230.15/41.47  | | | | |   (65)  all_48_0 = e2
% 230.15/41.47  | | | | | 
% 230.15/41.47  | | | | | SIMP: (65) implies:
% 230.15/41.47  | | | | |   (66)  all_48_0 = e2
% 230.15/41.47  | | | | | 
% 230.15/41.47  | | | | | REDUCE: (14), (66) imply:
% 230.15/41.47  | | | | |   (67)  $false
% 230.15/41.47  | | | | | 
% 230.15/41.47  | | | | | CLOSE: (67) is inconsistent.
% 230.15/41.47  | | | | | 
% 230.15/41.47  | | | | Case 2:
% 230.15/41.47  | | | | | 
% 230.15/41.47  | | | | |   (68)  all_55_8 = e1 | all_55_8 = e0
% 230.15/41.47  | | | | | 
% 230.15/41.47  | | | | | REF_CLOSE: (50), (51), (52), (68) are inconsistent by sub-proof #1878.
% 230.15/41.47  | | | | | 
% 230.15/41.47  | | | | End of split
% 230.15/41.47  | | | | 
% 230.15/41.47  | | | End of split
% 230.15/41.47  | | | 
% 230.15/41.47  | | End of split
% 230.15/41.47  | | 
% 230.15/41.47  | Case 2:
% 230.15/41.47  | | 
% 230.15/41.47  | |   (69)   ~ (all_48_1 = e1) & op(e3, e0) = all_48_1 & $i(all_48_1)
% 230.15/41.47  | | 
% 230.15/41.47  | | REF_CLOSE: (4), (5), (7), (69) are inconsistent by sub-proof #1000.
% 230.15/41.47  | | 
% 230.15/41.47  | End of split
% 230.15/41.47  | 
% 230.15/41.47  End of proof
% 230.15/41.47  
% 230.15/41.47  Sub-proof #1000 shows that the following formulas are inconsistent:
% 230.15/41.47  ----------------------------------------------------------------
% 230.15/41.47    (1)   ~ (all_48_1 = e1) & op(e3, e0) = all_48_1 & $i(all_48_1)
% 230.15/41.47    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.15/41.47           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.15/41.47    (3)  ( ~ (all_18_0 = e1) & op(all_18_1, e3) = all_18_0 & op(e3, e0) = all_18_1
% 230.15/41.47           & $i(all_18_0) & $i(all_18_1)) | ( ~ (all_18_1 = e2) & op(e3, e0) =
% 230.15/41.47           all_18_1 & $i(all_18_1))
% 230.15/41.47    (4)  op(e3, e0) = e1
% 230.15/41.47  
% 230.15/41.47  Begin of proof
% 230.15/41.47  | 
% 230.15/41.47  | ALPHA: (1) implies:
% 230.15/41.47  |   (5)   ~ (all_48_1 = e1)
% 230.15/41.47  |   (6)  op(e3, e0) = all_48_1
% 230.15/41.47  | 
% 230.15/41.47  | BETA: splitting (3) gives:
% 230.15/41.47  | 
% 230.15/41.47  | Case 1:
% 230.15/41.47  | | 
% 230.15/41.47  | |   (7)   ~ (all_18_0 = e1) & op(all_18_1, e3) = all_18_0 & op(e3, e0) =
% 230.15/41.47  | |        all_18_1 & $i(all_18_0) & $i(all_18_1)
% 230.15/41.47  | | 
% 230.15/41.47  | | ALPHA: (7) implies:
% 230.15/41.48  | |   (8)  op(e3, e0) = all_18_1
% 230.15/41.48  | | 
% 230.15/41.48  | | REF_CLOSE: (2), (4), (5), (6), (8) are inconsistent by sub-proof #1207.
% 230.15/41.48  | | 
% 230.15/41.48  | Case 2:
% 230.15/41.48  | | 
% 230.15/41.48  | |   (9)   ~ (all_18_1 = e2) & op(e3, e0) = all_18_1 & $i(all_18_1)
% 230.15/41.48  | | 
% 230.15/41.48  | | ALPHA: (9) implies:
% 230.15/41.48  | |   (10)  op(e3, e0) = all_18_1
% 230.15/41.48  | | 
% 230.15/41.48  | | REF_CLOSE: (2), (4), (5), (6), (10) are inconsistent by sub-proof #1207.
% 230.15/41.48  | | 
% 230.15/41.48  | End of split
% 230.15/41.48  | 
% 230.15/41.48  End of proof
% 230.15/41.48  
% 230.15/41.48  Sub-proof #1001 shows that the following formulas are inconsistent:
% 230.15/41.48  ----------------------------------------------------------------
% 230.15/41.48    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.15/41.48           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.15/41.48    (2)  ( ~ (all_18_0 = e1) & op(all_18_1, e3) = all_18_0 & op(e3, e0) = all_18_1
% 230.15/41.48           & $i(all_18_0) & $i(all_18_1)) | ( ~ (all_18_1 = e2) & op(e3, e0) =
% 230.15/41.48           all_18_1 & $i(all_18_1))
% 230.15/41.48    (3)  op(all_52_7, all_52_7) = e0
% 230.15/41.48    (4)  op(e3, e0) = e1
% 230.15/41.48    (5)  op(e1, e1) = e1
% 230.15/41.48    (6)   ~ (e1 = e0)
% 230.15/41.48    (7)  op(e3, e0) = all_52_7
% 230.15/41.48  
% 230.15/41.48  Begin of proof
% 230.15/41.48  | 
% 230.15/41.48  | BETA: splitting (2) gives:
% 230.15/41.48  | 
% 230.15/41.48  | Case 1:
% 230.15/41.48  | | 
% 230.15/41.48  | |   (8)   ~ (all_18_0 = e1) & op(all_18_1, e3) = all_18_0 & op(e3, e0) =
% 230.15/41.48  | |        all_18_1 & $i(all_18_0) & $i(all_18_1)
% 230.15/41.48  | | 
% 230.15/41.48  | | ALPHA: (8) implies:
% 230.15/41.48  | |   (9)  op(e3, e0) = all_18_1
% 230.15/41.48  | | 
% 230.15/41.48  | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (9) are inconsistent by sub-proof
% 230.15/41.48  | |            #1002.
% 230.15/41.48  | | 
% 230.15/41.48  | Case 2:
% 230.15/41.48  | | 
% 230.15/41.48  | |   (10)   ~ (all_18_1 = e2) & op(e3, e0) = all_18_1 & $i(all_18_1)
% 230.15/41.48  | | 
% 230.15/41.48  | | ALPHA: (10) implies:
% 230.15/41.48  | |   (11)  op(e3, e0) = all_18_1
% 230.15/41.48  | | 
% 230.15/41.48  | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (11) are inconsistent by sub-proof
% 230.15/41.48  | |            #1002.
% 230.15/41.48  | | 
% 230.15/41.48  | End of split
% 230.15/41.48  | 
% 230.15/41.48  End of proof
% 230.15/41.48  
% 230.15/41.48  Sub-proof #1002 shows that the following formulas are inconsistent:
% 230.15/41.48  ----------------------------------------------------------------
% 230.15/41.48    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.15/41.48           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.15/41.48    (2)  op(all_52_7, all_52_7) = e0
% 230.15/41.48    (3)  op(e3, e0) = e1
% 230.15/41.48    (4)  op(e1, e1) = e1
% 230.15/41.48    (5)   ~ (e1 = e0)
% 230.15/41.48    (6)  op(e3, e0) = all_18_1
% 230.15/41.48    (7)  op(e3, e0) = all_52_7
% 230.15/41.48  
% 230.15/41.48  Begin of proof
% 230.15/41.48  | 
% 230.15/41.48  | GROUND_INST: instantiating (1) with e1, all_52_7, e0, e3, simplifying with
% 230.15/41.48  |              (3), (7) gives:
% 230.15/41.48  |   (8)  all_52_7 = e1
% 230.15/41.48  | 
% 230.15/41.48  | GROUND_INST: instantiating (1) with all_18_1, all_52_7, e0, e3, simplifying
% 230.15/41.48  |              with (6), (7) gives:
% 230.15/41.48  |   (9)  all_52_7 = all_18_1
% 230.15/41.48  | 
% 230.15/41.48  | COMBINE_EQS: (8), (9) imply:
% 230.15/41.48  |   (10)  all_18_1 = e1
% 230.15/41.48  | 
% 230.15/41.48  | REDUCE: (2), (8) imply:
% 230.15/41.48  |   (11)  op(e1, e1) = e0
% 230.15/41.48  | 
% 230.15/41.48  | REF_CLOSE: (1), (4), (5), (11) are inconsistent by sub-proof #2427.
% 230.15/41.48  | 
% 230.15/41.48  End of proof
% 230.15/41.48  
% 230.15/41.48  Sub-proof #1003 shows that the following formulas are inconsistent:
% 230.15/41.48  ----------------------------------------------------------------
% 230.15/41.48    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.15/41.48         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.15/41.48    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.15/41.48         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.15/41.48    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.15/41.48         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.15/41.48    (4)   ~ (e3 = e1)
% 230.15/41.48    (5)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.15/41.48         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.15/41.48    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.15/41.48           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.15/41.48    (7)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.15/41.48         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.15/41.48    (8)   ~ (all_6_2 = e3)
% 230.15/41.48    (9)  op(e1, e1) = all_6_2
% 230.15/41.48    (10)  op(e2, e2) = e1
% 230.15/41.48    (11)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.15/41.48          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.15/41.48    (12)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 230.15/41.48            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 230.15/41.48              e3) = all_22_1 & $i(all_22_1))
% 230.15/41.48    (13)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.15/41.48          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.15/41.48    (14)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.15/41.48          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.15/41.48    (15)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 230.15/41.48          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.15/41.48    (16)   ~ (e3 = e2)
% 230.15/41.48    (17)   ~ (e3 = e0)
% 230.15/41.48    (18)  op(e0, e3) = e1
% 230.15/41.48    (19)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.15/41.48          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.15/41.48    (20)  op(e0, e3) = all_53_3
% 230.15/41.48    (21)  all_57_0 = e0
% 230.15/41.48    (22)  all_57_15 = e3
% 230.15/41.48    (23)  all_57_4 = e1
% 230.15/41.48    (24)  op(e3, e3) = e0
% 230.15/41.48    (25)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.15/41.48          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.15/41.48            e1)
% 230.15/41.48    (26)  all_57_12 = e1
% 230.15/41.48    (27)  op(e1, e1) = e1
% 230.15/41.48    (28)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.15/41.48          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.15/41.48    (29)   ~ (e2 = e0)
% 230.15/41.48    (30)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 230.15/41.48            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 230.15/41.48              e3) = all_12_1 & $i(all_12_1))
% 230.15/41.48    (31)  all_57_3 = e1
% 230.15/41.48    (32)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.15/41.48          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.15/41.48    (33)   ~ (e1 = e0)
% 230.15/41.48    (34)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 230.15/41.48          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 230.15/41.48    (35)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.15/41.48          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.15/41.48    (36)  op(e0, e0) = e3
% 230.15/41.48    (37)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.15/41.48          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.15/41.48            e2)
% 230.15/41.48    (38)   ~ (all_53_3 = e0)
% 230.15/41.48    (39)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.15/41.48              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.15/41.48                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.15/41.48                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.15/41.48    (40)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.15/41.48          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.15/41.48    (41)   ~ (all_53_12 = e3)
% 230.15/41.48    (42)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.15/41.48          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.15/41.48    (43)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.15/41.48          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.15/41.48    (44)   ~ (all_53_12 = e0)
% 230.15/41.48    (45)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.15/41.48          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 230.15/41.48    (46)   ~ (e2 = e1)
% 230.15/41.48    (47)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.15/41.48          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.15/41.48    (48)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.15/41.48          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.15/41.48    (49)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.15/41.48          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.15/41.48    (50)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.15/41.48          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.15/41.48    (51)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.15/41.48          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.15/41.48    (52)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.15/41.48          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.15/41.48    (53)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.15/41.48          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.15/41.48    (54)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.15/41.48          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.15/41.48    (55)  op(e3, e0) = all_53_12
% 230.15/41.48  
% 230.15/41.48  Begin of proof
% 230.15/41.48  | 
% 230.15/41.48  | BETA: splitting (32) gives:
% 230.15/41.48  | 
% 230.15/41.48  | Case 1:
% 230.15/41.48  | | 
% 230.15/41.48  | |   (56)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) =
% 230.15/41.48  | |           e3)
% 230.15/41.48  | | 
% 230.15/41.48  | | BETA: splitting (56) gives:
% 230.15/41.48  | | 
% 230.15/41.48  | | Case 1:
% 230.15/41.48  | | | 
% 230.15/41.48  | | |   (57)  all_57_0 = e3 & op(e3, e3) = e3
% 230.15/41.48  | | | 
% 230.15/41.48  | | | ALPHA: (57) implies:
% 230.15/41.48  | | |   (58)  op(e3, e3) = e3
% 230.15/41.48  | | | 
% 230.15/41.48  | | | REF_CLOSE: (6), (17), (24), (58) are inconsistent by sub-proof #2494.
% 230.15/41.48  | | | 
% 230.15/41.48  | | Case 2:
% 230.15/41.48  | | | 
% 230.15/41.48  | | |   (59)  all_57_1 = e3 & op(e3, e2) = e3
% 230.15/41.48  | | | 
% 230.15/41.48  | | | ALPHA: (59) implies:
% 230.15/41.48  | | |   (60)  all_57_1 = e3
% 230.15/41.48  | | | 
% 230.15/41.48  | | | BETA: splitting (34) gives:
% 230.15/41.48  | | | 
% 230.15/41.48  | | | Case 1:
% 230.15/41.48  | | | | 
% 230.15/41.48  | | | |   (61)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1)
% 230.15/41.48  | | | |           = e3)
% 230.15/41.48  | | | | 
% 230.15/41.48  | | | | BETA: splitting (61) gives:
% 230.15/41.48  | | | | 
% 230.15/41.48  | | | | Case 1:
% 230.15/41.48  | | | | | 
% 230.15/41.48  | | | | |   (62)  all_57_4 = e3 & op(e3, e1) = e3
% 230.15/41.48  | | | | | 
% 230.15/41.48  | | | | | ALPHA: (62) implies:
% 230.15/41.48  | | | | |   (63)  all_57_4 = e3
% 230.15/41.48  | | | | | 
% 230.15/41.48  | | | | | REF_CLOSE: (4), (6), (11), (13), (14), (16), (17), (24), (29), (33),
% 230.15/41.48  | | | | |            (46), (60), (63) are inconsistent by sub-proof #1220.
% 230.15/41.48  | | | | | 
% 230.15/41.48  | | | | Case 2:
% 230.15/41.48  | | | | | 
% 230.15/41.48  | | | | |   (64)  all_57_5 = e3 & op(e2, e1) = e3
% 230.15/41.48  | | | | | 
% 230.15/41.48  | | | | | ALPHA: (64) implies:
% 230.15/41.48  | | | | |   (65)  all_57_5 = e3
% 230.15/41.48  | | | | | 
% 230.15/41.48  | | | | | BETA: splitting (45) gives:
% 230.15/41.48  | | | | | 
% 230.15/41.48  | | | | | Case 1:
% 230.15/41.48  | | | | | | 
% 230.15/41.48  | | | | | |   (66)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2,
% 230.15/41.48  | | | | | |             e2) = e0)
% 230.15/41.48  | | | | | | 
% 230.15/41.48  | | | | | | BETA: splitting (66) gives:
% 230.15/41.48  | | | | | | 
% 230.15/41.48  | | | | | | Case 1:
% 230.15/41.48  | | | | | | | 
% 230.15/41.48  | | | | | | |   (67)  all_57_2 = e0 & op(e2, e3) = e0
% 230.15/41.48  | | | | | | | 
% 230.15/41.48  | | | | | | | ALPHA: (67) implies:
% 230.15/41.48  | | | | | | |   (68)  all_57_2 = e0
% 230.15/41.48  | | | | | | | 
% 230.15/41.48  | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 230.15/41.48  | | | | | | |            (11), (13), (14), (15), (16), (17), (19), (20), (22),
% 230.15/41.48  | | | | | | |            (24), (25), (28), (29), (31), (32), (33), (34), (35),
% 230.15/41.48  | | | | | | |            (36), (37), (38), (39), (41), (42), (43), (44), (46),
% 230.15/41.48  | | | | | | |            (47), (48), (49), (50), (51), (52), (53), (54), (55),
% 230.15/41.48  | | | | | | |            (65), (68) are inconsistent by sub-proof #1021.
% 230.15/41.48  | | | | | | | 
% 230.15/41.48  | | | | | | Case 2:
% 230.15/41.48  | | | | | | | 
% 230.15/41.48  | | | | | | |   (69)  all_57_3 = e0 & op(e2, e2) = e0
% 230.15/41.48  | | | | | | | 
% 230.15/41.48  | | | | | | | ALPHA: (69) implies:
% 230.15/41.48  | | | | | | |   (70)  op(e2, e2) = e0
% 230.15/41.48  | | | | | | | 
% 230.15/41.48  | | | | | | | REF_CLOSE: (6), (10), (33), (70) are inconsistent by sub-proof
% 230.15/41.48  | | | | | | |            #2352.
% 230.15/41.48  | | | | | | | 
% 230.15/41.48  | | | | | | End of split
% 230.15/41.48  | | | | | | 
% 230.15/41.48  | | | | | Case 2:
% 230.15/41.48  | | | | | | 
% 230.15/41.48  | | | | | |   (71)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2,
% 230.15/41.48  | | | | | |             e0) = e0)
% 230.15/41.48  | | | | | | 
% 230.15/41.48  | | | | | | BETA: splitting (71) gives:
% 230.15/41.48  | | | | | | 
% 230.15/41.48  | | | | | | Case 1:
% 230.15/41.48  | | | | | | | 
% 230.15/41.48  | | | | | | |   (72)  all_57_5 = e0 & op(e2, e1) = e0
% 230.15/41.48  | | | | | | | 
% 230.15/41.48  | | | | | | | REF_CLOSE: (4), (6), (17), (23), (24), (32), (41), (55), (60),
% 230.15/41.48  | | | | | | |            (65), (72) are inconsistent by sub-proof #1020.
% 230.15/41.48  | | | | | | | 
% 230.15/41.48  | | | | | | Case 2:
% 230.15/41.48  | | | | | | | 
% 230.15/41.48  | | | | | | |   (73)  all_57_10 = e0 & op(e2, e0) = e0
% 230.15/41.48  | | | | | | | 
% 230.15/41.48  | | | | | | | ALPHA: (73) implies:
% 230.15/41.48  | | | | | | |   (74)  all_57_10 = e0
% 230.15/41.48  | | | | | | | 
% 230.15/41.48  | | | | | | | BETA: splitting (51) gives:
% 230.15/41.48  | | | | | | | 
% 230.15/41.48  | | | | | | | Case 1:
% 230.15/41.48  | | | | | | | | 
% 230.15/41.48  | | | | | | | |   (75)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 &
% 230.15/41.48  | | | | | | | |           op(e2, e0) = e1)
% 230.15/41.48  | | | | | | | | 
% 230.15/41.48  | | | | | | | | BETA: splitting (75) gives:
% 230.15/41.48  | | | | | | | | 
% 230.15/41.48  | | | | | | | | Case 1:
% 230.15/41.48  | | | | | | | | | 
% 230.15/41.48  | | | | | | | | |   (76)  all_57_9 = e1 & op(e3, e0) = e1
% 230.15/41.48  | | | | | | | | | 
% 230.15/41.48  | | | | | | | | | ALPHA: (76) implies:
% 230.15/41.48  | | | | | | | | |   (77)  all_57_9 = e1
% 230.15/41.48  | | | | | | | | | 
% 230.15/41.48  | | | | | | | | | REF_CLOSE: (6), (12), (16), (18), (22), (29), (30), (46),
% 230.15/41.48  | | | | | | | | |            (47), (74), (77) are inconsistent by sub-proof
% 230.15/41.48  | | | | | | | | |            #1018.
% 230.15/41.48  | | | | | | | | | 
% 230.15/41.48  | | | | | | | | Case 2:
% 230.15/41.48  | | | | | | | | | 
% 230.15/41.48  | | | | | | | | |   (78)  all_57_10 = e1 & op(e2, e0) = e1
% 230.15/41.48  | | | | | | | | | 
% 230.15/41.48  | | | | | | | | | ALPHA: (78) implies:
% 230.15/41.48  | | | | | | | | |   (79)  all_57_10 = e1
% 230.15/41.48  | | | | | | | | | 
% 230.15/41.48  | | | | | | | | | COMBINE_EQS: (74), (79) imply:
% 230.15/41.48  | | | | | | | | |   (80)  e1 = e0
% 230.15/41.48  | | | | | | | | | 
% 230.15/41.48  | | | | | | | | | REF_CLOSE: (1), (4), (16), (29), (31), (33), (42), (46), (65),
% 230.15/41.48  | | | | | | | | |            (74), (80) are inconsistent by sub-proof #1017.
% 230.15/41.48  | | | | | | | | | 
% 230.15/41.48  | | | | | | | | End of split
% 230.15/41.48  | | | | | | | | 
% 230.15/41.48  | | | | | | | Case 2:
% 230.15/41.48  | | | | | | | | 
% 230.15/41.48  | | | | | | | |   (81)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 &
% 230.15/41.48  | | | | | | | |           op(e0, e0) = e1)
% 230.15/41.48  | | | | | | | | 
% 230.15/41.48  | | | | | | | | BETA: splitting (81) gives:
% 230.15/41.48  | | | | | | | | 
% 230.15/41.48  | | | | | | | | Case 1:
% 230.15/41.48  | | | | | | | | | 
% 230.15/41.48  | | | | | | | | |   (82)  all_57_11 = e1 & op(e1, e0) = e1
% 230.15/41.48  | | | | | | | | | 
% 230.15/41.48  | | | | | | | | | ALPHA: (82) implies:
% 230.15/41.48  | | | | | | | | |   (83)  all_57_11 = e1
% 230.15/41.48  | | | | | | | | | 
% 230.15/41.48  | | | | | | | | | BETA: splitting (42) gives:
% 230.15/41.48  | | | | | | | | | 
% 230.15/41.48  | | | | | | | | | Case 1:
% 230.15/41.48  | | | | | | | | | | 
% 230.15/41.48  | | | | | | | | | |   (84)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 &
% 230.15/41.48  | | | | | | | | | |           op(e2, e2) = e2)
% 230.15/41.48  | | | | | | | | | | 
% 230.15/41.48  | | | | | | | | | | BETA: splitting (84) gives:
% 230.15/41.48  | | | | | | | | | | 
% 230.15/41.48  | | | | | | | | | | Case 1:
% 230.15/41.48  | | | | | | | | | | | 
% 230.15/41.48  | | | | | | | | | | |   (85)  all_57_2 = e2 & op(e2, e3) = e2
% 230.15/41.48  | | | | | | | | | | | 
% 230.15/41.48  | | | | | | | | | | | ALPHA: (85) implies:
% 230.15/41.48  | | | | | | | | | | |   (86)  all_57_2 = e2
% 230.15/41.48  | | | | | | | | | | | 
% 230.15/41.48  | | | | | | | | | | | BETA: splitting (5) gives:
% 230.15/41.48  | | | | | | | | | | | 
% 230.15/41.48  | | | | | | | | | | | Case 1:
% 230.15/41.48  | | | | | | | | | | | | 
% 230.15/41.48  | | | | | | | | | | | |   (87)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 230.15/41.48  | | | | | | | | | | | |           & op(e1, e2) = e0)
% 230.15/41.48  | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | BETA: splitting (87) gives:
% 230.15/41.49  | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | Case 1:
% 230.15/41.49  | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | |   (88)  all_57_6 = e0 & op(e1, e3) = e0
% 230.15/41.49  | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | ALPHA: (88) implies:
% 230.15/41.49  | | | | | | | | | | | | |   (89)  all_57_6 = e0
% 230.15/41.49  | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | REF_CLOSE: (3), (4), (6), (7), (8), (9), (10), (16), (17),
% 230.15/41.49  | | | | | | | | | | | | |            (22), (28), (29), (33), (39), (46), (47), (51),
% 230.15/41.49  | | | | | | | | | | | | |            (53), (60), (89) are inconsistent by sub-proof
% 230.15/41.49  | | | | | | | | | | | | |            #1773.
% 230.15/41.49  | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | Case 2:
% 230.15/41.49  | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | |   (90)  all_57_7 = e0 & op(e1, e2) = e0
% 230.15/41.49  | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | ALPHA: (90) implies:
% 230.15/41.49  | | | | | | | | | | | | |   (91)  all_57_7 = e0
% 230.15/41.49  | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | BETA: splitting (43) gives:
% 230.15/41.49  | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | Case 1:
% 230.15/41.49  | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | |   (92)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 230.15/41.49  | | | | | | | | | | | | | |           & op(e2, e3) = e3)
% 230.15/41.49  | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | BETA: splitting (92) gives:
% 230.15/41.49  | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | Case 1:
% 230.15/41.49  | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | |   (93)  all_57_0 = e3 & op(e3, e3) = e3
% 230.15/41.49  | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | | ALPHA: (93) implies:
% 230.15/41.49  | | | | | | | | | | | | | | |   (94)  op(e3, e3) = e3
% 230.15/41.49  | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | | REF_CLOSE: (6), (17), (24), (94) are inconsistent by
% 230.15/41.49  | | | | | | | | | | | | | | |            sub-proof #2494.
% 230.15/41.49  | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | Case 2:
% 230.15/41.49  | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | |   (95)  all_57_2 = e3 & op(e2, e3) = e3
% 230.15/41.49  | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | | ALPHA: (95) implies:
% 230.15/41.49  | | | | | | | | | | | | | | |   (96)  all_57_2 = e3
% 230.15/41.49  | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 230.15/41.49  | | | | | | | | | | | | | | |            (11), (13), (14), (15), (16), (17), (19), (20),
% 230.15/41.49  | | | | | | | | | | | | | | |            (22), (24), (25), (26), (28), (29), (31), (32),
% 230.15/41.49  | | | | | | | | | | | | | | |            (33), (34), (35), (36), (37), (38), (39), (40),
% 230.15/41.49  | | | | | | | | | | | | | | |            (41), (42), (43), (44), (46), (47), (48), (49),
% 230.15/41.49  | | | | | | | | | | | | | | |            (50), (51), (52), (53), (54), (55), (91), (96) are
% 230.15/41.49  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1014.
% 230.15/41.49  | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | End of split
% 230.15/41.49  | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | Case 2:
% 230.15/41.49  | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | |   (97)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 230.15/41.49  | | | | | | | | | | | | | |           e3 & op(e0, e3) = e3)
% 230.15/41.49  | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | BETA: splitting (97) gives:
% 230.15/41.49  | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | Case 1:
% 230.15/41.49  | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | |   (98)  all_57_6 = e3 & op(e1, e3) = e3
% 230.15/41.49  | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | | ALPHA: (98) implies:
% 230.15/41.49  | | | | | | | | | | | | | | |   (99)  all_57_6 = e3
% 230.15/41.49  | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | | BETA: splitting (15) gives:
% 230.15/41.49  | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | | Case 1:
% 230.15/41.49  | | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | | |   (100)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 230.15/41.49  | | | | | | | | | | | | | | | |            & op(e2, e1) = e0)
% 230.15/41.49  | | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | | | BETA: splitting (100) gives:
% 230.15/41.49  | | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | | | Case 1:
% 230.15/41.49  | | | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | | | |   (101)  all_57_4 = e0 & op(e3, e1) = e0
% 230.15/41.49  | | | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | | | | ALPHA: (101) implies:
% 230.15/41.49  | | | | | | | | | | | | | | | | |   (102)  all_57_4 = e0
% 230.15/41.49  | | | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (6), (10), (11), (13), (16), (17), (21),
% 230.15/41.49  | | | | | | | | | | | | | | | | |            (24), (28), (29), (32), (33), (35), (41), (46),
% 230.15/41.49  | | | | | | | | | | | | | | | | |            (55), (102) are inconsistent by sub-proof #1012.
% 230.15/41.49  | | | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | | | Case 2:
% 230.15/41.49  | | | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | | | |   (103)  all_57_5 = e0 & op(e2, e1) = e0
% 230.15/41.49  | | | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (17), (23), (24), (32), (41), (55),
% 230.15/41.49  | | | | | | | | | | | | | | | | |            (60), (65), (103) are inconsistent by sub-proof
% 230.15/41.49  | | | | | | | | | | | | | | | | |            #1020.
% 230.15/41.49  | | | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | | | End of split
% 230.15/41.49  | | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | | Case 2:
% 230.15/41.49  | | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | | |   (104)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 230.15/41.49  | | | | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 230.15/41.49  | | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | | | BETA: splitting (104) gives:
% 230.15/41.49  | | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | | | Case 1:
% 230.15/41.49  | | | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | | | |   (105)  all_57_8 = e0 & op(e1, e1) = e0
% 230.15/41.49  | | | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 230.15/41.49  | | | | | | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 230.15/41.49  | | | | | | | | | | | | | | | | |            (19), (20), (22), (23), (24), (25), (26), (27),
% 230.15/41.49  | | | | | | | | | | | | | | | | |            (28), (29), (30), (31), (32), (33), (34), (35),
% 230.15/41.49  | | | | | | | | | | | | | | | | |            (36), (37), (38), (39), (41), (42), (43), (44),
% 230.15/41.49  | | | | | | | | | | | | | | | | |            (46), (47), (48), (49), (50), (51), (52), (53),
% 230.15/41.49  | | | | | | | | | | | | | | | | |            (54), (55), (60), (65), (74), (86), (105) are
% 230.15/41.49  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1010.
% 230.15/41.49  | | | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | | | Case 2:
% 230.15/41.49  | | | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | | | |   (106)  all_57_14 = e0 & op(e0, e1) = e0
% 230.15/41.49  | | | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | | | | ALPHA: (106) implies:
% 230.15/41.49  | | | | | | | | | | | | | | | | |   (107)  all_57_14 = e0
% 230.15/41.49  | | | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | | | | BETA: splitting (49) gives:
% 230.15/41.49  | | | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | | | | Case 1:
% 230.15/41.49  | | | | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | | | | |   (108)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 230.15/41.49  | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e2)
% 230.15/41.49  | | | | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | | | | | BETA: splitting (108) gives:
% 230.15/41.49  | | | | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | | | | | Case 1:
% 230.15/41.49  | | | | | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | | | | | |   (109)  all_57_4 = e2 & op(e3, e1) = e2
% 230.15/41.49  | | | | | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | | | | | | ALPHA: (109) implies:
% 230.15/41.49  | | | | | | | | | | | | | | | | | | |   (110)  all_57_4 = e2
% 230.15/41.49  | | | | | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (23), (110) imply:
% 230.15/41.49  | | | | | | | | | | | | | | | | | | |   (111)  e2 = e1
% 230.15/41.49  | | | | | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (86), (111) imply:
% 230.15/41.49  | | | | | | | | | | | | | | | | | | |   (112)  all_57_2 = e1
% 230.15/41.49  | | | | | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10),
% 230.15/41.49  | | | | | | | | | | | | | | | | | | |            (16), (17), (21), (22), (23), (24), (28), (29),
% 230.15/41.49  | | | | | | | | | | | | | | | | | | |            (31), (32), (33), (39), (41), (42), (45), (46),
% 230.15/41.49  | | | | | | | | | | | | | | | | | | |            (47), (48), (51), (53), (55), (60), (65), (91),
% 230.15/41.49  | | | | | | | | | | | | | | | | | | |            (112) are inconsistent by sub-proof #1006.
% 230.15/41.49  | | | | | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | | | | | Case 2:
% 230.15/41.49  | | | | | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | | | | | |   (113)  all_57_5 = e2 & op(e2, e1) = e2
% 230.15/41.49  | | | | | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (16), (17), (24), (26), (43), (65),
% 230.15/41.49  | | | | | | | | | | | | | | | | | | |            (86), (99), (113) are inconsistent by sub-proof
% 230.15/41.49  | | | | | | | | | | | | | | | | | | |            #1005.
% 230.15/41.49  | | | | | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | | | | | End of split
% 230.15/41.49  | | | | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | | | | Case 2:
% 230.15/41.49  | | | | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | | | | |   (114)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 230.15/41.49  | | | | | | | | | | | | | | | | | |            e2 & op(e0, e1) = e2)
% 230.15/41.49  | | | | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | | | | | BETA: splitting (114) gives:
% 230.15/41.49  | | | | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | | | | | Case 1:
% 230.15/41.49  | | | | | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | | | | | |   (115)  all_57_8 = e2 & op(e1, e1) = e2
% 230.15/41.49  | | | | | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | | | | | | ALPHA: (115) implies:
% 230.15/41.49  | | | | | | | | | | | | | | | | | | |   (116)  op(e1, e1) = e2
% 230.15/41.49  | | | | | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (27), (46), (116) are inconsistent by
% 230.15/41.49  | | | | | | | | | | | | | | | | | | |            sub-proof #2423.
% 230.15/41.49  | | | | | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | | | | | Case 2:
% 230.15/41.49  | | | | | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | | | | | |   (117)  all_57_14 = e2 & op(e0, e1) = e2
% 230.15/41.49  | | | | | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | | | | | | ALPHA: (117) implies:
% 230.15/41.49  | | | | | | | | | | | | | | | | | | |   (118)  all_57_14 = e2
% 230.15/41.49  | | | | | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (107), (118) imply:
% 230.15/41.49  | | | | | | | | | | | | | | | | | | |   (119)  e2 = e0
% 230.15/41.49  | | | | | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (86), (119) imply:
% 230.15/41.49  | | | | | | | | | | | | | | | | | | |   (120)  all_57_2 = e0
% 230.15/41.49  | | | | | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 230.15/41.49  | | | | | | | | | | | | | | | | | | |            (11), (13), (14), (15), (16), (17), (19), (20),
% 230.15/41.49  | | | | | | | | | | | | | | | | | | |            (22), (24), (25), (28), (29), (31), (32), (33),
% 230.15/41.49  | | | | | | | | | | | | | | | | | | |            (34), (35), (36), (37), (38), (39), (41), (42),
% 230.15/41.49  | | | | | | | | | | | | | | | | | | |            (43), (44), (46), (47), (48), (49), (50), (51),
% 230.15/41.49  | | | | | | | | | | | | | | | | | | |            (52), (53), (54), (55), (65), (120) are
% 230.15/41.49  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1021.
% 230.15/41.49  | | | | | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | | | | | End of split
% 230.15/41.49  | | | | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | | | | End of split
% 230.15/41.49  | | | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | | | End of split
% 230.15/41.49  | | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | | End of split
% 230.15/41.49  | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | Case 2:
% 230.15/41.49  | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | |   (121)  all_57_12 = e3 & op(e0, e3) = e3
% 230.15/41.49  | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | | ALPHA: (121) implies:
% 230.15/41.49  | | | | | | | | | | | | | | |   (122)  all_57_12 = e3
% 230.15/41.49  | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | | COMBINE_EQS: (26), (122) imply:
% 230.15/41.49  | | | | | | | | | | | | | | |   (123)  e3 = e1
% 230.15/41.49  | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | | SIMP: (123) implies:
% 230.15/41.49  | | | | | | | | | | | | | | |   (124)  e3 = e1
% 230.15/41.49  | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | | COMBINE_EQS: (60), (124) imply:
% 230.15/41.49  | | | | | | | | | | | | | | |   (125)  all_57_1 = e1
% 230.15/41.49  | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (6), (10), (16), (17), (28), (29), (33),
% 230.15/41.49  | | | | | | | | | | | | | | |            (35), (46), (125) are inconsistent by sub-proof
% 230.15/41.49  | | | | | | | | | | | | | | |            #1908.
% 230.15/41.49  | | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | | End of split
% 230.15/41.49  | | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | End of split
% 230.15/41.49  | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | End of split
% 230.15/41.49  | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | Case 2:
% 230.15/41.49  | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | |   (126)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 230.15/41.49  | | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 230.15/41.49  | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | BETA: splitting (126) gives:
% 230.15/41.49  | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | Case 1:
% 230.15/41.49  | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | |   (127)  all_57_8 = e0 & op(e1, e1) = e0
% 230.15/41.49  | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 230.15/41.49  | | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 230.15/41.49  | | | | | | | | | | | | |            (19), (20), (22), (23), (24), (25), (26), (27),
% 230.15/41.49  | | | | | | | | | | | | |            (28), (29), (30), (31), (32), (33), (34), (35),
% 230.15/41.49  | | | | | | | | | | | | |            (36), (37), (38), (39), (41), (42), (43), (44),
% 230.15/41.49  | | | | | | | | | | | | |            (46), (47), (48), (49), (50), (51), (52), (53),
% 230.15/41.49  | | | | | | | | | | | | |            (54), (55), (60), (65), (74), (86), (127) are
% 230.15/41.49  | | | | | | | | | | | | |            inconsistent by sub-proof #1010.
% 230.15/41.49  | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | Case 2:
% 230.15/41.49  | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | |   (128)  all_57_11 = e0 & op(e1, e0) = e0
% 230.15/41.49  | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | ALPHA: (128) implies:
% 230.15/41.49  | | | | | | | | | | | | |   (129)  all_57_11 = e0
% 230.15/41.49  | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | COMBINE_EQS: (83), (129) imply:
% 230.15/41.49  | | | | | | | | | | | | |   (130)  e1 = e0
% 230.15/41.49  | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | COMBINE_EQS: (31), (130) imply:
% 230.15/41.49  | | | | | | | | | | | | |   (131)  all_57_3 = e0
% 230.15/41.49  | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | | REF_CLOSE: (1), (4), (33), (46), (65), (74), (86), (131) are
% 230.15/41.49  | | | | | | | | | | | | |            inconsistent by sub-proof #1530.
% 230.15/41.49  | | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | | End of split
% 230.15/41.49  | | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | End of split
% 230.15/41.49  | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | Case 2:
% 230.15/41.49  | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | |   (132)  all_57_3 = e2 & op(e2, e2) = e2
% 230.15/41.49  | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | ALPHA: (132) implies:
% 230.15/41.49  | | | | | | | | | | |   (133)  op(e2, e2) = e2
% 230.15/41.49  | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | | REF_CLOSE: (6), (10), (46), (133) are inconsistent by
% 230.15/41.49  | | | | | | | | | | |            sub-proof #2306.
% 230.15/41.49  | | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | End of split
% 230.15/41.49  | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | Case 2:
% 230.15/41.49  | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | |   (134)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2
% 230.15/41.49  | | | | | | | | | |            & op(e2, e0) = e2)
% 230.15/41.49  | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | | REF_CLOSE: (16), (29), (65), (74), (134) are inconsistent by
% 230.15/41.49  | | | | | | | | | |            sub-proof #1827.
% 230.15/41.49  | | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | End of split
% 230.15/41.49  | | | | | | | | | 
% 230.15/41.49  | | | | | | | | Case 2:
% 230.15/41.49  | | | | | | | | | 
% 230.15/41.49  | | | | | | | | |   (135)  all_57_15 = e1 & op(e0, e0) = e1
% 230.15/41.49  | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | ALPHA: (135) implies:
% 230.15/41.49  | | | | | | | | |   (136)  op(e0, e0) = e1
% 230.15/41.49  | | | | | | | | | 
% 230.15/41.49  | | | | | | | | | REF_CLOSE: (4), (6), (36), (136) are inconsistent by sub-proof
% 230.15/41.49  | | | | | | | | |            #2183.
% 230.15/41.49  | | | | | | | | | 
% 230.15/41.49  | | | | | | | | End of split
% 230.15/41.49  | | | | | | | | 
% 230.15/41.49  | | | | | | | End of split
% 230.15/41.49  | | | | | | | 
% 230.15/41.49  | | | | | | End of split
% 230.15/41.49  | | | | | | 
% 230.15/41.49  | | | | | End of split
% 230.15/41.49  | | | | | 
% 230.15/41.49  | | | | End of split
% 230.15/41.49  | | | | 
% 230.15/41.49  | | | Case 2:
% 230.15/41.49  | | | | 
% 230.15/41.49  | | | |   (137)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0,
% 230.15/41.49  | | | |              e1) = e3)
% 230.15/41.49  | | | | 
% 230.15/41.49  | | | | REF_CLOSE: (4), (6), (8), (9), (16), (17), (22), (25), (29), (33), (37),
% 230.15/41.49  | | | |            (39), (46), (137) are inconsistent by sub-proof #1794.
% 230.15/41.49  | | | | 
% 230.15/41.49  | | | End of split
% 230.15/41.49  | | | 
% 230.15/41.49  | | End of split
% 230.15/41.49  | | 
% 230.15/41.49  | Case 2:
% 230.15/41.49  | | 
% 230.15/41.49  | |   (138)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) =
% 230.15/41.49  | |            e3)
% 230.15/41.49  | | 
% 230.15/41.49  | | REF_CLOSE: (4), (6), (23), (41), (55), (138) are inconsistent by sub-proof
% 230.15/41.49  | |            #1004.
% 230.15/41.49  | | 
% 230.15/41.49  | End of split
% 230.15/41.49  | 
% 230.15/41.49  End of proof
% 230.15/41.49  
% 230.15/41.49  Sub-proof #1004 shows that the following formulas are inconsistent:
% 230.15/41.49  ----------------------------------------------------------------
% 230.15/41.49    (1)   ~ (e3 = e1)
% 230.15/41.49    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.15/41.49           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.15/41.49    (3)  all_57_4 = e1
% 230.15/41.49    (4)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.15/41.49    (5)   ~ (all_53_12 = e3)
% 230.15/41.49    (6)  op(e3, e0) = all_53_12
% 230.15/41.49  
% 230.15/41.49  Begin of proof
% 230.15/41.49  | 
% 230.15/41.49  | BETA: splitting (4) gives:
% 230.15/41.49  | 
% 230.15/41.49  | Case 1:
% 230.15/41.49  | | 
% 230.15/41.49  | |   (7)  all_57_4 = e3 & op(e3, e1) = e3
% 230.15/41.49  | | 
% 230.15/41.49  | | REF_CLOSE: (1), (3), (7) are inconsistent by sub-proof #2415.
% 230.15/41.49  | | 
% 230.15/41.49  | Case 2:
% 230.15/41.49  | | 
% 230.15/41.49  | |   (8)  all_57_9 = e3 & op(e3, e0) = e3
% 230.15/41.49  | | 
% 230.15/41.49  | | ALPHA: (8) implies:
% 230.15/41.49  | |   (9)  op(e3, e0) = e3
% 230.15/41.49  | | 
% 230.15/41.49  | | REF_CLOSE: (2), (5), (6), (9) are inconsistent by sub-proof #2458.
% 230.15/41.49  | | 
% 230.15/41.49  | End of split
% 230.15/41.49  | 
% 230.15/41.49  End of proof
% 230.15/41.49  
% 230.15/41.49  Sub-proof #1005 shows that the following formulas are inconsistent:
% 230.15/41.49  ----------------------------------------------------------------
% 230.15/41.49    (1)   ~ (e3 = e1)
% 230.15/41.49    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.15/41.49           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.15/41.49    (3)  all_57_2 = e2
% 230.15/41.49    (4)   ~ (e3 = e2)
% 230.15/41.49    (5)   ~ (e3 = e0)
% 230.15/41.49    (6)  op(e3, e3) = e0
% 230.15/41.49    (7)  all_57_5 = e3
% 230.15/41.49    (8)  all_57_12 = e1
% 230.15/41.49    (9)  all_57_6 = e3
% 230.15/41.49    (10)  all_57_5 = e2 & op(e2, e1) = e2
% 230.15/41.49    (11)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.15/41.49          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.15/41.49  
% 230.15/41.49  Begin of proof
% 230.15/41.49  | 
% 230.15/41.49  | ALPHA: (10) implies:
% 230.15/41.49  |   (12)  all_57_5 = e2
% 230.15/41.49  | 
% 230.15/41.49  | COMBINE_EQS: (7), (12) imply:
% 230.15/41.49  |   (13)  e3 = e2
% 230.15/41.49  | 
% 230.15/41.49  | SIMP: (13) implies:
% 230.15/41.49  |   (14)  e3 = e2
% 230.15/41.49  | 
% 230.15/41.49  | COMBINE_EQS: (9), (14) imply:
% 230.15/41.49  |   (15)  all_57_6 = e2
% 230.15/41.49  | 
% 230.15/41.49  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (11), (15) are inconsistent by
% 230.15/41.49  |            sub-proof #1212.
% 230.15/41.49  | 
% 230.15/41.49  End of proof
% 230.15/41.49  
% 230.15/41.49  Sub-proof #1006 shows that the following formulas are inconsistent:
% 230.15/41.49  ----------------------------------------------------------------
% 230.15/41.49    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.15/41.49         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.15/41.49    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.15/41.49         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.15/41.49    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.15/41.49         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.15/41.49    (4)   ~ (e3 = e1)
% 230.15/41.49    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.15/41.49           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.15/41.49    (6)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.15/41.49         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.15/41.49    (7)   ~ (all_6_2 = e3)
% 230.15/41.49    (8)  op(e1, e1) = all_6_2
% 230.15/41.49    (9)  op(e2, e2) = e1
% 230.15/41.49    (10)   ~ (e3 = e2)
% 230.15/41.49    (11)   ~ (e3 = e0)
% 230.15/41.49    (12)  all_57_0 = e0
% 230.15/41.49    (13)  all_57_15 = e3
% 230.15/41.49    (14)  all_57_4 = e1
% 230.15/41.49    (15)  op(e3, e3) = e0
% 230.15/41.49    (16)  all_57_5 = e3
% 230.15/41.49    (17)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.15/41.49          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.15/41.49    (18)   ~ (e2 = e0)
% 230.15/41.49    (19)  all_57_3 = e1
% 230.15/41.49    (20)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.15/41.49          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.15/41.49    (21)   ~ (e1 = e0)
% 230.15/41.49    (22)  all_57_2 = e1
% 230.15/41.49    (23)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.15/41.49              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.15/41.49                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.15/41.49                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.15/41.49    (24)   ~ (all_53_12 = e3)
% 230.15/41.49    (25)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.15/41.49          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.15/41.49    (26)  all_57_1 = e3
% 230.15/41.49    (27)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.15/41.49          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 230.15/41.49    (28)   ~ (e2 = e1)
% 230.15/41.49    (29)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.15/41.49          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.15/41.49    (30)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.15/41.49          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.15/41.49    (31)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.15/41.49          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.15/41.49    (32)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.15/41.49          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.15/41.49    (33)  all_57_7 = e0
% 230.15/41.49    (34)  op(e3, e0) = all_53_12
% 230.15/41.49  
% 230.15/41.49  Begin of proof
% 230.15/41.49  | 
% 230.15/41.49  | BETA: splitting (6) gives:
% 230.15/41.49  | 
% 230.15/41.49  | Case 1:
% 230.15/41.49  | | 
% 230.15/41.49  | |   (35)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 230.15/41.49  | |           e3)
% 230.15/41.49  | | 
% 230.15/41.49  | | BETA: splitting (35) gives:
% 230.15/41.49  | | 
% 230.15/41.49  | | Case 1:
% 230.15/41.49  | | | 
% 230.15/41.49  | | |   (36)  all_57_6 = e3 & op(e1, e3) = e3
% 230.15/41.49  | | | 
% 230.15/41.49  | | | ALPHA: (36) implies:
% 230.15/41.49  | | |   (37)  all_57_6 = e3
% 230.15/41.49  | | | 
% 230.15/41.49  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 230.15/41.49  | | |            (13), (15), (16), (17), (18), (19), (21), (22), (23), (25),
% 230.15/41.49  | | |            (26), (27), (28), (29), (30), (31), (32), (37) are inconsistent
% 230.15/41.49  | | |            by sub-proof #1007.
% 230.15/41.49  | | | 
% 230.15/41.49  | | Case 2:
% 230.15/41.49  | | | 
% 230.15/41.49  | | |   (38)  all_57_7 = e3 & op(e1, e2) = e3
% 230.15/41.49  | | | 
% 230.15/41.49  | | | ALPHA: (38) implies:
% 230.15/41.49  | | |   (39)  all_57_7 = e3
% 230.15/41.49  | | | 
% 230.15/41.49  | | | COMBINE_EQS: (33), (39) imply:
% 230.15/41.49  | | |   (40)  e3 = e0
% 230.15/41.49  | | | 
% 230.15/41.49  | | | COMBINE_EQS: (26), (40) imply:
% 230.15/41.49  | | |   (41)  all_57_1 = e0
% 230.15/41.49  | | | 
% 230.15/41.49  | | | REF_CLOSE: (4), (5), (11), (14), (15), (20), (24), (34), (41) are
% 230.15/41.49  | | |            inconsistent by sub-proof #2280.
% 230.15/41.49  | | | 
% 230.15/41.49  | | End of split
% 230.15/41.49  | | 
% 230.15/41.49  | Case 2:
% 230.15/41.49  | | 
% 230.15/41.49  | |   (42)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 230.15/41.49  | |           e3)
% 230.15/41.49  | | 
% 230.15/41.49  | | REF_CLOSE: (4), (5), (7), (8), (10), (11), (13), (18), (21), (23), (28),
% 230.15/41.49  | |            (29), (31), (42) are inconsistent by sub-proof #1786.
% 230.15/41.49  | | 
% 230.15/41.49  | End of split
% 230.15/41.49  | 
% 230.15/41.49  End of proof
% 230.15/41.49  
% 230.15/41.49  Sub-proof #1007 shows that the following formulas are inconsistent:
% 230.15/41.49  ----------------------------------------------------------------
% 230.15/41.49    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.15/41.49         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.15/41.49    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.15/41.49         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.15/41.49    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.15/41.49         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.15/41.49    (4)   ~ (e3 = e1)
% 230.15/41.49    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.15/41.49           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.15/41.49    (6)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.15/41.49         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.15/41.49    (7)   ~ (all_6_2 = e3)
% 230.15/41.49    (8)  op(e1, e1) = all_6_2
% 230.15/41.49    (9)  op(e2, e2) = e1
% 230.15/41.49    (10)   ~ (e3 = e2)
% 230.15/41.49    (11)   ~ (e3 = e0)
% 230.15/41.49    (12)  all_57_0 = e0
% 230.15/41.49    (13)  all_57_15 = e3
% 230.15/41.49    (14)  op(e3, e3) = e0
% 230.15/41.49    (15)  all_57_5 = e3
% 230.15/41.49    (16)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.15/41.49          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.15/41.49    (17)   ~ (e2 = e0)
% 230.15/41.49    (18)  all_57_3 = e1
% 230.15/41.49    (19)   ~ (e1 = e0)
% 230.15/41.49    (20)  all_57_6 = e3
% 230.15/41.49    (21)  all_57_2 = e1
% 230.15/41.49    (22)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.15/41.49              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.15/41.49                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.15/41.49                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.15/41.49    (23)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.15/41.49          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.15/41.49    (24)  all_57_1 = e3
% 230.15/41.49    (25)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.15/41.49          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 230.15/41.49    (26)   ~ (e2 = e1)
% 230.15/41.49    (27)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.15/41.49          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.15/41.49    (28)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.15/41.49          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.15/41.49    (29)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.15/41.49          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.15/41.49    (30)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.15/41.49          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.15/41.49  
% 230.15/41.49  Begin of proof
% 230.15/41.49  | 
% 230.15/41.49  | BETA: splitting (23) gives:
% 230.15/41.49  | 
% 230.15/41.49  | Case 1:
% 230.15/41.49  | | 
% 230.15/41.49  | |   (31)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 230.15/41.49  | |           e2)
% 230.15/41.49  | | 
% 230.15/41.49  | | REF_CLOSE: (5), (9), (21), (26), (31) are inconsistent by sub-proof #1828.
% 230.15/41.49  | | 
% 230.15/41.49  | Case 2:
% 230.15/41.49  | | 
% 230.15/41.49  | |   (32)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 230.15/41.49  | |           e2)
% 230.15/41.49  | | 
% 230.15/41.49  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 230.15/41.49  | |            (13), (14), (15), (16), (17), (18), (19), (20), (22), (23), (24),
% 230.15/41.49  | |            (25), (26), (27), (28), (29), (30), (32) are inconsistent by
% 230.15/41.49  | |            sub-proof #1008.
% 230.15/41.49  | | 
% 230.15/41.49  | End of split
% 230.15/41.49  | 
% 230.15/41.49  End of proof
% 230.15/41.49  
% 230.15/41.49  Sub-proof #1008 shows that the following formulas are inconsistent:
% 230.15/41.49  ----------------------------------------------------------------
% 230.15/41.49    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.15/41.49         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.15/41.49    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.15/41.49         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.15/41.49    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.15/41.49         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.15/41.49    (4)   ~ (e3 = e1)
% 230.15/41.49    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.15/41.49           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.15/41.49    (6)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.15/41.49         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.15/41.49    (7)   ~ (all_6_2 = e3)
% 230.15/41.49    (8)  op(e1, e1) = all_6_2
% 230.15/41.49    (9)  op(e2, e2) = e1
% 230.15/41.49    (10)   ~ (e3 = e2)
% 230.15/41.49    (11)   ~ (e3 = e0)
% 230.15/41.49    (12)  all_57_0 = e0
% 230.15/41.49    (13)  all_57_15 = e3
% 230.15/41.49    (14)  op(e3, e3) = e0
% 230.15/41.49    (15)  all_57_5 = e3
% 230.15/41.49    (16)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.15/41.49          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.15/41.49    (17)   ~ (e2 = e0)
% 230.15/41.49    (18)  all_57_3 = e1
% 230.15/41.49    (19)   ~ (e1 = e0)
% 230.15/41.49    (20)  all_57_6 = e3
% 230.15/41.49    (21)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.15/41.49              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.15/41.49                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.15/41.49                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.15/41.49    (22)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.15/41.49          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.15/41.49    (23)  all_57_1 = e3
% 230.15/41.49    (24)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.15/41.49          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 230.15/41.49    (25)   ~ (e2 = e1)
% 230.15/41.49    (26)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.15/41.49    (27)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.15/41.49          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.15/41.49    (28)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.15/41.49          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.15/41.49    (29)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.15/41.49          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.15/41.49    (30)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.15/41.49          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.15/41.49  
% 230.15/41.49  Begin of proof
% 230.15/41.49  | 
% 230.15/41.49  | BETA: splitting (26) gives:
% 230.15/41.49  | 
% 230.15/41.49  | Case 1:
% 230.15/41.49  | | 
% 230.15/41.49  | |   (31)  all_57_5 = e2 & op(e2, e1) = e2
% 230.15/41.49  | | 
% 230.15/41.49  | | REF_CLOSE: (10), (15), (31) are inconsistent by sub-proof #2425.
% 230.15/41.49  | | 
% 230.15/41.49  | Case 2:
% 230.15/41.49  | | 
% 230.15/41.49  | |   (32)  all_57_10 = e2 & op(e2, e0) = e2
% 230.15/41.49  | | 
% 230.15/41.49  | | ALPHA: (32) implies:
% 230.15/41.49  | |   (33)  all_57_10 = e2
% 230.15/41.49  | | 
% 230.15/41.49  | | BETA: splitting (24) gives:
% 230.15/41.49  | | 
% 230.15/41.49  | | Case 1:
% 230.15/41.49  | | | 
% 230.15/41.49  | | |   (34)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) =
% 230.15/41.49  | | |           e0)
% 230.15/41.49  | | | 
% 230.15/41.50  | | | REF_CLOSE: (1), (2), (4), (5), (9), (10), (12), (14), (15), (17), (18),
% 230.15/41.50  | | |            (19), (20), (22), (25), (28), (34) are inconsistent by
% 230.15/41.50  | | |            sub-proof #1009.
% 230.15/41.50  | | | 
% 230.15/41.50  | | Case 2:
% 230.15/41.50  | | | 
% 230.15/41.50  | | |   (35)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 230.15/41.50  | | |           e0)
% 230.15/41.50  | | | 
% 230.15/41.50  | | | BETA: splitting (35) gives:
% 230.15/41.50  | | | 
% 230.15/41.50  | | | Case 1:
% 230.15/41.50  | | | | 
% 230.15/41.50  | | | |   (36)  all_57_5 = e0 & op(e2, e1) = e0
% 230.15/41.50  | | | | 
% 230.15/41.50  | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (10), (11), (13), (15),
% 230.15/41.50  | | | |            (16), (17), (19), (20), (21), (23), (25), (27), (29), (30),
% 230.15/41.50  | | | |            (36) are inconsistent by sub-proof #1772.
% 230.15/41.50  | | | | 
% 230.15/41.50  | | | Case 2:
% 230.15/41.50  | | | | 
% 230.15/41.50  | | | |   (37)  all_57_10 = e0 & op(e2, e0) = e0
% 230.15/41.50  | | | | 
% 230.15/41.50  | | | | REF_CLOSE: (17), (33), (37) are inconsistent by sub-proof #1751.
% 230.15/41.50  | | | | 
% 230.15/41.50  | | | End of split
% 230.15/41.50  | | | 
% 230.15/41.50  | | End of split
% 230.15/41.50  | | 
% 230.15/41.50  | End of split
% 230.15/41.50  | 
% 230.15/41.50  End of proof
% 230.15/41.50  
% 230.15/41.50  Sub-proof #1009 shows that the following formulas are inconsistent:
% 230.15/41.50  ----------------------------------------------------------------
% 230.15/41.50    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.15/41.50         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.15/41.50    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.15/41.50         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.15/41.50    (3)   ~ (e3 = e1)
% 230.15/41.50    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.15/41.50           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.15/41.50    (5)  op(e2, e2) = e1
% 230.15/41.50    (6)   ~ (e3 = e2)
% 230.15/41.50    (7)  all_57_0 = e0
% 230.15/41.50    (8)  op(e3, e3) = e0
% 230.15/41.50    (9)  all_57_5 = e3
% 230.15/41.50    (10)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0)
% 230.15/41.50    (11)   ~ (e2 = e0)
% 230.15/41.50    (12)  all_57_3 = e1
% 230.15/41.50    (13)   ~ (e1 = e0)
% 230.15/41.50    (14)  all_57_6 = e3
% 230.15/41.50    (15)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.15/41.50          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.15/41.50    (16)   ~ (e2 = e1)
% 230.15/41.50    (17)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.15/41.50          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.15/41.50  
% 230.15/41.50  Begin of proof
% 230.15/41.50  | 
% 230.15/41.50  | BETA: splitting (10) gives:
% 230.15/41.50  | 
% 230.15/41.50  | Case 1:
% 230.15/41.50  | | 
% 230.15/41.50  | |   (18)  all_57_2 = e0 & op(e2, e3) = e0
% 230.15/41.50  | | 
% 230.15/41.50  | | ALPHA: (18) implies:
% 230.15/41.50  | |   (19)  all_57_2 = e0
% 230.15/41.50  | | 
% 230.15/41.50  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (11), (12), (13), (14),
% 230.15/41.50  | |            (15), (16), (17), (19) are inconsistent by sub-proof #1066.
% 230.15/41.50  | | 
% 230.15/41.50  | Case 2:
% 230.15/41.50  | | 
% 230.15/41.50  | |   (20)  all_57_3 = e0 & op(e2, e2) = e0
% 230.15/41.50  | | 
% 230.15/41.50  | | ALPHA: (20) implies:
% 230.15/41.50  | |   (21)  op(e2, e2) = e0
% 230.15/41.50  | | 
% 230.15/41.50  | | REF_CLOSE: (4), (5), (13), (21) are inconsistent by sub-proof #2352.
% 230.15/41.50  | | 
% 230.15/41.50  | End of split
% 230.15/41.50  | 
% 230.15/41.50  End of proof
% 230.15/41.50  
% 230.15/41.50  Sub-proof #1010 shows that the following formulas are inconsistent:
% 230.15/41.50  ----------------------------------------------------------------
% 230.15/41.50    (1)  all_57_10 = e0
% 230.15/41.50    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.15/41.50         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.15/41.50    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.15/41.50         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.15/41.50    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.15/41.50         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.15/41.50    (5)   ~ (e3 = e1)
% 230.15/41.50    (6)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.15/41.50         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.15/41.50    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.15/41.50           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.15/41.50    (8)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.15/41.50         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.15/41.50    (9)   ~ (all_6_2 = e3)
% 230.15/41.50    (10)  op(e1, e1) = all_6_2
% 230.15/41.50    (11)  op(e2, e2) = e1
% 230.15/41.50    (12)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.15/41.50          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.15/41.50    (13)  all_57_8 = e0 & op(e1, e1) = e0
% 230.15/41.50    (14)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 230.15/41.50            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 230.15/41.50              e3) = all_22_1 & $i(all_22_1))
% 230.15/41.50    (15)  all_57_2 = e2
% 230.15/41.50    (16)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.15/41.50          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.15/41.50    (17)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.15/41.50          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.15/41.50    (18)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 230.15/41.50          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.15/41.50    (19)   ~ (e3 = e2)
% 230.15/41.50    (20)   ~ (e3 = e0)
% 230.15/41.50    (21)  op(e0, e3) = e1
% 230.15/41.50    (22)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.15/41.50          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.15/41.50    (23)  op(e0, e3) = all_53_3
% 230.15/41.50    (24)  all_57_15 = e3
% 230.15/41.50    (25)  all_57_4 = e1
% 230.15/41.50    (26)  op(e3, e3) = e0
% 230.15/41.50    (27)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.15/41.50          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.15/41.50            e1)
% 230.15/41.50    (28)  all_57_5 = e3
% 230.15/41.50    (29)  all_57_12 = e1
% 230.15/41.50    (30)  op(e1, e1) = e1
% 230.15/41.50    (31)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.15/41.50          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.15/41.50    (32)   ~ (e2 = e0)
% 230.15/41.50    (33)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 230.15/41.50            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 230.15/41.50              e3) = all_12_1 & $i(all_12_1))
% 230.15/41.50    (34)  all_57_3 = e1
% 230.15/41.50    (35)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.15/41.50          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.15/41.50    (36)   ~ (e1 = e0)
% 230.15/41.50    (37)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 230.15/41.50          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 230.15/41.50    (38)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.15/41.50          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.15/41.50    (39)  op(e0, e0) = e3
% 230.15/41.50    (40)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.15/41.50          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.15/41.50            e2)
% 230.15/41.50    (41)   ~ (all_53_3 = e0)
% 230.15/41.50    (42)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.15/41.50              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.15/41.50                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.15/41.50                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.15/41.50    (43)   ~ (all_53_12 = e3)
% 230.15/41.50    (44)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.15/41.50          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.15/41.50    (45)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.15/41.50          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.15/41.50    (46)  all_57_1 = e3
% 230.15/41.50    (47)   ~ (all_53_12 = e0)
% 230.15/41.50    (48)   ~ (e2 = e1)
% 230.15/41.50    (49)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.15/41.50          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.15/41.50    (50)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.15/41.50          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.15/41.50    (51)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.15/41.50          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.15/41.50    (52)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.15/41.50          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.15/41.50    (53)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.15/41.50          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.15/41.50    (54)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.15/41.50          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.15/41.50    (55)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.15/41.50          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.15/41.50    (56)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.15/41.50          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.15/41.50    (57)  op(e3, e0) = all_53_12
% 230.15/41.50  
% 230.15/41.50  Begin of proof
% 230.15/41.50  | 
% 230.15/41.50  | ALPHA: (13) implies:
% 230.15/41.50  |   (58)  op(e1, e1) = e0
% 230.15/41.50  | 
% 230.15/41.50  | BETA: splitting (56) gives:
% 230.15/41.50  | 
% 230.15/41.50  | Case 1:
% 230.15/41.50  | | 
% 230.15/41.50  | |   (59)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) =
% 230.15/41.50  | |           e2)
% 230.15/41.50  | | 
% 230.15/41.50  | | BETA: splitting (59) gives:
% 230.15/41.50  | | 
% 230.15/41.50  | | Case 1:
% 230.15/41.50  | | | 
% 230.15/41.50  | | |   (60)  all_57_6 = e2 & op(e1, e3) = e2
% 230.15/41.50  | | | 
% 230.15/41.50  | | | ALPHA: (60) implies:
% 230.15/41.50  | | |   (61)  all_57_6 = e2
% 230.15/41.50  | | | 
% 230.15/41.50  | | | REF_CLOSE: (5), (7), (15), (19), (20), (26), (29), (45), (61) are
% 230.15/41.50  | | |            inconsistent by sub-proof #1212.
% 230.15/41.50  | | | 
% 230.15/41.50  | | Case 2:
% 230.15/41.50  | | | 
% 230.15/41.50  | | |   (62)  all_57_7 = e2 & op(e1, e2) = e2
% 230.15/41.50  | | | 
% 230.15/41.50  | | | ALPHA: (62) implies:
% 230.15/41.50  | | |   (63)  all_57_7 = e2
% 230.15/41.50  | | | 
% 230.15/41.50  | | | BETA: splitting (31) gives:
% 230.15/41.50  | | | 
% 230.15/41.50  | | | Case 1:
% 230.15/41.50  | | | | 
% 230.15/41.50  | | | |   (64)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2)
% 230.15/41.50  | | | |           = e0)
% 230.15/41.50  | | | | 
% 230.15/41.50  | | | | BETA: splitting (64) gives:
% 230.15/41.50  | | | | 
% 230.15/41.50  | | | | Case 1:
% 230.15/41.50  | | | | | 
% 230.15/41.50  | | | | |   (65)  all_57_1 = e0 & op(e3, e2) = e0
% 230.15/41.50  | | | | | 
% 230.15/41.50  | | | | | ALPHA: (65) implies:
% 230.15/41.50  | | | | |   (66)  all_57_1 = e0
% 230.15/41.50  | | | | | 
% 230.15/41.50  | | | | | REF_CLOSE: (5), (7), (20), (25), (26), (35), (43), (57), (66) are
% 230.15/41.50  | | | | |            inconsistent by sub-proof #2280.
% 230.15/41.50  | | | | | 
% 230.15/41.50  | | | | Case 2:
% 230.15/41.50  | | | | | 
% 230.15/41.50  | | | | |   (67)  all_57_3 = e0 & op(e2, e2) = e0
% 230.15/41.50  | | | | | 
% 230.15/41.50  | | | | | ALPHA: (67) implies:
% 230.15/41.50  | | | | |   (68)  all_57_3 = e0
% 230.15/41.50  | | | | | 
% 230.15/41.50  | | | | | REF_CLOSE: (1), (2), (5), (15), (28), (36), (48), (68) are
% 230.15/41.50  | | | | |            inconsistent by sub-proof #1530.
% 230.15/41.50  | | | | | 
% 230.15/41.50  | | | | End of split
% 230.15/41.50  | | | | 
% 230.15/41.50  | | | Case 2:
% 230.15/41.50  | | | | 
% 230.15/41.50  | | | |   (69)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2)
% 230.15/41.50  | | | |           = e0)
% 230.15/41.50  | | | | 
% 230.15/41.50  | | | | BETA: splitting (69) gives:
% 230.15/41.50  | | | | 
% 230.15/41.50  | | | | Case 1:
% 230.15/41.50  | | | | | 
% 230.15/41.50  | | | | |   (70)  all_57_7 = e0 & op(e1, e2) = e0
% 230.15/41.50  | | | | | 
% 230.15/41.50  | | | | | ALPHA: (70) implies:
% 230.15/41.50  | | | | |   (71)  all_57_7 = e0
% 230.15/41.50  | | | | | 
% 230.15/41.50  | | | | | COMBINE_EQS: (63), (71) imply:
% 230.15/41.50  | | | | |   (72)  e2 = e0
% 230.15/41.50  | | | | | 
% 230.15/41.50  | | | | | COMBINE_EQS: (15), (72) imply:
% 230.15/41.50  | | | | |   (73)  all_57_2 = e0
% 230.15/41.50  | | | | | 
% 230.15/41.50  | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 230.15/41.50  | | | | |            (16), (17), (18), (19), (20), (22), (23), (24), (26), (27),
% 230.15/41.50  | | | | |            (28), (31), (32), (34), (35), (36), (37), (38), (39), (40),
% 230.15/41.50  | | | | |            (41), (42), (43), (44), (45), (47), (48), (49), (50), (51),
% 230.15/41.50  | | | | |            (52), (53), (54), (55), (56), (57), (73) are inconsistent
% 230.15/41.50  | | | | |            by sub-proof #1021.
% 230.15/41.50  | | | | | 
% 230.15/41.50  | | | | Case 2:
% 230.15/41.50  | | | | | 
% 230.15/41.50  | | | | |   (74)  all_57_13 = e0 & op(e0, e2) = e0
% 230.15/41.50  | | | | | 
% 230.15/41.50  | | | | | ALPHA: (74) implies:
% 230.15/41.50  | | | | |   (75)  all_57_13 = e0
% 230.15/41.50  | | | | | 
% 230.15/41.50  | | | | | GROUND_INST: instantiating (7) with e0, e1, e1, e1, simplifying with
% 230.15/41.50  | | | | |              (30), (58) gives:
% 230.15/41.50  | | | | |   (76)  e1 = e0
% 230.15/41.50  | | | | | 
% 230.15/41.50  | | | | | COMBINE_EQS: (34), (76) imply:
% 230.15/41.50  | | | | |   (77)  all_57_3 = e0
% 230.15/41.50  | | | | | 
% 230.15/41.50  | | | | | REF_CLOSE: (4), (5), (19), (32), (36), (46), (48), (55), (75), (77)
% 230.15/41.50  | | | | |            are inconsistent by sub-proof #1758.
% 230.15/41.50  | | | | | 
% 230.15/41.50  | | | | End of split
% 230.15/41.50  | | | | 
% 230.15/41.50  | | | End of split
% 230.15/41.50  | | | 
% 230.15/41.50  | | End of split
% 230.15/41.50  | | 
% 230.15/41.50  | Case 2:
% 230.15/41.50  | | 
% 230.15/41.50  | |   (78)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) =
% 230.15/41.50  | |           e2)
% 230.15/41.50  | | 
% 230.15/41.50  | | REF_CLOSE: (7), (14), (21), (30), (33), (48), (78) are inconsistent by
% 230.15/41.50  | |            sub-proof #1011.
% 230.15/41.50  | | 
% 230.15/41.50  | End of split
% 230.15/41.50  | 
% 230.15/41.50  End of proof
% 230.15/41.50  
% 230.15/41.50  Sub-proof #1011 shows that the following formulas are inconsistent:
% 230.15/41.50  ----------------------------------------------------------------
% 230.15/41.50    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.15/41.50           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.15/41.50    (2)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) = all_22_1
% 230.15/41.50           & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0, e3) =
% 230.15/41.50           all_22_1 & $i(all_22_1))
% 230.15/41.50    (3)  op(e0, e3) = e1
% 230.15/41.50    (4)  op(e1, e1) = e1
% 230.15/41.50    (5)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) = all_12_1
% 230.15/41.50           & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0, e3) =
% 230.15/41.50           all_12_1 & $i(all_12_1))
% 230.15/41.50    (6)   ~ (e2 = e1)
% 230.15/41.50    (7)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.15/41.50  
% 230.15/41.50  Begin of proof
% 230.15/41.50  | 
% 230.15/41.50  | BETA: splitting (7) gives:
% 230.15/41.50  | 
% 230.15/41.50  | Case 1:
% 230.15/41.50  | | 
% 230.15/41.50  | |   (8)  all_57_8 = e2 & op(e1, e1) = e2
% 230.15/41.50  | | 
% 230.15/41.50  | | ALPHA: (8) implies:
% 230.15/41.50  | |   (9)  op(e1, e1) = e2
% 230.15/41.50  | | 
% 230.15/41.50  | | REF_CLOSE: (1), (4), (6), (9) are inconsistent by sub-proof #2423.
% 230.15/41.50  | | 
% 230.15/41.50  | Case 2:
% 230.15/41.50  | | 
% 230.15/41.50  | |   (10)  all_57_11 = e2 & op(e1, e0) = e2
% 230.15/41.50  | | 
% 230.15/41.50  | | ALPHA: (10) implies:
% 230.15/41.50  | |   (11)  op(e1, e0) = e2
% 230.15/41.50  | | 
% 230.15/41.50  | | REF_CLOSE: (1), (2), (3), (5), (11) are inconsistent by sub-proof #1147.
% 230.15/41.50  | | 
% 230.15/41.50  | End of split
% 230.15/41.50  | 
% 230.15/41.50  End of proof
% 230.15/41.50  
% 230.15/41.50  Sub-proof #1012 shows that the following formulas are inconsistent:
% 230.15/41.50  ----------------------------------------------------------------
% 230.15/41.50    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.15/41.50         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.15/41.50    (2)   ~ (e3 = e1)
% 230.15/41.50    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.15/41.50           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.15/41.50    (4)  op(e2, e2) = e1
% 230.15/41.50    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.15/41.50         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.15/41.50    (6)  all_57_4 = e0
% 230.15/41.50    (7)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.15/41.50         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.15/41.50    (8)   ~ (e3 = e2)
% 230.15/41.50    (9)   ~ (e3 = e0)
% 230.15/41.50    (10)  all_57_0 = e0
% 230.15/41.50    (11)  op(e3, e3) = e0
% 230.15/41.50    (12)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.15/41.50          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.15/41.50    (13)   ~ (e2 = e0)
% 230.15/41.50    (14)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.15/41.50          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.15/41.50    (15)   ~ (e1 = e0)
% 230.15/41.50    (16)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.15/41.50          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.15/41.50    (17)   ~ (all_53_12 = e3)
% 230.15/41.50    (18)   ~ (e2 = e1)
% 230.15/41.50    (19)  op(e3, e0) = all_53_12
% 230.15/41.50  
% 230.15/41.50  Begin of proof
% 230.15/41.50  | 
% 230.15/41.50  | BETA: splitting (5) gives:
% 230.15/41.50  | 
% 230.15/41.50  | Case 1:
% 230.15/41.50  | | 
% 230.15/41.50  | |   (20)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) =
% 230.15/41.50  | |           e1)
% 230.15/41.50  | | 
% 230.15/41.50  | | REF_CLOSE: (1), (2), (3), (4), (8), (9), (10), (12), (13), (15), (16), (18),
% 230.15/41.50  | |            (20) are inconsistent by sub-proof #1551.
% 230.15/41.50  | | 
% 230.15/41.50  | Case 2:
% 230.15/41.50  | | 
% 230.15/41.50  | |   (21)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) =
% 230.15/41.50  | |           e1)
% 230.15/41.50  | | 
% 230.15/41.50  | | REF_CLOSE: (3), (6), (7), (8), (9), (11), (13), (14), (15), (17), (18),
% 230.15/41.50  | |            (19), (21) are inconsistent by sub-proof #1013.
% 230.15/41.50  | | 
% 230.15/41.50  | End of split
% 230.15/41.50  | 
% 230.15/41.50  End of proof
% 230.15/41.50  
% 230.15/41.50  Sub-proof #1013 shows that the following formulas are inconsistent:
% 230.15/41.50  ----------------------------------------------------------------
% 230.15/41.50    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.15/41.50           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.15/41.50    (2)  all_57_4 = e0
% 230.15/41.50    (3)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.15/41.50         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.15/41.50    (4)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.15/41.50    (5)   ~ (e3 = e2)
% 230.15/41.50    (6)   ~ (e3 = e0)
% 230.15/41.50    (7)  op(e3, e3) = e0
% 230.15/41.50    (8)   ~ (e2 = e0)
% 230.15/41.50    (9)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.15/41.50         (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.15/41.50    (10)   ~ (e1 = e0)
% 230.15/41.50    (11)   ~ (all_53_12 = e3)
% 230.15/41.50    (12)   ~ (e2 = e1)
% 230.15/41.50    (13)  op(e3, e0) = all_53_12
% 230.15/41.50  
% 230.15/41.50  Begin of proof
% 230.15/41.50  | 
% 230.15/41.50  | BETA: splitting (4) gives:
% 230.15/41.50  | 
% 230.15/41.50  | Case 1:
% 230.15/41.50  | | 
% 230.15/41.50  | |   (14)  all_57_4 = e1 & op(e3, e1) = e1
% 230.15/41.50  | | 
% 230.15/41.50  | | ALPHA: (14) implies:
% 230.15/41.50  | |   (15)  all_57_4 = e1
% 230.15/41.50  | | 
% 230.15/41.50  | | REF_CLOSE: (2), (10), (15) are inconsistent by sub-proof #2438.
% 230.15/41.50  | | 
% 230.15/41.50  | Case 2:
% 230.15/41.50  | | 
% 230.15/41.50  | |   (16)  all_57_9 = e1 & op(e3, e0) = e1
% 230.15/41.50  | | 
% 230.15/41.50  | | ALPHA: (16) implies:
% 230.15/41.50  | |   (17)  all_57_9 = e1
% 230.15/41.50  | | 
% 230.15/41.50  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (11), (12), (13), (17)
% 230.15/41.50  | |            are inconsistent by sub-proof #1403.
% 230.15/41.50  | | 
% 230.15/41.50  | End of split
% 230.15/41.50  | 
% 230.15/41.50  End of proof
% 230.15/41.50  
% 230.15/41.50  Sub-proof #1014 shows that the following formulas are inconsistent:
% 230.15/41.50  ----------------------------------------------------------------
% 230.15/41.50    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.15/41.50         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.15/41.50    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.15/41.50         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.15/41.50    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.15/41.50         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.15/41.50    (4)   ~ (e3 = e1)
% 230.15/41.50    (5)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.15/41.50         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.15/41.50    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.15/41.50           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.15/41.50    (7)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.15/41.50         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.15/41.50    (8)   ~ (all_6_2 = e3)
% 230.15/41.50    (9)  op(e1, e1) = all_6_2
% 230.15/41.50    (10)  op(e2, e2) = e1
% 230.15/41.50    (11)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.15/41.50          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.15/41.50    (12)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.15/41.50          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.15/41.50    (13)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.15/41.50          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.15/41.50    (14)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 230.15/41.50          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.15/41.50    (15)   ~ (e3 = e2)
% 230.15/41.50    (16)   ~ (e3 = e0)
% 230.15/41.50    (17)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.15/41.50          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.15/41.50    (18)  op(e0, e3) = all_53_3
% 230.15/41.50    (19)  all_57_15 = e3
% 230.15/41.50    (20)  op(e3, e3) = e0
% 230.15/41.50    (21)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.15/41.50          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.15/41.50            e1)
% 230.15/41.50    (22)  all_57_12 = e1
% 230.15/41.50    (23)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.15/41.50          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.15/41.50    (24)   ~ (e2 = e0)
% 230.15/41.50    (25)  all_57_2 = e3
% 230.15/41.50    (26)  all_57_3 = e1
% 230.15/41.50    (27)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.15/41.50          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.15/41.50    (28)   ~ (e1 = e0)
% 230.15/41.50    (29)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 230.15/41.50          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 230.15/41.50    (30)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.15/41.50          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.15/41.50    (31)  op(e0, e0) = e3
% 230.15/41.50    (32)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.15/41.50          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.15/41.50            e2)
% 230.15/41.50    (33)   ~ (all_53_3 = e0)
% 230.15/41.50    (34)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.15/41.50              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.15/41.50                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.15/41.50                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.15/41.50    (35)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.15/41.50          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.15/41.50    (36)   ~ (all_53_12 = e3)
% 230.15/41.50    (37)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.15/41.50          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.15/41.50    (38)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.15/41.50          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.15/41.50    (39)   ~ (all_53_12 = e0)
% 230.15/41.50    (40)   ~ (e2 = e1)
% 230.15/41.50    (41)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.15/41.50          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.15/41.50    (42)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.15/41.50          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.15/41.50    (43)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.15/41.50          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.15/41.50    (44)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.15/41.50          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.15/41.50    (45)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.15/41.50          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.15/41.50    (46)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.15/41.50          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.15/41.51    (47)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.15/41.51          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.15/41.51    (48)  all_57_7 = e0
% 230.15/41.51    (49)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.15/41.51          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.15/41.51    (50)  op(e3, e0) = all_53_12
% 230.15/41.51  
% 230.15/41.51  Begin of proof
% 230.15/41.51  | 
% 230.15/41.51  | BETA: splitting (7) gives:
% 230.15/41.51  | 
% 230.15/41.51  | Case 1:
% 230.15/41.51  | | 
% 230.15/41.51  | |   (51)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 230.15/41.51  | |           e3)
% 230.15/41.51  | | 
% 230.15/41.51  | | BETA: splitting (51) gives:
% 230.15/41.51  | | 
% 230.15/41.51  | | Case 1:
% 230.15/41.51  | | | 
% 230.15/41.51  | | |   (52)  all_57_6 = e3 & op(e1, e3) = e3
% 230.15/41.51  | | | 
% 230.15/41.51  | | | ALPHA: (52) implies:
% 230.15/41.51  | | |   (53)  all_57_6 = e3
% 230.15/41.51  | | | 
% 230.15/41.51  | | | REF_CLOSE: (6), (15), (20), (22), (24), (25), (40), (42), (53) are
% 230.15/41.51  | | |            inconsistent by sub-proof #1288.
% 230.15/41.51  | | | 
% 230.15/41.51  | | Case 2:
% 230.15/41.51  | | | 
% 230.15/41.51  | | |   (54)  all_57_7 = e3 & op(e1, e2) = e3
% 230.15/41.51  | | | 
% 230.15/41.51  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 230.15/41.51  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (23),
% 230.15/41.51  | | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 230.15/41.51  | | |            (34), (35), (36), (37), (38), (39), (40), (41), (42), (43),
% 230.15/41.51  | | |            (44), (45), (46), (47), (48), (49), (50), (54) are inconsistent
% 230.15/41.51  | | |            by sub-proof #1015.
% 230.15/41.51  | | | 
% 230.15/41.51  | | End of split
% 230.15/41.51  | | 
% 230.15/41.51  | Case 2:
% 230.15/41.51  | | 
% 230.15/41.51  | |   (55)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 230.15/41.51  | |           e3)
% 230.15/41.51  | | 
% 230.15/41.51  | | REF_CLOSE: (4), (6), (8), (9), (15), (16), (19), (24), (28), (34), (40),
% 230.15/41.51  | |            (41), (45), (55) are inconsistent by sub-proof #1786.
% 230.15/41.51  | | 
% 230.15/41.51  | End of split
% 230.15/41.51  | 
% 230.15/41.51  End of proof
% 230.15/41.51  
% 230.15/41.51  Sub-proof #1015 shows that the following formulas are inconsistent:
% 230.15/41.51  ----------------------------------------------------------------
% 230.15/41.51    (1)  all_57_7 = e3 & op(e1, e2) = e3
% 230.15/41.51    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.15/41.51         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.15/41.51    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.15/41.51         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.15/41.51    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.15/41.51         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.15/41.51    (5)   ~ (e3 = e1)
% 230.15/41.51    (6)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.15/41.51         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.15/41.51    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.15/41.51           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.15/41.51    (8)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.15/41.51         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.15/41.51    (9)   ~ (all_6_2 = e3)
% 230.15/41.51    (10)  op(e1, e1) = all_6_2
% 230.15/41.51    (11)  op(e2, e2) = e1
% 230.15/41.51    (12)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.15/41.51          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.15/41.51    (13)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.15/41.51          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.15/41.51    (14)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.15/41.51          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.15/41.51    (15)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 230.15/41.51          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.15/41.51    (16)   ~ (e3 = e2)
% 230.15/41.51    (17)   ~ (e3 = e0)
% 230.15/41.51    (18)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.15/41.51          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.15/41.51    (19)  op(e0, e3) = all_53_3
% 230.15/41.51    (20)  all_57_15 = e3
% 230.15/41.51    (21)  op(e3, e3) = e0
% 230.15/41.51    (22)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.15/41.51          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.15/41.51            e1)
% 230.15/41.51    (23)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.15/41.51          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.15/41.51    (24)   ~ (e2 = e0)
% 230.15/41.51    (25)  all_57_2 = e3
% 230.15/41.51    (26)  all_57_3 = e1
% 230.15/41.51    (27)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.15/41.51          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.15/41.51    (28)   ~ (e1 = e0)
% 230.15/41.51    (29)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 230.15/41.51          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 230.15/41.51    (30)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.15/41.51          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.15/41.51    (31)  op(e0, e0) = e3
% 230.15/41.51    (32)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.15/41.51          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.15/41.51            e2)
% 230.15/41.51    (33)   ~ (all_53_3 = e0)
% 230.15/41.51    (34)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.15/41.51              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.15/41.51                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.15/41.51                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.15/41.51    (35)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.15/41.51          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.15/41.51    (36)   ~ (all_53_12 = e3)
% 230.15/41.51    (37)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.15/41.51          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.15/41.51    (38)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.15/41.51          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.15/41.51    (39)   ~ (all_53_12 = e0)
% 230.15/41.51    (40)   ~ (e2 = e1)
% 230.15/41.51    (41)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.15/41.51          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.15/41.51    (42)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.15/41.51          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.15/41.51    (43)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.15/41.51          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.15/41.51    (44)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.15/41.51          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.15/41.51    (45)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.15/41.51          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.15/41.51    (46)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.15/41.51          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.15/41.51    (47)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.15/41.51          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.15/41.51    (48)  all_57_7 = e0
% 230.15/41.51    (49)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.15/41.51          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.15/41.51    (50)  op(e3, e0) = all_53_12
% 230.15/41.51  
% 230.15/41.51  Begin of proof
% 230.15/41.51  | 
% 230.15/41.51  | ALPHA: (1) implies:
% 230.15/41.51  |   (51)  all_57_7 = e3
% 230.15/41.51  | 
% 230.15/41.51  | COMBINE_EQS: (48), (51) imply:
% 230.15/41.51  |   (52)  e3 = e0
% 230.15/41.51  | 
% 230.15/41.51  | SIMP: (52) implies:
% 230.15/41.51  |   (53)  e3 = e0
% 230.15/41.51  | 
% 230.15/41.51  | COMBINE_EQS: (25), (53) imply:
% 230.15/41.51  |   (54)  all_57_2 = e0
% 230.15/41.51  | 
% 230.15/41.51  | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 230.15/41.51  |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 230.15/41.51  |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 230.15/41.51  |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 230.15/41.51  |            (49), (50), (54) are inconsistent by sub-proof #1016.
% 230.15/41.51  | 
% 230.15/41.51  End of proof
% 230.15/41.51  
% 230.15/41.51  Sub-proof #1016 shows that the following formulas are inconsistent:
% 230.15/41.51  ----------------------------------------------------------------
% 230.15/41.51    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.15/41.51         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.15/41.51    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.15/41.51         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.15/41.51    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.15/41.51         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.15/41.51    (4)   ~ (e3 = e1)
% 230.15/41.51    (5)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.15/41.51         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.15/41.51    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.15/41.51           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.15/41.51    (7)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.15/41.51         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.15/41.51    (8)   ~ (all_6_2 = e3)
% 230.15/41.51    (9)  op(e1, e1) = all_6_2
% 230.15/41.51    (10)  op(e2, e2) = e1
% 230.15/41.51    (11)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.15/41.51          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.15/41.51    (12)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.15/41.51          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.15/41.51    (13)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.15/41.51          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.15/41.51    (14)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 230.15/41.51          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.15/41.51    (15)   ~ (e3 = e2)
% 230.15/41.51    (16)   ~ (e3 = e0)
% 230.15/41.51    (17)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.15/41.51          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.15/41.51    (18)  op(e0, e3) = all_53_3
% 230.15/41.51    (19)  all_57_15 = e3
% 230.15/41.51    (20)  op(e3, e3) = e0
% 230.15/41.51    (21)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.15/41.51          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.15/41.51            e1)
% 230.15/41.51    (22)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.15/41.51          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.15/41.51    (23)   ~ (e2 = e0)
% 230.15/41.51    (24)  all_57_3 = e1
% 230.15/41.51    (25)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.15/41.51          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.15/41.51    (26)   ~ (e1 = e0)
% 230.15/41.51    (27)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 230.15/41.51          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 230.15/41.51    (28)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.15/41.51          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.15/41.51    (29)  op(e0, e0) = e3
% 230.15/41.51    (30)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.15/41.51          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.15/41.51            e2)
% 230.15/41.51    (31)   ~ (all_53_3 = e0)
% 230.15/41.51    (32)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.15/41.51              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.15/41.51                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.15/41.51                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.15/41.51    (33)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.15/41.51          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.15/41.51    (34)  all_57_2 = e0
% 230.15/41.51    (35)   ~ (all_53_12 = e3)
% 230.15/41.51    (36)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.15/41.51          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.15/41.51    (37)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.15/41.51          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.15/41.51    (38)   ~ (all_53_12 = e0)
% 230.15/41.51    (39)   ~ (e2 = e1)
% 230.15/41.51    (40)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.15/41.51          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.15/41.51    (41)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.15/41.51          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.15/41.51    (42)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.15/41.51          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.15/41.51    (43)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.15/41.51          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.15/41.51    (44)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.15/41.51          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.15/41.51    (45)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.15/41.51          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.15/41.51    (46)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.15/41.51          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.15/41.51    (47)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.15/41.51          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.15/41.51    (48)  op(e3, e0) = all_53_12
% 230.15/41.51  
% 230.15/41.51  Begin of proof
% 230.15/41.51  | 
% 230.15/41.51  | BETA: splitting (33) gives:
% 230.15/41.51  | 
% 230.15/41.51  | Case 1:
% 230.15/41.51  | | 
% 230.15/41.51  | |   (49)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 230.15/41.51  | |           e3)
% 230.15/41.51  | | 
% 230.15/41.51  | | REF_CLOSE: (4), (6), (10), (16), (34), (49) are inconsistent by sub-proof
% 230.15/41.51  | |            #1849.
% 230.15/41.51  | | 
% 230.15/41.51  | Case 2:
% 230.15/41.51  | | 
% 230.15/41.51  | |   (50)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 230.15/41.51  | |           e3)
% 230.15/41.51  | | 
% 230.15/41.51  | | BETA: splitting (50) gives:
% 230.15/41.51  | | 
% 230.15/41.51  | | Case 1:
% 230.15/41.51  | | | 
% 230.15/41.51  | | |   (51)  all_57_5 = e3 & op(e2, e1) = e3
% 230.15/41.51  | | | 
% 230.15/41.51  | | | ALPHA: (51) implies:
% 230.15/41.51  | | |   (52)  all_57_5 = e3
% 230.15/41.51  | | | 
% 230.15/41.51  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 230.15/41.51  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 230.15/41.51  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 230.15/41.51  | | |            (34), (35), (36), (37), (38), (39), (40), (41), (42), (43),
% 230.15/41.51  | | |            (44), (45), (46), (47), (48), (52) are inconsistent by
% 230.15/41.51  | | |            sub-proof #1021.
% 230.15/41.51  | | | 
% 230.15/41.51  | | Case 2:
% 230.15/41.51  | | | 
% 230.15/41.51  | | |   (53)  all_57_10 = e3 & op(e2, e0) = e3
% 230.15/41.51  | | | 
% 230.15/41.51  | | | ALPHA: (53) implies:
% 230.15/41.51  | | |   (54)  all_57_10 = e3
% 230.15/41.51  | | | 
% 230.15/41.51  | | | REF_CLOSE: (4), (6), (15), (16), (19), (23), (26), (29), (32), (39), (40),
% 230.15/41.51  | | |            (44), (54) are inconsistent by sub-proof #1746.
% 230.15/41.51  | | | 
% 230.15/41.51  | | End of split
% 230.15/41.51  | | 
% 230.15/41.51  | End of split
% 230.15/41.51  | 
% 230.15/41.51  End of proof
% 230.15/41.51  
% 230.15/41.51  Sub-proof #1017 shows that the following formulas are inconsistent:
% 230.15/41.51  ----------------------------------------------------------------
% 230.15/41.51    (1)  e1 = e0
% 230.15/41.51    (2)  all_57_10 = e0
% 230.15/41.51    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.15/41.51         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.15/41.51    (4)   ~ (e3 = e1)
% 230.15/41.51    (5)   ~ (e3 = e2)
% 230.15/41.51    (6)  all_57_5 = e3
% 230.15/41.51    (7)   ~ (e2 = e0)
% 230.15/41.51    (8)  all_57_3 = e1
% 230.15/41.51    (9)   ~ (e1 = e0)
% 230.15/41.51    (10)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.15/41.51          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.15/41.51    (11)   ~ (e2 = e1)
% 230.15/41.51  
% 230.15/41.51  Begin of proof
% 230.15/41.51  | 
% 230.15/41.51  | SIMP: (1) implies:
% 230.15/41.51  |   (12)  e1 = e0
% 230.15/41.51  | 
% 230.15/41.51  | COMBINE_EQS: (8), (12) imply:
% 230.15/41.51  |   (13)  all_57_3 = e0
% 230.15/41.51  | 
% 230.15/41.51  | REF_CLOSE: (2), (3), (4), (5), (6), (7), (9), (10), (11), (13) are
% 230.15/41.51  |            inconsistent by sub-proof #1518.
% 230.15/41.51  | 
% 230.15/41.51  End of proof
% 230.15/41.51  
% 230.15/41.51  Sub-proof #1018 shows that the following formulas are inconsistent:
% 230.15/41.51  ----------------------------------------------------------------
% 230.15/41.51    (1)  all_57_10 = e0
% 230.15/41.51    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.15/41.51           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.15/41.51    (3)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) = all_22_1
% 230.15/41.51           & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0, e3) =
% 230.15/41.51           all_22_1 & $i(all_22_1))
% 230.15/41.51    (4)  all_57_9 = e1
% 230.15/41.51    (5)   ~ (e3 = e2)
% 230.15/41.51    (6)  op(e0, e3) = e1
% 230.15/41.51    (7)  all_57_15 = e3
% 230.15/41.51    (8)   ~ (e2 = e0)
% 230.15/41.51    (9)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) = all_12_1
% 230.15/41.51           & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0, e3) =
% 230.15/41.51           all_12_1 & $i(all_12_1))
% 230.15/41.51    (10)   ~ (e2 = e1)
% 230.15/41.51    (11)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.15/41.51          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.15/41.51  
% 230.15/41.51  Begin of proof
% 230.15/41.51  | 
% 230.15/41.51  | BETA: splitting (11) gives:
% 230.15/41.51  | 
% 230.15/41.51  | Case 1:
% 230.15/41.51  | | 
% 230.15/41.51  | |   (12)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 230.15/41.51  | |           e2)
% 230.15/41.51  | | 
% 230.15/41.51  | | BETA: splitting (12) gives:
% 230.15/41.51  | | 
% 230.15/41.51  | | Case 1:
% 230.15/41.51  | | | 
% 230.15/41.51  | | |   (13)  all_57_9 = e2 & op(e3, e0) = e2
% 230.15/41.51  | | | 
% 230.15/41.51  | | | REF_CLOSE: (4), (10), (13) are inconsistent by sub-proof #2481.
% 230.15/41.51  | | | 
% 230.15/41.51  | | Case 2:
% 230.15/41.51  | | | 
% 230.15/41.51  | | |   (14)  all_57_10 = e2 & op(e2, e0) = e2
% 230.15/41.51  | | | 
% 230.15/41.51  | | | REF_CLOSE: (1), (8), (14) are inconsistent by sub-proof #1798.
% 230.15/41.51  | | | 
% 230.15/41.51  | | End of split
% 230.15/41.51  | | 
% 230.15/41.51  | Case 2:
% 230.15/41.51  | | 
% 230.15/41.51  | |   (15)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.15/41.51  | |           e2)
% 230.15/41.51  | | 
% 230.15/41.51  | | REF_CLOSE: (2), (3), (5), (6), (7), (9), (15) are inconsistent by sub-proof
% 230.15/41.51  | |            #1019.
% 230.15/41.51  | | 
% 230.15/41.51  | End of split
% 230.15/41.51  | 
% 230.15/41.51  End of proof
% 230.15/41.51  
% 230.15/41.51  Sub-proof #1019 shows that the following formulas are inconsistent:
% 230.15/41.51  ----------------------------------------------------------------
% 230.15/41.51    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.15/41.51           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.15/41.51    (2)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) = all_22_1
% 230.15/41.51           & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0, e3) =
% 230.15/41.51           all_22_1 & $i(all_22_1))
% 230.15/41.51    (3)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.15/41.51    (4)   ~ (e3 = e2)
% 230.15/41.51    (5)  op(e0, e3) = e1
% 230.15/41.51    (6)  all_57_15 = e3
% 230.15/41.51    (7)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) = all_12_1
% 230.15/41.51           & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0, e3) =
% 230.15/41.51           all_12_1 & $i(all_12_1))
% 230.15/41.51  
% 230.15/41.51  Begin of proof
% 230.15/41.51  | 
% 230.15/41.51  | BETA: splitting (3) gives:
% 230.15/41.51  | 
% 230.15/41.51  | Case 1:
% 230.15/41.51  | | 
% 230.15/41.51  | |   (8)  all_57_11 = e2 & op(e1, e0) = e2
% 230.15/41.51  | | 
% 230.15/41.51  | | ALPHA: (8) implies:
% 230.15/41.51  | |   (9)  op(e1, e0) = e2
% 230.15/41.51  | | 
% 230.15/41.51  | | REF_CLOSE: (1), (2), (5), (7), (9) are inconsistent by sub-proof #1147.
% 230.15/41.51  | | 
% 230.15/41.51  | Case 2:
% 230.15/41.51  | | 
% 230.15/41.51  | |   (10)  all_57_15 = e2 & op(e0, e0) = e2
% 230.15/41.51  | | 
% 230.15/41.51  | | REF_CLOSE: (4), (6), (10) are inconsistent by sub-proof #2323.
% 230.15/41.51  | | 
% 230.15/41.51  | End of split
% 230.15/41.51  | 
% 230.15/41.51  End of proof
% 230.15/41.51  
% 230.15/41.51  Sub-proof #1020 shows that the following formulas are inconsistent:
% 230.15/41.51  ----------------------------------------------------------------
% 230.15/41.51    (1)   ~ (e3 = e1)
% 230.15/41.51    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.15/41.51           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.15/41.51    (3)   ~ (e3 = e0)
% 230.15/41.51    (4)  all_57_4 = e1
% 230.15/41.51    (5)  op(e3, e3) = e0
% 230.15/41.51    (6)  all_57_5 = e3
% 230.15/41.51    (7)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.15/41.51         (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.15/41.51    (8)  all_57_5 = e0 & op(e2, e1) = e0
% 230.15/41.51    (9)   ~ (all_53_12 = e3)
% 230.15/41.51    (10)  all_57_1 = e3
% 230.15/41.51    (11)  op(e3, e0) = all_53_12
% 230.15/41.51  
% 230.15/41.51  Begin of proof
% 230.15/41.51  | 
% 230.15/41.51  | ALPHA: (8) implies:
% 230.15/41.51  |   (12)  all_57_5 = e0
% 230.15/41.51  | 
% 230.15/41.51  | COMBINE_EQS: (6), (12) imply:
% 230.15/41.51  |   (13)  e3 = e0
% 230.15/41.51  | 
% 230.15/41.51  | COMBINE_EQS: (10), (13) imply:
% 230.15/41.51  |   (14)  all_57_1 = e0
% 230.15/41.51  | 
% 230.15/41.51  | REF_CLOSE: (1), (2), (3), (4), (5), (7), (9), (11), (14) are inconsistent by
% 230.15/41.51  |            sub-proof #2280.
% 230.15/41.51  | 
% 230.15/41.51  End of proof
% 230.15/41.51  
% 230.15/41.51  Sub-proof #1021 shows that the following formulas are inconsistent:
% 230.15/41.51  ----------------------------------------------------------------
% 230.15/41.51    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.15/41.51         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.15/41.51    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.15/41.51         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.15/41.51    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.15/41.51         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.15/41.51    (4)   ~ (e3 = e1)
% 230.15/41.51    (5)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.15/41.51         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.15/41.51    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.15/41.51           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.15/41.51    (7)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.15/41.51         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.15/41.51    (8)   ~ (all_6_2 = e3)
% 230.15/41.51    (9)  op(e1, e1) = all_6_2
% 230.15/41.51    (10)  op(e2, e2) = e1
% 230.15/41.51    (11)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.15/41.51          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.15/41.51    (12)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.15/41.51          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.15/41.51    (13)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.15/41.51          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.15/41.51    (14)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 230.15/41.51          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.15/41.51    (15)   ~ (e3 = e2)
% 230.15/41.51    (16)   ~ (e3 = e0)
% 230.15/41.51    (17)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.15/41.51          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.15/41.51    (18)  op(e0, e3) = all_53_3
% 230.15/41.51    (19)  all_57_15 = e3
% 230.15/41.51    (20)  op(e3, e3) = e0
% 230.15/41.51    (21)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.15/41.51          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.15/41.51            e1)
% 230.15/41.51    (22)  all_57_5 = e3
% 230.15/41.51    (23)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.15/41.51          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.15/41.51    (24)   ~ (e2 = e0)
% 230.15/41.51    (25)  all_57_3 = e1
% 230.15/41.51    (26)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.15/41.51          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.15/41.51    (27)   ~ (e1 = e0)
% 230.15/41.51    (28)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 230.15/41.51          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 230.15/41.52    (29)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.15/41.52          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.15/41.52    (30)  op(e0, e0) = e3
% 230.15/41.52    (31)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.15/41.52          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.15/41.52            e2)
% 230.15/41.52    (32)   ~ (all_53_3 = e0)
% 230.15/41.52    (33)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.15/41.52              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.15/41.52                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.15/41.52                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.15/41.52    (34)  all_57_2 = e0
% 230.15/41.52    (35)   ~ (all_53_12 = e3)
% 230.15/41.52    (36)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.15/41.52          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.15/41.52    (37)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.15/41.52          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.15/41.52    (38)   ~ (all_53_12 = e0)
% 230.15/41.52    (39)   ~ (e2 = e1)
% 230.15/41.52    (40)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.15/41.52          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.15/41.52    (41)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.15/41.52          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.15/41.52    (42)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.15/41.52          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.15/41.52    (43)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.15/41.52          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.15/41.52    (44)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.15/41.52          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.15/41.52    (45)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.15/41.52          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.15/41.52    (46)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.15/41.52          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.15/41.52    (47)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.15/41.52          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.15/41.52    (48)  op(e3, e0) = all_53_12
% 230.15/41.52  
% 230.15/41.52  Begin of proof
% 230.15/41.52  | 
% 230.15/41.52  | BETA: splitting (13) gives:
% 230.15/41.52  | 
% 230.15/41.52  | Case 1:
% 230.15/41.52  | | 
% 230.15/41.52  | |   (49)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) =
% 230.15/41.52  | |           e0)
% 230.15/41.52  | | 
% 230.15/41.52  | | BETA: splitting (49) gives:
% 230.15/41.52  | | 
% 230.15/41.52  | | Case 1:
% 230.15/41.52  | | | 
% 230.15/41.52  | | |   (50)  all_57_0 = e0 & op(e3, e3) = e0
% 230.15/41.52  | | | 
% 230.15/41.52  | | | ALPHA: (50) implies:
% 230.15/41.52  | | |   (51)  all_57_0 = e0
% 230.15/41.52  | | | 
% 230.15/41.52  | | | BETA: splitting (37) gives:
% 230.15/41.52  | | | 
% 230.15/41.52  | | | Case 1:
% 230.15/41.52  | | | | 
% 230.15/41.52  | | | |   (52)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3)
% 230.15/41.52  | | | |           = e3)
% 230.15/41.52  | | | | 
% 230.15/41.52  | | | | REF_CLOSE: (6), (16), (20), (34), (52) are inconsistent by sub-proof
% 230.15/41.52  | | | |            #1559.
% 230.15/41.52  | | | | 
% 230.15/41.52  | | | Case 2:
% 230.15/41.52  | | | | 
% 230.15/41.52  | | | |   (53)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3)
% 230.15/41.52  | | | |           = e3)
% 230.15/41.52  | | | | 
% 230.15/41.52  | | | | BETA: splitting (53) gives:
% 230.15/41.52  | | | | 
% 230.15/41.52  | | | | Case 1:
% 230.15/41.52  | | | | | 
% 230.15/41.52  | | | | |   (54)  all_57_6 = e3 & op(e1, e3) = e3
% 230.15/41.52  | | | | | 
% 230.15/41.52  | | | | | ALPHA: (54) implies:
% 230.15/41.52  | | | | |   (55)  all_57_6 = e3
% 230.15/41.52  | | | | | 
% 230.15/41.52  | | | | | REF_CLOSE: (1), (2), (4), (6), (15), (20), (22), (24), (25), (27),
% 230.15/41.52  | | | | |            (34), (36), (39), (41), (51), (55) are inconsistent by
% 230.15/41.52  | | | | |            sub-proof #1066.
% 230.15/41.52  | | | | | 
% 230.15/41.52  | | | | Case 2:
% 230.15/41.52  | | | | | 
% 230.15/41.52  | | | | |   (56)  all_57_12 = e3 & op(e0, e3) = e3
% 230.15/41.52  | | | | | 
% 230.15/41.52  | | | | | ALPHA: (56) implies:
% 230.15/41.52  | | | | |   (57)  all_57_12 = e3
% 230.15/41.52  | | | | | 
% 230.15/41.52  | | | | | BETA: splitting (21) gives:
% 230.15/41.52  | | | | | 
% 230.15/41.52  | | | | | Case 1:
% 230.15/41.52  | | | | | | 
% 230.15/41.52  | | | | | |   (58)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 &
% 230.15/41.52  | | | | | |           op(e0, e2) = e1)
% 230.15/41.52  | | | | | | 
% 230.15/41.52  | | | | | | BETA: splitting (58) gives:
% 230.15/41.52  | | | | | | 
% 230.15/41.52  | | | | | | Case 1:
% 230.15/41.52  | | | | | | | 
% 230.15/41.52  | | | | | | |   (59)  all_57_12 = e1 & op(e0, e3) = e1
% 230.15/41.52  | | | | | | | 
% 230.15/41.52  | | | | | | | ALPHA: (59) implies:
% 230.15/41.52  | | | | | | |   (60)  all_57_12 = e1
% 230.15/41.52  | | | | | | | 
% 230.15/41.52  | | | | | | | REF_CLOSE: (4), (57), (60) are inconsistent by sub-proof #2151.
% 230.15/41.52  | | | | | | | 
% 230.15/41.52  | | | | | | Case 2:
% 230.15/41.52  | | | | | | | 
% 230.15/41.52  | | | | | | |   (61)  all_57_13 = e1 & op(e0, e2) = e1
% 230.15/41.52  | | | | | | | 
% 230.15/41.52  | | | | | | | ALPHA: (61) implies:
% 230.15/41.52  | | | | | | |   (62)  all_57_13 = e1
% 230.15/41.52  | | | | | | | 
% 230.15/41.52  | | | | | | | REF_CLOSE: (1), (4), (6), (15), (16), (18), (19), (21), (22),
% 230.15/41.52  | | | | | | |            (24), (25), (27), (30), (31), (32), (33), (34), (36),
% 230.15/41.52  | | | | | | |            (39), (57), (62) are inconsistent by sub-proof #1065.
% 230.15/41.52  | | | | | | | 
% 230.15/41.52  | | | | | | End of split
% 230.15/41.52  | | | | | | 
% 230.15/41.52  | | | | | Case 2:
% 230.15/41.52  | | | | | | 
% 230.15/41.52  | | | | | |   (63)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 &
% 230.15/41.52  | | | | | |           op(e0, e0) = e1)
% 230.15/41.52  | | | | | | 
% 230.15/41.52  | | | | | | BETA: splitting (63) gives:
% 230.15/41.52  | | | | | | 
% 230.15/41.52  | | | | | | Case 1:
% 230.15/41.52  | | | | | | | 
% 230.15/41.52  | | | | | | |   (64)  all_57_14 = e1 & op(e0, e1) = e1
% 230.15/41.52  | | | | | | | 
% 230.15/41.52  | | | | | | | ALPHA: (64) implies:
% 230.15/41.52  | | | | | | |   (65)  all_57_14 = e1
% 230.15/41.52  | | | | | | | 
% 230.15/41.52  | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 230.15/41.52  | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18), (19),
% 230.15/41.52  | | | | | | |            (20), (21), (22), (23), (24), (25), (26), (27), (28),
% 230.15/41.52  | | | | | | |            (29), (30), (31), (32), (33), (34), (35), (36), (37),
% 230.15/41.52  | | | | | | |            (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 230.15/41.52  | | | | | | |            (47), (48), (51), (57), (65) are inconsistent by
% 230.15/41.52  | | | | | | |            sub-proof #1022.
% 230.15/41.52  | | | | | | | 
% 230.15/41.52  | | | | | | Case 2:
% 230.15/41.52  | | | | | | | 
% 230.15/41.52  | | | | | | |   (66)  all_57_15 = e1 & op(e0, e0) = e1
% 230.15/41.52  | | | | | | | 
% 230.15/41.52  | | | | | | | ALPHA: (66) implies:
% 230.15/41.52  | | | | | | |   (67)  op(e0, e0) = e1
% 230.15/41.52  | | | | | | | 
% 230.15/41.52  | | | | | | | REF_CLOSE: (4), (6), (30), (67) are inconsistent by sub-proof
% 230.15/41.52  | | | | | | |            #2183.
% 230.15/41.52  | | | | | | | 
% 230.15/41.52  | | | | | | End of split
% 230.15/41.52  | | | | | | 
% 230.15/41.52  | | | | | End of split
% 230.15/41.52  | | | | | 
% 230.15/41.52  | | | | End of split
% 230.15/41.52  | | | | 
% 230.15/41.52  | | | End of split
% 230.15/41.52  | | | 
% 230.15/41.52  | | Case 2:
% 230.15/41.52  | | | 
% 230.15/41.52  | | |   (68)  all_57_1 = e0 & op(e3, e2) = e0
% 230.15/41.52  | | | 
% 230.15/41.52  | | | ALPHA: (68) implies:
% 230.15/41.52  | | |   (69)  all_57_1 = e0
% 230.15/41.52  | | | 
% 230.15/41.52  | | | REF_CLOSE: (3), (4), (6), (10), (15), (16), (18), (19), (20), (21), (24),
% 230.15/41.52  | | |            (25), (27), (29), (30), (31), (32), (33), (34), (37), (39),
% 230.15/41.52  | | |            (41), (46), (69) are inconsistent by sub-proof #1059.
% 230.15/41.52  | | | 
% 230.15/41.52  | | End of split
% 230.15/41.52  | | 
% 230.15/41.52  | Case 2:
% 230.15/41.52  | | 
% 230.15/41.52  | |   (70)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) =
% 230.15/41.52  | |           e0)
% 230.15/41.52  | | 
% 230.15/41.52  | | BETA: splitting (70) gives:
% 230.15/41.52  | | 
% 230.15/41.52  | | Case 1:
% 230.15/41.52  | | | 
% 230.15/41.52  | | |   (71)  all_57_4 = e0 & op(e3, e1) = e0
% 230.15/41.52  | | | 
% 230.15/41.52  | | | ALPHA: (71) implies:
% 230.15/41.52  | | |   (72)  all_57_4 = e0
% 230.15/41.52  | | | 
% 230.15/41.52  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 230.15/41.52  | | |            (13), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 230.15/41.52  | | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 230.15/41.52  | | |            (34), (35), (36), (37), (38), (39), (40), (41), (42), (43),
% 230.15/41.52  | | |            (44), (45), (46), (47), (48), (72) are inconsistent by
% 230.15/41.52  | | |            sub-proof #1024.
% 230.15/41.52  | | | 
% 230.15/41.52  | | Case 2:
% 230.15/41.52  | | | 
% 230.15/41.52  | | |   (73)  all_57_9 = e0 & op(e3, e0) = e0
% 230.15/41.52  | | | 
% 230.15/41.52  | | | REF_CLOSE: (6), (38), (48), (73) are inconsistent by sub-proof #2434.
% 230.15/41.52  | | | 
% 230.15/41.52  | | End of split
% 230.15/41.52  | | 
% 230.15/41.52  | End of split
% 230.15/41.52  | 
% 230.15/41.52  End of proof
% 230.15/41.52  
% 230.15/41.52  Sub-proof #1022 shows that the following formulas are inconsistent:
% 230.15/41.52  ----------------------------------------------------------------
% 230.15/41.52    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.15/41.52         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.15/41.52    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.15/41.52         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.15/41.52    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.15/41.52         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.15/41.52    (4)   ~ (e3 = e1)
% 230.15/41.52    (5)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.15/41.52         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.15/41.52    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.15/41.52           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.15/41.52    (7)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.15/41.52         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.15/41.52    (8)   ~ (all_6_2 = e3)
% 230.15/41.52    (9)  op(e1, e1) = all_6_2
% 230.15/41.52    (10)  op(e2, e2) = e1
% 230.15/41.52    (11)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.15/41.52          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.15/41.52    (12)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.15/41.52          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.15/41.52    (13)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.15/41.52          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.15/41.52    (14)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 230.15/41.52          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.15/41.52    (15)   ~ (e3 = e2)
% 230.15/41.52    (16)   ~ (e3 = e0)
% 230.15/41.52    (17)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.15/41.52          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.15/41.52    (18)  op(e0, e3) = all_53_3
% 230.15/41.52    (19)  all_57_0 = e0
% 230.15/41.52    (20)  all_57_15 = e3
% 230.15/41.52    (21)  op(e3, e3) = e0
% 230.15/41.52    (22)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.15/41.52          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.15/41.52            e1)
% 230.15/41.52    (23)  all_57_5 = e3
% 230.15/41.52    (24)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.15/41.52          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.15/41.52    (25)   ~ (e2 = e0)
% 230.15/41.52    (26)  all_57_3 = e1
% 230.15/41.52    (27)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.15/41.52          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.15/41.52    (28)   ~ (e1 = e0)
% 230.15/41.52    (29)  all_57_12 = e3
% 230.15/41.52    (30)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 230.15/41.52          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 230.15/41.52    (31)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.15/41.52          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.15/41.52    (32)  all_57_14 = e1
% 230.15/41.52    (33)  op(e0, e0) = e3
% 230.15/41.52    (34)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.15/41.52          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.15/41.52            e2)
% 230.15/41.52    (35)   ~ (all_53_3 = e0)
% 230.15/41.52    (36)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.15/41.52              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.15/41.52                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.15/41.52                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.15/41.52    (37)  all_57_2 = e0
% 230.15/41.52    (38)   ~ (all_53_12 = e3)
% 230.15/41.52    (39)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.15/41.52          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.15/41.52    (40)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.15/41.52          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.15/41.52    (41)   ~ (all_53_12 = e0)
% 230.15/41.52    (42)   ~ (e2 = e1)
% 230.15/41.52    (43)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.15/41.52          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.15/41.52    (44)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.15/41.52          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.15/41.52    (45)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.15/41.52          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.15/41.52    (46)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.15/41.52          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.15/41.52    (47)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.15/41.52          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.15/41.52    (48)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.15/41.52          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.15/41.52    (49)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.15/41.52          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.15/41.52    (50)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.15/41.52          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.15/41.52    (51)  op(e3, e0) = all_53_12
% 230.15/41.52  
% 230.15/41.52  Begin of proof
% 230.15/41.52  | 
% 230.15/41.52  | BETA: splitting (14) gives:
% 230.15/41.52  | 
% 230.15/41.52  | Case 1:
% 230.15/41.52  | | 
% 230.15/41.52  | |   (52)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) =
% 230.15/41.52  | |           e0)
% 230.15/41.52  | | 
% 230.15/41.52  | | BETA: splitting (52) gives:
% 230.15/41.52  | | 
% 230.15/41.52  | | Case 1:
% 230.15/41.52  | | | 
% 230.15/41.52  | | |   (53)  all_57_4 = e0 & op(e3, e1) = e0
% 230.15/41.52  | | | 
% 230.15/41.52  | | | ALPHA: (53) implies:
% 230.15/41.52  | | |   (54)  all_57_4 = e0
% 230.15/41.52  | | | 
% 230.15/41.52  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 230.15/41.52  | | |            (13), (15), (16), (17), (18), (20), (21), (22), (23), (24),
% 230.15/41.52  | | |            (25), (26), (27), (28), (30), (31), (33), (34), (35), (36),
% 230.15/41.52  | | |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 230.15/41.52  | | |            (47), (48), (49), (50), (51), (54) are inconsistent by
% 230.15/41.52  | | |            sub-proof #1024.
% 230.15/41.52  | | | 
% 230.15/41.52  | | Case 2:
% 230.15/41.52  | | | 
% 230.15/41.52  | | |   (55)  all_57_5 = e0 & op(e2, e1) = e0
% 230.15/41.52  | | | 
% 230.15/41.52  | | | REF_CLOSE: (16), (23), (55) are inconsistent by sub-proof #2414.
% 230.15/41.52  | | | 
% 230.15/41.52  | | End of split
% 230.15/41.52  | | 
% 230.15/41.52  | Case 2:
% 230.15/41.52  | | 
% 230.15/41.52  | |   (56)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 230.15/41.52  | |           e0)
% 230.15/41.52  | | 
% 230.15/41.52  | | BETA: splitting (56) gives:
% 230.15/41.52  | | 
% 230.15/41.52  | | Case 1:
% 230.15/41.52  | | | 
% 230.15/41.52  | | |   (57)  all_57_8 = e0 & op(e1, e1) = e0
% 230.15/41.52  | | | 
% 230.15/41.52  | | | ALPHA: (57) implies:
% 230.15/41.52  | | |   (58)  all_57_8 = e0
% 230.15/41.52  | | | 
% 230.15/41.52  | | | BETA: splitting (36) gives:
% 230.15/41.52  | | | 
% 230.15/41.52  | | | Case 1:
% 230.15/41.52  | | | | 
% 230.15/41.52  | | | |   (59)  all_57_15 = e0 & op(e0, e0) = e0
% 230.15/41.52  | | | | 
% 230.15/41.52  | | | | ALPHA: (59) implies:
% 230.15/41.52  | | | |   (60)  op(e0, e0) = e0
% 230.15/41.52  | | | | 
% 230.15/41.52  | | | | REF_CLOSE: (6), (16), (33), (60) are inconsistent by sub-proof #2304.
% 230.15/41.52  | | | | 
% 230.15/41.52  | | | Case 2:
% 230.15/41.52  | | | | 
% 230.15/41.52  | | | |   (61)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2,
% 230.15/41.52  | | | |               e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) &
% 230.15/41.52  | | | |         ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0,
% 230.15/41.52  | | | |               e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 230.15/41.52  | | | | 
% 230.15/41.52  | | | | ALPHA: (61) implies:
% 230.15/41.52  | | | |   (62)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0,
% 230.15/41.52  | | | |             e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.15/41.52  | | | | 
% 230.15/41.52  | | | | BETA: splitting (62) gives:
% 230.15/41.52  | | | | 
% 230.15/41.52  | | | | Case 1:
% 230.15/41.52  | | | | | 
% 230.15/41.52  | | | | |   (63)  all_57_12 = e0 & op(e0, e3) = e0
% 230.15/41.52  | | | | | 
% 230.15/41.52  | | | | | ALPHA: (63) implies:
% 230.15/41.52  | | | | |   (64)  op(e0, e3) = e0
% 230.15/41.52  | | | | | 
% 230.15/41.52  | | | | | REF_CLOSE: (6), (18), (35), (64) are inconsistent by sub-proof #2366.
% 230.15/41.52  | | | | | 
% 230.15/41.52  | | | | Case 2:
% 230.15/41.52  | | | | | 
% 230.15/41.52  | | | | |   (65)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 230.15/41.52  | | | | |             e1) = e0)
% 230.15/41.52  | | | | | 
% 230.15/41.52  | | | | | BETA: splitting (65) gives:
% 230.15/41.52  | | | | | 
% 230.15/41.52  | | | | | Case 1:
% 230.15/41.52  | | | | | | 
% 230.15/41.52  | | | | | |   (66)  all_57_13 = e0 & op(e0, e2) = e0
% 230.15/41.52  | | | | | | 
% 230.15/41.52  | | | | | | ALPHA: (66) implies:
% 230.15/41.52  | | | | | |   (67)  all_57_13 = e0
% 230.15/41.52  | | | | | | 
% 230.15/41.52  | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 230.15/41.52  | | | | | |            (12), (13), (15), (16), (17), (18), (19), (20), (21),
% 230.15/41.52  | | | | | |            (22), (23), (24), (25), (26), (27), (28), (29), (30),
% 230.15/41.52  | | | | | |            (31), (32), (33), (34), (35), (36), (37), (38), (39),
% 230.15/41.52  | | | | | |            (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 230.15/41.52  | | | | | |            (49), (50), (51), (58), (67) are inconsistent by
% 230.15/41.52  | | | | | |            sub-proof #1023.
% 230.15/41.52  | | | | | | 
% 230.15/41.52  | | | | | Case 2:
% 230.15/41.52  | | | | | | 
% 230.15/41.52  | | | | | |   (68)  all_57_14 = e0 & op(e0, e1) = e0
% 230.15/41.52  | | | | | | 
% 230.15/41.52  | | | | | | ALPHA: (68) implies:
% 230.15/41.52  | | | | | |   (69)  all_57_14 = e0
% 230.15/41.52  | | | | | | 
% 230.15/41.52  | | | | | | REF_CLOSE: (4), (15), (20), (22), (25), (28), (29), (34), (42), (69)
% 230.15/41.52  | | | | | |            are inconsistent by sub-proof #1763.
% 230.15/41.52  | | | | | | 
% 230.15/41.52  | | | | | End of split
% 230.15/41.52  | | | | | 
% 230.15/41.52  | | | | End of split
% 230.15/41.52  | | | | 
% 230.15/41.52  | | | End of split
% 230.15/41.52  | | | 
% 230.15/41.52  | | Case 2:
% 230.15/41.52  | | | 
% 230.15/41.52  | | |   (70)  all_57_14 = e0 & op(e0, e1) = e0
% 230.15/41.52  | | | 
% 230.15/41.52  | | | ALPHA: (70) implies:
% 230.15/41.52  | | |   (71)  all_57_14 = e0
% 230.15/41.52  | | | 
% 230.15/41.52  | | | REF_CLOSE: (4), (15), (20), (22), (25), (28), (29), (34), (42), (71) are
% 230.15/41.52  | | |            inconsistent by sub-proof #1763.
% 230.15/41.52  | | | 
% 230.15/41.52  | | End of split
% 230.15/41.52  | | 
% 230.15/41.52  | End of split
% 230.15/41.52  | 
% 230.15/41.52  End of proof
% 230.15/41.52  
% 230.15/41.52  Sub-proof #1023 shows that the following formulas are inconsistent:
% 230.15/41.52  ----------------------------------------------------------------
% 230.15/41.52    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.15/41.52         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.15/41.52    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.15/41.52         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.15/41.52    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.15/41.52         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.15/41.52    (4)   ~ (e3 = e1)
% 230.15/41.52    (5)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.15/41.52         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.15/41.52    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.15/41.52           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.15/41.52    (7)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.15/41.52         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.15/41.52    (8)   ~ (all_6_2 = e3)
% 230.15/41.52    (9)  op(e1, e1) = all_6_2
% 230.15/41.52    (10)  op(e2, e2) = e1
% 230.15/41.52    (11)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.15/41.52          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.15/41.52    (12)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.15/41.52          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.15/41.52    (13)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.15/41.52          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.15/41.52    (14)   ~ (e3 = e2)
% 230.15/41.52    (15)   ~ (e3 = e0)
% 230.15/41.52    (16)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.15/41.52          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.15/41.52    (17)  op(e0, e3) = all_53_3
% 230.15/41.52    (18)  all_57_0 = e0
% 230.15/41.52    (19)  all_57_15 = e3
% 230.15/41.52    (20)  op(e3, e3) = e0
% 230.15/41.52    (21)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.15/41.52          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.15/41.52            e1)
% 230.15/41.52    (22)  all_57_5 = e3
% 230.15/41.52    (23)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.15/41.52          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.15/41.52    (24)   ~ (e2 = e0)
% 230.15/41.52    (25)  all_57_3 = e1
% 230.15/41.52    (26)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.15/41.52          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.15/41.52    (27)   ~ (e1 = e0)
% 230.15/41.52    (28)  all_57_12 = e3
% 230.15/41.52    (29)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 230.15/41.52          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 230.15/41.52    (30)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.15/41.52          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.15/41.52    (31)  all_57_14 = e1
% 230.15/41.52    (32)  op(e0, e0) = e3
% 230.15/41.52    (33)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.15/41.52          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.15/41.52            e2)
% 230.15/41.52    (34)   ~ (all_53_3 = e0)
% 230.15/41.52    (35)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.15/41.52              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.15/41.52                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.15/41.52                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.15/41.52    (36)  all_57_13 = e0
% 230.15/41.52    (37)  all_57_2 = e0
% 230.15/41.52    (38)   ~ (all_53_12 = e3)
% 230.15/41.52    (39)  all_57_8 = e0
% 230.15/41.52    (40)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.15/41.52          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.15/41.52    (41)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.15/41.52          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.15/41.52    (42)   ~ (all_53_12 = e0)
% 230.15/41.52    (43)   ~ (e2 = e1)
% 230.15/41.52    (44)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.15/41.52          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.15/41.52    (45)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.15/41.52          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.15/41.52    (46)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.15/41.52          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.15/41.52    (47)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.15/41.52          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.15/41.52    (48)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.15/41.52          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.15/41.52    (49)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.15/41.52          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.15/41.52    (50)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.15/41.52          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.15/41.52    (51)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.15/41.52          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.15/41.52    (52)  op(e3, e0) = all_53_12
% 230.15/41.52  
% 230.15/41.52  Begin of proof
% 230.15/41.52  | 
% 230.15/41.52  | BETA: splitting (46) gives:
% 230.15/41.52  | 
% 230.15/41.52  | Case 1:
% 230.15/41.52  | | 
% 230.15/41.52  | |   (53)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) =
% 230.15/41.52  | |           e2)
% 230.15/41.52  | | 
% 230.15/41.52  | | BETA: splitting (53) gives:
% 230.15/41.52  | | 
% 230.15/41.52  | | Case 1:
% 230.15/41.52  | | | 
% 230.15/41.52  | | |   (54)  all_57_4 = e2 & op(e3, e1) = e2
% 230.15/41.52  | | | 
% 230.15/41.52  | | | ALPHA: (54) implies:
% 230.15/41.52  | | |   (55)  all_57_4 = e2
% 230.15/41.52  | | | 
% 230.15/41.52  | | | BETA: splitting (11) gives:
% 230.15/41.52  | | | 
% 230.15/41.52  | | | Case 1:
% 230.15/41.52  | | | | 
% 230.15/41.52  | | | |   (56)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2)
% 230.15/41.52  | | | |           = e1)
% 230.15/41.52  | | | | 
% 230.15/41.52  | | | | BETA: splitting (56) gives:
% 230.15/41.52  | | | | 
% 230.15/41.52  | | | | Case 1:
% 230.15/41.52  | | | | | 
% 230.15/41.52  | | | | |   (57)  all_57_0 = e1 & op(e3, e3) = e1
% 230.15/41.52  | | | | | 
% 230.15/41.52  | | | | | REF_CLOSE: (1), (4), (14), (18), (22), (24), (25), (27), (37), (40),
% 230.15/41.52  | | | | |            (43), (57) are inconsistent by sub-proof #1068.
% 230.15/41.52  | | | | | 
% 230.15/41.52  | | | | Case 2:
% 230.15/41.52  | | | | | 
% 230.15/41.52  | | | | |   (58)  all_57_1 = e1 & op(e3, e2) = e1
% 230.15/41.52  | | | | | 
% 230.15/41.52  | | | | | ALPHA: (58) implies:
% 230.15/41.52  | | | | |   (59)  all_57_1 = e1
% 230.15/41.52  | | | | | 
% 230.15/41.52  | | | | | REF_CLOSE: (3), (4), (6), (10), (14), (15), (23), (24), (27), (30),
% 230.15/41.52  | | | | |            (43), (59) are inconsistent by sub-proof #1908.
% 230.15/41.52  | | | | | 
% 230.15/41.52  | | | | End of split
% 230.15/41.52  | | | | 
% 230.15/41.52  | | | Case 2:
% 230.15/41.52  | | | | 
% 230.15/41.52  | | | |   (60)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0)
% 230.15/41.52  | | | |           = e1)
% 230.15/41.52  | | | | 
% 230.15/41.52  | | | | BETA: splitting (60) gives:
% 230.15/41.52  | | | | 
% 230.15/41.52  | | | | Case 1:
% 230.15/41.52  | | | | | 
% 230.15/41.52  | | | | |   (61)  all_57_4 = e1 & op(e3, e1) = e1
% 230.15/41.52  | | | | | 
% 230.15/41.52  | | | | | REF_CLOSE: (43), (55), (61) are inconsistent by sub-proof #2452.
% 230.15/41.52  | | | | | 
% 230.15/41.52  | | | | Case 2:
% 230.15/41.52  | | | | | 
% 230.15/41.52  | | | | |   (62)  all_57_9 = e1 & op(e3, e0) = e1
% 230.15/41.52  | | | | | 
% 230.15/41.52  | | | | | ALPHA: (62) implies:
% 230.15/41.52  | | | | |   (63)  all_57_9 = e1
% 230.15/41.52  | | | | | 
% 230.15/41.52  | | | | | BETA: splitting (33) gives:
% 230.15/41.52  | | | | | 
% 230.15/41.52  | | | | | Case 1:
% 230.15/41.52  | | | | | | 
% 230.15/41.52  | | | | | |   (64)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 &
% 230.15/41.52  | | | | | |           op(e0, e2) = e2)
% 230.15/41.52  | | | | | | 
% 230.15/41.52  | | | | | | BETA: splitting (64) gives:
% 230.15/41.52  | | | | | | 
% 230.15/41.52  | | | | | | Case 1:
% 230.15/41.52  | | | | | | | 
% 230.15/41.52  | | | | | | |   (65)  all_57_12 = e2 & op(e0, e3) = e2
% 230.15/41.52  | | | | | | | 
% 230.15/41.52  | | | | | | | REF_CLOSE: (14), (28), (65) are inconsistent by sub-proof #2232.
% 230.15/41.52  | | | | | | | 
% 230.15/41.52  | | | | | | Case 2:
% 230.15/41.52  | | | | | | | 
% 230.15/41.53  | | | | | | |   (66)  all_57_13 = e2 & op(e0, e2) = e2
% 230.15/41.53  | | | | | | | 
% 230.15/41.53  | | | | | | | ALPHA: (66) implies:
% 230.15/41.53  | | | | | | |   (67)  all_57_13 = e2
% 230.15/41.53  | | | | | | | 
% 230.15/41.53  | | | | | | | COMBINE_EQS: (36), (67) imply:
% 230.15/41.53  | | | | | | |   (68)  e2 = e0
% 230.15/41.53  | | | | | | | 
% 230.15/41.53  | | | | | | | COMBINE_EQS: (55), (68) imply:
% 230.15/41.53  | | | | | | |   (69)  all_57_4 = e0
% 230.15/41.53  | | | | | | | 
% 230.15/41.53  | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 230.15/41.53  | | | | | | |            (12), (13), (14), (15), (16), (17), (19), (20), (21),
% 230.15/41.53  | | | | | | |            (22), (23), (24), (25), (26), (27), (29), (30), (32),
% 230.15/41.53  | | | | | | |            (33), (34), (35), (37), (38), (40), (41), (42), (43),
% 230.15/41.53  | | | | | | |            (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 230.15/41.53  | | | | | | |            (63), (69) are inconsistent by sub-proof #1025.
% 230.15/41.53  | | | | | | | 
% 230.15/41.53  | | | | | | End of split
% 230.15/41.53  | | | | | | 
% 230.15/41.53  | | | | | Case 2:
% 230.15/41.53  | | | | | | 
% 230.15/41.53  | | | | | |   (70)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 &
% 230.15/41.53  | | | | | |           op(e0, e0) = e2)
% 230.15/41.53  | | | | | | 
% 230.15/41.53  | | | | | | REF_CLOSE: (14), (19), (31), (43), (70) are inconsistent by
% 230.15/41.53  | | | | | |            sub-proof #1418.
% 230.15/41.53  | | | | | | 
% 230.15/41.53  | | | | | End of split
% 230.15/41.53  | | | | | 
% 230.15/41.53  | | | | End of split
% 230.15/41.53  | | | | 
% 230.15/41.53  | | | End of split
% 230.15/41.53  | | | 
% 230.15/41.53  | | Case 2:
% 230.15/41.53  | | | 
% 230.15/41.53  | | |   (71)  all_57_5 = e2 & op(e2, e1) = e2
% 230.15/41.53  | | | 
% 230.15/41.53  | | | REF_CLOSE: (14), (22), (71) are inconsistent by sub-proof #2425.
% 230.15/41.53  | | | 
% 230.15/41.53  | | End of split
% 230.15/41.53  | | 
% 230.15/41.53  | Case 2:
% 230.15/41.53  | | 
% 230.15/41.53  | |   (72)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) =
% 230.15/41.53  | |           e2)
% 230.15/41.53  | | 
% 230.15/41.53  | | BETA: splitting (72) gives:
% 230.15/41.53  | | 
% 230.15/41.53  | | Case 1:
% 230.15/41.53  | | | 
% 230.15/41.53  | | |   (73)  all_57_8 = e2 & op(e1, e1) = e2
% 230.15/41.53  | | | 
% 230.15/41.53  | | | REF_CLOSE: (24), (39), (73) are inconsistent by sub-proof #2005.
% 230.15/41.53  | | | 
% 230.15/41.53  | | Case 2:
% 230.15/41.53  | | | 
% 230.15/41.53  | | |   (74)  all_57_14 = e2 & op(e0, e1) = e2
% 230.15/41.53  | | | 
% 230.15/41.53  | | | ALPHA: (74) implies:
% 230.15/41.53  | | |   (75)  all_57_14 = e2
% 230.15/41.53  | | | 
% 230.15/41.53  | | | REF_CLOSE: (31), (43), (75) are inconsistent by sub-proof #2178.
% 230.15/41.53  | | | 
% 230.15/41.53  | | End of split
% 230.15/41.53  | | 
% 230.15/41.53  | End of split
% 230.15/41.53  | 
% 230.15/41.53  End of proof
% 230.15/41.53  
% 230.15/41.53  Sub-proof #1024 shows that the following formulas are inconsistent:
% 230.15/41.53  ----------------------------------------------------------------
% 230.15/41.53    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.15/41.53         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.15/41.53    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.15/41.53         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.15/41.53    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.15/41.53         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.15/41.53    (4)   ~ (e3 = e1)
% 230.15/41.53    (5)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.15/41.53         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.15/41.53    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.15/41.53           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.15/41.53    (7)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.15/41.53         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.15/41.53    (8)   ~ (all_6_2 = e3)
% 230.15/41.53    (9)  op(e1, e1) = all_6_2
% 230.15/41.53    (10)  op(e2, e2) = e1
% 230.15/41.53    (11)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.15/41.53          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.15/41.53    (12)  all_57_4 = e0
% 230.15/41.53    (13)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.15/41.53          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.15/41.53    (14)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.15/41.53          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.15/41.53    (15)   ~ (e3 = e2)
% 230.15/41.53    (16)   ~ (e3 = e0)
% 230.15/41.53    (17)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.15/41.53          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.15/41.53    (18)  op(e0, e3) = all_53_3
% 230.15/41.53    (19)  all_57_15 = e3
% 230.15/41.53    (20)  op(e3, e3) = e0
% 230.15/41.53    (21)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.15/41.53          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.15/41.53            e1)
% 230.15/41.53    (22)  all_57_5 = e3
% 230.15/41.53    (23)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.15/41.53          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.15/41.53    (24)   ~ (e2 = e0)
% 230.15/41.53    (25)  all_57_3 = e1
% 230.15/41.53    (26)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.15/41.53          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.15/41.53    (27)   ~ (e1 = e0)
% 230.15/41.53    (28)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 230.15/41.53          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 230.15/41.53    (29)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.15/41.53          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.15/41.53    (30)  op(e0, e0) = e3
% 230.15/41.53    (31)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.15/41.53          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.15/41.53            e2)
% 230.15/41.53    (32)   ~ (all_53_3 = e0)
% 230.15/41.53    (33)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.15/41.53              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.15/41.53                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.15/41.53                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.15/41.53    (34)  all_57_2 = e0
% 230.15/41.53    (35)   ~ (all_53_12 = e3)
% 230.15/41.53    (36)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.15/41.53          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.15/41.53    (37)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.15/41.53          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.15/41.53    (38)   ~ (all_53_12 = e0)
% 230.15/41.53    (39)   ~ (e2 = e1)
% 230.15/41.53    (40)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.15/41.53          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.15/41.53    (41)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.15/41.53          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.15/41.53    (42)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.15/41.53          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.15/41.53    (43)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.15/41.53          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.15/41.53    (44)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.15/41.53          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.15/41.53    (45)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.15/41.53          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.15/41.53    (46)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.15/41.53          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.15/41.53    (47)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.15/41.53          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.15/41.53    (48)  op(e3, e0) = all_53_12
% 230.15/41.53  
% 230.15/41.53  Begin of proof
% 230.15/41.53  | 
% 230.15/41.53  | BETA: splitting (11) gives:
% 230.15/41.53  | 
% 230.15/41.53  | Case 1:
% 230.15/41.53  | | 
% 230.15/41.53  | |   (49)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) =
% 230.15/41.53  | |           e1)
% 230.15/41.53  | | 
% 230.15/41.53  | | BETA: splitting (49) gives:
% 230.15/41.53  | | 
% 230.15/41.53  | | Case 1:
% 230.15/41.53  | | | 
% 230.15/41.53  | | |   (50)  all_57_0 = e1 & op(e3, e3) = e1
% 230.15/41.53  | | | 
% 230.15/41.53  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 230.15/41.53  | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 230.15/41.53  | | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 230.15/41.53  | | |            (34), (35), (36), (37), (38), (39), (40), (41), (42), (44),
% 230.15/41.53  | | |            (45), (46), (47), (48), (50) are inconsistent by sub-proof
% 230.15/41.53  | | |            #1032.
% 230.15/41.53  | | | 
% 230.15/41.53  | | Case 2:
% 230.15/41.53  | | | 
% 230.15/41.53  | | |   (51)  all_57_1 = e1 & op(e3, e2) = e1
% 230.15/41.53  | | | 
% 230.15/41.53  | | | ALPHA: (51) implies:
% 230.15/41.53  | | |   (52)  all_57_1 = e1
% 230.15/41.53  | | | 
% 230.15/41.53  | | | REF_CLOSE: (3), (4), (6), (10), (15), (16), (23), (24), (27), (29), (39),
% 230.15/41.53  | | |            (52) are inconsistent by sub-proof #1908.
% 230.15/41.53  | | | 
% 230.15/41.53  | | End of split
% 230.15/41.53  | | 
% 230.15/41.53  | Case 2:
% 230.15/41.53  | | 
% 230.15/41.53  | |   (53)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) =
% 230.15/41.53  | |           e1)
% 230.15/41.53  | | 
% 230.15/41.53  | | BETA: splitting (53) gives:
% 230.15/41.53  | | 
% 230.15/41.53  | | Case 1:
% 230.15/41.53  | | | 
% 230.15/41.53  | | |   (54)  all_57_4 = e1 & op(e3, e1) = e1
% 230.15/41.53  | | | 
% 230.15/41.53  | | | ALPHA: (54) implies:
% 230.15/41.53  | | |   (55)  all_57_4 = e1
% 230.15/41.53  | | | 
% 230.15/41.53  | | | COMBINE_EQS: (12), (55) imply:
% 230.15/41.53  | | |   (56)  e1 = e0
% 230.15/41.53  | | | 
% 230.15/41.53  | | | SIMP: (56) implies:
% 230.15/41.53  | | |   (57)  e1 = e0
% 230.15/41.53  | | | 
% 230.15/41.53  | | | COMBINE_EQS: (25), (57) imply:
% 230.15/41.53  | | |   (58)  all_57_3 = e0
% 230.15/41.53  | | | 
% 230.15/41.53  | | | REF_CLOSE: (1), (4), (15), (22), (24), (27), (34), (36), (39), (58) are
% 230.15/41.53  | | |            inconsistent by sub-proof #2253.
% 230.15/41.53  | | | 
% 230.15/41.53  | | Case 2:
% 230.15/41.53  | | | 
% 230.15/41.53  | | |   (59)  all_57_9 = e1 & op(e3, e0) = e1
% 230.15/41.53  | | | 
% 230.15/41.53  | | | ALPHA: (59) implies:
% 230.15/41.53  | | |   (60)  all_57_9 = e1
% 230.15/41.53  | | | 
% 230.15/41.53  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 230.15/41.53  | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 230.15/41.53  | | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 230.15/41.53  | | |            (34), (35), (36), (37), (38), (39), (40), (41), (42), (43),
% 230.15/41.53  | | |            (44), (45), (46), (47), (48), (60) are inconsistent by
% 230.15/41.53  | | |            sub-proof #1025.
% 230.15/41.53  | | | 
% 230.15/41.53  | | End of split
% 230.15/41.53  | | 
% 230.15/41.53  | End of split
% 230.15/41.53  | 
% 230.15/41.53  End of proof
% 230.15/41.53  
% 230.15/41.53  Sub-proof #1025 shows that the following formulas are inconsistent:
% 230.15/41.53  ----------------------------------------------------------------
% 230.15/41.53    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.15/41.53         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.15/41.53    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.15/41.53         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.15/41.53    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.15/41.53         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.15/41.53    (4)   ~ (e3 = e1)
% 230.15/41.53    (5)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.15/41.53         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.15/41.53    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.15/41.53           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.15/41.53    (7)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.15/41.53         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.15/41.53    (8)   ~ (all_6_2 = e3)
% 230.15/41.53    (9)  op(e1, e1) = all_6_2
% 230.15/41.53    (10)  op(e2, e2) = e1
% 230.15/41.53    (11)  all_57_9 = e1
% 230.15/41.53    (12)  all_57_4 = e0
% 230.15/41.53    (13)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.15/41.53          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.15/41.53    (14)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.15/41.53          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.15/41.53    (15)   ~ (e3 = e2)
% 230.15/41.53    (16)   ~ (e3 = e0)
% 230.15/41.53    (17)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.15/41.53          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.15/41.53    (18)  op(e0, e3) = all_53_3
% 230.15/41.53    (19)  all_57_15 = e3
% 230.15/41.53    (20)  op(e3, e3) = e0
% 230.15/41.53    (21)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.15/41.53          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.15/41.53            e1)
% 230.15/41.53    (22)  all_57_5 = e3
% 230.15/41.53    (23)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.15/41.53          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.15/41.53    (24)   ~ (e2 = e0)
% 230.15/41.53    (25)  all_57_3 = e1
% 230.15/41.53    (26)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.15/41.53          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.15/41.53    (27)   ~ (e1 = e0)
% 230.15/41.53    (28)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 230.15/41.53          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 230.15/41.53    (29)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.15/41.53          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.15/41.53    (30)  op(e0, e0) = e3
% 230.15/41.53    (31)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.15/41.53          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.15/41.53            e2)
% 230.15/41.53    (32)   ~ (all_53_3 = e0)
% 230.15/41.53    (33)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.15/41.53              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.15/41.53                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.15/41.53                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.15/41.53    (34)  all_57_2 = e0
% 230.15/41.53    (35)   ~ (all_53_12 = e3)
% 230.15/41.53    (36)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.15/41.53          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.15/41.53    (37)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.15/41.53          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.15/41.53    (38)   ~ (all_53_12 = e0)
% 230.15/41.53    (39)   ~ (e2 = e1)
% 230.15/41.53    (40)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.15/41.53          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.15/41.53    (41)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.15/41.53          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.15/41.53    (42)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.15/41.53          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.15/41.53    (43)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.15/41.53          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.15/41.53    (44)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.15/41.53          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.15/41.53    (45)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.15/41.53          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.15/41.53    (46)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.15/41.53          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.15/41.53    (47)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.15/41.53          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.15/41.53    (48)  op(e3, e0) = all_53_12
% 230.15/41.53  
% 230.15/41.53  Begin of proof
% 230.15/41.53  | 
% 230.15/41.53  | BETA: splitting (13) gives:
% 230.15/41.53  | 
% 230.15/41.53  | Case 1:
% 230.15/41.53  | | 
% 230.15/41.53  | |   (49)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) =
% 230.15/41.53  | |           e2)
% 230.15/41.53  | | 
% 230.15/41.53  | | BETA: splitting (49) gives:
% 230.15/41.53  | | 
% 230.15/41.53  | | Case 1:
% 230.15/41.53  | | | 
% 230.15/41.53  | | |   (50)  all_57_0 = e2 & op(e3, e3) = e2
% 230.15/41.53  | | | 
% 230.15/41.53  | | | ALPHA: (50) implies:
% 230.15/41.53  | | |   (51)  op(e3, e3) = e2
% 230.15/41.53  | | | 
% 230.15/41.53  | | | REF_CLOSE: (6), (20), (24), (51) are inconsistent by sub-proof #2403.
% 230.15/41.53  | | | 
% 230.15/41.53  | | Case 2:
% 230.15/41.53  | | | 
% 230.15/41.53  | | |   (52)  all_57_1 = e2 & op(e3, e2) = e2
% 230.15/41.53  | | | 
% 230.15/41.53  | | | ALPHA: (52) implies:
% 230.15/41.53  | | |   (53)  all_57_1 = e2
% 230.15/41.53  | | | 
% 230.15/41.53  | | | BETA: splitting (29) gives:
% 230.15/41.53  | | | 
% 230.15/41.53  | | | Case 1:
% 230.15/41.53  | | | | 
% 230.15/41.53  | | | |   (54)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2)
% 230.15/41.53  | | | |           = e3)
% 230.15/41.53  | | | | 
% 230.15/41.53  | | | | REF_CLOSE: (4), (6), (10), (15), (53), (54) are inconsistent by
% 230.15/41.53  | | | |            sub-proof #1031.
% 230.15/41.53  | | | | 
% 230.15/41.53  | | | Case 2:
% 230.15/41.53  | | | | 
% 230.15/41.53  | | | |   (55)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2)
% 230.15/41.53  | | | |           = e3)
% 230.15/41.53  | | | | 
% 230.15/41.53  | | | | BETA: splitting (55) gives:
% 230.15/41.53  | | | | 
% 230.15/41.53  | | | | Case 1:
% 230.15/41.53  | | | | | 
% 230.15/41.53  | | | | |   (56)  all_57_7 = e3 & op(e1, e2) = e3
% 230.15/41.53  | | | | | 
% 230.15/41.53  | | | | | ALPHA: (56) implies:
% 230.15/41.53  | | | | |   (57)  all_57_7 = e3
% 230.15/41.53  | | | | | 
% 230.15/41.53  | | | | | BETA: splitting (37) gives:
% 230.15/41.53  | | | | | 
% 230.15/41.53  | | | | | Case 1:
% 230.15/41.53  | | | | | | 
% 230.15/41.53  | | | | | |   (58)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2,
% 230.15/41.53  | | | | | |             e3) = e3)
% 230.15/41.53  | | | | | | 
% 230.15/41.53  | | | | | | REF_CLOSE: (6), (16), (20), (34), (58) are inconsistent by sub-proof
% 230.15/41.53  | | | | | |            #1559.
% 230.15/41.53  | | | | | | 
% 230.15/41.53  | | | | | Case 2:
% 230.15/41.53  | | | | | | 
% 230.15/41.53  | | | | | |   (59)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0,
% 230.15/41.53  | | | | | |             e3) = e3)
% 230.15/41.53  | | | | | | 
% 230.15/41.53  | | | | | | BETA: splitting (59) gives:
% 230.15/41.53  | | | | | | 
% 230.15/41.53  | | | | | | Case 1:
% 230.15/41.53  | | | | | | | 
% 230.15/41.53  | | | | | | |   (60)  all_57_6 = e3 & op(e1, e3) = e3
% 230.15/41.53  | | | | | | | 
% 230.15/41.53  | | | | | | | ALPHA: (60) implies:
% 230.15/41.53  | | | | | | |   (61)  all_57_6 = e3
% 230.15/41.53  | | | | | | | 
% 230.15/41.53  | | | | | | | BETA: splitting (2) gives:
% 230.15/41.53  | | | | | | | 
% 230.15/41.53  | | | | | | | Case 1:
% 230.15/41.53  | | | | | | | | 
% 230.15/41.53  | | | | | | | |   (62)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 &
% 230.15/41.53  | | | | | | | |           op(e2, e3) = e1)
% 230.15/41.53  | | | | | | | | 
% 230.15/41.53  | | | | | | | | BETA: splitting (62) gives:
% 230.15/41.53  | | | | | | | | 
% 230.15/41.53  | | | | | | | | Case 1:
% 230.15/41.53  | | | | | | | | | 
% 230.15/41.53  | | | | | | | | |   (63)  all_57_0 = e1 & op(e3, e3) = e1
% 230.15/41.53  | | | | | | | | | 
% 230.15/41.53  | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 230.15/41.53  | | | | | | | | |            (12), (13), (14), (15), (16), (17), (18), (19),
% 230.15/41.53  | | | | | | | | |            (20), (21), (22), (23), (24), (25), (26), (27),
% 230.15/41.53  | | | | | | | | |            (28), (29), (30), (31), (32), (33), (34), (35),
% 230.15/41.53  | | | | | | | | |            (36), (37), (38), (39), (40), (41), (42), (44),
% 230.15/41.53  | | | | | | | | |            (45), (46), (47), (48), (63) are inconsistent by
% 230.15/41.53  | | | | | | | | |            sub-proof #1032.
% 230.15/41.53  | | | | | | | | | 
% 230.15/41.53  | | | | | | | | Case 2:
% 230.15/41.53  | | | | | | | | | 
% 230.15/41.53  | | | | | | | | |   (64)  all_57_2 = e1 & op(e2, e3) = e1
% 230.15/41.53  | | | | | | | | | 
% 230.15/41.53  | | | | | | | | | REF_CLOSE: (1), (4), (15), (22), (24), (25), (27), (34), (36),
% 230.15/41.53  | | | | | | | | |            (39), (64) are inconsistent by sub-proof #1067.
% 230.15/41.53  | | | | | | | | | 
% 230.15/41.53  | | | | | | | | End of split
% 230.15/41.53  | | | | | | | | 
% 230.15/41.53  | | | | | | | Case 2:
% 230.15/41.53  | | | | | | | | 
% 230.15/41.53  | | | | | | | |   (65)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 &
% 230.15/41.53  | | | | | | | |           op(e0, e3) = e1)
% 230.15/41.53  | | | | | | | | 
% 230.15/41.53  | | | | | | | | BETA: splitting (65) gives:
% 230.15/41.53  | | | | | | | | 
% 230.15/41.53  | | | | | | | | Case 1:
% 230.15/41.53  | | | | | | | | | 
% 230.15/41.53  | | | | | | | | |   (66)  all_57_6 = e1 & op(e1, e3) = e1
% 230.15/41.53  | | | | | | | | | 
% 230.15/41.53  | | | | | | | | | ALPHA: (66) implies:
% 230.15/41.53  | | | | | | | | |   (67)  all_57_6 = e1
% 230.15/41.53  | | | | | | | | | 
% 230.15/41.53  | | | | | | | | | REF_CLOSE: (4), (61), (67) are inconsistent by sub-proof
% 230.15/41.53  | | | | | | | | |            #2017.
% 230.15/41.53  | | | | | | | | | 
% 230.15/41.53  | | | | | | | | Case 2:
% 230.15/41.53  | | | | | | | | | 
% 230.15/41.53  | | | | | | | | |   (68)  all_57_12 = e1 & op(e0, e3) = e1
% 230.15/41.53  | | | | | | | | | 
% 230.15/41.53  | | | | | | | | | ALPHA: (68) implies:
% 230.15/41.53  | | | | | | | | |   (69)  all_57_12 = e1
% 230.15/41.53  | | | | | | | | | 
% 230.15/41.53  | | | | | | | | | BETA: splitting (26) gives:
% 230.15/41.53  | | | | | | | | | 
% 230.15/41.53  | | | | | | | | | Case 1:
% 230.15/41.53  | | | | | | | | | | 
% 230.15/41.53  | | | | | | | | | |   (70)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 &
% 230.15/41.53  | | | | | | | | | |           op(e3, e2) = e3)
% 230.15/41.53  | | | | | | | | | | 
% 230.15/41.53  | | | | | | | | | | BETA: splitting (70) gives:
% 230.15/41.53  | | | | | | | | | | 
% 230.15/41.53  | | | | | | | | | | Case 1:
% 230.15/41.53  | | | | | | | | | | | 
% 230.15/41.53  | | | | | | | | | | |   (71)  all_57_0 = e3 & op(e3, e3) = e3
% 230.15/41.53  | | | | | | | | | | | 
% 230.15/41.53  | | | | | | | | | | | ALPHA: (71) implies:
% 230.15/41.53  | | | | | | | | | | |   (72)  all_57_0 = e3
% 230.15/41.53  | | | | | | | | | | | 
% 230.15/41.53  | | | | | | | | | | | REF_CLOSE: (2), (4), (15), (16), (24), (27), (39), (41),
% 230.15/41.53  | | | | | | | | | | |            (43), (61), (72) are inconsistent by sub-proof
% 230.15/41.53  | | | | | | | | | | |            #2010.
% 230.15/41.53  | | | | | | | | | | | 
% 230.15/41.53  | | | | | | | | | | Case 2:
% 230.15/41.53  | | | | | | | | | | | 
% 230.15/41.53  | | | | | | | | | | |   (73)  all_57_1 = e3 & op(e3, e2) = e3
% 230.15/41.53  | | | | | | | | | | | 
% 230.15/41.53  | | | | | | | | | | | REF_CLOSE: (15), (53), (73) are inconsistent by sub-proof
% 230.15/41.53  | | | | | | | | | | |            #1664.
% 230.15/41.53  | | | | | | | | | | | 
% 230.15/41.53  | | | | | | | | | | End of split
% 230.15/41.53  | | | | | | | | | | 
% 230.15/41.53  | | | | | | | | | Case 2:
% 230.15/41.53  | | | | | | | | | | 
% 230.15/41.53  | | | | | | | | | |   (74)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 &
% 230.15/41.53  | | | | | | | | | |           op(e3, e0) = e3)
% 230.15/41.53  | | | | | | | | | | 
% 230.15/41.53  | | | | | | | | | | BETA: splitting (74) gives:
% 230.15/41.53  | | | | | | | | | | 
% 230.15/41.53  | | | | | | | | | | Case 1:
% 230.15/41.53  | | | | | | | | | | | 
% 230.15/41.53  | | | | | | | | | | |   (75)  all_57_4 = e3 & op(e3, e1) = e3
% 230.15/41.53  | | | | | | | | | | | 
% 230.15/41.53  | | | | | | | | | | | ALPHA: (75) implies:
% 230.15/41.53  | | | | | | | | | | |   (76)  all_57_4 = e3
% 230.15/41.53  | | | | | | | | | | | 
% 230.15/41.53  | | | | | | | | | | | COMBINE_EQS: (12), (76) imply:
% 230.15/41.53  | | | | | | | | | | |   (77)  e3 = e0
% 230.15/41.53  | | | | | | | | | | | 
% 230.15/41.53  | | | | | | | | | | | SIMP: (77) implies:
% 230.15/41.53  | | | | | | | | | | |   (78)  e3 = e0
% 230.15/41.53  | | | | | | | | | | | 
% 230.15/41.53  | | | | | | | | | | | COMBINE_EQS: (61), (78) imply:
% 230.15/41.53  | | | | | | | | | | |   (79)  all_57_6 = e0
% 230.15/41.53  | | | | | | | | | | | 
% 230.15/41.53  | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (15), (16), (19), (20),
% 230.15/41.53  | | | | | | | | | | |            (24), (27), (33), (37), (39), (40), (41), (44),
% 230.15/41.53  | | | | | | | | | | |            (69), (79) are inconsistent by sub-proof #1028.
% 230.15/41.53  | | | | | | | | | | | 
% 230.15/41.53  | | | | | | | | | | Case 2:
% 230.15/41.53  | | | | | | | | | | | 
% 230.15/41.53  | | | | | | | | | | |   (80)  all_57_9 = e3 & op(e3, e0) = e3
% 230.15/41.53  | | | | | | | | | | | 
% 230.15/41.53  | | | | | | | | | | | ALPHA: (80) implies:
% 230.15/41.53  | | | | | | | | | | |   (81)  op(e3, e0) = e3
% 230.15/41.53  | | | | | | | | | | | 
% 230.15/41.53  | | | | | | | | | | | REF_CLOSE: (6), (35), (48), (81) are inconsistent by
% 230.15/41.53  | | | | | | | | | | |            sub-proof #2458.
% 230.15/41.53  | | | | | | | | | | | 
% 230.15/41.53  | | | | | | | | | | End of split
% 230.15/41.53  | | | | | | | | | | 
% 230.15/41.53  | | | | | | | | | End of split
% 230.15/41.53  | | | | | | | | | 
% 230.15/41.53  | | | | | | | | End of split
% 230.15/41.53  | | | | | | | | 
% 230.15/41.53  | | | | | | | End of split
% 230.15/41.53  | | | | | | | 
% 230.15/41.53  | | | | | | Case 2:
% 230.15/41.53  | | | | | | | 
% 230.15/41.53  | | | | | | |   (82)  all_57_12 = e3 & op(e0, e3) = e3
% 230.15/41.53  | | | | | | | 
% 230.15/41.53  | | | | | | | ALPHA: (82) implies:
% 230.15/41.53  | | | | | | |   (83)  all_57_12 = e3
% 230.15/41.53  | | | | | | | 
% 230.15/41.53  | | | | | | | BETA: splitting (2) gives:
% 230.15/41.53  | | | | | | | 
% 230.15/41.53  | | | | | | | Case 1:
% 230.15/41.53  | | | | | | | | 
% 230.15/41.53  | | | | | | | |   (84)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 &
% 230.15/41.53  | | | | | | | |           op(e2, e3) = e1)
% 230.15/41.53  | | | | | | | | 
% 230.15/41.53  | | | | | | | | BETA: splitting (84) gives:
% 230.15/41.53  | | | | | | | | 
% 230.15/41.53  | | | | | | | | Case 1:
% 230.15/41.53  | | | | | | | | | 
% 230.15/41.53  | | | | | | | | |   (85)  all_57_0 = e1 & op(e3, e3) = e1
% 230.15/41.53  | | | | | | | | | 
% 230.15/41.53  | | | | | | | | | ALPHA: (85) implies:
% 230.15/41.53  | | | | | | | | |   (86)  op(e3, e3) = e1
% 230.15/41.53  | | | | | | | | | 
% 230.15/41.53  | | | | | | | | | REF_CLOSE: (3), (4), (6), (7), (8), (9), (10), (12), (15),
% 230.15/41.53  | | | | | | | | |            (16), (17), (18), (19), (20), (21), (22), (23),
% 230.15/41.53  | | | | | | | | |            (24), (25), (26), (27), (30), (31), (32), (33),
% 230.15/41.53  | | | | | | | | |            (34), (35), (37), (39), (40), (41), (42), (44),
% 230.15/41.53  | | | | | | | | |            (46), (48), (83), (86) are inconsistent by
% 230.15/41.53  | | | | | | | | |            sub-proof #1033.
% 230.15/41.53  | | | | | | | | | 
% 230.15/41.53  | | | | | | | | Case 2:
% 230.15/41.53  | | | | | | | | | 
% 230.15/41.53  | | | | | | | | |   (87)  all_57_2 = e1 & op(e2, e3) = e1
% 230.15/41.53  | | | | | | | | | 
% 230.15/41.53  | | | | | | | | | REF_CLOSE: (1), (4), (15), (22), (24), (25), (27), (34), (36),
% 230.15/41.53  | | | | | | | | |            (39), (87) are inconsistent by sub-proof #1067.
% 230.15/41.53  | | | | | | | | | 
% 230.15/41.53  | | | | | | | | End of split
% 230.15/41.53  | | | | | | | | 
% 230.15/41.53  | | | | | | | Case 2:
% 230.15/41.53  | | | | | | | | 
% 230.15/41.53  | | | | | | | |   (88)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 &
% 230.15/41.53  | | | | | | | |           op(e0, e3) = e1)
% 230.15/41.53  | | | | | | | | 
% 230.15/41.53  | | | | | | | | BETA: splitting (88) gives:
% 230.15/41.53  | | | | | | | | 
% 230.15/41.53  | | | | | | | | Case 1:
% 230.15/41.53  | | | | | | | | | 
% 230.15/41.53  | | | | | | | | |   (89)  all_57_6 = e1 & op(e1, e3) = e1
% 230.15/41.53  | | | | | | | | | 
% 230.15/41.53  | | | | | | | | | ALPHA: (89) implies:
% 230.15/41.53  | | | | | | | | |   (90)  all_57_6 = e1
% 230.15/41.53  | | | | | | | | | 
% 230.15/41.53  | | | | | | | | | BETA: splitting (26) gives:
% 230.15/41.53  | | | | | | | | | 
% 230.15/41.53  | | | | | | | | | Case 1:
% 230.15/41.53  | | | | | | | | | | 
% 230.15/41.53  | | | | | | | | | |   (91)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 &
% 230.15/41.53  | | | | | | | | | |           op(e3, e2) = e3)
% 230.15/41.53  | | | | | | | | | | 
% 230.15/41.53  | | | | | | | | | | REF_CLOSE: (6), (15), (16), (20), (53), (91) are inconsistent
% 230.15/41.53  | | | | | | | | | |            by sub-proof #1407.
% 230.15/41.53  | | | | | | | | | | 
% 230.15/41.53  | | | | | | | | | Case 2:
% 230.15/41.53  | | | | | | | | | | 
% 230.15/41.53  | | | | | | | | | |   (92)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 &
% 230.15/41.53  | | | | | | | | | |           op(e3, e0) = e3)
% 230.15/41.53  | | | | | | | | | | 
% 230.15/41.53  | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (12), (15), (16), (19),
% 230.15/41.53  | | | | | | | | | |            (24), (27), (33), (35), (39), (40), (44), (48),
% 230.15/41.53  | | | | | | | | | |            (57), (90), (92) are inconsistent by sub-proof
% 230.15/41.53  | | | | | | | | | |            #1026.
% 230.15/41.53  | | | | | | | | | | 
% 230.15/41.53  | | | | | | | | | End of split
% 230.15/41.53  | | | | | | | | | 
% 230.15/41.53  | | | | | | | | Case 2:
% 230.15/41.53  | | | | | | | | | 
% 230.15/41.53  | | | | | | | | |   (93)  all_57_12 = e1 & op(e0, e3) = e1
% 230.15/41.53  | | | | | | | | | 
% 230.15/41.53  | | | | | | | | | REF_CLOSE: (4), (83), (93) are inconsistent by sub-proof
% 230.15/41.53  | | | | | | | | |            #2230.
% 230.15/41.53  | | | | | | | | | 
% 230.15/41.53  | | | | | | | | End of split
% 230.15/41.53  | | | | | | | | 
% 230.15/41.53  | | | | | | | End of split
% 230.15/41.53  | | | | | | | 
% 230.15/41.53  | | | | | | End of split
% 230.15/41.53  | | | | | | 
% 230.15/41.53  | | | | | End of split
% 230.15/41.53  | | | | | 
% 230.15/41.53  | | | | Case 2:
% 230.15/41.53  | | | | | 
% 230.15/41.53  | | | | |   (94)  all_57_13 = e3 & op(e0, e2) = e3
% 230.15/41.53  | | | | | 
% 230.15/41.53  | | | | | ALPHA: (94) implies:
% 230.15/41.53  | | | | |   (95)  all_57_13 = e3
% 230.15/41.53  | | | | | 
% 230.15/41.53  | | | | | REF_CLOSE: (4), (6), (15), (16), (19), (21), (24), (27), (30), (31),
% 230.15/41.53  | | | | |            (33), (39), (95) are inconsistent by sub-proof #1792.
% 230.15/41.53  | | | | | 
% 230.15/41.53  | | | | End of split
% 230.15/41.53  | | | | 
% 230.15/41.53  | | | End of split
% 230.15/41.53  | | | 
% 230.15/41.53  | | End of split
% 230.15/41.53  | | 
% 230.15/41.53  | Case 2:
% 230.15/41.53  | | 
% 230.15/41.53  | |   (96)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) =
% 230.15/41.53  | |           e2)
% 230.15/41.53  | | 
% 230.15/41.53  | | BETA: splitting (96) gives:
% 230.15/41.53  | | 
% 230.15/41.53  | | Case 1:
% 230.15/41.53  | | | 
% 230.15/41.53  | | |   (97)  all_57_4 = e2 & op(e3, e1) = e2
% 230.15/41.53  | | | 
% 230.15/41.53  | | | REF_CLOSE: (12), (24), (97) are inconsistent by sub-proof #1404.
% 230.15/41.53  | | | 
% 230.15/41.53  | | Case 2:
% 230.15/41.53  | | | 
% 230.15/41.53  | | |   (98)  all_57_9 = e2 & op(e3, e0) = e2
% 230.15/41.53  | | | 
% 230.15/41.53  | | | REF_CLOSE: (11), (39), (98) are inconsistent by sub-proof #2481.
% 230.15/41.53  | | | 
% 230.15/41.53  | | End of split
% 230.15/41.53  | | 
% 230.15/41.53  | End of split
% 230.15/41.53  | 
% 230.15/41.53  End of proof
% 230.15/41.53  
% 230.15/41.53  Sub-proof #1026 shows that the following formulas are inconsistent:
% 230.15/41.53  ----------------------------------------------------------------
% 230.15/41.53    (1)   ~ (e3 = e1)
% 230.15/41.53    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.15/41.53           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.15/41.53    (3)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.15/41.53         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.15/41.53    (4)   ~ (all_6_2 = e3)
% 230.15/41.53    (5)  op(e1, e1) = all_6_2
% 230.15/41.53    (6)  all_57_4 = e0
% 230.15/41.53    (7)  all_57_6 = e1
% 230.15/41.53    (8)   ~ (e3 = e2)
% 230.15/41.53    (9)   ~ (e3 = e0)
% 230.15/41.53    (10)  all_57_15 = e3
% 230.15/41.53    (11)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.15/41.53    (12)   ~ (e2 = e0)
% 230.15/41.53    (13)   ~ (e1 = e0)
% 230.15/41.53    (14)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.15/41.53              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.15/41.53                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.15/41.53                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.15/41.53    (15)   ~ (all_53_12 = e3)
% 230.15/41.53    (16)  all_57_7 = e3
% 230.15/41.53    (17)   ~ (e2 = e1)
% 230.15/41.53    (18)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.15/41.53          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.15/41.53    (19)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.15/41.53          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.15/41.53    (20)  op(e3, e0) = all_53_12
% 230.15/41.53  
% 230.15/41.53  Begin of proof
% 230.15/41.53  | 
% 230.15/41.53  | BETA: splitting (11) gives:
% 230.15/41.53  | 
% 230.15/41.53  | Case 1:
% 230.15/41.53  | | 
% 230.15/41.53  | |   (21)  all_57_4 = e3 & op(e3, e1) = e3
% 230.15/41.54  | | 
% 230.15/41.54  | | ALPHA: (21) implies:
% 230.15/41.54  | |   (22)  all_57_4 = e3
% 230.15/41.54  | | 
% 230.15/41.54  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 230.15/41.54  | |            (14), (16), (17), (18), (19), (22) are inconsistent by sub-proof
% 230.15/41.54  | |            #1027.
% 230.15/41.54  | | 
% 230.15/41.54  | Case 2:
% 230.15/41.54  | | 
% 230.15/41.54  | |   (23)  all_57_9 = e3 & op(e3, e0) = e3
% 230.15/41.54  | | 
% 230.15/41.54  | | ALPHA: (23) implies:
% 230.15/41.54  | |   (24)  op(e3, e0) = e3
% 230.15/41.54  | | 
% 230.15/41.54  | | REF_CLOSE: (2), (15), (20), (24) are inconsistent by sub-proof #2458.
% 230.15/41.54  | | 
% 230.15/41.54  | End of split
% 230.15/41.54  | 
% 230.15/41.54  End of proof
% 230.15/41.54  
% 230.15/41.54  Sub-proof #1027 shows that the following formulas are inconsistent:
% 230.15/41.54  ----------------------------------------------------------------
% 230.15/41.54    (1)   ~ (e3 = e1)
% 230.15/41.54    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.15/41.54           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.15/41.54    (3)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.15/41.54         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.15/41.54    (4)   ~ (all_6_2 = e3)
% 230.15/41.54    (5)  op(e1, e1) = all_6_2
% 230.15/41.54    (6)  all_57_4 = e0
% 230.15/41.54    (7)  all_57_6 = e1
% 230.15/41.54    (8)  all_57_4 = e3
% 230.15/41.54    (9)   ~ (e3 = e2)
% 230.15/41.54    (10)   ~ (e3 = e0)
% 230.15/41.54    (11)  all_57_15 = e3
% 230.15/41.54    (12)   ~ (e2 = e0)
% 230.15/41.54    (13)   ~ (e1 = e0)
% 230.15/41.54    (14)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.15/41.54              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.15/41.54                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.15/41.54                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.15/41.54    (15)  all_57_7 = e3
% 230.15/41.54    (16)   ~ (e2 = e1)
% 230.15/41.54    (17)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.15/41.54          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.15/41.54    (18)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.15/41.54          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.15/41.54  
% 230.15/41.54  Begin of proof
% 230.15/41.54  | 
% 230.15/41.54  | COMBINE_EQS: (6), (8) imply:
% 230.15/41.54  |   (19)  e3 = e0
% 230.15/41.54  | 
% 230.15/41.54  | SIMP: (19) implies:
% 230.15/41.54  |   (20)  e3 = e0
% 230.15/41.54  | 
% 230.15/41.54  | COMBINE_EQS: (15), (20) imply:
% 230.15/41.54  |   (21)  all_57_7 = e0
% 230.15/41.54  | 
% 230.15/41.54  | REF_CLOSE: (1), (2), (3), (4), (5), (7), (9), (10), (11), (12), (13), (14),
% 230.15/41.54  |            (16), (17), (18), (21) are inconsistent by sub-proof #1735.
% 230.15/41.54  | 
% 230.15/41.54  End of proof
% 230.15/41.54  
% 230.15/41.54  Sub-proof #1028 shows that the following formulas are inconsistent:
% 230.15/41.54  ----------------------------------------------------------------
% 230.15/41.54    (1)   ~ (e3 = e1)
% 230.15/41.54    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.15/41.54           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.15/41.54    (3)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.15/41.54         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.15/41.54    (4)   ~ (all_6_2 = e3)
% 230.15/41.54    (5)  op(e1, e1) = all_6_2
% 230.15/41.54    (6)   ~ (e3 = e2)
% 230.15/41.54    (7)   ~ (e3 = e0)
% 230.15/41.54    (8)  all_57_6 = e0
% 230.15/41.54    (9)  all_57_15 = e3
% 230.15/41.54    (10)  op(e3, e3) = e0
% 230.15/41.54    (11)  all_57_12 = e1
% 230.15/41.54    (12)   ~ (e2 = e0)
% 230.15/41.54    (13)   ~ (e1 = e0)
% 230.15/41.54    (14)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.15/41.54              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.15/41.54                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.15/41.54                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.15/41.54    (15)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.15/41.54          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.15/41.54    (16)   ~ (e2 = e1)
% 230.15/41.54    (17)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.15/41.54          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.15/41.54    (18)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.15/41.54          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.15/41.54    (19)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.15/41.54          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.15/41.54  
% 230.15/41.54  Begin of proof
% 230.15/41.54  | 
% 230.15/41.54  | BETA: splitting (3) gives:
% 230.15/41.54  | 
% 230.15/41.54  | Case 1:
% 230.25/41.54  | | 
% 230.25/41.54  | |   (20)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 230.25/41.54  | |           e3)
% 230.25/41.54  | | 
% 230.25/41.54  | | BETA: splitting (20) gives:
% 230.25/41.54  | | 
% 230.25/41.54  | | Case 1:
% 230.25/41.54  | | | 
% 230.25/41.54  | | |   (21)  all_57_6 = e3 & op(e1, e3) = e3
% 230.25/41.54  | | | 
% 230.25/41.54  | | | ALPHA: (21) implies:
% 230.25/41.54  | | |   (22)  all_57_6 = e3
% 230.25/41.54  | | | 
% 230.25/41.54  | | | REF_CLOSE: (7), (8), (22) are inconsistent by sub-proof #1822.
% 230.25/41.54  | | | 
% 230.25/41.54  | | Case 2:
% 230.25/41.54  | | | 
% 230.25/41.54  | | |   (23)  all_57_7 = e3 & op(e1, e2) = e3
% 230.25/41.54  | | | 
% 230.25/41.54  | | | ALPHA: (23) implies:
% 230.25/41.54  | | |   (24)  all_57_7 = e3
% 230.25/41.54  | | | 
% 230.25/41.54  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 230.25/41.54  | | |            (13), (14), (15), (16), (17), (18), (19), (24) are inconsistent
% 230.25/41.54  | | |            by sub-proof #1029.
% 230.25/41.54  | | | 
% 230.25/41.54  | | End of split
% 230.25/41.54  | | 
% 230.25/41.54  | Case 2:
% 230.25/41.54  | | 
% 230.25/41.54  | |   (25)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 230.25/41.54  | |           e3)
% 230.25/41.54  | | 
% 230.25/41.54  | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (9), (12), (13), (14), (16), (17),
% 230.25/41.54  | |            (19), (25) are inconsistent by sub-proof #1786.
% 230.25/41.54  | | 
% 230.25/41.54  | End of split
% 230.25/41.54  | 
% 230.25/41.54  End of proof
% 230.25/41.54  
% 230.25/41.54  Sub-proof #1029 shows that the following formulas are inconsistent:
% 230.25/41.54  ----------------------------------------------------------------
% 230.25/41.54    (1)   ~ (e3 = e1)
% 230.25/41.54    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.25/41.54           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.25/41.54    (3)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.25/41.54         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.25/41.54    (4)   ~ (all_6_2 = e3)
% 230.25/41.54    (5)  op(e1, e1) = all_6_2
% 230.25/41.54    (6)   ~ (e3 = e2)
% 230.25/41.54    (7)   ~ (e3 = e0)
% 230.25/41.54    (8)  all_57_6 = e0
% 230.25/41.54    (9)  all_57_15 = e3
% 230.25/41.54    (10)  op(e3, e3) = e0
% 230.25/41.54    (11)  all_57_12 = e1
% 230.25/41.54    (12)   ~ (e2 = e0)
% 230.25/41.54    (13)   ~ (e1 = e0)
% 230.25/41.54    (14)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.25/41.54              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.25/41.54                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.25/41.54                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.25/41.54    (15)  all_57_7 = e3
% 230.25/41.54    (16)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.25/41.54          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.25/41.54    (17)   ~ (e2 = e1)
% 230.25/41.54    (18)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.25/41.54          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.25/41.54    (19)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.25/41.54          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.25/41.54    (20)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.25/41.54          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.25/41.54  
% 230.25/41.54  Begin of proof
% 230.25/41.54  | 
% 230.25/41.54  | BETA: splitting (16) gives:
% 230.25/41.54  | 
% 230.25/41.54  | Case 1:
% 230.25/41.54  | | 
% 230.25/41.54  | |   (21)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) =
% 230.25/41.54  | |           e3)
% 230.25/41.54  | | 
% 230.25/41.54  | | BETA: splitting (21) gives:
% 230.25/41.54  | | 
% 230.25/41.54  | | Case 1:
% 230.25/41.54  | | | 
% 230.25/41.54  | | |   (22)  all_57_0 = e3 & op(e3, e3) = e3
% 230.25/41.54  | | | 
% 230.25/41.54  | | | ALPHA: (22) implies:
% 230.25/41.54  | | |   (23)  op(e3, e3) = e3
% 230.25/41.54  | | | 
% 230.25/41.54  | | | REF_CLOSE: (2), (7), (10), (23) are inconsistent by sub-proof #2494.
% 230.25/41.54  | | | 
% 230.25/41.54  | | Case 2:
% 230.25/41.54  | | | 
% 230.25/41.54  | | |   (24)  all_57_2 = e3 & op(e2, e3) = e3
% 230.25/41.54  | | | 
% 230.25/41.54  | | | ALPHA: (24) implies:
% 230.25/41.54  | | |   (25)  all_57_2 = e3
% 230.25/41.54  | | | 
% 230.25/41.54  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 230.25/41.54  | | |            (13), (14), (15), (17), (18), (19), (20), (25) are inconsistent
% 230.25/41.54  | | |            by sub-proof #1030.
% 230.25/41.54  | | | 
% 230.25/41.54  | | End of split
% 230.25/41.54  | | 
% 230.25/41.54  | Case 2:
% 230.25/41.54  | | 
% 230.25/41.54  | |   (26)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) =
% 230.25/41.54  | |           e3)
% 230.25/41.54  | | 
% 230.25/41.54  | | BETA: splitting (26) gives:
% 230.25/41.54  | | 
% 230.25/41.54  | | Case 1:
% 230.25/41.54  | | | 
% 230.25/41.54  | | |   (27)  all_57_6 = e3 & op(e1, e3) = e3
% 230.25/41.54  | | | 
% 230.25/41.54  | | | REF_CLOSE: (7), (8), (27) are inconsistent by sub-proof #2395.
% 230.25/41.54  | | | 
% 230.25/41.54  | | Case 2:
% 230.25/41.54  | | | 
% 230.25/41.54  | | |   (28)  all_57_12 = e3 & op(e0, e3) = e3
% 230.25/41.54  | | | 
% 230.25/41.54  | | | REF_CLOSE: (1), (11), (28) are inconsistent by sub-proof #1285.
% 230.25/41.54  | | | 
% 230.25/41.54  | | End of split
% 230.25/41.54  | | 
% 230.25/41.54  | End of split
% 230.25/41.54  | 
% 230.25/41.54  End of proof
% 230.25/41.54  
% 230.25/41.54  Sub-proof #1030 shows that the following formulas are inconsistent:
% 230.25/41.54  ----------------------------------------------------------------
% 230.25/41.54    (1)   ~ (e3 = e1)
% 230.25/41.54    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.25/41.54           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.25/41.54    (3)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.25/41.54         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.25/41.54    (4)   ~ (all_6_2 = e3)
% 230.25/41.54    (5)  op(e1, e1) = all_6_2
% 230.25/41.54    (6)   ~ (e3 = e2)
% 230.25/41.54    (7)   ~ (e3 = e0)
% 230.25/41.54    (8)  all_57_6 = e0
% 230.25/41.54    (9)  all_57_15 = e3
% 230.25/41.54    (10)  op(e3, e3) = e0
% 230.25/41.54    (11)  all_57_12 = e1
% 230.25/41.54    (12)   ~ (e2 = e0)
% 230.25/41.54    (13)  all_57_2 = e3
% 230.25/41.54    (14)   ~ (e1 = e0)
% 230.25/41.54    (15)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.25/41.54              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.25/41.54                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.25/41.54                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.25/41.54    (16)  all_57_7 = e3
% 230.25/41.54    (17)   ~ (e2 = e1)
% 230.25/41.54    (18)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.25/41.54          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.25/41.54    (19)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.25/41.54          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.25/41.54    (20)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.25/41.54          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.25/41.54  
% 230.25/41.54  Begin of proof
% 230.25/41.54  | 
% 230.25/41.54  | BETA: splitting (19) gives:
% 230.25/41.54  | 
% 230.25/41.54  | Case 1:
% 230.25/41.54  | | 
% 230.25/41.54  | |   (21)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) =
% 230.25/41.54  | |           e2)
% 230.25/41.54  | | 
% 230.25/41.54  | | BETA: splitting (21) gives:
% 230.25/41.54  | | 
% 230.25/41.54  | | Case 1:
% 230.25/41.54  | | | 
% 230.25/41.54  | | |   (22)  all_57_0 = e2 & op(e3, e3) = e2
% 230.25/41.54  | | | 
% 230.25/41.54  | | | ALPHA: (22) implies:
% 230.25/41.54  | | |   (23)  op(e3, e3) = e2
% 230.25/41.54  | | | 
% 230.25/41.54  | | | REF_CLOSE: (2), (10), (12), (23) are inconsistent by sub-proof #2403.
% 230.25/41.54  | | | 
% 230.25/41.54  | | Case 2:
% 230.25/41.54  | | | 
% 230.25/41.54  | | |   (24)  all_57_2 = e2 & op(e2, e3) = e2
% 230.25/41.54  | | | 
% 230.25/41.54  | | | ALPHA: (24) implies:
% 230.25/41.54  | | |   (25)  all_57_2 = e2
% 230.25/41.54  | | | 
% 230.25/41.54  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (12), (13), (14),
% 230.25/41.54  | | |            (15), (16), (17), (18), (20), (25) are inconsistent by
% 230.25/41.54  | | |            sub-proof #1055.
% 230.25/41.54  | | | 
% 230.25/41.54  | | End of split
% 230.25/41.54  | | 
% 230.25/41.54  | Case 2:
% 230.25/41.54  | | 
% 230.25/41.54  | |   (26)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) =
% 230.25/41.54  | |           e2)
% 230.25/41.54  | | 
% 230.25/41.54  | | BETA: splitting (26) gives:
% 230.25/41.54  | | 
% 230.25/41.54  | | Case 1:
% 230.25/41.54  | | | 
% 230.25/41.54  | | |   (27)  all_57_6 = e2 & op(e1, e3) = e2
% 230.25/41.54  | | | 
% 230.25/41.54  | | | REF_CLOSE: (8), (12), (27) are inconsistent by sub-proof #2393.
% 230.25/41.54  | | | 
% 230.25/41.54  | | Case 2:
% 230.25/41.54  | | | 
% 230.25/41.54  | | |   (28)  all_57_12 = e2 & op(e0, e3) = e2
% 230.25/41.54  | | | 
% 230.25/41.54  | | | REF_CLOSE: (11), (17), (28) are inconsistent by sub-proof #1922.
% 230.25/41.54  | | | 
% 230.25/41.54  | | End of split
% 230.25/41.54  | | 
% 230.25/41.54  | End of split
% 230.25/41.54  | 
% 230.25/41.54  End of proof
% 230.25/41.54  
% 230.25/41.54  Sub-proof #1031 shows that the following formulas are inconsistent:
% 230.25/41.54  ----------------------------------------------------------------
% 230.25/41.54    (1)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3)
% 230.25/41.54    (2)   ~ (e3 = e1)
% 230.25/41.54    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.25/41.54           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.25/41.54    (4)  op(e2, e2) = e1
% 230.25/41.54    (5)   ~ (e3 = e2)
% 230.25/41.54    (6)  all_57_1 = e2
% 230.25/41.54  
% 230.25/41.54  Begin of proof
% 230.25/41.54  | 
% 230.25/41.54  | BETA: splitting (1) gives:
% 230.25/41.54  | 
% 230.25/41.54  | Case 1:
% 230.25/41.54  | | 
% 230.25/41.54  | |   (7)  all_57_1 = e3 & op(e3, e2) = e3
% 230.25/41.54  | | 
% 230.25/41.54  | | REF_CLOSE: (5), (6), (7) are inconsistent by sub-proof #1664.
% 230.25/41.54  | | 
% 230.25/41.54  | Case 2:
% 230.25/41.54  | | 
% 230.25/41.54  | |   (8)  all_57_3 = e3 & op(e2, e2) = e3
% 230.25/41.54  | | 
% 230.25/41.54  | | ALPHA: (8) implies:
% 230.25/41.54  | |   (9)  op(e2, e2) = e3
% 230.25/41.54  | | 
% 230.25/41.54  | | REF_CLOSE: (2), (3), (4), (9) are inconsistent by sub-proof #1912.
% 230.25/41.54  | | 
% 230.25/41.54  | End of split
% 230.25/41.54  | 
% 230.25/41.54  End of proof
% 230.25/41.54  
% 230.25/41.54  Sub-proof #1032 shows that the following formulas are inconsistent:
% 230.25/41.54  ----------------------------------------------------------------
% 230.25/41.54    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.25/41.54         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.25/41.54    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.25/41.54         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.25/41.54    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.25/41.54         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.25/41.54    (4)   ~ (e3 = e1)
% 230.25/41.54    (5)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.25/41.54         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.25/41.54    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.25/41.54           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.25/41.54    (7)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.25/41.54         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.25/41.54    (8)   ~ (all_6_2 = e3)
% 230.25/41.54    (9)  op(e1, e1) = all_6_2
% 230.25/41.54    (10)  op(e2, e2) = e1
% 230.25/41.54    (11)  all_57_4 = e0
% 230.25/41.54    (12)  all_57_0 = e1 & op(e3, e3) = e1
% 230.25/41.54    (13)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.25/41.54          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.25/41.54    (14)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.25/41.54          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.25/41.54    (15)   ~ (e3 = e2)
% 230.25/41.54    (16)   ~ (e3 = e0)
% 230.25/41.54    (17)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.25/41.54          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.25/41.54    (18)  op(e0, e3) = all_53_3
% 230.25/41.54    (19)  all_57_15 = e3
% 230.25/41.54    (20)  op(e3, e3) = e0
% 230.25/41.54    (21)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.25/41.54          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.25/41.54            e1)
% 230.25/41.54    (22)  all_57_5 = e3
% 230.25/41.54    (23)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.25/41.54          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.25/41.54    (24)   ~ (e2 = e0)
% 230.25/41.54    (25)  all_57_3 = e1
% 230.25/41.54    (26)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.25/41.54          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.25/41.54    (27)   ~ (e1 = e0)
% 230.25/41.54    (28)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 230.25/41.54          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 230.25/41.54    (29)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.25/41.54          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.25/41.54    (30)  op(e0, e0) = e3
% 230.25/41.54    (31)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.25/41.54          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.25/41.54            e2)
% 230.25/41.54    (32)   ~ (all_53_3 = e0)
% 230.25/41.54    (33)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.25/41.54              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.25/41.54                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.25/41.54                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.25/41.54    (34)  all_57_2 = e0
% 230.25/41.54    (35)   ~ (all_53_12 = e3)
% 230.25/41.54    (36)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.25/41.54          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.25/41.54    (37)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.25/41.54          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.25/41.54    (38)   ~ (all_53_12 = e0)
% 230.25/41.54    (39)   ~ (e2 = e1)
% 230.25/41.54    (40)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.25/41.54          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.25/41.54    (41)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.25/41.54          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.25/41.54    (42)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.25/41.54          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.25/41.54    (43)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.25/41.54          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.25/41.54    (44)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.25/41.54          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.25/41.54    (45)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.25/41.54          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.25/41.54    (46)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.25/41.54          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.25/41.54    (47)  op(e3, e0) = all_53_12
% 230.25/41.54  
% 230.25/41.54  Begin of proof
% 230.25/41.54  | 
% 230.25/41.54  | ALPHA: (12) implies:
% 230.25/41.54  |   (48)  all_57_0 = e1
% 230.25/41.54  |   (49)  op(e3, e3) = e1
% 230.25/41.54  | 
% 230.25/41.54  | BETA: splitting (37) gives:
% 230.25/41.54  | 
% 230.25/41.54  | Case 1:
% 230.25/41.54  | | 
% 230.25/41.54  | |   (50)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) =
% 230.25/41.54  | |           e3)
% 230.25/41.54  | | 
% 230.25/41.54  | | REF_CLOSE: (4), (6), (16), (34), (49), (50) are inconsistent by sub-proof
% 230.25/41.54  | |            #1064.
% 230.25/41.54  | | 
% 230.25/41.54  | Case 2:
% 230.25/41.54  | | 
% 230.25/41.54  | |   (51)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) =
% 230.25/41.54  | |           e3)
% 230.25/41.54  | | 
% 230.25/41.54  | | BETA: splitting (51) gives:
% 230.25/41.54  | | 
% 230.25/41.54  | | Case 1:
% 230.25/41.54  | | | 
% 230.25/41.54  | | |   (52)  all_57_6 = e3 & op(e1, e3) = e3
% 230.25/41.54  | | | 
% 230.25/41.54  | | | ALPHA: (52) implies:
% 230.25/41.54  | | |   (53)  all_57_6 = e3
% 230.25/41.54  | | | 
% 230.25/41.54  | | | BETA: splitting (41) gives:
% 230.25/41.54  | | | 
% 230.25/41.54  | | | Case 1:
% 230.25/41.54  | | | | 
% 230.25/41.54  | | | |   (54)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3)
% 230.25/41.54  | | | |           = e2)
% 230.25/41.54  | | | | 
% 230.25/41.54  | | | | REF_CLOSE: (6), (24), (34), (39), (49), (54) are inconsistent by
% 230.25/41.54  | | | |            sub-proof #1063.
% 230.25/41.54  | | | | 
% 230.25/41.54  | | | Case 2:
% 230.25/41.54  | | | | 
% 230.25/41.54  | | | |   (55)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3)
% 230.25/41.54  | | | |           = e2)
% 230.25/41.54  | | | | 
% 230.25/41.54  | | | | BETA: splitting (55) gives:
% 230.25/41.54  | | | | 
% 230.25/41.54  | | | | Case 1:
% 230.25/41.54  | | | | | 
% 230.25/41.54  | | | | |   (56)  all_57_6 = e2 & op(e1, e3) = e2
% 230.25/41.54  | | | | | 
% 230.25/41.54  | | | | | ALPHA: (56) implies:
% 230.25/41.54  | | | | |   (57)  all_57_6 = e2
% 230.25/41.54  | | | | | 
% 230.25/41.54  | | | | | REF_CLOSE: (15), (53), (57) are inconsistent by sub-proof #2463.
% 230.25/41.54  | | | | | 
% 230.25/41.54  | | | | Case 2:
% 230.25/41.54  | | | | | 
% 230.25/41.54  | | | | |   (58)  all_57_12 = e2 & op(e0, e3) = e2
% 230.25/41.54  | | | | | 
% 230.25/41.54  | | | | | ALPHA: (58) implies:
% 230.25/41.54  | | | | |   (59)  all_57_12 = e2
% 230.25/41.54  | | | | | 
% 230.25/41.54  | | | | | BETA: splitting (21) gives:
% 230.25/41.54  | | | | | 
% 230.25/41.54  | | | | | Case 1:
% 230.25/41.54  | | | | | | 
% 230.25/41.54  | | | | | |   (60)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 &
% 230.25/41.54  | | | | | |           op(e0, e2) = e1)
% 230.25/41.54  | | | | | | 
% 230.25/41.54  | | | | | | BETA: splitting (60) gives:
% 230.25/41.54  | | | | | | 
% 230.25/41.54  | | | | | | Case 1:
% 230.25/41.54  | | | | | | | 
% 230.25/41.54  | | | | | | |   (61)  all_57_12 = e1 & op(e0, e3) = e1
% 230.25/41.54  | | | | | | | 
% 230.25/41.54  | | | | | | | ALPHA: (61) implies:
% 230.25/41.54  | | | | | | |   (62)  all_57_12 = e1
% 230.25/41.54  | | | | | | | 
% 230.25/41.54  | | | | | | | REF_CLOSE: (39), (59), (62) are inconsistent by sub-proof #2321.
% 230.25/41.54  | | | | | | | 
% 230.25/41.54  | | | | | | Case 2:
% 230.25/41.54  | | | | | | | 
% 230.25/41.54  | | | | | | |   (63)  all_57_13 = e1 & op(e0, e2) = e1
% 230.25/41.54  | | | | | | | 
% 230.25/41.54  | | | | | | | ALPHA: (63) implies:
% 230.25/41.54  | | | | | | |   (64)  all_57_13 = e1
% 230.25/41.54  | | | | | | | 
% 230.25/41.54  | | | | | | | BETA: splitting (26) gives:
% 230.25/41.54  | | | | | | | 
% 230.25/41.54  | | | | | | | Case 1:
% 230.25/41.54  | | | | | | | | 
% 230.25/41.54  | | | | | | | |   (65)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 &
% 230.25/41.54  | | | | | | | |           op(e3, e2) = e3)
% 230.25/41.54  | | | | | | | | 
% 230.25/41.54  | | | | | | | | BETA: splitting (65) gives:
% 230.25/41.54  | | | | | | | | 
% 230.25/41.54  | | | | | | | | Case 1:
% 230.25/41.54  | | | | | | | | | 
% 230.25/41.54  | | | | | | | | |   (66)  all_57_0 = e3 & op(e3, e3) = e3
% 230.25/41.54  | | | | | | | | | 
% 230.25/41.54  | | | | | | | | | ALPHA: (66) implies:
% 230.25/41.54  | | | | | | | | |   (67)  all_57_0 = e3
% 230.25/41.54  | | | | | | | | | 
% 230.25/41.54  | | | | | | | | | REF_CLOSE: (2), (4), (27), (34), (39), (53), (59), (67) are
% 230.25/41.54  | | | | | | | | |            inconsistent by sub-proof #2015.
% 230.25/41.54  | | | | | | | | | 
% 230.25/41.54  | | | | | | | | Case 2:
% 230.25/41.54  | | | | | | | | | 
% 230.25/41.54  | | | | | | | | |   (68)  all_57_1 = e3 & op(e3, e2) = e3
% 230.25/41.54  | | | | | | | | | 
% 230.25/41.54  | | | | | | | | | ALPHA: (68) implies:
% 230.25/41.54  | | | | | | | | |   (69)  all_57_1 = e3
% 230.25/41.54  | | | | | | | | | 
% 230.25/41.54  | | | | | | | | | REF_CLOSE: (1), (3), (4), (6), (10), (15), (16), (18), (19),
% 230.25/41.54  | | | | | | | | |            (20), (21), (22), (23), (24), (25), (27), (29),
% 230.25/41.54  | | | | | | | | |            (30), (31), (32), (33), (34), (36), (37), (39),
% 230.25/41.54  | | | | | | | | |            (41), (45), (64), (69) are inconsistent by
% 230.25/41.54  | | | | | | | | |            sub-proof #1056.
% 230.25/41.54  | | | | | | | | | 
% 230.25/41.54  | | | | | | | | End of split
% 230.25/41.54  | | | | | | | | 
% 230.25/41.54  | | | | | | | Case 2:
% 230.25/41.54  | | | | | | | | 
% 230.25/41.54  | | | | | | | |   (70)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 &
% 230.25/41.54  | | | | | | | |           op(e3, e0) = e3)
% 230.25/41.54  | | | | | | | | 
% 230.25/41.54  | | | | | | | | REF_CLOSE: (3), (4), (6), (7), (8), (9), (10), (11), (14), (15),
% 230.25/41.54  | | | | | | | |            (16), (18), (19), (21), (23), (24), (25), (26), (27),
% 230.25/41.54  | | | | | | | |            (29), (30), (32), (33), (35), (37), (38), (39), (40),
% 230.25/41.54  | | | | | | | |            (41), (43), (45), (47), (48), (49), (53), (70) are
% 230.25/41.54  | | | | | | | |            inconsistent by sub-proof #1052.
% 230.25/41.54  | | | | | | | | 
% 230.25/41.54  | | | | | | | End of split
% 230.25/41.54  | | | | | | | 
% 230.25/41.54  | | | | | | End of split
% 230.25/41.54  | | | | | | 
% 230.25/41.54  | | | | | Case 2:
% 230.25/41.54  | | | | | | 
% 230.25/41.54  | | | | | |   (71)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 &
% 230.25/41.54  | | | | | |           op(e0, e0) = e1)
% 230.25/41.54  | | | | | | 
% 230.25/41.54  | | | | | | BETA: splitting (71) gives:
% 230.25/41.54  | | | | | | 
% 230.25/41.54  | | | | | | Case 1:
% 230.25/41.54  | | | | | | | 
% 230.25/41.54  | | | | | | |   (72)  all_57_14 = e1 & op(e0, e1) = e1
% 230.25/41.54  | | | | | | | 
% 230.25/41.54  | | | | | | | ALPHA: (72) implies:
% 230.25/41.54  | | | | | | |   (73)  all_57_14 = e1
% 230.25/41.54  | | | | | | | 
% 230.25/41.54  | | | | | | | BETA: splitting (26) gives:
% 230.25/41.54  | | | | | | | 
% 230.25/41.54  | | | | | | | Case 1:
% 230.25/41.54  | | | | | | | | 
% 230.25/41.54  | | | | | | | |   (74)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 &
% 230.25/41.54  | | | | | | | |           op(e3, e2) = e3)
% 230.25/41.54  | | | | | | | | 
% 230.25/41.54  | | | | | | | | BETA: splitting (74) gives:
% 230.25/41.54  | | | | | | | | 
% 230.25/41.54  | | | | | | | | Case 1:
% 230.25/41.54  | | | | | | | | | 
% 230.25/41.54  | | | | | | | | |   (75)  all_57_0 = e3 & op(e3, e3) = e3
% 230.25/41.54  | | | | | | | | | 
% 230.25/41.54  | | | | | | | | | ALPHA: (75) implies:
% 230.25/41.54  | | | | | | | | |   (76)  all_57_0 = e3
% 230.25/41.54  | | | | | | | | | 
% 230.25/41.54  | | | | | | | | | REF_CLOSE: (2), (4), (27), (34), (39), (53), (59), (76) are
% 230.25/41.54  | | | | | | | | |            inconsistent by sub-proof #2015.
% 230.25/41.54  | | | | | | | | | 
% 230.25/41.54  | | | | | | | | Case 2:
% 230.25/41.54  | | | | | | | | | 
% 230.25/41.54  | | | | | | | | |   (77)  all_57_1 = e3 & op(e3, e2) = e3
% 230.25/41.54  | | | | | | | | | 
% 230.25/41.54  | | | | | | | | | ALPHA: (77) implies:
% 230.25/41.54  | | | | | | | | |   (78)  all_57_1 = e3
% 230.25/41.54  | | | | | | | | | 
% 230.25/41.54  | | | | | | | | | BETA: splitting (42) gives:
% 230.25/41.54  | | | | | | | | | 
% 230.25/41.54  | | | | | | | | | Case 1:
% 230.25/41.54  | | | | | | | | | | 
% 230.25/41.54  | | | | | | | | | |   (79)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 &
% 230.25/41.54  | | | | | | | | | |           op(e2, e1) = e2)
% 230.25/41.54  | | | | | | | | | | 
% 230.25/41.54  | | | | | | | | | | BETA: splitting (79) gives:
% 230.25/41.54  | | | | | | | | | | 
% 230.25/41.54  | | | | | | | | | | Case 1:
% 230.25/41.54  | | | | | | | | | | | 
% 230.25/41.54  | | | | | | | | | | |   (80)  all_57_4 = e2 & op(e3, e1) = e2
% 230.25/41.54  | | | | | | | | | | | 
% 230.25/41.54  | | | | | | | | | | | REF_CLOSE: (11), (24), (80) are inconsistent by sub-proof
% 230.25/41.54  | | | | | | | | | | |            #1404.
% 230.25/41.54  | | | | | | | | | | | 
% 230.25/41.54  | | | | | | | | | | Case 2:
% 230.25/41.54  | | | | | | | | | | | 
% 230.25/41.54  | | | | | | | | | | |   (81)  all_57_5 = e2 & op(e2, e1) = e2
% 230.25/41.54  | | | | | | | | | | | 
% 230.25/41.54  | | | | | | | | | | | ALPHA: (81) implies:
% 230.25/41.54  | | | | | | | | | | |   (82)  all_57_5 = e2
% 230.25/41.54  | | | | | | | | | | | 
% 230.25/41.54  | | | | | | | | | | | REF_CLOSE: (15), (22), (82) are inconsistent by sub-proof
% 230.25/41.54  | | | | | | | | | | |            #2189.
% 230.25/41.54  | | | | | | | | | | | 
% 230.25/41.54  | | | | | | | | | | End of split
% 230.25/41.54  | | | | | | | | | | 
% 230.25/41.54  | | | | | | | | | Case 2:
% 230.25/41.54  | | | | | | | | | | 
% 230.25/41.54  | | | | | | | | | |   (83)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2
% 230.25/41.55  | | | | | | | | | |           & op(e0, e1) = e2)
% 230.25/41.55  | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | BETA: splitting (83) gives:
% 230.25/41.55  | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | Case 1:
% 230.25/41.55  | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | |   (84)  all_57_8 = e2 & op(e1, e1) = e2
% 230.25/41.55  | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | ALPHA: (84) implies:
% 230.25/41.55  | | | | | | | | | | |   (85)  all_57_8 = e2
% 230.25/41.55  | | | | | | | | | | |   (86)  op(e1, e1) = e2
% 230.25/41.55  | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | BETA: splitting (13) gives:
% 230.25/41.55  | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | Case 1:
% 230.25/41.55  | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | |   (87)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 230.25/41.55  | | | | | | | | | | | |           & op(e3, e2) = e2)
% 230.25/41.55  | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | REF_CLOSE: (6), (15), (39), (49), (78), (87) are inconsistent
% 230.25/41.55  | | | | | | | | | | | |            by sub-proof #1051.
% 230.25/41.55  | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | Case 2:
% 230.25/41.55  | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | |   (88)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 230.25/41.55  | | | | | | | | | | | |           & op(e3, e0) = e2)
% 230.25/41.55  | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | BETA: splitting (88) gives:
% 230.25/41.55  | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | Case 1:
% 230.25/41.55  | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | |   (89)  all_57_4 = e2 & op(e3, e1) = e2
% 230.25/41.55  | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | ALPHA: (89) implies:
% 230.25/41.55  | | | | | | | | | | | | |   (90)  all_57_4 = e2
% 230.25/41.55  | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | COMBINE_EQS: (11), (90) imply:
% 230.25/41.55  | | | | | | | | | | | | |   (91)  e2 = e0
% 230.25/41.55  | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | COMBINE_EQS: (85), (91) imply:
% 230.25/41.55  | | | | | | | | | | | | |   (92)  all_57_8 = e0
% 230.25/41.55  | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (6), (10), (11), (13), (15), (16),
% 230.25/41.55  | | | | | | | | | | | | |            (17), (18), (19), (20), (21), (22), (23), (24),
% 230.25/41.55  | | | | | | | | | | | | |            (25), (27), (29), (30), (31), (32), (33), (34),
% 230.25/41.55  | | | | | | | | | | | | |            (36), (37), (39), (40), (41), (42), (43), (44),
% 230.25/41.55  | | | | | | | | | | | | |            (45), (46), (49), (53), (73), (78), (92) are
% 230.25/41.55  | | | | | | | | | | | | |            inconsistent by sub-proof #1045.
% 230.25/41.55  | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | Case 2:
% 230.25/41.55  | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | |   (93)  all_57_9 = e2 & op(e3, e0) = e2
% 230.25/41.55  | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | ALPHA: (93) implies:
% 230.25/41.55  | | | | | | | | | | | | |   (94)  all_57_9 = e2
% 230.25/41.55  | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | BETA: splitting (36) gives:
% 230.25/41.55  | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | Case 1:
% 230.25/41.55  | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | |   (95)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 230.25/41.55  | | | | | | | | | | | | | |           & op(e2, e2) = e2)
% 230.25/41.55  | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | BETA: splitting (95) gives:
% 230.25/41.55  | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | Case 1:
% 230.25/41.55  | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | |   (96)  all_57_2 = e2 & op(e2, e3) = e2
% 230.25/41.55  | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | ALPHA: (96) implies:
% 230.25/41.55  | | | | | | | | | | | | | | |   (97)  all_57_2 = e2
% 230.25/41.55  | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | COMBINE_EQS: (34), (97) imply:
% 230.25/41.55  | | | | | | | | | | | | | | |   (98)  e2 = e0
% 230.25/41.55  | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | COMBINE_EQS: (85), (98) imply:
% 230.25/41.55  | | | | | | | | | | | | | | |   (99)  all_57_8 = e0
% 230.25/41.55  | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (6), (10), (11), (13), (15), (16),
% 230.25/41.55  | | | | | | | | | | | | | | |            (17), (18), (19), (20), (21), (22), (23), (24),
% 230.25/41.55  | | | | | | | | | | | | | | |            (25), (27), (29), (30), (31), (32), (33), (34),
% 230.25/41.55  | | | | | | | | | | | | | | |            (36), (37), (39), (40), (41), (42), (43), (44),
% 230.25/41.55  | | | | | | | | | | | | | | |            (45), (46), (49), (53), (73), (78), (99) are
% 230.25/41.55  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1045.
% 230.25/41.55  | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | Case 2:
% 230.25/41.55  | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | |   (100)  all_57_3 = e2 & op(e2, e2) = e2
% 230.25/41.55  | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | ALPHA: (100) implies:
% 230.25/41.55  | | | | | | | | | | | | | | |   (101)  op(e2, e2) = e2
% 230.25/41.55  | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | REF_CLOSE: (6), (10), (39), (101) are inconsistent by
% 230.25/41.55  | | | | | | | | | | | | | | |            sub-proof #2306.
% 230.25/41.55  | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | End of split
% 230.25/41.55  | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | Case 2:
% 230.25/41.55  | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | |   (102)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 230.25/41.55  | | | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 230.25/41.55  | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | BETA: splitting (102) gives:
% 230.25/41.55  | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | Case 1:
% 230.25/41.55  | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | |   (103)  all_57_5 = e2 & op(e2, e1) = e2
% 230.25/41.55  | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | ALPHA: (103) implies:
% 230.25/41.55  | | | | | | | | | | | | | | |   (104)  all_57_5 = e2
% 230.25/41.55  | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | REF_CLOSE: (15), (22), (104) are inconsistent by sub-proof
% 230.25/41.55  | | | | | | | | | | | | | | |            #2189.
% 230.25/41.55  | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | Case 2:
% 230.25/41.55  | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | |   (105)  all_57_10 = e2 & op(e2, e0) = e2
% 230.25/41.55  | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | ALPHA: (105) implies:
% 230.25/41.55  | | | | | | | | | | | | | | |   (106)  all_57_10 = e2
% 230.25/41.55  | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | BETA: splitting (43) gives:
% 230.25/41.55  | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | Case 1:
% 230.25/41.55  | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | |   (107)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 230.25/41.55  | | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 230.25/41.55  | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 230.25/41.55  | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | Case 1:
% 230.25/41.55  | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | |   (108)  all_57_9 = e1 & op(e3, e0) = e1
% 230.25/41.55  | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (94), (108) are inconsistent by sub-proof
% 230.25/41.55  | | | | | | | | | | | | | | | | |            #2451.
% 230.25/41.55  | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | Case 2:
% 230.25/41.55  | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | |   (109)  all_57_10 = e1 & op(e2, e0) = e1
% 230.25/41.55  | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | | ALPHA: (109) implies:
% 230.25/41.55  | | | | | | | | | | | | | | | | |   (110)  all_57_10 = e1
% 230.25/41.55  | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (106), (110) are inconsistent by sub-proof
% 230.25/41.55  | | | | | | | | | | | | | | | | |            #2144.
% 230.25/41.55  | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | End of split
% 230.25/41.55  | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | Case 2:
% 230.25/41.55  | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | |   (111)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 230.25/41.55  | | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 230.25/41.55  | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | BETA: splitting (111) gives:
% 230.25/41.55  | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | Case 1:
% 230.25/41.55  | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | |   (112)  all_57_11 = e1 & op(e1, e0) = e1
% 230.25/41.55  | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | | ALPHA: (112) implies:
% 230.25/41.55  | | | | | | | | | | | | | | | | |   (113)  all_57_11 = e1
% 230.25/41.55  | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | | BETA: splitting (5) gives:
% 230.25/41.55  | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | | Case 1:
% 230.25/41.55  | | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | | |   (114)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 230.25/41.55  | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e0)
% 230.25/41.55  | | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | | | BETA: splitting (114) gives:
% 230.25/41.55  | | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | | | Case 1:
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | | | |   (115)  all_57_6 = e0 & op(e1, e3) = e0
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | ALPHA: (115) implies:
% 230.25/41.55  | | | | | | | | | | | | | | | | | | |   (116)  all_57_6 = e0
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (6), (7), (8), (9), (10), (14), (15),
% 230.25/41.55  | | | | | | | | | | | | | | | | | | |            (16), (18), (19), (21), (23), (24), (25), (26),
% 230.25/41.55  | | | | | | | | | | | | | | | | | | |            (27), (29), (30), (32), (33), (35), (37), (38),
% 230.25/41.55  | | | | | | | | | | | | | | | | | | |            (39), (40), (41), (43), (45), (47), (48), (49),
% 230.25/41.55  | | | | | | | | | | | | | | | | | | |            (116) are inconsistent by sub-proof #1053.
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | | | Case 2:
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | | | |   (117)  all_57_7 = e0 & op(e1, e2) = e0
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | ALPHA: (117) implies:
% 230.25/41.55  | | | | | | | | | | | | | | | | | | |   (118)  all_57_7 = e0
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | BETA: splitting (3) gives:
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | Case 1:
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | |   (119)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10), (15), (39), (78), (119) are
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1768.
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | Case 2:
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | |   (120)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | | BETA: splitting (120) gives:
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | | |   (121)  all_57_7 = e2 & op(e1, e2) = e2
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | | | ALPHA: (121) implies:
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | | |   (122)  all_57_7 = e2
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (118), (122) imply:
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | | |   (123)  e2 = e0
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | | | SIMP: (123) implies:
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | | |   (124)  e2 = e0
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (85), (124) imply:
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | | |   (125)  all_57_8 = e0
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (6), (10), (11), (15), (16), (17),
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | | |            (18), (19), (20), (21), (22), (23), (24), (25),
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | | |            (27), (29), (30), (31), (32), (33), (34), (36),
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | | |            (37), (39), (40), (41), (42), (43), (45), (46),
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | | |            (53), (73), (78), (94), (122), (125) are
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1047.
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | | |   (126)  all_57_13 = e2 & op(e0, e2) = e2
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | | | ALPHA: (126) implies:
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | | |   (127)  all_57_13 = e2
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (11), (16), (17), (18), (22), (24),
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | | |            (27), (30), (32), (33), (39), (86), (127) are
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1050.
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | | End of split
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | End of split
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | | | End of split
% 230.25/41.55  | | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | | Case 2:
% 230.25/41.55  | | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | | |   (128)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 230.25/41.55  | | | | | | | | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 230.25/41.55  | | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | | | BETA: splitting (128) gives:
% 230.25/41.55  | | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | | | Case 1:
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | | | |   (129)  all_57_8 = e0 & op(e1, e1) = e0
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | ALPHA: (129) implies:
% 230.25/41.55  | | | | | | | | | | | | | | | | | | |   (130)  all_57_8 = e0
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (6), (10), (11), (13), (15), (16),
% 230.25/41.55  | | | | | | | | | | | | | | | | | | |            (17), (18), (19), (20), (21), (22), (23), (24),
% 230.25/41.55  | | | | | | | | | | | | | | | | | | |            (25), (27), (29), (30), (31), (32), (33), (34),
% 230.25/41.55  | | | | | | | | | | | | | | | | | | |            (36), (37), (39), (40), (41), (42), (43), (45),
% 230.25/41.55  | | | | | | | | | | | | | | | | | | |            (46), (49), (53), (73), (78), (113), (130) are
% 230.25/41.55  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1046.
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | | | Case 2:
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | | | |   (131)  all_57_11 = e0 & op(e1, e0) = e0
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | ALPHA: (131) implies:
% 230.25/41.55  | | | | | | | | | | | | | | | | | | |   (132)  all_57_11 = e0
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (113), (132) imply:
% 230.25/41.55  | | | | | | | | | | | | | | | | | | |   (133)  e1 = e0
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (6), (8), (9), (11), (15), (16), (19),
% 230.25/41.55  | | | | | | | | | | | | | | | | | | |            (21), (24), (25), (27), (28), (30), (31), (33),
% 230.25/41.55  | | | | | | | | | | | | | | | | | | |            (36), (39), (94), (113), (133) are inconsistent by
% 230.25/41.55  | | | | | | | | | | | | | | | | | | |            sub-proof #1040.
% 230.25/41.55  | | | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | | | End of split
% 230.25/41.55  | | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | | End of split
% 230.25/41.55  | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | Case 2:
% 230.25/41.55  | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | |   (134)  all_57_15 = e1 & op(e0, e0) = e1
% 230.25/41.55  | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | | ALPHA: (134) implies:
% 230.25/41.55  | | | | | | | | | | | | | | | | |   (135)  op(e0, e0) = e1
% 230.25/41.55  | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (30), (135) are inconsistent by
% 230.25/41.55  | | | | | | | | | | | | | | | | |            sub-proof #2183.
% 230.25/41.55  | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | End of split
% 230.25/41.55  | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | End of split
% 230.25/41.55  | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | End of split
% 230.25/41.55  | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | End of split
% 230.25/41.55  | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | End of split
% 230.25/41.55  | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | End of split
% 230.25/41.55  | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | Case 2:
% 230.25/41.55  | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | |   (136)  all_57_14 = e2 & op(e0, e1) = e2
% 230.25/41.55  | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | ALPHA: (136) implies:
% 230.25/41.55  | | | | | | | | | | |   (137)  all_57_14 = e2
% 230.25/41.55  | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | REF_CLOSE: (39), (73), (137) are inconsistent by sub-proof
% 230.25/41.55  | | | | | | | | | | |            #2178.
% 230.25/41.55  | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | End of split
% 230.25/41.55  | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | End of split
% 230.25/41.55  | | | | | | | | | 
% 230.25/41.55  | | | | | | | | End of split
% 230.25/41.55  | | | | | | | | 
% 230.25/41.55  | | | | | | | Case 2:
% 230.25/41.55  | | | | | | | | 
% 230.25/41.55  | | | | | | | |   (138)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 &
% 230.25/41.55  | | | | | | | |            op(e3, e0) = e3)
% 230.25/41.55  | | | | | | | | 
% 230.25/41.55  | | | | | | | | REF_CLOSE: (3), (4), (6), (7), (8), (9), (10), (11), (14), (15),
% 230.25/41.55  | | | | | | | |            (16), (18), (19), (21), (23), (24), (25), (26), (27),
% 230.25/41.55  | | | | | | | |            (29), (30), (32), (33), (35), (37), (38), (39), (40),
% 230.25/41.55  | | | | | | | |            (41), (43), (45), (47), (48), (49), (53), (138) are
% 230.25/41.55  | | | | | | | |            inconsistent by sub-proof #1052.
% 230.25/41.55  | | | | | | | | 
% 230.25/41.55  | | | | | | | End of split
% 230.25/41.55  | | | | | | | 
% 230.25/41.55  | | | | | | Case 2:
% 230.25/41.55  | | | | | | | 
% 230.25/41.55  | | | | | | |   (139)  all_57_15 = e1 & op(e0, e0) = e1
% 230.25/41.55  | | | | | | | 
% 230.25/41.55  | | | | | | | ALPHA: (139) implies:
% 230.25/41.55  | | | | | | |   (140)  op(e0, e0) = e1
% 230.25/41.55  | | | | | | | 
% 230.25/41.55  | | | | | | | REF_CLOSE: (4), (6), (30), (140) are inconsistent by sub-proof
% 230.25/41.55  | | | | | | |            #2183.
% 230.25/41.55  | | | | | | | 
% 230.25/41.55  | | | | | | End of split
% 230.25/41.55  | | | | | | 
% 230.25/41.55  | | | | | End of split
% 230.25/41.55  | | | | | 
% 230.25/41.55  | | | | End of split
% 230.25/41.55  | | | | 
% 230.25/41.55  | | | End of split
% 230.25/41.55  | | | 
% 230.25/41.55  | | Case 2:
% 230.25/41.55  | | | 
% 230.25/41.55  | | |   (141)  all_57_12 = e3 & op(e0, e3) = e3
% 230.25/41.55  | | | 
% 230.25/41.55  | | | ALPHA: (141) implies:
% 230.25/41.55  | | |   (142)  all_57_12 = e3
% 230.25/41.55  | | | 
% 230.25/41.55  | | | REF_CLOSE: (3), (4), (6), (7), (8), (9), (10), (11), (15), (16), (17),
% 230.25/41.55  | | |            (18), (19), (20), (21), (22), (23), (24), (25), (26), (27),
% 230.25/41.55  | | |            (30), (31), (32), (33), (34), (35), (37), (39), (40), (41),
% 230.25/41.55  | | |            (42), (43), (45), (47), (49), (142) are inconsistent by
% 230.25/41.55  | | |            sub-proof #1033.
% 230.25/41.55  | | | 
% 230.25/41.55  | | End of split
% 230.25/41.55  | | 
% 230.25/41.55  | End of split
% 230.25/41.55  | 
% 230.25/41.55  End of proof
% 230.25/41.55  
% 230.25/41.55  Sub-proof #1033 shows that the following formulas are inconsistent:
% 230.25/41.55  ----------------------------------------------------------------
% 230.25/41.55    (1)  op(e3, e3) = e1
% 230.25/41.55    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.25/41.55         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.25/41.55    (3)   ~ (e3 = e1)
% 230.25/41.55    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.25/41.55           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.25/41.55    (5)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.25/41.55         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.25/41.55    (6)   ~ (all_6_2 = e3)
% 230.25/41.55    (7)  op(e1, e1) = all_6_2
% 230.25/41.55    (8)  op(e2, e2) = e1
% 230.25/41.55    (9)  all_57_4 = e0
% 230.25/41.55    (10)   ~ (e3 = e2)
% 230.25/41.55    (11)   ~ (e3 = e0)
% 230.25/41.55    (12)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.25/41.55          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.25/41.55    (13)  op(e0, e3) = all_53_3
% 230.25/41.55    (14)  all_57_15 = e3
% 230.25/41.55    (15)  op(e3, e3) = e0
% 230.25/41.55    (16)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.25/41.55          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.25/41.55            e1)
% 230.25/41.55    (17)  all_57_5 = e3
% 230.25/41.55    (18)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.25/41.55          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.25/41.55    (19)   ~ (e2 = e0)
% 230.25/41.55    (20)  all_57_3 = e1
% 230.25/41.55    (21)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.25/41.55          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.25/41.55    (22)   ~ (e1 = e0)
% 230.25/41.55    (23)  all_57_12 = e3
% 230.25/41.55    (24)  op(e0, e0) = e3
% 230.25/41.55    (25)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.25/41.55          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.25/41.55            e2)
% 230.25/41.55    (26)   ~ (all_53_3 = e0)
% 230.25/41.55    (27)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.25/41.55              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.25/41.55                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.25/41.55                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.25/41.55    (28)  all_57_2 = e0
% 230.25/41.55    (29)   ~ (all_53_12 = e3)
% 230.25/41.55    (30)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.25/41.55          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.25/41.55    (31)   ~ (e2 = e1)
% 230.25/41.55    (32)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.25/41.55          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.25/41.55    (33)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.25/41.55          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.25/41.55    (34)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.25/41.55          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.25/41.55    (35)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.25/41.55          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.25/41.55    (36)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.25/41.55          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.25/41.55    (37)  op(e3, e0) = all_53_12
% 230.25/41.55  
% 230.25/41.55  Begin of proof
% 230.25/41.55  | 
% 230.25/41.55  | BETA: splitting (33) gives:
% 230.25/41.55  | 
% 230.25/41.55  | Case 1:
% 230.25/41.55  | | 
% 230.25/41.55  | |   (38)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) =
% 230.25/41.55  | |           e2)
% 230.25/41.55  | | 
% 230.25/41.55  | | REF_CLOSE: (1), (4), (19), (28), (31), (38) are inconsistent by sub-proof
% 230.25/41.55  | |            #1063.
% 230.25/41.55  | | 
% 230.25/41.55  | Case 2:
% 230.25/41.55  | | 
% 230.25/41.55  | |   (39)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) =
% 230.25/41.55  | |           e2)
% 230.25/41.55  | | 
% 230.25/41.55  | | BETA: splitting (39) gives:
% 230.25/41.55  | | 
% 230.25/41.55  | | Case 1:
% 230.25/41.55  | | | 
% 230.25/41.55  | | |   (40)  all_57_6 = e2 & op(e1, e3) = e2
% 230.25/41.55  | | | 
% 230.25/41.55  | | | ALPHA: (40) implies:
% 230.25/41.55  | | |   (41)  all_57_6 = e2
% 230.25/41.55  | | | 
% 230.25/41.55  | | | BETA: splitting (5) gives:
% 230.25/41.55  | | | 
% 230.25/41.55  | | | Case 1:
% 230.25/41.55  | | | | 
% 230.25/41.55  | | | |   (42)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2)
% 230.25/41.55  | | | |           = e3)
% 230.25/41.55  | | | | 
% 230.25/41.55  | | | | BETA: splitting (42) gives:
% 230.25/41.55  | | | | 
% 230.25/41.55  | | | | Case 1:
% 230.25/41.55  | | | | | 
% 230.25/41.55  | | | | |   (43)  all_57_6 = e3 & op(e1, e3) = e3
% 230.25/41.55  | | | | | 
% 230.25/41.55  | | | | | REF_CLOSE: (10), (41), (43) are inconsistent by sub-proof #1558.
% 230.25/41.55  | | | | | 
% 230.25/41.55  | | | | Case 2:
% 230.25/41.55  | | | | | 
% 230.25/41.55  | | | | |   (44)  all_57_7 = e3 & op(e1, e2) = e3
% 230.25/41.55  | | | | | 
% 230.25/41.55  | | | | | ALPHA: (44) implies:
% 230.25/41.55  | | | | |   (45)  all_57_7 = e3
% 230.25/41.55  | | | | | 
% 230.25/41.55  | | | | | BETA: splitting (21) gives:
% 230.25/41.55  | | | | | 
% 230.25/41.55  | | | | | Case 1:
% 230.25/41.55  | | | | | | 
% 230.25/41.55  | | | | | |   (46)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3,
% 230.25/41.55  | | | | | |             e2) = e3)
% 230.25/41.55  | | | | | | 
% 230.25/41.55  | | | | | | BETA: splitting (46) gives:
% 230.25/41.55  | | | | | | 
% 230.25/41.55  | | | | | | Case 1:
% 230.25/41.55  | | | | | | | 
% 230.25/41.55  | | | | | | |   (47)  all_57_0 = e3 & op(e3, e3) = e3
% 230.25/41.55  | | | | | | | 
% 230.25/41.55  | | | | | | | ALPHA: (47) implies:
% 230.25/41.55  | | | | | | |   (48)  op(e3, e3) = e3
% 230.25/41.55  | | | | | | | 
% 230.25/41.55  | | | | | | | REF_CLOSE: (1), (3), (4), (48) are inconsistent by sub-proof
% 230.25/41.55  | | | | | | |            #2495.
% 230.25/41.55  | | | | | | | 
% 230.25/41.55  | | | | | | Case 2:
% 230.25/41.55  | | | | | | | 
% 230.25/41.55  | | | | | | |   (49)  all_57_1 = e3 & op(e3, e2) = e3
% 230.25/41.55  | | | | | | | 
% 230.25/41.55  | | | | | | | ALPHA: (49) implies:
% 230.25/41.55  | | | | | | |   (50)  all_57_1 = e3
% 230.25/41.55  | | | | | | | 
% 230.25/41.55  | | | | | | | BETA: splitting (16) gives:
% 230.25/41.55  | | | | | | | 
% 230.25/41.55  | | | | | | | Case 1:
% 230.25/41.55  | | | | | | | | 
% 230.25/41.55  | | | | | | | |   (51)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 &
% 230.25/41.55  | | | | | | | |           op(e0, e2) = e1)
% 230.25/41.55  | | | | | | | | 
% 230.25/41.55  | | | | | | | | BETA: splitting (51) gives:
% 230.25/41.55  | | | | | | | | 
% 230.25/41.55  | | | | | | | | Case 1:
% 230.25/41.55  | | | | | | | | | 
% 230.25/41.55  | | | | | | | | |   (52)  all_57_12 = e1 & op(e0, e3) = e1
% 230.25/41.55  | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | ALPHA: (52) implies:
% 230.25/41.55  | | | | | | | | |   (53)  all_57_12 = e1
% 230.25/41.55  | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | REF_CLOSE: (2), (4), (8), (10), (11), (18), (19), (22), (23),
% 230.25/41.55  | | | | | | | | |            (31), (45), (50), (53) are inconsistent by
% 230.25/41.55  | | | | | | | | |            sub-proof #1039.
% 230.25/41.55  | | | | | | | | | 
% 230.25/41.55  | | | | | | | | Case 2:
% 230.25/41.55  | | | | | | | | | 
% 230.25/41.55  | | | | | | | | |   (54)  all_57_13 = e1 & op(e0, e2) = e1
% 230.25/41.55  | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | ALPHA: (54) implies:
% 230.25/41.55  | | | | | | | | |   (55)  all_57_13 = e1
% 230.25/41.55  | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | BETA: splitting (18) gives:
% 230.25/41.55  | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | Case 1:
% 230.25/41.55  | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | |   (56)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 &
% 230.25/41.55  | | | | | | | | | |           op(e2, e2) = e0)
% 230.25/41.55  | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | REF_CLOSE: (2), (3), (4), (8), (10), (11), (13), (14), (15),
% 230.25/41.55  | | | | | | | | | |            (16), (19), (20), (22), (23), (24), (25), (26),
% 230.25/41.55  | | | | | | | | | |            (27), (28), (30), (31), (33), (36), (45), (50),
% 230.25/41.55  | | | | | | | | | |            (56) are inconsistent by sub-proof #1036.
% 230.25/41.55  | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | Case 2:
% 230.25/41.55  | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | |   (57)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0
% 230.25/41.55  | | | | | | | | | |           & op(e0, e2) = e0)
% 230.25/41.55  | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | BETA: splitting (57) gives:
% 230.25/41.55  | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | Case 1:
% 230.25/41.55  | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | |   (58)  all_57_7 = e0 & op(e1, e2) = e0
% 230.25/41.55  | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (8), (10), (11), (13), (14), (15),
% 230.25/41.55  | | | | | | | | | | |            (16), (19), (20), (22), (24), (25), (26), (27),
% 230.25/41.55  | | | | | | | | | | |            (28), (30), (31), (33), (36), (45), (50), (58) are
% 230.25/41.55  | | | | | | | | | | |            inconsistent by sub-proof #1035.
% 230.25/41.55  | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | Case 2:
% 230.25/41.55  | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | |   (59)  all_57_13 = e0 & op(e0, e2) = e0
% 230.25/41.55  | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | REF_CLOSE: (2), (3), (10), (19), (20), (22), (31), (36),
% 230.25/41.55  | | | | | | | | | | |            (50), (55), (59) are inconsistent by sub-proof
% 230.25/41.55  | | | | | | | | | | |            #1058.
% 230.25/41.55  | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | End of split
% 230.25/41.55  | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | End of split
% 230.25/41.55  | | | | | | | | | 
% 230.25/41.55  | | | | | | | | End of split
% 230.25/41.55  | | | | | | | | 
% 230.25/41.55  | | | | | | | Case 2:
% 230.25/41.55  | | | | | | | | 
% 230.25/41.55  | | | | | | | |   (60)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 &
% 230.25/41.55  | | | | | | | |           op(e0, e0) = e1)
% 230.25/41.55  | | | | | | | | 
% 230.25/41.55  | | | | | | | | BETA: splitting (60) gives:
% 230.25/41.55  | | | | | | | | 
% 230.25/41.55  | | | | | | | | Case 1:
% 230.25/41.55  | | | | | | | | | 
% 230.25/41.55  | | | | | | | | |   (61)  all_57_14 = e1 & op(e0, e1) = e1
% 230.25/41.55  | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | ALPHA: (61) implies:
% 230.25/41.55  | | | | | | | | |   (62)  all_57_14 = e1
% 230.25/41.55  | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | BETA: splitting (18) gives:
% 230.25/41.55  | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | Case 1:
% 230.25/41.55  | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | |   (63)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 &
% 230.25/41.55  | | | | | | | | | |           op(e2, e2) = e0)
% 230.25/41.55  | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | REF_CLOSE: (2), (3), (4), (8), (10), (11), (13), (14), (15),
% 230.25/41.55  | | | | | | | | | |            (16), (19), (20), (22), (23), (24), (25), (26),
% 230.25/41.55  | | | | | | | | | |            (27), (28), (30), (31), (33), (36), (45), (50),
% 230.25/41.55  | | | | | | | | | |            (63) are inconsistent by sub-proof #1036.
% 230.25/41.55  | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | Case 2:
% 230.25/41.55  | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | |   (64)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0
% 230.25/41.55  | | | | | | | | | |           & op(e0, e2) = e0)
% 230.25/41.55  | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | BETA: splitting (64) gives:
% 230.25/41.55  | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | Case 1:
% 230.25/41.55  | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | |   (65)  all_57_7 = e0 & op(e1, e2) = e0
% 230.25/41.55  | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (8), (10), (11), (13), (14), (15),
% 230.25/41.55  | | | | | | | | | | |            (16), (19), (20), (22), (24), (25), (26), (27),
% 230.25/41.55  | | | | | | | | | | |            (28), (30), (31), (33), (36), (45), (50), (65) are
% 230.25/41.55  | | | | | | | | | | |            inconsistent by sub-proof #1035.
% 230.25/41.55  | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | Case 2:
% 230.25/41.55  | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | |   (66)  all_57_13 = e0 & op(e0, e2) = e0
% 230.25/41.55  | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | ALPHA: (66) implies:
% 230.25/41.55  | | | | | | | | | | |   (67)  all_57_13 = e0
% 230.25/41.55  | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | BETA: splitting (2) gives:
% 230.25/41.55  | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | Case 1:
% 230.25/41.55  | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | |   (68)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 230.25/41.55  | | | | | | | | | | | |           & op(e2, e2) = e2)
% 230.25/41.55  | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | REF_CLOSE: (4), (8), (10), (31), (50), (68) are inconsistent
% 230.25/41.55  | | | | | | | | | | | |            by sub-proof #1768.
% 230.25/41.55  | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | Case 2:
% 230.25/41.55  | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | |   (69)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 230.25/41.55  | | | | | | | | | | | |           e2 & op(e0, e2) = e2)
% 230.25/41.55  | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | BETA: splitting (69) gives:
% 230.25/41.55  | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | Case 1:
% 230.25/41.55  | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | |   (70)  all_57_7 = e2 & op(e1, e2) = e2
% 230.25/41.55  | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | REF_CLOSE: (10), (45), (70) are inconsistent by sub-proof
% 230.25/41.55  | | | | | | | | | | | | |            #2092.
% 230.25/41.55  | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | Case 2:
% 230.25/41.55  | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | |   (71)  all_57_13 = e2 & op(e0, e2) = e2
% 230.25/41.55  | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | ALPHA: (71) implies:
% 230.25/41.55  | | | | | | | | | | | | |   (72)  all_57_13 = e2
% 230.25/41.55  | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | COMBINE_EQS: (67), (72) imply:
% 230.25/41.55  | | | | | | | | | | | | |   (73)  e2 = e0
% 230.25/41.55  | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | COMBINE_EQS: (41), (73) imply:
% 230.25/41.55  | | | | | | | | | | | | |   (74)  all_57_6 = e0
% 230.25/41.55  | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | BETA: splitting (34) gives:
% 230.25/41.55  | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | Case 1:
% 230.25/41.55  | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | |   (75)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 230.25/41.55  | | | | | | | | | | | | | |           & op(e2, e1) = e2)
% 230.25/41.55  | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | BETA: splitting (75) gives:
% 230.25/41.55  | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | Case 1:
% 230.25/41.55  | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | |   (76)  all_57_4 = e2 & op(e3, e1) = e2
% 230.25/41.55  | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | REF_CLOSE: (9), (19), (76) are inconsistent by sub-proof
% 230.25/41.55  | | | | | | | | | | | | | | |            #1404.
% 230.25/41.55  | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | Case 2:
% 230.25/41.55  | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | |   (77)  all_57_5 = e2 & op(e2, e1) = e2
% 230.25/41.55  | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | ALPHA: (77) implies:
% 230.25/41.55  | | | | | | | | | | | | | | |   (78)  all_57_5 = e2
% 230.25/41.55  | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | COMBINE_EQS: (17), (78) imply:
% 230.25/41.55  | | | | | | | | | | | | | | |   (79)  e3 = e2
% 230.25/41.55  | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | SIMP: (79) implies:
% 230.25/41.55  | | | | | | | | | | | | | | |   (80)  e3 = e2
% 230.25/41.55  | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | COMBINE_EQS: (45), (80) imply:
% 230.25/41.55  | | | | | | | | | | | | | | |   (81)  all_57_7 = e2
% 230.25/41.55  | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (10), (11), (14), (19),
% 230.25/41.55  | | | | | | | | | | | | | | |            (22), (27), (31), (32), (35), (74), (81) are
% 230.25/41.55  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1775.
% 230.25/41.55  | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | End of split
% 230.25/41.55  | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | Case 2:
% 230.25/41.55  | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | |   (82)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 230.25/41.55  | | | | | | | | | | | | | |           e2 & op(e0, e1) = e2)
% 230.25/41.55  | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | BETA: splitting (82) gives:
% 230.25/41.55  | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | Case 1:
% 230.25/41.55  | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | |   (83)  all_57_8 = e2 & op(e1, e1) = e2
% 230.25/41.55  | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | ALPHA: (83) implies:
% 230.25/41.55  | | | | | | | | | | | | | | |   (84)  op(e1, e1) = e2
% 230.25/41.55  | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | BETA: splitting (25) gives:
% 230.25/41.55  | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | Case 1:
% 230.25/41.55  | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | |   (85)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 230.25/41.55  | | | | | | | | | | | | | | | |           e2 & op(e0, e2) = e2)
% 230.25/41.55  | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | BETA: splitting (85) gives:
% 230.25/41.55  | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | Case 1:
% 230.25/41.55  | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | |   (86)  all_57_12 = e2 & op(e0, e3) = e2
% 230.25/41.55  | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | | ALPHA: (86) implies:
% 230.25/41.55  | | | | | | | | | | | | | | | | |   (87)  all_57_12 = e2
% 230.25/41.55  | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | | COMBINE_EQS: (23), (87) imply:
% 230.25/41.55  | | | | | | | | | | | | | | | | |   (88)  e3 = e2
% 230.25/41.55  | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | | SIMP: (88) implies:
% 230.25/41.55  | | | | | | | | | | | | | | | | |   (89)  e3 = e2
% 230.25/41.55  | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | | COMBINE_EQS: (45), (89) imply:
% 230.25/41.55  | | | | | | | | | | | | | | | | |   (90)  all_57_7 = e2
% 230.25/41.55  | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (10), (11), (14), (19),
% 230.25/41.55  | | | | | | | | | | | | | | | | |            (22), (27), (31), (32), (35), (74), (90) are
% 230.25/41.55  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1775.
% 230.25/41.55  | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | Case 2:
% 230.25/41.55  | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (9), (11), (12), (13), (17), (19), (22),
% 230.25/41.55  | | | | | | | | | | | | | | | | |            (24), (26), (27), (31), (72), (84) are
% 230.25/41.55  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1050.
% 230.25/41.55  | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | End of split
% 230.25/41.55  | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | Case 2:
% 230.25/41.55  | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | |   (91)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 230.25/41.55  | | | | | | | | | | | | | | | |           e2 & op(e0, e0) = e2)
% 230.25/41.55  | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | BETA: splitting (91) gives:
% 230.25/41.55  | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | Case 1:
% 230.25/41.55  | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | |   (92)  all_57_14 = e2 & op(e0, e1) = e2
% 230.25/41.55  | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (62), (92) are inconsistent by sub-proof
% 230.25/41.55  | | | | | | | | | | | | | | | | |            #1968.
% 230.25/41.55  | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | Case 2:
% 230.25/41.55  | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | |   (93)  all_57_15 = e2 & op(e0, e0) = e2
% 230.25/41.55  | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (10), (11), (14), (19),
% 230.25/41.55  | | | | | | | | | | | | | | | | |            (22), (27), (31), (32), (35), (45), (74), (93) are
% 230.25/41.55  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1034.
% 230.25/41.55  | | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | | End of split
% 230.25/41.55  | | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | End of split
% 230.25/41.55  | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | Case 2:
% 230.25/41.55  | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | |   (94)  all_57_14 = e2 & op(e0, e1) = e2
% 230.25/41.55  | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | | REF_CLOSE: (31), (62), (94) are inconsistent by sub-proof
% 230.25/41.55  | | | | | | | | | | | | | | |            #1968.
% 230.25/41.55  | | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | | End of split
% 230.25/41.55  | | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | | End of split
% 230.25/41.55  | | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | | End of split
% 230.25/41.55  | | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | | End of split
% 230.25/41.55  | | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | | End of split
% 230.25/41.55  | | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | End of split
% 230.25/41.55  | | | | | | | | | 
% 230.25/41.55  | | | | | | | | Case 2:
% 230.25/41.55  | | | | | | | | | 
% 230.25/41.55  | | | | | | | | |   (95)  all_57_15 = e1 & op(e0, e0) = e1
% 230.25/41.55  | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | ALPHA: (95) implies:
% 230.25/41.55  | | | | | | | | |   (96)  op(e0, e0) = e1
% 230.25/41.55  | | | | | | | | | 
% 230.25/41.55  | | | | | | | | | REF_CLOSE: (3), (4), (24), (96) are inconsistent by sub-proof
% 230.25/41.55  | | | | | | | | |            #2183.
% 230.25/41.55  | | | | | | | | | 
% 230.25/41.55  | | | | | | | | End of split
% 230.25/41.55  | | | | | | | | 
% 230.25/41.55  | | | | | | | End of split
% 230.25/41.55  | | | | | | | 
% 230.25/41.55  | | | | | | End of split
% 230.25/41.55  | | | | | | 
% 230.25/41.55  | | | | | Case 2:
% 230.25/41.55  | | | | | | 
% 230.25/41.55  | | | | | |   (97)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3,
% 230.25/41.55  | | | | | |             e0) = e3)
% 230.25/41.55  | | | | | | 
% 230.25/41.55  | | | | | | REF_CLOSE: (4), (9), (11), (29), (37), (97) are inconsistent by
% 230.25/41.55  | | | | | |            sub-proof #1406.
% 230.25/41.55  | | | | | | 
% 230.25/41.55  | | | | | End of split
% 230.25/41.55  | | | | | 
% 230.25/41.55  | | | | End of split
% 230.25/41.55  | | | | 
% 230.25/41.55  | | | Case 2:
% 230.25/41.55  | | | | 
% 230.25/41.55  | | | |   (98)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0)
% 230.25/41.55  | | | |           = e3)
% 230.25/41.55  | | | | 
% 230.25/41.55  | | | | REF_CLOSE: (3), (4), (6), (7), (10), (11), (14), (19), (22), (27), (31),
% 230.25/41.55  | | | |            (32), (35), (98) are inconsistent by sub-proof #1786.
% 230.25/41.55  | | | | 
% 230.25/41.55  | | | End of split
% 230.25/41.55  | | | 
% 230.25/41.55  | | Case 2:
% 230.25/41.55  | | | 
% 230.25/41.55  | | |   (99)  all_57_12 = e2 & op(e0, e3) = e2
% 230.25/41.55  | | | 
% 230.25/41.55  | | | ALPHA: (99) implies:
% 230.25/41.55  | | |   (100)  all_57_12 = e2
% 230.25/41.55  | | | 
% 230.25/41.55  | | | REF_CLOSE: (10), (23), (100) are inconsistent by sub-proof #2392.
% 230.25/41.55  | | | 
% 230.25/41.55  | | End of split
% 230.25/41.55  | | 
% 230.25/41.55  | End of split
% 230.25/41.55  | 
% 230.25/41.55  End of proof
% 230.25/41.55  
% 230.25/41.55  Sub-proof #1034 shows that the following formulas are inconsistent:
% 230.25/41.55  ----------------------------------------------------------------
% 230.25/41.55    (1)   ~ (e3 = e1)
% 230.25/41.55    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.25/41.55           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.25/41.55    (3)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.25/41.55         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.25/41.55    (4)   ~ (all_6_2 = e3)
% 230.25/41.55    (5)  op(e1, e1) = all_6_2
% 230.25/41.55    (6)   ~ (e3 = e2)
% 230.25/41.55    (7)   ~ (e3 = e0)
% 230.25/41.55    (8)  all_57_6 = e0
% 230.25/41.55    (9)  all_57_15 = e3
% 230.25/41.55    (10)   ~ (e2 = e0)
% 230.25/41.55    (11)   ~ (e1 = e0)
% 230.25/41.56    (12)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.25/41.56              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.25/41.56                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.25/41.56                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.25/41.56    (13)  all_57_7 = e3
% 230.25/41.56    (14)   ~ (e2 = e1)
% 230.25/41.56    (15)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.25/41.56          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.25/41.56    (16)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.25/41.56          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.25/41.56    (17)  all_57_15 = e2 & op(e0, e0) = e2
% 230.25/41.56  
% 230.25/41.56  Begin of proof
% 230.25/41.56  | 
% 230.25/41.56  | ALPHA: (17) implies:
% 230.25/41.56  |   (18)  all_57_15 = e2
% 230.25/41.56  | 
% 230.25/41.56  | COMBINE_EQS: (9), (18) imply:
% 230.25/41.56  |   (19)  e3 = e2
% 230.25/41.56  | 
% 230.25/41.56  | SIMP: (19) implies:
% 230.25/41.56  |   (20)  e3 = e2
% 230.25/41.56  | 
% 230.25/41.56  | COMBINE_EQS: (13), (20) imply:
% 230.25/41.56  |   (21)  all_57_7 = e2
% 230.25/41.56  | 
% 230.25/41.56  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 230.25/41.56  |            (14), (15), (16), (21) are inconsistent by sub-proof #1775.
% 230.25/41.56  | 
% 230.25/41.56  End of proof
% 230.25/41.56  
% 230.25/41.56  Sub-proof #1035 shows that the following formulas are inconsistent:
% 230.25/41.56  ----------------------------------------------------------------
% 230.25/41.56    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.25/41.56         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.25/41.56    (2)   ~ (e3 = e1)
% 230.25/41.56    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.25/41.56           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.25/41.56    (4)  op(e2, e2) = e1
% 230.25/41.56    (5)  all_57_7 = e0 & op(e1, e2) = e0
% 230.25/41.56    (6)   ~ (e3 = e2)
% 230.25/41.56    (7)   ~ (e3 = e0)
% 230.25/41.56    (8)  op(e0, e3) = all_53_3
% 230.25/41.56    (9)  all_57_15 = e3
% 230.25/41.56    (10)  op(e3, e3) = e0
% 230.25/41.56    (11)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.25/41.56          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.25/41.56            e1)
% 230.25/41.56    (12)   ~ (e2 = e0)
% 230.25/41.56    (13)  all_57_3 = e1
% 230.25/41.56    (14)   ~ (e1 = e0)
% 230.25/41.56    (15)  op(e0, e0) = e3
% 230.25/41.56    (16)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.25/41.56          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.25/41.56            e2)
% 230.25/41.56    (17)   ~ (all_53_3 = e0)
% 230.25/41.56    (18)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.25/41.56              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.25/41.56                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.25/41.56                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.25/41.56    (19)  all_57_2 = e0
% 230.25/41.56    (20)  all_57_7 = e3
% 230.25/41.56    (21)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.25/41.56          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.25/41.56    (22)  all_57_1 = e3
% 230.25/41.56    (23)   ~ (e2 = e1)
% 230.25/41.56    (24)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.25/41.56          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.25/41.56    (25)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.25/41.56          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.25/41.56  
% 230.25/41.56  Begin of proof
% 230.25/41.56  | 
% 230.25/41.56  | ALPHA: (5) implies:
% 230.25/41.56  |   (26)  all_57_7 = e0
% 230.25/41.56  | 
% 230.25/41.56  | COMBINE_EQS: (20), (26) imply:
% 230.25/41.56  |   (27)  e3 = e0
% 230.25/41.56  | 
% 230.25/41.56  | COMBINE_EQS: (22), (27) imply:
% 230.25/41.56  |   (28)  all_57_1 = e0
% 230.25/41.56  | 
% 230.25/41.56  | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13),
% 230.25/41.56  |            (14), (15), (16), (17), (18), (19), (20), (21), (23), (24), (25),
% 230.25/41.56  |            (28) are inconsistent by sub-proof #1060.
% 230.25/41.56  | 
% 230.25/41.56  End of proof
% 230.25/41.56  
% 230.25/41.56  Sub-proof #1036 shows that the following formulas are inconsistent:
% 230.25/41.56  ----------------------------------------------------------------
% 230.25/41.56    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.25/41.56         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.25/41.56    (2)   ~ (e3 = e1)
% 230.25/41.56    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.25/41.56           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.25/41.56    (4)  op(e2, e2) = e1
% 230.25/41.56    (5)   ~ (e3 = e2)
% 230.25/41.56    (6)   ~ (e3 = e0)
% 230.25/41.56    (7)  op(e0, e3) = all_53_3
% 230.25/41.56    (8)  all_57_15 = e3
% 230.25/41.56    (9)  op(e3, e3) = e0
% 230.25/41.56    (10)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.25/41.56          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.25/41.56            e1)
% 230.25/41.56    (11)   ~ (e2 = e0)
% 230.25/41.56    (12)  all_57_3 = e1
% 230.25/41.56    (13)   ~ (e1 = e0)
% 230.25/41.56    (14)  all_57_12 = e3
% 230.25/41.56    (15)  op(e0, e0) = e3
% 230.25/41.56    (16)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0)
% 230.25/41.56    (17)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.25/41.56          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.25/41.56            e2)
% 230.25/41.56    (18)   ~ (all_53_3 = e0)
% 230.25/41.56    (19)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.25/41.56              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.25/41.56                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.25/41.56                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.25/41.56    (20)  all_57_2 = e0
% 230.25/41.56    (21)  all_57_7 = e3
% 230.25/41.56    (22)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.25/41.56          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.25/41.56    (23)  all_57_1 = e3
% 230.25/41.56    (24)   ~ (e2 = e1)
% 230.25/41.56    (25)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.25/41.56          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.25/41.56    (26)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.25/41.56          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.25/41.56  
% 230.25/41.56  Begin of proof
% 230.25/41.56  | 
% 230.25/41.56  | BETA: splitting (16) gives:
% 230.25/41.56  | 
% 230.25/41.56  | Case 1:
% 230.25/41.56  | | 
% 230.25/41.56  | |   (27)  all_57_1 = e0 & op(e3, e2) = e0
% 230.25/41.56  | | 
% 230.25/41.56  | | ALPHA: (27) implies:
% 230.25/41.56  | |   (28)  all_57_1 = e0
% 230.25/41.56  | | 
% 230.25/41.56  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 230.25/41.56  | |            (13), (15), (17), (18), (19), (20), (21), (22), (24), (25), (26),
% 230.25/41.56  | |            (28) are inconsistent by sub-proof #1060.
% 230.25/41.56  | | 
% 230.25/41.56  | Case 2:
% 230.25/41.56  | | 
% 230.25/41.56  | |   (29)  all_57_3 = e0 & op(e2, e2) = e0
% 230.25/41.56  | | 
% 230.25/41.56  | | ALPHA: (29) implies:
% 230.25/41.56  | |   (30)  all_57_3 = e0
% 230.25/41.56  | | 
% 230.25/41.56  | | REF_CLOSE: (1), (2), (5), (6), (8), (10), (11), (13), (14), (17), (19),
% 230.25/41.56  | |            (23), (24), (26), (30) are inconsistent by sub-proof #1037.
% 230.25/41.56  | | 
% 230.25/41.56  | End of split
% 230.25/41.56  | 
% 230.25/41.56  End of proof
% 230.25/41.56  
% 230.25/41.56  Sub-proof #1037 shows that the following formulas are inconsistent:
% 230.25/41.56  ----------------------------------------------------------------
% 230.25/41.56    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.25/41.56         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.25/41.56    (2)   ~ (e3 = e1)
% 230.25/41.56    (3)  all_57_3 = e0
% 230.25/41.56    (4)   ~ (e3 = e2)
% 230.25/41.56    (5)   ~ (e3 = e0)
% 230.25/41.56    (6)  all_57_15 = e3
% 230.25/41.56    (7)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 230.25/41.56         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.25/41.56    (8)   ~ (e2 = e0)
% 230.25/41.56    (9)   ~ (e1 = e0)
% 230.25/41.56    (10)  all_57_12 = e3
% 230.25/41.56    (11)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.25/41.56          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.25/41.56            e2)
% 230.25/41.56    (12)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.25/41.56              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.25/41.56                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.25/41.56                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.25/41.56    (13)  all_57_1 = e3
% 230.25/41.56    (14)   ~ (e2 = e1)
% 230.25/41.56    (15)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.25/41.56          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.25/41.56  
% 230.25/41.56  Begin of proof
% 230.25/41.56  | 
% 230.25/41.56  | BETA: splitting (12) gives:
% 230.25/41.56  | 
% 230.25/41.56  | Case 1:
% 230.25/41.56  | | 
% 230.25/41.56  | |   (16)  all_57_15 = e0 & op(e0, e0) = e0
% 230.25/41.56  | | 
% 230.25/41.56  | | REF_CLOSE: (5), (6), (16) are inconsistent by sub-proof #2329.
% 230.25/41.56  | | 
% 230.25/41.56  | Case 2:
% 230.25/41.56  | | 
% 230.25/41.56  | |   (17)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 230.25/41.56  | |             e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0 &
% 230.25/41.56  | |             op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 230.25/41.56  | |           (all_57_14 = e0 & op(e0, e1) = e0))
% 230.25/41.56  | | 
% 230.25/41.56  | | ALPHA: (17) implies:
% 230.25/41.56  | |   (18)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 230.25/41.56  | |           e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.25/41.56  | | 
% 230.25/41.56  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 230.25/41.56  | |            (14), (15), (18) are inconsistent by sub-proof #1038.
% 230.25/41.56  | | 
% 230.25/41.56  | End of split
% 230.25/41.56  | 
% 230.25/41.56  End of proof
% 230.25/41.56  
% 230.25/41.56  Sub-proof #1038 shows that the following formulas are inconsistent:
% 230.25/41.56  ----------------------------------------------------------------
% 230.25/41.56    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.25/41.56         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.25/41.56    (2)   ~ (e3 = e1)
% 230.25/41.56    (3)  all_57_3 = e0
% 230.25/41.56    (4)   ~ (e3 = e2)
% 230.25/41.56    (5)   ~ (e3 = e0)
% 230.25/41.56    (6)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 230.25/41.56         (all_57_14 = e0 & op(e0, e1) = e0)
% 230.25/41.56    (7)  all_57_15 = e3
% 230.25/41.56    (8)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 230.25/41.56         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.25/41.56    (9)   ~ (e2 = e0)
% 230.25/41.56    (10)   ~ (e1 = e0)
% 230.25/41.56    (11)  all_57_12 = e3
% 230.25/41.56    (12)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.25/41.56          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.25/41.56            e2)
% 230.25/41.56    (13)  all_57_1 = e3
% 230.25/41.56    (14)   ~ (e2 = e1)
% 230.25/41.56    (15)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.25/41.56          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.25/41.56  
% 230.25/41.56  Begin of proof
% 230.25/41.56  | 
% 230.25/41.56  | BETA: splitting (6) gives:
% 230.25/41.56  | 
% 230.25/41.56  | Case 1:
% 230.25/41.56  | | 
% 230.25/41.56  | |   (16)  all_57_12 = e0 & op(e0, e3) = e0
% 230.25/41.56  | | 
% 230.25/41.56  | | REF_CLOSE: (5), (11), (16) are inconsistent by sub-proof #2237.
% 230.25/41.56  | | 
% 230.25/41.56  | Case 2:
% 230.25/41.56  | | 
% 230.25/41.56  | |   (17)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 230.25/41.56  | |           e0)
% 230.25/41.56  | | 
% 230.25/41.56  | | BETA: splitting (17) gives:
% 230.25/41.56  | | 
% 230.25/41.56  | | Case 1:
% 230.25/41.56  | | | 
% 230.25/41.56  | | |   (18)  all_57_13 = e0 & op(e0, e2) = e0
% 230.25/41.56  | | | 
% 230.25/41.56  | | | ALPHA: (18) implies:
% 230.25/41.56  | | |   (19)  all_57_13 = e0
% 230.25/41.56  | | | 
% 230.25/41.56  | | | REF_CLOSE: (1), (2), (3), (4), (9), (10), (13), (14), (15), (19) are
% 230.25/41.56  | | |            inconsistent by sub-proof #1758.
% 230.25/41.56  | | | 
% 230.25/41.56  | | Case 2:
% 230.25/41.56  | | | 
% 230.25/41.56  | | |   (20)  all_57_14 = e0 & op(e0, e1) = e0
% 230.25/41.56  | | | 
% 230.25/41.56  | | | ALPHA: (20) implies:
% 230.25/41.56  | | |   (21)  all_57_14 = e0
% 230.25/41.56  | | | 
% 230.25/41.56  | | | REF_CLOSE: (2), (4), (7), (8), (9), (10), (11), (12), (14), (21) are
% 230.25/41.56  | | |            inconsistent by sub-proof #1763.
% 230.25/41.56  | | | 
% 230.25/41.56  | | End of split
% 230.25/41.56  | | 
% 230.25/41.56  | End of split
% 230.25/41.56  | 
% 230.25/41.56  End of proof
% 230.25/41.56  
% 230.25/41.56  Sub-proof #1039 shows that the following formulas are inconsistent:
% 230.25/41.56  ----------------------------------------------------------------
% 230.25/41.56    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.25/41.56         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.25/41.56    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.25/41.56           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.25/41.56    (3)  op(e2, e2) = e1
% 230.25/41.56    (4)   ~ (e3 = e2)
% 230.25/41.56    (5)   ~ (e3 = e0)
% 230.25/41.56    (6)  all_57_12 = e1
% 230.25/41.56    (7)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.25/41.56         (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.25/41.56    (8)   ~ (e2 = e0)
% 230.25/41.56    (9)   ~ (e1 = e0)
% 230.25/41.56    (10)  all_57_12 = e3
% 230.25/41.56    (11)  all_57_7 = e3
% 230.25/41.56    (12)  all_57_1 = e3
% 230.25/41.56    (13)   ~ (e2 = e1)
% 230.25/41.56  
% 230.25/41.56  Begin of proof
% 230.25/41.56  | 
% 230.25/41.56  | COMBINE_EQS: (6), (10) imply:
% 230.25/41.56  |   (14)  e3 = e1
% 230.25/41.56  | 
% 230.25/41.56  | COMBINE_EQS: (12), (14) imply:
% 230.25/41.56  |   (15)  all_57_1 = e1
% 230.25/41.56  | 
% 230.25/41.56  | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (11), (13), (15) are
% 230.25/41.56  |            inconsistent by sub-proof #1909.
% 230.25/41.56  | 
% 230.25/41.56  End of proof
% 230.25/41.56  
% 230.25/41.56  Sub-proof #1040 shows that the following formulas are inconsistent:
% 230.25/41.56  ----------------------------------------------------------------
% 230.25/41.56    (1)  e1 = e0
% 230.25/41.56    (2)  all_57_9 = e2
% 230.25/41.56    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.25/41.56         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.25/41.56    (4)   ~ (e3 = e1)
% 230.25/41.56    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.25/41.56           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.25/41.56    (6)   ~ (all_6_2 = e3)
% 230.25/41.56    (7)  op(e1, e1) = all_6_2
% 230.25/41.56    (8)  all_57_4 = e0
% 230.25/41.56    (9)   ~ (e3 = e2)
% 230.25/41.56    (10)   ~ (e3 = e0)
% 230.25/41.56    (11)  all_57_15 = e3
% 230.25/41.56    (12)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.25/41.56          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.25/41.56            e1)
% 230.25/41.56    (13)   ~ (e2 = e0)
% 230.25/41.56    (14)  all_57_3 = e1
% 230.25/41.56    (15)   ~ (e1 = e0)
% 230.25/41.56    (16)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 230.25/41.56          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 230.25/41.56    (17)  op(e0, e0) = e3
% 230.25/41.56    (18)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.25/41.56          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.25/41.56            e2)
% 230.25/41.56    (19)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.25/41.56              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.25/41.56                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.25/41.56                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.25/41.56    (20)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.25/41.56          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.25/41.56    (21)  all_57_11 = e1
% 230.25/41.56    (22)   ~ (e2 = e1)
% 230.25/41.56  
% 230.25/41.56  Begin of proof
% 230.25/41.56  | 
% 230.25/41.56  | SIMP: (1) implies:
% 230.25/41.56  |   (23)  e1 = e0
% 230.25/41.56  | 
% 230.25/41.56  | COMBINE_EQS: (14), (23) imply:
% 230.25/41.56  |   (24)  all_57_3 = e0
% 230.25/41.56  | 
% 230.25/41.56  | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 230.25/41.56  |            (15), (16), (17), (18), (19), (20), (21), (22), (24) are
% 230.25/41.56  |            inconsistent by sub-proof #1041.
% 230.25/41.56  | 
% 230.25/41.56  End of proof
% 230.25/41.56  
% 230.25/41.56  Sub-proof #1041 shows that the following formulas are inconsistent:
% 230.25/41.56  ----------------------------------------------------------------
% 230.25/41.56    (1)  all_57_9 = e2
% 230.25/41.56    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.25/41.56         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.25/41.56    (3)   ~ (e3 = e1)
% 230.25/41.56    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.25/41.56           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.25/41.56    (5)   ~ (all_6_2 = e3)
% 230.25/41.56    (6)  op(e1, e1) = all_6_2
% 230.25/41.56    (7)  all_57_4 = e0
% 230.25/41.56    (8)  all_57_3 = e0
% 230.25/41.56    (9)   ~ (e3 = e2)
% 230.25/41.56    (10)   ~ (e3 = e0)
% 230.25/41.56    (11)  all_57_15 = e3
% 230.25/41.56    (12)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.25/41.56          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.25/41.56            e1)
% 230.25/41.56    (13)   ~ (e2 = e0)
% 230.25/41.56    (14)   ~ (e1 = e0)
% 230.25/41.56    (15)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 230.25/41.56          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 230.25/41.56    (16)  op(e0, e0) = e3
% 230.25/41.56    (17)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.25/41.56          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.25/41.56            e2)
% 230.25/41.56    (18)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.25/41.56              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.25/41.56                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.25/41.56                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.25/41.56    (19)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.25/41.56          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.25/41.56    (20)  all_57_11 = e1
% 230.25/41.56    (21)   ~ (e2 = e1)
% 230.25/41.56  
% 230.25/41.56  Begin of proof
% 230.25/41.56  | 
% 230.25/41.56  | BETA: splitting (18) gives:
% 230.25/41.56  | 
% 230.25/41.56  | Case 1:
% 230.25/41.56  | | 
% 230.25/41.56  | |   (22)  all_57_15 = e0 & op(e0, e0) = e0
% 230.25/41.56  | | 
% 230.25/41.56  | | ALPHA: (22) implies:
% 230.25/41.56  | |   (23)  op(e0, e0) = e0
% 230.25/41.56  | | 
% 230.25/41.56  | | REF_CLOSE: (4), (10), (16), (23) are inconsistent by sub-proof #2304.
% 230.25/41.56  | | 
% 230.25/41.56  | Case 2:
% 230.25/41.56  | | 
% 230.25/41.56  | |   (24)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 230.25/41.56  | |             e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0 &
% 230.25/41.56  | |             op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 230.25/41.56  | |           (all_57_14 = e0 & op(e0, e1) = e0))
% 230.25/41.56  | | 
% 230.25/41.56  | | ALPHA: (24) implies:
% 230.25/41.56  | |   (25)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 230.25/41.56  | |           e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.25/41.56  | |   (26)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 230.25/41.56  | |           e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.25/41.56  | | 
% 230.25/41.56  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 230.25/41.56  | |            (13), (14), (15), (17), (19), (20), (21), (25), (26) are
% 230.25/41.56  | |            inconsistent by sub-proof #1042.
% 230.25/41.56  | | 
% 230.25/41.56  | End of split
% 230.25/41.56  | 
% 230.25/41.56  End of proof
% 230.25/41.56  
% 230.25/41.56  Sub-proof #1042 shows that the following formulas are inconsistent:
% 230.25/41.56  ----------------------------------------------------------------
% 230.25/41.56    (1)  all_57_9 = e2
% 230.25/41.56    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.25/41.56         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.25/41.56    (3)   ~ (e3 = e1)
% 230.25/41.56    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.25/41.56           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.25/41.56    (5)   ~ (all_6_2 = e3)
% 230.25/41.56    (6)  op(e1, e1) = all_6_2
% 230.25/41.56    (7)  all_57_4 = e0
% 230.25/41.56    (8)  all_57_3 = e0
% 230.25/41.56    (9)   ~ (e3 = e2)
% 230.25/41.56    (10)   ~ (e3 = e0)
% 230.25/41.56    (11)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.25/41.56          | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.25/41.56    (12)  all_57_15 = e3
% 230.25/41.56    (13)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.25/41.56          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.25/41.56            e1)
% 230.25/41.56    (14)   ~ (e2 = e0)
% 230.25/41.56    (15)   ~ (e1 = e0)
% 230.25/41.56    (16)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 230.25/41.56          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 230.25/41.56    (17)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.25/41.56          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.25/41.56            e2)
% 230.25/41.56    (18)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.25/41.56          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.25/41.56    (19)  all_57_11 = e1
% 230.25/41.56    (20)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) |
% 230.25/41.56          (all_57_11 = e0 & op(e1, e0) = e0)
% 230.25/41.56    (21)   ~ (e2 = e1)
% 230.25/41.56  
% 230.25/41.56  Begin of proof
% 230.25/41.56  | 
% 230.25/41.56  | BETA: splitting (20) gives:
% 230.25/41.56  | 
% 230.25/41.56  | Case 1:
% 230.25/41.56  | | 
% 230.25/41.56  | |   (22)  all_57_9 = e0 & op(e3, e0) = e0
% 230.25/41.56  | | 
% 230.25/41.56  | | REF_CLOSE: (1), (14), (22) are inconsistent by sub-proof #1973.
% 230.25/41.56  | | 
% 230.25/41.56  | Case 2:
% 230.25/41.56  | | 
% 230.25/41.56  | |   (23)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 230.25/41.56  | |           e0)
% 230.25/41.56  | | 
% 230.25/41.56  | | BETA: splitting (23) gives:
% 230.25/41.56  | | 
% 230.25/41.56  | | Case 1:
% 230.25/41.56  | | | 
% 230.25/41.56  | | |   (24)  all_57_10 = e0 & op(e2, e0) = e0
% 230.25/41.56  | | | 
% 230.25/41.56  | | | ALPHA: (24) implies:
% 230.25/41.56  | | |   (25)  all_57_10 = e0
% 230.25/41.56  | | | 
% 230.25/41.56  | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 230.25/41.56  | | |            (14), (15), (16), (17), (18), (21), (25) are inconsistent by
% 230.25/41.56  | | |            sub-proof #1043.
% 230.25/41.56  | | | 
% 230.25/41.56  | | Case 2:
% 230.25/41.56  | | | 
% 230.25/41.56  | | |   (26)  all_57_11 = e0 & op(e1, e0) = e0
% 230.25/41.56  | | | 
% 230.25/41.56  | | | REF_CLOSE: (15), (19), (26) are inconsistent by sub-proof #1257.
% 230.25/41.56  | | | 
% 230.25/41.56  | | End of split
% 230.25/41.56  | | 
% 230.25/41.56  | End of split
% 230.25/41.56  | 
% 230.25/41.56  End of proof
% 230.25/41.56  
% 230.25/41.56  Sub-proof #1043 shows that the following formulas are inconsistent:
% 230.25/41.56  ----------------------------------------------------------------
% 230.25/41.56    (1)  all_57_10 = e0
% 230.25/41.56    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.25/41.56         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.25/41.56    (3)   ~ (e3 = e1)
% 230.25/41.56    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.25/41.56           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.25/41.56    (5)   ~ (all_6_2 = e3)
% 230.25/41.56    (6)  op(e1, e1) = all_6_2
% 230.25/41.56    (7)  all_57_4 = e0
% 230.25/41.56    (8)  all_57_3 = e0
% 230.25/41.56    (9)   ~ (e3 = e2)
% 230.25/41.56    (10)   ~ (e3 = e0)
% 230.25/41.56    (11)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.25/41.56          | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.25/41.56    (12)  all_57_15 = e3
% 230.25/41.56    (13)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.25/41.56          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.25/41.56            e1)
% 230.25/41.56    (14)   ~ (e2 = e0)
% 230.25/41.56    (15)   ~ (e1 = e0)
% 230.25/41.56    (16)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 230.25/41.56          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 230.25/41.56    (17)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.25/41.56          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.25/41.56            e2)
% 230.25/41.56    (18)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.25/41.56          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.25/41.56    (19)   ~ (e2 = e1)
% 230.25/41.56  
% 230.25/41.56  Begin of proof
% 230.25/41.56  | 
% 230.25/41.56  | BETA: splitting (16) gives:
% 230.25/41.56  | 
% 230.25/41.56  | Case 1:
% 230.25/41.56  | | 
% 230.25/41.56  | |   (20)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) =
% 230.25/41.56  | |           e3)
% 230.25/41.56  | | 
% 230.25/41.56  | | BETA: splitting (20) gives:
% 230.25/41.56  | | 
% 230.25/41.56  | | Case 1:
% 230.25/41.56  | | | 
% 230.25/41.56  | | |   (21)  all_57_4 = e3 & op(e3, e1) = e3
% 230.25/41.56  | | | 
% 230.25/41.56  | | | ALPHA: (21) implies:
% 230.25/41.56  | | |   (22)  all_57_4 = e3
% 230.25/41.56  | | | 
% 230.25/41.56  | | | REF_CLOSE: (7), (10), (22) are inconsistent by sub-proof #2372.
% 230.25/41.56  | | | 
% 230.25/41.56  | | Case 2:
% 230.25/41.56  | | | 
% 230.25/41.56  | | |   (23)  all_57_5 = e3 & op(e2, e1) = e3
% 230.25/41.56  | | | 
% 230.25/41.56  | | | ALPHA: (23) implies:
% 230.25/41.56  | | |   (24)  all_57_5 = e3
% 230.25/41.56  | | | 
% 230.25/41.56  | | | REF_CLOSE: (1), (2), (3), (8), (9), (14), (15), (18), (19), (24) are
% 230.25/41.56  | | |            inconsistent by sub-proof #1518.
% 230.25/41.56  | | | 
% 230.25/41.56  | | End of split
% 230.25/41.56  | | 
% 230.25/41.56  | Case 2:
% 230.25/41.56  | | 
% 230.25/41.56  | |   (25)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) =
% 230.25/41.56  | |           e3)
% 230.25/41.56  | | 
% 230.25/41.56  | | REF_CLOSE: (3), (4), (5), (6), (9), (10), (11), (12), (13), (14), (15),
% 230.25/41.56  | |            (17), (19), (25) are inconsistent by sub-proof #1044.
% 230.25/41.56  | | 
% 230.25/41.56  | End of split
% 230.25/41.56  | 
% 230.25/41.56  End of proof
% 230.25/41.56  
% 230.25/41.56  Sub-proof #1044 shows that the following formulas are inconsistent:
% 230.25/41.56  ----------------------------------------------------------------
% 230.25/41.56    (1)   ~ (e3 = e1)
% 230.25/41.56    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.25/41.56           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.25/41.56    (3)   ~ (all_6_2 = e3)
% 230.25/41.56    (4)  op(e1, e1) = all_6_2
% 230.25/41.56    (5)   ~ (e3 = e2)
% 230.25/41.56    (6)   ~ (e3 = e0)
% 230.25/41.56    (7)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 230.25/41.56         (all_57_14 = e0 & op(e0, e1) = e0)
% 230.25/41.56    (8)  all_57_15 = e3
% 230.25/41.56    (9)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 230.25/41.56         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.25/41.56    (10)   ~ (e2 = e0)
% 230.25/41.56    (11)   ~ (e1 = e0)
% 230.25/41.56    (12)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.25/41.56          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.25/41.56            e2)
% 230.25/41.56    (13)   ~ (e2 = e1)
% 230.25/41.56    (14)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 230.25/41.56  
% 230.25/41.56  Begin of proof
% 230.25/41.56  | 
% 230.25/41.56  | BETA: splitting (14) gives:
% 230.25/41.56  | 
% 230.25/41.56  | Case 1:
% 230.25/41.56  | | 
% 230.25/41.56  | |   (15)  all_57_8 = e3 & op(e1, e1) = e3
% 230.25/41.56  | | 
% 230.25/41.56  | | ALPHA: (15) implies:
% 230.25/41.56  | |   (16)  op(e1, e1) = e3
% 230.25/41.56  | | 
% 230.25/41.56  | | REF_CLOSE: (2), (3), (4), (16) are inconsistent by sub-proof #2468.
% 230.25/41.56  | | 
% 230.25/41.56  | Case 2:
% 230.25/41.56  | | 
% 230.25/41.57  | |   (17)  all_57_14 = e3 & op(e0, e1) = e3
% 230.25/41.57  | | 
% 230.25/41.57  | | ALPHA: (17) implies:
% 230.25/41.57  | |   (18)  all_57_14 = e3
% 230.25/41.57  | | 
% 230.25/41.57  | | REF_CLOSE: (1), (5), (6), (7), (8), (9), (10), (11), (12), (13), (18) are
% 230.25/41.57  | |            inconsistent by sub-proof #2313.
% 230.25/41.57  | | 
% 230.25/41.57  | End of split
% 230.25/41.57  | 
% 230.25/41.57  End of proof
% 230.25/41.57  
% 230.25/41.57  Sub-proof #1045 shows that the following formulas are inconsistent:
% 230.25/41.57  ----------------------------------------------------------------
% 230.25/41.57    (1)  op(e3, e3) = e1
% 230.25/41.57    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.25/41.57         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.25/41.57    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.25/41.57         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.25/41.57    (4)   ~ (e3 = e1)
% 230.25/41.57    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.25/41.57           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.25/41.57    (6)  op(e2, e2) = e1
% 230.25/41.57    (7)  all_57_4 = e0
% 230.25/41.57    (8)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.25/41.57         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.25/41.57    (9)   ~ (e3 = e2)
% 230.25/41.57    (10)   ~ (e3 = e0)
% 230.25/41.57    (11)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.25/41.57          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.25/41.57    (12)  op(e0, e3) = all_53_3
% 230.25/41.57    (13)  all_57_15 = e3
% 230.25/41.57    (14)  op(e3, e3) = e0
% 230.25/41.57    (15)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.25/41.57          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.25/41.57            e1)
% 230.25/41.57    (16)  all_57_5 = e3
% 230.25/41.57    (17)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.25/41.57          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.25/41.57    (18)   ~ (e2 = e0)
% 230.25/41.57    (19)  all_57_3 = e1
% 230.25/41.57    (20)   ~ (e1 = e0)
% 230.25/41.57    (21)  all_57_6 = e3
% 230.25/41.57    (22)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.25/41.57          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.25/41.57    (23)  all_57_14 = e1
% 230.25/41.57    (24)  op(e0, e0) = e3
% 230.25/41.57    (25)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.25/41.57          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.25/41.57            e2)
% 230.25/41.57    (26)   ~ (all_53_3 = e0)
% 230.25/41.57    (27)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.25/41.57              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.25/41.57                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.25/41.57                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.25/41.57    (28)  all_57_2 = e0
% 230.25/41.57    (29)  all_57_8 = e0
% 230.25/41.57    (30)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.25/41.57          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.25/41.57    (31)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.25/41.57          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.25/41.57    (32)  all_57_1 = e3
% 230.25/41.57    (33)   ~ (e2 = e1)
% 230.25/41.57    (34)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.25/41.57          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.25/41.57    (35)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.25/41.57          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.25/41.57    (36)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.25/41.57          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.25/41.57    (37)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.25/41.57          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.25/41.57    (38)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.25/41.57          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.25/41.57    (39)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.25/41.57          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.25/41.57    (40)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.25/41.57          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.25/41.57  
% 230.25/41.57  Begin of proof
% 230.25/41.57  | 
% 230.25/41.57  | BETA: splitting (38) gives:
% 230.25/41.57  | 
% 230.25/41.57  | Case 1:
% 230.25/41.57  | | 
% 230.25/41.57  | |   (41)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) =
% 230.25/41.57  | |           e1)
% 230.25/41.57  | | 
% 230.25/41.57  | | BETA: splitting (41) gives:
% 230.25/41.57  | | 
% 230.25/41.57  | | Case 1:
% 230.25/41.57  | | | 
% 230.25/41.57  | | |   (42)  all_57_6 = e1 & op(e1, e3) = e1
% 230.25/41.57  | | | 
% 230.25/41.57  | | | ALPHA: (42) implies:
% 230.25/41.57  | | |   (43)  all_57_6 = e1
% 230.25/41.57  | | | 
% 230.25/41.57  | | | REF_CLOSE: (3), (4), (5), (6), (9), (10), (17), (18), (20), (21), (22),
% 230.25/41.57  | | |            (32), (33), (43) are inconsistent by sub-proof #1548.
% 230.25/41.57  | | | 
% 230.25/41.57  | | Case 2:
% 230.25/41.57  | | | 
% 230.25/41.57  | | |   (44)  all_57_7 = e1 & op(e1, e2) = e1
% 230.25/41.57  | | | 
% 230.25/41.57  | | | ALPHA: (44) implies:
% 230.25/41.57  | | |   (45)  all_57_7 = e1
% 230.25/41.57  | | | 
% 230.25/41.57  | | | BETA: splitting (8) gives:
% 230.25/41.57  | | | 
% 230.25/41.57  | | | Case 1:
% 230.25/41.57  | | | | 
% 230.25/41.57  | | | |   (46)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2)
% 230.25/41.57  | | | |           = e2)
% 230.25/41.57  | | | | 
% 230.25/41.57  | | | | REF_CLOSE: (1), (5), (9), (32), (33), (46) are inconsistent by sub-proof
% 230.25/41.57  | | | |            #1051.
% 230.25/41.57  | | | | 
% 230.25/41.57  | | | Case 2:
% 230.25/41.57  | | | | 
% 230.25/41.57  | | | |   (47)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0)
% 230.25/41.57  | | | |           = e2)
% 230.25/41.57  | | | | 
% 230.25/41.57  | | | | BETA: splitting (47) gives:
% 230.25/41.57  | | | | 
% 230.25/41.57  | | | | Case 1:
% 230.25/41.57  | | | | | 
% 230.25/41.57  | | | | |   (48)  all_57_4 = e2 & op(e3, e1) = e2
% 230.25/41.57  | | | | | 
% 230.25/41.57  | | | | | REF_CLOSE: (7), (18), (48) are inconsistent by sub-proof #1404.
% 230.25/41.57  | | | | | 
% 230.25/41.57  | | | | Case 2:
% 230.25/41.57  | | | | | 
% 230.25/41.57  | | | | |   (49)  all_57_9 = e2 & op(e3, e0) = e2
% 230.25/41.57  | | | | | 
% 230.25/41.57  | | | | | ALPHA: (49) implies:
% 230.25/41.57  | | | | |   (50)  all_57_9 = e2
% 230.25/41.57  | | | | | 
% 230.25/41.57  | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13),
% 230.25/41.57  | | | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 230.25/41.57  | | | | |            (24), (25), (26), (27), (28), (30), (31), (32), (33), (34),
% 230.25/41.57  | | | | |            (35), (36), (37), (39), (40), (45), (50) are inconsistent
% 230.25/41.57  | | | | |            by sub-proof #1048.
% 230.25/41.57  | | | | | 
% 230.25/41.57  | | | | End of split
% 230.25/41.57  | | | | 
% 230.25/41.57  | | | End of split
% 230.25/41.57  | | | 
% 230.25/41.57  | | End of split
% 230.25/41.57  | | 
% 230.25/41.57  | Case 2:
% 230.25/41.57  | | 
% 230.25/41.57  | |   (51)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) =
% 230.25/41.57  | |           e1)
% 230.25/41.57  | | 
% 230.25/41.57  | | BETA: splitting (51) gives:
% 230.25/41.57  | | 
% 230.25/41.57  | | Case 1:
% 230.25/41.57  | | | 
% 230.25/41.57  | | |   (52)  all_57_8 = e1 & op(e1, e1) = e1
% 230.25/41.57  | | | 
% 230.25/41.57  | | | ALPHA: (52) implies:
% 230.25/41.57  | | |   (53)  all_57_8 = e1
% 230.25/41.57  | | | 
% 230.25/41.57  | | | COMBINE_EQS: (29), (53) imply:
% 230.25/41.57  | | |   (54)  e1 = e0
% 230.25/41.57  | | | 
% 230.25/41.57  | | | SIMP: (54) implies:
% 230.25/41.57  | | |   (55)  e1 = e0
% 230.25/41.57  | | | 
% 230.25/41.57  | | | COMBINE_EQS: (19), (55) imply:
% 230.25/41.57  | | |   (56)  all_57_3 = e0
% 230.25/41.57  | | | 
% 230.25/41.57  | | | REF_CLOSE: (2), (4), (9), (16), (18), (20), (28), (30), (33), (56) are
% 230.25/41.57  | | |            inconsistent by sub-proof #2253.
% 230.25/41.57  | | | 
% 230.25/41.57  | | Case 2:
% 230.25/41.57  | | | 
% 230.25/41.57  | | |   (57)  all_57_11 = e1 & op(e1, e0) = e1
% 230.25/41.57  | | | 
% 230.25/41.57  | | | ALPHA: (57) implies:
% 230.25/41.57  | | |   (58)  all_57_11 = e1
% 230.25/41.57  | | | 
% 230.25/41.57  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 230.25/41.57  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 230.25/41.57  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 230.25/41.57  | | |            (33), (34), (35), (36), (37), (39), (40), (58) are inconsistent
% 230.25/41.57  | | |            by sub-proof #1046.
% 230.25/41.57  | | | 
% 230.25/41.57  | | End of split
% 230.25/41.57  | | 
% 230.25/41.57  | End of split
% 230.25/41.57  | 
% 230.25/41.57  End of proof
% 230.25/41.57  
% 230.25/41.57  Sub-proof #1046 shows that the following formulas are inconsistent:
% 230.25/41.57  ----------------------------------------------------------------
% 230.25/41.57    (1)  op(e3, e3) = e1
% 230.25/41.57    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.25/41.57         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.25/41.57    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.25/41.57         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.25/41.57    (4)   ~ (e3 = e1)
% 230.25/41.57    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.25/41.57           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.25/41.57    (6)  op(e2, e2) = e1
% 230.25/41.57    (7)  all_57_4 = e0
% 230.25/41.57    (8)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.25/41.57         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.25/41.57    (9)   ~ (e3 = e2)
% 230.25/41.57    (10)   ~ (e3 = e0)
% 230.25/41.57    (11)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.25/41.57          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.25/41.57    (12)  op(e0, e3) = all_53_3
% 230.25/41.57    (13)  all_57_15 = e3
% 230.25/41.57    (14)  op(e3, e3) = e0
% 230.25/41.57    (15)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.25/41.57          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.25/41.57            e1)
% 230.25/41.57    (16)  all_57_5 = e3
% 230.25/41.57    (17)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.25/41.57          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.25/41.57    (18)   ~ (e2 = e0)
% 230.25/41.57    (19)  all_57_3 = e1
% 230.25/41.57    (20)   ~ (e1 = e0)
% 230.25/41.57    (21)  all_57_6 = e3
% 230.25/41.57    (22)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.25/41.57          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.25/41.57    (23)  all_57_14 = e1
% 230.25/41.57    (24)  op(e0, e0) = e3
% 230.25/41.57    (25)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.25/41.57          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.25/41.57            e2)
% 230.25/41.57    (26)   ~ (all_53_3 = e0)
% 230.25/41.57    (27)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.25/41.57              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.25/41.57                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.25/41.57                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.25/41.57    (28)  all_57_2 = e0
% 230.25/41.57    (29)  all_57_8 = e0
% 230.25/41.57    (30)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.25/41.57          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.25/41.57    (31)  all_57_11 = e1
% 230.25/41.57    (32)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.25/41.57          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.25/41.57    (33)  all_57_1 = e3
% 230.25/41.57    (34)   ~ (e2 = e1)
% 230.25/41.57    (35)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.25/41.57          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.25/41.57    (36)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.25/41.57          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.25/41.57    (37)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.25/41.57          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.25/41.57    (38)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.25/41.57          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.25/41.57    (39)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.25/41.57          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.25/41.57    (40)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.25/41.57          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.25/41.57  
% 230.25/41.57  Begin of proof
% 230.25/41.57  | 
% 230.25/41.57  | BETA: splitting (8) gives:
% 230.25/41.57  | 
% 230.25/41.57  | Case 1:
% 230.25/41.57  | | 
% 230.25/41.57  | |   (41)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) =
% 230.25/41.57  | |           e2)
% 230.25/41.57  | | 
% 230.25/41.57  | | REF_CLOSE: (1), (5), (9), (33), (34), (41) are inconsistent by sub-proof
% 230.25/41.57  | |            #1051.
% 230.25/41.57  | | 
% 230.25/41.57  | Case 2:
% 230.25/41.57  | | 
% 230.25/41.57  | |   (42)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) =
% 230.25/41.57  | |           e2)
% 230.25/41.57  | | 
% 230.25/41.57  | | BETA: splitting (42) gives:
% 230.25/41.57  | | 
% 230.25/41.57  | | Case 1:
% 230.25/41.57  | | | 
% 230.25/41.57  | | |   (43)  all_57_4 = e2 & op(e3, e1) = e2
% 230.25/41.57  | | | 
% 230.25/41.57  | | | REF_CLOSE: (7), (18), (43) are inconsistent by sub-proof #1404.
% 230.25/41.57  | | | 
% 230.25/41.57  | | Case 2:
% 230.25/41.57  | | | 
% 230.25/41.57  | | |   (44)  all_57_9 = e2 & op(e3, e0) = e2
% 230.25/41.57  | | | 
% 230.25/41.57  | | | ALPHA: (44) implies:
% 230.25/41.57  | | |   (45)  all_57_9 = e2
% 230.25/41.57  | | | 
% 230.25/41.57  | | | BETA: splitting (40) gives:
% 230.25/41.57  | | | 
% 230.25/41.57  | | | Case 1:
% 230.25/41.57  | | | | 
% 230.25/41.57  | | | |   (46)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2)
% 230.25/41.57  | | | |           = e2)
% 230.25/41.57  | | | | 
% 230.25/41.57  | | | | BETA: splitting (46) gives:
% 230.25/41.57  | | | | 
% 230.25/41.57  | | | | Case 1:
% 230.25/41.57  | | | | | 
% 230.25/41.57  | | | | |   (47)  all_57_6 = e2 & op(e1, e3) = e2
% 230.25/41.57  | | | | | 
% 230.25/41.57  | | | | | ALPHA: (47) implies:
% 230.25/41.57  | | | | |   (48)  all_57_6 = e2
% 230.25/41.57  | | | | | 
% 230.25/41.57  | | | | | REF_CLOSE: (9), (21), (48) are inconsistent by sub-proof #2463.
% 230.25/41.57  | | | | | 
% 230.25/41.57  | | | | Case 2:
% 230.25/41.57  | | | | | 
% 230.25/41.57  | | | | |   (49)  all_57_7 = e2 & op(e1, e2) = e2
% 230.25/41.57  | | | | | 
% 230.25/41.57  | | | | | ALPHA: (49) implies:
% 230.25/41.57  | | | | |   (50)  all_57_7 = e2
% 230.25/41.57  | | | | | 
% 230.25/41.57  | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13),
% 230.25/41.57  | | | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 230.25/41.57  | | | | |            (24), (25), (26), (27), (28), (29), (30), (32), (33), (34),
% 230.25/41.57  | | | | |            (35), (36), (37), (38), (39), (40), (45), (50) are
% 230.25/41.57  | | | | |            inconsistent by sub-proof #1047.
% 230.25/41.57  | | | | | 
% 230.25/41.57  | | | | End of split
% 230.25/41.57  | | | | 
% 230.25/41.57  | | | Case 2:
% 230.25/41.57  | | | | 
% 230.25/41.57  | | | |   (51)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0)
% 230.25/41.57  | | | |           = e2)
% 230.25/41.57  | | | | 
% 230.25/41.57  | | | | BETA: splitting (51) gives:
% 230.25/41.57  | | | | 
% 230.25/41.57  | | | | Case 1:
% 230.25/41.57  | | | | | 
% 230.25/41.57  | | | | |   (52)  all_57_8 = e2 & op(e1, e1) = e2
% 230.25/41.57  | | | | | 
% 230.25/41.57  | | | | | ALPHA: (52) implies:
% 230.25/41.57  | | | | |   (53)  all_57_8 = e2
% 230.25/41.57  | | | | | 
% 230.25/41.57  | | | | | REF_CLOSE: (18), (29), (53) are inconsistent by sub-proof #1957.
% 230.25/41.57  | | | | | 
% 230.25/41.57  | | | | Case 2:
% 230.25/41.57  | | | | | 
% 230.25/41.57  | | | | |   (54)  all_57_11 = e2 & op(e1, e0) = e2
% 230.25/41.57  | | | | | 
% 230.25/41.57  | | | | | REF_CLOSE: (31), (34), (54) are inconsistent by sub-proof #2048.
% 230.25/41.57  | | | | | 
% 230.25/41.57  | | | | End of split
% 230.25/41.57  | | | | 
% 230.25/41.57  | | | End of split
% 230.25/41.57  | | | 
% 230.25/41.57  | | End of split
% 230.25/41.57  | | 
% 230.25/41.57  | End of split
% 230.25/41.57  | 
% 230.25/41.57  End of proof
% 230.25/41.57  
% 230.25/41.57  Sub-proof #1047 shows that the following formulas are inconsistent:
% 230.25/41.57  ----------------------------------------------------------------
% 230.25/41.57    (1)  all_57_9 = e2
% 230.25/41.57    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.25/41.57         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.25/41.57    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.25/41.57         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.25/41.57    (4)   ~ (e3 = e1)
% 230.25/41.57    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.25/41.57           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.25/41.57    (6)  op(e2, e2) = e1
% 230.25/41.57    (7)  all_57_7 = e2
% 230.25/41.57    (8)  all_57_4 = e0
% 230.25/41.57    (9)   ~ (e3 = e2)
% 230.25/41.57    (10)   ~ (e3 = e0)
% 230.25/41.57    (11)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.25/41.57          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.25/41.57    (12)  op(e0, e3) = all_53_3
% 230.25/41.57    (13)  all_57_15 = e3
% 230.25/41.57    (14)  op(e3, e3) = e0
% 230.25/41.57    (15)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.25/41.57          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.25/41.57            e1)
% 230.25/41.57    (16)  all_57_5 = e3
% 230.25/41.57    (17)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.25/41.57          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.25/41.57    (18)   ~ (e2 = e0)
% 230.25/41.57    (19)  all_57_3 = e1
% 230.25/41.57    (20)   ~ (e1 = e0)
% 230.25/41.57    (21)  all_57_6 = e3
% 230.25/41.57    (22)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.25/41.57          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.25/41.57    (23)  all_57_14 = e1
% 230.25/41.57    (24)  op(e0, e0) = e3
% 230.25/41.57    (25)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.25/41.57          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.25/41.57            e2)
% 230.25/41.57    (26)   ~ (all_53_3 = e0)
% 230.25/41.57    (27)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.25/41.57              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.25/41.57                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.25/41.57                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.25/41.57    (28)  all_57_2 = e0
% 230.25/41.57    (29)  all_57_8 = e0
% 230.25/41.57    (30)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.25/41.57          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.25/41.57    (31)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.25/41.57          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.25/41.57    (32)  all_57_1 = e3
% 230.25/41.57    (33)   ~ (e2 = e1)
% 230.25/41.57    (34)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.25/41.57          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.25/41.57    (35)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.25/41.57          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.25/41.57    (36)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.25/41.57          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.25/41.57    (37)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.25/41.57          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.25/41.57    (38)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.25/41.57          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.25/41.57    (39)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.25/41.57          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.25/41.57  
% 230.25/41.57  Begin of proof
% 230.25/41.57  | 
% 230.25/41.57  | BETA: splitting (36) gives:
% 230.25/41.57  | 
% 230.25/41.57  | Case 1:
% 230.25/41.57  | | 
% 230.25/41.57  | |   (40)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) =
% 230.25/41.57  | |           e2)
% 230.25/41.57  | | 
% 230.25/41.57  | | BETA: splitting (40) gives:
% 230.25/41.57  | | 
% 230.25/41.57  | | Case 1:
% 230.25/41.57  | | | 
% 230.25/41.57  | | |   (41)  all_57_4 = e2 & op(e3, e1) = e2
% 230.25/41.57  | | | 
% 230.25/41.57  | | | ALPHA: (41) implies:
% 230.25/41.57  | | |   (42)  all_57_4 = e2
% 230.25/41.57  | | | 
% 230.25/41.57  | | | REF_CLOSE: (8), (18), (42) are inconsistent by sub-proof #2441.
% 230.25/41.57  | | | 
% 230.25/41.57  | | Case 2:
% 230.25/41.57  | | | 
% 230.25/41.57  | | |   (43)  all_57_5 = e2 & op(e2, e1) = e2
% 230.25/41.57  | | | 
% 230.25/41.57  | | | ALPHA: (43) implies:
% 230.25/41.57  | | |   (44)  all_57_5 = e2
% 230.25/41.57  | | | 
% 230.25/41.57  | | | REF_CLOSE: (9), (16), (44) are inconsistent by sub-proof #2189.
% 230.25/41.57  | | | 
% 230.25/41.57  | | End of split
% 230.25/41.57  | | 
% 230.25/41.57  | Case 2:
% 230.25/41.57  | | 
% 230.25/41.57  | |   (45)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) =
% 230.25/41.57  | |           e2)
% 230.25/41.57  | | 
% 230.25/41.57  | | BETA: splitting (45) gives:
% 230.25/41.57  | | 
% 230.25/41.57  | | Case 1:
% 230.25/41.57  | | | 
% 230.25/41.57  | | |   (46)  all_57_8 = e2 & op(e1, e1) = e2
% 230.25/41.57  | | | 
% 230.25/41.57  | | | ALPHA: (46) implies:
% 230.25/41.57  | | |   (47)  all_57_8 = e2
% 230.25/41.57  | | | 
% 230.25/41.57  | | | REF_CLOSE: (18), (29), (47) are inconsistent by sub-proof #1957.
% 230.25/41.57  | | | 
% 230.25/41.57  | | Case 2:
% 230.25/41.57  | | | 
% 230.25/41.57  | | |   (48)  all_57_14 = e2 & op(e0, e1) = e2
% 230.25/41.57  | | | 
% 230.25/41.57  | | | ALPHA: (48) implies:
% 230.25/41.57  | | |   (49)  all_57_14 = e2
% 230.25/41.57  | | | 
% 230.25/41.57  | | | COMBINE_EQS: (23), (49) imply:
% 230.25/41.57  | | |   (50)  e2 = e1
% 230.25/41.57  | | | 
% 230.25/41.57  | | | COMBINE_EQS: (7), (50) imply:
% 230.25/41.57  | | |   (51)  all_57_7 = e1
% 230.25/41.57  | | | 
% 230.25/41.57  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13),
% 230.25/41.57  | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 230.25/41.57  | | |            (24), (25), (26), (27), (28), (30), (31), (32), (33), (34),
% 230.25/41.57  | | |            (35), (36), (37), (38), (39), (51) are inconsistent by
% 230.25/41.57  | | |            sub-proof #1048.
% 230.25/41.57  | | | 
% 230.25/41.57  | | End of split
% 230.25/41.57  | | 
% 230.25/41.57  | End of split
% 230.25/41.57  | 
% 230.25/41.57  End of proof
% 230.25/41.57  
% 230.25/41.57  Sub-proof #1048 shows that the following formulas are inconsistent:
% 230.25/41.57  ----------------------------------------------------------------
% 230.25/41.57    (1)  all_57_9 = e2
% 230.25/41.57    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.25/41.57         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.25/41.57    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.25/41.57         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.25/41.57    (4)   ~ (e3 = e1)
% 230.25/41.57    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.25/41.57           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.25/41.57    (6)  op(e2, e2) = e1
% 230.25/41.57    (7)  all_57_4 = e0
% 230.25/41.57    (8)  all_57_7 = e1
% 230.25/41.57    (9)   ~ (e3 = e2)
% 230.25/41.57    (10)   ~ (e3 = e0)
% 230.25/41.57    (11)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.25/41.57          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.25/41.57    (12)  op(e0, e3) = all_53_3
% 230.25/41.57    (13)  all_57_15 = e3
% 230.25/41.57    (14)  op(e3, e3) = e0
% 230.25/41.57    (15)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.25/41.57          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.25/41.57            e1)
% 230.25/41.57    (16)  all_57_5 = e3
% 230.25/41.57    (17)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.25/41.57          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.25/41.57    (18)   ~ (e2 = e0)
% 230.25/41.57    (19)  all_57_3 = e1
% 230.25/41.57    (20)   ~ (e1 = e0)
% 230.25/41.57    (21)  all_57_6 = e3
% 230.25/41.57    (22)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.25/41.57          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.25/41.57    (23)  all_57_14 = e1
% 230.25/41.57    (24)  op(e0, e0) = e3
% 230.25/41.57    (25)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.25/41.57          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.25/41.57            e2)
% 230.25/41.57    (26)   ~ (all_53_3 = e0)
% 230.25/41.57    (27)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.25/41.57              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.25/41.57                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.25/41.57                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.25/41.57    (28)  all_57_2 = e0
% 230.25/41.57    (29)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.25/41.57          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.25/41.57    (30)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.25/41.57          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.25/41.57    (31)  all_57_1 = e3
% 230.25/41.57    (32)   ~ (e2 = e1)
% 230.25/41.57    (33)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.25/41.57          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.25/41.57    (34)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.25/41.57          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.25/41.57    (35)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.25/41.57          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.25/41.57    (36)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.25/41.57          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.25/41.57    (37)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.25/41.57          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.25/41.57    (38)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.25/41.57          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.25/41.57  
% 230.25/41.57  Begin of proof
% 230.25/41.57  | 
% 230.25/41.57  | BETA: splitting (3) gives:
% 230.25/41.57  | 
% 230.25/41.57  | Case 1:
% 230.25/41.57  | | 
% 230.25/41.57  | |   (39)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 230.25/41.57  | |           e2)
% 230.25/41.57  | | 
% 230.25/41.57  | | REF_CLOSE: (5), (6), (9), (31), (32), (39) are inconsistent by sub-proof
% 230.25/41.57  | |            #1768.
% 230.25/41.57  | | 
% 230.25/41.57  | Case 2:
% 230.25/41.57  | | 
% 230.25/41.57  | |   (40)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 230.25/41.57  | |           e2)
% 230.25/41.57  | | 
% 230.25/41.57  | | BETA: splitting (40) gives:
% 230.25/41.57  | | 
% 230.25/41.57  | | Case 1:
% 230.25/41.57  | | | 
% 230.25/41.57  | | |   (41)  all_57_7 = e2 & op(e1, e2) = e2
% 230.25/41.57  | | | 
% 230.25/41.57  | | | ALPHA: (41) implies:
% 230.25/41.57  | | |   (42)  all_57_7 = e2
% 230.25/41.57  | | | 
% 230.25/41.57  | | | REF_CLOSE: (8), (32), (42) are inconsistent by sub-proof #1761.
% 230.25/41.57  | | | 
% 230.25/41.57  | | Case 2:
% 230.25/41.57  | | | 
% 230.25/41.57  | | |   (43)  all_57_13 = e2 & op(e0, e2) = e2
% 230.25/41.57  | | | 
% 230.25/41.57  | | | ALPHA: (43) implies:
% 230.25/41.57  | | |   (44)  all_57_13 = e2
% 230.25/41.57  | | | 
% 230.25/41.57  | | | BETA: splitting (38) gives:
% 230.25/41.57  | | | 
% 230.25/41.57  | | | Case 1:
% 230.25/41.57  | | | | 
% 230.25/41.57  | | | |   (45)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2)
% 230.25/41.57  | | | |           = e2)
% 230.25/41.57  | | | | 
% 230.25/41.57  | | | | BETA: splitting (45) gives:
% 230.25/41.57  | | | | 
% 230.25/41.57  | | | | Case 1:
% 230.25/41.57  | | | | | 
% 230.25/41.57  | | | | |   (46)  all_57_6 = e2 & op(e1, e3) = e2
% 230.25/41.57  | | | | | 
% 230.25/41.57  | | | | | ALPHA: (46) implies:
% 230.25/41.57  | | | | |   (47)  all_57_6 = e2
% 230.25/41.57  | | | | | 
% 230.25/41.57  | | | | | REF_CLOSE: (9), (21), (47) are inconsistent by sub-proof #2463.
% 230.25/41.57  | | | | | 
% 230.25/41.57  | | | | Case 2:
% 230.25/41.57  | | | | | 
% 230.25/41.57  | | | | |   (48)  all_57_7 = e2 & op(e1, e2) = e2
% 230.25/41.57  | | | | | 
% 230.25/41.57  | | | | | ALPHA: (48) implies:
% 230.25/41.57  | | | | |   (49)  all_57_7 = e2
% 230.25/41.57  | | | | | 
% 230.25/41.57  | | | | | COMBINE_EQS: (8), (49) imply:
% 230.25/41.57  | | | | |   (50)  e2 = e1
% 230.25/41.57  | | | | | 
% 230.25/41.57  | | | | | SIMP: (50) implies:
% 230.25/41.57  | | | | |   (51)  e2 = e1
% 230.25/41.57  | | | | | 
% 230.25/41.57  | | | | | COMBINE_EQS: (44), (51) imply:
% 230.25/41.57  | | | | |   (52)  all_57_13 = e1
% 230.25/41.57  | | | | | 
% 230.25/41.58  | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (9), (10), (12), (13), (14), (15),
% 230.25/41.58  | | | | |            (16), (17), (18), (19), (20), (22), (24), (25), (26), (27),
% 230.25/41.58  | | | | |            (28), (29), (30), (31), (32), (34), (37), (49), (52) are
% 230.25/41.58  | | | | |            inconsistent by sub-proof #1057.
% 230.25/41.58  | | | | | 
% 230.25/41.58  | | | | End of split
% 230.25/41.58  | | | | 
% 230.25/41.58  | | | Case 2:
% 230.25/41.58  | | | | 
% 230.25/41.58  | | | |   (53)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0)
% 230.25/41.58  | | | |           = e2)
% 230.25/41.58  | | | | 
% 230.25/41.58  | | | | BETA: splitting (53) gives:
% 230.25/41.58  | | | | 
% 230.25/41.58  | | | | Case 1:
% 230.25/41.58  | | | | | 
% 230.25/41.58  | | | | |   (54)  all_57_8 = e2 & op(e1, e1) = e2
% 230.25/41.58  | | | | | 
% 230.25/41.58  | | | | | ALPHA: (54) implies:
% 230.25/41.58  | | | | |   (55)  op(e1, e1) = e2
% 230.25/41.58  | | | | | 
% 230.25/41.58  | | | | | REF_CLOSE: (4), (5), (7), (10), (11), (12), (16), (18), (20), (24),
% 230.25/41.58  | | | | |            (26), (27), (32), (44), (55) are inconsistent by sub-proof
% 230.25/41.58  | | | | |            #1050.
% 230.25/41.58  | | | | | 
% 230.25/41.58  | | | | Case 2:
% 230.25/41.58  | | | | | 
% 230.25/41.58  | | | | |   (56)  all_57_11 = e2 & op(e1, e0) = e2
% 230.25/41.58  | | | | | 
% 230.25/41.58  | | | | | ALPHA: (56) implies:
% 230.25/41.58  | | | | |   (57)  all_57_11 = e2
% 230.25/41.58  | | | | | 
% 230.25/41.58  | | | | | BETA: splitting (35) gives:
% 230.25/41.58  | | | | | 
% 230.25/41.58  | | | | | Case 1:
% 230.25/41.58  | | | | | | 
% 230.25/41.58  | | | | | |   (58)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2,
% 230.25/41.58  | | | | | |             e1) = e2)
% 230.25/41.58  | | | | | | 
% 230.25/41.58  | | | | | | BETA: splitting (58) gives:
% 230.25/41.58  | | | | | | 
% 230.25/41.58  | | | | | | Case 1:
% 230.25/41.58  | | | | | | | 
% 230.25/41.58  | | | | | | |   (59)  all_57_4 = e2 & op(e3, e1) = e2
% 230.25/41.58  | | | | | | | 
% 230.25/41.58  | | | | | | | ALPHA: (59) implies:
% 230.25/41.58  | | | | | | |   (60)  all_57_4 = e2
% 230.25/41.58  | | | | | | | 
% 230.25/41.58  | | | | | | | COMBINE_EQS: (7), (60) imply:
% 230.25/41.58  | | | | | | |   (61)  e2 = e0
% 230.25/41.58  | | | | | | | 
% 230.25/41.58  | | | | | | | REF_CLOSE: (1), (4), (9), (13), (18), (20), (32), (33), (36),
% 230.25/41.58  | | | | | | |            (57), (61) are inconsistent by sub-proof #1049.
% 230.25/41.58  | | | | | | | 
% 230.25/41.58  | | | | | | Case 2:
% 230.25/41.58  | | | | | | | 
% 230.25/41.58  | | | | | | |   (62)  all_57_5 = e2 & op(e2, e1) = e2
% 230.25/41.58  | | | | | | | 
% 230.25/41.58  | | | | | | | ALPHA: (62) implies:
% 230.25/41.58  | | | | | | |   (63)  all_57_5 = e2
% 230.25/41.58  | | | | | | | 
% 230.25/41.58  | | | | | | | REF_CLOSE: (9), (16), (63) are inconsistent by sub-proof #2189.
% 230.25/41.58  | | | | | | | 
% 230.25/41.58  | | | | | | End of split
% 230.25/41.58  | | | | | | 
% 230.25/41.58  | | | | | Case 2:
% 230.25/41.58  | | | | | | 
% 230.25/41.58  | | | | | |   (64)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0,
% 230.25/41.58  | | | | | |             e1) = e2)
% 230.25/41.58  | | | | | | 
% 230.25/41.58  | | | | | | BETA: splitting (64) gives:
% 230.25/41.58  | | | | | | 
% 230.25/41.58  | | | | | | Case 1:
% 230.25/41.58  | | | | | | | 
% 230.25/41.58  | | | | | | |   (65)  all_57_8 = e2 & op(e1, e1) = e2
% 230.25/41.58  | | | | | | | 
% 230.25/41.58  | | | | | | | ALPHA: (65) implies:
% 230.25/41.58  | | | | | | |   (66)  op(e1, e1) = e2
% 230.25/41.58  | | | | | | | 
% 230.25/41.58  | | | | | | | REF_CLOSE: (4), (5), (7), (10), (11), (12), (16), (18), (20),
% 230.25/41.58  | | | | | | |            (24), (26), (27), (32), (44), (66) are inconsistent by
% 230.25/41.58  | | | | | | |            sub-proof #1050.
% 230.25/41.58  | | | | | | | 
% 230.25/41.58  | | | | | | Case 2:
% 230.25/41.58  | | | | | | | 
% 230.25/41.58  | | | | | | |   (67)  all_57_14 = e2 & op(e0, e1) = e2
% 230.25/41.58  | | | | | | | 
% 230.25/41.58  | | | | | | | ALPHA: (67) implies:
% 230.25/41.58  | | | | | | |   (68)  all_57_14 = e2
% 230.25/41.58  | | | | | | | 
% 230.25/41.58  | | | | | | | COMBINE_EQS: (23), (68) imply:
% 230.25/41.58  | | | | | | |   (69)  e2 = e1
% 230.25/41.58  | | | | | | | 
% 230.25/41.58  | | | | | | | COMBINE_EQS: (44), (69) imply:
% 230.25/41.58  | | | | | | |   (70)  all_57_13 = e1
% 230.25/41.58  | | | | | | | 
% 230.25/41.58  | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (9), (10), (12), (13), (14),
% 230.25/41.58  | | | | | | |            (15), (16), (17), (18), (19), (20), (22), (24), (25),
% 230.25/41.58  | | | | | | |            (26), (27), (28), (29), (30), (31), (32), (34), (37),
% 230.25/41.58  | | | | | | |            (70) are inconsistent by sub-proof #1056.
% 230.25/41.58  | | | | | | | 
% 230.25/41.58  | | | | | | End of split
% 230.25/41.58  | | | | | | 
% 230.25/41.58  | | | | | End of split
% 230.25/41.58  | | | | | 
% 230.25/41.58  | | | | End of split
% 230.25/41.58  | | | | 
% 230.25/41.58  | | | End of split
% 230.25/41.58  | | | 
% 230.25/41.58  | | End of split
% 230.25/41.58  | | 
% 230.25/41.58  | End of split
% 230.25/41.58  | 
% 230.25/41.58  End of proof
% 230.25/41.58  
% 230.25/41.58  Sub-proof #1049 shows that the following formulas are inconsistent:
% 230.25/41.58  ----------------------------------------------------------------
% 230.25/41.58    (1)  all_57_9 = e2
% 230.25/41.58    (2)   ~ (e3 = e1)
% 230.25/41.58    (3)   ~ (e3 = e2)
% 230.25/41.58    (4)  all_57_15 = e3
% 230.25/41.58    (5)  all_57_11 = e2
% 230.25/41.58    (6)  e2 = e0
% 230.25/41.58    (7)   ~ (e2 = e0)
% 230.25/41.58    (8)   ~ (e1 = e0)
% 230.25/41.58    (9)   ~ (e2 = e1)
% 230.25/41.58    (10)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.25/41.58          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.25/41.58    (11)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.25/41.58          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.25/41.58  
% 230.25/41.58  Begin of proof
% 230.25/41.58  | 
% 230.25/41.58  | SIMP: (6) implies:
% 230.25/41.58  |   (12)  e2 = e0
% 230.25/41.58  | 
% 230.25/41.58  | COMBINE_EQS: (5), (12) imply:
% 230.25/41.58  |   (13)  all_57_11 = e0
% 230.25/41.58  | 
% 230.25/41.58  | COMBINE_EQS: (1), (12) imply:
% 230.25/41.58  |   (14)  all_57_9 = e0
% 230.25/41.58  | 
% 230.25/41.58  | REF_CLOSE: (2), (3), (4), (7), (8), (9), (10), (11), (13), (14) are
% 230.25/41.58  |            inconsistent by sub-proof #1144.
% 230.25/41.58  | 
% 230.25/41.58  End of proof
% 230.25/41.58  
% 230.25/41.58  Sub-proof #1050 shows that the following formulas are inconsistent:
% 230.25/41.58  ----------------------------------------------------------------
% 230.25/41.58    (1)   ~ (e3 = e1)
% 230.25/41.58    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.25/41.58           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.25/41.58    (3)  all_57_4 = e0
% 230.25/41.58    (4)   ~ (e3 = e0)
% 230.25/41.58    (5)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.25/41.58         (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.25/41.58    (6)  op(e0, e3) = all_53_3
% 230.25/41.58    (7)  all_57_5 = e3
% 230.25/41.58    (8)   ~ (e2 = e0)
% 230.25/41.58    (9)  all_57_13 = e2
% 230.25/41.58    (10)   ~ (e1 = e0)
% 230.25/41.58    (11)  op(e0, e0) = e3
% 230.25/41.58    (12)   ~ (all_53_3 = e0)
% 230.25/41.58    (13)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.25/41.58              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.25/41.58                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.25/41.58                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.25/41.58    (14)  op(e1, e1) = e2
% 230.25/41.58    (15)   ~ (e2 = e1)
% 230.25/41.58  
% 230.25/41.58  Begin of proof
% 230.25/41.58  | 
% 230.25/41.58  | BETA: splitting (13) gives:
% 230.25/41.58  | 
% 230.25/41.58  | Case 1:
% 230.25/41.58  | | 
% 230.25/41.58  | |   (16)  all_57_15 = e0 & op(e0, e0) = e0
% 230.25/41.58  | | 
% 230.25/41.58  | | ALPHA: (16) implies:
% 230.25/41.58  | |   (17)  op(e0, e0) = e0
% 230.25/41.58  | | 
% 230.25/41.58  | | REF_CLOSE: (2), (4), (11), (17) are inconsistent by sub-proof #2304.
% 230.25/41.58  | | 
% 230.25/41.58  | Case 2:
% 230.25/41.58  | | 
% 230.25/41.58  | |   (18)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 230.25/41.58  | |             e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0 &
% 230.25/41.58  | |             op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 230.25/41.58  | |           (all_57_14 = e0 & op(e0, e1) = e0))
% 230.25/41.58  | | 
% 230.25/41.58  | | ALPHA: (18) implies:
% 230.25/41.58  | |   (19)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 230.25/41.58  | |           e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.25/41.58  | | 
% 230.25/41.58  | | BETA: splitting (19) gives:
% 230.25/41.58  | | 
% 230.25/41.58  | | Case 1:
% 230.25/41.58  | | | 
% 230.25/41.58  | | |   (20)  all_57_12 = e0 & op(e0, e3) = e0
% 230.25/41.58  | | | 
% 230.25/41.58  | | | ALPHA: (20) implies:
% 230.25/41.58  | | |   (21)  op(e0, e3) = e0
% 230.25/41.58  | | | 
% 230.25/41.58  | | | REF_CLOSE: (2), (6), (12), (21) are inconsistent by sub-proof #2366.
% 230.25/41.58  | | | 
% 230.25/41.58  | | Case 2:
% 230.25/41.58  | | | 
% 230.25/41.58  | | |   (22)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1)
% 230.25/41.58  | | |           = e0)
% 230.25/41.58  | | | 
% 230.25/41.58  | | | BETA: splitting (22) gives:
% 230.25/41.58  | | | 
% 230.25/41.58  | | | Case 1:
% 230.25/41.58  | | | | 
% 230.25/41.58  | | | |   (23)  all_57_13 = e0 & op(e0, e2) = e0
% 230.25/41.58  | | | | 
% 230.25/41.58  | | | | ALPHA: (23) implies:
% 230.25/41.58  | | | |   (24)  all_57_13 = e0
% 230.25/41.58  | | | | 
% 230.25/41.58  | | | | REF_CLOSE: (8), (9), (24) are inconsistent by sub-proof #1911.
% 230.25/41.58  | | | | 
% 230.25/41.58  | | | Case 2:
% 230.25/41.58  | | | | 
% 230.25/41.58  | | | |   (25)  all_57_14 = e0 & op(e0, e1) = e0
% 230.25/41.58  | | | | 
% 230.25/41.58  | | | | ALPHA: (25) implies:
% 230.25/41.58  | | | |   (26)  all_57_14 = e0
% 230.25/41.58  | | | | 
% 230.25/41.58  | | | | REF_CLOSE: (1), (2), (3), (5), (7), (10), (14), (15), (26) are
% 230.25/41.58  | | | |            inconsistent by sub-proof #2379.
% 230.25/41.58  | | | | 
% 230.25/41.58  | | | End of split
% 230.25/41.58  | | | 
% 230.25/41.58  | | End of split
% 230.25/41.58  | | 
% 230.25/41.58  | End of split
% 230.25/41.58  | 
% 230.25/41.58  End of proof
% 230.25/41.58  
% 230.25/41.58  Sub-proof #1051 shows that the following formulas are inconsistent:
% 230.25/41.58  ----------------------------------------------------------------
% 230.25/41.58    (1)  op(e3, e3) = e1
% 230.25/41.58    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.25/41.58           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.25/41.58    (3)   ~ (e3 = e2)
% 230.25/41.58    (4)  all_57_1 = e3
% 230.25/41.58    (5)   ~ (e2 = e1)
% 230.25/41.58    (6)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2)
% 230.25/41.58  
% 230.25/41.58  Begin of proof
% 230.25/41.58  | 
% 230.25/41.58  | BETA: splitting (6) gives:
% 230.25/41.58  | 
% 230.25/41.58  | Case 1:
% 230.25/41.58  | | 
% 230.25/41.58  | |   (7)  all_57_0 = e2 & op(e3, e3) = e2
% 230.25/41.58  | | 
% 230.25/41.58  | | ALPHA: (7) implies:
% 230.25/41.58  | |   (8)  op(e3, e3) = e2
% 230.25/41.58  | | 
% 230.25/41.58  | | REF_CLOSE: (1), (2), (5), (8) are inconsistent by sub-proof #1950.
% 230.25/41.58  | | 
% 230.25/41.58  | Case 2:
% 230.25/41.58  | | 
% 230.25/41.58  | |   (9)  all_57_1 = e2 & op(e3, e2) = e2
% 230.25/41.58  | | 
% 230.25/41.58  | | REF_CLOSE: (3), (4), (9) are inconsistent by sub-proof #1809.
% 230.25/41.58  | | 
% 230.25/41.58  | End of split
% 230.25/41.58  | 
% 230.25/41.58  End of proof
% 230.25/41.58  
% 230.25/41.58  Sub-proof #1052 shows that the following formulas are inconsistent:
% 230.25/41.58  ----------------------------------------------------------------
% 230.25/41.58    (1)  op(e3, e3) = e1
% 230.25/41.58    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.25/41.58         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.25/41.58    (3)   ~ (e3 = e1)
% 230.25/41.58    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.25/41.58           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.25/41.58    (5)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.25/41.58         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.25/41.58    (6)   ~ (all_6_2 = e3)
% 230.25/41.58    (7)  op(e1, e1) = all_6_2
% 230.25/41.58    (8)  op(e2, e2) = e1
% 230.25/41.58    (9)  all_57_4 = e0
% 230.25/41.58    (10)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.25/41.58          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.25/41.58    (11)   ~ (e3 = e2)
% 230.25/41.58    (12)   ~ (e3 = e0)
% 230.25/41.58    (13)  all_57_0 = e1
% 230.25/41.58    (14)  op(e0, e3) = all_53_3
% 230.25/41.58    (15)  all_57_15 = e3
% 230.25/41.58    (16)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.25/41.58          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.25/41.58            e1)
% 230.25/41.58    (17)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.25/41.58    (18)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.25/41.58          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.25/41.58    (19)   ~ (e2 = e0)
% 230.25/41.58    (20)  all_57_3 = e1
% 230.25/41.58    (21)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.25/41.58          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.25/41.58    (22)   ~ (e1 = e0)
% 230.25/41.58    (23)  all_57_6 = e3
% 230.25/41.58    (24)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.25/41.58          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.25/41.58    (25)  op(e0, e0) = e3
% 230.25/41.58    (26)   ~ (all_53_3 = e0)
% 230.25/41.58    (27)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.25/41.58              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.25/41.58                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.25/41.58                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.25/41.58    (28)   ~ (all_53_12 = e3)
% 230.25/41.58    (29)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.25/41.58          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.25/41.58    (30)   ~ (all_53_12 = e0)
% 230.25/41.58    (31)   ~ (e2 = e1)
% 230.25/41.58    (32)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.25/41.58          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.25/41.58    (33)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.25/41.58          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.25/41.58    (34)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.25/41.58          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.25/41.58    (35)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.25/41.58          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.25/41.58    (36)  op(e3, e0) = all_53_12
% 230.25/41.58  
% 230.25/41.58  Begin of proof
% 230.25/41.58  | 
% 230.25/41.58  | BETA: splitting (17) gives:
% 230.25/41.58  | 
% 230.25/41.58  | Case 1:
% 230.25/41.58  | | 
% 230.25/41.58  | |   (37)  all_57_4 = e3 & op(e3, e1) = e3
% 230.25/41.58  | | 
% 230.25/41.58  | | ALPHA: (37) implies:
% 230.25/41.58  | |   (38)  all_57_4 = e3
% 230.25/41.58  | | 
% 230.25/41.58  | | COMBINE_EQS: (9), (38) imply:
% 230.25/41.58  | |   (39)  e3 = e0
% 230.25/41.58  | | 
% 230.25/41.58  | | SIMP: (39) implies:
% 230.25/41.58  | |   (40)  e3 = e0
% 230.25/41.58  | | 
% 230.25/41.58  | | COMBINE_EQS: (23), (40) imply:
% 230.25/41.58  | |   (41)  all_57_6 = e0
% 230.25/41.58  | | 
% 230.25/41.58  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13),
% 230.25/41.58  | |            (14), (15), (16), (18), (19), (20), (21), (22), (24), (25), (26),
% 230.25/41.58  | |            (27), (28), (29), (30), (31), (32), (33), (34), (35), (36), (41)
% 230.25/41.58  | |            are inconsistent by sub-proof #1053.
% 230.25/41.58  | | 
% 230.25/41.58  | Case 2:
% 230.25/41.58  | | 
% 230.25/41.58  | |   (42)  all_57_9 = e3 & op(e3, e0) = e3
% 230.25/41.58  | | 
% 230.25/41.58  | | ALPHA: (42) implies:
% 230.25/41.58  | |   (43)  op(e3, e0) = e3
% 230.25/41.58  | | 
% 230.25/41.58  | | REF_CLOSE: (4), (28), (36), (43) are inconsistent by sub-proof #2458.
% 230.25/41.58  | | 
% 230.25/41.58  | End of split
% 230.25/41.58  | 
% 230.25/41.58  End of proof
% 230.25/41.58  
% 230.25/41.58  Sub-proof #1053 shows that the following formulas are inconsistent:
% 230.25/41.58  ----------------------------------------------------------------
% 230.25/41.58    (1)  op(e3, e3) = e1
% 230.25/41.58    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.25/41.58         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.25/41.58    (3)   ~ (e3 = e1)
% 230.25/41.58    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.25/41.58           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.25/41.58    (5)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.25/41.58         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.25/41.58    (6)   ~ (all_6_2 = e3)
% 230.25/41.58    (7)  op(e1, e1) = all_6_2
% 230.25/41.58    (8)  op(e2, e2) = e1
% 230.25/41.58    (9)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.25/41.58         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.25/41.58    (10)   ~ (e3 = e2)
% 230.25/41.58    (11)   ~ (e3 = e0)
% 230.25/41.58    (12)  all_57_6 = e0
% 230.25/41.58    (13)  all_57_0 = e1
% 230.25/41.58    (14)  op(e0, e3) = all_53_3
% 230.25/41.58    (15)  all_57_15 = e3
% 230.25/41.58    (16)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.25/41.58          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.25/41.58            e1)
% 230.25/41.58    (17)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.25/41.58          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.25/41.58    (18)   ~ (e2 = e0)
% 230.25/41.58    (19)  all_57_3 = e1
% 230.25/41.58    (20)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.25/41.58          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.25/41.58    (21)   ~ (e1 = e0)
% 230.25/41.58    (22)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.25/41.58          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.25/41.58    (23)  op(e0, e0) = e3
% 230.25/41.58    (24)   ~ (all_53_3 = e0)
% 230.25/41.58    (25)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.25/41.58              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.25/41.58                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.25/41.58                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.25/41.58    (26)   ~ (all_53_12 = e3)
% 230.25/41.58    (27)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.25/41.58          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.25/41.58    (28)   ~ (all_53_12 = e0)
% 230.25/41.58    (29)   ~ (e2 = e1)
% 230.25/41.58    (30)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.25/41.58          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.25/41.58    (31)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.25/41.58          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.25/41.58    (32)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.25/41.58          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.25/41.58    (33)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.25/41.58          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.25/41.58    (34)  op(e3, e0) = all_53_12
% 230.25/41.58  
% 230.25/41.58  Begin of proof
% 230.25/41.58  | 
% 230.25/41.58  | BETA: splitting (9) gives:
% 230.25/41.58  | 
% 230.25/41.58  | Case 1:
% 230.25/41.58  | | 
% 230.25/41.58  | |   (35)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) =
% 230.25/41.58  | |           e0)
% 230.25/41.58  | | 
% 230.25/41.58  | | BETA: splitting (35) gives:
% 230.25/41.58  | | 
% 230.25/41.58  | | Case 1:
% 230.25/41.58  | | | 
% 230.25/41.58  | | |   (36)  all_57_0 = e0 & op(e3, e3) = e0
% 230.25/41.58  | | | 
% 230.25/41.58  | | | REF_CLOSE: (13), (21), (36) are inconsistent by sub-proof #1812.
% 230.25/41.58  | | | 
% 230.25/41.58  | | Case 2:
% 230.25/41.58  | | | 
% 230.25/41.58  | | |   (37)  all_57_1 = e0 & op(e3, e2) = e0
% 230.25/41.58  | | | 
% 230.25/41.58  | | | ALPHA: (37) implies:
% 230.25/41.58  | | |   (38)  all_57_1 = e0
% 230.25/41.58  | | | 
% 230.25/41.58  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (14),
% 230.25/41.58  | | |            (15), (16), (17), (18), (19), (21), (22), (23), (24), (25),
% 230.25/41.58  | | |            (27), (29), (30), (31), (32), (33), (38) are inconsistent by
% 230.25/41.58  | | |            sub-proof #1054.
% 230.25/41.58  | | | 
% 230.25/41.58  | | End of split
% 230.25/41.58  | | 
% 230.25/41.58  | Case 2:
% 230.25/41.58  | | 
% 230.25/41.58  | |   (39)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) =
% 230.25/41.58  | |           e0)
% 230.25/41.58  | | 
% 230.25/41.58  | | BETA: splitting (39) gives:
% 230.25/41.58  | | 
% 230.25/41.58  | | Case 1:
% 230.25/41.58  | | | 
% 230.25/41.58  | | |   (40)  all_57_4 = e0 & op(e3, e1) = e0
% 230.25/41.58  | | | 
% 230.25/41.58  | | | ALPHA: (40) implies:
% 230.25/41.58  | | |   (41)  all_57_4 = e0
% 230.25/41.58  | | | 
% 230.25/41.58  | | | BETA: splitting (20) gives:
% 230.25/41.58  | | | 
% 230.25/41.58  | | | Case 1:
% 230.25/41.58  | | | | 
% 230.25/41.58  | | | |   (42)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2)
% 230.25/41.58  | | | |           = e3)
% 230.25/41.58  | | | | 
% 230.25/41.58  | | | | BETA: splitting (42) gives:
% 230.25/41.58  | | | | 
% 230.25/41.58  | | | | Case 1:
% 230.25/41.58  | | | | | 
% 230.25/41.58  | | | | |   (43)  all_57_0 = e3 & op(e3, e3) = e3
% 230.25/41.58  | | | | | 
% 230.25/41.58  | | | | | ALPHA: (43) implies:
% 230.25/41.58  | | | | |   (44)  op(e3, e3) = e3
% 230.25/41.58  | | | | | 
% 230.25/41.58  | | | | | REF_CLOSE: (1), (3), (4), (44) are inconsistent by sub-proof #2495.
% 230.25/41.58  | | | | | 
% 230.25/41.58  | | | | Case 2:
% 230.25/41.58  | | | | | 
% 230.25/41.58  | | | | |   (45)  all_57_1 = e3 & op(e3, e2) = e3
% 230.25/41.58  | | | | | 
% 230.25/41.58  | | | | | ALPHA: (45) implies:
% 230.25/41.58  | | | | |   (46)  all_57_1 = e3
% 230.25/41.58  | | | | | 
% 230.25/41.58  | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (15),
% 230.25/41.58  | | | | |            (17), (18), (21), (25), (29), (30), (32), (33), (46) are
% 230.25/41.58  | | | | |            inconsistent by sub-proof #1773.
% 230.25/41.58  | | | | | 
% 230.25/41.58  | | | | End of split
% 230.25/41.58  | | | | 
% 230.25/41.58  | | | Case 2:
% 230.25/41.58  | | | | 
% 230.25/41.58  | | | |   (47)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0)
% 230.25/41.58  | | | |           = e3)
% 230.25/41.58  | | | | 
% 230.25/41.58  | | | | REF_CLOSE: (4), (11), (26), (34), (41), (47) are inconsistent by
% 230.25/41.58  | | | |            sub-proof #1406.
% 230.25/41.58  | | | | 
% 230.25/41.58  | | | End of split
% 230.25/41.58  | | | 
% 230.25/41.58  | | Case 2:
% 230.25/41.58  | | | 
% 230.25/41.58  | | |   (48)  all_57_9 = e0 & op(e3, e0) = e0
% 230.25/41.58  | | | 
% 230.25/41.58  | | | REF_CLOSE: (4), (28), (34), (48) are inconsistent by sub-proof #2434.
% 230.25/41.58  | | | 
% 230.25/41.58  | | End of split
% 230.25/41.58  | | 
% 230.25/41.58  | End of split
% 230.25/41.58  | 
% 230.25/41.58  End of proof
% 230.25/41.58  
% 230.25/41.58  Sub-proof #1054 shows that the following formulas are inconsistent:
% 230.25/41.58  ----------------------------------------------------------------
% 230.25/41.58    (1)  op(e3, e3) = e1
% 230.25/41.58    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.25/41.58         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.25/41.58    (3)   ~ (e3 = e1)
% 230.25/41.58    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.25/41.58           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.25/41.58    (5)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.25/41.58         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.25/41.58    (6)   ~ (all_6_2 = e3)
% 230.25/41.58    (7)  op(e1, e1) = all_6_2
% 230.25/41.58    (8)  op(e2, e2) = e1
% 230.25/41.58    (9)   ~ (e3 = e2)
% 230.25/41.58    (10)   ~ (e3 = e0)
% 230.25/41.58    (11)  all_57_6 = e0
% 230.25/41.58    (12)  all_57_1 = e0
% 230.25/41.58    (13)  op(e0, e3) = all_53_3
% 230.25/41.58    (14)  all_57_15 = e3
% 230.25/41.58    (15)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.25/41.58          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.25/41.58            e1)
% 230.25/41.58    (16)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.25/41.58          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.25/41.58    (17)   ~ (e2 = e0)
% 230.25/41.58    (18)  all_57_3 = e1
% 230.25/41.58    (19)   ~ (e1 = e0)
% 230.25/41.58    (20)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.25/41.58          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.25/41.58    (21)  op(e0, e0) = e3
% 230.25/41.58    (22)   ~ (all_53_3 = e0)
% 230.25/41.58    (23)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.25/41.58              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.25/41.58                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.25/41.58                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.25/41.58    (24)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.25/41.58          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.25/41.58    (25)   ~ (e2 = e1)
% 230.25/41.58    (26)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.25/41.58          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.25/41.58    (27)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.25/41.58          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.25/41.58    (28)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.25/41.58          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.25/41.58    (29)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.25/41.58          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.25/41.58  
% 230.25/41.58  Begin of proof
% 230.25/41.58  | 
% 230.25/41.58  | BETA: splitting (20) gives:
% 230.25/41.58  | 
% 230.25/41.58  | Case 1:
% 230.25/41.58  | | 
% 230.25/41.58  | |   (30)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 230.25/41.58  | |           e3)
% 230.25/41.58  | | 
% 230.25/41.58  | | BETA: splitting (30) gives:
% 230.25/41.58  | | 
% 230.25/41.58  | | Case 1:
% 230.25/41.58  | | | 
% 230.25/41.58  | | |   (31)  all_57_1 = e3 & op(e3, e2) = e3
% 230.25/41.58  | | | 
% 230.25/41.58  | | | ALPHA: (31) implies:
% 230.25/41.58  | | |   (32)  all_57_1 = e3
% 230.25/41.58  | | | 
% 230.25/41.58  | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (14), (16),
% 230.25/41.58  | | |            (17), (19), (23), (25), (26), (28), (29), (32) are inconsistent
% 230.25/41.58  | | |            by sub-proof #1773.
% 230.25/41.58  | | | 
% 230.25/41.58  | | Case 2:
% 230.25/41.58  | | | 
% 230.25/41.58  | | |   (33)  all_57_3 = e3 & op(e2, e2) = e3
% 230.25/41.58  | | | 
% 230.25/41.58  | | | ALPHA: (33) implies:
% 230.25/41.58  | | |   (34)  op(e2, e2) = e3
% 230.25/41.58  | | | 
% 230.25/41.58  | | | REF_CLOSE: (3), (4), (8), (34) are inconsistent by sub-proof #1912.
% 230.25/41.58  | | | 
% 230.25/41.58  | | End of split
% 230.25/41.58  | | 
% 230.25/41.58  | Case 2:
% 230.25/41.58  | | 
% 230.25/41.58  | |   (35)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 230.25/41.58  | |           e3)
% 230.25/41.58  | | 
% 230.25/41.58  | | BETA: splitting (35) gives:
% 230.25/41.58  | | 
% 230.25/41.58  | | Case 1:
% 230.25/41.58  | | | 
% 230.25/41.58  | | |   (36)  all_57_7 = e3 & op(e1, e2) = e3
% 230.25/41.58  | | | 
% 230.25/41.58  | | | ALPHA: (36) implies:
% 230.25/41.58  | | |   (37)  all_57_7 = e3
% 230.25/41.58  | | | 
% 230.25/41.58  | | | BETA: splitting (2) gives:
% 230.25/41.58  | | | 
% 230.25/41.58  | | | Case 1:
% 230.25/41.58  | | | | 
% 230.25/41.58  | | | |   (38)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2)
% 230.25/41.58  | | | |           = e2)
% 230.25/41.58  | | | | 
% 230.25/41.58  | | | | REF_CLOSE: (4), (8), (12), (17), (25), (38) are inconsistent by
% 230.25/41.58  | | | |            sub-proof #1738.
% 230.25/41.58  | | | | 
% 230.25/41.58  | | | Case 2:
% 230.25/41.58  | | | | 
% 230.25/41.58  | | | |   (39)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2)
% 230.25/41.58  | | | |           = e2)
% 230.25/41.58  | | | | 
% 230.25/41.58  | | | | BETA: splitting (39) gives:
% 230.25/41.58  | | | | 
% 230.25/41.58  | | | | Case 1:
% 230.25/41.58  | | | | | 
% 230.25/41.58  | | | | |   (40)  all_57_7 = e2 & op(e1, e2) = e2
% 230.25/41.58  | | | | | 
% 230.25/41.58  | | | | | ALPHA: (40) implies:
% 230.25/41.58  | | | | |   (41)  all_57_7 = e2
% 230.25/41.58  | | | | | 
% 230.25/41.58  | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (9), (10), (11), (14), (17), (19),
% 230.25/41.58  | | | | |            (23), (25), (26), (28), (41) are inconsistent by sub-proof
% 230.25/41.58  | | | | |            #1775.
% 230.25/41.58  | | | | | 
% 230.25/41.58  | | | | Case 2:
% 230.25/41.58  | | | | | 
% 230.25/41.58  | | | | |   (42)  all_57_13 = e2 & op(e0, e2) = e2
% 230.25/41.58  | | | | | 
% 230.25/41.58  | | | | | ALPHA: (42) implies:
% 230.25/41.58  | | | | |   (43)  all_57_13 = e2
% 230.25/41.58  | | | | | 
% 230.25/41.58  | | | | | BETA: splitting (23) gives:
% 230.25/41.58  | | | | | 
% 230.25/41.58  | | | | | Case 1:
% 230.25/41.58  | | | | | | 
% 230.25/41.58  | | | | | |   (44)  all_57_15 = e0 & op(e0, e0) = e0
% 230.25/41.58  | | | | | | 
% 230.25/41.58  | | | | | | ALPHA: (44) implies:
% 230.25/41.58  | | | | | |   (45)  op(e0, e0) = e0
% 230.25/41.58  | | | | | | 
% 230.25/41.58  | | | | | | REF_CLOSE: (4), (10), (21), (45) are inconsistent by sub-proof
% 230.25/41.58  | | | | | |            #2304.
% 230.25/41.58  | | | | | | 
% 230.25/41.58  | | | | | Case 2:
% 230.25/41.58  | | | | | | 
% 230.25/41.58  | | | | | |   (46)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 &
% 230.25/41.58  | | | | | |             op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) &
% 230.25/41.58  | | | | | |         ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.25/41.58  | | | | | |             op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 230.25/41.58  | | | | | | 
% 230.25/41.58  | | | | | | ALPHA: (46) implies:
% 230.25/41.58  | | | | | |   (47)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.25/41.58  | | | | | |           op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.25/41.58  | | | | | | 
% 230.25/41.58  | | | | | | BETA: splitting (47) gives:
% 230.25/41.58  | | | | | | 
% 230.25/41.58  | | | | | | Case 1:
% 230.25/41.58  | | | | | | | 
% 230.25/41.58  | | | | | | |   (48)  all_57_12 = e0 & op(e0, e3) = e0
% 230.25/41.58  | | | | | | | 
% 230.25/41.58  | | | | | | | ALPHA: (48) implies:
% 230.25/41.58  | | | | | | |   (49)  op(e0, e3) = e0
% 230.25/41.58  | | | | | | | 
% 230.25/41.58  | | | | | | | REF_CLOSE: (4), (13), (22), (49) are inconsistent by sub-proof
% 230.25/41.58  | | | | | | |            #2366.
% 230.25/41.58  | | | | | | | 
% 230.25/41.58  | | | | | | Case 2:
% 230.25/41.58  | | | | | | | 
% 230.25/41.58  | | | | | | |   (50)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 &
% 230.25/41.58  | | | | | | |           op(e0, e1) = e0)
% 230.25/41.58  | | | | | | | 
% 230.25/41.58  | | | | | | | BETA: splitting (50) gives:
% 230.25/41.58  | | | | | | | 
% 230.25/41.58  | | | | | | | Case 1:
% 230.25/41.58  | | | | | | | | 
% 230.25/41.58  | | | | | | | |   (51)  all_57_13 = e0 & op(e0, e2) = e0
% 230.25/41.58  | | | | | | | | 
% 230.25/41.58  | | | | | | | | ALPHA: (51) implies:
% 230.25/41.58  | | | | | | | |   (52)  all_57_13 = e0
% 230.25/41.58  | | | | | | | | 
% 230.25/41.58  | | | | | | | | REF_CLOSE: (17), (43), (52) are inconsistent by sub-proof #1911.
% 230.25/41.58  | | | | | | | | 
% 230.25/41.58  | | | | | | | Case 2:
% 230.25/41.58  | | | | | | | | 
% 230.25/41.58  | | | | | | | |   (53)  all_57_14 = e0 & op(e0, e1) = e0
% 230.25/41.58  | | | | | | | | 
% 230.25/41.58  | | | | | | | | ALPHA: (53) implies:
% 230.25/41.58  | | | | | | | |   (54)  all_57_14 = e0
% 230.25/41.58  | | | | | | | | 
% 230.25/41.58  | | | | | | | | BETA: splitting (24) gives:
% 230.25/41.58  | | | | | | | | 
% 230.25/41.58  | | | | | | | | Case 1:
% 230.25/41.58  | | | | | | | | | 
% 230.25/41.58  | | | | | | | | |   (55)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 &
% 230.25/41.58  | | | | | | | | |           op(e2, e3) = e3)
% 230.25/41.58  | | | | | | | | | 
% 230.25/41.58  | | | | | | | | | BETA: splitting (55) gives:
% 230.25/41.58  | | | | | | | | | 
% 230.25/41.58  | | | | | | | | | Case 1:
% 230.25/41.58  | | | | | | | | | | 
% 230.25/41.58  | | | | | | | | | |   (56)  all_57_0 = e3 & op(e3, e3) = e3
% 230.25/41.58  | | | | | | | | | | 
% 230.25/41.58  | | | | | | | | | | ALPHA: (56) implies:
% 230.25/41.58  | | | | | | | | | |   (57)  op(e3, e3) = e3
% 230.25/41.58  | | | | | | | | | | 
% 230.25/41.58  | | | | | | | | | | REF_CLOSE: (1), (3), (4), (57) are inconsistent by sub-proof
% 230.25/41.58  | | | | | | | | | |            #2495.
% 230.25/41.58  | | | | | | | | | | 
% 230.25/41.58  | | | | | | | | | Case 2:
% 230.25/41.58  | | | | | | | | | | 
% 230.25/41.58  | | | | | | | | | |   (58)  all_57_2 = e3 & op(e2, e3) = e3
% 230.25/41.58  | | | | | | | | | | 
% 230.25/41.58  | | | | | | | | | | ALPHA: (58) implies:
% 230.25/41.58  | | | | | | | | | |   (59)  all_57_2 = e3
% 230.25/41.58  | | | | | | | | | | 
% 230.25/41.58  | | | | | | | | | | BETA: splitting (15) gives:
% 230.25/41.58  | | | | | | | | | | 
% 230.25/41.58  | | | | | | | | | | Case 1:
% 230.25/41.58  | | | | | | | | | | | 
% 230.25/41.59  | | | | | | | | | | |   (60)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 230.25/41.59  | | | | | | | | | | |           e1 & op(e0, e2) = e1)
% 230.25/41.59  | | | | | | | | | | | 
% 230.25/41.59  | | | | | | | | | | | BETA: splitting (60) gives:
% 230.25/41.59  | | | | | | | | | | | 
% 230.25/41.59  | | | | | | | | | | | Case 1:
% 230.25/41.59  | | | | | | | | | | | | 
% 230.25/41.59  | | | | | | | | | | | |   (61)  all_57_12 = e1 & op(e0, e3) = e1
% 230.25/41.59  | | | | | | | | | | | | 
% 230.25/41.59  | | | | | | | | | | | | ALPHA: (61) implies:
% 230.25/41.59  | | | | | | | | | | | |   (62)  all_57_12 = e1
% 230.25/41.59  | | | | | | | | | | | | 
% 230.25/41.59  | | | | | | | | | | | | BETA: splitting (27) gives:
% 230.25/41.59  | | | | | | | | | | | | 
% 230.25/41.59  | | | | | | | | | | | | Case 1:
% 230.25/41.59  | | | | | | | | | | | | | 
% 230.25/41.59  | | | | | | | | | | | | |   (63)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 230.25/41.59  | | | | | | | | | | | | |           & op(e2, e3) = e2)
% 230.25/41.59  | | | | | | | | | | | | | 
% 230.25/41.59  | | | | | | | | | | | | | BETA: splitting (63) gives:
% 230.25/41.59  | | | | | | | | | | | | | 
% 230.25/41.59  | | | | | | | | | | | | | Case 1:
% 230.25/41.59  | | | | | | | | | | | | | | 
% 230.25/41.59  | | | | | | | | | | | | | |   (64)  all_57_0 = e2 & op(e3, e3) = e2
% 230.25/41.59  | | | | | | | | | | | | | | 
% 230.25/41.59  | | | | | | | | | | | | | | ALPHA: (64) implies:
% 230.25/41.59  | | | | | | | | | | | | | |   (65)  op(e3, e3) = e2
% 230.25/41.59  | | | | | | | | | | | | | | 
% 230.25/41.59  | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (25), (65) are inconsistent by sub-proof
% 230.25/41.59  | | | | | | | | | | | | | |            #1950.
% 230.25/41.59  | | | | | | | | | | | | | | 
% 230.25/41.59  | | | | | | | | | | | | | Case 2:
% 230.25/41.59  | | | | | | | | | | | | | | 
% 230.25/41.59  | | | | | | | | | | | | | |   (66)  all_57_2 = e2 & op(e2, e3) = e2
% 230.25/41.59  | | | | | | | | | | | | | | 
% 230.25/41.59  | | | | | | | | | | | | | | ALPHA: (66) implies:
% 230.25/41.59  | | | | | | | | | | | | | |   (67)  all_57_2 = e2
% 230.25/41.59  | | | | | | | | | | | | | | 
% 230.25/41.59  | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (9), (10), (11), (14),
% 230.25/41.59  | | | | | | | | | | | | | |            (17), (19), (23), (25), (26), (28), (37), (59),
% 230.25/41.59  | | | | | | | | | | | | | |            (67) are inconsistent by sub-proof #1055.
% 230.25/41.59  | | | | | | | | | | | | | | 
% 230.25/41.59  | | | | | | | | | | | | | End of split
% 230.25/41.59  | | | | | | | | | | | | | 
% 230.25/41.59  | | | | | | | | | | | | Case 2:
% 230.25/41.59  | | | | | | | | | | | | | 
% 230.25/41.59  | | | | | | | | | | | | |   (68)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 230.25/41.59  | | | | | | | | | | | | |           e2 & op(e0, e3) = e2)
% 230.25/41.59  | | | | | | | | | | | | | 
% 230.25/41.59  | | | | | | | | | | | | | BETA: splitting (68) gives:
% 230.25/41.59  | | | | | | | | | | | | | 
% 230.25/41.59  | | | | | | | | | | | | | Case 1:
% 230.25/41.59  | | | | | | | | | | | | | | 
% 230.25/41.59  | | | | | | | | | | | | | |   (69)  all_57_6 = e2 & op(e1, e3) = e2
% 230.25/41.59  | | | | | | | | | | | | | | 
% 230.25/41.59  | | | | | | | | | | | | | | REF_CLOSE: (11), (17), (69) are inconsistent by sub-proof
% 230.25/41.59  | | | | | | | | | | | | | |            #2393.
% 230.25/41.59  | | | | | | | | | | | | | | 
% 230.25/41.59  | | | | | | | | | | | | | Case 2:
% 230.25/41.59  | | | | | | | | | | | | | | 
% 230.25/41.59  | | | | | | | | | | | | | |   (70)  all_57_12 = e2 & op(e0, e3) = e2
% 230.25/41.59  | | | | | | | | | | | | | | 
% 230.25/41.59  | | | | | | | | | | | | | | ALPHA: (70) implies:
% 230.25/41.59  | | | | | | | | | | | | | |   (71)  all_57_12 = e2
% 230.25/41.59  | | | | | | | | | | | | | | 
% 230.25/41.59  | | | | | | | | | | | | | | REF_CLOSE: (25), (62), (71) are inconsistent by sub-proof
% 230.25/41.59  | | | | | | | | | | | | | |            #2321.
% 230.25/41.59  | | | | | | | | | | | | | | 
% 230.25/41.59  | | | | | | | | | | | | | End of split
% 230.25/41.59  | | | | | | | | | | | | | 
% 230.25/41.59  | | | | | | | | | | | | End of split
% 230.25/41.59  | | | | | | | | | | | | 
% 230.25/41.59  | | | | | | | | | | | Case 2:
% 230.25/41.59  | | | | | | | | | | | | 
% 230.25/41.59  | | | | | | | | | | | |   (72)  all_57_13 = e1 & op(e0, e2) = e1
% 230.25/41.59  | | | | | | | | | | | | 
% 230.25/41.59  | | | | | | | | | | | | ALPHA: (72) implies:
% 230.25/41.59  | | | | | | | | | | | |   (73)  all_57_13 = e1
% 230.25/41.59  | | | | | | | | | | | | 
% 230.25/41.59  | | | | | | | | | | | | REF_CLOSE: (25), (43), (73) are inconsistent by sub-proof
% 230.25/41.59  | | | | | | | | | | | |            #2327.
% 230.25/41.59  | | | | | | | | | | | | 
% 230.25/41.59  | | | | | | | | | | | End of split
% 230.25/41.59  | | | | | | | | | | | 
% 230.25/41.59  | | | | | | | | | | Case 2:
% 230.25/41.59  | | | | | | | | | | | 
% 230.25/41.59  | | | | | | | | | | |   (74)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 230.25/41.59  | | | | | | | | | | |           e1 & op(e0, e0) = e1)
% 230.25/41.59  | | | | | | | | | | | 
% 230.25/41.59  | | | | | | | | | | | BETA: splitting (74) gives:
% 230.25/41.59  | | | | | | | | | | | 
% 230.25/41.59  | | | | | | | | | | | Case 1:
% 230.25/41.59  | | | | | | | | | | | | 
% 230.25/41.59  | | | | | | | | | | | |   (75)  all_57_14 = e1 & op(e0, e1) = e1
% 230.25/41.59  | | | | | | | | | | | | 
% 230.25/41.59  | | | | | | | | | | | | ALPHA: (75) implies:
% 230.25/41.59  | | | | | | | | | | | |   (76)  all_57_14 = e1
% 230.25/41.59  | | | | | | | | | | | | 
% 230.25/41.59  | | | | | | | | | | | | COMBINE_EQS: (54), (76) imply:
% 230.25/41.59  | | | | | | | | | | | |   (77)  e1 = e0
% 230.25/41.59  | | | | | | | | | | | | 
% 230.25/41.59  | | | | | | | | | | | | REF_CLOSE: (2), (3), (9), (12), (17), (18), (19), (25), (29),
% 230.25/41.59  | | | | | | | | | | | |            (37), (77) are inconsistent by sub-proof #1708.
% 230.25/41.59  | | | | | | | | | | | | 
% 230.25/41.59  | | | | | | | | | | | Case 2:
% 230.25/41.59  | | | | | | | | | | | | 
% 230.25/41.59  | | | | | | | | | | | |   (78)  all_57_15 = e1 & op(e0, e0) = e1
% 230.25/41.59  | | | | | | | | | | | | 
% 230.25/41.59  | | | | | | | | | | | | ALPHA: (78) implies:
% 230.25/41.59  | | | | | | | | | | | |   (79)  op(e0, e0) = e1
% 230.25/41.59  | | | | | | | | | | | | 
% 230.25/41.59  | | | | | | | | | | | | REF_CLOSE: (3), (4), (21), (79) are inconsistent by sub-proof
% 230.25/41.59  | | | | | | | | | | | |            #2183.
% 230.25/41.59  | | | | | | | | | | | | 
% 230.25/41.59  | | | | | | | | | | | End of split
% 230.25/41.59  | | | | | | | | | | | 
% 230.25/41.59  | | | | | | | | | | End of split
% 230.25/41.59  | | | | | | | | | | 
% 230.25/41.59  | | | | | | | | | End of split
% 230.25/41.59  | | | | | | | | | 
% 230.25/41.59  | | | | | | | | Case 2:
% 230.25/41.59  | | | | | | | | | 
% 230.25/41.59  | | | | | | | | |   (80)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 &
% 230.25/41.59  | | | | | | | | |           op(e0, e3) = e3)
% 230.25/41.59  | | | | | | | | | 
% 230.25/41.59  | | | | | | | | | BETA: splitting (80) gives:
% 230.25/41.59  | | | | | | | | | 
% 230.25/41.59  | | | | | | | | | Case 1:
% 230.25/41.59  | | | | | | | | | | 
% 230.25/41.59  | | | | | | | | | |   (81)  all_57_6 = e3 & op(e1, e3) = e3
% 230.25/41.59  | | | | | | | | | | 
% 230.25/41.59  | | | | | | | | | | ALPHA: (81) implies:
% 230.25/41.59  | | | | | | | | | |   (82)  all_57_6 = e3
% 230.25/41.59  | | | | | | | | | | 
% 230.25/41.59  | | | | | | | | | | REF_CLOSE: (10), (11), (82) are inconsistent by sub-proof
% 230.25/41.59  | | | | | | | | | |            #1822.
% 230.25/41.59  | | | | | | | | | | 
% 230.25/41.59  | | | | | | | | | Case 2:
% 230.25/41.59  | | | | | | | | | | 
% 230.25/41.59  | | | | | | | | | |   (83)  all_57_12 = e3 & op(e0, e3) = e3
% 230.25/41.59  | | | | | | | | | | 
% 230.25/41.59  | | | | | | | | | | ALPHA: (83) implies:
% 230.25/41.59  | | | | | | | | | |   (84)  all_57_12 = e3
% 230.25/41.59  | | | | | | | | | | 
% 230.25/41.59  | | | | | | | | | | REF_CLOSE: (3), (14), (15), (19), (25), (43), (54), (84) are
% 230.25/41.59  | | | | | | | | | |            inconsistent by sub-proof #1764.
% 230.25/41.59  | | | | | | | | | | 
% 230.25/41.59  | | | | | | | | | End of split
% 230.25/41.59  | | | | | | | | | 
% 230.25/41.59  | | | | | | | | End of split
% 230.25/41.59  | | | | | | | | 
% 230.25/41.59  | | | | | | | End of split
% 230.25/41.59  | | | | | | | 
% 230.25/41.59  | | | | | | End of split
% 230.25/41.59  | | | | | | 
% 230.25/41.59  | | | | | End of split
% 230.25/41.59  | | | | | 
% 230.25/41.59  | | | | End of split
% 230.25/41.59  | | | | 
% 230.25/41.59  | | | End of split
% 230.25/41.59  | | | 
% 230.25/41.59  | | Case 2:
% 230.25/41.59  | | | 
% 230.25/41.59  | | |   (85)  all_57_13 = e3 & op(e0, e2) = e3
% 230.25/41.59  | | | 
% 230.25/41.59  | | | ALPHA: (85) implies:
% 230.25/41.59  | | |   (86)  all_57_13 = e3
% 230.25/41.59  | | | 
% 230.25/41.59  | | | BETA: splitting (2) gives:
% 230.25/41.59  | | | 
% 230.25/41.59  | | | Case 1:
% 230.25/41.59  | | | | 
% 230.25/41.59  | | | |   (87)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2)
% 230.25/41.59  | | | |           = e2)
% 230.25/41.59  | | | | 
% 230.25/41.59  | | | | REF_CLOSE: (4), (8), (12), (17), (25), (87) are inconsistent by
% 230.25/41.59  | | | |            sub-proof #1738.
% 230.25/41.59  | | | | 
% 230.25/41.59  | | | Case 2:
% 230.25/41.59  | | | | 
% 230.25/41.59  | | | |   (88)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2)
% 230.25/41.59  | | | |           = e2)
% 230.25/41.59  | | | | 
% 230.25/41.59  | | | | BETA: splitting (88) gives:
% 230.25/41.59  | | | | 
% 230.25/41.59  | | | | Case 1:
% 230.25/41.59  | | | | | 
% 230.25/41.59  | | | | |   (89)  all_57_7 = e2 & op(e1, e2) = e2
% 230.25/41.59  | | | | | 
% 230.25/41.59  | | | | | ALPHA: (89) implies:
% 230.25/41.59  | | | | |   (90)  all_57_7 = e2
% 230.25/41.59  | | | | | 
% 230.25/41.59  | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (9), (10), (11), (14), (17), (19),
% 230.25/41.59  | | | | |            (23), (25), (26), (28), (90) are inconsistent by sub-proof
% 230.25/41.59  | | | | |            #1775.
% 230.25/41.59  | | | | | 
% 230.25/41.59  | | | | Case 2:
% 230.25/41.59  | | | | | 
% 230.25/41.59  | | | | |   (91)  all_57_13 = e2 & op(e0, e2) = e2
% 230.25/41.59  | | | | | 
% 230.25/41.59  | | | | | ALPHA: (91) implies:
% 230.25/41.59  | | | | |   (92)  all_57_13 = e2
% 230.25/41.59  | | | | | 
% 230.25/41.59  | | | | | REF_CLOSE: (9), (86), (92) are inconsistent by sub-proof #2203.
% 230.25/41.59  | | | | | 
% 230.25/41.59  | | | | End of split
% 230.25/41.59  | | | | 
% 230.25/41.59  | | | End of split
% 230.25/41.59  | | | 
% 230.25/41.59  | | End of split
% 230.25/41.59  | | 
% 230.25/41.59  | End of split
% 230.25/41.59  | 
% 230.25/41.59  End of proof
% 230.25/41.59  
% 230.25/41.59  Sub-proof #1055 shows that the following formulas are inconsistent:
% 230.25/41.59  ----------------------------------------------------------------
% 230.25/41.59    (1)   ~ (e3 = e1)
% 230.25/41.59    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.25/41.59           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.25/41.59    (3)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.25/41.59         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.25/41.59    (4)   ~ (all_6_2 = e3)
% 230.25/41.59    (5)  op(e1, e1) = all_6_2
% 230.25/41.59    (6)  all_57_2 = e2
% 230.25/41.59    (7)   ~ (e3 = e2)
% 230.25/41.59    (8)   ~ (e3 = e0)
% 230.25/41.59    (9)  all_57_6 = e0
% 230.25/41.59    (10)  all_57_15 = e3
% 230.25/41.59    (11)   ~ (e2 = e0)
% 230.25/41.59    (12)  all_57_2 = e3
% 230.25/41.59    (13)   ~ (e1 = e0)
% 230.25/41.59    (14)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.25/41.59              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.25/41.59                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.25/41.59                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.25/41.59    (15)  all_57_7 = e3
% 230.25/41.59    (16)   ~ (e2 = e1)
% 230.25/41.59    (17)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.25/41.59          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.25/41.59    (18)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.25/41.59          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.25/41.59  
% 230.25/41.59  Begin of proof
% 230.25/41.59  | 
% 230.25/41.59  | COMBINE_EQS: (6), (12) imply:
% 230.25/41.59  |   (19)  e3 = e2
% 230.25/41.59  | 
% 230.25/41.59  | SIMP: (19) implies:
% 230.25/41.59  |   (20)  e3 = e2
% 230.25/41.59  | 
% 230.25/41.59  | COMBINE_EQS: (15), (20) imply:
% 230.25/41.59  |   (21)  all_57_7 = e2
% 230.25/41.59  | 
% 230.25/41.59  | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (13), (14),
% 230.25/41.59  |            (16), (17), (18), (21) are inconsistent by sub-proof #1775.
% 230.25/41.59  | 
% 230.25/41.59  End of proof
% 230.25/41.59  
% 230.25/41.59  Sub-proof #1056 shows that the following formulas are inconsistent:
% 230.25/41.59  ----------------------------------------------------------------
% 230.25/41.59    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.25/41.59         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.25/41.59    (2)  all_57_13 = e1
% 230.25/41.59    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.25/41.59         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.25/41.59    (4)   ~ (e3 = e1)
% 230.25/41.59    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.25/41.59           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.25/41.59    (6)  op(e2, e2) = e1
% 230.25/41.59    (7)   ~ (e3 = e2)
% 230.25/41.59    (8)   ~ (e3 = e0)
% 230.25/41.59    (9)  op(e0, e3) = all_53_3
% 230.25/41.59    (10)  all_57_15 = e3
% 230.25/41.59    (11)  op(e3, e3) = e0
% 230.25/41.59    (12)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.25/41.59          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.25/41.59            e1)
% 230.25/41.59    (13)  all_57_5 = e3
% 230.25/41.59    (14)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.25/41.59          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.25/41.59    (15)   ~ (e2 = e0)
% 230.25/41.59    (16)  all_57_3 = e1
% 230.25/41.59    (17)   ~ (e1 = e0)
% 230.25/41.59    (18)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.25/41.59          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.25/41.59    (19)  op(e0, e0) = e3
% 230.25/41.59    (20)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.25/41.59          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.25/41.59            e2)
% 230.25/41.59    (21)   ~ (all_53_3 = e0)
% 230.25/41.59    (22)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.25/41.59              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.25/41.59                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.25/41.59                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.25/41.59    (23)  all_57_2 = e0
% 230.25/41.59    (24)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.25/41.59          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.25/41.59    (25)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.25/41.59          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.25/41.59    (26)  all_57_1 = e3
% 230.25/41.59    (27)   ~ (e2 = e1)
% 230.25/41.59    (28)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.25/41.59          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.25/41.59    (29)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.25/41.59          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.25/41.59  
% 230.25/41.59  Begin of proof
% 230.25/41.59  | 
% 230.25/41.59  | BETA: splitting (3) gives:
% 230.25/41.59  | 
% 230.25/41.59  | Case 1:
% 230.25/41.59  | | 
% 230.25/41.59  | |   (30)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 230.25/41.59  | |           e2)
% 230.25/41.59  | | 
% 230.25/41.59  | | REF_CLOSE: (5), (6), (7), (26), (27), (30) are inconsistent by sub-proof
% 230.25/41.59  | |            #1768.
% 230.25/41.59  | | 
% 230.25/41.59  | Case 2:
% 230.25/41.59  | | 
% 230.25/41.59  | |   (31)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 230.25/41.59  | |           e2)
% 230.25/41.59  | | 
% 230.25/41.59  | | BETA: splitting (31) gives:
% 230.25/41.59  | | 
% 230.25/41.59  | | Case 1:
% 230.25/41.59  | | | 
% 230.25/41.59  | | |   (32)  all_57_7 = e2 & op(e1, e2) = e2
% 230.25/41.59  | | | 
% 230.25/41.59  | | | ALPHA: (32) implies:
% 230.25/41.59  | | |   (33)  all_57_7 = e2
% 230.25/41.59  | | | 
% 230.25/41.59  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 230.25/41.59  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 230.25/41.59  | | |            (23), (24), (25), (26), (27), (28), (29), (33) are inconsistent
% 230.25/41.59  | | |            by sub-proof #1057.
% 230.25/41.59  | | | 
% 230.25/41.59  | | Case 2:
% 230.25/41.59  | | | 
% 230.25/41.59  | | |   (34)  all_57_13 = e2 & op(e0, e2) = e2
% 230.25/41.59  | | | 
% 230.25/41.59  | | | ALPHA: (34) implies:
% 230.25/41.59  | | |   (35)  all_57_13 = e2
% 230.25/41.59  | | | 
% 230.25/41.59  | | | REF_CLOSE: (2), (27), (35) are inconsistent by sub-proof #2327.
% 230.25/41.59  | | | 
% 230.25/41.59  | | End of split
% 230.25/41.59  | | 
% 230.25/41.59  | End of split
% 230.25/41.59  | 
% 230.25/41.59  End of proof
% 230.25/41.59  
% 230.25/41.59  Sub-proof #1057 shows that the following formulas are inconsistent:
% 230.25/41.59  ----------------------------------------------------------------
% 230.25/41.59    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.25/41.59         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.25/41.59    (2)  all_57_13 = e1
% 230.25/41.59    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.25/41.59         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.25/41.59    (4)   ~ (e3 = e1)
% 230.25/41.59    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.25/41.59           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.25/41.59    (6)  op(e2, e2) = e1
% 230.25/41.59    (7)  all_57_7 = e2
% 230.25/41.59    (8)   ~ (e3 = e2)
% 230.25/41.59    (9)   ~ (e3 = e0)
% 230.25/41.59    (10)  op(e0, e3) = all_53_3
% 230.25/41.59    (11)  all_57_15 = e3
% 230.25/41.59    (12)  op(e3, e3) = e0
% 230.25/41.59    (13)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.25/41.59          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.25/41.59            e1)
% 230.25/41.59    (14)  all_57_5 = e3
% 230.25/41.59    (15)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.25/41.59          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.25/41.59    (16)   ~ (e2 = e0)
% 230.25/41.59    (17)  all_57_3 = e1
% 230.25/41.59    (18)   ~ (e1 = e0)
% 230.25/41.59    (19)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.25/41.59          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.25/41.59    (20)  op(e0, e0) = e3
% 230.25/41.59    (21)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.25/41.59          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.25/41.59            e2)
% 230.25/41.59    (22)   ~ (all_53_3 = e0)
% 230.25/41.59    (23)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.25/41.59              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.25/41.59                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.25/41.59                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.25/41.59    (24)  all_57_2 = e0
% 230.25/41.59    (25)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.25/41.59          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.25/41.59    (26)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.25/41.59          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.25/41.59    (27)  all_57_1 = e3
% 230.25/41.59    (28)   ~ (e2 = e1)
% 230.25/41.59    (29)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.25/41.59          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.25/41.59    (30)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.25/41.59          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.25/41.59  
% 230.25/41.59  Begin of proof
% 230.25/41.59  | 
% 230.25/41.59  | BETA: splitting (15) gives:
% 230.25/41.59  | 
% 230.25/41.59  | Case 1:
% 230.25/41.59  | | 
% 230.25/41.59  | |   (31)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) =
% 230.25/41.59  | |           e0)
% 230.25/41.59  | | 
% 230.25/41.59  | | BETA: splitting (31) gives:
% 230.25/41.59  | | 
% 230.25/41.59  | | Case 1:
% 230.25/41.59  | | | 
% 230.25/41.59  | | |   (32)  all_57_1 = e0 & op(e3, e2) = e0
% 230.25/41.59  | | | 
% 230.25/41.59  | | | ALPHA: (32) implies:
% 230.25/41.59  | | |   (33)  all_57_1 = e0
% 230.25/41.59  | | | 
% 230.25/41.59  | | | REF_CLOSE: (3), (4), (5), (6), (8), (9), (10), (11), (12), (13), (16),
% 230.25/41.59  | | |            (17), (18), (19), (20), (21), (22), (23), (24), (26), (28),
% 230.25/41.59  | | |            (29), (30), (33) are inconsistent by sub-proof #1059.
% 230.25/41.59  | | | 
% 230.25/41.59  | | Case 2:
% 230.25/41.59  | | | 
% 230.25/41.59  | | |   (34)  all_57_3 = e0 & op(e2, e2) = e0
% 230.25/41.59  | | | 
% 230.25/41.59  | | | ALPHA: (34) implies:
% 230.25/41.59  | | |   (35)  all_57_3 = e0
% 230.25/41.59  | | | 
% 230.25/41.59  | | | REF_CLOSE: (1), (4), (8), (14), (16), (18), (24), (25), (28), (35) are
% 230.25/41.59  | | |            inconsistent by sub-proof #2253.
% 230.25/41.59  | | | 
% 230.25/41.59  | | End of split
% 230.25/41.59  | | 
% 230.25/41.59  | Case 2:
% 230.25/41.59  | | 
% 230.25/41.59  | |   (36)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 230.25/41.59  | |           e0)
% 230.25/41.59  | | 
% 230.25/41.59  | | BETA: splitting (36) gives:
% 230.25/41.59  | | 
% 230.25/41.59  | | Case 1:
% 230.25/41.59  | | | 
% 230.25/41.59  | | |   (37)  all_57_7 = e0 & op(e1, e2) = e0
% 230.25/41.59  | | | 
% 230.25/41.59  | | | REF_CLOSE: (7), (16), (37) are inconsistent by sub-proof #2148.
% 230.25/41.59  | | | 
% 230.25/41.59  | | Case 2:
% 230.25/41.59  | | | 
% 230.25/41.59  | | |   (38)  all_57_13 = e0 & op(e0, e2) = e0
% 230.25/41.59  | | | 
% 230.25/41.59  | | | REF_CLOSE: (2), (3), (4), (8), (16), (17), (18), (27), (28), (30), (38)
% 230.25/41.59  | | |            are inconsistent by sub-proof #1058.
% 230.25/41.59  | | | 
% 230.25/41.59  | | End of split
% 230.25/41.59  | | 
% 230.25/41.59  | End of split
% 230.25/41.59  | 
% 230.25/41.59  End of proof
% 230.25/41.59  
% 230.25/41.59  Sub-proof #1058 shows that the following formulas are inconsistent:
% 230.25/41.59  ----------------------------------------------------------------
% 230.25/41.59    (1)  all_57_13 = e1
% 230.25/41.59    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.25/41.59         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.25/41.59    (3)   ~ (e3 = e1)
% 230.25/41.59    (4)  all_57_13 = e0 & op(e0, e2) = e0
% 230.25/41.59    (5)   ~ (e3 = e2)
% 230.25/41.59    (6)   ~ (e2 = e0)
% 230.25/41.59    (7)  all_57_3 = e1
% 230.25/41.59    (8)   ~ (e1 = e0)
% 230.25/41.59    (9)  all_57_1 = e3
% 230.25/41.59    (10)   ~ (e2 = e1)
% 230.25/41.59    (11)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.25/41.59          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.25/41.59  
% 230.25/41.59  Begin of proof
% 230.25/41.59  | 
% 230.25/41.59  | ALPHA: (4) implies:
% 230.25/41.59  |   (12)  all_57_13 = e0
% 230.25/41.59  | 
% 230.25/41.59  | COMBINE_EQS: (1), (12) imply:
% 230.25/41.59  |   (13)  e1 = e0
% 230.25/41.59  | 
% 230.25/41.59  | SIMP: (13) implies:
% 230.25/41.59  |   (14)  e1 = e0
% 230.25/41.59  | 
% 230.25/41.59  | COMBINE_EQS: (7), (14) imply:
% 230.25/41.59  |   (15)  all_57_3 = e0
% 230.25/41.59  | 
% 230.25/41.59  | REF_CLOSE: (2), (3), (5), (6), (8), (9), (10), (11), (12), (15) are
% 230.25/41.59  |            inconsistent by sub-proof #1758.
% 230.25/41.59  | 
% 230.25/41.59  End of proof
% 230.25/41.59  
% 230.25/41.59  Sub-proof #1059 shows that the following formulas are inconsistent:
% 230.25/41.59  ----------------------------------------------------------------
% 230.25/41.59    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.25/41.59         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.25/41.59    (2)   ~ (e3 = e1)
% 230.25/41.59    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.25/41.59           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.25/41.59    (4)  op(e2, e2) = e1
% 230.25/41.59    (5)   ~ (e3 = e2)
% 230.25/41.59    (6)   ~ (e3 = e0)
% 230.25/41.59    (7)  all_57_1 = e0
% 230.25/41.59    (8)  op(e0, e3) = all_53_3
% 230.25/41.59    (9)  all_57_15 = e3
% 230.25/41.59    (10)  op(e3, e3) = e0
% 230.25/41.59    (11)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.25/41.59          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.25/41.59            e1)
% 230.25/41.59    (12)   ~ (e2 = e0)
% 230.25/41.59    (13)  all_57_3 = e1
% 230.25/41.59    (14)   ~ (e1 = e0)
% 230.25/41.59    (15)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.25/41.59          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.25/41.59    (16)  op(e0, e0) = e3
% 230.25/41.59    (17)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.25/41.59          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.25/41.59            e2)
% 230.25/41.59    (18)   ~ (all_53_3 = e0)
% 230.25/41.59    (19)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.25/41.59              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.25/41.59                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.25/41.59                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.25/41.59    (20)  all_57_2 = e0
% 230.25/41.59    (21)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.25/41.59          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.25/41.59    (22)   ~ (e2 = e1)
% 230.25/41.59    (23)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.25/41.59          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.25/41.59    (24)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.25/41.59          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.25/41.59  
% 230.25/41.59  Begin of proof
% 230.25/41.59  | 
% 230.25/41.59  | BETA: splitting (15) gives:
% 230.25/41.59  | 
% 230.25/41.59  | Case 1:
% 230.25/41.59  | | 
% 230.25/41.59  | |   (25)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 230.25/41.59  | |           e3)
% 230.25/41.59  | | 
% 230.25/41.59  | | REF_CLOSE: (2), (3), (4), (6), (7), (25) are inconsistent by sub-proof
% 230.25/41.59  | |            #1737.
% 230.25/41.59  | | 
% 230.25/41.59  | Case 2:
% 230.25/41.59  | | 
% 230.25/41.59  | |   (26)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 230.25/41.59  | |           e3)
% 230.25/41.59  | | 
% 230.25/41.59  | | BETA: splitting (26) gives:
% 230.25/41.59  | | 
% 230.25/41.59  | | Case 1:
% 230.25/41.59  | | | 
% 230.25/41.59  | | |   (27)  all_57_7 = e3 & op(e1, e2) = e3
% 230.25/41.59  | | | 
% 230.25/41.59  | | | ALPHA: (27) implies:
% 230.25/41.59  | | |   (28)  all_57_7 = e3
% 230.25/41.59  | | | 
% 230.25/41.59  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 230.25/41.59  | | |            (13), (14), (16), (17), (18), (19), (20), (21), (22), (23),
% 230.25/41.59  | | |            (24), (28) are inconsistent by sub-proof #1060.
% 230.25/41.59  | | | 
% 230.25/41.59  | | Case 2:
% 230.25/41.59  | | | 
% 230.25/41.59  | | |   (29)  all_57_13 = e3 & op(e0, e2) = e3
% 230.25/41.59  | | | 
% 230.25/41.59  | | | ALPHA: (29) implies:
% 230.25/41.59  | | |   (30)  all_57_13 = e3
% 230.25/41.59  | | | 
% 230.25/41.59  | | | REF_CLOSE: (2), (3), (5), (6), (9), (11), (12), (14), (16), (17), (19),
% 230.25/41.59  | | |            (22), (30) are inconsistent by sub-proof #1792.
% 230.25/41.59  | | | 
% 230.25/41.59  | | End of split
% 230.25/41.59  | | 
% 230.25/41.59  | End of split
% 230.25/41.59  | 
% 230.25/41.59  End of proof
% 230.25/41.59  
% 230.25/41.59  Sub-proof #1060 shows that the following formulas are inconsistent:
% 230.25/41.59  ----------------------------------------------------------------
% 230.25/41.59    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.25/41.59         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.25/41.59    (2)   ~ (e3 = e1)
% 230.25/41.59    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.25/41.59           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.25/41.59    (4)  op(e2, e2) = e1
% 230.25/41.59    (5)   ~ (e3 = e2)
% 230.25/41.59    (6)   ~ (e3 = e0)
% 230.25/41.59    (7)  all_57_1 = e0
% 230.25/41.59    (8)  op(e0, e3) = all_53_3
% 230.25/41.59    (9)  all_57_15 = e3
% 230.25/41.59    (10)  op(e3, e3) = e0
% 230.25/41.59    (11)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.25/41.59          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.25/41.59            e1)
% 230.25/41.59    (12)   ~ (e2 = e0)
% 230.25/41.59    (13)  all_57_3 = e1
% 230.25/41.59    (14)   ~ (e1 = e0)
% 230.25/41.59    (15)  op(e0, e0) = e3
% 230.25/41.59    (16)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.25/41.59          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.25/41.59            e2)
% 230.25/41.59    (17)   ~ (all_53_3 = e0)
% 230.25/41.59    (18)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.25/41.59              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.25/41.59                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.25/41.59                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.25/41.59    (19)  all_57_2 = e0
% 230.25/41.59    (20)  all_57_7 = e3
% 230.25/41.59    (21)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.25/41.59          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.25/41.59    (22)   ~ (e2 = e1)
% 230.25/41.59    (23)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.25/41.59          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.25/41.59    (24)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.25/41.59          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.25/41.59  
% 230.25/41.59  Begin of proof
% 230.25/41.59  | 
% 230.25/41.59  | BETA: splitting (1) gives:
% 230.25/41.59  | 
% 230.25/41.59  | Case 1:
% 230.25/41.59  | | 
% 230.25/41.59  | |   (25)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 230.25/41.59  | |           e2)
% 230.25/41.59  | | 
% 230.25/41.59  | | REF_CLOSE: (3), (4), (7), (12), (22), (25) are inconsistent by sub-proof
% 230.25/41.59  | |            #1738.
% 230.25/41.59  | | 
% 230.25/41.59  | Case 2:
% 230.25/41.59  | | 
% 230.25/41.59  | |   (26)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 230.25/41.59  | |           e2)
% 230.25/41.59  | | 
% 230.25/41.59  | | BETA: splitting (26) gives:
% 230.25/41.59  | | 
% 230.25/41.59  | | Case 1:
% 230.25/41.59  | | | 
% 230.25/41.59  | | |   (27)  all_57_7 = e2 & op(e1, e2) = e2
% 230.25/41.59  | | | 
% 230.25/41.59  | | | ALPHA: (27) implies:
% 230.25/41.59  | | |   (28)  all_57_7 = e2
% 230.25/41.59  | | | 
% 230.25/41.59  | | | REF_CLOSE: (5), (20), (28) are inconsistent by sub-proof #2102.
% 230.25/41.59  | | | 
% 230.25/41.59  | | Case 2:
% 230.25/41.59  | | | 
% 230.25/41.59  | | |   (29)  all_57_13 = e2 & op(e0, e2) = e2
% 230.25/41.59  | | | 
% 230.25/41.59  | | | ALPHA: (29) implies:
% 230.25/41.59  | | |   (30)  all_57_13 = e2
% 230.25/41.59  | | | 
% 230.25/41.59  | | | BETA: splitting (18) gives:
% 230.25/41.59  | | | 
% 230.25/41.59  | | | Case 1:
% 230.25/41.59  | | | | 
% 230.25/41.59  | | | |   (31)  all_57_15 = e0 & op(e0, e0) = e0
% 230.25/41.59  | | | | 
% 230.25/41.59  | | | | ALPHA: (31) implies:
% 230.25/41.59  | | | |   (32)  op(e0, e0) = e0
% 230.25/41.59  | | | | 
% 230.25/41.59  | | | | REF_CLOSE: (3), (6), (15), (32) are inconsistent by sub-proof #2304.
% 230.25/41.59  | | | | 
% 230.25/41.59  | | | Case 2:
% 230.25/41.59  | | | | 
% 230.25/41.59  | | | |   (33)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2,
% 230.25/41.59  | | | |               e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) &
% 230.25/41.59  | | | |         ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0,
% 230.25/41.59  | | | |               e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 230.25/41.59  | | | | 
% 230.25/41.59  | | | | ALPHA: (33) implies:
% 230.25/41.59  | | | |   (34)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0,
% 230.25/41.59  | | | |             e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.25/41.59  | | | | 
% 230.25/41.59  | | | | BETA: splitting (34) gives:
% 230.25/41.59  | | | | 
% 230.25/41.59  | | | | Case 1:
% 230.25/41.59  | | | | | 
% 230.25/41.59  | | | | |   (35)  all_57_12 = e0 & op(e0, e3) = e0
% 230.25/41.59  | | | | | 
% 230.25/41.59  | | | | | ALPHA: (35) implies:
% 230.25/41.59  | | | | |   (36)  op(e0, e3) = e0
% 230.25/41.59  | | | | | 
% 230.25/41.59  | | | | | REF_CLOSE: (3), (8), (17), (36) are inconsistent by sub-proof #2366.
% 230.25/41.59  | | | | | 
% 230.25/41.59  | | | | Case 2:
% 230.25/41.59  | | | | | 
% 230.25/41.59  | | | | |   (37)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 230.25/41.59  | | | | |             e1) = e0)
% 230.25/41.59  | | | | | 
% 230.25/41.59  | | | | | BETA: splitting (37) gives:
% 230.25/41.59  | | | | | 
% 230.25/41.59  | | | | | Case 1:
% 230.25/41.59  | | | | | | 
% 230.25/41.59  | | | | | |   (38)  all_57_13 = e0 & op(e0, e2) = e0
% 230.25/41.59  | | | | | | 
% 230.25/41.59  | | | | | | ALPHA: (38) implies:
% 230.25/41.59  | | | | | |   (39)  all_57_13 = e0
% 230.25/41.59  | | | | | | 
% 230.25/41.59  | | | | | | REF_CLOSE: (12), (30), (39) are inconsistent by sub-proof #1911.
% 230.25/41.59  | | | | | | 
% 230.25/41.59  | | | | | Case 2:
% 230.25/41.59  | | | | | | 
% 230.25/41.59  | | | | | |   (40)  all_57_14 = e0 & op(e0, e1) = e0
% 230.25/41.59  | | | | | | 
% 230.25/41.59  | | | | | | ALPHA: (40) implies:
% 230.25/41.59  | | | | | |   (41)  all_57_14 = e0
% 230.25/41.59  | | | | | | 
% 230.25/41.59  | | | | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (9), (10), (11), (12),
% 230.25/41.59  | | | | | |            (13), (14), (15), (16), (19), (20), (21), (22), (23),
% 230.25/41.59  | | | | | |            (24), (30), (41) are inconsistent by sub-proof #1061.
% 230.25/41.59  | | | | | | 
% 230.25/41.59  | | | | | End of split
% 230.25/41.59  | | | | | 
% 230.25/41.59  | | | | End of split
% 230.25/41.59  | | | | 
% 230.25/41.59  | | | End of split
% 230.25/41.59  | | | 
% 230.25/41.59  | | End of split
% 230.25/41.59  | | 
% 230.25/41.59  | End of split
% 230.25/41.59  | 
% 230.25/41.59  End of proof
% 230.25/41.60  
% 230.25/41.60  Sub-proof #1061 shows that the following formulas are inconsistent:
% 230.25/41.60  ----------------------------------------------------------------
% 230.25/41.60    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.25/41.60         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.25/41.60    (2)   ~ (e3 = e1)
% 230.25/41.60    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.25/41.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.25/41.60    (4)   ~ (e3 = e2)
% 230.25/41.60    (5)   ~ (e3 = e0)
% 230.25/41.60    (6)  all_57_1 = e0
% 230.25/41.60    (7)  all_57_15 = e3
% 230.25/41.60    (8)  op(e3, e3) = e0
% 230.25/41.60    (9)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 230.25/41.60         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.25/41.60    (10)   ~ (e2 = e0)
% 230.25/41.60    (11)  all_57_13 = e2
% 230.25/41.60    (12)  all_57_3 = e1
% 230.25/41.60    (13)   ~ (e1 = e0)
% 230.25/41.60    (14)  op(e0, e0) = e3
% 230.25/41.60    (15)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.25/41.60          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.25/41.60            e2)
% 230.25/41.60    (16)  all_57_2 = e0
% 230.25/41.60    (17)  all_57_7 = e3
% 230.25/41.60    (18)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.25/41.60          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.25/41.60    (19)   ~ (e2 = e1)
% 230.25/41.60    (20)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.25/41.60          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.25/41.60    (21)  all_57_14 = e0
% 230.25/41.60    (22)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.25/41.60          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.25/41.60  
% 230.25/41.60  Begin of proof
% 230.25/41.60  | 
% 230.25/41.60  | BETA: splitting (9) gives:
% 230.25/41.60  | 
% 230.25/41.60  | Case 1:
% 230.25/41.60  | | 
% 230.25/41.60  | |   (23)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 230.25/41.60  | |           e1)
% 230.25/41.60  | | 
% 230.25/41.60  | | BETA: splitting (23) gives:
% 230.25/41.60  | | 
% 230.25/41.60  | | Case 1:
% 230.25/41.60  | | | 
% 230.25/41.60  | | |   (24)  all_57_12 = e1 & op(e0, e3) = e1
% 230.25/41.60  | | | 
% 230.25/41.60  | | | ALPHA: (24) implies:
% 230.25/41.60  | | |   (25)  all_57_12 = e1
% 230.25/41.60  | | | 
% 230.25/41.60  | | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (10), (13), (15), (16),
% 230.25/41.60  | | |            (18), (19), (20), (21), (25) are inconsistent by sub-proof
% 230.25/41.60  | | |            #1555.
% 230.25/41.60  | | | 
% 230.25/41.60  | | Case 2:
% 230.25/41.60  | | | 
% 230.25/41.60  | | |   (26)  all_57_13 = e1 & op(e0, e2) = e1
% 230.25/41.60  | | | 
% 230.25/41.60  | | | ALPHA: (26) implies:
% 230.25/41.60  | | |   (27)  all_57_13 = e1
% 230.25/41.60  | | | 
% 230.25/41.60  | | | REF_CLOSE: (11), (19), (27) are inconsistent by sub-proof #2327.
% 230.25/41.60  | | | 
% 230.25/41.60  | | End of split
% 230.25/41.60  | | 
% 230.25/41.60  | Case 2:
% 230.25/41.60  | | 
% 230.25/41.60  | |   (28)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.25/41.60  | |           e1)
% 230.25/41.60  | | 
% 230.25/41.60  | | BETA: splitting (28) gives:
% 230.25/41.60  | | 
% 230.25/41.60  | | Case 1:
% 230.25/41.60  | | | 
% 230.25/41.60  | | |   (29)  all_57_14 = e1 & op(e0, e1) = e1
% 230.25/41.60  | | | 
% 230.25/41.60  | | | REF_CLOSE: (1), (2), (4), (6), (10), (12), (13), (17), (19), (21), (22),
% 230.25/41.60  | | |            (29) are inconsistent by sub-proof #1062.
% 230.25/41.60  | | | 
% 230.25/41.60  | | Case 2:
% 230.25/41.60  | | | 
% 230.25/41.60  | | |   (30)  all_57_15 = e1 & op(e0, e0) = e1
% 230.25/41.60  | | | 
% 230.25/41.60  | | | ALPHA: (30) implies:
% 230.25/41.60  | | |   (31)  op(e0, e0) = e1
% 230.25/41.60  | | | 
% 230.25/41.60  | | | REF_CLOSE: (2), (3), (14), (31) are inconsistent by sub-proof #2183.
% 230.25/41.60  | | | 
% 230.25/41.60  | | End of split
% 230.25/41.60  | | 
% 230.25/41.60  | End of split
% 230.25/41.60  | 
% 230.25/41.60  End of proof
% 230.25/41.60  
% 230.25/41.60  Sub-proof #1062 shows that the following formulas are inconsistent:
% 230.25/41.60  ----------------------------------------------------------------
% 230.25/41.60    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.25/41.60         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.25/41.60    (2)   ~ (e3 = e1)
% 230.25/41.60    (3)   ~ (e3 = e2)
% 230.25/41.60    (4)  all_57_1 = e0
% 230.25/41.60    (5)   ~ (e2 = e0)
% 230.25/41.60    (6)  all_57_3 = e1
% 230.25/41.60    (7)   ~ (e1 = e0)
% 230.25/41.60    (8)  all_57_7 = e3
% 230.25/41.60    (9)   ~ (e2 = e1)
% 230.25/41.60    (10)  all_57_14 = e0
% 230.25/41.60    (11)  all_57_14 = e1 & op(e0, e1) = e1
% 230.25/41.60    (12)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.25/41.60          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.25/41.60  
% 230.25/41.60  Begin of proof
% 230.25/41.60  | 
% 230.25/41.60  | ALPHA: (11) implies:
% 230.25/41.60  |   (13)  all_57_14 = e1
% 230.25/41.60  | 
% 230.25/41.60  | COMBINE_EQS: (10), (13) imply:
% 230.25/41.60  |   (14)  e1 = e0
% 230.25/41.60  | 
% 230.25/41.60  | COMBINE_EQS: (6), (14) imply:
% 230.25/41.60  |   (15)  all_57_3 = e0
% 230.25/41.60  | 
% 230.25/41.60  | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (12), (15) are inconsistent
% 230.25/41.60  |            by sub-proof #2098.
% 230.25/41.60  | 
% 230.25/41.60  End of proof
% 230.25/41.60  
% 230.25/41.60  Sub-proof #1063 shows that the following formulas are inconsistent:
% 230.25/41.60  ----------------------------------------------------------------
% 230.25/41.60    (1)  op(e3, e3) = e1
% 230.25/41.60    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.25/41.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.25/41.60    (3)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2)
% 230.25/41.60    (4)   ~ (e2 = e0)
% 230.25/41.60    (5)  all_57_2 = e0
% 230.32/41.60    (6)   ~ (e2 = e1)
% 230.32/41.60  
% 230.32/41.60  Begin of proof
% 230.32/41.60  | 
% 230.32/41.60  | BETA: splitting (3) gives:
% 230.32/41.60  | 
% 230.32/41.60  | Case 1:
% 230.32/41.60  | | 
% 230.32/41.60  | |   (7)  all_57_0 = e2 & op(e3, e3) = e2
% 230.32/41.60  | | 
% 230.32/41.60  | | ALPHA: (7) implies:
% 230.32/41.60  | |   (8)  op(e3, e3) = e2
% 230.32/41.60  | | 
% 230.32/41.60  | | REF_CLOSE: (1), (2), (6), (8) are inconsistent by sub-proof #1950.
% 230.32/41.60  | | 
% 230.32/41.60  | Case 2:
% 230.32/41.60  | | 
% 230.32/41.60  | |   (9)  all_57_2 = e2 & op(e2, e3) = e2
% 230.32/41.60  | | 
% 230.32/41.60  | | REF_CLOSE: (4), (5), (9) are inconsistent by sub-proof #2257.
% 230.32/41.60  | | 
% 230.32/41.60  | End of split
% 230.32/41.60  | 
% 230.32/41.60  End of proof
% 230.32/41.60  
% 230.32/41.60  Sub-proof #1064 shows that the following formulas are inconsistent:
% 230.32/41.60  ----------------------------------------------------------------
% 230.32/41.60    (1)  op(e3, e3) = e1
% 230.32/41.60    (2)   ~ (e3 = e1)
% 230.32/41.60    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.32/41.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.32/41.60    (4)   ~ (e3 = e0)
% 230.32/41.60    (5)  all_57_2 = e0
% 230.32/41.60    (6)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3)
% 230.32/41.60  
% 230.32/41.60  Begin of proof
% 230.32/41.60  | 
% 230.32/41.60  | BETA: splitting (6) gives:
% 230.32/41.60  | 
% 230.32/41.60  | Case 1:
% 230.32/41.60  | | 
% 230.32/41.60  | |   (7)  all_57_0 = e3 & op(e3, e3) = e3
% 230.32/41.60  | | 
% 230.32/41.60  | | ALPHA: (7) implies:
% 230.32/41.60  | |   (8)  op(e3, e3) = e3
% 230.32/41.60  | | 
% 230.32/41.60  | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #2495.
% 230.32/41.60  | | 
% 230.32/41.60  | Case 2:
% 230.32/41.60  | | 
% 230.32/41.60  | |   (9)  all_57_2 = e3 & op(e2, e3) = e3
% 230.32/41.60  | | 
% 230.32/41.60  | | ALPHA: (9) implies:
% 230.32/41.60  | |   (10)  all_57_2 = e3
% 230.32/41.60  | | 
% 230.32/41.60  | | REF_CLOSE: (4), (5), (10) are inconsistent by sub-proof #2258.
% 230.32/41.60  | | 
% 230.32/41.60  | End of split
% 230.32/41.60  | 
% 230.32/41.60  End of proof
% 230.32/41.60  
% 230.32/41.60  Sub-proof #1065 shows that the following formulas are inconsistent:
% 230.32/41.60  ----------------------------------------------------------------
% 230.32/41.60    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.32/41.60         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.32/41.60    (2)  all_57_13 = e1
% 230.32/41.60    (3)   ~ (e3 = e1)
% 230.32/41.60    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.32/41.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.32/41.60    (5)   ~ (e3 = e2)
% 230.32/41.60    (6)   ~ (e3 = e0)
% 230.32/41.60    (7)  op(e0, e3) = all_53_3
% 230.32/41.60    (8)  all_57_15 = e3
% 230.32/41.60    (9)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 230.32/41.60         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.32/41.60    (10)  all_57_5 = e3
% 230.32/41.60    (11)   ~ (e2 = e0)
% 230.32/41.60    (12)  all_57_3 = e1
% 230.32/41.60    (13)   ~ (e1 = e0)
% 230.32/41.60    (14)  all_57_12 = e3
% 230.32/41.60    (15)  op(e0, e0) = e3
% 230.32/41.60    (16)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.32/41.60          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.32/41.60            e2)
% 230.32/41.60    (17)   ~ (all_53_3 = e0)
% 230.32/41.60    (18)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.32/41.60              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.32/41.60                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.32/41.60                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.32/41.60    (19)  all_57_2 = e0
% 230.32/41.60    (20)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.32/41.60          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.32/41.60    (21)   ~ (e2 = e1)
% 230.32/41.60  
% 230.32/41.60  Begin of proof
% 230.32/41.60  | 
% 230.32/41.60  | BETA: splitting (18) gives:
% 230.32/41.60  | 
% 230.32/41.60  | Case 1:
% 230.32/41.60  | | 
% 230.32/41.60  | |   (22)  all_57_15 = e0 & op(e0, e0) = e0
% 230.32/41.60  | | 
% 230.32/41.60  | | ALPHA: (22) implies:
% 230.32/41.60  | |   (23)  op(e0, e0) = e0
% 230.32/41.60  | | 
% 230.32/41.60  | | REF_CLOSE: (4), (6), (15), (23) are inconsistent by sub-proof #2304.
% 230.32/41.60  | | 
% 230.32/41.60  | Case 2:
% 230.32/41.60  | | 
% 230.32/41.60  | |   (24)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 230.32/41.60  | |             e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0 &
% 230.32/41.60  | |             op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 230.32/41.60  | |           (all_57_14 = e0 & op(e0, e1) = e0))
% 230.32/41.60  | | 
% 230.32/41.60  | | ALPHA: (24) implies:
% 230.32/41.60  | |   (25)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 230.32/41.60  | |           e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.32/41.60  | | 
% 230.32/41.60  | | BETA: splitting (25) gives:
% 230.32/41.60  | | 
% 230.32/41.60  | | Case 1:
% 230.32/41.60  | | | 
% 230.32/41.60  | | |   (26)  all_57_12 = e0 & op(e0, e3) = e0
% 230.32/41.60  | | | 
% 230.32/41.60  | | | ALPHA: (26) implies:
% 230.32/41.60  | | |   (27)  op(e0, e3) = e0
% 230.32/41.60  | | | 
% 230.32/41.60  | | | REF_CLOSE: (4), (7), (17), (27) are inconsistent by sub-proof #2366.
% 230.32/41.60  | | | 
% 230.32/41.60  | | Case 2:
% 230.32/41.60  | | | 
% 230.32/41.60  | | |   (28)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1)
% 230.32/41.60  | | |           = e0)
% 230.32/41.60  | | | 
% 230.32/41.60  | | | BETA: splitting (28) gives:
% 230.32/41.60  | | | 
% 230.32/41.60  | | | Case 1:
% 230.32/41.60  | | | | 
% 230.32/41.60  | | | |   (29)  all_57_13 = e0 & op(e0, e2) = e0
% 230.32/41.60  | | | | 
% 230.32/41.60  | | | | ALPHA: (29) implies:
% 230.32/41.60  | | | |   (30)  all_57_13 = e0
% 230.32/41.60  | | | | 
% 230.32/41.60  | | | | COMBINE_EQS: (2), (30) imply:
% 230.32/41.60  | | | |   (31)  e1 = e0
% 230.32/41.60  | | | | 
% 230.32/41.60  | | | | SIMP: (31) implies:
% 230.32/41.60  | | | |   (32)  e1 = e0
% 230.32/41.60  | | | | 
% 230.32/41.60  | | | | COMBINE_EQS: (12), (32) imply:
% 230.32/41.60  | | | |   (33)  all_57_3 = e0
% 230.32/41.60  | | | | 
% 230.32/41.60  | | | | REF_CLOSE: (1), (3), (5), (10), (11), (13), (19), (20), (21), (33) are
% 230.32/41.60  | | | |            inconsistent by sub-proof #2253.
% 230.32/41.60  | | | | 
% 230.32/41.60  | | | Case 2:
% 230.32/41.60  | | | | 
% 230.32/41.60  | | | |   (34)  all_57_14 = e0 & op(e0, e1) = e0
% 230.32/41.60  | | | | 
% 230.32/41.60  | | | | ALPHA: (34) implies:
% 230.32/41.60  | | | |   (35)  all_57_14 = e0
% 230.32/41.60  | | | | 
% 230.32/41.60  | | | | REF_CLOSE: (3), (5), (8), (9), (11), (13), (14), (16), (21), (35) are
% 230.32/41.60  | | | |            inconsistent by sub-proof #1763.
% 230.32/41.60  | | | | 
% 230.32/41.60  | | | End of split
% 230.32/41.60  | | | 
% 230.32/41.60  | | End of split
% 230.32/41.60  | | 
% 230.32/41.60  | End of split
% 230.32/41.60  | 
% 230.32/41.60  End of proof
% 230.32/41.60  
% 230.32/41.60  Sub-proof #1066 shows that the following formulas are inconsistent:
% 230.32/41.60  ----------------------------------------------------------------
% 230.32/41.60    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.32/41.60         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.32/41.60    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.32/41.60         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.32/41.60    (3)   ~ (e3 = e1)
% 230.32/41.60    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.32/41.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.32/41.60    (5)   ~ (e3 = e2)
% 230.32/41.60    (6)  all_57_0 = e0
% 230.32/41.60    (7)  op(e3, e3) = e0
% 230.32/41.60    (8)  all_57_5 = e3
% 230.32/41.60    (9)   ~ (e2 = e0)
% 230.32/41.60    (10)  all_57_3 = e1
% 230.32/41.60    (11)   ~ (e1 = e0)
% 230.32/41.60    (12)  all_57_6 = e3
% 230.32/41.60    (13)  all_57_2 = e0
% 230.32/41.60    (14)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.32/41.60          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.32/41.60    (15)   ~ (e2 = e1)
% 230.32/41.60    (16)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.32/41.60          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.32/41.60  
% 230.32/41.60  Begin of proof
% 230.32/41.60  | 
% 230.32/41.60  | BETA: splitting (16) gives:
% 230.32/41.60  | 
% 230.32/41.60  | Case 1:
% 230.32/41.60  | | 
% 230.32/41.60  | |   (17)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) =
% 230.32/41.60  | |           e2)
% 230.32/41.60  | | 
% 230.32/41.60  | | REF_CLOSE: (4), (7), (9), (13), (17) are inconsistent by sub-proof #1560.
% 230.32/41.60  | | 
% 230.32/41.60  | Case 2:
% 230.32/41.60  | | 
% 230.32/41.60  | |   (18)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) =
% 230.32/41.60  | |           e2)
% 230.32/41.60  | | 
% 230.32/41.60  | | BETA: splitting (18) gives:
% 230.32/41.60  | | 
% 230.32/41.60  | | Case 1:
% 230.32/41.60  | | | 
% 230.32/41.60  | | |   (19)  all_57_6 = e2 & op(e1, e3) = e2
% 230.32/41.60  | | | 
% 230.32/41.60  | | | ALPHA: (19) implies:
% 230.32/41.60  | | |   (20)  all_57_6 = e2
% 230.32/41.60  | | | 
% 230.32/41.60  | | | REF_CLOSE: (5), (12), (20) are inconsistent by sub-proof #2463.
% 230.32/41.60  | | | 
% 230.32/41.60  | | Case 2:
% 230.32/41.60  | | | 
% 230.32/41.60  | | |   (21)  all_57_12 = e2 & op(e0, e3) = e2
% 230.32/41.60  | | | 
% 230.32/41.60  | | | ALPHA: (21) implies:
% 230.32/41.60  | | |   (22)  all_57_12 = e2
% 230.32/41.60  | | | 
% 230.32/41.60  | | | BETA: splitting (2) gives:
% 230.32/41.60  | | | 
% 230.32/41.60  | | | Case 1:
% 230.32/41.60  | | | | 
% 230.32/41.60  | | | |   (23)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3)
% 230.32/41.60  | | | |           = e1)
% 230.32/41.60  | | | | 
% 230.32/41.60  | | | | BETA: splitting (23) gives:
% 230.32/41.60  | | | | 
% 230.32/41.60  | | | | Case 1:
% 230.32/41.60  | | | | | 
% 230.32/41.60  | | | | |   (24)  all_57_0 = e1 & op(e3, e3) = e1
% 230.32/41.60  | | | | | 
% 230.32/41.60  | | | | | REF_CLOSE: (1), (3), (5), (6), (8), (9), (10), (11), (13), (14), (15),
% 230.32/41.60  | | | | |            (24) are inconsistent by sub-proof #1068.
% 230.32/41.60  | | | | | 
% 230.32/41.60  | | | | Case 2:
% 230.32/41.60  | | | | | 
% 230.32/41.60  | | | | |   (25)  all_57_2 = e1 & op(e2, e3) = e1
% 230.32/41.60  | | | | | 
% 230.32/41.60  | | | | | REF_CLOSE: (1), (3), (5), (8), (9), (10), (11), (13), (14), (15), (25)
% 230.32/41.60  | | | | |            are inconsistent by sub-proof #1067.
% 230.32/41.60  | | | | | 
% 230.32/41.60  | | | | End of split
% 230.32/41.60  | | | | 
% 230.32/41.60  | | | Case 2:
% 230.32/41.60  | | | | 
% 230.32/41.60  | | | |   (26)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3)
% 230.32/41.60  | | | |           = e1)
% 230.32/41.60  | | | | 
% 230.32/41.60  | | | | REF_CLOSE: (3), (12), (15), (22), (26) are inconsistent by sub-proof
% 230.32/41.60  | | | |            #2016.
% 230.32/41.60  | | | | 
% 230.32/41.60  | | | End of split
% 230.32/41.60  | | | 
% 230.32/41.60  | | End of split
% 230.32/41.60  | | 
% 230.32/41.60  | End of split
% 230.32/41.60  | 
% 230.32/41.60  End of proof
% 230.32/41.60  
% 230.32/41.60  Sub-proof #1067 shows that the following formulas are inconsistent:
% 230.32/41.60  ----------------------------------------------------------------
% 230.32/41.60    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.32/41.60         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.32/41.60    (2)   ~ (e3 = e1)
% 230.32/41.60    (3)   ~ (e3 = e2)
% 230.32/41.60    (4)  all_57_5 = e3
% 230.32/41.60    (5)  all_57_2 = e1 & op(e2, e3) = e1
% 230.32/41.60    (6)   ~ (e2 = e0)
% 230.32/41.60    (7)  all_57_3 = e1
% 230.32/41.60    (8)   ~ (e1 = e0)
% 230.32/41.60    (9)  all_57_2 = e0
% 230.32/41.60    (10)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.32/41.60          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.32/41.60    (11)   ~ (e2 = e1)
% 230.32/41.60  
% 230.32/41.60  Begin of proof
% 230.32/41.60  | 
% 230.32/41.60  | ALPHA: (5) implies:
% 230.32/41.60  |   (12)  all_57_2 = e1
% 230.32/41.60  | 
% 230.32/41.60  | COMBINE_EQS: (9), (12) imply:
% 230.32/41.60  |   (13)  e1 = e0
% 230.32/41.60  | 
% 230.32/41.60  | SIMP: (13) implies:
% 230.32/41.60  |   (14)  e1 = e0
% 230.32/41.60  | 
% 230.32/41.60  | COMBINE_EQS: (7), (14) imply:
% 230.32/41.60  |   (15)  all_57_3 = e0
% 230.32/41.60  | 
% 230.32/41.60  | REF_CLOSE: (1), (2), (3), (4), (6), (8), (9), (10), (11), (15) are
% 230.32/41.60  |            inconsistent by sub-proof #2253.
% 230.32/41.60  | 
% 230.32/41.60  End of proof
% 230.32/41.60  
% 230.32/41.60  Sub-proof #1068 shows that the following formulas are inconsistent:
% 230.32/41.60  ----------------------------------------------------------------
% 230.32/41.60    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.32/41.60         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.32/41.60    (2)   ~ (e3 = e1)
% 230.32/41.60    (3)  all_57_0 = e1 & op(e3, e3) = e1
% 230.32/41.60    (4)   ~ (e3 = e2)
% 230.32/41.60    (5)  all_57_0 = e0
% 230.32/41.60    (6)  all_57_5 = e3
% 230.32/41.60    (7)   ~ (e2 = e0)
% 230.32/41.60    (8)  all_57_3 = e1
% 230.32/41.60    (9)   ~ (e1 = e0)
% 230.32/41.60    (10)  all_57_2 = e0
% 230.32/41.60    (11)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.32/41.60          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.32/41.60    (12)   ~ (e2 = e1)
% 230.32/41.60  
% 230.32/41.60  Begin of proof
% 230.32/41.60  | 
% 230.32/41.60  | ALPHA: (3) implies:
% 230.32/41.60  |   (13)  all_57_0 = e1
% 230.32/41.60  | 
% 230.32/41.60  | COMBINE_EQS: (5), (13) imply:
% 230.32/41.60  |   (14)  e1 = e0
% 230.32/41.60  | 
% 230.32/41.60  | SIMP: (14) implies:
% 230.32/41.60  |   (15)  e1 = e0
% 230.32/41.60  | 
% 230.32/41.60  | COMBINE_EQS: (8), (15) imply:
% 230.32/41.60  |   (16)  all_57_3 = e0
% 230.32/41.60  | 
% 230.32/41.60  | REF_CLOSE: (1), (2), (4), (6), (7), (9), (10), (11), (12), (16) are
% 230.32/41.60  |            inconsistent by sub-proof #2253.
% 230.32/41.60  | 
% 230.32/41.60  End of proof
% 230.32/41.60  
% 230.32/41.60  Sub-proof #1069 shows that the following formulas are inconsistent:
% 230.32/41.60  ----------------------------------------------------------------
% 230.32/41.60    (1)   ~ (e3 = e1)
% 230.32/41.60    (2)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.32/41.60         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.32/41.60    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.32/41.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.32/41.60    (4)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.32/41.60         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.32/41.60    (5)   ~ (all_6_2 = e3)
% 230.32/41.60    (6)  op(e1, e1) = all_6_2
% 230.32/41.60    (7)  all_57_7 = e1
% 230.32/41.60    (8)   ~ (e3 = e2)
% 230.32/41.60    (9)   ~ (e3 = e0)
% 230.32/41.60    (10)  all_57_15 = e3
% 230.32/41.60    (11)  op(e1, e1) = e1
% 230.32/41.60    (12)   ~ (e2 = e0)
% 230.32/41.60    (13)   ~ (e1 = e0)
% 230.32/41.60    (14)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.32/41.60              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.32/41.60                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.32/41.60                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.32/41.60    (15)   ~ (e2 = e1)
% 230.32/41.60    (16)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.32/41.60          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.32/41.60    (17)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.32/41.60          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.32/41.60    (18)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.32/41.60          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.32/41.60  
% 230.32/41.60  Begin of proof
% 230.32/41.60  | 
% 230.32/41.60  | BETA: splitting (18) gives:
% 230.32/41.60  | 
% 230.32/41.60  | Case 1:
% 230.32/41.60  | | 
% 230.32/41.60  | |   (19)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) =
% 230.32/41.60  | |           e2)
% 230.32/41.60  | | 
% 230.32/41.60  | | BETA: splitting (19) gives:
% 230.32/41.60  | | 
% 230.32/41.60  | | Case 1:
% 230.32/41.60  | | | 
% 230.32/41.60  | | |   (20)  all_57_6 = e2 & op(e1, e3) = e2
% 230.32/41.60  | | | 
% 230.32/41.60  | | | ALPHA: (20) implies:
% 230.32/41.60  | | |   (21)  all_57_6 = e2
% 230.32/41.60  | | | 
% 230.32/41.60  | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13), (14),
% 230.32/41.60  | | |            (15), (16), (17), (21) are inconsistent by sub-proof #1245.
% 230.32/41.60  | | | 
% 230.32/41.60  | | Case 2:
% 230.32/41.60  | | | 
% 230.32/41.60  | | |   (22)  all_57_7 = e2 & op(e1, e2) = e2
% 230.32/41.60  | | | 
% 230.32/41.60  | | | REF_CLOSE: (7), (15), (22) are inconsistent by sub-proof #1268.
% 230.32/41.60  | | | 
% 230.32/41.60  | | End of split
% 230.32/41.60  | | 
% 230.32/41.60  | Case 2:
% 230.32/41.60  | | 
% 230.32/41.60  | |   (23)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) =
% 230.32/41.60  | |           e2)
% 230.32/41.60  | | 
% 230.32/41.60  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 230.32/41.60  | |            (13), (14), (15), (16), (17), (23) are inconsistent by sub-proof
% 230.32/41.60  | |            #1070.
% 230.32/41.60  | | 
% 230.32/41.60  | End of split
% 230.32/41.60  | 
% 230.32/41.60  End of proof
% 230.32/41.60  
% 230.32/41.60  Sub-proof #1070 shows that the following formulas are inconsistent:
% 230.32/41.60  ----------------------------------------------------------------
% 230.32/41.60    (1)   ~ (e3 = e1)
% 230.32/41.60    (2)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.32/41.60         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.32/41.60    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.32/41.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.32/41.60    (4)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.32/41.60         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.32/41.60    (5)   ~ (all_6_2 = e3)
% 230.32/41.60    (6)  op(e1, e1) = all_6_2
% 230.32/41.60    (7)  all_57_7 = e1
% 230.32/41.60    (8)   ~ (e3 = e2)
% 230.32/41.60    (9)   ~ (e3 = e0)
% 230.32/41.60    (10)  all_57_15 = e3
% 230.32/41.60    (11)  op(e1, e1) = e1
% 230.32/41.60    (12)   ~ (e2 = e0)
% 230.32/41.60    (13)   ~ (e1 = e0)
% 230.32/41.60    (14)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.32/41.60              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.32/41.60                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.32/41.60                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.32/41.60    (15)   ~ (e2 = e1)
% 230.32/41.60    (16)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.32/41.60          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.32/41.60    (17)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.32/41.60    (18)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.32/41.60          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.32/41.60  
% 230.32/41.60  Begin of proof
% 230.32/41.60  | 
% 230.32/41.60  | BETA: splitting (17) gives:
% 230.32/41.60  | 
% 230.32/41.60  | Case 1:
% 230.32/41.60  | | 
% 230.32/41.60  | |   (19)  all_57_8 = e2 & op(e1, e1) = e2
% 230.32/41.60  | | 
% 230.32/41.60  | | ALPHA: (19) implies:
% 230.32/41.60  | |   (20)  op(e1, e1) = e2
% 230.32/41.60  | | 
% 230.32/41.60  | | REF_CLOSE: (3), (11), (15), (20) are inconsistent by sub-proof #2423.
% 230.32/41.60  | | 
% 230.32/41.60  | Case 2:
% 230.32/41.60  | | 
% 230.32/41.60  | |   (21)  all_57_11 = e2 & op(e1, e0) = e2
% 230.32/41.60  | | 
% 230.32/41.60  | | ALPHA: (21) implies:
% 230.32/41.60  | |   (22)  all_57_11 = e2
% 230.32/41.60  | | 
% 230.32/41.60  | | BETA: splitting (2) gives:
% 230.32/41.60  | | 
% 230.32/41.60  | | Case 1:
% 230.32/41.60  | | | 
% 230.32/41.60  | | |   (23)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) =
% 230.32/41.60  | | |           e0)
% 230.32/41.60  | | | 
% 230.32/41.60  | | | BETA: splitting (23) gives:
% 230.32/41.60  | | | 
% 230.32/41.60  | | | Case 1:
% 230.32/41.60  | | | | 
% 230.32/41.60  | | | |   (24)  all_57_6 = e0 & op(e1, e3) = e0
% 230.32/41.60  | | | | 
% 230.32/41.60  | | | | ALPHA: (24) implies:
% 230.32/41.60  | | | |   (25)  all_57_6 = e0
% 230.32/41.60  | | | | 
% 230.32/41.60  | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 230.32/41.60  | | | |            (14), (15), (16), (18), (25) are inconsistent by sub-proof
% 230.32/41.60  | | | |            #1157.
% 230.32/41.60  | | | | 
% 230.32/41.60  | | | Case 2:
% 230.32/41.60  | | | | 
% 230.32/41.60  | | | |   (26)  all_57_7 = e0 & op(e1, e2) = e0
% 230.32/41.60  | | | | 
% 230.32/41.60  | | | | ALPHA: (26) implies:
% 230.32/41.60  | | | |   (27)  all_57_7 = e0
% 230.32/41.60  | | | | 
% 230.32/41.60  | | | | REF_CLOSE: (7), (13), (27) are inconsistent by sub-proof #2211.
% 230.32/41.60  | | | | 
% 230.32/41.60  | | | End of split
% 230.32/41.60  | | | 
% 230.32/41.60  | | Case 2:
% 230.32/41.60  | | | 
% 230.32/41.60  | | |   (28)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 230.32/41.60  | | |           e0)
% 230.32/41.60  | | | 
% 230.32/41.60  | | | REF_CLOSE: (3), (11), (12), (13), (22), (28) are inconsistent by sub-proof
% 230.32/41.60  | | |            #1622.
% 230.32/41.60  | | | 
% 230.32/41.60  | | End of split
% 230.32/41.60  | | 
% 230.32/41.60  | End of split
% 230.32/41.60  | 
% 230.32/41.60  End of proof
% 230.32/41.60  
% 230.32/41.60  Sub-proof #1071 shows that the following formulas are inconsistent:
% 230.32/41.60  ----------------------------------------------------------------
% 230.32/41.60    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.32/41.60         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.32/41.60    (2)   ~ (e3 = e1)
% 230.32/41.60    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.32/41.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.32/41.60    (4)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.32/41.60         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.32/41.60    (5)   ~ (all_6_2 = e3)
% 230.32/41.60    (6)  op(e1, e1) = all_6_2
% 230.32/41.60    (7)  all_57_6 = e1
% 230.32/41.60    (8)   ~ (e3 = e2)
% 230.32/41.60    (9)   ~ (e3 = e0)
% 230.32/41.60    (10)  all_57_15 = e3
% 230.32/41.60    (11)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.32/41.60          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.32/41.60    (12)   ~ (e2 = e0)
% 230.32/41.60    (13)  op(e2, e2) = e2
% 230.32/41.60    (14)   ~ (e1 = e0)
% 230.32/41.60    (15)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.32/41.60              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.32/41.60                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.32/41.60                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.32/41.60    (16)  all_57_1 = e3
% 230.32/41.60    (17)   ~ (e2 = e1)
% 230.32/41.60    (18)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.32/41.60          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.32/41.60    (19)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.32/41.60          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.32/41.60    (20)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.32/41.60          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.32/41.60  
% 230.32/41.60  Begin of proof
% 230.32/41.60  | 
% 230.32/41.60  | BETA: splitting (4) gives:
% 230.32/41.60  | 
% 230.32/41.60  | Case 1:
% 230.32/41.60  | | 
% 230.32/41.60  | |   (21)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 230.32/41.60  | |           e3)
% 230.32/41.60  | | 
% 230.32/41.60  | | BETA: splitting (21) gives:
% 230.32/41.60  | | 
% 230.32/41.60  | | Case 1:
% 230.32/41.60  | | | 
% 230.32/41.60  | | |   (22)  all_57_6 = e3 & op(e1, e3) = e3
% 230.32/41.60  | | | 
% 230.32/41.60  | | | ALPHA: (22) implies:
% 230.32/41.60  | | |   (23)  all_57_6 = e3
% 230.32/41.60  | | | 
% 230.32/41.60  | | | REF_CLOSE: (2), (7), (23) are inconsistent by sub-proof #2017.
% 230.32/41.60  | | | 
% 230.32/41.60  | | Case 2:
% 230.32/41.60  | | | 
% 230.32/41.60  | | |   (24)  all_57_7 = e3 & op(e1, e2) = e3
% 230.32/41.60  | | | 
% 230.32/41.60  | | | ALPHA: (24) implies:
% 230.32/41.60  | | |   (25)  all_57_7 = e3
% 230.32/41.60  | | | 
% 230.32/41.60  | | | REF_CLOSE: (1), (2), (3), (8), (9), (11), (12), (13), (14), (16), (17),
% 230.32/41.60  | | |            (20), (25) are inconsistent by sub-proof #1167.
% 230.32/41.60  | | | 
% 230.32/41.60  | | End of split
% 230.32/41.60  | | 
% 230.32/41.60  | Case 2:
% 230.32/41.60  | | 
% 230.32/41.61  | |   (26)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 230.32/41.61  | |           e3)
% 230.32/41.61  | | 
% 230.32/41.61  | | REF_CLOSE: (2), (3), (5), (6), (8), (9), (10), (12), (14), (15), (17), (18),
% 230.32/41.61  | |            (19), (26) are inconsistent by sub-proof #1786.
% 230.32/41.61  | | 
% 230.32/41.61  | End of split
% 230.32/41.61  | 
% 230.32/41.61  End of proof
% 230.32/41.61  
% 230.32/41.61  Sub-proof #1072 shows that the following formulas are inconsistent:
% 230.32/41.61  ----------------------------------------------------------------
% 230.32/41.61    (1)  op(e0, e1) = all_53_11
% 230.32/41.61    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 230.32/41.61    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.32/41.61           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.32/41.61    (4)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 230.32/41.61           op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 230.32/41.61             e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 230.32/41.61    (5)   ~ (all_6_2 = e3)
% 230.32/41.61    (6)  op(e1, e1) = all_6_2
% 230.32/41.61    (7)  all_34_2 = all_6_2
% 230.32/41.61    (8)   ~ (all_53_13 = e2)
% 230.32/41.61    (9)   ~ (all_53_7 = e2)
% 230.32/41.61    (10)   ~ (all_53_9 = all_53_11)
% 230.32/41.61    (11)   ~ (all_53_9 = all_6_2)
% 230.32/41.61    (12)   ~ (all_53_14 = all_6_2)
% 230.32/41.61    (13)   ~ (e3 = e2)
% 230.32/41.61    (14)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 230.32/41.61    (15)  op(e1, e0) = all_53_14
% 230.32/41.61    (16)  op(e0, e3) = all_53_3
% 230.32/41.61    (17)  all_57_15 = e3
% 230.32/41.61    (18)  op(e3, e3) = e2
% 230.32/41.61    (19)   ~ (all_53_3 = e2)
% 230.32/41.61    (20)   ~ (all_53_14 = e3)
% 230.32/41.61    (21)  all_55_6 = all_53_9
% 230.32/41.61    (22)   ~ (e2 = e0)
% 230.32/41.61    (23)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 230.32/41.61            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 230.32/41.61            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 230.32/41.61            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 230.32/41.61              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 230.32/41.61            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 230.32/41.61            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 230.32/41.61              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 230.32/41.61              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 230.32/41.61            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 230.32/41.61            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 230.32/41.61            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 230.32/41.61              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 230.32/41.61              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 230.32/41.61            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 230.32/41.61              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 230.32/41.61            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 230.32/41.61            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 230.32/41.61              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 230.32/41.61              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 230.32/41.61            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 230.32/41.61            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 230.32/41.61    (24)  op(e2, e2) = e2
% 230.32/41.61    (25)  op(e0, e0) = e3
% 230.32/41.61    (26)  op(e0, e2) = all_53_7
% 230.32/41.61    (27)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.32/41.61          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.32/41.61            e2)
% 230.32/41.61    (28)  all_55_10 = all_6_2
% 230.32/41.61    (29)  op(e2, e0) = all_53_13
% 230.32/41.61    (30)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.32/41.61          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.32/41.61    (31)  op(e2, e1) = all_53_9
% 230.32/41.61    (32)  all_24_2 = all_6_2
% 230.32/41.61    (33)   ~ (all_53_12 = e2)
% 230.32/41.61    (34)   ~ (all_34_2 = e0) | ( ~ (all_34_0 = e3) & op(all_34_1, e1) = all_34_0 &
% 230.32/41.61            op(e1, e0) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 230.32/41.61              e2) & op(e1, e0) = all_34_1 & $i(all_34_1))
% 230.32/41.61    (35)  op(e3, e0) = all_53_12
% 230.32/41.61  
% 230.32/41.61  Begin of proof
% 230.32/41.61  | 
% 230.32/41.61  | BETA: splitting (27) gives:
% 230.32/41.61  | 
% 230.32/41.61  | Case 1:
% 230.32/41.61  | | 
% 230.32/41.61  | |   (36)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 230.32/41.61  | |           e2)
% 230.32/41.61  | | 
% 230.32/41.61  | | REF_CLOSE: (3), (9), (16), (19), (26), (36) are inconsistent by sub-proof
% 230.32/41.61  | |            #1979.
% 230.32/41.61  | | 
% 230.32/41.61  | Case 2:
% 230.32/41.61  | | 
% 230.32/41.61  | |   (37)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.32/41.61  | |           e2)
% 230.32/41.61  | | 
% 230.32/41.61  | | BETA: splitting (37) gives:
% 230.32/41.61  | | 
% 230.32/41.61  | | Case 1:
% 230.32/41.61  | | | 
% 230.32/41.61  | | |   (38)  all_57_14 = e2 & op(e0, e1) = e2
% 230.32/41.61  | | | 
% 230.32/41.61  | | | ALPHA: (38) implies:
% 230.32/41.61  | | |   (39)  op(e0, e1) = e2
% 230.32/41.61  | | | 
% 230.32/41.61  | | | BETA: splitting (30) gives:
% 230.32/41.61  | | | 
% 230.32/41.61  | | | Case 1:
% 230.32/41.61  | | | | 
% 230.32/41.61  | | | |   (40)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0)
% 230.32/41.61  | | | |           = e2)
% 230.32/41.61  | | | | 
% 230.32/41.61  | | | | REF_CLOSE: (3), (8), (29), (33), (35), (40) are inconsistent by
% 230.32/41.61  | | | |            sub-proof #1952.
% 230.32/41.61  | | | | 
% 230.32/41.61  | | | Case 2:
% 230.32/41.61  | | | | 
% 230.32/41.61  | | | |   (41)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0,
% 230.32/41.61  | | | |             e0) = e2)
% 230.32/41.61  | | | | 
% 230.32/41.61  | | | | BETA: splitting (41) gives:
% 230.32/41.61  | | | | 
% 230.32/41.61  | | | | Case 1:
% 230.32/41.61  | | | | | 
% 230.32/41.61  | | | | |   (42)  all_57_11 = e2 & op(e1, e0) = e2
% 230.32/41.61  | | | | | 
% 230.32/41.61  | | | | | ALPHA: (42) implies:
% 230.32/41.61  | | | | |   (43)  op(e1, e0) = e2
% 230.32/41.61  | | | | | 
% 230.32/41.61  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (10), (11), (12), (14),
% 230.32/41.61  | | | | |            (15), (18), (20), (21), (22), (23), (24), (25), (28), (31),
% 230.32/41.61  | | | | |            (32), (34), (39), (43) are inconsistent by sub-proof #1114.
% 230.32/41.61  | | | | | 
% 230.32/41.61  | | | | Case 2:
% 230.32/41.61  | | | | | 
% 230.32/41.61  | | | | |   (44)  all_57_15 = e2 & op(e0, e0) = e2
% 230.32/41.61  | | | | | 
% 230.32/41.61  | | | | | REF_CLOSE: (13), (17), (44) are inconsistent by sub-proof #2323.
% 230.32/41.61  | | | | | 
% 230.32/41.61  | | | | End of split
% 230.32/41.61  | | | | 
% 230.32/41.61  | | | End of split
% 230.32/41.61  | | | 
% 230.32/41.61  | | Case 2:
% 230.32/41.61  | | | 
% 230.32/41.61  | | |   (45)  all_57_15 = e2 & op(e0, e0) = e2
% 230.32/41.61  | | | 
% 230.32/41.61  | | | REF_CLOSE: (13), (17), (45) are inconsistent by sub-proof #2323.
% 230.32/41.61  | | | 
% 230.32/41.61  | | End of split
% 230.32/41.61  | | 
% 230.32/41.61  | End of split
% 230.32/41.61  | 
% 230.32/41.61  End of proof
% 230.32/41.61  
% 230.32/41.61  Sub-proof #1073 shows that the following formulas are inconsistent:
% 230.32/41.61  ----------------------------------------------------------------
% 230.32/41.61    (1)  op(e0, e1) = all_53_11
% 230.32/41.61    (2)   ~ (all_53_6 = all_53_14)
% 230.32/41.61    (3)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 230.32/41.61    (4)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.32/41.61         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.32/41.61    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.32/41.61         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.32/41.61    (6)   ~ (all_53_8 = all_53_12)
% 230.32/41.61    (7)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.32/41.61         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.32/41.61    (8)   ~ (e3 = e1)
% 230.32/41.61    (9)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.32/41.61         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.32/41.61    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.32/41.61            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.32/41.61    (11)  all_22_2 = e3
% 230.32/41.61    (12)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.32/41.61          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.32/41.61    (13)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 230.32/41.61            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 230.32/41.61              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 230.32/41.61    (14)   ~ (all_6_2 = e3)
% 230.32/41.61    (15)  op(e1, e1) = all_6_2
% 230.32/41.61    (16)  all_34_2 = all_6_2
% 230.32/41.61    (17)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.32/41.61          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.32/41.61    (18)   ~ (all_53_13 = e2)
% 230.32/41.61    (19)   ~ (all_53_4 = all_53_12)
% 230.32/41.61    (20)   ~ (all_53_7 = e2)
% 230.32/41.61    (21)   ~ (all_53_8 = all_53_9)
% 230.32/41.61    (22)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.32/41.61          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.32/41.61    (23)   ~ (all_53_9 = all_53_11)
% 230.32/41.61    (24)   ~ (all_53_9 = all_6_2)
% 230.32/41.61    (25)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.32/41.61          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.32/41.61    (26)   ~ (all_53_14 = all_6_2)
% 230.32/41.61    (27)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 230.32/41.61          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.32/41.61    (28)   ~ (e3 = e2)
% 230.32/41.61    (29)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 230.32/41.61    (30)  op(e1, e0) = all_53_14
% 230.32/41.61    (31)   ~ (e3 = e0)
% 230.32/41.61    (32)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.32/41.61          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.32/41.61    (33)  op(e3, e3) = e3
% 230.32/41.61    (34)   ~ (all_53_8 = all_6_2)
% 230.32/41.61    (35)  all_57_15 = e3
% 230.32/41.61    (36)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.32/41.61          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.32/41.61            e1)
% 230.32/41.61    (37)  all_55_6 = all_53_9
% 230.32/41.61    (38)  op(e3, e2) = all_53_4
% 230.32/41.61    (39)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.32/41.61          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.32/41.61    (40)   ~ (e2 = e0)
% 230.32/41.61    (41)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 230.32/41.61            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 230.32/41.61            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 230.32/41.61            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 230.32/41.61              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 230.32/41.61            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 230.32/41.61            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 230.32/41.61              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 230.32/41.61              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 230.32/41.61            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 230.32/41.61            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 230.32/41.61            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 230.32/41.61              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 230.32/41.61              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 230.32/41.61            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 230.32/41.61              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 230.32/41.61            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 230.32/41.61            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 230.32/41.61              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 230.32/41.61              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 230.32/41.61            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 230.32/41.61            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 230.32/41.61    (42)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 230.32/41.61            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 230.32/41.61              e3) = all_12_1 & $i(all_12_1))
% 230.32/41.61    (43)   ~ (all_53_9 = e2)
% 230.32/41.61    (44)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.32/41.61          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.32/41.61    (45)  op(e2, e2) = e2
% 230.32/41.61    (46)   ~ (e1 = e0)
% 230.32/41.61    (47)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 230.32/41.61            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 230.32/41.61              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 230.32/41.61    (48)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 230.32/41.61          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 230.32/41.61    (49)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.32/41.61          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.32/41.61    (50)  op(e0, e0) = e3
% 230.32/41.61    (51)  op(e0, e2) = all_53_7
% 230.32/41.61    (52)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.32/41.61          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.32/41.61            e2)
% 230.32/41.61    (53)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.32/41.61              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.32/41.61                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.32/41.61                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.32/41.61    (54)  all_55_10 = all_6_2
% 230.32/41.61    (55)  op(e2, e0) = all_53_13
% 230.32/41.61    (56)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.32/41.61          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.32/41.61    (57)  all_38_2 = all_6_2
% 230.32/41.61    (58)   ~ (all_53_12 = e3)
% 230.32/41.61    (59)   ~ (all_53_4 = e2)
% 230.32/41.61    (60)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.32/41.61          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.32/41.61    (61)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.32/41.61          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.32/41.61    (62)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.32/41.61          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 230.32/41.61    (63)   ~ (e2 = e1)
% 230.32/41.61    (64)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.32/41.61          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.32/41.61    (65)  op(e2, e1) = all_53_9
% 230.32/41.61    (66)  op(e1, e2) = all_53_6
% 230.32/41.61    (67)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.32/41.61          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.32/41.61    (68)  all_24_2 = all_6_2
% 230.32/41.61    (69)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.32/41.61          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.32/41.61    (70)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.32/41.61          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.32/41.61    (71)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.32/41.61          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.32/41.61    (72)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.32/41.61          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.32/41.61    (73)   ~ (all_22_2 = e3) | ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 &
% 230.32/41.61            op(e0, e3) = all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 =
% 230.32/41.61              e2) & op(e0, e3) = all_22_1 & $i(all_22_1))
% 230.32/41.61    (74)  all_57_3 = e2
% 230.32/41.61    (75)  op(e3, e1) = all_53_8
% 230.32/41.61    (76)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.32/41.61          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.32/41.61    (77)   ~ (all_34_2 = e0) | ( ~ (all_34_0 = e3) & op(all_34_1, e1) = all_34_0 &
% 230.32/41.61            op(e1, e0) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 230.32/41.61              e2) & op(e1, e0) = all_34_1 & $i(all_34_1))
% 230.32/41.61    (78)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.32/41.61          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.32/41.61    (79)  op(e3, e0) = all_53_12
% 230.32/41.61  
% 230.32/41.61  Begin of proof
% 230.32/41.61  | 
% 230.32/41.61  | BETA: splitting (49) gives:
% 230.32/41.61  | 
% 230.32/41.61  | Case 1:
% 230.32/41.61  | | 
% 230.32/41.61  | |   (80)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 230.32/41.61  | |           e3)
% 230.32/41.61  | | 
% 230.32/41.61  | | BETA: splitting (80) gives:
% 230.32/41.61  | | 
% 230.32/41.61  | | Case 1:
% 230.32/41.61  | | | 
% 230.32/41.61  | | |   (81)  all_57_1 = e3 & op(e3, e2) = e3
% 230.32/41.61  | | | 
% 230.32/41.61  | | | ALPHA: (81) implies:
% 230.32/41.61  | | |   (82)  all_57_1 = e3
% 230.32/41.61  | | | 
% 230.32/41.61  | | | BETA: splitting (48) gives:
% 230.32/41.61  | | | 
% 230.32/41.61  | | | Case 1:
% 230.32/41.61  | | | | 
% 230.32/41.61  | | | |   (83)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1)
% 230.32/41.61  | | | |           = e3)
% 230.32/41.61  | | | | 
% 230.32/41.61  | | | | BETA: splitting (83) gives:
% 230.32/41.61  | | | | 
% 230.32/41.61  | | | | Case 1:
% 230.32/41.61  | | | | | 
% 230.32/41.61  | | | | |   (84)  all_57_4 = e3 & op(e3, e1) = e3
% 230.32/41.61  | | | | | 
% 230.32/41.61  | | | | | ALPHA: (84) implies:
% 230.32/41.61  | | | | |   (85)  all_57_4 = e3
% 230.32/41.61  | | | | | 
% 230.32/41.61  | | | | | REF_CLOSE: (8), (10), (17), (22), (25), (28), (31), (33), (40), (46),
% 230.32/41.61  | | | | |            (63), (82), (85) are inconsistent by sub-proof #1806.
% 230.32/41.61  | | | | | 
% 230.32/41.61  | | | | Case 2:
% 230.32/41.61  | | | | | 
% 230.32/41.61  | | | | |   (86)  all_57_5 = e3 & op(e2, e1) = e3
% 230.32/41.61  | | | | | 
% 230.32/41.61  | | | | | ALPHA: (86) implies:
% 230.32/41.61  | | | | |   (87)  all_57_5 = e3
% 230.32/41.61  | | | | | 
% 230.32/41.61  | | | | | BETA: splitting (12) gives:
% 230.32/41.61  | | | | | 
% 230.32/41.61  | | | | | Case 1:
% 230.32/41.61  | | | | | | 
% 230.32/41.61  | | | | | |   (88)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1,
% 230.32/41.61  | | | | | |             e2) = e3)
% 230.32/41.61  | | | | | | 
% 230.32/41.61  | | | | | | BETA: splitting (88) gives:
% 230.32/41.61  | | | | | | 
% 230.32/41.61  | | | | | | Case 1:
% 230.32/41.61  | | | | | | | 
% 230.32/41.61  | | | | | | |   (89)  all_57_6 = e3 & op(e1, e3) = e3
% 230.32/41.61  | | | | | | | 
% 230.32/41.61  | | | | | | | ALPHA: (89) implies:
% 230.32/41.61  | | | | | | |   (90)  all_57_6 = e3
% 230.32/41.61  | | | | | | | 
% 230.32/41.61  | | | | | | | BETA: splitting (67) gives:
% 230.32/41.61  | | | | | | | 
% 230.32/41.61  | | | | | | | Case 1:
% 230.32/41.61  | | | | | | | | 
% 230.32/41.61  | | | | | | | |   (91)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 &
% 230.32/41.61  | | | | | | | |           op(e2, e3) = e2)
% 230.32/41.61  | | | | | | | | 
% 230.32/41.61  | | | | | | | | BETA: splitting (91) gives:
% 230.32/41.61  | | | | | | | | 
% 230.32/41.61  | | | | | | | | Case 1:
% 230.32/41.61  | | | | | | | | | 
% 230.32/41.61  | | | | | | | | |   (92)  all_57_0 = e2 & op(e3, e3) = e2
% 230.32/41.61  | | | | | | | | | 
% 230.32/41.61  | | | | | | | | | ALPHA: (92) implies:
% 230.32/41.61  | | | | | | | | |   (93)  op(e3, e3) = e2
% 230.32/41.61  | | | | | | | | | 
% 230.32/41.61  | | | | | | | | | REF_CLOSE: (10), (28), (33), (93) are inconsistent by
% 230.32/41.61  | | | | | | | | |            sub-proof #2490.
% 230.32/41.61  | | | | | | | | | 
% 230.32/41.61  | | | | | | | | Case 2:
% 230.32/41.61  | | | | | | | | | 
% 230.32/41.61  | | | | | | | | |   (94)  all_57_2 = e2 & op(e2, e3) = e2
% 230.32/41.61  | | | | | | | | | 
% 230.32/41.61  | | | | | | | | | ALPHA: (94) implies:
% 230.32/41.61  | | | | | | | | |   (95)  all_57_2 = e2
% 230.32/41.61  | | | | | | | | | 
% 230.32/41.61  | | | | | | | | | BETA: splitting (4) gives:
% 230.32/41.61  | | | | | | | | | 
% 230.32/41.61  | | | | | | | | | Case 1:
% 230.32/41.61  | | | | | | | | | | 
% 230.32/41.61  | | | | | | | | | |   (96)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 &
% 230.32/41.61  | | | | | | | | | |           op(e2, e2) = e1)
% 230.32/41.61  | | | | | | | | | | 
% 230.32/41.61  | | | | | | | | | | BETA: splitting (96) gives:
% 230.32/41.61  | | | | | | | | | | 
% 230.32/41.61  | | | | | | | | | | Case 1:
% 230.32/41.61  | | | | | | | | | | | 
% 230.32/41.61  | | | | | | | | | | |   (97)  all_57_2 = e1 & op(e2, e3) = e1
% 230.32/41.61  | | | | | | | | | | | 
% 230.32/41.61  | | | | | | | | | | | ALPHA: (97) implies:
% 230.32/41.61  | | | | | | | | | | |   (98)  all_57_2 = e1
% 230.32/41.61  | | | | | | | | | | | 
% 230.32/41.61  | | | | | | | | | | | REF_CLOSE: (10), (28), (31), (33), (40), (46), (63), (67),
% 230.32/41.61  | | | | | | | | | | |            (70), (90), (98) are inconsistent by sub-proof
% 230.32/41.61  | | | | | | | | | | |            #2459.
% 230.32/41.61  | | | | | | | | | | | 
% 230.32/41.61  | | | | | | | | | | Case 2:
% 230.32/41.61  | | | | | | | | | | | 
% 230.32/41.61  | | | | | | | | | | |   (99)  all_57_3 = e1 & op(e2, e2) = e1
% 230.32/41.61  | | | | | | | | | | | 
% 230.32/41.61  | | | | | | | | | | | ALPHA: (99) implies:
% 230.32/41.61  | | | | | | | | | | |   (100)  all_57_3 = e1
% 230.32/41.61  | | | | | | | | | | |   (101)  op(e2, e2) = e1
% 230.32/41.61  | | | | | | | | | | | 
% 230.32/41.61  | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (10), (12), (14), (15), (28),
% 230.32/41.61  | | | | | | | | | | |            (31), (33), (35), (39), (40), (46), (49), (53),
% 230.32/41.61  | | | | | | | | | | |            (60), (62), (63), (64), (67), (70), (71), (76),
% 230.32/41.61  | | | | | | | | | | |            (82), (87), (90), (100), (101) are inconsistent by
% 230.32/41.61  | | | | | | | | | | |            sub-proof #1770.
% 230.32/41.61  | | | | | | | | | | | 
% 230.32/41.61  | | | | | | | | | | End of split
% 230.32/41.61  | | | | | | | | | | 
% 230.32/41.61  | | | | | | | | | Case 2:
% 230.32/41.61  | | | | | | | | | | 
% 230.32/41.61  | | | | | | | | | |   (102)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1
% 230.32/41.61  | | | | | | | | | |            & op(e2, e0) = e1)
% 230.32/41.61  | | | | | | | | | | 
% 230.32/41.61  | | | | | | | | | | BETA: splitting (102) gives:
% 230.32/41.61  | | | | | | | | | | 
% 230.32/41.61  | | | | | | | | | | Case 1:
% 230.32/41.61  | | | | | | | | | | | 
% 230.32/41.61  | | | | | | | | | | |   (103)  all_57_5 = e1 & op(e2, e1) = e1
% 230.32/41.61  | | | | | | | | | | | 
% 230.32/41.61  | | | | | | | | | | | REF_CLOSE: (8), (87), (103) are inconsistent by sub-proof
% 230.32/41.61  | | | | | | | | | | |            #2376.
% 230.32/41.61  | | | | | | | | | | | 
% 230.32/41.61  | | | | | | | | | | Case 2:
% 230.32/41.61  | | | | | | | | | | | 
% 230.32/41.61  | | | | | | | | | | |   (104)  all_57_10 = e1 & op(e2, e0) = e1
% 230.32/41.61  | | | | | | | | | | | 
% 230.32/41.61  | | | | | | | | | | | ALPHA: (104) implies:
% 230.32/41.61  | | | | | | | | | | |   (105)  all_57_10 = e1
% 230.32/41.61  | | | | | | | | | | | 
% 230.32/41.61  | | | | | | | | | | | BETA: splitting (62) gives:
% 230.32/41.61  | | | | | | | | | | | 
% 230.32/41.61  | | | | | | | | | | | Case 1:
% 230.32/41.61  | | | | | | | | | | | | 
% 230.32/41.61  | | | | | | | | | | | |   (106)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 230.32/41.61  | | | | | | | | | | | |            & op(e2, e2) = e0)
% 230.32/41.61  | | | | | | | | | | | | 
% 230.32/41.61  | | | | | | | | | | | | BETA: splitting (106) gives:
% 230.32/41.61  | | | | | | | | | | | | 
% 230.32/41.61  | | | | | | | | | | | | Case 1:
% 230.32/41.61  | | | | | | | | | | | | | 
% 230.32/41.61  | | | | | | | | | | | | |   (107)  all_57_2 = e0 & op(e2, e3) = e0
% 230.32/41.61  | | | | | | | | | | | | | 
% 230.32/41.61  | | | | | | | | | | | | | ALPHA: (107) implies:
% 230.32/41.61  | | | | | | | | | | | | |   (108)  all_57_2 = e0
% 230.32/41.61  | | | | | | | | | | | | | 
% 230.32/41.61  | | | | | | | | | | | | | COMBINE_EQS: (95), (108) imply:
% 230.32/41.61  | | | | | | | | | | | | |   (109)  e2 = e0
% 230.32/41.61  | | | | | | | | | | | | | 
% 230.32/41.61  | | | | | | | | | | | | | REF_CLOSE: (4), (8), (28), (31), (40), (46), (56), (60),
% 230.32/41.61  | | | | | | | | | | | | |            (63), (74), (95), (109) are inconsistent by
% 230.32/41.61  | | | | | | | | | | | | |            sub-proof #2245.
% 230.32/41.61  | | | | | | | | | | | | | 
% 230.32/41.61  | | | | | | | | | | | | Case 2:
% 230.32/41.61  | | | | | | | | | | | | | 
% 230.32/41.61  | | | | | | | | | | | | |   (110)  all_57_3 = e0 & op(e2, e2) = e0
% 230.32/41.61  | | | | | | | | | | | | | 
% 230.32/41.61  | | | | | | | | | | | | | ALPHA: (110) implies:
% 230.32/41.61  | | | | | | | | | | | | |   (111)  all_57_3 = e0
% 230.32/41.61  | | | | | | | | | | | | | 
% 230.32/41.61  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (10), (12), (14), (15), (28),
% 230.32/41.61  | | | | | | | | | | | | |            (31), (33), (35), (40), (46), (53), (60), (63),
% 230.32/41.61  | | | | | | | | | | | | |            (64), (67), (70), (71), (76), (82), (87), (111)
% 230.32/41.61  | | | | | | | | | | | | |            are inconsistent by sub-proof #1777.
% 230.32/41.61  | | | | | | | | | | | | | 
% 230.32/41.61  | | | | | | | | | | | | End of split
% 230.32/41.61  | | | | | | | | | | | | 
% 230.32/41.61  | | | | | | | | | | | Case 2:
% 230.32/41.61  | | | | | | | | | | | | 
% 230.32/41.61  | | | | | | | | | | | |   (112)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 230.32/41.61  | | | | | | | | | | | |            e0 & op(e2, e0) = e0)
% 230.32/41.61  | | | | | | | | | | | | 
% 230.32/41.61  | | | | | | | | | | | | BETA: splitting (112) gives:
% 230.32/41.61  | | | | | | | | | | | | 
% 230.32/41.61  | | | | | | | | | | | | Case 1:
% 230.32/41.61  | | | | | | | | | | | | | 
% 230.32/41.61  | | | | | | | | | | | | |   (113)  all_57_5 = e0 & op(e2, e1) = e0
% 230.32/41.61  | | | | | | | | | | | | | 
% 230.32/41.61  | | | | | | | | | | | | | REF_CLOSE: (31), (87), (113) are inconsistent by sub-proof
% 230.32/41.61  | | | | | | | | | | | | |            #2414.
% 230.32/41.61  | | | | | | | | | | | | | 
% 230.32/41.61  | | | | | | | | | | | | Case 2:
% 230.32/41.61  | | | | | | | | | | | | | 
% 230.32/41.61  | | | | | | | | | | | | |   (114)  all_57_10 = e0 & op(e2, e0) = e0
% 230.32/41.61  | | | | | | | | | | | | | 
% 230.32/41.61  | | | | | | | | | | | | | REF_CLOSE: (46), (105), (114) are inconsistent by sub-proof
% 230.32/41.61  | | | | | | | | | | | | |            #1332.
% 230.32/41.61  | | | | | | | | | | | | | 
% 230.32/41.61  | | | | | | | | | | | | End of split
% 230.32/41.61  | | | | | | | | | | | | 
% 230.32/41.61  | | | | | | | | | | | End of split
% 230.32/41.61  | | | | | | | | | | | 
% 230.32/41.61  | | | | | | | | | | End of split
% 230.32/41.61  | | | | | | | | | | 
% 230.32/41.61  | | | | | | | | | End of split
% 230.32/41.61  | | | | | | | | | 
% 230.32/41.61  | | | | | | | | End of split
% 230.32/41.61  | | | | | | | | 
% 230.32/41.61  | | | | | | | Case 2:
% 230.32/41.61  | | | | | | | | 
% 230.32/41.61  | | | | | | | |   (115)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 &
% 230.32/41.61  | | | | | | | |            op(e0, e3) = e2)
% 230.32/41.61  | | | | | | | | 
% 230.32/41.61  | | | | | | | | BETA: splitting (115) gives:
% 230.32/41.61  | | | | | | | | 
% 230.32/41.61  | | | | | | | | Case 1:
% 230.32/41.61  | | | | | | | | | 
% 230.32/41.61  | | | | | | | | |   (116)  all_57_6 = e2 & op(e1, e3) = e2
% 230.32/41.61  | | | | | | | | | 
% 230.32/41.61  | | | | | | | | | REF_CLOSE: (28), (90), (116) are inconsistent by sub-proof
% 230.32/41.61  | | | | | | | | |            #2012.
% 230.32/41.61  | | | | | | | | | 
% 230.32/41.61  | | | | | | | | Case 2:
% 230.32/41.61  | | | | | | | | | 
% 230.32/41.61  | | | | | | | | |   (117)  all_57_12 = e2 & op(e0, e3) = e2
% 230.32/41.61  | | | | | | | | | 
% 230.32/41.61  | | | | | | | | | ALPHA: (117) implies:
% 230.32/41.61  | | | | | | | | |   (118)  all_57_12 = e2
% 230.32/41.61  | | | | | | | | | 
% 230.32/41.61  | | | | | | | | | REF_CLOSE: (5), (8), (10), (28), (31), (33), (40), (46), (63),
% 230.32/41.61  | | | | | | | | |            (67), (70), (90), (118) are inconsistent by
% 230.32/41.61  | | | | | | | | |            sub-proof #2116.
% 230.32/41.61  | | | | | | | | | 
% 230.32/41.61  | | | | | | | | End of split
% 230.32/41.61  | | | | | | | | 
% 230.32/41.61  | | | | | | | End of split
% 230.32/41.61  | | | | | | | 
% 230.32/41.61  | | | | | | Case 2:
% 230.32/41.61  | | | | | | | 
% 230.32/41.61  | | | | | | |   (119)  all_57_7 = e3 & op(e1, e2) = e3
% 230.32/41.61  | | | | | | | 
% 230.32/41.61  | | | | | | | ALPHA: (119) implies:
% 230.32/41.61  | | | | | | |   (120)  all_57_7 = e3
% 230.32/41.61  | | | | | | | 
% 230.32/41.61  | | | | | | | REF_CLOSE: (7), (8), (10), (28), (31), (39), (40), (45), (46),
% 230.32/41.61  | | | | | | |            (63), (76), (82), (120) are inconsistent by sub-proof
% 230.32/41.61  | | | | | | |            #1167.
% 230.32/41.61  | | | | | | | 
% 230.32/41.61  | | | | | | End of split
% 230.32/41.61  | | | | | | 
% 230.32/41.61  | | | | | Case 2:
% 230.32/41.61  | | | | | | 
% 230.32/41.61  | | | | | |   (121)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 &
% 230.32/41.61  | | | | | |            op(e1, e0) = e3)
% 230.32/41.61  | | | | | | 
% 230.32/41.61  | | | | | | REF_CLOSE: (8), (10), (14), (15), (28), (31), (35), (40), (46),
% 230.32/41.61  | | | | | |            (53), (63), (64), (71), (121) are inconsistent by
% 230.32/41.61  | | | | | |            sub-proof #1786.
% 230.32/41.61  | | | | | | 
% 230.32/41.61  | | | | | End of split
% 230.32/41.61  | | | | | 
% 230.32/41.61  | | | | End of split
% 230.32/41.61  | | | | 
% 230.32/41.61  | | | Case 2:
% 230.32/41.61  | | | | 
% 230.32/41.61  | | | |   (122)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0,
% 230.32/41.61  | | | |              e1) = e3)
% 230.32/41.61  | | | | 
% 230.32/41.61  | | | | REF_CLOSE: (8), (10), (14), (15), (28), (31), (35), (36), (40), (46),
% 230.32/41.61  | | | |            (52), (53), (63), (122) are inconsistent by sub-proof #1794.
% 230.32/41.61  | | | | 
% 230.32/41.61  | | | End of split
% 230.32/41.61  | | | 
% 230.32/41.61  | | Case 2:
% 230.32/41.61  | | | 
% 230.32/41.61  | | |   (123)  all_57_3 = e3 & op(e2, e2) = e3
% 230.32/41.61  | | | 
% 230.32/41.61  | | | ALPHA: (123) implies:
% 230.32/41.61  | | |   (124)  all_57_3 = e3
% 230.32/41.61  | | | 
% 230.32/41.61  | | | REF_CLOSE: (28), (74), (124) are inconsistent by sub-proof #1166.
% 230.32/41.61  | | | 
% 230.32/41.61  | | End of split
% 230.32/41.61  | | 
% 230.32/41.61  | Case 2:
% 230.32/41.61  | | 
% 230.32/41.61  | |   (125)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 230.32/41.61  | |            e3)
% 230.32/41.61  | | 
% 230.32/41.61  | | BETA: splitting (125) gives:
% 230.32/41.61  | | 
% 230.32/41.61  | | Case 1:
% 230.32/41.61  | | | 
% 230.32/41.61  | | |   (126)  all_57_7 = e3 & op(e1, e2) = e3
% 230.32/41.61  | | | 
% 230.32/41.61  | | | ALPHA: (126) implies:
% 230.32/41.61  | | |   (127)  all_57_7 = e3
% 230.32/41.61  | | |   (128)  op(e1, e2) = e3
% 230.32/41.61  | | | 
% 230.32/41.61  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 230.32/41.61  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 230.32/41.61  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 230.32/41.61  | | |            (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 230.32/41.61  | | |            (43), (44), (45), (46), (47), (48), (50), (51), (52), (53),
% 230.32/41.61  | | |            (54), (55), (56), (57), (58), (59), (60), (61), (62), (63),
% 230.32/41.61  | | |            (64), (65), (66), (67), (68), (69), (70), (71), (72), (73),
% 230.32/41.61  | | |            (74), (75), (76), (77), (78), (79), (127), (128) are
% 230.32/41.61  | | |            inconsistent by sub-proof #1074.
% 230.32/41.61  | | | 
% 230.32/41.61  | | Case 2:
% 230.32/41.61  | | | 
% 230.32/41.61  | | |   (129)  all_57_13 = e3 & op(e0, e2) = e3
% 230.32/41.61  | | | 
% 230.32/41.61  | | | ALPHA: (129) implies:
% 230.32/41.61  | | |   (130)  all_57_13 = e3
% 230.32/41.61  | | | 
% 230.32/41.61  | | | REF_CLOSE: (8), (10), (28), (31), (35), (36), (40), (46), (50), (52),
% 230.32/41.61  | | |            (53), (63), (130) are inconsistent by sub-proof #1792.
% 230.32/41.61  | | | 
% 230.32/41.61  | | End of split
% 230.32/41.61  | | 
% 230.32/41.61  | End of split
% 230.32/41.61  | 
% 230.32/41.61  End of proof
% 230.32/41.61  
% 230.32/41.61  Sub-proof #1074 shows that the following formulas are inconsistent:
% 230.32/41.61  ----------------------------------------------------------------
% 230.32/41.61    (1)  op(e0, e1) = all_53_11
% 230.32/41.61    (2)   ~ (all_53_6 = all_53_14)
% 230.32/41.61    (3)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 230.32/41.61    (4)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.32/41.61         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.32/41.61    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.32/41.61         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.32/41.61    (6)   ~ (all_53_8 = all_53_12)
% 230.32/41.61    (7)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.32/41.61         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.32/41.61    (8)   ~ (e3 = e1)
% 230.32/41.61    (9)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.32/41.61         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.32/41.61    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.32/41.61            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.32/41.61    (11)  op(e1, e2) = e3
% 230.32/41.61    (12)  all_22_2 = e3
% 230.32/41.62    (13)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.32/41.62          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.32/41.62    (14)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 230.32/41.62            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 230.32/41.62              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 230.32/41.62    (15)   ~ (all_6_2 = e3)
% 230.32/41.62    (16)  op(e1, e1) = all_6_2
% 230.32/41.62    (17)  all_34_2 = all_6_2
% 230.32/41.62    (18)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.32/41.62          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.32/41.62    (19)   ~ (all_53_13 = e2)
% 230.32/41.62    (20)   ~ (all_53_4 = all_53_12)
% 230.32/41.62    (21)   ~ (all_53_7 = e2)
% 230.32/41.62    (22)   ~ (all_53_8 = all_53_9)
% 230.32/41.62    (23)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.32/41.62          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.32/41.62    (24)   ~ (all_53_9 = all_53_11)
% 230.32/41.62    (25)   ~ (all_53_9 = all_6_2)
% 230.32/41.62    (26)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.32/41.62          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.32/41.62    (27)   ~ (all_53_14 = all_6_2)
% 230.32/41.62    (28)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 230.32/41.62          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.32/41.62    (29)   ~ (e3 = e2)
% 230.32/41.62    (30)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 230.32/41.62    (31)  op(e1, e0) = all_53_14
% 230.32/41.62    (32)   ~ (e3 = e0)
% 230.32/41.62    (33)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.32/41.62          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.32/41.62    (34)  op(e3, e3) = e3
% 230.32/41.62    (35)   ~ (all_53_8 = all_6_2)
% 230.32/41.62    (36)  all_57_15 = e3
% 230.32/41.62    (37)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.32/41.62          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.32/41.62            e1)
% 230.32/41.62    (38)  all_55_6 = all_53_9
% 230.32/41.62    (39)  op(e3, e2) = all_53_4
% 230.32/41.62    (40)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.32/41.62          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.32/41.62    (41)   ~ (e2 = e0)
% 230.32/41.62    (42)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 230.32/41.62            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 230.32/41.62            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 230.32/41.62            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 230.32/41.62              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 230.32/41.62            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 230.32/41.62            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 230.32/41.62              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 230.32/41.62              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 230.32/41.62            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 230.32/41.62            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 230.32/41.62            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 230.32/41.62              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 230.32/41.62              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 230.32/41.62            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 230.32/41.62              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 230.32/41.62            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 230.32/41.62            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 230.32/41.62              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 230.32/41.62              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 230.32/41.62            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 230.32/41.62            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 230.32/41.62    (43)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 230.32/41.62            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 230.32/41.62              e3) = all_12_1 & $i(all_12_1))
% 230.32/41.62    (44)   ~ (all_53_9 = e2)
% 230.32/41.62    (45)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.32/41.62          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.32/41.62    (46)  op(e2, e2) = e2
% 230.32/41.62    (47)   ~ (e1 = e0)
% 230.32/41.62    (48)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 230.32/41.62            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 230.32/41.62              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 230.32/41.62    (49)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 230.32/41.62          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 230.32/41.62    (50)  op(e0, e0) = e3
% 230.32/41.62    (51)  op(e0, e2) = all_53_7
% 230.32/41.62    (52)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.32/41.62          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.32/41.62            e2)
% 230.32/41.62    (53)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.32/41.62              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.32/41.62                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.32/41.62                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.32/41.62    (54)  all_55_10 = all_6_2
% 230.32/41.62    (55)  op(e2, e0) = all_53_13
% 230.32/41.62    (56)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.32/41.62          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.32/41.62    (57)  all_38_2 = all_6_2
% 230.32/41.62    (58)   ~ (all_53_12 = e3)
% 230.32/41.62    (59)   ~ (all_53_4 = e2)
% 230.32/41.62    (60)  all_57_7 = e3
% 230.32/41.62    (61)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.32/41.62          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.32/41.62    (62)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.32/41.62          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.32/41.62    (63)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.32/41.62          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 230.32/41.62    (64)   ~ (e2 = e1)
% 230.32/41.62    (65)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.32/41.62          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.32/41.62    (66)  op(e2, e1) = all_53_9
% 230.32/41.62    (67)  op(e1, e2) = all_53_6
% 230.32/41.62    (68)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.32/41.62          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.32/41.62    (69)  all_24_2 = all_6_2
% 230.32/41.62    (70)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.32/41.62          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.32/41.62    (71)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.32/41.62          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.32/41.62    (72)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.32/41.62          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.32/41.62    (73)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.32/41.62          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.32/41.62    (74)   ~ (all_22_2 = e3) | ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 &
% 230.32/41.62            op(e0, e3) = all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 =
% 230.32/41.62              e2) & op(e0, e3) = all_22_1 & $i(all_22_1))
% 230.32/41.62    (75)  all_57_3 = e2
% 230.32/41.62    (76)  op(e3, e1) = all_53_8
% 230.32/41.62    (77)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.32/41.62          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.32/41.62    (78)   ~ (all_34_2 = e0) | ( ~ (all_34_0 = e3) & op(all_34_1, e1) = all_34_0 &
% 230.32/41.62            op(e1, e0) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 230.32/41.62              e2) & op(e1, e0) = all_34_1 & $i(all_34_1))
% 230.32/41.62    (79)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.32/41.62          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.32/41.62    (80)  op(e3, e0) = all_53_12
% 230.32/41.62  
% 230.32/41.62  Begin of proof
% 230.32/41.62  | 
% 230.32/41.62  | BETA: splitting (56) gives:
% 230.32/41.62  | 
% 230.32/41.62  | Case 1:
% 230.32/41.62  | | 
% 230.32/41.62  | |   (81)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 230.32/41.62  | |           e3)
% 230.32/41.62  | | 
% 230.32/41.62  | | BETA: splitting (81) gives:
% 230.32/41.62  | | 
% 230.32/41.62  | | Case 1:
% 230.32/41.62  | | | 
% 230.32/41.62  | | |   (82)  all_57_2 = e3 & op(e2, e3) = e3
% 230.32/41.62  | | | 
% 230.32/41.62  | | | ALPHA: (82) implies:
% 230.32/41.62  | | |   (83)  all_57_2 = e3
% 230.32/41.62  | | | 
% 230.32/41.62  | | | REF_CLOSE: (4), (7), (8), (10), (15), (16), (18), (23), (26), (29), (32),
% 230.32/41.62  | | |            (34), (36), (37), (40), (41), (47), (49), (52), (53), (60),
% 230.32/41.62  | | |            (61), (63), (64), (83) are inconsistent by sub-proof #1330.
% 230.32/41.62  | | | 
% 230.32/41.62  | | Case 2:
% 230.32/41.62  | | | 
% 230.32/41.62  | | |   (84)  all_57_3 = e3 & op(e2, e2) = e3
% 230.32/41.62  | | | 
% 230.32/41.62  | | | ALPHA: (84) implies:
% 230.32/41.62  | | |   (85)  all_57_3 = e3
% 230.32/41.62  | | | 
% 230.32/41.62  | | | REF_CLOSE: (29), (75), (85) are inconsistent by sub-proof #1166.
% 230.32/41.62  | | | 
% 230.32/41.62  | | End of split
% 230.32/41.62  | | 
% 230.32/41.62  | Case 2:
% 230.32/41.62  | | 
% 230.32/41.62  | |   (86)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 230.32/41.62  | |           e3)
% 230.32/41.62  | | 
% 230.32/41.62  | | BETA: splitting (86) gives:
% 230.32/41.62  | | 
% 230.32/41.62  | | Case 1:
% 230.32/41.62  | | | 
% 230.32/41.62  | | |   (87)  all_57_5 = e3 & op(e2, e1) = e3
% 230.32/41.62  | | | 
% 230.32/41.62  | | | ALPHA: (87) implies:
% 230.32/41.62  | | |   (88)  all_57_5 = e3
% 230.32/41.62  | | |   (89)  op(e2, e1) = e3
% 230.32/41.62  | | | 
% 230.32/41.62  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 230.32/41.62  | | |            (13), (14), (16), (17), (18), (19), (20), (21), (22), (23),
% 230.32/41.62  | | |            (24), (25), (26), (27), (28), (30), (31), (32), (33), (34),
% 230.32/41.62  | | |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44),
% 230.32/41.62  | | |            (45), (46), (47), (48), (50), (51), (52), (53), (54), (55),
% 230.32/41.62  | | |            (56), (57), (58), (59), (60), (61), (62), (63), (64), (65),
% 230.32/41.62  | | |            (66), (67), (68), (69), (70), (71), (72), (73), (74), (75),
% 230.32/41.62  | | |            (76), (77), (78), (79), (80), (88), (89) are inconsistent by
% 230.32/41.62  | | |            sub-proof #1075.
% 230.32/41.62  | | | 
% 230.32/41.62  | | Case 2:
% 230.32/41.62  | | | 
% 230.32/41.62  | | |   (90)  all_57_10 = e3 & op(e2, e0) = e3
% 230.32/41.62  | | | 
% 230.32/41.62  | | | ALPHA: (90) implies:
% 230.32/41.62  | | |   (91)  all_57_10 = e3
% 230.32/41.62  | | | 
% 230.32/41.62  | | | REF_CLOSE: (8), (10), (29), (32), (36), (41), (47), (50), (53), (64),
% 230.32/41.62  | | |            (65), (72), (91) are inconsistent by sub-proof #1746.
% 230.32/41.62  | | | 
% 230.32/41.62  | | End of split
% 230.32/41.62  | | 
% 230.32/41.62  | End of split
% 230.32/41.62  | 
% 230.32/41.62  End of proof
% 230.32/41.62  
% 230.32/41.62  Sub-proof #1075 shows that the following formulas are inconsistent:
% 230.32/41.62  ----------------------------------------------------------------
% 230.32/41.62    (1)  op(e0, e1) = all_53_11
% 230.32/41.62    (2)   ~ (all_53_6 = all_53_14)
% 230.32/41.62    (3)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 230.32/41.62    (4)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.32/41.62         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.32/41.62    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.32/41.62         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.32/41.62    (6)  op(e2, e1) = e3
% 230.32/41.62    (7)   ~ (all_53_8 = all_53_12)
% 230.32/41.62    (8)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.32/41.62         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.32/41.62    (9)   ~ (e3 = e1)
% 230.32/41.62    (10)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.32/41.62          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.32/41.62    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.32/41.62            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.32/41.62    (12)  op(e1, e2) = e3
% 230.32/41.62    (13)  all_22_2 = e3
% 230.32/41.62    (14)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.32/41.62          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.32/41.62    (15)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 230.32/41.62            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 230.32/41.62              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 230.32/41.62    (16)  op(e1, e1) = all_6_2
% 230.32/41.62    (17)  all_34_2 = all_6_2
% 230.32/41.62    (18)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.32/41.62          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.32/41.62    (19)   ~ (all_53_13 = e2)
% 230.32/41.62    (20)   ~ (all_53_4 = all_53_12)
% 230.32/41.62    (21)   ~ (all_53_7 = e2)
% 230.32/41.62    (22)   ~ (all_53_8 = all_53_9)
% 230.32/41.62    (23)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.32/41.62          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.32/41.62    (24)   ~ (all_53_9 = all_53_11)
% 230.32/41.62    (25)   ~ (all_53_9 = all_6_2)
% 230.32/41.62    (26)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.32/41.62          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.32/41.62    (27)   ~ (all_53_14 = all_6_2)
% 230.32/41.62    (28)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 230.32/41.62          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.32/41.62    (29)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 230.32/41.62    (30)  op(e1, e0) = all_53_14
% 230.32/41.62    (31)   ~ (e3 = e0)
% 230.32/41.62    (32)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.32/41.62          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.32/41.62    (33)  op(e3, e3) = e3
% 230.32/41.62    (34)   ~ (all_53_8 = all_6_2)
% 230.32/41.62    (35)  all_57_15 = e3
% 230.32/41.62    (36)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.32/41.62          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.32/41.62            e1)
% 230.32/41.62    (37)  all_57_5 = e3
% 230.32/41.62    (38)  all_55_6 = all_53_9
% 230.32/41.62    (39)  op(e3, e2) = all_53_4
% 230.32/41.62    (40)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.32/41.62          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.32/41.62    (41)   ~ (e2 = e0)
% 230.32/41.62    (42)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 230.32/41.62            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 230.32/41.62            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 230.32/41.62            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 230.32/41.62              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 230.32/41.62            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 230.32/41.62            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 230.32/41.62              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 230.32/41.62              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 230.32/41.62            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 230.32/41.62            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 230.32/41.62            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 230.32/41.62              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 230.32/41.62              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 230.32/41.62            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 230.32/41.62              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 230.32/41.62            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 230.32/41.62            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 230.32/41.62              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 230.32/41.62              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 230.32/41.62            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 230.32/41.62            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 230.32/41.62    (43)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 230.32/41.62            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 230.32/41.62              e3) = all_12_1 & $i(all_12_1))
% 230.32/41.62    (44)   ~ (all_53_9 = e2)
% 230.32/41.62    (45)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.32/41.62          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.32/41.62    (46)  op(e2, e2) = e2
% 230.32/41.62    (47)   ~ (e1 = e0)
% 230.32/41.62    (48)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 230.32/41.62            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 230.32/41.62              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 230.32/41.62    (49)  op(e0, e0) = e3
% 230.32/41.62    (50)  op(e0, e2) = all_53_7
% 230.32/41.62    (51)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.32/41.62          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.32/41.62            e2)
% 230.32/41.62    (52)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.32/41.62              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.32/41.62                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.32/41.62                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.32/41.62    (53)  all_55_10 = all_6_2
% 230.32/41.62    (54)  op(e2, e0) = all_53_13
% 230.32/41.62    (55)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.32/41.62          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.32/41.62    (56)  all_38_2 = all_6_2
% 230.32/41.62    (57)   ~ (all_53_12 = e3)
% 230.32/41.62    (58)   ~ (all_53_4 = e2)
% 230.32/41.62    (59)  all_57_7 = e3
% 230.32/41.62    (60)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.32/41.62          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.32/41.62    (61)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.32/41.62          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.32/41.62    (62)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.32/41.62          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 230.32/41.62    (63)   ~ (e2 = e1)
% 230.32/41.62    (64)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.32/41.62          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.32/41.62    (65)  op(e2, e1) = all_53_9
% 230.32/41.62    (66)  op(e1, e2) = all_53_6
% 230.32/41.62    (67)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.32/41.62          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.32/41.62    (68)  all_24_2 = all_6_2
% 230.32/41.62    (69)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.32/41.62          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.32/41.62    (70)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.32/41.62          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.32/41.62    (71)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.32/41.62          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.32/41.62    (72)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.32/41.62          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.32/41.62    (73)   ~ (all_22_2 = e3) | ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 &
% 230.32/41.62            op(e0, e3) = all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 =
% 230.32/41.62              e2) & op(e0, e3) = all_22_1 & $i(all_22_1))
% 230.32/41.62    (74)  all_57_3 = e2
% 230.32/41.62    (75)  op(e3, e1) = all_53_8
% 230.32/41.62    (76)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.32/41.62          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.32/41.62    (77)   ~ (all_34_2 = e0) | ( ~ (all_34_0 = e3) & op(all_34_1, e1) = all_34_0 &
% 230.32/41.62            op(e1, e0) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 230.32/41.62              e2) & op(e1, e0) = all_34_1 & $i(all_34_1))
% 230.32/41.62    (78)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.32/41.62          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.32/41.62    (79)  op(e3, e0) = all_53_12
% 230.32/41.62  
% 230.32/41.62  Begin of proof
% 230.32/41.62  | 
% 230.32/41.62  | GROUND_INST: instantiating (11) with all_53_6, e3, e2, e1, simplifying with
% 230.32/41.62  |              (12), (66) gives:
% 230.32/41.62  |   (80)  all_53_6 = e3
% 230.32/41.62  | 
% 230.32/41.62  | GROUND_INST: instantiating (11) with all_53_9, e3, e1, e2, simplifying with
% 230.32/41.62  |              (6), (65) gives:
% 230.32/41.62  |   (81)  all_53_9 = e3
% 230.32/41.62  | 
% 230.32/41.62  | REDUCE: (2), (80) imply:
% 230.32/41.62  |   (82)   ~ (all_53_14 = e3)
% 230.32/41.62  | 
% 230.32/41.62  | SIMP: (82) implies:
% 230.32/41.62  |   (83)   ~ (all_53_14 = e3)
% 230.32/41.62  | 
% 230.32/41.62  | REDUCE: (22), (81) imply:
% 230.32/41.62  |   (84)   ~ (all_53_8 = e3)
% 230.32/41.62  | 
% 230.32/41.62  | REDUCE: (25), (81) imply:
% 230.32/41.62  |   (85)   ~ (all_6_2 = e3)
% 230.32/41.62  | 
% 230.32/41.62  | SIMP: (85) implies:
% 230.32/41.62  |   (86)   ~ (all_6_2 = e3)
% 230.32/41.62  | 
% 230.32/41.62  | REDUCE: (44), (81) imply:
% 230.32/41.62  |   (87)   ~ (e3 = e2)
% 230.32/41.62  | 
% 230.32/41.62  | BETA: splitting (42) gives:
% 230.32/41.62  | 
% 230.32/41.62  | Case 1:
% 230.32/41.62  | | 
% 230.32/41.62  | |   (88)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 230.32/41.62  | |           op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 230.32/41.62  | |           op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3,
% 230.32/41.62  | |             e3) = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 &
% 230.32/41.62  | |           op(e3, e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5)
% 230.32/41.62  | |           & $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1
% 230.32/41.62  | |           & all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 230.32/41.62  | |             all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 230.32/41.62  | |             all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11
% 230.32/41.62  | |           & op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 230.32/41.62  | |           $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 230.32/41.62  | | 
% 230.32/41.62  | | BETA: splitting (88) gives:
% 230.32/41.62  | | 
% 230.32/41.62  | | Case 1:
% 230.32/41.62  | | | 
% 230.32/41.62  | | |   (89)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 230.32/41.62  | | |         op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 230.32/41.62  | | |         op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3,
% 230.32/41.62  | | |           e3) = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 &
% 230.32/41.62  | | |         op(e3, e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5)
% 230.32/41.62  | | |         & $i(all_52_7)
% 230.32/41.62  | | | 
% 230.32/41.62  | | | ALPHA: (89) implies:
% 230.32/41.62  | | |   (90)  op(e3, e0) = all_52_7
% 230.32/41.62  | | |   (91)  op(e3, e1) = all_52_5
% 230.32/41.62  | | |   (92)  op(e3, e2) = all_52_3
% 230.32/41.62  | | |   (93)  op(e3, e3) = all_52_1
% 230.32/41.62  | | |   (94)  op(all_52_7, all_52_7) = e0
% 230.32/41.62  | | |   (95)  op(all_52_1, all_52_1) = e3
% 230.32/41.62  | | | 
% 230.32/41.62  | | | GROUND_INST: instantiating (11) with all_53_12, all_52_7, e0, e3,
% 230.32/41.62  | | |              simplifying with (79), (90) gives:
% 230.32/41.62  | | |   (96)  all_53_12 = all_52_7
% 230.32/41.62  | | | 
% 230.32/41.62  | | | GROUND_INST: instantiating (11) with all_53_8, all_52_5, e1, e3,
% 230.32/41.62  | | |              simplifying with (75), (91) gives:
% 230.32/41.62  | | |   (97)  all_53_8 = all_52_5
% 230.32/41.62  | | | 
% 230.32/41.62  | | | GROUND_INST: instantiating (11) with all_53_4, all_52_3, e2, e3,
% 230.32/41.62  | | |              simplifying with (39), (92) gives:
% 230.32/41.62  | | |   (98)  all_53_4 = all_52_3
% 230.32/41.62  | | | 
% 230.32/41.62  | | | GROUND_INST: instantiating (11) with e3, all_52_1, e3, e3, simplifying
% 230.32/41.62  | | |              with (33), (93) gives:
% 230.32/41.62  | | |   (99)  all_52_1 = e3
% 230.32/41.62  | | | 
% 230.32/41.62  | | | REDUCE: (20), (96), (98) imply:
% 230.32/41.62  | | |   (100)   ~ (all_52_3 = all_52_7)
% 230.32/41.62  | | | 
% 230.32/41.62  | | | REDUCE: (58), (98) imply:
% 230.32/41.62  | | |   (101)   ~ (all_52_3 = e2)
% 230.32/41.62  | | | 
% 230.32/41.62  | | | REDUCE: (7), (96), (97) imply:
% 230.32/41.62  | | |   (102)   ~ (all_52_5 = all_52_7)
% 230.32/41.62  | | | 
% 230.32/41.62  | | | REDUCE: (34), (97) imply:
% 230.32/41.62  | | |   (103)   ~ (all_52_5 = all_6_2)
% 230.32/41.62  | | | 
% 230.32/41.62  | | | REDUCE: (84), (97) imply:
% 230.32/41.62  | | |   (104)   ~ (all_52_5 = e3)
% 230.32/41.62  | | | 
% 230.32/41.62  | | | REDUCE: (57), (96) imply:
% 230.32/41.62  | | |   (105)   ~ (all_52_7 = e3)
% 230.32/41.62  | | | 
% 230.32/41.62  | | | BETA: splitting (73) gives:
% 230.32/41.62  | | | 
% 230.32/41.62  | | | Case 1:
% 230.32/41.62  | | | | 
% 230.32/41.62  | | | |   (106)   ~ (all_22_2 = e3)
% 230.32/41.62  | | | | 
% 230.32/41.62  | | | | REDUCE: (13), (106) imply:
% 230.32/41.62  | | | |   (107)  $false
% 230.32/41.62  | | | | 
% 230.32/41.62  | | | | CLOSE: (107) is inconsistent.
% 230.32/41.62  | | | | 
% 230.32/41.62  | | | Case 2:
% 230.32/41.62  | | | | 
% 230.32/41.62  | | | |   (108)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3)
% 230.32/41.62  | | | |            = all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 =
% 230.32/41.62  | | | |              e2) & op(e0, e3) = all_22_1 & $i(all_22_1))
% 230.32/41.62  | | | | 
% 230.32/41.62  | | | | BETA: splitting (15) gives:
% 230.32/41.62  | | | | 
% 230.32/41.62  | | | | Case 1:
% 230.32/41.62  | | | | | 
% 230.32/41.62  | | | | |   (109)   ~ (all_24_2 = e0)
% 230.32/41.62  | | | | | 
% 230.32/41.62  | | | | | REDUCE: (68), (109) imply:
% 230.32/41.62  | | | | |   (110)   ~ (all_6_2 = e0)
% 230.32/41.62  | | | | | 
% 230.32/41.62  | | | | | BETA: splitting (48) gives:
% 230.32/41.63  | | | | | 
% 230.32/41.63  | | | | | Case 1:
% 230.32/41.63  | | | | | | 
% 230.32/41.63  | | | | | |   (111)   ~ (all_38_2 = e2)
% 230.32/41.63  | | | | | | 
% 230.32/41.63  | | | | | | REDUCE: (56), (111) imply:
% 230.32/41.63  | | | | | |   (112)   ~ (all_6_2 = e2)
% 230.32/41.63  | | | | | | 
% 230.32/41.63  | | | | | | BETA: splitting (3) gives:
% 230.32/41.63  | | | | | | 
% 230.32/41.63  | | | | | | Case 1:
% 230.32/41.63  | | | | | | | 
% 230.32/41.63  | | | | | | |   (113)  all_55_10 = e3
% 230.32/41.63  | | | | | | | 
% 230.32/41.63  | | | | | | | REF_CLOSE: (53), (86), (113) are inconsistent by sub-proof #2500.
% 230.32/41.63  | | | | | | | 
% 230.32/41.63  | | | | | | Case 2:
% 230.32/41.63  | | | | | | | 
% 230.32/41.63  | | | | | | |   (114)   ~ (all_55_10 = e3)
% 230.32/41.63  | | | | | | |   (115)  all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 230.32/41.63  | | | | | | | 
% 230.32/41.63  | | | | | | | BETA: splitting (115) gives:
% 230.32/41.63  | | | | | | | 
% 230.32/41.63  | | | | | | | Case 1:
% 230.32/41.63  | | | | | | | | 
% 230.32/41.63  | | | | | | | |   (116)  all_55_10 = e2
% 230.32/41.63  | | | | | | | | 
% 230.32/41.63  | | | | | | | | REF_CLOSE: (53), (112), (116) are inconsistent by sub-proof
% 230.32/41.63  | | | | | | | |            #2499.
% 230.32/41.63  | | | | | | | | 
% 230.32/41.63  | | | | | | | Case 2:
% 230.32/41.63  | | | | | | | | 
% 230.32/41.63  | | | | | | | |   (117)   ~ (all_55_10 = e2)
% 230.32/41.63  | | | | | | | |   (118)  all_55_10 = e1 | all_55_10 = e0
% 230.32/41.63  | | | | | | | | 
% 230.32/41.63  | | | | | | | | BETA: splitting (118) gives:
% 230.32/41.63  | | | | | | | | 
% 230.32/41.63  | | | | | | | | Case 1:
% 230.32/41.63  | | | | | | | | | 
% 230.32/41.63  | | | | | | | | |   (119)  all_55_10 = e1
% 230.32/41.63  | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | COMBINE_EQS: (53), (119) imply:
% 230.32/41.63  | | | | | | | | |   (120)  all_6_2 = e1
% 230.32/41.63  | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | SIMP: (120) implies:
% 230.32/41.63  | | | | | | | | |   (121)  all_6_2 = e1
% 230.32/41.63  | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | REDUCE: (86), (121) imply:
% 230.32/41.63  | | | | | | | | |   (122)   ~ (e3 = e1)
% 230.32/41.63  | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | REDUCE: (112), (121) imply:
% 230.32/41.63  | | | | | | | | |   (123)   ~ (e2 = e1)
% 230.32/41.63  | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | REDUCE: (16), (121) imply:
% 230.32/41.63  | | | | | | | | |   (124)  op(e1, e1) = e1
% 230.32/41.63  | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | BETA: splitting (78) gives:
% 230.32/41.63  | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | Case 1:
% 230.32/41.63  | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | |   (125)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 230.32/41.63  | | | | | | | | | |            & op(e1, e2) = e2)
% 230.32/41.63  | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | BETA: splitting (125) gives:
% 230.32/41.63  | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | Case 1:
% 230.32/41.63  | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | |   (126)  all_57_6 = e2 & op(e1, e3) = e2
% 230.32/41.63  | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | ALPHA: (126) implies:
% 230.32/41.63  | | | | | | | | | | |   (127)  all_57_6 = e2
% 230.32/41.63  | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | REF_CLOSE: (4), (5), (8), (9), (10), (11), (14), (16), (18),
% 230.32/41.63  | | | | | | | | | | |            (19), (21), (23), (26), (28), (31), (32), (33),
% 230.32/41.63  | | | | | | | | | | |            (35), (36), (37), (40), (41), (43), (46), (47),
% 230.32/41.63  | | | | | | | | | | |            (49), (50), (51), (52), (54), (55), (59), (60),
% 230.32/41.63  | | | | | | | | | | |            (63), (64), (67), (69), (70), (71), (72), (74),
% 230.32/41.63  | | | | | | | | | | |            (76), (78), (86), (87), (90), (91), (93), (94),
% 230.32/41.63  | | | | | | | | | | |            (95), (102), (105), (108), (124), (127) are
% 230.32/41.63  | | | | | | | | | | |            inconsistent by sub-proof #1119.
% 230.32/41.63  | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | Case 2:
% 230.32/41.63  | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | |   (128)  all_57_7 = e2 & op(e1, e2) = e2
% 230.32/41.63  | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | REF_CLOSE: (59), (87), (128) are inconsistent by sub-proof
% 230.32/41.63  | | | | | | | | | | |            #2092.
% 230.32/41.63  | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | End of split
% 230.32/41.63  | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | Case 2:
% 230.32/41.63  | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | |   (129)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2
% 230.32/41.63  | | | | | | | | | |            & op(e1, e0) = e2)
% 230.32/41.63  | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | BETA: splitting (129) gives:
% 230.32/41.63  | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | Case 1:
% 230.32/41.63  | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | |   (130)  all_57_8 = e2 & op(e1, e1) = e2
% 230.32/41.63  | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | ALPHA: (130) implies:
% 230.32/41.63  | | | | | | | | | | |   (131)  op(e1, e1) = e2
% 230.32/41.63  | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | REF_CLOSE: (11), (63), (124), (131) are inconsistent by
% 230.32/41.63  | | | | | | | | | | |            sub-proof #2423.
% 230.32/41.63  | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | Case 2:
% 230.32/41.63  | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | |   (132)  all_57_11 = e2 & op(e1, e0) = e2
% 230.32/41.63  | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | ALPHA: (132) implies:
% 230.32/41.63  | | | | | | | | | | |   (133)  all_57_11 = e2
% 230.32/41.63  | | | | | | | | | | |   (134)  op(e1, e0) = e2
% 230.32/41.63  | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (8), (9), (10), (11), (14),
% 230.32/41.63  | | | | | | | | | | |            (15), (16), (17), (18), (19), (21), (23), (24),
% 230.32/41.63  | | | | | | | | | | |            (25), (26), (27), (28), (29), (30), (31), (32),
% 230.32/41.63  | | | | | | | | | | |            (33), (35), (36), (37), (38), (40), (41), (42),
% 230.32/41.63  | | | | | | | | | | |            (43), (46), (47), (49), (50), (51), (52), (53),
% 230.32/41.63  | | | | | | | | | | |            (54), (55), (59), (60), (61), (62), (63), (64),
% 230.32/41.63  | | | | | | | | | | |            (65), (67), (68), (69), (70), (71), (72), (74),
% 230.32/41.63  | | | | | | | | | | |            (76), (77), (78), (83), (86), (87), (90), (91),
% 230.32/41.63  | | | | | | | | | | |            (92), (93), (94), (95), (100), (102), (105),
% 230.32/41.63  | | | | | | | | | | |            (108), (124), (133), (134) are inconsistent by
% 230.32/41.63  | | | | | | | | | | |            sub-proof #1107.
% 230.32/41.63  | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | End of split
% 230.32/41.63  | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | End of split
% 230.32/41.63  | | | | | | | | | 
% 230.32/41.63  | | | | | | | | Case 2:
% 230.32/41.63  | | | | | | | | | 
% 230.32/41.63  | | | | | | | | |   (135)  all_55_10 = e0
% 230.32/41.63  | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | REF_CLOSE: (53), (110), (135) are inconsistent by sub-proof
% 230.32/41.63  | | | | | | | | |            #2118.
% 230.32/41.63  | | | | | | | | | 
% 230.32/41.63  | | | | | | | | End of split
% 230.32/41.63  | | | | | | | | 
% 230.32/41.63  | | | | | | | End of split
% 230.32/41.63  | | | | | | | 
% 230.32/41.63  | | | | | | End of split
% 230.32/41.63  | | | | | | 
% 230.32/41.63  | | | | | Case 2:
% 230.32/41.63  | | | | | | 
% 230.32/41.63  | | | | | |   (136)  all_38_2 = e2
% 230.32/41.63  | | | | | | 
% 230.32/41.63  | | | | | | COMBINE_EQS: (56), (136) imply:
% 230.32/41.63  | | | | | |   (137)  all_6_2 = e2
% 230.32/41.63  | | | | | | 
% 230.32/41.63  | | | | | | REDUCE: (86), (137) imply:
% 230.32/41.63  | | | | | |   (138)   ~ (e3 = e2)
% 230.32/41.63  | | | | | | 
% 230.32/41.63  | | | | | | REDUCE: (16), (137) imply:
% 230.32/41.63  | | | | | |   (139)  op(e1, e1) = e2
% 230.32/41.63  | | | | | | 
% 230.32/41.63  | | | | | | REF_CLOSE: (4), (5), (8), (9), (10), (11), (14), (16), (18), (19),
% 230.32/41.63  | | | | | |            (21), (23), (26), (28), (31), (32), (33), (35), (36),
% 230.32/41.63  | | | | | |            (37), (40), (41), (43), (46), (47), (49), (50), (51),
% 230.32/41.63  | | | | | |            (52), (54), (55), (59), (60), (62), (63), (64), (67),
% 230.32/41.63  | | | | | |            (69), (70), (71), (72), (74), (76), (78), (86), (87),
% 230.32/41.63  | | | | | |            (90), (93), (94), (95), (105), (108), (139) are
% 230.32/41.63  | | | | | |            inconsistent by sub-proof #1090.
% 230.32/41.63  | | | | | | 
% 230.32/41.63  | | | | | End of split
% 230.32/41.63  | | | | | 
% 230.32/41.63  | | | | Case 2:
% 230.32/41.63  | | | | | 
% 230.32/41.63  | | | | |   (140)  all_24_2 = e0
% 230.32/41.63  | | | | | 
% 230.32/41.63  | | | | | COMBINE_EQS: (68), (140) imply:
% 230.32/41.63  | | | | |   (141)  all_6_2 = e0
% 230.32/41.63  | | | | | 
% 230.32/41.63  | | | | | SIMP: (141) implies:
% 230.32/41.63  | | | | |   (142)  all_6_2 = e0
% 230.32/41.63  | | | | | 
% 230.32/41.63  | | | | | REDUCE: (103), (142) imply:
% 230.32/41.63  | | | | |   (143)   ~ (all_52_5 = e0)
% 230.32/41.63  | | | | | 
% 230.32/41.63  | | | | | REDUCE: (86), (142) imply:
% 230.32/41.63  | | | | |   (144)   ~ (e3 = e0)
% 230.32/41.63  | | | | | 
% 230.32/41.63  | | | | | REDUCE: (16), (142) imply:
% 230.32/41.63  | | | | |   (145)  op(e1, e1) = e0
% 230.32/41.63  | | | | | 
% 230.32/41.63  | | | | | BETA: splitting (10) gives:
% 230.32/41.63  | | | | | 
% 230.32/41.63  | | | | | Case 1:
% 230.32/41.63  | | | | | | 
% 230.32/41.63  | | | | | |   (146)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1,
% 230.32/41.63  | | | | | |              e2) = e0)
% 230.32/41.63  | | | | | | 
% 230.32/41.63  | | | | | | BETA: splitting (146) gives:
% 230.32/41.63  | | | | | | 
% 230.32/41.63  | | | | | | Case 1:
% 230.32/41.63  | | | | | | | 
% 230.32/41.63  | | | | | | |   (147)  all_57_6 = e0 & op(e1, e3) = e0
% 230.32/41.63  | | | | | | | 
% 230.32/41.63  | | | | | | | ALPHA: (147) implies:
% 230.32/41.63  | | | | | | |   (148)  all_57_6 = e0
% 230.32/41.63  | | | | | | | 
% 230.32/41.63  | | | | | | | REF_CLOSE: (4), (5), (8), (9), (10), (11), (14), (16), (18), (19),
% 230.32/41.63  | | | | | | |            (21), (23), (26), (28), (31), (32), (33), (35), (36),
% 230.32/41.63  | | | | | | |            (37), (40), (41), (43), (46), (47), (49), (50), (51),
% 230.32/41.63  | | | | | | |            (52), (54), (55), (59), (60), (62), (63), (64), (67),
% 230.32/41.63  | | | | | | |            (69), (70), (71), (72), (74), (76), (78), (86), (87),
% 230.32/41.63  | | | | | | |            (90), (93), (94), (95), (105), (108), (145), (148) are
% 230.32/41.63  | | | | | | |            inconsistent by sub-proof #1088.
% 230.32/41.63  | | | | | | | 
% 230.32/41.63  | | | | | | Case 2:
% 230.32/41.63  | | | | | | | 
% 230.32/41.63  | | | | | | |   (149)  all_57_7 = e0 & op(e1, e2) = e0
% 230.32/41.63  | | | | | | | 
% 230.32/41.63  | | | | | | | REF_CLOSE: (31), (59), (149) are inconsistent by sub-proof #2042.
% 230.32/41.63  | | | | | | | 
% 230.32/41.63  | | | | | | End of split
% 230.32/41.63  | | | | | | 
% 230.32/41.63  | | | | | Case 2:
% 230.32/41.63  | | | | | | 
% 230.32/41.63  | | | | | |   (150)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 &
% 230.32/41.63  | | | | | |            op(e1, e0) = e0)
% 230.32/41.63  | | | | | | 
% 230.32/41.63  | | | | | | BETA: splitting (150) gives:
% 230.32/41.63  | | | | | | 
% 230.32/41.63  | | | | | | Case 1:
% 230.32/41.63  | | | | | | | 
% 230.32/41.63  | | | | | | |   (151)  all_57_8 = e0 & op(e1, e1) = e0
% 230.32/41.63  | | | | | | | 
% 230.32/41.63  | | | | | | | ALPHA: (151) implies:
% 230.32/41.63  | | | | | | |   (152)  all_57_8 = e0
% 230.32/41.63  | | | | | | | 
% 230.32/41.63  | | | | | | | BETA: splitting (78) gives:
% 230.32/41.63  | | | | | | | 
% 230.32/41.63  | | | | | | | Case 1:
% 230.32/41.63  | | | | | | | | 
% 230.32/41.63  | | | | | | | |   (153)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 &
% 230.32/41.63  | | | | | | | |            op(e1, e2) = e2)
% 230.32/41.63  | | | | | | | | 
% 230.32/41.63  | | | | | | | | BETA: splitting (153) gives:
% 230.32/41.63  | | | | | | | | 
% 230.32/41.63  | | | | | | | | Case 1:
% 230.32/41.63  | | | | | | | | | 
% 230.32/41.63  | | | | | | | | |   (154)  all_57_6 = e2 & op(e1, e3) = e2
% 230.32/41.63  | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | ALPHA: (154) implies:
% 230.32/41.63  | | | | | | | | |   (155)  all_57_6 = e2
% 230.32/41.63  | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | BETA: splitting (72) gives:
% 230.32/41.63  | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | Case 1:
% 230.32/41.63  | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | |   (156)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 230.32/41.63  | | | | | | | | | |            & op(e1, e2) = e1)
% 230.32/41.63  | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | REF_CLOSE: (9), (11), (14), (16), (31), (35), (41), (47),
% 230.32/41.63  | | | | | | | | | |            (52), (63), (64), (71), (86), (87), (155), (156)
% 230.32/41.63  | | | | | | | | | |            are inconsistent by sub-proof #1123.
% 230.32/41.63  | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | Case 2:
% 230.32/41.63  | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | |   (157)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1
% 230.32/41.63  | | | | | | | | | |            & op(e1, e0) = e1)
% 230.32/41.63  | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | BETA: splitting (157) gives:
% 230.32/41.63  | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | Case 1:
% 230.32/41.63  | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | |   (158)  all_57_8 = e1 & op(e1, e1) = e1
% 230.32/41.63  | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | ALPHA: (158) implies:
% 230.32/41.63  | | | | | | | | | | |   (159)  op(e1, e1) = e1
% 230.32/41.63  | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | REF_CLOSE: (4), (5), (8), (9), (10), (11), (14), (16), (18),
% 230.32/41.63  | | | | | | | | | | |            (19), (21), (23), (26), (28), (31), (32), (33),
% 230.32/41.63  | | | | | | | | | | |            (35), (36), (37), (40), (41), (43), (46), (47),
% 230.32/41.63  | | | | | | | | | | |            (49), (50), (51), (52), (54), (55), (59), (60),
% 230.32/41.63  | | | | | | | | | | |            (63), (64), (67), (69), (70), (71), (72), (74),
% 230.32/41.63  | | | | | | | | | | |            (76), (78), (86), (87), (90), (91), (93), (94),
% 230.32/41.63  | | | | | | | | | | |            (95), (102), (105), (108), (155), (159) are
% 230.32/41.63  | | | | | | | | | | |            inconsistent by sub-proof #1119.
% 230.32/41.63  | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | Case 2:
% 230.32/41.63  | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | |   (160)  all_57_11 = e1 & op(e1, e0) = e1
% 230.32/41.63  | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | ALPHA: (160) implies:
% 230.32/41.63  | | | | | | | | | | |   (161)  all_57_11 = e1
% 230.32/41.63  | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | BETA: splitting (64) gives:
% 230.32/41.63  | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | Case 1:
% 230.32/41.63  | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | |   (162)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 230.32/41.63  | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 230.32/41.63  | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | BETA: splitting (162) gives:
% 230.32/41.63  | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | Case 1:
% 230.32/41.63  | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | |   (163)  all_57_9 = e2 & op(e3, e0) = e2
% 230.32/41.63  | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | ALPHA: (163) implies:
% 230.32/41.63  | | | | | | | | | | | | |   (164)  all_57_9 = e2
% 230.32/41.63  | | | | | | | | | | | | |   (165)  op(e3, e0) = e2
% 230.32/41.63  | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | BETA: splitting (52) gives:
% 230.32/41.63  | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | Case 1:
% 230.32/41.63  | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | |   (166)  all_57_15 = e0 & op(e0, e0) = e0
% 230.32/41.63  | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | ALPHA: (166) implies:
% 230.32/41.63  | | | | | | | | | | | | | |   (167)  op(e0, e0) = e0
% 230.32/41.63  | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | REF_CLOSE: (11), (31), (49), (167) are inconsistent by
% 230.32/41.63  | | | | | | | | | | | | | |            sub-proof #2304.
% 230.32/41.63  | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | Case 2:
% 230.32/41.63  | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | |   (168)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 230.32/41.63  | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 230.32/41.63  | | | | | | | | | | | | | |              op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 230.32/41.63  | | | | | | | | | | | | | |                e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 230.32/41.63  | | | | | | | | | | | | | |              e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 230.32/41.63  | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | ALPHA: (168) implies:
% 230.32/41.63  | | | | | | | | | | | | | |   (169)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 230.32/41.63  | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 230.32/41.63  | | | | | | | | | | | | | |              e1) = e0)
% 230.32/41.63  | | | | | | | | | | | | | |   (170)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 230.32/41.63  | | | | | | | | | | | | | |            e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 230.32/41.63  | | | | | | | | | | | | | |              e0) = e0)
% 230.32/41.63  | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | BETA: splitting (26) gives:
% 230.32/41.63  | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | Case 1:
% 230.32/41.63  | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | |   (171)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 230.32/41.63  | | | | | | | | | | | | | | |            & op(e3, e2) = e0)
% 230.32/41.63  | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | BETA: splitting (171) gives:
% 230.32/41.63  | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | Case 1:
% 230.32/41.63  | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | |   (172)  all_57_0 = e0 & op(e3, e3) = e0
% 230.32/41.63  | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | ALPHA: (172) implies:
% 230.32/41.63  | | | | | | | | | | | | | | | |   (173)  op(e3, e3) = e0
% 230.32/41.63  | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | REF_CLOSE: (11), (31), (33), (173) are inconsistent by
% 230.32/41.63  | | | | | | | | | | | | | | | |            sub-proof #2494.
% 230.32/41.63  | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | Case 2:
% 230.32/41.63  | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | |   (174)  all_57_1 = e0 & op(e3, e2) = e0
% 230.32/41.63  | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | ALPHA: (174) implies:
% 230.32/41.63  | | | | | | | | | | | | | | | |   (175)  all_57_1 = e0
% 230.32/41.63  | | | | | | | | | | | | | | | |   (176)  op(e3, e2) = e0
% 230.32/41.63  | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | BETA: splitting (18) gives:
% 230.32/41.63  | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | Case 1:
% 230.32/41.63  | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | |   (177)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 230.32/41.63  | | | | | | | | | | | | | | | | |            & op(e3, e2) = e1)
% 230.32/41.63  | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | BETA: splitting (177) gives:
% 230.32/41.63  | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | Case 1:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | |   (178)  all_57_0 = e1 & op(e3, e3) = e1
% 230.32/41.63  | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | ALPHA: (178) implies:
% 230.32/41.63  | | | | | | | | | | | | | | | | | |   (179)  op(e3, e3) = e1
% 230.32/41.63  | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11), (33), (179) are inconsistent by
% 230.32/41.63  | | | | | | | | | | | | | | | | | |            sub-proof #2495.
% 230.32/41.63  | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | Case 2:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | |   (180)  all_57_1 = e1 & op(e3, e2) = e1
% 230.32/41.63  | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | ALPHA: (180) implies:
% 230.32/41.63  | | | | | | | | | | | | | | | | | |   (181)  all_57_1 = e1
% 230.32/41.63  | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (175), (181) imply:
% 230.32/41.63  | | | | | | | | | | | | | | | | | |   (182)  e1 = e0
% 230.32/41.63  | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | SIMP: (182) implies:
% 230.32/41.63  | | | | | | | | | | | | | | | | | |   (183)  e1 = e0
% 230.32/41.63  | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (161), (183) imply:
% 230.32/41.63  | | | | | | | | | | | | | | | | | |   (184)  all_57_11 = e0
% 230.32/41.63  | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (8), (9), (10), (11), (14), (16), (18),
% 230.32/41.63  | | | | | | | | | | | | | | | | | |            (19), (21), (23), (26), (28), (31), (32), (33),
% 230.32/41.63  | | | | | | | | | | | | | | | | | |            (35), (36), (37), (40), (41), (43), (46), (47),
% 230.32/41.63  | | | | | | | | | | | | | | | | | |            (49), (50), (51), (52), (54), (55), (59), (60),
% 230.32/41.63  | | | | | | | | | | | | | | | | | |            (62), (63), (64), (67), (69), (70), (71), (72),
% 230.32/41.63  | | | | | | | | | | | | | | | | | |            (74), (76), (78), (86), (87), (90), (91), (93),
% 230.32/41.63  | | | | | | | | | | | | | | | | | |            (94), (95), (102), (105), (108), (145), (164),
% 230.32/41.63  | | | | | | | | | | | | | | | | | |            (165), (184) are inconsistent by sub-proof #1083.
% 230.32/41.63  | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | End of split
% 230.32/41.63  | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | Case 2:
% 230.32/41.63  | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | |   (185)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 230.32/41.63  | | | | | | | | | | | | | | | | |            & op(e3, e0) = e1)
% 230.32/41.63  | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 230.32/41.63  | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | Case 1:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | |   (186)  all_57_4 = e1 & op(e3, e1) = e1
% 230.32/41.63  | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | ALPHA: (186) implies:
% 230.32/41.63  | | | | | | | | | | | | | | | | | |   (187)  all_57_4 = e1
% 230.32/41.63  | | | | | | | | | | | | | | | | | |   (188)  op(e3, e1) = e1
% 230.32/41.63  | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | BETA: splitting (69) gives:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | Case 1:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | |   (189)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 230.32/41.63  | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e2)
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | Case 1:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | |   (190)  all_57_4 = e2 & op(e3, e1) = e2
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | ALPHA: (190) implies:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | |   (191)  all_57_4 = e2
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11), (18), (33), (47), (63), (164), (175),
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | |            (191) are inconsistent by sub-proof #2442.
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | Case 2:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | |   (192)  all_57_5 = e2 & op(e2, e1) = e2
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (37), (87), (192) are inconsistent by sub-proof
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | |            #2425.
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | End of split
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | Case 2:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | |   (193)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 230.32/41.63  | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e1) = e2)
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | Case 1:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | |   (194)  all_57_8 = e2 & op(e1, e1) = e2
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | ALPHA: (194) implies:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | |   (195)  op(e1, e1) = e2
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (8), (9), (10), (11), (14), (16), (18),
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | |            (21), (23), (26), (28), (31), (32), (33), (35),
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | |            (36), (37), (41), (46), (47), (49), (50), (51),
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | |            (52), (59), (60), (63), (64), (67), (69), (70),
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | |            (71), (72), (74), (76), (78), (86), (87), (90),
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | |            (94), (105), (155), (164), (195) are inconsistent
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | |            by sub-proof #1121.
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | Case 2:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | |   (196)  all_57_14 = e2 & op(e0, e1) = e2
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | ALPHA: (196) implies:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | |   (197)  all_57_14 = e2
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | BETA: splitting (76) gives:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | |   (198)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11), (18), (33), (46), (47), (63), (164),
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | |            (175), (187), (198) are inconsistent by sub-proof
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | |            #1085.
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | |   (199)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | |   (200)  all_57_7 = e1 & op(e1, e2) = e1
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (200) implies:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | |   (201)  all_57_7 = e1
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11), (14), (16), (31), (35), (41), (47),
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | |            (52), (63), (64), (71), (86), (87), (155), (201)
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1245.
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | |   (202)  all_57_13 = e1 & op(e0, e2) = e1
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (202) implies:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | |   (203)  all_57_13 = e1
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (169) gives:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | |   (204)  all_57_12 = e0 & op(e0, e3) = e0
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (204) implies:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | |   (205)  all_57_12 = e0
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5) gives:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | |   (206)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e1)
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (207)  all_57_0 = e1 & op(e3, e3) = e1
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (207) implies:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (208)  op(e3, e3) = e1
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11), (33), (208) are inconsistent by
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2495.
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (209)  all_57_2 = e1 & op(e2, e3) = e1
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (209) implies:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (210)  all_57_2 = e1
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (70) gives:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | |   (211)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e0)
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (212)  all_57_0 = e0 & op(e3, e3) = e0
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (212) implies:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (213)  op(e3, e3) = e0
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11), (31), (45), (57), (79), (175), (187),
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (213) are inconsistent by sub-proof #2280.
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (214)  all_57_2 = e0 & op(e2, e3) = e0
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (214) implies:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (215)  all_57_2 = e0
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (210), (215) imply:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (216)  e1 = e0
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (187), (216) imply:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (217)  all_57_4 = e0
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11), (18), (23), (31), (33), (40), (41),
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (47), (59), (63), (74), (87), (164), (203), (217)
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1128.
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | |   (218)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e3) = e0)
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (219)  all_57_6 = e0 & op(e1, e3) = e0
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (219) implies:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (220)  all_57_6 = e0
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (8), (9), (10), (11), (14), (16), (18),
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (19), (21), (23), (26), (28), (31), (32), (33),
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (35), (36), (37), (40), (41), (43), (46), (47),
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (49), (50), (51), (52), (54), (55), (59), (60),
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (62), (63), (64), (67), (69), (70), (71), (72),
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (74), (76), (78), (86), (87), (90), (93), (94),
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (95), (105), (108), (145), (161), (220) are
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1089.
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_52_7, e2, e0, e3,
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (90), (165) gives:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (221)  all_52_7 = e2
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_52_5, e1, e1, e3,
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (91), (188) gives:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (222)  all_52_5 = e1
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_52_3, e0, e2, e3,
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (92), (176) gives:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (223)  all_52_3 = e0
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (101), (223) imply:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (224)   ~ (e2 = e0)
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (102), (221), (222) imply:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (225)   ~ (e2 = e1)
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (104), (222) imply:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (226)   ~ (e3 = e1)
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (105), (221) imply:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (227)   ~ (e3 = e2)
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (94), (221) imply:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (228)  op(e2, e2) = e0
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (11), (41), (47), (59), (63), (76),
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (87), (175), (228) are inconsistent by sub-proof
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1282.
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | |   (229)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e3) = e1)
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (230)  all_57_6 = e1 & op(e1, e3) = e1
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (230) implies:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (231)  all_57_6 = e1
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (155), (231) imply:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (232)  e2 = e1
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (197), (232) imply:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (233)  all_57_14 = e1
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (8), (9), (10), (11), (14), (16), (18),
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | |            (19), (21), (23), (26), (28), (31), (32), (33),
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | |            (35), (36), (37), (40), (41), (43), (46), (47),
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | |            (49), (50), (51), (52), (54), (59), (60), (63),
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | |            (64), (67), (69), (70), (71), (72), (74), (76),
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | |            (78), (86), (87), (90), (93), (94), (95), (105),
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | |            (108), (164), (233) are inconsistent by sub-proof
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | |            #1126.
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (234)  all_57_12 = e1 & op(e0, e3) = e1
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (234) implies:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (235)  all_57_12 = e1
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (205), (235) imply:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (236)  e1 = e0
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11), (18), (23), (31), (33), (40), (41),
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | |            (47), (59), (63), (74), (87), (164), (187), (203),
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | |            (236) are inconsistent by sub-proof #1084.
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | |   (237)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | |   (238)  all_57_13 = e0 & op(e0, e2) = e0
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (238) implies:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | |   (239)  all_57_13 = e0
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (203), (239) imply:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | |   (240)  e1 = e0
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (187), (240) imply:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | |   (241)  all_57_4 = e0
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11), (18), (23), (31), (33), (40), (41),
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | |            (47), (59), (63), (74), (87), (164), (203), (241)
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1128.
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | |   (242)  all_57_14 = e0 & op(e0, e1) = e0
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (242) implies:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | |   (243)  all_57_14 = e0
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (197), (243) imply:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | |   (244)  e2 = e0
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (244) implies:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | |   (245)  e2 = e0
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (74), (245) imply:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | |   (246)  all_57_3 = e0
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (9), (10), (11), (18), (23), (26), (28),
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | |            (31), (32), (33), (35), (37), (41), (47), (59),
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | |            (60), (63), (64), (69), (71), (72), (76), (78),
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | |            (87), (145), (170), (243), (246) are inconsistent
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1488.
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | End of split
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | End of split
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | End of split
% 230.32/41.63  | | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | End of split
% 230.32/41.63  | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | Case 2:
% 230.32/41.63  | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | |   (247)  all_57_9 = e1 & op(e3, e0) = e1
% 230.32/41.63  | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | | REF_CLOSE: (63), (164), (247) are inconsistent by sub-proof
% 230.32/41.63  | | | | | | | | | | | | | | | | | |            #2451.
% 230.32/41.63  | | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | | End of split
% 230.32/41.63  | | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | | End of split
% 230.32/41.63  | | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | | End of split
% 230.32/41.63  | | | | | | | | | | | | | | | 
% 230.32/41.63  | | | | | | | | | | | | | | Case 2:
% 230.32/41.63  | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | |   (248)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 230.32/41.64  | | | | | | | | | | | | | | |            & op(e3, e0) = e0)
% 230.32/41.64  | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | BETA: splitting (248) gives:
% 230.32/41.64  | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | Case 1:
% 230.32/41.64  | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | |   (249)  all_57_4 = e0 & op(e3, e1) = e0
% 230.32/41.64  | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | REF_CLOSE: (11), (31), (46), (49), (52), (90), (91), (94),
% 230.32/41.64  | | | | | | | | | | | | | | | |            (102), (165), (249) are inconsistent by sub-proof
% 230.32/41.64  | | | | | | | | | | | | | | | |            #1163.
% 230.32/41.64  | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | Case 2:
% 230.32/41.64  | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | |   (250)  all_57_9 = e0 & op(e3, e0) = e0
% 230.32/41.64  | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | ALPHA: (250) implies:
% 230.32/41.64  | | | | | | | | | | | | | | | |   (251)  all_57_9 = e0
% 230.32/41.64  | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | COMBINE_EQS: (164), (251) imply:
% 230.32/41.64  | | | | | | | | | | | | | | | |   (252)  e2 = e0
% 230.32/41.64  | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (8), (9), (10), (11), (18), (23), (26),
% 230.32/41.64  | | | | | | | | | | | | | | | |            (28), (31), (32), (33), (35), (37), (41), (47),
% 230.32/41.64  | | | | | | | | | | | | | | | |            (49), (51), (52), (59), (60), (63), (64), (67),
% 230.32/41.64  | | | | | | | | | | | | | | | |            (69), (70), (71), (72), (74), (76), (78), (87),
% 230.32/41.64  | | | | | | | | | | | | | | | |            (90), (94), (105), (145), (252) are inconsistent
% 230.32/41.64  | | | | | | | | | | | | | | | |            by sub-proof #1140.
% 230.32/41.64  | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | End of split
% 230.32/41.64  | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | End of split
% 230.32/41.64  | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | End of split
% 230.32/41.64  | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | Case 2:
% 230.32/41.64  | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | |   (253)  all_57_10 = e2 & op(e2, e0) = e2
% 230.32/41.64  | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | REF_CLOSE: (11), (19), (54), (253) are inconsistent by
% 230.32/41.64  | | | | | | | | | | | | |            sub-proof #2432.
% 230.32/41.64  | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | End of split
% 230.32/41.64  | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | Case 2:
% 230.32/41.64  | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | |   (254)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 230.32/41.64  | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 230.32/41.64  | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | BETA: splitting (254) gives:
% 230.32/41.64  | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | Case 1:
% 230.32/41.64  | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | |   (255)  all_57_11 = e2 & op(e1, e0) = e2
% 230.32/41.64  | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | ALPHA: (255) implies:
% 230.32/41.64  | | | | | | | | | | | | |   (256)  all_57_11 = e2
% 230.32/41.64  | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | REF_CLOSE: (9), (11), (14), (16), (31), (35), (41), (47),
% 230.32/41.64  | | | | | | | | | | | | |            (52), (63), (64), (71), (72), (86), (87), (145),
% 230.32/41.64  | | | | | | | | | | | | |            (155), (256) are inconsistent by sub-proof #1092.
% 230.32/41.64  | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | Case 2:
% 230.32/41.64  | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | |   (257)  all_57_15 = e2 & op(e0, e0) = e2
% 230.32/41.64  | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | REF_CLOSE: (35), (87), (257) are inconsistent by sub-proof
% 230.32/41.64  | | | | | | | | | | | | |            #2323.
% 230.32/41.64  | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | End of split
% 230.32/41.64  | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | End of split
% 230.32/41.64  | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | End of split
% 230.32/41.64  | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | End of split
% 230.32/41.64  | | | | | | | | | 
% 230.32/41.64  | | | | | | | | Case 2:
% 230.32/41.64  | | | | | | | | | 
% 230.32/41.64  | | | | | | | | |   (258)  all_57_7 = e2 & op(e1, e2) = e2
% 230.32/41.64  | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | REF_CLOSE: (59), (87), (258) are inconsistent by sub-proof
% 230.32/41.64  | | | | | | | | |            #2092.
% 230.32/41.64  | | | | | | | | | 
% 230.32/41.64  | | | | | | | | End of split
% 230.32/41.64  | | | | | | | | 
% 230.32/41.64  | | | | | | | Case 2:
% 230.32/41.64  | | | | | | | | 
% 230.32/41.64  | | | | | | | |   (259)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 &
% 230.32/41.64  | | | | | | | |            op(e1, e0) = e2)
% 230.32/41.64  | | | | | | | | 
% 230.32/41.64  | | | | | | | | BETA: splitting (259) gives:
% 230.32/41.64  | | | | | | | | 
% 230.32/41.64  | | | | | | | | Case 1:
% 230.32/41.64  | | | | | | | | | 
% 230.32/41.64  | | | | | | | | |   (260)  all_57_8 = e2 & op(e1, e1) = e2
% 230.32/41.64  | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | ALPHA: (260) implies:
% 230.32/41.64  | | | | | | | | |   (261)  op(e1, e1) = e2
% 230.32/41.64  | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | REF_CLOSE: (4), (5), (8), (9), (10), (11), (14), (16), (18),
% 230.32/41.64  | | | | | | | | |            (19), (21), (23), (26), (28), (31), (32), (33),
% 230.32/41.64  | | | | | | | | |            (35), (36), (37), (40), (41), (43), (46), (47),
% 230.32/41.64  | | | | | | | | |            (49), (50), (51), (52), (54), (55), (59), (60),
% 230.32/41.64  | | | | | | | | |            (62), (63), (64), (67), (69), (70), (71), (72),
% 230.32/41.64  | | | | | | | | |            (74), (76), (78), (86), (87), (90), (93), (94),
% 230.32/41.64  | | | | | | | | |            (95), (105), (108), (261) are inconsistent by
% 230.32/41.64  | | | | | | | | |            sub-proof #1090.
% 230.32/41.64  | | | | | | | | | 
% 230.32/41.64  | | | | | | | | Case 2:
% 230.32/41.64  | | | | | | | | | 
% 230.32/41.64  | | | | | | | | |   (262)  all_57_11 = e2 & op(e1, e0) = e2
% 230.32/41.64  | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | ALPHA: (262) implies:
% 230.32/41.64  | | | | | | | | |   (263)  all_57_11 = e2
% 230.32/41.64  | | | | | | | | |   (264)  op(e1, e0) = e2
% 230.32/41.64  | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | BETA: splitting (72) gives:
% 230.32/41.64  | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | Case 1:
% 230.32/41.64  | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | |   (265)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 230.32/41.64  | | | | | | | | | |            & op(e1, e2) = e1)
% 230.32/41.64  | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | BETA: splitting (265) gives:
% 230.32/41.64  | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | Case 1:
% 230.32/41.64  | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | |   (266)  all_57_6 = e1 & op(e1, e3) = e1
% 230.32/41.64  | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | ALPHA: (266) implies:
% 230.32/41.64  | | | | | | | | | | |   (267)  all_57_6 = e1
% 230.32/41.64  | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | BETA: splitting (67) gives:
% 230.32/41.64  | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | Case 1:
% 230.32/41.64  | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | |   (268)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 230.32/41.64  | | | | | | | | | | | |            & op(e2, e3) = e2)
% 230.32/41.64  | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | BETA: splitting (268) gives:
% 230.32/41.64  | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | Case 1:
% 230.32/41.64  | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | |   (269)  all_57_0 = e2 & op(e3, e3) = e2
% 230.32/41.64  | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | ALPHA: (269) implies:
% 230.32/41.64  | | | | | | | | | | | | |   (270)  op(e3, e3) = e2
% 230.32/41.64  | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | REF_CLOSE: (11), (46), (87), (93), (95), (270) are
% 230.32/41.64  | | | | | | | | | | | | |            inconsistent by sub-proof #1951.
% 230.32/41.64  | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | Case 2:
% 230.32/41.64  | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | |   (271)  all_57_2 = e2 & op(e2, e3) = e2
% 230.32/41.64  | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | ALPHA: (271) implies:
% 230.32/41.64  | | | | | | | | | | | | |   (272)  all_57_2 = e2
% 230.32/41.64  | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | REF_CLOSE: (4), (9), (11), (14), (16), (31), (35), (37),
% 230.32/41.64  | | | | | | | | | | | | |            (41), (46), (47), (52), (55), (59), (60), (62),
% 230.32/41.64  | | | | | | | | | | | | |            (63), (64), (71), (74), (86), (87), (267), (272)
% 230.32/41.64  | | | | | | | | | | | | |            are inconsistent by sub-proof #1082.
% 230.32/41.64  | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | End of split
% 230.32/41.64  | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | Case 2:
% 230.32/41.64  | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | |   (273)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 230.32/41.64  | | | | | | | | | | | |            e2 & op(e0, e3) = e2)
% 230.32/41.64  | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | BETA: splitting (273) gives:
% 230.32/41.64  | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | Case 1:
% 230.32/41.64  | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | |   (274)  all_57_6 = e2 & op(e1, e3) = e2
% 230.32/41.64  | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | ALPHA: (274) implies:
% 230.32/41.64  | | | | | | | | | | | | |   (275)  all_57_6 = e2
% 230.32/41.64  | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | REF_CLOSE: (9), (11), (14), (16), (31), (35), (41), (47),
% 230.32/41.64  | | | | | | | | | | | | |            (52), (63), (64), (71), (72), (86), (87), (145),
% 230.32/41.64  | | | | | | | | | | | | |            (263), (275) are inconsistent by sub-proof #1092.
% 230.32/41.64  | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | Case 2:
% 230.32/41.64  | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | |   (276)  all_57_12 = e2 & op(e0, e3) = e2
% 230.32/41.64  | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | ALPHA: (276) implies:
% 230.32/41.64  | | | | | | | | | | | | |   (277)  all_57_12 = e2
% 230.32/41.64  | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | BETA: splitting (52) gives:
% 230.32/41.64  | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | Case 1:
% 230.32/41.64  | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | |   (278)  all_57_15 = e0 & op(e0, e0) = e0
% 230.32/41.64  | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | ALPHA: (278) implies:
% 230.32/41.64  | | | | | | | | | | | | | |   (279)  op(e0, e0) = e0
% 230.32/41.64  | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | REF_CLOSE: (11), (31), (49), (279) are inconsistent by
% 230.32/41.64  | | | | | | | | | | | | | |            sub-proof #2304.
% 230.32/41.64  | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | Case 2:
% 230.32/41.64  | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | |   (280)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 230.32/41.64  | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 230.32/41.64  | | | | | | | | | | | | | |              op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 230.32/41.64  | | | | | | | | | | | | | |                e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 230.32/41.64  | | | | | | | | | | | | | |              e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 230.32/41.64  | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | ALPHA: (280) implies:
% 230.32/41.64  | | | | | | | | | | | | | |   (281)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 230.32/41.64  | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 230.32/41.64  | | | | | | | | | | | | | |              e1) = e0)
% 230.32/41.64  | | | | | | | | | | | | | |   (282)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 230.32/41.64  | | | | | | | | | | | | | |            e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 230.32/41.64  | | | | | | | | | | | | | |              e0) = e0)
% 230.32/41.64  | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | BETA: splitting (70) gives:
% 230.32/41.64  | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | Case 1:
% 230.32/41.64  | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | |   (283)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 230.32/41.64  | | | | | | | | | | | | | | |            & op(e2, e3) = e0)
% 230.32/41.64  | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | BETA: splitting (283) gives:
% 230.32/41.64  | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | Case 1:
% 230.32/41.64  | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | |   (284)  all_57_0 = e0 & op(e3, e3) = e0
% 230.32/41.64  | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | ALPHA: (284) implies:
% 230.32/41.64  | | | | | | | | | | | | | | | |   (285)  op(e3, e3) = e0
% 230.32/41.64  | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | REF_CLOSE: (11), (31), (33), (285) are inconsistent by
% 230.32/41.64  | | | | | | | | | | | | | | | |            sub-proof #2494.
% 230.32/41.64  | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | Case 2:
% 230.32/41.64  | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | |   (286)  all_57_2 = e0 & op(e2, e3) = e0
% 230.32/41.64  | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | ALPHA: (286) implies:
% 230.32/41.64  | | | | | | | | | | | | | | | |   (287)  all_57_2 = e0
% 230.32/41.64  | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | BETA: splitting (4) gives:
% 230.32/41.64  | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | Case 1:
% 230.32/41.64  | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | |   (288)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 230.32/41.64  | | | | | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 230.32/41.64  | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | BETA: splitting (288) gives:
% 230.32/41.64  | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | Case 1:
% 230.32/41.64  | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | |   (289)  all_57_2 = e1 & op(e2, e3) = e1
% 230.32/41.64  | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | ALPHA: (289) implies:
% 230.32/41.64  | | | | | | | | | | | | | | | | | |   (290)  all_57_2 = e1
% 230.32/41.64  | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (287), (290) imply:
% 230.32/41.64  | | | | | | | | | | | | | | | | | |   (291)  e1 = e0
% 230.32/41.64  | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (8), (9), (10), (11), (14), (16), (18),
% 230.32/41.64  | | | | | | | | | | | | | | | | | |            (19), (21), (23), (26), (28), (31), (32), (33),
% 230.32/41.64  | | | | | | | | | | | | | | | | | |            (35), (36), (37), (40), (41), (43), (46), (47),
% 230.32/41.64  | | | | | | | | | | | | | | | | | |            (49), (50), (51), (52), (54), (55), (59), (60),
% 230.32/41.64  | | | | | | | | | | | | | | | | | |            (62), (63), (64), (67), (69), (70), (71), (72),
% 230.32/41.64  | | | | | | | | | | | | | | | | | |            (74), (76), (78), (86), (87), (90), (93), (94),
% 230.32/41.64  | | | | | | | | | | | | | | | | | |            (95), (105), (108), (145), (267), (291) are
% 230.32/41.64  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1081.
% 230.32/41.64  | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | Case 2:
% 230.32/41.64  | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | |   (292)  all_57_3 = e1 & op(e2, e2) = e1
% 230.32/41.64  | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | ALPHA: (292) implies:
% 230.32/41.64  | | | | | | | | | | | | | | | | | |   (293)  op(e2, e2) = e1
% 230.32/41.64  | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (46), (63), (293) are inconsistent by
% 230.32/41.64  | | | | | | | | | | | | | | | | | |            sub-proof #2306.
% 230.32/41.64  | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | End of split
% 230.32/41.64  | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | Case 2:
% 230.32/41.64  | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | |   (294)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 230.32/41.64  | | | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 230.32/41.64  | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | BETA: splitting (294) gives:
% 230.32/41.64  | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | Case 1:
% 230.32/41.64  | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | |   (295)  all_57_5 = e1 & op(e2, e1) = e1
% 230.32/41.64  | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (37), (295) are inconsistent by sub-proof
% 230.32/41.64  | | | | | | | | | | | | | | | | | |            #2376.
% 230.32/41.64  | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | Case 2:
% 230.32/41.64  | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | |   (296)  all_57_10 = e1 & op(e2, e0) = e1
% 230.32/41.64  | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | ALPHA: (296) implies:
% 230.32/41.64  | | | | | | | | | | | | | | | | | |   (297)  all_57_10 = e1
% 230.32/41.64  | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | BETA: splitting (282) gives:
% 230.32/41.64  | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | Case 1:
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | |   (298)  all_57_9 = e0 & op(e3, e0) = e0
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | ALPHA: (298) implies:
% 230.32/41.64  | | | | | | | | | | | | | | | | | | |   (299)  all_57_9 = e0
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | BETA: splitting (18) gives:
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | Case 1:
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | |   (300)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e1)
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | BETA: splitting (300) gives:
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | |   (301)  all_57_0 = e1 & op(e3, e3) = e1
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | ALPHA: (301) implies:
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | |   (302)  op(e3, e3) = e1
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11), (33), (302) are inconsistent by
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | |            sub-proof #2495.
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | ALPHA: (298) implies:
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | |   (303)  op(e3, e0) = e0
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_52_7, e0, e0, e3,
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | |              simplifying with (90), (303) gives:
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | |   (304)  all_52_7 = e0
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (49), (94), (105), (304) are inconsistent by
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | |            sub-proof #1505.
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | End of split
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | Case 2:
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | |   (305)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e1)
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | BETA: splitting (305) gives:
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | |   (306)  all_57_4 = e1 & op(e3, e1) = e1
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | ALPHA: (306) implies:
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | |   (307)  all_57_4 = e1
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (69) gives:
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | |   (308)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e2)
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (308) gives:
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | |   (309)  all_57_4 = e2 & op(e3, e1) = e2
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (309) implies:
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | |   (310)  all_57_4 = e2
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (63), (307), (310) are inconsistent by sub-proof
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | |            #2430.
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | |   (311)  all_57_5 = e2 & op(e2, e1) = e2
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (311) implies:
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | |   (312)  all_57_5 = e2
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (37), (312) imply:
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | |   (313)  e3 = e2
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (59), (313) imply:
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | |   (314)  all_57_7 = e2
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11), (14), (16), (31), (35), (41), (47),
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | |            (49), (52), (63), (64), (71), (86), (87), (267),
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | |            (314) are inconsistent by sub-proof #1078.
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | |   (315)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e1) = e2)
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (315) gives:
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | |   (316)  all_57_8 = e2 & op(e1, e1) = e2
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (316) implies:
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | |   (317)  op(e1, e1) = e2
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (8), (9), (10), (11), (18), (23), (26),
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | |            (28), (31), (32), (33), (35), (36), (37), (41),
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | |            (43), (46), (47), (49), (51), (52), (59), (60),
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | |            (63), (64), (67), (69), (70), (71), (72), (74),
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | |            (76), (78), (87), (90), (94), (105), (108), (145),
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | |            (152), (263), (264), (277), (317) are inconsistent
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1137.
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | |   (318)  all_57_14 = e2 & op(e0, e1) = e2
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (318) implies:
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | |   (319)  all_57_14 = e2
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (281) gives:
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | |   (320)  all_57_12 = e0 & op(e0, e3) = e0
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (320) implies:
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | |   (321)  all_57_12 = e0
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (277), (321) imply:
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | |   (322)  e2 = e0
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (74), (322) imply:
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | |   (323)  all_57_3 = e0
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (37), (41), (60), (63), (87), (287), (297), (323)
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2254.
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | |   (324)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (324) gives:
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | | |   (325)  all_57_13 = e0 & op(e0, e2) = e0
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (325) implies:
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | | |   (326)  all_57_13 = e0
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11), (36), (43), (47), (49), (63), (108),
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | | |            (264), (319), (326) are inconsistent by sub-proof
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | | |            #1100.
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | | |   (327)  all_57_14 = e0 & op(e0, e1) = e0
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (327) implies:
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | | |   (328)  all_57_14 = e0
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (319), (328) imply:
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | | |   (329)  e2 = e0
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (37), (41), (60), (63), (74), (87), (287), (297),
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | | |            (329) are inconsistent by sub-proof #1077.
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | End of split
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | |   (330)  all_57_9 = e1 & op(e3, e0) = e1
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | ALPHA: (330) implies:
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | |   (331)  all_57_9 = e1
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (299), (331) imply:
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | |   (332)  e1 = e0
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (8), (9), (10), (11), (14), (16), (18),
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | |            (19), (21), (23), (26), (28), (31), (32), (33),
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | |            (35), (36), (37), (40), (41), (43), (46), (47),
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | |            (49), (50), (51), (52), (54), (55), (59), (60),
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | |            (62), (63), (64), (67), (69), (70), (71), (72),
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | |            (74), (76), (78), (86), (87), (90), (93), (94),
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | |            (95), (105), (108), (145), (267), (332) are
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1081.
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | End of split
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | End of split
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | Case 2:
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | |   (333)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 =
% 230.32/41.64  | | | | | | | | | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | BETA: splitting (333) gives:
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | Case 1:
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | |   (334)  all_57_10 = e0 & op(e2, e0) = e0
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | ALPHA: (334) implies:
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | |   (335)  all_57_10 = e0
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (297), (335) imply:
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | |   (336)  e1 = e0
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (336) imply:
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | |   (337)  all_57_6 = e0
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (8), (9), (10), (11), (14), (16), (18),
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | |            (19), (21), (23), (26), (28), (31), (32), (33),
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | |            (35), (36), (37), (40), (41), (43), (46), (47),
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | |            (49), (50), (51), (52), (54), (55), (59), (60),
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | |            (62), (63), (64), (67), (69), (70), (71), (72),
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | |            (74), (76), (78), (86), (87), (90), (93), (94),
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | |            (95), (105), (108), (145), (337) are inconsistent
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | |            by sub-proof #1088.
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | Case 2:
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | |   (338)  all_57_11 = e0 & op(e1, e0) = e0
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | ALPHA: (338) implies:
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | |   (339)  all_57_11 = e0
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (8), (9), (10), (11), (14), (16), (18),
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | |            (19), (21), (23), (26), (28), (31), (32), (33),
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | |            (35), (36), (37), (40), (41), (43), (46), (47),
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | |            (49), (50), (51), (52), (54), (55), (59), (60),
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | |            (62), (63), (64), (67), (69), (70), (71), (72),
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | |            (74), (76), (78), (86), (87), (90), (91), (93),
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | |            (94), (95), (102), (105), (108), (145), (339) are
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1076.
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | End of split
% 230.32/41.64  | | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | | End of split
% 230.32/41.64  | | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | | End of split
% 230.32/41.64  | | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | End of split
% 230.32/41.64  | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | End of split
% 230.32/41.64  | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | Case 2:
% 230.32/41.64  | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | |   (340)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 230.32/41.64  | | | | | | | | | | | | | | |            e0 & op(e0, e3) = e0)
% 230.32/41.64  | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | BETA: splitting (340) gives:
% 230.32/41.64  | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | Case 1:
% 230.32/41.64  | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | |   (341)  all_57_6 = e0 & op(e1, e3) = e0
% 230.32/41.64  | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | ALPHA: (341) implies:
% 230.32/41.64  | | | | | | | | | | | | | | | |   (342)  all_57_6 = e0
% 230.32/41.64  | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (8), (9), (10), (11), (14), (16), (18),
% 230.32/41.64  | | | | | | | | | | | | | | | |            (19), (21), (23), (26), (28), (31), (32), (33),
% 230.32/41.64  | | | | | | | | | | | | | | | |            (35), (36), (37), (40), (41), (43), (46), (47),
% 230.32/41.64  | | | | | | | | | | | | | | | |            (49), (50), (51), (52), (54), (55), (59), (60),
% 230.32/41.64  | | | | | | | | | | | | | | | |            (62), (63), (64), (67), (69), (70), (71), (72),
% 230.32/41.64  | | | | | | | | | | | | | | | |            (74), (76), (78), (86), (87), (90), (93), (94),
% 230.32/41.64  | | | | | | | | | | | | | | | |            (95), (105), (108), (145), (342) are inconsistent
% 230.32/41.64  | | | | | | | | | | | | | | | |            by sub-proof #1088.
% 230.32/41.64  | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | Case 2:
% 230.32/41.64  | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | |   (343)  all_57_12 = e0 & op(e0, e3) = e0
% 230.32/41.64  | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (8), (9), (11), (23), (26), (31), (32),
% 230.32/41.64  | | | | | | | | | | | | | | | |            (33), (35), (37), (41), (47), (49), (51), (59),
% 230.32/41.64  | | | | | | | | | | | | | | | |            (60), (63), (64), (67), (70), (71), (72), (74),
% 230.32/41.64  | | | | | | | | | | | | | | | |            (76), (78), (87), (90), (94), (105), (145), (277),
% 230.32/41.64  | | | | | | | | | | | | | | | |            (282), (343) are inconsistent by sub-proof #1151.
% 230.32/41.64  | | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | | End of split
% 230.32/41.64  | | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | | End of split
% 230.32/41.64  | | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | | End of split
% 230.32/41.64  | | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | | End of split
% 230.32/41.64  | | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | End of split
% 230.32/41.64  | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | Case 2:
% 230.32/41.64  | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | |   (344)  all_57_7 = e1 & op(e1, e2) = e1
% 230.32/41.64  | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | REF_CLOSE: (9), (59), (344) are inconsistent by sub-proof
% 230.32/41.64  | | | | | | | | | | |            #2104.
% 230.32/41.64  | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | End of split
% 230.32/41.64  | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | Case 2:
% 230.32/41.64  | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | |   (345)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1
% 230.32/41.64  | | | | | | | | | |            & op(e1, e0) = e1)
% 230.32/41.64  | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | BETA: splitting (345) gives:
% 230.32/41.64  | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | Case 1:
% 230.32/41.64  | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | |   (346)  all_57_8 = e1 & op(e1, e1) = e1
% 230.32/41.64  | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | ALPHA: (346) implies:
% 230.32/41.64  | | | | | | | | | | |   (347)  op(e1, e1) = e1
% 230.32/41.64  | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (8), (9), (10), (11), (14),
% 230.32/41.64  | | | | | | | | | | |            (15), (16), (17), (18), (19), (21), (23), (24),
% 230.32/41.64  | | | | | | | | | | |            (25), (26), (27), (28), (29), (30), (31), (32),
% 230.32/41.64  | | | | | | | | | | |            (33), (35), (36), (37), (38), (40), (41), (42),
% 230.32/41.64  | | | | | | | | | | |            (43), (46), (47), (49), (50), (51), (52), (53),
% 230.32/41.64  | | | | | | | | | | |            (54), (55), (59), (60), (61), (62), (63), (64),
% 230.32/41.64  | | | | | | | | | | |            (65), (67), (68), (69), (70), (71), (72), (74),
% 230.32/41.64  | | | | | | | | | | |            (76), (77), (78), (83), (86), (87), (90), (91),
% 230.32/41.64  | | | | | | | | | | |            (92), (93), (94), (95), (100), (102), (105),
% 230.32/41.64  | | | | | | | | | | |            (108), (263), (264), (347) are inconsistent by
% 230.32/41.64  | | | | | | | | | | |            sub-proof #1107.
% 230.32/41.64  | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | Case 2:
% 230.32/41.64  | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | |   (348)  all_57_11 = e1 & op(e1, e0) = e1
% 230.32/41.64  | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | ALPHA: (348) implies:
% 230.32/41.64  | | | | | | | | | | |   (349)  all_57_11 = e1
% 230.32/41.64  | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | | REF_CLOSE: (63), (263), (349) are inconsistent by sub-proof
% 230.32/41.64  | | | | | | | | | | |            #2113.
% 230.32/41.64  | | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | | End of split
% 230.32/41.64  | | | | | | | | | | 
% 230.32/41.64  | | | | | | | | | End of split
% 230.32/41.64  | | | | | | | | | 
% 230.32/41.64  | | | | | | | | End of split
% 230.32/41.64  | | | | | | | | 
% 230.32/41.64  | | | | | | | End of split
% 230.32/41.64  | | | | | | | 
% 230.32/41.64  | | | | | | Case 2:
% 230.32/41.64  | | | | | | | 
% 230.32/41.64  | | | | | | |   (350)  all_57_11 = e0 & op(e1, e0) = e0
% 230.32/41.64  | | | | | | | 
% 230.32/41.64  | | | | | | | ALPHA: (350) implies:
% 230.32/41.64  | | | | | | |   (351)  all_57_11 = e0
% 230.32/41.64  | | | | | | | 
% 230.32/41.64  | | | | | | | REF_CLOSE: (4), (5), (8), (9), (10), (11), (14), (16), (18), (19),
% 230.32/41.64  | | | | | | |            (21), (23), (26), (28), (31), (32), (33), (35), (36),
% 230.32/41.64  | | | | | | |            (37), (40), (41), (43), (46), (47), (49), (50), (51),
% 230.32/41.64  | | | | | | |            (52), (54), (55), (59), (60), (62), (63), (64), (67),
% 230.32/41.64  | | | | | | |            (69), (70), (71), (72), (74), (76), (78), (86), (87),
% 230.32/41.64  | | | | | | |            (90), (91), (93), (94), (95), (102), (105), (108),
% 230.32/41.64  | | | | | | |            (145), (351) are inconsistent by sub-proof #1076.
% 230.32/41.64  | | | | | | | 
% 230.32/41.64  | | | | | | End of split
% 230.32/41.64  | | | | | | 
% 230.32/41.64  | | | | | End of split
% 230.32/41.64  | | | | | 
% 230.32/41.64  | | | | End of split
% 230.32/41.64  | | | | 
% 230.32/41.64  | | | End of split
% 230.32/41.64  | | | 
% 230.32/41.64  | | Case 2:
% 230.32/41.64  | | | 
% 230.32/41.64  | | |   (352)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 230.32/41.64  | | |          & op(all_52_9, all_52_9) = e3 & op(all_52_11, all_52_11) = e2 &
% 230.32/41.64  | | |          op(all_52_13, all_52_13) = e1 & op(all_52_15, all_52_15) = e0 &
% 230.32/41.64  | | |          op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 & op(e2, e1) =
% 230.32/41.64  | | |          all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) & $i(all_52_11)
% 230.32/41.64  | | |          & $i(all_52_13) & $i(all_52_15)
% 230.32/41.64  | | | 
% 230.32/41.64  | | | REF_CLOSE: (6), (9), (11), (33), (352) are inconsistent by sub-proof
% 230.32/41.64  | | |            #1443.
% 230.32/41.64  | | | 
% 230.32/41.64  | | End of split
% 230.32/41.64  | | 
% 230.32/41.64  | Case 2:
% 230.32/41.64  | | 
% 230.32/41.64  | |   (353)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 230.32/41.64  | |            & op(all_52_17, all_52_17) = e3 & op(all_52_19, all_52_19) = e2 &
% 230.32/41.64  | |            op(all_52_21, all_52_21) = e1 & op(all_52_23, all_52_23) = e0 &
% 230.32/41.64  | |            op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) =
% 230.32/41.64  | |            all_52_21 & op(e1, e0) = all_52_23 & $i(all_52_17) &
% 230.32/41.64  | |            $i(all_52_19) & $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 230.32/41.64  | |            & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0 &
% 230.32/41.64  | |            op(all_52_25, all_52_25) = e3 & op(all_52_27, all_52_27) = e2 &
% 230.32/41.64  | |            op(all_52_29, all_52_29) = e1 & op(all_52_31, all_52_31) = e0 &
% 230.32/41.64  | |            op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 & op(e0, e1) =
% 230.32/41.64  | |            all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 230.32/41.64  | |            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 230.32/41.64  | | 
% 230.32/41.64  | | BETA: splitting (353) gives:
% 230.32/41.64  | | 
% 230.32/41.64  | | Case 1:
% 230.32/41.64  | | | 
% 230.32/41.64  | | |   (354)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 230.32/41.64  | | |          & op(all_52_17, all_52_17) = e3 & op(all_52_19, all_52_19) = e2 &
% 230.32/41.64  | | |          op(all_52_21, all_52_21) = e1 & op(all_52_23, all_52_23) = e0 &
% 230.32/41.64  | | |          op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) =
% 230.32/41.64  | | |          all_52_21 & op(e1, e0) = all_52_23 & $i(all_52_17) &
% 230.32/41.64  | | |          $i(all_52_19) & $i(all_52_21) & $i(all_52_23)
% 230.32/41.64  | | | 
% 230.32/41.64  | | | REF_CLOSE: (11), (12), (33), (87), (354) are inconsistent by sub-proof
% 230.32/41.64  | | |            #1790.
% 230.32/41.64  | | | 
% 230.32/41.64  | | Case 2:
% 230.32/41.64  | | | 
% 230.32/41.64  | | |   (355)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 230.32/41.64  | | |          & op(all_52_25, all_52_25) = e3 & op(all_52_27, all_52_27) = e2 &
% 230.32/41.64  | | |          op(all_52_29, all_52_29) = e1 & op(all_52_31, all_52_31) = e0 &
% 230.32/41.64  | | |          op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 & op(e0, e1) =
% 230.32/41.64  | | |          all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 230.32/41.64  | | |          $i(all_52_27) & $i(all_52_29) & $i(all_52_31)
% 230.32/41.64  | | | 
% 230.32/41.64  | | | REF_CLOSE: (11), (31), (33), (49), (355) are inconsistent by sub-proof
% 230.32/41.64  | | |            #1442.
% 230.32/41.64  | | | 
% 230.32/41.64  | | End of split
% 230.32/41.64  | | 
% 230.32/41.64  | End of split
% 230.32/41.64  | 
% 230.32/41.64  End of proof
% 230.32/41.64  
% 230.32/41.64  Sub-proof #1076 shows that the following formulas are inconsistent:
% 230.32/41.64  ----------------------------------------------------------------
% 230.32/41.64    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.32/41.64         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.32/41.64    (2)  op(e3, e1) = all_52_5
% 230.32/41.64    (3)   ~ (all_52_7 = e3)
% 230.32/41.64    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.32/41.64         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.32/41.64    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.32/41.64         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.32/41.64    (6)   ~ (e3 = e1)
% 230.32/41.64    (7)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.32/41.64         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.32/41.64    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.32/41.64           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.32/41.64    (9)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.32/41.64         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.32/41.65    (10)   ~ (all_6_2 = e3)
% 230.32/41.65    (11)  op(e1, e1) = all_6_2
% 230.32/41.65    (12)  op(all_52_7, all_52_7) = e0
% 230.32/41.65    (13)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.32/41.65          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.32/41.65    (14)   ~ (all_52_5 = all_52_7)
% 230.32/41.65    (15)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 230.32/41.65            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 230.32/41.65              e3) = all_22_1 & $i(all_22_1))
% 230.32/41.65    (16)   ~ (all_53_13 = e2)
% 230.32/41.65    (17)   ~ (all_53_7 = e2)
% 230.32/41.65    (18)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.32/41.65          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.32/41.65    (19)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.32/41.65          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.32/41.65    (20)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 230.32/41.65          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.32/41.65    (21)   ~ (e3 = e2)
% 230.32/41.65    (22)   ~ (e3 = e0)
% 230.32/41.65    (23)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.32/41.65          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.32/41.65    (24)  op(e3, e3) = e3
% 230.32/41.65    (25)  all_57_15 = e3
% 230.32/41.65    (26)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.32/41.65          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.32/41.65            e1)
% 230.32/41.65    (27)  all_57_5 = e3
% 230.32/41.65    (28)  op(e3, e3) = all_52_1
% 230.32/41.65    (29)  all_57_11 = e0
% 230.32/41.65    (30)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.32/41.65          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.32/41.65    (31)  op(all_52_1, all_52_1) = e3
% 230.32/41.65    (32)   ~ (e2 = e0)
% 230.32/41.65    (33)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 230.32/41.65            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 230.32/41.65              e3) = all_12_1 & $i(all_12_1))
% 230.32/41.65    (34)  op(e2, e2) = e2
% 230.32/41.65    (35)   ~ (e1 = e0)
% 230.32/41.65    (36)  op(e0, e0) = e3
% 230.32/41.65    (37)  op(e0, e2) = all_53_7
% 230.32/41.65    (38)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.32/41.65          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.32/41.65            e2)
% 230.32/41.65    (39)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.32/41.65              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.32/41.65                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.32/41.65                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.32/41.65    (40)  op(e1, e1) = e0
% 230.32/41.65    (41)  op(e2, e0) = all_53_13
% 230.32/41.65    (42)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.32/41.65          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.32/41.65    (43)  all_57_7 = e3
% 230.32/41.65    (44)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.32/41.65          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.32/41.65    (45)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.32/41.65          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 230.32/41.65    (46)   ~ (e2 = e1)
% 230.32/41.65    (47)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.32/41.65          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.32/41.65    (48)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.32/41.65          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.32/41.65    (49)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.32/41.65          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.32/41.65    (50)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.32/41.65          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.32/41.65    (51)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.32/41.65          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.32/41.65    (52)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.32/41.65          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.32/41.65    (53)  all_57_3 = e2
% 230.32/41.65    (54)  op(e3, e0) = all_52_7
% 230.32/41.65    (55)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.32/41.65          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.32/41.65    (56)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.32/41.65          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.32/41.65  
% 230.32/41.65  Begin of proof
% 230.32/41.65  | 
% 230.32/41.65  | BETA: splitting (47) gives:
% 230.32/41.65  | 
% 230.32/41.65  | Case 1:
% 230.32/41.65  | | 
% 230.32/41.65  | |   (57)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 230.32/41.65  | |           e2)
% 230.32/41.65  | | 
% 230.32/41.65  | | BETA: splitting (57) gives:
% 230.32/41.65  | | 
% 230.32/41.65  | | Case 1:
% 230.32/41.65  | | | 
% 230.32/41.65  | | |   (58)  all_57_9 = e2 & op(e3, e0) = e2
% 230.32/41.65  | | | 
% 230.32/41.65  | | | ALPHA: (58) implies:
% 230.32/41.65  | | |   (59)  all_57_9 = e2
% 230.32/41.65  | | |   (60)  op(e3, e0) = e2
% 230.32/41.65  | | | 
% 230.32/41.65  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 230.32/41.65  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 230.32/41.65  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 230.32/41.65  | | |            (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 230.32/41.65  | | |            (43), (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 230.32/41.65  | | |            (53), (54), (55), (56), (59), (60) are inconsistent by
% 230.32/41.65  | | |            sub-proof #1083.
% 230.32/41.65  | | | 
% 230.32/41.65  | | Case 2:
% 230.32/41.65  | | | 
% 230.32/41.65  | | |   (61)  all_57_10 = e2 & op(e2, e0) = e2
% 230.32/41.65  | | | 
% 230.32/41.65  | | | REF_CLOSE: (8), (16), (41), (61) are inconsistent by sub-proof #2432.
% 230.32/41.65  | | | 
% 230.32/41.65  | | End of split
% 230.32/41.65  | | 
% 230.32/41.65  | Case 2:
% 230.32/41.65  | | 
% 230.32/41.65  | |   (62)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.32/41.65  | |           e2)
% 230.32/41.65  | | 
% 230.32/41.65  | | BETA: splitting (62) gives:
% 230.32/41.65  | | 
% 230.32/41.65  | | Case 1:
% 230.32/41.65  | | | 
% 230.32/41.65  | | |   (63)  all_57_11 = e2 & op(e1, e0) = e2
% 230.32/41.65  | | | 
% 230.32/41.65  | | | ALPHA: (63) implies:
% 230.32/41.65  | | |   (64)  all_57_11 = e2
% 230.32/41.65  | | | 
% 230.32/41.65  | | | COMBINE_EQS: (29), (64) imply:
% 230.32/41.65  | | |   (65)  e2 = e0
% 230.32/41.65  | | | 
% 230.32/41.65  | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (12), (13), (18), (19),
% 230.32/41.65  | | |            (20), (21), (22), (23), (24), (25), (27), (32), (35), (36),
% 230.32/41.65  | | |            (38), (39), (40), (43), (44), (46), (47), (48), (49), (50),
% 230.32/41.65  | | |            (51), (52), (53), (54), (55), (56), (65) are inconsistent by
% 230.32/41.65  | | |            sub-proof #1140.
% 230.32/41.65  | | | 
% 230.32/41.65  | | Case 2:
% 230.32/41.65  | | | 
% 230.32/41.65  | | |   (66)  all_57_15 = e2 & op(e0, e0) = e2
% 230.32/41.65  | | | 
% 230.32/41.65  | | | ALPHA: (66) implies:
% 230.32/41.65  | | |   (67)  all_57_15 = e2
% 230.32/41.65  | | | 
% 230.32/41.65  | | | REF_CLOSE: (21), (25), (67) are inconsistent by sub-proof #2058.
% 230.32/41.65  | | | 
% 230.32/41.65  | | End of split
% 230.32/41.65  | | 
% 230.32/41.65  | End of split
% 230.32/41.65  | 
% 230.32/41.65  End of proof
% 230.32/41.65  
% 230.32/41.65  Sub-proof #1077 shows that the following formulas are inconsistent:
% 230.32/41.65  ----------------------------------------------------------------
% 230.32/41.65    (1)  all_57_10 = e1
% 230.32/41.65    (2)   ~ (e3 = e2)
% 230.32/41.65    (3)  all_57_5 = e3
% 230.32/41.65    (4)  e2 = e0
% 230.32/41.65    (5)   ~ (e2 = e0)
% 230.32/41.65    (6)  all_57_2 = e0
% 230.32/41.65    (7)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.32/41.65         (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.32/41.65    (8)   ~ (e2 = e1)
% 230.32/41.65    (9)  all_57_3 = e2
% 230.32/41.65  
% 230.32/41.65  Begin of proof
% 230.32/41.65  | 
% 230.32/41.65  | SIMP: (4) implies:
% 230.32/41.65  |   (10)  e2 = e0
% 230.32/41.65  | 
% 230.32/41.65  | COMBINE_EQS: (9), (10) imply:
% 230.32/41.65  |   (11)  all_57_3 = e0
% 230.32/41.65  | 
% 230.32/41.65  | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (11) are inconsistent by
% 230.32/41.65  |            sub-proof #2254.
% 230.32/41.65  | 
% 230.32/41.65  End of proof
% 230.32/41.65  
% 230.32/41.65  Sub-proof #1078 shows that the following formulas are inconsistent:
% 230.32/41.65  ----------------------------------------------------------------
% 230.32/41.65    (1)   ~ (e3 = e1)
% 230.32/41.65    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.32/41.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.32/41.65    (3)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.32/41.65         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.32/41.65    (4)   ~ (all_6_2 = e3)
% 230.32/41.65    (5)  op(e1, e1) = all_6_2
% 230.32/41.65    (6)  all_57_7 = e2
% 230.32/41.65    (7)  all_57_6 = e1
% 230.32/41.65    (8)   ~ (e3 = e2)
% 230.32/41.65    (9)   ~ (e3 = e0)
% 230.32/41.65    (10)  all_57_15 = e3
% 230.32/41.65    (11)   ~ (e2 = e0)
% 230.32/41.65    (12)   ~ (e1 = e0)
% 230.32/41.65    (13)  op(e0, e0) = e3
% 230.32/41.65    (14)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.32/41.65              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.32/41.65                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.32/41.65                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.32/41.65    (15)   ~ (e2 = e1)
% 230.32/41.65    (16)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.32/41.65          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.32/41.65    (17)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.32/41.65          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.32/41.65  
% 230.32/41.65  Begin of proof
% 230.32/41.65  | 
% 230.32/41.65  | BETA: splitting (14) gives:
% 230.32/41.65  | 
% 230.32/41.65  | Case 1:
% 230.32/41.65  | | 
% 230.32/41.65  | |   (18)  all_57_15 = e0 & op(e0, e0) = e0
% 230.32/41.65  | | 
% 230.32/41.65  | | ALPHA: (18) implies:
% 230.32/41.65  | |   (19)  op(e0, e0) = e0
% 230.32/41.65  | | 
% 230.32/41.65  | | REF_CLOSE: (2), (9), (13), (19) are inconsistent by sub-proof #2304.
% 230.32/41.65  | | 
% 230.32/41.65  | Case 2:
% 230.32/41.65  | | 
% 230.32/41.65  | |   (20)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 230.32/41.65  | |             e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0 &
% 230.32/41.65  | |             op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 230.32/41.65  | |           (all_57_14 = e0 & op(e0, e1) = e0))
% 230.32/41.65  | | 
% 230.32/41.65  | | ALPHA: (20) implies:
% 230.32/41.65  | |   (21)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 230.32/41.65  | |           e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.32/41.65  | | 
% 230.32/41.65  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 230.32/41.65  | |            (15), (16), (17), (21) are inconsistent by sub-proof #1079.
% 230.32/41.65  | | 
% 230.32/41.65  | End of split
% 230.32/41.65  | 
% 230.32/41.65  End of proof
% 230.32/41.65  
% 230.32/41.65  Sub-proof #1079 shows that the following formulas are inconsistent:
% 230.32/41.65  ----------------------------------------------------------------
% 230.32/41.65    (1)   ~ (e3 = e1)
% 230.32/41.65    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.32/41.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.32/41.65    (3)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.32/41.65         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.32/41.65    (4)   ~ (all_6_2 = e3)
% 230.32/41.65    (5)  op(e1, e1) = all_6_2
% 230.32/41.65    (6)  all_57_7 = e2
% 230.32/41.65    (7)  all_57_6 = e1
% 230.32/41.65    (8)   ~ (e3 = e2)
% 230.32/41.65    (9)   ~ (e3 = e0)
% 230.32/41.65    (10)  all_57_15 = e3
% 230.32/41.65    (11)   ~ (e2 = e0)
% 230.32/41.65    (12)   ~ (e1 = e0)
% 230.32/41.65    (13)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) |
% 230.32/41.65          (all_57_11 = e0 & op(e1, e0) = e0)
% 230.32/41.65    (14)   ~ (e2 = e1)
% 230.32/41.65    (15)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.32/41.65          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.32/41.65    (16)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.32/41.65          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.32/41.65  
% 230.32/41.65  Begin of proof
% 230.32/41.65  | 
% 230.32/41.65  | BETA: splitting (3) gives:
% 230.32/41.65  | 
% 230.32/41.65  | Case 1:
% 230.32/41.65  | | 
% 230.32/41.65  | |   (17)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 230.32/41.65  | |           e3)
% 230.32/41.65  | | 
% 230.32/41.65  | | BETA: splitting (17) gives:
% 230.32/41.65  | | 
% 230.32/41.65  | | Case 1:
% 230.32/41.65  | | | 
% 230.32/41.65  | | |   (18)  all_57_6 = e3 & op(e1, e3) = e3
% 230.32/41.65  | | | 
% 230.32/41.65  | | | ALPHA: (18) implies:
% 230.32/41.65  | | |   (19)  all_57_6 = e3
% 230.32/41.65  | | | 
% 230.32/41.65  | | | REF_CLOSE: (1), (7), (19) are inconsistent by sub-proof #2017.
% 230.32/41.65  | | | 
% 230.32/41.65  | | Case 2:
% 230.32/41.65  | | | 
% 230.32/41.65  | | |   (20)  all_57_7 = e3 & op(e1, e2) = e3
% 230.32/41.65  | | | 
% 230.32/41.65  | | | ALPHA: (20) implies:
% 230.32/41.65  | | |   (21)  all_57_7 = e3
% 230.32/41.65  | | | 
% 230.32/41.65  | | | REF_CLOSE: (6), (8), (21) are inconsistent by sub-proof #2102.
% 230.32/41.65  | | | 
% 230.32/41.65  | | End of split
% 230.32/41.65  | | 
% 230.32/41.65  | Case 2:
% 230.32/41.65  | | 
% 230.32/41.65  | |   (22)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 230.32/41.65  | |           e3)
% 230.32/41.65  | | 
% 230.32/41.65  | | REF_CLOSE: (1), (2), (4), (5), (8), (9), (10), (11), (12), (13), (14), (15),
% 230.32/41.65  | |            (16), (22) are inconsistent by sub-proof #1080.
% 230.32/41.65  | | 
% 230.32/41.65  | End of split
% 230.32/41.65  | 
% 230.32/41.65  End of proof
% 230.32/41.65  
% 230.32/41.65  Sub-proof #1080 shows that the following formulas are inconsistent:
% 230.32/41.65  ----------------------------------------------------------------
% 230.32/41.65    (1)   ~ (e3 = e1)
% 230.32/41.65    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.32/41.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.32/41.65    (3)   ~ (all_6_2 = e3)
% 230.32/41.65    (4)  op(e1, e1) = all_6_2
% 230.32/41.65    (5)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.32/41.65    (6)   ~ (e3 = e2)
% 230.32/41.65    (7)   ~ (e3 = e0)
% 230.32/41.65    (8)  all_57_15 = e3
% 230.32/41.65    (9)   ~ (e2 = e0)
% 230.32/41.65    (10)   ~ (e1 = e0)
% 230.32/41.65    (11)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) |
% 230.32/41.65          (all_57_11 = e0 & op(e1, e0) = e0)
% 230.32/41.65    (12)   ~ (e2 = e1)
% 230.32/41.65    (13)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.32/41.65          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.32/41.65    (14)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.32/41.65          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.32/41.65  
% 230.32/41.65  Begin of proof
% 230.32/41.65  | 
% 230.32/41.65  | BETA: splitting (5) gives:
% 230.32/41.65  | 
% 230.32/41.65  | Case 1:
% 230.32/41.65  | | 
% 230.32/41.65  | |   (15)  all_57_8 = e3 & op(e1, e1) = e3
% 230.32/41.65  | | 
% 230.32/41.65  | | ALPHA: (15) implies:
% 230.32/41.65  | |   (16)  op(e1, e1) = e3
% 230.32/41.65  | | 
% 230.32/41.65  | | REF_CLOSE: (2), (3), (4), (16) are inconsistent by sub-proof #2468.
% 230.32/41.65  | | 
% 230.32/41.65  | Case 2:
% 230.32/41.65  | | 
% 230.32/41.65  | |   (17)  all_57_11 = e3 & op(e1, e0) = e3
% 230.32/41.65  | | 
% 230.32/41.65  | | ALPHA: (17) implies:
% 230.32/41.65  | |   (18)  all_57_11 = e3
% 230.32/41.65  | | 
% 230.32/41.65  | | REF_CLOSE: (1), (6), (7), (8), (9), (10), (11), (12), (13), (14), (18) are
% 230.32/41.65  | |            inconsistent by sub-proof #2135.
% 230.32/41.65  | | 
% 230.32/41.65  | End of split
% 230.32/41.65  | 
% 230.32/41.65  End of proof
% 230.32/41.65  
% 230.32/41.65  Sub-proof #1081 shows that the following formulas are inconsistent:
% 230.32/41.65  ----------------------------------------------------------------
% 230.32/41.65    (1)  e1 = e0
% 230.32/41.65    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.32/41.65         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.32/41.65    (3)   ~ (all_52_7 = e3)
% 230.32/41.65    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.32/41.65         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.32/41.65    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.32/41.65         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.32/41.65    (6)   ~ (e3 = e1)
% 230.32/41.65    (7)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.32/41.65         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.32/41.65    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.32/41.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.32/41.65    (9)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.32/41.65         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.32/41.65    (10)   ~ (all_6_2 = e3)
% 230.32/41.65    (11)  op(e1, e1) = all_6_2
% 230.32/41.65    (12)  op(all_52_7, all_52_7) = e0
% 230.32/41.65    (13)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.32/41.65          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.32/41.65    (14)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 230.32/41.65            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 230.32/41.65              e3) = all_22_1 & $i(all_22_1))
% 230.32/41.65    (15)   ~ (all_53_13 = e2)
% 230.32/41.65    (16)   ~ (all_53_7 = e2)
% 230.32/41.65    (17)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.32/41.65          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.32/41.65    (18)  all_57_6 = e1
% 230.32/41.65    (19)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.32/41.65          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.32/41.65    (20)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 230.32/41.65          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.32/41.65    (21)   ~ (e3 = e2)
% 230.32/41.65    (22)   ~ (e3 = e0)
% 230.32/41.65    (23)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.32/41.65          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.32/41.65    (24)  op(e3, e3) = e3
% 230.32/41.65    (25)  all_57_15 = e3
% 230.32/41.65    (26)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.32/41.65          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.32/41.65            e1)
% 230.32/41.65    (27)  all_57_5 = e3
% 230.32/41.65    (28)  op(e3, e3) = all_52_1
% 230.32/41.65    (29)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.32/41.65          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.32/41.65    (30)  op(all_52_1, all_52_1) = e3
% 230.32/41.65    (31)   ~ (e2 = e0)
% 230.32/41.65    (32)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 230.32/41.65            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 230.32/41.65              e3) = all_12_1 & $i(all_12_1))
% 230.32/41.65    (33)  op(e2, e2) = e2
% 230.32/41.65    (34)   ~ (e1 = e0)
% 230.32/41.65    (35)  op(e0, e0) = e3
% 230.32/41.65    (36)  op(e0, e2) = all_53_7
% 230.32/41.65    (37)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.32/41.65          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.32/41.65            e2)
% 230.32/41.65    (38)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.32/41.65              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.32/41.65                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.32/41.65                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.32/41.65    (39)  op(e1, e1) = e0
% 230.32/41.65    (40)  op(e2, e0) = all_53_13
% 230.32/41.65    (41)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.32/41.65          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.32/41.65    (42)  all_57_7 = e3
% 230.32/41.65    (43)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.32/41.65          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.32/41.65    (44)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.32/41.65          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 230.32/41.65    (45)   ~ (e2 = e1)
% 230.32/41.65    (46)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.32/41.65          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.32/41.65    (47)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.32/41.65          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.32/41.65    (48)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.32/41.65          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.32/41.65    (49)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.32/41.65          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.32/41.65    (50)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.32/41.65          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.32/41.65    (51)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.32/41.65          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.32/41.65    (52)  all_57_3 = e2
% 230.32/41.65    (53)  op(e3, e0) = all_52_7
% 230.32/41.65    (54)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.32/41.65          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.32/41.65    (55)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.32/41.65          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.32/41.65  
% 230.32/41.65  Begin of proof
% 230.32/41.65  | 
% 230.32/41.65  | SIMP: (1) implies:
% 230.32/41.65  |   (56)  e1 = e0
% 230.32/41.65  | 
% 230.32/41.65  | COMBINE_EQS: (18), (56) imply:
% 230.32/41.65  |   (57)  all_57_6 = e0
% 230.32/41.65  | 
% 230.32/41.65  | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 230.32/41.65  |            (14), (15), (16), (17), (19), (20), (21), (22), (23), (24), (25),
% 230.32/41.65  |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 230.32/41.65  |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 230.32/41.65  |            (48), (49), (50), (51), (52), (53), (54), (55), (57) are
% 230.32/41.65  |            inconsistent by sub-proof #1088.
% 230.32/41.65  | 
% 230.32/41.65  End of proof
% 230.32/41.65  
% 230.32/41.65  Sub-proof #1082 shows that the following formulas are inconsistent:
% 230.32/41.65  ----------------------------------------------------------------
% 230.32/41.65    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.32/41.65         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.32/41.65    (2)   ~ (e3 = e1)
% 230.32/41.65    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.32/41.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.32/41.65    (4)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.32/41.65         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.32/41.65    (5)   ~ (all_6_2 = e3)
% 230.32/41.65    (6)  op(e1, e1) = all_6_2
% 230.32/41.65    (7)  all_57_2 = e2
% 230.32/41.65    (8)  all_57_6 = e1
% 230.32/41.65    (9)   ~ (e3 = e2)
% 230.32/41.65    (10)   ~ (e3 = e0)
% 230.32/41.65    (11)  all_57_15 = e3
% 230.32/41.65    (12)  all_57_5 = e3
% 230.32/41.65    (13)   ~ (e2 = e0)
% 230.32/41.65    (14)  op(e2, e2) = e2
% 230.32/41.65    (15)   ~ (e1 = e0)
% 230.32/41.65    (16)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.32/41.65              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.32/41.65                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.32/41.65                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.32/41.65    (17)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.32/41.65          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.32/41.65    (18)  all_57_7 = e3
% 230.32/41.65    (19)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.32/41.65          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.32/41.65    (20)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.32/41.65          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 230.32/41.65    (21)   ~ (e2 = e1)
% 230.32/41.65    (22)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.32/41.65          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.32/41.65    (23)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.32/41.65          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.32/41.65    (24)  all_57_3 = e2
% 230.32/41.65  
% 230.32/41.65  Begin of proof
% 230.32/41.65  | 
% 230.32/41.65  | BETA: splitting (1) gives:
% 230.32/41.65  | 
% 230.32/41.65  | Case 1:
% 230.32/41.65  | | 
% 230.32/41.65  | |   (25)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) =
% 230.32/41.65  | |           e1)
% 230.32/41.65  | | 
% 230.32/41.65  | | REF_CLOSE: (3), (7), (14), (21), (25) are inconsistent by sub-proof #2243.
% 230.32/41.65  | | 
% 230.32/41.65  | Case 2:
% 230.32/41.65  | | 
% 230.32/41.65  | |   (26)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) =
% 230.32/41.65  | |           e1)
% 230.32/41.65  | | 
% 230.32/41.65  | | BETA: splitting (26) gives:
% 230.32/41.65  | | 
% 230.32/41.65  | | Case 1:
% 230.32/41.65  | | | 
% 230.32/41.65  | | |   (27)  all_57_5 = e1 & op(e2, e1) = e1
% 230.32/41.65  | | | 
% 230.32/41.65  | | | REF_CLOSE: (2), (12), (27) are inconsistent by sub-proof #2376.
% 230.32/41.65  | | | 
% 230.32/41.65  | | Case 2:
% 230.32/41.65  | | | 
% 230.32/41.65  | | |   (28)  all_57_10 = e1 & op(e2, e0) = e1
% 230.32/41.65  | | | 
% 230.32/41.65  | | | ALPHA: (28) implies:
% 230.32/41.66  | | |   (29)  all_57_10 = e1
% 230.32/41.66  | | | 
% 230.32/41.66  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 230.32/41.66  | | |            (13), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 230.32/41.66  | | |            (24), (29) are inconsistent by sub-proof #1106.
% 230.32/41.66  | | | 
% 230.32/41.66  | | End of split
% 230.32/41.66  | | 
% 230.32/41.66  | End of split
% 230.32/41.66  | 
% 230.32/41.66  End of proof
% 230.32/41.66  
% 230.32/41.66  Sub-proof #1083 shows that the following formulas are inconsistent:
% 230.32/41.66  ----------------------------------------------------------------
% 230.32/41.66    (1)  all_57_9 = e2
% 230.32/41.66    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.32/41.66         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.32/41.66    (3)  op(e3, e1) = all_52_5
% 230.32/41.66    (4)   ~ (all_52_7 = e3)
% 230.32/41.66    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.32/41.66         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.32/41.66    (6)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.32/41.66         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.32/41.66    (7)   ~ (e3 = e1)
% 230.32/41.66    (8)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.32/41.66         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.32/41.66    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.32/41.66           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.32/41.66    (10)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.32/41.66          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.32/41.66    (11)   ~ (all_6_2 = e3)
% 230.32/41.66    (12)  op(e1, e1) = all_6_2
% 230.32/41.66    (13)  op(all_52_7, all_52_7) = e0
% 230.32/41.66    (14)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.32/41.66          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.32/41.66    (15)   ~ (all_52_5 = all_52_7)
% 230.32/41.66    (16)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 230.32/41.66            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 230.32/41.66              e3) = all_22_1 & $i(all_22_1))
% 230.32/41.66    (17)   ~ (all_53_13 = e2)
% 230.32/41.66    (18)   ~ (all_53_7 = e2)
% 230.32/41.66    (19)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.32/41.66          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.32/41.66    (20)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.32/41.66          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.32/41.66    (21)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 230.32/41.66          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.32/41.66    (22)   ~ (e3 = e2)
% 230.32/41.66    (23)   ~ (e3 = e0)
% 230.32/41.66    (24)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.32/41.66          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.32/41.66    (25)  op(e3, e3) = e3
% 230.32/41.66    (26)  op(e3, e0) = e2
% 230.32/41.66    (27)  all_57_15 = e3
% 230.32/41.66    (28)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.32/41.66          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.32/41.66            e1)
% 230.32/41.66    (29)  all_57_5 = e3
% 230.32/41.66    (30)  op(e3, e3) = all_52_1
% 230.32/41.66    (31)  all_57_11 = e0
% 230.32/41.66    (32)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.32/41.66          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.32/41.66    (33)  op(all_52_1, all_52_1) = e3
% 230.32/41.66    (34)   ~ (e2 = e0)
% 230.38/41.66    (35)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 230.38/41.66            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 230.38/41.66              e3) = all_12_1 & $i(all_12_1))
% 230.38/41.66    (36)  op(e2, e2) = e2
% 230.38/41.66    (37)   ~ (e1 = e0)
% 230.38/41.66    (38)  op(e0, e0) = e3
% 230.38/41.66    (39)  op(e0, e2) = all_53_7
% 230.38/41.66    (40)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.38/41.66          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.38/41.66            e2)
% 230.38/41.66    (41)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.38/41.66              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.38/41.66                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.38/41.66                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.38/41.66    (42)  op(e1, e1) = e0
% 230.38/41.66    (43)  op(e2, e0) = all_53_13
% 230.38/41.66    (44)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.38/41.66          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.38/41.66    (45)  all_57_7 = e3
% 230.38/41.66    (46)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.38/41.66          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.38/41.66    (47)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.38/41.66          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 230.38/41.66    (48)   ~ (e2 = e1)
% 230.38/41.66    (49)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.38/41.66          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.38/41.66    (50)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.38/41.66          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.38/41.66    (51)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.38/41.66          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.38/41.66    (52)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.38/41.66          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.38/41.66    (53)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.38/41.66          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.38/41.66    (54)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.38/41.66          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.38/41.66    (55)  all_57_3 = e2
% 230.38/41.66    (56)  op(e3, e0) = all_52_7
% 230.38/41.66    (57)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.38/41.66          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.38/41.66    (58)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.38/41.66          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.38/41.66  
% 230.38/41.66  Begin of proof
% 230.38/41.66  | 
% 230.38/41.66  | BETA: splitting (58) gives:
% 230.38/41.66  | 
% 230.38/41.66  | Case 1:
% 230.38/41.66  | | 
% 230.38/41.66  | |   (59)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) =
% 230.38/41.66  | |           e2)
% 230.38/41.66  | | 
% 230.38/41.66  | | BETA: splitting (59) gives:
% 230.38/41.66  | | 
% 230.38/41.66  | | Case 1:
% 230.38/41.66  | | | 
% 230.38/41.66  | | |   (60)  all_57_6 = e2 & op(e1, e3) = e2
% 230.38/41.66  | | | 
% 230.38/41.66  | | | ALPHA: (60) implies:
% 230.38/41.66  | | |   (61)  all_57_6 = e2
% 230.38/41.66  | | | 
% 230.38/41.66  | | | BETA: splitting (20) gives:
% 230.38/41.66  | | | 
% 230.38/41.66  | | | Case 1:
% 230.38/41.66  | | | | 
% 230.38/41.66  | | | |   (62)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2)
% 230.38/41.66  | | | |           = e0)
% 230.38/41.66  | | | | 
% 230.38/41.66  | | | | BETA: splitting (62) gives:
% 230.38/41.66  | | | | 
% 230.38/41.66  | | | | Case 1:
% 230.38/41.66  | | | | | 
% 230.38/41.66  | | | | |   (63)  all_57_0 = e0 & op(e3, e3) = e0
% 230.38/41.66  | | | | | 
% 230.38/41.66  | | | | | ALPHA: (63) implies:
% 230.38/41.66  | | | | |   (64)  op(e3, e3) = e0
% 230.38/41.66  | | | | | 
% 230.38/41.66  | | | | | REF_CLOSE: (9), (23), (25), (64) are inconsistent by sub-proof #2494.
% 230.38/41.66  | | | | | 
% 230.38/41.66  | | | | Case 2:
% 230.38/41.66  | | | | | 
% 230.38/41.66  | | | | |   (65)  all_57_1 = e0 & op(e3, e2) = e0
% 230.38/41.66  | | | | | 
% 230.38/41.66  | | | | | ALPHA: (65) implies:
% 230.38/41.66  | | | | |   (66)  all_57_1 = e0
% 230.38/41.66  | | | | | 
% 230.38/41.66  | | | | | BETA: splitting (53) gives:
% 230.38/41.66  | | | | | 
% 230.38/41.66  | | | | | Case 1:
% 230.38/41.66  | | | | | | 
% 230.38/41.66  | | | | | |   (67)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2,
% 230.38/41.66  | | | | | |             e0) = e1)
% 230.38/41.66  | | | | | | 
% 230.38/41.66  | | | | | | BETA: splitting (67) gives:
% 230.38/41.66  | | | | | | 
% 230.38/41.66  | | | | | | Case 1:
% 230.38/41.66  | | | | | | | 
% 230.38/41.66  | | | | | | |   (68)  all_57_9 = e1 & op(e3, e0) = e1
% 230.38/41.66  | | | | | | | 
% 230.38/41.66  | | | | | | | ALPHA: (68) implies:
% 230.38/41.66  | | | | | | |   (69)  all_57_9 = e1
% 230.38/41.66  | | | | | | | 
% 230.38/41.66  | | | | | | | REF_CLOSE: (1), (48), (69) are inconsistent by sub-proof #2444.
% 230.38/41.66  | | | | | | | 
% 230.38/41.66  | | | | | | Case 2:
% 230.38/41.66  | | | | | | | 
% 230.38/41.66  | | | | | | |   (70)  all_57_10 = e1 & op(e2, e0) = e1
% 230.38/41.66  | | | | | | | 
% 230.38/41.66  | | | | | | | ALPHA: (70) implies:
% 230.38/41.66  | | | | | | |   (71)  all_57_10 = e1
% 230.38/41.66  | | | | | | | 
% 230.38/41.66  | | | | | | | BETA: splitting (14) gives:
% 230.38/41.66  | | | | | | | 
% 230.38/41.66  | | | | | | | Case 1:
% 230.38/41.66  | | | | | | | | 
% 230.38/41.66  | | | | | | | |   (72)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 &
% 230.38/41.66  | | | | | | | |           op(e3, e2) = e1)
% 230.38/41.66  | | | | | | | | 
% 230.38/41.66  | | | | | | | | BETA: splitting (72) gives:
% 230.38/41.66  | | | | | | | | 
% 230.38/41.66  | | | | | | | | Case 1:
% 230.38/41.66  | | | | | | | | | 
% 230.38/41.66  | | | | | | | | |   (73)  all_57_0 = e1 & op(e3, e3) = e1
% 230.38/41.66  | | | | | | | | | 
% 230.38/41.66  | | | | | | | | | ALPHA: (73) implies:
% 230.38/41.66  | | | | | | | | |   (74)  op(e3, e3) = e1
% 230.38/41.66  | | | | | | | | | 
% 230.38/41.66  | | | | | | | | | REF_CLOSE: (7), (9), (25), (74) are inconsistent by sub-proof
% 230.38/41.66  | | | | | | | | |            #2495.
% 230.38/41.66  | | | | | | | | | 
% 230.38/41.66  | | | | | | | | Case 2:
% 230.38/41.66  | | | | | | | | | 
% 230.38/41.66  | | | | | | | | |   (75)  all_57_1 = e1 & op(e3, e2) = e1
% 230.38/41.66  | | | | | | | | | 
% 230.38/41.66  | | | | | | | | | ALPHA: (75) implies:
% 230.38/41.66  | | | | | | | | |   (76)  all_57_1 = e1
% 230.38/41.66  | | | | | | | | | 
% 230.38/41.66  | | | | | | | | | COMBINE_EQS: (66), (76) imply:
% 230.38/41.66  | | | | | | | | |   (77)  e1 = e0
% 230.38/41.66  | | | | | | | | | 
% 230.38/41.66  | | | | | | | | | REF_CLOSE: (7), (9), (22), (27), (31), (34), (37), (38), (48),
% 230.38/41.66  | | | | | | | | |            (49), (53), (71), (77) are inconsistent by
% 230.38/41.66  | | | | | | | | |            sub-proof #1086.
% 230.38/41.66  | | | | | | | | | 
% 230.38/41.66  | | | | | | | | End of split
% 230.38/41.66  | | | | | | | | 
% 230.38/41.66  | | | | | | | Case 2:
% 230.38/41.66  | | | | | | | | 
% 230.38/41.66  | | | | | | | |   (78)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 &
% 230.38/41.66  | | | | | | | |           op(e3, e0) = e1)
% 230.38/41.66  | | | | | | | | 
% 230.38/41.66  | | | | | | | | BETA: splitting (78) gives:
% 230.38/41.66  | | | | | | | | 
% 230.38/41.66  | | | | | | | | Case 1:
% 230.38/41.66  | | | | | | | | | 
% 230.38/41.66  | | | | | | | | |   (79)  all_57_4 = e1 & op(e3, e1) = e1
% 230.38/41.66  | | | | | | | | | 
% 230.38/41.66  | | | | | | | | | ALPHA: (79) implies:
% 230.38/41.66  | | | | | | | | |   (80)  all_57_4 = e1
% 230.38/41.66  | | | | | | | | | 
% 230.38/41.66  | | | | | | | | | BETA: splitting (57) gives:
% 230.38/41.66  | | | | | | | | | 
% 230.38/41.66  | | | | | | | | | Case 1:
% 230.38/41.66  | | | | | | | | | | 
% 230.38/41.66  | | | | | | | | | |   (81)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 &
% 230.38/41.66  | | | | | | | | | |           op(e2, e2) = e1)
% 230.38/41.66  | | | | | | | | | | 
% 230.38/41.66  | | | | | | | | | | REF_CLOSE: (1), (7), (9), (14), (25), (36), (37), (48), (66),
% 230.38/41.66  | | | | | | | | | |            (80), (81) are inconsistent by sub-proof #1085.
% 230.38/41.66  | | | | | | | | | | 
% 230.38/41.66  | | | | | | | | | Case 2:
% 230.38/41.66  | | | | | | | | | | 
% 230.38/41.66  | | | | | | | | | |   (82)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1
% 230.38/41.66  | | | | | | | | | |           & op(e0, e2) = e1)
% 230.38/41.66  | | | | | | | | | | 
% 230.38/41.66  | | | | | | | | | | BETA: splitting (82) gives:
% 230.38/41.66  | | | | | | | | | | 
% 230.38/41.66  | | | | | | | | | | Case 1:
% 230.38/41.66  | | | | | | | | | | | 
% 230.38/41.66  | | | | | | | | | | |   (83)  all_57_7 = e1 & op(e1, e2) = e1
% 230.38/41.66  | | | | | | | | | | | 
% 230.38/41.66  | | | | | | | | | | | ALPHA: (83) implies:
% 230.38/41.66  | | | | | | | | | | |   (84)  all_57_7 = e1
% 230.38/41.66  | | | | | | | | | | | 
% 230.38/41.66  | | | | | | | | | | | REF_CLOSE: (7), (9), (10), (11), (12), (22), (23), (27),
% 230.38/41.66  | | | | | | | | | | |            (34), (37), (41), (48), (49), (53), (61), (84) are
% 230.38/41.66  | | | | | | | | | | |            inconsistent by sub-proof #1245.
% 230.38/41.66  | | | | | | | | | | | 
% 230.38/41.66  | | | | | | | | | | Case 2:
% 230.38/41.66  | | | | | | | | | | | 
% 230.38/41.66  | | | | | | | | | | |   (85)  all_57_13 = e1 & op(e0, e2) = e1
% 230.38/41.66  | | | | | | | | | | | 
% 230.38/41.66  | | | | | | | | | | | ALPHA: (85) implies:
% 230.38/41.66  | | | | | | | | | | |   (86)  all_57_13 = e1
% 230.38/41.66  | | | | | | | | | | | 
% 230.38/41.66  | | | | | | | | | | | BETA: splitting (54) gives:
% 230.38/41.66  | | | | | | | | | | | 
% 230.38/41.66  | | | | | | | | | | | Case 1:
% 230.38/41.66  | | | | | | | | | | | | 
% 230.38/41.66  | | | | | | | | | | | |   (87)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 230.38/41.66  | | | | | | | | | | | |           & op(e1, e2) = e1)
% 230.38/41.66  | | | | | | | | | | | | 
% 230.38/41.66  | | | | | | | | | | | | REF_CLOSE: (7), (9), (10), (11), (12), (22), (23), (27),
% 230.38/41.66  | | | | | | | | | | | |            (34), (37), (41), (48), (49), (53), (61), (87) are
% 230.38/41.66  | | | | | | | | | | | |            inconsistent by sub-proof #1123.
% 230.38/41.66  | | | | | | | | | | | | 
% 230.38/41.66  | | | | | | | | | | | Case 2:
% 230.38/41.66  | | | | | | | | | | | | 
% 230.38/41.66  | | | | | | | | | | | |   (88)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 230.38/41.66  | | | | | | | | | | | |           e1 & op(e1, e0) = e1)
% 230.38/41.66  | | | | | | | | | | | | 
% 230.38/41.66  | | | | | | | | | | | | BETA: splitting (88) gives:
% 230.38/41.66  | | | | | | | | | | | | 
% 230.38/41.66  | | | | | | | | | | | | Case 1:
% 230.38/41.66  | | | | | | | | | | | | | 
% 230.38/41.66  | | | | | | | | | | | | |   (89)  all_57_8 = e1 & op(e1, e1) = e1
% 230.38/41.66  | | | | | | | | | | | | | 
% 230.38/41.66  | | | | | | | | | | | | | ALPHA: (89) implies:
% 230.38/41.66  | | | | | | | | | | | | |   (90)  op(e1, e1) = e1
% 230.38/41.66  | | | | | | | | | | | | | 
% 230.38/41.66  | | | | | | | | | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10),
% 230.38/41.66  | | | | | | | | | | | | |            (11), (12), (13), (14), (18), (19), (20), (21),
% 230.38/41.66  | | | | | | | | | | | | |            (22), (23), (24), (25), (27), (28), (29), (31),
% 230.38/41.66  | | | | | | | | | | | | |            (34), (36), (37), (38), (39), (40), (41), (45),
% 230.38/41.66  | | | | | | | | | | | | |            (46), (48), (49), (50), (51), (52), (53), (54),
% 230.38/41.66  | | | | | | | | | | | | |            (55), (56), (57), (58), (61), (80), (90) are
% 230.38/41.66  | | | | | | | | | | | | |            inconsistent by sub-proof #1120.
% 230.38/41.66  | | | | | | | | | | | | | 
% 230.38/41.66  | | | | | | | | | | | | Case 2:
% 230.38/41.66  | | | | | | | | | | | | | 
% 230.38/41.66  | | | | | | | | | | | | |   (91)  all_57_11 = e1 & op(e1, e0) = e1
% 230.38/41.66  | | | | | | | | | | | | | 
% 230.38/41.66  | | | | | | | | | | | | | ALPHA: (91) implies:
% 230.38/41.66  | | | | | | | | | | | | |   (92)  all_57_11 = e1
% 230.38/41.66  | | | | | | | | | | | | | 
% 230.38/41.66  | | | | | | | | | | | | | COMBINE_EQS: (31), (92) imply:
% 230.38/41.66  | | | | | | | | | | | | |   (93)  e1 = e0
% 230.38/41.66  | | | | | | | | | | | | | 
% 230.38/41.66  | | | | | | | | | | | | | REF_CLOSE: (1), (7), (9), (14), (19), (22), (23), (25), (32),
% 230.38/41.66  | | | | | | | | | | | | |            (34), (37), (45), (48), (55), (80), (86), (93) are
% 230.38/41.66  | | | | | | | | | | | | |            inconsistent by sub-proof #1084.
% 230.38/41.66  | | | | | | | | | | | | | 
% 230.38/41.66  | | | | | | | | | | | | End of split
% 230.38/41.66  | | | | | | | | | | | | 
% 230.38/41.66  | | | | | | | | | | | End of split
% 230.38/41.66  | | | | | | | | | | | 
% 230.38/41.66  | | | | | | | | | | End of split
% 230.38/41.66  | | | | | | | | | | 
% 230.38/41.66  | | | | | | | | | End of split
% 230.38/41.66  | | | | | | | | | 
% 230.38/41.66  | | | | | | | | Case 2:
% 230.38/41.66  | | | | | | | | | 
% 230.38/41.66  | | | | | | | | |   (94)  all_57_9 = e1 & op(e3, e0) = e1
% 230.38/41.66  | | | | | | | | | 
% 230.38/41.66  | | | | | | | | | ALPHA: (94) implies:
% 230.38/41.66  | | | | | | | | |   (95)  all_57_9 = e1
% 230.38/41.66  | | | | | | | | | 
% 230.38/41.66  | | | | | | | | | REF_CLOSE: (1), (48), (95) are inconsistent by sub-proof
% 230.38/41.66  | | | | | | | | |            #2444.
% 230.38/41.66  | | | | | | | | | 
% 230.38/41.66  | | | | | | | | End of split
% 230.38/41.66  | | | | | | | | 
% 230.38/41.66  | | | | | | | End of split
% 230.38/41.66  | | | | | | | 
% 230.38/41.66  | | | | | | End of split
% 230.38/41.66  | | | | | | 
% 230.38/41.66  | | | | | Case 2:
% 230.38/41.66  | | | | | | 
% 230.38/41.66  | | | | | |   (96)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 &
% 230.38/41.66  | | | | | |           op(e0, e0) = e1)
% 230.38/41.66  | | | | | | 
% 230.38/41.66  | | | | | | REF_CLOSE: (7), (9), (31), (37), (38), (96) are inconsistent by
% 230.38/41.66  | | | | | |            sub-proof #1105.
% 230.38/41.66  | | | | | | 
% 230.38/41.66  | | | | | End of split
% 230.38/41.66  | | | | | 
% 230.38/41.66  | | | | End of split
% 230.38/41.66  | | | | 
% 230.38/41.66  | | | Case 2:
% 230.38/41.66  | | | | 
% 230.38/41.66  | | | |   (97)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0)
% 230.38/41.66  | | | |           = e0)
% 230.38/41.66  | | | | 
% 230.38/41.66  | | | | BETA: splitting (97) gives:
% 230.38/41.66  | | | | 
% 230.38/41.66  | | | | Case 1:
% 230.38/41.66  | | | | | 
% 230.38/41.66  | | | | |   (98)  all_57_4 = e0 & op(e3, e1) = e0
% 230.38/41.66  | | | | | 
% 230.38/41.66  | | | | | REF_CLOSE: (3), (9), (13), (15), (23), (26), (36), (38), (41), (56),
% 230.38/41.66  | | | | |            (98) are inconsistent by sub-proof #1163.
% 230.38/41.66  | | | | | 
% 230.38/41.66  | | | | Case 2:
% 230.38/41.66  | | | | | 
% 230.38/41.66  | | | | |   (99)  all_57_9 = e0 & op(e3, e0) = e0
% 230.38/41.66  | | | | | 
% 230.38/41.66  | | | | | ALPHA: (99) implies:
% 230.38/41.66  | | | | |   (100)  all_57_9 = e0
% 230.38/41.66  | | | | | 
% 230.38/41.66  | | | | | REF_CLOSE: (7), (22), (27), (31), (34), (37), (48), (49), (53), (100)
% 230.38/41.66  | | | | |            are inconsistent by sub-proof #1144.
% 230.38/41.66  | | | | | 
% 230.38/41.66  | | | | End of split
% 230.38/41.66  | | | | 
% 230.38/41.66  | | | End of split
% 230.38/41.66  | | | 
% 230.38/41.66  | | Case 2:
% 230.38/41.66  | | | 
% 230.38/41.66  | | |   (101)  all_57_7 = e2 & op(e1, e2) = e2
% 230.38/41.66  | | | 
% 230.38/41.66  | | | REF_CLOSE: (22), (45), (101) are inconsistent by sub-proof #2092.
% 230.38/41.66  | | | 
% 230.38/41.66  | | End of split
% 230.38/41.66  | | 
% 230.38/41.66  | Case 2:
% 230.38/41.66  | | 
% 230.38/41.66  | |   (102)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) =
% 230.38/41.66  | |            e2)
% 230.38/41.66  | | 
% 230.38/41.66  | | BETA: splitting (102) gives:
% 230.38/41.66  | | 
% 230.38/41.66  | | Case 1:
% 230.38/41.66  | | | 
% 230.38/41.66  | | |   (103)  all_57_8 = e2 & op(e1, e1) = e2
% 230.38/41.66  | | | 
% 230.38/41.66  | | | ALPHA: (103) implies:
% 230.38/41.66  | | |   (104)  op(e1, e1) = e2
% 230.38/41.66  | | | 
% 230.38/41.66  | | | REF_CLOSE: (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 230.38/41.66  | | |            (14), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 230.38/41.66  | | |            (25), (27), (28), (29), (30), (32), (33), (34), (35), (36),
% 230.38/41.66  | | |            (37), (38), (39), (40), (41), (43), (44), (45), (46), (47),
% 230.38/41.66  | | |            (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 230.38/41.66  | | |            (58), (104) are inconsistent by sub-proof #1090.
% 230.38/41.66  | | | 
% 230.38/41.66  | | Case 2:
% 230.38/41.66  | | | 
% 230.38/41.66  | | |   (105)  all_57_11 = e2 & op(e1, e0) = e2
% 230.38/41.66  | | | 
% 230.38/41.66  | | | ALPHA: (105) implies:
% 230.38/41.66  | | |   (106)  all_57_11 = e2
% 230.38/41.66  | | | 
% 230.38/41.66  | | | COMBINE_EQS: (31), (106) imply:
% 230.38/41.66  | | |   (107)  e2 = e0
% 230.38/41.66  | | | 
% 230.38/41.66  | | | REF_CLOSE: (2), (4), (5), (6), (7), (8), (9), (13), (14), (19), (20),
% 230.38/41.66  | | |            (21), (22), (23), (24), (25), (27), (29), (34), (37), (38),
% 230.38/41.66  | | |            (40), (41), (42), (45), (46), (48), (49), (50), (51), (52),
% 230.38/41.66  | | |            (53), (54), (55), (56), (57), (58), (107) are inconsistent by
% 230.38/41.66  | | |            sub-proof #1140.
% 230.38/41.66  | | | 
% 230.38/41.66  | | End of split
% 230.38/41.66  | | 
% 230.38/41.66  | End of split
% 230.38/41.66  | 
% 230.38/41.66  End of proof
% 230.38/41.66  
% 230.38/41.66  Sub-proof #1084 shows that the following formulas are inconsistent:
% 230.38/41.66  ----------------------------------------------------------------
% 230.38/41.66    (1)  e1 = e0
% 230.38/41.66    (2)  all_57_9 = e2
% 230.38/41.66    (3)  all_57_13 = e1
% 230.38/41.66    (4)   ~ (e3 = e1)
% 230.38/41.66    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.38/41.66           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.38/41.66    (6)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.38/41.66         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.38/41.66    (7)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.38/41.66         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.38/41.66    (8)   ~ (e3 = e2)
% 230.38/41.66    (9)   ~ (e3 = e0)
% 230.38/41.66    (10)  op(e3, e3) = e3
% 230.38/41.66    (11)  all_57_4 = e1
% 230.38/41.66    (12)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.38/41.66          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.38/41.66    (13)   ~ (e2 = e0)
% 230.38/41.66    (14)   ~ (e1 = e0)
% 230.38/41.66    (15)  all_57_7 = e3
% 230.38/41.66    (16)   ~ (e2 = e1)
% 230.38/41.66    (17)  all_57_3 = e2
% 230.38/41.66  
% 230.38/41.66  Begin of proof
% 230.38/41.66  | 
% 230.38/41.66  | SIMP: (1) implies:
% 230.38/41.66  |   (18)  e1 = e0
% 230.38/41.66  | 
% 230.38/41.66  | COMBINE_EQS: (11), (18) imply:
% 230.38/41.66  |   (19)  all_57_4 = e0
% 230.38/41.66  | 
% 230.38/41.66  | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13), (14),
% 230.38/41.66  |            (15), (16), (17), (19) are inconsistent by sub-proof #1128.
% 230.38/41.66  | 
% 230.38/41.66  End of proof
% 230.38/41.66  
% 230.38/41.66  Sub-proof #1085 shows that the following formulas are inconsistent:
% 230.38/41.66  ----------------------------------------------------------------
% 230.38/41.66    (1)  all_57_9 = e2
% 230.38/41.66    (2)   ~ (e3 = e1)
% 230.38/41.66    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.38/41.66           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.38/41.66    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.38/41.66         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.38/41.66    (5)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1)
% 230.38/41.66    (6)  op(e3, e3) = e3
% 230.38/41.66    (7)  all_57_1 = e0
% 230.38/41.66    (8)  all_57_4 = e1
% 230.38/41.66    (9)  op(e2, e2) = e2
% 230.38/41.66    (10)   ~ (e1 = e0)
% 230.38/41.66    (11)   ~ (e2 = e1)
% 230.38/41.66  
% 230.38/41.66  Begin of proof
% 230.38/41.66  | 
% 230.38/41.66  | BETA: splitting (5) gives:
% 230.38/41.66  | 
% 230.38/41.66  | Case 1:
% 230.38/41.66  | | 
% 230.38/41.66  | |   (12)  all_57_1 = e1 & op(e3, e2) = e1
% 230.38/41.66  | | 
% 230.38/41.66  | | ALPHA: (12) implies:
% 230.38/41.66  | |   (13)  all_57_1 = e1
% 230.38/41.66  | | 
% 230.38/41.66  | | COMBINE_EQS: (7), (13) imply:
% 230.38/41.66  | |   (14)  e1 = e0
% 230.38/41.66  | | 
% 230.38/41.66  | | SIMP: (14) implies:
% 230.38/41.66  | |   (15)  e1 = e0
% 230.38/41.66  | | 
% 230.38/41.66  | | COMBINE_EQS: (8), (15) imply:
% 230.38/41.66  | |   (16)  all_57_4 = e0
% 230.38/41.66  | | 
% 230.38/41.66  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (10), (11), (16) are inconsistent
% 230.38/41.66  | |            by sub-proof #2219.
% 230.38/41.66  | | 
% 230.38/41.66  | Case 2:
% 230.38/41.66  | | 
% 230.38/41.66  | |   (17)  all_57_3 = e1 & op(e2, e2) = e1
% 230.38/41.66  | | 
% 230.38/41.66  | | ALPHA: (17) implies:
% 230.38/41.66  | |   (18)  op(e2, e2) = e1
% 230.38/41.66  | | 
% 230.38/41.66  | | REF_CLOSE: (3), (9), (11), (18) are inconsistent by sub-proof #2306.
% 230.38/41.66  | | 
% 230.38/41.66  | End of split
% 230.38/41.66  | 
% 230.38/41.66  End of proof
% 230.38/41.66  
% 230.38/41.66  Sub-proof #1086 shows that the following formulas are inconsistent:
% 230.38/41.66  ----------------------------------------------------------------
% 230.38/41.66    (1)  e1 = e0
% 230.38/41.66    (2)   ~ (e3 = e1)
% 230.38/41.66    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.38/41.66           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.38/41.66    (4)  all_57_10 = e1
% 230.38/41.66    (5)   ~ (e3 = e2)
% 230.38/41.66    (6)  all_57_15 = e3
% 230.38/41.66    (7)  all_57_11 = e0
% 230.38/41.66    (8)   ~ (e2 = e0)
% 230.38/41.66    (9)   ~ (e1 = e0)
% 230.38/41.66    (10)  op(e0, e0) = e3
% 230.38/41.66    (11)   ~ (e2 = e1)
% 230.38/41.66    (12)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.38/41.66          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.38/41.66    (13)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.38/41.66          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.38/41.66  
% 230.38/41.66  Begin of proof
% 230.38/41.66  | 
% 230.38/41.66  | SIMP: (1) implies:
% 230.38/41.66  |   (14)  e1 = e0
% 230.38/41.66  | 
% 230.38/41.66  | COMBINE_EQS: (4), (14) imply:
% 230.38/41.66  |   (15)  all_57_10 = e0
% 230.38/41.66  | 
% 230.38/41.66  | REF_CLOSE: (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13), (15) are
% 230.38/41.66  |            inconsistent by sub-proof #1087.
% 230.38/41.66  | 
% 230.38/41.66  End of proof
% 230.38/41.66  
% 230.38/41.66  Sub-proof #1087 shows that the following formulas are inconsistent:
% 230.38/41.66  ----------------------------------------------------------------
% 230.38/41.66    (1)  all_57_10 = e0
% 230.38/41.66    (2)   ~ (e3 = e1)
% 230.38/41.66    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.38/41.66           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.38/41.66    (4)   ~ (e3 = e2)
% 230.38/41.66    (5)  all_57_15 = e3
% 230.38/41.66    (6)  all_57_11 = e0
% 230.38/41.66    (7)   ~ (e2 = e0)
% 230.38/41.66    (8)   ~ (e1 = e0)
% 230.38/41.66    (9)  op(e0, e0) = e3
% 230.38/41.66    (10)   ~ (e2 = e1)
% 230.38/41.66    (11)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.38/41.66          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.38/41.66    (12)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.38/41.66          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.38/41.66  
% 230.38/41.66  Begin of proof
% 230.38/41.66  | 
% 230.38/41.66  | BETA: splitting (11) gives:
% 230.38/41.66  | 
% 230.38/41.66  | Case 1:
% 230.38/41.66  | | 
% 230.38/41.66  | |   (13)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 230.38/41.66  | |           e2)
% 230.38/41.66  | | 
% 230.38/41.66  | | BETA: splitting (13) gives:
% 230.38/41.66  | | 
% 230.38/41.66  | | Case 1:
% 230.38/41.66  | | | 
% 230.38/41.66  | | |   (14)  all_57_9 = e2 & op(e3, e0) = e2
% 230.38/41.66  | | | 
% 230.38/41.66  | | | ALPHA: (14) implies:
% 230.38/41.66  | | |   (15)  all_57_9 = e2
% 230.38/41.66  | | | 
% 230.38/41.66  | | | REF_CLOSE: (1), (2), (3), (6), (8), (9), (10), (12), (15) are inconsistent
% 230.38/41.66  | | |            by sub-proof #1104.
% 230.38/41.66  | | | 
% 230.38/41.66  | | Case 2:
% 230.38/41.66  | | | 
% 230.38/41.66  | | |   (16)  all_57_10 = e2 & op(e2, e0) = e2
% 230.38/41.66  | | | 
% 230.38/41.66  | | | ALPHA: (16) implies:
% 230.38/41.66  | | |   (17)  all_57_10 = e2
% 230.38/41.66  | | | 
% 230.38/41.66  | | | REF_CLOSE: (1), (7), (17) are inconsistent by sub-proof #2138.
% 230.38/41.66  | | | 
% 230.38/41.66  | | End of split
% 230.38/41.66  | | 
% 230.38/41.66  | Case 2:
% 230.38/41.66  | | 
% 230.38/41.66  | |   (18)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.38/41.66  | |           e2)
% 230.38/41.66  | | 
% 230.38/41.66  | | REF_CLOSE: (4), (5), (6), (7), (18) are inconsistent by sub-proof #1146.
% 230.38/41.66  | | 
% 230.38/41.66  | End of split
% 230.38/41.66  | 
% 230.38/41.66  End of proof
% 230.38/41.66  
% 230.38/41.66  Sub-proof #1088 shows that the following formulas are inconsistent:
% 230.38/41.66  ----------------------------------------------------------------
% 230.38/41.66    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.38/41.66         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.38/41.66    (2)   ~ (all_52_7 = e3)
% 230.38/41.66    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.38/41.66         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.38/41.66    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.38/41.66         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.38/41.66    (5)   ~ (e3 = e1)
% 230.38/41.66    (6)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.38/41.66         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.38/41.66    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.38/41.66           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.38/41.66    (8)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.38/41.66         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.38/41.66    (9)   ~ (all_6_2 = e3)
% 230.38/41.66    (10)  op(e1, e1) = all_6_2
% 230.38/41.66    (11)  op(all_52_7, all_52_7) = e0
% 230.38/41.66    (12)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.38/41.66          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.38/41.66    (13)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 230.38/41.66            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 230.38/41.66              e3) = all_22_1 & $i(all_22_1))
% 230.38/41.66    (14)   ~ (all_53_13 = e2)
% 230.38/41.66    (15)   ~ (all_53_7 = e2)
% 230.38/41.66    (16)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.38/41.66          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.38/41.66    (17)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.38/41.66          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.38/41.66    (18)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 230.38/41.66          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.38/41.66    (19)   ~ (e3 = e2)
% 230.38/41.66    (20)   ~ (e3 = e0)
% 230.38/41.67    (21)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.38/41.67          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.38/41.67    (22)  op(e3, e3) = e3
% 230.38/41.67    (23)  all_57_6 = e0
% 230.38/41.67    (24)  all_57_15 = e3
% 230.38/41.67    (25)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.38/41.67          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.38/41.67            e1)
% 230.38/41.67    (26)  all_57_5 = e3
% 230.38/41.67    (27)  op(e3, e3) = all_52_1
% 230.38/41.67    (28)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.38/41.67          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.38/41.67    (29)  op(all_52_1, all_52_1) = e3
% 230.38/41.67    (30)   ~ (e2 = e0)
% 230.38/41.67    (31)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 230.38/41.67            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 230.38/41.67              e3) = all_12_1 & $i(all_12_1))
% 230.38/41.67    (32)  op(e2, e2) = e2
% 230.38/41.67    (33)   ~ (e1 = e0)
% 230.38/41.67    (34)  op(e0, e0) = e3
% 230.38/41.67    (35)  op(e0, e2) = all_53_7
% 230.38/41.67    (36)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.38/41.67          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.38/41.67            e2)
% 230.38/41.67    (37)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.38/41.67              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.38/41.67                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.38/41.67                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.38/41.67    (38)  op(e1, e1) = e0
% 230.38/41.67    (39)  op(e2, e0) = all_53_13
% 230.38/41.67    (40)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.38/41.67          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.38/41.67    (41)  all_57_7 = e3
% 230.38/41.67    (42)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.38/41.67          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.38/41.67    (43)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.38/41.67          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 230.38/41.67    (44)   ~ (e2 = e1)
% 230.38/41.67    (45)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.38/41.67          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.38/41.67    (46)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.38/41.67          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.38/41.67    (47)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.38/41.67          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.38/41.67    (48)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.38/41.67          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.38/41.67    (49)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.38/41.67          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.38/41.67    (50)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.38/41.67          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.38/41.67    (51)  all_57_3 = e2
% 230.38/41.67    (52)  op(e3, e0) = all_52_7
% 230.38/41.67    (53)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.38/41.67          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.38/41.67    (54)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.38/41.67          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.38/41.67  
% 230.38/41.67  Begin of proof
% 230.38/41.67  | 
% 230.38/41.67  | BETA: splitting (50) gives:
% 230.38/41.67  | 
% 230.38/41.67  | Case 1:
% 230.38/41.67  | | 
% 230.38/41.67  | |   (55)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) =
% 230.38/41.67  | |           e1)
% 230.38/41.67  | | 
% 230.38/41.67  | | REF_CLOSE: (5), (7), (8), (9), (10), (19), (20), (23), (24), (30), (33),
% 230.38/41.67  | |            (37), (44), (45), (49), (55) are inconsistent by sub-proof #1156.
% 230.38/41.67  | | 
% 230.38/41.67  | Case 2:
% 230.38/41.67  | | 
% 230.38/41.67  | |   (56)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) =
% 230.38/41.67  | |           e1)
% 230.38/41.67  | | 
% 230.38/41.67  | | BETA: splitting (56) gives:
% 230.38/41.67  | | 
% 230.38/41.67  | | Case 1:
% 230.38/41.67  | | | 
% 230.38/41.67  | | |   (57)  all_57_8 = e1 & op(e1, e1) = e1
% 230.38/41.67  | | | 
% 230.38/41.67  | | | ALPHA: (57) implies:
% 230.38/41.67  | | |   (58)  op(e1, e1) = e1
% 230.38/41.67  | | | 
% 230.38/41.67  | | | REF_CLOSE: (7), (33), (38), (58) are inconsistent by sub-proof #2427.
% 230.38/41.67  | | | 
% 230.38/41.67  | | Case 2:
% 230.38/41.67  | | | 
% 230.38/41.67  | | |   (59)  all_57_11 = e1 & op(e1, e0) = e1
% 230.38/41.67  | | | 
% 230.38/41.67  | | | ALPHA: (59) implies:
% 230.38/41.67  | | |   (60)  all_57_11 = e1
% 230.38/41.67  | | | 
% 230.38/41.67  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 230.38/41.67  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 230.38/41.67  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 230.38/41.67  | | |            (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 230.38/41.67  | | |            (43), (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 230.38/41.67  | | |            (53), (54), (60) are inconsistent by sub-proof #1089.
% 230.38/41.67  | | | 
% 230.38/41.67  | | End of split
% 230.38/41.67  | | 
% 230.38/41.67  | End of split
% 230.38/41.67  | 
% 230.38/41.67  End of proof
% 230.38/41.67  
% 230.38/41.67  Sub-proof #1089 shows that the following formulas are inconsistent:
% 230.38/41.67  ----------------------------------------------------------------
% 230.38/41.67    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.38/41.67         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.38/41.67    (2)   ~ (all_52_7 = e3)
% 230.38/41.67    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.38/41.67         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.38/41.67    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.38/41.67         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.38/41.67    (5)   ~ (e3 = e1)
% 230.38/41.67    (6)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.38/41.67         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.38/41.67    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.38/41.67           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.38/41.67    (8)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.38/41.67         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.38/41.67    (9)   ~ (all_6_2 = e3)
% 230.38/41.67    (10)  op(e1, e1) = all_6_2
% 230.38/41.67    (11)  op(all_52_7, all_52_7) = e0
% 230.38/41.67    (12)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.38/41.67          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.38/41.67    (13)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 230.38/41.67            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 230.38/41.67              e3) = all_22_1 & $i(all_22_1))
% 230.38/41.67    (14)   ~ (all_53_13 = e2)
% 230.38/41.67    (15)   ~ (all_53_7 = e2)
% 230.38/41.67    (16)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.38/41.67          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.38/41.67    (17)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.38/41.67          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.38/41.67    (18)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 230.38/41.67          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.38/41.67    (19)   ~ (e3 = e2)
% 230.38/41.67    (20)   ~ (e3 = e0)
% 230.38/41.67    (21)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.38/41.67          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.38/41.67    (22)  op(e3, e3) = e3
% 230.38/41.67    (23)  all_57_6 = e0
% 230.38/41.67    (24)  all_57_15 = e3
% 230.38/41.67    (25)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.38/41.67          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.38/41.67            e1)
% 230.38/41.67    (26)  all_57_5 = e3
% 230.38/41.67    (27)  op(e3, e3) = all_52_1
% 230.38/41.67    (28)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.38/41.67          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.38/41.67    (29)  op(all_52_1, all_52_1) = e3
% 230.38/41.67    (30)   ~ (e2 = e0)
% 230.38/41.67    (31)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 230.38/41.67            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 230.38/41.67              e3) = all_12_1 & $i(all_12_1))
% 230.38/41.67    (32)  op(e2, e2) = e2
% 230.38/41.67    (33)   ~ (e1 = e0)
% 230.38/41.67    (34)  op(e0, e0) = e3
% 230.38/41.67    (35)  op(e0, e2) = all_53_7
% 230.38/41.67    (36)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.38/41.67          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.38/41.67            e2)
% 230.38/41.67    (37)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.38/41.67              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.38/41.67                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.38/41.67                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.38/41.67    (38)  op(e1, e1) = e0
% 230.38/41.67    (39)  op(e2, e0) = all_53_13
% 230.38/41.67    (40)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.38/41.67          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.38/41.67    (41)  all_57_7 = e3
% 230.38/41.67    (42)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.38/41.67          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.38/41.67    (43)  all_57_11 = e1
% 230.38/41.67    (44)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.38/41.67          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 230.38/41.67    (45)   ~ (e2 = e1)
% 230.38/41.67    (46)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.38/41.67          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.38/41.67    (47)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.38/41.67          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.38/41.67    (48)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.38/41.67          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.38/41.67    (49)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.38/41.67          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.38/41.67    (50)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.38/41.67          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.38/41.67    (51)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.38/41.67          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.38/41.67    (52)  all_57_3 = e2
% 230.38/41.67    (53)  op(e3, e0) = all_52_7
% 230.38/41.67    (54)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.38/41.67          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.38/41.67    (55)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.38/41.67          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.38/41.67  
% 230.38/41.67  Begin of proof
% 230.38/41.67  | 
% 230.38/41.67  | BETA: splitting (55) gives:
% 230.38/41.67  | 
% 230.38/41.67  | Case 1:
% 230.38/41.67  | | 
% 230.38/41.67  | |   (56)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) =
% 230.38/41.67  | |           e2)
% 230.38/41.67  | | 
% 230.38/41.67  | | BETA: splitting (56) gives:
% 230.38/41.67  | | 
% 230.38/41.67  | | Case 1:
% 230.38/41.67  | | | 
% 230.38/41.67  | | |   (57)  all_57_6 = e2 & op(e1, e3) = e2
% 230.38/41.67  | | | 
% 230.38/41.67  | | | ALPHA: (57) implies:
% 230.38/41.67  | | |   (58)  all_57_6 = e2
% 230.38/41.67  | | | 
% 230.38/41.67  | | | COMBINE_EQS: (23), (58) imply:
% 230.38/41.67  | | |   (59)  e2 = e0
% 230.38/41.67  | | | 
% 230.38/41.67  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (11), (12), (16), (17),
% 230.38/41.67  | | |            (18), (19), (20), (21), (22), (24), (26), (30), (33), (34),
% 230.38/41.67  | | |            (36), (37), (38), (41), (42), (45), (46), (47), (48), (49),
% 230.38/41.67  | | |            (50), (51), (52), (53), (54), (55), (59) are inconsistent by
% 230.38/41.67  | | |            sub-proof #1140.
% 230.38/41.67  | | | 
% 230.38/41.67  | | Case 2:
% 230.38/41.67  | | | 
% 230.38/41.67  | | |   (60)  all_57_7 = e2 & op(e1, e2) = e2
% 230.38/41.67  | | | 
% 230.38/41.67  | | | ALPHA: (60) implies:
% 230.38/41.67  | | |   (61)  all_57_7 = e2
% 230.38/41.67  | | | 
% 230.38/41.67  | | | REF_CLOSE: (5), (7), (8), (9), (10), (19), (20), (23), (24), (30), (33),
% 230.38/41.67  | | |            (37), (45), (46), (50), (61) are inconsistent by sub-proof
% 230.38/41.67  | | |            #1775.
% 230.38/41.67  | | | 
% 230.38/41.67  | | End of split
% 230.38/41.67  | | 
% 230.38/41.67  | Case 2:
% 230.38/41.67  | | 
% 230.38/41.67  | |   (62)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) =
% 230.38/41.67  | |           e2)
% 230.38/41.67  | | 
% 230.38/41.67  | | BETA: splitting (62) gives:
% 230.38/41.67  | | 
% 230.38/41.67  | | Case 1:
% 230.38/41.67  | | | 
% 230.38/41.67  | | |   (63)  all_57_8 = e2 & op(e1, e1) = e2
% 230.38/41.67  | | | 
% 230.38/41.67  | | | ALPHA: (63) implies:
% 230.38/41.67  | | |   (64)  op(e1, e1) = e2
% 230.38/41.67  | | | 
% 230.38/41.67  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 230.38/41.67  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 230.38/41.67  | | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 230.38/41.67  | | |            (34), (35), (36), (37), (39), (40), (41), (42), (44), (45),
% 230.38/41.67  | | |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (55),
% 230.38/41.67  | | |            (64) are inconsistent by sub-proof #1090.
% 230.38/41.67  | | | 
% 230.38/41.67  | | Case 2:
% 230.38/41.67  | | | 
% 230.38/41.67  | | |   (65)  all_57_11 = e2 & op(e1, e0) = e2
% 230.38/41.67  | | | 
% 230.38/41.67  | | | ALPHA: (65) implies:
% 230.38/41.67  | | |   (66)  all_57_11 = e2
% 230.38/41.67  | | | 
% 230.38/41.67  | | | REF_CLOSE: (43), (45), (66) are inconsistent by sub-proof #2113.
% 230.38/41.67  | | | 
% 230.38/41.67  | | End of split
% 230.38/41.67  | | 
% 230.38/41.67  | End of split
% 230.38/41.67  | 
% 230.38/41.67  End of proof
% 230.38/41.67  
% 230.38/41.67  Sub-proof #1090 shows that the following formulas are inconsistent:
% 230.38/41.67  ----------------------------------------------------------------
% 230.38/41.67    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.38/41.67         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.38/41.67    (2)   ~ (all_52_7 = e3)
% 230.38/41.67    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.38/41.67         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.38/41.67    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.38/41.67         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.38/41.67    (5)   ~ (e3 = e1)
% 230.38/41.67    (6)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.38/41.67         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.38/41.67    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.38/41.67           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.38/41.67    (8)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.38/41.67         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.38/41.67    (9)   ~ (all_6_2 = e3)
% 230.38/41.67    (10)  op(e1, e1) = all_6_2
% 230.38/41.67    (11)  op(all_52_7, all_52_7) = e0
% 230.38/41.67    (12)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.38/41.67          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.38/41.67    (13)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 230.38/41.67            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 230.38/41.67              e3) = all_22_1 & $i(all_22_1))
% 230.38/41.67    (14)   ~ (all_53_13 = e2)
% 230.38/41.67    (15)   ~ (all_53_7 = e2)
% 230.38/41.67    (16)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.38/41.67          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.38/41.67    (17)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.38/41.67          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.38/41.67    (18)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 230.38/41.67          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.38/41.67    (19)   ~ (e3 = e2)
% 230.38/41.67    (20)   ~ (e3 = e0)
% 230.38/41.67    (21)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.38/41.67          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.38/41.67    (22)  op(e3, e3) = e3
% 230.38/41.67    (23)  all_57_15 = e3
% 230.38/41.67    (24)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.38/41.67          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.38/41.67            e1)
% 230.38/41.67    (25)  all_57_5 = e3
% 230.38/41.67    (26)  op(e3, e3) = all_52_1
% 230.38/41.67    (27)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.38/41.67          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.38/41.67    (28)  op(all_52_1, all_52_1) = e3
% 230.38/41.67    (29)   ~ (e2 = e0)
% 230.38/41.67    (30)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 230.38/41.67            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 230.38/41.67              e3) = all_12_1 & $i(all_12_1))
% 230.38/41.67    (31)  op(e2, e2) = e2
% 230.38/41.67    (32)   ~ (e1 = e0)
% 230.38/41.67    (33)  op(e0, e0) = e3
% 230.38/41.67    (34)  op(e0, e2) = all_53_7
% 230.38/41.67    (35)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.38/41.67          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.38/41.67            e2)
% 230.38/41.67    (36)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.38/41.67              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.38/41.67                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.38/41.67                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.38/41.67    (37)  op(e1, e1) = e2
% 230.38/41.67    (38)  op(e2, e0) = all_53_13
% 230.38/41.67    (39)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.38/41.67          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.38/41.67    (40)  all_57_7 = e3
% 230.38/41.67    (41)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.38/41.67          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.38/41.67    (42)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.38/41.67          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 230.38/41.67    (43)   ~ (e2 = e1)
% 230.38/41.67    (44)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.38/41.67          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.38/41.67    (45)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.38/41.67          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.38/41.67    (46)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.38/41.67          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.38/41.67    (47)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.38/41.67          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.38/41.67    (48)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.38/41.67          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.38/41.67    (49)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.38/41.67          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.38/41.67    (50)  all_57_3 = e2
% 230.38/41.67    (51)  op(e3, e0) = all_52_7
% 230.38/41.67    (52)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.38/41.67          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.38/41.67    (53)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.38/41.67          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.38/41.67  
% 230.38/41.67  Begin of proof
% 230.38/41.67  | 
% 230.38/41.67  | BETA: splitting (45) gives:
% 230.38/41.67  | 
% 230.38/41.67  | Case 1:
% 230.38/41.67  | | 
% 230.38/41.67  | |   (54)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) =
% 230.38/41.67  | |           e2)
% 230.38/41.67  | | 
% 230.38/41.67  | | BETA: splitting (54) gives:
% 230.38/41.67  | | 
% 230.38/41.67  | | Case 1:
% 230.38/41.67  | | | 
% 230.38/41.67  | | |   (55)  all_57_0 = e2 & op(e3, e3) = e2
% 230.38/41.67  | | | 
% 230.38/41.67  | | | ALPHA: (55) implies:
% 230.38/41.67  | | |   (56)  op(e3, e3) = e2
% 230.38/41.67  | | | 
% 230.38/41.67  | | | REF_CLOSE: (7), (19), (26), (28), (31), (56) are inconsistent by sub-proof
% 230.38/41.67  | | |            #1951.
% 230.38/41.67  | | | 
% 230.38/41.67  | | Case 2:
% 230.38/41.67  | | | 
% 230.38/41.67  | | |   (57)  all_57_2 = e2 & op(e2, e3) = e2
% 230.38/41.67  | | | 
% 230.38/41.67  | | | ALPHA: (57) implies:
% 230.38/41.67  | | |   (58)  all_57_2 = e2
% 230.38/41.67  | | | 
% 230.38/41.67  | | | BETA: splitting (16) gives:
% 230.38/41.67  | | | 
% 230.38/41.67  | | | Case 1:
% 230.38/41.67  | | | | 
% 230.38/41.67  | | | |   (59)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2)
% 230.38/41.67  | | | |           = e2)
% 230.38/41.67  | | | | 
% 230.38/41.67  | | | | BETA: splitting (59) gives:
% 230.38/41.67  | | | | 
% 230.38/41.67  | | | | Case 1:
% 230.38/41.67  | | | | | 
% 230.38/41.67  | | | | |   (60)  all_57_0 = e2 & op(e3, e3) = e2
% 230.38/41.67  | | | | | 
% 230.38/41.67  | | | | | ALPHA: (60) implies:
% 230.38/41.67  | | | | |   (61)  op(e3, e3) = e2
% 230.38/41.67  | | | | | 
% 230.38/41.67  | | | | | REF_CLOSE: (7), (19), (26), (28), (31), (61) are inconsistent by
% 230.38/41.67  | | | | |            sub-proof #1951.
% 230.38/41.67  | | | | | 
% 230.38/41.67  | | | | Case 2:
% 230.38/41.67  | | | | | 
% 230.38/41.67  | | | | |   (62)  all_57_1 = e2 & op(e3, e2) = e2
% 230.38/41.67  | | | | | 
% 230.38/41.67  | | | | | ALPHA: (62) implies:
% 230.38/41.67  | | | | |   (63)  all_57_1 = e2
% 230.38/41.67  | | | | | 
% 230.38/41.67  | | | | | BETA: splitting (35) gives:
% 230.38/41.67  | | | | | 
% 230.38/41.67  | | | | | Case 1:
% 230.38/41.67  | | | | | | 
% 230.38/41.67  | | | | | |   (64)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 &
% 230.38/41.67  | | | | | |           op(e0, e2) = e2)
% 230.38/41.67  | | | | | | 
% 230.38/41.67  | | | | | | BETA: splitting (64) gives:
% 230.38/41.67  | | | | | | 
% 230.38/41.67  | | | | | | Case 1:
% 230.38/41.67  | | | | | | | 
% 230.38/41.67  | | | | | | |   (65)  all_57_12 = e2 & op(e0, e3) = e2
% 230.38/41.67  | | | | | | | 
% 230.38/41.67  | | | | | | | ALPHA: (65) implies:
% 230.38/41.67  | | | | | | |   (66)  all_57_12 = e2
% 230.38/41.67  | | | | | | | 
% 230.38/41.67  | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 230.38/41.67  | | | | | | |            (11), (12), (13), (14), (16), (17), (18), (19), (20),
% 230.38/41.67  | | | | | | |            (21), (22), (23), (24), (25), (27), (29), (30), (31),
% 230.38/41.67  | | | | | | |            (32), (33), (35), (36), (37), (38), (40), (41), (43),
% 230.38/41.67  | | | | | | |            (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 230.38/41.67  | | | | | | |            (53), (63), (66) are inconsistent by sub-proof #1131.
% 230.38/41.67  | | | | | | | 
% 230.38/41.67  | | | | | | Case 2:
% 230.38/41.67  | | | | | | | 
% 230.38/41.67  | | | | | | |   (67)  all_57_13 = e2 & op(e0, e2) = e2
% 230.38/41.67  | | | | | | | 
% 230.38/41.67  | | | | | | | ALPHA: (67) implies:
% 230.38/41.67  | | | | | | |   (68)  op(e0, e2) = e2
% 230.38/41.67  | | | | | | | 
% 230.38/41.67  | | | | | | | REF_CLOSE: (7), (15), (34), (68) are inconsistent by sub-proof
% 230.38/41.67  | | | | | | |            #2335.
% 230.38/41.67  | | | | | | | 
% 230.38/41.67  | | | | | | End of split
% 230.38/41.67  | | | | | | 
% 230.38/41.67  | | | | | Case 2:
% 230.38/41.67  | | | | | | 
% 230.38/41.67  | | | | | |   (69)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 &
% 230.38/41.67  | | | | | |           op(e0, e0) = e2)
% 230.38/41.67  | | | | | | 
% 230.38/41.67  | | | | | | BETA: splitting (69) gives:
% 230.38/41.67  | | | | | | 
% 230.38/41.67  | | | | | | Case 1:
% 230.38/41.67  | | | | | | | 
% 230.38/41.67  | | | | | | |   (70)  all_57_14 = e2 & op(e0, e1) = e2
% 230.38/41.67  | | | | | | | 
% 230.38/41.67  | | | | | | | ALPHA: (70) implies:
% 230.38/41.67  | | | | | | |   (71)  all_57_14 = e2
% 230.38/41.67  | | | | | | | 
% 230.38/41.67  | | | | | | | BETA: splitting (44) gives:
% 230.38/41.67  | | | | | | | 
% 230.38/41.67  | | | | | | | Case 1:
% 230.38/41.67  | | | | | | | | 
% 230.38/41.67  | | | | | | | |   (72)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 &
% 230.38/41.67  | | | | | | | |           op(e2, e0) = e2)
% 230.38/41.67  | | | | | | | | 
% 230.38/41.67  | | | | | | | | BETA: splitting (72) gives:
% 230.38/41.67  | | | | | | | | 
% 230.38/41.67  | | | | | | | | Case 1:
% 230.38/41.67  | | | | | | | | | 
% 230.38/41.67  | | | | | | | | |   (73)  all_57_9 = e2 & op(e3, e0) = e2
% 230.38/41.67  | | | | | | | | | 
% 230.38/41.67  | | | | | | | | | ALPHA: (73) implies:
% 230.38/41.67  | | | | | | | | |   (74)  all_57_9 = e2
% 230.38/41.67  | | | | | | | | | 
% 230.38/41.67  | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 230.38/41.67  | | | | | | | | |            (11), (12), (16), (17), (18), (19), (20), (21),
% 230.38/41.67  | | | | | | | | |            (22), (23), (25), (27), (29), (31), (32), (33),
% 230.38/41.67  | | | | | | | | |            (35), (36), (39), (40), (41), (42), (43), (44),
% 230.38/41.67  | | | | | | | | |            (45), (46), (47), (48), (49), (50), (51), (52),
% 230.38/41.67  | | | | | | | | |            (53), (58), (71), (74) are inconsistent by
% 230.38/41.67  | | | | | | | | |            sub-proof #1101.
% 230.38/41.67  | | | | | | | | | 
% 230.38/41.67  | | | | | | | | Case 2:
% 230.38/41.67  | | | | | | | | | 
% 230.38/41.67  | | | | | | | | |   (75)  all_57_10 = e2 & op(e2, e0) = e2
% 230.38/41.67  | | | | | | | | | 
% 230.38/41.67  | | | | | | | | | REF_CLOSE: (7), (14), (38), (75) are inconsistent by sub-proof
% 230.38/41.67  | | | | | | | | |            #2432.
% 230.38/41.67  | | | | | | | | | 
% 230.38/41.67  | | | | | | | | End of split
% 230.38/41.67  | | | | | | | | 
% 230.38/41.67  | | | | | | | Case 2:
% 230.38/41.67  | | | | | | | | 
% 230.38/41.67  | | | | | | | |   (76)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 &
% 230.38/41.67  | | | | | | | |           op(e0, e0) = e2)
% 230.38/41.67  | | | | | | | | 
% 230.38/41.67  | | | | | | | | BETA: splitting (76) gives:
% 230.38/41.67  | | | | | | | | 
% 230.38/41.67  | | | | | | | | Case 1:
% 230.38/41.67  | | | | | | | | | 
% 230.38/41.68  | | | | | | | | |   (77)  all_57_11 = e2 & op(e1, e0) = e2
% 230.38/41.68  | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | ALPHA: (77) implies:
% 230.38/41.68  | | | | | | | | |   (78)  all_57_11 = e2
% 230.38/41.68  | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (7), (8), (9), (10), (19),
% 230.38/41.68  | | | | | | | | |            (20), (22), (23), (25), (27), (29), (31), (32),
% 230.38/41.68  | | | | | | | | |            (36), (37), (40), (41), (43), (44), (45), (47),
% 230.38/41.68  | | | | | | | | |            (48), (49), (50), (52), (63), (78) are inconsistent
% 230.38/41.68  | | | | | | | | |            by sub-proof #1132.
% 230.38/41.68  | | | | | | | | | 
% 230.38/41.68  | | | | | | | | Case 2:
% 230.38/41.68  | | | | | | | | | 
% 230.38/41.68  | | | | | | | | |   (79)  all_57_15 = e2 & op(e0, e0) = e2
% 230.38/41.68  | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | REF_CLOSE: (19), (23), (79) are inconsistent by sub-proof
% 230.38/41.68  | | | | | | | | |            #2323.
% 230.38/41.68  | | | | | | | | | 
% 230.38/41.68  | | | | | | | | End of split
% 230.38/41.68  | | | | | | | | 
% 230.38/41.68  | | | | | | | End of split
% 230.38/41.68  | | | | | | | 
% 230.38/41.68  | | | | | | Case 2:
% 230.38/41.68  | | | | | | | 
% 230.38/41.68  | | | | | | |   (80)  all_57_15 = e2 & op(e0, e0) = e2
% 230.38/41.68  | | | | | | | 
% 230.38/41.68  | | | | | | | ALPHA: (80) implies:
% 230.38/41.68  | | | | | | |   (81)  all_57_15 = e2
% 230.38/41.68  | | | | | | | 
% 230.38/41.68  | | | | | | | REF_CLOSE: (19), (23), (81) are inconsistent by sub-proof #2058.
% 230.38/41.68  | | | | | | | 
% 230.38/41.68  | | | | | | End of split
% 230.38/41.68  | | | | | | 
% 230.38/41.68  | | | | | End of split
% 230.38/41.68  | | | | | 
% 230.38/41.68  | | | | End of split
% 230.38/41.68  | | | | 
% 230.38/41.68  | | | Case 2:
% 230.38/41.68  | | | | 
% 230.38/41.68  | | | |   (82)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0)
% 230.38/41.68  | | | |           = e2)
% 230.38/41.68  | | | | 
% 230.38/41.68  | | | | BETA: splitting (82) gives:
% 230.38/41.68  | | | | 
% 230.38/41.68  | | | | Case 1:
% 230.38/41.68  | | | | | 
% 230.38/41.68  | | | | |   (83)  all_57_4 = e2 & op(e3, e1) = e2
% 230.38/41.68  | | | | | 
% 230.38/41.68  | | | | | ALPHA: (83) implies:
% 230.38/41.68  | | | | |   (84)  all_57_4 = e2
% 230.38/41.68  | | | | | 
% 230.38/41.68  | | | | | BETA: splitting (35) gives:
% 230.38/41.68  | | | | | 
% 230.38/41.68  | | | | | Case 1:
% 230.38/41.68  | | | | | | 
% 230.38/41.68  | | | | | |   (85)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 &
% 230.38/41.68  | | | | | |           op(e0, e2) = e2)
% 230.38/41.68  | | | | | | 
% 230.38/41.68  | | | | | | BETA: splitting (85) gives:
% 230.38/41.68  | | | | | | 
% 230.38/41.68  | | | | | | Case 1:
% 230.38/41.68  | | | | | | | 
% 230.38/41.68  | | | | | | |   (86)  all_57_12 = e2 & op(e0, e3) = e2
% 230.38/41.68  | | | | | | | 
% 230.38/41.68  | | | | | | | ALPHA: (86) implies:
% 230.38/41.68  | | | | | | |   (87)  all_57_12 = e2
% 230.38/41.68  | | | | | | | 
% 230.38/41.68  | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 230.38/41.68  | | | | | | |            (11), (12), (13), (14), (16), (17), (18), (19), (20),
% 230.38/41.68  | | | | | | |            (21), (22), (23), (24), (25), (27), (29), (30), (31),
% 230.38/41.68  | | | | | | |            (32), (33), (35), (36), (37), (38), (40), (41), (43),
% 230.38/41.68  | | | | | | |            (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 230.38/41.68  | | | | | | |            (53), (84), (87) are inconsistent by sub-proof #1130.
% 230.38/41.68  | | | | | | | 
% 230.38/41.68  | | | | | | Case 2:
% 230.38/41.68  | | | | | | | 
% 230.38/41.68  | | | | | | |   (88)  all_57_13 = e2 & op(e0, e2) = e2
% 230.38/41.68  | | | | | | | 
% 230.38/41.68  | | | | | | | ALPHA: (88) implies:
% 230.38/41.68  | | | | | | |   (89)  op(e0, e2) = e2
% 230.38/41.68  | | | | | | | 
% 230.38/41.68  | | | | | | | REF_CLOSE: (7), (15), (34), (89) are inconsistent by sub-proof
% 230.38/41.68  | | | | | | |            #2335.
% 230.38/41.68  | | | | | | | 
% 230.38/41.68  | | | | | | End of split
% 230.38/41.68  | | | | | | 
% 230.38/41.68  | | | | | Case 2:
% 230.38/41.68  | | | | | | 
% 230.38/41.68  | | | | | |   (90)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 &
% 230.38/41.68  | | | | | |           op(e0, e0) = e2)
% 230.38/41.68  | | | | | | 
% 230.38/41.68  | | | | | | BETA: splitting (90) gives:
% 230.38/41.68  | | | | | | 
% 230.38/41.68  | | | | | | Case 1:
% 230.38/41.68  | | | | | | | 
% 230.38/41.68  | | | | | | |   (91)  all_57_14 = e2 & op(e0, e1) = e2
% 230.38/41.68  | | | | | | | 
% 230.38/41.68  | | | | | | | ALPHA: (91) implies:
% 230.38/41.68  | | | | | | |   (92)  all_57_14 = e2
% 230.38/41.68  | | | | | | | 
% 230.38/41.68  | | | | | | | BETA: splitting (44) gives:
% 230.38/41.68  | | | | | | | 
% 230.38/41.68  | | | | | | | Case 1:
% 230.38/41.68  | | | | | | | | 
% 230.38/41.68  | | | | | | | |   (93)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 &
% 230.38/41.68  | | | | | | | |           op(e2, e0) = e2)
% 230.38/41.68  | | | | | | | | 
% 230.38/41.68  | | | | | | | | BETA: splitting (93) gives:
% 230.38/41.68  | | | | | | | | 
% 230.38/41.68  | | | | | | | | Case 1:
% 230.38/41.68  | | | | | | | | | 
% 230.38/41.68  | | | | | | | | |   (94)  all_57_9 = e2 & op(e3, e0) = e2
% 230.38/41.68  | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | ALPHA: (94) implies:
% 230.38/41.68  | | | | | | | | |   (95)  all_57_9 = e2
% 230.38/41.68  | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | BETA: splitting (18) gives:
% 230.38/41.68  | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | Case 1:
% 230.38/41.68  | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | |   (96)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 &
% 230.38/41.68  | | | | | | | | | |           op(e2, e1) = e0)
% 230.38/41.68  | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | BETA: splitting (96) gives:
% 230.38/41.68  | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | Case 1:
% 230.38/41.68  | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | |   (97)  all_57_4 = e0 & op(e3, e1) = e0
% 230.38/41.68  | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | REF_CLOSE: (5), (7), (12), (16), (19), (22), (29), (32),
% 230.38/41.68  | | | | | | | | | | |            (43), (84), (95), (97) are inconsistent by
% 230.38/41.68  | | | | | | | | | | |            sub-proof #2435.
% 230.38/41.68  | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | Case 2:
% 230.38/41.68  | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | |   (98)  all_57_5 = e0 & op(e2, e1) = e0
% 230.38/41.68  | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | REF_CLOSE: (20), (25), (98) are inconsistent by sub-proof
% 230.38/41.68  | | | | | | | | | | |            #2414.
% 230.38/41.68  | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | End of split
% 230.38/41.68  | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | Case 2:
% 230.38/41.68  | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | |   (99)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0
% 230.38/41.68  | | | | | | | | | |           & op(e0, e1) = e0)
% 230.38/41.68  | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | BETA: splitting (99) gives:
% 230.38/41.68  | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | Case 1:
% 230.38/41.68  | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | |   (100)  all_57_8 = e0 & op(e1, e1) = e0
% 230.38/41.68  | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (11), (12),
% 230.38/41.68  | | | | | | | | | | |            (16), (17), (18), (19), (20), (21), (22), (23),
% 230.38/41.68  | | | | | | | | | | |            (25), (29), (32), (33), (35), (36), (40), (41),
% 230.38/41.68  | | | | | | | | | | |            (43), (44), (45), (46), (47), (48), (49), (50),
% 230.38/41.68  | | | | | | | | | | |            (51), (52), (53), (84), (95), (100) are
% 230.38/41.68  | | | | | | | | | | |            inconsistent by sub-proof #1159.
% 230.38/41.68  | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | Case 2:
% 230.38/41.68  | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | |   (101)  all_57_14 = e0 & op(e0, e1) = e0
% 230.38/41.68  | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | ALPHA: (101) implies:
% 230.38/41.68  | | | | | | | | | | |   (102)  all_57_14 = e0
% 230.38/41.68  | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | COMBINE_EQS: (92), (102) imply:
% 230.38/41.68  | | | | | | | | | | |   (103)  e2 = e0
% 230.38/41.68  | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | REF_CLOSE: (5), (7), (19), (21), (25), (29), (32), (43),
% 230.38/41.68  | | | | | | | | | | |            (46), (84), (92), (103) are inconsistent by
% 230.38/41.68  | | | | | | | | | | |            sub-proof #2377.
% 230.38/41.68  | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | End of split
% 230.38/41.68  | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | End of split
% 230.38/41.68  | | | | | | | | | 
% 230.38/41.68  | | | | | | | | Case 2:
% 230.38/41.68  | | | | | | | | | 
% 230.38/41.68  | | | | | | | | |   (104)  all_57_10 = e2 & op(e2, e0) = e2
% 230.38/41.68  | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | REF_CLOSE: (7), (14), (38), (104) are inconsistent by
% 230.38/41.68  | | | | | | | | |            sub-proof #2432.
% 230.38/41.68  | | | | | | | | | 
% 230.38/41.68  | | | | | | | | End of split
% 230.38/41.68  | | | | | | | | 
% 230.38/41.68  | | | | | | | Case 2:
% 230.38/41.68  | | | | | | | | 
% 230.38/41.68  | | | | | | | |   (105)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 &
% 230.38/41.68  | | | | | | | |            op(e0, e0) = e2)
% 230.38/41.68  | | | | | | | | 
% 230.38/41.68  | | | | | | | | BETA: splitting (105) gives:
% 230.38/41.68  | | | | | | | | 
% 230.38/41.68  | | | | | | | | Case 1:
% 230.38/41.68  | | | | | | | | | 
% 230.38/41.68  | | | | | | | | |   (106)  all_57_11 = e2 & op(e1, e0) = e2
% 230.38/41.68  | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | ALPHA: (106) implies:
% 230.38/41.68  | | | | | | | | |   (107)  all_57_11 = e2
% 230.38/41.68  | | | | | | | | |   (108)  op(e1, e0) = e2
% 230.38/41.68  | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | BETA: splitting (6) gives:
% 230.38/41.68  | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | Case 1:
% 230.38/41.68  | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | |   (109)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 230.38/41.68  | | | | | | | | | |            & op(e1, e2) = e0)
% 230.38/41.68  | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | BETA: splitting (109) gives:
% 230.38/41.68  | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | Case 1:
% 230.38/41.68  | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | |   (110)  all_57_6 = e0 & op(e1, e3) = e0
% 230.38/41.68  | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | ALPHA: (110) implies:
% 230.38/41.68  | | | | | | | | | | |   (111)  all_57_6 = e0
% 230.38/41.68  | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | BETA: splitting (18) gives:
% 230.38/41.68  | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | Case 1:
% 230.38/41.68  | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | |   (112)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 230.38/41.68  | | | | | | | | | | | |            & op(e2, e1) = e0)
% 230.38/41.68  | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | BETA: splitting (112) gives:
% 230.38/41.68  | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | Case 1:
% 230.38/41.68  | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | |   (113)  all_57_4 = e0 & op(e3, e1) = e0
% 230.38/41.68  | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | ALPHA: (113) implies:
% 230.38/41.68  | | | | | | | | | | | | |   (114)  all_57_4 = e0
% 230.38/41.68  | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | COMBINE_EQS: (84), (114) imply:
% 230.38/41.68  | | | | | | | | | | | | |   (115)  e2 = e0
% 230.38/41.68  | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (12), (16), (17), (19), (20), (22),
% 230.38/41.68  | | | | | | | | | | | | |            (23), (25), (29), (32), (40), (41), (43), (44),
% 230.38/41.68  | | | | | | | | | | | | |            (48), (50), (52), (84), (107), (115) are
% 230.38/41.68  | | | | | | | | | | | | |            inconsistent by sub-proof #1111.
% 230.38/41.68  | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | Case 2:
% 230.38/41.68  | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | |   (116)  all_57_5 = e0 & op(e2, e1) = e0
% 230.38/41.68  | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | ALPHA: (116) implies:
% 230.38/41.68  | | | | | | | | | | | | |   (117)  all_57_5 = e0
% 230.38/41.68  | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | COMBINE_EQS: (25), (117) imply:
% 230.38/41.68  | | | | | | | | | | | | |   (118)  e3 = e0
% 230.38/41.68  | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | COMBINE_EQS: (40), (118) imply:
% 230.38/41.68  | | | | | | | | | | | | |   (119)  all_57_7 = e0
% 230.38/41.68  | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (9), (10), (19), (20), (23), (29),
% 230.38/41.68  | | | | | | | | | | | | |            (32), (36), (37), (43), (44), (48), (49), (107),
% 230.38/41.68  | | | | | | | | | | | | |            (119) are inconsistent by sub-proof #1154.
% 230.38/41.68  | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | End of split
% 230.38/41.68  | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | Case 2:
% 230.38/41.68  | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | |   (120)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 230.38/41.68  | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 230.38/41.68  | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | BETA: splitting (120) gives:
% 230.38/41.68  | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | Case 1:
% 230.38/41.68  | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | |   (121)  all_57_8 = e0 & op(e1, e1) = e0
% 230.38/41.68  | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | ALPHA: (121) implies:
% 230.38/41.68  | | | | | | | | | | | | |   (122)  op(e1, e1) = e0
% 230.38/41.68  | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | BETA: splitting (24) gives:
% 230.38/41.68  | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | Case 1:
% 230.38/41.68  | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | |   (123)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 230.38/41.68  | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 230.38/41.68  | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | BETA: splitting (123) gives:
% 230.38/41.68  | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | Case 1:
% 230.38/41.68  | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | |   (124)  all_57_12 = e1 & op(e0, e3) = e1
% 230.38/41.68  | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | ALPHA: (124) implies:
% 230.38/41.68  | | | | | | | | | | | | | | |   (125)  op(e0, e3) = e1
% 230.38/41.68  | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | REF_CLOSE: (7), (13), (30), (108), (125) are inconsistent by
% 230.38/41.68  | | | | | | | | | | | | | | |            sub-proof #1147.
% 230.38/41.68  | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | Case 2:
% 230.38/41.68  | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | |   (126)  all_57_13 = e1 & op(e0, e2) = e1
% 230.38/41.68  | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | ALPHA: (126) implies:
% 230.38/41.68  | | | | | | | | | | | | | | |   (127)  all_57_13 = e1
% 230.38/41.68  | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | BETA: splitting (49) gives:
% 230.38/41.68  | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | Case 1:
% 230.38/41.68  | | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | |   (128)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 230.38/41.68  | | | | | | | | | | | | | | | |            & op(e1, e2) = e1)
% 230.38/41.68  | | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | | BETA: splitting (128) gives:
% 230.38/41.68  | | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | | Case 1:
% 230.38/41.68  | | | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | | |   (129)  all_57_6 = e1 & op(e1, e3) = e1
% 230.38/41.68  | | | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | | | ALPHA: (129) implies:
% 230.38/41.68  | | | | | | | | | | | | | | | | |   (130)  all_57_6 = e1
% 230.38/41.68  | | | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | | | COMBINE_EQS: (111), (130) imply:
% 230.38/41.68  | | | | | | | | | | | | | | | | |   (131)  e1 = e0
% 230.38/41.68  | | | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | | | SIMP: (131) implies:
% 230.38/41.68  | | | | | | | | | | | | | | | | |   (132)  e1 = e0
% 230.38/41.68  | | | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | | | COMBINE_EQS: (127), (132) imply:
% 230.38/41.68  | | | | | | | | | | | | | | | | |   (133)  all_57_13 = e0
% 230.38/41.68  | | | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (13), (24), (30), (32), (33), (43),
% 230.38/41.68  | | | | | | | | | | | | | | | | |            (92), (108), (133) are inconsistent by sub-proof
% 230.38/41.68  | | | | | | | | | | | | | | | | |            #1100.
% 230.38/41.68  | | | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | | Case 2:
% 230.38/41.68  | | | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | | |   (134)  all_57_7 = e1 & op(e1, e2) = e1
% 230.38/41.68  | | | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | | | ALPHA: (134) implies:
% 230.38/41.68  | | | | | | | | | | | | | | | | |   (135)  all_57_7 = e1
% 230.38/41.68  | | | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (9), (10), (19), (20), (23), (29),
% 230.38/41.68  | | | | | | | | | | | | | | | | |            (32), (36), (43), (44), (48), (111), (135) are
% 230.38/41.68  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1157.
% 230.38/41.68  | | | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | | End of split
% 230.38/41.68  | | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | Case 2:
% 230.38/41.68  | | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | |   (136)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 230.38/41.68  | | | | | | | | | | | | | | | |            e1 & op(e1, e0) = e1)
% 230.38/41.68  | | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | | REF_CLOSE: (7), (32), (43), (107), (122), (136) are
% 230.38/41.68  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1315.
% 230.38/41.68  | | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | End of split
% 230.38/41.68  | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | End of split
% 230.38/41.68  | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | Case 2:
% 230.38/41.68  | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | |   (137)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 230.38/41.68  | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 230.38/41.68  | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (33), (43), (92), (137) are inconsistent
% 230.38/41.68  | | | | | | | | | | | | | |            by sub-proof #1139.
% 230.38/41.68  | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | End of split
% 230.38/41.68  | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | Case 2:
% 230.38/41.68  | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | |   (138)  all_57_14 = e0 & op(e0, e1) = e0
% 230.38/41.68  | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | ALPHA: (138) implies:
% 230.38/41.68  | | | | | | | | | | | | |   (139)  all_57_14 = e0
% 230.38/41.68  | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | COMBINE_EQS: (92), (139) imply:
% 230.38/41.68  | | | | | | | | | | | | |   (140)  e2 = e0
% 230.38/41.68  | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | REF_CLOSE: (5), (7), (19), (21), (25), (29), (32), (43),
% 230.38/41.68  | | | | | | | | | | | | |            (46), (84), (92), (140) are inconsistent by
% 230.38/41.68  | | | | | | | | | | | | |            sub-proof #2377.
% 230.38/41.68  | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | End of split
% 230.38/41.68  | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | End of split
% 230.38/41.68  | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | Case 2:
% 230.38/41.68  | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | |   (141)  all_57_7 = e0 & op(e1, e2) = e0
% 230.38/41.68  | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | ALPHA: (141) implies:
% 230.38/41.68  | | | | | | | | | | |   (142)  all_57_7 = e0
% 230.38/41.68  | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (9), (10), (19), (20), (23), (29),
% 230.38/41.68  | | | | | | | | | | |            (32), (36), (37), (43), (44), (48), (49), (107),
% 230.38/41.68  | | | | | | | | | | |            (142) are inconsistent by sub-proof #1154.
% 230.38/41.68  | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | End of split
% 230.38/41.68  | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | Case 2:
% 230.38/41.68  | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | |   (143)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0
% 230.38/41.68  | | | | | | | | | |            & op(e1, e0) = e0)
% 230.38/41.68  | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | BETA: splitting (143) gives:
% 230.38/41.68  | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | Case 1:
% 230.38/41.68  | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | |   (144)  all_57_8 = e0 & op(e1, e1) = e0
% 230.38/41.68  | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | REF_CLOSE: (5), (7), (21), (25), (32), (43), (84), (92),
% 230.38/41.68  | | | | | | | | | | |            (144) are inconsistent by sub-proof #2373.
% 230.38/41.68  | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | Case 2:
% 230.38/41.68  | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | |   (145)  all_57_11 = e0 & op(e1, e0) = e0
% 230.38/41.68  | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | ALPHA: (145) implies:
% 230.38/41.68  | | | | | | | | | | |   (146)  all_57_11 = e0
% 230.38/41.68  | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | COMBINE_EQS: (107), (146) imply:
% 230.38/41.68  | | | | | | | | | | |   (147)  e2 = e0
% 230.38/41.68  | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (12), (16), (17), (19), (20), (22),
% 230.38/41.68  | | | | | | | | | | |            (23), (25), (29), (32), (40), (41), (43), (44),
% 230.38/41.68  | | | | | | | | | | |            (48), (50), (52), (84), (107), (147) are
% 230.38/41.68  | | | | | | | | | | |            inconsistent by sub-proof #1111.
% 230.38/41.68  | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | End of split
% 230.38/41.68  | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | End of split
% 230.38/41.68  | | | | | | | | | 
% 230.38/41.68  | | | | | | | | Case 2:
% 230.38/41.68  | | | | | | | | | 
% 230.38/41.68  | | | | | | | | |   (148)  all_57_15 = e2 & op(e0, e0) = e2
% 230.38/41.68  | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | REF_CLOSE: (19), (23), (148) are inconsistent by sub-proof
% 230.38/41.68  | | | | | | | | |            #2323.
% 230.38/41.68  | | | | | | | | | 
% 230.38/41.68  | | | | | | | | End of split
% 230.38/41.68  | | | | | | | | 
% 230.38/41.68  | | | | | | | End of split
% 230.38/41.68  | | | | | | | 
% 230.38/41.68  | | | | | | Case 2:
% 230.38/41.68  | | | | | | | 
% 230.38/41.68  | | | | | | |   (149)  all_57_15 = e2 & op(e0, e0) = e2
% 230.38/41.68  | | | | | | | 
% 230.38/41.68  | | | | | | | ALPHA: (149) implies:
% 230.38/41.68  | | | | | | |   (150)  all_57_15 = e2
% 230.38/41.68  | | | | | | | 
% 230.38/41.68  | | | | | | | REF_CLOSE: (19), (23), (150) are inconsistent by sub-proof #2058.
% 230.38/41.68  | | | | | | | 
% 230.38/41.68  | | | | | | End of split
% 230.38/41.68  | | | | | | 
% 230.38/41.68  | | | | | End of split
% 230.38/41.68  | | | | | 
% 230.38/41.68  | | | | Case 2:
% 230.38/41.68  | | | | | 
% 230.38/41.68  | | | | |   (151)  all_57_9 = e2 & op(e3, e0) = e2
% 230.38/41.68  | | | | | 
% 230.38/41.68  | | | | | ALPHA: (151) implies:
% 230.38/41.68  | | | | |   (152)  all_57_9 = e2
% 230.38/41.68  | | | | | 
% 230.38/41.68  | | | | | BETA: splitting (35) gives:
% 230.38/41.68  | | | | | 
% 230.38/41.68  | | | | | Case 1:
% 230.38/41.68  | | | | | | 
% 230.38/41.68  | | | | | |   (153)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 &
% 230.38/41.68  | | | | | |            op(e0, e2) = e2)
% 230.38/41.68  | | | | | | 
% 230.38/41.68  | | | | | | BETA: splitting (153) gives:
% 230.38/41.68  | | | | | | 
% 230.38/41.68  | | | | | | Case 1:
% 230.38/41.68  | | | | | | | 
% 230.38/41.68  | | | | | | |   (154)  all_57_12 = e2 & op(e0, e3) = e2
% 230.38/41.68  | | | | | | | 
% 230.38/41.68  | | | | | | | ALPHA: (154) implies:
% 230.38/41.68  | | | | | | |   (155)  all_57_12 = e2
% 230.38/41.68  | | | | | | | 
% 230.38/41.68  | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 230.38/41.68  | | | | | | |            (11), (12), (13), (14), (16), (17), (18), (19), (20),
% 230.38/41.68  | | | | | | |            (21), (22), (23), (24), (25), (29), (30), (31), (32),
% 230.38/41.68  | | | | | | |            (33), (35), (36), (37), (38), (40), (41), (43), (44),
% 230.38/41.68  | | | | | | |            (45), (46), (47), (48), (49), (50), (51), (52), (53),
% 230.38/41.68  | | | | | | |            (152), (155) are inconsistent by sub-proof #1135.
% 230.38/41.68  | | | | | | | 
% 230.38/41.68  | | | | | | Case 2:
% 230.38/41.68  | | | | | | | 
% 230.38/41.68  | | | | | | |   (156)  all_57_13 = e2 & op(e0, e2) = e2
% 230.38/41.68  | | | | | | | 
% 230.38/41.68  | | | | | | | ALPHA: (156) implies:
% 230.38/41.68  | | | | | | |   (157)  op(e0, e2) = e2
% 230.38/41.68  | | | | | | | 
% 230.38/41.68  | | | | | | | REF_CLOSE: (7), (15), (34), (157) are inconsistent by sub-proof
% 230.38/41.68  | | | | | | |            #2335.
% 230.38/41.68  | | | | | | | 
% 230.38/41.68  | | | | | | End of split
% 230.38/41.68  | | | | | | 
% 230.38/41.68  | | | | | Case 2:
% 230.38/41.68  | | | | | | 
% 230.38/41.68  | | | | | |   (158)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 &
% 230.38/41.68  | | | | | |            op(e0, e0) = e2)
% 230.38/41.68  | | | | | | 
% 230.38/41.68  | | | | | | BETA: splitting (158) gives:
% 230.38/41.68  | | | | | | 
% 230.38/41.68  | | | | | | Case 1:
% 230.38/41.68  | | | | | | | 
% 230.38/41.68  | | | | | | |   (159)  all_57_14 = e2 & op(e0, e1) = e2
% 230.38/41.68  | | | | | | | 
% 230.38/41.68  | | | | | | | ALPHA: (159) implies:
% 230.38/41.68  | | | | | | |   (160)  all_57_14 = e2
% 230.38/41.68  | | | | | | | 
% 230.38/41.68  | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 230.38/41.68  | | | | | | |            (11), (12), (16), (17), (18), (19), (20), (21), (22),
% 230.38/41.68  | | | | | | |            (23), (25), (27), (29), (31), (32), (33), (35), (36),
% 230.38/41.68  | | | | | | |            (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 230.38/41.68  | | | | | | |            (48), (49), (50), (51), (52), (53), (58), (152), (160)
% 230.38/41.68  | | | | | | |            are inconsistent by sub-proof #1101.
% 230.38/41.68  | | | | | | | 
% 230.38/41.68  | | | | | | Case 2:
% 230.38/41.68  | | | | | | | 
% 230.38/41.68  | | | | | | |   (161)  all_57_15 = e2 & op(e0, e0) = e2
% 230.38/41.68  | | | | | | | 
% 230.38/41.68  | | | | | | | ALPHA: (161) implies:
% 230.38/41.68  | | | | | | |   (162)  all_57_15 = e2
% 230.38/41.68  | | | | | | | 
% 230.38/41.68  | | | | | | | REF_CLOSE: (19), (23), (162) are inconsistent by sub-proof #2058.
% 230.38/41.68  | | | | | | | 
% 230.38/41.68  | | | | | | End of split
% 230.38/41.68  | | | | | | 
% 230.38/41.68  | | | | | End of split
% 230.38/41.68  | | | | | 
% 230.38/41.68  | | | | End of split
% 230.38/41.68  | | | | 
% 230.38/41.68  | | | End of split
% 230.38/41.68  | | | 
% 230.38/41.68  | | End of split
% 230.38/41.68  | | 
% 230.38/41.68  | Case 2:
% 230.38/41.68  | | 
% 230.38/41.68  | |   (163)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) =
% 230.38/41.68  | |            e2)
% 230.38/41.68  | | 
% 230.38/41.68  | | BETA: splitting (163) gives:
% 230.38/41.68  | | 
% 230.38/41.68  | | Case 1:
% 230.38/41.68  | | | 
% 230.38/41.68  | | |   (164)  all_57_6 = e2 & op(e1, e3) = e2
% 230.38/41.68  | | | 
% 230.38/41.68  | | | ALPHA: (164) implies:
% 230.38/41.68  | | |   (165)  all_57_6 = e2
% 230.38/41.68  | | | 
% 230.38/41.68  | | | BETA: splitting (16) gives:
% 230.38/41.68  | | | 
% 230.38/41.68  | | | Case 1:
% 230.38/41.68  | | | | 
% 230.38/41.68  | | | |   (166)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2)
% 230.38/41.68  | | | |            = e2)
% 230.38/41.68  | | | | 
% 230.38/41.68  | | | | BETA: splitting (166) gives:
% 230.38/41.68  | | | | 
% 230.38/41.68  | | | | Case 1:
% 230.38/41.68  | | | | | 
% 230.38/41.68  | | | | |   (167)  all_57_0 = e2 & op(e3, e3) = e2
% 230.38/41.68  | | | | | 
% 230.38/41.68  | | | | | ALPHA: (167) implies:
% 230.38/41.68  | | | | |   (168)  op(e3, e3) = e2
% 230.38/41.68  | | | | | 
% 230.38/41.68  | | | | | REF_CLOSE: (7), (19), (26), (28), (31), (168) are inconsistent by
% 230.38/41.68  | | | | |            sub-proof #1951.
% 230.38/41.68  | | | | | 
% 230.38/41.68  | | | | Case 2:
% 230.38/41.68  | | | | | 
% 230.38/41.68  | | | | |   (169)  all_57_1 = e2 & op(e3, e2) = e2
% 230.38/41.68  | | | | | 
% 230.38/41.68  | | | | | ALPHA: (169) implies:
% 230.38/41.68  | | | | |   (170)  all_57_1 = e2
% 230.38/41.68  | | | | | 
% 230.38/41.68  | | | | | BETA: splitting (27) gives:
% 230.38/41.68  | | | | | 
% 230.38/41.68  | | | | | Case 1:
% 230.38/41.68  | | | | | | 
% 230.38/41.68  | | | | | |   (171)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2,
% 230.38/41.68  | | | | | |              e2) = e0)
% 230.38/41.68  | | | | | | 
% 230.38/41.68  | | | | | | BETA: splitting (171) gives:
% 230.38/41.68  | | | | | | 
% 230.38/41.68  | | | | | | Case 1:
% 230.38/41.68  | | | | | | | 
% 230.38/41.68  | | | | | | |   (172)  all_57_1 = e0 & op(e3, e2) = e0
% 230.38/41.68  | | | | | | | 
% 230.38/41.68  | | | | | | | REF_CLOSE: (1), (3), (4), (5), (7), (8), (9), (10), (19), (20),
% 230.38/41.68  | | | | | | |            (22), (23), (25), (29), (32), (36), (41), (43), (44),
% 230.38/41.68  | | | | | | |            (45), (47), (48), (50), (52), (170), (172) are
% 230.38/41.68  | | | | | | |            inconsistent by sub-proof #1134.
% 230.38/41.68  | | | | | | | 
% 230.38/41.68  | | | | | | Case 2:
% 230.38/41.68  | | | | | | | 
% 230.38/41.68  | | | | | | |   (173)  all_57_3 = e0 & op(e2, e2) = e0
% 230.38/41.68  | | | | | | | 
% 230.38/41.68  | | | | | | | ALPHA: (173) implies:
% 230.38/41.68  | | | | | | |   (174)  all_57_3 = e0
% 230.38/41.68  | | | | | | | 
% 230.38/41.68  | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (11), (12), (16),
% 230.38/41.68  | | | | | | |            (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 230.38/41.68  | | | | | | |            (29), (32), (33), (35), (36), (37), (40), (41), (43),
% 230.38/41.68  | | | | | | |            (44), (45), (46), (47), (48), (49), (51), (52), (53),
% 230.38/41.68  | | | | | | |            (165), (174) are inconsistent by sub-proof #1461.
% 230.38/41.68  | | | | | | | 
% 230.38/41.68  | | | | | | End of split
% 230.38/41.68  | | | | | | 
% 230.38/41.68  | | | | | Case 2:
% 230.38/41.68  | | | | | | 
% 230.38/41.68  | | | | | |   (175)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 &
% 230.38/41.68  | | | | | |            op(e0, e2) = e0)
% 230.38/41.68  | | | | | | 
% 230.38/41.68  | | | | | | BETA: splitting (175) gives:
% 230.38/41.68  | | | | | | 
% 230.38/41.68  | | | | | | Case 1:
% 230.38/41.68  | | | | | | | 
% 230.38/41.68  | | | | | | |   (176)  all_57_7 = e0 & op(e1, e2) = e0
% 230.38/41.68  | | | | | | | 
% 230.38/41.68  | | | | | | | REF_CLOSE: (20), (40), (176) are inconsistent by sub-proof #2042.
% 230.38/41.68  | | | | | | | 
% 230.38/41.68  | | | | | | Case 2:
% 230.38/41.68  | | | | | | | 
% 230.38/41.68  | | | | | | |   (177)  all_57_13 = e0 & op(e0, e2) = e0
% 230.38/41.68  | | | | | | | 
% 230.38/41.68  | | | | | | | ALPHA: (177) implies:
% 230.38/41.68  | | | | | | |   (178)  all_57_13 = e0
% 230.38/41.68  | | | | | | | 
% 230.38/41.68  | | | | | | | REF_CLOSE: (5), (7), (8), (9), (10), (19), (20), (23), (29), (31),
% 230.38/41.68  | | | | | | |            (32), (36), (43), (44), (48), (52), (165), (170), (178)
% 230.38/41.68  | | | | | | |            are inconsistent by sub-proof #1099.
% 230.38/41.68  | | | | | | | 
% 230.38/41.68  | | | | | | End of split
% 230.38/41.68  | | | | | | 
% 230.38/41.68  | | | | | End of split
% 230.38/41.68  | | | | | 
% 230.38/41.68  | | | | End of split
% 230.38/41.68  | | | | 
% 230.38/41.68  | | | Case 2:
% 230.38/41.68  | | | | 
% 230.38/41.68  | | | |   (179)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0)
% 230.38/41.68  | | | |            = e2)
% 230.38/41.68  | | | | 
% 230.38/41.68  | | | | BETA: splitting (179) gives:
% 230.38/41.68  | | | | 
% 230.38/41.68  | | | | Case 1:
% 230.38/41.68  | | | | | 
% 230.38/41.68  | | | | |   (180)  all_57_4 = e2 & op(e3, e1) = e2
% 230.38/41.68  | | | | | 
% 230.38/41.68  | | | | | ALPHA: (180) implies:
% 230.38/41.68  | | | | |   (181)  all_57_4 = e2
% 230.38/41.68  | | | | | 
% 230.38/41.68  | | | | | BETA: splitting (35) gives:
% 230.38/41.68  | | | | | 
% 230.38/41.68  | | | | | Case 1:
% 230.38/41.68  | | | | | | 
% 230.38/41.68  | | | | | |   (182)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 &
% 230.38/41.68  | | | | | |            op(e0, e2) = e2)
% 230.38/41.68  | | | | | | 
% 230.38/41.68  | | | | | | BETA: splitting (182) gives:
% 230.38/41.68  | | | | | | 
% 230.38/41.68  | | | | | | Case 1:
% 230.38/41.68  | | | | | | | 
% 230.38/41.68  | | | | | | |   (183)  all_57_12 = e2 & op(e0, e3) = e2
% 230.38/41.68  | | | | | | | 
% 230.38/41.68  | | | | | | | ALPHA: (183) implies:
% 230.38/41.68  | | | | | | |   (184)  all_57_12 = e2
% 230.38/41.68  | | | | | | | 
% 230.38/41.68  | | | | | | | BETA: splitting (44) gives:
% 230.38/41.68  | | | | | | | 
% 230.38/41.68  | | | | | | | Case 1:
% 230.38/41.68  | | | | | | | | 
% 230.38/41.68  | | | | | | | |   (185)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 &
% 230.38/41.68  | | | | | | | |            op(e2, e0) = e2)
% 230.38/41.68  | | | | | | | | 
% 230.38/41.68  | | | | | | | | BETA: splitting (185) gives:
% 230.38/41.68  | | | | | | | | 
% 230.38/41.68  | | | | | | | | Case 1:
% 230.38/41.68  | | | | | | | | | 
% 230.38/41.68  | | | | | | | | |   (186)  all_57_9 = e2 & op(e3, e0) = e2
% 230.38/41.68  | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | ALPHA: (186) implies:
% 230.38/41.68  | | | | | | | | |   (187)  all_57_9 = e2
% 230.38/41.68  | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | BETA: splitting (6) gives:
% 230.38/41.68  | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | Case 1:
% 230.38/41.68  | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | |   (188)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 230.38/41.68  | | | | | | | | | |            & op(e1, e2) = e0)
% 230.38/41.68  | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | BETA: splitting (188) gives:
% 230.38/41.68  | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | Case 1:
% 230.38/41.68  | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | |   (189)  all_57_6 = e0 & op(e1, e3) = e0
% 230.38/41.68  | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (11), (12),
% 230.38/41.68  | | | | | | | | | | |            (16), (17), (18), (19), (20), (21), (22), (23),
% 230.38/41.68  | | | | | | | | | | |            (24), (25), (29), (32), (33), (35), (36), (37),
% 230.38/41.68  | | | | | | | | | | |            (40), (41), (43), (44), (45), (46), (47), (48),
% 230.38/41.68  | | | | | | | | | | |            (49), (50), (51), (52), (53), (165), (189) are
% 230.38/41.68  | | | | | | | | | | |            inconsistent by sub-proof #1124.
% 230.38/41.68  | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | Case 2:
% 230.38/41.68  | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | |   (190)  all_57_7 = e0 & op(e1, e2) = e0
% 230.38/41.68  | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | REF_CLOSE: (20), (40), (190) are inconsistent by sub-proof
% 230.38/41.68  | | | | | | | | | | |            #2042.
% 230.38/41.68  | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | End of split
% 230.38/41.68  | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | Case 2:
% 230.38/41.68  | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | |   (191)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0
% 230.38/41.68  | | | | | | | | | |            & op(e1, e0) = e0)
% 230.38/41.68  | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | BETA: splitting (191) gives:
% 230.38/41.68  | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | Case 1:
% 230.38/41.68  | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | |   (192)  all_57_8 = e0 & op(e1, e1) = e0
% 230.38/41.68  | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (11), (12),
% 230.38/41.68  | | | | | | | | | | |            (16), (17), (18), (19), (20), (21), (22), (23),
% 230.38/41.68  | | | | | | | | | | |            (25), (29), (32), (33), (35), (36), (40), (41),
% 230.38/41.68  | | | | | | | | | | |            (43), (44), (45), (46), (47), (48), (49), (50),
% 230.38/41.68  | | | | | | | | | | |            (51), (52), (53), (181), (187), (192) are
% 230.38/41.68  | | | | | | | | | | |            inconsistent by sub-proof #1159.
% 230.38/41.68  | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | Case 2:
% 230.38/41.68  | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | |   (193)  all_57_11 = e0 & op(e1, e0) = e0
% 230.38/41.68  | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | ALPHA: (193) implies:
% 230.38/41.68  | | | | | | | | | | |   (194)  all_57_11 = e0
% 230.38/41.68  | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | BETA: splitting (18) gives:
% 230.38/41.68  | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | Case 1:
% 230.38/41.68  | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | |   (195)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 230.38/41.68  | | | | | | | | | | | |            & op(e2, e1) = e0)
% 230.38/41.68  | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (7), (12), (16), (17), (19),
% 230.38/41.68  | | | | | | | | | | | |            (20), (22), (23), (24), (25), (29), (32), (37),
% 230.38/41.68  | | | | | | | | | | | |            (40), (41), (43), (44), (46), (47), (48), (49),
% 230.38/41.68  | | | | | | | | | | | |            (50), (52), (165), (181), (194), (195) are
% 230.38/41.68  | | | | | | | | | | | |            inconsistent by sub-proof #1098.
% 230.38/41.68  | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | Case 2:
% 230.38/41.68  | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | |   (196)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 230.38/41.68  | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 230.38/41.68  | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | BETA: splitting (196) gives:
% 230.38/41.68  | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | Case 1:
% 230.38/41.68  | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | |   (197)  all_57_8 = e0 & op(e1, e1) = e0
% 230.38/41.68  | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (11), (12),
% 230.38/41.68  | | | | | | | | | | | | |            (16), (17), (18), (19), (20), (21), (22), (23),
% 230.38/41.68  | | | | | | | | | | | | |            (25), (29), (32), (33), (35), (36), (40), (41),
% 230.38/41.68  | | | | | | | | | | | | |            (43), (44), (45), (46), (47), (48), (49), (50),
% 230.38/41.68  | | | | | | | | | | | | |            (51), (52), (53), (181), (187), (194), (197) are
% 230.38/41.68  | | | | | | | | | | | | |            inconsistent by sub-proof #1097.
% 230.38/41.68  | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | Case 2:
% 230.38/41.68  | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | |   (198)  all_57_14 = e0 & op(e0, e1) = e0
% 230.38/41.68  | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | ALPHA: (198) implies:
% 230.38/41.68  | | | | | | | | | | | | |   (199)  all_57_14 = e0
% 230.38/41.68  | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | BETA: splitting (12) gives:
% 230.38/41.68  | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | Case 1:
% 230.38/41.68  | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | |   (200)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 230.38/41.68  | | | | | | | | | | | | | |            & op(e3, e2) = e1)
% 230.38/41.68  | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 230.38/41.68  | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | Case 1:
% 230.38/41.68  | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | |   (201)  all_57_0 = e1 & op(e3, e3) = e1
% 230.38/41.68  | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | ALPHA: (201) implies:
% 230.38/41.68  | | | | | | | | | | | | | | |   (202)  op(e3, e3) = e1
% 230.38/41.68  | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (22), (202) are inconsistent by
% 230.38/41.68  | | | | | | | | | | | | | | |            sub-proof #2495.
% 230.38/41.68  | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | Case 2:
% 230.38/41.68  | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | |   (203)  all_57_1 = e1 & op(e3, e2) = e1
% 230.38/41.68  | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | ALPHA: (203) implies:
% 230.38/41.68  | | | | | | | | | | | | | | |   (204)  all_57_1 = e1
% 230.38/41.68  | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | BETA: splitting (24) gives:
% 230.38/41.68  | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | Case 1:
% 230.38/41.68  | | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | |   (205)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 230.38/41.68  | | | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 230.38/41.68  | | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | | BETA: splitting (205) gives:
% 230.38/41.68  | | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | | Case 1:
% 230.38/41.68  | | | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | | |   (206)  all_57_12 = e1 & op(e0, e3) = e1
% 230.38/41.68  | | | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (184), (206) are inconsistent by sub-proof
% 230.38/41.68  | | | | | | | | | | | | | | | | |            #2388.
% 230.38/41.68  | | | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | | Case 2:
% 230.38/41.68  | | | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | | |   (207)  all_57_13 = e1 & op(e0, e2) = e1
% 230.38/41.68  | | | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | | | ALPHA: (207) implies:
% 230.38/41.68  | | | | | | | | | | | | | | | | |   (208)  all_57_13 = e1
% 230.38/41.68  | | | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | | | BETA: splitting (3) gives:
% 230.38/41.68  | | | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | | | Case 1:
% 230.38/41.68  | | | | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | | | |   (209)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 230.38/41.68  | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e1)
% 230.38/41.68  | | | | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 230.38/41.68  | | | | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/41.68  | | | | | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | | | | |   (210)  all_57_0 = e1 & op(e3, e3) = e1
% 230.38/41.68  | | | | | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | | | | | ALPHA: (210) implies:
% 230.38/41.68  | | | | | | | | | | | | | | | | | | |   (211)  op(e3, e3) = e1
% 230.38/41.68  | | | | | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (22), (211) are inconsistent by
% 230.38/41.68  | | | | | | | | | | | | | | | | | | |            sub-proof #2495.
% 230.38/41.68  | | | | | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/41.68  | | | | | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | | | | |   (212)  all_57_2 = e1 & op(e2, e3) = e1
% 230.38/41.68  | | | | | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | | | | | ALPHA: (212) implies:
% 230.38/41.68  | | | | | | | | | | | | | | | | | | |   (213)  all_57_2 = e1
% 230.38/41.68  | | | | | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | | | | | BETA: splitting (27) gives:
% 230.38/41.68  | | | | | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/41.68  | | | | | | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | | | | | |   (214)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 230.38/41.68  | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e0)
% 230.38/41.68  | | | | | | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 230.38/41.68  | | | | | | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/41.68  | | | | | | | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | | | | | | |   (215)  all_57_1 = e0 & op(e3, e2) = e0
% 230.38/41.68  | | | | | | | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (32), (204), (215) are inconsistent by sub-proof
% 230.38/41.68  | | | | | | | | | | | | | | | | | | | | |            #2493.
% 230.38/41.68  | | | | | | | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/41.68  | | | | | | | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | | | | | | |   (216)  all_57_3 = e0 & op(e2, e2) = e0
% 230.38/41.68  | | | | | | | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | | | | | | | ALPHA: (216) implies:
% 230.38/41.68  | | | | | | | | | | | | | | | | | | | | |   (217)  all_57_3 = e0
% 230.38/41.68  | | | | | | | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (5), (7), (19), (23), (25), (29), (32), (33),
% 230.38/41.68  | | | | | | | | | | | | | | | | | | | | |            (41), (43), (44), (48), (187), (194), (213), (217)
% 230.38/41.68  | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1093.
% 230.38/41.68  | | | | | | | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | | | | | | End of split
% 230.38/41.68  | | | | | | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/41.68  | | | | | | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | | | | | |   (218)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 230.38/41.68  | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0)
% 230.38/41.68  | | | | | | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 230.38/41.68  | | | | | | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/41.68  | | | | | | | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | | | | | | |   (219)  all_57_7 = e0 & op(e1, e2) = e0
% 230.38/41.68  | | | | | | | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (40), (219) are inconsistent by sub-proof
% 230.38/41.68  | | | | | | | | | | | | | | | | | | | | |            #2042.
% 230.38/41.68  | | | | | | | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/41.68  | | | | | | | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | | | | | | |   (220)  all_57_13 = e0 & op(e0, e2) = e0
% 230.38/41.68  | | | | | | | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (32), (208), (220) are inconsistent by sub-proof
% 230.38/41.68  | | | | | | | | | | | | | | | | | | | | |            #1920.
% 230.38/41.68  | | | | | | | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | | | | | | End of split
% 230.38/41.68  | | | | | | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | | | | | End of split
% 230.38/41.68  | | | | | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | | | | End of split
% 230.38/41.68  | | | | | | | | | | | | | | | | | | 
% 230.38/41.68  | | | | | | | | | | | | | | | | | Case 2:
% 230.38/41.68  | | | | | | | | | | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | | | | | | | | | |   (221)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 230.38/41.69  | | | | | | | | | | | | | | | | | |            e1 & op(e0, e3) = e1)
% 230.38/41.69  | | | | | | | | | | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 230.38/41.69  | | | | | | | | | | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | | | | | | | | | | Case 1:
% 230.38/41.69  | | | | | | | | | | | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | | | | | | | | | | |   (222)  all_57_6 = e1 & op(e1, e3) = e1
% 230.38/41.69  | | | | | | | | | | | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (165), (222) are inconsistent by sub-proof
% 230.38/41.69  | | | | | | | | | | | | | | | | | | |            #2389.
% 230.38/41.69  | | | | | | | | | | | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | | | | | | | | | | Case 2:
% 230.38/41.69  | | | | | | | | | | | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | | | | | | | | | | |   (223)  all_57_12 = e1 & op(e0, e3) = e1
% 230.38/41.69  | | | | | | | | | | | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (184), (223) are inconsistent by sub-proof
% 230.38/41.69  | | | | | | | | | | | | | | | | | | |            #2388.
% 230.38/41.69  | | | | | | | | | | | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | | | | | | | | | | End of split
% 230.38/41.69  | | | | | | | | | | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | | | | | | | | | End of split
% 230.38/41.69  | | | | | | | | | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | | | | | | | | End of split
% 230.38/41.69  | | | | | | | | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | | | | | | | Case 2:
% 230.38/41.69  | | | | | | | | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | | | | | | | |   (224)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 230.38/41.69  | | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 230.38/41.69  | | | | | | | | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (32), (33), (199), (224) are
% 230.38/41.69  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2056.
% 230.38/41.69  | | | | | | | | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | | | | | | | End of split
% 230.38/41.69  | | | | | | | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | | | | | | End of split
% 230.38/41.69  | | | | | | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | | | | | Case 2:
% 230.38/41.69  | | | | | | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | | | | | |   (225)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 230.38/41.69  | | | | | | | | | | | | | |            & op(e3, e0) = e1)
% 230.38/41.69  | | | | | | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | | | | | | REF_CLOSE: (43), (181), (187), (225) are inconsistent by
% 230.38/41.69  | | | | | | | | | | | | | |            sub-proof #2443.
% 230.38/41.69  | | | | | | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | | | | | End of split
% 230.38/41.69  | | | | | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | | | | End of split
% 230.38/41.69  | | | | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | | | End of split
% 230.38/41.69  | | | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | | End of split
% 230.38/41.69  | | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | End of split
% 230.38/41.69  | | | | | | | | | 
% 230.38/41.69  | | | | | | | | Case 2:
% 230.38/41.69  | | | | | | | | | 
% 230.38/41.69  | | | | | | | | |   (226)  all_57_10 = e2 & op(e2, e0) = e2
% 230.38/41.69  | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | REF_CLOSE: (7), (14), (38), (226) are inconsistent by
% 230.38/41.69  | | | | | | | | |            sub-proof #2432.
% 230.38/41.69  | | | | | | | | | 
% 230.38/41.69  | | | | | | | | End of split
% 230.38/41.69  | | | | | | | | 
% 230.38/41.69  | | | | | | | Case 2:
% 230.38/41.69  | | | | | | | | 
% 230.38/41.69  | | | | | | | |   (227)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 &
% 230.38/41.69  | | | | | | | |            op(e0, e0) = e2)
% 230.38/41.69  | | | | | | | | 
% 230.38/41.69  | | | | | | | | BETA: splitting (227) gives:
% 230.38/41.69  | | | | | | | | 
% 230.38/41.69  | | | | | | | | Case 1:
% 230.38/41.69  | | | | | | | | | 
% 230.38/41.69  | | | | | | | | |   (228)  all_57_11 = e2 & op(e1, e0) = e2
% 230.38/41.69  | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | ALPHA: (228) implies:
% 230.38/41.69  | | | | | | | | |   (229)  all_57_11 = e2
% 230.38/41.69  | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 230.38/41.69  | | | | | | | | |            (11), (12), (16), (17), (18), (19), (20), (21),
% 230.38/41.69  | | | | | | | | |            (22), (23), (24), (25), (29), (32), (33), (35),
% 230.38/41.69  | | | | | | | | |            (36), (37), (40), (41), (43), (44), (45), (46),
% 230.38/41.69  | | | | | | | | |            (47), (48), (49), (50), (51), (52), (53), (165),
% 230.38/41.69  | | | | | | | | |            (229) are inconsistent by sub-proof #1091.
% 230.38/41.69  | | | | | | | | | 
% 230.38/41.69  | | | | | | | | Case 2:
% 230.38/41.69  | | | | | | | | | 
% 230.38/41.69  | | | | | | | | |   (230)  all_57_15 = e2 & op(e0, e0) = e2
% 230.38/41.69  | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | REF_CLOSE: (19), (23), (230) are inconsistent by sub-proof
% 230.38/41.69  | | | | | | | | |            #2323.
% 230.38/41.69  | | | | | | | | | 
% 230.38/41.69  | | | | | | | | End of split
% 230.38/41.69  | | | | | | | | 
% 230.38/41.69  | | | | | | | End of split
% 230.38/41.69  | | | | | | | 
% 230.38/41.69  | | | | | | Case 2:
% 230.38/41.69  | | | | | | | 
% 230.38/41.69  | | | | | | |   (231)  all_57_13 = e2 & op(e0, e2) = e2
% 230.38/41.69  | | | | | | | 
% 230.38/41.69  | | | | | | | ALPHA: (231) implies:
% 230.38/41.69  | | | | | | |   (232)  op(e0, e2) = e2
% 230.38/41.69  | | | | | | | 
% 230.38/41.69  | | | | | | | REF_CLOSE: (7), (15), (34), (232) are inconsistent by sub-proof
% 230.38/41.69  | | | | | | |            #2335.
% 230.38/41.69  | | | | | | | 
% 230.38/41.69  | | | | | | End of split
% 230.38/41.69  | | | | | | 
% 230.38/41.69  | | | | | Case 2:
% 230.38/41.69  | | | | | | 
% 230.38/41.69  | | | | | |   (233)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 &
% 230.38/41.69  | | | | | |            op(e0, e0) = e2)
% 230.38/41.69  | | | | | | 
% 230.38/41.69  | | | | | | BETA: splitting (233) gives:
% 230.38/41.69  | | | | | | 
% 230.38/41.69  | | | | | | Case 1:
% 230.38/41.69  | | | | | | | 
% 230.38/41.69  | | | | | | |   (234)  all_57_14 = e2 & op(e0, e1) = e2
% 230.38/41.69  | | | | | | | 
% 230.38/41.69  | | | | | | | ALPHA: (234) implies:
% 230.38/41.69  | | | | | | |   (235)  all_57_14 = e2
% 230.38/41.69  | | | | | | | 
% 230.38/41.69  | | | | | | | BETA: splitting (44) gives:
% 230.38/41.69  | | | | | | | 
% 230.38/41.69  | | | | | | | Case 1:
% 230.38/41.69  | | | | | | | | 
% 230.38/41.69  | | | | | | | |   (236)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 &
% 230.38/41.69  | | | | | | | |            op(e2, e0) = e2)
% 230.38/41.69  | | | | | | | | 
% 230.38/41.69  | | | | | | | | BETA: splitting (236) gives:
% 230.38/41.69  | | | | | | | | 
% 230.38/41.69  | | | | | | | | Case 1:
% 230.38/41.69  | | | | | | | | | 
% 230.38/41.69  | | | | | | | | |   (237)  all_57_9 = e2 & op(e3, e0) = e2
% 230.38/41.69  | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | ALPHA: (237) implies:
% 230.38/41.69  | | | | | | | | |   (238)  all_57_9 = e2
% 230.38/41.69  | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | BETA: splitting (6) gives:
% 230.38/41.69  | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | Case 1:
% 230.38/41.69  | | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | |   (239)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 230.38/41.69  | | | | | | | | | |            & op(e1, e2) = e0)
% 230.38/41.69  | | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | | BETA: splitting (239) gives:
% 230.38/41.69  | | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | | Case 1:
% 230.38/41.69  | | | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | | |   (240)  all_57_6 = e0 & op(e1, e3) = e0
% 230.38/41.69  | | | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (11), (12),
% 230.38/41.69  | | | | | | | | | | |            (16), (17), (18), (19), (20), (21), (22), (23),
% 230.38/41.69  | | | | | | | | | | |            (24), (25), (29), (32), (33), (35), (36), (37),
% 230.38/41.69  | | | | | | | | | | |            (40), (41), (43), (44), (45), (46), (47), (48),
% 230.38/41.69  | | | | | | | | | | |            (49), (50), (51), (52), (53), (165), (240) are
% 230.38/41.69  | | | | | | | | | | |            inconsistent by sub-proof #1124.
% 230.38/41.69  | | | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | | Case 2:
% 230.38/41.69  | | | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | | |   (241)  all_57_7 = e0 & op(e1, e2) = e0
% 230.38/41.69  | | | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | | | REF_CLOSE: (20), (40), (241) are inconsistent by sub-proof
% 230.38/41.69  | | | | | | | | | | |            #2042.
% 230.38/41.69  | | | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | | End of split
% 230.38/41.69  | | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | Case 2:
% 230.38/41.69  | | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | |   (242)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0
% 230.38/41.69  | | | | | | | | | |            & op(e1, e0) = e0)
% 230.38/41.69  | | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | | BETA: splitting (242) gives:
% 230.38/41.69  | | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | | Case 1:
% 230.38/41.69  | | | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | | |   (243)  all_57_8 = e0 & op(e1, e1) = e0
% 230.38/41.69  | | | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (11), (12),
% 230.38/41.69  | | | | | | | | | | |            (16), (17), (18), (19), (20), (21), (22), (23),
% 230.38/41.69  | | | | | | | | | | |            (25), (29), (32), (33), (35), (36), (40), (41),
% 230.38/41.69  | | | | | | | | | | |            (43), (44), (45), (46), (47), (48), (49), (50),
% 230.38/41.69  | | | | | | | | | | |            (51), (52), (53), (181), (238), (243) are
% 230.38/41.69  | | | | | | | | | | |            inconsistent by sub-proof #1159.
% 230.38/41.69  | | | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | | Case 2:
% 230.38/41.69  | | | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | | |   (244)  all_57_11 = e0 & op(e1, e0) = e0
% 230.38/41.69  | | | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | | | ALPHA: (244) implies:
% 230.38/41.69  | | | | | | | | | | |   (245)  all_57_11 = e0
% 230.38/41.69  | | | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | | | BETA: splitting (18) gives:
% 230.38/41.69  | | | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | | | Case 1:
% 230.38/41.69  | | | | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | | | |   (246)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 230.38/41.69  | | | | | | | | | | | |            & op(e2, e1) = e0)
% 230.38/41.69  | | | | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (7), (12), (16), (17), (19),
% 230.38/41.69  | | | | | | | | | | | |            (20), (22), (23), (24), (25), (29), (32), (37),
% 230.38/41.69  | | | | | | | | | | | |            (40), (41), (43), (44), (46), (47), (48), (49),
% 230.38/41.69  | | | | | | | | | | | |            (50), (52), (165), (181), (245), (246) are
% 230.38/41.69  | | | | | | | | | | | |            inconsistent by sub-proof #1098.
% 230.38/41.69  | | | | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | | | Case 2:
% 230.38/41.69  | | | | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | | | |   (247)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 230.38/41.69  | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 230.38/41.69  | | | | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | | | | BETA: splitting (247) gives:
% 230.38/41.69  | | | | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | | | | Case 1:
% 230.38/41.69  | | | | | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | | | | |   (248)  all_57_8 = e0 & op(e1, e1) = e0
% 230.38/41.69  | | | | | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (11), (12),
% 230.38/41.69  | | | | | | | | | | | | |            (16), (17), (18), (19), (20), (21), (22), (23),
% 230.38/41.69  | | | | | | | | | | | | |            (25), (29), (32), (33), (35), (36), (40), (41),
% 230.38/41.69  | | | | | | | | | | | | |            (43), (44), (45), (46), (47), (48), (49), (50),
% 230.38/41.69  | | | | | | | | | | | | |            (51), (52), (53), (181), (238), (245), (248) are
% 230.38/41.69  | | | | | | | | | | | | |            inconsistent by sub-proof #1097.
% 230.38/41.69  | | | | | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | | | | Case 2:
% 230.38/41.69  | | | | | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | | | | |   (249)  all_57_14 = e0 & op(e0, e1) = e0
% 230.38/41.69  | | | | | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | | | | | ALPHA: (249) implies:
% 230.38/41.69  | | | | | | | | | | | | |   (250)  all_57_14 = e0
% 230.38/41.69  | | | | | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | | | | | COMBINE_EQS: (235), (250) imply:
% 230.38/41.69  | | | | | | | | | | | | |   (251)  e2 = e0
% 230.38/41.69  | | | | | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | | | | | COMBINE_EQS: (50), (251) imply:
% 230.38/41.69  | | | | | | | | | | | | |   (252)  all_57_3 = e0
% 230.38/41.69  | | | | | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (7), (12), (16), (17), (19),
% 230.38/41.69  | | | | | | | | | | | | |            (20), (22), (23), (24), (25), (29), (32), (37),
% 230.38/41.69  | | | | | | | | | | | | |            (40), (41), (43), (44), (46), (47), (48), (49),
% 230.38/41.69  | | | | | | | | | | | | |            (52), (165), (245), (252) are inconsistent by
% 230.38/41.69  | | | | | | | | | | | | |            sub-proof #1462.
% 230.38/41.69  | | | | | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | | | | End of split
% 230.38/41.69  | | | | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | | | End of split
% 230.38/41.69  | | | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | | End of split
% 230.38/41.69  | | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | End of split
% 230.38/41.69  | | | | | | | | | 
% 230.38/41.69  | | | | | | | | Case 2:
% 230.38/41.69  | | | | | | | | | 
% 230.38/41.69  | | | | | | | | |   (253)  all_57_10 = e2 & op(e2, e0) = e2
% 230.38/41.69  | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | REF_CLOSE: (7), (14), (38), (253) are inconsistent by
% 230.38/41.69  | | | | | | | | |            sub-proof #2432.
% 230.38/41.69  | | | | | | | | | 
% 230.38/41.69  | | | | | | | | End of split
% 230.38/41.69  | | | | | | | | 
% 230.38/41.69  | | | | | | | Case 2:
% 230.38/41.69  | | | | | | | | 
% 230.38/41.69  | | | | | | | |   (254)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 &
% 230.38/41.69  | | | | | | | |            op(e0, e0) = e2)
% 230.38/41.69  | | | | | | | | 
% 230.38/41.69  | | | | | | | | BETA: splitting (254) gives:
% 230.38/41.69  | | | | | | | | 
% 230.38/41.69  | | | | | | | | Case 1:
% 230.38/41.69  | | | | | | | | | 
% 230.38/41.69  | | | | | | | | |   (255)  all_57_11 = e2 & op(e1, e0) = e2
% 230.38/41.69  | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | ALPHA: (255) implies:
% 230.38/41.69  | | | | | | | | |   (256)  all_57_11 = e2
% 230.38/41.69  | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 230.38/41.69  | | | | | | | | |            (11), (12), (16), (17), (18), (19), (20), (21),
% 230.38/41.69  | | | | | | | | |            (22), (23), (24), (25), (29), (32), (33), (35),
% 230.38/41.69  | | | | | | | | |            (36), (37), (40), (41), (43), (44), (45), (46),
% 230.38/41.69  | | | | | | | | |            (47), (48), (49), (50), (51), (52), (53), (165),
% 230.38/41.69  | | | | | | | | |            (256) are inconsistent by sub-proof #1091.
% 230.38/41.69  | | | | | | | | | 
% 230.38/41.69  | | | | | | | | Case 2:
% 230.38/41.69  | | | | | | | | | 
% 230.38/41.69  | | | | | | | | |   (257)  all_57_15 = e2 & op(e0, e0) = e2
% 230.38/41.69  | | | | | | | | | 
% 230.38/41.69  | | | | | | | | | REF_CLOSE: (19), (23), (257) are inconsistent by sub-proof
% 230.38/41.69  | | | | | | | | |            #2323.
% 230.38/41.69  | | | | | | | | | 
% 230.38/41.69  | | | | | | | | End of split
% 230.38/41.69  | | | | | | | | 
% 230.38/41.69  | | | | | | | End of split
% 230.38/41.69  | | | | | | | 
% 230.38/41.69  | | | | | | Case 2:
% 230.38/41.69  | | | | | | | 
% 230.38/41.69  | | | | | | |   (258)  all_57_15 = e2 & op(e0, e0) = e2
% 230.38/41.69  | | | | | | | 
% 230.38/41.69  | | | | | | | ALPHA: (258) implies:
% 230.38/41.69  | | | | | | |   (259)  all_57_15 = e2
% 230.38/41.69  | | | | | | | 
% 230.38/41.69  | | | | | | | REF_CLOSE: (19), (23), (259) are inconsistent by sub-proof #2058.
% 230.38/41.69  | | | | | | | 
% 230.38/41.69  | | | | | | End of split
% 230.38/41.69  | | | | | | 
% 230.38/41.69  | | | | | End of split
% 230.38/41.69  | | | | | 
% 230.38/41.69  | | | | Case 2:
% 230.38/41.69  | | | | | 
% 230.38/41.69  | | | | |   (260)  all_57_9 = e2 & op(e3, e0) = e2
% 230.38/41.69  | | | | | 
% 230.38/41.69  | | | | | ALPHA: (260) implies:
% 230.38/41.69  | | | | |   (261)  all_57_9 = e2
% 230.38/41.69  | | | | | 
% 230.38/41.69  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 230.38/41.69  | | | | |            (12), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 230.38/41.69  | | | | |            (24), (25), (29), (31), (32), (33), (34), (35), (36), (37),
% 230.38/41.69  | | | | |            (40), (41), (43), (44), (45), (46), (47), (48), (49), (50),
% 230.38/41.69  | | | | |            (51), (52), (53), (165), (261) are inconsistent by
% 230.38/41.69  | | | | |            sub-proof #1121.
% 230.38/41.69  | | | | | 
% 230.38/41.69  | | | | End of split
% 230.38/41.69  | | | | 
% 230.38/41.69  | | | End of split
% 230.38/41.69  | | | 
% 230.38/41.69  | | Case 2:
% 230.38/41.69  | | | 
% 230.38/41.69  | | |   (262)  all_57_12 = e2 & op(e0, e3) = e2
% 230.38/41.69  | | | 
% 230.38/41.69  | | | ALPHA: (262) implies:
% 230.38/41.69  | | |   (263)  all_57_12 = e2
% 230.38/41.69  | | | 
% 230.38/41.69  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 230.38/41.69  | | |            (13), (14), (16), (17), (18), (19), (20), (21), (22), (23),
% 230.38/41.69  | | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 230.38/41.69  | | |            (35), (36), (37), (38), (40), (41), (43), (44), (45), (46),
% 230.38/41.69  | | |            (47), (48), (49), (50), (51), (52), (53), (263) are
% 230.38/41.69  | | |            inconsistent by sub-proof #1129.
% 230.38/41.69  | | | 
% 230.38/41.69  | | End of split
% 230.38/41.69  | | 
% 230.38/41.69  | End of split
% 230.38/41.69  | 
% 230.38/41.69  End of proof
% 230.38/41.69  
% 230.38/41.69  Sub-proof #1091 shows that the following formulas are inconsistent:
% 230.38/41.69  ----------------------------------------------------------------
% 230.38/41.69    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.38/41.69         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.38/41.69    (2)   ~ (all_52_7 = e3)
% 230.38/41.69    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.38/41.69         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.38/41.69    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.38/41.69         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.38/41.69    (5)   ~ (e3 = e1)
% 230.38/41.69    (6)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.38/41.69         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.38/41.69    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.38/41.69           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.38/41.69    (8)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.38/41.69         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.38/41.69    (9)   ~ (all_6_2 = e3)
% 230.38/41.69    (10)  op(e1, e1) = all_6_2
% 230.38/41.69    (11)  op(all_52_7, all_52_7) = e0
% 230.38/41.69    (12)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.38/41.69          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.38/41.69    (13)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.38/41.69          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.38/41.69    (14)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.38/41.69          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.38/41.69    (15)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 230.38/41.69          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.38/41.69    (16)   ~ (e3 = e2)
% 230.38/41.69    (17)   ~ (e3 = e0)
% 230.38/41.69    (18)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.38/41.69          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.38/41.69    (19)  op(e3, e3) = e3
% 230.38/41.69    (20)  all_57_15 = e3
% 230.38/41.69    (21)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.38/41.69          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.38/41.69            e1)
% 230.38/41.69    (22)  all_57_5 = e3
% 230.38/41.69    (23)  all_57_6 = e2
% 230.38/41.69    (24)  all_57_11 = e2
% 230.38/41.69    (25)   ~ (e2 = e0)
% 230.38/41.69    (26)   ~ (e1 = e0)
% 230.38/41.69    (27)  op(e0, e0) = e3
% 230.38/41.69    (28)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.38/41.69          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.38/41.69            e2)
% 230.38/41.69    (29)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.38/41.69              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.38/41.69                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.38/41.69                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.38/41.69    (30)  op(e1, e1) = e2
% 230.38/41.69    (31)  all_57_7 = e3
% 230.38/41.69    (32)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.38/41.69          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.38/41.69    (33)   ~ (e2 = e1)
% 230.38/41.69    (34)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.38/41.69          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.38/41.69    (35)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.38/41.69          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.38/41.69    (36)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.38/41.69          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.38/41.69    (37)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.38/41.69          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.38/41.69    (38)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.38/41.69          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.38/41.69    (39)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.38/41.69          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.38/41.69    (40)  all_57_3 = e2
% 230.38/41.69    (41)  op(e3, e0) = all_52_7
% 230.38/41.69    (42)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.38/41.69          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.38/41.69    (43)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.38/41.69          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.38/41.69  
% 230.38/41.69  Begin of proof
% 230.38/41.69  | 
% 230.38/41.69  | BETA: splitting (6) gives:
% 230.38/41.69  | 
% 230.38/41.69  | Case 1:
% 230.38/41.69  | | 
% 230.38/41.69  | |   (44)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) =
% 230.38/41.69  | |           e0)
% 230.38/41.69  | | 
% 230.38/41.69  | | BETA: splitting (44) gives:
% 230.38/41.69  | | 
% 230.38/41.69  | | Case 1:
% 230.38/41.69  | | | 
% 230.38/41.69  | | |   (45)  all_57_6 = e0 & op(e1, e3) = e0
% 230.38/41.69  | | | 
% 230.38/41.69  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (11), (12), (13), (14),
% 230.38/41.69  | | |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (25),
% 230.38/41.69  | | |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 230.38/41.69  | | |            (36), (37), (38), (39), (40), (41), (42), (43), (45) are
% 230.38/41.69  | | |            inconsistent by sub-proof #1124.
% 230.38/41.69  | | | 
% 230.38/41.69  | | Case 2:
% 230.38/41.69  | | | 
% 230.38/41.69  | | |   (46)  all_57_7 = e0 & op(e1, e2) = e0
% 230.38/41.69  | | | 
% 230.38/41.69  | | | ALPHA: (46) implies:
% 230.38/41.69  | | |   (47)  all_57_7 = e0
% 230.38/41.69  | | | 
% 230.38/41.69  | | | REF_CLOSE: (5), (7), (8), (9), (10), (16), (17), (20), (24), (25), (26),
% 230.38/41.69  | | |            (29), (30), (33), (34), (38), (39), (47) are inconsistent by
% 230.38/41.69  | | |            sub-proof #1154.
% 230.38/41.69  | | | 
% 230.38/41.69  | | End of split
% 230.38/41.69  | | 
% 230.38/41.69  | Case 2:
% 230.38/41.69  | | 
% 230.38/41.69  | |   (48)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 230.38/41.69  | |           e0)
% 230.38/41.69  | | 
% 230.38/41.69  | | BETA: splitting (48) gives:
% 230.38/41.69  | | 
% 230.38/41.69  | | Case 1:
% 230.38/41.69  | | | 
% 230.38/41.69  | | |   (49)  all_57_8 = e0 & op(e1, e1) = e0
% 230.38/41.69  | | | 
% 230.38/41.69  | | | ALPHA: (49) implies:
% 230.38/41.69  | | |   (50)  op(e1, e1) = e0
% 230.38/41.69  | | | 
% 230.38/41.69  | | | REF_CLOSE: (5), (7), (8), (9), (10), (16), (17), (20), (23), (24), (25),
% 230.38/41.69  | | |            (26), (29), (33), (34), (38), (39), (50) are inconsistent by
% 230.38/41.69  | | |            sub-proof #1092.
% 230.38/41.69  | | | 
% 230.38/41.69  | | Case 2:
% 230.38/41.69  | | | 
% 230.38/41.69  | | |   (51)  all_57_11 = e0 & op(e1, e0) = e0
% 230.38/41.69  | | | 
% 230.38/41.69  | | | ALPHA: (51) implies:
% 230.38/41.69  | | |   (52)  all_57_11 = e0
% 230.38/41.69  | | | 
% 230.38/41.69  | | | COMBINE_EQS: (24), (52) imply:
% 230.38/41.69  | | |   (53)  e2 = e0
% 230.38/41.69  | | | 
% 230.38/41.69  | | | SIMP: (53) implies:
% 230.38/41.69  | | |   (54)  e2 = e0
% 230.38/41.69  | | | 
% 230.38/41.69  | | | COMBINE_EQS: (40), (54) imply:
% 230.38/41.69  | | |   (55)  all_57_3 = e0
% 230.38/41.69  | | | 
% 230.38/41.69  | | | REF_CLOSE: (1), (3), (4), (5), (7), (12), (13), (14), (16), (17), (19),
% 230.38/41.69  | | |            (20), (21), (22), (23), (25), (26), (30), (31), (32), (33),
% 230.38/41.69  | | |            (34), (36), (37), (38), (39), (42), (52), (55) are inconsistent
% 230.38/41.69  | | |            by sub-proof #1462.
% 230.38/41.69  | | | 
% 230.38/41.69  | | End of split
% 230.38/41.69  | | 
% 230.38/41.69  | End of split
% 230.38/41.69  | 
% 230.38/41.69  End of proof
% 230.38/41.69  
% 230.38/41.69  Sub-proof #1092 shows that the following formulas are inconsistent:
% 230.38/41.69  ----------------------------------------------------------------
% 230.38/41.69    (1)   ~ (e3 = e1)
% 230.38/41.69    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.38/41.69           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.38/41.69    (3)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.38/41.69         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.38/41.69    (4)   ~ (all_6_2 = e3)
% 230.38/41.69    (5)  op(e1, e1) = all_6_2
% 230.38/41.69    (6)   ~ (e3 = e2)
% 230.38/41.69    (7)   ~ (e3 = e0)
% 230.38/41.69    (8)  all_57_15 = e3
% 230.38/41.69    (9)  all_57_6 = e2
% 230.38/41.69    (10)  all_57_11 = e2
% 230.38/41.69    (11)   ~ (e2 = e0)
% 230.38/41.69    (12)   ~ (e1 = e0)
% 230.38/41.69    (13)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.38/41.69              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.38/41.69                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.38/41.69                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.38/41.69    (14)  op(e1, e1) = e0
% 230.38/41.69    (15)   ~ (e2 = e1)
% 230.38/41.69    (16)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.38/41.69          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.38/41.69    (17)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.38/41.69          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.38/41.69    (18)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.38/41.69          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.38/41.69  
% 230.38/41.69  Begin of proof
% 230.38/41.69  | 
% 230.38/41.69  | BETA: splitting (18) gives:
% 230.38/41.69  | 
% 230.38/41.69  | Case 1:
% 230.38/41.69  | | 
% 230.38/41.69  | |   (19)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) =
% 230.38/41.69  | |           e1)
% 230.38/41.69  | | 
% 230.38/41.69  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13),
% 230.38/41.69  | |            (15), (16), (17), (19) are inconsistent by sub-proof #1123.
% 230.38/41.69  | | 
% 230.38/41.69  | Case 2:
% 230.38/41.69  | | 
% 230.38/41.69  | |   (20)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) =
% 230.38/41.69  | |           e1)
% 230.38/41.69  | | 
% 230.38/41.69  | | REF_CLOSE: (2), (10), (12), (14), (15), (20) are inconsistent by sub-proof
% 230.38/41.69  | |            #1315.
% 230.38/41.69  | | 
% 230.38/41.69  | End of split
% 230.38/41.69  | 
% 230.38/41.69  End of proof
% 230.38/41.69  
% 230.38/41.69  Sub-proof #1093 shows that the following formulas are inconsistent:
% 230.38/41.69  ----------------------------------------------------------------
% 230.38/41.69    (1)  all_57_9 = e2
% 230.38/41.69    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.38/41.69         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.38/41.69    (3)   ~ (e3 = e1)
% 230.38/41.69    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.38/41.69           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.38/41.69    (5)  all_57_3 = e0
% 230.38/41.69    (6)   ~ (e3 = e2)
% 230.38/41.69    (7)  all_57_15 = e3
% 230.38/41.69    (8)  all_57_5 = e3
% 230.38/41.69    (9)  all_57_11 = e0
% 230.38/41.69    (10)   ~ (e2 = e0)
% 230.38/41.69    (11)   ~ (e1 = e0)
% 230.38/41.69    (12)  op(e0, e0) = e3
% 230.38/41.69    (13)  all_57_2 = e1
% 230.38/41.69    (14)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.38/41.69          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.38/41.69    (15)   ~ (e2 = e1)
% 230.38/41.69    (16)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.38/41.69          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.38/41.69    (17)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.38/41.69          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.38/41.69  
% 230.38/41.69  Begin of proof
% 230.38/41.69  | 
% 230.38/41.69  | BETA: splitting (14) gives:
% 230.38/41.69  | 
% 230.38/41.69  | Case 1:
% 230.38/41.69  | | 
% 230.38/41.69  | |   (18)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 230.38/41.69  | |           e2)
% 230.38/41.69  | | 
% 230.38/41.69  | | REF_CLOSE: (1), (3), (5), (6), (7), (9), (10), (11), (13), (15), (16), (17),
% 230.38/41.69  | |            (18) are inconsistent by sub-proof #1095.
% 230.38/41.69  | | 
% 230.38/41.69  | Case 2:
% 230.38/41.69  | | 
% 230.38/41.69  | |   (19)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 230.38/41.69  | |           e2)
% 230.38/41.69  | | 
% 230.38/41.69  | | BETA: splitting (19) gives:
% 230.38/41.69  | | 
% 230.38/41.69  | | Case 1:
% 230.38/41.69  | | | 
% 230.38/41.69  | | |   (20)  all_57_5 = e2 & op(e2, e1) = e2
% 230.38/41.69  | | | 
% 230.38/41.69  | | | REF_CLOSE: (6), (8), (20) are inconsistent by sub-proof #2425.
% 230.38/41.69  | | | 
% 230.38/41.69  | | Case 2:
% 230.38/41.69  | | | 
% 230.38/41.69  | | |   (21)  all_57_10 = e2 & op(e2, e0) = e2
% 230.38/41.69  | | | 
% 230.38/41.69  | | | ALPHA: (21) implies:
% 230.38/41.69  | | |   (22)  all_57_10 = e2
% 230.38/41.69  | | | 
% 230.38/41.69  | | | BETA: splitting (17) gives:
% 230.38/41.69  | | | 
% 230.38/41.69  | | | Case 1:
% 230.38/41.69  | | | | 
% 230.38/41.69  | | | |   (23)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0)
% 230.38/41.69  | | | |           = e1)
% 230.38/41.69  | | | | 
% 230.38/41.69  | | | | BETA: splitting (23) gives:
% 230.38/41.69  | | | | 
% 230.38/41.69  | | | | Case 1:
% 230.38/41.69  | | | | | 
% 230.38/41.69  | | | | |   (24)  all_57_9 = e1 & op(e3, e0) = e1
% 230.38/41.69  | | | | | 
% 230.38/41.69  | | | | | REF_CLOSE: (1), (15), (24) are inconsistent by sub-proof #2451.
% 230.38/41.69  | | | | | 
% 230.38/41.69  | | | | Case 2:
% 230.38/41.69  | | | | | 
% 230.38/41.69  | | | | |   (25)  all_57_10 = e1 & op(e2, e0) = e1
% 230.38/41.69  | | | | | 
% 230.38/41.69  | | | | | REF_CLOSE: (15), (22), (25) are inconsistent by sub-proof #2360.
% 230.38/41.69  | | | | | 
% 230.38/41.69  | | | | End of split
% 230.38/41.69  | | | | 
% 230.38/41.69  | | | Case 2:
% 230.38/41.69  | | | | 
% 230.38/41.69  | | | |   (26)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0,
% 230.38/41.69  | | | |             e0) = e1)
% 230.38/41.69  | | | | 
% 230.38/41.69  | | | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13),
% 230.38/41.69  | | | |            (14), (15), (26) are inconsistent by sub-proof #1094.
% 230.38/41.69  | | | | 
% 230.38/41.69  | | | End of split
% 230.38/41.69  | | | 
% 230.38/41.69  | | End of split
% 230.38/41.69  | | 
% 230.38/41.69  | End of split
% 230.38/41.69  | 
% 230.38/41.69  End of proof
% 230.38/41.69  
% 230.38/41.69  Sub-proof #1094 shows that the following formulas are inconsistent:
% 230.38/41.69  ----------------------------------------------------------------
% 230.38/41.69    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.38/41.69         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.38/41.69    (2)   ~ (e3 = e1)
% 230.38/41.69    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.38/41.69           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.38/41.69    (4)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.38/41.69    (5)  all_57_3 = e0
% 230.38/41.69    (6)   ~ (e3 = e2)
% 230.38/41.69    (7)  all_57_5 = e3
% 230.38/41.69    (8)  all_57_11 = e0
% 230.38/41.69    (9)   ~ (e2 = e0)
% 230.38/41.69    (10)   ~ (e1 = e0)
% 230.38/41.69    (11)  op(e0, e0) = e3
% 230.38/41.69    (12)  all_57_2 = e1
% 230.38/41.69    (13)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.38/41.69          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.38/41.69    (14)   ~ (e2 = e1)
% 230.38/41.69  
% 230.38/41.69  Begin of proof
% 230.38/41.69  | 
% 230.38/41.69  | BETA: splitting (4) gives:
% 230.38/41.69  | 
% 230.38/41.69  | Case 1:
% 230.38/41.69  | | 
% 230.38/41.69  | |   (15)  all_57_11 = e1 & op(e1, e0) = e1
% 230.38/41.69  | | 
% 230.38/41.69  | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (9), (10), (12), (13), (14), (15)
% 230.38/41.69  | |            are inconsistent by sub-proof #1515.
% 230.38/41.69  | | 
% 230.38/41.69  | Case 2:
% 230.38/41.69  | | 
% 230.38/41.69  | |   (16)  all_57_15 = e1 & op(e0, e0) = e1
% 230.38/41.69  | | 
% 230.38/41.69  | | ALPHA: (16) implies:
% 230.38/41.69  | |   (17)  op(e0, e0) = e1
% 230.38/41.69  | | 
% 230.38/41.69  | | REF_CLOSE: (2), (3), (11), (17) are inconsistent by sub-proof #2183.
% 230.38/41.69  | | 
% 230.38/41.69  | End of split
% 230.38/41.69  | 
% 230.38/41.69  End of proof
% 230.38/41.69  
% 230.38/41.69  Sub-proof #1095 shows that the following formulas are inconsistent:
% 230.38/41.69  ----------------------------------------------------------------
% 230.38/41.69    (1)  all_57_9 = e2
% 230.38/41.69    (2)   ~ (e3 = e1)
% 230.38/41.69    (3)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2)
% 230.38/41.69    (4)  all_57_3 = e0
% 230.38/41.69    (5)   ~ (e3 = e2)
% 230.38/41.69    (6)  all_57_15 = e3
% 230.38/41.69    (7)  all_57_11 = e0
% 230.38/41.69    (8)   ~ (e2 = e0)
% 230.38/41.69    (9)   ~ (e1 = e0)
% 230.38/41.69    (10)  all_57_2 = e1
% 230.38/41.69    (11)   ~ (e2 = e1)
% 230.38/41.70    (12)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.38/41.70          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.38/41.70    (13)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.38/41.70          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.38/41.70  
% 230.38/41.70  Begin of proof
% 230.38/41.70  | 
% 230.38/41.70  | BETA: splitting (3) gives:
% 230.38/41.70  | 
% 230.38/41.70  | Case 1:
% 230.38/41.70  | | 
% 230.38/41.70  | |   (14)  all_57_2 = e2 & op(e2, e3) = e2
% 230.38/41.70  | | 
% 230.38/41.70  | | ALPHA: (14) implies:
% 230.38/41.70  | |   (15)  all_57_2 = e2
% 230.38/41.70  | | 
% 230.38/41.70  | | REF_CLOSE: (10), (11), (15) are inconsistent by sub-proof #2464.
% 230.38/41.70  | | 
% 230.38/41.70  | Case 2:
% 230.38/41.70  | | 
% 230.38/41.70  | |   (16)  all_57_3 = e2 & op(e2, e2) = e2
% 230.38/41.70  | | 
% 230.38/41.70  | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (11), (12), (13), (16)
% 230.38/41.70  | |            are inconsistent by sub-proof #1096.
% 230.38/41.70  | | 
% 230.38/41.70  | End of split
% 230.38/41.70  | 
% 230.38/41.70  End of proof
% 230.38/41.70  
% 230.38/41.70  Sub-proof #1096 shows that the following formulas are inconsistent:
% 230.38/41.70  ----------------------------------------------------------------
% 230.38/41.70    (1)  all_57_9 = e2
% 230.38/41.70    (2)  all_57_3 = e2 & op(e2, e2) = e2
% 230.38/41.70    (3)   ~ (e3 = e1)
% 230.38/41.70    (4)  all_57_3 = e0
% 230.38/41.70    (5)   ~ (e3 = e2)
% 230.38/41.70    (6)  all_57_15 = e3
% 230.38/41.70    (7)  all_57_11 = e0
% 230.38/41.70    (8)   ~ (e2 = e0)
% 230.38/41.70    (9)   ~ (e1 = e0)
% 230.38/41.70    (10)   ~ (e2 = e1)
% 230.38/41.70    (11)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.38/41.70          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.38/41.70    (12)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.38/41.70          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.38/41.70  
% 230.38/41.70  Begin of proof
% 230.38/41.70  | 
% 230.38/41.70  | ALPHA: (2) implies:
% 230.38/41.70  |   (13)  all_57_3 = e2
% 230.38/41.70  | 
% 230.38/41.70  | COMBINE_EQS: (4), (13) imply:
% 230.38/41.70  |   (14)  e2 = e0
% 230.38/41.70  | 
% 230.38/41.70  | SIMP: (14) implies:
% 230.38/41.70  |   (15)  e2 = e0
% 230.38/41.70  | 
% 230.38/41.70  | COMBINE_EQS: (1), (15) imply:
% 230.38/41.70  |   (16)  all_57_9 = e0
% 230.38/41.70  | 
% 230.38/41.70  | REF_CLOSE: (3), (5), (6), (7), (8), (9), (10), (11), (12), (16) are
% 230.38/41.70  |            inconsistent by sub-proof #1144.
% 230.38/41.70  | 
% 230.38/41.70  End of proof
% 230.38/41.70  
% 230.38/41.70  Sub-proof #1097 shows that the following formulas are inconsistent:
% 230.38/41.70  ----------------------------------------------------------------
% 230.38/41.70    (1)  all_57_9 = e2
% 230.38/41.70    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.38/41.70         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.38/41.70    (3)   ~ (all_52_7 = e3)
% 230.38/41.70    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.38/41.70         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.38/41.70    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.38/41.70         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.38/41.70    (6)   ~ (e3 = e1)
% 230.38/41.70    (7)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.38/41.70         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.38/41.70    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.38/41.70           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.38/41.70    (9)  op(all_52_7, all_52_7) = e0
% 230.38/41.70    (10)  all_57_4 = e2
% 230.38/41.70    (11)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.38/41.70          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.38/41.70    (12)  all_57_8 = e0 & op(e1, e1) = e0
% 230.38/41.70    (13)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.38/41.70          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.38/41.70    (14)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.38/41.70          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.38/41.70    (15)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 230.38/41.70          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.38/41.70    (16)   ~ (e3 = e2)
% 230.38/41.70    (17)   ~ (e3 = e0)
% 230.38/41.70    (18)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.38/41.70          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.38/41.70    (19)  op(e3, e3) = e3
% 230.38/41.70    (20)  all_57_15 = e3
% 230.38/41.70    (21)  all_57_5 = e3
% 230.38/41.70    (22)  all_57_11 = e0
% 230.38/41.70    (23)   ~ (e2 = e0)
% 230.38/41.70    (24)   ~ (e1 = e0)
% 230.38/41.70    (25)  op(e0, e0) = e3
% 230.38/41.70    (26)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.38/41.70          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.38/41.70            e2)
% 230.38/41.70    (27)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.38/41.70              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.38/41.70                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.38/41.70                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.38/41.70    (28)  all_57_7 = e3
% 230.38/41.70    (29)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.38/41.70          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.38/41.70    (30)   ~ (e2 = e1)
% 230.38/41.70    (31)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.38/41.70          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.38/41.70    (32)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.38/41.70          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.38/41.70    (33)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.38/41.70          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.38/41.70    (34)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.38/41.70          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.38/41.70    (35)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.38/41.70          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.38/41.70    (36)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.38/41.70          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.38/41.70    (37)  all_57_3 = e2
% 230.38/41.70    (38)  op(e3, e0) = all_52_7
% 230.38/41.70    (39)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.38/41.70          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.38/41.70    (40)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.38/41.70          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.38/41.70  
% 230.38/41.70  Begin of proof
% 230.38/41.70  | 
% 230.38/41.70  | ALPHA: (12) implies:
% 230.38/41.70  |   (41)  op(e1, e1) = e0
% 230.38/41.70  | 
% 230.38/41.70  | BETA: splitting (11) gives:
% 230.38/41.70  | 
% 230.38/41.70  | Case 1:
% 230.38/41.70  | | 
% 230.38/41.70  | |   (42)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) =
% 230.38/41.70  | |           e1)
% 230.38/41.70  | | 
% 230.38/41.70  | | BETA: splitting (42) gives:
% 230.38/41.70  | | 
% 230.38/41.70  | | Case 1:
% 230.38/41.70  | | | 
% 230.38/41.70  | | |   (43)  all_57_0 = e1 & op(e3, e3) = e1
% 230.38/41.70  | | | 
% 230.38/41.70  | | | ALPHA: (43) implies:
% 230.38/41.70  | | |   (44)  op(e3, e3) = e1
% 230.38/41.70  | | | 
% 230.38/41.70  | | | REF_CLOSE: (6), (8), (19), (44) are inconsistent by sub-proof #2495.
% 230.38/41.70  | | | 
% 230.38/41.70  | | Case 2:
% 230.38/41.70  | | | 
% 230.38/41.70  | | |   (45)  all_57_1 = e1 & op(e3, e2) = e1
% 230.38/41.70  | | | 
% 230.38/41.70  | | | ALPHA: (45) implies:
% 230.38/41.70  | | |   (46)  all_57_1 = e1
% 230.38/41.70  | | | 
% 230.38/41.70  | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13), (14),
% 230.38/41.70  | | |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 230.38/41.70  | | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 230.38/41.70  | | |            (35), (36), (37), (38), (39), (40), (41), (46) are inconsistent
% 230.38/41.70  | | |            by sub-proof #1143.
% 230.38/41.70  | | | 
% 230.38/41.70  | | End of split
% 230.38/41.70  | | 
% 230.38/41.70  | Case 2:
% 230.38/41.70  | | 
% 230.38/41.70  | |   (47)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) =
% 230.38/41.70  | |           e1)
% 230.38/41.70  | | 
% 230.38/41.70  | | BETA: splitting (47) gives:
% 230.38/41.70  | | 
% 230.38/41.70  | | Case 1:
% 230.38/41.70  | | | 
% 230.38/41.70  | | |   (48)  all_57_4 = e1 & op(e3, e1) = e1
% 230.38/41.70  | | | 
% 230.38/41.70  | | | REF_CLOSE: (10), (30), (48) are inconsistent by sub-proof #2452.
% 230.38/41.70  | | | 
% 230.38/41.70  | | Case 2:
% 230.38/41.70  | | | 
% 230.38/41.70  | | |   (49)  all_57_9 = e1 & op(e3, e0) = e1
% 230.38/41.70  | | | 
% 230.38/41.70  | | | REF_CLOSE: (1), (30), (49) are inconsistent by sub-proof #2451.
% 230.38/41.70  | | | 
% 230.38/41.70  | | End of split
% 230.38/41.70  | | 
% 230.38/41.70  | End of split
% 230.38/41.70  | 
% 230.38/41.70  End of proof
% 230.38/41.70  
% 230.38/41.70  Sub-proof #1098 shows that the following formulas are inconsistent:
% 230.38/41.70  ----------------------------------------------------------------
% 230.38/41.70    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.38/41.70         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.38/41.70    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.38/41.70         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.38/41.70    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.38/41.70         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.38/41.70    (4)   ~ (e3 = e1)
% 230.38/41.70    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.38/41.70           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.38/41.70    (6)  all_57_4 = e2
% 230.38/41.70    (7)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.38/41.70         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.38/41.70    (8)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0)
% 230.38/41.70    (9)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.38/41.70         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.38/41.70    (10)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.38/41.70          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.38/41.70    (11)   ~ (e3 = e2)
% 230.38/41.70    (12)   ~ (e3 = e0)
% 230.38/41.70    (13)  op(e3, e3) = e3
% 230.38/41.70    (14)  all_57_15 = e3
% 230.38/41.70    (15)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.38/41.70          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.38/41.70            e1)
% 230.38/41.70    (16)  all_57_5 = e3
% 230.38/41.70    (17)  all_57_6 = e2
% 230.38/41.70    (18)  all_57_11 = e0
% 230.38/41.70    (19)   ~ (e2 = e0)
% 230.38/41.70    (20)   ~ (e1 = e0)
% 230.38/41.70    (21)  op(e1, e1) = e2
% 230.38/41.70    (22)  all_57_7 = e3
% 230.38/41.70    (23)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.38/41.70          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.38/41.70    (24)   ~ (e2 = e1)
% 230.38/41.70    (25)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.38/41.70          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.38/41.70    (26)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.38/41.70          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.38/41.70    (27)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.38/41.70          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.38/41.70    (28)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.38/41.70          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.38/41.70    (29)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.38/41.70          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.38/41.70    (30)  all_57_3 = e2
% 230.38/41.70    (31)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.38/41.70          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.38/41.70  
% 230.38/41.70  Begin of proof
% 230.38/41.70  | 
% 230.38/41.70  | BETA: splitting (8) gives:
% 230.38/41.70  | 
% 230.38/41.70  | Case 1:
% 230.38/41.70  | | 
% 230.38/41.70  | |   (32)  all_57_4 = e0 & op(e3, e1) = e0
% 230.38/41.70  | | 
% 230.38/41.70  | | ALPHA: (32) implies:
% 230.38/41.70  | |   (33)  all_57_4 = e0
% 230.38/41.70  | | 
% 230.38/41.70  | | COMBINE_EQS: (6), (33) imply:
% 230.38/41.70  | |   (34)  e2 = e0
% 230.38/41.70  | | 
% 230.38/41.70  | | COMBINE_EQS: (30), (34) imply:
% 230.38/41.70  | |   (35)  all_57_3 = e0
% 230.38/41.70  | | 
% 230.38/41.70  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (9), (10), (11), (12), (13), (14),
% 230.38/41.70  | |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 230.38/41.70  | |            (26), (27), (28), (29), (31), (35) are inconsistent by sub-proof
% 230.38/41.70  | |            #1462.
% 230.38/41.70  | | 
% 230.38/41.70  | Case 2:
% 230.38/41.70  | | 
% 230.38/41.70  | |   (36)  all_57_5 = e0 & op(e2, e1) = e0
% 230.38/41.70  | | 
% 230.38/41.70  | | REF_CLOSE: (12), (16), (36) are inconsistent by sub-proof #2414.
% 230.38/41.70  | | 
% 230.38/41.70  | End of split
% 230.38/41.70  | 
% 230.38/41.70  End of proof
% 230.38/41.70  
% 230.38/41.70  Sub-proof #1099 shows that the following formulas are inconsistent:
% 230.38/41.70  ----------------------------------------------------------------
% 230.38/41.70    (1)   ~ (e3 = e1)
% 230.38/41.70    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.38/41.70           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.38/41.70    (3)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.38/41.70         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.38/41.70    (4)   ~ (all_6_2 = e3)
% 230.38/41.70    (5)  op(e1, e1) = all_6_2
% 230.38/41.70    (6)   ~ (e3 = e2)
% 230.38/41.70    (7)   ~ (e3 = e0)
% 230.38/41.70    (8)  all_57_1 = e2
% 230.38/41.70    (9)  all_57_15 = e3
% 230.38/41.70    (10)  all_57_6 = e2
% 230.38/41.70    (11)   ~ (e2 = e0)
% 230.38/41.70    (12)  op(e2, e2) = e2
% 230.38/41.70    (13)   ~ (e1 = e0)
% 230.38/41.70    (14)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.38/41.70              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.38/41.70                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.38/41.70                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.38/41.70    (15)  all_57_13 = e0
% 230.38/41.70    (16)   ~ (e2 = e1)
% 230.38/41.70    (17)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.38/41.70          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.38/41.70    (18)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.38/41.70          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.38/41.70    (19)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.38/41.70          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.38/41.70  
% 230.38/41.70  Begin of proof
% 230.38/41.70  | 
% 230.38/41.70  | BETA: splitting (19) gives:
% 230.38/41.70  | 
% 230.38/41.70  | Case 1:
% 230.38/41.70  | | 
% 230.38/41.70  | |   (20)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) =
% 230.38/41.70  | |           e1)
% 230.38/41.70  | | 
% 230.38/41.70  | | REF_CLOSE: (2), (8), (12), (16), (20) are inconsistent by sub-proof #1133.
% 230.38/41.70  | | 
% 230.38/41.70  | Case 2:
% 230.38/41.70  | | 
% 230.38/41.70  | |   (21)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 230.38/41.70  | |           e1)
% 230.38/41.70  | | 
% 230.38/41.70  | | BETA: splitting (21) gives:
% 230.38/41.70  | | 
% 230.38/41.70  | | Case 1:
% 230.38/41.70  | | | 
% 230.38/41.70  | | |   (22)  all_57_7 = e1 & op(e1, e2) = e1
% 230.38/41.70  | | | 
% 230.38/41.70  | | | ALPHA: (22) implies:
% 230.38/41.70  | | |   (23)  all_57_7 = e1
% 230.38/41.70  | | | 
% 230.38/41.70  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (13), (14),
% 230.38/41.70  | | |            (16), (17), (18), (23) are inconsistent by sub-proof #1245.
% 230.38/41.70  | | | 
% 230.38/41.70  | | Case 2:
% 230.38/41.70  | | | 
% 230.38/41.70  | | |   (24)  all_57_13 = e1 & op(e0, e2) = e1
% 230.38/41.70  | | | 
% 230.38/41.70  | | | ALPHA: (24) implies:
% 230.38/41.70  | | |   (25)  all_57_13 = e1
% 230.38/41.70  | | | 
% 230.38/41.70  | | | REF_CLOSE: (13), (15), (25) are inconsistent by sub-proof #1760.
% 230.38/41.70  | | | 
% 230.38/41.70  | | End of split
% 230.38/41.70  | | 
% 230.38/41.70  | End of split
% 230.38/41.70  | 
% 230.38/41.70  End of proof
% 230.38/41.70  
% 230.38/41.70  Sub-proof #1100 shows that the following formulas are inconsistent:
% 230.38/41.70  ----------------------------------------------------------------
% 230.38/41.70    (1)  op(e1, e0) = e2
% 230.38/41.70    (2)   ~ (e3 = e1)
% 230.38/41.70    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.38/41.70           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.38/41.70    (4)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) = all_22_1
% 230.38/41.70           & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0, e3) =
% 230.38/41.70           all_22_1 & $i(all_22_1))
% 230.38/41.70    (5)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 230.38/41.70         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.38/41.70    (6)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) = all_12_1
% 230.38/41.70           & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0, e3) =
% 230.38/41.70           all_12_1 & $i(all_12_1))
% 230.38/41.70    (7)   ~ (e1 = e0)
% 230.38/41.70    (8)  all_57_14 = e2
% 230.38/41.70    (9)  op(e0, e0) = e3
% 230.38/41.70    (10)  all_57_13 = e0
% 230.38/41.70    (11)   ~ (e2 = e1)
% 230.38/41.70  
% 230.38/41.70  Begin of proof
% 230.38/41.70  | 
% 230.38/41.70  | BETA: splitting (5) gives:
% 230.38/41.70  | 
% 230.38/41.70  | Case 1:
% 230.38/41.70  | | 
% 230.38/41.70  | |   (12)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 230.38/41.70  | |           e1)
% 230.38/41.70  | | 
% 230.38/41.70  | | BETA: splitting (12) gives:
% 230.38/41.70  | | 
% 230.38/41.70  | | Case 1:
% 230.38/41.70  | | | 
% 230.38/41.70  | | |   (13)  all_57_12 = e1 & op(e0, e3) = e1
% 230.38/41.70  | | | 
% 230.38/41.70  | | | ALPHA: (13) implies:
% 230.38/41.70  | | |   (14)  op(e0, e3) = e1
% 230.38/41.70  | | | 
% 230.38/41.70  | | | REF_CLOSE: (1), (3), (4), (6), (14) are inconsistent by sub-proof #1147.
% 230.38/41.70  | | | 
% 230.38/41.70  | | Case 2:
% 230.38/41.70  | | | 
% 230.38/41.70  | | |   (15)  all_57_13 = e1 & op(e0, e2) = e1
% 230.38/41.70  | | | 
% 230.38/41.70  | | | REF_CLOSE: (7), (10), (15) are inconsistent by sub-proof #2320.
% 230.38/41.70  | | | 
% 230.38/41.70  | | End of split
% 230.38/41.70  | | 
% 230.38/41.70  | Case 2:
% 230.38/41.70  | | 
% 230.38/41.70  | |   (16)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.38/41.70  | |           e1)
% 230.38/41.70  | | 
% 230.38/41.70  | | REF_CLOSE: (2), (3), (8), (9), (11), (16) are inconsistent by sub-proof
% 230.38/41.70  | |            #1139.
% 230.38/41.70  | | 
% 230.38/41.70  | End of split
% 230.38/41.70  | 
% 230.38/41.70  End of proof
% 230.38/41.70  
% 230.38/41.70  Sub-proof #1101 shows that the following formulas are inconsistent:
% 230.38/41.70  ----------------------------------------------------------------
% 230.38/41.70    (1)  all_57_9 = e2
% 230.38/41.70    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.38/41.70         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.38/41.70    (3)   ~ (all_52_7 = e3)
% 230.38/41.70    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.38/41.70         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.38/41.70    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.38/41.70         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.38/41.70    (6)   ~ (e3 = e1)
% 230.38/41.70    (7)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.38/41.70         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.38/41.70    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.38/41.70           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.38/41.70    (9)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.38/41.70         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.38/41.70    (10)   ~ (all_6_2 = e3)
% 230.38/41.70    (11)  op(e1, e1) = all_6_2
% 230.38/41.70    (12)  op(all_52_7, all_52_7) = e0
% 230.38/41.70    (13)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.38/41.70          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.38/41.70    (14)  all_57_2 = e2
% 230.38/41.70    (15)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.38/41.70          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.38/41.70    (16)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.38/41.70          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.38/41.70    (17)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 230.38/41.70          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.38/41.70    (18)   ~ (e3 = e2)
% 230.38/41.70    (19)   ~ (e3 = e0)
% 230.38/41.70    (20)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.38/41.70          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.38/41.70    (21)  op(e3, e3) = e3
% 230.38/41.70    (22)  all_57_15 = e3
% 230.38/41.70    (23)  all_57_5 = e3
% 230.38/41.70    (24)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.38/41.70          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.38/41.70    (25)   ~ (e2 = e0)
% 230.38/41.70    (26)  op(e2, e2) = e2
% 230.38/41.70    (27)   ~ (e1 = e0)
% 230.38/41.70    (28)  all_57_14 = e2
% 230.38/41.70    (29)  op(e0, e0) = e3
% 230.38/41.70    (30)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.38/41.70          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.38/41.70            e2)
% 230.38/41.70    (31)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.38/41.70              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.38/41.70                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.38/41.70                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.38/41.70    (32)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.38/41.70          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.38/41.70    (33)  all_57_7 = e3
% 230.38/41.70    (34)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.38/41.70          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.38/41.70    (35)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.38/41.70          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 230.38/41.70    (36)   ~ (e2 = e1)
% 230.38/41.70    (37)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.38/41.70          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.38/41.70    (38)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.38/41.70          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.38/41.70    (39)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.38/41.70          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.38/41.70    (40)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.38/41.70          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.38/41.70    (41)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.38/41.70          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.38/41.70    (42)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.38/41.70          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.38/41.70    (43)  all_57_3 = e2
% 230.38/41.70    (44)  op(e3, e0) = all_52_7
% 230.38/41.70    (45)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.38/41.70          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.38/41.70    (46)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.38/41.70          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.38/41.70  
% 230.38/41.70  Begin of proof
% 230.38/41.70  | 
% 230.38/41.70  | BETA: splitting (17) gives:
% 230.38/41.70  | 
% 230.38/41.70  | Case 1:
% 230.38/41.70  | | 
% 230.38/41.70  | |   (47)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) =
% 230.38/41.70  | |           e0)
% 230.38/41.70  | | 
% 230.38/41.70  | | BETA: splitting (47) gives:
% 230.38/41.70  | | 
% 230.38/41.70  | | Case 1:
% 230.38/41.70  | | | 
% 230.38/41.70  | | |   (48)  all_57_4 = e0 & op(e3, e1) = e0
% 230.38/41.70  | | | 
% 230.38/41.70  | | | ALPHA: (48) implies:
% 230.38/41.70  | | |   (49)  all_57_4 = e0
% 230.38/41.70  | | | 
% 230.38/41.70  | | | BETA: splitting (2) gives:
% 230.38/41.70  | | | 
% 230.38/41.70  | | | Case 1:
% 230.38/41.70  | | | | 
% 230.38/41.71  | | | |   (50)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2)
% 230.38/41.71  | | | |           = e1)
% 230.38/41.71  | | | | 
% 230.38/41.71  | | | | REF_CLOSE: (8), (14), (26), (36), (50) are inconsistent by sub-proof
% 230.38/41.71  | | | |            #2243.
% 230.38/41.71  | | | | 
% 230.38/41.71  | | | Case 2:
% 230.38/41.71  | | | | 
% 230.38/41.71  | | | |   (51)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0)
% 230.38/41.71  | | | |           = e1)
% 230.38/41.71  | | | | 
% 230.38/41.71  | | | | BETA: splitting (51) gives:
% 230.38/41.71  | | | | 
% 230.38/41.71  | | | | Case 1:
% 230.38/41.71  | | | | | 
% 230.38/41.71  | | | | |   (52)  all_57_5 = e1 & op(e2, e1) = e1
% 230.38/41.71  | | | | | 
% 230.38/41.71  | | | | | REF_CLOSE: (6), (23), (52) are inconsistent by sub-proof #2376.
% 230.38/41.71  | | | | | 
% 230.38/41.71  | | | | Case 2:
% 230.38/41.71  | | | | | 
% 230.38/41.71  | | | | |   (53)  all_57_10 = e1 & op(e2, e0) = e1
% 230.38/41.71  | | | | | 
% 230.38/41.71  | | | | | ALPHA: (53) implies:
% 230.38/41.71  | | | | |   (54)  all_57_10 = e1
% 230.38/41.71  | | | | | 
% 230.38/41.71  | | | | | BETA: splitting (13) gives:
% 230.38/41.71  | | | | | 
% 230.38/41.71  | | | | | Case 1:
% 230.38/41.71  | | | | | | 
% 230.38/41.71  | | | | | |   (55)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3,
% 230.38/41.71  | | | | | |             e2) = e1)
% 230.38/41.71  | | | | | | 
% 230.38/41.71  | | | | | | BETA: splitting (55) gives:
% 230.38/41.71  | | | | | | 
% 230.38/41.71  | | | | | | Case 1:
% 230.38/41.71  | | | | | | | 
% 230.38/41.71  | | | | | | |   (56)  all_57_0 = e1 & op(e3, e3) = e1
% 230.38/41.71  | | | | | | | 
% 230.38/41.71  | | | | | | | ALPHA: (56) implies:
% 230.38/41.71  | | | | | | |   (57)  op(e3, e3) = e1
% 230.38/41.71  | | | | | | | 
% 230.38/41.71  | | | | | | | REF_CLOSE: (6), (8), (21), (57) are inconsistent by sub-proof
% 230.38/41.71  | | | | | | |            #2495.
% 230.38/41.71  | | | | | | | 
% 230.38/41.71  | | | | | | Case 2:
% 230.38/41.71  | | | | | | | 
% 230.38/41.71  | | | | | | |   (58)  all_57_1 = e1 & op(e3, e2) = e1
% 230.38/41.71  | | | | | | | 
% 230.38/41.71  | | | | | | | ALPHA: (58) implies:
% 230.38/41.71  | | | | | | |   (59)  all_57_1 = e1
% 230.38/41.71  | | | | | | | 
% 230.38/41.71  | | | | | | | BETA: splitting (24) gives:
% 230.38/41.71  | | | | | | | 
% 230.38/41.71  | | | | | | | Case 1:
% 230.38/41.71  | | | | | | | | 
% 230.38/41.71  | | | | | | | |   (60)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 &
% 230.38/41.71  | | | | | | | |           op(e2, e2) = e0)
% 230.38/41.71  | | | | | | | | 
% 230.38/41.71  | | | | | | | | BETA: splitting (60) gives:
% 230.38/41.71  | | | | | | | | 
% 230.38/41.71  | | | | | | | | Case 1:
% 230.38/41.71  | | | | | | | | | 
% 230.38/41.71  | | | | | | | | |   (61)  all_57_1 = e0 & op(e3, e2) = e0
% 230.38/41.71  | | | | | | | | | 
% 230.38/41.71  | | | | | | | | | ALPHA: (61) implies:
% 230.38/41.71  | | | | | | | | |   (62)  all_57_1 = e0
% 230.38/41.71  | | | | | | | | | 
% 230.38/41.71  | | | | | | | | | REF_CLOSE: (1), (6), (8), (13), (21), (27), (36), (49), (62)
% 230.38/41.71  | | | | | | | | |            are inconsistent by sub-proof #2219.
% 230.38/41.71  | | | | | | | | | 
% 230.38/41.71  | | | | | | | | Case 2:
% 230.38/41.71  | | | | | | | | | 
% 230.38/41.71  | | | | | | | | |   (63)  all_57_3 = e0 & op(e2, e2) = e0
% 230.38/41.71  | | | | | | | | | 
% 230.38/41.71  | | | | | | | | | ALPHA: (63) implies:
% 230.38/41.71  | | | | | | | | |   (64)  op(e2, e2) = e0
% 230.38/41.71  | | | | | | | | | 
% 230.38/41.71  | | | | | | | | | REF_CLOSE: (8), (25), (26), (64) are inconsistent by sub-proof
% 230.38/41.71  | | | | | | | | |            #2472.
% 230.38/41.71  | | | | | | | | | 
% 230.38/41.71  | | | | | | | | End of split
% 230.38/41.71  | | | | | | | | 
% 230.38/41.71  | | | | | | | Case 2:
% 230.38/41.71  | | | | | | | | 
% 230.38/41.71  | | | | | | | |   (65)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 &
% 230.38/41.71  | | | | | | | |           op(e0, e2) = e0)
% 230.38/41.71  | | | | | | | | 
% 230.38/41.71  | | | | | | | | BETA: splitting (65) gives:
% 230.38/41.71  | | | | | | | | 
% 230.38/41.71  | | | | | | | | Case 1:
% 230.38/41.71  | | | | | | | | | 
% 230.38/41.71  | | | | | | | | |   (66)  all_57_7 = e0 & op(e1, e2) = e0
% 230.38/41.71  | | | | | | | | | 
% 230.38/41.71  | | | | | | | | | ALPHA: (66) implies:
% 230.38/41.71  | | | | | | | | |   (67)  all_57_7 = e0
% 230.38/41.71  | | | | | | | | | 
% 230.38/41.71  | | | | | | | | | REF_CLOSE: (19), (33), (67) are inconsistent by sub-proof
% 230.38/41.71  | | | | | | | | |            #2269.
% 230.38/41.71  | | | | | | | | | 
% 230.38/41.71  | | | | | | | | Case 2:
% 230.38/41.71  | | | | | | | | | 
% 230.38/41.71  | | | | | | | | |   (68)  all_57_13 = e0 & op(e0, e2) = e0
% 230.38/41.71  | | | | | | | | | 
% 230.38/41.71  | | | | | | | | | ALPHA: (68) implies:
% 230.38/41.71  | | | | | | | | |   (69)  all_57_13 = e0
% 230.38/41.71  | | | | | | | | | 
% 230.38/41.71  | | | | | | | | | BETA: splitting (35) gives:
% 230.38/41.71  | | | | | | | | | 
% 230.38/41.71  | | | | | | | | | Case 1:
% 230.38/41.71  | | | | | | | | | | 
% 230.38/41.71  | | | | | | | | | |   (70)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 &
% 230.38/41.71  | | | | | | | | | |           op(e2, e2) = e0)
% 230.38/41.71  | | | | | | | | | | 
% 230.38/41.71  | | | | | | | | | | BETA: splitting (70) gives:
% 230.38/41.71  | | | | | | | | | | 
% 230.38/41.71  | | | | | | | | | | Case 1:
% 230.38/41.71  | | | | | | | | | | | 
% 230.38/41.71  | | | | | | | | | | |   (71)  all_57_2 = e0 & op(e2, e3) = e0
% 230.38/41.71  | | | | | | | | | | | 
% 230.38/41.71  | | | | | | | | | | | ALPHA: (71) implies:
% 230.38/41.71  | | | | | | | | | | |   (72)  all_57_2 = e0
% 230.38/41.71  | | | | | | | | | | | 
% 230.38/41.71  | | | | | | | | | | | COMBINE_EQS: (14), (72) imply:
% 230.38/41.71  | | | | | | | | | | |   (73)  e2 = e0
% 230.38/41.71  | | | | | | | | | | | 
% 230.38/41.71  | | | | | | | | | | | REF_CLOSE: (14), (18), (23), (25), (34), (36), (43), (54),
% 230.38/41.71  | | | | | | | | | | |            (73) are inconsistent by sub-proof #1482.
% 230.38/41.71  | | | | | | | | | | | 
% 230.38/41.71  | | | | | | | | | | Case 2:
% 230.38/41.71  | | | | | | | | | | | 
% 230.38/41.71  | | | | | | | | | | |   (74)  all_57_3 = e0 & op(e2, e2) = e0
% 230.38/41.71  | | | | | | | | | | | 
% 230.38/41.71  | | | | | | | | | | | ALPHA: (74) implies:
% 230.38/41.71  | | | | | | | | | | |   (75)  all_57_3 = e0
% 230.38/41.71  | | | | | | | | | | | 
% 230.38/41.71  | | | | | | | | | | | REF_CLOSE: (5), (6), (8), (13), (15), (16), (18), (19), (21),
% 230.38/41.71  | | | | | | | | | | |            (25), (27), (33), (36), (45), (69), (75) are
% 230.38/41.71  | | | | | | | | | | |            inconsistent by sub-proof #2091.
% 230.38/41.71  | | | | | | | | | | | 
% 230.38/41.71  | | | | | | | | | | End of split
% 230.38/41.71  | | | | | | | | | | 
% 230.38/41.71  | | | | | | | | | Case 2:
% 230.38/41.71  | | | | | | | | | | 
% 230.38/41.71  | | | | | | | | | |   (76)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0
% 230.38/41.71  | | | | | | | | | |           & op(e2, e0) = e0)
% 230.38/41.71  | | | | | | | | | | 
% 230.38/41.71  | | | | | | | | | | BETA: splitting (76) gives:
% 230.38/41.71  | | | | | | | | | | 
% 230.38/41.71  | | | | | | | | | | Case 1:
% 230.38/41.71  | | | | | | | | | | | 
% 230.38/41.71  | | | | | | | | | | |   (77)  all_57_5 = e0 & op(e2, e1) = e0
% 230.38/41.71  | | | | | | | | | | | 
% 230.38/41.71  | | | | | | | | | | | REF_CLOSE: (19), (23), (77) are inconsistent by sub-proof
% 230.38/41.71  | | | | | | | | | | |            #2414.
% 230.38/41.71  | | | | | | | | | | | 
% 230.38/41.71  | | | | | | | | | | Case 2:
% 230.38/41.71  | | | | | | | | | | | 
% 230.38/41.71  | | | | | | | | | | |   (78)  all_57_10 = e0 & op(e2, e0) = e0
% 230.38/41.71  | | | | | | | | | | | 
% 230.38/41.71  | | | | | | | | | | | ALPHA: (78) implies:
% 230.38/41.71  | | | | | | | | | | |   (79)  all_57_10 = e0
% 230.38/41.71  | | | | | | | | | | | 
% 230.38/41.71  | | | | | | | | | | | COMBINE_EQS: (54), (79) imply:
% 230.38/41.71  | | | | | | | | | | |   (80)  e1 = e0
% 230.38/41.71  | | | | | | | | | | | 
% 230.38/41.71  | | | | | | | | | | | COMBINE_EQS: (59), (80) imply:
% 230.38/41.71  | | | | | | | | | | |   (81)  all_57_1 = e0
% 230.38/41.71  | | | | | | | | | | | 
% 230.38/41.71  | | | | | | | | | | | REF_CLOSE: (1), (6), (8), (13), (21), (27), (36), (49), (81)
% 230.38/41.71  | | | | | | | | | | |            are inconsistent by sub-proof #2219.
% 230.38/41.71  | | | | | | | | | | | 
% 230.38/41.71  | | | | | | | | | | End of split
% 230.38/41.71  | | | | | | | | | | 
% 230.38/41.71  | | | | | | | | | End of split
% 230.38/41.71  | | | | | | | | | 
% 230.38/41.71  | | | | | | | | End of split
% 230.38/41.71  | | | | | | | | 
% 230.38/41.71  | | | | | | | End of split
% 230.38/41.71  | | | | | | | 
% 230.38/41.71  | | | | | | End of split
% 230.38/41.71  | | | | | | 
% 230.38/41.71  | | | | | Case 2:
% 230.38/41.71  | | | | | | 
% 230.38/41.71  | | | | | |   (82)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3,
% 230.38/41.71  | | | | | |             e0) = e1)
% 230.38/41.71  | | | | | | 
% 230.38/41.71  | | | | | | BETA: splitting (82) gives:
% 230.38/41.71  | | | | | | 
% 230.38/41.71  | | | | | | Case 1:
% 230.38/41.71  | | | | | | | 
% 230.38/41.71  | | | | | | |   (83)  all_57_4 = e1 & op(e3, e1) = e1
% 230.38/41.71  | | | | | | | 
% 230.38/41.71  | | | | | | | ALPHA: (83) implies:
% 230.38/41.71  | | | | | | |   (84)  all_57_4 = e1
% 230.38/41.71  | | | | | | | 
% 230.38/41.71  | | | | | | | REF_CLOSE: (27), (49), (84) are inconsistent by sub-proof #2438.
% 230.38/41.71  | | | | | | | 
% 230.38/41.71  | | | | | | Case 2:
% 230.38/41.71  | | | | | | | 
% 230.38/41.71  | | | | | | |   (85)  all_57_9 = e1 & op(e3, e0) = e1
% 230.38/41.71  | | | | | | | 
% 230.38/41.71  | | | | | | | ALPHA: (85) implies:
% 230.38/41.71  | | | | | | |   (86)  all_57_9 = e1
% 230.38/41.71  | | | | | | | 
% 230.38/41.71  | | | | | | | REF_CLOSE: (1), (36), (86) are inconsistent by sub-proof #2444.
% 230.38/41.71  | | | | | | | 
% 230.38/41.71  | | | | | | End of split
% 230.38/41.71  | | | | | | 
% 230.38/41.71  | | | | | End of split
% 230.38/41.71  | | | | | 
% 230.38/41.71  | | | | End of split
% 230.38/41.71  | | | | 
% 230.38/41.71  | | | End of split
% 230.38/41.71  | | | 
% 230.38/41.71  | | Case 2:
% 230.38/41.71  | | | 
% 230.38/41.71  | | |   (87)  all_57_5 = e0 & op(e2, e1) = e0
% 230.38/41.71  | | | 
% 230.38/41.71  | | | REF_CLOSE: (19), (23), (87) are inconsistent by sub-proof #2414.
% 230.38/41.71  | | | 
% 230.38/41.71  | | End of split
% 230.38/41.71  | | 
% 230.38/41.71  | Case 2:
% 230.38/41.71  | | 
% 230.38/41.71  | |   (88)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 230.38/41.71  | |           e0)
% 230.38/41.71  | | 
% 230.38/41.71  | | BETA: splitting (88) gives:
% 230.38/41.71  | | 
% 230.38/41.71  | | Case 1:
% 230.38/41.71  | | | 
% 230.38/41.71  | | |   (89)  all_57_8 = e0 & op(e1, e1) = e0
% 230.38/41.71  | | | 
% 230.38/41.71  | | | ALPHA: (89) implies:
% 230.38/41.71  | | |   (90)  op(e1, e1) = e0
% 230.38/41.71  | | | 
% 230.38/41.71  | | | BETA: splitting (2) gives:
% 230.38/41.71  | | | 
% 230.38/41.71  | | | Case 1:
% 230.38/41.71  | | | | 
% 230.38/41.71  | | | |   (91)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2)
% 230.38/41.71  | | | |           = e1)
% 230.38/41.71  | | | | 
% 230.38/41.71  | | | | REF_CLOSE: (8), (14), (26), (36), (91) are inconsistent by sub-proof
% 230.38/41.71  | | | |            #2243.
% 230.38/41.71  | | | | 
% 230.38/41.71  | | | Case 2:
% 230.38/41.71  | | | | 
% 230.38/41.71  | | | |   (92)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0)
% 230.38/41.71  | | | |           = e1)
% 230.38/41.71  | | | | 
% 230.38/41.71  | | | | BETA: splitting (92) gives:
% 230.38/41.71  | | | | 
% 230.38/41.71  | | | | Case 1:
% 230.38/41.71  | | | | | 
% 230.38/41.71  | | | | |   (93)  all_57_5 = e1 & op(e2, e1) = e1
% 230.38/41.71  | | | | | 
% 230.38/41.71  | | | | | REF_CLOSE: (6), (23), (93) are inconsistent by sub-proof #2376.
% 230.38/41.71  | | | | | 
% 230.38/41.71  | | | | Case 2:
% 230.38/41.71  | | | | | 
% 230.38/41.71  | | | | |   (94)  all_57_10 = e1 & op(e2, e0) = e1
% 230.38/41.71  | | | | | 
% 230.38/41.71  | | | | | ALPHA: (94) implies:
% 230.38/41.71  | | | | |   (95)  all_57_10 = e1
% 230.38/41.71  | | | | | 
% 230.38/41.71  | | | | | BETA: splitting (31) gives:
% 230.38/41.71  | | | | | 
% 230.38/41.71  | | | | | Case 1:
% 230.38/41.71  | | | | | | 
% 230.38/41.71  | | | | | |   (96)  all_57_15 = e0 & op(e0, e0) = e0
% 230.38/41.71  | | | | | | 
% 230.38/41.71  | | | | | | ALPHA: (96) implies:
% 230.38/41.71  | | | | | |   (97)  op(e0, e0) = e0
% 230.38/41.71  | | | | | | 
% 230.38/41.71  | | | | | | REF_CLOSE: (8), (19), (29), (97) are inconsistent by sub-proof
% 230.38/41.71  | | | | | |            #2304.
% 230.38/41.71  | | | | | | 
% 230.38/41.71  | | | | | Case 2:
% 230.38/41.71  | | | | | | 
% 230.38/41.71  | | | | | |   (98)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 &
% 230.38/41.71  | | | | | |             op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) &
% 230.38/41.71  | | | | | |         ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.38/41.71  | | | | | |             op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 230.38/41.71  | | | | | | 
% 230.38/41.71  | | | | | | ALPHA: (98) implies:
% 230.38/41.71  | | | | | |   (99)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.38/41.71  | | | | | |           op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.38/41.71  | | | | | |   (100)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 &
% 230.38/41.71  | | | | | |            op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.38/41.71  | | | | | | 
% 230.38/41.71  | | | | | | BETA: splitting (100) gives:
% 230.38/41.71  | | | | | | 
% 230.38/41.71  | | | | | | Case 1:
% 230.38/41.71  | | | | | | | 
% 230.38/41.71  | | | | | | |   (101)  all_57_9 = e0 & op(e3, e0) = e0
% 230.38/41.71  | | | | | | | 
% 230.38/41.71  | | | | | | | ALPHA: (101) implies:
% 230.38/41.71  | | | | | | |   (102)  all_57_9 = e0
% 230.38/41.71  | | | | | | | 
% 230.38/41.71  | | | | | | | COMBINE_EQS: (1), (102) imply:
% 230.38/41.71  | | | | | | |   (103)  e2 = e0
% 230.38/41.71  | | | | | | | 
% 230.38/41.71  | | | | | | | SIMP: (103) implies:
% 230.38/41.71  | | | | | | |   (104)  e2 = e0
% 230.38/41.71  | | | | | | | 
% 230.38/41.71  | | | | | | | COMBINE_EQS: (43), (104) imply:
% 230.38/41.71  | | | | | | |   (105)  all_57_3 = e0
% 230.38/41.71  | | | | | | | 
% 230.38/41.71  | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (12), (13), (15),
% 230.38/41.71  | | | | | | |            (16), (17), (18), (19), (20), (21), (22), (23), (25),
% 230.38/41.71  | | | | | | |            (27), (29), (30), (33), (34), (36), (37), (38), (39),
% 230.38/41.71  | | | | | | |            (40), (41), (42), (44), (45), (46), (90), (99), (100),
% 230.38/41.71  | | | | | | |            (105) are inconsistent by sub-proof #1487.
% 230.38/41.71  | | | | | | | 
% 230.38/41.71  | | | | | | Case 2:
% 230.38/41.71  | | | | | | | 
% 230.38/41.71  | | | | | | |   (106)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 230.38/41.71  | | | | | | |            op(e1, e0) = e0)
% 230.38/41.71  | | | | | | | 
% 230.38/41.71  | | | | | | | BETA: splitting (106) gives:
% 230.38/41.71  | | | | | | | 
% 230.38/41.71  | | | | | | | Case 1:
% 230.38/41.71  | | | | | | | | 
% 230.38/41.71  | | | | | | | |   (107)  all_57_10 = e0 & op(e2, e0) = e0
% 230.38/41.71  | | | | | | | | 
% 230.38/41.71  | | | | | | | | REF_CLOSE: (27), (95), (107) are inconsistent by sub-proof
% 230.38/41.71  | | | | | | | |            #1332.
% 230.38/41.71  | | | | | | | | 
% 230.38/41.71  | | | | | | | Case 2:
% 230.38/41.71  | | | | | | | | 
% 230.38/41.71  | | | | | | | |   (108)  all_57_11 = e0 & op(e1, e0) = e0
% 230.38/41.71  | | | | | | | | 
% 230.38/41.71  | | | | | | | | ALPHA: (108) implies:
% 230.38/41.71  | | | | | | | |   (109)  all_57_11 = e0
% 230.38/41.71  | | | | | | | | 
% 230.38/41.71  | | | | | | | | BETA: splitting (42) gives:
% 230.38/41.71  | | | | | | | | 
% 230.38/41.71  | | | | | | | | Case 1:
% 230.38/41.71  | | | | | | | | | 
% 230.38/41.71  | | | | | | | | |   (110)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 &
% 230.38/41.71  | | | | | | | | |            op(e1, e2) = e1)
% 230.38/41.71  | | | | | | | | | 
% 230.38/41.71  | | | | | | | | | BETA: splitting (110) gives:
% 230.38/41.71  | | | | | | | | | 
% 230.38/41.71  | | | | | | | | | Case 1:
% 230.38/41.71  | | | | | | | | | | 
% 230.38/41.71  | | | | | | | | | |   (111)  all_57_6 = e1 & op(e1, e3) = e1
% 230.38/41.71  | | | | | | | | | | 
% 230.38/41.71  | | | | | | | | | | ALPHA: (111) implies:
% 230.38/41.71  | | | | | | | | | |   (112)  all_57_6 = e1
% 230.38/41.71  | | | | | | | | | | 
% 230.38/41.71  | | | | | | | | | | REF_CLOSE: (2), (6), (8), (9), (10), (11), (14), (18), (19),
% 230.38/41.71  | | | | | | | | | |            (22), (23), (25), (27), (31), (32), (33), (34),
% 230.38/41.71  | | | | | | | | | |            (35), (36), (37), (41), (43), (95), (112) are
% 230.38/41.71  | | | | | | | | | |            inconsistent by sub-proof #1106.
% 230.38/41.71  | | | | | | | | | | 
% 230.38/41.71  | | | | | | | | | Case 2:
% 230.38/41.71  | | | | | | | | | | 
% 230.38/41.71  | | | | | | | | | |   (113)  all_57_7 = e1 & op(e1, e2) = e1
% 230.38/41.71  | | | | | | | | | | 
% 230.38/41.71  | | | | | | | | | | REF_CLOSE: (6), (33), (113) are inconsistent by sub-proof
% 230.38/41.71  | | | | | | | | | |            #2104.
% 230.38/41.71  | | | | | | | | | | 
% 230.38/41.71  | | | | | | | | | End of split
% 230.38/41.71  | | | | | | | | | 
% 230.38/41.71  | | | | | | | | Case 2:
% 230.38/41.71  | | | | | | | | | 
% 230.38/41.71  | | | | | | | | |   (114)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 &
% 230.38/41.71  | | | | | | | | |            op(e1, e0) = e1)
% 230.38/41.71  | | | | | | | | | 
% 230.38/41.71  | | | | | | | | | REF_CLOSE: (1), (6), (8), (27), (29), (36), (41), (90), (95),
% 230.38/41.71  | | | | | | | | |            (109), (114) are inconsistent by sub-proof #1102.
% 230.38/41.71  | | | | | | | | | 
% 230.38/41.71  | | | | | | | | End of split
% 230.38/41.71  | | | | | | | | 
% 230.38/41.71  | | | | | | | End of split
% 230.38/41.71  | | | | | | | 
% 230.38/41.71  | | | | | | End of split
% 230.38/41.71  | | | | | | 
% 230.38/41.71  | | | | | End of split
% 230.38/41.71  | | | | | 
% 230.38/41.71  | | | | End of split
% 230.38/41.71  | | | | 
% 230.38/41.71  | | | End of split
% 230.38/41.71  | | | 
% 230.38/41.71  | | Case 2:
% 230.38/41.71  | | | 
% 230.38/41.71  | | |   (115)  all_57_14 = e0 & op(e0, e1) = e0
% 230.38/41.71  | | | 
% 230.38/41.71  | | | ALPHA: (115) implies:
% 230.38/41.71  | | |   (116)  all_57_14 = e0
% 230.38/41.71  | | | 
% 230.38/41.71  | | | COMBINE_EQS: (28), (116) imply:
% 230.38/41.71  | | |   (117)  e2 = e0
% 230.38/41.71  | | | 
% 230.38/41.71  | | | SIMP: (117) implies:
% 230.38/41.71  | | |   (118)  e2 = e0
% 230.38/41.71  | | | 
% 230.38/41.71  | | | REF_CLOSE: (2), (6), (14), (18), (19), (25), (27), (32), (34), (36), (43),
% 230.38/41.71  | | |            (118) are inconsistent by sub-proof #2245.
% 230.38/41.71  | | | 
% 230.38/41.71  | | End of split
% 230.38/41.71  | | 
% 230.38/41.71  | End of split
% 230.38/41.71  | 
% 230.38/41.71  End of proof
% 230.38/41.71  
% 230.38/41.71  Sub-proof #1102 shows that the following formulas are inconsistent:
% 230.38/41.71  ----------------------------------------------------------------
% 230.38/41.71    (1)  all_57_9 = e2
% 230.38/41.71    (2)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.38/41.71    (3)   ~ (e3 = e1)
% 230.38/41.71    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.38/41.71           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.38/41.71    (5)  all_57_10 = e1
% 230.38/41.71    (6)  all_57_11 = e0
% 230.38/41.71    (7)   ~ (e1 = e0)
% 230.38/41.71    (8)  op(e0, e0) = e3
% 230.38/41.71    (9)  op(e1, e1) = e0
% 230.38/41.71    (10)   ~ (e2 = e1)
% 230.38/41.71    (11)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.38/41.71          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.38/41.71  
% 230.38/41.71  Begin of proof
% 230.38/41.71  | 
% 230.38/41.71  | BETA: splitting (2) gives:
% 230.38/41.71  | 
% 230.38/41.71  | Case 1:
% 230.38/41.71  | | 
% 230.38/41.71  | |   (12)  all_57_8 = e1 & op(e1, e1) = e1
% 230.38/41.71  | | 
% 230.38/41.71  | | ALPHA: (12) implies:
% 230.38/41.71  | |   (13)  op(e1, e1) = e1
% 230.38/41.71  | | 
% 230.38/41.71  | | REF_CLOSE: (4), (7), (9), (13) are inconsistent by sub-proof #2427.
% 230.38/41.71  | | 
% 230.38/41.71  | Case 2:
% 230.38/41.71  | | 
% 230.38/41.71  | |   (14)  all_57_11 = e1 & op(e1, e0) = e1
% 230.38/41.71  | | 
% 230.38/41.71  | | ALPHA: (14) implies:
% 230.38/41.71  | |   (15)  all_57_11 = e1
% 230.38/41.71  | | 
% 230.38/41.71  | | COMBINE_EQS: (6), (15) imply:
% 230.38/41.71  | |   (16)  e1 = e0
% 230.38/41.71  | | 
% 230.38/41.71  | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (10), (11), (16) are
% 230.38/41.71  | |            inconsistent by sub-proof #1103.
% 230.38/41.71  | | 
% 230.38/41.71  | End of split
% 230.38/41.71  | 
% 230.38/41.71  End of proof
% 230.38/41.71  
% 230.38/41.71  Sub-proof #1103 shows that the following formulas are inconsistent:
% 230.38/41.71  ----------------------------------------------------------------
% 230.38/41.71    (1)  e1 = e0
% 230.38/41.71    (2)  all_57_9 = e2
% 230.38/41.71    (3)   ~ (e3 = e1)
% 230.38/41.71    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.38/41.71           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.38/41.71    (5)  all_57_10 = e1
% 230.38/41.71    (6)  all_57_11 = e0
% 230.38/41.71    (7)   ~ (e1 = e0)
% 230.38/41.71    (8)  op(e0, e0) = e3
% 230.38/41.71    (9)   ~ (e2 = e1)
% 230.38/41.71    (10)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.38/41.71          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.38/41.71  
% 230.38/41.71  Begin of proof
% 230.38/41.71  | 
% 230.38/41.71  | SIMP: (1) implies:
% 230.38/41.71  |   (11)  e1 = e0
% 230.38/41.71  | 
% 230.38/41.71  | COMBINE_EQS: (5), (11) imply:
% 230.38/41.71  |   (12)  all_57_10 = e0
% 230.38/41.71  | 
% 230.38/41.71  | REF_CLOSE: (2), (3), (4), (6), (7), (8), (9), (10), (12) are inconsistent by
% 230.38/41.71  |            sub-proof #1104.
% 230.38/41.71  | 
% 230.38/41.71  End of proof
% 230.38/41.71  
% 230.38/41.71  Sub-proof #1104 shows that the following formulas are inconsistent:
% 230.38/41.71  ----------------------------------------------------------------
% 230.38/41.71    (1)  all_57_9 = e2
% 230.38/41.71    (2)  all_57_10 = e0
% 230.38/41.71    (3)   ~ (e3 = e1)
% 230.38/41.71    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.38/41.71           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.38/41.71    (5)  all_57_11 = e0
% 230.38/41.71    (6)   ~ (e1 = e0)
% 230.38/41.71    (7)  op(e0, e0) = e3
% 230.38/41.71    (8)   ~ (e2 = e1)
% 230.38/41.71    (9)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.38/41.71         (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.38/41.71  
% 230.38/41.71  Begin of proof
% 230.38/41.71  | 
% 230.38/41.71  | BETA: splitting (9) gives:
% 230.38/41.71  | 
% 230.38/41.71  | Case 1:
% 230.38/41.71  | | 
% 230.38/41.71  | |   (10)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) =
% 230.38/41.71  | |           e1)
% 230.38/41.71  | | 
% 230.38/41.71  | | BETA: splitting (10) gives:
% 230.38/41.71  | | 
% 230.38/41.71  | | Case 1:
% 230.38/41.71  | | | 
% 230.38/41.71  | | |   (11)  all_57_9 = e1 & op(e3, e0) = e1
% 230.38/41.71  | | | 
% 230.38/41.71  | | | REF_CLOSE: (1), (8), (11) are inconsistent by sub-proof #2451.
% 230.38/41.71  | | | 
% 230.38/41.71  | | Case 2:
% 230.38/41.71  | | | 
% 230.38/41.71  | | |   (12)  all_57_10 = e1 & op(e2, e0) = e1
% 230.38/41.71  | | | 
% 230.38/41.71  | | | ALPHA: (12) implies:
% 230.38/41.71  | | |   (13)  all_57_10 = e1
% 230.38/41.71  | | | 
% 230.38/41.71  | | | REF_CLOSE: (2), (6), (13) are inconsistent by sub-proof #1531.
% 230.38/41.71  | | | 
% 230.38/41.71  | | End of split
% 230.38/41.71  | | 
% 230.38/41.71  | Case 2:
% 230.38/41.71  | | 
% 230.38/41.71  | |   (14)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.38/41.71  | |           e1)
% 230.38/41.71  | | 
% 230.38/41.71  | | REF_CLOSE: (3), (4), (5), (6), (7), (14) are inconsistent by sub-proof
% 230.38/41.71  | |            #1105.
% 230.38/41.71  | | 
% 230.38/41.71  | End of split
% 230.38/41.71  | 
% 230.38/41.71  End of proof
% 230.38/41.71  
% 230.38/41.71  Sub-proof #1105 shows that the following formulas are inconsistent:
% 230.38/41.71  ----------------------------------------------------------------
% 230.38/41.71    (1)   ~ (e3 = e1)
% 230.38/41.71    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.38/41.71           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.38/41.71    (3)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.38/41.71    (4)  all_57_11 = e0
% 230.38/41.71    (5)   ~ (e1 = e0)
% 230.38/41.71    (6)  op(e0, e0) = e3
% 230.38/41.71  
% 230.38/41.71  Begin of proof
% 230.38/41.71  | 
% 230.38/41.71  | BETA: splitting (3) gives:
% 230.38/41.71  | 
% 230.38/41.71  | Case 1:
% 230.38/41.71  | | 
% 230.38/41.71  | |   (7)  all_57_11 = e1 & op(e1, e0) = e1
% 230.38/41.71  | | 
% 230.38/41.71  | | ALPHA: (7) implies:
% 230.38/41.71  | |   (8)  all_57_11 = e1
% 230.38/41.71  | | 
% 230.38/41.71  | | REF_CLOSE: (4), (5), (8) are inconsistent by sub-proof #1862.
% 230.38/41.71  | | 
% 230.38/41.71  | Case 2:
% 230.38/41.71  | | 
% 230.38/41.71  | |   (9)  all_57_15 = e1 & op(e0, e0) = e1
% 230.38/41.71  | | 
% 230.38/41.71  | | ALPHA: (9) implies:
% 230.38/41.71  | |   (10)  op(e0, e0) = e1
% 230.38/41.71  | | 
% 230.38/41.71  | | REF_CLOSE: (1), (2), (6), (10) are inconsistent by sub-proof #2183.
% 230.38/41.71  | | 
% 230.38/41.71  | End of split
% 230.38/41.71  | 
% 230.38/41.71  End of proof
% 230.38/41.71  
% 230.38/41.71  Sub-proof #1106 shows that the following formulas are inconsistent:
% 230.38/41.71  ----------------------------------------------------------------
% 230.38/41.71    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.38/41.71         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.38/41.71    (2)   ~ (e3 = e1)
% 230.38/41.71    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.38/41.71           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.38/41.71    (4)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.38/41.71         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.38/41.71    (5)   ~ (all_6_2 = e3)
% 230.38/41.71    (6)  all_57_10 = e1
% 230.38/41.71    (7)  op(e1, e1) = all_6_2
% 230.38/41.71    (8)  all_57_2 = e2
% 230.38/41.71    (9)  all_57_6 = e1
% 230.38/41.71    (10)   ~ (e3 = e2)
% 230.38/41.71    (11)   ~ (e3 = e0)
% 230.38/41.71    (12)  all_57_15 = e3
% 230.38/41.71    (13)  all_57_5 = e3
% 230.38/41.71    (14)   ~ (e2 = e0)
% 230.38/41.71    (15)   ~ (e1 = e0)
% 230.38/41.71    (16)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.38/41.71              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.38/41.71                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.38/41.71                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.38/41.71    (17)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.38/41.71          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.38/41.71    (18)  all_57_7 = e3
% 230.38/41.71    (19)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.38/41.71          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.38/41.71    (20)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.38/41.71          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 230.38/41.71    (21)   ~ (e2 = e1)
% 230.38/41.71    (22)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.38/41.71          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.38/41.71    (23)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.38/41.71          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.38/41.71    (24)  all_57_3 = e2
% 230.38/41.71  
% 230.38/41.71  Begin of proof
% 230.38/41.71  | 
% 230.38/41.71  | BETA: splitting (20) gives:
% 230.38/41.71  | 
% 230.38/41.71  | Case 1:
% 230.38/41.71  | | 
% 230.38/41.71  | |   (25)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) =
% 230.38/41.71  | |           e0)
% 230.38/41.71  | | 
% 230.38/41.71  | | BETA: splitting (25) gives:
% 230.38/41.71  | | 
% 230.38/41.71  | | Case 1:
% 230.38/41.71  | | | 
% 230.38/41.71  | | |   (26)  all_57_2 = e0 & op(e2, e3) = e0
% 230.38/41.71  | | | 
% 230.38/41.71  | | | ALPHA: (26) implies:
% 230.38/41.71  | | |   (27)  all_57_2 = e0
% 230.38/41.71  | | | 
% 230.38/41.71  | | | COMBINE_EQS: (8), (27) imply:
% 230.38/41.71  | | |   (28)  e2 = e0
% 230.38/41.71  | | | 
% 230.38/41.71  | | | REF_CLOSE: (1), (2), (8), (10), (11), (14), (15), (17), (19), (21), (24),
% 230.38/41.71  | | |            (28) are inconsistent by sub-proof #2245.
% 230.38/41.71  | | | 
% 230.38/41.71  | | Case 2:
% 230.38/41.71  | | | 
% 230.38/41.71  | | |   (29)  all_57_3 = e0 & op(e2, e2) = e0
% 230.38/41.71  | | | 
% 230.38/41.71  | | | ALPHA: (29) implies:
% 230.38/41.71  | | |   (30)  all_57_3 = e0
% 230.38/41.71  | | | 
% 230.38/41.71  | | | COMBINE_EQS: (24), (30) imply:
% 230.38/41.71  | | |   (31)  e2 = e0
% 230.38/41.71  | | | 
% 230.38/41.71  | | | REF_CLOSE: (6), (8), (10), (13), (14), (19), (21), (30), (31) are
% 230.38/41.71  | | |            inconsistent by sub-proof #1532.
% 230.38/41.71  | | | 
% 230.38/41.71  | | End of split
% 230.38/41.71  | | 
% 230.38/41.71  | Case 2:
% 230.38/41.71  | | 
% 230.38/41.71  | |   (32)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 230.38/41.71  | |           e0)
% 230.38/41.71  | | 
% 230.38/41.71  | | BETA: splitting (32) gives:
% 230.38/41.71  | | 
% 230.38/41.71  | | Case 1:
% 230.38/41.71  | | | 
% 230.38/41.71  | | |   (33)  all_57_5 = e0 & op(e2, e1) = e0
% 230.38/41.71  | | | 
% 230.38/41.71  | | | ALPHA: (33) implies:
% 230.38/41.71  | | |   (34)  all_57_5 = e0
% 230.38/41.71  | | | 
% 230.38/41.71  | | | COMBINE_EQS: (13), (34) imply:
% 230.38/41.71  | | |   (35)  e3 = e0
% 230.38/41.71  | | | 
% 230.38/41.71  | | | COMBINE_EQS: (18), (35) imply:
% 230.38/41.71  | | |   (36)  all_57_7 = e0
% 230.38/41.71  | | | 
% 230.38/41.71  | | | REF_CLOSE: (2), (3), (4), (5), (7), (9), (10), (11), (12), (14), (15),
% 230.38/41.71  | | |            (16), (21), (22), (23), (36) are inconsistent by sub-proof
% 230.38/41.71  | | |            #1735.
% 230.38/41.71  | | | 
% 230.38/41.71  | | Case 2:
% 230.38/41.71  | | | 
% 230.38/41.71  | | |   (37)  all_57_10 = e0 & op(e2, e0) = e0
% 230.38/41.71  | | | 
% 230.38/41.71  | | | ALPHA: (37) implies:
% 230.38/41.71  | | |   (38)  all_57_10 = e0
% 230.38/41.71  | | | 
% 230.38/41.71  | | | REF_CLOSE: (6), (15), (38) are inconsistent by sub-proof #1531.
% 230.38/41.71  | | | 
% 230.38/41.71  | | End of split
% 230.38/41.71  | | 
% 230.38/41.71  | End of split
% 230.38/41.71  | 
% 230.38/41.71  End of proof
% 230.38/41.71  
% 230.38/41.71  Sub-proof #1107 shows that the following formulas are inconsistent:
% 230.38/41.71  ----------------------------------------------------------------
% 230.38/41.71    (1)  op(e0, e1) = all_53_11
% 230.38/41.71    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 230.38/41.71    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.38/41.71         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.38/41.71    (4)  op(e1, e0) = e2
% 230.38/41.71    (5)  op(e3, e1) = all_52_5
% 230.38/41.71    (6)   ~ (all_52_7 = e3)
% 230.38/41.71    (7)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.38/41.71         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.38/41.71    (8)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.38/41.71         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.38/41.71    (9)   ~ (e3 = e1)
% 230.38/41.71    (10)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.38/41.71          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.38/41.71    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.38/41.71            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.38/41.71    (12)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.38/41.71          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.38/41.71    (13)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 230.38/41.71            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 230.38/41.71              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 230.38/41.71    (14)   ~ (all_6_2 = e3)
% 230.38/41.71    (15)  op(e1, e1) = all_6_2
% 230.38/41.71    (16)  op(all_52_7, all_52_7) = e0
% 230.38/41.71    (17)  op(e3, e2) = all_52_3
% 230.38/41.71    (18)  all_34_2 = all_6_2
% 230.38/41.71    (19)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.38/41.71          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.38/41.71    (20)   ~ (all_52_5 = all_52_7)
% 230.38/41.71    (21)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 230.38/41.71            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 230.38/41.71              e3) = all_22_1 & $i(all_22_1))
% 230.38/41.71    (22)   ~ (all_53_13 = e2)
% 230.38/41.71    (23)   ~ (all_53_7 = e2)
% 230.38/41.71    (24)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.38/41.71          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.38/41.71    (25)   ~ (all_53_9 = all_53_11)
% 230.38/41.71    (26)   ~ (all_53_9 = all_6_2)
% 230.38/41.71    (27)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.38/41.71          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.38/41.71    (28)   ~ (all_53_14 = all_6_2)
% 230.38/41.71    (29)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 230.38/41.72          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.38/41.72    (30)   ~ (e3 = e2)
% 230.38/41.72    (31)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 230.38/41.72    (32)  op(e1, e0) = all_53_14
% 230.38/41.72    (33)   ~ (e3 = e0)
% 230.38/41.72    (34)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.38/41.72          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.38/41.72    (35)  op(e3, e3) = e3
% 230.38/41.72    (36)  all_57_15 = e3
% 230.38/41.72    (37)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.38/41.72          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.38/41.72            e1)
% 230.38/41.72    (38)  all_57_5 = e3
% 230.38/41.72    (39)  op(e3, e3) = all_52_1
% 230.38/41.72    (40)  all_57_11 = e2
% 230.38/41.72    (41)   ~ (all_53_14 = e3)
% 230.38/41.72    (42)  all_55_6 = all_53_9
% 230.38/41.72    (43)  op(e1, e1) = e1
% 230.38/41.72    (44)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.38/41.72          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.38/41.72    (45)  op(all_52_1, all_52_1) = e3
% 230.38/41.72    (46)   ~ (e2 = e0)
% 230.38/41.72    (47)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 230.38/41.72            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 230.38/41.72            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 230.38/41.72            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 230.38/41.72              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 230.38/41.72            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 230.38/41.72            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 230.38/41.72              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 230.38/41.72              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 230.38/41.72            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 230.38/41.72            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 230.38/41.72            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 230.38/41.72              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 230.38/41.72              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 230.38/41.72            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 230.38/41.72              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 230.38/41.72            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 230.38/41.72            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 230.38/41.72              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 230.38/41.72              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 230.38/41.72            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 230.38/41.72            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 230.38/41.72    (48)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 230.38/41.72            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 230.38/41.72              e3) = all_12_1 & $i(all_12_1))
% 230.38/41.72    (49)  op(e2, e2) = e2
% 230.38/41.72    (50)   ~ (e1 = e0)
% 230.38/41.72    (51)   ~ (all_52_3 = all_52_7)
% 230.38/41.72    (52)  op(e0, e0) = e3
% 230.38/41.72    (53)  op(e0, e2) = all_53_7
% 230.38/41.72    (54)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.38/41.72          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.38/41.72            e2)
% 230.38/41.72    (55)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.38/41.72              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.38/41.72                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.38/41.72                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.38/41.72    (56)  all_55_10 = all_6_2
% 230.38/41.72    (57)  op(e2, e0) = all_53_13
% 230.38/41.72    (58)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.38/41.72          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.38/41.72    (59)  all_57_7 = e3
% 230.38/41.72    (60)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.38/41.72          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.38/41.72    (61)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.38/41.72          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.38/41.72    (62)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.38/41.72          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 230.38/41.72    (63)   ~ (e2 = e1)
% 230.38/41.72    (64)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.38/41.72          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.38/41.72    (65)  op(e2, e1) = all_53_9
% 230.38/41.72    (66)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.38/41.72          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.38/41.72    (67)  all_24_2 = all_6_2
% 230.38/41.72    (68)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.38/41.72          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.38/41.72    (69)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.38/41.72          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.38/41.72    (70)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.38/41.72          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.38/41.72    (71)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.38/41.72          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.38/41.72    (72)  all_57_3 = e2
% 230.38/41.72    (73)  op(e3, e0) = all_52_7
% 230.38/41.72    (74)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.38/41.72          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.38/41.72    (75)   ~ (all_34_2 = e0) | ( ~ (all_34_0 = e3) & op(all_34_1, e1) = all_34_0 &
% 230.38/41.72            op(e1, e0) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 230.38/41.72              e2) & op(e1, e0) = all_34_1 & $i(all_34_1))
% 230.38/41.72    (76)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.38/41.72          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.38/41.72  
% 230.38/41.72  Begin of proof
% 230.38/41.72  | 
% 230.38/41.72  | BETA: splitting (10) gives:
% 230.38/41.72  | 
% 230.38/41.72  | Case 1:
% 230.38/41.72  | | 
% 230.38/41.72  | |   (77)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) =
% 230.38/41.72  | |           e0)
% 230.38/41.72  | | 
% 230.38/41.72  | | BETA: splitting (77) gives:
% 230.38/41.72  | | 
% 230.38/41.72  | | Case 1:
% 230.38/41.72  | | | 
% 230.38/41.72  | | |   (78)  all_57_6 = e0 & op(e1, e3) = e0
% 230.38/41.72  | | | 
% 230.38/41.72  | | | ALPHA: (78) implies:
% 230.38/41.72  | | |   (79)  all_57_6 = e0
% 230.38/41.72  | | | 
% 230.38/41.72  | | | BETA: splitting (66) gives:
% 230.38/41.72  | | | 
% 230.38/41.72  | | | Case 1:
% 230.38/41.72  | | | | 
% 230.38/41.72  | | | |   (80)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3)
% 230.38/41.72  | | | |           = e2)
% 230.38/41.72  | | | | 
% 230.38/41.72  | | | | BETA: splitting (80) gives:
% 230.38/41.72  | | | | 
% 230.38/41.72  | | | | Case 1:
% 230.38/41.72  | | | | | 
% 230.38/41.72  | | | | |   (81)  all_57_0 = e2 & op(e3, e3) = e2
% 230.38/41.72  | | | | | 
% 230.38/41.72  | | | | | ALPHA: (81) implies:
% 230.38/41.72  | | | | |   (82)  op(e3, e3) = e2
% 230.38/41.72  | | | | | 
% 230.38/41.72  | | | | | REF_CLOSE: (11), (30), (39), (45), (49), (82) are inconsistent by
% 230.38/41.72  | | | | |            sub-proof #1951.
% 230.38/41.72  | | | | | 
% 230.38/41.72  | | | | Case 2:
% 230.38/41.72  | | | | | 
% 230.38/41.72  | | | | |   (83)  all_57_2 = e2 & op(e2, e3) = e2
% 230.38/41.72  | | | | | 
% 230.38/41.72  | | | | | ALPHA: (83) implies:
% 230.38/41.72  | | | | |   (84)  all_57_2 = e2
% 230.38/41.72  | | | | | 
% 230.38/41.72  | | | | | BETA: splitting (7) gives:
% 230.38/41.72  | | | | | 
% 230.38/41.72  | | | | | Case 1:
% 230.38/41.72  | | | | | | 
% 230.38/41.72  | | | | | |   (85)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2,
% 230.38/41.72  | | | | | |             e3) = e1)
% 230.38/41.72  | | | | | | 
% 230.38/41.72  | | | | | | REF_CLOSE: (9), (11), (35), (63), (84), (85) are inconsistent by
% 230.38/41.72  | | | | | |            sub-proof #2228.
% 230.38/41.72  | | | | | | 
% 230.38/41.72  | | | | | Case 2:
% 230.38/41.72  | | | | | | 
% 230.38/41.72  | | | | | |   (86)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0,
% 230.38/41.72  | | | | | |             e3) = e1)
% 230.38/41.72  | | | | | | 
% 230.38/41.72  | | | | | | REF_CLOSE: (4), (11), (21), (48), (50), (79), (86) are inconsistent
% 230.38/41.72  | | | | | |            by sub-proof #1118.
% 230.38/41.72  | | | | | | 
% 230.38/41.72  | | | | | End of split
% 230.38/41.72  | | | | | 
% 230.38/41.72  | | | | End of split
% 230.38/41.72  | | | | 
% 230.38/41.72  | | | Case 2:
% 230.38/41.72  | | | | 
% 230.38/41.72  | | | |   (87)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3)
% 230.38/41.72  | | | |           = e2)
% 230.38/41.72  | | | | 
% 230.38/41.72  | | | | BETA: splitting (87) gives:
% 230.38/41.72  | | | | 
% 230.38/41.72  | | | | Case 1:
% 230.38/41.72  | | | | | 
% 230.38/41.72  | | | | |   (88)  all_57_6 = e2 & op(e1, e3) = e2
% 230.38/41.72  | | | | | 
% 230.38/41.72  | | | | | ALPHA: (88) implies:
% 230.38/41.72  | | | | |   (89)  all_57_6 = e2
% 230.38/41.72  | | | | | 
% 230.38/41.72  | | | | | REF_CLOSE: (3), (5), (6), (7), (8), (9), (10), (11), (12), (14), (15),
% 230.38/41.72  | | | | |            (16), (19), (20), (21), (22), (23), (24), (27), (29), (30),
% 230.38/41.72  | | | | |            (33), (34), (35), (36), (37), (38), (39), (43), (44), (45),
% 230.38/41.72  | | | | |            (46), (48), (49), (50), (52), (53), (54), (55), (57), (58),
% 230.38/41.72  | | | | |            (59), (60), (63), (64), (66), (68), (69), (70), (71), (72),
% 230.38/41.72  | | | | |            (73), (74), (76), (89) are inconsistent by sub-proof #1119.
% 230.38/41.72  | | | | | 
% 230.38/41.72  | | | | Case 2:
% 230.38/41.72  | | | | | 
% 230.38/41.72  | | | | |   (90)  all_57_12 = e2 & op(e0, e3) = e2
% 230.38/41.72  | | | | | 
% 230.38/41.72  | | | | | ALPHA: (90) implies:
% 230.38/41.72  | | | | |   (91)  all_57_12 = e2
% 230.38/41.72  | | | | | 
% 230.38/41.72  | | | | | BETA: splitting (7) gives:
% 230.38/41.72  | | | | | 
% 230.38/41.72  | | | | | Case 1:
% 230.38/41.72  | | | | | | 
% 230.38/41.72  | | | | | |   (92)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2,
% 230.38/41.72  | | | | | |             e3) = e1)
% 230.38/41.72  | | | | | | 
% 230.38/41.72  | | | | | | BETA: splitting (92) gives:
% 230.38/41.72  | | | | | | 
% 230.38/41.72  | | | | | | Case 1:
% 230.38/41.72  | | | | | | | 
% 230.38/41.72  | | | | | | |   (93)  all_57_0 = e1 & op(e3, e3) = e1
% 230.38/41.72  | | | | | | | 
% 230.38/41.72  | | | | | | | ALPHA: (93) implies:
% 230.38/41.72  | | | | | | |   (94)  op(e3, e3) = e1
% 230.38/41.72  | | | | | | | 
% 230.38/41.72  | | | | | | | REF_CLOSE: (9), (11), (35), (94) are inconsistent by sub-proof
% 230.38/41.72  | | | | | | |            #2495.
% 230.38/41.72  | | | | | | | 
% 230.38/41.72  | | | | | | Case 2:
% 230.38/41.72  | | | | | | | 
% 230.38/41.72  | | | | | | |   (95)  all_57_2 = e1 & op(e2, e3) = e1
% 230.38/41.72  | | | | | | | 
% 230.38/41.72  | | | | | | | ALPHA: (95) implies:
% 230.38/41.72  | | | | | | |   (96)  all_57_2 = e1
% 230.38/41.72  | | | | | | | 
% 230.38/41.72  | | | | | | | BETA: splitting (37) gives:
% 230.38/41.72  | | | | | | | 
% 230.38/41.72  | | | | | | | Case 1:
% 230.38/41.72  | | | | | | | | 
% 230.38/41.72  | | | | | | | |   (97)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 &
% 230.38/41.72  | | | | | | | |           op(e0, e2) = e1)
% 230.38/41.72  | | | | | | | | 
% 230.38/41.72  | | | | | | | | BETA: splitting (97) gives:
% 230.38/41.72  | | | | | | | | 
% 230.38/41.72  | | | | | | | | Case 1:
% 230.38/41.72  | | | | | | | | | 
% 230.38/41.72  | | | | | | | | |   (98)  all_57_12 = e1 & op(e0, e3) = e1
% 230.38/41.72  | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | ALPHA: (98) implies:
% 230.38/41.72  | | | | | | | | |   (99)  op(e0, e3) = e1
% 230.38/41.72  | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | REF_CLOSE: (4), (11), (21), (48), (99) are inconsistent by
% 230.38/41.72  | | | | | | | | |            sub-proof #1147.
% 230.38/41.72  | | | | | | | | | 
% 230.38/41.72  | | | | | | | | Case 2:
% 230.38/41.72  | | | | | | | | | 
% 230.38/41.72  | | | | | | | | |   (100)  all_57_13 = e1 & op(e0, e2) = e1
% 230.38/41.72  | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | ALPHA: (100) implies:
% 230.38/41.72  | | | | | | | | |   (101)  all_57_13 = e1
% 230.38/41.72  | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | BETA: splitting (55) gives:
% 230.38/41.72  | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | Case 1:
% 230.38/41.72  | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | |   (102)  all_57_15 = e0 & op(e0, e0) = e0
% 230.38/41.72  | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | ALPHA: (102) implies:
% 230.38/41.72  | | | | | | | | | |   (103)  op(e0, e0) = e0
% 230.38/41.72  | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | REF_CLOSE: (11), (33), (52), (103) are inconsistent by
% 230.38/41.72  | | | | | | | | | |            sub-proof #2304.
% 230.38/41.72  | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | Case 2:
% 230.38/41.72  | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | |   (104)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 230.38/41.72  | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 230.38/41.72  | | | | | | | | | |              op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 230.38/41.72  | | | | | | | | | |                e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 230.38/41.72  | | | | | | | | | |              e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 230.38/41.72  | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | ALPHA: (104) implies:
% 230.38/41.72  | | | | | | | | | |   (105)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0
% 230.38/41.72  | | | | | | | | | |            & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.38/41.72  | | | | | | | | | |            = e0)
% 230.38/41.72  | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | BETA: splitting (44) gives:
% 230.38/41.72  | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | Case 1:
% 230.38/41.72  | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | |   (106)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 230.38/41.72  | | | | | | | | | | |            & op(e2, e2) = e0)
% 230.38/41.72  | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | BETA: splitting (106) gives:
% 230.38/41.72  | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | Case 1:
% 230.38/41.72  | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | |   (107)  all_57_1 = e0 & op(e3, e2) = e0
% 230.38/41.72  | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | ALPHA: (107) implies:
% 230.38/41.72  | | | | | | | | | | | |   (108)  all_57_1 = e0
% 230.38/41.72  | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | BETA: splitting (19) gives:
% 230.38/41.72  | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | Case 1:
% 230.38/41.72  | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | |   (109)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 230.38/41.72  | | | | | | | | | | | | |            & op(e3, e2) = e1)
% 230.38/41.72  | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | REF_CLOSE: (9), (11), (35), (50), (108), (109) are
% 230.38/41.72  | | | | | | | | | | | | |            inconsistent by sub-proof #2445.
% 230.38/41.72  | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | Case 2:
% 230.38/41.72  | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | |   (110)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 230.38/41.72  | | | | | | | | | | | | |            & op(e3, e0) = e1)
% 230.38/41.72  | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | BETA: splitting (110) gives:
% 230.38/41.72  | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | Case 1:
% 230.38/41.72  | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | |   (111)  all_57_4 = e1 & op(e3, e1) = e1
% 230.38/41.72  | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | ALPHA: (111) implies:
% 230.38/41.72  | | | | | | | | | | | | | |   (112)  all_57_4 = e1
% 230.38/41.72  | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | BETA: splitting (68) gives:
% 230.38/41.72  | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | Case 1:
% 230.38/41.72  | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | |   (113)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 230.38/41.72  | | | | | | | | | | | | | | |            & op(e2, e1) = e2)
% 230.38/41.72  | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | BETA: splitting (113) gives:
% 230.38/41.72  | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | Case 1:
% 230.38/41.72  | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | |   (114)  all_57_4 = e2 & op(e3, e1) = e2
% 230.38/41.72  | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | | ALPHA: (114) implies:
% 230.38/41.72  | | | | | | | | | | | | | | | |   (115)  all_57_4 = e2
% 230.38/41.72  | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | | REF_CLOSE: (63), (112), (115) are inconsistent by sub-proof
% 230.38/41.72  | | | | | | | | | | | | | | | |            #2430.
% 230.38/41.72  | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | Case 2:
% 230.38/41.72  | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | |   (116)  all_57_5 = e2 & op(e2, e1) = e2
% 230.38/41.72  | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11), (12), (14), (15), (30), (33), (36),
% 230.38/41.72  | | | | | | | | | | | | | | | |            (38), (46), (50), (55), (59), (63), (64), (70),
% 230.38/41.72  | | | | | | | | | | | | | | | |            (79), (116) are inconsistent by sub-proof #1117.
% 230.38/41.72  | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | End of split
% 230.38/41.72  | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | Case 2:
% 230.38/41.72  | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | |   (117)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 230.38/41.72  | | | | | | | | | | | | | | |            e2 & op(e0, e1) = e2)
% 230.38/41.72  | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | BETA: splitting (117) gives:
% 230.38/41.72  | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | Case 1:
% 230.38/41.72  | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | |   (118)  all_57_8 = e2 & op(e1, e1) = e2
% 230.38/41.72  | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | | ALPHA: (118) implies:
% 230.38/41.72  | | | | | | | | | | | | | | | |   (119)  op(e1, e1) = e2
% 230.38/41.72  | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (7), (8), (9), (10), (11), (12), (14),
% 230.38/41.72  | | | | | | | | | | | | | | | |            (15), (16), (19), (21), (22), (24), (27), (29),
% 230.38/41.72  | | | | | | | | | | | | | | | |            (30), (33), (34), (35), (36), (37), (38), (39),
% 230.38/41.72  | | | | | | | | | | | | | | | |            (44), (45), (46), (48), (49), (50), (52), (54),
% 230.38/41.72  | | | | | | | | | | | | | | | |            (55), (57), (59), (60), (63), (64), (66), (68),
% 230.38/41.72  | | | | | | | | | | | | | | | |            (69), (70), (71), (72), (73), (74), (76), (91),
% 230.38/41.72  | | | | | | | | | | | | | | | |            (119) are inconsistent by sub-proof #1129.
% 230.38/41.72  | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | Case 2:
% 230.38/41.72  | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | |   (120)  all_57_14 = e2 & op(e0, e1) = e2
% 230.38/41.72  | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | | ALPHA: (120) implies:
% 230.38/41.72  | | | | | | | | | | | | | | | |   (121)  all_57_14 = e2
% 230.38/41.72  | | | | | | | | | | | | | | | |   (122)  op(e0, e1) = e2
% 230.38/41.72  | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | | BETA: splitting (24) gives:
% 230.38/41.72  | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | | Case 1:
% 230.38/41.72  | | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | | |   (123)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 230.38/41.72  | | | | | | | | | | | | | | | | |            & op(e3, e2) = e2)
% 230.38/41.72  | | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | | | BETA: splitting (123) gives:
% 230.38/41.72  | | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | | | Case 1:
% 230.38/41.72  | | | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | | | |   (124)  all_57_0 = e2 & op(e3, e3) = e2
% 230.38/41.72  | | | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | | | | ALPHA: (124) implies:
% 230.38/41.72  | | | | | | | | | | | | | | | | | |   (125)  op(e3, e3) = e2
% 230.38/41.72  | | | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (4), (11), (13), (14), (15), (18), (25),
% 230.38/41.72  | | | | | | | | | | | | | | | | | |            (26), (28), (31), (32), (41), (42), (46), (47),
% 230.38/41.72  | | | | | | | | | | | | | | | | | |            (49), (52), (56), (65), (67), (75), (122), (125)
% 230.38/41.72  | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1114.
% 230.38/41.72  | | | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | | | Case 2:
% 230.38/41.72  | | | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | | | |   (126)  all_57_1 = e2 & op(e3, e2) = e2
% 230.38/41.72  | | | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (30), (46), (59), (63), (72), (101), (108),
% 230.38/41.72  | | | | | | | | | | | | | | | | | |            (126) are inconsistent by sub-proof #1113.
% 230.38/41.72  | | | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | | | End of split
% 230.38/41.72  | | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | | Case 2:
% 230.38/41.72  | | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | | |   (127)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 230.38/41.72  | | | | | | | | | | | | | | | | |            & op(e3, e0) = e2)
% 230.38/41.72  | | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | | | BETA: splitting (127) gives:
% 230.38/41.72  | | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | | | Case 1:
% 230.38/41.72  | | | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | | | |   (128)  all_57_4 = e2 & op(e3, e1) = e2
% 230.38/41.72  | | | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | | | | ALPHA: (128) implies:
% 230.38/41.72  | | | | | | | | | | | | | | | | | |   (129)  all_57_4 = e2
% 230.38/41.72  | | | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (112), (129) imply:
% 230.38/41.72  | | | | | | | | | | | | | | | | | |   (130)  e2 = e1
% 230.38/41.72  | | | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | | | | SIMP: (130) implies:
% 230.38/41.72  | | | | | | | | | | | | | | | | | |   (131)  e2 = e1
% 230.38/41.72  | | | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (121), (131) imply:
% 230.38/41.72  | | | | | | | | | | | | | | | | | |   (132)  all_57_14 = e1
% 230.38/41.72  | | | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (11), (12), (14), (15), (29), (30),
% 230.38/41.72  | | | | | | | | | | | | | | | | | |            (33), (36), (38), (43), (46), (50), (55), (59),
% 230.38/41.72  | | | | | | | | | | | | | | | | | |            (60), (62), (63), (64), (70), (72), (74), (79),
% 230.38/41.72  | | | | | | | | | | | | | | | | | |            (96), (108), (129), (132) are inconsistent by
% 230.38/41.72  | | | | | | | | | | | | | | | | | |            sub-proof #1112.
% 230.38/41.72  | | | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | | | Case 2:
% 230.38/41.72  | | | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | | | |   (133)  all_57_9 = e2 & op(e3, e0) = e2
% 230.38/41.72  | | | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | | | | ALPHA: (133) implies:
% 230.38/41.72  | | | | | | | | | | | | | | | | | |   (134)  all_57_9 = e2
% 230.38/41.72  | | | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (7), (8), (9), (11), (12), (14), (15), (19),
% 230.38/41.72  | | | | | | | | | | | | | | | | | |            (29), (30), (33), (35), (36), (38), (43), (46),
% 230.38/41.72  | | | | | | | | | | | | | | | | | |            (50), (55), (60), (63), (64), (66), (69), (70),
% 230.38/41.72  | | | | | | | | | | | | | | | | | |            (72), (74), (108), (121), (134) are inconsistent
% 230.38/41.72  | | | | | | | | | | | | | | | | | |            by sub-proof #1162.
% 230.38/41.72  | | | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | | | End of split
% 230.38/41.72  | | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | | End of split
% 230.38/41.72  | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | End of split
% 230.38/41.72  | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | End of split
% 230.38/41.72  | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | Case 2:
% 230.38/41.72  | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | |   (135)  all_57_9 = e1 & op(e3, e0) = e1
% 230.38/41.72  | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | ALPHA: (135) implies:
% 230.38/41.72  | | | | | | | | | | | | | |   (136)  all_57_9 = e1
% 230.38/41.72  | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | BETA: splitting (24) gives:
% 230.38/41.72  | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | Case 1:
% 230.38/41.72  | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | |   (137)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 230.38/41.72  | | | | | | | | | | | | | | |            & op(e3, e2) = e2)
% 230.38/41.72  | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | BETA: splitting (137) gives:
% 230.38/41.72  | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | Case 1:
% 230.38/41.72  | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | |   (138)  all_57_0 = e2 & op(e3, e3) = e2
% 230.38/41.72  | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | | ALPHA: (138) implies:
% 230.38/41.72  | | | | | | | | | | | | | | | |   (139)  op(e3, e3) = e2
% 230.38/41.72  | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | | REF_CLOSE: (11), (30), (39), (45), (49), (139) are
% 230.38/41.72  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1951.
% 230.38/41.72  | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | Case 2:
% 230.38/41.72  | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | |   (140)  all_57_1 = e2 & op(e3, e2) = e2
% 230.38/41.72  | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | | REF_CLOSE: (8), (30), (46), (59), (63), (72), (101), (108),
% 230.38/41.72  | | | | | | | | | | | | | | | |            (140) are inconsistent by sub-proof #1113.
% 230.38/41.72  | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | End of split
% 230.38/41.72  | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | Case 2:
% 230.38/41.72  | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | |   (141)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 230.38/41.72  | | | | | | | | | | | | | | |            & op(e3, e0) = e2)
% 230.38/41.72  | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | BETA: splitting (141) gives:
% 230.38/41.72  | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | Case 1:
% 230.38/41.72  | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | |   (142)  all_57_4 = e2 & op(e3, e1) = e2
% 230.38/41.72  | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | | ALPHA: (142) implies:
% 230.38/41.72  | | | | | | | | | | | | | | | |   (143)  all_57_4 = e2
% 230.38/41.72  | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | | BETA: splitting (105) gives:
% 230.38/41.72  | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | | Case 1:
% 230.38/41.72  | | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | | |   (144)  all_57_9 = e0 & op(e3, e0) = e0
% 230.38/41.72  | | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | | | REF_CLOSE: (50), (136), (144) are inconsistent by sub-proof
% 230.38/41.72  | | | | | | | | | | | | | | | | |            #1990.
% 230.38/41.72  | | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | | Case 2:
% 230.38/41.72  | | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | | |   (145)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 =
% 230.38/41.72  | | | | | | | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 230.38/41.72  | | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | | | BETA: splitting (145) gives:
% 230.38/41.72  | | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | | | Case 1:
% 230.38/41.72  | | | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | | | | ALPHA: (135) implies:
% 230.38/41.72  | | | | | | | | | | | | | | | | | |   (146)  op(e3, e0) = e1
% 230.38/41.72  | | | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | | | | ALPHA: (107) implies:
% 230.38/41.72  | | | | | | | | | | | | | | | | | |   (147)  op(e3, e2) = e0
% 230.38/41.72  | | | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_52_7, e1, e0, e3,
% 230.38/41.72  | | | | | | | | | | | | | | | | | |              simplifying with (73), (146) gives:
% 230.38/41.72  | | | | | | | | | | | | | | | | | |   (148)  all_52_7 = e1
% 230.38/41.72  | | | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (11) with all_52_3, e0, e2, e3,
% 230.38/41.72  | | | | | | | | | | | | | | | | | |              simplifying with (17), (147) gives:
% 230.38/41.72  | | | | | | | | | | | | | | | | | |   (149)  all_52_3 = e0
% 230.38/41.72  | | | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | | | | REDUCE: (51), (148), (149) imply:
% 230.38/41.72  | | | | | | | | | | | | | | | | | |   (150)   ~ (e1 = e0)
% 230.38/41.72  | | | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | | | | REDUCE: (16), (148) imply:
% 230.38/41.72  | | | | | | | | | | | | | | | | | |   (151)  op(e1, e1) = e0
% 230.38/41.72  | | | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (43), (50), (151) are inconsistent by
% 230.38/41.72  | | | | | | | | | | | | | | | | | |            sub-proof #2427.
% 230.38/41.72  | | | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | | | Case 2:
% 230.38/41.72  | | | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | | | |   (152)  all_57_11 = e0 & op(e1, e0) = e0
% 230.38/41.72  | | | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | | | | ALPHA: (152) implies:
% 230.38/41.72  | | | | | | | | | | | | | | | | | |   (153)  all_57_11 = e0
% 230.38/41.72  | | | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (40), (153) imply:
% 230.38/41.72  | | | | | | | | | | | | | | | | | |   (154)  e2 = e0
% 230.38/41.72  | | | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (11), (19), (24), (27), (30), (33),
% 230.38/41.72  | | | | | | | | | | | | | | | | | |            (35), (36), (38), (40), (46), (50), (59), (60),
% 230.38/41.72  | | | | | | | | | | | | | | | | | |            (63), (64), (70), (72), (74), (143), (154) are
% 230.38/41.72  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1111.
% 230.38/41.72  | | | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | | | End of split
% 230.38/41.72  | | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | | End of split
% 230.38/41.72  | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | Case 2:
% 230.38/41.72  | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | |   (155)  all_57_9 = e2 & op(e3, e0) = e2
% 230.38/41.72  | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | | ALPHA: (155) implies:
% 230.38/41.72  | | | | | | | | | | | | | | | |   (156)  all_57_9 = e2
% 230.38/41.72  | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (7), (8), (9), (10), (11), (12), (14),
% 230.38/41.72  | | | | | | | | | | | | | | | |            (15), (16), (19), (21), (22), (24), (27), (29),
% 230.38/41.72  | | | | | | | | | | | | | | | |            (30), (33), (34), (35), (36), (37), (38), (39),
% 230.38/41.72  | | | | | | | | | | | | | | | |            (44), (45), (46), (48), (49), (50), (52), (54),
% 230.38/41.72  | | | | | | | | | | | | | | | |            (55), (57), (59), (60), (63), (64), (66), (68),
% 230.38/41.72  | | | | | | | | | | | | | | | |            (69), (70), (71), (72), (73), (74), (76), (91),
% 230.38/41.72  | | | | | | | | | | | | | | | |            (156) are inconsistent by sub-proof #1127.
% 230.38/41.72  | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | End of split
% 230.38/41.72  | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | End of split
% 230.38/41.72  | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | End of split
% 230.38/41.72  | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | End of split
% 230.38/41.72  | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | Case 2:
% 230.38/41.72  | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | |   (157)  all_57_3 = e0 & op(e2, e2) = e0
% 230.38/41.72  | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | ALPHA: (157) implies:
% 230.38/41.72  | | | | | | | | | | | |   (158)  op(e2, e2) = e0
% 230.38/41.72  | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | REF_CLOSE: (11), (46), (49), (158) are inconsistent by
% 230.38/41.72  | | | | | | | | | | | |            sub-proof #2472.
% 230.38/41.72  | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | End of split
% 230.38/41.72  | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | Case 2:
% 230.38/41.72  | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | |   (159)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 230.38/41.72  | | | | | | | | | | |            e0 & op(e0, e2) = e0)
% 230.38/41.72  | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | BETA: splitting (159) gives:
% 230.38/41.72  | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | Case 1:
% 230.38/41.72  | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | |   (160)  all_57_7 = e0 & op(e1, e2) = e0
% 230.38/41.72  | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | ALPHA: (160) implies:
% 230.38/41.72  | | | | | | | | | | | |   (161)  all_57_7 = e0
% 230.38/41.72  | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | REF_CLOSE: (33), (59), (161) are inconsistent by sub-proof
% 230.38/41.72  | | | | | | | | | | | |            #2269.
% 230.38/41.72  | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | Case 2:
% 230.38/41.72  | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | |   (162)  all_57_13 = e0 & op(e0, e2) = e0
% 230.38/41.72  | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | REF_CLOSE: (50), (101), (162) are inconsistent by sub-proof
% 230.38/41.72  | | | | | | | | | | | |            #1920.
% 230.38/41.72  | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | End of split
% 230.38/41.72  | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | End of split
% 230.38/41.72  | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | End of split
% 230.38/41.72  | | | | | | | | | 
% 230.38/41.72  | | | | | | | | End of split
% 230.38/41.72  | | | | | | | | 
% 230.38/41.72  | | | | | | | Case 2:
% 230.38/41.72  | | | | | | | | 
% 230.38/41.72  | | | | | | | |   (163)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 &
% 230.38/41.72  | | | | | | | |            op(e0, e0) = e1)
% 230.38/41.72  | | | | | | | | 
% 230.38/41.72  | | | | | | | | BETA: splitting (163) gives:
% 230.38/41.72  | | | | | | | | 
% 230.38/41.72  | | | | | | | | Case 1:
% 230.38/41.72  | | | | | | | | | 
% 230.38/41.72  | | | | | | | | |   (164)  all_57_14 = e1 & op(e0, e1) = e1
% 230.38/41.72  | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | ALPHA: (164) implies:
% 230.38/41.72  | | | | | | | | |   (165)  all_57_14 = e1
% 230.38/41.72  | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | BETA: splitting (62) gives:
% 230.38/41.72  | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | Case 1:
% 230.38/41.72  | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | |   (166)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 230.38/41.72  | | | | | | | | | |            & op(e2, e2) = e0)
% 230.38/41.72  | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | REF_CLOSE: (11), (46), (49), (50), (96), (166) are
% 230.38/41.72  | | | | | | | | | |            inconsistent by sub-proof #2457.
% 230.38/41.72  | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | Case 2:
% 230.38/41.72  | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | |   (167)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0
% 230.38/41.72  | | | | | | | | | |            & op(e2, e0) = e0)
% 230.38/41.72  | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | BETA: splitting (167) gives:
% 230.38/41.72  | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | Case 1:
% 230.38/41.72  | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | |   (168)  all_57_5 = e0 & op(e2, e1) = e0
% 230.38/41.72  | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | REF_CLOSE: (33), (38), (168) are inconsistent by sub-proof
% 230.38/41.72  | | | | | | | | | | |            #2414.
% 230.38/41.72  | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | Case 2:
% 230.38/41.72  | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | |   (169)  all_57_10 = e0 & op(e2, e0) = e0
% 230.38/41.72  | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | ALPHA: (169) implies:
% 230.38/41.72  | | | | | | | | | | |   (170)  all_57_10 = e0
% 230.38/41.72  | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | BETA: splitting (70) gives:
% 230.38/41.72  | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | Case 1:
% 230.38/41.72  | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | |   (171)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 230.38/41.72  | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 230.38/41.72  | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | BETA: splitting (171) gives:
% 230.38/41.72  | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | Case 1:
% 230.38/41.72  | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | |   (172)  all_57_9 = e1 & op(e3, e0) = e1
% 230.38/41.72  | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | ALPHA: (172) implies:
% 230.38/41.72  | | | | | | | | | | | | |   (173)  all_57_9 = e1
% 230.38/41.72  | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | BETA: splitting (24) gives:
% 230.38/41.72  | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | Case 1:
% 230.38/41.72  | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | |   (174)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 230.38/41.72  | | | | | | | | | | | | | |            & op(e3, e2) = e2)
% 230.38/41.72  | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | BETA: splitting (174) gives:
% 230.38/41.72  | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | Case 1:
% 230.38/41.72  | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | |   (175)  all_57_0 = e2 & op(e3, e3) = e2
% 230.38/41.72  | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | ALPHA: (175) implies:
% 230.38/41.72  | | | | | | | | | | | | | | |   (176)  op(e3, e3) = e2
% 230.38/41.72  | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | REF_CLOSE: (11), (30), (39), (45), (49), (176) are
% 230.38/41.72  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1951.
% 230.38/41.72  | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | Case 2:
% 230.38/41.72  | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | |   (177)  all_57_1 = e2 & op(e3, e2) = e2
% 230.38/41.72  | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | ALPHA: (177) implies:
% 230.38/41.72  | | | | | | | | | | | | | | |   (178)  all_57_1 = e2
% 230.38/41.72  | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | BETA: splitting (68) gives:
% 230.38/41.72  | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | Case 1:
% 230.38/41.72  | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | |   (179)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 230.38/41.72  | | | | | | | | | | | | | | | |            & op(e2, e1) = e2)
% 230.38/41.72  | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | | BETA: splitting (179) gives:
% 230.38/41.72  | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | | Case 1:
% 230.38/41.72  | | | | | | | | | | | | | | | | | 
% 230.38/41.72  | | | | | | | | | | | | | | | | |   (180)  all_57_4 = e2 & op(e3, e1) = e2
% 230.38/41.72  | | | | | | | | | | | | | | | | | 
% 230.38/41.73  | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (8), (9), (11), (12), (14), (15), (27), (29),
% 230.38/41.73  | | | | | | | | | | | | | | | | |            (30), (33), (36), (38), (43), (46), (50), (55),
% 230.38/41.73  | | | | | | | | | | | | | | | | |            (59), (60), (61), (62), (63), (64), (66), (70),
% 230.38/41.73  | | | | | | | | | | | | | | | | |            (72), (74), (79), (96), (165), (170), (173), (180)
% 230.38/41.73  | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1110.
% 230.38/41.73  | | | | | | | | | | | | | | | | | 
% 230.38/41.73  | | | | | | | | | | | | | | | | Case 2:
% 230.38/41.73  | | | | | | | | | | | | | | | | | 
% 230.38/41.73  | | | | | | | | | | | | | | | | |   (181)  all_57_5 = e2 & op(e2, e1) = e2
% 230.38/41.73  | | | | | | | | | | | | | | | | | 
% 230.38/41.73  | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11), (12), (14), (15), (30), (33), (36),
% 230.38/41.73  | | | | | | | | | | | | | | | | |            (38), (46), (50), (55), (59), (63), (64), (70),
% 230.38/41.73  | | | | | | | | | | | | | | | | |            (79), (181) are inconsistent by sub-proof #1117.
% 230.38/41.73  | | | | | | | | | | | | | | | | | 
% 230.38/41.73  | | | | | | | | | | | | | | | | End of split
% 230.38/41.73  | | | | | | | | | | | | | | | | 
% 230.38/41.73  | | | | | | | | | | | | | | | Case 2:
% 230.38/41.73  | | | | | | | | | | | | | | | | 
% 230.38/41.73  | | | | | | | | | | | | | | | |   (182)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 230.38/41.73  | | | | | | | | | | | | | | | |            e2 & op(e0, e1) = e2)
% 230.38/41.73  | | | | | | | | | | | | | | | | 
% 230.38/41.73  | | | | | | | | | | | | | | | | BETA: splitting (182) gives:
% 230.38/41.73  | | | | | | | | | | | | | | | | 
% 230.38/41.73  | | | | | | | | | | | | | | | | Case 1:
% 230.38/41.73  | | | | | | | | | | | | | | | | | 
% 230.38/41.73  | | | | | | | | | | | | | | | | |   (183)  all_57_8 = e2 & op(e1, e1) = e2
% 230.38/41.73  | | | | | | | | | | | | | | | | | 
% 230.38/41.73  | | | | | | | | | | | | | | | | | ALPHA: (183) implies:
% 230.38/41.73  | | | | | | | | | | | | | | | | |   (184)  op(e1, e1) = e2
% 230.38/41.73  | | | | | | | | | | | | | | | | | 
% 230.38/41.73  | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (7), (8), (9), (10), (11), (12), (14),
% 230.38/41.73  | | | | | | | | | | | | | | | | |            (15), (16), (19), (21), (22), (24), (27), (29),
% 230.38/41.73  | | | | | | | | | | | | | | | | |            (30), (33), (34), (35), (36), (37), (38), (44),
% 230.38/41.73  | | | | | | | | | | | | | | | | |            (46), (48), (49), (50), (52), (54), (55), (57),
% 230.38/41.73  | | | | | | | | | | | | | | | | |            (59), (60), (63), (64), (66), (68), (69), (70),
% 230.38/41.73  | | | | | | | | | | | | | | | | |            (71), (72), (73), (74), (76), (91), (178), (184)
% 230.38/41.73  | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1131.
% 230.38/41.73  | | | | | | | | | | | | | | | | | 
% 230.38/41.73  | | | | | | | | | | | | | | | | Case 2:
% 230.38/41.73  | | | | | | | | | | | | | | | | | 
% 230.38/41.73  | | | | | | | | | | | | | | | | |   (185)  all_57_14 = e2 & op(e0, e1) = e2
% 230.38/41.73  | | | | | | | | | | | | | | | | | 
% 230.38/41.73  | | | | | | | | | | | | | | | | | REF_CLOSE: (63), (165), (185) are inconsistent by sub-proof
% 230.38/41.73  | | | | | | | | | | | | | | | | |            #1968.
% 230.38/41.73  | | | | | | | | | | | | | | | | | 
% 230.38/41.73  | | | | | | | | | | | | | | | | End of split
% 230.38/41.73  | | | | | | | | | | | | | | | | 
% 230.38/41.73  | | | | | | | | | | | | | | | End of split
% 230.38/41.73  | | | | | | | | | | | | | | | 
% 230.38/41.73  | | | | | | | | | | | | | | End of split
% 230.38/41.73  | | | | | | | | | | | | | | 
% 230.38/41.73  | | | | | | | | | | | | | Case 2:
% 230.38/41.73  | | | | | | | | | | | | | | 
% 230.38/41.73  | | | | | | | | | | | | | |   (186)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 230.38/41.73  | | | | | | | | | | | | | |            & op(e3, e0) = e2)
% 230.38/41.73  | | | | | | | | | | | | | | 
% 230.38/41.73  | | | | | | | | | | | | | | BETA: splitting (186) gives:
% 230.38/41.73  | | | | | | | | | | | | | | 
% 230.38/41.73  | | | | | | | | | | | | | | Case 1:
% 230.38/41.73  | | | | | | | | | | | | | | | 
% 230.38/41.73  | | | | | | | | | | | | | | |   (187)  all_57_4 = e2 & op(e3, e1) = e2
% 230.38/41.73  | | | | | | | | | | | | | | | 
% 230.38/41.73  | | | | | | | | | | | | | | | REF_CLOSE: (3), (8), (9), (11), (12), (14), (15), (27), (29),
% 230.38/41.73  | | | | | | | | | | | | | | |            (30), (33), (36), (38), (43), (46), (50), (55),
% 230.38/41.73  | | | | | | | | | | | | | | |            (59), (60), (61), (62), (63), (64), (66), (70),
% 230.38/41.73  | | | | | | | | | | | | | | |            (72), (74), (79), (96), (165), (170), (173), (187)
% 230.38/41.73  | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1110.
% 230.38/41.73  | | | | | | | | | | | | | | | 
% 230.38/41.73  | | | | | | | | | | | | | | Case 2:
% 230.38/41.73  | | | | | | | | | | | | | | | 
% 230.38/41.73  | | | | | | | | | | | | | | |   (188)  all_57_9 = e2 & op(e3, e0) = e2
% 230.38/41.73  | | | | | | | | | | | | | | | 
% 230.38/41.73  | | | | | | | | | | | | | | | ALPHA: (188) implies:
% 230.38/41.73  | | | | | | | | | | | | | | |   (189)  all_57_9 = e2
% 230.38/41.73  | | | | | | | | | | | | | | | 
% 230.38/41.73  | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (7), (8), (9), (10), (11), (12), (14),
% 230.38/41.73  | | | | | | | | | | | | | | |            (15), (16), (19), (21), (22), (23), (24), (27),
% 230.38/41.73  | | | | | | | | | | | | | | |            (29), (30), (33), (34), (35), (36), (37), (38),
% 230.38/41.73  | | | | | | | | | | | | | | |            (39), (44), (45), (46), (48), (49), (50), (52),
% 230.38/41.73  | | | | | | | | | | | | | | |            (53), (54), (55), (57), (59), (60), (63), (64),
% 230.38/41.73  | | | | | | | | | | | | | | |            (66), (68), (69), (70), (71), (72), (73), (74),
% 230.38/41.73  | | | | | | | | | | | | | | |            (76), (165), (189) are inconsistent by sub-proof
% 230.38/41.73  | | | | | | | | | | | | | | |            #1126.
% 230.38/41.73  | | | | | | | | | | | | | | | 
% 230.38/41.73  | | | | | | | | | | | | | | End of split
% 230.38/41.73  | | | | | | | | | | | | | | 
% 230.38/41.73  | | | | | | | | | | | | | End of split
% 230.38/41.73  | | | | | | | | | | | | | 
% 230.38/41.73  | | | | | | | | | | | | Case 2:
% 230.38/41.73  | | | | | | | | | | | | | 
% 230.38/41.73  | | | | | | | | | | | | |   (190)  all_57_10 = e1 & op(e2, e0) = e1
% 230.38/41.73  | | | | | | | | | | | | | 
% 230.38/41.73  | | | | | | | | | | | | | ALPHA: (190) implies:
% 230.38/41.73  | | | | | | | | | | | | |   (191)  all_57_10 = e1
% 230.38/41.73  | | | | | | | | | | | | | 
% 230.38/41.73  | | | | | | | | | | | | | REF_CLOSE: (50), (170), (191) are inconsistent by sub-proof
% 230.38/41.73  | | | | | | | | | | | | |            #1531.
% 230.38/41.73  | | | | | | | | | | | | | 
% 230.38/41.73  | | | | | | | | | | | | End of split
% 230.38/41.73  | | | | | | | | | | | | 
% 230.38/41.73  | | | | | | | | | | | Case 2:
% 230.38/41.73  | | | | | | | | | | | | 
% 230.38/41.73  | | | | | | | | | | | |   (192)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 230.38/41.73  | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 230.38/41.73  | | | | | | | | | | | | 
% 230.38/41.73  | | | | | | | | | | | | REF_CLOSE: (9), (11), (40), (52), (63), (192) are
% 230.38/41.73  | | | | | | | | | | | |            inconsistent by sub-proof #1109.
% 230.38/41.73  | | | | | | | | | | | | 
% 230.38/41.73  | | | | | | | | | | | End of split
% 230.38/41.73  | | | | | | | | | | | 
% 230.38/41.73  | | | | | | | | | | End of split
% 230.38/41.73  | | | | | | | | | | 
% 230.38/41.73  | | | | | | | | | End of split
% 230.38/41.73  | | | | | | | | | 
% 230.38/41.73  | | | | | | | | Case 2:
% 230.38/41.73  | | | | | | | | | 
% 230.38/41.73  | | | | | | | | |   (193)  all_57_15 = e1 & op(e0, e0) = e1
% 230.38/41.73  | | | | | | | | | 
% 230.38/41.73  | | | | | | | | | ALPHA: (193) implies:
% 230.38/41.73  | | | | | | | | |   (194)  op(e0, e0) = e1
% 230.38/41.73  | | | | | | | | | 
% 230.38/41.73  | | | | | | | | | REF_CLOSE: (9), (11), (52), (194) are inconsistent by
% 230.38/41.73  | | | | | | | | |            sub-proof #2183.
% 230.38/41.73  | | | | | | | | | 
% 230.38/41.73  | | | | | | | | End of split
% 230.38/41.73  | | | | | | | | 
% 230.38/41.73  | | | | | | | End of split
% 230.38/41.73  | | | | | | | 
% 230.38/41.73  | | | | | | End of split
% 230.38/41.73  | | | | | | 
% 230.38/41.73  | | | | | Case 2:
% 230.38/41.73  | | | | | | 
% 230.38/41.73  | | | | | |   (195)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 &
% 230.38/41.73  | | | | | |            op(e0, e3) = e1)
% 230.38/41.73  | | | | | | 
% 230.38/41.73  | | | | | | REF_CLOSE: (4), (11), (21), (48), (50), (79), (195) are inconsistent
% 230.38/41.73  | | | | | |            by sub-proof #1118.
% 230.38/41.73  | | | | | | 
% 230.38/41.73  | | | | | End of split
% 230.38/41.73  | | | | | 
% 230.38/41.73  | | | | End of split
% 230.38/41.73  | | | | 
% 230.38/41.73  | | | End of split
% 230.38/41.73  | | | 
% 230.38/41.73  | | Case 2:
% 230.38/41.73  | | | 
% 230.38/41.73  | | |   (196)  all_57_7 = e0 & op(e1, e2) = e0
% 230.38/41.73  | | | 
% 230.38/41.73  | | | REF_CLOSE: (33), (59), (196) are inconsistent by sub-proof #2042.
% 230.38/41.73  | | | 
% 230.38/41.73  | | End of split
% 230.38/41.73  | | 
% 230.38/41.73  | Case 2:
% 230.38/41.73  | | 
% 230.38/41.73  | |   (197)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 230.38/41.73  | |            e0)
% 230.38/41.73  | | 
% 230.38/41.73  | | REF_CLOSE: (11), (40), (43), (46), (50), (197) are inconsistent by sub-proof
% 230.38/41.73  | |            #1108.
% 230.38/41.73  | | 
% 230.38/41.73  | End of split
% 230.38/41.73  | 
% 230.38/41.73  End of proof
% 230.38/41.73  
% 230.38/41.73  Sub-proof #1108 shows that the following formulas are inconsistent:
% 230.38/41.73  ----------------------------------------------------------------
% 230.38/41.73    (1)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.38/41.73    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.38/41.73           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.38/41.73    (3)  all_57_11 = e2
% 230.38/41.73    (4)  op(e1, e1) = e1
% 230.38/41.73    (5)   ~ (e2 = e0)
% 230.38/41.73    (6)   ~ (e1 = e0)
% 230.38/41.73  
% 230.38/41.73  Begin of proof
% 230.38/41.73  | 
% 230.38/41.73  | BETA: splitting (1) gives:
% 230.38/41.73  | 
% 230.38/41.73  | Case 1:
% 230.38/41.73  | | 
% 230.38/41.73  | |   (7)  all_57_8 = e0 & op(e1, e1) = e0
% 230.38/41.73  | | 
% 230.38/41.73  | | ALPHA: (7) implies:
% 230.38/41.73  | |   (8)  op(e1, e1) = e0
% 230.38/41.73  | | 
% 230.38/41.73  | | REF_CLOSE: (2), (4), (6), (8) are inconsistent by sub-proof #2427.
% 230.38/41.73  | | 
% 230.38/41.73  | Case 2:
% 230.38/41.73  | | 
% 230.38/41.73  | |   (9)  all_57_11 = e0 & op(e1, e0) = e0
% 230.38/41.73  | | 
% 230.38/41.73  | | ALPHA: (9) implies:
% 230.38/41.73  | |   (10)  all_57_11 = e0
% 230.38/41.73  | | 
% 230.38/41.73  | | REF_CLOSE: (3), (5), (10) are inconsistent by sub-proof #1949.
% 230.38/41.73  | | 
% 230.38/41.73  | End of split
% 230.38/41.73  | 
% 230.38/41.73  End of proof
% 230.38/41.73  
% 230.38/41.73  Sub-proof #1109 shows that the following formulas are inconsistent:
% 230.38/41.73  ----------------------------------------------------------------
% 230.38/41.73    (1)   ~ (e3 = e1)
% 230.38/41.73    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.38/41.73           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.38/41.73    (3)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.38/41.73    (4)  all_57_11 = e2
% 230.38/41.73    (5)  op(e0, e0) = e3
% 230.38/41.73    (6)   ~ (e2 = e1)
% 230.38/41.73  
% 230.38/41.73  Begin of proof
% 230.38/41.73  | 
% 230.38/41.73  | BETA: splitting (3) gives:
% 230.38/41.73  | 
% 230.38/41.73  | Case 1:
% 230.38/41.73  | | 
% 230.38/41.73  | |   (7)  all_57_11 = e1 & op(e1, e0) = e1
% 230.38/41.73  | | 
% 230.38/41.73  | | REF_CLOSE: (4), (6), (7) are inconsistent by sub-proof #1726.
% 230.38/41.73  | | 
% 230.38/41.73  | Case 2:
% 230.38/41.73  | | 
% 230.38/41.73  | |   (8)  all_57_15 = e1 & op(e0, e0) = e1
% 230.38/41.73  | | 
% 230.38/41.73  | | ALPHA: (8) implies:
% 230.38/41.73  | |   (9)  op(e0, e0) = e1
% 230.38/41.73  | | 
% 230.38/41.73  | | REF_CLOSE: (1), (2), (5), (9) are inconsistent by sub-proof #2183.
% 230.38/41.73  | | 
% 230.38/41.73  | End of split
% 230.38/41.73  | 
% 230.38/41.73  End of proof
% 230.38/41.73  
% 230.38/41.73  Sub-proof #1110 shows that the following formulas are inconsistent:
% 230.38/41.73  ----------------------------------------------------------------
% 230.38/41.73    (1)  all_57_10 = e0
% 230.38/41.73    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.38/41.73         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.38/41.73    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.38/41.73         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.38/41.73    (4)   ~ (e3 = e1)
% 230.38/41.73    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.38/41.73           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.38/41.73    (6)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.38/41.73         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.38/41.73    (7)   ~ (all_6_2 = e3)
% 230.38/41.73    (8)  op(e1, e1) = all_6_2
% 230.38/41.73    (9)  all_57_9 = e1
% 230.38/41.73    (10)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.38/41.73          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.38/41.73    (11)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 230.38/41.73          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.38/41.73    (12)   ~ (e3 = e2)
% 230.38/41.73    (13)   ~ (e3 = e0)
% 230.38/41.73    (14)  all_57_6 = e0
% 230.38/41.73    (15)  all_57_15 = e3
% 230.38/41.73    (16)  all_57_5 = e3
% 230.38/41.73    (17)  op(e1, e1) = e1
% 230.38/41.73    (18)   ~ (e2 = e0)
% 230.38/41.73    (19)   ~ (e1 = e0)
% 230.38/41.73    (20)  all_57_4 = e2 & op(e3, e1) = e2
% 230.38/41.73    (21)  all_57_14 = e1
% 230.38/41.73    (22)  all_57_2 = e1
% 230.38/41.73    (23)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.38/41.73              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.38/41.73                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.38/41.73                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.38/41.73    (24)  all_57_7 = e3
% 230.38/41.73    (25)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.38/41.73          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.38/41.73    (26)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.38/41.73          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.38/41.73    (27)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.38/41.73          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 230.38/41.73    (28)   ~ (e2 = e1)
% 230.38/41.73    (29)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.38/41.73          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.38/41.73    (30)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.38/41.73          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.38/41.73    (31)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.38/41.73          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.38/41.73    (32)  all_57_3 = e2
% 230.38/41.73    (33)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.38/41.73          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.38/41.73  
% 230.38/41.73  Begin of proof
% 230.38/41.73  | 
% 230.38/41.73  | ALPHA: (20) implies:
% 230.38/41.73  |   (34)  all_57_4 = e2
% 230.38/41.73  | 
% 230.38/41.73  | BETA: splitting (10) gives:
% 230.38/41.73  | 
% 230.38/41.73  | Case 1:
% 230.38/41.73  | | 
% 230.38/41.73  | |   (35)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) =
% 230.38/41.73  | |           e0)
% 230.38/41.73  | | 
% 230.38/41.73  | | BETA: splitting (35) gives:
% 230.38/41.73  | | 
% 230.38/41.73  | | Case 1:
% 230.38/41.73  | | | 
% 230.38/41.73  | | |   (36)  all_57_0 = e0 & op(e3, e3) = e0
% 230.38/41.73  | | | 
% 230.38/41.73  | | | ALPHA: (36) implies:
% 230.38/41.73  | | |   (37)  op(e3, e3) = e0
% 230.38/41.73  | | | 
% 230.38/41.73  | | | REF_CLOSE: (4), (5), (12), (13), (14), (18), (22), (26), (28), (30), (37)
% 230.38/41.73  | | |            are inconsistent by sub-proof #2390.
% 230.38/41.73  | | | 
% 230.38/41.73  | | Case 2:
% 230.38/41.73  | | | 
% 230.38/41.73  | | |   (38)  all_57_1 = e0 & op(e3, e2) = e0
% 230.38/41.73  | | | 
% 230.38/41.73  | | | ALPHA: (38) implies:
% 230.38/41.73  | | |   (39)  all_57_1 = e0
% 230.38/41.73  | | | 
% 230.38/41.73  | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (11), (12), (13), (14), (15),
% 230.38/41.73  | | |            (16), (17), (18), (19), (21), (22), (23), (24), (25), (27),
% 230.38/41.73  | | |            (28), (29), (31), (32), (33), (34), (39) are inconsistent by
% 230.38/41.73  | | |            sub-proof #1112.
% 230.38/41.73  | | | 
% 230.38/41.73  | | End of split
% 230.38/41.73  | | 
% 230.38/41.73  | Case 2:
% 230.38/41.73  | | 
% 230.38/41.73  | |   (40)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) =
% 230.38/41.73  | |           e0)
% 230.38/41.73  | | 
% 230.38/41.73  | | BETA: splitting (40) gives:
% 230.38/41.73  | | 
% 230.38/41.73  | | Case 1:
% 230.38/41.73  | | | 
% 230.38/41.73  | | |   (41)  all_57_4 = e0 & op(e3, e1) = e0
% 230.38/41.73  | | | 
% 230.38/41.73  | | | ALPHA: (41) implies:
% 230.38/41.73  | | |   (42)  all_57_4 = e0
% 230.38/41.73  | | | 
% 230.38/41.73  | | | COMBINE_EQS: (34), (42) imply:
% 230.38/41.73  | | |   (43)  e2 = e0
% 230.38/41.73  | | | 
% 230.38/41.73  | | | COMBINE_EQS: (32), (43) imply:
% 230.38/41.73  | | |   (44)  all_57_3 = e0
% 230.38/41.73  | | | 
% 230.38/41.73  | | | REF_CLOSE: (1), (2), (4), (12), (16), (18), (19), (25), (28), (44) are
% 230.38/41.73  | | |            inconsistent by sub-proof #1518.
% 230.38/41.73  | | | 
% 230.38/41.73  | | Case 2:
% 230.38/41.73  | | | 
% 230.38/41.73  | | |   (45)  all_57_9 = e0 & op(e3, e0) = e0
% 230.38/41.73  | | | 
% 230.38/41.73  | | | REF_CLOSE: (9), (19), (45) are inconsistent by sub-proof #1990.
% 230.38/41.73  | | | 
% 230.38/41.73  | | End of split
% 230.38/41.73  | | 
% 230.38/41.73  | End of split
% 230.38/41.73  | 
% 230.38/41.73  End of proof
% 230.38/41.73  
% 230.38/41.73  Sub-proof #1111 shows that the following formulas are inconsistent:
% 230.38/41.73  ----------------------------------------------------------------
% 230.38/41.73    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.38/41.73         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.38/41.73    (2)   ~ (e3 = e1)
% 230.38/41.73    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.38/41.73           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.38/41.73    (4)  all_57_4 = e2
% 230.38/41.73    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.38/41.73         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.38/41.73    (6)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.38/41.73         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.38/41.73    (7)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.38/41.73         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.38/41.73    (8)   ~ (e3 = e2)
% 230.38/41.73    (9)   ~ (e3 = e0)
% 230.38/41.73    (10)  op(e3, e3) = e3
% 230.38/41.73    (11)  all_57_15 = e3
% 230.38/41.73    (12)  all_57_5 = e3
% 230.38/41.73    (13)  all_57_11 = e2
% 230.38/41.73    (14)   ~ (e2 = e0)
% 230.38/41.73    (15)  e2 = e0
% 230.38/41.73    (16)   ~ (e1 = e0)
% 230.38/41.73    (17)  all_57_7 = e3
% 230.38/41.73    (18)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.38/41.73          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.38/41.73    (19)   ~ (e2 = e1)
% 230.38/41.73    (20)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.38/41.73          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.38/41.73    (21)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.38/41.73          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.38/41.73    (22)  all_57_3 = e2
% 230.38/41.73    (23)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.38/41.73          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.38/41.73  
% 230.38/41.73  Begin of proof
% 230.38/41.73  | 
% 230.38/41.73  | COMBINE_EQS: (13), (15) imply:
% 230.38/41.73  |   (24)  all_57_11 = e0
% 230.38/41.73  | 
% 230.38/41.73  | COMBINE_EQS: (15), (22) imply:
% 230.38/41.73  |   (25)  all_57_3 = e0
% 230.38/41.73  | 
% 230.38/41.73  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 230.38/41.73  |            (14), (16), (17), (18), (19), (20), (21), (23), (24), (25) are
% 230.38/41.73  |            inconsistent by sub-proof #1480.
% 230.38/41.73  | 
% 230.38/41.73  End of proof
% 230.38/41.73  
% 230.38/41.73  Sub-proof #1112 shows that the following formulas are inconsistent:
% 230.38/41.73  ----------------------------------------------------------------
% 230.38/41.73    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.38/41.73         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.38/41.73    (2)   ~ (e3 = e1)
% 230.38/41.73    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.38/41.73           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.38/41.73    (4)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.38/41.73         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.38/41.73    (5)   ~ (all_6_2 = e3)
% 230.38/41.73    (6)  op(e1, e1) = all_6_2
% 230.38/41.73    (7)  all_57_4 = e2
% 230.38/41.73    (8)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 230.38/41.73         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.38/41.73    (9)   ~ (e3 = e2)
% 230.38/41.73    (10)   ~ (e3 = e0)
% 230.38/41.73    (11)  all_57_6 = e0
% 230.38/41.73    (12)  all_57_1 = e0
% 230.38/41.73    (13)  all_57_15 = e3
% 230.38/41.73    (14)  all_57_5 = e3
% 230.38/41.73    (15)  op(e1, e1) = e1
% 230.38/41.73    (16)   ~ (e2 = e0)
% 230.38/41.73    (17)   ~ (e1 = e0)
% 230.38/41.73    (18)  all_57_14 = e1
% 230.38/41.73    (19)  all_57_2 = e1
% 230.38/41.73    (20)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.38/41.73              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.38/41.73                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.38/41.73                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.38/41.73    (21)  all_57_7 = e3
% 230.38/41.73    (22)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.38/41.73          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.38/41.73    (23)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.38/41.73          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 230.38/41.73    (24)   ~ (e2 = e1)
% 230.38/41.73    (25)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.38/41.73          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.38/41.73    (26)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.38/41.73          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.38/41.73    (27)  all_57_3 = e2
% 230.38/41.73    (28)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.38/41.73          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.38/41.73  
% 230.38/41.73  Begin of proof
% 230.38/41.73  | 
% 230.38/41.73  | BETA: splitting (28) gives:
% 230.38/41.73  | 
% 230.38/41.73  | Case 1:
% 230.38/41.73  | | 
% 230.38/41.73  | |   (29)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) =
% 230.38/41.73  | |           e1)
% 230.38/41.73  | | 
% 230.38/41.73  | | BETA: splitting (29) gives:
% 230.38/41.73  | | 
% 230.38/41.73  | | Case 1:
% 230.38/41.73  | | | 
% 230.38/41.73  | | |   (30)  all_57_1 = e1 & op(e3, e2) = e1
% 230.38/41.73  | | | 
% 230.38/41.73  | | | REF_CLOSE: (12), (17), (30) are inconsistent by sub-proof #2446.
% 230.38/41.73  | | | 
% 230.38/41.73  | | Case 2:
% 230.38/41.73  | | | 
% 230.38/41.73  | | |   (31)  all_57_3 = e1 & op(e2, e2) = e1
% 230.38/41.73  | | | 
% 230.38/41.73  | | | ALPHA: (31) implies:
% 230.38/41.73  | | |   (32)  op(e2, e2) = e1
% 230.38/41.73  | | | 
% 230.38/41.73  | | | REF_CLOSE: (3), (9), (10), (14), (16), (17), (19), (22), (23), (24), (32)
% 230.38/41.73  | | |            are inconsistent by sub-proof #1825.
% 230.38/41.73  | | | 
% 230.38/41.73  | | End of split
% 230.38/41.73  | | 
% 230.38/41.73  | Case 2:
% 230.38/41.73  | | 
% 230.38/41.73  | |   (33)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 230.38/41.73  | |           e1)
% 230.38/41.73  | | 
% 230.38/41.73  | | BETA: splitting (33) gives:
% 230.38/41.73  | | 
% 230.38/41.73  | | Case 1:
% 230.38/41.73  | | | 
% 230.38/41.73  | | |   (34)  all_57_7 = e1 & op(e1, e2) = e1
% 230.38/41.73  | | | 
% 230.38/41.73  | | | ALPHA: (34) implies:
% 230.38/41.73  | | |   (35)  all_57_7 = e1
% 230.38/41.73  | | | 
% 230.38/41.73  | | | REF_CLOSE: (2), (3), (4), (5), (6), (9), (10), (11), (13), (16), (17),
% 230.38/41.73  | | |            (20), (24), (25), (26), (35) are inconsistent by sub-proof
% 230.38/41.73  | | |            #1157.
% 230.38/41.73  | | | 
% 230.38/41.73  | | Case 2:
% 230.38/41.73  | | | 
% 230.38/41.73  | | |   (36)  all_57_13 = e1 & op(e0, e2) = e1
% 230.38/41.73  | | | 
% 230.38/41.73  | | | ALPHA: (36) implies:
% 230.38/41.73  | | |   (37)  all_57_13 = e1
% 230.38/41.73  | | | 
% 230.38/41.73  | | | BETA: splitting (8) gives:
% 230.38/41.73  | | | 
% 230.38/41.73  | | | Case 1:
% 230.38/41.73  | | | | 
% 230.38/41.73  | | | |   (38)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1)
% 230.38/41.73  | | | |           = e0)
% 230.38/41.73  | | | | 
% 230.38/41.73  | | | | BETA: splitting (38) gives:
% 230.38/41.73  | | | | 
% 230.38/41.73  | | | | Case 1:
% 230.38/41.73  | | | | | 
% 230.38/41.73  | | | | |   (39)  all_57_4 = e0 & op(e3, e1) = e0
% 230.38/41.73  | | | | | 
% 230.38/41.73  | | | | | ALPHA: (39) implies:
% 230.38/41.73  | | | | |   (40)  all_57_4 = e0
% 230.38/41.73  | | | | | 
% 230.38/41.73  | | | | | COMBINE_EQS: (7), (40) imply:
% 230.38/41.73  | | | | |   (41)  e2 = e0
% 230.38/41.73  | | | | | 
% 230.38/41.73  | | | | | COMBINE_EQS: (27), (41) imply:
% 230.38/41.73  | | | | |   (42)  all_57_3 = e0
% 230.38/41.73  | | | | | 
% 230.38/41.73  | | | | | REF_CLOSE: (1), (9), (12), (16), (21), (24), (37), (42) are
% 230.38/41.73  | | | | |            inconsistent by sub-proof #2099.
% 230.38/41.73  | | | | | 
% 230.38/41.73  | | | | Case 2:
% 230.38/41.73  | | | | | 
% 230.38/41.73  | | | | |   (43)  all_57_5 = e0 & op(e2, e1) = e0
% 230.38/41.73  | | | | | 
% 230.38/41.73  | | | | | REF_CLOSE: (10), (14), (43) are inconsistent by sub-proof #2414.
% 230.38/41.73  | | | | | 
% 230.38/41.73  | | | | End of split
% 230.38/41.73  | | | | 
% 230.38/41.73  | | | Case 2:
% 230.38/41.73  | | | | 
% 230.38/41.73  | | | |   (44)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1)
% 230.38/41.73  | | | |           = e0)
% 230.38/41.73  | | | | 
% 230.38/41.73  | | | | BETA: splitting (44) gives:
% 230.38/41.73  | | | | 
% 230.38/41.73  | | | | Case 1:
% 230.38/41.73  | | | | | 
% 230.38/41.73  | | | | |   (45)  all_57_8 = e0 & op(e1, e1) = e0
% 230.38/41.73  | | | | | 
% 230.38/41.73  | | | | | ALPHA: (45) implies:
% 230.38/41.73  | | | | |   (46)  op(e1, e1) = e0
% 230.38/41.73  | | | | | 
% 230.38/41.73  | | | | | REF_CLOSE: (3), (15), (17), (46) are inconsistent by sub-proof #2427.
% 230.38/41.73  | | | | | 
% 230.38/41.73  | | | | Case 2:
% 230.38/41.73  | | | | | 
% 230.38/41.73  | | | | |   (47)  all_57_14 = e0 & op(e0, e1) = e0
% 230.38/41.73  | | | | | 
% 230.38/41.73  | | | | | ALPHA: (47) implies:
% 230.38/41.73  | | | | |   (48)  all_57_14 = e0
% 230.38/41.73  | | | | | 
% 230.38/41.73  | | | | | REF_CLOSE: (17), (18), (48) are inconsistent by sub-proof #2122.
% 230.38/41.73  | | | | | 
% 230.38/41.73  | | | | End of split
% 230.38/41.73  | | | | 
% 230.38/41.73  | | | End of split
% 230.38/41.73  | | | 
% 230.38/41.73  | | End of split
% 230.38/41.73  | | 
% 230.38/41.73  | End of split
% 230.38/41.73  | 
% 230.38/41.73  End of proof
% 230.38/41.73  
% 230.38/41.73  Sub-proof #1113 shows that the following formulas are inconsistent:
% 230.38/41.73  ----------------------------------------------------------------
% 230.38/41.73    (1)  all_57_13 = e1
% 230.38/41.73    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.38/41.73         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.38/41.73    (3)   ~ (e3 = e2)
% 230.38/41.73    (4)  all_57_1 = e0
% 230.38/41.73    (5)   ~ (e2 = e0)
% 230.38/41.73    (6)  all_57_1 = e2 & op(e3, e2) = e2
% 230.38/41.73    (7)  all_57_7 = e3
% 230.38/41.73    (8)   ~ (e2 = e1)
% 230.38/41.73    (9)  all_57_3 = e2
% 230.38/41.73  
% 230.38/41.73  Begin of proof
% 230.38/41.73  | 
% 230.38/41.73  | ALPHA: (6) implies:
% 230.38/41.73  |   (10)  all_57_1 = e2
% 230.38/41.73  | 
% 230.38/41.73  | COMBINE_EQS: (4), (10) imply:
% 230.38/41.73  |   (11)  e2 = e0
% 230.38/41.73  | 
% 230.38/41.73  | SIMP: (11) implies:
% 230.38/41.73  |   (12)  e2 = e0
% 230.38/41.73  | 
% 230.38/41.73  | COMBINE_EQS: (9), (12) imply:
% 230.38/41.73  |   (13)  all_57_3 = e0
% 230.38/41.73  | 
% 230.38/41.73  | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (13) are inconsistent by
% 230.38/41.73  |            sub-proof #2099.
% 230.38/41.73  | 
% 230.38/41.73  End of proof
% 230.38/41.73  
% 230.38/41.73  Sub-proof #1114 shows that the following formulas are inconsistent:
% 230.38/41.73  ----------------------------------------------------------------
% 230.38/41.73    (1)  op(e0, e1) = all_53_11
% 230.38/41.73    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 230.38/41.73    (3)  op(e1, e0) = e2
% 230.38/41.73    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.38/41.73           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.38/41.73    (5)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 230.38/41.73           op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 230.38/41.73             e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 230.38/41.73    (6)   ~ (all_6_2 = e3)
% 230.38/41.73    (7)  op(e1, e1) = all_6_2
% 230.38/41.73    (8)  all_34_2 = all_6_2
% 230.38/41.73    (9)   ~ (all_53_9 = all_53_11)
% 230.38/41.73    (10)   ~ (all_53_9 = all_6_2)
% 230.38/41.73    (11)   ~ (all_53_14 = all_6_2)
% 230.38/41.73    (12)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 230.38/41.73    (13)  op(e1, e0) = all_53_14
% 230.38/41.73    (14)  op(e3, e3) = e2
% 230.38/41.73    (15)   ~ (all_53_14 = e3)
% 230.38/41.73    (16)  all_55_6 = all_53_9
% 230.38/41.73    (17)   ~ (e2 = e0)
% 230.38/41.73    (18)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 230.38/41.73            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 230.38/41.73            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 230.38/41.73            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 230.38/41.73              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 230.38/41.73            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 230.38/41.73            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 230.38/41.73              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 230.38/41.73              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 230.38/41.73            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 230.38/41.73            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 230.38/41.73            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 230.38/41.73              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 230.38/41.73              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 230.38/41.73            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 230.38/41.73              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 230.38/41.73            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 230.38/41.73            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 230.38/41.73              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 230.38/41.73              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 230.38/41.73            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 230.38/41.73            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 230.38/41.73    (19)  op(e2, e2) = e2
% 230.38/41.73    (20)  op(e0, e0) = e3
% 230.38/41.74    (21)  all_55_10 = all_6_2
% 230.38/41.74    (22)  op(e0, e1) = e2
% 230.38/41.74    (23)  op(e2, e1) = all_53_9
% 230.38/41.74    (24)  all_24_2 = all_6_2
% 230.38/41.74    (25)   ~ (all_34_2 = e0) | ( ~ (all_34_0 = e3) & op(all_34_1, e1) = all_34_0 &
% 230.38/41.74            op(e1, e0) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 230.38/41.74              e2) & op(e1, e0) = all_34_1 & $i(all_34_1))
% 230.38/41.74  
% 230.38/41.74  Begin of proof
% 230.38/41.74  | 
% 230.38/41.74  | GROUND_INST: instantiating (4) with all_53_11, e2, e1, e0, simplifying with
% 230.38/41.74  |              (1), (22) gives:
% 230.38/41.74  |   (26)  all_53_11 = e2
% 230.38/41.74  | 
% 230.38/41.74  | GROUND_INST: instantiating (4) with all_53_14, e2, e0, e1, simplifying with
% 230.38/41.74  |              (3), (13) gives:
% 230.38/41.74  |   (27)  all_53_14 = e2
% 230.38/41.74  | 
% 230.38/41.74  | REDUCE: (9), (26) imply:
% 230.38/41.74  |   (28)   ~ (all_53_9 = e2)
% 230.38/41.74  | 
% 230.38/41.74  | REDUCE: (11), (27) imply:
% 230.38/41.74  |   (29)   ~ (all_6_2 = e2)
% 230.38/41.74  | 
% 230.38/41.74  | SIMP: (29) implies:
% 230.38/41.74  |   (30)   ~ (all_6_2 = e2)
% 230.38/41.74  | 
% 230.38/41.74  | REDUCE: (15), (27) imply:
% 230.38/41.74  |   (31)   ~ (e3 = e2)
% 230.38/41.74  | 
% 230.38/41.74  | SIMP: (31) implies:
% 230.38/41.74  |   (32)   ~ (e3 = e2)
% 230.38/41.74  | 
% 230.38/41.74  | BETA: splitting (18) gives:
% 230.38/41.74  | 
% 230.38/41.74  | Case 1:
% 230.38/41.74  | | 
% 230.38/41.74  | |   (33)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 230.38/41.74  | |           op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 230.38/41.74  | |           op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3,
% 230.38/41.74  | |             e3) = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 &
% 230.38/41.74  | |           op(e3, e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5)
% 230.38/41.74  | |           & $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1
% 230.38/41.74  | |           & all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 230.38/41.74  | |             all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 230.38/41.74  | |             all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11
% 230.38/41.74  | |           & op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 230.38/41.74  | |           $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 230.38/41.74  | | 
% 230.38/41.74  | | BETA: splitting (33) gives:
% 230.38/41.74  | | 
% 230.38/41.74  | | Case 1:
% 230.38/41.74  | | | 
% 230.38/41.74  | | |   (34)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 230.38/41.74  | | |         op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 230.38/41.74  | | |         op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3,
% 230.38/41.74  | | |           e3) = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 &
% 230.38/41.74  | | |         op(e3, e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5)
% 230.38/41.74  | | |         & $i(all_52_7)
% 230.38/41.74  | | | 
% 230.38/41.74  | | | ALPHA: (34) implies:
% 230.38/41.74  | | |   (35)  op(e3, e3) = all_52_1
% 230.38/41.74  | | |   (36)  op(all_52_1, all_52_1) = e3
% 230.38/41.74  | | | 
% 230.38/41.74  | | | REF_CLOSE: (4), (14), (19), (32), (35), (36) are inconsistent by sub-proof
% 230.38/41.74  | | |            #1951.
% 230.38/41.74  | | | 
% 230.38/41.74  | | Case 2:
% 230.38/41.74  | | | 
% 230.38/41.74  | | |   (37)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0 &
% 230.38/41.74  | | |         op(all_52_9, all_52_9) = e3 & op(all_52_11, all_52_11) = e2 &
% 230.38/41.74  | | |         op(all_52_13, all_52_13) = e1 & op(all_52_15, all_52_15) = e0 &
% 230.38/41.74  | | |         op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 & op(e2, e1) =
% 230.38/41.74  | | |         all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) & $i(all_52_11)
% 230.38/41.74  | | |         & $i(all_52_13) & $i(all_52_15)
% 230.38/41.74  | | | 
% 230.38/41.74  | | | ALPHA: (37) implies:
% 230.38/41.74  | | |   (38)  op(e2, e1) = all_52_13
% 230.38/41.74  | | |   (39)  op(all_52_13, all_52_13) = e1
% 230.38/41.74  | | | 
% 230.38/41.74  | | | GROUND_INST: instantiating (4) with all_53_9, all_52_13, e1, e2,
% 230.38/41.74  | | |              simplifying with (23), (38) gives:
% 230.38/41.74  | | |   (40)  all_53_9 = all_52_13
% 230.38/41.74  | | | 
% 230.38/41.74  | | | COMBINE_EQS: (16), (40) imply:
% 230.38/41.74  | | |   (41)  all_55_6 = all_52_13
% 230.38/41.74  | | | 
% 230.38/41.74  | | | REDUCE: (10), (40) imply:
% 230.38/41.74  | | |   (42)   ~ (all_52_13 = all_6_2)
% 230.38/41.74  | | | 
% 230.38/41.74  | | | REDUCE: (28), (40) imply:
% 230.38/41.74  | | |   (43)   ~ (all_52_13 = e2)
% 230.38/41.74  | | | 
% 230.38/41.74  | | | BETA: splitting (5) gives:
% 230.38/41.74  | | | 
% 230.38/41.74  | | | Case 1:
% 230.38/41.74  | | | | 
% 230.38/41.74  | | | |   (44)   ~ (all_24_2 = e0)
% 230.38/41.74  | | | | 
% 230.38/41.74  | | | | REDUCE: (24), (44) imply:
% 230.38/41.74  | | | |   (45)   ~ (all_6_2 = e0)
% 230.38/41.74  | | | | 
% 230.38/41.74  | | | | BETA: splitting (2) gives:
% 230.38/41.74  | | | | 
% 230.38/41.74  | | | | Case 1:
% 230.38/41.74  | | | | | 
% 230.38/41.74  | | | | |   (46)  all_55_10 = e3
% 230.38/41.74  | | | | | 
% 230.38/41.74  | | | | | REF_CLOSE: (6), (21), (46) are inconsistent by sub-proof #2500.
% 230.38/41.74  | | | | | 
% 230.38/41.74  | | | | Case 2:
% 230.38/41.74  | | | | | 
% 230.38/41.74  | | | | |   (47)   ~ (all_55_10 = e3)
% 230.38/41.74  | | | | |   (48)  all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 230.38/41.74  | | | | | 
% 230.38/41.74  | | | | | BETA: splitting (48) gives:
% 230.38/41.74  | | | | | 
% 230.38/41.74  | | | | | Case 1:
% 230.38/41.74  | | | | | | 
% 230.38/41.74  | | | | | |   (49)  all_55_10 = e2
% 230.38/41.74  | | | | | | 
% 230.38/41.74  | | | | | | REF_CLOSE: (21), (30), (49) are inconsistent by sub-proof #2499.
% 230.38/41.74  | | | | | | 
% 230.38/41.74  | | | | | Case 2:
% 230.38/41.74  | | | | | | 
% 230.38/41.74  | | | | | |   (50)   ~ (all_55_10 = e2)
% 230.38/41.74  | | | | | |   (51)  all_55_10 = e1 | all_55_10 = e0
% 230.38/41.74  | | | | | | 
% 230.38/41.74  | | | | | | BETA: splitting (51) gives:
% 230.38/41.74  | | | | | | 
% 230.38/41.74  | | | | | | Case 1:
% 230.38/41.74  | | | | | | | 
% 230.38/41.74  | | | | | | |   (52)  all_55_10 = e1
% 230.38/41.74  | | | | | | | 
% 230.38/41.74  | | | | | | | COMBINE_EQS: (21), (52) imply:
% 230.38/41.74  | | | | | | |   (53)  all_6_2 = e1
% 230.38/41.74  | | | | | | | 
% 230.38/41.74  | | | | | | | SIMP: (53) implies:
% 230.38/41.74  | | | | | | |   (54)  all_6_2 = e1
% 230.38/41.74  | | | | | | | 
% 230.38/41.74  | | | | | | | REDUCE: (42), (54) imply:
% 230.38/41.74  | | | | | | |   (55)   ~ (all_52_13 = e1)
% 230.38/41.74  | | | | | | | 
% 230.38/41.74  | | | | | | | REDUCE: (6), (54) imply:
% 230.38/41.74  | | | | | | |   (56)   ~ (e3 = e1)
% 230.38/41.74  | | | | | | | 
% 230.38/41.74  | | | | | | | SIMP: (56) implies:
% 230.38/41.74  | | | | | | |   (57)   ~ (e3 = e1)
% 230.38/41.74  | | | | | | | 
% 230.38/41.74  | | | | | | | REDUCE: (30), (54) imply:
% 230.38/41.74  | | | | | | |   (58)   ~ (e2 = e1)
% 230.38/41.74  | | | | | | | 
% 230.38/41.74  | | | | | | | SIMP: (58) implies:
% 230.38/41.74  | | | | | | |   (59)   ~ (e2 = e1)
% 230.38/41.74  | | | | | | | 
% 230.38/41.74  | | | | | | | BETA: splitting (12) gives:
% 230.38/41.74  | | | | | | | 
% 230.38/41.74  | | | | | | | Case 1:
% 230.38/41.74  | | | | | | | | 
% 230.38/41.74  | | | | | | | |   (60)  all_55_6 = e3
% 230.38/41.74  | | | | | | | | 
% 230.38/41.74  | | | | | | | | COMBINE_EQS: (41), (60) imply:
% 230.38/41.74  | | | | | | | |   (61)  all_52_13 = e3
% 230.38/41.74  | | | | | | | | 
% 230.38/41.74  | | | | | | | | REDUCE: (39), (61) imply:
% 230.38/41.74  | | | | | | | |   (62)  op(e3, e3) = e1
% 230.38/41.74  | | | | | | | | 
% 230.38/41.74  | | | | | | | | REF_CLOSE: (4), (14), (59), (62) are inconsistent by sub-proof
% 230.38/41.74  | | | | | | | |            #1950.
% 230.38/41.74  | | | | | | | | 
% 230.38/41.74  | | | | | | | Case 2:
% 230.38/41.74  | | | | | | | | 
% 230.38/41.74  | | | | | | | |   (63)  all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 230.38/41.74  | | | | | | | | 
% 230.38/41.74  | | | | | | | | REF_CLOSE: (4), (20), (39), (41), (43), (55), (57), (63) are
% 230.38/41.74  | | | | | | | |            inconsistent by sub-proof #1116.
% 230.38/41.74  | | | | | | | | 
% 230.38/41.74  | | | | | | | End of split
% 230.38/41.74  | | | | | | | 
% 230.38/41.74  | | | | | | Case 2:
% 230.38/41.74  | | | | | | | 
% 230.38/41.74  | | | | | | |   (64)  all_55_10 = e0
% 230.38/41.74  | | | | | | | 
% 230.38/41.74  | | | | | | | REF_CLOSE: (21), (45), (64) are inconsistent by sub-proof #2118.
% 230.38/41.74  | | | | | | | 
% 230.38/41.74  | | | | | | End of split
% 230.38/41.74  | | | | | | 
% 230.38/41.74  | | | | | End of split
% 230.38/41.74  | | | | | 
% 230.38/41.74  | | | | End of split
% 230.38/41.74  | | | | 
% 230.38/41.74  | | | Case 2:
% 230.38/41.74  | | | | 
% 230.38/41.74  | | | |   (65)  all_24_2 = e0
% 230.38/41.74  | | | |   (66)  ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 & op(e1, e0) =
% 230.38/41.74  | | | |           all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 = e3)
% 230.38/41.74  | | | |           & op(e1, e0) = all_24_1 & $i(all_24_1))
% 230.38/41.74  | | | | 
% 230.38/41.74  | | | | COMBINE_EQS: (24), (65) imply:
% 230.38/41.74  | | | |   (67)  all_6_2 = e0
% 230.38/41.74  | | | | 
% 230.38/41.74  | | | | COMBINE_EQS: (8), (67) imply:
% 230.38/41.74  | | | |   (68)  all_34_2 = e0
% 230.38/41.74  | | | | 
% 230.38/41.74  | | | | REDUCE: (42), (67) imply:
% 230.38/41.74  | | | |   (69)   ~ (all_52_13 = e0)
% 230.38/41.74  | | | | 
% 230.38/41.74  | | | | REDUCE: (7), (67) imply:
% 230.38/41.74  | | | |   (70)  op(e1, e1) = e0
% 230.38/41.74  | | | | 
% 230.38/41.74  | | | | REF_CLOSE: (3), (4), (12), (25), (38), (39), (41), (43), (66), (68),
% 230.38/41.74  | | | |            (69), (70) are inconsistent by sub-proof #1945.
% 230.38/41.74  | | | | 
% 230.38/41.74  | | | End of split
% 230.38/41.74  | | | 
% 230.38/41.74  | | End of split
% 230.38/41.74  | | 
% 230.38/41.74  | Case 2:
% 230.38/41.74  | | 
% 230.38/41.74  | |   (71)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 &
% 230.38/41.74  | |           op(all_52_17, all_52_17) = e3 & op(all_52_19, all_52_19) = e2 &
% 230.38/41.74  | |           op(all_52_21, all_52_21) = e1 & op(all_52_23, all_52_23) = e0 &
% 230.38/41.74  | |           op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) =
% 230.38/41.74  | |           all_52_21 & op(e1, e0) = all_52_23 & $i(all_52_17) & $i(all_52_19)
% 230.38/41.74  | |           & $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3 & all_52_26 =
% 230.38/41.74  | |           e2 & all_52_28 = e1 & all_52_30 = e0 & op(all_52_25, all_52_25) =
% 230.38/41.74  | |           e3 & op(all_52_27, all_52_27) = e2 & op(all_52_29, all_52_29) = e1
% 230.38/41.74  | |           & op(all_52_31, all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0,
% 230.38/41.74  | |             e2) = all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0) =
% 230.38/41.74  | |           all_52_31 & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 230.38/41.74  | |           $i(all_52_31))
% 230.38/41.74  | | 
% 230.38/41.74  | | BETA: splitting (71) gives:
% 230.38/41.74  | | 
% 230.38/41.74  | | Case 1:
% 230.38/41.74  | | | 
% 230.38/41.74  | | |   (72)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 230.38/41.74  | | |         & op(all_52_17, all_52_17) = e3 & op(all_52_19, all_52_19) = e2 &
% 230.38/41.74  | | |         op(all_52_21, all_52_21) = e1 & op(all_52_23, all_52_23) = e0 &
% 230.38/41.74  | | |         op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) =
% 230.38/41.74  | | |         all_52_21 & op(e1, e0) = all_52_23 & $i(all_52_17) & $i(all_52_19)
% 230.38/41.74  | | |         & $i(all_52_21) & $i(all_52_23)
% 230.38/41.74  | | | 
% 230.38/41.74  | | | ALPHA: (72) implies:
% 230.38/41.74  | | |   (73)  op(e1, e0) = all_52_23
% 230.38/41.74  | | |   (74)  op(all_52_23, all_52_23) = e0
% 230.38/41.74  | | | 
% 230.38/41.74  | | | REF_CLOSE: (3), (4), (17), (19), (73), (74) are inconsistent by sub-proof
% 230.38/41.74  | | |            #2369.
% 230.38/41.74  | | | 
% 230.38/41.74  | | Case 2:
% 230.38/41.74  | | | 
% 230.38/41.74  | | |   (75)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 230.38/41.74  | | |         & op(all_52_25, all_52_25) = e3 & op(all_52_27, all_52_27) = e2 &
% 230.38/41.74  | | |         op(all_52_29, all_52_29) = e1 & op(all_52_31, all_52_31) = e0 &
% 230.38/41.74  | | |         op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 & op(e0, e1) =
% 230.38/41.74  | | |         all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) & $i(all_52_27)
% 230.38/41.74  | | |         & $i(all_52_29) & $i(all_52_31)
% 230.38/41.74  | | | 
% 230.38/41.74  | | | REF_CLOSE: (4), (14), (17), (20), (75) are inconsistent by sub-proof
% 230.38/41.74  | | |            #1115.
% 230.38/41.74  | | | 
% 230.38/41.74  | | End of split
% 230.38/41.74  | | 
% 230.38/41.74  | End of split
% 230.38/41.74  | 
% 230.38/41.74  End of proof
% 230.38/41.74  
% 230.38/41.74  Sub-proof #1115 shows that the following formulas are inconsistent:
% 230.38/41.74  ----------------------------------------------------------------
% 230.38/41.74    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.38/41.74           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.38/41.74    (2)  op(e3, e3) = e2
% 230.38/41.74    (3)   ~ (e2 = e0)
% 230.38/41.74    (4)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0 &
% 230.38/41.74         op(all_52_25, all_52_25) = e3 & op(all_52_27, all_52_27) = e2 &
% 230.38/41.74         op(all_52_29, all_52_29) = e1 & op(all_52_31, all_52_31) = e0 & op(e0,
% 230.38/41.74           e3) = all_52_25 & op(e0, e2) = all_52_27 & op(e0, e1) = all_52_29 &
% 230.38/41.74         op(e0, e0) = all_52_31 & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 230.38/41.74         $i(all_52_31)
% 230.38/41.74    (5)  op(e0, e0) = e3
% 230.38/41.74  
% 230.38/41.74  Begin of proof
% 230.38/41.74  | 
% 230.38/41.74  | ALPHA: (4) implies:
% 230.38/41.74  |   (6)  op(e0, e0) = all_52_31
% 230.38/41.74  |   (7)  op(all_52_31, all_52_31) = e0
% 230.38/41.74  | 
% 230.38/41.74  | GROUND_INST: instantiating (1) with e3, all_52_31, e0, e0, simplifying with
% 230.38/41.74  |              (5), (6) gives:
% 230.38/41.74  |   (8)  all_52_31 = e3
% 230.38/41.74  | 
% 230.38/41.74  | REDUCE: (7), (8) imply:
% 230.38/41.74  |   (9)  op(e3, e3) = e0
% 230.38/41.74  | 
% 230.38/41.74  | REF_CLOSE: (1), (2), (3), (9) are inconsistent by sub-proof #2403.
% 230.38/41.74  | 
% 230.38/41.74  End of proof
% 230.38/41.74  
% 230.38/41.74  Sub-proof #1116 shows that the following formulas are inconsistent:
% 230.38/41.74  ----------------------------------------------------------------
% 230.38/41.74    (1)   ~ (e3 = e1)
% 230.38/41.74    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.38/41.74           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.38/41.74    (3)  all_55_6 = all_52_13
% 230.38/41.74    (4)   ~ (all_52_13 = e2)
% 230.38/41.74    (5)  op(all_52_13, all_52_13) = e1
% 230.38/41.74    (6)   ~ (all_52_13 = e1)
% 230.38/41.74    (7)  op(e0, e0) = e3
% 230.38/41.74    (8)  all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 230.38/41.74  
% 230.38/41.74  Begin of proof
% 230.38/41.74  | 
% 230.38/41.74  | BETA: splitting (8) gives:
% 230.38/41.74  | 
% 230.38/41.74  | Case 1:
% 230.38/41.74  | | 
% 230.38/41.74  | |   (9)  all_55_6 = e2
% 230.38/41.74  | | 
% 230.38/41.74  | | COMBINE_EQS: (3), (9) imply:
% 230.38/41.74  | |   (10)  all_52_13 = e2
% 230.38/41.74  | | 
% 230.38/41.74  | | REDUCE: (4), (10) imply:
% 230.38/41.74  | |   (11)  $false
% 230.38/41.74  | | 
% 230.38/41.74  | | CLOSE: (11) is inconsistent.
% 230.38/41.74  | | 
% 230.38/41.74  | Case 2:
% 230.38/41.74  | | 
% 230.38/41.74  | |   (12)  all_55_6 = e1 | all_55_6 = e0
% 230.38/41.74  | | 
% 230.38/41.74  | | BETA: splitting (12) gives:
% 230.38/41.74  | | 
% 230.38/41.74  | | Case 1:
% 230.38/41.74  | | | 
% 230.38/41.74  | | |   (13)  all_55_6 = e1
% 230.38/41.74  | | | 
% 230.38/41.74  | | | REF_CLOSE: (3), (6), (13) are inconsistent by sub-proof #2291.
% 230.38/41.74  | | | 
% 230.38/41.74  | | Case 2:
% 230.38/41.74  | | | 
% 230.38/41.74  | | |   (14)  all_55_6 = e0
% 230.38/41.74  | | | 
% 230.38/41.74  | | | COMBINE_EQS: (3), (14) imply:
% 230.38/41.74  | | |   (15)  all_52_13 = e0
% 230.38/41.74  | | | 
% 230.38/41.74  | | | SIMP: (15) implies:
% 230.38/41.74  | | |   (16)  all_52_13 = e0
% 230.38/41.74  | | | 
% 230.38/41.74  | | | REDUCE: (5), (16) imply:
% 230.38/41.74  | | |   (17)  op(e0, e0) = e1
% 230.38/41.74  | | | 
% 230.38/41.74  | | | REF_CLOSE: (1), (2), (7), (17) are inconsistent by sub-proof #2183.
% 230.38/41.74  | | | 
% 230.38/41.74  | | End of split
% 230.38/41.74  | | 
% 230.38/41.74  | End of split
% 230.38/41.74  | 
% 230.38/41.74  End of proof
% 230.38/41.74  
% 230.38/41.74  Sub-proof #1117 shows that the following formulas are inconsistent:
% 230.38/41.74  ----------------------------------------------------------------
% 230.38/41.74    (1)   ~ (e3 = e1)
% 230.38/41.74    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.38/41.74           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.38/41.74    (3)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.38/41.74         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.38/41.74    (4)   ~ (all_6_2 = e3)
% 230.38/41.74    (5)  op(e1, e1) = all_6_2
% 230.38/41.74    (6)   ~ (e3 = e2)
% 230.38/41.74    (7)   ~ (e3 = e0)
% 230.38/41.74    (8)  all_57_6 = e0
% 230.38/41.74    (9)  all_57_15 = e3
% 230.38/41.74    (10)  all_57_5 = e3
% 230.38/41.74    (11)   ~ (e2 = e0)
% 230.38/41.74    (12)   ~ (e1 = e0)
% 230.38/41.74    (13)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.38/41.74              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.38/41.74                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.38/41.74                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.38/41.74    (14)  all_57_5 = e2 & op(e2, e1) = e2
% 230.38/41.74    (15)  all_57_7 = e3
% 230.38/41.74    (16)   ~ (e2 = e1)
% 230.38/41.74    (17)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.38/41.74          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.38/41.74    (18)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.38/41.74          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.38/41.74  
% 230.38/41.74  Begin of proof
% 230.38/41.74  | 
% 230.38/41.74  | ALPHA: (14) implies:
% 230.38/41.74  |   (19)  all_57_5 = e2
% 230.38/41.74  | 
% 230.38/41.74  | COMBINE_EQS: (10), (19) imply:
% 230.38/41.74  |   (20)  e3 = e2
% 230.38/41.74  | 
% 230.38/41.74  | COMBINE_EQS: (15), (20) imply:
% 230.38/41.74  |   (21)  all_57_7 = e2
% 230.38/41.74  | 
% 230.38/41.74  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13),
% 230.38/41.74  |            (16), (17), (18), (21) are inconsistent by sub-proof #1775.
% 230.38/41.74  | 
% 230.38/41.74  End of proof
% 230.38/41.74  
% 230.38/41.74  Sub-proof #1118 shows that the following formulas are inconsistent:
% 230.38/41.74  ----------------------------------------------------------------
% 230.38/41.74    (1)  op(e1, e0) = e2
% 230.38/41.74    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.38/41.74           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.38/41.74    (3)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) = all_22_1
% 230.38/41.74           & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0, e3) =
% 230.38/41.74           all_22_1 & $i(all_22_1))
% 230.38/41.74    (4)  all_57_6 = e0
% 230.38/41.74    (5)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) = all_12_1
% 230.38/41.74           & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0, e3) =
% 230.38/41.74           all_12_1 & $i(all_12_1))
% 230.38/41.74    (6)   ~ (e1 = e0)
% 230.38/41.74    (7)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.38/41.74  
% 230.38/41.74  Begin of proof
% 230.38/41.74  | 
% 230.38/41.74  | BETA: splitting (7) gives:
% 230.38/41.74  | 
% 230.38/41.74  | Case 1:
% 230.38/41.74  | | 
% 230.38/41.74  | |   (8)  all_57_6 = e1 & op(e1, e3) = e1
% 230.38/41.74  | | 
% 230.38/41.74  | | ALPHA: (8) implies:
% 230.38/41.74  | |   (9)  all_57_6 = e1
% 230.38/41.74  | | 
% 230.38/41.74  | | REF_CLOSE: (4), (6), (9) are inconsistent by sub-proof #2227.
% 230.38/41.74  | | 
% 230.38/41.74  | Case 2:
% 230.38/41.74  | | 
% 230.38/41.74  | |   (10)  all_57_12 = e1 & op(e0, e3) = e1
% 230.38/41.74  | | 
% 230.38/41.74  | | ALPHA: (10) implies:
% 230.38/41.74  | |   (11)  op(e0, e3) = e1
% 230.38/41.74  | | 
% 230.38/41.74  | | REF_CLOSE: (1), (2), (3), (5), (11) are inconsistent by sub-proof #1147.
% 230.38/41.74  | | 
% 230.38/41.74  | End of split
% 230.38/41.74  | 
% 230.38/41.74  End of proof
% 230.38/41.74  
% 230.38/41.74  Sub-proof #1119 shows that the following formulas are inconsistent:
% 230.38/41.74  ----------------------------------------------------------------
% 230.38/41.74    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.38/41.74         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.38/41.74    (2)  op(e3, e1) = all_52_5
% 230.38/41.74    (3)   ~ (all_52_7 = e3)
% 230.38/41.74    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.38/41.74         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.38/41.74    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.38/41.74         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.38/41.74    (6)   ~ (e3 = e1)
% 230.38/41.74    (7)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.38/41.74         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.38/41.74    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.38/41.74           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.38/41.74    (9)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.38/41.74         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.38/41.74    (10)   ~ (all_6_2 = e3)
% 230.38/41.74    (11)  op(e1, e1) = all_6_2
% 230.38/41.74    (12)  op(all_52_7, all_52_7) = e0
% 230.38/41.74    (13)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.38/41.74          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.38/41.74    (14)   ~ (all_52_5 = all_52_7)
% 230.38/41.74    (15)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 230.38/41.74            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 230.38/41.74              e3) = all_22_1 & $i(all_22_1))
% 230.38/41.74    (16)   ~ (all_53_13 = e2)
% 230.38/41.74    (17)   ~ (all_53_7 = e2)
% 230.38/41.74    (18)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.38/41.74          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.38/41.74    (19)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.38/41.74          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.38/41.74    (20)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 230.38/41.74          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.38/41.74    (21)   ~ (e3 = e2)
% 230.38/41.74    (22)   ~ (e3 = e0)
% 230.38/41.74    (23)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.38/41.74          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.38/41.74    (24)  op(e3, e3) = e3
% 230.38/41.74    (25)  all_57_15 = e3
% 230.38/41.74    (26)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.38/41.74          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.38/41.74            e1)
% 230.38/41.74    (27)  all_57_5 = e3
% 230.38/41.74    (28)  op(e3, e3) = all_52_1
% 230.38/41.74    (29)  all_57_6 = e2
% 230.38/41.74    (30)  op(e1, e1) = e1
% 230.38/41.74    (31)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.38/41.74          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.38/41.74    (32)  op(all_52_1, all_52_1) = e3
% 230.38/41.74    (33)   ~ (e2 = e0)
% 230.38/41.74    (34)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 230.38/41.74            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 230.38/41.74              e3) = all_12_1 & $i(all_12_1))
% 230.38/41.74    (35)  op(e2, e2) = e2
% 230.38/41.74    (36)   ~ (e1 = e0)
% 230.38/41.74    (37)  op(e0, e0) = e3
% 230.38/41.74    (38)  op(e0, e2) = all_53_7
% 230.38/41.74    (39)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.38/41.74          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.38/41.74            e2)
% 230.38/41.74    (40)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.38/41.74              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.38/41.74                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.38/41.74                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.38/41.74    (41)  op(e2, e0) = all_53_13
% 230.38/41.74    (42)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.38/41.74          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.38/41.74    (43)  all_57_7 = e3
% 230.38/41.74    (44)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.38/41.74          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.38/41.74    (45)   ~ (e2 = e1)
% 230.38/41.74    (46)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.38/41.74          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.38/41.74    (47)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.38/41.74          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.38/41.74    (48)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.38/41.74          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.38/41.74    (49)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.38/41.74          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.38/41.74    (50)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.38/41.74          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.38/41.74    (51)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.38/41.74          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.38/41.74    (52)  all_57_3 = e2
% 230.38/41.74    (53)  op(e3, e0) = all_52_7
% 230.38/41.74    (54)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.38/41.74          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.38/41.74    (55)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.38/41.74          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.38/41.74  
% 230.38/41.74  Begin of proof
% 230.38/41.74  | 
% 230.38/41.74  | BETA: splitting (7) gives:
% 230.38/41.74  | 
% 230.38/41.74  | Case 1:
% 230.38/41.74  | | 
% 230.38/41.74  | |   (56)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) =
% 230.38/41.74  | |           e0)
% 230.38/41.74  | | 
% 230.38/41.74  | | REF_CLOSE: (22), (29), (33), (43), (56) are inconsistent by sub-proof #1165.
% 230.38/41.74  | | 
% 230.38/41.74  | Case 2:
% 230.38/41.74  | | 
% 230.38/41.74  | |   (57)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 230.38/41.74  | |           e0)
% 230.38/41.74  | | 
% 230.38/41.74  | | BETA: splitting (57) gives:
% 230.38/41.74  | | 
% 230.38/41.74  | | Case 1:
% 230.38/41.74  | | | 
% 230.38/41.74  | | |   (58)  all_57_8 = e0 & op(e1, e1) = e0
% 230.38/41.74  | | | 
% 230.38/41.74  | | | ALPHA: (58) implies:
% 230.38/41.74  | | |   (59)  op(e1, e1) = e0
% 230.38/41.74  | | | 
% 230.38/41.74  | | | REF_CLOSE: (8), (30), (36), (59) are inconsistent by sub-proof #2427.
% 230.38/41.74  | | | 
% 230.38/41.74  | | Case 2:
% 230.38/41.74  | | | 
% 230.38/41.74  | | |   (60)  all_57_11 = e0 & op(e1, e0) = e0
% 230.38/41.74  | | | 
% 230.38/41.74  | | | ALPHA: (60) implies:
% 230.38/41.74  | | |   (61)  all_57_11 = e0
% 230.38/41.74  | | | 
% 230.38/41.74  | | | BETA: splitting (46) gives:
% 230.38/41.74  | | | 
% 230.38/41.74  | | | Case 1:
% 230.38/41.74  | | | | 
% 230.38/41.74  | | | |   (62)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0)
% 230.38/41.74  | | | |           = e2)
% 230.38/41.74  | | | | 
% 230.38/41.74  | | | | BETA: splitting (62) gives:
% 230.38/41.74  | | | | 
% 230.38/41.74  | | | | Case 1:
% 230.38/41.74  | | | | | 
% 230.38/41.74  | | | | |   (63)  all_57_9 = e2 & op(e3, e0) = e2
% 230.38/41.74  | | | | | 
% 230.38/41.74  | | | | | ALPHA: (63) implies:
% 230.38/41.74  | | | | |   (64)  all_57_9 = e2
% 230.38/41.74  | | | | |   (65)  op(e3, e0) = e2
% 230.38/41.74  | | | | | 
% 230.38/41.74  | | | | | BETA: splitting (13) gives:
% 230.38/41.74  | | | | | 
% 230.38/41.74  | | | | | Case 1:
% 230.38/41.74  | | | | | | 
% 230.38/41.74  | | | | | |   (66)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3,
% 230.38/41.74  | | | | | |             e2) = e1)
% 230.38/41.74  | | | | | | 
% 230.38/41.74  | | | | | | BETA: splitting (66) gives:
% 230.38/41.74  | | | | | | 
% 230.38/41.74  | | | | | | Case 1:
% 230.38/41.74  | | | | | | | 
% 230.38/41.74  | | | | | | |   (67)  all_57_0 = e1 & op(e3, e3) = e1
% 230.38/41.74  | | | | | | | 
% 230.38/41.74  | | | | | | | ALPHA: (67) implies:
% 230.38/41.74  | | | | | | |   (68)  op(e3, e3) = e1
% 230.38/41.74  | | | | | | | 
% 230.38/41.74  | | | | | | | REF_CLOSE: (6), (8), (24), (68) are inconsistent by sub-proof
% 230.38/41.74  | | | | | | |            #2495.
% 230.38/41.74  | | | | | | | 
% 230.38/41.74  | | | | | | Case 2:
% 230.38/41.74  | | | | | | | 
% 230.38/41.74  | | | | | | |   (69)  all_57_1 = e1 & op(e3, e2) = e1
% 230.38/41.74  | | | | | | | 
% 230.38/41.74  | | | | | | | ALPHA: (69) implies:
% 230.38/41.74  | | | | | | |   (70)  all_57_1 = e1
% 230.38/41.74  | | | | | | | 
% 230.38/41.74  | | | | | | | BETA: splitting (31) gives:
% 230.38/41.74  | | | | | | | 
% 230.38/41.74  | | | | | | | Case 1:
% 230.38/41.74  | | | | | | | | 
% 230.38/41.74  | | | | | | | |   (71)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 &
% 230.38/41.74  | | | | | | | |           op(e2, e2) = e0)
% 230.38/41.74  | | | | | | | | 
% 230.38/41.74  | | | | | | | | REF_CLOSE: (8), (33), (35), (36), (70), (71) are inconsistent by
% 230.38/41.74  | | | | | | | |            sub-proof #1164.
% 230.38/41.74  | | | | | | | | 
% 230.38/41.74  | | | | | | | Case 2:
% 230.38/41.74  | | | | | | | | 
% 230.38/41.74  | | | | | | | |   (72)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 &
% 230.38/41.74  | | | | | | | |           op(e0, e2) = e0)
% 230.38/41.74  | | | | | | | | 
% 230.38/41.74  | | | | | | | | BETA: splitting (72) gives:
% 230.38/41.74  | | | | | | | | 
% 230.38/41.74  | | | | | | | | Case 1:
% 230.38/41.74  | | | | | | | | | 
% 230.38/41.74  | | | | | | | | |   (73)  all_57_7 = e0 & op(e1, e2) = e0
% 230.38/41.74  | | | | | | | | | 
% 230.38/41.74  | | | | | | | | | ALPHA: (73) implies:
% 230.38/41.74  | | | | | | | | |   (74)  all_57_7 = e0
% 230.38/41.74  | | | | | | | | | 
% 230.38/41.74  | | | | | | | | | REF_CLOSE: (22), (43), (74) are inconsistent by sub-proof
% 230.38/41.74  | | | | | | | | |            #2269.
% 230.38/41.74  | | | | | | | | | 
% 230.38/41.74  | | | | | | | | Case 2:
% 230.38/41.74  | | | | | | | | | 
% 230.38/41.74  | | | | | | | | |   (75)  all_57_13 = e0 & op(e0, e2) = e0
% 230.38/41.74  | | | | | | | | | 
% 230.38/41.74  | | | | | | | | | ALPHA: (75) implies:
% 230.38/41.74  | | | | | | | | |   (76)  all_57_13 = e0
% 230.38/41.74  | | | | | | | | | 
% 230.38/41.74  | | | | | | | | | BETA: splitting (26) gives:
% 230.38/41.74  | | | | | | | | | 
% 230.38/41.74  | | | | | | | | | Case 1:
% 230.38/41.74  | | | | | | | | | | 
% 230.38/41.74  | | | | | | | | | |   (77)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1
% 230.38/41.74  | | | | | | | | | |           & op(e0, e2) = e1)
% 230.38/41.74  | | | | | | | | | | 
% 230.38/41.74  | | | | | | | | | | BETA: splitting (77) gives:
% 230.38/41.74  | | | | | | | | | | 
% 230.38/41.74  | | | | | | | | | | Case 1:
% 230.38/41.74  | | | | | | | | | | | 
% 230.38/41.74  | | | | | | | | | | |   (78)  all_57_12 = e1 & op(e0, e3) = e1
% 230.38/41.74  | | | | | | | | | | | 
% 230.38/41.74  | | | | | | | | | | | ALPHA: (78) implies:
% 230.38/41.74  | | | | | | | | | | |   (79)  all_57_12 = e1
% 230.38/41.74  | | | | | | | | | | | 
% 230.38/41.74  | | | | | | | | | | | BETA: splitting (39) gives:
% 230.38/41.74  | | | | | | | | | | | 
% 230.38/41.74  | | | | | | | | | | | Case 1:
% 230.38/41.74  | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | |   (80)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 230.38/41.75  | | | | | | | | | | | |           e2 & op(e0, e2) = e2)
% 230.38/41.75  | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | | REF_CLOSE: (8), (17), (38), (45), (79), (80) are inconsistent
% 230.38/41.75  | | | | | | | | | | | |            by sub-proof #2128.
% 230.38/41.75  | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | Case 2:
% 230.38/41.75  | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | |   (81)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 230.38/41.75  | | | | | | | | | | | |           e2 & op(e0, e0) = e2)
% 230.38/41.75  | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | | BETA: splitting (81) gives:
% 230.38/41.75  | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | | Case 1:
% 230.38/41.75  | | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | | |   (82)  all_57_14 = e2 & op(e0, e1) = e2
% 230.38/41.75  | | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | | | ALPHA: (82) implies:
% 230.38/41.75  | | | | | | | | | | | | |   (83)  all_57_14 = e2
% 230.38/41.75  | | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | | | BETA: splitting (49) gives:
% 230.38/41.75  | | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | | | Case 1:
% 230.38/41.75  | | | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | | | |   (84)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 230.38/41.75  | | | | | | | | | | | | | |           & op(e2, e3) = e0)
% 230.38/41.75  | | | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | | | | BETA: splitting (84) gives:
% 230.38/41.75  | | | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | | | | Case 1:
% 230.38/41.75  | | | | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | | | | |   (85)  all_57_0 = e0 & op(e3, e3) = e0
% 230.38/41.75  | | | | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | | | | | ALPHA: (85) implies:
% 230.38/41.75  | | | | | | | | | | | | | | |   (86)  op(e3, e3) = e0
% 230.38/41.75  | | | | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | | | | | REF_CLOSE: (8), (22), (24), (86) are inconsistent by
% 230.38/41.75  | | | | | | | | | | | | | | |            sub-proof #2494.
% 230.38/41.75  | | | | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | | | | Case 2:
% 230.38/41.75  | | | | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | | | | |   (87)  all_57_2 = e0 & op(e2, e3) = e0
% 230.38/41.75  | | | | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | | | | | ALPHA: (87) implies:
% 230.38/41.75  | | | | | | | | | | | | | | |   (88)  all_57_2 = e0
% 230.38/41.75  | | | | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | | | | | BETA: splitting (20) gives:
% 230.38/41.75  | | | | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | | | | | Case 1:
% 230.38/41.75  | | | | | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | | | | | |   (89)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 230.38/41.75  | | | | | | | | | | | | | | | |           & op(e2, e1) = e0)
% 230.38/41.75  | | | | | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | | | | | | BETA: splitting (89) gives:
% 230.38/41.75  | | | | | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | | | | | | Case 1:
% 230.38/41.75  | | | | | | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | | | | | | |   (90)  all_57_4 = e0 & op(e3, e1) = e0
% 230.38/41.75  | | | | | | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (8), (12), (14), (22), (35), (37), (40),
% 230.38/41.75  | | | | | | | | | | | | | | | | |            (53), (65), (90) are inconsistent by sub-proof
% 230.38/41.75  | | | | | | | | | | | | | | | | |            #1163.
% 230.38/41.75  | | | | | | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | | | | | | Case 2:
% 230.38/41.75  | | | | | | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | | | | | | |   (91)  all_57_5 = e0 & op(e2, e1) = e0
% 230.38/41.75  | | | | | | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | | | | | | | REF_CLOSE: (22), (27), (91) are inconsistent by sub-proof
% 230.38/41.75  | | | | | | | | | | | | | | | | |            #2414.
% 230.38/41.75  | | | | | | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | | | | | | End of split
% 230.38/41.75  | | | | | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | | | | | Case 2:
% 230.38/41.75  | | | | | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | | | | | |   (92)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 230.38/41.75  | | | | | | | | | | | | | | | |           e0 & op(e0, e1) = e0)
% 230.38/41.75  | | | | | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | | | | | | BETA: splitting (92) gives:
% 230.38/41.75  | | | | | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | | | | | | Case 1:
% 230.38/41.75  | | | | | | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | | | | | | |   (93)  all_57_8 = e0 & op(e1, e1) = e0
% 230.38/41.75  | | | | | | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | | | | | | | ALPHA: (93) implies:
% 230.38/41.75  | | | | | | | | | | | | | | | | |   (94)  op(e1, e1) = e0
% 230.38/41.75  | | | | | | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (30), (36), (94) are inconsistent by
% 230.38/41.75  | | | | | | | | | | | | | | | | |            sub-proof #2427.
% 230.38/41.75  | | | | | | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | | | | | | Case 2:
% 230.38/41.75  | | | | | | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | | | | | | |   (95)  all_57_14 = e0 & op(e0, e1) = e0
% 230.38/41.75  | | | | | | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | | | | | | | ALPHA: (95) implies:
% 230.38/41.75  | | | | | | | | | | | | | | | | |   (96)  all_57_14 = e0
% 230.38/41.75  | | | | | | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | | | | | | | COMBINE_EQS: (83), (96) imply:
% 230.38/41.75  | | | | | | | | | | | | | | | | |   (97)  e2 = e0
% 230.38/41.75  | | | | | | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | | | | | | | SIMP: (97) implies:
% 230.38/41.75  | | | | | | | | | | | | | | | | |   (98)  e2 = e0
% 230.38/41.75  | | | | | | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | | | | | | | COMBINE_EQS: (52), (98) imply:
% 230.38/41.75  | | | | | | | | | | | | | | | | |   (99)  all_57_3 = e0
% 230.38/41.75  | | | | | | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (6), (21), (22), (33), (36), (42), (44),
% 230.38/41.75  | | | | | | | | | | | | | | | | |            (45), (88), (99) are inconsistent by sub-proof
% 230.38/41.75  | | | | | | | | | | | | | | | | |            #2246.
% 230.38/41.75  | | | | | | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | | | | | | End of split
% 230.38/41.75  | | | | | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | | | | | End of split
% 230.38/41.75  | | | | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | | | | End of split
% 230.38/41.75  | | | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | | | Case 2:
% 230.38/41.75  | | | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | | | |   (100)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 230.38/41.75  | | | | | | | | | | | | | |            e0 & op(e0, e3) = e0)
% 230.38/41.75  | | | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | | | | BETA: splitting (100) gives:
% 230.38/41.75  | | | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | | | | Case 1:
% 230.38/41.75  | | | | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | | | | |   (101)  all_57_6 = e0 & op(e1, e3) = e0
% 230.38/41.75  | | | | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | | | | | ALPHA: (101) implies:
% 230.38/41.75  | | | | | | | | | | | | | | |   (102)  all_57_6 = e0
% 230.38/41.75  | | | | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | | | | | COMBINE_EQS: (29), (102) imply:
% 230.38/41.75  | | | | | | | | | | | | | | |   (103)  e2 = e0
% 230.38/41.75  | | | | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | | | | | COMBINE_EQS: (52), (103) imply:
% 230.38/41.75  | | | | | | | | | | | | | | |   (104)  all_57_3 = e0
% 230.38/41.75  | | | | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (8), (13), (18), (19), (21), (22), (24),
% 230.38/41.75  | | | | | | | | | | | | | | |            (33), (36), (43), (45), (54), (76), (104) are
% 230.38/41.75  | | | | | | | | | | | | | | |            inconsistent by sub-proof #2091.
% 230.38/41.75  | | | | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | | | | Case 2:
% 230.38/41.75  | | | | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | | | | |   (105)  all_57_12 = e0 & op(e0, e3) = e0
% 230.38/41.75  | | | | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | | | | | ALPHA: (105) implies:
% 230.38/41.75  | | | | | | | | | | | | | | |   (106)  all_57_12 = e0
% 230.38/41.75  | | | | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | | | | | COMBINE_EQS: (79), (106) imply:
% 230.38/41.75  | | | | | | | | | | | | | | |   (107)  e1 = e0
% 230.38/41.75  | | | | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | | | | | COMBINE_EQS: (70), (107) imply:
% 230.38/41.75  | | | | | | | | | | | | | | |   (108)  all_57_1 = e0
% 230.38/41.75  | | | | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (5), (6), (8), (9), (10), (11), (13),
% 230.38/41.75  | | | | | | | | | | | | | | |            (20), (21), (22), (24), (25), (27), (30), (33),
% 230.38/41.75  | | | | | | | | | | | | | | |            (36), (40), (44), (45), (46), (47), (49), (50),
% 230.38/41.75  | | | | | | | | | | | | | | |            (52), (54), (64), (83), (108) are inconsistent by
% 230.38/41.75  | | | | | | | | | | | | | | |            sub-proof #1162.
% 230.38/41.75  | | | | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | | | | End of split
% 230.38/41.75  | | | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | | | End of split
% 230.38/41.75  | | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | | Case 2:
% 230.38/41.75  | | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | | |   (109)  all_57_15 = e2 & op(e0, e0) = e2
% 230.38/41.75  | | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | | | ALPHA: (109) implies:
% 230.38/41.75  | | | | | | | | | | | | |   (110)  all_57_15 = e2
% 230.38/41.75  | | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | | | REF_CLOSE: (21), (25), (110) are inconsistent by sub-proof
% 230.38/41.75  | | | | | | | | | | | | |            #2058.
% 230.38/41.75  | | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | | End of split
% 230.38/41.75  | | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | End of split
% 230.38/41.75  | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | Case 2:
% 230.38/41.75  | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | |   (111)  all_57_13 = e1 & op(e0, e2) = e1
% 230.38/41.75  | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | ALPHA: (111) implies:
% 230.38/41.75  | | | | | | | | | | |   (112)  all_57_13 = e1
% 230.38/41.75  | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | REF_CLOSE: (36), (76), (112) are inconsistent by sub-proof
% 230.38/41.75  | | | | | | | | | | |            #1760.
% 230.38/41.75  | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | End of split
% 230.38/41.75  | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | Case 2:
% 230.38/41.75  | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | |   (113)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 230.38/41.75  | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 230.38/41.75  | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | BETA: splitting (113) gives:
% 230.38/41.75  | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | Case 1:
% 230.38/41.75  | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | |   (114)  all_57_14 = e1 & op(e0, e1) = e1
% 230.38/41.75  | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | ALPHA: (114) implies:
% 230.38/41.75  | | | | | | | | | | |   (115)  all_57_14 = e1
% 230.38/41.75  | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10),
% 230.38/41.75  | | | | | | | | | | |            (11), (12), (13), (15), (16), (17), (18), (19),
% 230.38/41.75  | | | | | | | | | | |            (20), (21), (22), (23), (24), (25), (26), (27),
% 230.38/41.75  | | | | | | | | | | |            (28), (31), (32), (33), (34), (35), (36), (37),
% 230.38/41.75  | | | | | | | | | | |            (38), (39), (40), (41), (43), (44), (45), (46),
% 230.38/41.75  | | | | | | | | | | |            (47), (48), (49), (50), (51), (52), (53), (54),
% 230.38/41.75  | | | | | | | | | | |            (55), (64), (115) are inconsistent by sub-proof
% 230.38/41.75  | | | | | | | | | | |            #1126.
% 230.38/41.75  | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | Case 2:
% 230.38/41.75  | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | |   (116)  all_57_15 = e1 & op(e0, e0) = e1
% 230.38/41.75  | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | ALPHA: (116) implies:
% 230.38/41.75  | | | | | | | | | | |   (117)  op(e0, e0) = e1
% 230.38/41.75  | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | | REF_CLOSE: (6), (8), (37), (117) are inconsistent by
% 230.38/41.75  | | | | | | | | | | |            sub-proof #2183.
% 230.38/41.75  | | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | | End of split
% 230.38/41.75  | | | | | | | | | | 
% 230.38/41.75  | | | | | | | | | End of split
% 230.38/41.75  | | | | | | | | | 
% 230.38/41.75  | | | | | | | | End of split
% 230.38/41.75  | | | | | | | | 
% 230.38/41.75  | | | | | | | End of split
% 230.38/41.75  | | | | | | | 
% 230.38/41.75  | | | | | | End of split
% 230.38/41.75  | | | | | | 
% 230.38/41.75  | | | | | Case 2:
% 230.38/41.75  | | | | | | 
% 230.38/41.75  | | | | | |   (118)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3,
% 230.38/41.75  | | | | | |              e0) = e1)
% 230.38/41.75  | | | | | | 
% 230.38/41.75  | | | | | | BETA: splitting (118) gives:
% 230.38/41.75  | | | | | | 
% 230.38/41.75  | | | | | | Case 1:
% 230.38/41.75  | | | | | | | 
% 230.38/41.75  | | | | | | |   (119)  all_57_4 = e1 & op(e3, e1) = e1
% 230.38/41.75  | | | | | | | 
% 230.38/41.75  | | | | | | | ALPHA: (119) implies:
% 230.38/41.75  | | | | | | |   (120)  all_57_4 = e1
% 230.38/41.75  | | | | | | | 
% 230.38/41.75  | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 230.38/41.75  | | | | | | |            (12), (13), (17), (18), (19), (20), (21), (22), (23),
% 230.38/41.75  | | | | | | |            (24), (25), (26), (27), (29), (30), (33), (35), (36),
% 230.38/41.75  | | | | | | |            (37), (38), (39), (40), (43), (44), (45), (46), (47),
% 230.38/41.75  | | | | | | |            (48), (49), (50), (51), (52), (53), (54), (55), (61),
% 230.38/41.75  | | | | | | |            (64), (120) are inconsistent by sub-proof #1120.
% 230.38/41.75  | | | | | | | 
% 230.38/41.75  | | | | | | Case 2:
% 230.38/41.75  | | | | | | | 
% 230.38/41.75  | | | | | | |   (121)  all_57_9 = e1 & op(e3, e0) = e1
% 230.38/41.75  | | | | | | | 
% 230.38/41.75  | | | | | | | ALPHA: (121) implies:
% 230.38/41.75  | | | | | | |   (122)  all_57_9 = e1
% 230.38/41.75  | | | | | | | 
% 230.38/41.75  | | | | | | | REF_CLOSE: (45), (64), (122) are inconsistent by sub-proof #2444.
% 230.38/41.75  | | | | | | | 
% 230.38/41.75  | | | | | | End of split
% 230.38/41.75  | | | | | | 
% 230.38/41.75  | | | | | End of split
% 230.38/41.75  | | | | | 
% 230.38/41.75  | | | | Case 2:
% 230.38/41.75  | | | | | 
% 230.38/41.75  | | | | |   (123)  all_57_10 = e2 & op(e2, e0) = e2
% 230.38/41.75  | | | | | 
% 230.38/41.75  | | | | | REF_CLOSE: (8), (16), (41), (123) are inconsistent by sub-proof #2432.
% 230.38/41.75  | | | | | 
% 230.38/41.75  | | | | End of split
% 230.38/41.75  | | | | 
% 230.38/41.75  | | | Case 2:
% 230.38/41.75  | | | | 
% 230.38/41.75  | | | |   (124)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0,
% 230.38/41.75  | | | |              e0) = e2)
% 230.38/41.75  | | | | 
% 230.38/41.75  | | | | BETA: splitting (124) gives:
% 230.38/41.75  | | | | 
% 230.38/41.75  | | | | Case 1:
% 230.38/41.75  | | | | | 
% 230.38/41.75  | | | | |   (125)  all_57_11 = e2 & op(e1, e0) = e2
% 230.38/41.75  | | | | | 
% 230.38/41.75  | | | | | REF_CLOSE: (33), (61), (125) are inconsistent by sub-proof #1988.
% 230.38/41.75  | | | | | 
% 230.38/41.75  | | | | Case 2:
% 230.38/41.75  | | | | | 
% 230.38/41.75  | | | | |   (126)  all_57_15 = e2 & op(e0, e0) = e2
% 230.38/41.75  | | | | | 
% 230.38/41.75  | | | | | REF_CLOSE: (21), (25), (126) are inconsistent by sub-proof #2323.
% 230.38/41.75  | | | | | 
% 230.38/41.75  | | | | End of split
% 230.38/41.75  | | | | 
% 230.38/41.75  | | | End of split
% 230.38/41.75  | | | 
% 230.38/41.75  | | End of split
% 230.38/41.75  | | 
% 230.38/41.75  | End of split
% 230.38/41.75  | 
% 230.38/41.75  End of proof
% 230.38/41.75  
% 230.38/41.75  Sub-proof #1120 shows that the following formulas are inconsistent:
% 230.38/41.75  ----------------------------------------------------------------
% 230.38/41.75    (1)  all_57_9 = e2
% 230.38/41.75    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.38/41.75         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.38/41.75    (3)   ~ (all_52_7 = e3)
% 230.38/41.75    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.38/41.75         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.38/41.75    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.38/41.75         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.38/41.75    (6)   ~ (e3 = e1)
% 230.38/41.75    (7)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.38/41.75         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.38/41.75    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.38/41.75           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.38/41.75    (9)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.38/41.75         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.38/41.75    (10)   ~ (all_6_2 = e3)
% 230.38/41.75    (11)  op(e1, e1) = all_6_2
% 230.38/41.75    (12)  op(all_52_7, all_52_7) = e0
% 230.38/41.75    (13)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.38/41.75          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.38/41.75    (14)   ~ (all_53_7 = e2)
% 230.38/41.75    (15)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.38/41.75          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.38/41.75    (16)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.38/41.75          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.38/41.75    (17)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 230.38/41.75          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.38/41.75    (18)   ~ (e3 = e2)
% 230.38/41.75    (19)   ~ (e3 = e0)
% 230.38/41.75    (20)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.38/41.75          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.38/41.75    (21)  op(e3, e3) = e3
% 230.38/41.75    (22)  all_57_15 = e3
% 230.38/41.75    (23)  all_57_4 = e1
% 230.38/41.75    (24)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.38/41.75          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.38/41.75            e1)
% 230.38/41.75    (25)  all_57_5 = e3
% 230.38/41.75    (26)  all_57_6 = e2
% 230.38/41.75    (27)  all_57_11 = e0
% 230.38/41.75    (28)  op(e1, e1) = e1
% 230.38/41.75    (29)   ~ (e2 = e0)
% 230.38/41.75    (30)  op(e2, e2) = e2
% 230.38/41.75    (31)   ~ (e1 = e0)
% 230.38/41.75    (32)  op(e0, e0) = e3
% 230.38/41.75    (33)  op(e0, e2) = all_53_7
% 230.38/41.75    (34)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.38/41.75          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.38/41.75            e2)
% 230.38/41.75    (35)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.38/41.75              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.38/41.75                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.38/41.75                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.38/41.75    (36)  all_57_7 = e3
% 230.38/41.75    (37)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.38/41.75          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.38/41.75    (38)   ~ (e2 = e1)
% 230.38/41.75    (39)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.38/41.75          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.38/41.75    (40)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.38/41.75          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.38/41.75    (41)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.38/41.75          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.38/41.75    (42)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.38/41.75          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.38/41.75    (43)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.38/41.75          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.38/41.75    (44)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.38/41.75          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.38/41.75    (45)  all_57_3 = e2
% 230.38/41.75    (46)  op(e3, e0) = all_52_7
% 230.38/41.75    (47)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.38/41.75          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.38/41.75    (48)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.38/41.75          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.38/41.75  
% 230.38/41.75  Begin of proof
% 230.38/41.75  | 
% 230.38/41.75  | BETA: splitting (41) gives:
% 230.38/41.75  | 
% 230.38/41.75  | Case 1:
% 230.38/41.75  | | 
% 230.38/41.75  | |   (49)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) =
% 230.38/41.75  | |           e2)
% 230.38/41.75  | | 
% 230.38/41.75  | | BETA: splitting (49) gives:
% 230.38/41.75  | | 
% 230.38/41.75  | | Case 1:
% 230.38/41.75  | | | 
% 230.38/41.75  | | |   (50)  all_57_4 = e2 & op(e3, e1) = e2
% 230.38/41.75  | | | 
% 230.38/41.75  | | | REF_CLOSE: (23), (38), (50) are inconsistent by sub-proof #1125.
% 230.38/41.75  | | | 
% 230.38/41.75  | | Case 2:
% 230.38/41.75  | | | 
% 230.38/41.75  | | |   (51)  all_57_5 = e2 & op(e2, e1) = e2
% 230.38/41.75  | | | 
% 230.38/41.75  | | | REF_CLOSE: (18), (25), (51) are inconsistent by sub-proof #2425.
% 230.38/41.75  | | | 
% 230.38/41.75  | | End of split
% 230.38/41.75  | | 
% 230.38/41.75  | Case 2:
% 230.38/41.75  | | 
% 230.38/41.75  | |   (52)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) =
% 230.38/41.75  | |           e2)
% 230.38/41.75  | | 
% 230.38/41.75  | | BETA: splitting (52) gives:
% 230.38/41.75  | | 
% 230.38/41.75  | | Case 1:
% 230.38/41.75  | | | 
% 230.38/41.75  | | |   (53)  all_57_8 = e2 & op(e1, e1) = e2
% 230.38/41.75  | | | 
% 230.38/41.75  | | | ALPHA: (53) implies:
% 230.38/41.75  | | |   (54)  op(e1, e1) = e2
% 230.38/41.75  | | | 
% 230.38/41.75  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 230.38/41.75  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 230.38/41.75  | | |            (24), (25), (26), (29), (30), (31), (32), (33), (34), (35),
% 230.38/41.75  | | |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 230.38/41.75  | | |            (46), (47), (48), (54) are inconsistent by sub-proof #1121.
% 230.38/41.75  | | | 
% 230.38/41.75  | | Case 2:
% 230.38/41.75  | | | 
% 230.38/41.75  | | |   (55)  all_57_14 = e2 & op(e0, e1) = e2
% 230.38/41.75  | | | 
% 230.38/41.75  | | | ALPHA: (55) implies:
% 230.38/41.75  | | |   (56)  all_57_14 = e2
% 230.38/41.75  | | | 
% 230.38/41.75  | | | BETA: splitting (16) gives:
% 230.38/41.75  | | | 
% 230.38/41.75  | | | Case 1:
% 230.38/41.75  | | | | 
% 230.38/41.75  | | | |   (57)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2)
% 230.38/41.75  | | | |           = e0)
% 230.38/41.75  | | | | 
% 230.38/41.75  | | | | BETA: splitting (57) gives:
% 230.38/41.75  | | | | 
% 230.38/41.75  | | | | Case 1:
% 230.38/41.75  | | | | | 
% 230.38/41.75  | | | | |   (58)  all_57_0 = e0 & op(e3, e3) = e0
% 230.38/41.75  | | | | | 
% 230.38/41.75  | | | | | ALPHA: (58) implies:
% 230.38/41.75  | | | | |   (59)  op(e3, e3) = e0
% 230.38/41.75  | | | | | 
% 230.38/41.75  | | | | | REF_CLOSE: (8), (19), (21), (59) are inconsistent by sub-proof #2494.
% 230.38/41.75  | | | | | 
% 230.38/41.75  | | | | Case 2:
% 230.38/41.75  | | | | | 
% 230.38/41.75  | | | | |   (60)  all_57_1 = e0 & op(e3, e2) = e0
% 230.38/41.75  | | | | | 
% 230.38/41.75  | | | | | ALPHA: (60) implies:
% 230.38/41.75  | | | | |   (61)  all_57_1 = e0
% 230.38/41.75  | | | | | 
% 230.38/41.75  | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (8), (9), (10), (11), (13), (17),
% 230.38/41.75  | | | | |            (18), (19), (21), (22), (25), (28), (29), (31), (35), (37),
% 230.38/41.75  | | | | |            (38), (39), (40), (42), (43), (45), (47), (56), (61) are
% 230.38/41.75  | | | | |            inconsistent by sub-proof #1162.
% 230.38/41.75  | | | | | 
% 230.38/41.75  | | | | End of split
% 230.38/41.75  | | | | 
% 230.38/41.75  | | | Case 2:
% 230.38/41.75  | | | | 
% 230.38/41.75  | | | |   (62)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0)
% 230.38/41.75  | | | |           = e0)
% 230.38/41.75  | | | | 
% 230.38/41.75  | | | | BETA: splitting (62) gives:
% 230.38/41.75  | | | | 
% 230.38/41.75  | | | | Case 1:
% 230.38/41.75  | | | | | 
% 230.38/41.75  | | | | |   (63)  all_57_4 = e0 & op(e3, e1) = e0
% 230.38/41.75  | | | | | 
% 230.38/41.75  | | | | | ALPHA: (63) implies:
% 230.38/41.75  | | | | |   (64)  all_57_4 = e0
% 230.38/41.75  | | | | | 
% 230.38/41.75  | | | | | REF_CLOSE: (23), (31), (64) are inconsistent by sub-proof #2438.
% 230.38/41.75  | | | | | 
% 230.38/41.75  | | | | Case 2:
% 230.38/41.75  | | | | | 
% 230.38/41.75  | | | | |   (65)  all_57_9 = e0 & op(e3, e0) = e0
% 230.38/41.75  | | | | | 
% 230.38/41.75  | | | | | ALPHA: (65) implies:
% 230.38/41.75  | | | | |   (66)  all_57_9 = e0
% 230.38/41.75  | | | | | 
% 230.38/41.75  | | | | | REF_CLOSE: (6), (18), (22), (27), (29), (31), (38), (39), (43), (66)
% 230.38/41.75  | | | | |            are inconsistent by sub-proof #1144.
% 230.38/41.75  | | | | | 
% 230.38/41.75  | | | | End of split
% 230.38/41.75  | | | | 
% 230.38/41.75  | | | End of split
% 230.38/41.75  | | | 
% 230.38/41.75  | | End of split
% 230.38/41.75  | | 
% 230.38/41.75  | End of split
% 230.38/41.75  | 
% 230.38/41.75  End of proof
% 230.38/41.75  
% 230.38/41.75  Sub-proof #1121 shows that the following formulas are inconsistent:
% 230.38/41.75  ----------------------------------------------------------------
% 230.38/41.75    (1)  all_57_9 = e2
% 230.38/41.75    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.38/41.75         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.38/41.75    (3)   ~ (all_52_7 = e3)
% 230.38/41.75    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.38/41.75         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.38/41.75    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.38/41.75         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.38/41.75    (6)   ~ (e3 = e1)
% 230.38/41.75    (7)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.38/41.75         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.38/41.75    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.38/41.75           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.38/41.75    (9)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.38/41.75         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.38/41.75    (10)   ~ (all_6_2 = e3)
% 230.38/41.75    (11)  op(e1, e1) = all_6_2
% 230.38/41.75    (12)  op(all_52_7, all_52_7) = e0
% 230.38/41.75    (13)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.38/41.75          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.38/41.75    (14)   ~ (all_53_7 = e2)
% 230.38/41.75    (15)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.38/41.75          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.38/41.75    (16)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.38/41.75          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.38/41.75    (17)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 230.38/41.75          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.38/41.75    (18)   ~ (e3 = e2)
% 230.38/41.75    (19)   ~ (e3 = e0)
% 230.38/41.75    (20)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.38/41.75          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.38/41.75    (21)  op(e3, e3) = e3
% 230.38/41.75    (22)  all_57_15 = e3
% 230.38/41.75    (23)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.38/41.75          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.38/41.75            e1)
% 230.38/41.75    (24)  all_57_5 = e3
% 230.38/41.75    (25)  all_57_6 = e2
% 230.38/41.75    (26)   ~ (e2 = e0)
% 230.38/41.75    (27)  op(e2, e2) = e2
% 230.38/41.75    (28)   ~ (e1 = e0)
% 230.38/41.75    (29)  op(e0, e0) = e3
% 230.38/41.75    (30)  op(e0, e2) = all_53_7
% 230.38/41.75    (31)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.38/41.75          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.38/41.75            e2)
% 230.38/41.75    (32)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.38/41.75              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.38/41.75                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.38/41.75                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.38/41.75    (33)  op(e1, e1) = e2
% 230.38/41.75    (34)  all_57_7 = e3
% 230.38/41.75    (35)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.38/41.75          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.38/41.75    (36)   ~ (e2 = e1)
% 230.38/41.75    (37)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.38/41.75          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.38/41.75    (38)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.38/41.75          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.38/41.75    (39)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.38/41.75          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.38/41.75    (40)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.38/41.75          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.38/41.75    (41)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.38/41.75          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.38/41.75    (42)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.38/41.75          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.38/41.75    (43)  all_57_3 = e2
% 230.38/41.75    (44)  op(e3, e0) = all_52_7
% 230.38/41.75    (45)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.38/41.75          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.38/41.75    (46)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.38/41.75          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.38/41.75  
% 230.38/41.75  Begin of proof
% 230.38/41.75  | 
% 230.38/41.75  | BETA: splitting (31) gives:
% 230.38/41.75  | 
% 230.38/41.75  | Case 1:
% 230.38/41.75  | | 
% 230.38/41.75  | |   (47)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 230.38/41.75  | |           e2)
% 230.38/41.75  | | 
% 230.38/41.75  | | BETA: splitting (47) gives:
% 230.38/41.75  | | 
% 230.38/41.75  | | Case 1:
% 230.38/41.75  | | | 
% 230.38/41.75  | | |   (48)  all_57_12 = e2 & op(e0, e3) = e2
% 230.38/41.75  | | | 
% 230.38/41.75  | | | ALPHA: (48) implies:
% 230.38/41.75  | | |   (49)  all_57_12 = e2
% 230.38/41.75  | | | 
% 230.38/41.75  | | | BETA: splitting (7) gives:
% 230.38/41.75  | | | 
% 230.38/41.75  | | | Case 1:
% 230.38/41.75  | | | | 
% 230.38/41.75  | | | |   (50)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2)
% 230.38/41.75  | | | |           = e0)
% 230.38/41.75  | | | | 
% 230.38/41.75  | | | | BETA: splitting (50) gives:
% 230.38/41.75  | | | | 
% 230.38/41.75  | | | | Case 1:
% 230.38/41.75  | | | | | 
% 230.38/41.75  | | | | |   (51)  all_57_6 = e0 & op(e1, e3) = e0
% 230.38/41.75  | | | | | 
% 230.38/41.75  | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (12), (13), (15), (16),
% 230.38/41.75  | | | | |            (17), (18), (19), (20), (21), (22), (23), (24), (25), (26),
% 230.38/41.75  | | | | |            (28), (29), (31), (32), (33), (34), (35), (36), (37), (38),
% 230.38/41.75  | | | | |            (39), (40), (41), (42), (43), (44), (45), (46), (51) are
% 230.38/41.75  | | | | |            inconsistent by sub-proof #1124.
% 230.38/41.75  | | | | | 
% 230.38/41.75  | | | | Case 2:
% 230.38/41.75  | | | | | 
% 230.38/41.75  | | | | |   (52)  all_57_7 = e0 & op(e1, e2) = e0
% 230.38/41.75  | | | | | 
% 230.38/41.75  | | | | | REF_CLOSE: (19), (34), (52) are inconsistent by sub-proof #2042.
% 230.38/41.75  | | | | | 
% 230.38/41.75  | | | | End of split
% 230.38/41.75  | | | | 
% 230.38/41.75  | | | Case 2:
% 230.38/41.75  | | | | 
% 230.38/41.75  | | | |   (53)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.38/41.75  | | | |           = e0)
% 230.38/41.75  | | | | 
% 230.38/41.75  | | | | BETA: splitting (53) gives:
% 230.38/41.75  | | | | 
% 230.38/41.75  | | | | Case 1:
% 230.38/41.75  | | | | | 
% 230.38/41.75  | | | | |   (54)  all_57_8 = e0 & op(e1, e1) = e0
% 230.38/41.75  | | | | | 
% 230.38/41.75  | | | | | ALPHA: (54) implies:
% 230.38/41.75  | | | | |   (55)  op(e1, e1) = e0
% 230.38/41.75  | | | | | 
% 230.38/41.75  | | | | | BETA: splitting (32) gives:
% 230.38/41.75  | | | | | 
% 230.38/41.75  | | | | | Case 1:
% 230.38/41.75  | | | | | | 
% 230.38/41.75  | | | | | |   (56)  all_57_15 = e0 & op(e0, e0) = e0
% 230.38/41.75  | | | | | | 
% 230.38/41.75  | | | | | | ALPHA: (56) implies:
% 230.38/41.75  | | | | | |   (57)  op(e0, e0) = e0
% 230.38/41.75  | | | | | | 
% 230.38/41.75  | | | | | | REF_CLOSE: (8), (19), (29), (57) are inconsistent by sub-proof
% 230.38/41.75  | | | | | |            #2304.
% 230.38/41.75  | | | | | | 
% 230.38/41.75  | | | | | Case 2:
% 230.38/41.75  | | | | | | 
% 230.38/41.75  | | | | | |   (58)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 &
% 230.38/41.75  | | | | | |             op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) &
% 230.38/41.75  | | | | | |         ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.38/41.75  | | | | | |             op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 230.38/41.75  | | | | | | 
% 230.38/41.75  | | | | | | ALPHA: (58) implies:
% 230.38/41.75  | | | | | |   (59)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2,
% 230.38/41.75  | | | | | |             e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.38/41.75  | | | | | | 
% 230.38/41.75  | | | | | | BETA: splitting (40) gives:
% 230.38/41.75  | | | | | | 
% 230.38/41.75  | | | | | | Case 1:
% 230.38/41.75  | | | | | | | 
% 230.38/41.75  | | | | | | |   (60)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 &
% 230.38/41.75  | | | | | | |           op(e2, e3) = e0)
% 230.38/41.75  | | | | | | | 
% 230.38/41.75  | | | | | | | BETA: splitting (60) gives:
% 230.38/41.75  | | | | | | | 
% 230.38/41.75  | | | | | | | Case 1:
% 230.38/41.75  | | | | | | | | 
% 230.38/41.75  | | | | | | | |   (61)  all_57_0 = e0 & op(e3, e3) = e0
% 230.38/41.75  | | | | | | | | 
% 230.38/41.75  | | | | | | | | ALPHA: (61) implies:
% 230.38/41.75  | | | | | | | |   (62)  op(e3, e3) = e0
% 230.38/41.75  | | | | | | | | 
% 230.38/41.75  | | | | | | | | REF_CLOSE: (8), (19), (21), (62) are inconsistent by sub-proof
% 230.38/41.75  | | | | | | | |            #2494.
% 230.38/41.75  | | | | | | | | 
% 230.38/41.75  | | | | | | | Case 2:
% 230.38/41.75  | | | | | | | | 
% 230.38/41.75  | | | | | | | |   (63)  all_57_2 = e0 & op(e2, e3) = e0
% 230.38/41.75  | | | | | | | | 
% 230.38/41.75  | | | | | | | | ALPHA: (63) implies:
% 230.38/41.75  | | | | | | | |   (64)  all_57_2 = e0
% 230.38/41.75  | | | | | | | | 
% 230.38/41.75  | | | | | | | | REF_CLOSE: (4), (6), (8), (21), (25), (28), (36), (49), (64) are
% 230.38/41.75  | | | | | | | |            inconsistent by sub-proof #2387.
% 230.38/41.75  | | | | | | | | 
% 230.38/41.75  | | | | | | | End of split
% 230.38/41.75  | | | | | | | 
% 230.38/41.75  | | | | | | Case 2:
% 230.38/41.75  | | | | | | | 
% 230.38/41.76  | | | | | | |   (65)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 &
% 230.38/41.76  | | | | | | |           op(e0, e3) = e0)
% 230.38/41.76  | | | | | | | 
% 230.38/41.76  | | | | | | | BETA: splitting (65) gives:
% 230.38/41.76  | | | | | | | 
% 230.38/41.76  | | | | | | | Case 1:
% 230.38/41.76  | | | | | | | | 
% 230.38/41.76  | | | | | | | |   (66)  all_57_6 = e0 & op(e1, e3) = e0
% 230.38/41.76  | | | | | | | | 
% 230.38/41.76  | | | | | | | | ALPHA: (66) implies:
% 230.38/41.76  | | | | | | | |   (67)  all_57_6 = e0
% 230.38/41.76  | | | | | | | | 
% 230.38/41.76  | | | | | | | | COMBINE_EQS: (25), (67) imply:
% 230.38/41.76  | | | | | | | |   (68)  e2 = e0
% 230.38/41.76  | | | | | | | | 
% 230.38/41.76  | | | | | | | | COMBINE_EQS: (43), (68) imply:
% 230.38/41.76  | | | | | | | |   (69)  all_57_3 = e0
% 230.38/41.76  | | | | | | | | 
% 230.38/41.76  | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (12), (13), (15),
% 230.38/41.76  | | | | | | | |            (16), (17), (18), (19), (20), (21), (22), (24), (26),
% 230.38/41.76  | | | | | | | |            (28), (29), (31), (32), (34), (35), (36), (37), (38),
% 230.38/41.76  | | | | | | | |            (39), (40), (41), (42), (44), (45), (46), (55), (69)
% 230.38/41.76  | | | | | | | |            are inconsistent by sub-proof #1486.
% 230.38/41.76  | | | | | | | | 
% 230.38/41.76  | | | | | | | Case 2:
% 230.38/41.76  | | | | | | | | 
% 230.38/41.76  | | | | | | | |   (70)  all_57_12 = e0 & op(e0, e3) = e0
% 230.38/41.76  | | | | | | | | 
% 230.38/41.76  | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (12), (15), (16), (18),
% 230.38/41.76  | | | | | | | |            (19), (20), (21), (22), (24), (26), (28), (29), (31),
% 230.38/41.76  | | | | | | | |            (34), (35), (36), (37), (38), (40), (41), (42), (43),
% 230.38/41.76  | | | | | | | |            (44), (45), (46), (49), (55), (59), (70) are
% 230.38/41.76  | | | | | | | |            inconsistent by sub-proof #1151.
% 230.38/41.76  | | | | | | | | 
% 230.38/41.76  | | | | | | | End of split
% 230.38/41.76  | | | | | | | 
% 230.38/41.76  | | | | | | End of split
% 230.38/41.76  | | | | | | 
% 230.38/41.76  | | | | | End of split
% 230.38/41.76  | | | | | 
% 230.38/41.76  | | | | Case 2:
% 230.38/41.76  | | | | | 
% 230.38/41.76  | | | | |   (71)  all_57_11 = e0 & op(e1, e0) = e0
% 230.38/41.76  | | | | | 
% 230.38/41.76  | | | | | ALPHA: (71) implies:
% 230.38/41.76  | | | | |   (72)  all_57_11 = e0
% 230.38/41.76  | | | | | 
% 230.38/41.76  | | | | | REF_CLOSE: (6), (8), (9), (10), (11), (18), (19), (22), (25), (26),
% 230.38/41.76  | | | | |            (28), (32), (33), (36), (37), (41), (42), (72) are
% 230.38/41.76  | | | | |            inconsistent by sub-proof #1122.
% 230.38/41.76  | | | | | 
% 230.38/41.76  | | | | End of split
% 230.38/41.76  | | | | 
% 230.38/41.76  | | | End of split
% 230.38/41.76  | | | 
% 230.38/41.76  | | Case 2:
% 230.38/41.76  | | | 
% 230.38/41.76  | | |   (73)  all_57_13 = e2 & op(e0, e2) = e2
% 230.38/41.76  | | | 
% 230.38/41.76  | | | ALPHA: (73) implies:
% 230.38/41.76  | | |   (74)  op(e0, e2) = e2
% 230.38/41.76  | | | 
% 230.38/41.76  | | | REF_CLOSE: (8), (14), (30), (74) are inconsistent by sub-proof #2335.
% 230.38/41.76  | | | 
% 230.38/41.76  | | End of split
% 230.38/41.76  | | 
% 230.38/41.76  | Case 2:
% 230.38/41.76  | | 
% 230.38/41.76  | |   (75)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.38/41.76  | |           e2)
% 230.38/41.76  | | 
% 230.38/41.76  | | BETA: splitting (75) gives:
% 230.38/41.76  | | 
% 230.38/41.76  | | Case 1:
% 230.38/41.76  | | | 
% 230.38/41.76  | | |   (76)  all_57_14 = e2 & op(e0, e1) = e2
% 230.38/41.76  | | | 
% 230.38/41.76  | | | ALPHA: (76) implies:
% 230.38/41.76  | | |   (77)  all_57_14 = e2
% 230.38/41.76  | | | 
% 230.38/41.76  | | | BETA: splitting (7) gives:
% 230.38/41.76  | | | 
% 230.38/41.76  | | | Case 1:
% 230.38/41.76  | | | | 
% 230.38/41.76  | | | |   (78)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2)
% 230.38/41.76  | | | |           = e0)
% 230.38/41.76  | | | | 
% 230.38/41.76  | | | | BETA: splitting (78) gives:
% 230.38/41.76  | | | | 
% 230.38/41.76  | | | | Case 1:
% 230.38/41.76  | | | | | 
% 230.38/41.76  | | | | |   (79)  all_57_6 = e0 & op(e1, e3) = e0
% 230.38/41.76  | | | | | 
% 230.38/41.76  | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (12), (13), (15), (16),
% 230.38/41.76  | | | | |            (17), (18), (19), (20), (21), (22), (23), (24), (25), (26),
% 230.38/41.76  | | | | |            (28), (29), (31), (32), (33), (34), (35), (36), (37), (38),
% 230.38/41.76  | | | | |            (39), (40), (41), (42), (43), (44), (45), (46), (79) are
% 230.38/41.76  | | | | |            inconsistent by sub-proof #1124.
% 230.38/41.76  | | | | | 
% 230.38/41.76  | | | | Case 2:
% 230.38/41.76  | | | | | 
% 230.38/41.76  | | | | |   (80)  all_57_7 = e0 & op(e1, e2) = e0
% 230.38/41.76  | | | | | 
% 230.38/41.76  | | | | | REF_CLOSE: (19), (34), (80) are inconsistent by sub-proof #2042.
% 230.38/41.76  | | | | | 
% 230.38/41.76  | | | | End of split
% 230.38/41.76  | | | | 
% 230.38/41.76  | | | Case 2:
% 230.38/41.76  | | | | 
% 230.38/41.76  | | | |   (81)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.38/41.76  | | | |           = e0)
% 230.38/41.76  | | | | 
% 230.38/41.76  | | | | BETA: splitting (81) gives:
% 230.38/41.76  | | | | 
% 230.38/41.76  | | | | Case 1:
% 230.38/41.76  | | | | | 
% 230.38/41.76  | | | | |   (82)  all_57_8 = e0 & op(e1, e1) = e0
% 230.38/41.76  | | | | | 
% 230.38/41.76  | | | | | ALPHA: (82) implies:
% 230.48/41.76  | | | | |   (83)  op(e1, e1) = e0
% 230.48/41.76  | | | | | 
% 230.48/41.76  | | | | | BETA: splitting (42) gives:
% 230.48/41.76  | | | | | 
% 230.48/41.76  | | | | | Case 1:
% 230.48/41.76  | | | | | | 
% 230.48/41.76  | | | | | |   (84)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1,
% 230.48/41.76  | | | | | |             e2) = e1)
% 230.48/41.76  | | | | | | 
% 230.48/41.76  | | | | | | REF_CLOSE: (6), (8), (9), (10), (11), (18), (19), (22), (25), (26),
% 230.48/41.76  | | | | | |            (28), (32), (36), (37), (41), (84) are inconsistent by
% 230.48/41.76  | | | | | |            sub-proof #1123.
% 230.48/41.76  | | | | | | 
% 230.48/41.76  | | | | | Case 2:
% 230.48/41.76  | | | | | | 
% 230.48/41.76  | | | | | |   (85)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1,
% 230.48/41.76  | | | | | |             e0) = e1)
% 230.48/41.76  | | | | | | 
% 230.48/41.76  | | | | | | BETA: splitting (85) gives:
% 230.48/41.76  | | | | | | 
% 230.48/41.76  | | | | | | Case 1:
% 230.48/41.76  | | | | | | | 
% 230.48/41.76  | | | | | | |   (86)  all_57_8 = e1 & op(e1, e1) = e1
% 230.48/41.76  | | | | | | | 
% 230.48/41.76  | | | | | | | ALPHA: (86) implies:
% 230.48/41.76  | | | | | | |   (87)  op(e1, e1) = e1
% 230.48/41.76  | | | | | | | 
% 230.48/41.76  | | | | | | | REF_CLOSE: (8), (28), (83), (87) are inconsistent by sub-proof
% 230.48/41.76  | | | | | | |            #2427.
% 230.48/41.76  | | | | | | | 
% 230.48/41.76  | | | | | | Case 2:
% 230.48/41.76  | | | | | | | 
% 230.48/41.76  | | | | | | |   (88)  all_57_11 = e1 & op(e1, e0) = e1
% 230.48/41.76  | | | | | | | 
% 230.48/41.76  | | | | | | | ALPHA: (88) implies:
% 230.48/41.76  | | | | | | |   (89)  all_57_11 = e1
% 230.48/41.76  | | | | | | | 
% 230.48/41.76  | | | | | | | BETA: splitting (32) gives:
% 230.48/41.76  | | | | | | | 
% 230.48/41.76  | | | | | | | Case 1:
% 230.48/41.76  | | | | | | | | 
% 230.48/41.76  | | | | | | | |   (90)  all_57_15 = e0 & op(e0, e0) = e0
% 230.48/41.76  | | | | | | | | 
% 230.48/41.76  | | | | | | | | ALPHA: (90) implies:
% 230.48/41.76  | | | | | | | |   (91)  op(e0, e0) = e0
% 230.48/41.76  | | | | | | | | 
% 230.48/41.76  | | | | | | | | REF_CLOSE: (8), (19), (29), (91) are inconsistent by sub-proof
% 230.48/41.76  | | | | | | | |            #2304.
% 230.48/41.76  | | | | | | | | 
% 230.48/41.76  | | | | | | | Case 2:
% 230.48/41.76  | | | | | | | | 
% 230.48/41.76  | | | | | | | |   (92)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 &
% 230.48/41.76  | | | | | | | |             op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 230.48/41.76  | | | | | | | |             e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) |
% 230.48/41.76  | | | | | | | |           (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 &
% 230.48/41.76  | | | | | | | |             op(e0, e1) = e0))
% 230.48/41.76  | | | | | | | | 
% 230.48/41.76  | | | | | | | | ALPHA: (92) implies:
% 230.48/41.76  | | | | | | | |   (93)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.48/41.76  | | | | | | | |           op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.48/41.76  | | | | | | | |   (94)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 &
% 230.48/41.76  | | | | | | | |           op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.48/41.76  | | | | | | | | 
% 230.48/41.76  | | | | | | | | BETA: splitting (20) gives:
% 230.48/41.76  | | | | | | | | 
% 230.48/41.76  | | | | | | | | Case 1:
% 230.48/41.76  | | | | | | | | | 
% 230.48/41.76  | | | | | | | | |   (95)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 &
% 230.48/41.76  | | | | | | | | |           op(e2, e1) = e1)
% 230.48/41.76  | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | BETA: splitting (95) gives:
% 230.48/41.76  | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | Case 1:
% 230.48/41.76  | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | |   (96)  all_57_4 = e1 & op(e3, e1) = e1
% 230.48/41.76  | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | ALPHA: (96) implies:
% 230.48/41.76  | | | | | | | | | |   (97)  all_57_4 = e1
% 230.48/41.76  | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | BETA: splitting (16) gives:
% 230.48/41.76  | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | Case 1:
% 230.48/41.76  | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | |   (98)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 230.48/41.76  | | | | | | | | | | |           & op(e3, e2) = e0)
% 230.48/41.76  | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | BETA: splitting (98) gives:
% 230.48/41.76  | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | Case 1:
% 230.48/41.76  | | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | |   (99)  all_57_0 = e0 & op(e3, e3) = e0
% 230.48/41.76  | | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | | ALPHA: (99) implies:
% 230.48/41.76  | | | | | | | | | | | |   (100)  op(e3, e3) = e0
% 230.48/41.76  | | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | | REF_CLOSE: (8), (19), (21), (100) are inconsistent by
% 230.48/41.76  | | | | | | | | | | | |            sub-proof #2494.
% 230.48/41.76  | | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | Case 2:
% 230.48/41.76  | | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | |   (101)  all_57_1 = e0 & op(e3, e2) = e0
% 230.48/41.76  | | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | | ALPHA: (101) implies:
% 230.48/41.76  | | | | | | | | | | | |   (102)  all_57_1 = e0
% 230.48/41.76  | | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | | BETA: splitting (45) gives:
% 230.48/41.76  | | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | | Case 1:
% 230.48/41.76  | | | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | | |   (103)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 230.48/41.76  | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 230.48/41.76  | | | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | | | BETA: splitting (103) gives:
% 230.48/41.76  | | | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | | | Case 1:
% 230.48/41.76  | | | | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | | | |   (104)  all_57_1 = e1 & op(e3, e2) = e1
% 230.48/41.76  | | | | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | | | | ALPHA: (104) implies:
% 230.48/41.76  | | | | | | | | | | | | | |   (105)  all_57_1 = e1
% 230.48/41.76  | | | | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | | | | COMBINE_EQS: (102), (105) imply:
% 230.48/41.76  | | | | | | | | | | | | | |   (106)  e1 = e0
% 230.48/41.76  | | | | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | | | | SIMP: (106) implies:
% 230.48/41.76  | | | | | | | | | | | | | |   (107)  e1 = e0
% 230.48/41.76  | | | | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | | | | COMBINE_EQS: (89), (107) imply:
% 230.48/41.76  | | | | | | | | | | | | | |   (108)  all_57_11 = e0
% 230.48/41.76  | | | | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (10), (11), (18), (19), (22), (25),
% 230.48/41.76  | | | | | | | | | | | | | |            (26), (28), (32), (33), (36), (37), (41), (42),
% 230.48/41.76  | | | | | | | | | | | | | |            (108) are inconsistent by sub-proof #1122.
% 230.48/41.76  | | | | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | | | Case 2:
% 230.48/41.76  | | | | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | | | |   (109)  all_57_3 = e1 & op(e2, e2) = e1
% 230.48/41.76  | | | | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | | | | ALPHA: (109) implies:
% 230.48/41.76  | | | | | | | | | | | | | |   (110)  op(e2, e2) = e1
% 230.48/41.76  | | | | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | | | | REF_CLOSE: (8), (27), (36), (110) are inconsistent by
% 230.48/41.76  | | | | | | | | | | | | | |            sub-proof #2306.
% 230.48/41.76  | | | | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | | | End of split
% 230.48/41.76  | | | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | | Case 2:
% 230.48/41.76  | | | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | | |   (111)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 230.48/41.76  | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 230.48/41.76  | | | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | | | BETA: splitting (111) gives:
% 230.48/41.76  | | | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | | | Case 1:
% 230.48/41.76  | | | | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | | | |   (112)  all_57_7 = e1 & op(e1, e2) = e1
% 230.48/41.76  | | | | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | | | | ALPHA: (112) implies:
% 230.48/41.76  | | | | | | | | | | | | | |   (113)  all_57_7 = e1
% 230.48/41.76  | | | | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (10), (11), (18), (19), (22), (25),
% 230.48/41.76  | | | | | | | | | | | | | |            (26), (28), (32), (36), (37), (41), (113) are
% 230.48/41.76  | | | | | | | | | | | | | |            inconsistent by sub-proof #1245.
% 230.48/41.76  | | | | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | | | Case 2:
% 230.48/41.76  | | | | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | | | |   (114)  all_57_13 = e1 & op(e0, e2) = e1
% 230.48/41.76  | | | | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | | | | ALPHA: (114) implies:
% 230.48/41.76  | | | | | | | | | | | | | |   (115)  all_57_13 = e1
% 230.48/41.76  | | | | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | | | | BETA: splitting (93) gives:
% 230.48/41.76  | | | | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | | | | Case 1:
% 230.48/41.76  | | | | | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | | | | |   (116)  all_57_12 = e0 & op(e0, e3) = e0
% 230.48/41.76  | | | | | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | | | | | ALPHA: (116) implies:
% 230.48/41.76  | | | | | | | | | | | | | | |   (117)  all_57_12 = e0
% 230.48/41.76  | | | | | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with e0, e2, e1, e1, simplifying
% 230.48/41.76  | | | | | | | | | | | | | | |              with (33), (83) gives:
% 230.48/41.76  | | | | | | | | | | | | | | |   (118)  e2 = e0
% 230.48/41.76  | | | | | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | | | | | COMBINE_EQS: (43), (118) imply:
% 230.48/41.76  | | | | | | | | | | | | | | |   (119)  all_57_3 = e0
% 230.48/41.76  | | | | | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (12), (15), (16),
% 230.48/41.76  | | | | | | | | | | | | | | |            (18), (19), (20), (21), (22), (24), (26), (28),
% 230.48/41.76  | | | | | | | | | | | | | | |            (29), (31), (34), (35), (36), (37), (38), (40),
% 230.48/41.76  | | | | | | | | | | | | | | |            (41), (42), (44), (45), (46), (83), (94), (117),
% 230.48/41.76  | | | | | | | | | | | | | | |            (119) are inconsistent by sub-proof #1500.
% 230.48/41.76  | | | | | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | | | | Case 2:
% 230.48/41.76  | | | | | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | | | | |   (120)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 230.48/41.76  | | | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 230.48/41.76  | | | | | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | | | | | BETA: splitting (120) gives:
% 230.48/41.76  | | | | | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | | | | | Case 1:
% 230.48/41.76  | | | | | | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | | | | | |   (121)  all_57_13 = e0 & op(e0, e2) = e0
% 230.48/41.76  | | | | | | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | | | | | | ALPHA: (121) implies:
% 230.48/41.76  | | | | | | | | | | | | | | | |   (122)  all_57_13 = e0
% 230.48/41.76  | | | | | | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | | | | | | COMBINE_EQS: (115), (122) imply:
% 230.48/41.76  | | | | | | | | | | | | | | | |   (123)  e1 = e0
% 230.48/41.76  | | | | | | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | | | | | | COMBINE_EQS: (89), (123) imply:
% 230.48/41.76  | | | | | | | | | | | | | | | |   (124)  all_57_11 = e0
% 230.48/41.76  | | | | | | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (10), (11), (18), (19), (22), (25),
% 230.48/41.76  | | | | | | | | | | | | | | | |            (26), (28), (32), (33), (36), (37), (41), (42),
% 230.48/41.76  | | | | | | | | | | | | | | | |            (124) are inconsistent by sub-proof #1122.
% 230.48/41.76  | | | | | | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | | | | | Case 2:
% 230.48/41.76  | | | | | | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | | | | | |   (125)  all_57_14 = e0 & op(e0, e1) = e0
% 230.48/41.76  | | | | | | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | | | | | | ALPHA: (125) implies:
% 230.48/41.76  | | | | | | | | | | | | | | | |   (126)  all_57_14 = e0
% 230.48/41.76  | | | | | | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | | | | | | COMBINE_EQS: (77), (126) imply:
% 230.48/41.76  | | | | | | | | | | | | | | | |   (127)  e2 = e0
% 230.48/41.76  | | | | | | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | | | | | | COMBINE_EQS: (43), (127) imply:
% 230.48/41.76  | | | | | | | | | | | | | | | |   (128)  all_57_3 = e0
% 230.48/41.76  | | | | | | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (5), (6), (8), (9), (10), (11), (18),
% 230.48/41.76  | | | | | | | | | | | | | | | |            (19), (21), (22), (24), (26), (28), (32), (35),
% 230.48/41.76  | | | | | | | | | | | | | | | |            (36), (37), (38), (40), (41), (45), (102), (128)
% 230.48/41.76  | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1439.
% 230.48/41.76  | | | | | | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | | | | | End of split
% 230.48/41.76  | | | | | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | | | | End of split
% 230.48/41.76  | | | | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | | | End of split
% 230.48/41.76  | | | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | | End of split
% 230.48/41.76  | | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | End of split
% 230.48/41.76  | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | Case 2:
% 230.48/41.76  | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | |   (129)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 230.48/41.76  | | | | | | | | | | |            & op(e3, e0) = e0)
% 230.48/41.76  | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | BETA: splitting (129) gives:
% 230.48/41.76  | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | Case 1:
% 230.48/41.76  | | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | |   (130)  all_57_4 = e0 & op(e3, e1) = e0
% 230.48/41.76  | | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | | ALPHA: (130) implies:
% 230.48/41.76  | | | | | | | | | | | |   (131)  all_57_4 = e0
% 230.48/41.76  | | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | | COMBINE_EQS: (97), (131) imply:
% 230.48/41.76  | | | | | | | | | | | |   (132)  e1 = e0
% 230.48/41.76  | | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | | COMBINE_EQS: (89), (132) imply:
% 230.48/41.76  | | | | | | | | | | | |   (133)  all_57_11 = e0
% 230.48/41.76  | | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (10), (11), (18), (19), (22), (25),
% 230.48/41.76  | | | | | | | | | | | |            (26), (28), (32), (33), (36), (37), (41), (42),
% 230.48/41.76  | | | | | | | | | | | |            (133) are inconsistent by sub-proof #1122.
% 230.48/41.76  | | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | Case 2:
% 230.48/41.76  | | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | |   (134)  all_57_9 = e0 & op(e3, e0) = e0
% 230.48/41.76  | | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (12),
% 230.48/41.76  | | | | | | | | | | | |            (13), (15), (16), (17), (18), (19), (20), (21),
% 230.48/41.76  | | | | | | | | | | | |            (22), (24), (26), (28), (29), (31), (32), (34),
% 230.48/41.76  | | | | | | | | | | | |            (35), (36), (37), (38), (39), (40), (41), (42),
% 230.48/41.76  | | | | | | | | | | | |            (43), (44), (45), (46), (83), (134) are
% 230.48/41.76  | | | | | | | | | | | |            inconsistent by sub-proof #1160.
% 230.48/41.76  | | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | | End of split
% 230.48/41.76  | | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | End of split
% 230.48/41.76  | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | Case 2:
% 230.48/41.76  | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | |   (135)  all_57_5 = e1 & op(e2, e1) = e1
% 230.48/41.76  | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | ALPHA: (135) implies:
% 230.48/41.76  | | | | | | | | | |   (136)  all_57_5 = e1
% 230.48/41.76  | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | COMBINE_EQS: (24), (136) imply:
% 230.48/41.76  | | | | | | | | | |   (137)  e3 = e1
% 230.48/41.76  | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | COMBINE_EQS: (34), (137) imply:
% 230.48/41.76  | | | | | | | | | |   (138)  all_57_7 = e1
% 230.48/41.76  | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | | REF_CLOSE: (6), (8), (9), (10), (11), (18), (19), (22), (25),
% 230.48/41.76  | | | | | | | | | |            (26), (28), (32), (36), (37), (41), (138) are
% 230.48/41.76  | | | | | | | | | |            inconsistent by sub-proof #1245.
% 230.48/41.76  | | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | End of split
% 230.48/41.76  | | | | | | | | | 
% 230.48/41.76  | | | | | | | | Case 2:
% 230.48/41.76  | | | | | | | | | 
% 230.48/41.76  | | | | | | | | |   (139)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 &
% 230.48/41.76  | | | | | | | | |            op(e0, e1) = e1)
% 230.48/41.76  | | | | | | | | | 
% 230.48/41.76  | | | | | | | | | REF_CLOSE: (8), (28), (36), (77), (83), (139) are inconsistent
% 230.48/41.76  | | | | | | | | |            by sub-proof #2374.
% 230.48/41.76  | | | | | | | | | 
% 230.48/41.76  | | | | | | | | End of split
% 230.48/41.76  | | | | | | | | 
% 230.48/41.76  | | | | | | | End of split
% 230.48/41.76  | | | | | | | 
% 230.48/41.76  | | | | | | End of split
% 230.48/41.76  | | | | | | 
% 230.48/41.76  | | | | | End of split
% 230.48/41.76  | | | | | 
% 230.48/41.76  | | | | Case 2:
% 230.48/41.76  | | | | | 
% 230.48/41.76  | | | | |   (140)  all_57_11 = e0 & op(e1, e0) = e0
% 230.48/41.76  | | | | | 
% 230.48/41.76  | | | | | ALPHA: (140) implies:
% 230.48/41.76  | | | | |   (141)  all_57_11 = e0
% 230.48/41.76  | | | | | 
% 230.48/41.76  | | | | | REF_CLOSE: (6), (8), (9), (10), (11), (18), (19), (22), (25), (26),
% 230.48/41.76  | | | | |            (28), (32), (33), (36), (37), (41), (42), (141) are
% 230.48/41.76  | | | | |            inconsistent by sub-proof #1122.
% 230.48/41.76  | | | | | 
% 230.48/41.76  | | | | End of split
% 230.48/41.76  | | | | 
% 230.48/41.76  | | | End of split
% 230.48/41.76  | | | 
% 230.48/41.76  | | Case 2:
% 230.48/41.76  | | | 
% 230.48/41.76  | | |   (142)  all_57_15 = e2 & op(e0, e0) = e2
% 230.48/41.76  | | | 
% 230.48/41.76  | | | ALPHA: (142) implies:
% 230.48/41.76  | | |   (143)  all_57_15 = e2
% 230.48/41.76  | | | 
% 230.48/41.76  | | | REF_CLOSE: (18), (22), (143) are inconsistent by sub-proof #2058.
% 230.48/41.76  | | | 
% 230.48/41.76  | | End of split
% 230.48/41.76  | | 
% 230.48/41.76  | End of split
% 230.48/41.76  | 
% 230.48/41.76  End of proof
% 230.48/41.76  
% 230.48/41.76  Sub-proof #1122 shows that the following formulas are inconsistent:
% 230.48/41.76  ----------------------------------------------------------------
% 230.48/41.76    (1)   ~ (e3 = e1)
% 230.48/41.76    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.48/41.76           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.48/41.76    (3)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.48/41.76         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.48/41.76    (4)   ~ (all_6_2 = e3)
% 230.48/41.76    (5)  op(e1, e1) = all_6_2
% 230.48/41.76    (6)   ~ (e3 = e2)
% 230.48/41.76    (7)   ~ (e3 = e0)
% 230.48/41.76    (8)  all_57_15 = e3
% 230.48/41.76    (9)  all_57_6 = e2
% 230.48/41.76    (10)  all_57_11 = e0
% 230.48/41.76    (11)   ~ (e2 = e0)
% 230.48/41.76    (12)   ~ (e1 = e0)
% 230.48/41.76    (13)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.48/41.76              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.48/41.76                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.48/41.76                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.48/41.76    (14)  op(e1, e1) = e2
% 230.48/41.76    (15)   ~ (e2 = e1)
% 230.48/41.76    (16)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.48/41.76          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.48/41.76    (17)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.48/41.76          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.48/41.76    (18)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.48/41.76          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.48/41.76  
% 230.48/41.76  Begin of proof
% 230.48/41.76  | 
% 230.48/41.76  | BETA: splitting (18) gives:
% 230.48/41.76  | 
% 230.48/41.76  | Case 1:
% 230.48/41.76  | | 
% 230.48/41.76  | |   (19)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) =
% 230.48/41.76  | |           e1)
% 230.48/41.76  | | 
% 230.48/41.76  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13),
% 230.48/41.76  | |            (15), (16), (17), (19) are inconsistent by sub-proof #1123.
% 230.48/41.76  | | 
% 230.48/41.76  | Case 2:
% 230.48/41.76  | | 
% 230.48/41.76  | |   (20)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) =
% 230.48/41.76  | |           e1)
% 230.48/41.76  | | 
% 230.48/41.76  | | REF_CLOSE: (2), (10), (12), (14), (15), (20) are inconsistent by sub-proof
% 230.48/41.76  | |            #1861.
% 230.48/41.76  | | 
% 230.48/41.76  | End of split
% 230.48/41.76  | 
% 230.48/41.76  End of proof
% 230.48/41.76  
% 230.48/41.76  Sub-proof #1123 shows that the following formulas are inconsistent:
% 230.48/41.76  ----------------------------------------------------------------
% 230.48/41.76    (1)   ~ (e3 = e1)
% 230.48/41.76    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.48/41.76           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.48/41.76    (3)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.48/41.76         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.48/41.76    (4)   ~ (all_6_2 = e3)
% 230.48/41.76    (5)  op(e1, e1) = all_6_2
% 230.48/41.76    (6)   ~ (e3 = e2)
% 230.48/41.76    (7)   ~ (e3 = e0)
% 230.48/41.76    (8)  all_57_15 = e3
% 230.48/41.76    (9)  all_57_6 = e2
% 230.48/41.76    (10)   ~ (e2 = e0)
% 230.48/41.76    (11)   ~ (e1 = e0)
% 230.48/41.76    (12)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.48/41.76              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.48/41.76                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.48/41.76                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.48/41.76    (13)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1)
% 230.48/41.76    (14)   ~ (e2 = e1)
% 230.48/41.76    (15)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.48/41.76          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.48/41.76    (16)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.48/41.76          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.48/41.76  
% 230.48/41.76  Begin of proof
% 230.48/41.76  | 
% 230.48/41.76  | BETA: splitting (13) gives:
% 230.48/41.76  | 
% 230.48/41.76  | Case 1:
% 230.48/41.76  | | 
% 230.48/41.76  | |   (17)  all_57_6 = e1 & op(e1, e3) = e1
% 230.48/41.76  | | 
% 230.48/41.76  | | REF_CLOSE: (9), (14), (17) are inconsistent by sub-proof #2389.
% 230.48/41.76  | | 
% 230.48/41.76  | Case 2:
% 230.48/41.76  | | 
% 230.48/41.76  | |   (18)  all_57_7 = e1 & op(e1, e2) = e1
% 230.48/41.76  | | 
% 230.48/41.76  | | ALPHA: (18) implies:
% 230.48/41.76  | |   (19)  all_57_7 = e1
% 230.48/41.76  | | 
% 230.48/41.76  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 230.48/41.76  | |            (14), (15), (16), (19) are inconsistent by sub-proof #1245.
% 230.48/41.76  | | 
% 230.48/41.76  | End of split
% 230.48/41.76  | 
% 230.48/41.76  End of proof
% 230.48/41.76  
% 230.48/41.76  Sub-proof #1124 shows that the following formulas are inconsistent:
% 230.48/41.76  ----------------------------------------------------------------
% 230.48/41.76    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.48/41.76         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.48/41.76    (2)   ~ (all_52_7 = e3)
% 230.48/41.76    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.48/41.76         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.48/41.76    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.48/41.76         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.48/41.76    (5)   ~ (e3 = e1)
% 230.48/41.76    (6)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.48/41.76         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.48/41.76    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.48/41.76           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.48/41.76    (8)  op(all_52_7, all_52_7) = e0
% 230.48/41.76    (9)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.48/41.76         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.48/41.76    (10)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.48/41.76          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.48/41.76    (11)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.48/41.76          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.48/41.76    (12)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 230.48/41.76          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.48/41.76    (13)   ~ (e3 = e2)
% 230.48/41.76    (14)   ~ (e3 = e0)
% 230.48/41.76    (15)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.48/41.76          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.48/41.76    (16)  op(e3, e3) = e3
% 230.48/41.76    (17)  all_57_15 = e3
% 230.48/41.76    (18)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.48/41.76          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.48/41.76            e1)
% 230.48/41.76    (19)  all_57_5 = e3
% 230.48/41.76    (20)  all_57_6 = e2
% 230.48/41.76    (21)   ~ (e2 = e0)
% 230.48/41.76    (22)   ~ (e1 = e0)
% 230.48/41.76    (23)  op(e0, e0) = e3
% 230.48/41.76    (24)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.48/41.76          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.48/41.76            e2)
% 230.48/41.76    (25)  all_57_6 = e0 & op(e1, e3) = e0
% 230.48/41.76    (26)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.48/41.76              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.48/41.76                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.48/41.76                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.48/41.76    (27)  op(e1, e1) = e2
% 230.48/41.76    (28)  all_57_7 = e3
% 230.48/41.76    (29)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.48/41.76          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.48/41.76    (30)   ~ (e2 = e1)
% 230.48/41.76    (31)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.48/41.76          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.48/41.76    (32)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.48/41.76          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.48/41.76    (33)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.48/41.76          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.48/41.76    (34)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.48/41.76          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.48/41.76    (35)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.48/41.76          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.48/41.76    (36)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.48/41.76          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.48/41.76    (37)  all_57_3 = e2
% 230.48/41.76    (38)  op(e3, e0) = all_52_7
% 230.48/41.76    (39)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.48/41.76          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.48/41.76    (40)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.48/41.76          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.48/41.76  
% 230.48/41.76  Begin of proof
% 230.48/41.76  | 
% 230.48/41.76  | ALPHA: (25) implies:
% 230.48/41.76  |   (41)  all_57_6 = e0
% 230.48/41.76  | 
% 230.48/41.76  | COMBINE_EQS: (20), (41) imply:
% 230.48/41.76  |   (42)  e2 = e0
% 230.48/41.76  | 
% 230.48/41.76  | COMBINE_EQS: (37), (42) imply:
% 230.48/41.76  |   (43)  all_57_3 = e0
% 230.48/41.76  | 
% 230.48/41.76  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 230.48/41.76  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 230.48/41.76  |            (24), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 230.48/41.76  |            (36), (38), (39), (40), (43) are inconsistent by sub-proof #1461.
% 230.48/41.76  | 
% 230.48/41.76  End of proof
% 230.48/41.76  
% 230.48/41.76  Sub-proof #1125 shows that the following formulas are inconsistent:
% 230.48/41.76  ----------------------------------------------------------------
% 230.48/41.76    (1)  all_57_4 = e2 & op(e3, e1) = e2
% 230.48/41.76    (2)  all_57_4 = e1
% 230.48/41.76    (3)   ~ (e2 = e1)
% 230.48/41.76  
% 230.48/41.76  Begin of proof
% 230.48/41.76  | 
% 230.48/41.76  | ALPHA: (1) implies:
% 230.48/41.76  |   (4)  all_57_4 = e2
% 230.48/41.76  | 
% 230.48/41.76  | COMBINE_EQS: (2), (4) imply:
% 230.48/41.76  |   (5)  e2 = e1
% 230.48/41.76  | 
% 230.48/41.76  | REDUCE: (3), (5) imply:
% 230.48/41.76  |   (6)  $false
% 230.48/41.76  | 
% 230.48/41.76  | CLOSE: (6) is inconsistent.
% 230.48/41.76  | 
% 230.48/41.76  End of proof
% 230.48/41.76  
% 230.48/41.76  Sub-proof #1126 shows that the following formulas are inconsistent:
% 230.48/41.76  ----------------------------------------------------------------
% 230.48/41.76    (1)  all_57_9 = e2
% 230.48/41.76    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.48/41.76         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.48/41.77    (3)   ~ (all_52_7 = e3)
% 230.48/41.77    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.48/41.77         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.48/41.77    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.48/41.77         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.48/41.77    (6)   ~ (e3 = e1)
% 230.48/41.77    (7)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.48/41.77         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.48/41.77    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.48/41.77           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.48/41.77    (9)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.48/41.77         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.48/41.77    (10)   ~ (all_6_2 = e3)
% 230.48/41.77    (11)  op(e1, e1) = all_6_2
% 230.48/41.77    (12)  op(all_52_7, all_52_7) = e0
% 230.48/41.77    (13)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.48/41.77          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.48/41.77    (14)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 230.48/41.77            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 230.48/41.77              e3) = all_22_1 & $i(all_22_1))
% 230.48/41.77    (15)   ~ (all_53_13 = e2)
% 230.48/41.77    (16)   ~ (all_53_7 = e2)
% 230.48/41.77    (17)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.48/41.77          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.48/41.77    (18)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.48/41.77          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.48/41.77    (19)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 230.48/41.77          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.48/41.77    (20)   ~ (e3 = e2)
% 230.48/41.77    (21)   ~ (e3 = e0)
% 230.48/41.77    (22)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.48/41.77          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.48/41.77    (23)  op(e3, e3) = e3
% 230.48/41.77    (24)  all_57_15 = e3
% 230.48/41.77    (25)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.48/41.77          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.48/41.77            e1)
% 230.48/41.77    (26)  all_57_5 = e3
% 230.48/41.77    (27)  op(e3, e3) = all_52_1
% 230.48/41.77    (28)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.48/41.77          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.48/41.77    (29)  op(all_52_1, all_52_1) = e3
% 230.48/41.77    (30)   ~ (e2 = e0)
% 230.48/41.77    (31)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 230.48/41.77            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 230.48/41.77              e3) = all_12_1 & $i(all_12_1))
% 230.48/41.77    (32)  op(e2, e2) = e2
% 230.48/41.77    (33)   ~ (e1 = e0)
% 230.48/41.77    (34)  all_57_14 = e1
% 230.48/41.77    (35)  op(e0, e0) = e3
% 230.48/41.77    (36)  op(e0, e2) = all_53_7
% 230.48/41.77    (37)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.48/41.77          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.48/41.77            e2)
% 230.48/41.77    (38)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.48/41.77              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.48/41.77                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.48/41.77                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.48/41.77    (39)  op(e2, e0) = all_53_13
% 230.48/41.77    (40)  all_57_7 = e3
% 230.48/41.77    (41)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.48/41.77          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.48/41.77    (42)   ~ (e2 = e1)
% 230.48/41.77    (43)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.48/41.77          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.48/41.77    (44)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.48/41.77          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.48/41.77    (45)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.48/41.77          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.48/41.77    (46)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.48/41.77          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.48/41.77    (47)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.48/41.77          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.48/41.77    (48)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.48/41.77          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.48/41.77    (49)  all_57_3 = e2
% 230.48/41.77    (50)  op(e3, e0) = all_52_7
% 230.48/41.77    (51)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.48/41.77          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.48/41.77    (52)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.48/41.77          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.48/41.77  
% 230.48/41.77  Begin of proof
% 230.48/41.77  | 
% 230.48/41.77  | BETA: splitting (37) gives:
% 230.48/41.77  | 
% 230.48/41.77  | Case 1:
% 230.48/41.77  | | 
% 230.48/41.77  | |   (53)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 230.48/41.77  | |           e2)
% 230.48/41.77  | | 
% 230.48/41.77  | | BETA: splitting (53) gives:
% 230.48/41.77  | | 
% 230.48/41.77  | | Case 1:
% 230.48/41.77  | | | 
% 230.48/41.77  | | |   (54)  all_57_12 = e2 & op(e0, e3) = e2
% 230.48/41.77  | | | 
% 230.48/41.77  | | | ALPHA: (54) implies:
% 230.48/41.77  | | |   (55)  all_57_12 = e2
% 230.48/41.77  | | | 
% 230.48/41.77  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 230.48/41.77  | | |            (13), (14), (15), (17), (18), (19), (20), (21), (22), (23),
% 230.48/41.77  | | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 230.48/41.77  | | |            (35), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 230.48/41.77  | | |            (46), (47), (48), (49), (50), (51), (52), (55) are inconsistent
% 230.48/41.77  | | |            by sub-proof #1127.
% 230.48/41.77  | | | 
% 230.48/41.77  | | Case 2:
% 230.48/41.77  | | | 
% 230.48/41.77  | | |   (56)  all_57_13 = e2 & op(e0, e2) = e2
% 230.48/41.77  | | | 
% 230.48/41.77  | | | ALPHA: (56) implies:
% 230.48/41.77  | | |   (57)  op(e0, e2) = e2
% 230.48/41.77  | | | 
% 230.48/41.77  | | | REF_CLOSE: (8), (16), (36), (57) are inconsistent by sub-proof #2335.
% 230.48/41.77  | | | 
% 230.48/41.77  | | End of split
% 230.48/41.77  | | 
% 230.48/41.77  | Case 2:
% 230.48/41.77  | | 
% 230.48/41.77  | |   (58)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.48/41.77  | |           e2)
% 230.48/41.77  | | 
% 230.48/41.77  | | REF_CLOSE: (20), (24), (34), (42), (58) are inconsistent by sub-proof #1418.
% 230.48/41.77  | | 
% 230.48/41.77  | End of split
% 230.48/41.77  | 
% 230.48/41.77  End of proof
% 230.48/41.77  
% 230.48/41.77  Sub-proof #1127 shows that the following formulas are inconsistent:
% 230.48/41.77  ----------------------------------------------------------------
% 230.48/41.77    (1)  all_57_9 = e2
% 230.48/41.77    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.48/41.77         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.48/41.77    (3)   ~ (all_52_7 = e3)
% 230.48/41.77    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.48/41.77         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.48/41.77    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.48/41.77         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.48/41.77    (6)   ~ (e3 = e1)
% 230.48/41.77    (7)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.48/41.77         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.48/41.77    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.48/41.77           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.48/41.77    (9)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.48/41.77         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.48/41.77    (10)   ~ (all_6_2 = e3)
% 230.48/41.77    (11)  op(e1, e1) = all_6_2
% 230.48/41.77    (12)  op(all_52_7, all_52_7) = e0
% 230.48/41.77    (13)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.48/41.77          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.48/41.77    (14)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 230.48/41.77            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 230.48/41.77              e3) = all_22_1 & $i(all_22_1))
% 230.48/41.77    (15)   ~ (all_53_13 = e2)
% 230.48/41.77    (16)  all_57_12 = e2
% 230.48/41.77    (17)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.48/41.77          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.48/41.77    (18)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.48/41.77          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.48/41.77    (19)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 230.48/41.77          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.48/41.77    (20)   ~ (e3 = e2)
% 230.48/41.77    (21)   ~ (e3 = e0)
% 230.48/41.77    (22)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.48/41.77          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.48/41.77    (23)  op(e3, e3) = e3
% 230.48/41.77    (24)  all_57_15 = e3
% 230.48/41.77    (25)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.48/41.77          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.48/41.77            e1)
% 230.48/41.77    (26)  all_57_5 = e3
% 230.48/41.77    (27)  op(e3, e3) = all_52_1
% 230.48/41.77    (28)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.48/41.77          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.48/41.77    (29)  op(all_52_1, all_52_1) = e3
% 230.48/41.77    (30)   ~ (e2 = e0)
% 230.48/41.77    (31)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 230.48/41.77            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 230.48/41.77              e3) = all_12_1 & $i(all_12_1))
% 230.48/41.77    (32)  op(e2, e2) = e2
% 230.48/41.77    (33)   ~ (e1 = e0)
% 230.48/41.77    (34)  op(e0, e0) = e3
% 230.48/41.77    (35)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.48/41.77          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.48/41.77            e2)
% 230.48/41.77    (36)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.48/41.77              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.48/41.77                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.48/41.77                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.48/41.77    (37)  op(e2, e0) = all_53_13
% 230.48/41.77    (38)  all_57_7 = e3
% 230.48/41.77    (39)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.48/41.77          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.48/41.77    (40)   ~ (e2 = e1)
% 230.48/41.77    (41)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.48/41.77          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.48/41.77    (42)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.48/41.77          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.48/41.77    (43)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.48/41.77          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.48/41.77    (44)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.48/41.77          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.48/41.77    (45)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.48/41.77          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.48/41.77    (46)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.48/41.77          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.48/41.77    (47)  all_57_3 = e2
% 230.48/41.77    (48)  op(e3, e0) = all_52_7
% 230.48/41.77    (49)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.48/41.77          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.48/41.77    (50)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.48/41.77          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.48/41.77  
% 230.48/41.77  Begin of proof
% 230.48/41.77  | 
% 230.48/41.77  | BETA: splitting (43) gives:
% 230.48/41.77  | 
% 230.48/41.77  | Case 1:
% 230.48/41.77  | | 
% 230.48/41.77  | |   (51)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) =
% 230.48/41.77  | |           e2)
% 230.48/41.77  | | 
% 230.48/41.77  | | BETA: splitting (51) gives:
% 230.48/41.77  | | 
% 230.48/41.77  | | Case 1:
% 230.48/41.77  | | | 
% 230.48/41.77  | | |   (52)  all_57_4 = e2 & op(e3, e1) = e2
% 230.48/41.77  | | | 
% 230.48/41.77  | | | ALPHA: (52) implies:
% 230.48/41.77  | | |   (53)  all_57_4 = e2
% 230.48/41.77  | | | 
% 230.48/41.77  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (12), (13), (16), (17),
% 230.48/41.77  | | |            (18), (19), (20), (21), (22), (23), (24), (25), (26), (28),
% 230.48/41.77  | | |            (30), (33), (34), (35), (36), (38), (39), (40), (41), (42),
% 230.48/41.77  | | |            (43), (44), (45), (46), (47), (48), (49), (50), (53) are
% 230.48/41.77  | | |            inconsistent by sub-proof #1158.
% 230.48/41.77  | | | 
% 230.48/41.77  | | Case 2:
% 230.48/41.77  | | | 
% 230.48/41.77  | | |   (54)  all_57_5 = e2 & op(e2, e1) = e2
% 230.48/41.77  | | | 
% 230.48/41.77  | | | REF_CLOSE: (20), (26), (54) are inconsistent by sub-proof #2425.
% 230.48/41.77  | | | 
% 230.48/41.77  | | End of split
% 230.48/41.77  | | 
% 230.48/41.77  | Case 2:
% 230.48/41.77  | | 
% 230.48/41.77  | |   (55)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) =
% 230.48/41.77  | |           e2)
% 230.48/41.77  | | 
% 230.48/41.77  | | BETA: splitting (55) gives:
% 230.48/41.77  | | 
% 230.48/41.77  | | Case 1:
% 230.48/41.77  | | | 
% 230.48/41.77  | | |   (56)  all_57_8 = e2 & op(e1, e1) = e2
% 230.48/41.77  | | | 
% 230.48/41.77  | | | ALPHA: (56) implies:
% 230.48/41.77  | | |   (57)  op(e1, e1) = e2
% 230.48/41.77  | | | 
% 230.48/41.77  | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 230.48/41.77  | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 230.48/41.77  | | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 230.48/41.77  | | |            (34), (35), (36), (37), (38), (39), (40), (41), (42), (43),
% 230.48/41.77  | | |            (44), (45), (46), (47), (48), (49), (50), (57) are inconsistent
% 230.48/41.77  | | |            by sub-proof #1129.
% 230.48/41.77  | | | 
% 230.48/41.77  | | Case 2:
% 230.48/41.77  | | | 
% 230.48/41.77  | | |   (58)  all_57_14 = e2 & op(e0, e1) = e2
% 230.48/41.77  | | | 
% 230.48/41.77  | | | ALPHA: (58) implies:
% 230.48/41.77  | | |   (59)  all_57_14 = e2
% 230.48/41.77  | | | 
% 230.48/41.77  | | | BETA: splitting (19) gives:
% 230.48/41.77  | | | 
% 230.48/41.77  | | | Case 1:
% 230.48/41.77  | | | | 
% 230.48/41.77  | | | |   (60)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1)
% 230.48/41.77  | | | |           = e0)
% 230.48/41.77  | | | | 
% 230.48/41.77  | | | | BETA: splitting (60) gives:
% 230.48/41.77  | | | | 
% 230.48/41.77  | | | | Case 1:
% 230.48/41.77  | | | | | 
% 230.48/41.77  | | | | |   (61)  all_57_4 = e0 & op(e3, e1) = e0
% 230.48/41.77  | | | | | 
% 230.48/41.77  | | | | | ALPHA: (61) implies:
% 230.48/41.77  | | | | |   (62)  all_57_4 = e0
% 230.48/41.77  | | | | | 
% 230.48/41.77  | | | | | BETA: splitting (25) gives:
% 230.48/41.77  | | | | | 
% 230.48/41.77  | | | | | Case 1:
% 230.48/41.77  | | | | | | 
% 230.48/41.77  | | | | | |   (63)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 &
% 230.48/41.77  | | | | | |           op(e0, e2) = e1)
% 230.48/41.77  | | | | | | 
% 230.48/41.77  | | | | | | BETA: splitting (63) gives:
% 230.48/41.77  | | | | | | 
% 230.48/41.77  | | | | | | Case 1:
% 230.48/41.77  | | | | | | | 
% 230.48/41.77  | | | | | | |   (64)  all_57_12 = e1 & op(e0, e3) = e1
% 230.48/41.77  | | | | | | | 
% 230.48/41.77  | | | | | | | REF_CLOSE: (16), (40), (64) are inconsistent by sub-proof #2388.
% 230.48/41.77  | | | | | | | 
% 230.48/41.77  | | | | | | Case 2:
% 230.48/41.77  | | | | | | | 
% 230.48/41.77  | | | | | | |   (65)  all_57_13 = e1 & op(e0, e2) = e1
% 230.48/41.77  | | | | | | | 
% 230.48/41.77  | | | | | | | ALPHA: (65) implies:
% 230.48/41.77  | | | | | | |   (66)  all_57_13 = e1
% 230.48/41.77  | | | | | | | 
% 230.48/41.77  | | | | | | | REF_CLOSE: (1), (6), (8), (13), (17), (20), (21), (23), (28),
% 230.48/41.77  | | | | | | |            (30), (33), (38), (40), (47), (62), (66) are
% 230.48/41.77  | | | | | | |            inconsistent by sub-proof #1128.
% 230.48/41.77  | | | | | | | 
% 230.48/41.77  | | | | | | End of split
% 230.48/41.77  | | | | | | 
% 230.48/41.77  | | | | | Case 2:
% 230.48/41.77  | | | | | | 
% 230.48/41.77  | | | | | |   (67)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 &
% 230.48/41.77  | | | | | |           op(e0, e0) = e1)
% 230.48/41.77  | | | | | | 
% 230.48/41.77  | | | | | | REF_CLOSE: (6), (8), (34), (40), (59), (67) are inconsistent by
% 230.48/41.77  | | | | | |            sub-proof #1139.
% 230.48/41.77  | | | | | | 
% 230.48/41.77  | | | | | End of split
% 230.48/41.77  | | | | | 
% 230.48/41.77  | | | | Case 2:
% 230.48/41.77  | | | | | 
% 230.48/41.77  | | | | |   (68)  all_57_5 = e0 & op(e2, e1) = e0
% 230.48/41.77  | | | | | 
% 230.48/41.77  | | | | | ALPHA: (68) implies:
% 230.48/41.77  | | | | |   (69)  all_57_5 = e0
% 230.48/41.77  | | | | | 
% 230.48/41.77  | | | | | REF_CLOSE: (21), (26), (69) are inconsistent by sub-proof #2471.
% 230.48/41.77  | | | | | 
% 230.48/41.77  | | | | End of split
% 230.48/41.77  | | | | 
% 230.48/41.77  | | | Case 2:
% 230.48/41.77  | | | | 
% 230.48/41.77  | | | |   (70)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1)
% 230.48/41.77  | | | |           = e0)
% 230.48/41.77  | | | | 
% 230.48/41.77  | | | | BETA: splitting (70) gives:
% 230.48/41.77  | | | | 
% 230.48/41.77  | | | | Case 1:
% 230.48/41.77  | | | | | 
% 230.48/41.77  | | | | |   (71)  all_57_8 = e0 & op(e1, e1) = e0
% 230.48/41.77  | | | | | 
% 230.48/41.77  | | | | | ALPHA: (71) implies:
% 230.48/41.77  | | | | |   (72)  op(e1, e1) = e0
% 230.48/41.77  | | | | | 
% 230.48/41.77  | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (12), (13), (16), (17),
% 230.48/41.77  | | | | |            (18), (19), (20), (21), (22), (23), (24), (25), (26), (30),
% 230.48/41.77  | | | | |            (33), (34), (35), (36), (38), (39), (40), (41), (42), (43),
% 230.48/41.77  | | | | |            (44), (45), (46), (47), (48), (49), (50), (59), (72) are
% 230.48/41.77  | | | | |            inconsistent by sub-proof #1138.
% 230.48/41.77  | | | | | 
% 230.48/41.77  | | | | Case 2:
% 230.48/41.77  | | | | | 
% 230.48/41.77  | | | | |   (73)  all_57_14 = e0 & op(e0, e1) = e0
% 230.48/41.77  | | | | | 
% 230.48/41.77  | | | | | ALPHA: (73) implies:
% 230.48/41.77  | | | | |   (74)  all_57_14 = e0
% 230.48/41.77  | | | | | 
% 230.48/41.77  | | | | | REF_CLOSE: (30), (59), (74) are inconsistent by sub-proof #2422.
% 230.48/41.77  | | | | | 
% 230.48/41.77  | | | | End of split
% 230.48/41.77  | | | | 
% 230.48/41.77  | | | End of split
% 230.48/41.77  | | | 
% 230.48/41.77  | | End of split
% 230.48/41.77  | | 
% 230.48/41.77  | End of split
% 230.48/41.77  | 
% 230.48/41.77  End of proof
% 230.48/41.77  
% 230.48/41.77  Sub-proof #1128 shows that the following formulas are inconsistent:
% 230.48/41.77  ----------------------------------------------------------------
% 230.48/41.77    (1)  all_57_9 = e2
% 230.48/41.77    (2)  all_57_13 = e1
% 230.48/41.77    (3)   ~ (e3 = e1)
% 230.48/41.77    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.48/41.77           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.48/41.77    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.48/41.77         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.48/41.77    (6)  all_57_4 = e0
% 230.48/41.77    (7)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.48/41.77         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.48/41.77    (8)   ~ (e3 = e2)
% 230.48/41.77    (9)   ~ (e3 = e0)
% 230.48/41.77    (10)  op(e3, e3) = e3
% 230.48/41.77    (11)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.48/41.77          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.48/41.77    (12)   ~ (e2 = e0)
% 230.48/41.77    (13)   ~ (e1 = e0)
% 230.48/41.77    (14)  all_57_7 = e3
% 230.48/41.77    (15)   ~ (e2 = e1)
% 230.48/41.77    (16)  all_57_3 = e2
% 230.48/41.77  
% 230.48/41.77  Begin of proof
% 230.48/41.77  | 
% 230.48/41.77  | BETA: splitting (11) gives:
% 230.48/41.77  | 
% 230.48/41.77  | Case 1:
% 230.48/41.77  | | 
% 230.48/41.77  | |   (17)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) =
% 230.48/41.77  | |           e0)
% 230.48/41.77  | | 
% 230.48/41.77  | | BETA: splitting (17) gives:
% 230.48/41.77  | | 
% 230.48/41.77  | | Case 1:
% 230.48/41.77  | | | 
% 230.48/41.77  | | |   (18)  all_57_1 = e0 & op(e3, e2) = e0
% 230.48/41.77  | | | 
% 230.48/41.77  | | | ALPHA: (18) implies:
% 230.48/41.77  | | |   (19)  all_57_1 = e0
% 230.48/41.77  | | | 
% 230.48/41.77  | | | REF_CLOSE: (1), (3), (4), (5), (6), (10), (13), (15), (19) are
% 230.48/41.77  | | |            inconsistent by sub-proof #2219.
% 230.48/41.77  | | | 
% 230.48/41.77  | | Case 2:
% 230.48/41.77  | | | 
% 230.48/41.77  | | |   (20)  all_57_3 = e0 & op(e2, e2) = e0
% 230.48/41.77  | | | 
% 230.48/41.77  | | | ALPHA: (20) implies:
% 230.48/41.77  | | |   (21)  all_57_3 = e0
% 230.48/41.77  | | | 
% 230.48/41.77  | | | COMBINE_EQS: (16), (21) imply:
% 230.48/41.77  | | |   (22)  e2 = e0
% 230.48/41.77  | | | 
% 230.48/41.77  | | | COMBINE_EQS: (1), (22) imply:
% 230.48/41.77  | | |   (23)  all_57_9 = e0
% 230.48/41.77  | | | 
% 230.48/41.77  | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (10), (12), (13), (15), (23) are
% 230.48/41.77  | | |            inconsistent by sub-proof #2436.
% 230.48/41.77  | | | 
% 230.48/41.77  | | End of split
% 230.48/41.77  | | 
% 230.48/41.77  | Case 2:
% 230.48/41.77  | | 
% 230.48/41.77  | |   (24)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 230.48/41.77  | |           e0)
% 230.48/41.77  | | 
% 230.48/41.77  | | BETA: splitting (24) gives:
% 230.48/41.77  | | 
% 230.48/41.77  | | Case 1:
% 230.48/41.77  | | | 
% 230.48/41.77  | | |   (25)  all_57_7 = e0 & op(e1, e2) = e0
% 230.48/41.77  | | | 
% 230.48/41.77  | | | REF_CLOSE: (9), (14), (25) are inconsistent by sub-proof #2042.
% 230.48/41.77  | | | 
% 230.48/41.77  | | Case 2:
% 230.48/41.77  | | | 
% 230.48/41.77  | | |   (26)  all_57_13 = e0 & op(e0, e2) = e0
% 230.48/41.77  | | | 
% 230.48/41.77  | | | REF_CLOSE: (2), (13), (26) are inconsistent by sub-proof #1920.
% 230.48/41.77  | | | 
% 230.48/41.77  | | End of split
% 230.48/41.77  | | 
% 230.48/41.77  | End of split
% 230.48/41.77  | 
% 230.48/41.77  End of proof
% 230.48/41.77  
% 230.48/41.77  Sub-proof #1129 shows that the following formulas are inconsistent:
% 230.48/41.77  ----------------------------------------------------------------
% 230.48/41.77    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.48/41.77         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.48/41.77    (2)   ~ (all_52_7 = e3)
% 230.48/41.77    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.48/41.77         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.48/41.77    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.48/41.77         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.48/41.77    (5)   ~ (e3 = e1)
% 230.48/41.77    (6)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.48/41.77         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.48/41.77    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.48/41.77           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.48/41.77    (8)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.48/41.77         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.48/41.77    (9)   ~ (all_6_2 = e3)
% 230.48/41.77    (10)  op(e1, e1) = all_6_2
% 230.48/41.77    (11)  op(all_52_7, all_52_7) = e0
% 230.48/41.77    (12)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.48/41.77          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.48/41.77    (13)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 230.48/41.77            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 230.48/41.77              e3) = all_22_1 & $i(all_22_1))
% 230.48/41.77    (14)   ~ (all_53_13 = e2)
% 230.48/41.77    (15)  all_57_12 = e2
% 230.48/41.77    (16)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.48/41.77          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.48/41.77    (17)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.48/41.77          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.48/41.77    (18)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 230.48/41.77          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.48/41.77    (19)   ~ (e3 = e2)
% 230.48/41.77    (20)   ~ (e3 = e0)
% 230.48/41.77    (21)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.48/41.77          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.48/41.77    (22)  op(e3, e3) = e3
% 230.48/41.77    (23)  all_57_15 = e3
% 230.48/41.77    (24)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.48/41.77          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.48/41.77            e1)
% 230.48/41.77    (25)  all_57_5 = e3
% 230.48/41.77    (26)  op(e3, e3) = all_52_1
% 230.48/41.77    (27)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.48/41.77          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.48/41.77    (28)  op(all_52_1, all_52_1) = e3
% 230.48/41.77    (29)   ~ (e2 = e0)
% 230.48/41.77    (30)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 230.48/41.77            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 230.48/41.77              e3) = all_12_1 & $i(all_12_1))
% 230.48/41.77    (31)  op(e2, e2) = e2
% 230.48/41.77    (32)   ~ (e1 = e0)
% 230.48/41.77    (33)  op(e0, e0) = e3
% 230.48/41.77    (34)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.48/41.77          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.48/41.77            e2)
% 230.48/41.78    (35)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.48/41.78              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.48/41.78                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.48/41.78                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.48/41.78    (36)  op(e1, e1) = e2
% 230.48/41.78    (37)  op(e2, e0) = all_53_13
% 230.48/41.78    (38)  all_57_7 = e3
% 230.48/41.78    (39)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.48/41.78          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.48/41.78    (40)   ~ (e2 = e1)
% 230.48/41.78    (41)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.48/41.78          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.48/41.78    (42)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.48/41.78          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.48/41.78    (43)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.48/41.78          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.48/41.78    (44)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.48/41.78          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.48/41.78    (45)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.48/41.78          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.48/41.78    (46)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.48/41.78          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.48/41.78    (47)  all_57_3 = e2
% 230.48/41.78    (48)  op(e3, e0) = all_52_7
% 230.48/41.78    (49)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.48/41.78          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.48/41.78    (50)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.48/41.78          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.48/41.78  
% 230.48/41.78  Begin of proof
% 230.48/41.78  | 
% 230.48/41.78  | BETA: splitting (16) gives:
% 230.48/41.78  | 
% 230.48/41.78  | Case 1:
% 230.48/41.78  | | 
% 230.48/41.78  | |   (51)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) =
% 230.48/41.78  | |           e2)
% 230.48/41.78  | | 
% 230.48/41.78  | | BETA: splitting (51) gives:
% 230.48/41.78  | | 
% 230.48/41.78  | | Case 1:
% 230.48/41.78  | | | 
% 230.48/41.78  | | |   (52)  all_57_0 = e2 & op(e3, e3) = e2
% 230.48/41.78  | | | 
% 230.48/41.78  | | | ALPHA: (52) implies:
% 230.48/41.78  | | |   (53)  op(e3, e3) = e2
% 230.48/41.78  | | | 
% 230.48/41.78  | | | REF_CLOSE: (7), (19), (26), (28), (31), (53) are inconsistent by sub-proof
% 230.48/41.78  | | |            #1951.
% 230.48/41.78  | | | 
% 230.48/41.78  | | Case 2:
% 230.48/41.78  | | | 
% 230.48/41.78  | | |   (54)  all_57_1 = e2 & op(e3, e2) = e2
% 230.48/41.78  | | | 
% 230.48/41.78  | | | ALPHA: (54) implies:
% 230.48/41.78  | | |   (55)  all_57_1 = e2
% 230.48/41.78  | | | 
% 230.48/41.78  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 230.48/41.78  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 230.48/41.78  | | |            (23), (24), (25), (27), (29), (30), (31), (32), (33), (34),
% 230.48/41.78  | | |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44),
% 230.48/41.78  | | |            (45), (46), (47), (48), (49), (50), (55) are inconsistent by
% 230.48/41.78  | | |            sub-proof #1131.
% 230.48/41.78  | | | 
% 230.48/41.78  | | End of split
% 230.48/41.78  | | 
% 230.48/41.78  | Case 2:
% 230.48/41.78  | | 
% 230.48/41.78  | |   (56)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) =
% 230.48/41.78  | |           e2)
% 230.48/41.78  | | 
% 230.48/41.78  | | BETA: splitting (56) gives:
% 230.48/41.78  | | 
% 230.48/41.78  | | Case 1:
% 230.48/41.78  | | | 
% 230.48/41.78  | | |   (57)  all_57_4 = e2 & op(e3, e1) = e2
% 230.48/41.78  | | | 
% 230.48/41.78  | | | ALPHA: (57) implies:
% 230.48/41.78  | | |   (58)  all_57_4 = e2
% 230.48/41.78  | | | 
% 230.48/41.78  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 230.48/41.78  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 230.48/41.78  | | |            (23), (24), (25), (27), (29), (30), (31), (32), (33), (34),
% 230.48/41.78  | | |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44),
% 230.48/41.78  | | |            (45), (46), (47), (48), (49), (50), (58) are inconsistent by
% 230.48/41.78  | | |            sub-proof #1130.
% 230.48/41.78  | | | 
% 230.48/41.78  | | Case 2:
% 230.48/41.78  | | | 
% 230.48/41.78  | | |   (59)  all_57_9 = e2 & op(e3, e0) = e2
% 230.48/41.78  | | | 
% 230.48/41.78  | | | ALPHA: (59) implies:
% 230.48/41.78  | | |   (60)  all_57_9 = e2
% 230.48/41.78  | | | 
% 230.48/41.78  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 230.48/41.78  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 230.48/41.78  | | |            (23), (24), (25), (29), (30), (31), (32), (33), (34), (35),
% 230.48/41.78  | | |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 230.48/41.78  | | |            (46), (47), (48), (49), (50), (60) are inconsistent by
% 230.48/41.78  | | |            sub-proof #1135.
% 230.48/41.78  | | | 
% 230.48/41.78  | | End of split
% 230.48/41.78  | | 
% 230.48/41.78  | End of split
% 230.48/41.78  | 
% 230.48/41.78  End of proof
% 230.48/41.78  
% 230.48/41.78  Sub-proof #1130 shows that the following formulas are inconsistent:
% 230.48/41.78  ----------------------------------------------------------------
% 230.48/41.78    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.48/41.78         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.48/41.78    (2)   ~ (all_52_7 = e3)
% 230.48/41.78    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.48/41.78         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.48/41.78    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.48/41.78         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.48/41.78    (5)   ~ (e3 = e1)
% 230.48/41.78    (6)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.48/41.78         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.48/41.78    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.48/41.78           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.48/41.78    (8)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.48/41.78         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.48/41.78    (9)   ~ (all_6_2 = e3)
% 230.48/41.78    (10)  op(e1, e1) = all_6_2
% 230.48/41.78    (11)  op(all_52_7, all_52_7) = e0
% 230.48/41.78    (12)  all_57_4 = e2
% 230.48/41.78    (13)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.48/41.78          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.48/41.78    (14)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 230.48/41.78            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 230.48/41.78              e3) = all_22_1 & $i(all_22_1))
% 230.48/41.78    (15)   ~ (all_53_13 = e2)
% 230.48/41.78    (16)  all_57_12 = e2
% 230.48/41.78    (17)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.48/41.78          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.48/41.78    (18)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.48/41.78          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.48/41.78    (19)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 230.48/41.78          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.48/41.78    (20)   ~ (e3 = e2)
% 230.48/41.78    (21)   ~ (e3 = e0)
% 230.48/41.78    (22)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.48/41.78          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.48/41.78    (23)  op(e3, e3) = e3
% 230.48/41.78    (24)  all_57_15 = e3
% 230.48/41.78    (25)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.48/41.78          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.48/41.78            e1)
% 230.48/41.78    (26)  all_57_5 = e3
% 230.48/41.78    (27)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.48/41.78          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.48/41.78    (28)   ~ (e2 = e0)
% 230.48/41.78    (29)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 230.48/41.78            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 230.48/41.78              e3) = all_12_1 & $i(all_12_1))
% 230.48/41.78    (30)  op(e2, e2) = e2
% 230.48/41.78    (31)   ~ (e1 = e0)
% 230.48/41.78    (32)  op(e0, e0) = e3
% 230.48/41.78    (33)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.48/41.78          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.48/41.78            e2)
% 230.48/41.78    (34)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.48/41.78              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.48/41.78                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.48/41.78                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.48/41.78    (35)  op(e1, e1) = e2
% 230.48/41.78    (36)  op(e2, e0) = all_53_13
% 230.48/41.78    (37)  all_57_7 = e3
% 230.48/41.78    (38)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.48/41.78          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.48/41.78    (39)   ~ (e2 = e1)
% 230.48/41.78    (40)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.48/41.78          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.48/41.78    (41)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.48/41.78          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.48/41.78    (42)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.48/41.78          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.48/41.78    (43)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.48/41.78          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.48/41.78    (44)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.48/41.78          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.48/41.78    (45)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.48/41.78          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.48/41.78    (46)  all_57_3 = e2
% 230.48/41.78    (47)  op(e3, e0) = all_52_7
% 230.48/41.78    (48)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.48/41.78          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.48/41.78    (49)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.48/41.78          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.48/41.78  
% 230.48/41.78  Begin of proof
% 230.48/41.78  | 
% 230.48/41.78  | BETA: splitting (40) gives:
% 230.48/41.78  | 
% 230.48/41.78  | Case 1:
% 230.48/41.78  | | 
% 230.48/41.78  | |   (50)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 230.48/41.78  | |           e2)
% 230.48/41.78  | | 
% 230.48/41.78  | | BETA: splitting (50) gives:
% 230.48/41.78  | | 
% 230.48/41.78  | | Case 1:
% 230.48/41.78  | | | 
% 230.48/41.78  | | |   (51)  all_57_9 = e2 & op(e3, e0) = e2
% 230.48/41.78  | | | 
% 230.48/41.78  | | | ALPHA: (51) implies:
% 230.48/41.78  | | |   (52)  all_57_9 = e2
% 230.48/41.78  | | | 
% 230.48/41.78  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (11), (12), (13), (16),
% 230.48/41.78  | | |            (17), (18), (19), (20), (21), (22), (23), (24), (25), (26),
% 230.48/41.78  | | |            (27), (28), (31), (32), (33), (34), (37), (38), (39), (40),
% 230.48/41.78  | | |            (41), (42), (43), (44), (45), (46), (47), (48), (49), (52) are
% 230.48/41.78  | | |            inconsistent by sub-proof #1158.
% 230.48/41.78  | | | 
% 230.48/41.78  | | Case 2:
% 230.48/41.78  | | | 
% 230.48/41.78  | | |   (53)  all_57_10 = e2 & op(e2, e0) = e2
% 230.48/41.78  | | | 
% 230.48/41.78  | | | REF_CLOSE: (7), (15), (36), (53) are inconsistent by sub-proof #2432.
% 230.48/41.78  | | | 
% 230.48/41.78  | | End of split
% 230.48/41.78  | | 
% 230.48/41.78  | Case 2:
% 230.48/41.78  | | 
% 230.48/41.78  | |   (54)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.48/41.78  | |           e2)
% 230.48/41.78  | | 
% 230.48/41.78  | | BETA: splitting (54) gives:
% 230.48/41.78  | | 
% 230.48/41.78  | | Case 1:
% 230.48/41.78  | | | 
% 230.48/41.78  | | |   (55)  all_57_11 = e2 & op(e1, e0) = e2
% 230.48/41.78  | | | 
% 230.48/41.78  | | | ALPHA: (55) implies:
% 230.48/41.78  | | |   (56)  all_57_11 = e2
% 230.48/41.78  | | |   (57)  op(e1, e0) = e2
% 230.48/41.78  | | | 
% 230.48/41.78  | | | BETA: splitting (6) gives:
% 230.48/41.78  | | | 
% 230.48/41.78  | | | Case 1:
% 230.48/41.78  | | | | 
% 230.48/41.78  | | | |   (58)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2)
% 230.48/41.78  | | | |           = e0)
% 230.48/41.78  | | | | 
% 230.48/41.78  | | | | REF_CLOSE: (5), (7), (8), (9), (10), (20), (21), (24), (28), (31), (34),
% 230.48/41.78  | | | |            (35), (39), (40), (44), (45), (56), (58) are inconsistent by
% 230.48/41.78  | | | |            sub-proof #1153.
% 230.48/41.78  | | | | 
% 230.48/41.78  | | | Case 2:
% 230.48/41.78  | | | | 
% 230.48/41.78  | | | |   (59)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.48/41.78  | | | |           = e0)
% 230.48/41.78  | | | | 
% 230.48/41.78  | | | | BETA: splitting (59) gives:
% 230.48/41.78  | | | | 
% 230.48/41.78  | | | | Case 1:
% 230.48/41.78  | | | | | 
% 230.48/41.78  | | | | |   (60)  all_57_8 = e0 & op(e1, e1) = e0
% 230.48/41.78  | | | | | 
% 230.48/41.78  | | | | | ALPHA: (60) implies:
% 230.48/41.78  | | | | |   (61)  op(e1, e1) = e0
% 230.48/41.78  | | | | | 
% 230.48/41.78  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (11), (12), (13), (14),
% 230.48/41.78  | | | | |            (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 230.48/41.78  | | | | |            (26), (28), (29), (30), (31), (32), (33), (34), (35), (37),
% 230.48/41.78  | | | | |            (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 230.48/41.78  | | | | |            (48), (49), (56), (57), (61) are inconsistent by sub-proof
% 230.48/41.78  | | | | |            #1141.
% 230.48/41.78  | | | | | 
% 230.48/41.78  | | | | Case 2:
% 230.48/41.78  | | | | | 
% 230.48/41.78  | | | | |   (62)  all_57_11 = e0 & op(e1, e0) = e0
% 230.48/41.78  | | | | | 
% 230.48/41.78  | | | | | ALPHA: (62) implies:
% 230.48/41.78  | | | | |   (63)  all_57_11 = e0
% 230.48/41.78  | | | | | 
% 230.48/41.78  | | | | | COMBINE_EQS: (56), (63) imply:
% 230.48/41.78  | | | | |   (64)  e2 = e0
% 230.48/41.78  | | | | | 
% 230.48/41.78  | | | | | SIMP: (64) implies:
% 230.48/41.78  | | | | |   (65)  e2 = e0
% 230.48/41.78  | | | | | 
% 230.48/41.78  | | | | | COMBINE_EQS: (46), (65) imply:
% 230.48/41.78  | | | | |   (66)  all_57_3 = e0
% 230.48/41.78  | | | | | 
% 230.48/41.78  | | | | | REF_CLOSE: (4), (5), (7), (12), (13), (17), (18), (20), (21), (23),
% 230.48/41.78  | | | | |            (24), (26), (28), (31), (37), (38), (39), (40), (44), (48),
% 230.48/41.78  | | | | |            (63), (66) are inconsistent by sub-proof #1480.
% 230.48/41.78  | | | | | 
% 230.48/41.78  | | | | End of split
% 230.48/41.78  | | | | 
% 230.48/41.78  | | | End of split
% 230.48/41.78  | | | 
% 230.48/41.78  | | Case 2:
% 230.48/41.78  | | | 
% 230.48/41.78  | | |   (67)  all_57_15 = e2 & op(e0, e0) = e2
% 230.48/41.78  | | | 
% 230.48/41.78  | | | ALPHA: (67) implies:
% 230.48/41.78  | | |   (68)  all_57_15 = e2
% 230.48/41.78  | | | 
% 230.48/41.78  | | | REF_CLOSE: (20), (24), (68) are inconsistent by sub-proof #2058.
% 230.48/41.78  | | | 
% 230.48/41.78  | | End of split
% 230.48/41.78  | | 
% 230.48/41.78  | End of split
% 230.48/41.78  | 
% 230.48/41.78  End of proof
% 230.48/41.78  
% 230.48/41.78  Sub-proof #1131 shows that the following formulas are inconsistent:
% 230.48/41.78  ----------------------------------------------------------------
% 230.48/41.78    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.48/41.78         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.48/41.78    (2)   ~ (all_52_7 = e3)
% 230.48/41.78    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.48/41.78         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.48/41.78    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.48/41.78         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.48/41.78    (5)   ~ (e3 = e1)
% 230.48/41.78    (6)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.48/41.78         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.48/41.78    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.48/41.78           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.48/41.78    (8)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.48/41.78         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.48/41.78    (9)   ~ (all_6_2 = e3)
% 230.48/41.78    (10)  op(e1, e1) = all_6_2
% 230.48/41.78    (11)  op(all_52_7, all_52_7) = e0
% 230.48/41.78    (12)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.48/41.78          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.48/41.78    (13)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 230.48/41.78            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 230.48/41.78              e3) = all_22_1 & $i(all_22_1))
% 230.48/41.78    (14)   ~ (all_53_13 = e2)
% 230.48/41.78    (15)  all_57_12 = e2
% 230.48/41.78    (16)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.48/41.78          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.48/41.78    (17)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.48/41.78          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.48/41.78    (18)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 230.48/41.78          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.48/41.78    (19)   ~ (e3 = e2)
% 230.48/41.78    (20)   ~ (e3 = e0)
% 230.48/41.78    (21)  all_57_1 = e2
% 230.48/41.78    (22)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.48/41.78          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.48/41.78    (23)  op(e3, e3) = e3
% 230.48/41.78    (24)  all_57_15 = e3
% 230.48/41.78    (25)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.48/41.78          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.48/41.78            e1)
% 230.48/41.78    (26)  all_57_5 = e3
% 230.48/41.78    (27)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.48/41.78          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.48/41.78    (28)   ~ (e2 = e0)
% 230.48/41.78    (29)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 230.48/41.78            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 230.48/41.78              e3) = all_12_1 & $i(all_12_1))
% 230.48/41.78    (30)  op(e2, e2) = e2
% 230.48/41.78    (31)   ~ (e1 = e0)
% 230.48/41.78    (32)  op(e0, e0) = e3
% 230.48/41.78    (33)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.48/41.78          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.48/41.78            e2)
% 230.48/41.78    (34)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.48/41.78              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.48/41.78                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.48/41.78                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.48/41.78    (35)  op(e1, e1) = e2
% 230.48/41.78    (36)  op(e2, e0) = all_53_13
% 230.48/41.78    (37)  all_57_7 = e3
% 230.48/41.78    (38)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.48/41.78          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.48/41.78    (39)   ~ (e2 = e1)
% 230.48/41.78    (40)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.48/41.78          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.48/41.78    (41)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.48/41.78          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.48/41.78    (42)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.48/41.78          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.48/41.78    (43)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.48/41.78          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.48/41.78    (44)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.48/41.78          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.48/41.78    (45)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.48/41.78          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.48/41.78    (46)  all_57_3 = e2
% 230.48/41.78    (47)  op(e3, e0) = all_52_7
% 230.48/41.78    (48)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.48/41.78          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.48/41.78    (49)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.48/41.78          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.48/41.78  
% 230.48/41.78  Begin of proof
% 230.48/41.78  | 
% 230.48/41.78  | BETA: splitting (40) gives:
% 230.48/41.78  | 
% 230.48/41.78  | Case 1:
% 230.48/41.78  | | 
% 230.48/41.78  | |   (50)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 230.48/41.78  | |           e2)
% 230.48/41.78  | | 
% 230.48/41.78  | | BETA: splitting (50) gives:
% 230.48/41.78  | | 
% 230.48/41.78  | | Case 1:
% 230.48/41.78  | | | 
% 230.48/41.78  | | |   (51)  all_57_9 = e2 & op(e3, e0) = e2
% 230.48/41.78  | | | 
% 230.48/41.78  | | | ALPHA: (51) implies:
% 230.48/41.78  | | |   (52)  all_57_9 = e2
% 230.48/41.78  | | | 
% 230.48/41.78  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 230.48/41.78  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (22), (23),
% 230.48/41.78  | | |            (24), (25), (26), (28), (29), (30), (31), (32), (33), (34),
% 230.48/41.78  | | |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44),
% 230.48/41.78  | | |            (45), (46), (47), (48), (49), (52) are inconsistent by
% 230.48/41.78  | | |            sub-proof #1135.
% 230.48/41.78  | | | 
% 230.48/41.78  | | Case 2:
% 230.48/41.78  | | | 
% 230.48/41.78  | | |   (53)  all_57_10 = e2 & op(e2, e0) = e2
% 230.48/41.78  | | | 
% 230.48/41.78  | | | REF_CLOSE: (7), (14), (36), (53) are inconsistent by sub-proof #2432.
% 230.48/41.78  | | | 
% 230.48/41.78  | | End of split
% 230.48/41.78  | | 
% 230.48/41.78  | Case 2:
% 230.48/41.78  | | 
% 230.48/41.78  | |   (54)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.48/41.78  | |           e2)
% 230.48/41.78  | | 
% 230.48/41.78  | | BETA: splitting (54) gives:
% 230.48/41.78  | | 
% 230.48/41.78  | | Case 1:
% 230.48/41.78  | | | 
% 230.48/41.78  | | |   (55)  all_57_11 = e2 & op(e1, e0) = e2
% 230.48/41.78  | | | 
% 230.48/41.78  | | | ALPHA: (55) implies:
% 230.48/41.78  | | |   (56)  all_57_11 = e2
% 230.48/41.78  | | | 
% 230.48/41.78  | | | REF_CLOSE: (1), (3), (4), (5), (7), (8), (9), (10), (19), (20), (21),
% 230.48/41.78  | | |            (23), (24), (26), (27), (28), (30), (31), (34), (35), (37),
% 230.48/41.78  | | |            (38), (39), (40), (41), (43), (44), (45), (46), (48), (56) are
% 230.48/41.78  | | |            inconsistent by sub-proof #1132.
% 230.48/41.78  | | | 
% 230.48/41.78  | | Case 2:
% 230.48/41.78  | | | 
% 230.48/41.78  | | |   (57)  all_57_15 = e2 & op(e0, e0) = e2
% 230.48/41.78  | | | 
% 230.48/41.78  | | | ALPHA: (57) implies:
% 230.48/41.78  | | |   (58)  all_57_15 = e2
% 230.48/41.78  | | | 
% 230.48/41.78  | | | REF_CLOSE: (19), (24), (58) are inconsistent by sub-proof #2058.
% 230.48/41.78  | | | 
% 230.48/41.78  | | End of split
% 230.48/41.78  | | 
% 230.48/41.78  | End of split
% 230.48/41.78  | 
% 230.48/41.78  End of proof
% 230.48/41.78  
% 230.48/41.78  Sub-proof #1132 shows that the following formulas are inconsistent:
% 230.48/41.78  ----------------------------------------------------------------
% 230.48/41.78    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.48/41.78         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.48/41.78    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.48/41.78         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.48/41.78    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.48/41.78         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.48/41.78    (4)   ~ (e3 = e1)
% 230.48/41.78    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.48/41.78           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.48/41.78    (6)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.48/41.78         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.48/41.78    (7)   ~ (all_6_2 = e3)
% 230.48/41.78    (8)  op(e1, e1) = all_6_2
% 230.48/41.78    (9)   ~ (e3 = e2)
% 230.48/41.78    (10)   ~ (e3 = e0)
% 230.48/41.78    (11)  all_57_1 = e2
% 230.48/41.78    (12)  op(e3, e3) = e3
% 230.48/41.78    (13)  all_57_15 = e3
% 230.48/41.78    (14)  all_57_5 = e3
% 230.48/41.78    (15)  all_57_11 = e2
% 230.48/41.78    (16)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.48/41.78          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.48/41.78    (17)   ~ (e2 = e0)
% 230.48/41.78    (18)  op(e2, e2) = e2
% 230.48/41.78    (19)   ~ (e1 = e0)
% 230.48/41.78    (20)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.48/41.78              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.48/41.78                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.48/41.78                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.48/41.78    (21)  op(e1, e1) = e2
% 230.48/41.78    (22)  all_57_7 = e3
% 230.48/41.78    (23)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.48/41.78          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.48/41.78    (24)   ~ (e2 = e1)
% 230.48/41.78    (25)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.48/41.78          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.48/41.79    (26)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.48/41.79          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.48/41.79    (27)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.48/41.79          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.48/41.79    (28)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.48/41.79          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.48/41.79    (29)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.48/41.79          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.48/41.79    (30)  all_57_3 = e2
% 230.48/41.79    (31)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.48/41.79          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.48/41.79  
% 230.48/41.79  Begin of proof
% 230.48/41.79  | 
% 230.48/41.79  | BETA: splitting (16) gives:
% 230.48/41.79  | 
% 230.48/41.79  | Case 1:
% 230.48/41.79  | | 
% 230.48/41.79  | |   (32)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) =
% 230.48/41.79  | |           e0)
% 230.48/41.79  | | 
% 230.48/41.79  | | BETA: splitting (32) gives:
% 230.48/41.79  | | 
% 230.48/41.79  | | Case 1:
% 230.48/41.79  | | | 
% 230.48/41.79  | | |   (33)  all_57_1 = e0 & op(e3, e2) = e0
% 230.48/41.79  | | | 
% 230.48/41.79  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 230.48/41.79  | | |            (13), (14), (17), (19), (20), (23), (24), (25), (26), (27),
% 230.48/41.79  | | |            (28), (30), (31), (33) are inconsistent by sub-proof #1134.
% 230.48/41.79  | | | 
% 230.48/41.79  | | Case 2:
% 230.48/41.79  | | | 
% 230.48/41.79  | | |   (34)  all_57_3 = e0 & op(e2, e2) = e0
% 230.48/41.79  | | | 
% 230.48/41.79  | | | ALPHA: (34) implies:
% 230.48/41.79  | | |   (35)  op(e2, e2) = e0
% 230.48/41.79  | | | 
% 230.48/41.79  | | | REF_CLOSE: (5), (17), (18), (35) are inconsistent by sub-proof #2472.
% 230.48/41.79  | | | 
% 230.48/41.79  | | End of split
% 230.48/41.79  | | 
% 230.48/41.79  | Case 2:
% 230.48/41.79  | | 
% 230.48/41.79  | |   (36)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 230.48/41.79  | |           e0)
% 230.48/41.79  | | 
% 230.48/41.79  | | BETA: splitting (36) gives:
% 230.48/41.79  | | 
% 230.48/41.79  | | Case 1:
% 230.48/41.79  | | | 
% 230.48/41.79  | | |   (37)  all_57_7 = e0 & op(e1, e2) = e0
% 230.48/41.79  | | | 
% 230.48/41.79  | | | ALPHA: (37) implies:
% 230.48/41.79  | | |   (38)  all_57_7 = e0
% 230.48/41.79  | | | 
% 230.48/41.79  | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (10), (13), (15), (17), (19),
% 230.48/41.79  | | |            (20), (21), (24), (25), (28), (29), (38) are inconsistent by
% 230.48/41.79  | | |            sub-proof #1154.
% 230.48/41.79  | | | 
% 230.48/41.79  | | Case 2:
% 230.48/41.79  | | | 
% 230.48/41.79  | | |   (39)  all_57_13 = e0 & op(e0, e2) = e0
% 230.48/41.79  | | | 
% 230.48/41.79  | | | ALPHA: (39) implies:
% 230.48/41.79  | | |   (40)  all_57_13 = e0
% 230.48/41.79  | | | 
% 230.48/41.79  | | | BETA: splitting (31) gives:
% 230.48/41.79  | | | 
% 230.48/41.79  | | | Case 1:
% 230.48/41.79  | | | | 
% 230.48/41.79  | | | |   (41)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2)
% 230.48/41.79  | | | |           = e1)
% 230.48/41.79  | | | | 
% 230.48/41.79  | | | | REF_CLOSE: (5), (11), (18), (24), (41) are inconsistent by sub-proof
% 230.48/41.79  | | | |            #1133.
% 230.48/41.79  | | | | 
% 230.48/41.79  | | | Case 2:
% 230.48/41.79  | | | | 
% 230.48/41.79  | | | |   (42)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2)
% 230.48/41.79  | | | |           = e1)
% 230.48/41.79  | | | | 
% 230.48/41.79  | | | | REF_CLOSE: (4), (19), (22), (40), (42) are inconsistent by sub-proof
% 230.48/41.79  | | | |            #1142.
% 230.48/41.79  | | | | 
% 230.48/41.79  | | | End of split
% 230.48/41.79  | | | 
% 230.48/41.79  | | End of split
% 230.48/41.79  | | 
% 230.48/41.79  | End of split
% 230.48/41.79  | 
% 230.48/41.79  End of proof
% 230.48/41.79  
% 230.48/41.79  Sub-proof #1133 shows that the following formulas are inconsistent:
% 230.48/41.79  ----------------------------------------------------------------
% 230.48/41.79    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.48/41.79           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.48/41.79    (2)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1)
% 230.48/41.79    (3)  all_57_1 = e2
% 230.48/41.79    (4)  op(e2, e2) = e2
% 230.48/41.79    (5)   ~ (e2 = e1)
% 230.48/41.79  
% 230.48/41.79  Begin of proof
% 230.48/41.79  | 
% 230.48/41.79  | BETA: splitting (2) gives:
% 230.48/41.79  | 
% 230.48/41.79  | Case 1:
% 230.48/41.79  | | 
% 230.48/41.79  | |   (6)  all_57_1 = e1 & op(e3, e2) = e1
% 230.48/41.79  | | 
% 230.48/41.79  | | REF_CLOSE: (3), (5), (6) are inconsistent by sub-proof #2210.
% 230.48/41.79  | | 
% 230.48/41.79  | Case 2:
% 230.48/41.79  | | 
% 230.48/41.79  | |   (7)  all_57_3 = e1 & op(e2, e2) = e1
% 230.48/41.79  | | 
% 230.48/41.79  | | ALPHA: (7) implies:
% 230.48/41.79  | |   (8)  op(e2, e2) = e1
% 230.48/41.79  | | 
% 230.48/41.79  | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #2306.
% 230.48/41.79  | | 
% 230.48/41.79  | End of split
% 230.48/41.79  | 
% 230.48/41.79  End of proof
% 230.48/41.79  
% 230.48/41.79  Sub-proof #1134 shows that the following formulas are inconsistent:
% 230.48/41.79  ----------------------------------------------------------------
% 230.48/41.79    (1)  all_57_1 = e0 & op(e3, e2) = e0
% 230.48/41.79    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.48/41.79         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.48/41.79    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.48/41.79         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.48/41.79    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.48/41.79         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.48/41.79    (5)   ~ (e3 = e1)
% 230.48/41.79    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.48/41.79           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.48/41.79    (7)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.48/41.79         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.48/41.79    (8)   ~ (all_6_2 = e3)
% 230.48/41.79    (9)  op(e1, e1) = all_6_2
% 230.48/41.79    (10)   ~ (e3 = e2)
% 230.48/41.79    (11)   ~ (e3 = e0)
% 230.48/41.79    (12)  all_57_1 = e2
% 230.48/41.79    (13)  op(e3, e3) = e3
% 230.48/41.79    (14)  all_57_15 = e3
% 230.48/41.79    (15)  all_57_5 = e3
% 230.48/41.79    (16)   ~ (e2 = e0)
% 230.48/41.79    (17)   ~ (e1 = e0)
% 230.48/41.79    (18)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.48/41.79              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.48/41.79                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.48/41.79                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.48/41.79    (19)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.48/41.79          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.48/41.79    (20)   ~ (e2 = e1)
% 230.48/41.79    (21)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.48/41.79          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.48/41.79    (22)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.48/41.79          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.48/41.79    (23)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.48/41.79          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.48/41.79    (24)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.48/41.79          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.48/41.79    (25)  all_57_3 = e2
% 230.48/41.79    (26)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.48/41.79          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.48/41.79  
% 230.48/41.79  Begin of proof
% 230.48/41.79  | 
% 230.48/41.79  | ALPHA: (1) implies:
% 230.48/41.79  |   (27)  all_57_1 = e0
% 230.48/41.79  | 
% 230.48/41.79  | COMBINE_EQS: (12), (27) imply:
% 230.48/41.79  |   (28)  e2 = e0
% 230.48/41.79  | 
% 230.48/41.79  | COMBINE_EQS: (25), (28) imply:
% 230.48/41.79  |   (29)  all_57_3 = e0
% 230.48/41.79  | 
% 230.48/41.79  | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13), (14),
% 230.48/41.79  |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (26),
% 230.48/41.79  |            (27), (29) are inconsistent by sub-proof #1439.
% 230.48/41.79  | 
% 230.48/41.79  End of proof
% 230.48/41.79  
% 230.48/41.79  Sub-proof #1135 shows that the following formulas are inconsistent:
% 230.48/41.79  ----------------------------------------------------------------
% 230.48/41.79    (1)  all_57_9 = e2
% 230.48/41.79    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.48/41.79         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.48/41.79    (3)   ~ (all_52_7 = e3)
% 230.48/41.79    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.48/41.79         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.48/41.79    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.48/41.79         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.48/41.79    (6)   ~ (e3 = e1)
% 230.48/41.79    (7)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.48/41.79         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.48/41.79    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.48/41.79           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.48/41.79    (9)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.48/41.79         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.48/41.79    (10)   ~ (all_6_2 = e3)
% 230.48/41.79    (11)  op(e1, e1) = all_6_2
% 230.48/41.79    (12)  op(all_52_7, all_52_7) = e0
% 230.48/41.79    (13)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.48/41.79          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.48/41.79    (14)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 230.48/41.79            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 230.48/41.79              e3) = all_22_1 & $i(all_22_1))
% 230.48/41.79    (15)   ~ (all_53_13 = e2)
% 230.48/41.79    (16)  all_57_12 = e2
% 230.48/41.79    (17)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.48/41.79          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.48/41.79    (18)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.48/41.79          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.48/41.79    (19)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 230.48/41.79          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.48/41.79    (20)   ~ (e3 = e2)
% 230.48/41.79    (21)   ~ (e3 = e0)
% 230.48/41.79    (22)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.48/41.79          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.48/41.79    (23)  op(e3, e3) = e3
% 230.48/41.79    (24)  all_57_15 = e3
% 230.48/41.79    (25)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.48/41.79          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.48/41.79            e1)
% 230.48/41.79    (26)  all_57_5 = e3
% 230.48/41.79    (27)   ~ (e2 = e0)
% 230.48/41.79    (28)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 230.48/41.79            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 230.48/41.79              e3) = all_12_1 & $i(all_12_1))
% 230.48/41.79    (29)  op(e2, e2) = e2
% 230.48/41.79    (30)   ~ (e1 = e0)
% 230.48/41.79    (31)  op(e0, e0) = e3
% 230.48/41.79    (32)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.48/41.79          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.48/41.79            e2)
% 230.48/41.79    (33)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.48/41.79              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.48/41.79                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.48/41.79                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.48/41.79    (34)  op(e1, e1) = e2
% 230.48/41.79    (35)  op(e2, e0) = all_53_13
% 230.48/41.79    (36)  all_57_7 = e3
% 230.48/41.79    (37)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.48/41.79          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.48/41.79    (38)   ~ (e2 = e1)
% 230.48/41.79    (39)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.48/41.79          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.48/41.79    (40)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.48/41.79          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.48/41.79    (41)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.48/41.79          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.48/41.79    (42)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.48/41.79          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.48/41.79    (43)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.48/41.79          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.48/41.79    (44)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.48/41.79          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.48/41.79    (45)  all_57_3 = e2
% 230.48/41.79    (46)  op(e3, e0) = all_52_7
% 230.48/41.79    (47)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.48/41.79          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.48/41.79    (48)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.48/41.79          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.48/41.79  
% 230.48/41.79  Begin of proof
% 230.48/41.79  | 
% 230.48/41.79  | BETA: splitting (39) gives:
% 230.48/41.79  | 
% 230.48/41.79  | Case 1:
% 230.48/41.79  | | 
% 230.48/41.79  | |   (49)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 230.48/41.79  | |           e2)
% 230.48/41.79  | | 
% 230.48/41.79  | | BETA: splitting (49) gives:
% 230.48/41.79  | | 
% 230.48/41.79  | | Case 1:
% 230.48/41.79  | | | 
% 230.48/41.79  | | |   (50)  all_57_9 = e2 & op(e3, e0) = e2
% 230.48/41.79  | | | 
% 230.48/41.79  | | | ALPHA: (50) implies:
% 230.48/41.79  | | |   (51)  op(e3, e0) = e2
% 230.48/41.79  | | | 
% 230.48/41.79  | | | GROUND_INST: instantiating (8) with all_52_7, e2, e0, e3, simplifying with
% 230.48/41.79  | | |              (46), (51) gives:
% 230.48/41.79  | | |   (52)  all_52_7 = e2
% 230.48/41.79  | | | 
% 230.48/41.79  | | | REDUCE: (12), (52) imply:
% 230.48/41.79  | | |   (53)  op(e2, e2) = e0
% 230.48/41.79  | | | 
% 230.48/41.79  | | | REF_CLOSE: (8), (27), (29), (53) are inconsistent by sub-proof #2472.
% 230.48/41.79  | | | 
% 230.48/41.79  | | Case 2:
% 230.48/41.79  | | | 
% 230.48/41.79  | | |   (54)  all_57_10 = e2 & op(e2, e0) = e2
% 230.48/41.79  | | | 
% 230.48/41.79  | | | REF_CLOSE: (8), (15), (35), (54) are inconsistent by sub-proof #2432.
% 230.48/41.79  | | | 
% 230.48/41.79  | | End of split
% 230.48/41.79  | | 
% 230.48/41.79  | Case 2:
% 230.48/41.79  | | 
% 230.48/41.79  | |   (55)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.48/41.79  | |           e2)
% 230.48/41.79  | | 
% 230.48/41.79  | | BETA: splitting (55) gives:
% 230.48/41.79  | | 
% 230.48/41.79  | | Case 1:
% 230.48/41.79  | | | 
% 230.48/41.79  | | |   (56)  all_57_11 = e2 & op(e1, e0) = e2
% 230.48/41.79  | | | 
% 230.48/41.79  | | | ALPHA: (56) implies:
% 230.48/41.79  | | |   (57)  all_57_11 = e2
% 230.48/41.79  | | |   (58)  op(e1, e0) = e2
% 230.48/41.79  | | | 
% 230.48/41.79  | | | BETA: splitting (7) gives:
% 230.48/41.79  | | | 
% 230.48/41.79  | | | Case 1:
% 230.48/41.79  | | | | 
% 230.48/41.79  | | | |   (59)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2)
% 230.48/41.79  | | | |           = e0)
% 230.48/41.79  | | | | 
% 230.48/41.79  | | | | REF_CLOSE: (6), (8), (9), (10), (11), (20), (21), (24), (27), (30),
% 230.48/41.79  | | | |            (33), (34), (38), (39), (43), (44), (57), (59) are
% 230.48/41.79  | | | |            inconsistent by sub-proof #1153.
% 230.48/41.79  | | | | 
% 230.48/41.79  | | | Case 2:
% 230.48/41.79  | | | | 
% 230.48/41.79  | | | |   (60)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.48/41.79  | | | |           = e0)
% 230.48/41.79  | | | | 
% 230.48/41.79  | | | | BETA: splitting (60) gives:
% 230.48/41.79  | | | | 
% 230.48/41.79  | | | | Case 1:
% 230.48/41.79  | | | | | 
% 230.48/41.79  | | | | |   (61)  all_57_8 = e0 & op(e1, e1) = e0
% 230.48/41.79  | | | | | 
% 230.48/41.79  | | | | | ALPHA: (61) implies:
% 230.48/41.79  | | | | |   (62)  all_57_8 = e0
% 230.48/41.79  | | | | |   (63)  op(e1, e1) = e0
% 230.48/41.79  | | | | | 
% 230.48/41.79  | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (12), (13), (14), (16),
% 230.48/41.79  | | | | |            (17), (18), (19), (20), (21), (22), (23), (24), (25), (26),
% 230.48/41.79  | | | | |            (27), (28), (29), (30), (31), (32), (33), (34), (36), (37),
% 230.48/41.79  | | | | |            (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 230.48/41.79  | | | | |            (48), (57), (58), (62), (63) are inconsistent by sub-proof
% 230.48/41.79  | | | | |            #1137.
% 230.48/41.79  | | | | | 
% 230.48/41.79  | | | | Case 2:
% 230.48/41.79  | | | | | 
% 230.48/41.79  | | | | |   (64)  all_57_11 = e0 & op(e1, e0) = e0
% 230.48/41.79  | | | | | 
% 230.48/41.79  | | | | | ALPHA: (64) implies:
% 230.48/41.79  | | | | |   (65)  all_57_11 = e0
% 230.48/41.79  | | | | | 
% 230.48/41.79  | | | | | REF_CLOSE: (1), (6), (20), (24), (27), (30), (38), (39), (43), (57),
% 230.48/41.79  | | | | |            (65) are inconsistent by sub-proof #1136.
% 230.48/41.79  | | | | | 
% 230.48/41.79  | | | | End of split
% 230.48/41.79  | | | | 
% 230.48/41.79  | | | End of split
% 230.48/41.79  | | | 
% 230.48/41.79  | | Case 2:
% 230.48/41.79  | | | 
% 230.48/41.79  | | |   (66)  all_57_15 = e2 & op(e0, e0) = e2
% 230.48/41.79  | | | 
% 230.48/41.79  | | | ALPHA: (66) implies:
% 230.48/41.79  | | |   (67)  all_57_15 = e2
% 230.48/41.79  | | | 
% 230.48/41.79  | | | REF_CLOSE: (20), (24), (67) are inconsistent by sub-proof #2058.
% 230.48/41.79  | | | 
% 230.48/41.79  | | End of split
% 230.48/41.79  | | 
% 230.48/41.79  | End of split
% 230.48/41.79  | 
% 230.48/41.79  End of proof
% 230.48/41.79  
% 230.48/41.79  Sub-proof #1136 shows that the following formulas are inconsistent:
% 230.48/41.79  ----------------------------------------------------------------
% 230.48/41.79    (1)  all_57_9 = e2
% 230.48/41.79    (2)   ~ (e3 = e1)
% 230.48/41.79    (3)   ~ (e3 = e2)
% 230.48/41.79    (4)  all_57_15 = e3
% 230.48/41.79    (5)  all_57_11 = e0
% 230.48/41.79    (6)  all_57_11 = e2
% 230.48/41.79    (7)   ~ (e2 = e0)
% 230.48/41.79    (8)   ~ (e1 = e0)
% 230.48/41.79    (9)   ~ (e2 = e1)
% 230.48/41.79    (10)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.48/41.79          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.48/41.79    (11)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.48/41.79          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.48/41.79  
% 230.48/41.79  Begin of proof
% 230.48/41.79  | 
% 230.48/41.79  | COMBINE_EQS: (5), (6) imply:
% 230.48/41.79  |   (12)  e2 = e0
% 230.48/41.79  | 
% 230.48/41.79  | SIMP: (12) implies:
% 230.48/41.79  |   (13)  e2 = e0
% 230.48/41.79  | 
% 230.48/41.79  | COMBINE_EQS: (1), (13) imply:
% 230.48/41.79  |   (14)  all_57_9 = e0
% 230.48/41.79  | 
% 230.48/41.79  | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (10), (11), (14) are
% 230.48/41.79  |            inconsistent by sub-proof #1144.
% 230.48/41.79  | 
% 230.48/41.79  End of proof
% 230.48/41.79  
% 230.48/41.79  Sub-proof #1137 shows that the following formulas are inconsistent:
% 230.48/41.79  ----------------------------------------------------------------
% 230.48/41.79    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.48/41.79         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.48/41.79    (2)  op(e1, e0) = e2
% 230.48/41.79    (3)   ~ (all_52_7 = e3)
% 230.48/41.79    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.48/41.79         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.48/41.79    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.48/41.79         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.48/41.79    (6)   ~ (e3 = e1)
% 230.48/41.79    (7)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.48/41.79         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.48/41.79    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.48/41.79           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.48/41.79    (9)  op(all_52_7, all_52_7) = e0
% 230.48/41.79    (10)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.48/41.79          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.48/41.79    (11)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 230.48/41.79            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 230.48/41.79              e3) = all_22_1 & $i(all_22_1))
% 230.48/41.79    (12)  all_57_12 = e2
% 230.48/41.79    (13)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.48/41.79          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.48/41.79    (14)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.48/41.79          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.48/41.79    (15)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 230.48/41.79          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.48/41.79    (16)   ~ (e3 = e2)
% 230.48/41.79    (17)   ~ (e3 = e0)
% 230.48/41.79    (18)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.48/41.79          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.48/41.79    (19)  op(e3, e3) = e3
% 230.48/41.79    (20)  all_57_15 = e3
% 230.48/41.79    (21)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.48/41.79          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.48/41.79            e1)
% 230.48/41.79    (22)  all_57_5 = e3
% 230.48/41.79    (23)  all_57_11 = e2
% 230.48/41.79    (24)   ~ (e2 = e0)
% 230.48/41.79    (25)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 230.48/41.79            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 230.48/41.79              e3) = all_12_1 & $i(all_12_1))
% 230.48/41.79    (26)  op(e2, e2) = e2
% 230.48/41.79    (27)   ~ (e1 = e0)
% 230.48/41.79    (28)  op(e0, e0) = e3
% 230.48/41.79    (29)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.48/41.79          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.48/41.79            e2)
% 230.48/41.79    (30)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.48/41.79              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.48/41.79                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.48/41.79                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.48/41.79    (31)  op(e1, e1) = e0
% 230.48/41.79    (32)  op(e1, e1) = e2
% 230.48/41.79    (33)  all_57_7 = e3
% 230.48/41.79    (34)  all_57_8 = e0
% 230.48/41.79    (35)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.48/41.79          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.48/41.79    (36)   ~ (e2 = e1)
% 230.48/41.79    (37)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.48/41.79          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.48/41.79    (38)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.48/41.79          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.48/41.79    (39)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.48/41.79          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.48/41.79    (40)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.48/41.79          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.48/41.79    (41)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.48/41.79          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.48/41.79    (42)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.48/41.79          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.48/41.79    (43)  all_57_3 = e2
% 230.48/41.79    (44)  op(e3, e0) = all_52_7
% 230.48/41.79    (45)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.48/41.79          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.48/41.79    (46)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.48/41.79          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.48/41.79  
% 230.48/41.79  Begin of proof
% 230.48/41.79  | 
% 230.48/41.79  | BETA: splitting (39) gives:
% 230.48/41.79  | 
% 230.48/41.79  | Case 1:
% 230.48/41.79  | | 
% 230.48/41.79  | |   (47)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) =
% 230.48/41.79  | |           e2)
% 230.48/41.79  | | 
% 230.48/41.79  | | BETA: splitting (47) gives:
% 230.48/41.79  | | 
% 230.48/41.79  | | Case 1:
% 230.48/41.79  | | | 
% 230.48/41.79  | | |   (48)  all_57_4 = e2 & op(e3, e1) = e2
% 230.48/41.79  | | | 
% 230.48/41.79  | | | ALPHA: (48) implies:
% 230.48/41.79  | | |   (49)  all_57_4 = e2
% 230.48/41.79  | | | 
% 230.48/41.79  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 230.48/41.79  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 230.48/41.79  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 230.48/41.79  | | |            (33), (35), (36), (37), (38), (39), (40), (41), (42), (43),
% 230.48/41.79  | | |            (44), (45), (46), (49) are inconsistent by sub-proof #1141.
% 230.48/41.79  | | | 
% 230.48/41.79  | | Case 2:
% 230.48/41.79  | | | 
% 230.48/41.79  | | |   (50)  all_57_5 = e2 & op(e2, e1) = e2
% 230.48/41.79  | | | 
% 230.48/41.79  | | | REF_CLOSE: (16), (22), (50) are inconsistent by sub-proof #2425.
% 230.48/41.79  | | | 
% 230.48/41.79  | | End of split
% 230.48/41.79  | | 
% 230.48/41.79  | Case 2:
% 230.48/41.79  | | 
% 230.48/41.79  | |   (51)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) =
% 230.48/41.79  | |           e2)
% 230.48/41.79  | | 
% 230.48/41.79  | | BETA: splitting (51) gives:
% 230.48/41.79  | | 
% 230.48/41.79  | | Case 1:
% 230.48/41.79  | | | 
% 230.48/41.79  | | |   (52)  all_57_8 = e2 & op(e1, e1) = e2
% 230.48/41.79  | | | 
% 230.48/41.79  | | | ALPHA: (52) implies:
% 230.48/41.79  | | |   (53)  all_57_8 = e2
% 230.48/41.79  | | | 
% 230.48/41.79  | | | COMBINE_EQS: (34), (53) imply:
% 230.48/41.79  | | |   (54)  e2 = e0
% 230.48/41.79  | | | 
% 230.48/41.79  | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (13), (14), (15),
% 230.48/41.79  | | |            (16), (17), (18), (19), (20), (22), (24), (27), (28), (29),
% 230.48/41.79  | | |            (30), (31), (33), (35), (36), (37), (38), (39), (40), (41),
% 230.48/41.79  | | |            (42), (43), (44), (45), (46), (54) are inconsistent by
% 230.48/41.79  | | |            sub-proof #1140.
% 230.48/41.79  | | | 
% 230.48/41.79  | | Case 2:
% 230.48/41.79  | | | 
% 230.48/41.79  | | |   (55)  all_57_14 = e2 & op(e0, e1) = e2
% 230.48/41.80  | | | 
% 230.48/41.80  | | | ALPHA: (55) implies:
% 230.48/41.80  | | |   (56)  all_57_14 = e2
% 230.48/41.80  | | | 
% 230.48/41.80  | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13), (14),
% 230.48/41.80  | | |            (15), (16), (17), (18), (19), (20), (21), (22), (24), (27),
% 230.48/41.80  | | |            (28), (29), (30), (31), (33), (35), (36), (37), (38), (39),
% 230.48/41.80  | | |            (40), (41), (42), (43), (44), (45), (46), (56) are inconsistent
% 230.48/41.80  | | |            by sub-proof #1138.
% 230.48/41.80  | | | 
% 230.48/41.80  | | End of split
% 230.48/41.80  | | 
% 230.48/41.80  | End of split
% 230.48/41.80  | 
% 230.48/41.80  End of proof
% 230.48/41.80  
% 230.48/41.80  Sub-proof #1138 shows that the following formulas are inconsistent:
% 230.48/41.80  ----------------------------------------------------------------
% 230.48/41.80    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.48/41.80         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.48/41.80    (2)   ~ (all_52_7 = e3)
% 230.48/41.80    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.48/41.80         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.48/41.80    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.48/41.80         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.48/41.80    (5)   ~ (e3 = e1)
% 230.48/41.80    (6)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.48/41.80         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.48/41.80    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.48/41.80           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.48/41.80    (8)  op(all_52_7, all_52_7) = e0
% 230.48/41.80    (9)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.48/41.80         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.48/41.80    (10)  all_57_12 = e2
% 230.48/41.80    (11)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.48/41.80          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.48/41.80    (12)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.48/41.80          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.48/41.80    (13)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 230.48/41.80          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.48/41.80    (14)   ~ (e3 = e2)
% 230.48/41.80    (15)   ~ (e3 = e0)
% 230.48/41.80    (16)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.48/41.80          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.48/41.80    (17)  op(e3, e3) = e3
% 230.48/41.80    (18)  all_57_15 = e3
% 230.48/41.80    (19)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.48/41.80          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.48/41.80            e1)
% 230.48/41.80    (20)  all_57_5 = e3
% 230.48/41.80    (21)   ~ (e2 = e0)
% 230.48/41.80    (22)   ~ (e1 = e0)
% 230.48/41.80    (23)  all_57_14 = e2
% 230.48/41.80    (24)  op(e0, e0) = e3
% 230.48/41.80    (25)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.48/41.80          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.48/41.80            e2)
% 230.48/41.80    (26)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.48/41.80              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.48/41.80                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.48/41.80                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.48/41.80    (27)  op(e1, e1) = e0
% 230.48/41.80    (28)  all_57_7 = e3
% 230.48/41.80    (29)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.48/41.80          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.48/41.80    (30)   ~ (e2 = e1)
% 230.48/41.80    (31)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.48/41.80          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.52/41.80    (32)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.52/41.80          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.52/41.80    (33)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.52/41.80          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.52/41.80    (34)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.52/41.80          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.52/41.80    (35)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.52/41.80          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.52/41.80    (36)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.52/41.80          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.52/41.80    (37)  all_57_3 = e2
% 230.52/41.80    (38)  op(e3, e0) = all_52_7
% 230.52/41.80    (39)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.52/41.80          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.52/41.80    (40)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.52/41.80          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.52/41.80  
% 230.52/41.80  Begin of proof
% 230.52/41.80  | 
% 230.52/41.80  | BETA: splitting (19) gives:
% 230.52/41.80  | 
% 230.52/41.80  | Case 1:
% 230.52/41.80  | | 
% 230.52/41.80  | |   (41)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 230.52/41.80  | |           e1)
% 230.52/41.80  | | 
% 230.52/41.80  | | BETA: splitting (41) gives:
% 230.52/41.80  | | 
% 230.52/41.80  | | Case 1:
% 230.52/41.80  | | | 
% 230.52/41.80  | | |   (42)  all_57_12 = e1 & op(e0, e3) = e1
% 230.52/41.80  | | | 
% 230.52/41.80  | | | ALPHA: (42) implies:
% 230.52/41.80  | | |   (43)  all_57_12 = e1
% 230.52/41.80  | | | 
% 230.52/41.80  | | | REF_CLOSE: (10), (30), (43) are inconsistent by sub-proof #2321.
% 230.52/41.80  | | | 
% 230.52/41.80  | | Case 2:
% 230.52/41.80  | | | 
% 230.52/41.80  | | |   (44)  all_57_13 = e1 & op(e0, e2) = e1
% 230.52/41.80  | | | 
% 230.52/41.80  | | | ALPHA: (44) implies:
% 230.52/41.80  | | |   (45)  all_57_13 = e1
% 230.52/41.80  | | | 
% 230.52/41.80  | | | BETA: splitting (26) gives:
% 230.52/41.80  | | | 
% 230.52/41.80  | | | Case 1:
% 230.52/41.80  | | | | 
% 230.52/41.80  | | | |   (46)  all_57_15 = e0 & op(e0, e0) = e0
% 230.52/41.80  | | | | 
% 230.52/41.80  | | | | ALPHA: (46) implies:
% 230.52/41.80  | | | |   (47)  op(e0, e0) = e0
% 230.52/41.80  | | | | 
% 230.52/41.80  | | | | REF_CLOSE: (7), (15), (24), (47) are inconsistent by sub-proof #2304.
% 230.52/41.80  | | | | 
% 230.52/41.80  | | | Case 2:
% 230.52/41.80  | | | | 
% 230.52/41.80  | | | |   (48)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2,
% 230.52/41.80  | | | |               e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) &
% 230.52/41.80  | | | |         ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0,
% 230.52/41.80  | | | |               e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 230.52/41.80  | | | | 
% 230.52/41.80  | | | | ALPHA: (48) implies:
% 230.52/41.80  | | | |   (49)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0,
% 230.52/41.80  | | | |             e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.52/41.80  | | | |   (50)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0)
% 230.52/41.80  | | | |           = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.52/41.80  | | | | 
% 230.52/41.80  | | | | BETA: splitting (49) gives:
% 230.52/41.80  | | | | 
% 230.52/41.80  | | | | Case 1:
% 230.52/41.80  | | | | | 
% 230.52/41.80  | | | | |   (51)  all_57_12 = e0 & op(e0, e3) = e0
% 230.52/41.80  | | | | | 
% 230.52/41.80  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (10), (11), (12), (14),
% 230.52/41.80  | | | | |            (15), (16), (17), (18), (20), (21), (22), (24), (25), (27),
% 230.52/41.80  | | | | |            (28), (29), (30), (31), (32), (34), (35), (36), (37), (38),
% 230.52/41.80  | | | | |            (39), (40), (50), (51) are inconsistent by sub-proof #1151.
% 230.52/41.80  | | | | | 
% 230.52/41.80  | | | | Case 2:
% 230.52/41.80  | | | | | 
% 230.52/41.80  | | | | |   (52)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 230.52/41.80  | | | | |             e1) = e0)
% 230.52/41.80  | | | | | 
% 230.52/41.80  | | | | | BETA: splitting (52) gives:
% 230.52/41.80  | | | | | 
% 230.52/41.80  | | | | | Case 1:
% 230.52/41.80  | | | | | | 
% 230.52/41.80  | | | | | |   (53)  all_57_13 = e0 & op(e0, e2) = e0
% 230.52/41.80  | | | | | | 
% 230.52/41.80  | | | | | | REF_CLOSE: (22), (45), (53) are inconsistent by sub-proof #1920.
% 230.52/41.80  | | | | | | 
% 230.52/41.80  | | | | | Case 2:
% 230.52/41.80  | | | | | | 
% 230.52/41.80  | | | | | |   (54)  all_57_14 = e0 & op(e0, e1) = e0
% 230.52/41.80  | | | | | | 
% 230.52/41.80  | | | | | | ALPHA: (54) implies:
% 230.52/41.80  | | | | | |   (55)  all_57_14 = e0
% 230.52/41.80  | | | | | | 
% 230.52/41.80  | | | | | | COMBINE_EQS: (23), (55) imply:
% 230.52/41.80  | | | | | |   (56)  e2 = e0
% 230.52/41.80  | | | | | | 
% 230.52/41.80  | | | | | | COMBINE_EQS: (37), (56) imply:
% 230.52/41.80  | | | | | |   (57)  all_57_3 = e0
% 230.52/41.80  | | | | | | 
% 230.52/41.80  | | | | | | REF_CLOSE: (1), (4), (5), (6), (7), (9), (11), (12), (13), (14),
% 230.52/41.80  | | | | | |            (15), (16), (17), (18), (20), (21), (22), (27), (28),
% 230.52/41.80  | | | | | |            (29), (30), (31), (33), (35), (36), (39), (40), (50),
% 230.52/41.80  | | | | | |            (55), (57) are inconsistent by sub-proof #1488.
% 230.52/41.80  | | | | | | 
% 230.52/41.80  | | | | | End of split
% 230.52/41.80  | | | | | 
% 230.52/41.80  | | | | End of split
% 230.52/41.80  | | | | 
% 230.52/41.80  | | | End of split
% 230.52/41.80  | | | 
% 230.52/41.80  | | End of split
% 230.52/41.80  | | 
% 230.52/41.80  | Case 2:
% 230.52/41.80  | | 
% 230.52/41.80  | |   (58)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.52/41.80  | |           e1)
% 230.52/41.80  | | 
% 230.52/41.80  | | REF_CLOSE: (5), (7), (23), (24), (30), (58) are inconsistent by sub-proof
% 230.52/41.80  | |            #1139.
% 230.52/41.80  | | 
% 230.52/41.80  | End of split
% 230.52/41.80  | 
% 230.52/41.80  End of proof
% 230.52/41.80  
% 230.52/41.80  Sub-proof #1139 shows that the following formulas are inconsistent:
% 230.52/41.80  ----------------------------------------------------------------
% 230.52/41.80    (1)   ~ (e3 = e1)
% 230.52/41.80    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.80           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.80    (3)  all_57_14 = e2
% 230.52/41.80    (4)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.52/41.80    (5)  op(e0, e0) = e3
% 230.52/41.80    (6)   ~ (e2 = e1)
% 230.52/41.80  
% 230.52/41.80  Begin of proof
% 230.52/41.80  | 
% 230.52/41.80  | BETA: splitting (4) gives:
% 230.52/41.80  | 
% 230.52/41.80  | Case 1:
% 230.52/41.80  | | 
% 230.52/41.80  | |   (7)  all_57_14 = e1 & op(e0, e1) = e1
% 230.52/41.80  | | 
% 230.52/41.80  | | REF_CLOSE: (3), (6), (7) are inconsistent by sub-proof #2375.
% 230.52/41.80  | | 
% 230.52/41.80  | Case 2:
% 230.52/41.80  | | 
% 230.52/41.80  | |   (8)  all_57_15 = e1 & op(e0, e0) = e1
% 230.52/41.80  | | 
% 230.52/41.80  | | ALPHA: (8) implies:
% 230.52/41.80  | |   (9)  op(e0, e0) = e1
% 230.52/41.80  | | 
% 230.52/41.80  | | REF_CLOSE: (1), (2), (5), (9) are inconsistent by sub-proof #2183.
% 230.52/41.80  | | 
% 230.52/41.80  | End of split
% 230.52/41.80  | 
% 230.52/41.80  End of proof
% 230.52/41.80  
% 230.52/41.80  Sub-proof #1140 shows that the following formulas are inconsistent:
% 230.52/41.80  ----------------------------------------------------------------
% 230.52/41.80    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.52/41.80         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.52/41.80    (2)   ~ (all_52_7 = e3)
% 230.52/41.80    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.52/41.80         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.52/41.80    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.52/41.80         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.52/41.80    (5)   ~ (e3 = e1)
% 230.52/41.80    (6)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.52/41.80         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.52/41.80    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.80           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.80    (8)  op(all_52_7, all_52_7) = e0
% 230.52/41.80    (9)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.52/41.80         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.52/41.80    (10)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.52/41.80          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.52/41.80    (11)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.52/41.80          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.52/41.80    (12)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 230.52/41.80          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.52/41.80    (13)   ~ (e3 = e2)
% 230.52/41.80    (14)   ~ (e3 = e0)
% 230.52/41.80    (15)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.52/41.80          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.52/41.80    (16)  op(e3, e3) = e3
% 230.52/41.80    (17)  all_57_15 = e3
% 230.52/41.80    (18)  all_57_5 = e3
% 230.52/41.80    (19)  e2 = e0
% 230.52/41.80    (20)   ~ (e2 = e0)
% 230.52/41.80    (21)   ~ (e1 = e0)
% 230.52/41.80    (22)  op(e0, e0) = e3
% 230.52/41.80    (23)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.52/41.80          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.52/41.80            e2)
% 230.52/41.80    (24)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.52/41.80              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.52/41.80                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.52/41.80                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.52/41.80    (25)  op(e1, e1) = e0
% 230.52/41.80    (26)  all_57_7 = e3
% 230.52/41.80    (27)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.52/41.80          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.52/41.80    (28)   ~ (e2 = e1)
% 230.52/41.80    (29)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.52/41.80          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.52/41.80    (30)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.52/41.80          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.52/41.80    (31)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.52/41.80          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.52/41.80    (32)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.52/41.80          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.52/41.80    (33)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.52/41.80          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.52/41.80    (34)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.52/41.80          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.52/41.80    (35)  all_57_3 = e2
% 230.52/41.80    (36)  op(e3, e0) = all_52_7
% 230.52/41.80    (37)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.52/41.80          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.52/41.80    (38)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.52/41.80          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.52/41.80  
% 230.52/41.80  Begin of proof
% 230.52/41.80  | 
% 230.52/41.80  | SIMP: (19) implies:
% 230.52/41.80  |   (39)  e2 = e0
% 230.52/41.80  | 
% 230.52/41.80  | COMBINE_EQS: (35), (39) imply:
% 230.52/41.80  |   (40)  all_57_3 = e0
% 230.52/41.80  | 
% 230.52/41.80  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 230.52/41.80  |            (13), (14), (15), (16), (17), (18), (20), (21), (22), (23), (24),
% 230.52/41.80  |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (36),
% 230.52/41.80  |            (37), (38), (40) are inconsistent by sub-proof #1486.
% 230.52/41.80  | 
% 230.52/41.80  End of proof
% 230.52/41.80  
% 230.52/41.80  Sub-proof #1141 shows that the following formulas are inconsistent:
% 230.52/41.80  ----------------------------------------------------------------
% 230.52/41.80    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.52/41.80         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.52/41.80    (2)  op(e1, e0) = e2
% 230.52/41.80    (3)   ~ (all_52_7 = e3)
% 230.52/41.80    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.52/41.80         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.52/41.80    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.52/41.80         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.52/41.80    (6)   ~ (e3 = e1)
% 230.52/41.80    (7)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.52/41.80         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.52/41.80    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.80           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.80    (9)  op(all_52_7, all_52_7) = e0
% 230.52/41.80    (10)  all_57_4 = e2
% 230.52/41.80    (11)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.52/41.80          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.52/41.80    (12)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 230.52/41.80            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0,
% 230.52/41.80              e3) = all_22_1 & $i(all_22_1))
% 230.52/41.80    (13)  all_57_12 = e2
% 230.52/41.80    (14)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.52/41.80          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.52/41.80    (15)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.52/41.80          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.52/41.80    (16)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 230.52/41.80          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.52/41.80    (17)   ~ (e3 = e2)
% 230.52/41.80    (18)   ~ (e3 = e0)
% 230.52/41.80    (19)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.52/41.80          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.52/41.80    (20)  op(e3, e3) = e3
% 230.52/41.80    (21)  all_57_15 = e3
% 230.52/41.80    (22)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.52/41.80          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.52/41.80            e1)
% 230.52/41.80    (23)  all_57_5 = e3
% 230.52/41.80    (24)  all_57_11 = e2
% 230.52/41.80    (25)   ~ (e2 = e0)
% 230.52/41.80    (26)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 230.52/41.80            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0,
% 230.52/41.80              e3) = all_12_1 & $i(all_12_1))
% 230.52/41.80    (27)  op(e2, e2) = e2
% 230.52/41.80    (28)   ~ (e1 = e0)
% 230.52/41.80    (29)  op(e0, e0) = e3
% 230.52/41.80    (30)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.52/41.80          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.52/41.80            e2)
% 230.52/41.80    (31)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.52/41.80              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.52/41.80                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.52/41.80                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.52/41.80    (32)  op(e1, e1) = e0
% 230.52/41.80    (33)  op(e1, e1) = e2
% 230.52/41.80    (34)  all_57_7 = e3
% 230.52/41.80    (35)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.52/41.80          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.52/41.80    (36)   ~ (e2 = e1)
% 230.52/41.80    (37)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.52/41.80          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.52/41.80    (38)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.52/41.80          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.52/41.80    (39)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.52/41.80          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.52/41.80    (40)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.52/41.80          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.52/41.80    (41)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.52/41.80          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.52/41.80    (42)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.52/41.80          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.52/41.80    (43)  all_57_3 = e2
% 230.52/41.80    (44)  op(e3, e0) = all_52_7
% 230.52/41.80    (45)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.52/41.80          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.52/41.80    (46)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.52/41.80          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.52/41.80  
% 230.52/41.80  Begin of proof
% 230.52/41.80  | 
% 230.52/41.80  | BETA: splitting (42) gives:
% 230.52/41.80  | 
% 230.52/41.80  | Case 1:
% 230.52/41.80  | | 
% 230.52/41.80  | |   (47)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) =
% 230.52/41.80  | |           e1)
% 230.52/41.80  | | 
% 230.52/41.80  | | BETA: splitting (47) gives:
% 230.52/41.80  | | 
% 230.52/41.80  | | Case 1:
% 230.52/41.80  | | | 
% 230.52/41.80  | | |   (48)  all_57_6 = e1 & op(e1, e3) = e1
% 230.52/41.80  | | | 
% 230.52/41.80  | | | ALPHA: (48) implies:
% 230.52/41.80  | | |   (49)  all_57_6 = e1
% 230.52/41.80  | | | 
% 230.52/41.80  | | | BETA: splitting (40) gives:
% 230.52/41.80  | | | 
% 230.52/41.80  | | | Case 1:
% 230.52/41.80  | | | | 
% 230.52/41.80  | | | |   (50)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3)
% 230.52/41.80  | | | |           = e0)
% 230.52/41.80  | | | | 
% 230.52/41.80  | | | | BETA: splitting (50) gives:
% 230.52/41.80  | | | | 
% 230.52/41.80  | | | | Case 1:
% 230.52/41.80  | | | | | 
% 230.52/41.80  | | | | |   (51)  all_57_0 = e0 & op(e3, e3) = e0
% 230.52/41.80  | | | | | 
% 230.52/41.80  | | | | | ALPHA: (51) implies:
% 230.52/41.80  | | | | |   (52)  op(e3, e3) = e0
% 230.52/41.80  | | | | | 
% 230.52/41.80  | | | | | REF_CLOSE: (8), (18), (20), (52) are inconsistent by sub-proof #2494.
% 230.52/41.80  | | | | | 
% 230.52/41.80  | | | | Case 2:
% 230.52/41.80  | | | | | 
% 230.52/41.80  | | | | |   (53)  all_57_2 = e0 & op(e2, e3) = e0
% 230.52/41.80  | | | | | 
% 230.52/41.80  | | | | | ALPHA: (53) implies:
% 230.52/41.80  | | | | |   (54)  all_57_2 = e0
% 230.52/41.80  | | | | | 
% 230.52/41.80  | | | | | BETA: splitting (1) gives:
% 230.52/41.80  | | | | | 
% 230.52/41.80  | | | | | Case 1:
% 230.52/41.80  | | | | | | 
% 230.52/41.80  | | | | | |   (55)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2,
% 230.52/41.80  | | | | | |             e2) = e1)
% 230.52/41.80  | | | | | | 
% 230.52/41.80  | | | | | | REF_CLOSE: (8), (27), (28), (36), (54), (55) are inconsistent by
% 230.52/41.80  | | | | | |            sub-proof #1152.
% 230.52/41.80  | | | | | | 
% 230.52/41.80  | | | | | Case 2:
% 230.52/41.80  | | | | | | 
% 230.52/41.80  | | | | | |   (56)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2,
% 230.52/41.80  | | | | | |             e0) = e1)
% 230.52/41.80  | | | | | | 
% 230.52/41.80  | | | | | | BETA: splitting (56) gives:
% 230.52/41.80  | | | | | | 
% 230.52/41.80  | | | | | | Case 1:
% 230.52/41.80  | | | | | | | 
% 230.52/41.80  | | | | | | |   (57)  all_57_5 = e1 & op(e2, e1) = e1
% 230.52/41.80  | | | | | | | 
% 230.52/41.80  | | | | | | | REF_CLOSE: (6), (23), (57) are inconsistent by sub-proof #2376.
% 230.52/41.80  | | | | | | | 
% 230.52/41.80  | | | | | | Case 2:
% 230.52/41.80  | | | | | | | 
% 230.52/41.80  | | | | | | |   (58)  all_57_10 = e1 & op(e2, e0) = e1
% 230.52/41.80  | | | | | | | 
% 230.52/41.80  | | | | | | | ALPHA: (58) implies:
% 230.52/41.80  | | | | | | |   (59)  all_57_10 = e1
% 230.52/41.80  | | | | | | | 
% 230.52/41.80  | | | | | | | BETA: splitting (19) gives:
% 230.52/41.80  | | | | | | | 
% 230.52/41.80  | | | | | | | Case 1:
% 230.52/41.80  | | | | | | | | 
% 230.52/41.80  | | | | | | | |   (60)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 &
% 230.52/41.80  | | | | | | | |           op(e2, e1) = e1)
% 230.52/41.80  | | | | | | | | 
% 230.52/41.80  | | | | | | | | BETA: splitting (60) gives:
% 230.52/41.80  | | | | | | | | 
% 230.52/41.80  | | | | | | | | Case 1:
% 230.52/41.80  | | | | | | | | | 
% 230.52/41.80  | | | | | | | | |   (61)  all_57_4 = e1 & op(e3, e1) = e1
% 230.52/41.80  | | | | | | | | | 
% 230.52/41.80  | | | | | | | | | REF_CLOSE: (10), (36), (61) are inconsistent by sub-proof
% 230.52/41.80  | | | | | | | | |            #2452.
% 230.52/41.80  | | | | | | | | | 
% 230.52/41.80  | | | | | | | | Case 2:
% 230.52/41.80  | | | | | | | | | 
% 230.52/41.80  | | | | | | | | |   (62)  all_57_5 = e1 & op(e2, e1) = e1
% 230.52/41.80  | | | | | | | | | 
% 230.52/41.80  | | | | | | | | | REF_CLOSE: (6), (23), (62) are inconsistent by sub-proof
% 230.52/41.80  | | | | | | | | |            #2376.
% 230.52/41.80  | | | | | | | | | 
% 230.52/41.80  | | | | | | | | End of split
% 230.52/41.80  | | | | | | | | 
% 230.52/41.80  | | | | | | | Case 2:
% 230.52/41.80  | | | | | | | | 
% 230.52/41.80  | | | | | | | |   (63)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 &
% 230.52/41.80  | | | | | | | |           op(e0, e1) = e1)
% 230.52/41.80  | | | | | | | | 
% 230.52/41.80  | | | | | | | | BETA: splitting (63) gives:
% 230.52/41.80  | | | | | | | | 
% 230.52/41.80  | | | | | | | | Case 1:
% 230.52/41.80  | | | | | | | | | 
% 230.52/41.80  | | | | | | | | |   (64)  all_57_8 = e1 & op(e1, e1) = e1
% 230.52/41.80  | | | | | | | | | 
% 230.52/41.80  | | | | | | | | | ALPHA: (64) implies:
% 230.52/41.80  | | | | | | | | |   (65)  op(e1, e1) = e1
% 230.52/41.80  | | | | | | | | | 
% 230.52/41.80  | | | | | | | | | REF_CLOSE: (8), (28), (32), (65) are inconsistent by sub-proof
% 230.52/41.80  | | | | | | | | |            #2427.
% 230.52/41.80  | | | | | | | | | 
% 230.52/41.80  | | | | | | | | Case 2:
% 230.52/41.80  | | | | | | | | | 
% 230.52/41.80  | | | | | | | | |   (66)  all_57_14 = e1 & op(e0, e1) = e1
% 230.52/41.80  | | | | | | | | | 
% 230.52/41.80  | | | | | | | | | ALPHA: (66) implies:
% 230.52/41.80  | | | | | | | | |   (67)  all_57_14 = e1
% 230.52/41.80  | | | | | | | | | 
% 230.52/41.80  | | | | | | | | | BETA: splitting (31) gives:
% 230.52/41.80  | | | | | | | | | 
% 230.52/41.80  | | | | | | | | | Case 1:
% 230.52/41.80  | | | | | | | | | | 
% 230.52/41.80  | | | | | | | | | |   (68)  all_57_15 = e0 & op(e0, e0) = e0
% 230.52/41.80  | | | | | | | | | | 
% 230.52/41.80  | | | | | | | | | | ALPHA: (68) implies:
% 230.52/41.80  | | | | | | | | | |   (69)  op(e0, e0) = e0
% 230.52/41.80  | | | | | | | | | | 
% 230.52/41.80  | | | | | | | | | | REF_CLOSE: (8), (18), (29), (69) are inconsistent by
% 230.52/41.80  | | | | | | | | | |            sub-proof #2304.
% 230.52/41.80  | | | | | | | | | | 
% 230.52/41.80  | | | | | | | | | Case 2:
% 230.52/41.80  | | | | | | | | | | 
% 230.52/41.80  | | | | | | | | | |   (70)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0
% 230.52/41.80  | | | | | | | | | |             & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 230.52/41.80  | | | | | | | | | |               e0) = e0)) & ((all_57_12 = e0 & op(e0, e3) =
% 230.52/41.80  | | | | | | | | | |             e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 230.52/41.80  | | | | | | | | | |           (all_57_14 = e0 & op(e0, e1) = e0))
% 230.52/41.80  | | | | | | | | | | 
% 230.52/41.80  | | | | | | | | | | ALPHA: (70) implies:
% 230.52/41.80  | | | | | | | | | |   (71)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0
% 230.52/41.80  | | | | | | | | | |           & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1)
% 230.52/41.80  | | | | | | | | | |           = e0)
% 230.52/41.80  | | | | | | | | | |   (72)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0
% 230.52/41.80  | | | | | | | | | |           & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.52/41.80  | | | | | | | | | |           = e0)
% 230.52/41.80  | | | | | | | | | | 
% 230.52/41.80  | | | | | | | | | | BETA: splitting (71) gives:
% 230.52/41.80  | | | | | | | | | | 
% 230.52/41.80  | | | | | | | | | | Case 1:
% 230.52/41.80  | | | | | | | | | | | 
% 230.52/41.80  | | | | | | | | | | |   (73)  all_57_12 = e0 & op(e0, e3) = e0
% 230.52/41.80  | | | | | | | | | | | 
% 230.52/41.80  | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (13), (14),
% 230.52/41.80  | | | | | | | | | | |            (15), (17), (18), (19), (20), (21), (23), (25),
% 230.52/41.80  | | | | | | | | | | |            (28), (29), (30), (32), (34), (35), (36), (37),
% 230.52/41.80  | | | | | | | | | | |            (38), (40), (41), (42), (43), (44), (45), (46),
% 230.52/41.80  | | | | | | | | | | |            (72), (73) are inconsistent by sub-proof #1151.
% 230.52/41.80  | | | | | | | | | | | 
% 230.52/41.80  | | | | | | | | | | Case 2:
% 230.52/41.80  | | | | | | | | | | | 
% 230.52/41.80  | | | | | | | | | | |   (74)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 230.52/41.80  | | | | | | | | | | |           e0 & op(e0, e1) = e0)
% 230.52/41.80  | | | | | | | | | | | 
% 230.52/41.80  | | | | | | | | | | | BETA: splitting (74) gives:
% 230.52/41.80  | | | | | | | | | | | 
% 230.52/41.80  | | | | | | | | | | | Case 1:
% 230.52/41.80  | | | | | | | | | | | | 
% 230.52/41.80  | | | | | | | | | | | |   (75)  all_57_13 = e0 & op(e0, e2) = e0
% 230.52/41.80  | | | | | | | | | | | | 
% 230.52/41.80  | | | | | | | | | | | | ALPHA: (75) implies:
% 230.52/41.81  | | | | | | | | | | | |   (76)  all_57_13 = e0
% 230.52/41.81  | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | BETA: splitting (45) gives:
% 230.52/41.81  | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | Case 1:
% 230.52/41.81  | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | |   (77)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 230.52/41.81  | | | | | | | | | | | | |           & op(e2, e2) = e1)
% 230.52/41.81  | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | BETA: splitting (77) gives:
% 230.52/41.81  | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | Case 1:
% 230.52/41.81  | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | |   (78)  all_57_1 = e1 & op(e3, e2) = e1
% 230.52/41.81  | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | | ALPHA: (78) implies:
% 230.52/41.81  | | | | | | | | | | | | | |   (79)  all_57_1 = e1
% 230.52/41.81  | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | | BETA: splitting (72) gives:
% 230.52/41.81  | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | | Case 1:
% 230.52/41.81  | | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | | |   (80)  all_57_9 = e0 & op(e3, e0) = e0
% 230.52/41.81  | | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | | | BETA: splitting (22) gives:
% 230.52/41.81  | | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | | | Case 1:
% 230.52/41.81  | | | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | | | |   (81)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 230.52/41.81  | | | | | | | | | | | | | | | |           e1 & op(e0, e2) = e1)
% 230.52/41.81  | | | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | | | | BETA: splitting (81) gives:
% 230.52/41.81  | | | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | | | | Case 1:
% 230.52/41.81  | | | | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | | | | |   (82)  all_57_12 = e1 & op(e0, e3) = e1
% 230.52/41.81  | | | | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | | | | | ALPHA: (82) implies:
% 230.52/41.81  | | | | | | | | | | | | | | | | |   (83)  op(e0, e3) = e1
% 230.52/41.81  | | | | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (8), (12), (26), (83) are inconsistent by
% 230.52/41.81  | | | | | | | | | | | | | | | | |            sub-proof #1147.
% 230.52/41.81  | | | | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | | | | Case 2:
% 230.52/41.81  | | | | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | | | | |   (84)  all_57_13 = e1 & op(e0, e2) = e1
% 230.52/41.81  | | | | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | | | | | ALPHA: (84) implies:
% 230.52/41.81  | | | | | | | | | | | | | | | | |   (85)  all_57_13 = e1
% 230.52/41.81  | | | | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | | | | | REF_CLOSE: (28), (76), (85) are inconsistent by sub-proof
% 230.52/41.81  | | | | | | | | | | | | | | | | |            #1760.
% 230.52/41.81  | | | | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | | | | End of split
% 230.52/41.81  | | | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | | | Case 2:
% 230.52/41.81  | | | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | | | |   (86)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 230.52/41.81  | | | | | | | | | | | | | | | |           e1 & op(e0, e0) = e1)
% 230.52/41.81  | | | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | | | | BETA: splitting (86) gives:
% 230.52/41.81  | | | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | | | | Case 1:
% 230.52/41.81  | | | | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | | | | | ALPHA: (80) implies:
% 230.52/41.81  | | | | | | | | | | | | | | | | |   (87)  all_57_9 = e0
% 230.52/41.81  | | | | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with e0, e2, e1, e1, simplifying
% 230.52/41.81  | | | | | | | | | | | | | | | | |              with (32), (33) gives:
% 230.52/41.81  | | | | | | | | | | | | | | | | |   (88)  e2 = e0
% 230.52/41.81  | | | | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | | | | | COMBINE_EQS: (43), (88) imply:
% 230.52/41.81  | | | | | | | | | | | | | | | | |   (89)  all_57_3 = e0
% 230.52/41.81  | | | | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | | | | | BETA: splitting (5) gives:
% 230.52/41.81  | | | | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | | | | | Case 1:
% 230.52/41.81  | | | | | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | | | | | |   (90)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 230.52/41.81  | | | | | | | | | | | | | | | | | |           & op(e2, e2) = e2)
% 230.52/41.81  | | | | | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | | | | | | BETA: splitting (90) gives:
% 230.52/41.81  | | | | | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | | | | | | Case 1:
% 230.52/41.81  | | | | | | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | | | | | | |   (91)  all_57_1 = e2 & op(e3, e2) = e2
% 230.52/41.81  | | | | | | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | | | | | | | ALPHA: (91) implies:
% 230.52/41.81  | | | | | | | | | | | | | | | | | | |   (92)  all_57_1 = e2
% 230.52/41.81  | | | | | | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (11), (14), (17), (20), (25), (28),
% 230.52/41.81  | | | | | | | | | | | | | | | | | | |            (34), (36), (45), (76), (87), (89), (92) are
% 230.52/41.81  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2094.
% 230.52/41.81  | | | | | | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | | | | | | Case 2:
% 230.52/41.81  | | | | | | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | | | | | | |   (93)  all_57_3 = e2 & op(e2, e2) = e2
% 230.52/41.81  | | | | | | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (89), (93) are inconsistent by sub-proof
% 230.52/41.81  | | | | | | | | | | | | | | | | | | |            #2103.
% 230.52/41.81  | | | | | | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | | | | | | End of split
% 230.52/41.81  | | | | | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | | | | | Case 2:
% 230.52/41.81  | | | | | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | | | | | |   (94)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 230.52/41.81  | | | | | | | | | | | | | | | | | |           e2 & op(e0, e2) = e2)
% 230.52/41.81  | | | | | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | | | | | | BETA: splitting (94) gives:
% 230.52/41.81  | | | | | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | | | | | | Case 1:
% 230.52/41.81  | | | | | | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | | | | | | |   (95)  all_57_7 = e2 & op(e1, e2) = e2
% 230.52/41.81  | | | | | | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (34), (95) are inconsistent by sub-proof
% 230.52/41.81  | | | | | | | | | | | | | | | | | | |            #2092.
% 230.52/41.81  | | | | | | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | | | | | | Case 2:
% 230.52/41.81  | | | | | | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | | | | | | |   (96)  all_57_13 = e2 & op(e0, e2) = e2
% 230.52/41.81  | | | | | | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | | | | | | | ALPHA: (96) implies:
% 230.52/41.81  | | | | | | | | | | | | | | | | | | |   (97)  all_57_13 = e2
% 230.52/41.81  | | | | | | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (76), (97) are inconsistent by sub-proof
% 230.52/41.81  | | | | | | | | | | | | | | | | | | |            #1911.
% 230.52/41.81  | | | | | | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | | | | | | End of split
% 230.52/41.81  | | | | | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | | | | | End of split
% 230.52/41.81  | | | | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | | | | Case 2:
% 230.52/41.81  | | | | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | | | | |   (98)  all_57_15 = e1 & op(e0, e0) = e1
% 230.52/41.81  | | | | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | | | | | ALPHA: (98) implies:
% 230.52/41.81  | | | | | | | | | | | | | | | | |   (99)  op(e0, e0) = e1
% 230.52/41.81  | | | | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (29), (99) are inconsistent by sub-proof
% 230.52/41.81  | | | | | | | | | | | | | | | | |            #2183.
% 230.52/41.81  | | | | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | | | | End of split
% 230.52/41.81  | | | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | | | End of split
% 230.52/41.81  | | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | | Case 2:
% 230.52/41.81  | | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | | |   (100)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 =
% 230.52/41.81  | | | | | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 230.52/41.81  | | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | | | BETA: splitting (100) gives:
% 230.52/41.81  | | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | | | Case 1:
% 230.52/41.81  | | | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | | | |   (101)  all_57_10 = e0 & op(e2, e0) = e0
% 230.52/41.81  | | | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | | | | REF_CLOSE: (28), (59), (101) are inconsistent by sub-proof
% 230.52/41.81  | | | | | | | | | | | | | | | |            #1332.
% 230.52/41.81  | | | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | | | Case 2:
% 230.52/41.81  | | | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | | | |   (102)  all_57_11 = e0 & op(e1, e0) = e0
% 230.52/41.81  | | | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | | | | ALPHA: (102) implies:
% 230.52/41.81  | | | | | | | | | | | | | | | |   (103)  all_57_11 = e0
% 230.52/41.81  | | | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10),
% 230.52/41.81  | | | | | | | | | | | | | | | |            (11), (14), (15), (16), (17), (18), (19), (20),
% 230.52/41.81  | | | | | | | | | | | | | | | |            (21), (23), (25), (28), (29), (30), (31), (32),
% 230.52/41.81  | | | | | | | | | | | | | | | |            (34), (35), (36), (37), (38), (39), (40), (41),
% 230.52/41.81  | | | | | | | | | | | | | | | |            (42), (43), (44), (45), (46), (79), (103) are
% 230.52/41.81  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1143.
% 230.52/41.81  | | | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | | | End of split
% 230.52/41.81  | | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | | End of split
% 230.52/41.81  | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | Case 2:
% 230.52/41.81  | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | |   (104)  all_57_3 = e1 & op(e2, e2) = e1
% 230.52/41.81  | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | | ALPHA: (104) implies:
% 230.52/41.81  | | | | | | | | | | | | | |   (105)  op(e2, e2) = e1
% 230.52/41.81  | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | | REF_CLOSE: (8), (27), (36), (105) are inconsistent by
% 230.52/41.81  | | | | | | | | | | | | | |            sub-proof #2306.
% 230.52/41.81  | | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | End of split
% 230.52/41.81  | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | Case 2:
% 230.52/41.81  | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | |   (106)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 230.52/41.81  | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 230.52/41.81  | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | | REF_CLOSE: (6), (28), (34), (76), (106) are inconsistent by
% 230.52/41.81  | | | | | | | | | | | | |            sub-proof #1142.
% 230.52/41.81  | | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | End of split
% 230.52/41.81  | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | Case 2:
% 230.52/41.81  | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | |   (107)  all_57_14 = e0 & op(e0, e1) = e0
% 230.52/41.81  | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | | REF_CLOSE: (28), (67), (107) are inconsistent by sub-proof
% 230.52/41.81  | | | | | | | | | | | |            #2181.
% 230.52/41.81  | | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | | End of split
% 230.52/41.81  | | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | | End of split
% 230.52/41.81  | | | | | | | | | | 
% 230.52/41.81  | | | | | | | | | End of split
% 230.52/41.81  | | | | | | | | | 
% 230.52/41.81  | | | | | | | | End of split
% 230.52/41.81  | | | | | | | | 
% 230.52/41.81  | | | | | | | End of split
% 230.52/41.81  | | | | | | | 
% 230.52/41.81  | | | | | | End of split
% 230.52/41.81  | | | | | | 
% 230.52/41.81  | | | | | End of split
% 230.52/41.81  | | | | | 
% 230.52/41.81  | | | | End of split
% 230.52/41.81  | | | | 
% 230.52/41.81  | | | Case 2:
% 230.52/41.81  | | | | 
% 230.52/41.81  | | | |   (108)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0,
% 230.52/41.81  | | | |              e3) = e0)
% 230.52/41.81  | | | | 
% 230.52/41.81  | | | | BETA: splitting (108) gives:
% 230.52/41.81  | | | | 
% 230.52/41.81  | | | | Case 1:
% 230.52/41.81  | | | | | 
% 230.52/41.81  | | | | |   (109)  all_57_6 = e0 & op(e1, e3) = e0
% 230.52/41.81  | | | | | 
% 230.52/41.81  | | | | | REF_CLOSE: (28), (49), (109) are inconsistent by sub-proof #2347.
% 230.52/41.81  | | | | | 
% 230.52/41.81  | | | | Case 2:
% 230.52/41.81  | | | | | 
% 230.52/41.81  | | | | |   (110)  all_57_12 = e0 & op(e0, e3) = e0
% 230.52/41.81  | | | | | 
% 230.52/41.81  | | | | | ALPHA: (110) implies:
% 230.52/41.81  | | | | |   (111)  all_57_12 = e0
% 230.52/41.81  | | | | | 
% 230.52/41.81  | | | | | COMBINE_EQS: (13), (111) imply:
% 230.52/41.81  | | | | |   (112)  e2 = e0
% 230.52/41.81  | | | | | 
% 230.52/41.81  | | | | | COMBINE_EQS: (43), (112) imply:
% 230.52/41.81  | | | | |   (113)  all_57_3 = e0
% 230.52/41.81  | | | | | 
% 230.52/41.81  | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (11), (14), (15),
% 230.52/41.81  | | | | |            (16), (17), (18), (19), (20), (21), (23), (25), (28), (29),
% 230.52/41.81  | | | | |            (30), (31), (32), (34), (35), (36), (37), (38), (39), (40),
% 230.52/41.81  | | | | |            (41), (42), (44), (45), (46), (113) are inconsistent by
% 230.52/41.81  | | | | |            sub-proof #1486.
% 230.52/41.81  | | | | | 
% 230.52/41.81  | | | | End of split
% 230.52/41.81  | | | | 
% 230.52/41.81  | | | End of split
% 230.52/41.81  | | | 
% 230.52/41.81  | | Case 2:
% 230.52/41.81  | | | 
% 230.52/41.81  | | |   (114)  all_57_7 = e1 & op(e1, e2) = e1
% 230.52/41.81  | | | 
% 230.52/41.81  | | | REF_CLOSE: (6), (34), (114) are inconsistent by sub-proof #2104.
% 230.52/41.81  | | | 
% 230.52/41.81  | | End of split
% 230.52/41.81  | | 
% 230.52/41.81  | Case 2:
% 230.52/41.81  | | 
% 230.52/41.81  | |   (115)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) =
% 230.52/41.81  | |            e1)
% 230.52/41.81  | | 
% 230.52/41.81  | | REF_CLOSE: (8), (24), (28), (32), (36), (115) are inconsistent by sub-proof
% 230.52/41.81  | |            #1201.
% 230.52/41.81  | | 
% 230.52/41.81  | End of split
% 230.52/41.81  | 
% 230.52/41.81  End of proof
% 230.52/41.81  
% 230.52/41.81  Sub-proof #1142 shows that the following formulas are inconsistent:
% 230.52/41.81  ----------------------------------------------------------------
% 230.52/41.81    (1)   ~ (e3 = e1)
% 230.52/41.81    (2)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.52/41.81    (3)   ~ (e1 = e0)
% 230.52/41.81    (4)  all_57_13 = e0
% 230.52/41.81    (5)  all_57_7 = e3
% 230.52/41.81  
% 230.52/41.81  Begin of proof
% 230.52/41.81  | 
% 230.52/41.81  | BETA: splitting (2) gives:
% 230.52/41.81  | 
% 230.52/41.81  | Case 1:
% 230.52/41.81  | | 
% 230.52/41.81  | |   (6)  all_57_7 = e1 & op(e1, e2) = e1
% 230.52/41.81  | | 
% 230.52/41.81  | | REF_CLOSE: (1), (5), (6) are inconsistent by sub-proof #2104.
% 230.52/41.81  | | 
% 230.52/41.81  | Case 2:
% 230.52/41.81  | | 
% 230.52/41.81  | |   (7)  all_57_13 = e1 & op(e0, e2) = e1
% 230.52/41.81  | | 
% 230.52/41.81  | | ALPHA: (7) implies:
% 230.52/41.81  | |   (8)  all_57_13 = e1
% 230.52/41.81  | | 
% 230.52/41.81  | | REF_CLOSE: (3), (4), (8) are inconsistent by sub-proof #1760.
% 230.52/41.81  | | 
% 230.52/41.81  | End of split
% 230.52/41.81  | 
% 230.52/41.81  End of proof
% 230.52/41.81  
% 230.52/41.81  Sub-proof #1143 shows that the following formulas are inconsistent:
% 230.52/41.81  ----------------------------------------------------------------
% 230.52/41.81    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.52/41.81         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.52/41.81    (2)   ~ (all_52_7 = e3)
% 230.52/41.81    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.52/41.81         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.52/41.81    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.52/41.81         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.52/41.81    (5)   ~ (e3 = e1)
% 230.52/41.81    (6)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.52/41.81         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.52/41.81    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.81           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.81    (8)  op(all_52_7, all_52_7) = e0
% 230.52/41.81    (9)  all_57_4 = e2
% 230.52/41.81    (10)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.52/41.81          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.52/41.81    (11)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.52/41.81          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.52/41.81    (12)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.52/41.81          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.52/41.81    (13)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 230.52/41.81          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.52/41.81    (14)   ~ (e3 = e2)
% 230.52/41.81    (15)   ~ (e3 = e0)
% 230.52/41.81    (16)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.52/41.81          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.52/41.81    (17)  op(e3, e3) = e3
% 230.52/41.81    (18)  all_57_15 = e3
% 230.52/41.81    (19)  all_57_1 = e1
% 230.52/41.81    (20)  all_57_5 = e3
% 230.52/41.81    (21)  all_57_11 = e0
% 230.52/41.81    (22)   ~ (e2 = e0)
% 230.52/41.81    (23)   ~ (e1 = e0)
% 230.52/41.81    (24)  op(e0, e0) = e3
% 230.52/41.81    (25)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.52/41.81          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.52/41.81            e2)
% 230.52/41.81    (26)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.52/41.81              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.52/41.81                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.52/41.81                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.52/41.81    (27)  op(e1, e1) = e0
% 230.52/41.81    (28)  all_57_7 = e3
% 230.52/41.81    (29)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.52/41.81          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.52/41.81    (30)   ~ (e2 = e1)
% 230.52/41.81    (31)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.52/41.81          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.52/41.81    (32)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.52/41.81          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.52/41.81    (33)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.52/41.81          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.52/41.81    (34)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.52/41.81          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.52/41.81    (35)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.52/41.81          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.52/41.81    (36)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.52/41.81          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.52/41.81    (37)  all_57_3 = e2
% 230.52/41.81    (38)  op(e3, e0) = all_52_7
% 230.52/41.81    (39)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.52/41.81          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.52/41.81    (40)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.52/41.81          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.52/41.81  
% 230.52/41.81  Begin of proof
% 230.52/41.81  | 
% 230.52/41.81  | BETA: splitting (12) gives:
% 230.52/41.81  | 
% 230.52/41.81  | Case 1:
% 230.52/41.81  | | 
% 230.52/41.81  | |   (41)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) =
% 230.52/41.81  | |           e0)
% 230.52/41.81  | | 
% 230.52/41.81  | | REF_CLOSE: (7), (15), (17), (19), (23), (41) are inconsistent by sub-proof
% 230.52/41.81  | |            #2492.
% 230.52/41.81  | | 
% 230.52/41.81  | Case 2:
% 230.52/41.81  | | 
% 230.52/41.81  | |   (42)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) =
% 230.52/41.81  | |           e0)
% 230.52/41.81  | | 
% 230.52/41.81  | | BETA: splitting (42) gives:
% 230.52/41.81  | | 
% 230.52/41.81  | | Case 1:
% 230.52/41.81  | | | 
% 230.52/41.81  | | |   (43)  all_57_4 = e0 & op(e3, e1) = e0
% 230.52/41.81  | | | 
% 230.52/41.81  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 230.52/41.81  | | |            (13), (14), (15), (16), (17), (18), (20), (22), (23), (24),
% 230.52/41.81  | | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 230.52/41.81  | | |            (35), (36), (37), (38), (39), (40), (43) are inconsistent by
% 230.52/41.81  | | |            sub-proof #1161.
% 230.52/41.81  | | | 
% 230.52/41.81  | | Case 2:
% 230.52/41.81  | | | 
% 230.52/41.81  | | |   (44)  all_57_9 = e0 & op(e3, e0) = e0
% 230.52/41.81  | | | 
% 230.52/41.81  | | | ALPHA: (44) implies:
% 230.52/41.81  | | |   (45)  all_57_9 = e0
% 230.52/41.81  | | | 
% 230.52/41.81  | | | REF_CLOSE: (5), (14), (18), (21), (22), (23), (30), (31), (35), (45) are
% 230.52/41.81  | | |            inconsistent by sub-proof #1144.
% 230.52/41.81  | | | 
% 230.52/41.81  | | End of split
% 230.52/41.81  | | 
% 230.52/41.81  | End of split
% 230.52/41.81  | 
% 230.52/41.81  End of proof
% 230.52/41.81  
% 230.52/41.81  Sub-proof #1144 shows that the following formulas are inconsistent:
% 230.52/41.81  ----------------------------------------------------------------
% 230.52/41.81    (1)   ~ (e3 = e1)
% 230.52/41.81    (2)   ~ (e3 = e2)
% 230.52/41.81    (3)  all_57_15 = e3
% 230.52/41.81    (4)  all_57_9 = e0
% 230.52/41.81    (5)  all_57_11 = e0
% 230.52/41.81    (6)   ~ (e2 = e0)
% 230.52/41.81    (7)   ~ (e1 = e0)
% 230.52/41.81    (8)   ~ (e2 = e1)
% 230.52/41.81    (9)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.52/41.81         (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.52/41.81    (10)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.52/41.81          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.52/41.81  
% 230.52/41.81  Begin of proof
% 230.52/41.81  | 
% 230.52/41.81  | BETA: splitting (10) gives:
% 230.52/41.81  | 
% 230.52/41.81  | Case 1:
% 230.52/41.81  | | 
% 230.52/41.81  | |   (11)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) =
% 230.52/41.81  | |           e1)
% 230.52/41.81  | | 
% 230.52/41.81  | | BETA: splitting (11) gives:
% 230.52/41.81  | | 
% 230.52/41.81  | | Case 1:
% 230.52/41.81  | | | 
% 230.52/41.81  | | |   (12)  all_57_9 = e1 & op(e3, e0) = e1
% 230.52/41.81  | | | 
% 230.52/41.81  | | | ALPHA: (12) implies:
% 230.52/41.81  | | |   (13)  all_57_9 = e1
% 230.52/41.81  | | | 
% 230.52/41.81  | | | REF_CLOSE: (4), (7), (13) are inconsistent by sub-proof #2479.
% 230.52/41.81  | | | 
% 230.52/41.81  | | Case 2:
% 230.52/41.81  | | | 
% 230.52/41.81  | | |   (14)  all_57_10 = e1 & op(e2, e0) = e1
% 230.52/41.81  | | | 
% 230.52/41.81  | | | ALPHA: (14) implies:
% 230.52/41.81  | | |   (15)  all_57_10 = e1
% 230.52/41.81  | | | 
% 230.52/41.81  | | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (9), (15) are inconsistent by
% 230.52/41.81  | | |            sub-proof #1145.
% 230.52/41.81  | | | 
% 230.52/41.81  | | End of split
% 230.52/41.81  | | 
% 230.52/41.81  | Case 2:
% 230.52/41.81  | | 
% 230.52/41.81  | |   (16)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.52/41.81  | |           e1)
% 230.52/41.81  | | 
% 230.52/41.81  | | REF_CLOSE: (1), (3), (5), (7), (16) are inconsistent by sub-proof #1512.
% 230.52/41.81  | | 
% 230.52/41.81  | End of split
% 230.52/41.81  | 
% 230.52/41.81  End of proof
% 230.52/41.81  
% 230.52/41.81  Sub-proof #1145 shows that the following formulas are inconsistent:
% 230.52/41.81  ----------------------------------------------------------------
% 230.52/41.81    (1)  all_57_10 = e1
% 230.52/41.81    (2)   ~ (e3 = e2)
% 230.52/41.81    (3)  all_57_15 = e3
% 230.52/41.81    (4)  all_57_9 = e0
% 230.52/41.81    (5)  all_57_11 = e0
% 230.52/41.81    (6)   ~ (e2 = e0)
% 230.52/41.81    (7)   ~ (e2 = e1)
% 230.52/41.81    (8)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.52/41.81         (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.52/41.81  
% 230.52/41.81  Begin of proof
% 230.52/41.81  | 
% 230.52/41.81  | BETA: splitting (8) gives:
% 230.52/41.81  | 
% 230.52/41.81  | Case 1:
% 230.52/41.81  | | 
% 230.52/41.81  | |   (9)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 230.52/41.81  | |          e2)
% 230.52/41.81  | | 
% 230.52/41.81  | | BETA: splitting (9) gives:
% 230.52/41.81  | | 
% 230.52/41.81  | | Case 1:
% 230.52/41.81  | | | 
% 230.52/41.81  | | |   (10)  all_57_9 = e2 & op(e3, e0) = e2
% 230.52/41.81  | | | 
% 230.52/41.81  | | | ALPHA: (10) implies:
% 230.52/41.81  | | |   (11)  all_57_9 = e2
% 230.52/41.81  | | | 
% 230.52/41.81  | | | REF_CLOSE: (4), (6), (11) are inconsistent by sub-proof #2440.
% 230.52/41.81  | | | 
% 230.52/41.81  | | Case 2:
% 230.52/41.81  | | | 
% 230.52/41.81  | | |   (12)  all_57_10 = e2 & op(e2, e0) = e2
% 230.52/41.81  | | | 
% 230.52/41.81  | | | ALPHA: (12) implies:
% 230.52/41.81  | | |   (13)  all_57_10 = e2
% 230.52/41.81  | | | 
% 230.52/41.81  | | | REF_CLOSE: (1), (7), (13) are inconsistent by sub-proof #2144.
% 230.52/41.81  | | | 
% 230.52/41.81  | | End of split
% 230.52/41.81  | | 
% 230.52/41.81  | Case 2:
% 230.52/41.81  | | 
% 230.52/41.81  | |   (14)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.52/41.81  | |           e2)
% 230.52/41.81  | | 
% 230.52/41.81  | | REF_CLOSE: (2), (3), (5), (6), (14) are inconsistent by sub-proof #1146.
% 230.52/41.81  | | 
% 230.52/41.81  | End of split
% 230.52/41.81  | 
% 230.52/41.81  End of proof
% 230.52/41.81  
% 230.52/41.81  Sub-proof #1146 shows that the following formulas are inconsistent:
% 230.52/41.81  ----------------------------------------------------------------
% 230.52/41.81    (1)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.52/41.81    (2)   ~ (e3 = e2)
% 230.52/41.81    (3)  all_57_15 = e3
% 230.52/41.81    (4)  all_57_11 = e0
% 230.52/41.81    (5)   ~ (e2 = e0)
% 230.52/41.81  
% 230.52/41.81  Begin of proof
% 230.52/41.81  | 
% 230.52/41.81  | BETA: splitting (1) gives:
% 230.52/41.81  | 
% 230.52/41.81  | Case 1:
% 230.52/41.81  | | 
% 230.52/41.81  | |   (6)  all_57_11 = e2 & op(e1, e0) = e2
% 230.52/41.81  | | 
% 230.52/41.81  | | ALPHA: (6) implies:
% 230.52/41.81  | |   (7)  all_57_11 = e2
% 230.52/41.81  | | 
% 230.52/41.81  | | REF_CLOSE: (4), (5), (7) are inconsistent by sub-proof #1949.
% 230.52/41.81  | | 
% 230.52/41.81  | Case 2:
% 230.52/41.81  | | 
% 230.52/41.81  | |   (8)  all_57_15 = e2 & op(e0, e0) = e2
% 230.52/41.81  | | 
% 230.52/41.81  | | REF_CLOSE: (2), (3), (8) are inconsistent by sub-proof #2323.
% 230.52/41.81  | | 
% 230.52/41.81  | End of split
% 230.52/41.81  | 
% 230.52/41.81  End of proof
% 230.52/41.81  
% 230.52/41.81  Sub-proof #1147 shows that the following formulas are inconsistent:
% 230.52/41.81  ----------------------------------------------------------------
% 230.52/41.81    (1)  op(e1, e0) = e2
% 230.52/41.81    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.81           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.81    (3)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) = all_22_1
% 230.52/41.81           & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0, e3) =
% 230.52/41.81           all_22_1 & $i(all_22_1))
% 230.52/41.81    (4)  op(e0, e3) = e1
% 230.52/41.81    (5)  ( ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) = all_12_1
% 230.52/41.81           & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e1) & op(e0, e3) =
% 230.52/41.81           all_12_1 & $i(all_12_1))
% 230.52/41.81  
% 230.52/41.81  Begin of proof
% 230.52/41.81  | 
% 230.52/41.81  | BETA: splitting (5) gives:
% 230.52/41.81  | 
% 230.52/41.81  | Case 1:
% 230.52/41.81  | | 
% 230.52/41.81  | |   (6)   ~ (all_12_0 = e2) & op(all_12_1, e0) = all_12_0 & op(e0, e3) =
% 230.52/41.81  | |        all_12_1 & $i(all_12_0) & $i(all_12_1)
% 230.52/41.81  | | 
% 230.52/41.81  | | ALPHA: (6) implies:
% 230.52/41.81  | |   (7)   ~ (all_12_0 = e2)
% 230.52/41.81  | |   (8)  op(e0, e3) = all_12_1
% 230.52/41.81  | |   (9)  op(all_12_1, e0) = all_12_0
% 230.52/41.81  | | 
% 230.52/41.81  | | BETA: splitting (3) gives:
% 230.52/41.81  | | 
% 230.52/41.81  | | Case 1:
% 230.52/41.81  | | | 
% 230.52/41.81  | | |   (10)   ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 230.52/41.81  | | |         all_22_1 & $i(all_22_0) & $i(all_22_1)
% 230.52/41.81  | | | 
% 230.52/41.81  | | | ALPHA: (10) implies:
% 230.52/41.81  | | |   (11)  op(e0, e3) = all_22_1
% 230.52/41.81  | | | 
% 230.52/41.81  | | | REF_CLOSE: (1), (2), (4), (7), (8), (9), (11) are inconsistent by
% 230.52/41.81  | | |            sub-proof #1150.
% 230.52/41.81  | | | 
% 230.52/41.81  | | Case 2:
% 230.52/41.81  | | | 
% 230.52/41.81  | | |   (12)   ~ (all_22_1 = e2) & op(e0, e3) = all_22_1 & $i(all_22_1)
% 230.52/41.81  | | | 
% 230.52/41.81  | | | ALPHA: (12) implies:
% 230.52/41.81  | | |   (13)  op(e0, e3) = all_22_1
% 230.52/41.81  | | | 
% 230.52/41.81  | | | REF_CLOSE: (1), (2), (4), (7), (8), (9), (13) are inconsistent by
% 230.52/41.81  | | |            sub-proof #1150.
% 230.52/41.81  | | | 
% 230.52/41.81  | | End of split
% 230.52/41.81  | | 
% 230.52/41.81  | Case 2:
% 230.52/41.81  | | 
% 230.52/41.81  | |   (14)   ~ (all_12_1 = e1) & op(e0, e3) = all_12_1 & $i(all_12_1)
% 230.52/41.81  | | 
% 230.52/41.81  | | REF_CLOSE: (2), (3), (4), (14) are inconsistent by sub-proof #1148.
% 230.52/41.81  | | 
% 230.52/41.81  | End of split
% 230.52/41.81  | 
% 230.52/41.81  End of proof
% 230.52/41.81  
% 230.52/41.81  Sub-proof #1148 shows that the following formulas are inconsistent:
% 230.52/41.81  ----------------------------------------------------------------
% 230.52/41.81    (1)   ~ (all_12_1 = e1) & op(e0, e3) = all_12_1 & $i(all_12_1)
% 230.52/41.81    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.81           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.81    (3)  ( ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) = all_22_1
% 230.52/41.81           & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e0, e3) =
% 230.52/41.81           all_22_1 & $i(all_22_1))
% 230.52/41.81    (4)  op(e0, e3) = e1
% 230.52/41.81  
% 230.52/41.81  Begin of proof
% 230.52/41.81  | 
% 230.52/41.81  | ALPHA: (1) implies:
% 230.52/41.81  |   (5)   ~ (all_12_1 = e1)
% 230.52/41.81  |   (6)  op(e0, e3) = all_12_1
% 230.52/41.81  | 
% 230.52/41.81  | BETA: splitting (3) gives:
% 230.52/41.81  | 
% 230.52/41.81  | Case 1:
% 230.52/41.81  | | 
% 230.52/41.81  | |   (7)   ~ (all_22_0 = e1) & op(all_22_1, e0) = all_22_0 & op(e0, e3) =
% 230.52/41.81  | |        all_22_1 & $i(all_22_0) & $i(all_22_1)
% 230.52/41.81  | | 
% 230.52/41.81  | | ALPHA: (7) implies:
% 230.52/41.81  | |   (8)  op(e0, e3) = all_22_1
% 230.52/41.81  | | 
% 230.52/41.81  | | REF_CLOSE: (2), (4), (5), (6), (8) are inconsistent by sub-proof #1149.
% 230.52/41.81  | | 
% 230.52/41.81  | Case 2:
% 230.52/41.81  | | 
% 230.52/41.81  | |   (9)   ~ (all_22_1 = e2) & op(e0, e3) = all_22_1 & $i(all_22_1)
% 230.52/41.81  | | 
% 230.52/41.81  | | ALPHA: (9) implies:
% 230.52/41.81  | |   (10)  op(e0, e3) = all_22_1
% 230.52/41.81  | | 
% 230.52/41.81  | | REF_CLOSE: (2), (4), (5), (6), (10) are inconsistent by sub-proof #1149.
% 230.52/41.81  | | 
% 230.52/41.81  | End of split
% 230.52/41.81  | 
% 230.52/41.81  End of proof
% 230.52/41.81  
% 230.52/41.81  Sub-proof #1149 shows that the following formulas are inconsistent:
% 230.52/41.81  ----------------------------------------------------------------
% 230.52/41.81    (1)  op(e0, e3) = all_12_1
% 230.52/41.81    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.81           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.81    (3)  op(e0, e3) = e1
% 230.52/41.81    (4)  op(e0, e3) = all_22_1
% 230.52/41.81    (5)   ~ (all_12_1 = e1)
% 230.52/41.81  
% 230.52/41.81  Begin of proof
% 230.52/41.81  | 
% 230.52/41.81  | GROUND_INST: instantiating (2) with all_12_1, all_22_1, e3, e0, simplifying
% 230.52/41.81  |              with (1), (4) gives:
% 230.52/41.81  |   (6)  all_22_1 = all_12_1
% 230.52/41.81  | 
% 230.52/41.81  | GROUND_INST: instantiating (2) with e1, all_22_1, e3, e0, simplifying with
% 230.52/41.81  |              (3), (4) gives:
% 230.52/41.81  |   (7)  all_22_1 = e1
% 230.52/41.81  | 
% 230.52/41.81  | COMBINE_EQS: (6), (7) imply:
% 230.52/41.81  |   (8)  all_12_1 = e1
% 230.52/41.81  | 
% 230.52/41.81  | SIMP: (8) implies:
% 230.52/41.81  |   (9)  all_12_1 = e1
% 230.52/41.81  | 
% 230.52/41.81  | REDUCE: (5), (9) imply:
% 230.52/41.81  |   (10)  $false
% 230.52/41.81  | 
% 230.52/41.81  | CLOSE: (10) is inconsistent.
% 230.52/41.81  | 
% 230.52/41.81  End of proof
% 230.52/41.81  
% 230.52/41.81  Sub-proof #1150 shows that the following formulas are inconsistent:
% 230.52/41.81  ----------------------------------------------------------------
% 230.52/41.81    (1)  op(e1, e0) = e2
% 230.52/41.81    (2)  op(e0, e3) = all_12_1
% 230.52/41.81    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.81           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.81    (4)  op(e0, e3) = e1
% 230.52/41.81    (5)  op(e0, e3) = all_22_1
% 230.52/41.81    (6)  op(all_12_1, e0) = all_12_0
% 230.52/41.81    (7)   ~ (all_12_0 = e2)
% 230.52/41.81  
% 230.52/41.81  Begin of proof
% 230.52/41.81  | 
% 230.52/41.81  | GROUND_INST: instantiating (3) with all_12_1, all_22_1, e3, e0, simplifying
% 230.52/41.81  |              with (2), (5) gives:
% 230.52/41.81  |   (8)  all_22_1 = all_12_1
% 230.52/41.81  | 
% 230.52/41.81  | GROUND_INST: instantiating (3) with e1, all_22_1, e3, e0, simplifying with
% 230.52/41.81  |              (4), (5) gives:
% 230.52/41.81  |   (9)  all_22_1 = e1
% 230.52/41.81  | 
% 230.52/41.81  | COMBINE_EQS: (8), (9) imply:
% 230.52/41.81  |   (10)  all_12_1 = e1
% 230.52/41.81  | 
% 230.52/41.81  | SIMP: (10) implies:
% 230.52/41.81  |   (11)  all_12_1 = e1
% 230.52/41.81  | 
% 230.52/41.81  | REDUCE: (6), (11) imply:
% 230.52/41.81  |   (12)  op(e1, e0) = all_12_0
% 230.52/41.81  | 
% 230.52/41.81  | GROUND_INST: instantiating (3) with e2, all_12_0, e0, e1, simplifying with
% 230.52/41.81  |              (1), (12) gives:
% 230.52/41.81  |   (13)  all_12_0 = e2
% 230.52/41.81  | 
% 230.52/41.81  | REDUCE: (7), (13) imply:
% 230.52/41.81  |   (14)  $false
% 230.52/41.81  | 
% 230.52/41.81  | CLOSE: (14) is inconsistent.
% 230.52/41.81  | 
% 230.52/41.81  End of proof
% 230.52/41.81  
% 230.52/41.81  Sub-proof #1151 shows that the following formulas are inconsistent:
% 230.52/41.81  ----------------------------------------------------------------
% 230.52/41.81    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.52/41.81         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.52/41.81    (2)   ~ (all_52_7 = e3)
% 230.52/41.81    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.52/41.81         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.52/41.81    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.52/41.81         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.52/41.81    (5)   ~ (e3 = e1)
% 230.52/41.81    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.81           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.81    (7)  op(all_52_7, all_52_7) = e0
% 230.52/41.81    (8)  all_57_12 = e2
% 230.52/41.81    (9)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.52/41.81         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.52/41.81    (10)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.52/41.81          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.52/41.81    (11)   ~ (e3 = e2)
% 230.52/41.81    (12)   ~ (e3 = e0)
% 230.52/41.81    (13)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.52/41.81          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.52/41.81    (14)  op(e3, e3) = e3
% 230.52/41.81    (15)  all_57_15 = e3
% 230.52/41.81    (16)  all_57_5 = e3
% 230.52/41.81    (17)   ~ (e2 = e0)
% 230.52/41.81    (18)   ~ (e1 = e0)
% 230.52/41.81    (19)  op(e0, e0) = e3
% 230.52/41.81    (20)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.52/41.81          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.52/41.81            e2)
% 230.52/41.81    (21)  op(e1, e1) = e0
% 230.52/41.81    (22)  all_57_7 = e3
% 230.52/41.82    (23)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.52/41.82          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.52/41.82    (24)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) |
% 230.52/41.82          (all_57_11 = e0 & op(e1, e0) = e0)
% 230.52/41.82    (25)   ~ (e2 = e1)
% 230.52/41.82    (26)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.52/41.82          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.52/41.82    (27)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.52/41.82          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.52/41.82    (28)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.52/41.82          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.52/41.82    (29)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.52/41.82          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.52/41.82    (30)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.52/41.82          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.52/41.82    (31)  all_57_3 = e2
% 230.52/41.82    (32)  op(e3, e0) = all_52_7
% 230.52/41.82    (33)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.52/41.82          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.52/41.82    (34)  all_57_12 = e0 & op(e0, e3) = e0
% 230.52/41.82    (35)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.52/41.82          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.52/41.82  
% 230.52/41.82  Begin of proof
% 230.52/41.82  | 
% 230.52/41.82  | ALPHA: (34) implies:
% 230.52/41.82  |   (36)  all_57_12 = e0
% 230.52/41.82  | 
% 230.52/41.82  | COMBINE_EQS: (8), (36) imply:
% 230.52/41.82  |   (37)  e2 = e0
% 230.52/41.82  | 
% 230.52/41.82  | COMBINE_EQS: (31), (37) imply:
% 230.52/41.82  |   (38)  all_57_3 = e0
% 230.52/41.82  | 
% 230.52/41.82  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13),
% 230.52/41.82  |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 230.52/41.82  |            (25), (26), (27), (28), (29), (30), (32), (33), (35), (36), (38)
% 230.52/41.82  |            are inconsistent by sub-proof #1500.
% 230.52/41.82  | 
% 230.52/41.82  End of proof
% 230.52/41.82  
% 230.52/41.82  Sub-proof #1152 shows that the following formulas are inconsistent:
% 230.52/41.82  ----------------------------------------------------------------
% 230.52/41.82    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.82           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.82    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1)
% 230.52/41.82    (3)  op(e2, e2) = e2
% 230.52/41.82    (4)   ~ (e1 = e0)
% 230.52/41.82    (5)  all_57_2 = e0
% 230.52/41.82    (6)   ~ (e2 = e1)
% 230.52/41.82  
% 230.52/41.82  Begin of proof
% 230.52/41.82  | 
% 230.52/41.82  | BETA: splitting (2) gives:
% 230.52/41.82  | 
% 230.52/41.82  | Case 1:
% 230.52/41.82  | | 
% 230.52/41.82  | |   (7)  all_57_2 = e1 & op(e2, e3) = e1
% 230.52/41.82  | | 
% 230.52/41.82  | | ALPHA: (7) implies:
% 230.52/41.82  | |   (8)  all_57_2 = e1
% 230.52/41.82  | | 
% 230.52/41.82  | | REF_CLOSE: (4), (5), (8) are inconsistent by sub-proof #2473.
% 230.52/41.82  | | 
% 230.52/41.82  | Case 2:
% 230.52/41.82  | | 
% 230.52/41.82  | |   (9)  all_57_3 = e1 & op(e2, e2) = e1
% 230.52/41.82  | | 
% 230.52/41.82  | | ALPHA: (9) implies:
% 230.52/41.82  | |   (10)  op(e2, e2) = e1
% 230.52/41.82  | | 
% 230.52/41.82  | | REF_CLOSE: (1), (3), (6), (10) are inconsistent by sub-proof #2306.
% 230.52/41.82  | | 
% 230.52/41.82  | End of split
% 230.52/41.82  | 
% 230.52/41.82  End of proof
% 230.52/41.82  
% 230.52/41.82  Sub-proof #1153 shows that the following formulas are inconsistent:
% 230.52/41.82  ----------------------------------------------------------------
% 230.52/41.82    (1)   ~ (e3 = e1)
% 230.52/41.82    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.82           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.82    (3)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.52/41.82         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.52/41.82    (4)   ~ (all_6_2 = e3)
% 230.52/41.82    (5)  op(e1, e1) = all_6_2
% 230.52/41.82    (6)   ~ (e3 = e2)
% 230.52/41.82    (7)   ~ (e3 = e0)
% 230.52/41.82    (8)  all_57_15 = e3
% 230.52/41.82    (9)  all_57_11 = e2
% 230.52/41.82    (10)   ~ (e2 = e0)
% 230.52/41.82    (11)   ~ (e1 = e0)
% 230.52/41.82    (12)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.52/41.82              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.52/41.82                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.52/41.82                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.52/41.82    (13)  op(e1, e1) = e2
% 230.52/41.82    (14)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0)
% 230.52/41.82    (15)   ~ (e2 = e1)
% 230.52/41.82    (16)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.52/41.82          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.52/41.82    (17)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.52/41.82          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.52/41.82    (18)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.52/41.82          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.52/41.82  
% 230.52/41.82  Begin of proof
% 230.52/41.82  | 
% 230.52/41.82  | BETA: splitting (14) gives:
% 230.52/41.82  | 
% 230.52/41.82  | Case 1:
% 230.52/41.82  | | 
% 230.52/41.82  | |   (19)  all_57_6 = e0 & op(e1, e3) = e0
% 230.52/41.82  | | 
% 230.52/41.82  | | ALPHA: (19) implies:
% 230.52/41.82  | |   (20)  all_57_6 = e0
% 230.52/41.82  | | 
% 230.52/41.82  | | BETA: splitting (18) gives:
% 230.52/41.82  | | 
% 230.52/41.82  | | Case 1:
% 230.52/41.82  | | | 
% 230.52/41.82  | | |   (21)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) =
% 230.52/41.82  | | |           e1)
% 230.52/41.82  | | | 
% 230.52/41.82  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (15),
% 230.52/41.82  | | |            (16), (17), (20), (21) are inconsistent by sub-proof #1156.
% 230.52/41.82  | | | 
% 230.52/41.82  | | Case 2:
% 230.52/41.82  | | | 
% 230.52/41.82  | | |   (22)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) =
% 230.52/41.82  | | |           e1)
% 230.52/41.82  | | | 
% 230.52/41.82  | | | REF_CLOSE: (2), (9), (13), (15), (22) are inconsistent by sub-proof #1725.
% 230.52/41.82  | | | 
% 230.52/41.82  | | End of split
% 230.52/41.82  | | 
% 230.52/41.82  | Case 2:
% 230.52/41.82  | | 
% 230.52/41.82  | |   (23)  all_57_7 = e0 & op(e1, e2) = e0
% 230.52/41.82  | | 
% 230.52/41.82  | | ALPHA: (23) implies:
% 230.52/41.82  | |   (24)  all_57_7 = e0
% 230.52/41.82  | | 
% 230.52/41.82  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 230.52/41.82  | |            (13), (15), (16), (17), (18), (24) are inconsistent by sub-proof
% 230.52/41.82  | |            #1154.
% 230.52/41.82  | | 
% 230.52/41.82  | End of split
% 230.52/41.82  | 
% 230.52/41.82  End of proof
% 230.52/41.82  
% 230.52/41.82  Sub-proof #1154 shows that the following formulas are inconsistent:
% 230.52/41.82  ----------------------------------------------------------------
% 230.52/41.82    (1)   ~ (e3 = e1)
% 230.52/41.82    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.82           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.82    (3)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.52/41.82         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.52/41.82    (4)   ~ (all_6_2 = e3)
% 230.52/41.82    (5)  op(e1, e1) = all_6_2
% 230.52/41.82    (6)   ~ (e3 = e2)
% 230.52/41.82    (7)   ~ (e3 = e0)
% 230.52/41.82    (8)  all_57_15 = e3
% 230.52/41.82    (9)  all_57_11 = e2
% 230.52/41.82    (10)   ~ (e2 = e0)
% 230.52/41.82    (11)   ~ (e1 = e0)
% 230.52/41.82    (12)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.52/41.82              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.52/41.82                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.52/41.82                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.52/41.82    (13)  op(e1, e1) = e2
% 230.52/41.82    (14)   ~ (e2 = e1)
% 230.52/41.82    (15)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.52/41.82          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.52/41.82    (16)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.52/41.82          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.52/41.82    (17)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.52/41.82          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.52/41.82    (18)  all_57_7 = e0
% 230.52/41.82  
% 230.52/41.82  Begin of proof
% 230.52/41.82  | 
% 230.52/41.82  | BETA: splitting (17) gives:
% 230.52/41.82  | 
% 230.52/41.82  | Case 1:
% 230.52/41.82  | | 
% 230.52/41.82  | |   (19)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) =
% 230.52/41.82  | |           e1)
% 230.52/41.82  | | 
% 230.52/41.82  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (14),
% 230.52/41.82  | |            (15), (16), (18), (19) are inconsistent by sub-proof #1155.
% 230.52/41.82  | | 
% 230.52/41.82  | Case 2:
% 230.52/41.82  | | 
% 230.52/41.82  | |   (20)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) =
% 230.52/41.82  | |           e1)
% 230.52/41.82  | | 
% 230.52/41.82  | | REF_CLOSE: (2), (9), (13), (14), (20) are inconsistent by sub-proof #1725.
% 230.52/41.82  | | 
% 230.52/41.82  | End of split
% 230.52/41.82  | 
% 230.52/41.82  End of proof
% 230.52/41.82  
% 230.52/41.82  Sub-proof #1155 shows that the following formulas are inconsistent:
% 230.52/41.82  ----------------------------------------------------------------
% 230.52/41.82    (1)   ~ (e3 = e1)
% 230.52/41.82    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.82           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.82    (3)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.52/41.82         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.52/41.82    (4)   ~ (all_6_2 = e3)
% 230.52/41.82    (5)  op(e1, e1) = all_6_2
% 230.52/41.82    (6)   ~ (e3 = e2)
% 230.52/41.82    (7)   ~ (e3 = e0)
% 230.52/41.82    (8)  all_57_15 = e3
% 230.52/41.82    (9)   ~ (e2 = e0)
% 230.52/41.82    (10)   ~ (e1 = e0)
% 230.52/41.82    (11)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.52/41.82              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.52/41.82                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.52/41.82                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.52/41.82    (12)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1)
% 230.52/41.82    (13)   ~ (e2 = e1)
% 230.52/41.82    (14)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.52/41.82          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.52/41.82    (15)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.52/41.82          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.52/41.82    (16)  all_57_7 = e0
% 230.52/41.82  
% 230.52/41.82  Begin of proof
% 230.52/41.82  | 
% 230.52/41.82  | BETA: splitting (12) gives:
% 230.52/41.82  | 
% 230.52/41.82  | Case 1:
% 230.52/41.82  | | 
% 230.52/41.82  | |   (17)  all_57_6 = e1 & op(e1, e3) = e1
% 230.52/41.82  | | 
% 230.52/41.82  | | ALPHA: (17) implies:
% 230.52/41.82  | |   (18)  all_57_6 = e1
% 230.52/41.82  | | 
% 230.52/41.82  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 230.52/41.82  | |            (14), (15), (16), (18) are inconsistent by sub-proof #1735.
% 230.52/41.82  | | 
% 230.52/41.82  | Case 2:
% 230.52/41.82  | | 
% 230.52/41.82  | |   (19)  all_57_7 = e1 & op(e1, e2) = e1
% 230.52/41.82  | | 
% 230.52/41.82  | | ALPHA: (19) implies:
% 230.52/41.82  | |   (20)  all_57_7 = e1
% 230.52/41.82  | | 
% 230.52/41.82  | | REF_CLOSE: (10), (16), (20) are inconsistent by sub-proof #2211.
% 230.52/41.82  | | 
% 230.52/41.82  | End of split
% 230.52/41.82  | 
% 230.52/41.82  End of proof
% 230.52/41.82  
% 230.52/41.82  Sub-proof #1156 shows that the following formulas are inconsistent:
% 230.52/41.82  ----------------------------------------------------------------
% 230.52/41.82    (1)   ~ (e3 = e1)
% 230.52/41.82    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.82           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.82    (3)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.52/41.82         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.52/41.82    (4)   ~ (all_6_2 = e3)
% 230.52/41.82    (5)  op(e1, e1) = all_6_2
% 230.52/41.82    (6)   ~ (e3 = e2)
% 230.52/41.82    (7)   ~ (e3 = e0)
% 230.52/41.82    (8)  all_57_6 = e0
% 230.52/41.82    (9)  all_57_15 = e3
% 230.52/41.82    (10)   ~ (e2 = e0)
% 230.52/41.82    (11)   ~ (e1 = e0)
% 230.52/41.82    (12)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.52/41.82              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.52/41.82                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.52/41.82                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.52/41.82    (13)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1)
% 230.52/41.82    (14)   ~ (e2 = e1)
% 230.52/41.82    (15)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.52/41.82          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.52/41.82    (16)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.52/41.82          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.52/41.82  
% 230.52/41.82  Begin of proof
% 230.52/41.82  | 
% 230.52/41.82  | BETA: splitting (13) gives:
% 230.52/41.82  | 
% 230.52/41.82  | Case 1:
% 230.52/41.82  | | 
% 230.52/41.82  | |   (17)  all_57_6 = e1 & op(e1, e3) = e1
% 230.52/41.82  | | 
% 230.52/41.82  | | ALPHA: (17) implies:
% 230.52/41.82  | |   (18)  all_57_6 = e1
% 230.52/41.82  | | 
% 230.52/41.82  | | REF_CLOSE: (8), (11), (18) are inconsistent by sub-proof #2227.
% 230.52/41.82  | | 
% 230.52/41.82  | Case 2:
% 230.52/41.82  | | 
% 230.52/41.82  | |   (19)  all_57_7 = e1 & op(e1, e2) = e1
% 230.52/41.82  | | 
% 230.52/41.82  | | ALPHA: (19) implies:
% 230.52/41.82  | |   (20)  all_57_7 = e1
% 230.52/41.82  | | 
% 230.52/41.82  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 230.52/41.82  | |            (14), (15), (16), (20) are inconsistent by sub-proof #1157.
% 230.52/41.82  | | 
% 230.52/41.82  | End of split
% 230.52/41.82  | 
% 230.52/41.82  End of proof
% 230.52/41.82  
% 230.52/41.82  Sub-proof #1157 shows that the following formulas are inconsistent:
% 230.52/41.82  ----------------------------------------------------------------
% 230.52/41.82    (1)   ~ (e3 = e1)
% 230.52/41.82    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.82           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.82    (3)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.52/41.82         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.52/41.82    (4)   ~ (all_6_2 = e3)
% 230.52/41.82    (5)  op(e1, e1) = all_6_2
% 230.52/41.82    (6)  all_57_7 = e1
% 230.52/41.82    (7)   ~ (e3 = e2)
% 230.52/41.82    (8)   ~ (e3 = e0)
% 230.52/41.82    (9)  all_57_6 = e0
% 230.52/41.82    (10)  all_57_15 = e3
% 230.52/41.82    (11)   ~ (e2 = e0)
% 230.52/41.82    (12)   ~ (e1 = e0)
% 230.52/41.82    (13)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.52/41.82              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.52/41.82                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.52/41.82                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.52/41.82    (14)   ~ (e2 = e1)
% 230.52/41.82    (15)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.52/41.82          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.52/41.82    (16)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.52/41.82          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.52/41.82  
% 230.52/41.82  Begin of proof
% 230.52/41.82  | 
% 230.52/41.82  | BETA: splitting (3) gives:
% 230.52/41.82  | 
% 230.52/41.82  | Case 1:
% 230.52/41.82  | | 
% 230.52/41.82  | |   (17)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 230.52/41.82  | |           e3)
% 230.52/41.82  | | 
% 230.52/41.82  | | BETA: splitting (17) gives:
% 230.52/41.82  | | 
% 230.52/41.82  | | Case 1:
% 230.52/41.82  | | | 
% 230.52/41.82  | | |   (18)  all_57_6 = e3 & op(e1, e3) = e3
% 230.52/41.82  | | | 
% 230.52/41.82  | | | ALPHA: (18) implies:
% 230.52/41.82  | | |   (19)  all_57_6 = e3
% 230.52/41.82  | | | 
% 230.52/41.82  | | | REF_CLOSE: (8), (9), (19) are inconsistent by sub-proof #1822.
% 230.52/41.82  | | | 
% 230.52/41.82  | | Case 2:
% 230.52/41.82  | | | 
% 230.52/41.82  | | |   (20)  all_57_7 = e3 & op(e1, e2) = e3
% 230.52/41.82  | | | 
% 230.52/41.82  | | | ALPHA: (20) implies:
% 230.52/41.82  | | |   (21)  all_57_7 = e3
% 230.52/41.82  | | | 
% 230.52/41.82  | | | REF_CLOSE: (1), (6), (21) are inconsistent by sub-proof #2115.
% 230.52/41.82  | | | 
% 230.52/41.82  | | End of split
% 230.52/41.82  | | 
% 230.52/41.82  | Case 2:
% 230.52/41.82  | | 
% 230.52/41.82  | |   (22)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 230.52/41.82  | |           e3)
% 230.52/41.82  | | 
% 230.52/41.82  | | REF_CLOSE: (1), (2), (4), (5), (7), (8), (10), (11), (12), (13), (14), (15),
% 230.52/41.82  | |            (16), (22) are inconsistent by sub-proof #1786.
% 230.52/41.82  | | 
% 230.52/41.82  | End of split
% 230.52/41.82  | 
% 230.52/41.82  End of proof
% 230.52/41.82  
% 230.52/41.82  Sub-proof #1158 shows that the following formulas are inconsistent:
% 230.52/41.82  ----------------------------------------------------------------
% 230.52/41.82    (1)  all_57_9 = e2
% 230.52/41.82    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.52/41.82         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.52/41.82    (3)   ~ (all_52_7 = e3)
% 230.52/41.82    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.52/41.82         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.52/41.82    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.52/41.82         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.52/41.82    (6)   ~ (e3 = e1)
% 230.52/41.82    (7)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.52/41.82         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.52/41.82    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.82           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.82    (9)  op(all_52_7, all_52_7) = e0
% 230.52/41.82    (10)  all_57_4 = e2
% 230.52/41.82    (11)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.52/41.82          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.52/41.82    (12)  all_57_12 = e2
% 230.52/41.82    (13)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.52/41.82          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.52/41.82    (14)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.52/41.82          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.52/41.82    (15)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 230.52/41.82          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.52/41.82    (16)   ~ (e3 = e2)
% 230.52/41.82    (17)   ~ (e3 = e0)
% 230.52/41.82    (18)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.52/41.82          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.52/41.82    (19)  op(e3, e3) = e3
% 230.52/41.82    (20)  all_57_15 = e3
% 230.52/41.82    (21)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.52/41.82          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.52/41.82            e1)
% 230.52/41.82    (22)  all_57_5 = e3
% 230.52/41.82    (23)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.52/41.82          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.52/41.82    (24)   ~ (e2 = e0)
% 230.52/41.82    (25)   ~ (e1 = e0)
% 230.52/41.82    (26)  op(e0, e0) = e3
% 230.52/41.82    (27)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.52/41.82          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.52/41.82            e2)
% 230.52/41.82    (28)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.52/41.82              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.52/41.82                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.52/41.82                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.52/41.82    (29)  all_57_7 = e3
% 230.52/41.82    (30)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.52/41.82          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.52/41.82    (31)   ~ (e2 = e1)
% 230.52/41.82    (32)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.52/41.82          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.52/41.82    (33)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.52/41.82          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.52/41.82    (34)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.52/41.82          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.52/41.82    (35)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.52/41.82          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.52/41.82    (36)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.52/41.82          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.52/41.82    (37)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.52/41.82          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.52/41.82    (38)  all_57_3 = e2
% 230.52/41.82    (39)  op(e3, e0) = all_52_7
% 230.52/41.82    (40)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.52/41.82          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.52/41.82    (41)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.52/41.82          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.52/41.82  
% 230.52/41.82  Begin of proof
% 230.52/41.82  | 
% 230.52/41.82  | BETA: splitting (15) gives:
% 230.52/41.82  | 
% 230.52/41.82  | Case 1:
% 230.52/41.82  | | 
% 230.52/41.82  | |   (42)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) =
% 230.52/41.82  | |           e0)
% 230.52/41.82  | | 
% 230.52/41.82  | | BETA: splitting (42) gives:
% 230.52/41.82  | | 
% 230.52/41.82  | | Case 1:
% 230.52/41.82  | | | 
% 230.52/41.82  | | |   (43)  all_57_4 = e0 & op(e3, e1) = e0
% 230.52/41.82  | | | 
% 230.52/41.82  | | | ALPHA: (43) implies:
% 230.52/41.82  | | |   (44)  all_57_4 = e0
% 230.52/41.82  | | | 
% 230.52/41.82  | | | COMBINE_EQS: (10), (44) imply:
% 230.52/41.82  | | |   (45)  e2 = e0
% 230.52/41.82  | | | 
% 230.52/41.82  | | | SIMP: (45) implies:
% 230.52/41.82  | | |   (46)  e2 = e0
% 230.52/41.82  | | | 
% 230.52/41.82  | | | COMBINE_EQS: (1), (46) imply:
% 230.52/41.82  | | |   (47)  all_57_9 = e0
% 230.52/41.82  | | | 
% 230.52/41.82  | | | REF_CLOSE: (6), (8), (11), (13), (16), (19), (24), (25), (31), (44), (47)
% 230.52/41.82  | | |            are inconsistent by sub-proof #2436.
% 230.52/41.82  | | | 
% 230.52/41.82  | | Case 2:
% 230.52/41.82  | | | 
% 230.52/41.82  | | |   (48)  all_57_5 = e0 & op(e2, e1) = e0
% 230.52/41.82  | | | 
% 230.52/41.82  | | | REF_CLOSE: (17), (22), (48) are inconsistent by sub-proof #2414.
% 230.52/41.82  | | | 
% 230.52/41.82  | | End of split
% 230.52/41.82  | | 
% 230.52/41.82  | Case 2:
% 230.52/41.82  | | 
% 230.52/41.82  | |   (49)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 230.52/41.82  | |           e0)
% 230.52/41.82  | | 
% 230.52/41.82  | | BETA: splitting (49) gives:
% 230.52/41.82  | | 
% 230.52/41.82  | | Case 1:
% 230.52/41.82  | | | 
% 230.52/41.82  | | |   (50)  all_57_8 = e0 & op(e1, e1) = e0
% 230.52/41.82  | | | 
% 230.52/41.82  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 230.52/41.82  | | |            (14), (15), (16), (17), (18), (19), (20), (22), (24), (25),
% 230.52/41.82  | | |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 230.52/41.82  | | |            (36), (37), (38), (39), (40), (41), (50) are inconsistent by
% 230.52/41.82  | | |            sub-proof #1159.
% 230.52/41.82  | | | 
% 230.52/41.82  | | Case 2:
% 230.52/41.82  | | | 
% 230.52/41.82  | | |   (51)  all_57_14 = e0 & op(e0, e1) = e0
% 230.52/41.82  | | | 
% 230.52/41.82  | | | ALPHA: (51) implies:
% 230.52/41.82  | | |   (52)  all_57_14 = e0
% 230.52/41.82  | | | 
% 230.52/41.82  | | | BETA: splitting (21) gives:
% 230.52/41.82  | | | 
% 230.52/41.82  | | | Case 1:
% 230.52/41.82  | | | | 
% 230.52/41.82  | | | |   (53)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0,
% 230.52/41.82  | | | |             e2) = e1)
% 230.52/41.82  | | | | 
% 230.52/41.82  | | | | BETA: splitting (53) gives:
% 230.52/41.82  | | | | 
% 230.52/41.82  | | | | Case 1:
% 230.52/41.82  | | | | | 
% 230.52/41.82  | | | | |   (54)  all_57_12 = e1 & op(e0, e3) = e1
% 230.52/41.82  | | | | | 
% 230.52/41.82  | | | | | ALPHA: (54) implies:
% 230.52/41.82  | | | | |   (55)  all_57_12 = e1
% 230.52/41.82  | | | | | 
% 230.52/41.82  | | | | | REF_CLOSE: (12), (31), (55) are inconsistent by sub-proof #2321.
% 230.52/41.82  | | | | | 
% 230.52/41.82  | | | | Case 2:
% 230.52/41.82  | | | | | 
% 230.52/41.82  | | | | |   (56)  all_57_13 = e1 & op(e0, e2) = e1
% 230.52/41.82  | | | | | 
% 230.52/41.82  | | | | | ALPHA: (56) implies:
% 230.52/41.82  | | | | |   (57)  all_57_13 = e1
% 230.52/41.82  | | | | | 
% 230.52/41.82  | | | | | BETA: splitting (23) gives:
% 230.52/41.82  | | | | | 
% 230.52/41.82  | | | | | Case 1:
% 230.52/41.82  | | | | | | 
% 230.52/41.82  | | | | | |   (58)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2,
% 230.52/41.82  | | | | | |             e2) = e0)
% 230.52/41.82  | | | | | | 
% 230.52/41.82  | | | | | | BETA: splitting (58) gives:
% 230.52/41.82  | | | | | | 
% 230.52/41.82  | | | | | | Case 1:
% 230.52/41.82  | | | | | | | 
% 230.52/41.82  | | | | | | |   (59)  all_57_1 = e0 & op(e3, e2) = e0
% 230.52/41.82  | | | | | | | 
% 230.52/41.82  | | | | | | | ALPHA: (59) implies:
% 230.52/41.82  | | | | | | |   (60)  all_57_1 = e0
% 230.52/41.82  | | | | | | | 
% 230.52/41.82  | | | | | | | REF_CLOSE: (1), (6), (8), (10), (11), (19), (25), (31), (60) are
% 230.52/41.82  | | | | | | |            inconsistent by sub-proof #2442.
% 230.52/41.82  | | | | | | | 
% 230.52/41.82  | | | | | | Case 2:
% 230.52/41.82  | | | | | | | 
% 230.52/41.82  | | | | | | |   (61)  all_57_3 = e0 & op(e2, e2) = e0
% 230.52/41.82  | | | | | | | 
% 230.52/41.82  | | | | | | | ALPHA: (61) implies:
% 230.52/41.82  | | | | | | |   (62)  all_57_3 = e0
% 230.52/41.82  | | | | | | | 
% 230.52/41.82  | | | | | | | COMBINE_EQS: (38), (62) imply:
% 230.52/41.82  | | | | | | |   (63)  e2 = e0
% 230.52/41.82  | | | | | | | 
% 230.52/41.82  | | | | | | | COMBINE_EQS: (10), (63) imply:
% 230.52/41.82  | | | | | | |   (64)  all_57_4 = e0
% 230.52/41.82  | | | | | | | 
% 230.52/41.82  | | | | | | | REF_CLOSE: (6), (8), (16), (18), (22), (24), (25), (31), (34),
% 230.52/41.82  | | | | | | |            (52), (64) are inconsistent by sub-proof #2378.
% 230.52/41.82  | | | | | | | 
% 230.52/41.82  | | | | | | End of split
% 230.52/41.82  | | | | | | 
% 230.52/41.82  | | | | | Case 2:
% 230.52/41.82  | | | | | | 
% 230.52/41.82  | | | | | |   (65)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0,
% 230.52/41.82  | | | | | |             e2) = e0)
% 230.52/41.82  | | | | | | 
% 230.52/41.82  | | | | | | BETA: splitting (65) gives:
% 230.52/41.82  | | | | | | 
% 230.52/41.82  | | | | | | Case 1:
% 230.52/41.82  | | | | | | | 
% 230.52/41.82  | | | | | | |   (66)  all_57_7 = e0 & op(e1, e2) = e0
% 230.52/41.82  | | | | | | | 
% 230.52/41.82  | | | | | | | REF_CLOSE: (17), (29), (66) are inconsistent by sub-proof #2042.
% 230.52/41.82  | | | | | | | 
% 230.52/41.82  | | | | | | Case 2:
% 230.52/41.82  | | | | | | | 
% 230.52/41.82  | | | | | | |   (67)  all_57_13 = e0 & op(e0, e2) = e0
% 230.52/41.82  | | | | | | | 
% 230.52/41.82  | | | | | | | REF_CLOSE: (25), (57), (67) are inconsistent by sub-proof #1920.
% 230.52/41.82  | | | | | | | 
% 230.52/41.82  | | | | | | End of split
% 230.52/41.82  | | | | | | 
% 230.52/41.82  | | | | | End of split
% 230.52/41.82  | | | | | 
% 230.52/41.82  | | | | End of split
% 230.52/41.82  | | | | 
% 230.52/41.82  | | | Case 2:
% 230.52/41.82  | | | | 
% 230.52/41.82  | | | |   (68)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0,
% 230.52/41.82  | | | |             e0) = e1)
% 230.52/41.82  | | | | 
% 230.52/41.82  | | | | REF_CLOSE: (6), (8), (25), (26), (52), (68) are inconsistent by
% 230.52/41.82  | | | |            sub-proof #2056.
% 230.52/41.82  | | | | 
% 230.52/41.82  | | | End of split
% 230.52/41.82  | | | 
% 230.52/41.82  | | End of split
% 230.52/41.82  | | 
% 230.52/41.82  | End of split
% 230.52/41.82  | 
% 230.52/41.82  End of proof
% 230.52/41.82  
% 230.52/41.82  Sub-proof #1159 shows that the following formulas are inconsistent:
% 230.52/41.82  ----------------------------------------------------------------
% 230.52/41.82    (1)  all_57_9 = e2
% 230.52/41.82    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.52/41.82         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.52/41.82    (3)   ~ (all_52_7 = e3)
% 230.52/41.82    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.52/41.82         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.52/41.82    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.52/41.82         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.52/41.82    (6)   ~ (e3 = e1)
% 230.52/41.82    (7)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.52/41.82         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.52/41.82    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.82           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.82    (9)  op(all_52_7, all_52_7) = e0
% 230.52/41.83    (10)  all_57_4 = e2
% 230.52/41.83    (11)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.52/41.83          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.52/41.83    (12)  all_57_8 = e0 & op(e1, e1) = e0
% 230.52/41.83    (13)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.52/41.83          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.52/41.83    (14)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.52/41.83          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.52/41.83    (15)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 230.52/41.83          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.52/41.83    (16)   ~ (e3 = e2)
% 230.52/41.83    (17)   ~ (e3 = e0)
% 230.52/41.83    (18)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.52/41.83          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.52/41.83    (19)  op(e3, e3) = e3
% 230.52/41.83    (20)  all_57_15 = e3
% 230.52/41.83    (21)  all_57_5 = e3
% 230.52/41.83    (22)   ~ (e2 = e0)
% 230.52/41.83    (23)   ~ (e1 = e0)
% 230.52/41.83    (24)  op(e0, e0) = e3
% 230.52/41.83    (25)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.52/41.83          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.52/41.83            e2)
% 230.52/41.83    (26)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.52/41.83              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.52/41.83                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.52/41.83                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.52/41.83    (27)  all_57_7 = e3
% 230.52/41.83    (28)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.52/41.83          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.52/41.83    (29)   ~ (e2 = e1)
% 230.52/41.83    (30)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.52/41.83          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.52/41.83    (31)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.52/41.83          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.52/41.83    (32)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.52/41.83          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.52/41.83    (33)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.52/41.83          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.52/41.83    (34)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.52/41.83          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.52/41.83    (35)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.52/41.83          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.52/41.83    (36)  all_57_3 = e2
% 230.52/41.83    (37)  op(e3, e0) = all_52_7
% 230.52/41.83    (38)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.52/41.83          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.52/41.83    (39)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.52/41.83          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.52/41.83  
% 230.52/41.83  Begin of proof
% 230.52/41.83  | 
% 230.52/41.83  | ALPHA: (12) implies:
% 230.52/41.83  |   (40)  op(e1, e1) = e0
% 230.52/41.83  | 
% 230.52/41.83  | BETA: splitting (11) gives:
% 230.52/41.83  | 
% 230.52/41.83  | Case 1:
% 230.52/41.83  | | 
% 230.52/41.83  | |   (41)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) =
% 230.52/41.83  | |           e1)
% 230.52/41.83  | | 
% 230.52/41.83  | | BETA: splitting (41) gives:
% 230.52/41.83  | | 
% 230.52/41.83  | | Case 1:
% 230.52/41.83  | | | 
% 230.52/41.83  | | |   (42)  all_57_0 = e1 & op(e3, e3) = e1
% 230.52/41.83  | | | 
% 230.52/41.83  | | | ALPHA: (42) implies:
% 230.52/41.83  | | |   (43)  op(e3, e3) = e1
% 230.52/41.83  | | | 
% 230.52/41.83  | | | REF_CLOSE: (6), (8), (19), (43) are inconsistent by sub-proof #2495.
% 230.52/41.83  | | | 
% 230.52/41.83  | | Case 2:
% 230.52/41.83  | | | 
% 230.52/41.83  | | |   (44)  all_57_1 = e1 & op(e3, e2) = e1
% 230.52/41.83  | | | 
% 230.52/41.83  | | | ALPHA: (44) implies:
% 230.52/41.83  | | |   (45)  all_57_1 = e1
% 230.52/41.83  | | | 
% 230.52/41.83  | | | BETA: splitting (14) gives:
% 230.52/41.83  | | | 
% 230.52/41.83  | | | Case 1:
% 230.52/41.83  | | | | 
% 230.52/41.83  | | | |   (46)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2)
% 230.52/41.83  | | | |           = e0)
% 230.52/41.83  | | | | 
% 230.52/41.83  | | | | REF_CLOSE: (8), (17), (19), (23), (45), (46) are inconsistent by
% 230.52/41.83  | | | |            sub-proof #2492.
% 230.52/41.83  | | | | 
% 230.52/41.83  | | | Case 2:
% 230.52/41.83  | | | | 
% 230.52/41.83  | | | |   (47)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0)
% 230.52/41.83  | | | |           = e0)
% 230.52/41.83  | | | | 
% 230.52/41.83  | | | | BETA: splitting (47) gives:
% 230.52/41.83  | | | | 
% 230.52/41.83  | | | | Case 1:
% 230.52/41.83  | | | | | 
% 230.52/41.83  | | | | |   (48)  all_57_4 = e0 & op(e3, e1) = e0
% 230.52/41.83  | | | | | 
% 230.52/41.83  | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 230.52/41.83  | | | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 230.52/41.83  | | | | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 230.52/41.83  | | | | |            (34), (35), (36), (37), (38), (39), (40), (48) are
% 230.52/41.83  | | | | |            inconsistent by sub-proof #1161.
% 230.52/41.83  | | | | | 
% 230.52/41.83  | | | | Case 2:
% 230.52/41.83  | | | | | 
% 230.52/41.83  | | | | |   (49)  all_57_9 = e0 & op(e3, e0) = e0
% 230.52/41.83  | | | | | 
% 230.52/41.83  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (13),
% 230.52/41.83  | | | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 230.52/41.83  | | | | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 230.52/41.83  | | | | |            (34), (35), (36), (37), (38), (39), (40), (49) are
% 230.52/41.83  | | | | |            inconsistent by sub-proof #1160.
% 230.52/41.83  | | | | | 
% 230.52/41.83  | | | | End of split
% 230.52/41.83  | | | | 
% 230.52/41.83  | | | End of split
% 230.52/41.83  | | | 
% 230.52/41.83  | | End of split
% 230.52/41.83  | | 
% 230.52/41.83  | Case 2:
% 230.52/41.83  | | 
% 230.52/41.83  | |   (50)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) =
% 230.52/41.83  | |           e1)
% 230.52/41.83  | | 
% 230.52/41.83  | | BETA: splitting (50) gives:
% 230.52/41.83  | | 
% 230.52/41.83  | | Case 1:
% 230.52/41.83  | | | 
% 230.52/41.83  | | |   (51)  all_57_4 = e1 & op(e3, e1) = e1
% 230.52/41.83  | | | 
% 230.52/41.83  | | | REF_CLOSE: (10), (29), (51) are inconsistent by sub-proof #2452.
% 230.52/41.83  | | | 
% 230.52/41.83  | | Case 2:
% 230.52/41.83  | | | 
% 230.52/41.83  | | |   (52)  all_57_9 = e1 & op(e3, e0) = e1
% 230.52/41.83  | | | 
% 230.52/41.83  | | | REF_CLOSE: (1), (29), (52) are inconsistent by sub-proof #2451.
% 230.52/41.83  | | | 
% 230.52/41.83  | | End of split
% 230.52/41.83  | | 
% 230.52/41.83  | End of split
% 230.52/41.83  | 
% 230.52/41.83  End of proof
% 230.52/41.83  
% 230.52/41.83  Sub-proof #1160 shows that the following formulas are inconsistent:
% 230.52/41.83  ----------------------------------------------------------------
% 230.52/41.83    (1)  all_57_9 = e2
% 230.52/41.83    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.52/41.83         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.52/41.83    (3)   ~ (all_52_7 = e3)
% 230.52/41.83    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.52/41.83         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.52/41.83    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.52/41.83         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.52/41.83    (6)   ~ (e3 = e1)
% 230.52/41.83    (7)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.52/41.83         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.52/41.83    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.83           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.83    (9)  op(all_52_7, all_52_7) = e0
% 230.52/41.83    (10)  all_57_9 = e0 & op(e3, e0) = e0
% 230.52/41.83    (11)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.52/41.83          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.52/41.83    (12)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.52/41.83          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.52/41.83    (13)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.52/41.83          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.52/41.83    (14)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 230.52/41.83          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.52/41.83    (15)   ~ (e3 = e2)
% 230.52/41.83    (16)   ~ (e3 = e0)
% 230.52/41.83    (17)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.52/41.83          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.52/41.83    (18)  op(e3, e3) = e3
% 230.52/41.83    (19)  all_57_15 = e3
% 230.52/41.83    (20)  all_57_5 = e3
% 230.52/41.83    (21)   ~ (e2 = e0)
% 230.52/41.83    (22)   ~ (e1 = e0)
% 230.52/41.83    (23)  op(e0, e0) = e3
% 230.52/41.83    (24)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.52/41.83          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.52/41.83            e2)
% 230.52/41.83    (25)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.52/41.83              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.52/41.83                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.52/41.83                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.52/41.83    (26)  op(e1, e1) = e0
% 230.52/41.83    (27)  all_57_7 = e3
% 230.52/41.83    (28)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.52/41.83          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.52/41.83    (29)   ~ (e2 = e1)
% 230.52/41.83    (30)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.52/41.83          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.52/41.83    (31)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.52/41.83          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.52/41.83    (32)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.52/41.83          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.52/41.83    (33)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.52/41.83          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.52/41.83    (34)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.52/41.83          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.52/41.83    (35)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.52/41.83          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.52/41.83    (36)  all_57_3 = e2
% 230.52/41.83    (37)  op(e3, e0) = all_52_7
% 230.52/41.83    (38)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.52/41.83          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.52/41.83    (39)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.52/41.83          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.52/41.83  
% 230.52/41.83  Begin of proof
% 230.52/41.83  | 
% 230.52/41.83  | ALPHA: (10) implies:
% 230.52/41.83  |   (40)  all_57_9 = e0
% 230.52/41.83  | 
% 230.52/41.83  | COMBINE_EQS: (1), (40) imply:
% 230.52/41.83  |   (41)  e2 = e0
% 230.52/41.83  | 
% 230.52/41.83  | COMBINE_EQS: (36), (41) imply:
% 230.52/41.83  |   (42)  all_57_3 = e0
% 230.52/41.83  | 
% 230.52/41.83  | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13), (14),
% 230.52/41.83  |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 230.52/41.83  |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (37),
% 230.52/41.83  |            (38), (39), (42) are inconsistent by sub-proof #1486.
% 230.52/41.83  | 
% 230.52/41.83  End of proof
% 230.52/41.83  
% 230.52/41.83  Sub-proof #1161 shows that the following formulas are inconsistent:
% 230.52/41.83  ----------------------------------------------------------------
% 230.52/41.83    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.52/41.83         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.52/41.83    (2)   ~ (all_52_7 = e3)
% 230.52/41.83    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.52/41.83         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.52/41.83    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.52/41.83         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.52/41.83    (5)   ~ (e3 = e1)
% 230.52/41.83    (6)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.52/41.83         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.52/41.83    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.83           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.83    (8)  op(all_52_7, all_52_7) = e0
% 230.52/41.83    (9)  all_57_4 = e2
% 230.52/41.83    (10)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.52/41.83          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.52/41.83    (11)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.52/41.83          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.52/41.83    (12)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.52/41.83          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.52/41.83    (13)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 230.52/41.83          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.52/41.83    (14)   ~ (e3 = e2)
% 230.52/41.83    (15)   ~ (e3 = e0)
% 230.52/41.83    (16)  all_57_4 = e0 & op(e3, e1) = e0
% 230.52/41.83    (17)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.52/41.83          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.52/41.83    (18)  op(e3, e3) = e3
% 230.52/41.83    (19)  all_57_15 = e3
% 230.52/41.83    (20)  all_57_5 = e3
% 230.52/41.83    (21)   ~ (e2 = e0)
% 230.52/41.83    (22)   ~ (e1 = e0)
% 230.52/41.83    (23)  op(e0, e0) = e3
% 230.52/41.83    (24)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.52/41.83          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.52/41.83            e2)
% 230.52/41.83    (25)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.52/41.83              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.52/41.83                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.52/41.83                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.52/41.83    (26)  op(e1, e1) = e0
% 230.52/41.83    (27)  all_57_7 = e3
% 230.52/41.83    (28)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.52/41.83          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.52/41.83    (29)   ~ (e2 = e1)
% 230.52/41.83    (30)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.52/41.83          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.52/41.83    (31)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.52/41.83          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.52/41.83    (32)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.52/41.83          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.52/41.83    (33)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.52/41.83          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.52/41.83    (34)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.52/41.83          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.52/41.83    (35)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.52/41.83          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.52/41.83    (36)  all_57_3 = e2
% 230.52/41.83    (37)  op(e3, e0) = all_52_7
% 230.52/41.83    (38)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.52/41.83          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.52/41.83    (39)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.52/41.83          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.52/41.83  
% 230.52/41.83  Begin of proof
% 230.52/41.83  | 
% 230.52/41.83  | ALPHA: (16) implies:
% 230.52/41.83  |   (40)  all_57_4 = e0
% 230.52/41.83  | 
% 230.52/41.83  | COMBINE_EQS: (9), (40) imply:
% 230.52/41.83  |   (41)  e2 = e0
% 230.52/41.83  | 
% 230.52/41.83  | COMBINE_EQS: (36), (41) imply:
% 230.52/41.83  |   (42)  all_57_3 = e0
% 230.52/41.83  | 
% 230.52/41.83  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13),
% 230.52/41.83  |            (14), (15), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 230.52/41.83  |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (37),
% 230.52/41.83  |            (38), (39), (42) are inconsistent by sub-proof #1486.
% 230.52/41.83  | 
% 230.52/41.83  End of proof
% 230.52/41.83  
% 230.52/41.83  Sub-proof #1162 shows that the following formulas are inconsistent:
% 230.52/41.83  ----------------------------------------------------------------
% 230.52/41.83    (1)  all_57_9 = e2
% 230.52/41.83    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.52/41.83         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.52/41.83    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.52/41.83         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.52/41.83    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.52/41.83         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.52/41.83    (5)   ~ (e3 = e1)
% 230.52/41.83    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.83           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.83    (7)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.52/41.83         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.52/41.83    (8)   ~ (all_6_2 = e3)
% 230.52/41.83    (9)  op(e1, e1) = all_6_2
% 230.52/41.83    (10)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.52/41.83          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.52/41.83    (11)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 230.52/41.83          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.52/41.83    (12)   ~ (e3 = e2)
% 230.52/41.83    (13)   ~ (e3 = e0)
% 230.52/41.83    (14)  op(e3, e3) = e3
% 230.52/41.83    (15)  all_57_1 = e0
% 230.52/41.83    (16)  all_57_15 = e3
% 230.52/41.83    (17)  all_57_5 = e3
% 230.52/41.83    (18)  op(e1, e1) = e1
% 230.52/41.83    (19)   ~ (e2 = e0)
% 230.52/41.83    (20)   ~ (e1 = e0)
% 230.52/41.83    (21)  all_57_14 = e2
% 230.52/41.83    (22)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.52/41.83              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.52/41.83                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.52/41.83                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.52/41.83    (23)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.52/41.83          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.52/41.83    (24)   ~ (e2 = e1)
% 230.52/41.83    (25)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.52/41.83          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.52/41.83    (26)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.52/41.83          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.52/41.83    (27)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.52/41.83          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.52/41.83    (28)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.52/41.83          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.52/41.83    (29)  all_57_3 = e2
% 230.52/41.83    (30)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.52/41.83          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.52/41.83  
% 230.52/41.83  Begin of proof
% 230.52/41.83  | 
% 230.52/41.83  | BETA: splitting (11) gives:
% 230.52/41.83  | 
% 230.52/41.83  | Case 1:
% 230.52/41.83  | | 
% 230.52/41.83  | |   (31)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) =
% 230.52/41.83  | |           e0)
% 230.52/41.83  | | 
% 230.52/41.83  | | BETA: splitting (31) gives:
% 230.52/41.83  | | 
% 230.52/41.83  | | Case 1:
% 230.52/41.83  | | | 
% 230.52/41.83  | | |   (32)  all_57_4 = e0 & op(e3, e1) = e0
% 230.52/41.83  | | | 
% 230.52/41.83  | | | ALPHA: (32) implies:
% 230.52/41.83  | | |   (33)  all_57_4 = e0
% 230.52/41.83  | | | 
% 230.52/41.83  | | | REF_CLOSE: (1), (5), (6), (10), (14), (15), (20), (24), (33) are
% 230.52/41.83  | | |            inconsistent by sub-proof #2219.
% 230.52/41.83  | | | 
% 230.52/41.83  | | Case 2:
% 230.52/41.83  | | | 
% 230.52/41.83  | | |   (34)  all_57_5 = e0 & op(e2, e1) = e0
% 230.52/41.83  | | | 
% 230.52/41.83  | | | REF_CLOSE: (13), (17), (34) are inconsistent by sub-proof #2414.
% 230.52/41.83  | | | 
% 230.52/41.83  | | End of split
% 230.52/41.83  | | 
% 230.52/41.83  | Case 2:
% 230.52/41.83  | | 
% 230.52/41.83  | |   (35)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 230.52/41.83  | |           e0)
% 230.52/41.83  | | 
% 230.52/41.83  | | BETA: splitting (35) gives:
% 230.52/41.83  | | 
% 230.52/41.83  | | Case 1:
% 230.52/41.83  | | | 
% 230.52/41.83  | | |   (36)  all_57_8 = e0 & op(e1, e1) = e0
% 230.52/41.83  | | | 
% 230.52/41.83  | | | ALPHA: (36) implies:
% 230.52/41.83  | | |   (37)  op(e1, e1) = e0
% 230.52/41.83  | | | 
% 230.52/41.83  | | | REF_CLOSE: (6), (18), (20), (37) are inconsistent by sub-proof #2427.
% 230.52/41.83  | | | 
% 230.52/41.83  | | Case 2:
% 230.52/41.83  | | | 
% 230.52/41.83  | | |   (38)  all_57_14 = e0 & op(e0, e1) = e0
% 230.52/41.83  | | | 
% 230.52/41.83  | | | ALPHA: (38) implies:
% 230.52/41.83  | | |   (39)  all_57_14 = e0
% 230.52/41.83  | | | 
% 230.52/41.83  | | | COMBINE_EQS: (21), (39) imply:
% 230.52/41.83  | | |   (40)  e2 = e0
% 230.52/41.83  | | | 
% 230.52/41.83  | | | SIMP: (40) implies:
% 230.52/41.83  | | |   (41)  e2 = e0
% 230.52/41.83  | | | 
% 230.52/41.83  | | | COMBINE_EQS: (29), (41) imply:
% 230.52/41.83  | | |   (42)  all_57_3 = e0
% 230.52/41.83  | | | 
% 230.52/41.83  | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (12), (13), (14), (15),
% 230.52/41.83  | | |            (16), (17), (19), (20), (22), (23), (24), (25), (26), (27),
% 230.52/41.83  | | |            (28), (30), (42) are inconsistent by sub-proof #1439.
% 230.52/41.83  | | | 
% 230.52/41.83  | | End of split
% 230.52/41.83  | | 
% 230.52/41.83  | End of split
% 230.52/41.83  | 
% 230.52/41.83  End of proof
% 230.52/41.83  
% 230.52/41.83  Sub-proof #1163 shows that the following formulas are inconsistent:
% 230.52/41.83  ----------------------------------------------------------------
% 230.52/41.83    (1)  op(e3, e1) = all_52_5
% 230.52/41.83    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.83           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.83    (3)  op(all_52_7, all_52_7) = e0
% 230.52/41.83    (4)   ~ (all_52_5 = all_52_7)
% 230.52/41.83    (5)   ~ (e3 = e0)
% 230.52/41.83    (6)  all_57_4 = e0 & op(e3, e1) = e0
% 230.52/41.83    (7)  op(e3, e0) = e2
% 230.52/41.83    (8)  op(e2, e2) = e2
% 230.52/41.83    (9)  op(e0, e0) = e3
% 230.52/41.83    (10)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.52/41.83              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.52/41.83                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.52/41.83                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.52/41.83    (11)  op(e3, e0) = all_52_7
% 230.52/41.83  
% 230.52/41.83  Begin of proof
% 230.52/41.83  | 
% 230.52/41.83  | BETA: splitting (10) gives:
% 230.52/41.83  | 
% 230.52/41.83  | Case 1:
% 230.52/41.83  | | 
% 230.52/41.83  | |   (12)  all_57_15 = e0 & op(e0, e0) = e0
% 230.52/41.83  | | 
% 230.52/41.83  | | ALPHA: (12) implies:
% 230.52/41.83  | |   (13)  op(e0, e0) = e0
% 230.52/41.83  | | 
% 230.52/41.83  | | REF_CLOSE: (2), (5), (9), (13) are inconsistent by sub-proof #2304.
% 230.52/41.83  | | 
% 230.52/41.83  | Case 2:
% 230.52/41.83  | | 
% 230.52/41.83  | | 
% 230.52/41.83  | | ALPHA: (6) implies:
% 230.52/41.83  | |   (14)  op(e3, e1) = e0
% 230.52/41.83  | | 
% 230.52/41.83  | | GROUND_INST: instantiating (2) with all_52_7, e2, e0, e3, simplifying with
% 230.52/41.83  | |              (7), (11) gives:
% 230.52/41.83  | |   (15)  all_52_7 = e2
% 230.52/41.83  | | 
% 230.52/41.83  | | GROUND_INST: instantiating (2) with all_52_5, e0, e1, e3, simplifying with
% 230.52/41.83  | |              (1), (14) gives:
% 230.52/41.83  | |   (16)  all_52_5 = e0
% 230.52/41.83  | | 
% 230.52/41.83  | | REDUCE: (4), (15), (16) imply:
% 230.52/41.83  | |   (17)   ~ (e2 = e0)
% 230.52/41.83  | | 
% 230.52/41.83  | | SIMP: (17) implies:
% 230.52/41.83  | |   (18)   ~ (e2 = e0)
% 230.52/41.83  | | 
% 230.52/41.83  | | REDUCE: (3), (15) imply:
% 230.52/41.83  | |   (19)  op(e2, e2) = e0
% 230.52/41.83  | | 
% 230.52/41.83  | | REF_CLOSE: (2), (8), (18), (19) are inconsistent by sub-proof #2472.
% 230.52/41.83  | | 
% 230.52/41.83  | End of split
% 230.52/41.83  | 
% 230.52/41.83  End of proof
% 230.52/41.83  
% 230.52/41.83  Sub-proof #1164 shows that the following formulas are inconsistent:
% 230.52/41.83  ----------------------------------------------------------------
% 230.52/41.83    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.83           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.83    (2)  all_57_1 = e1
% 230.52/41.83    (3)   ~ (e2 = e0)
% 230.52/41.83    (4)  op(e2, e2) = e2
% 230.52/41.83    (5)   ~ (e1 = e0)
% 230.52/41.83    (6)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0)
% 230.52/41.83  
% 230.52/41.83  Begin of proof
% 230.52/41.83  | 
% 230.52/41.83  | BETA: splitting (6) gives:
% 230.52/41.83  | 
% 230.52/41.83  | Case 1:
% 230.52/41.83  | | 
% 230.52/41.83  | |   (7)  all_57_1 = e0 & op(e3, e2) = e0
% 230.52/41.83  | | 
% 230.52/41.83  | | REF_CLOSE: (2), (5), (7) are inconsistent by sub-proof #2493.
% 230.52/41.83  | | 
% 230.52/41.83  | Case 2:
% 230.52/41.83  | | 
% 230.52/41.83  | |   (8)  all_57_3 = e0 & op(e2, e2) = e0
% 230.52/41.83  | | 
% 230.52/41.83  | | ALPHA: (8) implies:
% 230.52/41.83  | |   (9)  op(e2, e2) = e0
% 230.52/41.83  | | 
% 230.52/41.83  | | REF_CLOSE: (1), (3), (4), (9) are inconsistent by sub-proof #2472.
% 230.52/41.83  | | 
% 230.52/41.83  | End of split
% 230.52/41.83  | 
% 230.52/41.83  End of proof
% 230.52/41.83  
% 230.52/41.83  Sub-proof #1165 shows that the following formulas are inconsistent:
% 230.52/41.83  ----------------------------------------------------------------
% 230.52/41.83    (1)   ~ (e3 = e0)
% 230.52/41.83    (2)  all_57_6 = e2
% 230.52/41.83    (3)   ~ (e2 = e0)
% 230.52/41.83    (4)  all_57_7 = e3
% 230.52/41.83    (5)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0)
% 230.52/41.83  
% 230.52/41.83  Begin of proof
% 230.52/41.83  | 
% 230.52/41.83  | BETA: splitting (5) gives:
% 230.52/41.83  | 
% 230.52/41.83  | Case 1:
% 230.52/41.83  | | 
% 230.52/41.83  | |   (6)  all_57_6 = e0 & op(e1, e3) = e0
% 230.52/41.83  | | 
% 230.52/41.83  | | REF_CLOSE: (2), (3), (6) are inconsistent by sub-proof #2386.
% 230.52/41.83  | | 
% 230.52/41.83  | Case 2:
% 230.52/41.83  | | 
% 230.52/41.83  | |   (7)  all_57_7 = e0 & op(e1, e2) = e0
% 230.52/41.83  | | 
% 230.52/41.83  | | ALPHA: (7) implies:
% 230.52/41.83  | |   (8)  all_57_7 = e0
% 230.52/41.83  | | 
% 230.52/41.83  | | REF_CLOSE: (1), (4), (8) are inconsistent by sub-proof #2269.
% 230.52/41.83  | | 
% 230.52/41.83  | End of split
% 230.52/41.83  | 
% 230.52/41.83  End of proof
% 230.52/41.83  
% 230.52/41.83  Sub-proof #1166 shows that the following formulas are inconsistent:
% 230.52/41.83  ----------------------------------------------------------------
% 230.52/41.83    (1)  all_57_3 = e3
% 230.52/41.83    (2)  all_57_3 = e2
% 230.52/41.83    (3)   ~ (e3 = e2)
% 230.52/41.83  
% 230.52/41.83  Begin of proof
% 230.52/41.83  | 
% 230.52/41.83  | COMBINE_EQS: (1), (2) imply:
% 230.52/41.83  |   (4)  e3 = e2
% 230.52/41.83  | 
% 230.52/41.83  | SIMP: (4) implies:
% 230.52/41.83  |   (5)  e3 = e2
% 230.52/41.84  | 
% 230.52/41.84  | REDUCE: (3), (5) imply:
% 230.52/41.84  |   (6)  $false
% 230.52/41.84  | 
% 230.52/41.84  | CLOSE: (6) is inconsistent.
% 230.52/41.84  | 
% 230.52/41.84  End of proof
% 230.52/41.84  
% 230.52/41.84  Sub-proof #1167 shows that the following formulas are inconsistent:
% 230.52/41.84  ----------------------------------------------------------------
% 230.52/41.84    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.52/41.84         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.52/41.84    (2)   ~ (e3 = e1)
% 230.52/41.84    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.84           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.84    (4)   ~ (e3 = e2)
% 230.52/41.84    (5)   ~ (e3 = e0)
% 230.52/41.84    (6)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.52/41.84         (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.52/41.84    (7)   ~ (e2 = e0)
% 230.52/41.84    (8)  op(e2, e2) = e2
% 230.52/41.84    (9)   ~ (e1 = e0)
% 230.52/41.84    (10)  all_57_7 = e3
% 230.52/41.84    (11)  all_57_1 = e3
% 230.52/41.84    (12)   ~ (e2 = e1)
% 230.52/41.84    (13)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.52/41.84          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.52/41.84  
% 230.52/41.84  Begin of proof
% 230.52/41.84  | 
% 230.52/41.84  | BETA: splitting (13) gives:
% 230.52/41.84  | 
% 230.52/41.84  | Case 1:
% 230.52/41.84  | | 
% 230.52/41.84  | |   (14)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) =
% 230.52/41.84  | |           e1)
% 230.52/41.84  | | 
% 230.52/41.84  | | REF_CLOSE: (2), (3), (8), (11), (12), (14) are inconsistent by sub-proof
% 230.52/41.84  | |            #1168.
% 230.52/41.84  | | 
% 230.52/41.84  | Case 2:
% 230.52/41.84  | | 
% 230.52/41.84  | |   (15)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 230.52/41.84  | |           e1)
% 230.52/41.84  | | 
% 230.52/41.84  | | BETA: splitting (15) gives:
% 230.52/41.84  | | 
% 230.52/41.84  | | Case 1:
% 230.52/41.84  | | | 
% 230.52/41.84  | | |   (16)  all_57_7 = e1 & op(e1, e2) = e1
% 230.52/41.84  | | | 
% 230.52/41.84  | | | REF_CLOSE: (2), (10), (16) are inconsistent by sub-proof #2104.
% 230.52/41.84  | | | 
% 230.52/41.84  | | Case 2:
% 230.52/41.84  | | | 
% 230.52/41.84  | | |   (17)  all_57_13 = e1 & op(e0, e2) = e1
% 230.52/41.84  | | | 
% 230.52/41.84  | | | ALPHA: (17) implies:
% 230.52/41.84  | | |   (18)  all_57_13 = e1
% 230.52/41.84  | | | 
% 230.52/41.84  | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (9), (10), (11), (12), (13), (18)
% 230.52/41.84  | | |            are inconsistent by sub-proof #1214.
% 230.52/41.84  | | | 
% 230.52/41.84  | | End of split
% 230.52/41.84  | | 
% 230.52/41.84  | End of split
% 230.52/41.84  | 
% 230.52/41.84  End of proof
% 230.52/41.84  
% 230.52/41.84  Sub-proof #1168 shows that the following formulas are inconsistent:
% 230.52/41.84  ----------------------------------------------------------------
% 230.52/41.84    (1)   ~ (e3 = e1)
% 230.52/41.84    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.84           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.84    (3)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1)
% 230.52/41.84    (4)  op(e2, e2) = e2
% 230.52/41.84    (5)  all_57_1 = e3
% 230.52/41.84    (6)   ~ (e2 = e1)
% 230.52/41.84  
% 230.52/41.84  Begin of proof
% 230.52/41.84  | 
% 230.52/41.84  | BETA: splitting (3) gives:
% 230.52/41.84  | 
% 230.52/41.84  | Case 1:
% 230.52/41.84  | | 
% 230.52/41.84  | |   (7)  all_57_1 = e1 & op(e3, e2) = e1
% 230.52/41.84  | | 
% 230.52/41.84  | | REF_CLOSE: (1), (5), (7) are inconsistent by sub-proof #2453.
% 230.52/41.84  | | 
% 230.52/41.84  | Case 2:
% 230.52/41.84  | | 
% 230.52/41.84  | |   (8)  all_57_3 = e1 & op(e2, e2) = e1
% 230.52/41.84  | | 
% 230.52/41.84  | | ALPHA: (8) implies:
% 230.52/41.84  | |   (9)  op(e2, e2) = e1
% 230.52/41.84  | | 
% 230.52/41.84  | | REF_CLOSE: (2), (4), (6), (9) are inconsistent by sub-proof #2306.
% 230.52/41.84  | | 
% 230.52/41.84  | End of split
% 230.52/41.84  | 
% 230.52/41.84  End of proof
% 230.52/41.84  
% 230.52/41.84  Sub-proof #1169 shows that the following formulas are inconsistent:
% 230.52/41.84  ----------------------------------------------------------------
% 230.52/41.84    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.52/41.84         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.52/41.84    (2)   ~ (e3 = e1)
% 230.52/41.84    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.84           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.84    (4)  all_57_2 = e2
% 230.52/41.84    (5)   ~ (e3 = e2)
% 230.52/41.84    (6)   ~ (e3 = e0)
% 230.52/41.84    (7)  all_57_15 = e3
% 230.52/41.84    (8)   ~ (e2 = e0)
% 230.52/41.84    (9)  op(e2, e2) = e2
% 230.52/41.84    (10)   ~ (e1 = e0)
% 230.52/41.84    (11)  op(e0, e0) = e3
% 230.52/41.84    (12)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.52/41.84              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.52/41.84                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.52/41.84                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.52/41.84    (13)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.52/41.84          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.52/41.84    (14)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.52/41.84          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 230.52/41.84    (15)   ~ (e2 = e1)
% 230.52/41.84    (16)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.52/41.84          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.52/41.84    (17)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.52/41.84          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.52/41.84  
% 230.52/41.84  Begin of proof
% 230.52/41.84  | 
% 230.52/41.84  | BETA: splitting (13) gives:
% 230.52/41.84  | 
% 230.52/41.84  | Case 1:
% 230.52/41.84  | | 
% 230.52/41.84  | |   (18)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 230.52/41.84  | |           e3)
% 230.52/41.84  | | 
% 230.52/41.84  | | BETA: splitting (18) gives:
% 230.52/41.84  | | 
% 230.52/41.84  | | Case 1:
% 230.52/41.84  | | | 
% 230.52/41.84  | | |   (19)  all_57_2 = e3 & op(e2, e3) = e3
% 230.52/41.84  | | | 
% 230.52/41.84  | | | ALPHA: (19) implies:
% 230.52/41.84  | | |   (20)  all_57_2 = e3
% 230.52/41.84  | | | 
% 230.52/41.84  | | | REF_CLOSE: (4), (5), (20) are inconsistent by sub-proof #1800.
% 230.52/41.84  | | | 
% 230.52/41.84  | | Case 2:
% 230.52/41.84  | | | 
% 230.52/41.84  | | |   (21)  all_57_3 = e3 & op(e2, e2) = e3
% 230.52/41.84  | | | 
% 230.52/41.84  | | | ALPHA: (21) implies:
% 230.52/41.84  | | |   (22)  op(e2, e2) = e3
% 230.52/41.84  | | | 
% 230.52/41.84  | | | REF_CLOSE: (3), (5), (9), (22) are inconsistent by sub-proof #2298.
% 230.52/41.84  | | | 
% 230.52/41.84  | | End of split
% 230.52/41.84  | | 
% 230.52/41.84  | Case 2:
% 230.52/41.84  | | 
% 230.52/41.84  | |   (23)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 230.52/41.84  | |           e3)
% 230.52/41.84  | | 
% 230.52/41.84  | | BETA: splitting (23) gives:
% 230.52/41.84  | | 
% 230.52/41.84  | | Case 1:
% 230.52/41.84  | | | 
% 230.52/41.84  | | |   (24)  all_57_5 = e3 & op(e2, e1) = e3
% 230.52/41.84  | | | 
% 230.52/41.84  | | | ALPHA: (24) implies:
% 230.52/41.84  | | |   (25)  all_57_5 = e3
% 230.52/41.84  | | | 
% 230.52/41.84  | | | BETA: splitting (14) gives:
% 230.52/41.84  | | | 
% 230.52/41.84  | | | Case 1:
% 230.52/41.84  | | | | 
% 230.52/41.84  | | | |   (26)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2)
% 230.52/41.84  | | | |           = e0)
% 230.52/41.84  | | | | 
% 230.52/41.84  | | | | BETA: splitting (26) gives:
% 230.52/41.84  | | | | 
% 230.52/41.84  | | | | Case 1:
% 230.52/41.84  | | | | | 
% 230.52/41.84  | | | | |   (27)  all_57_2 = e0 & op(e2, e3) = e0
% 230.52/41.84  | | | | | 
% 230.52/41.84  | | | | | REF_CLOSE: (4), (8), (27) are inconsistent by sub-proof #1700.
% 230.52/41.84  | | | | | 
% 230.52/41.84  | | | | Case 2:
% 230.52/41.84  | | | | | 
% 230.52/41.84  | | | | |   (28)  all_57_3 = e0 & op(e2, e2) = e0
% 230.52/41.84  | | | | | 
% 230.52/41.84  | | | | | ALPHA: (28) implies:
% 230.52/41.84  | | | | |   (29)  op(e2, e2) = e0
% 230.52/41.84  | | | | | 
% 230.52/41.84  | | | | | REF_CLOSE: (3), (8), (9), (29) are inconsistent by sub-proof #2472.
% 230.52/41.84  | | | | | 
% 230.52/41.84  | | | | End of split
% 230.52/41.84  | | | | 
% 230.52/41.84  | | | Case 2:
% 230.52/41.84  | | | | 
% 230.52/41.84  | | | |   (30)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0)
% 230.52/41.84  | | | |           = e0)
% 230.52/41.84  | | | | 
% 230.52/41.84  | | | | REF_CLOSE: (1), (2), (3), (4), (6), (9), (10), (15), (25), (30) are
% 230.52/41.84  | | | |            inconsistent by sub-proof #2240.
% 230.52/41.84  | | | | 
% 230.52/41.84  | | | End of split
% 230.52/41.84  | | | 
% 230.52/41.84  | | Case 2:
% 230.52/41.84  | | | 
% 230.52/41.84  | | |   (31)  all_57_10 = e3 & op(e2, e0) = e3
% 230.52/41.84  | | | 
% 230.52/41.84  | | | ALPHA: (31) implies:
% 230.52/41.84  | | |   (32)  all_57_10 = e3
% 230.52/41.84  | | | 
% 230.52/41.84  | | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (10), (11), (12), (15), (16),
% 230.52/41.84  | | |            (17), (32) are inconsistent by sub-proof #1746.
% 230.52/41.84  | | | 
% 230.52/41.84  | | End of split
% 230.52/41.84  | | 
% 230.52/41.84  | End of split
% 230.52/41.84  | 
% 230.52/41.84  End of proof
% 230.52/41.84  
% 230.52/41.84  Sub-proof #1170 shows that the following formulas are inconsistent:
% 230.52/41.84  ----------------------------------------------------------------
% 230.52/41.84    (1)  all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 230.52/41.84    (2)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 230.52/41.84    (3)   ~ (all_53_6 = all_53_14)
% 230.52/41.84    (4)  all_57_15 = e0
% 230.52/41.84    (5)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.52/41.84         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.52/41.84    (6)  ( ~ (all_50_0 = e3) & op(all_50_1, e2) = all_50_0 & op(e2, e0) = all_50_1
% 230.52/41.84           & $i(all_50_0) & $i(all_50_1)) | ( ~ (all_50_1 = e1) & op(e2, e0) =
% 230.52/41.84           all_50_1 & $i(all_50_1))
% 230.52/41.84    (7)  op(e2, e3) = all_53_1
% 230.52/41.84    (8)   ~ (all_53_6 = e0)
% 230.52/41.84    (9)  ( ~ (all_14_0 = e1) & op(all_14_1, e2) = all_14_0 & op(e2, e0) = all_14_1
% 230.52/41.84           & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e3) & op(e2, e0) =
% 230.52/41.84           all_14_1 & $i(all_14_1))
% 230.52/41.84    (10)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.52/41.84          (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.52/41.84    (11)  op(e2, e1) = e3
% 230.52/41.84    (12)   ~ (e3 = e1)
% 230.52/41.84    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.84            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.84    (14)   ~ (all_53_2 = all_52_25)
% 230.52/41.84    (15)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 230.52/41.84    (16)  all_55_9 = all_53_6
% 230.52/41.84    (17)  ( ~ (all_34_0 = e3) & op(all_34_1, e1) = all_34_0 & op(e1, e0) =
% 230.52/41.84            all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 = e2) & op(e1,
% 230.52/41.84              e0) = all_34_1 & $i(all_34_1))
% 230.52/41.84    (18)   ~ (all_53_13 = e3)
% 230.52/41.84    (19)  op(e2, e2) = e0
% 230.52/41.84    (20)  all_57_3 = e0
% 230.52/41.84    (21)  all_55_12 = all_52_25
% 230.52/41.84    (22)   ~ (e3 = e2)
% 230.52/41.84    (23)  all_55_1 = all_53_4
% 230.52/41.84    (24)  op(e1, e0) = all_53_14
% 230.52/41.84    (25)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 230.52/41.84    (26)   ~ (all_53_2 = e0)
% 230.52/41.84    (27)   ~ (all_18_1 = e2)
% 230.52/41.84    (28)  op(e3, e3) = e0
% 230.52/41.84    (29)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.52/41.84          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.52/41.84            e1)
% 230.52/41.84    (30)  all_57_5 = e3
% 230.52/41.84    (31)  op(all_52_25, all_52_25) = e3
% 230.52/41.84    (32)   ~ (e2 = e0)
% 230.52/41.84    (33)  all_57_9 = e3
% 230.52/41.84    (34)  all_55_13 = all_52_27
% 230.52/41.84    (35)   ~ (all_53_2 = all_53_14)
% 230.52/41.84    (36)   ~ (e1 = e0)
% 230.52/41.84    (37)   ~ (all_53_1 = all_52_25)
% 230.52/41.84    (38)  op(e0, e1) = all_52_29
% 230.52/41.84    (39)   ~ (all_53_4 = e0)
% 230.52/41.84    (40)  op(e3, e0) = all_18_1
% 230.52/41.84    (41)  op(e0, e0) = e0
% 230.52/41.84    (42)   ~ (all_53_14 = e0)
% 230.52/41.84    (43)  all_55_8 = all_53_2
% 230.52/41.84    (44)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.52/41.84          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 230.52/41.84            e3)
% 230.52/41.84    (45)   ~ (all_53_4 = all_53_6)
% 230.52/41.84    (46)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.52/41.84          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.52/41.84            e2)
% 230.52/41.84    (47)   ~ (all_53_13 = e0)
% 230.52/41.84    (48)  op(all_52_29, all_52_29) = e1
% 230.52/41.84    (49)   ~ (all_52_27 = e0)
% 230.52/41.84    (50)  op(e2, e0) = all_53_13
% 230.52/41.84    (51)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.52/41.84          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.52/41.84    (52)   ~ (all_53_4 = all_52_27)
% 230.52/41.84    (53)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.52/41.84          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.52/41.84    (54)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.52/41.84          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.52/41.84    (55)   ~ (all_53_13 = all_53_14)
% 230.52/41.84    (56)   ~ (e2 = e1)
% 230.52/41.84    (57)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.52/41.84          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.52/41.84    (58)  op(e3, e0) = all_48_1
% 230.52/41.84    (59)   ~ (all_53_2 = all_53_6)
% 230.52/41.84    (60)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.52/41.84          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.52/41.84    (61)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 230.52/41.84    (62)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.52/41.84          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.52/41.84    (63)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.52/41.84          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.52/41.84    (64)  op(all_52_27, all_52_27) = e2
% 230.52/41.84    (65)   ~ (all_52_25 = e0)
% 230.52/41.84    (66)   ~ (all_53_4 = e3)
% 230.52/41.84  
% 230.52/41.84  Begin of proof
% 230.52/41.84  | 
% 230.52/41.84  | BETA: splitting (2) gives:
% 230.52/41.84  | 
% 230.52/41.84  | Case 1:
% 230.52/41.84  | | 
% 230.52/41.84  | |   (67)  all_55_1 = e3
% 230.52/41.84  | | 
% 230.52/41.84  | | REF_CLOSE: (23), (66), (67) are inconsistent by sub-proof #2295.
% 230.52/41.84  | | 
% 230.52/41.84  | Case 2:
% 230.52/41.84  | | 
% 230.52/41.84  | |   (68)  all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 230.52/41.84  | | 
% 230.52/41.84  | | BETA: splitting (53) gives:
% 230.52/41.84  | | 
% 230.52/41.84  | | Case 1:
% 230.52/41.84  | | | 
% 230.52/41.84  | | |   (69)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 230.52/41.84  | | |           e2)
% 230.52/41.84  | | | 
% 230.52/41.84  | | | BETA: splitting (69) gives:
% 230.52/41.84  | | | 
% 230.52/41.84  | | | Case 1:
% 230.52/41.84  | | | | 
% 230.52/41.84  | | | |   (70)  all_57_2 = e2 & op(e2, e3) = e2
% 230.52/41.84  | | | | 
% 230.52/41.84  | | | | ALPHA: (70) implies:
% 230.52/41.84  | | | |   (71)  all_57_2 = e2
% 230.52/41.84  | | | | 
% 230.52/41.84  | | | | BETA: splitting (5) gives:
% 230.52/41.84  | | | | 
% 230.52/41.84  | | | | Case 1:
% 230.52/41.84  | | | | | 
% 230.52/41.84  | | | | |   (72)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2,
% 230.52/41.84  | | | | |             e2) = e1)
% 230.52/41.84  | | | | | 
% 230.52/41.84  | | | | | REF_CLOSE: (13), (19), (36), (56), (71), (72) are inconsistent by
% 230.52/41.84  | | | | |            sub-proof #1540.
% 230.52/41.84  | | | | | 
% 230.52/41.84  | | | | Case 2:
% 230.52/41.84  | | | | | 
% 230.52/41.84  | | | | |   (73)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2,
% 230.52/41.84  | | | | |             e0) = e1)
% 230.52/41.84  | | | | | 
% 230.52/41.84  | | | | | BETA: splitting (73) gives:
% 230.52/41.84  | | | | | 
% 230.52/41.84  | | | | | Case 1:
% 230.52/41.84  | | | | | | 
% 230.52/41.84  | | | | | |   (74)  all_57_5 = e1 & op(e2, e1) = e1
% 230.52/41.84  | | | | | | 
% 230.52/41.84  | | | | | | REF_CLOSE: (12), (30), (74) are inconsistent by sub-proof #2376.
% 230.52/41.84  | | | | | | 
% 230.52/41.84  | | | | | Case 2:
% 230.52/41.84  | | | | | | 
% 230.52/41.84  | | | | | |   (75)  all_57_10 = e1 & op(e2, e0) = e1
% 230.52/41.84  | | | | | | 
% 230.52/41.84  | | | | | | ALPHA: (75) implies:
% 230.52/41.84  | | | | | |   (76)  all_57_10 = e1
% 230.52/41.84  | | | | | | 
% 230.52/41.84  | | | | | | BETA: splitting (57) gives:
% 230.52/41.84  | | | | | | 
% 230.52/41.84  | | | | | | Case 1:
% 230.52/41.84  | | | | | | | 
% 230.52/41.84  | | | | | | |   (77)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 &
% 230.52/41.84  | | | | | | |           op(e2, e0) = e2)
% 230.52/41.84  | | | | | | | 
% 230.52/41.84  | | | | | | | BETA: splitting (77) gives:
% 230.52/41.84  | | | | | | | 
% 230.52/41.84  | | | | | | | Case 1:
% 230.52/41.84  | | | | | | | | 
% 230.52/41.84  | | | | | | | |   (78)  all_57_9 = e2 & op(e3, e0) = e2
% 230.52/41.84  | | | | | | | | 
% 230.52/41.84  | | | | | | | | ALPHA: (78) implies:
% 230.52/41.84  | | | | | | | |   (79)  op(e3, e0) = e2
% 230.52/41.84  | | | | | | | | 
% 230.52/41.84  | | | | | | | | REF_CLOSE: (13), (27), (40), (58), (79) are inconsistent by
% 230.52/41.84  | | | | | | | |            sub-proof #1900.
% 230.52/41.84  | | | | | | | | 
% 230.52/41.84  | | | | | | | Case 2:
% 230.52/41.84  | | | | | | | | 
% 230.52/41.84  | | | | | | | |   (80)  all_57_10 = e2 & op(e2, e0) = e2
% 230.52/41.84  | | | | | | | | 
% 230.52/41.84  | | | | | | | | ALPHA: (80) implies:
% 230.52/41.84  | | | | | | | |   (81)  all_57_10 = e2
% 230.52/41.84  | | | | | | | |   (82)  op(e2, e0) = e2
% 230.52/41.84  | | | | | | | | 
% 230.52/41.84  | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (12),
% 230.52/41.84  | | | | | | | |            (13), (14), (15), (16), (18), (19), (20), (21), (23),
% 230.52/41.84  | | | | | | | |            (24), (25), (26), (28), (29), (30), (31), (33), (34),
% 230.52/41.84  | | | | | | | |            (35), (36), (37), (38), (39), (41), (42), (43), (44),
% 230.52/41.84  | | | | | | | |            (45), (46), (47), (48), (49), (50), (51), (52), (53),
% 230.52/41.84  | | | | | | | |            (54), (55), (56), (59), (60), (61), (62), (63), (64),
% 230.52/41.84  | | | | | | | |            (65), (68), (81), (82) are inconsistent by sub-proof
% 230.52/41.84  | | | | | | | |            #1174.
% 230.52/41.84  | | | | | | | | 
% 230.52/41.84  | | | | | | | End of split
% 230.52/41.84  | | | | | | | 
% 230.52/41.84  | | | | | | Case 2:
% 230.52/41.84  | | | | | | | 
% 230.52/41.84  | | | | | | |   (83)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 &
% 230.52/41.84  | | | | | | |           op(e0, e0) = e2)
% 230.52/41.84  | | | | | | | 
% 230.52/41.84  | | | | | | | REF_CLOSE: (4), (11), (13), (17), (20), (22), (30), (32), (53),
% 230.52/41.84  | | | | | | |            (56), (71), (76), (83) are inconsistent by sub-proof
% 230.52/41.84  | | | | | | |            #1172.
% 230.52/41.84  | | | | | | | 
% 230.52/41.84  | | | | | | End of split
% 230.52/41.84  | | | | | | 
% 230.52/41.84  | | | | | End of split
% 230.52/41.84  | | | | | 
% 230.52/41.84  | | | | End of split
% 230.52/41.84  | | | | 
% 230.52/41.84  | | | Case 2:
% 230.52/41.84  | | | | 
% 230.52/41.84  | | | |   (84)  all_57_3 = e2 & op(e2, e2) = e2
% 230.52/41.84  | | | | 
% 230.52/41.84  | | | | ALPHA: (84) implies:
% 230.52/41.84  | | | |   (85)  op(e2, e2) = e2
% 230.52/41.84  | | | | 
% 230.52/41.84  | | | | REF_CLOSE: (13), (19), (32), (85) are inconsistent by sub-proof #2472.
% 230.52/41.84  | | | | 
% 230.52/41.84  | | | End of split
% 230.52/41.84  | | | 
% 230.52/41.84  | | Case 2:
% 230.52/41.84  | | | 
% 230.52/41.84  | | |   (86)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 230.52/41.84  | | |           e2)
% 230.52/41.84  | | | 
% 230.52/41.84  | | | BETA: splitting (86) gives:
% 230.52/41.84  | | | 
% 230.52/41.84  | | | Case 1:
% 230.52/41.84  | | | | 
% 230.52/41.84  | | | |   (87)  all_57_5 = e2 & op(e2, e1) = e2
% 230.52/41.84  | | | | 
% 230.52/41.84  | | | | ALPHA: (87) implies:
% 230.52/41.84  | | | |   (88)  all_57_5 = e2
% 230.52/41.84  | | | | 
% 230.52/41.84  | | | | REF_CLOSE: (22), (30), (88) are inconsistent by sub-proof #2189.
% 230.52/41.84  | | | | 
% 230.52/41.84  | | | Case 2:
% 230.52/41.84  | | | | 
% 230.52/41.84  | | | |   (89)  all_57_10 = e2 & op(e2, e0) = e2
% 230.52/41.84  | | | | 
% 230.52/41.84  | | | | ALPHA: (89) implies:
% 230.52/41.84  | | | |   (90)  all_57_10 = e2
% 230.52/41.84  | | | |   (91)  op(e2, e0) = e2
% 230.52/41.84  | | | | 
% 230.52/41.84  | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 230.52/41.84  | | | |            (14), (15), (16), (18), (19), (20), (21), (23), (24), (25),
% 230.52/41.84  | | | |            (26), (28), (29), (30), (31), (33), (34), (35), (36), (37),
% 230.52/41.84  | | | |            (38), (39), (41), (42), (43), (44), (45), (46), (47), (48),
% 230.52/41.84  | | | |            (49), (50), (51), (52), (53), (54), (55), (56), (59), (60),
% 230.52/41.84  | | | |            (61), (62), (63), (64), (65), (68), (90), (91) are
% 230.52/41.84  | | | |            inconsistent by sub-proof #1174.
% 230.52/41.84  | | | | 
% 230.52/41.84  | | | End of split
% 230.52/41.84  | | | 
% 230.52/41.84  | | End of split
% 230.52/41.84  | | 
% 230.52/41.84  | End of split
% 230.52/41.84  | 
% 230.52/41.84  End of proof
% 230.52/41.84  
% 230.52/41.84  Sub-proof #1171 shows that the following formulas are inconsistent:
% 230.52/41.84  ----------------------------------------------------------------
% 230.52/41.84    (1)  all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 230.52/41.84    (2)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 230.52/41.84    (3)   ~ (all_53_6 = all_53_14)
% 230.52/41.84    (4)  all_57_15 = e0
% 230.52/41.84    (5)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.52/41.84         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.52/41.84    (6)  ( ~ (all_50_0 = e3) & op(all_50_1, e2) = all_50_0 & op(e2, e0) = all_50_1
% 230.52/41.84           & $i(all_50_0) & $i(all_50_1)) | ( ~ (all_50_1 = e1) & op(e2, e0) =
% 230.52/41.84           all_50_1 & $i(all_50_1))
% 230.52/41.84    (7)  op(e2, e3) = all_53_1
% 230.52/41.84    (8)   ~ (all_53_6 = e0)
% 230.52/41.84    (9)  ( ~ (all_14_0 = e1) & op(all_14_1, e2) = all_14_0 & op(e2, e0) = all_14_1
% 230.52/41.84           & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e3) & op(e2, e0) =
% 230.52/41.84           all_14_1 & $i(all_14_1))
% 230.52/41.84    (10)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.52/41.84          (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.52/41.84    (11)  op(e2, e1) = e3
% 230.52/41.84    (12)   ~ (e3 = e1)
% 230.52/41.84    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.84            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.84    (14)   ~ (all_53_2 = all_52_25)
% 230.52/41.84    (15)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 230.52/41.84    (16)  all_55_9 = all_53_6
% 230.52/41.84    (17)  ( ~ (all_34_0 = e3) & op(all_34_1, e1) = all_34_0 & op(e1, e0) =
% 230.52/41.84            all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 = e2) & op(e1,
% 230.52/41.84              e0) = all_34_1 & $i(all_34_1))
% 230.52/41.84    (18)   ~ (all_53_13 = e3)
% 230.52/41.84    (19)  op(e2, e2) = e0
% 230.52/41.84    (20)  all_57_3 = e0
% 230.52/41.84    (21)  all_18_0 = e0
% 230.52/41.84    (22)  all_55_12 = all_52_25
% 230.52/41.84    (23)   ~ (e3 = e2)
% 230.52/41.84    (24)  all_55_1 = all_53_4
% 230.52/41.84    (25)  op(e1, e0) = all_53_14
% 230.52/41.84    (26)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 230.52/41.84    (27)   ~ (all_53_2 = e0)
% 230.52/41.84    (28)  op(e3, e3) = all_18_0
% 230.52/41.84    (29)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.52/41.84          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.52/41.84            e1)
% 230.52/41.84    (30)  all_57_5 = e3
% 230.52/41.84    (31)  op(all_52_25, all_52_25) = e3
% 230.52/41.84    (32)   ~ (e2 = e0)
% 230.52/41.84    (33)  all_57_9 = e3
% 230.52/41.84    (34)  all_55_13 = all_52_27
% 230.52/41.84    (35)   ~ (all_53_2 = all_53_14)
% 230.52/41.84    (36)   ~ (all_53_1 = all_52_25)
% 230.52/41.84    (37)  op(e0, e1) = all_52_29
% 230.52/41.84    (38)   ~ (all_53_4 = e0)
% 230.52/41.84    (39)  op(e0, e0) = e0
% 230.52/41.84    (40)   ~ (all_53_14 = e0)
% 230.52/41.84    (41)  all_55_8 = all_53_2
% 230.52/41.84    (42)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.52/41.84          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 230.52/41.84            e3)
% 230.52/41.84    (43)   ~ (all_53_4 = all_53_6)
% 230.52/41.84    (44)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.52/41.84          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.52/41.84            e2)
% 230.52/41.84    (45)   ~ (all_53_13 = e0)
% 230.52/41.84    (46)  op(all_52_29, all_52_29) = e1
% 230.52/41.84    (47)   ~ (all_52_27 = e0)
% 230.52/41.84    (48)  op(e2, e0) = all_53_13
% 230.52/41.84    (49)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.52/41.84          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.52/41.84    (50)   ~ (all_53_4 = all_52_27)
% 230.52/41.84    (51)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.52/41.84          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.52/41.84    (52)   ~ (all_18_0 = e1)
% 230.52/41.84    (53)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.52/41.84          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.52/41.84    (54)   ~ (all_53_13 = all_53_14)
% 230.52/41.84    (55)   ~ (e2 = e1)
% 230.52/41.84    (56)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.52/41.84          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.52/41.84    (57)   ~ (all_53_2 = all_53_6)
% 230.52/41.84    (58)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.52/41.84          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.52/41.84    (59)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 230.52/41.84    (60)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.52/41.84          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.52/41.84    (61)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.52/41.84          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.52/41.84    (62)  op(all_52_27, all_52_27) = e2
% 230.52/41.84    (63)   ~ (all_52_25 = e0)
% 230.52/41.84    (64)   ~ (all_53_4 = e3)
% 230.52/41.84  
% 230.52/41.84  Begin of proof
% 230.52/41.84  | 
% 230.52/41.84  | REDUCE: (21), (52) imply:
% 230.52/41.84  |   (65)   ~ (e1 = e0)
% 230.52/41.84  | 
% 230.52/41.84  | SIMP: (65) implies:
% 230.52/41.84  |   (66)   ~ (e1 = e0)
% 230.52/41.84  | 
% 230.52/41.84  | REDUCE: (21), (28) imply:
% 230.52/41.84  |   (67)  op(e3, e3) = e0
% 230.52/41.84  | 
% 230.52/41.84  | BETA: splitting (2) gives:
% 230.52/41.84  | 
% 230.52/41.84  | Case 1:
% 230.52/41.84  | | 
% 230.52/41.84  | |   (68)  all_55_1 = e3
% 230.52/41.84  | | 
% 230.52/41.84  | | REF_CLOSE: (24), (64), (68) are inconsistent by sub-proof #2295.
% 230.52/41.84  | | 
% 230.52/41.84  | Case 2:
% 230.52/41.84  | | 
% 230.52/41.84  | |   (69)  all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 230.52/41.84  | | 
% 230.52/41.84  | | BETA: splitting (51) gives:
% 230.52/41.84  | | 
% 230.52/41.84  | | Case 1:
% 230.52/41.84  | | | 
% 230.52/41.84  | | |   (70)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 230.52/41.84  | | |           e2)
% 230.52/41.84  | | | 
% 230.52/41.84  | | | BETA: splitting (70) gives:
% 230.52/41.84  | | | 
% 230.52/41.84  | | | Case 1:
% 230.52/41.84  | | | | 
% 230.52/41.84  | | | |   (71)  all_57_2 = e2 & op(e2, e3) = e2
% 230.52/41.84  | | | | 
% 230.52/41.84  | | | | ALPHA: (71) implies:
% 230.52/41.84  | | | |   (72)  all_57_2 = e2
% 230.52/41.84  | | | | 
% 230.52/41.84  | | | | BETA: splitting (5) gives:
% 230.52/41.84  | | | | 
% 230.52/41.84  | | | | Case 1:
% 230.52/41.84  | | | | | 
% 230.52/41.84  | | | | |   (73)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2,
% 230.52/41.84  | | | | |             e2) = e1)
% 230.52/41.84  | | | | | 
% 230.52/41.84  | | | | | REF_CLOSE: (13), (19), (55), (66), (72), (73) are inconsistent by
% 230.52/41.84  | | | | |            sub-proof #1540.
% 230.52/41.84  | | | | | 
% 230.52/41.84  | | | | Case 2:
% 230.52/41.84  | | | | | 
% 230.52/41.84  | | | | |   (74)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2,
% 230.52/41.84  | | | | |             e0) = e1)
% 230.52/41.84  | | | | | 
% 230.52/41.84  | | | | | BETA: splitting (74) gives:
% 230.52/41.84  | | | | | 
% 230.52/41.84  | | | | | Case 1:
% 230.52/41.84  | | | | | | 
% 230.52/41.84  | | | | | |   (75)  all_57_5 = e1 & op(e2, e1) = e1
% 230.52/41.84  | | | | | | 
% 230.52/41.84  | | | | | | REF_CLOSE: (12), (30), (75) are inconsistent by sub-proof #2376.
% 230.52/41.84  | | | | | | 
% 230.52/41.84  | | | | | Case 2:
% 230.52/41.84  | | | | | | 
% 230.52/41.84  | | | | | |   (76)  all_57_10 = e1 & op(e2, e0) = e1
% 230.52/41.84  | | | | | | 
% 230.52/41.84  | | | | | | ALPHA: (76) implies:
% 230.52/41.84  | | | | | |   (77)  all_57_10 = e1
% 230.52/41.84  | | | | | | 
% 230.52/41.84  | | | | | | BETA: splitting (56) gives:
% 230.52/41.84  | | | | | | 
% 230.52/41.84  | | | | | | Case 1:
% 230.52/41.84  | | | | | | | 
% 230.52/41.84  | | | | | | |   (78)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 &
% 230.52/41.84  | | | | | | |           op(e2, e0) = e2)
% 230.52/41.84  | | | | | | | 
% 230.52/41.84  | | | | | | | BETA: splitting (78) gives:
% 230.52/41.84  | | | | | | | 
% 230.52/41.84  | | | | | | | Case 1:
% 230.52/41.84  | | | | | | | | 
% 230.52/41.84  | | | | | | | |   (79)  all_57_9 = e2 & op(e3, e0) = e2
% 230.52/41.84  | | | | | | | | 
% 230.52/41.84  | | | | | | | | ALPHA: (79) implies:
% 230.52/41.84  | | | | | | | |   (80)  all_57_9 = e2
% 230.52/41.84  | | | | | | | | 
% 230.52/41.84  | | | | | | | | REF_CLOSE: (23), (33), (80) are inconsistent by sub-proof #1192.
% 230.52/41.84  | | | | | | | | 
% 230.52/41.84  | | | | | | | Case 2:
% 230.52/41.84  | | | | | | | | 
% 230.52/41.84  | | | | | | | |   (81)  all_57_10 = e2 & op(e2, e0) = e2
% 230.52/41.84  | | | | | | | | 
% 230.52/41.84  | | | | | | | | ALPHA: (81) implies:
% 230.52/41.85  | | | | | | | |   (82)  all_57_10 = e2
% 230.52/41.85  | | | | | | | |   (83)  op(e2, e0) = e2
% 230.52/41.85  | | | | | | | | 
% 230.52/41.85  | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (12),
% 230.52/41.85  | | | | | | | |            (13), (14), (15), (16), (18), (19), (20), (22), (24),
% 230.52/41.85  | | | | | | | |            (25), (26), (27), (29), (30), (31), (33), (34), (35),
% 230.52/41.85  | | | | | | | |            (36), (37), (38), (39), (40), (41), (42), (43), (44),
% 230.52/41.85  | | | | | | | |            (45), (46), (47), (48), (49), (50), (51), (53), (54),
% 230.52/41.85  | | | | | | | |            (55), (57), (58), (59), (60), (61), (62), (63), (66),
% 230.52/41.85  | | | | | | | |            (67), (69), (82), (83) are inconsistent by sub-proof
% 230.52/41.85  | | | | | | | |            #1174.
% 230.52/41.85  | | | | | | | | 
% 230.52/41.85  | | | | | | | End of split
% 230.52/41.85  | | | | | | | 
% 230.52/41.85  | | | | | | Case 2:
% 230.52/41.85  | | | | | | | 
% 230.52/41.85  | | | | | | |   (84)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 &
% 230.52/41.85  | | | | | | |           op(e0, e0) = e2)
% 230.52/41.85  | | | | | | | 
% 230.52/41.85  | | | | | | | REF_CLOSE: (4), (11), (13), (17), (20), (23), (30), (32), (51),
% 230.52/41.85  | | | | | | |            (55), (72), (77), (84) are inconsistent by sub-proof
% 230.52/41.85  | | | | | | |            #1172.
% 230.52/41.85  | | | | | | | 
% 230.52/41.85  | | | | | | End of split
% 230.52/41.85  | | | | | | 
% 230.52/41.85  | | | | | End of split
% 230.52/41.85  | | | | | 
% 230.52/41.85  | | | | End of split
% 230.52/41.85  | | | | 
% 230.52/41.85  | | | Case 2:
% 230.52/41.85  | | | | 
% 230.52/41.85  | | | |   (85)  all_57_3 = e2 & op(e2, e2) = e2
% 230.52/41.85  | | | | 
% 230.52/41.85  | | | | ALPHA: (85) implies:
% 230.52/41.85  | | | |   (86)  op(e2, e2) = e2
% 230.52/41.85  | | | | 
% 230.52/41.85  | | | | REF_CLOSE: (13), (19), (32), (86) are inconsistent by sub-proof #2472.
% 230.52/41.85  | | | | 
% 230.52/41.85  | | | End of split
% 230.52/41.85  | | | 
% 230.52/41.85  | | Case 2:
% 230.52/41.85  | | | 
% 230.52/41.85  | | |   (87)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 230.52/41.85  | | |           e2)
% 230.52/41.85  | | | 
% 230.52/41.85  | | | BETA: splitting (87) gives:
% 230.52/41.85  | | | 
% 230.52/41.85  | | | Case 1:
% 230.52/41.85  | | | | 
% 230.52/41.85  | | | |   (88)  all_57_5 = e2 & op(e2, e1) = e2
% 230.52/41.85  | | | | 
% 230.52/41.85  | | | | ALPHA: (88) implies:
% 230.52/41.85  | | | |   (89)  all_57_5 = e2
% 230.52/41.85  | | | | 
% 230.52/41.85  | | | | REF_CLOSE: (23), (30), (89) are inconsistent by sub-proof #2189.
% 230.52/41.85  | | | | 
% 230.52/41.85  | | | Case 2:
% 230.52/41.85  | | | | 
% 230.52/41.85  | | | |   (90)  all_57_10 = e2 & op(e2, e0) = e2
% 230.52/41.85  | | | | 
% 230.52/41.85  | | | | ALPHA: (90) implies:
% 230.52/41.85  | | | |   (91)  all_57_10 = e2
% 230.52/41.85  | | | |   (92)  op(e2, e0) = e2
% 230.52/41.85  | | | | 
% 230.52/41.85  | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 230.52/41.85  | | | |            (14), (15), (16), (18), (19), (20), (22), (24), (25), (26),
% 230.52/41.85  | | | |            (27), (29), (30), (31), (33), (34), (35), (36), (37), (38),
% 230.52/41.85  | | | |            (39), (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 230.52/41.85  | | | |            (49), (50), (51), (53), (54), (55), (57), (58), (59), (60),
% 230.52/41.85  | | | |            (61), (62), (63), (66), (67), (69), (91), (92) are
% 230.52/41.85  | | | |            inconsistent by sub-proof #1174.
% 230.52/41.85  | | | | 
% 230.52/41.85  | | | End of split
% 230.52/41.85  | | | 
% 230.52/41.85  | | End of split
% 230.52/41.85  | | 
% 230.52/41.85  | End of split
% 230.52/41.85  | 
% 230.52/41.85  End of proof
% 230.52/41.85  
% 230.52/41.85  Sub-proof #1172 shows that the following formulas are inconsistent:
% 230.52/41.85  ----------------------------------------------------------------
% 230.52/41.85    (1)  all_57_15 = e0
% 230.52/41.85    (2)  op(e2, e1) = e3
% 230.52/41.85    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.85           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.85    (4)  all_57_10 = e1
% 230.52/41.85    (5)  ( ~ (all_34_0 = e3) & op(all_34_1, e1) = all_34_0 & op(e1, e0) = all_34_1
% 230.52/41.85           & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 = e2) & op(e1, e0) =
% 230.52/41.85           all_34_1 & $i(all_34_1))
% 230.52/41.85    (6)  all_57_2 = e2
% 230.52/41.85    (7)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.52/41.85    (8)  all_57_3 = e0
% 230.52/41.85    (9)   ~ (e3 = e2)
% 230.52/41.85    (10)  all_57_5 = e3
% 230.52/41.85    (11)   ~ (e2 = e0)
% 230.52/41.85    (12)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.52/41.85          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.52/41.85    (13)   ~ (e2 = e1)
% 230.52/41.85  
% 230.52/41.85  Begin of proof
% 230.52/41.85  | 
% 230.52/41.85  | BETA: splitting (7) gives:
% 230.52/41.85  | 
% 230.52/41.85  | Case 1:
% 230.52/41.85  | | 
% 230.52/41.85  | |   (14)  all_57_11 = e2 & op(e1, e0) = e2
% 230.52/41.85  | | 
% 230.52/41.85  | | ALPHA: (14) implies:
% 230.52/41.85  | |   (15)  op(e1, e0) = e2
% 230.52/41.85  | | 
% 230.52/41.85  | | REF_CLOSE: (2), (3), (5), (15) are inconsistent by sub-proof #1173.
% 230.52/41.85  | | 
% 230.52/41.85  | Case 2:
% 230.52/41.85  | | 
% 230.52/41.85  | |   (16)  all_57_15 = e2 & op(e0, e0) = e2
% 230.52/41.85  | | 
% 230.52/41.85  | | ALPHA: (16) implies:
% 230.52/41.85  | |   (17)  all_57_15 = e2
% 230.52/41.85  | | 
% 230.52/41.85  | | COMBINE_EQS: (1), (17) imply:
% 230.52/41.85  | |   (18)  e2 = e0
% 230.52/41.85  | | 
% 230.52/41.85  | | REF_CLOSE: (4), (6), (8), (9), (10), (11), (12), (13), (18) are inconsistent
% 230.52/41.85  | |            by sub-proof #1532.
% 230.52/41.85  | | 
% 230.52/41.85  | End of split
% 230.52/41.85  | 
% 230.52/41.85  End of proof
% 230.52/41.85  
% 230.52/41.85  Sub-proof #1173 shows that the following formulas are inconsistent:
% 230.52/41.85  ----------------------------------------------------------------
% 230.52/41.85    (1)  ( ~ (all_34_0 = e3) & op(all_34_1, e1) = all_34_0 & op(e1, e0) = all_34_1
% 230.52/41.85           & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 = e2) & op(e1, e0) =
% 230.52/41.85           all_34_1 & $i(all_34_1))
% 230.52/41.85    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.85           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.85    (3)  op(e1, e0) = e2
% 230.52/41.85    (4)  op(e2, e1) = e3
% 230.52/41.85  
% 230.52/41.85  Begin of proof
% 230.52/41.85  | 
% 230.52/41.85  | BETA: splitting (1) gives:
% 230.52/41.85  | 
% 230.52/41.85  | Case 1:
% 230.52/41.85  | | 
% 230.52/41.85  | |   (5)   ~ (all_34_0 = e3) & op(all_34_1, e1) = all_34_0 & op(e1, e0) =
% 230.52/41.85  | |        all_34_1 & $i(all_34_0) & $i(all_34_1)
% 230.52/41.85  | | 
% 230.52/41.85  | | ALPHA: (5) implies:
% 230.52/41.85  | |   (6)   ~ (all_34_0 = e3)
% 230.52/41.85  | |   (7)  op(e1, e0) = all_34_1
% 230.52/41.85  | |   (8)  op(all_34_1, e1) = all_34_0
% 230.52/41.85  | | 
% 230.52/41.85  | | GROUND_INST: instantiating (2) with e2, all_34_1, e0, e1, simplifying with
% 230.52/41.85  | |              (3), (7) gives:
% 230.52/41.85  | |   (9)  all_34_1 = e2
% 230.52/41.85  | | 
% 230.52/41.85  | | REDUCE: (8), (9) imply:
% 230.52/41.85  | |   (10)  op(e2, e1) = all_34_0
% 230.52/41.85  | | 
% 230.52/41.85  | | GROUND_INST: instantiating (2) with e3, all_34_0, e1, e2, simplifying with
% 230.52/41.85  | |              (4), (10) gives:
% 230.52/41.85  | |   (11)  all_34_0 = e3
% 230.52/41.85  | | 
% 230.52/41.85  | | REDUCE: (6), (11) imply:
% 230.52/41.85  | |   (12)  $false
% 230.52/41.85  | | 
% 230.52/41.85  | | CLOSE: (12) is inconsistent.
% 230.52/41.85  | | 
% 230.52/41.85  | Case 2:
% 230.52/41.85  | | 
% 230.52/41.85  | |   (13)   ~ (all_34_1 = e2) & op(e1, e0) = all_34_1 & $i(all_34_1)
% 230.52/41.85  | | 
% 230.52/41.85  | | ALPHA: (13) implies:
% 230.52/41.85  | |   (14)   ~ (all_34_1 = e2)
% 230.52/41.85  | |   (15)  op(e1, e0) = all_34_1
% 230.52/41.85  | | 
% 230.52/41.85  | | REF_CLOSE: (2), (3), (14), (15) are inconsistent by sub-proof #1190.
% 230.52/41.85  | | 
% 230.52/41.85  | End of split
% 230.52/41.85  | 
% 230.52/41.85  End of proof
% 230.52/41.85  
% 230.52/41.85  Sub-proof #1174 shows that the following formulas are inconsistent:
% 230.52/41.85  ----------------------------------------------------------------
% 230.52/41.85    (1)  all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 230.52/41.85    (2)   ~ (all_53_6 = all_53_14)
% 230.52/41.85    (3)  all_57_15 = e0
% 230.52/41.85    (4)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.52/41.85         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.52/41.85    (5)  ( ~ (all_50_0 = e3) & op(all_50_1, e2) = all_50_0 & op(e2, e0) = all_50_1
% 230.52/41.85           & $i(all_50_0) & $i(all_50_1)) | ( ~ (all_50_1 = e1) & op(e2, e0) =
% 230.52/41.85           all_50_1 & $i(all_50_1))
% 230.52/41.85    (6)  op(e2, e3) = all_53_1
% 230.52/41.85    (7)   ~ (all_53_6 = e0)
% 230.52/41.85    (8)  ( ~ (all_14_0 = e1) & op(all_14_1, e2) = all_14_0 & op(e2, e0) = all_14_1
% 230.52/41.85           & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e3) & op(e2, e0) =
% 230.52/41.85           all_14_1 & $i(all_14_1))
% 230.52/41.85    (9)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.52/41.85         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.52/41.85    (10)   ~ (e3 = e1)
% 230.52/41.85    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.85            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.85    (12)   ~ (all_53_2 = all_52_25)
% 230.52/41.85    (13)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 230.52/41.85    (14)  all_55_9 = all_53_6
% 230.52/41.85    (15)   ~ (all_53_13 = e3)
% 230.52/41.85    (16)  op(e2, e2) = e0
% 230.52/41.85    (17)  all_57_3 = e0
% 230.52/41.85    (18)  all_55_12 = all_52_25
% 230.52/41.85    (19)  all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 230.52/41.85    (20)  all_55_1 = all_53_4
% 230.52/41.85    (21)  op(e1, e0) = all_53_14
% 230.52/41.85    (22)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 230.52/41.85    (23)   ~ (all_53_2 = e0)
% 230.52/41.85    (24)  op(e3, e3) = e0
% 230.52/41.85    (25)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.52/41.85          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.52/41.85            e1)
% 230.52/41.85    (26)  all_57_10 = e2
% 230.52/41.85    (27)  op(e2, e0) = e2
% 230.52/41.85    (28)  all_57_5 = e3
% 230.52/41.85    (29)  op(all_52_25, all_52_25) = e3
% 230.52/41.85    (30)  all_57_9 = e3
% 230.52/41.85    (31)  all_55_13 = all_52_27
% 230.52/41.85    (32)   ~ (all_53_2 = all_53_14)
% 230.52/41.85    (33)   ~ (e1 = e0)
% 230.52/41.85    (34)   ~ (all_53_1 = all_52_25)
% 230.52/41.85    (35)  op(e0, e1) = all_52_29
% 230.52/41.85    (36)   ~ (all_53_4 = e0)
% 230.52/41.85    (37)  op(e0, e0) = e0
% 230.52/41.85    (38)   ~ (all_53_14 = e0)
% 230.52/41.85    (39)  all_55_8 = all_53_2
% 230.52/41.85    (40)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.52/41.85          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 230.52/41.85            e3)
% 230.52/41.85    (41)   ~ (all_53_4 = all_53_6)
% 230.52/41.85    (42)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.52/41.85          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.52/41.85            e2)
% 230.52/41.85    (43)   ~ (all_53_13 = e0)
% 230.52/41.85    (44)  op(all_52_29, all_52_29) = e1
% 230.52/41.85    (45)   ~ (all_52_27 = e0)
% 230.52/41.85    (46)  op(e2, e0) = all_53_13
% 230.52/41.85    (47)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.52/41.85          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.52/41.85    (48)   ~ (all_53_4 = all_52_27)
% 230.52/41.85    (49)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.52/41.85          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.52/41.85    (50)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.52/41.85          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.52/41.85    (51)   ~ (all_53_13 = all_53_14)
% 230.52/41.85    (52)   ~ (e2 = e1)
% 230.52/41.85    (53)   ~ (all_53_2 = all_53_6)
% 230.52/41.85    (54)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.52/41.85          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.52/41.85    (55)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 230.52/41.85    (56)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.52/41.85          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.52/41.85    (57)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.52/41.85          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.52/41.85    (58)  op(all_52_27, all_52_27) = e2
% 230.52/41.85    (59)   ~ (all_52_25 = e0)
% 230.52/41.85  
% 230.52/41.85  Begin of proof
% 230.52/41.85  | 
% 230.52/41.85  | BETA: splitting (57) gives:
% 230.52/41.85  | 
% 230.52/41.85  | Case 1:
% 230.52/41.85  | | 
% 230.52/41.85  | |   (60)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) =
% 230.52/41.85  | |           e1)
% 230.52/41.85  | | 
% 230.52/41.85  | | BETA: splitting (60) gives:
% 230.52/41.85  | | 
% 230.52/41.85  | | Case 1:
% 230.52/41.85  | | | 
% 230.52/41.85  | | |   (61)  all_57_9 = e1 & op(e3, e0) = e1
% 230.52/41.85  | | | 
% 230.52/41.85  | | | ALPHA: (61) implies:
% 230.52/41.85  | | |   (62)  all_57_9 = e1
% 230.52/41.85  | | | 
% 230.52/41.85  | | | REF_CLOSE: (10), (30), (62) are inconsistent by sub-proof #1673.
% 230.52/41.85  | | | 
% 230.52/41.85  | | Case 2:
% 230.52/41.85  | | | 
% 230.52/41.85  | | |   (63)  all_57_10 = e1 & op(e2, e0) = e1
% 230.52/41.85  | | | 
% 230.52/41.85  | | | ALPHA: (63) implies:
% 230.52/41.85  | | |   (64)  all_57_10 = e1
% 230.52/41.85  | | | 
% 230.52/41.85  | | | REF_CLOSE: (26), (52), (64) are inconsistent by sub-proof #2144.
% 230.52/41.85  | | | 
% 230.52/41.85  | | End of split
% 230.52/41.85  | | 
% 230.52/41.85  | Case 2:
% 230.52/41.85  | | 
% 230.52/41.85  | |   (65)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.52/41.85  | |           e1)
% 230.52/41.85  | | 
% 230.52/41.85  | | BETA: splitting (65) gives:
% 230.52/41.85  | | 
% 230.52/41.85  | | Case 1:
% 230.52/41.85  | | | 
% 230.52/41.85  | | |   (66)  all_57_11 = e1 & op(e1, e0) = e1
% 230.52/41.85  | | | 
% 230.52/41.85  | | | ALPHA: (66) implies:
% 230.52/41.85  | | |   (67)  op(e1, e0) = e1
% 230.52/41.85  | | | 
% 230.52/41.85  | | | BETA: splitting (4) gives:
% 230.52/41.85  | | | 
% 230.52/41.85  | | | Case 1:
% 230.52/41.85  | | | | 
% 230.52/41.85  | | | |   (68)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2)
% 230.52/41.85  | | | |           = e1)
% 230.52/41.85  | | | | 
% 230.52/41.85  | | | | BETA: splitting (68) gives:
% 230.52/41.85  | | | | 
% 230.52/41.85  | | | | Case 1:
% 230.52/41.85  | | | | | 
% 230.52/41.85  | | | | |   (69)  all_57_2 = e1 & op(e2, e3) = e1
% 230.52/41.85  | | | | | 
% 230.52/41.85  | | | | | ALPHA: (69) implies:
% 230.52/41.85  | | | | |   (70)  all_57_2 = e1
% 230.52/41.85  | | | | |   (71)  op(e2, e3) = e1
% 230.52/41.85  | | | | | 
% 230.52/41.85  | | | | | GROUND_INST: instantiating (11) with all_53_14, e1, e0, e1,
% 230.52/41.85  | | | | |              simplifying with (21), (67) gives:
% 230.52/41.85  | | | | |   (72)  all_53_14 = e1
% 230.52/41.85  | | | | | 
% 230.52/41.85  | | | | | GROUND_INST: instantiating (11) with all_53_13, e2, e0, e2,
% 230.52/41.85  | | | | |              simplifying with (27), (46) gives:
% 230.52/41.85  | | | | |   (73)  all_53_13 = e2
% 230.52/41.85  | | | | | 
% 230.52/41.85  | | | | | GROUND_INST: instantiating (11) with all_53_1, e1, e3, e2, simplifying
% 230.52/41.85  | | | | |              with (6), (71) gives:
% 230.52/41.85  | | | | |   (74)  all_53_1 = e1
% 230.52/41.85  | | | | | 
% 230.52/41.85  | | | | | REDUCE: (34), (74) imply:
% 230.52/41.85  | | | | |   (75)   ~ (all_52_25 = e1)
% 230.52/41.85  | | | | | 
% 230.52/41.85  | | | | | SIMP: (75) implies:
% 230.52/41.85  | | | | |   (76)   ~ (all_52_25 = e1)
% 230.52/41.85  | | | | | 
% 230.52/41.85  | | | | | REDUCE: (32), (72) imply:
% 230.52/41.85  | | | | |   (77)   ~ (all_53_2 = e1)
% 230.52/41.85  | | | | | 
% 230.52/41.85  | | | | | REDUCE: (2), (72) imply:
% 230.52/41.85  | | | | |   (78)   ~ (all_53_6 = e1)
% 230.52/41.85  | | | | | 
% 230.52/41.85  | | | | | REDUCE: (15), (73) imply:
% 230.52/41.85  | | | | |   (79)   ~ (e3 = e2)
% 230.52/41.85  | | | | | 
% 230.52/41.85  | | | | | SIMP: (79) implies:
% 230.52/41.85  | | | | |   (80)   ~ (e3 = e2)
% 230.52/41.85  | | | | | 
% 230.52/41.85  | | | | | REDUCE: (43), (73) imply:
% 230.52/41.85  | | | | |   (81)   ~ (e2 = e0)
% 230.52/41.85  | | | | | 
% 230.52/41.85  | | | | | BETA: splitting (8) gives:
% 230.52/41.85  | | | | | 
% 230.52/41.85  | | | | | Case 1:
% 230.52/41.85  | | | | | | 
% 230.52/41.85  | | | | | |   (82)   ~ (all_14_0 = e1) & op(all_14_1, e2) = all_14_0 & op(e2,
% 230.52/41.85  | | | | | |           e0) = all_14_1 & $i(all_14_0) & $i(all_14_1)
% 230.52/41.85  | | | | | | 
% 230.52/41.85  | | | | | | ALPHA: (82) implies:
% 230.52/41.85  | | | | | |   (83)   ~ (all_14_0 = e1)
% 230.52/41.85  | | | | | |   (84)  op(e2, e0) = all_14_1
% 230.52/41.85  | | | | | |   (85)  op(all_14_1, e2) = all_14_0
% 230.52/41.85  | | | | | | 
% 230.52/41.85  | | | | | | BETA: splitting (5) gives:
% 230.52/41.85  | | | | | | 
% 230.52/41.85  | | | | | | Case 1:
% 230.52/41.85  | | | | | | | 
% 230.52/41.85  | | | | | | |   (86)   ~ (all_50_0 = e3) & op(all_50_1, e2) = all_50_0 & op(e2,
% 230.52/41.85  | | | | | | |           e0) = all_50_1 & $i(all_50_0) & $i(all_50_1)
% 230.52/41.85  | | | | | | | 
% 230.52/41.85  | | | | | | | ALPHA: (86) implies:
% 230.52/41.85  | | | | | | |   (87)  op(e2, e0) = all_50_1
% 230.52/41.85  | | | | | | |   (88)  op(all_50_1, e2) = all_50_0
% 230.52/41.85  | | | | | | | 
% 230.52/41.85  | | | | | | | GROUND_INST: instantiating (11) with e2, all_50_1, e0, e2,
% 230.52/41.85  | | | | | | |              simplifying with (27), (87) gives:
% 230.52/41.85  | | | | | | |   (89)  all_50_1 = e2
% 230.52/41.85  | | | | | | | 
% 230.52/41.85  | | | | | | | GROUND_INST: instantiating (11) with all_14_1, all_50_1, e0, e2,
% 230.52/41.85  | | | | | | |              simplifying with (84), (87) gives:
% 230.52/41.85  | | | | | | |   (90)  all_50_1 = all_14_1
% 230.52/41.85  | | | | | | | 
% 230.52/41.85  | | | | | | | COMBINE_EQS: (89), (90) imply:
% 230.52/41.85  | | | | | | |   (91)  all_14_1 = e2
% 230.52/41.85  | | | | | | | 
% 230.52/41.85  | | | | | | | REDUCE: (88), (89) imply:
% 230.52/41.85  | | | | | | |   (92)  op(e2, e2) = all_50_0
% 230.52/41.85  | | | | | | | 
% 230.52/41.85  | | | | | | | REDUCE: (85), (91) imply:
% 230.52/41.85  | | | | | | |   (93)  op(e2, e2) = all_14_0
% 230.52/41.85  | | | | | | | 
% 230.52/41.85  | | | | | | | GROUND_INST: instantiating (11) with e0, all_50_0, e2, e2,
% 230.52/41.85  | | | | | | |              simplifying with (16), (92) gives:
% 230.52/41.85  | | | | | | |   (94)  all_50_0 = e0
% 230.52/41.85  | | | | | | | 
% 230.52/41.85  | | | | | | | GROUND_INST: instantiating (11) with all_14_0, all_50_0, e2, e2,
% 230.52/41.85  | | | | | | |              simplifying with (92), (93) gives:
% 230.52/41.85  | | | | | | |   (95)  all_50_0 = all_14_0
% 230.52/41.85  | | | | | | | 
% 230.52/41.85  | | | | | | | COMBINE_EQS: (94), (95) imply:
% 230.52/41.85  | | | | | | |   (96)  all_14_0 = e0
% 230.52/41.85  | | | | | | | 
% 230.52/41.85  | | | | | | | SIMP: (96) implies:
% 230.52/41.85  | | | | | | |   (97)  all_14_0 = e0
% 230.52/41.85  | | | | | | | 
% 230.52/41.85  | | | | | | | REDUCE: (83), (97) imply:
% 230.52/41.85  | | | | | | |   (98)   ~ (e1 = e0)
% 230.52/41.85  | | | | | | | 
% 230.52/41.85  | | | | | | | BETA: splitting (13) gives:
% 230.52/41.85  | | | | | | | 
% 230.52/41.85  | | | | | | | Case 1:
% 230.52/41.85  | | | | | | | | 
% 230.52/41.85  | | | | | | | |   (99)  all_55_9 = e3
% 230.52/41.85  | | | | | | | | 
% 230.52/41.85  | | | | | | | | COMBINE_EQS: (14), (99) imply:
% 230.52/41.85  | | | | | | | |   (100)  all_53_6 = e3
% 230.52/41.85  | | | | | | | | 
% 230.52/41.85  | | | | | | | | SIMP: (100) implies:
% 230.52/41.85  | | | | | | | |   (101)  all_53_6 = e3
% 230.52/41.85  | | | | | | | | 
% 230.52/41.85  | | | | | | | | REDUCE: (53), (101) imply:
% 230.52/41.85  | | | | | | | |   (102)   ~ (all_53_2 = e3)
% 230.52/41.85  | | | | | | | | 
% 230.52/41.85  | | | | | | | | REDUCE: (7), (101) imply:
% 230.52/41.85  | | | | | | | |   (103)   ~ (e3 = e0)
% 230.52/41.85  | | | | | | | | 
% 230.52/41.85  | | | | | | | | REF_CLOSE: (3), (4), (9), (10), (11), (12), (16), (17), (18),
% 230.52/41.85  | | | | | | | |            (22), (23), (24), (25), (26), (28), (29), (33), (35),
% 230.52/41.85  | | | | | | | |            (37), (39), (40), (42), (44), (47), (49), (50), (52),
% 230.52/41.85  | | | | | | | |            (54), (55), (56), (59), (70), (76), (77), (80), (81),
% 230.52/41.85  | | | | | | | |            (102), (103) are inconsistent by sub-proof #1178.
% 230.52/41.85  | | | | | | | | 
% 230.52/41.85  | | | | | | | Case 2:
% 230.52/41.85  | | | | | | | | 
% 230.52/41.85  | | | | | | | |   (104)  all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 230.52/41.85  | | | | | | | | 
% 230.52/41.85  | | | | | | | | REF_CLOSE: (1), (7), (11), (14), (16), (19), (20), (24), (31),
% 230.52/41.85  | | | | | | | |            (36), (41), (45), (48), (58), (78), (104) are
% 230.52/41.85  | | | | | | | |            inconsistent by sub-proof #1176.
% 230.52/41.85  | | | | | | | | 
% 230.52/41.85  | | | | | | | End of split
% 230.52/41.85  | | | | | | | 
% 230.52/41.85  | | | | | | Case 2:
% 230.52/41.85  | | | | | | | 
% 230.52/41.85  | | | | | | |   (105)   ~ (all_50_1 = e1) & op(e2, e0) = all_50_1 & $i(all_50_1)
% 230.52/41.85  | | | | | | | 
% 230.52/41.85  | | | | | | | ALPHA: (105) implies:
% 230.52/41.85  | | | | | | |   (106)   ~ (all_50_1 = e1)
% 230.52/41.85  | | | | | | |   (107)  op(e2, e0) = all_50_1
% 230.52/41.85  | | | | | | | 
% 230.52/41.85  | | | | | | | GROUND_INST: instantiating (11) with e2, all_50_1, e0, e2,
% 230.52/41.85  | | | | | | |              simplifying with (27), (107) gives:
% 230.52/41.85  | | | | | | |   (108)  all_50_1 = e2
% 230.52/41.85  | | | | | | | 
% 230.52/41.85  | | | | | | | GROUND_INST: instantiating (11) with all_14_1, all_50_1, e0, e2,
% 230.52/41.85  | | | | | | |              simplifying with (84), (107) gives:
% 230.52/41.85  | | | | | | |   (109)  all_50_1 = all_14_1
% 230.52/41.85  | | | | | | | 
% 230.52/41.85  | | | | | | | COMBINE_EQS: (108), (109) imply:
% 230.52/41.85  | | | | | | |   (110)  all_14_1 = e2
% 230.52/41.85  | | | | | | | 
% 230.52/41.85  | | | | | | | REDUCE: (85), (110) imply:
% 230.52/41.85  | | | | | | |   (111)  op(e2, e2) = all_14_0
% 230.52/41.85  | | | | | | | 
% 230.52/41.85  | | | | | | | GROUND_INST: instantiating (11) with e0, all_14_0, e2, e2,
% 230.52/41.85  | | | | | | |              simplifying with (16), (111) gives:
% 230.52/41.85  | | | | | | |   (112)  all_14_0 = e0
% 230.52/41.85  | | | | | | | 
% 230.52/41.85  | | | | | | | REDUCE: (83), (112) imply:
% 230.52/41.85  | | | | | | |   (113)   ~ (e1 = e0)
% 230.52/41.85  | | | | | | | 
% 230.52/41.85  | | | | | | | REF_CLOSE: (1), (3), (4), (7), (9), (11), (12), (13), (14), (16),
% 230.52/41.85  | | | | | | |            (17), (18), (19), (20), (22), (23), (24), (25), (26),
% 230.52/41.85  | | | | | | |            (28), (29), (31), (33), (35), (36), (37), (39), (40),
% 230.52/41.85  | | | | | | |            (41), (42), (44), (45), (47), (48), (49), (50), (52),
% 230.52/41.85  | | | | | | |            (53), (54), (55), (56), (58), (59), (70), (76), (77),
% 230.52/41.85  | | | | | | |            (78), (80), (81) are inconsistent by sub-proof #1175.
% 230.52/41.85  | | | | | | | 
% 230.52/41.85  | | | | | | End of split
% 230.52/41.85  | | | | | | 
% 230.52/41.85  | | | | | Case 2:
% 230.52/41.85  | | | | | | 
% 230.52/41.85  | | | | | |   (114)   ~ (all_14_1 = e3) & op(e2, e0) = all_14_1 & $i(all_14_1)
% 230.52/41.85  | | | | | | 
% 230.52/41.85  | | | | | | ALPHA: (114) implies:
% 230.52/41.85  | | | | | |   (115)   ~ (all_14_1 = e3)
% 230.52/41.85  | | | | | |   (116)  op(e2, e0) = all_14_1
% 230.52/41.85  | | | | | | 
% 230.52/41.85  | | | | | | BETA: splitting (5) gives:
% 230.52/41.85  | | | | | | 
% 230.52/41.85  | | | | | | Case 1:
% 230.52/41.85  | | | | | | | 
% 230.52/41.85  | | | | | | |   (117)   ~ (all_50_0 = e3) & op(all_50_1, e2) = all_50_0 & op(e2,
% 230.52/41.85  | | | | | | |            e0) = all_50_1 & $i(all_50_0) & $i(all_50_1)
% 230.52/41.85  | | | | | | | 
% 230.52/41.85  | | | | | | | ALPHA: (117) implies:
% 230.52/41.85  | | | | | | |   (118)  op(e2, e0) = all_50_1
% 230.52/41.85  | | | | | | |   (119)  op(all_50_1, e2) = all_50_0
% 230.52/41.85  | | | | | | | 
% 230.52/41.85  | | | | | | | GROUND_INST: instantiating (11) with e2, all_50_1, e0, e2,
% 230.52/41.85  | | | | | | |              simplifying with (27), (118) gives:
% 230.52/41.85  | | | | | | |   (120)  all_50_1 = e2
% 230.52/41.85  | | | | | | | 
% 230.52/41.85  | | | | | | | GROUND_INST: instantiating (11) with all_14_1, all_50_1, e0, e2,
% 230.52/41.85  | | | | | | |              simplifying with (116), (118) gives:
% 230.52/41.85  | | | | | | |   (121)  all_50_1 = all_14_1
% 230.52/41.85  | | | | | | | 
% 230.52/41.85  | | | | | | | COMBINE_EQS: (120), (121) imply:
% 230.52/41.85  | | | | | | |   (122)  all_14_1 = e2
% 230.52/41.85  | | | | | | | 
% 230.52/41.85  | | | | | | | REDUCE: (119), (120) imply:
% 230.52/41.85  | | | | | | |   (123)  op(e2, e2) = all_50_0
% 230.52/41.85  | | | | | | | 
% 230.52/41.85  | | | | | | | GROUND_INST: instantiating (11) with e0, all_50_0, e2, e2,
% 230.52/41.85  | | | | | | |              simplifying with (16), (123) gives:
% 230.52/41.85  | | | | | | |   (124)  all_50_0 = e0
% 230.52/41.85  | | | | | | | 
% 230.52/41.85  | | | | | | | REF_CLOSE: (1), (3), (4), (7), (9), (11), (12), (13), (14), (16),
% 230.52/41.85  | | | | | | |            (17), (18), (19), (20), (22), (23), (24), (25), (26),
% 230.52/41.85  | | | | | | |            (28), (29), (31), (33), (35), (36), (37), (39), (40),
% 230.52/41.85  | | | | | | |            (41), (42), (44), (45), (47), (48), (49), (50), (52),
% 230.52/41.85  | | | | | | |            (53), (54), (55), (56), (58), (59), (70), (76), (77),
% 230.52/41.85  | | | | | | |            (78), (80), (81) are inconsistent by sub-proof #1175.
% 230.52/41.85  | | | | | | | 
% 230.52/41.85  | | | | | | Case 2:
% 230.52/41.85  | | | | | | | 
% 230.52/41.85  | | | | | | |   (125)   ~ (all_50_1 = e1) & op(e2, e0) = all_50_1 & $i(all_50_1)
% 230.52/41.85  | | | | | | | 
% 230.52/41.85  | | | | | | | ALPHA: (125) implies:
% 230.52/41.85  | | | | | | |   (126)   ~ (all_50_1 = e1)
% 230.52/41.85  | | | | | | |   (127)  op(e2, e0) = all_50_1
% 230.52/41.85  | | | | | | | 
% 230.52/41.85  | | | | | | | GROUND_INST: instantiating (11) with e2, all_50_1, e0, e2,
% 230.52/41.85  | | | | | | |              simplifying with (27), (127) gives:
% 230.52/41.85  | | | | | | |   (128)  all_50_1 = e2
% 230.52/41.85  | | | | | | | 
% 230.52/41.85  | | | | | | | GROUND_INST: instantiating (11) with all_14_1, all_50_1, e0, e2,
% 230.52/41.85  | | | | | | |              simplifying with (116), (127) gives:
% 230.52/41.85  | | | | | | |   (129)  all_50_1 = all_14_1
% 230.52/41.85  | | | | | | | 
% 230.52/41.85  | | | | | | | COMBINE_EQS: (128), (129) imply:
% 230.52/41.85  | | | | | | |   (130)  all_14_1 = e2
% 230.52/41.85  | | | | | | | 
% 230.52/41.85  | | | | | | | REF_CLOSE: (1), (3), (4), (7), (9), (11), (12), (13), (14), (16),
% 230.52/41.85  | | | | | | |            (17), (18), (19), (20), (22), (23), (24), (25), (26),
% 230.52/41.85  | | | | | | |            (28), (29), (31), (33), (35), (36), (37), (39), (40),
% 230.52/41.85  | | | | | | |            (41), (42), (44), (45), (47), (48), (49), (50), (52),
% 230.52/41.85  | | | | | | |            (53), (54), (55), (56), (58), (59), (70), (76), (77),
% 230.52/41.85  | | | | | | |            (78), (80), (81) are inconsistent by sub-proof #1175.
% 230.52/41.85  | | | | | | | 
% 230.52/41.85  | | | | | | End of split
% 230.52/41.85  | | | | | | 
% 230.52/41.85  | | | | | End of split
% 230.52/41.85  | | | | | 
% 230.52/41.85  | | | | Case 2:
% 230.52/41.85  | | | | | 
% 230.52/41.85  | | | | |   (131)  all_57_3 = e1 & op(e2, e2) = e1
% 230.52/41.85  | | | | | 
% 230.52/41.85  | | | | | ALPHA: (131) implies:
% 230.52/41.85  | | | | |   (132)  op(e2, e2) = e1
% 230.52/41.85  | | | | | 
% 230.52/41.85  | | | | | REF_CLOSE: (11), (16), (33), (132) are inconsistent by sub-proof
% 230.52/41.85  | | | | |            #2352.
% 230.52/41.85  | | | | | 
% 230.52/41.85  | | | | End of split
% 230.52/41.85  | | | | 
% 230.52/41.85  | | | Case 2:
% 230.52/41.85  | | | | 
% 230.52/41.85  | | | |   (133)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2,
% 230.52/41.85  | | | |              e0) = e1)
% 230.52/41.85  | | | | 
% 230.52/41.85  | | | | REF_CLOSE: (10), (26), (28), (52), (133) are inconsistent by sub-proof
% 230.52/41.85  | | | |            #1466.
% 230.52/41.85  | | | | 
% 230.52/41.85  | | | End of split
% 230.52/41.85  | | | 
% 230.52/41.85  | | Case 2:
% 230.52/41.85  | | | 
% 230.52/41.85  | | |   (134)  all_57_15 = e1 & op(e0, e0) = e1
% 230.52/41.85  | | | 
% 230.52/41.85  | | | ALPHA: (134) implies:
% 230.52/41.85  | | |   (135)  op(e0, e0) = e1
% 230.52/41.85  | | | 
% 230.52/41.85  | | | REF_CLOSE: (11), (33), (37), (135) are inconsistent by sub-proof #2290.
% 230.52/41.85  | | | 
% 230.52/41.85  | | End of split
% 230.52/41.85  | | 
% 230.52/41.85  | End of split
% 230.52/41.85  | 
% 230.52/41.85  End of proof
% 230.52/41.85  
% 230.52/41.85  Sub-proof #1175 shows that the following formulas are inconsistent:
% 230.52/41.85  ----------------------------------------------------------------
% 230.52/41.85    (1)  all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 230.52/41.85    (2)   ~ (all_53_2 = e1)
% 230.52/41.85    (3)   ~ (all_52_25 = e1)
% 230.52/41.85    (4)  all_57_15 = e0
% 230.52/41.85    (5)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.52/41.85         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.52/41.85    (6)   ~ (all_53_6 = e0)
% 230.52/41.85    (7)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.52/41.85         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.52/41.86    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.86           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.86    (9)   ~ (all_53_2 = all_52_25)
% 230.52/41.86    (10)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 230.52/41.86    (11)  all_55_9 = all_53_6
% 230.52/41.86    (12)  op(e2, e2) = e0
% 230.52/41.86    (13)  all_57_3 = e0
% 230.52/41.86    (14)  all_55_12 = all_52_25
% 230.52/41.86    (15)  all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 230.52/41.86    (16)   ~ (e3 = e2)
% 230.52/41.86    (17)  all_55_1 = all_53_4
% 230.52/41.86    (18)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 230.52/41.86    (19)   ~ (all_53_2 = e0)
% 230.52/41.86    (20)  op(e3, e3) = e0
% 230.52/41.86    (21)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.52/41.86          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.52/41.86            e1)
% 230.52/41.86    (22)  all_57_10 = e2
% 230.52/41.86    (23)  all_57_5 = e3
% 230.52/41.86    (24)  op(all_52_25, all_52_25) = e3
% 230.52/41.86    (25)   ~ (e2 = e0)
% 230.52/41.86    (26)   ~ (all_53_6 = e1)
% 230.52/41.86    (27)  all_55_13 = all_52_27
% 230.52/41.86    (28)   ~ (e1 = e0)
% 230.52/41.86    (29)  op(e0, e1) = all_52_29
% 230.52/41.86    (30)   ~ (all_53_4 = e0)
% 230.52/41.86    (31)  op(e0, e0) = e0
% 230.52/41.86    (32)  all_55_8 = all_53_2
% 230.52/41.86    (33)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.52/41.86          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 230.52/41.86            e3)
% 230.52/41.86    (34)   ~ (all_53_4 = all_53_6)
% 230.52/41.86    (35)  all_57_2 = e1
% 230.52/41.86    (36)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.52/41.86          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.52/41.86            e2)
% 230.52/41.86    (37)  op(all_52_29, all_52_29) = e1
% 230.52/41.86    (38)   ~ (all_52_27 = e0)
% 230.52/41.86    (39)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.52/41.86          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.52/41.86    (40)   ~ (all_53_4 = all_52_27)
% 230.52/41.86    (41)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.52/41.86          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.52/41.86    (42)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.52/41.86          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.52/41.86    (43)   ~ (e2 = e1)
% 230.52/41.86    (44)   ~ (all_53_2 = all_53_6)
% 230.52/41.86    (45)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.52/41.86          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.52/41.86    (46)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 230.52/41.86    (47)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.52/41.86          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.52/41.86    (48)  op(all_52_27, all_52_27) = e2
% 230.52/41.86    (49)   ~ (all_52_25 = e0)
% 230.52/41.86  
% 230.52/41.86  Begin of proof
% 230.52/41.86  | 
% 230.52/41.86  | BETA: splitting (10) gives:
% 230.52/41.86  | 
% 230.52/41.86  | Case 1:
% 230.52/41.86  | | 
% 230.52/41.86  | |   (50)  all_55_9 = e3
% 230.52/41.86  | | 
% 230.52/41.86  | | COMBINE_EQS: (11), (50) imply:
% 230.52/41.86  | |   (51)  all_53_6 = e3
% 230.52/41.86  | | 
% 230.52/41.86  | | SIMP: (51) implies:
% 230.52/41.86  | |   (52)  all_53_6 = e3
% 230.52/41.86  | | 
% 230.52/41.86  | | REDUCE: (44), (52) imply:
% 230.52/41.86  | |   (53)   ~ (all_53_2 = e3)
% 230.52/41.86  | | 
% 230.52/41.86  | | REDUCE: (26), (52) imply:
% 230.52/41.86  | |   (54)   ~ (e3 = e1)
% 230.52/41.86  | | 
% 230.52/41.86  | | REDUCE: (6), (52) imply:
% 230.52/41.86  | |   (55)   ~ (e3 = e0)
% 230.52/41.86  | | 
% 230.52/41.86  | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (12), (13), (14), (16), (18),
% 230.52/41.86  | |            (19), (20), (21), (22), (23), (24), (25), (28), (29), (31), (32),
% 230.52/41.86  | |            (33), (35), (36), (37), (39), (41), (42), (43), (45), (46), (47),
% 230.52/41.86  | |            (49), (53), (54), (55) are inconsistent by sub-proof #1178.
% 230.52/41.86  | | 
% 230.52/41.86  | Case 2:
% 230.52/41.86  | | 
% 230.52/41.86  | |   (56)  all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 230.52/41.86  | | 
% 230.52/41.86  | | REF_CLOSE: (1), (6), (8), (11), (12), (15), (17), (20), (26), (27), (30),
% 230.52/41.86  | |            (34), (38), (40), (48), (56) are inconsistent by sub-proof #1176.
% 230.52/41.86  | | 
% 230.52/41.86  | End of split
% 230.52/41.86  | 
% 230.52/41.86  End of proof
% 230.52/41.86  
% 230.52/41.86  Sub-proof #1176 shows that the following formulas are inconsistent:
% 230.52/41.86  ----------------------------------------------------------------
% 230.52/41.86    (1)  all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 230.52/41.86    (2)   ~ (all_53_6 = e0)
% 230.52/41.86    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.86           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.86    (4)  all_55_9 = all_53_6
% 230.52/41.86    (5)  op(e2, e2) = e0
% 230.52/41.86    (6)  all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 230.52/41.86    (7)  all_55_1 = all_53_4
% 230.52/41.86    (8)  all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 230.52/41.86    (9)  op(e3, e3) = e0
% 230.52/41.86    (10)   ~ (all_53_6 = e1)
% 230.52/41.86    (11)  all_55_13 = all_52_27
% 230.52/41.86    (12)   ~ (all_53_4 = e0)
% 230.52/41.86    (13)   ~ (all_53_4 = all_53_6)
% 230.52/41.86    (14)   ~ (all_52_27 = e0)
% 230.52/41.86    (15)   ~ (all_53_4 = all_52_27)
% 230.52/41.86    (16)  op(all_52_27, all_52_27) = e2
% 230.52/41.86  
% 230.52/41.86  Begin of proof
% 230.52/41.86  | 
% 230.52/41.86  | BETA: splitting (8) gives:
% 230.52/41.86  | 
% 230.52/41.86  | Case 1:
% 230.52/41.86  | | 
% 230.52/41.86  | |   (17)  all_55_9 = e2
% 230.52/41.86  | | 
% 230.52/41.86  | | COMBINE_EQS: (4), (17) imply:
% 230.52/41.86  | |   (18)  all_53_6 = e2
% 230.52/41.86  | | 
% 230.52/41.86  | | SIMP: (18) implies:
% 230.52/41.86  | |   (19)  all_53_6 = e2
% 230.52/41.86  | | 
% 230.52/41.86  | | REDUCE: (13), (19) imply:
% 230.52/41.86  | |   (20)   ~ (all_53_4 = e2)
% 230.52/41.86  | | 
% 230.52/41.86  | | REDUCE: (2), (19) imply:
% 230.52/41.86  | |   (21)   ~ (e2 = e0)
% 230.52/41.86  | | 
% 230.52/41.86  | | BETA: splitting (6) gives:
% 230.52/41.86  | | 
% 230.52/41.86  | | Case 1:
% 230.52/41.86  | | | 
% 230.52/41.86  | | |   (22)  all_55_1 = e2
% 230.52/41.86  | | | 
% 230.52/41.86  | | | REF_CLOSE: (7), (20), (22) are inconsistent by sub-proof #2284.
% 230.52/41.86  | | | 
% 230.52/41.86  | | Case 2:
% 230.52/41.86  | | | 
% 230.52/41.86  | | |   (23)  all_55_1 = e1 | all_55_1 = e0
% 230.52/41.86  | | | 
% 230.52/41.86  | | | BETA: splitting (23) gives:
% 230.52/41.86  | | | 
% 230.52/41.86  | | | Case 1:
% 230.52/41.86  | | | | 
% 230.52/41.86  | | | |   (24)  all_55_1 = e1
% 230.52/41.86  | | | | 
% 230.52/41.86  | | | | COMBINE_EQS: (7), (24) imply:
% 230.52/41.86  | | | |   (25)  all_53_4 = e1
% 230.52/41.86  | | | | 
% 230.52/41.86  | | | | SIMP: (25) implies:
% 230.52/41.86  | | | |   (26)  all_53_4 = e1
% 230.52/41.86  | | | | 
% 230.52/41.86  | | | | REDUCE: (15), (26) imply:
% 230.52/41.86  | | | |   (27)   ~ (all_52_27 = e1)
% 230.52/41.86  | | | | 
% 230.52/41.86  | | | | SIMP: (27) implies:
% 230.52/41.86  | | | |   (28)   ~ (all_52_27 = e1)
% 230.52/41.86  | | | | 
% 230.52/41.86  | | | | REF_CLOSE: (1), (3), (5), (9), (11), (14), (16), (21), (28) are
% 230.52/41.86  | | | |            inconsistent by sub-proof #1177.
% 230.52/41.86  | | | | 
% 230.52/41.86  | | | Case 2:
% 230.52/41.86  | | | | 
% 230.52/41.86  | | | |   (29)  all_55_1 = e0
% 230.52/41.86  | | | | 
% 230.52/41.86  | | | | REF_CLOSE: (7), (12), (29) are inconsistent by sub-proof #2076.
% 230.52/41.86  | | | | 
% 230.52/41.86  | | | End of split
% 230.52/41.86  | | | 
% 230.52/41.86  | | End of split
% 230.52/41.86  | | 
% 230.52/41.86  | Case 2:
% 230.52/41.86  | | 
% 230.52/41.86  | |   (30)  all_55_9 = e1 | all_55_9 = e0
% 230.52/41.86  | | 
% 230.52/41.86  | | REF_CLOSE: (2), (4), (10), (30) are inconsistent by sub-proof #1835.
% 230.52/41.86  | | 
% 230.52/41.86  | End of split
% 230.52/41.86  | 
% 230.52/41.86  End of proof
% 230.52/41.86  
% 230.52/41.86  Sub-proof #1177 shows that the following formulas are inconsistent:
% 230.52/41.86  ----------------------------------------------------------------
% 230.52/41.86    (1)  all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 230.52/41.86    (2)   ~ (all_52_27 = e1)
% 230.52/41.86    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.86           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.86    (4)  op(e2, e2) = e0
% 230.52/41.86    (5)  op(e3, e3) = e0
% 230.52/41.86    (6)   ~ (e2 = e0)
% 230.52/41.86    (7)  all_55_13 = all_52_27
% 230.52/41.86    (8)   ~ (all_52_27 = e0)
% 230.52/41.86    (9)  op(all_52_27, all_52_27) = e2
% 230.52/41.86  
% 230.52/41.86  Begin of proof
% 230.52/41.86  | 
% 230.52/41.86  | BETA: splitting (1) gives:
% 230.52/41.86  | 
% 230.52/41.86  | Case 1:
% 230.52/41.86  | | 
% 230.52/41.86  | |   (10)  all_55_13 = e3
% 230.52/41.86  | | 
% 230.52/41.86  | | COMBINE_EQS: (7), (10) imply:
% 230.52/41.86  | |   (11)  all_52_27 = e3
% 230.52/41.86  | | 
% 230.52/41.86  | | SIMP: (11) implies:
% 230.52/41.86  | |   (12)  all_52_27 = e3
% 230.52/41.86  | | 
% 230.52/41.86  | | REDUCE: (9), (12) imply:
% 230.52/41.86  | |   (13)  op(e3, e3) = e2
% 230.52/41.86  | | 
% 230.52/41.86  | | REF_CLOSE: (3), (5), (6), (13) are inconsistent by sub-proof #2403.
% 230.52/41.86  | | 
% 230.52/41.86  | Case 2:
% 230.52/41.86  | | 
% 230.52/41.86  | |   (14)  all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 230.52/41.86  | | 
% 230.52/41.86  | | REF_CLOSE: (2), (3), (4), (7), (8), (9), (14) are inconsistent by sub-proof
% 230.52/41.86  | |            #1614.
% 230.52/41.86  | | 
% 230.52/41.86  | End of split
% 230.52/41.86  | 
% 230.52/41.86  End of proof
% 230.52/41.86  
% 230.52/41.86  Sub-proof #1178 shows that the following formulas are inconsistent:
% 230.52/41.86  ----------------------------------------------------------------
% 230.52/41.86    (1)   ~ (all_53_2 = e1)
% 230.52/41.86    (2)   ~ (all_52_25 = e1)
% 230.52/41.86    (3)  all_57_15 = e0
% 230.52/41.86    (4)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.52/41.86         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.52/41.86    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.52/41.86         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.52/41.86    (6)   ~ (e3 = e1)
% 230.52/41.86    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.86           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.86    (8)   ~ (all_53_2 = all_52_25)
% 230.52/41.86    (9)   ~ (all_53_2 = e3)
% 230.52/41.86    (10)  op(e2, e2) = e0
% 230.52/41.86    (11)  all_57_3 = e0
% 230.52/41.86    (12)  all_55_12 = all_52_25
% 230.52/41.86    (13)   ~ (e3 = e2)
% 230.52/41.86    (14)   ~ (e3 = e0)
% 230.52/41.86    (15)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 230.52/41.86    (16)   ~ (all_53_2 = e0)
% 230.52/41.86    (17)  op(e3, e3) = e0
% 230.52/41.86    (18)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.52/41.86          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.52/41.86            e1)
% 230.52/41.86    (19)  all_57_10 = e2
% 230.52/41.86    (20)  all_57_5 = e3
% 230.52/41.86    (21)  op(all_52_25, all_52_25) = e3
% 230.52/41.86    (22)   ~ (e2 = e0)
% 230.52/41.86    (23)   ~ (e1 = e0)
% 230.52/41.86    (24)  op(e0, e1) = all_52_29
% 230.52/41.86    (25)  op(e0, e0) = e0
% 230.52/41.86    (26)  all_55_8 = all_53_2
% 230.52/41.86    (27)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.52/41.86          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 230.52/41.86            e3)
% 230.52/41.86    (28)  all_57_2 = e1
% 230.52/41.86    (29)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.52/41.86          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.52/41.86            e2)
% 230.52/41.86    (30)  op(all_52_29, all_52_29) = e1
% 230.52/41.86    (31)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.52/41.86          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.52/41.86    (32)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.52/41.86          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.52/41.86    (33)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.52/41.86          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.52/41.86    (34)   ~ (e2 = e1)
% 230.52/41.86    (35)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.52/41.86          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.52/41.86    (36)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 230.52/41.86    (37)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.52/41.86          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.52/41.86    (38)   ~ (all_52_25 = e0)
% 230.52/41.86  
% 230.52/41.86  Begin of proof
% 230.52/41.86  | 
% 230.52/41.86  | BETA: splitting (27) gives:
% 230.52/41.86  | 
% 230.52/41.86  | Case 1:
% 230.52/41.86  | | 
% 230.52/41.86  | |   (39)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 230.52/41.86  | |           e3)
% 230.52/41.86  | | 
% 230.52/41.86  | | BETA: splitting (39) gives:
% 230.52/41.86  | | 
% 230.52/41.86  | | Case 1:
% 230.52/41.86  | | | 
% 230.52/41.86  | | |   (40)  all_57_12 = e3 & op(e0, e3) = e3
% 230.52/41.86  | | | 
% 230.52/41.86  | | | ALPHA: (40) implies:
% 230.52/41.86  | | |   (41)  all_57_12 = e3
% 230.52/41.86  | | | 
% 230.52/41.86  | | | BETA: splitting (15) gives:
% 230.52/41.86  | | | 
% 230.52/41.86  | | | Case 1:
% 230.52/41.86  | | | | 
% 230.52/41.86  | | | |   (42)  all_55_8 = e3
% 230.52/41.86  | | | | 
% 230.52/41.86  | | | | REF_CLOSE: (9), (26), (42) are inconsistent by sub-proof #2496.
% 230.52/41.86  | | | | 
% 230.52/41.86  | | | Case 2:
% 230.52/41.86  | | | | 
% 230.52/41.86  | | | |   (43)  all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 230.52/41.86  | | | | 
% 230.52/41.86  | | | | BETA: splitting (43) gives:
% 230.52/41.86  | | | | 
% 230.52/41.86  | | | | Case 1:
% 230.52/41.86  | | | | | 
% 230.52/41.86  | | | | |   (44)  all_55_8 = e2
% 230.52/41.86  | | | | | 
% 230.52/41.86  | | | | | COMBINE_EQS: (26), (44) imply:
% 230.52/41.86  | | | | |   (45)  all_53_2 = e2
% 230.52/41.86  | | | | | 
% 230.52/41.86  | | | | | SIMP: (45) implies:
% 230.52/41.86  | | | | |   (46)  all_53_2 = e2
% 230.52/41.86  | | | | | 
% 230.52/41.86  | | | | | REDUCE: (8), (46) imply:
% 230.52/41.86  | | | | |   (47)   ~ (all_52_25 = e2)
% 230.52/41.86  | | | | | 
% 230.52/41.86  | | | | | SIMP: (47) implies:
% 230.52/41.86  | | | | |   (48)   ~ (all_52_25 = e2)
% 230.52/41.86  | | | | | 
% 230.52/41.86  | | | | | BETA: splitting (36) gives:
% 230.52/41.86  | | | | | 
% 230.52/41.86  | | | | | Case 1:
% 230.52/41.86  | | | | | | 
% 230.52/41.86  | | | | | |   (49)  all_55_12 = e3
% 230.52/41.86  | | | | | | 
% 230.52/41.86  | | | | | | COMBINE_EQS: (12), (49) imply:
% 230.52/41.86  | | | | | |   (50)  all_52_25 = e3
% 230.52/41.86  | | | | | | 
% 230.52/41.86  | | | | | | SIMP: (50) implies:
% 230.52/41.86  | | | | | |   (51)  all_52_25 = e3
% 230.52/41.86  | | | | | | 
% 230.52/41.86  | | | | | | REF_CLOSE: (4), (5), (6), (7), (11), (13), (21), (22), (23), (31),
% 230.52/41.86  | | | | | |            (32), (34), (35), (37), (38), (41), (51) are inconsistent
% 230.52/41.86  | | | | | |            by sub-proof #1185.
% 230.52/41.86  | | | | | | 
% 230.52/41.86  | | | | | Case 2:
% 230.52/41.86  | | | | | | 
% 230.52/41.86  | | | | | |   (52)  all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 230.52/41.86  | | | | | | 
% 230.52/41.86  | | | | | | REF_CLOSE: (2), (12), (38), (48), (52) are inconsistent by sub-proof
% 230.52/41.86  | | | | | |            #1563.
% 230.52/41.86  | | | | | | 
% 230.52/41.86  | | | | | End of split
% 230.52/41.86  | | | | | 
% 230.52/41.86  | | | | Case 2:
% 230.52/41.86  | | | | | 
% 230.52/41.86  | | | | |   (53)  all_55_8 = e1 | all_55_8 = e0
% 230.52/41.86  | | | | | 
% 230.52/41.86  | | | | | REF_CLOSE: (1), (16), (26), (53) are inconsistent by sub-proof #1974.
% 230.52/41.86  | | | | | 
% 230.52/41.86  | | | | End of split
% 230.52/41.86  | | | | 
% 230.52/41.86  | | | End of split
% 230.52/41.86  | | | 
% 230.52/41.86  | | Case 2:
% 230.52/41.86  | | | 
% 230.52/41.86  | | |   (54)  all_57_13 = e3 & op(e0, e2) = e3
% 230.52/41.86  | | | 
% 230.52/41.86  | | | ALPHA: (54) implies:
% 230.52/41.86  | | |   (55)  all_57_13 = e3
% 230.52/41.86  | | | 
% 230.52/41.86  | | | BETA: splitting (15) gives:
% 230.52/41.86  | | | 
% 230.52/41.86  | | | Case 1:
% 230.52/41.86  | | | | 
% 230.52/41.86  | | | |   (56)  all_55_8 = e3
% 230.52/41.86  | | | | 
% 230.52/41.86  | | | | REF_CLOSE: (9), (26), (56) are inconsistent by sub-proof #2496.
% 230.52/41.86  | | | | 
% 230.52/41.86  | | | Case 2:
% 230.52/41.86  | | | | 
% 230.52/41.86  | | | |   (57)  all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 230.52/41.86  | | | | 
% 230.52/41.86  | | | | BETA: splitting (33) gives:
% 230.52/41.86  | | | | 
% 230.52/41.86  | | | | Case 1:
% 230.52/41.86  | | | | | 
% 230.52/41.86  | | | | |   (58)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2,
% 230.52/41.86  | | | | |             e3) = e3)
% 230.52/41.86  | | | | | 
% 230.52/41.86  | | | | | REF_CLOSE: (4), (6), (7), (11), (14), (17), (19), (20), (23), (34),
% 230.52/41.86  | | | | |            (58) are inconsistent by sub-proof #1180.
% 230.52/41.86  | | | | | 
% 230.52/41.86  | | | | Case 2:
% 230.52/41.86  | | | | | 
% 230.52/41.86  | | | | |   (59)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0,
% 230.52/41.86  | | | | |             e3) = e3)
% 230.52/41.86  | | | | | 
% 230.52/41.86  | | | | | BETA: splitting (59) gives:
% 230.52/41.86  | | | | | 
% 230.52/41.86  | | | | | Case 1:
% 230.52/41.86  | | | | | | 
% 230.52/41.86  | | | | | |   (60)  all_57_6 = e3 & op(e1, e3) = e3
% 230.52/41.86  | | | | | | 
% 230.52/41.86  | | | | | | ALPHA: (60) implies:
% 230.52/41.86  | | | | | |   (61)  all_57_6 = e3
% 230.52/41.86  | | | | | | 
% 230.52/41.86  | | | | | | BETA: splitting (57) gives:
% 230.52/41.86  | | | | | | 
% 230.52/41.86  | | | | | | Case 1:
% 230.52/41.86  | | | | | | | 
% 230.52/41.86  | | | | | | |   (62)  all_55_8 = e2
% 230.52/41.86  | | | | | | | 
% 230.52/41.86  | | | | | | | COMBINE_EQS: (26), (62) imply:
% 230.52/41.86  | | | | | | |   (63)  all_53_2 = e2
% 230.52/41.86  | | | | | | | 
% 230.52/41.86  | | | | | | | SIMP: (63) implies:
% 230.52/41.86  | | | | | | |   (64)  all_53_2 = e2
% 230.52/41.86  | | | | | | | 
% 230.52/41.86  | | | | | | | REDUCE: (8), (64) imply:
% 230.52/41.86  | | | | | | |   (65)   ~ (all_52_25 = e2)
% 230.52/41.86  | | | | | | | 
% 230.52/41.86  | | | | | | | SIMP: (65) implies:
% 230.52/41.86  | | | | | | |   (66)   ~ (all_52_25 = e2)
% 230.52/41.86  | | | | | | | 
% 230.52/41.86  | | | | | | | BETA: splitting (36) gives:
% 230.52/41.86  | | | | | | | 
% 230.52/41.86  | | | | | | | Case 1:
% 230.52/41.86  | | | | | | | | 
% 230.52/41.86  | | | | | | | |   (67)  all_55_12 = e3
% 230.52/41.86  | | | | | | | | 
% 230.52/41.86  | | | | | | | | COMBINE_EQS: (12), (67) imply:
% 230.52/41.86  | | | | | | | |   (68)  all_52_25 = e3
% 230.52/41.86  | | | | | | | | 
% 230.52/41.86  | | | | | | | | SIMP: (68) implies:
% 230.52/41.86  | | | | | | | |   (69)  all_52_25 = e3
% 230.52/41.86  | | | | | | | | 
% 230.52/41.86  | | | | | | | | REDUCE: (21), (69) imply:
% 230.52/41.86  | | | | | | | |   (70)  op(e3, e3) = e3
% 230.52/41.86  | | | | | | | | 
% 230.52/41.86  | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (11), (13), (14), (20), (22),
% 230.52/41.86  | | | | | | | |            (23), (32), (34), (35), (37), (61), (70) are
% 230.52/41.86  | | | | | | | |            inconsistent by sub-proof #1781.
% 230.52/41.86  | | | | | | | | 
% 230.52/41.86  | | | | | | | Case 2:
% 230.52/41.86  | | | | | | | | 
% 230.52/41.86  | | | | | | | |   (71)  all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 230.52/41.86  | | | | | | | | 
% 230.52/41.86  | | | | | | | | REF_CLOSE: (2), (12), (38), (66), (71) are inconsistent by
% 230.52/41.86  | | | | | | | |            sub-proof #1563.
% 230.52/41.86  | | | | | | | | 
% 230.52/41.86  | | | | | | | End of split
% 230.52/41.86  | | | | | | | 
% 230.52/41.86  | | | | | | Case 2:
% 230.52/41.86  | | | | | | | 
% 230.52/41.86  | | | | | | |   (72)  all_55_8 = e1 | all_55_8 = e0
% 230.52/41.86  | | | | | | | 
% 230.52/41.86  | | | | | | | REF_CLOSE: (1), (16), (26), (72) are inconsistent by sub-proof
% 230.52/41.86  | | | | | | |            #1974.
% 230.52/41.86  | | | | | | | 
% 230.52/41.86  | | | | | | End of split
% 230.52/41.86  | | | | | | 
% 230.52/41.86  | | | | | Case 2:
% 230.52/41.86  | | | | | | 
% 230.52/41.86  | | | | | |   (73)  all_57_12 = e3 & op(e0, e3) = e3
% 230.52/41.86  | | | | | | 
% 230.52/41.86  | | | | | | ALPHA: (73) implies:
% 230.52/41.86  | | | | | |   (74)  all_57_12 = e3
% 230.52/41.86  | | | | | | 
% 230.52/41.86  | | | | | | BETA: splitting (35) gives:
% 230.52/41.86  | | | | | | 
% 230.52/41.86  | | | | | | Case 1:
% 230.52/41.86  | | | | | | | 
% 230.52/41.86  | | | | | | |   (75)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 &
% 230.52/41.86  | | | | | | |           op(e2, e3) = e2)
% 230.52/41.86  | | | | | | | 
% 230.52/41.86  | | | | | | | REF_CLOSE: (7), (17), (22), (28), (34), (75) are inconsistent by
% 230.52/41.86  | | | | | | |            sub-proof #2394.
% 230.52/41.86  | | | | | | | 
% 230.52/41.86  | | | | | | Case 2:
% 230.52/41.86  | | | | | | | 
% 230.52/41.86  | | | | | | |   (76)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 &
% 230.52/41.86  | | | | | | |           op(e0, e3) = e2)
% 230.52/41.86  | | | | | | | 
% 230.52/41.86  | | | | | | | BETA: splitting (76) gives:
% 230.52/41.86  | | | | | | | 
% 230.52/41.86  | | | | | | | Case 1:
% 230.52/41.86  | | | | | | | | 
% 230.52/41.86  | | | | | | | |   (77)  all_57_6 = e2 & op(e1, e3) = e2
% 230.52/41.86  | | | | | | | | 
% 230.52/41.86  | | | | | | | | ALPHA: (77) implies:
% 230.52/41.86  | | | | | | | |   (78)  all_57_6 = e2
% 230.52/41.86  | | | | | | | | 
% 230.52/41.86  | | | | | | | | BETA: splitting (29) gives:
% 230.52/41.86  | | | | | | | | 
% 230.52/41.86  | | | | | | | | Case 1:
% 230.52/41.86  | | | | | | | | | 
% 230.52/41.86  | | | | | | | | |   (79)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 &
% 230.52/41.86  | | | | | | | | |           op(e0, e2) = e2)
% 230.52/41.86  | | | | | | | | | 
% 230.52/41.86  | | | | | | | | | BETA: splitting (79) gives:
% 230.52/41.86  | | | | | | | | | 
% 230.52/41.86  | | | | | | | | | Case 1:
% 230.52/41.86  | | | | | | | | | | 
% 230.52/41.86  | | | | | | | | | |   (80)  all_57_12 = e2 & op(e0, e3) = e2
% 230.52/41.86  | | | | | | | | | | 
% 230.52/41.86  | | | | | | | | | | REF_CLOSE: (13), (74), (80) are inconsistent by sub-proof
% 230.52/41.86  | | | | | | | | | |            #2232.
% 230.52/41.86  | | | | | | | | | | 
% 230.52/41.86  | | | | | | | | | Case 2:
% 230.52/41.86  | | | | | | | | | | 
% 230.52/41.86  | | | | | | | | | |   (81)  all_57_13 = e2 & op(e0, e2) = e2
% 230.52/41.86  | | | | | | | | | | 
% 230.52/41.86  | | | | | | | | | | ALPHA: (81) implies:
% 230.52/41.86  | | | | | | | | | |   (82)  all_57_13 = e2
% 230.52/41.86  | | | | | | | | | | 
% 230.52/41.86  | | | | | | | | | | REF_CLOSE: (13), (55), (82) are inconsistent by sub-proof
% 230.52/41.86  | | | | | | | | | |            #2203.
% 230.52/41.86  | | | | | | | | | | 
% 230.52/41.86  | | | | | | | | | End of split
% 230.52/41.86  | | | | | | | | | 
% 230.52/41.86  | | | | | | | | Case 2:
% 230.52/41.86  | | | | | | | | | 
% 230.52/41.86  | | | | | | | | |   (83)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 &
% 230.52/41.86  | | | | | | | | |           op(e0, e0) = e2)
% 230.52/41.86  | | | | | | | | | 
% 230.52/41.86  | | | | | | | | | BETA: splitting (83) gives:
% 230.52/41.86  | | | | | | | | | 
% 230.52/41.86  | | | | | | | | | Case 1:
% 230.52/41.86  | | | | | | | | | | 
% 230.52/41.86  | | | | | | | | | |   (84)  all_57_14 = e2 & op(e0, e1) = e2
% 230.52/41.86  | | | | | | | | | | 
% 230.52/41.86  | | | | | | | | | | ALPHA: (84) implies:
% 230.52/41.86  | | | | | | | | | |   (85)  all_57_14 = e2
% 230.52/41.86  | | | | | | | | | | 
% 230.52/41.86  | | | | | | | | | | BETA: splitting (18) gives:
% 230.52/41.86  | | | | | | | | | | 
% 230.52/41.86  | | | | | | | | | | Case 1:
% 230.52/41.86  | | | | | | | | | | | 
% 230.52/41.86  | | | | | | | | | | |   (86)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 230.52/41.86  | | | | | | | | | | |           e1 & op(e0, e2) = e1)
% 230.52/41.86  | | | | | | | | | | | 
% 230.52/41.86  | | | | | | | | | | | BETA: splitting (86) gives:
% 230.52/41.86  | | | | | | | | | | | 
% 230.52/41.86  | | | | | | | | | | | Case 1:
% 230.52/41.86  | | | | | | | | | | | | 
% 230.52/41.86  | | | | | | | | | | | |   (87)  all_57_12 = e1 & op(e0, e3) = e1
% 230.52/41.86  | | | | | | | | | | | | 
% 230.52/41.86  | | | | | | | | | | | | ALPHA: (87) implies:
% 230.52/41.86  | | | | | | | | | | | |   (88)  all_57_12 = e1
% 230.52/41.86  | | | | | | | | | | | | 
% 230.52/41.86  | | | | | | | | | | | | BETA: splitting (33) gives:
% 230.52/41.86  | | | | | | | | | | | | 
% 230.52/41.86  | | | | | | | | | | | | Case 1:
% 230.52/41.86  | | | | | | | | | | | | | 
% 230.52/41.86  | | | | | | | | | | | | |   (89)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 230.52/41.86  | | | | | | | | | | | | |           & op(e2, e3) = e3)
% 230.52/41.86  | | | | | | | | | | | | | 
% 230.52/41.86  | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (11), (14), (17), (19), (20), (23),
% 230.52/41.86  | | | | | | | | | | | | |            (34), (89) are inconsistent by sub-proof #1180.
% 230.52/41.86  | | | | | | | | | | | | | 
% 230.52/41.86  | | | | | | | | | | | | Case 2:
% 230.52/41.86  | | | | | | | | | | | | | 
% 230.52/41.86  | | | | | | | | | | | | | 
% 230.52/41.86  | | | | | | | | | | | | | BETA: splitting (59) gives:
% 230.52/41.86  | | | | | | | | | | | | | 
% 230.52/41.86  | | | | | | | | | | | | | Case 1:
% 230.52/41.86  | | | | | | | | | | | | | | 
% 230.52/41.86  | | | | | | | | | | | | | |   (90)  all_57_6 = e3 & op(e1, e3) = e3
% 230.52/41.86  | | | | | | | | | | | | | | 
% 230.52/41.86  | | | | | | | | | | | | | | REF_CLOSE: (13), (78), (90) are inconsistent by sub-proof
% 230.52/41.86  | | | | | | | | | | | | | |            #1558.
% 230.52/41.86  | | | | | | | | | | | | | | 
% 230.52/41.86  | | | | | | | | | | | | | Case 2:
% 230.52/41.86  | | | | | | | | | | | | | | 
% 230.52/41.86  | | | | | | | | | | | | | | 
% 230.52/41.86  | | | | | | | | | | | | | | COMBINE_EQS: (74), (88) imply:
% 230.52/41.86  | | | | | | | | | | | | | |   (91)  e3 = e1
% 230.52/41.86  | | | | | | | | | | | | | | 
% 230.52/41.86  | | | | | | | | | | | | | | SIMP: (91) implies:
% 230.52/41.86  | | | | | | | | | | | | | |   (92)  e3 = e1
% 230.52/41.86  | | | | | | | | | | | | | | 
% 230.52/41.86  | | | | | | | | | | | | | | COMBINE_EQS: (20), (92) imply:
% 230.52/41.86  | | | | | | | | | | | | | |   (93)  all_57_5 = e1
% 230.52/41.86  | | | | | | | | | | | | | | 
% 230.52/41.86  | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (10), (11), (13), (14), (22), (28),
% 230.52/41.86  | | | | | | | | | | | | | |            (31), (32), (34), (93) are inconsistent by
% 230.52/41.86  | | | | | | | | | | | | | |            sub-proof #1536.
% 230.52/41.86  | | | | | | | | | | | | | | 
% 230.52/41.86  | | | | | | | | | | | | | End of split
% 230.52/41.86  | | | | | | | | | | | | | 
% 230.52/41.86  | | | | | | | | | | | | End of split
% 230.52/41.86  | | | | | | | | | | | | 
% 230.52/41.86  | | | | | | | | | | | Case 2:
% 230.52/41.86  | | | | | | | | | | | | 
% 230.52/41.86  | | | | | | | | | | | |   (94)  all_57_13 = e1 & op(e0, e2) = e1
% 230.52/41.86  | | | | | | | | | | | | 
% 230.52/41.86  | | | | | | | | | | | | ALPHA: (94) implies:
% 230.52/41.86  | | | | | | | | | | | |   (95)  all_57_13 = e1
% 230.52/41.86  | | | | | | | | | | | | 
% 230.52/41.86  | | | | | | | | | | | | COMBINE_EQS: (55), (95) imply:
% 230.52/41.86  | | | | | | | | | | | |   (96)  e3 = e1
% 230.52/41.86  | | | | | | | | | | | | 
% 230.52/41.86  | | | | | | | | | | | | SIMP: (96) implies:
% 230.52/41.86  | | | | | | | | | | | |   (97)  e3 = e1
% 230.52/41.86  | | | | | | | | | | | | 
% 230.52/41.86  | | | | | | | | | | | | COMBINE_EQS: (20), (97) imply:
% 230.52/41.86  | | | | | | | | | | | |   (98)  all_57_5 = e1
% 230.52/41.86  | | | | | | | | | | | | 
% 230.52/41.86  | | | | | | | | | | | | REF_CLOSE: (6), (7), (10), (11), (13), (14), (22), (28),
% 230.52/41.86  | | | | | | | | | | | |            (31), (32), (34), (98) are inconsistent by
% 230.52/41.86  | | | | | | | | | | | |            sub-proof #1536.
% 230.52/41.86  | | | | | | | | | | | | 
% 230.52/41.86  | | | | | | | | | | | End of split
% 230.52/41.86  | | | | | | | | | | | 
% 230.52/41.86  | | | | | | | | | | Case 2:
% 230.52/41.86  | | | | | | | | | | | 
% 230.52/41.86  | | | | | | | | | | |   (99)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 230.52/41.86  | | | | | | | | | | |           e1 & op(e0, e0) = e1)
% 230.52/41.86  | | | | | | | | | | | 
% 230.52/41.86  | | | | | | | | | | | REF_CLOSE: (7), (23), (25), (34), (85), (99) are inconsistent
% 230.52/41.86  | | | | | | | | | | |            by sub-proof #1179.
% 230.52/41.86  | | | | | | | | | | | 
% 230.52/41.86  | | | | | | | | | | End of split
% 230.52/41.86  | | | | | | | | | | 
% 230.52/41.86  | | | | | | | | | Case 2:
% 230.52/41.86  | | | | | | | | | | 
% 230.52/41.86  | | | | | | | | | |   (100)  all_57_15 = e2 & op(e0, e0) = e2
% 230.52/41.86  | | | | | | | | | | 
% 230.52/41.86  | | | | | | | | | | ALPHA: (100) implies:
% 230.52/41.86  | | | | | | | | | |   (101)  all_57_15 = e2
% 230.52/41.86  | | | | | | | | | | 
% 230.52/41.86  | | | | | | | | | | COMBINE_EQS: (3), (101) imply:
% 230.52/41.86  | | | | | | | | | |   (102)  e2 = e0
% 230.52/41.86  | | | | | | | | | | 
% 230.52/41.86  | | | | | | | | | | COMBINE_EQS: (78), (102) imply:
% 230.52/41.86  | | | | | | | | | |   (103)  all_57_6 = e0
% 230.52/41.86  | | | | | | | | | | 
% 230.52/41.86  | | | | | | | | | | REF_CLOSE: (6), (7), (13), (14), (17), (22), (28), (33),
% 230.52/41.86  | | | | | | | | | |            (34), (35), (103) are inconsistent by sub-proof
% 230.52/41.86  | | | | | | | | | |            #2390.
% 230.52/41.86  | | | | | | | | | | 
% 230.52/41.86  | | | | | | | | | End of split
% 230.52/41.86  | | | | | | | | | 
% 230.52/41.86  | | | | | | | | End of split
% 230.52/41.86  | | | | | | | | 
% 230.52/41.86  | | | | | | | Case 2:
% 230.52/41.86  | | | | | | | | 
% 230.52/41.86  | | | | | | | |   (104)  all_57_12 = e2 & op(e0, e3) = e2
% 230.52/41.86  | | | | | | | | 
% 230.52/41.86  | | | | | | | | REF_CLOSE: (13), (74), (104) are inconsistent by sub-proof
% 230.52/41.86  | | | | | | | |            #2232.
% 230.52/41.86  | | | | | | | | 
% 230.52/41.86  | | | | | | | End of split
% 230.52/41.86  | | | | | | | 
% 230.52/41.86  | | | | | | End of split
% 230.52/41.86  | | | | | | 
% 230.52/41.86  | | | | | End of split
% 230.52/41.86  | | | | | 
% 230.52/41.86  | | | | End of split
% 230.52/41.86  | | | | 
% 230.52/41.86  | | | End of split
% 230.52/41.86  | | | 
% 230.52/41.86  | | End of split
% 230.52/41.86  | | 
% 230.52/41.86  | Case 2:
% 230.52/41.86  | | 
% 230.52/41.86  | |   (105)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 230.52/41.86  | |            e3)
% 230.52/41.86  | | 
% 230.52/41.86  | | BETA: splitting (105) gives:
% 230.52/41.86  | | 
% 230.52/41.86  | | Case 1:
% 230.52/41.86  | | | 
% 230.52/41.86  | | |   (106)  all_57_14 = e3 & op(e0, e1) = e3
% 230.52/41.86  | | | 
% 230.52/41.86  | | | ALPHA: (106) implies:
% 230.52/41.86  | | |   (107)  op(e0, e1) = e3
% 230.52/41.86  | | | 
% 230.52/41.86  | | | REF_CLOSE: (7), (17), (23), (24), (30), (107) are inconsistent by
% 230.52/41.86  | | |            sub-proof #1934.
% 230.52/41.86  | | | 
% 230.52/41.86  | | Case 2:
% 230.52/41.86  | | | 
% 230.52/41.86  | | |   (108)  all_57_15 = e3 & op(e0, e0) = e3
% 230.52/41.86  | | | 
% 230.52/41.86  | | | ALPHA: (108) implies:
% 230.52/41.86  | | |   (109)  op(e0, e0) = e3
% 230.52/41.86  | | | 
% 230.52/41.86  | | | REF_CLOSE: (7), (14), (25), (109) are inconsistent by sub-proof #2304.
% 230.52/41.86  | | | 
% 230.52/41.86  | | End of split
% 230.52/41.86  | | 
% 230.52/41.86  | End of split
% 230.52/41.86  | 
% 230.52/41.86  End of proof
% 230.52/41.86  
% 230.52/41.86  Sub-proof #1179 shows that the following formulas are inconsistent:
% 230.52/41.86  ----------------------------------------------------------------
% 230.52/41.86    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.86           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.86    (2)   ~ (e1 = e0)
% 230.52/41.86    (3)  all_57_14 = e2
% 230.52/41.86    (4)  op(e0, e0) = e0
% 230.52/41.86    (5)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.52/41.86    (6)   ~ (e2 = e1)
% 230.52/41.86  
% 230.52/41.86  Begin of proof
% 230.52/41.86  | 
% 230.52/41.86  | BETA: splitting (5) gives:
% 230.52/41.86  | 
% 230.52/41.86  | Case 1:
% 230.52/41.86  | | 
% 230.52/41.86  | |   (7)  all_57_14 = e1 & op(e0, e1) = e1
% 230.52/41.86  | | 
% 230.52/41.86  | | ALPHA: (7) implies:
% 230.52/41.86  | |   (8)  all_57_14 = e1
% 230.52/41.86  | | 
% 230.52/41.86  | | REF_CLOSE: (3), (6), (8) are inconsistent by sub-proof #2178.
% 230.52/41.86  | | 
% 230.52/41.86  | Case 2:
% 230.52/41.86  | | 
% 230.52/41.86  | |   (9)  all_57_15 = e1 & op(e0, e0) = e1
% 230.52/41.86  | | 
% 230.52/41.86  | | ALPHA: (9) implies:
% 230.52/41.86  | |   (10)  op(e0, e0) = e1
% 230.52/41.86  | | 
% 230.52/41.86  | | REF_CLOSE: (1), (2), (4), (10) are inconsistent by sub-proof #2290.
% 230.52/41.86  | | 
% 230.52/41.86  | End of split
% 230.52/41.86  | 
% 230.52/41.86  End of proof
% 230.52/41.86  
% 230.52/41.86  Sub-proof #1180 shows that the following formulas are inconsistent:
% 230.52/41.86  ----------------------------------------------------------------
% 230.52/41.86    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.52/41.86         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.52/41.86    (2)   ~ (e3 = e1)
% 230.52/41.86    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.86           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.86    (4)  all_57_3 = e0
% 230.52/41.86    (5)   ~ (e3 = e0)
% 230.52/41.86    (6)  op(e3, e3) = e0
% 230.52/41.86    (7)  all_57_10 = e2
% 230.52/41.86    (8)  all_57_5 = e3
% 230.52/41.86    (9)   ~ (e1 = e0)
% 230.52/41.86    (10)   ~ (e2 = e1)
% 230.52/41.86    (11)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3)
% 230.52/41.86  
% 230.52/41.86  Begin of proof
% 230.52/41.86  | 
% 230.52/41.86  | BETA: splitting (11) gives:
% 230.52/41.86  | 
% 230.52/41.86  | Case 1:
% 230.52/41.86  | | 
% 230.52/41.86  | |   (12)  all_57_0 = e3 & op(e3, e3) = e3
% 230.52/41.86  | | 
% 230.52/41.86  | | ALPHA: (12) implies:
% 230.52/41.86  | |   (13)  op(e3, e3) = e3
% 230.52/41.86  | | 
% 230.52/41.86  | | REF_CLOSE: (3), (5), (6), (13) are inconsistent by sub-proof #2494.
% 230.52/41.86  | | 
% 230.52/41.86  | Case 2:
% 230.52/41.86  | | 
% 230.52/41.86  | |   (14)  all_57_2 = e3 & op(e2, e3) = e3
% 230.52/41.86  | | 
% 230.52/41.86  | | ALPHA: (14) implies:
% 230.52/41.86  | |   (15)  all_57_2 = e3
% 230.52/41.86  | | 
% 230.52/41.86  | | REF_CLOSE: (1), (2), (4), (7), (8), (9), (10), (15) are inconsistent by
% 230.52/41.86  | |            sub-proof #1804.
% 230.52/41.86  | | 
% 230.52/41.86  | End of split
% 230.52/41.86  | 
% 230.52/41.86  End of proof
% 230.52/41.86  
% 230.52/41.86  Sub-proof #1181 shows that the following formulas are inconsistent:
% 230.52/41.86  ----------------------------------------------------------------
% 230.52/41.86    (1)   ~ (e3 = e1)
% 230.52/41.86    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.86           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.86    (3)  all_57_4 = e3
% 230.52/41.86    (4)   ~ (e3 = e2)
% 230.52/41.86    (5)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.52/41.86         (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.52/41.86    (6)  all_57_5 = e3
% 230.52/41.86    (7)   ~ (e2 = e0)
% 230.52/41.86    (8)   ~ (e1 = e0)
% 230.52/41.86    (9)  op(e1, e1) = e0
% 230.52/41.86    (10)  all_57_8 = e0
% 230.52/41.87    (11)   ~ (e2 = e1)
% 230.52/41.87    (12)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.52/41.87          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.52/41.87  
% 230.52/41.87  Begin of proof
% 230.52/41.87  | 
% 230.52/41.87  | BETA: splitting (12) gives:
% 230.52/41.87  | 
% 230.52/41.87  | Case 1:
% 230.52/41.87  | | 
% 230.52/41.87  | |   (13)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) =
% 230.52/41.87  | |           e2)
% 230.52/41.87  | | 
% 230.52/41.87  | | BETA: splitting (13) gives:
% 230.52/41.87  | | 
% 230.52/41.87  | | Case 1:
% 230.52/41.87  | | | 
% 230.52/41.87  | | |   (14)  all_57_4 = e2 & op(e3, e1) = e2
% 230.52/41.87  | | | 
% 230.52/41.87  | | | ALPHA: (14) implies:
% 230.52/41.87  | | |   (15)  all_57_4 = e2
% 230.52/41.87  | | | 
% 230.52/41.87  | | | REF_CLOSE: (3), (4), (15) are inconsistent by sub-proof #2482.
% 230.52/41.87  | | | 
% 230.52/41.87  | | Case 2:
% 230.52/41.87  | | | 
% 230.52/41.87  | | |   (16)  all_57_5 = e2 & op(e2, e1) = e2
% 230.52/41.87  | | | 
% 230.52/41.87  | | | REF_CLOSE: (4), (6), (16) are inconsistent by sub-proof #2425.
% 230.52/41.87  | | | 
% 230.52/41.87  | | End of split
% 230.52/41.87  | | 
% 230.52/41.87  | Case 2:
% 230.52/41.87  | | 
% 230.52/41.87  | |   (17)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) =
% 230.52/41.87  | |           e2)
% 230.52/41.87  | | 
% 230.52/41.87  | | BETA: splitting (17) gives:
% 230.52/41.87  | | 
% 230.52/41.87  | | Case 1:
% 230.52/41.87  | | | 
% 230.52/41.87  | | |   (18)  all_57_8 = e2 & op(e1, e1) = e2
% 230.52/41.87  | | | 
% 230.52/41.87  | | | REF_CLOSE: (7), (10), (18) are inconsistent by sub-proof #2005.
% 230.52/41.87  | | | 
% 230.52/41.87  | | Case 2:
% 230.52/41.87  | | | 
% 230.52/41.87  | | |   (19)  all_57_14 = e2 & op(e0, e1) = e2
% 230.52/41.87  | | | 
% 230.52/41.87  | | | ALPHA: (19) implies:
% 230.52/41.87  | | |   (20)  all_57_14 = e2
% 230.52/41.87  | | | 
% 230.52/41.87  | | | REF_CLOSE: (1), (2), (3), (5), (6), (8), (9), (11), (20) are inconsistent
% 230.52/41.87  | | |            by sub-proof #1904.
% 230.52/41.87  | | | 
% 230.52/41.87  | | End of split
% 230.52/41.87  | | 
% 230.52/41.87  | End of split
% 230.52/41.87  | 
% 230.52/41.87  End of proof
% 230.52/41.87  
% 230.52/41.87  Sub-proof #1182 shows that the following formulas are inconsistent:
% 230.52/41.87  ----------------------------------------------------------------
% 230.52/41.87    (1)   ~ (e3 = e1)
% 230.52/41.87    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.87           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.87    (3)  all_57_1 = e1 & op(e3, e2) = e1
% 230.52/41.87    (4)  all_57_6 = e1
% 230.52/41.87    (5)   ~ (e3 = e2)
% 230.52/41.87    (6)   ~ (e3 = e0)
% 230.52/41.87    (7)  op(e3, e3) = e0
% 230.52/41.87    (8)   ~ (e2 = e0)
% 230.52/41.87    (9)  all_57_12 = e3
% 230.52/41.87    (10)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.52/41.87          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.52/41.87    (11)  all_57_1 = e3
% 230.52/41.87    (12)   ~ (e2 = e1)
% 230.52/41.87    (13)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.52/41.87          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.52/41.87  
% 230.52/41.87  Begin of proof
% 230.52/41.87  | 
% 230.52/41.87  | ALPHA: (3) implies:
% 230.52/41.87  |   (14)  all_57_1 = e1
% 230.52/41.87  | 
% 230.52/41.87  | COMBINE_EQS: (11), (14) imply:
% 230.52/41.87  |   (15)  e3 = e1
% 230.52/41.87  | 
% 230.52/41.87  | COMBINE_EQS: (9), (15) imply:
% 230.52/41.87  |   (16)  all_57_12 = e1
% 230.52/41.87  | 
% 230.52/41.87  | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (10), (12), (13), (16) are
% 230.52/41.87  |            inconsistent by sub-proof #1205.
% 230.52/41.87  | 
% 230.52/41.87  End of proof
% 230.52/41.87  
% 230.52/41.87  Sub-proof #1183 shows that the following formulas are inconsistent:
% 230.52/41.87  ----------------------------------------------------------------
% 230.52/41.87    (1)   ~ (e3 = e1)
% 230.52/41.87    (2)  all_57_7 = e2
% 230.52/41.87    (3)  all_57_3 = e0
% 230.52/41.87    (4)   ~ (e3 = e2)
% 230.52/41.87    (5)   ~ (e3 = e0)
% 230.52/41.87    (6)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.52/41.87         (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.52/41.87    (7)  all_57_13 = e3
% 230.52/41.87    (8)  e3 = e1
% 230.52/41.87    (9)  all_57_1 = e3
% 230.52/41.87  
% 230.52/41.87  Begin of proof
% 230.52/41.87  | 
% 230.52/41.87  | SIMP: (8) implies:
% 230.52/41.87  |   (10)  e3 = e1
% 230.52/41.87  | 
% 230.52/41.87  | COMBINE_EQS: (7), (10) imply:
% 230.52/41.87  |   (11)  all_57_13 = e1
% 230.52/41.87  | 
% 230.52/41.87  | COMBINE_EQS: (9), (10) imply:
% 230.52/41.87  |   (12)  all_57_1 = e1
% 230.52/41.87  | 
% 230.52/41.87  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (11), (12) are inconsistent by
% 230.52/41.87  |            sub-proof #2193.
% 230.52/41.87  | 
% 230.52/41.87  End of proof
% 230.52/41.87  
% 230.52/41.87  Sub-proof #1184 shows that the following formulas are inconsistent:
% 230.52/41.87  ----------------------------------------------------------------
% 230.52/41.87    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.87           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.87    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2)
% 230.52/41.87    (3)  op(e2, e2) = e0
% 230.52/41.87    (4)   ~ (e3 = e2)
% 230.52/41.87    (5)   ~ (e2 = e0)
% 230.52/41.87    (6)  op(e3, e2) = e3
% 230.52/41.87  
% 230.52/41.87  Begin of proof
% 230.52/41.87  | 
% 230.52/41.87  | BETA: splitting (2) gives:
% 230.52/41.87  | 
% 230.52/41.87  | Case 1:
% 230.52/41.87  | | 
% 230.52/41.87  | |   (7)  all_57_1 = e2 & op(e3, e2) = e2
% 230.52/41.87  | | 
% 230.52/41.87  | | ALPHA: (7) implies:
% 230.52/41.87  | |   (8)  op(e3, e2) = e2
% 230.52/41.87  | | 
% 230.52/41.87  | | REF_CLOSE: (1), (4), (6), (8) are inconsistent by sub-proof #1549.
% 230.52/41.87  | | 
% 230.52/41.87  | Case 2:
% 230.52/41.87  | | 
% 230.52/41.87  | |   (9)  all_57_3 = e2 & op(e2, e2) = e2
% 230.52/41.87  | | 
% 230.52/41.87  | | ALPHA: (9) implies:
% 230.52/41.87  | |   (10)  op(e2, e2) = e2
% 230.52/41.87  | | 
% 230.52/41.87  | | REF_CLOSE: (1), (3), (5), (10) are inconsistent by sub-proof #2472.
% 230.52/41.87  | | 
% 230.52/41.87  | End of split
% 230.52/41.87  | 
% 230.52/41.87  End of proof
% 230.52/41.87  
% 230.52/41.87  Sub-proof #1185 shows that the following formulas are inconsistent:
% 230.52/41.87  ----------------------------------------------------------------
% 230.52/41.87    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.52/41.87         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.52/41.87    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.52/41.87         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.52/41.87    (3)   ~ (e3 = e1)
% 230.52/41.87    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.87           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.87    (5)  all_52_25 = e3
% 230.52/41.87    (6)  all_57_3 = e0
% 230.52/41.87    (7)   ~ (e3 = e2)
% 230.52/41.87    (8)  op(all_52_25, all_52_25) = e3
% 230.52/41.87    (9)   ~ (e2 = e0)
% 230.52/41.87    (10)   ~ (e1 = e0)
% 230.52/41.87    (11)  all_57_12 = e3
% 230.52/41.87    (12)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.52/41.87          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.52/41.87    (13)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.52/41.87          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.52/41.87    (14)   ~ (e2 = e1)
% 230.52/41.87    (15)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.52/41.87          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.52/41.87    (16)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.52/41.87          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.52/41.87    (17)   ~ (all_52_25 = e0)
% 230.52/41.87  
% 230.52/41.87  Begin of proof
% 230.52/41.87  | 
% 230.52/41.87  | REDUCE: (5), (17) imply:
% 230.52/41.87  |   (18)   ~ (e3 = e0)
% 230.52/41.87  | 
% 230.52/41.87  | REDUCE: (5), (8) imply:
% 230.52/41.87  |   (19)  op(e3, e3) = e3
% 230.52/41.87  | 
% 230.52/41.87  | REF_CLOSE: (1), (2), (3), (4), (6), (7), (9), (10), (11), (12), (13), (14),
% 230.52/41.87  |            (15), (16), (18), (19) are inconsistent by sub-proof #2223.
% 230.52/41.87  | 
% 230.52/41.87  End of proof
% 230.52/41.87  
% 230.52/41.87  Sub-proof #1186 shows that the following formulas are inconsistent:
% 230.52/41.87  ----------------------------------------------------------------
% 230.52/41.87    (1)   ~ (e3 = e1)
% 230.52/41.87    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.87           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.87    (3)   ~ (e3 = e2)
% 230.52/41.87    (4)   ~ (e3 = e0)
% 230.52/41.87    (5)  op(e3, e3) = e0
% 230.52/41.87    (6)   ~ (e2 = e0)
% 230.52/41.87    (7)   ~ (e1 = e0)
% 230.52/41.87    (8)  op(e0, e1) = all_52_29
% 230.52/41.87    (9)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.52/41.87             | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 230.52/41.87               e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.52/41.87               op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.52/41.87    (10)  op(all_52_29, all_52_29) = e1
% 230.52/41.87    (11)  all_57_11 = e3
% 230.52/41.87    (12)   ~ (e2 = e1)
% 230.52/41.87    (13)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.52/41.87          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.52/41.87    (14)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 230.52/41.87    (15)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.52/41.87          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.52/41.87  
% 230.52/41.87  Begin of proof
% 230.52/41.87  | 
% 230.52/41.87  | BETA: splitting (14) gives:
% 230.52/41.87  | 
% 230.52/41.87  | Case 1:
% 230.52/41.87  | | 
% 230.52/41.87  | |   (16)  all_57_14 = e3 & op(e0, e1) = e3
% 230.52/41.87  | | 
% 230.52/41.87  | | ALPHA: (16) implies:
% 230.52/41.87  | |   (17)  op(e0, e1) = e3
% 230.52/41.87  | | 
% 230.52/41.87  | | REF_CLOSE: (2), (5), (7), (8), (10), (17) are inconsistent by sub-proof
% 230.52/41.87  | |            #1934.
% 230.52/41.87  | | 
% 230.52/41.87  | Case 2:
% 230.52/41.87  | | 
% 230.52/41.87  | |   (18)  all_57_15 = e3 & op(e0, e0) = e3
% 230.52/41.87  | | 
% 230.52/41.87  | | ALPHA: (18) implies:
% 230.52/41.87  | |   (19)  all_57_15 = e3
% 230.52/41.87  | | 
% 230.52/41.87  | | REF_CLOSE: (1), (3), (4), (6), (7), (9), (11), (12), (13), (15), (19) are
% 230.52/41.87  | |            inconsistent by sub-proof #2134.
% 230.52/41.87  | | 
% 230.52/41.87  | End of split
% 230.52/41.87  | 
% 230.52/41.87  End of proof
% 230.52/41.87  
% 230.52/41.87  Sub-proof #1187 shows that the following formulas are inconsistent:
% 230.52/41.87  ----------------------------------------------------------------
% 230.52/41.87    (1)  all_57_4 = e3
% 230.52/41.87    (2)   ~ (e3 = e2)
% 230.52/41.87    (3)   ~ (e2 = e0)
% 230.52/41.87    (4)  all_57_14 = e1
% 230.52/41.87    (5)  all_57_5 = e1
% 230.52/41.87    (6)  all_57_8 = e0
% 230.52/41.87    (7)   ~ (e2 = e1)
% 230.52/41.87    (8)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.52/41.87         (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.52/41.87  
% 230.52/41.87  Begin of proof
% 230.52/41.87  | 
% 230.52/41.87  | BETA: splitting (8) gives:
% 230.52/41.87  | 
% 230.52/41.87  | Case 1:
% 230.52/41.87  | | 
% 230.52/41.87  | |   (9)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2)
% 230.52/41.87  | | 
% 230.52/41.87  | | REF_CLOSE: (1), (2), (5), (7), (9) are inconsistent by sub-proof #1232.
% 230.52/41.87  | | 
% 230.52/41.87  | Case 2:
% 230.52/41.87  | | 
% 230.52/41.87  | |   (10)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) =
% 230.52/41.87  | |           e2)
% 230.52/41.87  | | 
% 230.52/41.87  | | REF_CLOSE: (3), (4), (6), (7), (10) are inconsistent by sub-proof #1188.
% 230.52/41.87  | | 
% 230.52/41.87  | End of split
% 230.52/41.87  | 
% 230.52/41.87  End of proof
% 230.52/41.87  
% 230.52/41.87  Sub-proof #1188 shows that the following formulas are inconsistent:
% 230.52/41.87  ----------------------------------------------------------------
% 230.52/41.87    (1)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.52/41.87    (2)   ~ (e2 = e0)
% 230.52/41.87    (3)  all_57_14 = e1
% 230.52/41.87    (4)  all_57_8 = e0
% 230.52/41.87    (5)   ~ (e2 = e1)
% 230.52/41.87  
% 230.52/41.87  Begin of proof
% 230.52/41.87  | 
% 230.52/41.87  | BETA: splitting (1) gives:
% 230.52/41.87  | 
% 230.52/41.87  | Case 1:
% 230.52/41.87  | | 
% 230.52/41.87  | |   (6)  all_57_8 = e2 & op(e1, e1) = e2
% 230.52/41.87  | | 
% 230.52/41.87  | | ALPHA: (6) implies:
% 230.52/41.87  | |   (7)  all_57_8 = e2
% 230.52/41.87  | | 
% 230.52/41.87  | | REF_CLOSE: (2), (4), (7) are inconsistent by sub-proof #1957.
% 230.52/41.87  | | 
% 230.52/41.87  | Case 2:
% 230.52/41.87  | | 
% 230.52/41.87  | |   (8)  all_57_14 = e2 & op(e0, e1) = e2
% 230.52/41.87  | | 
% 230.52/41.87  | | ALPHA: (8) implies:
% 230.52/41.87  | |   (9)  all_57_14 = e2
% 230.52/41.87  | | 
% 230.52/41.87  | | REF_CLOSE: (3), (5), (9) are inconsistent by sub-proof #2178.
% 230.52/41.87  | | 
% 230.52/41.87  | End of split
% 230.52/41.87  | 
% 230.52/41.87  End of proof
% 230.52/41.87  
% 230.52/41.87  Sub-proof #1189 shows that the following formulas are inconsistent:
% 230.52/41.87  ----------------------------------------------------------------
% 230.52/41.87    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.87           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.87    (2)   ~ (all_34_1 = e2)
% 230.52/41.87    (3)  op(e1, e0) = all_34_1
% 230.52/41.87    (4)   ~ (e2 = e0)
% 230.52/41.87    (5)  all_57_8 = e0
% 230.52/41.87    (6)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.52/41.87  
% 230.52/41.87  Begin of proof
% 230.52/41.87  | 
% 230.52/41.87  | BETA: splitting (6) gives:
% 230.52/41.87  | 
% 230.52/41.87  | Case 1:
% 230.52/41.87  | | 
% 230.52/41.87  | |   (7)  all_57_8 = e2 & op(e1, e1) = e2
% 230.52/41.87  | | 
% 230.52/41.87  | | REF_CLOSE: (4), (5), (7) are inconsistent by sub-proof #2005.
% 230.52/41.87  | | 
% 230.52/41.87  | Case 2:
% 230.52/41.87  | | 
% 230.52/41.87  | |   (8)  all_57_11 = e2 & op(e1, e0) = e2
% 230.52/41.87  | | 
% 230.52/41.87  | | ALPHA: (8) implies:
% 230.52/41.87  | |   (9)  op(e1, e0) = e2
% 230.52/41.87  | | 
% 230.52/41.87  | | REF_CLOSE: (1), (2), (3), (9) are inconsistent by sub-proof #1190.
% 230.52/41.87  | | 
% 230.52/41.87  | End of split
% 230.52/41.87  | 
% 230.52/41.87  End of proof
% 230.52/41.87  
% 230.52/41.87  Sub-proof #1190 shows that the following formulas are inconsistent:
% 230.52/41.87  ----------------------------------------------------------------
% 230.52/41.87    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.87           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.87    (2)  op(e1, e0) = all_34_1
% 230.52/41.87    (3)  op(e1, e0) = e2
% 230.52/41.87    (4)   ~ (all_34_1 = e2)
% 230.52/41.87  
% 230.52/41.87  Begin of proof
% 230.52/41.87  | 
% 230.52/41.87  | GROUND_INST: instantiating (1) with e2, all_34_1, e0, e1, simplifying with
% 230.52/41.87  |              (2), (3) gives:
% 230.52/41.87  |   (5)  all_34_1 = e2
% 230.52/41.87  | 
% 230.52/41.87  | REDUCE: (4), (5) imply:
% 230.52/41.87  |   (6)  $false
% 230.52/41.87  | 
% 230.52/41.87  | CLOSE: (6) is inconsistent.
% 230.52/41.87  | 
% 230.52/41.87  End of proof
% 230.52/41.87  
% 230.52/41.87  Sub-proof #1191 shows that the following formulas are inconsistent:
% 230.52/41.87  ----------------------------------------------------------------
% 230.52/41.87    (1)   ~ (all_52_29 = e0)
% 230.52/41.87    (2)   ~ (all_52_29 = e2)
% 230.52/41.87    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.87           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.87    (4)  all_55_14 = all_52_29
% 230.52/41.87    (5)  op(e3, e3) = e0
% 230.52/41.87    (6)   ~ (all_52_29 = e1)
% 230.52/41.87    (7)   ~ (e1 = e0)
% 230.52/41.87    (8)  op(e0, e1) = all_52_29
% 230.52/41.87    (9)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 230.52/41.87    (10)  op(all_52_29, all_52_29) = e1
% 230.52/41.87  
% 230.52/41.87  Begin of proof
% 230.52/41.87  | 
% 230.52/41.87  | SIMP: (2) implies:
% 230.52/41.87  |   (11)   ~ (all_52_29 = e2)
% 230.52/41.87  | 
% 230.52/41.87  | BETA: splitting (9) gives:
% 230.52/41.87  | 
% 230.52/41.87  | Case 1:
% 230.52/41.87  | | 
% 230.52/41.87  | |   (12)  all_55_14 = e3
% 230.52/41.87  | | 
% 230.52/41.87  | | COMBINE_EQS: (4), (12) imply:
% 230.52/41.87  | |   (13)  all_52_29 = e3
% 230.52/41.87  | | 
% 230.52/41.87  | | SIMP: (13) implies:
% 230.52/41.87  | |   (14)  all_52_29 = e3
% 230.52/41.87  | | 
% 230.52/41.87  | | REDUCE: (8), (14) imply:
% 230.52/41.87  | |   (15)  op(e0, e1) = e3
% 230.52/41.87  | | 
% 230.52/41.87  | | REF_CLOSE: (3), (5), (7), (8), (10), (15) are inconsistent by sub-proof
% 230.52/41.87  | |            #1934.
% 230.52/41.87  | | 
% 230.52/41.87  | Case 2:
% 230.52/41.87  | | 
% 230.52/41.87  | |   (16)  all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 230.52/41.87  | | 
% 230.52/41.87  | | REF_CLOSE: (1), (4), (6), (11), (16) are inconsistent by sub-proof #2034.
% 230.52/41.87  | | 
% 230.52/41.87  | End of split
% 230.52/41.87  | 
% 230.52/41.87  End of proof
% 230.52/41.87  
% 230.52/41.87  Sub-proof #1192 shows that the following formulas are inconsistent:
% 230.52/41.87  ----------------------------------------------------------------
% 230.52/41.87    (1)  all_57_9 = e3
% 230.52/41.87    (2)  all_57_9 = e2
% 230.52/41.87    (3)   ~ (e3 = e2)
% 230.52/41.87  
% 230.52/41.87  Begin of proof
% 230.52/41.87  | 
% 230.52/41.87  | COMBINE_EQS: (1), (2) imply:
% 230.52/41.87  |   (4)  e3 = e2
% 230.52/41.87  | 
% 230.52/41.87  | SIMP: (4) implies:
% 230.52/41.87  |   (5)  e3 = e2
% 230.52/41.87  | 
% 230.52/41.87  | REDUCE: (3), (5) imply:
% 230.52/41.87  |   (6)  $false
% 230.52/41.87  | 
% 230.52/41.87  | CLOSE: (6) is inconsistent.
% 230.52/41.87  | 
% 230.52/41.87  End of proof
% 230.52/41.87  
% 230.52/41.87  Sub-proof #1193 shows that the following formulas are inconsistent:
% 230.52/41.87  ----------------------------------------------------------------
% 230.52/41.87    (1)  all_57_13 = e1
% 230.52/41.87    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.52/41.87         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.52/41.87    (3)   ~ (e3 = e1)
% 230.52/41.87    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.87           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.87    (5)  op(e2, e2) = e0
% 230.52/41.87    (6)  all_57_3 = e0
% 230.52/41.87    (7)   ~ (e3 = e2)
% 230.52/41.87    (8)   ~ (e3 = e0)
% 230.52/41.87    (9)  all_57_1 = e1
% 230.52/41.87    (10)   ~ (e2 = e0)
% 230.52/41.87    (11)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.52/41.87          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.52/41.87    (12)   ~ (e2 = e1)
% 230.52/41.87  
% 230.52/41.87  Begin of proof
% 230.52/41.87  | 
% 230.52/41.87  | BETA: splitting (2) gives:
% 230.52/41.87  | 
% 230.52/41.87  | Case 1:
% 230.52/41.87  | | 
% 230.52/41.87  | |   (13)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 230.52/41.87  | |           e2)
% 230.52/41.87  | | 
% 230.52/41.87  | | REF_CLOSE: (4), (5), (9), (10), (12), (13) are inconsistent by sub-proof
% 230.52/41.87  | |            #2208.
% 230.52/41.87  | | 
% 230.52/41.87  | Case 2:
% 230.52/41.87  | | 
% 230.52/41.87  | |   (14)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 230.52/41.87  | |           e2)
% 230.52/41.87  | | 
% 230.52/41.87  | | BETA: splitting (14) gives:
% 230.52/41.87  | | 
% 230.52/41.87  | | Case 1:
% 230.52/41.87  | | | 
% 230.52/41.87  | | |   (15)  all_57_7 = e2 & op(e1, e2) = e2
% 230.52/41.87  | | | 
% 230.52/41.87  | | | ALPHA: (15) implies:
% 230.52/41.87  | | |   (16)  all_57_7 = e2
% 230.52/41.87  | | | 
% 230.52/41.87  | | | REF_CLOSE: (1), (3), (6), (7), (8), (9), (11), (16) are inconsistent by
% 230.52/41.87  | | |            sub-proof #2193.
% 230.52/41.87  | | | 
% 230.52/41.87  | | Case 2:
% 230.52/41.87  | | | 
% 230.52/41.87  | | |   (17)  all_57_13 = e2 & op(e0, e2) = e2
% 230.52/41.87  | | | 
% 230.52/41.87  | | | ALPHA: (17) implies:
% 230.52/41.87  | | |   (18)  all_57_13 = e2
% 230.52/41.87  | | | 
% 230.52/41.87  | | | REF_CLOSE: (1), (12), (18) are inconsistent by sub-proof #2327.
% 230.52/41.87  | | | 
% 230.52/41.87  | | End of split
% 230.52/41.87  | | 
% 230.52/41.87  | End of split
% 230.52/41.87  | 
% 230.52/41.87  End of proof
% 230.52/41.87  
% 230.52/41.87  Sub-proof #1194 shows that the following formulas are inconsistent:
% 230.52/41.87  ----------------------------------------------------------------
% 230.52/41.87    (1)  all_57_9 = e2
% 230.52/41.87    (2)   ~ (e3 = e1)
% 230.52/41.87    (3)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.52/41.87    (4)  all_57_4 = e3
% 230.52/41.87    (5)   ~ (e2 = e1)
% 230.52/41.87  
% 230.52/41.87  Begin of proof
% 230.52/41.87  | 
% 230.52/41.87  | BETA: splitting (3) gives:
% 230.52/41.87  | 
% 230.52/41.87  | Case 1:
% 230.52/41.87  | | 
% 230.52/41.87  | |   (6)  all_57_4 = e1 & op(e3, e1) = e1
% 230.52/41.87  | | 
% 230.52/41.87  | | ALPHA: (6) implies:
% 230.52/41.87  | |   (7)  all_57_4 = e1
% 230.52/41.87  | | 
% 230.52/41.87  | | REF_CLOSE: (2), (4), (7) are inconsistent by sub-proof #2426.
% 230.52/41.87  | | 
% 230.52/41.87  | Case 2:
% 230.52/41.87  | | 
% 230.52/41.87  | |   (8)  all_57_9 = e1 & op(e3, e0) = e1
% 230.52/41.87  | | 
% 230.52/41.87  | | ALPHA: (8) implies:
% 230.52/41.87  | |   (9)  all_57_9 = e1
% 230.52/41.87  | | 
% 230.52/41.87  | | REF_CLOSE: (1), (5), (9) are inconsistent by sub-proof #2444.
% 230.52/41.87  | | 
% 230.52/41.87  | End of split
% 230.52/41.87  | 
% 230.52/41.87  End of proof
% 230.52/41.87  
% 230.52/41.87  Sub-proof #1195 shows that the following formulas are inconsistent:
% 230.52/41.87  ----------------------------------------------------------------
% 230.52/41.87    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.87           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.87    (2)   ~ (e3 = e2)
% 230.52/41.87    (3)  op(e3, e3) = e0
% 230.52/41.87    (4)   ~ (e2 = e0)
% 230.52/41.87    (5)  op(e3, e2) = e3
% 230.52/41.87    (6)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2)
% 230.52/41.87  
% 230.52/41.87  Begin of proof
% 230.52/41.87  | 
% 230.52/41.87  | BETA: splitting (6) gives:
% 230.52/41.87  | 
% 230.52/41.87  | Case 1:
% 230.52/41.87  | | 
% 230.52/41.87  | |   (7)  all_57_0 = e2 & op(e3, e3) = e2
% 230.52/41.87  | | 
% 230.52/41.87  | | ALPHA: (7) implies:
% 230.52/41.87  | |   (8)  op(e3, e3) = e2
% 230.52/41.87  | | 
% 230.52/41.87  | | REF_CLOSE: (1), (3), (4), (8) are inconsistent by sub-proof #2403.
% 230.52/41.87  | | 
% 230.52/41.87  | Case 2:
% 230.52/41.87  | | 
% 230.52/41.87  | |   (9)  all_57_1 = e2 & op(e3, e2) = e2
% 230.52/41.87  | | 
% 230.52/41.87  | | ALPHA: (9) implies:
% 230.52/41.87  | |   (10)  op(e3, e2) = e2
% 230.52/41.87  | | 
% 230.52/41.87  | | REF_CLOSE: (1), (2), (5), (10) are inconsistent by sub-proof #1549.
% 230.52/41.87  | | 
% 230.52/41.87  | End of split
% 230.52/41.87  | 
% 230.52/41.87  End of proof
% 230.52/41.87  
% 230.52/41.87  Sub-proof #1196 shows that the following formulas are inconsistent:
% 230.52/41.87  ----------------------------------------------------------------
% 230.52/41.87    (1)  all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 230.52/41.87    (2)  ( ~ (all_48_0 = e2) & op(all_48_1, e3) = all_48_0 & op(e3, e0) = all_48_1
% 230.52/41.87           & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 = e1) & op(e3, e0) =
% 230.52/41.87           all_48_1 & $i(all_48_1))
% 230.52/41.87    (3)   ~ (all_52_29 = e0)
% 230.52/41.87    (4)   ~ (all_14_0 = e1)
% 230.52/41.87    (5)  all_57_15 = e0
% 230.52/41.87    (6)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.52/41.87         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.52/41.87    (7)   ~ (all_53_8 = all_52_29)
% 230.52/41.87    (8)   ~ (all_52_27 = all_52_29)
% 230.52/41.87    (9)   ~ (all_53_6 = e0)
% 230.52/41.87    (10)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.52/41.87          (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.52/41.87    (11)   ~ (all_53_8 = all_53_12)
% 230.52/41.87    (12)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.52/41.87          (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.52/41.87    (13)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.52/41.87          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.52/41.87    (14)  op(all_14_1, e2) = all_14_0
% 230.52/41.87    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.87            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.87    (16)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.52/41.87          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.52/41.87    (17)  op(e2, e0) = e3
% 230.52/41.87    (18)   ~ (all_53_6 = all_14_0)
% 230.52/41.87    (19)   ~ (all_6_2 = e3)
% 230.52/41.87    (20)  ( ~ (all_18_0 = e1) & op(all_18_1, e3) = all_18_0 & op(e3, e0) =
% 230.52/41.87            all_18_1 & $i(all_18_0) & $i(all_18_1)) | ( ~ (all_18_1 = e2) & op(e3,
% 230.52/41.87              e0) = all_18_1 & $i(all_18_1))
% 230.52/41.87    (21)  op(e1, e1) = all_6_2
% 230.52/41.87    (22)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 230.52/41.87    (23)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.52/41.87          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.52/41.87    (24)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 230.52/41.87    (25)  all_55_9 = all_53_6
% 230.52/41.87    (26)   ~ (all_53_8 = all_14_0)
% 230.52/41.87    (27)   ~ (all_53_12 = all_14_0)
% 230.52/41.87    (28)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.52/41.87          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.52/41.87    (29)  op(e2, e2) = e0
% 230.52/41.87    (30)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.52/41.87          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.52/41.87    (31)  all_57_3 = e0
% 230.52/41.87    (32)  all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 230.52/41.87    (33)   ~ (all_14_0 = e3)
% 230.52/41.87    (34)  op(e1, e0) = all_53_14
% 230.52/41.87    (35)   ~ (e3 = e0)
% 230.52/41.87    (36)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.52/41.87          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.52/41.87    (37)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 230.52/41.87    (38)   ~ (all_53_2 = e0)
% 230.52/41.87    (39)  all_57_0 = e0
% 230.52/41.87    (40)  all_55_2 = all_53_8
% 230.52/41.87    (41)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 230.52/41.87    (42)  all_55_14 = all_52_29
% 230.52/41.87    (43)  op(e3, e3) = e0
% 230.52/41.87    (44)   ~ (all_52_27 = all_14_0)
% 230.52/41.87    (45)   ~ (all_53_14 = e3)
% 230.52/41.87    (46)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.52/41.87          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.52/41.87    (47)  all_55_13 = all_52_27
% 230.52/41.87    (48)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.52/41.87          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.52/41.87    (49)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 230.52/41.87          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 230.52/41.87    (50)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.52/41.87          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.52/41.87    (51)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 230.52/41.87    (52)  op(e0, e0) = e0
% 230.52/41.87    (53)  op(e2, e0) = all_14_1
% 230.52/41.87    (54)  all_55_8 = all_53_2
% 230.52/41.87    (55)   ~ (all_14_0 = e0)
% 230.52/41.87    (56)  all_57_10 = e3
% 230.52/41.87    (57)  op(e3, e2) = all_14_0
% 230.52/41.87    (58)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.52/41.87          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.52/41.87            e2)
% 230.52/41.87    (59)  all_55_1 = all_14_0
% 230.52/41.87    (60)  op(e1, e1) = e0
% 230.52/41.87    (61)  op(all_52_29, all_52_29) = e1
% 230.52/41.87    (62)   ~ (all_52_27 = e0)
% 230.52/41.87    (63)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.52/41.87          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.52/41.87    (64)  all_55_3 = all_53_12
% 230.52/41.87    (65)   ~ (all_53_12 = e3)
% 230.52/41.87    (66)  op(e1, e3) = all_53_2
% 230.52/41.87    (67)  all_57_8 = e0
% 230.52/41.87    (68)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.52/41.87          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.52/41.88    (69)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.52/41.88          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.52/41.88    (70)   ~ (all_53_12 = e0)
% 230.52/41.88    (71)   ~ (all_53_8 = e0)
% 230.52/41.88    (72)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.52/41.88          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.52/41.88    (73)   ~ (all_53_2 = all_53_6)
% 230.52/41.88    (74)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.52/41.88          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.52/41.88    (75)  op(e2, e0) = all_50_1
% 230.52/41.88    (76)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.52/41.88          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.52/41.88    (77)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.52/41.88          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.52/41.88    (78)  op(all_52_27, all_52_27) = e2
% 230.52/41.88    (79)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.52/41.88          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.52/41.88    (80)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.52/41.88          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.52/41.88    (81)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.52/41.88          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.52/41.88    (82)   ~ (all_53_6 = all_52_27)
% 230.52/41.88    (83)  op(e3, e0) = all_53_12
% 230.52/41.88  
% 230.52/41.88  Begin of proof
% 230.52/41.88  | 
% 230.52/41.88  | BETA: splitting (32) gives:
% 230.52/41.88  | 
% 230.52/41.88  | Case 1:
% 230.52/41.88  | | 
% 230.52/41.88  | |   (84)  all_55_1 = e2
% 230.52/41.88  | | 
% 230.52/41.88  | | COMBINE_EQS: (59), (84) imply:
% 230.52/41.88  | |   (85)  all_14_0 = e2
% 230.52/41.88  | | 
% 230.52/41.88  | | SIMP: (85) implies:
% 230.52/41.88  | |   (86)  all_14_0 = e2
% 230.52/41.88  | | 
% 230.52/41.88  | | REDUCE: (18), (86) imply:
% 230.52/41.88  | |   (87)   ~ (all_53_6 = e2)
% 230.52/41.88  | | 
% 230.52/41.88  | | REDUCE: (26), (86) imply:
% 230.52/41.88  | |   (88)   ~ (all_53_8 = e2)
% 230.52/41.88  | | 
% 230.52/41.88  | | REDUCE: (27), (86) imply:
% 230.52/41.88  | |   (89)   ~ (all_53_12 = e2)
% 230.52/41.88  | | 
% 230.52/41.88  | | REDUCE: (44), (86) imply:
% 230.52/41.88  | |   (90)   ~ (all_52_27 = e2)
% 230.52/41.88  | | 
% 230.52/41.88  | | REDUCE: (33), (86) imply:
% 230.52/41.88  | |   (91)   ~ (e3 = e2)
% 230.52/41.88  | | 
% 230.52/41.88  | | SIMP: (91) implies:
% 230.52/41.88  | |   (92)   ~ (e3 = e2)
% 230.52/41.88  | | 
% 230.52/41.88  | | REDUCE: (55), (86) imply:
% 230.52/41.88  | |   (93)   ~ (e2 = e0)
% 230.52/41.88  | | 
% 230.52/41.88  | | REDUCE: (57), (86) imply:
% 230.52/41.88  | |   (94)  op(e3, e2) = e2
% 230.52/41.88  | | 
% 230.52/41.88  | | BETA: splitting (22) gives:
% 230.52/41.88  | | 
% 230.52/41.88  | | Case 1:
% 230.52/41.88  | | | 
% 230.52/41.88  | | |   (95)  all_55_3 = e3
% 230.52/41.88  | | | 
% 230.52/41.88  | | | COMBINE_EQS: (64), (95) imply:
% 230.52/41.88  | | |   (96)  all_53_12 = e3
% 230.52/41.88  | | | 
% 230.52/41.88  | | | REDUCE: (65), (96) imply:
% 230.52/41.88  | | |   (97)  $false
% 230.52/41.88  | | | 
% 230.52/41.88  | | | CLOSE: (97) is inconsistent.
% 230.52/41.88  | | | 
% 230.52/41.88  | | Case 2:
% 230.52/41.88  | | | 
% 230.52/41.88  | | |   (98)   ~ (all_55_3 = e3)
% 230.52/41.88  | | |   (99)  all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 230.52/41.88  | | | 
% 230.52/41.88  | | | BETA: splitting (99) gives:
% 230.52/41.88  | | | 
% 230.52/41.88  | | | Case 1:
% 230.52/41.88  | | | | 
% 230.52/41.88  | | | |   (100)  all_55_3 = e2
% 230.52/41.88  | | | | 
% 230.52/41.88  | | | | COMBINE_EQS: (64), (100) imply:
% 230.52/41.88  | | | |   (101)  all_53_12 = e2
% 230.52/41.88  | | | | 
% 230.52/41.88  | | | | REDUCE: (89), (101) imply:
% 230.52/41.88  | | | |   (102)  $false
% 230.52/41.88  | | | | 
% 230.52/41.88  | | | | CLOSE: (102) is inconsistent.
% 230.52/41.88  | | | | 
% 230.52/41.88  | | | Case 2:
% 230.52/41.88  | | | | 
% 230.52/41.88  | | | |   (103)   ~ (all_55_3 = e2)
% 230.52/41.88  | | | |   (104)  all_55_3 = e1 | all_55_3 = e0
% 230.52/41.88  | | | | 
% 230.52/41.88  | | | | BETA: splitting (104) gives:
% 230.52/41.88  | | | | 
% 230.52/41.88  | | | | Case 1:
% 230.52/41.88  | | | | | 
% 230.52/41.88  | | | | |   (105)  all_55_3 = e1
% 230.52/41.88  | | | | | 
% 230.52/41.88  | | | | | COMBINE_EQS: (64), (105) imply:
% 230.52/41.88  | | | | |   (106)  all_53_12 = e1
% 230.52/41.88  | | | | | 
% 230.52/41.88  | | | | | REDUCE: (11), (106) imply:
% 230.52/41.88  | | | | |   (107)   ~ (all_53_8 = e1)
% 230.52/41.88  | | | | | 
% 230.52/41.88  | | | | | REDUCE: (65), (106) imply:
% 230.52/41.88  | | | | |   (108)   ~ (e3 = e1)
% 230.52/41.88  | | | | | 
% 230.52/41.88  | | | | | SIMP: (108) implies:
% 230.52/41.88  | | | | |   (109)   ~ (e3 = e1)
% 230.52/41.88  | | | | | 
% 230.52/41.88  | | | | | REDUCE: (89), (106) imply:
% 230.52/41.88  | | | | |   (110)   ~ (e2 = e1)
% 230.52/41.88  | | | | | 
% 230.52/41.88  | | | | | SIMP: (110) implies:
% 230.52/41.88  | | | | |   (111)   ~ (e2 = e1)
% 230.52/41.88  | | | | | 
% 230.52/41.88  | | | | | REDUCE: (70), (106) imply:
% 230.52/41.88  | | | | |   (112)   ~ (e1 = e0)
% 230.52/41.88  | | | | | 
% 230.52/41.88  | | | | | BETA: splitting (77) gives:
% 230.52/41.88  | | | | | 
% 230.52/41.88  | | | | | Case 1:
% 230.52/41.88  | | | | | | 
% 230.52/41.88  | | | | | |   (113)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 &
% 230.52/41.88  | | | | | |            op(e2, e0) = e1)
% 230.52/41.88  | | | | | | 
% 230.52/41.88  | | | | | | BETA: splitting (113) gives:
% 230.52/41.88  | | | | | | 
% 230.52/41.88  | | | | | | Case 1:
% 230.52/41.88  | | | | | | | 
% 230.52/41.88  | | | | | | |   (114)  all_57_9 = e1 & op(e3, e0) = e1
% 230.52/41.88  | | | | | | | 
% 230.52/41.88  | | | | | | | ALPHA: (114) implies:
% 230.52/41.88  | | | | | | |   (115)  all_57_9 = e1
% 230.52/41.88  | | | | | | |   (116)  op(e3, e0) = e1
% 230.52/41.88  | | | | | | | 
% 230.52/41.88  | | | | | | | BETA: splitting (20) gives:
% 230.52/41.88  | | | | | | | 
% 230.52/41.88  | | | | | | | Case 1:
% 230.52/41.88  | | | | | | | | 
% 230.52/41.88  | | | | | | | |   (117)   ~ (all_18_0 = e1) & op(all_18_1, e3) = all_18_0 &
% 230.52/41.88  | | | | | | | |          op(e3, e0) = all_18_1 & $i(all_18_0) & $i(all_18_1)
% 230.52/41.88  | | | | | | | | 
% 230.52/41.88  | | | | | | | | ALPHA: (117) implies:
% 230.52/41.88  | | | | | | | |   (118)   ~ (all_18_0 = e1)
% 230.52/41.88  | | | | | | | |   (119)  op(e3, e0) = all_18_1
% 230.52/41.88  | | | | | | | |   (120)  op(all_18_1, e3) = all_18_0
% 230.52/41.88  | | | | | | | | 
% 230.52/41.88  | | | | | | | | BETA: splitting (48) gives:
% 230.52/41.88  | | | | | | | | 
% 230.52/41.88  | | | | | | | | Case 1:
% 230.52/41.88  | | | | | | | | | 
% 230.52/41.88  | | | | | | | | |   (121)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 &
% 230.52/41.88  | | | | | | | | |            op(e3, e2) = e3)
% 230.52/41.88  | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | REF_CLOSE: (4), (5), (6), (10), (12), (13), (14), (15), (16),
% 230.52/41.88  | | | | | | | | |            (17), (19), (21), (23), (28), (29), (30), (31),
% 230.52/41.88  | | | | | | | | |            (34), (35), (36), (39), (43), (45), (46), (49),
% 230.52/41.88  | | | | | | | | |            (50), (53), (56), (58), (60), (63), (68), (69),
% 230.52/41.88  | | | | | | | | |            (72), (74), (75), (76), (80), (83), (89), (92),
% 230.52/41.88  | | | | | | | | |            (93), (94), (109), (111), (112), (121) are
% 230.52/41.88  | | | | | | | | |            inconsistent by sub-proof #1210.
% 230.52/41.88  | | | | | | | | | 
% 230.52/41.88  | | | | | | | | Case 2:
% 230.52/41.88  | | | | | | | | | 
% 230.52/41.88  | | | | | | | | |   (122)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 &
% 230.52/41.88  | | | | | | | | |            op(e3, e0) = e3)
% 230.52/41.88  | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | BETA: splitting (122) gives:
% 230.52/41.88  | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | Case 1:
% 230.52/41.88  | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | |   (123)  all_57_4 = e3 & op(e3, e1) = e3
% 230.52/41.88  | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | ALPHA: (123) implies:
% 230.52/41.88  | | | | | | | | | |   (124)  all_57_4 = e3
% 230.52/41.88  | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | BETA: splitting (2) gives:
% 230.52/41.88  | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | Case 1:
% 230.52/41.88  | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | |   (125)   ~ (all_48_0 = e2) & op(all_48_1, e3) = all_48_0 &
% 230.52/41.88  | | | | | | | | | | |          op(e3, e0) = all_48_1 & $i(all_48_0) &
% 230.52/41.88  | | | | | | | | | | |          $i(all_48_1)
% 230.52/41.88  | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | ALPHA: (125) implies:
% 230.52/41.88  | | | | | | | | | | |   (126)   ~ (all_48_0 = e2)
% 230.52/41.88  | | | | | | | | | | |   (127)  op(e3, e0) = all_48_1
% 230.52/41.88  | | | | | | | | | | |   (128)  op(all_48_1, e3) = all_48_0
% 230.52/41.88  | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | BETA: splitting (28) gives:
% 230.52/41.88  | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | Case 1:
% 230.52/41.88  | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | |   (129)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 230.52/41.88  | | | | | | | | | | | |            & op(e3, e2) = e2)
% 230.52/41.88  | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | BETA: splitting (129) gives:
% 230.52/41.88  | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | Case 1:
% 230.52/41.88  | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | |   (130)  all_57_0 = e2 & op(e3, e3) = e2
% 230.52/41.88  | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | ALPHA: (130) implies:
% 230.52/41.88  | | | | | | | | | | | | |   (131)  op(e3, e3) = e2
% 230.52/41.88  | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | REF_CLOSE: (15), (43), (93), (131) are inconsistent by
% 230.52/41.88  | | | | | | | | | | | | |            sub-proof #2403.
% 230.52/41.88  | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | Case 2:
% 230.52/41.88  | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | |   (132)  all_57_1 = e2 & op(e3, e2) = e2
% 230.52/41.88  | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | ALPHA: (132) implies:
% 230.52/41.88  | | | | | | | | | | | | |   (133)  all_57_1 = e2
% 230.52/41.88  | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | GROUND_INST: instantiating (15) with all_18_1, all_48_1, e0,
% 230.52/41.88  | | | | | | | | | | | | |              e3, simplifying with (119), (127) gives:
% 230.52/41.88  | | | | | | | | | | | | |   (134)  all_48_1 = all_18_1
% 230.52/41.88  | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | GROUND_INST: instantiating (15) with e1, all_48_1, e0, e3,
% 230.52/41.88  | | | | | | | | | | | | |              simplifying with (116), (127) gives:
% 230.52/41.88  | | | | | | | | | | | | |   (135)  all_48_1 = e1
% 230.52/41.88  | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | COMBINE_EQS: (134), (135) imply:
% 230.52/41.88  | | | | | | | | | | | | |   (136)  all_18_1 = e1
% 230.52/41.88  | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | REDUCE: (128), (135) imply:
% 230.52/41.88  | | | | | | | | | | | | |   (137)  op(e1, e3) = all_48_0
% 230.52/41.88  | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | REDUCE: (120), (136) imply:
% 230.52/41.88  | | | | | | | | | | | | |   (138)  op(e1, e3) = all_18_0
% 230.52/41.88  | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | GROUND_INST: instantiating (15) with all_53_2, all_18_0, e3,
% 230.52/41.88  | | | | | | | | | | | | |              e1, simplifying with (66), (138) gives:
% 230.52/41.88  | | | | | | | | | | | | |   (139)  all_53_2 = all_18_0
% 230.52/41.88  | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | GROUND_INST: instantiating (15) with all_53_2, all_48_0, e3,
% 230.52/41.88  | | | | | | | | | | | | |              e1, simplifying with (66), (137) gives:
% 230.52/41.88  | | | | | | | | | | | | |   (140)  all_53_2 = all_48_0
% 230.52/41.88  | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | COMBINE_EQS: (139), (140) imply:
% 230.52/41.88  | | | | | | | | | | | | |   (141)  all_48_0 = all_18_0
% 230.52/41.88  | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | SIMP: (141) implies:
% 230.52/41.88  | | | | | | | | | | | | |   (142)  all_48_0 = all_18_0
% 230.52/41.88  | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | COMBINE_EQS: (54), (139) imply:
% 230.52/41.88  | | | | | | | | | | | | |   (143)  all_55_8 = all_18_0
% 230.52/41.88  | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | REDUCE: (73), (139) imply:
% 230.52/41.88  | | | | | | | | | | | | |   (144)   ~ (all_53_6 = all_18_0)
% 230.52/41.88  | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | SIMP: (144) implies:
% 230.52/41.88  | | | | | | | | | | | | |   (145)   ~ (all_53_6 = all_18_0)
% 230.52/41.88  | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | REDUCE: (38), (139) imply:
% 230.52/41.88  | | | | | | | | | | | | |   (146)   ~ (all_18_0 = e0)
% 230.52/41.88  | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | REDUCE: (126), (142) imply:
% 230.52/41.88  | | | | | | | | | | | | |   (147)   ~ (all_18_0 = e2)
% 230.52/41.88  | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | BETA: splitting (37) gives:
% 230.52/41.88  | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | Case 1:
% 230.52/41.88  | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | |   (148)  all_55_8 = e3
% 230.52/41.88  | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | COMBINE_EQS: (143), (148) imply:
% 230.52/41.88  | | | | | | | | | | | | | |   (149)  all_18_0 = e3
% 230.52/41.88  | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | REDUCE: (145), (149) imply:
% 230.52/41.88  | | | | | | | | | | | | | |   (150)   ~ (all_53_6 = e3)
% 230.52/41.88  | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | BETA: splitting (24) gives:
% 230.52/41.88  | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | Case 1:
% 230.52/41.88  | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | |   (151)  all_55_9 = e3
% 230.52/41.88  | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | COMBINE_EQS: (25), (151) imply:
% 230.52/41.88  | | | | | | | | | | | | | | |   (152)  all_53_6 = e3
% 230.52/41.88  | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | REDUCE: (150), (152) imply:
% 230.52/41.88  | | | | | | | | | | | | | | |   (153)  $false
% 230.52/41.88  | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | CLOSE: (153) is inconsistent.
% 230.52/41.88  | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | Case 2:
% 230.52/41.88  | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | |   (154)  all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 230.52/41.88  | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | BETA: splitting (154) gives:
% 230.52/41.88  | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | Case 1:
% 230.52/41.88  | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | |   (155)  all_55_9 = e2
% 230.52/41.88  | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | REF_CLOSE: (25), (87), (155) are inconsistent by sub-proof
% 230.52/41.88  | | | | | | | | | | | | | | | |            #2274.
% 230.52/41.88  | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | Case 2:
% 230.52/41.88  | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | |   (156)   ~ (all_55_9 = e2)
% 230.52/41.88  | | | | | | | | | | | | | | | |   (157)  all_55_9 = e1 | all_55_9 = e0
% 230.52/41.88  | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | BETA: splitting (157) gives:
% 230.52/41.88  | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | Case 1:
% 230.52/41.88  | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | |   (158)  all_55_9 = e1
% 230.52/41.88  | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | COMBINE_EQS: (25), (158) imply:
% 230.52/41.88  | | | | | | | | | | | | | | | | |   (159)  all_53_6 = e1
% 230.52/41.88  | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | SIMP: (159) implies:
% 230.52/41.88  | | | | | | | | | | | | | | | | |   (160)  all_53_6 = e1
% 230.52/41.88  | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | REDUCE: (82), (160) imply:
% 230.52/41.88  | | | | | | | | | | | | | | | | |   (161)   ~ (all_52_27 = e1)
% 230.52/41.88  | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | SIMP: (161) implies:
% 230.52/41.88  | | | | | | | | | | | | | | | | |   (162)   ~ (all_52_27 = e1)
% 230.52/41.88  | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | BETA: splitting (1) gives:
% 230.52/41.88  | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | Case 1:
% 230.52/41.88  | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | |   (163)  all_55_13 = e3
% 230.52/41.88  | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (47), (163) imply:
% 230.52/41.88  | | | | | | | | | | | | | | | | | |   (164)  all_52_27 = e3
% 230.52/41.88  | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | SIMP: (164) implies:
% 230.52/41.88  | | | | | | | | | | | | | | | | | |   (165)  all_52_27 = e3
% 230.52/41.88  | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | REDUCE: (78), (165) imply:
% 230.52/41.88  | | | | | | | | | | | | | | | | | |   (166)  op(e3, e3) = e2
% 230.52/41.88  | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (23), (30), (35), (93), (109), (111), (112),
% 230.52/41.88  | | | | | | | | | | | | | | | | | |            (124), (133), (166) are inconsistent by sub-proof
% 230.52/41.88  | | | | | | | | | | | | | | | | | |            #1659.
% 230.52/41.88  | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | Case 2:
% 230.52/41.88  | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | |   (167)  all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 230.52/41.88  | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (29), (47), (62), (78), (162), (167) are
% 230.52/41.88  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1614.
% 230.52/41.88  | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | End of split
% 230.52/41.88  | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | Case 2:
% 230.52/41.88  | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | |   (168)  all_55_9 = e0
% 230.52/41.88  | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (25), (168) are inconsistent by sub-proof
% 230.52/41.88  | | | | | | | | | | | | | | | | |            #2272.
% 230.52/41.88  | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | End of split
% 230.52/41.88  | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | End of split
% 230.52/41.88  | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | End of split
% 230.52/41.88  | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | Case 2:
% 230.52/41.88  | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | |   (169)  all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 230.52/41.88  | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | BETA: splitting (169) gives:
% 230.52/41.88  | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | Case 1:
% 230.52/41.88  | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | |   (170)  all_55_8 = e2
% 230.52/41.88  | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | REF_CLOSE: (143), (147), (170) are inconsistent by sub-proof
% 230.52/41.88  | | | | | | | | | | | | | | |            #1209.
% 230.52/41.88  | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | Case 2:
% 230.52/41.88  | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | |   (171)  all_55_8 = e1 | all_55_8 = e0
% 230.52/41.88  | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | BETA: splitting (171) gives:
% 230.52/41.88  | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | Case 1:
% 230.52/41.88  | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | |   (172)  all_55_8 = e1
% 230.52/41.88  | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | COMBINE_EQS: (143), (172) imply:
% 230.52/41.88  | | | | | | | | | | | | | | | |   (173)  all_18_0 = e1
% 230.52/41.88  | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | SIMP: (173) implies:
% 230.52/41.88  | | | | | | | | | | | | | | | |   (174)  all_18_0 = e1
% 230.52/41.88  | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | REDUCE: (118), (174) imply:
% 230.52/41.88  | | | | | | | | | | | | | | | |   (175)  $false
% 230.52/41.88  | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | CLOSE: (175) is inconsistent.
% 230.52/41.88  | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | Case 2:
% 230.52/41.88  | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | |   (176)  all_55_8 = e0
% 230.52/41.88  | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | COMBINE_EQS: (143), (176) imply:
% 230.52/41.88  | | | | | | | | | | | | | | | |   (177)  all_18_0 = e0
% 230.52/41.88  | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | SIMP: (177) implies:
% 230.52/41.88  | | | | | | | | | | | | | | | |   (178)  all_18_0 = e0
% 230.52/41.88  | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | REDUCE: (146), (178) imply:
% 230.52/41.88  | | | | | | | | | | | | | | | |   (179)  $false
% 230.52/41.88  | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | CLOSE: (179) is inconsistent.
% 230.52/41.88  | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | End of split
% 230.52/41.88  | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | End of split
% 230.52/41.88  | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | End of split
% 230.52/41.88  | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | End of split
% 230.52/41.88  | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | Case 2:
% 230.52/41.88  | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | |   (180)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 230.52/41.88  | | | | | | | | | | | |            & op(e3, e0) = e2)
% 230.52/41.88  | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | REF_CLOSE: (15), (83), (89), (92), (124), (180) are
% 230.52/41.88  | | | | | | | | | | | |            inconsistent by sub-proof #1208.
% 230.52/41.88  | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | End of split
% 230.52/41.88  | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | Case 2:
% 230.52/41.88  | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | |   (181)   ~ (all_48_1 = e1) & op(e3, e0) = all_48_1 &
% 230.52/41.88  | | | | | | | | | | |          $i(all_48_1)
% 230.52/41.88  | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | ALPHA: (181) implies:
% 230.52/41.88  | | | | | | | | | | |   (182)   ~ (all_48_1 = e1)
% 230.52/41.88  | | | | | | | | | | |   (183)  op(e3, e0) = all_48_1
% 230.52/41.88  | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | REF_CLOSE: (15), (116), (119), (182), (183) are inconsistent
% 230.52/41.88  | | | | | | | | | | |            by sub-proof #1207.
% 230.52/41.88  | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | End of split
% 230.52/41.88  | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | Case 2:
% 230.52/41.88  | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | |   (184)  all_57_9 = e3 & op(e3, e0) = e3
% 230.52/41.88  | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | ALPHA: (184) implies:
% 230.52/41.88  | | | | | | | | | |   (185)  op(e3, e0) = e3
% 230.52/41.88  | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | REF_CLOSE: (15), (65), (83), (185) are inconsistent by
% 230.52/41.88  | | | | | | | | | |            sub-proof #2458.
% 230.52/41.88  | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | End of split
% 230.52/41.88  | | | | | | | | | 
% 230.52/41.88  | | | | | | | | End of split
% 230.52/41.88  | | | | | | | | 
% 230.52/41.88  | | | | | | | Case 2:
% 230.52/41.88  | | | | | | | | 
% 230.52/41.88  | | | | | | | |   (186)   ~ (all_18_1 = e2) & op(e3, e0) = all_18_1 &
% 230.52/41.88  | | | | | | | |          $i(all_18_1)
% 230.52/41.88  | | | | | | | | 
% 230.52/41.88  | | | | | | | | ALPHA: (186) implies:
% 230.52/41.88  | | | | | | | |   (187)   ~ (all_18_1 = e2)
% 230.52/41.88  | | | | | | | |   (188)  op(e3, e0) = all_18_1
% 230.52/41.88  | | | | | | | | 
% 230.52/41.88  | | | | | | | | BETA: splitting (48) gives:
% 230.52/41.88  | | | | | | | | 
% 230.52/41.88  | | | | | | | | Case 1:
% 230.52/41.88  | | | | | | | | | 
% 230.52/41.88  | | | | | | | | |   (189)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 &
% 230.52/41.88  | | | | | | | | |            op(e3, e2) = e3)
% 230.52/41.88  | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | REF_CLOSE: (4), (5), (6), (10), (12), (13), (14), (15), (16),
% 230.52/41.88  | | | | | | | | |            (17), (19), (21), (23), (28), (29), (30), (31),
% 230.52/41.88  | | | | | | | | |            (34), (35), (36), (39), (43), (45), (46), (49),
% 230.52/41.88  | | | | | | | | |            (50), (53), (56), (58), (60), (63), (68), (69),
% 230.52/41.88  | | | | | | | | |            (72), (74), (75), (76), (80), (83), (89), (92),
% 230.52/41.88  | | | | | | | | |            (93), (94), (109), (111), (112), (189) are
% 230.52/41.88  | | | | | | | | |            inconsistent by sub-proof #1210.
% 230.52/41.88  | | | | | | | | | 
% 230.52/41.88  | | | | | | | | Case 2:
% 230.52/41.88  | | | | | | | | | 
% 230.52/41.88  | | | | | | | | |   (190)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 &
% 230.52/41.88  | | | | | | | | |            op(e3, e0) = e3)
% 230.52/41.88  | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | BETA: splitting (190) gives:
% 230.52/41.88  | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | Case 1:
% 230.52/41.88  | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | |   (191)  all_57_4 = e3 & op(e3, e1) = e3
% 230.52/41.88  | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | ALPHA: (191) implies:
% 230.52/41.88  | | | | | | | | | |   (192)  all_57_4 = e3
% 230.52/41.88  | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | BETA: splitting (41) gives:
% 230.52/41.88  | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | Case 1:
% 230.52/41.88  | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | |   (193)  all_55_2 = e3
% 230.52/41.88  | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | COMBINE_EQS: (40), (193) imply:
% 230.52/41.88  | | | | | | | | | | |   (194)  all_53_8 = e3
% 230.52/41.88  | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | REDUCE: (7), (194) imply:
% 230.52/41.88  | | | | | | | | | | |   (195)   ~ (all_52_29 = e3)
% 230.52/41.88  | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | SIMP: (195) implies:
% 230.52/41.88  | | | | | | | | | | |   (196)   ~ (all_52_29 = e3)
% 230.52/41.88  | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | BETA: splitting (2) gives:
% 230.52/41.88  | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | Case 1:
% 230.52/41.88  | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | |   (197)   ~ (all_48_0 = e2) & op(all_48_1, e3) = all_48_0 &
% 230.52/41.88  | | | | | | | | | | | |          op(e3, e0) = all_48_1 & $i(all_48_0) &
% 230.52/41.88  | | | | | | | | | | | |          $i(all_48_1)
% 230.52/41.88  | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | ALPHA: (197) implies:
% 230.52/41.88  | | | | | | | | | | | |   (198)  op(e3, e0) = all_48_1
% 230.52/41.88  | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | BETA: splitting (81) gives:
% 230.52/41.88  | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | Case 1:
% 230.52/41.88  | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | |   (199)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 230.52/41.88  | | | | | | | | | | | | |            & op(e1, e2) = e2)
% 230.52/41.88  | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | BETA: splitting (199) gives:
% 230.52/41.88  | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | Case 1:
% 230.52/41.88  | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | |   (200)  all_57_6 = e2 & op(e1, e3) = e2
% 230.52/41.88  | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | ALPHA: (200) implies:
% 230.52/41.88  | | | | | | | | | | | | | |   (201)  all_57_6 = e2
% 230.52/41.88  | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | BETA: splitting (69) gives:
% 230.52/41.88  | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | Case 1:
% 230.52/41.88  | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | |   (202)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 230.52/41.88  | | | | | | | | | | | | | | |            & op(e2, e3) = e3)
% 230.52/41.88  | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 230.52/41.88  | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | Case 1:
% 230.52/41.88  | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | |   (203)  all_57_0 = e3 & op(e3, e3) = e3
% 230.52/41.88  | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | ALPHA: (203) implies:
% 230.52/41.88  | | | | | | | | | | | | | | | |   (204)  op(e3, e3) = e3
% 230.52/41.88  | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | REF_CLOSE: (15), (23), (28), (30), (35), (92), (93), (109),
% 230.52/41.88  | | | | | | | | | | | | | | | |            (111), (112), (192), (204) are inconsistent by
% 230.52/41.88  | | | | | | | | | | | | | | | |            sub-proof #2474.
% 230.52/41.88  | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | Case 2:
% 230.52/41.88  | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | |   (205)  all_57_2 = e3 & op(e2, e3) = e3
% 230.52/41.88  | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | ALPHA: (205) implies:
% 230.52/41.88  | | | | | | | | | | | | | | | |   (206)  all_57_2 = e3
% 230.52/41.88  | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (31), (56), (68), (92), (93), (109), (111),
% 230.52/41.88  | | | | | | | | | | | | | | | |            (112), (206) are inconsistent by sub-proof #1433.
% 230.52/41.88  | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | End of split
% 230.52/41.88  | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | Case 2:
% 230.52/41.88  | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | |   (207)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 230.52/41.88  | | | | | | | | | | | | | | |            e3 & op(e0, e3) = e3)
% 230.52/41.88  | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 230.52/41.88  | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | Case 1:
% 230.52/41.88  | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | |   (208)  all_57_6 = e3 & op(e1, e3) = e3
% 230.52/41.88  | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | ALPHA: (208) implies:
% 230.52/41.88  | | | | | | | | | | | | | | | |   (209)  all_57_6 = e3
% 230.52/41.88  | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | REF_CLOSE: (92), (201), (209) are inconsistent by sub-proof
% 230.52/41.88  | | | | | | | | | | | | | | | |            #2463.
% 230.52/41.88  | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | Case 2:
% 230.52/41.88  | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | |   (210)  all_57_12 = e3 & op(e0, e3) = e3
% 230.52/41.88  | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | ALPHA: (210) implies:
% 230.52/41.88  | | | | | | | | | | | | | | | |   (211)  all_57_12 = e3
% 230.52/41.88  | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | BETA: splitting (58) gives:
% 230.52/41.88  | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | Case 1:
% 230.52/41.88  | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | |   (212)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 230.52/41.88  | | | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 230.52/41.88  | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 230.52/41.88  | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | Case 1:
% 230.52/41.88  | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | |   (213)  all_57_12 = e2 & op(e0, e3) = e2
% 230.52/41.88  | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | REF_CLOSE: (92), (211), (213) are inconsistent by sub-proof
% 230.52/41.88  | | | | | | | | | | | | | | | | | |            #2232.
% 230.52/41.88  | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | Case 2:
% 230.52/41.88  | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | |   (214)  all_57_13 = e2 & op(e0, e2) = e2
% 230.52/41.88  | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | ALPHA: (214) implies:
% 230.52/41.88  | | | | | | | | | | | | | | | | | |   (215)  all_57_13 = e2
% 230.52/41.88  | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | BETA: splitting (80) gives:
% 230.52/41.88  | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | Case 1:
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | |   (216)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 230.52/41.88  | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (14), (15), (17), (29), (53), (75), (112),
% 230.52/41.88  | | | | | | | | | | | | | | | | | | |            (216) are inconsistent by sub-proof #1218.
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | Case 2:
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | |   (217)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 230.52/41.88  | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | Case 1:
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | |   (218)  all_57_7 = e1 & op(e1, e2) = e1
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | ALPHA: (218) implies:
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | |   (219)  all_57_7 = e1
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | BETA: splitting (28) gives:
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | |   (220)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e2)
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | |   (221)  all_57_0 = e2 & op(e3, e3) = e2
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (221) implies:
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | |   (222)  op(e3, e3) = e2
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (43), (93), (222) are inconsistent by
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2403.
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | |   (223)  all_57_1 = e2 & op(e3, e2) = e2
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (223) implies:
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | |   (224)  all_57_1 = e2
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16) gives:
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | |   (225)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e3)
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | |   (226)  all_57_6 = e3 & op(e1, e3) = e3
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (226) implies:
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | |   (227)  all_57_6 = e3
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (50) gives:
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | |   (228)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e3)
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | |   (229)  all_57_1 = e3 & op(e3, e2) = e3
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (229) implies:
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | |   (230)  all_57_1 = e3
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (23), (28), (30), (35), (43), (92), (93),
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | |            (109), (111), (112), (192), (230) are inconsistent
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1220.
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | |   (231)  all_57_3 = e3 & op(e2, e2) = e3
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (231) implies:
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | |   (232)  all_57_3 = e3
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (31), (232) imply:
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | |   (233)  e3 = e0
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (233) implies:
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | |   (234)  e3 = e0
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (192), (234) imply:
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | |   (235)  all_57_4 = e0
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (35), (43), (48), (65), (83), (92), (224),
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | |            (235) are inconsistent by sub-proof #1405.
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | |   (236)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | |   (237)  all_57_7 = e3 & op(e1, e2) = e3
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (237) implies:
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | |   (238)  all_57_7 = e3
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (219), (238) imply:
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | |   (239)  e3 = e1
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (239) implies:
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | |   (240)  e3 = e1
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (227), (240) imply:
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | |   (241)  all_57_6 = e1
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16) gives:
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (211), (240) imply:
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (242)  all_57_12 = e1
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (35), (43), (69), (74), (92), (93), (109),
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (111), (241), (242) are inconsistent by sub-proof
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1205.
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (211), (240) imply:
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (243)  all_57_12 = e1
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (35), (43), (69), (74), (92), (93), (109),
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (111), (241), (243) are inconsistent by sub-proof
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1205.
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (244)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e1, e0) = e3)
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (19), (21), (34), (45), (244) are
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2310.
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | |   (245)  all_57_13 = e3 & op(e0, e2) = e3
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (92), (215), (245) are inconsistent by sub-proof
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | |            #1358.
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | |   (246)  all_57_7 = e3 & op(e1, e2) = e3
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (109), (219), (246) are inconsistent by sub-proof
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | |            #1247.
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | |   (247)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e1, e0) = e3)
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (19), (21), (34), (45), (247) are
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2310.
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | End of split
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | |   (248)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e2)
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (248) gives:
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | |   (249)  all_57_4 = e2 & op(e3, e1) = e2
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (92), (192), (249) are inconsistent by sub-proof
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | |            #2487.
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | |   (250)  all_57_9 = e2 & op(e3, e0) = e2
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (250) implies:
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | |   (251)  op(e3, e0) = e2
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (15), (187), (188), (251) are inconsistent by
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1899.
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | End of split
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | End of split
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | Case 2:
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | |   (252)  all_57_13 = e1 & op(e0, e2) = e1
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | ALPHA: (252) implies:
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | |   (253)  all_57_13 = e1
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (215), (253) are inconsistent by sub-proof
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | |            #2327.
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | End of split
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | End of split
% 230.52/41.88  | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | End of split
% 230.52/41.88  | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | Case 2:
% 230.52/41.88  | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | |   (254)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 230.52/41.88  | | | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 230.52/41.88  | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | BETA: splitting (254) gives:
% 230.52/41.88  | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | Case 1:
% 230.52/41.88  | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | |   (255)  all_57_14 = e2 & op(e0, e1) = e2
% 230.52/41.88  | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | ALPHA: (255) implies:
% 230.52/41.88  | | | | | | | | | | | | | | | | | |   (256)  all_57_14 = e2
% 230.52/41.88  | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | BETA: splitting (10) gives:
% 230.52/41.88  | | | | | | | | | | | | | | | | | | 
% 230.52/41.88  | | | | | | | | | | | | | | | | | | Case 1:
% 230.52/41.88  | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | |   (257)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 230.52/41.89  | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e1)
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | BETA: splitting (257) gives:
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | Case 1:
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | |   (258)  all_57_0 = e1 & op(e3, e3) = e1
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (112), (258) are inconsistent by sub-proof
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | |            #2454.
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | Case 2:
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | |   (259)  all_57_2 = e1 & op(e2, e3) = e1
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | ALPHA: (259) implies:
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | |   (260)  all_57_2 = e1
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | BETA: splitting (68) gives:
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | |   (261)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (261) gives:
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | |   (262)  all_57_2 = e2 & op(e2, e3) = e2
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (260), (262) are inconsistent by sub-proof
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | |            #1351.
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | |   (263)  all_57_3 = e2 & op(e2, e2) = e2
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (263) implies:
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | |   (264)  op(e2, e2) = e2
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (29), (93), (264) are inconsistent by
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2472.
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | End of split
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | |   (265)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (265) gives:
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | |   (266)  all_57_5 = e2 & op(e2, e1) = e2
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (266) implies:
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | |   (267)  all_57_5 = e2
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (36) gives:
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | |   (268)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e1)
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (268) gives:
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | | |   (269)  all_57_4 = e1 & op(e3, e1) = e1
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (269) implies:
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | | |   (270)  all_57_4 = e1
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (109), (192), (270) are inconsistent by sub-proof
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | | |            #2426.
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | | |   (271)  all_57_5 = e1 & op(e2, e1) = e1
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (271) implies:
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | | |   (272)  all_57_5 = e1
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (29), (31), (35), (63), (68), (92), (93),
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | | |            (109), (111), (260), (272) are inconsistent by
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1536.
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | |   (273)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e1) = e1)
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (273) gives:
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | | |   (274)  all_57_8 = e1 & op(e1, e1) = e1
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (274) implies:
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | | |   (275)  op(e1, e1) = e1
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (60), (112), (275) are inconsistent by
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2427.
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | | |   (276)  all_57_14 = e1 & op(e0, e1) = e1
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (276) implies:
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | | |   (277)  all_57_14 = e1
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (277) imply:
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | | |   (278)  e2 = e1
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (278) implies:
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | | |   (279)  e2 = e1
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (279) imply:
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | | |   (280)  all_57_5 = e1
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (29), (31), (35), (63), (68), (92), (93),
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | | |            (109), (111), (260), (280) are inconsistent by
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1536.
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | |   (281)  all_57_10 = e2 & op(e2, e0) = e2
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (281) implies:
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | |   (282)  all_57_10 = e2
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (56), (92), (282) are inconsistent by sub-proof
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | |            #2356.
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | End of split
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | End of split
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | End of split
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | Case 2:
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | |   (283)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 230.52/41.89  | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e3) = e1)
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | BETA: splitting (283) gives:
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | Case 1:
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | |   (284)  all_57_6 = e1 & op(e1, e3) = e1
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | ALPHA: (284) implies:
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | |   (285)  all_57_6 = e1
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (201), (285) are inconsistent by sub-proof
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | |            #2233.
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | Case 2:
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | |   (286)  all_57_12 = e1 & op(e0, e3) = e1
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | ALPHA: (286) implies:
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | |   (287)  all_57_12 = e1
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (109), (211), (287) are inconsistent by sub-proof
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | |            #2151.
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | End of split
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | End of split
% 230.52/41.89  | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | Case 2:
% 230.52/41.89  | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | |   (288)  all_57_15 = e2 & op(e0, e0) = e2
% 230.52/41.89  | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | ALPHA: (288) implies:
% 230.52/41.89  | | | | | | | | | | | | | | | | | |   (289)  all_57_15 = e2
% 230.52/41.89  | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (93), (289) are inconsistent by sub-proof
% 230.52/41.89  | | | | | | | | | | | | | | | | | |            #2126.
% 230.52/41.89  | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | End of split
% 230.52/41.89  | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | End of split
% 230.52/41.89  | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | End of split
% 230.52/41.89  | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | End of split
% 230.52/41.89  | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | Case 2:
% 230.52/41.89  | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | |   (290)  all_57_7 = e2 & op(e1, e2) = e2
% 230.52/41.89  | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | ALPHA: (290) implies:
% 230.52/41.89  | | | | | | | | | | | | | |   (291)  all_57_7 = e2
% 230.52/41.89  | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | BETA: splitting (50) gives:
% 230.52/41.89  | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | Case 1:
% 230.52/41.89  | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | |   (292)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 230.52/41.89  | | | | | | | | | | | | | | |            & op(e2, e2) = e3)
% 230.52/41.89  | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | REF_CLOSE: (15), (23), (28), (30), (31), (35), (43), (48),
% 230.52/41.89  | | | | | | | | | | | | | | |            (65), (83), (92), (93), (109), (111), (112),
% 230.52/41.89  | | | | | | | | | | | | | | |            (115), (192), (292) are inconsistent by sub-proof
% 230.52/41.89  | | | | | | | | | | | | | | |            #1203.
% 230.52/41.89  | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | Case 2:
% 230.52/41.89  | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | |   (293)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 230.52/41.89  | | | | | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 230.52/41.89  | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | BETA: splitting (293) gives:
% 230.52/41.89  | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | Case 1:
% 230.52/41.89  | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | |   (294)  all_57_7 = e3 & op(e1, e2) = e3
% 230.52/41.89  | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | ALPHA: (294) implies:
% 230.52/41.89  | | | | | | | | | | | | | | | |   (295)  all_57_7 = e3
% 230.52/41.89  | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | REF_CLOSE: (92), (291), (295) are inconsistent by sub-proof
% 230.52/41.89  | | | | | | | | | | | | | | | |            #2102.
% 230.52/41.89  | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | Case 2:
% 230.52/41.89  | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | |   (296)  all_57_13 = e3 & op(e0, e2) = e3
% 230.52/41.89  | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | ALPHA: (296) implies:
% 230.52/41.89  | | | | | | | | | | | | | | | |   (297)  all_57_13 = e3
% 230.52/41.89  | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | BETA: splitting (80) gives:
% 230.52/41.89  | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | Case 1:
% 230.52/41.89  | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | |   (298)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 230.52/41.89  | | | | | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 230.52/41.89  | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (14), (15), (17), (29), (53), (75), (112),
% 230.52/41.89  | | | | | | | | | | | | | | | | |            (298) are inconsistent by sub-proof #1218.
% 230.52/41.89  | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | Case 2:
% 230.52/41.89  | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | |   (299)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 230.52/41.89  | | | | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 230.52/41.89  | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | BETA: splitting (299) gives:
% 230.52/41.89  | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | Case 1:
% 230.52/41.89  | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | |   (300)  all_57_7 = e1 & op(e1, e2) = e1
% 230.52/41.89  | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (291), (300) are inconsistent by sub-proof
% 230.52/41.89  | | | | | | | | | | | | | | | | | |            #2190.
% 230.52/41.89  | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | Case 2:
% 230.52/41.89  | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | |   (301)  all_57_13 = e1 & op(e0, e2) = e1
% 230.52/41.89  | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | REF_CLOSE: (109), (297), (301) are inconsistent by sub-proof
% 230.52/41.89  | | | | | | | | | | | | | | | | | |            #2264.
% 230.52/41.89  | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | End of split
% 230.52/41.89  | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | End of split
% 230.52/41.89  | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | End of split
% 230.52/41.89  | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | End of split
% 230.52/41.89  | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | End of split
% 230.52/41.89  | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | Case 2:
% 230.52/41.89  | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | |   (302)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 230.52/41.89  | | | | | | | | | | | | |            e2 & op(e1, e0) = e2)
% 230.52/41.89  | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | BETA: splitting (302) gives:
% 230.52/41.89  | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | Case 1:
% 230.52/41.89  | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | |   (303)  all_57_8 = e2 & op(e1, e1) = e2
% 230.52/41.89  | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | ALPHA: (303) implies:
% 230.52/41.89  | | | | | | | | | | | | | |   (304)  all_57_8 = e2
% 230.52/41.89  | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | REF_CLOSE: (67), (93), (304) are inconsistent by sub-proof
% 230.52/41.89  | | | | | | | | | | | | | |            #1957.
% 230.52/41.89  | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | Case 2:
% 230.52/41.89  | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | |   (305)  all_57_11 = e2 & op(e1, e0) = e2
% 230.52/41.89  | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | ALPHA: (305) implies:
% 230.52/41.89  | | | | | | | | | | | | | |   (306)  all_57_11 = e2
% 230.52/41.89  | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | BETA: splitting (12) gives:
% 230.52/41.89  | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | Case 1:
% 230.52/41.89  | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | |   (307)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 230.52/41.89  | | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 230.52/41.89  | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | BETA: splitting (307) gives:
% 230.52/41.89  | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | Case 1:
% 230.52/41.89  | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | |   (308)  all_57_1 = e2 & op(e3, e2) = e2
% 230.52/41.89  | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (8), (15), (23), (29), (30), (42), (47),
% 230.52/41.89  | | | | | | | | | | | | | | | |            (51), (61), (62), (78), (90), (93), (109), (112),
% 230.52/41.89  | | | | | | | | | | | | | | | |            (116), (187), (188), (192), (196), (198), (308)
% 230.52/41.89  | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1202.
% 230.52/41.89  | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | Case 2:
% 230.52/41.89  | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | |   (309)  all_57_3 = e2 & op(e2, e2) = e2
% 230.52/41.89  | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | ALPHA: (309) implies:
% 230.52/41.89  | | | | | | | | | | | | | | | |   (310)  op(e2, e2) = e2
% 230.52/41.89  | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | REF_CLOSE: (15), (29), (93), (310) are inconsistent by
% 230.52/41.89  | | | | | | | | | | | | | | | |            sub-proof #2472.
% 230.52/41.89  | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | End of split
% 230.52/41.89  | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | Case 2:
% 230.52/41.89  | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | |   (311)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 230.52/41.89  | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 230.52/41.89  | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | BETA: splitting (311) gives:
% 230.52/41.89  | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | Case 1:
% 230.52/41.89  | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | |   (312)  all_57_7 = e2 & op(e1, e2) = e2
% 230.52/41.89  | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | ALPHA: (312) implies:
% 230.52/41.89  | | | | | | | | | | | | | | | |   (313)  all_57_7 = e2
% 230.52/41.89  | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (19), (21), (34), (45), (60), (79),
% 230.52/41.89  | | | | | | | | | | | | | | | |            (92), (109), (111), (112), (306), (313) are
% 230.52/41.89  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1199.
% 230.52/41.89  | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | Case 2:
% 230.52/41.89  | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | |   (314)  all_57_13 = e2 & op(e0, e2) = e2
% 230.52/41.89  | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | ALPHA: (314) implies:
% 230.52/41.89  | | | | | | | | | | | | | | | |   (315)  all_57_13 = e2
% 230.52/41.89  | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | BETA: splitting (50) gives:
% 230.52/41.89  | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | Case 1:
% 230.52/41.89  | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | |   (316)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 230.52/41.89  | | | | | | | | | | | | | | | | |            & op(e2, e2) = e3)
% 230.52/41.89  | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (23), (28), (30), (31), (35), (43), (48),
% 230.52/41.89  | | | | | | | | | | | | | | | | |            (65), (83), (92), (93), (109), (111), (112),
% 230.52/41.89  | | | | | | | | | | | | | | | | |            (115), (192), (316) are inconsistent by sub-proof
% 230.52/41.89  | | | | | | | | | | | | | | | | |            #1203.
% 230.52/41.89  | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | Case 2:
% 230.52/41.89  | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | |   (317)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 230.52/41.89  | | | | | | | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 230.52/41.89  | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | BETA: splitting (317) gives:
% 230.52/41.89  | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | Case 1:
% 230.52/41.89  | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | |   (318)  all_57_7 = e3 & op(e1, e2) = e3
% 230.52/41.89  | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | ALPHA: (318) implies:
% 230.52/41.89  | | | | | | | | | | | | | | | | | |   (319)  all_57_7 = e3
% 230.52/41.89  | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | BETA: splitting (28) gives:
% 230.52/41.89  | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | Case 1:
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | |   (320)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 230.52/41.89  | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e2)
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | BETA: splitting (320) gives:
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | Case 1:
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | |   (321)  all_57_0 = e2 & op(e3, e3) = e2
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | ALPHA: (321) implies:
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | |   (322)  op(e3, e3) = e2
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (43), (93), (322) are inconsistent by
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | |            sub-proof #2403.
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | Case 2:
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | |   (323)  all_57_1 = e2 & op(e3, e2) = e2
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (8), (15), (23), (29), (30), (42), (47),
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | |            (51), (61), (62), (78), (90), (93), (109), (112),
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | |            (116), (187), (188), (192), (196), (198), (323)
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1202.
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | End of split
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | Case 2:
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | |   (324)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 230.52/41.89  | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e2)
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | BETA: splitting (324) gives:
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | Case 1:
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | |   (325)  all_57_4 = e2 & op(e3, e1) = e2
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | ALPHA: (325) implies:
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | |   (326)  all_57_4 = e2
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (192), (326) imply:
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | |   (327)  e3 = e2
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | SIMP: (327) implies:
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | |   (328)  e3 = e2
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (319), (328) imply:
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | |   (329)  all_57_7 = e2
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (19), (21), (34), (45), (60), (79),
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | |            (92), (109), (111), (112), (306), (329) are
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1199.
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | Case 2:
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | |   (330)  all_57_9 = e2 & op(e3, e0) = e2
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | ALPHA: (330) implies:
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | |   (331)  op(e3, e0) = e2
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (15), (187), (188), (331) are inconsistent by
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | |            sub-proof #1899.
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | End of split
% 230.52/41.89  | | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | End of split
% 230.52/41.89  | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | Case 2:
% 230.52/41.89  | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | |   (332)  all_57_13 = e3 & op(e0, e2) = e3
% 230.52/41.89  | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | ALPHA: (332) implies:
% 230.52/41.89  | | | | | | | | | | | | | | | | | |   (333)  all_57_13 = e3
% 230.52/41.89  | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | | REF_CLOSE: (92), (315), (333) are inconsistent by sub-proof
% 230.52/41.89  | | | | | | | | | | | | | | | | | |            #2203.
% 230.52/41.89  | | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | | End of split
% 230.52/41.89  | | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | | End of split
% 230.52/41.89  | | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | | End of split
% 230.52/41.89  | | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | | End of split
% 230.52/41.89  | | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | End of split
% 230.52/41.89  | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | End of split
% 230.52/41.89  | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | Case 2:
% 230.52/41.89  | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | |   (334)   ~ (all_48_1 = e1) & op(e3, e0) = all_48_1 &
% 230.52/41.89  | | | | | | | | | | | |          $i(all_48_1)
% 230.52/41.89  | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | ALPHA: (334) implies:
% 230.52/41.89  | | | | | | | | | | | |   (335)   ~ (all_48_1 = e1)
% 230.52/41.89  | | | | | | | | | | | |   (336)  op(e3, e0) = all_48_1
% 230.52/41.89  | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | REF_CLOSE: (15), (116), (188), (335), (336) are inconsistent
% 230.52/41.89  | | | | | | | | | | | |            by sub-proof #1207.
% 230.52/41.89  | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | End of split
% 230.52/41.89  | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | Case 2:
% 230.52/41.89  | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | |   (337)  all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 230.52/41.89  | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | REF_CLOSE: (40), (71), (88), (107), (337) are inconsistent by
% 230.52/41.89  | | | | | | | | | | |            sub-proof #1937.
% 230.52/41.89  | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | End of split
% 230.52/41.89  | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | Case 2:
% 230.52/41.89  | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | |   (338)  all_57_9 = e3 & op(e3, e0) = e3
% 230.52/41.89  | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | ALPHA: (338) implies:
% 230.52/41.89  | | | | | | | | | |   (339)  op(e3, e0) = e3
% 230.52/41.89  | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | REF_CLOSE: (15), (65), (83), (339) are inconsistent by
% 230.52/41.89  | | | | | | | | | |            sub-proof #2458.
% 230.52/41.89  | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | End of split
% 230.52/41.89  | | | | | | | | | 
% 230.52/41.89  | | | | | | | | End of split
% 230.52/41.89  | | | | | | | | 
% 230.52/41.89  | | | | | | | End of split
% 230.52/41.89  | | | | | | | 
% 230.52/41.89  | | | | | | Case 2:
% 230.52/41.89  | | | | | | | 
% 230.52/41.89  | | | | | | |   (340)  all_57_10 = e1 & op(e2, e0) = e1
% 230.52/41.89  | | | | | | | 
% 230.52/41.89  | | | | | | | REF_CLOSE: (56), (109), (340) are inconsistent by sub-proof #2349.
% 230.52/41.89  | | | | | | | 
% 230.52/41.89  | | | | | | End of split
% 230.52/41.89  | | | | | | 
% 230.52/41.89  | | | | | Case 2:
% 230.52/41.89  | | | | | | 
% 230.52/41.89  | | | | | |   (341)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 &
% 230.52/41.89  | | | | | |            op(e0, e0) = e1)
% 230.52/41.89  | | | | | | 
% 230.52/41.89  | | | | | | BETA: splitting (341) gives:
% 230.52/41.89  | | | | | | 
% 230.52/41.89  | | | | | | Case 1:
% 230.52/41.89  | | | | | | | 
% 230.52/41.89  | | | | | | |   (342)  all_57_11 = e1 & op(e1, e0) = e1
% 230.52/41.89  | | | | | | | 
% 230.52/41.89  | | | | | | | ALPHA: (342) implies:
% 230.52/41.89  | | | | | | |   (343)  all_57_11 = e1
% 230.52/41.89  | | | | | | | 
% 230.52/41.89  | | | | | | | BETA: splitting (81) gives:
% 230.52/41.89  | | | | | | | 
% 230.52/41.89  | | | | | | | Case 1:
% 230.52/41.89  | | | | | | | | 
% 230.52/41.89  | | | | | | | |   (344)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 &
% 230.52/41.89  | | | | | | | |            op(e1, e2) = e2)
% 230.52/41.89  | | | | | | | | 
% 230.52/41.89  | | | | | | | | BETA: splitting (344) gives:
% 230.52/41.89  | | | | | | | | 
% 230.52/41.89  | | | | | | | | Case 1:
% 230.52/41.89  | | | | | | | | | 
% 230.52/41.89  | | | | | | | | |   (345)  all_57_6 = e2 & op(e1, e3) = e2
% 230.52/41.89  | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | ALPHA: (345) implies:
% 230.52/41.89  | | | | | | | | |   (346)  all_57_6 = e2
% 230.52/41.89  | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | BETA: splitting (16) gives:
% 230.52/41.89  | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | Case 1:
% 230.52/41.89  | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | |   (347)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 230.52/41.89  | | | | | | | | | |            & op(e1, e2) = e3)
% 230.52/41.89  | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | BETA: splitting (347) gives:
% 230.52/41.89  | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | Case 1:
% 230.52/41.89  | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | |   (348)  all_57_6 = e3 & op(e1, e3) = e3
% 230.52/41.89  | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | ALPHA: (348) implies:
% 230.52/41.89  | | | | | | | | | | |   (349)  all_57_6 = e3
% 230.52/41.89  | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | REF_CLOSE: (92), (346), (349) are inconsistent by sub-proof
% 230.52/41.89  | | | | | | | | | | |            #2463.
% 230.52/41.89  | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | Case 2:
% 230.52/41.89  | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | |   (350)  all_57_7 = e3 & op(e1, e2) = e3
% 230.52/41.89  | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | ALPHA: (350) implies:
% 230.52/41.89  | | | | | | | | | | |   (351)  all_57_7 = e3
% 230.52/41.89  | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | BETA: splitting (72) gives:
% 230.52/41.89  | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | Case 1:
% 230.52/41.89  | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | |   (352)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 230.52/41.89  | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 230.52/41.89  | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | BETA: splitting (352) gives:
% 230.52/41.89  | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | Case 1:
% 230.52/41.89  | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | |   (353)  all_57_9 = e2 & op(e3, e0) = e2
% 230.52/41.89  | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | ALPHA: (353) implies:
% 230.52/41.89  | | | | | | | | | | | | |   (354)  op(e3, e0) = e2
% 230.52/41.89  | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | REF_CLOSE: (15), (83), (89), (354) are inconsistent by
% 230.52/41.89  | | | | | | | | | | | | |            sub-proof #2331.
% 230.52/41.89  | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | Case 2:
% 230.52/41.89  | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | |   (355)  all_57_10 = e2 & op(e2, e0) = e2
% 230.52/41.89  | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | ALPHA: (355) implies:
% 230.52/41.89  | | | | | | | | | | | | |   (356)  all_57_10 = e2
% 230.52/41.89  | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | COMBINE_EQS: (56), (356) imply:
% 230.52/41.89  | | | | | | | | | | | | |   (357)  e3 = e2
% 230.52/41.89  | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | COMBINE_EQS: (351), (357) imply:
% 230.52/41.89  | | | | | | | | | | | | |   (358)  all_57_7 = e2
% 230.52/41.89  | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | | REF_CLOSE: (5), (15), (16), (19), (21), (34), (45), (56),
% 230.52/41.89  | | | | | | | | | | | | |            (60), (72), (79), (83), (89), (92), (93), (109),
% 230.52/41.89  | | | | | | | | | | | | |            (111), (112), (358) are inconsistent by sub-proof
% 230.52/41.89  | | | | | | | | | | | | |            #1198.
% 230.52/41.89  | | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | End of split
% 230.52/41.89  | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | Case 2:
% 230.52/41.89  | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | |   (359)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 230.52/41.89  | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 230.52/41.89  | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | | REF_CLOSE: (5), (93), (111), (343), (359) are inconsistent by
% 230.52/41.89  | | | | | | | | | | | |            sub-proof #1666.
% 230.52/41.89  | | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | | End of split
% 230.52/41.89  | | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | End of split
% 230.52/41.89  | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | Case 2:
% 230.52/41.89  | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | |   (360)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3
% 230.52/41.89  | | | | | | | | | |            & op(e1, e0) = e3)
% 230.52/41.89  | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | | REF_CLOSE: (15), (19), (21), (34), (45), (360) are
% 230.52/41.89  | | | | | | | | | |            inconsistent by sub-proof #2310.
% 230.52/41.89  | | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | End of split
% 230.52/41.89  | | | | | | | | | 
% 230.52/41.89  | | | | | | | | Case 2:
% 230.52/41.89  | | | | | | | | | 
% 230.52/41.89  | | | | | | | | |   (361)  all_57_7 = e2 & op(e1, e2) = e2
% 230.52/41.89  | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | ALPHA: (361) implies:
% 230.52/41.89  | | | | | | | | |   (362)  all_57_7 = e2
% 230.52/41.89  | | | | | | | | | 
% 230.52/41.89  | | | | | | | | | REF_CLOSE: (5), (15), (16), (19), (21), (34), (45), (56),
% 230.52/41.89  | | | | | | | | |            (60), (72), (79), (83), (89), (92), (93), (109),
% 230.52/41.89  | | | | | | | | |            (111), (112), (362) are inconsistent by sub-proof
% 230.52/41.89  | | | | | | | | |            #1198.
% 230.52/41.89  | | | | | | | | | 
% 230.52/41.89  | | | | | | | | End of split
% 230.52/41.89  | | | | | | | | 
% 230.52/41.89  | | | | | | | Case 2:
% 230.52/41.89  | | | | | | | | 
% 230.52/41.89  | | | | | | | |   (363)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 &
% 230.52/41.89  | | | | | | | |            op(e1, e0) = e2)
% 230.52/41.89  | | | | | | | | 
% 230.52/41.89  | | | | | | | | REF_CLOSE: (67), (93), (111), (343), (363) are inconsistent by
% 230.52/41.89  | | | | | | | |            sub-proof #1251.
% 230.52/41.89  | | | | | | | | 
% 230.52/41.89  | | | | | | | End of split
% 230.52/41.89  | | | | | | | 
% 230.52/41.89  | | | | | | Case 2:
% 230.52/41.89  | | | | | | | 
% 230.52/41.89  | | | | | | |   (364)  all_57_15 = e1 & op(e0, e0) = e1
% 230.52/41.89  | | | | | | | 
% 230.52/41.89  | | | | | | | ALPHA: (364) implies:
% 230.52/41.89  | | | | | | |   (365)  op(e0, e0) = e1
% 230.52/41.89  | | | | | | | 
% 230.52/41.89  | | | | | | | REF_CLOSE: (15), (52), (112), (365) are inconsistent by sub-proof
% 230.52/41.89  | | | | | | |            #2290.
% 230.52/41.89  | | | | | | | 
% 230.52/41.89  | | | | | | End of split
% 230.52/41.89  | | | | | | 
% 230.52/41.89  | | | | | End of split
% 230.52/41.89  | | | | | 
% 230.52/41.89  | | | | Case 2:
% 230.52/41.89  | | | | | 
% 230.52/41.89  | | | | |   (366)  all_55_3 = e0
% 230.52/41.89  | | | | | 
% 230.52/41.89  | | | | | COMBINE_EQS: (64), (366) imply:
% 230.52/41.89  | | | | |   (367)  all_53_12 = e0
% 230.52/41.89  | | | | | 
% 230.52/41.89  | | | | | REDUCE: (70), (367) imply:
% 230.52/41.89  | | | | |   (368)  $false
% 230.52/41.89  | | | | | 
% 230.52/41.89  | | | | | CLOSE: (368) is inconsistent.
% 230.52/41.89  | | | | | 
% 230.52/41.89  | | | | End of split
% 230.52/41.89  | | | | 
% 230.52/41.89  | | | End of split
% 230.52/41.89  | | | 
% 230.52/41.89  | | End of split
% 230.52/41.89  | | 
% 230.52/41.89  | Case 2:
% 230.52/41.89  | | 
% 230.52/41.89  | |   (369)  all_55_1 = e1 | all_55_1 = e0
% 230.52/41.89  | | 
% 230.52/41.89  | | REF_CLOSE: (4), (55), (59), (369) are inconsistent by sub-proof #1197.
% 230.52/41.89  | | 
% 230.52/41.89  | End of split
% 230.52/41.89  | 
% 230.52/41.89  End of proof
% 230.52/41.89  
% 230.52/41.89  Sub-proof #1197 shows that the following formulas are inconsistent:
% 230.52/41.89  ----------------------------------------------------------------
% 230.52/41.89    (1)  all_55_1 = e1 | all_55_1 = e0
% 230.52/41.89    (2)  all_55_1 = all_14_0
% 230.52/41.89    (3)   ~ (all_14_0 = e1)
% 230.52/41.89    (4)   ~ (all_14_0 = e0)
% 230.52/41.89  
% 230.52/41.89  Begin of proof
% 230.52/41.89  | 
% 230.52/41.89  | BETA: splitting (1) gives:
% 230.52/41.89  | 
% 230.52/41.89  | Case 1:
% 230.52/41.89  | | 
% 230.52/41.89  | |   (5)  all_55_1 = e1
% 230.52/41.89  | | 
% 230.52/41.89  | | COMBINE_EQS: (2), (5) imply:
% 230.52/41.89  | |   (6)  all_14_0 = e1
% 230.52/41.89  | | 
% 230.52/41.89  | | SIMP: (6) implies:
% 230.52/41.89  | |   (7)  all_14_0 = e1
% 230.52/41.89  | | 
% 230.52/41.89  | | REDUCE: (3), (7) imply:
% 230.52/41.89  | |   (8)  $false
% 230.52/41.89  | | 
% 230.52/41.89  | | CLOSE: (8) is inconsistent.
% 230.52/41.89  | | 
% 230.52/41.89  | Case 2:
% 230.52/41.89  | | 
% 230.52/41.89  | |   (9)  all_55_1 = e0
% 230.52/41.89  | | 
% 230.52/41.89  | | COMBINE_EQS: (2), (9) imply:
% 230.52/41.89  | |   (10)  all_14_0 = e0
% 230.52/41.89  | | 
% 230.52/41.89  | | SIMP: (10) implies:
% 230.52/41.89  | |   (11)  all_14_0 = e0
% 230.52/41.89  | | 
% 230.52/41.89  | | REDUCE: (4), (11) imply:
% 230.52/41.89  | |   (12)  $false
% 230.52/41.89  | | 
% 230.52/41.89  | | CLOSE: (12) is inconsistent.
% 230.52/41.89  | | 
% 230.52/41.89  | End of split
% 230.52/41.89  | 
% 230.52/41.89  End of proof
% 230.52/41.89  
% 230.52/41.89  Sub-proof #1198 shows that the following formulas are inconsistent:
% 230.52/41.89  ----------------------------------------------------------------
% 230.52/41.89    (1)  all_57_15 = e0
% 230.52/41.89    (2)   ~ (e3 = e1)
% 230.52/41.89    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.89           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.89    (4)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.52/41.89         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.52/41.89    (5)   ~ (all_6_2 = e3)
% 230.52/41.89    (6)  op(e1, e1) = all_6_2
% 230.52/41.89    (7)  all_57_7 = e2
% 230.52/41.89    (8)   ~ (e3 = e2)
% 230.52/41.89    (9)  op(e1, e0) = all_53_14
% 230.52/41.89    (10)   ~ (all_53_14 = e3)
% 230.52/41.89    (11)   ~ (e2 = e0)
% 230.52/41.89    (12)   ~ (e1 = e0)
% 230.52/41.89    (13)  all_57_10 = e3
% 230.52/41.89    (14)  op(e1, e1) = e0
% 230.52/41.89    (15)   ~ (e2 = e1)
% 230.52/41.89    (16)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.52/41.89          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.52/41.89    (17)   ~ (all_53_12 = e2)
% 230.52/41.89    (18)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.52/41.89          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.52/41.89    (19)  op(e3, e0) = all_53_12
% 230.52/41.89  
% 230.52/41.89  Begin of proof
% 230.52/41.89  | 
% 230.52/41.89  | BETA: splitting (4) gives:
% 230.52/41.89  | 
% 230.52/41.89  | Case 1:
% 230.52/41.89  | | 
% 230.52/41.89  | |   (20)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 230.52/41.89  | |           e3)
% 230.52/41.89  | | 
% 230.52/41.89  | | BETA: splitting (20) gives:
% 230.52/41.89  | | 
% 230.52/41.89  | | Case 1:
% 230.52/41.89  | | | 
% 230.52/41.89  | | |   (21)  all_57_6 = e3 & op(e1, e3) = e3
% 230.52/41.89  | | | 
% 230.52/41.89  | | | ALPHA: (21) implies:
% 230.52/41.89  | | |   (22)  all_57_6 = e3
% 230.52/41.89  | | | 
% 230.52/41.89  | | | BETA: splitting (16) gives:
% 230.52/41.89  | | | 
% 230.52/41.89  | | | Case 1:
% 230.52/41.89  | | | | 
% 230.52/41.89  | | | |   (23)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0)
% 230.52/41.89  | | | |           = e2)
% 230.52/41.89  | | | | 
% 230.52/41.89  | | | | REF_CLOSE: (3), (8), (13), (17), (19), (23) are inconsistent by
% 230.52/41.89  | | | |            sub-proof #1219.
% 230.52/41.89  | | | | 
% 230.52/41.89  | | | Case 2:
% 230.52/41.89  | | | | 
% 230.52/41.89  | | | |   (24)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0,
% 230.52/41.89  | | | |             e0) = e2)
% 230.52/41.89  | | | | 
% 230.52/41.89  | | | | BETA: splitting (24) gives:
% 230.52/41.89  | | | | 
% 230.52/41.89  | | | | Case 1:
% 230.52/41.89  | | | | | 
% 230.52/41.89  | | | | |   (25)  all_57_11 = e2 & op(e1, e0) = e2
% 230.52/41.89  | | | | | 
% 230.52/41.89  | | | | | ALPHA: (25) implies:
% 230.52/41.89  | | | | |   (26)  all_57_11 = e2
% 230.52/41.89  | | | | | 
% 230.52/41.89  | | | | | REF_CLOSE: (2), (3), (7), (12), (14), (15), (18), (22), (26) are
% 230.52/41.89  | | | | |            inconsistent by sub-proof #1200.
% 230.52/41.89  | | | | | 
% 230.52/41.89  | | | | Case 2:
% 230.52/41.89  | | | | | 
% 230.52/41.89  | | | | |   (27)  all_57_15 = e2 & op(e0, e0) = e2
% 230.52/41.89  | | | | | 
% 230.52/41.89  | | | | | ALPHA: (27) implies:
% 230.52/41.89  | | | | |   (28)  all_57_15 = e2
% 230.52/41.89  | | | | | 
% 230.52/41.89  | | | | | REF_CLOSE: (1), (11), (28) are inconsistent by sub-proof #2126.
% 230.52/41.89  | | | | | 
% 230.52/41.89  | | | | End of split
% 230.52/41.89  | | | | 
% 230.52/41.89  | | | End of split
% 230.52/41.89  | | | 
% 230.52/41.89  | | Case 2:
% 230.52/41.89  | | | 
% 230.52/41.89  | | |   (29)  all_57_7 = e3 & op(e1, e2) = e3
% 230.52/41.89  | | | 
% 230.52/41.89  | | | ALPHA: (29) implies:
% 230.52/41.89  | | |   (30)  all_57_7 = e3
% 230.52/41.89  | | | 
% 230.52/41.89  | | | REF_CLOSE: (7), (8), (30) are inconsistent by sub-proof #2102.
% 230.52/41.89  | | | 
% 230.52/41.89  | | End of split
% 230.52/41.89  | | 
% 230.52/41.89  | Case 2:
% 230.52/41.89  | | 
% 230.52/41.89  | |   (31)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 230.52/41.89  | |           e3)
% 230.52/41.89  | | 
% 230.52/41.89  | | REF_CLOSE: (3), (5), (6), (9), (10), (31) are inconsistent by sub-proof
% 230.52/41.89  | |            #2310.
% 230.52/41.89  | | 
% 230.52/41.89  | End of split
% 230.52/41.89  | 
% 230.52/41.89  End of proof
% 230.52/41.89  
% 230.52/41.89  Sub-proof #1199 shows that the following formulas are inconsistent:
% 230.52/41.89  ----------------------------------------------------------------
% 230.52/41.89    (1)   ~ (e3 = e1)
% 230.52/41.89    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.89           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.89    (3)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.52/41.89         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.52/41.89    (4)   ~ (all_6_2 = e3)
% 230.52/41.89    (5)  op(e1, e1) = all_6_2
% 230.52/41.89    (6)  all_57_7 = e2
% 230.52/41.89    (7)   ~ (e3 = e2)
% 230.52/41.89    (8)  op(e1, e0) = all_53_14
% 230.52/41.89    (9)  all_57_11 = e2
% 230.52/41.89    (10)   ~ (all_53_14 = e3)
% 230.52/41.89    (11)   ~ (e1 = e0)
% 230.52/41.89    (12)  op(e1, e1) = e0
% 230.52/41.89    (13)   ~ (e2 = e1)
% 230.52/41.89    (14)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.52/41.89          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.52/41.89  
% 230.52/41.89  Begin of proof
% 230.52/41.89  | 
% 230.52/41.89  | BETA: splitting (3) gives:
% 230.52/41.89  | 
% 230.52/41.89  | Case 1:
% 230.52/41.89  | | 
% 230.52/41.89  | |   (15)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 230.52/41.89  | |           e3)
% 230.52/41.89  | | 
% 230.52/41.89  | | BETA: splitting (15) gives:
% 230.52/41.89  | | 
% 230.52/41.89  | | Case 1:
% 230.52/41.89  | | | 
% 230.52/41.89  | | |   (16)  all_57_6 = e3 & op(e1, e3) = e3
% 230.52/41.89  | | | 
% 230.52/41.89  | | | ALPHA: (16) implies:
% 230.52/41.89  | | |   (17)  all_57_6 = e3
% 230.52/41.89  | | | 
% 230.52/41.89  | | | REF_CLOSE: (1), (2), (6), (9), (11), (12), (13), (14), (17) are
% 230.52/41.89  | | |            inconsistent by sub-proof #1200.
% 230.52/41.89  | | | 
% 230.52/41.89  | | Case 2:
% 230.52/41.89  | | | 
% 230.52/41.89  | | |   (18)  all_57_7 = e3 & op(e1, e2) = e3
% 230.52/41.89  | | | 
% 230.52/41.89  | | | ALPHA: (18) implies:
% 230.52/41.89  | | |   (19)  all_57_7 = e3
% 230.52/41.89  | | | 
% 230.52/41.89  | | | REF_CLOSE: (6), (7), (19) are inconsistent by sub-proof #2102.
% 230.52/41.89  | | | 
% 230.52/41.89  | | End of split
% 230.52/41.89  | | 
% 230.52/41.89  | Case 2:
% 230.52/41.89  | | 
% 230.52/41.89  | |   (20)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 230.52/41.89  | |           e3)
% 230.52/41.89  | | 
% 230.52/41.89  | | REF_CLOSE: (2), (4), (5), (8), (10), (20) are inconsistent by sub-proof
% 230.52/41.89  | |            #2310.
% 230.52/41.89  | | 
% 230.52/41.89  | End of split
% 230.52/41.89  | 
% 230.52/41.89  End of proof
% 230.52/41.89  
% 230.52/41.89  Sub-proof #1200 shows that the following formulas are inconsistent:
% 230.52/41.89  ----------------------------------------------------------------
% 230.52/41.89    (1)   ~ (e3 = e1)
% 230.52/41.89    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.89           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.89    (3)  all_57_7 = e2
% 230.52/41.89    (4)  all_57_11 = e2
% 230.52/41.89    (5)   ~ (e1 = e0)
% 230.52/41.89    (6)  all_57_6 = e3
% 230.52/41.89    (7)  op(e1, e1) = e0
% 230.52/41.89    (8)   ~ (e2 = e1)
% 230.52/41.89    (9)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.52/41.89         (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.52/41.89  
% 230.52/41.89  Begin of proof
% 230.52/41.89  | 
% 230.52/41.89  | BETA: splitting (9) gives:
% 230.52/41.89  | 
% 230.52/41.89  | Case 1:
% 230.52/41.89  | | 
% 230.52/41.89  | |   (10)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) =
% 230.52/41.89  | |           e1)
% 230.52/41.89  | | 
% 230.52/41.89  | | BETA: splitting (10) gives:
% 230.52/41.89  | | 
% 230.52/41.89  | | Case 1:
% 230.52/41.89  | | | 
% 230.52/41.89  | | |   (11)  all_57_6 = e1 & op(e1, e3) = e1
% 230.52/41.89  | | | 
% 230.52/41.89  | | | ALPHA: (11) implies:
% 230.52/41.89  | | |   (12)  all_57_6 = e1
% 230.52/41.90  | | | 
% 230.52/41.90  | | | REF_CLOSE: (1), (6), (12) are inconsistent by sub-proof #2017.
% 230.52/41.90  | | | 
% 230.52/41.90  | | Case 2:
% 230.52/41.90  | | | 
% 230.52/41.90  | | |   (13)  all_57_7 = e1 & op(e1, e2) = e1
% 230.52/41.90  | | | 
% 230.52/41.90  | | | ALPHA: (13) implies:
% 230.52/41.90  | | |   (14)  all_57_7 = e1
% 230.52/41.90  | | | 
% 230.52/41.90  | | | REF_CLOSE: (3), (8), (14) are inconsistent by sub-proof #1761.
% 230.52/41.90  | | | 
% 230.52/41.90  | | End of split
% 230.52/41.90  | | 
% 230.52/41.90  | Case 2:
% 230.52/41.90  | | 
% 230.52/41.90  | |   (15)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) =
% 230.52/41.90  | |           e1)
% 230.52/41.90  | | 
% 230.52/41.90  | | REF_CLOSE: (2), (4), (5), (7), (8), (15) are inconsistent by sub-proof
% 230.52/41.90  | |            #1201.
% 230.52/41.90  | | 
% 230.52/41.90  | End of split
% 230.52/41.90  | 
% 230.52/41.90  End of proof
% 230.52/41.90  
% 230.52/41.90  Sub-proof #1201 shows that the following formulas are inconsistent:
% 230.52/41.90  ----------------------------------------------------------------
% 230.52/41.90    (1)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.52/41.90    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.90           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.90    (3)  all_57_11 = e2
% 230.52/41.90    (4)   ~ (e1 = e0)
% 230.52/41.90    (5)  op(e1, e1) = e0
% 230.52/41.90    (6)   ~ (e2 = e1)
% 230.52/41.90  
% 230.52/41.90  Begin of proof
% 230.52/41.90  | 
% 230.52/41.90  | BETA: splitting (1) gives:
% 230.52/41.90  | 
% 230.52/41.90  | Case 1:
% 230.52/41.90  | | 
% 230.52/41.90  | |   (7)  all_57_8 = e1 & op(e1, e1) = e1
% 230.52/41.90  | | 
% 230.52/41.90  | | ALPHA: (7) implies:
% 230.52/41.90  | |   (8)  op(e1, e1) = e1
% 230.52/41.90  | | 
% 230.52/41.90  | | REF_CLOSE: (2), (4), (5), (8) are inconsistent by sub-proof #2427.
% 230.52/41.90  | | 
% 230.52/41.90  | Case 2:
% 230.52/41.90  | | 
% 230.52/41.90  | |   (9)  all_57_11 = e1 & op(e1, e0) = e1
% 230.52/41.90  | | 
% 230.52/41.90  | | ALPHA: (9) implies:
% 230.52/41.90  | |   (10)  all_57_11 = e1
% 230.52/41.90  | | 
% 230.52/41.90  | | REF_CLOSE: (3), (6), (10) are inconsistent by sub-proof #2113.
% 230.52/41.90  | | 
% 230.52/41.90  | End of split
% 230.52/41.90  | 
% 230.52/41.90  End of proof
% 230.52/41.90  
% 230.52/41.90  Sub-proof #1202 shows that the following formulas are inconsistent:
% 230.52/41.90  ----------------------------------------------------------------
% 230.52/41.90    (1)  all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 230.52/41.90    (2)   ~ (all_52_29 = e0)
% 230.52/41.90    (3)   ~ (all_52_27 = all_52_29)
% 230.52/41.90    (4)   ~ (e3 = e1)
% 230.52/41.90    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.90           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.90    (6)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.52/41.90         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.52/41.90    (7)  op(e2, e2) = e0
% 230.52/41.90    (8)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.52/41.90         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.52/41.90    (9)  all_57_4 = e3
% 230.52/41.90    (10)  op(e3, e0) = e1
% 230.52/41.90    (11)  all_55_14 = all_52_29
% 230.52/41.90    (12)   ~ (all_18_1 = e2)
% 230.52/41.90    (13)   ~ (all_52_29 = e3)
% 230.52/41.90    (14)   ~ (e2 = e0)
% 230.52/41.90    (15)  all_55_13 = all_52_27
% 230.52/41.90    (16)   ~ (e1 = e0)
% 230.52/41.90    (17)  op(e3, e0) = all_18_1
% 230.52/41.90    (18)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 230.52/41.90    (19)  all_57_1 = e2 & op(e3, e2) = e2
% 230.52/41.90    (20)  op(all_52_29, all_52_29) = e1
% 230.52/41.90    (21)   ~ (all_52_27 = e0)
% 230.52/41.90    (22)   ~ (all_52_27 = e2)
% 230.52/41.90    (23)  op(e3, e0) = all_48_1
% 230.52/41.90    (24)  op(all_52_27, all_52_27) = e2
% 230.52/41.90  
% 230.52/41.90  Begin of proof
% 230.52/41.90  | 
% 230.52/41.90  | ALPHA: (19) implies:
% 230.52/41.90  |   (25)  all_57_1 = e2
% 230.52/41.90  | 
% 230.52/41.90  | GROUND_INST: instantiating (5) with all_18_1, all_48_1, e0, e3, simplifying
% 230.52/41.90  |              with (17), (23) gives:
% 230.52/41.90  |   (26)  all_48_1 = all_18_1
% 230.52/41.90  | 
% 230.52/41.90  | GROUND_INST: instantiating (5) with e1, all_48_1, e0, e3, simplifying with
% 230.52/41.90  |              (10), (23) gives:
% 230.52/41.90  |   (27)  all_48_1 = e1
% 230.52/41.90  | 
% 230.52/41.90  | COMBINE_EQS: (26), (27) imply:
% 230.52/41.90  |   (28)  all_18_1 = e1
% 230.52/41.90  | 
% 230.52/41.90  | REDUCE: (12), (28) imply:
% 230.52/41.90  |   (29)   ~ (e2 = e1)
% 230.52/41.90  | 
% 230.52/41.90  | SIMP: (29) implies:
% 230.52/41.90  |   (30)   ~ (e2 = e1)
% 230.52/41.90  | 
% 230.52/41.90  | BETA: splitting (1) gives:
% 230.52/41.90  | 
% 230.52/41.90  | Case 1:
% 230.52/41.90  | | 
% 230.52/41.90  | |   (31)  all_55_13 = e3
% 230.52/41.90  | | 
% 230.52/41.90  | | COMBINE_EQS: (15), (31) imply:
% 230.52/41.90  | |   (32)  all_52_27 = e3
% 230.52/41.90  | | 
% 230.52/41.90  | | SIMP: (32) implies:
% 230.52/41.90  | |   (33)  all_52_27 = e3
% 230.52/41.90  | | 
% 230.52/41.90  | | REDUCE: (21), (33) imply:
% 230.52/41.90  | |   (34)   ~ (e3 = e0)
% 230.52/41.90  | | 
% 230.52/41.90  | | REDUCE: (24), (33) imply:
% 230.52/41.90  | |   (35)  op(e3, e3) = e2
% 230.52/41.90  | | 
% 230.52/41.90  | | REF_CLOSE: (4), (5), (6), (8), (9), (14), (16), (25), (30), (34), (35) are
% 230.52/41.90  | |            inconsistent by sub-proof #1659.
% 230.52/41.90  | | 
% 230.52/41.90  | Case 2:
% 230.52/41.90  | | 
% 230.52/41.90  | |   (36)  all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 230.52/41.90  | | 
% 230.52/41.90  | | BETA: splitting (36) gives:
% 230.52/41.90  | | 
% 230.52/41.90  | | Case 1:
% 230.52/41.90  | | | 
% 230.52/41.90  | | |   (37)  all_55_13 = e2
% 230.52/41.90  | | | 
% 230.52/41.90  | | | REF_CLOSE: (15), (22), (37) are inconsistent by sub-proof #1647.
% 230.52/41.90  | | | 
% 230.52/41.90  | | Case 2:
% 230.52/41.90  | | | 
% 230.52/41.90  | | |   (38)  all_55_13 = e1 | all_55_13 = e0
% 230.52/41.90  | | | 
% 230.52/41.90  | | | BETA: splitting (38) gives:
% 230.52/41.90  | | | 
% 230.52/41.90  | | | Case 1:
% 230.52/41.90  | | | | 
% 230.52/41.90  | | | |   (39)  all_55_13 = e1
% 230.52/41.90  | | | | 
% 230.52/41.90  | | | | COMBINE_EQS: (15), (39) imply:
% 230.52/41.90  | | | |   (40)  all_52_27 = e1
% 230.52/41.90  | | | | 
% 230.52/41.90  | | | | SIMP: (40) implies:
% 230.52/41.90  | | | |   (41)  all_52_27 = e1
% 230.52/41.90  | | | | 
% 230.52/41.90  | | | | REDUCE: (3), (41) imply:
% 230.52/41.90  | | | |   (42)   ~ (all_52_29 = e1)
% 230.52/41.90  | | | | 
% 230.52/41.90  | | | | SIMP: (42) implies:
% 230.52/41.90  | | | |   (43)   ~ (all_52_29 = e1)
% 230.52/41.90  | | | | 
% 230.52/41.90  | | | | REF_CLOSE: (2), (5), (7), (11), (13), (16), (18), (20), (43) are
% 230.52/41.90  | | | |            inconsistent by sub-proof #1542.
% 230.52/41.90  | | | | 
% 230.52/41.90  | | | Case 2:
% 230.52/41.90  | | | | 
% 230.52/41.90  | | | |   (44)  all_55_13 = e0
% 230.52/41.90  | | | | 
% 230.52/41.90  | | | | REF_CLOSE: (15), (21), (44) are inconsistent by sub-proof #1639.
% 230.52/41.90  | | | | 
% 230.52/41.90  | | | End of split
% 230.52/41.90  | | | 
% 230.52/41.90  | | End of split
% 230.52/41.90  | | 
% 230.52/41.90  | End of split
% 230.52/41.90  | 
% 230.52/41.90  End of proof
% 230.52/41.90  
% 230.52/41.90  Sub-proof #1203 shows that the following formulas are inconsistent:
% 230.52/41.90  ----------------------------------------------------------------
% 230.52/41.90    (1)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3)
% 230.52/41.90    (2)   ~ (e3 = e1)
% 230.52/41.90    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.90           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.90    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.52/41.90         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.52/41.90    (5)  all_57_9 = e1
% 230.52/41.90    (6)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.52/41.90         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.52/41.90    (7)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.52/41.90         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.52/41.90    (8)  all_57_3 = e0
% 230.52/41.90    (9)  all_57_4 = e3
% 230.52/41.90    (10)   ~ (e3 = e2)
% 230.52/41.90    (11)   ~ (e3 = e0)
% 230.52/41.90    (12)  op(e3, e3) = e0
% 230.52/41.90    (13)   ~ (e2 = e0)
% 230.52/41.90    (14)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.52/41.90          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.52/41.90    (15)   ~ (e1 = e0)
% 230.52/41.90    (16)   ~ (all_53_12 = e3)
% 230.52/41.90    (17)   ~ (e2 = e1)
% 230.52/41.90    (18)  op(e3, e0) = all_53_12
% 230.52/41.90  
% 230.52/41.90  Begin of proof
% 230.52/41.90  | 
% 230.52/41.90  | BETA: splitting (1) gives:
% 230.52/41.90  | 
% 230.52/41.90  | Case 1:
% 230.52/41.90  | | 
% 230.52/41.90  | |   (19)  all_57_1 = e3 & op(e3, e2) = e3
% 230.52/41.90  | | 
% 230.52/41.90  | | ALPHA: (19) implies:
% 230.52/41.90  | |   (20)  all_57_1 = e3
% 230.52/41.90  | | 
% 230.52/41.90  | | REF_CLOSE: (2), (3), (4), (6), (7), (9), (10), (11), (12), (13), (15), (17),
% 230.52/41.90  | |            (20) are inconsistent by sub-proof #1220.
% 230.52/41.90  | | 
% 230.52/41.90  | Case 2:
% 230.52/41.90  | | 
% 230.52/41.90  | |   (21)  all_57_3 = e3 & op(e2, e2) = e3
% 230.52/41.90  | | 
% 230.52/41.90  | | ALPHA: (21) implies:
% 230.52/41.90  | |   (22)  all_57_3 = e3
% 230.52/41.90  | | 
% 230.52/41.90  | | REF_CLOSE: (3), (5), (6), (8), (9), (10), (11), (12), (13), (14), (16),
% 230.52/41.90  | |            (17), (18), (22) are inconsistent by sub-proof #1204.
% 230.52/41.90  | | 
% 230.52/41.90  | End of split
% 230.52/41.90  | 
% 230.52/41.90  End of proof
% 230.52/41.90  
% 230.52/41.90  Sub-proof #1204 shows that the following formulas are inconsistent:
% 230.52/41.90  ----------------------------------------------------------------
% 230.52/41.90    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.90           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.90    (2)  all_57_3 = e3
% 230.52/41.90    (3)  all_57_9 = e1
% 230.52/41.90    (4)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.52/41.90         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.52/41.90    (5)  all_57_3 = e0
% 230.52/41.90    (6)  all_57_4 = e3
% 230.52/41.90    (7)   ~ (e3 = e2)
% 230.52/41.90    (8)   ~ (e3 = e0)
% 230.52/41.90    (9)  op(e3, e3) = e0
% 230.52/41.90    (10)   ~ (e2 = e0)
% 230.52/41.90    (11)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.52/41.90          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.52/41.90    (12)   ~ (all_53_12 = e3)
% 230.52/41.90    (13)   ~ (e2 = e1)
% 230.52/41.90    (14)  op(e3, e0) = all_53_12
% 230.52/41.90  
% 230.52/41.90  Begin of proof
% 230.52/41.90  | 
% 230.52/41.90  | COMBINE_EQS: (2), (5) imply:
% 230.52/41.90  |   (15)  e3 = e0
% 230.52/41.90  | 
% 230.52/41.90  | SIMP: (15) implies:
% 230.52/41.90  |   (16)  e3 = e0
% 230.52/41.90  | 
% 230.52/41.90  | COMBINE_EQS: (6), (16) imply:
% 230.52/41.90  |   (17)  all_57_4 = e0
% 230.52/41.90  | 
% 230.52/41.90  | REF_CLOSE: (1), (3), (4), (7), (8), (9), (10), (11), (12), (13), (14), (17)
% 230.52/41.90  |            are inconsistent by sub-proof #1403.
% 230.52/41.90  | 
% 230.52/41.90  End of proof
% 230.52/41.90  
% 230.52/41.90  Sub-proof #1205 shows that the following formulas are inconsistent:
% 230.52/41.90  ----------------------------------------------------------------
% 230.52/41.90    (1)   ~ (e3 = e1)
% 230.52/41.90    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.90           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.90    (3)  all_57_6 = e1
% 230.52/41.90    (4)   ~ (e3 = e2)
% 230.52/41.90    (5)   ~ (e3 = e0)
% 230.52/41.90    (6)  op(e3, e3) = e0
% 230.52/41.90    (7)  all_57_12 = e1
% 230.52/41.90    (8)   ~ (e2 = e0)
% 230.52/41.90    (9)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.52/41.90         (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.52/41.90    (10)   ~ (e2 = e1)
% 230.52/41.90    (11)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.52/41.90          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.52/41.90  
% 230.52/41.90  Begin of proof
% 230.52/41.90  | 
% 230.52/41.90  | BETA: splitting (9) gives:
% 230.52/41.90  | 
% 230.52/41.90  | Case 1:
% 230.52/41.90  | | 
% 230.52/41.90  | |   (12)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) =
% 230.52/41.90  | |           e3)
% 230.52/41.90  | | 
% 230.52/41.90  | | BETA: splitting (12) gives:
% 230.52/41.90  | | 
% 230.52/41.90  | | Case 1:
% 230.52/41.90  | | | 
% 230.52/41.90  | | |   (13)  all_57_0 = e3 & op(e3, e3) = e3
% 230.52/41.90  | | | 
% 230.52/41.90  | | | ALPHA: (13) implies:
% 230.52/41.90  | | |   (14)  op(e3, e3) = e3
% 230.52/41.90  | | | 
% 230.52/41.90  | | | REF_CLOSE: (2), (5), (6), (14) are inconsistent by sub-proof #2494.
% 230.52/41.90  | | | 
% 230.52/41.90  | | Case 2:
% 230.52/41.90  | | | 
% 230.52/41.90  | | |   (15)  all_57_2 = e3 & op(e2, e3) = e3
% 230.52/41.90  | | | 
% 230.52/41.90  | | | ALPHA: (15) implies:
% 230.52/41.90  | | |   (16)  all_57_2 = e3
% 230.52/41.90  | | | 
% 230.52/41.90  | | | REF_CLOSE: (2), (3), (4), (6), (7), (8), (10), (11), (16) are inconsistent
% 230.52/41.90  | | |            by sub-proof #1923.
% 230.52/41.90  | | | 
% 230.52/41.90  | | End of split
% 230.52/41.90  | | 
% 230.52/41.90  | Case 2:
% 230.52/41.90  | | 
% 230.52/41.90  | |   (17)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) =
% 230.52/41.90  | |           e3)
% 230.52/41.90  | | 
% 230.52/41.90  | | REF_CLOSE: (1), (3), (7), (17) are inconsistent by sub-proof #1206.
% 230.52/41.90  | | 
% 230.52/41.90  | End of split
% 230.52/41.90  | 
% 230.52/41.90  End of proof
% 230.52/41.90  
% 230.52/41.90  Sub-proof #1206 shows that the following formulas are inconsistent:
% 230.52/41.90  ----------------------------------------------------------------
% 230.52/41.90    (1)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.52/41.90    (2)  all_57_6 = e1
% 230.52/41.90    (3)   ~ (e3 = e1)
% 230.52/41.90    (4)  all_57_12 = e1
% 230.52/41.90  
% 230.52/41.90  Begin of proof
% 230.52/41.90  | 
% 230.52/41.90  | BETA: splitting (1) gives:
% 230.52/41.90  | 
% 230.52/41.90  | Case 1:
% 230.52/41.90  | | 
% 230.52/41.90  | |   (5)  all_57_6 = e3 & op(e1, e3) = e3
% 230.52/41.90  | | 
% 230.52/41.90  | | ALPHA: (5) implies:
% 230.52/41.90  | |   (6)  all_57_6 = e3
% 230.52/41.90  | | 
% 230.52/41.90  | | REF_CLOSE: (2), (3), (6) are inconsistent by sub-proof #2017.
% 230.52/41.90  | | 
% 230.52/41.90  | Case 2:
% 230.52/41.90  | | 
% 230.52/41.90  | |   (7)  all_57_12 = e3 & op(e0, e3) = e3
% 230.52/41.90  | | 
% 230.52/41.90  | | ALPHA: (7) implies:
% 230.52/41.90  | |   (8)  all_57_12 = e3
% 230.52/41.90  | | 
% 230.52/41.90  | | REF_CLOSE: (3), (4), (8) are inconsistent by sub-proof #2151.
% 230.52/41.90  | | 
% 230.52/41.90  | End of split
% 230.52/41.90  | 
% 230.52/41.90  End of proof
% 230.52/41.90  
% 230.52/41.90  Sub-proof #1207 shows that the following formulas are inconsistent:
% 230.52/41.90  ----------------------------------------------------------------
% 230.52/41.90    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.90           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.90    (2)   ~ (all_48_1 = e1)
% 230.52/41.90    (3)  op(e3, e0) = e1
% 230.52/41.90    (4)  op(e3, e0) = all_18_1
% 230.52/41.90    (5)  op(e3, e0) = all_48_1
% 230.52/41.90  
% 230.52/41.90  Begin of proof
% 230.52/41.90  | 
% 230.52/41.90  | GROUND_INST: instantiating (1) with all_18_1, all_48_1, e0, e3, simplifying
% 230.52/41.90  |              with (4), (5) gives:
% 230.52/41.90  |   (6)  all_48_1 = all_18_1
% 230.52/41.90  | 
% 230.52/41.90  | GROUND_INST: instantiating (1) with e1, all_48_1, e0, e3, simplifying with
% 230.52/41.90  |              (3), (5) gives:
% 230.52/41.90  |   (7)  all_48_1 = e1
% 230.52/41.90  | 
% 230.52/41.90  | COMBINE_EQS: (6), (7) imply:
% 230.52/41.90  |   (8)  all_18_1 = e1
% 230.52/41.90  | 
% 230.52/41.90  | REDUCE: (2), (7) imply:
% 230.52/41.90  |   (9)  $false
% 230.52/41.90  | 
% 230.52/41.90  | CLOSE: (9) is inconsistent.
% 230.52/41.90  | 
% 230.52/41.90  End of proof
% 230.52/41.90  
% 230.52/41.90  Sub-proof #1208 shows that the following formulas are inconsistent:
% 230.52/41.90  ----------------------------------------------------------------
% 230.52/41.90    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.90           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.90    (2)  all_57_4 = e3
% 230.52/41.90    (3)   ~ (e3 = e2)
% 230.52/41.90    (4)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.52/41.90    (5)   ~ (all_53_12 = e2)
% 230.52/41.90    (6)  op(e3, e0) = all_53_12
% 230.52/41.90  
% 230.52/41.90  Begin of proof
% 230.52/41.90  | 
% 230.52/41.90  | BETA: splitting (4) gives:
% 230.52/41.90  | 
% 230.52/41.90  | Case 1:
% 230.52/41.90  | | 
% 230.52/41.90  | |   (7)  all_57_4 = e2 & op(e3, e1) = e2
% 230.52/41.90  | | 
% 230.52/41.90  | | ALPHA: (7) implies:
% 230.52/41.90  | |   (8)  all_57_4 = e2
% 230.52/41.90  | | 
% 230.52/41.90  | | REF_CLOSE: (2), (3), (8) are inconsistent by sub-proof #2482.
% 230.52/41.90  | | 
% 230.52/41.90  | Case 2:
% 230.52/41.90  | | 
% 230.52/41.90  | |   (9)  all_57_9 = e2 & op(e3, e0) = e2
% 230.52/41.90  | | 
% 230.52/41.90  | | ALPHA: (9) implies:
% 230.52/41.90  | |   (10)  op(e3, e0) = e2
% 230.52/41.90  | | 
% 230.52/41.90  | | REF_CLOSE: (1), (5), (6), (10) are inconsistent by sub-proof #2331.
% 230.52/41.90  | | 
% 230.52/41.90  | End of split
% 230.52/41.90  | 
% 230.52/41.90  End of proof
% 230.52/41.90  
% 230.52/41.90  Sub-proof #1209 shows that the following formulas are inconsistent:
% 230.52/41.90  ----------------------------------------------------------------
% 230.52/41.90    (1)  all_55_8 = all_18_0
% 230.52/41.90    (2)  all_55_8 = e2
% 230.52/41.90    (3)   ~ (all_18_0 = e2)
% 230.52/41.90  
% 230.52/41.90  Begin of proof
% 230.52/41.90  | 
% 230.52/41.90  | COMBINE_EQS: (1), (2) imply:
% 230.52/41.90  |   (4)  all_18_0 = e2
% 230.52/41.90  | 
% 230.52/41.90  | SIMP: (4) implies:
% 230.52/41.90  |   (5)  all_18_0 = e2
% 230.52/41.90  | 
% 230.52/41.90  | REDUCE: (3), (5) imply:
% 230.52/41.90  |   (6)  $false
% 230.52/41.90  | 
% 230.52/41.90  | CLOSE: (6) is inconsistent.
% 230.52/41.90  | 
% 230.52/41.90  End of proof
% 230.52/41.90  
% 230.52/41.90  Sub-proof #1210 shows that the following formulas are inconsistent:
% 230.52/41.90  ----------------------------------------------------------------
% 230.52/41.90    (1)   ~ (all_14_0 = e1)
% 230.52/41.90    (2)  all_57_15 = e0
% 230.52/41.90    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.52/41.90         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.52/41.90    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.52/41.90         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.52/41.90    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.52/41.90         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.52/41.90    (6)   ~ (e3 = e1)
% 230.52/41.90    (7)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.52/41.90         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.52/41.90    (8)  op(all_14_1, e2) = all_14_0
% 230.52/41.90    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.90           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.90    (10)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.52/41.90          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.52/41.90    (11)  op(e2, e0) = e3
% 230.52/41.90    (12)   ~ (all_6_2 = e3)
% 230.52/41.90    (13)  op(e1, e1) = all_6_2
% 230.52/41.90    (14)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.52/41.90          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.52/41.90    (15)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3)
% 230.52/41.90    (16)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.52/41.90          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.52/41.90    (17)  op(e2, e2) = e0
% 230.52/41.90    (18)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.52/41.90          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.52/41.90    (19)  all_57_3 = e0
% 230.52/41.90    (20)   ~ (e3 = e2)
% 230.52/41.90    (21)  op(e1, e0) = all_53_14
% 230.52/41.90    (22)   ~ (e3 = e0)
% 230.52/41.90    (23)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.52/41.90          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.52/41.90    (24)  all_57_0 = e0
% 230.52/41.90    (25)  op(e3, e3) = e0
% 230.52/41.90    (26)   ~ (all_53_14 = e3)
% 230.52/41.90    (27)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.52/41.90          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.52/41.90    (28)   ~ (e2 = e0)
% 230.52/41.90    (29)   ~ (e1 = e0)
% 230.52/41.90    (30)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 230.52/41.90          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 230.52/41.90    (31)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.52/41.90          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.52/41.90    (32)  op(e2, e0) = all_14_1
% 230.52/41.90    (33)  all_57_10 = e3
% 230.52/41.90    (34)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.52/41.90          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.52/41.90            e2)
% 230.52/41.90    (35)  op(e1, e1) = e0
% 230.52/41.90    (36)  op(e3, e2) = e2
% 230.52/41.90    (37)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.52/41.90          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.52/41.90    (38)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.52/41.90          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.52/41.90    (39)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.52/41.90          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.52/41.90    (40)   ~ (e2 = e1)
% 230.52/41.90    (41)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.52/41.90          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.52/41.90    (42)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.52/41.90          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.52/41.90    (43)  op(e2, e0) = all_50_1
% 230.52/41.90    (44)   ~ (all_53_12 = e2)
% 230.52/41.90    (45)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.52/41.90          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.52/41.90    (46)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.52/41.90          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.52/41.90    (47)  op(e3, e0) = all_53_12
% 230.52/41.90  
% 230.52/41.90  Begin of proof
% 230.52/41.90  | 
% 230.52/41.90  | BETA: splitting (15) gives:
% 230.52/41.90  | 
% 230.52/41.90  | Case 1:
% 230.52/41.90  | | 
% 230.52/41.90  | |   (48)  all_57_0 = e3 & op(e3, e3) = e3
% 230.52/41.90  | | 
% 230.52/41.90  | | ALPHA: (48) implies:
% 230.52/41.90  | |   (49)  op(e3, e3) = e3
% 230.52/41.90  | | 
% 230.52/41.90  | | REF_CLOSE: (9), (22), (25), (49) are inconsistent by sub-proof #2494.
% 230.52/41.90  | | 
% 230.52/41.90  | Case 2:
% 230.52/41.90  | | 
% 230.52/41.90  | |   (50)  all_57_1 = e3 & op(e3, e2) = e3
% 230.52/41.90  | | 
% 230.52/41.90  | | ALPHA: (50) implies:
% 230.52/41.90  | |   (51)  all_57_1 = e3
% 230.52/41.90  | |   (52)  op(e3, e2) = e3
% 230.52/41.90  | | 
% 230.52/41.90  | | BETA: splitting (30) gives:
% 230.52/41.90  | | 
% 230.52/41.90  | | Case 1:
% 230.52/41.90  | | | 
% 230.52/41.90  | | |   (53)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) =
% 230.52/41.90  | | |           e3)
% 230.52/41.90  | | | 
% 230.52/41.90  | | | BETA: splitting (53) gives:
% 230.52/41.90  | | | 
% 230.52/41.90  | | | Case 1:
% 230.52/41.90  | | | | 
% 230.52/41.90  | | | |   (54)  all_57_4 = e3 & op(e3, e1) = e3
% 230.52/41.90  | | | | 
% 230.52/41.90  | | | | ALPHA: (54) implies:
% 230.52/41.90  | | | |   (55)  all_57_4 = e3
% 230.52/41.90  | | | | 
% 230.52/41.90  | | | | REF_CLOSE: (6), (9), (14), (16), (18), (20), (22), (25), (28), (29),
% 230.52/41.90  | | | |            (40), (51), (55) are inconsistent by sub-proof #1220.
% 230.52/41.90  | | | | 
% 230.52/41.90  | | | Case 2:
% 230.52/41.90  | | | | 
% 230.52/41.90  | | | |   (56)  all_57_5 = e3 & op(e2, e1) = e3
% 230.52/41.90  | | | | 
% 230.52/41.90  | | | | ALPHA: (56) implies:
% 230.52/41.90  | | | |   (57)  all_57_5 = e3
% 230.52/41.90  | | | | 
% 230.52/41.90  | | | | REF_CLOSE: (3), (6), (19), (20), (28), (29), (33), (38), (40), (57) are
% 230.52/41.90  | | | |            inconsistent by sub-proof #1693.
% 230.52/41.90  | | | | 
% 230.52/41.90  | | | End of split
% 230.52/41.90  | | | 
% 230.52/41.90  | | Case 2:
% 230.52/41.90  | | | 
% 230.52/41.90  | | |   (58)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) =
% 230.52/41.90  | | |           e3)
% 230.52/41.90  | | | 
% 230.52/41.90  | | | BETA: splitting (58) gives:
% 230.52/41.90  | | | 
% 230.52/41.90  | | | Case 1:
% 230.52/41.90  | | | | 
% 230.52/41.90  | | | |   (59)  all_57_8 = e3 & op(e1, e1) = e3
% 230.52/41.90  | | | | 
% 230.52/41.90  | | | | ALPHA: (59) implies:
% 230.52/41.90  | | | |   (60)  op(e1, e1) = e3
% 230.52/41.90  | | | | 
% 230.52/41.90  | | | | REF_CLOSE: (9), (12), (13), (60) are inconsistent by sub-proof #2468.
% 230.52/41.90  | | | | 
% 230.52/41.90  | | | Case 2:
% 230.52/41.90  | | | | 
% 230.52/41.90  | | | |   (61)  all_57_14 = e3 & op(e0, e1) = e3
% 230.52/41.90  | | | | 
% 230.52/41.90  | | | | ALPHA: (61) implies:
% 230.52/41.90  | | | |   (62)  all_57_14 = e3
% 230.52/41.90  | | | | 
% 230.52/41.90  | | | | BETA: splitting (41) gives:
% 230.52/41.90  | | | | 
% 230.52/41.90  | | | | Case 1:
% 230.52/41.90  | | | | | 
% 230.52/41.90  | | | | |   (63)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2,
% 230.52/41.90  | | | | |             e0) = e2)
% 230.52/41.90  | | | | | 
% 230.52/41.90  | | | | | REF_CLOSE: (9), (20), (33), (44), (47), (63) are inconsistent by
% 230.52/41.90  | | | | |            sub-proof #1219.
% 230.52/41.90  | | | | | 
% 230.52/41.90  | | | | Case 2:
% 230.52/41.90  | | | | | 
% 230.52/41.90  | | | | |   (64)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0,
% 230.52/41.90  | | | | |             e0) = e2)
% 230.52/41.90  | | | | | 
% 230.52/41.90  | | | | | BETA: splitting (64) gives:
% 230.52/41.90  | | | | | 
% 230.52/41.90  | | | | | Case 1:
% 230.52/41.90  | | | | | | 
% 230.52/41.90  | | | | | |   (65)  all_57_11 = e2 & op(e1, e0) = e2
% 230.52/41.90  | | | | | | 
% 230.52/41.90  | | | | | | ALPHA: (65) implies:
% 230.52/41.90  | | | | | |   (66)  all_57_11 = e2
% 230.52/41.90  | | | | | | 
% 230.52/41.90  | | | | | | BETA: splitting (5) gives:
% 230.52/41.90  | | | | | | 
% 230.52/41.90  | | | | | | Case 1:
% 230.52/41.90  | | | | | | | 
% 230.52/41.90  | | | | | | |   (67)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 &
% 230.52/41.90  | | | | | | |           op(e2, e2) = e2)
% 230.52/41.90  | | | | | | | 
% 230.52/41.90  | | | | | | | BETA: splitting (67) gives:
% 230.52/41.90  | | | | | | | 
% 230.52/41.90  | | | | | | | Case 1:
% 230.52/41.90  | | | | | | | | 
% 230.52/41.90  | | | | | | | |   (68)  all_57_1 = e2 & op(e3, e2) = e2
% 230.52/41.90  | | | | | | | | 
% 230.52/41.90  | | | | | | | | REF_CLOSE: (20), (51), (68) are inconsistent by sub-proof #1809.
% 230.52/41.90  | | | | | | | | 
% 230.52/41.90  | | | | | | | Case 2:
% 230.52/41.90  | | | | | | | | 
% 230.52/41.90  | | | | | | | |   (69)  all_57_3 = e2 & op(e2, e2) = e2
% 230.52/41.90  | | | | | | | | 
% 230.52/41.90  | | | | | | | | ALPHA: (69) implies:
% 230.52/41.90  | | | | | | | |   (70)  op(e2, e2) = e2
% 230.52/41.90  | | | | | | | | 
% 230.52/41.90  | | | | | | | | REF_CLOSE: (9), (17), (28), (70) are inconsistent by sub-proof
% 230.52/41.90  | | | | | | | |            #2472.
% 230.52/41.90  | | | | | | | | 
% 230.52/41.90  | | | | | | | End of split
% 230.52/41.90  | | | | | | | 
% 230.52/41.90  | | | | | | Case 2:
% 230.52/41.90  | | | | | | | 
% 230.52/41.90  | | | | | | |   (71)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 &
% 230.52/41.90  | | | | | | |           op(e0, e2) = e2)
% 230.52/41.90  | | | | | | | 
% 230.52/41.90  | | | | | | | BETA: splitting (71) gives:
% 230.52/41.90  | | | | | | | 
% 230.52/41.90  | | | | | | | Case 1:
% 230.52/41.90  | | | | | | | | 
% 230.52/41.90  | | | | | | | |   (72)  all_57_7 = e2 & op(e1, e2) = e2
% 230.52/41.90  | | | | | | | | 
% 230.52/41.90  | | | | | | | | ALPHA: (72) implies:
% 230.52/41.90  | | | | | | | |   (73)  all_57_7 = e2
% 230.52/41.90  | | | | | | | | 
% 230.52/41.90  | | | | | | | | BETA: splitting (46) gives:
% 230.52/41.90  | | | | | | | | 
% 230.52/41.90  | | | | | | | | Case 1:
% 230.52/41.90  | | | | | | | | | 
% 230.52/41.90  | | | | | | | | |   (74)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 &
% 230.52/41.90  | | | | | | | | |           op(e2, e2) = e1)
% 230.52/41.90  | | | | | | | | | 
% 230.52/41.90  | | | | | | | | | REF_CLOSE: (1), (8), (9), (11), (17), (29), (32), (43), (74)
% 230.52/41.90  | | | | | | | | |            are inconsistent by sub-proof #1218.
% 230.52/41.90  | | | | | | | | | 
% 230.52/41.90  | | | | | | | | Case 2:
% 230.52/41.90  | | | | | | | | | 
% 230.52/41.90  | | | | | | | | |   (75)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 &
% 230.52/41.90  | | | | | | | | |           op(e0, e2) = e1)
% 230.52/41.90  | | | | | | | | | 
% 230.52/41.90  | | | | | | | | | BETA: splitting (75) gives:
% 230.52/41.90  | | | | | | | | | 
% 230.52/41.90  | | | | | | | | | Case 1:
% 230.52/41.90  | | | | | | | | | | 
% 230.52/41.90  | | | | | | | | | |   (76)  all_57_7 = e1 & op(e1, e2) = e1
% 230.52/41.90  | | | | | | | | | | 
% 230.52/41.90  | | | | | | | | | | REF_CLOSE: (40), (73), (76) are inconsistent by sub-proof
% 230.52/41.90  | | | | | | | | | |            #2190.
% 230.52/41.90  | | | | | | | | | | 
% 230.52/41.90  | | | | | | | | | Case 2:
% 230.52/41.90  | | | | | | | | | | 
% 230.52/41.90  | | | | | | | | | |   (77)  all_57_13 = e1 & op(e0, e2) = e1
% 230.52/41.90  | | | | | | | | | | 
% 230.52/41.90  | | | | | | | | | | ALPHA: (77) implies:
% 230.52/41.90  | | | | | | | | | |   (78)  all_57_13 = e1
% 230.52/41.90  | | | | | | | | | | 
% 230.52/41.90  | | | | | | | | | | BETA: splitting (10) gives:
% 230.52/41.90  | | | | | | | | | | 
% 230.52/41.90  | | | | | | | | | | Case 1:
% 230.52/41.90  | | | | | | | | | | | 
% 230.52/41.90  | | | | | | | | | | |   (79)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 230.52/41.90  | | | | | | | | | | |           & op(e1, e2) = e3)
% 230.52/41.90  | | | | | | | | | | | 
% 230.52/41.90  | | | | | | | | | | | BETA: splitting (79) gives:
% 230.52/41.90  | | | | | | | | | | | 
% 230.52/41.90  | | | | | | | | | | | Case 1:
% 230.52/41.90  | | | | | | | | | | | | 
% 230.52/41.90  | | | | | | | | | | | |   (80)  all_57_6 = e3 & op(e1, e3) = e3
% 230.52/41.90  | | | | | | | | | | | | 
% 230.52/41.90  | | | | | | | | | | | | ALPHA: (80) implies:
% 230.52/41.90  | | | | | | | | | | | |   (81)  all_57_6 = e3
% 230.52/41.90  | | | | | | | | | | | | 
% 230.52/41.90  | | | | | | | | | | | | BETA: splitting (16) gives:
% 230.52/41.90  | | | | | | | | | | | | 
% 230.52/41.90  | | | | | | | | | | | | Case 1:
% 230.52/41.90  | | | | | | | | | | | | | 
% 230.52/41.90  | | | | | | | | | | | | |   (82)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 230.52/41.90  | | | | | | | | | | | | |           & op(e3, e2) = e2)
% 230.52/41.90  | | | | | | | | | | | | | 
% 230.52/41.90  | | | | | | | | | | | | | REF_CLOSE: (9), (20), (25), (28), (51), (82) are inconsistent
% 230.52/41.90  | | | | | | | | | | | | |            by sub-proof #1224.
% 230.52/41.90  | | | | | | | | | | | | | 
% 230.52/41.90  | | | | | | | | | | | | Case 2:
% 230.52/41.90  | | | | | | | | | | | | | 
% 230.52/41.90  | | | | | | | | | | | | |   (83)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 230.52/41.90  | | | | | | | | | | | | |           & op(e3, e0) = e2)
% 230.52/41.90  | | | | | | | | | | | | | 
% 230.52/41.90  | | | | | | | | | | | | | BETA: splitting (83) gives:
% 230.52/41.90  | | | | | | | | | | | | | 
% 230.52/41.90  | | | | | | | | | | | | | Case 1:
% 230.52/41.90  | | | | | | | | | | | | | | 
% 230.52/41.90  | | | | | | | | | | | | | |   (84)  all_57_4 = e2 & op(e3, e1) = e2
% 230.52/41.90  | | | | | | | | | | | | | | 
% 230.52/41.90  | | | | | | | | | | | | | | ALPHA: (84) implies:
% 230.52/41.90  | | | | | | | | | | | | | |   (85)  all_57_4 = e2
% 230.52/41.90  | | | | | | | | | | | | | | 
% 230.52/41.90  | | | | | | | | | | | | | | BETA: splitting (23) gives:
% 230.52/41.90  | | | | | | | | | | | | | | 
% 230.52/41.90  | | | | | | | | | | | | | | Case 1:
% 230.52/41.90  | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | |   (86)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 230.52/41.91  | | | | | | | | | | | | | | |           & op(e2, e1) = e1)
% 230.52/41.91  | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | BETA: splitting (86) gives:
% 230.52/41.91  | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | Case 1:
% 230.52/41.91  | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | |   (87)  all_57_4 = e1 & op(e3, e1) = e1
% 230.52/41.91  | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | REF_CLOSE: (40), (85), (87) are inconsistent by sub-proof
% 230.52/41.91  | | | | | | | | | | | | | | | |            #2452.
% 230.52/41.91  | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | Case 2:
% 230.52/41.91  | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | |   (88)  all_57_5 = e1 & op(e2, e1) = e1
% 230.52/41.91  | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | ALPHA: (88) implies:
% 230.52/41.91  | | | | | | | | | | | | | | | |   (89)  all_57_5 = e1
% 230.52/41.91  | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | BETA: splitting (38) gives:
% 230.52/41.91  | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | Case 1:
% 230.52/41.91  | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | |   (90)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 230.52/41.91  | | | | | | | | | | | | | | | | |           & op(e2, e2) = e2)
% 230.52/41.91  | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | BETA: splitting (90) gives:
% 230.52/41.91  | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | Case 1:
% 230.52/41.91  | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | |   (91)  all_57_2 = e2 & op(e2, e3) = e2
% 230.52/41.91  | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | ALPHA: (91) implies:
% 230.52/41.91  | | | | | | | | | | | | | | | | | |   (92)  all_57_2 = e2
% 230.52/41.91  | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | BETA: splitting (34) gives:
% 230.52/41.91  | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | Case 1:
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | |   (93)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 230.52/41.91  | | | | | | | | | | | | | | | | | | |           e2 & op(e0, e2) = e2)
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | BETA: splitting (93) gives:
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | Case 1:
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | |   (94)  all_57_12 = e2 & op(e0, e3) = e2
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | ALPHA: (94) implies:
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | |   (95)  all_57_12 = e2
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | BETA: splitting (4) gives:
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | |   (96)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | |           & op(e2, e3) = e1)
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (9), (17), (19), (20), (22), (24), (28),
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | |            (29), (33), (37), (38), (40), (89), (96) are
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1217.
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | |   (97)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | |           e1 & op(e0, e3) = e1)
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (97) gives:
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | |   (98)  all_57_6 = e1 & op(e1, e3) = e1
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (98) implies:
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | |   (99)  all_57_6 = e1
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (81), (99) imply:
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | |   (100)  e3 = e1
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | | SIMP: (100) implies:
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | |   (101)  e3 = e1
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (51), (101) imply:
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | |   (102)  all_57_1 = e1
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (19), (20), (22), (31), (73), (78), (102) are
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2193.
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | |   (103)  all_57_12 = e1 & op(e0, e3) = e1
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (103) implies:
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | |   (104)  all_57_12 = e1
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (95), (104) imply:
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | |   (105)  e2 = e1
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | | SIMP: (105) implies:
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | |   (106)  e2 = e1
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (92), (106) imply:
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | |   (107)  all_57_2 = e1
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (17), (19), (20), (22), (28), (37),
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | |            (38), (40), (89), (107) are inconsistent by
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1536.
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | End of split
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | End of split
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | Case 2:
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | |   (108)  all_57_13 = e2 & op(e0, e2) = e2
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | ALPHA: (108) implies:
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | |   (109)  all_57_13 = e2
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (19), (29), (40), (46), (51), (73), (109) are
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1698.
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | End of split
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | Case 2:
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | |   (110)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 230.52/41.91  | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | BETA: splitting (110) gives:
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | Case 1:
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | |   (111)  all_57_14 = e2 & op(e0, e1) = e2
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | ALPHA: (111) implies:
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | |   (112)  all_57_14 = e2
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (62), (112) are inconsistent by sub-proof
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | |            #2410.
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | Case 2:
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | |   (113)  all_57_15 = e2 & op(e0, e0) = e2
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (19), (20), (28), (33), (38), (40), (89),
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | |            (92), (113) are inconsistent by sub-proof #1412.
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | End of split
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | End of split
% 230.52/41.91  | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | Case 2:
% 230.52/41.91  | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | |   (114)  all_57_3 = e2 & op(e2, e2) = e2
% 230.52/41.91  | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | ALPHA: (114) implies:
% 230.52/41.91  | | | | | | | | | | | | | | | | | |   (115)  op(e2, e2) = e2
% 230.52/41.91  | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (17), (28), (115) are inconsistent by
% 230.52/41.91  | | | | | | | | | | | | | | | | | |            sub-proof #2472.
% 230.52/41.91  | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | End of split
% 230.52/41.91  | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | Case 2:
% 230.52/41.91  | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | |   (116)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 230.52/41.91  | | | | | | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 230.52/41.91  | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | BETA: splitting (116) gives:
% 230.52/41.91  | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | Case 1:
% 230.52/41.91  | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | |   (117)  all_57_5 = e2 & op(e2, e1) = e2
% 230.52/41.91  | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | ALPHA: (117) implies:
% 230.52/41.91  | | | | | | | | | | | | | | | | | |   (118)  all_57_5 = e2
% 230.52/41.91  | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | BETA: splitting (23) gives:
% 230.52/41.91  | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | Case 1:
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (40), (85), (86), (118) are inconsistent by
% 230.52/41.91  | | | | | | | | | | | | | | | | | | |            sub-proof #1216.
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | Case 2:
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | |   (119)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 230.52/41.91  | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e1) = e1)
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (19), (20), (22), (29), (31), (35),
% 230.52/41.91  | | | | | | | | | | | | | | | | | | |            (51), (62), (73), (78), (119) are inconsistent by
% 230.52/41.91  | | | | | | | | | | | | | | | | | | |            sub-proof #1215.
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | End of split
% 230.52/41.91  | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | Case 2:
% 230.52/41.91  | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | |   (120)  all_57_10 = e2 & op(e2, e0) = e2
% 230.52/41.91  | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | ALPHA: (120) implies:
% 230.52/41.91  | | | | | | | | | | | | | | | | | |   (121)  all_57_10 = e2
% 230.52/41.91  | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (33), (121) are inconsistent by sub-proof
% 230.52/41.91  | | | | | | | | | | | | | | | | | |            #2356.
% 230.52/41.91  | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | End of split
% 230.52/41.91  | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | End of split
% 230.52/41.91  | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | End of split
% 230.52/41.91  | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | Case 2:
% 230.52/41.91  | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | |   (122)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 230.52/41.91  | | | | | | | | | | | | | | |            e1 & op(e0, e1) = e1)
% 230.52/41.91  | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (19), (20), (22), (29), (31), (35),
% 230.52/41.91  | | | | | | | | | | | | | | |            (51), (62), (73), (78), (122) are inconsistent by
% 230.52/41.91  | | | | | | | | | | | | | | |            sub-proof #1215.
% 230.52/41.91  | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | End of split
% 230.52/41.91  | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | Case 2:
% 230.52/41.91  | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | |   (123)  all_57_9 = e2 & op(e3, e0) = e2
% 230.52/41.91  | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | ALPHA: (123) implies:
% 230.52/41.91  | | | | | | | | | | | | | |   (124)  op(e3, e0) = e2
% 230.52/41.91  | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | REF_CLOSE: (9), (44), (47), (124) are inconsistent by
% 230.52/41.91  | | | | | | | | | | | | | |            sub-proof #2331.
% 230.52/41.91  | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | End of split
% 230.52/41.91  | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | End of split
% 230.52/41.91  | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | Case 2:
% 230.52/41.91  | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | |   (125)  all_57_7 = e3 & op(e1, e2) = e3
% 230.52/41.91  | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | ALPHA: (125) implies:
% 230.52/41.91  | | | | | | | | | | | |   (126)  all_57_7 = e3
% 230.52/41.91  | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | REF_CLOSE: (5), (6), (20), (22), (27), (28), (29), (40),
% 230.52/41.91  | | | | | | | | | | | |            (46), (51), (78), (126) are inconsistent by
% 230.52/41.91  | | | | | | | | | | | |            sub-proof #1214.
% 230.52/41.91  | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | End of split
% 230.52/41.91  | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | Case 2:
% 230.52/41.91  | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | |   (127)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 230.52/41.91  | | | | | | | | | | |            e3 & op(e1, e0) = e3)
% 230.52/41.91  | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | REF_CLOSE: (9), (12), (13), (21), (26), (127) are
% 230.52/41.91  | | | | | | | | | | |            inconsistent by sub-proof #2310.
% 230.52/41.91  | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | End of split
% 230.52/41.91  | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | End of split
% 230.52/41.91  | | | | | | | | | 
% 230.52/41.91  | | | | | | | | End of split
% 230.52/41.91  | | | | | | | | 
% 230.52/41.91  | | | | | | | Case 2:
% 230.52/41.91  | | | | | | | | 
% 230.52/41.91  | | | | | | | |   (128)  all_57_13 = e2 & op(e0, e2) = e2
% 230.52/41.91  | | | | | | | | 
% 230.52/41.91  | | | | | | | | ALPHA: (128) implies:
% 230.52/41.91  | | | | | | | |   (129)  all_57_13 = e2
% 230.52/41.91  | | | | | | | | 
% 230.52/41.91  | | | | | | | | BETA: splitting (46) gives:
% 230.52/41.91  | | | | | | | | 
% 230.52/41.91  | | | | | | | | Case 1:
% 230.52/41.91  | | | | | | | | | 
% 230.52/41.91  | | | | | | | | |   (130)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 &
% 230.52/41.91  | | | | | | | | |            op(e2, e2) = e1)
% 230.52/41.91  | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | REF_CLOSE: (1), (8), (9), (11), (17), (29), (32), (43), (130)
% 230.52/41.91  | | | | | | | | |            are inconsistent by sub-proof #1218.
% 230.52/41.91  | | | | | | | | | 
% 230.52/41.91  | | | | | | | | Case 2:
% 230.52/41.91  | | | | | | | | | 
% 230.52/41.91  | | | | | | | | |   (131)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 &
% 230.52/41.91  | | | | | | | | |            op(e0, e2) = e1)
% 230.52/41.91  | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | BETA: splitting (131) gives:
% 230.52/41.91  | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | Case 1:
% 230.52/41.91  | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | |   (132)  all_57_7 = e1 & op(e1, e2) = e1
% 230.52/41.91  | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | ALPHA: (132) implies:
% 230.52/41.91  | | | | | | | | | |   (133)  all_57_7 = e1
% 230.52/41.91  | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | BETA: splitting (10) gives:
% 230.52/41.91  | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | Case 1:
% 230.52/41.91  | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | |   (134)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 230.52/41.91  | | | | | | | | | | |            & op(e1, e2) = e3)
% 230.52/41.91  | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | BETA: splitting (134) gives:
% 230.52/41.91  | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | Case 1:
% 230.52/41.91  | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | |   (135)  all_57_6 = e3 & op(e1, e3) = e3
% 230.52/41.91  | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | ALPHA: (135) implies:
% 230.52/41.91  | | | | | | | | | | | |   (136)  all_57_6 = e3
% 230.52/41.91  | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | BETA: splitting (16) gives:
% 230.52/41.91  | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | Case 1:
% 230.52/41.91  | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | |   (137)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 230.52/41.91  | | | | | | | | | | | | |            & op(e3, e2) = e2)
% 230.52/41.91  | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | REF_CLOSE: (9), (20), (25), (28), (51), (137) are
% 230.52/41.91  | | | | | | | | | | | | |            inconsistent by sub-proof #1224.
% 230.52/41.91  | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | Case 2:
% 230.52/41.91  | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | |   (138)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 230.52/41.91  | | | | | | | | | | | | |            & op(e3, e0) = e2)
% 230.52/41.91  | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | BETA: splitting (138) gives:
% 230.52/41.91  | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | Case 1:
% 230.52/41.91  | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | |   (139)  all_57_4 = e2 & op(e3, e1) = e2
% 230.52/41.91  | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | ALPHA: (139) implies:
% 230.52/41.91  | | | | | | | | | | | | | |   (140)  all_57_4 = e2
% 230.52/41.91  | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | BETA: splitting (23) gives:
% 230.52/41.91  | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | Case 1:
% 230.52/41.91  | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | |   (141)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 230.52/41.91  | | | | | | | | | | | | | | |            & op(e2, e1) = e1)
% 230.52/41.91  | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | BETA: splitting (141) gives:
% 230.52/41.91  | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | Case 1:
% 230.52/41.91  | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | |   (142)  all_57_4 = e1 & op(e3, e1) = e1
% 230.52/41.91  | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | REF_CLOSE: (40), (140), (142) are inconsistent by sub-proof
% 230.52/41.91  | | | | | | | | | | | | | | | |            #2452.
% 230.52/41.91  | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | Case 2:
% 230.52/41.91  | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | |   (143)  all_57_5 = e1 & op(e2, e1) = e1
% 230.52/41.91  | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | ALPHA: (143) implies:
% 230.52/41.91  | | | | | | | | | | | | | | | |   (144)  all_57_5 = e1
% 230.52/41.91  | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | BETA: splitting (38) gives:
% 230.52/41.91  | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | Case 1:
% 230.52/41.91  | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | |   (145)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 230.52/41.91  | | | | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 230.52/41.91  | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | BETA: splitting (145) gives:
% 230.52/41.91  | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | Case 1:
% 230.52/41.91  | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | |   (146)  all_57_2 = e2 & op(e2, e3) = e2
% 230.52/41.91  | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | ALPHA: (146) implies:
% 230.52/41.91  | | | | | | | | | | | | | | | | | |   (147)  all_57_2 = e2
% 230.52/41.91  | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | BETA: splitting (4) gives:
% 230.52/41.91  | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | Case 1:
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | |   (148)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 230.52/41.91  | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e1)
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (9), (17), (19), (20), (22), (24), (28),
% 230.52/41.91  | | | | | | | | | | | | | | | | | | |            (29), (33), (37), (38), (40), (144), (148) are
% 230.52/41.91  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1217.
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | Case 2:
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | |   (149)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 230.52/41.91  | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e3) = e1)
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | BETA: splitting (149) gives:
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | Case 1:
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | |   (150)  all_57_6 = e1 & op(e1, e3) = e1
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | ALPHA: (150) implies:
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | |   (151)  all_57_6 = e1
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (136), (151) are inconsistent by sub-proof
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | |            #2017.
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | Case 2:
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | |   (152)  all_57_12 = e1 & op(e0, e3) = e1
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | ALPHA: (152) implies:
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | |   (153)  all_57_12 = e1
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | BETA: splitting (42) gives:
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | |   (154)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e2)
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (154) gives:
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | |   (155)  all_57_0 = e2 & op(e3, e3) = e2
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (155) implies:
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | |   (156)  op(e3, e3) = e2
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (9), (19), (20), (22), (28), (29), (37),
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | |            (38), (39), (40), (45), (147), (153), (156) are
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1629.
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with e2, e3, e2, e3, simplifying
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | |              with (36), (52) gives:
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | |   (157)  e3 = e2
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (136), (157) imply:
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | |   (158)  all_57_6 = e2
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (20), (22), (25), (39), (147), (153),
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | |            (158) are inconsistent by sub-proof #1212.
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | End of split
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | |   (159)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e3) = e2)
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (159) gives:
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | |   (160)  all_57_6 = e2 & op(e1, e3) = e2
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (160) implies:
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | |   (161)  all_57_6 = e2
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (20), (22), (25), (39), (147), (153),
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | |            (161) are inconsistent by sub-proof #1212.
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | |   (162)  all_57_12 = e2 & op(e0, e3) = e2
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (162) implies:
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | |   (163)  all_57_12 = e2
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (153), (163) imply:
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | |   (164)  e2 = e1
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (147), (164) imply:
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | |   (165)  all_57_2 = e1
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (17), (19), (20), (22), (28), (37),
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | |            (38), (40), (144), (165) are inconsistent by
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1536.
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | End of split
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | End of split
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | End of split
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | End of split
% 230.52/41.91  | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | Case 2:
% 230.52/41.91  | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | |   (166)  all_57_3 = e2 & op(e2, e2) = e2
% 230.52/41.91  | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | ALPHA: (166) implies:
% 230.52/41.91  | | | | | | | | | | | | | | | | | |   (167)  op(e2, e2) = e2
% 230.52/41.91  | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (17), (28), (167) are inconsistent by
% 230.52/41.91  | | | | | | | | | | | | | | | | | |            sub-proof #2472.
% 230.52/41.91  | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | End of split
% 230.52/41.91  | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | Case 2:
% 230.52/41.91  | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | |   (168)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 230.52/41.91  | | | | | | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 230.52/41.91  | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | BETA: splitting (168) gives:
% 230.52/41.91  | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | Case 1:
% 230.52/41.91  | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | |   (169)  all_57_5 = e2 & op(e2, e1) = e2
% 230.52/41.91  | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | ALPHA: (169) implies:
% 230.52/41.91  | | | | | | | | | | | | | | | | | |   (170)  all_57_5 = e2
% 230.52/41.91  | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | BETA: splitting (23) gives:
% 230.52/41.91  | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | Case 1:
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (40), (140), (141), (170) are inconsistent by
% 230.52/41.91  | | | | | | | | | | | | | | | | | | |            sub-proof #1216.
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | Case 2:
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | |   (171)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 230.52/41.91  | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e1) = e1)
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (9), (10), (12), (13), (17), (19), (20),
% 230.52/41.91  | | | | | | | | | | | | | | | | | | |            (22), (28), (29), (31), (40), (46), (62), (66),
% 230.52/41.91  | | | | | | | | | | | | | | | | | | |            (129), (133), (171) are inconsistent by sub-proof
% 230.52/41.91  | | | | | | | | | | | | | | | | | | |            #1211.
% 230.52/41.91  | | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | End of split
% 230.52/41.91  | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | Case 2:
% 230.52/41.91  | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | |   (172)  all_57_10 = e2 & op(e2, e0) = e2
% 230.52/41.91  | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | ALPHA: (172) implies:
% 230.52/41.91  | | | | | | | | | | | | | | | | | |   (173)  all_57_10 = e2
% 230.52/41.91  | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (33), (173) are inconsistent by sub-proof
% 230.52/41.91  | | | | | | | | | | | | | | | | | |            #2356.
% 230.52/41.91  | | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | | End of split
% 230.52/41.91  | | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | | End of split
% 230.52/41.91  | | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | End of split
% 230.52/41.91  | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | Case 2:
% 230.52/41.91  | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | |   (174)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 230.52/41.91  | | | | | | | | | | | | | | |            e1 & op(e0, e1) = e1)
% 230.52/41.91  | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (9), (10), (12), (13), (17), (19), (20),
% 230.52/41.91  | | | | | | | | | | | | | | |            (22), (28), (29), (31), (40), (46), (62), (66),
% 230.52/41.91  | | | | | | | | | | | | | | |            (129), (133), (174) are inconsistent by sub-proof
% 230.52/41.91  | | | | | | | | | | | | | | |            #1211.
% 230.52/41.91  | | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | End of split
% 230.52/41.91  | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | Case 2:
% 230.52/41.91  | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | |   (175)  all_57_9 = e2 & op(e3, e0) = e2
% 230.52/41.91  | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | ALPHA: (175) implies:
% 230.52/41.91  | | | | | | | | | | | | | |   (176)  op(e3, e0) = e2
% 230.52/41.91  | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | | REF_CLOSE: (9), (44), (47), (176) are inconsistent by
% 230.52/41.91  | | | | | | | | | | | | | |            sub-proof #2331.
% 230.52/41.91  | | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | | End of split
% 230.52/41.91  | | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | End of split
% 230.52/41.91  | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | Case 2:
% 230.52/41.91  | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | |   (177)  all_57_7 = e3 & op(e1, e2) = e3
% 230.52/41.91  | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | ALPHA: (177) implies:
% 230.52/41.91  | | | | | | | | | | | |   (178)  all_57_7 = e3
% 230.52/41.91  | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | | REF_CLOSE: (6), (19), (29), (40), (46), (51), (129), (178)
% 230.52/41.91  | | | | | | | | | | | |            are inconsistent by sub-proof #1779.
% 230.52/41.91  | | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | End of split
% 230.52/41.91  | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | Case 2:
% 230.52/41.91  | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | |   (179)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 230.52/41.91  | | | | | | | | | | |            e3 & op(e1, e0) = e3)
% 230.52/41.91  | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | | REF_CLOSE: (9), (12), (13), (21), (26), (179) are
% 230.52/41.91  | | | | | | | | | | |            inconsistent by sub-proof #2310.
% 230.52/41.91  | | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | End of split
% 230.52/41.91  | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | Case 2:
% 230.52/41.91  | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | |   (180)  all_57_13 = e1 & op(e0, e2) = e1
% 230.52/41.91  | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | | REF_CLOSE: (40), (129), (180) are inconsistent by sub-proof
% 230.52/41.91  | | | | | | | | | |            #2205.
% 230.52/41.91  | | | | | | | | | | 
% 230.52/41.91  | | | | | | | | | End of split
% 230.52/41.91  | | | | | | | | | 
% 230.52/41.91  | | | | | | | | End of split
% 230.52/41.91  | | | | | | | | 
% 230.52/41.91  | | | | | | | End of split
% 230.52/41.91  | | | | | | | 
% 230.52/41.91  | | | | | | End of split
% 230.52/41.91  | | | | | | 
% 230.52/41.91  | | | | | Case 2:
% 230.52/41.91  | | | | | | 
% 230.52/41.91  | | | | | |   (181)  all_57_15 = e2 & op(e0, e0) = e2
% 230.52/41.91  | | | | | | 
% 230.52/41.91  | | | | | | ALPHA: (181) implies:
% 230.52/41.91  | | | | | |   (182)  all_57_15 = e2
% 230.52/41.91  | | | | | | 
% 230.52/41.91  | | | | | | REF_CLOSE: (2), (28), (182) are inconsistent by sub-proof #2126.
% 230.52/41.91  | | | | | | 
% 230.52/41.91  | | | | | End of split
% 230.52/41.91  | | | | | 
% 230.52/41.91  | | | | End of split
% 230.52/41.91  | | | | 
% 230.52/41.91  | | | End of split
% 230.52/41.91  | | | 
% 230.52/41.91  | | End of split
% 230.52/41.91  | | 
% 230.52/41.91  | End of split
% 230.52/41.91  | 
% 230.52/41.91  End of proof
% 230.52/41.91  
% 230.52/41.91  Sub-proof #1211 shows that the following formulas are inconsistent:
% 230.52/41.91  ----------------------------------------------------------------
% 230.52/41.91    (1)   ~ (e3 = e1)
% 230.52/41.91    (2)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.52/41.91         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.52/41.91    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.91           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.91    (4)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.52/41.91         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.52/41.91    (5)   ~ (all_6_2 = e3)
% 230.52/41.91    (6)  op(e1, e1) = all_6_2
% 230.52/41.91    (7)  all_57_14 = e3
% 230.52/41.91    (8)  all_57_7 = e1
% 230.52/41.91    (9)  op(e2, e2) = e0
% 230.52/41.91    (10)  all_57_3 = e0
% 230.52/41.91    (11)   ~ (e3 = e2)
% 230.52/41.91    (12)   ~ (e3 = e0)
% 230.52/41.91    (13)  all_57_11 = e2
% 230.52/41.91    (14)   ~ (e2 = e0)
% 230.52/41.91    (15)  all_57_13 = e2
% 230.52/41.91    (16)   ~ (e1 = e0)
% 230.52/41.91    (17)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.52/41.91          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.52/41.91    (18)   ~ (e2 = e1)
% 230.52/41.91    (19)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.52/41.91    (20)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.52/41.91          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.52/41.91  
% 230.52/41.91  Begin of proof
% 230.52/41.91  | 
% 230.52/41.91  | BETA: splitting (19) gives:
% 230.52/41.91  | 
% 230.52/41.91  | Case 1:
% 230.52/41.91  | | 
% 230.52/41.91  | |   (21)  all_57_8 = e1 & op(e1, e1) = e1
% 230.52/41.91  | | 
% 230.52/41.91  | | ALPHA: (21) implies:
% 230.52/41.91  | |   (22)  op(e1, e1) = e1
% 230.52/41.91  | | 
% 230.52/41.91  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13),
% 230.52/41.91  | |            (14), (15), (16), (17), (18), (20), (22) are inconsistent by
% 230.52/41.91  | |            sub-proof #1621.
% 230.52/41.91  | | 
% 230.52/41.91  | Case 2:
% 230.52/41.91  | | 
% 230.52/41.91  | |   (23)  all_57_14 = e1 & op(e0, e1) = e1
% 230.52/41.91  | | 
% 230.52/41.91  | | ALPHA: (23) implies:
% 230.52/41.91  | |   (24)  all_57_14 = e1
% 230.52/41.91  | | 
% 230.52/41.91  | | REF_CLOSE: (1), (7), (24) are inconsistent by sub-proof #2326.
% 230.52/41.91  | | 
% 230.52/41.91  | End of split
% 230.52/41.91  | 
% 230.52/41.91  End of proof
% 230.52/41.91  
% 230.52/41.91  Sub-proof #1212 shows that the following formulas are inconsistent:
% 230.52/41.91  ----------------------------------------------------------------
% 230.52/41.91    (1)   ~ (e3 = e1)
% 230.52/41.91    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.91           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.91    (3)  all_57_2 = e2
% 230.52/41.91    (4)   ~ (e3 = e2)
% 230.52/41.91    (5)   ~ (e3 = e0)
% 230.52/41.91    (6)  op(e3, e3) = e0
% 230.52/41.91    (7)  all_57_6 = e2
% 230.52/41.91    (8)  all_57_12 = e1
% 230.52/41.91    (9)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.52/41.91         (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.52/41.91  
% 230.52/41.91  Begin of proof
% 230.52/41.91  | 
% 230.52/41.91  | BETA: splitting (9) gives:
% 230.52/41.91  | 
% 230.52/41.91  | Case 1:
% 230.52/41.91  | | 
% 230.52/41.91  | |   (10)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) =
% 230.52/41.91  | |           e3)
% 230.52/41.91  | | 
% 230.52/41.91  | | BETA: splitting (10) gives:
% 230.52/41.91  | | 
% 230.52/41.91  | | Case 1:
% 230.52/41.91  | | | 
% 230.52/41.91  | | |   (11)  all_57_0 = e3 & op(e3, e3) = e3
% 230.52/41.91  | | | 
% 230.52/41.91  | | | ALPHA: (11) implies:
% 230.52/41.91  | | |   (12)  op(e3, e3) = e3
% 230.52/41.91  | | | 
% 230.52/41.91  | | | REF_CLOSE: (2), (5), (6), (12) are inconsistent by sub-proof #2494.
% 230.52/41.91  | | | 
% 230.52/41.91  | | Case 2:
% 230.52/41.91  | | | 
% 230.52/41.91  | | |   (13)  all_57_2 = e3 & op(e2, e3) = e3
% 230.52/41.91  | | | 
% 230.52/41.91  | | | ALPHA: (13) implies:
% 230.52/41.91  | | |   (14)  all_57_2 = e3
% 230.52/41.91  | | | 
% 230.52/41.91  | | | REF_CLOSE: (3), (4), (14) are inconsistent by sub-proof #1800.
% 230.52/41.91  | | | 
% 230.52/41.91  | | End of split
% 230.52/41.91  | | 
% 230.52/41.91  | Case 2:
% 230.52/41.91  | | 
% 230.52/41.91  | |   (15)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) =
% 230.52/41.91  | |           e3)
% 230.52/41.91  | | 
% 230.52/41.91  | | REF_CLOSE: (1), (4), (7), (8), (15) are inconsistent by sub-proof #1213.
% 230.52/41.91  | | 
% 230.52/41.91  | End of split
% 230.52/41.91  | 
% 230.52/41.91  End of proof
% 230.52/41.91  
% 230.52/41.91  Sub-proof #1213 shows that the following formulas are inconsistent:
% 230.52/41.91  ----------------------------------------------------------------
% 230.52/41.91    (1)   ~ (e3 = e1)
% 230.52/41.91    (2)   ~ (e3 = e2)
% 230.52/41.91    (3)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.52/41.91    (4)  all_57_6 = e2
% 230.52/41.91    (5)  all_57_12 = e1
% 230.52/41.91  
% 230.52/41.91  Begin of proof
% 230.52/41.91  | 
% 230.52/41.91  | BETA: splitting (3) gives:
% 230.52/41.91  | 
% 230.52/41.91  | Case 1:
% 230.52/41.91  | | 
% 230.52/41.91  | |   (6)  all_57_6 = e3 & op(e1, e3) = e3
% 230.52/41.91  | | 
% 230.52/41.91  | | ALPHA: (6) implies:
% 230.52/41.91  | |   (7)  all_57_6 = e3
% 230.52/41.91  | | 
% 230.52/41.91  | | REF_CLOSE: (2), (4), (7) are inconsistent by sub-proof #2463.
% 230.52/41.91  | | 
% 230.52/41.91  | Case 2:
% 230.52/41.91  | | 
% 230.52/41.91  | |   (8)  all_57_12 = e3 & op(e0, e3) = e3
% 230.52/41.91  | | 
% 230.52/41.91  | | REF_CLOSE: (1), (5), (8) are inconsistent by sub-proof #1285.
% 230.52/41.91  | | 
% 230.52/41.91  | End of split
% 230.52/41.91  | 
% 230.52/41.91  End of proof
% 230.52/41.91  
% 230.52/41.91  Sub-proof #1214 shows that the following formulas are inconsistent:
% 230.52/41.91  ----------------------------------------------------------------
% 230.52/41.91    (1)  all_57_13 = e1
% 230.52/41.91    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.52/41.91         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.52/41.91    (3)   ~ (e3 = e1)
% 230.52/41.91    (4)   ~ (e3 = e2)
% 230.52/41.91    (5)   ~ (e3 = e0)
% 230.52/41.91    (6)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.52/41.91         (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.52/41.91    (7)   ~ (e2 = e0)
% 230.52/41.91    (8)   ~ (e1 = e0)
% 230.52/41.91    (9)  all_57_7 = e3
% 230.52/41.91    (10)  all_57_1 = e3
% 230.52/41.91    (11)   ~ (e2 = e1)
% 230.52/41.91    (12)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.52/41.91          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.52/41.91  
% 230.52/41.91  Begin of proof
% 230.52/41.91  | 
% 230.52/41.91  | BETA: splitting (6) gives:
% 230.52/41.91  | 
% 230.52/41.91  | Case 1:
% 230.52/41.91  | | 
% 230.52/41.91  | |   (13)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) =
% 230.52/41.91  | |           e0)
% 230.52/41.91  | | 
% 230.52/41.91  | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13) are
% 230.52/41.91  | |            inconsistent by sub-proof #1776.
% 230.52/41.91  | | 
% 230.52/41.91  | Case 2:
% 230.52/41.91  | | 
% 230.52/41.91  | |   (14)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 230.52/41.91  | |           e0)
% 230.52/41.91  | | 
% 230.52/41.91  | | BETA: splitting (14) gives:
% 230.52/41.91  | | 
% 230.52/41.91  | | Case 1:
% 230.52/41.91  | | | 
% 230.52/41.91  | | |   (15)  all_57_7 = e0 & op(e1, e2) = e0
% 230.52/41.91  | | | 
% 230.52/41.91  | | | REF_CLOSE: (5), (9), (15) are inconsistent by sub-proof #2042.
% 230.52/41.91  | | | 
% 230.52/41.91  | | Case 2:
% 230.52/41.91  | | | 
% 230.52/41.91  | | |   (16)  all_57_13 = e0 & op(e0, e2) = e0
% 230.52/41.91  | | | 
% 230.52/41.91  | | | REF_CLOSE: (1), (8), (16) are inconsistent by sub-proof #1920.
% 230.52/41.91  | | | 
% 230.52/41.91  | | End of split
% 230.52/41.91  | | 
% 230.52/41.91  | End of split
% 230.52/41.91  | 
% 230.52/41.91  End of proof
% 230.52/41.91  
% 230.52/41.91  Sub-proof #1215 shows that the following formulas are inconsistent:
% 230.52/41.91  ----------------------------------------------------------------
% 230.52/41.91    (1)  all_57_13 = e1
% 230.52/41.91    (2)   ~ (e3 = e1)
% 230.52/41.91    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.91           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.91    (4)  all_57_7 = e2
% 230.52/41.91    (5)  all_57_14 = e3
% 230.52/41.91    (6)  all_57_3 = e0
% 230.52/41.91    (7)   ~ (e3 = e2)
% 230.52/41.91    (8)   ~ (e3 = e0)
% 230.52/41.91    (9)   ~ (e1 = e0)
% 230.52/41.91    (10)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.52/41.91          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.52/41.91    (11)  op(e1, e1) = e0
% 230.52/41.91    (12)  all_57_1 = e3
% 230.52/41.91    (13)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.52/41.91  
% 230.52/41.91  Begin of proof
% 230.52/41.91  | 
% 230.52/41.91  | BETA: splitting (13) gives:
% 230.52/41.91  | 
% 230.52/41.91  | Case 1:
% 230.52/41.91  | | 
% 230.52/41.91  | |   (14)  all_57_8 = e1 & op(e1, e1) = e1
% 230.52/41.91  | | 
% 230.52/41.91  | | ALPHA: (14) implies:
% 230.52/41.91  | |   (15)  op(e1, e1) = e1
% 230.52/41.91  | | 
% 230.52/41.91  | | REF_CLOSE: (3), (9), (11), (15) are inconsistent by sub-proof #2427.
% 230.52/41.91  | | 
% 230.52/41.91  | Case 2:
% 230.52/41.91  | | 
% 230.52/41.91  | |   (16)  all_57_14 = e1 & op(e0, e1) = e1
% 230.52/41.91  | | 
% 230.52/41.91  | | ALPHA: (16) implies:
% 230.52/41.91  | |   (17)  all_57_14 = e1
% 230.52/41.91  | | 
% 230.52/41.91  | | COMBINE_EQS: (5), (17) imply:
% 230.52/41.91  | |   (18)  e3 = e1
% 230.52/41.91  | | 
% 230.52/41.91  | | SIMP: (18) implies:
% 230.52/41.91  | |   (19)  e3 = e1
% 230.52/41.91  | | 
% 230.52/41.91  | | COMBINE_EQS: (12), (19) imply:
% 230.52/41.91  | |   (20)  all_57_1 = e1
% 230.52/41.91  | | 
% 230.52/41.91  | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (10), (20) are inconsistent by
% 230.52/41.91  | |            sub-proof #2193.
% 230.52/41.91  | | 
% 230.52/41.91  | End of split
% 230.52/41.91  | 
% 230.52/41.91  End of proof
% 230.52/41.91  
% 230.52/41.91  Sub-proof #1216 shows that the following formulas are inconsistent:
% 230.52/41.91  ----------------------------------------------------------------
% 230.52/41.91    (1)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1)
% 230.52/41.91    (2)  all_57_4 = e2
% 230.52/41.91    (3)   ~ (e2 = e1)
% 230.52/41.91    (4)  all_57_5 = e2
% 230.52/41.91  
% 230.52/41.91  Begin of proof
% 230.52/41.91  | 
% 230.52/41.91  | BETA: splitting (1) gives:
% 230.52/41.91  | 
% 230.52/41.91  | Case 1:
% 230.52/41.91  | | 
% 230.52/41.91  | |   (5)  all_57_4 = e1 & op(e3, e1) = e1
% 230.52/41.91  | | 
% 230.52/41.91  | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #2452.
% 230.52/41.91  | | 
% 230.52/41.91  | Case 2:
% 230.52/41.91  | | 
% 230.52/41.91  | |   (6)  all_57_5 = e1 & op(e2, e1) = e1
% 230.52/41.91  | | 
% 230.52/41.91  | | ALPHA: (6) implies:
% 230.52/41.91  | |   (7)  all_57_5 = e1
% 230.52/41.91  | | 
% 230.52/41.91  | | REF_CLOSE: (3), (4), (7) are inconsistent by sub-proof #1885.
% 230.52/41.91  | | 
% 230.52/41.91  | End of split
% 230.52/41.91  | 
% 230.52/41.91  End of proof
% 230.52/41.91  
% 230.52/41.91  Sub-proof #1217 shows that the following formulas are inconsistent:
% 230.52/41.91  ----------------------------------------------------------------
% 230.52/41.91    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.52/41.91         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.52/41.91    (2)   ~ (e3 = e1)
% 230.52/41.91    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.91           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.91    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1)
% 230.52/41.91    (5)  op(e2, e2) = e0
% 230.52/41.91    (6)  all_57_3 = e0
% 230.52/41.91    (7)   ~ (e3 = e2)
% 230.52/41.91    (8)   ~ (e3 = e0)
% 230.52/41.91    (9)  all_57_0 = e0
% 230.52/41.91    (10)   ~ (e2 = e0)
% 230.52/41.91    (11)   ~ (e1 = e0)
% 230.52/41.91    (12)  all_57_10 = e3
% 230.52/41.91    (13)  all_57_5 = e1
% 230.52/41.91    (14)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.52/41.91          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.52/41.92    (15)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.52/41.92          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.52/41.92    (16)   ~ (e2 = e1)
% 230.52/41.92  
% 230.52/41.92  Begin of proof
% 230.52/41.92  | 
% 230.52/41.92  | BETA: splitting (4) gives:
% 230.52/41.92  | 
% 230.52/41.92  | Case 1:
% 230.52/41.92  | | 
% 230.52/41.92  | |   (17)  all_57_0 = e1 & op(e3, e3) = e1
% 230.52/41.92  | | 
% 230.52/41.92  | | ALPHA: (17) implies:
% 230.52/41.92  | |   (18)  all_57_0 = e1
% 230.52/41.92  | | 
% 230.52/41.92  | | COMBINE_EQS: (9), (18) imply:
% 230.52/41.92  | |   (19)  e1 = e0
% 230.52/41.92  | | 
% 230.52/41.92  | | SIMP: (19) implies:
% 230.52/41.92  | |   (20)  e1 = e0
% 230.52/41.92  | | 
% 230.52/41.92  | | COMBINE_EQS: (13), (20) imply:
% 230.52/41.92  | |   (21)  all_57_5 = e0
% 230.52/41.92  | | 
% 230.52/41.92  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (10), (11), (12), (14), (15),
% 230.52/41.92  | |            (16), (21) are inconsistent by sub-proof #2348.
% 230.52/41.92  | | 
% 230.52/41.92  | Case 2:
% 230.52/41.92  | | 
% 230.52/41.92  | |   (22)  all_57_2 = e1 & op(e2, e3) = e1
% 230.52/41.92  | | 
% 230.52/41.92  | | ALPHA: (22) implies:
% 230.52/41.92  | |   (23)  all_57_2 = e1
% 230.52/41.92  | | 
% 230.52/41.92  | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (10), (13), (14), (15), (16), (23)
% 230.52/41.92  | |            are inconsistent by sub-proof #1536.
% 230.52/41.92  | | 
% 230.52/41.92  | End of split
% 230.52/41.92  | 
% 230.52/41.92  End of proof
% 230.52/41.92  
% 230.52/41.92  Sub-proof #1218 shows that the following formulas are inconsistent:
% 230.52/41.92  ----------------------------------------------------------------
% 230.52/41.92    (1)   ~ (all_14_0 = e1)
% 230.52/41.92    (2)  op(all_14_1, e2) = all_14_0
% 230.52/41.92    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.92           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.92    (4)  op(e2, e0) = e3
% 230.52/41.92    (5)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1)
% 230.52/41.92    (6)  op(e2, e2) = e0
% 230.52/41.92    (7)   ~ (e1 = e0)
% 230.52/41.92    (8)  op(e2, e0) = all_14_1
% 230.52/41.92    (9)  op(e2, e0) = all_50_1
% 230.52/41.92  
% 230.52/41.92  Begin of proof
% 230.52/41.92  | 
% 230.52/41.92  | BETA: splitting (5) gives:
% 230.52/41.92  | 
% 230.52/41.92  | Case 1:
% 230.52/41.92  | | 
% 230.52/41.92  | |   (10)  all_57_1 = e1 & op(e3, e2) = e1
% 230.52/41.92  | | 
% 230.52/41.92  | | ALPHA: (10) implies:
% 230.52/41.92  | |   (11)  op(e3, e2) = e1
% 230.52/41.92  | | 
% 230.52/41.92  | | REF_CLOSE: (1), (2), (3), (4), (8), (9), (11) are inconsistent by sub-proof
% 230.52/41.92  | |            #1328.
% 230.52/41.92  | | 
% 230.52/41.92  | Case 2:
% 230.52/41.92  | | 
% 230.52/41.92  | |   (12)  all_57_3 = e1 & op(e2, e2) = e1
% 230.52/41.92  | | 
% 230.52/41.92  | | ALPHA: (12) implies:
% 230.52/41.92  | |   (13)  op(e2, e2) = e1
% 230.52/41.92  | | 
% 230.52/41.92  | | REF_CLOSE: (3), (6), (7), (13) are inconsistent by sub-proof #2352.
% 230.52/41.92  | | 
% 230.52/41.92  | End of split
% 230.52/41.92  | 
% 230.52/41.92  End of proof
% 230.52/41.92  
% 230.52/41.92  Sub-proof #1219 shows that the following formulas are inconsistent:
% 230.52/41.92  ----------------------------------------------------------------
% 230.52/41.92    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.92           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.92    (2)   ~ (e3 = e2)
% 230.52/41.92    (3)  all_57_10 = e3
% 230.52/41.92    (4)   ~ (all_53_12 = e2)
% 230.52/41.92    (5)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.52/41.92    (6)  op(e3, e0) = all_53_12
% 230.52/41.92  
% 230.52/41.92  Begin of proof
% 230.52/41.92  | 
% 230.52/41.92  | BETA: splitting (5) gives:
% 230.52/41.92  | 
% 230.52/41.92  | Case 1:
% 230.52/41.92  | | 
% 230.52/41.92  | |   (7)  all_57_9 = e2 & op(e3, e0) = e2
% 230.52/41.92  | | 
% 230.52/41.92  | | ALPHA: (7) implies:
% 230.52/41.92  | |   (8)  op(e3, e0) = e2
% 230.52/41.92  | | 
% 230.52/41.92  | | REF_CLOSE: (1), (4), (6), (8) are inconsistent by sub-proof #2331.
% 230.52/41.92  | | 
% 230.52/41.92  | Case 2:
% 230.52/41.92  | | 
% 230.52/41.92  | |   (9)  all_57_10 = e2 & op(e2, e0) = e2
% 230.52/41.92  | | 
% 230.52/41.92  | | REF_CLOSE: (2), (3), (9) are inconsistent by sub-proof #2250.
% 230.52/41.92  | | 
% 230.52/41.92  | End of split
% 230.52/41.92  | 
% 230.52/41.92  End of proof
% 230.52/41.92  
% 230.52/41.92  Sub-proof #1220 shows that the following formulas are inconsistent:
% 230.52/41.92  ----------------------------------------------------------------
% 230.52/41.92    (1)   ~ (e3 = e1)
% 230.52/41.92    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.92           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.92    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.52/41.92         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.52/41.92    (4)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.52/41.92         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.52/41.92    (5)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.52/41.92         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.52/41.92    (6)  all_57_4 = e3
% 230.52/41.92    (7)   ~ (e3 = e2)
% 230.52/41.92    (8)   ~ (e3 = e0)
% 230.52/41.92    (9)  op(e3, e3) = e0
% 230.52/41.92    (10)   ~ (e2 = e0)
% 230.52/41.92    (11)   ~ (e1 = e0)
% 230.52/41.92    (12)  all_57_1 = e3
% 230.52/41.92    (13)   ~ (e2 = e1)
% 230.52/41.92  
% 230.52/41.92  Begin of proof
% 230.52/41.92  | 
% 230.52/41.92  | BETA: splitting (4) gives:
% 230.52/41.92  | 
% 230.52/41.92  | Case 1:
% 230.52/41.92  | | 
% 230.52/41.92  | |   (14)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) =
% 230.52/41.92  | |           e2)
% 230.52/41.92  | | 
% 230.52/41.92  | | REF_CLOSE: (2), (7), (9), (10), (12), (14) are inconsistent by sub-proof
% 230.52/41.92  | |            #1224.
% 230.52/41.92  | | 
% 230.52/41.92  | Case 2:
% 230.52/41.92  | | 
% 230.52/41.92  | |   (15)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) =
% 230.52/41.92  | |           e2)
% 230.52/41.92  | | 
% 230.52/41.92  | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13), (15)
% 230.52/41.92  | |            are inconsistent by sub-proof #1221.
% 230.52/41.92  | | 
% 230.52/41.92  | End of split
% 230.52/41.92  | 
% 230.52/41.92  End of proof
% 230.52/41.92  
% 230.52/41.92  Sub-proof #1221 shows that the following formulas are inconsistent:
% 230.52/41.92  ----------------------------------------------------------------
% 230.52/41.92    (1)   ~ (e3 = e1)
% 230.52/41.92    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.52/41.92         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.52/41.92    (3)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.52/41.92         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.52/41.92    (4)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.52/41.92         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.52/41.92    (5)  all_57_4 = e3
% 230.52/41.92    (6)   ~ (e3 = e2)
% 230.52/41.92    (7)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.52/41.92    (8)   ~ (e3 = e0)
% 230.52/41.92    (9)   ~ (e2 = e0)
% 230.52/41.92    (10)   ~ (e1 = e0)
% 230.52/41.92    (11)  all_57_1 = e3
% 230.52/41.92    (12)   ~ (e2 = e1)
% 230.52/41.92  
% 230.52/41.92  Begin of proof
% 230.52/41.92  | 
% 230.52/41.92  | BETA: splitting (7) gives:
% 230.52/41.92  | 
% 230.52/41.92  | Case 1:
% 230.52/41.92  | | 
% 230.52/41.92  | |   (13)  all_57_4 = e2 & op(e3, e1) = e2
% 230.52/41.92  | | 
% 230.52/41.92  | | REF_CLOSE: (5), (6), (13) are inconsistent by sub-proof #2487.
% 230.52/41.92  | | 
% 230.52/41.92  | Case 2:
% 230.52/41.92  | | 
% 230.52/41.92  | |   (14)  all_57_9 = e2 & op(e3, e0) = e2
% 230.52/41.92  | | 
% 230.52/41.92  | | ALPHA: (14) implies:
% 230.52/41.92  | |   (15)  all_57_9 = e2
% 230.52/41.92  | | 
% 230.52/41.92  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (15)
% 230.52/41.92  | |            are inconsistent by sub-proof #1222.
% 230.52/41.92  | | 
% 230.52/41.92  | End of split
% 230.52/41.92  | 
% 230.52/41.92  End of proof
% 230.52/41.92  
% 230.52/41.92  Sub-proof #1222 shows that the following formulas are inconsistent:
% 230.52/41.92  ----------------------------------------------------------------
% 230.52/41.92    (1)  all_57_9 = e2
% 230.52/41.92    (2)   ~ (e3 = e1)
% 230.52/41.92    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.52/41.92         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.52/41.92    (4)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.52/41.92         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.52/41.92    (5)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.52/41.92         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.52/41.92    (6)  all_57_4 = e3
% 230.52/41.92    (7)   ~ (e3 = e2)
% 230.52/41.92    (8)   ~ (e3 = e0)
% 230.52/41.92    (9)   ~ (e2 = e0)
% 230.52/41.92    (10)   ~ (e1 = e0)
% 230.52/41.92    (11)  all_57_1 = e3
% 230.52/41.92    (12)   ~ (e2 = e1)
% 230.52/41.92  
% 230.52/41.92  Begin of proof
% 230.52/41.92  | 
% 230.52/41.92  | BETA: splitting (3) gives:
% 230.52/41.92  | 
% 230.52/41.92  | Case 1:
% 230.52/41.92  | | 
% 230.52/41.92  | |   (13)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) =
% 230.52/41.92  | |           e1)
% 230.52/41.92  | | 
% 230.52/41.92  | | REF_CLOSE: (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13) are
% 230.52/41.92  | |            inconsistent by sub-proof #1807.
% 230.52/41.92  | | 
% 230.52/41.92  | Case 2:
% 230.52/41.92  | | 
% 230.52/41.92  | |   (14)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) =
% 230.52/41.92  | |           e1)
% 230.52/41.92  | | 
% 230.52/41.92  | | REF_CLOSE: (1), (2), (6), (12), (14) are inconsistent by sub-proof #1223.
% 230.52/41.92  | | 
% 230.52/41.92  | End of split
% 230.52/41.92  | 
% 230.52/41.92  End of proof
% 230.52/41.92  
% 230.52/41.92  Sub-proof #1223 shows that the following formulas are inconsistent:
% 230.52/41.92  ----------------------------------------------------------------
% 230.52/41.92    (1)  all_57_9 = e2
% 230.52/41.92    (2)   ~ (e3 = e1)
% 230.52/41.92    (3)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.52/41.92    (4)  all_57_4 = e3
% 230.52/41.92    (5)   ~ (e2 = e1)
% 230.52/41.92  
% 230.52/41.92  Begin of proof
% 230.52/41.92  | 
% 230.52/41.92  | BETA: splitting (3) gives:
% 230.52/41.92  | 
% 230.52/41.92  | Case 1:
% 230.52/41.92  | | 
% 230.52/41.92  | |   (6)  all_57_4 = e1 & op(e3, e1) = e1
% 230.52/41.92  | | 
% 230.52/41.92  | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #2484.
% 230.52/41.92  | | 
% 230.52/41.92  | Case 2:
% 230.52/41.92  | | 
% 230.52/41.92  | |   (7)  all_57_9 = e1 & op(e3, e0) = e1
% 230.52/41.92  | | 
% 230.52/41.92  | | ALPHA: (7) implies:
% 230.52/41.92  | |   (8)  all_57_9 = e1
% 230.52/41.92  | | 
% 230.52/41.92  | | REF_CLOSE: (1), (5), (8) are inconsistent by sub-proof #2444.
% 230.52/41.92  | | 
% 230.52/41.92  | End of split
% 230.52/41.92  | 
% 230.52/41.92  End of proof
% 230.52/41.92  
% 230.52/41.92  Sub-proof #1224 shows that the following formulas are inconsistent:
% 230.52/41.92  ----------------------------------------------------------------
% 230.52/41.92    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.92           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.92    (2)   ~ (e3 = e2)
% 230.52/41.92    (3)  op(e3, e3) = e0
% 230.52/41.92    (4)   ~ (e2 = e0)
% 230.52/41.92    (5)  all_57_1 = e3
% 230.52/41.92    (6)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2)
% 230.52/41.92  
% 230.52/41.92  Begin of proof
% 230.52/41.92  | 
% 230.52/41.92  | BETA: splitting (6) gives:
% 230.52/41.92  | 
% 230.52/41.92  | Case 1:
% 230.52/41.92  | | 
% 230.52/41.92  | |   (7)  all_57_0 = e2 & op(e3, e3) = e2
% 230.52/41.92  | | 
% 230.52/41.92  | | ALPHA: (7) implies:
% 230.52/41.92  | |   (8)  op(e3, e3) = e2
% 230.52/41.92  | | 
% 230.52/41.92  | | REF_CLOSE: (1), (3), (4), (8) are inconsistent by sub-proof #2403.
% 230.52/41.92  | | 
% 230.52/41.92  | Case 2:
% 230.52/41.92  | | 
% 230.52/41.92  | |   (9)  all_57_1 = e2 & op(e3, e2) = e2
% 230.52/41.92  | | 
% 230.52/41.92  | | REF_CLOSE: (2), (5), (9) are inconsistent by sub-proof #1809.
% 230.52/41.92  | | 
% 230.52/41.92  | End of split
% 230.52/41.92  | 
% 230.52/41.92  End of proof
% 230.52/41.92  
% 230.52/41.92  Sub-proof #1225 shows that the following formulas are inconsistent:
% 230.52/41.92  ----------------------------------------------------------------
% 230.52/41.92    (1)  all_55_1 = all_14_0
% 230.52/41.92    (2)  all_55_1 = e3
% 230.52/41.92    (3)   ~ (all_14_0 = e3)
% 230.52/41.92  
% 230.52/41.92  Begin of proof
% 230.52/41.92  | 
% 230.52/41.92  | COMBINE_EQS: (1), (2) imply:
% 230.52/41.92  |   (4)  all_14_0 = e3
% 230.52/41.92  | 
% 230.52/41.92  | SIMP: (4) implies:
% 230.52/41.92  |   (5)  all_14_0 = e3
% 230.52/41.92  | 
% 230.52/41.92  | REDUCE: (3), (5) imply:
% 230.52/41.92  |   (6)  $false
% 230.52/41.92  | 
% 230.52/41.92  | CLOSE: (6) is inconsistent.
% 230.52/41.92  | 
% 230.52/41.92  End of proof
% 230.52/41.92  
% 230.52/41.92  Sub-proof #1226 shows that the following formulas are inconsistent:
% 230.52/41.92  ----------------------------------------------------------------
% 230.52/41.92    (1)  op(e0, e0) = all_4_2
% 230.52/41.92    (2)  op(e0, e1) = all_53_11
% 230.52/41.92    (3)  all_55_15 = e3 | all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 230.52/41.92    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.92           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.92    (5)  all_55_15 = all_4_2
% 230.52/41.92    (6)  op(e1, e1) = all_6_2
% 230.52/41.92    (7)  op(e0, e1) = e0
% 230.52/41.92    (8)  op(e2, e2) = e0
% 230.52/41.92    (9)   ~ (all_53_14 = all_6_2)
% 230.52/41.92    (10)   ~ (all_53_14 = all_4_2)
% 230.52/41.92    (11)   ~ (e3 = e2)
% 230.52/41.92    (12)  op(e1, e0) = all_53_14
% 230.52/41.92    (13)   ~ (e3 = e0)
% 230.52/41.92    (14)   ~ (all_4_2 = e2)
% 230.52/41.92    (15)  op(e3, e3) = e0
% 230.52/41.92    (16)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.52/41.92          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.52/41.92            e1)
% 230.52/41.92    (17)   ~ (e2 = e0)
% 230.52/41.92    (18)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 230.52/41.92            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 230.52/41.92            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 230.52/41.92            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 230.52/41.92              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 230.52/41.92            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 230.52/41.92            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 230.52/41.92              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 230.52/41.92              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 230.52/41.92            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 230.52/41.92            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 230.52/41.92            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 230.52/41.92              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 230.52/41.92              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 230.52/41.92            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 230.52/41.92              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 230.52/41.92            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 230.52/41.92            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 230.52/41.92              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 230.52/41.92              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 230.52/41.92            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 230.52/41.92            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 230.52/41.92    (19)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.52/41.92          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 230.52/41.92            e3)
% 230.52/41.92    (20)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.52/41.92          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.52/41.92            e2)
% 230.52/41.92    (21)   ~ (all_4_2 = e3)
% 230.52/41.92    (22)  op(e1, e0) = e0
% 230.52/41.92    (23)  all_40_2 = all_4_2
% 230.52/41.92    (24)  all_57_14 = e0
% 230.52/41.92    (25)   ~ (all_40_2 = e1) | ( ~ (all_40_0 = e3) & op(all_40_1, e0) = all_40_0 &
% 230.52/41.92            op(e0, e1) = all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 =
% 230.52/41.92              e2) & op(e0, e1) = all_40_1 & $i(all_40_1))
% 230.52/41.92  
% 230.52/41.92  Begin of proof
% 230.52/41.92  | 
% 230.52/41.92  | GROUND_INST: instantiating (4) with all_53_11, e0, e1, e0, simplifying with
% 230.52/41.92  |              (2), (7) gives:
% 230.52/41.92  |   (26)  all_53_11 = e0
% 230.52/41.92  | 
% 230.52/41.92  | GROUND_INST: instantiating (4) with all_53_14, e0, e0, e1, simplifying with
% 230.52/41.92  |              (12), (22) gives:
% 230.52/41.92  |   (27)  all_53_14 = e0
% 230.52/41.92  | 
% 230.52/41.92  | REDUCE: (9), (27) imply:
% 230.52/41.92  |   (28)   ~ (all_6_2 = e0)
% 230.52/41.92  | 
% 230.52/41.92  | SIMP: (28) implies:
% 230.52/41.92  |   (29)   ~ (all_6_2 = e0)
% 230.52/41.92  | 
% 230.52/41.92  | REDUCE: (10), (27) imply:
% 230.52/41.92  |   (30)   ~ (all_4_2 = e0)
% 230.52/41.92  | 
% 230.52/41.92  | SIMP: (30) implies:
% 230.52/41.92  |   (31)   ~ (all_4_2 = e0)
% 230.52/41.92  | 
% 230.52/41.92  | BETA: splitting (18) gives:
% 230.52/41.92  | 
% 230.52/41.92  | Case 1:
% 230.52/41.92  | | 
% 230.52/41.92  | |   (32)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 230.52/41.92  | |           op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 230.52/41.92  | |           op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3,
% 230.52/41.92  | |             e3) = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 &
% 230.52/41.92  | |           op(e3, e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5)
% 230.52/41.92  | |           & $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1
% 230.52/41.92  | |           & all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 230.52/41.92  | |             all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 230.52/41.92  | |             all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11
% 230.52/41.92  | |           & op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 230.52/41.92  | |           $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 230.52/41.92  | | 
% 230.52/41.92  | | BETA: splitting (32) gives:
% 230.52/41.92  | | 
% 230.52/41.92  | | Case 1:
% 230.52/41.92  | | | 
% 230.52/41.92  | | |   (33)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 230.52/41.92  | | |         op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 230.52/41.92  | | |         op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3,
% 230.52/41.92  | | |           e3) = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 &
% 230.52/41.92  | | |         op(e3, e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5)
% 230.52/41.92  | | |         & $i(all_52_7)
% 230.52/41.92  | | | 
% 230.52/41.92  | | | ALPHA: (33) implies:
% 230.52/41.92  | | |   (34)  op(e3, e3) = all_52_1
% 230.52/41.92  | | |   (35)  op(all_52_1, all_52_1) = e3
% 230.52/41.92  | | | 
% 230.52/41.92  | | | BETA: splitting (3) gives:
% 230.52/41.92  | | | 
% 230.52/41.92  | | | Case 1:
% 230.52/41.92  | | | | 
% 230.52/41.92  | | | |   (36)  all_55_15 = e3
% 230.52/41.92  | | | | 
% 230.52/41.92  | | | | REF_CLOSE: (5), (21), (36) are inconsistent by sub-proof #2503.
% 230.52/41.92  | | | | 
% 230.52/41.92  | | | Case 2:
% 230.52/41.92  | | | | 
% 230.52/41.92  | | | |   (37)   ~ (all_55_15 = e3)
% 230.52/41.92  | | | |   (38)  all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 230.52/41.92  | | | | 
% 230.52/41.92  | | | | BETA: splitting (38) gives:
% 230.52/41.92  | | | | 
% 230.52/41.92  | | | | Case 1:
% 230.52/41.92  | | | | | 
% 230.52/41.92  | | | | |   (39)  all_55_15 = e2
% 230.52/41.92  | | | | | 
% 230.52/41.92  | | | | | REF_CLOSE: (5), (14), (39) are inconsistent by sub-proof #2502.
% 230.52/41.92  | | | | | 
% 230.52/41.92  | | | | Case 2:
% 230.52/41.92  | | | | | 
% 230.52/41.92  | | | | |   (40)   ~ (all_55_15 = e2)
% 230.52/41.92  | | | | |   (41)  all_55_15 = e1 | all_55_15 = e0
% 230.52/41.92  | | | | | 
% 230.52/41.92  | | | | | BETA: splitting (41) gives:
% 230.52/41.92  | | | | | 
% 230.52/41.92  | | | | | Case 1:
% 230.52/41.92  | | | | | | 
% 230.52/41.92  | | | | | |   (42)  all_55_15 = e1
% 230.52/41.92  | | | | | | 
% 230.52/41.92  | | | | | | COMBINE_EQS: (5), (42) imply:
% 230.52/41.92  | | | | | |   (43)  all_4_2 = e1
% 230.52/41.92  | | | | | | 
% 230.52/41.92  | | | | | | SIMP: (43) implies:
% 230.52/41.92  | | | | | |   (44)  all_4_2 = e1
% 230.52/41.92  | | | | | | 
% 230.52/41.92  | | | | | | REDUCE: (21), (44) imply:
% 230.52/41.92  | | | | | |   (45)   ~ (e3 = e1)
% 230.52/41.92  | | | | | | 
% 230.52/41.92  | | | | | | SIMP: (45) implies:
% 230.52/41.92  | | | | | |   (46)   ~ (e3 = e1)
% 230.52/41.92  | | | | | | 
% 230.52/41.92  | | | | | | REDUCE: (14), (44) imply:
% 230.52/41.92  | | | | | |   (47)   ~ (e2 = e1)
% 230.52/41.92  | | | | | | 
% 230.52/41.92  | | | | | | SIMP: (47) implies:
% 230.52/41.92  | | | | | |   (48)   ~ (e2 = e1)
% 230.52/41.92  | | | | | | 
% 230.52/41.92  | | | | | | REDUCE: (31), (44) imply:
% 230.52/41.92  | | | | | |   (49)   ~ (e1 = e0)
% 230.52/41.92  | | | | | | 
% 230.52/41.92  | | | | | | REDUCE: (1), (44) imply:
% 230.52/41.92  | | | | | |   (50)  op(e0, e0) = e1
% 230.52/41.92  | | | | | | 
% 230.52/41.92  | | | | | | BETA: splitting (16) gives:
% 230.52/41.92  | | | | | | 
% 230.52/41.92  | | | | | | Case 1:
% 230.52/41.92  | | | | | | | 
% 230.52/41.92  | | | | | | |   (51)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 &
% 230.52/41.92  | | | | | | |           op(e0, e2) = e1)
% 230.52/41.92  | | | | | | | 
% 230.52/41.92  | | | | | | | REF_CLOSE: (4), (11), (13), (17), (19), (20), (24), (46), (48),
% 230.52/41.92  | | | | | | |            (50), (51) are inconsistent by sub-proof #2067.
% 230.52/41.92  | | | | | | | 
% 230.52/41.92  | | | | | | Case 2:
% 230.52/41.92  | | | | | | | 
% 230.52/41.92  | | | | | | |   (52)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 &
% 230.52/41.92  | | | | | | |           op(e0, e0) = e1)
% 230.52/41.92  | | | | | | | 
% 230.52/41.92  | | | | | | | BETA: splitting (52) gives:
% 230.52/41.92  | | | | | | | 
% 230.52/41.92  | | | | | | | Case 1:
% 230.52/41.92  | | | | | | | | 
% 230.52/41.92  | | | | | | | |   (53)  all_57_14 = e1 & op(e0, e1) = e1
% 230.52/41.92  | | | | | | | | 
% 230.52/41.92  | | | | | | | | ALPHA: (53) implies:
% 230.52/41.92  | | | | | | | |   (54)  all_57_14 = e1
% 230.52/41.92  | | | | | | | | 
% 230.52/41.92  | | | | | | | | REF_CLOSE: (24), (49), (54) are inconsistent by sub-proof #2122.
% 230.52/41.92  | | | | | | | | 
% 230.52/41.92  | | | | | | | Case 2:
% 230.52/41.92  | | | | | | | | 
% 230.52/41.92  | | | | | | | |   (55)  all_57_15 = e1 & op(e0, e0) = e1
% 230.52/41.92  | | | | | | | | 
% 230.52/41.92  | | | | | | | | REF_CLOSE: (4), (15), (34), (35), (46), (55) are inconsistent by
% 230.52/41.92  | | | | | | | |            sub-proof #1916.
% 230.52/41.92  | | | | | | | | 
% 230.52/41.92  | | | | | | | End of split
% 230.52/41.92  | | | | | | | 
% 230.52/41.92  | | | | | | End of split
% 230.52/41.92  | | | | | | 
% 230.52/41.92  | | | | | Case 2:
% 230.52/41.92  | | | | | | 
% 230.52/41.92  | | | | | |   (56)  all_55_15 = e0
% 230.52/41.92  | | | | | | 
% 230.52/41.92  | | | | | | REF_CLOSE: (5), (31), (56) are inconsistent by sub-proof #1884.
% 230.52/41.92  | | | | | | 
% 230.52/41.92  | | | | | End of split
% 230.52/41.92  | | | | | 
% 230.52/41.92  | | | | End of split
% 230.52/41.92  | | | | 
% 230.52/41.92  | | | End of split
% 230.52/41.92  | | | 
% 230.52/41.92  | | Case 2:
% 230.52/41.92  | | | 
% 230.52/41.92  | | |   (57)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0 &
% 230.52/41.92  | | |         op(all_52_9, all_52_9) = e3 & op(all_52_11, all_52_11) = e2 &
% 230.52/41.92  | | |         op(all_52_13, all_52_13) = e1 & op(all_52_15, all_52_15) = e0 &
% 230.52/41.92  | | |         op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 & op(e2, e1) =
% 230.52/41.92  | | |         all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) & $i(all_52_11)
% 230.52/41.92  | | |         & $i(all_52_13) & $i(all_52_15)
% 230.52/41.92  | | | 
% 230.52/41.92  | | | ALPHA: (57) implies:
% 230.52/41.92  | | |   (58)  op(e2, e2) = all_52_11
% 230.52/41.92  | | |   (59)  op(all_52_11, all_52_11) = e2
% 230.52/41.92  | | | 
% 230.52/41.92  | | | BETA: splitting (3) gives:
% 230.52/41.92  | | | 
% 230.52/41.92  | | | Case 1:
% 230.52/41.92  | | | | 
% 230.52/41.92  | | | |   (60)  all_55_15 = e3
% 230.52/41.92  | | | | 
% 230.52/41.92  | | | | REF_CLOSE: (5), (21), (60) are inconsistent by sub-proof #2503.
% 230.52/41.92  | | | | 
% 230.52/41.92  | | | Case 2:
% 230.52/41.92  | | | | 
% 230.52/41.92  | | | |   (61)   ~ (all_55_15 = e3)
% 230.52/41.92  | | | |   (62)  all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 230.52/41.92  | | | | 
% 230.52/41.92  | | | | BETA: splitting (62) gives:
% 230.52/41.92  | | | | 
% 230.52/41.92  | | | | Case 1:
% 230.52/41.92  | | | | | 
% 230.52/41.92  | | | | |   (63)  all_55_15 = e2
% 230.52/41.92  | | | | | 
% 230.52/41.92  | | | | | REF_CLOSE: (5), (14), (63) are inconsistent by sub-proof #2502.
% 230.52/41.92  | | | | | 
% 230.52/41.92  | | | | Case 2:
% 230.52/41.92  | | | | | 
% 230.52/41.92  | | | | |   (64)   ~ (all_55_15 = e2)
% 230.52/41.92  | | | | |   (65)  all_55_15 = e1 | all_55_15 = e0
% 230.52/41.92  | | | | | 
% 230.52/41.92  | | | | | BETA: splitting (65) gives:
% 230.52/41.92  | | | | | 
% 230.52/41.92  | | | | | Case 1:
% 230.52/41.92  | | | | | | 
% 230.52/41.92  | | | | | |   (66)  all_55_15 = e1
% 230.52/41.92  | | | | | | 
% 230.52/41.92  | | | | | | COMBINE_EQS: (5), (66) imply:
% 230.52/41.92  | | | | | |   (67)  all_4_2 = e1
% 230.52/41.92  | | | | | | 
% 230.52/41.92  | | | | | | SIMP: (67) implies:
% 230.52/41.92  | | | | | |   (68)  all_4_2 = e1
% 230.52/41.92  | | | | | | 
% 230.52/41.92  | | | | | | REDUCE: (21), (68) imply:
% 230.52/41.92  | | | | | |   (69)   ~ (e3 = e1)
% 230.52/41.92  | | | | | | 
% 230.52/41.92  | | | | | | SIMP: (69) implies:
% 230.52/41.92  | | | | | |   (70)   ~ (e3 = e1)
% 230.52/41.92  | | | | | | 
% 230.52/41.92  | | | | | | REDUCE: (14), (68) imply:
% 230.52/41.92  | | | | | |   (71)   ~ (e2 = e1)
% 230.52/41.92  | | | | | | 
% 230.52/41.92  | | | | | | SIMP: (71) implies:
% 230.52/41.92  | | | | | |   (72)   ~ (e2 = e1)
% 230.52/41.92  | | | | | | 
% 230.52/41.92  | | | | | | REDUCE: (31), (68) imply:
% 230.52/41.92  | | | | | |   (73)   ~ (e1 = e0)
% 230.52/41.92  | | | | | | 
% 230.52/41.92  | | | | | | REDUCE: (1), (68) imply:
% 230.52/41.92  | | | | | |   (74)  op(e0, e0) = e1
% 230.52/41.92  | | | | | | 
% 230.52/41.92  | | | | | | REF_CLOSE: (4), (8), (11), (13), (16), (17), (19), (20), (24), (58),
% 230.52/41.92  | | | | | |            (59), (70), (72), (73), (74) are inconsistent by
% 230.52/41.92  | | | | | |            sub-proof #2065.
% 230.52/41.92  | | | | | | 
% 230.52/41.92  | | | | | Case 2:
% 230.52/41.92  | | | | | | 
% 230.52/41.92  | | | | | |   (75)  all_55_15 = e0
% 230.52/41.92  | | | | | | 
% 230.52/41.92  | | | | | | REF_CLOSE: (5), (31), (75) are inconsistent by sub-proof #1884.
% 230.52/41.92  | | | | | | 
% 230.52/41.92  | | | | | End of split
% 230.52/41.92  | | | | | 
% 230.52/41.92  | | | | End of split
% 230.52/41.92  | | | | 
% 230.52/41.92  | | | End of split
% 230.52/41.92  | | | 
% 230.52/41.92  | | End of split
% 230.52/41.92  | | 
% 230.52/41.92  | Case 2:
% 230.52/41.92  | | 
% 230.52/41.92  | |   (76)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 &
% 230.52/41.92  | |           op(all_52_17, all_52_17) = e3 & op(all_52_19, all_52_19) = e2 &
% 230.52/41.92  | |           op(all_52_21, all_52_21) = e1 & op(all_52_23, all_52_23) = e0 &
% 230.52/41.92  | |           op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) =
% 230.52/41.92  | |           all_52_21 & op(e1, e0) = all_52_23 & $i(all_52_17) & $i(all_52_19)
% 230.52/41.92  | |           & $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3 & all_52_26 =
% 230.52/41.92  | |           e2 & all_52_28 = e1 & all_52_30 = e0 & op(all_52_25, all_52_25) =
% 230.52/41.92  | |           e3 & op(all_52_27, all_52_27) = e2 & op(all_52_29, all_52_29) = e1
% 230.52/41.92  | |           & op(all_52_31, all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0,
% 230.52/41.92  | |             e2) = all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0) =
% 230.52/41.92  | |           all_52_31 & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 230.52/41.92  | |           $i(all_52_31))
% 230.52/41.92  | | 
% 230.52/41.92  | | BETA: splitting (76) gives:
% 230.52/41.92  | | 
% 230.52/41.92  | | Case 1:
% 230.52/41.92  | | | 
% 230.52/41.92  | | |   (77)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 230.52/41.92  | | |         & op(all_52_17, all_52_17) = e3 & op(all_52_19, all_52_19) = e2 &
% 230.52/41.92  | | |         op(all_52_21, all_52_21) = e1 & op(all_52_23, all_52_23) = e0 &
% 230.52/41.92  | | |         op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) =
% 230.52/41.92  | | |         all_52_21 & op(e1, e0) = all_52_23 & $i(all_52_17) & $i(all_52_19)
% 230.52/41.92  | | |         & $i(all_52_21) & $i(all_52_23)
% 230.52/41.92  | | | 
% 230.52/41.92  | | | ALPHA: (77) implies:
% 230.52/41.92  | | |   (78)  op(e1, e0) = all_52_23
% 230.52/41.92  | | |   (79)  op(all_52_23, all_52_23) = e0
% 230.52/41.92  | | | 
% 230.52/41.92  | | | BETA: splitting (3) gives:
% 230.52/41.92  | | | 
% 230.52/41.92  | | | Case 1:
% 230.52/41.92  | | | | 
% 230.52/41.92  | | | |   (80)  all_55_15 = e3
% 230.52/41.92  | | | | 
% 230.52/41.92  | | | | REF_CLOSE: (5), (21), (80) are inconsistent by sub-proof #2503.
% 230.52/41.92  | | | | 
% 230.52/41.92  | | | Case 2:
% 230.52/41.92  | | | | 
% 230.52/41.92  | | | |   (81)  all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 230.52/41.92  | | | | 
% 230.52/41.92  | | | | BETA: splitting (81) gives:
% 230.52/41.92  | | | | 
% 230.52/41.92  | | | | Case 1:
% 230.52/41.92  | | | | | 
% 230.52/41.92  | | | | |   (82)  all_55_15 = e2
% 230.52/41.92  | | | | | 
% 230.52/41.92  | | | | | REF_CLOSE: (5), (14), (82) are inconsistent by sub-proof #2502.
% 230.52/41.92  | | | | | 
% 230.52/41.92  | | | | Case 2:
% 230.52/41.92  | | | | | 
% 230.52/41.92  | | | | |   (83)  all_55_15 = e1 | all_55_15 = e0
% 230.52/41.92  | | | | | 
% 230.52/41.92  | | | | | BETA: splitting (83) gives:
% 230.52/41.92  | | | | | 
% 230.52/41.92  | | | | | Case 1:
% 230.52/41.92  | | | | | | 
% 230.52/41.92  | | | | | |   (84)  all_55_15 = e1
% 230.52/41.92  | | | | | | 
% 230.52/41.92  | | | | | | COMBINE_EQS: (5), (84) imply:
% 230.52/41.92  | | | | | |   (85)  all_4_2 = e1
% 230.52/41.92  | | | | | | 
% 230.52/41.92  | | | | | | SIMP: (85) implies:
% 230.52/41.92  | | | | | |   (86)  all_4_2 = e1
% 230.52/41.92  | | | | | | 
% 230.52/41.92  | | | | | | COMBINE_EQS: (23), (86) imply:
% 230.52/41.92  | | | | | |   (87)  all_40_2 = e1
% 230.52/41.92  | | | | | | 
% 230.52/41.92  | | | | | | REDUCE: (31), (86) imply:
% 230.52/41.92  | | | | | |   (88)   ~ (e1 = e0)
% 230.52/41.92  | | | | | | 
% 230.52/41.92  | | | | | | REDUCE: (1), (86) imply:
% 230.52/41.92  | | | | | |   (89)  op(e0, e0) = e1
% 230.52/41.92  | | | | | | 
% 230.52/41.92  | | | | | | BETA: splitting (25) gives:
% 230.52/41.92  | | | | | | 
% 230.52/41.92  | | | | | | Case 1:
% 230.52/41.92  | | | | | | | 
% 230.52/41.92  | | | | | | |   (90)   ~ (all_40_2 = e1)
% 230.52/41.92  | | | | | | | 
% 230.52/41.92  | | | | | | | REDUCE: (87), (90) imply:
% 230.52/41.92  | | | | | | |   (91)  $false
% 230.52/41.92  | | | | | | | 
% 230.52/41.92  | | | | | | | CLOSE: (91) is inconsistent.
% 230.52/41.92  | | | | | | | 
% 230.52/41.92  | | | | | | Case 2:
% 230.52/41.92  | | | | | | | 
% 230.52/41.92  | | | | | | |   (92)  ( ~ (all_40_0 = e3) & op(all_40_1, e0) = all_40_0 & op(e0,
% 230.52/41.92  | | | | | | |             e1) = all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~
% 230.52/41.92  | | | | | | |           (all_40_1 = e2) & op(e0, e1) = all_40_1 & $i(all_40_1))
% 230.52/41.92  | | | | | | | 
% 230.52/41.92  | | | | | | | REF_CLOSE: (4), (7), (22), (78), (79), (88), (89), (92) are
% 230.52/41.92  | | | | | | |            inconsistent by sub-proof #1227.
% 230.52/41.92  | | | | | | | 
% 230.52/41.92  | | | | | | End of split
% 230.52/41.92  | | | | | | 
% 230.52/41.92  | | | | | Case 2:
% 230.52/41.92  | | | | | | 
% 230.52/41.92  | | | | | |   (93)  all_55_15 = e0
% 230.52/41.92  | | | | | | 
% 230.52/41.92  | | | | | | REF_CLOSE: (5), (31), (93) are inconsistent by sub-proof #1884.
% 230.52/41.92  | | | | | | 
% 230.52/41.92  | | | | | End of split
% 230.52/41.92  | | | | | 
% 230.52/41.92  | | | | End of split
% 230.52/41.92  | | | | 
% 230.52/41.92  | | | End of split
% 230.52/41.92  | | | 
% 230.52/41.92  | | Case 2:
% 230.52/41.92  | | | 
% 230.52/41.92  | | |   (94)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 230.52/41.92  | | |         & op(all_52_25, all_52_25) = e3 & op(all_52_27, all_52_27) = e2 &
% 230.52/41.92  | | |         op(all_52_29, all_52_29) = e1 & op(all_52_31, all_52_31) = e0 &
% 230.52/41.92  | | |         op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 & op(e0, e1) =
% 230.52/41.92  | | |         all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) & $i(all_52_27)
% 230.52/41.92  | | |         & $i(all_52_29) & $i(all_52_31)
% 230.52/41.92  | | | 
% 230.52/41.92  | | | ALPHA: (94) implies:
% 230.52/41.92  | | |   (95)  op(e0, e0) = all_52_31
% 230.52/41.92  | | |   (96)  op(all_52_31, all_52_31) = e0
% 230.52/41.92  | | | 
% 230.52/41.92  | | | BETA: splitting (3) gives:
% 230.52/41.92  | | | 
% 230.52/41.92  | | | Case 1:
% 230.52/41.92  | | | | 
% 230.52/41.92  | | | |   (97)  all_55_15 = e3
% 230.52/41.92  | | | | 
% 230.52/41.92  | | | | REF_CLOSE: (5), (21), (97) are inconsistent by sub-proof #2503.
% 230.52/41.92  | | | | 
% 230.52/41.92  | | | Case 2:
% 230.52/41.92  | | | | 
% 230.52/41.92  | | | |   (98)  all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 230.52/41.92  | | | | 
% 230.52/41.92  | | | | BETA: splitting (98) gives:
% 230.52/41.92  | | | | 
% 230.52/41.92  | | | | Case 1:
% 230.52/41.92  | | | | | 
% 230.52/41.92  | | | | |   (99)  all_55_15 = e2
% 230.52/41.92  | | | | | 
% 230.52/41.92  | | | | | REF_CLOSE: (5), (14), (99) are inconsistent by sub-proof #2502.
% 230.52/41.92  | | | | | 
% 230.52/41.92  | | | | Case 2:
% 230.52/41.92  | | | | | 
% 230.52/41.92  | | | | |   (100)  all_55_15 = e1 | all_55_15 = e0
% 230.52/41.92  | | | | | 
% 230.52/41.92  | | | | | BETA: splitting (100) gives:
% 230.52/41.92  | | | | | 
% 230.52/41.92  | | | | | Case 1:
% 230.52/41.92  | | | | | | 
% 230.52/41.92  | | | | | |   (101)  all_55_15 = e1
% 230.52/41.92  | | | | | | 
% 230.52/41.92  | | | | | | COMBINE_EQS: (5), (101) imply:
% 230.52/41.92  | | | | | |   (102)  all_4_2 = e1
% 230.52/41.92  | | | | | | 
% 230.52/41.92  | | | | | | SIMP: (102) implies:
% 230.52/41.92  | | | | | |   (103)  all_4_2 = e1
% 230.52/41.92  | | | | | | 
% 230.52/41.92  | | | | | | REDUCE: (1), (103) imply:
% 230.52/41.92  | | | | | |   (104)  op(e0, e0) = e1
% 230.52/41.92  | | | | | | 
% 230.52/41.92  | | | | | | REF_CLOSE: (4), (6), (29), (95), (96), (104) are inconsistent by
% 230.52/41.92  | | | | | |            sub-proof #2086.
% 230.52/41.92  | | | | | | 
% 230.52/41.92  | | | | | Case 2:
% 230.52/41.92  | | | | | | 
% 230.52/41.92  | | | | | |   (105)  all_55_15 = e0
% 230.52/41.92  | | | | | | 
% 230.52/41.92  | | | | | | REF_CLOSE: (5), (31), (105) are inconsistent by sub-proof #1884.
% 230.52/41.92  | | | | | | 
% 230.52/41.92  | | | | | End of split
% 230.52/41.92  | | | | | 
% 230.52/41.92  | | | | End of split
% 230.52/41.92  | | | | 
% 230.52/41.92  | | | End of split
% 230.52/41.92  | | | 
% 230.52/41.92  | | End of split
% 230.52/41.92  | | 
% 230.52/41.92  | End of split
% 230.52/41.92  | 
% 230.52/41.92  End of proof
% 230.52/41.92  
% 230.52/41.92  Sub-proof #1227 shows that the following formulas are inconsistent:
% 230.52/41.92  ----------------------------------------------------------------
% 230.52/41.92    (1)  ( ~ (all_40_0 = e3) & op(all_40_1, e0) = all_40_0 & op(e0, e1) = all_40_1
% 230.52/41.92           & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 = e2) & op(e0, e1) =
% 230.52/41.92           all_40_1 & $i(all_40_1))
% 230.52/41.92    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.92           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.93    (3)  op(e0, e1) = e0
% 230.52/41.93    (4)  op(e1, e0) = all_52_23
% 230.52/41.93    (5)   ~ (e1 = e0)
% 230.52/41.93    (6)  op(all_52_23, all_52_23) = e0
% 230.52/41.93    (7)  op(e0, e0) = e1
% 230.52/41.93    (8)  op(e1, e0) = e0
% 230.52/41.93  
% 230.52/41.93  Begin of proof
% 230.52/41.93  | 
% 230.52/41.93  | BETA: splitting (1) gives:
% 230.52/41.93  | 
% 230.52/41.93  | Case 1:
% 230.52/41.93  | | 
% 230.52/41.93  | |   (9)   ~ (all_40_0 = e3) & op(all_40_1, e0) = all_40_0 & op(e0, e1) =
% 230.52/41.93  | |        all_40_1 & $i(all_40_0) & $i(all_40_1)
% 230.52/41.93  | | 
% 230.52/41.93  | | ALPHA: (9) implies:
% 230.52/41.93  | |   (10)  op(e0, e1) = all_40_1
% 230.52/41.93  | |   (11)  op(all_40_1, e0) = all_40_0
% 230.52/41.93  | | 
% 230.52/41.93  | | GROUND_INST: instantiating (2) with e0, all_40_1, e1, e0, simplifying with
% 230.52/41.93  | |              (3), (10) gives:
% 230.52/41.93  | |   (12)  all_40_1 = e0
% 230.52/41.93  | | 
% 230.52/41.93  | | GROUND_INST: instantiating (2) with e0, all_52_23, e0, e1, simplifying with
% 230.52/41.93  | |              (4), (8) gives:
% 230.52/41.93  | |   (13)  all_52_23 = e0
% 230.52/41.93  | | 
% 230.52/41.93  | | REDUCE: (6), (13) imply:
% 230.52/41.93  | |   (14)  op(e0, e0) = e0
% 230.52/41.93  | | 
% 230.52/41.93  | | REDUCE: (11), (12) imply:
% 230.52/41.93  | |   (15)  op(e0, e0) = all_40_0
% 230.52/41.93  | | 
% 230.52/41.93  | | GROUND_INST: instantiating (2) with e1, all_40_0, e0, e0, simplifying with
% 230.52/41.93  | |              (7), (15) gives:
% 230.52/41.93  | |   (16)  all_40_0 = e1
% 230.52/41.93  | | 
% 230.52/41.93  | | GROUND_INST: instantiating (2) with e0, all_40_0, e0, e0, simplifying with
% 230.52/41.93  | |              (14), (15) gives:
% 230.52/41.93  | |   (17)  all_40_0 = e0
% 230.52/41.93  | | 
% 230.52/41.93  | | COMBINE_EQS: (16), (17) imply:
% 230.52/41.93  | |   (18)  e1 = e0
% 230.52/41.93  | | 
% 230.52/41.93  | | SIMP: (18) implies:
% 230.52/41.93  | |   (19)  e1 = e0
% 230.52/41.93  | | 
% 230.52/41.93  | | REDUCE: (5), (19) imply:
% 230.52/41.93  | |   (20)  $false
% 230.52/41.93  | | 
% 230.52/41.93  | | CLOSE: (20) is inconsistent.
% 230.52/41.93  | | 
% 230.52/41.93  | Case 2:
% 230.52/41.93  | | 
% 230.52/41.93  | | 
% 230.52/41.93  | | GROUND_INST: instantiating (2) with e0, all_52_23, e0, e1, simplifying with
% 230.52/41.93  | |              (4), (8) gives:
% 230.52/41.93  | |   (21)  all_52_23 = e0
% 230.52/41.93  | | 
% 230.52/41.93  | | REDUCE: (6), (21) imply:
% 230.52/41.93  | |   (22)  op(e0, e0) = e0
% 230.52/41.93  | | 
% 230.52/41.93  | | REF_CLOSE: (2), (5), (7), (22) are inconsistent by sub-proof #2290.
% 230.52/41.93  | | 
% 230.52/41.93  | End of split
% 230.52/41.93  | 
% 230.52/41.93  End of proof
% 230.52/41.93  
% 230.52/41.93  Sub-proof #1228 shows that the following formulas are inconsistent:
% 230.52/41.93  ----------------------------------------------------------------
% 230.52/41.93    (1)  all_57_12 = e0
% 230.52/41.93    (2)   ~ (e3 = e1)
% 230.52/41.93    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.93           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.93    (4)  op(e2, e2) = e0
% 230.52/41.93    (5)   ~ (e3 = e2)
% 230.52/41.93    (6)   ~ (e3 = e0)
% 230.52/41.93    (7)  op(e0, e3) = all_53_3
% 230.52/41.93    (8)  op(e2, e2) = all_52_11
% 230.52/41.93    (9)   ~ (all_53_3 = e2)
% 230.52/41.93    (10)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.52/41.93          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.52/41.93            e1)
% 230.52/41.93    (11)   ~ (e1 = e0)
% 230.52/41.93    (12)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.52/41.93          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 230.52/41.93            e3)
% 230.52/41.93    (13)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.52/41.93          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.52/41.93            e2)
% 230.52/41.93    (14)  op(e0, e0) = e1
% 230.52/41.93    (15)   ~ (e2 = e1)
% 230.52/41.93    (16)  op(all_52_11, all_52_11) = e2
% 230.52/41.93  
% 230.52/41.93  Begin of proof
% 230.52/41.93  | 
% 230.52/41.93  | BETA: splitting (10) gives:
% 230.52/41.93  | 
% 230.52/41.93  | Case 1:
% 230.52/41.93  | | 
% 230.52/41.93  | |   (17)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 230.52/41.93  | |           e1)
% 230.52/41.93  | | 
% 230.52/41.93  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (9), (11), (12), (13), (14), (15),
% 230.52/41.93  | |            (17) are inconsistent by sub-proof #1969.
% 230.52/41.93  | | 
% 230.52/41.93  | Case 2:
% 230.52/41.93  | | 
% 230.52/41.93  | |   (18)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.52/41.93  | |           e1)
% 230.52/41.93  | | 
% 230.52/41.93  | | BETA: splitting (18) gives:
% 230.52/41.93  | | 
% 230.52/41.93  | | Case 1:
% 230.52/41.93  | | | 
% 230.52/41.93  | | |   (19)  all_57_14 = e1 & op(e0, e1) = e1
% 230.52/41.93  | | | 
% 230.52/41.93  | | | ALPHA: (19) implies:
% 230.52/41.93  | | |   (20)  all_57_14 = e1
% 230.52/41.93  | | | 
% 230.52/41.93  | | | BETA: splitting (12) gives:
% 230.52/41.93  | | | 
% 230.52/41.93  | | | Case 1:
% 230.52/41.93  | | | | 
% 230.52/41.93  | | | |   (21)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0,
% 230.52/41.93  | | | |             e2) = e3)
% 230.52/41.93  | | | | 
% 230.52/41.93  | | | | BETA: splitting (21) gives:
% 230.52/41.93  | | | | 
% 230.52/41.93  | | | | Case 1:
% 230.52/41.93  | | | | | 
% 230.52/41.93  | | | | |   (22)  all_57_12 = e3 & op(e0, e3) = e3
% 230.52/41.93  | | | | | 
% 230.52/41.93  | | | | | REF_CLOSE: (1), (6), (22) are inconsistent by sub-proof #1978.
% 230.52/41.93  | | | | | 
% 230.52/41.93  | | | | Case 2:
% 230.52/41.93  | | | | | 
% 230.52/41.93  | | | | |   (23)  all_57_13 = e3 & op(e0, e2) = e3
% 230.52/41.93  | | | | | 
% 230.52/41.93  | | | | | ALPHA: (23) implies:
% 230.52/41.93  | | | | |   (24)  all_57_13 = e3
% 230.52/41.93  | | | | | 
% 230.52/41.93  | | | | | REF_CLOSE: (3), (5), (7), (9), (13), (14), (15), (20), (24) are
% 230.52/41.93  | | | | |            inconsistent by sub-proof #1967.
% 230.52/41.93  | | | | | 
% 230.52/41.93  | | | | End of split
% 230.52/41.93  | | | | 
% 230.52/41.93  | | | Case 2:
% 230.52/41.93  | | | | 
% 230.52/41.93  | | | |   (25)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0,
% 230.52/41.93  | | | |             e0) = e3)
% 230.52/41.93  | | | | 
% 230.52/41.93  | | | | BETA: splitting (25) gives:
% 230.52/41.93  | | | | 
% 230.52/41.93  | | | | Case 1:
% 230.52/41.93  | | | | | 
% 230.52/41.93  | | | | |   (26)  all_57_14 = e3 & op(e0, e1) = e3
% 230.52/41.93  | | | | | 
% 230.52/41.93  | | | | | REF_CLOSE: (2), (20), (26) are inconsistent by sub-proof #1966.
% 230.52/41.93  | | | | | 
% 230.52/41.93  | | | | Case 2:
% 230.52/41.93  | | | | | 
% 230.52/41.93  | | | | |   (27)  all_57_15 = e3 & op(e0, e0) = e3
% 230.52/41.93  | | | | | 
% 230.52/41.93  | | | | | ALPHA: (27) implies:
% 230.52/41.93  | | | | |   (28)  op(e0, e0) = e3
% 230.52/41.93  | | | | | 
% 230.52/41.93  | | | | | REF_CLOSE: (3), (4), (5), (8), (16), (28) are inconsistent by
% 230.52/41.93  | | | | |            sub-proof #1229.
% 230.52/41.93  | | | | | 
% 230.52/41.93  | | | | End of split
% 230.52/41.93  | | | | 
% 230.52/41.93  | | | End of split
% 230.52/41.93  | | | 
% 230.52/41.93  | | Case 2:
% 230.52/41.93  | | | 
% 230.52/41.93  | | |   (29)  all_57_15 = e1 & op(e0, e0) = e1
% 230.52/41.93  | | | 
% 230.52/41.93  | | | REF_CLOSE: (3), (4), (8), (15), (16), (29) are inconsistent by sub-proof
% 230.52/41.93  | | |            #2066.
% 230.52/41.93  | | | 
% 230.52/41.93  | | End of split
% 230.52/41.93  | | 
% 230.52/41.93  | End of split
% 230.52/41.93  | 
% 230.52/41.93  End of proof
% 230.52/41.93  
% 230.52/41.93  Sub-proof #1229 shows that the following formulas are inconsistent:
% 230.52/41.93  ----------------------------------------------------------------
% 230.52/41.93    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.93           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.93    (2)  op(e2, e2) = e0
% 230.52/41.93    (3)   ~ (e3 = e2)
% 230.52/41.93    (4)  op(e2, e2) = all_52_11
% 230.52/41.93    (5)  op(e0, e0) = e3
% 230.52/41.93    (6)  op(all_52_11, all_52_11) = e2
% 230.52/41.93  
% 230.52/41.93  Begin of proof
% 230.52/41.93  | 
% 230.52/41.93  | GROUND_INST: instantiating (1) with e0, all_52_11, e2, e2, simplifying with
% 230.52/41.93  |              (2), (4) gives:
% 230.52/41.93  |   (7)  all_52_11 = e0
% 230.52/41.93  | 
% 230.52/41.93  | REDUCE: (6), (7) imply:
% 230.52/41.93  |   (8)  op(e0, e0) = e2
% 230.52/41.93  | 
% 230.52/41.93  | GROUND_INST: instantiating (1) with e3, e2, e0, e0, simplifying with (5), (8)
% 230.52/41.93  |              gives:
% 230.52/41.93  |   (9)  e3 = e2
% 230.52/41.93  | 
% 230.52/41.93  | REDUCE: (3), (9) imply:
% 230.52/41.93  |   (10)  $false
% 230.52/41.93  | 
% 230.52/41.93  | CLOSE: (10) is inconsistent.
% 230.52/41.93  | 
% 230.52/41.93  End of proof
% 230.52/41.93  
% 230.52/41.93  Sub-proof #1230 shows that the following formulas are inconsistent:
% 230.52/41.93  ----------------------------------------------------------------
% 230.52/41.93    (1)   ~ (e3 = e1)
% 230.52/41.93    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.93           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.93    (3)   ~ (all_6_2 = e3)
% 230.52/41.93    (4)  op(e1, e1) = all_6_2
% 230.52/41.93    (5)   ~ (e3 = e2)
% 230.52/41.93    (6)   ~ (e3 = e0)
% 230.52/41.93    (7)  all_57_15 = e3
% 230.52/41.93    (8)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 230.52/41.93         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.52/41.93    (9)  op(e1, e1) = e1
% 230.52/41.93    (10)   ~ (e2 = e0)
% 230.52/41.93    (11)   ~ (e1 = e0)
% 230.52/41.93    (12)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 230.52/41.93          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 230.52/41.93    (13)  all_57_5 = e1
% 230.52/41.93    (14)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.52/41.93          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.52/41.93            e2)
% 230.52/41.93    (15)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.52/41.93              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.52/41.93                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.52/41.93                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.52/41.93    (16)   ~ (e2 = e1)
% 230.52/41.93    (17)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.52/41.93          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.52/41.93    (18)  all_57_14 = e0
% 230.52/41.93  
% 230.52/41.93  Begin of proof
% 230.52/41.93  | 
% 230.52/41.93  | BETA: splitting (12) gives:
% 230.52/41.93  | 
% 230.52/41.93  | Case 1:
% 230.52/41.93  | | 
% 230.52/41.93  | |   (19)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) =
% 230.52/41.93  | |           e3)
% 230.52/41.93  | | 
% 230.52/41.93  | | BETA: splitting (19) gives:
% 230.52/41.93  | | 
% 230.52/41.93  | | Case 1:
% 230.52/41.93  | | | 
% 230.52/41.93  | | |   (20)  all_57_4 = e3 & op(e3, e1) = e3
% 230.52/41.93  | | | 
% 230.52/41.93  | | | ALPHA: (20) implies:
% 230.52/41.93  | | |   (21)  all_57_4 = e3
% 230.52/41.93  | | | 
% 230.52/41.93  | | | REF_CLOSE: (2), (5), (9), (10), (13), (16), (17), (18), (21) are
% 230.52/41.93  | | |            inconsistent by sub-proof #1231.
% 230.52/41.93  | | | 
% 230.52/41.93  | | Case 2:
% 230.52/41.93  | | | 
% 230.52/41.93  | | |   (22)  all_57_5 = e3 & op(e2, e1) = e3
% 230.52/41.93  | | | 
% 230.52/41.93  | | | ALPHA: (22) implies:
% 230.52/41.93  | | |   (23)  all_57_5 = e3
% 230.52/41.93  | | | 
% 230.52/41.93  | | | REF_CLOSE: (1), (13), (23) are inconsistent by sub-proof #2382.
% 230.52/41.93  | | | 
% 230.52/41.93  | | End of split
% 230.52/41.93  | | 
% 230.52/41.93  | Case 2:
% 230.52/41.93  | | 
% 230.52/41.93  | |   (24)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) =
% 230.52/41.93  | |           e3)
% 230.52/41.93  | | 
% 230.52/41.93  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (14), (15),
% 230.52/41.93  | |            (16), (24) are inconsistent by sub-proof #1794.
% 230.52/41.93  | | 
% 230.52/41.93  | End of split
% 230.52/41.93  | 
% 230.52/41.93  End of proof
% 230.52/41.93  
% 230.52/41.93  Sub-proof #1231 shows that the following formulas are inconsistent:
% 230.52/41.93  ----------------------------------------------------------------
% 230.52/41.93    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.93           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.93    (2)  all_57_4 = e3
% 230.52/41.93    (3)   ~ (e3 = e2)
% 230.52/41.93    (4)  op(e1, e1) = e1
% 230.52/41.93    (5)   ~ (e2 = e0)
% 230.52/41.93    (6)  all_57_5 = e1
% 230.52/41.93    (7)   ~ (e2 = e1)
% 230.52/41.93    (8)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.52/41.93         (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.52/41.93    (9)  all_57_14 = e0
% 230.52/41.93  
% 230.52/41.93  Begin of proof
% 230.52/41.93  | 
% 230.52/41.93  | BETA: splitting (8) gives:
% 230.52/41.93  | 
% 230.52/41.93  | Case 1:
% 230.52/41.93  | | 
% 230.52/41.93  | |   (10)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) =
% 230.52/41.93  | |           e2)
% 230.52/41.93  | | 
% 230.52/41.93  | | REF_CLOSE: (2), (3), (6), (7), (10) are inconsistent by sub-proof #1232.
% 230.52/41.93  | | 
% 230.52/41.93  | Case 2:
% 230.52/41.93  | | 
% 230.52/41.93  | |   (11)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) =
% 230.52/41.93  | |           e2)
% 230.52/41.93  | | 
% 230.52/41.93  | | REF_CLOSE: (1), (4), (5), (7), (9), (11) are inconsistent by sub-proof
% 230.52/41.93  | |            #2421.
% 230.52/41.93  | | 
% 230.52/41.93  | End of split
% 230.52/41.93  | 
% 230.52/41.93  End of proof
% 230.52/41.93  
% 230.52/41.93  Sub-proof #1232 shows that the following formulas are inconsistent:
% 230.52/41.93  ----------------------------------------------------------------
% 230.52/41.93    (1)  all_57_4 = e3
% 230.52/41.93    (2)   ~ (e3 = e2)
% 230.52/41.93    (3)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2)
% 230.52/41.93    (4)  all_57_5 = e1
% 230.52/41.93    (5)   ~ (e2 = e1)
% 230.52/41.93  
% 230.52/41.93  Begin of proof
% 230.52/41.93  | 
% 230.52/41.93  | BETA: splitting (3) gives:
% 230.52/41.93  | 
% 230.52/41.93  | Case 1:
% 230.52/41.93  | | 
% 230.52/41.93  | |   (6)  all_57_4 = e2 & op(e3, e1) = e2
% 230.52/41.93  | | 
% 230.52/41.93  | | REF_CLOSE: (1), (2), (6) are inconsistent by sub-proof #2487.
% 230.52/41.93  | | 
% 230.52/41.93  | Case 2:
% 230.52/41.93  | | 
% 230.52/41.93  | |   (7)  all_57_5 = e2 & op(e2, e1) = e2
% 230.52/41.93  | | 
% 230.52/41.93  | | ALPHA: (7) implies:
% 230.52/41.93  | |   (8)  all_57_5 = e2
% 230.52/41.93  | | 
% 230.52/41.93  | | REF_CLOSE: (4), (5), (8) are inconsistent by sub-proof #1885.
% 230.52/41.93  | | 
% 230.52/41.93  | End of split
% 230.52/41.93  | 
% 230.52/41.93  End of proof
% 230.52/41.93  
% 230.52/41.93  Sub-proof #1233 shows that the following formulas are inconsistent:
% 230.52/41.93  ----------------------------------------------------------------
% 230.52/41.93    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.52/41.93         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.52/41.93    (2)   ~ (e3 = e1)
% 230.52/41.93    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.93           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.93    (4)  all_57_4 = e2
% 230.52/41.93    (5)  all_57_14 = e3
% 230.52/41.93    (6)  all_57_3 = e0
% 230.52/41.93    (7)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 230.52/41.93         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.52/41.93    (8)   ~ (e3 = e2)
% 230.52/41.93    (9)   ~ (e3 = e0)
% 230.52/41.93    (10)  all_57_10 = e2
% 230.52/41.93    (11)  op(e1, e1) = e1
% 230.52/41.93    (12)   ~ (e2 = e0)
% 230.52/41.93    (13)   ~ (e1 = e0)
% 230.52/41.93    (14)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.52/41.93          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.52/41.93    (15)   ~ (e2 = e1)
% 230.52/41.93  
% 230.52/41.93  Begin of proof
% 230.52/41.93  | 
% 230.52/41.93  | BETA: splitting (7) gives:
% 230.52/41.93  | 
% 230.52/41.93  | Case 1:
% 230.52/41.93  | | 
% 230.52/41.93  | |   (16)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) =
% 230.52/41.93  | |           e0)
% 230.52/41.93  | | 
% 230.52/41.93  | | BETA: splitting (16) gives:
% 230.52/41.93  | | 
% 230.52/41.93  | | Case 1:
% 230.52/41.93  | | | 
% 230.52/41.93  | | |   (17)  all_57_4 = e0 & op(e3, e1) = e0
% 230.52/41.93  | | | 
% 230.52/41.93  | | | REF_CLOSE: (4), (12), (17) are inconsistent by sub-proof #2045.
% 230.52/41.93  | | | 
% 230.52/41.93  | | Case 2:
% 230.52/41.93  | | | 
% 230.52/41.93  | | |   (18)  all_57_5 = e0 & op(e2, e1) = e0
% 230.52/41.93  | | | 
% 230.52/41.93  | | | ALPHA: (18) implies:
% 230.52/41.93  | | |   (19)  all_57_5 = e0
% 230.52/41.93  | | | 
% 230.52/41.93  | | | REF_CLOSE: (1), (2), (6), (8), (9), (10), (13), (14), (15), (19) are
% 230.52/41.93  | | |            inconsistent by sub-proof #2355.
% 230.52/41.93  | | | 
% 230.52/41.93  | | End of split
% 230.52/41.93  | | 
% 230.52/41.93  | Case 2:
% 230.52/41.93  | | 
% 230.52/41.93  | |   (20)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 230.52/41.93  | |           e0)
% 230.52/41.93  | | 
% 230.52/41.93  | | REF_CLOSE: (3), (5), (9), (11), (13), (20) are inconsistent by sub-proof
% 230.52/41.93  | |            #1234.
% 230.52/41.93  | | 
% 230.52/41.93  | End of split
% 230.52/41.93  | 
% 230.52/41.93  End of proof
% 230.52/41.93  
% 230.52/41.93  Sub-proof #1234 shows that the following formulas are inconsistent:
% 230.52/41.93  ----------------------------------------------------------------
% 230.52/41.93    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.93           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.93    (2)  all_57_14 = e3
% 230.52/41.93    (3)   ~ (e3 = e0)
% 230.52/41.93    (4)  op(e1, e1) = e1
% 230.52/41.93    (5)   ~ (e1 = e0)
% 230.52/41.93    (6)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.52/41.93  
% 230.52/41.93  Begin of proof
% 230.52/41.93  | 
% 230.52/41.93  | BETA: splitting (6) gives:
% 230.52/41.93  | 
% 230.52/41.93  | Case 1:
% 230.52/41.93  | | 
% 230.52/41.93  | |   (7)  all_57_8 = e0 & op(e1, e1) = e0
% 230.52/41.93  | | 
% 230.52/41.93  | | ALPHA: (7) implies:
% 230.52/41.93  | |   (8)  op(e1, e1) = e0
% 230.52/41.93  | | 
% 230.52/41.93  | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #2427.
% 230.52/41.93  | | 
% 230.52/41.93  | Case 2:
% 230.52/41.93  | | 
% 230.52/41.93  | |   (9)  all_57_14 = e0 & op(e0, e1) = e0
% 230.52/41.93  | | 
% 230.52/41.93  | | ALPHA: (9) implies:
% 230.52/41.93  | |   (10)  all_57_14 = e0
% 230.52/41.93  | | 
% 230.52/41.93  | | REF_CLOSE: (2), (3), (10) are inconsistent by sub-proof #2420.
% 230.52/41.93  | | 
% 230.52/41.93  | End of split
% 230.52/41.93  | 
% 230.52/41.93  End of proof
% 230.52/41.93  
% 230.52/41.93  Sub-proof #1235 shows that the following formulas are inconsistent:
% 230.52/41.93  ----------------------------------------------------------------
% 230.52/41.93    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.52/41.93         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.52/41.93    (2)   ~ (e3 = e1)
% 230.52/41.93    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.93           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.93    (4)  all_57_15 = e1
% 230.52/41.93    (5)   ~ (all_6_2 = e3)
% 230.52/41.93    (6)  op(e1, e1) = all_6_2
% 230.52/41.93    (7)  all_57_3 = e0
% 230.52/41.93    (8)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 230.52/41.93         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.52/41.93    (9)   ~ (e3 = e2)
% 230.52/41.93    (10)   ~ (e3 = e0)
% 230.52/41.93    (11)  all_57_6 = e0
% 230.52/41.93    (12)  op(e3, e3) = e2
% 230.52/41.93    (13)   ~ (all_53_7 = e0)
% 230.52/41.93    (14)  all_57_10 = e2
% 230.52/41.93    (15)  all_57_12 = e1
% 230.52/41.93    (16)  op(e1, e1) = e1
% 230.52/41.93    (17)   ~ (e2 = e0)
% 230.52/41.93    (18)   ~ (e1 = e0)
% 230.52/41.93    (19)  all_57_14 = e2
% 230.52/41.93    (20)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 230.52/41.93          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 230.52/41.93    (21)  op(e0, e2) = all_53_7
% 230.52/41.93    (22)  all_57_5 = e1
% 230.52/41.93    (23)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.52/41.93              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.52/41.93                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.52/41.93                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.52/41.93    (24)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.52/41.93          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.52/41.93    (25)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.52/41.93          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.52/41.93    (26)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.52/41.93          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.52/41.93    (27)   ~ (e2 = e1)
% 230.52/41.93  
% 230.52/41.93  Begin of proof
% 230.52/41.93  | 
% 230.52/41.93  | BETA: splitting (8) gives:
% 230.52/41.93  | 
% 230.52/41.93  | Case 1:
% 230.52/41.93  | | 
% 230.52/41.93  | |   (28)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) =
% 230.52/41.93  | |           e0)
% 230.52/41.93  | | 
% 230.52/41.93  | | BETA: splitting (28) gives:
% 230.52/41.93  | | 
% 230.52/41.93  | | Case 1:
% 230.52/41.93  | | | 
% 230.52/41.93  | | |   (29)  all_57_4 = e0 & op(e3, e1) = e0
% 230.52/41.93  | | | 
% 230.52/41.93  | | | ALPHA: (29) implies:
% 230.52/41.93  | | |   (30)  all_57_4 = e0
% 230.52/41.93  | | | 
% 230.52/41.93  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13),
% 230.52/41.93  | | |            (14), (15), (17), (18), (20), (21), (22), (23), (24), (25),
% 230.52/41.93  | | |            (26), (27), (30) are inconsistent by sub-proof #1238.
% 230.52/41.93  | | | 
% 230.52/41.93  | | Case 2:
% 230.52/41.93  | | | 
% 230.52/41.93  | | |   (31)  all_57_5 = e0 & op(e2, e1) = e0
% 230.52/41.93  | | | 
% 230.52/41.93  | | | ALPHA: (31) implies:
% 230.52/41.93  | | |   (32)  all_57_5 = e0
% 230.52/41.93  | | | 
% 230.52/41.93  | | | REF_CLOSE: (1), (2), (7), (9), (10), (14), (18), (24), (27), (32) are
% 230.52/41.93  | | |            inconsistent by sub-proof #2355.
% 230.52/41.93  | | | 
% 230.52/41.93  | | End of split
% 230.52/41.93  | | 
% 230.52/41.93  | Case 2:
% 230.52/41.93  | | 
% 230.52/41.93  | |   (33)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 230.52/41.93  | |           e0)
% 230.52/41.93  | | 
% 230.52/41.93  | | BETA: splitting (33) gives:
% 230.52/41.93  | | 
% 230.52/41.93  | | Case 1:
% 230.52/41.93  | | | 
% 230.52/41.93  | | |   (34)  all_57_8 = e0 & op(e1, e1) = e0
% 230.52/41.93  | | | 
% 230.52/41.93  | | | ALPHA: (34) implies:
% 230.52/41.93  | | |   (35)  op(e1, e1) = e0
% 230.52/41.93  | | | 
% 230.52/41.93  | | | REF_CLOSE: (3), (16), (18), (35) are inconsistent by sub-proof #2427.
% 230.52/41.93  | | | 
% 230.52/41.93  | | Case 2:
% 230.52/41.93  | | | 
% 230.52/41.93  | | |   (36)  all_57_14 = e0 & op(e0, e1) = e0
% 230.52/41.93  | | | 
% 230.52/41.93  | | | REF_CLOSE: (17), (19), (36) are inconsistent by sub-proof #2173.
% 230.52/41.93  | | | 
% 230.52/41.93  | | End of split
% 230.52/41.93  | | 
% 230.52/41.93  | End of split
% 230.52/41.93  | 
% 230.52/41.93  End of proof
% 230.52/41.93  
% 230.52/41.93  Sub-proof #1236 shows that the following formulas are inconsistent:
% 230.52/41.93  ----------------------------------------------------------------
% 230.52/41.93    (1)   ~ (e3 = e1)
% 230.52/41.93    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.93           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.93    (3)  e2 = e1
% 230.52/41.93    (4)  all_57_15 = e1
% 230.52/41.93    (5)  op(e2, e2) = e0
% 230.52/41.93    (6)  all_57_3 = e0
% 230.52/41.93    (7)   ~ (e3 = e2)
% 230.52/41.93    (8)   ~ (e3 = e0)
% 230.52/41.93    (9)  op(e0, e3) = all_53_3
% 230.52/41.93    (10)  all_57_1 = e1
% 230.52/41.93    (11)   ~ (all_53_3 = e2)
% 230.52/41.93    (12)   ~ (all_53_7 = e0)
% 230.52/41.93    (13)   ~ (e1 = e0)
% 230.52/41.93    (14)  all_57_14 = e2
% 230.52/41.93    (15)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.52/41.93          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.52/41.93    (16)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.52/41.93          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 230.52/41.93            e3)
% 230.52/41.93    (17)  op(e0, e2) = all_53_7
% 230.52/41.93    (18)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.52/41.93          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.52/41.93            e2)
% 230.52/41.93    (19)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.52/41.93              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.52/41.93                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.52/41.93                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.52/41.93    (20)  op(e0, e0) = e1
% 230.52/41.93    (21)   ~ (e2 = e1)
% 230.52/41.93    (22)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.52/41.93          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.52/41.93  
% 230.52/41.93  Begin of proof
% 230.52/41.93  | 
% 230.52/41.93  | SIMP: (3) implies:
% 230.52/41.93  |   (23)  e2 = e1
% 230.52/41.93  | 
% 230.52/41.93  | COMBINE_EQS: (14), (23) imply:
% 230.52/41.93  |   (24)  all_57_14 = e1
% 230.52/41.93  | 
% 230.52/41.93  | BETA: splitting (18) gives:
% 230.52/41.93  | 
% 230.52/41.93  | Case 1:
% 230.52/41.93  | | 
% 230.52/41.93  | |   (25)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 230.52/41.93  | |           e2)
% 230.52/41.93  | | 
% 230.52/41.93  | | BETA: splitting (25) gives:
% 230.52/41.93  | | 
% 230.52/41.93  | | Case 1:
% 230.52/41.93  | | | 
% 230.52/41.93  | | |   (26)  all_57_12 = e2 & op(e0, e3) = e2
% 230.52/41.93  | | | 
% 230.52/41.93  | | | ALPHA: (26) implies:
% 230.52/41.93  | | |   (27)  op(e0, e3) = e2
% 230.52/41.93  | | | 
% 230.52/41.93  | | | REF_CLOSE: (2), (9), (11), (27) are inconsistent by sub-proof #1980.
% 230.52/41.93  | | | 
% 230.52/41.93  | | Case 2:
% 230.52/41.93  | | | 
% 230.52/41.93  | | |   (28)  all_57_13 = e2 & op(e0, e2) = e2
% 230.52/41.93  | | | 
% 230.52/41.93  | | | ALPHA: (28) implies:
% 230.52/41.93  | | |   (29)  all_57_13 = e2
% 230.52/41.93  | | | 
% 230.52/41.93  | | | BETA: splitting (15) gives:
% 230.52/41.93  | | | 
% 230.52/41.93  | | | Case 1:
% 230.52/41.93  | | | | 
% 230.52/41.93  | | | |   (30)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2)
% 230.52/41.93  | | | |           = e3)
% 230.52/41.93  | | | | 
% 230.52/41.93  | | | | REF_CLOSE: (1), (6), (8), (10), (30) are inconsistent by sub-proof
% 230.52/41.93  | | | |            #2195.
% 230.52/41.93  | | | | 
% 230.52/41.93  | | | Case 2:
% 230.52/41.93  | | | | 
% 230.52/41.93  | | | |   (31)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2)
% 230.52/41.93  | | | |           = e3)
% 230.52/41.93  | | | | 
% 230.52/41.93  | | | | BETA: splitting (31) gives:
% 230.52/41.93  | | | | 
% 230.52/41.93  | | | | Case 1:
% 230.52/41.93  | | | | | 
% 230.52/41.93  | | | | |   (32)  all_57_7 = e3 & op(e1, e2) = e3
% 230.52/41.93  | | | | | 
% 230.52/41.93  | | | | | ALPHA: (32) implies:
% 230.52/41.93  | | | | |   (33)  all_57_7 = e3
% 230.52/41.93  | | | | | 
% 230.52/41.93  | | | | | BETA: splitting (19) gives:
% 230.52/41.93  | | | | | 
% 230.52/41.93  | | | | | Case 1:
% 230.52/41.93  | | | | | | 
% 230.52/41.93  | | | | | |   (34)  all_57_15 = e0 & op(e0, e0) = e0
% 230.52/41.93  | | | | | | 
% 230.52/41.93  | | | | | | ALPHA: (34) implies:
% 230.52/41.93  | | | | | |   (35)  all_57_15 = e0
% 230.52/41.93  | | | | | | 
% 230.52/41.93  | | | | | | COMBINE_EQS: (4), (35) imply:
% 230.52/41.93  | | | | | |   (36)  e1 = e0
% 230.52/41.93  | | | | | | 
% 230.52/41.93  | | | | | | REF_CLOSE: (1), (2), (5), (10), (13), (21), (22), (29), (33), (36)
% 230.52/41.93  | | | | | |            are inconsistent by sub-proof #1237.
% 230.52/41.93  | | | | | | 
% 230.52/41.93  | | | | | Case 2:
% 230.52/41.93  | | | | | | 
% 230.52/41.93  | | | | | |   (37)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 &
% 230.52/41.93  | | | | | |             op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) &
% 230.52/41.93  | | | | | |         ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.52/41.93  | | | | | |             op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 230.52/41.93  | | | | | | 
% 230.52/41.93  | | | | | | ALPHA: (37) implies:
% 230.52/41.93  | | | | | |   (38)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.52/41.93  | | | | | |           op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.52/41.93  | | | | | | 
% 230.52/41.93  | | | | | | BETA: splitting (38) gives:
% 230.52/41.93  | | | | | | 
% 230.52/41.93  | | | | | | Case 1:
% 230.52/41.93  | | | | | | | 
% 230.52/41.93  | | | | | | |   (39)  all_57_12 = e0 & op(e0, e3) = e0
% 230.52/41.93  | | | | | | | 
% 230.52/41.93  | | | | | | | ALPHA: (39) implies:
% 230.52/41.93  | | | | | | |   (40)  all_57_12 = e0
% 230.52/41.93  | | | | | | | 
% 230.52/41.93  | | | | | | | REF_CLOSE: (1), (2), (7), (8), (9), (11), (16), (18), (20), (21),
% 230.52/41.93  | | | | | | |            (24), (40) are inconsistent by sub-proof #1964.
% 230.52/41.93  | | | | | | | 
% 230.52/41.93  | | | | | | Case 2:
% 230.52/41.93  | | | | | | | 
% 230.52/41.93  | | | | | | |   (41)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 &
% 230.52/41.93  | | | | | | |           op(e0, e1) = e0)
% 230.52/41.93  | | | | | | | 
% 230.52/41.93  | | | | | | | BETA: splitting (41) gives:
% 230.52/41.93  | | | | | | | 
% 230.52/41.93  | | | | | | | Case 1:
% 230.52/41.93  | | | | | | | | 
% 230.52/41.93  | | | | | | | |   (42)  all_57_13 = e0 & op(e0, e2) = e0
% 230.52/41.93  | | | | | | | | 
% 230.52/41.93  | | | | | | | | ALPHA: (42) implies:
% 230.52/41.93  | | | | | | | |   (43)  op(e0, e2) = e0
% 230.52/41.93  | | | | | | | | 
% 230.52/41.93  | | | | | | | | REF_CLOSE: (2), (12), (17), (43) are inconsistent by sub-proof
% 230.52/41.93  | | | | | | | |            #2332.
% 230.52/41.93  | | | | | | | | 
% 230.52/41.93  | | | | | | | Case 2:
% 230.52/41.93  | | | | | | | | 
% 230.52/41.93  | | | | | | | |   (44)  all_57_14 = e0 & op(e0, e1) = e0
% 230.52/41.93  | | | | | | | | 
% 230.52/41.93  | | | | | | | | ALPHA: (44) implies:
% 230.52/41.93  | | | | | | | |   (45)  all_57_14 = e0
% 230.52/41.93  | | | | | | | | 
% 230.52/41.93  | | | | | | | | COMBINE_EQS: (24), (45) imply:
% 230.52/41.93  | | | | | | | |   (46)  e1 = e0
% 230.52/41.93  | | | | | | | | 
% 230.52/41.93  | | | | | | | | REF_CLOSE: (1), (2), (5), (10), (13), (21), (22), (29), (33),
% 230.52/41.93  | | | | | | | |            (46) are inconsistent by sub-proof #1237.
% 230.52/41.93  | | | | | | | | 
% 230.52/41.93  | | | | | | | End of split
% 230.52/41.93  | | | | | | | 
% 230.52/41.93  | | | | | | End of split
% 230.52/41.93  | | | | | | 
% 230.52/41.93  | | | | | End of split
% 230.52/41.93  | | | | | 
% 230.52/41.93  | | | | Case 2:
% 230.52/41.93  | | | | | 
% 230.52/41.93  | | | | |   (47)  all_57_13 = e3 & op(e0, e2) = e3
% 230.52/41.93  | | | | | 
% 230.52/41.93  | | | | | ALPHA: (47) implies:
% 230.52/41.93  | | | | |   (48)  all_57_13 = e3
% 230.52/41.93  | | | | | 
% 230.52/41.93  | | | | | REF_CLOSE: (2), (7), (9), (11), (18), (20), (21), (24), (48) are
% 230.52/41.93  | | | | |            inconsistent by sub-proof #1967.
% 230.52/41.93  | | | | | 
% 230.52/41.93  | | | | End of split
% 230.52/41.93  | | | | 
% 230.52/41.93  | | | End of split
% 230.52/41.93  | | | 
% 230.52/41.93  | | End of split
% 230.52/41.93  | | 
% 230.52/41.93  | Case 2:
% 230.52/41.93  | | 
% 230.52/41.93  | |   (49)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.52/41.93  | |           e2)
% 230.52/41.93  | | 
% 230.52/41.93  | | REF_CLOSE: (2), (20), (21), (24), (49) are inconsistent by sub-proof #2176.
% 230.52/41.93  | | 
% 230.52/41.93  | End of split
% 230.52/41.93  | 
% 230.52/41.93  End of proof
% 230.52/41.93  
% 230.52/41.93  Sub-proof #1237 shows that the following formulas are inconsistent:
% 230.52/41.93  ----------------------------------------------------------------
% 230.52/41.93    (1)  e1 = e0
% 230.52/41.94    (2)   ~ (e3 = e1)
% 230.52/41.94    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.94    (4)  op(e2, e2) = e0
% 230.52/41.94    (5)  all_57_1 = e1
% 230.52/41.94    (6)  all_57_13 = e2
% 230.52/41.94    (7)   ~ (e1 = e0)
% 230.52/41.94    (8)  all_57_7 = e3
% 230.52/41.94    (9)   ~ (e2 = e1)
% 230.52/41.94    (10)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.52/41.94          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.52/41.94  
% 230.52/41.94  Begin of proof
% 230.52/41.94  | 
% 230.52/41.94  | SIMP: (1) implies:
% 230.52/41.94  |   (11)  e1 = e0
% 230.52/41.94  | 
% 230.52/41.94  | COMBINE_EQS: (5), (11) imply:
% 230.52/41.94  |   (12)  all_57_1 = e0
% 230.52/41.94  | 
% 230.52/41.94  | REF_CLOSE: (2), (3), (4), (6), (7), (8), (9), (10), (12) are inconsistent by
% 230.52/41.94  |            sub-proof #1283.
% 230.52/41.94  | 
% 230.52/41.94  End of proof
% 230.52/41.94  
% 230.52/41.94  Sub-proof #1238 shows that the following formulas are inconsistent:
% 230.52/41.94  ----------------------------------------------------------------
% 230.52/41.94    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.52/41.94         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.52/41.94    (2)   ~ (e3 = e1)
% 230.52/41.94    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.94    (4)  all_57_15 = e1
% 230.52/41.94    (5)   ~ (all_6_2 = e3)
% 230.52/41.94    (6)  op(e1, e1) = all_6_2
% 230.52/41.94    (7)  all_57_4 = e0
% 230.52/41.94    (8)  all_57_3 = e0
% 230.52/41.94    (9)   ~ (e3 = e2)
% 230.52/41.94    (10)   ~ (e3 = e0)
% 230.52/41.94    (11)  all_57_6 = e0
% 230.52/41.94    (12)  op(e3, e3) = e2
% 230.52/41.94    (13)   ~ (all_53_7 = e0)
% 230.52/41.94    (14)  all_57_10 = e2
% 230.52/41.94    (15)  all_57_12 = e1
% 230.52/41.94    (16)   ~ (e2 = e0)
% 230.52/41.94    (17)   ~ (e1 = e0)
% 230.52/41.94    (18)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 230.52/41.94          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 230.52/41.94    (19)  op(e0, e2) = all_53_7
% 230.52/41.94    (20)  all_57_5 = e1
% 230.52/41.94    (21)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.52/41.94              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.52/41.94                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.52/41.94                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.52/41.94    (22)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.52/41.94          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.52/41.94    (23)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.52/41.94          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.52/41.94    (24)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.52/41.94          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.52/41.94    (25)   ~ (e2 = e1)
% 230.52/41.94  
% 230.52/41.94  Begin of proof
% 230.52/41.94  | 
% 230.52/41.94  | BETA: splitting (24) gives:
% 230.52/41.94  | 
% 230.52/41.94  | Case 1:
% 230.52/41.94  | | 
% 230.52/41.94  | |   (26)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) =
% 230.52/41.94  | |           e3)
% 230.52/41.94  | | 
% 230.52/41.94  | | BETA: splitting (26) gives:
% 230.52/41.94  | | 
% 230.52/41.94  | | Case 1:
% 230.52/41.94  | | | 
% 230.52/41.94  | | |   (27)  all_57_0 = e3 & op(e3, e3) = e3
% 230.52/41.94  | | | 
% 230.52/41.94  | | | ALPHA: (27) implies:
% 230.52/41.94  | | |   (28)  op(e3, e3) = e3
% 230.52/41.94  | | | 
% 230.52/41.94  | | | REF_CLOSE: (3), (9), (12), (28) are inconsistent by sub-proof #2490.
% 230.52/41.94  | | | 
% 230.52/41.94  | | Case 2:
% 230.52/41.94  | | | 
% 230.52/41.94  | | |   (29)  all_57_2 = e3 & op(e2, e3) = e3
% 230.52/41.94  | | | 
% 230.52/41.94  | | | ALPHA: (29) implies:
% 230.52/41.94  | | |   (30)  all_57_2 = e3
% 230.52/41.94  | | | 
% 230.52/41.94  | | | BETA: splitting (21) gives:
% 230.52/41.94  | | | 
% 230.52/41.94  | | | Case 1:
% 230.52/41.94  | | | | 
% 230.52/41.94  | | | |   (31)  all_57_15 = e0 & op(e0, e0) = e0
% 230.52/41.94  | | | | 
% 230.52/41.94  | | | | ALPHA: (31) implies:
% 230.52/41.94  | | | |   (32)  all_57_15 = e0
% 230.52/41.94  | | | | 
% 230.52/41.94  | | | | COMBINE_EQS: (4), (32) imply:
% 230.52/41.94  | | | |   (33)  e1 = e0
% 230.52/41.94  | | | | 
% 230.52/41.94  | | | | COMBINE_EQS: (20), (33) imply:
% 230.52/41.94  | | | |   (34)  all_57_5 = e0
% 230.52/41.94  | | | | 
% 230.52/41.94  | | | | REF_CLOSE: (1), (2), (8), (14), (17), (25), (30), (34) are inconsistent
% 230.52/41.94  | | | |            by sub-proof #2359.
% 230.52/41.94  | | | | 
% 230.52/41.94  | | | Case 2:
% 230.52/41.94  | | | | 
% 230.52/41.94  | | | |   (35)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2,
% 230.52/41.94  | | | |               e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) &
% 230.52/41.94  | | | |         ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0,
% 230.52/41.94  | | | |               e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 230.52/41.94  | | | | 
% 230.52/41.94  | | | | ALPHA: (35) implies:
% 230.52/41.94  | | | |   (36)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0,
% 230.52/41.94  | | | |             e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.52/41.94  | | | | 
% 230.52/41.94  | | | | BETA: splitting (36) gives:
% 230.52/41.94  | | | | 
% 230.52/41.94  | | | | Case 1:
% 230.52/41.94  | | | | | 
% 230.52/41.94  | | | | |   (37)  all_57_12 = e0 & op(e0, e3) = e0
% 230.52/41.94  | | | | | 
% 230.52/41.94  | | | | | ALPHA: (37) implies:
% 230.52/41.94  | | | | |   (38)  all_57_12 = e0
% 230.52/41.94  | | | | | 
% 230.52/41.94  | | | | | COMBINE_EQS: (15), (38) imply:
% 230.52/41.94  | | | | |   (39)  e1 = e0
% 230.52/41.94  | | | | | 
% 230.52/41.94  | | | | | COMBINE_EQS: (20), (39) imply:
% 230.52/41.94  | | | | |   (40)  all_57_5 = e0
% 230.52/41.94  | | | | | 
% 230.52/41.94  | | | | | REF_CLOSE: (1), (2), (8), (14), (17), (25), (30), (40) are
% 230.52/41.94  | | | | |            inconsistent by sub-proof #2359.
% 230.52/41.94  | | | | | 
% 230.52/41.94  | | | | Case 2:
% 230.52/41.94  | | | | | 
% 230.52/41.94  | | | | |   (41)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 230.52/41.94  | | | | |             e1) = e0)
% 230.52/41.94  | | | | | 
% 230.52/41.94  | | | | | BETA: splitting (41) gives:
% 230.52/41.94  | | | | | 
% 230.52/41.94  | | | | | Case 1:
% 230.52/41.94  | | | | | | 
% 230.52/41.94  | | | | | |   (42)  all_57_13 = e0 & op(e0, e2) = e0
% 230.52/41.94  | | | | | | 
% 230.52/41.94  | | | | | | ALPHA: (42) implies:
% 230.52/41.94  | | | | | |   (43)  op(e0, e2) = e0
% 230.52/41.94  | | | | | | 
% 230.52/41.94  | | | | | | REF_CLOSE: (3), (13), (19), (43) are inconsistent by sub-proof
% 230.52/41.94  | | | | | |            #2332.
% 230.52/41.94  | | | | | | 
% 230.52/41.94  | | | | | Case 2:
% 230.52/41.94  | | | | | | 
% 230.52/41.94  | | | | | |   (44)  all_57_14 = e0 & op(e0, e1) = e0
% 230.52/41.94  | | | | | | 
% 230.52/41.94  | | | | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (16), (17),
% 230.52/41.94  | | | | | |            (18), (22), (23), (25), (30), (44) are inconsistent by
% 230.52/41.94  | | | | | |            sub-proof #1278.
% 230.52/41.94  | | | | | | 
% 230.52/41.94  | | | | | End of split
% 230.52/41.94  | | | | | 
% 230.52/41.94  | | | | End of split
% 230.52/41.94  | | | | 
% 230.52/41.94  | | | End of split
% 230.52/41.94  | | | 
% 230.52/41.94  | | End of split
% 230.52/41.94  | | 
% 230.52/41.94  | Case 2:
% 230.52/41.94  | | 
% 230.52/41.94  | |   (45)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) =
% 230.52/41.94  | |           e3)
% 230.52/41.94  | | 
% 230.52/41.94  | | REF_CLOSE: (2), (10), (11), (15), (45) are inconsistent by sub-proof #1631.
% 230.52/41.94  | | 
% 230.52/41.94  | End of split
% 230.52/41.94  | 
% 230.52/41.94  End of proof
% 230.52/41.94  
% 230.52/41.94  Sub-proof #1239 shows that the following formulas are inconsistent:
% 230.52/41.94  ----------------------------------------------------------------
% 230.52/41.94    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.52/41.94         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.52/41.94    (2)   ~ (e3 = e1)
% 230.52/41.94    (3)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.52/41.94         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.52/41.94    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.94    (5)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.52/41.94         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.52/41.94    (6)   ~ (all_6_2 = e3)
% 230.52/41.94    (7)  op(e1, e1) = all_6_2
% 230.52/41.94    (8)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.52/41.94         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.52/41.94    (9)  all_57_6 = e1
% 230.52/41.94    (10)  op(e2, e2) = e0
% 230.52/41.94    (11)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.52/41.94          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.52/41.94    (12)  all_57_3 = e0
% 230.52/41.94    (13)   ~ (e3 = e2)
% 230.52/41.94    (14)   ~ (e3 = e0)
% 230.52/41.94    (15)  op(e3, e3) = e2
% 230.52/41.94    (16)  op(e1, e1) = e1
% 230.52/41.94    (17)   ~ (e2 = e0)
% 230.52/41.94    (18)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.52/41.94          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.52/41.94    (19)   ~ (e1 = e0)
% 230.52/41.94    (20)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.52/41.94          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.52/41.94    (21)   ~ (e2 = e1)
% 230.52/41.94    (22)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.52/41.94          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.52/41.94    (23)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.52/41.94          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.52/41.94  
% 230.52/41.94  Begin of proof
% 230.52/41.94  | 
% 230.52/41.94  | BETA: splitting (3) gives:
% 230.52/41.94  | 
% 230.52/41.94  | Case 1:
% 230.52/41.94  | | 
% 230.52/41.94  | |   (24)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) =
% 230.52/41.94  | |           e0)
% 230.52/41.94  | | 
% 230.52/41.94  | | BETA: splitting (24) gives:
% 230.52/41.94  | | 
% 230.52/41.94  | | Case 1:
% 230.52/41.94  | | | 
% 230.52/41.94  | | |   (25)  all_57_6 = e0 & op(e1, e3) = e0
% 230.52/41.94  | | | 
% 230.52/41.94  | | | ALPHA: (25) implies:
% 230.52/41.94  | | |   (26)  all_57_6 = e0
% 230.52/41.94  | | | 
% 230.52/41.94  | | | REF_CLOSE: (9), (19), (26) are inconsistent by sub-proof #2227.
% 230.52/41.94  | | | 
% 230.52/41.94  | | Case 2:
% 230.52/41.94  | | | 
% 230.52/41.94  | | |   (27)  all_57_7 = e0 & op(e1, e2) = e0
% 230.52/41.94  | | | 
% 230.52/41.94  | | | ALPHA: (27) implies:
% 230.52/41.94  | | |   (28)  all_57_7 = e0
% 230.52/41.94  | | | 
% 230.52/41.94  | | | REF_CLOSE: (1), (2), (4), (8), (10), (11), (12), (13), (14), (15), (17),
% 230.52/41.94  | | |            (18), (19), (20), (21), (22), (28) are inconsistent by
% 230.52/41.94  | | |            sub-proof #1296.
% 230.52/41.94  | | | 
% 230.52/41.94  | | End of split
% 230.52/41.94  | | 
% 230.52/41.94  | Case 2:
% 230.52/41.94  | | 
% 230.52/41.94  | |   (29)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 230.52/41.94  | |           e0)
% 230.52/41.94  | | 
% 230.52/41.94  | | REF_CLOSE: (2), (4), (5), (6), (7), (9), (13), (14), (16), (17), (19), (21),
% 230.52/41.94  | |            (23), (29) are inconsistent by sub-proof #1593.
% 230.52/41.94  | | 
% 230.52/41.94  | End of split
% 230.52/41.94  | 
% 230.52/41.94  End of proof
% 230.52/41.94  
% 230.52/41.94  Sub-proof #1240 shows that the following formulas are inconsistent:
% 230.52/41.94  ----------------------------------------------------------------
% 230.52/41.94    (1)  all_57_0 = e2
% 230.52/41.94    (2)  op(e1, e3) = all_52_17
% 230.52/41.94    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.52/41.94         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.52/41.94    (4)  op(e2, e3) = all_53_1
% 230.52/41.94    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.52/41.94         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.52/41.94    (6)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.52/41.94         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.52/41.94    (7)   ~ (e3 = e1)
% 230.52/41.94    (8)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.52/41.94         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.52/41.94    (9)   ~ (all_53_13 = e1)
% 230.52/41.94    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.94            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.94    (11)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.52/41.94          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.52/41.94    (12)   ~ (all_6_2 = e3)
% 230.52/41.94    (13)  ( ~ (all_28_0 = e0) & op(all_28_1, e3) = all_28_0 & op(e3, e2) =
% 230.52/41.94            all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 = e1) & op(e3,
% 230.52/41.94              e2) = all_28_1 & $i(all_28_1))
% 230.52/41.94    (14)  op(e1, e1) = all_6_2
% 230.52/41.94    (15)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.52/41.94          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.52/41.94    (16)   ~ (all_52_17 = e2)
% 230.52/41.94    (17)  op(all_52_17, all_52_17) = e3
% 230.52/41.94    (18)  op(e2, e2) = e0
% 230.52/41.94    (19)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.52/41.94          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.52/41.94    (20)  all_57_3 = e0
% 230.52/41.94    (21)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 230.52/41.94          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.52/41.94    (22)   ~ (e3 = e2)
% 230.52/41.94    (23)   ~ (all_53_1 = all_52_17)
% 230.52/41.94    (24)   ~ (e3 = e0)
% 230.52/41.94    (25)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.52/41.94          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.52/41.94    (26)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 230.52/41.94    (27)  op(e0, e3) = all_53_3
% 230.52/41.94    (28)  op(e3, e3) = e2
% 230.52/41.94    (29)   ~ (all_53_3 = e2)
% 230.52/41.94    (30)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.52/41.94          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.52/41.94            e1)
% 230.52/41.94    (31)  op(e3, e2) = all_53_4
% 230.52/41.94    (32)  op(e1, e1) = e1
% 230.52/41.94    (33)  all_57_2 = e1 & op(e2, e3) = e1
% 230.52/41.94    (34)   ~ (e2 = e0)
% 230.52/41.94    (35)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.52/41.94          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.52/41.94    (36)   ~ (e1 = e0)
% 230.52/41.94    (37)   ~ (all_53_4 = e0)
% 230.52/41.94    (38)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 230.52/41.94          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 230.52/41.94    (39)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.52/41.94          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.52/41.94    (40)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.52/41.94          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 230.52/41.94            e3)
% 230.52/41.94    (41)  ( ~ (all_20_0 = e1) & op(all_20_1, e3) = all_20_0 & op(e3, e2) =
% 230.52/41.94            all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e0) & op(e3,
% 230.52/41.94              e2) = all_20_1 & $i(all_20_1))
% 230.52/41.94    (42)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.52/41.94          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.52/41.94            e2)
% 230.52/41.94    (43)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.52/41.94              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.52/41.94                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.52/41.94                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.52/41.94    (44)   ~ (all_53_13 = e0)
% 230.52/41.94    (45)  op(e0, e0) = e1
% 230.52/41.94    (46)  op(e2, e0) = all_53_13
% 230.52/41.94    (47)  all_55_8 = all_52_17
% 230.52/41.94    (48)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.52/41.94          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.52/41.94    (49)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.52/41.94          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.52/41.94    (50)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.52/41.94          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.52/41.94    (51)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 230.52/41.94          (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 230.52/41.94    (52)   ~ (e2 = e1)
% 230.52/41.94    (53)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.52/41.94          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.52/41.94    (54)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.52/41.94          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.52/41.94    (55)   ~ (all_53_12 = e2)
% 230.52/41.94    (56)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.52/41.94          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.52/41.94    (57)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.52/41.94          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.52/41.94    (58)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.52/41.94          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.52/41.94    (59)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.52/41.94          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.52/41.94    (60)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.52/41.94          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.52/41.94    (61)  op(e3, e0) = all_53_12
% 230.52/41.94  
% 230.52/41.94  Begin of proof
% 230.52/41.94  | 
% 230.52/41.94  | ALPHA: (33) implies:
% 230.52/41.94  |   (62)  all_57_2 = e1
% 230.52/41.94  |   (63)  op(e2, e3) = e1
% 230.52/41.94  | 
% 230.52/41.94  | BETA: splitting (59) gives:
% 230.52/41.94  | 
% 230.52/41.94  | Case 1:
% 230.52/41.94  | | 
% 230.52/41.94  | |   (64)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) =
% 230.52/41.94  | |           e1)
% 230.52/41.94  | | 
% 230.52/41.94  | | BETA: splitting (64) gives:
% 230.52/41.94  | | 
% 230.52/41.94  | | Case 1:
% 230.52/41.94  | | | 
% 230.52/41.94  | | |   (65)  all_57_1 = e1 & op(e3, e2) = e1
% 230.52/41.94  | | | 
% 230.52/41.94  | | | ALPHA: (65) implies:
% 230.52/41.94  | | |   (66)  op(e3, e2) = e1
% 230.52/41.94  | | | 
% 230.52/41.94  | | | GROUND_INST: instantiating (10) with all_53_1, e1, e3, e2, simplifying
% 230.52/41.94  | | |              with (4), (63) gives:
% 230.52/41.94  | | |   (67)  all_53_1 = e1
% 230.52/41.94  | | | 
% 230.52/41.94  | | | GROUND_INST: instantiating (10) with all_53_4, e1, e2, e3, simplifying
% 230.52/41.94  | | |              with (31), (66) gives:
% 230.52/41.94  | | |   (68)  all_53_4 = e1
% 230.52/41.94  | | | 
% 230.52/41.94  | | | REDUCE: (23), (67) imply:
% 230.52/41.94  | | |   (69)   ~ (all_52_17 = e1)
% 230.52/41.94  | | | 
% 230.52/41.94  | | | SIMP: (69) implies:
% 230.52/41.94  | | |   (70)   ~ (all_52_17 = e1)
% 230.52/41.94  | | | 
% 230.52/41.94  | | | BETA: splitting (41) gives:
% 230.52/41.94  | | | 
% 230.52/41.94  | | | Case 1:
% 230.52/41.94  | | | | 
% 230.52/41.94  | | | |   (71)   ~ (all_20_0 = e1) & op(all_20_1, e3) = all_20_0 & op(e3, e2) =
% 230.52/41.94  | | | |         all_20_1 & $i(all_20_0) & $i(all_20_1)
% 230.52/41.94  | | | | 
% 230.52/41.94  | | | | ALPHA: (71) implies:
% 230.52/41.94  | | | |   (72)  op(e3, e2) = all_20_1
% 230.52/41.94  | | | | 
% 230.52/41.94  | | | | REF_CLOSE: (2), (10), (13), (16), (17), (26), (28), (47), (66), (70),
% 230.52/41.94  | | | |            (72) are inconsistent by sub-proof #1248.
% 230.52/41.94  | | | | 
% 230.52/41.94  | | | Case 2:
% 230.52/41.94  | | | | 
% 230.52/41.94  | | | |   (73)   ~ (all_20_1 = e0) & op(e3, e2) = all_20_1 & $i(all_20_1)
% 230.52/41.94  | | | | 
% 230.52/41.94  | | | | ALPHA: (73) implies:
% 230.52/41.94  | | | |   (74)  op(e3, e2) = all_20_1
% 230.52/41.94  | | | | 
% 230.52/41.94  | | | | REF_CLOSE: (2), (10), (13), (16), (17), (26), (28), (47), (66), (70),
% 230.52/41.94  | | | |            (74) are inconsistent by sub-proof #1248.
% 230.52/41.94  | | | | 
% 230.52/41.94  | | | End of split
% 230.52/41.94  | | | 
% 230.52/41.94  | | Case 2:
% 230.52/41.94  | | | 
% 230.52/41.94  | | |   (75)  all_57_3 = e1 & op(e2, e2) = e1
% 230.52/41.94  | | | 
% 230.52/41.94  | | | ALPHA: (75) implies:
% 230.52/41.94  | | |   (76)  op(e2, e2) = e1
% 230.52/41.94  | | | 
% 230.52/41.94  | | | REF_CLOSE: (10), (18), (36), (76) are inconsistent by sub-proof #2352.
% 230.52/41.94  | | | 
% 230.52/41.94  | | End of split
% 230.52/41.94  | | 
% 230.52/41.94  | Case 2:
% 230.52/41.94  | | 
% 230.52/41.94  | |   (77)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 230.52/41.94  | |           e1)
% 230.52/41.94  | | 
% 230.52/41.94  | | BETA: splitting (77) gives:
% 230.52/41.94  | | 
% 230.52/41.94  | | Case 1:
% 230.52/41.94  | | | 
% 230.52/41.94  | | |   (78)  all_57_7 = e1 & op(e1, e2) = e1
% 230.52/41.94  | | | 
% 230.52/41.94  | | | ALPHA: (78) implies:
% 230.52/41.94  | | |   (79)  all_57_7 = e1
% 230.52/41.94  | | | 
% 230.52/41.94  | | | BETA: splitting (6) gives:
% 230.52/41.94  | | | 
% 230.52/41.94  | | | Case 1:
% 230.52/41.94  | | | | 
% 230.52/41.94  | | | |   (80)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2)
% 230.52/41.94  | | | |           = e2)
% 230.52/41.94  | | | | 
% 230.52/41.94  | | | | REF_CLOSE: (7), (10), (15), (18), (19), (22), (24), (28), (34), (35),
% 230.52/41.94  | | | |            (36), (52), (80) are inconsistent by sub-proof #1297.
% 230.52/41.94  | | | | 
% 230.52/41.94  | | | Case 2:
% 230.52/41.94  | | | | 
% 230.52/41.94  | | | |   (81)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2)
% 230.52/41.94  | | | |           = e2)
% 230.52/41.94  | | | | 
% 230.52/41.94  | | | | BETA: splitting (81) gives:
% 230.52/41.94  | | | | 
% 230.52/41.94  | | | | Case 1:
% 230.52/41.94  | | | | | 
% 230.52/41.94  | | | | |   (82)  all_57_7 = e2 & op(e1, e2) = e2
% 230.52/41.94  | | | | | 
% 230.52/41.94  | | | | | ALPHA: (82) implies:
% 230.52/41.94  | | | | |   (83)  all_57_7 = e2
% 230.52/41.94  | | | | | 
% 230.52/41.94  | | | | | REF_CLOSE: (52), (79), (83) are inconsistent by sub-proof #1761.
% 230.52/41.94  | | | | | 
% 230.52/41.94  | | | | Case 2:
% 230.52/41.94  | | | | | 
% 230.52/41.94  | | | | |   (84)  all_57_13 = e2 & op(e0, e2) = e2
% 230.52/41.94  | | | | | 
% 230.52/41.94  | | | | | ALPHA: (84) implies:
% 230.52/41.94  | | | | |   (85)  all_57_13 = e2
% 230.52/41.94  | | | | | 
% 230.52/41.94  | | | | | BETA: splitting (60) gives:
% 230.52/41.94  | | | | | 
% 230.52/41.94  | | | | | Case 1:
% 230.52/41.94  | | | | | | 
% 230.52/41.94  | | | | | |   (86)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1,
% 230.52/41.94  | | | | | |             e2) = e2)
% 230.52/41.94  | | | | | | 
% 230.52/41.94  | | | | | | BETA: splitting (86) gives:
% 230.52/41.94  | | | | | | 
% 230.52/41.94  | | | | | | Case 1:
% 230.52/41.94  | | | | | | | 
% 230.52/41.94  | | | | | | |   (87)  all_57_6 = e2 & op(e1, e3) = e2
% 230.52/41.94  | | | | | | | 
% 230.52/41.94  | | | | | | | ALPHA: (87) implies:
% 230.52/41.94  | | | | | | |   (88)  all_57_6 = e2
% 230.52/41.94  | | | | | | | 
% 230.52/41.94  | | | | | | | REF_CLOSE: (1), (3), (5), (6), (7), (8), (9), (10), (11), (12),
% 230.52/41.94  | | | | | | |            (14), (15), (18), (19), (20), (22), (24), (25), (27),
% 230.52/41.94  | | | | | | |            (28), (29), (30), (31), (32), (34), (35), (36), (37),
% 230.52/41.94  | | | | | | |            (38), (39), (40), (42), (43), (44), (45), (46), (48),
% 230.52/41.94  | | | | | | |            (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 230.52/41.94  | | | | | | |            (58), (59), (60), (61), (62), (79), (85), (88) are
% 230.52/41.94  | | | | | | |            inconsistent by sub-proof #1244.
% 230.52/41.94  | | | | | | | 
% 230.52/41.94  | | | | | | Case 2:
% 230.52/41.94  | | | | | | | 
% 230.52/41.94  | | | | | | |   (89)  all_57_7 = e2 & op(e1, e2) = e2
% 230.52/41.94  | | | | | | | 
% 230.52/41.94  | | | | | | | ALPHA: (89) implies:
% 230.52/41.94  | | | | | | |   (90)  all_57_7 = e2
% 230.52/41.94  | | | | | | | 
% 230.52/41.94  | | | | | | | COMBINE_EQS: (79), (90) imply:
% 230.52/41.94  | | | | | | |   (91)  e2 = e1
% 230.52/41.94  | | | | | | | 
% 230.52/41.94  | | | | | | | SIMP: (91) implies:
% 230.52/41.94  | | | | | | |   (92)  e2 = e1
% 230.52/41.94  | | | | | | | 
% 230.52/41.94  | | | | | | | COMBINE_EQS: (85), (92) imply:
% 230.52/41.94  | | | | | | |   (93)  all_57_13 = e1
% 230.52/41.94  | | | | | | | 
% 230.52/41.94  | | | | | | | REF_CLOSE: (1), (3), (5), (6), (7), (8), (9), (10), (11), (12),
% 230.52/41.94  | | | | | | |            (14), (15), (18), (19), (20), (21), (22), (24), (25),
% 230.52/41.94  | | | | | | |            (27), (28), (29), (30), (31), (32), (34), (35), (36),
% 230.52/41.94  | | | | | | |            (37), (38), (39), (40), (42), (43), (44), (45), (46),
% 230.52/41.94  | | | | | | |            (48), (49), (50), (51), (52), (53), (54), (55), (56),
% 230.52/41.94  | | | | | | |            (57), (58), (59), (60), (61), (62), (93) are
% 230.52/41.94  | | | | | | |            inconsistent by sub-proof #1241.
% 230.52/41.94  | | | | | | | 
% 230.52/41.94  | | | | | | End of split
% 230.52/41.94  | | | | | | 
% 230.52/41.94  | | | | | Case 2:
% 230.52/41.94  | | | | | | 
% 230.52/41.94  | | | | | |   (94)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1,
% 230.52/41.94  | | | | | |             e0) = e2)
% 230.52/41.94  | | | | | | 
% 230.52/41.94  | | | | | | BETA: splitting (94) gives:
% 230.52/41.94  | | | | | | 
% 230.52/41.94  | | | | | | Case 1:
% 230.52/41.94  | | | | | | | 
% 230.52/41.94  | | | | | | |   (95)  all_57_8 = e2 & op(e1, e1) = e2
% 230.52/41.94  | | | | | | | 
% 230.52/41.94  | | | | | | | ALPHA: (95) implies:
% 230.52/41.94  | | | | | | |   (96)  op(e1, e1) = e2
% 230.52/41.94  | | | | | | | 
% 230.52/41.94  | | | | | | | REF_CLOSE: (10), (32), (52), (96) are inconsistent by sub-proof
% 230.52/41.94  | | | | | | |            #2423.
% 230.52/41.94  | | | | | | | 
% 230.52/41.94  | | | | | | Case 2:
% 230.52/41.94  | | | | | | | 
% 230.52/41.94  | | | | | | |   (97)  all_57_11 = e2 & op(e1, e0) = e2
% 230.52/41.94  | | | | | | | 
% 230.52/41.94  | | | | | | | ALPHA: (97) implies:
% 230.52/41.94  | | | | | | |   (98)  all_57_11 = e2
% 230.52/41.94  | | | | | | | 
% 230.52/41.94  | | | | | | | REF_CLOSE: (7), (8), (10), (11), (12), (14), (18), (20), (22),
% 230.52/41.94  | | | | | | |            (24), (32), (34), (36), (39), (52), (59), (79), (85),
% 230.52/41.94  | | | | | | |            (98) are inconsistent by sub-proof #1621.
% 230.52/41.94  | | | | | | | 
% 230.52/41.94  | | | | | | End of split
% 230.52/41.94  | | | | | | 
% 230.52/41.94  | | | | | End of split
% 230.52/41.94  | | | | | 
% 230.52/41.94  | | | | End of split
% 230.52/41.94  | | | | 
% 230.52/41.94  | | | End of split
% 230.52/41.94  | | | 
% 230.52/41.94  | | Case 2:
% 230.52/41.94  | | | 
% 230.52/41.94  | | |   (99)  all_57_13 = e1 & op(e0, e2) = e1
% 230.52/41.94  | | | 
% 230.52/41.94  | | | ALPHA: (99) implies:
% 230.52/41.94  | | |   (100)  all_57_13 = e1
% 230.52/41.94  | | | 
% 230.52/41.94  | | | REF_CLOSE: (1), (3), (5), (6), (7), (8), (9), (10), (11), (12), (14),
% 230.52/41.94  | | |            (15), (18), (19), (20), (21), (22), (24), (25), (27), (28),
% 230.52/41.94  | | |            (29), (30), (31), (32), (34), (35), (36), (37), (38), (39),
% 230.52/41.94  | | |            (40), (42), (43), (44), (45), (46), (48), (49), (50), (51),
% 230.52/41.94  | | |            (52), (53), (54), (55), (56), (57), (58), (59), (60), (61),
% 230.52/41.94  | | |            (62), (100) are inconsistent by sub-proof #1241.
% 230.52/41.94  | | | 
% 230.52/41.94  | | End of split
% 230.52/41.94  | | 
% 230.52/41.94  | End of split
% 230.52/41.94  | 
% 230.52/41.94  End of proof
% 230.52/41.94  
% 230.52/41.94  Sub-proof #1241 shows that the following formulas are inconsistent:
% 230.52/41.94  ----------------------------------------------------------------
% 230.52/41.94    (1)  all_57_0 = e2
% 230.52/41.94    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.52/41.94         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.52/41.94    (3)  all_57_13 = e1
% 230.52/41.94    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.52/41.94         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.52/41.95    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.52/41.95         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.52/41.95    (6)   ~ (e3 = e1)
% 230.52/41.95    (7)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.52/41.95         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.52/41.95    (8)   ~ (all_53_13 = e1)
% 230.52/41.95    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.95           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.95    (10)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.52/41.95          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.52/41.95    (11)   ~ (all_6_2 = e3)
% 230.52/41.95    (12)  op(e1, e1) = all_6_2
% 230.52/41.95    (13)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.52/41.95          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.52/41.95    (14)  op(e2, e2) = e0
% 230.52/41.95    (15)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.52/41.95          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.52/41.95    (16)  all_57_3 = e0
% 230.52/41.95    (17)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 230.52/41.95          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.52/41.95    (18)   ~ (e3 = e2)
% 230.52/41.95    (19)   ~ (e3 = e0)
% 230.52/41.95    (20)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.52/41.95          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.52/41.95    (21)  op(e0, e3) = all_53_3
% 230.52/41.95    (22)  op(e3, e3) = e2
% 230.52/41.95    (23)   ~ (all_53_3 = e2)
% 230.52/41.95    (24)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.52/41.95          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.52/41.95            e1)
% 230.52/41.95    (25)  op(e3, e2) = all_53_4
% 230.52/41.95    (26)  op(e1, e1) = e1
% 230.52/41.95    (27)   ~ (e2 = e0)
% 230.52/41.95    (28)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.52/41.95          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.52/41.95    (29)   ~ (e1 = e0)
% 230.52/41.95    (30)   ~ (all_53_4 = e0)
% 230.52/41.95    (31)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 230.52/41.95          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 230.52/41.95    (32)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.52/41.95          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.52/41.95    (33)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.52/41.95          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 230.52/41.95            e3)
% 230.52/41.95    (34)  all_57_2 = e1
% 230.52/41.95    (35)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.52/41.95          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.52/41.95            e2)
% 230.52/41.95    (36)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.52/41.95              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.52/41.95                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.52/41.95                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.52/41.95    (37)   ~ (all_53_13 = e0)
% 230.52/41.95    (38)  op(e0, e0) = e1
% 230.52/41.95    (39)  op(e2, e0) = all_53_13
% 230.52/41.95    (40)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.52/41.95          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.52/41.95    (41)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.52/41.95          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.52/41.95    (42)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.52/41.95          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.52/41.95    (43)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 230.52/41.95          (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 230.52/41.95    (44)   ~ (e2 = e1)
% 230.52/41.95    (45)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.52/41.95          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.52/41.95    (46)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.52/41.95          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.52/41.95    (47)   ~ (all_53_12 = e2)
% 230.52/41.95    (48)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.52/41.95          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.52/41.95    (49)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.52/41.95          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.52/41.95    (50)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.52/41.95          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.52/41.95    (51)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.52/41.95          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.52/41.95    (52)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.52/41.95          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.52/41.95    (53)  op(e3, e0) = all_53_12
% 230.52/41.95  
% 230.52/41.95  Begin of proof
% 230.52/41.95  | 
% 230.52/41.95  | BETA: splitting (35) gives:
% 230.52/41.95  | 
% 230.52/41.95  | Case 1:
% 230.52/41.95  | | 
% 230.52/41.95  | |   (54)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 230.52/41.95  | |           e2)
% 230.52/41.95  | | 
% 230.52/41.95  | | REF_CLOSE: (3), (9), (21), (23), (44), (54) are inconsistent by sub-proof
% 230.52/41.95  | |            #1243.
% 230.52/41.95  | | 
% 230.52/41.95  | Case 2:
% 230.52/41.95  | | 
% 230.52/41.95  | |   (55)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.52/41.95  | |           e2)
% 230.52/41.95  | | 
% 230.52/41.95  | | BETA: splitting (55) gives:
% 230.52/41.95  | | 
% 230.52/41.95  | | Case 1:
% 230.52/41.95  | | | 
% 230.52/41.95  | | |   (56)  all_57_14 = e2 & op(e0, e1) = e2
% 230.52/41.95  | | | 
% 230.52/41.95  | | | ALPHA: (56) implies:
% 230.52/41.95  | | |   (57)  all_57_14 = e2
% 230.52/41.95  | | | 
% 230.52/41.95  | | | BETA: splitting (13) gives:
% 230.52/41.95  | | | 
% 230.52/41.95  | | | Case 1:
% 230.52/41.95  | | | | 
% 230.52/41.95  | | | |   (58)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2)
% 230.52/41.95  | | | |           = e1)
% 230.52/41.95  | | | | 
% 230.52/41.95  | | | | BETA: splitting (58) gives:
% 230.52/41.95  | | | | 
% 230.52/41.95  | | | | Case 1:
% 230.52/41.95  | | | | | 
% 230.52/41.95  | | | | |   (59)  all_57_0 = e1 & op(e3, e3) = e1
% 230.52/41.95  | | | | | 
% 230.52/41.95  | | | | | ALPHA: (59) implies:
% 230.52/41.95  | | | | |   (60)  op(e3, e3) = e1
% 230.52/41.95  | | | | | 
% 230.52/41.95  | | | | | REF_CLOSE: (9), (22), (44), (60) are inconsistent by sub-proof #1950.
% 230.52/41.95  | | | | | 
% 230.52/41.95  | | | | Case 2:
% 230.52/41.95  | | | | | 
% 230.52/41.95  | | | | |   (61)  all_57_1 = e1 & op(e3, e2) = e1
% 230.52/41.95  | | | | | 
% 230.52/41.95  | | | | | ALPHA: (61) implies:
% 230.52/41.95  | | | | |   (62)  all_57_1 = e1
% 230.52/41.95  | | | | | 
% 230.52/41.95  | | | | | BETA: splitting (5) gives:
% 230.52/41.95  | | | | | 
% 230.52/41.95  | | | | | Case 1:
% 230.52/41.95  | | | | | | 
% 230.52/41.95  | | | | | |   (63)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2,
% 230.52/41.95  | | | | | |             e2) = e2)
% 230.52/41.95  | | | | | | 
% 230.52/41.95  | | | | | | REF_CLOSE: (6), (9), (13), (14), (15), (18), (19), (22), (27), (28),
% 230.52/41.95  | | | | | |            (29), (44), (63) are inconsistent by sub-proof #1297.
% 230.52/41.95  | | | | | | 
% 230.52/41.95  | | | | | Case 2:
% 230.52/41.95  | | | | | | 
% 230.52/41.95  | | | | | |   (64)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0,
% 230.52/41.95  | | | | | |             e2) = e2)
% 230.52/41.95  | | | | | | 
% 230.52/41.95  | | | | | | BETA: splitting (64) gives:
% 230.52/41.95  | | | | | | 
% 230.52/41.95  | | | | | | Case 1:
% 230.52/41.95  | | | | | | | 
% 230.52/41.95  | | | | | | |   (65)  all_57_7 = e2 & op(e1, e2) = e2
% 230.52/41.95  | | | | | | | 
% 230.52/41.95  | | | | | | | ALPHA: (65) implies:
% 230.52/41.95  | | | | | | |   (66)  all_57_7 = e2
% 230.52/41.95  | | | | | | | 
% 230.52/41.95  | | | | | | | REF_CLOSE: (3), (6), (16), (18), (19), (32), (62), (66) are
% 230.52/41.95  | | | | | | |            inconsistent by sub-proof #2193.
% 230.52/41.95  | | | | | | | 
% 230.52/41.95  | | | | | | Case 2:
% 230.52/41.95  | | | | | | | 
% 230.52/41.95  | | | | | | |   (67)  all_57_13 = e2 & op(e0, e2) = e2
% 230.52/41.95  | | | | | | | 
% 230.52/41.95  | | | | | | | ALPHA: (67) implies:
% 230.52/41.95  | | | | | | |   (68)  all_57_13 = e2
% 230.52/41.95  | | | | | | | 
% 230.52/41.95  | | | | | | | COMBINE_EQS: (3), (68) imply:
% 230.52/41.95  | | | | | | |   (69)  e2 = e1
% 230.52/41.95  | | | | | | | 
% 230.52/41.95  | | | | | | | COMBINE_EQS: (57), (69) imply:
% 230.52/41.95  | | | | | | |   (70)  all_57_14 = e1
% 230.52/41.95  | | | | | | | 
% 230.52/41.95  | | | | | | | BETA: splitting (35) gives:
% 230.52/41.95  | | | | | | | 
% 230.52/41.95  | | | | | | | Case 1:
% 230.52/41.95  | | | | | | | | 
% 230.52/41.95  | | | | | | | |   (71)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 &
% 230.52/41.95  | | | | | | | |           op(e0, e2) = e2)
% 230.52/41.95  | | | | | | | | 
% 230.52/41.95  | | | | | | | | REF_CLOSE: (3), (9), (21), (23), (44), (71) are inconsistent by
% 230.52/41.95  | | | | | | | |            sub-proof #1243.
% 230.52/41.95  | | | | | | | | 
% 230.52/41.95  | | | | | | | Case 2:
% 230.52/41.95  | | | | | | | | 
% 230.52/41.95  | | | | | | | | 
% 230.52/41.95  | | | | | | | | REF_CLOSE: (9), (38), (44), (55), (70) are inconsistent by
% 230.52/41.95  | | | | | | | |            sub-proof #2176.
% 230.52/41.95  | | | | | | | | 
% 230.52/41.95  | | | | | | | End of split
% 230.52/41.95  | | | | | | | 
% 230.52/41.95  | | | | | | End of split
% 230.52/41.95  | | | | | | 
% 230.52/41.95  | | | | | End of split
% 230.52/41.95  | | | | | 
% 230.52/41.95  | | | | End of split
% 230.52/41.95  | | | | 
% 230.52/41.95  | | | Case 2:
% 230.52/41.95  | | | | 
% 230.52/41.95  | | | |   (72)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0)
% 230.52/41.95  | | | |           = e1)
% 230.52/41.95  | | | | 
% 230.52/41.95  | | | | BETA: splitting (72) gives:
% 230.52/41.95  | | | | 
% 230.52/41.95  | | | | Case 1:
% 230.52/41.95  | | | | | 
% 230.52/41.95  | | | | |   (73)  all_57_4 = e1 & op(e3, e1) = e1
% 230.52/41.95  | | | | | 
% 230.52/41.95  | | | | | ALPHA: (73) implies:
% 230.52/41.95  | | | | |   (74)  all_57_4 = e1
% 230.52/41.95  | | | | | 
% 230.52/41.95  | | | | | REF_CLOSE: (2), (6), (9), (11), (12), (14), (16), (17), (18), (19),
% 230.52/41.95  | | | | |            (26), (27), (29), (31), (34), (40), (41), (44), (48), (74)
% 230.52/41.95  | | | | |            are inconsistent by sub-proof #1242.
% 230.52/41.95  | | | | | 
% 230.52/41.95  | | | | Case 2:
% 230.52/41.95  | | | | | 
% 230.52/41.95  | | | | |   (75)  all_57_9 = e1 & op(e3, e0) = e1
% 230.52/41.95  | | | | | 
% 230.52/41.95  | | | | | ALPHA: (75) implies:
% 230.52/41.95  | | | | |   (76)  all_57_9 = e1
% 230.52/41.95  | | | | | 
% 230.52/41.95  | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 230.52/41.95  | | | | |            (13), (14), (15), (16), (18), (19), (20), (21), (22), (23),
% 230.52/41.95  | | | | |            (24), (25), (27), (28), (29), (30), (31), (32), (33), (35),
% 230.52/41.95  | | | | |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 230.52/41.95  | | | | |            (46), (47), (48), (49), (50), (51), (52), (53), (76) are
% 230.52/41.95  | | | | |            inconsistent by sub-proof #1266.
% 230.52/41.95  | | | | | 
% 230.52/41.95  | | | | End of split
% 230.52/41.95  | | | | 
% 230.52/41.95  | | | End of split
% 230.52/41.95  | | | 
% 230.52/41.95  | | Case 2:
% 230.52/41.95  | | | 
% 230.52/41.95  | | |   (77)  all_57_15 = e2 & op(e0, e0) = e2
% 230.52/41.95  | | | 
% 230.52/41.95  | | | ALPHA: (77) implies:
% 230.52/41.95  | | |   (78)  op(e0, e0) = e2
% 230.52/41.95  | | | 
% 230.52/41.95  | | | REF_CLOSE: (9), (38), (44), (78) are inconsistent by sub-proof #2177.
% 230.52/41.95  | | | 
% 230.52/41.95  | | End of split
% 230.52/41.95  | | 
% 230.52/41.95  | End of split
% 230.52/41.95  | 
% 230.52/41.95  End of proof
% 230.52/41.95  
% 230.52/41.95  Sub-proof #1242 shows that the following formulas are inconsistent:
% 230.52/41.95  ----------------------------------------------------------------
% 230.52/41.95    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.52/41.95         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.52/41.95    (2)   ~ (e3 = e1)
% 230.52/41.95    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.95           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.95    (4)   ~ (all_6_2 = e3)
% 230.52/41.95    (5)  op(e1, e1) = all_6_2
% 230.52/41.95    (6)  op(e2, e2) = e0
% 230.52/41.95    (7)  all_57_3 = e0
% 230.52/41.95    (8)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 230.52/41.95         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.52/41.95    (9)   ~ (e3 = e2)
% 230.52/41.95    (10)   ~ (e3 = e0)
% 230.52/41.95    (11)  all_57_4 = e1
% 230.52/41.95    (12)  op(e1, e1) = e1
% 230.52/41.95    (13)   ~ (e2 = e0)
% 230.52/41.95    (14)   ~ (e1 = e0)
% 230.52/41.95    (15)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 230.52/41.95          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 230.52/41.95    (16)  all_57_2 = e1
% 230.52/41.95    (17)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.52/41.95          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.52/41.95    (18)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.52/41.95          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.52/41.95    (19)   ~ (e2 = e1)
% 230.52/41.96    (20)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.52/41.96          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.52/41.96  
% 230.52/41.96  Begin of proof
% 230.52/41.96  | 
% 230.52/41.96  | BETA: splitting (8) gives:
% 230.52/41.96  | 
% 230.52/41.96  | Case 1:
% 230.52/41.96  | | 
% 230.52/41.96  | |   (21)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) =
% 230.52/41.96  | |           e0)
% 230.52/41.96  | | 
% 230.52/41.96  | | BETA: splitting (21) gives:
% 230.52/41.96  | | 
% 230.52/41.96  | | Case 1:
% 230.52/41.96  | | | 
% 230.52/41.96  | | |   (22)  all_57_4 = e0 & op(e3, e1) = e0
% 230.52/41.96  | | | 
% 230.52/41.96  | | | ALPHA: (22) implies:
% 230.52/41.96  | | |   (23)  all_57_4 = e0
% 230.52/41.96  | | | 
% 230.52/41.96  | | | COMBINE_EQS: (11), (23) imply:
% 230.52/41.96  | | |   (24)  e1 = e0
% 230.52/41.96  | | | 
% 230.52/41.96  | | | COMBINE_EQS: (16), (24) imply:
% 230.52/41.96  | | |   (25)  all_57_2 = e0
% 230.52/41.96  | | | 
% 230.52/41.96  | | | REF_CLOSE: (1), (2), (7), (9), (10), (13), (14), (17), (18), (19), (25)
% 230.52/41.96  | | |            are inconsistent by sub-proof #2246.
% 230.52/41.96  | | | 
% 230.52/41.96  | | Case 2:
% 230.52/41.96  | | | 
% 230.52/41.96  | | |   (26)  all_57_5 = e0 & op(e2, e1) = e0
% 230.52/41.96  | | | 
% 230.52/41.96  | | | ALPHA: (26) implies:
% 230.52/41.96  | | |   (27)  all_57_5 = e0
% 230.52/41.96  | | | 
% 230.52/41.96  | | | BETA: splitting (18) gives:
% 230.52/41.96  | | | 
% 230.52/41.96  | | | Case 1:
% 230.52/41.96  | | | | 
% 230.52/41.96  | | | |   (28)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2)
% 230.52/41.96  | | | |           = e2)
% 230.52/41.96  | | | | 
% 230.52/41.96  | | | | REF_CLOSE: (3), (6), (13), (16), (19), (28) are inconsistent by
% 230.52/41.96  | | | |            sub-proof #2364.
% 230.52/41.96  | | | | 
% 230.52/41.96  | | | Case 2:
% 230.52/41.96  | | | | 
% 230.52/41.96  | | | |   (29)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0)
% 230.52/41.96  | | | |           = e2)
% 230.52/41.96  | | | | 
% 230.52/41.96  | | | | REF_CLOSE: (1), (2), (7), (9), (10), (13), (14), (17), (19), (27), (29)
% 230.52/41.96  | | | |            are inconsistent by sub-proof #2354.
% 230.52/41.96  | | | | 
% 230.52/41.96  | | | End of split
% 230.52/41.96  | | | 
% 230.52/41.96  | | End of split
% 230.52/41.96  | | 
% 230.52/41.96  | Case 2:
% 230.52/41.96  | | 
% 230.52/41.96  | |   (30)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 230.52/41.96  | |           e0)
% 230.52/41.96  | | 
% 230.52/41.96  | | BETA: splitting (30) gives:
% 230.52/41.96  | | 
% 230.52/41.96  | | Case 1:
% 230.52/41.96  | | | 
% 230.52/41.96  | | |   (31)  all_57_8 = e0 & op(e1, e1) = e0
% 230.52/41.96  | | | 
% 230.52/41.96  | | | ALPHA: (31) implies:
% 230.52/41.96  | | |   (32)  op(e1, e1) = e0
% 230.52/41.96  | | | 
% 230.52/41.96  | | | REF_CLOSE: (3), (12), (14), (32) are inconsistent by sub-proof #2427.
% 230.52/41.96  | | | 
% 230.52/41.96  | | Case 2:
% 230.52/41.96  | | | 
% 230.52/41.96  | | |   (33)  all_57_14 = e0 & op(e0, e1) = e0
% 230.52/41.96  | | | 
% 230.52/41.96  | | | ALPHA: (33) implies:
% 230.52/41.96  | | |   (34)  all_57_14 = e0
% 230.52/41.96  | | | 
% 230.52/41.96  | | | REF_CLOSE: (2), (3), (4), (5), (9), (10), (11), (12), (13), (15), (19),
% 230.52/41.96  | | |            (20), (34) are inconsistent by sub-proof #2418.
% 230.52/41.96  | | | 
% 230.52/41.96  | | End of split
% 230.52/41.96  | | 
% 230.52/41.96  | End of split
% 230.52/41.96  | 
% 230.52/41.96  End of proof
% 230.52/41.96  
% 230.52/41.96  Sub-proof #1243 shows that the following formulas are inconsistent:
% 230.52/41.96  ----------------------------------------------------------------
% 230.52/41.96    (1)  all_57_13 = e1
% 230.52/41.96    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.96           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.96    (3)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.52/41.96    (4)  op(e0, e3) = all_53_3
% 230.52/41.96    (5)   ~ (all_53_3 = e2)
% 230.52/41.96    (6)   ~ (e2 = e1)
% 230.52/41.96  
% 230.52/41.96  Begin of proof
% 230.52/41.96  | 
% 230.52/41.96  | BETA: splitting (3) gives:
% 230.52/41.96  | 
% 230.52/41.96  | Case 1:
% 230.52/41.96  | | 
% 230.52/41.96  | |   (7)  all_57_12 = e2 & op(e0, e3) = e2
% 230.52/41.96  | | 
% 230.52/41.96  | | ALPHA: (7) implies:
% 230.52/41.96  | |   (8)  op(e0, e3) = e2
% 230.52/41.96  | | 
% 230.52/41.96  | | REF_CLOSE: (2), (4), (5), (8) are inconsistent by sub-proof #1980.
% 230.52/41.96  | | 
% 230.52/41.96  | Case 2:
% 230.52/41.96  | | 
% 230.52/41.96  | |   (9)  all_57_13 = e2 & op(e0, e2) = e2
% 230.52/41.96  | | 
% 230.52/41.96  | | ALPHA: (9) implies:
% 230.52/41.96  | |   (10)  all_57_13 = e2
% 230.52/41.96  | | 
% 230.52/41.96  | | REF_CLOSE: (1), (6), (10) are inconsistent by sub-proof #2327.
% 230.52/41.96  | | 
% 230.52/41.96  | End of split
% 230.52/41.96  | 
% 230.52/41.96  End of proof
% 230.52/41.96  
% 230.52/41.96  Sub-proof #1244 shows that the following formulas are inconsistent:
% 230.52/41.96  ----------------------------------------------------------------
% 230.52/41.96    (1)  all_57_0 = e2
% 230.52/41.96    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.52/41.96         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.52/41.96    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.52/41.96         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.52/41.96    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.52/41.96         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.52/41.96    (5)   ~ (e3 = e1)
% 230.52/41.96    (6)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.52/41.96         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.52/41.96    (7)   ~ (all_53_13 = e1)
% 230.52/41.96    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.96           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.96    (9)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.52/41.96         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.52/41.96    (10)   ~ (all_6_2 = e3)
% 230.52/41.96    (11)  op(e1, e1) = all_6_2
% 230.52/41.96    (12)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.52/41.96          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.52/41.96    (13)  all_57_7 = e1
% 230.52/41.96    (14)  op(e2, e2) = e0
% 230.52/41.96    (15)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.52/41.96          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.52/41.96    (16)  all_57_3 = e0
% 230.52/41.96    (17)   ~ (e3 = e2)
% 230.52/41.96    (18)   ~ (e3 = e0)
% 230.52/41.96    (19)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.52/41.96          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.52/41.96    (20)  op(e0, e3) = all_53_3
% 230.52/41.96    (21)  op(e3, e3) = e2
% 230.52/41.96    (22)   ~ (all_53_3 = e2)
% 230.52/41.96    (23)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.52/41.96          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.52/41.96            e1)
% 230.52/41.96    (24)  all_57_6 = e2
% 230.52/41.96    (25)  op(e3, e2) = all_53_4
% 230.52/41.96    (26)  op(e1, e1) = e1
% 230.52/41.96    (27)   ~ (e2 = e0)
% 230.52/41.96    (28)  all_57_13 = e2
% 230.52/41.96    (29)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.52/41.96          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.52/41.96    (30)   ~ (e1 = e0)
% 230.52/41.96    (31)   ~ (all_53_4 = e0)
% 230.52/41.96    (32)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 230.52/41.96          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 230.52/41.96    (33)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.52/41.96          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.52/41.96    (34)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.52/41.96          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 230.52/41.96            e3)
% 230.52/41.96    (35)  all_57_2 = e1
% 230.52/41.96    (36)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.52/41.96          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.52/41.96            e2)
% 230.52/41.96    (37)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.52/41.96              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.52/41.96                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.52/41.96                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.52/41.96    (38)   ~ (all_53_13 = e0)
% 230.52/41.96    (39)  op(e0, e0) = e1
% 230.52/41.96    (40)  op(e2, e0) = all_53_13
% 230.52/41.96    (41)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.52/41.96          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.52/41.96    (42)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.52/41.96          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.52/41.96    (43)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.52/41.96          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.52/41.96    (44)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 230.52/41.96          (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 230.52/41.96    (45)   ~ (e2 = e1)
% 230.52/41.96    (46)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.52/41.96          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.52/41.96    (47)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.52/41.96          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.52/41.96    (48)   ~ (all_53_12 = e2)
% 230.52/41.96    (49)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.52/41.96          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.52/41.96    (50)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.52/41.96          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.52/41.96    (51)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.52/41.96          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.52/41.96    (52)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.52/41.96          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.52/41.96    (53)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.52/41.96          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.52/41.96    (54)  op(e3, e0) = all_53_12
% 230.52/41.96  
% 230.52/41.96  Begin of proof
% 230.52/41.96  | 
% 230.52/41.96  | BETA: splitting (6) gives:
% 230.52/41.96  | 
% 230.52/41.96  | Case 1:
% 230.52/41.96  | | 
% 230.52/41.96  | |   (55)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) =
% 230.52/41.96  | |           e0)
% 230.52/41.96  | | 
% 230.52/41.96  | | BETA: splitting (55) gives:
% 230.52/41.96  | | 
% 230.52/41.96  | | Case 1:
% 230.52/41.96  | | | 
% 230.52/41.96  | | |   (56)  all_57_6 = e0 & op(e1, e3) = e0
% 230.52/41.96  | | | 
% 230.52/41.96  | | | REF_CLOSE: (24), (27), (56) are inconsistent by sub-proof #2386.
% 230.52/41.96  | | | 
% 230.52/41.96  | | Case 2:
% 230.52/41.96  | | | 
% 230.52/41.96  | | |   (57)  all_57_7 = e0 & op(e1, e2) = e0
% 230.52/41.96  | | | 
% 230.52/41.96  | | | ALPHA: (57) implies:
% 230.52/41.96  | | |   (58)  all_57_7 = e0
% 230.52/41.96  | | | 
% 230.52/41.96  | | | REF_CLOSE: (5), (8), (14), (16), (17), (18), (28), (30), (33), (45), (52),
% 230.52/41.96  | | |            (58) are inconsistent by sub-proof #2202.
% 230.52/41.96  | | | 
% 230.52/41.96  | | End of split
% 230.52/41.96  | | 
% 230.52/41.96  | Case 2:
% 230.52/41.96  | | 
% 230.52/41.96  | |   (59)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 230.52/41.96  | |           e0)
% 230.52/41.96  | | 
% 230.52/41.96  | | BETA: splitting (59) gives:
% 230.52/41.96  | | 
% 230.52/41.96  | | Case 1:
% 230.52/41.96  | | | 
% 230.52/41.96  | | |   (60)  all_57_8 = e0 & op(e1, e1) = e0
% 230.52/41.96  | | | 
% 230.52/41.96  | | | ALPHA: (60) implies:
% 230.52/41.96  | | |   (61)  op(e1, e1) = e0
% 230.52/41.96  | | | 
% 230.52/41.96  | | | REF_CLOSE: (8), (26), (30), (61) are inconsistent by sub-proof #2427.
% 230.52/41.96  | | | 
% 230.52/41.96  | | Case 2:
% 230.52/41.96  | | | 
% 230.52/41.96  | | |   (62)  all_57_11 = e0 & op(e1, e0) = e0
% 230.52/41.96  | | | 
% 230.52/41.96  | | | ALPHA: (62) implies:
% 230.52/41.96  | | |   (63)  all_57_11 = e0
% 230.52/41.96  | | | 
% 230.52/41.96  | | | BETA: splitting (46) gives:
% 230.52/41.96  | | | 
% 230.52/41.96  | | | Case 1:
% 230.52/41.96  | | | | 
% 230.52/41.96  | | | |   (64)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0)
% 230.52/41.96  | | | |           = e2)
% 230.52/41.96  | | | | 
% 230.52/41.96  | | | | BETA: splitting (64) gives:
% 230.52/41.96  | | | | 
% 230.52/41.96  | | | | Case 1:
% 230.52/41.96  | | | | | 
% 230.52/41.96  | | | | |   (65)  all_57_9 = e2 & op(e3, e0) = e2
% 230.52/41.96  | | | | | 
% 230.52/41.96  | | | | | ALPHA: (65) implies:
% 230.52/41.96  | | | | |   (66)  op(e3, e0) = e2
% 230.52/41.96  | | | | | 
% 230.52/41.96  | | | | | REF_CLOSE: (8), (48), (54), (66) are inconsistent by sub-proof #2331.
% 230.52/41.96  | | | | | 
% 230.52/41.96  | | | | Case 2:
% 230.52/41.96  | | | | | 
% 230.52/41.96  | | | | |   (67)  all_57_10 = e2 & op(e2, e0) = e2
% 230.52/41.96  | | | | | 
% 230.52/41.96  | | | | | ALPHA: (67) implies:
% 230.52/41.96  | | | | |   (68)  all_57_10 = e2
% 230.52/41.96  | | | | | 
% 230.52/41.96  | | | | | BETA: splitting (44) gives:
% 230.52/41.96  | | | | | 
% 230.52/41.96  | | | | | Case 1:
% 230.52/41.96  | | | | | | 
% 230.52/41.96  | | | | | |   (69)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2,
% 230.52/41.96  | | | | | |             e0) = e3)
% 230.52/41.96  | | | | | | 
% 230.52/41.96  | | | | | | BETA: splitting (69) gives:
% 230.52/41.96  | | | | | | 
% 230.52/41.96  | | | | | | Case 1:
% 230.52/41.96  | | | | | | | 
% 230.52/41.96  | | | | | | |   (70)  all_57_9 = e3 & op(e3, e0) = e3
% 230.52/41.96  | | | | | | | 
% 230.52/41.96  | | | | | | | ALPHA: (70) implies:
% 230.52/41.96  | | | | | | |   (71)  all_57_9 = e3
% 230.52/41.96  | | | | | | | 
% 230.52/41.96  | | | | | | | BETA: splitting (41) gives:
% 230.52/41.96  | | | | | | | 
% 230.52/41.96  | | | | | | | Case 1:
% 230.52/41.96  | | | | | | | | 
% 230.52/41.96  | | | | | | | |   (72)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 &
% 230.52/41.96  | | | | | | | |           op(e2, e2) = e3)
% 230.52/41.96  | | | | | | | | 
% 230.52/41.96  | | | | | | | | BETA: splitting (72) gives:
% 230.52/41.96  | | | | | | | | 
% 230.52/41.96  | | | | | | | | Case 1:
% 230.52/41.96  | | | | | | | | | 
% 230.52/41.96  | | | | | | | | |   (73)  all_57_2 = e3 & op(e2, e3) = e3
% 230.52/41.96  | | | | | | | | | 
% 230.52/41.96  | | | | | | | | | ALPHA: (73) implies:
% 230.52/41.96  | | | | | | | | |   (74)  all_57_2 = e3
% 230.52/41.96  | | | | | | | | | 
% 230.52/41.96  | | | | | | | | | COMBINE_EQS: (35), (74) imply:
% 230.52/41.96  | | | | | | | | |   (75)  e3 = e1
% 230.52/41.96  | | | | | | | | | 
% 230.52/41.96  | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 230.52/41.96  | | | | | | | | |            (11), (12), (14), (15), (16), (17), (18), (19),
% 230.52/41.96  | | | | | | | | |            (20), (21), (22), (23), (25), (27), (29), (30),
% 230.52/41.96  | | | | | | | | |            (31), (32), (33), (34), (36), (37), (38), (39),
% 230.52/41.96  | | | | | | | | |            (40), (41), (42), (43), (44), (45), (46), (47),
% 230.52/41.96  | | | | | | | | |            (48), (49), (50), (51), (52), (53), (54), (71),
% 230.52/41.96  | | | | | | | | |            (75) are inconsistent by sub-proof #1260.
% 230.52/41.96  | | | | | | | | | 
% 230.52/41.96  | | | | | | | | Case 2:
% 230.52/41.96  | | | | | | | | | 
% 230.52/41.96  | | | | | | | | |   (76)  all_57_3 = e3 & op(e2, e2) = e3
% 230.52/41.96  | | | | | | | | | 
% 230.52/41.96  | | | | | | | | | ALPHA: (76) implies:
% 230.52/41.96  | | | | | | | | |   (77)  all_57_3 = e3
% 230.52/41.97  | | | | | | | | | 
% 230.52/41.97  | | | | | | | | | REF_CLOSE: (16), (18), (77) are inconsistent by sub-proof
% 230.52/41.97  | | | | | | | | |            #2358.
% 230.52/41.97  | | | | | | | | | 
% 230.52/41.97  | | | | | | | | End of split
% 230.52/41.97  | | | | | | | | 
% 230.52/41.97  | | | | | | | Case 2:
% 230.52/41.97  | | | | | | | | 
% 230.52/41.97  | | | | | | | |   (78)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 &
% 230.52/41.97  | | | | | | | |           op(e2, e0) = e3)
% 230.52/41.97  | | | | | | | | 
% 230.52/41.97  | | | | | | | | BETA: splitting (78) gives:
% 230.52/41.97  | | | | | | | | 
% 230.52/41.97  | | | | | | | | Case 1:
% 230.52/41.97  | | | | | | | | | 
% 230.52/41.97  | | | | | | | | |   (79)  all_57_5 = e3 & op(e2, e1) = e3
% 230.52/41.97  | | | | | | | | | 
% 230.52/41.97  | | | | | | | | | ALPHA: (79) implies:
% 230.52/41.97  | | | | | | | | |   (80)  all_57_5 = e3
% 230.52/41.97  | | | | | | | | | 
% 230.52/41.97  | | | | | | | | | BETA: splitting (15) gives:
% 230.52/41.97  | | | | | | | | | 
% 230.52/41.97  | | | | | | | | | Case 1:
% 230.52/41.97  | | | | | | | | | | 
% 230.52/41.97  | | | | | | | | | |   (81)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 &
% 230.52/41.97  | | | | | | | | | |           op(e3, e2) = e0)
% 230.52/41.97  | | | | | | | | | | 
% 230.52/41.97  | | | | | | | | | | REF_CLOSE: (4), (5), (8), (14), (16), (17), (18), (21), (27),
% 230.52/41.97  | | | | | | | | | |            (28), (30), (33), (45), (52), (81) are
% 230.52/41.97  | | | | | | | | | |            inconsistent by sub-proof #1265.
% 230.52/41.97  | | | | | | | | | | 
% 230.52/41.97  | | | | | | | | | Case 2:
% 230.52/41.97  | | | | | | | | | | 
% 230.52/41.97  | | | | | | | | | |   (82)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 &
% 230.52/41.97  | | | | | | | | | |           op(e3, e0) = e0)
% 230.52/41.97  | | | | | | | | | | 
% 230.52/41.97  | | | | | | | | | | BETA: splitting (82) gives:
% 230.52/41.97  | | | | | | | | | | 
% 230.52/41.97  | | | | | | | | | | Case 1:
% 230.52/41.97  | | | | | | | | | | | 
% 230.52/41.97  | | | | | | | | | | |   (83)  all_57_4 = e0 & op(e3, e1) = e0
% 230.52/41.97  | | | | | | | | | | | 
% 230.52/41.97  | | | | | | | | | | | ALPHA: (83) implies:
% 230.52/41.97  | | | | | | | | | | |   (84)  all_57_4 = e0
% 230.52/41.97  | | | | | | | | | | | 
% 230.52/41.97  | | | | | | | | | | | BETA: splitting (9) gives:
% 230.52/41.97  | | | | | | | | | | | 
% 230.52/41.97  | | | | | | | | | | | Case 1:
% 230.52/41.97  | | | | | | | | | | | | 
% 230.52/41.97  | | | | | | | | | | | |   (85)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 230.52/41.97  | | | | | | | | | | | |           & op(e1, e2) = e3)
% 230.52/41.97  | | | | | | | | | | | | 
% 230.52/41.97  | | | | | | | | | | | | BETA: splitting (85) gives:
% 230.52/41.97  | | | | | | | | | | | | 
% 230.52/41.97  | | | | | | | | | | | | Case 1:
% 230.52/41.97  | | | | | | | | | | | | | 
% 230.52/41.97  | | | | | | | | | | | | |   (86)  all_57_6 = e3 & op(e1, e3) = e3
% 230.52/41.97  | | | | | | | | | | | | | 
% 230.52/41.97  | | | | | | | | | | | | | REF_CLOSE: (17), (24), (86) are inconsistent by sub-proof
% 230.52/41.97  | | | | | | | | | | | | |            #1558.
% 230.52/41.97  | | | | | | | | | | | | | 
% 230.52/41.97  | | | | | | | | | | | | Case 2:
% 230.52/41.97  | | | | | | | | | | | | | 
% 230.52/41.97  | | | | | | | | | | | | |   (87)  all_57_7 = e3 & op(e1, e2) = e3
% 230.52/41.97  | | | | | | | | | | | | | 
% 230.52/41.97  | | | | | | | | | | | | | ALPHA: (87) implies:
% 230.52/41.97  | | | | | | | | | | | | |   (88)  all_57_7 = e3
% 230.52/41.97  | | | | | | | | | | | | | 
% 230.52/41.97  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (8), (12), (13), (14), (15), (16), (17),
% 230.52/41.97  | | | | | | | | | | | | |            (18), (21), (27), (29), (30), (33), (35), (41),
% 230.52/41.97  | | | | | | | | | | | | |            (45), (52), (68), (80), (84), (88) are
% 230.52/41.97  | | | | | | | | | | | | |            inconsistent by sub-proof #1263.
% 230.52/41.97  | | | | | | | | | | | | | 
% 230.52/41.97  | | | | | | | | | | | | End of split
% 230.52/41.97  | | | | | | | | | | | | 
% 230.52/41.97  | | | | | | | | | | | Case 2:
% 230.52/41.97  | | | | | | | | | | | | 
% 230.52/41.97  | | | | | | | | | | | |   (89)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 230.52/41.97  | | | | | | | | | | | |           e3 & op(e1, e0) = e3)
% 230.52/41.97  | | | | | | | | | | | | 
% 230.52/41.97  | | | | | | | | | | | | BETA: splitting (89) gives:
% 230.52/41.97  | | | | | | | | | | | | 
% 230.52/41.97  | | | | | | | | | | | | Case 1:
% 230.52/41.97  | | | | | | | | | | | | | 
% 230.52/41.97  | | | | | | | | | | | | |   (90)  all_57_8 = e3 & op(e1, e1) = e3
% 230.52/41.97  | | | | | | | | | | | | | 
% 230.52/41.97  | | | | | | | | | | | | | ALPHA: (90) implies:
% 230.52/41.97  | | | | | | | | | | | | |   (91)  op(e1, e1) = e3
% 230.52/41.97  | | | | | | | | | | | | | 
% 230.52/41.97  | | | | | | | | | | | | | REF_CLOSE: (8), (10), (11), (91) are inconsistent by
% 230.52/41.97  | | | | | | | | | | | | |            sub-proof #2468.
% 230.52/41.97  | | | | | | | | | | | | | 
% 230.52/41.97  | | | | | | | | | | | | Case 2:
% 230.52/41.97  | | | | | | | | | | | | | 
% 230.52/41.97  | | | | | | | | | | | | |   (92)  all_57_11 = e3 & op(e1, e0) = e3
% 230.52/41.97  | | | | | | | | | | | | | 
% 230.52/41.97  | | | | | | | | | | | | | ALPHA: (92) implies:
% 230.52/41.97  | | | | | | | | | | | | |   (93)  all_57_11 = e3
% 230.52/41.97  | | | | | | | | | | | | | 
% 230.52/41.97  | | | | | | | | | | | | | COMBINE_EQS: (63), (93) imply:
% 230.52/41.97  | | | | | | | | | | | | |   (94)  e3 = e0
% 230.52/41.97  | | | | | | | | | | | | | 
% 230.52/41.97  | | | | | | | | | | | | | COMBINE_EQS: (80), (94) imply:
% 230.52/41.97  | | | | | | | | | | | | |   (95)  all_57_5 = e0
% 230.52/41.97  | | | | | | | | | | | | | 
% 230.52/41.97  | | | | | | | | | | | | | REF_CLOSE: (2), (5), (16), (17), (18), (30), (41), (45),
% 230.52/41.97  | | | | | | | | | | | | |            (68), (95) are inconsistent by sub-proof #2355.
% 230.52/41.97  | | | | | | | | | | | | | 
% 230.52/41.97  | | | | | | | | | | | | End of split
% 230.52/41.97  | | | | | | | | | | | | 
% 230.52/41.97  | | | | | | | | | | | End of split
% 230.52/41.97  | | | | | | | | | | | 
% 230.52/41.97  | | | | | | | | | | Case 2:
% 230.52/41.97  | | | | | | | | | | | 
% 230.52/41.97  | | | | | | | | | | |   (96)  all_57_9 = e0 & op(e3, e0) = e0
% 230.52/41.97  | | | | | | | | | | | 
% 230.52/41.97  | | | | | | | | | | | ALPHA: (96) implies:
% 230.52/41.97  | | | | | | | | | | |   (97)  all_57_9 = e0
% 230.52/41.97  | | | | | | | | | | | 
% 230.52/41.97  | | | | | | | | | | | COMBINE_EQS: (71), (97) imply:
% 230.52/41.97  | | | | | | | | | | |   (98)  e3 = e0
% 230.52/41.97  | | | | | | | | | | | 
% 230.52/41.97  | | | | | | | | | | | COMBINE_EQS: (80), (98) imply:
% 230.52/41.97  | | | | | | | | | | |   (99)  all_57_5 = e0
% 230.52/41.97  | | | | | | | | | | | 
% 230.52/41.97  | | | | | | | | | | | REF_CLOSE: (2), (5), (16), (17), (18), (30), (41), (45),
% 230.52/41.97  | | | | | | | | | | |            (68), (99) are inconsistent by sub-proof #2355.
% 230.52/41.97  | | | | | | | | | | | 
% 230.52/41.97  | | | | | | | | | | End of split
% 230.52/41.97  | | | | | | | | | | 
% 230.52/41.97  | | | | | | | | | End of split
% 230.52/41.97  | | | | | | | | | 
% 230.52/41.97  | | | | | | | | Case 2:
% 230.52/41.97  | | | | | | | | | 
% 230.52/41.97  | | | | | | | | |   (100)  all_57_10 = e3 & op(e2, e0) = e3
% 230.52/41.97  | | | | | | | | | 
% 230.52/41.97  | | | | | | | | | ALPHA: (100) implies:
% 230.52/41.97  | | | | | | | | |   (101)  all_57_10 = e3
% 230.52/41.97  | | | | | | | | | 
% 230.52/41.97  | | | | | | | | | REF_CLOSE: (17), (68), (101) are inconsistent by sub-proof
% 230.52/41.97  | | | | | | | | |            #2356.
% 230.52/41.97  | | | | | | | | | 
% 230.52/41.97  | | | | | | | | End of split
% 230.52/41.97  | | | | | | | | 
% 230.52/41.97  | | | | | | | End of split
% 230.52/41.97  | | | | | | | 
% 230.52/41.97  | | | | | | Case 2:
% 230.52/41.97  | | | | | | | 
% 230.52/41.97  | | | | | | |   (102)  all_57_10 = e3 & op(e2, e0) = e3
% 230.52/41.97  | | | | | | | 
% 230.52/41.97  | | | | | | | ALPHA: (102) implies:
% 230.52/41.97  | | | | | | |   (103)  all_57_10 = e3
% 230.52/41.97  | | | | | | | 
% 230.52/41.97  | | | | | | | REF_CLOSE: (17), (68), (103) are inconsistent by sub-proof #2356.
% 230.52/41.97  | | | | | | | 
% 230.52/41.97  | | | | | | End of split
% 230.52/41.97  | | | | | | 
% 230.52/41.97  | | | | | Case 2:
% 230.52/41.97  | | | | | | 
% 230.52/41.97  | | | | | |   (104)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 &
% 230.52/41.97  | | | | | |            op(e0, e0) = e3)
% 230.52/41.97  | | | | | | 
% 230.52/41.97  | | | | | | BETA: splitting (104) gives:
% 230.52/41.97  | | | | | | 
% 230.52/41.97  | | | | | | Case 1:
% 230.52/41.97  | | | | | | | 
% 230.52/41.97  | | | | | | |   (105)  all_57_11 = e3 & op(e1, e0) = e3
% 230.52/41.97  | | | | | | | 
% 230.52/41.97  | | | | | | | ALPHA: (105) implies:
% 230.52/41.97  | | | | | | |   (106)  all_57_11 = e3
% 230.52/41.97  | | | | | | | 
% 230.52/41.97  | | | | | | | REF_CLOSE: (18), (63), (106) are inconsistent by sub-proof #1595.
% 230.52/41.97  | | | | | | | 
% 230.52/41.97  | | | | | | Case 2:
% 230.52/41.97  | | | | | | | 
% 230.52/41.97  | | | | | | |   (107)  all_57_15 = e3 & op(e0, e0) = e3
% 230.52/41.97  | | | | | | | 
% 230.52/41.97  | | | | | | | ALPHA: (107) implies:
% 230.52/41.97  | | | | | | |   (108)  all_57_15 = e3
% 230.52/41.97  | | | | | | | 
% 230.52/41.97  | | | | | | | REF_CLOSE: (5), (8), (9), (10), (11), (13), (17), (18), (24),
% 230.52/41.97  | | | | | | |            (27), (30), (37), (45), (46), (51), (108) are
% 230.52/41.97  | | | | | | |            inconsistent by sub-proof #1245.
% 230.52/41.97  | | | | | | | 
% 230.52/41.97  | | | | | | End of split
% 230.52/41.97  | | | | | | 
% 230.52/41.97  | | | | | End of split
% 230.52/41.97  | | | | | 
% 230.52/41.97  | | | | End of split
% 230.52/41.97  | | | | 
% 230.52/41.97  | | | Case 2:
% 230.52/41.97  | | | | 
% 230.52/41.97  | | | |   (109)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0,
% 230.52/41.97  | | | |              e0) = e2)
% 230.52/41.97  | | | | 
% 230.52/41.97  | | | | BETA: splitting (109) gives:
% 230.52/41.97  | | | | 
% 230.52/41.97  | | | | Case 1:
% 230.52/41.97  | | | | | 
% 230.52/41.97  | | | | |   (110)  all_57_11 = e2 & op(e1, e0) = e2
% 230.52/41.97  | | | | | 
% 230.52/41.97  | | | | | ALPHA: (110) implies:
% 230.52/41.97  | | | | |   (111)  all_57_11 = e2
% 230.52/41.97  | | | | | 
% 230.52/41.97  | | | | | COMBINE_EQS: (63), (111) imply:
% 230.52/41.97  | | | | |   (112)  e2 = e0
% 230.52/41.97  | | | | | 
% 230.52/41.97  | | | | | COMBINE_EQS: (24), (112) imply:
% 230.52/41.97  | | | | |   (113)  all_57_6 = e0
% 230.52/41.97  | | | | | 
% 230.52/41.97  | | | | | REF_CLOSE: (5), (8), (9), (10), (11), (13), (17), (18), (111), (113)
% 230.52/41.97  | | | | |            are inconsistent by sub-proof #2114.
% 230.52/41.97  | | | | | 
% 230.52/41.97  | | | | Case 2:
% 230.52/41.97  | | | | | 
% 230.52/41.97  | | | | |   (114)  all_57_15 = e2 & op(e0, e0) = e2
% 230.52/41.97  | | | | | 
% 230.52/41.97  | | | | | ALPHA: (114) implies:
% 230.52/41.97  | | | | |   (115)  op(e0, e0) = e2
% 230.52/41.97  | | | | | 
% 230.52/41.97  | | | | | REF_CLOSE: (8), (39), (45), (115) are inconsistent by sub-proof #2177.
% 230.52/41.97  | | | | | 
% 230.52/41.97  | | | | End of split
% 230.52/41.97  | | | | 
% 230.52/41.97  | | | End of split
% 230.52/41.97  | | | 
% 230.52/41.97  | | End of split
% 230.52/41.97  | | 
% 230.52/41.97  | End of split
% 230.52/41.97  | 
% 230.52/41.97  End of proof
% 230.52/41.97  
% 230.52/41.97  Sub-proof #1245 shows that the following formulas are inconsistent:
% 230.52/41.97  ----------------------------------------------------------------
% 230.52/41.97    (1)   ~ (e3 = e1)
% 230.52/41.97    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.97           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.97    (3)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.52/41.97         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.52/41.97    (4)   ~ (all_6_2 = e3)
% 230.52/41.97    (5)  op(e1, e1) = all_6_2
% 230.52/41.97    (6)  all_57_7 = e1
% 230.52/41.97    (7)   ~ (e3 = e2)
% 230.52/41.97    (8)   ~ (e3 = e0)
% 230.52/41.97    (9)  all_57_15 = e3
% 230.52/41.97    (10)  all_57_6 = e2
% 230.52/41.97    (11)   ~ (e2 = e0)
% 230.52/41.97    (12)   ~ (e1 = e0)
% 230.52/41.97    (13)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.52/41.97              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.52/41.97                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.52/41.97                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.52/41.97    (14)   ~ (e2 = e1)
% 230.52/41.97    (15)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.52/41.97          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.52/41.97    (16)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.52/41.97          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.52/41.97  
% 230.52/41.97  Begin of proof
% 230.52/41.97  | 
% 230.52/41.97  | BETA: splitting (3) gives:
% 230.52/41.97  | 
% 230.52/41.97  | Case 1:
% 230.52/41.97  | | 
% 230.52/41.97  | |   (17)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 230.52/41.97  | |           e3)
% 230.52/41.97  | | 
% 230.52/41.97  | | REF_CLOSE: (1), (6), (7), (10), (17) are inconsistent by sub-proof #1246.
% 230.52/41.97  | | 
% 230.52/41.97  | Case 2:
% 230.52/41.97  | | 
% 230.52/41.97  | |   (18)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 230.52/41.97  | |           e3)
% 230.52/41.97  | | 
% 230.52/41.97  | | REF_CLOSE: (1), (2), (4), (5), (7), (8), (9), (11), (12), (13), (14), (15),
% 230.52/41.97  | |            (16), (18) are inconsistent by sub-proof #1786.
% 230.52/41.97  | | 
% 230.52/41.97  | End of split
% 230.52/41.97  | 
% 230.52/41.97  End of proof
% 230.52/41.97  
% 230.52/41.97  Sub-proof #1246 shows that the following formulas are inconsistent:
% 230.52/41.97  ----------------------------------------------------------------
% 230.52/41.97    (1)   ~ (e3 = e1)
% 230.52/41.97    (2)  all_57_7 = e1
% 230.52/41.97    (3)   ~ (e3 = e2)
% 230.52/41.97    (4)  all_57_6 = e2
% 230.52/41.97    (5)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3)
% 230.52/41.97  
% 230.52/41.97  Begin of proof
% 230.52/41.97  | 
% 230.52/41.97  | BETA: splitting (5) gives:
% 230.52/41.97  | 
% 230.52/41.97  | Case 1:
% 230.52/41.97  | | 
% 230.52/41.97  | |   (6)  all_57_6 = e3 & op(e1, e3) = e3
% 230.52/41.97  | | 
% 230.52/41.97  | | ALPHA: (6) implies:
% 230.52/41.97  | |   (7)  all_57_6 = e3
% 230.52/41.97  | | 
% 230.52/41.97  | | REF_CLOSE: (3), (4), (7) are inconsistent by sub-proof #2463.
% 230.52/41.97  | | 
% 230.52/41.97  | Case 2:
% 230.52/41.97  | | 
% 230.52/41.97  | |   (8)  all_57_7 = e3 & op(e1, e2) = e3
% 230.52/41.97  | | 
% 230.52/41.97  | | REF_CLOSE: (1), (2), (8) are inconsistent by sub-proof #1247.
% 230.52/41.97  | | 
% 230.52/41.97  | End of split
% 230.52/41.97  | 
% 230.52/41.97  End of proof
% 230.52/41.97  
% 230.52/41.97  Sub-proof #1247 shows that the following formulas are inconsistent:
% 230.52/41.97  ----------------------------------------------------------------
% 230.52/41.97    (1)  all_57_7 = e3 & op(e1, e2) = e3
% 230.52/41.97    (2)  all_57_7 = e1
% 230.52/41.97    (3)   ~ (e3 = e1)
% 230.52/41.97  
% 230.52/41.97  Begin of proof
% 230.52/41.97  | 
% 230.52/41.97  | ALPHA: (1) implies:
% 230.52/41.97  |   (4)  all_57_7 = e3
% 230.52/41.97  | 
% 230.52/41.97  | COMBINE_EQS: (2), (4) imply:
% 230.52/41.97  |   (5)  e3 = e1
% 230.52/41.97  | 
% 230.52/41.97  | REDUCE: (3), (5) imply:
% 230.52/41.97  |   (6)  $false
% 230.52/41.97  | 
% 230.52/41.97  | CLOSE: (6) is inconsistent.
% 230.52/41.97  | 
% 230.52/41.97  End of proof
% 230.52/41.97  
% 230.52/41.97  Sub-proof #1248 shows that the following formulas are inconsistent:
% 230.52/41.97  ----------------------------------------------------------------
% 230.52/41.97    (1)  op(e1, e3) = all_52_17
% 230.52/41.97    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.97           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.97    (3)  ( ~ (all_28_0 = e0) & op(all_28_1, e3) = all_28_0 & op(e3, e2) = all_28_1
% 230.52/41.97           & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 = e1) & op(e3, e2) =
% 230.52/41.97           all_28_1 & $i(all_28_1))
% 230.52/41.97    (4)  op(e3, e2) = e1
% 230.52/41.97    (5)   ~ (all_52_17 = e2)
% 230.52/41.97    (6)  op(all_52_17, all_52_17) = e3
% 230.52/41.97    (7)  op(e3, e2) = all_20_1
% 230.52/41.97    (8)   ~ (all_52_17 = e1)
% 230.52/41.97    (9)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 230.52/41.97    (10)  op(e3, e3) = e2
% 230.52/41.97    (11)  all_55_8 = all_52_17
% 230.52/41.97  
% 230.52/41.97  Begin of proof
% 230.52/41.97  | 
% 230.52/41.97  | BETA: splitting (3) gives:
% 230.52/41.97  | 
% 230.52/41.97  | Case 1:
% 230.52/41.97  | | 
% 230.52/41.97  | |   (12)   ~ (all_28_0 = e0) & op(all_28_1, e3) = all_28_0 & op(e3, e2) =
% 230.52/41.97  | |         all_28_1 & $i(all_28_0) & $i(all_28_1)
% 230.52/41.97  | | 
% 230.52/41.97  | | ALPHA: (12) implies:
% 230.52/41.97  | |   (13)   ~ (all_28_0 = e0)
% 230.52/41.97  | |   (14)  op(e3, e2) = all_28_1
% 230.52/41.97  | |   (15)  op(all_28_1, e3) = all_28_0
% 230.52/41.97  | | 
% 230.52/41.97  | | GROUND_INST: instantiating (2) with e1, all_28_1, e2, e3, simplifying with
% 230.52/41.97  | |              (4), (14) gives:
% 230.52/41.97  | |   (16)  all_28_1 = e1
% 230.52/41.97  | | 
% 230.52/41.97  | | GROUND_INST: instantiating (2) with all_20_1, all_28_1, e2, e3, simplifying
% 230.52/41.97  | |              with (7), (14) gives:
% 230.52/41.97  | |   (17)  all_28_1 = all_20_1
% 230.52/41.97  | | 
% 230.52/41.97  | | COMBINE_EQS: (16), (17) imply:
% 230.52/41.97  | |   (18)  all_20_1 = e1
% 230.52/41.97  | | 
% 230.52/41.97  | | REDUCE: (15), (16) imply:
% 230.52/41.97  | |   (19)  op(e1, e3) = all_28_0
% 230.52/41.97  | | 
% 230.52/41.97  | | GROUND_INST: instantiating (2) with all_52_17, all_28_0, e3, e1, simplifying
% 230.52/41.97  | |              with (1), (19) gives:
% 230.52/41.97  | |   (20)  all_52_17 = all_28_0
% 230.52/41.97  | | 
% 230.52/41.97  | | COMBINE_EQS: (11), (20) imply:
% 230.52/41.97  | |   (21)  all_55_8 = all_28_0
% 230.52/41.97  | | 
% 230.52/41.97  | | REDUCE: (5), (20) imply:
% 230.52/41.97  | |   (22)   ~ (all_28_0 = e2)
% 230.52/41.97  | | 
% 230.52/41.97  | | REDUCE: (8), (20) imply:
% 230.52/41.97  | |   (23)   ~ (all_28_0 = e1)
% 230.52/41.97  | | 
% 230.52/41.97  | | REDUCE: (6), (20) imply:
% 230.52/41.97  | |   (24)  op(all_28_0, all_28_0) = e3
% 230.52/41.97  | | 
% 230.52/41.97  | | BETA: splitting (9) gives:
% 230.52/41.97  | | 
% 230.52/41.97  | | Case 1:
% 230.52/41.97  | | | 
% 230.52/41.97  | | |   (25)  all_55_8 = e3
% 230.52/41.97  | | | 
% 230.52/41.97  | | | COMBINE_EQS: (21), (25) imply:
% 230.52/41.97  | | |   (26)  all_28_0 = e3
% 230.52/41.97  | | | 
% 230.52/41.97  | | | REDUCE: (22), (26) imply:
% 230.52/41.97  | | |   (27)   ~ (e3 = e2)
% 230.52/41.97  | | | 
% 230.52/41.97  | | | REDUCE: (24), (26) imply:
% 230.52/41.97  | | |   (28)  op(e3, e3) = e3
% 230.52/41.97  | | | 
% 230.52/41.97  | | | REF_CLOSE: (2), (10), (27), (28) are inconsistent by sub-proof #2490.
% 230.52/41.97  | | | 
% 230.52/41.97  | | Case 2:
% 230.52/41.97  | | | 
% 230.52/41.97  | | |   (29)  all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 230.52/41.97  | | | 
% 230.52/41.97  | | | BETA: splitting (29) gives:
% 230.52/41.97  | | | 
% 230.52/41.97  | | | Case 1:
% 230.52/41.97  | | | | 
% 230.52/41.97  | | | |   (30)  all_55_8 = e2
% 230.52/41.97  | | | | 
% 230.52/41.97  | | | | COMBINE_EQS: (21), (30) imply:
% 230.52/41.97  | | | |   (31)  all_28_0 = e2
% 230.52/41.97  | | | | 
% 230.52/41.97  | | | | REDUCE: (22), (31) imply:
% 230.52/41.97  | | | |   (32)  $false
% 230.52/41.97  | | | | 
% 230.52/41.97  | | | | CLOSE: (32) is inconsistent.
% 230.52/41.97  | | | | 
% 230.52/41.97  | | | Case 2:
% 230.52/41.97  | | | | 
% 230.52/41.97  | | | |   (33)  all_55_8 = e1 | all_55_8 = e0
% 230.52/41.97  | | | | 
% 230.52/41.97  | | | | BETA: splitting (33) gives:
% 230.52/41.97  | | | | 
% 230.52/41.97  | | | | Case 1:
% 230.52/41.97  | | | | | 
% 230.52/41.97  | | | | |   (34)  all_55_8 = e1
% 230.52/41.97  | | | | | 
% 230.52/41.97  | | | | | COMBINE_EQS: (21), (34) imply:
% 230.52/41.97  | | | | |   (35)  all_28_0 = e1
% 230.52/41.97  | | | | | 
% 230.52/41.97  | | | | | REDUCE: (23), (35) imply:
% 230.52/41.97  | | | | |   (36)  $false
% 230.52/41.97  | | | | | 
% 230.52/41.97  | | | | | CLOSE: (36) is inconsistent.
% 230.52/41.97  | | | | | 
% 230.52/41.97  | | | | Case 2:
% 230.52/41.97  | | | | | 
% 230.52/41.97  | | | | |   (37)  all_55_8 = e0
% 230.52/41.97  | | | | | 
% 230.52/41.97  | | | | | COMBINE_EQS: (21), (37) imply:
% 230.52/41.97  | | | | |   (38)  all_28_0 = e0
% 230.52/41.97  | | | | | 
% 230.52/41.97  | | | | | REDUCE: (13), (38) imply:
% 230.52/41.97  | | | | |   (39)  $false
% 230.52/41.97  | | | | | 
% 230.52/41.97  | | | | | CLOSE: (39) is inconsistent.
% 230.52/41.97  | | | | | 
% 230.52/41.97  | | | | End of split
% 230.52/41.97  | | | | 
% 230.52/41.97  | | | End of split
% 230.52/41.97  | | | 
% 230.52/41.97  | | End of split
% 230.52/41.97  | | 
% 230.52/41.97  | Case 2:
% 230.52/41.97  | | 
% 230.52/41.98  | |   (40)   ~ (all_28_1 = e1) & op(e3, e2) = all_28_1 & $i(all_28_1)
% 230.52/41.98  | | 
% 230.52/41.98  | | REF_CLOSE: (2), (4), (40) are inconsistent by sub-proof #1249.
% 230.52/41.98  | | 
% 230.52/41.98  | End of split
% 230.52/41.98  | 
% 230.52/41.98  End of proof
% 230.52/41.98  
% 230.52/41.98  Sub-proof #1249 shows that the following formulas are inconsistent:
% 230.52/41.98  ----------------------------------------------------------------
% 230.52/41.98    (1)   ~ (all_28_1 = e1) & op(e3, e2) = all_28_1 & $i(all_28_1)
% 230.52/41.98    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.98           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.98    (3)  op(e3, e2) = e1
% 230.52/41.98  
% 230.52/41.98  Begin of proof
% 230.52/41.98  | 
% 230.52/41.98  | ALPHA: (1) implies:
% 230.52/41.98  |   (4)   ~ (all_28_1 = e1)
% 230.52/41.98  |   (5)  op(e3, e2) = all_28_1
% 230.52/41.98  | 
% 230.52/41.98  | GROUND_INST: instantiating (2) with e1, all_28_1, e2, e3, simplifying with
% 230.52/41.98  |              (3), (5) gives:
% 230.52/41.98  |   (6)  all_28_1 = e1
% 230.52/41.98  | 
% 230.52/41.98  | REDUCE: (4), (6) imply:
% 230.52/41.98  |   (7)  $false
% 230.52/41.98  | 
% 230.52/41.98  | CLOSE: (7) is inconsistent.
% 230.52/41.98  | 
% 230.52/41.98  End of proof
% 230.52/41.98  
% 230.52/41.98  Sub-proof #1250 shows that the following formulas are inconsistent:
% 230.52/41.98  ----------------------------------------------------------------
% 230.52/41.98    (1)  all_57_0 = e2
% 230.52/41.98    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.52/41.98         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.52/41.98    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.52/41.98         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.52/41.98    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.52/41.98         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.52/41.98    (5)   ~ (e3 = e1)
% 230.52/41.98    (6)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.52/41.98         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.52/41.98    (7)   ~ (all_53_13 = e1)
% 230.52/41.98    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.52/41.98           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.52/41.98    (9)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.52/41.98         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.52/41.98    (10)   ~ (all_6_2 = e3)
% 230.52/41.98    (11)  op(e1, e1) = all_6_2
% 230.52/41.98    (12)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.52/41.98          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.52/41.98    (13)  op(e2, e2) = e0
% 230.52/41.98    (14)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.52/41.98          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.52/41.98    (15)  all_57_3 = e0
% 230.52/41.98    (16)   ~ (e3 = e2)
% 230.52/41.98    (17)   ~ (e3 = e0)
% 230.52/41.98    (18)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.52/41.98          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.52/41.98    (19)  op(e0, e3) = all_53_3
% 230.52/41.98    (20)  op(e3, e3) = e2
% 230.52/41.98    (21)   ~ (all_53_3 = e2)
% 230.52/41.98    (22)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.52/41.98          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.52/41.98            e1)
% 230.52/41.98    (23)  op(e3, e2) = all_53_4
% 230.52/41.98    (24)   ~ (e2 = e0)
% 230.52/41.98    (25)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.52/41.98          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.52/41.98    (26)   ~ (e1 = e0)
% 230.52/41.98    (27)   ~ (all_53_4 = e0)
% 230.52/41.98    (28)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 230.52/41.98          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 230.52/41.98    (29)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.52/41.98          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.52/41.98    (30)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.52/41.98          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 230.52/41.98            e3)
% 230.52/41.98    (31)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.52/41.98          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.52/41.98            e2)
% 230.52/41.98    (32)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.52/41.98              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.52/41.98                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.52/41.98                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.52/41.98    (33)   ~ (all_53_13 = e0)
% 230.52/41.98    (34)  op(e0, e0) = e1
% 230.52/41.98    (35)  op(e2, e0) = all_53_13
% 230.52/41.98    (36)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.52/41.98          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.52/41.98    (37)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.52/41.98          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.52/41.98    (38)  all_57_11 = e1
% 230.52/41.98    (39)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.52/41.98          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.52/41.98    (40)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 230.52/41.98          (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 230.52/41.98    (41)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.52/41.98          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 230.52/41.98    (42)   ~ (e2 = e1)
% 230.52/41.98    (43)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.52/41.98          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.52/41.98    (44)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.52/41.98          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.52/41.98    (45)   ~ (all_53_12 = e2)
% 230.52/41.98    (46)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.52/41.98          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.52/41.98    (47)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.52/41.98          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.52/41.98    (48)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.52/41.98          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.52/41.98    (49)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.52/41.98          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.52/41.98    (50)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.52/41.98          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.52/41.98    (51)  op(e3, e0) = all_53_12
% 230.52/41.98  
% 230.52/41.98  Begin of proof
% 230.52/41.98  | 
% 230.52/41.98  | BETA: splitting (43) gives:
% 230.52/41.98  | 
% 230.52/41.98  | Case 1:
% 230.52/41.98  | | 
% 230.52/41.98  | |   (52)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 230.52/41.98  | |           e2)
% 230.52/41.98  | | 
% 230.52/41.98  | | BETA: splitting (52) gives:
% 230.52/41.98  | | 
% 230.52/41.98  | | Case 1:
% 230.52/41.98  | | | 
% 230.52/41.98  | | |   (53)  all_57_9 = e2 & op(e3, e0) = e2
% 230.52/41.98  | | | 
% 230.52/41.98  | | | ALPHA: (53) implies:
% 230.52/41.98  | | |   (54)  op(e3, e0) = e2
% 230.52/41.98  | | | 
% 230.52/41.98  | | | REF_CLOSE: (8), (45), (51), (54) are inconsistent by sub-proof #2331.
% 230.52/41.98  | | | 
% 230.52/41.98  | | Case 2:
% 230.52/41.98  | | | 
% 230.52/41.98  | | |   (55)  all_57_10 = e2 & op(e2, e0) = e2
% 230.52/41.98  | | | 
% 230.52/41.98  | | | ALPHA: (55) implies:
% 230.52/41.98  | | |   (56)  all_57_10 = e2
% 230.52/41.98  | | | 
% 230.52/41.98  | | | BETA: splitting (6) gives:
% 230.52/41.98  | | | 
% 230.52/41.98  | | | Case 1:
% 230.52/41.98  | | | | 
% 230.52/41.98  | | | |   (57)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2)
% 230.52/41.98  | | | |           = e0)
% 230.52/41.98  | | | | 
% 230.52/41.98  | | | | BETA: splitting (57) gives:
% 230.52/41.98  | | | | 
% 230.52/41.98  | | | | Case 1:
% 230.52/41.98  | | | | | 
% 230.52/41.98  | | | | |   (58)  all_57_6 = e0 & op(e1, e3) = e0
% 230.52/41.98  | | | | | 
% 230.52/41.98  | | | | | ALPHA: (58) implies:
% 230.52/41.98  | | | | |   (59)  all_57_6 = e0
% 230.52/41.98  | | | | | 
% 230.52/41.98  | | | | | BETA: splitting (32) gives:
% 230.52/41.98  | | | | | 
% 230.52/41.98  | | | | | Case 1:
% 230.52/41.98  | | | | | | 
% 230.52/41.98  | | | | | |   (60)  all_57_15 = e0 & op(e0, e0) = e0
% 230.52/41.98  | | | | | | 
% 230.52/41.98  | | | | | | ALPHA: (60) implies:
% 230.52/41.98  | | | | | |   (61)  all_57_15 = e0
% 230.52/41.98  | | | | | |   (62)  op(e0, e0) = e0
% 230.52/41.98  | | | | | | 
% 230.52/41.98  | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 230.52/41.98  | | | | | |            (12), (13), (14), (15), (16), (17), (18), (19), (20),
% 230.52/41.98  | | | | | |            (21), (22), (23), (24), (25), (26), (27), (28), (29),
% 230.52/41.98  | | | | | |            (30), (31), (32), (33), (34), (35), (36), (37), (38),
% 230.52/41.98  | | | | | |            (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 230.52/41.98  | | | | | |            (48), (49), (50), (51), (56), (59), (61), (62) are
% 230.52/41.98  | | | | | |            inconsistent by sub-proof #1258.
% 230.52/41.98  | | | | | | 
% 230.52/41.98  | | | | | Case 2:
% 230.52/41.98  | | | | | | 
% 230.52/41.98  | | | | | |   (63)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 &
% 230.52/41.98  | | | | | |             op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) &
% 230.52/41.98  | | | | | |         ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.52/41.98  | | | | | |             op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 230.52/41.98  | | | | | | 
% 230.52/41.98  | | | | | | ALPHA: (63) implies:
% 230.52/41.98  | | | | | |   (64)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2,
% 230.52/41.98  | | | | | |             e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.52/41.98  | | | | | | 
% 230.52/41.98  | | | | | | BETA: splitting (64) gives:
% 230.52/41.98  | | | | | | 
% 230.52/41.98  | | | | | | Case 1:
% 230.52/41.98  | | | | | | | 
% 230.52/41.98  | | | | | | |   (65)  all_57_9 = e0 & op(e3, e0) = e0
% 230.52/41.98  | | | | | | | 
% 230.52/41.98  | | | | | | | ALPHA: (65) implies:
% 230.52/41.98  | | | | | | |   (66)  all_57_9 = e0
% 230.52/41.98  | | | | | | | 
% 230.52/41.98  | | | | | | | BETA: splitting (9) gives:
% 230.52/41.98  | | | | | | | 
% 230.52/41.98  | | | | | | | Case 1:
% 230.52/41.98  | | | | | | | | 
% 230.52/41.98  | | | | | | | |   (67)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 &
% 230.52/41.98  | | | | | | | |           op(e1, e2) = e3)
% 230.52/41.98  | | | | | | | | 
% 230.52/41.98  | | | | | | | | BETA: splitting (67) gives:
% 230.52/41.98  | | | | | | | | 
% 230.52/41.98  | | | | | | | | Case 1:
% 230.52/41.98  | | | | | | | | | 
% 230.52/41.98  | | | | | | | | |   (68)  all_57_6 = e3 & op(e1, e3) = e3
% 230.52/41.98  | | | | | | | | | 
% 230.52/41.98  | | | | | | | | | ALPHA: (68) implies:
% 230.52/41.98  | | | | | | | | |   (69)  all_57_6 = e3
% 230.52/41.98  | | | | | | | | | 
% 230.52/41.98  | | | | | | | | | REF_CLOSE: (17), (59), (69) are inconsistent by sub-proof
% 230.52/41.98  | | | | | | | | |            #1822.
% 230.52/41.98  | | | | | | | | | 
% 230.52/41.98  | | | | | | | | Case 2:
% 230.52/41.98  | | | | | | | | | 
% 230.52/41.98  | | | | | | | | |   (70)  all_57_7 = e3 & op(e1, e2) = e3
% 230.52/41.98  | | | | | | | | | 
% 230.52/41.98  | | | | | | | | | ALPHA: (70) implies:
% 230.52/41.98  | | | | | | | | |   (71)  all_57_7 = e3
% 230.52/41.98  | | | | | | | | | 
% 230.52/41.98  | | | | | | | | | BETA: splitting (4) gives:
% 230.52/41.98  | | | | | | | | | 
% 230.52/41.98  | | | | | | | | | Case 1:
% 230.52/41.98  | | | | | | | | | | 
% 230.52/41.98  | | | | | | | | | |   (72)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 &
% 230.52/41.98  | | | | | | | | | |           op(e2, e2) = e2)
% 230.52/41.98  | | | | | | | | | | 
% 230.52/41.98  | | | | | | | | | | BETA: splitting (72) gives:
% 230.52/41.98  | | | | | | | | | | 
% 230.52/41.98  | | | | | | | | | | Case 1:
% 230.52/41.98  | | | | | | | | | | | 
% 230.52/41.98  | | | | | | | | | | |   (73)  all_57_1 = e2 & op(e3, e2) = e2
% 230.52/41.98  | | | | | | | | | | | 
% 230.52/41.98  | | | | | | | | | | | ALPHA: (73) implies:
% 230.52/41.98  | | | | | | | | | | |   (74)  all_57_1 = e2
% 230.52/41.98  | | | | | | | | | | | 
% 230.52/41.98  | | | | | | | | | | | REF_CLOSE: (5), (8), (12), (14), (16), (17), (20), (24),
% 230.52/41.98  | | | | | | | | | | |            (25), (26), (42), (66), (74) are inconsistent by
% 230.52/41.98  | | | | | | | | | | |            sub-proof #1656.
% 230.52/41.98  | | | | | | | | | | | 
% 230.52/41.98  | | | | | | | | | | Case 2:
% 230.52/41.98  | | | | | | | | | | | 
% 230.52/41.98  | | | | | | | | | | |   (75)  all_57_3 = e2 & op(e2, e2) = e2
% 230.52/41.98  | | | | | | | | | | | 
% 230.52/41.98  | | | | | | | | | | | ALPHA: (75) implies:
% 230.52/41.98  | | | | | | | | | | |   (76)  op(e2, e2) = e2
% 230.52/41.98  | | | | | | | | | | | 
% 230.52/41.98  | | | | | | | | | | | REF_CLOSE: (8), (13), (24), (76) are inconsistent by
% 230.52/41.98  | | | | | | | | | | |            sub-proof #2472.
% 230.52/41.98  | | | | | | | | | | | 
% 230.52/41.98  | | | | | | | | | | End of split
% 230.52/41.98  | | | | | | | | | | 
% 230.52/41.98  | | | | | | | | | Case 2:
% 230.52/41.98  | | | | | | | | | | 
% 230.52/41.98  | | | | | | | | | |   (77)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2
% 230.52/41.98  | | | | | | | | | |           & op(e0, e2) = e2)
% 230.52/41.98  | | | | | | | | | | 
% 230.52/41.98  | | | | | | | | | | BETA: splitting (77) gives:
% 230.52/41.98  | | | | | | | | | | 
% 230.52/41.98  | | | | | | | | | | Case 1:
% 230.52/41.98  | | | | | | | | | | | 
% 230.52/41.98  | | | | | | | | | | |   (78)  all_57_7 = e2 & op(e1, e2) = e2
% 230.52/41.98  | | | | | | | | | | | 
% 230.52/41.98  | | | | | | | | | | | ALPHA: (78) implies:
% 230.52/41.98  | | | | | | | | | | |   (79)  all_57_7 = e2
% 230.52/41.98  | | | | | | | | | | | 
% 230.52/41.98  | | | | | | | | | | | REF_CLOSE: (5), (8), (9), (10), (11), (16), (17), (24), (26),
% 230.52/41.98  | | | | | | | | | | |            (32), (38), (40), (42), (43), (48), (56), (59),
% 230.52/41.98  | | | | | | | | | | |            (66), (79) are inconsistent by sub-proof #1262.
% 230.52/41.98  | | | | | | | | | | | 
% 230.52/41.98  | | | | | | | | | | Case 2:
% 230.52/41.98  | | | | | | | | | | | 
% 230.52/41.98  | | | | | | | | | | |   (80)  all_57_13 = e2 & op(e0, e2) = e2
% 230.52/41.98  | | | | | | | | | | | 
% 230.52/41.98  | | | | | | | | | | | ALPHA: (80) implies:
% 230.52/41.98  | | | | | | | | | | |   (81)  all_57_13 = e2
% 230.52/41.98  | | | | | | | | | | | 
% 230.52/41.98  | | | | | | | | | | | REF_CLOSE: (5), (8), (9), (10), (11), (13), (15), (16), (17),
% 230.52/41.98  | | | | | | | | | | |            (24), (26), (29), (32), (34), (38), (40), (42),
% 230.52/41.98  | | | | | | | | | | |            (43), (48), (49), (56), (59), (66), (71), (81) are
% 230.52/41.98  | | | | | | | | | | |            inconsistent by sub-proof #1261.
% 230.52/41.98  | | | | | | | | | | | 
% 230.52/41.98  | | | | | | | | | | End of split
% 230.52/41.98  | | | | | | | | | | 
% 230.52/41.98  | | | | | | | | | End of split
% 230.52/41.98  | | | | | | | | | 
% 230.52/41.98  | | | | | | | | End of split
% 230.52/41.98  | | | | | | | | 
% 230.52/41.98  | | | | | | | Case 2:
% 230.52/41.98  | | | | | | | | 
% 230.52/41.98  | | | | | | | |   (82)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 &
% 230.52/41.98  | | | | | | | |           op(e1, e0) = e3)
% 230.52/41.98  | | | | | | | | 
% 230.52/41.98  | | | | | | | | REF_CLOSE: (5), (8), (10), (11), (38), (82) are inconsistent by
% 230.52/41.98  | | | | | | | |            sub-proof #2004.
% 230.52/41.99  | | | | | | | | 
% 230.52/41.99  | | | | | | | End of split
% 230.52/41.99  | | | | | | | 
% 230.52/41.99  | | | | | | Case 2:
% 230.52/41.99  | | | | | | | 
% 230.52/41.99  | | | | | | |   (83)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 230.52/41.99  | | | | | | |           op(e1, e0) = e0)
% 230.52/41.99  | | | | | | | 
% 230.52/41.99  | | | | | | | REF_CLOSE: (8), (26), (33), (35), (38), (83) are inconsistent by
% 230.52/41.99  | | | | | | |            sub-proof #1256.
% 230.52/41.99  | | | | | | | 
% 230.52/41.99  | | | | | | End of split
% 230.52/41.99  | | | | | | 
% 230.52/41.99  | | | | | End of split
% 230.52/41.99  | | | | | 
% 230.52/41.99  | | | | Case 2:
% 230.52/41.99  | | | | | 
% 230.52/41.99  | | | | |   (84)  all_57_7 = e0 & op(e1, e2) = e0
% 230.52/41.99  | | | | | 
% 230.52/41.99  | | | | | ALPHA: (84) implies:
% 230.52/41.99  | | | | |   (85)  all_57_7 = e0
% 230.52/41.99  | | | | | 
% 230.52/41.99  | | | | | REF_CLOSE: (4), (5), (8), (12), (13), (14), (15), (16), (17), (20),
% 230.52/41.99  | | | | |            (24), (25), (26), (29), (42), (49), (85) are inconsistent
% 230.52/41.99  | | | | |            by sub-proof #1296.
% 230.52/41.99  | | | | | 
% 230.52/41.99  | | | | End of split
% 230.52/41.99  | | | | 
% 230.52/41.99  | | | Case 2:
% 230.52/41.99  | | | | 
% 230.52/41.99  | | | |   (86)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.52/41.99  | | | |           = e0)
% 230.52/41.99  | | | | 
% 230.52/41.99  | | | | BETA: splitting (86) gives:
% 230.52/41.99  | | | | 
% 230.52/41.99  | | | | Case 1:
% 230.52/41.99  | | | | | 
% 230.52/41.99  | | | | |   (87)  all_57_8 = e0 & op(e1, e1) = e0
% 230.52/41.99  | | | | | 
% 230.52/41.99  | | | | | ALPHA: (87) implies:
% 230.52/41.99  | | | | |   (88)  all_57_8 = e0
% 230.52/41.99  | | | | | 
% 230.52/41.99  | | | | | BETA: splitting (32) gives:
% 230.52/41.99  | | | | | 
% 230.52/41.99  | | | | | Case 1:
% 230.52/41.99  | | | | | | 
% 230.52/41.99  | | | | | |   (89)  all_57_15 = e0 & op(e0, e0) = e0
% 230.52/41.99  | | | | | | 
% 230.52/41.99  | | | | | | ALPHA: (89) implies:
% 230.52/41.99  | | | | | |   (90)  all_57_15 = e0
% 230.52/41.99  | | | | | |   (91)  op(e0, e0) = e0
% 230.52/41.99  | | | | | | 
% 230.52/41.99  | | | | | | BETA: splitting (50) gives:
% 230.52/41.99  | | | | | | 
% 230.52/41.99  | | | | | | Case 1:
% 230.52/41.99  | | | | | | | 
% 230.52/41.99  | | | | | | |   (92)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 &
% 230.52/41.99  | | | | | | |           op(e1, e2) = e2)
% 230.52/41.99  | | | | | | | 
% 230.52/41.99  | | | | | | | BETA: splitting (92) gives:
% 230.52/41.99  | | | | | | | 
% 230.52/41.99  | | | | | | | Case 1:
% 230.52/41.99  | | | | | | | | 
% 230.52/41.99  | | | | | | | |   (93)  all_57_6 = e2 & op(e1, e3) = e2
% 230.52/41.99  | | | | | | | | 
% 230.52/41.99  | | | | | | | | ALPHA: (93) implies:
% 230.52/41.99  | | | | | | | |   (94)  all_57_6 = e2
% 230.52/41.99  | | | | | | | | 
% 230.52/41.99  | | | | | | | | BETA: splitting (3) gives:
% 230.52/41.99  | | | | | | | | 
% 230.52/41.99  | | | | | | | | Case 1:
% 230.52/41.99  | | | | | | | | | 
% 230.52/41.99  | | | | | | | | |   (95)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 &
% 230.52/41.99  | | | | | | | | |           op(e2, e3) = e1)
% 230.52/41.99  | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | BETA: splitting (95) gives:
% 230.52/41.99  | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | Case 1:
% 230.52/41.99  | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | |   (96)  all_57_0 = e1 & op(e3, e3) = e1
% 230.52/41.99  | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | | ALPHA: (96) implies:
% 230.52/41.99  | | | | | | | | | |   (97)  op(e3, e3) = e1
% 230.52/41.99  | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | | REF_CLOSE: (8), (20), (42), (97) are inconsistent by
% 230.52/41.99  | | | | | | | | | |            sub-proof #1950.
% 230.52/41.99  | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | Case 2:
% 230.52/41.99  | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | |   (98)  all_57_2 = e1 & op(e2, e3) = e1
% 230.52/41.99  | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | | ALPHA: (98) implies:
% 230.52/41.99  | | | | | | | | | |   (99)  all_57_2 = e1
% 230.52/41.99  | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | | BETA: splitting (22) gives:
% 230.52/41.99  | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | | Case 1:
% 230.52/41.99  | | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | | |   (100)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 230.52/41.99  | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 230.52/41.99  | | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | | | BETA: splitting (100) gives:
% 230.52/41.99  | | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | | | Case 1:
% 230.52/41.99  | | | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | | | |   (101)  all_57_12 = e1 & op(e0, e3) = e1
% 230.52/41.99  | | | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 230.52/41.99  | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 230.52/41.99  | | | | | | | | | | | |            (19), (20), (21), (22), (23), (24), (25), (26),
% 230.52/41.99  | | | | | | | | | | | |            (27), (28), (29), (30), (31), (32), (33), (34),
% 230.52/41.99  | | | | | | | | | | | |            (35), (36), (37), (38), (39), (40), (41), (42),
% 230.52/41.99  | | | | | | | | | | | |            (43), (44), (45), (46), (47), (48), (49), (50),
% 230.52/41.99  | | | | | | | | | | | |            (51), (56), (90), (91), (101) are inconsistent by
% 230.52/41.99  | | | | | | | | | | | |            sub-proof #1255.
% 230.52/41.99  | | | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | | | Case 2:
% 230.52/41.99  | | | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | | | |   (102)  all_57_13 = e1 & op(e0, e2) = e1
% 230.52/41.99  | | | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | | | | REF_CLOSE: (2), (4), (5), (7), (8), (10), (11), (12), (13),
% 230.52/41.99  | | | | | | | | | | | |            (14), (15), (16), (17), (18), (19), (20), (21),
% 230.52/41.99  | | | | | | | | | | | |            (23), (24), (25), (26), (27), (28), (29), (30),
% 230.52/41.99  | | | | | | | | | | | |            (31), (32), (34), (35), (37), (38), (40), (42),
% 230.52/41.99  | | | | | | | | | | | |            (46), (49), (56), (102) are inconsistent by
% 230.52/41.99  | | | | | | | | | | | |            sub-proof #1254.
% 230.52/41.99  | | | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | | | End of split
% 230.52/41.99  | | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | | Case 2:
% 230.52/41.99  | | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | | |   (103)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 230.52/41.99  | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 230.52/41.99  | | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | | | BETA: splitting (103) gives:
% 230.52/41.99  | | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | | | Case 1:
% 230.52/41.99  | | | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | | | |   (104)  all_57_14 = e1 & op(e0, e1) = e1
% 230.52/41.99  | | | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 230.52/41.99  | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 230.52/41.99  | | | | | | | | | | | |            (19), (20), (21), (22), (23), (24), (25), (26),
% 230.52/41.99  | | | | | | | | | | | |            (27), (28), (29), (30), (31), (32), (33), (34),
% 230.52/41.99  | | | | | | | | | | | |            (35), (36), (37), (38), (39), (40), (41), (42),
% 230.52/41.99  | | | | | | | | | | | |            (43), (44), (45), (46), (47), (48), (49), (50),
% 230.52/41.99  | | | | | | | | | | | |            (51), (56), (90), (91), (104) are inconsistent by
% 230.52/41.99  | | | | | | | | | | | |            sub-proof #1253.
% 230.52/41.99  | | | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | | | Case 2:
% 230.52/41.99  | | | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | | | |   (105)  all_57_15 = e1 & op(e0, e0) = e1
% 230.52/41.99  | | | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | | | | ALPHA: (105) implies:
% 230.52/41.99  | | | | | | | | | | | |   (106)  all_57_15 = e1
% 230.52/41.99  | | | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | | | | COMBINE_EQS: (90), (106) imply:
% 230.52/41.99  | | | | | | | | | | | |   (107)  e1 = e0
% 230.52/41.99  | | | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | | | | REF_CLOSE: (2), (5), (15), (16), (17), (24), (26), (36),
% 230.52/41.99  | | | | | | | | | | | |            (37), (42), (99), (107) are inconsistent by
% 230.52/41.99  | | | | | | | | | | | |            sub-proof #1252.
% 230.52/41.99  | | | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | | | End of split
% 230.52/41.99  | | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | | End of split
% 230.52/41.99  | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | End of split
% 230.52/41.99  | | | | | | | | | 
% 230.52/41.99  | | | | | | | | Case 2:
% 230.52/41.99  | | | | | | | | | 
% 230.52/41.99  | | | | | | | | |   (108)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 &
% 230.52/41.99  | | | | | | | | |            op(e0, e3) = e1)
% 230.52/41.99  | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | BETA: splitting (108) gives:
% 230.52/41.99  | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | Case 1:
% 230.52/41.99  | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | |   (109)  all_57_6 = e1 & op(e1, e3) = e1
% 230.52/41.99  | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | | ALPHA: (109) implies:
% 230.52/41.99  | | | | | | | | | |   (110)  all_57_6 = e1
% 230.52/41.99  | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | | REF_CLOSE: (42), (94), (110) are inconsistent by sub-proof
% 230.52/41.99  | | | | | | | | | |            #2233.
% 230.52/41.99  | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | Case 2:
% 230.52/41.99  | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | |   (111)  all_57_12 = e1 & op(e0, e3) = e1
% 230.52/41.99  | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 230.52/41.99  | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 230.52/41.99  | | | | | | | | | |            (19), (20), (21), (22), (23), (24), (25), (26),
% 230.52/41.99  | | | | | | | | | |            (27), (28), (29), (30), (31), (32), (33), (34),
% 230.52/41.99  | | | | | | | | | |            (35), (36), (37), (38), (39), (40), (41), (42),
% 230.52/41.99  | | | | | | | | | |            (43), (44), (45), (46), (47), (48), (49), (50),
% 230.52/41.99  | | | | | | | | | |            (51), (56), (90), (91), (111) are inconsistent by
% 230.52/41.99  | | | | | | | | | |            sub-proof #1255.
% 230.52/41.99  | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | End of split
% 230.52/41.99  | | | | | | | | | 
% 230.52/41.99  | | | | | | | | End of split
% 230.52/41.99  | | | | | | | | 
% 230.52/41.99  | | | | | | | Case 2:
% 230.52/41.99  | | | | | | | | 
% 230.52/41.99  | | | | | | | |   (112)  all_57_7 = e2 & op(e1, e2) = e2
% 230.52/41.99  | | | | | | | | 
% 230.52/41.99  | | | | | | | | ALPHA: (112) implies:
% 230.52/41.99  | | | | | | | |   (113)  all_57_7 = e2
% 230.52/41.99  | | | | | | | | 
% 230.52/41.99  | | | | | | | | BETA: splitting (49) gives:
% 230.52/41.99  | | | | | | | | 
% 230.52/41.99  | | | | | | | | Case 1:
% 230.52/41.99  | | | | | | | | | 
% 230.52/41.99  | | | | | | | | |   (114)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 &
% 230.52/41.99  | | | | | | | | |            op(e2, e2) = e1)
% 230.52/41.99  | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | BETA: splitting (114) gives:
% 230.52/41.99  | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | Case 1:
% 230.52/41.99  | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | |   (115)  all_57_1 = e1 & op(e3, e2) = e1
% 230.52/41.99  | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | | ALPHA: (115) implies:
% 230.52/41.99  | | | | | | | | | |   (116)  all_57_1 = e1
% 230.52/41.99  | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | | BETA: splitting (22) gives:
% 230.52/41.99  | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | | Case 1:
% 230.52/41.99  | | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | | |   (117)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 230.52/41.99  | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 230.52/41.99  | | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | | | BETA: splitting (117) gives:
% 230.52/41.99  | | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | | | Case 1:
% 230.52/41.99  | | | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | | | |   (118)  all_57_12 = e1 & op(e0, e3) = e1
% 230.52/41.99  | | | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 230.52/41.99  | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 230.52/41.99  | | | | | | | | | | | |            (19), (20), (21), (22), (23), (24), (25), (26),
% 230.52/41.99  | | | | | | | | | | | |            (27), (28), (29), (30), (31), (32), (33), (34),
% 230.52/41.99  | | | | | | | | | | | |            (35), (36), (37), (38), (39), (40), (41), (42),
% 230.52/41.99  | | | | | | | | | | | |            (43), (44), (45), (46), (47), (48), (49), (50),
% 230.52/41.99  | | | | | | | | | | | |            (51), (56), (90), (91), (118) are inconsistent by
% 230.52/41.99  | | | | | | | | | | | |            sub-proof #1255.
% 230.52/41.99  | | | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | | | Case 2:
% 230.52/41.99  | | | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | | | |   (119)  all_57_13 = e1 & op(e0, e2) = e1
% 230.52/41.99  | | | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | | | | ALPHA: (119) implies:
% 230.52/41.99  | | | | | | | | | | | |   (120)  all_57_13 = e1
% 230.52/41.99  | | | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | | | | REF_CLOSE: (5), (15), (16), (17), (29), (113), (116), (120)
% 230.52/41.99  | | | | | | | | | | | |            are inconsistent by sub-proof #2193.
% 230.52/41.99  | | | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | | | End of split
% 230.52/41.99  | | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | | Case 2:
% 230.52/41.99  | | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | | |   (121)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 230.52/41.99  | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 230.52/41.99  | | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | | | BETA: splitting (121) gives:
% 230.52/41.99  | | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | | | Case 1:
% 230.52/41.99  | | | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | | | |   (122)  all_57_14 = e1 & op(e0, e1) = e1
% 230.52/41.99  | | | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 230.52/41.99  | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 230.52/41.99  | | | | | | | | | | | |            (19), (20), (21), (22), (23), (24), (25), (26),
% 230.52/41.99  | | | | | | | | | | | |            (27), (28), (29), (30), (31), (32), (33), (34),
% 230.52/41.99  | | | | | | | | | | | |            (35), (36), (37), (38), (39), (40), (41), (42),
% 230.52/41.99  | | | | | | | | | | | |            (43), (44), (45), (46), (47), (48), (49), (50),
% 230.52/41.99  | | | | | | | | | | | |            (51), (56), (90), (91), (122) are inconsistent by
% 230.52/41.99  | | | | | | | | | | | |            sub-proof #1253.
% 230.52/41.99  | | | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | | | Case 2:
% 230.52/41.99  | | | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | | | |   (123)  all_57_15 = e1 & op(e0, e0) = e1
% 230.52/41.99  | | | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | | | | ALPHA: (123) implies:
% 230.52/41.99  | | | | | | | | | | | |   (124)  all_57_15 = e1
% 230.52/41.99  | | | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | | | | COMBINE_EQS: (90), (124) imply:
% 230.52/41.99  | | | | | | | | | | | |   (125)  e1 = e0
% 230.52/41.99  | | | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | | | | SIMP: (125) implies:
% 230.52/41.99  | | | | | | | | | | | |   (126)  e1 = e0
% 230.52/41.99  | | | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | | | | REDUCE: (26), (126) imply:
% 230.52/41.99  | | | | | | | | | | | |   (127)  $false
% 230.52/41.99  | | | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | | | | CLOSE: (127) is inconsistent.
% 230.52/41.99  | | | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | | | End of split
% 230.52/41.99  | | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | | End of split
% 230.52/41.99  | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | Case 2:
% 230.52/41.99  | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | |   (128)  all_57_3 = e1 & op(e2, e2) = e1
% 230.52/41.99  | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | | ALPHA: (128) implies:
% 230.52/41.99  | | | | | | | | | |   (129)  op(e2, e2) = e1
% 230.52/41.99  | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | | REF_CLOSE: (8), (13), (26), (129) are inconsistent by
% 230.52/41.99  | | | | | | | | | |            sub-proof #2352.
% 230.52/41.99  | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | End of split
% 230.52/41.99  | | | | | | | | | 
% 230.52/41.99  | | | | | | | | Case 2:
% 230.52/41.99  | | | | | | | | | 
% 230.52/41.99  | | | | | | | | |   (130)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 &
% 230.52/41.99  | | | | | | | | |            op(e0, e2) = e1)
% 230.52/41.99  | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | BETA: splitting (130) gives:
% 230.52/41.99  | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | Case 1:
% 230.52/41.99  | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | |   (131)  all_57_7 = e1 & op(e1, e2) = e1
% 230.52/41.99  | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | | ALPHA: (131) implies:
% 230.52/41.99  | | | | | | | | | |   (132)  all_57_7 = e1
% 230.52/41.99  | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | | REF_CLOSE: (42), (113), (132) are inconsistent by sub-proof
% 230.52/41.99  | | | | | | | | | |            #1761.
% 230.52/41.99  | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | Case 2:
% 230.52/41.99  | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | |   (133)  all_57_13 = e1 & op(e0, e2) = e1
% 230.52/41.99  | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | | REF_CLOSE: (2), (4), (5), (7), (8), (10), (11), (12), (13),
% 230.52/41.99  | | | | | | | | | |            (14), (15), (16), (17), (18), (19), (20), (21),
% 230.52/41.99  | | | | | | | | | |            (23), (24), (25), (26), (27), (28), (29), (30),
% 230.52/41.99  | | | | | | | | | |            (31), (32), (34), (35), (37), (38), (40), (42),
% 230.52/41.99  | | | | | | | | | |            (46), (49), (56), (133) are inconsistent by
% 230.52/41.99  | | | | | | | | | |            sub-proof #1254.
% 230.52/41.99  | | | | | | | | | | 
% 230.52/41.99  | | | | | | | | | End of split
% 230.52/41.99  | | | | | | | | | 
% 230.52/41.99  | | | | | | | | End of split
% 230.52/41.99  | | | | | | | | 
% 230.52/41.99  | | | | | | | End of split
% 230.52/41.99  | | | | | | | 
% 230.52/41.99  | | | | | | Case 2:
% 230.52/41.99  | | | | | | | 
% 230.52/41.99  | | | | | | |   (134)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 &
% 230.52/41.99  | | | | | | |            op(e1, e0) = e2)
% 230.52/41.99  | | | | | | | 
% 230.52/41.99  | | | | | | | REF_CLOSE: (24), (38), (42), (88), (134) are inconsistent by
% 230.52/41.99  | | | | | | |            sub-proof #1251.
% 230.52/41.99  | | | | | | | 
% 230.52/41.99  | | | | | | End of split
% 230.52/41.99  | | | | | | 
% 230.52/41.99  | | | | | Case 2:
% 230.52/41.99  | | | | | | 
% 230.52/41.99  | | | | | |   (135)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 &
% 230.52/41.99  | | | | | |              op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0))
% 230.52/41.99  | | | | | |          & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.52/41.99  | | | | | |              op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 230.52/41.99  | | | | | | 
% 230.52/41.99  | | | | | | ALPHA: (135) implies:
% 230.52/41.99  | | | | | |   (136)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 &
% 230.52/41.99  | | | | | |            op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.52/41.99  | | | | | | 
% 230.52/41.99  | | | | | | BETA: splitting (136) gives:
% 230.52/41.99  | | | | | | 
% 230.52/41.99  | | | | | | Case 1:
% 230.52/41.99  | | | | | | | 
% 230.52/41.99  | | | | | | |   (137)  all_57_9 = e0 & op(e3, e0) = e0
% 230.52/41.99  | | | | | | | 
% 230.52/41.99  | | | | | | | ALPHA: (137) implies:
% 230.52/41.99  | | | | | | |   (138)  all_57_9 = e0
% 230.52/41.99  | | | | | | | 
% 230.52/41.99  | | | | | | | REF_CLOSE: (5), (8), (16), (17), (34), (38), (40), (56), (138) are
% 230.52/41.99  | | | | | | |            inconsistent by sub-proof #2049.
% 230.52/41.99  | | | | | | | 
% 230.52/41.99  | | | | | | Case 2:
% 230.52/41.99  | | | | | | | 
% 230.52/41.99  | | | | | | |   (139)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 230.52/41.99  | | | | | | |            op(e1, e0) = e0)
% 230.52/41.99  | | | | | | | 
% 230.52/41.99  | | | | | | | REF_CLOSE: (8), (26), (33), (35), (38), (139) are inconsistent by
% 230.52/41.99  | | | | | | |            sub-proof #1256.
% 230.52/41.99  | | | | | | | 
% 230.52/41.99  | | | | | | End of split
% 230.52/41.99  | | | | | | 
% 230.52/41.99  | | | | | End of split
% 230.52/41.99  | | | | | 
% 230.52/41.99  | | | | Case 2:
% 230.52/41.99  | | | | | 
% 230.52/41.99  | | | | |   (140)  all_57_11 = e0 & op(e1, e0) = e0
% 230.52/41.99  | | | | | 
% 230.52/41.99  | | | | | REF_CLOSE: (26), (38), (140) are inconsistent by sub-proof #1257.
% 230.52/41.99  | | | | | 
% 230.52/41.99  | | | | End of split
% 230.52/41.99  | | | | 
% 230.52/41.99  | | | End of split
% 230.52/41.99  | | | 
% 230.52/41.99  | | End of split
% 230.52/41.99  | | 
% 230.52/41.99  | Case 2:
% 230.52/41.99  | | 
% 230.52/42.00  | |   (141)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.52/42.00  | |            e2)
% 230.52/42.00  | | 
% 230.52/42.00  | | BETA: splitting (141) gives:
% 230.52/42.00  | | 
% 230.52/42.00  | | Case 1:
% 230.52/42.00  | | | 
% 230.52/42.00  | | |   (142)  all_57_11 = e2 & op(e1, e0) = e2
% 230.52/42.00  | | | 
% 230.52/42.00  | | | ALPHA: (142) implies:
% 230.52/42.00  | | |   (143)  all_57_11 = e2
% 230.52/42.00  | | | 
% 230.52/42.00  | | | REF_CLOSE: (38), (42), (143) are inconsistent by sub-proof #2113.
% 230.52/42.00  | | | 
% 230.52/42.00  | | Case 2:
% 230.52/42.00  | | | 
% 230.52/42.00  | | |   (144)  all_57_15 = e2 & op(e0, e0) = e2
% 230.52/42.00  | | | 
% 230.52/42.00  | | | ALPHA: (144) implies:
% 230.52/42.00  | | |   (145)  op(e0, e0) = e2
% 230.52/42.00  | | | 
% 230.52/42.00  | | | REF_CLOSE: (8), (34), (42), (145) are inconsistent by sub-proof #2177.
% 230.52/42.00  | | | 
% 230.52/42.00  | | End of split
% 230.52/42.00  | | 
% 230.52/42.00  | End of split
% 230.52/42.00  | 
% 230.52/42.00  End of proof
% 230.52/42.00  
% 230.52/42.00  Sub-proof #1251 shows that the following formulas are inconsistent:
% 230.52/42.00  ----------------------------------------------------------------
% 230.52/42.00    (1)   ~ (e2 = e0)
% 230.52/42.00    (2)  all_57_8 = e0
% 230.52/42.00    (3)  all_57_11 = e1
% 230.52/42.00    (4)   ~ (e2 = e1)
% 230.52/42.00    (5)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.52/42.00  
% 230.52/42.00  Begin of proof
% 230.52/42.00  | 
% 230.52/42.00  | BETA: splitting (5) gives:
% 230.52/42.00  | 
% 230.52/42.00  | Case 1:
% 230.52/42.00  | | 
% 230.52/42.00  | |   (6)  all_57_8 = e2 & op(e1, e1) = e2
% 230.52/42.00  | | 
% 230.52/42.00  | | ALPHA: (6) implies:
% 230.52/42.00  | |   (7)  all_57_8 = e2
% 230.52/42.00  | | 
% 230.52/42.00  | | REF_CLOSE: (1), (2), (7) are inconsistent by sub-proof #1957.
% 230.52/42.00  | | 
% 230.52/42.00  | Case 2:
% 230.52/42.00  | | 
% 230.52/42.00  | |   (8)  all_57_11 = e2 & op(e1, e0) = e2
% 230.52/42.00  | | 
% 230.52/42.00  | | ALPHA: (8) implies:
% 230.52/42.00  | |   (9)  all_57_11 = e2
% 230.52/42.00  | | 
% 230.52/42.00  | | REF_CLOSE: (3), (4), (9) are inconsistent by sub-proof #2113.
% 230.52/42.00  | | 
% 230.52/42.00  | End of split
% 230.52/42.00  | 
% 230.52/42.00  End of proof
% 230.52/42.00  
% 230.52/42.00  Sub-proof #1252 shows that the following formulas are inconsistent:
% 230.52/42.00  ----------------------------------------------------------------
% 230.52/42.00    (1)  e1 = e0
% 230.52/42.00    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.52/42.00         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.52/42.00    (3)   ~ (e3 = e1)
% 230.52/42.00    (4)  all_57_3 = e0
% 230.52/42.00    (5)   ~ (e3 = e2)
% 230.52/42.00    (6)   ~ (e3 = e0)
% 230.52/42.00    (7)   ~ (e2 = e0)
% 230.52/42.00    (8)   ~ (e1 = e0)
% 230.52/42.00    (9)  all_57_2 = e1
% 230.52/42.00    (10)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.52/42.00          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.52/42.00    (11)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.52/42.00          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.52/42.00    (12)   ~ (e2 = e1)
% 230.52/42.00  
% 230.52/42.00  Begin of proof
% 230.52/42.00  | 
% 230.52/42.00  | SIMP: (1) implies:
% 230.75/42.00  |   (13)  e1 = e0
% 230.75/42.00  | 
% 230.75/42.00  | COMBINE_EQS: (9), (13) imply:
% 230.75/42.00  |   (14)  all_57_2 = e0
% 230.75/42.00  | 
% 230.75/42.00  | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (14) are
% 230.75/42.00  |            inconsistent by sub-proof #2246.
% 230.75/42.00  | 
% 230.75/42.00  End of proof
% 230.75/42.00  
% 230.75/42.00  Sub-proof #1253 shows that the following formulas are inconsistent:
% 230.75/42.00  ----------------------------------------------------------------
% 230.75/42.00    (1)  all_57_0 = e2
% 230.75/42.00    (2)  all_57_15 = e0
% 230.75/42.00    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.75/42.00         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.75/42.00    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.75/42.00         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.75/42.00    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.75/42.00         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.75/42.00    (6)   ~ (e3 = e1)
% 230.75/42.00    (7)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.75/42.00         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.75/42.00    (8)   ~ (all_53_13 = e1)
% 230.75/42.00    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.75/42.00           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.75/42.00    (10)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.75/42.00          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.75/42.00    (11)   ~ (all_6_2 = e3)
% 230.75/42.00    (12)  op(e1, e1) = all_6_2
% 230.75/42.00    (13)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.75/42.00          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.75/42.00    (14)  op(e2, e2) = e0
% 230.75/42.00    (15)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.75/42.00          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.75/42.00    (16)  all_57_3 = e0
% 230.75/42.00    (17)   ~ (e3 = e2)
% 230.75/42.00    (18)   ~ (e3 = e0)
% 230.75/42.00    (19)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.75/42.00          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.75/42.00    (20)  op(e0, e3) = all_53_3
% 230.75/42.00    (21)  op(e3, e3) = e2
% 230.75/42.00    (22)   ~ (all_53_3 = e2)
% 230.75/42.00    (23)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.75/42.00          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.75/42.00            e1)
% 230.75/42.00    (24)  all_57_10 = e2
% 230.75/42.00    (25)  op(e3, e2) = all_53_4
% 230.75/42.00    (26)   ~ (e2 = e0)
% 230.75/42.00    (27)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.75/42.00          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.75/42.00    (28)   ~ (e1 = e0)
% 230.75/42.00    (29)   ~ (all_53_4 = e0)
% 230.75/42.00    (30)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 230.75/42.00          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 230.75/42.00    (31)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.75/42.00          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.75/42.00    (32)  op(e0, e0) = e0
% 230.75/42.00    (33)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.75/42.00          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 230.75/42.00            e3)
% 230.75/42.00    (34)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.75/42.00          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.75/42.00            e2)
% 230.75/42.00    (35)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.75/42.00              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.75/42.00                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.75/42.00                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.75/42.00    (36)   ~ (all_53_13 = e0)
% 230.75/42.00    (37)  op(e0, e0) = e1
% 230.75/42.00    (38)  op(e2, e0) = all_53_13
% 230.75/42.00    (39)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.75/42.00          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.75/42.00    (40)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.75/42.00          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.75/42.00    (41)  all_57_11 = e1
% 230.75/42.00    (42)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.75/42.00          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.75/42.00    (43)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 230.75/42.00          (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 230.75/42.00    (44)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.75/42.00          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 230.75/42.00    (45)   ~ (e2 = e1)
% 230.75/42.00    (46)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.75/42.00          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.75/42.00    (47)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.75/42.00          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.75/42.00    (48)   ~ (all_53_12 = e2)
% 230.75/42.00    (49)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.75/42.00          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.75/42.00    (50)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.75/42.00          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.75/42.00    (51)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.75/42.00          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.75/42.00    (52)  all_57_14 = e1 & op(e0, e1) = e1
% 230.75/42.00    (53)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.75/42.00          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.75/42.00    (54)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.75/42.00          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.75/42.00    (55)  op(e3, e0) = all_53_12
% 230.75/42.00  
% 230.75/42.00  Begin of proof
% 230.75/42.00  | 
% 230.75/42.00  | ALPHA: (52) implies:
% 230.75/42.00  |   (56)  all_57_14 = e1
% 230.75/42.00  | 
% 230.75/42.00  | BETA: splitting (50) gives:
% 230.75/42.00  | 
% 230.75/42.00  | Case 1:
% 230.75/42.00  | | 
% 230.75/42.00  | |   (57)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) =
% 230.75/42.00  | |           e0)
% 230.75/42.00  | | 
% 230.75/42.00  | | REF_CLOSE: (3), (6), (9), (16), (17), (18), (21), (26), (28), (39), (40),
% 230.75/42.00  | |            (45), (57) are inconsistent by sub-proof #1654.
% 230.75/42.00  | | 
% 230.75/42.00  | Case 2:
% 230.75/42.00  | | 
% 230.75/42.00  | |   (58)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) =
% 230.75/42.00  | |           e0)
% 230.75/42.00  | | 
% 230.75/42.00  | | BETA: splitting (58) gives:
% 230.75/42.00  | | 
% 230.75/42.00  | | Case 1:
% 230.75/42.00  | | | 
% 230.75/42.00  | | |   (59)  all_57_6 = e0 & op(e1, e3) = e0
% 230.75/42.00  | | | 
% 230.75/42.00  | | | ALPHA: (59) implies:
% 230.75/42.00  | | |   (60)  all_57_6 = e0
% 230.75/42.00  | | | 
% 230.75/42.00  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 230.75/42.00  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 230.75/42.00  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 230.75/42.00  | | |            (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 230.75/42.00  | | |            (43), (44), (45), (46), (47), (48), (49), (50), (51), (53),
% 230.75/42.00  | | |            (54), (55), (60) are inconsistent by sub-proof #1258.
% 230.75/42.00  | | | 
% 230.75/42.00  | | Case 2:
% 230.75/42.00  | | | 
% 230.75/42.00  | | |   (61)  all_57_12 = e0 & op(e0, e3) = e0
% 230.75/42.00  | | | 
% 230.75/42.00  | | | ALPHA: (61) implies:
% 230.75/42.00  | | |   (62)  all_57_12 = e0
% 230.75/42.00  | | | 
% 230.75/42.00  | | | REF_CLOSE: (6), (9), (17), (18), (20), (22), (33), (34), (37), (45), (56),
% 230.75/42.00  | | |            (62) are inconsistent by sub-proof #1964.
% 230.75/42.00  | | | 
% 230.75/42.00  | | End of split
% 230.75/42.00  | | 
% 230.75/42.00  | End of split
% 230.75/42.00  | 
% 230.75/42.00  End of proof
% 230.75/42.00  
% 230.75/42.00  Sub-proof #1254 shows that the following formulas are inconsistent:
% 230.75/42.00  ----------------------------------------------------------------
% 230.75/42.00    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.75/42.00         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.75/42.00    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.75/42.00         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.75/42.00    (3)   ~ (e3 = e1)
% 230.75/42.00    (4)   ~ (all_53_13 = e1)
% 230.75/42.00    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.75/42.00           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.75/42.00    (6)   ~ (all_6_2 = e3)
% 230.75/42.00    (7)  op(e1, e1) = all_6_2
% 230.75/42.00    (8)  all_57_13 = e1 & op(e0, e2) = e1
% 230.75/42.00    (9)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.75/42.00         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.75/42.00    (10)  op(e2, e2) = e0
% 230.75/42.00    (11)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.75/42.00          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.75/42.00    (12)  all_57_3 = e0
% 230.75/42.00    (13)   ~ (e3 = e2)
% 230.75/42.00    (14)   ~ (e3 = e0)
% 230.75/42.00    (15)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.75/42.00          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.75/42.00    (16)  op(e0, e3) = all_53_3
% 230.75/42.00    (17)  op(e3, e3) = e2
% 230.75/42.00    (18)   ~ (all_53_3 = e2)
% 230.75/42.00    (19)  all_57_10 = e2
% 230.75/42.00    (20)  op(e3, e2) = all_53_4
% 230.75/42.00    (21)   ~ (e2 = e0)
% 230.75/42.00    (22)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.75/42.00          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.75/42.00    (23)   ~ (e1 = e0)
% 230.75/42.00    (24)   ~ (all_53_4 = e0)
% 230.75/42.01    (25)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 230.75/42.01          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 230.75/42.01    (26)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.75/42.01          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.75/42.01    (27)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.75/42.01          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 230.75/42.01            e3)
% 230.75/42.01    (28)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.75/42.01          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.75/42.01            e2)
% 230.75/42.01    (29)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.75/42.01              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.75/42.01                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.75/42.01                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.75/42.01    (30)  op(e0, e0) = e1
% 230.75/42.01    (31)  op(e2, e0) = all_53_13
% 230.75/42.01    (32)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.75/42.01          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.75/42.01    (33)  all_57_11 = e1
% 230.75/42.01    (34)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 230.75/42.01          (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 230.75/42.01    (35)   ~ (e2 = e1)
% 230.75/42.01    (36)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.75/42.01          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.75/42.01    (37)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.75/42.01          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.75/42.01  
% 230.75/42.01  Begin of proof
% 230.75/42.01  | 
% 230.75/42.01  | ALPHA: (8) implies:
% 230.75/42.01  |   (38)  all_57_13 = e1
% 230.75/42.01  | 
% 230.75/42.01  | BETA: splitting (34) gives:
% 230.75/42.01  | 
% 230.75/42.01  | Case 1:
% 230.75/42.01  | | 
% 230.75/42.01  | |   (39)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 230.75/42.01  | |           e3)
% 230.75/42.01  | | 
% 230.75/42.01  | | BETA: splitting (39) gives:
% 230.75/42.01  | | 
% 230.75/42.01  | | Case 1:
% 230.75/42.01  | | | 
% 230.75/42.01  | | |   (40)  all_57_9 = e3 & op(e3, e0) = e3
% 230.75/42.01  | | | 
% 230.75/42.01  | | | ALPHA: (40) implies:
% 230.75/42.01  | | |   (41)  all_57_9 = e3
% 230.75/42.01  | | | 
% 230.75/42.01  | | | BETA: splitting (11) gives:
% 230.75/42.01  | | | 
% 230.75/42.01  | | | Case 1:
% 230.75/42.01  | | | | 
% 230.75/42.01  | | | |   (42)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2)
% 230.75/42.01  | | | |           = e0)
% 230.75/42.01  | | | | 
% 230.75/42.01  | | | | REF_CLOSE: (5), (17), (20), (21), (24), (42) are inconsistent by
% 230.75/42.01  | | | |            sub-proof #1321.
% 230.75/42.01  | | | | 
% 230.75/42.01  | | | Case 2:
% 230.75/42.01  | | | | 
% 230.75/42.01  | | | |   (43)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0)
% 230.75/42.01  | | | |           = e0)
% 230.75/42.01  | | | | 
% 230.75/42.01  | | | | BETA: splitting (43) gives:
% 230.75/42.01  | | | | 
% 230.75/42.01  | | | | Case 1:
% 230.75/42.01  | | | | | 
% 230.75/42.01  | | | | |   (44)  all_57_4 = e0 & op(e3, e1) = e0
% 230.75/42.01  | | | | | 
% 230.75/42.01  | | | | | ALPHA: (44) implies:
% 230.75/42.01  | | | | |   (45)  all_57_4 = e0
% 230.75/42.01  | | | | | 
% 230.75/42.01  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12),
% 230.75/42.01  | | | | |            (13), (14), (15), (16), (17), (18), (21), (22), (23), (25),
% 230.75/42.01  | | | | |            (26), (27), (28), (29), (30), (31), (32), (35), (36), (37),
% 230.75/42.01  | | | | |            (38), (45) are inconsistent by sub-proof #1275.
% 230.75/42.01  | | | | | 
% 230.75/42.01  | | | | Case 2:
% 230.75/42.01  | | | | | 
% 230.75/42.01  | | | | |   (46)  all_57_9 = e0 & op(e3, e0) = e0
% 230.75/42.01  | | | | | 
% 230.75/42.01  | | | | | ALPHA: (46) implies:
% 230.75/42.01  | | | | |   (47)  all_57_9 = e0
% 230.75/42.01  | | | | | 
% 230.75/42.01  | | | | | REF_CLOSE: (14), (41), (47) are inconsistent by sub-proof #1657.
% 230.75/42.01  | | | | | 
% 230.75/42.01  | | | | End of split
% 230.75/42.01  | | | | 
% 230.75/42.01  | | | End of split
% 230.75/42.01  | | | 
% 230.75/42.01  | | Case 2:
% 230.75/42.01  | | | 
% 230.75/42.01  | | |   (48)  all_57_10 = e3 & op(e2, e0) = e3
% 230.75/42.01  | | | 
% 230.75/42.01  | | | REF_CLOSE: (13), (19), (48) are inconsistent by sub-proof #2051.
% 230.75/42.01  | | | 
% 230.75/42.01  | | End of split
% 230.75/42.01  | | 
% 230.75/42.01  | Case 2:
% 230.75/42.01  | | 
% 230.75/42.01  | |   (49)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 230.75/42.01  | |           e3)
% 230.75/42.01  | | 
% 230.75/42.01  | | REF_CLOSE: (3), (5), (30), (33), (49) are inconsistent by sub-proof #1259.
% 230.75/42.01  | | 
% 230.75/42.01  | End of split
% 230.75/42.01  | 
% 230.75/42.01  End of proof
% 230.75/42.01  
% 230.75/42.01  Sub-proof #1255 shows that the following formulas are inconsistent:
% 230.75/42.01  ----------------------------------------------------------------
% 230.75/42.01    (1)  all_57_0 = e2
% 230.75/42.01    (2)  all_57_15 = e0
% 230.75/42.01    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.75/42.01         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.75/42.01    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.75/42.01         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.75/42.01    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.75/42.01         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.75/42.01    (6)   ~ (e3 = e1)
% 230.75/42.01    (7)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.75/42.01         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.75/42.01    (8)   ~ (all_53_13 = e1)
% 230.75/42.01    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.75/42.01           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.75/42.01    (10)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.75/42.01          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.75/42.01    (11)   ~ (all_6_2 = e3)
% 230.75/42.01    (12)  op(e1, e1) = all_6_2
% 230.75/42.01    (13)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.75/42.01          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.75/42.01    (14)  op(e2, e2) = e0
% 230.75/42.01    (15)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.75/42.01          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.75/42.01    (16)  all_57_3 = e0
% 230.75/42.01    (17)   ~ (e3 = e2)
% 230.75/42.01    (18)   ~ (e3 = e0)
% 230.75/42.01    (19)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.75/42.01          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.75/42.01    (20)  op(e0, e3) = all_53_3
% 230.75/42.01    (21)  op(e3, e3) = e2
% 230.75/42.01    (22)   ~ (all_53_3 = e2)
% 230.75/42.01    (23)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.75/42.01          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.75/42.01            e1)
% 230.75/42.01    (24)  all_57_10 = e2
% 230.75/42.01    (25)  op(e3, e2) = all_53_4
% 230.75/42.01    (26)   ~ (e2 = e0)
% 230.75/42.01    (27)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.75/42.01          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.75/42.01    (28)   ~ (e1 = e0)
% 230.75/42.01    (29)   ~ (all_53_4 = e0)
% 230.75/42.01    (30)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 230.75/42.01          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 230.75/42.01    (31)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.75/42.01          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.75/42.01    (32)  op(e0, e0) = e0
% 230.75/42.01    (33)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.75/42.01          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 230.75/42.01            e3)
% 230.75/42.01    (34)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.75/42.01          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.75/42.01            e2)
% 230.75/42.01    (35)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.75/42.01              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.75/42.01                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.75/42.01                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.75/42.01    (36)   ~ (all_53_13 = e0)
% 230.75/42.01    (37)  op(e0, e0) = e1
% 230.75/42.01    (38)  op(e2, e0) = all_53_13
% 230.75/42.01    (39)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.75/42.01          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.75/42.01    (40)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.75/42.01          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.75/42.01    (41)  all_57_11 = e1
% 230.75/42.01    (42)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.75/42.01          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.75/42.01    (43)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 230.75/42.01          (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 230.75/42.01    (44)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.75/42.01          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 230.75/42.01    (45)   ~ (e2 = e1)
% 230.75/42.01    (46)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.75/42.01          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.75/42.01    (47)  all_57_12 = e1 & op(e0, e3) = e1
% 230.75/42.01    (48)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.75/42.01          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.75/42.01    (49)   ~ (all_53_12 = e2)
% 230.75/42.01    (50)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.75/42.01          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.75/42.01    (51)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.75/42.01          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.75/42.01    (52)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.75/42.01          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.75/42.01    (53)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.75/42.01          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.75/42.01    (54)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.75/42.01          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.75/42.01    (55)  op(e3, e0) = all_53_12
% 230.75/42.01  
% 230.75/42.01  Begin of proof
% 230.75/42.01  | 
% 230.75/42.01  | ALPHA: (47) implies:
% 230.75/42.01  |   (56)  all_57_12 = e1
% 230.75/42.01  | 
% 230.75/42.01  | BETA: splitting (51) gives:
% 230.75/42.01  | 
% 230.75/42.01  | Case 1:
% 230.75/42.01  | | 
% 230.75/42.01  | |   (57)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) =
% 230.75/42.01  | |           e0)
% 230.75/42.01  | | 
% 230.75/42.01  | | REF_CLOSE: (3), (6), (9), (16), (17), (18), (21), (26), (28), (39), (40),
% 230.75/42.01  | |            (45), (57) are inconsistent by sub-proof #1654.
% 230.75/42.01  | | 
% 230.75/42.01  | Case 2:
% 230.75/42.01  | | 
% 230.75/42.01  | |   (58)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) =
% 230.75/42.01  | |           e0)
% 230.75/42.01  | | 
% 230.75/42.01  | | BETA: splitting (58) gives:
% 230.75/42.01  | | 
% 230.75/42.01  | | Case 1:
% 230.75/42.01  | | | 
% 230.75/42.01  | | |   (59)  all_57_6 = e0 & op(e1, e3) = e0
% 230.75/42.01  | | | 
% 230.75/42.01  | | | ALPHA: (59) implies:
% 230.75/42.01  | | |   (60)  all_57_6 = e0
% 230.75/42.01  | | | 
% 230.75/42.01  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 230.75/42.01  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 230.75/42.01  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 230.75/42.01  | | |            (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 230.75/42.01  | | |            (43), (44), (45), (46), (48), (49), (50), (51), (52), (53),
% 230.75/42.01  | | |            (54), (55), (60) are inconsistent by sub-proof #1258.
% 230.75/42.01  | | | 
% 230.75/42.01  | | Case 2:
% 230.75/42.01  | | | 
% 230.75/42.01  | | |   (61)  all_57_12 = e0 & op(e0, e3) = e0
% 230.75/42.01  | | | 
% 230.75/42.01  | | | ALPHA: (61) implies:
% 230.75/42.01  | | |   (62)  all_57_12 = e0
% 230.75/42.01  | | | 
% 230.75/42.01  | | | REF_CLOSE: (28), (56), (62) are inconsistent by sub-proof #2014.
% 230.75/42.01  | | | 
% 230.75/42.01  | | End of split
% 230.75/42.01  | | 
% 230.75/42.01  | End of split
% 230.75/42.01  | 
% 230.75/42.01  End of proof
% 230.75/42.01  
% 230.75/42.01  Sub-proof #1256 shows that the following formulas are inconsistent:
% 230.75/42.01  ----------------------------------------------------------------
% 230.75/42.01    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.75/42.01           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.75/42.01    (2)   ~ (e1 = e0)
% 230.75/42.01    (3)   ~ (all_53_13 = e0)
% 230.75/42.01    (4)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.75/42.01    (5)  op(e2, e0) = all_53_13
% 230.75/42.01    (6)  all_57_11 = e1
% 230.75/42.01  
% 230.75/42.01  Begin of proof
% 230.75/42.01  | 
% 230.75/42.01  | BETA: splitting (4) gives:
% 230.75/42.01  | 
% 230.75/42.01  | Case 1:
% 230.75/42.01  | | 
% 230.75/42.01  | |   (7)  all_57_10 = e0 & op(e2, e0) = e0
% 230.75/42.01  | | 
% 230.75/42.01  | | ALPHA: (7) implies:
% 230.75/42.01  | |   (8)  op(e2, e0) = e0
% 230.75/42.01  | | 
% 230.75/42.01  | | REF_CLOSE: (1), (3), (5), (8) are inconsistent by sub-proof #2470.
% 230.75/42.01  | | 
% 230.75/42.01  | Case 2:
% 230.75/42.01  | | 
% 230.75/42.02  | |   (9)  all_57_11 = e0 & op(e1, e0) = e0
% 230.75/42.02  | | 
% 230.75/42.02  | | REF_CLOSE: (2), (6), (9) are inconsistent by sub-proof #1257.
% 230.75/42.02  | | 
% 230.75/42.02  | End of split
% 230.75/42.02  | 
% 230.75/42.02  End of proof
% 230.75/42.02  
% 230.75/42.02  Sub-proof #1257 shows that the following formulas are inconsistent:
% 230.75/42.02  ----------------------------------------------------------------
% 230.75/42.02    (1)  all_57_11 = e0 & op(e1, e0) = e0
% 230.75/42.02    (2)  all_57_11 = e1
% 230.75/42.02    (3)   ~ (e1 = e0)
% 230.75/42.02  
% 230.75/42.02  Begin of proof
% 230.75/42.02  | 
% 230.75/42.02  | ALPHA: (1) implies:
% 230.75/42.02  |   (4)  all_57_11 = e0
% 230.75/42.02  | 
% 230.75/42.02  | COMBINE_EQS: (2), (4) imply:
% 230.75/42.02  |   (5)  e1 = e0
% 230.75/42.02  | 
% 230.75/42.02  | REDUCE: (3), (5) imply:
% 230.75/42.02  |   (6)  $false
% 230.75/42.02  | 
% 230.75/42.02  | CLOSE: (6) is inconsistent.
% 230.75/42.02  | 
% 230.75/42.02  End of proof
% 230.75/42.02  
% 230.75/42.02  Sub-proof #1258 shows that the following formulas are inconsistent:
% 230.75/42.02  ----------------------------------------------------------------
% 230.75/42.02    (1)  all_57_0 = e2
% 230.75/42.02    (2)  all_57_15 = e0
% 230.75/42.02    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.75/42.02         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.75/42.02    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.75/42.02         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.75/42.02    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.75/42.02         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.75/42.02    (6)   ~ (e3 = e1)
% 230.75/42.02    (7)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.75/42.02         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.75/42.02    (8)   ~ (all_53_13 = e1)
% 230.75/42.02    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.75/42.02           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.75/42.02    (10)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.75/42.02          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.75/42.02    (11)   ~ (all_6_2 = e3)
% 230.75/42.02    (12)  op(e1, e1) = all_6_2
% 230.75/42.02    (13)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.75/42.02          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.75/42.02    (14)  op(e2, e2) = e0
% 230.75/42.02    (15)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.75/42.02          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.75/42.02    (16)  all_57_3 = e0
% 230.75/42.02    (17)   ~ (e3 = e2)
% 230.75/42.02    (18)   ~ (e3 = e0)
% 230.75/42.02    (19)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.75/42.02          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.75/42.02    (20)  all_57_6 = e0
% 230.75/42.02    (21)  op(e0, e3) = all_53_3
% 230.75/42.02    (22)  op(e3, e3) = e2
% 230.75/42.02    (23)   ~ (all_53_3 = e2)
% 230.75/42.02    (24)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.75/42.02          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.75/42.02            e1)
% 230.75/42.02    (25)  all_57_10 = e2
% 230.75/42.02    (26)  op(e3, e2) = all_53_4
% 230.75/42.02    (27)   ~ (e2 = e0)
% 230.75/42.02    (28)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.75/42.02          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.75/42.02    (29)   ~ (e1 = e0)
% 230.75/42.02    (30)   ~ (all_53_4 = e0)
% 230.75/42.02    (31)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 230.75/42.02          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 230.75/42.02    (32)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.75/42.02          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.75/42.02    (33)  op(e0, e0) = e0
% 230.75/42.02    (34)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.75/42.02          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 230.75/42.02            e3)
% 230.75/42.02    (35)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.75/42.02          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.75/42.02            e2)
% 230.75/42.02    (36)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.75/42.02              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.75/42.02                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.75/42.02                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.75/42.02    (37)   ~ (all_53_13 = e0)
% 230.75/42.02    (38)  op(e0, e0) = e1
% 230.75/42.02    (39)  op(e2, e0) = all_53_13
% 230.75/42.02    (40)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.75/42.02          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.75/42.02    (41)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.75/42.02          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.75/42.02    (42)  all_57_11 = e1
% 230.75/42.02    (43)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.75/42.02          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.75/42.02    (44)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 230.75/42.02          (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 230.75/42.02    (45)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.75/42.02          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 230.75/42.02    (46)   ~ (e2 = e1)
% 230.75/42.02    (47)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.75/42.02          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.75/42.02    (48)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.75/42.02          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.75/42.02    (49)   ~ (all_53_12 = e2)
% 230.75/42.02    (50)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.75/42.02          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.75/42.02    (51)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.75/42.02          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.75/42.02    (52)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.75/42.02          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.75/42.02    (53)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.75/42.02          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.75/42.02    (54)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.75/42.02          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.75/42.02    (55)  op(e3, e0) = all_53_12
% 230.75/42.02  
% 230.75/42.02  Begin of proof
% 230.75/42.02  | 
% 230.75/42.02  | BETA: splitting (10) gives:
% 230.75/42.02  | 
% 230.75/42.02  | Case 1:
% 230.75/42.02  | | 
% 230.75/42.02  | |   (56)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 230.75/42.02  | |           e3)
% 230.75/42.02  | | 
% 230.75/42.02  | | BETA: splitting (56) gives:
% 230.75/42.02  | | 
% 230.75/42.02  | | Case 1:
% 230.75/42.02  | | | 
% 230.75/42.02  | | |   (57)  all_57_6 = e3 & op(e1, e3) = e3
% 230.75/42.02  | | | 
% 230.75/42.02  | | | ALPHA: (57) implies:
% 230.75/42.02  | | |   (58)  all_57_6 = e3
% 230.75/42.02  | | | 
% 230.75/42.02  | | | REF_CLOSE: (18), (20), (58) are inconsistent by sub-proof #1822.
% 230.75/42.02  | | | 
% 230.75/42.02  | | Case 2:
% 230.75/42.02  | | | 
% 230.75/42.02  | | |   (59)  all_57_7 = e3 & op(e1, e2) = e3
% 230.75/42.02  | | | 
% 230.75/42.02  | | | ALPHA: (59) implies:
% 230.75/42.02  | | |   (60)  all_57_7 = e3
% 230.75/42.02  | | | 
% 230.75/42.02  | | | BETA: splitting (5) gives:
% 230.75/42.02  | | | 
% 230.75/42.02  | | | Case 1:
% 230.75/42.02  | | | | 
% 230.75/42.02  | | | |   (61)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2)
% 230.75/42.02  | | | |           = e2)
% 230.75/42.02  | | | | 
% 230.75/42.02  | | | | REF_CLOSE: (6), (9), (13), (14), (15), (17), (18), (22), (27), (28),
% 230.75/42.02  | | | |            (29), (46), (61) are inconsistent by sub-proof #1297.
% 230.75/42.02  | | | | 
% 230.75/42.02  | | | Case 2:
% 230.75/42.02  | | | | 
% 230.75/42.02  | | | |   (62)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2)
% 230.75/42.02  | | | |           = e2)
% 230.75/42.02  | | | | 
% 230.75/42.02  | | | | BETA: splitting (62) gives:
% 230.75/42.02  | | | | 
% 230.75/42.02  | | | | Case 1:
% 230.75/42.02  | | | | | 
% 230.75/42.02  | | | | |   (63)  all_57_7 = e2 & op(e1, e2) = e2
% 230.75/42.02  | | | | | 
% 230.75/42.02  | | | | | REF_CLOSE: (17), (60), (63) are inconsistent by sub-proof #2092.
% 230.75/42.02  | | | | | 
% 230.75/42.02  | | | | Case 2:
% 230.75/42.02  | | | | | 
% 230.75/42.02  | | | | |   (64)  all_57_13 = e2 & op(e0, e2) = e2
% 230.75/42.02  | | | | | 
% 230.75/42.02  | | | | | ALPHA: (64) implies:
% 230.75/42.02  | | | | |   (65)  all_57_13 = e2
% 230.75/42.02  | | | | | 
% 230.75/42.02  | | | | | BETA: splitting (44) gives:
% 230.75/42.02  | | | | | 
% 230.75/42.02  | | | | | Case 1:
% 230.75/42.02  | | | | | | 
% 230.75/42.02  | | | | | |   (66)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2,
% 230.75/42.02  | | | | | |             e0) = e3)
% 230.75/42.02  | | | | | | 
% 230.75/42.02  | | | | | | BETA: splitting (66) gives:
% 230.75/42.02  | | | | | | 
% 230.75/42.02  | | | | | | Case 1:
% 230.75/42.02  | | | | | | | 
% 230.75/42.02  | | | | | | |   (67)  all_57_9 = e3 & op(e3, e0) = e3
% 230.75/42.02  | | | | | | | 
% 230.75/42.02  | | | | | | | ALPHA: (67) implies:
% 230.75/42.02  | | | | | | |   (68)  all_57_9 = e3
% 230.75/42.02  | | | | | | | 
% 230.75/42.02  | | | | | | | BETA: splitting (4) gives:
% 230.75/42.02  | | | | | | | 
% 230.75/42.02  | | | | | | | Case 1:
% 230.75/42.02  | | | | | | | | 
% 230.75/42.02  | | | | | | | |   (69)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 &
% 230.75/42.02  | | | | | | | |           op(e2, e3) = e1)
% 230.75/42.02  | | | | | | | | 
% 230.75/42.02  | | | | | | | | BETA: splitting (69) gives:
% 230.75/42.02  | | | | | | | | 
% 230.75/42.02  | | | | | | | | Case 1:
% 230.75/42.02  | | | | | | | | | 
% 230.75/42.02  | | | | | | | | |   (70)  all_57_0 = e1 & op(e3, e3) = e1
% 230.75/42.02  | | | | | | | | | 
% 230.75/42.02  | | | | | | | | | ALPHA: (70) implies:
% 230.75/42.02  | | | | | | | | |   (71)  op(e3, e3) = e1
% 230.75/42.02  | | | | | | | | | 
% 230.75/42.02  | | | | | | | | | REF_CLOSE: (9), (22), (46), (71) are inconsistent by sub-proof
% 230.75/42.02  | | | | | | | | |            #1950.
% 230.75/42.02  | | | | | | | | | 
% 230.75/42.02  | | | | | | | | Case 2:
% 230.75/42.02  | | | | | | | | | 
% 230.75/42.02  | | | | | | | | |   (72)  all_57_2 = e1 & op(e2, e3) = e1
% 230.75/42.02  | | | | | | | | | 
% 230.75/42.02  | | | | | | | | | ALPHA: (72) implies:
% 230.75/42.02  | | | | | | | | |   (73)  all_57_2 = e1
% 230.75/42.02  | | | | | | | | | 
% 230.75/42.02  | | | | | | | | | BETA: splitting (15) gives:
% 230.75/42.02  | | | | | | | | | 
% 230.75/42.02  | | | | | | | | | Case 1:
% 230.75/42.02  | | | | | | | | | | 
% 230.75/42.02  | | | | | | | | | |   (74)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 &
% 230.75/42.02  | | | | | | | | | |           op(e3, e2) = e0)
% 230.75/42.02  | | | | | | | | | | 
% 230.75/42.02  | | | | | | | | | | BETA: splitting (74) gives:
% 230.75/42.02  | | | | | | | | | | 
% 230.75/42.02  | | | | | | | | | | Case 1:
% 230.75/42.02  | | | | | | | | | | | 
% 230.75/42.02  | | | | | | | | | | |   (75)  all_57_0 = e0 & op(e3, e3) = e0
% 230.75/42.02  | | | | | | | | | | | 
% 230.75/42.02  | | | | | | | | | | | ALPHA: (75) implies:
% 230.75/42.02  | | | | | | | | | | |   (76)  op(e3, e3) = e0
% 230.75/42.02  | | | | | | | | | | | 
% 230.75/42.02  | | | | | | | | | | | REF_CLOSE: (6), (9), (17), (18), (20), (27), (43), (46),
% 230.75/42.02  | | | | | | | | | | |            (48), (73), (76) are inconsistent by sub-proof
% 230.75/42.02  | | | | | | | | | | |            #2390.
% 230.75/42.02  | | | | | | | | | | | 
% 230.75/42.02  | | | | | | | | | | Case 2:
% 230.75/42.02  | | | | | | | | | | | 
% 230.75/42.02  | | | | | | | | | | |   (77)  all_57_1 = e0 & op(e3, e2) = e0
% 230.75/42.02  | | | | | | | | | | | 
% 230.75/42.02  | | | | | | | | | | | ALPHA: (77) implies:
% 230.75/42.02  | | | | | | | | | | |   (78)  all_57_1 = e0
% 230.75/42.02  | | | | | | | | | | | 
% 230.75/42.02  | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (14), (16), (17), (18), (27), (29),
% 230.75/42.02  | | | | | | | | | | |            (32), (46), (53), (65), (78) are inconsistent by
% 230.75/42.02  | | | | | | | | | | |            sub-proof #1281.
% 230.75/42.02  | | | | | | | | | | | 
% 230.75/42.02  | | | | | | | | | | End of split
% 230.75/42.02  | | | | | | | | | | 
% 230.75/42.02  | | | | | | | | | Case 2:
% 230.75/42.02  | | | | | | | | | | 
% 230.75/42.02  | | | | | | | | | |   (79)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 &
% 230.75/42.02  | | | | | | | | | |           op(e3, e0) = e0)
% 230.75/42.02  | | | | | | | | | | 
% 230.75/42.02  | | | | | | | | | | BETA: splitting (79) gives:
% 230.75/42.02  | | | | | | | | | | 
% 230.75/42.02  | | | | | | | | | | Case 1:
% 230.75/42.02  | | | | | | | | | | | 
% 230.75/42.02  | | | | | | | | | | |   (80)  all_57_4 = e0 & op(e3, e1) = e0
% 230.75/42.02  | | | | | | | | | | | 
% 230.75/42.02  | | | | | | | | | | | ALPHA: (80) implies:
% 230.75/42.02  | | | | | | | | | | |   (81)  all_57_4 = e0
% 230.75/42.02  | | | | | | | | | | | 
% 230.75/42.02  | | | | | | | | | | | BETA: splitting (40) gives:
% 230.75/42.02  | | | | | | | | | | | 
% 230.75/42.02  | | | | | | | | | | | Case 1:
% 230.75/42.02  | | | | | | | | | | | | 
% 230.75/42.02  | | | | | | | | | | | |   (82)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 230.75/42.02  | | | | | | | | | | | |           & op(e2, e2) = e3)
% 230.75/42.02  | | | | | | | | | | | | 
% 230.75/42.02  | | | | | | | | | | | | BETA: splitting (82) gives:
% 230.75/42.02  | | | | | | | | | | | | 
% 230.75/42.02  | | | | | | | | | | | | Case 1:
% 230.75/42.02  | | | | | | | | | | | | | 
% 230.75/42.02  | | | | | | | | | | | | |   (83)  all_57_2 = e3 & op(e2, e3) = e3
% 230.75/42.02  | | | | | | | | | | | | | 
% 230.75/42.02  | | | | | | | | | | | | | ALPHA: (83) implies:
% 230.75/42.02  | | | | | | | | | | | | |   (84)  all_57_2 = e3
% 230.75/42.02  | | | | | | | | | | | | | 
% 230.75/42.02  | | | | | | | | | | | | | COMBINE_EQS: (73), (84) imply:
% 230.75/42.02  | | | | | | | | | | | | |   (85)  e3 = e1
% 230.75/42.02  | | | | | | | | | | | | | 
% 230.75/42.02  | | | | | | | | | | | | | SIMP: (85) implies:
% 230.75/42.02  | | | | | | | | | | | | |   (86)  e3 = e1
% 230.75/42.02  | | | | | | | | | | | | | 
% 230.75/42.02  | | | | | | | | | | | | | COMBINE_EQS: (68), (86) imply:
% 230.75/42.02  | | | | | | | | | | | | |   (87)  all_57_9 = e1
% 230.75/42.02  | | | | | | | | | | | | | 
% 230.75/42.02  | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10),
% 230.75/42.02  | | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 230.75/42.02  | | | | | | | | | | | | |            (19), (21), (22), (23), (24), (27), (28), (29),
% 230.75/42.02  | | | | | | | | | | | | |            (31), (32), (34), (35), (36), (37), (38), (39),
% 230.75/42.02  | | | | | | | | | | | | |            (40), (41), (43), (44), (46), (47), (48), (49),
% 230.75/42.02  | | | | | | | | | | | | |            (50), (51), (52), (53), (54), (55), (81), (87) are
% 230.75/42.02  | | | | | | | | | | | | |            inconsistent by sub-proof #1267.
% 230.75/42.02  | | | | | | | | | | | | | 
% 230.75/42.02  | | | | | | | | | | | | Case 2:
% 230.75/42.02  | | | | | | | | | | | | | 
% 230.75/42.02  | | | | | | | | | | | | |   (88)  all_57_3 = e3 & op(e2, e2) = e3
% 230.75/42.02  | | | | | | | | | | | | | 
% 230.75/42.02  | | | | | | | | | | | | | ALPHA: (88) implies:
% 230.75/42.02  | | | | | | | | | | | | |   (89)  all_57_3 = e3
% 230.75/42.02  | | | | | | | | | | | | | 
% 230.75/42.02  | | | | | | | | | | | | | COMBINE_EQS: (16), (89) imply:
% 230.75/42.02  | | | | | | | | | | | | |   (90)  e3 = e0
% 230.75/42.02  | | | | | | | | | | | | | 
% 230.75/42.02  | | | | | | | | | | | | | COMBINE_EQS: (60), (90) imply:
% 230.75/42.02  | | | | | | | | | | | | |   (91)  all_57_7 = e0
% 230.75/42.02  | | | | | | | | | | | | | 
% 230.75/42.02  | | | | | | | | | | | | | REF_CLOSE: (6), (9), (14), (16), (17), (18), (29), (32),
% 230.75/42.02  | | | | | | | | | | | | |            (46), (53), (65), (91) are inconsistent by
% 230.75/42.02  | | | | | | | | | | | | |            sub-proof #2202.
% 230.75/42.02  | | | | | | | | | | | | | 
% 230.75/42.02  | | | | | | | | | | | | End of split
% 230.75/42.02  | | | | | | | | | | | | 
% 230.75/42.02  | | | | | | | | | | | Case 2:
% 230.75/42.02  | | | | | | | | | | | | 
% 230.75/42.02  | | | | | | | | | | | |   (92)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 230.75/42.02  | | | | | | | | | | | |           e3 & op(e2, e0) = e3)
% 230.75/42.02  | | | | | | | | | | | | 
% 230.75/42.02  | | | | | | | | | | | | BETA: splitting (92) gives:
% 230.75/42.02  | | | | | | | | | | | | 
% 230.75/42.02  | | | | | | | | | | | | Case 1:
% 230.75/42.02  | | | | | | | | | | | | | 
% 230.75/42.02  | | | | | | | | | | | | |   (93)  all_57_5 = e3 & op(e2, e1) = e3
% 230.75/42.02  | | | | | | | | | | | | | 
% 230.75/42.02  | | | | | | | | | | | | | ALPHA: (93) implies:
% 230.75/42.03  | | | | | | | | | | | | |   (94)  all_57_5 = e3
% 230.75/42.03  | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | BETA: splitting (54) gives:
% 230.75/42.03  | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | Case 1:
% 230.75/42.03  | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | |   (95)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 230.75/42.03  | | | | | | | | | | | | | |           & op(e1, e2) = e2)
% 230.75/42.03  | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | BETA: splitting (95) gives:
% 230.75/42.03  | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | Case 1:
% 230.75/42.03  | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | |   (96)  all_57_6 = e2 & op(e1, e3) = e2
% 230.75/42.03  | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | ALPHA: (96) implies:
% 230.75/42.03  | | | | | | | | | | | | | | |   (97)  all_57_6 = e2
% 230.75/42.03  | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (16), (17), (20), (25), (27), (29),
% 230.75/42.03  | | | | | | | | | | | | | | |            (41), (46), (94), (97) are inconsistent by
% 230.75/42.03  | | | | | | | | | | | | | | |            sub-proof #1469.
% 230.75/42.03  | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | Case 2:
% 230.75/42.03  | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | |   (98)  all_57_7 = e2 & op(e1, e2) = e2
% 230.75/42.03  | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | ALPHA: (98) implies:
% 230.75/42.03  | | | | | | | | | | | | | | |   (99)  all_57_7 = e2
% 230.75/42.03  | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | REF_CLOSE: (17), (60), (99) are inconsistent by sub-proof
% 230.75/42.03  | | | | | | | | | | | | | | |            #2102.
% 230.75/42.03  | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | End of split
% 230.75/42.03  | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | Case 2:
% 230.75/42.03  | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | |   (100)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 230.75/42.03  | | | | | | | | | | | | | |            e2 & op(e1, e0) = e2)
% 230.75/42.03  | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | BETA: splitting (100) gives:
% 230.75/42.03  | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | Case 1:
% 230.75/42.03  | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | |   (101)  all_57_8 = e2 & op(e1, e1) = e2
% 230.75/42.03  | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | ALPHA: (101) implies:
% 230.75/42.03  | | | | | | | | | | | | | | |   (102)  op(e1, e1) = e2
% 230.75/42.03  | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | BETA: splitting (53) gives:
% 230.75/42.03  | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | Case 1:
% 230.75/42.03  | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | |   (103)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 230.75/42.03  | | | | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 230.75/42.03  | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | BETA: splitting (103) gives:
% 230.75/42.03  | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | Case 1:
% 230.75/42.03  | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | |   (104)  all_57_1 = e1 & op(e3, e2) = e1
% 230.75/42.03  | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | ALPHA: (104) implies:
% 230.75/42.03  | | | | | | | | | | | | | | | | |   (105)  all_57_1 = e1
% 230.75/42.03  | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | BETA: splitting (19) gives:
% 230.75/42.03  | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | Case 1:
% 230.75/42.03  | | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | |   (106)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 230.75/42.03  | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e1)
% 230.75/42.03  | | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | | BETA: splitting (106) gives:
% 230.75/42.03  | | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | | Case 1:
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | | |   (107)  all_57_4 = e1 & op(e3, e1) = e1
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | ALPHA: (107) implies:
% 230.75/42.03  | | | | | | | | | | | | | | | | | | |   (108)  all_57_4 = e1
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | BETA: splitting (15) gives:
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | Case 1:
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | |   (109)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e0)
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (14), (16), (17), (18), (22), (27),
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | |            (29), (32), (46), (53), (65), (109) are
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1265.
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | Case 2:
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | | BETA: splitting (79) gives:
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (81), (108) imply:
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | | |   (110)  e1 = e0
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | | | SIMP: (110) implies:
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | | |   (111)  e1 = e0
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (105), (111) imply:
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | | |   (112)  all_57_1 = e0
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (14), (16), (17), (18), (27), (29),
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | | |            (32), (46), (53), (65), (112) are inconsistent by
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | | |            sub-proof #1281.
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | | |   (113)  all_57_9 = e0 & op(e3, e0) = e0
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | | | ALPHA: (113) implies:
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | | |   (114)  all_57_9 = e0
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (68), (114) are inconsistent by sub-proof
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | | |            #1657.
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | | End of split
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | End of split
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | | Case 2:
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | | |   (115)  all_57_5 = e1 & op(e2, e1) = e1
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | ALPHA: (115) implies:
% 230.75/42.03  | | | | | | | | | | | | | | | | | | |   (116)  all_57_5 = e1
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (13), (14), (15), (16), (17), (18),
% 230.75/42.03  | | | | | | | | | | | | | | | | | | |            (22), (25), (27), (28), (29), (32), (40), (46),
% 230.75/42.03  | | | | | | | | | | | | | | | | | | |            (53), (60), (73), (81), (116) are inconsistent by
% 230.75/42.03  | | | | | | | | | | | | | | | | | | |            sub-proof #1264.
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | | End of split
% 230.75/42.03  | | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | Case 2:
% 230.75/42.03  | | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | |   (117)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 230.75/42.03  | | | | | | | | | | | | | | | | | |            e1 & op(e0, e1) = e1)
% 230.75/42.03  | | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | | BETA: splitting (117) gives:
% 230.75/42.03  | | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | | Case 1:
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | | |   (118)  all_57_8 = e1 & op(e1, e1) = e1
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | ALPHA: (118) implies:
% 230.75/42.03  | | | | | | | | | | | | | | | | | | |   (119)  op(e1, e1) = e1
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (46), (102), (119) are inconsistent by
% 230.75/42.03  | | | | | | | | | | | | | | | | | | |            sub-proof #2423.
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | | Case 2:
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with e0, e1, e0, e0, simplifying
% 230.75/42.03  | | | | | | | | | | | | | | | | | | |              with (33), (38) gives:
% 230.75/42.03  | | | | | | | | | | | | | | | | | | |   (120)  e1 = e0
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (105), (120) imply:
% 230.75/42.03  | | | | | | | | | | | | | | | | | | |   (121)  all_57_1 = e0
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (14), (16), (17), (18), (27), (29),
% 230.75/42.03  | | | | | | | | | | | | | | | | | | |            (32), (46), (53), (65), (121) are inconsistent by
% 230.75/42.03  | | | | | | | | | | | | | | | | | | |            sub-proof #1281.
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | | End of split
% 230.75/42.03  | | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | End of split
% 230.75/42.03  | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | Case 2:
% 230.75/42.03  | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | |   (122)  all_57_3 = e1 & op(e2, e2) = e1
% 230.75/42.03  | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | ALPHA: (122) implies:
% 230.75/42.03  | | | | | | | | | | | | | | | | |   (123)  op(e2, e2) = e1
% 230.75/42.03  | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (17), (18), (27), (29), (41), (45), (46),
% 230.75/42.03  | | | | | | | | | | | | | | | | |            (73), (94), (123) are inconsistent by sub-proof
% 230.75/42.03  | | | | | | | | | | | | | | | | |            #1825.
% 230.75/42.03  | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | End of split
% 230.75/42.03  | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | Case 2:
% 230.75/42.03  | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | |   (124)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 230.75/42.03  | | | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 230.75/42.03  | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | BETA: splitting (124) gives:
% 230.75/42.03  | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | Case 1:
% 230.75/42.03  | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | |   (125)  all_57_7 = e1 & op(e1, e2) = e1
% 230.75/42.03  | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | ALPHA: (125) implies:
% 230.75/42.03  | | | | | | | | | | | | | | | | |   (126)  all_57_7 = e1
% 230.75/42.03  | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (13), (14), (15), (16), (17), (18),
% 230.75/42.03  | | | | | | | | | | | | | | | | |            (22), (25), (27), (28), (29), (32), (40), (46),
% 230.75/42.03  | | | | | | | | | | | | | | | | |            (53), (60), (73), (81), (94), (126) are
% 230.75/42.03  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1263.
% 230.75/42.03  | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | Case 2:
% 230.75/42.03  | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | |   (127)  all_57_13 = e1 & op(e0, e2) = e1
% 230.75/42.03  | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | ALPHA: (127) implies:
% 230.75/42.03  | | | | | | | | | | | | | | | | |   (128)  all_57_13 = e1
% 230.75/42.03  | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (5), (6), (8), (9), (11), (12), (13), (14),
% 230.75/42.03  | | | | | | | | | | | | | | | | |            (15), (16), (17), (18), (19), (21), (22), (23),
% 230.75/42.03  | | | | | | | | | | | | | | | | |            (27), (28), (29), (31), (32), (34), (35), (36),
% 230.75/42.03  | | | | | | | | | | | | | | | | |            (38), (39), (41), (46), (50), (53), (81), (128)
% 230.75/42.03  | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1275.
% 230.75/42.03  | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | End of split
% 230.75/42.03  | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | End of split
% 230.75/42.03  | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | Case 2:
% 230.75/42.03  | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | |   (129)  all_57_11 = e2 & op(e1, e0) = e2
% 230.75/42.03  | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | ALPHA: (129) implies:
% 230.75/42.03  | | | | | | | | | | | | | | |   (130)  all_57_11 = e2
% 230.75/42.03  | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (25), (29), (46), (52), (68), (130) are
% 230.75/42.03  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1668.
% 230.75/42.03  | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | End of split
% 230.75/42.03  | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | End of split
% 230.75/42.03  | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | Case 2:
% 230.75/42.03  | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | |   (131)  all_57_10 = e3 & op(e2, e0) = e3
% 230.75/42.03  | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | ALPHA: (131) implies:
% 230.75/42.03  | | | | | | | | | | | | |   (132)  all_57_10 = e3
% 230.75/42.03  | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | REF_CLOSE: (17), (25), (132) are inconsistent by sub-proof
% 230.75/42.03  | | | | | | | | | | | | |            #2356.
% 230.75/42.03  | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | End of split
% 230.75/42.03  | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | End of split
% 230.75/42.03  | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | Case 2:
% 230.75/42.03  | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | |   (133)  all_57_9 = e0 & op(e3, e0) = e0
% 230.75/42.03  | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | ALPHA: (133) implies:
% 230.75/42.03  | | | | | | | | | | |   (134)  all_57_9 = e0
% 230.75/42.03  | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | REF_CLOSE: (6), (9), (10), (11), (12), (14), (16), (17),
% 230.75/42.03  | | | | | | | | | | |            (18), (20), (25), (27), (29), (32), (36), (38),
% 230.75/42.03  | | | | | | | | | | |            (42), (44), (46), (47), (52), (53), (60), (65),
% 230.75/42.03  | | | | | | | | | | |            (134) are inconsistent by sub-proof #1261.
% 230.75/42.03  | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | End of split
% 230.75/42.03  | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | End of split
% 230.75/42.03  | | | | | | | | | 
% 230.75/42.03  | | | | | | | | End of split
% 230.75/42.03  | | | | | | | | 
% 230.75/42.03  | | | | | | | Case 2:
% 230.75/42.03  | | | | | | | | 
% 230.75/42.03  | | | | | | | |   (135)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 &
% 230.75/42.03  | | | | | | | |            op(e0, e3) = e1)
% 230.75/42.03  | | | | | | | | 
% 230.75/42.03  | | | | | | | | BETA: splitting (135) gives:
% 230.75/42.03  | | | | | | | | 
% 230.75/42.03  | | | | | | | | Case 1:
% 230.75/42.03  | | | | | | | | | 
% 230.75/42.03  | | | | | | | | |   (136)  all_57_6 = e1 & op(e1, e3) = e1
% 230.75/42.03  | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | REF_CLOSE: (20), (29), (136) are inconsistent by sub-proof
% 230.75/42.03  | | | | | | | | |            #2044.
% 230.75/42.03  | | | | | | | | | 
% 230.75/42.03  | | | | | | | | Case 2:
% 230.75/42.03  | | | | | | | | | 
% 230.75/42.03  | | | | | | | | |   (137)  all_57_12 = e1 & op(e0, e3) = e1
% 230.75/42.03  | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | ALPHA: (137) implies:
% 230.75/42.03  | | | | | | | | |   (138)  all_57_12 = e1
% 230.75/42.03  | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | BETA: splitting (34) gives:
% 230.75/42.03  | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | Case 1:
% 230.75/42.03  | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | |   (139)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 230.75/42.03  | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 230.75/42.03  | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | BETA: splitting (139) gives:
% 230.75/42.03  | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | Case 1:
% 230.75/42.03  | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | |   (140)  all_57_12 = e3 & op(e0, e3) = e3
% 230.75/42.03  | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | ALPHA: (140) implies:
% 230.75/42.03  | | | | | | | | | | |   (141)  all_57_12 = e3
% 230.75/42.03  | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | COMBINE_EQS: (138), (141) imply:
% 230.75/42.03  | | | | | | | | | | |   (142)  e3 = e1
% 230.75/42.03  | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10),
% 230.75/42.03  | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 230.75/42.03  | | | | | | | | | | |            (19), (21), (22), (23), (24), (26), (27), (28),
% 230.75/42.03  | | | | | | | | | | |            (29), (30), (31), (32), (34), (35), (36), (37),
% 230.75/42.03  | | | | | | | | | | |            (38), (39), (40), (41), (43), (44), (46), (47),
% 230.75/42.03  | | | | | | | | | | |            (48), (49), (50), (51), (52), (53), (54), (55),
% 230.75/42.03  | | | | | | | | | | |            (68), (142) are inconsistent by sub-proof #1260.
% 230.75/42.03  | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | Case 2:
% 230.75/42.03  | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | |   (143)  all_57_13 = e3 & op(e0, e2) = e3
% 230.75/42.03  | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | REF_CLOSE: (17), (65), (143) are inconsistent by sub-proof
% 230.75/42.03  | | | | | | | | | | |            #1358.
% 230.75/42.03  | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | End of split
% 230.75/42.03  | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | Case 2:
% 230.75/42.03  | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | |   (144)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 230.75/42.03  | | | | | | | | | |            e3 & op(e0, e0) = e3)
% 230.75/42.03  | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | BETA: splitting (144) gives:
% 230.75/42.03  | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | Case 1:
% 230.75/42.03  | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | |   (145)  all_57_14 = e3 & op(e0, e1) = e3
% 230.75/42.03  | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | ALPHA: (145) implies:
% 230.75/42.03  | | | | | | | | | | |   (146)  all_57_14 = e3
% 230.75/42.03  | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | BETA: splitting (53) gives:
% 230.75/42.03  | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | Case 1:
% 230.75/42.03  | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | |   (147)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 230.75/42.03  | | | | | | | | | | | |            & op(e2, e2) = e1)
% 230.75/42.03  | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | BETA: splitting (147) gives:
% 230.75/42.03  | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | Case 1:
% 230.75/42.03  | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | |   (148)  all_57_1 = e1 & op(e3, e2) = e1
% 230.75/42.03  | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | ALPHA: (148) implies:
% 230.75/42.03  | | | | | | | | | | | | |   (149)  all_57_1 = e1
% 230.75/42.03  | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | BETA: splitting (15) gives:
% 230.75/42.03  | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | Case 1:
% 230.75/42.03  | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | |   (150)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 230.75/42.03  | | | | | | | | | | | | | |            & op(e3, e2) = e0)
% 230.75/42.03  | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (14), (16), (17), (18), (22), (27),
% 230.75/42.03  | | | | | | | | | | | | | |            (29), (32), (46), (53), (65), (150) are
% 230.75/42.03  | | | | | | | | | | | | | |            inconsistent by sub-proof #1265.
% 230.75/42.03  | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | Case 2:
% 230.75/42.03  | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | |   (151)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 230.75/42.03  | | | | | | | | | | | | | |            & op(e3, e0) = e0)
% 230.75/42.03  | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | BETA: splitting (151) gives:
% 230.75/42.03  | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | Case 1:
% 230.75/42.03  | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | |   (152)  all_57_4 = e0 & op(e3, e1) = e0
% 230.75/42.03  | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | ALPHA: (152) implies:
% 230.75/42.03  | | | | | | | | | | | | | | |   (153)  all_57_4 = e0
% 230.75/42.03  | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | BETA: splitting (43) gives:
% 230.75/42.03  | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | Case 1:
% 230.75/42.03  | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | |   (154)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 230.75/42.03  | | | | | | | | | | | | | | | |            & op(e2, e3) = e3)
% 230.75/42.03  | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | BETA: splitting (154) gives:
% 230.75/42.03  | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | Case 1:
% 230.75/42.03  | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | |   (155)  all_57_0 = e3 & op(e3, e3) = e3
% 230.75/42.03  | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | ALPHA: (155) implies:
% 230.75/42.03  | | | | | | | | | | | | | | | | |   (156)  op(e3, e3) = e3
% 230.75/42.03  | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (17), (22), (156) are inconsistent by
% 230.75/42.03  | | | | | | | | | | | | | | | | |            sub-proof #2490.
% 230.75/42.03  | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | Case 2:
% 230.75/42.03  | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | |   (157)  all_57_2 = e3 & op(e2, e3) = e3
% 230.75/42.03  | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | ALPHA: (157) implies:
% 230.75/42.03  | | | | | | | | | | | | | | | | |   (158)  all_57_2 = e3
% 230.75/42.03  | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | BETA: splitting (40) gives:
% 230.75/42.03  | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | Case 1:
% 230.75/42.03  | | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | |   (159)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 230.75/42.03  | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e3)
% 230.75/42.03  | | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | | BETA: splitting (159) gives:
% 230.75/42.03  | | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | | Case 1:
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (9) with e0, e1, e0, e0, simplifying
% 230.75/42.03  | | | | | | | | | | | | | | | | | | |              with (33), (38) gives:
% 230.75/42.03  | | | | | | | | | | | | | | | | | | |   (160)  e1 = e0
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (149), (160) imply:
% 230.75/42.03  | | | | | | | | | | | | | | | | | | |   (161)  all_57_1 = e0
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (14), (16), (17), (18), (27), (29),
% 230.75/42.03  | | | | | | | | | | | | | | | | | | |            (32), (46), (53), (65), (161) are inconsistent by
% 230.75/42.03  | | | | | | | | | | | | | | | | | | |            sub-proof #1281.
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | | Case 2:
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | | |   (162)  all_57_3 = e3 & op(e2, e2) = e3
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | ALPHA: (162) implies:
% 230.75/42.03  | | | | | | | | | | | | | | | | | | |   (163)  all_57_3 = e3
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (16), (163) imply:
% 230.75/42.03  | | | | | | | | | | | | | | | | | | |   (164)  e3 = e0
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (16), (17), (18), (27), (29), (40),
% 230.75/42.03  | | | | | | | | | | | | | | | | | | |            (41), (46), (158), (164) are inconsistent by
% 230.75/42.03  | | | | | | | | | | | | | | | | | | |            sub-proof #1333.
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | | End of split
% 230.75/42.03  | | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | Case 2:
% 230.75/42.03  | | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | |   (165)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 230.75/42.03  | | | | | | | | | | | | | | | | | |            e3 & op(e2, e0) = e3)
% 230.75/42.03  | | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | | BETA: splitting (165) gives:
% 230.75/42.03  | | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | | Case 1:
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | | |   (166)  all_57_5 = e3 & op(e2, e1) = e3
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | ALPHA: (166) implies:
% 230.75/42.03  | | | | | | | | | | | | | | | | | | |   (167)  all_57_5 = e3
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (16), (25), (29), (46), (158), (167) are
% 230.75/42.03  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1804.
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | | Case 2:
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | | |   (168)  all_57_10 = e3 & op(e2, e0) = e3
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | ALPHA: (168) implies:
% 230.75/42.03  | | | | | | | | | | | | | | | | | | |   (169)  all_57_10 = e3
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (16), (17), (27), (29), (41), (46),
% 230.75/42.03  | | | | | | | | | | | | | | | | | | |            (158), (169) are inconsistent by sub-proof #1433.
% 230.75/42.03  | | | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | | End of split
% 230.75/42.03  | | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | | End of split
% 230.75/42.03  | | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | End of split
% 230.75/42.03  | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | Case 2:
% 230.75/42.03  | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | |   (170)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 230.75/42.03  | | | | | | | | | | | | | | | |            e3 & op(e0, e3) = e3)
% 230.75/42.03  | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | BETA: splitting (170) gives:
% 230.75/42.03  | | | | | | | | | | | | | | | | 
% 230.75/42.03  | | | | | | | | | | | | | | | | Case 1:
% 230.75/42.03  | | | | | | | | | | | | | | | | | 
% 230.75/42.04  | | | | | | | | | | | | | | | | |   (171)  all_57_6 = e3 & op(e1, e3) = e3
% 230.75/42.04  | | | | | | | | | | | | | | | | | 
% 230.75/42.04  | | | | | | | | | | | | | | | | | ALPHA: (171) implies:
% 230.75/42.04  | | | | | | | | | | | | | | | | |   (172)  all_57_6 = e3
% 230.75/42.04  | | | | | | | | | | | | | | | | | 
% 230.75/42.04  | | | | | | | | | | | | | | | | | COMBINE_EQS: (20), (172) imply:
% 230.75/42.04  | | | | | | | | | | | | | | | | |   (173)  e3 = e0
% 230.75/42.04  | | | | | | | | | | | | | | | | | 
% 230.75/42.04  | | | | | | | | | | | | | | | | | COMBINE_EQS: (60), (173) imply:
% 230.75/42.04  | | | | | | | | | | | | | | | | |   (174)  all_57_7 = e0
% 230.75/42.04  | | | | | | | | | | | | | | | | | 
% 230.75/42.04  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (14), (16), (17), (18), (29), (32),
% 230.75/42.04  | | | | | | | | | | | | | | | | |            (46), (53), (65), (174) are inconsistent by
% 230.75/42.04  | | | | | | | | | | | | | | | | |            sub-proof #2202.
% 230.75/42.04  | | | | | | | | | | | | | | | | | 
% 230.75/42.04  | | | | | | | | | | | | | | | | Case 2:
% 230.75/42.04  | | | | | | | | | | | | | | | | | 
% 230.75/42.04  | | | | | | | | | | | | | | | | |   (175)  all_57_12 = e3 & op(e0, e3) = e3
% 230.75/42.04  | | | | | | | | | | | | | | | | | 
% 230.75/42.04  | | | | | | | | | | | | | | | | | ALPHA: (175) implies:
% 230.75/42.04  | | | | | | | | | | | | | | | | |   (176)  all_57_12 = e3
% 230.75/42.04  | | | | | | | | | | | | | | | | | 
% 230.75/42.04  | | | | | | | | | | | | | | | | | COMBINE_EQS: (138), (176) imply:
% 230.75/42.04  | | | | | | | | | | | | | | | | |   (177)  e3 = e1
% 230.75/42.04  | | | | | | | | | | | | | | | | | 
% 230.75/42.04  | | | | | | | | | | | | | | | | | COMBINE_EQS: (68), (177) imply:
% 230.75/42.04  | | | | | | | | | | | | | | | | |   (178)  all_57_9 = e1
% 230.75/42.04  | | | | | | | | | | | | | | | | | 
% 230.75/42.04  | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10),
% 230.75/42.04  | | | | | | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 230.75/42.04  | | | | | | | | | | | | | | | | |            (21), (22), (23), (27), (28), (29), (31), (32),
% 230.75/42.04  | | | | | | | | | | | | | | | | |            (34), (35), (36), (38), (39), (40), (41), (43),
% 230.75/42.04  | | | | | | | | | | | | | | | | |            (46), (47), (48), (50), (51), (52), (53), (138),
% 230.75/42.04  | | | | | | | | | | | | | | | | |            (153), (178) are inconsistent by sub-proof #1276.
% 230.75/42.04  | | | | | | | | | | | | | | | | | 
% 230.75/42.04  | | | | | | | | | | | | | | | | End of split
% 230.75/42.04  | | | | | | | | | | | | | | | | 
% 230.75/42.04  | | | | | | | | | | | | | | | End of split
% 230.75/42.04  | | | | | | | | | | | | | | | 
% 230.75/42.04  | | | | | | | | | | | | | | Case 2:
% 230.75/42.04  | | | | | | | | | | | | | | | 
% 230.75/42.04  | | | | | | | | | | | | | | |   (179)  all_57_9 = e0 & op(e3, e0) = e0
% 230.75/42.04  | | | | | | | | | | | | | | | 
% 230.75/42.04  | | | | | | | | | | | | | | | ALPHA: (179) implies:
% 230.75/42.04  | | | | | | | | | | | | | | |   (180)  all_57_9 = e0
% 230.75/42.04  | | | | | | | | | | | | | | | 
% 230.75/42.04  | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (10), (11), (12), (14), (16), (17),
% 230.75/42.04  | | | | | | | | | | | | | | |            (18), (20), (25), (27), (29), (32), (36), (38),
% 230.75/42.04  | | | | | | | | | | | | | | |            (42), (44), (46), (47), (52), (53), (60), (65),
% 230.75/42.04  | | | | | | | | | | | | | | |            (180) are inconsistent by sub-proof #1261.
% 230.75/42.04  | | | | | | | | | | | | | | | 
% 230.75/42.04  | | | | | | | | | | | | | | End of split
% 230.75/42.04  | | | | | | | | | | | | | | 
% 230.75/42.04  | | | | | | | | | | | | | End of split
% 230.75/42.04  | | | | | | | | | | | | | 
% 230.75/42.04  | | | | | | | | | | | | Case 2:
% 230.75/42.04  | | | | | | | | | | | | | 
% 230.75/42.04  | | | | | | | | | | | | |   (181)  all_57_3 = e1 & op(e2, e2) = e1
% 230.75/42.04  | | | | | | | | | | | | | 
% 230.75/42.04  | | | | | | | | | | | | | ALPHA: (181) implies:
% 230.75/42.04  | | | | | | | | | | | | |   (182)  op(e2, e2) = e1
% 230.75/42.04  | | | | | | | | | | | | | 
% 230.75/42.04  | | | | | | | | | | | | | REF_CLOSE: (9), (14), (29), (182) are inconsistent by
% 230.75/42.04  | | | | | | | | | | | | |            sub-proof #2352.
% 230.75/42.04  | | | | | | | | | | | | | 
% 230.75/42.04  | | | | | | | | | | | | End of split
% 230.75/42.04  | | | | | | | | | | | | 
% 230.75/42.04  | | | | | | | | | | | Case 2:
% 230.75/42.04  | | | | | | | | | | | | 
% 230.75/42.04  | | | | | | | | | | | |   (183)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 230.75/42.04  | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 230.75/42.04  | | | | | | | | | | | | 
% 230.75/42.04  | | | | | | | | | | | | BETA: splitting (183) gives:
% 230.75/42.04  | | | | | | | | | | | | 
% 230.75/42.04  | | | | | | | | | | | | Case 1:
% 230.75/42.04  | | | | | | | | | | | | | 
% 230.75/42.04  | | | | | | | | | | | | |   (184)  all_57_7 = e1 & op(e1, e2) = e1
% 230.75/42.04  | | | | | | | | | | | | | 
% 230.75/42.04  | | | | | | | | | | | | | ALPHA: (184) implies:
% 230.75/42.04  | | | | | | | | | | | | |   (185)  all_57_7 = e1
% 230.75/42.04  | | | | | | | | | | | | | 
% 230.75/42.04  | | | | | | | | | | | | | COMBINE_EQS: (60), (185) imply:
% 230.75/42.04  | | | | | | | | | | | | |   (186)  e3 = e1
% 230.75/42.04  | | | | | | | | | | | | | 
% 230.75/42.04  | | | | | | | | | | | | | COMBINE_EQS: (68), (186) imply:
% 230.75/42.04  | | | | | | | | | | | | |   (187)  all_57_9 = e1
% 230.75/42.04  | | | | | | | | | | | | | 
% 230.75/42.04  | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10),
% 230.75/42.04  | | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 230.75/42.04  | | | | | | | | | | | | |            (19), (21), (22), (23), (24), (26), (27), (28),
% 230.75/42.04  | | | | | | | | | | | | |            (29), (30), (31), (32), (34), (35), (36), (37),
% 230.75/42.04  | | | | | | | | | | | | |            (38), (39), (40), (41), (43), (44), (46), (47),
% 230.75/42.04  | | | | | | | | | | | | |            (48), (49), (50), (51), (52), (53), (54), (55),
% 230.75/42.04  | | | | | | | | | | | | |            (187) are inconsistent by sub-proof #1266.
% 230.75/42.04  | | | | | | | | | | | | | 
% 230.75/42.04  | | | | | | | | | | | | Case 2:
% 230.75/42.04  | | | | | | | | | | | | | 
% 230.75/42.04  | | | | | | | | | | | | |   (188)  all_57_13 = e1 & op(e0, e2) = e1
% 230.75/42.04  | | | | | | | | | | | | | 
% 230.75/42.04  | | | | | | | | | | | | | ALPHA: (188) implies:
% 230.75/42.04  | | | | | | | | | | | | |   (189)  all_57_13 = e1
% 230.75/42.04  | | | | | | | | | | | | | 
% 230.75/42.04  | | | | | | | | | | | | | REF_CLOSE: (9), (17), (21), (23), (35), (38), (46), (146),
% 230.75/42.04  | | | | | | | | | | | | |            (189) are inconsistent by sub-proof #1976.
% 230.75/42.04  | | | | | | | | | | | | | 
% 230.75/42.04  | | | | | | | | | | | | End of split
% 230.75/42.04  | | | | | | | | | | | | 
% 230.75/42.04  | | | | | | | | | | | End of split
% 230.75/42.04  | | | | | | | | | | | 
% 230.75/42.04  | | | | | | | | | | Case 2:
% 230.75/42.04  | | | | | | | | | | | 
% 230.75/42.04  | | | | | | | | | | |   (190)  all_57_15 = e3 & op(e0, e0) = e3
% 230.75/42.04  | | | | | | | | | | | 
% 230.75/42.04  | | | | | | | | | | | ALPHA: (190) implies:
% 230.75/42.04  | | | | | | | | | | |   (191)  op(e0, e0) = e3
% 230.75/42.04  | | | | | | | | | | | 
% 230.75/42.04  | | | | | | | | | | | REF_CLOSE: (6), (9), (38), (191) are inconsistent by
% 230.75/42.04  | | | | | | | | | | |            sub-proof #2183.
% 230.75/42.04  | | | | | | | | | | | 
% 230.75/42.04  | | | | | | | | | | End of split
% 230.75/42.04  | | | | | | | | | | 
% 230.75/42.04  | | | | | | | | | End of split
% 230.75/42.04  | | | | | | | | | 
% 230.75/42.04  | | | | | | | | End of split
% 230.75/42.04  | | | | | | | | 
% 230.75/42.04  | | | | | | | End of split
% 230.75/42.04  | | | | | | | 
% 230.75/42.04  | | | | | | Case 2:
% 230.75/42.04  | | | | | | | 
% 230.75/42.04  | | | | | | |   (192)  all_57_10 = e3 & op(e2, e0) = e3
% 230.75/42.04  | | | | | | | 
% 230.75/42.04  | | | | | | | REF_CLOSE: (17), (25), (192) are inconsistent by sub-proof #2051.
% 230.75/42.04  | | | | | | | 
% 230.75/42.04  | | | | | | End of split
% 230.75/42.04  | | | | | | 
% 230.75/42.04  | | | | | Case 2:
% 230.75/42.04  | | | | | | 
% 230.75/42.04  | | | | | |   (193)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 &
% 230.75/42.04  | | | | | |            op(e0, e0) = e3)
% 230.75/42.04  | | | | | | 
% 230.75/42.04  | | | | | | REF_CLOSE: (6), (9), (38), (42), (193) are inconsistent by sub-proof
% 230.75/42.04  | | | | | |            #1259.
% 230.75/42.04  | | | | | | 
% 230.75/42.04  | | | | | End of split
% 230.75/42.04  | | | | | 
% 230.75/42.04  | | | | End of split
% 230.75/42.04  | | | | 
% 230.75/42.04  | | | End of split
% 230.75/42.04  | | | 
% 230.75/42.04  | | End of split
% 230.75/42.04  | | 
% 230.75/42.04  | Case 2:
% 230.75/42.04  | | 
% 230.75/42.04  | |   (194)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 230.75/42.04  | |            e3)
% 230.75/42.04  | | 
% 230.75/42.04  | | REF_CLOSE: (6), (9), (11), (12), (42), (194) are inconsistent by sub-proof
% 230.75/42.04  | |            #2004.
% 230.75/42.04  | | 
% 230.75/42.04  | End of split
% 230.75/42.04  | 
% 230.75/42.04  End of proof
% 230.75/42.04  
% 230.75/42.04  Sub-proof #1259 shows that the following formulas are inconsistent:
% 230.75/42.04  ----------------------------------------------------------------
% 230.75/42.04    (1)   ~ (e3 = e1)
% 230.75/42.04    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.75/42.04           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.75/42.04    (3)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 230.75/42.04    (4)  op(e0, e0) = e1
% 230.75/42.04    (5)  all_57_11 = e1
% 230.75/42.04  
% 230.75/42.04  Begin of proof
% 230.75/42.04  | 
% 230.75/42.04  | BETA: splitting (3) gives:
% 230.75/42.04  | 
% 230.75/42.04  | Case 1:
% 230.75/42.04  | | 
% 230.75/42.04  | |   (6)  all_57_11 = e3 & op(e1, e0) = e3
% 230.75/42.04  | | 
% 230.75/42.04  | | REF_CLOSE: (1), (5), (6) are inconsistent by sub-proof #1820.
% 230.75/42.04  | | 
% 230.75/42.04  | Case 2:
% 230.75/42.04  | | 
% 230.75/42.04  | |   (7)  all_57_15 = e3 & op(e0, e0) = e3
% 230.75/42.04  | | 
% 230.75/42.04  | | ALPHA: (7) implies:
% 230.75/42.04  | |   (8)  op(e0, e0) = e3
% 230.75/42.04  | | 
% 230.75/42.04  | | REF_CLOSE: (1), (2), (4), (8) are inconsistent by sub-proof #2183.
% 230.75/42.04  | | 
% 230.75/42.04  | End of split
% 230.75/42.04  | 
% 230.75/42.04  End of proof
% 230.75/42.04  
% 230.75/42.04  Sub-proof #1260 shows that the following formulas are inconsistent:
% 230.75/42.04  ----------------------------------------------------------------
% 230.75/42.04    (1)  all_57_0 = e2
% 230.75/42.04    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.75/42.04         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.75/42.04    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.75/42.04         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.75/42.04    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.75/42.04         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.75/42.04    (5)   ~ (e3 = e1)
% 230.75/42.04    (6)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.75/42.04         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.75/42.04    (7)   ~ (all_53_13 = e1)
% 230.75/42.04    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.75/42.04           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.75/42.04    (9)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.75/42.04         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.75/42.04    (10)   ~ (all_6_2 = e3)
% 230.75/42.04    (11)  op(e1, e1) = all_6_2
% 230.75/42.04    (12)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.75/42.04          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.75/42.04    (13)  op(e2, e2) = e0
% 230.75/42.04    (14)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.75/42.04          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.75/42.04    (15)  all_57_3 = e0
% 230.75/42.04    (16)   ~ (e3 = e2)
% 230.75/42.04    (17)   ~ (e3 = e0)
% 230.75/42.04    (18)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.75/42.04          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.75/42.04    (19)  op(e0, e3) = all_53_3
% 230.75/42.04    (20)  op(e3, e3) = e2
% 230.75/42.04    (21)   ~ (all_53_3 = e2)
% 230.75/42.04    (22)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.75/42.04          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.75/42.04            e1)
% 230.75/42.04    (23)  op(e3, e2) = all_53_4
% 230.75/42.04    (24)   ~ (e2 = e0)
% 230.75/42.04    (25)  all_57_9 = e3
% 230.75/42.04    (26)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.75/42.04          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.75/42.04    (27)   ~ (e1 = e0)
% 230.75/42.04    (28)   ~ (all_53_4 = e0)
% 230.75/42.04    (29)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 230.75/42.04          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 230.75/42.04    (30)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.75/42.04          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.75/42.04    (31)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.75/42.04          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 230.75/42.04            e3)
% 230.75/42.04    (32)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.75/42.04          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.75/42.04            e2)
% 230.75/42.04    (33)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.75/42.04              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.75/42.04                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.75/42.04                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.75/42.04    (34)   ~ (all_53_13 = e0)
% 230.75/42.04    (35)  op(e0, e0) = e1
% 230.75/42.04    (36)  op(e2, e0) = all_53_13
% 230.75/42.04    (37)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.75/42.04          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.75/42.04    (38)  e3 = e1
% 230.75/42.04    (39)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.75/42.04          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.75/42.04    (40)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.75/42.04          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.75/42.04    (41)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 230.75/42.04          (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 230.75/42.04    (42)   ~ (e2 = e1)
% 230.75/42.04    (43)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.75/42.04          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.75/42.04    (44)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.75/42.04          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.75/42.04    (45)   ~ (all_53_12 = e2)
% 230.75/42.04    (46)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.75/42.04          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.75/42.04    (47)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.75/42.04          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.75/42.04    (48)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.75/42.04          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.75/42.04    (49)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.75/42.04          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.75/42.04    (50)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.75/42.04          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.75/42.04    (51)  op(e3, e0) = all_53_12
% 230.75/42.04  
% 230.75/42.04  Begin of proof
% 230.75/42.04  | 
% 230.75/42.04  | SIMP: (38) implies:
% 230.75/42.04  |   (52)  e3 = e1
% 230.75/42.04  | 
% 230.75/42.04  | COMBINE_EQS: (25), (52) imply:
% 230.75/42.04  |   (53)  all_57_9 = e1
% 230.75/42.04  | 
% 230.75/42.04  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 230.75/42.04  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 230.75/42.04  |            (24), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 230.75/42.04  |            (36), (37), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 230.75/42.04  |            (48), (49), (50), (51), (53) are inconsistent by sub-proof #1266.
% 230.75/42.04  | 
% 230.75/42.04  End of proof
% 230.75/42.04  
% 230.75/42.04  Sub-proof #1261 shows that the following formulas are inconsistent:
% 230.75/42.04  ----------------------------------------------------------------
% 230.75/42.04    (1)   ~ (e3 = e1)
% 230.75/42.04    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.75/42.04           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.75/42.04    (3)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.75/42.04         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.75/42.04    (4)   ~ (all_6_2 = e3)
% 230.75/42.04    (5)  op(e1, e1) = all_6_2
% 230.75/42.05    (6)  op(e2, e2) = e0
% 230.75/42.05    (7)  all_57_3 = e0
% 230.75/42.05    (8)   ~ (e3 = e2)
% 230.75/42.05    (9)   ~ (e3 = e0)
% 230.75/42.05    (10)  all_57_6 = e0
% 230.75/42.05    (11)  all_57_10 = e2
% 230.75/42.05    (12)  all_57_9 = e0
% 230.75/42.05    (13)   ~ (e2 = e0)
% 230.75/42.05    (14)  all_57_13 = e2
% 230.75/42.05    (15)   ~ (e1 = e0)
% 230.75/42.05    (16)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.75/42.05          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.75/42.05    (17)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.75/42.05              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.75/42.05                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.75/42.05                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.75/42.05    (18)  op(e0, e0) = e1
% 230.75/42.05    (19)  all_57_7 = e3
% 230.75/42.05    (20)  all_57_11 = e1
% 230.75/42.05    (21)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 230.75/42.05          (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 230.75/42.05    (22)   ~ (e2 = e1)
% 230.75/42.05    (23)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.75/42.05          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.75/42.05    (24)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.75/42.05          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.75/42.05    (25)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.75/42.05          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.75/42.05  
% 230.75/42.05  Begin of proof
% 230.75/42.05  | 
% 230.75/42.05  | BETA: splitting (21) gives:
% 230.75/42.05  | 
% 230.75/42.05  | Case 1:
% 230.75/42.05  | | 
% 230.75/42.05  | |   (26)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 230.75/42.05  | |           e3)
% 230.75/42.05  | | 
% 230.75/42.05  | | BETA: splitting (26) gives:
% 230.75/42.05  | | 
% 230.75/42.05  | | Case 1:
% 230.75/42.05  | | | 
% 230.75/42.05  | | |   (27)  all_57_9 = e3 & op(e3, e0) = e3
% 230.75/42.05  | | | 
% 230.75/42.05  | | | ALPHA: (27) implies:
% 230.75/42.05  | | |   (28)  all_57_9 = e3
% 230.75/42.05  | | | 
% 230.75/42.05  | | | COMBINE_EQS: (12), (28) imply:
% 230.75/42.05  | | |   (29)  e3 = e0
% 230.75/42.05  | | | 
% 230.75/42.05  | | | COMBINE_EQS: (19), (29) imply:
% 230.75/42.05  | | |   (30)  all_57_7 = e0
% 230.75/42.05  | | | 
% 230.75/42.05  | | | REF_CLOSE: (1), (2), (6), (7), (8), (9), (14), (15), (16), (22), (25),
% 230.75/42.05  | | |            (30) are inconsistent by sub-proof #2202.
% 230.75/42.05  | | | 
% 230.75/42.05  | | Case 2:
% 230.75/42.05  | | | 
% 230.75/42.05  | | |   (31)  all_57_10 = e3 & op(e2, e0) = e3
% 230.75/42.05  | | | 
% 230.75/42.05  | | | ALPHA: (31) implies:
% 230.75/42.05  | | |   (32)  all_57_10 = e3
% 230.75/42.05  | | | 
% 230.75/42.05  | | | COMBINE_EQS: (11), (32) imply:
% 230.75/42.05  | | |   (33)  e3 = e2
% 230.75/42.05  | | | 
% 230.75/42.05  | | | COMBINE_EQS: (19), (33) imply:
% 230.75/42.05  | | |   (34)  all_57_7 = e2
% 230.75/42.05  | | | 
% 230.75/42.05  | | | REF_CLOSE: (1), (2), (3), (4), (5), (8), (9), (10), (11), (12), (13),
% 230.75/42.05  | | |            (15), (17), (20), (21), (22), (23), (24), (34) are inconsistent
% 230.75/42.05  | | |            by sub-proof #1262.
% 230.75/42.05  | | | 
% 230.75/42.05  | | End of split
% 230.75/42.05  | | 
% 230.75/42.05  | Case 2:
% 230.75/42.05  | | 
% 230.75/42.05  | |   (35)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 230.75/42.05  | |           e3)
% 230.75/42.05  | | 
% 230.75/42.05  | | REF_CLOSE: (1), (2), (18), (20), (35) are inconsistent by sub-proof #2050.
% 230.75/42.05  | | 
% 230.75/42.05  | End of split
% 230.75/42.05  | 
% 230.75/42.05  End of proof
% 230.75/42.05  
% 230.75/42.05  Sub-proof #1262 shows that the following formulas are inconsistent:
% 230.75/42.05  ----------------------------------------------------------------
% 230.75/42.05    (1)   ~ (e3 = e1)
% 230.75/42.05    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.75/42.05           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.75/42.05    (3)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.75/42.05         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.75/42.05    (4)   ~ (all_6_2 = e3)
% 230.75/42.05    (5)  op(e1, e1) = all_6_2
% 230.75/42.05    (6)  all_57_7 = e2
% 230.75/42.05    (7)   ~ (e3 = e2)
% 230.75/42.05    (8)   ~ (e3 = e0)
% 230.75/42.05    (9)  all_57_6 = e0
% 230.75/42.05    (10)  all_57_10 = e2
% 230.75/42.05    (11)  all_57_9 = e0
% 230.75/42.05    (12)   ~ (e2 = e0)
% 230.75/42.05    (13)   ~ (e1 = e0)
% 230.75/42.05    (14)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.75/42.05              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.75/42.05                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.75/42.05                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.75/42.05    (15)  all_57_11 = e1
% 230.75/42.05    (16)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 230.75/42.05          (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 230.75/42.05    (17)   ~ (e2 = e1)
% 230.75/42.05    (18)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.75/42.05          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.75/42.05    (19)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.75/42.05          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.75/42.05  
% 230.75/42.05  Begin of proof
% 230.75/42.05  | 
% 230.75/42.05  | BETA: splitting (16) gives:
% 230.75/42.05  | 
% 230.75/42.05  | Case 1:
% 230.75/42.05  | | 
% 230.75/42.05  | |   (20)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 230.75/42.05  | |           e3)
% 230.75/42.05  | | 
% 230.75/42.05  | | BETA: splitting (20) gives:
% 230.75/42.05  | | 
% 230.75/42.05  | | Case 1:
% 230.75/42.05  | | | 
% 230.75/42.05  | | |   (21)  all_57_9 = e3 & op(e3, e0) = e3
% 230.75/42.05  | | | 
% 230.75/42.05  | | | ALPHA: (21) implies:
% 230.75/42.05  | | |   (22)  all_57_9 = e3
% 230.75/42.05  | | | 
% 230.75/42.05  | | | REF_CLOSE: (8), (11), (22) are inconsistent by sub-proof #1657.
% 230.75/42.05  | | | 
% 230.75/42.05  | | Case 2:
% 230.75/42.05  | | | 
% 230.75/42.05  | | |   (23)  all_57_10 = e3 & op(e2, e0) = e3
% 230.75/42.05  | | | 
% 230.75/42.05  | | | ALPHA: (23) implies:
% 230.75/42.05  | | |   (24)  all_57_10 = e3
% 230.75/42.05  | | | 
% 230.75/42.05  | | | REF_CLOSE: (7), (10), (24) are inconsistent by sub-proof #2356.
% 230.75/42.05  | | | 
% 230.75/42.05  | | End of split
% 230.75/42.05  | | 
% 230.75/42.05  | Case 2:
% 230.75/42.05  | | 
% 230.75/42.05  | |   (25)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 230.75/42.05  | |           e3)
% 230.75/42.05  | | 
% 230.75/42.05  | | BETA: splitting (25) gives:
% 230.75/42.05  | | 
% 230.75/42.05  | | Case 1:
% 230.75/42.05  | | | 
% 230.75/42.05  | | |   (26)  all_57_11 = e3 & op(e1, e0) = e3
% 230.75/42.05  | | | 
% 230.75/42.05  | | | ALPHA: (26) implies:
% 230.75/42.05  | | |   (27)  all_57_11 = e3
% 230.75/42.05  | | | 
% 230.75/42.05  | | | REF_CLOSE: (1), (15), (27) are inconsistent by sub-proof #2218.
% 230.75/42.05  | | | 
% 230.75/42.05  | | Case 2:
% 230.75/42.05  | | | 
% 230.75/42.05  | | |   (28)  all_57_15 = e3 & op(e0, e0) = e3
% 230.75/42.05  | | | 
% 230.75/42.05  | | | ALPHA: (28) implies:
% 230.75/42.05  | | |   (29)  all_57_15 = e3
% 230.75/42.05  | | | 
% 230.75/42.05  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (12), (13), (14),
% 230.75/42.05  | | |            (17), (18), (19), (29) are inconsistent by sub-proof #1775.
% 230.75/42.05  | | | 
% 230.75/42.05  | | End of split
% 230.75/42.05  | | 
% 230.75/42.05  | End of split
% 230.75/42.05  | 
% 230.75/42.05  End of proof
% 230.75/42.05  
% 230.75/42.05  Sub-proof #1263 shows that the following formulas are inconsistent:
% 230.75/42.05  ----------------------------------------------------------------
% 230.75/42.05    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.75/42.05         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.75/42.05    (2)   ~ (e3 = e1)
% 230.75/42.05    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.75/42.05           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.75/42.05    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.75/42.05         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.75/42.05    (5)  all_57_4 = e0
% 230.75/42.05    (6)  all_57_7 = e1
% 230.75/42.05    (7)  op(e2, e2) = e0
% 230.75/42.05    (8)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.75/42.05         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.75/42.05    (9)  all_57_3 = e0
% 230.75/42.05    (10)   ~ (e3 = e2)
% 230.75/42.05    (11)   ~ (e3 = e0)
% 230.75/42.05    (12)  op(e3, e3) = e2
% 230.75/42.05    (13)  all_57_10 = e2
% 230.75/42.05    (14)  all_57_5 = e3
% 230.75/42.05    (15)   ~ (e2 = e0)
% 230.75/42.05    (16)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.75/42.05          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.75/42.05    (17)   ~ (e1 = e0)
% 230.75/42.05    (18)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.75/42.05          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.75/42.05    (19)  all_57_2 = e1
% 230.75/42.05    (20)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.75/42.05          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.75/42.05    (21)  all_57_7 = e3
% 230.75/42.05    (22)   ~ (e2 = e1)
% 230.75/42.05    (23)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.75/42.05          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.75/42.05  
% 230.75/42.05  Begin of proof
% 230.75/42.05  | 
% 230.75/42.05  | COMBINE_EQS: (6), (21) imply:
% 230.75/42.05  |   (24)  e3 = e1
% 230.75/42.05  | 
% 230.75/42.05  | SIMP: (24) implies:
% 230.75/42.05  |   (25)  e3 = e1
% 230.75/42.05  | 
% 230.75/42.05  | COMBINE_EQS: (14), (25) imply:
% 230.75/42.05  |   (26)  all_57_5 = e1
% 230.75/42.05  | 
% 230.75/42.05  | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 230.75/42.05  |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (26) are
% 230.75/42.05  |            inconsistent by sub-proof #1264.
% 230.75/42.05  | 
% 230.75/42.05  End of proof
% 230.75/42.05  
% 230.75/42.05  Sub-proof #1264 shows that the following formulas are inconsistent:
% 230.75/42.05  ----------------------------------------------------------------
% 230.75/42.05    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.75/42.05         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.75/42.05    (2)   ~ (e3 = e1)
% 230.75/42.05    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.75/42.05           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.75/42.05    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.75/42.05         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.75/42.05    (5)  all_57_4 = e0
% 230.75/42.05    (6)  op(e2, e2) = e0
% 230.75/42.05    (7)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.75/42.05         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.75/42.05    (8)  all_57_3 = e0
% 230.75/42.05    (9)   ~ (e3 = e2)
% 230.75/42.05    (10)   ~ (e3 = e0)
% 230.75/42.05    (11)  op(e3, e3) = e2
% 230.75/42.05    (12)  all_57_10 = e2
% 230.75/42.05    (13)   ~ (e2 = e0)
% 230.75/42.05    (14)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.75/42.05          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.75/42.05    (15)   ~ (e1 = e0)
% 230.75/42.05    (16)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.75/42.05          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.75/42.05    (17)  all_57_2 = e1
% 230.75/42.05    (18)  all_57_5 = e1
% 230.75/42.05    (19)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.75/42.05          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.75/42.05    (20)  all_57_7 = e3
% 230.75/42.05    (21)   ~ (e2 = e1)
% 230.75/42.05    (22)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.75/42.05          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.75/42.05  
% 230.75/42.05  Begin of proof
% 230.75/42.05  | 
% 230.75/42.05  | BETA: splitting (19) gives:
% 230.75/42.05  | 
% 230.75/42.05  | Case 1:
% 230.75/42.05  | | 
% 230.75/42.05  | |   (23)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 230.75/42.05  | |           e3)
% 230.75/42.05  | | 
% 230.75/42.05  | | BETA: splitting (23) gives:
% 230.75/42.05  | | 
% 230.75/42.05  | | Case 1:
% 230.75/42.05  | | | 
% 230.75/42.05  | | |   (24)  all_57_2 = e3 & op(e2, e3) = e3
% 230.75/42.05  | | | 
% 230.75/42.05  | | | ALPHA: (24) implies:
% 230.75/42.05  | | |   (25)  all_57_2 = e3
% 230.75/42.05  | | | 
% 230.75/42.05  | | | REF_CLOSE: (2), (17), (25) are inconsistent by sub-proof #2397.
% 230.75/42.05  | | | 
% 230.75/42.05  | | Case 2:
% 230.75/42.05  | | | 
% 230.75/42.05  | | |   (26)  all_57_3 = e3 & op(e2, e2) = e3
% 230.75/42.05  | | | 
% 230.75/42.05  | | | ALPHA: (26) implies:
% 230.75/42.05  | | |   (27)  all_57_3 = e3
% 230.75/42.05  | | | 
% 230.75/42.05  | | | COMBINE_EQS: (8), (27) imply:
% 230.75/42.05  | | |   (28)  e3 = e0
% 230.75/42.05  | | | 
% 230.75/42.05  | | | SIMP: (28) implies:
% 230.75/42.05  | | |   (29)  e3 = e0
% 230.75/42.05  | | | 
% 230.75/42.05  | | | COMBINE_EQS: (20), (29) imply:
% 230.75/42.05  | | |   (30)  all_57_7 = e0
% 230.75/42.05  | | | 
% 230.75/42.05  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 230.75/42.05  | | |            (14), (15), (16), (21), (22), (30) are inconsistent by
% 230.75/42.05  | | |            sub-proof #1636.
% 230.75/42.05  | | | 
% 230.75/42.05  | | End of split
% 230.75/42.05  | | 
% 230.75/42.05  | Case 2:
% 230.75/42.05  | | 
% 230.75/42.05  | |   (31)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 230.75/42.05  | |           e3)
% 230.75/42.05  | | 
% 230.75/42.05  | | BETA: splitting (31) gives:
% 230.75/42.05  | | 
% 230.75/42.05  | | Case 1:
% 230.75/42.05  | | | 
% 230.75/42.05  | | |   (32)  all_57_5 = e3 & op(e2, e1) = e3
% 230.75/42.05  | | | 
% 230.75/42.05  | | | ALPHA: (32) implies:
% 230.75/42.05  | | |   (33)  all_57_5 = e3
% 230.75/42.05  | | | 
% 230.75/42.05  | | | REF_CLOSE: (2), (18), (33) are inconsistent by sub-proof #2382.
% 230.75/42.05  | | | 
% 230.75/42.05  | | Case 2:
% 230.75/42.05  | | | 
% 230.75/42.05  | | |   (34)  all_57_10 = e3 & op(e2, e0) = e3
% 230.75/42.05  | | | 
% 230.75/42.05  | | | ALPHA: (34) implies:
% 230.75/42.05  | | |   (35)  all_57_10 = e3
% 230.75/42.05  | | | 
% 230.75/42.05  | | | REF_CLOSE: (9), (12), (35) are inconsistent by sub-proof #2356.
% 230.75/42.05  | | | 
% 230.75/42.05  | | End of split
% 230.75/42.05  | | 
% 230.75/42.05  | End of split
% 230.75/42.05  | 
% 230.75/42.05  End of proof
% 230.75/42.05  
% 230.75/42.05  Sub-proof #1265 shows that the following formulas are inconsistent:
% 230.75/42.05  ----------------------------------------------------------------
% 230.75/42.06    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.75/42.06         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.75/42.06    (2)   ~ (e3 = e1)
% 230.75/42.06    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.75/42.06           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.75/42.06    (4)  op(e2, e2) = e0
% 230.75/42.06    (5)  all_57_3 = e0
% 230.75/42.06    (6)   ~ (e3 = e2)
% 230.75/42.06    (7)   ~ (e3 = e0)
% 230.75/42.06    (8)  op(e3, e3) = e2
% 230.75/42.06    (9)   ~ (e2 = e0)
% 230.75/42.06    (10)  all_57_13 = e2
% 230.75/42.06    (11)   ~ (e1 = e0)
% 230.75/42.06    (12)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.75/42.06          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.75/42.06    (13)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0)
% 230.75/42.06    (14)   ~ (e2 = e1)
% 230.75/42.06    (15)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.75/42.06          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.75/42.06  
% 230.75/42.06  Begin of proof
% 230.75/42.06  | 
% 230.75/42.06  | BETA: splitting (13) gives:
% 230.75/42.06  | 
% 230.75/42.06  | Case 1:
% 230.75/42.06  | | 
% 230.75/42.06  | |   (16)  all_57_0 = e0 & op(e3, e3) = e0
% 230.75/42.06  | | 
% 230.75/42.06  | | ALPHA: (16) implies:
% 230.75/42.06  | |   (17)  op(e3, e3) = e0
% 230.75/42.06  | | 
% 230.75/42.06  | | REF_CLOSE: (3), (8), (9), (17) are inconsistent by sub-proof #2403.
% 230.75/42.06  | | 
% 230.75/42.06  | Case 2:
% 230.75/42.06  | | 
% 230.75/42.06  | |   (18)  all_57_1 = e0 & op(e3, e2) = e0
% 230.75/42.06  | | 
% 230.75/42.06  | | ALPHA: (18) implies:
% 230.75/42.06  | |   (19)  all_57_1 = e0
% 230.75/42.06  | | 
% 230.75/42.06  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (14),
% 230.75/42.06  | |            (15), (19) are inconsistent by sub-proof #1281.
% 230.75/42.06  | | 
% 230.75/42.06  | End of split
% 230.75/42.06  | 
% 230.75/42.06  End of proof
% 230.75/42.06  
% 230.75/42.06  Sub-proof #1266 shows that the following formulas are inconsistent:
% 230.75/42.06  ----------------------------------------------------------------
% 230.75/42.06    (1)  all_57_0 = e2
% 230.75/42.06    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.75/42.06         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.75/42.06    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.75/42.06         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.75/42.06    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.75/42.06         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.75/42.06    (5)   ~ (e3 = e1)
% 230.75/42.06    (6)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.75/42.06         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.75/42.06    (7)   ~ (all_53_13 = e1)
% 230.75/42.06    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.75/42.06           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.75/42.06    (9)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.75/42.06         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.75/42.06    (10)   ~ (all_6_2 = e3)
% 230.75/42.06    (11)  op(e1, e1) = all_6_2
% 230.75/42.06    (12)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.75/42.06          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.75/42.06    (13)  all_57_9 = e1
% 230.75/42.06    (14)  op(e2, e2) = e0
% 230.75/42.06    (15)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.75/42.06          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.75/42.06    (16)  all_57_3 = e0
% 230.75/42.06    (17)   ~ (e3 = e2)
% 230.75/42.06    (18)   ~ (e3 = e0)
% 230.75/42.06    (19)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.75/42.06          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.75/42.06    (20)  op(e0, e3) = all_53_3
% 230.75/42.06    (21)  op(e3, e3) = e2
% 230.75/42.06    (22)   ~ (all_53_3 = e2)
% 230.75/42.06    (23)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.75/42.06          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.75/42.06            e1)
% 230.75/42.06    (24)  op(e3, e2) = all_53_4
% 230.75/42.06    (25)   ~ (e2 = e0)
% 230.75/42.06    (26)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.75/42.06          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.75/42.06    (27)   ~ (e1 = e0)
% 230.75/42.06    (28)   ~ (all_53_4 = e0)
% 230.75/42.06    (29)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 230.75/42.06          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 230.75/42.06    (30)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.75/42.06          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.75/42.06    (31)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.75/42.06          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 230.75/42.06            e3)
% 230.75/42.06    (32)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.75/42.06          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.75/42.06            e2)
% 230.75/42.06    (33)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.75/42.06              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.75/42.06                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.75/42.06                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.75/42.06    (34)   ~ (all_53_13 = e0)
% 230.75/42.06    (35)  op(e0, e0) = e1
% 230.75/42.06    (36)  op(e2, e0) = all_53_13
% 230.75/42.06    (37)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.75/42.06          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.75/42.06    (38)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.75/42.06          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.75/42.06    (39)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.75/42.06          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.75/42.06    (40)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 230.75/42.06          (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 230.75/42.06    (41)   ~ (e2 = e1)
% 230.75/42.06    (42)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.75/42.06          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.75/42.06    (43)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.75/42.06          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.75/42.06    (44)   ~ (all_53_12 = e2)
% 230.75/42.06    (45)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.75/42.06          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.75/42.06    (46)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.75/42.06          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.75/42.06    (47)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.75/42.06          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.75/42.06    (48)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.75/42.06          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.75/42.06    (49)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.75/42.06          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.75/42.06    (50)  op(e3, e0) = all_53_12
% 230.75/42.06  
% 230.75/42.06  Begin of proof
% 230.75/42.06  | 
% 230.75/42.06  | BETA: splitting (15) gives:
% 230.75/42.06  | 
% 230.75/42.06  | Case 1:
% 230.75/42.06  | | 
% 230.75/42.06  | |   (51)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) =
% 230.75/42.06  | |           e0)
% 230.75/42.06  | | 
% 230.75/42.06  | | REF_CLOSE: (8), (21), (24), (25), (28), (51) are inconsistent by sub-proof
% 230.75/42.06  | |            #1321.
% 230.75/42.06  | | 
% 230.75/42.06  | Case 2:
% 230.75/42.06  | | 
% 230.75/42.06  | |   (52)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) =
% 230.75/42.06  | |           e0)
% 230.75/42.06  | | 
% 230.75/42.06  | | BETA: splitting (52) gives:
% 230.75/42.06  | | 
% 230.75/42.06  | | Case 1:
% 230.75/42.06  | | | 
% 230.75/42.06  | | |   (53)  all_57_4 = e0 & op(e3, e1) = e0
% 230.75/42.06  | | | 
% 230.75/42.06  | | | ALPHA: (53) implies:
% 230.75/42.06  | | |   (54)  all_57_4 = e0
% 230.75/42.06  | | | 
% 230.75/42.06  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 230.75/42.06  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 230.75/42.06  | | |            (23), (25), (26), (27), (29), (30), (31), (32), (33), (34),
% 230.75/42.06  | | |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44),
% 230.75/42.06  | | |            (45), (46), (47), (48), (49), (50), (54) are inconsistent by
% 230.75/42.06  | | |            sub-proof #1267.
% 230.75/42.06  | | | 
% 230.75/42.06  | | Case 2:
% 230.75/42.06  | | | 
% 230.75/42.06  | | |   (55)  all_57_9 = e0 & op(e3, e0) = e0
% 230.75/42.06  | | | 
% 230.75/42.06  | | | REF_CLOSE: (13), (27), (55) are inconsistent by sub-proof #1990.
% 230.75/42.06  | | | 
% 230.75/42.06  | | End of split
% 230.75/42.06  | | 
% 230.75/42.06  | End of split
% 230.75/42.06  | 
% 230.75/42.06  End of proof
% 230.75/42.06  
% 230.75/42.06  Sub-proof #1267 shows that the following formulas are inconsistent:
% 230.75/42.06  ----------------------------------------------------------------
% 230.75/42.06    (1)  all_57_0 = e2
% 230.75/42.06    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.75/42.06         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.75/42.06    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.75/42.06         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.75/42.06    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.75/42.06         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.75/42.06    (5)   ~ (e3 = e1)
% 230.75/42.06    (6)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.75/42.06         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.75/42.06    (7)   ~ (all_53_13 = e1)
% 230.75/42.06    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.75/42.06           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.75/42.06    (9)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.75/42.06         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.75/42.06    (10)   ~ (all_6_2 = e3)
% 230.75/42.06    (11)  op(e1, e1) = all_6_2
% 230.75/42.06    (12)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.75/42.06          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.75/42.06    (13)  all_57_9 = e1
% 230.75/42.06    (14)  all_57_4 = e0
% 230.75/42.06    (15)  op(e2, e2) = e0
% 230.75/42.06    (16)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.75/42.06          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.75/42.06    (17)  all_57_3 = e0
% 230.75/42.06    (18)   ~ (e3 = e2)
% 230.75/42.06    (19)   ~ (e3 = e0)
% 230.75/42.06    (20)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.75/42.06          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.75/42.06    (21)  op(e0, e3) = all_53_3
% 230.75/42.06    (22)  op(e3, e3) = e2
% 230.75/42.06    (23)   ~ (all_53_3 = e2)
% 230.75/42.06    (24)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.75/42.06          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.75/42.06            e1)
% 230.75/42.06    (25)   ~ (e2 = e0)
% 230.75/42.06    (26)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.75/42.06          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.75/42.06    (27)   ~ (e1 = e0)
% 230.75/42.06    (28)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 230.75/42.06          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 230.75/42.06    (29)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.75/42.06          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.75/42.06    (30)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.75/42.06          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 230.75/42.06            e3)
% 230.75/42.06    (31)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.75/42.06          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.75/42.06            e2)
% 230.75/42.07    (32)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.75/42.07              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.75/42.07                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.75/42.07                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.75/42.07    (33)   ~ (all_53_13 = e0)
% 230.75/42.07    (34)  op(e0, e0) = e1
% 230.75/42.07    (35)  op(e2, e0) = all_53_13
% 230.75/42.07    (36)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.75/42.07          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.75/42.07    (37)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.75/42.07          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.75/42.07    (38)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.75/42.07          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.75/42.07    (39)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 230.75/42.07          (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 230.75/42.07    (40)   ~ (e2 = e1)
% 230.75/42.07    (41)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.75/42.07          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.75/42.07    (42)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.75/42.07          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.75/42.07    (43)   ~ (all_53_12 = e2)
% 230.75/42.07    (44)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.75/42.07          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.75/42.07    (45)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.75/42.07          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.75/42.07    (46)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.75/42.07          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.75/42.07    (47)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.75/42.07          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.75/42.07    (48)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.75/42.07          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.75/42.07    (49)  op(e3, e0) = all_53_12
% 230.75/42.07  
% 230.75/42.07  Begin of proof
% 230.75/42.07  | 
% 230.75/42.07  | BETA: splitting (24) gives:
% 230.75/42.07  | 
% 230.75/42.07  | Case 1:
% 230.75/42.07  | | 
% 230.75/42.07  | |   (50)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 230.75/42.07  | |           e1)
% 230.75/42.07  | | 
% 230.75/42.07  | | BETA: splitting (50) gives:
% 230.75/42.07  | | 
% 230.75/42.07  | | Case 1:
% 230.75/42.07  | | | 
% 230.75/42.07  | | |   (51)  all_57_12 = e1 & op(e0, e3) = e1
% 230.75/42.07  | | | 
% 230.75/42.07  | | | ALPHA: (51) implies:
% 230.75/42.07  | | |   (52)  all_57_12 = e1
% 230.75/42.07  | | | 
% 230.75/42.07  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 230.75/42.07  | | |            (13), (14), (15), (16), (17), (18), (19), (21), (22), (23),
% 230.75/42.07  | | |            (25), (26), (27), (28), (29), (30), (31), (32), (34), (35),
% 230.75/42.07  | | |            (36), (37), (38), (40), (41), (42), (44), (45), (46), (47),
% 230.75/42.07  | | |            (52) are inconsistent by sub-proof #1276.
% 230.75/42.07  | | | 
% 230.75/42.07  | | Case 2:
% 230.75/42.07  | | | 
% 230.75/42.07  | | |   (53)  all_57_13 = e1 & op(e0, e2) = e1
% 230.75/42.07  | | | 
% 230.75/42.07  | | | ALPHA: (53) implies:
% 230.75/42.07  | | |   (54)  all_57_13 = e1
% 230.75/42.07  | | | 
% 230.75/42.07  | | | REF_CLOSE: (2), (4), (5), (7), (8), (10), (11), (12), (14), (15), (16),
% 230.75/42.07  | | |            (17), (18), (19), (20), (21), (22), (23), (25), (26), (27),
% 230.75/42.07  | | |            (28), (29), (30), (31), (32), (34), (35), (37), (40), (44),
% 230.75/42.07  | | |            (47), (54) are inconsistent by sub-proof #1275.
% 230.75/42.07  | | | 
% 230.75/42.07  | | End of split
% 230.75/42.07  | | 
% 230.75/42.07  | Case 2:
% 230.75/42.07  | | 
% 230.75/42.07  | |   (55)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.75/42.07  | |           e1)
% 230.75/42.07  | | 
% 230.75/42.07  | | BETA: splitting (55) gives:
% 230.75/42.07  | | 
% 230.75/42.07  | | Case 1:
% 230.75/42.07  | | | 
% 230.75/42.07  | | |   (56)  all_57_14 = e1 & op(e0, e1) = e1
% 230.75/42.07  | | | 
% 230.75/42.07  | | | ALPHA: (56) implies:
% 230.75/42.07  | | |   (57)  all_57_14 = e1
% 230.75/42.07  | | | 
% 230.75/42.07  | | | BETA: splitting (31) gives:
% 230.75/42.07  | | | 
% 230.75/42.07  | | | Case 1:
% 230.75/42.07  | | | | 
% 230.75/42.07  | | | |   (58)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0,
% 230.75/42.07  | | | |             e2) = e2)
% 230.75/42.07  | | | | 
% 230.75/42.07  | | | | BETA: splitting (58) gives:
% 230.75/42.07  | | | | 
% 230.75/42.07  | | | | Case 1:
% 230.75/42.07  | | | | | 
% 230.75/42.07  | | | | |   (59)  all_57_12 = e2 & op(e0, e3) = e2
% 230.75/42.07  | | | | | 
% 230.75/42.07  | | | | | ALPHA: (59) implies:
% 230.75/42.07  | | | | |   (60)  op(e0, e3) = e2
% 230.75/42.07  | | | | | 
% 230.75/42.07  | | | | | REF_CLOSE: (8), (21), (23), (60) are inconsistent by sub-proof #1980.
% 230.75/42.07  | | | | | 
% 230.75/42.07  | | | | Case 2:
% 230.75/42.07  | | | | | 
% 230.75/42.07  | | | | |   (61)  all_57_13 = e2 & op(e0, e2) = e2
% 230.75/42.07  | | | | | 
% 230.75/42.07  | | | | | ALPHA: (61) implies:
% 230.75/42.07  | | | | |   (62)  all_57_13 = e2
% 230.75/42.07  | | | | | 
% 230.75/42.07  | | | | | BETA: splitting (28) gives:
% 230.75/42.07  | | | | | 
% 230.75/42.07  | | | | | Case 1:
% 230.75/42.07  | | | | | | 
% 230.75/42.07  | | | | | |   (63)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2,
% 230.75/42.07  | | | | | |             e1) = e3)
% 230.75/42.07  | | | | | | 
% 230.75/42.07  | | | | | | BETA: splitting (63) gives:
% 230.75/42.07  | | | | | | 
% 230.75/42.07  | | | | | | Case 1:
% 230.75/42.07  | | | | | | | 
% 230.75/42.07  | | | | | | |   (64)  all_57_4 = e3 & op(e3, e1) = e3
% 230.75/42.07  | | | | | | | 
% 230.75/42.07  | | | | | | | ALPHA: (64) implies:
% 230.75/42.07  | | | | | | |   (65)  all_57_4 = e3
% 230.75/42.07  | | | | | | | 
% 230.75/42.07  | | | | | | | REF_CLOSE: (14), (19), (65) are inconsistent by sub-proof #2372.
% 230.75/42.07  | | | | | | | 
% 230.75/42.07  | | | | | | Case 2:
% 230.75/42.07  | | | | | | | 
% 230.75/42.07  | | | | | | |   (66)  all_57_5 = e3 & op(e2, e1) = e3
% 230.75/42.07  | | | | | | | 
% 230.75/42.07  | | | | | | | ALPHA: (66) implies:
% 230.75/42.07  | | | | | | |   (67)  all_57_5 = e3
% 230.75/42.07  | | | | | | | 
% 230.75/42.07  | | | | | | | BETA: splitting (26) gives:
% 230.75/42.07  | | | | | | | 
% 230.75/42.07  | | | | | | | Case 1:
% 230.75/42.07  | | | | | | | | 
% 230.75/42.07  | | | | | | | |   (68)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 &
% 230.75/42.07  | | | | | | | |           op(e3, e2) = e3)
% 230.75/42.07  | | | | | | | | 
% 230.75/42.07  | | | | | | | | BETA: splitting (68) gives:
% 230.75/42.07  | | | | | | | | 
% 230.75/42.07  | | | | | | | | Case 1:
% 230.75/42.07  | | | | | | | | | 
% 230.75/42.07  | | | | | | | | |   (69)  all_57_0 = e3 & op(e3, e3) = e3
% 230.75/42.07  | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | ALPHA: (69) implies:
% 230.75/42.07  | | | | | | | | |   (70)  op(e3, e3) = e3
% 230.75/42.07  | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | REF_CLOSE: (8), (18), (22), (70) are inconsistent by sub-proof
% 230.75/42.07  | | | | | | | | |            #2490.
% 230.75/42.07  | | | | | | | | | 
% 230.75/42.07  | | | | | | | | Case 2:
% 230.75/42.07  | | | | | | | | | 
% 230.75/42.07  | | | | | | | | |   (71)  all_57_1 = e3 & op(e3, e2) = e3
% 230.75/42.07  | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | ALPHA: (71) implies:
% 230.75/42.07  | | | | | | | | |   (72)  all_57_1 = e3
% 230.75/42.07  | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | BETA: splitting (37) gives:
% 230.75/42.07  | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | Case 1:
% 230.75/42.07  | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | |   (73)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 &
% 230.75/42.07  | | | | | | | | | |           op(e2, e2) = e2)
% 230.75/42.07  | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | BETA: splitting (73) gives:
% 230.75/42.07  | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | Case 1:
% 230.75/42.07  | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | |   (74)  all_57_2 = e2 & op(e2, e3) = e2
% 230.75/42.07  | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | ALPHA: (74) implies:
% 230.75/42.07  | | | | | | | | | | |   (75)  all_57_2 = e2
% 230.75/42.07  | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | BETA: splitting (3) gives:
% 230.75/42.07  | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | Case 1:
% 230.75/42.07  | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | |   (76)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 230.75/42.07  | | | | | | | | | | | |           & op(e2, e3) = e1)
% 230.75/42.07  | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | BETA: splitting (76) gives:
% 230.75/42.07  | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | Case 1:
% 230.75/42.07  | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | |   (77)  all_57_0 = e1 & op(e3, e3) = e1
% 230.75/42.07  | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | ALPHA: (77) implies:
% 230.75/42.07  | | | | | | | | | | | | |   (78)  op(e3, e3) = e1
% 230.75/42.07  | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | REF_CLOSE: (8), (22), (40), (78) are inconsistent by
% 230.75/42.07  | | | | | | | | | | | | |            sub-proof #1950.
% 230.75/42.07  | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | Case 2:
% 230.75/42.07  | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | |   (79)  all_57_2 = e1 & op(e2, e3) = e1
% 230.75/42.07  | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | ALPHA: (79) implies:
% 230.75/42.07  | | | | | | | | | | | | |   (80)  all_57_2 = e1
% 230.75/42.07  | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | COMBINE_EQS: (75), (80) imply:
% 230.75/42.07  | | | | | | | | | | | | |   (81)  e2 = e1
% 230.75/42.07  | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | SIMP: (81) implies:
% 230.75/42.07  | | | | | | | | | | | | |   (82)  e2 = e1
% 230.75/42.07  | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | COMBINE_EQS: (62), (82) imply:
% 230.75/42.07  | | | | | | | | | | | | |   (83)  all_57_13 = e1
% 230.75/42.07  | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | REF_CLOSE: (2), (4), (5), (7), (8), (10), (11), (12), (14),
% 230.75/42.07  | | | | | | | | | | | | |            (15), (16), (17), (18), (19), (20), (21), (22),
% 230.75/42.07  | | | | | | | | | | | | |            (23), (25), (26), (27), (28), (29), (30), (31),
% 230.75/42.07  | | | | | | | | | | | | |            (32), (34), (35), (37), (40), (44), (47), (83) are
% 230.75/42.07  | | | | | | | | | | | | |            inconsistent by sub-proof #1275.
% 230.75/42.07  | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | End of split
% 230.75/42.07  | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | Case 2:
% 230.75/42.07  | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | |   (84)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 230.75/42.07  | | | | | | | | | | | |           e1 & op(e0, e3) = e1)
% 230.75/42.07  | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | BETA: splitting (84) gives:
% 230.75/42.07  | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | Case 1:
% 230.75/42.07  | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | |   (85)  all_57_6 = e1 & op(e1, e3) = e1
% 230.75/42.07  | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | ALPHA: (85) implies:
% 230.75/42.07  | | | | | | | | | | | | |   (86)  all_57_6 = e1
% 230.75/42.07  | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | BETA: splitting (30) gives:
% 230.75/42.07  | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | Case 1:
% 230.75/42.07  | | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | |   (87)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 230.75/42.07  | | | | | | | | | | | | | |           e3 & op(e0, e2) = e3)
% 230.75/42.07  | | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | | BETA: splitting (87) gives:
% 230.75/42.07  | | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | | Case 1:
% 230.75/42.07  | | | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | | |   (88)  all_57_12 = e3 & op(e0, e3) = e3
% 230.75/42.07  | | | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | | | ALPHA: (88) implies:
% 230.75/42.07  | | | | | | | | | | | | | | |   (89)  all_57_12 = e3
% 230.75/42.07  | | | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | | | REF_CLOSE: (2), (5), (8), (17), (18), (19), (22), (25), (27),
% 230.75/42.07  | | | | | | | | | | | | | | |            (36), (37), (40), (45), (86), (89) are
% 230.75/42.07  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1632.
% 230.75/42.07  | | | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | | Case 2:
% 230.75/42.07  | | | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | | |   (90)  all_57_13 = e3 & op(e0, e2) = e3
% 230.75/42.07  | | | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | | | ALPHA: (90) implies:
% 230.75/42.07  | | | | | | | | | | | | | | |   (91)  all_57_13 = e3
% 230.75/42.07  | | | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | | | REF_CLOSE: (8), (18), (21), (23), (31), (34), (40), (57),
% 230.75/42.07  | | | | | | | | | | | | | | |            (91) are inconsistent by sub-proof #1967.
% 230.75/42.07  | | | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | | End of split
% 230.75/42.07  | | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | Case 2:
% 230.75/42.07  | | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | |   (92)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 230.75/42.07  | | | | | | | | | | | | | |           e3 & op(e0, e0) = e3)
% 230.75/42.07  | | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (34), (57), (92) are inconsistent by
% 230.75/42.07  | | | | | | | | | | | | | |            sub-proof #1965.
% 230.75/42.07  | | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | End of split
% 230.75/42.07  | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | Case 2:
% 230.75/42.07  | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | |   (93)  all_57_12 = e1 & op(e0, e3) = e1
% 230.75/42.07  | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | ALPHA: (93) implies:
% 230.75/42.07  | | | | | | | | | | | | |   (94)  all_57_12 = e1
% 230.75/42.07  | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 230.75/42.07  | | | | | | | | | | | | |            (11), (12), (14), (15), (16), (17), (18), (19),
% 230.75/42.07  | | | | | | | | | | | | |            (21), (22), (23), (25), (26), (27), (28), (29),
% 230.75/42.07  | | | | | | | | | | | | |            (30), (31), (32), (34), (35), (36), (37), (38),
% 230.75/42.07  | | | | | | | | | | | | |            (40), (41), (42), (44), (45), (46), (47), (72),
% 230.75/42.07  | | | | | | | | | | | | |            (94) are inconsistent by sub-proof #1277.
% 230.75/42.07  | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | End of split
% 230.75/42.07  | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | End of split
% 230.75/42.07  | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | Case 2:
% 230.75/42.07  | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | |   (95)  all_57_3 = e2 & op(e2, e2) = e2
% 230.75/42.07  | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | ALPHA: (95) implies:
% 230.75/42.07  | | | | | | | | | | |   (96)  op(e2, e2) = e2
% 230.75/42.07  | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | REF_CLOSE: (8), (15), (25), (96) are inconsistent by
% 230.75/42.07  | | | | | | | | | | |            sub-proof #2472.
% 230.75/42.07  | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | End of split
% 230.75/42.07  | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | Case 2:
% 230.75/42.07  | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | |   (97)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2
% 230.75/42.07  | | | | | | | | | |           & op(e2, e0) = e2)
% 230.75/42.07  | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | BETA: splitting (97) gives:
% 230.75/42.07  | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | Case 1:
% 230.75/42.07  | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | |   (98)  all_57_5 = e2 & op(e2, e1) = e2
% 230.75/42.07  | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | REF_CLOSE: (5), (8), (12), (14), (16), (18), (19), (22),
% 230.75/42.07  | | | | | | | | | | |            (25), (26), (27), (40), (67), (72), (98) are
% 230.75/42.07  | | | | | | | | | | |            inconsistent by sub-proof #1274.
% 230.75/42.07  | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | Case 2:
% 230.75/42.07  | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | |   (99)  all_57_10 = e2 & op(e2, e0) = e2
% 230.75/42.07  | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | ALPHA: (99) implies:
% 230.75/42.07  | | | | | | | | | | |   (100)  all_57_10 = e2
% 230.75/42.07  | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | BETA: splitting (30) gives:
% 230.75/42.07  | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | Case 1:
% 230.75/42.07  | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | |   (101)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 230.75/42.07  | | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 230.75/42.07  | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | BETA: splitting (101) gives:
% 230.75/42.07  | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | Case 1:
% 230.75/42.07  | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | |   (102)  all_57_12 = e3 & op(e0, e3) = e3
% 230.75/42.07  | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | ALPHA: (102) implies:
% 230.75/42.07  | | | | | | | | | | | | |   (103)  all_57_12 = e3
% 230.75/42.07  | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | BETA: splitting (2) gives:
% 230.75/42.07  | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | Case 1:
% 230.75/42.07  | | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | |   (104)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 230.75/42.07  | | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 230.75/42.07  | | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | | BETA: splitting (104) gives:
% 230.75/42.07  | | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | | Case 1:
% 230.75/42.07  | | | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | | |   (105)  all_57_2 = e1 & op(e2, e3) = e1
% 230.75/42.07  | | | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | | | ALPHA: (105) implies:
% 230.75/42.07  | | | | | | | | | | | | | | |   (106)  all_57_2 = e1
% 230.75/42.07  | | | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | | | BETA: splitting (32) gives:
% 230.75/42.07  | | | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | | | Case 1:
% 230.75/42.07  | | | | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | | | |   (107)  all_57_15 = e0 & op(e0, e0) = e0
% 230.75/42.07  | | | | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | | | | ALPHA: (107) implies:
% 230.75/42.07  | | | | | | | | | | | | | | | |   (108)  op(e0, e0) = e0
% 230.75/42.07  | | | | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | | | | BETA: splitting (48) gives:
% 230.75/42.07  | | | | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | | | | Case 1:
% 230.75/42.07  | | | | | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | | | | |   (109)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 230.75/42.07  | | | | | | | | | | | | | | | | |            & op(e1, e2) = e2)
% 230.75/42.07  | | | | | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (5), (8), (17), (18), (19), (21), (22), (23),
% 230.75/42.07  | | | | | | | | | | | | | | | | |            (25), (27), (30), (31), (34), (37), (40), (45),
% 230.75/42.07  | | | | | | | | | | | | | | | | |            (47), (57), (62), (67), (72), (100), (109) are
% 230.75/42.07  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1273.
% 230.75/42.07  | | | | | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | | | | Case 2:
% 230.75/42.07  | | | | | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | | | | |   (110)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 230.75/42.07  | | | | | | | | | | | | | | | | |            e2 & op(e1, e0) = e2)
% 230.75/42.07  | | | | | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | | | | | BETA: splitting (110) gives:
% 230.75/42.07  | | | | | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | | | | | Case 1:
% 230.75/42.07  | | | | | | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | | | | | |   (111)  all_57_8 = e2 & op(e1, e1) = e2
% 230.75/42.07  | | | | | | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | | | | | | ALPHA: (111) implies:
% 230.75/42.07  | | | | | | | | | | | | | | | | | |   (112)  all_57_8 = e2
% 230.75/42.07  | | | | | | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | | | | | | BETA: splitting (44) gives:
% 230.75/42.07  | | | | | | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | | | | | | Case 1:
% 230.75/42.07  | | | | | | | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | | | | | | |   (113)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 230.75/42.07  | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e2)
% 230.75/42.07  | | | | | | | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | | | | | | | BETA: splitting (113) gives:
% 230.75/42.07  | | | | | | | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | | | | | | | Case 1:
% 230.75/42.07  | | | | | | | | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | | | | | | | |   (114)  all_57_4 = e2 & op(e3, e1) = e2
% 230.75/42.07  | | | | | | | | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | | | | | | | | ALPHA: (114) implies:
% 230.75/42.07  | | | | | | | | | | | | | | | | | | | |   (115)  all_57_4 = e2
% 230.75/42.07  | | | | | | | | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14), (115) imply:
% 230.75/42.07  | | | | | | | | | | | | | | | | | | | |   (116)  e2 = e0
% 230.75/42.07  | | | | | | | | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | | | | | | | | SIMP: (116) implies:
% 230.75/42.07  | | | | | | | | | | | | | | | | | | | |   (117)  e2 = e0
% 230.75/42.07  | | | | | | | | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (112), (117) imply:
% 230.75/42.07  | | | | | | | | | | | | | | | | | | | |   (118)  all_57_8 = e0
% 230.75/42.07  | | | | | | | | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | | | | | | | | BETA: splitting (48) gives:
% 230.75/42.07  | | | | | | | | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.75/42.07  | | | | | | | | | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | | | | | | | | |   (119)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 230.75/42.07  | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e2)
% 230.75/42.07  | | | | | | | | | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (5), (8), (17), (18), (19), (21), (22), (23),
% 230.75/42.07  | | | | | | | | | | | | | | | | | | | | |            (25), (27), (30), (31), (34), (37), (40), (45),
% 230.75/42.07  | | | | | | | | | | | | | | | | | | | | |            (47), (57), (62), (67), (72), (100), (119) are
% 230.75/42.07  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1273.
% 230.75/42.07  | | | | | | | | | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.75/42.07  | | | | | | | | | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (110) gives:
% 230.75/42.07  | | | | | | | | | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.75/42.07  | | | | | | | | | | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (5), (17), (18), (25), (27), (37), (40),
% 230.75/42.07  | | | | | | | | | | | | | | | | | | | | | |            (67), (100), (112), (118) are inconsistent by
% 230.75/42.07  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1272.
% 230.75/42.07  | | | | | | | | | | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.75/42.07  | | | | | | | | | | | | | | | | | | | | | | 
% 230.75/42.07  | | | | | | | | | | | | | | | | | | | | | |   (120)  all_57_11 = e2 & op(e1, e0) = e2
% 230.75/42.07  | | | | | | | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (5), (8), (12), (13), (14), (16), (17), (18),
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | | | |            (19), (22), (25), (26), (27), (34), (37), (39),
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | | | |            (40), (67), (72), (120) are inconsistent by
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1271.
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | | | End of split
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | | End of split
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | Case 2:
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | |   (121)  all_57_5 = e2 & op(e2, e1) = e2
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (12), (14), (16), (18), (19), (22),
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | |            (25), (26), (27), (40), (67), (72), (121) are
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1274.
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | End of split
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | | | Case 2:
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | | | |   (122)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 230.75/42.08  | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e1) = e2)
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | BETA: splitting (122) gives:
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | Case 1:
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with e0, e1, e0, e0, simplifying
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | |              with (34), (108) gives:
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | |   (123)  e1 = e0
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (106), (123) imply:
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | |   (124)  all_57_2 = e0
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (5), (17), (18), (25), (27), (37), (40),
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | |            (67), (124) are inconsistent by sub-proof #2253.
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | Case 2:
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | |   (125)  all_57_14 = e2 & op(e0, e1) = e2
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (5), (7), (8), (10), (11), (12), (14),
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | |            (15), (16), (17), (18), (19), (20), (21), (22),
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | |            (23), (25), (26), (27), (28), (29), (30), (31),
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | |            (32), (34), (35), (37), (40), (44), (47), (57),
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | |            (62), (125) are inconsistent by sub-proof #1270.
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | End of split
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | | | End of split
% 230.75/42.08  | | | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | | Case 2:
% 230.75/42.08  | | | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | | |   (126)  all_57_11 = e2 & op(e1, e0) = e2
% 230.75/42.08  | | | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (5), (8), (12), (13), (14), (16), (17), (18),
% 230.75/42.08  | | | | | | | | | | | | | | | | | |            (19), (22), (25), (26), (27), (34), (37), (39),
% 230.75/42.08  | | | | | | | | | | | | | | | | | |            (40), (67), (72), (126) are inconsistent by
% 230.75/42.08  | | | | | | | | | | | | | | | | | |            sub-proof #1271.
% 230.75/42.08  | | | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | | End of split
% 230.75/42.08  | | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | End of split
% 230.75/42.08  | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | Case 2:
% 230.75/42.08  | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | |   (127)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 230.75/42.08  | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 230.75/42.08  | | | | | | | | | | | | | | | |              op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 230.75/42.08  | | | | | | | | | | | | | | | |                e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 230.75/42.08  | | | | | | | | | | | | | | | |              e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 230.75/42.08  | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | ALPHA: (127) implies:
% 230.75/42.08  | | | | | | | | | | | | | | | |   (128)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 230.75/42.08  | | | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 230.75/42.08  | | | | | | | | | | | | | | | |              e1) = e0)
% 230.75/42.08  | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | BETA: splitting (44) gives:
% 230.75/42.08  | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | Case 1:
% 230.75/42.08  | | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | |   (129)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 230.75/42.08  | | | | | | | | | | | | | | | | |            & op(e2, e1) = e2)
% 230.75/42.08  | | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | | BETA: splitting (129) gives:
% 230.75/42.08  | | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | | Case 1:
% 230.75/42.08  | | | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | | |   (130)  all_57_4 = e2 & op(e3, e1) = e2
% 230.75/42.08  | | | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | | | ALPHA: (130) implies:
% 230.75/42.08  | | | | | | | | | | | | | | | | | |   (131)  all_57_4 = e2
% 230.75/42.08  | | | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14), (131) imply:
% 230.75/42.08  | | | | | | | | | | | | | | | | | |   (132)  e2 = e0
% 230.75/42.08  | | | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (100), (132) imply:
% 230.75/42.08  | | | | | | | | | | | | | | | | | |   (133)  all_57_10 = e0
% 230.75/42.08  | | | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (5), (17), (18), (25), (27), (37), (40),
% 230.75/42.08  | | | | | | | | | | | | | | | | | |            (67), (133) are inconsistent by sub-proof #1518.
% 230.75/42.08  | | | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | | Case 2:
% 230.75/42.08  | | | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | | |   (134)  all_57_5 = e2 & op(e2, e1) = e2
% 230.75/42.08  | | | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (12), (14), (16), (18), (19), (22),
% 230.75/42.08  | | | | | | | | | | | | | | | | | |            (25), (26), (27), (40), (67), (72), (134) are
% 230.75/42.08  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1274.
% 230.75/42.08  | | | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | | End of split
% 230.75/42.08  | | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | Case 2:
% 230.75/42.08  | | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | |   (135)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 230.75/42.08  | | | | | | | | | | | | | | | | |            e2 & op(e0, e1) = e2)
% 230.75/42.08  | | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | | BETA: splitting (135) gives:
% 230.75/42.08  | | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | | Case 1:
% 230.75/42.08  | | | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | | |   (136)  all_57_8 = e2 & op(e1, e1) = e2
% 230.75/42.08  | | | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | | | ALPHA: (136) implies:
% 230.75/42.08  | | | | | | | | | | | | | | | | | |   (137)  op(e1, e1) = e2
% 230.75/42.08  | | | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | | | BETA: splitting (128) gives:
% 230.75/42.08  | | | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | | | Case 1:
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | | | |   (138)  all_57_12 = e0 & op(e0, e3) = e0
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | ALPHA: (138) implies:
% 230.75/42.08  | | | | | | | | | | | | | | | | | | |   (139)  all_57_12 = e0
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (18), (19), (21), (23), (30), (31),
% 230.75/42.08  | | | | | | | | | | | | | | | | | | |            (34), (40), (57), (139) are inconsistent by
% 230.75/42.08  | | | | | | | | | | | | | | | | | | |            sub-proof #1964.
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | | | Case 2:
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | | | |   (140)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 230.75/42.08  | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | BETA: splitting (140) gives:
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | Case 1:
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | |   (141)  all_57_13 = e0 & op(e0, e2) = e0
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | | ALPHA: (141) implies:
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | |   (142)  all_57_13 = e0
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (17), (18), (25), (27), (40), (47),
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | |            (72), (142) are inconsistent by sub-proof #1758.
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | Case 2:
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | |   (143)  all_57_14 = e0 & op(e0, e1) = e0
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | | ALPHA: (143) implies:
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | |   (144)  all_57_14 = e0
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (14), (20), (27), (40), (67), (137),
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | |            (144) are inconsistent by sub-proof #2379.
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | End of split
% 230.75/42.08  | | | | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | | | End of split
% 230.75/42.08  | | | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | | Case 2:
% 230.75/42.08  | | | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | | |   (145)  all_57_14 = e2 & op(e0, e1) = e2
% 230.75/42.08  | | | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (5), (7), (8), (10), (11), (12), (14),
% 230.75/42.08  | | | | | | | | | | | | | | | | | |            (15), (16), (17), (18), (19), (20), (21), (22),
% 230.75/42.08  | | | | | | | | | | | | | | | | | |            (23), (25), (26), (27), (28), (29), (30), (31),
% 230.75/42.08  | | | | | | | | | | | | | | | | | |            (32), (34), (35), (37), (40), (44), (47), (57),
% 230.75/42.08  | | | | | | | | | | | | | | | | | |            (62), (145) are inconsistent by sub-proof #1270.
% 230.75/42.08  | | | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | | End of split
% 230.75/42.08  | | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | End of split
% 230.75/42.08  | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | End of split
% 230.75/42.08  | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | Case 2:
% 230.75/42.08  | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | |   (146)  all_57_3 = e1 & op(e2, e2) = e1
% 230.75/42.08  | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | ALPHA: (146) implies:
% 230.75/42.08  | | | | | | | | | | | | | | |   (147)  op(e2, e2) = e1
% 230.75/42.08  | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | REF_CLOSE: (8), (15), (27), (147) are inconsistent by
% 230.75/42.08  | | | | | | | | | | | | | | |            sub-proof #2352.
% 230.75/42.08  | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | End of split
% 230.75/42.08  | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | Case 2:
% 230.75/42.08  | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | |   (148)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 230.75/42.08  | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 230.75/42.08  | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | BETA: splitting (148) gives:
% 230.75/42.08  | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | Case 1:
% 230.75/42.08  | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | |   (149)  all_57_5 = e1 & op(e2, e1) = e1
% 230.75/42.08  | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | ALPHA: (149) implies:
% 230.75/42.08  | | | | | | | | | | | | | | |   (150)  all_57_5 = e1
% 230.75/42.08  | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | COMBINE_EQS: (67), (150) imply:
% 230.75/42.08  | | | | | | | | | | | | | | |   (151)  e3 = e1
% 230.75/42.08  | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | SIMP: (151) implies:
% 230.75/42.08  | | | | | | | | | | | | | | |   (152)  e3 = e1
% 230.75/42.08  | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | COMBINE_EQS: (103), (152) imply:
% 230.75/42.08  | | | | | | | | | | | | | | |   (153)  all_57_12 = e1
% 230.75/42.08  | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 230.75/42.08  | | | | | | | | | | | | | | |            (11), (12), (14), (15), (16), (17), (18), (19),
% 230.75/42.08  | | | | | | | | | | | | | | |            (21), (22), (23), (25), (26), (27), (28), (29),
% 230.75/42.08  | | | | | | | | | | | | | | |            (30), (31), (32), (34), (35), (36), (37), (38),
% 230.75/42.08  | | | | | | | | | | | | | | |            (40), (41), (42), (44), (45), (46), (47), (72),
% 230.75/42.08  | | | | | | | | | | | | | | |            (153) are inconsistent by sub-proof #1277.
% 230.75/42.08  | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | Case 2:
% 230.75/42.08  | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | |   (154)  all_57_10 = e1 & op(e2, e0) = e1
% 230.75/42.08  | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (35), (154) are inconsistent by
% 230.75/42.08  | | | | | | | | | | | | | | |            sub-proof #2084.
% 230.75/42.08  | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | End of split
% 230.75/42.08  | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | End of split
% 230.75/42.08  | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | Case 2:
% 230.75/42.08  | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | |   (155)  all_57_13 = e3 & op(e0, e2) = e3
% 230.75/42.08  | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | ALPHA: (155) implies:
% 230.75/42.08  | | | | | | | | | | | | |   (156)  all_57_13 = e3
% 230.75/42.08  | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | REF_CLOSE: (8), (18), (21), (23), (31), (34), (40), (57),
% 230.75/42.08  | | | | | | | | | | | | |            (156) are inconsistent by sub-proof #1967.
% 230.75/42.08  | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | End of split
% 230.75/42.08  | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | Case 2:
% 230.75/42.08  | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | |   (157)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 230.75/42.08  | | | | | | | | | | | |            e3 & op(e0, e0) = e3)
% 230.75/42.08  | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | REF_CLOSE: (5), (8), (34), (57), (157) are inconsistent by
% 230.75/42.08  | | | | | | | | | | | |            sub-proof #1965.
% 230.75/42.08  | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | End of split
% 230.75/42.08  | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | End of split
% 230.75/42.08  | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | End of split
% 230.75/42.08  | | | | | | | | | 
% 230.75/42.08  | | | | | | | | End of split
% 230.75/42.08  | | | | | | | | 
% 230.75/42.08  | | | | | | | Case 2:
% 230.75/42.08  | | | | | | | | 
% 230.75/42.08  | | | | | | | |   (158)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 &
% 230.75/42.08  | | | | | | | |            op(e3, e0) = e3)
% 230.75/42.08  | | | | | | | | 
% 230.75/42.08  | | | | | | | | BETA: splitting (158) gives:
% 230.75/42.08  | | | | | | | | 
% 230.75/42.08  | | | | | | | | Case 1:
% 230.75/42.08  | | | | | | | | | 
% 230.75/42.08  | | | | | | | | |   (159)  all_57_4 = e3 & op(e3, e1) = e3
% 230.75/42.08  | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | REF_CLOSE: (14), (19), (159) are inconsistent by sub-proof
% 230.75/42.08  | | | | | | | | |            #1618.
% 230.75/42.08  | | | | | | | | | 
% 230.75/42.08  | | | | | | | | Case 2:
% 230.75/42.08  | | | | | | | | | 
% 230.75/42.08  | | | | | | | | |   (160)  all_57_9 = e3 & op(e3, e0) = e3
% 230.75/42.08  | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | REF_CLOSE: (5), (13), (160) are inconsistent by sub-proof
% 230.75/42.08  | | | | | | | | |            #1269.
% 230.75/42.08  | | | | | | | | | 
% 230.75/42.08  | | | | | | | | End of split
% 230.75/42.08  | | | | | | | | 
% 230.75/42.08  | | | | | | | End of split
% 230.75/42.08  | | | | | | | 
% 230.75/42.08  | | | | | | End of split
% 230.75/42.08  | | | | | | 
% 230.75/42.08  | | | | | Case 2:
% 230.75/42.08  | | | | | | 
% 230.75/42.08  | | | | | |   (161)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 &
% 230.75/42.08  | | | | | |            op(e0, e1) = e3)
% 230.75/42.08  | | | | | | 
% 230.75/42.08  | | | | | | REF_CLOSE: (5), (8), (10), (11), (57), (161) are inconsistent by
% 230.75/42.08  | | | | | |            sub-proof #2263.
% 230.75/42.08  | | | | | | 
% 230.75/42.08  | | | | | End of split
% 230.75/42.08  | | | | | 
% 230.75/42.08  | | | | End of split
% 230.75/42.08  | | | | 
% 230.75/42.08  | | | Case 2:
% 230.75/42.08  | | | | 
% 230.75/42.08  | | | |   (162)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0,
% 230.75/42.08  | | | |              e0) = e2)
% 230.75/42.08  | | | | 
% 230.75/42.08  | | | | REF_CLOSE: (8), (34), (40), (57), (162) are inconsistent by sub-proof
% 230.75/42.08  | | | |            #2176.
% 230.75/42.08  | | | | 
% 230.75/42.08  | | | End of split
% 230.75/42.08  | | | 
% 230.75/42.08  | | Case 2:
% 230.75/42.08  | | | 
% 230.75/42.08  | | |   (163)  all_57_15 = e1 & op(e0, e0) = e1
% 230.75/42.08  | | | 
% 230.75/42.08  | | | ALPHA: (163) implies:
% 230.75/42.08  | | |   (164)  all_57_15 = e1
% 230.75/42.08  | | | 
% 230.75/42.08  | | | BETA: splitting (26) gives:
% 230.75/42.08  | | | 
% 230.75/42.08  | | | Case 1:
% 230.75/42.08  | | | | 
% 230.75/42.08  | | | |   (165)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2)
% 230.75/42.08  | | | |            = e3)
% 230.75/42.08  | | | | 
% 230.75/42.08  | | | | BETA: splitting (165) gives:
% 230.75/42.08  | | | | 
% 230.75/42.08  | | | | Case 1:
% 230.75/42.08  | | | | | 
% 230.75/42.08  | | | | |   (166)  all_57_0 = e3 & op(e3, e3) = e3
% 230.75/42.08  | | | | | 
% 230.75/42.08  | | | | | ALPHA: (166) implies:
% 230.75/42.08  | | | | |   (167)  op(e3, e3) = e3
% 230.75/42.08  | | | | | 
% 230.75/42.08  | | | | | REF_CLOSE: (8), (18), (22), (167) are inconsistent by sub-proof #2490.
% 230.75/42.08  | | | | | 
% 230.75/42.08  | | | | Case 2:
% 230.75/42.08  | | | | | 
% 230.75/42.08  | | | | |   (168)  all_57_1 = e3 & op(e3, e2) = e3
% 230.75/42.08  | | | | | 
% 230.75/42.08  | | | | | ALPHA: (168) implies:
% 230.75/42.08  | | | | |   (169)  all_57_1 = e3
% 230.75/42.08  | | | | | 
% 230.75/42.08  | | | | | BETA: splitting (47) gives:
% 230.75/42.08  | | | | | 
% 230.75/42.08  | | | | | Case 1:
% 230.75/42.08  | | | | | | 
% 230.75/42.08  | | | | | |   (170)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2,
% 230.75/42.08  | | | | | |              e2) = e1)
% 230.75/42.08  | | | | | | 
% 230.75/42.08  | | | | | | REF_CLOSE: (5), (8), (15), (27), (169), (170) are inconsistent by
% 230.75/42.08  | | | | | |            sub-proof #2206.
% 230.75/42.08  | | | | | | 
% 230.75/42.08  | | | | | Case 2:
% 230.75/42.08  | | | | | | 
% 230.75/42.08  | | | | | |   (171)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 &
% 230.75/42.08  | | | | | |            op(e0, e2) = e1)
% 230.75/42.08  | | | | | | 
% 230.75/42.08  | | | | | | BETA: splitting (171) gives:
% 230.75/42.08  | | | | | | 
% 230.75/42.08  | | | | | | Case 1:
% 230.75/42.08  | | | | | | | 
% 230.75/42.08  | | | | | | |   (172)  all_57_7 = e1 & op(e1, e2) = e1
% 230.75/42.08  | | | | | | | 
% 230.75/42.08  | | | | | | | ALPHA: (172) implies:
% 230.75/42.08  | | | | | | |   (173)  all_57_7 = e1
% 230.75/42.08  | | | | | | | 
% 230.75/42.08  | | | | | | | BETA: splitting (4) gives:
% 230.75/42.08  | | | | | | | 
% 230.75/42.08  | | | | | | | Case 1:
% 230.75/42.08  | | | | | | | | 
% 230.75/42.08  | | | | | | | |   (174)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 &
% 230.75/42.08  | | | | | | | |            op(e2, e2) = e2)
% 230.75/42.08  | | | | | | | | 
% 230.75/42.08  | | | | | | | | REF_CLOSE: (5), (8), (12), (14), (15), (16), (18), (19), (22),
% 230.75/42.08  | | | | | | | |            (25), (26), (27), (40), (174) are inconsistent by
% 230.75/42.08  | | | | | | | |            sub-proof #1637.
% 230.75/42.08  | | | | | | | | 
% 230.75/42.08  | | | | | | | Case 2:
% 230.75/42.08  | | | | | | | | 
% 230.75/42.08  | | | | | | | |   (175)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 &
% 230.75/42.08  | | | | | | | |            op(e0, e2) = e2)
% 230.75/42.08  | | | | | | | | 
% 230.75/42.08  | | | | | | | | BETA: splitting (175) gives:
% 230.75/42.08  | | | | | | | | 
% 230.75/42.08  | | | | | | | | Case 1:
% 230.75/42.08  | | | | | | | | | 
% 230.75/42.08  | | | | | | | | |   (176)  all_57_7 = e2 & op(e1, e2) = e2
% 230.75/42.08  | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | REF_CLOSE: (40), (173), (176) are inconsistent by sub-proof
% 230.75/42.08  | | | | | | | | |            #1268.
% 230.75/42.08  | | | | | | | | | 
% 230.75/42.08  | | | | | | | | Case 2:
% 230.75/42.08  | | | | | | | | | 
% 230.75/42.08  | | | | | | | | |   (177)  all_57_13 = e2 & op(e0, e2) = e2
% 230.75/42.08  | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | ALPHA: (177) implies:
% 230.75/42.08  | | | | | | | | |   (178)  all_57_13 = e2
% 230.75/42.08  | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | BETA: splitting (32) gives:
% 230.75/42.08  | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | Case 1:
% 230.75/42.08  | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | |   (179)  all_57_15 = e0 & op(e0, e0) = e0
% 230.75/42.08  | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | ALPHA: (179) implies:
% 230.75/42.08  | | | | | | | | | |   (180)  all_57_15 = e0
% 230.75/42.08  | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | COMBINE_EQS: (164), (180) imply:
% 230.75/42.08  | | | | | | | | | |   (181)  e1 = e0
% 230.75/42.08  | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | COMBINE_EQS: (173), (181) imply:
% 230.75/42.08  | | | | | | | | | |   (182)  all_57_7 = e0
% 230.75/42.08  | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | REF_CLOSE: (4), (5), (8), (12), (14), (15), (16), (17), (18),
% 230.75/42.08  | | | | | | | | | |            (19), (22), (25), (26), (27), (29), (40), (47),
% 230.75/42.08  | | | | | | | | | |            (182) are inconsistent by sub-proof #1636.
% 230.75/42.08  | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | Case 2:
% 230.75/42.08  | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | |   (183)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 230.75/42.08  | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 230.75/42.08  | | | | | | | | | |              op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 230.75/42.08  | | | | | | | | | |                e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 230.75/42.08  | | | | | | | | | |              e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 230.75/42.08  | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | ALPHA: (183) implies:
% 230.75/42.08  | | | | | | | | | |   (184)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0
% 230.75/42.08  | | | | | | | | | |            & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.75/42.08  | | | | | | | | | |            = e0)
% 230.75/42.08  | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | BETA: splitting (184) gives:
% 230.75/42.08  | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | Case 1:
% 230.75/42.08  | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | |   (185)  all_57_9 = e0 & op(e3, e0) = e0
% 230.75/42.08  | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | ALPHA: (185) implies:
% 230.75/42.08  | | | | | | | | | | |   (186)  all_57_9 = e0
% 230.75/42.08  | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | COMBINE_EQS: (13), (186) imply:
% 230.75/42.08  | | | | | | | | | | |   (187)  e1 = e0
% 230.75/42.08  | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | SIMP: (187) implies:
% 230.75/42.08  | | | | | | | | | | |   (188)  e1 = e0
% 230.75/42.08  | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | COMBINE_EQS: (173), (188) imply:
% 230.75/42.08  | | | | | | | | | | |   (189)  all_57_7 = e0
% 230.75/42.08  | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | REF_CLOSE: (4), (5), (8), (12), (14), (15), (16), (17), (18),
% 230.75/42.08  | | | | | | | | | | |            (19), (22), (25), (26), (27), (29), (40), (47),
% 230.75/42.08  | | | | | | | | | | |            (189) are inconsistent by sub-proof #1636.
% 230.75/42.08  | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | Case 2:
% 230.75/42.08  | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | |   (190)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 =
% 230.75/42.08  | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 230.75/42.08  | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | BETA: splitting (190) gives:
% 230.75/42.08  | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | Case 1:
% 230.75/42.08  | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | |   (191)  all_57_10 = e0 & op(e2, e0) = e0
% 230.75/42.08  | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | ALPHA: (191) implies:
% 230.75/42.08  | | | | | | | | | | | |   (192)  op(e2, e0) = e0
% 230.75/42.08  | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | REF_CLOSE: (8), (33), (35), (192) are inconsistent by
% 230.75/42.08  | | | | | | | | | | | |            sub-proof #2470.
% 230.75/42.08  | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | Case 2:
% 230.75/42.08  | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | |   (193)  all_57_11 = e0 & op(e1, e0) = e0
% 230.75/42.08  | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | ALPHA: (193) implies:
% 230.75/42.08  | | | | | | | | | | | |   (194)  all_57_11 = e0
% 230.75/42.08  | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | BETA: splitting (41) gives:
% 230.75/42.08  | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | Case 1:
% 230.75/42.08  | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | |   (195)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 230.75/42.08  | | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 230.75/42.08  | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | BETA: splitting (195) gives:
% 230.75/42.08  | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | Case 1:
% 230.75/42.08  | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | |   (196)  all_57_9 = e2 & op(e3, e0) = e2
% 230.75/42.08  | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | ALPHA: (196) implies:
% 230.75/42.08  | | | | | | | | | | | | | |   (197)  op(e3, e0) = e2
% 230.75/42.08  | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | REF_CLOSE: (8), (43), (49), (197) are inconsistent by
% 230.75/42.08  | | | | | | | | | | | | | |            sub-proof #2331.
% 230.75/42.08  | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | Case 2:
% 230.75/42.08  | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | |   (198)  all_57_10 = e2 & op(e2, e0) = e2
% 230.75/42.08  | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | ALPHA: (198) implies:
% 230.75/42.08  | | | | | | | | | | | | | |   (199)  all_57_10 = e2
% 230.75/42.08  | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | BETA: splitting (39) gives:
% 230.75/42.08  | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | Case 1:
% 230.75/42.08  | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | |   (200)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 230.75/42.08  | | | | | | | | | | | | | | |            e3 & op(e2, e0) = e3)
% 230.75/42.08  | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 230.75/42.08  | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | Case 1:
% 230.75/42.08  | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | |   (201)  all_57_9 = e3 & op(e3, e0) = e3
% 230.75/42.08  | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | REF_CLOSE: (5), (13), (201) are inconsistent by sub-proof
% 230.75/42.08  | | | | | | | | | | | | | | | |            #1269.
% 230.75/42.08  | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | Case 2:
% 230.75/42.08  | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | |   (202)  all_57_10 = e3 & op(e2, e0) = e3
% 230.75/42.08  | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | ALPHA: (202) implies:
% 230.75/42.08  | | | | | | | | | | | | | | | |   (203)  all_57_10 = e3
% 230.75/42.08  | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | COMBINE_EQS: (199), (203) imply:
% 230.75/42.08  | | | | | | | | | | | | | | | |   (204)  e3 = e2
% 230.75/42.08  | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | COMBINE_EQS: (169), (204) imply:
% 230.75/42.08  | | | | | | | | | | | | | | | |   (205)  all_57_1 = e2
% 230.75/42.08  | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (12), (14), (16), (18), (19), (22),
% 230.75/42.08  | | | | | | | | | | | | | | | |            (25), (26), (27), (40), (205) are inconsistent by
% 230.75/42.08  | | | | | | | | | | | | | | | |            sub-proof #1658.
% 230.75/42.08  | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | End of split
% 230.75/42.08  | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | Case 2:
% 230.75/42.08  | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | |   (206)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 230.75/42.08  | | | | | | | | | | | | | | |            e3 & op(e0, e0) = e3)
% 230.75/42.08  | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 230.75/42.08  | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | Case 1:
% 230.75/42.08  | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | |   (207)  all_57_11 = e3 & op(e1, e0) = e3
% 230.75/42.08  | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | ALPHA: (207) implies:
% 230.75/42.08  | | | | | | | | | | | | | | | |   (208)  all_57_11 = e3
% 230.75/42.08  | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (8), (15), (17), (18), (19), (25), (27),
% 230.75/42.08  | | | | | | | | | | | | | | | |            (29), (40), (47), (169), (178), (194), (208) are
% 230.75/42.08  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1280.
% 230.75/42.08  | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | Case 2:
% 230.75/42.08  | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | |   (209)  all_57_15 = e3 & op(e0, e0) = e3
% 230.75/42.08  | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | ALPHA: (209) implies:
% 230.75/42.08  | | | | | | | | | | | | | | | |   (210)  op(e0, e0) = e3
% 230.75/42.08  | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (34), (210) are inconsistent by
% 230.75/42.08  | | | | | | | | | | | | | | | |            sub-proof #2183.
% 230.75/42.08  | | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | | End of split
% 230.75/42.08  | | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | End of split
% 230.75/42.08  | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | End of split
% 230.75/42.08  | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | Case 2:
% 230.75/42.08  | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | |   (211)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 230.75/42.08  | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 230.75/42.08  | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | BETA: splitting (211) gives:
% 230.75/42.08  | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | Case 1:
% 230.75/42.08  | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | |   (212)  all_57_11 = e2 & op(e1, e0) = e2
% 230.75/42.08  | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | ALPHA: (212) implies:
% 230.75/42.08  | | | | | | | | | | | | | |   (213)  all_57_11 = e2
% 230.75/42.08  | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | COMBINE_EQS: (194), (213) imply:
% 230.75/42.08  | | | | | | | | | | | | | |   (214)  e2 = e0
% 230.75/42.08  | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | COMBINE_EQS: (178), (214) imply:
% 230.75/42.08  | | | | | | | | | | | | | |   (215)  all_57_13 = e0
% 230.75/42.08  | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (17), (18), (25), (27), (40), (47),
% 230.75/42.08  | | | | | | | | | | | | | |            (169), (215) are inconsistent by sub-proof #1758.
% 230.75/42.08  | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | Case 2:
% 230.75/42.08  | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | |   (216)  all_57_15 = e2 & op(e0, e0) = e2
% 230.75/42.08  | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | ALPHA: (216) implies:
% 230.75/42.08  | | | | | | | | | | | | | |   (217)  op(e0, e0) = e2
% 230.75/42.08  | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | | REF_CLOSE: (8), (34), (40), (217) are inconsistent by
% 230.75/42.08  | | | | | | | | | | | | | |            sub-proof #2177.
% 230.75/42.08  | | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | | End of split
% 230.75/42.08  | | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | | End of split
% 230.75/42.08  | | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | | End of split
% 230.75/42.08  | | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | | End of split
% 230.75/42.08  | | | | | | | | | | 
% 230.75/42.08  | | | | | | | | | End of split
% 230.75/42.08  | | | | | | | | | 
% 230.75/42.08  | | | | | | | | End of split
% 230.75/42.08  | | | | | | | | 
% 230.75/42.08  | | | | | | | End of split
% 230.75/42.08  | | | | | | | 
% 230.75/42.08  | | | | | | Case 2:
% 230.75/42.08  | | | | | | | 
% 230.75/42.08  | | | | | | |   (218)  all_57_13 = e1 & op(e0, e2) = e1
% 230.75/42.08  | | | | | | | 
% 230.75/42.08  | | | | | | | ALPHA: (218) implies:
% 230.75/42.08  | | | | | | |   (219)  all_57_13 = e1
% 230.75/42.08  | | | | | | | 
% 230.75/42.08  | | | | | | | REF_CLOSE: (2), (4), (5), (7), (8), (10), (11), (12), (14), (15),
% 230.75/42.08  | | | | | | |            (16), (17), (18), (19), (20), (21), (22), (23), (25),
% 230.75/42.08  | | | | | | |            (26), (27), (28), (29), (30), (31), (32), (34), (35),
% 230.75/42.08  | | | | | | |            (37), (40), (44), (47), (219) are inconsistent by
% 230.75/42.08  | | | | | | |            sub-proof #1275.
% 230.75/42.08  | | | | | | | 
% 230.75/42.08  | | | | | | End of split
% 230.75/42.08  | | | | | | 
% 230.75/42.08  | | | | | End of split
% 230.75/42.08  | | | | | 
% 230.75/42.08  | | | | End of split
% 230.75/42.08  | | | | 
% 230.75/42.08  | | | Case 2:
% 230.75/42.08  | | | | 
% 230.75/42.08  | | | |   (220)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0)
% 230.75/42.08  | | | |            = e3)
% 230.75/42.08  | | | | 
% 230.75/42.08  | | | | REF_CLOSE: (5), (13), (14), (19), (220) are inconsistent by sub-proof
% 230.75/42.08  | | | |            #1641.
% 230.75/42.08  | | | | 
% 230.75/42.08  | | | End of split
% 230.75/42.08  | | | 
% 230.75/42.08  | | End of split
% 230.75/42.08  | | 
% 230.75/42.08  | End of split
% 230.75/42.08  | 
% 230.75/42.08  End of proof
% 230.75/42.08  
% 230.75/42.08  Sub-proof #1268 shows that the following formulas are inconsistent:
% 230.75/42.08  ----------------------------------------------------------------
% 230.75/42.08    (1)  all_57_7 = e2 & op(e1, e2) = e2
% 230.75/42.08    (2)  all_57_7 = e1
% 230.75/42.08    (3)   ~ (e2 = e1)
% 230.75/42.08  
% 230.75/42.08  Begin of proof
% 230.75/42.08  | 
% 230.75/42.08  | ALPHA: (1) implies:
% 230.75/42.08  |   (4)  all_57_7 = e2
% 230.75/42.08  | 
% 230.75/42.08  | COMBINE_EQS: (2), (4) imply:
% 230.75/42.08  |   (5)  e2 = e1
% 230.75/42.08  | 
% 230.75/42.08  | REDUCE: (3), (5) imply:
% 230.75/42.08  |   (6)  $false
% 230.75/42.08  | 
% 230.75/42.08  | CLOSE: (6) is inconsistent.
% 230.75/42.08  | 
% 230.75/42.08  End of proof
% 230.75/42.08  
% 230.75/42.08  Sub-proof #1269 shows that the following formulas are inconsistent:
% 230.75/42.08  ----------------------------------------------------------------
% 230.75/42.08    (1)  all_57_9 = e3 & op(e3, e0) = e3
% 230.75/42.08    (2)  all_57_9 = e1
% 230.75/42.08    (3)   ~ (e3 = e1)
% 230.75/42.08  
% 230.75/42.08  Begin of proof
% 230.75/42.08  | 
% 230.75/42.08  | ALPHA: (1) implies:
% 230.75/42.08  |   (4)  all_57_9 = e3
% 230.75/42.08  | 
% 230.75/42.08  | COMBINE_EQS: (2), (4) imply:
% 230.75/42.08  |   (5)  e3 = e1
% 230.75/42.08  | 
% 230.75/42.08  | REDUCE: (3), (5) imply:
% 230.75/42.08  |   (6)  $false
% 230.75/42.08  | 
% 230.75/42.08  | CLOSE: (6) is inconsistent.
% 230.75/42.08  | 
% 230.75/42.08  End of proof
% 230.75/42.08  
% 230.75/42.08  Sub-proof #1270 shows that the following formulas are inconsistent:
% 230.75/42.08  ----------------------------------------------------------------
% 230.75/42.08    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.75/42.08         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.75/42.08    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.75/42.08         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.75/42.08    (3)   ~ (e3 = e1)
% 230.75/42.08    (4)   ~ (all_53_13 = e1)
% 230.75/42.08    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.75/42.08           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.75/42.08    (6)   ~ (all_6_2 = e3)
% 230.75/42.08    (7)  op(e1, e1) = all_6_2
% 230.75/42.08    (8)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.75/42.08         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.75/42.08    (9)  all_57_4 = e0
% 230.75/42.08    (10)  op(e2, e2) = e0
% 230.75/42.08    (11)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.75/42.08          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.75/42.08    (12)  all_57_3 = e0
% 230.75/42.08    (13)   ~ (e3 = e2)
% 230.75/42.08    (14)   ~ (e3 = e0)
% 230.75/42.08    (15)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.75/42.08          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.75/42.09    (16)  op(e0, e3) = all_53_3
% 230.75/42.09    (17)  op(e3, e3) = e2
% 230.75/42.09    (18)   ~ (all_53_3 = e2)
% 230.75/42.09    (19)   ~ (e2 = e0)
% 230.75/42.09    (20)  all_57_13 = e2
% 230.75/42.09    (21)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.75/42.09          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.75/42.09    (22)   ~ (e1 = e0)
% 230.75/42.09    (23)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 230.75/42.09          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 230.75/42.09    (24)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.75/42.09          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.75/42.09    (25)  all_57_14 = e1
% 230.75/42.09    (26)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.75/42.09          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 230.75/42.09            e3)
% 230.75/42.09    (27)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.75/42.09          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.75/42.09            e2)
% 230.75/42.09    (28)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.75/42.09              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.75/42.09                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.75/42.09                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.75/42.09    (29)  op(e0, e0) = e1
% 230.75/42.09    (30)  op(e2, e0) = all_53_13
% 230.75/42.09    (31)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.75/42.09          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.75/42.09    (32)   ~ (e2 = e1)
% 230.75/42.09    (33)  all_57_14 = e2 & op(e0, e1) = e2
% 230.75/42.09    (34)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.75/42.09          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.75/42.09    (35)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.75/42.09          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.75/42.09  
% 230.75/42.09  Begin of proof
% 230.75/42.09  | 
% 230.75/42.09  | ALPHA: (33) implies:
% 230.75/42.09  |   (36)  all_57_14 = e2
% 230.75/42.09  | 
% 230.75/42.09  | COMBINE_EQS: (25), (36) imply:
% 230.75/42.09  |   (37)  e2 = e1
% 230.75/42.09  | 
% 230.75/42.09  | COMBINE_EQS: (20), (37) imply:
% 230.75/42.09  |   (38)  all_57_13 = e1
% 230.75/42.09  | 
% 230.75/42.09  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 230.75/42.09  |            (13), (14), (15), (16), (17), (18), (19), (21), (22), (23), (24),
% 230.75/42.09  |            (26), (27), (28), (29), (30), (31), (32), (34), (35), (38) are
% 230.75/42.09  |            inconsistent by sub-proof #1275.
% 230.75/42.09  | 
% 230.75/42.09  End of proof
% 230.75/42.09  
% 230.75/42.09  Sub-proof #1271 shows that the following formulas are inconsistent:
% 230.75/42.09  ----------------------------------------------------------------
% 230.75/42.09    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.75/42.09         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.75/42.09    (2)   ~ (e3 = e1)
% 230.75/42.09    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.75/42.09           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.75/42.09    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.75/42.09         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.75/42.09    (5)  all_57_9 = e1
% 230.75/42.09    (6)  all_57_11 = e2 & op(e1, e0) = e2
% 230.75/42.09    (7)  all_57_4 = e0
% 230.75/42.09    (8)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.75/42.09         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.75/42.09    (9)  all_57_3 = e0
% 230.75/42.09    (10)   ~ (e3 = e2)
% 230.75/42.09    (11)   ~ (e3 = e0)
% 230.75/42.09    (12)  op(e3, e3) = e2
% 230.75/42.09    (13)  all_57_5 = e3
% 230.75/42.09    (14)   ~ (e2 = e0)
% 230.75/42.09    (15)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.75/42.09          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.75/42.09    (16)   ~ (e1 = e0)
% 230.75/42.09    (17)  op(e0, e0) = e1
% 230.75/42.09    (18)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.75/42.09          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.75/42.09    (19)  all_57_1 = e3
% 230.75/42.09    (20)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 230.75/42.09          (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 230.75/42.09    (21)   ~ (e2 = e1)
% 230.75/42.09  
% 230.75/42.09  Begin of proof
% 230.75/42.09  | 
% 230.75/42.09  | ALPHA: (6) implies:
% 230.75/42.09  |   (22)  all_57_11 = e2
% 230.75/42.09  | 
% 230.75/42.09  | BETA: splitting (20) gives:
% 230.75/42.09  | 
% 230.75/42.09  | Case 1:
% 230.75/42.09  | | 
% 230.75/42.09  | |   (23)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 230.75/42.09  | |           e3)
% 230.75/42.09  | | 
% 230.75/42.09  | | BETA: splitting (23) gives:
% 230.75/42.09  | | 
% 230.75/42.09  | | Case 1:
% 230.75/42.09  | | | 
% 230.75/42.09  | | |   (24)  all_57_9 = e3 & op(e3, e0) = e3
% 230.75/42.09  | | | 
% 230.75/42.09  | | | ALPHA: (24) implies:
% 230.75/42.09  | | |   (25)  all_57_9 = e3
% 230.75/42.09  | | | 
% 230.75/42.09  | | | REF_CLOSE: (2), (5), (25) are inconsistent by sub-proof #1673.
% 230.75/42.09  | | | 
% 230.75/42.09  | | Case 2:
% 230.75/42.09  | | | 
% 230.75/42.09  | | |   (26)  all_57_10 = e3 & op(e2, e0) = e3
% 230.75/42.09  | | | 
% 230.75/42.09  | | | ALPHA: (26) implies:
% 230.75/42.09  | | |   (27)  all_57_10 = e3
% 230.75/42.09  | | | 
% 230.75/42.09  | | | REF_CLOSE: (1), (2), (9), (10), (13), (14), (16), (18), (21), (27) are
% 230.75/42.09  | | |            inconsistent by sub-proof #1693.
% 230.75/42.09  | | | 
% 230.75/42.09  | | End of split
% 230.75/42.09  | | 
% 230.75/42.09  | Case 2:
% 230.75/42.09  | | 
% 230.75/42.09  | |   (28)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 230.75/42.09  | |           e3)
% 230.75/42.09  | | 
% 230.75/42.09  | | BETA: splitting (28) gives:
% 230.75/42.09  | | 
% 230.75/42.09  | | Case 1:
% 230.75/42.09  | | | 
% 230.75/42.09  | | |   (29)  all_57_11 = e3 & op(e1, e0) = e3
% 230.75/42.09  | | | 
% 230.75/42.09  | | | ALPHA: (29) implies:
% 230.75/42.09  | | |   (30)  all_57_11 = e3
% 230.75/42.09  | | | 
% 230.75/42.09  | | | COMBINE_EQS: (22), (30) imply:
% 230.75/42.09  | | |   (31)  e3 = e2
% 230.75/42.09  | | | 
% 230.75/42.09  | | | COMBINE_EQS: (19), (31) imply:
% 230.75/42.09  | | |   (32)  all_57_1 = e2
% 230.75/42.09  | | | 
% 230.75/42.09  | | | REF_CLOSE: (2), (3), (4), (7), (8), (10), (11), (12), (14), (15), (16),
% 230.75/42.09  | | |            (21), (32) are inconsistent by sub-proof #1658.
% 230.75/42.09  | | | 
% 230.75/42.09  | | Case 2:
% 230.75/42.09  | | | 
% 230.75/42.09  | | |   (33)  all_57_15 = e3 & op(e0, e0) = e3
% 230.75/42.09  | | | 
% 230.75/42.09  | | | ALPHA: (33) implies:
% 230.75/42.09  | | |   (34)  op(e0, e0) = e3
% 230.75/42.09  | | | 
% 230.75/42.09  | | | REF_CLOSE: (2), (3), (17), (34) are inconsistent by sub-proof #2183.
% 230.75/42.09  | | | 
% 230.75/42.09  | | End of split
% 230.75/42.09  | | 
% 230.75/42.09  | End of split
% 230.75/42.09  | 
% 230.75/42.09  End of proof
% 230.75/42.09  
% 230.75/42.09  Sub-proof #1272 shows that the following formulas are inconsistent:
% 230.75/42.09  ----------------------------------------------------------------
% 230.75/42.09    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.75/42.09         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.75/42.09    (2)   ~ (e3 = e1)
% 230.75/42.09    (3)  all_57_3 = e0
% 230.75/42.09    (4)   ~ (e3 = e2)
% 230.75/42.09    (5)  all_57_10 = e2
% 230.75/42.09    (6)  all_57_5 = e3
% 230.75/42.09    (7)   ~ (e2 = e0)
% 230.75/42.09    (8)   ~ (e1 = e0)
% 230.75/42.09    (9)  all_57_8 = e2
% 230.75/42.09    (10)  all_57_8 = e0
% 230.75/42.09    (11)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.75/42.09          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.75/42.09    (12)   ~ (e2 = e1)
% 230.75/42.09  
% 230.75/42.09  Begin of proof
% 230.75/42.09  | 
% 230.75/42.09  | COMBINE_EQS: (9), (10) imply:
% 230.75/42.09  |   (13)  e2 = e0
% 230.75/42.09  | 
% 230.75/42.09  | COMBINE_EQS: (5), (13) imply:
% 230.75/42.09  |   (14)  all_57_10 = e0
% 230.75/42.09  | 
% 230.75/42.09  | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (11), (12), (14) are
% 230.75/42.09  |            inconsistent by sub-proof #1518.
% 230.75/42.09  | 
% 230.75/42.09  End of proof
% 230.75/42.09  
% 230.75/42.09  Sub-proof #1273 shows that the following formulas are inconsistent:
% 230.75/42.09  ----------------------------------------------------------------
% 230.75/42.09    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.75/42.09         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.75/42.09    (2)   ~ (e3 = e1)
% 230.75/42.09    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.75/42.09           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.75/42.09    (4)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2)
% 230.75/42.09    (5)  all_57_3 = e0
% 230.75/42.09    (6)   ~ (e3 = e2)
% 230.75/42.09    (7)   ~ (e3 = e0)
% 230.75/42.09    (8)  op(e0, e3) = all_53_3
% 230.75/42.09    (9)  op(e3, e3) = e2
% 230.75/42.09    (10)   ~ (all_53_3 = e2)
% 230.75/42.09    (11)  all_57_10 = e2
% 230.75/42.09    (12)  all_57_5 = e3
% 230.75/42.09    (13)   ~ (e2 = e0)
% 230.75/42.09    (14)  all_57_13 = e2
% 230.75/42.09    (15)   ~ (e1 = e0)
% 230.75/42.09    (16)  all_57_14 = e1
% 230.75/42.09    (17)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.75/42.09          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 230.75/42.09            e3)
% 230.75/42.09    (18)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.75/42.09          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.75/42.09            e2)
% 230.75/42.09    (19)  op(e0, e0) = e1
% 230.75/42.09    (20)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.75/42.09          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.75/42.09    (21)  all_57_1 = e3
% 230.75/42.09    (22)   ~ (e2 = e1)
% 230.75/42.09    (23)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.75/42.09          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.75/42.09    (24)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.75/42.09          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.75/42.09  
% 230.75/42.09  Begin of proof
% 230.75/42.09  | 
% 230.75/42.09  | BETA: splitting (4) gives:
% 230.75/42.09  | 
% 230.75/42.09  | Case 1:
% 230.75/42.09  | | 
% 230.75/42.09  | |   (25)  all_57_6 = e2 & op(e1, e3) = e2
% 230.75/42.09  | | 
% 230.75/42.09  | | ALPHA: (25) implies:
% 230.75/42.09  | |   (26)  all_57_6 = e2
% 230.75/42.09  | | 
% 230.75/42.09  | | BETA: splitting (23) gives:
% 230.75/42.09  | | 
% 230.75/42.09  | | Case 1:
% 230.75/42.09  | | | 
% 230.75/42.09  | | |   (27)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) =
% 230.75/42.09  | | |           e0)
% 230.75/42.09  | | | 
% 230.75/42.09  | | | REF_CLOSE: (1), (2), (3), (5), (6), (9), (12), (13), (15), (20), (22),
% 230.75/42.09  | | |            (27) are inconsistent by sub-proof #1644.
% 230.75/42.09  | | | 
% 230.75/42.09  | | Case 2:
% 230.75/42.09  | | | 
% 230.75/42.09  | | |   (28)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) =
% 230.75/42.09  | | |           e0)
% 230.75/42.09  | | | 
% 230.75/42.09  | | | BETA: splitting (28) gives:
% 230.75/42.09  | | | 
% 230.75/42.09  | | | Case 1:
% 230.75/42.09  | | | | 
% 230.75/42.09  | | | |   (29)  all_57_6 = e0 & op(e1, e3) = e0
% 230.75/42.09  | | | | 
% 230.75/42.09  | | | | ALPHA: (29) implies:
% 230.75/42.09  | | | |   (30)  all_57_6 = e0
% 230.75/42.09  | | | | 
% 230.75/42.09  | | | | COMBINE_EQS: (26), (30) imply:
% 230.75/42.09  | | | |   (31)  e2 = e0
% 230.75/42.09  | | | | 
% 230.75/42.09  | | | | REF_CLOSE: (1), (2), (5), (6), (11), (12), (13), (15), (20), (22), (31)
% 230.75/42.09  | | | |            are inconsistent by sub-proof #1517.
% 230.75/42.09  | | | | 
% 230.75/42.09  | | | Case 2:
% 230.75/42.09  | | | | 
% 230.75/42.09  | | | |   (32)  all_57_12 = e0 & op(e0, e3) = e0
% 230.75/42.09  | | | | 
% 230.75/42.09  | | | | ALPHA: (32) implies:
% 230.75/42.09  | | | |   (33)  all_57_12 = e0
% 230.75/42.09  | | | | 
% 230.75/42.09  | | | | REF_CLOSE: (2), (3), (6), (7), (8), (10), (16), (17), (18), (19), (22),
% 230.75/42.09  | | | |            (33) are inconsistent by sub-proof #1964.
% 230.75/42.09  | | | | 
% 230.75/42.09  | | | End of split
% 230.75/42.09  | | | 
% 230.75/42.09  | | End of split
% 230.75/42.09  | | 
% 230.75/42.09  | Case 2:
% 230.75/42.09  | | 
% 230.75/42.09  | |   (34)  all_57_7 = e2 & op(e1, e2) = e2
% 230.75/42.09  | | 
% 230.75/42.09  | | ALPHA: (34) implies:
% 230.75/42.09  | |   (35)  all_57_7 = e2
% 230.75/42.09  | | 
% 230.75/42.09  | | REF_CLOSE: (2), (5), (14), (15), (21), (22), (24), (35) are inconsistent by
% 230.75/42.09  | |            sub-proof #1698.
% 230.75/42.09  | | 
% 230.75/42.09  | End of split
% 230.75/42.09  | 
% 230.75/42.09  End of proof
% 230.75/42.09  
% 230.75/42.09  Sub-proof #1274 shows that the following formulas are inconsistent:
% 230.75/42.09  ----------------------------------------------------------------
% 230.75/42.09    (1)   ~ (e3 = e1)
% 230.75/42.09    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.75/42.09           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.75/42.09    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.75/42.09         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.75/42.09    (4)  all_57_4 = e0
% 230.75/42.09    (5)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.75/42.09         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.75/42.09    (6)   ~ (e3 = e2)
% 230.75/42.09    (7)   ~ (e3 = e0)
% 230.75/42.09    (8)  op(e3, e3) = e2
% 230.75/42.09    (9)  all_57_5 = e3
% 230.75/42.09    (10)   ~ (e2 = e0)
% 230.75/42.09    (11)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.75/42.09          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.75/42.09    (12)   ~ (e1 = e0)
% 230.75/42.09    (13)  all_57_5 = e2 & op(e2, e1) = e2
% 230.75/42.09    (14)  all_57_1 = e3
% 230.75/42.09    (15)   ~ (e2 = e1)
% 230.75/42.09  
% 230.75/42.09  Begin of proof
% 230.75/42.09  | 
% 230.75/42.09  | ALPHA: (13) implies:
% 230.75/42.09  |   (16)  all_57_5 = e2
% 230.75/42.09  | 
% 230.75/42.09  | COMBINE_EQS: (9), (16) imply:
% 230.75/42.09  |   (17)  e3 = e2
% 230.75/42.09  | 
% 230.75/42.09  | SIMP: (17) implies:
% 230.75/42.09  |   (18)  e3 = e2
% 230.75/42.09  | 
% 230.75/42.09  | COMBINE_EQS: (14), (18) imply:
% 230.75/42.09  |   (19)  all_57_1 = e2
% 230.75/42.09  | 
% 230.75/42.09  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (15),
% 230.75/42.09  |            (19) are inconsistent by sub-proof #1658.
% 230.75/42.09  | 
% 230.75/42.09  End of proof
% 230.75/42.09  
% 230.75/42.09  Sub-proof #1275 shows that the following formulas are inconsistent:
% 230.75/42.09  ----------------------------------------------------------------
% 230.75/42.09    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.75/42.09         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.75/42.09    (2)  all_57_13 = e1
% 230.75/42.09    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.75/42.09         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.75/42.09    (4)   ~ (e3 = e1)
% 230.75/42.09    (5)   ~ (all_53_13 = e1)
% 230.75/42.09    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.75/42.09           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.75/42.09    (7)   ~ (all_6_2 = e3)
% 230.75/42.09    (8)  op(e1, e1) = all_6_2
% 230.75/42.09    (9)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.75/42.09         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.75/42.09    (10)  all_57_4 = e0
% 230.75/42.09    (11)  op(e2, e2) = e0
% 230.75/42.09    (12)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.75/42.09          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.75/42.09    (13)  all_57_3 = e0
% 230.75/42.09    (14)   ~ (e3 = e2)
% 230.75/42.09    (15)   ~ (e3 = e0)
% 230.75/42.09    (16)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.75/42.09          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.75/42.09    (17)  op(e0, e3) = all_53_3
% 230.75/42.09    (18)  op(e3, e3) = e2
% 230.75/42.09    (19)   ~ (all_53_3 = e2)
% 230.75/42.09    (20)   ~ (e2 = e0)
% 230.75/42.09    (21)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.75/42.09          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.75/42.09    (22)   ~ (e1 = e0)
% 230.75/42.09    (23)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 230.75/42.09          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 230.75/42.09    (24)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.75/42.09          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.75/42.09    (25)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.75/42.09          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 230.75/42.09            e3)
% 230.75/42.09    (26)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.75/42.09          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.75/42.09            e2)
% 230.75/42.09    (27)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.75/42.09              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.75/42.09                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.75/42.09                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.75/42.09    (28)  op(e0, e0) = e1
% 230.75/42.09    (29)  op(e2, e0) = all_53_13
% 230.75/42.09    (30)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.75/42.09          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.75/42.09    (31)   ~ (e2 = e1)
% 230.75/42.09    (32)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.75/42.09          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.75/42.09    (33)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.75/42.09          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.75/42.09  
% 230.75/42.09  Begin of proof
% 230.75/42.09  | 
% 230.75/42.09  | BETA: splitting (3) gives:
% 230.75/42.09  | 
% 230.75/42.09  | Case 1:
% 230.75/42.09  | | 
% 230.75/42.09  | |   (34)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 230.75/42.09  | |           e2)
% 230.75/42.09  | | 
% 230.75/42.09  | | REF_CLOSE: (4), (6), (9), (10), (11), (12), (14), (15), (18), (20), (21),
% 230.75/42.09  | |            (22), (31), (34) are inconsistent by sub-proof #1637.
% 230.75/42.09  | | 
% 230.75/42.09  | Case 2:
% 230.75/42.09  | | 
% 230.75/42.09  | |   (35)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 230.75/42.09  | |           e2)
% 230.75/42.09  | | 
% 230.75/42.09  | | BETA: splitting (35) gives:
% 230.75/42.09  | | 
% 230.75/42.09  | | Case 1:
% 230.75/42.09  | | | 
% 230.75/42.09  | | |   (36)  all_57_7 = e2 & op(e1, e2) = e2
% 230.75/42.09  | | | 
% 230.75/42.09  | | | ALPHA: (36) implies:
% 230.75/42.09  | | |   (37)  all_57_7 = e2
% 230.75/42.09  | | | 
% 230.75/42.09  | | | BETA: splitting (23) gives:
% 230.75/42.09  | | | 
% 230.75/42.09  | | | Case 1:
% 230.75/42.09  | | | | 
% 230.75/42.09  | | | |   (38)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1)
% 230.75/42.09  | | | |           = e3)
% 230.75/42.09  | | | | 
% 230.75/42.09  | | | | BETA: splitting (38) gives:
% 230.75/42.09  | | | | 
% 230.75/42.09  | | | | Case 1:
% 230.75/42.09  | | | | | 
% 230.75/42.09  | | | | |   (39)  all_57_4 = e3 & op(e3, e1) = e3
% 230.75/42.09  | | | | | 
% 230.75/42.09  | | | | | REF_CLOSE: (10), (15), (39) are inconsistent by sub-proof #1618.
% 230.75/42.09  | | | | | 
% 230.75/42.09  | | | | Case 2:
% 230.75/42.09  | | | | | 
% 230.75/42.09  | | | | |   (40)  all_57_5 = e3 & op(e2, e1) = e3
% 230.75/42.09  | | | | | 
% 230.75/42.09  | | | | | ALPHA: (40) implies:
% 230.75/42.09  | | | | |   (41)  all_57_5 = e3
% 230.75/42.09  | | | | | 
% 230.75/42.09  | | | | | BETA: splitting (24) gives:
% 230.75/42.09  | | | | | 
% 230.75/42.09  | | | | | Case 1:
% 230.75/42.09  | | | | | | 
% 230.75/42.09  | | | | | |   (42)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2,
% 230.75/42.09  | | | | | |             e2) = e3)
% 230.75/42.09  | | | | | | 
% 230.75/42.09  | | | | | | BETA: splitting (42) gives:
% 230.75/42.09  | | | | | | 
% 230.75/42.09  | | | | | | Case 1:
% 230.75/42.09  | | | | | | | 
% 230.75/42.09  | | | | | | |   (43)  all_57_1 = e3 & op(e3, e2) = e3
% 230.75/42.09  | | | | | | | 
% 230.75/42.09  | | | | | | | ALPHA: (43) implies:
% 230.75/42.09  | | | | | | |   (44)  all_57_1 = e3
% 230.75/42.09  | | | | | | | 
% 230.75/42.09  | | | | | | | BETA: splitting (27) gives:
% 230.75/42.09  | | | | | | | 
% 230.75/42.09  | | | | | | | Case 1:
% 230.75/42.09  | | | | | | | | 
% 230.75/42.09  | | | | | | | |   (45)  all_57_15 = e0 & op(e0, e0) = e0
% 230.75/42.09  | | | | | | | | 
% 230.75/42.09  | | | | | | | | ALPHA: (45) implies:
% 230.75/42.09  | | | | | | | |   (46)  op(e0, e0) = e0
% 230.75/42.09  | | | | | | | | 
% 230.75/42.09  | | | | | | | | BETA: splitting (1) gives:
% 230.75/42.09  | | | | | | | | 
% 230.75/42.09  | | | | | | | | Case 1:
% 230.75/42.09  | | | | | | | | | 
% 230.75/42.09  | | | | | | | | |   (47)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 &
% 230.75/42.09  | | | | | | | | |           op(e2, e2) = e1)
% 230.75/42.09  | | | | | | | | | 
% 230.75/42.09  | | | | | | | | | BETA: splitting (47) gives:
% 230.75/42.09  | | | | | | | | | 
% 230.75/42.09  | | | | | | | | | Case 1:
% 230.75/42.09  | | | | | | | | | | 
% 230.75/42.09  | | | | | | | | | |   (48)  all_57_2 = e1 & op(e2, e3) = e1
% 230.75/42.09  | | | | | | | | | | 
% 230.75/42.09  | | | | | | | | | | ALPHA: (48) implies:
% 230.75/42.09  | | | | | | | | | |   (49)  all_57_2 = e1
% 230.75/42.09  | | | | | | | | | | 
% 230.75/42.09  | | | | | | | | | | GROUND_INST: instantiating (6) with e0, e1, e0, e0, simplifying
% 230.75/42.09  | | | | | | | | | |              with (28), (46) gives:
% 230.75/42.09  | | | | | | | | | |   (50)  e1 = e0
% 230.75/42.09  | | | | | | | | | | 
% 230.75/42.09  | | | | | | | | | | COMBINE_EQS: (49), (50) imply:
% 230.75/42.09  | | | | | | | | | |   (51)  all_57_2 = e0
% 230.75/42.09  | | | | | | | | | | 
% 230.75/42.09  | | | | | | | | | | REF_CLOSE: (1), (4), (13), (14), (20), (22), (30), (31),
% 230.75/42.09  | | | | | | | | | |            (41), (51) are inconsistent by sub-proof #2253.
% 230.75/42.09  | | | | | | | | | | 
% 230.75/42.09  | | | | | | | | | Case 2:
% 230.75/42.09  | | | | | | | | | | 
% 230.75/42.09  | | | | | | | | | |   (52)  all_57_3 = e1 & op(e2, e2) = e1
% 230.75/42.09  | | | | | | | | | | 
% 230.75/42.09  | | | | | | | | | | ALPHA: (52) implies:
% 230.75/42.09  | | | | | | | | | |   (53)  op(e2, e2) = e1
% 230.75/42.09  | | | | | | | | | | 
% 230.75/42.09  | | | | | | | | | | REF_CLOSE: (6), (11), (22), (53) are inconsistent by
% 230.75/42.09  | | | | | | | | | |            sub-proof #2352.
% 230.75/42.09  | | | | | | | | | | 
% 230.75/42.09  | | | | | | | | | End of split
% 230.75/42.09  | | | | | | | | | 
% 230.75/42.09  | | | | | | | | Case 2:
% 230.75/42.09  | | | | | | | | | 
% 230.75/42.09  | | | | | | | | |   (54)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 &
% 230.75/42.09  | | | | | | | | |           op(e2, e0) = e1)
% 230.75/42.09  | | | | | | | | | 
% 230.75/42.09  | | | | | | | | | BETA: splitting (54) gives:
% 230.75/42.09  | | | | | | | | | 
% 230.75/42.09  | | | | | | | | | Case 1:
% 230.75/42.09  | | | | | | | | | | 
% 230.75/42.09  | | | | | | | | | |   (55)  all_57_5 = e1 & op(e2, e1) = e1
% 230.75/42.09  | | | | | | | | | | 
% 230.75/42.09  | | | | | | | | | | ALPHA: (55) implies:
% 230.75/42.09  | | | | | | | | | |   (56)  all_57_5 = e1
% 230.75/42.09  | | | | | | | | | | 
% 230.75/42.09  | | | | | | | | | | COMBINE_EQS: (41), (56) imply:
% 230.75/42.09  | | | | | | | | | |   (57)  e3 = e1
% 230.75/42.09  | | | | | | | | | | 
% 230.75/42.09  | | | | | | | | | | SIMP: (57) implies:
% 230.75/42.09  | | | | | | | | | |   (58)  e3 = e1
% 230.75/42.09  | | | | | | | | | | 
% 230.75/42.09  | | | | | | | | | | COMBINE_EQS: (44), (58) imply:
% 230.75/42.09  | | | | | | | | | |   (59)  all_57_1 = e1
% 230.75/42.09  | | | | | | | | | | 
% 230.75/42.09  | | | | | | | | | | REF_CLOSE: (2), (4), (13), (14), (15), (24), (37), (59) are
% 230.75/42.09  | | | | | | | | | |            inconsistent by sub-proof #2193.
% 230.75/42.09  | | | | | | | | | | 
% 230.75/42.09  | | | | | | | | | Case 2:
% 230.75/42.09  | | | | | | | | | | 
% 230.75/42.09  | | | | | | | | | |   (60)  all_57_10 = e1 & op(e2, e0) = e1
% 230.75/42.09  | | | | | | | | | | 
% 230.75/42.09  | | | | | | | | | | REF_CLOSE: (5), (6), (29), (60) are inconsistent by sub-proof
% 230.75/42.09  | | | | | | | | | |            #2084.
% 230.75/42.09  | | | | | | | | | | 
% 230.75/42.09  | | | | | | | | | End of split
% 230.75/42.09  | | | | | | | | | 
% 230.75/42.09  | | | | | | | | End of split
% 230.75/42.09  | | | | | | | | 
% 230.75/42.09  | | | | | | | Case 2:
% 230.75/42.09  | | | | | | | | 
% 230.75/42.09  | | | | | | | |   (61)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 &
% 230.75/42.09  | | | | | | | |             op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 230.75/42.09  | | | | | | | |             e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) |
% 230.75/42.09  | | | | | | | |           (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 &
% 230.75/42.09  | | | | | | | |             op(e0, e1) = e0))
% 230.75/42.09  | | | | | | | | 
% 230.75/42.09  | | | | | | | | ALPHA: (61) implies:
% 230.75/42.09  | | | | | | | |   (62)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.75/42.09  | | | | | | | |           op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.75/42.09  | | | | | | | | 
% 230.75/42.09  | | | | | | | | BETA: splitting (62) gives:
% 230.75/42.09  | | | | | | | | 
% 230.75/42.09  | | | | | | | | Case 1:
% 230.75/42.09  | | | | | | | | | 
% 230.75/42.09  | | | | | | | | |   (63)  all_57_12 = e0 & op(e0, e3) = e0
% 230.75/42.09  | | | | | | | | | 
% 230.75/42.09  | | | | | | | | | ALPHA: (63) implies:
% 230.75/42.09  | | | | | | | | |   (64)  all_57_12 = e0
% 230.75/42.09  | | | | | | | | | 
% 230.75/42.10  | | | | | | | | | REF_CLOSE: (2), (4), (6), (14), (15), (17), (19), (25), (26),
% 230.75/42.10  | | | | | | | | |            (28), (31), (64) are inconsistent by sub-proof
% 230.75/42.10  | | | | | | | | |            #1975.
% 230.75/42.10  | | | | | | | | | 
% 230.75/42.10  | | | | | | | | Case 2:
% 230.75/42.10  | | | | | | | | | 
% 230.75/42.10  | | | | | | | | |   (65)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 &
% 230.75/42.10  | | | | | | | | |           op(e0, e1) = e0)
% 230.75/42.10  | | | | | | | | | 
% 230.75/42.10  | | | | | | | | | BETA: splitting (65) gives:
% 230.75/42.10  | | | | | | | | | 
% 230.75/42.10  | | | | | | | | | Case 1:
% 230.75/42.10  | | | | | | | | | | 
% 230.75/42.10  | | | | | | | | | |   (66)  all_57_13 = e0 & op(e0, e2) = e0
% 230.75/42.10  | | | | | | | | | | 
% 230.75/42.10  | | | | | | | | | | ALPHA: (66) implies:
% 230.75/42.10  | | | | | | | | | |   (67)  all_57_13 = e0
% 230.75/42.10  | | | | | | | | | | 
% 230.75/42.10  | | | | | | | | | | REF_CLOSE: (4), (13), (22), (31), (33), (37), (44), (67) are
% 230.75/42.10  | | | | | | | | | |            inconsistent by sub-proof #1759.
% 230.75/42.10  | | | | | | | | | | 
% 230.75/42.10  | | | | | | | | | Case 2:
% 230.75/42.10  | | | | | | | | | | 
% 230.75/42.10  | | | | | | | | | |   (68)  all_57_14 = e0 & op(e0, e1) = e0
% 230.75/42.10  | | | | | | | | | | 
% 230.75/42.10  | | | | | | | | | | ALPHA: (68) implies:
% 230.75/42.10  | | | | | | | | | |   (69)  all_57_14 = e0
% 230.75/42.10  | | | | | | | | | | 
% 230.75/42.10  | | | | | | | | | | REF_CLOSE: (4), (6), (10), (14), (16), (20), (22), (31),
% 230.75/42.10  | | | | | | | | | |            (32), (41), (69) are inconsistent by sub-proof
% 230.75/42.10  | | | | | | | | | |            #2378.
% 230.75/42.10  | | | | | | | | | | 
% 230.75/42.10  | | | | | | | | | End of split
% 230.75/42.10  | | | | | | | | | 
% 230.75/42.10  | | | | | | | | End of split
% 230.75/42.10  | | | | | | | | 
% 230.75/42.10  | | | | | | | End of split
% 230.75/42.10  | | | | | | | 
% 230.75/42.10  | | | | | | Case 2:
% 230.75/42.10  | | | | | | | 
% 230.75/42.10  | | | | | | |   (70)  all_57_3 = e3 & op(e2, e2) = e3
% 230.75/42.10  | | | | | | | 
% 230.75/42.10  | | | | | | | ALPHA: (70) implies:
% 230.75/42.10  | | | | | | |   (71)  all_57_3 = e3
% 230.75/42.10  | | | | | | | 
% 230.75/42.10  | | | | | | | REF_CLOSE: (13), (15), (71) are inconsistent by sub-proof #2358.
% 230.75/42.10  | | | | | | | 
% 230.75/42.10  | | | | | | End of split
% 230.75/42.10  | | | | | | 
% 230.75/42.10  | | | | | Case 2:
% 230.75/42.10  | | | | | | 
% 230.75/42.10  | | | | | |   (72)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0,
% 230.75/42.10  | | | | | |             e2) = e3)
% 230.75/42.10  | | | | | | 
% 230.75/42.10  | | | | | | BETA: splitting (72) gives:
% 230.75/42.10  | | | | | | 
% 230.75/42.10  | | | | | | Case 1:
% 230.75/42.10  | | | | | | | 
% 230.75/42.10  | | | | | | |   (73)  all_57_7 = e3 & op(e1, e2) = e3
% 230.75/42.10  | | | | | | | 
% 230.75/42.10  | | | | | | | REF_CLOSE: (14), (37), (73) are inconsistent by sub-proof #2194.
% 230.75/42.10  | | | | | | | 
% 230.75/42.10  | | | | | | Case 2:
% 230.75/42.10  | | | | | | | 
% 230.75/42.10  | | | | | | |   (74)  all_57_13 = e3 & op(e0, e2) = e3
% 230.75/42.10  | | | | | | | 
% 230.75/42.10  | | | | | | | REF_CLOSE: (2), (4), (74) are inconsistent by sub-proof #1977.
% 230.75/42.10  | | | | | | | 
% 230.75/42.10  | | | | | | End of split
% 230.75/42.10  | | | | | | 
% 230.75/42.10  | | | | | End of split
% 230.75/42.10  | | | | | 
% 230.75/42.10  | | | | End of split
% 230.75/42.10  | | | | 
% 230.75/42.10  | | | Case 2:
% 230.75/42.10  | | | | 
% 230.75/42.10  | | | |   (75)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1)
% 230.75/42.10  | | | |           = e3)
% 230.75/42.10  | | | | 
% 230.75/42.10  | | | | REF_CLOSE: (2), (6), (7), (8), (14), (17), (19), (26), (28), (31), (75)
% 230.75/42.10  | | | |            are inconsistent by sub-proof #1290.
% 230.75/42.10  | | | | 
% 230.75/42.10  | | | End of split
% 230.75/42.10  | | | 
% 230.75/42.10  | | Case 2:
% 230.75/42.10  | | | 
% 230.75/42.10  | | |   (76)  all_57_13 = e2 & op(e0, e2) = e2
% 230.75/42.10  | | | 
% 230.75/42.10  | | | ALPHA: (76) implies:
% 230.75/42.10  | | |   (77)  all_57_13 = e2
% 230.75/42.10  | | | 
% 230.75/42.10  | | | REF_CLOSE: (2), (31), (77) are inconsistent by sub-proof #2327.
% 230.75/42.10  | | | 
% 230.75/42.10  | | End of split
% 230.75/42.10  | | 
% 230.75/42.10  | End of split
% 230.75/42.10  | 
% 230.75/42.10  End of proof
% 230.75/42.10  
% 230.75/42.10  Sub-proof #1276 shows that the following formulas are inconsistent:
% 230.75/42.10  ----------------------------------------------------------------
% 230.75/42.10    (1)  all_57_0 = e2
% 230.75/42.10    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.75/42.10         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.75/42.10    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.75/42.10         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.75/42.10    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.75/42.10         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.75/42.10    (5)   ~ (e3 = e1)
% 230.75/42.10    (6)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.75/42.10         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.75/42.10    (7)   ~ (all_53_13 = e1)
% 230.75/42.10    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.75/42.10           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.75/42.10    (9)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.75/42.10         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.75/42.10    (10)   ~ (all_6_2 = e3)
% 230.75/42.10    (11)  op(e1, e1) = all_6_2
% 230.75/42.10    (12)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.75/42.10          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.75/42.10    (13)  all_57_9 = e1
% 230.75/42.10    (14)  all_57_4 = e0
% 230.75/42.10    (15)  op(e2, e2) = e0
% 230.75/42.10    (16)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.75/42.10          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.75/42.10    (17)  all_57_3 = e0
% 230.75/42.10    (18)   ~ (e3 = e2)
% 230.75/42.10    (19)   ~ (e3 = e0)
% 230.75/42.10    (20)  op(e0, e3) = all_53_3
% 230.75/42.10    (21)  op(e3, e3) = e2
% 230.75/42.10    (22)   ~ (all_53_3 = e2)
% 230.75/42.10    (23)  all_57_12 = e1
% 230.75/42.10    (24)   ~ (e2 = e0)
% 230.75/42.10    (25)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.75/42.10          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.75/42.10    (26)   ~ (e1 = e0)
% 230.75/42.10    (27)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 230.75/42.10          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 230.75/42.10    (28)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.75/42.10          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.75/42.10    (29)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.75/42.10          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 230.75/42.10            e3)
% 230.75/42.10    (30)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.75/42.10          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.75/42.10            e2)
% 230.75/42.10    (31)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.75/42.10              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.75/42.10                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.75/42.10                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.75/42.10    (32)  op(e0, e0) = e1
% 230.75/42.10    (33)  op(e2, e0) = all_53_13
% 230.75/42.10    (34)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.75/42.10          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.75/42.10    (35)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.75/42.10          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.75/42.10    (36)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.75/42.10          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.75/42.10    (37)   ~ (e2 = e1)
% 230.75/42.10    (38)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.75/42.10          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.75/42.10    (39)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.75/42.10          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.75/42.10    (40)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.75/42.10          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.75/42.10    (41)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.75/42.10          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.75/42.10    (42)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.75/42.10          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.75/42.10    (43)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.75/42.10          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.75/42.10  
% 230.75/42.10  Begin of proof
% 230.75/42.10  | 
% 230.75/42.10  | BETA: splitting (25) gives:
% 230.75/42.10  | 
% 230.75/42.10  | Case 1:
% 230.75/42.10  | | 
% 230.75/42.10  | |   (44)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) =
% 230.75/42.10  | |           e3)
% 230.75/42.10  | | 
% 230.75/42.10  | | BETA: splitting (44) gives:
% 230.75/42.10  | | 
% 230.75/42.10  | | Case 1:
% 230.75/42.10  | | | 
% 230.75/42.10  | | |   (45)  all_57_0 = e3 & op(e3, e3) = e3
% 230.75/42.10  | | | 
% 230.75/42.10  | | | ALPHA: (45) implies:
% 230.75/42.10  | | |   (46)  op(e3, e3) = e3
% 230.75/42.10  | | | 
% 230.75/42.10  | | | REF_CLOSE: (8), (18), (21), (46) are inconsistent by sub-proof #2490.
% 230.75/42.10  | | | 
% 230.75/42.10  | | Case 2:
% 230.75/42.10  | | | 
% 230.75/42.10  | | |   (47)  all_57_1 = e3 & op(e3, e2) = e3
% 230.75/42.10  | | | 
% 230.75/42.10  | | | ALPHA: (47) implies:
% 230.75/42.10  | | |   (48)  all_57_1 = e3
% 230.75/42.10  | | | 
% 230.75/42.10  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 230.75/42.10  | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 230.75/42.10  | | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 230.75/42.10  | | |            (34), (35), (36), (37), (38), (39), (40), (41), (42), (43),
% 230.75/42.10  | | |            (48) are inconsistent by sub-proof #1277.
% 230.75/42.10  | | | 
% 230.75/42.10  | | End of split
% 230.75/42.10  | | 
% 230.75/42.10  | Case 2:
% 230.75/42.10  | | 
% 230.75/42.10  | |   (49)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) =
% 230.75/42.10  | |           e3)
% 230.75/42.10  | | 
% 230.75/42.10  | | REF_CLOSE: (5), (13), (14), (19), (49) are inconsistent by sub-proof #1641.
% 230.75/42.10  | | 
% 230.75/42.10  | End of split
% 230.75/42.10  | 
% 230.75/42.10  End of proof
% 230.75/42.10  
% 230.75/42.10  Sub-proof #1277 shows that the following formulas are inconsistent:
% 230.75/42.10  ----------------------------------------------------------------
% 230.75/42.10    (1)  all_57_0 = e2
% 230.75/42.10    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.75/42.10         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.75/42.10    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.75/42.10         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.75/42.10    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.75/42.10         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.93/42.10    (5)   ~ (e3 = e1)
% 230.93/42.10    (6)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.93/42.10         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.93/42.10    (7)   ~ (all_53_13 = e1)
% 230.93/42.10    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.93/42.10           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.93/42.10    (9)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.93/42.10         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.93/42.10    (10)   ~ (all_6_2 = e3)
% 230.93/42.10    (11)  op(e1, e1) = all_6_2
% 230.93/42.10    (12)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.93/42.10          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.93/42.10    (13)  all_57_4 = e0
% 230.93/42.10    (14)  op(e2, e2) = e0
% 230.93/42.10    (15)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.93/42.10          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.93/42.10    (16)  all_57_3 = e0
% 230.93/42.10    (17)   ~ (e3 = e2)
% 230.93/42.10    (18)   ~ (e3 = e0)
% 230.93/42.10    (19)  op(e0, e3) = all_53_3
% 230.93/42.10    (20)  op(e3, e3) = e2
% 230.93/42.10    (21)   ~ (all_53_3 = e2)
% 230.93/42.10    (22)  all_57_12 = e1
% 230.93/42.10    (23)   ~ (e2 = e0)
% 230.93/42.10    (24)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.93/42.10          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.93/42.10    (25)   ~ (e1 = e0)
% 230.93/42.10    (26)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 230.93/42.10          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 230.93/42.10    (27)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.93/42.10          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.93/42.10    (28)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.93/42.10          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 230.93/42.10            e3)
% 230.93/42.10    (29)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.93/42.10          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.93/42.10            e2)
% 230.93/42.10    (30)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.93/42.10              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.93/42.10                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.93/42.10                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.93/42.10    (31)  op(e0, e0) = e1
% 230.93/42.10    (32)  op(e2, e0) = all_53_13
% 230.93/42.10    (33)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.93/42.10          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.93/42.10    (34)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.93/42.10          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.93/42.10    (35)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.93/42.10          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.93/42.10    (36)  all_57_1 = e3
% 230.93/42.10    (37)   ~ (e2 = e1)
% 230.93/42.10    (38)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.93/42.10          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.93/42.10    (39)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.93/42.10          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.93/42.10    (40)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.93/42.10          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.93/42.10    (41)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.93/42.10          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.93/42.10    (42)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.93/42.10          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.93/42.10    (43)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.93/42.10          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.93/42.10  
% 230.93/42.10  Begin of proof
% 230.93/42.10  | 
% 230.93/42.10  | BETA: splitting (41) gives:
% 230.93/42.10  | 
% 230.93/42.10  | Case 1:
% 230.93/42.10  | | 
% 230.93/42.10  | |   (44)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) =
% 230.93/42.10  | |           e0)
% 230.93/42.10  | | 
% 230.93/42.10  | | REF_CLOSE: (2), (5), (8), (16), (17), (18), (20), (23), (25), (33), (34),
% 230.93/42.10  | |            (37), (44) are inconsistent by sub-proof #1654.
% 230.93/42.10  | | 
% 230.93/42.10  | Case 2:
% 230.93/42.10  | | 
% 230.93/42.10  | |   (45)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) =
% 230.93/42.10  | |           e0)
% 230.93/42.10  | | 
% 230.93/42.10  | | BETA: splitting (45) gives:
% 230.93/42.10  | | 
% 230.93/42.10  | | Case 1:
% 230.93/42.10  | | | 
% 230.93/42.10  | | |   (46)  all_57_6 = e0 & op(e1, e3) = e0
% 230.93/42.10  | | | 
% 230.93/42.10  | | | ALPHA: (46) implies:
% 230.93/42.10  | | |   (47)  all_57_6 = e0
% 230.93/42.10  | | | 
% 230.93/42.10  | | | BETA: splitting (35) gives:
% 230.93/42.10  | | | 
% 230.93/42.10  | | | Case 1:
% 230.93/42.10  | | | | 
% 230.93/42.10  | | | |   (48)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3)
% 230.93/42.10  | | | |           = e3)
% 230.93/42.10  | | | | 
% 230.93/42.10  | | | | BETA: splitting (48) gives:
% 230.93/42.10  | | | | 
% 230.93/42.10  | | | | Case 1:
% 230.93/42.10  | | | | | 
% 230.93/42.10  | | | | |   (49)  all_57_0 = e3 & op(e3, e3) = e3
% 230.93/42.10  | | | | | 
% 230.93/42.10  | | | | | ALPHA: (49) implies:
% 230.93/42.10  | | | | |   (50)  op(e3, e3) = e3
% 230.93/42.10  | | | | | 
% 230.93/42.10  | | | | | REF_CLOSE: (8), (17), (20), (50) are inconsistent by sub-proof #2490.
% 230.93/42.10  | | | | | 
% 230.93/42.10  | | | | Case 2:
% 230.93/42.10  | | | | | 
% 230.93/42.10  | | | | |   (51)  all_57_2 = e3 & op(e2, e3) = e3
% 230.93/42.10  | | | | | 
% 230.93/42.10  | | | | | ALPHA: (51) implies:
% 230.93/42.10  | | | | |   (52)  all_57_2 = e3
% 230.93/42.10  | | | | | 
% 230.93/42.10  | | | | | BETA: splitting (30) gives:
% 230.93/42.10  | | | | | 
% 230.93/42.10  | | | | | Case 1:
% 230.93/42.10  | | | | | | 
% 230.93/42.10  | | | | | |   (53)  all_57_15 = e0 & op(e0, e0) = e0
% 230.93/42.10  | | | | | | 
% 230.93/42.10  | | | | | | ALPHA: (53) implies:
% 230.93/42.10  | | | | | |   (54)  op(e0, e0) = e0
% 230.93/42.10  | | | | | | 
% 230.93/42.10  | | | | | | BETA: splitting (43) gives:
% 230.93/42.10  | | | | | | 
% 230.93/42.10  | | | | | | Case 1:
% 230.93/42.10  | | | | | | | 
% 230.93/42.10  | | | | | | |   (55)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 &
% 230.93/42.10  | | | | | | |           op(e2, e2) = e1)
% 230.93/42.10  | | | | | | | 
% 230.93/42.10  | | | | | | | REF_CLOSE: (5), (8), (14), (25), (36), (55) are inconsistent by
% 230.93/42.10  | | | | | | |            sub-proof #2206.
% 230.93/42.10  | | | | | | | 
% 230.93/42.10  | | | | | | Case 2:
% 230.93/42.10  | | | | | | | 
% 230.93/42.10  | | | | | | |   (56)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 &
% 230.93/42.10  | | | | | | |           op(e0, e2) = e1)
% 230.93/42.10  | | | | | | | 
% 230.93/42.10  | | | | | | | BETA: splitting (56) gives:
% 230.93/42.10  | | | | | | | 
% 230.93/42.10  | | | | | | | Case 1:
% 230.93/42.10  | | | | | | | | 
% 230.93/42.10  | | | | | | | |   (57)  all_57_7 = e1 & op(e1, e2) = e1
% 230.93/42.10  | | | | | | | | 
% 230.93/42.10  | | | | | | | | ALPHA: (57) implies:
% 230.93/42.10  | | | | | | | |   (58)  all_57_7 = e1
% 230.93/42.10  | | | | | | | | 
% 230.93/42.10  | | | | | | | | BETA: splitting (2) gives:
% 230.93/42.10  | | | | | | | | 
% 230.93/42.10  | | | | | | | | Case 1:
% 230.93/42.10  | | | | | | | | | 
% 230.93/42.10  | | | | | | | | |   (59)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 &
% 230.93/42.10  | | | | | | | | |           op(e2, e2) = e1)
% 230.93/42.10  | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | BETA: splitting (59) gives:
% 230.93/42.10  | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | Case 1:
% 230.93/42.10  | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | |   (60)  all_57_2 = e1 & op(e2, e3) = e1
% 230.93/42.10  | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | ALPHA: (60) implies:
% 230.93/42.10  | | | | | | | | | |   (61)  all_57_2 = e1
% 230.93/42.10  | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | REF_CLOSE: (5), (52), (61) are inconsistent by sub-proof
% 230.93/42.10  | | | | | | | | | |            #2397.
% 230.93/42.10  | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | Case 2:
% 230.93/42.10  | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | |   (62)  all_57_3 = e1 & op(e2, e2) = e1
% 230.93/42.10  | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | ALPHA: (62) implies:
% 230.93/42.10  | | | | | | | | | |   (63)  op(e2, e2) = e1
% 230.93/42.10  | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | REF_CLOSE: (8), (14), (25), (63) are inconsistent by
% 230.93/42.10  | | | | | | | | | |            sub-proof #2352.
% 230.93/42.10  | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | End of split
% 230.93/42.10  | | | | | | | | | 
% 230.93/42.10  | | | | | | | | Case 2:
% 230.93/42.10  | | | | | | | | | 
% 230.93/42.10  | | | | | | | | |   (64)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 &
% 230.93/42.10  | | | | | | | | |           op(e2, e0) = e1)
% 230.93/42.10  | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | BETA: splitting (64) gives:
% 230.93/42.10  | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | Case 1:
% 230.93/42.10  | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | |   (65)  all_57_5 = e1 & op(e2, e1) = e1
% 230.93/42.10  | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | ALPHA: (65) implies:
% 230.93/42.10  | | | | | | | | | |   (66)  all_57_5 = e1
% 230.93/42.10  | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | BETA: splitting (4) gives:
% 230.93/42.10  | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | Case 1:
% 230.93/42.10  | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | |   (67)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 230.93/42.10  | | | | | | | | | | |           & op(e2, e2) = e2)
% 230.93/42.10  | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | | REF_CLOSE: (5), (8), (12), (13), (14), (15), (17), (18),
% 230.93/42.10  | | | | | | | | | | |            (20), (23), (24), (25), (37), (67) are
% 230.93/42.10  | | | | | | | | | | |            inconsistent by sub-proof #1637.
% 230.93/42.10  | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | Case 2:
% 230.93/42.10  | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | |   (68)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 230.93/42.10  | | | | | | | | | | |           e2 & op(e0, e2) = e2)
% 230.93/42.10  | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | | BETA: splitting (68) gives:
% 230.93/42.10  | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | | Case 1:
% 230.93/42.10  | | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | | |   (69)  all_57_7 = e2 & op(e1, e2) = e2
% 230.93/42.10  | | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | | | ALPHA: (69) implies:
% 230.93/42.10  | | | | | | | | | | | |   (70)  all_57_7 = e2
% 230.93/42.10  | | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | | | REF_CLOSE: (37), (58), (70) are inconsistent by sub-proof
% 230.93/42.10  | | | | | | | | | | | |            #1761.
% 230.93/42.10  | | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | | Case 2:
% 230.93/42.10  | | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | | |   (71)  all_57_13 = e2 & op(e0, e2) = e2
% 230.93/42.10  | | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | | | ALPHA: (71) implies:
% 230.93/42.10  | | | | | | | | | | | |   (72)  all_57_13 = e2
% 230.93/42.10  | | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | | | BETA: splitting (34) gives:
% 230.93/42.10  | | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | | | Case 1:
% 230.93/42.10  | | | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | | | |   (73)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 230.93/42.10  | | | | | | | | | | | | |           & op(e2, e2) = e2)
% 230.93/42.10  | | | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | | | | BETA: splitting (73) gives:
% 230.93/42.10  | | | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | | | | Case 1:
% 230.93/42.10  | | | | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | | | | |   (74)  all_57_2 = e2 & op(e2, e3) = e2
% 230.93/42.10  | | | | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | | | | | ALPHA: (74) implies:
% 230.93/42.10  | | | | | | | | | | | | | |   (75)  all_57_2 = e2
% 230.93/42.10  | | | | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | | | | | COMBINE_EQS: (52), (75) imply:
% 230.93/42.10  | | | | | | | | | | | | | |   (76)  e3 = e2
% 230.93/42.10  | | | | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | | | | | SIMP: (76) implies:
% 230.93/42.10  | | | | | | | | | | | | | |   (77)  e3 = e2
% 230.93/42.10  | | | | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | | | | | COMBINE_EQS: (36), (77) imply:
% 230.93/42.10  | | | | | | | | | | | | | |   (78)  all_57_1 = e2
% 230.93/42.10  | | | | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (12), (13), (15), (17), (18), (20),
% 230.93/42.10  | | | | | | | | | | | | | |            (23), (24), (25), (37), (78) are inconsistent by
% 230.93/42.10  | | | | | | | | | | | | | |            sub-proof #1658.
% 230.93/42.10  | | | | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | | | | Case 2:
% 230.93/42.10  | | | | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | | | | |   (79)  all_57_3 = e2 & op(e2, e2) = e2
% 230.93/42.10  | | | | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | | | | | ALPHA: (79) implies:
% 230.93/42.10  | | | | | | | | | | | | | |   (80)  op(e2, e2) = e2
% 230.93/42.10  | | | | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | | | | | REF_CLOSE: (8), (14), (23), (80) are inconsistent by
% 230.93/42.10  | | | | | | | | | | | | | |            sub-proof #2472.
% 230.93/42.10  | | | | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | | | | End of split
% 230.93/42.10  | | | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | | | Case 2:
% 230.93/42.10  | | | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | | | |   (81)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 230.93/42.10  | | | | | | | | | | | | |           e2 & op(e2, e0) = e2)
% 230.93/42.10  | | | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | | | | BETA: splitting (81) gives:
% 230.93/42.10  | | | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | | | | Case 1:
% 230.93/42.10  | | | | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | | | | |   (82)  all_57_5 = e2 & op(e2, e1) = e2
% 230.93/42.10  | | | | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | | | | | ALPHA: (82) implies:
% 230.93/42.10  | | | | | | | | | | | | | |   (83)  all_57_5 = e2
% 230.93/42.10  | | | | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | | | | | COMBINE_EQS: (66), (83) imply:
% 230.93/42.10  | | | | | | | | | | | | | |   (84)  e2 = e1
% 230.93/42.10  | | | | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | | | | | COMBINE_EQS: (72), (84) imply:
% 230.93/42.10  | | | | | | | | | | | | | |   (85)  all_57_13 = e1
% 230.93/42.10  | | | | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | | | | | REF_CLOSE: (2), (5), (8), (10), (11), (13), (16), (17), (18),
% 230.93/42.10  | | | | | | | | | | | | | |            (19), (21), (23), (25), (26), (29), (31), (33),
% 230.93/42.10  | | | | | | | | | | | | | |            (34), (37), (52), (85) are inconsistent by
% 230.93/42.10  | | | | | | | | | | | | | |            sub-proof #1289.
% 230.93/42.10  | | | | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | | | | Case 2:
% 230.93/42.10  | | | | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | | | | |   (86)  all_57_10 = e2 & op(e2, e0) = e2
% 230.93/42.10  | | | | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | | | | | ALPHA: (86) implies:
% 230.93/42.10  | | | | | | | | | | | | | |   (87)  all_57_10 = e2
% 230.93/42.10  | | | | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | | | | | BETA: splitting (9) gives:
% 230.93/42.10  | | | | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | | | | | Case 1:
% 230.93/42.10  | | | | | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | | | | | |   (88)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 230.93/42.10  | | | | | | | | | | | | | | |           & op(e1, e2) = e3)
% 230.93/42.10  | | | | | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | | | | | | BETA: splitting (88) gives:
% 230.93/42.10  | | | | | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | | | | | | Case 1:
% 230.93/42.10  | | | | | | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | | | | | | |   (89)  all_57_6 = e3 & op(e1, e3) = e3
% 230.93/42.10  | | | | | | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | | | | | | | ALPHA: (89) implies:
% 230.93/42.10  | | | | | | | | | | | | | | | |   (90)  all_57_6 = e3
% 230.93/42.10  | | | | | | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (5), (8), (17), (18), (23), (25), (37),
% 230.93/42.10  | | | | | | | | | | | | | | | |            (39), (41), (52), (90) are inconsistent by
% 230.93/42.10  | | | | | | | | | | | | | | | |            sub-proof #1286.
% 230.93/42.10  | | | | | | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | | | | | | Case 2:
% 230.93/42.10  | | | | | | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | | | | | | |   (91)  all_57_7 = e3 & op(e1, e2) = e3
% 230.93/42.10  | | | | | | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | | | | | | | ALPHA: (91) implies:
% 230.93/42.10  | | | | | | | | | | | | | | | |   (92)  all_57_7 = e3
% 230.93/42.10  | | | | | | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | | | | | | | REF_CLOSE: (5), (16), (25), (36), (37), (43), (72), (92) are
% 230.93/42.10  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1779.
% 230.93/42.10  | | | | | | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | | | | | | End of split
% 230.93/42.10  | | | | | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | | | | | Case 2:
% 230.93/42.10  | | | | | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | | | | | |   (93)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 230.93/42.10  | | | | | | | | | | | | | | |           e3 & op(e1, e0) = e3)
% 230.93/42.10  | | | | | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | | | | | | BETA: splitting (93) gives:
% 230.93/42.10  | | | | | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | | | | | | Case 1:
% 230.93/42.10  | | | | | | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | | | | | | |   (94)  all_57_8 = e3 & op(e1, e1) = e3
% 230.93/42.10  | | | | | | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | | | | | | | ALPHA: (94) implies:
% 230.93/42.10  | | | | | | | | | | | | | | | |   (95)  op(e1, e1) = e3
% 230.93/42.10  | | | | | | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10), (11), (95) are inconsistent by
% 230.93/42.10  | | | | | | | | | | | | | | | |            sub-proof #2468.
% 230.93/42.10  | | | | | | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | | | | | | Case 2:
% 230.93/42.10  | | | | | | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | | | | | | |   (96)  all_57_11 = e3 & op(e1, e0) = e3
% 230.93/42.10  | | | | | | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | | | | | | | ALPHA: (96) implies:
% 230.93/42.10  | | | | | | | | | | | | | | | |   (97)  all_57_11 = e3
% 230.93/42.10  | | | | | | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | | | | | | | BETA: splitting (28) gives:
% 230.93/42.10  | | | | | | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | | | | | | | Case 1:
% 230.93/42.10  | | | | | | | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | | | | | | | |   (98)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 230.93/42.10  | | | | | | | | | | | | | | | | |           e3 & op(e0, e2) = e3)
% 230.93/42.10  | | | | | | | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | | | | | | | | BETA: splitting (98) gives:
% 230.93/42.10  | | | | | | | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | | | | | | | | Case 1:
% 230.93/42.10  | | | | | | | | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | | | | | | | | |   (99)  all_57_12 = e3 & op(e0, e3) = e3
% 230.93/42.10  | | | | | | | | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (22), (99) are inconsistent by sub-proof
% 230.93/42.10  | | | | | | | | | | | | | | | | | |            #1285.
% 230.93/42.10  | | | | | | | | | | | | | | | | | | 
% 230.93/42.10  | | | | | | | | | | | | | | | | | Case 2:
% 230.93/42.10  | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | |   (100)  all_57_13 = e3 & op(e0, e2) = e3
% 230.93/42.11  | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | | ALPHA: (100) implies:
% 230.93/42.11  | | | | | | | | | | | | | | | | | |   (101)  all_57_13 = e3
% 230.93/42.11  | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (72), (101) imply:
% 230.93/42.11  | | | | | | | | | | | | | | | | | |   (102)  e3 = e2
% 230.93/42.11  | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (36), (102) imply:
% 230.93/42.11  | | | | | | | | | | | | | | | | | |   (103)  all_57_1 = e2
% 230.93/42.11  | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (12), (13), (15), (17), (18), (20),
% 230.93/42.11  | | | | | | | | | | | | | | | | | |            (23), (24), (25), (37), (103) are inconsistent by
% 230.93/42.11  | | | | | | | | | | | | | | | | | |            sub-proof #1658.
% 230.93/42.11  | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | End of split
% 230.93/42.11  | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | Case 2:
% 230.93/42.11  | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | |   (104)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 230.93/42.11  | | | | | | | | | | | | | | | | |            e3 & op(e0, e0) = e3)
% 230.93/42.11  | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | BETA: splitting (104) gives:
% 230.93/42.11  | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | Case 1:
% 230.93/42.11  | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | |   (105)  all_57_14 = e3 & op(e0, e1) = e3
% 230.93/42.11  | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | | ALPHA: (105) implies:
% 230.93/42.11  | | | | | | | | | | | | | | | | | |   (106)  all_57_14 = e3
% 230.93/42.11  | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | | BETA: splitting (40) gives:
% 230.93/42.11  | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | | Case 1:
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | | |   (107)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 230.93/42.11  | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e2)
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | Case 1:
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | |   (108)  all_57_4 = e2 & op(e3, e1) = e2
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | ALPHA: (108) implies:
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | |   (109)  all_57_4 = e2
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13), (109) imply:
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | |   (110)  e2 = e0
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | SIMP: (110) implies:
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | |   (111)  e2 = e0
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (72), (111) imply:
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | |   (112)  all_57_13 = e0
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (16), (17), (23), (25), (36), (37),
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | |            (43), (112) are inconsistent by sub-proof #1758.
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | Case 2:
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | |   (113)  all_57_5 = e2 & op(e2, e1) = e2
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | ALPHA: (113) implies:
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | |   (114)  all_57_5 = e2
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (66), (114) imply:
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | |   (115)  e2 = e1
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (72), (115) imply:
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | |   (116)  all_57_13 = e1
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (17), (19), (21), (29), (31), (37), (106),
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | |            (116) are inconsistent by sub-proof #1976.
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | End of split
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | | Case 2:
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | | |   (117)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 230.93/42.11  | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e1) = e2)
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | BETA: splitting (117) gives:
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | Case 1:
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | |   (118)  all_57_8 = e2 & op(e1, e1) = e2
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | ALPHA: (118) implies:
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | |   (119)  all_57_8 = e2
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | BETA: splitting (6) gives:
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | |   (120)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e0)
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (120) gives:
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with e0, e1, e0, e0, simplifying
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | | |              with (31), (54) gives:
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | | |   (121)  e1 = e0
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (66), (121) imply:
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | | |   (122)  all_57_5 = e0
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (5), (16), (25), (37), (52), (87), (122) are
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2359.
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | | |   (123)  all_57_7 = e0 & op(e1, e2) = e0
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (123) implies:
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | | |   (124)  all_57_7 = e0
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (8), (12), (13), (14), (15), (16), (17),
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | | |            (18), (20), (23), (24), (25), (27), (37), (43),
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | | |            (124) are inconsistent by sub-proof #1636.
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | | End of split
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | |   (125)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (125) gives:
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | | |   (126)  all_57_8 = e0 & op(e1, e1) = e0
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (126) implies:
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | | |   (127)  all_57_8 = e0
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (119), (127) imply:
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | | |   (128)  e2 = e0
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (72), (128) imply:
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | | |   (129)  all_57_13 = e0
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (16), (17), (23), (25), (36), (37),
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | | |            (43), (129) are inconsistent by sub-proof #1758.
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | | |   (130)  all_57_11 = e0 & op(e1, e0) = e0
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (130) implies:
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | | |   (131)  all_57_11 = e0
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (8), (14), (16), (17), (18), (23), (25),
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | | |            (27), (36), (37), (43), (72), (97), (131) are
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1280.
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | | End of split
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | End of split
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | Case 2:
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | |   (132)  all_57_14 = e2 & op(e0, e1) = e2
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | ALPHA: (132) implies:
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | |   (133)  all_57_14 = e2
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (12), (13), (15), (17), (18), (20),
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | |            (23), (24), (25), (36), (37), (106), (133) are
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1642.
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | End of split
% 230.93/42.11  | | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | | End of split
% 230.93/42.11  | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | Case 2:
% 230.93/42.11  | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | |   (134)  all_57_15 = e3 & op(e0, e0) = e3
% 230.93/42.11  | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | | ALPHA: (134) implies:
% 230.93/42.11  | | | | | | | | | | | | | | | | | |   (135)  all_57_15 = e3
% 230.93/42.11  | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (17), (18), (23), (25), (30), (37), (38),
% 230.93/42.11  | | | | | | | | | | | | | | | | | |            (42), (97), (135) are inconsistent by sub-proof
% 230.93/42.11  | | | | | | | | | | | | | | | | | |            #2134.
% 230.93/42.11  | | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | | End of split
% 230.93/42.11  | | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | | End of split
% 230.93/42.11  | | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | | End of split
% 230.93/42.11  | | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | | End of split
% 230.93/42.11  | | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | | End of split
% 230.93/42.11  | | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | | End of split
% 230.93/42.11  | | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | | End of split
% 230.93/42.11  | | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | End of split
% 230.93/42.11  | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | Case 2:
% 230.93/42.11  | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | |   (136)  all_57_10 = e1 & op(e2, e0) = e1
% 230.93/42.11  | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | | REF_CLOSE: (7), (8), (32), (136) are inconsistent by
% 230.93/42.11  | | | | | | | | | |            sub-proof #2084.
% 230.93/42.11  | | | | | | | | | | 
% 230.93/42.11  | | | | | | | | | End of split
% 230.93/42.11  | | | | | | | | | 
% 230.93/42.11  | | | | | | | | End of split
% 230.93/42.11  | | | | | | | | 
% 230.93/42.11  | | | | | | | Case 2:
% 230.93/42.11  | | | | | | | | 
% 230.93/42.11  | | | | | | | |   (137)  all_57_13 = e1 & op(e0, e2) = e1
% 230.93/42.11  | | | | | | | | 
% 230.93/42.11  | | | | | | | | ALPHA: (137) implies:
% 230.93/42.11  | | | | | | | |   (138)  all_57_13 = e1
% 230.93/42.11  | | | | | | | | 
% 230.93/42.11  | | | | | | | | REF_CLOSE: (2), (5), (8), (10), (11), (13), (16), (17), (18),
% 230.93/42.11  | | | | | | | |            (19), (21), (23), (25), (26), (29), (31), (33), (34),
% 230.93/42.11  | | | | | | | |            (37), (52), (138) are inconsistent by sub-proof
% 230.93/42.11  | | | | | | | |            #1289.
% 230.93/42.11  | | | | | | | | 
% 230.93/42.11  | | | | | | | End of split
% 230.93/42.11  | | | | | | | 
% 230.93/42.11  | | | | | | End of split
% 230.93/42.11  | | | | | | 
% 230.93/42.11  | | | | | Case 2:
% 230.93/42.11  | | | | | | 
% 230.93/42.11  | | | | | |   (139)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 &
% 230.93/42.11  | | | | | |              op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0))
% 230.93/42.11  | | | | | |          & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.93/42.11  | | | | | |              op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 230.93/42.11  | | | | | | 
% 230.93/42.11  | | | | | | ALPHA: (139) implies:
% 230.93/42.11  | | | | | |   (140)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.93/42.11  | | | | | |            op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.93/42.11  | | | | | | 
% 230.93/42.11  | | | | | | BETA: splitting (140) gives:
% 230.93/42.11  | | | | | | 
% 230.93/42.11  | | | | | | Case 1:
% 230.93/42.11  | | | | | | | 
% 230.93/42.11  | | | | | | |   (141)  all_57_12 = e0 & op(e0, e3) = e0
% 230.93/42.11  | | | | | | | 
% 230.93/42.11  | | | | | | | REF_CLOSE: (22), (25), (141) are inconsistent by sub-proof #1279.
% 230.93/42.11  | | | | | | | 
% 230.93/42.11  | | | | | | Case 2:
% 230.93/42.11  | | | | | | | 
% 230.93/42.11  | | | | | | |   (142)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 &
% 230.93/42.11  | | | | | | |            op(e0, e1) = e0)
% 230.93/42.11  | | | | | | | 
% 230.93/42.11  | | | | | | | BETA: splitting (142) gives:
% 230.93/42.11  | | | | | | | 
% 230.93/42.11  | | | | | | | Case 1:
% 230.93/42.11  | | | | | | | | 
% 230.93/42.11  | | | | | | | |   (143)  all_57_13 = e0 & op(e0, e2) = e0
% 230.93/42.11  | | | | | | | | 
% 230.93/42.11  | | | | | | | | ALPHA: (143) implies:
% 230.93/42.11  | | | | | | | |   (144)  all_57_13 = e0
% 230.93/42.11  | | | | | | | | 
% 230.93/42.11  | | | | | | | | REF_CLOSE: (4), (5), (16), (17), (23), (25), (36), (37), (43),
% 230.93/42.11  | | | | | | | |            (144) are inconsistent by sub-proof #1758.
% 230.93/42.11  | | | | | | | | 
% 230.93/42.11  | | | | | | | Case 2:
% 230.93/42.11  | | | | | | | | 
% 230.93/42.11  | | | | | | | |   (145)  all_57_14 = e0 & op(e0, e1) = e0
% 230.93/42.11  | | | | | | | | 
% 230.93/42.11  | | | | | | | | REF_CLOSE: (2), (5), (8), (10), (11), (13), (16), (17), (18),
% 230.93/42.11  | | | | | | | |            (23), (25), (26), (33), (34), (37), (52), (145) are
% 230.93/42.11  | | | | | | | |            inconsistent by sub-proof #1278.
% 230.93/42.11  | | | | | | | | 
% 230.93/42.11  | | | | | | | End of split
% 230.93/42.11  | | | | | | | 
% 230.93/42.11  | | | | | | End of split
% 230.93/42.11  | | | | | | 
% 230.93/42.11  | | | | | End of split
% 230.93/42.11  | | | | | 
% 230.93/42.11  | | | | End of split
% 230.93/42.11  | | | | 
% 230.93/42.11  | | | Case 2:
% 230.93/42.11  | | | | 
% 230.93/42.11  | | | |   (146)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0,
% 230.93/42.11  | | | |              e3) = e3)
% 230.93/42.11  | | | | 
% 230.93/42.11  | | | | BETA: splitting (146) gives:
% 230.93/42.11  | | | | 
% 230.93/42.11  | | | | Case 1:
% 230.93/42.11  | | | | | 
% 230.93/42.11  | | | | |   (147)  all_57_6 = e3 & op(e1, e3) = e3
% 230.93/42.11  | | | | | 
% 230.93/42.11  | | | | | REF_CLOSE: (18), (47), (147) are inconsistent by sub-proof #2395.
% 230.93/42.11  | | | | | 
% 230.93/42.11  | | | | Case 2:
% 230.93/42.11  | | | | | 
% 230.93/42.11  | | | | |   (148)  all_57_12 = e3 & op(e0, e3) = e3
% 230.93/42.11  | | | | | 
% 230.93/42.11  | | | | | REF_CLOSE: (5), (22), (148) are inconsistent by sub-proof #1285.
% 230.93/42.11  | | | | | 
% 230.93/42.11  | | | | End of split
% 230.93/42.11  | | | | 
% 230.93/42.11  | | | End of split
% 230.93/42.11  | | | 
% 230.93/42.11  | | Case 2:
% 230.93/42.11  | | | 
% 230.93/42.11  | | |   (149)  all_57_12 = e0 & op(e0, e3) = e0
% 230.93/42.11  | | | 
% 230.93/42.11  | | | REF_CLOSE: (22), (25), (149) are inconsistent by sub-proof #1279.
% 230.93/42.11  | | | 
% 230.93/42.11  | | End of split
% 230.93/42.11  | | 
% 230.93/42.11  | End of split
% 230.93/42.11  | 
% 230.93/42.11  End of proof
% 230.93/42.11  
% 230.93/42.11  Sub-proof #1278 shows that the following formulas are inconsistent:
% 230.93/42.11  ----------------------------------------------------------------
% 230.93/42.11    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.93/42.11         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.93/42.11    (2)   ~ (e3 = e1)
% 230.93/42.11    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.93/42.11           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.93/42.11    (4)   ~ (all_6_2 = e3)
% 230.93/42.11    (5)  op(e1, e1) = all_6_2
% 230.93/42.11    (6)  all_57_4 = e0
% 230.93/42.11    (7)  all_57_3 = e0
% 230.93/42.11    (8)   ~ (e3 = e2)
% 230.93/42.11    (9)   ~ (e3 = e0)
% 230.93/42.11    (10)   ~ (e2 = e0)
% 230.93/42.11    (11)  all_57_2 = e3
% 230.93/42.11    (12)   ~ (e1 = e0)
% 230.93/42.11    (13)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 230.93/42.11          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 230.93/42.11    (14)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.93/42.11          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.93/42.11    (15)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.93/42.11          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.93/42.11    (16)   ~ (e2 = e1)
% 230.93/42.11    (17)  all_57_14 = e0 & op(e0, e1) = e0
% 230.93/42.11  
% 230.93/42.11  Begin of proof
% 230.93/42.11  | 
% 230.93/42.11  | ALPHA: (17) implies:
% 230.93/42.11  |   (18)  all_57_14 = e0
% 230.93/42.11  | 
% 230.93/42.11  | BETA: splitting (13) gives:
% 230.93/42.11  | 
% 230.93/42.11  | Case 1:
% 230.93/42.11  | | 
% 230.93/42.11  | |   (19)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) =
% 230.93/42.11  | |           e3)
% 230.93/42.11  | | 
% 230.93/42.11  | | REF_CLOSE: (1), (2), (6), (7), (8), (9), (10), (11), (12), (14), (15), (16),
% 230.93/42.11  | |            (19) are inconsistent by sub-proof #1291.
% 230.93/42.11  | | 
% 230.93/42.11  | Case 2:
% 230.93/42.11  | | 
% 230.93/42.11  | |   (20)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) =
% 230.93/42.11  | |           e3)
% 230.93/42.11  | | 
% 230.93/42.11  | | BETA: splitting (20) gives:
% 230.93/42.11  | | 
% 230.93/42.11  | | Case 1:
% 230.93/42.11  | | | 
% 230.93/42.11  | | |   (21)  all_57_8 = e3 & op(e1, e1) = e3
% 230.93/42.11  | | | 
% 230.93/42.11  | | | ALPHA: (21) implies:
% 230.93/42.11  | | |   (22)  op(e1, e1) = e3
% 230.93/42.11  | | | 
% 230.93/42.11  | | | REF_CLOSE: (3), (4), (5), (22) are inconsistent by sub-proof #2468.
% 230.93/42.11  | | | 
% 230.93/42.11  | | Case 2:
% 230.93/42.11  | | | 
% 230.93/42.11  | | |   (23)  all_57_14 = e3 & op(e0, e1) = e3
% 230.93/42.11  | | | 
% 230.93/42.11  | | | ALPHA: (23) implies:
% 230.93/42.11  | | |   (24)  all_57_14 = e3
% 230.93/42.11  | | | 
% 230.93/42.11  | | | COMBINE_EQS: (18), (24) imply:
% 230.93/42.11  | | |   (25)  e3 = e0
% 230.93/42.11  | | | 
% 230.93/42.11  | | | COMBINE_EQS: (11), (25) imply:
% 230.93/42.11  | | |   (26)  all_57_2 = e0
% 230.93/42.11  | | | 
% 230.93/42.11  | | | REF_CLOSE: (1), (2), (7), (8), (9), (10), (12), (14), (15), (16), (26) are
% 230.93/42.11  | | |            inconsistent by sub-proof #2246.
% 230.93/42.11  | | | 
% 230.93/42.11  | | End of split
% 230.93/42.11  | | 
% 230.93/42.11  | End of split
% 230.93/42.11  | 
% 230.93/42.11  End of proof
% 230.93/42.11  
% 230.93/42.11  Sub-proof #1279 shows that the following formulas are inconsistent:
% 230.93/42.11  ----------------------------------------------------------------
% 230.93/42.11    (1)  all_57_12 = e0 & op(e0, e3) = e0
% 230.93/42.11    (2)  all_57_12 = e1
% 230.93/42.11    (3)   ~ (e1 = e0)
% 230.93/42.11  
% 230.93/42.11  Begin of proof
% 230.93/42.11  | 
% 230.93/42.11  | ALPHA: (1) implies:
% 230.93/42.11  |   (4)  all_57_12 = e0
% 230.93/42.11  | 
% 230.93/42.11  | COMBINE_EQS: (2), (4) imply:
% 230.93/42.11  |   (5)  e1 = e0
% 230.93/42.11  | 
% 230.93/42.11  | REDUCE: (3), (5) imply:
% 230.93/42.11  |   (6)  $false
% 230.93/42.11  | 
% 230.93/42.11  | CLOSE: (6) is inconsistent.
% 230.93/42.11  | 
% 230.93/42.11  End of proof
% 230.93/42.11  
% 230.93/42.11  Sub-proof #1280 shows that the following formulas are inconsistent:
% 230.93/42.11  ----------------------------------------------------------------
% 230.93/42.11    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.93/42.11         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.93/42.11    (2)   ~ (e3 = e1)
% 230.93/42.11    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.93/42.11           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.93/42.11    (4)  op(e2, e2) = e0
% 230.93/42.11    (5)  all_57_3 = e0
% 230.93/42.11    (6)   ~ (e3 = e2)
% 230.93/42.11    (7)   ~ (e3 = e0)
% 230.93/42.11    (8)  all_57_11 = e0
% 230.93/42.11    (9)   ~ (e2 = e0)
% 230.93/42.11    (10)  all_57_13 = e2
% 230.93/42.11    (11)   ~ (e1 = e0)
% 230.93/42.11    (12)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.93/42.11          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.93/42.11    (13)  all_57_11 = e3
% 230.93/42.11    (14)  all_57_1 = e3
% 230.93/42.11    (15)   ~ (e2 = e1)
% 230.93/42.11    (16)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.93/42.11          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.93/42.11  
% 230.93/42.11  Begin of proof
% 230.93/42.11  | 
% 230.93/42.11  | COMBINE_EQS: (8), (13) imply:
% 230.93/42.11  |   (17)  e3 = e0
% 230.93/42.11  | 
% 230.93/42.11  | SIMP: (17) implies:
% 230.93/42.11  |   (18)  e3 = e0
% 230.93/42.11  | 
% 230.93/42.11  | COMBINE_EQS: (14), (18) imply:
% 230.93/42.11  |   (19)  all_57_1 = e0
% 230.93/42.11  | 
% 230.93/42.11  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (15),
% 230.93/42.11  |            (16), (19) are inconsistent by sub-proof #1281.
% 230.93/42.11  | 
% 230.93/42.11  End of proof
% 230.93/42.11  
% 230.93/42.11  Sub-proof #1281 shows that the following formulas are inconsistent:
% 230.93/42.11  ----------------------------------------------------------------
% 230.93/42.11    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.93/42.11         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.93/42.11    (2)   ~ (e3 = e1)
% 230.93/42.11    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.93/42.11           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.93/42.11    (4)  op(e2, e2) = e0
% 230.93/42.11    (5)  all_57_3 = e0
% 230.93/42.11    (6)   ~ (e3 = e2)
% 230.93/42.11    (7)   ~ (e3 = e0)
% 230.93/42.11    (8)  all_57_1 = e0
% 230.93/42.11    (9)   ~ (e2 = e0)
% 230.93/42.11    (10)  all_57_13 = e2
% 230.93/42.11    (11)   ~ (e1 = e0)
% 230.93/42.11    (12)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.93/42.11          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.93/42.11    (13)   ~ (e2 = e1)
% 230.93/42.11    (14)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.93/42.11          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.93/42.11  
% 230.93/42.11  Begin of proof
% 230.93/42.11  | 
% 230.93/42.11  | BETA: splitting (12) gives:
% 230.93/42.11  | 
% 230.93/42.11  | Case 1:
% 230.93/42.11  | | 
% 230.93/42.11  | |   (15)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 230.93/42.11  | |           e3)
% 230.93/42.11  | | 
% 230.93/42.11  | | REF_CLOSE: (5), (7), (8), (15) are inconsistent by sub-proof #1284.
% 230.93/42.11  | | 
% 230.93/42.11  | Case 2:
% 230.93/42.11  | | 
% 230.93/42.11  | |   (16)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 230.93/42.11  | |           e3)
% 230.93/42.11  | | 
% 230.93/42.11  | | BETA: splitting (16) gives:
% 230.93/42.11  | | 
% 230.93/42.11  | | Case 1:
% 230.93/42.11  | | | 
% 230.93/42.11  | | |   (17)  all_57_7 = e3 & op(e1, e2) = e3
% 230.93/42.11  | | | 
% 230.93/42.11  | | | ALPHA: (17) implies:
% 230.93/42.11  | | |   (18)  all_57_7 = e3
% 230.93/42.11  | | | 
% 230.93/42.11  | | | REF_CLOSE: (1), (2), (3), (4), (6), (8), (9), (11), (13), (14), (18) are
% 230.93/42.11  | | |            inconsistent by sub-proof #1282.
% 230.93/42.11  | | | 
% 230.93/42.11  | | Case 2:
% 230.93/42.11  | | | 
% 230.93/42.11  | | |   (19)  all_57_13 = e3 & op(e0, e2) = e3
% 230.93/42.11  | | | 
% 230.93/42.11  | | | ALPHA: (19) implies:
% 230.93/42.11  | | |   (20)  all_57_13 = e3
% 230.93/42.11  | | | 
% 230.93/42.11  | | | REF_CLOSE: (6), (10), (20) are inconsistent by sub-proof #2203.
% 230.93/42.11  | | | 
% 230.93/42.11  | | End of split
% 230.93/42.11  | | 
% 230.93/42.11  | End of split
% 230.93/42.11  | 
% 230.93/42.11  End of proof
% 230.93/42.11  
% 230.93/42.11  Sub-proof #1282 shows that the following formulas are inconsistent:
% 230.93/42.11  ----------------------------------------------------------------
% 230.93/42.11    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.93/42.11         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.93/42.11    (2)   ~ (e3 = e1)
% 230.93/42.11    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.93/42.11           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.93/42.11    (4)  op(e2, e2) = e0
% 230.93/42.11    (5)   ~ (e3 = e2)
% 230.93/42.11    (6)  all_57_1 = e0
% 230.93/42.11    (7)   ~ (e2 = e0)
% 230.93/42.11    (8)   ~ (e1 = e0)
% 230.93/42.11    (9)  all_57_7 = e3
% 230.93/42.11    (10)   ~ (e2 = e1)
% 230.93/42.11    (11)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.93/42.11          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.93/42.11  
% 230.93/42.11  Begin of proof
% 230.93/42.11  | 
% 230.93/42.11  | BETA: splitting (1) gives:
% 230.93/42.11  | 
% 230.93/42.11  | Case 1:
% 230.93/42.11  | | 
% 230.93/42.11  | |   (12)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 230.93/42.11  | |           e2)
% 230.93/42.11  | | 
% 230.93/42.11  | | BETA: splitting (12) gives:
% 230.93/42.11  | | 
% 230.93/42.11  | | Case 1:
% 230.93/42.11  | | | 
% 230.93/42.11  | | |   (13)  all_57_1 = e2 & op(e3, e2) = e2
% 230.93/42.11  | | | 
% 230.93/42.11  | | | REF_CLOSE: (6), (7), (13) are inconsistent by sub-proof #2483.
% 230.93/42.11  | | | 
% 230.93/42.11  | | Case 2:
% 230.93/42.11  | | | 
% 230.93/42.11  | | |   (14)  all_57_3 = e2 & op(e2, e2) = e2
% 230.93/42.11  | | | 
% 230.93/42.11  | | | ALPHA: (14) implies:
% 230.93/42.11  | | |   (15)  all_57_3 = e2
% 230.93/42.11  | | |   (16)  op(e2, e2) = e2
% 230.93/42.11  | | | 
% 230.93/42.11  | | | GROUND_INST: instantiating (3) with e0, e2, e2, e2, simplifying with (4),
% 230.93/42.11  | | |              (16) gives:
% 230.93/42.11  | | |   (17)  e2 = e0
% 230.93/42.11  | | | 
% 230.93/42.11  | | | COMBINE_EQS: (15), (17) imply:
% 230.93/42.11  | | |   (18)  all_57_3 = e0
% 230.93/42.11  | | | 
% 230.93/42.11  | | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (9), (10), (11), (18) are
% 230.93/42.11  | | |            inconsistent by sub-proof #2098.
% 230.93/42.11  | | | 
% 230.93/42.11  | | End of split
% 230.93/42.11  | | 
% 230.93/42.11  | Case 2:
% 230.93/42.11  | | 
% 230.93/42.11  | |   (19)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 230.93/42.11  | |           e2)
% 230.93/42.11  | | 
% 230.93/42.11  | | BETA: splitting (19) gives:
% 230.93/42.11  | | 
% 230.93/42.11  | | Case 1:
% 230.93/42.11  | | | 
% 230.93/42.11  | | |   (20)  all_57_7 = e2 & op(e1, e2) = e2
% 230.93/42.11  | | | 
% 230.93/42.11  | | | REF_CLOSE: (5), (9), (20) are inconsistent by sub-proof #2092.
% 230.93/42.11  | | | 
% 230.93/42.11  | | Case 2:
% 230.93/42.11  | | | 
% 230.93/42.11  | | |   (21)  all_57_13 = e2 & op(e0, e2) = e2
% 230.93/42.11  | | | 
% 230.93/42.11  | | | ALPHA: (21) implies:
% 230.93/42.11  | | |   (22)  all_57_13 = e2
% 230.93/42.11  | | | 
% 230.93/42.11  | | | REF_CLOSE: (2), (3), (4), (6), (8), (9), (10), (11), (22) are inconsistent
% 230.93/42.11  | | |            by sub-proof #1283.
% 230.93/42.11  | | | 
% 230.93/42.11  | | End of split
% 230.93/42.11  | | 
% 230.93/42.11  | End of split
% 230.93/42.11  | 
% 230.93/42.11  End of proof
% 230.93/42.11  
% 230.93/42.11  Sub-proof #1283 shows that the following formulas are inconsistent:
% 230.93/42.11  ----------------------------------------------------------------
% 230.93/42.11    (1)   ~ (e3 = e1)
% 230.93/42.11    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.93/42.11           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.93/42.11    (3)  op(e2, e2) = e0
% 230.93/42.11    (4)  all_57_1 = e0
% 230.93/42.11    (5)  all_57_13 = e2
% 230.93/42.11    (6)   ~ (e1 = e0)
% 230.93/42.11    (7)  all_57_7 = e3
% 230.93/42.11    (8)   ~ (e2 = e1)
% 230.93/42.11    (9)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.93/42.11         (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.93/42.11  
% 230.93/42.11  Begin of proof
% 230.93/42.11  | 
% 230.93/42.11  | BETA: splitting (9) gives:
% 230.93/42.11  | 
% 230.93/42.11  | Case 1:
% 230.93/42.11  | | 
% 230.93/42.11  | |   (10)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) =
% 230.93/42.11  | |           e1)
% 230.93/42.11  | | 
% 230.93/42.11  | | BETA: splitting (10) gives:
% 230.93/42.11  | | 
% 230.93/42.11  | | Case 1:
% 230.93/42.11  | | | 
% 230.93/42.11  | | |   (11)  all_57_1 = e1 & op(e3, e2) = e1
% 230.93/42.11  | | | 
% 230.93/42.11  | | | REF_CLOSE: (4), (6), (11) are inconsistent by sub-proof #2446.
% 230.93/42.11  | | | 
% 230.93/42.11  | | Case 2:
% 230.93/42.11  | | | 
% 230.93/42.11  | | |   (12)  all_57_3 = e1 & op(e2, e2) = e1
% 230.93/42.11  | | | 
% 230.93/42.11  | | | ALPHA: (12) implies:
% 230.93/42.11  | | |   (13)  op(e2, e2) = e1
% 230.93/42.11  | | | 
% 230.93/42.11  | | | REF_CLOSE: (2), (3), (6), (13) are inconsistent by sub-proof #2352.
% 230.93/42.11  | | | 
% 230.93/42.11  | | End of split
% 230.93/42.11  | | 
% 230.93/42.11  | Case 2:
% 230.93/42.11  | | 
% 230.93/42.11  | |   (14)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 230.93/42.11  | |           e1)
% 230.93/42.11  | | 
% 230.93/42.11  | | REF_CLOSE: (1), (5), (7), (8), (14) are inconsistent by sub-proof #1780.
% 230.93/42.11  | | 
% 230.93/42.11  | End of split
% 230.93/42.11  | 
% 230.93/42.11  End of proof
% 230.93/42.11  
% 230.93/42.11  Sub-proof #1284 shows that the following formulas are inconsistent:
% 230.93/42.11  ----------------------------------------------------------------
% 230.93/42.11    (1)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3)
% 230.93/42.11    (2)  all_57_1 = e0
% 230.93/42.11    (3)   ~ (e3 = e0)
% 230.93/42.11    (4)  all_57_3 = e0
% 230.93/42.11  
% 230.93/42.11  Begin of proof
% 230.93/42.11  | 
% 230.93/42.11  | BETA: splitting (1) gives:
% 230.93/42.11  | 
% 230.93/42.11  | Case 1:
% 230.93/42.11  | | 
% 230.93/42.11  | |   (5)  all_57_1 = e3 & op(e3, e2) = e3
% 230.93/42.11  | | 
% 230.93/42.11  | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #2405.
% 230.93/42.11  | | 
% 230.93/42.11  | Case 2:
% 230.93/42.11  | | 
% 230.93/42.11  | |   (6)  all_57_3 = e3 & op(e2, e2) = e3
% 230.93/42.11  | | 
% 230.93/42.11  | | ALPHA: (6) implies:
% 230.93/42.11  | |   (7)  all_57_3 = e3
% 230.93/42.11  | | 
% 230.93/42.11  | | REF_CLOSE: (3), (4), (7) are inconsistent by sub-proof #2358.
% 230.93/42.11  | | 
% 230.93/42.11  | End of split
% 230.93/42.11  | 
% 230.93/42.11  End of proof
% 230.93/42.11  
% 230.93/42.11  Sub-proof #1285 shows that the following formulas are inconsistent:
% 230.93/42.11  ----------------------------------------------------------------
% 230.93/42.11    (1)  all_57_12 = e3 & op(e0, e3) = e3
% 230.93/42.11    (2)  all_57_12 = e1
% 230.93/42.11    (3)   ~ (e3 = e1)
% 230.93/42.11  
% 230.93/42.11  Begin of proof
% 230.93/42.11  | 
% 230.93/42.11  | ALPHA: (1) implies:
% 230.93/42.11  |   (4)  all_57_12 = e3
% 230.93/42.11  | 
% 230.93/42.11  | COMBINE_EQS: (2), (4) imply:
% 230.93/42.11  |   (5)  e3 = e1
% 230.93/42.11  | 
% 230.93/42.11  | REDUCE: (3), (5) imply:
% 230.93/42.11  |   (6)  $false
% 230.93/42.11  | 
% 230.93/42.11  | CLOSE: (6) is inconsistent.
% 230.93/42.11  | 
% 230.93/42.11  End of proof
% 230.93/42.11  
% 230.93/42.11  Sub-proof #1286 shows that the following formulas are inconsistent:
% 230.93/42.11  ----------------------------------------------------------------
% 230.93/42.11    (1)  all_57_0 = e2
% 230.93/42.11    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.93/42.11         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.93/42.11    (3)   ~ (e3 = e1)
% 230.93/42.11    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.93/42.11           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.93/42.11    (5)   ~ (e3 = e2)
% 230.93/42.11    (6)   ~ (e3 = e0)
% 230.93/42.11    (7)   ~ (e2 = e0)
% 230.93/42.11    (8)  all_57_2 = e3
% 230.93/42.11    (9)   ~ (e1 = e0)
% 230.93/42.11    (10)  all_57_6 = e3
% 230.93/42.11    (11)   ~ (e2 = e1)
% 230.93/42.11    (12)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.93/42.11          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.93/42.11    (13)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.93/42.11          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.93/42.11  
% 230.93/42.11  Begin of proof
% 230.93/42.11  | 
% 230.93/42.11  | BETA: splitting (13) gives:
% 230.93/42.11  | 
% 230.93/42.11  | Case 1:
% 230.93/42.11  | | 
% 230.93/42.11  | |   (14)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) =
% 230.93/42.11  | |           e0)
% 230.93/42.11  | | 
% 230.93/42.11  | | BETA: splitting (14) gives:
% 230.93/42.11  | | 
% 230.93/42.11  | | Case 1:
% 230.93/42.11  | | | 
% 230.93/42.12  | | |   (15)  all_57_0 = e0 & op(e3, e3) = e0
% 230.93/42.12  | | | 
% 230.93/42.12  | | | ALPHA: (15) implies:
% 230.93/42.12  | | |   (16)  all_57_0 = e0
% 230.93/42.12  | | |   (17)  op(e3, e3) = e0
% 230.93/42.12  | | | 
% 230.93/42.12  | | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (16), (17)
% 230.93/42.12  | | |            are inconsistent by sub-proof #1287.
% 230.93/42.12  | | | 
% 230.93/42.12  | | Case 2:
% 230.93/42.12  | | | 
% 230.93/42.12  | | |   (18)  all_57_2 = e0 & op(e2, e3) = e0
% 230.93/42.12  | | | 
% 230.93/42.12  | | | REF_CLOSE: (6), (8), (18) are inconsistent by sub-proof #1805.
% 230.93/42.12  | | | 
% 230.93/42.12  | | End of split
% 230.93/42.12  | | 
% 230.93/42.12  | Case 2:
% 230.93/42.12  | | 
% 230.93/42.12  | |   (19)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) =
% 230.93/42.12  | |           e0)
% 230.93/42.12  | | 
% 230.93/42.12  | | BETA: splitting (19) gives:
% 230.93/42.12  | | 
% 230.93/42.12  | | Case 1:
% 230.93/42.12  | | | 
% 230.93/42.12  | | |   (20)  all_57_6 = e0 & op(e1, e3) = e0
% 230.93/42.12  | | | 
% 230.93/42.12  | | | REF_CLOSE: (6), (10), (20) are inconsistent by sub-proof #2465.
% 230.93/42.12  | | | 
% 230.93/42.12  | | Case 2:
% 230.93/42.12  | | | 
% 230.93/42.12  | | |   (21)  all_57_12 = e0 & op(e0, e3) = e0
% 230.93/42.12  | | | 
% 230.93/42.12  | | | ALPHA: (21) implies:
% 230.93/42.12  | | |   (22)  all_57_12 = e0
% 230.93/42.12  | | | 
% 230.93/42.12  | | | REF_CLOSE: (1), (2), (3), (8), (9), (10), (11), (22) are inconsistent by
% 230.93/42.12  | | |            sub-proof #1535.
% 230.93/42.12  | | | 
% 230.93/42.12  | | End of split
% 230.93/42.12  | | 
% 230.93/42.12  | End of split
% 230.93/42.12  | 
% 230.93/42.12  End of proof
% 230.93/42.12  
% 230.93/42.12  Sub-proof #1287 shows that the following formulas are inconsistent:
% 230.93/42.12  ----------------------------------------------------------------
% 230.93/42.12    (1)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.93/42.12         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.93/42.12    (2)   ~ (e3 = e1)
% 230.93/42.12    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.93/42.12           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.93/42.12    (4)   ~ (e3 = e2)
% 230.93/42.12    (5)  all_57_0 = e0
% 230.93/42.12    (6)  op(e3, e3) = e0
% 230.93/42.12    (7)   ~ (e2 = e0)
% 230.93/42.12    (8)  all_57_2 = e3
% 230.93/42.12    (9)   ~ (e1 = e0)
% 230.93/42.12    (10)  all_57_6 = e3
% 230.93/42.12    (11)   ~ (e2 = e1)
% 230.93/42.12    (12)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.93/42.12          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.93/42.12  
% 230.93/42.12  Begin of proof
% 230.93/42.12  | 
% 230.93/42.12  | BETA: splitting (1) gives:
% 230.93/42.12  | 
% 230.93/42.12  | Case 1:
% 230.93/42.12  | | 
% 230.93/42.12  | |   (13)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) =
% 230.93/42.12  | |           e1)
% 230.93/42.12  | | 
% 230.93/42.12  | | BETA: splitting (13) gives:
% 230.93/42.12  | | 
% 230.93/42.12  | | Case 1:
% 230.93/42.12  | | | 
% 230.93/42.12  | | |   (14)  all_57_0 = e1 & op(e3, e3) = e1
% 230.93/42.12  | | | 
% 230.93/42.12  | | | REF_CLOSE: (5), (9), (14) are inconsistent by sub-proof #2454.
% 230.93/42.12  | | | 
% 230.93/42.12  | | Case 2:
% 230.93/42.12  | | | 
% 230.93/42.12  | | |   (15)  all_57_2 = e1 & op(e2, e3) = e1
% 230.93/42.12  | | | 
% 230.93/42.12  | | | REF_CLOSE: (2), (8), (15) are inconsistent by sub-proof #1928.
% 230.93/42.12  | | | 
% 230.93/42.12  | | End of split
% 230.93/42.12  | | 
% 230.93/42.12  | Case 2:
% 230.93/42.12  | | 
% 230.93/42.12  | |   (16)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) =
% 230.93/42.12  | |           e1)
% 230.93/42.12  | | 
% 230.93/42.12  | | BETA: splitting (16) gives:
% 230.93/42.12  | | 
% 230.93/42.12  | | Case 1:
% 230.93/42.12  | | | 
% 230.93/42.12  | | |   (17)  all_57_6 = e1 & op(e1, e3) = e1
% 230.93/42.12  | | | 
% 230.93/42.12  | | | REF_CLOSE: (2), (10), (17) are inconsistent by sub-proof #2117.
% 230.93/42.12  | | | 
% 230.93/42.12  | | Case 2:
% 230.93/42.12  | | | 
% 230.93/42.12  | | |   (18)  all_57_12 = e1 & op(e0, e3) = e1
% 230.93/42.12  | | | 
% 230.93/42.12  | | | ALPHA: (18) implies:
% 230.93/42.12  | | |   (19)  all_57_12 = e1
% 230.93/42.12  | | | 
% 230.93/42.12  | | | REF_CLOSE: (3), (4), (6), (7), (8), (10), (11), (12), (19) are
% 230.93/42.12  | | |            inconsistent by sub-proof #1288.
% 230.93/42.12  | | | 
% 230.93/42.12  | | End of split
% 230.93/42.12  | | 
% 230.93/42.12  | End of split
% 230.93/42.12  | 
% 230.93/42.12  End of proof
% 230.93/42.12  
% 230.93/42.12  Sub-proof #1288 shows that the following formulas are inconsistent:
% 230.93/42.12  ----------------------------------------------------------------
% 230.93/42.12    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.93/42.12           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.93/42.12    (2)   ~ (e3 = e2)
% 230.93/42.12    (3)  op(e3, e3) = e0
% 230.93/42.12    (4)  all_57_12 = e1
% 230.93/42.12    (5)   ~ (e2 = e0)
% 230.93/42.12    (6)  all_57_2 = e3
% 230.93/42.12    (7)  all_57_6 = e3
% 230.93/42.12    (8)   ~ (e2 = e1)
% 230.93/42.12    (9)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.93/42.12         (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.93/42.12  
% 230.93/42.12  Begin of proof
% 230.93/42.12  | 
% 230.93/42.12  | BETA: splitting (9) gives:
% 230.93/42.12  | 
% 230.93/42.12  | Case 1:
% 230.93/42.12  | | 
% 230.93/42.12  | |   (10)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) =
% 230.93/42.12  | |           e2)
% 230.93/42.12  | | 
% 230.93/42.12  | | BETA: splitting (10) gives:
% 230.93/42.12  | | 
% 230.93/42.12  | | Case 1:
% 230.93/42.12  | | | 
% 230.93/42.12  | | |   (11)  all_57_0 = e2 & op(e3, e3) = e2
% 230.93/42.12  | | | 
% 230.93/42.12  | | | ALPHA: (11) implies:
% 230.93/42.12  | | |   (12)  op(e3, e3) = e2
% 230.93/42.12  | | | 
% 230.93/42.12  | | | REF_CLOSE: (1), (3), (5), (12) are inconsistent by sub-proof #2403.
% 230.93/42.12  | | | 
% 230.93/42.12  | | Case 2:
% 230.93/42.12  | | | 
% 230.93/42.12  | | |   (13)  all_57_2 = e2 & op(e2, e3) = e2
% 230.93/42.12  | | | 
% 230.93/42.12  | | | ALPHA: (13) implies:
% 230.93/42.12  | | |   (14)  all_57_2 = e2
% 230.93/42.12  | | | 
% 230.93/42.12  | | | REF_CLOSE: (2), (6), (14) are inconsistent by sub-proof #1800.
% 230.93/42.12  | | | 
% 230.93/42.12  | | End of split
% 230.93/42.12  | | 
% 230.93/42.12  | Case 2:
% 230.93/42.12  | | 
% 230.93/42.12  | |   (15)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) =
% 230.93/42.12  | |           e2)
% 230.93/42.12  | | 
% 230.93/42.12  | | BETA: splitting (15) gives:
% 230.93/42.12  | | 
% 230.93/42.12  | | Case 1:
% 230.93/42.12  | | | 
% 230.93/42.12  | | |   (16)  all_57_6 = e2 & op(e1, e3) = e2
% 230.93/42.12  | | | 
% 230.93/42.12  | | | ALPHA: (16) implies:
% 230.93/42.12  | | |   (17)  all_57_6 = e2
% 230.93/42.12  | | | 
% 230.93/42.12  | | | REF_CLOSE: (2), (7), (17) are inconsistent by sub-proof #2463.
% 230.93/42.12  | | | 
% 230.93/42.12  | | Case 2:
% 230.93/42.12  | | | 
% 230.93/42.12  | | |   (18)  all_57_12 = e2 & op(e0, e3) = e2
% 230.93/42.12  | | | 
% 230.93/42.12  | | | ALPHA: (18) implies:
% 230.93/42.12  | | |   (19)  all_57_12 = e2
% 230.93/42.12  | | | 
% 230.93/42.12  | | | REF_CLOSE: (4), (8), (19) are inconsistent by sub-proof #2321.
% 230.93/42.12  | | | 
% 230.93/42.12  | | End of split
% 230.93/42.12  | | 
% 230.93/42.12  | End of split
% 230.93/42.12  | 
% 230.93/42.12  End of proof
% 230.93/42.12  
% 230.93/42.12  Sub-proof #1289 shows that the following formulas are inconsistent:
% 230.93/42.12  ----------------------------------------------------------------
% 230.93/42.12    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.93/42.12         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.93/42.12    (2)  all_57_13 = e1
% 230.93/42.12    (3)   ~ (e3 = e1)
% 230.93/42.12    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.93/42.12           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.93/42.12    (5)   ~ (all_6_2 = e3)
% 230.93/42.12    (6)  op(e1, e1) = all_6_2
% 230.93/42.12    (7)  all_57_4 = e0
% 230.93/42.12    (8)  all_57_3 = e0
% 230.93/42.12    (9)   ~ (e3 = e2)
% 230.93/42.12    (10)   ~ (e3 = e0)
% 230.93/42.12    (11)  op(e0, e3) = all_53_3
% 230.93/42.12    (12)   ~ (all_53_3 = e2)
% 230.93/42.12    (13)   ~ (e2 = e0)
% 230.93/42.12    (14)  all_57_2 = e3
% 230.93/42.12    (15)   ~ (e1 = e0)
% 230.93/42.12    (16)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 230.93/42.12          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 230.93/42.12    (17)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.93/42.12          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.93/42.12            e2)
% 230.93/42.12    (18)  op(e0, e0) = e1
% 230.93/42.12    (19)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.93/42.12          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.93/42.12    (20)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.93/42.12          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.93/42.12    (21)   ~ (e2 = e1)
% 230.93/42.12  
% 230.93/42.12  Begin of proof
% 230.93/42.12  | 
% 230.93/42.12  | BETA: splitting (16) gives:
% 230.93/42.12  | 
% 230.93/42.12  | Case 1:
% 230.93/42.12  | | 
% 230.93/42.12  | |   (22)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) =
% 230.93/42.12  | |           e3)
% 230.93/42.12  | | 
% 230.93/42.12  | | REF_CLOSE: (1), (3), (7), (8), (9), (10), (13), (14), (15), (19), (20),
% 230.93/42.12  | |            (21), (22) are inconsistent by sub-proof #1291.
% 230.93/42.12  | | 
% 230.93/42.12  | Case 2:
% 230.93/42.12  | | 
% 230.93/42.12  | |   (23)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) =
% 230.93/42.12  | |           e3)
% 230.93/42.12  | | 
% 230.93/42.12  | | REF_CLOSE: (2), (4), (5), (6), (9), (11), (12), (17), (18), (21), (23) are
% 230.93/42.12  | |            inconsistent by sub-proof #1290.
% 230.93/42.12  | | 
% 230.93/42.12  | End of split
% 230.93/42.12  | 
% 230.93/42.12  End of proof
% 230.93/42.12  
% 230.93/42.12  Sub-proof #1290 shows that the following formulas are inconsistent:
% 230.93/42.12  ----------------------------------------------------------------
% 230.93/42.12    (1)  all_57_13 = e1
% 230.93/42.12    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.93/42.12           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.93/42.12    (3)   ~ (all_6_2 = e3)
% 230.93/42.12    (4)  op(e1, e1) = all_6_2
% 230.93/42.12    (5)   ~ (e3 = e2)
% 230.93/42.12    (6)  op(e0, e3) = all_53_3
% 230.93/42.12    (7)   ~ (all_53_3 = e2)
% 230.93/42.12    (8)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2) |
% 230.93/42.12         (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.93/42.12    (9)  op(e0, e0) = e1
% 230.93/42.12    (10)   ~ (e2 = e1)
% 230.93/42.12    (11)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 230.93/42.12  
% 230.93/42.12  Begin of proof
% 230.93/42.12  | 
% 230.93/42.12  | BETA: splitting (11) gives:
% 230.93/42.12  | 
% 230.93/42.12  | Case 1:
% 230.93/42.12  | | 
% 230.93/42.12  | |   (12)  all_57_8 = e3 & op(e1, e1) = e3
% 230.93/42.12  | | 
% 230.93/42.12  | | ALPHA: (12) implies:
% 230.93/42.12  | |   (13)  op(e1, e1) = e3
% 230.93/42.12  | | 
% 230.93/42.12  | | REF_CLOSE: (2), (3), (4), (13) are inconsistent by sub-proof #2468.
% 230.93/42.12  | | 
% 230.93/42.12  | Case 2:
% 230.93/42.12  | | 
% 230.93/42.12  | |   (14)  all_57_14 = e3 & op(e0, e1) = e3
% 230.93/42.12  | | 
% 230.93/42.12  | | ALPHA: (14) implies:
% 230.93/42.12  | |   (15)  all_57_14 = e3
% 230.93/42.12  | | 
% 230.93/42.12  | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (9), (10), (15) are inconsistent by
% 230.93/42.12  | |            sub-proof #1976.
% 230.93/42.12  | | 
% 230.93/42.12  | End of split
% 230.93/42.12  | 
% 230.93/42.12  End of proof
% 230.93/42.12  
% 230.93/42.12  Sub-proof #1291 shows that the following formulas are inconsistent:
% 230.93/42.12  ----------------------------------------------------------------
% 230.93/42.12    (1)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3)
% 230.93/42.12    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.93/42.12         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.93/42.12    (3)   ~ (e3 = e1)
% 230.93/42.12    (4)  all_57_4 = e0
% 230.93/42.12    (5)  all_57_3 = e0
% 230.93/42.12    (6)   ~ (e3 = e2)
% 230.93/42.12    (7)   ~ (e3 = e0)
% 230.93/42.12    (8)   ~ (e2 = e0)
% 230.93/42.12    (9)  all_57_2 = e3
% 230.93/42.12    (10)   ~ (e1 = e0)
% 230.93/42.12    (11)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.93/42.12          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.93/42.12    (12)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.93/42.12          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.93/42.12    (13)   ~ (e2 = e1)
% 230.93/42.12  
% 230.93/42.12  Begin of proof
% 230.93/42.12  | 
% 230.93/42.12  | BETA: splitting (1) gives:
% 230.93/42.12  | 
% 230.93/42.12  | Case 1:
% 230.93/42.12  | | 
% 230.93/42.12  | |   (14)  all_57_4 = e3 & op(e3, e1) = e3
% 230.93/42.12  | | 
% 230.93/42.12  | | ALPHA: (14) implies:
% 230.93/42.12  | |   (15)  all_57_4 = e3
% 230.93/42.12  | | 
% 230.93/42.12  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 230.93/42.12  | |            (15) are inconsistent by sub-proof #1292.
% 230.93/42.12  | | 
% 230.93/42.12  | Case 2:
% 230.93/42.12  | | 
% 230.93/42.12  | |   (16)  all_57_5 = e3 & op(e2, e1) = e3
% 230.93/42.12  | | 
% 230.93/42.12  | | ALPHA: (16) implies:
% 230.93/42.12  | |   (17)  all_57_5 = e3
% 230.93/42.12  | | 
% 230.93/42.12  | | REF_CLOSE: (2), (3), (5), (6), (8), (9), (10), (12), (13), (17) are
% 230.93/42.12  | |            inconsistent by sub-proof #1802.
% 230.93/42.12  | | 
% 230.93/42.12  | End of split
% 230.93/42.12  | 
% 230.93/42.12  End of proof
% 230.93/42.12  
% 230.93/42.12  Sub-proof #1292 shows that the following formulas are inconsistent:
% 230.93/42.12  ----------------------------------------------------------------
% 230.93/42.12    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.93/42.12         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.93/42.12    (2)   ~ (e3 = e1)
% 230.93/42.12    (3)  all_57_4 = e0
% 230.93/42.12    (4)  all_57_3 = e0
% 230.93/42.12    (5)  all_57_4 = e3
% 230.93/42.12    (6)   ~ (e3 = e2)
% 230.93/42.12    (7)   ~ (e3 = e0)
% 230.93/42.12    (8)   ~ (e2 = e0)
% 230.93/42.12    (9)  all_57_2 = e3
% 230.93/42.12    (10)   ~ (e1 = e0)
% 230.93/42.12    (11)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.93/42.12          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.93/42.12    (12)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.93/42.12          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.93/42.12    (13)   ~ (e2 = e1)
% 230.93/42.12  
% 230.93/42.12  Begin of proof
% 230.93/42.12  | 
% 230.93/42.12  | COMBINE_EQS: (3), (5) imply:
% 230.93/42.12  |   (14)  e3 = e0
% 230.93/42.12  | 
% 230.93/42.12  | COMBINE_EQS: (9), (14) imply:
% 230.93/42.12  |   (15)  all_57_2 = e0
% 230.93/42.12  | 
% 230.93/42.12  | REF_CLOSE: (1), (2), (4), (6), (7), (8), (10), (11), (12), (13), (15) are
% 230.93/42.12  |            inconsistent by sub-proof #2246.
% 230.93/42.12  | 
% 230.93/42.12  End of proof
% 230.93/42.12  
% 230.93/42.12  Sub-proof #1293 shows that the following formulas are inconsistent:
% 230.93/42.12  ----------------------------------------------------------------
% 230.93/42.12    (1)   ~ (e3 = e1)
% 230.93/42.12    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.93/42.12           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.93/42.12    (3)   ~ (all_6_2 = e3)
% 230.93/42.12    (4)  op(e1, e1) = all_6_2
% 230.93/42.12    (5)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.93/42.12         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.93/42.12    (6)   ~ (e3 = e2)
% 230.93/42.12    (7)   ~ (e3 = e0)
% 230.93/42.12    (8)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.93/42.12         (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.93/42.12    (9)  op(e3, e3) = e2
% 230.93/42.12    (10)  op(e3, e2) = all_53_4
% 230.93/42.12    (11)   ~ (e2 = e0)
% 230.93/42.12    (12)   ~ (e1 = e0)
% 230.93/42.12    (13)   ~ (all_53_4 = e0)
% 230.93/42.12    (14)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 230.93/42.12          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 230.93/42.12    (15)   ~ (all_53_12 = e0)
% 230.93/42.12    (16)   ~ (e2 = e1)
% 230.93/42.12    (17)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.93/42.12          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.93/42.12    (18)  all_57_14 = e0
% 230.93/42.12    (19)  op(e3, e0) = all_53_12
% 230.93/42.12  
% 230.93/42.12  Begin of proof
% 230.93/42.12  | 
% 230.93/42.12  | BETA: splitting (5) gives:
% 230.93/42.12  | 
% 230.93/42.12  | Case 1:
% 230.93/42.12  | | 
% 230.93/42.12  | |   (20)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) =
% 230.93/42.12  | |           e0)
% 230.93/42.12  | | 
% 230.93/42.12  | | REF_CLOSE: (2), (9), (10), (11), (13), (20) are inconsistent by sub-proof
% 230.93/42.12  | |            #1321.
% 230.93/42.12  | | 
% 230.93/42.12  | Case 2:
% 230.93/42.12  | | 
% 230.93/42.12  | |   (21)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) =
% 230.93/42.12  | |           e0)
% 230.93/42.12  | | 
% 230.93/42.12  | | BETA: splitting (21) gives:
% 230.93/42.12  | | 
% 230.93/42.12  | | Case 1:
% 230.93/42.12  | | | 
% 230.93/42.12  | | |   (22)  all_57_4 = e0 & op(e3, e1) = e0
% 230.93/42.12  | | | 
% 230.93/42.12  | | | ALPHA: (22) implies:
% 230.93/42.12  | | |   (23)  all_57_4 = e0
% 230.93/42.12  | | | 
% 230.93/42.12  | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (11), (12), (14), (16),
% 230.93/42.12  | | |            (17), (18), (23) are inconsistent by sub-proof #2371.
% 230.93/42.12  | | | 
% 230.93/42.12  | | Case 2:
% 230.93/42.12  | | | 
% 230.93/42.12  | | |   (24)  all_57_9 = e0 & op(e3, e0) = e0
% 230.93/42.12  | | | 
% 230.93/42.12  | | | REF_CLOSE: (2), (15), (19), (24) are inconsistent by sub-proof #2434.
% 230.93/42.12  | | | 
% 230.93/42.12  | | End of split
% 230.93/42.12  | | 
% 230.93/42.12  | End of split
% 230.93/42.12  | 
% 230.93/42.12  End of proof
% 230.93/42.12  
% 230.93/42.12  Sub-proof #1294 shows that the following formulas are inconsistent:
% 230.93/42.12  ----------------------------------------------------------------
% 230.93/42.12    (1)   ~ (all_10_2 = e2)
% 230.93/42.12    (2)  op(e3, e3) = all_10_2
% 230.93/42.12    (3)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 230.93/42.12    (4)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 230.93/42.12    (5)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.93/42.12         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.93/42.12    (6)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.93/42.12         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.93/42.12    (7)   ~ (all_53_8 = all_53_12)
% 230.93/42.12    (8)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.93/42.12         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.93/42.12    (9)   ~ (e3 = e1)
% 230.93/42.12    (10)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.93/42.12          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.93/42.12    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.93/42.12            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.93/42.12    (12)  all_55_0 = all_10_2
% 230.93/42.12    (13)   ~ (all_10_2 = e0)
% 230.93/42.12    (14)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.93/42.12          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.93/42.12    (15)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 230.93/42.12            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 230.93/42.12              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 230.93/42.12    (16)   ~ (all_6_2 = e3)
% 230.93/42.12    (17)  op(e1, e1) = all_6_2
% 230.93/42.12    (18)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 230.93/42.12    (19)   ~ (all_53_9 = e0)
% 230.93/42.12    (20)  all_55_0 = e3 | all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 230.93/42.12    (21)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.93/42.12          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.93/42.12    (22)   ~ (all_53_4 = all_53_12)
% 230.93/42.12    (23)   ~ (all_53_8 = all_53_9)
% 230.93/42.12    (24)  all_42_2 = all_6_2
% 230.93/42.12    (25)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.93/42.12          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.93/42.12    (26)  op(e2, e2) = e0
% 230.93/42.12    (27)   ~ (all_53_9 = all_6_2)
% 230.93/42.12    (28)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.93/42.12          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.93/42.12    (29)  all_57_3 = e0
% 230.93/42.12    (30)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 230.93/42.12          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.93/42.12    (31)   ~ (e3 = e2)
% 230.93/42.12    (32)  all_55_1 = all_53_4
% 230.93/42.12    (33)   ~ (e3 = e0)
% 230.93/42.12    (34)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.93/42.12          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.93/42.12    (35)  op(e3, e3) = e3
% 230.93/42.12    (36)   ~ (all_53_8 = all_6_2)
% 230.93/42.12    (37)   ~ (all_53_2 = e0)
% 230.93/42.12    (38)  all_55_2 = all_53_8
% 230.93/42.12    (39)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 230.93/42.12    (40)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.93/42.12          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.93/42.12            e1)
% 230.93/42.12    (41)  all_57_11 = e0
% 230.93/42.12    (42)   ~ (all_53_4 = all_53_8)
% 230.93/42.12    (43)  op(e3, e2) = all_53_4
% 230.93/42.12    (44)   ~ (e2 = e0)
% 230.93/42.12    (45)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 230.93/42.12            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 230.93/42.12            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 230.93/42.12            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 230.93/42.12              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 230.93/42.12            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 230.93/42.12            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 230.93/42.12              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 230.93/42.12              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 230.93/42.12            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 230.93/42.12            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 230.93/42.12            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 230.93/42.12              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 230.93/42.12              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 230.93/42.12            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 230.93/42.12              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 230.93/42.12            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 230.93/42.12            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 230.93/42.12              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 230.93/42.12              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 230.93/42.12            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 230.93/42.12            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 230.93/42.12    (46)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.93/42.12          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.93/42.12    (47)   ~ (e1 = e0)
% 230.93/42.12    (48)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 230.93/42.12            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 230.93/42.12              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 230.93/42.12    (49)   ~ (all_53_4 = e0)
% 230.93/42.12    (50)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 230.93/42.12          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 230.93/42.12    (51)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.93/42.12          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.93/42.12    (52)   ~ (all_10_2 = e1)
% 230.93/42.12    (53)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.93/42.12          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 230.93/42.12            e3)
% 230.93/42.12    (54)   ~ (all_53_4 = all_53_6)
% 230.93/42.12    (55)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.93/42.12          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.93/42.12            e2)
% 230.93/42.12    (56)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.93/42.12              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.93/42.12                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.93/42.12                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.93/42.12    (57)  op(e1, e1) = e0
% 230.93/42.13    (58)  all_55_10 = all_6_2
% 230.93/42.13    (59)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.93/42.13          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.93/42.13    (60)  all_38_2 = all_6_2
% 230.93/42.13    (61)  all_55_3 = all_53_12
% 230.93/42.13    (62)   ~ (all_53_12 = e3)
% 230.93/42.13    (63)  all_57_0 = e3
% 230.93/42.13    (64)  op(e1, e3) = all_53_2
% 230.93/42.13    (65)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 230.93/42.13            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 230.93/42.13              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 230.93/42.13    (66)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.93/42.13          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.93/42.13    (67)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.93/42.13          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.93/42.13    (68)   ~ (all_53_12 = all_10_2)
% 230.93/42.13    (69)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 230.93/42.13          (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 230.93/42.13    (70)   ~ (all_53_8 = e0)
% 230.93/42.13    (71)   ~ (e2 = e1)
% 230.93/42.13    (72)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.93/42.13          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.93/42.13    (73)  op(e2, e1) = all_53_9
% 230.93/42.13    (74)  op(e1, e2) = all_53_6
% 230.93/42.13    (75)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.93/42.13          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.93/42.13    (76)  all_24_2 = all_6_2
% 230.93/42.13    (77)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.93/42.13          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.93/42.13    (78)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.93/42.13          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.93/42.13    (79)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.93/42.13          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.93/42.13    (80)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.93/42.13          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.93/42.13    (81)  op(e3, e1) = all_53_8
% 230.93/42.13    (82)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.93/42.13          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.93/42.13    (83)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.93/42.13          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.93/42.13    (84)  op(e3, e0) = all_53_12
% 230.93/42.13  
% 230.93/42.13  Begin of proof
% 230.93/42.13  | 
% 230.93/42.13  | BETA: splitting (78) gives:
% 230.93/42.13  | 
% 230.93/42.13  | Case 1:
% 230.93/42.13  | | 
% 230.93/42.13  | |   (85)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) =
% 230.93/42.13  | |           e0)
% 230.93/42.13  | | 
% 230.93/42.13  | | REF_CLOSE: (5), (9), (11), (29), (31), (33), (35), (44), (47), (59), (66),
% 230.93/42.13  | |            (71), (85) are inconsistent by sub-proof #2229.
% 230.93/42.13  | | 
% 230.93/42.13  | Case 2:
% 230.93/42.13  | | 
% 230.93/42.13  | |   (86)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) =
% 230.93/42.13  | |           e0)
% 230.93/42.13  | | 
% 230.93/42.13  | | BETA: splitting (86) gives:
% 230.93/42.13  | | 
% 230.93/42.13  | | Case 1:
% 230.93/42.13  | | | 
% 230.93/42.13  | | |   (87)  all_57_6 = e0 & op(e1, e3) = e0
% 230.93/42.13  | | | 
% 230.93/42.13  | | | ALPHA: (87) implies:
% 230.93/42.13  | | |   (88)  op(e1, e3) = e0
% 230.93/42.13  | | | 
% 230.93/42.13  | | | REF_CLOSE: (11), (37), (64), (88) are inconsistent by sub-proof #2154.
% 230.93/42.13  | | | 
% 230.93/42.13  | | Case 2:
% 230.93/42.13  | | | 
% 230.93/42.13  | | |   (89)  all_57_12 = e0 & op(e0, e3) = e0
% 230.93/42.13  | | | 
% 230.93/42.13  | | | ALPHA: (89) implies:
% 230.93/42.13  | | |   (90)  all_57_12 = e0
% 230.93/42.13  | | | 
% 230.93/42.13  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 230.93/42.13  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 230.93/42.13  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 230.93/42.13  | | |            (33), (34), (35), (36), (38), (39), (40), (41), (42), (43),
% 230.93/42.13  | | |            (44), (45), (46), (47), (48), (49), (50), (51), (52), (53),
% 230.93/42.13  | | |            (54), (55), (56), (57), (58), (59), (60), (61), (62), (63),
% 230.93/42.13  | | |            (65), (66), (67), (68), (69), (70), (71), (72), (73), (74),
% 230.93/42.13  | | |            (75), (76), (77), (78), (79), (80), (81), (82), (83), (84),
% 230.93/42.13  | | |            (90) are inconsistent by sub-proof #1295.
% 230.93/42.13  | | | 
% 230.93/42.13  | | End of split
% 230.93/42.13  | | 
% 230.93/42.13  | End of split
% 230.93/42.13  | 
% 230.93/42.13  End of proof
% 230.93/42.13  
% 230.93/42.13  Sub-proof #1295 shows that the following formulas are inconsistent:
% 230.93/42.13  ----------------------------------------------------------------
% 230.93/42.13    (1)   ~ (all_10_2 = e2)
% 230.93/42.13    (2)  op(e3, e3) = all_10_2
% 230.93/42.13    (3)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 230.93/42.13    (4)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 230.93/42.13    (5)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.93/42.13         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.93/42.13    (6)  all_57_12 = e0
% 230.93/42.13    (7)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.93/42.13         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.93/42.13    (8)   ~ (all_53_8 = all_53_12)
% 230.93/42.13    (9)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.93/42.13         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.93/42.13    (10)   ~ (e3 = e1)
% 230.93/42.13    (11)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.93/42.13          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.93/42.13    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.93/42.13            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.93/42.13    (13)  all_55_0 = all_10_2
% 230.93/42.13    (14)   ~ (all_10_2 = e0)
% 230.93/42.13    (15)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.93/42.13          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.93/42.13    (16)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 230.93/42.13            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 230.93/42.13              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 230.93/42.13    (17)   ~ (all_6_2 = e3)
% 230.93/42.13    (18)  op(e1, e1) = all_6_2
% 230.93/42.13    (19)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 230.93/42.13    (20)   ~ (all_53_9 = e0)
% 230.93/42.13    (21)  all_55_0 = e3 | all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 230.93/42.13    (22)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.93/42.13          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.93/42.13    (23)   ~ (all_53_4 = all_53_12)
% 230.93/42.13    (24)   ~ (all_53_8 = all_53_9)
% 230.93/42.13    (25)  all_42_2 = all_6_2
% 230.93/42.13    (26)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.93/42.13          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.93/42.13    (27)  op(e2, e2) = e0
% 230.93/42.13    (28)   ~ (all_53_9 = all_6_2)
% 230.93/42.13    (29)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.93/42.13          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.93/42.13    (30)  all_57_3 = e0
% 230.93/42.13    (31)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 230.93/42.13          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.93/42.13    (32)   ~ (e3 = e2)
% 230.93/42.13    (33)  all_55_1 = all_53_4
% 230.93/42.13    (34)   ~ (e3 = e0)
% 230.93/42.13    (35)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.93/42.13          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.93/42.13    (36)  op(e3, e3) = e3
% 230.93/42.13    (37)   ~ (all_53_8 = all_6_2)
% 230.93/42.13    (38)  all_55_2 = all_53_8
% 230.93/42.13    (39)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 230.93/42.13    (40)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.93/42.13          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.93/42.13            e1)
% 230.93/42.13    (41)  all_57_11 = e0
% 230.93/42.13    (42)   ~ (all_53_4 = all_53_8)
% 230.93/42.13    (43)  op(e3, e2) = all_53_4
% 230.93/42.13    (44)   ~ (e2 = e0)
% 230.93/42.13    (45)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 230.93/42.13            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 230.93/42.13            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 230.93/42.13            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 230.93/42.13              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 230.93/42.13            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 230.93/42.13            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 230.93/42.13              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 230.93/42.13              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 230.93/42.13            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 230.93/42.13            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 230.93/42.13            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 230.93/42.13              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 230.93/42.13              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 230.93/42.13            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 230.93/42.13              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 230.93/42.13            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 230.93/42.13            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 230.93/42.13              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 230.93/42.13              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 230.93/42.13            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 230.93/42.13            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 230.93/42.13    (46)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.93/42.13          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.93/42.13    (47)   ~ (e1 = e0)
% 230.93/42.13    (48)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 230.93/42.13            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 230.93/42.13              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 230.93/42.13    (49)   ~ (all_53_4 = e0)
% 230.93/42.13    (50)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 230.93/42.13          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 230.93/42.13    (51)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.93/42.13          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.93/42.13    (52)   ~ (all_10_2 = e1)
% 230.93/42.13    (53)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.93/42.13          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 230.93/42.13            e3)
% 230.93/42.13    (54)   ~ (all_53_4 = all_53_6)
% 230.93/42.13    (55)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.93/42.13          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.93/42.13            e2)
% 230.93/42.13    (56)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.93/42.13              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.93/42.13                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.93/42.13                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.93/42.13    (57)  op(e1, e1) = e0
% 230.93/42.13    (58)  all_55_10 = all_6_2
% 230.93/42.13    (59)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.93/42.13          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.93/42.13    (60)  all_38_2 = all_6_2
% 230.93/42.13    (61)  all_55_3 = all_53_12
% 230.93/42.13    (62)   ~ (all_53_12 = e3)
% 230.93/42.13    (63)  all_57_0 = e3
% 230.93/42.13    (64)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 230.93/42.13            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 230.93/42.13              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 230.93/42.13    (65)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.93/42.13          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.93/42.13    (66)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.93/42.13          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.93/42.13    (67)   ~ (all_53_12 = all_10_2)
% 230.93/42.13    (68)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 230.93/42.13          (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 230.93/42.13    (69)   ~ (all_53_8 = e0)
% 230.93/42.13    (70)   ~ (e2 = e1)
% 230.93/42.13    (71)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.93/42.13          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.93/42.13    (72)  op(e2, e1) = all_53_9
% 230.93/42.13    (73)  op(e1, e2) = all_53_6
% 230.93/42.13    (74)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.93/42.13          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.93/42.13    (75)  all_24_2 = all_6_2
% 230.93/42.13    (76)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.93/42.13          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.93/42.13    (77)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.93/42.13          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.93/42.13    (78)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.93/42.13          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.93/42.13    (79)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.93/42.13          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.93/42.13    (80)  op(e3, e1) = all_53_8
% 230.93/42.13    (81)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.93/42.13          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.93/42.13    (82)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.93/42.13          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.93/42.13    (83)  op(e3, e0) = all_53_12
% 230.93/42.13  
% 230.93/42.13  Begin of proof
% 230.93/42.13  | 
% 230.93/42.13  | BETA: splitting (15) gives:
% 230.93/42.13  | 
% 230.93/42.13  | Case 1:
% 230.93/42.13  | | 
% 230.93/42.13  | |   (84)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 230.93/42.13  | |           e3)
% 230.93/42.13  | | 
% 230.93/42.13  | | BETA: splitting (84) gives:
% 230.93/42.13  | | 
% 230.93/42.13  | | Case 1:
% 230.93/42.13  | | | 
% 230.93/42.13  | | |   (85)  all_57_6 = e3 & op(e1, e3) = e3
% 230.93/42.13  | | | 
% 230.93/42.13  | | | ALPHA: (85) implies:
% 230.93/42.13  | | |   (86)  all_57_6 = e3
% 230.93/42.13  | | | 
% 230.93/42.13  | | | REF_CLOSE: (6), (7), (10), (32), (44), (47), (63), (70), (74), (86) are
% 230.93/42.13  | | |            inconsistent by sub-proof #2011.
% 230.93/42.13  | | | 
% 230.93/42.13  | | Case 2:
% 230.93/42.13  | | | 
% 230.93/42.13  | | |   (87)  all_57_7 = e3 & op(e1, e2) = e3
% 230.93/42.13  | | | 
% 230.93/42.13  | | | ALPHA: (87) implies:
% 230.93/42.13  | | |   (88)  all_57_7 = e3
% 230.93/42.13  | | | 
% 230.93/42.13  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 230.93/42.13  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 230.93/42.13  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 230.93/42.13  | | |            (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 230.93/42.13  | | |            (43), (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 230.93/42.13  | | |            (53), (54), (55), (56), (57), (58), (59), (60), (61), (62),
% 230.93/42.13  | | |            (64), (65), (66), (67), (68), (69), (70), (71), (72), (73),
% 230.93/42.13  | | |            (74), (75), (76), (77), (78), (79), (80), (81), (82), (83),
% 230.93/42.13  | | |            (88) are inconsistent by sub-proof #1311.
% 230.93/42.13  | | | 
% 230.93/42.13  | | End of split
% 230.93/42.13  | | 
% 230.93/42.13  | Case 2:
% 230.93/42.13  | | 
% 230.93/42.13  | |   (89)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 230.93/42.13  | |           e3)
% 230.93/42.13  | | 
% 230.93/42.13  | | REF_CLOSE: (12), (17), (18), (34), (41), (89) are inconsistent by sub-proof
% 230.93/42.13  | |            #1594.
% 230.93/42.13  | | 
% 230.93/42.13  | End of split
% 230.93/42.13  | 
% 230.93/42.13  End of proof
% 230.93/42.13  
% 230.93/42.13  Sub-proof #1296 shows that the following formulas are inconsistent:
% 230.93/42.13  ----------------------------------------------------------------
% 230.93/42.13    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.93/42.13         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.93/42.13    (2)   ~ (e3 = e1)
% 230.93/42.13    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.93/42.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.93/42.13    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.93/42.13         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.93/42.13    (5)  op(e2, e2) = e0
% 230.93/42.13    (6)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.93/42.13         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.93/42.13    (7)  all_57_3 = e0
% 230.93/42.13    (8)   ~ (e3 = e2)
% 230.93/42.13    (9)   ~ (e3 = e0)
% 230.93/42.13    (10)  op(e3, e3) = e2
% 230.93/42.13    (11)   ~ (e2 = e0)
% 230.93/42.13    (12)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.93/42.13          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.93/42.13    (13)   ~ (e1 = e0)
% 230.93/42.13    (14)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.93/42.13          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.93/42.13    (15)   ~ (e2 = e1)
% 230.93/42.13    (16)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.93/42.13          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.93/42.13    (17)  all_57_7 = e0
% 230.93/42.13  
% 230.93/42.13  Begin of proof
% 230.93/42.13  | 
% 230.93/42.13  | BETA: splitting (1) gives:
% 230.93/42.13  | 
% 230.93/42.13  | Case 1:
% 230.93/42.13  | | 
% 230.93/42.13  | |   (18)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 230.93/42.13  | |           e2)
% 230.93/42.13  | | 
% 230.93/42.13  | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13), (15),
% 230.93/42.13  | |            (18) are inconsistent by sub-proof #1297.
% 230.93/42.13  | | 
% 230.93/42.13  | Case 2:
% 230.93/42.13  | | 
% 230.93/42.13  | |   (19)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 230.93/42.13  | |           e2)
% 230.93/42.13  | | 
% 230.93/42.13  | | REF_CLOSE: (2), (3), (5), (7), (8), (9), (11), (13), (14), (15), (16), (17),
% 230.93/42.13  | |            (19) are inconsistent by sub-proof #2201.
% 230.93/42.13  | | 
% 230.93/42.13  | End of split
% 230.93/42.13  | 
% 230.93/42.13  End of proof
% 230.93/42.13  
% 230.93/42.13  Sub-proof #1297 shows that the following formulas are inconsistent:
% 230.93/42.13  ----------------------------------------------------------------
% 230.93/42.13    (1)   ~ (e3 = e1)
% 230.93/42.13    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.93/42.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.93/42.13    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.93/42.13         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.93/42.13    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2)
% 230.93/42.13    (5)  op(e2, e2) = e0
% 230.93/42.13    (6)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.93/42.13         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.93/42.13    (7)   ~ (e3 = e2)
% 230.93/42.13    (8)   ~ (e3 = e0)
% 230.93/42.13    (9)  op(e3, e3) = e2
% 230.93/42.13    (10)   ~ (e2 = e0)
% 230.93/42.13    (11)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.93/42.13          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.93/42.13    (12)   ~ (e1 = e0)
% 230.93/42.13    (13)   ~ (e2 = e1)
% 230.93/42.13  
% 230.93/42.13  Begin of proof
% 230.93/42.13  | 
% 230.93/42.13  | BETA: splitting (4) gives:
% 230.93/42.13  | 
% 230.93/42.13  | Case 1:
% 230.93/42.13  | | 
% 230.93/42.13  | |   (14)  all_57_1 = e2 & op(e3, e2) = e2
% 230.93/42.13  | | 
% 230.93/42.13  | | ALPHA: (14) implies:
% 230.93/42.13  | |   (15)  all_57_1 = e2
% 230.93/42.13  | | 
% 230.93/42.13  | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (9), (10), (11), (12), (13), (15)
% 230.93/42.13  | |            are inconsistent by sub-proof #1655.
% 230.93/42.13  | | 
% 230.93/42.13  | Case 2:
% 230.93/42.13  | | 
% 230.93/42.13  | |   (16)  all_57_3 = e2 & op(e2, e2) = e2
% 230.93/42.13  | | 
% 230.93/42.13  | | ALPHA: (16) implies:
% 230.93/42.13  | |   (17)  op(e2, e2) = e2
% 230.93/42.13  | | 
% 230.93/42.13  | | REF_CLOSE: (2), (5), (10), (17) are inconsistent by sub-proof #2472.
% 230.93/42.13  | | 
% 230.93/42.13  | End of split
% 230.93/42.13  | 
% 230.93/42.13  End of proof
% 230.93/42.13  
% 230.93/42.13  Sub-proof #1298 shows that the following formulas are inconsistent:
% 230.93/42.13  ----------------------------------------------------------------
% 230.93/42.13    (1)   ~ (all_10_2 = e2)
% 230.93/42.13    (2)  all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 230.93/42.13    (3)  op(e3, e3) = all_10_2
% 230.93/42.13    (4)  op(e0, e1) = all_53_11
% 230.93/42.13    (5)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 230.93/42.13    (6)   ~ (all_53_6 = all_53_14)
% 230.93/42.13    (7)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 230.93/42.13    (8)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.93/42.13         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.93/42.13    (9)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.93/42.13         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.93/42.13    (10)   ~ (all_53_8 = all_53_12)
% 230.93/42.13    (11)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.93/42.13          (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.93/42.13    (12)   ~ (all_53_8 = all_53_11)
% 230.93/42.13    (13)   ~ (e3 = e1)
% 230.93/42.13    (14)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.93/42.13          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.93/42.13    (15)   ~ (all_53_13 = e1)
% 230.93/42.14    (16)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.93/42.14            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.93/42.14    (17)  all_55_0 = all_10_2
% 230.93/42.14    (18)  all_57_15 = e1
% 230.93/42.14    (19)   ~ (all_10_2 = e0)
% 230.93/42.14    (20)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.93/42.14          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.93/42.14    (21)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 230.93/42.14            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 230.93/42.14              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 230.93/42.14    (22)   ~ (all_6_2 = e3)
% 230.93/42.14    (23)  op(e1, e1) = all_6_2
% 230.93/42.14    (24)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 230.93/42.14    (25)   ~ (all_53_9 = e0)
% 230.93/42.14    (26)  all_55_0 = e3 | all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 230.93/42.14    (27)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 230.93/42.14    (28)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.93/42.14          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.93/42.14    (29)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 230.93/42.14    (30)  all_55_9 = all_53_6
% 230.93/42.14    (31)   ~ (all_53_11 = all_6_2)
% 230.93/42.14    (32)   ~ (all_53_4 = all_53_12)
% 230.93/42.14    (33)   ~ (all_53_8 = e3)
% 230.93/42.14    (34)   ~ (all_53_8 = all_53_9)
% 230.93/42.14    (35)  all_42_2 = all_6_2
% 230.93/42.14    (36)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.93/42.14          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.93/42.14    (37)  op(e2, e2) = e0
% 230.93/42.14    (38)   ~ (all_53_9 = all_53_11)
% 230.93/42.14    (39)   ~ (all_53_9 = all_6_2)
% 230.93/42.14    (40)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.93/42.14          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.93/42.14    (41)   ~ (all_53_14 = all_6_2)
% 230.93/42.14    (42)  all_57_3 = e0
% 230.93/42.14    (43)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 230.93/42.14          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.93/42.14    (44)   ~ (e3 = e2)
% 230.93/42.14    (45)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 230.93/42.14    (46)  all_55_1 = all_53_4
% 230.93/42.14    (47)  op(e1, e0) = all_53_14
% 230.93/42.14    (48)   ~ (all_53_6 = all_53_7)
% 230.93/42.14    (49)   ~ (e3 = e0)
% 230.93/42.14    (50)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.93/42.14          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.93/42.14    (51)  op(e3, e3) = e3
% 230.93/42.14    (52)   ~ (all_53_8 = all_6_2)
% 230.93/42.14    (53)  all_55_2 = all_53_8
% 230.93/42.14    (54)   ~ (all_53_4 = all_53_7)
% 230.93/42.14    (55)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 230.93/42.14    (56)   ~ (all_53_7 = e0)
% 230.93/42.14    (57)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.93/42.14          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.93/42.14            e1)
% 230.93/42.14    (58)   ~ (all_53_4 = all_53_8)
% 230.93/42.14    (59)  all_55_6 = all_53_9
% 230.93/42.14    (60)  op(e3, e2) = all_53_4
% 230.93/42.14    (61)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.93/42.14          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.93/42.14    (62)   ~ (e2 = e0)
% 230.93/42.14    (63)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 230.93/42.14            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 230.93/42.14            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 230.93/42.14            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 230.93/42.14              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 230.93/42.14            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 230.93/42.14            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 230.93/42.14              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 230.93/42.14              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 230.93/42.14            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 230.93/42.14            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 230.93/42.14            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 230.93/42.14              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 230.93/42.14              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 230.93/42.14            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 230.93/42.14              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 230.93/42.14            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 230.93/42.14            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 230.93/42.14              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 230.93/42.14              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 230.93/42.14            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 230.93/42.14            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 230.93/42.14    (64)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.93/42.14          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.93/42.14    (65)   ~ (all_53_2 = all_53_14)
% 230.93/42.14    (66)   ~ (e1 = e0)
% 230.93/42.14    (67)  all_57_14 = e2
% 230.93/42.14    (68)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 230.93/42.14            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 230.93/42.14              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 230.93/42.14    (69)   ~ (all_53_4 = e0)
% 230.93/42.14    (70)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 230.93/42.14          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 230.93/42.14    (71)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.93/42.14          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.93/42.14    (72)   ~ (all_10_2 = e1)
% 230.93/42.14    (73)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 230.93/42.14    (74)  all_57_13 = e3
% 230.93/42.14    (75)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.93/42.14          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 230.93/42.14            e3)
% 230.93/42.14    (76)   ~ (all_53_4 = all_53_6)
% 230.93/42.14    (77)  op(e0, e2) = all_53_7
% 230.93/42.14    (78)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.93/42.14          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.93/42.14            e2)
% 230.93/42.14    (79)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.93/42.14              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.93/42.14                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.93/42.14                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.93/42.14    (80)  all_55_10 = all_6_2
% 230.93/42.14    (81)   ~ (all_53_6 = all_6_2)
% 230.93/42.14    (82)   ~ (all_53_13 = e0)
% 230.93/42.14    (83)  op(e1, e1) = e2
% 230.93/42.14    (84)  all_55_13 = all_53_7
% 230.93/42.14    (85)  op(e0, e0) = e1
% 230.93/42.14    (86)  op(e2, e0) = all_53_13
% 230.93/42.14    (87)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.93/42.14          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.93/42.14    (88)  all_38_2 = all_6_2
% 230.93/42.14    (89)  all_55_11 = all_53_14
% 230.93/42.14    (90)  all_55_3 = all_53_12
% 230.93/42.14    (91)   ~ (all_53_12 = e3)
% 230.93/42.14    (92)  all_57_0 = e3
% 230.93/42.14    (93)  op(e1, e3) = all_53_2
% 230.93/42.14    (94)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 230.93/42.14            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 230.93/42.14              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 230.93/42.14    (95)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.93/42.14          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.93/42.14    (96)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.93/42.14          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.93/42.14    (97)   ~ (all_53_12 = all_10_2)
% 230.93/42.14    (98)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 230.93/42.14          (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 230.93/42.14    (99)   ~ (all_53_13 = all_53_14)
% 230.93/42.14    (100)   ~ (e2 = e1)
% 230.93/42.14    (101)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.93/42.14           | (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.93/42.14             e2)
% 230.93/42.14    (102)  op(e2, e1) = all_53_9
% 230.93/42.14    (103)  op(e1, e2) = all_53_6
% 230.93/42.14    (104)   ~ (all_6_2 = e0)
% 230.93/42.14    (105)   ~ (all_53_2 = all_53_6)
% 230.93/42.14    (106)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.93/42.14           (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.93/42.14    (107)  all_24_2 = all_6_2
% 230.93/42.14    (108)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.93/42.14           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.93/42.14    (109)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.93/42.14           (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.93/42.14    (110)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.93/42.14           | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.93/42.14             e1)
% 230.93/42.14    (111)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.93/42.14           (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.93/42.14    (112)   ~ (all_53_12 = all_53_14)
% 230.93/42.14    (113)  all_55_14 = all_53_11
% 230.93/42.14    (114)  op(e3, e1) = all_53_8
% 230.93/42.14    (115)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.93/42.14           (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.93/42.14    (116)   ~ (all_53_4 = e3)
% 230.93/42.14    (117)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.93/42.14           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.93/42.14    (118)  op(e3, e0) = all_53_12
% 230.93/42.14  
% 230.93/42.14  Begin of proof
% 230.93/42.14  | 
% 230.93/42.14  | BETA: splitting (11) gives:
% 230.93/42.14  | 
% 230.93/42.14  | Case 1:
% 230.93/42.14  | | 
% 230.93/42.14  | |   (119)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 230.93/42.14  | |            e2)
% 230.93/42.14  | | 
% 230.93/42.14  | | BETA: splitting (119) gives:
% 230.93/42.14  | | 
% 230.93/42.14  | | Case 1:
% 230.93/42.14  | | | 
% 230.93/42.14  | | |   (120)  all_57_1 = e2 & op(e3, e2) = e2
% 230.93/42.14  | | | 
% 230.93/42.14  | | | ALPHA: (120) implies:
% 230.93/42.14  | | |   (121)  all_57_1 = e2
% 230.93/42.14  | | | 
% 230.93/42.14  | | | BETA: splitting (28) gives:
% 230.93/42.14  | | | 
% 230.93/42.14  | | | Case 1:
% 230.93/42.14  | | | | 
% 230.93/42.14  | | | |   (122)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2)
% 230.93/42.14  | | | |            = e1)
% 230.93/42.14  | | | | 
% 230.93/42.14  | | | | REF_CLOSE: (13), (16), (51), (100), (121), (122) are inconsistent by
% 230.93/42.14  | | | |            sub-proof #2096.
% 230.93/42.14  | | | | 
% 230.93/42.14  | | | Case 2:
% 230.93/42.14  | | | | 
% 230.93/42.14  | | | |   (123)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0)
% 230.93/42.14  | | | |            = e1)
% 230.93/42.14  | | | | 
% 230.93/42.14  | | | | BETA: splitting (123) gives:
% 230.93/42.14  | | | | 
% 230.93/42.14  | | | | Case 1:
% 230.93/42.14  | | | | | 
% 230.93/42.14  | | | | |   (124)  all_57_4 = e1 & op(e3, e1) = e1
% 230.93/42.14  | | | | | 
% 230.93/42.14  | | | | | ALPHA: (124) implies:
% 230.93/42.14  | | | | |   (125)  all_57_4 = e1
% 230.93/42.14  | | | | | 
% 230.93/42.14  | | | | | BETA: splitting (70) gives:
% 230.93/42.14  | | | | | 
% 230.93/42.14  | | | | | Case 1:
% 230.93/42.14  | | | | | | 
% 230.93/42.14  | | | | | |   (126)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2,
% 230.93/42.14  | | | | | |              e1) = e3)
% 230.93/42.14  | | | | | | 
% 230.93/42.14  | | | | | | BETA: splitting (126) gives:
% 230.93/42.14  | | | | | | 
% 230.93/42.14  | | | | | | Case 1:
% 230.93/42.14  | | | | | | | 
% 230.93/42.14  | | | | | | |   (127)  all_57_4 = e3 & op(e3, e1) = e3
% 230.93/42.14  | | | | | | | 
% 230.93/42.14  | | | | | | | REF_CLOSE: (13), (16), (28), (36), (40), (44), (49), (51), (62),
% 230.93/42.14  | | | | | | |            (66), (100), (121), (127) are inconsistent by sub-proof
% 230.93/42.14  | | | | | | |            #1829.
% 230.93/42.14  | | | | | | | 
% 230.93/42.14  | | | | | | Case 2:
% 230.93/42.14  | | | | | | | 
% 230.93/42.14  | | | | | | |   (128)  all_57_5 = e3 & op(e2, e1) = e3
% 230.93/42.14  | | | | | | | 
% 230.93/42.14  | | | | | | | ALPHA: (128) implies:
% 230.93/42.14  | | | | | | |   (129)  all_57_5 = e3
% 230.93/42.14  | | | | | | |   (130)  op(e2, e1) = e3
% 230.93/42.14  | | | | | | | 
% 230.93/42.14  | | | | | | | BETA: splitting (20) gives:
% 230.93/42.14  | | | | | | | 
% 230.93/42.14  | | | | | | | Case 1:
% 230.93/42.14  | | | | | | | | 
% 230.93/42.14  | | | | | | | |   (131)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 &
% 230.93/42.14  | | | | | | | |            op(e1, e2) = e3)
% 230.93/42.14  | | | | | | | | 
% 230.93/42.14  | | | | | | | | REF_CLOSE: (8), (9), (13), (16), (42), (44), (49), (51), (62),
% 230.93/42.14  | | | | | | | |            (66), (74), (95), (100), (106), (109), (115), (121),
% 230.93/42.14  | | | | | | | |            (129), (131) are inconsistent by sub-proof #1352.
% 230.93/42.14  | | | | | | | | 
% 230.93/42.14  | | | | | | | Case 2:
% 230.93/42.14  | | | | | | | | 
% 230.93/42.14  | | | | | | | |   (132)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 &
% 230.93/42.14  | | | | | | | |            op(e1, e0) = e3)
% 230.93/42.14  | | | | | | | | 
% 230.93/42.14  | | | | | | | | BETA: splitting (132) gives:
% 230.93/42.14  | | | | | | | | 
% 230.93/42.14  | | | | | | | | Case 1:
% 230.93/42.14  | | | | | | | | | 
% 230.93/42.14  | | | | | | | | |   (133)  all_57_8 = e3 & op(e1, e1) = e3
% 230.93/42.14  | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | ALPHA: (133) implies:
% 230.93/42.14  | | | | | | | | |   (134)  op(e1, e1) = e3
% 230.93/42.14  | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | REF_CLOSE: (16), (22), (23), (134) are inconsistent by
% 230.93/42.14  | | | | | | | | |            sub-proof #2468.
% 230.93/42.14  | | | | | | | | | 
% 230.93/42.14  | | | | | | | | Case 2:
% 230.93/42.14  | | | | | | | | | 
% 230.93/42.14  | | | | | | | | |   (135)  all_57_11 = e3 & op(e1, e0) = e3
% 230.93/42.14  | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | ALPHA: (135) implies:
% 230.93/42.14  | | | | | | | | |   (136)  all_57_11 = e3
% 230.93/42.14  | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | BETA: splitting (14) gives:
% 230.93/42.14  | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | Case 1:
% 230.93/42.14  | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | |   (137)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 230.93/42.14  | | | | | | | | | |            & op(e1, e2) = e0)
% 230.93/42.14  | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | BETA: splitting (137) gives:
% 230.93/42.14  | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | Case 1:
% 230.93/42.14  | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | |   (138)  all_57_6 = e0 & op(e1, e3) = e0
% 230.93/42.14  | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | ALPHA: (138) implies:
% 230.93/42.14  | | | | | | | | | | |   (139)  all_57_6 = e0
% 230.93/42.14  | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | BETA: splitting (8) gives:
% 230.93/42.14  | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | Case 1:
% 230.93/42.14  | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | |   (140)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 230.93/42.14  | | | | | | | | | | | |            & op(e2, e2) = e1)
% 230.93/42.14  | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | BETA: splitting (140) gives:
% 230.93/42.14  | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | Case 1:
% 230.93/42.14  | | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | |   (141)  all_57_2 = e1 & op(e2, e3) = e1
% 230.93/42.14  | | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | | ALPHA: (141) implies:
% 230.93/42.14  | | | | | | | | | | | | |   (142)  all_57_2 = e1
% 230.93/42.14  | | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | | BETA: splitting (106) gives:
% 230.93/42.14  | | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | | Case 1:
% 230.93/42.14  | | | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | | |   (143)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 230.93/42.14  | | | | | | | | | | | | | |            & op(e2, e3) = e2)
% 230.93/42.14  | | | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | | | BETA: splitting (143) gives:
% 230.93/42.14  | | | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | | | Case 1:
% 230.93/42.14  | | | | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | | | |   (144)  all_57_0 = e2 & op(e3, e3) = e2
% 230.93/42.14  | | | | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | | | | ALPHA: (144) implies:
% 230.93/42.14  | | | | | | | | | | | | | | |   (145)  op(e3, e3) = e2
% 230.93/42.14  | | | | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | | | | REF_CLOSE: (13), (16), (44), (64), (91), (118), (121), (125),
% 230.93/42.14  | | | | | | | | | | | | | | |            (145) are inconsistent by sub-proof #1308.
% 230.93/42.14  | | | | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | | | Case 2:
% 230.93/42.14  | | | | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | | | |   (146)  all_57_2 = e2 & op(e2, e3) = e2
% 230.93/42.14  | | | | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | | | | REF_CLOSE: (100), (142), (146) are inconsistent by sub-proof
% 230.93/42.14  | | | | | | | | | | | | | | |            #1351.
% 230.93/42.14  | | | | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | | | End of split
% 230.93/42.14  | | | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | | Case 2:
% 230.93/42.14  | | | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | | |   (147)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 230.93/42.14  | | | | | | | | | | | | | |            e2 & op(e0, e3) = e2)
% 230.93/42.14  | | | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | | | BETA: splitting (147) gives:
% 230.93/42.14  | | | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | | | Case 1:
% 230.93/42.14  | | | | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | | | |   (148)  all_57_6 = e2 & op(e1, e3) = e2
% 230.93/42.14  | | | | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | | | | REF_CLOSE: (62), (139), (148) are inconsistent by sub-proof
% 230.93/42.14  | | | | | | | | | | | | | | |            #2393.
% 230.93/42.14  | | | | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | | | Case 2:
% 230.93/42.14  | | | | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | | | |   (149)  all_57_12 = e2 & op(e0, e3) = e2
% 230.93/42.14  | | | | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | | | | ALPHA: (149) implies:
% 230.93/42.14  | | | | | | | | | | | | | | |   (150)  all_57_12 = e2
% 230.93/42.14  | | | | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | | | | BETA: splitting (79) gives:
% 230.93/42.14  | | | | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | | | | Case 1:
% 230.93/42.14  | | | | | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | | | | |   (151)  all_57_15 = e0 & op(e0, e0) = e0
% 230.93/42.14  | | | | | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | | | | | ALPHA: (151) implies:
% 230.93/42.14  | | | | | | | | | | | | | | | |   (152)  all_57_15 = e0
% 230.93/42.14  | | | | | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | | | | | COMBINE_EQS: (18), (152) imply:
% 230.93/42.14  | | | | | | | | | | | | | | | |   (153)  e1 = e0
% 230.93/42.14  | | | | | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | | | | | SIMP: (153) implies:
% 230.93/42.14  | | | | | | | | | | | | | | | |   (154)  e1 = e0
% 230.93/42.14  | | | | | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | | | | | COMBINE_EQS: (142), (154) imply:
% 230.93/42.14  | | | | | | | | | | | | | | | |   (155)  all_57_2 = e0
% 230.93/42.14  | | | | | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | | | | | REF_CLOSE: (8), (13), (42), (44), (62), (66), (95), (100),
% 230.93/42.14  | | | | | | | | | | | | | | | |            (129), (155) are inconsistent by sub-proof #2253.
% 230.93/42.14  | | | | | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | | | | Case 2:
% 230.93/42.14  | | | | | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | | | | |   (156)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 230.93/42.14  | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 230.93/42.14  | | | | | | | | | | | | | | | |              op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 230.93/42.14  | | | | | | | | | | | | | | | |                e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 230.93/42.14  | | | | | | | | | | | | | | | |              e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 230.93/42.14  | | | | | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | | | | | ALPHA: (156) implies:
% 230.93/42.14  | | | | | | | | | | | | | | | |   (157)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 230.93/42.14  | | | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 230.93/42.14  | | | | | | | | | | | | | | | |              e1) = e0)
% 230.93/42.14  | | | | | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | | | | | BETA: splitting (157) gives:
% 230.93/42.14  | | | | | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | | | | | Case 1:
% 230.93/42.14  | | | | | | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | | | | | |   (158)  all_57_12 = e0 & op(e0, e3) = e0
% 230.93/42.14  | | | | | | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | | | | | | ALPHA: (158) implies:
% 230.93/42.14  | | | | | | | | | | | | | | | | |   (159)  all_57_12 = e0
% 230.93/42.14  | | | | | | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | | | | | | REF_CLOSE: (62), (150), (159) are inconsistent by sub-proof
% 230.93/42.14  | | | | | | | | | | | | | | | | |            #2385.
% 230.93/42.14  | | | | | | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | | | | | Case 2:
% 230.93/42.14  | | | | | | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | | | | | |   (160)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 230.93/42.14  | | | | | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 230.93/42.14  | | | | | | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | | | | | | BETA: splitting (160) gives:
% 230.93/42.14  | | | | | | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | | | | | | Case 1:
% 230.93/42.14  | | | | | | | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | | | | | | |   (161)  all_57_13 = e0 & op(e0, e2) = e0
% 230.93/42.14  | | | | | | | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | | | | | | | ALPHA: (161) implies:
% 230.93/42.14  | | | | | | | | | | | | | | | | | |   (162)  op(e0, e2) = e0
% 230.93/42.14  | | | | | | | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (56), (77), (162) are inconsistent by
% 230.93/42.14  | | | | | | | | | | | | | | | | | |            sub-proof #2332.
% 230.93/42.14  | | | | | | | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | | | | | | Case 2:
% 230.93/42.14  | | | | | | | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | | | | | | |   (163)  all_57_14 = e0 & op(e0, e1) = e0
% 230.93/42.14  | | | | | | | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | | | | | | | ALPHA: (163) implies:
% 230.93/42.14  | | | | | | | | | | | | | | | | | |   (164)  all_57_14 = e0
% 230.93/42.14  | | | | | | | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | | | | | | | REF_CLOSE: (62), (67), (164) are inconsistent by sub-proof
% 230.93/42.14  | | | | | | | | | | | | | | | | | |            #2422.
% 230.93/42.14  | | | | | | | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | | | | | | End of split
% 230.93/42.14  | | | | | | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | | | | | End of split
% 230.93/42.14  | | | | | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | | | | End of split
% 230.93/42.14  | | | | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | | | End of split
% 230.93/42.14  | | | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | | End of split
% 230.93/42.14  | | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | Case 2:
% 230.93/42.14  | | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | |   (165)  all_57_3 = e1 & op(e2, e2) = e1
% 230.93/42.14  | | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | | ALPHA: (165) implies:
% 230.93/42.14  | | | | | | | | | | | | |   (166)  op(e2, e2) = e1
% 230.93/42.14  | | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | | REF_CLOSE: (16), (37), (66), (166) are inconsistent by
% 230.93/42.14  | | | | | | | | | | | | |            sub-proof #2352.
% 230.93/42.14  | | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | End of split
% 230.93/42.14  | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | Case 2:
% 230.93/42.14  | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | |   (167)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 230.93/42.14  | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 230.93/42.14  | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | BETA: splitting (167) gives:
% 230.93/42.14  | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | Case 1:
% 230.93/42.14  | | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | |   (168)  all_57_5 = e1 & op(e2, e1) = e1
% 230.93/42.14  | | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 230.93/42.14  | | | | | | | | | | | | |            (11), (12), (13), (14), (16), (17), (19), (20),
% 230.93/42.14  | | | | | | | | | | | | |            (21), (22), (23), (24), (25), (26), (27), (28),
% 230.93/42.14  | | | | | | | | | | | | |            (29), (30), (31), (32), (33), (34), (35), (36),
% 230.93/42.14  | | | | | | | | | | | | |            (37), (38), (39), (40), (41), (42), (43), (44),
% 230.93/42.14  | | | | | | | | | | | | |            (45), (46), (47), (48), (49), (50), (51), (52),
% 230.93/42.14  | | | | | | | | | | | | |            (53), (54), (55), (56), (57), (58), (59), (60),
% 230.93/42.14  | | | | | | | | | | | | |            (62), (63), (64), (65), (66), (68), (69), (70),
% 230.93/42.14  | | | | | | | | | | | | |            (71), (72), (73), (75), (76), (77), (78), (79),
% 230.93/42.14  | | | | | | | | | | | | |            (80), (81), (82), (84), (85), (86), (87), (88),
% 230.93/42.14  | | | | | | | | | | | | |            (89), (90), (91), (92), (93), (94), (95), (96),
% 230.93/42.14  | | | | | | | | | | | | |            (97), (98), (99), (100), (101), (102), (103),
% 230.93/42.14  | | | | | | | | | | | | |            (104), (105), (106), (107), (108), (109), (110),
% 230.93/42.14  | | | | | | | | | | | | |            (111), (112), (113), (114), (115), (116), (117),
% 230.93/42.14  | | | | | | | | | | | | |            (118), (129), (136), (168) are inconsistent by
% 230.93/42.14  | | | | | | | | | | | | |            sub-proof #1353.
% 230.93/42.14  | | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | Case 2:
% 230.93/42.14  | | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | |   (169)  all_57_10 = e1 & op(e2, e0) = e1
% 230.93/42.14  | | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | | REF_CLOSE: (15), (16), (86), (169) are inconsistent by
% 230.93/42.14  | | | | | | | | | | | | |            sub-proof #2084.
% 230.93/42.14  | | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | | End of split
% 230.93/42.14  | | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | End of split
% 230.93/42.14  | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | Case 2:
% 230.93/42.14  | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | |   (170)  all_57_7 = e0 & op(e1, e2) = e0
% 230.93/42.14  | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | ALPHA: (170) implies:
% 230.93/42.14  | | | | | | | | | | |   (171)  all_57_7 = e0
% 230.93/42.14  | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | | REF_CLOSE: (11), (13), (16), (37), (42), (44), (49), (62),
% 230.93/42.14  | | | | | | | | | | |            (66), (71), (74), (100), (115), (171) are
% 230.93/42.14  | | | | | | | | | | |            inconsistent by sub-proof #2199.
% 230.93/42.14  | | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | End of split
% 230.93/42.14  | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | Case 2:
% 230.93/42.14  | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | |   (172)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0
% 230.93/42.14  | | | | | | | | | |            & op(e1, e0) = e0)
% 230.93/42.14  | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | | REF_CLOSE: (5), (7), (8), (9), (10), (11), (13), (14), (16),
% 230.93/42.14  | | | | | | | | | |            (20), (21), (22), (23), (24), (25), (28), (32),
% 230.93/42.14  | | | | | | | | | |            (34), (35), (36), (37), (39), (40), (42), (43),
% 230.93/42.14  | | | | | | | | | |            (44), (46), (49), (50), (51), (52), (53), (55),
% 230.93/42.14  | | | | | | | | | |            (57), (58), (60), (62), (63), (66), (68), (69),
% 230.93/42.14  | | | | | | | | | |            (71), (74), (76), (78), (79), (80), (88), (90),
% 230.93/42.14  | | | | | | | | | |            (91), (92), (94), (95), (98), (100), (101), (102),
% 230.93/42.14  | | | | | | | | | |            (103), (104), (106), (107), (108), (109), (110),
% 230.93/42.14  | | | | | | | | | |            (111), (114), (115), (117), (118), (129), (130),
% 230.93/42.14  | | | | | | | | | |            (172) are inconsistent by sub-proof #1350.
% 230.93/42.14  | | | | | | | | | | 
% 230.93/42.14  | | | | | | | | | End of split
% 230.93/42.14  | | | | | | | | | 
% 230.93/42.14  | | | | | | | | End of split
% 230.93/42.14  | | | | | | | | 
% 230.93/42.14  | | | | | | | End of split
% 230.93/42.14  | | | | | | | 
% 230.93/42.14  | | | | | | End of split
% 230.93/42.14  | | | | | | 
% 230.93/42.14  | | | | | Case 2:
% 230.93/42.14  | | | | | | 
% 230.93/42.14  | | | | | |   (173)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 &
% 230.93/42.14  | | | | | |            op(e0, e1) = e3)
% 230.93/42.14  | | | | | | 
% 230.93/42.14  | | | | | | REF_CLOSE: (16), (22), (23), (44), (67), (173) are inconsistent by
% 230.93/42.14  | | | | | |            sub-proof #2409.
% 230.93/42.14  | | | | | | 
% 230.93/42.14  | | | | | End of split
% 230.93/42.14  | | | | | 
% 230.93/42.14  | | | | Case 2:
% 230.93/42.14  | | | | | 
% 230.93/42.14  | | | | |   (174)  all_57_9 = e1 & op(e3, e0) = e1
% 230.93/42.14  | | | | | 
% 230.93/42.14  | | | | | ALPHA: (174) implies:
% 230.93/42.14  | | | | |   (175)  all_57_9 = e1
% 230.93/42.14  | | | | | 
% 230.93/42.14  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 230.93/42.14  | | | | |            (12), (13), (14), (16), (17), (19), (20), (21), (22), (23),
% 230.93/42.14  | | | | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 230.93/42.14  | | | | |            (34), (35), (36), (37), (38), (39), (40), (41), (42), (43),
% 230.93/42.14  | | | | |            (44), (45), (46), (47), (48), (49), (50), (51), (52), (53),
% 230.93/42.14  | | | | |            (54), (55), (56), (57), (58), (59), (60), (62), (63), (64),
% 230.93/42.14  | | | | |            (65), (66), (68), (69), (70), (71), (72), (73), (75), (76),
% 230.93/42.14  | | | | |            (77), (78), (79), (80), (81), (82), (84), (85), (86), (87),
% 230.93/42.14  | | | | |            (88), (89), (90), (91), (92), (93), (94), (95), (96), (97),
% 230.93/42.14  | | | | |            (98), (99), (100), (101), (102), (103), (105), (106),
% 230.93/42.14  | | | | |            (107), (108), (109), (110), (111), (112), (113), (114),
% 230.93/42.14  | | | | |            (115), (116), (117), (118), (175) are inconsistent by
% 230.93/42.14  | | | | |            sub-proof #1384.
% 230.93/42.14  | | | | | 
% 230.93/42.14  | | | | End of split
% 230.93/42.14  | | | | 
% 230.93/42.14  | | | End of split
% 230.93/42.14  | | | 
% 230.93/42.14  | | Case 2:
% 230.93/42.14  | | | 
% 230.93/42.14  | | |   (176)  all_57_3 = e2 & op(e2, e2) = e2
% 230.93/42.14  | | | 
% 230.93/42.14  | | | ALPHA: (176) implies:
% 230.93/42.14  | | |   (177)  op(e2, e2) = e2
% 230.93/42.14  | | | 
% 230.93/42.14  | | | REF_CLOSE: (16), (37), (62), (177) are inconsistent by sub-proof #2472.
% 230.93/42.14  | | | 
% 230.93/42.14  | | End of split
% 230.93/42.14  | | 
% 230.93/42.14  | Case 2:
% 230.93/42.14  | | 
% 230.93/42.14  | |   (178)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 230.93/42.14  | |            e2)
% 230.93/42.14  | | 
% 230.93/42.14  | | BETA: splitting (178) gives:
% 230.93/42.14  | | 
% 230.93/42.14  | | Case 1:
% 230.93/42.14  | | | 
% 230.93/42.14  | | |   (179)  all_57_7 = e2 & op(e1, e2) = e2
% 230.93/42.14  | | | 
% 230.93/42.15  | | | ALPHA: (179) implies:
% 230.93/42.15  | | |   (180)  all_57_7 = e2
% 230.93/42.15  | | | 
% 230.93/42.15  | | | BETA: splitting (70) gives:
% 230.93/42.15  | | | 
% 230.93/42.15  | | | Case 1:
% 230.93/42.15  | | | | 
% 230.93/42.15  | | | |   (181)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1)
% 230.93/42.15  | | | |            = e3)
% 230.93/42.15  | | | | 
% 230.93/42.15  | | | | BETA: splitting (181) gives:
% 230.93/42.15  | | | | 
% 230.93/42.15  | | | | Case 1:
% 230.93/42.15  | | | | | 
% 230.93/42.15  | | | | |   (182)  all_57_4 = e3 & op(e3, e1) = e3
% 230.93/42.15  | | | | | 
% 230.93/42.15  | | | | | ALPHA: (182) implies:
% 230.93/42.15  | | | | |   (183)  all_57_4 = e3
% 230.93/42.15  | | | | | 
% 230.93/42.15  | | | | | REF_CLOSE: (13), (16), (28), (36), (40), (44), (49), (51), (62), (66),
% 230.93/42.15  | | | | |            (100), (183) are inconsistent by sub-proof #2474.
% 230.93/42.15  | | | | | 
% 230.93/42.15  | | | | Case 2:
% 230.93/42.15  | | | | | 
% 230.93/42.15  | | | | |   (184)  all_57_5 = e3 & op(e2, e1) = e3
% 230.93/42.15  | | | | | 
% 230.93/42.15  | | | | | ALPHA: (184) implies:
% 230.93/42.15  | | | | |   (185)  all_57_5 = e3
% 230.93/42.15  | | | | | 
% 230.93/42.15  | | | | | BETA: splitting (115) gives:
% 230.93/42.15  | | | | | 
% 230.93/42.15  | | | | | Case 1:
% 230.93/42.15  | | | | | | 
% 230.93/42.15  | | | | | |   (186)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2,
% 230.93/42.15  | | | | | |              e2) = e1)
% 230.93/42.15  | | | | | | 
% 230.93/42.15  | | | | | | BETA: splitting (186) gives:
% 230.93/42.15  | | | | | | 
% 230.93/42.15  | | | | | | Case 1:
% 230.93/42.15  | | | | | | | 
% 230.93/42.15  | | | | | | |   (187)  all_57_1 = e1 & op(e3, e2) = e1
% 230.93/42.15  | | | | | | | 
% 230.93/42.15  | | | | | | | ALPHA: (187) implies:
% 230.93/42.15  | | | | | | |   (188)  all_57_1 = e1
% 230.93/42.15  | | | | | | | 
% 230.93/42.15  | | | | | | | BETA: splitting (8) gives:
% 230.93/42.15  | | | | | | | 
% 230.93/42.15  | | | | | | | Case 1:
% 230.93/42.15  | | | | | | | | 
% 230.93/42.15  | | | | | | | |   (189)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 &
% 230.93/42.15  | | | | | | | |            op(e2, e2) = e1)
% 230.93/42.15  | | | | | | | | 
% 230.93/42.15  | | | | | | | | BETA: splitting (189) gives:
% 230.93/42.15  | | | | | | | | 
% 230.93/42.15  | | | | | | | | Case 1:
% 230.93/42.15  | | | | | | | | | 
% 230.93/42.15  | | | | | | | | |   (190)  all_57_2 = e1 & op(e2, e3) = e1
% 230.93/42.15  | | | | | | | | | 
% 230.93/42.15  | | | | | | | | | ALPHA: (190) implies:
% 230.93/42.15  | | | | | | | | |   (191)  all_57_2 = e1
% 230.93/42.15  | | | | | | | | | 
% 230.93/42.15  | | | | | | | | | BETA: splitting (43) gives:
% 230.93/42.15  | | | | | | | | | 
% 230.93/42.15  | | | | | | | | | Case 1:
% 230.93/42.15  | | | | | | | | | | 
% 230.93/42.15  | | | | | | | | | |   (192)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 230.93/42.15  | | | | | | | | | |            & op(e2, e1) = e0)
% 230.93/42.15  | | | | | | | | | | 
% 230.93/42.15  | | | | | | | | | | REF_CLOSE: (8), (13), (16), (37), (42), (44), (49), (50),
% 230.93/42.15  | | | | | | | | | |            (62), (66), (67), (71), (74), (83), (87), (95),
% 230.93/42.15  | | | | | | | | | |            (100), (180), (185), (188), (191), (192) are
% 230.93/42.15  | | | | | | | | | |            inconsistent by sub-proof #1349.
% 230.93/42.15  | | | | | | | | | | 
% 230.93/42.15  | | | | | | | | | Case 2:
% 230.93/42.15  | | | | | | | | | | 
% 230.93/42.15  | | | | | | | | | |   (193)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0
% 230.93/42.15  | | | | | | | | | |            & op(e0, e1) = e0)
% 230.93/42.15  | | | | | | | | | | 
% 230.93/42.15  | | | | | | | | | | BETA: splitting (193) gives:
% 230.93/42.15  | | | | | | | | | | 
% 230.93/42.15  | | | | | | | | | | Case 1:
% 230.93/42.15  | | | | | | | | | | | 
% 230.93/42.15  | | | | | | | | | | |   (194)  all_57_8 = e0 & op(e1, e1) = e0
% 230.93/42.15  | | | | | | | | | | | 
% 230.93/42.15  | | | | | | | | | | | REF_CLOSE: (16), (23), (104), (194) are inconsistent by
% 230.93/42.15  | | | | | | | | | | |            sub-proof #2412.
% 230.93/42.15  | | | | | | | | | | | 
% 230.93/42.15  | | | | | | | | | | Case 2:
% 230.93/42.15  | | | | | | | | | | | 
% 230.93/42.15  | | | | | | | | | | |   (195)  all_57_14 = e0 & op(e0, e1) = e0
% 230.93/42.15  | | | | | | | | | | | 
% 230.93/42.15  | | | | | | | | | | | ALPHA: (195) implies:
% 230.93/42.15  | | | | | | | | | | |   (196)  all_57_14 = e0
% 230.93/42.15  | | | | | | | | | | | 
% 230.93/42.15  | | | | | | | | | | | COMBINE_EQS: (67), (196) imply:
% 230.93/42.15  | | | | | | | | | | |   (197)  e2 = e0
% 230.93/42.15  | | | | | | | | | | | 
% 230.93/42.15  | | | | | | | | | | | SIMP: (197) implies:
% 230.93/42.15  | | | | | | | | | | |   (198)  e2 = e0
% 230.93/42.15  | | | | | | | | | | | 
% 230.93/42.15  | | | | | | | | | | | COMBINE_EQS: (180), (198) imply:
% 230.93/42.15  | | | | | | | | | | |   (199)  all_57_7 = e0
% 230.93/42.15  | | | | | | | | | | | 
% 230.93/42.15  | | | | | | | | | | | REF_CLOSE: (11), (13), (16), (37), (42), (44), (49), (62),
% 230.93/42.15  | | | | | | | | | | |            (66), (71), (74), (100), (115), (199) are
% 230.93/42.15  | | | | | | | | | | |            inconsistent by sub-proof #2199.
% 230.93/42.15  | | | | | | | | | | | 
% 230.93/42.15  | | | | | | | | | | End of split
% 230.93/42.15  | | | | | | | | | | 
% 230.93/42.15  | | | | | | | | | End of split
% 230.93/42.15  | | | | | | | | | 
% 230.93/42.15  | | | | | | | | Case 2:
% 230.93/42.15  | | | | | | | | | 
% 230.93/42.15  | | | | | | | | |   (200)  all_57_3 = e1 & op(e2, e2) = e1
% 230.93/42.15  | | | | | | | | | 
% 230.93/42.15  | | | | | | | | | ALPHA: (200) implies:
% 230.93/42.15  | | | | | | | | |   (201)  op(e2, e2) = e1
% 230.93/42.15  | | | | | | | | | 
% 230.93/42.15  | | | | | | | | | REF_CLOSE: (16), (49), (61), (62), (66), (74), (180), (188),
% 230.93/42.15  | | | | | | | | |            (201) are inconsistent by sub-proof #2147.
% 230.93/42.15  | | | | | | | | | 
% 230.93/42.15  | | | | | | | | End of split
% 230.93/42.15  | | | | | | | | 
% 230.93/42.15  | | | | | | | Case 2:
% 230.93/42.15  | | | | | | | | 
% 230.93/42.15  | | | | | | | |   (202)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 &
% 230.93/42.15  | | | | | | | |            op(e2, e0) = e1)
% 230.93/42.15  | | | | | | | | 
% 230.93/42.15  | | | | | | | | BETA: splitting (202) gives:
% 230.93/42.15  | | | | | | | | 
% 230.93/42.15  | | | | | | | | Case 1:
% 230.93/42.15  | | | | | | | | | 
% 230.93/42.15  | | | | | | | | |   (203)  all_57_5 = e1 & op(e2, e1) = e1
% 230.93/42.15  | | | | | | | | | 
% 230.93/42.15  | | | | | | | | | REF_CLOSE: (13), (42), (44), (49), (71), (74), (180), (185),
% 230.93/42.15  | | | | | | | | |            (188), (203) are inconsistent by sub-proof #2192.
% 230.93/42.15  | | | | | | | | | 
% 230.93/42.15  | | | | | | | | Case 2:
% 230.93/42.15  | | | | | | | | | 
% 230.93/42.15  | | | | | | | | |   (204)  all_57_10 = e1 & op(e2, e0) = e1
% 230.93/42.15  | | | | | | | | | 
% 230.93/42.15  | | | | | | | | | REF_CLOSE: (15), (16), (86), (204) are inconsistent by
% 230.93/42.15  | | | | | | | | |            sub-proof #2084.
% 230.93/42.15  | | | | | | | | | 
% 230.93/42.15  | | | | | | | | End of split
% 230.93/42.15  | | | | | | | | 
% 230.93/42.15  | | | | | | | End of split
% 230.93/42.15  | | | | | | | 
% 230.93/42.15  | | | | | | Case 2:
% 230.93/42.15  | | | | | | | 
% 230.93/42.15  | | | | | | |   (205)  all_57_3 = e1 & op(e2, e2) = e1
% 230.93/42.15  | | | | | | | 
% 230.93/42.15  | | | | | | | ALPHA: (205) implies:
% 230.93/42.15  | | | | | | |   (206)  op(e2, e2) = e1
% 230.93/42.15  | | | | | | | 
% 230.93/42.15  | | | | | | | REF_CLOSE: (16), (37), (66), (206) are inconsistent by sub-proof
% 230.93/42.15  | | | | | | |            #2352.
% 230.93/42.15  | | | | | | | 
% 230.93/42.15  | | | | | | End of split
% 230.93/42.15  | | | | | | 
% 230.93/42.15  | | | | | Case 2:
% 230.93/42.15  | | | | | | 
% 230.93/42.15  | | | | | |   (207)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 &
% 230.93/42.15  | | | | | |            op(e0, e2) = e1)
% 230.93/42.15  | | | | | | 
% 230.93/42.15  | | | | | | BETA: splitting (207) gives:
% 230.93/42.15  | | | | | | 
% 230.93/42.15  | | | | | | Case 1:
% 230.93/42.15  | | | | | | | 
% 230.93/42.15  | | | | | | |   (208)  all_57_7 = e1 & op(e1, e2) = e1
% 230.93/42.15  | | | | | | | 
% 230.93/42.15  | | | | | | | REF_CLOSE: (100), (180), (208) are inconsistent by sub-proof
% 230.93/42.15  | | | | | | |            #2190.
% 230.93/42.15  | | | | | | | 
% 230.93/42.15  | | | | | | Case 2:
% 230.93/42.15  | | | | | | | 
% 230.93/42.15  | | | | | | |   (209)  all_57_13 = e1 & op(e0, e2) = e1
% 230.93/42.15  | | | | | | | 
% 230.93/42.15  | | | | | | | REF_CLOSE: (13), (74), (209) are inconsistent by sub-proof #2264.
% 230.93/42.15  | | | | | | | 
% 230.93/42.15  | | | | | | End of split
% 230.93/42.15  | | | | | | 
% 230.93/42.15  | | | | | End of split
% 230.93/42.15  | | | | | 
% 230.93/42.15  | | | | End of split
% 230.93/42.15  | | | | 
% 230.93/42.15  | | | Case 2:
% 230.93/42.15  | | | | 
% 230.93/42.15  | | | |   (210)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0,
% 230.93/42.15  | | | |              e1) = e3)
% 230.93/42.15  | | | | 
% 230.93/42.15  | | | | REF_CLOSE: (16), (22), (23), (44), (67), (210) are inconsistent by
% 230.93/42.15  | | | |            sub-proof #2409.
% 230.93/42.15  | | | | 
% 230.93/42.15  | | | End of split
% 230.93/42.15  | | | 
% 230.93/42.15  | | Case 2:
% 230.93/42.15  | | | 
% 230.93/42.15  | | |   (211)  all_57_13 = e2 & op(e0, e2) = e2
% 230.93/42.15  | | | 
% 230.93/42.15  | | | REF_CLOSE: (44), (74), (211) are inconsistent by sub-proof #2146.
% 230.93/42.15  | | | 
% 230.93/42.15  | | End of split
% 230.93/42.15  | | 
% 230.93/42.15  | End of split
% 230.93/42.15  | 
% 230.93/42.15  End of proof
% 230.93/42.15  
% 230.93/42.15  Sub-proof #1299 shows that the following formulas are inconsistent:
% 230.93/42.15  ----------------------------------------------------------------
% 230.93/42.15    (1)   ~ (all_10_2 = e2)
% 230.93/42.15    (2)  all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 230.93/42.15    (3)  op(e3, e3) = all_10_2
% 230.93/42.15    (4)  op(e0, e0) = all_4_2
% 230.93/42.15    (5)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 230.93/42.15    (6)   ~ (all_53_12 = all_4_2)
% 230.93/42.15    (7)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 230.93/42.15    (8)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.93/42.15         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.93/42.15    (9)  all_55_15 = e3 | all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 230.93/42.15    (10)   ~ (all_53_6 = e0)
% 230.93/42.15    (11)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.93/42.15          (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.93/42.15    (12)   ~ (all_53_8 = all_53_12)
% 230.93/42.15    (13)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.93/42.15          (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.93/42.15    (14)   ~ (all_53_8 = all_53_11)
% 230.93/42.15    (15)   ~ (e3 = e1)
% 230.93/42.15    (16)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.93/42.15          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.93/42.15    (17)   ~ (all_53_13 = e1)
% 230.93/42.15    (18)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.93/42.15            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.93/42.15    (19)  all_55_15 = all_4_2
% 230.93/42.15    (20)  all_55_0 = all_10_2
% 230.93/42.15    (21)  all_57_15 = e1
% 230.93/42.15    (22)   ~ (all_10_2 = e0)
% 230.93/42.15    (23)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.93/42.15          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.93/42.15    (24)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 230.93/42.15            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 230.93/42.15              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 230.93/42.15    (25)   ~ (all_53_3 = all_53_7)
% 230.93/42.15    (26)   ~ (all_6_2 = e3)
% 230.93/42.15    (27)  op(e1, e1) = all_6_2
% 230.93/42.15    (28)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 230.93/42.15    (29)   ~ (all_53_9 = e0)
% 230.93/42.15    (30)  all_55_0 = e3 | all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 230.93/42.15    (31)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 230.93/42.15    (32)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.93/42.15          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.93/42.15    (33)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 230.93/42.15    (34)  all_55_9 = all_53_6
% 230.93/42.15    (35)   ~ (all_53_4 = all_53_12)
% 230.93/42.15    (36)   ~ (all_53_8 = e3)
% 230.93/42.15    (37)   ~ (all_53_8 = all_53_9)
% 230.93/42.15    (38)  all_42_2 = all_6_2
% 230.93/42.15    (39)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.93/42.15          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.93/42.15    (40)  op(e2, e2) = e0
% 230.93/42.15    (41)   ~ (all_53_9 = all_53_11)
% 230.93/42.15    (42)   ~ (all_53_9 = all_6_2)
% 230.93/42.15    (43)   ~ (all_53_12 = all_53_13)
% 230.93/42.15    (44)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.93/42.15          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.93/42.15    (45)  all_57_3 = e0
% 230.93/42.15    (46)   ~ (all_53_14 = all_4_2)
% 230.93/42.15    (47)   ~ (all_53_11 = all_4_2)
% 230.93/42.15    (48)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 230.93/42.15          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.93/42.15    (49)   ~ (e3 = e2)
% 230.93/42.15    (50)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 230.93/42.15    (51)  all_55_1 = all_53_4
% 230.93/42.15    (52)  op(e1, e0) = all_53_14
% 230.93/42.15    (53)   ~ (all_53_6 = all_53_7)
% 230.93/42.15    (54)  all_55_7 = e3 | all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 230.93/42.15    (55)   ~ (e3 = e0)
% 230.93/42.15    (56)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.93/42.15          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.93/42.15    (57)  op(e3, e3) = e3
% 230.93/42.15    (58)   ~ (all_53_8 = all_6_2)
% 230.93/42.15    (59)   ~ (all_4_2 = e2)
% 230.93/42.15    (60)  op(e0, e3) = all_53_3
% 230.93/42.15    (61)   ~ (all_53_7 = all_4_2)
% 230.93/42.15    (62)  all_55_2 = all_53_8
% 230.93/42.15    (63)   ~ (all_53_4 = all_53_7)
% 230.93/42.15    (64)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 230.93/42.15    (65)   ~ (all_53_9 = all_53_13)
% 230.93/42.15    (66)   ~ (all_53_7 = e0)
% 230.93/42.15    (67)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.93/42.15          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.93/42.15            e1)
% 230.93/42.15    (68)  all_57_5 = e3
% 230.93/42.15    (69)   ~ (all_53_4 = all_53_8)
% 230.93/42.15    (70)  all_55_6 = all_53_9
% 230.93/42.15    (71)  op(e3, e2) = all_53_4
% 230.93/42.15    (72)   ~ (e2 = e0)
% 230.93/42.15    (73)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 230.93/42.15            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 230.93/42.15            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 230.93/42.15            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 230.93/42.15              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 230.93/42.15            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 230.93/42.15            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 230.93/42.15              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 230.93/42.15              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 230.93/42.15            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 230.93/42.15            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 230.93/42.15            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 230.93/42.15              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 230.93/42.15              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 230.93/42.15            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 230.93/42.15              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 230.93/42.15            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 230.93/42.15            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 230.93/42.15              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 230.93/42.15              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 230.93/42.15            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 230.93/42.15            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 230.93/42.15    (74)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.93/42.15          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.93/42.15    (75)   ~ (e1 = e0)
% 230.93/42.15    (76)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 230.93/42.15            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 230.93/42.15              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 230.93/42.15    (77)   ~ (all_53_3 = all_53_11)
% 230.93/42.15    (78)   ~ (all_53_4 = e0)
% 230.93/42.15    (79)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 230.93/42.15          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 230.93/42.15    (80)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.93/42.15          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.93/42.15    (81)   ~ (all_10_2 = e1)
% 230.93/42.15    (82)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 230.93/42.15    (83)  all_57_13 = e3
% 230.93/42.15    (84)   ~ (all_53_7 = all_53_11)
% 230.93/42.15    (85)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.93/42.15          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 230.93/42.15            e3)
% 230.93/42.15    (86)   ~ (all_53_13 = all_4_2)
% 230.93/42.15    (87)   ~ (all_53_4 = all_53_6)
% 230.93/42.15    (88)  op(e0, e2) = all_53_7
% 230.93/42.15    (89)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.93/42.15          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.93/42.15            e2)
% 230.93/42.15    (90)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.93/42.15              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.93/42.15                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.93/42.15                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.93/42.15    (91)  all_55_10 = all_6_2
% 230.93/42.15    (92)  op(e1, e1) = e2
% 230.93/42.15    (93)  all_55_13 = all_53_7
% 230.93/42.15    (94)  op(e2, e0) = all_53_13
% 230.93/42.15    (95)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.93/42.15          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.93/42.15    (96)  all_38_2 = all_6_2
% 230.93/42.15    (97)  all_55_11 = all_53_14
% 230.93/42.15    (98)  all_55_3 = all_53_12
% 230.93/42.15    (99)   ~ (all_53_12 = e3)
% 230.93/42.15    (100)  all_57_0 = e3
% 230.93/42.15    (101)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0
% 230.93/42.15             & op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~
% 230.93/42.15             (all_42_1 = e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 230.93/42.15    (102)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.93/42.15           (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.93/42.15    (103)   ~ (all_4_2 = e3)
% 230.93/42.15    (104)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.93/42.15           (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.93/42.15    (105)   ~ (all_53_12 = all_10_2)
% 230.93/42.15    (106)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.93/42.15           | (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 230.93/42.15             e3)
% 230.93/42.15    (107)   ~ (all_53_13 = all_53_14)
% 230.93/42.15    (108)   ~ (e2 = e1)
% 230.93/42.15    (109)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.93/42.15           | (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.93/42.15             e2)
% 230.93/42.15    (110)  op(e2, e1) = all_53_9
% 230.93/42.15    (111)  op(e1, e2) = all_53_6
% 230.93/42.15    (112)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.93/42.15           (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.93/42.15    (113)  all_24_2 = all_6_2
% 230.93/42.15    (114)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.93/42.15           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.93/42.15    (115)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.93/42.15           (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.93/42.15    (116)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.93/42.15           | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.93/42.15             e1)
% 230.93/42.15    (117)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.93/42.15           (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.93/42.15    (118)   ~ (all_53_12 = all_53_14)
% 230.93/42.15    (119)  all_55_14 = all_53_11
% 230.93/42.15    (120)  op(e3, e1) = all_53_8
% 230.93/42.15    (121)  all_55_7 = all_53_13
% 230.93/42.15    (122)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.93/42.15           (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.93/42.15    (123)   ~ (all_53_4 = e3)
% 230.93/42.15    (124)  all_57_13 = e2 & op(e0, e2) = e2
% 230.93/42.15    (125)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.93/42.15           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.93/42.15    (126)  op(e3, e0) = all_53_12
% 230.93/42.15  
% 230.93/42.15  Begin of proof
% 230.93/42.15  | 
% 230.93/42.15  | ALPHA: (124) implies:
% 230.93/42.15  |   (127)  all_57_13 = e2
% 230.93/42.15  | 
% 230.93/42.15  | COMBINE_EQS: (83), (127) imply:
% 230.93/42.15  |   (128)  e3 = e2
% 230.93/42.15  | 
% 230.93/42.15  | COMBINE_EQS: (68), (128) imply:
% 230.93/42.15  |   (129)  all_57_5 = e2
% 230.93/42.15  | 
% 230.93/42.15  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 230.93/42.15  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 230.93/42.15  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 230.93/42.15  |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 230.93/42.15  |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), (56),
% 230.93/42.15  |            (57), (58), (59), (60), (61), (62), (63), (64), (65), (66), (67),
% 230.93/42.15  |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 230.93/42.15  |            (80), (81), (82), (84), (85), (86), (87), (88), (89), (90), (91),
% 230.93/42.15  |            (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 230.93/42.15  |            (102), (103), (104), (105), (106), (107), (108), (109), (110),
% 230.93/42.15  |            (111), (112), (113), (114), (115), (116), (117), (118), (119),
% 230.93/42.15  |            (120), (121), (122), (123), (125), (126), (129) are inconsistent by
% 230.93/42.15  |            sub-proof #1300.
% 230.93/42.15  | 
% 230.93/42.15  End of proof
% 230.93/42.15  
% 230.93/42.15  Sub-proof #1300 shows that the following formulas are inconsistent:
% 230.93/42.15  ----------------------------------------------------------------
% 230.93/42.15    (1)   ~ (all_10_2 = e2)
% 230.93/42.15    (2)  all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 230.93/42.15    (3)  op(e3, e3) = all_10_2
% 230.93/42.15    (4)  op(e0, e0) = all_4_2
% 230.93/42.15    (5)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 230.93/42.15    (6)   ~ (all_53_12 = all_4_2)
% 230.93/42.15    (7)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 230.93/42.15    (8)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.93/42.15         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.93/42.15    (9)  all_55_15 = e3 | all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 230.93/42.15    (10)   ~ (all_53_6 = e0)
% 230.93/42.15    (11)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.93/42.15          (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.93/42.15    (12)   ~ (all_53_8 = all_53_12)
% 230.93/42.15    (13)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.93/42.15          (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.93/42.15    (14)   ~ (all_53_8 = all_53_11)
% 230.93/42.15    (15)   ~ (e3 = e1)
% 230.93/42.15    (16)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.93/42.15          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.93/42.15    (17)   ~ (all_53_13 = e1)
% 230.93/42.15    (18)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.93/42.15            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.93/42.15    (19)  all_55_15 = all_4_2
% 230.93/42.15    (20)  all_55_0 = all_10_2
% 230.93/42.15    (21)  all_57_15 = e1
% 230.93/42.15    (22)   ~ (all_10_2 = e0)
% 230.93/42.15    (23)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.93/42.15          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.93/42.15    (24)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 230.93/42.15            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 230.93/42.15              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 230.93/42.15    (25)   ~ (all_53_3 = all_53_7)
% 230.93/42.15    (26)   ~ (all_6_2 = e3)
% 230.93/42.15    (27)  op(e1, e1) = all_6_2
% 230.93/42.15    (28)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 230.93/42.15    (29)   ~ (all_53_9 = e0)
% 230.93/42.15    (30)  all_55_0 = e3 | all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 230.93/42.15    (31)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 230.93/42.15    (32)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.93/42.15          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.93/42.15    (33)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 230.93/42.15    (34)  all_55_9 = all_53_6
% 230.93/42.15    (35)   ~ (all_53_4 = all_53_12)
% 230.93/42.15    (36)   ~ (all_53_8 = e3)
% 230.93/42.15    (37)   ~ (all_53_8 = all_53_9)
% 230.93/42.15    (38)  all_42_2 = all_6_2
% 230.93/42.15    (39)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.93/42.16          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.93/42.16    (40)  op(e2, e2) = e0
% 230.93/42.16    (41)   ~ (all_53_9 = all_53_11)
% 230.93/42.16    (42)   ~ (all_53_9 = all_6_2)
% 230.93/42.16    (43)   ~ (all_53_12 = all_53_13)
% 230.93/42.16    (44)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.93/42.16          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.93/42.16    (45)  all_57_3 = e0
% 230.93/42.16    (46)   ~ (all_53_14 = all_4_2)
% 230.93/42.16    (47)   ~ (all_53_11 = all_4_2)
% 230.93/42.16    (48)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 230.93/42.16          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.93/42.16    (49)   ~ (e3 = e2)
% 230.93/42.16    (50)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 230.93/42.16    (51)  all_55_1 = all_53_4
% 230.93/42.16    (52)  op(e1, e0) = all_53_14
% 230.93/42.16    (53)   ~ (all_53_6 = all_53_7)
% 230.93/42.16    (54)  all_55_7 = e3 | all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 230.93/42.16    (55)   ~ (e3 = e0)
% 230.93/42.16    (56)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.93/42.16          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.93/42.16    (57)  op(e3, e3) = e3
% 230.93/42.16    (58)   ~ (all_53_8 = all_6_2)
% 230.93/42.16    (59)   ~ (all_4_2 = e2)
% 230.93/42.16    (60)  op(e0, e3) = all_53_3
% 230.93/42.16    (61)   ~ (all_53_7 = all_4_2)
% 230.93/42.16    (62)  all_55_2 = all_53_8
% 230.93/42.16    (63)   ~ (all_53_4 = all_53_7)
% 230.93/42.16    (64)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 230.93/42.16    (65)   ~ (all_53_9 = all_53_13)
% 230.93/42.16    (66)   ~ (all_53_7 = e0)
% 230.93/42.16    (67)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.93/42.16          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.93/42.16            e1)
% 230.93/42.16    (68)   ~ (all_53_4 = all_53_8)
% 230.93/42.16    (69)  all_55_6 = all_53_9
% 230.93/42.16    (70)  op(e3, e2) = all_53_4
% 230.93/42.16    (71)   ~ (e2 = e0)
% 230.93/42.16    (72)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 230.93/42.16            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 230.93/42.16            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 230.93/42.16            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 230.93/42.16              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 230.93/42.16            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 230.93/42.16            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 230.93/42.16              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 230.93/42.16              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 230.93/42.16            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 230.93/42.16            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 230.93/42.16            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 230.93/42.16              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 230.93/42.16              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 230.93/42.16            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 230.93/42.16              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 230.93/42.16            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 230.93/42.16            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 230.93/42.16              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 230.93/42.16              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 230.93/42.16            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 230.93/42.16            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 230.93/42.16    (73)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.93/42.16          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.93/42.16    (74)   ~ (e1 = e0)
% 230.93/42.16    (75)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 230.93/42.16            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 230.93/42.16              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 230.93/42.16    (76)   ~ (all_53_3 = all_53_11)
% 230.93/42.16    (77)  all_57_5 = e2
% 230.93/42.16    (78)   ~ (all_53_4 = e0)
% 230.93/42.16    (79)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 230.93/42.16          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 230.93/42.16    (80)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.93/42.16          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.93/42.16    (81)   ~ (all_10_2 = e1)
% 230.93/42.16    (82)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 230.93/42.16    (83)   ~ (all_53_7 = all_53_11)
% 230.93/42.16    (84)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.93/42.16          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 230.93/42.16            e3)
% 230.93/42.16    (85)   ~ (all_53_13 = all_4_2)
% 230.93/42.16    (86)   ~ (all_53_4 = all_53_6)
% 230.93/42.16    (87)  op(e0, e2) = all_53_7
% 230.93/42.16    (88)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.93/42.16          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.93/42.16            e2)
% 230.93/42.16    (89)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.93/42.16              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.93/42.16                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.93/42.16                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.93/42.16    (90)  all_55_10 = all_6_2
% 230.93/42.16    (91)  op(e1, e1) = e2
% 230.93/42.16    (92)  all_55_13 = all_53_7
% 230.93/42.16    (93)  op(e2, e0) = all_53_13
% 230.93/42.16    (94)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.93/42.16          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.93/42.16    (95)  all_38_2 = all_6_2
% 230.93/42.16    (96)  all_55_11 = all_53_14
% 230.93/42.16    (97)  all_55_3 = all_53_12
% 230.93/42.16    (98)   ~ (all_53_12 = e3)
% 230.93/42.16    (99)  all_57_0 = e3
% 230.93/42.16    (100)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0
% 230.93/42.16             & op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~
% 230.93/42.16             (all_42_1 = e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 230.93/42.16    (101)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.93/42.16           (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.93/42.16    (102)   ~ (all_4_2 = e3)
% 230.93/42.16    (103)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.93/42.16           (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.93/42.16    (104)   ~ (all_53_12 = all_10_2)
% 230.93/42.16    (105)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.93/42.16           | (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 230.93/42.16             e3)
% 230.93/42.16    (106)   ~ (all_53_13 = all_53_14)
% 230.93/42.16    (107)   ~ (e2 = e1)
% 230.93/42.16    (108)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.93/42.16           | (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.93/42.16             e2)
% 230.93/42.16    (109)  op(e2, e1) = all_53_9
% 230.93/42.16    (110)  op(e1, e2) = all_53_6
% 230.93/42.16    (111)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.93/42.16           (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.93/42.16    (112)  all_24_2 = all_6_2
% 230.93/42.16    (113)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.93/42.16           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.93/42.16    (114)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.93/42.16           (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.93/42.16    (115)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.93/42.16           | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.93/42.16             e1)
% 230.93/42.16    (116)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.93/42.16           (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.93/42.16    (117)   ~ (all_53_12 = all_53_14)
% 230.93/42.16    (118)  all_55_14 = all_53_11
% 230.93/42.16    (119)  op(e3, e1) = all_53_8
% 230.93/42.16    (120)  all_55_7 = all_53_13
% 230.93/42.16    (121)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.93/42.16           (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.93/42.16    (122)   ~ (all_53_4 = e3)
% 230.93/42.16    (123)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.93/42.16           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.93/42.16    (124)  op(e3, e0) = all_53_12
% 230.93/42.16  
% 230.93/42.16  Begin of proof
% 230.93/42.16  | 
% 230.93/42.16  | BETA: splitting (79) gives:
% 230.93/42.16  | 
% 230.93/42.16  | Case 1:
% 230.93/42.16  | | 
% 230.93/42.16  | |   (125)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) =
% 230.93/42.16  | |            e3)
% 230.93/42.16  | | 
% 230.93/42.16  | | BETA: splitting (125) gives:
% 230.93/42.16  | | 
% 230.93/42.16  | | Case 1:
% 230.93/42.16  | | | 
% 230.93/42.16  | | |   (126)  all_57_4 = e3 & op(e3, e1) = e3
% 230.93/42.16  | | | 
% 230.93/42.16  | | | ALPHA: (126) implies:
% 230.93/42.16  | | |   (127)  all_57_4 = e3
% 230.93/42.16  | | | 
% 230.93/42.16  | | | REF_CLOSE: (15), (18), (32), (39), (44), (49), (55), (57), (71), (74),
% 230.93/42.16  | | |            (107), (127) are inconsistent by sub-proof #2474.
% 230.93/42.16  | | | 
% 230.93/42.16  | | Case 2:
% 230.93/42.16  | | | 
% 230.93/42.16  | | |   (128)  all_57_5 = e3 & op(e2, e1) = e3
% 230.93/42.16  | | | 
% 230.93/42.16  | | | ALPHA: (128) implies:
% 230.93/42.16  | | |   (129)  all_57_5 = e3
% 230.93/42.16  | | | 
% 230.93/42.16  | | | REF_CLOSE: (49), (77), (129) are inconsistent by sub-proof #2189.
% 230.93/42.16  | | | 
% 230.93/42.16  | | End of split
% 230.93/42.16  | | 
% 230.93/42.16  | Case 2:
% 230.93/42.16  | | 
% 230.93/42.16  | |   (130)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) =
% 230.93/42.16  | |            e3)
% 230.93/42.16  | | 
% 230.93/42.16  | | BETA: splitting (130) gives:
% 230.93/42.16  | | 
% 230.93/42.16  | | Case 1:
% 230.93/42.16  | | | 
% 230.93/42.16  | | |   (131)  all_57_8 = e3 & op(e1, e1) = e3
% 230.93/42.16  | | | 
% 230.93/42.16  | | | ALPHA: (131) implies:
% 230.93/42.16  | | |   (132)  op(e1, e1) = e3
% 230.93/42.16  | | | 
% 230.93/42.16  | | | REF_CLOSE: (18), (26), (27), (132) are inconsistent by sub-proof #2468.
% 230.93/42.16  | | | 
% 230.93/42.16  | | Case 2:
% 230.93/42.16  | | | 
% 230.93/42.16  | | |   (133)  all_57_14 = e3 & op(e0, e1) = e3
% 230.93/42.16  | | | 
% 230.93/42.16  | | | ALPHA: (133) implies:
% 230.93/42.16  | | |   (134)  all_57_14 = e3
% 230.93/42.16  | | | 
% 230.93/42.16  | | | BETA: splitting (89) gives:
% 230.93/42.16  | | | 
% 230.93/42.16  | | | Case 1:
% 230.93/42.16  | | | | 
% 230.93/42.16  | | | |   (135)  all_57_15 = e0 & op(e0, e0) = e0
% 230.93/42.16  | | | | 
% 230.93/42.16  | | | | ALPHA: (135) implies:
% 230.93/42.16  | | | |   (136)  all_57_15 = e0
% 230.93/42.16  | | | | 
% 230.93/42.16  | | | | COMBINE_EQS: (21), (136) imply:
% 230.93/42.16  | | | |   (137)  e1 = e0
% 230.93/42.16  | | | | 
% 230.93/42.16  | | | | REDUCE: (74), (137) imply:
% 230.93/42.16  | | | |   (138)  $false
% 230.93/42.16  | | | | 
% 230.93/42.16  | | | | CLOSE: (138) is inconsistent.
% 230.93/42.16  | | | | 
% 230.93/42.16  | | | Case 2:
% 230.93/42.16  | | | | 
% 230.93/42.16  | | | |   (139)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2,
% 230.93/42.16  | | | |                e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) &
% 230.93/42.16  | | | |          ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0,
% 230.93/42.16  | | | |                e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 230.93/42.16  | | | | 
% 230.93/42.16  | | | | ALPHA: (139) implies:
% 230.99/42.16  | | | |   (140)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0,
% 230.99/42.16  | | | |              e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.99/42.16  | | | | 
% 230.99/42.16  | | | | BETA: splitting (56) gives:
% 230.99/42.16  | | | | 
% 230.99/42.16  | | | | Case 1:
% 230.99/42.16  | | | | | 
% 230.99/42.16  | | | | |   (141)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2,
% 230.99/42.16  | | | | |              e1) = e1)
% 230.99/42.16  | | | | | 
% 230.99/42.16  | | | | | BETA: splitting (141) gives:
% 230.99/42.16  | | | | | 
% 230.99/42.16  | | | | | Case 1:
% 230.99/42.16  | | | | | | 
% 230.99/42.16  | | | | | |   (142)  all_57_4 = e1 & op(e3, e1) = e1
% 230.99/42.16  | | | | | | 
% 230.99/42.16  | | | | | | ALPHA: (142) implies:
% 230.99/42.16  | | | | | |   (143)  all_57_4 = e1
% 230.99/42.16  | | | | | | 
% 230.99/42.16  | | | | | | BETA: splitting (44) gives:
% 230.99/42.16  | | | | | | 
% 230.99/42.16  | | | | | | Case 1:
% 230.99/42.16  | | | | | | | 
% 230.99/42.16  | | | | | | |   (144)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 &
% 230.99/42.16  | | | | | | |            op(e3, e2) = e0)
% 230.99/42.16  | | | | | | | 
% 230.99/42.16  | | | | | | | REF_CLOSE: (18), (55), (57), (70), (78), (144) are inconsistent by
% 230.99/42.16  | | | | | | |            sub-proof #1543.
% 230.99/42.16  | | | | | | | 
% 230.99/42.16  | | | | | | Case 2:
% 230.99/42.16  | | | | | | | 
% 230.99/42.16  | | | | | | |   (145)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 &
% 230.99/42.16  | | | | | | |            op(e3, e0) = e0)
% 230.99/42.16  | | | | | | | 
% 230.99/42.16  | | | | | | | BETA: splitting (145) gives:
% 230.99/42.16  | | | | | | | 
% 230.99/42.16  | | | | | | | Case 1:
% 230.99/42.16  | | | | | | | | 
% 230.99/42.16  | | | | | | | |   (146)  all_57_4 = e0 & op(e3, e1) = e0
% 230.99/42.16  | | | | | | | | 
% 230.99/42.16  | | | | | | | | REF_CLOSE: (74), (143), (146) are inconsistent by sub-proof
% 230.99/42.16  | | | | | | | |            #2429.
% 230.99/42.16  | | | | | | | | 
% 230.99/42.16  | | | | | | | Case 2:
% 230.99/42.16  | | | | | | | | 
% 230.99/42.16  | | | | | | | |   (147)  all_57_9 = e0 & op(e3, e0) = e0
% 230.99/42.16  | | | | | | | | 
% 230.99/42.16  | | | | | | | | ALPHA: (147) implies:
% 230.99/42.16  | | | | | | | |   (148)  all_57_9 = e0
% 230.99/42.16  | | | | | | | |   (149)  op(e3, e0) = e0
% 230.99/42.16  | | | | | | | | 
% 230.99/42.16  | | | | | | | | BETA: splitting (8) gives:
% 230.99/42.16  | | | | | | | | 
% 230.99/42.16  | | | | | | | | Case 1:
% 230.99/42.16  | | | | | | | | | 
% 230.99/42.16  | | | | | | | | |   (150)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 &
% 230.99/42.16  | | | | | | | | |            op(e2, e2) = e1)
% 230.99/42.16  | | | | | | | | | 
% 230.99/42.16  | | | | | | | | | BETA: splitting (150) gives:
% 230.99/42.16  | | | | | | | | | 
% 230.99/42.16  | | | | | | | | | Case 1:
% 230.99/42.16  | | | | | | | | | | 
% 230.99/42.16  | | | | | | | | | |   (151)  all_57_2 = e1 & op(e2, e3) = e1
% 230.99/42.16  | | | | | | | | | | 
% 230.99/42.16  | | | | | | | | | | ALPHA: (151) implies:
% 230.99/42.16  | | | | | | | | | |   (152)  all_57_2 = e1
% 230.99/42.16  | | | | | | | | | | 
% 230.99/42.16  | | | | | | | | | | BETA: splitting (140) gives:
% 230.99/42.16  | | | | | | | | | | 
% 230.99/42.16  | | | | | | | | | | Case 1:
% 230.99/42.16  | | | | | | | | | | | 
% 230.99/42.16  | | | | | | | | | | |   (153)  all_57_12 = e0 & op(e0, e3) = e0
% 230.99/42.16  | | | | | | | | | | | 
% 230.99/42.16  | | | | | | | | | | | ALPHA: (153) implies:
% 230.99/42.16  | | | | | | | | | | |   (154)  all_57_12 = e0
% 230.99/42.16  | | | | | | | | | | |   (155)  op(e0, e3) = e0
% 230.99/42.16  | | | | | | | | | | | 
% 230.99/42.16  | | | | | | | | | | | BETA: splitting (48) gives:
% 230.99/42.16  | | | | | | | | | | | 
% 230.99/42.16  | | | | | | | | | | | Case 1:
% 230.99/42.16  | | | | | | | | | | | | 
% 230.99/42.16  | | | | | | | | | | | |   (156)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 230.99/42.16  | | | | | | | | | | | |            & op(e2, e1) = e0)
% 230.99/42.16  | | | | | | | | | | | | 
% 230.99/42.16  | | | | | | | | | | | | BETA: splitting (156) gives:
% 230.99/42.16  | | | | | | | | | | | | 
% 230.99/42.16  | | | | | | | | | | | | Case 1:
% 230.99/42.16  | | | | | | | | | | | | | 
% 230.99/42.16  | | | | | | | | | | | | |   (157)  all_57_4 = e0 & op(e3, e1) = e0
% 230.99/42.16  | | | | | | | | | | | | | 
% 230.99/42.16  | | | | | | | | | | | | | ALPHA: (157) implies:
% 230.99/42.16  | | | | | | | | | | | | |   (158)  all_57_4 = e0
% 230.99/42.16  | | | | | | | | | | | | | 
% 230.99/42.16  | | | | | | | | | | | | | REF_CLOSE: (15), (18), (32), (39), (49), (57), (71), (74),
% 230.99/42.16  | | | | | | | | | | | | |            (107), (148), (158) are inconsistent by sub-proof
% 230.99/42.16  | | | | | | | | | | | | |            #2436.
% 230.99/42.16  | | | | | | | | | | | | | 
% 230.99/42.16  | | | | | | | | | | | | Case 2:
% 230.99/42.16  | | | | | | | | | | | | | 
% 230.99/42.16  | | | | | | | | | | | | |   (159)  all_57_5 = e0 & op(e2, e1) = e0
% 230.99/42.16  | | | | | | | | | | | | | 
% 230.99/42.16  | | | | | | | | | | | | | ALPHA: (159) implies:
% 230.99/42.16  | | | | | | | | | | | | |   (160)  all_57_5 = e0
% 230.99/42.16  | | | | | | | | | | | | | 
% 230.99/42.16  | | | | | | | | | | | | | REF_CLOSE: (8), (15), (18), (40), (45), (49), (55), (71),
% 230.99/42.16  | | | | | | | | | | | | |            (74), (94), (101), (107), (152), (160) are
% 230.99/42.16  | | | | | | | | | | | | |            inconsistent by sub-proof #2353.
% 230.99/42.16  | | | | | | | | | | | | | 
% 230.99/42.16  | | | | | | | | | | | | End of split
% 230.99/42.16  | | | | | | | | | | | | 
% 230.99/42.16  | | | | | | | | | | | Case 2:
% 230.99/42.16  | | | | | | | | | | | | 
% 230.99/42.16  | | | | | | | | | | | |   (161)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 230.99/42.16  | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 230.99/42.16  | | | | | | | | | | | | 
% 230.99/42.16  | | | | | | | | | | | | BETA: splitting (161) gives:
% 230.99/42.16  | | | | | | | | | | | | 
% 230.99/42.16  | | | | | | | | | | | | Case 1:
% 230.99/42.16  | | | | | | | | | | | | | 
% 230.99/42.16  | | | | | | | | | | | | |   (162)  all_57_8 = e0 & op(e1, e1) = e0
% 230.99/42.16  | | | | | | | | | | | | | 
% 230.99/42.16  | | | | | | | | | | | | | ALPHA: (162) implies:
% 230.99/42.16  | | | | | | | | | | | | |   (163)  all_57_8 = e0
% 230.99/42.16  | | | | | | | | | | | | |   (164)  op(e1, e1) = e0
% 230.99/42.16  | | | | | | | | | | | | | 
% 230.99/42.16  | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 230.99/42.16  | | | | | | | | | | | | |            (11), (12), (13), (14), (16), (18), (19), (20),
% 230.99/42.16  | | | | | | | | | | | | |            (22), (23), (24), (25), (26), (27), (28), (29),
% 230.99/42.16  | | | | | | | | | | | | |            (30), (31), (32), (33), (34), (35), (36), (37),
% 230.99/42.16  | | | | | | | | | | | | |            (38), (39), (40), (41), (42), (43), (44), (45),
% 230.99/42.16  | | | | | | | | | | | | |            (46), (47), (48), (49), (50), (51), (52), (53),
% 230.99/42.16  | | | | | | | | | | | | |            (54), (56), (57), (58), (59), (60), (61), (62),
% 230.99/42.16  | | | | | | | | | | | | |            (63), (64), (65), (67), (68), (69), (70), (71),
% 230.99/42.16  | | | | | | | | | | | | |            (72), (73), (75), (76), (79), (80), (81), (82),
% 230.99/42.16  | | | | | | | | | | | | |            (83), (84), (85), (86), (88), (89), (90), (92),
% 230.99/42.16  | | | | | | | | | | | | |            (93), (94), (95), (96), (97), (98), (99), (100),
% 230.99/42.16  | | | | | | | | | | | | |            (101), (102), (103), (104), (105), (106), (108),
% 230.99/42.16  | | | | | | | | | | | | |            (109), (110), (111), (112), (113), (114), (115),
% 230.99/42.16  | | | | | | | | | | | | |            (116), (117), (118), (119), (120), (121), (122),
% 230.99/42.16  | | | | | | | | | | | | |            (123), (124), (148), (149), (154), (155), (163),
% 230.99/42.16  | | | | | | | | | | | | |            (164) are inconsistent by sub-proof #1301.
% 230.99/42.16  | | | | | | | | | | | | | 
% 230.99/42.16  | | | | | | | | | | | | Case 2:
% 230.99/42.16  | | | | | | | | | | | | | 
% 230.99/42.16  | | | | | | | | | | | | |   (165)  all_57_14 = e0 & op(e0, e1) = e0
% 230.99/42.16  | | | | | | | | | | | | | 
% 230.99/42.16  | | | | | | | | | | | | | ALPHA: (165) implies:
% 230.99/42.16  | | | | | | | | | | | | |   (166)  all_57_14 = e0
% 230.99/42.16  | | | | | | | | | | | | | 
% 230.99/42.16  | | | | | | | | | | | | | REF_CLOSE: (55), (134), (166) are inconsistent by sub-proof
% 230.99/42.16  | | | | | | | | | | | | |            #2420.
% 230.99/42.16  | | | | | | | | | | | | | 
% 230.99/42.16  | | | | | | | | | | | | End of split
% 230.99/42.16  | | | | | | | | | | | | 
% 230.99/42.16  | | | | | | | | | | | End of split
% 230.99/42.16  | | | | | | | | | | | 
% 230.99/42.16  | | | | | | | | | | Case 2:
% 230.99/42.16  | | | | | | | | | | | 
% 230.99/42.16  | | | | | | | | | | |   (167)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 230.99/42.16  | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 230.99/42.16  | | | | | | | | | | | 
% 230.99/42.16  | | | | | | | | | | | BETA: splitting (167) gives:
% 230.99/42.16  | | | | | | | | | | | 
% 230.99/42.16  | | | | | | | | | | | Case 1:
% 230.99/42.16  | | | | | | | | | | | | 
% 230.99/42.16  | | | | | | | | | | | |   (168)  all_57_13 = e0 & op(e0, e2) = e0
% 230.99/42.16  | | | | | | | | | | | | 
% 230.99/42.16  | | | | | | | | | | | | ALPHA: (168) implies:
% 230.99/42.16  | | | | | | | | | | | |   (169)  op(e0, e2) = e0
% 230.99/42.16  | | | | | | | | | | | | 
% 230.99/42.16  | | | | | | | | | | | | REF_CLOSE: (18), (66), (87), (169) are inconsistent by
% 230.99/42.16  | | | | | | | | | | | |            sub-proof #2332.
% 230.99/42.16  | | | | | | | | | | | | 
% 230.99/42.16  | | | | | | | | | | | Case 2:
% 230.99/42.16  | | | | | | | | | | | | 
% 230.99/42.16  | | | | | | | | | | | |   (170)  all_57_14 = e0 & op(e0, e1) = e0
% 230.99/42.16  | | | | | | | | | | | | 
% 230.99/42.16  | | | | | | | | | | | | ALPHA: (170) implies:
% 230.99/42.16  | | | | | | | | | | | |   (171)  all_57_14 = e0
% 230.99/42.16  | | | | | | | | | | | | 
% 230.99/42.16  | | | | | | | | | | | | REF_CLOSE: (55), (134), (171) are inconsistent by sub-proof
% 230.99/42.16  | | | | | | | | | | | |            #2420.
% 230.99/42.16  | | | | | | | | | | | | 
% 230.99/42.16  | | | | | | | | | | | End of split
% 230.99/42.16  | | | | | | | | | | | 
% 230.99/42.16  | | | | | | | | | | End of split
% 230.99/42.16  | | | | | | | | | | 
% 230.99/42.16  | | | | | | | | | Case 2:
% 230.99/42.16  | | | | | | | | | | 
% 230.99/42.16  | | | | | | | | | |   (172)  all_57_3 = e1 & op(e2, e2) = e1
% 230.99/42.16  | | | | | | | | | | 
% 230.99/42.16  | | | | | | | | | | ALPHA: (172) implies:
% 230.99/42.16  | | | | | | | | | |   (173)  op(e2, e2) = e1
% 230.99/42.16  | | | | | | | | | | 
% 230.99/42.16  | | | | | | | | | | REF_CLOSE: (18), (40), (74), (173) are inconsistent by
% 230.99/42.16  | | | | | | | | | |            sub-proof #2352.
% 230.99/42.16  | | | | | | | | | | 
% 230.99/42.16  | | | | | | | | | End of split
% 230.99/42.16  | | | | | | | | | 
% 230.99/42.16  | | | | | | | | Case 2:
% 230.99/42.16  | | | | | | | | | 
% 230.99/42.16  | | | | | | | | |   (174)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 &
% 230.99/42.16  | | | | | | | | |            op(e2, e0) = e1)
% 230.99/42.16  | | | | | | | | | 
% 230.99/42.16  | | | | | | | | | BETA: splitting (174) gives:
% 230.99/42.16  | | | | | | | | | 
% 230.99/42.16  | | | | | | | | | Case 1:
% 230.99/42.16  | | | | | | | | | | 
% 230.99/42.16  | | | | | | | | | |   (175)  all_57_5 = e1 & op(e2, e1) = e1
% 230.99/42.16  | | | | | | | | | | 
% 230.99/42.16  | | | | | | | | | | REF_CLOSE: (77), (107), (175) are inconsistent by sub-proof
% 230.99/42.16  | | | | | | | | | |            #1886.
% 230.99/42.16  | | | | | | | | | | 
% 230.99/42.16  | | | | | | | | | Case 2:
% 230.99/42.16  | | | | | | | | | | 
% 230.99/42.16  | | | | | | | | | |   (176)  all_57_10 = e1 & op(e2, e0) = e1
% 230.99/42.16  | | | | | | | | | | 
% 230.99/42.16  | | | | | | | | | | REF_CLOSE: (17), (18), (93), (176) are inconsistent by
% 230.99/42.16  | | | | | | | | | |            sub-proof #2084.
% 230.99/42.16  | | | | | | | | | | 
% 230.99/42.16  | | | | | | | | | End of split
% 230.99/42.16  | | | | | | | | | 
% 230.99/42.16  | | | | | | | | End of split
% 230.99/42.16  | | | | | | | | 
% 230.99/42.16  | | | | | | | End of split
% 230.99/42.16  | | | | | | | 
% 230.99/42.16  | | | | | | End of split
% 230.99/42.16  | | | | | | 
% 230.99/42.16  | | | | | Case 2:
% 230.99/42.16  | | | | | | 
% 230.99/42.16  | | | | | |   (177)  all_57_5 = e1 & op(e2, e1) = e1
% 230.99/42.16  | | | | | | 
% 230.99/42.16  | | | | | | REF_CLOSE: (77), (107), (177) are inconsistent by sub-proof #1886.
% 230.99/42.16  | | | | | | 
% 230.99/42.16  | | | | | End of split
% 230.99/42.16  | | | | | 
% 230.99/42.16  | | | | Case 2:
% 230.99/42.16  | | | | | 
% 230.99/42.16  | | | | |   (178)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0,
% 230.99/42.16  | | | | |              e1) = e1)
% 230.99/42.16  | | | | | 
% 230.99/42.16  | | | | | BETA: splitting (178) gives:
% 230.99/42.16  | | | | | 
% 230.99/42.16  | | | | | Case 1:
% 230.99/42.16  | | | | | | 
% 230.99/42.16  | | | | | |   (179)  all_57_8 = e1 & op(e1, e1) = e1
% 230.99/42.16  | | | | | | 
% 230.99/42.16  | | | | | | ALPHA: (179) implies:
% 230.99/42.16  | | | | | |   (180)  op(e1, e1) = e1
% 230.99/42.16  | | | | | | 
% 230.99/42.16  | | | | | | REF_CLOSE: (18), (91), (107), (180) are inconsistent by sub-proof
% 230.99/42.16  | | | | | |            #2423.
% 230.99/42.16  | | | | | | 
% 230.99/42.16  | | | | | Case 2:
% 230.99/42.16  | | | | | | 
% 230.99/42.16  | | | | | |   (181)  all_57_14 = e1 & op(e0, e1) = e1
% 230.99/42.16  | | | | | | 
% 230.99/42.16  | | | | | | REF_CLOSE: (15), (134), (181) are inconsistent by sub-proof #2319.
% 230.99/42.16  | | | | | | 
% 230.99/42.16  | | | | | End of split
% 230.99/42.16  | | | | | 
% 230.99/42.16  | | | | End of split
% 230.99/42.16  | | | | 
% 230.99/42.16  | | | End of split
% 230.99/42.16  | | | 
% 230.99/42.16  | | End of split
% 230.99/42.16  | | 
% 230.99/42.16  | End of split
% 230.99/42.16  | 
% 230.99/42.16  End of proof
% 230.99/42.16  
% 230.99/42.16  Sub-proof #1301 shows that the following formulas are inconsistent:
% 230.99/42.16  ----------------------------------------------------------------
% 230.99/42.16    (1)   ~ (all_10_2 = e2)
% 230.99/42.16    (2)  all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 230.99/42.16    (3)  op(e3, e3) = all_10_2
% 230.99/42.16    (4)  op(e0, e0) = all_4_2
% 230.99/42.16    (5)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 230.99/42.16    (6)   ~ (all_53_12 = all_4_2)
% 230.99/42.16    (7)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 230.99/42.16    (8)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.99/42.16         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.99/42.16    (9)  all_55_15 = e3 | all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 230.99/42.16    (10)  all_57_12 = e0
% 230.99/42.16    (11)   ~ (all_53_6 = e0)
% 230.99/42.16    (12)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.99/42.16          (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.99/42.16    (13)   ~ (all_53_8 = all_53_12)
% 230.99/42.16    (14)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.99/42.16          (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.99/42.16    (15)   ~ (all_53_8 = all_53_11)
% 230.99/42.16    (16)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.99/42.16          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.99/42.16    (17)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.99/42.16            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.99/42.16    (18)  all_55_15 = all_4_2
% 230.99/42.16    (19)  all_55_0 = all_10_2
% 230.99/42.16    (20)   ~ (all_10_2 = e0)
% 230.99/42.16    (21)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.99/42.16          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.99/42.16    (22)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 230.99/42.16            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 230.99/42.16              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 230.99/42.16    (23)  op(e0, e3) = e0
% 230.99/42.16    (24)   ~ (all_53_3 = all_53_7)
% 230.99/42.16    (25)   ~ (all_6_2 = e3)
% 230.99/42.16    (26)  op(e1, e1) = all_6_2
% 230.99/42.16    (27)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 230.99/42.16    (28)   ~ (all_53_9 = e0)
% 230.99/42.16    (29)  all_55_0 = e3 | all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 230.99/42.16    (30)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 230.99/42.16    (31)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.99/42.16          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.99/42.16    (32)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 230.99/42.16    (33)  all_55_9 = all_53_6
% 230.99/42.16    (34)   ~ (all_53_4 = all_53_12)
% 230.99/42.16    (35)   ~ (all_53_8 = e3)
% 230.99/42.16    (36)   ~ (all_53_8 = all_53_9)
% 230.99/42.16    (37)  all_42_2 = all_6_2
% 230.99/42.17    (38)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.99/42.17          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.99/42.17    (39)  op(e2, e2) = e0
% 230.99/42.17    (40)   ~ (all_53_9 = all_53_11)
% 230.99/42.17    (41)   ~ (all_53_9 = all_6_2)
% 230.99/42.17    (42)   ~ (all_53_12 = all_53_13)
% 230.99/42.17    (43)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.99/42.17          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.99/42.17    (44)  all_57_3 = e0
% 230.99/42.17    (45)   ~ (all_53_14 = all_4_2)
% 230.99/42.17    (46)   ~ (all_53_11 = all_4_2)
% 230.99/42.17    (47)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 230.99/42.17          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.99/42.17    (48)   ~ (e3 = e2)
% 230.99/42.17    (49)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 230.99/42.17    (50)  all_55_1 = all_53_4
% 230.99/42.17    (51)  op(e1, e0) = all_53_14
% 230.99/42.17    (52)   ~ (all_53_6 = all_53_7)
% 230.99/42.17    (53)  all_55_7 = e3 | all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 230.99/42.17    (54)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.99/42.17          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.99/42.17    (55)  op(e3, e3) = e3
% 230.99/42.17    (56)  op(e3, e0) = e0
% 230.99/42.17    (57)   ~ (all_53_8 = all_6_2)
% 230.99/42.17    (58)   ~ (all_4_2 = e2)
% 230.99/42.17    (59)  op(e0, e3) = all_53_3
% 230.99/42.17    (60)   ~ (all_53_7 = all_4_2)
% 230.99/42.17    (61)  all_55_2 = all_53_8
% 230.99/42.17    (62)   ~ (all_53_4 = all_53_7)
% 230.99/42.17    (63)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 230.99/42.17    (64)   ~ (all_53_9 = all_53_13)
% 230.99/42.17    (65)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.99/42.17          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.99/42.17            e1)
% 230.99/42.17    (66)  all_57_9 = e0
% 230.99/42.17    (67)   ~ (all_53_4 = all_53_8)
% 230.99/42.17    (68)  all_55_6 = all_53_9
% 230.99/42.17    (69)  op(e3, e2) = all_53_4
% 230.99/42.17    (70)   ~ (e2 = e0)
% 230.99/42.17    (71)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 230.99/42.17            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 230.99/42.17            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 230.99/42.17            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 230.99/42.17              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 230.99/42.17            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 230.99/42.17            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 230.99/42.17              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 230.99/42.17              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 230.99/42.17            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 230.99/42.17            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 230.99/42.17            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 230.99/42.17              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 230.99/42.17              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 230.99/42.17            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 230.99/42.17              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 230.99/42.17            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 230.99/42.17            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 230.99/42.17              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 230.99/42.17              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 230.99/42.17            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 230.99/42.17            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 230.99/42.17    (72)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.99/42.17          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.99/42.17    (73)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 230.99/42.17            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 230.99/42.17              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 230.99/42.17    (74)   ~ (all_53_3 = all_53_11)
% 230.99/42.17    (75)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 230.99/42.17          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 230.99/42.17    (76)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.99/42.17          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.99/42.17    (77)   ~ (all_10_2 = e1)
% 230.99/42.17    (78)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 230.99/42.17    (79)   ~ (all_53_7 = all_53_11)
% 230.99/42.17    (80)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.99/42.17          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 230.99/42.17            e3)
% 230.99/42.17    (81)   ~ (all_53_13 = all_4_2)
% 230.99/42.17    (82)   ~ (all_53_4 = all_53_6)
% 230.99/42.17    (83)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.99/42.17          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.99/42.17            e2)
% 230.99/42.17    (84)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.99/42.17              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.99/42.17                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.99/42.17                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.99/42.17    (85)  op(e1, e1) = e0
% 230.99/42.17    (86)  all_55_10 = all_6_2
% 230.99/42.17    (87)  all_55_13 = all_53_7
% 230.99/42.17    (88)  op(e2, e0) = all_53_13
% 230.99/42.17    (89)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.99/42.17          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.99/42.17    (90)  all_38_2 = all_6_2
% 230.99/42.17    (91)  all_55_11 = all_53_14
% 230.99/42.17    (92)  all_55_3 = all_53_12
% 230.99/42.17    (93)   ~ (all_53_12 = e3)
% 230.99/42.17    (94)  all_57_0 = e3
% 230.99/42.17    (95)  all_57_8 = e0
% 230.99/42.17    (96)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 230.99/42.17            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 230.99/42.17              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 230.99/42.17    (97)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.99/42.17          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.99/42.17    (98)   ~ (all_4_2 = e3)
% 230.99/42.17    (99)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.99/42.17          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.99/42.17    (100)   ~ (all_53_12 = all_10_2)
% 230.99/42.17    (101)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.99/42.17           | (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 230.99/42.17             e3)
% 230.99/42.17    (102)   ~ (all_53_13 = all_53_14)
% 230.99/42.17    (103)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.99/42.17           | (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.99/42.17             e2)
% 230.99/42.17    (104)  op(e2, e1) = all_53_9
% 230.99/42.17    (105)  op(e1, e2) = all_53_6
% 230.99/42.17    (106)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.99/42.17           (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.99/42.17    (107)  all_24_2 = all_6_2
% 230.99/42.17    (108)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.99/42.17           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.99/42.17    (109)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.99/42.17           (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.99/42.17    (110)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.99/42.17           | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.99/42.17             e1)
% 230.99/42.17    (111)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.99/42.17           (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.99/42.17    (112)   ~ (all_53_12 = all_53_14)
% 230.99/42.17    (113)  all_55_14 = all_53_11
% 230.99/42.17    (114)  op(e3, e1) = all_53_8
% 230.99/42.17    (115)  all_55_7 = all_53_13
% 230.99/42.17    (116)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.99/42.17           (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.99/42.17    (117)   ~ (all_53_4 = e3)
% 230.99/42.17    (118)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.99/42.17           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.99/42.17    (119)  op(e3, e0) = all_53_12
% 230.99/42.17  
% 230.99/42.17  Begin of proof
% 230.99/42.17  | 
% 230.99/42.17  | GROUND_INST: instantiating (17) with all_53_3, e0, e3, e0, simplifying with
% 230.99/42.17  |              (23), (59) gives:
% 230.99/42.17  |   (120)  all_53_3 = e0
% 230.99/42.17  | 
% 230.99/42.17  | GROUND_INST: instantiating (17) with all_53_12, e0, e0, e3, simplifying with
% 230.99/42.17  |              (56), (119) gives:
% 230.99/42.17  |   (121)  all_53_12 = e0
% 230.99/42.17  | 
% 230.99/42.17  | REDUCE: (24), (120) imply:
% 230.99/42.17  |   (122)   ~ (all_53_7 = e0)
% 230.99/42.17  | 
% 230.99/42.17  | SIMP: (122) implies:
% 230.99/42.17  |   (123)   ~ (all_53_7 = e0)
% 230.99/42.17  | 
% 230.99/42.17  | REDUCE: (74), (120) imply:
% 230.99/42.17  |   (124)   ~ (all_53_11 = e0)
% 230.99/42.17  | 
% 230.99/42.17  | SIMP: (124) implies:
% 230.99/42.17  |   (125)   ~ (all_53_11 = e0)
% 230.99/42.17  | 
% 230.99/42.17  | REDUCE: (34), (121) imply:
% 230.99/42.17  |   (126)   ~ (all_53_4 = e0)
% 230.99/42.17  | 
% 230.99/42.17  | REDUCE: (13), (121) imply:
% 230.99/42.17  |   (127)   ~ (all_53_8 = e0)
% 230.99/42.17  | 
% 230.99/42.17  | REDUCE: (42), (121) imply:
% 230.99/42.17  |   (128)   ~ (all_53_13 = e0)
% 230.99/42.17  | 
% 230.99/42.17  | SIMP: (128) implies:
% 230.99/42.17  |   (129)   ~ (all_53_13 = e0)
% 230.99/42.17  | 
% 230.99/42.17  | REDUCE: (112), (121) imply:
% 230.99/42.17  |   (130)   ~ (all_53_14 = e0)
% 230.99/42.17  | 
% 230.99/42.17  | SIMP: (130) implies:
% 230.99/42.17  |   (131)   ~ (all_53_14 = e0)
% 230.99/42.17  | 
% 230.99/42.17  | REDUCE: (6), (121) imply:
% 230.99/42.17  |   (132)   ~ (all_4_2 = e0)
% 230.99/42.17  | 
% 230.99/42.17  | SIMP: (132) implies:
% 230.99/42.17  |   (133)   ~ (all_4_2 = e0)
% 230.99/42.17  | 
% 230.99/42.17  | REDUCE: (93), (121) imply:
% 230.99/42.17  |   (134)   ~ (e3 = e0)
% 230.99/42.17  | 
% 230.99/42.17  | SIMP: (134) implies:
% 230.99/42.17  |   (135)   ~ (e3 = e0)
% 230.99/42.17  | 
% 230.99/42.17  | BETA: splitting (9) gives:
% 230.99/42.17  | 
% 230.99/42.17  | Case 1:
% 230.99/42.17  | | 
% 230.99/42.17  | |   (136)  all_55_15 = e3
% 230.99/42.17  | | 
% 230.99/42.17  | | REF_CLOSE: (18), (98), (136) are inconsistent by sub-proof #2503.
% 230.99/42.17  | | 
% 230.99/42.17  | Case 2:
% 230.99/42.17  | | 
% 230.99/42.17  | |   (137)   ~ (all_55_15 = e3)
% 230.99/42.17  | |   (138)  all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 230.99/42.17  | | 
% 230.99/42.17  | | BETA: splitting (138) gives:
% 230.99/42.17  | | 
% 230.99/42.17  | | Case 1:
% 230.99/42.17  | | | 
% 230.99/42.17  | | |   (139)  all_55_15 = e2
% 230.99/42.17  | | | 
% 230.99/42.17  | | | REF_CLOSE: (18), (58), (139) are inconsistent by sub-proof #2502.
% 230.99/42.17  | | | 
% 230.99/42.17  | | Case 2:
% 230.99/42.17  | | | 
% 230.99/42.17  | | |   (140)   ~ (all_55_15 = e2)
% 230.99/42.17  | | |   (141)  all_55_15 = e1 | all_55_15 = e0
% 230.99/42.17  | | | 
% 230.99/42.17  | | | BETA: splitting (71) gives:
% 230.99/42.17  | | | 
% 230.99/42.17  | | | Case 1:
% 230.99/42.17  | | | | 
% 230.99/42.17  | | | |   (142)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 230.99/42.17  | | | |            & op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 230.99/42.17  | | | |            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 230.99/42.17  | | | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) =
% 230.99/42.17  | | | |            all_52_5 & op(e3, e0) = all_52_7 & $i(all_52_1) &
% 230.99/42.17  | | | |            $i(all_52_3) & $i(all_52_5) & $i(all_52_7)) | (all_52_8 = e3
% 230.99/42.17  | | | |            & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0 &
% 230.99/42.17  | | | |            op(all_52_9, all_52_9) = e3 & op(all_52_11, all_52_11) = e2 &
% 230.99/42.17  | | | |            op(all_52_13, all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 230.99/42.17  | | | |            & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 & op(e2, e1)
% 230.99/42.17  | | | |            = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 230.99/42.17  | | | |            $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 230.99/42.17  | | | | 
% 230.99/42.17  | | | | BETA: splitting (142) gives:
% 230.99/42.17  | | | | 
% 230.99/42.17  | | | | Case 1:
% 230.99/42.17  | | | | | 
% 230.99/42.17  | | | | |   (143)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 230.99/42.17  | | | | |          & op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 230.99/42.17  | | | | |          op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 230.99/42.17  | | | | |          op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) =
% 230.99/42.17  | | | | |          all_52_5 & op(e3, e0) = all_52_7 & $i(all_52_1) &
% 230.99/42.17  | | | | |          $i(all_52_3) & $i(all_52_5) & $i(all_52_7)
% 230.99/42.17  | | | | | 
% 230.99/42.17  | | | | | ALPHA: (143) implies:
% 230.99/42.17  | | | | |   (144)  op(e3, e0) = all_52_7
% 230.99/42.17  | | | | |   (145)  op(all_52_7, all_52_7) = e0
% 230.99/42.17  | | | | | 
% 230.99/42.17  | | | | | REF_CLOSE: (4), (17), (18), (56), (133), (141), (144), (145) are
% 230.99/42.17  | | | | |            inconsistent by sub-proof #1325.
% 230.99/42.17  | | | | | 
% 230.99/42.17  | | | | Case 2:
% 230.99/42.17  | | | | | 
% 230.99/42.17  | | | | |   (146)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 230.99/42.17  | | | | |          e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11, all_52_11) =
% 230.99/42.17  | | | | |          e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15, all_52_15)
% 230.99/42.17  | | | | |          = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 230.99/42.17  | | | | |          op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 230.99/42.17  | | | | |          $i(all_52_9) & $i(all_52_11) & $i(all_52_13) & $i(all_52_15)
% 230.99/42.17  | | | | | 
% 230.99/42.17  | | | | | ALPHA: (146) implies:
% 230.99/42.17  | | | | |   (147)  op(e2, e2) = all_52_11
% 230.99/42.17  | | | | |   (148)  op(all_52_11, all_52_11) = e2
% 230.99/42.17  | | | | | 
% 230.99/42.17  | | | | | REF_CLOSE: (4), (17), (18), (39), (48), (58), (66), (70), (81), (88),
% 230.99/42.17  | | | | |            (98), (101), (103), (110), (133), (135), (141), (147),
% 230.99/42.17  | | | | |            (148) are inconsistent by sub-proof #1323.
% 230.99/42.17  | | | | | 
% 230.99/42.17  | | | | End of split
% 230.99/42.17  | | | | 
% 230.99/42.17  | | | Case 2:
% 230.99/42.17  | | | | 
% 230.99/42.17  | | | |   (149)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 230.99/42.17  | | | |            e0 & op(all_52_17, all_52_17) = e3 & op(all_52_19, all_52_19)
% 230.99/42.17  | | | |            = e2 & op(all_52_21, all_52_21) = e1 & op(all_52_23,
% 230.99/42.17  | | | |              all_52_23) = e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 230.99/42.17  | | | |            all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23 &
% 230.99/42.17  | | | |            $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 230.99/42.17  | | | |            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28
% 230.99/42.17  | | | |            = e1 & all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 230.99/42.17  | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29, all_52_29) = e1
% 230.99/42.17  | | | |            & op(all_52_31, all_52_31) = e0 & op(e0, e3) = all_52_25 &
% 230.99/42.17  | | | |            op(e0, e2) = all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 230.99/42.17  | | | |            = all_52_31 & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 230.99/42.17  | | | |            $i(all_52_31))
% 230.99/42.17  | | | | 
% 230.99/42.17  | | | | BETA: splitting (149) gives:
% 230.99/42.17  | | | | 
% 230.99/42.17  | | | | Case 1:
% 230.99/42.17  | | | | | 
% 230.99/42.17  | | | | |   (150)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22
% 230.99/42.17  | | | | |          = e0 & op(all_52_17, all_52_17) = e3 & op(all_52_19,
% 230.99/42.17  | | | | |            all_52_19) = e2 & op(all_52_21, all_52_21) = e1 &
% 230.99/42.17  | | | | |          op(all_52_23, all_52_23) = e0 & op(e1, e3) = all_52_17 &
% 230.99/42.17  | | | | |          op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 230.99/42.17  | | | | |          = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 230.99/42.17  | | | | |          $i(all_52_23)
% 230.99/42.17  | | | | | 
% 230.99/42.17  | | | | | ALPHA: (150) implies:
% 230.99/42.17  | | | | |   (151)  op(e1, e0) = all_52_23
% 230.99/42.17  | | | | |   (152)  op(e1, e1) = all_52_21
% 230.99/42.17  | | | | |   (153)  op(e1, e2) = all_52_19
% 230.99/42.17  | | | | |   (154)  op(all_52_23, all_52_23) = e0
% 230.99/42.17  | | | | |   (155)  op(all_52_21, all_52_21) = e1
% 230.99/42.17  | | | | |   (156)  op(all_52_19, all_52_19) = e2
% 230.99/42.17  | | | | | 
% 230.99/42.17  | | | | | BETA: splitting (141) gives:
% 230.99/42.17  | | | | | 
% 230.99/42.17  | | | | | Case 1:
% 230.99/42.17  | | | | | | 
% 230.99/42.17  | | | | | |   (157)  all_55_15 = e1
% 230.99/42.17  | | | | | | 
% 230.99/42.17  | | | | | | COMBINE_EQS: (18), (157) imply:
% 230.99/42.17  | | | | | |   (158)  all_4_2 = e1
% 230.99/42.17  | | | | | | 
% 230.99/42.17  | | | | | | SIMP: (158) implies:
% 230.99/42.17  | | | | | |   (159)  all_4_2 = e1
% 230.99/42.17  | | | | | | 
% 230.99/42.17  | | | | | | REDUCE: (60), (159) imply:
% 230.99/42.17  | | | | | |   (160)   ~ (all_53_7 = e1)
% 230.99/42.17  | | | | | | 
% 230.99/42.17  | | | | | | REDUCE: (46), (159) imply:
% 230.99/42.17  | | | | | |   (161)   ~ (all_53_11 = e1)
% 230.99/42.17  | | | | | | 
% 230.99/42.17  | | | | | | REDUCE: (81), (159) imply:
% 230.99/42.17  | | | | | |   (162)   ~ (all_53_13 = e1)
% 230.99/42.17  | | | | | | 
% 230.99/42.17  | | | | | | REDUCE: (45), (159) imply:
% 230.99/42.17  | | | | | |   (163)   ~ (all_53_14 = e1)
% 230.99/42.17  | | | | | | 
% 230.99/42.17  | | | | | | REDUCE: (98), (159) imply:
% 230.99/42.17  | | | | | |   (164)   ~ (e3 = e1)
% 230.99/42.17  | | | | | | 
% 230.99/42.17  | | | | | | SIMP: (164) implies:
% 230.99/42.17  | | | | | |   (165)   ~ (e3 = e1)
% 230.99/42.17  | | | | | | 
% 230.99/42.17  | | | | | | REDUCE: (58), (159) imply:
% 230.99/42.17  | | | | | |   (166)   ~ (e2 = e1)
% 230.99/42.17  | | | | | | 
% 230.99/42.17  | | | | | | SIMP: (166) implies:
% 230.99/42.17  | | | | | |   (167)   ~ (e2 = e1)
% 230.99/42.17  | | | | | | 
% 230.99/42.17  | | | | | | REDUCE: (133), (159) imply:
% 230.99/42.17  | | | | | |   (168)   ~ (e1 = e0)
% 230.99/42.17  | | | | | | 
% 230.99/42.17  | | | | | | GROUND_INST: instantiating (17) with all_53_14, all_52_23, e0, e1,
% 230.99/42.17  | | | | | |              simplifying with (51), (151) gives:
% 230.99/42.17  | | | | | |   (169)  all_53_14 = all_52_23
% 230.99/42.17  | | | | | | 
% 230.99/42.17  | | | | | | GROUND_INST: instantiating (17) with e0, all_52_21, e1, e1,
% 230.99/42.17  | | | | | |              simplifying with (85), (152) gives:
% 230.99/42.17  | | | | | |   (170)  all_52_21 = e0
% 230.99/42.17  | | | | | | 
% 230.99/42.17  | | | | | | GROUND_INST: instantiating (17) with all_53_6, all_52_19, e2, e1,
% 230.99/42.17  | | | | | |              simplifying with (105), (153) gives:
% 230.99/42.17  | | | | | |   (171)  all_53_6 = all_52_19
% 230.99/42.17  | | | | | | 
% 230.99/42.17  | | | | | | COMBINE_EQS: (91), (169) imply:
% 230.99/42.17  | | | | | |   (172)  all_55_11 = all_52_23
% 230.99/42.17  | | | | | | 
% 230.99/42.17  | | | | | | COMBINE_EQS: (33), (171) imply:
% 230.99/42.17  | | | | | |   (173)  all_55_9 = all_52_19
% 230.99/42.17  | | | | | | 
% 230.99/42.17  | | | | | | REDUCE: (82), (171) imply:
% 230.99/42.17  | | | | | |   (174)   ~ (all_53_4 = all_52_19)
% 230.99/42.17  | | | | | | 
% 230.99/42.17  | | | | | | REDUCE: (52), (171) imply:
% 230.99/42.17  | | | | | |   (175)   ~ (all_53_7 = all_52_19)
% 230.99/42.17  | | | | | | 
% 230.99/42.17  | | | | | | SIMP: (175) implies:
% 230.99/42.17  | | | | | |   (176)   ~ (all_53_7 = all_52_19)
% 230.99/42.17  | | | | | | 
% 230.99/42.17  | | | | | | REDUCE: (11), (171) imply:
% 230.99/42.17  | | | | | |   (177)   ~ (all_52_19 = e0)
% 230.99/42.17  | | | | | | 
% 230.99/42.17  | | | | | | REDUCE: (102), (169) imply:
% 230.99/42.17  | | | | | |   (178)   ~ (all_53_13 = all_52_23)
% 230.99/42.17  | | | | | | 
% 230.99/42.17  | | | | | | REDUCE: (163), (169) imply:
% 230.99/42.17  | | | | | |   (179)   ~ (all_52_23 = e1)
% 230.99/42.17  | | | | | | 
% 230.99/42.17  | | | | | | REDUCE: (131), (169) imply:
% 230.99/42.17  | | | | | |   (180)   ~ (all_52_23 = e0)
% 230.99/42.17  | | | | | | 
% 230.99/42.17  | | | | | | REDUCE: (155), (170) imply:
% 230.99/42.17  | | | | | |   (181)  op(e0, e0) = e1
% 230.99/42.17  | | | | | | 
% 230.99/42.17  | | | | | | BETA: splitting (5) gives:
% 230.99/42.17  | | | | | | 
% 230.99/42.17  | | | | | | Case 1:
% 230.99/42.17  | | | | | | | 
% 230.99/42.17  | | | | | | |   (182)  all_55_1 = e3
% 230.99/42.17  | | | | | | | 
% 230.99/42.17  | | | | | | | REF_CLOSE: (50), (117), (182) are inconsistent by sub-proof #2295.
% 230.99/42.17  | | | | | | | 
% 230.99/42.17  | | | | | | Case 2:
% 230.99/42.17  | | | | | | | 
% 230.99/42.17  | | | | | | |   (183)  all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 230.99/42.17  | | | | | | | 
% 230.99/42.17  | | | | | | | BETA: splitting (63) gives:
% 230.99/42.17  | | | | | | | 
% 230.99/42.17  | | | | | | | Case 1:
% 230.99/42.17  | | | | | | | | 
% 230.99/42.17  | | | | | | | |   (184)  all_55_2 = e3
% 230.99/42.17  | | | | | | | | 
% 230.99/42.17  | | | | | | | | REF_CLOSE: (35), (61), (184) are inconsistent by sub-proof
% 230.99/42.17  | | | | | | | |            #2028.
% 230.99/42.17  | | | | | | | | 
% 230.99/42.17  | | | | | | | Case 2:
% 230.99/42.17  | | | | | | | | 
% 230.99/42.17  | | | | | | | |   (185)  all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 230.99/42.17  | | | | | | | | 
% 230.99/42.17  | | | | | | | | BETA: splitting (2) gives:
% 230.99/42.17  | | | | | | | | 
% 230.99/42.17  | | | | | | | | Case 1:
% 230.99/42.17  | | | | | | | | | 
% 230.99/42.17  | | | | | | | | |   (186)  all_55_13 = e3
% 230.99/42.17  | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | COMBINE_EQS: (87), (186) imply:
% 230.99/42.17  | | | | | | | | |   (187)  all_53_7 = e3
% 230.99/42.17  | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | SIMP: (187) implies:
% 230.99/42.17  | | | | | | | | |   (188)  all_53_7 = e3
% 230.99/42.17  | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | REDUCE: (79), (188) imply:
% 230.99/42.17  | | | | | | | | |   (189)   ~ (all_53_11 = e3)
% 230.99/42.17  | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | SIMP: (189) implies:
% 230.99/42.17  | | | | | | | | |   (190)   ~ (all_53_11 = e3)
% 230.99/42.17  | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | BETA: splitting (78) gives:
% 230.99/42.17  | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | Case 1:
% 230.99/42.17  | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | |   (191)  all_55_14 = e3
% 230.99/42.17  | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | | REF_CLOSE: (113), (190), (191) are inconsistent by sub-proof
% 230.99/42.17  | | | | | | | | | |            #2294.
% 230.99/42.17  | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | Case 2:
% 230.99/42.17  | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | |   (192)  all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 230.99/42.17  | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | | BETA: splitting (192) gives:
% 230.99/42.17  | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | | Case 1:
% 230.99/42.17  | | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | | |   (193)  all_55_14 = e2
% 230.99/42.17  | | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | | | COMBINE_EQS: (113), (193) imply:
% 230.99/42.17  | | | | | | | | | | |   (194)  all_53_11 = e2
% 230.99/42.17  | | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | | | REDUCE: (15), (194) imply:
% 230.99/42.17  | | | | | | | | | | |   (195)   ~ (all_53_8 = e2)
% 230.99/42.17  | | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | | | REDUCE: (40), (194) imply:
% 230.99/42.17  | | | | | | | | | | |   (196)   ~ (all_53_9 = e2)
% 230.99/42.17  | | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | | | BETA: splitting (185) gives:
% 230.99/42.17  | | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | | | Case 1:
% 230.99/42.17  | | | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | | | |   (197)  all_55_2 = e2
% 230.99/42.17  | | | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | | | | REF_CLOSE: (61), (195), (197) are inconsistent by sub-proof
% 230.99/42.17  | | | | | | | | | | | |            #2027.
% 230.99/42.17  | | | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | | | Case 2:
% 230.99/42.17  | | | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | | | |   (198)  all_55_2 = e1 | all_55_2 = e0
% 230.99/42.17  | | | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | | | | BETA: splitting (198) gives:
% 230.99/42.17  | | | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | | | | Case 1:
% 230.99/42.17  | | | | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | | | | |   (199)  all_55_2 = e1
% 230.99/42.17  | | | | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | | | | | COMBINE_EQS: (61), (199) imply:
% 230.99/42.17  | | | | | | | | | | | | |   (200)  all_53_8 = e1
% 230.99/42.17  | | | | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | | | | | SIMP: (200) implies:
% 230.99/42.17  | | | | | | | | | | | | |   (201)  all_53_8 = e1
% 230.99/42.17  | | | | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | | | | | REDUCE: (36), (201) imply:
% 230.99/42.17  | | | | | | | | | | | | |   (202)   ~ (all_53_9 = e1)
% 230.99/42.17  | | | | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | | | | | SIMP: (202) implies:
% 230.99/42.17  | | | | | | | | | | | | |   (203)   ~ (all_53_9 = e1)
% 230.99/42.17  | | | | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | | | | | BETA: splitting (49) gives:
% 230.99/42.17  | | | | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | | | | | Case 1:
% 230.99/42.17  | | | | | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | | | | | |   (204)  all_55_6 = e3
% 230.99/42.17  | | | | | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | | | | | | COMBINE_EQS: (68), (204) imply:
% 230.99/42.17  | | | | | | | | | | | | | |   (205)  all_53_9 = e3
% 230.99/42.17  | | | | | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | | | | | | SIMP: (205) implies:
% 230.99/42.17  | | | | | | | | | | | | | |   (206)  all_53_9 = e3
% 230.99/42.17  | | | | | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | | | | | | REDUCE: (64), (206) imply:
% 230.99/42.17  | | | | | | | | | | | | | |   (207)   ~ (all_53_13 = e3)
% 230.99/42.17  | | | | | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | | | | | | SIMP: (207) implies:
% 230.99/42.17  | | | | | | | | | | | | | |   (208)   ~ (all_53_13 = e3)
% 230.99/42.17  | | | | | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | | | | | | BETA: splitting (53) gives:
% 230.99/42.17  | | | | | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | | | | | | Case 1:
% 230.99/42.17  | | | | | | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | | | | | | |   (209)  all_55_7 = e3
% 230.99/42.17  | | | | | | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | | | | | | | REF_CLOSE: (115), (208), (209) are inconsistent by sub-proof
% 230.99/42.17  | | | | | | | | | | | | | | |            #2109.
% 230.99/42.17  | | | | | | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | | | | | | Case 2:
% 230.99/42.17  | | | | | | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | | | | | | |   (210)  all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 230.99/42.17  | | | | | | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 230.99/42.17  | | | | | | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | | | | | | | Case 1:
% 230.99/42.17  | | | | | | | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | | | | | | | |   (211)  all_55_7 = e2
% 230.99/42.17  | | | | | | | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | | | | | | | | COMBINE_EQS: (115), (211) imply:
% 230.99/42.17  | | | | | | | | | | | | | | | |   (212)  all_53_13 = e2
% 230.99/42.17  | | | | | | | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | | | | | | | | SIMP: (212) implies:
% 230.99/42.17  | | | | | | | | | | | | | | | |   (213)  all_53_13 = e2
% 230.99/42.17  | | | | | | | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | | | | | | | | REDUCE: (178), (213) imply:
% 230.99/42.17  | | | | | | | | | | | | | | | |   (214)   ~ (all_52_23 = e2)
% 230.99/42.17  | | | | | | | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | | | | | | | | SIMP: (214) implies:
% 230.99/42.17  | | | | | | | | | | | | | | | |   (215)   ~ (all_52_23 = e2)
% 230.99/42.17  | | | | | | | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | | | | | | | | BETA: splitting (30) gives:
% 230.99/42.17  | | | | | | | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | | | | | | | | Case 1:
% 230.99/42.17  | | | | | | | | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | | | | | | | | |   (216)  all_55_11 = e3
% 230.99/42.17  | | | | | | | | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (55), (154), (172), (180), (216) are
% 230.99/42.17  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2108.
% 230.99/42.17  | | | | | | | | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | | | | | | | | Case 2:
% 230.99/42.17  | | | | | | | | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | | | | | | | | |   (217)  all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 230.99/42.17  | | | | | | | | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | | | | | | | | | REF_CLOSE: (172), (179), (180), (215), (217) are inconsistent
% 230.99/42.17  | | | | | | | | | | | | | | | | |            by sub-proof #2106.
% 230.99/42.17  | | | | | | | | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | | | | | | | | End of split
% 230.99/42.17  | | | | | | | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | | | | | | | Case 2:
% 230.99/42.17  | | | | | | | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | | | | | | | |   (218)  all_55_7 = e1 | all_55_7 = e0
% 230.99/42.17  | | | | | | | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | | | | | | | | REF_CLOSE: (115), (129), (162), (218) are inconsistent by
% 230.99/42.17  | | | | | | | | | | | | | | | |            sub-proof #1322.
% 230.99/42.17  | | | | | | | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | | | | | | | End of split
% 230.99/42.17  | | | | | | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | | | | | | End of split
% 230.99/42.17  | | | | | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | | | | | Case 2:
% 230.99/42.17  | | | | | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | | | | | |   (219)  all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 230.99/42.17  | | | | | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | | | | | | REF_CLOSE: (28), (68), (196), (203), (219) are inconsistent
% 230.99/42.17  | | | | | | | | | | | | | |            by sub-proof #2160.
% 230.99/42.17  | | | | | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | | | | | End of split
% 230.99/42.17  | | | | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | | | | Case 2:
% 230.99/42.17  | | | | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | | | | |   (220)  all_55_2 = e0
% 230.99/42.17  | | | | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | | | | | REF_CLOSE: (61), (127), (220) are inconsistent by sub-proof
% 230.99/42.17  | | | | | | | | | | | | |            #2031.
% 230.99/42.17  | | | | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | | | | End of split
% 230.99/42.17  | | | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | | | End of split
% 230.99/42.17  | | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | | Case 2:
% 230.99/42.17  | | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | | |   (221)  all_55_14 = e1 | all_55_14 = e0
% 230.99/42.17  | | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | | | REF_CLOSE: (113), (125), (161), (221) are inconsistent by
% 230.99/42.17  | | | | | | | | | | |            sub-proof #1720.
% 230.99/42.17  | | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | | End of split
% 230.99/42.17  | | | | | | | | | | 
% 230.99/42.17  | | | | | | | | | End of split
% 230.99/42.17  | | | | | | | | | 
% 230.99/42.17  | | | | | | | | Case 2:
% 230.99/42.17  | | | | | | | | | 
% 230.99/42.18  | | | | | | | | |   (222)   ~ (all_55_13 = e3)
% 230.99/42.18  | | | | | | | | |   (223)  all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 230.99/42.18  | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | REDUCE: (87), (222) imply:
% 230.99/42.18  | | | | | | | | |   (224)   ~ (all_53_7 = e3)
% 230.99/42.18  | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | BETA: splitting (76) gives:
% 230.99/42.18  | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | Case 1:
% 230.99/42.18  | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | |   (225)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 230.99/42.18  | | | | | | | | | |            & op(e2, e2) = e3)
% 230.99/42.18  | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | BETA: splitting (225) gives:
% 230.99/42.18  | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | Case 1:
% 230.99/42.18  | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | |   (226)  all_57_1 = e3 & op(e3, e2) = e3
% 230.99/42.18  | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | ALPHA: (226) implies:
% 230.99/42.18  | | | | | | | | | | |   (227)  all_57_1 = e3
% 230.99/42.18  | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | BETA: splitting (38) gives:
% 230.99/42.18  | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | Case 1:
% 230.99/42.18  | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | |   (228)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 230.99/42.18  | | | | | | | | | | | |            & op(e3, e2) = e2)
% 230.99/42.18  | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | BETA: splitting (228) gives:
% 230.99/42.18  | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | Case 1:
% 230.99/42.18  | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | |   (229)  all_57_0 = e2 & op(e3, e3) = e2
% 230.99/42.18  | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | ALPHA: (229) implies:
% 230.99/42.18  | | | | | | | | | | | | |   (230)  op(e3, e3) = e2
% 230.99/42.18  | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | REF_CLOSE: (17), (48), (55), (230) are inconsistent by
% 230.99/42.18  | | | | | | | | | | | | |            sub-proof #2490.
% 230.99/42.18  | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | Case 2:
% 230.99/42.18  | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | |   (231)  all_57_1 = e2 & op(e3, e2) = e2
% 230.99/42.18  | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | REF_CLOSE: (48), (227), (231) are inconsistent by sub-proof
% 230.99/42.18  | | | | | | | | | | | | |            #1809.
% 230.99/42.18  | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | End of split
% 230.99/42.18  | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | Case 2:
% 230.99/42.18  | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | |   (232)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 230.99/42.18  | | | | | | | | | | | |            & op(e3, e0) = e2)
% 230.99/42.18  | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | BETA: splitting (232) gives:
% 230.99/42.18  | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | Case 1:
% 230.99/42.18  | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | |   (233)  all_57_4 = e2 & op(e3, e1) = e2
% 230.99/42.18  | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | REF_CLOSE: (17), (31), (32), (43), (50), (62), (69), (72),
% 230.99/42.18  | | | | | | | | | | | | |            (87), (123), (126), (156), (160), (173), (174),
% 230.99/42.18  | | | | | | | | | | | | |            (176), (177), (183), (223), (233) are inconsistent
% 230.99/42.18  | | | | | | | | | | | | |            by sub-proof #1318.
% 230.99/42.18  | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | Case 2:
% 230.99/42.18  | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | |   (234)  all_57_9 = e2 & op(e3, e0) = e2
% 230.99/42.18  | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | REF_CLOSE: (66), (70), (234) are inconsistent by sub-proof
% 230.99/42.18  | | | | | | | | | | | | |            #2486.
% 230.99/42.18  | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | End of split
% 230.99/42.18  | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | End of split
% 230.99/42.18  | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | Case 2:
% 230.99/42.18  | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | |   (235)  all_57_3 = e3 & op(e2, e2) = e3
% 230.99/42.18  | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | ALPHA: (235) implies:
% 230.99/42.18  | | | | | | | | | | |   (236)  all_57_3 = e3
% 230.99/42.18  | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | REF_CLOSE: (44), (135), (236) are inconsistent by sub-proof
% 230.99/42.18  | | | | | | | | | | |            #2358.
% 230.99/42.18  | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | End of split
% 230.99/42.18  | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | Case 2:
% 230.99/42.18  | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | |   (237)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3
% 230.99/42.18  | | | | | | | | | |            & op(e0, e2) = e3)
% 230.99/42.18  | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | BETA: splitting (237) gives:
% 230.99/42.18  | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | Case 1:
% 230.99/42.18  | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | |   (238)  all_57_7 = e3 & op(e1, e2) = e3
% 230.99/42.18  | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | ALPHA: (238) implies:
% 230.99/42.18  | | | | | | | | | | |   (239)  all_57_7 = e3
% 230.99/42.18  | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | BETA: splitting (111) gives:
% 230.99/42.18  | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | Case 1:
% 230.99/42.18  | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | |   (240)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 230.99/42.18  | | | | | | | | | | | |            & op(e1, e2) = e1)
% 230.99/42.18  | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | BETA: splitting (240) gives:
% 230.99/42.18  | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | Case 1:
% 230.99/42.18  | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | |   (241)  all_57_6 = e1 & op(e1, e3) = e1
% 230.99/42.18  | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | ALPHA: (241) implies:
% 230.99/42.18  | | | | | | | | | | | | |   (242)  all_57_6 = e1
% 230.99/42.18  | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | BETA: splitting (118) gives:
% 230.99/42.18  | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | Case 1:
% 230.99/42.18  | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | |   (243)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 230.99/42.18  | | | | | | | | | | | | | |            & op(e1, e2) = e2)
% 230.99/42.18  | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 230.99/42.18  | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | Case 1:
% 230.99/42.18  | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | |   (244)  all_57_6 = e2 & op(e1, e3) = e2
% 230.99/42.18  | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | REF_CLOSE: (167), (242), (244) are inconsistent by sub-proof
% 230.99/42.18  | | | | | | | | | | | | | | |            #1317.
% 230.99/42.18  | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | Case 2:
% 230.99/42.18  | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | |   (245)  all_57_7 = e2 & op(e1, e2) = e2
% 230.99/42.18  | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | REF_CLOSE: (48), (239), (245) are inconsistent by sub-proof
% 230.99/42.18  | | | | | | | | | | | | | | |            #2092.
% 230.99/42.18  | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | End of split
% 230.99/42.18  | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | Case 2:
% 230.99/42.18  | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | |   (246)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 230.99/42.18  | | | | | | | | | | | | | |            e2 & op(e1, e0) = e2)
% 230.99/42.18  | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 230.99/42.18  | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | Case 1:
% 230.99/42.18  | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | |   (247)  all_57_8 = e2 & op(e1, e1) = e2
% 230.99/42.18  | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | REF_CLOSE: (70), (95), (247) are inconsistent by sub-proof
% 230.99/42.18  | | | | | | | | | | | | | | |            #2005.
% 230.99/42.18  | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | Case 2:
% 230.99/42.18  | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | |   (248)  all_57_11 = e2 & op(e1, e0) = e2
% 230.99/42.18  | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | ALPHA: (248) implies:
% 230.99/42.18  | | | | | | | | | | | | | | |   (249)  all_57_11 = e2
% 230.99/42.18  | | | | | | | | | | | | | | |   (250)  op(e1, e0) = e2
% 230.99/42.18  | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | BETA: splitting (106) gives:
% 230.99/42.18  | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | Case 1:
% 230.99/42.18  | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | |   (251)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 230.99/42.18  | | | | | | | | | | | | | | | |            & op(e2, e3) = e2)
% 230.99/42.18  | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | BETA: splitting (251) gives:
% 230.99/42.18  | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | Case 1:
% 230.99/42.18  | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | |   (252)  all_57_0 = e2 & op(e3, e3) = e2
% 230.99/42.18  | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | ALPHA: (252) implies:
% 230.99/42.18  | | | | | | | | | | | | | | | | |   (253)  op(e3, e3) = e2
% 230.99/42.18  | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (48), (55), (253) are inconsistent by
% 230.99/42.18  | | | | | | | | | | | | | | | | |            sub-proof #2490.
% 230.99/42.18  | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | Case 2:
% 230.99/42.18  | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | |   (254)  all_57_2 = e2 & op(e2, e3) = e2
% 230.99/42.18  | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | ALPHA: (254) implies:
% 230.99/42.18  | | | | | | | | | | | | | | | | |   (255)  all_57_2 = e2
% 230.99/42.18  | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | BETA: splitting (116) gives:
% 230.99/42.18  | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | Case 1:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | |   (256)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 230.99/42.18  | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 230.99/42.18  | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | BETA: splitting (256) gives:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | Case 1:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | |   (257)  all_57_1 = e1 & op(e3, e2) = e1
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | ALPHA: (257) implies:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | |   (258)  all_57_1 = e1
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (17), (31), (32), (38), (43), (44), (48),
% 230.99/42.18  | | | | | | | | | | | | | | | | | | |            (50), (55), (62), (66), (69), (70), (72), (87),
% 230.99/42.18  | | | | | | | | | | | | | | | | | | |            (89), (97), (123), (126), (135), (156), (160),
% 230.99/42.18  | | | | | | | | | | | | | | | | | | |            (165), (167), (168), (173), (174), (176), (177),
% 230.99/42.18  | | | | | | | | | | | | | | | | | | |            (183), (223), (255), (258) are inconsistent by
% 230.99/42.18  | | | | | | | | | | | | | | | | | | |            sub-proof #1316.
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | Case 2:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | |   (259)  all_57_3 = e1 & op(e2, e2) = e1
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | ALPHA: (259) implies:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | |   (260)  op(e2, e2) = e1
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (39), (168), (260) are inconsistent by
% 230.99/42.18  | | | | | | | | | | | | | | | | | | |            sub-proof #2352.
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | End of split
% 230.99/42.18  | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | Case 2:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | |   (261)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 230.99/42.18  | | | | | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 230.99/42.18  | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | BETA: splitting (261) gives:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | Case 1:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | |   (262)  all_57_7 = e1 & op(e1, e2) = e1
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (239), (262) are inconsistent by sub-proof
% 230.99/42.18  | | | | | | | | | | | | | | | | | | |            #2104.
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | Case 2:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | |   (263)  all_57_13 = e1 & op(e0, e2) = e1
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | ALPHA: (263) implies:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | |   (264)  all_57_13 = e1
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | BETA: splitting (14) gives:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | Case 1:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | |   (265)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | BETA: splitting (265) gives:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | |   (266)  all_57_1 = e2 & op(e3, e2) = e2
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | ALPHA: (266) implies:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | |   (267)  all_57_1 = e2
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (83) gives:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | |   (268)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (268) gives:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | |   (269)  all_57_12 = e2 & op(e0, e3) = e2
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (269) implies:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | |   (270)  all_57_12 = e2
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10), (270) imply:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | |   (271)  e2 = e0
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (271) implies:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | |   (272)  e2 = e0
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (272) imply:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | |   (273)  all_57_1 = e0
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (44), (48), (70), (167), (239), (264), (273)
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2099.
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | |   (274)  all_57_13 = e2 & op(e0, e2) = e2
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (274) implies:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | |   (275)  all_57_13 = e2
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (264), (275) imply:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | |   (276)  e2 = e1
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (276) imply:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | |   (277)  all_57_1 = e1
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (17), (31), (32), (38), (43), (44), (48),
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | |            (50), (55), (62), (66), (69), (70), (72), (87),
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | |            (89), (97), (123), (126), (135), (156), (160),
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | |            (165), (167), (168), (173), (174), (176), (177),
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | |            (183), (223), (255), (277) are inconsistent by
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1316.
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | |   (278)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (278) gives:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | |   (279)  all_57_14 = e2 & op(e0, e1) = e2
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (279) implies:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | |   (280)  all_57_14 = e2
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8) gives:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | |   (281)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (281) gives:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | |   (282)  all_57_2 = e1 & op(e2, e3) = e1
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (282) implies:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | |   (283)  all_57_2 = e1
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (255), (283) imply:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | |   (284)  e2 = e1
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (267), (284) imply:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | |   (285)  all_57_1 = e1
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (17), (31), (32), (38), (43), (44), (48),
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | |            (50), (55), (62), (66), (69), (70), (72), (87),
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | |            (89), (97), (123), (126), (135), (156), (160),
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | |            (165), (167), (168), (173), (174), (176), (177),
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | |            (183), (223), (255), (285) are inconsistent by
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1316.
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | |   (286)  all_57_3 = e1 & op(e2, e2) = e1
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (286) implies:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | |   (287)  op(e2, e2) = e1
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (39), (168), (287) are inconsistent by
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2352.
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | |   (288)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (288) gives:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | |   (289)  all_57_5 = e1 & op(e2, e1) = e1
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (289) implies:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | |   (290)  all_57_5 = e1
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (89) gives:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | |   (291)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e3)
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (291) gives:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (292)  all_57_2 = e3 & op(e2, e3) = e3
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (292) implies:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (293)  all_57_2 = e3
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (255), (293) are inconsistent by sub-proof
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1800.
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (294)  all_57_3 = e3 & op(e2, e2) = e3
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (294) implies:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (295)  all_57_3 = e3
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (44), (295) imply:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (296)  e3 = e0
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (296) implies:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (297)  e3 = e0
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (239), (297) imply:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (298)  all_57_7 = e0
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (21), (25), (26), (48), (85), (111), (135),
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (165), (167), (168), (249), (298) are inconsistent
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1314.
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | |   (299)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e2, e0) = e3)
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (299) gives:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (300)  all_57_5 = e3 & op(e2, e1) = e3
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (300) implies:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (301)  all_57_5 = e3
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (290), (301) are inconsistent by sub-proof
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #2382.
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (302)  all_57_10 = e3 & op(e2, e0) = e3
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (302) implies:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (303)  all_57_10 = e3
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (80) gives:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (304)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (304) gives:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (305)  all_57_12 = e3 & op(e0, e3) = e3
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (305) implies:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (306)  all_57_12 = e3
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10), (306) imply:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (307)  e3 = e0
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (239), (307) imply:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (308)  all_57_7 = e0
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (21), (25), (26), (48), (85), (111), (135),
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (165), (167), (168), (249), (308) are inconsistent
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1314.
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (309)  all_57_13 = e3 & op(e0, e2) = e3
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (309) implies:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (310)  all_57_13 = e3
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (14), (44), (48), (70), (97), (116), (165),
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (167), (168), (239), (255), (303), (310) are
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1699.
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (311)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e0) = e3)
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (311) gives:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (312)  all_57_14 = e3 & op(e0, e1) = e3
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (280), (312) are inconsistent by sub-proof
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1891.
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (313)  all_57_15 = e3 & op(e0, e0) = e3
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (313) implies:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (314)  all_57_15 = e3
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (66), (70), (84), (103), (110), (135),
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (165), (167), (168), (303), (314) are inconsistent
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1982.
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | |   (315)  all_57_10 = e1 & op(e2, e0) = e1
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (88), (162), (315) are inconsistent by
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2084.
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | |   (316)  all_57_15 = e2 & op(e0, e0) = e2
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (316) implies:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | |   (317)  op(e0, e0) = e2
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (167), (181), (317) are inconsistent by
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2177.
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | End of split
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | End of split
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | |   (318)  all_57_3 = e2 & op(e2, e2) = e2
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | ALPHA: (318) implies:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | |   (319)  op(e2, e2) = e2
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (70), (151), (154), (250), (319) are
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2369.
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | End of split
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | Case 2:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | |   (320)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | BETA: splitting (320) gives:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | Case 1:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | |   (321)  all_57_7 = e2 & op(e1, e2) = e2
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (239), (321) are inconsistent by sub-proof
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | |            #2092.
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | Case 2:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | |   (322)  all_57_13 = e2 & op(e0, e2) = e2
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | ALPHA: (322) implies:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | |   (323)  all_57_13 = e2
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (264), (323) are inconsistent by sub-proof
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | |            #2327.
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | End of split
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | End of split
% 230.99/42.18  | | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | End of split
% 230.99/42.18  | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | End of split
% 230.99/42.18  | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | End of split
% 230.99/42.18  | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | Case 2:
% 230.99/42.18  | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | |   (324)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 230.99/42.18  | | | | | | | | | | | | | | | |            e2 & op(e0, e3) = e2)
% 230.99/42.18  | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | BETA: splitting (324) gives:
% 230.99/42.18  | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | Case 1:
% 230.99/42.18  | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | |   (325)  all_57_6 = e2 & op(e1, e3) = e2
% 230.99/42.18  | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (242), (325) are inconsistent by sub-proof
% 230.99/42.18  | | | | | | | | | | | | | | | | |            #1317.
% 230.99/42.18  | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | Case 2:
% 230.99/42.18  | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | |   (326)  all_57_12 = e2 & op(e0, e3) = e2
% 230.99/42.18  | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | ALPHA: (326) implies:
% 230.99/42.18  | | | | | | | | | | | | | | | | |   (327)  all_57_12 = e2
% 230.99/42.18  | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | COMBINE_EQS: (10), (327) imply:
% 230.99/42.18  | | | | | | | | | | | | | | | | |   (328)  e2 = e0
% 230.99/42.18  | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | SIMP: (328) implies:
% 230.99/42.18  | | | | | | | | | | | | | | | | |   (329)  e2 = e0
% 230.99/42.18  | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (329) imply:
% 230.99/42.18  | | | | | | | | | | | | | | | | |   (330)  all_57_11 = e0
% 230.99/42.18  | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (5), (7), (8), (10), (12), (13), (14),
% 230.99/42.18  | | | | | | | | | | | | | | | | |            (16), (17), (19), (20), (21), (22), (25), (26),
% 230.99/42.18  | | | | | | | | | | | | | | | | |            (27), (28), (29), (31), (34), (36), (37), (38),
% 230.99/42.18  | | | | | | | | | | | | | | | | |            (39), (41), (43), (44), (47), (48), (50), (54),
% 230.99/42.18  | | | | | | | | | | | | | | | | |            (55), (57), (61), (63), (65), (67), (69), (70),
% 230.99/42.18  | | | | | | | | | | | | | | | | |            (71), (72), (73), (75), (76), (77), (80), (82),
% 230.99/42.18  | | | | | | | | | | | | | | | | |            (83), (84), (85), (86), (89), (90), (92), (93),
% 230.99/42.18  | | | | | | | | | | | | | | | | |            (96), (97), (99), (100), (101), (103), (104),
% 230.99/42.18  | | | | | | | | | | | | | | | | |            (105), (106), (107), (108), (109), (110), (111),
% 230.99/42.18  | | | | | | | | | | | | | | | | |            (114), (116), (118), (119), (126), (127), (135),
% 230.99/42.18  | | | | | | | | | | | | | | | | |            (165), (167), (168), (239), (330) are inconsistent
% 230.99/42.18  | | | | | | | | | | | | | | | | |            by sub-proof #1311.
% 230.99/42.18  | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | End of split
% 230.99/42.18  | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | End of split
% 230.99/42.18  | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | End of split
% 230.99/42.18  | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | End of split
% 230.99/42.18  | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | Case 2:
% 230.99/42.18  | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | |   (331)  all_57_7 = e1 & op(e1, e2) = e1
% 230.99/42.18  | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | ALPHA: (331) implies:
% 230.99/42.18  | | | | | | | | | | | | |   (332)  all_57_7 = e1
% 230.99/42.18  | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | REF_CLOSE: (165), (239), (332) are inconsistent by sub-proof
% 230.99/42.18  | | | | | | | | | | | | |            #2115.
% 230.99/42.18  | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | End of split
% 230.99/42.18  | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | Case 2:
% 230.99/42.18  | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | |   (333)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 230.99/42.18  | | | | | | | | | | | |            e1 & op(e1, e0) = e1)
% 230.99/42.18  | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | REF_CLOSE: (17), (48), (66), (70), (85), (101), (103), (135),
% 230.99/42.18  | | | | | | | | | | | |            (165), (167), (168), (181), (333) are inconsistent
% 230.99/42.18  | | | | | | | | | | | |            by sub-proof #2009.
% 230.99/42.18  | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | End of split
% 230.99/42.18  | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | Case 2:
% 230.99/42.18  | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | |   (334)  all_57_13 = e3 & op(e0, e2) = e3
% 230.99/42.18  | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | ALPHA: (334) implies:
% 230.99/42.18  | | | | | | | | | | |   (335)  all_57_13 = e3
% 230.99/42.18  | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | BETA: splitting (83) gives:
% 230.99/42.18  | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | Case 1:
% 230.99/42.18  | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | |   (336)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 230.99/42.18  | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 230.99/42.18  | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | BETA: splitting (336) gives:
% 230.99/42.18  | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | Case 1:
% 230.99/42.18  | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | |   (337)  all_57_12 = e2 & op(e0, e3) = e2
% 230.99/42.18  | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | REF_CLOSE: (10), (70), (337) are inconsistent by sub-proof
% 230.99/42.18  | | | | | | | | | | | | |            #2462.
% 230.99/42.18  | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | Case 2:
% 230.99/42.18  | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | |   (338)  all_57_13 = e2 & op(e0, e2) = e2
% 230.99/42.18  | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | ALPHA: (338) implies:
% 230.99/42.18  | | | | | | | | | | | | |   (339)  all_57_13 = e2
% 230.99/42.18  | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | REF_CLOSE: (48), (335), (339) are inconsistent by sub-proof
% 230.99/42.18  | | | | | | | | | | | | |            #2203.
% 230.99/42.18  | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | End of split
% 230.99/42.18  | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | Case 2:
% 230.99/42.18  | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | |   (340)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 230.99/42.18  | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 230.99/42.18  | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | BETA: splitting (340) gives:
% 230.99/42.18  | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | Case 1:
% 230.99/42.18  | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | |   (341)  all_57_14 = e2 & op(e0, e1) = e2
% 230.99/42.18  | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | ALPHA: (341) implies:
% 230.99/42.18  | | | | | | | | | | | | |   (342)  all_57_14 = e2
% 230.99/42.18  | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | BETA: splitting (223) gives:
% 230.99/42.18  | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | Case 1:
% 230.99/42.18  | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | |   (343)  all_55_13 = e2
% 230.99/42.18  | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | COMBINE_EQS: (87), (343) imply:
% 230.99/42.18  | | | | | | | | | | | | | |   (344)  all_53_7 = e2
% 230.99/42.18  | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | REDUCE: (62), (344) imply:
% 230.99/42.18  | | | | | | | | | | | | | |   (345)   ~ (all_53_4 = e2)
% 230.99/42.18  | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | REDUCE: (176), (344) imply:
% 230.99/42.18  | | | | | | | | | | | | | |   (346)   ~ (all_52_19 = e2)
% 230.99/42.18  | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | SIMP: (346) implies:
% 230.99/42.18  | | | | | | | | | | | | | |   (347)   ~ (all_52_19 = e2)
% 230.99/42.18  | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | REDUCE: (224), (344) imply:
% 230.99/42.18  | | | | | | | | | | | | | |   (348)   ~ (e3 = e2)
% 230.99/42.18  | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | BETA: splitting (14) gives:
% 230.99/42.18  | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | Case 1:
% 230.99/42.18  | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | |   (349)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 230.99/42.18  | | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 230.99/42.18  | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | BETA: splitting (349) gives:
% 230.99/42.18  | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | Case 1:
% 230.99/42.18  | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | |   (350)  all_57_1 = e2 & op(e3, e2) = e2
% 230.99/42.18  | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | ALPHA: (350) implies:
% 230.99/42.18  | | | | | | | | | | | | | | | |   (351)  all_57_1 = e2
% 230.99/42.18  | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | BETA: splitting (89) gives:
% 230.99/42.18  | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | Case 1:
% 230.99/42.18  | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | |   (352)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 230.99/42.18  | | | | | | | | | | | | | | | | |            & op(e2, e2) = e3)
% 230.99/42.18  | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | BETA: splitting (352) gives:
% 230.99/42.18  | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | Case 1:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | |   (353)  all_57_2 = e3 & op(e2, e3) = e3
% 230.99/42.18  | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | ALPHA: (353) implies:
% 230.99/42.18  | | | | | | | | | | | | | | | | | |   (354)  all_57_2 = e3
% 230.99/42.18  | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (12), (17), (21), (25), (26), (31), (38),
% 230.99/42.18  | | | | | | | | | | | | | | | | | |            (44), (48), (55), (66), (70), (75), (103), (106),
% 230.99/42.18  | | | | | | | | | | | | | | | | | |            (109), (116), (135), (165), (167), (168), (181),
% 230.99/42.18  | | | | | | | | | | | | | | | | | |            (335), (342), (351), (354) are inconsistent by
% 230.99/42.18  | | | | | | | | | | | | | | | | | |            sub-proof #1310.
% 230.99/42.18  | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | Case 2:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | |   (355)  all_57_3 = e3 & op(e2, e2) = e3
% 230.99/42.18  | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | | REF_CLOSE: (44), (135), (355) are inconsistent by sub-proof
% 230.99/42.18  | | | | | | | | | | | | | | | | | |            #1309.
% 230.99/42.18  | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | End of split
% 230.99/42.18  | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | Case 2:
% 230.99/42.18  | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | |   (356)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 230.99/42.18  | | | | | | | | | | | | | | | | |            e3 & op(e2, e0) = e3)
% 230.99/42.18  | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | BETA: splitting (356) gives:
% 230.99/42.18  | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | Case 1:
% 230.99/42.18  | | | | | | | | | | | | | | | | | | 
% 230.99/42.18  | | | | | | | | | | | | | | | | | |   (357)  all_57_5 = e3 & op(e2, e1) = e3
% 230.99/42.19  | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | ALPHA: (357) implies:
% 230.99/42.19  | | | | | | | | | | | | | | | | | |   (358)  all_57_5 = e3
% 230.99/42.19  | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (32), (50), (54), (72), (85), (93), (119),
% 230.99/42.19  | | | | | | | | | | | | | | | | | |            (126), (156), (165), (167), (168), (173), (174),
% 230.99/42.19  | | | | | | | | | | | | | | | | | |            (177), (183), (342), (345), (347), (351), (358)
% 230.99/42.19  | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1307.
% 230.99/42.19  | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | Case 2:
% 230.99/42.19  | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | |   (359)  all_57_10 = e3 & op(e2, e0) = e3
% 230.99/42.19  | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | ALPHA: (359) implies:
% 230.99/42.19  | | | | | | | | | | | | | | | | | |   (360)  all_57_10 = e3
% 230.99/42.19  | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (12), (17), (21), (25), (26), (44), (48),
% 230.99/42.19  | | | | | | | | | | | | | | | | | |            (66), (70), (94), (103), (106), (116), (165),
% 230.99/42.19  | | | | | | | | | | | | | | | | | |            (167), (168), (181), (335), (351), (360) are
% 230.99/42.19  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1305.
% 230.99/42.19  | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | End of split
% 230.99/42.19  | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | End of split
% 230.99/42.19  | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | Case 2:
% 230.99/42.19  | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | |   (361)  all_57_3 = e2 & op(e2, e2) = e2
% 230.99/42.19  | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | ALPHA: (361) implies:
% 230.99/42.19  | | | | | | | | | | | | | | | |   (362)  op(e2, e2) = e2
% 230.99/42.19  | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | REF_CLOSE: (17), (39), (70), (362) are inconsistent by
% 230.99/42.19  | | | | | | | | | | | | | | | |            sub-proof #2472.
% 230.99/42.19  | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | End of split
% 230.99/42.19  | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | Case 2:
% 230.99/42.19  | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | |   (363)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 230.99/42.19  | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 230.99/42.19  | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | BETA: splitting (363) gives:
% 230.99/42.19  | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | Case 1:
% 230.99/42.19  | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | |   (364)  all_57_7 = e2 & op(e1, e2) = e2
% 230.99/42.19  | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | ALPHA: (364) implies:
% 230.99/42.19  | | | | | | | | | | | | | | | |   (365)  all_57_7 = e2
% 230.99/42.19  | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | BETA: splitting (89) gives:
% 230.99/42.19  | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | Case 1:
% 230.99/42.19  | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | |   (366)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 230.99/42.19  | | | | | | | | | | | | | | | | |            & op(e2, e2) = e3)
% 230.99/42.19  | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | BETA: splitting (366) gives:
% 230.99/42.19  | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | Case 1:
% 230.99/42.19  | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | |   (367)  all_57_2 = e3 & op(e2, e3) = e3
% 230.99/42.19  | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | ALPHA: (367) implies:
% 230.99/42.19  | | | | | | | | | | | | | | | | | |   (368)  all_57_2 = e3
% 230.99/42.19  | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | BETA: splitting (38) gives:
% 230.99/42.19  | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | Case 1:
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | |   (369)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 230.99/42.19  | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e2)
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | BETA: splitting (369) gives:
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | Case 1:
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | |   (370)  all_57_0 = e2 & op(e3, e3) = e2
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | | ALPHA: (370) implies:
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | |   (371)  op(e3, e3) = e2
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (48), (55), (371) are inconsistent by
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | |            sub-proof #2490.
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | Case 2:
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | |   (372)  all_57_1 = e2 & op(e3, e2) = e2
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | | ALPHA: (372) implies:
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | |   (373)  all_57_1 = e2
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (12), (17), (21), (25), (26), (31), (38),
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | |            (44), (48), (55), (66), (70), (75), (103), (106),
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | |            (109), (116), (135), (165), (167), (168), (181),
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | |            (335), (342), (368), (373) are inconsistent by
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | |            sub-proof #1310.
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | End of split
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | Case 2:
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | |   (374)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 230.99/42.19  | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e2)
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (17), (31), (32), (39), (43), (44), (48),
% 230.99/42.19  | | | | | | | | | | | | | | | | | | |            (50), (66), (69), (70), (72), (76), (116), (126),
% 230.99/42.19  | | | | | | | | | | | | | | | | | | |            (135), (156), (165), (167), (168), (173), (174),
% 230.99/42.19  | | | | | | | | | | | | | | | | | | |            (177), (183), (335), (345), (347), (365), (374)
% 230.99/42.19  | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1304.
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | End of split
% 230.99/42.19  | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | Case 2:
% 230.99/42.19  | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | |   (375)  all_57_3 = e3 & op(e2, e2) = e3
% 230.99/42.19  | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | ALPHA: (375) implies:
% 230.99/42.19  | | | | | | | | | | | | | | | | | |   (376)  all_57_3 = e3
% 230.99/42.19  | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | REF_CLOSE: (44), (135), (376) are inconsistent by sub-proof
% 230.99/42.19  | | | | | | | | | | | | | | | | | |            #2358.
% 230.99/42.19  | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | End of split
% 230.99/42.19  | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | Case 2:
% 230.99/42.19  | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | |   (377)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 230.99/42.19  | | | | | | | | | | | | | | | | |            e3 & op(e2, e0) = e3)
% 230.99/42.19  | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | BETA: splitting (377) gives:
% 230.99/42.19  | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | Case 1:
% 230.99/42.19  | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | |   (378)  all_57_5 = e3 & op(e2, e1) = e3
% 230.99/42.19  | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | ALPHA: (378) implies:
% 230.99/42.19  | | | | | | | | | | | | | | | | | |   (379)  all_57_5 = e3
% 230.99/42.19  | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | BETA: splitting (38) gives:
% 230.99/42.19  | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | Case 1:
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | |   (380)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 230.99/42.19  | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e2)
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | BETA: splitting (380) gives:
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | Case 1:
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | |   (381)  all_57_0 = e2 & op(e3, e3) = e2
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | | ALPHA: (381) implies:
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | |   (382)  op(e3, e3) = e2
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (48), (55), (382) are inconsistent by
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | |            sub-proof #2490.
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | Case 2:
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | |   (383)  all_57_1 = e2 & op(e3, e2) = e2
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | | ALPHA: (383) implies:
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | |   (384)  all_57_1 = e2
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (32), (50), (54), (72), (85), (93), (119),
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | |            (126), (156), (165), (167), (168), (173), (174),
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | |            (177), (183), (342), (345), (347), (379), (384)
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1307.
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | End of split
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | Case 2:
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | |   (385)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 230.99/42.19  | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e2)
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (17), (31), (32), (39), (43), (44), (48),
% 230.99/42.19  | | | | | | | | | | | | | | | | | | |            (50), (66), (69), (70), (72), (76), (116), (126),
% 230.99/42.19  | | | | | | | | | | | | | | | | | | |            (135), (156), (165), (167), (168), (173), (174),
% 230.99/42.19  | | | | | | | | | | | | | | | | | | |            (177), (183), (335), (345), (347), (365), (385)
% 230.99/42.19  | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1304.
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | End of split
% 230.99/42.19  | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | Case 2:
% 230.99/42.19  | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | |   (386)  all_57_10 = e3 & op(e2, e0) = e3
% 230.99/42.19  | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | ALPHA: (386) implies:
% 230.99/42.19  | | | | | | | | | | | | | | | | | |   (387)  all_57_10 = e3
% 230.99/42.19  | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | BETA: splitting (38) gives:
% 230.99/42.19  | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | Case 1:
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | |   (388)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 230.99/42.19  | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e2)
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | BETA: splitting (388) gives:
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | Case 1:
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | |   (389)  all_57_0 = e2 & op(e3, e3) = e2
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | | ALPHA: (389) implies:
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | |   (390)  op(e3, e3) = e2
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (48), (55), (390) are inconsistent by
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | |            sub-proof #2490.
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | Case 2:
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | |   (391)  all_57_1 = e2 & op(e3, e2) = e2
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | | ALPHA: (391) implies:
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | |   (392)  all_57_1 = e2
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (12), (17), (21), (25), (26), (44), (48),
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | |            (66), (70), (94), (103), (106), (116), (165),
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | |            (167), (168), (181), (335), (387), (392) are
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1305.
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | End of split
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | Case 2:
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | |   (393)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 230.99/42.19  | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e2)
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | BETA: splitting (393) gives:
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | Case 1:
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | |   (394)  all_57_4 = e2 & op(e3, e1) = e2
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | | ALPHA: (394) implies:
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | |   (395)  all_57_4 = e2
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (31), (32), (43), (50), (69), (70), (72),
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | |            (126), (156), (173), (174), (177), (183), (345),
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | |            (347), (395) are inconsistent by sub-proof #1319.
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | Case 2:
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | |   (396)  all_57_9 = e2 & op(e3, e0) = e2
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | | ALPHA: (396) implies:
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | |   (397)  all_57_9 = e2
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (66), (397) imply:
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | |   (398)  e2 = e0
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | | SIMP: (398) implies:
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | |   (399)  e2 = e0
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (365), (399) imply:
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | |   (400)  all_57_7 = e0
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (17), (39), (44), (48), (70), (76), (116),
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | |            (135), (165), (167), (168), (335), (400) are
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2199.
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | End of split
% 230.99/42.19  | | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | | End of split
% 230.99/42.19  | | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | | End of split
% 230.99/42.19  | | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | End of split
% 230.99/42.19  | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | Case 2:
% 230.99/42.19  | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | |   (401)  all_57_13 = e2 & op(e0, e2) = e2
% 230.99/42.19  | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | ALPHA: (401) implies:
% 230.99/42.19  | | | | | | | | | | | | | | | |   (402)  all_57_13 = e2
% 230.99/42.19  | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | | REF_CLOSE: (48), (335), (402) are inconsistent by sub-proof
% 230.99/42.19  | | | | | | | | | | | | | | | |            #2203.
% 230.99/42.19  | | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | | End of split
% 230.99/42.19  | | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | End of split
% 230.99/42.19  | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | Case 2:
% 230.99/42.19  | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | |   (403)  all_55_13 = e1 | all_55_13 = e0
% 230.99/42.19  | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | | REF_CLOSE: (87), (123), (160), (403) are inconsistent by
% 230.99/42.19  | | | | | | | | | | | | | |            sub-proof #1837.
% 230.99/42.19  | | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | End of split
% 230.99/42.19  | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | Case 2:
% 230.99/42.19  | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | |   (404)  all_57_15 = e2 & op(e0, e0) = e2
% 230.99/42.19  | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | ALPHA: (404) implies:
% 230.99/42.19  | | | | | | | | | | | | |   (405)  op(e0, e0) = e2
% 230.99/42.19  | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | | REF_CLOSE: (17), (167), (181), (405) are inconsistent by
% 230.99/42.19  | | | | | | | | | | | | |            sub-proof #2177.
% 230.99/42.19  | | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | | End of split
% 230.99/42.19  | | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | | End of split
% 230.99/42.19  | | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | | End of split
% 230.99/42.19  | | | | | | | | | | 
% 230.99/42.19  | | | | | | | | | End of split
% 230.99/42.19  | | | | | | | | | 
% 230.99/42.19  | | | | | | | | End of split
% 230.99/42.19  | | | | | | | | 
% 230.99/42.19  | | | | | | | End of split
% 230.99/42.19  | | | | | | | 
% 230.99/42.19  | | | | | | End of split
% 230.99/42.19  | | | | | | 
% 230.99/42.19  | | | | | Case 2:
% 230.99/42.19  | | | | | | 
% 230.99/42.19  | | | | | |   (406)  all_55_15 = e0
% 230.99/42.19  | | | | | | 
% 230.99/42.19  | | | | | | REF_CLOSE: (18), (133), (406) are inconsistent by sub-proof #1884.
% 230.99/42.19  | | | | | | 
% 230.99/42.19  | | | | | End of split
% 230.99/42.19  | | | | | 
% 230.99/42.19  | | | | Case 2:
% 230.99/42.19  | | | | | 
% 230.99/42.19  | | | | |   (407)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30
% 230.99/42.19  | | | | |          = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 230.99/42.19  | | | | |            all_52_27) = e2 & op(all_52_29, all_52_29) = e1 &
% 230.99/42.19  | | | | |          op(all_52_31, all_52_31) = e0 & op(e0, e3) = all_52_25 &
% 230.99/42.19  | | | | |          op(e0, e2) = all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 230.99/42.19  | | | | |          = all_52_31 & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 230.99/42.19  | | | | |          $i(all_52_31)
% 230.99/42.19  | | | | | 
% 230.99/42.19  | | | | | ALPHA: (407) implies:
% 230.99/42.19  | | | | |   (408)  op(e0, e0) = all_52_31
% 230.99/42.19  | | | | |   (409)  op(e0, e3) = all_52_25
% 230.99/42.19  | | | | |   (410)  op(all_52_25, all_52_25) = e3
% 230.99/42.19  | | | | | 
% 230.99/42.19  | | | | | REF_CLOSE: (4), (17), (18), (23), (48), (58), (66), (70), (81), (88),
% 230.99/42.19  | | | | |            (98), (101), (103), (110), (133), (135), (141), (408),
% 230.99/42.19  | | | | |            (409), (410) are inconsistent by sub-proof #1302.
% 230.99/42.19  | | | | | 
% 230.99/42.19  | | | | End of split
% 230.99/42.19  | | | | 
% 230.99/42.19  | | | End of split
% 230.99/42.19  | | | 
% 230.99/42.19  | | End of split
% 230.99/42.19  | | 
% 230.99/42.19  | End of split
% 230.99/42.19  | 
% 230.99/42.19  End of proof
% 230.99/42.19  
% 230.99/42.19  Sub-proof #1302 shows that the following formulas are inconsistent:
% 230.99/42.19  ----------------------------------------------------------------
% 230.99/42.19    (1)  op(e0, e0) = all_4_2
% 230.99/42.19    (2)   ~ (all_4_2 = e0)
% 230.99/42.19    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.99/42.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.99/42.19    (4)  all_55_15 = all_4_2
% 230.99/42.19    (5)  op(e0, e3) = e0
% 230.99/42.19    (6)  op(e0, e3) = all_52_25
% 230.99/42.19    (7)   ~ (e3 = e2)
% 230.99/42.19    (8)   ~ (e3 = e0)
% 230.99/42.19    (9)   ~ (all_4_2 = e2)
% 230.99/42.19    (10)  op(e0, e0) = all_52_31
% 230.99/42.19    (11)  op(all_52_25, all_52_25) = e3
% 230.99/42.19    (12)  all_57_9 = e0
% 230.99/42.19    (13)   ~ (e2 = e0)
% 230.99/42.19    (14)   ~ (all_53_13 = all_4_2)
% 230.99/42.19    (15)  op(e2, e0) = all_53_13
% 230.99/42.19    (16)  all_55_15 = e1 | all_55_15 = e0
% 230.99/42.19    (17)   ~ (all_4_2 = e3)
% 230.99/42.19    (18)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 230.99/42.19          (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 230.99/42.19    (19)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.99/42.19          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.99/42.19    (20)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.99/42.19          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.99/42.19  
% 230.99/42.19  Begin of proof
% 230.99/42.19  | 
% 230.99/42.19  | BETA: splitting (16) gives:
% 230.99/42.19  | 
% 230.99/42.19  | Case 1:
% 230.99/42.19  | | 
% 230.99/42.19  | |   (21)  all_55_15 = e1
% 230.99/42.19  | | 
% 230.99/42.19  | | COMBINE_EQS: (4), (21) imply:
% 230.99/42.19  | |   (22)  all_4_2 = e1
% 230.99/42.19  | | 
% 230.99/42.19  | | SIMP: (22) implies:
% 230.99/42.19  | |   (23)  all_4_2 = e1
% 230.99/42.19  | | 
% 230.99/42.19  | | REDUCE: (14), (23) imply:
% 230.99/42.19  | |   (24)   ~ (all_53_13 = e1)
% 230.99/42.19  | | 
% 230.99/42.19  | | REDUCE: (17), (23) imply:
% 230.99/42.19  | |   (25)   ~ (e3 = e1)
% 230.99/42.19  | | 
% 230.99/42.19  | | SIMP: (25) implies:
% 230.99/42.19  | |   (26)   ~ (e3 = e1)
% 230.99/42.19  | | 
% 230.99/42.19  | | REDUCE: (9), (23) imply:
% 230.99/42.19  | |   (27)   ~ (e2 = e1)
% 230.99/42.19  | | 
% 230.99/42.19  | | SIMP: (27) implies:
% 230.99/42.19  | |   (28)   ~ (e2 = e1)
% 230.99/42.19  | | 
% 230.99/42.19  | | REDUCE: (2), (23) imply:
% 230.99/42.19  | |   (29)   ~ (e1 = e0)
% 230.99/42.19  | | 
% 230.99/42.19  | | REDUCE: (1), (23) imply:
% 230.99/42.19  | |   (30)  op(e0, e0) = e1
% 230.99/42.19  | | 
% 230.99/42.19  | | REF_CLOSE: (3), (5), (6), (7), (8), (10), (11), (12), (13), (15), (18),
% 230.99/42.19  | |            (19), (20), (24), (26), (28), (29), (30) are inconsistent by
% 230.99/42.19  | |            sub-proof #1303.
% 230.99/42.19  | | 
% 230.99/42.19  | Case 2:
% 230.99/42.19  | | 
% 230.99/42.19  | |   (31)  all_55_15 = e0
% 230.99/42.19  | | 
% 230.99/42.19  | | REF_CLOSE: (2), (4), (31) are inconsistent by sub-proof #1884.
% 230.99/42.19  | | 
% 230.99/42.19  | End of split
% 230.99/42.19  | 
% 230.99/42.19  End of proof
% 230.99/42.19  
% 230.99/42.19  Sub-proof #1303 shows that the following formulas are inconsistent:
% 230.99/42.19  ----------------------------------------------------------------
% 230.99/42.19    (1)   ~ (e3 = e1)
% 230.99/42.19    (2)   ~ (all_53_13 = e1)
% 230.99/42.19    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.99/42.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.99/42.19    (4)  op(e0, e3) = e0
% 230.99/42.19    (5)  op(e0, e3) = all_52_25
% 230.99/42.19    (6)   ~ (e3 = e2)
% 230.99/42.19    (7)   ~ (e3 = e0)
% 230.99/42.19    (8)  op(e0, e0) = all_52_31
% 230.99/42.19    (9)  op(all_52_25, all_52_25) = e3
% 230.99/42.19    (10)  all_57_9 = e0
% 230.99/42.19    (11)   ~ (e2 = e0)
% 230.99/42.19    (12)   ~ (e1 = e0)
% 230.99/42.19    (13)  op(e0, e0) = e1
% 230.99/42.19    (14)  op(e2, e0) = all_53_13
% 230.99/42.19    (15)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 230.99/42.19          (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 230.99/42.19    (16)   ~ (e2 = e1)
% 230.99/42.19    (17)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.99/42.19          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.99/42.19    (18)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.99/42.19          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.99/42.19  
% 230.99/42.19  Begin of proof
% 230.99/42.19  | 
% 230.99/42.19  | BETA: splitting (18) gives:
% 230.99/42.19  | 
% 230.99/42.19  | Case 1:
% 230.99/42.19  | | 
% 230.99/42.19  | |   (19)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) =
% 230.99/42.19  | |           e1)
% 230.99/42.19  | | 
% 230.99/42.19  | | REF_CLOSE: (2), (3), (10), (12), (14), (19) are inconsistent by sub-proof
% 230.99/42.19  | |            #1324.
% 230.99/42.19  | | 
% 230.99/42.19  | Case 2:
% 230.99/42.19  | | 
% 230.99/42.19  | |   (20)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.99/42.19  | |           e1)
% 230.99/42.19  | | 
% 230.99/42.19  | | BETA: splitting (20) gives:
% 230.99/42.19  | | 
% 230.99/42.19  | | Case 1:
% 230.99/42.19  | | | 
% 230.99/42.19  | | |   (21)  all_57_11 = e1 & op(e1, e0) = e1
% 230.99/42.19  | | | 
% 230.99/42.19  | | | ALPHA: (21) implies:
% 230.99/42.19  | | |   (22)  all_57_11 = e1
% 230.99/42.19  | | | 
% 230.99/42.19  | | | REF_CLOSE: (1), (3), (6), (7), (10), (11), (13), (15), (16), (17), (22)
% 230.99/42.19  | | |            are inconsistent by sub-proof #2047.
% 230.99/42.19  | | | 
% 230.99/42.19  | | Case 2:
% 230.99/42.19  | | | 
% 230.99/42.19  | | |   (23)  all_57_15 = e1 & op(e0, e0) = e1
% 230.99/42.19  | | | 
% 230.99/42.19  | | | REF_CLOSE: (1), (3), (4), (5), (8), (9), (23) are inconsistent by
% 230.99/42.19  | | |            sub-proof #1963.
% 230.99/42.19  | | | 
% 230.99/42.19  | | End of split
% 230.99/42.19  | | 
% 230.99/42.19  | End of split
% 230.99/42.19  | 
% 230.99/42.19  End of proof
% 230.99/42.19  
% 230.99/42.19  Sub-proof #1304 shows that the following formulas are inconsistent:
% 230.99/42.19  ----------------------------------------------------------------
% 230.99/42.19    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.99/42.19         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.99/42.19    (2)   ~ (e3 = e1)
% 230.99/42.19    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.99/42.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.99/42.19    (4)  all_55_9 = all_52_19
% 230.99/42.19    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.99/42.19         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.99/42.19    (6)  all_57_7 = e2
% 230.99/42.19    (7)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 230.99/42.19    (8)  op(e2, e2) = e0
% 230.99/42.19    (9)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.99/42.19         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.99/42.19    (10)  all_57_3 = e0
% 230.99/42.19    (11)  all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 230.99/42.19    (12)   ~ (e3 = e2)
% 230.99/42.19    (13)  all_55_1 = all_53_4
% 230.99/42.19    (14)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.99/42.19    (15)   ~ (e3 = e0)
% 230.99/42.19    (16)  all_57_9 = e0
% 230.99/42.19    (17)  op(e3, e2) = all_53_4
% 230.99/42.19    (18)   ~ (all_53_4 = all_52_19)
% 230.99/42.19    (19)   ~ (e2 = e0)
% 230.99/42.19    (20)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.99/42.19          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.99/42.19    (21)   ~ (e1 = e0)
% 230.99/42.19    (22)   ~ (all_53_4 = e0)
% 230.99/42.19    (23)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.99/42.19          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.99/42.19    (24)  all_57_13 = e3
% 230.99/42.19    (25)   ~ (all_52_19 = e0)
% 230.99/42.19    (26)   ~ (all_53_4 = e2)
% 230.99/42.19    (27)  op(all_52_19, all_52_19) = e2
% 230.99/42.19    (28)   ~ (all_52_19 = e2)
% 230.99/42.19    (29)   ~ (e2 = e1)
% 230.99/42.19    (30)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.99/42.19          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.99/42.19  
% 230.99/42.19  Begin of proof
% 230.99/42.19  | 
% 230.99/42.19  | BETA: splitting (14) gives:
% 230.99/42.19  | 
% 230.99/42.19  | Case 1:
% 230.99/42.19  | | 
% 230.99/42.19  | |   (31)  all_57_4 = e2 & op(e3, e1) = e2
% 230.99/42.19  | | 
% 230.99/42.19  | | ALPHA: (31) implies:
% 230.99/42.19  | |   (32)  all_57_4 = e2
% 230.99/42.19  | | 
% 230.99/42.19  | | REF_CLOSE: (3), (4), (5), (7), (9), (11), (13), (17), (18), (19), (20),
% 230.99/42.19  | |            (22), (25), (26), (27), (28), (32) are inconsistent by sub-proof
% 230.99/42.19  | |            #1319.
% 230.99/42.19  | | 
% 230.99/42.19  | Case 2:
% 230.99/42.19  | | 
% 230.99/42.19  | |   (33)  all_57_9 = e2 & op(e3, e0) = e2
% 230.99/42.19  | | 
% 230.99/42.19  | | ALPHA: (33) implies:
% 230.99/42.19  | |   (34)  all_57_9 = e2
% 230.99/42.19  | | 
% 230.99/42.19  | | COMBINE_EQS: (16), (34) imply:
% 230.99/42.19  | |   (35)  e2 = e0
% 230.99/42.19  | | 
% 230.99/42.19  | | COMBINE_EQS: (6), (35) imply:
% 230.99/42.19  | |   (36)  all_57_7 = e0
% 230.99/42.19  | | 
% 230.99/42.19  | | REF_CLOSE: (1), (2), (3), (8), (10), (12), (15), (19), (21), (23), (24),
% 230.99/42.19  | |            (29), (30), (36) are inconsistent by sub-proof #2199.
% 230.99/42.19  | | 
% 230.99/42.19  | End of split
% 230.99/42.19  | 
% 230.99/42.19  End of proof
% 230.99/42.19  
% 230.99/42.19  Sub-proof #1305 shows that the following formulas are inconsistent:
% 230.99/42.19  ----------------------------------------------------------------
% 230.99/42.19    (1)  all_57_12 = e0
% 230.99/42.19    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.99/42.19         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.99/42.19    (3)   ~ (e3 = e1)
% 230.99/42.19    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.99/42.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.99/42.19    (5)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.99/42.19         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.99/42.19    (6)   ~ (all_6_2 = e3)
% 230.99/42.19    (7)  op(e1, e1) = all_6_2
% 230.99/42.19    (8)  all_57_3 = e0
% 230.99/42.19    (9)   ~ (e3 = e2)
% 230.99/42.19    (10)  all_57_1 = e2
% 230.99/42.19    (11)  all_57_9 = e0
% 230.99/42.19    (12)   ~ (e2 = e0)
% 230.99/42.19    (13)   ~ (e1 = e0)
% 230.99/42.19    (14)  all_57_13 = e3
% 230.99/42.19    (15)  all_57_10 = e3
% 230.99/42.19    (16)  op(e0, e0) = e1
% 230.99/42.19    (17)  all_57_0 = e3
% 230.99/42.19    (18)   ~ (e2 = e1)
% 230.99/42.19    (19)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.99/42.19          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.99/42.19    (20)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.99/42.19          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.99/42.19    (21)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.99/42.19          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.99/42.19  
% 230.99/42.19  Begin of proof
% 230.99/42.19  | 
% 230.99/42.19  | BETA: splitting (19) gives:
% 230.99/42.19  | 
% 230.99/42.19  | Case 1:
% 230.99/42.19  | | 
% 230.99/42.19  | |   (22)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 230.99/42.19  | |           e2)
% 230.99/42.19  | | 
% 230.99/42.19  | | BETA: splitting (22) gives:
% 230.99/42.19  | | 
% 230.99/42.19  | | Case 1:
% 230.99/42.19  | | | 
% 230.99/42.19  | | |   (23)  all_57_9 = e2 & op(e3, e0) = e2
% 230.99/42.19  | | | 
% 230.99/42.19  | | | ALPHA: (23) implies:
% 230.99/42.19  | | |   (24)  all_57_9 = e2
% 230.99/42.19  | | | 
% 230.99/42.19  | | | REF_CLOSE: (11), (12), (24) are inconsistent by sub-proof #2440.
% 230.99/42.19  | | | 
% 230.99/42.19  | | Case 2:
% 230.99/42.19  | | | 
% 230.99/42.19  | | |   (25)  all_57_10 = e2 & op(e2, e0) = e2
% 230.99/42.19  | | | 
% 230.99/42.19  | | | ALPHA: (25) implies:
% 230.99/42.19  | | |   (26)  all_57_10 = e2
% 230.99/42.19  | | | 
% 230.99/42.19  | | | REF_CLOSE: (9), (15), (26) are inconsistent by sub-proof #2356.
% 230.99/42.19  | | | 
% 230.99/42.19  | | End of split
% 230.99/42.19  | | 
% 230.99/42.19  | Case 2:
% 230.99/42.19  | | 
% 230.99/42.20  | |   (27)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.99/42.20  | |           e2)
% 230.99/42.20  | | 
% 230.99/42.20  | | BETA: splitting (27) gives:
% 230.99/42.20  | | 
% 230.99/42.20  | | Case 1:
% 230.99/42.20  | | | 
% 230.99/42.20  | | |   (28)  all_57_11 = e2 & op(e1, e0) = e2
% 230.99/42.20  | | | 
% 230.99/42.20  | | | ALPHA: (28) implies:
% 230.99/42.20  | | |   (29)  all_57_11 = e2
% 230.99/42.20  | | | 
% 230.99/42.20  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 230.99/42.20  | | |            (14), (17), (18), (20), (21), (29) are inconsistent by
% 230.99/42.20  | | |            sub-proof #1306.
% 230.99/42.20  | | | 
% 230.99/42.20  | | Case 2:
% 230.99/42.20  | | | 
% 230.99/42.20  | | |   (30)  all_57_15 = e2 & op(e0, e0) = e2
% 230.99/42.20  | | | 
% 230.99/42.20  | | | ALPHA: (30) implies:
% 230.99/42.20  | | |   (31)  op(e0, e0) = e2
% 230.99/42.20  | | | 
% 230.99/42.20  | | | REF_CLOSE: (4), (16), (18), (31) are inconsistent by sub-proof #2177.
% 230.99/42.20  | | | 
% 230.99/42.20  | | End of split
% 230.99/42.20  | | 
% 230.99/42.20  | End of split
% 230.99/42.20  | 
% 230.99/42.20  End of proof
% 230.99/42.20  
% 230.99/42.20  Sub-proof #1306 shows that the following formulas are inconsistent:
% 230.99/42.20  ----------------------------------------------------------------
% 230.99/42.20    (1)  all_57_12 = e0
% 230.99/42.20    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.99/42.20         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.99/42.20    (3)   ~ (e3 = e1)
% 230.99/42.20    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.99/42.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.99/42.20    (5)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.99/42.20         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.99/42.20    (6)   ~ (all_6_2 = e3)
% 230.99/42.20    (7)  op(e1, e1) = all_6_2
% 230.99/42.20    (8)  all_57_3 = e0
% 230.99/42.20    (9)   ~ (e3 = e2)
% 230.99/42.20    (10)  all_57_1 = e2
% 230.99/42.20    (11)  all_57_11 = e2
% 230.99/42.20    (12)   ~ (e2 = e0)
% 230.99/42.20    (13)   ~ (e1 = e0)
% 230.99/42.20    (14)  all_57_13 = e3
% 230.99/42.20    (15)  all_57_0 = e3
% 230.99/42.20    (16)   ~ (e2 = e1)
% 230.99/42.20    (17)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.99/42.20          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.99/42.20    (18)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.99/42.20          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.99/42.20  
% 230.99/42.20  Begin of proof
% 230.99/42.20  | 
% 230.99/42.20  | BETA: splitting (5) gives:
% 230.99/42.20  | 
% 230.99/42.20  | Case 1:
% 230.99/42.20  | | 
% 230.99/42.20  | |   (19)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 230.99/42.20  | |           e3)
% 230.99/42.20  | | 
% 230.99/42.20  | | BETA: splitting (19) gives:
% 230.99/42.20  | | 
% 230.99/42.20  | | Case 1:
% 230.99/42.20  | | | 
% 230.99/42.20  | | |   (20)  all_57_6 = e3 & op(e1, e3) = e3
% 230.99/42.20  | | | 
% 230.99/42.20  | | | ALPHA: (20) implies:
% 230.99/42.20  | | |   (21)  all_57_6 = e3
% 230.99/42.20  | | | 
% 230.99/42.20  | | | REF_CLOSE: (1), (2), (3), (9), (12), (13), (15), (16), (17), (21) are
% 230.99/42.20  | | |            inconsistent by sub-proof #2011.
% 230.99/42.20  | | | 
% 230.99/42.20  | | Case 2:
% 230.99/42.20  | | | 
% 230.99/42.20  | | |   (22)  all_57_7 = e3 & op(e1, e2) = e3
% 230.99/42.20  | | | 
% 230.99/42.20  | | | ALPHA: (22) implies:
% 230.99/42.20  | | |   (23)  all_57_7 = e3
% 230.99/42.20  | | | 
% 230.99/42.20  | | | REF_CLOSE: (3), (8), (10), (13), (14), (16), (18), (23) are inconsistent
% 230.99/42.20  | | |            by sub-proof #2008.
% 230.99/42.20  | | | 
% 230.99/42.20  | | End of split
% 230.99/42.20  | | 
% 230.99/42.20  | Case 2:
% 230.99/42.20  | | 
% 230.99/42.20  | |   (24)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 230.99/42.20  | |           e3)
% 230.99/42.20  | | 
% 230.99/42.20  | | REF_CLOSE: (4), (6), (7), (9), (11), (24) are inconsistent by sub-proof
% 230.99/42.20  | |            #2344.
% 230.99/42.20  | | 
% 230.99/42.20  | End of split
% 230.99/42.20  | 
% 230.99/42.20  End of proof
% 230.99/42.20  
% 230.99/42.20  Sub-proof #1307 shows that the following formulas are inconsistent:
% 230.99/42.20  ----------------------------------------------------------------
% 230.99/42.20    (1)   ~ (e3 = e1)
% 230.99/42.20    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.99/42.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.99/42.20    (3)  all_55_9 = all_52_19
% 230.99/42.20    (4)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 230.99/42.20    (5)  all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 230.99/42.20    (6)  all_55_1 = all_53_4
% 230.99/42.20    (7)  all_57_1 = e2
% 230.99/42.20    (8)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.99/42.20         (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.99/42.20    (9)  all_57_5 = e3
% 230.99/42.20    (10)   ~ (all_53_4 = all_52_19)
% 230.99/42.20    (11)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.99/42.20          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.99/42.20    (12)   ~ (e1 = e0)
% 230.99/42.20    (13)  all_57_14 = e2
% 230.99/42.20    (14)   ~ (all_53_4 = e0)
% 230.99/42.20    (15)   ~ (all_52_19 = e0)
% 230.99/42.20    (16)  op(e1, e1) = e0
% 230.99/42.20    (17)   ~ (all_53_12 = e3)
% 230.99/42.20    (18)   ~ (all_53_4 = e2)
% 230.99/42.20    (19)  op(all_52_19, all_52_19) = e2
% 230.99/42.20    (20)   ~ (all_52_19 = e2)
% 230.99/42.20    (21)   ~ (e2 = e1)
% 230.99/42.20    (22)  op(e3, e0) = all_53_12
% 230.99/42.20  
% 230.99/42.20  Begin of proof
% 230.99/42.20  | 
% 230.99/42.20  | BETA: splitting (8) gives:
% 230.99/42.20  | 
% 230.99/42.20  | Case 1:
% 230.99/42.20  | | 
% 230.99/42.20  | |   (23)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) =
% 230.99/42.20  | |           e1)
% 230.99/42.20  | | 
% 230.99/42.20  | | BETA: splitting (23) gives:
% 230.99/42.20  | | 
% 230.99/42.20  | | Case 1:
% 230.99/42.20  | | | 
% 230.99/42.20  | | |   (24)  all_57_4 = e1 & op(e3, e1) = e1
% 230.99/42.20  | | | 
% 230.99/42.20  | | | ALPHA: (24) implies:
% 230.99/42.20  | | |   (25)  all_57_4 = e1
% 230.99/42.20  | | | 
% 230.99/42.20  | | | BETA: splitting (5) gives:
% 230.99/42.20  | | | 
% 230.99/42.20  | | | Case 1:
% 230.99/42.20  | | | | 
% 230.99/42.20  | | | |   (26)  all_55_1 = e2
% 230.99/42.20  | | | | 
% 230.99/42.20  | | | | REF_CLOSE: (6), (18), (26) are inconsistent by sub-proof #2284.
% 230.99/42.20  | | | | 
% 230.99/42.20  | | | Case 2:
% 230.99/42.20  | | | | 
% 230.99/42.20  | | | |   (27)  all_55_1 = e1 | all_55_1 = e0
% 230.99/42.20  | | | | 
% 230.99/42.20  | | | | BETA: splitting (27) gives:
% 230.99/42.20  | | | | 
% 230.99/42.20  | | | | Case 1:
% 230.99/42.20  | | | | | 
% 230.99/42.20  | | | | |   (28)  all_55_1 = e1
% 230.99/42.20  | | | | | 
% 230.99/42.20  | | | | | COMBINE_EQS: (6), (28) imply:
% 230.99/42.20  | | | | |   (29)  all_53_4 = e1
% 230.99/42.20  | | | | | 
% 230.99/42.20  | | | | | SIMP: (29) implies:
% 230.99/42.20  | | | | |   (30)  all_53_4 = e1
% 230.99/42.20  | | | | | 
% 230.99/42.20  | | | | | REDUCE: (10), (30) imply:
% 230.99/42.20  | | | | |   (31)   ~ (all_52_19 = e1)
% 230.99/42.20  | | | | | 
% 230.99/42.20  | | | | | SIMP: (31) implies:
% 230.99/42.20  | | | | |   (32)   ~ (all_52_19 = e1)
% 230.99/42.20  | | | | | 
% 230.99/42.20  | | | | | BETA: splitting (4) gives:
% 230.99/42.20  | | | | | 
% 230.99/42.20  | | | | | Case 1:
% 230.99/42.20  | | | | | | 
% 230.99/42.20  | | | | | |   (33)  all_55_9 = e3
% 230.99/42.20  | | | | | | 
% 230.99/42.20  | | | | | | COMBINE_EQS: (3), (33) imply:
% 230.99/42.20  | | | | | |   (34)  all_52_19 = e3
% 230.99/42.20  | | | | | | 
% 230.99/42.20  | | | | | | REDUCE: (20), (34) imply:
% 230.99/42.20  | | | | | |   (35)   ~ (e3 = e2)
% 230.99/42.20  | | | | | | 
% 230.99/42.20  | | | | | | REDUCE: (19), (34) imply:
% 230.99/42.20  | | | | | |   (36)  op(e3, e3) = e2
% 230.99/42.20  | | | | | | 
% 230.99/42.20  | | | | | | REF_CLOSE: (1), (2), (7), (11), (17), (22), (25), (35), (36) are
% 230.99/42.20  | | | | | |            inconsistent by sub-proof #1308.
% 230.99/42.20  | | | | | | 
% 230.99/42.20  | | | | | Case 2:
% 230.99/42.20  | | | | | | 
% 230.99/42.20  | | | | | |   (37)  all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 230.99/42.20  | | | | | | 
% 230.99/42.20  | | | | | | REF_CLOSE: (3), (15), (20), (32), (37) are inconsistent by sub-proof
% 230.99/42.20  | | | | | |            #1882.
% 230.99/42.20  | | | | | | 
% 230.99/42.20  | | | | | End of split
% 230.99/42.20  | | | | | 
% 230.99/42.20  | | | | Case 2:
% 230.99/42.20  | | | | | 
% 230.99/42.20  | | | | |   (38)  all_55_1 = e0
% 230.99/42.20  | | | | | 
% 230.99/42.20  | | | | | REF_CLOSE: (6), (14), (38) are inconsistent by sub-proof #2076.
% 230.99/42.20  | | | | | 
% 230.99/42.20  | | | | End of split
% 230.99/42.20  | | | | 
% 230.99/42.20  | | | End of split
% 230.99/42.20  | | | 
% 230.99/42.20  | | Case 2:
% 230.99/42.20  | | | 
% 230.99/42.20  | | |   (39)  all_57_5 = e1 & op(e2, e1) = e1
% 230.99/42.20  | | | 
% 230.99/42.20  | | | REF_CLOSE: (1), (9), (39) are inconsistent by sub-proof #2376.
% 230.99/42.20  | | | 
% 230.99/42.20  | | End of split
% 230.99/42.20  | | 
% 230.99/42.20  | Case 2:
% 230.99/42.20  | | 
% 230.99/42.20  | |   (40)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) =
% 230.99/42.20  | |           e1)
% 230.99/42.20  | | 
% 230.99/42.20  | | REF_CLOSE: (2), (12), (13), (16), (21), (40) are inconsistent by sub-proof
% 230.99/42.20  | |            #2374.
% 230.99/42.20  | | 
% 230.99/42.20  | End of split
% 230.99/42.20  | 
% 230.99/42.20  End of proof
% 230.99/42.20  
% 230.99/42.20  Sub-proof #1308 shows that the following formulas are inconsistent:
% 230.99/42.20  ----------------------------------------------------------------
% 230.99/42.20    (1)   ~ (e3 = e1)
% 230.99/42.20    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.99/42.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.99/42.20    (3)   ~ (e3 = e2)
% 230.99/42.20    (4)  all_57_1 = e2
% 230.99/42.20    (5)  op(e3, e3) = e2
% 230.99/42.20    (6)  all_57_4 = e1
% 230.99/42.20    (7)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.99/42.20         (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.99/42.20    (8)   ~ (all_53_12 = e3)
% 230.99/42.20    (9)  op(e3, e0) = all_53_12
% 230.99/42.20  
% 230.99/42.20  Begin of proof
% 230.99/42.20  | 
% 230.99/42.20  | BETA: splitting (7) gives:
% 230.99/42.20  | 
% 230.99/42.20  | Case 1:
% 230.99/42.20  | | 
% 230.99/42.20  | |   (10)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) =
% 230.99/42.20  | |           e3)
% 230.99/42.20  | | 
% 230.99/42.20  | | REF_CLOSE: (2), (3), (4), (5), (10) are inconsistent by sub-proof #1663.
% 230.99/42.20  | | 
% 230.99/42.20  | Case 2:
% 230.99/42.20  | | 
% 230.99/42.20  | |   (11)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) =
% 230.99/42.20  | |           e3)
% 230.99/42.20  | | 
% 230.99/42.20  | | REF_CLOSE: (1), (2), (6), (8), (9), (11) are inconsistent by sub-proof
% 230.99/42.20  | |            #2281.
% 230.99/42.20  | | 
% 230.99/42.20  | End of split
% 230.99/42.20  | 
% 230.99/42.20  End of proof
% 230.99/42.20  
% 230.99/42.20  Sub-proof #1309 shows that the following formulas are inconsistent:
% 230.99/42.20  ----------------------------------------------------------------
% 230.99/42.20    (1)  all_57_3 = e3 & op(e2, e2) = e3
% 230.99/42.20    (2)  all_57_3 = e0
% 230.99/42.20    (3)   ~ (e3 = e0)
% 230.99/42.20  
% 230.99/42.20  Begin of proof
% 230.99/42.20  | 
% 230.99/42.20  | ALPHA: (1) implies:
% 230.99/42.20  |   (4)  all_57_3 = e3
% 230.99/42.20  | 
% 230.99/42.20  | COMBINE_EQS: (2), (4) imply:
% 230.99/42.20  |   (5)  e3 = e0
% 230.99/42.20  | 
% 230.99/42.20  | REDUCE: (3), (5) imply:
% 230.99/42.20  |   (6)  $false
% 230.99/42.20  | 
% 230.99/42.20  | CLOSE: (6) is inconsistent.
% 230.99/42.20  | 
% 230.99/42.20  End of proof
% 230.99/42.20  
% 230.99/42.20  Sub-proof #1310 shows that the following formulas are inconsistent:
% 230.99/42.20  ----------------------------------------------------------------
% 230.99/42.20    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.99/42.20         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.99/42.20    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.99/42.20         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.99/42.20    (3)   ~ (e3 = e1)
% 230.99/42.20    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.99/42.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.99/42.20    (5)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.99/42.20         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.99/42.20    (6)   ~ (all_6_2 = e3)
% 230.99/42.20    (7)  op(e1, e1) = all_6_2
% 230.99/42.20    (8)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.99/42.20         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.99/42.20    (9)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.99/42.20         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.99/42.20    (10)  all_57_3 = e0
% 230.99/42.20    (11)   ~ (e3 = e2)
% 230.99/42.20    (12)   ~ (e3 = e0)
% 230.99/42.20    (13)  all_57_1 = e2
% 230.99/42.20    (14)  op(e3, e3) = e3
% 230.99/42.20    (15)  all_57_9 = e0
% 230.99/42.20    (16)   ~ (e2 = e0)
% 230.99/42.20    (17)  all_57_2 = e3
% 230.99/42.20    (18)   ~ (e1 = e0)
% 230.99/42.20    (19)  all_57_14 = e2
% 230.99/42.20    (20)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 230.99/42.20          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 230.99/42.20    (21)  all_57_13 = e3
% 230.99/42.20    (22)  op(e0, e0) = e1
% 230.99/42.20    (23)   ~ (e2 = e1)
% 230.99/42.20    (24)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.99/42.20          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.99/42.20    (25)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.99/42.20          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.99/42.20    (26)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.99/42.20          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.99/42.20    (27)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.99/42.20          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.99/42.20  
% 230.99/42.20  Begin of proof
% 230.99/42.20  | 
% 230.99/42.20  | BETA: splitting (5) gives:
% 230.99/42.20  | 
% 230.99/42.20  | Case 1:
% 230.99/42.20  | | 
% 230.99/42.20  | |   (28)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 230.99/42.20  | |           e3)
% 230.99/42.20  | | 
% 230.99/42.20  | | BETA: splitting (28) gives:
% 230.99/42.20  | | 
% 230.99/42.20  | | Case 1:
% 230.99/42.20  | | | 
% 230.99/42.20  | | |   (29)  all_57_6 = e3 & op(e1, e3) = e3
% 230.99/42.20  | | | 
% 230.99/42.20  | | | REF_CLOSE: (2), (3), (4), (11), (12), (14), (16), (17), (18), (23), (25),
% 230.99/42.20  | | |            (26), (29) are inconsistent by sub-proof #1534.
% 230.99/42.20  | | | 
% 230.99/42.20  | | Case 2:
% 230.99/42.20  | | | 
% 230.99/42.20  | | |   (30)  all_57_7 = e3 & op(e1, e2) = e3
% 230.99/42.20  | | | 
% 230.99/42.20  | | | ALPHA: (30) implies:
% 230.99/42.20  | | |   (31)  all_57_7 = e3
% 230.99/42.20  | | | 
% 230.99/42.20  | | | REF_CLOSE: (3), (10), (13), (18), (21), (23), (27), (31) are inconsistent
% 230.99/42.20  | | |            by sub-proof #2008.
% 230.99/42.20  | | | 
% 230.99/42.20  | | End of split
% 230.99/42.20  | | 
% 230.99/42.20  | Case 2:
% 230.99/42.20  | | 
% 230.99/42.20  | |   (32)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 230.99/42.20  | |           e3)
% 230.99/42.20  | | 
% 230.99/42.20  | | BETA: splitting (32) gives:
% 230.99/42.20  | | 
% 230.99/42.20  | | Case 1:
% 230.99/42.20  | | | 
% 230.99/42.20  | | |   (33)  all_57_8 = e3 & op(e1, e1) = e3
% 230.99/42.20  | | | 
% 230.99/42.20  | | | ALPHA: (33) implies:
% 230.99/42.20  | | |   (34)  op(e1, e1) = e3
% 230.99/42.20  | | | 
% 230.99/42.20  | | | REF_CLOSE: (4), (6), (7), (34) are inconsistent by sub-proof #2468.
% 230.99/42.20  | | | 
% 230.99/42.20  | | Case 2:
% 230.99/42.20  | | | 
% 230.99/42.20  | | |   (35)  all_57_11 = e3 & op(e1, e0) = e3
% 230.99/42.20  | | | 
% 230.99/42.20  | | | ALPHA: (35) implies:
% 230.99/42.20  | | |   (36)  all_57_11 = e3
% 230.99/42.20  | | | 
% 230.99/42.20  | | | BETA: splitting (24) gives:
% 230.99/42.20  | | | 
% 230.99/42.20  | | | Case 1:
% 230.99/42.20  | | | | 
% 230.99/42.20  | | | |   (37)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0)
% 230.99/42.20  | | | |           = e2)
% 230.99/42.20  | | | | 
% 230.99/42.20  | | | | BETA: splitting (37) gives:
% 230.99/42.20  | | | | 
% 230.99/42.20  | | | | Case 1:
% 230.99/42.20  | | | | | 
% 230.99/42.20  | | | | |   (38)  all_57_9 = e2 & op(e3, e0) = e2
% 230.99/42.20  | | | | | 
% 230.99/42.20  | | | | | ALPHA: (38) implies:
% 230.99/42.20  | | | | |   (39)  all_57_9 = e2
% 230.99/42.20  | | | | | 
% 230.99/42.20  | | | | | REF_CLOSE: (15), (16), (39) are inconsistent by sub-proof #2440.
% 230.99/42.20  | | | | | 
% 230.99/42.20  | | | | Case 2:
% 230.99/42.20  | | | | | 
% 230.99/42.20  | | | | |   (40)  all_57_10 = e2 & op(e2, e0) = e2
% 230.99/42.20  | | | | | 
% 230.99/42.20  | | | | | ALPHA: (40) implies:
% 230.99/42.20  | | | | |   (41)  all_57_10 = e2
% 230.99/42.20  | | | | | 
% 230.99/42.20  | | | | | BETA: splitting (20) gives:
% 230.99/42.20  | | | | | 
% 230.99/42.20  | | | | | Case 1:
% 230.99/42.20  | | | | | | 
% 230.99/42.20  | | | | | |   (42)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2,
% 230.99/42.20  | | | | | |             e1) = e3)
% 230.99/42.20  | | | | | | 
% 230.99/42.20  | | | | | | BETA: splitting (42) gives:
% 230.99/42.20  | | | | | | 
% 230.99/42.20  | | | | | | Case 1:
% 230.99/42.20  | | | | | | | 
% 230.99/42.20  | | | | | | |   (43)  all_57_4 = e3 & op(e3, e1) = e3
% 230.99/42.20  | | | | | | | 
% 230.99/42.20  | | | | | | | ALPHA: (43) implies:
% 230.99/42.20  | | | | | | |   (44)  all_57_4 = e3
% 230.99/42.20  | | | | | | | 
% 230.99/42.20  | | | | | | | REF_CLOSE: (3), (4), (8), (9), (11), (14), (15), (16), (18), (23),
% 230.99/42.20  | | | | | | |            (44) are inconsistent by sub-proof #2477.
% 230.99/42.20  | | | | | | | 
% 230.99/42.20  | | | | | | Case 2:
% 230.99/42.20  | | | | | | | 
% 230.99/42.20  | | | | | | |   (45)  all_57_5 = e3 & op(e2, e1) = e3
% 230.99/42.20  | | | | | | | 
% 230.99/42.20  | | | | | | | ALPHA: (45) implies:
% 230.99/42.20  | | | | | | |   (46)  all_57_5 = e3
% 230.99/42.20  | | | | | | | 
% 230.99/42.20  | | | | | | | REF_CLOSE: (1), (3), (10), (17), (18), (23), (41), (46) are
% 230.99/42.20  | | | | | | |            inconsistent by sub-proof #1804.
% 230.99/42.20  | | | | | | | 
% 230.99/42.20  | | | | | | End of split
% 230.99/42.20  | | | | | | 
% 230.99/42.20  | | | | | Case 2:
% 230.99/42.20  | | | | | | 
% 230.99/42.20  | | | | | |   (47)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0,
% 230.99/42.20  | | | | | |             e1) = e3)
% 230.99/42.20  | | | | | | 
% 230.99/42.20  | | | | | | REF_CLOSE: (4), (6), (7), (11), (19), (47) are inconsistent by
% 230.99/42.20  | | | | | |            sub-proof #1890.
% 230.99/42.20  | | | | | | 
% 230.99/42.20  | | | | | End of split
% 230.99/42.20  | | | | | 
% 230.99/42.20  | | | | End of split
% 230.99/42.20  | | | | 
% 230.99/42.20  | | | Case 2:
% 230.99/42.20  | | | | 
% 230.99/42.20  | | | |   (48)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0,
% 230.99/42.20  | | | |             e0) = e2)
% 230.99/42.20  | | | | 
% 230.99/42.20  | | | | REF_CLOSE: (4), (11), (22), (23), (36), (48) are inconsistent by
% 230.99/42.20  | | | |            sub-proof #1956.
% 230.99/42.20  | | | | 
% 230.99/42.20  | | | End of split
% 230.99/42.20  | | | 
% 230.99/42.20  | | End of split
% 230.99/42.20  | | 
% 230.99/42.20  | End of split
% 230.99/42.20  | 
% 230.99/42.20  End of proof
% 230.99/42.20  
% 230.99/42.20  Sub-proof #1311 shows that the following formulas are inconsistent:
% 230.99/42.20  ----------------------------------------------------------------
% 230.99/42.20    (1)   ~ (all_10_2 = e2)
% 230.99/42.20    (2)  op(e3, e3) = all_10_2
% 230.99/42.20    (3)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 230.99/42.20    (4)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 230.99/42.20    (5)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.99/42.20         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.99/42.20    (6)  all_57_12 = e0
% 230.99/42.20    (7)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.99/42.20         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.99/42.20    (8)   ~ (all_53_8 = all_53_12)
% 230.99/42.20    (9)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.99/42.20         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.99/42.20    (10)   ~ (e3 = e1)
% 230.99/42.20    (11)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.99/42.20          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.99/42.20    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.99/42.20            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.99/42.20    (13)  all_55_0 = all_10_2
% 230.99/42.20    (14)   ~ (all_10_2 = e0)
% 230.99/42.20    (15)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.99/42.20          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.99/42.20    (16)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 230.99/42.20            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 230.99/42.20              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 230.99/42.20    (17)   ~ (all_6_2 = e3)
% 230.99/42.20    (18)  op(e1, e1) = all_6_2
% 230.99/42.20    (19)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 230.99/42.20    (20)   ~ (all_53_9 = e0)
% 230.99/42.20    (21)  all_55_0 = e3 | all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 230.99/42.20    (22)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.99/42.20          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.99/42.20    (23)   ~ (all_53_4 = all_53_12)
% 230.99/42.20    (24)   ~ (all_53_8 = all_53_9)
% 230.99/42.20    (25)  all_42_2 = all_6_2
% 230.99/42.20    (26)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.99/42.20          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.99/42.20    (27)  op(e2, e2) = e0
% 230.99/42.20    (28)   ~ (all_53_9 = all_6_2)
% 230.99/42.20    (29)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.99/42.20          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.99/42.20    (30)  all_57_3 = e0
% 230.99/42.20    (31)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 230.99/42.20          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.99/42.20    (32)   ~ (e3 = e2)
% 230.99/42.20    (33)  all_55_1 = all_53_4
% 230.99/42.20    (34)   ~ (e3 = e0)
% 230.99/42.20    (35)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.99/42.20          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.99/42.20    (36)  op(e3, e3) = e3
% 230.99/42.20    (37)   ~ (all_53_8 = all_6_2)
% 230.99/42.20    (38)  all_55_2 = all_53_8
% 230.99/42.20    (39)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 230.99/42.20    (40)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.99/42.20          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.99/42.20            e1)
% 230.99/42.20    (41)  all_57_11 = e0
% 230.99/42.20    (42)   ~ (all_53_4 = all_53_8)
% 230.99/42.20    (43)  op(e3, e2) = all_53_4
% 230.99/42.20    (44)   ~ (e2 = e0)
% 230.99/42.20    (45)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 230.99/42.20            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 230.99/42.20            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 230.99/42.20            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 230.99/42.20              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 230.99/42.20            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 230.99/42.20            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 230.99/42.20              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 230.99/42.20              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 230.99/42.20            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 230.99/42.20            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 230.99/42.20            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 230.99/42.20              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 230.99/42.20              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 230.99/42.20            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 230.99/42.20              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 230.99/42.20            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 230.99/42.20            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 230.99/42.20              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 230.99/42.20              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 230.99/42.20            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 230.99/42.20            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 230.99/42.20    (46)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.99/42.20          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.99/42.20    (47)   ~ (e1 = e0)
% 230.99/42.20    (48)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 230.99/42.20            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 230.99/42.20              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 230.99/42.20    (49)   ~ (all_53_4 = e0)
% 230.99/42.20    (50)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 230.99/42.20          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 230.99/42.20    (51)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.99/42.20          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.99/42.20    (52)   ~ (all_10_2 = e1)
% 230.99/42.20    (53)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.99/42.20          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 230.99/42.20            e3)
% 230.99/42.20    (54)   ~ (all_53_4 = all_53_6)
% 230.99/42.20    (55)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.99/42.20          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.99/42.20            e2)
% 230.99/42.21    (56)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.99/42.21              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.99/42.21                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.99/42.21                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.99/42.21    (57)  op(e1, e1) = e0
% 230.99/42.21    (58)  all_55_10 = all_6_2
% 230.99/42.21    (59)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.99/42.21          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.99/42.21    (60)  all_38_2 = all_6_2
% 230.99/42.21    (61)  all_55_3 = all_53_12
% 230.99/42.21    (62)   ~ (all_53_12 = e3)
% 230.99/42.21    (63)  all_57_7 = e3
% 230.99/42.21    (64)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 230.99/42.21            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 230.99/42.21              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 230.99/42.21    (65)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.99/42.21          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.99/42.21    (66)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.99/42.21          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.99/42.21    (67)   ~ (all_53_12 = all_10_2)
% 230.99/42.21    (68)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 230.99/42.21          (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 230.99/42.21    (69)   ~ (all_53_8 = e0)
% 230.99/42.21    (70)   ~ (e2 = e1)
% 230.99/42.21    (71)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.99/42.21          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.99/42.21    (72)  op(e2, e1) = all_53_9
% 230.99/42.21    (73)  op(e1, e2) = all_53_6
% 230.99/42.21    (74)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.99/42.21          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.99/42.21    (75)  all_24_2 = all_6_2
% 230.99/42.21    (76)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.99/42.21          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.99/42.21    (77)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.99/42.21          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.99/42.21    (78)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.99/42.21          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.99/42.21    (79)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.99/42.21          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.99/42.21    (80)  op(e3, e1) = all_53_8
% 230.99/42.21    (81)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.99/42.21          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.99/42.21    (82)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.99/42.21          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.99/42.21    (83)  op(e3, e0) = all_53_12
% 230.99/42.21  
% 230.99/42.21  Begin of proof
% 230.99/42.21  | 
% 230.99/42.21  | BETA: splitting (68) gives:
% 230.99/42.21  | 
% 230.99/42.21  | Case 1:
% 230.99/42.21  | | 
% 230.99/42.21  | |   (84)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 230.99/42.21  | |           e3)
% 230.99/42.21  | | 
% 230.99/42.21  | | BETA: splitting (84) gives:
% 230.99/42.21  | | 
% 230.99/42.21  | | Case 1:
% 230.99/42.21  | | | 
% 230.99/42.21  | | |   (85)  all_57_9 = e3 & op(e3, e0) = e3
% 230.99/42.21  | | | 
% 230.99/42.21  | | | ALPHA: (85) implies:
% 230.99/42.21  | | |   (86)  op(e3, e0) = e3
% 230.99/42.21  | | | 
% 230.99/42.21  | | | REF_CLOSE: (12), (62), (83), (86) are inconsistent by sub-proof #2458.
% 230.99/42.21  | | | 
% 230.99/42.21  | | Case 2:
% 230.99/42.21  | | | 
% 230.99/42.21  | | |   (87)  all_57_10 = e3 & op(e2, e0) = e3
% 230.99/42.21  | | | 
% 230.99/42.21  | | | ALPHA: (87) implies:
% 230.99/42.21  | | |   (88)  all_57_10 = e3
% 230.99/42.21  | | | 
% 230.99/42.21  | | | BETA: splitting (31) gives:
% 230.99/42.21  | | | 
% 230.99/42.21  | | | Case 1:
% 230.99/42.21  | | | | 
% 230.99/42.21  | | | |   (89)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1)
% 230.99/42.21  | | | |           = e0)
% 230.99/42.21  | | | | 
% 230.99/42.21  | | | | BETA: splitting (89) gives:
% 230.99/42.21  | | | | 
% 230.99/42.21  | | | | Case 1:
% 230.99/42.21  | | | | | 
% 230.99/42.21  | | | | |   (90)  all_57_4 = e0 & op(e3, e1) = e0
% 230.99/42.21  | | | | | 
% 230.99/42.21  | | | | | ALPHA: (90) implies:
% 230.99/42.21  | | | | |   (91)  op(e3, e1) = e0
% 230.99/42.21  | | | | | 
% 230.99/42.21  | | | | | REF_CLOSE: (12), (69), (80), (91) are inconsistent by sub-proof #2267.
% 230.99/42.21  | | | | | 
% 230.99/42.21  | | | | Case 2:
% 230.99/42.21  | | | | | 
% 230.99/42.21  | | | | |   (92)  all_57_5 = e0 & op(e2, e1) = e0
% 230.99/42.21  | | | | | 
% 230.99/42.21  | | | | | ALPHA: (92) implies:
% 230.99/42.21  | | | | |   (93)  all_57_5 = e0
% 230.99/42.21  | | | | | 
% 230.99/42.21  | | | | | REF_CLOSE: (5), (10), (12), (27), (30), (32), (34), (44), (47), (59),
% 230.99/42.21  | | | | |            (65), (70), (88), (93) are inconsistent by sub-proof #2348.
% 230.99/42.21  | | | | | 
% 230.99/42.21  | | | | End of split
% 230.99/42.21  | | | | 
% 230.99/42.21  | | | Case 2:
% 230.99/42.21  | | | | 
% 230.99/42.21  | | | |   (94)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1)
% 230.99/42.21  | | | |           = e0)
% 230.99/42.21  | | | | 
% 230.99/42.21  | | | | BETA: splitting (94) gives:
% 230.99/42.21  | | | | 
% 230.99/42.21  | | | | Case 1:
% 230.99/42.21  | | | | | 
% 230.99/42.21  | | | | |   (95)  all_57_8 = e0 & op(e1, e1) = e0
% 230.99/42.21  | | | | | 
% 230.99/42.21  | | | | | ALPHA: (95) implies:
% 230.99/42.21  | | | | |   (96)  all_57_8 = e0
% 230.99/42.21  | | | | | 
% 230.99/42.21  | | | | | BETA: splitting (82) gives:
% 230.99/42.21  | | | | | 
% 230.99/42.21  | | | | | Case 1:
% 230.99/42.21  | | | | | | 
% 230.99/42.21  | | | | | |   (97)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1,
% 230.99/42.21  | | | | | |             e2) = e2)
% 230.99/42.21  | | | | | | 
% 230.99/42.21  | | | | | | REF_CLOSE: (5), (6), (7), (10), (12), (30), (32), (36), (41), (44),
% 230.99/42.21  | | | | | |            (47), (57), (63), (65), (70), (79), (88), (97) are
% 230.99/42.21  | | | | | |            inconsistent by sub-proof #1312.
% 230.99/42.21  | | | | | | 
% 230.99/42.21  | | | | | Case 2:
% 230.99/42.21  | | | | | | 
% 230.99/42.21  | | | | | |   (98)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1,
% 230.99/42.21  | | | | | |             e0) = e2)
% 230.99/42.21  | | | | | | 
% 230.99/42.21  | | | | | | BETA: splitting (98) gives:
% 230.99/42.21  | | | | | | 
% 230.99/42.21  | | | | | | Case 1:
% 230.99/42.21  | | | | | | | 
% 230.99/42.21  | | | | | | |   (99)  all_57_8 = e2 & op(e1, e1) = e2
% 230.99/42.21  | | | | | | | 
% 230.99/42.21  | | | | | | | ALPHA: (99) implies:
% 230.99/42.21  | | | | | | |   (100)  all_57_8 = e2
% 230.99/42.21  | | | | | | | 
% 230.99/42.21  | | | | | | | REF_CLOSE: (44), (96), (100) are inconsistent by sub-proof #1957.
% 230.99/42.21  | | | | | | | 
% 230.99/42.21  | | | | | | Case 2:
% 230.99/42.21  | | | | | | | 
% 230.99/42.21  | | | | | | |   (101)  all_57_11 = e2 & op(e1, e0) = e2
% 230.99/42.21  | | | | | | | 
% 230.99/42.21  | | | | | | | ALPHA: (101) implies:
% 230.99/42.21  | | | | | | |   (102)  all_57_11 = e2
% 230.99/42.21  | | | | | | | 
% 230.99/42.21  | | | | | | | REF_CLOSE: (41), (44), (102) are inconsistent by sub-proof #1949.
% 230.99/42.21  | | | | | | | 
% 230.99/42.21  | | | | | | End of split
% 230.99/42.21  | | | | | | 
% 230.99/42.21  | | | | | End of split
% 230.99/42.21  | | | | | 
% 230.99/42.21  | | | | Case 2:
% 230.99/42.21  | | | | | 
% 230.99/42.21  | | | | |   (103)  all_57_14 = e0 & op(e0, e1) = e0
% 230.99/42.21  | | | | | 
% 230.99/42.21  | | | | | ALPHA: (103) implies:
% 230.99/42.21  | | | | |   (104)  all_57_14 = e0
% 230.99/42.21  | | | | | 
% 230.99/42.21  | | | | | BETA: splitting (82) gives:
% 230.99/42.21  | | | | | 
% 230.99/42.21  | | | | | Case 1:
% 230.99/42.21  | | | | | | 
% 230.99/42.21  | | | | | |   (105)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1,
% 230.99/42.21  | | | | | |              e2) = e2)
% 230.99/42.21  | | | | | | 
% 230.99/42.21  | | | | | | REF_CLOSE: (5), (6), (7), (10), (12), (30), (32), (36), (41), (44),
% 230.99/42.21  | | | | | |            (47), (57), (63), (65), (70), (79), (88), (105) are
% 230.99/42.21  | | | | | |            inconsistent by sub-proof #1312.
% 230.99/42.21  | | | | | | 
% 230.99/42.21  | | | | | Case 2:
% 230.99/42.21  | | | | | | 
% 230.99/42.21  | | | | | |   (106)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 &
% 230.99/42.21  | | | | | |            op(e1, e0) = e2)
% 230.99/42.21  | | | | | | 
% 230.99/42.21  | | | | | | BETA: splitting (106) gives:
% 230.99/42.21  | | | | | | 
% 230.99/42.21  | | | | | | Case 1:
% 230.99/42.21  | | | | | | | 
% 230.99/42.21  | | | | | | |   (107)  all_57_8 = e2 & op(e1, e1) = e2
% 230.99/42.21  | | | | | | | 
% 230.99/42.21  | | | | | | | ALPHA: (107) implies:
% 230.99/42.21  | | | | | | |   (108)  all_57_8 = e2
% 230.99/42.21  | | | | | | |   (109)  op(e1, e1) = e2
% 230.99/42.21  | | | | | | | 
% 230.99/42.21  | | | | | | | BETA: splitting (9) gives:
% 230.99/42.21  | | | | | | | 
% 230.99/42.21  | | | | | | | Case 1:
% 230.99/42.21  | | | | | | | | 
% 230.99/42.21  | | | | | | | |   (110)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 &
% 230.99/42.21  | | | | | | | |            op(e2, e2) = e2)
% 230.99/42.21  | | | | | | | | 
% 230.99/42.21  | | | | | | | | BETA: splitting (110) gives:
% 230.99/42.21  | | | | | | | | 
% 230.99/42.21  | | | | | | | | Case 1:
% 230.99/42.21  | | | | | | | | | 
% 230.99/42.21  | | | | | | | | |   (111)  all_57_1 = e2 & op(e3, e2) = e2
% 230.99/42.21  | | | | | | | | | 
% 230.99/42.21  | | | | | | | | | ALPHA: (111) implies:
% 230.99/42.21  | | | | | | | | |   (112)  all_57_1 = e2
% 230.99/42.21  | | | | | | | | | 
% 230.99/42.21  | | | | | | | | | BETA: splitting (50) gives:
% 230.99/42.21  | | | | | | | | | 
% 230.99/42.21  | | | | | | | | | Case 1:
% 230.99/42.21  | | | | | | | | | | 
% 230.99/42.21  | | | | | | | | | |   (113)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 230.99/42.21  | | | | | | | | | |            & op(e2, e1) = e3)
% 230.99/42.21  | | | | | | | | | | 
% 230.99/42.21  | | | | | | | | | | BETA: splitting (113) gives:
% 230.99/42.21  | | | | | | | | | | 
% 230.99/42.21  | | | | | | | | | | Case 1:
% 230.99/42.21  | | | | | | | | | | | 
% 230.99/42.21  | | | | | | | | | | |   (114)  all_57_4 = e3 & op(e3, e1) = e3
% 230.99/42.21  | | | | | | | | | | | 
% 230.99/42.21  | | | | | | | | | | | REF_CLOSE: (10), (12), (22), (26), (29), (32), (34), (36),
% 230.99/42.21  | | | | | | | | | | |            (44), (47), (70), (112), (114) are inconsistent by
% 230.99/42.21  | | | | | | | | | | |            sub-proof #1829.
% 230.99/42.21  | | | | | | | | | | | 
% 230.99/42.21  | | | | | | | | | | Case 2:
% 230.99/42.21  | | | | | | | | | | | 
% 230.99/42.21  | | | | | | | | | | |   (115)  all_57_5 = e3 & op(e2, e1) = e3
% 230.99/42.21  | | | | | | | | | | | 
% 230.99/42.21  | | | | | | | | | | | ALPHA: (115) implies:
% 230.99/42.21  | | | | | | | | | | |   (116)  all_57_5 = e3
% 230.99/42.21  | | | | | | | | | | | 
% 230.99/42.21  | | | | | | | | | | | REF_CLOSE: (9), (10), (12), (22), (26), (29), (30), (31),
% 230.99/42.21  | | | | | | | | | | |            (32), (34), (35), (36), (44), (47), (57), (63),
% 230.99/42.21  | | | | | | | | | | |            (70), (81), (104), (108), (109), (116) are
% 230.99/42.21  | | | | | | | | | | |            inconsistent by sub-proof #1489.
% 230.99/42.21  | | | | | | | | | | | 
% 230.99/42.21  | | | | | | | | | | End of split
% 230.99/42.21  | | | | | | | | | | 
% 230.99/42.21  | | | | | | | | | Case 2:
% 230.99/42.21  | | | | | | | | | | 
% 230.99/42.21  | | | | | | | | | |   (117)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3
% 230.99/42.21  | | | | | | | | | |            & op(e0, e1) = e3)
% 230.99/42.21  | | | | | | | | | | 
% 230.99/42.21  | | | | | | | | | | REF_CLOSE: (12), (17), (18), (34), (104), (117) are
% 230.99/42.21  | | | | | | | | | |            inconsistent by sub-proof #2337.
% 230.99/42.21  | | | | | | | | | | 
% 230.99/42.21  | | | | | | | | | End of split
% 230.99/42.21  | | | | | | | | | 
% 230.99/42.21  | | | | | | | | Case 2:
% 230.99/42.21  | | | | | | | | | 
% 230.99/42.21  | | | | | | | | |   (118)  all_57_3 = e2 & op(e2, e2) = e2
% 230.99/42.21  | | | | | | | | | 
% 230.99/42.21  | | | | | | | | | ALPHA: (118) implies:
% 230.99/42.21  | | | | | | | | |   (119)  op(e2, e2) = e2
% 230.99/42.21  | | | | | | | | | 
% 230.99/42.21  | | | | | | | | | REF_CLOSE: (12), (27), (44), (119) are inconsistent by
% 230.99/42.21  | | | | | | | | |            sub-proof #2472.
% 230.99/42.21  | | | | | | | | | 
% 230.99/42.21  | | | | | | | | End of split
% 230.99/42.21  | | | | | | | | 
% 230.99/42.21  | | | | | | | Case 2:
% 230.99/42.21  | | | | | | | | 
% 230.99/42.21  | | | | | | | |   (120)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 &
% 230.99/42.21  | | | | | | | |            op(e0, e2) = e2)
% 230.99/42.21  | | | | | | | | 
% 230.99/42.21  | | | | | | | | BETA: splitting (120) gives:
% 230.99/42.21  | | | | | | | | 
% 230.99/42.21  | | | | | | | | Case 1:
% 230.99/42.21  | | | | | | | | | 
% 230.99/42.21  | | | | | | | | |   (121)  all_57_7 = e2 & op(e1, e2) = e2
% 230.99/42.21  | | | | | | | | | 
% 230.99/42.21  | | | | | | | | | ALPHA: (121) implies:
% 230.99/42.21  | | | | | | | | |   (122)  all_57_7 = e2
% 230.99/42.21  | | | | | | | | | 
% 230.99/42.21  | | | | | | | | | REF_CLOSE: (32), (63), (122) are inconsistent by sub-proof
% 230.99/42.21  | | | | | | | | |            #2102.
% 230.99/42.21  | | | | | | | | | 
% 230.99/42.21  | | | | | | | | Case 2:
% 230.99/42.21  | | | | | | | | | 
% 230.99/42.21  | | | | | | | | |   (123)  all_57_13 = e2 & op(e0, e2) = e2
% 230.99/42.21  | | | | | | | | | 
% 230.99/42.21  | | | | | | | | | ALPHA: (123) implies:
% 230.99/42.21  | | | | | | | | |   (124)  all_57_13 = e2
% 230.99/42.21  | | | | | | | | | 
% 230.99/42.21  | | | | | | | | | BETA: splitting (53) gives:
% 230.99/42.21  | | | | | | | | | 
% 230.99/42.21  | | | | | | | | | Case 1:
% 230.99/42.21  | | | | | | | | | | 
% 230.99/42.21  | | | | | | | | | |   (125)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 230.99/42.21  | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 230.99/42.21  | | | | | | | | | | 
% 230.99/42.21  | | | | | | | | | | BETA: splitting (125) gives:
% 230.99/42.21  | | | | | | | | | | 
% 230.99/42.21  | | | | | | | | | | Case 1:
% 230.99/42.21  | | | | | | | | | | | 
% 230.99/42.21  | | | | | | | | | | |   (126)  all_57_12 = e3 & op(e0, e3) = e3
% 230.99/42.21  | | | | | | | | | | | 
% 230.99/42.21  | | | | | | | | | | | ALPHA: (126) implies:
% 230.99/42.21  | | | | | | | | | | |   (127)  all_57_12 = e3
% 230.99/42.21  | | | | | | | | | | | 
% 230.99/42.21  | | | | | | | | | | | COMBINE_EQS: (6), (127) imply:
% 230.99/42.21  | | | | | | | | | | |   (128)  e3 = e0
% 230.99/42.21  | | | | | | | | | | | 
% 230.99/42.21  | | | | | | | | | | | SIMP: (128) implies:
% 230.99/42.21  | | | | | | | | | | |   (129)  e3 = e0
% 230.99/42.21  | | | | | | | | | | | 
% 230.99/42.21  | | | | | | | | | | | COMBINE_EQS: (63), (129) imply:
% 230.99/42.21  | | | | | | | | | | |   (130)  all_57_7 = e0
% 230.99/42.21  | | | | | | | | | | | 
% 230.99/42.21  | | | | | | | | | | | REF_CLOSE: (10), (12), (27), (30), (32), (34), (47), (51),
% 230.99/42.21  | | | | | | | | | | |            (70), (81), (124), (130) are inconsistent by
% 230.99/42.21  | | | | | | | | | | |            sub-proof #2202.
% 230.99/42.21  | | | | | | | | | | | 
% 230.99/42.21  | | | | | | | | | | Case 2:
% 230.99/42.21  | | | | | | | | | | | 
% 230.99/42.21  | | | | | | | | | | |   (131)  all_57_13 = e3 & op(e0, e2) = e3
% 230.99/42.21  | | | | | | | | | | | 
% 230.99/42.21  | | | | | | | | | | | REF_CLOSE: (32), (124), (131) are inconsistent by sub-proof
% 230.99/42.21  | | | | | | | | | | |            #1358.
% 230.99/42.21  | | | | | | | | | | | 
% 230.99/42.21  | | | | | | | | | | End of split
% 230.99/42.21  | | | | | | | | | | 
% 230.99/42.21  | | | | | | | | | Case 2:
% 230.99/42.21  | | | | | | | | | | 
% 230.99/42.21  | | | | | | | | | |   (132)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 230.99/42.21  | | | | | | | | | |            e3 & op(e0, e0) = e3)
% 230.99/42.21  | | | | | | | | | | 
% 230.99/42.21  | | | | | | | | | | BETA: splitting (132) gives:
% 230.99/42.21  | | | | | | | | | | 
% 230.99/42.21  | | | | | | | | | | Case 1:
% 230.99/42.21  | | | | | | | | | | | 
% 230.99/42.21  | | | | | | | | | | |   (133)  all_57_14 = e3 & op(e0, e1) = e3
% 230.99/42.21  | | | | | | | | | | | 
% 230.99/42.21  | | | | | | | | | | | ALPHA: (133) implies:
% 230.99/42.21  | | | | | | | | | | |   (134)  all_57_14 = e3
% 230.99/42.21  | | | | | | | | | | | 
% 230.99/42.21  | | | | | | | | | | | COMBINE_EQS: (104), (134) imply:
% 230.99/42.21  | | | | | | | | | | |   (135)  e3 = e0
% 230.99/42.21  | | | | | | | | | | | 
% 230.99/42.21  | | | | | | | | | | | COMBINE_EQS: (63), (135) imply:
% 230.99/42.21  | | | | | | | | | | |   (136)  all_57_7 = e0
% 230.99/42.21  | | | | | | | | | | | 
% 230.99/42.21  | | | | | | | | | | | REF_CLOSE: (10), (12), (27), (30), (32), (34), (47), (51),
% 230.99/42.21  | | | | | | | | | | |            (70), (81), (124), (136) are inconsistent by
% 230.99/42.21  | | | | | | | | | | |            sub-proof #2202.
% 230.99/42.21  | | | | | | | | | | | 
% 230.99/42.21  | | | | | | | | | | Case 2:
% 230.99/42.21  | | | | | | | | | | | 
% 230.99/42.21  | | | | | | | | | | |   (137)  all_57_15 = e3 & op(e0, e0) = e3
% 230.99/42.21  | | | | | | | | | | | 
% 230.99/42.21  | | | | | | | | | | | ALPHA: (137) implies:
% 230.99/42.21  | | | | | | | | | | |   (138)  all_57_15 = e3
% 230.99/42.21  | | | | | | | | | | | 
% 230.99/42.21  | | | | | | | | | | | REF_CLOSE: (5), (7), (9), (10), (11), (12), (15), (17), (18),
% 230.99/42.21  | | | | | | | | | | |            (22), (26), (29), (30), (31), (32), (34), (36),
% 230.99/42.21  | | | | | | | | | | |            (40), (44), (47), (50), (51), (55), (56), (65),
% 230.99/42.21  | | | | | | | | | | |            (66), (70), (71), (74), (76), (77), (78), (81),
% 230.99/42.21  | | | | | | | | | | |            (88), (138) are inconsistent by sub-proof #1416.
% 230.99/42.21  | | | | | | | | | | | 
% 230.99/42.21  | | | | | | | | | | End of split
% 230.99/42.21  | | | | | | | | | | 
% 230.99/42.21  | | | | | | | | | End of split
% 230.99/42.21  | | | | | | | | | 
% 230.99/42.21  | | | | | | | | End of split
% 230.99/42.21  | | | | | | | | 
% 230.99/42.21  | | | | | | | End of split
% 230.99/42.21  | | | | | | | 
% 230.99/42.21  | | | | | | Case 2:
% 230.99/42.21  | | | | | | | 
% 230.99/42.21  | | | | | | |   (139)  all_57_11 = e2 & op(e1, e0) = e2
% 230.99/42.21  | | | | | | | 
% 230.99/42.21  | | | | | | | ALPHA: (139) implies:
% 230.99/42.21  | | | | | | |   (140)  all_57_11 = e2
% 230.99/42.21  | | | | | | | 
% 230.99/42.21  | | | | | | | REF_CLOSE: (41), (44), (140) are inconsistent by sub-proof #1949.
% 230.99/42.21  | | | | | | | 
% 230.99/42.21  | | | | | | End of split
% 230.99/42.21  | | | | | | 
% 230.99/42.21  | | | | | End of split
% 230.99/42.21  | | | | | 
% 230.99/42.21  | | | | End of split
% 230.99/42.21  | | | | 
% 230.99/42.21  | | | End of split
% 230.99/42.21  | | | 
% 230.99/42.21  | | End of split
% 230.99/42.21  | | 
% 230.99/42.21  | Case 2:
% 230.99/42.21  | | 
% 230.99/42.21  | |   (141)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 230.99/42.21  | |            e3)
% 230.99/42.21  | | 
% 230.99/42.21  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (11), (12), (13), (14),
% 230.99/42.21  | |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 230.99/42.21  | |            (26), (28), (29), (30), (31), (33), (34), (35), (37), (38), (39),
% 230.99/42.21  | |            (40), (41), (42), (43), (44), (45), (46), (47), (48), (49), (50),
% 230.99/42.21  | |            (51), (52), (54), (55), (56), (58), (59), (60), (61), (64), (65),
% 230.99/42.21  | |            (66), (67), (70), (71), (72), (73), (74), (75), (76), (77), (78),
% 230.99/42.21  | |            (79), (80), (81), (82), (83), (141) are inconsistent by sub-proof
% 230.99/42.21  | |            #1391.
% 230.99/42.21  | | 
% 230.99/42.21  | End of split
% 230.99/42.21  | 
% 230.99/42.21  End of proof
% 230.99/42.21  
% 230.99/42.21  Sub-proof #1312 shows that the following formulas are inconsistent:
% 230.99/42.21  ----------------------------------------------------------------
% 230.99/42.21    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.99/42.21         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.99/42.21    (2)  all_57_12 = e0
% 230.99/42.21    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.99/42.21         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.99/42.21    (4)   ~ (e3 = e1)
% 230.99/42.21    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.99/42.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.99/42.21    (6)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2)
% 230.99/42.21    (7)  all_57_3 = e0
% 230.99/42.21    (8)   ~ (e3 = e2)
% 230.99/42.21    (9)  op(e3, e3) = e3
% 230.99/42.21    (10)  all_57_11 = e0
% 230.99/42.21    (11)   ~ (e2 = e0)
% 230.99/42.21    (12)   ~ (e1 = e0)
% 230.99/42.21    (13)  all_57_10 = e3
% 230.99/42.21    (14)  op(e1, e1) = e0
% 230.99/42.21    (15)  all_57_7 = e3
% 230.99/42.21    (16)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.99/42.21          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.99/42.21    (17)   ~ (e2 = e1)
% 230.99/42.21    (18)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.99/42.21          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.99/42.21  
% 230.99/42.21  Begin of proof
% 230.99/42.21  | 
% 230.99/42.21  | BETA: splitting (6) gives:
% 230.99/42.21  | 
% 230.99/42.21  | Case 1:
% 230.99/42.21  | | 
% 230.99/42.21  | |   (19)  all_57_6 = e2 & op(e1, e3) = e2
% 230.99/42.21  | | 
% 230.99/42.21  | | ALPHA: (19) implies:
% 230.99/42.21  | |   (20)  all_57_6 = e2
% 230.99/42.21  | | 
% 230.99/42.21  | | BETA: splitting (3) gives:
% 230.99/42.21  | | 
% 230.99/42.21  | | Case 1:
% 230.99/42.21  | | | 
% 230.99/42.21  | | |   (21)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) =
% 230.99/42.21  | | |           e1)
% 230.99/42.21  | | | 
% 230.99/42.21  | | | BETA: splitting (21) gives:
% 230.99/42.21  | | | 
% 230.99/42.21  | | | Case 1:
% 230.99/42.21  | | | | 
% 230.99/42.21  | | | |   (22)  all_57_0 = e1 & op(e3, e3) = e1
% 230.99/42.21  | | | | 
% 230.99/42.21  | | | | ALPHA: (22) implies:
% 230.99/42.21  | | | |   (23)  op(e3, e3) = e1
% 230.99/42.21  | | | | 
% 230.99/42.21  | | | | REF_CLOSE: (4), (5), (9), (23) are inconsistent by sub-proof #2495.
% 230.99/42.21  | | | | 
% 230.99/42.21  | | | Case 2:
% 230.99/42.21  | | | | 
% 230.99/42.21  | | | |   (24)  all_57_2 = e1 & op(e2, e3) = e1
% 230.99/42.21  | | | | 
% 230.99/42.21  | | | | ALPHA: (24) implies:
% 230.99/42.21  | | | |   (25)  all_57_2 = e1
% 230.99/42.21  | | | | 
% 230.99/42.21  | | | | BETA: splitting (18) gives:
% 230.99/42.21  | | | | 
% 230.99/42.21  | | | | Case 1:
% 230.99/42.21  | | | | | 
% 230.99/42.21  | | | | |   (26)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1,
% 230.99/42.21  | | | | |             e2) = e1)
% 230.99/42.21  | | | | | 
% 230.99/42.21  | | | | | BETA: splitting (26) gives:
% 230.99/42.21  | | | | | 
% 230.99/42.21  | | | | | Case 1:
% 230.99/42.21  | | | | | | 
% 230.99/42.21  | | | | | |   (27)  all_57_6 = e1 & op(e1, e3) = e1
% 230.99/42.21  | | | | | | 
% 230.99/42.21  | | | | | | REF_CLOSE: (17), (20), (27) are inconsistent by sub-proof #2389.
% 230.99/42.21  | | | | | | 
% 230.99/42.21  | | | | | Case 2:
% 230.99/42.21  | | | | | | 
% 230.99/42.21  | | | | | |   (28)  all_57_7 = e1 & op(e1, e2) = e1
% 230.99/42.21  | | | | | | 
% 230.99/42.21  | | | | | | ALPHA: (28) implies:
% 230.99/42.21  | | | | | |   (29)  all_57_7 = e1
% 230.99/42.21  | | | | | | 
% 230.99/42.21  | | | | | | REF_CLOSE: (4), (15), (29) are inconsistent by sub-proof #2115.
% 230.99/42.21  | | | | | | 
% 230.99/42.21  | | | | | End of split
% 230.99/42.21  | | | | | 
% 230.99/42.21  | | | | Case 2:
% 230.99/42.21  | | | | | 
% 230.99/42.21  | | | | |   (30)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1,
% 230.99/42.21  | | | | |             e0) = e1)
% 230.99/42.21  | | | | | 
% 230.99/42.21  | | | | | BETA: splitting (30) gives:
% 230.99/42.21  | | | | | 
% 230.99/42.21  | | | | | Case 1:
% 230.99/42.21  | | | | | | 
% 230.99/42.21  | | | | | |   (31)  all_57_8 = e1 & op(e1, e1) = e1
% 230.99/42.21  | | | | | | 
% 230.99/42.21  | | | | | | ALPHA: (31) implies:
% 230.99/42.21  | | | | | |   (32)  op(e1, e1) = e1
% 230.99/42.21  | | | | | | 
% 230.99/42.21  | | | | | | REF_CLOSE: (5), (12), (14), (32) are inconsistent by sub-proof
% 230.99/42.21  | | | | | |            #2427.
% 230.99/42.21  | | | | | | 
% 230.99/42.21  | | | | | Case 2:
% 230.99/42.21  | | | | | | 
% 230.99/42.21  | | | | | |   (33)  all_57_11 = e1 & op(e1, e0) = e1
% 230.99/42.21  | | | | | | 
% 230.99/42.21  | | | | | | ALPHA: (33) implies:
% 230.99/42.21  | | | | | |   (34)  all_57_11 = e1
% 230.99/42.21  | | | | | | 
% 230.99/42.21  | | | | | | COMBINE_EQS: (10), (34) imply:
% 230.99/42.21  | | | | | |   (35)  e1 = e0
% 230.99/42.21  | | | | | | 
% 230.99/42.21  | | | | | | COMBINE_EQS: (25), (35) imply:
% 230.99/42.21  | | | | | |   (36)  all_57_2 = e0
% 230.99/42.21  | | | | | | 
% 230.99/42.21  | | | | | | REF_CLOSE: (1), (4), (7), (8), (11), (12), (13), (16), (17), (36)
% 230.99/42.21  | | | | | |            are inconsistent by sub-proof #2247.
% 230.99/42.21  | | | | | | 
% 230.99/42.21  | | | | | End of split
% 230.99/42.21  | | | | | 
% 230.99/42.21  | | | | End of split
% 230.99/42.21  | | | | 
% 230.99/42.21  | | | End of split
% 230.99/42.21  | | | 
% 230.99/42.21  | | Case 2:
% 230.99/42.21  | | | 
% 230.99/42.21  | | |   (37)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) =
% 230.99/42.21  | | |           e1)
% 230.99/42.21  | | | 
% 230.99/42.21  | | | REF_CLOSE: (2), (12), (17), (20), (37) are inconsistent by sub-proof
% 230.99/42.21  | | |            #1313.
% 230.99/42.21  | | | 
% 230.99/42.21  | | End of split
% 230.99/42.21  | | 
% 230.99/42.21  | Case 2:
% 230.99/42.21  | | 
% 230.99/42.21  | |   (38)  all_57_7 = e2 & op(e1, e2) = e2
% 230.99/42.21  | | 
% 230.99/42.21  | | REF_CLOSE: (8), (15), (38) are inconsistent by sub-proof #2092.
% 230.99/42.21  | | 
% 230.99/42.21  | End of split
% 230.99/42.21  | 
% 230.99/42.21  End of proof
% 230.99/42.21  
% 230.99/42.21  Sub-proof #1313 shows that the following formulas are inconsistent:
% 230.99/42.21  ----------------------------------------------------------------
% 230.99/42.21    (1)  all_57_12 = e0
% 230.99/42.21    (2)  all_57_6 = e2
% 230.99/42.21    (3)   ~ (e1 = e0)
% 230.99/42.21    (4)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.99/42.21    (5)   ~ (e2 = e1)
% 230.99/42.21  
% 230.99/42.21  Begin of proof
% 230.99/42.21  | 
% 230.99/42.21  | BETA: splitting (4) gives:
% 230.99/42.21  | 
% 230.99/42.21  | Case 1:
% 230.99/42.21  | | 
% 230.99/42.21  | |   (6)  all_57_6 = e1 & op(e1, e3) = e1
% 230.99/42.21  | | 
% 230.99/42.21  | | ALPHA: (6) implies:
% 230.99/42.21  | |   (7)  all_57_6 = e1
% 230.99/42.21  | | 
% 230.99/42.21  | | REF_CLOSE: (2), (5), (7) are inconsistent by sub-proof #2233.
% 230.99/42.21  | | 
% 230.99/42.21  | Case 2:
% 230.99/42.21  | | 
% 230.99/42.21  | |   (8)  all_57_12 = e1 & op(e0, e3) = e1
% 230.99/42.21  | | 
% 230.99/42.21  | | ALPHA: (8) implies:
% 230.99/42.21  | |   (9)  all_57_12 = e1
% 230.99/42.21  | | 
% 230.99/42.21  | | REF_CLOSE: (1), (3), (9) are inconsistent by sub-proof #2014.
% 230.99/42.21  | | 
% 230.99/42.21  | End of split
% 230.99/42.21  | 
% 230.99/42.21  End of proof
% 230.99/42.21  
% 230.99/42.21  Sub-proof #1314 shows that the following formulas are inconsistent:
% 230.99/42.21  ----------------------------------------------------------------
% 230.99/42.21    (1)   ~ (e3 = e1)
% 230.99/42.21    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.99/42.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.99/42.21    (3)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.99/42.21         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.99/42.21    (4)   ~ (all_6_2 = e3)
% 230.99/42.21    (5)  op(e1, e1) = all_6_2
% 230.99/42.21    (6)   ~ (e3 = e2)
% 230.99/42.21    (7)   ~ (e3 = e0)
% 230.99/42.21    (8)  all_57_11 = e2
% 230.99/42.21    (9)   ~ (e1 = e0)
% 230.99/42.21    (10)  op(e1, e1) = e0
% 230.99/42.21    (11)   ~ (e2 = e1)
% 230.99/42.21    (12)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.99/42.21          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.99/42.21    (13)  all_57_7 = e0
% 230.99/42.21  
% 230.99/42.21  Begin of proof
% 230.99/42.21  | 
% 230.99/42.21  | BETA: splitting (12) gives:
% 230.99/42.21  | 
% 230.99/42.21  | Case 1:
% 230.99/42.21  | | 
% 230.99/42.21  | |   (14)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) =
% 230.99/42.21  | |           e1)
% 230.99/42.21  | | 
% 230.99/42.21  | | BETA: splitting (14) gives:
% 230.99/42.21  | | 
% 230.99/42.21  | | Case 1:
% 230.99/42.21  | | | 
% 230.99/42.21  | | |   (15)  all_57_6 = e1 & op(e1, e3) = e1
% 230.99/42.21  | | | 
% 230.99/42.21  | | | ALPHA: (15) implies:
% 230.99/42.21  | | |   (16)  all_57_6 = e1
% 230.99/42.21  | | | 
% 230.99/42.21  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (13), (16) are
% 230.99/42.21  | | |            inconsistent by sub-proof #2343.
% 230.99/42.21  | | | 
% 230.99/42.21  | | Case 2:
% 230.99/42.21  | | | 
% 230.99/42.21  | | |   (17)  all_57_7 = e1 & op(e1, e2) = e1
% 230.99/42.21  | | | 
% 230.99/42.21  | | | REF_CLOSE: (9), (13), (17) are inconsistent by sub-proof #2200.
% 230.99/42.21  | | | 
% 230.99/42.21  | | End of split
% 230.99/42.21  | | 
% 230.99/42.21  | Case 2:
% 230.99/42.21  | | 
% 230.99/42.21  | |   (18)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) =
% 230.99/42.21  | |           e1)
% 230.99/42.21  | | 
% 230.99/42.21  | | REF_CLOSE: (2), (8), (9), (10), (11), (18) are inconsistent by sub-proof
% 230.99/42.21  | |            #1315.
% 230.99/42.21  | | 
% 230.99/42.21  | End of split
% 230.99/42.21  | 
% 230.99/42.21  End of proof
% 230.99/42.21  
% 230.99/42.21  Sub-proof #1315 shows that the following formulas are inconsistent:
% 230.99/42.21  ----------------------------------------------------------------
% 230.99/42.21    (1)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.99/42.21    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.99/42.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.99/42.21    (3)  all_57_11 = e2
% 230.99/42.21    (4)   ~ (e1 = e0)
% 230.99/42.21    (5)  op(e1, e1) = e0
% 230.99/42.21    (6)   ~ (e2 = e1)
% 230.99/42.21  
% 230.99/42.21  Begin of proof
% 230.99/42.21  | 
% 230.99/42.21  | BETA: splitting (1) gives:
% 230.99/42.21  | 
% 230.99/42.21  | Case 1:
% 230.99/42.21  | | 
% 230.99/42.21  | |   (7)  all_57_8 = e1 & op(e1, e1) = e1
% 230.99/42.21  | | 
% 230.99/42.21  | | ALPHA: (7) implies:
% 230.99/42.21  | |   (8)  op(e1, e1) = e1
% 230.99/42.21  | | 
% 230.99/42.21  | | REF_CLOSE: (2), (4), (5), (8) are inconsistent by sub-proof #2427.
% 230.99/42.21  | | 
% 230.99/42.21  | Case 2:
% 230.99/42.21  | | 
% 230.99/42.21  | |   (9)  all_57_11 = e1 & op(e1, e0) = e1
% 230.99/42.21  | | 
% 230.99/42.21  | | REF_CLOSE: (3), (6), (9) are inconsistent by sub-proof #1726.
% 230.99/42.21  | | 
% 230.99/42.21  | End of split
% 230.99/42.21  | 
% 230.99/42.21  End of proof
% 230.99/42.21  
% 230.99/42.21  Sub-proof #1316 shows that the following formulas are inconsistent:
% 230.99/42.21  ----------------------------------------------------------------
% 230.99/42.21    (1)   ~ (all_53_7 = all_52_19)
% 230.99/42.21    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.99/42.21         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.99/42.21    (3)   ~ (e3 = e1)
% 230.99/42.21    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.99/42.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.99/42.21    (5)   ~ (all_53_7 = e1)
% 230.99/42.21    (6)  all_55_9 = all_52_19
% 230.99/42.21    (7)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.99/42.22         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.99/42.22    (8)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 230.99/42.22    (9)  all_57_2 = e2
% 230.99/42.22    (10)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.99/42.22          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.99/42.22    (11)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.99/42.22          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.99/42.22    (12)  all_57_3 = e0
% 230.99/42.22    (13)  all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 230.99/42.22    (14)   ~ (e3 = e2)
% 230.99/42.22    (15)  all_55_1 = all_53_4
% 230.99/42.22    (16)   ~ (e3 = e0)
% 230.99/42.22    (17)  op(e3, e3) = e3
% 230.99/42.22    (18)   ~ (all_53_4 = all_53_7)
% 230.99/42.22    (19)  all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 230.99/42.22    (20)  all_57_1 = e1
% 230.99/42.22    (21)   ~ (all_53_7 = e0)
% 230.99/42.22    (22)  all_57_9 = e0
% 230.99/42.22    (23)  op(e3, e2) = all_53_4
% 230.99/42.22    (24)   ~ (all_53_4 = all_52_19)
% 230.99/42.22    (25)   ~ (e2 = e0)
% 230.99/42.22    (26)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.99/42.22          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.99/42.22    (27)   ~ (e1 = e0)
% 230.99/42.22    (28)   ~ (all_53_4 = e0)
% 230.99/42.22    (29)   ~ (all_52_19 = e0)
% 230.99/42.22    (30)  all_55_13 = all_53_7
% 230.99/42.22    (31)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.99/42.22          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.99/42.22    (32)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.99/42.22          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.99/42.22    (33)  op(all_52_19, all_52_19) = e2
% 230.99/42.22    (34)   ~ (e2 = e1)
% 230.99/42.22  
% 230.99/42.22  Begin of proof
% 230.99/42.22  | 
% 230.99/42.22  | BETA: splitting (10) gives:
% 230.99/42.22  | 
% 230.99/42.22  | Case 1:
% 230.99/42.22  | | 
% 230.99/42.22  | |   (35)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) =
% 230.99/42.22  | |           e2)
% 230.99/42.22  | | 
% 230.99/42.22  | | REF_CLOSE: (4), (14), (17), (20), (34), (35) are inconsistent by sub-proof
% 230.99/42.22  | |            #2488.
% 230.99/42.22  | | 
% 230.99/42.22  | Case 2:
% 230.99/42.22  | | 
% 230.99/42.22  | |   (36)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) =
% 230.99/42.22  | |           e2)
% 230.99/42.22  | | 
% 230.99/42.22  | | BETA: splitting (36) gives:
% 230.99/42.22  | | 
% 230.99/42.22  | | Case 1:
% 230.99/42.22  | | | 
% 230.99/42.22  | | |   (37)  all_57_4 = e2 & op(e3, e1) = e2
% 230.99/42.22  | | | 
% 230.99/42.22  | | | REF_CLOSE: (1), (4), (5), (6), (7), (8), (11), (13), (15), (18), (19),
% 230.99/42.22  | | |            (21), (23), (24), (26), (28), (29), (30), (33), (37) are
% 230.99/42.22  | | |            inconsistent by sub-proof #1318.
% 230.99/42.22  | | | 
% 230.99/42.22  | | Case 2:
% 230.99/42.22  | | | 
% 230.99/42.22  | | |   (38)  all_57_9 = e2 & op(e3, e0) = e2
% 230.99/42.22  | | | 
% 230.99/42.22  | | | ALPHA: (38) implies:
% 230.99/42.22  | | |   (39)  all_57_9 = e2
% 230.99/42.22  | | | 
% 230.99/42.22  | | | COMBINE_EQS: (22), (39) imply:
% 230.99/42.22  | | |   (40)  e2 = e0
% 230.99/42.22  | | | 
% 230.99/42.22  | | | SIMP: (40) implies:
% 230.99/42.22  | | |   (41)  e2 = e0
% 230.99/42.22  | | | 
% 230.99/42.22  | | | COMBINE_EQS: (9), (41) imply:
% 230.99/42.22  | | |   (42)  all_57_2 = e0
% 230.99/42.22  | | | 
% 230.99/42.22  | | | REF_CLOSE: (2), (3), (12), (14), (16), (25), (27), (31), (32), (34), (42)
% 230.99/42.22  | | |            are inconsistent by sub-proof #2246.
% 230.99/42.22  | | | 
% 230.99/42.22  | | End of split
% 230.99/42.22  | | 
% 230.99/42.22  | End of split
% 230.99/42.22  | 
% 230.99/42.22  End of proof
% 230.99/42.22  
% 230.99/42.22  Sub-proof #1317 shows that the following formulas are inconsistent:
% 230.99/42.22  ----------------------------------------------------------------
% 230.99/42.22    (1)  all_57_6 = e2 & op(e1, e3) = e2
% 230.99/42.22    (2)  all_57_6 = e1
% 230.99/42.22    (3)   ~ (e2 = e1)
% 230.99/42.22  
% 230.99/42.22  Begin of proof
% 230.99/42.22  | 
% 230.99/42.22  | ALPHA: (1) implies:
% 230.99/42.22  |   (4)  all_57_6 = e2
% 230.99/42.22  | 
% 230.99/42.22  | COMBINE_EQS: (2), (4) imply:
% 230.99/42.22  |   (5)  e2 = e1
% 230.99/42.22  | 
% 230.99/42.22  | REDUCE: (3), (5) imply:
% 230.99/42.22  |   (6)  $false
% 230.99/42.22  | 
% 230.99/42.22  | CLOSE: (6) is inconsistent.
% 230.99/42.22  | 
% 230.99/42.22  End of proof
% 230.99/42.22  
% 230.99/42.22  Sub-proof #1318 shows that the following formulas are inconsistent:
% 230.99/42.22  ----------------------------------------------------------------
% 230.99/42.22    (1)   ~ (all_53_7 = all_52_19)
% 230.99/42.22    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.99/42.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.99/42.22    (3)   ~ (all_53_7 = e1)
% 230.99/42.22    (4)  all_55_9 = all_52_19
% 230.99/42.22    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.99/42.22         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.99/42.22    (6)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 230.99/42.22    (7)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.99/42.22         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.99/42.22    (8)  all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 230.99/42.22    (9)  all_55_1 = all_53_4
% 230.99/42.22    (10)   ~ (all_53_4 = all_53_7)
% 230.99/42.22    (11)  all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 230.99/42.22    (12)   ~ (all_53_7 = e0)
% 230.99/42.22    (13)  op(e3, e2) = all_53_4
% 230.99/42.22    (14)   ~ (all_53_4 = all_52_19)
% 230.99/42.22    (15)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.99/42.22          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.99/42.22    (16)   ~ (all_53_4 = e0)
% 230.99/42.22    (17)  all_57_4 = e2 & op(e3, e1) = e2
% 230.99/42.22    (18)   ~ (all_52_19 = e0)
% 230.99/42.22    (19)  all_55_13 = all_53_7
% 230.99/42.22    (20)  op(all_52_19, all_52_19) = e2
% 230.99/42.22  
% 230.99/42.22  Begin of proof
% 230.99/42.22  | 
% 230.99/42.22  | ALPHA: (17) implies:
% 230.99/42.22  |   (21)  all_57_4 = e2
% 230.99/42.22  | 
% 230.99/42.22  | BETA: splitting (11) gives:
% 230.99/42.22  | 
% 230.99/42.22  | Case 1:
% 230.99/42.22  | | 
% 230.99/42.22  | |   (22)  all_55_13 = e2
% 230.99/42.22  | | 
% 230.99/42.22  | | COMBINE_EQS: (19), (22) imply:
% 230.99/42.22  | |   (23)  all_53_7 = e2
% 230.99/42.22  | | 
% 230.99/42.22  | | SIMP: (23) implies:
% 230.99/42.22  | |   (24)  all_53_7 = e2
% 230.99/42.22  | | 
% 230.99/42.22  | | REDUCE: (10), (24) imply:
% 230.99/42.22  | |   (25)   ~ (all_53_4 = e2)
% 230.99/42.22  | | 
% 230.99/42.22  | | REDUCE: (1), (24) imply:
% 230.99/42.22  | |   (26)   ~ (all_52_19 = e2)
% 230.99/42.22  | | 
% 230.99/42.22  | | SIMP: (26) implies:
% 230.99/42.22  | |   (27)   ~ (all_52_19 = e2)
% 230.99/42.22  | | 
% 230.99/42.22  | | REDUCE: (12), (24) imply:
% 230.99/42.22  | |   (28)   ~ (e2 = e0)
% 230.99/42.22  | | 
% 230.99/42.22  | | REF_CLOSE: (2), (4), (5), (6), (7), (8), (9), (13), (14), (15), (16), (18),
% 230.99/42.22  | |            (20), (21), (25), (27), (28) are inconsistent by sub-proof #1319.
% 230.99/42.22  | | 
% 230.99/42.22  | Case 2:
% 230.99/42.22  | | 
% 230.99/42.22  | |   (29)  all_55_13 = e1 | all_55_13 = e0
% 230.99/42.22  | | 
% 230.99/42.22  | | REF_CLOSE: (3), (12), (19), (29) are inconsistent by sub-proof #1837.
% 230.99/42.22  | | 
% 230.99/42.22  | End of split
% 230.99/42.22  | 
% 230.99/42.22  End of proof
% 230.99/42.22  
% 230.99/42.22  Sub-proof #1319 shows that the following formulas are inconsistent:
% 230.99/42.22  ----------------------------------------------------------------
% 230.99/42.22    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.99/42.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.99/42.22    (2)  all_55_9 = all_52_19
% 230.99/42.22    (3)  all_57_4 = e2
% 230.99/42.22    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.99/42.22         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.99/42.22    (5)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 230.99/42.22    (6)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.99/42.22         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.99/42.22    (7)  all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 230.99/42.22    (8)  all_55_1 = all_53_4
% 230.99/42.22    (9)  op(e3, e2) = all_53_4
% 230.99/42.22    (10)   ~ (all_53_4 = all_52_19)
% 230.99/42.22    (11)   ~ (e2 = e0)
% 230.99/42.22    (12)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.99/42.22          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.99/42.22    (13)   ~ (all_53_4 = e0)
% 230.99/42.22    (14)   ~ (all_52_19 = e0)
% 230.99/42.22    (15)   ~ (all_53_4 = e2)
% 230.99/42.22    (16)  op(all_52_19, all_52_19) = e2
% 230.99/42.22    (17)   ~ (all_52_19 = e2)
% 230.99/42.22  
% 230.99/42.22  Begin of proof
% 230.99/42.22  | 
% 230.99/42.22  | BETA: splitting (7) gives:
% 230.99/42.22  | 
% 230.99/42.22  | Case 1:
% 230.99/42.22  | | 
% 230.99/42.22  | |   (18)  all_55_1 = e2
% 230.99/42.22  | | 
% 230.99/42.22  | | REF_CLOSE: (8), (15), (18) are inconsistent by sub-proof #2284.
% 230.99/42.22  | | 
% 230.99/42.22  | Case 2:
% 230.99/42.22  | | 
% 230.99/42.22  | |   (19)   ~ (all_55_1 = e2)
% 230.99/42.22  | |   (20)  all_55_1 = e1 | all_55_1 = e0
% 230.99/42.22  | | 
% 230.99/42.22  | | BETA: splitting (20) gives:
% 230.99/42.22  | | 
% 230.99/42.22  | | Case 1:
% 230.99/42.22  | | | 
% 230.99/42.22  | | |   (21)  all_55_1 = e1
% 230.99/42.22  | | | 
% 230.99/42.22  | | | COMBINE_EQS: (8), (21) imply:
% 230.99/42.22  | | |   (22)  all_53_4 = e1
% 230.99/42.22  | | | 
% 230.99/42.22  | | | SIMP: (22) implies:
% 230.99/42.22  | | |   (23)  all_53_4 = e1
% 230.99/42.22  | | | 
% 230.99/42.22  | | | REDUCE: (10), (23) imply:
% 230.99/42.22  | | |   (24)   ~ (all_52_19 = e1)
% 230.99/42.22  | | | 
% 230.99/42.22  | | | SIMP: (24) implies:
% 230.99/42.22  | | |   (25)   ~ (all_52_19 = e1)
% 230.99/42.22  | | | 
% 230.99/42.22  | | | REDUCE: (15), (23) imply:
% 230.99/42.22  | | |   (26)   ~ (e2 = e1)
% 230.99/42.22  | | | 
% 230.99/42.22  | | | SIMP: (26) implies:
% 230.99/42.22  | | |   (27)   ~ (e2 = e1)
% 230.99/42.22  | | | 
% 230.99/42.22  | | | REDUCE: (13), (23) imply:
% 230.99/42.22  | | |   (28)   ~ (e1 = e0)
% 230.99/42.22  | | | 
% 230.99/42.22  | | | BETA: splitting (5) gives:
% 230.99/42.22  | | | 
% 230.99/42.22  | | | Case 1:
% 230.99/42.22  | | | | 
% 230.99/42.22  | | | |   (29)  all_55_9 = e3
% 230.99/42.22  | | | | 
% 230.99/42.22  | | | | COMBINE_EQS: (2), (29) imply:
% 230.99/42.22  | | | |   (30)  all_52_19 = e3
% 230.99/42.22  | | | | 
% 230.99/42.22  | | | | REDUCE: (17), (30) imply:
% 230.99/42.22  | | | |   (31)   ~ (e3 = e2)
% 230.99/42.22  | | | | 
% 230.99/42.22  | | | | REDUCE: (25), (30) imply:
% 230.99/42.22  | | | |   (32)   ~ (e3 = e1)
% 230.99/42.22  | | | | 
% 230.99/42.22  | | | | REDUCE: (14), (30) imply:
% 230.99/42.22  | | | |   (33)   ~ (e3 = e0)
% 230.99/42.22  | | | | 
% 230.99/42.22  | | | | REDUCE: (16), (30) imply:
% 230.99/42.22  | | | |   (34)  op(e3, e3) = e2
% 230.99/42.22  | | | | 
% 230.99/42.22  | | | | REF_CLOSE: (1), (3), (4), (6), (9), (11), (12), (13), (27), (28), (31),
% 230.99/42.22  | | | |            (32), (33), (34) are inconsistent by sub-proof #1320.
% 230.99/42.22  | | | | 
% 230.99/42.22  | | | Case 2:
% 230.99/42.22  | | | | 
% 230.99/42.22  | | | |   (35)  all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 230.99/42.22  | | | | 
% 230.99/42.22  | | | | REF_CLOSE: (2), (14), (17), (25), (35) are inconsistent by sub-proof
% 230.99/42.22  | | | |            #1882.
% 230.99/42.22  | | | | 
% 230.99/42.22  | | | End of split
% 230.99/42.22  | | | 
% 230.99/42.22  | | Case 2:
% 230.99/42.22  | | | 
% 230.99/42.22  | | |   (36)  all_55_1 = e0
% 230.99/42.22  | | | 
% 230.99/42.22  | | | REF_CLOSE: (8), (13), (36) are inconsistent by sub-proof #2076.
% 230.99/42.22  | | | 
% 230.99/42.22  | | End of split
% 230.99/42.22  | | 
% 230.99/42.22  | End of split
% 230.99/42.22  | 
% 230.99/42.22  End of proof
% 230.99/42.22  
% 230.99/42.22  Sub-proof #1320 shows that the following formulas are inconsistent:
% 230.99/42.22  ----------------------------------------------------------------
% 230.99/42.22    (1)   ~ (e3 = e1)
% 230.99/42.22    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.99/42.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.99/42.22    (3)  all_57_4 = e2
% 230.99/42.22    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.99/42.22         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.99/42.22    (5)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.99/42.22         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.99/42.22    (6)   ~ (e3 = e2)
% 230.99/42.22    (7)   ~ (e3 = e0)
% 230.99/42.22    (8)  op(e3, e3) = e2
% 230.99/42.22    (9)  op(e3, e2) = all_53_4
% 230.99/42.22    (10)   ~ (e2 = e0)
% 230.99/42.22    (11)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.99/42.22          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.99/42.22    (12)   ~ (e1 = e0)
% 230.99/42.22    (13)   ~ (all_53_4 = e0)
% 230.99/42.22    (14)   ~ (e2 = e1)
% 230.99/42.22  
% 230.99/42.22  Begin of proof
% 230.99/42.22  | 
% 230.99/42.22  | BETA: splitting (5) gives:
% 230.99/42.22  | 
% 230.99/42.22  | Case 1:
% 230.99/42.22  | | 
% 230.99/42.22  | |   (15)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) =
% 230.99/42.22  | |           e0)
% 230.99/42.22  | | 
% 230.99/42.22  | | REF_CLOSE: (2), (8), (9), (10), (13), (15) are inconsistent by sub-proof
% 230.99/42.22  | |            #1321.
% 230.99/42.22  | | 
% 230.99/42.22  | Case 2:
% 230.99/42.22  | | 
% 230.99/42.22  | |   (16)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) =
% 230.99/42.22  | |           e0)
% 230.99/42.22  | | 
% 230.99/42.22  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (10), (11), (12), (14), (16)
% 230.99/42.22  | |            are inconsistent by sub-proof #1605.
% 230.99/42.22  | | 
% 230.99/42.22  | End of split
% 230.99/42.22  | 
% 230.99/42.22  End of proof
% 230.99/42.22  
% 230.99/42.22  Sub-proof #1321 shows that the following formulas are inconsistent:
% 230.99/42.22  ----------------------------------------------------------------
% 230.99/42.22    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.99/42.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.99/42.22    (2)  op(e3, e3) = e2
% 230.99/42.22    (3)  op(e3, e2) = all_53_4
% 230.99/42.22    (4)   ~ (e2 = e0)
% 230.99/42.22    (5)   ~ (all_53_4 = e0)
% 230.99/42.22    (6)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0)
% 230.99/42.22  
% 230.99/42.22  Begin of proof
% 230.99/42.22  | 
% 230.99/42.22  | BETA: splitting (6) gives:
% 230.99/42.22  | 
% 230.99/42.22  | Case 1:
% 230.99/42.22  | | 
% 230.99/42.22  | |   (7)  all_57_0 = e0 & op(e3, e3) = e0
% 230.99/42.22  | | 
% 230.99/42.22  | | ALPHA: (7) implies:
% 230.99/42.22  | |   (8)  op(e3, e3) = e0
% 230.99/42.22  | | 
% 230.99/42.22  | | REF_CLOSE: (1), (2), (4), (8) are inconsistent by sub-proof #2403.
% 230.99/42.22  | | 
% 230.99/42.22  | Case 2:
% 230.99/42.22  | | 
% 230.99/42.22  | |   (9)  all_57_1 = e0 & op(e3, e2) = e0
% 230.99/42.22  | | 
% 230.99/42.22  | | ALPHA: (9) implies:
% 230.99/42.22  | |   (10)  op(e3, e2) = e0
% 230.99/42.22  | | 
% 230.99/42.22  | | REF_CLOSE: (1), (3), (5), (10) are inconsistent by sub-proof #1941.
% 230.99/42.22  | | 
% 230.99/42.22  | End of split
% 230.99/42.22  | 
% 230.99/42.22  End of proof
% 230.99/42.22  
% 230.99/42.22  Sub-proof #1322 shows that the following formulas are inconsistent:
% 230.99/42.22  ----------------------------------------------------------------
% 230.99/42.22    (1)  all_55_7 = e1 | all_55_7 = e0
% 230.99/42.22    (2)  all_55_7 = all_53_13
% 230.99/42.22    (3)   ~ (all_53_13 = e1)
% 230.99/42.22    (4)   ~ (all_53_13 = e0)
% 230.99/42.22  
% 230.99/42.22  Begin of proof
% 230.99/42.22  | 
% 230.99/42.22  | BETA: splitting (1) gives:
% 230.99/42.22  | 
% 230.99/42.22  | Case 1:
% 230.99/42.22  | | 
% 230.99/42.22  | |   (5)  all_55_7 = e1
% 230.99/42.22  | | 
% 230.99/42.22  | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #1970.
% 230.99/42.22  | | 
% 230.99/42.22  | Case 2:
% 230.99/42.22  | | 
% 230.99/42.22  | |   (6)  all_55_7 = e0
% 230.99/42.22  | | 
% 230.99/42.22  | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #2130.
% 230.99/42.22  | | 
% 230.99/42.22  | End of split
% 230.99/42.22  | 
% 230.99/42.22  End of proof
% 230.99/42.22  
% 230.99/42.22  Sub-proof #1323 shows that the following formulas are inconsistent:
% 230.99/42.22  ----------------------------------------------------------------
% 230.99/42.22    (1)  op(e0, e0) = all_4_2
% 230.99/42.22    (2)   ~ (all_4_2 = e0)
% 230.99/42.22    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.99/42.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.99/42.22    (4)  all_55_15 = all_4_2
% 230.99/42.22    (5)  op(e2, e2) = e0
% 230.99/42.22    (6)   ~ (e3 = e2)
% 230.99/42.22    (7)   ~ (e3 = e0)
% 230.99/42.22    (8)   ~ (all_4_2 = e2)
% 230.99/42.22    (9)  op(e2, e2) = all_52_11
% 230.99/42.22    (10)  all_57_9 = e0
% 230.99/42.22    (11)   ~ (e2 = e0)
% 230.99/42.22    (12)   ~ (all_53_13 = all_4_2)
% 230.99/42.22    (13)  op(e2, e0) = all_53_13
% 230.99/42.22    (14)  all_55_15 = e1 | all_55_15 = e0
% 230.99/42.22    (15)   ~ (all_4_2 = e3)
% 230.99/42.22    (16)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 230.99/42.22          (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 230.99/42.22    (17)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 230.99/42.22          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 230.99/42.22    (18)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 230.99/42.22          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 230.99/42.22    (19)  op(all_52_11, all_52_11) = e2
% 230.99/42.22  
% 230.99/42.22  Begin of proof
% 230.99/42.22  | 
% 230.99/42.22  | BETA: splitting (14) gives:
% 230.99/42.22  | 
% 230.99/42.22  | Case 1:
% 230.99/42.22  | | 
% 230.99/42.22  | |   (20)  all_55_15 = e1
% 230.99/42.22  | | 
% 230.99/42.22  | | COMBINE_EQS: (4), (20) imply:
% 230.99/42.22  | |   (21)  all_4_2 = e1
% 230.99/42.22  | | 
% 230.99/42.22  | | SIMP: (21) implies:
% 230.99/42.22  | |   (22)  all_4_2 = e1
% 230.99/42.22  | | 
% 230.99/42.22  | | REDUCE: (12), (22) imply:
% 230.99/42.22  | |   (23)   ~ (all_53_13 = e1)
% 230.99/42.22  | | 
% 230.99/42.22  | | REDUCE: (15), (22) imply:
% 230.99/42.22  | |   (24)   ~ (e3 = e1)
% 230.99/42.22  | | 
% 230.99/42.22  | | SIMP: (24) implies:
% 230.99/42.22  | |   (25)   ~ (e3 = e1)
% 230.99/42.22  | | 
% 230.99/42.22  | | REDUCE: (8), (22) imply:
% 230.99/42.22  | |   (26)   ~ (e2 = e1)
% 230.99/42.22  | | 
% 230.99/42.22  | | SIMP: (26) implies:
% 230.99/42.22  | |   (27)   ~ (e2 = e1)
% 230.99/42.22  | | 
% 230.99/42.22  | | REDUCE: (2), (22) imply:
% 230.99/42.22  | |   (28)   ~ (e1 = e0)
% 230.99/42.22  | | 
% 230.99/42.22  | | REDUCE: (1), (22) imply:
% 230.99/42.22  | |   (29)  op(e0, e0) = e1
% 230.99/42.22  | | 
% 230.99/42.22  | | BETA: splitting (18) gives:
% 230.99/42.22  | | 
% 230.99/42.22  | | Case 1:
% 230.99/42.22  | | | 
% 230.99/42.22  | | |   (30)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) =
% 230.99/42.22  | | |           e1)
% 230.99/42.22  | | | 
% 230.99/42.22  | | | REF_CLOSE: (3), (10), (13), (23), (28), (30) are inconsistent by sub-proof
% 230.99/42.22  | | |            #1324.
% 230.99/42.22  | | | 
% 230.99/42.22  | | Case 2:
% 230.99/42.22  | | | 
% 230.99/42.22  | | |   (31)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0)
% 230.99/42.22  | | |           = e1)
% 230.99/42.22  | | | 
% 230.99/42.22  | | | BETA: splitting (31) gives:
% 230.99/42.22  | | | 
% 230.99/42.22  | | | Case 1:
% 230.99/42.22  | | | | 
% 230.99/42.22  | | | |   (32)  all_57_11 = e1 & op(e1, e0) = e1
% 230.99/42.22  | | | | 
% 230.99/42.22  | | | | ALPHA: (32) implies:
% 230.99/42.22  | | | |   (33)  all_57_11 = e1
% 230.99/42.22  | | | | 
% 230.99/42.22  | | | | REF_CLOSE: (3), (6), (7), (10), (11), (16), (17), (25), (27), (29), (33)
% 230.99/42.22  | | | |            are inconsistent by sub-proof #2047.
% 230.99/42.22  | | | | 
% 230.99/42.22  | | | Case 2:
% 230.99/42.22  | | | | 
% 230.99/42.22  | | | |   (34)  all_57_15 = e1 & op(e0, e0) = e1
% 230.99/42.22  | | | | 
% 230.99/42.22  | | | | REF_CLOSE: (3), (5), (9), (19), (27), (34) are inconsistent by sub-proof
% 230.99/42.22  | | | |            #2066.
% 230.99/42.22  | | | | 
% 230.99/42.22  | | | End of split
% 230.99/42.22  | | | 
% 230.99/42.22  | | End of split
% 230.99/42.22  | | 
% 230.99/42.22  | Case 2:
% 230.99/42.22  | | 
% 230.99/42.22  | |   (35)  all_55_15 = e0
% 230.99/42.22  | | 
% 230.99/42.22  | | REF_CLOSE: (2), (4), (35) are inconsistent by sub-proof #1884.
% 230.99/42.22  | | 
% 230.99/42.22  | End of split
% 230.99/42.22  | 
% 230.99/42.22  End of proof
% 230.99/42.22  
% 230.99/42.22  Sub-proof #1324 shows that the following formulas are inconsistent:
% 230.99/42.22  ----------------------------------------------------------------
% 230.99/42.22    (1)   ~ (all_53_13 = e1)
% 230.99/42.22    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.99/42.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.99/42.22    (3)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.99/42.22    (4)  all_57_9 = e0
% 230.99/42.22    (5)   ~ (e1 = e0)
% 230.99/42.22    (6)  op(e2, e0) = all_53_13
% 230.99/42.22  
% 230.99/42.22  Begin of proof
% 230.99/42.22  | 
% 230.99/42.22  | BETA: splitting (3) gives:
% 230.99/42.22  | 
% 230.99/42.22  | Case 1:
% 230.99/42.22  | | 
% 230.99/42.22  | |   (7)  all_57_9 = e1 & op(e3, e0) = e1
% 230.99/42.22  | | 
% 230.99/42.22  | | ALPHA: (7) implies:
% 230.99/42.22  | |   (8)  all_57_9 = e1
% 230.99/42.22  | | 
% 230.99/42.22  | | REF_CLOSE: (4), (5), (8) are inconsistent by sub-proof #2479.
% 230.99/42.22  | | 
% 230.99/42.22  | Case 2:
% 230.99/42.22  | | 
% 230.99/42.22  | |   (9)  all_57_10 = e1 & op(e2, e0) = e1
% 230.99/42.22  | | 
% 230.99/42.22  | | REF_CLOSE: (1), (2), (6), (9) are inconsistent by sub-proof #2084.
% 230.99/42.22  | | 
% 230.99/42.22  | End of split
% 230.99/42.22  | 
% 230.99/42.22  End of proof
% 230.99/42.22  
% 230.99/42.22  Sub-proof #1325 shows that the following formulas are inconsistent:
% 230.99/42.22  ----------------------------------------------------------------
% 230.99/42.22    (1)  op(e0, e0) = all_4_2
% 230.99/42.22    (2)   ~ (all_4_2 = e0)
% 230.99/42.22    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.99/42.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.99/42.22    (4)  all_55_15 = all_4_2
% 230.99/42.22    (5)  op(all_52_7, all_52_7) = e0
% 230.99/42.22    (6)  op(e3, e0) = e0
% 230.99/42.22    (7)  all_55_15 = e1 | all_55_15 = e0
% 230.99/42.22    (8)  op(e3, e0) = all_52_7
% 230.99/42.22  
% 230.99/42.22  Begin of proof
% 230.99/42.22  | 
% 230.99/42.22  | BETA: splitting (7) gives:
% 230.99/42.22  | 
% 230.99/42.22  | Case 1:
% 230.99/42.22  | | 
% 230.99/42.22  | |   (9)  all_55_15 = e1
% 230.99/42.22  | | 
% 230.99/42.22  | | COMBINE_EQS: (4), (9) imply:
% 230.99/42.22  | |   (10)  all_4_2 = e1
% 230.99/42.22  | | 
% 230.99/42.22  | | SIMP: (10) implies:
% 230.99/42.22  | |   (11)  all_4_2 = e1
% 230.99/42.22  | | 
% 230.99/42.22  | | REDUCE: (2), (11) imply:
% 230.99/42.22  | |   (12)   ~ (e1 = e0)
% 230.99/42.22  | | 
% 230.99/42.22  | | REDUCE: (1), (11) imply:
% 230.99/42.22  | |   (13)  op(e0, e0) = e1
% 230.99/42.22  | | 
% 230.99/42.22  | | REF_CLOSE: (3), (5), (6), (8), (12), (13) are inconsistent by sub-proof
% 230.99/42.22  | |            #2000.
% 230.99/42.22  | | 
% 230.99/42.22  | Case 2:
% 230.99/42.22  | | 
% 230.99/42.22  | |   (14)  all_55_15 = e0
% 230.99/42.22  | | 
% 230.99/42.22  | | REF_CLOSE: (2), (4), (14) are inconsistent by sub-proof #1884.
% 230.99/42.22  | | 
% 230.99/42.22  | End of split
% 230.99/42.22  | 
% 230.99/42.22  End of proof
% 230.99/42.22  
% 230.99/42.22  Sub-proof #1326 shows that the following formulas are inconsistent:
% 230.99/42.22  ----------------------------------------------------------------
% 230.99/42.22    (1)   ~ (all_14_1 = e3) & op(e2, e0) = all_14_1 & $i(all_14_1)
% 230.99/42.22    (2)  ( ~ (all_50_0 = e3) & op(all_50_1, e2) = all_50_0 & op(e2, e0) = all_50_1
% 230.99/42.22           & $i(all_50_0) & $i(all_50_1)) | ( ~ (all_50_1 = e1) & op(e2, e0) =
% 230.99/42.22           all_50_1 & $i(all_50_1))
% 230.99/42.22    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.99/42.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.99/42.22    (4)  op(e2, e0) = e3
% 230.99/42.22  
% 230.99/42.22  Begin of proof
% 230.99/42.22  | 
% 230.99/42.22  | ALPHA: (1) implies:
% 230.99/42.22  |   (5)   ~ (all_14_1 = e3)
% 230.99/42.22  |   (6)  op(e2, e0) = all_14_1
% 230.99/42.22  | 
% 230.99/42.22  | BETA: splitting (2) gives:
% 230.99/42.22  | 
% 230.99/42.22  | Case 1:
% 230.99/42.22  | | 
% 230.99/42.22  | |   (7)   ~ (all_50_0 = e3) & op(all_50_1, e2) = all_50_0 & op(e2, e0) =
% 230.99/42.22  | |        all_50_1 & $i(all_50_0) & $i(all_50_1)
% 230.99/42.22  | | 
% 230.99/42.22  | | ALPHA: (7) implies:
% 230.99/42.22  | |   (8)  op(e2, e0) = all_50_1
% 230.99/42.22  | | 
% 230.99/42.22  | | REF_CLOSE: (3), (4), (5), (6), (8) are inconsistent by sub-proof #1327.
% 230.99/42.22  | | 
% 230.99/42.22  | Case 2:
% 230.99/42.22  | | 
% 230.99/42.22  | |   (9)   ~ (all_50_1 = e1) & op(e2, e0) = all_50_1 & $i(all_50_1)
% 230.99/42.22  | | 
% 230.99/42.22  | | ALPHA: (9) implies:
% 230.99/42.22  | |   (10)  op(e2, e0) = all_50_1
% 230.99/42.22  | | 
% 230.99/42.22  | | REF_CLOSE: (3), (4), (5), (6), (10) are inconsistent by sub-proof #1327.
% 230.99/42.22  | | 
% 230.99/42.22  | End of split
% 230.99/42.22  | 
% 230.99/42.22  End of proof
% 230.99/42.22  
% 230.99/42.22  Sub-proof #1327 shows that the following formulas are inconsistent:
% 230.99/42.22  ----------------------------------------------------------------
% 230.99/42.22    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.99/42.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.99/42.22    (2)  op(e2, e0) = e3
% 230.99/42.22    (3)  op(e2, e0) = all_14_1
% 230.99/42.22    (4)  op(e2, e0) = all_50_1
% 230.99/42.22    (5)   ~ (all_14_1 = e3)
% 230.99/42.22  
% 230.99/42.22  Begin of proof
% 230.99/42.22  | 
% 230.99/42.22  | GROUND_INST: instantiating (1) with all_14_1, all_50_1, e0, e2, simplifying
% 230.99/42.22  |              with (3), (4) gives:
% 230.99/42.22  |   (6)  all_50_1 = all_14_1
% 230.99/42.22  | 
% 230.99/42.22  | GROUND_INST: instantiating (1) with e3, all_50_1, e0, e2, simplifying with
% 230.99/42.22  |              (2), (4) gives:
% 230.99/42.22  |   (7)  all_50_1 = e3
% 230.99/42.22  | 
% 230.99/42.23  | COMBINE_EQS: (6), (7) imply:
% 230.99/42.23  |   (8)  all_14_1 = e3
% 230.99/42.23  | 
% 230.99/42.23  | SIMP: (8) implies:
% 230.99/42.23  |   (9)  all_14_1 = e3
% 230.99/42.23  | 
% 230.99/42.23  | REDUCE: (5), (9) imply:
% 230.99/42.23  |   (10)  $false
% 230.99/42.23  | 
% 230.99/42.23  | CLOSE: (10) is inconsistent.
% 230.99/42.23  | 
% 230.99/42.23  End of proof
% 230.99/42.23  
% 230.99/42.23  Sub-proof #1328 shows that the following formulas are inconsistent:
% 230.99/42.23  ----------------------------------------------------------------
% 230.99/42.23    (1)   ~ (all_14_0 = e1)
% 230.99/42.23    (2)  op(all_14_1, e2) = all_14_0
% 230.99/42.23    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.99/42.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.99/42.23    (4)  op(e2, e0) = e3
% 230.99/42.23    (5)  op(e3, e2) = e1
% 230.99/42.23    (6)  op(e2, e0) = all_14_1
% 230.99/42.23    (7)  op(e2, e0) = all_50_1
% 230.99/42.23  
% 230.99/42.23  Begin of proof
% 230.99/42.23  | 
% 230.99/42.23  | GROUND_INST: instantiating (3) with all_14_1, all_50_1, e0, e2, simplifying
% 230.99/42.23  |              with (6), (7) gives:
% 230.99/42.23  |   (8)  all_50_1 = all_14_1
% 230.99/42.23  | 
% 230.99/42.23  | GROUND_INST: instantiating (3) with e3, all_50_1, e0, e2, simplifying with
% 230.99/42.23  |              (4), (7) gives:
% 230.99/42.23  |   (9)  all_50_1 = e3
% 230.99/42.23  | 
% 230.99/42.23  | COMBINE_EQS: (8), (9) imply:
% 230.99/42.23  |   (10)  all_14_1 = e3
% 230.99/42.23  | 
% 230.99/42.23  | SIMP: (10) implies:
% 230.99/42.23  |   (11)  all_14_1 = e3
% 230.99/42.23  | 
% 230.99/42.23  | REDUCE: (2), (11) imply:
% 230.99/42.23  |   (12)  op(e3, e2) = all_14_0
% 230.99/42.23  | 
% 230.99/42.23  | GROUND_INST: instantiating (3) with e1, all_14_0, e2, e3, simplifying with
% 230.99/42.23  |              (5), (12) gives:
% 230.99/42.23  |   (13)  all_14_0 = e1
% 230.99/42.23  | 
% 230.99/42.23  | REDUCE: (1), (13) imply:
% 230.99/42.23  |   (14)  $false
% 230.99/42.23  | 
% 230.99/42.23  | CLOSE: (14) is inconsistent.
% 230.99/42.23  | 
% 230.99/42.23  End of proof
% 230.99/42.23  
% 230.99/42.23  Sub-proof #1329 shows that the following formulas are inconsistent:
% 230.99/42.23  ----------------------------------------------------------------
% 230.99/42.23    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.99/42.23         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.99/42.23    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.99/42.23         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.99/42.23    (3)   ~ (e3 = e1)
% 230.99/42.23    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.99/42.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.99/42.23    (5)   ~ (all_6_2 = e3)
% 230.99/42.23    (6)  op(e1, e1) = all_6_2
% 230.99/42.23    (7)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.99/42.23         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.99/42.23    (8)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.99/42.23         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.99/42.23    (9)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.99/42.23         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.99/42.23    (10)  all_57_3 = e0
% 230.99/42.23    (11)   ~ (e3 = e2)
% 230.99/42.23    (12)   ~ (e3 = e0)
% 230.99/42.23    (13)  op(e3, e3) = e3
% 230.99/42.23    (14)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.99/42.23          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.99/42.23            e1)
% 230.99/42.23    (15)  all_57_11 = e0
% 230.99/42.23    (16)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.99/42.23          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.99/42.23    (17)   ~ (e2 = e0)
% 230.99/42.23    (18)  all_57_2 = e3
% 230.99/42.23    (19)   ~ (e1 = e0)
% 230.99/42.23    (20)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 230.99/42.23          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 230.99/42.23    (21)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.99/42.23          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.99/42.23            e2)
% 230.99/42.23    (22)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.99/42.23              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.99/42.23                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.99/42.23                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.99/42.23    (23)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.99/42.23          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.99/42.23    (24)   ~ (all_53_12 = e3)
% 230.99/42.23    (25)  all_57_7 = e3
% 230.99/42.23    (26)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.99/42.23          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.99/42.23    (27)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 230.99/42.23          (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 230.99/42.23    (28)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.99/42.23          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 230.99/42.23    (29)   ~ (e2 = e1)
% 230.99/42.23    (30)  op(e3, e0) = all_53_12
% 230.99/42.23  
% 230.99/42.23  Begin of proof
% 230.99/42.23  | 
% 230.99/42.23  | BETA: splitting (27) gives:
% 230.99/42.23  | 
% 230.99/42.23  | Case 1:
% 230.99/42.23  | | 
% 230.99/42.23  | |   (31)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 230.99/42.23  | |           e3)
% 230.99/42.23  | | 
% 230.99/42.23  | | REF_CLOSE: (1), (3), (4), (10), (11), (17), (18), (19), (24), (26), (29),
% 230.99/42.23  | |            (30), (31) are inconsistent by sub-proof #1334.
% 230.99/42.23  | | 
% 230.99/42.23  | Case 2:
% 230.99/42.23  | | 
% 230.99/42.23  | |   (32)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 230.99/42.23  | |           e3)
% 230.99/42.23  | | 
% 230.99/42.23  | | BETA: splitting (32) gives:
% 230.99/42.23  | | 
% 230.99/42.23  | | Case 1:
% 230.99/42.23  | | | 
% 230.99/42.23  | | |   (33)  all_57_11 = e3 & op(e1, e0) = e3
% 230.99/42.23  | | | 
% 230.99/42.23  | | | ALPHA: (33) implies:
% 230.99/42.23  | | |   (34)  all_57_11 = e3
% 230.99/42.23  | | | 
% 230.99/42.23  | | | COMBINE_EQS: (15), (34) imply:
% 230.99/42.23  | | |   (35)  e3 = e0
% 230.99/42.23  | | | 
% 230.99/42.23  | | | REF_CLOSE: (1), (3), (10), (11), (12), (17), (18), (19), (23), (26), (29),
% 230.99/42.23  | | |            (35) are inconsistent by sub-proof #1333.
% 230.99/42.23  | | | 
% 230.99/42.23  | | Case 2:
% 230.99/42.23  | | | 
% 230.99/42.23  | | |   (36)  all_57_15 = e3 & op(e0, e0) = e3
% 230.99/42.23  | | | 
% 230.99/42.23  | | | ALPHA: (36) implies:
% 230.99/42.23  | | |   (37)  all_57_15 = e3
% 230.99/42.23  | | | 
% 230.99/42.23  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13),
% 230.99/42.23  | | |            (14), (16), (17), (18), (19), (20), (21), (22), (25), (26),
% 230.99/42.23  | | |            (28), (29), (37) are inconsistent by sub-proof #1330.
% 230.99/42.23  | | | 
% 230.99/42.23  | | End of split
% 230.99/42.23  | | 
% 230.99/42.23  | End of split
% 230.99/42.23  | 
% 230.99/42.23  End of proof
% 230.99/42.23  
% 230.99/42.23  Sub-proof #1330 shows that the following formulas are inconsistent:
% 230.99/42.23  ----------------------------------------------------------------
% 230.99/42.23    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.99/42.23         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.99/42.23    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.99/42.23         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.99/42.23    (3)   ~ (e3 = e1)
% 230.99/42.23    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.99/42.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.99/42.23    (5)   ~ (all_6_2 = e3)
% 230.99/42.23    (6)  op(e1, e1) = all_6_2
% 230.99/42.23    (7)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.99/42.23         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.99/42.23    (8)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.99/42.23         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.99/42.23    (9)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.99/42.23         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.99/42.23    (10)   ~ (e3 = e2)
% 230.99/42.23    (11)   ~ (e3 = e0)
% 230.99/42.23    (12)  op(e3, e3) = e3
% 230.99/42.23    (13)  all_57_15 = e3
% 230.99/42.23    (14)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.99/42.23          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.99/42.23            e1)
% 230.99/42.23    (15)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.99/42.23          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.99/42.23    (16)   ~ (e2 = e0)
% 230.99/42.23    (17)  all_57_2 = e3
% 230.99/42.23    (18)   ~ (e1 = e0)
% 230.99/42.23    (19)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 230.99/42.23          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 230.99/42.23    (20)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.99/42.23          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.99/42.23            e2)
% 230.99/42.23    (21)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.99/42.23              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.99/42.23                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.99/42.23                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.99/42.23    (22)  all_57_7 = e3
% 230.99/42.23    (23)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.99/42.23          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.99/42.23    (24)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.99/42.23          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 230.99/42.23    (25)   ~ (e2 = e1)
% 230.99/42.23  
% 230.99/42.23  Begin of proof
% 230.99/42.23  | 
% 230.99/42.23  | BETA: splitting (19) gives:
% 230.99/42.23  | 
% 230.99/42.23  | Case 1:
% 230.99/42.23  | | 
% 230.99/42.23  | |   (26)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) =
% 230.99/42.23  | |           e3)
% 230.99/42.23  | | 
% 230.99/42.23  | | BETA: splitting (26) gives:
% 230.99/42.23  | | 
% 230.99/42.23  | | Case 1:
% 230.99/42.23  | | | 
% 230.99/42.23  | | |   (27)  all_57_4 = e3 & op(e3, e1) = e3
% 230.99/42.23  | | | 
% 230.99/42.23  | | | ALPHA: (27) implies:
% 230.99/42.23  | | |   (28)  all_57_4 = e3
% 230.99/42.23  | | | 
% 230.99/42.23  | | | REF_CLOSE: (3), (4), (7), (8), (9), (10), (11), (12), (16), (18), (25),
% 230.99/42.23  | | |            (28) are inconsistent by sub-proof #2474.
% 230.99/42.23  | | | 
% 230.99/42.23  | | Case 2:
% 230.99/42.23  | | | 
% 230.99/42.23  | | |   (29)  all_57_5 = e3 & op(e2, e1) = e3
% 230.99/42.23  | | | 
% 230.99/42.23  | | | ALPHA: (29) implies:
% 230.99/42.23  | | |   (30)  all_57_5 = e3
% 230.99/42.23  | | | 
% 230.99/42.23  | | | BETA: splitting (1) gives:
% 230.99/42.23  | | | 
% 230.99/42.23  | | | Case 1:
% 230.99/42.23  | | | | 
% 230.99/42.23  | | | |   (31)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2)
% 230.99/42.23  | | | |           = e1)
% 230.99/42.23  | | | | 
% 230.99/42.23  | | | | BETA: splitting (31) gives:
% 230.99/42.23  | | | | 
% 230.99/42.23  | | | | Case 1:
% 230.99/42.23  | | | | | 
% 230.99/42.23  | | | | |   (32)  all_57_2 = e1 & op(e2, e3) = e1
% 230.99/42.23  | | | | | 
% 230.99/42.23  | | | | | REF_CLOSE: (3), (17), (32) are inconsistent by sub-proof #1928.
% 230.99/42.23  | | | | | 
% 230.99/42.23  | | | | Case 2:
% 230.99/42.23  | | | | | 
% 230.99/42.23  | | | | |   (33)  all_57_3 = e1 & op(e2, e2) = e1
% 230.99/42.23  | | | | | 
% 230.99/42.23  | | | | | ALPHA: (33) implies:
% 230.99/42.23  | | | | |   (34)  op(e2, e2) = e1
% 230.99/42.23  | | | | | 
% 230.99/42.23  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 230.99/42.23  | | | | |            (12), (13), (14), (15), (16), (17), (18), (19), (20), (21),
% 230.99/42.23  | | | | |            (22), (23), (24), (25), (34) are inconsistent by sub-proof
% 230.99/42.23  | | | | |            #1793.
% 230.99/42.23  | | | | | 
% 230.99/42.23  | | | | End of split
% 230.99/42.23  | | | | 
% 230.99/42.23  | | | Case 2:
% 230.99/42.23  | | | | 
% 230.99/42.23  | | | |   (35)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0)
% 230.99/42.23  | | | |           = e1)
% 230.99/42.23  | | | | 
% 230.99/42.23  | | | | BETA: splitting (35) gives:
% 230.99/42.23  | | | | 
% 230.99/42.23  | | | | Case 1:
% 230.99/42.23  | | | | | 
% 230.99/42.23  | | | | |   (36)  all_57_5 = e1 & op(e2, e1) = e1
% 230.99/42.23  | | | | | 
% 230.99/42.23  | | | | | REF_CLOSE: (3), (30), (36) are inconsistent by sub-proof #2376.
% 230.99/42.23  | | | | | 
% 230.99/42.23  | | | | Case 2:
% 230.99/42.23  | | | | | 
% 230.99/42.23  | | | | |   (37)  all_57_10 = e1 & op(e2, e0) = e1
% 230.99/42.23  | | | | | 
% 230.99/42.23  | | | | | ALPHA: (37) implies:
% 230.99/42.23  | | | | |   (38)  all_57_10 = e1
% 230.99/42.23  | | | | | 
% 230.99/42.23  | | | | | REF_CLOSE: (1), (3), (10), (11), (16), (17), (18), (23), (24), (25),
% 230.99/42.23  | | | | |            (30), (38) are inconsistent by sub-proof #1331.
% 230.99/42.23  | | | | | 
% 230.99/42.23  | | | | End of split
% 230.99/42.23  | | | | 
% 230.99/42.23  | | | End of split
% 230.99/42.23  | | | 
% 230.99/42.23  | | End of split
% 230.99/42.23  | | 
% 230.99/42.23  | Case 2:
% 230.99/42.23  | | 
% 230.99/42.23  | |   (39)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) =
% 230.99/42.23  | |           e3)
% 230.99/42.23  | | 
% 230.99/42.23  | | REF_CLOSE: (3), (4), (5), (6), (10), (11), (13), (14), (16), (18), (20),
% 230.99/42.23  | |            (21), (25), (39) are inconsistent by sub-proof #1794.
% 230.99/42.23  | | 
% 230.99/42.23  | End of split
% 230.99/42.23  | 
% 230.99/42.23  End of proof
% 230.99/42.23  
% 230.99/42.23  Sub-proof #1331 shows that the following formulas are inconsistent:
% 230.99/42.23  ----------------------------------------------------------------
% 230.99/42.23    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.99/42.23         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.99/42.23    (2)   ~ (e3 = e1)
% 230.99/42.23    (3)  all_57_10 = e1
% 230.99/42.23    (4)   ~ (e3 = e2)
% 230.99/42.23    (5)   ~ (e3 = e0)
% 230.99/42.23    (6)  all_57_5 = e3
% 230.99/42.23    (7)   ~ (e2 = e0)
% 230.99/42.23    (8)  all_57_2 = e3
% 230.99/42.23    (9)   ~ (e1 = e0)
% 230.99/42.23    (10)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.99/42.23          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.99/42.23    (11)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.99/42.23          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 230.99/42.23    (12)   ~ (e2 = e1)
% 230.99/42.23  
% 230.99/42.23  Begin of proof
% 230.99/42.23  | 
% 230.99/42.23  | BETA: splitting (11) gives:
% 230.99/42.23  | 
% 230.99/42.23  | Case 1:
% 230.99/42.23  | | 
% 230.99/42.23  | |   (13)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) =
% 230.99/42.23  | |           e0)
% 230.99/42.23  | | 
% 230.99/42.23  | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (12), (13) are
% 230.99/42.23  | |            inconsistent by sub-proof #1801.
% 230.99/42.23  | | 
% 230.99/42.23  | Case 2:
% 230.99/42.23  | | 
% 230.99/42.23  | |   (14)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 230.99/42.23  | |           e0)
% 230.99/42.23  | | 
% 230.99/42.23  | | BETA: splitting (14) gives:
% 230.99/42.23  | | 
% 230.99/42.23  | | Case 1:
% 230.99/42.23  | | | 
% 230.99/42.23  | | |   (15)  all_57_5 = e0 & op(e2, e1) = e0
% 230.99/42.23  | | | 
% 230.99/42.23  | | | REF_CLOSE: (5), (6), (15) are inconsistent by sub-proof #2414.
% 230.99/42.23  | | | 
% 230.99/42.23  | | Case 2:
% 230.99/42.23  | | | 
% 230.99/42.23  | | |   (16)  all_57_10 = e0 & op(e2, e0) = e0
% 230.99/42.23  | | | 
% 230.99/42.23  | | | REF_CLOSE: (3), (9), (16) are inconsistent by sub-proof #1332.
% 230.99/42.23  | | | 
% 230.99/42.23  | | End of split
% 230.99/42.23  | | 
% 230.99/42.23  | End of split
% 230.99/42.23  | 
% 230.99/42.23  End of proof
% 230.99/42.23  
% 230.99/42.23  Sub-proof #1332 shows that the following formulas are inconsistent:
% 230.99/42.23  ----------------------------------------------------------------
% 230.99/42.23    (1)  all_57_10 = e0 & op(e2, e0) = e0
% 230.99/42.23    (2)  all_57_10 = e1
% 230.99/42.23    (3)   ~ (e1 = e0)
% 230.99/42.23  
% 230.99/42.23  Begin of proof
% 230.99/42.23  | 
% 230.99/42.23  | ALPHA: (1) implies:
% 230.99/42.23  |   (4)  all_57_10 = e0
% 230.99/42.23  | 
% 230.99/42.23  | COMBINE_EQS: (2), (4) imply:
% 230.99/42.23  |   (5)  e1 = e0
% 230.99/42.23  | 
% 230.99/42.23  | REDUCE: (3), (5) imply:
% 230.99/42.23  |   (6)  $false
% 230.99/42.23  | 
% 230.99/42.23  | CLOSE: (6) is inconsistent.
% 230.99/42.23  | 
% 230.99/42.23  End of proof
% 230.99/42.23  
% 230.99/42.23  Sub-proof #1333 shows that the following formulas are inconsistent:
% 230.99/42.23  ----------------------------------------------------------------
% 230.99/42.23    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.99/42.23         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.99/42.23    (2)   ~ (e3 = e1)
% 230.99/42.23    (3)  e3 = e0
% 230.99/42.23    (4)  all_57_3 = e0
% 230.99/42.23    (5)   ~ (e3 = e2)
% 230.99/42.23    (6)   ~ (e3 = e0)
% 230.99/42.23    (7)   ~ (e2 = e0)
% 230.99/42.23    (8)  all_57_2 = e3
% 230.99/42.23    (9)   ~ (e1 = e0)
% 230.99/42.23    (10)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.99/42.23          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.99/42.23    (11)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.99/42.23          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.99/42.23    (12)   ~ (e2 = e1)
% 230.99/42.23  
% 230.99/42.23  Begin of proof
% 230.99/42.23  | 
% 230.99/42.23  | SIMP: (3) implies:
% 230.99/42.23  |   (13)  e3 = e0
% 230.99/42.23  | 
% 230.99/42.23  | COMBINE_EQS: (8), (13) imply:
% 230.99/42.23  |   (14)  all_57_2 = e0
% 230.99/42.23  | 
% 230.99/42.23  | REF_CLOSE: (1), (2), (4), (5), (6), (7), (9), (10), (11), (12), (14) are
% 230.99/42.23  |            inconsistent by sub-proof #2246.
% 230.99/42.23  | 
% 230.99/42.23  End of proof
% 230.99/42.23  
% 230.99/42.23  Sub-proof #1334 shows that the following formulas are inconsistent:
% 230.99/42.23  ----------------------------------------------------------------
% 230.99/42.23    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.99/42.23         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.99/42.23    (2)   ~ (e3 = e1)
% 230.99/42.23    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.99/42.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.99/42.23    (4)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.99/42.23    (5)  all_57_3 = e0
% 230.99/42.23    (6)   ~ (e3 = e2)
% 230.99/42.23    (7)   ~ (e2 = e0)
% 230.99/42.23    (8)  all_57_2 = e3
% 230.99/42.23    (9)   ~ (e1 = e0)
% 230.99/42.23    (10)   ~ (all_53_12 = e3)
% 230.99/42.23    (11)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.99/42.23          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.99/42.23    (12)   ~ (e2 = e1)
% 230.99/42.23    (13)  op(e3, e0) = all_53_12
% 230.99/42.23  
% 230.99/42.23  Begin of proof
% 230.99/42.23  | 
% 230.99/42.23  | BETA: splitting (4) gives:
% 230.99/42.23  | 
% 230.99/42.23  | Case 1:
% 230.99/42.23  | | 
% 230.99/42.23  | |   (14)  all_57_9 = e3 & op(e3, e0) = e3
% 230.99/42.23  | | 
% 230.99/42.23  | | ALPHA: (14) implies:
% 230.99/42.23  | |   (15)  op(e3, e0) = e3
% 230.99/42.23  | | 
% 230.99/42.23  | | REF_CLOSE: (3), (10), (13), (15) are inconsistent by sub-proof #2458.
% 230.99/42.23  | | 
% 230.99/42.23  | Case 2:
% 230.99/42.23  | | 
% 230.99/42.23  | |   (16)  all_57_10 = e3 & op(e2, e0) = e3
% 230.99/42.23  | | 
% 230.99/42.23  | | ALPHA: (16) implies:
% 230.99/42.23  | |   (17)  all_57_10 = e3
% 230.99/42.23  | | 
% 230.99/42.23  | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (9), (11), (12), (17) are
% 230.99/42.23  | |            inconsistent by sub-proof #1433.
% 230.99/42.23  | | 
% 230.99/42.23  | End of split
% 230.99/42.23  | 
% 230.99/42.23  End of proof
% 230.99/42.23  
% 230.99/42.23  Sub-proof #1335 shows that the following formulas are inconsistent:
% 230.99/42.23  ----------------------------------------------------------------
% 230.99/42.23    (1)  op(e1, e3) = e0
% 230.99/42.23    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.99/42.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.99/42.23    (3)   ~ (all_53_7 = e1)
% 230.99/42.23    (4)   ~ (all_53_3 = e3)
% 230.99/42.23    (5)   ~ (all_53_3 = all_53_7)
% 230.99/42.23    (6)  all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 230.99/42.23    (7)   ~ (all_53_7 = e0)
% 230.99/42.23    (8)  all_55_12 = all_53_3
% 230.99/42.23    (9)   ~ (all_53_2 = all_53_3)
% 230.99/42.23    (10)   ~ (all_53_3 = e1)
% 230.99/42.23    (11)  all_55_13 = all_53_7
% 230.99/42.23    (12)  op(e1, e3) = all_53_2
% 230.99/42.23    (13)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 230.99/42.23  
% 230.99/42.23  Begin of proof
% 230.99/42.23  | 
% 230.99/42.23  | BETA: splitting (6) gives:
% 230.99/42.23  | 
% 230.99/42.23  | Case 1:
% 230.99/42.23  | | 
% 230.99/42.23  | |   (14)  all_55_13 = e2
% 230.99/42.23  | | 
% 230.99/42.23  | | COMBINE_EQS: (11), (14) imply:
% 230.99/42.23  | |   (15)  all_53_7 = e2
% 230.99/42.23  | | 
% 230.99/42.23  | | SIMP: (15) implies:
% 230.99/42.23  | |   (16)  all_53_7 = e2
% 230.99/42.23  | | 
% 230.99/42.23  | | REDUCE: (5), (16) imply:
% 230.99/42.23  | |   (17)   ~ (all_53_3 = e2)
% 230.99/42.23  | | 
% 230.99/42.23  | | BETA: splitting (13) gives:
% 230.99/42.23  | | 
% 230.99/42.23  | | Case 1:
% 230.99/42.23  | | | 
% 230.99/42.23  | | |   (18)  all_55_12 = e3
% 230.99/42.23  | | | 
% 230.99/42.23  | | | REF_CLOSE: (4), (8), (18) are inconsistent by sub-proof #2001.
% 230.99/42.23  | | | 
% 230.99/42.23  | | Case 2:
% 230.99/42.23  | | | 
% 230.99/42.23  | | |   (19)  all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 230.99/42.23  | | | 
% 230.99/42.23  | | | REF_CLOSE: (1), (2), (8), (9), (10), (12), (17), (19) are inconsistent by
% 230.99/42.23  | | |            sub-proof #1336.
% 230.99/42.23  | | | 
% 230.99/42.23  | | End of split
% 230.99/42.23  | | 
% 230.99/42.23  | Case 2:
% 230.99/42.23  | | 
% 230.99/42.23  | |   (20)  all_55_13 = e1 | all_55_13 = e0
% 230.99/42.23  | | 
% 230.99/42.23  | | REF_CLOSE: (3), (7), (11), (20) are inconsistent by sub-proof #1837.
% 230.99/42.23  | | 
% 230.99/42.23  | End of split
% 230.99/42.23  | 
% 230.99/42.23  End of proof
% 230.99/42.23  
% 230.99/42.23  Sub-proof #1336 shows that the following formulas are inconsistent:
% 230.99/42.23  ----------------------------------------------------------------
% 230.99/42.23    (1)  op(e1, e3) = e0
% 230.99/42.23    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.99/42.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.99/42.23    (3)   ~ (all_53_3 = e2)
% 230.99/42.23    (4)  all_55_12 = all_53_3
% 230.99/42.23    (5)   ~ (all_53_2 = all_53_3)
% 230.99/42.23    (6)   ~ (all_53_3 = e1)
% 230.99/42.23    (7)  op(e1, e3) = all_53_2
% 230.99/42.23    (8)  all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 230.99/42.23  
% 230.99/42.23  Begin of proof
% 230.99/42.23  | 
% 230.99/42.23  | BETA: splitting (8) gives:
% 230.99/42.23  | 
% 230.99/42.23  | Case 1:
% 230.99/42.23  | | 
% 230.99/42.23  | |   (9)  all_55_12 = e2
% 230.99/42.23  | | 
% 230.99/42.23  | | REF_CLOSE: (3), (4), (9) are inconsistent by sub-proof #1337.
% 230.99/42.23  | | 
% 230.99/42.23  | Case 2:
% 230.99/42.23  | | 
% 230.99/42.23  | |   (10)  all_55_12 = e1 | all_55_12 = e0
% 230.99/42.23  | | 
% 230.99/42.23  | | BETA: splitting (10) gives:
% 230.99/42.23  | | 
% 230.99/42.23  | | Case 1:
% 230.99/42.23  | | | 
% 230.99/42.23  | | |   (11)  all_55_12 = e1
% 230.99/42.23  | | | 
% 230.99/42.23  | | | REF_CLOSE: (4), (6), (11) are inconsistent by sub-proof #1994.
% 230.99/42.23  | | | 
% 230.99/42.23  | | Case 2:
% 230.99/42.23  | | | 
% 230.99/42.23  | | |   (12)  all_55_12 = e0
% 230.99/42.23  | | | 
% 230.99/42.23  | | | COMBINE_EQS: (4), (12) imply:
% 230.99/42.23  | | |   (13)  all_53_3 = e0
% 230.99/42.23  | | | 
% 230.99/42.23  | | | SIMP: (13) implies:
% 230.99/42.23  | | |   (14)  all_53_3 = e0
% 230.99/42.23  | | | 
% 230.99/42.23  | | | REDUCE: (5), (14) imply:
% 230.99/42.23  | | |   (15)   ~ (all_53_2 = e0)
% 230.99/42.23  | | | 
% 230.99/42.23  | | | REF_CLOSE: (1), (2), (7), (15) are inconsistent by sub-proof #2154.
% 230.99/42.23  | | | 
% 230.99/42.23  | | End of split
% 230.99/42.23  | | 
% 230.99/42.23  | End of split
% 230.99/42.23  | 
% 230.99/42.23  End of proof
% 230.99/42.23  
% 230.99/42.23  Sub-proof #1337 shows that the following formulas are inconsistent:
% 230.99/42.23  ----------------------------------------------------------------
% 230.99/42.23    (1)  all_55_12 = all_53_3
% 230.99/42.23    (2)  all_55_12 = e2
% 230.99/42.23    (3)   ~ (all_53_3 = e2)
% 230.99/42.23  
% 230.99/42.23  Begin of proof
% 230.99/42.23  | 
% 230.99/42.23  | COMBINE_EQS: (1), (2) imply:
% 230.99/42.23  |   (4)  all_53_3 = e2
% 230.99/42.23  | 
% 230.99/42.23  | SIMP: (4) implies:
% 230.99/42.23  |   (5)  all_53_3 = e2
% 230.99/42.23  | 
% 230.99/42.23  | REDUCE: (3), (5) imply:
% 230.99/42.23  |   (6)  $false
% 230.99/42.23  | 
% 230.99/42.23  | CLOSE: (6) is inconsistent.
% 230.99/42.23  | 
% 230.99/42.23  End of proof
% 230.99/42.23  
% 230.99/42.23  Sub-proof #1338 shows that the following formulas are inconsistent:
% 230.99/42.23  ----------------------------------------------------------------
% 230.99/42.23    (1)   ~ (all_10_2 = e2)
% 230.99/42.23    (2)  all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 230.99/42.24    (3)   ~ (all_53_2 = e2)
% 230.99/42.24    (4)  op(e3, e3) = all_10_2
% 230.99/42.24    (5)  op(e0, e1) = all_53_11
% 230.99/42.24    (6)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 230.99/42.24    (7)   ~ (all_53_6 = all_53_14)
% 230.99/42.24    (8)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 230.99/42.24    (9)   ~ (all_53_6 = e2)
% 230.99/42.24    (10)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.99/42.24          (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.99/42.24    (11)  op(e3, e1) = all_52_5
% 230.99/42.24    (12)   ~ (all_53_6 = e0)
% 230.99/42.24    (13)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.99/42.24          (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.99/42.24    (14)   ~ (all_53_8 = all_53_12)
% 230.99/42.24    (15)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.99/42.24          (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.99/42.24    (16)   ~ (all_53_8 = all_53_11)
% 230.99/42.24    (17)   ~ (e3 = e1)
% 230.99/42.24    (18)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.99/42.24          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.99/42.24    (19)   ~ (all_53_13 = e1)
% 230.99/42.24    (20)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.99/42.24            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.99/42.24    (21)  op(all_52_5, all_52_5) = e1
% 230.99/42.24    (22)  all_55_0 = all_10_2
% 230.99/42.24    (23)  all_57_15 = e1
% 230.99/42.24    (24)   ~ (all_10_2 = e0)
% 230.99/42.24    (25)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.99/42.24          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.99/42.24    (26)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 230.99/42.24            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 230.99/42.24              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 230.99/42.24    (27)   ~ (all_6_2 = e3)
% 230.99/42.24    (28)  op(e1, e1) = all_6_2
% 230.99/42.24    (29)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 230.99/42.24    (30)  op(all_52_7, all_52_7) = e0
% 230.99/42.24    (31)   ~ (all_53_9 = e0)
% 230.99/42.24    (32)  all_55_0 = e3 | all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 230.99/42.24    (33)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 230.99/42.24    (34)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.99/42.24          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.99/42.24    (35)  all_55_9 = e1 | all_55_9 = e0
% 230.99/42.24    (36)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 230.99/42.24    (37)  all_55_9 = all_53_6
% 230.99/42.24    (38)   ~ (all_53_2 = e3)
% 230.99/42.24    (39)   ~ (all_53_11 = all_6_2)
% 230.99/42.24    (40)   ~ (all_53_4 = all_53_12)
% 230.99/42.24    (41)   ~ (all_53_8 = e3)
% 230.99/42.24    (42)   ~ (all_53_8 = all_53_9)
% 230.99/42.24    (43)  all_42_2 = all_6_2
% 230.99/42.24    (44)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.99/42.24          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.99/42.24    (45)  op(e2, e2) = e0
% 230.99/42.24    (46)   ~ (all_53_9 = all_53_11)
% 230.99/42.24    (47)   ~ (all_53_9 = all_6_2)
% 230.99/42.24    (48)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.99/42.24          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.99/42.24    (49)   ~ (all_53_14 = all_6_2)
% 230.99/42.24    (50)  all_57_3 = e0
% 230.99/42.24    (51)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 230.99/42.24          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.99/42.24    (52)   ~ (e3 = e2)
% 230.99/42.24    (53)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 230.99/42.24    (54)  all_55_1 = all_53_4
% 230.99/42.24    (55)  op(e1, e0) = all_53_14
% 230.99/42.24    (56)   ~ (all_53_6 = all_53_7)
% 230.99/42.24    (57)   ~ (e3 = e0)
% 230.99/42.24    (58)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.99/42.24          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.99/42.24    (59)  op(e3, e3) = e3
% 230.99/42.24    (60)   ~ (all_53_8 = all_6_2)
% 230.99/42.24    (61)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 230.99/42.24    (62)  op(e0, e3) = all_53_3
% 230.99/42.24    (63)  all_55_2 = all_53_8
% 230.99/42.24    (64)   ~ (all_53_4 = all_53_7)
% 230.99/42.24    (65)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 230.99/42.24    (66)   ~ (all_53_7 = e0)
% 230.99/42.24    (67)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.99/42.24          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.99/42.24            e1)
% 230.99/42.24    (68)  op(e3, e3) = all_52_1
% 230.99/42.24    (69)   ~ (all_53_4 = all_53_8)
% 230.99/42.24    (70)  all_55_6 = all_53_9
% 230.99/42.24    (71)  op(e3, e2) = all_53_4
% 230.99/42.24    (72)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.99/42.24          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.99/42.24    (73)  op(all_52_1, all_52_1) = e3
% 230.99/42.24    (74)   ~ (e2 = e0)
% 230.99/42.24    (75)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 230.99/42.24            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 230.99/42.24            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 230.99/42.24            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 230.99/42.24              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 230.99/42.24            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 230.99/42.24            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 230.99/42.24              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 230.99/42.24              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 230.99/42.24            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 230.99/42.24            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 230.99/42.24            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 230.99/42.24              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 230.99/42.24              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 230.99/42.24            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 230.99/42.24              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 230.99/42.24            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 230.99/42.24            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 230.99/42.24              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 230.99/42.24              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 230.99/42.24            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 230.99/42.24            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 230.99/42.24    (76)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.99/42.24          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.99/42.24    (77)   ~ (all_53_2 = all_53_14)
% 230.99/42.24    (78)   ~ (e1 = e0)
% 230.99/42.24    (79)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 230.99/42.24            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 230.99/42.24              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 230.99/42.24    (80)   ~ (all_53_4 = e0)
% 230.99/42.24    (81)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 230.99/42.24          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 230.99/42.24    (82)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.99/42.24          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.99/42.24    (83)   ~ (all_53_2 = all_53_3)
% 230.99/42.24    (84)   ~ (all_10_2 = e1)
% 230.99/42.24    (85)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 230.99/42.24    (86)  all_55_8 = all_53_2
% 230.99/42.24    (87)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.99/42.24          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 230.99/42.24            e3)
% 230.99/42.24    (88)   ~ (all_53_4 = all_53_6)
% 230.99/42.24    (89)  op(e0, e2) = all_53_7
% 230.99/42.24    (90)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.99/42.24          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.99/42.24            e2)
% 230.99/42.24    (91)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.99/42.24              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.99/42.24                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.99/42.24                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.99/42.24    (92)  all_55_10 = all_6_2
% 230.99/42.24    (93)   ~ (all_53_6 = all_6_2)
% 230.99/42.24    (94)   ~ (all_53_13 = e0)
% 230.99/42.24    (95)  op(e1, e1) = e2
% 230.99/42.24    (96)  all_55_13 = all_53_7
% 230.99/42.24    (97)  op(e0, e0) = e1
% 230.99/42.24    (98)  op(e2, e0) = all_53_13
% 230.99/42.24    (99)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.99/42.24          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.99/42.24    (100)  all_38_2 = all_6_2
% 230.99/42.24    (101)  all_55_11 = all_53_14
% 230.99/42.24    (102)  all_55_3 = all_53_12
% 230.99/42.24    (103)   ~ (all_53_12 = e3)
% 230.99/42.24    (104)  all_57_0 = e3
% 230.99/42.24    (105)  op(e1, e3) = all_53_2
% 230.99/42.24    (106)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0
% 230.99/42.24             & op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~
% 230.99/42.24             (all_42_1 = e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 230.99/42.24    (107)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.99/42.24           (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.99/42.24    (108)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.99/42.24           (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.99/42.24    (109)   ~ (all_53_12 = all_10_2)
% 230.99/42.24    (110)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.99/42.24           | (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 230.99/42.24             e3)
% 230.99/42.24    (111)   ~ (all_53_13 = all_53_14)
% 230.99/42.24    (112)   ~ (all_53_6 = e3)
% 230.99/42.24    (113)   ~ (e2 = e1)
% 230.99/42.24    (114)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.99/42.24           | (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.99/42.24             e2)
% 230.99/42.24    (115)  all_57_14 = e3 & op(e0, e1) = e3
% 230.99/42.24    (116)  op(e2, e1) = all_53_9
% 230.99/42.24    (117)  op(e1, e2) = all_53_6
% 230.99/42.24    (118)   ~ (all_6_2 = e0)
% 230.99/42.24    (119)   ~ (all_53_2 = all_53_6)
% 230.99/42.24    (120)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.99/42.24           (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.99/42.24    (121)  all_24_2 = all_6_2
% 230.99/42.24    (122)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.99/42.24           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.99/42.24    (123)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.99/42.24           (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.99/42.24    (124)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.99/42.24           | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.99/42.24             e1)
% 230.99/42.24    (125)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.99/42.24           (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.99/42.24    (126)   ~ (all_53_12 = all_53_14)
% 230.99/42.24    (127)  all_55_14 = all_53_11
% 230.99/42.24    (128)  op(e3, e0) = all_52_7
% 230.99/42.24    (129)  op(e3, e1) = all_53_8
% 230.99/42.24    (130)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.99/42.24           (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.99/42.24    (131)   ~ (all_53_4 = e3)
% 230.99/42.24    (132)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.99/42.24           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.99/42.24    (133)  op(e3, e0) = all_53_12
% 230.99/42.24  
% 230.99/42.24  Begin of proof
% 230.99/42.24  | 
% 230.99/42.24  | ALPHA: (115) implies:
% 230.99/42.24  |   (134)  all_57_14 = e3
% 230.99/42.24  | 
% 230.99/42.24  | BETA: splitting (25) gives:
% 230.99/42.24  | 
% 230.99/42.24  | Case 1:
% 230.99/42.24  | | 
% 230.99/42.24  | |   (135)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 230.99/42.24  | |            e3)
% 230.99/42.24  | | 
% 230.99/42.24  | | BETA: splitting (135) gives:
% 230.99/42.24  | | 
% 230.99/42.24  | | Case 1:
% 230.99/42.24  | | | 
% 230.99/42.24  | | |   (136)  all_57_6 = e3 & op(e1, e3) = e3
% 230.99/42.24  | | | 
% 230.99/42.24  | | | ALPHA: (136) implies:
% 230.99/42.24  | | |   (137)  all_57_6 = e3
% 230.99/42.24  | | | 
% 230.99/42.24  | | | REF_CLOSE: (13), (17), (52), (57), (74), (78), (104), (113), (120), (123),
% 230.99/42.24  | | |            (137) are inconsistent by sub-proof #2010.
% 230.99/42.24  | | | 
% 230.99/42.24  | | Case 2:
% 230.99/42.24  | | | 
% 230.99/42.24  | | |   (138)  all_57_7 = e3 & op(e1, e2) = e3
% 230.99/42.24  | | | 
% 230.99/42.24  | | | REF_CLOSE: (3), (9), (10), (11), (12), (15), (17), (19), (20), (21), (27),
% 230.99/42.24  | | |            (28), (30), (34), (35), (37), (38), (44), (45), (48), (50),
% 230.99/42.24  | | |            (51), (52), (57), (58), (59), (61), (62), (71), (74), (78),
% 230.99/42.24  | | |            (80), (81), (83), (86), (91), (97), (98), (99), (107), (112),
% 230.99/42.24  | | |            (113), (118), (119), (122), (128), (130), (138) are
% 230.99/42.24  | | |            inconsistent by sub-proof #1365.
% 230.99/42.24  | | | 
% 230.99/42.24  | | End of split
% 230.99/42.24  | | 
% 230.99/42.24  | Case 2:
% 230.99/42.24  | | 
% 230.99/42.24  | |   (139)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 230.99/42.24  | |            e3)
% 230.99/42.24  | | 
% 230.99/42.24  | | BETA: splitting (139) gives:
% 230.99/42.24  | | 
% 230.99/42.24  | | Case 1:
% 230.99/42.24  | | | 
% 230.99/42.24  | | |   (140)  all_57_8 = e3 & op(e1, e1) = e3
% 230.99/42.24  | | | 
% 230.99/42.24  | | | ALPHA: (140) implies:
% 230.99/42.24  | | |   (141)  op(e1, e1) = e3
% 230.99/42.24  | | | 
% 230.99/42.24  | | | REF_CLOSE: (20), (27), (28), (141) are inconsistent by sub-proof #2468.
% 230.99/42.24  | | | 
% 230.99/42.24  | | Case 2:
% 230.99/42.24  | | | 
% 230.99/42.24  | | |   (142)  all_57_11 = e3 & op(e1, e0) = e3
% 230.99/42.24  | | | 
% 230.99/42.24  | | | ALPHA: (142) implies:
% 230.99/42.24  | | |   (143)  all_57_11 = e3
% 230.99/42.24  | | | 
% 230.99/42.24  | | | BETA: splitting (90) gives:
% 230.99/42.24  | | | 
% 230.99/42.24  | | | Case 1:
% 230.99/42.24  | | | | 
% 230.99/42.24  | | | |   (144)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0,
% 230.99/42.24  | | | |              e2) = e2)
% 230.99/42.24  | | | | 
% 230.99/42.24  | | | | BETA: splitting (144) gives:
% 230.99/42.24  | | | | 
% 230.99/42.24  | | | | Case 1:
% 230.99/42.24  | | | | | 
% 230.99/42.24  | | | | |   (145)  all_57_12 = e2 & op(e0, e3) = e2
% 230.99/42.24  | | | | | 
% 230.99/42.24  | | | | | ALPHA: (145) implies:
% 230.99/42.24  | | | | |   (146)  all_57_12 = e2
% 230.99/42.24  | | | | | 
% 230.99/42.24  | | | | | BETA: splitting (82) gives:
% 230.99/42.24  | | | | | 
% 230.99/42.24  | | | | | Case 1:
% 230.99/42.24  | | | | | | 
% 230.99/42.24  | | | | | |   (147)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2,
% 230.99/42.24  | | | | | |              e2) = e3)
% 230.99/42.24  | | | | | | 
% 230.99/42.24  | | | | | | BETA: splitting (147) gives:
% 230.99/42.24  | | | | | | 
% 230.99/42.24  | | | | | | Case 1:
% 230.99/42.24  | | | | | | | 
% 230.99/42.24  | | | | | | |   (148)  all_57_1 = e3 & op(e3, e2) = e3
% 230.99/42.24  | | | | | | | 
% 230.99/42.24  | | | | | | | ALPHA: (148) implies:
% 230.99/42.24  | | | | | | |   (149)  all_57_1 = e3
% 230.99/42.24  | | | | | | | 
% 230.99/42.24  | | | | | | | BETA: splitting (44) gives:
% 230.99/42.24  | | | | | | | 
% 230.99/42.24  | | | | | | | Case 1:
% 230.99/42.24  | | | | | | | | 
% 230.99/42.24  | | | | | | | |   (150)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 &
% 230.99/42.24  | | | | | | | |            op(e3, e2) = e2)
% 230.99/42.24  | | | | | | | | 
% 230.99/42.24  | | | | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (10), (13), (14),
% 230.99/42.24  | | | | | | | |            (15), (16), (17), (18), (19), (20), (22), (23), (24),
% 230.99/42.24  | | | | | | | |            (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 230.99/42.24  | | | | | | | |            (34), (36), (37), (39), (40), (41), (42), (43), (44),
% 230.99/42.24  | | | | | | | |            (45), (46), (47), (48), (49), (50), (51), (52), (53),
% 230.99/42.24  | | | | | | | |            (54), (55), (56), (57), (58), (59), (60), (63), (64),
% 230.99/42.24  | | | | | | | |            (65), (66), (67), (68), (69), (70), (71), (72), (73),
% 230.99/42.24  | | | | | | | |            (74), (75), (76), (77), (78), (79), (80), (81), (82),
% 230.99/42.24  | | | | | | | |            (84), (85), (87), (88), (89), (90), (91), (92), (93),
% 230.99/42.24  | | | | | | | |            (94), (95), (96), (97), (98), (99), (100), (101),
% 230.99/42.24  | | | | | | | |            (102), (103), (104), (105), (106), (107), (108),
% 230.99/42.24  | | | | | | | |            (109), (110), (111), (113), (114), (116), (117),
% 230.99/42.24  | | | | | | | |            (118), (119), (120), (121), (122), (123), (124),
% 230.99/42.24  | | | | | | | |            (125), (126), (127), (128), (129), (130), (131),
% 230.99/42.24  | | | | | | | |            (132), (133), (134), (149), (150) are inconsistent by
% 230.99/42.24  | | | | | | | |            sub-proof #1345.
% 230.99/42.24  | | | | | | | | 
% 230.99/42.24  | | | | | | | Case 2:
% 230.99/42.24  | | | | | | | | 
% 230.99/42.24  | | | | | | | |   (151)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 &
% 230.99/42.24  | | | | | | | |            op(e3, e0) = e2)
% 230.99/42.24  | | | | | | | | 
% 230.99/42.24  | | | | | | | | BETA: splitting (151) gives:
% 230.99/42.24  | | | | | | | | 
% 230.99/42.24  | | | | | | | | Case 1:
% 230.99/42.24  | | | | | | | | | 
% 230.99/42.24  | | | | | | | | |   (152)  all_57_4 = e2 & op(e3, e1) = e2
% 230.99/42.24  | | | | | | | | | 
% 230.99/42.24  | | | | | | | | | REF_CLOSE: (10), (17), (19), (20), (27), (28), (30), (34),
% 230.99/42.24  | | | | | | | | |            (44), (45), (48), (50), (51), (52), (57), (58),
% 230.99/42.24  | | | | | | | | |            (59), (71), (74), (78), (80), (81), (97), (98),
% 230.99/42.24  | | | | | | | | |            (99), (107), (113), (118), (122), (128), (152) are
% 230.99/42.24  | | | | | | | | |            inconsistent by sub-proof #1361.
% 230.99/42.24  | | | | | | | | | 
% 230.99/42.24  | | | | | | | | Case 2:
% 230.99/42.24  | | | | | | | | | 
% 230.99/42.24  | | | | | | | | |   (153)  all_57_9 = e2 & op(e3, e0) = e2
% 230.99/42.24  | | | | | | | | | 
% 230.99/42.24  | | | | | | | | | ALPHA: (153) implies:
% 230.99/42.24  | | | | | | | | |   (154)  all_57_9 = e2
% 230.99/42.24  | | | | | | | | | 
% 230.99/42.24  | | | | | | | | | BETA: splitting (51) gives:
% 230.99/42.24  | | | | | | | | | 
% 230.99/42.24  | | | | | | | | | Case 1:
% 230.99/42.24  | | | | | | | | | | 
% 230.99/42.24  | | | | | | | | | |   (155)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 230.99/42.24  | | | | | | | | | |            & op(e2, e1) = e0)
% 230.99/42.24  | | | | | | | | | | 
% 230.99/42.24  | | | | | | | | | | BETA: splitting (155) gives:
% 230.99/42.24  | | | | | | | | | | 
% 230.99/42.24  | | | | | | | | | | Case 1:
% 230.99/42.24  | | | | | | | | | | | 
% 230.99/42.24  | | | | | | | | | | |   (156)  all_57_4 = e0 & op(e3, e1) = e0
% 230.99/42.24  | | | | | | | | | | | 
% 230.99/42.24  | | | | | | | | | | | ALPHA: (156) implies:
% 230.99/42.24  | | | | | | | | | | |   (157)  all_57_4 = e0
% 230.99/42.24  | | | | | | | | | | |   (158)  op(e3, e1) = e0
% 230.99/42.24  | | | | | | | | | | | 
% 230.99/42.24  | | | | | | | | | | | BETA: splitting (123) gives:
% 230.99/42.24  | | | | | | | | | | | 
% 230.99/42.24  | | | | | | | | | | | Case 1:
% 230.99/42.24  | | | | | | | | | | | | 
% 230.99/42.24  | | | | | | | | | | | |   (159)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 230.99/42.24  | | | | | | | | | | | |            & op(e2, e3) = e0)
% 230.99/42.24  | | | | | | | | | | | | 
% 230.99/42.24  | | | | | | | | | | | | REF_CLOSE: (10), (17), (20), (50), (52), (57), (59), (74),
% 230.99/42.24  | | | | | | | | | | | |            (78), (99), (107), (113), (159) are inconsistent
% 230.99/42.24  | | | | | | | | | | | |            by sub-proof #2229.
% 230.99/42.24  | | | | | | | | | | | | 
% 230.99/42.24  | | | | | | | | | | | Case 2:
% 230.99/42.24  | | | | | | | | | | | | 
% 230.99/42.24  | | | | | | | | | | | |   (160)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 230.99/42.24  | | | | | | | | | | | |            e0 & op(e0, e3) = e0)
% 230.99/42.24  | | | | | | | | | | | | 
% 230.99/42.24  | | | | | | | | | | | | BETA: splitting (160) gives:
% 230.99/42.24  | | | | | | | | | | | | 
% 230.99/42.24  | | | | | | | | | | | | Case 1:
% 230.99/42.24  | | | | | | | | | | | | | 
% 230.99/42.24  | | | | | | | | | | | | |   (161)  all_57_6 = e0 & op(e1, e3) = e0
% 230.99/42.24  | | | | | | | | | | | | | 
% 230.99/42.24  | | | | | | | | | | | | | ALPHA: (161) implies:
% 230.99/42.24  | | | | | | | | | | | | |   (162)  all_57_6 = e0
% 230.99/42.24  | | | | | | | | | | | | |   (163)  op(e1, e3) = e0
% 230.99/42.24  | | | | | | | | | | | | | 
% 230.99/42.24  | | | | | | | | | | | | | BETA: splitting (91) gives:
% 230.99/42.24  | | | | | | | | | | | | | 
% 230.99/42.24  | | | | | | | | | | | | | Case 1:
% 230.99/42.24  | | | | | | | | | | | | | | 
% 230.99/42.24  | | | | | | | | | | | | | |   (164)  all_57_15 = e0 & op(e0, e0) = e0
% 230.99/42.24  | | | | | | | | | | | | | | 
% 230.99/42.24  | | | | | | | | | | | | | | ALPHA: (164) implies:
% 230.99/42.24  | | | | | | | | | | | | | |   (165)  all_57_15 = e0
% 230.99/42.24  | | | | | | | | | | | | | |   (166)  op(e0, e0) = e0
% 230.99/42.24  | | | | | | | | | | | | | | 
% 230.99/42.24  | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (10), (13),
% 230.99/42.24  | | | | | | | | | | | | | |            (14), (15), (16), (17), (18), (20), (22), (24),
% 230.99/42.24  | | | | | | | | | | | | | |            (25), (26), (27), (28), (29), (32), (33), (34),
% 230.99/42.24  | | | | | | | | | | | | | |            (36), (37), (39), (40), (41), (42), (43), (44),
% 230.99/42.24  | | | | | | | | | | | | | |            (45), (46), (47), (48), (49), (50), (51), (53),
% 230.99/42.24  | | | | | | | | | | | | | |            (54), (55), (56), (58), (59), (60), (63), (64),
% 230.99/42.24  | | | | | | | | | | | | | |            (65), (66), (67), (69), (70), (71), (74), (75),
% 230.99/42.24  | | | | | | | | | | | | | |            (76), (77), (78), (79), (81), (82), (84), (85),
% 230.99/42.24  | | | | | | | | | | | | | |            (87), (88), (89), (90), (91), (92), (93), (96),
% 230.99/42.24  | | | | | | | | | | | | | |            (98), (99), (100), (101), (102), (103), (104),
% 230.99/42.24  | | | | | | | | | | | | | |            (105), (106), (107), (108), (109), (110), (111),
% 230.99/42.24  | | | | | | | | | | | | | |            (113), (114), (116), (117), (119), (120), (121),
% 230.99/42.24  | | | | | | | | | | | | | |            (122), (123), (124), (125), (126), (127), (129),
% 230.99/42.24  | | | | | | | | | | | | | |            (130), (131), (132), (133), (157), (158), (162),
% 230.99/42.24  | | | | | | | | | | | | | |            (163), (165), (166) are inconsistent by sub-proof
% 230.99/42.24  | | | | | | | | | | | | | |            #1410.
% 230.99/42.24  | | | | | | | | | | | | | | 
% 230.99/42.24  | | | | | | | | | | | | | Case 2:
% 230.99/42.24  | | | | | | | | | | | | | | 
% 230.99/42.24  | | | | | | | | | | | | | |   (167)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 230.99/42.24  | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 230.99/42.24  | | | | | | | | | | | | | |              op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 230.99/42.24  | | | | | | | | | | | | | |                e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 230.99/42.24  | | | | | | | | | | | | | |              e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 230.99/42.24  | | | | | | | | | | | | | | 
% 230.99/42.24  | | | | | | | | | | | | | | ALPHA: (167) implies:
% 230.99/42.24  | | | | | | | | | | | | | |   (168)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 230.99/42.24  | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 230.99/42.24  | | | | | | | | | | | | | |              e1) = e0)
% 230.99/42.24  | | | | | | | | | | | | | | 
% 230.99/42.24  | | | | | | | | | | | | | | BETA: splitting (168) gives:
% 230.99/42.24  | | | | | | | | | | | | | | 
% 230.99/42.24  | | | | | | | | | | | | | | Case 1:
% 230.99/42.24  | | | | | | | | | | | | | | | 
% 230.99/42.24  | | | | | | | | | | | | | | |   (169)  all_57_12 = e0 & op(e0, e3) = e0
% 230.99/42.24  | | | | | | | | | | | | | | | 
% 230.99/42.24  | | | | | | | | | | | | | | | REF_CLOSE: (17), (20), (34), (44), (52), (59), (74), (78),
% 230.99/42.24  | | | | | | | | | | | | | | |            (113), (146), (154), (157), (169) are inconsistent
% 230.99/42.24  | | | | | | | | | | | | | | |            by sub-proof #1344.
% 230.99/42.24  | | | | | | | | | | | | | | | 
% 230.99/42.24  | | | | | | | | | | | | | | Case 2:
% 230.99/42.24  | | | | | | | | | | | | | | | 
% 230.99/42.24  | | | | | | | | | | | | | | |   (170)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 230.99/42.24  | | | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 230.99/42.24  | | | | | | | | | | | | | | | 
% 230.99/42.24  | | | | | | | | | | | | | | | BETA: splitting (170) gives:
% 230.99/42.24  | | | | | | | | | | | | | | | 
% 230.99/42.24  | | | | | | | | | | | | | | | Case 1:
% 230.99/42.24  | | | | | | | | | | | | | | | | 
% 230.99/42.24  | | | | | | | | | | | | | | | |   (171)  all_57_13 = e0 & op(e0, e2) = e0
% 230.99/42.24  | | | | | | | | | | | | | | | | 
% 230.99/42.24  | | | | | | | | | | | | | | | | ALPHA: (171) implies:
% 230.99/42.24  | | | | | | | | | | | | | | | |   (172)  all_57_13 = e0
% 230.99/42.24  | | | | | | | | | | | | | | | | 
% 230.99/42.24  | | | | | | | | | | | | | | | | REF_CLOSE: (15), (17), (50), (52), (74), (78), (113), (130),
% 230.99/42.24  | | | | | | | | | | | | | | | |            (149), (172) are inconsistent by sub-proof #1758.
% 230.99/42.24  | | | | | | | | | | | | | | | | 
% 230.99/42.24  | | | | | | | | | | | | | | | Case 2:
% 230.99/42.24  | | | | | | | | | | | | | | | | 
% 230.99/42.24  | | | | | | | | | | | | | | | |   (173)  all_57_14 = e0 & op(e0, e1) = e0
% 230.99/42.24  | | | | | | | | | | | | | | | | 
% 230.99/42.24  | | | | | | | | | | | | | | | | ALPHA: (173) implies:
% 230.99/42.24  | | | | | | | | | | | | | | | |   (174)  all_57_14 = e0
% 230.99/42.24  | | | | | | | | | | | | | | | | 
% 230.99/42.24  | | | | | | | | | | | | | | | | REF_CLOSE: (17), (20), (27), (28), (52), (57), (58), (74),
% 230.99/42.25  | | | | | | | | | | | | | | | |            (78), (81), (113), (122), (157), (174) are
% 230.99/42.25  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2371.
% 230.99/42.25  | | | | | | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | | | | | End of split
% 230.99/42.25  | | | | | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | | | | End of split
% 230.99/42.25  | | | | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | | | End of split
% 230.99/42.25  | | | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | | Case 2:
% 230.99/42.25  | | | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | | |   (175)  all_57_12 = e0 & op(e0, e3) = e0
% 230.99/42.25  | | | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | | | REF_CLOSE: (17), (20), (34), (44), (52), (59), (74), (78),
% 230.99/42.25  | | | | | | | | | | | | |            (113), (146), (154), (157), (175) are inconsistent
% 230.99/42.25  | | | | | | | | | | | | |            by sub-proof #1344.
% 230.99/42.25  | | | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | | End of split
% 230.99/42.25  | | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | End of split
% 230.99/42.25  | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | Case 2:
% 230.99/42.25  | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | |   (176)  all_57_5 = e0 & op(e2, e1) = e0
% 230.99/42.25  | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | ALPHA: (176) implies:
% 230.99/42.25  | | | | | | | | | | |   (177)  all_57_5 = e0
% 230.99/42.25  | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | REF_CLOSE: (10), (17), (19), (20), (45), (50), (52), (57),
% 230.99/42.25  | | | | | | | | | | |            (74), (78), (98), (99), (107), (113), (177) are
% 230.99/42.25  | | | | | | | | | | |            inconsistent by sub-proof #1689.
% 230.99/42.25  | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | End of split
% 230.99/42.25  | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | Case 2:
% 230.99/42.25  | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | |   (178)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0
% 230.99/42.25  | | | | | | | | | |            & op(e0, e1) = e0)
% 230.99/42.25  | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | REF_CLOSE: (17), (20), (27), (28), (30), (34), (44), (48),
% 230.99/42.25  | | | | | | | | | |            (52), (57), (58), (59), (71), (74), (78), (80),
% 230.99/42.25  | | | | | | | | | |            (81), (97), (113), (118), (122), (128), (178) are
% 230.99/42.25  | | | | | | | | | |            inconsistent by sub-proof #1366.
% 230.99/42.25  | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | End of split
% 230.99/42.25  | | | | | | | | | 
% 230.99/42.25  | | | | | | | | End of split
% 230.99/42.25  | | | | | | | | 
% 230.99/42.25  | | | | | | | End of split
% 230.99/42.25  | | | | | | | 
% 230.99/42.25  | | | | | | Case 2:
% 230.99/42.25  | | | | | | | 
% 230.99/42.25  | | | | | | |   (179)  all_57_3 = e3 & op(e2, e2) = e3
% 230.99/42.25  | | | | | | | 
% 230.99/42.25  | | | | | | | REF_CLOSE: (17), (20), (27), (28), (30), (34), (44), (48), (50),
% 230.99/42.25  | | | | | | |            (52), (57), (58), (59), (71), (74), (78), (80), (81),
% 230.99/42.25  | | | | | | |            (97), (113), (122), (128), (134), (179) are
% 230.99/42.25  | | | | | | |            inconsistent by sub-proof #1343.
% 230.99/42.25  | | | | | | | 
% 230.99/42.25  | | | | | | End of split
% 230.99/42.25  | | | | | | 
% 230.99/42.25  | | | | | Case 2:
% 230.99/42.25  | | | | | | 
% 230.99/42.25  | | | | | |   (180)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 &
% 230.99/42.25  | | | | | |            op(e0, e2) = e3)
% 230.99/42.25  | | | | | | 
% 230.99/42.25  | | | | | | BETA: splitting (180) gives:
% 230.99/42.25  | | | | | | 
% 230.99/42.25  | | | | | | Case 1:
% 230.99/42.25  | | | | | | | 
% 230.99/42.25  | | | | | | |   (181)  all_57_7 = e3 & op(e1, e2) = e3
% 230.99/42.25  | | | | | | | 
% 230.99/42.25  | | | | | | | ALPHA: (181) implies:
% 230.99/42.25  | | | | | | |   (182)  all_57_7 = e3
% 230.99/42.25  | | | | | | | 
% 230.99/42.25  | | | | | | | BETA: splitting (130) gives:
% 230.99/42.25  | | | | | | | 
% 230.99/42.25  | | | | | | | Case 1:
% 230.99/42.25  | | | | | | | | 
% 230.99/42.25  | | | | | | | |   (183)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 &
% 230.99/42.25  | | | | | | | |            op(e2, e2) = e1)
% 230.99/42.25  | | | | | | | | 
% 230.99/42.25  | | | | | | | | BETA: splitting (183) gives:
% 230.99/42.25  | | | | | | | | 
% 230.99/42.25  | | | | | | | | Case 1:
% 230.99/42.25  | | | | | | | | | 
% 230.99/42.25  | | | | | | | | |   (184)  all_57_1 = e1 & op(e3, e2) = e1
% 230.99/42.25  | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | ALPHA: (184) implies:
% 230.99/42.25  | | | | | | | | |   (185)  all_57_1 = e1
% 230.99/42.25  | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | BETA: splitting (44) gives:
% 230.99/42.25  | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | Case 1:
% 230.99/42.25  | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | |   (186)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 230.99/42.25  | | | | | | | | | |            & op(e3, e2) = e2)
% 230.99/42.25  | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | REF_CLOSE: (20), (45), (57), (68), (73), (113), (185), (186)
% 230.99/42.25  | | | | | | | | | |            are inconsistent by sub-proof #1342.
% 230.99/42.25  | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | Case 2:
% 230.99/42.25  | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | |   (187)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 230.99/42.25  | | | | | | | | | |            & op(e3, e0) = e2)
% 230.99/42.25  | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | BETA: splitting (187) gives:
% 230.99/42.25  | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | Case 1:
% 230.99/42.25  | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | |   (188)  all_57_4 = e2 & op(e3, e1) = e2
% 230.99/42.25  | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | REF_CLOSE: (10), (17), (19), (20), (27), (28), (30), (34),
% 230.99/42.25  | | | | | | | | | | |            (44), (45), (48), (50), (51), (52), (57), (58),
% 230.99/42.25  | | | | | | | | | | |            (59), (71), (74), (78), (80), (81), (97), (98),
% 230.99/42.25  | | | | | | | | | | |            (99), (107), (113), (118), (122), (128), (188) are
% 230.99/42.25  | | | | | | | | | | |            inconsistent by sub-proof #1361.
% 230.99/42.25  | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | Case 2:
% 230.99/42.25  | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | |   (189)  all_57_9 = e2 & op(e3, e0) = e2
% 230.99/42.25  | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | ALPHA: (189) implies:
% 230.99/42.25  | | | | | | | | | | |   (190)  all_57_9 = e2
% 230.99/42.25  | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | BETA: splitting (51) gives:
% 230.99/42.25  | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | Case 1:
% 230.99/42.25  | | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | |   (191)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 230.99/42.25  | | | | | | | | | | | |            & op(e2, e1) = e0)
% 230.99/42.25  | | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | | BETA: splitting (191) gives:
% 230.99/42.25  | | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | | Case 1:
% 230.99/42.25  | | | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | | |   (192)  all_57_4 = e0 & op(e3, e1) = e0
% 230.99/42.25  | | | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | | | ALPHA: (192) implies:
% 230.99/42.25  | | | | | | | | | | | | |   (193)  all_57_4 = e0
% 230.99/42.25  | | | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | | | BETA: splitting (123) gives:
% 230.99/42.25  | | | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | | | Case 1:
% 230.99/42.25  | | | | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | | | |   (194)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 230.99/42.25  | | | | | | | | | | | | | |            & op(e2, e3) = e0)
% 230.99/42.25  | | | | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | | | | REF_CLOSE: (10), (17), (20), (50), (52), (57), (59), (74),
% 230.99/42.25  | | | | | | | | | | | | | |            (78), (99), (107), (113), (194) are inconsistent
% 230.99/42.25  | | | | | | | | | | | | | |            by sub-proof #2229.
% 230.99/42.25  | | | | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | | | Case 2:
% 230.99/42.25  | | | | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | | | |   (195)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 230.99/42.25  | | | | | | | | | | | | | |            e0 & op(e0, e3) = e0)
% 230.99/42.25  | | | | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 230.99/42.25  | | | | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | | | | Case 1:
% 230.99/42.25  | | | | | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | | | | |   (196)  all_57_6 = e0 & op(e1, e3) = e0
% 230.99/42.25  | | | | | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | | | | | ALPHA: (196) implies:
% 230.99/42.25  | | | | | | | | | | | | | | |   (197)  all_57_6 = e0
% 230.99/42.25  | | | | | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (10), (13),
% 230.99/42.25  | | | | | | | | | | | | | | |            (14), (15), (16), (17), (18), (20), (22), (24),
% 230.99/42.25  | | | | | | | | | | | | | | |            (25), (26), (27), (28), (29), (31), (32), (33),
% 230.99/42.25  | | | | | | | | | | | | | | |            (34), (36), (37), (39), (40), (41), (42), (43),
% 230.99/42.25  | | | | | | | | | | | | | | |            (44), (45), (46), (47), (48), (49), (50), (51),
% 230.99/42.25  | | | | | | | | | | | | | | |            (52), (53), (54), (55), (56), (57), (58), (59),
% 230.99/42.25  | | | | | | | | | | | | | | |            (60), (63), (64), (65), (66), (67), (69), (70),
% 230.99/42.25  | | | | | | | | | | | | | | |            (71), (74), (75), (76), (77), (78), (79), (80),
% 230.99/42.25  | | | | | | | | | | | | | | |            (81), (82), (84), (85), (87), (88), (89), (90),
% 230.99/42.25  | | | | | | | | | | | | | | |            (91), (92), (93), (94), (95), (96), (97), (98),
% 230.99/42.25  | | | | | | | | | | | | | | |            (99), (100), (101), (102), (103), (104), (105),
% 230.99/42.25  | | | | | | | | | | | | | | |            (106), (107), (108), (109), (110), (111), (113),
% 230.99/42.25  | | | | | | | | | | | | | | |            (114), (116), (117), (118), (119), (120), (121),
% 230.99/42.25  | | | | | | | | | | | | | | |            (122), (123), (124), (125), (126), (127), (129),
% 230.99/42.25  | | | | | | | | | | | | | | |            (130), (131), (132), (133), (182), (185), (190),
% 230.99/42.25  | | | | | | | | | | | | | | |            (193), (197) are inconsistent by sub-proof #1341.
% 230.99/42.25  | | | | | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | | | | Case 2:
% 230.99/42.25  | | | | | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | | | | |   (198)  all_57_12 = e0 & op(e0, e3) = e0
% 230.99/42.25  | | | | | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | | | | | ALPHA: (198) implies:
% 230.99/42.25  | | | | | | | | | | | | | | |   (199)  all_57_12 = e0
% 230.99/42.25  | | | | | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | | | | | COMBINE_EQS: (146), (199) imply:
% 230.99/42.25  | | | | | | | | | | | | | | |   (200)  e2 = e0
% 230.99/42.25  | | | | | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | | | | | COMBINE_EQS: (190), (200) imply:
% 230.99/42.25  | | | | | | | | | | | | | | |   (201)  all_57_9 = e0
% 230.99/42.25  | | | | | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | | | | | REF_CLOSE: (20), (44), (52), (59), (74), (113), (185), (193),
% 230.99/42.25  | | | | | | | | | | | | | | |            (201) are inconsistent by sub-proof #2439.
% 230.99/42.25  | | | | | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | | | | End of split
% 230.99/42.25  | | | | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | | | End of split
% 230.99/42.25  | | | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | | Case 2:
% 230.99/42.25  | | | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | | |   (202)  all_57_5 = e0 & op(e2, e1) = e0
% 230.99/42.25  | | | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | | | ALPHA: (202) implies:
% 230.99/42.25  | | | | | | | | | | | | |   (203)  all_57_5 = e0
% 230.99/42.25  | | | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | | | REF_CLOSE: (10), (17), (19), (20), (45), (50), (52), (57),
% 230.99/42.25  | | | | | | | | | | | | |            (74), (78), (98), (99), (107), (113), (203) are
% 230.99/42.25  | | | | | | | | | | | | |            inconsistent by sub-proof #1689.
% 230.99/42.25  | | | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | | End of split
% 230.99/42.25  | | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | Case 2:
% 230.99/42.25  | | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | |   (204)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 230.99/42.25  | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 230.99/42.25  | | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | | REF_CLOSE: (17), (20), (27), (28), (30), (34), (44), (48),
% 230.99/42.25  | | | | | | | | | | | |            (52), (57), (58), (59), (71), (74), (78), (80),
% 230.99/42.25  | | | | | | | | | | | |            (81), (97), (113), (118), (122), (128), (204) are
% 230.99/42.25  | | | | | | | | | | | |            inconsistent by sub-proof #1366.
% 230.99/42.25  | | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | End of split
% 230.99/42.25  | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | End of split
% 230.99/42.25  | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | End of split
% 230.99/42.25  | | | | | | | | | 
% 230.99/42.25  | | | | | | | | Case 2:
% 230.99/42.25  | | | | | | | | | 
% 230.99/42.25  | | | | | | | | |   (205)  all_57_3 = e1 & op(e2, e2) = e1
% 230.99/42.25  | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | ALPHA: (205) implies:
% 230.99/42.25  | | | | | | | | |   (206)  op(e2, e2) = e1
% 230.99/42.25  | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | REF_CLOSE: (20), (45), (78), (206) are inconsistent by
% 230.99/42.25  | | | | | | | | |            sub-proof #2352.
% 230.99/42.25  | | | | | | | | | 
% 230.99/42.25  | | | | | | | | End of split
% 230.99/42.25  | | | | | | | | 
% 230.99/42.25  | | | | | | | Case 2:
% 230.99/42.25  | | | | | | | | 
% 230.99/42.25  | | | | | | | |   (207)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 &
% 230.99/42.25  | | | | | | | |            op(e0, e2) = e1)
% 230.99/42.25  | | | | | | | | 
% 230.99/42.25  | | | | | | | | BETA: splitting (207) gives:
% 230.99/42.25  | | | | | | | | 
% 230.99/42.25  | | | | | | | | Case 1:
% 230.99/42.25  | | | | | | | | | 
% 230.99/42.25  | | | | | | | | |   (208)  all_57_7 = e1 & op(e1, e2) = e1
% 230.99/42.25  | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | ALPHA: (208) implies:
% 230.99/42.25  | | | | | | | | |   (209)  all_57_7 = e1
% 230.99/42.25  | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | REF_CLOSE: (17), (182), (209) are inconsistent by sub-proof
% 230.99/42.25  | | | | | | | | |            #2115.
% 230.99/42.25  | | | | | | | | | 
% 230.99/42.25  | | | | | | | | Case 2:
% 230.99/42.25  | | | | | | | | | 
% 230.99/42.25  | | | | | | | | |   (210)  all_57_13 = e1 & op(e0, e2) = e1
% 230.99/42.25  | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | ALPHA: (210) implies:
% 230.99/42.25  | | | | | | | | |   (211)  all_57_13 = e1
% 230.99/42.25  | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | BETA: splitting (123) gives:
% 230.99/42.25  | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | Case 1:
% 230.99/42.25  | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | |   (212)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 230.99/42.25  | | | | | | | | | |            & op(e2, e3) = e0)
% 230.99/42.25  | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | REF_CLOSE: (10), (17), (20), (50), (52), (57), (59), (74),
% 230.99/42.25  | | | | | | | | | |            (78), (99), (107), (113), (212) are inconsistent
% 230.99/42.25  | | | | | | | | | |            by sub-proof #2229.
% 230.99/42.25  | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | Case 2:
% 230.99/42.25  | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | |   (213)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0
% 230.99/42.25  | | | | | | | | | |            & op(e0, e3) = e0)
% 230.99/42.25  | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | BETA: splitting (213) gives:
% 230.99/42.25  | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | Case 1:
% 230.99/42.25  | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | |   (214)  all_57_6 = e0 & op(e1, e3) = e0
% 230.99/42.25  | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | ALPHA: (214) implies:
% 230.99/42.25  | | | | | | | | | | |   (215)  all_57_6 = e0
% 230.99/42.25  | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | BETA: splitting (125) gives:
% 230.99/42.25  | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | Case 1:
% 230.99/42.25  | | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | |   (216)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 230.99/42.25  | | | | | | | | | | | |            & op(e1, e2) = e1)
% 230.99/42.25  | | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | | BETA: splitting (216) gives:
% 230.99/42.25  | | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | | Case 1:
% 230.99/42.25  | | | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | | |   (217)  all_57_6 = e1 & op(e1, e3) = e1
% 230.99/42.25  | | | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | | | ALPHA: (217) implies:
% 230.99/42.25  | | | | | | | | | | | | |   (218)  all_57_6 = e1
% 230.99/42.25  | | | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | | | COMBINE_EQS: (215), (218) imply:
% 230.99/42.25  | | | | | | | | | | | | |   (219)  e1 = e0
% 230.99/42.25  | | | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | | | SIMP: (219) implies:
% 230.99/42.25  | | | | | | | | | | | | |   (220)  e1 = e0
% 230.99/42.25  | | | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | | | COMBINE_EQS: (211), (220) imply:
% 230.99/42.25  | | | | | | | | | | | | |   (221)  all_57_13 = e0
% 230.99/42.25  | | | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | | | REF_CLOSE: (15), (17), (20), (34), (44), (48), (50), (52),
% 230.99/42.25  | | | | | | | | | | | | |            (57), (59), (74), (78), (113), (130), (182), (221)
% 230.99/42.25  | | | | | | | | | | | | |            are inconsistent by sub-proof #2091.
% 230.99/42.25  | | | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | | Case 2:
% 230.99/42.25  | | | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | | |   (222)  all_57_7 = e1 & op(e1, e2) = e1
% 230.99/42.25  | | | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | | | REF_CLOSE: (17), (182), (222) are inconsistent by sub-proof
% 230.99/42.25  | | | | | | | | | | | | |            #2104.
% 230.99/42.25  | | | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | | End of split
% 230.99/42.25  | | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | Case 2:
% 230.99/42.25  | | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | |   (223)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 230.99/42.25  | | | | | | | | | | | |            e1 & op(e1, e0) = e1)
% 230.99/42.25  | | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | | BETA: splitting (223) gives:
% 230.99/42.25  | | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | | Case 1:
% 230.99/42.25  | | | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | | |   (224)  all_57_8 = e1 & op(e1, e1) = e1
% 230.99/42.25  | | | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | | | ALPHA: (224) implies:
% 230.99/42.25  | | | | | | | | | | | | |   (225)  op(e1, e1) = e1
% 230.99/42.25  | | | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | | | REF_CLOSE: (20), (95), (113), (225) are inconsistent by
% 230.99/42.25  | | | | | | | | | | | | |            sub-proof #2423.
% 230.99/42.25  | | | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | | Case 2:
% 230.99/42.25  | | | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | | |   (226)  all_57_11 = e1 & op(e1, e0) = e1
% 230.99/42.25  | | | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | | | ALPHA: (226) implies:
% 230.99/42.25  | | | | | | | | | | | | |   (227)  all_57_11 = e1
% 230.99/42.25  | | | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (10), (13),
% 230.99/42.25  | | | | | | | | | | | | |            (14), (15), (16), (17), (18), (20), (22), (24),
% 230.99/42.25  | | | | | | | | | | | | |            (25), (26), (27), (28), (29), (31), (32), (33),
% 230.99/42.25  | | | | | | | | | | | | |            (34), (36), (37), (39), (40), (41), (42), (43),
% 230.99/42.25  | | | | | | | | | | | | |            (44), (45), (46), (47), (48), (49), (50), (51),
% 230.99/42.25  | | | | | | | | | | | | |            (52), (53), (54), (55), (56), (57), (58), (59),
% 230.99/42.25  | | | | | | | | | | | | |            (60), (63), (64), (65), (66), (67), (69), (70),
% 230.99/42.25  | | | | | | | | | | | | |            (71), (74), (75), (76), (77), (78), (79), (80),
% 230.99/42.25  | | | | | | | | | | | | |            (81), (82), (84), (85), (87), (88), (89), (90),
% 230.99/42.25  | | | | | | | | | | | | |            (91), (92), (93), (94), (96), (97), (98), (99),
% 230.99/42.25  | | | | | | | | | | | | |            (100), (101), (102), (103), (104), (105), (106),
% 230.99/42.25  | | | | | | | | | | | | |            (107), (108), (109), (110), (111), (113), (114),
% 230.99/42.25  | | | | | | | | | | | | |            (116), (117), (118), (119), (120), (121), (122),
% 230.99/42.25  | | | | | | | | | | | | |            (123), (124), (125), (126), (127), (129), (130),
% 230.99/42.25  | | | | | | | | | | | | |            (131), (132), (133), (182), (227) are inconsistent
% 230.99/42.25  | | | | | | | | | | | | |            by sub-proof #1374.
% 230.99/42.25  | | | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | | End of split
% 230.99/42.25  | | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | End of split
% 230.99/42.25  | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | Case 2:
% 230.99/42.25  | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | |   (228)  all_57_12 = e0 & op(e0, e3) = e0
% 230.99/42.25  | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | ALPHA: (228) implies:
% 230.99/42.25  | | | | | | | | | | |   (229)  all_57_12 = e0
% 230.99/42.25  | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | | REF_CLOSE: (74), (146), (229) are inconsistent by sub-proof
% 230.99/42.25  | | | | | | | | | | |            #2385.
% 230.99/42.25  | | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | | End of split
% 230.99/42.25  | | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | End of split
% 230.99/42.25  | | | | | | | | | 
% 230.99/42.25  | | | | | | | | End of split
% 230.99/42.25  | | | | | | | | 
% 230.99/42.25  | | | | | | | End of split
% 230.99/42.25  | | | | | | | 
% 230.99/42.25  | | | | | | Case 2:
% 230.99/42.25  | | | | | | | 
% 230.99/42.25  | | | | | | |   (230)  all_57_13 = e3 & op(e0, e2) = e3
% 230.99/42.25  | | | | | | | 
% 230.99/42.25  | | | | | | | ALPHA: (230) implies:
% 230.99/42.25  | | | | | | |   (231)  all_57_13 = e3
% 230.99/42.25  | | | | | | | 
% 230.99/42.25  | | | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (10), (13), (14),
% 230.99/42.25  | | | | | | |            (15), (16), (17), (18), (19), (20), (22), (24), (25),
% 230.99/42.25  | | | | | | |            (26), (27), (28), (29), (30), (32), (33), (34), (36),
% 230.99/42.25  | | | | | | |            (37), (39), (40), (41), (42), (43), (44), (45), (46),
% 230.99/42.25  | | | | | | |            (47), (48), (49), (50), (51), (52), (53), (54), (55),
% 230.99/42.25  | | | | | | |            (56), (57), (58), (59), (60), (63), (64), (65), (66),
% 230.99/42.25  | | | | | | |            (67), (69), (70), (71), (74), (75), (76), (77), (78),
% 230.99/42.25  | | | | | | |            (79), (80), (81), (82), (84), (85), (87), (88), (89),
% 230.99/42.25  | | | | | | |            (90), (91), (92), (93), (96), (97), (98), (99), (100),
% 230.99/42.25  | | | | | | |            (101), (102), (103), (104), (105), (106), (107), (108),
% 230.99/42.25  | | | | | | |            (109), (110), (111), (113), (114), (116), (117), (118),
% 230.99/42.25  | | | | | | |            (119), (120), (121), (122), (123), (124), (125), (126),
% 230.99/42.25  | | | | | | |            (127), (128), (129), (130), (131), (132), (133), (134),
% 230.99/42.25  | | | | | | |            (146), (231) are inconsistent by sub-proof #1340.
% 230.99/42.25  | | | | | | | 
% 230.99/42.25  | | | | | | End of split
% 230.99/42.25  | | | | | | 
% 230.99/42.25  | | | | | End of split
% 230.99/42.25  | | | | | 
% 230.99/42.25  | | | | Case 2:
% 230.99/42.25  | | | | | 
% 230.99/42.25  | | | | |   (232)  all_57_13 = e2 & op(e0, e2) = e2
% 230.99/42.25  | | | | | 
% 230.99/42.25  | | | | | ALPHA: (232) implies:
% 230.99/42.25  | | | | |   (233)  all_57_13 = e2
% 230.99/42.25  | | | | | 
% 230.99/42.25  | | | | | BETA: splitting (82) gives:
% 230.99/42.25  | | | | | 
% 230.99/42.25  | | | | | Case 1:
% 230.99/42.25  | | | | | | 
% 230.99/42.25  | | | | | |   (234)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2,
% 230.99/42.25  | | | | | |              e2) = e3)
% 230.99/42.25  | | | | | | 
% 230.99/42.25  | | | | | | BETA: splitting (234) gives:
% 230.99/42.25  | | | | | | 
% 230.99/42.25  | | | | | | Case 1:
% 230.99/42.25  | | | | | | | 
% 230.99/42.25  | | | | | | |   (235)  all_57_1 = e3 & op(e3, e2) = e3
% 230.99/42.25  | | | | | | | 
% 230.99/42.25  | | | | | | | ALPHA: (235) implies:
% 230.99/42.25  | | | | | | |   (236)  all_57_1 = e3
% 230.99/42.25  | | | | | | | 
% 230.99/42.25  | | | | | | | BETA: splitting (44) gives:
% 230.99/42.25  | | | | | | | 
% 230.99/42.25  | | | | | | | Case 1:
% 230.99/42.25  | | | | | | | | 
% 230.99/42.25  | | | | | | | |   (237)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 &
% 230.99/42.25  | | | | | | | |            op(e3, e2) = e2)
% 230.99/42.25  | | | | | | | | 
% 230.99/42.25  | | | | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (10), (13), (14),
% 230.99/42.25  | | | | | | | |            (15), (16), (17), (18), (19), (20), (22), (23), (24),
% 230.99/42.25  | | | | | | | |            (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 230.99/42.25  | | | | | | | |            (34), (36), (37), (39), (40), (41), (42), (43), (44),
% 230.99/42.25  | | | | | | | |            (45), (46), (47), (48), (49), (50), (51), (52), (53),
% 230.99/42.25  | | | | | | | |            (54), (55), (56), (57), (58), (59), (60), (63), (64),
% 230.99/42.25  | | | | | | | |            (65), (66), (67), (68), (69), (70), (71), (72), (73),
% 230.99/42.25  | | | | | | | |            (74), (75), (76), (77), (78), (79), (80), (81), (82),
% 230.99/42.25  | | | | | | | |            (84), (85), (87), (88), (89), (90), (91), (92), (93),
% 230.99/42.25  | | | | | | | |            (94), (95), (96), (97), (98), (99), (100), (101),
% 230.99/42.25  | | | | | | | |            (102), (103), (104), (105), (106), (107), (108),
% 230.99/42.25  | | | | | | | |            (109), (110), (111), (113), (114), (116), (117),
% 230.99/42.25  | | | | | | | |            (118), (119), (120), (121), (122), (123), (124),
% 230.99/42.25  | | | | | | | |            (125), (126), (127), (128), (129), (130), (131),
% 230.99/42.25  | | | | | | | |            (132), (133), (134), (236), (237) are inconsistent by
% 230.99/42.25  | | | | | | | |            sub-proof #1345.
% 230.99/42.25  | | | | | | | | 
% 230.99/42.25  | | | | | | | Case 2:
% 230.99/42.25  | | | | | | | | 
% 230.99/42.25  | | | | | | | |   (238)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 &
% 230.99/42.25  | | | | | | | |            op(e3, e0) = e2)
% 230.99/42.25  | | | | | | | | 
% 230.99/42.25  | | | | | | | | BETA: splitting (238) gives:
% 230.99/42.25  | | | | | | | | 
% 230.99/42.25  | | | | | | | | Case 1:
% 230.99/42.25  | | | | | | | | | 
% 230.99/42.25  | | | | | | | | |   (239)  all_57_4 = e2 & op(e3, e1) = e2
% 230.99/42.25  | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | REF_CLOSE: (10), (17), (19), (20), (27), (28), (30), (34),
% 230.99/42.25  | | | | | | | | |            (44), (45), (48), (50), (51), (52), (57), (58),
% 230.99/42.25  | | | | | | | | |            (59), (71), (74), (78), (80), (81), (97), (98),
% 230.99/42.25  | | | | | | | | |            (99), (107), (113), (118), (122), (128), (239) are
% 230.99/42.25  | | | | | | | | |            inconsistent by sub-proof #1361.
% 230.99/42.25  | | | | | | | | | 
% 230.99/42.25  | | | | | | | | Case 2:
% 230.99/42.25  | | | | | | | | | 
% 230.99/42.25  | | | | | | | | |   (240)  all_57_9 = e2 & op(e3, e0) = e2
% 230.99/42.25  | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | ALPHA: (240) implies:
% 230.99/42.25  | | | | | | | | |   (241)  all_57_9 = e2
% 230.99/42.25  | | | | | | | | | 
% 230.99/42.25  | | | | | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (10), (13),
% 230.99/42.25  | | | | | | | | |            (14), (15), (16), (17), (18), (19), (20), (22),
% 230.99/42.25  | | | | | | | | |            (24), (25), (26), (27), (28), (29), (30), (31),
% 230.99/42.25  | | | | | | | | |            (32), (33), (34), (36), (37), (39), (40), (41),
% 230.99/42.25  | | | | | | | | |            (42), (43), (44), (45), (46), (47), (48), (49),
% 230.99/42.25  | | | | | | | | |            (50), (51), (52), (53), (54), (55), (56), (57),
% 230.99/42.25  | | | | | | | | |            (58), (59), (60), (63), (64), (65), (66), (67),
% 230.99/42.25  | | | | | | | | |            (69), (70), (71), (74), (75), (76), (77), (78),
% 230.99/42.25  | | | | | | | | |            (79), (80), (81), (82), (84), (85), (87), (88),
% 230.99/42.25  | | | | | | | | |            (89), (90), (91), (92), (93), (94), (96), (97),
% 230.99/42.25  | | | | | | | | |            (98), (99), (100), (101), (102), (103), (104),
% 230.99/42.25  | | | | | | | | |            (105), (106), (107), (108), (109), (110), (111),
% 230.99/42.25  | | | | | | | | |            (113), (114), (116), (117), (118), (119), (120),
% 230.99/42.25  | | | | | | | | |            (121), (122), (123), (124), (125), (126), (127),
% 230.99/42.25  | | | | | | | | |            (128), (129), (130), (131), (132), (133), (143),
% 230.99/42.25  | | | | | | | | |            (233), (236), (241) are inconsistent by sub-proof
% 230.99/42.25  | | | | | | | | |            #1359.
% 230.99/42.25  | | | | | | | | | 
% 230.99/42.25  | | | | | | | | End of split
% 230.99/42.25  | | | | | | | | 
% 230.99/42.25  | | | | | | | End of split
% 230.99/42.25  | | | | | | | 
% 230.99/42.25  | | | | | | Case 2:
% 230.99/42.25  | | | | | | | 
% 230.99/42.25  | | | | | | |   (242)  all_57_3 = e3 & op(e2, e2) = e3
% 230.99/42.25  | | | | | | | 
% 230.99/42.25  | | | | | | | REF_CLOSE: (17), (20), (27), (28), (30), (34), (44), (48), (50),
% 230.99/42.25  | | | | | | |            (52), (57), (58), (59), (71), (74), (78), (80), (81),
% 230.99/42.25  | | | | | | |            (97), (113), (122), (128), (134), (242) are
% 230.99/42.25  | | | | | | |            inconsistent by sub-proof #1343.
% 230.99/42.25  | | | | | | | 
% 230.99/42.25  | | | | | | End of split
% 230.99/42.25  | | | | | | 
% 230.99/42.25  | | | | | Case 2:
% 230.99/42.25  | | | | | | 
% 230.99/42.25  | | | | | |   (243)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 &
% 230.99/42.25  | | | | | |            op(e0, e2) = e3)
% 230.99/42.25  | | | | | | 
% 230.99/42.25  | | | | | | BETA: splitting (243) gives:
% 230.99/42.25  | | | | | | 
% 230.99/42.25  | | | | | | Case 1:
% 230.99/42.25  | | | | | | | 
% 230.99/42.25  | | | | | | |   (244)  all_57_7 = e3 & op(e1, e2) = e3
% 230.99/42.25  | | | | | | | 
% 230.99/42.25  | | | | | | | REF_CLOSE: (3), (9), (10), (11), (12), (15), (17), (19), (20),
% 230.99/42.25  | | | | | | |            (21), (27), (28), (30), (34), (35), (37), (38), (44),
% 230.99/42.25  | | | | | | |            (45), (48), (50), (51), (52), (57), (58), (59), (61),
% 230.99/42.25  | | | | | | |            (62), (71), (74), (78), (80), (81), (83), (86), (91),
% 230.99/42.25  | | | | | | |            (97), (98), (99), (107), (112), (113), (118), (119),
% 230.99/42.25  | | | | | | |            (122), (128), (130), (244) are inconsistent by
% 230.99/42.25  | | | | | | |            sub-proof #1365.
% 230.99/42.25  | | | | | | | 
% 230.99/42.25  | | | | | | Case 2:
% 230.99/42.25  | | | | | | | 
% 230.99/42.25  | | | | | | |   (245)  all_57_13 = e3 & op(e0, e2) = e3
% 230.99/42.25  | | | | | | | 
% 230.99/42.25  | | | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (10), (13), (14),
% 230.99/42.25  | | | | | | |            (15), (16), (17), (18), (19), (20), (22), (23), (24),
% 230.99/42.25  | | | | | | |            (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 230.99/42.25  | | | | | | |            (34), (36), (37), (39), (40), (41), (42), (43), (44),
% 230.99/42.25  | | | | | | |            (45), (46), (47), (48), (49), (50), (51), (52), (53),
% 230.99/42.25  | | | | | | |            (54), (55), (56), (57), (58), (59), (60), (63), (64),
% 230.99/42.25  | | | | | | |            (65), (66), (67), (68), (69), (70), (71), (72), (73),
% 230.99/42.25  | | | | | | |            (74), (75), (76), (77), (78), (79), (80), (81), (82),
% 230.99/42.25  | | | | | | |            (84), (85), (87), (88), (89), (90), (91), (92), (93),
% 230.99/42.25  | | | | | | |            (94), (95), (96), (97), (98), (99), (100), (101),
% 230.99/42.25  | | | | | | |            (102), (103), (104), (105), (106), (107), (108), (109),
% 230.99/42.25  | | | | | | |            (110), (111), (113), (114), (116), (117), (118), (119),
% 230.99/42.25  | | | | | | |            (120), (121), (122), (123), (124), (125), (126), (127),
% 230.99/42.25  | | | | | | |            (128), (129), (130), (131), (132), (133), (134), (245)
% 230.99/42.25  | | | | | | |            are inconsistent by sub-proof #1339.
% 230.99/42.25  | | | | | | | 
% 230.99/42.25  | | | | | | End of split
% 230.99/42.25  | | | | | | 
% 230.99/42.25  | | | | | End of split
% 230.99/42.25  | | | | | 
% 230.99/42.25  | | | | End of split
% 230.99/42.25  | | | | 
% 230.99/42.25  | | | Case 2:
% 230.99/42.25  | | | | 
% 230.99/42.25  | | | |   (246)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0,
% 230.99/42.25  | | | |              e0) = e2)
% 230.99/42.25  | | | | 
% 230.99/42.25  | | | | BETA: splitting (246) gives:
% 230.99/42.25  | | | | 
% 230.99/42.25  | | | | Case 1:
% 230.99/42.25  | | | | | 
% 230.99/42.25  | | | | |   (247)  all_57_14 = e2 & op(e0, e1) = e2
% 230.99/42.25  | | | | | 
% 230.99/42.25  | | | | | ALPHA: (247) implies:
% 230.99/42.25  | | | | |   (248)  all_57_14 = e2
% 230.99/42.25  | | | | | 
% 230.99/42.25  | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (10), (13), (14), (15),
% 230.99/42.25  | | | | |            (16), (17), (18), (19), (20), (22), (23), (24), (25), (26),
% 230.99/42.25  | | | | |            (27), (28), (29), (30), (31), (32), (33), (34), (36), (37),
% 230.99/42.25  | | | | |            (39), (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 230.99/42.25  | | | | |            (49), (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 230.99/42.25  | | | | |            (59), (60), (63), (64), (65), (66), (67), (68), (69), (70),
% 230.99/42.25  | | | | |            (71), (72), (73), (74), (75), (76), (77), (78), (79), (80),
% 230.99/42.25  | | | | |            (81), (82), (84), (85), (87), (88), (89), (90), (91), (92),
% 230.99/42.25  | | | | |            (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 230.99/42.25  | | | | |            (102), (103), (104), (105), (106), (107), (108), (109),
% 230.99/42.25  | | | | |            (110), (111), (113), (114), (116), (117), (118), (119),
% 230.99/42.25  | | | | |            (120), (121), (122), (123), (124), (125), (126), (127),
% 230.99/42.25  | | | | |            (128), (129), (130), (131), (132), (133), (248) are
% 230.99/42.25  | | | | |            inconsistent by sub-proof #1346.
% 230.99/42.25  | | | | | 
% 230.99/42.25  | | | | Case 2:
% 230.99/42.25  | | | | | 
% 230.99/42.25  | | | | |   (249)  all_57_15 = e2 & op(e0, e0) = e2
% 230.99/42.25  | | | | | 
% 230.99/42.25  | | | | | ALPHA: (249) implies:
% 230.99/42.25  | | | | |   (250)  op(e0, e0) = e2
% 230.99/42.25  | | | | | 
% 230.99/42.25  | | | | | REF_CLOSE: (20), (97), (113), (250) are inconsistent by sub-proof
% 230.99/42.25  | | | | |            #2177.
% 230.99/42.25  | | | | | 
% 230.99/42.25  | | | | End of split
% 230.99/42.25  | | | | 
% 230.99/42.25  | | | End of split
% 230.99/42.25  | | | 
% 230.99/42.25  | | End of split
% 230.99/42.25  | | 
% 230.99/42.25  | End of split
% 230.99/42.25  | 
% 230.99/42.25  End of proof
% 230.99/42.25  
% 230.99/42.25  Sub-proof #1339 shows that the following formulas are inconsistent:
% 230.99/42.25  ----------------------------------------------------------------
% 230.99/42.25    (1)   ~ (all_10_2 = e2)
% 230.99/42.25    (2)  all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 230.99/42.25    (3)  op(e3, e3) = all_10_2
% 230.99/42.25    (4)  op(e0, e1) = all_53_11
% 230.99/42.25    (5)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 230.99/42.25    (6)   ~ (all_53_6 = all_53_14)
% 230.99/42.25    (7)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 230.99/42.25    (8)  all_57_13 = e3 & op(e0, e2) = e3
% 230.99/42.25    (9)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.99/42.25         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.99/42.25    (10)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 230.99/42.25          (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 230.99/42.25    (11)   ~ (all_53_8 = all_53_12)
% 230.99/42.25    (12)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.99/42.25          (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.99/42.25    (13)   ~ (all_53_8 = all_53_11)
% 230.99/42.25    (14)   ~ (e3 = e1)
% 230.99/42.25    (15)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 230.99/42.25          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 230.99/42.25    (16)   ~ (all_53_13 = e1)
% 230.99/42.25    (17)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 230.99/42.25            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 230.99/42.25    (18)  all_55_0 = all_10_2
% 230.99/42.25    (19)  all_57_15 = e1
% 230.99/42.25    (20)   ~ (all_10_2 = e0)
% 230.99/42.25    (21)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 230.99/42.25          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 230.99/42.25    (22)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 230.99/42.25            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 230.99/42.26              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 230.99/42.26    (23)   ~ (all_6_2 = e3)
% 230.99/42.26    (24)  op(e1, e1) = all_6_2
% 230.99/42.26    (25)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 230.99/42.26    (26)  op(all_52_7, all_52_7) = e0
% 230.99/42.26    (27)   ~ (all_53_9 = e0)
% 230.99/42.26    (28)  all_55_0 = e3 | all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 230.99/42.26    (29)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 230.99/42.26    (30)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 230.99/42.26          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 230.99/42.26    (31)  all_57_14 = e3
% 230.99/42.26    (32)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 230.99/42.26    (33)  all_55_9 = all_53_6
% 230.99/42.26    (34)   ~ (all_53_11 = all_6_2)
% 230.99/42.26    (35)   ~ (all_53_4 = all_53_12)
% 230.99/42.26    (36)   ~ (all_53_8 = e3)
% 230.99/42.26    (37)   ~ (all_53_8 = all_53_9)
% 230.99/42.26    (38)  all_42_2 = all_6_2
% 230.99/42.26    (39)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 230.99/42.26          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 230.99/42.26    (40)  op(e2, e2) = e0
% 230.99/42.26    (41)   ~ (all_53_9 = all_53_11)
% 230.99/42.26    (42)   ~ (all_53_9 = all_6_2)
% 230.99/42.26    (43)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 230.99/42.26          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 230.99/42.26    (44)   ~ (all_53_14 = all_6_2)
% 230.99/42.26    (45)  all_57_3 = e0
% 230.99/42.26    (46)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 230.99/42.26          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 230.99/42.26    (47)   ~ (e3 = e2)
% 230.99/42.26    (48)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 230.99/42.26    (49)  all_55_1 = all_53_4
% 230.99/42.26    (50)  op(e1, e0) = all_53_14
% 230.99/42.26    (51)   ~ (all_53_6 = all_53_7)
% 230.99/42.26    (52)   ~ (e3 = e0)
% 230.99/42.26    (53)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 230.99/42.26          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 230.99/42.26    (54)  op(e3, e3) = e3
% 230.99/42.26    (55)   ~ (all_53_8 = all_6_2)
% 230.99/42.26    (56)  all_55_2 = all_53_8
% 230.99/42.26    (57)   ~ (all_53_4 = all_53_7)
% 230.99/42.26    (58)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 230.99/42.26    (59)   ~ (all_53_7 = e0)
% 230.99/42.26    (60)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.99/42.26          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.99/42.26            e1)
% 230.99/42.26    (61)  op(e3, e3) = all_52_1
% 230.99/42.26    (62)   ~ (all_53_4 = all_53_8)
% 230.99/42.26    (63)  all_55_6 = all_53_9
% 230.99/42.26    (64)  op(e3, e2) = all_53_4
% 230.99/42.26    (65)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 230.99/42.26          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 230.99/42.26    (66)  op(all_52_1, all_52_1) = e3
% 230.99/42.26    (67)   ~ (e2 = e0)
% 230.99/42.26    (68)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 230.99/42.26            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 230.99/42.26            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 230.99/42.26            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 230.99/42.26              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 230.99/42.26            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 230.99/42.26            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 230.99/42.26              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 230.99/42.26              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 230.99/42.26            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 230.99/42.26            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 230.99/42.26            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 230.99/42.26              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 230.99/42.26              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 230.99/42.26            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 230.99/42.26              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 230.99/42.26            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 230.99/42.26            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 230.99/42.26              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 230.99/42.26              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 230.99/42.26            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 230.99/42.26            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 230.99/42.26    (69)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 230.99/42.26          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 230.99/42.26    (70)   ~ (all_53_2 = all_53_14)
% 230.99/42.26    (71)   ~ (e1 = e0)
% 230.99/42.26    (72)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 230.99/42.26            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 230.99/42.26              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 230.99/42.26    (73)   ~ (all_53_4 = e0)
% 230.99/42.26    (74)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 230.99/42.26          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 230.99/42.26    (75)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.99/42.26          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.99/42.26    (76)   ~ (all_10_2 = e1)
% 230.99/42.26    (77)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 230.99/42.26    (78)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 230.99/42.26          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 230.99/42.26            e3)
% 230.99/42.26    (79)   ~ (all_53_4 = all_53_6)
% 230.99/42.26    (80)  op(e0, e2) = all_53_7
% 230.99/42.26    (81)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 230.99/42.26          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.99/42.26            e2)
% 230.99/42.26    (82)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 230.99/42.26              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 230.99/42.26                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 230.99/42.26                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 230.99/42.26    (83)  all_55_10 = all_6_2
% 230.99/42.26    (84)   ~ (all_53_6 = all_6_2)
% 230.99/42.26    (85)   ~ (all_53_13 = e0)
% 230.99/42.26    (86)  op(e1, e1) = e2
% 230.99/42.26    (87)  all_55_13 = all_53_7
% 230.99/42.26    (88)  op(e0, e0) = e1
% 230.99/42.26    (89)  op(e2, e0) = all_53_13
% 230.99/42.26    (90)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 230.99/42.26          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.99/42.26    (91)  all_38_2 = all_6_2
% 230.99/42.26    (92)  all_55_11 = all_53_14
% 230.99/42.26    (93)  all_55_3 = all_53_12
% 230.99/42.26    (94)   ~ (all_53_12 = e3)
% 230.99/42.26    (95)  all_57_0 = e3
% 230.99/42.26    (96)  op(e1, e3) = all_53_2
% 230.99/42.26    (97)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 230.99/42.26            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 230.99/42.26              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 230.99/42.26    (98)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 230.99/42.26          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.99/42.26    (99)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 230.99/42.26          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 230.99/42.26    (100)   ~ (all_53_12 = all_10_2)
% 230.99/42.26    (101)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 230.99/42.26           | (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 230.99/42.26             e3)
% 230.99/42.26    (102)   ~ (all_53_13 = all_53_14)
% 230.99/42.26    (103)   ~ (e2 = e1)
% 230.99/42.26    (104)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 230.99/42.26           | (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 230.99/42.26             e2)
% 230.99/42.26    (105)  op(e2, e1) = all_53_9
% 230.99/42.26    (106)  op(e1, e2) = all_53_6
% 230.99/42.26    (107)   ~ (all_6_2 = e0)
% 230.99/42.26    (108)   ~ (all_53_2 = all_53_6)
% 230.99/42.26    (109)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 230.99/42.26           (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 230.99/42.26    (110)  all_24_2 = all_6_2
% 230.99/42.26    (111)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 230.99/42.26           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 230.99/42.26    (112)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 230.99/42.26           (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 230.99/42.26    (113)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 230.99/42.26           | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 230.99/42.26             e1)
% 230.99/42.26    (114)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 230.99/42.26           (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 230.99/42.26    (115)   ~ (all_53_12 = all_53_14)
% 230.99/42.26    (116)  all_55_14 = all_53_11
% 230.99/42.26    (117)  op(e3, e0) = all_52_7
% 230.99/42.26    (118)  op(e3, e1) = all_53_8
% 230.99/42.26    (119)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 230.99/42.26           (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 230.99/42.26    (120)   ~ (all_53_4 = e3)
% 230.99/42.26    (121)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 230.99/42.26           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 230.99/42.26    (122)  op(e3, e0) = all_53_12
% 230.99/42.26  
% 230.99/42.26  Begin of proof
% 230.99/42.26  | 
% 231.09/42.26  | ALPHA: (8) implies:
% 231.09/42.26  |   (123)  all_57_13 = e3
% 231.09/42.26  | 
% 231.09/42.26  | BETA: splitting (81) gives:
% 231.09/42.26  | 
% 231.09/42.26  | Case 1:
% 231.09/42.26  | | 
% 231.09/42.26  | |   (124)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 231.09/42.26  | |            e2)
% 231.09/42.26  | | 
% 231.09/42.26  | | BETA: splitting (124) gives:
% 231.09/42.26  | | 
% 231.09/42.26  | | Case 1:
% 231.09/42.26  | | | 
% 231.09/42.26  | | |   (125)  all_57_12 = e2 & op(e0, e3) = e2
% 231.09/42.26  | | | 
% 231.09/42.26  | | | ALPHA: (125) implies:
% 231.09/42.26  | | |   (126)  all_57_12 = e2
% 231.09/42.26  | | | 
% 231.09/42.26  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13),
% 231.09/42.26  | | |            (14), (15), (16), (17), (18), (20), (21), (22), (23), (24),
% 231.09/42.26  | | |            (25), (26), (28), (29), (30), (31), (32), (33), (34), (35),
% 231.09/42.26  | | |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 231.09/42.26  | | |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (55),
% 231.09/42.26  | | |            (56), (57), (58), (59), (60), (62), (63), (64), (67), (68),
% 231.09/42.26  | | |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78),
% 231.09/42.26  | | |            (79), (80), (81), (82), (83), (84), (87), (88), (89), (90),
% 231.09/42.26  | | |            (91), (92), (93), (94), (95), (96), (97), (98), (99), (100),
% 231.09/42.26  | | |            (101), (102), (103), (104), (105), (106), (107), (108), (109),
% 231.09/42.26  | | |            (110), (111), (112), (113), (114), (115), (116), (117), (118),
% 231.09/42.26  | | |            (119), (120), (121), (122), (123), (126) are inconsistent by
% 231.09/42.26  | | |            sub-proof #1340.
% 231.09/42.26  | | | 
% 231.09/42.26  | | Case 2:
% 231.09/42.26  | | | 
% 231.09/42.26  | | |   (127)  all_57_13 = e2 & op(e0, e2) = e2
% 231.09/42.26  | | | 
% 231.09/42.26  | | | ALPHA: (127) implies:
% 231.09/42.26  | | |   (128)  all_57_13 = e2
% 231.09/42.26  | | | 
% 231.09/42.26  | | | COMBINE_EQS: (123), (128) imply:
% 231.09/42.26  | | |   (129)  e3 = e2
% 231.09/42.26  | | | 
% 231.09/42.26  | | | COMBINE_EQS: (31), (129) imply:
% 231.09/42.26  | | |   (130)  all_57_14 = e2
% 231.09/42.26  | | | 
% 231.09/42.26  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13),
% 231.09/42.26  | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 231.09/42.26  | | |            (24), (25), (26), (27), (28), (29), (30), (32), (33), (34),
% 231.09/42.26  | | |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44),
% 231.09/42.26  | | |            (45), (46), (47), (48), (49), (50), (51), (52), (53), (54),
% 231.09/42.26  | | |            (55), (56), (57), (58), (59), (60), (61), (62), (63), (64),
% 231.09/42.26  | | |            (65), (66), (67), (68), (69), (70), (71), (72), (73), (74),
% 231.09/42.26  | | |            (75), (76), (77), (78), (79), (80), (81), (82), (83), (84),
% 231.09/42.26  | | |            (85), (86), (87), (88), (89), (90), (91), (92), (93), (94),
% 231.09/42.26  | | |            (95), (96), (97), (98), (99), (100), (101), (102), (103),
% 231.09/42.26  | | |            (104), (105), (106), (107), (108), (109), (110), (111), (112),
% 231.09/42.26  | | |            (113), (114), (115), (116), (117), (118), (119), (120), (121),
% 231.09/42.26  | | |            (122), (123), (130) are inconsistent by sub-proof #1348.
% 231.09/42.26  | | | 
% 231.09/42.26  | | End of split
% 231.09/42.26  | | 
% 231.09/42.26  | Case 2:
% 231.09/42.26  | | 
% 231.09/42.26  | |   (131)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.09/42.26  | |            e2)
% 231.09/42.26  | | 
% 231.09/42.26  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13),
% 231.09/42.26  | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 231.09/42.26  | |            (25), (26), (27), (28), (29), (30), (32), (33), (34), (35), (36),
% 231.09/42.26  | |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 231.09/42.26  | |            (48), (49), (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 231.09/42.26  | |            (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 231.09/42.26  | |            (70), (71), (72), (73), (74), (75), (76), (77), (78), (79), (80),
% 231.09/42.26  | |            (81), (82), (83), (84), (85), (86), (87), (88), (89), (90), (91),
% 231.09/42.26  | |            (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 231.09/42.26  | |            (102), (103), (104), (105), (106), (107), (108), (109), (110),
% 231.09/42.26  | |            (111), (112), (113), (114), (115), (116), (117), (118), (119),
% 231.09/42.26  | |            (120), (121), (122), (123), (131) are inconsistent by sub-proof
% 231.09/42.26  | |            #1347.
% 231.09/42.26  | | 
% 231.09/42.26  | End of split
% 231.09/42.26  | 
% 231.09/42.26  End of proof
% 231.09/42.26  
% 231.09/42.26  Sub-proof #1340 shows that the following formulas are inconsistent:
% 231.09/42.26  ----------------------------------------------------------------
% 231.09/42.26    (1)   ~ (all_10_2 = e2)
% 231.09/42.26    (2)  all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 231.09/42.26    (3)  op(e3, e3) = all_10_2
% 231.09/42.26    (4)  op(e0, e1) = all_53_11
% 231.09/42.26    (5)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 231.09/42.26    (6)   ~ (all_53_6 = all_53_14)
% 231.09/42.26    (7)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 231.09/42.26    (8)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.09/42.26         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.09/42.26    (9)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.09/42.26         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.09/42.26    (10)   ~ (all_53_8 = all_53_12)
% 231.09/42.26    (11)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.09/42.26          (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.09/42.26    (12)   ~ (all_53_8 = all_53_11)
% 231.09/42.26    (13)   ~ (e3 = e1)
% 231.09/42.26    (14)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 231.09/42.26          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.09/42.26    (15)   ~ (all_53_13 = e1)
% 231.09/42.26    (16)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.09/42.26            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.09/42.26    (17)  all_55_0 = all_10_2
% 231.09/42.26    (18)   ~ (all_10_2 = e0)
% 231.09/42.26    (19)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.09/42.26          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.09/42.26    (20)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 231.09/42.26            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 231.09/42.26              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 231.09/42.26    (21)   ~ (all_6_2 = e3)
% 231.09/42.26    (22)  op(e1, e1) = all_6_2
% 231.09/42.26    (23)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 231.09/42.26    (24)  op(all_52_7, all_52_7) = e0
% 231.09/42.26    (25)  all_55_0 = e3 | all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 231.09/42.26    (26)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 231.09/42.26    (27)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.09/42.26          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.09/42.26    (28)  all_57_14 = e3
% 231.09/42.26    (29)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 231.09/42.26    (30)  all_55_9 = all_53_6
% 231.09/42.26    (31)   ~ (all_53_11 = all_6_2)
% 231.09/42.26    (32)   ~ (all_53_4 = all_53_12)
% 231.09/42.26    (33)   ~ (all_53_8 = e3)
% 231.09/42.26    (34)   ~ (all_53_8 = all_53_9)
% 231.09/42.26    (35)  all_57_12 = e2
% 231.09/42.26    (36)  all_42_2 = all_6_2
% 231.09/42.26    (37)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.09/42.26          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.09/42.26    (38)  op(e2, e2) = e0
% 231.09/42.26    (39)   ~ (all_53_9 = all_53_11)
% 231.09/42.26    (40)   ~ (all_53_9 = all_6_2)
% 231.09/42.26    (41)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.09/42.26          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.09/42.26    (42)   ~ (all_53_14 = all_6_2)
% 231.09/42.26    (43)  all_57_3 = e0
% 231.09/42.26    (44)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.09/42.26          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.09/42.26    (45)   ~ (e3 = e2)
% 231.09/42.26    (46)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 231.09/42.26    (47)  all_55_1 = all_53_4
% 231.09/42.26    (48)  op(e1, e0) = all_53_14
% 231.09/42.26    (49)   ~ (all_53_6 = all_53_7)
% 231.09/42.26    (50)   ~ (e3 = e0)
% 231.09/42.26    (51)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.09/42.26          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.09/42.26    (52)  op(e3, e3) = e3
% 231.09/42.26    (53)   ~ (all_53_8 = all_6_2)
% 231.09/42.26    (54)  all_55_2 = all_53_8
% 231.09/42.26    (55)   ~ (all_53_4 = all_53_7)
% 231.09/42.26    (56)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 231.09/42.26    (57)   ~ (all_53_7 = e0)
% 231.09/42.26    (58)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.09/42.26          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.09/42.26            e1)
% 231.09/42.26    (59)   ~ (all_53_4 = all_53_8)
% 231.09/42.26    (60)  all_55_6 = all_53_9
% 231.09/42.26    (61)  op(e3, e2) = all_53_4
% 231.09/42.26    (62)   ~ (e2 = e0)
% 231.09/42.26    (63)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 231.09/42.26            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 231.09/42.26            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 231.09/42.26            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 231.09/42.26              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 231.09/42.26            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 231.09/42.26            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 231.09/42.26              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 231.09/42.26              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 231.09/42.26            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 231.09/42.26            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 231.09/42.26            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 231.09/42.26              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 231.09/42.26              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 231.09/42.26            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 231.09/42.26              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 231.09/42.26            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 231.09/42.26            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 231.09/42.26              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 231.09/42.26              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 231.09/42.26            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 231.09/42.26            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 231.09/42.26    (64)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 231.09/42.26          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.09/42.26    (65)   ~ (all_53_2 = all_53_14)
% 231.09/42.26    (66)   ~ (e1 = e0)
% 231.09/42.26    (67)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 231.09/42.26            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 231.09/42.26              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 231.09/42.26    (68)   ~ (all_53_4 = e0)
% 231.09/42.26    (69)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.09/42.26          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.09/42.26    (70)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.09/42.26          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.09/42.26    (71)   ~ (all_10_2 = e1)
% 231.09/42.26    (72)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 231.09/42.26    (73)  all_57_13 = e3
% 231.09/42.26    (74)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.09/42.26          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 231.09/42.26            e3)
% 231.09/42.26    (75)   ~ (all_53_4 = all_53_6)
% 231.09/42.26    (76)  op(e0, e2) = all_53_7
% 231.09/42.27    (77)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.09/42.27          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.09/42.27            e2)
% 231.09/42.27    (78)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.09/42.27              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.09/42.27                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.09/42.27                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.09/42.27    (79)  all_55_10 = all_6_2
% 231.09/42.27    (80)   ~ (all_53_6 = all_6_2)
% 231.09/42.27    (81)  all_55_13 = all_53_7
% 231.09/42.27    (82)  op(e0, e0) = e1
% 231.09/42.27    (83)  op(e2, e0) = all_53_13
% 231.09/42.27    (84)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.09/42.27          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.09/42.27    (85)  all_38_2 = all_6_2
% 231.09/42.27    (86)  all_55_11 = all_53_14
% 231.09/42.27    (87)  all_55_3 = all_53_12
% 231.09/42.27    (88)   ~ (all_53_12 = e3)
% 231.09/42.27    (89)  all_57_0 = e3
% 231.09/42.27    (90)  op(e1, e3) = all_53_2
% 231.09/42.27    (91)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 231.09/42.27            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 231.09/42.27              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 231.09/42.27    (92)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.09/42.27          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.09/42.27    (93)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 231.09/42.27          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 231.09/42.27    (94)   ~ (all_53_12 = all_10_2)
% 231.09/42.27    (95)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 231.09/42.27          (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 231.09/42.27    (96)   ~ (all_53_13 = all_53_14)
% 231.09/42.27    (97)   ~ (e2 = e1)
% 231.09/42.27    (98)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.09/42.27          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.09/42.27    (99)  op(e2, e1) = all_53_9
% 231.09/42.27    (100)  op(e1, e2) = all_53_6
% 231.09/42.27    (101)   ~ (all_6_2 = e0)
% 231.09/42.27    (102)   ~ (all_53_2 = all_53_6)
% 231.09/42.27    (103)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.09/42.27           (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.09/42.27    (104)  all_24_2 = all_6_2
% 231.09/42.27    (105)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.09/42.27           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.09/42.27    (106)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.09/42.27           (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.09/42.27    (107)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.09/42.27           | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.09/42.27             e1)
% 231.09/42.27    (108)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 231.09/42.27           (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 231.09/42.27    (109)   ~ (all_53_12 = all_53_14)
% 231.09/42.27    (110)  all_55_14 = all_53_11
% 231.09/42.27    (111)  op(e3, e0) = all_52_7
% 231.09/42.27    (112)  op(e3, e1) = all_53_8
% 231.09/42.27    (113)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.09/42.27           (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.09/42.27    (114)   ~ (all_53_4 = e3)
% 231.09/42.27    (115)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 231.09/42.27           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 231.09/42.27    (116)  op(e3, e0) = all_53_12
% 231.09/42.27  
% 231.09/42.27  Begin of proof
% 231.09/42.27  | 
% 231.09/42.27  | BETA: splitting (44) gives:
% 231.09/42.27  | 
% 231.09/42.27  | Case 1:
% 231.09/42.27  | | 
% 231.09/42.27  | |   (117)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) =
% 231.09/42.27  | |            e0)
% 231.09/42.27  | | 
% 231.09/42.27  | | BETA: splitting (117) gives:
% 231.09/42.27  | | 
% 231.09/42.27  | | Case 1:
% 231.09/42.27  | | | 
% 231.09/42.27  | | |   (118)  all_57_4 = e0 & op(e3, e1) = e0
% 231.09/42.27  | | | 
% 231.09/42.27  | | | ALPHA: (118) implies:
% 231.09/42.27  | | |   (119)  all_57_4 = e0
% 231.09/42.27  | | |   (120)  op(e3, e1) = e0
% 231.09/42.27  | | | 
% 231.09/42.27  | | | BETA: splitting (106) gives:
% 231.09/42.27  | | | 
% 231.09/42.27  | | | Case 1:
% 231.09/42.27  | | | | 
% 231.09/42.27  | | | |   (121)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3)
% 231.09/42.27  | | | |            = e0)
% 231.09/42.27  | | | | 
% 231.09/42.27  | | | | REF_CLOSE: (8), (13), (16), (43), (45), (50), (52), (62), (66), (84),
% 231.09/42.27  | | | |            (92), (97), (121) are inconsistent by sub-proof #2229.
% 231.09/42.27  | | | | 
% 231.09/42.27  | | | Case 2:
% 231.09/42.27  | | | | 
% 231.09/42.27  | | | |   (122)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0,
% 231.09/42.27  | | | |              e3) = e0)
% 231.09/42.27  | | | | 
% 231.09/42.27  | | | | BETA: splitting (122) gives:
% 231.09/42.27  | | | | 
% 231.09/42.27  | | | | Case 1:
% 231.09/42.27  | | | | | 
% 231.09/42.27  | | | | |   (123)  all_57_6 = e0 & op(e1, e3) = e0
% 231.09/42.27  | | | | | 
% 231.09/42.27  | | | | | ALPHA: (123) implies:
% 231.09/42.27  | | | | |   (124)  all_57_6 = e0
% 231.09/42.27  | | | | |   (125)  op(e1, e3) = e0
% 231.09/42.27  | | | | | 
% 231.09/42.27  | | | | | BETA: splitting (78) gives:
% 231.09/42.27  | | | | | 
% 231.09/42.27  | | | | | Case 1:
% 231.09/42.27  | | | | | | 
% 231.09/42.27  | | | | | |   (126)  all_57_15 = e0 & op(e0, e0) = e0
% 231.09/42.27  | | | | | | 
% 231.09/42.27  | | | | | | ALPHA: (126) implies:
% 231.09/42.27  | | | | | |   (127)  all_57_15 = e0
% 231.09/42.27  | | | | | |   (128)  op(e0, e0) = e0
% 231.09/42.27  | | | | | | 
% 231.09/42.27  | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 231.09/42.27  | | | | | |            (12), (13), (14), (16), (17), (18), (19), (20), (21),
% 231.09/42.27  | | | | | |            (22), (23), (25), (26), (27), (29), (30), (31), (32),
% 231.09/42.27  | | | | | |            (33), (34), (36), (37), (38), (39), (40), (41), (42),
% 231.09/42.27  | | | | | |            (43), (44), (46), (47), (48), (49), (51), (52), (53),
% 231.09/42.27  | | | | | |            (54), (55), (56), (57), (58), (59), (60), (61), (62),
% 231.09/42.27  | | | | | |            (63), (64), (65), (66), (67), (69), (70), (71), (72),
% 231.09/42.27  | | | | | |            (74), (75), (76), (77), (78), (79), (80), (81), (83),
% 231.09/42.27  | | | | | |            (84), (85), (86), (87), (88), (89), (90), (91), (92),
% 231.09/42.27  | | | | | |            (93), (94), (95), (96), (97), (98), (99), (100), (102),
% 231.09/42.27  | | | | | |            (103), (104), (105), (106), (107), (108), (109), (110),
% 231.09/42.27  | | | | | |            (112), (113), (114), (115), (116), (119), (120), (124),
% 231.09/42.27  | | | | | |            (125), (127), (128) are inconsistent by sub-proof #1410.
% 231.09/42.27  | | | | | | 
% 231.09/42.27  | | | | | Case 2:
% 231.09/42.27  | | | | | | 
% 231.09/42.27  | | | | | |   (129)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 &
% 231.09/42.27  | | | | | |              op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0))
% 231.09/42.27  | | | | | |          & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.09/42.27  | | | | | |              op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 231.09/42.27  | | | | | | 
% 231.09/42.27  | | | | | | ALPHA: (129) implies:
% 231.09/42.27  | | | | | |   (130)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.09/42.27  | | | | | |            op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.09/42.27  | | | | | | 
% 231.09/42.27  | | | | | | REF_CLOSE: (28), (35), (50), (62), (73), (130) are inconsistent by
% 231.09/42.27  | | | | | |            sub-proof #2088.
% 231.09/42.27  | | | | | | 
% 231.09/42.27  | | | | | End of split
% 231.09/42.27  | | | | | 
% 231.09/42.27  | | | | Case 2:
% 231.09/42.27  | | | | | 
% 231.09/42.27  | | | | |   (131)  all_57_12 = e0 & op(e0, e3) = e0
% 231.09/42.27  | | | | | 
% 231.09/42.27  | | | | | REF_CLOSE: (35), (62), (131) are inconsistent by sub-proof #2185.
% 231.09/42.27  | | | | | 
% 231.09/42.27  | | | | End of split
% 231.09/42.27  | | | | 
% 231.09/42.27  | | | End of split
% 231.09/42.27  | | | 
% 231.09/42.27  | | Case 2:
% 231.09/42.27  | | | 
% 231.09/42.27  | | |   (132)  all_57_5 = e0 & op(e2, e1) = e0
% 231.09/42.27  | | | 
% 231.09/42.27  | | | ALPHA: (132) implies:
% 231.09/42.27  | | |   (133)  all_57_5 = e0
% 231.09/42.27  | | | 
% 231.09/42.27  | | | REF_CLOSE: (8), (13), (15), (16), (38), (43), (45), (50), (62), (66),
% 231.09/42.27  | | |            (83), (84), (92), (97), (133) are inconsistent by sub-proof
% 231.09/42.27  | | |            #1689.
% 231.09/42.27  | | | 
% 231.09/42.27  | | End of split
% 231.09/42.27  | | 
% 231.09/42.27  | Case 2:
% 231.09/42.27  | | 
% 231.09/42.27  | |   (134)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 231.09/42.27  | |            e0)
% 231.09/42.27  | | 
% 231.09/42.27  | | REF_CLOSE: (13), (16), (21), (22), (24), (27), (37), (41), (45), (50), (51),
% 231.09/42.27  | |            (52), (61), (62), (66), (68), (69), (82), (97), (101), (105),
% 231.09/42.27  | |            (111), (134) are inconsistent by sub-proof #1366.
% 231.09/42.27  | | 
% 231.09/42.27  | End of split
% 231.09/42.27  | 
% 231.09/42.27  End of proof
% 231.09/42.27  
% 231.09/42.27  Sub-proof #1341 shows that the following formulas are inconsistent:
% 231.09/42.27  ----------------------------------------------------------------
% 231.09/42.27    (1)   ~ (all_10_2 = e2)
% 231.09/42.27    (2)  all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 231.09/42.27    (3)  op(e3, e3) = all_10_2
% 231.09/42.27    (4)  op(e0, e1) = all_53_11
% 231.09/42.27    (5)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 231.09/42.27    (6)  all_57_9 = e2
% 231.09/42.27    (7)   ~ (all_53_6 = all_53_14)
% 231.09/42.27    (8)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 231.09/42.27    (9)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.09/42.27         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.09/42.27    (10)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.09/42.27          (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.09/42.27    (11)   ~ (all_53_8 = all_53_12)
% 231.09/42.27    (12)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.09/42.27          (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.09/42.27    (13)   ~ (all_53_8 = all_53_11)
% 231.09/42.27    (14)   ~ (e3 = e1)
% 231.09/42.27    (15)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 231.09/42.27          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.09/42.27    (16)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.09/42.27            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.09/42.27    (17)  all_55_0 = all_10_2
% 231.09/42.27    (18)   ~ (all_10_2 = e0)
% 231.09/42.27    (19)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.09/42.27          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.09/42.27    (20)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 231.09/42.27            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 231.09/42.27              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 231.09/42.27    (21)   ~ (all_6_2 = e3)
% 231.09/42.27    (22)  op(e1, e1) = all_6_2
% 231.09/42.27    (23)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 231.09/42.27    (24)   ~ (all_53_9 = e0)
% 231.09/42.27    (25)  all_55_0 = e3 | all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 231.09/42.27    (26)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 231.09/42.27    (27)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.09/42.27          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.09/42.27    (28)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 231.09/42.27    (29)  all_55_9 = all_53_6
% 231.09/42.27    (30)   ~ (all_53_11 = all_6_2)
% 231.09/42.27    (31)   ~ (all_53_4 = all_53_12)
% 231.09/42.27    (32)  all_57_4 = e0
% 231.09/42.27    (33)   ~ (all_53_8 = e3)
% 231.09/42.27    (34)   ~ (all_53_8 = all_53_9)
% 231.09/42.27    (35)  all_42_2 = all_6_2
% 231.09/42.27    (36)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.09/42.27          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.09/42.27    (37)  op(e2, e2) = e0
% 231.09/42.27    (38)   ~ (all_53_9 = all_53_11)
% 231.09/42.27    (39)   ~ (all_53_9 = all_6_2)
% 231.09/42.27    (40)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.09/42.27          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.09/42.27    (41)   ~ (all_53_14 = all_6_2)
% 231.09/42.27    (42)  all_57_3 = e0
% 231.09/42.27    (43)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.09/42.27          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.09/42.27    (44)   ~ (e3 = e2)
% 231.09/42.27    (45)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 231.09/42.27    (46)  all_55_1 = all_53_4
% 231.09/42.27    (47)  op(e1, e0) = all_53_14
% 231.09/42.27    (48)   ~ (all_53_6 = all_53_7)
% 231.09/42.27    (49)   ~ (e3 = e0)
% 231.09/42.27    (50)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.09/42.27          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.09/42.27    (51)  op(e3, e3) = e3
% 231.09/42.27    (52)  all_57_6 = e0
% 231.09/42.27    (53)   ~ (all_53_8 = all_6_2)
% 231.09/42.27    (54)  all_55_2 = all_53_8
% 231.09/42.27    (55)   ~ (all_53_4 = all_53_7)
% 231.09/42.27    (56)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 231.09/42.27    (57)  all_57_1 = e1
% 231.09/42.27    (58)   ~ (all_53_7 = e0)
% 231.09/42.27    (59)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.09/42.27          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.09/42.27            e1)
% 231.09/42.27    (60)   ~ (all_53_4 = all_53_8)
% 231.09/42.27    (61)  all_55_6 = all_53_9
% 231.09/42.27    (62)  op(e3, e2) = all_53_4
% 231.09/42.27    (63)   ~ (e2 = e0)
% 231.09/42.27    (64)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 231.09/42.27            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 231.09/42.27            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 231.09/42.27            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 231.09/42.27              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 231.09/42.27            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 231.09/42.27            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 231.09/42.27              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 231.09/42.27              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 231.09/42.27            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 231.09/42.27            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 231.09/42.27            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 231.09/42.27              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 231.09/42.27              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 231.09/42.27            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 231.09/42.27              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 231.09/42.27            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 231.09/42.27            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 231.09/42.27              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 231.09/42.27              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 231.09/42.27            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 231.09/42.27            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 231.09/42.27    (65)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 231.09/42.27          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.09/42.27    (66)   ~ (all_53_2 = all_53_14)
% 231.09/42.27    (67)   ~ (e1 = e0)
% 231.09/42.27    (68)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 231.09/42.27            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 231.09/42.27              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 231.09/42.27    (69)   ~ (all_53_4 = e0)
% 231.09/42.27    (70)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.09/42.27          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.09/42.27    (71)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.09/42.27          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.09/42.27    (72)   ~ (all_10_2 = e1)
% 231.09/42.27    (73)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 231.09/42.27    (74)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.09/42.27          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 231.09/42.27            e3)
% 231.09/42.27    (75)   ~ (all_53_4 = all_53_6)
% 231.09/42.27    (76)  op(e0, e2) = all_53_7
% 231.09/42.27    (77)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.09/42.27          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.09/42.27            e2)
% 231.09/42.27    (78)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.09/42.27              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.09/42.27                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.09/42.27                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.09/42.27    (79)  all_55_10 = all_6_2
% 231.09/42.27    (80)   ~ (all_53_6 = all_6_2)
% 231.09/42.27    (81)   ~ (all_53_13 = e0)
% 231.09/42.27    (82)  op(e1, e1) = e2
% 231.09/42.27    (83)  all_55_13 = all_53_7
% 231.09/42.27    (84)  op(e0, e0) = e1
% 231.09/42.27    (85)  op(e2, e0) = all_53_13
% 231.09/42.27    (86)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.09/42.27          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.09/42.27    (87)  all_38_2 = all_6_2
% 231.09/42.27    (88)  all_55_11 = all_53_14
% 231.09/42.27    (89)  all_55_3 = all_53_12
% 231.09/42.27    (90)   ~ (all_53_12 = e3)
% 231.09/42.27    (91)  all_57_0 = e3
% 231.09/42.27    (92)  all_57_7 = e3
% 231.09/42.27    (93)  op(e1, e3) = all_53_2
% 231.09/42.27    (94)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 231.09/42.27            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 231.09/42.27              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 231.09/42.27    (95)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.09/42.27          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.09/42.27    (96)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 231.09/42.27          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 231.09/42.27    (97)   ~ (all_53_12 = all_10_2)
% 231.09/42.27    (98)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 231.09/42.27          (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 231.09/42.27    (99)   ~ (all_53_13 = all_53_14)
% 231.09/42.27    (100)   ~ (e2 = e1)
% 231.09/42.27    (101)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.09/42.27           | (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.09/42.27             e2)
% 231.09/42.27    (102)  op(e2, e1) = all_53_9
% 231.09/42.27    (103)  op(e1, e2) = all_53_6
% 231.09/42.27    (104)   ~ (all_6_2 = e0)
% 231.09/42.27    (105)   ~ (all_53_2 = all_53_6)
% 231.09/42.27    (106)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.09/42.27           (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.09/42.27    (107)  all_24_2 = all_6_2
% 231.09/42.27    (108)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.09/42.27           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.09/42.27    (109)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.09/42.27           (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.09/42.27    (110)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.09/42.27           | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.09/42.27             e1)
% 231.09/42.27    (111)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 231.09/42.27           (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 231.09/42.27    (112)   ~ (all_53_12 = all_53_14)
% 231.09/42.27    (113)  all_55_14 = all_53_11
% 231.09/42.27    (114)  op(e3, e1) = all_53_8
% 231.09/42.27    (115)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.09/42.27           (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.09/42.27    (116)   ~ (all_53_4 = e3)
% 231.09/42.27    (117)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 231.09/42.27           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 231.09/42.27    (118)  op(e3, e0) = all_53_12
% 231.09/42.27  
% 231.09/42.27  Begin of proof
% 231.09/42.27  | 
% 231.09/42.27  | BETA: splitting (111) gives:
% 231.09/42.27  | 
% 231.09/42.27  | Case 1:
% 231.09/42.27  | | 
% 231.09/42.27  | |   (119)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) =
% 231.09/42.27  | |            e1)
% 231.09/42.27  | | 
% 231.09/42.27  | | BETA: splitting (119) gives:
% 231.09/42.27  | | 
% 231.09/42.27  | | Case 1:
% 231.09/42.27  | | | 
% 231.09/42.27  | | |   (120)  all_57_6 = e1 & op(e1, e3) = e1
% 231.09/42.27  | | | 
% 231.09/42.27  | | | ALPHA: (120) implies:
% 231.09/42.27  | | |   (121)  all_57_6 = e1
% 231.09/42.27  | | | 
% 231.09/42.27  | | | COMBINE_EQS: (52), (121) imply:
% 231.09/42.27  | | |   (122)  e1 = e0
% 231.09/42.27  | | | 
% 231.09/42.27  | | | SIMP: (122) implies:
% 231.09/42.27  | | |   (123)  e1 = e0
% 231.09/42.27  | | | 
% 231.09/42.27  | | | COMBINE_EQS: (57), (123) imply:
% 231.09/42.27  | | |   (124)  all_57_1 = e0
% 231.09/42.27  | | | 
% 231.09/42.27  | | | REF_CLOSE: (6), (14), (16), (27), (32), (51), (67), (100), (124) are
% 231.09/42.27  | | |            inconsistent by sub-proof #2219.
% 231.09/42.27  | | | 
% 231.09/42.27  | | Case 2:
% 231.09/42.27  | | | 
% 231.09/42.27  | | |   (125)  all_57_7 = e1 & op(e1, e2) = e1
% 231.09/42.27  | | | 
% 231.09/42.27  | | | REF_CLOSE: (14), (92), (125) are inconsistent by sub-proof #2104.
% 231.09/42.27  | | | 
% 231.09/42.27  | | End of split
% 231.09/42.27  | | 
% 231.09/42.27  | Case 2:
% 231.09/42.27  | | 
% 231.09/42.27  | |   (126)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) =
% 231.09/42.27  | |            e1)
% 231.09/42.27  | | 
% 231.09/42.27  | | BETA: splitting (126) gives:
% 231.09/42.27  | | 
% 231.09/42.28  | | Case 1:
% 231.09/42.28  | | | 
% 231.09/42.28  | | |   (127)  all_57_8 = e1 & op(e1, e1) = e1
% 231.09/42.28  | | | 
% 231.09/42.28  | | | ALPHA: (127) implies:
% 231.09/42.28  | | |   (128)  op(e1, e1) = e1
% 231.09/42.28  | | | 
% 231.09/42.28  | | | REF_CLOSE: (16), (82), (100), (128) are inconsistent by sub-proof #2423.
% 231.09/42.28  | | | 
% 231.09/42.28  | | Case 2:
% 231.09/42.28  | | | 
% 231.09/42.28  | | |   (129)  all_57_11 = e1 & op(e1, e0) = e1
% 231.09/42.28  | | | 
% 231.09/42.28  | | | ALPHA: (129) implies:
% 231.09/42.28  | | |   (130)  all_57_11 = e1
% 231.09/42.28  | | | 
% 231.09/42.28  | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 231.09/42.28  | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 231.09/42.28  | | |            (24), (25), (26), (27), (28), (29), (30), (31), (33), (34),
% 231.09/42.28  | | |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44),
% 231.09/42.28  | | |            (45), (46), (47), (48), (49), (50), (51), (53), (54), (55),
% 231.09/42.28  | | |            (56), (57), (58), (59), (60), (61), (62), (63), (64), (65),
% 231.09/42.28  | | |            (66), (67), (68), (69), (70), (71), (72), (73), (74), (75),
% 231.09/42.28  | | |            (76), (77), (78), (79), (80), (81), (83), (84), (85), (86),
% 231.09/42.28  | | |            (87), (88), (89), (90), (91), (92), (93), (94), (95), (96),
% 231.09/42.28  | | |            (97), (98), (99), (100), (101), (102), (103), (104), (105),
% 231.09/42.28  | | |            (106), (107), (108), (109), (110), (111), (112), (113), (114),
% 231.09/42.28  | | |            (115), (116), (117), (118), (130) are inconsistent by sub-proof
% 231.09/42.28  | | |            #1376.
% 231.09/42.28  | | | 
% 231.09/42.28  | | End of split
% 231.09/42.28  | | 
% 231.09/42.28  | End of split
% 231.09/42.28  | 
% 231.09/42.28  End of proof
% 231.09/42.28  
% 231.09/42.28  Sub-proof #1342 shows that the following formulas are inconsistent:
% 231.09/42.28  ----------------------------------------------------------------
% 231.09/42.28    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.09/42.28           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.09/42.28    (2)  op(e2, e2) = e0
% 231.09/42.28    (3)   ~ (e3 = e0)
% 231.09/42.28    (4)  all_57_1 = e1
% 231.09/42.28    (5)  op(e3, e3) = all_52_1
% 231.09/42.28    (6)  op(all_52_1, all_52_1) = e3
% 231.09/42.28    (7)   ~ (e2 = e1)
% 231.09/42.28    (8)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2)
% 231.09/42.28  
% 231.09/42.28  Begin of proof
% 231.09/42.28  | 
% 231.09/42.28  | BETA: splitting (8) gives:
% 231.09/42.28  | 
% 231.09/42.28  | Case 1:
% 231.09/42.28  | | 
% 231.09/42.28  | |   (9)  all_57_0 = e2 & op(e3, e3) = e2
% 231.09/42.28  | | 
% 231.09/42.28  | | ALPHA: (9) implies:
% 231.09/42.28  | |   (10)  op(e3, e3) = e2
% 231.09/42.28  | | 
% 231.09/42.28  | | REF_CLOSE: (1), (2), (3), (5), (6), (10) are inconsistent by sub-proof
% 231.09/42.28  | |            #1653.
% 231.09/42.28  | | 
% 231.09/42.28  | Case 2:
% 231.09/42.28  | | 
% 231.09/42.28  | |   (11)  all_57_1 = e2 & op(e3, e2) = e2
% 231.09/42.28  | | 
% 231.09/42.28  | | REF_CLOSE: (4), (7), (11) are inconsistent by sub-proof #2489.
% 231.09/42.28  | | 
% 231.09/42.28  | End of split
% 231.09/42.28  | 
% 231.09/42.28  End of proof
% 231.09/42.28  
% 231.09/42.28  Sub-proof #1343 shows that the following formulas are inconsistent:
% 231.09/42.28  ----------------------------------------------------------------
% 231.09/42.28    (1)   ~ (e3 = e1)
% 231.09/42.28    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.09/42.28           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.09/42.28    (3)   ~ (all_6_2 = e3)
% 231.09/42.28    (4)  op(e1, e1) = all_6_2
% 231.09/42.28    (5)  op(all_52_7, all_52_7) = e0
% 231.09/42.28    (6)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.09/42.28         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.09/42.28    (7)  all_57_14 = e3
% 231.09/42.28    (8)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.09/42.28         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.09/42.28    (9)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.09/42.28         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.09/42.28    (10)  all_57_3 = e0
% 231.09/42.28    (11)   ~ (e3 = e2)
% 231.09/42.28    (12)   ~ (e3 = e0)
% 231.09/42.28    (13)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.09/42.28          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.09/42.28    (14)  op(e3, e3) = e3
% 231.09/42.28    (15)  op(e3, e2) = all_53_4
% 231.09/42.28    (16)   ~ (e2 = e0)
% 231.09/42.28    (17)  all_57_3 = e3 & op(e2, e2) = e3
% 231.09/42.28    (18)   ~ (e1 = e0)
% 231.09/42.28    (19)   ~ (all_53_4 = e0)
% 231.09/42.28    (20)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.09/42.28          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.09/42.28    (21)  op(e0, e0) = e1
% 231.09/42.28    (22)   ~ (e2 = e1)
% 231.09/42.28    (23)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.09/42.28          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.09/42.28    (24)  op(e3, e0) = all_52_7
% 231.09/42.28  
% 231.09/42.28  Begin of proof
% 231.09/42.28  | 
% 231.09/42.28  | ALPHA: (17) implies:
% 231.09/42.28  |   (25)  all_57_3 = e3
% 231.09/42.28  | 
% 231.09/42.28  | COMBINE_EQS: (10), (25) imply:
% 231.09/42.28  |   (26)  e3 = e0
% 231.09/42.28  | 
% 231.09/42.28  | SIMP: (26) implies:
% 231.09/42.28  |   (27)  e3 = e0
% 231.09/42.28  | 
% 231.09/42.28  | COMBINE_EQS: (7), (27) imply:
% 231.09/42.28  |   (28)  all_57_14 = e0
% 231.09/42.28  | 
% 231.09/42.28  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (11), (12), (13), (14),
% 231.09/42.28  |            (15), (16), (18), (19), (20), (21), (22), (23), (24), (28) are
% 231.09/42.28  |            inconsistent by sub-proof #1367.
% 231.09/42.28  | 
% 231.09/42.28  End of proof
% 231.09/42.28  
% 231.09/42.28  Sub-proof #1344 shows that the following formulas are inconsistent:
% 231.09/42.28  ----------------------------------------------------------------
% 231.09/42.28    (1)  all_57_9 = e2
% 231.09/42.28    (2)   ~ (e3 = e1)
% 231.09/42.28    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.09/42.28           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.09/42.28    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.09/42.28         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.09/42.28    (5)  all_57_4 = e0
% 231.09/42.28    (6)  all_57_12 = e2
% 231.09/42.28    (7)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.09/42.28         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.09/42.28    (8)   ~ (e3 = e2)
% 231.09/42.28    (9)  op(e3, e3) = e3
% 231.09/42.28    (10)   ~ (e2 = e0)
% 231.09/42.28    (11)   ~ (e1 = e0)
% 231.09/42.28    (12)   ~ (e2 = e1)
% 231.09/42.28    (13)  all_57_12 = e0 & op(e0, e3) = e0
% 231.09/42.28  
% 231.09/42.28  Begin of proof
% 231.09/42.28  | 
% 231.09/42.28  | ALPHA: (13) implies:
% 231.09/42.28  |   (14)  all_57_12 = e0
% 231.09/42.28  | 
% 231.09/42.28  | COMBINE_EQS: (6), (14) imply:
% 231.09/42.28  |   (15)  e2 = e0
% 231.09/42.28  | 
% 231.09/42.28  | COMBINE_EQS: (1), (15) imply:
% 231.09/42.28  |   (16)  all_57_9 = e0
% 231.09/42.28  | 
% 231.09/42.28  | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (16) are
% 231.09/42.28  |            inconsistent by sub-proof #2436.
% 231.09/42.28  | 
% 231.09/42.28  End of proof
% 231.09/42.28  
% 231.09/42.28  Sub-proof #1345 shows that the following formulas are inconsistent:
% 231.09/42.28  ----------------------------------------------------------------
% 231.09/42.28    (1)   ~ (all_10_2 = e2)
% 231.09/42.28    (2)  all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 231.09/42.28    (3)  op(e3, e3) = all_10_2
% 231.09/42.28    (4)  op(e0, e1) = all_53_11
% 231.09/42.28    (5)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 231.09/42.28    (6)   ~ (all_53_6 = all_53_14)
% 231.09/42.28    (7)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 231.09/42.28    (8)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.09/42.28         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.09/42.28    (9)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.09/42.28         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.09/42.28    (10)   ~ (all_53_8 = all_53_12)
% 231.09/42.28    (11)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.09/42.28          (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.09/42.28    (12)   ~ (all_53_8 = all_53_11)
% 231.09/42.28    (13)   ~ (e3 = e1)
% 231.09/42.28    (14)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 231.09/42.28          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.09/42.28    (15)   ~ (all_53_13 = e1)
% 231.09/42.28    (16)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.09/42.28            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.09/42.28    (17)  all_55_0 = all_10_2
% 231.09/42.28    (18)  all_57_15 = e1
% 231.09/42.28    (19)   ~ (all_10_2 = e0)
% 231.09/42.28    (20)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.09/42.28          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.09/42.28    (21)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 231.09/42.28            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 231.09/42.28              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 231.09/42.28    (22)   ~ (all_6_2 = e3)
% 231.09/42.28    (23)  op(e1, e1) = all_6_2
% 231.09/42.28    (24)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 231.09/42.28    (25)  op(all_52_7, all_52_7) = e0
% 231.09/42.28    (26)   ~ (all_53_9 = e0)
% 231.09/42.28    (27)  all_55_0 = e3 | all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 231.09/42.28    (28)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 231.09/42.28    (29)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.09/42.28          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.09/42.28    (30)  all_57_14 = e3
% 231.09/42.28    (31)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 231.09/42.28    (32)  all_55_9 = all_53_6
% 231.09/42.28    (33)   ~ (all_53_11 = all_6_2)
% 231.09/42.28    (34)   ~ (all_53_4 = all_53_12)
% 231.09/42.28    (35)   ~ (all_53_8 = e3)
% 231.09/42.28    (36)   ~ (all_53_8 = all_53_9)
% 231.09/42.28    (37)  all_42_2 = all_6_2
% 231.09/42.28    (38)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.09/42.28          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.09/42.28    (39)  op(e2, e2) = e0
% 231.09/42.28    (40)   ~ (all_53_9 = all_53_11)
% 231.09/42.28    (41)   ~ (all_53_9 = all_6_2)
% 231.09/42.28    (42)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.09/42.28          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.09/42.28    (43)   ~ (all_53_14 = all_6_2)
% 231.09/42.28    (44)  all_57_3 = e0
% 231.09/42.28    (45)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.09/42.28          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.09/42.28    (46)   ~ (e3 = e2)
% 231.09/42.28    (47)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 231.09/42.28    (48)  all_55_1 = all_53_4
% 231.09/42.28    (49)  op(e1, e0) = all_53_14
% 231.09/42.28    (50)   ~ (all_53_6 = all_53_7)
% 231.09/42.28    (51)   ~ (e3 = e0)
% 231.09/42.28    (52)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.09/42.28          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.09/42.28    (53)  op(e3, e3) = e3
% 231.09/42.28    (54)   ~ (all_53_8 = all_6_2)
% 231.09/42.28    (55)  all_55_2 = all_53_8
% 231.09/42.28    (56)   ~ (all_53_4 = all_53_7)
% 231.09/42.28    (57)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 231.09/42.28    (58)   ~ (all_53_7 = e0)
% 231.09/42.28    (59)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.09/42.28          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.09/42.28            e1)
% 231.09/42.28    (60)  op(e3, e3) = all_52_1
% 231.09/42.28    (61)   ~ (all_53_4 = all_53_8)
% 231.09/42.28    (62)  all_55_6 = all_53_9
% 231.09/42.28    (63)  op(e3, e2) = all_53_4
% 231.09/42.28    (64)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 231.09/42.28          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 231.09/42.28    (65)  op(all_52_1, all_52_1) = e3
% 231.09/42.28    (66)   ~ (e2 = e0)
% 231.09/42.28    (67)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 231.09/42.28            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 231.09/42.28            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 231.09/42.28            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 231.09/42.28              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 231.09/42.28            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 231.09/42.28            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 231.09/42.28              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 231.09/42.28              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 231.09/42.28            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 231.09/42.28            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 231.09/42.28            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 231.09/42.28              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 231.09/42.28              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 231.09/42.28            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 231.09/42.28              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 231.09/42.28            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 231.09/42.28            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 231.09/42.28              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 231.09/42.28              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 231.09/42.28            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 231.09/42.28            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 231.09/42.28    (68)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 231.09/42.28          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.09/42.28    (69)   ~ (all_53_2 = all_53_14)
% 231.09/42.28    (70)   ~ (e1 = e0)
% 231.09/42.28    (71)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 231.09/42.28            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 231.09/42.28              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 231.09/42.28    (72)   ~ (all_53_4 = e0)
% 231.09/42.28    (73)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.09/42.28          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.09/42.28    (74)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.09/42.28          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.09/42.28    (75)   ~ (all_10_2 = e1)
% 231.09/42.28    (76)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 231.09/42.28    (77)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.09/42.28          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 231.09/42.28            e3)
% 231.09/42.28    (78)   ~ (all_53_4 = all_53_6)
% 231.09/42.28    (79)  op(e0, e2) = all_53_7
% 231.09/42.28    (80)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.09/42.28          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.09/42.28            e2)
% 231.09/42.28    (81)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.09/42.28              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.09/42.28                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.09/42.28                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.09/42.28    (82)  all_55_10 = all_6_2
% 231.09/42.28    (83)   ~ (all_53_6 = all_6_2)
% 231.09/42.28    (84)   ~ (all_53_13 = e0)
% 231.09/42.28    (85)  op(e1, e1) = e2
% 231.09/42.28    (86)  all_55_13 = all_53_7
% 231.09/42.28    (87)  op(e0, e0) = e1
% 231.09/42.28    (88)  op(e2, e0) = all_53_13
% 231.09/42.28    (89)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.09/42.28          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.09/42.28    (90)  all_38_2 = all_6_2
% 231.09/42.28    (91)  all_55_11 = all_53_14
% 231.09/42.28    (92)  all_55_3 = all_53_12
% 231.09/42.28    (93)   ~ (all_53_12 = e3)
% 231.09/42.28    (94)  all_57_0 = e3
% 231.09/42.28    (95)  op(e1, e3) = all_53_2
% 231.09/42.28    (96)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 231.09/42.28            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 231.09/42.28              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 231.09/42.28    (97)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.09/42.28          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.09/42.28    (98)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 231.09/42.28          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 231.09/42.28    (99)  all_57_1 = e3
% 231.09/42.28    (100)   ~ (all_53_12 = all_10_2)
% 231.09/42.28    (101)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.09/42.28           | (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 231.09/42.28             e3)
% 231.09/42.28    (102)   ~ (all_53_13 = all_53_14)
% 231.09/42.28    (103)   ~ (e2 = e1)
% 231.09/42.28    (104)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.09/42.28           | (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.09/42.28             e2)
% 231.09/42.28    (105)  op(e2, e1) = all_53_9
% 231.09/42.28    (106)  op(e1, e2) = all_53_6
% 231.09/42.28    (107)   ~ (all_6_2 = e0)
% 231.09/42.28    (108)   ~ (all_53_2 = all_53_6)
% 231.09/42.28    (109)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.09/42.28           (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.09/42.28    (110)  all_24_2 = all_6_2
% 231.09/42.28    (111)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.09/42.28           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.09/42.28    (112)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.09/42.28           (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.09/42.28    (113)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.09/42.28           | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.09/42.28             e1)
% 231.09/42.28    (114)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 231.09/42.28           (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 231.09/42.28    (115)   ~ (all_53_12 = all_53_14)
% 231.09/42.28    (116)  all_55_14 = all_53_11
% 231.09/42.28    (117)  op(e3, e0) = all_52_7
% 231.09/42.28    (118)  op(e3, e1) = all_53_8
% 231.09/42.28    (119)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2)
% 231.09/42.28    (120)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.09/42.28           (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.09/42.28    (121)   ~ (all_53_4 = e3)
% 231.09/42.28    (122)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 231.09/42.28           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 231.09/42.28    (123)  op(e3, e0) = all_53_12
% 231.09/42.28  
% 231.09/42.28  Begin of proof
% 231.09/42.28  | 
% 231.09/42.28  | BETA: splitting (119) gives:
% 231.09/42.28  | 
% 231.09/42.28  | Case 1:
% 231.09/42.28  | | 
% 231.09/42.28  | |   (124)  all_57_0 = e2 & op(e3, e3) = e2
% 231.09/42.28  | | 
% 231.09/42.28  | | ALPHA: (124) implies:
% 231.09/42.28  | |   (125)  op(e3, e3) = e2
% 231.09/42.28  | | 
% 231.09/42.28  | | REF_CLOSE: (16), (39), (51), (60), (65), (125) are inconsistent by sub-proof
% 231.09/42.28  | |            #1653.
% 231.09/42.28  | | 
% 231.09/42.28  | Case 2:
% 231.09/42.28  | | 
% 231.09/42.28  | |   (126)  all_57_1 = e2 & op(e3, e2) = e2
% 231.09/42.28  | | 
% 231.09/42.28  | | ALPHA: (126) implies:
% 231.09/42.28  | |   (127)  all_57_1 = e2
% 231.09/42.28  | | 
% 231.09/42.28  | | COMBINE_EQS: (99), (127) imply:
% 231.09/42.28  | |   (128)  e3 = e2
% 231.09/42.28  | | 
% 231.09/42.28  | | COMBINE_EQS: (30), (128) imply:
% 231.09/42.28  | |   (129)  all_57_14 = e2
% 231.09/42.28  | | 
% 231.09/42.28  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 231.09/42.28  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 231.09/42.28  | |            (24), (25), (26), (27), (28), (29), (31), (32), (33), (34), (35),
% 231.09/42.28  | |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 231.09/42.28  | |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 231.09/42.28  | |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 231.09/42.28  | |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 231.09/42.28  | |            (80), (81), (82), (83), (84), (85), (86), (87), (88), (89), (90),
% 231.09/42.28  | |            (91), (92), (93), (94), (95), (96), (97), (98), (100), (101),
% 231.09/42.28  | |            (102), (103), (104), (105), (106), (107), (108), (109), (110),
% 231.09/42.28  | |            (111), (112), (113), (114), (115), (116), (117), (118), (120),
% 231.09/42.28  | |            (121), (122), (123), (129) are inconsistent by sub-proof #1346.
% 231.09/42.28  | | 
% 231.09/42.28  | End of split
% 231.09/42.28  | 
% 231.09/42.28  End of proof
% 231.09/42.28  
% 231.09/42.28  Sub-proof #1346 shows that the following formulas are inconsistent:
% 231.09/42.28  ----------------------------------------------------------------
% 231.09/42.28    (1)   ~ (all_10_2 = e2)
% 231.09/42.28    (2)  all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 231.09/42.28    (3)  op(e3, e3) = all_10_2
% 231.09/42.28    (4)  op(e0, e1) = all_53_11
% 231.09/42.28    (5)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 231.09/42.28    (6)   ~ (all_53_6 = all_53_14)
% 231.09/42.28    (7)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 231.09/42.28    (8)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.09/42.28         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.09/42.28    (9)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.09/42.28         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.09/42.28    (10)   ~ (all_53_8 = all_53_12)
% 231.09/42.28    (11)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.09/42.28          (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.09/42.28    (12)   ~ (all_53_8 = all_53_11)
% 231.09/42.28    (13)   ~ (e3 = e1)
% 231.09/42.28    (14)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 231.09/42.28          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.09/42.28    (15)   ~ (all_53_13 = e1)
% 231.09/42.29    (16)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.09/42.29            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.09/42.29    (17)  all_55_0 = all_10_2
% 231.09/42.29    (18)  all_57_15 = e1
% 231.09/42.29    (19)   ~ (all_10_2 = e0)
% 231.09/42.29    (20)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.09/42.29          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.09/42.29    (21)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 231.09/42.29            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 231.09/42.29              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 231.09/42.29    (22)   ~ (all_6_2 = e3)
% 231.09/42.29    (23)  op(e1, e1) = all_6_2
% 231.09/42.29    (24)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 231.09/42.29    (25)  op(all_52_7, all_52_7) = e0
% 231.09/42.29    (26)   ~ (all_53_9 = e0)
% 231.09/42.29    (27)  all_55_0 = e3 | all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 231.09/42.29    (28)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 231.09/42.29    (29)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.09/42.29          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.09/42.29    (30)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 231.09/42.29    (31)  all_55_9 = all_53_6
% 231.09/42.29    (32)   ~ (all_53_11 = all_6_2)
% 231.09/42.29    (33)   ~ (all_53_4 = all_53_12)
% 231.09/42.29    (34)   ~ (all_53_8 = e3)
% 231.09/42.29    (35)   ~ (all_53_8 = all_53_9)
% 231.09/42.29    (36)  all_42_2 = all_6_2
% 231.09/42.29    (37)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.09/42.29          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.09/42.29    (38)  op(e2, e2) = e0
% 231.09/42.29    (39)   ~ (all_53_9 = all_53_11)
% 231.09/42.29    (40)   ~ (all_53_9 = all_6_2)
% 231.09/42.29    (41)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.09/42.29          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.09/42.29    (42)   ~ (all_53_14 = all_6_2)
% 231.09/42.29    (43)  all_57_3 = e0
% 231.09/42.29    (44)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.09/42.29          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.09/42.29    (45)   ~ (e3 = e2)
% 231.09/42.29    (46)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 231.09/42.29    (47)  all_55_1 = all_53_4
% 231.09/42.29    (48)  op(e1, e0) = all_53_14
% 231.09/42.29    (49)   ~ (all_53_6 = all_53_7)
% 231.09/42.29    (50)   ~ (e3 = e0)
% 231.09/42.29    (51)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.09/42.29          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.09/42.29    (52)  op(e3, e3) = e3
% 231.09/42.29    (53)   ~ (all_53_8 = all_6_2)
% 231.09/42.29    (54)  all_55_2 = all_53_8
% 231.09/42.29    (55)   ~ (all_53_4 = all_53_7)
% 231.09/42.29    (56)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 231.09/42.29    (57)   ~ (all_53_7 = e0)
% 231.09/42.29    (58)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.09/42.29          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.09/42.29            e1)
% 231.09/42.29    (59)  op(e3, e3) = all_52_1
% 231.09/42.29    (60)   ~ (all_53_4 = all_53_8)
% 231.09/42.29    (61)  all_55_6 = all_53_9
% 231.09/42.29    (62)  op(e3, e2) = all_53_4
% 231.09/42.29    (63)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 231.09/42.29          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 231.09/42.29    (64)  op(all_52_1, all_52_1) = e3
% 231.09/42.29    (65)   ~ (e2 = e0)
% 231.09/42.29    (66)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 231.09/42.29            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 231.09/42.29            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 231.09/42.29            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 231.09/42.29              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 231.09/42.29            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 231.09/42.29            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 231.09/42.29              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 231.09/42.29              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 231.09/42.29            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 231.09/42.29            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 231.09/42.29            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 231.09/42.29              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 231.09/42.29              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 231.09/42.29            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 231.09/42.29              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 231.09/42.29            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 231.09/42.29            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 231.09/42.29              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 231.09/42.29              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 231.09/42.29            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 231.09/42.29            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 231.09/42.29    (67)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 231.09/42.29          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.09/42.29    (68)   ~ (all_53_2 = all_53_14)
% 231.09/42.29    (69)   ~ (e1 = e0)
% 231.09/42.29    (70)  all_57_14 = e2
% 231.09/42.29    (71)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 231.09/42.29            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 231.09/42.29              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 231.09/42.29    (72)   ~ (all_53_4 = e0)
% 231.09/42.29    (73)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.09/42.29          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.09/42.29    (74)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.09/42.29          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.09/42.29    (75)   ~ (all_10_2 = e1)
% 231.09/42.29    (76)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 231.09/42.29    (77)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.09/42.29          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 231.09/42.29            e3)
% 231.09/42.29    (78)   ~ (all_53_4 = all_53_6)
% 231.09/42.29    (79)  op(e0, e2) = all_53_7
% 231.09/42.29    (80)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.09/42.29          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.09/42.29            e2)
% 231.09/42.29    (81)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.09/42.29              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.09/42.29                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.09/42.29                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.09/42.29    (82)  all_55_10 = all_6_2
% 231.09/42.29    (83)   ~ (all_53_6 = all_6_2)
% 231.09/42.29    (84)   ~ (all_53_13 = e0)
% 231.09/42.29    (85)  op(e1, e1) = e2
% 231.09/42.29    (86)  all_55_13 = all_53_7
% 231.09/42.29    (87)  op(e0, e0) = e1
% 231.09/42.29    (88)  op(e2, e0) = all_53_13
% 231.09/42.29    (89)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.09/42.29          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.09/42.29    (90)  all_38_2 = all_6_2
% 231.09/42.29    (91)  all_55_11 = all_53_14
% 231.09/42.29    (92)  all_55_3 = all_53_12
% 231.09/42.29    (93)   ~ (all_53_12 = e3)
% 231.09/42.29    (94)  all_57_0 = e3
% 231.09/42.29    (95)  op(e1, e3) = all_53_2
% 231.09/42.29    (96)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 231.09/42.29            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 231.09/42.29              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 231.09/42.29    (97)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.09/42.29          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.09/42.29    (98)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 231.09/42.29          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 231.09/42.29    (99)   ~ (all_53_12 = all_10_2)
% 231.09/42.29    (100)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.09/42.29           | (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 231.09/42.29             e3)
% 231.09/42.29    (101)   ~ (all_53_13 = all_53_14)
% 231.09/42.29    (102)   ~ (e2 = e1)
% 231.09/42.29    (103)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.09/42.29           | (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.09/42.29             e2)
% 231.09/42.29    (104)  op(e2, e1) = all_53_9
% 231.09/42.29    (105)  op(e1, e2) = all_53_6
% 231.09/42.29    (106)   ~ (all_6_2 = e0)
% 231.09/42.29    (107)   ~ (all_53_2 = all_53_6)
% 231.09/42.29    (108)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.09/42.29           (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.09/42.29    (109)  all_24_2 = all_6_2
% 231.09/42.29    (110)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.09/42.29           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.09/42.29    (111)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.09/42.29           (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.09/42.29    (112)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.09/42.29           | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.09/42.29             e1)
% 231.09/42.29    (113)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 231.09/42.29           (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 231.09/42.29    (114)   ~ (all_53_12 = all_53_14)
% 231.09/42.29    (115)  all_55_14 = all_53_11
% 231.09/42.29    (116)  op(e3, e0) = all_52_7
% 231.09/42.29    (117)  op(e3, e1) = all_53_8
% 231.09/42.29    (118)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.09/42.29           (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.09/42.29    (119)   ~ (all_53_4 = e3)
% 231.09/42.29    (120)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 231.09/42.29           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 231.09/42.29    (121)  op(e3, e0) = all_53_12
% 231.09/42.29  
% 231.09/42.29  Begin of proof
% 231.09/42.29  | 
% 231.09/42.29  | BETA: splitting (77) gives:
% 231.09/42.29  | 
% 231.09/42.29  | Case 1:
% 231.09/42.29  | | 
% 231.09/42.29  | |   (122)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 231.09/42.29  | |            e3)
% 231.09/42.29  | | 
% 231.09/42.29  | | BETA: splitting (122) gives:
% 231.09/42.29  | | 
% 231.09/42.29  | | Case 1:
% 231.09/42.29  | | | 
% 231.09/42.29  | | |   (123)  all_57_12 = e3 & op(e0, e3) = e3
% 231.09/42.29  | | | 
% 231.09/42.29  | | | ALPHA: (123) implies:
% 231.09/42.29  | | |   (124)  all_57_12 = e3
% 231.09/42.29  | | | 
% 231.09/42.29  | | | REF_CLOSE: (8), (9), (13), (16), (22), (23), (25), (29), (37), (38), (41),
% 231.09/42.29  | | |            (43), (45), (50), (51), (52), (59), (62), (64), (65), (69),
% 231.09/42.29  | | |            (70), (72), (73), (87), (89), (97), (102), (108), (110), (111),
% 231.09/42.29  | | |            (116), (124) are inconsistent by sub-proof #1356.
% 231.09/42.29  | | | 
% 231.09/42.29  | | Case 2:
% 231.09/42.29  | | | 
% 231.09/42.29  | | |   (125)  all_57_13 = e3 & op(e0, e2) = e3
% 231.09/42.29  | | | 
% 231.09/42.29  | | | ALPHA: (125) implies:
% 231.09/42.29  | | |   (126)  all_57_13 = e3
% 231.09/42.29  | | | 
% 231.09/42.29  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 231.09/42.29  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 231.09/42.29  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 231.09/42.29  | | |            (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 231.09/42.29  | | |            (43), (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 231.09/42.29  | | |            (53), (54), (55), (56), (57), (58), (59), (60), (61), (62),
% 231.09/42.29  | | |            (63), (64), (65), (66), (67), (68), (69), (70), (71), (72),
% 231.09/42.29  | | |            (73), (74), (75), (76), (77), (78), (79), (80), (81), (82),
% 231.09/42.29  | | |            (83), (84), (85), (86), (87), (88), (89), (90), (91), (92),
% 231.09/42.29  | | |            (93), (94), (95), (96), (97), (98), (99), (100), (101), (102),
% 231.09/42.29  | | |            (103), (104), (105), (106), (107), (108), (109), (110), (111),
% 231.09/42.29  | | |            (112), (113), (114), (115), (116), (117), (118), (119), (120),
% 231.09/42.29  | | |            (121), (126) are inconsistent by sub-proof #1348.
% 231.09/42.29  | | | 
% 231.09/42.29  | | End of split
% 231.09/42.29  | | 
% 231.09/42.29  | Case 2:
% 231.09/42.29  | | 
% 231.09/42.29  | |   (127)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 231.09/42.29  | |            e3)
% 231.09/42.29  | | 
% 231.09/42.29  | | REF_CLOSE: (1), (3), (5), (7), (8), (9), (10), (11), (14), (16), (17), (19),
% 231.09/42.29  | |            (20), (21), (22), (23), (24), (26), (27), (29), (33), (35), (36),
% 231.09/42.29  | |            (37), (40), (41), (43), (44), (45), (47), (51), (53), (54), (56),
% 231.09/42.29  | |            (58), (60), (62), (65), (66), (67), (69), (70), (71), (72), (73),
% 231.09/42.29  | |            (74), (75), (78), (80), (81), (82), (89), (90), (92), (96), (97),
% 231.09/42.29  | |            (98), (99), (102), (103), (104), (105), (108), (109), (110),
% 231.09/42.29  | |            (111), (112), (113), (117), (118), (120), (121), (127) are
% 231.09/42.29  | |            inconsistent by sub-proof #1413.
% 231.09/42.29  | | 
% 231.09/42.29  | End of split
% 231.09/42.29  | 
% 231.09/42.29  End of proof
% 231.09/42.29  
% 231.09/42.29  Sub-proof #1347 shows that the following formulas are inconsistent:
% 231.09/42.29  ----------------------------------------------------------------
% 231.09/42.29    (1)   ~ (all_10_2 = e2)
% 231.09/42.29    (2)  all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 231.09/42.29    (3)  op(e3, e3) = all_10_2
% 231.09/42.29    (4)  op(e0, e1) = all_53_11
% 231.09/42.29    (5)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 231.09/42.29    (6)   ~ (all_53_6 = all_53_14)
% 231.09/42.29    (7)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 231.09/42.29    (8)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.09/42.29         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.09/42.29    (9)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.09/42.29         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.09/42.29    (10)   ~ (all_53_8 = all_53_12)
% 231.09/42.29    (11)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.09/42.29          (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.09/42.29    (12)   ~ (all_53_8 = all_53_11)
% 231.09/42.29    (13)   ~ (e3 = e1)
% 231.09/42.29    (14)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 231.09/42.29          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.09/42.29    (15)   ~ (all_53_13 = e1)
% 231.09/42.29    (16)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.09/42.29            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.09/42.29    (17)  all_55_0 = all_10_2
% 231.09/42.29    (18)  all_57_15 = e1
% 231.09/42.29    (19)   ~ (all_10_2 = e0)
% 231.09/42.29    (20)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.09/42.29          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.09/42.29    (21)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 231.09/42.29            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 231.09/42.29              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 231.09/42.29    (22)   ~ (all_6_2 = e3)
% 231.09/42.29    (23)  op(e1, e1) = all_6_2
% 231.09/42.29    (24)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 231.09/42.29    (25)  op(all_52_7, all_52_7) = e0
% 231.09/42.29    (26)   ~ (all_53_9 = e0)
% 231.09/42.29    (27)  all_55_0 = e3 | all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 231.09/42.29    (28)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 231.09/42.29    (29)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.09/42.29          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.09/42.29    (30)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 231.09/42.29    (31)  all_55_9 = all_53_6
% 231.09/42.29    (32)   ~ (all_53_11 = all_6_2)
% 231.09/42.29    (33)   ~ (all_53_4 = all_53_12)
% 231.09/42.29    (34)   ~ (all_53_8 = e3)
% 231.09/42.29    (35)   ~ (all_53_8 = all_53_9)
% 231.09/42.29    (36)  all_42_2 = all_6_2
% 231.09/42.29    (37)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.09/42.29          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.09/42.29    (38)  op(e2, e2) = e0
% 231.09/42.29    (39)   ~ (all_53_9 = all_53_11)
% 231.09/42.29    (40)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.09/42.29    (41)   ~ (all_53_9 = all_6_2)
% 231.09/42.29    (42)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.09/42.29          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.09/42.29    (43)   ~ (all_53_14 = all_6_2)
% 231.09/42.29    (44)  all_57_3 = e0
% 231.09/42.29    (45)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.09/42.29          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.09/42.29    (46)   ~ (e3 = e2)
% 231.09/42.29    (47)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 231.09/42.29    (48)  all_55_1 = all_53_4
% 231.09/42.29    (49)  op(e1, e0) = all_53_14
% 231.09/42.29    (50)   ~ (all_53_6 = all_53_7)
% 231.09/42.29    (51)   ~ (e3 = e0)
% 231.09/42.29    (52)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.09/42.29          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.09/42.29    (53)  op(e3, e3) = e3
% 231.09/42.29    (54)   ~ (all_53_8 = all_6_2)
% 231.09/42.29    (55)  all_55_2 = all_53_8
% 231.09/42.29    (56)   ~ (all_53_4 = all_53_7)
% 231.09/42.29    (57)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 231.09/42.29    (58)   ~ (all_53_7 = e0)
% 231.09/42.29    (59)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.09/42.29          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.09/42.29            e1)
% 231.09/42.29    (60)  op(e3, e3) = all_52_1
% 231.09/42.29    (61)   ~ (all_53_4 = all_53_8)
% 231.09/42.29    (62)  all_55_6 = all_53_9
% 231.09/42.29    (63)  op(e3, e2) = all_53_4
% 231.09/42.29    (64)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 231.09/42.29          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 231.09/42.29    (65)  op(all_52_1, all_52_1) = e3
% 231.09/42.29    (66)   ~ (e2 = e0)
% 231.09/42.29    (67)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 231.09/42.29            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 231.09/42.29            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 231.09/42.29            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 231.09/42.29              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 231.09/42.29            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 231.09/42.29            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 231.09/42.29              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 231.09/42.29              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 231.09/42.29            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 231.09/42.29            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 231.09/42.29            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 231.09/42.29              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 231.09/42.29              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 231.09/42.29            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 231.09/42.29              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 231.09/42.29            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 231.09/42.29            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 231.09/42.29              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 231.09/42.29              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 231.09/42.29            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 231.09/42.29            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 231.09/42.29    (68)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 231.09/42.29          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.09/42.29    (69)   ~ (all_53_2 = all_53_14)
% 231.09/42.29    (70)   ~ (e1 = e0)
% 231.09/42.29    (71)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 231.09/42.29            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 231.09/42.29              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 231.09/42.29    (72)   ~ (all_53_4 = e0)
% 231.09/42.29    (73)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.09/42.29          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.09/42.29    (74)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.09/42.29          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.09/42.29    (75)   ~ (all_10_2 = e1)
% 231.09/42.29    (76)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 231.09/42.29    (77)  all_57_13 = e3
% 231.09/42.29    (78)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.09/42.29          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 231.09/42.29            e3)
% 231.09/42.29    (79)   ~ (all_53_4 = all_53_6)
% 231.09/42.29    (80)  op(e0, e2) = all_53_7
% 231.09/42.29    (81)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.09/42.29          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.09/42.29            e2)
% 231.09/42.29    (82)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.09/42.29              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.09/42.29                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.09/42.29                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.09/42.29    (83)  all_55_10 = all_6_2
% 231.09/42.29    (84)   ~ (all_53_6 = all_6_2)
% 231.09/42.29    (85)   ~ (all_53_13 = e0)
% 231.09/42.29    (86)  op(e1, e1) = e2
% 231.09/42.29    (87)  all_55_13 = all_53_7
% 231.09/42.30    (88)  op(e0, e0) = e1
% 231.09/42.30    (89)  op(e2, e0) = all_53_13
% 231.09/42.30    (90)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.09/42.30          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.09/42.30    (91)  all_38_2 = all_6_2
% 231.09/42.30    (92)  all_55_11 = all_53_14
% 231.09/42.30    (93)  all_55_3 = all_53_12
% 231.09/42.30    (94)   ~ (all_53_12 = e3)
% 231.09/42.30    (95)  all_57_0 = e3
% 231.09/42.30    (96)  op(e1, e3) = all_53_2
% 231.09/42.30    (97)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 231.09/42.30            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 231.09/42.30              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 231.09/42.30    (98)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.09/42.30          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.09/42.30    (99)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 231.09/42.30          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 231.09/42.30    (100)   ~ (all_53_12 = all_10_2)
% 231.09/42.30    (101)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.09/42.30           | (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 231.09/42.30             e3)
% 231.09/42.30    (102)   ~ (all_53_13 = all_53_14)
% 231.09/42.30    (103)   ~ (e2 = e1)
% 231.09/42.30    (104)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.09/42.30           | (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.09/42.30             e2)
% 231.09/42.30    (105)  op(e2, e1) = all_53_9
% 231.09/42.30    (106)  op(e1, e2) = all_53_6
% 231.09/42.30    (107)   ~ (all_6_2 = e0)
% 231.09/42.30    (108)   ~ (all_53_2 = all_53_6)
% 231.09/42.30    (109)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.09/42.30           (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.09/42.30    (110)  all_24_2 = all_6_2
% 231.09/42.30    (111)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.09/42.30           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.09/42.30    (112)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.09/42.30           (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.09/42.30    (113)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.09/42.30           | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.09/42.30             e1)
% 231.09/42.30    (114)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 231.09/42.30           (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 231.09/42.30    (115)   ~ (all_53_12 = all_53_14)
% 231.09/42.30    (116)  all_55_14 = all_53_11
% 231.09/42.30    (117)  op(e3, e0) = all_52_7
% 231.09/42.30    (118)  op(e3, e1) = all_53_8
% 231.09/42.30    (119)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.09/42.30           (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.09/42.30    (120)   ~ (all_53_4 = e3)
% 231.09/42.30    (121)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 231.09/42.30           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 231.09/42.30    (122)  op(e3, e0) = all_53_12
% 231.09/42.30  
% 231.09/42.30  Begin of proof
% 231.09/42.30  | 
% 231.09/42.30  | BETA: splitting (40) gives:
% 231.09/42.30  | 
% 231.09/42.30  | Case 1:
% 231.09/42.30  | | 
% 231.09/42.30  | |   (123)  all_57_14 = e2 & op(e0, e1) = e2
% 231.09/42.30  | | 
% 231.09/42.30  | | ALPHA: (123) implies:
% 231.09/42.30  | |   (124)  all_57_14 = e2
% 231.09/42.30  | | 
% 231.09/42.30  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 231.09/42.30  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 231.09/42.30  | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 231.09/42.30  | |            (35), (36), (37), (38), (39), (41), (42), (43), (44), (45), (46),
% 231.09/42.30  | |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 231.09/42.30  | |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 231.09/42.30  | |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 231.09/42.30  | |            (80), (81), (82), (83), (84), (85), (86), (87), (88), (89), (90),
% 231.09/42.30  | |            (91), (92), (93), (94), (95), (96), (97), (98), (99), (100),
% 231.09/42.30  | |            (101), (102), (103), (104), (105), (106), (107), (108), (109),
% 231.09/42.30  | |            (110), (111), (112), (113), (114), (115), (116), (117), (118),
% 231.09/42.30  | |            (119), (120), (121), (122), (124) are inconsistent by sub-proof
% 231.09/42.30  | |            #1348.
% 231.09/42.30  | | 
% 231.09/42.30  | Case 2:
% 231.09/42.30  | | 
% 231.09/42.30  | |   (125)  all_57_15 = e2 & op(e0, e0) = e2
% 231.09/42.30  | | 
% 231.09/42.30  | | ALPHA: (125) implies:
% 231.09/42.30  | |   (126)  op(e0, e0) = e2
% 231.09/42.30  | | 
% 231.09/42.30  | | REF_CLOSE: (16), (88), (103), (126) are inconsistent by sub-proof #2177.
% 231.09/42.30  | | 
% 231.09/42.30  | End of split
% 231.09/42.30  | 
% 231.09/42.30  End of proof
% 231.09/42.30  
% 231.09/42.30  Sub-proof #1348 shows that the following formulas are inconsistent:
% 231.09/42.30  ----------------------------------------------------------------
% 231.09/42.30    (1)   ~ (all_10_2 = e2)
% 231.09/42.30    (2)  all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 231.09/42.30    (3)  op(e3, e3) = all_10_2
% 231.13/42.30    (4)  op(e0, e1) = all_53_11
% 231.13/42.30    (5)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 231.13/42.30    (6)   ~ (all_53_6 = all_53_14)
% 231.13/42.30    (7)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 231.13/42.30    (8)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.13/42.30         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.13/42.30    (9)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.13/42.30         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.13/42.30    (10)   ~ (all_53_8 = all_53_12)
% 231.13/42.30    (11)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.13/42.30          (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.13/42.30    (12)   ~ (all_53_8 = all_53_11)
% 231.13/42.30    (13)   ~ (e3 = e1)
% 231.13/42.30    (14)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 231.13/42.30          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.13/42.30    (15)   ~ (all_53_13 = e1)
% 231.13/42.30    (16)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.13/42.30            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.13/42.30    (17)  all_55_0 = all_10_2
% 231.13/42.30    (18)  all_57_15 = e1
% 231.13/42.30    (19)   ~ (all_10_2 = e0)
% 231.13/42.30    (20)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.13/42.30          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.13/42.30    (21)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 231.13/42.30            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 231.13/42.30              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 231.13/42.30    (22)   ~ (all_6_2 = e3)
% 231.13/42.30    (23)  op(e1, e1) = all_6_2
% 231.13/42.30    (24)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 231.13/42.30    (25)  op(all_52_7, all_52_7) = e0
% 231.13/42.30    (26)   ~ (all_53_9 = e0)
% 231.13/42.30    (27)  all_55_0 = e3 | all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 231.13/42.30    (28)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 231.13/42.30    (29)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.13/42.30          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.13/42.30    (30)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 231.13/42.30    (31)  all_55_9 = all_53_6
% 231.13/42.30    (32)   ~ (all_53_11 = all_6_2)
% 231.13/42.30    (33)   ~ (all_53_4 = all_53_12)
% 231.13/42.30    (34)   ~ (all_53_8 = e3)
% 231.13/42.30    (35)   ~ (all_53_8 = all_53_9)
% 231.13/42.30    (36)  all_42_2 = all_6_2
% 231.13/42.30    (37)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.13/42.30          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.13/42.30    (38)  op(e2, e2) = e0
% 231.13/42.30    (39)   ~ (all_53_9 = all_53_11)
% 231.13/42.30    (40)   ~ (all_53_9 = all_6_2)
% 231.13/42.30    (41)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.13/42.30          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.13/42.30    (42)   ~ (all_53_14 = all_6_2)
% 231.13/42.30    (43)  all_57_3 = e0
% 231.13/42.30    (44)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.13/42.30          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.13/42.30    (45)   ~ (e3 = e2)
% 231.13/42.30    (46)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 231.13/42.30    (47)  all_55_1 = all_53_4
% 231.13/42.30    (48)  op(e1, e0) = all_53_14
% 231.13/42.30    (49)   ~ (all_53_6 = all_53_7)
% 231.13/42.30    (50)   ~ (e3 = e0)
% 231.13/42.30    (51)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.13/42.30          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.13/42.30    (52)  op(e3, e3) = e3
% 231.13/42.30    (53)   ~ (all_53_8 = all_6_2)
% 231.13/42.30    (54)  all_55_2 = all_53_8
% 231.13/42.30    (55)   ~ (all_53_4 = all_53_7)
% 231.13/42.30    (56)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 231.13/42.30    (57)   ~ (all_53_7 = e0)
% 231.13/42.30    (58)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.13/42.30          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.13/42.30            e1)
% 231.13/42.30    (59)  op(e3, e3) = all_52_1
% 231.13/42.30    (60)   ~ (all_53_4 = all_53_8)
% 231.13/42.30    (61)  all_55_6 = all_53_9
% 231.13/42.30    (62)  op(e3, e2) = all_53_4
% 231.13/42.30    (63)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 231.13/42.30          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 231.13/42.30    (64)  op(all_52_1, all_52_1) = e3
% 231.13/42.30    (65)   ~ (e2 = e0)
% 231.13/42.30    (66)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 231.13/42.30            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 231.13/42.30            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 231.13/42.30            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 231.13/42.30              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 231.13/42.30            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 231.13/42.30            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 231.13/42.30              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 231.13/42.30              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 231.13/42.30            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 231.13/42.30            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 231.13/42.30            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 231.13/42.30              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 231.13/42.30              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 231.13/42.30            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 231.13/42.30              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 231.13/42.30            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 231.13/42.30            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 231.13/42.30              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 231.13/42.30              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 231.13/42.30            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 231.13/42.30            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 231.13/42.30    (67)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 231.13/42.30          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.13/42.30    (68)   ~ (all_53_2 = all_53_14)
% 231.13/42.30    (69)   ~ (e1 = e0)
% 231.13/42.30    (70)  all_57_14 = e2
% 231.13/42.30    (71)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 231.13/42.30            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 231.13/42.30              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 231.13/42.30    (72)   ~ (all_53_4 = e0)
% 231.13/42.30    (73)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.13/42.30          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.13/42.30    (74)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.13/42.30          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.13/42.30    (75)   ~ (all_10_2 = e1)
% 231.13/42.30    (76)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 231.13/42.30    (77)  all_57_13 = e3
% 231.13/42.30    (78)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.13/42.30          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 231.13/42.30            e3)
% 231.13/42.30    (79)   ~ (all_53_4 = all_53_6)
% 231.13/42.30    (80)  op(e0, e2) = all_53_7
% 231.13/42.30    (81)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.13/42.30          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.13/42.30            e2)
% 231.13/42.30    (82)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.13/42.30              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.13/42.30                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.13/42.30                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.13/42.30    (83)  all_55_10 = all_6_2
% 231.13/42.30    (84)   ~ (all_53_6 = all_6_2)
% 231.13/42.30    (85)   ~ (all_53_13 = e0)
% 231.13/42.30    (86)  op(e1, e1) = e2
% 231.13/42.30    (87)  all_55_13 = all_53_7
% 231.13/42.30    (88)  op(e0, e0) = e1
% 231.13/42.30    (89)  op(e2, e0) = all_53_13
% 231.13/42.30    (90)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.13/42.30          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.13/42.30    (91)  all_38_2 = all_6_2
% 231.13/42.30    (92)  all_55_11 = all_53_14
% 231.13/42.30    (93)  all_55_3 = all_53_12
% 231.13/42.30    (94)   ~ (all_53_12 = e3)
% 231.13/42.30    (95)  all_57_0 = e3
% 231.13/42.30    (96)  op(e1, e3) = all_53_2
% 231.13/42.30    (97)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 231.13/42.30            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 231.13/42.30              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 231.13/42.30    (98)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.13/42.30          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.13/42.30    (99)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 231.13/42.30          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 231.13/42.30    (100)   ~ (all_53_12 = all_10_2)
% 231.13/42.30    (101)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.13/42.30           | (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 231.13/42.30             e3)
% 231.13/42.30    (102)   ~ (all_53_13 = all_53_14)
% 231.13/42.30    (103)   ~ (e2 = e1)
% 231.13/42.30    (104)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.13/42.30           | (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.13/42.30             e2)
% 231.13/42.30    (105)  op(e2, e1) = all_53_9
% 231.13/42.30    (106)  op(e1, e2) = all_53_6
% 231.13/42.30    (107)   ~ (all_6_2 = e0)
% 231.13/42.30    (108)   ~ (all_53_2 = all_53_6)
% 231.13/42.30    (109)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.13/42.30           (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.13/42.30    (110)  all_24_2 = all_6_2
% 231.13/42.30    (111)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.13/42.30           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.13/42.30    (112)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.13/42.30           (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.13/42.30    (113)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.13/42.30           | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.13/42.30             e1)
% 231.13/42.30    (114)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 231.13/42.30           (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 231.13/42.30    (115)   ~ (all_53_12 = all_53_14)
% 231.13/42.30    (116)  all_55_14 = all_53_11
% 231.13/42.30    (117)  op(e3, e0) = all_52_7
% 231.13/42.30    (118)  op(e3, e1) = all_53_8
% 231.13/42.30    (119)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.13/42.30           (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.13/42.30    (120)   ~ (all_53_4 = e3)
% 231.13/42.30    (121)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 231.13/42.30           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 231.13/42.30    (122)  op(e3, e0) = all_53_12
% 231.13/42.30  
% 231.13/42.30  Begin of proof
% 231.13/42.30  | 
% 231.13/42.30  | BETA: splitting (11) gives:
% 231.13/42.30  | 
% 231.13/42.30  | Case 1:
% 231.13/42.30  | | 
% 231.13/42.30  | |   (123)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 231.13/42.30  | |            e2)
% 231.13/42.30  | | 
% 231.13/42.30  | | BETA: splitting (123) gives:
% 231.13/42.30  | | 
% 231.13/42.30  | | Case 1:
% 231.13/42.30  | | | 
% 231.13/42.30  | | |   (124)  all_57_1 = e2 & op(e3, e2) = e2
% 231.13/42.30  | | | 
% 231.13/42.30  | | | ALPHA: (124) implies:
% 231.13/42.30  | | |   (125)  all_57_1 = e2
% 231.13/42.30  | | | 
% 231.13/42.30  | | | BETA: splitting (29) gives:
% 231.13/42.30  | | | 
% 231.13/42.30  | | | Case 1:
% 231.13/42.30  | | | | 
% 231.13/42.30  | | | |   (126)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2)
% 231.13/42.30  | | | |            = e1)
% 231.13/42.30  | | | | 
% 231.13/42.30  | | | | REF_CLOSE: (13), (16), (52), (103), (125), (126) are inconsistent by
% 231.13/42.30  | | | |            sub-proof #2096.
% 231.13/42.30  | | | | 
% 231.13/42.30  | | | Case 2:
% 231.13/42.30  | | | | 
% 231.13/42.30  | | | |   (127)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0)
% 231.13/42.30  | | | |            = e1)
% 231.13/42.30  | | | | 
% 231.13/42.30  | | | | BETA: splitting (127) gives:
% 231.13/42.30  | | | | 
% 231.13/42.30  | | | | Case 1:
% 231.13/42.30  | | | | | 
% 231.13/42.30  | | | | |   (128)  all_57_4 = e1 & op(e3, e1) = e1
% 231.13/42.30  | | | | | 
% 231.13/42.30  | | | | | ALPHA: (128) implies:
% 231.13/42.30  | | | | |   (129)  all_57_4 = e1
% 231.13/42.30  | | | | | 
% 231.13/42.30  | | | | | BETA: splitting (73) gives:
% 231.13/42.30  | | | | | 
% 231.13/42.30  | | | | | Case 1:
% 231.13/42.30  | | | | | | 
% 231.13/42.30  | | | | | |   (130)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2,
% 231.13/42.30  | | | | | |              e1) = e3)
% 231.13/42.30  | | | | | | 
% 231.13/42.30  | | | | | | BETA: splitting (130) gives:
% 231.13/42.30  | | | | | | 
% 231.13/42.30  | | | | | | Case 1:
% 231.13/42.30  | | | | | | | 
% 231.13/42.30  | | | | | | |   (131)  all_57_4 = e3 & op(e3, e1) = e3
% 231.13/42.30  | | | | | | | 
% 231.13/42.30  | | | | | | | REF_CLOSE: (13), (16), (29), (37), (41), (45), (50), (52), (65),
% 231.13/42.30  | | | | | | |            (69), (103), (125), (131) are inconsistent by sub-proof
% 231.13/42.30  | | | | | | |            #1829.
% 231.13/42.30  | | | | | | | 
% 231.13/42.30  | | | | | | Case 2:
% 231.13/42.30  | | | | | | | 
% 231.13/42.30  | | | | | | |   (132)  all_57_5 = e3 & op(e2, e1) = e3
% 231.13/42.30  | | | | | | | 
% 231.13/42.30  | | | | | | | ALPHA: (132) implies:
% 231.13/42.30  | | | | | | |   (133)  all_57_5 = e3
% 231.13/42.30  | | | | | | |   (134)  op(e2, e1) = e3
% 231.13/42.30  | | | | | | | 
% 231.13/42.30  | | | | | | | BETA: splitting (20) gives:
% 231.13/42.30  | | | | | | | 
% 231.13/42.30  | | | | | | | Case 1:
% 231.13/42.30  | | | | | | | | 
% 231.13/42.30  | | | | | | | |   (135)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 &
% 231.13/42.30  | | | | | | | |            op(e1, e2) = e3)
% 231.13/42.30  | | | | | | | | 
% 231.13/42.30  | | | | | | | | REF_CLOSE: (8), (9), (13), (16), (43), (45), (50), (52), (65),
% 231.13/42.30  | | | | | | | |            (69), (77), (98), (103), (109), (112), (119), (125),
% 231.13/42.30  | | | | | | | |            (133), (135) are inconsistent by sub-proof #1352.
% 231.13/42.30  | | | | | | | | 
% 231.13/42.30  | | | | | | | Case 2:
% 231.13/42.30  | | | | | | | | 
% 231.13/42.30  | | | | | | | |   (136)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 &
% 231.13/42.30  | | | | | | | |            op(e1, e0) = e3)
% 231.13/42.30  | | | | | | | | 
% 231.13/42.30  | | | | | | | | BETA: splitting (136) gives:
% 231.13/42.30  | | | | | | | | 
% 231.13/42.30  | | | | | | | | Case 1:
% 231.13/42.30  | | | | | | | | | 
% 231.13/42.30  | | | | | | | | |   (137)  all_57_8 = e3 & op(e1, e1) = e3
% 231.13/42.30  | | | | | | | | | 
% 231.13/42.30  | | | | | | | | | ALPHA: (137) implies:
% 231.13/42.30  | | | | | | | | |   (138)  op(e1, e1) = e3
% 231.13/42.30  | | | | | | | | | 
% 231.13/42.30  | | | | | | | | | REF_CLOSE: (16), (22), (23), (138) are inconsistent by
% 231.13/42.30  | | | | | | | | |            sub-proof #2468.
% 231.13/42.30  | | | | | | | | | 
% 231.13/42.30  | | | | | | | | Case 2:
% 231.13/42.30  | | | | | | | | | 
% 231.13/42.30  | | | | | | | | |   (139)  all_57_11 = e3 & op(e1, e0) = e3
% 231.13/42.30  | | | | | | | | | 
% 231.13/42.30  | | | | | | | | | ALPHA: (139) implies:
% 231.13/42.30  | | | | | | | | |   (140)  all_57_11 = e3
% 231.13/42.30  | | | | | | | | | 
% 231.13/42.30  | | | | | | | | | BETA: splitting (14) gives:
% 231.13/42.30  | | | | | | | | | 
% 231.13/42.30  | | | | | | | | | Case 1:
% 231.13/42.30  | | | | | | | | | | 
% 231.13/42.30  | | | | | | | | | |   (141)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 231.13/42.30  | | | | | | | | | |            & op(e1, e2) = e0)
% 231.13/42.30  | | | | | | | | | | 
% 231.13/42.30  | | | | | | | | | | BETA: splitting (141) gives:
% 231.13/42.30  | | | | | | | | | | 
% 231.13/42.30  | | | | | | | | | | Case 1:
% 231.13/42.30  | | | | | | | | | | | 
% 231.13/42.30  | | | | | | | | | | |   (142)  all_57_6 = e0 & op(e1, e3) = e0
% 231.13/42.30  | | | | | | | | | | | 
% 231.13/42.30  | | | | | | | | | | | ALPHA: (142) implies:
% 231.13/42.30  | | | | | | | | | | |   (143)  all_57_6 = e0
% 231.13/42.30  | | | | | | | | | | | 
% 231.13/42.30  | | | | | | | | | | | BETA: splitting (82) gives:
% 231.13/42.30  | | | | | | | | | | | 
% 231.13/42.30  | | | | | | | | | | | Case 1:
% 231.13/42.30  | | | | | | | | | | | | 
% 231.13/42.30  | | | | | | | | | | | |   (144)  all_57_15 = e0 & op(e0, e0) = e0
% 231.13/42.30  | | | | | | | | | | | | 
% 231.13/42.30  | | | | | | | | | | | | ALPHA: (144) implies:
% 231.13/42.30  | | | | | | | | | | | |   (145)  all_57_15 = e0
% 231.13/42.30  | | | | | | | | | | | | 
% 231.13/42.30  | | | | | | | | | | | | COMBINE_EQS: (18), (145) imply:
% 231.13/42.30  | | | | | | | | | | | |   (146)  e1 = e0
% 231.13/42.30  | | | | | | | | | | | | 
% 231.13/42.30  | | | | | | | | | | | | SIMP: (146) implies:
% 231.13/42.30  | | | | | | | | | | | |   (147)  e1 = e0
% 231.13/42.30  | | | | | | | | | | | | 
% 231.13/42.30  | | | | | | | | | | | | COMBINE_EQS: (129), (147) imply:
% 231.13/42.30  | | | | | | | | | | | |   (148)  all_57_4 = e0
% 231.13/42.30  | | | | | | | | | | | | 
% 231.13/42.30  | | | | | | | | | | | | REF_CLOSE: (11), (13), (16), (38), (43), (45), (50), (51),
% 231.13/42.30  | | | | | | | | | | | |            (65), (69), (70), (74), (77), (86), (103), (119),
% 231.13/42.30  | | | | | | | | | | | |            (125), (133), (148) are inconsistent by sub-proof
% 231.13/42.30  | | | | | | | | | | | |            #2197.
% 231.13/42.30  | | | | | | | | | | | | 
% 231.13/42.30  | | | | | | | | | | | Case 2:
% 231.13/42.30  | | | | | | | | | | | | 
% 231.13/42.30  | | | | | | | | | | | |   (149)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 231.13/42.30  | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 231.13/42.30  | | | | | | | | | | | |              op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 231.13/42.30  | | | | | | | | | | | |                e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 231.13/42.30  | | | | | | | | | | | |              e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 231.13/42.30  | | | | | | | | | | | | 
% 231.13/42.30  | | | | | | | | | | | | ALPHA: (149) implies:
% 231.13/42.30  | | | | | | | | | | | |   (150)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 231.13/42.30  | | | | | | | | | | | |            e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 231.13/42.30  | | | | | | | | | | | |              e1) = e0)
% 231.13/42.30  | | | | | | | | | | | | 
% 231.13/42.30  | | | | | | | | | | | | BETA: splitting (8) gives:
% 231.13/42.30  | | | | | | | | | | | | 
% 231.13/42.30  | | | | | | | | | | | | Case 1:
% 231.13/42.30  | | | | | | | | | | | | | 
% 231.13/42.30  | | | | | | | | | | | | |   (151)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 231.13/42.30  | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 231.13/42.30  | | | | | | | | | | | | | 
% 231.13/42.30  | | | | | | | | | | | | | BETA: splitting (151) gives:
% 231.13/42.30  | | | | | | | | | | | | | 
% 231.13/42.30  | | | | | | | | | | | | | Case 1:
% 231.13/42.30  | | | | | | | | | | | | | | 
% 231.13/42.30  | | | | | | | | | | | | | |   (152)  all_57_2 = e1 & op(e2, e3) = e1
% 231.13/42.30  | | | | | | | | | | | | | | 
% 231.13/42.30  | | | | | | | | | | | | | | ALPHA: (152) implies:
% 231.13/42.31  | | | | | | | | | | | | | |   (153)  all_57_2 = e1
% 231.13/42.31  | | | | | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | | | | | BETA: splitting (109) gives:
% 231.13/42.31  | | | | | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | | | | | Case 1:
% 231.13/42.31  | | | | | | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | | | | | |   (154)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 231.13/42.31  | | | | | | | | | | | | | | |            & op(e2, e3) = e2)
% 231.13/42.31  | | | | | | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | | | | | | BETA: splitting (154) gives:
% 231.13/42.31  | | | | | | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | | | | | | Case 1:
% 231.13/42.31  | | | | | | | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | | | | | | |   (155)  all_57_0 = e2 & op(e3, e3) = e2
% 231.13/42.31  | | | | | | | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | | | | | | | ALPHA: (155) implies:
% 231.13/42.31  | | | | | | | | | | | | | | | |   (156)  op(e3, e3) = e2
% 231.13/42.31  | | | | | | | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | | | | | | | REF_CLOSE: (16), (38), (50), (59), (64), (156) are
% 231.13/42.31  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1653.
% 231.13/42.31  | | | | | | | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | | | | | | Case 2:
% 231.13/42.31  | | | | | | | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | | | | | | |   (157)  all_57_2 = e2 & op(e2, e3) = e2
% 231.13/42.31  | | | | | | | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | | | | | | | REF_CLOSE: (103), (153), (157) are inconsistent by sub-proof
% 231.13/42.31  | | | | | | | | | | | | | | | |            #1351.
% 231.13/42.31  | | | | | | | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | | | | | | End of split
% 231.13/42.31  | | | | | | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | | | | | Case 2:
% 231.13/42.31  | | | | | | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | | | | | |   (158)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 231.13/42.31  | | | | | | | | | | | | | | |            e2 & op(e0, e3) = e2)
% 231.13/42.31  | | | | | | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | | | | | | BETA: splitting (158) gives:
% 231.13/42.31  | | | | | | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | | | | | | Case 1:
% 231.13/42.31  | | | | | | | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | | | | | | |   (159)  all_57_6 = e2 & op(e1, e3) = e2
% 231.13/42.31  | | | | | | | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | | | | | | | ALPHA: (159) implies:
% 231.13/42.31  | | | | | | | | | | | | | | | |   (160)  all_57_6 = e2
% 231.13/42.31  | | | | | | | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | | | | | | | COMBINE_EQS: (143), (160) imply:
% 231.13/42.31  | | | | | | | | | | | | | | | |   (161)  e2 = e0
% 231.13/42.31  | | | | | | | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | | | | | | | COMBINE_EQS: (70), (161) imply:
% 231.13/42.31  | | | | | | | | | | | | | | | |   (162)  all_57_14 = e0
% 231.13/42.31  | | | | | | | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | | | | | | | REF_CLOSE: (13), (16), (25), (41), (45), (50), (51), (52),
% 231.13/42.31  | | | | | | | | | | | | | | | |            (62), (65), (69), (72), (88), (103), (111), (117),
% 231.13/42.31  | | | | | | | | | | | | | | | |            (133), (162) are inconsistent by sub-proof #1368.
% 231.13/42.31  | | | | | | | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | | | | | | Case 2:
% 231.13/42.31  | | | | | | | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | | | | | | |   (163)  all_57_12 = e2 & op(e0, e3) = e2
% 231.13/42.31  | | | | | | | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | | | | | | | ALPHA: (163) implies:
% 231.13/42.31  | | | | | | | | | | | | | | | |   (164)  all_57_12 = e2
% 231.13/42.31  | | | | | | | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | | | | | | | BETA: splitting (150) gives:
% 231.13/42.31  | | | | | | | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | | | | | | | Case 1:
% 231.13/42.31  | | | | | | | | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | | | | | | | |   (165)  all_57_12 = e0 & op(e0, e3) = e0
% 231.13/42.31  | | | | | | | | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | | | | | | | | ALPHA: (165) implies:
% 231.13/42.31  | | | | | | | | | | | | | | | | |   (166)  all_57_12 = e0
% 231.13/42.31  | | | | | | | | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | | | | | | | | COMBINE_EQS: (164), (166) imply:
% 231.13/42.31  | | | | | | | | | | | | | | | | |   (167)  e2 = e0
% 231.13/42.31  | | | | | | | | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | | | | | | | | SIMP: (167) implies:
% 231.13/42.31  | | | | | | | | | | | | | | | | |   (168)  e2 = e0
% 231.13/42.31  | | | | | | | | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | | | | | | | | COMBINE_EQS: (70), (168) imply:
% 231.13/42.31  | | | | | | | | | | | | | | | | |   (169)  all_57_14 = e0
% 231.13/42.31  | | | | | | | | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (16), (25), (41), (45), (50), (51), (52),
% 231.13/42.31  | | | | | | | | | | | | | | | | |            (62), (65), (69), (72), (88), (103), (111), (117),
% 231.13/42.31  | | | | | | | | | | | | | | | | |            (133), (169) are inconsistent by sub-proof #1368.
% 231.13/42.31  | | | | | | | | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | | | | | | | Case 2:
% 231.13/42.31  | | | | | | | | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | | | | | | | |   (170)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 231.13/42.31  | | | | | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 231.13/42.31  | | | | | | | | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | | | | | | | | BETA: splitting (170) gives:
% 231.13/42.31  | | | | | | | | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | | | | | | | | Case 1:
% 231.13/42.31  | | | | | | | | | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | | | | | | | | |   (171)  all_57_13 = e0 & op(e0, e2) = e0
% 231.13/42.31  | | | | | | | | | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | | | | | | | | | ALPHA: (171) implies:
% 231.13/42.31  | | | | | | | | | | | | | | | | | |   (172)  op(e0, e2) = e0
% 231.13/42.31  | | | | | | | | | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (57), (80), (172) are inconsistent by
% 231.13/42.31  | | | | | | | | | | | | | | | | | |            sub-proof #2332.
% 231.13/42.31  | | | | | | | | | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | | | | | | | | Case 2:
% 231.13/42.31  | | | | | | | | | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | | | | | | | | |   (173)  all_57_14 = e0 & op(e0, e1) = e0
% 231.13/42.31  | | | | | | | | | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | | | | | | | | | ALPHA: (173) implies:
% 231.13/42.31  | | | | | | | | | | | | | | | | | |   (174)  all_57_14 = e0
% 231.13/42.31  | | | | | | | | | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (16), (25), (41), (45), (50), (51), (52),
% 231.13/42.31  | | | | | | | | | | | | | | | | | |            (62), (65), (69), (72), (88), (103), (111), (117),
% 231.13/42.31  | | | | | | | | | | | | | | | | | |            (133), (174) are inconsistent by sub-proof #1368.
% 231.13/42.31  | | | | | | | | | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | | | | | | | | End of split
% 231.13/42.31  | | | | | | | | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | | | | | | | End of split
% 231.13/42.31  | | | | | | | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | | | | | | End of split
% 231.13/42.31  | | | | | | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | | | | | End of split
% 231.13/42.31  | | | | | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | | | | Case 2:
% 231.13/42.31  | | | | | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | | | | |   (175)  all_57_3 = e1 & op(e2, e2) = e1
% 231.13/42.31  | | | | | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | | | | | ALPHA: (175) implies:
% 231.13/42.31  | | | | | | | | | | | | | |   (176)  op(e2, e2) = e1
% 231.13/42.31  | | | | | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | | | | | REF_CLOSE: (16), (38), (69), (176) are inconsistent by
% 231.13/42.31  | | | | | | | | | | | | | |            sub-proof #2352.
% 231.13/42.31  | | | | | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | | | | End of split
% 231.13/42.31  | | | | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | | | Case 2:
% 231.13/42.31  | | | | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | | | |   (177)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 231.13/42.31  | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 231.13/42.31  | | | | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | | | | BETA: splitting (177) gives:
% 231.13/42.31  | | | | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | | | | Case 1:
% 231.13/42.31  | | | | | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | | | | |   (178)  all_57_5 = e1 & op(e2, e1) = e1
% 231.13/42.31  | | | | | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 231.13/42.31  | | | | | | | | | | | | | |            (11), (12), (13), (14), (16), (17), (19), (20),
% 231.13/42.31  | | | | | | | | | | | | | |            (21), (22), (23), (24), (26), (27), (28), (29),
% 231.13/42.31  | | | | | | | | | | | | | |            (30), (31), (32), (33), (34), (35), (36), (37),
% 231.13/42.31  | | | | | | | | | | | | | |            (38), (39), (40), (41), (42), (43), (44), (45),
% 231.13/42.31  | | | | | | | | | | | | | |            (46), (47), (48), (49), (50), (51), (52), (53),
% 231.13/42.31  | | | | | | | | | | | | | |            (54), (55), (56), (57), (58), (60), (61), (62),
% 231.13/42.31  | | | | | | | | | | | | | |            (65), (66), (67), (68), (69), (71), (72), (73),
% 231.13/42.31  | | | | | | | | | | | | | |            (74), (75), (76), (78), (79), (80), (81), (82),
% 231.13/42.31  | | | | | | | | | | | | | |            (83), (84), (85), (87), (88), (89), (90), (91),
% 231.13/42.31  | | | | | | | | | | | | | |            (92), (93), (94), (95), (96), (97), (98), (99),
% 231.13/42.31  | | | | | | | | | | | | | |            (100), (101), (102), (103), (104), (105), (106),
% 231.13/42.31  | | | | | | | | | | | | | |            (107), (108), (109), (110), (111), (112), (113),
% 231.13/42.31  | | | | | | | | | | | | | |            (114), (115), (116), (118), (119), (120), (121),
% 231.13/42.31  | | | | | | | | | | | | | |            (122), (133), (140), (178) are inconsistent by
% 231.13/42.31  | | | | | | | | | | | | | |            sub-proof #1353.
% 231.13/42.31  | | | | | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | | | | Case 2:
% 231.13/42.31  | | | | | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | | | | |   (179)  all_57_10 = e1 & op(e2, e0) = e1
% 231.13/42.31  | | | | | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (89), (179) are inconsistent by
% 231.13/42.31  | | | | | | | | | | | | | |            sub-proof #2084.
% 231.13/42.31  | | | | | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | | | | End of split
% 231.13/42.31  | | | | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | | | End of split
% 231.13/42.31  | | | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | | End of split
% 231.13/42.31  | | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | Case 2:
% 231.13/42.31  | | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | |   (180)  all_57_7 = e0 & op(e1, e2) = e0
% 231.13/42.31  | | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | | ALPHA: (180) implies:
% 231.13/42.31  | | | | | | | | | | |   (181)  all_57_7 = e0
% 231.13/42.31  | | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | | REF_CLOSE: (11), (13), (16), (38), (43), (45), (50), (65),
% 231.13/42.31  | | | | | | | | | | |            (69), (74), (77), (103), (119), (181) are
% 231.13/42.31  | | | | | | | | | | |            inconsistent by sub-proof #2199.
% 231.13/42.31  | | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | End of split
% 231.13/42.31  | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | Case 2:
% 231.13/42.31  | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | |   (182)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0
% 231.13/42.31  | | | | | | | | | |            & op(e1, e0) = e0)
% 231.13/42.31  | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | REF_CLOSE: (5), (7), (8), (9), (10), (11), (13), (14), (16),
% 231.13/42.31  | | | | | | | | | |            (20), (21), (22), (23), (24), (26), (29), (33),
% 231.13/42.31  | | | | | | | | | |            (35), (36), (37), (38), (40), (41), (43), (44),
% 231.13/42.31  | | | | | | | | | |            (45), (47), (50), (51), (52), (53), (54), (56),
% 231.13/42.31  | | | | | | | | | |            (58), (60), (62), (65), (66), (69), (71), (72),
% 231.13/42.31  | | | | | | | | | |            (74), (77), (79), (81), (82), (83), (91), (93),
% 231.13/42.31  | | | | | | | | | |            (94), (95), (97), (98), (101), (103), (104),
% 231.13/42.31  | | | | | | | | | |            (105), (106), (107), (109), (110), (111), (112),
% 231.13/42.31  | | | | | | | | | |            (113), (114), (118), (119), (121), (122), (133),
% 231.13/42.31  | | | | | | | | | |            (134), (182) are inconsistent by sub-proof #1350.
% 231.13/42.31  | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | End of split
% 231.13/42.31  | | | | | | | | | 
% 231.13/42.31  | | | | | | | | End of split
% 231.13/42.31  | | | | | | | | 
% 231.13/42.31  | | | | | | | End of split
% 231.13/42.31  | | | | | | | 
% 231.13/42.31  | | | | | | End of split
% 231.13/42.31  | | | | | | 
% 231.13/42.31  | | | | | Case 2:
% 231.13/42.31  | | | | | | 
% 231.13/42.31  | | | | | |   (183)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 &
% 231.13/42.31  | | | | | |            op(e0, e1) = e3)
% 231.13/42.31  | | | | | | 
% 231.13/42.31  | | | | | | REF_CLOSE: (16), (22), (23), (45), (70), (183) are inconsistent by
% 231.13/42.31  | | | | | |            sub-proof #2409.
% 231.13/42.31  | | | | | | 
% 231.13/42.31  | | | | | End of split
% 231.13/42.31  | | | | | 
% 231.13/42.31  | | | | Case 2:
% 231.13/42.31  | | | | | 
% 231.13/42.31  | | | | |   (184)  all_57_9 = e1 & op(e3, e0) = e1
% 231.13/42.31  | | | | | 
% 231.13/42.31  | | | | | ALPHA: (184) implies:
% 231.13/42.31  | | | | |   (185)  all_57_9 = e1
% 231.13/42.31  | | | | | 
% 231.13/42.31  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 231.13/42.31  | | | | |            (12), (13), (14), (16), (17), (19), (20), (21), (22), (23),
% 231.13/42.31  | | | | |            (24), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 231.13/42.31  | | | | |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44),
% 231.13/42.31  | | | | |            (45), (46), (47), (48), (49), (50), (51), (52), (53), (54),
% 231.13/42.31  | | | | |            (55), (56), (57), (58), (60), (61), (62), (65), (66), (67),
% 231.13/42.31  | | | | |            (68), (69), (71), (72), (73), (74), (75), (76), (78), (79),
% 231.13/42.31  | | | | |            (80), (81), (82), (83), (84), (85), (87), (88), (89), (90),
% 231.13/42.31  | | | | |            (91), (92), (93), (94), (95), (96), (97), (98), (99),
% 231.13/42.31  | | | | |            (100), (101), (102), (103), (104), (105), (106), (108),
% 231.13/42.31  | | | | |            (109), (110), (111), (112), (113), (114), (115), (116),
% 231.13/42.31  | | | | |            (118), (119), (120), (121), (122), (185) are inconsistent
% 231.13/42.31  | | | | |            by sub-proof #1384.
% 231.13/42.31  | | | | | 
% 231.13/42.31  | | | | End of split
% 231.13/42.31  | | | | 
% 231.13/42.31  | | | End of split
% 231.13/42.31  | | | 
% 231.13/42.31  | | Case 2:
% 231.13/42.31  | | | 
% 231.13/42.31  | | |   (186)  all_57_3 = e2 & op(e2, e2) = e2
% 231.13/42.31  | | | 
% 231.13/42.31  | | | ALPHA: (186) implies:
% 231.13/42.31  | | |   (187)  op(e2, e2) = e2
% 231.13/42.31  | | | 
% 231.13/42.31  | | | REF_CLOSE: (16), (38), (65), (187) are inconsistent by sub-proof #2472.
% 231.13/42.31  | | | 
% 231.13/42.31  | | End of split
% 231.13/42.31  | | 
% 231.13/42.31  | Case 2:
% 231.13/42.31  | | 
% 231.13/42.31  | |   (188)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 231.13/42.31  | |            e2)
% 231.13/42.31  | | 
% 231.13/42.31  | | BETA: splitting (188) gives:
% 231.13/42.31  | | 
% 231.13/42.31  | | Case 1:
% 231.13/42.31  | | | 
% 231.13/42.31  | | |   (189)  all_57_7 = e2 & op(e1, e2) = e2
% 231.13/42.31  | | | 
% 231.13/42.31  | | | ALPHA: (189) implies:
% 231.13/42.31  | | |   (190)  all_57_7 = e2
% 231.13/42.31  | | | 
% 231.13/42.31  | | | BETA: splitting (73) gives:
% 231.13/42.31  | | | 
% 231.13/42.31  | | | Case 1:
% 231.13/42.31  | | | | 
% 231.13/42.31  | | | |   (191)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1)
% 231.13/42.31  | | | |            = e3)
% 231.13/42.31  | | | | 
% 231.13/42.31  | | | | BETA: splitting (191) gives:
% 231.13/42.31  | | | | 
% 231.13/42.31  | | | | Case 1:
% 231.13/42.31  | | | | | 
% 231.13/42.31  | | | | |   (192)  all_57_4 = e3 & op(e3, e1) = e3
% 231.13/42.31  | | | | | 
% 231.13/42.31  | | | | | ALPHA: (192) implies:
% 231.13/42.31  | | | | |   (193)  all_57_4 = e3
% 231.13/42.31  | | | | | 
% 231.13/42.31  | | | | | REF_CLOSE: (13), (16), (29), (37), (41), (45), (50), (52), (65), (69),
% 231.13/42.31  | | | | |            (103), (193) are inconsistent by sub-proof #2474.
% 231.13/42.31  | | | | | 
% 231.13/42.31  | | | | Case 2:
% 231.13/42.31  | | | | | 
% 231.13/42.31  | | | | |   (194)  all_57_5 = e3 & op(e2, e1) = e3
% 231.13/42.31  | | | | | 
% 231.13/42.31  | | | | | ALPHA: (194) implies:
% 231.13/42.31  | | | | |   (195)  all_57_5 = e3
% 231.13/42.31  | | | | | 
% 231.13/42.31  | | | | | BETA: splitting (119) gives:
% 231.13/42.31  | | | | | 
% 231.13/42.31  | | | | | Case 1:
% 231.13/42.31  | | | | | | 
% 231.13/42.31  | | | | | |   (196)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2,
% 231.13/42.31  | | | | | |              e2) = e1)
% 231.13/42.31  | | | | | | 
% 231.13/42.31  | | | | | | BETA: splitting (196) gives:
% 231.13/42.31  | | | | | | 
% 231.13/42.31  | | | | | | Case 1:
% 231.13/42.31  | | | | | | | 
% 231.13/42.31  | | | | | | |   (197)  all_57_1 = e1 & op(e3, e2) = e1
% 231.13/42.31  | | | | | | | 
% 231.13/42.31  | | | | | | | ALPHA: (197) implies:
% 231.13/42.31  | | | | | | |   (198)  all_57_1 = e1
% 231.13/42.31  | | | | | | | 
% 231.13/42.31  | | | | | | | BETA: splitting (8) gives:
% 231.13/42.31  | | | | | | | 
% 231.13/42.31  | | | | | | | Case 1:
% 231.13/42.31  | | | | | | | | 
% 231.13/42.31  | | | | | | | |   (199)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 &
% 231.13/42.31  | | | | | | | |            op(e2, e2) = e1)
% 231.13/42.31  | | | | | | | | 
% 231.13/42.31  | | | | | | | | BETA: splitting (199) gives:
% 231.13/42.31  | | | | | | | | 
% 231.13/42.31  | | | | | | | | Case 1:
% 231.13/42.31  | | | | | | | | | 
% 231.13/42.31  | | | | | | | | |   (200)  all_57_2 = e1 & op(e2, e3) = e1
% 231.13/42.31  | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | ALPHA: (200) implies:
% 231.13/42.31  | | | | | | | | |   (201)  all_57_2 = e1
% 231.13/42.31  | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | BETA: splitting (44) gives:
% 231.13/42.31  | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | Case 1:
% 231.13/42.31  | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | |   (202)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 231.13/42.31  | | | | | | | | | |            & op(e2, e1) = e0)
% 231.13/42.31  | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | REF_CLOSE: (8), (13), (16), (38), (43), (45), (50), (51),
% 231.13/42.31  | | | | | | | | | |            (65), (69), (70), (74), (77), (86), (90), (98),
% 231.13/42.31  | | | | | | | | | |            (103), (190), (195), (198), (201), (202) are
% 231.13/42.31  | | | | | | | | | |            inconsistent by sub-proof #1349.
% 231.13/42.31  | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | Case 2:
% 231.13/42.31  | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | |   (203)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0
% 231.13/42.31  | | | | | | | | | |            & op(e0, e1) = e0)
% 231.13/42.31  | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | | REF_CLOSE: (13), (16), (23), (25), (41), (45), (50), (51),
% 231.13/42.31  | | | | | | | | | |            (52), (62), (65), (69), (72), (88), (103), (107),
% 231.13/42.31  | | | | | | | | | |            (111), (117), (195), (203) are inconsistent by
% 231.13/42.31  | | | | | | | | | |            sub-proof #1354.
% 231.13/42.31  | | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | End of split
% 231.13/42.31  | | | | | | | | | 
% 231.13/42.31  | | | | | | | | Case 2:
% 231.13/42.31  | | | | | | | | | 
% 231.13/42.31  | | | | | | | | |   (204)  all_57_3 = e1 & op(e2, e2) = e1
% 231.13/42.31  | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | ALPHA: (204) implies:
% 231.13/42.31  | | | | | | | | |   (205)  op(e2, e2) = e1
% 231.13/42.31  | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | REF_CLOSE: (16), (50), (63), (65), (69), (77), (190), (198),
% 231.13/42.31  | | | | | | | | |            (205) are inconsistent by sub-proof #2147.
% 231.13/42.31  | | | | | | | | | 
% 231.13/42.31  | | | | | | | | End of split
% 231.13/42.31  | | | | | | | | 
% 231.13/42.31  | | | | | | | Case 2:
% 231.13/42.31  | | | | | | | | 
% 231.13/42.31  | | | | | | | |   (206)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 &
% 231.13/42.31  | | | | | | | |            op(e2, e0) = e1)
% 231.13/42.31  | | | | | | | | 
% 231.13/42.31  | | | | | | | | BETA: splitting (206) gives:
% 231.13/42.31  | | | | | | | | 
% 231.13/42.31  | | | | | | | | Case 1:
% 231.13/42.31  | | | | | | | | | 
% 231.13/42.31  | | | | | | | | |   (207)  all_57_5 = e1 & op(e2, e1) = e1
% 231.13/42.31  | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | REF_CLOSE: (13), (43), (45), (50), (74), (77), (190), (195),
% 231.13/42.31  | | | | | | | | |            (198), (207) are inconsistent by sub-proof #2192.
% 231.13/42.31  | | | | | | | | | 
% 231.13/42.31  | | | | | | | | Case 2:
% 231.13/42.31  | | | | | | | | | 
% 231.13/42.31  | | | | | | | | |   (208)  all_57_10 = e1 & op(e2, e0) = e1
% 231.13/42.31  | | | | | | | | | 
% 231.13/42.31  | | | | | | | | | REF_CLOSE: (15), (16), (89), (208) are inconsistent by
% 231.13/42.31  | | | | | | | | |            sub-proof #2084.
% 231.13/42.31  | | | | | | | | | 
% 231.13/42.31  | | | | | | | | End of split
% 231.13/42.31  | | | | | | | | 
% 231.13/42.31  | | | | | | | End of split
% 231.13/42.31  | | | | | | | 
% 231.13/42.31  | | | | | | Case 2:
% 231.13/42.31  | | | | | | | 
% 231.13/42.31  | | | | | | |   (209)  all_57_3 = e1 & op(e2, e2) = e1
% 231.13/42.31  | | | | | | | 
% 231.13/42.31  | | | | | | | ALPHA: (209) implies:
% 231.13/42.31  | | | | | | |   (210)  op(e2, e2) = e1
% 231.13/42.31  | | | | | | | 
% 231.13/42.31  | | | | | | | REF_CLOSE: (16), (38), (69), (210) are inconsistent by sub-proof
% 231.13/42.31  | | | | | | |            #2352.
% 231.13/42.31  | | | | | | | 
% 231.13/42.31  | | | | | | End of split
% 231.13/42.31  | | | | | | 
% 231.13/42.31  | | | | | Case 2:
% 231.13/42.31  | | | | | | 
% 231.13/42.31  | | | | | |   (211)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 &
% 231.13/42.31  | | | | | |            op(e0, e2) = e1)
% 231.13/42.31  | | | | | | 
% 231.13/42.31  | | | | | | BETA: splitting (211) gives:
% 231.13/42.31  | | | | | | 
% 231.13/42.31  | | | | | | Case 1:
% 231.13/42.31  | | | | | | | 
% 231.13/42.31  | | | | | | |   (212)  all_57_7 = e1 & op(e1, e2) = e1
% 231.13/42.31  | | | | | | | 
% 231.13/42.31  | | | | | | | REF_CLOSE: (103), (190), (212) are inconsistent by sub-proof
% 231.13/42.31  | | | | | | |            #2190.
% 231.13/42.31  | | | | | | | 
% 231.13/42.31  | | | | | | Case 2:
% 231.13/42.31  | | | | | | | 
% 231.13/42.31  | | | | | | |   (213)  all_57_13 = e1 & op(e0, e2) = e1
% 231.13/42.31  | | | | | | | 
% 231.13/42.31  | | | | | | | REF_CLOSE: (13), (77), (213) are inconsistent by sub-proof #2264.
% 231.13/42.31  | | | | | | | 
% 231.13/42.31  | | | | | | End of split
% 231.13/42.31  | | | | | | 
% 231.13/42.31  | | | | | End of split
% 231.13/42.31  | | | | | 
% 231.13/42.31  | | | | End of split
% 231.13/42.31  | | | | 
% 231.13/42.31  | | | Case 2:
% 231.13/42.31  | | | | 
% 231.13/42.31  | | | |   (214)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0,
% 231.13/42.31  | | | |              e1) = e3)
% 231.13/42.31  | | | | 
% 231.13/42.31  | | | | REF_CLOSE: (16), (22), (23), (45), (70), (214) are inconsistent by
% 231.13/42.31  | | | |            sub-proof #2409.
% 231.13/42.31  | | | | 
% 231.13/42.31  | | | End of split
% 231.13/42.31  | | | 
% 231.13/42.31  | | Case 2:
% 231.13/42.31  | | | 
% 231.13/42.31  | | |   (215)  all_57_13 = e2 & op(e0, e2) = e2
% 231.13/42.31  | | | 
% 231.13/42.31  | | | REF_CLOSE: (45), (77), (215) are inconsistent by sub-proof #2146.
% 231.13/42.31  | | | 
% 231.13/42.31  | | End of split
% 231.13/42.31  | | 
% 231.13/42.31  | End of split
% 231.13/42.31  | 
% 231.13/42.31  End of proof
% 231.13/42.31  
% 231.13/42.31  Sub-proof #1349 shows that the following formulas are inconsistent:
% 231.13/42.31  ----------------------------------------------------------------
% 231.13/42.31    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.13/42.31         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.13/42.31    (2)   ~ (e3 = e1)
% 231.13/42.31    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.13/42.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.13/42.31    (4)  all_57_7 = e2
% 231.13/42.31    (5)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0)
% 231.13/42.31    (6)  op(e2, e2) = e0
% 231.13/42.31    (7)  all_57_3 = e0
% 231.13/42.31    (8)   ~ (e3 = e2)
% 231.13/42.31    (9)   ~ (e3 = e0)
% 231.13/42.31    (10)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.13/42.31          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.13/42.31    (11)  all_57_1 = e1
% 231.13/42.31    (12)  all_57_5 = e3
% 231.13/42.31    (13)   ~ (e2 = e0)
% 231.13/42.31    (14)   ~ (e1 = e0)
% 231.13/42.31    (15)  all_57_14 = e2
% 231.13/42.31    (16)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.13/42.31          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.13/42.31    (17)  all_57_13 = e3
% 231.13/42.31    (18)  all_57_2 = e1
% 231.13/42.31    (19)  op(e1, e1) = e2
% 231.13/42.31    (20)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.13/42.31          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.13/42.31    (21)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.13/42.31          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.13/42.31    (22)   ~ (e2 = e1)
% 231.13/42.31  
% 231.13/42.31  Begin of proof
% 231.13/42.31  | 
% 231.13/42.31  | BETA: splitting (5) gives:
% 231.13/42.31  | 
% 231.13/42.31  | Case 1:
% 231.13/42.31  | | 
% 231.13/42.31  | |   (23)  all_57_4 = e0 & op(e3, e1) = e0
% 231.13/42.31  | | 
% 231.13/42.31  | | ALPHA: (23) implies:
% 231.13/42.31  | |   (24)  all_57_4 = e0
% 231.13/42.31  | | 
% 231.13/42.31  | | REF_CLOSE: (2), (3), (4), (7), (8), (9), (10), (11), (12), (14), (15), (16),
% 231.13/42.31  | |            (17), (19), (22), (24) are inconsistent by sub-proof #2191.
% 231.13/42.31  | | 
% 231.13/42.31  | Case 2:
% 231.13/42.31  | | 
% 231.13/42.31  | |   (25)  all_57_5 = e0 & op(e2, e1) = e0
% 231.13/42.31  | | 
% 231.13/42.31  | | ALPHA: (25) implies:
% 231.13/42.31  | |   (26)  all_57_5 = e0
% 231.13/42.31  | | 
% 231.13/42.31  | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (9), (13), (14), (18), (20), (21),
% 231.13/42.31  | |            (22), (26) are inconsistent by sub-proof #2353.
% 231.13/42.31  | | 
% 231.13/42.31  | End of split
% 231.13/42.31  | 
% 231.13/42.31  End of proof
% 231.13/42.31  
% 231.13/42.31  Sub-proof #1350 shows that the following formulas are inconsistent:
% 231.13/42.31  ----------------------------------------------------------------
% 231.13/42.31    (1)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.13/42.31    (2)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 231.13/42.31    (3)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 231.13/42.31    (4)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.13/42.31         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.13/42.31    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.13/42.31         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.13/42.31    (6)  op(e2, e1) = e3
% 231.13/42.31    (7)   ~ (all_53_8 = all_53_12)
% 231.13/42.31    (8)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.13/42.31         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.13/42.31    (9)   ~ (e3 = e1)
% 231.13/42.31    (10)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 231.13/42.31          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.13/42.31    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.13/42.31            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.13/42.31    (12)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.13/42.31          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.13/42.31    (13)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 231.13/42.31            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 231.13/42.31              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 231.13/42.31    (14)   ~ (all_6_2 = e3)
% 231.13/42.31    (15)  op(e1, e1) = all_6_2
% 231.13/42.31    (16)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 231.13/42.31    (17)   ~ (all_53_9 = e0)
% 231.13/42.31    (18)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.13/42.31          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.13/42.31    (19)   ~ (all_53_4 = all_53_12)
% 231.13/42.31    (20)   ~ (all_53_8 = all_53_9)
% 231.13/42.31    (21)  all_42_2 = all_6_2
% 231.13/42.31    (22)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.13/42.31          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.13/42.31    (23)  op(e2, e2) = e0
% 231.13/42.31    (24)   ~ (all_53_9 = all_6_2)
% 231.13/42.31    (25)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.13/42.31          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.13/42.31    (26)  all_57_3 = e0
% 231.13/42.31    (27)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.13/42.31          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.13/42.31    (28)   ~ (e3 = e2)
% 231.13/42.31    (29)  all_55_1 = all_53_4
% 231.13/42.31    (30)   ~ (e3 = e0)
% 231.13/42.31    (31)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.13/42.31          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.13/42.31    (32)  op(e3, e3) = e3
% 231.13/42.31    (33)   ~ (all_53_8 = all_6_2)
% 231.13/42.31    (34)  all_55_2 = all_53_8
% 231.13/42.31    (35)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 231.13/42.31    (36)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.13/42.31          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.13/42.31            e1)
% 231.13/42.31    (37)  all_57_5 = e3
% 231.13/42.31    (38)   ~ (all_53_4 = all_53_8)
% 231.13/42.31    (39)  op(e3, e2) = all_53_4
% 231.13/42.31    (40)   ~ (e2 = e0)
% 231.13/42.31    (41)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 231.13/42.31            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 231.13/42.31            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 231.13/42.31            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 231.13/42.31              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 231.13/42.31            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 231.13/42.31            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 231.13/42.31              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 231.13/42.31              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 231.13/42.31            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 231.13/42.31            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 231.13/42.31            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 231.13/42.31              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 231.13/42.31              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 231.13/42.31            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 231.13/42.31              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 231.13/42.31            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 231.13/42.31            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 231.13/42.31              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 231.13/42.31              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 231.13/42.31            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 231.13/42.31            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 231.13/42.31    (42)   ~ (e1 = e0)
% 231.13/42.31    (43)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 231.13/42.31            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 231.13/42.31              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 231.13/42.31    (44)   ~ (all_53_4 = e0)
% 231.13/42.31    (45)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.13/42.31          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.13/42.31    (46)  all_57_13 = e3
% 231.13/42.31    (47)   ~ (all_53_4 = all_53_6)
% 231.13/42.31    (48)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.13/42.31          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.13/42.31            e2)
% 231.13/42.31    (49)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.13/42.31              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.13/42.31                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.13/42.31                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.13/42.31    (50)  all_55_10 = all_6_2
% 231.13/42.31    (51)  all_38_2 = all_6_2
% 231.13/42.31    (52)  all_55_3 = all_53_12
% 231.13/42.31    (53)   ~ (all_53_12 = e3)
% 231.13/42.31    (54)  all_57_0 = e3
% 231.13/42.31    (55)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 231.13/42.31            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 231.13/42.31              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 231.13/42.32    (56)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.13/42.32          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.13/42.32    (57)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 231.13/42.32          (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 231.13/42.32    (58)   ~ (e2 = e1)
% 231.13/42.32    (59)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.13/42.32          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.13/42.32    (60)  op(e2, e1) = all_53_9
% 231.13/42.32    (61)  op(e1, e2) = all_53_6
% 231.13/42.32    (62)   ~ (all_6_2 = e0)
% 231.13/42.32    (63)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.13/42.32          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.13/42.32    (64)  all_24_2 = all_6_2
% 231.13/42.32    (65)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.13/42.32          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.13/42.32    (66)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.13/42.32          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.13/42.32    (67)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.13/42.32          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.13/42.32    (68)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 231.13/42.32          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 231.13/42.32    (69)  op(e3, e1) = all_53_8
% 231.13/42.32    (70)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.13/42.32          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.13/42.32    (71)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 231.13/42.32          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 231.13/42.32    (72)  op(e3, e0) = all_53_12
% 231.13/42.32  
% 231.13/42.32  Begin of proof
% 231.13/42.32  | 
% 231.13/42.32  | BETA: splitting (1) gives:
% 231.13/42.32  | 
% 231.13/42.32  | Case 1:
% 231.13/42.32  | | 
% 231.13/42.32  | |   (73)  all_57_8 = e0 & op(e1, e1) = e0
% 231.13/42.32  | | 
% 231.13/42.32  | | REF_CLOSE: (11), (15), (62), (73) are inconsistent by sub-proof #2412.
% 231.13/42.32  | | 
% 231.13/42.32  | Case 2:
% 231.13/42.32  | | 
% 231.13/42.32  | |   (74)  all_57_11 = e0 & op(e1, e0) = e0
% 231.13/42.32  | | 
% 231.13/42.32  | | ALPHA: (74) implies:
% 231.13/42.32  | |   (75)  all_57_11 = e0
% 231.13/42.32  | | 
% 231.13/42.32  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 231.13/42.32  | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 231.13/42.32  | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 231.13/42.32  | |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 231.13/42.32  | |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 231.13/42.32  | |            (58), (59), (60), (61), (63), (64), (65), (66), (67), (68), (69),
% 231.13/42.32  | |            (70), (71), (72), (75) are inconsistent by sub-proof #1408.
% 231.13/42.32  | | 
% 231.13/42.32  | End of split
% 231.13/42.32  | 
% 231.13/42.32  End of proof
% 231.13/42.32  
% 231.13/42.32  Sub-proof #1351 shows that the following formulas are inconsistent:
% 231.13/42.32  ----------------------------------------------------------------
% 231.13/42.32    (1)  all_57_2 = e2 & op(e2, e3) = e2
% 231.13/42.32    (2)  all_57_2 = e1
% 231.13/42.32    (3)   ~ (e2 = e1)
% 231.13/42.32  
% 231.13/42.32  Begin of proof
% 231.13/42.32  | 
% 231.13/42.32  | ALPHA: (1) implies:
% 231.13/42.32  |   (4)  all_57_2 = e2
% 231.13/42.32  | 
% 231.13/42.32  | COMBINE_EQS: (2), (4) imply:
% 231.13/42.32  |   (5)  e2 = e1
% 231.13/42.32  | 
% 231.13/42.32  | REDUCE: (3), (5) imply:
% 231.13/42.32  |   (6)  $false
% 231.13/42.32  | 
% 231.13/42.32  | CLOSE: (6) is inconsistent.
% 231.13/42.32  | 
% 231.13/42.32  End of proof
% 231.13/42.32  
% 231.13/42.32  Sub-proof #1352 shows that the following formulas are inconsistent:
% 231.13/42.32  ----------------------------------------------------------------
% 231.13/42.32    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.13/42.32         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.13/42.32    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.13/42.32         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.13/42.32    (3)   ~ (e3 = e1)
% 231.13/42.32    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.13/42.32           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.13/42.32    (5)  all_57_3 = e0
% 231.13/42.32    (6)   ~ (e3 = e2)
% 231.13/42.32    (7)   ~ (e3 = e0)
% 231.13/42.32    (8)  all_57_1 = e2
% 231.13/42.32    (9)  op(e3, e3) = e3
% 231.13/42.32    (10)  all_57_5 = e3
% 231.13/42.32    (11)   ~ (e2 = e0)
% 231.13/42.32    (12)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3)
% 231.13/42.32    (13)   ~ (e1 = e0)
% 231.13/42.32    (14)  all_57_13 = e3
% 231.13/42.32    (15)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.13/42.32          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.13/42.32    (16)   ~ (e2 = e1)
% 231.13/42.32    (17)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.13/42.32          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.13/42.32    (18)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.13/42.32          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.13/42.32    (19)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.13/42.32          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.13/42.32  
% 231.13/42.32  Begin of proof
% 231.13/42.32  | 
% 231.13/42.32  | BETA: splitting (12) gives:
% 231.13/42.32  | 
% 231.13/42.32  | Case 1:
% 231.13/42.32  | | 
% 231.13/42.32  | |   (20)  all_57_6 = e3 & op(e1, e3) = e3
% 231.13/42.32  | | 
% 231.13/42.32  | | ALPHA: (20) implies:
% 231.13/42.32  | |   (21)  all_57_6 = e3
% 231.13/42.32  | | 
% 231.13/42.32  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (13), (15),
% 231.13/42.32  | |            (16), (17), (18), (21) are inconsistent by sub-proof #1781.
% 231.13/42.32  | | 
% 231.13/42.32  | Case 2:
% 231.13/42.32  | | 
% 231.13/42.32  | |   (22)  all_57_7 = e3 & op(e1, e2) = e3
% 231.13/42.32  | | 
% 231.13/42.32  | | ALPHA: (22) implies:
% 231.13/42.32  | |   (23)  all_57_7 = e3
% 231.13/42.32  | | 
% 231.13/42.32  | | REF_CLOSE: (3), (5), (8), (13), (14), (16), (19), (23) are inconsistent by
% 231.13/42.32  | |            sub-proof #2008.
% 231.13/42.32  | | 
% 231.13/42.32  | End of split
% 231.13/42.32  | 
% 231.13/42.32  End of proof
% 231.13/42.32  
% 231.13/42.32  Sub-proof #1353 shows that the following formulas are inconsistent:
% 231.13/42.32  ----------------------------------------------------------------
% 231.13/42.32    (1)   ~ (all_10_2 = e2)
% 231.13/42.32    (2)  all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 231.13/42.32    (3)  op(e3, e3) = all_10_2
% 231.13/42.32    (4)  op(e0, e1) = all_53_11
% 231.13/42.32    (5)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 231.13/42.32    (6)   ~ (all_53_6 = all_53_14)
% 231.13/42.32    (7)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 231.13/42.32    (8)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.13/42.32         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.13/42.32    (9)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.13/42.32         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.13/42.32    (10)   ~ (all_53_8 = all_53_12)
% 231.13/42.32    (11)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.13/42.32          (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.13/42.32    (12)   ~ (all_53_8 = all_53_11)
% 231.13/42.32    (13)   ~ (e3 = e1)
% 231.13/42.32    (14)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 231.13/42.32          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.13/42.32    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.13/42.32            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.13/42.32    (16)  all_55_0 = all_10_2
% 231.13/42.32    (17)   ~ (all_10_2 = e0)
% 231.13/42.32    (18)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.13/42.32          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.13/42.32    (19)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 231.13/42.32            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 231.13/42.32              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 231.13/42.32    (20)   ~ (all_6_2 = e3)
% 231.13/42.32    (21)  op(e1, e1) = all_6_2
% 231.13/42.32    (22)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 231.13/42.32    (23)   ~ (all_53_9 = e0)
% 231.13/42.32    (24)  all_55_0 = e3 | all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 231.13/42.32    (25)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 231.13/42.32    (26)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.13/42.32          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.13/42.32    (27)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 231.13/42.32    (28)  all_55_9 = all_53_6
% 231.13/42.32    (29)   ~ (all_53_11 = all_6_2)
% 231.13/42.32    (30)   ~ (all_53_4 = all_53_12)
% 231.13/42.32    (31)   ~ (all_53_8 = e3)
% 231.13/42.32    (32)   ~ (all_53_8 = all_53_9)
% 231.13/42.32    (33)  all_42_2 = all_6_2
% 231.13/42.32    (34)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.13/42.32          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.13/42.32    (35)  op(e2, e2) = e0
% 231.13/42.32    (36)   ~ (all_53_9 = all_53_11)
% 231.13/42.32    (37)   ~ (all_53_9 = all_6_2)
% 231.13/42.32    (38)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.13/42.32          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.13/42.32    (39)   ~ (all_53_14 = all_6_2)
% 231.13/42.32    (40)  all_57_3 = e0
% 231.13/42.32    (41)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.13/42.32          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.13/42.32    (42)   ~ (e3 = e2)
% 231.13/42.32    (43)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 231.13/42.32    (44)  all_55_1 = all_53_4
% 231.13/42.32    (45)  op(e1, e0) = all_53_14
% 231.13/42.32    (46)   ~ (all_53_6 = all_53_7)
% 231.13/42.32    (47)   ~ (e3 = e0)
% 231.13/42.32    (48)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.13/42.32          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.13/42.32    (49)  op(e3, e3) = e3
% 231.13/42.32    (50)   ~ (all_53_8 = all_6_2)
% 231.13/42.32    (51)  all_55_2 = all_53_8
% 231.13/42.32    (52)   ~ (all_53_4 = all_53_7)
% 231.13/42.32    (53)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 231.13/42.32    (54)  all_57_5 = e1 & op(e2, e1) = e1
% 231.13/42.32    (55)   ~ (all_53_7 = e0)
% 231.13/42.32    (56)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.13/42.32          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.13/42.32            e1)
% 231.13/42.32    (57)  all_57_5 = e3
% 231.13/42.32    (58)   ~ (all_53_4 = all_53_8)
% 231.13/42.32    (59)  all_55_6 = all_53_9
% 231.13/42.32    (60)  op(e3, e2) = all_53_4
% 231.13/42.32    (61)   ~ (e2 = e0)
% 231.13/42.32    (62)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 231.13/42.32            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 231.13/42.32            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 231.13/42.32            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 231.13/42.32              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 231.13/42.32            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 231.13/42.32            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 231.13/42.32              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 231.13/42.32              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 231.13/42.32            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 231.13/42.32            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 231.13/42.32            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 231.13/42.32              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 231.13/42.32              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 231.13/42.32            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 231.13/42.32              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 231.13/42.32            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 231.13/42.32            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 231.13/42.32              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 231.13/42.32              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 231.13/42.32            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 231.13/42.32            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 231.13/42.32    (63)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 231.13/42.32          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.13/42.32    (64)   ~ (all_53_2 = all_53_14)
% 231.13/42.32    (65)   ~ (e1 = e0)
% 231.13/42.32    (66)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 231.13/42.32            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 231.13/42.32              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 231.13/42.32    (67)   ~ (all_53_4 = e0)
% 231.13/42.32    (68)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.13/42.32          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.13/42.32    (69)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.13/42.32          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.13/42.32    (70)   ~ (all_10_2 = e1)
% 231.13/42.32    (71)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 231.13/42.32    (72)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.13/42.32          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 231.13/42.32            e3)
% 231.13/42.32    (73)   ~ (all_53_4 = all_53_6)
% 231.13/42.32    (74)  op(e0, e2) = all_53_7
% 231.13/42.32    (75)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.13/42.32          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.13/42.32            e2)
% 231.13/42.32    (76)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.13/42.32              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.13/42.32                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.13/42.32                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.13/42.32    (77)  all_55_10 = all_6_2
% 231.13/42.32    (78)   ~ (all_53_6 = all_6_2)
% 231.13/42.32    (79)   ~ (all_53_13 = e0)
% 231.13/42.32    (80)  all_57_11 = e3
% 231.13/42.32    (81)  all_55_13 = all_53_7
% 231.13/42.32    (82)  op(e0, e0) = e1
% 231.13/42.32    (83)  op(e2, e0) = all_53_13
% 231.13/42.32    (84)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.13/42.32          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.13/42.32    (85)  all_38_2 = all_6_2
% 231.13/42.32    (86)  all_55_11 = all_53_14
% 231.13/42.32    (87)  all_55_3 = all_53_12
% 231.13/42.32    (88)   ~ (all_53_12 = e3)
% 231.13/42.32    (89)  all_57_0 = e3
% 231.13/42.32    (90)  op(e1, e3) = all_53_2
% 231.13/42.32    (91)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 231.13/42.32            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 231.13/42.32              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 231.13/42.32    (92)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.13/42.32          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.13/42.32    (93)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 231.13/42.32          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 231.13/42.32    (94)   ~ (all_53_12 = all_10_2)
% 231.13/42.32    (95)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 231.13/42.32          (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 231.13/42.32    (96)   ~ (all_53_13 = all_53_14)
% 231.13/42.32    (97)   ~ (e2 = e1)
% 231.13/42.32    (98)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.13/42.32          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.13/42.32    (99)  op(e2, e1) = all_53_9
% 231.13/42.32    (100)  op(e1, e2) = all_53_6
% 231.13/42.32    (101)   ~ (all_6_2 = e0)
% 231.13/42.32    (102)   ~ (all_53_2 = all_53_6)
% 231.13/42.32    (103)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.13/42.32           (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.13/42.32    (104)  all_24_2 = all_6_2
% 231.13/42.32    (105)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.13/42.32           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.13/42.32    (106)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.13/42.32           (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.13/42.32    (107)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.13/42.32           | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.13/42.32             e1)
% 231.13/42.32    (108)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 231.13/42.32           (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 231.13/42.32    (109)   ~ (all_53_12 = all_53_14)
% 231.13/42.32    (110)  all_55_14 = all_53_11
% 231.13/42.32    (111)  op(e3, e1) = all_53_8
% 231.13/42.32    (112)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.13/42.32           (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.13/42.32    (113)   ~ (all_53_4 = e3)
% 231.13/42.32    (114)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 231.13/42.32           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 231.13/42.32    (115)  op(e3, e0) = all_53_12
% 231.13/42.32  
% 231.13/42.32  Begin of proof
% 231.13/42.32  | 
% 231.13/42.32  | ALPHA: (54) implies:
% 231.13/42.32  |   (116)  all_57_5 = e1
% 231.13/42.32  | 
% 231.13/42.32  | COMBINE_EQS: (57), (116) imply:
% 231.13/42.32  |   (117)  e3 = e1
% 231.13/42.32  | 
% 231.13/42.32  | SIMP: (117) implies:
% 231.13/42.32  |   (118)  e3 = e1
% 231.13/42.32  | 
% 231.13/42.32  | COMBINE_EQS: (80), (118) imply:
% 231.13/42.32  |   (119)  all_57_11 = e1
% 231.13/42.32  | 
% 231.13/42.32  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 231.13/42.32  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 231.13/42.32  |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 231.13/42.32  |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 231.13/42.32  |            (46), (47), (48), (49), (50), (51), (52), (53), (55), (56), (58),
% 231.13/42.32  |            (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 231.13/42.32  |            (70), (71), (72), (73), (74), (75), (76), (77), (78), (79), (81),
% 231.13/42.32  |            (82), (83), (84), (85), (86), (87), (88), (89), (90), (91), (92),
% 231.13/42.32  |            (93), (94), (95), (96), (97), (98), (99), (100), (101), (102),
% 231.13/42.32  |            (103), (104), (105), (106), (107), (108), (109), (110), (111),
% 231.13/42.32  |            (112), (113), (114), (115), (119) are inconsistent by sub-proof
% 231.13/42.32  |            #1373.
% 231.13/42.32  | 
% 231.13/42.32  End of proof
% 231.13/42.32  
% 231.13/42.32  Sub-proof #1354 shows that the following formulas are inconsistent:
% 231.13/42.32  ----------------------------------------------------------------
% 231.13/42.32    (1)   ~ (e3 = e1)
% 231.13/42.32    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.13/42.32           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.13/42.32    (3)  op(e1, e1) = all_6_2
% 231.13/42.32    (4)  op(all_52_7, all_52_7) = e0
% 231.13/42.32    (5)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.13/42.32         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.13/42.32    (6)   ~ (e3 = e2)
% 231.13/42.32    (7)   ~ (e3 = e0)
% 231.13/42.32    (8)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.13/42.32         (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.13/42.32    (9)  op(e3, e3) = e3
% 231.13/42.32    (10)  all_57_5 = e3
% 231.13/42.32    (11)  op(e3, e2) = all_53_4
% 231.13/42.32    (12)   ~ (e2 = e0)
% 231.13/42.32    (13)   ~ (e1 = e0)
% 231.13/42.32    (14)   ~ (all_53_4 = e0)
% 231.13/42.32    (15)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.13/42.32    (16)  op(e0, e0) = e1
% 231.13/42.32    (17)   ~ (e2 = e1)
% 231.13/42.32    (18)   ~ (all_6_2 = e0)
% 231.13/42.32    (19)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.13/42.32          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.13/42.32    (20)  op(e3, e0) = all_52_7
% 231.13/42.32  
% 231.13/42.32  Begin of proof
% 231.13/42.32  | 
% 231.13/42.32  | BETA: splitting (15) gives:
% 231.13/42.32  | 
% 231.13/42.32  | Case 1:
% 231.13/42.32  | | 
% 231.13/42.32  | |   (21)  all_57_8 = e0 & op(e1, e1) = e0
% 231.13/42.32  | | 
% 231.13/42.32  | | REF_CLOSE: (2), (3), (18), (21) are inconsistent by sub-proof #2412.
% 231.13/42.32  | | 
% 231.13/42.32  | Case 2:
% 231.13/42.32  | | 
% 231.13/42.32  | |   (22)  all_57_14 = e0 & op(e0, e1) = e0
% 231.13/42.32  | | 
% 231.13/42.32  | | ALPHA: (22) implies:
% 231.13/42.32  | |   (23)  all_57_14 = e0
% 231.13/42.32  | | 
% 231.13/42.32  | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 231.13/42.32  | |            (14), (16), (17), (19), (20), (23) are inconsistent by sub-proof
% 231.13/42.32  | |            #1368.
% 231.13/42.32  | | 
% 231.13/42.32  | End of split
% 231.13/42.32  | 
% 231.13/42.32  End of proof
% 231.13/42.32  
% 231.13/42.32  Sub-proof #1355 shows that the following formulas are inconsistent:
% 231.13/42.32  ----------------------------------------------------------------
% 231.13/42.32    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.13/42.32         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.13/42.32    (2)   ~ (e3 = e1)
% 231.13/42.32    (3)  all_57_3 = e0
% 231.13/42.32    (4)   ~ (e3 = e2)
% 231.13/42.32    (5)  all_57_4 = e0 & op(e3, e1) = e0
% 231.13/42.32    (6)  all_57_4 = e1
% 231.13/42.32    (7)  all_57_5 = e3
% 231.13/42.33    (8)   ~ (e2 = e0)
% 231.13/42.33    (9)   ~ (e1 = e0)
% 231.13/42.33    (10)  all_57_2 = e1
% 231.13/42.33    (11)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.13/42.33          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.13/42.33    (12)   ~ (e2 = e1)
% 231.13/42.33  
% 231.13/42.33  Begin of proof
% 231.13/42.33  | 
% 231.13/42.33  | ALPHA: (5) implies:
% 231.13/42.33  |   (13)  all_57_4 = e0
% 231.13/42.33  | 
% 231.13/42.33  | COMBINE_EQS: (6), (13) imply:
% 231.13/42.33  |   (14)  e1 = e0
% 231.13/42.33  | 
% 231.13/42.33  | COMBINE_EQS: (10), (14) imply:
% 231.13/42.33  |   (15)  all_57_2 = e0
% 231.13/42.33  | 
% 231.13/42.33  | REF_CLOSE: (1), (2), (3), (4), (7), (8), (9), (11), (12), (15) are
% 231.13/42.33  |            inconsistent by sub-proof #2253.
% 231.13/42.33  | 
% 231.13/42.33  End of proof
% 231.13/42.33  
% 231.13/42.33  Sub-proof #1356 shows that the following formulas are inconsistent:
% 231.13/42.33  ----------------------------------------------------------------
% 231.13/42.33    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.13/42.33         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.13/42.33    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.13/42.33         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.13/42.33    (3)   ~ (e3 = e1)
% 231.13/42.33    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.13/42.33           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.13/42.33    (5)   ~ (all_6_2 = e3)
% 231.13/42.33    (6)  op(e1, e1) = all_6_2
% 231.13/42.33    (7)  op(all_52_7, all_52_7) = e0
% 231.13/42.33    (8)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.13/42.33         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.13/42.33    (9)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.13/42.33         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.13/42.33    (10)  op(e2, e2) = e0
% 231.13/42.33    (11)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.13/42.33          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.13/42.33    (12)  all_57_3 = e0
% 231.13/42.33    (13)   ~ (e3 = e2)
% 231.13/42.33    (14)   ~ (e3 = e0)
% 231.13/42.33    (15)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.13/42.33          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.13/42.33    (16)  op(e3, e3) = e3
% 231.13/42.33    (17)  op(e3, e3) = all_52_1
% 231.13/42.33    (18)  op(e3, e2) = all_53_4
% 231.13/42.33    (19)  op(all_52_1, all_52_1) = e3
% 231.13/42.33    (20)   ~ (e2 = e0)
% 231.13/42.33    (21)   ~ (e1 = e0)
% 231.13/42.33    (22)  all_57_12 = e3
% 231.13/42.33    (23)  all_57_14 = e2
% 231.13/42.33    (24)   ~ (all_53_4 = e0)
% 231.13/42.33    (25)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.13/42.33          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.13/42.33    (26)  op(e0, e0) = e1
% 231.13/42.33    (27)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.13/42.33          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.13/42.33    (28)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.13/42.33          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.13/42.33    (29)   ~ (e2 = e1)
% 231.13/42.33    (30)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.13/42.33          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.13/42.33    (31)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.13/42.33          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.13/42.33    (32)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.13/42.33          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.13/42.33    (33)  op(e3, e0) = all_52_7
% 231.13/42.33  
% 231.13/42.33  Begin of proof
% 231.13/42.33  | 
% 231.13/42.33  | BETA: splitting (30) gives:
% 231.13/42.33  | 
% 231.13/42.33  | Case 1:
% 231.13/42.33  | | 
% 231.13/42.33  | |   (34)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) =
% 231.13/42.33  | |           e2)
% 231.13/42.33  | | 
% 231.13/42.33  | | BETA: splitting (34) gives:
% 231.13/42.33  | | 
% 231.13/42.33  | | Case 1:
% 231.13/42.33  | | | 
% 231.13/42.33  | | |   (35)  all_57_0 = e2 & op(e3, e3) = e2
% 231.13/42.33  | | | 
% 231.13/42.33  | | | ALPHA: (35) implies:
% 231.13/42.33  | | |   (36)  op(e3, e3) = e2
% 231.13/42.33  | | | 
% 231.13/42.33  | | | REF_CLOSE: (4), (10), (14), (17), (19), (36) are inconsistent by sub-proof
% 231.13/42.33  | | |            #1653.
% 231.13/42.33  | | | 
% 231.13/42.33  | | Case 2:
% 231.13/42.33  | | | 
% 231.13/42.33  | | |   (37)  all_57_2 = e2 & op(e2, e3) = e2
% 231.13/42.33  | | | 
% 231.13/42.33  | | | ALPHA: (37) implies:
% 231.13/42.33  | | |   (38)  all_57_2 = e2
% 231.13/42.33  | | | 
% 231.13/42.33  | | | REF_CLOSE: (1), (2), (3), (4), (12), (13), (14), (16), (20), (21), (22),
% 231.13/42.33  | | |            (27), (28), (29), (32), (38) are inconsistent by sub-proof
% 231.13/42.33  | | |            #2224.
% 231.13/42.33  | | | 
% 231.13/42.33  | | End of split
% 231.13/42.33  | | 
% 231.13/42.33  | Case 2:
% 231.13/42.33  | | 
% 231.13/42.33  | |   (39)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) =
% 231.13/42.33  | |           e2)
% 231.13/42.33  | | 
% 231.13/42.33  | | BETA: splitting (39) gives:
% 231.13/42.33  | | 
% 231.13/42.33  | | Case 1:
% 231.13/42.33  | | | 
% 231.13/42.33  | | |   (40)  all_57_6 = e2 & op(e1, e3) = e2
% 231.13/42.33  | | | 
% 231.13/42.33  | | | ALPHA: (40) implies:
% 231.13/42.33  | | |   (41)  all_57_6 = e2
% 231.13/42.33  | | | 
% 231.13/42.33  | | | BETA: splitting (32) gives:
% 231.13/42.33  | | | 
% 231.13/42.33  | | | Case 1:
% 231.13/42.33  | | | | 
% 231.13/42.33  | | | |   (42)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3)
% 231.13/42.33  | | | |           = e0)
% 231.13/42.33  | | | | 
% 231.13/42.33  | | | | REF_CLOSE: (1), (3), (4), (12), (13), (14), (16), (20), (21), (27),
% 231.13/42.33  | | | |            (28), (29), (42) are inconsistent by sub-proof #2229.
% 231.13/42.33  | | | | 
% 231.13/42.33  | | | Case 2:
% 231.13/42.33  | | | | 
% 231.13/42.33  | | | |   (43)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3)
% 231.13/42.33  | | | |           = e0)
% 231.13/42.33  | | | | 
% 231.13/42.33  | | | | BETA: splitting (43) gives:
% 231.13/42.33  | | | | 
% 231.13/42.33  | | | | Case 1:
% 231.13/42.33  | | | | | 
% 231.13/42.33  | | | | |   (44)  all_57_6 = e0 & op(e1, e3) = e0
% 231.13/42.33  | | | | | 
% 231.13/42.33  | | | | | ALPHA: (44) implies:
% 231.13/42.33  | | | | |   (45)  all_57_6 = e0
% 231.13/42.33  | | | | | 
% 231.13/42.33  | | | | | COMBINE_EQS: (41), (45) imply:
% 231.13/42.33  | | | | |   (46)  e2 = e0
% 231.13/42.33  | | | | | 
% 231.13/42.33  | | | | | COMBINE_EQS: (23), (46) imply:
% 231.13/42.33  | | | | |   (47)  all_57_14 = e0
% 231.13/42.33  | | | | | 
% 231.13/42.33  | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (11), (13), (14), (15),
% 231.13/42.33  | | | | |            (16), (18), (20), (21), (24), (25), (26), (29), (31), (33),
% 231.13/42.33  | | | | |            (47) are inconsistent by sub-proof #1367.
% 231.13/42.33  | | | | | 
% 231.13/42.33  | | | | Case 2:
% 231.13/42.33  | | | | | 
% 231.13/42.33  | | | | |   (48)  all_57_12 = e0 & op(e0, e3) = e0
% 231.13/42.33  | | | | | 
% 231.13/42.33  | | | | | REF_CLOSE: (14), (22), (48) are inconsistent by sub-proof #2237.
% 231.13/42.33  | | | | | 
% 231.13/42.33  | | | | End of split
% 231.13/42.33  | | | | 
% 231.13/42.33  | | | End of split
% 231.13/42.33  | | | 
% 231.13/42.33  | | Case 2:
% 231.13/42.33  | | | 
% 231.13/42.33  | | |   (49)  all_57_12 = e2 & op(e0, e3) = e2
% 231.13/42.33  | | | 
% 231.13/42.33  | | | REF_CLOSE: (13), (22), (49) are inconsistent by sub-proof #2232.
% 231.13/42.33  | | | 
% 231.13/42.33  | | End of split
% 231.13/42.33  | | 
% 231.13/42.33  | End of split
% 231.13/42.33  | 
% 231.13/42.33  End of proof
% 231.13/42.33  
% 231.13/42.33  Sub-proof #1357 shows that the following formulas are inconsistent:
% 231.13/42.33  ----------------------------------------------------------------
% 231.13/42.33    (1)   ~ (all_10_2 = e2)
% 231.13/42.33    (2)  all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 231.13/42.33    (3)   ~ (all_53_2 = e2)
% 231.13/42.33    (4)  op(e3, e3) = all_10_2
% 231.13/42.33    (5)  op(e0, e1) = all_53_11
% 231.13/42.33    (6)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 231.13/42.33    (7)   ~ (all_53_6 = all_53_14)
% 231.13/42.33    (8)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 231.13/42.33    (9)   ~ (all_53_6 = e2)
% 231.13/42.33    (10)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.13/42.33          (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.13/42.33    (11)  op(e3, e1) = all_52_5
% 231.13/42.33    (12)   ~ (all_53_6 = e0)
% 231.13/42.33    (13)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.13/42.33          (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.13/42.33    (14)   ~ (all_53_8 = all_53_12)
% 231.13/42.33    (15)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.13/42.33          (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.13/42.33    (16)   ~ (all_53_8 = all_53_11)
% 231.13/42.33    (17)   ~ (e3 = e1)
% 231.13/42.33    (18)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 231.13/42.33          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.13/42.33    (19)   ~ (all_53_13 = e1)
% 231.13/42.33    (20)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.13/42.33            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.13/42.33    (21)  op(all_52_5, all_52_5) = e1
% 231.13/42.33    (22)  all_55_0 = all_10_2
% 231.13/42.33    (23)   ~ (all_10_2 = e0)
% 231.13/42.33    (24)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.13/42.33          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.13/42.33    (25)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 231.13/42.33            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 231.13/42.33              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 231.13/42.33    (26)   ~ (all_6_2 = e3)
% 231.13/42.33    (27)  op(e1, e1) = all_6_2
% 231.13/42.33    (28)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 231.13/42.33    (29)  op(all_52_7, all_52_7) = e0
% 231.13/42.33    (30)   ~ (all_53_9 = e0)
% 231.13/42.33    (31)  all_55_0 = e3 | all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 231.13/42.33    (32)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 231.13/42.33    (33)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.13/42.33          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.13/42.33    (34)  all_55_9 = e1 | all_55_9 = e0
% 231.13/42.33    (35)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 231.13/42.33    (36)  all_55_9 = all_53_6
% 231.13/42.33    (37)   ~ (all_53_2 = e3)
% 231.13/42.33    (38)   ~ (all_53_11 = all_6_2)
% 231.13/42.33    (39)   ~ (all_53_4 = all_53_12)
% 231.13/42.33    (40)   ~ (all_53_8 = e3)
% 231.13/42.33    (41)   ~ (all_53_8 = all_53_9)
% 231.13/42.33    (42)  all_42_2 = all_6_2
% 231.13/42.33    (43)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.13/42.33          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.13/42.33    (44)  op(e2, e2) = e0
% 231.13/42.33    (45)   ~ (all_53_9 = all_53_11)
% 231.13/42.33    (46)   ~ (all_53_9 = all_6_2)
% 231.13/42.33    (47)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.13/42.33          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.13/42.33    (48)   ~ (all_53_14 = all_6_2)
% 231.13/42.33    (49)  all_57_3 = e0
% 231.13/42.33    (50)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.13/42.33          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.13/42.33    (51)   ~ (e3 = e2)
% 231.13/42.33    (52)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 231.13/42.33    (53)  all_55_1 = all_53_4
% 231.13/42.33    (54)  op(e1, e0) = all_53_14
% 231.13/42.33    (55)   ~ (all_53_6 = all_53_7)
% 231.13/42.33    (56)   ~ (e3 = e0)
% 231.13/42.33    (57)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.13/42.33          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.13/42.33    (58)  op(e3, e3) = e3
% 231.13/42.33    (59)   ~ (all_53_8 = all_6_2)
% 231.13/42.33    (60)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 231.13/42.33    (61)  op(e0, e3) = all_53_3
% 231.13/42.33    (62)  all_55_2 = all_53_8
% 231.13/42.33    (63)   ~ (all_53_4 = all_53_7)
% 231.13/42.33    (64)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 231.13/42.33    (65)   ~ (all_53_7 = e0)
% 231.13/42.33    (66)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.13/42.33          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.13/42.33            e1)
% 231.13/42.33    (67)  all_57_5 = e3
% 231.13/42.33    (68)  op(e3, e3) = all_52_1
% 231.13/42.33    (69)   ~ (all_53_4 = all_53_8)
% 231.13/42.33    (70)  all_55_6 = all_53_9
% 231.13/42.33    (71)  op(e3, e2) = all_53_4
% 231.13/42.33    (72)  op(all_52_1, all_52_1) = e3
% 231.13/42.33    (73)   ~ (e2 = e0)
% 231.13/42.33    (74)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 231.13/42.33            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 231.13/42.33            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 231.13/42.33            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 231.13/42.33              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 231.13/42.33            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 231.13/42.33            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 231.13/42.33              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 231.13/42.33              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 231.13/42.33            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 231.13/42.33            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 231.13/42.33            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 231.13/42.33              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 231.13/42.33              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 231.13/42.33            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 231.13/42.33              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 231.13/42.33            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 231.13/42.33            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 231.13/42.33              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 231.13/42.33              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 231.13/42.33            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 231.13/42.33            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 231.13/42.33    (75)  all_57_13 = e2
% 231.13/42.33    (76)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 231.13/42.33          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.13/42.33    (77)   ~ (all_53_2 = all_53_14)
% 231.13/42.33    (78)   ~ (e1 = e0)
% 231.13/42.33    (79)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 231.13/42.33            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 231.13/42.33              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 231.13/42.33    (80)   ~ (all_53_4 = e0)
% 231.13/42.33    (81)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.13/42.33          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.13/42.33    (82)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.13/42.33          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.13/42.33    (83)   ~ (all_53_2 = all_53_3)
% 231.13/42.33    (84)   ~ (all_10_2 = e1)
% 231.13/42.33    (85)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 231.13/42.33    (86)  all_55_8 = all_53_2
% 231.13/42.33    (87)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.13/42.33          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 231.13/42.33            e3)
% 231.13/42.33    (88)   ~ (all_53_4 = all_53_6)
% 231.13/42.33    (89)  op(e0, e2) = all_53_7
% 231.13/42.33    (90)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.13/42.33          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.13/42.33            e2)
% 231.13/42.33    (91)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.13/42.33              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.13/42.33                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.13/42.33                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.13/42.33    (92)  all_55_10 = all_6_2
% 231.13/42.33    (93)   ~ (all_53_6 = all_6_2)
% 231.13/42.33    (94)   ~ (all_53_13 = e0)
% 231.13/42.33    (95)  all_57_11 = e3
% 231.13/42.33    (96)  all_55_13 = all_53_7
% 231.13/42.33    (97)  op(e0, e0) = e1
% 231.13/42.33    (98)  op(e2, e0) = all_53_13
% 231.13/42.33    (99)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.13/42.33          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.13/42.33    (100)  all_38_2 = all_6_2
% 231.13/42.33    (101)  all_55_11 = all_53_14
% 231.13/42.33    (102)  all_55_3 = all_53_12
% 231.13/42.33    (103)   ~ (all_53_12 = e3)
% 231.13/42.33    (104)  all_57_0 = e3
% 231.13/42.33    (105)  op(e1, e3) = all_53_2
% 231.13/42.33    (106)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0
% 231.13/42.33             & op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~
% 231.13/42.33             (all_42_1 = e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 231.13/42.33    (107)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.13/42.33           (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.13/42.33    (108)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 231.13/42.33           (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 231.13/42.33    (109)   ~ (all_53_12 = all_10_2)
% 231.13/42.33    (110)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.13/42.33           | (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 231.13/42.33             e3)
% 231.13/42.33    (111)   ~ (all_53_13 = all_53_14)
% 231.13/42.33    (112)   ~ (all_53_6 = e3)
% 231.13/42.33    (113)   ~ (e2 = e1)
% 231.13/42.33    (114)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.13/42.33           | (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.13/42.33             e2)
% 231.13/42.33    (115)  op(e2, e1) = all_53_9
% 231.13/42.33    (116)  op(e1, e2) = all_53_6
% 231.13/42.33    (117)   ~ (all_6_2 = e0)
% 231.13/42.33    (118)   ~ (all_53_2 = all_53_6)
% 231.13/42.33    (119)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.13/42.33           (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.13/42.33    (120)  all_24_2 = all_6_2
% 231.13/42.33    (121)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.13/42.33           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.13/42.33    (122)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.13/42.33           (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.13/42.33    (123)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.13/42.33           | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.13/42.33             e1)
% 231.13/42.33    (124)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 231.13/42.33           (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 231.13/42.33    (125)   ~ (all_53_12 = all_53_14)
% 231.13/42.33    (126)  all_55_14 = all_53_11
% 231.13/42.33    (127)  op(e3, e0) = all_52_7
% 231.13/42.33    (128)  op(e3, e1) = all_53_8
% 231.13/42.33    (129)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.13/42.33           (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.13/42.33    (130)   ~ (all_53_4 = e3)
% 231.16/42.33    (131)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 231.16/42.33           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 231.16/42.33    (132)  op(e3, e0) = all_53_12
% 231.16/42.33  
% 231.16/42.33  Begin of proof
% 231.16/42.33  | 
% 231.16/42.33  | BETA: splitting (82) gives:
% 231.16/42.33  | 
% 231.16/42.33  | Case 1:
% 231.16/42.33  | | 
% 231.16/42.33  | |   (133)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 231.16/42.33  | |            e3)
% 231.16/42.33  | | 
% 231.16/42.33  | | BETA: splitting (133) gives:
% 231.16/42.33  | | 
% 231.16/42.33  | | Case 1:
% 231.16/42.33  | | | 
% 231.16/42.33  | | |   (134)  all_57_1 = e3 & op(e3, e2) = e3
% 231.16/42.33  | | | 
% 231.16/42.33  | | | ALPHA: (134) implies:
% 231.16/42.33  | | |   (135)  all_57_1 = e3
% 231.16/42.33  | | | 
% 231.16/42.33  | | | BETA: splitting (43) gives:
% 231.16/42.33  | | | 
% 231.16/42.33  | | | Case 1:
% 231.16/42.33  | | | | 
% 231.16/42.33  | | | |   (136)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2)
% 231.16/42.33  | | | |            = e2)
% 231.16/42.33  | | | | 
% 231.16/42.33  | | | | REF_CLOSE: (20), (44), (51), (56), (68), (72), (135), (136) are
% 231.16/42.33  | | | |            inconsistent by sub-proof #1363.
% 231.16/42.33  | | | | 
% 231.16/42.33  | | | Case 2:
% 231.16/42.33  | | | | 
% 231.16/42.33  | | | |   (137)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0)
% 231.16/42.33  | | | |            = e2)
% 231.16/42.33  | | | | 
% 231.16/42.33  | | | | BETA: splitting (137) gives:
% 231.16/42.33  | | | | 
% 231.16/42.33  | | | | Case 1:
% 231.16/42.33  | | | | | 
% 231.16/42.33  | | | | |   (138)  all_57_4 = e2 & op(e3, e1) = e2
% 231.16/42.33  | | | | | 
% 231.16/42.33  | | | | | REF_CLOSE: (10), (17), (19), (20), (26), (27), (29), (33), (43), (44),
% 231.16/42.33  | | | | |            (47), (49), (50), (51), (56), (57), (58), (71), (73), (78),
% 231.16/42.33  | | | | |            (80), (81), (97), (98), (99), (107), (113), (117), (121),
% 231.16/42.33  | | | | |            (127), (138) are inconsistent by sub-proof #1361.
% 231.16/42.33  | | | | | 
% 231.16/42.33  | | | | Case 2:
% 231.16/42.33  | | | | | 
% 231.16/42.33  | | | | |   (139)  all_57_9 = e2 & op(e3, e0) = e2
% 231.16/42.33  | | | | | 
% 231.16/42.33  | | | | | ALPHA: (139) implies:
% 231.16/42.33  | | | | |   (140)  all_57_9 = e2
% 231.16/42.33  | | | | | 
% 231.16/42.34  | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (10), (13), (14), (15),
% 231.16/42.34  | | | | |            (16), (17), (18), (19), (20), (22), (23), (24), (25), (26),
% 231.16/42.34  | | | | |            (27), (28), (29), (30), (31), (32), (33), (35), (36), (38),
% 231.16/42.34  | | | | |            (39), (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 231.16/42.34  | | | | |            (49), (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 231.16/42.34  | | | | |            (59), (62), (63), (64), (65), (66), (69), (70), (71), (73),
% 231.16/42.34  | | | | |            (74), (75), (76), (77), (78), (79), (80), (81), (82), (84),
% 231.16/42.34  | | | | |            (85), (87), (88), (89), (90), (91), (92), (93), (94), (95),
% 231.16/42.34  | | | | |            (96), (97), (98), (99), (100), (101), (102), (103), (104),
% 231.16/42.34  | | | | |            (105), (106), (107), (108), (109), (110), (111), (113),
% 231.16/42.34  | | | | |            (114), (115), (116), (117), (118), (119), (120), (121),
% 231.16/42.34  | | | | |            (122), (123), (124), (125), (126), (127), (128), (129),
% 231.16/42.34  | | | | |            (130), (131), (132), (135), (140) are inconsistent by
% 231.16/42.34  | | | | |            sub-proof #1359.
% 231.16/42.34  | | | | | 
% 231.16/42.34  | | | | End of split
% 231.16/42.34  | | | | 
% 231.16/42.34  | | | End of split
% 231.16/42.34  | | | 
% 231.16/42.34  | | Case 2:
% 231.16/42.34  | | | 
% 231.16/42.34  | | |   (141)  all_57_3 = e3 & op(e2, e2) = e3
% 231.16/42.34  | | | 
% 231.16/42.34  | | | ALPHA: (141) implies:
% 231.16/42.34  | | |   (142)  all_57_3 = e3
% 231.16/42.34  | | | 
% 231.16/42.34  | | | COMBINE_EQS: (49), (142) imply:
% 231.16/42.34  | | |   (143)  e3 = e0
% 231.16/42.34  | | | 
% 231.16/42.34  | | | SIMP: (143) implies:
% 231.16/42.34  | | |   (144)  e3 = e0
% 231.16/42.34  | | | 
% 231.16/42.34  | | | COMBINE_EQS: (67), (144) imply:
% 231.16/42.34  | | |   (145)  all_57_5 = e0
% 231.16/42.34  | | | 
% 231.16/42.34  | | | REF_CLOSE: (10), (17), (19), (20), (44), (49), (51), (56), (73), (78),
% 231.16/42.34  | | |            (98), (99), (107), (113), (145) are inconsistent by sub-proof
% 231.16/42.34  | | |            #1689.
% 231.16/42.34  | | | 
% 231.16/42.34  | | End of split
% 231.16/42.34  | | 
% 231.16/42.34  | Case 2:
% 231.16/42.34  | | 
% 231.16/42.34  | |   (146)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 231.16/42.34  | |            e3)
% 231.16/42.34  | | 
% 231.16/42.34  | | BETA: splitting (146) gives:
% 231.16/42.34  | | 
% 231.16/42.34  | | Case 1:
% 231.16/42.34  | | | 
% 231.16/42.34  | | |   (147)  all_57_7 = e3 & op(e1, e2) = e3
% 231.16/42.34  | | | 
% 231.16/42.34  | | | REF_CLOSE: (3), (9), (10), (11), (12), (15), (17), (19), (20), (21), (26),
% 231.16/42.34  | | |            (27), (29), (33), (34), (36), (37), (43), (44), (47), (49),
% 231.16/42.34  | | |            (50), (51), (56), (57), (58), (60), (61), (71), (73), (78),
% 231.16/42.34  | | |            (80), (81), (83), (86), (91), (97), (98), (99), (107), (112),
% 231.16/42.34  | | |            (113), (117), (118), (121), (127), (129), (147) are
% 231.16/42.34  | | |            inconsistent by sub-proof #1365.
% 231.16/42.34  | | | 
% 231.16/42.34  | | Case 2:
% 231.16/42.34  | | | 
% 231.16/42.34  | | |   (148)  all_57_13 = e3 & op(e0, e2) = e3
% 231.16/42.34  | | | 
% 231.16/42.34  | | | REF_CLOSE: (51), (75), (148) are inconsistent by sub-proof #1358.
% 231.16/42.34  | | | 
% 231.16/42.34  | | End of split
% 231.16/42.34  | | 
% 231.16/42.34  | End of split
% 231.16/42.34  | 
% 231.16/42.34  End of proof
% 231.16/42.34  
% 231.16/42.34  Sub-proof #1358 shows that the following formulas are inconsistent:
% 231.16/42.34  ----------------------------------------------------------------
% 231.16/42.34    (1)  all_57_13 = e3 & op(e0, e2) = e3
% 231.16/42.34    (2)  all_57_13 = e2
% 231.16/42.34    (3)   ~ (e3 = e2)
% 231.16/42.34  
% 231.16/42.34  Begin of proof
% 231.16/42.34  | 
% 231.16/42.34  | ALPHA: (1) implies:
% 231.16/42.34  |   (4)  all_57_13 = e3
% 231.16/42.34  | 
% 231.16/42.34  | COMBINE_EQS: (2), (4) imply:
% 231.16/42.34  |   (5)  e3 = e2
% 231.16/42.34  | 
% 231.16/42.34  | REDUCE: (3), (5) imply:
% 231.16/42.34  |   (6)  $false
% 231.16/42.34  | 
% 231.16/42.34  | CLOSE: (6) is inconsistent.
% 231.16/42.34  | 
% 231.16/42.34  End of proof
% 231.16/42.34  
% 231.16/42.34  Sub-proof #1359 shows that the following formulas are inconsistent:
% 231.16/42.34  ----------------------------------------------------------------
% 231.16/42.34    (1)   ~ (all_10_2 = e2)
% 231.16/42.34    (2)  all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 231.16/42.34    (3)  op(e3, e3) = all_10_2
% 231.16/42.34    (4)  op(e0, e1) = all_53_11
% 231.16/42.34    (5)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 231.16/42.34    (6)  all_57_9 = e2
% 231.16/42.34    (7)   ~ (all_53_6 = all_53_14)
% 231.16/42.34    (8)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 231.16/42.34    (9)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.16/42.34         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.16/42.34    (10)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.16/42.34          (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.16/42.34    (11)   ~ (all_53_8 = all_53_12)
% 231.16/42.34    (12)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.16/42.34          (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.16/42.34    (13)   ~ (all_53_8 = all_53_11)
% 231.16/42.34    (14)   ~ (e3 = e1)
% 231.16/42.34    (15)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 231.16/42.34          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.16/42.34    (16)   ~ (all_53_13 = e1)
% 231.16/42.34    (17)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.16/42.34            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.16/42.34    (18)  all_55_0 = all_10_2
% 231.16/42.34    (19)   ~ (all_10_2 = e0)
% 231.16/42.34    (20)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.16/42.34          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.16/42.34    (21)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 231.16/42.34            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 231.16/42.34              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 231.16/42.34    (22)   ~ (all_6_2 = e3)
% 231.16/42.34    (23)  op(e1, e1) = all_6_2
% 231.16/42.34    (24)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 231.16/42.34    (25)  op(all_52_7, all_52_7) = e0
% 231.16/42.34    (26)   ~ (all_53_9 = e0)
% 231.16/42.34    (27)  all_55_0 = e3 | all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 231.16/42.34    (28)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 231.16/42.34    (29)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.16/42.34          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.16/42.34    (30)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 231.16/42.34    (31)  all_55_9 = all_53_6
% 231.16/42.34    (32)   ~ (all_53_11 = all_6_2)
% 231.16/42.34    (33)   ~ (all_53_4 = all_53_12)
% 231.16/42.34    (34)   ~ (all_53_8 = e3)
% 231.16/42.34    (35)   ~ (all_53_8 = all_53_9)
% 231.16/42.34    (36)  all_42_2 = all_6_2
% 231.16/42.34    (37)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.16/42.34          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.16/42.34    (38)  op(e2, e2) = e0
% 231.16/42.34    (39)   ~ (all_53_9 = all_53_11)
% 231.16/42.34    (40)   ~ (all_53_9 = all_6_2)
% 231.16/42.34    (41)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.16/42.34          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.16/42.34    (42)   ~ (all_53_14 = all_6_2)
% 231.16/42.34    (43)  all_57_3 = e0
% 231.16/42.34    (44)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.16/42.34          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.16/42.34    (45)   ~ (e3 = e2)
% 231.16/42.34    (46)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 231.16/42.34    (47)  all_55_1 = all_53_4
% 231.16/42.34    (48)  op(e1, e0) = all_53_14
% 231.16/42.34    (49)   ~ (all_53_6 = all_53_7)
% 231.16/42.34    (50)   ~ (e3 = e0)
% 231.16/42.34    (51)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.16/42.34          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.16/42.34    (52)  op(e3, e3) = e3
% 231.16/42.34    (53)   ~ (all_53_8 = all_6_2)
% 231.16/42.34    (54)  all_55_2 = all_53_8
% 231.16/42.34    (55)   ~ (all_53_4 = all_53_7)
% 231.16/42.34    (56)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 231.16/42.34    (57)   ~ (all_53_7 = e0)
% 231.16/42.34    (58)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.16/42.34          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.16/42.34            e1)
% 231.16/42.34    (59)   ~ (all_53_4 = all_53_8)
% 231.16/42.34    (60)  all_55_6 = all_53_9
% 231.16/42.34    (61)  op(e3, e2) = all_53_4
% 231.16/42.34    (62)   ~ (e2 = e0)
% 231.16/42.34    (63)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 231.16/42.34            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 231.16/42.34            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 231.16/42.34            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 231.16/42.34              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 231.16/42.34            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 231.16/42.34            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 231.16/42.34              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 231.16/42.34              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 231.16/42.34            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 231.16/42.34            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 231.16/42.34            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 231.16/42.34              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 231.16/42.34              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 231.16/42.34            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 231.16/42.34              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 231.16/42.34            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 231.16/42.34            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 231.16/42.34              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 231.16/42.34              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 231.16/42.34            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 231.16/42.34            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 231.16/42.34    (64)  all_57_13 = e2
% 231.16/42.34    (65)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 231.16/42.34          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.16/42.34    (66)   ~ (all_53_2 = all_53_14)
% 231.16/42.34    (67)   ~ (e1 = e0)
% 231.16/42.34    (68)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 231.16/42.34            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 231.16/42.34              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 231.16/42.34    (69)   ~ (all_53_4 = e0)
% 231.16/42.34    (70)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.16/42.34          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.16/42.34    (71)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.16/42.34          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.16/42.34    (72)   ~ (all_10_2 = e1)
% 231.16/42.34    (73)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 231.16/42.34    (74)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.16/42.34          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 231.16/42.34            e3)
% 231.16/42.34    (75)   ~ (all_53_4 = all_53_6)
% 231.16/42.34    (76)  op(e0, e2) = all_53_7
% 231.16/42.34    (77)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.16/42.34          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.16/42.34            e2)
% 231.16/42.34    (78)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.16/42.34              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.16/42.34                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.16/42.34                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.16/42.34    (79)  all_55_10 = all_6_2
% 231.16/42.34    (80)   ~ (all_53_6 = all_6_2)
% 231.16/42.34    (81)   ~ (all_53_13 = e0)
% 231.16/42.34    (82)  all_57_11 = e3
% 231.16/42.34    (83)  all_55_13 = all_53_7
% 231.16/42.34    (84)  op(e0, e0) = e1
% 231.16/42.34    (85)  op(e2, e0) = all_53_13
% 231.16/42.34    (86)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.16/42.34          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.16/42.34    (87)  all_38_2 = all_6_2
% 231.16/42.34    (88)  all_55_11 = all_53_14
% 231.16/42.34    (89)  all_55_3 = all_53_12
% 231.16/42.34    (90)   ~ (all_53_12 = e3)
% 231.16/42.34    (91)  all_57_0 = e3
% 231.16/42.34    (92)  op(e1, e3) = all_53_2
% 231.16/42.34    (93)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 231.16/42.34            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 231.16/42.34              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 231.16/42.34    (94)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.16/42.34          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.16/42.34    (95)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 231.16/42.34          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 231.16/42.34    (96)  all_57_1 = e3
% 231.16/42.34    (97)   ~ (all_53_12 = all_10_2)
% 231.16/42.34    (98)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 231.16/42.34          (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 231.16/42.34    (99)   ~ (all_53_13 = all_53_14)
% 231.16/42.34    (100)   ~ (e2 = e1)
% 231.16/42.34    (101)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.16/42.34           | (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.16/42.34             e2)
% 231.16/42.34    (102)  op(e2, e1) = all_53_9
% 231.16/42.34    (103)  op(e1, e2) = all_53_6
% 231.16/42.34    (104)   ~ (all_6_2 = e0)
% 231.16/42.34    (105)   ~ (all_53_2 = all_53_6)
% 231.16/42.34    (106)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.16/42.34           (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.16/42.34    (107)  all_24_2 = all_6_2
% 231.16/42.34    (108)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.16/42.34           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.16/42.34    (109)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.16/42.34           (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.16/42.34    (110)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.16/42.34           | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.16/42.34             e1)
% 231.16/42.34    (111)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 231.16/42.34           (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 231.16/42.34    (112)   ~ (all_53_12 = all_53_14)
% 231.16/42.34    (113)  all_55_14 = all_53_11
% 231.16/42.34    (114)  op(e3, e0) = all_52_7
% 231.16/42.34    (115)  op(e3, e1) = all_53_8
% 231.16/42.34    (116)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.16/42.34           (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.16/42.34    (117)   ~ (all_53_4 = e3)
% 231.16/42.34    (118)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 231.16/42.34           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 231.16/42.34    (119)  op(e3, e0) = all_53_12
% 231.16/42.34  
% 231.16/42.34  Begin of proof
% 231.16/42.34  | 
% 231.16/42.34  | BETA: splitting (116) gives:
% 231.16/42.34  | 
% 231.16/42.34  | Case 1:
% 231.16/42.34  | | 
% 231.16/42.34  | |   (120)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) =
% 231.16/42.34  | |            e1)
% 231.16/42.34  | | 
% 231.16/42.34  | | BETA: splitting (120) gives:
% 231.16/42.34  | | 
% 231.16/42.34  | | Case 1:
% 231.16/42.34  | | | 
% 231.16/42.34  | | |   (121)  all_57_1 = e1 & op(e3, e2) = e1
% 231.16/42.34  | | | 
% 231.16/42.34  | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 231.16/42.34  | | |            (14), (15), (17), (18), (19), (20), (21), (22), (23), (24),
% 231.16/42.34  | | |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 231.16/42.34  | | |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 231.16/42.34  | | |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (55),
% 231.16/42.34  | | |            (56), (57), (58), (59), (60), (61), (62), (63), (65), (66),
% 231.16/42.34  | | |            (67), (68), (69), (70), (71), (72), (73), (74), (75), (76),
% 231.16/42.34  | | |            (77), (78), (79), (80), (81), (82), (83), (84), (85), (86),
% 231.16/42.34  | | |            (87), (88), (89), (90), (91), (92), (93), (94), (95), (96),
% 231.16/42.34  | | |            (97), (98), (99), (100), (101), (102), (103), (104), (105),
% 231.16/42.34  | | |            (106), (107), (108), (109), (110), (111), (112), (113), (115),
% 231.16/42.34  | | |            (116), (117), (118), (119), (121) are inconsistent by sub-proof
% 231.16/42.34  | | |            #1360.
% 231.16/42.34  | | | 
% 231.16/42.34  | | Case 2:
% 231.16/42.34  | | | 
% 231.16/42.34  | | |   (122)  all_57_3 = e1 & op(e2, e2) = e1
% 231.16/42.34  | | | 
% 231.16/42.34  | | | ALPHA: (122) implies:
% 231.16/42.34  | | |   (123)  op(e2, e2) = e1
% 231.16/42.34  | | | 
% 231.16/42.34  | | | REF_CLOSE: (17), (38), (67), (123) are inconsistent by sub-proof #2352.
% 231.16/42.34  | | | 
% 231.16/42.34  | | End of split
% 231.16/42.34  | | 
% 231.16/42.34  | Case 2:
% 231.16/42.34  | | 
% 231.16/42.34  | |   (124)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 231.16/42.34  | |            e1)
% 231.16/42.34  | | 
% 231.16/42.34  | | BETA: splitting (124) gives:
% 231.16/42.34  | | 
% 231.16/42.34  | | Case 1:
% 231.16/42.34  | | | 
% 231.16/42.34  | | |   (125)  all_57_7 = e1 & op(e1, e2) = e1
% 231.16/42.34  | | | 
% 231.16/42.34  | | | ALPHA: (125) implies:
% 231.16/42.34  | | |   (126)  all_57_7 = e1
% 231.16/42.34  | | | 
% 231.16/42.34  | | | BETA: splitting (44) gives:
% 231.16/42.34  | | | 
% 231.16/42.34  | | | Case 1:
% 231.16/42.34  | | | | 
% 231.16/42.34  | | | |   (127)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1)
% 231.16/42.34  | | | |            = e0)
% 231.16/42.34  | | | | 
% 231.16/42.34  | | | | BETA: splitting (127) gives:
% 231.16/42.34  | | | | 
% 231.16/42.34  | | | | Case 1:
% 231.16/42.34  | | | | | 
% 231.16/42.34  | | | | |   (128)  all_57_4 = e0 & op(e3, e1) = e0
% 231.16/42.34  | | | | | 
% 231.16/42.34  | | | | | ALPHA: (128) implies:
% 231.16/42.34  | | | | |   (129)  all_57_4 = e0
% 231.16/42.34  | | | | |   (130)  op(e3, e1) = e0
% 231.16/42.34  | | | | | 
% 231.16/42.34  | | | | | BETA: splitting (29) gives:
% 231.16/42.34  | | | | | 
% 231.16/42.34  | | | | | Case 1:
% 231.16/42.34  | | | | | | 
% 231.16/42.34  | | | | | |   (131)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3,
% 231.16/42.34  | | | | | |              e2) = e1)
% 231.16/42.34  | | | | | | 
% 231.16/42.34  | | | | | | BETA: splitting (131) gives:
% 231.16/42.34  | | | | | | 
% 231.16/42.34  | | | | | | Case 1:
% 231.16/42.34  | | | | | | | 
% 231.16/42.34  | | | | | | |   (132)  all_57_0 = e1 & op(e3, e3) = e1
% 231.16/42.34  | | | | | | | 
% 231.16/42.34  | | | | | | | ALPHA: (132) implies:
% 231.16/42.34  | | | | | | |   (133)  op(e3, e3) = e1
% 231.16/42.34  | | | | | | | 
% 231.16/42.34  | | | | | | | REF_CLOSE: (14), (17), (52), (133) are inconsistent by sub-proof
% 231.16/42.34  | | | | | | |            #2495.
% 231.16/42.34  | | | | | | | 
% 231.16/42.34  | | | | | | Case 2:
% 231.16/42.34  | | | | | | | 
% 231.16/42.34  | | | | | | |   (134)  all_57_1 = e1 & op(e3, e2) = e1
% 231.16/42.34  | | | | | | | 
% 231.16/42.34  | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11),
% 231.16/42.34  | | | | | | |            (12), (13), (14), (15), (17), (18), (19), (20), (21),
% 231.16/42.34  | | | | | | |            (22), (23), (24), (26), (27), (28), (29), (30), (31),
% 231.16/42.34  | | | | | | |            (32), (33), (34), (35), (36), (37), (38), (39), (40),
% 231.16/42.34  | | | | | | |            (41), (42), (43), (44), (45), (46), (47), (48), (49),
% 231.16/42.34  | | | | | | |            (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 231.16/42.34  | | | | | | |            (59), (60), (61), (62), (63), (65), (66), (67), (68),
% 231.16/42.34  | | | | | | |            (69), (70), (71), (72), (73), (74), (75), (76), (77),
% 231.16/42.34  | | | | | | |            (78), (79), (80), (81), (82), (83), (84), (85), (86),
% 231.16/42.34  | | | | | | |            (87), (88), (89), (90), (91), (92), (93), (94), (95),
% 231.16/42.34  | | | | | | |            (96), (97), (98), (99), (100), (101), (102), (103),
% 231.16/42.34  | | | | | | |            (104), (105), (106), (107), (108), (109), (110), (111),
% 231.16/42.34  | | | | | | |            (112), (113), (115), (116), (117), (118), (119), (134)
% 231.16/42.34  | | | | | | |            are inconsistent by sub-proof #1360.
% 231.16/42.34  | | | | | | | 
% 231.16/42.34  | | | | | | End of split
% 231.16/42.34  | | | | | | 
% 231.16/42.34  | | | | | Case 2:
% 231.16/42.34  | | | | | | 
% 231.16/42.34  | | | | | |   (135)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3,
% 231.16/42.34  | | | | | |              e0) = e1)
% 231.16/42.34  | | | | | | 
% 231.16/42.34  | | | | | | BETA: splitting (135) gives:
% 231.16/42.34  | | | | | | 
% 231.16/42.34  | | | | | | Case 1:
% 231.16/42.34  | | | | | | | 
% 231.16/42.34  | | | | | | |   (136)  all_57_4 = e1 & op(e3, e1) = e1
% 231.16/42.34  | | | | | | | 
% 231.16/42.34  | | | | | | | ALPHA: (136) implies:
% 231.16/42.34  | | | | | | |   (137)  all_57_4 = e1
% 231.16/42.34  | | | | | | | 
% 231.16/42.34  | | | | | | | COMBINE_EQS: (129), (137) imply:
% 231.16/42.34  | | | | | | |   (138)  e1 = e0
% 231.16/42.34  | | | | | | | 
% 231.16/42.34  | | | | | | | SIMP: (138) implies:
% 231.16/42.34  | | | | | | |   (139)  e1 = e0
% 231.16/42.34  | | | | | | | 
% 231.16/42.34  | | | | | | | COMBINE_EQS: (126), (139) imply:
% 231.16/42.34  | | | | | | |   (140)  all_57_7 = e0
% 231.16/42.34  | | | | | | | 
% 231.16/42.34  | | | | | | | REF_CLOSE: (14), (17), (38), (64), (67), (96), (100), (116), (140)
% 231.16/42.34  | | | | | | |            are inconsistent by sub-proof #2204.
% 231.16/42.34  | | | | | | | 
% 231.16/42.34  | | | | | | Case 2:
% 231.16/42.34  | | | | | | | 
% 231.16/42.34  | | | | | | |   (141)  all_57_9 = e1 & op(e3, e0) = e1
% 231.16/42.34  | | | | | | | 
% 231.16/42.34  | | | | | | | ALPHA: (141) implies:
% 231.16/42.34  | | | | | | |   (142)  all_57_9 = e1
% 231.16/42.34  | | | | | | | 
% 231.16/42.34  | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11),
% 231.16/42.34  | | | | | | |            (12), (13), (14), (15), (17), (18), (19), (20), (21),
% 231.16/42.34  | | | | | | |            (22), (23), (24), (26), (27), (28), (29), (30), (31),
% 231.16/42.34  | | | | | | |            (32), (33), (34), (35), (36), (37), (38), (39), (40),
% 231.16/42.34  | | | | | | |            (41), (42), (43), (44), (45), (46), (47), (48), (49),
% 231.16/42.34  | | | | | | |            (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 231.16/42.34  | | | | | | |            (59), (60), (61), (62), (63), (65), (66), (67), (68),
% 231.16/42.34  | | | | | | |            (69), (70), (71), (72), (73), (74), (75), (76), (77),
% 231.16/42.34  | | | | | | |            (78), (79), (80), (81), (83), (84), (85), (86), (87),
% 231.16/42.34  | | | | | | |            (88), (89), (90), (91), (92), (93), (94), (95), (97),
% 231.16/42.34  | | | | | | |            (98), (99), (100), (101), (102), (103), (105), (106),
% 231.16/42.34  | | | | | | |            (107), (108), (109), (110), (111), (112), (113), (115),
% 231.16/42.34  | | | | | | |            (116), (117), (118), (119), (129), (130), (142) are
% 231.16/42.34  | | | | | | |            inconsistent by sub-proof #1385.
% 231.16/42.34  | | | | | | | 
% 231.16/42.34  | | | | | | End of split
% 231.16/42.34  | | | | | | 
% 231.16/42.34  | | | | | End of split
% 231.16/42.34  | | | | | 
% 231.16/42.34  | | | | Case 2:
% 231.16/42.34  | | | | | 
% 231.16/42.34  | | | | |   (143)  all_57_5 = e0 & op(e2, e1) = e0
% 231.16/42.34  | | | | | 
% 231.16/42.34  | | | | | ALPHA: (143) implies:
% 231.16/42.34  | | | | |   (144)  all_57_5 = e0
% 231.16/42.34  | | | | | 
% 231.16/42.34  | | | | | REF_CLOSE: (9), (14), (16), (17), (38), (43), (45), (50), (62), (67),
% 231.16/42.34  | | | | |            (85), (86), (94), (100), (144) are inconsistent by
% 231.16/42.34  | | | | |            sub-proof #1689.
% 231.16/42.34  | | | | | 
% 231.16/42.34  | | | | End of split
% 231.16/42.34  | | | | 
% 231.16/42.34  | | | Case 2:
% 231.16/42.34  | | | | 
% 231.16/42.34  | | | |   (145)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0,
% 231.16/42.34  | | | |              e1) = e0)
% 231.16/42.34  | | | | 
% 231.16/42.34  | | | | REF_CLOSE: (14), (17), (22), (23), (25), (29), (37), (41), (45), (50),
% 231.16/42.34  | | | |            (51), (52), (61), (62), (67), (69), (70), (84), (100), (104),
% 231.16/42.34  | | | |            (108), (114), (145) are inconsistent by sub-proof #1366.
% 231.16/42.34  | | | | 
% 231.16/42.34  | | | End of split
% 231.16/42.34  | | | 
% 231.16/42.34  | | Case 2:
% 231.16/42.34  | | | 
% 231.16/42.34  | | |   (146)  all_57_13 = e1 & op(e0, e2) = e1
% 231.16/42.34  | | | 
% 231.16/42.34  | | | ALPHA: (146) implies:
% 231.16/42.34  | | |   (147)  all_57_13 = e1
% 231.16/42.34  | | | 
% 231.16/42.34  | | | COMBINE_EQS: (64), (147) imply:
% 231.16/42.34  | | |   (148)  e2 = e1
% 231.16/42.34  | | | 
% 231.16/42.34  | | | SIMP: (148) implies:
% 231.16/42.34  | | |   (149)  e2 = e1
% 231.16/42.34  | | | 
% 231.16/42.34  | | | COMBINE_EQS: (6), (149) imply:
% 231.16/42.34  | | |   (150)  all_57_9 = e1
% 231.16/42.34  | | | 
% 231.16/42.34  | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 231.16/42.34  | | |            (14), (15), (17), (18), (19), (20), (21), (22), (23), (24),
% 231.16/42.34  | | |            (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 231.16/42.34  | | |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 231.16/42.34  | | |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (55),
% 231.16/42.34  | | |            (56), (57), (58), (59), (60), (61), (62), (63), (65), (66),
% 231.16/42.34  | | |            (67), (68), (69), (70), (71), (72), (73), (74), (75), (76),
% 231.16/42.34  | | |            (77), (78), (79), (80), (81), (83), (84), (85), (86), (87),
% 231.16/42.34  | | |            (88), (89), (90), (91), (92), (93), (94), (95), (97), (98),
% 231.16/42.34  | | |            (99), (100), (101), (102), (103), (105), (106), (107), (108),
% 231.16/42.34  | | |            (109), (110), (111), (112), (113), (115), (116), (117), (118),
% 231.16/42.34  | | |            (119), (150) are inconsistent by sub-proof #1384.
% 231.16/42.34  | | | 
% 231.16/42.34  | | End of split
% 231.16/42.34  | | 
% 231.16/42.34  | End of split
% 231.16/42.34  | 
% 231.16/42.34  End of proof
% 231.16/42.34  
% 231.16/42.34  Sub-proof #1360 shows that the following formulas are inconsistent:
% 231.16/42.34  ----------------------------------------------------------------
% 231.16/42.34    (1)   ~ (all_10_2 = e2)
% 231.16/42.34    (2)  all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 231.16/42.34    (3)  op(e3, e3) = all_10_2
% 231.16/42.34    (4)  op(e0, e1) = all_53_11
% 231.16/42.34    (5)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 231.16/42.35    (6)   ~ (all_53_6 = all_53_14)
% 231.16/42.35    (7)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 231.16/42.35    (8)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.16/42.35         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.16/42.35    (9)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.16/42.35         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.16/42.35    (10)   ~ (all_53_8 = all_53_12)
% 231.16/42.35    (11)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.16/42.35          (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.16/42.35    (12)   ~ (all_53_8 = all_53_11)
% 231.16/42.35    (13)   ~ (e3 = e1)
% 231.16/42.35    (14)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 231.16/42.35          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.16/42.35    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.16/42.35            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.16/42.35    (16)  all_55_0 = all_10_2
% 231.16/42.35    (17)   ~ (all_10_2 = e0)
% 231.16/42.35    (18)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.16/42.35          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.16/42.35    (19)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 231.16/42.35            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 231.16/42.35              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 231.16/42.35    (20)   ~ (all_6_2 = e3)
% 231.16/42.35    (21)  op(e1, e1) = all_6_2
% 231.16/42.35    (22)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 231.16/42.35    (23)   ~ (all_53_9 = e0)
% 231.16/42.35    (24)  all_55_0 = e3 | all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 231.16/42.35    (25)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 231.16/42.35    (26)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.16/42.35          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.16/42.35    (27)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 231.16/42.35    (28)  all_55_9 = all_53_6
% 231.16/42.35    (29)   ~ (all_53_11 = all_6_2)
% 231.16/42.35    (30)   ~ (all_53_4 = all_53_12)
% 231.16/42.35    (31)  all_57_1 = e1 & op(e3, e2) = e1
% 231.16/42.35    (32)   ~ (all_53_8 = e3)
% 231.16/42.35    (33)   ~ (all_53_8 = all_53_9)
% 231.16/42.35    (34)  all_42_2 = all_6_2
% 231.16/42.35    (35)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.16/42.35          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.16/42.35    (36)  op(e2, e2) = e0
% 231.16/42.35    (37)   ~ (all_53_9 = all_53_11)
% 231.16/42.35    (38)   ~ (all_53_9 = all_6_2)
% 231.16/42.35    (39)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.16/42.35          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.16/42.35    (40)   ~ (all_53_14 = all_6_2)
% 231.16/42.35    (41)  all_57_3 = e0
% 231.16/42.35    (42)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.16/42.35          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.16/42.35    (43)   ~ (e3 = e2)
% 231.16/42.35    (44)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 231.16/42.35    (45)  all_55_1 = all_53_4
% 231.16/42.35    (46)  op(e1, e0) = all_53_14
% 231.16/42.35    (47)   ~ (all_53_6 = all_53_7)
% 231.16/42.35    (48)   ~ (e3 = e0)
% 231.16/42.35    (49)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.16/42.35          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.16/42.35    (50)  op(e3, e3) = e3
% 231.16/42.35    (51)   ~ (all_53_8 = all_6_2)
% 231.16/42.35    (52)  all_55_2 = all_53_8
% 231.16/42.35    (53)   ~ (all_53_4 = all_53_7)
% 231.16/42.35    (54)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 231.16/42.35    (55)   ~ (all_53_7 = e0)
% 231.16/42.35    (56)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.16/42.35          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.16/42.35            e1)
% 231.16/42.35    (57)   ~ (all_53_4 = all_53_8)
% 231.16/42.35    (58)  all_55_6 = all_53_9
% 231.16/42.35    (59)  op(e3, e2) = all_53_4
% 231.16/42.35    (60)   ~ (e2 = e0)
% 231.16/42.35    (61)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 231.16/42.35            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 231.16/42.35            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 231.16/42.35            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 231.16/42.35              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 231.16/42.35            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 231.16/42.35            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 231.16/42.35              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 231.16/42.35              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 231.16/42.35            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 231.16/42.35            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 231.16/42.35            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 231.16/42.35              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 231.16/42.35              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 231.16/42.35            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 231.16/42.35              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 231.16/42.35            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 231.16/42.35            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 231.16/42.35              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 231.16/42.35              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 231.16/42.35            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 231.16/42.35            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 231.16/42.35    (62)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 231.16/42.35          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.16/42.35    (63)   ~ (all_53_2 = all_53_14)
% 231.16/42.35    (64)   ~ (e1 = e0)
% 231.16/42.35    (65)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 231.16/42.35            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 231.16/42.35              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 231.16/42.35    (66)   ~ (all_53_4 = e0)
% 231.16/42.35    (67)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.16/42.35          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.16/42.35    (68)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.16/42.35          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.16/42.35    (69)   ~ (all_10_2 = e1)
% 231.16/42.35    (70)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 231.16/42.35    (71)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.16/42.35          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 231.16/42.35            e3)
% 231.16/42.35    (72)   ~ (all_53_4 = all_53_6)
% 231.16/42.35    (73)  op(e0, e2) = all_53_7
% 231.16/42.35    (74)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.16/42.35          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.16/42.35            e2)
% 231.16/42.35    (75)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.16/42.35              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.16/42.35                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.16/42.35                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.16/42.35    (76)  all_55_10 = all_6_2
% 231.16/42.35    (77)   ~ (all_53_6 = all_6_2)
% 231.16/42.35    (78)   ~ (all_53_13 = e0)
% 231.16/42.35    (79)  all_57_11 = e3
% 231.16/42.35    (80)  all_55_13 = all_53_7
% 231.16/42.35    (81)  op(e0, e0) = e1
% 231.16/42.35    (82)  op(e2, e0) = all_53_13
% 231.16/42.35    (83)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.16/42.35          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.16/42.35    (84)  all_38_2 = all_6_2
% 231.16/42.35    (85)  all_55_11 = all_53_14
% 231.16/42.35    (86)  all_55_3 = all_53_12
% 231.16/42.35    (87)   ~ (all_53_12 = e3)
% 231.16/42.35    (88)  all_57_0 = e3
% 231.16/42.35    (89)  op(e1, e3) = all_53_2
% 231.16/42.35    (90)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 231.16/42.35            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 231.16/42.35              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 231.16/42.35    (91)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.16/42.35          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.16/42.35    (92)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 231.16/42.35          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 231.16/42.35    (93)  all_57_1 = e3
% 231.16/42.35    (94)   ~ (all_53_12 = all_10_2)
% 231.16/42.35    (95)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 231.16/42.35          (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 231.16/42.35    (96)   ~ (all_53_13 = all_53_14)
% 231.16/42.35    (97)   ~ (e2 = e1)
% 231.16/42.35    (98)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.16/42.35          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.16/42.35    (99)  op(e2, e1) = all_53_9
% 231.16/42.35    (100)  op(e1, e2) = all_53_6
% 231.16/42.35    (101)   ~ (all_6_2 = e0)
% 231.16/42.35    (102)   ~ (all_53_2 = all_53_6)
% 231.16/42.35    (103)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.16/42.35           (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.16/42.35    (104)  all_24_2 = all_6_2
% 231.16/42.35    (105)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.16/42.35           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.16/42.35    (106)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.16/42.35           (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.16/42.35    (107)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.16/42.35           | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.16/42.35             e1)
% 231.16/42.35    (108)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 231.16/42.35           (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 231.16/42.35    (109)   ~ (all_53_12 = all_53_14)
% 231.16/42.35    (110)  all_55_14 = all_53_11
% 231.16/42.35    (111)  op(e3, e1) = all_53_8
% 231.16/42.35    (112)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.16/42.35           (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.16/42.35    (113)   ~ (all_53_4 = e3)
% 231.16/42.35    (114)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 231.16/42.35           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 231.16/42.35    (115)  op(e3, e0) = all_53_12
% 231.16/42.35  
% 231.16/42.35  Begin of proof
% 231.16/42.35  | 
% 231.16/42.35  | ALPHA: (31) implies:
% 231.16/42.35  |   (116)  all_57_1 = e1
% 231.16/42.35  | 
% 231.16/42.35  | COMBINE_EQS: (93), (116) imply:
% 231.16/42.35  |   (117)  e3 = e1
% 231.16/42.35  | 
% 231.16/42.35  | COMBINE_EQS: (79), (117) imply:
% 231.16/42.35  |   (118)  all_57_11 = e1
% 231.16/42.35  | 
% 231.16/42.35  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 231.16/42.35  |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 231.16/42.35  |            (24), (25), (26), (27), (28), (29), (30), (32), (33), (34), (35),
% 231.16/42.35  |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 231.16/42.35  |            (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 231.16/42.35  |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68),
% 231.16/42.35  |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (80),
% 231.16/42.35  |            (81), (82), (83), (84), (85), (86), (87), (88), (89), (90), (91),
% 231.16/42.35  |            (92), (94), (95), (96), (97), (98), (99), (100), (101), (102),
% 231.16/42.35  |            (103), (104), (105), (106), (107), (108), (109), (110), (111),
% 231.16/42.35  |            (112), (113), (114), (115), (118) are inconsistent by sub-proof
% 231.16/42.35  |            #1373.
% 231.16/42.35  | 
% 231.16/42.35  End of proof
% 231.16/42.35  
% 231.16/42.35  Sub-proof #1361 shows that the following formulas are inconsistent:
% 231.16/42.35  ----------------------------------------------------------------
% 231.16/42.35    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.16/42.35         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.16/42.35    (2)   ~ (e3 = e1)
% 231.16/42.35    (3)   ~ (all_53_13 = e1)
% 231.16/42.35    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.16/42.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.16/42.35    (5)   ~ (all_6_2 = e3)
% 231.16/42.35    (6)  op(e1, e1) = all_6_2
% 231.16/42.35    (7)  op(all_52_7, all_52_7) = e0
% 231.16/42.35    (8)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.16/42.35         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.16/42.35    (9)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.16/42.35         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.16/42.35    (10)  op(e2, e2) = e0
% 231.16/42.35    (11)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.16/42.35          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.16/42.35    (12)  all_57_3 = e0
% 231.16/42.35    (13)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.16/42.35          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.16/42.35    (14)   ~ (e3 = e2)
% 231.16/42.35    (15)   ~ (e3 = e0)
% 231.16/42.35    (16)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.16/42.35          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.16/42.35    (17)  op(e3, e3) = e3
% 231.16/42.35    (18)  op(e3, e2) = all_53_4
% 231.16/42.35    (19)   ~ (e2 = e0)
% 231.16/42.35    (20)   ~ (e1 = e0)
% 231.16/42.35    (21)   ~ (all_53_4 = e0)
% 231.16/42.35    (22)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.16/42.35          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.16/42.35    (23)  all_57_4 = e2 & op(e3, e1) = e2
% 231.16/42.35    (24)  op(e0, e0) = e1
% 231.16/42.35    (25)  op(e2, e0) = all_53_13
% 231.16/42.35    (26)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.16/42.35          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.16/42.35    (27)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.16/42.35          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.16/42.35    (28)   ~ (e2 = e1)
% 231.16/42.35    (29)   ~ (all_6_2 = e0)
% 231.16/42.35    (30)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.16/42.35          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.16/42.35    (31)  op(e3, e0) = all_52_7
% 231.16/42.35  
% 231.16/42.35  Begin of proof
% 231.16/42.35  | 
% 231.16/42.35  | ALPHA: (23) implies:
% 231.16/42.35  |   (32)  all_57_4 = e2
% 231.16/42.35  | 
% 231.16/42.35  | BETA: splitting (13) gives:
% 231.16/42.35  | 
% 231.16/42.35  | Case 1:
% 231.16/42.35  | | 
% 231.16/42.35  | |   (33)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) =
% 231.16/42.35  | |           e0)
% 231.16/42.35  | | 
% 231.16/42.35  | | REF_CLOSE: (1), (2), (3), (4), (10), (12), (14), (15), (19), (20), (25),
% 231.16/42.35  | |            (26), (27), (28), (32), (33) are inconsistent by sub-proof #1362.
% 231.16/42.35  | | 
% 231.16/42.35  | Case 2:
% 231.16/42.35  | | 
% 231.16/42.35  | |   (34)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 231.16/42.35  | |           e0)
% 231.16/42.35  | | 
% 231.16/42.35  | | BETA: splitting (34) gives:
% 231.16/42.35  | | 
% 231.16/42.35  | | Case 1:
% 231.16/42.35  | | | 
% 231.16/42.35  | | |   (35)  all_57_8 = e0 & op(e1, e1) = e0
% 231.16/42.35  | | | 
% 231.16/42.35  | | | REF_CLOSE: (4), (6), (29), (35) are inconsistent by sub-proof #2412.
% 231.16/42.35  | | | 
% 231.16/42.35  | | Case 2:
% 231.16/42.35  | | | 
% 231.16/42.35  | | |   (36)  all_57_14 = e0 & op(e0, e1) = e0
% 231.16/42.35  | | | 
% 231.16/42.35  | | | ALPHA: (36) implies:
% 231.16/42.35  | | |   (37)  all_57_14 = e0
% 231.16/42.35  | | | 
% 231.16/42.35  | | | REF_CLOSE: (2), (4), (5), (6), (7), (8), (9), (11), (14), (15), (16),
% 231.16/42.35  | | |            (17), (18), (19), (20), (21), (22), (24), (28), (30), (31),
% 231.16/42.35  | | |            (37) are inconsistent by sub-proof #1367.
% 231.16/42.35  | | | 
% 231.16/42.35  | | End of split
% 231.16/42.35  | | 
% 231.16/42.35  | End of split
% 231.16/42.35  | 
% 231.16/42.35  End of proof
% 231.16/42.35  
% 231.16/42.35  Sub-proof #1362 shows that the following formulas are inconsistent:
% 231.16/42.35  ----------------------------------------------------------------
% 231.16/42.35    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.16/42.35         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.16/42.35    (2)   ~ (e3 = e1)
% 231.16/42.35    (3)   ~ (all_53_13 = e1)
% 231.16/42.35    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.16/42.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.16/42.35    (5)  all_57_4 = e2
% 231.16/42.35    (6)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0)
% 231.16/42.35    (7)  op(e2, e2) = e0
% 231.16/42.35    (8)  all_57_3 = e0
% 231.16/42.35    (9)   ~ (e3 = e2)
% 231.16/42.35    (10)   ~ (e3 = e0)
% 231.16/42.35    (11)   ~ (e2 = e0)
% 231.16/42.35    (12)   ~ (e1 = e0)
% 231.16/42.35    (13)  op(e2, e0) = all_53_13
% 231.16/42.35    (14)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.16/42.35          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.16/42.35    (15)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.16/42.35          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.16/42.35    (16)   ~ (e2 = e1)
% 231.16/42.35  
% 231.16/42.35  Begin of proof
% 231.16/42.35  | 
% 231.16/42.35  | BETA: splitting (6) gives:
% 231.16/42.35  | 
% 231.16/42.35  | Case 1:
% 231.16/42.35  | | 
% 231.16/42.35  | |   (17)  all_57_4 = e0 & op(e3, e1) = e0
% 231.16/42.35  | | 
% 231.16/42.35  | | REF_CLOSE: (5), (11), (17) are inconsistent by sub-proof #2045.
% 231.16/42.35  | | 
% 231.16/42.35  | Case 2:
% 231.16/42.35  | | 
% 231.16/42.35  | |   (18)  all_57_5 = e0 & op(e2, e1) = e0
% 231.16/42.35  | | 
% 231.16/42.35  | | ALPHA: (18) implies:
% 231.16/42.35  | |   (19)  all_57_5 = e0
% 231.16/42.35  | | 
% 231.16/42.35  | | REF_CLOSE: (1), (2), (3), (4), (7), (8), (9), (10), (11), (12), (13), (14),
% 231.16/42.35  | |            (15), (16), (19) are inconsistent by sub-proof #1689.
% 231.16/42.35  | | 
% 231.16/42.35  | End of split
% 231.16/42.35  | 
% 231.16/42.35  End of proof
% 231.16/42.35  
% 231.16/42.35  Sub-proof #1363 shows that the following formulas are inconsistent:
% 231.16/42.35  ----------------------------------------------------------------
% 231.16/42.35    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.16/42.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.16/42.35    (2)  op(e2, e2) = e0
% 231.16/42.35    (3)   ~ (e3 = e2)
% 231.16/42.35    (4)   ~ (e3 = e0)
% 231.16/42.35    (5)  op(e3, e3) = all_52_1
% 231.16/42.35    (6)  op(all_52_1, all_52_1) = e3
% 231.16/42.35    (7)  all_57_1 = e3
% 231.16/42.35    (8)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2)
% 231.16/42.35  
% 231.16/42.35  Begin of proof
% 231.16/42.35  | 
% 231.16/42.35  | BETA: splitting (8) gives:
% 231.16/42.35  | 
% 231.16/42.35  | Case 1:
% 231.16/42.35  | | 
% 231.16/42.35  | |   (9)  all_57_0 = e2 & op(e3, e3) = e2
% 231.16/42.35  | | 
% 231.16/42.35  | | ALPHA: (9) implies:
% 231.16/42.35  | |   (10)  op(e3, e3) = e2
% 231.16/42.35  | | 
% 231.16/42.35  | | REF_CLOSE: (1), (2), (4), (5), (6), (10) are inconsistent by sub-proof
% 231.16/42.35  | |            #1653.
% 231.16/42.35  | | 
% 231.16/42.35  | Case 2:
% 231.16/42.35  | | 
% 231.16/42.35  | |   (11)  all_57_1 = e2 & op(e3, e2) = e2
% 231.16/42.35  | | 
% 231.16/42.35  | | REF_CLOSE: (3), (7), (11) are inconsistent by sub-proof #1809.
% 231.16/42.35  | | 
% 231.16/42.35  | End of split
% 231.16/42.35  | 
% 231.16/42.35  End of proof
% 231.16/42.35  
% 231.16/42.35  Sub-proof #1364 shows that the following formulas are inconsistent:
% 231.16/42.35  ----------------------------------------------------------------
% 231.16/42.35    (1)   ~ (all_53_2 = e2)
% 231.16/42.35    (2)   ~ (all_53_6 = e2)
% 231.16/42.35    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.16/42.35         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.16/42.35    (4)  op(e3, e1) = all_52_5
% 231.16/42.35    (5)   ~ (all_53_6 = e0)
% 231.16/42.35    (6)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.16/42.35         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.16/42.35    (7)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.16/42.35         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.16/42.35    (8)   ~ (e3 = e1)
% 231.16/42.35    (9)   ~ (all_53_13 = e1)
% 231.16/42.35    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.16/42.35            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.16/42.35    (11)  op(all_52_5, all_52_5) = e1
% 231.16/42.35    (12)   ~ (all_6_2 = e3)
% 231.16/42.35    (13)  op(e1, e1) = all_6_2
% 231.16/42.35    (14)  op(all_52_7, all_52_7) = e0
% 231.16/42.35    (15)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.16/42.35          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.16/42.35    (16)  all_55_9 = e1 | all_55_9 = e0
% 231.16/42.35    (17)  all_55_9 = all_53_6
% 231.16/42.35    (18)   ~ (all_53_2 = e3)
% 231.16/42.35    (19)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.16/42.35          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.16/42.35    (20)  op(e2, e2) = e0
% 231.16/42.35    (21)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.16/42.35          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.16/42.35    (22)  all_57_3 = e0
% 231.16/42.35    (23)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.16/42.35          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.16/42.35    (24)   ~ (e3 = e2)
% 231.16/42.36    (25)   ~ (e3 = e0)
% 231.16/42.36    (26)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.16/42.36          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.16/42.36    (27)  op(e3, e3) = e3
% 231.16/42.36    (28)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 231.16/42.36    (29)  op(e0, e3) = all_53_3
% 231.16/42.36    (30)  all_57_5 = e3
% 231.16/42.36    (31)  op(e3, e2) = all_53_4
% 231.16/42.36    (32)   ~ (e2 = e0)
% 231.16/42.36    (33)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3)
% 231.16/42.36    (34)   ~ (e1 = e0)
% 231.16/42.36    (35)   ~ (all_53_4 = e0)
% 231.16/42.36    (36)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.16/42.36          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.16/42.36    (37)   ~ (all_53_2 = all_53_3)
% 231.16/42.36    (38)  all_55_8 = all_53_2
% 231.16/42.36    (39)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.16/42.36              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.16/42.36                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.16/42.36                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.16/42.36    (40)  op(e0, e0) = e1
% 231.16/42.36    (41)  op(e2, e0) = all_53_13
% 231.16/42.36    (42)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.16/42.36          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.16/42.36    (43)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.16/42.36          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.16/42.36    (44)   ~ (all_53_6 = e3)
% 231.16/42.36    (45)   ~ (e2 = e1)
% 231.16/42.36    (46)   ~ (all_6_2 = e0)
% 231.16/42.36    (47)   ~ (all_53_2 = all_53_6)
% 231.16/42.36    (48)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.16/42.36          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.16/42.36    (49)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.16/42.36          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.16/42.36    (50)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.16/42.36          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.16/42.36    (51)  op(e3, e0) = all_52_7
% 231.16/42.36    (52)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.16/42.36          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.16/42.36  
% 231.16/42.36  Begin of proof
% 231.16/42.36  | 
% 231.16/42.36  | BETA: splitting (33) gives:
% 231.16/42.36  | 
% 231.16/42.36  | Case 1:
% 231.16/42.36  | | 
% 231.16/42.36  | |   (53)  all_57_6 = e3 & op(e1, e3) = e3
% 231.16/42.36  | | 
% 231.16/42.36  | | ALPHA: (53) implies:
% 231.16/42.36  | |   (54)  all_57_6 = e3
% 231.16/42.36  | | 
% 231.16/42.36  | | REF_CLOSE: (3), (6), (8), (10), (22), (24), (25), (27), (30), (32), (34),
% 231.16/42.36  | |            (43), (45), (48), (50), (54) are inconsistent by sub-proof #1781.
% 231.16/42.36  | | 
% 231.16/42.36  | Case 2:
% 231.16/42.36  | | 
% 231.16/42.36  | |   (55)  all_57_7 = e3 & op(e1, e2) = e3
% 231.16/42.36  | | 
% 231.16/42.36  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 231.16/42.36  | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 231.16/42.36  | |            (25), (26), (27), (28), (29), (31), (32), (34), (35), (36), (37),
% 231.16/42.36  | |            (38), (39), (40), (41), (42), (43), (44), (45), (46), (47), (49),
% 231.16/42.36  | |            (51), (52), (55) are inconsistent by sub-proof #1365.
% 231.16/42.36  | | 
% 231.16/42.36  | End of split
% 231.16/42.36  | 
% 231.16/42.36  End of proof
% 231.16/42.36  
% 231.16/42.36  Sub-proof #1365 shows that the following formulas are inconsistent:
% 231.16/42.36  ----------------------------------------------------------------
% 231.16/42.36    (1)   ~ (all_53_2 = e2)
% 231.16/42.36    (2)  all_57_7 = e3 & op(e1, e2) = e3
% 231.16/42.36    (3)   ~ (all_53_6 = e2)
% 231.16/42.36    (4)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.16/42.36         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.16/42.36    (5)  op(e3, e1) = all_52_5
% 231.16/42.36    (6)   ~ (all_53_6 = e0)
% 231.16/42.36    (7)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.16/42.36         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.16/42.36    (8)   ~ (e3 = e1)
% 231.16/42.36    (9)   ~ (all_53_13 = e1)
% 231.16/42.36    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.16/42.36            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.16/42.36    (11)  op(all_52_5, all_52_5) = e1
% 231.16/42.36    (12)   ~ (all_6_2 = e3)
% 231.16/42.36    (13)  op(e1, e1) = all_6_2
% 231.16/42.36    (14)  op(all_52_7, all_52_7) = e0
% 231.16/42.36    (15)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.16/42.36          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.16/42.36    (16)  all_55_9 = e1 | all_55_9 = e0
% 231.16/42.36    (17)  all_55_9 = all_53_6
% 231.16/42.36    (18)   ~ (all_53_2 = e3)
% 231.16/42.36    (19)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.16/42.36          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.16/42.36    (20)  op(e2, e2) = e0
% 231.16/42.36    (21)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.16/42.36          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.16/42.36    (22)  all_57_3 = e0
% 231.16/42.36    (23)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.16/42.36          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.16/42.36    (24)   ~ (e3 = e2)
% 231.16/42.36    (25)   ~ (e3 = e0)
% 231.16/42.36    (26)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.16/42.36          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.16/42.36    (27)  op(e3, e3) = e3
% 231.16/42.36    (28)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 231.16/42.36    (29)  op(e0, e3) = all_53_3
% 231.16/42.36    (30)  op(e3, e2) = all_53_4
% 231.16/42.36    (31)   ~ (e2 = e0)
% 231.16/42.36    (32)   ~ (e1 = e0)
% 231.16/42.36    (33)   ~ (all_53_4 = e0)
% 231.16/42.36    (34)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.16/42.36          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.16/42.36    (35)   ~ (all_53_2 = all_53_3)
% 231.16/42.36    (36)  all_55_8 = all_53_2
% 231.16/42.36    (37)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.16/42.36              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.16/42.36                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.16/42.36                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.16/42.36    (38)  op(e0, e0) = e1
% 231.16/42.36    (39)  op(e2, e0) = all_53_13
% 231.16/42.36    (40)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.16/42.36          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.16/42.36    (41)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.16/42.36          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.16/42.36    (42)   ~ (all_53_6 = e3)
% 231.16/42.36    (43)   ~ (e2 = e1)
% 231.16/42.36    (44)   ~ (all_6_2 = e0)
% 231.16/42.36    (45)   ~ (all_53_2 = all_53_6)
% 231.16/42.36    (46)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.16/42.36          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.16/42.36    (47)  op(e3, e0) = all_52_7
% 231.16/42.36    (48)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.16/42.36          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.16/42.36  
% 231.16/42.36  Begin of proof
% 231.16/42.36  | 
% 231.16/42.36  | ALPHA: (2) implies:
% 231.16/42.36  |   (49)  all_57_7 = e3
% 231.16/42.36  | 
% 231.16/42.36  | BETA: splitting (23) gives:
% 231.16/42.36  | 
% 231.16/42.36  | Case 1:
% 231.16/42.36  | | 
% 231.16/42.36  | |   (50)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) =
% 231.16/42.36  | |           e0)
% 231.16/42.36  | | 
% 231.16/42.36  | | BETA: splitting (50) gives:
% 231.16/42.36  | | 
% 231.16/42.36  | | Case 1:
% 231.16/42.36  | | | 
% 231.16/42.36  | | |   (51)  all_57_4 = e0 & op(e3, e1) = e0
% 231.16/42.36  | | | 
% 231.16/42.36  | | | ALPHA: (51) implies:
% 231.16/42.36  | | |   (52)  all_57_4 = e0
% 231.16/42.36  | | |   (53)  op(e3, e1) = e0
% 231.16/42.36  | | | 
% 231.16/42.36  | | | BETA: splitting (37) gives:
% 231.16/42.36  | | | 
% 231.16/42.36  | | | Case 1:
% 231.16/42.36  | | | | 
% 231.16/42.36  | | | |   (54)  all_57_15 = e0 & op(e0, e0) = e0
% 231.16/42.36  | | | | 
% 231.16/42.36  | | | | ALPHA: (54) implies:
% 231.16/42.36  | | | |   (55)  op(e0, e0) = e0
% 231.16/42.36  | | | | 
% 231.16/42.36  | | | | REF_CLOSE: (5), (10), (11), (32), (53), (55) are inconsistent by
% 231.16/42.36  | | | |            sub-proof #2167.
% 231.16/42.36  | | | | 
% 231.16/42.36  | | | Case 2:
% 231.16/42.36  | | | | 
% 231.16/42.36  | | | |   (56)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2,
% 231.16/42.36  | | | |               e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) &
% 231.16/42.36  | | | |         ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0,
% 231.16/42.36  | | | |               e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 231.16/42.36  | | | | 
% 231.16/42.36  | | | | ALPHA: (56) implies:
% 231.16/42.36  | | | |   (57)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0,
% 231.16/42.36  | | | |             e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.16/42.36  | | | | 
% 231.16/42.36  | | | | BETA: splitting (16) gives:
% 231.16/42.36  | | | | 
% 231.16/42.36  | | | | Case 1:
% 231.16/42.36  | | | | | 
% 231.16/42.36  | | | | |   (58)  all_55_9 = e1
% 231.16/42.36  | | | | | 
% 231.16/42.36  | | | | | COMBINE_EQS: (17), (58) imply:
% 231.16/42.36  | | | | |   (59)  all_53_6 = e1
% 231.16/42.36  | | | | | 
% 231.16/42.36  | | | | | REDUCE: (45), (59) imply:
% 231.16/42.36  | | | | |   (60)   ~ (all_53_2 = e1)
% 231.16/42.36  | | | | | 
% 231.16/42.36  | | | | | REDUCE: (42), (59) imply:
% 231.16/42.36  | | | | |   (61)   ~ (e3 = e1)
% 231.16/42.36  | | | | | 
% 231.16/42.36  | | | | | REDUCE: (3), (59) imply:
% 231.16/42.36  | | | | |   (62)   ~ (e2 = e1)
% 231.16/42.36  | | | | | 
% 231.16/42.36  | | | | | BETA: splitting (57) gives:
% 231.16/42.36  | | | | | 
% 231.16/42.36  | | | | | Case 1:
% 231.16/42.36  | | | | | | 
% 231.16/42.36  | | | | | |   (63)  all_57_12 = e0 & op(e0, e3) = e0
% 231.16/42.36  | | | | | | 
% 231.16/42.36  | | | | | | REF_CLOSE: (1), (10), (18), (28), (29), (35), (36), (60), (63) are
% 231.16/42.36  | | | | | |            inconsistent by sub-proof #1369.
% 231.16/42.36  | | | | | | 
% 231.16/42.36  | | | | | Case 2:
% 231.16/42.36  | | | | | | 
% 231.16/42.36  | | | | | |   (64)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 &
% 231.16/42.36  | | | | | |           op(e0, e1) = e0)
% 231.16/42.36  | | | | | | 
% 231.16/42.36  | | | | | | BETA: splitting (64) gives:
% 231.16/42.36  | | | | | | 
% 231.16/42.36  | | | | | | Case 1:
% 231.16/42.36  | | | | | | | 
% 231.16/42.36  | | | | | | |   (65)  all_57_13 = e0 & op(e0, e2) = e0
% 231.16/42.36  | | | | | | | 
% 231.16/42.36  | | | | | | | ALPHA: (65) implies:
% 231.16/42.36  | | | | | | |   (66)  all_57_13 = e0
% 231.16/42.36  | | | | | | | 
% 231.16/42.36  | | | | | | | REF_CLOSE: (7), (8), (10), (15), (19), (21), (22), (24), (25),
% 231.16/42.36  | | | | | | |            (27), (31), (32), (43), (48), (49), (66) are
% 231.16/42.36  | | | | | | |            inconsistent by sub-proof #2091.
% 231.16/42.36  | | | | | | | 
% 231.16/42.36  | | | | | | Case 2:
% 231.16/42.36  | | | | | | | 
% 231.16/42.36  | | | | | | |   (67)  all_57_14 = e0 & op(e0, e1) = e0
% 231.16/42.36  | | | | | | | 
% 231.16/42.36  | | | | | | | ALPHA: (67) implies:
% 231.16/42.36  | | | | | | |   (68)  all_57_14 = e0
% 231.16/42.36  | | | | | | | 
% 231.16/42.36  | | | | | | | REF_CLOSE: (8), (10), (12), (13), (24), (25), (26), (31), (32),
% 231.16/42.36  | | | | | | |            (34), (43), (46), (52), (68) are inconsistent by
% 231.16/42.36  | | | | | | |            sub-proof #2371.
% 231.16/42.36  | | | | | | | 
% 231.16/42.36  | | | | | | End of split
% 231.16/42.36  | | | | | | 
% 231.16/42.36  | | | | | End of split
% 231.16/42.36  | | | | | 
% 231.16/42.36  | | | | Case 2:
% 231.16/42.36  | | | | | 
% 231.16/42.36  | | | | |   (69)  all_55_9 = e0
% 231.16/42.36  | | | | | 
% 231.16/42.36  | | | | | COMBINE_EQS: (17), (69) imply:
% 231.16/42.36  | | | | |   (70)  all_53_6 = e0
% 231.16/42.36  | | | | | 
% 231.16/42.36  | | | | | REDUCE: (6), (70) imply:
% 231.16/42.36  | | | | |   (71)  $false
% 231.16/42.36  | | | | | 
% 231.16/42.36  | | | | | CLOSE: (71) is inconsistent.
% 231.16/42.36  | | | | | 
% 231.16/42.36  | | | | End of split
% 231.16/42.36  | | | | 
% 231.16/42.36  | | | End of split
% 231.16/42.36  | | | 
% 231.16/42.36  | | Case 2:
% 231.16/42.36  | | | 
% 231.16/42.36  | | |   (72)  all_57_5 = e0 & op(e2, e1) = e0
% 231.16/42.36  | | | 
% 231.16/42.36  | | | ALPHA: (72) implies:
% 231.16/42.36  | | |   (73)  all_57_5 = e0
% 231.16/42.36  | | | 
% 231.16/42.36  | | | REF_CLOSE: (4), (8), (9), (10), (20), (22), (24), (25), (31), (32), (39),
% 231.16/42.36  | | |            (40), (41), (43), (73) are inconsistent by sub-proof #1689.
% 231.16/42.36  | | | 
% 231.16/42.36  | | End of split
% 231.16/42.36  | | 
% 231.16/42.36  | Case 2:
% 231.16/42.36  | | 
% 231.16/42.36  | |   (74)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 231.16/42.36  | |           e0)
% 231.16/42.36  | | 
% 231.16/42.36  | | REF_CLOSE: (8), (10), (12), (13), (14), (15), (19), (21), (24), (25), (26),
% 231.16/42.36  | |            (27), (30), (31), (32), (33), (34), (38), (43), (44), (46), (47),
% 231.16/42.36  | |            (74) are inconsistent by sub-proof #1366.
% 231.16/42.36  | | 
% 231.16/42.36  | End of split
% 231.16/42.36  | 
% 231.16/42.36  End of proof
% 231.16/42.36  
% 231.16/42.36  Sub-proof #1366 shows that the following formulas are inconsistent:
% 231.16/42.36  ----------------------------------------------------------------
% 231.16/42.36    (1)   ~ (e3 = e1)
% 231.16/42.36    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.16/42.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.16/42.36    (3)   ~ (all_6_2 = e3)
% 231.16/42.36    (4)  op(e1, e1) = all_6_2
% 231.16/42.36    (5)  op(all_52_7, all_52_7) = e0
% 231.16/42.36    (6)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.16/42.36         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.16/42.36    (7)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.16/42.36         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.16/42.36    (8)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.16/42.36         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.16/42.36    (9)   ~ (e3 = e2)
% 231.16/42.36    (10)   ~ (e3 = e0)
% 231.16/42.36    (11)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.16/42.36          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.16/42.36    (12)  op(e3, e3) = e3
% 231.16/42.36    (13)  op(e3, e2) = all_53_4
% 231.16/42.36    (14)   ~ (e2 = e0)
% 231.16/42.36    (15)   ~ (e1 = e0)
% 231.16/42.36    (16)   ~ (all_53_4 = e0)
% 231.16/42.36    (17)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.16/42.36          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.16/42.36    (18)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.16/42.36    (19)  op(e0, e0) = e1
% 231.16/42.36    (20)   ~ (e2 = e1)
% 231.16/42.36    (21)   ~ (all_6_2 = e0)
% 231.16/42.36    (22)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.16/42.36          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.16/42.36    (23)  op(e3, e0) = all_52_7
% 231.16/42.36  
% 231.16/42.36  Begin of proof
% 231.16/42.36  | 
% 231.16/42.36  | BETA: splitting (18) gives:
% 231.16/42.36  | 
% 231.16/42.36  | Case 1:
% 231.16/42.36  | | 
% 231.16/42.36  | |   (24)  all_57_8 = e0 & op(e1, e1) = e0
% 231.16/42.36  | | 
% 231.16/42.36  | | REF_CLOSE: (2), (4), (21), (24) are inconsistent by sub-proof #2412.
% 231.16/42.36  | | 
% 231.16/42.36  | Case 2:
% 231.16/42.36  | | 
% 231.16/42.36  | |   (25)  all_57_14 = e0 & op(e0, e1) = e0
% 231.16/42.36  | | 
% 231.16/42.36  | | ALPHA: (25) implies:
% 231.16/42.36  | |   (26)  all_57_14 = e0
% 231.16/42.36  | | 
% 231.16/42.36  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 231.16/42.36  | |            (13), (14), (15), (16), (17), (19), (20), (22), (23), (26) are
% 231.16/42.36  | |            inconsistent by sub-proof #1367.
% 231.16/42.36  | | 
% 231.16/42.36  | End of split
% 231.16/42.36  | 
% 231.16/42.36  End of proof
% 231.16/42.36  
% 231.16/42.36  Sub-proof #1367 shows that the following formulas are inconsistent:
% 231.16/42.36  ----------------------------------------------------------------
% 231.16/42.36    (1)   ~ (e3 = e1)
% 231.16/42.36    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.16/42.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.16/42.36    (3)   ~ (all_6_2 = e3)
% 231.16/42.36    (4)  op(e1, e1) = all_6_2
% 231.16/42.36    (5)  op(all_52_7, all_52_7) = e0
% 231.16/42.36    (6)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.16/42.36         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.16/42.36    (7)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.16/42.36         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.16/42.36    (8)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.16/42.36         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.16/42.36    (9)   ~ (e3 = e2)
% 231.16/42.36    (10)   ~ (e3 = e0)
% 231.16/42.36    (11)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.16/42.36          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.16/42.36    (12)  op(e3, e3) = e3
% 231.16/42.36    (13)  op(e3, e2) = all_53_4
% 231.16/42.36    (14)   ~ (e2 = e0)
% 231.16/42.36    (15)   ~ (e1 = e0)
% 231.16/42.36    (16)   ~ (all_53_4 = e0)
% 231.16/42.36    (17)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.16/42.36          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.16/42.36    (18)  op(e0, e0) = e1
% 231.16/42.36    (19)   ~ (e2 = e1)
% 231.16/42.36    (20)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.16/42.36          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.16/42.36    (21)  all_57_14 = e0
% 231.16/42.36    (22)  op(e3, e0) = all_52_7
% 231.16/42.36  
% 231.16/42.36  Begin of proof
% 231.16/42.36  | 
% 231.16/42.36  | BETA: splitting (17) gives:
% 231.16/42.36  | 
% 231.16/42.36  | Case 1:
% 231.16/42.36  | | 
% 231.16/42.36  | |   (23)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) =
% 231.16/42.36  | |           e3)
% 231.16/42.36  | | 
% 231.16/42.36  | | BETA: splitting (23) gives:
% 231.16/42.36  | | 
% 231.16/42.36  | | Case 1:
% 231.16/42.36  | | | 
% 231.16/42.36  | | |   (24)  all_57_4 = e3 & op(e3, e1) = e3
% 231.16/42.36  | | | 
% 231.16/42.36  | | | ALPHA: (24) implies:
% 231.16/42.36  | | |   (25)  all_57_4 = e3
% 231.16/42.36  | | | 
% 231.16/42.36  | | | REF_CLOSE: (1), (2), (6), (7), (8), (9), (10), (12), (14), (15), (19),
% 231.16/42.36  | | |            (25) are inconsistent by sub-proof #2474.
% 231.16/42.36  | | | 
% 231.16/42.36  | | Case 2:
% 231.16/42.36  | | | 
% 231.16/42.36  | | |   (26)  all_57_5 = e3 & op(e2, e1) = e3
% 231.16/42.36  | | | 
% 231.16/42.36  | | | ALPHA: (26) implies:
% 231.16/42.36  | | |   (27)  all_57_5 = e3
% 231.16/42.36  | | | 
% 231.16/42.36  | | | REF_CLOSE: (1), (2), (5), (8), (9), (10), (11), (12), (13), (14), (15),
% 231.16/42.36  | | |            (16), (18), (19), (20), (21), (22), (27) are inconsistent by
% 231.16/42.36  | | |            sub-proof #1368.
% 231.16/42.36  | | | 
% 231.16/42.36  | | End of split
% 231.16/42.36  | | 
% 231.16/42.36  | Case 2:
% 231.16/42.36  | | 
% 231.16/42.36  | |   (28)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) =
% 231.16/42.36  | |           e3)
% 231.16/42.36  | | 
% 231.16/42.36  | | REF_CLOSE: (2), (3), (4), (10), (21), (28) are inconsistent by sub-proof
% 231.16/42.36  | |            #2419.
% 231.16/42.36  | | 
% 231.16/42.36  | End of split
% 231.16/42.36  | 
% 231.16/42.36  End of proof
% 231.16/42.36  
% 231.16/42.36  Sub-proof #1368 shows that the following formulas are inconsistent:
% 231.16/42.36  ----------------------------------------------------------------
% 231.16/42.36    (1)   ~ (e3 = e1)
% 231.16/42.36    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.16/42.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.16/42.36    (3)  op(all_52_7, all_52_7) = e0
% 231.16/42.36    (4)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.16/42.36         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.16/42.36    (5)   ~ (e3 = e2)
% 231.16/42.36    (6)   ~ (e3 = e0)
% 231.16/42.36    (7)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.16/42.36         (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.16/42.36    (8)  op(e3, e3) = e3
% 231.16/42.36    (9)  all_57_5 = e3
% 231.16/42.36    (10)  op(e3, e2) = all_53_4
% 231.16/42.36    (11)   ~ (e2 = e0)
% 231.16/42.36    (12)   ~ (e1 = e0)
% 231.16/42.36    (13)   ~ (all_53_4 = e0)
% 231.16/42.36    (14)  op(e0, e0) = e1
% 231.16/42.36    (15)   ~ (e2 = e1)
% 231.16/42.36    (16)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.16/42.36          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.16/42.36    (17)  all_57_14 = e0
% 231.16/42.36    (18)  op(e3, e0) = all_52_7
% 231.16/42.36  
% 231.16/42.36  Begin of proof
% 231.16/42.36  | 
% 231.16/42.36  | BETA: splitting (4) gives:
% 231.16/42.36  | 
% 231.16/42.36  | Case 1:
% 231.16/42.36  | | 
% 231.16/42.36  | |   (19)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) =
% 231.16/42.36  | |           e0)
% 231.16/42.36  | | 
% 231.16/42.36  | | REF_CLOSE: (2), (6), (8), (10), (13), (19) are inconsistent by sub-proof
% 231.16/42.36  | |            #1543.
% 231.16/42.36  | | 
% 231.16/42.36  | Case 2:
% 231.16/42.36  | | 
% 231.16/42.36  | |   (20)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) =
% 231.16/42.36  | |           e0)
% 231.16/42.36  | | 
% 231.16/42.36  | | BETA: splitting (20) gives:
% 231.16/42.36  | | 
% 231.16/42.36  | | Case 1:
% 231.16/42.36  | | | 
% 231.16/42.36  | | |   (21)  all_57_4 = e0 & op(e3, e1) = e0
% 231.16/42.36  | | | 
% 231.16/42.36  | | | ALPHA: (21) implies:
% 231.16/42.36  | | |   (22)  all_57_4 = e0
% 231.16/42.36  | | | 
% 231.16/42.36  | | | REF_CLOSE: (1), (2), (5), (7), (9), (11), (12), (15), (16), (17), (22) are
% 231.16/42.36  | | |            inconsistent by sub-proof #2378.
% 231.16/42.36  | | | 
% 231.16/42.36  | | Case 2:
% 231.16/42.36  | | | 
% 231.16/42.36  | | |   (23)  all_57_9 = e0 & op(e3, e0) = e0
% 231.16/42.36  | | | 
% 231.16/42.36  | | | ALPHA: (23) implies:
% 231.16/42.36  | | |   (24)  op(e3, e0) = e0
% 231.16/42.36  | | | 
% 231.16/42.36  | | | REF_CLOSE: (2), (3), (12), (14), (18), (24) are inconsistent by sub-proof
% 231.16/42.36  | | |            #2000.
% 231.16/42.36  | | | 
% 231.16/42.36  | | End of split
% 231.16/42.36  | | 
% 231.16/42.36  | End of split
% 231.16/42.36  | 
% 231.16/42.36  End of proof
% 231.16/42.36  
% 231.16/42.36  Sub-proof #1369 shows that the following formulas are inconsistent:
% 231.16/42.36  ----------------------------------------------------------------
% 231.16/42.36    (1)   ~ (all_53_2 = e2)
% 231.16/42.36    (2)   ~ (all_53_2 = e1)
% 231.16/42.36    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.16/42.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.16/42.36    (4)   ~ (all_53_2 = e3)
% 231.16/42.36    (5)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 231.16/42.36    (6)  op(e0, e3) = all_53_3
% 231.16/42.36    (7)   ~ (all_53_2 = all_53_3)
% 231.16/42.36    (8)  all_55_8 = all_53_2
% 231.16/42.36    (9)  all_57_12 = e0 & op(e0, e3) = e0
% 231.16/42.36  
% 231.16/42.36  Begin of proof
% 231.16/42.36  | 
% 231.16/42.36  | ALPHA: (9) implies:
% 231.16/42.36  |   (10)  op(e0, e3) = e0
% 231.16/42.36  | 
% 231.16/42.36  | BETA: splitting (5) gives:
% 231.16/42.36  | 
% 231.16/42.36  | Case 1:
% 231.16/42.36  | | 
% 231.16/42.36  | |   (11)  all_55_8 = e3
% 231.16/42.36  | | 
% 231.16/42.36  | | REF_CLOSE: (4), (8), (11) are inconsistent by sub-proof #2496.
% 231.16/42.36  | | 
% 231.16/42.36  | Case 2:
% 231.16/42.36  | | 
% 231.16/42.36  | |   (12)  all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 231.16/42.36  | | 
% 231.16/42.36  | | BETA: splitting (12) gives:
% 231.16/42.36  | | 
% 231.16/42.36  | | Case 1:
% 231.16/42.36  | | | 
% 231.16/42.36  | | |   (13)  all_55_8 = e2
% 231.16/42.36  | | | 
% 231.16/42.36  | | | REF_CLOSE: (1), (8), (13) are inconsistent by sub-proof #2406.
% 231.16/42.36  | | | 
% 231.16/42.36  | | Case 2:
% 231.16/42.36  | | | 
% 231.16/42.36  | | |   (14)  all_55_8 = e1 | all_55_8 = e0
% 231.16/42.36  | | | 
% 231.16/42.36  | | | REF_CLOSE: (2), (3), (6), (7), (8), (10), (14) are inconsistent by
% 231.16/42.37  | | |            sub-proof #2365.
% 231.16/42.37  | | | 
% 231.16/42.37  | | End of split
% 231.16/42.37  | | 
% 231.16/42.37  | End of split
% 231.16/42.37  | 
% 231.16/42.37  End of proof
% 231.16/42.37  
% 231.16/42.37  Sub-proof #1370 shows that the following formulas are inconsistent:
% 231.16/42.37  ----------------------------------------------------------------
% 231.16/42.37    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.16/42.37           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.16/42.37    (2)  all_55_9 = all_52_19
% 231.16/42.37    (3)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 231.16/42.37    (4)  op(e3, e3) = e3
% 231.16/42.37    (5)   ~ (all_52_19 = e0)
% 231.16/42.37    (6)  op(all_52_19, all_52_19) = e2
% 231.16/42.37    (7)   ~ (all_52_19 = e2)
% 231.16/42.37    (8)   ~ (all_52_19 = e1)
% 231.16/42.37  
% 231.16/42.37  Begin of proof
% 231.16/42.37  | 
% 231.16/42.37  | BETA: splitting (3) gives:
% 231.16/42.37  | 
% 231.16/42.37  | Case 1:
% 231.16/42.37  | | 
% 231.16/42.37  | |   (9)  all_55_9 = e3
% 231.16/42.37  | | 
% 231.16/42.37  | | COMBINE_EQS: (2), (9) imply:
% 231.16/42.37  | |   (10)  all_52_19 = e3
% 231.16/42.37  | | 
% 231.16/42.37  | | SIMP: (10) implies:
% 231.16/42.37  | |   (11)  all_52_19 = e3
% 231.16/42.37  | | 
% 231.16/42.37  | | REDUCE: (7), (11) imply:
% 231.16/42.37  | |   (12)   ~ (e3 = e2)
% 231.16/42.37  | | 
% 231.16/42.37  | | REDUCE: (6), (11) imply:
% 231.16/42.37  | |   (13)  op(e3, e3) = e2
% 231.16/42.37  | | 
% 231.16/42.37  | | REF_CLOSE: (1), (4), (12), (13) are inconsistent by sub-proof #2490.
% 231.16/42.37  | | 
% 231.16/42.37  | Case 2:
% 231.16/42.37  | | 
% 231.16/42.37  | |   (14)  all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 231.16/42.37  | | 
% 231.16/42.37  | | REF_CLOSE: (2), (5), (7), (8), (14) are inconsistent by sub-proof #1882.
% 231.16/42.37  | | 
% 231.16/42.37  | End of split
% 231.16/42.37  | 
% 231.16/42.37  End of proof
% 231.16/42.37  
% 231.16/42.37  Sub-proof #1371 shows that the following formulas are inconsistent:
% 231.16/42.37  ----------------------------------------------------------------
% 231.16/42.37    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.16/42.37           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.16/42.37    (2)  all_55_9 = all_52_19
% 231.16/42.37    (3)  op(e2, e2) = e0
% 231.16/42.37    (4)  all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 231.16/42.37    (5)   ~ (all_52_19 = e0)
% 231.16/42.37    (6)  op(all_52_19, all_52_19) = e2
% 231.16/42.37    (7)   ~ (all_52_19 = e1)
% 231.16/42.37  
% 231.16/42.37  Begin of proof
% 231.16/42.37  | 
% 231.16/42.37  | BETA: splitting (4) gives:
% 231.16/42.37  | 
% 231.16/42.37  | Case 1:
% 231.16/42.37  | | 
% 231.16/42.37  | |   (8)  all_55_9 = e2
% 231.16/42.37  | | 
% 231.16/42.37  | | COMBINE_EQS: (2), (8) imply:
% 231.16/42.37  | |   (9)  all_52_19 = e2
% 231.16/42.37  | | 
% 231.16/42.37  | | REDUCE: (5), (9) imply:
% 231.16/42.37  | |   (10)   ~ (e2 = e0)
% 231.16/42.37  | | 
% 231.16/42.37  | | REDUCE: (6), (9) imply:
% 231.16/42.37  | |   (11)  op(e2, e2) = e2
% 231.16/42.37  | | 
% 231.16/42.37  | | REF_CLOSE: (1), (3), (10), (11) are inconsistent by sub-proof #2472.
% 231.16/42.37  | | 
% 231.16/42.37  | Case 2:
% 231.16/42.37  | | 
% 231.16/42.37  | |   (12)  all_55_9 = e1 | all_55_9 = e0
% 231.16/42.37  | | 
% 231.16/42.37  | | REF_CLOSE: (2), (5), (7), (12) are inconsistent by sub-proof #1883.
% 231.16/42.37  | | 
% 231.16/42.37  | End of split
% 231.16/42.37  | 
% 231.16/42.37  End of proof
% 231.16/42.37  
% 231.16/42.37  Sub-proof #1372 shows that the following formulas are inconsistent:
% 231.16/42.37  ----------------------------------------------------------------
% 231.16/42.37    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.16/42.37           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.16/42.37    (2)  op(e2, e2) = e0
% 231.16/42.37    (3)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0 &
% 231.16/42.37         op(all_52_9, all_52_9) = e3 & op(all_52_11, all_52_11) = e2 &
% 231.16/42.37         op(all_52_13, all_52_13) = e1 & op(all_52_15, all_52_15) = e0 & op(e2,
% 231.16/42.37           e3) = all_52_9 & op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13 &
% 231.16/42.37         op(e2, e0) = all_52_15 & $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 231.16/42.37         $i(all_52_15)
% 231.16/42.37    (4)  op(e0, e0) = e1
% 231.16/42.37    (5)   ~ (e2 = e1)
% 231.16/42.37  
% 231.16/42.37  Begin of proof
% 231.16/42.37  | 
% 231.16/42.37  | ALPHA: (3) implies:
% 231.16/42.37  |   (6)  op(e2, e2) = all_52_11
% 231.16/42.37  |   (7)  op(all_52_11, all_52_11) = e2
% 231.16/42.37  | 
% 231.16/42.37  | GROUND_INST: instantiating (1) with e0, all_52_11, e2, e2, simplifying with
% 231.16/42.37  |              (2), (6) gives:
% 231.16/42.37  |   (8)  all_52_11 = e0
% 231.16/42.37  | 
% 231.16/42.37  | REDUCE: (7), (8) imply:
% 231.16/42.37  |   (9)  op(e0, e0) = e2
% 231.16/42.37  | 
% 231.16/42.37  | REF_CLOSE: (1), (4), (5), (9) are inconsistent by sub-proof #2177.
% 231.16/42.37  | 
% 231.16/42.37  End of proof
% 231.16/42.37  
% 231.16/42.37  Sub-proof #1373 shows that the following formulas are inconsistent:
% 231.16/42.37  ----------------------------------------------------------------
% 231.16/42.37    (1)   ~ (all_10_2 = e2)
% 231.16/42.37    (2)  all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 231.16/42.37    (3)  op(e3, e3) = all_10_2
% 231.16/42.37    (4)  op(e0, e1) = all_53_11
% 231.16/42.37    (5)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 231.16/42.37    (6)   ~ (all_53_6 = all_53_14)
% 231.16/42.37    (7)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 231.16/42.37    (8)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.16/42.37         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.16/42.37    (9)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.16/42.37         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.16/42.37    (10)   ~ (all_53_8 = all_53_12)
% 231.16/42.37    (11)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.16/42.37          (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.16/42.37    (12)   ~ (all_53_8 = all_53_11)
% 231.16/42.37    (13)   ~ (e3 = e1)
% 231.16/42.37    (14)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 231.16/42.37          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.16/42.37    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.16/42.37            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.16/42.37    (16)  all_55_0 = all_10_2
% 231.16/42.37    (17)   ~ (all_10_2 = e0)
% 231.16/42.37    (18)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.16/42.37          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.16/42.37    (19)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 231.16/42.37            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 231.16/42.37              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 231.16/42.37    (20)   ~ (all_6_2 = e3)
% 231.16/42.37    (21)  op(e1, e1) = all_6_2
% 231.16/42.37    (22)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 231.16/42.37    (23)   ~ (all_53_9 = e0)
% 231.16/42.37    (24)  all_55_0 = e3 | all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 231.16/42.37    (25)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 231.16/42.37    (26)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.16/42.37          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.16/42.37    (27)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 231.16/42.37    (28)  all_55_9 = all_53_6
% 231.16/42.37    (29)   ~ (all_53_11 = all_6_2)
% 231.16/42.37    (30)   ~ (all_53_4 = all_53_12)
% 231.16/42.37    (31)   ~ (all_53_8 = e3)
% 231.16/42.37    (32)   ~ (all_53_8 = all_53_9)
% 231.16/42.37    (33)  all_42_2 = all_6_2
% 231.16/42.37    (34)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.16/42.37          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.16/42.37    (35)  op(e2, e2) = e0
% 231.16/42.37    (36)   ~ (all_53_9 = all_53_11)
% 231.16/42.37    (37)   ~ (all_53_9 = all_6_2)
% 231.16/42.37    (38)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.16/42.37          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.16/42.37    (39)   ~ (all_53_14 = all_6_2)
% 231.16/42.37    (40)  all_57_3 = e0
% 231.16/42.37    (41)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.16/42.37          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.16/42.37    (42)   ~ (e3 = e2)
% 231.16/42.37    (43)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 231.16/42.37    (44)  all_55_1 = all_53_4
% 231.16/42.37    (45)  op(e1, e0) = all_53_14
% 231.16/42.37    (46)   ~ (all_53_6 = all_53_7)
% 231.16/42.37    (47)   ~ (e3 = e0)
% 231.16/42.37    (48)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.16/42.37          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.16/42.37    (49)  op(e3, e3) = e3
% 231.16/42.37    (50)   ~ (all_53_8 = all_6_2)
% 231.16/42.37    (51)  all_55_2 = all_53_8
% 231.16/42.37    (52)   ~ (all_53_4 = all_53_7)
% 231.16/42.37    (53)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 231.16/42.37    (54)   ~ (all_53_7 = e0)
% 231.16/42.37    (55)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.16/42.37          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.16/42.37            e1)
% 231.16/42.37    (56)   ~ (all_53_4 = all_53_8)
% 231.16/42.37    (57)  all_55_6 = all_53_9
% 231.16/42.37    (58)  op(e3, e2) = all_53_4
% 231.16/42.37    (59)   ~ (e2 = e0)
% 231.16/42.37    (60)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 231.16/42.37            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 231.16/42.37            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 231.16/42.37            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 231.16/42.37              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 231.16/42.37            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 231.16/42.37            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 231.16/42.37              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 231.16/42.37              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 231.16/42.37            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 231.16/42.37            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 231.16/42.37            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 231.16/42.37              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 231.16/42.37              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 231.16/42.37            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 231.16/42.37              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 231.16/42.37            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 231.16/42.37            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 231.16/42.37              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 231.16/42.37              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 231.16/42.37            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 231.16/42.37            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 231.16/42.37    (61)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 231.16/42.37          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.16/42.37    (62)   ~ (all_53_2 = all_53_14)
% 231.16/42.37    (63)   ~ (e1 = e0)
% 231.16/42.37    (64)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 231.16/42.37            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 231.16/42.37              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 231.16/42.37    (65)   ~ (all_53_4 = e0)
% 231.16/42.37    (66)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.16/42.37          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.16/42.37    (67)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.16/42.37          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.16/42.37    (68)   ~ (all_10_2 = e1)
% 231.16/42.37    (69)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 231.16/42.37    (70)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.16/42.37          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 231.16/42.37            e3)
% 231.16/42.37    (71)   ~ (all_53_4 = all_53_6)
% 231.16/42.37    (72)  op(e0, e2) = all_53_7
% 231.16/42.37    (73)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.16/42.37          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.16/42.37            e2)
% 231.16/42.37    (74)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.16/42.37              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.16/42.37                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.16/42.37                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.16/42.37    (75)  all_55_10 = all_6_2
% 231.16/42.37    (76)   ~ (all_53_6 = all_6_2)
% 231.16/42.37    (77)   ~ (all_53_13 = e0)
% 231.16/42.37    (78)  all_55_13 = all_53_7
% 231.16/42.37    (79)  op(e0, e0) = e1
% 231.16/42.37    (80)  op(e2, e0) = all_53_13
% 231.16/42.37    (81)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.16/42.37          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.16/42.37    (82)  all_38_2 = all_6_2
% 231.16/42.37    (83)  all_55_11 = all_53_14
% 231.16/42.37    (84)  all_55_3 = all_53_12
% 231.16/42.37    (85)   ~ (all_53_12 = e3)
% 231.16/42.37    (86)  all_57_0 = e3
% 231.16/42.37    (87)  op(e1, e3) = all_53_2
% 231.16/42.37    (88)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 231.16/42.37            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 231.16/42.37              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 231.16/42.37    (89)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.16/42.37          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.16/42.37    (90)  all_57_11 = e1
% 231.16/42.37    (91)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 231.16/42.37          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 231.16/42.37    (92)   ~ (all_53_12 = all_10_2)
% 231.16/42.37    (93)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 231.16/42.37          (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 231.16/42.37    (94)   ~ (all_53_13 = all_53_14)
% 231.16/42.37    (95)   ~ (e2 = e1)
% 231.16/42.37    (96)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.16/42.37          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.16/42.37    (97)  op(e2, e1) = all_53_9
% 231.16/42.37    (98)  op(e1, e2) = all_53_6
% 231.16/42.37    (99)   ~ (all_6_2 = e0)
% 231.16/42.37    (100)   ~ (all_53_2 = all_53_6)
% 231.16/42.37    (101)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.16/42.37           (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.16/42.37    (102)  all_24_2 = all_6_2
% 231.16/42.37    (103)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.16/42.37           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.16/42.37    (104)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.16/42.37           (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.16/42.37    (105)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.16/42.37           | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.16/42.37             e1)
% 231.16/42.37    (106)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 231.16/42.37           (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 231.16/42.37    (107)   ~ (all_53_12 = all_53_14)
% 231.16/42.37    (108)  all_55_14 = all_53_11
% 231.16/42.37    (109)  op(e3, e1) = all_53_8
% 231.16/42.37    (110)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.16/42.37           (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.16/42.37    (111)   ~ (all_53_4 = e3)
% 231.16/42.37    (112)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 231.16/42.37           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 231.16/42.37    (113)  op(e3, e0) = all_53_12
% 231.16/42.37  
% 231.16/42.37  Begin of proof
% 231.16/42.37  | 
% 231.16/42.37  | BETA: splitting (18) gives:
% 231.16/42.37  | 
% 231.16/42.37  | Case 1:
% 231.16/42.37  | | 
% 231.16/42.37  | |   (114)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 231.16/42.37  | |            e3)
% 231.16/42.37  | | 
% 231.16/42.37  | | BETA: splitting (114) gives:
% 231.16/42.37  | | 
% 231.16/42.37  | | Case 1:
% 231.16/42.37  | | | 
% 231.16/42.37  | | |   (115)  all_57_6 = e3 & op(e1, e3) = e3
% 231.16/42.37  | | | 
% 231.16/42.37  | | | ALPHA: (115) implies:
% 231.16/42.37  | | |   (116)  all_57_6 = e3
% 231.16/42.37  | | | 
% 231.16/42.37  | | | REF_CLOSE: (9), (13), (42), (47), (59), (63), (86), (95), (101), (104),
% 231.16/42.37  | | |            (116) are inconsistent by sub-proof #2010.
% 231.16/42.37  | | | 
% 231.16/42.37  | | Case 2:
% 231.16/42.37  | | | 
% 231.16/42.37  | | |   (117)  all_57_7 = e3 & op(e1, e2) = e3
% 231.16/42.37  | | | 
% 231.16/42.37  | | | ALPHA: (117) implies:
% 231.16/42.37  | | |   (118)  all_57_7 = e3
% 231.16/42.37  | | | 
% 231.16/42.37  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 231.16/42.37  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 231.16/42.37  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 231.16/42.37  | | |            (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 231.16/42.37  | | |            (43), (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 231.16/42.37  | | |            (53), (54), (55), (56), (57), (58), (59), (60), (61), (62),
% 231.16/42.37  | | |            (63), (64), (65), (66), (67), (68), (69), (70), (71), (72),
% 231.16/42.37  | | |            (73), (74), (75), (76), (77), (78), (79), (80), (81), (82),
% 231.16/42.37  | | |            (83), (84), (85), (86), (87), (88), (89), (90), (91), (92),
% 231.16/42.37  | | |            (93), (94), (95), (96), (97), (98), (99), (100), (101), (102),
% 231.16/42.37  | | |            (103), (104), (105), (106), (107), (108), (109), (110), (111),
% 231.16/42.37  | | |            (112), (113), (118) are inconsistent by sub-proof #1374.
% 231.16/42.37  | | | 
% 231.16/42.37  | | End of split
% 231.16/42.37  | | 
% 231.16/42.37  | Case 2:
% 231.16/42.37  | | 
% 231.16/42.37  | |   (119)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 231.16/42.37  | |            e3)
% 231.16/42.37  | | 
% 231.16/42.37  | | REF_CLOSE: (13), (15), (20), (21), (90), (119) are inconsistent by sub-proof
% 231.16/42.37  | |            #2004.
% 231.16/42.37  | | 
% 231.16/42.37  | End of split
% 231.16/42.37  | 
% 231.16/42.37  End of proof
% 231.16/42.37  
% 231.16/42.37  Sub-proof #1374 shows that the following formulas are inconsistent:
% 231.16/42.37  ----------------------------------------------------------------
% 231.16/42.37    (1)   ~ (all_10_2 = e2)
% 231.16/42.37    (2)  all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 231.16/42.37    (3)  op(e3, e3) = all_10_2
% 231.16/42.37    (4)  op(e0, e1) = all_53_11
% 231.16/42.37    (5)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 231.16/42.37    (6)   ~ (all_53_6 = all_53_14)
% 231.16/42.37    (7)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 231.16/42.37    (8)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.16/42.37         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.16/42.37    (9)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.16/42.37         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.16/42.37    (10)   ~ (all_53_8 = all_53_12)
% 231.16/42.37    (11)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.16/42.37          (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.16/42.37    (12)   ~ (all_53_8 = all_53_11)
% 231.16/42.37    (13)   ~ (e3 = e1)
% 231.16/42.37    (14)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 231.16/42.37          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.16/42.37    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.16/42.37            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.16/42.37    (16)  all_55_0 = all_10_2
% 231.16/42.37    (17)   ~ (all_10_2 = e0)
% 231.16/42.37    (18)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.16/42.37          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.16/42.37    (19)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 231.16/42.37            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 231.16/42.37              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 231.16/42.37    (20)   ~ (all_6_2 = e3)
% 231.16/42.37    (21)  op(e1, e1) = all_6_2
% 231.16/42.37    (22)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 231.16/42.37    (23)   ~ (all_53_9 = e0)
% 231.16/42.37    (24)  all_55_0 = e3 | all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 231.16/42.37    (25)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 231.16/42.37    (26)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.16/42.37          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.16/42.37    (27)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 231.16/42.37    (28)  all_55_9 = all_53_6
% 231.16/42.37    (29)   ~ (all_53_11 = all_6_2)
% 231.16/42.37    (30)   ~ (all_53_4 = all_53_12)
% 231.16/42.37    (31)   ~ (all_53_8 = e3)
% 231.16/42.37    (32)   ~ (all_53_8 = all_53_9)
% 231.16/42.37    (33)  all_42_2 = all_6_2
% 231.16/42.37    (34)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.16/42.37          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.16/42.37    (35)  op(e2, e2) = e0
% 231.16/42.37    (36)   ~ (all_53_9 = all_53_11)
% 231.16/42.37    (37)   ~ (all_53_9 = all_6_2)
% 231.16/42.37    (38)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.16/42.37          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.16/42.37    (39)   ~ (all_53_14 = all_6_2)
% 231.16/42.37    (40)  all_57_3 = e0
% 231.16/42.37    (41)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.16/42.37          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.16/42.37    (42)   ~ (e3 = e2)
% 231.16/42.37    (43)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 231.16/42.37    (44)  all_55_1 = all_53_4
% 231.16/42.37    (45)  op(e1, e0) = all_53_14
% 231.16/42.37    (46)   ~ (all_53_6 = all_53_7)
% 231.16/42.37    (47)   ~ (e3 = e0)
% 231.16/42.37    (48)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.16/42.37          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.16/42.37    (49)  op(e3, e3) = e3
% 231.16/42.37    (50)   ~ (all_53_8 = all_6_2)
% 231.16/42.37    (51)  all_55_2 = all_53_8
% 231.16/42.38    (52)   ~ (all_53_4 = all_53_7)
% 231.16/42.38    (53)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 231.16/42.38    (54)   ~ (all_53_7 = e0)
% 231.16/42.38    (55)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.16/42.38          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.16/42.38            e1)
% 231.16/42.38    (56)   ~ (all_53_4 = all_53_8)
% 231.16/42.38    (57)  all_55_6 = all_53_9
% 231.16/42.38    (58)  op(e3, e2) = all_53_4
% 231.16/42.38    (59)   ~ (e2 = e0)
% 231.16/42.38    (60)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 231.16/42.38            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 231.16/42.38            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 231.16/42.38            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 231.16/42.38              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 231.16/42.38            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 231.16/42.38            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 231.16/42.38              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 231.16/42.38              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 231.16/42.38            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 231.16/42.38            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 231.16/42.38            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 231.16/42.38              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 231.16/42.38              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 231.16/42.38            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 231.16/42.38              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 231.16/42.38            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 231.16/42.38            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 231.16/42.38              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 231.16/42.38              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 231.16/42.38            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 231.16/42.38            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 231.16/42.38    (61)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 231.16/42.38          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.16/42.38    (62)   ~ (all_53_2 = all_53_14)
% 231.16/42.38    (63)   ~ (e1 = e0)
% 231.16/42.38    (64)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 231.16/42.38            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 231.16/42.38              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 231.16/42.38    (65)   ~ (all_53_4 = e0)
% 231.16/42.38    (66)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.16/42.38          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.16/42.38    (67)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.16/42.38          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.16/42.38    (68)   ~ (all_10_2 = e1)
% 231.16/42.38    (69)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 231.16/42.38    (70)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.16/42.38          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 231.16/42.38            e3)
% 231.16/42.38    (71)   ~ (all_53_4 = all_53_6)
% 231.16/42.38    (72)  op(e0, e2) = all_53_7
% 231.16/42.38    (73)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.16/42.38          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.16/42.38            e2)
% 231.16/42.38    (74)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.16/42.38              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.16/42.38                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.16/42.38                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.16/42.38    (75)  all_55_10 = all_6_2
% 231.16/42.38    (76)   ~ (all_53_6 = all_6_2)
% 231.16/42.38    (77)   ~ (all_53_13 = e0)
% 231.16/42.38    (78)  all_55_13 = all_53_7
% 231.16/42.38    (79)  op(e0, e0) = e1
% 231.16/42.38    (80)  op(e2, e0) = all_53_13
% 231.16/42.38    (81)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.16/42.38          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.16/42.38    (82)  all_38_2 = all_6_2
% 231.16/42.38    (83)  all_55_11 = all_53_14
% 231.16/42.38    (84)  all_55_3 = all_53_12
% 231.16/42.38    (85)   ~ (all_53_12 = e3)
% 231.16/42.38    (86)  all_57_0 = e3
% 231.16/42.38    (87)  all_57_7 = e3
% 231.16/42.38    (88)  op(e1, e3) = all_53_2
% 231.16/42.38    (89)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 231.16/42.38            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 231.16/42.38              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 231.16/42.38    (90)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.16/42.38          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.16/42.38    (91)  all_57_11 = e1
% 231.16/42.38    (92)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 231.16/42.38          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 231.16/42.38    (93)   ~ (all_53_12 = all_10_2)
% 231.16/42.38    (94)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 231.16/42.38          (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 231.16/42.38    (95)   ~ (all_53_13 = all_53_14)
% 231.16/42.38    (96)   ~ (e2 = e1)
% 231.16/42.38    (97)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.16/42.38          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.16/42.38    (98)  op(e2, e1) = all_53_9
% 231.16/42.38    (99)  op(e1, e2) = all_53_6
% 231.16/42.38    (100)   ~ (all_6_2 = e0)
% 231.16/42.38    (101)   ~ (all_53_2 = all_53_6)
% 231.16/42.38    (102)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.16/42.38           (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.16/42.38    (103)  all_24_2 = all_6_2
% 231.16/42.38    (104)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.16/42.38           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.16/42.38    (105)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.16/42.38           (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.16/42.38    (106)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.16/42.38           | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.16/42.38             e1)
% 231.16/42.38    (107)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 231.16/42.38           (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 231.16/42.38    (108)   ~ (all_53_12 = all_53_14)
% 231.16/42.38    (109)  all_55_14 = all_53_11
% 231.16/42.38    (110)  op(e3, e1) = all_53_8
% 231.16/42.38    (111)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.16/42.38           (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.16/42.38    (112)   ~ (all_53_4 = e3)
% 231.16/42.38    (113)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 231.16/42.38           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 231.16/42.38    (114)  op(e3, e0) = all_53_12
% 231.16/42.38  
% 231.16/42.38  Begin of proof
% 231.16/42.38  | 
% 231.16/42.38  | BETA: splitting (111) gives:
% 231.16/42.38  | 
% 231.16/42.38  | Case 1:
% 231.16/42.38  | | 
% 231.16/42.38  | |   (115)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) =
% 231.16/42.38  | |            e1)
% 231.16/42.38  | | 
% 231.16/42.38  | | BETA: splitting (115) gives:
% 231.16/42.38  | | 
% 231.16/42.38  | | Case 1:
% 231.16/42.38  | | | 
% 231.16/42.38  | | |   (116)  all_57_1 = e1 & op(e3, e2) = e1
% 231.16/42.38  | | | 
% 231.16/42.38  | | | ALPHA: (116) implies:
% 231.16/42.38  | | |   (117)  all_57_1 = e1
% 231.16/42.38  | | | 
% 231.16/42.38  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 231.16/42.38  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 231.16/42.38  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 231.16/42.38  | | |            (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 231.16/42.38  | | |            (43), (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 231.16/42.38  | | |            (53), (54), (55), (56), (57), (58), (59), (60), (61), (62),
% 231.16/42.38  | | |            (63), (64), (65), (66), (67), (68), (69), (70), (71), (72),
% 231.16/42.38  | | |            (73), (74), (75), (76), (77), (78), (79), (80), (81), (82),
% 231.16/42.38  | | |            (83), (84), (85), (86), (87), (88), (89), (90), (91), (92),
% 231.16/42.38  | | |            (93), (94), (95), (96), (97), (98), (99), (100), (101), (102),
% 231.16/42.38  | | |            (103), (104), (105), (106), (107), (108), (109), (110), (111),
% 231.16/42.38  | | |            (112), (113), (114), (117) are inconsistent by sub-proof #1376.
% 231.16/42.38  | | | 
% 231.16/42.38  | | Case 2:
% 231.16/42.38  | | | 
% 231.16/42.38  | | |   (118)  all_57_3 = e1 & op(e2, e2) = e1
% 231.16/42.38  | | | 
% 231.16/42.38  | | | ALPHA: (118) implies:
% 231.16/42.38  | | |   (119)  op(e2, e2) = e1
% 231.16/42.38  | | | 
% 231.16/42.38  | | | REF_CLOSE: (15), (35), (63), (119) are inconsistent by sub-proof #2352.
% 231.16/42.38  | | | 
% 231.16/42.38  | | End of split
% 231.16/42.38  | | 
% 231.16/42.38  | Case 2:
% 231.16/42.38  | | 
% 231.16/42.38  | |   (120)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 231.16/42.38  | |            e1)
% 231.16/42.38  | | 
% 231.16/42.38  | | BETA: splitting (120) gives:
% 231.16/42.38  | | 
% 231.16/42.38  | | Case 1:
% 231.16/42.38  | | | 
% 231.16/42.38  | | |   (121)  all_57_7 = e1 & op(e1, e2) = e1
% 231.16/42.38  | | | 
% 231.16/42.38  | | | REF_CLOSE: (13), (87), (121) are inconsistent by sub-proof #2104.
% 231.16/42.38  | | | 
% 231.16/42.38  | | Case 2:
% 231.16/42.38  | | | 
% 231.16/42.38  | | |   (122)  all_57_13 = e1 & op(e0, e2) = e1
% 231.16/42.38  | | | 
% 231.16/42.38  | | | ALPHA: (122) implies:
% 231.16/42.38  | | |   (123)  all_57_13 = e1
% 231.16/42.38  | | | 
% 231.16/42.38  | | | BETA: splitting (74) gives:
% 231.16/42.38  | | | 
% 231.16/42.38  | | | Case 1:
% 231.16/42.38  | | | | 
% 231.16/42.38  | | | |   (124)  all_57_15 = e0 & op(e0, e0) = e0
% 231.16/42.38  | | | | 
% 231.16/42.38  | | | | ALPHA: (124) implies:
% 231.16/42.38  | | | |   (125)  all_57_15 = e0
% 231.16/42.38  | | | |   (126)  op(e0, e0) = e0
% 231.16/42.38  | | | | 
% 231.16/42.38  | | | | BETA: splitting (70) gives:
% 231.16/42.38  | | | | 
% 231.16/42.38  | | | | Case 1:
% 231.16/42.38  | | | | | 
% 231.16/42.38  | | | | |   (127)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0,
% 231.16/42.38  | | | | |              e2) = e3)
% 231.16/42.38  | | | | | 
% 231.16/42.38  | | | | | BETA: splitting (127) gives:
% 231.16/42.38  | | | | | 
% 231.16/42.38  | | | | | Case 1:
% 231.16/42.38  | | | | | | 
% 231.16/42.38  | | | | | |   (128)  all_57_12 = e3 & op(e0, e3) = e3
% 231.16/42.38  | | | | | | 
% 231.16/42.38  | | | | | | ALPHA: (128) implies:
% 231.16/42.38  | | | | | |   (129)  all_57_12 = e3
% 231.16/42.38  | | | | | | 
% 231.16/42.38  | | | | | | BETA: splitting (94) gives:
% 231.16/42.38  | | | | | | 
% 231.16/42.38  | | | | | | Case 1:
% 231.16/42.38  | | | | | | | 
% 231.16/42.38  | | | | | | |   (130)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 &
% 231.16/42.38  | | | | | | |            op(e2, e0) = e3)
% 231.16/42.38  | | | | | | | 
% 231.16/42.38  | | | | | | | BETA: splitting (130) gives:
% 231.16/42.38  | | | | | | | 
% 231.16/42.38  | | | | | | | Case 1:
% 231.16/42.38  | | | | | | | | 
% 231.16/42.38  | | | | | | | |   (131)  all_57_9 = e3 & op(e3, e0) = e3
% 231.16/42.38  | | | | | | | | 
% 231.16/42.38  | | | | | | | | ALPHA: (131) implies:
% 231.16/42.38  | | | | | | | |   (132)  op(e3, e0) = e3
% 231.16/42.38  | | | | | | | | 
% 231.16/42.38  | | | | | | | | REF_CLOSE: (15), (85), (114), (132) are inconsistent by
% 231.16/42.38  | | | | | | | |            sub-proof #2458.
% 231.16/42.38  | | | | | | | | 
% 231.16/42.38  | | | | | | | Case 2:
% 231.16/42.38  | | | | | | | | 
% 231.16/42.38  | | | | | | | |   (133)  all_57_10 = e3 & op(e2, e0) = e3
% 231.16/42.38  | | | | | | | | 
% 231.16/42.38  | | | | | | | | ALPHA: (133) implies:
% 231.16/42.38  | | | | | | | |   (134)  all_57_10 = e3
% 231.16/42.38  | | | | | | | | 
% 231.16/42.38  | | | | | | | | BETA: splitting (105) gives:
% 231.16/42.38  | | | | | | | | 
% 231.16/42.38  | | | | | | | | Case 1:
% 231.16/42.38  | | | | | | | | | 
% 231.16/42.38  | | | | | | | | |   (135)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 &
% 231.16/42.38  | | | | | | | | |            op(e2, e3) = e0)
% 231.16/42.38  | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | REF_CLOSE: (8), (13), (15), (40), (42), (47), (49), (59),
% 231.16/42.38  | | | | | | | | |            (63), (90), (96), (134), (135) are inconsistent by
% 231.16/42.38  | | | | | | | | |            sub-proof #1432.
% 231.16/42.38  | | | | | | | | | 
% 231.16/42.38  | | | | | | | | Case 2:
% 231.16/42.38  | | | | | | | | | 
% 231.16/42.38  | | | | | | | | |   (136)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 &
% 231.16/42.38  | | | | | | | | |            op(e0, e3) = e0)
% 231.16/42.38  | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | BETA: splitting (136) gives:
% 231.16/42.38  | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | Case 1:
% 231.16/42.38  | | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | |   (137)  all_57_6 = e0 & op(e1, e3) = e0
% 231.16/42.38  | | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | | ALPHA: (137) implies:
% 231.16/42.38  | | | | | | | | | |   (138)  all_57_6 = e0
% 231.16/42.38  | | | | | | | | | |   (139)  op(e1, e3) = e0
% 231.16/42.38  | | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | | BETA: splitting (73) gives:
% 231.16/42.38  | | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | | Case 1:
% 231.16/42.38  | | | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | | |   (140)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 231.16/42.38  | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 231.16/42.38  | | | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | | | BETA: splitting (140) gives:
% 231.16/42.38  | | | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | | | Case 1:
% 231.16/42.38  | | | | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | | | |   (141)  all_57_12 = e2 & op(e0, e3) = e2
% 231.16/42.38  | | | | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | | | | REF_CLOSE: (42), (129), (141) are inconsistent by sub-proof
% 231.16/42.38  | | | | | | | | | | | |            #2232.
% 231.16/42.38  | | | | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | | | Case 2:
% 231.16/42.38  | | | | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | | | |   (142)  all_57_13 = e2 & op(e0, e2) = e2
% 231.16/42.38  | | | | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | | | | ALPHA: (142) implies:
% 231.16/42.38  | | | | | | | | | | | |   (143)  all_57_13 = e2
% 231.16/42.38  | | | | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 231.16/42.38  | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 231.16/42.38  | | | | | | | | | | | |            (19), (20), (21), (22), (24), (25), (26), (27),
% 231.16/42.38  | | | | | | | | | | | |            (28), (29), (30), (31), (32), (33), (34), (35),
% 231.16/42.38  | | | | | | | | | | | |            (36), (37), (38), (39), (40), (41), (42), (43),
% 231.16/42.38  | | | | | | | | | | | |            (44), (45), (46), (47), (48), (49), (50), (51),
% 231.16/42.38  | | | | | | | | | | | |            (52), (53), (54), (55), (56), (57), (58), (59),
% 231.16/42.38  | | | | | | | | | | | |            (60), (61), (62), (63), (64), (66), (67), (68),
% 231.16/42.38  | | | | | | | | | | | |            (69), (70), (71), (72), (73), (74), (75), (76),
% 231.16/42.38  | | | | | | | | | | | |            (78), (80), (81), (82), (83), (84), (85), (86),
% 231.16/42.38  | | | | | | | | | | | |            (87), (88), (89), (90), (92), (93), (94), (95),
% 231.16/42.38  | | | | | | | | | | | |            (96), (97), (98), (99), (100), (101), (102),
% 231.16/42.38  | | | | | | | | | | | |            (103), (104), (105), (106), (107), (108), (109),
% 231.16/42.38  | | | | | | | | | | | |            (110), (111), (112), (113), (114), (125), (126),
% 231.16/42.38  | | | | | | | | | | | |            (134), (138), (139), (143) are inconsistent by
% 231.16/42.38  | | | | | | | | | | | |            sub-proof #1380.
% 231.16/42.38  | | | | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | | | End of split
% 231.16/42.38  | | | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | | Case 2:
% 231.16/42.38  | | | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | | |   (144)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 231.16/42.38  | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 231.16/42.38  | | | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | | | BETA: splitting (144) gives:
% 231.16/42.38  | | | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | | | Case 1:
% 231.16/42.38  | | | | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | | | |   (145)  all_57_14 = e2 & op(e0, e1) = e2
% 231.16/42.38  | | | | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | | | | ALPHA: (145) implies:
% 231.16/42.38  | | | | | | | | | | | |   (146)  all_57_14 = e2
% 231.16/42.38  | | | | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | | | | BETA: splitting (66) gives:
% 231.16/42.38  | | | | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | | | | Case 1:
% 231.16/42.38  | | | | | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | | | | |   (147)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 231.16/42.38  | | | | | | | | | | | | |            & op(e2, e1) = e3)
% 231.16/42.38  | | | | | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | | | | | REF_CLOSE: (8), (11), (13), (15), (26), (34), (38), (40),
% 231.16/42.38  | | | | | | | | | | | | |            (42), (47), (49), (59), (63), (87), (90), (96),
% 231.16/42.38  | | | | | | | | | | | | |            (111), (134), (147) are inconsistent by sub-proof
% 231.16/42.38  | | | | | | | | | | | | |            #1383.
% 231.16/42.38  | | | | | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | | | | Case 2:
% 231.16/42.38  | | | | | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | | | | |   (148)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 231.16/42.38  | | | | | | | | | | | | |            e3 & op(e0, e1) = e3)
% 231.16/42.38  | | | | | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | | | | | REF_CLOSE: (15), (20), (21), (42), (146), (148) are
% 231.16/42.38  | | | | | | | | | | | | |            inconsistent by sub-proof #1890.
% 231.16/42.38  | | | | | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | | | | End of split
% 231.16/42.38  | | | | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | | | Case 2:
% 231.16/42.38  | | | | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | | | |   (149)  all_57_15 = e2 & op(e0, e0) = e2
% 231.16/42.38  | | | | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | | | | ALPHA: (149) implies:
% 231.16/42.38  | | | | | | | | | | | |   (150)  op(e0, e0) = e2
% 231.16/42.38  | | | | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | | | | REF_CLOSE: (15), (79), (96), (150) are inconsistent by
% 231.16/42.38  | | | | | | | | | | | |            sub-proof #2177.
% 231.16/42.38  | | | | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | | | End of split
% 231.16/42.38  | | | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | | End of split
% 231.16/42.38  | | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | Case 2:
% 231.16/42.38  | | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | |   (151)  all_57_12 = e0 & op(e0, e3) = e0
% 231.16/42.38  | | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | | REF_CLOSE: (47), (129), (151) are inconsistent by sub-proof
% 231.16/42.38  | | | | | | | | | |            #2237.
% 231.16/42.38  | | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | End of split
% 231.16/42.38  | | | | | | | | | 
% 231.16/42.38  | | | | | | | | End of split
% 231.16/42.38  | | | | | | | | 
% 231.16/42.38  | | | | | | | End of split
% 231.16/42.38  | | | | | | | 
% 231.16/42.38  | | | | | | Case 2:
% 231.16/42.38  | | | | | | | 
% 231.16/42.38  | | | | | | |   (152)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 &
% 231.16/42.38  | | | | | | |            op(e0, e0) = e3)
% 231.16/42.38  | | | | | | | 
% 231.16/42.38  | | | | | | | REF_CLOSE: (1), (3), (5), (7), (8), (9), (10), (11), (13), (14),
% 231.16/42.38  | | | | | | |            (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 231.16/42.38  | | | | | | |            (24), (26), (30), (32), (33), (34), (37), (38), (40),
% 231.16/42.38  | | | | | | |            (41), (44), (48), (50), (51), (53), (55), (56), (58),
% 231.16/42.38  | | | | | | |            (59), (60), (61), (63), (64), (65), (66), (67), (68),
% 231.16/42.38  | | | | | | |            (71), (73), (74), (75), (81), (82), (84), (89), (90),
% 231.16/42.38  | | | | | | |            (91), (92), (93), (96), (97), (98), (99), (102), (103),
% 231.16/42.38  | | | | | | |            (104), (105), (106), (107), (110), (111), (113), (114),
% 231.16/42.38  | | | | | | |            (152) are inconsistent by sub-proof #1379.
% 231.16/42.38  | | | | | | | 
% 231.16/42.38  | | | | | | End of split
% 231.16/42.38  | | | | | | 
% 231.16/42.38  | | | | | Case 2:
% 231.16/42.38  | | | | | | 
% 231.16/42.38  | | | | | |   (153)  all_57_13 = e3 & op(e0, e2) = e3
% 231.16/42.38  | | | | | | 
% 231.16/42.38  | | | | | | ALPHA: (153) implies:
% 231.16/42.38  | | | | | |   (154)  all_57_13 = e3
% 231.16/42.38  | | | | | | 
% 231.16/42.38  | | | | | | REF_CLOSE: (13), (123), (154) are inconsistent by sub-proof #2268.
% 231.16/42.38  | | | | | | 
% 231.16/42.38  | | | | | End of split
% 231.16/42.38  | | | | | 
% 231.16/42.38  | | | | Case 2:
% 231.16/42.38  | | | | | 
% 231.16/42.38  | | | | |   (155)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0,
% 231.16/42.38  | | | | |              e0) = e3)
% 231.16/42.38  | | | | | 
% 231.16/42.38  | | | | | BETA: splitting (155) gives:
% 231.16/42.38  | | | | | 
% 231.16/42.38  | | | | | Case 1:
% 231.16/42.38  | | | | | | 
% 231.16/42.38  | | | | | |   (156)  all_57_14 = e3 & op(e0, e1) = e3
% 231.16/42.38  | | | | | | 
% 231.16/42.38  | | | | | | ALPHA: (156) implies:
% 231.16/42.38  | | | | | |   (157)  all_57_14 = e3
% 231.16/42.38  | | | | | | 
% 231.16/42.38  | | | | | | BETA: splitting (94) gives:
% 231.16/42.38  | | | | | | 
% 231.16/42.38  | | | | | | Case 1:
% 231.16/42.38  | | | | | | | 
% 231.16/42.38  | | | | | | |   (158)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 &
% 231.16/42.38  | | | | | | |            op(e2, e0) = e3)
% 231.16/42.38  | | | | | | | 
% 231.16/42.38  | | | | | | | BETA: splitting (158) gives:
% 231.16/42.38  | | | | | | | 
% 231.16/42.38  | | | | | | | Case 1:
% 231.16/42.38  | | | | | | | | 
% 231.16/42.38  | | | | | | | |   (159)  all_57_9 = e3 & op(e3, e0) = e3
% 231.16/42.38  | | | | | | | | 
% 231.16/42.38  | | | | | | | | ALPHA: (159) implies:
% 231.16/42.38  | | | | | | | |   (160)  op(e3, e0) = e3
% 231.16/42.38  | | | | | | | | 
% 231.16/42.38  | | | | | | | | REF_CLOSE: (15), (85), (114), (160) are inconsistent by
% 231.16/42.38  | | | | | | | |            sub-proof #2458.
% 231.16/42.38  | | | | | | | | 
% 231.16/42.38  | | | | | | | Case 2:
% 231.16/42.38  | | | | | | | | 
% 231.16/42.38  | | | | | | | |   (161)  all_57_10 = e3 & op(e2, e0) = e3
% 231.16/42.38  | | | | | | | | 
% 231.16/42.38  | | | | | | | | ALPHA: (161) implies:
% 231.16/42.38  | | | | | | | |   (162)  all_57_10 = e3
% 231.16/42.38  | | | | | | | | 
% 231.16/42.38  | | | | | | | | BETA: splitting (14) gives:
% 231.16/42.38  | | | | | | | | 
% 231.16/42.38  | | | | | | | | Case 1:
% 231.16/42.38  | | | | | | | | | 
% 231.16/42.38  | | | | | | | | |   (163)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 &
% 231.16/42.38  | | | | | | | | |            op(e1, e2) = e0)
% 231.16/42.38  | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | BETA: splitting (163) gives:
% 231.16/42.38  | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | Case 1:
% 231.16/42.38  | | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | |   (164)  all_57_6 = e0 & op(e1, e3) = e0
% 231.16/42.38  | | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | | ALPHA: (164) implies:
% 231.16/42.38  | | | | | | | | | |   (165)  all_57_6 = e0
% 231.16/42.38  | | | | | | | | | |   (166)  op(e1, e3) = e0
% 231.16/42.38  | | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | | BETA: splitting (41) gives:
% 231.16/42.38  | | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | | Case 1:
% 231.16/42.38  | | | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | | |   (167)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 231.16/42.38  | | | | | | | | | | |            & op(e2, e1) = e0)
% 231.16/42.38  | | | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 231.16/42.38  | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 231.16/42.38  | | | | | | | | | | |            (19), (20), (21), (22), (24), (25), (26), (27),
% 231.16/42.38  | | | | | | | | | | |            (28), (29), (30), (31), (32), (33), (34), (35),
% 231.16/42.38  | | | | | | | | | | |            (36), (37), (38), (39), (40), (41), (42), (43),
% 231.16/42.38  | | | | | | | | | | |            (44), (45), (46), (47), (48), (49), (50), (51),
% 231.16/42.38  | | | | | | | | | | |            (52), (53), (54), (55), (56), (57), (58), (59),
% 231.16/42.38  | | | | | | | | | | |            (60), (61), (62), (63), (64), (66), (67), (68),
% 231.16/42.38  | | | | | | | | | | |            (69), (70), (71), (72), (73), (74), (75), (76),
% 231.16/42.38  | | | | | | | | | | |            (78), (80), (81), (82), (83), (84), (85), (86),
% 231.16/42.38  | | | | | | | | | | |            (88), (89), (90), (92), (93), (94), (95), (96),
% 231.16/42.38  | | | | | | | | | | |            (97), (98), (99), (101), (102), (103), (104),
% 231.16/42.38  | | | | | | | | | | |            (105), (106), (107), (108), (109), (110), (111),
% 231.16/42.38  | | | | | | | | | | |            (112), (113), (114), (125), (126), (162), (165),
% 231.16/42.38  | | | | | | | | | | |            (166), (167) are inconsistent by sub-proof #1382.
% 231.16/42.38  | | | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | | Case 2:
% 231.16/42.38  | | | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | | |   (168)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 231.16/42.38  | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 231.16/42.38  | | | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | | | BETA: splitting (168) gives:
% 231.16/42.38  | | | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | | | Case 1:
% 231.16/42.38  | | | | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | | | |   (169)  all_57_8 = e0 & op(e1, e1) = e0
% 231.16/42.38  | | | | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | | | | REF_CLOSE: (15), (21), (100), (169) are inconsistent by
% 231.16/42.38  | | | | | | | | | | | |            sub-proof #2412.
% 231.16/42.38  | | | | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | | | Case 2:
% 231.16/42.38  | | | | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | | | |   (170)  all_57_14 = e0 & op(e0, e1) = e0
% 231.16/42.38  | | | | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | | | | REF_CLOSE: (47), (157), (170) are inconsistent by sub-proof
% 231.16/42.38  | | | | | | | | | | | |            #2314.
% 231.16/42.38  | | | | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | | | End of split
% 231.16/42.38  | | | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | | End of split
% 231.16/42.38  | | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | Case 2:
% 231.16/42.38  | | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | |   (171)  all_57_7 = e0 & op(e1, e2) = e0
% 231.16/42.38  | | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | | REF_CLOSE: (47), (87), (171) are inconsistent by sub-proof
% 231.16/42.38  | | | | | | | | | |            #2042.
% 231.16/42.38  | | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | End of split
% 231.16/42.38  | | | | | | | | | 
% 231.16/42.38  | | | | | | | | Case 2:
% 231.16/42.38  | | | | | | | | | 
% 231.16/42.38  | | | | | | | | |   (172)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 &
% 231.16/42.38  | | | | | | | | |            op(e1, e0) = e0)
% 231.16/42.38  | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | BETA: splitting (172) gives:
% 231.16/42.38  | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | Case 1:
% 231.16/42.38  | | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | |   (173)  all_57_8 = e0 & op(e1, e1) = e0
% 231.16/42.38  | | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | | REF_CLOSE: (15), (21), (100), (173) are inconsistent by
% 231.16/42.38  | | | | | | | | | |            sub-proof #2412.
% 231.16/42.38  | | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | Case 2:
% 231.16/42.38  | | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | |   (174)  all_57_11 = e0 & op(e1, e0) = e0
% 231.16/42.38  | | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | | REF_CLOSE: (11), (13), (15), (26), (34), (38), (40), (42),
% 231.16/42.38  | | | | | | | | | |            (47), (49), (59), (63), (87), (91), (96), (111),
% 231.16/42.38  | | | | | | | | | |            (123), (174) are inconsistent by sub-proof #1375.
% 231.16/42.38  | | | | | | | | | | 
% 231.16/42.38  | | | | | | | | | End of split
% 231.16/42.38  | | | | | | | | | 
% 231.16/42.38  | | | | | | | | End of split
% 231.16/42.38  | | | | | | | | 
% 231.16/42.38  | | | | | | | End of split
% 231.16/42.38  | | | | | | | 
% 231.16/42.38  | | | | | | Case 2:
% 231.16/42.38  | | | | | | | 
% 231.16/42.38  | | | | | | |   (175)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 &
% 231.16/42.38  | | | | | | |            op(e0, e0) = e3)
% 231.16/42.38  | | | | | | | 
% 231.16/42.38  | | | | | | | BETA: splitting (175) gives:
% 231.16/42.38  | | | | | | | 
% 231.16/42.38  | | | | | | | Case 1:
% 231.16/42.38  | | | | | | | | 
% 231.16/42.38  | | | | | | | |   (176)  all_57_11 = e3 & op(e1, e0) = e3
% 231.16/42.38  | | | | | | | | 
% 231.16/42.38  | | | | | | | | ALPHA: (176) implies:
% 231.16/42.38  | | | | | | | |   (177)  all_57_11 = e3
% 231.16/42.38  | | | | | | | | 
% 231.16/42.38  | | | | | | | | REF_CLOSE: (13), (91), (177) are inconsistent by sub-proof
% 231.16/42.38  | | | | | | | |            #2218.
% 231.16/42.38  | | | | | | | | 
% 231.16/42.38  | | | | | | | Case 2:
% 231.16/42.38  | | | | | | | | 
% 231.16/42.38  | | | | | | | |   (178)  all_57_15 = e3 & op(e0, e0) = e3
% 231.16/42.38  | | | | | | | | 
% 231.16/42.38  | | | | | | | | ALPHA: (178) implies:
% 231.16/42.38  | | | | | | | |   (179)  all_57_15 = e3
% 231.16/42.38  | | | | | | | | 
% 231.16/42.38  | | | | | | | | REF_CLOSE: (13), (42), (47), (55), (59), (63), (73), (74), (96),
% 231.16/42.38  | | | | | | | |            (157), (179) are inconsistent by sub-proof #2312.
% 231.16/42.38  | | | | | | | | 
% 231.16/42.38  | | | | | | | End of split
% 231.16/42.38  | | | | | | | 
% 231.16/42.38  | | | | | | End of split
% 231.16/42.38  | | | | | | 
% 231.16/42.38  | | | | | Case 2:
% 231.16/42.38  | | | | | | 
% 231.16/42.38  | | | | | |   (180)  all_57_15 = e3 & op(e0, e0) = e3
% 231.16/42.38  | | | | | | 
% 231.16/42.38  | | | | | | ALPHA: (180) implies:
% 231.16/42.38  | | | | | |   (181)  all_57_15 = e3
% 231.16/42.38  | | | | | |   (182)  op(e0, e0) = e3
% 231.16/42.38  | | | | | | 
% 231.16/42.38  | | | | | | REF_CLOSE: (1), (3), (5), (7), (8), (9), (10), (11), (14), (15),
% 231.16/42.38  | | | | | |            (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 231.16/42.38  | | | | | |            (26), (30), (32), (33), (34), (37), (38), (40), (41),
% 231.16/42.38  | | | | | |            (44), (48), (50), (51), (53), (55), (56), (58), (59),
% 231.16/42.38  | | | | | |            (60), (61), (63), (64), (65), (66), (67), (68), (71),
% 231.16/42.38  | | | | | |            (73), (74), (75), (81), (82), (84), (89), (90), (92),
% 231.16/42.38  | | | | | |            (93), (96), (97), (98), (99), (102), (103), (104), (105),
% 231.16/42.38  | | | | | |            (106), (107), (110), (111), (113), (114), (181), (182)
% 231.16/42.38  | | | | | |            are inconsistent by sub-proof #1414.
% 231.16/42.38  | | | | | | 
% 231.16/42.38  | | | | | End of split
% 231.16/42.38  | | | | | 
% 231.16/42.38  | | | | End of split
% 231.16/42.38  | | | | 
% 231.16/42.38  | | | Case 2:
% 231.16/42.38  | | | | 
% 231.16/42.38  | | | |   (183)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2,
% 231.16/42.39  | | | |                e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) &
% 231.16/42.39  | | | |          ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0,
% 231.16/42.39  | | | |                e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 231.16/42.39  | | | | 
% 231.16/42.39  | | | | ALPHA: (183) implies:
% 231.16/42.39  | | | |   (184)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2,
% 231.16/42.39  | | | |              e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.16/42.39  | | | | 
% 231.16/42.39  | | | | BETA: splitting (184) gives:
% 231.16/42.39  | | | | 
% 231.16/42.39  | | | | Case 1:
% 231.16/42.39  | | | | | 
% 231.16/42.39  | | | | |   (185)  all_57_9 = e0 & op(e3, e0) = e0
% 231.16/42.39  | | | | | 
% 231.16/42.39  | | | | | ALPHA: (185) implies:
% 231.16/42.39  | | | | |   (186)  all_57_9 = e0
% 231.16/42.39  | | | | | 
% 231.16/42.39  | | | | | REF_CLOSE: (13), (15), (42), (47), (59), (79), (91), (94), (96), (97),
% 231.16/42.39  | | | | |            (186) are inconsistent by sub-proof #2047.
% 231.16/42.39  | | | | | 
% 231.16/42.39  | | | | Case 2:
% 231.16/42.39  | | | | | 
% 231.16/42.39  | | | | |   (187)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 231.16/42.39  | | | | |              e0) = e0)
% 231.16/42.39  | | | | | 
% 231.16/42.39  | | | | | BETA: splitting (187) gives:
% 231.16/42.39  | | | | | 
% 231.16/42.39  | | | | | Case 1:
% 231.16/42.39  | | | | | | 
% 231.16/42.39  | | | | | |   (188)  all_57_10 = e0 & op(e2, e0) = e0
% 231.16/42.39  | | | | | | 
% 231.16/42.39  | | | | | | ALPHA: (188) implies:
% 231.16/42.39  | | | | | |   (189)  op(e2, e0) = e0
% 231.16/42.39  | | | | | | 
% 231.16/42.39  | | | | | | REF_CLOSE: (15), (77), (80), (189) are inconsistent by sub-proof
% 231.16/42.39  | | | | | |            #2470.
% 231.16/42.39  | | | | | | 
% 231.16/42.39  | | | | | Case 2:
% 231.16/42.39  | | | | | | 
% 231.16/42.39  | | | | | |   (190)  all_57_11 = e0 & op(e1, e0) = e0
% 231.16/42.39  | | | | | | 
% 231.16/42.39  | | | | | | REF_CLOSE: (11), (13), (15), (26), (34), (38), (40), (42), (47),
% 231.16/42.39  | | | | | |            (49), (59), (63), (87), (91), (96), (111), (123), (190)
% 231.16/42.39  | | | | | |            are inconsistent by sub-proof #1375.
% 231.16/42.39  | | | | | | 
% 231.16/42.39  | | | | | End of split
% 231.16/42.39  | | | | | 
% 231.16/42.39  | | | | End of split
% 231.16/42.39  | | | | 
% 231.16/42.39  | | | End of split
% 231.16/42.39  | | | 
% 231.16/42.39  | | End of split
% 231.16/42.39  | | 
% 231.16/42.39  | End of split
% 231.16/42.39  | 
% 231.16/42.39  End of proof
% 231.16/42.39  
% 231.16/42.39  Sub-proof #1375 shows that the following formulas are inconsistent:
% 231.16/42.39  ----------------------------------------------------------------
% 231.16/42.39    (1)  all_57_11 = e0 & op(e1, e0) = e0
% 231.16/42.39    (2)  all_57_13 = e1
% 231.16/42.39    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.16/42.39         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.16/42.39    (4)   ~ (e3 = e1)
% 231.16/42.39    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.16/42.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.16/42.39    (6)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.16/42.39         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.16/42.39    (7)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.16/42.39         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.16/42.39    (8)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.16/42.39         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.16/42.39    (9)  all_57_3 = e0
% 231.16/42.39    (10)   ~ (e3 = e2)
% 231.16/42.39    (11)   ~ (e3 = e0)
% 231.16/42.39    (12)  op(e3, e3) = e3
% 231.16/42.39    (13)   ~ (e2 = e0)
% 231.16/42.39    (14)   ~ (e1 = e0)
% 231.16/42.39    (15)  all_57_7 = e3
% 231.16/42.39    (16)  all_57_11 = e1
% 231.16/42.39    (17)   ~ (e2 = e1)
% 231.16/42.39    (18)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.16/42.39          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.16/42.39  
% 231.16/42.39  Begin of proof
% 231.16/42.39  | 
% 231.16/42.39  | ALPHA: (1) implies:
% 231.16/42.39  |   (19)  all_57_11 = e0
% 231.16/42.39  | 
% 231.16/42.39  | COMBINE_EQS: (16), (19) imply:
% 231.16/42.39  |   (20)  e1 = e0
% 231.16/42.39  | 
% 231.16/42.39  | COMBINE_EQS: (2), (20) imply:
% 231.16/42.39  |   (21)  all_57_13 = e0
% 231.16/42.39  | 
% 231.16/42.39  | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), (14),
% 231.16/42.39  |            (15), (17), (18), (21) are inconsistent by sub-proof #2091.
% 231.16/42.39  | 
% 231.16/42.39  End of proof
% 231.16/42.39  
% 231.16/42.39  Sub-proof #1376 shows that the following formulas are inconsistent:
% 231.16/42.39  ----------------------------------------------------------------
% 231.16/42.39    (1)   ~ (all_10_2 = e2)
% 231.16/42.39    (2)  all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 231.16/42.39    (3)  op(e3, e3) = all_10_2
% 231.16/42.39    (4)  op(e0, e1) = all_53_11
% 231.16/42.39    (5)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 231.16/42.39    (6)   ~ (all_53_6 = all_53_14)
% 231.16/42.39    (7)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 231.16/42.39    (8)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.16/42.39         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.16/42.39    (9)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.16/42.39         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.16/42.39    (10)   ~ (all_53_8 = all_53_12)
% 231.16/42.39    (11)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.16/42.39          (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.16/42.39    (12)   ~ (all_53_8 = all_53_11)
% 231.16/42.39    (13)   ~ (e3 = e1)
% 231.16/42.39    (14)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 231.16/42.39          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.16/42.39    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.16/42.39            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.16/42.39    (16)  all_55_0 = all_10_2
% 231.16/42.39    (17)   ~ (all_10_2 = e0)
% 231.16/42.39    (18)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.16/42.39          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.16/42.39    (19)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 231.16/42.39            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 231.16/42.39              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 231.16/42.39    (20)   ~ (all_6_2 = e3)
% 231.16/42.39    (21)  op(e1, e1) = all_6_2
% 231.16/42.39    (22)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 231.16/42.39    (23)   ~ (all_53_9 = e0)
% 231.16/42.39    (24)  all_55_0 = e3 | all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 231.16/42.39    (25)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 231.16/42.39    (26)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.16/42.39          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.16/42.39    (27)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 231.16/42.39    (28)  all_55_9 = all_53_6
% 231.16/42.39    (29)   ~ (all_53_11 = all_6_2)
% 231.16/42.39    (30)   ~ (all_53_4 = all_53_12)
% 231.16/42.39    (31)   ~ (all_53_8 = e3)
% 231.16/42.39    (32)   ~ (all_53_8 = all_53_9)
% 231.16/42.39    (33)  all_42_2 = all_6_2
% 231.16/42.39    (34)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.16/42.39          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.16/42.39    (35)  op(e2, e2) = e0
% 231.16/42.39    (36)   ~ (all_53_9 = all_53_11)
% 231.16/42.39    (37)   ~ (all_53_9 = all_6_2)
% 231.16/42.39    (38)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.16/42.39          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.16/42.39    (39)   ~ (all_53_14 = all_6_2)
% 231.16/42.39    (40)  all_57_3 = e0
% 231.16/42.39    (41)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.16/42.39          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.16/42.39    (42)   ~ (e3 = e2)
% 231.16/42.39    (43)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 231.16/42.39    (44)  all_55_1 = all_53_4
% 231.16/42.39    (45)  op(e1, e0) = all_53_14
% 231.16/42.39    (46)   ~ (all_53_6 = all_53_7)
% 231.16/42.39    (47)   ~ (e3 = e0)
% 231.16/42.39    (48)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.16/42.39          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.16/42.39    (49)  op(e3, e3) = e3
% 231.16/42.39    (50)   ~ (all_53_8 = all_6_2)
% 231.16/42.39    (51)  all_55_2 = all_53_8
% 231.16/42.39    (52)   ~ (all_53_4 = all_53_7)
% 231.16/42.39    (53)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 231.16/42.39    (54)  all_57_1 = e1
% 231.16/42.39    (55)   ~ (all_53_7 = e0)
% 231.16/42.39    (56)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.16/42.39          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.16/42.39            e1)
% 231.16/42.39    (57)   ~ (all_53_4 = all_53_8)
% 231.16/42.39    (58)  all_55_6 = all_53_9
% 231.16/42.39    (59)  op(e3, e2) = all_53_4
% 231.16/42.39    (60)   ~ (e2 = e0)
% 231.16/42.39    (61)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 231.16/42.39            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 231.16/42.39            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 231.16/42.39            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 231.16/42.39              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 231.16/42.39            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 231.16/42.39            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 231.16/42.39              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 231.16/42.39              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 231.16/42.39            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 231.16/42.39            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 231.16/42.39            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 231.16/42.39              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 231.16/42.39              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 231.16/42.39            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 231.16/42.39              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 231.16/42.39            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 231.16/42.39            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 231.16/42.39              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 231.16/42.39              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 231.16/42.39            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 231.16/42.39            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 231.16/42.39    (62)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 231.16/42.39          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.16/42.39    (63)   ~ (all_53_2 = all_53_14)
% 231.16/42.39    (64)   ~ (e1 = e0)
% 231.16/42.39    (65)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 231.16/42.39            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 231.16/42.39              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 231.16/42.39    (66)   ~ (all_53_4 = e0)
% 231.16/42.39    (67)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.16/42.39          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.16/42.39    (68)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.16/42.39          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.16/42.39    (69)   ~ (all_10_2 = e1)
% 231.16/42.39    (70)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 231.16/42.39    (71)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.16/42.39          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 231.16/42.39            e3)
% 231.16/42.39    (72)   ~ (all_53_4 = all_53_6)
% 231.16/42.39    (73)  op(e0, e2) = all_53_7
% 231.16/42.39    (74)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.16/42.39          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.16/42.39            e2)
% 231.16/42.39    (75)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.16/42.39              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.16/42.39                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.16/42.39                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.16/42.39    (76)  all_55_10 = all_6_2
% 231.16/42.39    (77)   ~ (all_53_6 = all_6_2)
% 231.16/42.39    (78)   ~ (all_53_13 = e0)
% 231.16/42.39    (79)  all_55_13 = all_53_7
% 231.16/42.39    (80)  op(e0, e0) = e1
% 231.16/42.39    (81)  op(e2, e0) = all_53_13
% 231.16/42.39    (82)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.16/42.39          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.16/42.39    (83)  all_38_2 = all_6_2
% 231.16/42.39    (84)  all_55_11 = all_53_14
% 231.16/42.39    (85)  all_55_3 = all_53_12
% 231.16/42.39    (86)   ~ (all_53_12 = e3)
% 231.16/42.39    (87)  all_57_0 = e3
% 231.16/42.39    (88)  all_57_7 = e3
% 231.16/42.39    (89)  op(e1, e3) = all_53_2
% 231.16/42.39    (90)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 231.16/42.39            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 231.16/42.39              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 231.16/42.39    (91)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.16/42.39          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.16/42.39    (92)  all_57_11 = e1
% 231.16/42.39    (93)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 231.16/42.39          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 231.16/42.39    (94)   ~ (all_53_12 = all_10_2)
% 231.16/42.39    (95)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 231.16/42.39          (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 231.16/42.39    (96)   ~ (all_53_13 = all_53_14)
% 231.16/42.39    (97)   ~ (e2 = e1)
% 231.16/42.39    (98)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.16/42.39          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.16/42.39    (99)  op(e2, e1) = all_53_9
% 231.16/42.39    (100)  op(e1, e2) = all_53_6
% 231.16/42.39    (101)   ~ (all_6_2 = e0)
% 231.16/42.39    (102)   ~ (all_53_2 = all_53_6)
% 231.16/42.39    (103)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.16/42.39           (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.16/42.39    (104)  all_24_2 = all_6_2
% 231.16/42.39    (105)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.16/42.39           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.16/42.39    (106)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.16/42.39           (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.16/42.39    (107)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.16/42.39           | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.16/42.39             e1)
% 231.16/42.39    (108)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 231.16/42.39           (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 231.16/42.39    (109)   ~ (all_53_12 = all_53_14)
% 231.16/42.39    (110)  all_55_14 = all_53_11
% 231.16/42.39    (111)  op(e3, e1) = all_53_8
% 231.16/42.39    (112)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.16/42.39           (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.16/42.39    (113)   ~ (all_53_4 = e3)
% 231.16/42.39    (114)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 231.16/42.39           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 231.16/42.39    (115)  op(e3, e0) = all_53_12
% 231.16/42.39  
% 231.16/42.39  Begin of proof
% 231.16/42.39  | 
% 231.16/42.39  | BETA: splitting (75) gives:
% 231.16/42.39  | 
% 231.16/42.39  | Case 1:
% 231.16/42.39  | | 
% 231.16/42.39  | |   (116)  all_57_15 = e0 & op(e0, e0) = e0
% 231.16/42.39  | | 
% 231.16/42.39  | | ALPHA: (116) implies:
% 231.16/42.39  | |   (117)  all_57_15 = e0
% 231.16/42.39  | |   (118)  op(e0, e0) = e0
% 231.16/42.39  | | 
% 231.16/42.39  | | BETA: splitting (14) gives:
% 231.16/42.39  | | 
% 231.16/42.39  | | Case 1:
% 231.16/42.39  | | | 
% 231.16/42.39  | | |   (119)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) =
% 231.16/42.39  | | |            e0)
% 231.16/42.39  | | | 
% 231.16/42.39  | | | BETA: splitting (119) gives:
% 231.16/42.39  | | | 
% 231.16/42.39  | | | Case 1:
% 231.16/42.39  | | | | 
% 231.16/42.39  | | | |   (120)  all_57_6 = e0 & op(e1, e3) = e0
% 231.16/42.39  | | | | 
% 231.16/42.39  | | | | ALPHA: (120) implies:
% 231.16/42.39  | | | |   (121)  all_57_6 = e0
% 231.16/42.39  | | | |   (122)  op(e1, e3) = e0
% 231.16/42.39  | | | | 
% 231.16/42.39  | | | | BETA: splitting (95) gives:
% 231.16/42.39  | | | | 
% 231.16/42.39  | | | | Case 1:
% 231.16/42.39  | | | | | 
% 231.16/42.39  | | | | |   (123)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2,
% 231.16/42.39  | | | | |              e0) = e3)
% 231.16/42.39  | | | | | 
% 231.16/42.39  | | | | | BETA: splitting (123) gives:
% 231.16/42.39  | | | | | 
% 231.16/42.39  | | | | | Case 1:
% 231.16/42.39  | | | | | | 
% 231.16/42.39  | | | | | |   (124)  all_57_9 = e3 & op(e3, e0) = e3
% 231.16/42.39  | | | | | | 
% 231.16/42.39  | | | | | | ALPHA: (124) implies:
% 231.16/42.39  | | | | | |   (125)  op(e3, e0) = e3
% 231.16/42.39  | | | | | | 
% 231.16/42.39  | | | | | | REF_CLOSE: (15), (86), (115), (125) are inconsistent by sub-proof
% 231.16/42.39  | | | | | |            #2458.
% 231.16/42.39  | | | | | | 
% 231.16/42.39  | | | | | Case 2:
% 231.16/42.39  | | | | | | 
% 231.16/42.39  | | | | | |   (126)  all_57_10 = e3 & op(e2, e0) = e3
% 231.16/42.39  | | | | | | 
% 231.16/42.39  | | | | | | ALPHA: (126) implies:
% 231.16/42.39  | | | | | |   (127)  all_57_10 = e3
% 231.16/42.39  | | | | | | 
% 231.16/42.39  | | | | | | BETA: splitting (9) gives:
% 231.16/42.39  | | | | | | 
% 231.16/42.39  | | | | | | Case 1:
% 231.16/42.39  | | | | | | | 
% 231.16/42.39  | | | | | | |   (128)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 &
% 231.16/42.39  | | | | | | |            op(e2, e3) = e1)
% 231.16/42.39  | | | | | | | 
% 231.16/42.39  | | | | | | | BETA: splitting (128) gives:
% 231.16/42.39  | | | | | | | 
% 231.16/42.39  | | | | | | | Case 1:
% 231.16/42.39  | | | | | | | | 
% 231.16/42.39  | | | | | | | |   (129)  all_57_0 = e1 & op(e3, e3) = e1
% 231.16/42.39  | | | | | | | | 
% 231.16/42.39  | | | | | | | | ALPHA: (129) implies:
% 231.16/42.39  | | | | | | | |   (130)  op(e3, e3) = e1
% 231.16/42.39  | | | | | | | | 
% 231.16/42.39  | | | | | | | | REF_CLOSE: (13), (15), (49), (130) are inconsistent by sub-proof
% 231.16/42.39  | | | | | | | |            #2495.
% 231.16/42.39  | | | | | | | | 
% 231.16/42.39  | | | | | | | Case 2:
% 231.16/42.39  | | | | | | | | 
% 231.16/42.39  | | | | | | | |   (131)  all_57_2 = e1 & op(e2, e3) = e1
% 231.16/42.39  | | | | | | | | 
% 231.16/42.39  | | | | | | | | ALPHA: (131) implies:
% 231.16/42.39  | | | | | | | |   (132)  all_57_2 = e1
% 231.16/42.39  | | | | | | | | 
% 231.16/42.39  | | | | | | | | BETA: splitting (91) gives:
% 231.16/42.39  | | | | | | | | 
% 231.16/42.39  | | | | | | | | Case 1:
% 231.16/42.39  | | | | | | | | | 
% 231.16/42.39  | | | | | | | | |   (133)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 &
% 231.16/42.39  | | | | | | | | |            op(e2, e2) = e2)
% 231.16/42.39  | | | | | | | | | 
% 231.16/42.39  | | | | | | | | | REF_CLOSE: (15), (35), (60), (97), (132), (133) are
% 231.16/42.39  | | | | | | | | |            inconsistent by sub-proof #2364.
% 231.16/42.39  | | | | | | | | | 
% 231.16/42.39  | | | | | | | | Case 2:
% 231.16/42.39  | | | | | | | | | 
% 231.16/42.39  | | | | | | | | |   (134)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 &
% 231.16/42.39  | | | | | | | | |            op(e2, e0) = e2)
% 231.16/42.39  | | | | | | | | | 
% 231.16/42.39  | | | | | | | | | BETA: splitting (134) gives:
% 231.16/42.39  | | | | | | | | | 
% 231.16/42.39  | | | | | | | | | Case 1:
% 231.16/42.39  | | | | | | | | | | 
% 231.16/42.39  | | | | | | | | | |   (135)  all_57_5 = e2 & op(e2, e1) = e2
% 231.16/42.39  | | | | | | | | | | 
% 231.16/42.39  | | | | | | | | | | ALPHA: (135) implies:
% 231.16/42.39  | | | | | | | | | |   (136)  all_57_5 = e2
% 231.16/42.39  | | | | | | | | | | 
% 231.16/42.39  | | | | | | | | | | BETA: splitting (11) gives:
% 231.16/42.39  | | | | | | | | | | 
% 231.16/42.39  | | | | | | | | | | Case 1:
% 231.16/42.39  | | | | | | | | | | | 
% 231.16/42.39  | | | | | | | | | | |   (137)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 231.16/42.39  | | | | | | | | | | |            & op(e2, e2) = e2)
% 231.16/42.39  | | | | | | | | | | | 
% 231.16/42.39  | | | | | | | | | | | BETA: splitting (137) gives:
% 231.16/42.39  | | | | | | | | | | | 
% 231.16/42.39  | | | | | | | | | | | Case 1:
% 231.16/42.39  | | | | | | | | | | | | 
% 231.16/42.39  | | | | | | | | | | | |   (138)  all_57_1 = e2 & op(e3, e2) = e2
% 231.16/42.39  | | | | | | | | | | | | 
% 231.16/42.39  | | | | | | | | | | | | ALPHA: (138) implies:
% 231.16/42.39  | | | | | | | | | | | |   (139)  all_57_1 = e2
% 231.16/42.39  | | | | | | | | | | | | 
% 231.16/42.39  | | | | | | | | | | | | COMBINE_EQS: (54), (139) imply:
% 231.16/42.39  | | | | | | | | | | | |   (140)  e2 = e1
% 231.16/42.39  | | | | | | | | | | | | 
% 231.16/42.39  | | | | | | | | | | | | SIMP: (140) implies:
% 231.16/42.39  | | | | | | | | | | | |   (141)  e2 = e1
% 231.16/42.39  | | | | | | | | | | | | 
% 231.16/42.39  | | | | | | | | | | | | COMBINE_EQS: (136), (141) imply:
% 231.16/42.39  | | | | | | | | | | | |   (142)  all_57_5 = e1
% 231.16/42.39  | | | | | | | | | | | | 
% 231.16/42.39  | | | | | | | | | | | | REF_CLOSE: (13), (15), (35), (40), (42), (47), (60), (82),
% 231.16/42.39  | | | | | | | | | | | |            (91), (97), (132), (142) are inconsistent by
% 231.16/42.39  | | | | | | | | | | | |            sub-proof #1536.
% 231.16/42.39  | | | | | | | | | | | | 
% 231.16/42.39  | | | | | | | | | | | Case 2:
% 231.16/42.39  | | | | | | | | | | | | 
% 231.16/42.39  | | | | | | | | | | | |   (143)  all_57_3 = e2 & op(e2, e2) = e2
% 231.16/42.39  | | | | | | | | | | | | 
% 231.16/42.39  | | | | | | | | | | | | ALPHA: (143) implies:
% 231.16/42.39  | | | | | | | | | | | |   (144)  op(e2, e2) = e2
% 231.16/42.39  | | | | | | | | | | | | 
% 231.16/42.39  | | | | | | | | | | | | REF_CLOSE: (15), (35), (60), (144) are inconsistent by
% 231.16/42.39  | | | | | | | | | | | |            sub-proof #2472.
% 231.16/42.39  | | | | | | | | | | | | 
% 231.16/42.39  | | | | | | | | | | | End of split
% 231.16/42.39  | | | | | | | | | | | 
% 231.16/42.39  | | | | | | | | | | Case 2:
% 231.16/42.39  | | | | | | | | | | | 
% 231.16/42.39  | | | | | | | | | | |   (145)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 231.16/42.39  | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 231.16/42.39  | | | | | | | | | | | 
% 231.16/42.39  | | | | | | | | | | | BETA: splitting (145) gives:
% 231.16/42.39  | | | | | | | | | | | 
% 231.16/42.39  | | | | | | | | | | | Case 1:
% 231.16/42.39  | | | | | | | | | | | | 
% 231.16/42.39  | | | | | | | | | | | |   (146)  all_57_7 = e2 & op(e1, e2) = e2
% 231.16/42.39  | | | | | | | | | | | | 
% 231.16/42.39  | | | | | | | | | | | | REF_CLOSE: (42), (88), (146) are inconsistent by sub-proof
% 231.16/42.39  | | | | | | | | | | | |            #2092.
% 231.16/42.39  | | | | | | | | | | | | 
% 231.16/42.39  | | | | | | | | | | | Case 2:
% 231.16/42.39  | | | | | | | | | | | | 
% 231.16/42.39  | | | | | | | | | | | |   (147)  all_57_13 = e2 & op(e0, e2) = e2
% 231.16/42.39  | | | | | | | | | | | | 
% 231.16/42.39  | | | | | | | | | | | | ALPHA: (147) implies:
% 231.16/42.39  | | | | | | | | | | | |   (148)  all_57_13 = e2
% 231.16/42.39  | | | | | | | | | | | | 
% 231.16/42.39  | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 231.16/42.39  | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 231.16/42.39  | | | | | | | | | | | |            (19), (20), (21), (22), (24), (25), (26), (27),
% 231.16/42.39  | | | | | | | | | | | |            (28), (29), (30), (31), (32), (33), (34), (35),
% 231.16/42.39  | | | | | | | | | | | |            (36), (37), (38), (39), (40), (41), (42), (43),
% 231.16/42.39  | | | | | | | | | | | |            (44), (45), (46), (47), (48), (49), (50), (51),
% 231.16/42.39  | | | | | | | | | | | |            (52), (53), (55), (56), (57), (58), (59), (60),
% 231.16/42.39  | | | | | | | | | | | |            (61), (62), (63), (64), (65), (67), (68), (69),
% 231.16/42.39  | | | | | | | | | | | |            (70), (71), (72), (73), (74), (75), (76), (77),
% 231.16/42.39  | | | | | | | | | | | |            (79), (81), (82), (83), (84), (85), (86), (87),
% 231.16/42.39  | | | | | | | | | | | |            (88), (89), (90), (91), (93), (94), (95), (96),
% 231.16/42.39  | | | | | | | | | | | |            (97), (98), (99), (100), (101), (102), (103),
% 231.16/42.39  | | | | | | | | | | | |            (104), (105), (106), (107), (108), (109), (110),
% 231.16/42.39  | | | | | | | | | | | |            (111), (112), (113), (114), (115), (117), (118),
% 231.16/42.39  | | | | | | | | | | | |            (121), (122), (127), (148) are inconsistent by
% 231.16/42.39  | | | | | | | | | | | |            sub-proof #1380.
% 231.16/42.39  | | | | | | | | | | | | 
% 231.16/42.39  | | | | | | | | | | | End of split
% 231.16/42.39  | | | | | | | | | | | 
% 231.16/42.39  | | | | | | | | | | End of split
% 231.16/42.39  | | | | | | | | | | 
% 231.16/42.39  | | | | | | | | | Case 2:
% 231.16/42.39  | | | | | | | | | | 
% 231.16/42.39  | | | | | | | | | |   (149)  all_57_10 = e2 & op(e2, e0) = e2
% 231.16/42.39  | | | | | | | | | | 
% 231.16/42.40  | | | | | | | | | | REF_CLOSE: (42), (127), (149) are inconsistent by sub-proof
% 231.16/42.40  | | | | | | | | | |            #2250.
% 231.16/42.40  | | | | | | | | | | 
% 231.16/42.40  | | | | | | | | | End of split
% 231.16/42.40  | | | | | | | | | 
% 231.16/42.40  | | | | | | | | End of split
% 231.16/42.40  | | | | | | | | 
% 231.16/42.40  | | | | | | | End of split
% 231.16/42.40  | | | | | | | 
% 231.16/42.40  | | | | | | Case 2:
% 231.16/42.40  | | | | | | | 
% 231.16/42.40  | | | | | | |   (150)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 &
% 231.16/42.40  | | | | | | |            op(e0, e3) = e1)
% 231.16/42.40  | | | | | | | 
% 231.16/42.40  | | | | | | | BETA: splitting (150) gives:
% 231.16/42.40  | | | | | | | 
% 231.16/42.40  | | | | | | | Case 1:
% 231.16/42.40  | | | | | | | | 
% 231.16/42.40  | | | | | | | |   (151)  all_57_6 = e1 & op(e1, e3) = e1
% 231.16/42.40  | | | | | | | | 
% 231.16/42.40  | | | | | | | | ALPHA: (151) implies:
% 231.16/42.40  | | | | | | | |   (152)  all_57_6 = e1
% 231.16/42.40  | | | | | | | | 
% 231.16/42.40  | | | | | | | | COMBINE_EQS: (121), (152) imply:
% 231.16/42.40  | | | | | | | |   (153)  e1 = e0
% 231.16/42.40  | | | | | | | | 
% 231.16/42.40  | | | | | | | | REF_CLOSE: (11), (13), (40), (42), (54), (60), (64), (88), (97),
% 231.16/42.40  | | | | | | | |            (112), (153) are inconsistent by sub-proof #1626.
% 231.16/42.40  | | | | | | | | 
% 231.16/42.40  | | | | | | | Case 2:
% 231.16/42.40  | | | | | | | | 
% 231.16/42.40  | | | | | | | |   (154)  all_57_12 = e1 & op(e0, e3) = e1
% 231.16/42.40  | | | | | | | | 
% 231.16/42.40  | | | | | | | | ALPHA: (154) implies:
% 231.16/42.40  | | | | | | | |   (155)  all_57_12 = e1
% 231.16/42.40  | | | | | | | | 
% 231.16/42.40  | | | | | | | | BETA: splitting (11) gives:
% 231.16/42.40  | | | | | | | | 
% 231.16/42.40  | | | | | | | | Case 1:
% 231.16/42.40  | | | | | | | | | 
% 231.16/42.40  | | | | | | | | |   (156)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 &
% 231.16/42.40  | | | | | | | | |            op(e2, e2) = e2)
% 231.16/42.40  | | | | | | | | | 
% 231.16/42.40  | | | | | | | | | REF_CLOSE: (15), (35), (54), (60), (97), (156) are
% 231.16/42.40  | | | | | | | | |            inconsistent by sub-proof #2208.
% 231.16/42.40  | | | | | | | | | 
% 231.16/42.40  | | | | | | | | Case 2:
% 231.16/42.40  | | | | | | | | | 
% 231.16/42.40  | | | | | | | | |   (157)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 &
% 231.16/42.40  | | | | | | | | |            op(e0, e2) = e2)
% 231.16/42.40  | | | | | | | | | 
% 231.16/42.40  | | | | | | | | | BETA: splitting (157) gives:
% 231.16/42.40  | | | | | | | | | 
% 231.16/42.40  | | | | | | | | | Case 1:
% 231.16/42.40  | | | | | | | | | | 
% 231.16/42.40  | | | | | | | | | |   (158)  all_57_7 = e2 & op(e1, e2) = e2
% 231.16/42.40  | | | | | | | | | | 
% 231.16/42.40  | | | | | | | | | | REF_CLOSE: (42), (88), (158) are inconsistent by sub-proof
% 231.16/42.40  | | | | | | | | | |            #2092.
% 231.16/42.40  | | | | | | | | | | 
% 231.16/42.40  | | | | | | | | | Case 2:
% 231.16/42.40  | | | | | | | | | | 
% 231.16/42.40  | | | | | | | | | |   (159)  all_57_13 = e2 & op(e0, e2) = e2
% 231.16/42.40  | | | | | | | | | | 
% 231.16/42.40  | | | | | | | | | | ALPHA: (159) implies:
% 231.16/42.40  | | | | | | | | | |   (160)  all_57_13 = e2
% 231.16/42.40  | | | | | | | | | | 
% 231.16/42.40  | | | | | | | | | | BETA: splitting (71) gives:
% 231.16/42.40  | | | | | | | | | | 
% 231.16/42.40  | | | | | | | | | | Case 1:
% 231.16/42.40  | | | | | | | | | | | 
% 231.16/42.40  | | | | | | | | | | |   (161)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 231.16/42.40  | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 231.16/42.40  | | | | | | | | | | | 
% 231.16/42.40  | | | | | | | | | | | REF_CLOSE: (13), (42), (155), (160), (161) are inconsistent
% 231.16/42.40  | | | | | | | | | | |            by sub-proof #1585.
% 231.16/42.40  | | | | | | | | | | | 
% 231.16/42.40  | | | | | | | | | | Case 2:
% 231.16/42.40  | | | | | | | | | | | 
% 231.16/42.40  | | | | | | | | | | |   (162)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 231.16/42.40  | | | | | | | | | | |            e3 & op(e0, e0) = e3)
% 231.16/42.40  | | | | | | | | | | | 
% 231.16/42.40  | | | | | | | | | | | BETA: splitting (162) gives:
% 231.16/42.40  | | | | | | | | | | | 
% 231.16/42.40  | | | | | | | | | | | Case 1:
% 231.16/42.40  | | | | | | | | | | | | 
% 231.16/42.40  | | | | | | | | | | | |   (163)  all_57_14 = e3 & op(e0, e1) = e3
% 231.16/42.40  | | | | | | | | | | | | 
% 231.16/42.40  | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 231.16/42.40  | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 231.16/42.40  | | | | | | | | | | | |            (19), (20), (21), (22), (24), (25), (26), (27),
% 231.16/42.40  | | | | | | | | | | | |            (28), (29), (30), (31), (32), (33), (34), (35),
% 231.16/42.40  | | | | | | | | | | | |            (36), (37), (38), (39), (40), (41), (42), (43),
% 231.16/42.40  | | | | | | | | | | | |            (44), (45), (46), (47), (48), (49), (50), (51),
% 231.16/42.40  | | | | | | | | | | | |            (52), (53), (55), (56), (57), (58), (59), (60),
% 231.16/42.40  | | | | | | | | | | | |            (61), (62), (63), (64), (65), (67), (68), (69),
% 231.16/42.40  | | | | | | | | | | | |            (70), (71), (72), (73), (74), (75), (76), (77),
% 231.16/42.40  | | | | | | | | | | | |            (79), (81), (82), (83), (84), (85), (86), (87),
% 231.16/42.40  | | | | | | | | | | | |            (88), (89), (90), (91), (93), (94), (95), (96),
% 231.16/42.40  | | | | | | | | | | | |            (97), (98), (99), (100), (101), (102), (103),
% 231.16/42.40  | | | | | | | | | | | |            (104), (105), (106), (107), (108), (109), (110),
% 231.16/42.40  | | | | | | | | | | | |            (111), (112), (113), (114), (115), (117), (118),
% 231.16/42.40  | | | | | | | | | | | |            (121), (122), (127), (160), (163) are inconsistent
% 231.16/42.40  | | | | | | | | | | | |            by sub-proof #1381.
% 231.16/42.40  | | | | | | | | | | | | 
% 231.16/42.40  | | | | | | | | | | | Case 2:
% 231.16/42.40  | | | | | | | | | | | | 
% 231.16/42.40  | | | | | | | | | | | |   (164)  all_57_15 = e3 & op(e0, e0) = e3
% 231.16/42.40  | | | | | | | | | | | | 
% 231.16/42.40  | | | | | | | | | | | | ALPHA: (164) implies:
% 231.16/42.40  | | | | | | | | | | | |   (165)  all_57_15 = e3
% 231.16/42.40  | | | | | | | | | | | | 
% 231.16/42.40  | | | | | | | | | | | | REF_CLOSE: (8), (9), (11), (13), (14), (15), (18), (20),
% 231.16/42.40  | | | | | | | | | | | |            (21), (26), (34), (38), (40), (41), (42), (47),
% 231.16/42.40  | | | | | | | | | | | |            (49), (56), (60), (64), (67), (68), (74), (75),
% 231.16/42.40  | | | | | | | | | | | |            (91), (93), (97), (98), (103), (105), (106),
% 231.16/42.40  | | | | | | | | | | | |            (107), (112), (127), (165) are inconsistent by
% 231.16/42.40  | | | | | | | | | | | |            sub-proof #1416.
% 231.16/42.40  | | | | | | | | | | | | 
% 231.16/42.40  | | | | | | | | | | | End of split
% 231.16/42.40  | | | | | | | | | | | 
% 231.16/42.40  | | | | | | | | | | End of split
% 231.16/42.40  | | | | | | | | | | 
% 231.16/42.40  | | | | | | | | | End of split
% 231.16/42.40  | | | | | | | | | 
% 231.16/42.40  | | | | | | | | End of split
% 231.16/42.40  | | | | | | | | 
% 231.16/42.40  | | | | | | | End of split
% 231.16/42.40  | | | | | | | 
% 231.16/42.40  | | | | | | End of split
% 231.16/42.40  | | | | | | 
% 231.16/42.40  | | | | | End of split
% 231.16/42.40  | | | | | 
% 231.16/42.40  | | | | Case 2:
% 231.16/42.40  | | | | | 
% 231.16/42.40  | | | | |   (166)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0,
% 231.16/42.40  | | | | |              e0) = e3)
% 231.16/42.40  | | | | | 
% 231.16/42.40  | | | | | REF_CLOSE: (1), (3), (5), (7), (8), (9), (10), (11), (13), (14), (15),
% 231.16/42.40  | | | | |            (16), (17), (18), (19), (20), (21), (22), (23), (24), (26),
% 231.16/42.40  | | | | |            (30), (32), (33), (34), (37), (38), (40), (41), (44), (48),
% 231.16/42.40  | | | | |            (50), (51), (53), (56), (57), (59), (60), (61), (62), (64),
% 231.16/42.40  | | | | |            (65), (66), (67), (68), (69), (72), (74), (75), (76), (82),
% 231.16/42.40  | | | | |            (83), (85), (90), (91), (92), (93), (94), (97), (98), (99),
% 231.16/42.40  | | | | |            (100), (103), (104), (105), (106), (107), (108), (111),
% 231.16/42.40  | | | | |            (112), (114), (115), (166) are inconsistent by sub-proof
% 231.16/42.40  | | | | |            #1379.
% 231.16/42.40  | | | | | 
% 231.16/42.40  | | | | End of split
% 231.16/42.40  | | | | 
% 231.16/42.40  | | | Case 2:
% 231.16/42.40  | | | | 
% 231.16/42.40  | | | |   (167)  all_57_7 = e0 & op(e1, e2) = e0
% 231.16/42.40  | | | | 
% 231.16/42.40  | | | | ALPHA: (167) implies:
% 231.16/42.40  | | | |   (168)  all_57_7 = e0
% 231.16/42.40  | | | | 
% 231.16/42.40  | | | | REF_CLOSE: (11), (13), (15), (35), (40), (42), (47), (54), (60), (64),
% 231.16/42.40  | | | |            (68), (97), (112), (168) are inconsistent by sub-proof #1378.
% 231.16/42.40  | | | | 
% 231.16/42.40  | | | End of split
% 231.16/42.40  | | | 
% 231.16/42.40  | | Case 2:
% 231.16/42.40  | | | 
% 231.16/42.40  | | |   (169)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.16/42.40  | | |            = e0)
% 231.16/42.40  | | | 
% 231.16/42.40  | | | BETA: splitting (169) gives:
% 231.16/42.40  | | | 
% 231.16/42.40  | | | Case 1:
% 231.16/42.40  | | | | 
% 231.16/42.40  | | | |   (170)  all_57_8 = e0 & op(e1, e1) = e0
% 231.16/42.40  | | | | 
% 231.16/42.40  | | | | REF_CLOSE: (15), (21), (101), (170) are inconsistent by sub-proof #2412.
% 231.16/42.40  | | | | 
% 231.16/42.40  | | | Case 2:
% 231.16/42.40  | | | | 
% 231.16/42.40  | | | |   (171)  all_57_11 = e0 & op(e1, e0) = e0
% 231.16/42.40  | | | | 
% 231.16/42.40  | | | | ALPHA: (171) implies:
% 231.16/42.40  | | | |   (172)  all_57_11 = e0
% 231.16/42.40  | | | | 
% 231.16/42.40  | | | | REF_CLOSE: (11), (13), (40), (42), (54), (60), (64), (88), (92), (97),
% 231.16/42.40  | | | |            (112), (172) are inconsistent by sub-proof #1377.
% 231.16/42.40  | | | | 
% 231.16/42.40  | | | End of split
% 231.16/42.40  | | | 
% 231.16/42.40  | | End of split
% 231.16/42.40  | | 
% 231.16/42.40  | Case 2:
% 231.16/42.40  | | 
% 231.16/42.40  | |   (173)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 231.16/42.40  | |              e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0 &
% 231.16/42.40  | |              op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 231.16/42.40  | |            (all_57_14 = e0 & op(e0, e1) = e0))
% 231.16/42.40  | | 
% 231.16/42.40  | | ALPHA: (173) implies:
% 231.16/42.40  | |   (174)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 231.16/42.40  | |            e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.16/42.40  | | 
% 231.16/42.40  | | BETA: splitting (174) gives:
% 231.16/42.40  | | 
% 231.16/42.40  | | Case 1:
% 231.16/42.40  | | | 
% 231.16/42.40  | | |   (175)  all_57_9 = e0 & op(e3, e0) = e0
% 231.16/42.40  | | | 
% 231.16/42.40  | | | ALPHA: (175) implies:
% 231.16/42.40  | | |   (176)  all_57_9 = e0
% 231.16/42.40  | | | 
% 231.16/42.40  | | | REF_CLOSE: (13), (15), (42), (47), (60), (80), (92), (95), (97), (98),
% 231.16/42.40  | | |            (176) are inconsistent by sub-proof #2047.
% 231.16/42.40  | | | 
% 231.16/42.40  | | Case 2:
% 231.16/42.40  | | | 
% 231.16/42.40  | | |   (177)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.16/42.40  | | |            = e0)
% 231.16/42.40  | | | 
% 231.16/42.40  | | | BETA: splitting (177) gives:
% 231.16/42.40  | | | 
% 231.16/42.40  | | | Case 1:
% 231.16/42.40  | | | | 
% 231.16/42.40  | | | |   (178)  all_57_10 = e0 & op(e2, e0) = e0
% 231.16/42.40  | | | | 
% 231.16/42.40  | | | | ALPHA: (178) implies:
% 231.16/42.40  | | | |   (179)  op(e2, e0) = e0
% 231.16/42.40  | | | | 
% 231.16/42.40  | | | | REF_CLOSE: (15), (78), (81), (179) are inconsistent by sub-proof #2470.
% 231.16/42.40  | | | | 
% 231.16/42.40  | | | Case 2:
% 231.16/42.40  | | | | 
% 231.16/42.40  | | | |   (180)  all_57_11 = e0 & op(e1, e0) = e0
% 231.16/42.40  | | | | 
% 231.16/42.40  | | | | ALPHA: (180) implies:
% 231.16/42.40  | | | |   (181)  all_57_11 = e0
% 231.16/42.40  | | | | 
% 231.16/42.40  | | | | REF_CLOSE: (11), (13), (40), (42), (54), (60), (64), (88), (92), (97),
% 231.16/42.40  | | | |            (112), (181) are inconsistent by sub-proof #1377.
% 231.16/42.40  | | | | 
% 231.16/42.40  | | | End of split
% 231.16/42.40  | | | 
% 231.16/42.40  | | End of split
% 231.16/42.40  | | 
% 231.16/42.40  | End of split
% 231.16/42.40  | 
% 231.16/42.40  End of proof
% 231.16/42.40  
% 231.16/42.40  Sub-proof #1377 shows that the following formulas are inconsistent:
% 231.16/42.40  ----------------------------------------------------------------
% 231.16/42.40    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.16/42.40         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.16/42.40    (2)   ~ (e3 = e1)
% 231.16/42.40    (3)  all_57_3 = e0
% 231.16/42.40    (4)   ~ (e3 = e2)
% 231.16/42.40    (5)  all_57_1 = e1
% 231.16/42.40    (6)  all_57_11 = e0
% 231.16/42.40    (7)   ~ (e2 = e0)
% 231.16/42.40    (8)   ~ (e1 = e0)
% 231.16/42.40    (9)  all_57_7 = e3
% 231.16/42.40    (10)  all_57_11 = e1
% 231.16/42.40    (11)   ~ (e2 = e1)
% 231.16/42.40    (12)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.16/42.40          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.16/42.40  
% 231.16/42.40  Begin of proof
% 231.16/42.40  | 
% 231.16/42.40  | COMBINE_EQS: (6), (10) imply:
% 231.16/42.40  |   (13)  e1 = e0
% 231.16/42.40  | 
% 231.16/42.40  | COMBINE_EQS: (5), (13) imply:
% 231.16/42.40  |   (14)  all_57_1 = e0
% 231.16/42.40  | 
% 231.16/42.40  | REF_CLOSE: (1), (2), (3), (4), (7), (8), (9), (11), (12), (14) are
% 231.16/42.40  |            inconsistent by sub-proof #2098.
% 231.16/42.40  | 
% 231.16/42.40  End of proof
% 231.16/42.40  
% 231.16/42.40  Sub-proof #1378 shows that the following formulas are inconsistent:
% 231.16/42.40  ----------------------------------------------------------------
% 231.16/42.40    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.16/42.40         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.16/42.40    (2)   ~ (e3 = e1)
% 231.16/42.40    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.16/42.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.16/42.40    (4)  op(e2, e2) = e0
% 231.16/42.40    (5)  all_57_3 = e0
% 231.16/42.40    (6)   ~ (e3 = e2)
% 231.16/42.40    (7)   ~ (e3 = e0)
% 231.16/42.40    (8)  all_57_1 = e1
% 231.16/42.40    (9)   ~ (e2 = e0)
% 231.16/42.40    (10)   ~ (e1 = e0)
% 231.16/42.40    (11)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.16/42.40          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.16/42.40    (12)   ~ (e2 = e1)
% 231.16/42.40    (13)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.16/42.40          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.16/42.40    (14)  all_57_7 = e0
% 231.16/42.40  
% 231.16/42.40  Begin of proof
% 231.16/42.40  | 
% 231.16/42.40  | BETA: splitting (1) gives:
% 231.16/42.40  | 
% 231.16/42.40  | Case 1:
% 231.16/42.40  | | 
% 231.16/42.40  | |   (15)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 231.16/42.40  | |           e2)
% 231.16/42.40  | | 
% 231.16/42.40  | | REF_CLOSE: (3), (4), (8), (9), (12), (15) are inconsistent by sub-proof
% 231.16/42.40  | |            #2208.
% 231.16/42.40  | | 
% 231.16/42.40  | Case 2:
% 231.16/42.40  | | 
% 231.16/42.40  | |   (16)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 231.16/42.40  | |           e2)
% 231.16/42.40  | | 
% 231.16/42.40  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13), (14),
% 231.16/42.40  | |            (16) are inconsistent by sub-proof #2201.
% 231.16/42.40  | | 
% 231.16/42.40  | End of split
% 231.16/42.40  | 
% 231.16/42.40  End of proof
% 231.16/42.40  
% 231.16/42.40  Sub-proof #1379 shows that the following formulas are inconsistent:
% 231.16/42.40  ----------------------------------------------------------------
% 231.16/42.40    (1)   ~ (all_10_2 = e2)
% 231.16/42.40    (2)  op(e3, e3) = all_10_2
% 231.16/42.40    (3)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 231.16/42.40    (4)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 231.16/42.40    (5)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.16/42.40         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.16/42.40    (6)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.16/42.40         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.16/42.40    (7)   ~ (all_53_8 = all_53_12)
% 231.16/42.40    (8)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.16/42.40         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.16/42.40    (9)   ~ (e3 = e1)
% 231.16/42.40    (10)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 231.16/42.40          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.16/42.40    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.16/42.40            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.16/42.40    (12)  all_55_0 = all_10_2
% 231.16/42.40    (13)   ~ (all_10_2 = e0)
% 231.16/42.40    (14)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.16/42.40          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.16/42.40    (15)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 231.16/42.40            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 231.16/42.40              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 231.16/42.40    (16)   ~ (all_6_2 = e3)
% 231.16/42.40    (17)  op(e1, e1) = all_6_2
% 231.16/42.40    (18)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 231.16/42.40    (19)   ~ (all_53_9 = e0)
% 231.16/42.40    (20)  all_55_0 = e3 | all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 231.16/42.40    (21)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.16/42.40          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.16/42.40    (22)   ~ (all_53_4 = all_53_12)
% 231.16/42.40    (23)   ~ (all_53_8 = all_53_9)
% 231.16/42.40    (24)  all_42_2 = all_6_2
% 231.16/42.40    (25)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.16/42.40          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.16/42.40    (26)   ~ (all_53_9 = all_6_2)
% 231.16/42.40    (27)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.16/42.40          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.16/42.40    (28)  all_57_3 = e0
% 231.16/42.40    (29)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.16/42.40          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.16/42.40    (30)  all_55_1 = all_53_4
% 231.16/42.40    (31)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.16/42.40          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.16/42.40    (32)   ~ (all_53_8 = all_6_2)
% 231.16/42.40    (33)  all_55_2 = all_53_8
% 231.16/42.40    (34)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 231.16/42.40    (35)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.16/42.40          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.16/42.40            e1)
% 231.16/42.40    (36)   ~ (all_53_4 = all_53_8)
% 231.16/42.40    (37)  op(e3, e2) = all_53_4
% 231.16/42.40    (38)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 231.16/42.40    (39)   ~ (e2 = e0)
% 231.16/42.40    (40)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 231.16/42.40            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 231.16/42.40            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 231.16/42.40            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 231.16/42.40              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 231.16/42.40            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 231.16/42.40            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 231.16/42.40              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 231.16/42.40              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 231.16/42.40            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 231.16/42.40            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 231.16/42.40            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 231.16/42.40              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 231.16/42.40              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 231.16/42.40            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 231.16/42.40              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 231.16/42.40            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 231.16/42.40            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 231.16/42.40              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 231.16/42.40              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 231.16/42.40            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 231.16/42.40            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 231.16/42.40    (41)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 231.16/42.40          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.16/42.40    (42)   ~ (e1 = e0)
% 231.16/42.40    (43)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 231.16/42.40            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 231.16/42.40              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 231.16/42.40    (44)   ~ (all_53_4 = e0)
% 231.16/42.40    (45)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.16/42.40          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.16/42.40    (46)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.16/42.40          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.16/42.40    (47)   ~ (all_10_2 = e1)
% 231.16/42.40    (48)   ~ (all_53_4 = all_53_6)
% 231.16/42.40    (49)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.16/42.40          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.16/42.40            e2)
% 231.16/42.40    (50)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.16/42.40              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.16/42.40                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.16/42.40                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.16/42.40    (51)  all_55_10 = all_6_2
% 231.16/42.40    (52)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.16/42.40          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.16/42.40    (53)  all_38_2 = all_6_2
% 231.16/42.40    (54)  all_55_3 = all_53_12
% 231.16/42.40    (55)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 231.16/42.40            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 231.16/42.40              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 231.16/42.40    (56)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.16/42.40          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.16/42.40    (57)  all_57_11 = e1
% 231.16/42.40    (58)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 231.16/42.40          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 231.16/42.40    (59)   ~ (all_53_12 = all_10_2)
% 231.16/42.40    (60)   ~ (e2 = e1)
% 231.16/42.40    (61)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.16/42.40          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.16/42.40    (62)  op(e2, e1) = all_53_9
% 231.16/42.40    (63)  op(e1, e2) = all_53_6
% 231.16/42.40    (64)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.16/42.40          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.16/42.40    (65)  all_24_2 = all_6_2
% 231.16/42.40    (66)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.16/42.40          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.16/42.40    (67)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.16/42.40          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.16/42.40    (68)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.16/42.40          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.16/42.40    (69)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 231.16/42.40          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 231.16/42.40    (70)  op(e3, e1) = all_53_8
% 231.16/42.40    (71)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.16/42.40          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.16/42.40    (72)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 231.16/42.40          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 231.16/42.40    (73)  op(e3, e0) = all_53_12
% 231.16/42.40  
% 231.16/42.40  Begin of proof
% 231.16/42.40  | 
% 231.16/42.40  | BETA: splitting (38) gives:
% 231.16/42.40  | 
% 231.16/42.40  | Case 1:
% 231.16/42.40  | | 
% 231.16/42.40  | |   (74)  all_57_11 = e3 & op(e1, e0) = e3
% 231.16/42.40  | | 
% 231.16/42.40  | | ALPHA: (74) implies:
% 231.16/42.40  | |   (75)  all_57_11 = e3
% 231.16/42.40  | | 
% 231.16/42.40  | | REF_CLOSE: (9), (57), (75) are inconsistent by sub-proof #2218.
% 231.16/42.40  | | 
% 231.16/42.40  | Case 2:
% 231.16/42.40  | | 
% 231.16/42.40  | |   (76)  all_57_15 = e3 & op(e0, e0) = e3
% 231.16/42.40  | | 
% 231.16/42.40  | | ALPHA: (76) implies:
% 231.16/42.40  | |   (77)  all_57_15 = e3
% 231.16/42.40  | |   (78)  op(e0, e0) = e3
% 231.16/42.40  | | 
% 231.16/42.40  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13),
% 231.16/42.40  | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 231.16/42.40  | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 231.16/42.40  | |            (36), (37), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 231.16/42.40  | |            (48), (49), (50), (51), (52), (53), (54), (55), (56), (58), (59),
% 231.16/42.40  | |            (60), (61), (62), (63), (64), (65), (66), (67), (68), (69), (70),
% 231.16/42.40  | |            (71), (72), (73), (77), (78) are inconsistent by sub-proof #1414.
% 231.16/42.40  | | 
% 231.16/42.40  | End of split
% 231.16/42.40  | 
% 231.16/42.40  End of proof
% 231.16/42.40  
% 231.16/42.40  Sub-proof #1380 shows that the following formulas are inconsistent:
% 231.16/42.40  ----------------------------------------------------------------
% 231.16/42.40    (1)   ~ (all_10_2 = e2)
% 231.16/42.40    (2)  all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 231.16/42.40    (3)  op(e3, e3) = all_10_2
% 231.16/42.40    (4)  op(e0, e1) = all_53_11
% 231.16/42.40    (5)  op(e1, e3) = e0
% 231.16/42.41    (6)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 231.16/42.41    (7)   ~ (all_53_6 = all_53_14)
% 231.16/42.41    (8)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 231.16/42.41    (9)  all_57_15 = e0
% 231.16/42.41    (10)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.16/42.41          (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.16/42.41    (11)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.16/42.41          (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.16/42.41    (12)   ~ (all_53_8 = all_53_12)
% 231.16/42.41    (13)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.16/42.41          (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.16/42.41    (14)   ~ (all_53_8 = all_53_11)
% 231.16/42.41    (15)   ~ (e3 = e1)
% 231.16/42.41    (16)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 231.16/42.41          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.16/42.41    (17)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.16/42.41            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.16/42.41    (18)  all_55_0 = all_10_2
% 231.16/42.41    (19)   ~ (all_10_2 = e0)
% 231.16/42.41    (20)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.16/42.41          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.16/42.41    (21)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 231.16/42.41            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 231.16/42.41              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 231.16/42.41    (22)   ~ (all_6_2 = e3)
% 231.16/42.41    (23)  op(e1, e1) = all_6_2
% 231.16/42.41    (24)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 231.16/42.41    (25)  all_55_0 = e3 | all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 231.16/42.41    (26)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 231.16/42.41    (27)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.16/42.41          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.16/42.41    (28)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 231.16/42.41    (29)  all_55_9 = all_53_6
% 231.16/42.41    (30)   ~ (all_53_11 = all_6_2)
% 231.16/42.41    (31)   ~ (all_53_4 = all_53_12)
% 231.16/42.41    (32)   ~ (all_53_8 = e3)
% 231.16/42.41    (33)   ~ (all_53_8 = all_53_9)
% 231.16/42.41    (34)  all_42_2 = all_6_2
% 231.16/42.41    (35)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.16/42.41          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.16/42.41    (36)  op(e2, e2) = e0
% 231.16/42.41    (37)   ~ (all_53_9 = all_53_11)
% 231.16/42.41    (38)   ~ (all_53_9 = all_6_2)
% 231.16/42.41    (39)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.16/42.41          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.16/42.41    (40)   ~ (all_53_14 = all_6_2)
% 231.16/42.41    (41)  all_57_3 = e0
% 231.16/42.41    (42)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.16/42.41          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.16/42.41    (43)   ~ (e3 = e2)
% 231.16/42.41    (44)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 231.16/42.41    (45)  all_55_1 = all_53_4
% 231.16/42.41    (46)  op(e1, e0) = all_53_14
% 231.16/42.41    (47)   ~ (all_53_6 = all_53_7)
% 231.16/42.41    (48)   ~ (e3 = e0)
% 231.16/42.41    (49)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.16/42.41          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.16/42.41    (50)  op(e3, e3) = e3
% 231.16/42.41    (51)  all_57_6 = e0
% 231.16/42.41    (52)   ~ (all_53_8 = all_6_2)
% 231.16/42.41    (53)  all_55_2 = all_53_8
% 231.16/42.41    (54)   ~ (all_53_4 = all_53_7)
% 231.16/42.41    (55)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 231.16/42.41    (56)   ~ (all_53_7 = e0)
% 231.16/42.41    (57)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.16/42.41          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.16/42.41            e1)
% 231.16/42.41    (58)   ~ (all_53_4 = all_53_8)
% 231.16/42.41    (59)  all_55_6 = all_53_9
% 231.16/42.41    (60)  op(e3, e2) = all_53_4
% 231.16/42.41    (61)   ~ (e2 = e0)
% 231.16/42.41    (62)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 231.16/42.41            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 231.16/42.41            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 231.16/42.41            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 231.16/42.41              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 231.16/42.41            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 231.16/42.41            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 231.16/42.41              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 231.16/42.41              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 231.16/42.41            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 231.16/42.41            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 231.16/42.41            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 231.16/42.41              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 231.16/42.41              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 231.16/42.41            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 231.16/42.41              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 231.16/42.41            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 231.16/42.41            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 231.16/42.41              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 231.16/42.41              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 231.16/42.41            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 231.16/42.41            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 231.16/42.41    (63)  all_57_13 = e2
% 231.16/42.41    (64)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 231.16/42.41          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.16/42.41    (65)   ~ (all_53_2 = all_53_14)
% 231.16/42.41    (66)   ~ (e1 = e0)
% 231.16/42.41    (67)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 231.16/42.41            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 231.16/42.41              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 231.16/42.41    (68)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.16/42.41          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.16/42.41    (69)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.16/42.41          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.16/42.41    (70)   ~ (all_10_2 = e1)
% 231.16/42.41    (71)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 231.16/42.41    (72)  op(e0, e0) = e0
% 231.16/42.41    (73)  all_57_10 = e3
% 231.16/42.41    (74)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.16/42.41          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 231.16/42.41            e3)
% 231.16/42.41    (75)   ~ (all_53_4 = all_53_6)
% 231.16/42.41    (76)  op(e0, e2) = all_53_7
% 231.16/42.41    (77)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.16/42.41          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.16/42.41            e2)
% 231.16/42.41    (78)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.16/42.41              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.16/42.41                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.16/42.41                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.16/42.41    (79)  all_55_10 = all_6_2
% 231.16/42.41    (80)   ~ (all_53_6 = all_6_2)
% 231.16/42.41    (81)  all_55_13 = all_53_7
% 231.16/42.41    (82)  op(e2, e0) = all_53_13
% 231.16/42.41    (83)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.16/42.41          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.16/42.41    (84)  all_38_2 = all_6_2
% 231.16/42.41    (85)  all_55_11 = all_53_14
% 231.16/42.41    (86)  all_55_3 = all_53_12
% 231.16/42.41    (87)   ~ (all_53_12 = e3)
% 231.16/42.41    (88)  all_57_0 = e3
% 231.16/42.41    (89)  all_57_7 = e3
% 231.16/42.41    (90)  op(e1, e3) = all_53_2
% 231.16/42.41    (91)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 231.16/42.41            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 231.16/42.41              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 231.16/42.41    (92)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.16/42.41          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.16/42.41    (93)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 231.16/42.41          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 231.16/42.41    (94)   ~ (all_53_12 = all_10_2)
% 231.16/42.41    (95)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 231.16/42.41          (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 231.16/42.41    (96)   ~ (all_53_13 = all_53_14)
% 231.16/42.41    (97)   ~ (e2 = e1)
% 231.16/42.41    (98)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.16/42.41          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.16/42.41    (99)  op(e2, e1) = all_53_9
% 231.16/42.41    (100)  op(e1, e2) = all_53_6
% 231.16/42.41    (101)   ~ (all_6_2 = e0)
% 231.16/42.41    (102)   ~ (all_53_2 = all_53_6)
% 231.16/42.41    (103)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.16/42.41           (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.16/42.41    (104)  all_24_2 = all_6_2
% 231.16/42.41    (105)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.16/42.41           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.16/42.41    (106)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.16/42.41           (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.16/42.41    (107)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.16/42.41           | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.16/42.41             e1)
% 231.16/42.41    (108)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 231.16/42.41           (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 231.16/42.41    (109)   ~ (all_53_12 = all_53_14)
% 231.16/42.41    (110)  all_55_14 = all_53_11
% 231.16/42.41    (111)  op(e3, e1) = all_53_8
% 231.16/42.41    (112)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.16/42.41           (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.16/42.41    (113)   ~ (all_53_4 = e3)
% 231.16/42.41    (114)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 231.16/42.41           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 231.16/42.41    (115)  op(e3, e0) = all_53_12
% 231.16/42.41  
% 231.16/42.41  Begin of proof
% 231.16/42.41  | 
% 231.16/42.41  | BETA: splitting (68) gives:
% 231.16/42.41  | 
% 231.16/42.41  | Case 1:
% 231.16/42.41  | | 
% 231.16/42.41  | |   (116)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) =
% 231.16/42.41  | |            e3)
% 231.16/42.41  | | 
% 231.16/42.41  | | REF_CLOSE: (10), (13), (15), (17), (27), (35), (39), (41), (43), (48), (50),
% 231.16/42.41  | |            (61), (66), (73), (89), (92), (97), (112), (116) are inconsistent
% 231.16/42.41  | |            by sub-proof #1383.
% 231.16/42.41  | | 
% 231.16/42.41  | Case 2:
% 231.16/42.41  | | 
% 231.16/42.41  | |   (117)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) =
% 231.16/42.41  | |            e3)
% 231.16/42.41  | | 
% 231.16/42.41  | | BETA: splitting (117) gives:
% 231.16/42.41  | | 
% 231.16/42.41  | | Case 1:
% 231.16/42.41  | | | 
% 231.16/42.41  | | |   (118)  all_57_8 = e3 & op(e1, e1) = e3
% 231.16/42.41  | | | 
% 231.16/42.41  | | | ALPHA: (118) implies:
% 231.16/42.41  | | |   (119)  op(e1, e1) = e3
% 231.16/42.41  | | | 
% 231.16/42.41  | | | REF_CLOSE: (17), (22), (23), (119) are inconsistent by sub-proof #2468.
% 231.16/42.41  | | | 
% 231.16/42.41  | | Case 2:
% 231.16/42.41  | | | 
% 231.16/42.41  | | |   (120)  all_57_14 = e3 & op(e0, e1) = e3
% 231.16/42.41  | | | 
% 231.16/42.41  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 231.16/42.41  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 231.16/42.41  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 231.16/42.41  | | |            (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 231.16/42.41  | | |            (43), (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 231.16/42.41  | | |            (53), (54), (55), (56), (57), (58), (59), (60), (61), (62),
% 231.16/42.41  | | |            (63), (64), (65), (66), (67), (68), (69), (70), (71), (72),
% 231.16/42.41  | | |            (73), (74), (75), (76), (77), (78), (79), (80), (81), (82),
% 231.16/42.41  | | |            (83), (84), (85), (86), (87), (88), (89), (90), (91), (92),
% 231.16/42.41  | | |            (93), (94), (95), (96), (97), (98), (99), (100), (101), (102),
% 231.16/42.41  | | |            (103), (104), (105), (106), (107), (108), (109), (110), (111),
% 231.16/42.41  | | |            (112), (113), (114), (115), (120) are inconsistent by sub-proof
% 231.16/42.41  | | |            #1381.
% 231.16/42.41  | | | 
% 231.16/42.41  | | End of split
% 231.16/42.41  | | 
% 231.16/42.41  | End of split
% 231.16/42.41  | 
% 231.16/42.41  End of proof
% 231.16/42.41  
% 231.16/42.41  Sub-proof #1381 shows that the following formulas are inconsistent:
% 231.16/42.41  ----------------------------------------------------------------
% 231.16/42.41    (1)   ~ (all_10_2 = e2)
% 231.16/42.41    (2)  all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 231.16/42.41    (3)  op(e3, e3) = all_10_2
% 231.16/42.41    (4)  op(e0, e1) = all_53_11
% 231.16/42.41    (5)  op(e1, e3) = e0
% 231.16/42.41    (6)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 231.16/42.41    (7)   ~ (all_53_6 = all_53_14)
% 231.16/42.41    (8)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 231.16/42.41    (9)  all_57_15 = e0
% 231.16/42.41    (10)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.16/42.41          (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.16/42.41    (11)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.16/42.41          (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.16/42.41    (12)   ~ (all_53_8 = all_53_12)
% 231.16/42.41    (13)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.16/42.41          (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.16/42.41    (14)   ~ (all_53_8 = all_53_11)
% 231.16/42.41    (15)   ~ (e3 = e1)
% 231.16/42.41    (16)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 231.16/42.41          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.16/42.41    (17)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.16/42.41            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.16/42.41    (18)  all_55_0 = all_10_2
% 231.16/42.41    (19)   ~ (all_10_2 = e0)
% 231.16/42.41    (20)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.16/42.41          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.16/42.41    (21)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 231.16/42.41            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 231.16/42.41              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 231.16/42.41    (22)   ~ (all_6_2 = e3)
% 231.16/42.41    (23)  op(e1, e1) = all_6_2
% 231.16/42.41    (24)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 231.16/42.41    (25)  all_55_0 = e3 | all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 231.16/42.41    (26)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 231.16/42.41    (27)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.16/42.41          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.16/42.41    (28)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 231.16/42.41    (29)  all_55_9 = all_53_6
% 231.16/42.41    (30)   ~ (all_53_11 = all_6_2)
% 231.16/42.41    (31)   ~ (all_53_4 = all_53_12)
% 231.16/42.41    (32)   ~ (all_53_8 = e3)
% 231.16/42.41    (33)   ~ (all_53_8 = all_53_9)
% 231.16/42.41    (34)  all_42_2 = all_6_2
% 231.16/42.41    (35)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.16/42.41          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.16/42.41    (36)  op(e2, e2) = e0
% 231.16/42.41    (37)   ~ (all_53_9 = all_53_11)
% 231.16/42.41    (38)   ~ (all_53_9 = all_6_2)
% 231.16/42.41    (39)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.16/42.41          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.16/42.41    (40)   ~ (all_53_14 = all_6_2)
% 231.16/42.41    (41)  all_57_3 = e0
% 231.16/42.41    (42)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.16/42.41          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.16/42.41    (43)   ~ (e3 = e2)
% 231.16/42.41    (44)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 231.16/42.41    (45)  all_55_1 = all_53_4
% 231.16/42.41    (46)  op(e1, e0) = all_53_14
% 231.16/42.41    (47)   ~ (all_53_6 = all_53_7)
% 231.16/42.41    (48)   ~ (e3 = e0)
% 231.16/42.41    (49)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.16/42.41          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.16/42.41    (50)  op(e3, e3) = e3
% 231.16/42.41    (51)  all_57_6 = e0
% 231.16/42.41    (52)   ~ (all_53_8 = all_6_2)
% 231.16/42.41    (53)  all_55_2 = all_53_8
% 231.16/42.41    (54)   ~ (all_53_4 = all_53_7)
% 231.16/42.41    (55)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 231.16/42.41    (56)   ~ (all_53_7 = e0)
% 231.16/42.41    (57)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.16/42.41          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.16/42.41            e1)
% 231.16/42.41    (58)   ~ (all_53_4 = all_53_8)
% 231.16/42.41    (59)  all_55_6 = all_53_9
% 231.16/42.41    (60)  op(e3, e2) = all_53_4
% 231.16/42.41    (61)   ~ (e2 = e0)
% 231.16/42.41    (62)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 231.16/42.41            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 231.16/42.41            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 231.16/42.41            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 231.16/42.41              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 231.16/42.41            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 231.16/42.41            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 231.16/42.41              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 231.16/42.41              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 231.16/42.41            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 231.16/42.41            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 231.16/42.41            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 231.16/42.41              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 231.16/42.41              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 231.16/42.41            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 231.16/42.41              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 231.16/42.41            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 231.16/42.41            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 231.16/42.41              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 231.16/42.41              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 231.16/42.41            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 231.16/42.41            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 231.16/42.41    (63)  all_57_13 = e2
% 231.16/42.41    (64)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 231.16/42.41          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.16/42.41    (65)   ~ (all_53_2 = all_53_14)
% 231.16/42.41    (66)   ~ (e1 = e0)
% 231.16/42.41    (67)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 231.16/42.41            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 231.16/42.41              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 231.16/42.41    (68)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.16/42.41          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.16/42.41    (69)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.16/42.41          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.16/42.41    (70)   ~ (all_10_2 = e1)
% 231.16/42.41    (71)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 231.16/42.41    (72)  op(e0, e0) = e0
% 231.16/42.41    (73)  all_57_10 = e3
% 231.16/42.41    (74)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.16/42.41          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 231.16/42.41            e3)
% 231.16/42.41    (75)   ~ (all_53_4 = all_53_6)
% 231.16/42.41    (76)  op(e0, e2) = all_53_7
% 231.16/42.41    (77)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.16/42.41          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.16/42.41            e2)
% 231.16/42.41    (78)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.16/42.41              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.16/42.41                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.16/42.41                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.16/42.41    (79)  all_55_10 = all_6_2
% 231.16/42.41    (80)   ~ (all_53_6 = all_6_2)
% 231.16/42.42    (81)  all_55_13 = all_53_7
% 231.16/42.42    (82)  op(e2, e0) = all_53_13
% 231.16/42.42    (83)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.16/42.42          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.16/42.42    (84)  all_38_2 = all_6_2
% 231.16/42.42    (85)  all_55_11 = all_53_14
% 231.16/42.42    (86)  all_55_3 = all_53_12
% 231.16/42.42    (87)   ~ (all_53_12 = e3)
% 231.16/42.42    (88)  all_57_0 = e3
% 231.16/42.42    (89)  all_57_7 = e3
% 231.16/42.42    (90)  op(e1, e3) = all_53_2
% 231.16/42.42    (91)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 231.16/42.42            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 231.16/42.42              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 231.16/42.42    (92)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.16/42.42          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.16/42.42    (93)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 231.16/42.42          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 231.16/42.42    (94)   ~ (all_53_12 = all_10_2)
% 231.16/42.42    (95)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 231.16/42.42          (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 231.16/42.42    (96)   ~ (all_53_13 = all_53_14)
% 231.16/42.42    (97)   ~ (e2 = e1)
% 231.16/42.42    (98)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.16/42.42          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.16/42.42    (99)  all_57_14 = e3 & op(e0, e1) = e3
% 231.16/42.42    (100)  op(e2, e1) = all_53_9
% 231.16/42.42    (101)  op(e1, e2) = all_53_6
% 231.16/42.42    (102)   ~ (all_6_2 = e0)
% 231.16/42.42    (103)   ~ (all_53_2 = all_53_6)
% 231.16/42.42    (104)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.16/42.42           (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.16/42.42    (105)  all_24_2 = all_6_2
% 231.16/42.42    (106)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.16/42.42           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.16/42.42    (107)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.16/42.42           (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.16/42.42    (108)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.16/42.42           | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.16/42.42             e1)
% 231.16/42.42    (109)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 231.16/42.42           (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 231.16/42.42    (110)   ~ (all_53_12 = all_53_14)
% 231.16/42.42    (111)  all_55_14 = all_53_11
% 231.16/42.42    (112)  op(e3, e1) = all_53_8
% 231.16/42.42    (113)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.16/42.42           (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.16/42.42    (114)   ~ (all_53_4 = e3)
% 231.16/42.42    (115)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 231.16/42.42           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 231.16/42.42    (116)  op(e3, e0) = all_53_12
% 231.16/42.42  
% 231.16/42.42  Begin of proof
% 231.16/42.42  | 
% 231.16/42.42  | ALPHA: (99) implies:
% 231.16/42.42  |   (117)  all_57_14 = e3
% 231.16/42.42  | 
% 231.16/42.42  | BETA: splitting (42) gives:
% 231.16/42.42  | 
% 231.16/42.42  | Case 1:
% 231.16/42.42  | | 
% 231.16/42.42  | |   (118)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) =
% 231.16/42.42  | |            e0)
% 231.16/42.42  | | 
% 231.16/42.42  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 231.16/42.42  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 231.16/42.42  | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 231.16/42.42  | |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 231.16/42.42  | |            (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), (56),
% 231.16/42.42  | |            (57), (58), (59), (60), (61), (62), (64), (65), (66), (67), (68),
% 231.16/42.42  | |            (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79),
% 231.16/42.42  | |            (80), (81), (82), (83), (84), (85), (86), (87), (88), (90), (91),
% 231.16/42.42  | |            (92), (93), (94), (95), (96), (97), (98), (100), (101), (103),
% 231.16/42.42  | |            (104), (105), (106), (107), (108), (109), (110), (111), (112),
% 231.16/42.42  | |            (113), (114), (115), (116), (118) are inconsistent by sub-proof
% 231.16/42.42  | |            #1382.
% 231.16/42.42  | | 
% 231.16/42.42  | Case 2:
% 231.16/42.42  | | 
% 231.16/42.42  | |   (119)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 231.16/42.42  | |            e0)
% 231.16/42.42  | | 
% 231.16/42.42  | | BETA: splitting (119) gives:
% 231.16/42.42  | | 
% 231.16/42.42  | | Case 1:
% 231.16/42.42  | | | 
% 231.16/42.42  | | |   (120)  all_57_8 = e0 & op(e1, e1) = e0
% 231.16/42.42  | | | 
% 231.16/42.42  | | | REF_CLOSE: (17), (23), (102), (120) are inconsistent by sub-proof #2412.
% 231.16/42.42  | | | 
% 231.16/42.42  | | Case 2:
% 231.16/42.42  | | | 
% 231.16/42.42  | | |   (121)  all_57_14 = e0 & op(e0, e1) = e0
% 231.16/42.42  | | | 
% 231.16/42.42  | | | ALPHA: (121) implies:
% 231.16/42.42  | | |   (122)  all_57_14 = e0
% 231.16/42.42  | | | 
% 231.16/42.42  | | | COMBINE_EQS: (117), (122) imply:
% 231.16/42.42  | | |   (123)  e3 = e0
% 231.16/42.42  | | | 
% 231.16/42.42  | | | SIMP: (123) implies:
% 231.16/42.42  | | |   (124)  e3 = e0
% 231.16/42.42  | | | 
% 231.16/42.42  | | | COMBINE_EQS: (89), (124) imply:
% 231.16/42.42  | | |   (125)  all_57_7 = e0
% 231.16/42.42  | | | 
% 231.16/42.42  | | | REF_CLOSE: (15), (17), (36), (41), (43), (48), (63), (66), (69), (97),
% 231.16/42.42  | | |            (113), (125) are inconsistent by sub-proof #2202.
% 231.16/42.42  | | | 
% 231.16/42.42  | | End of split
% 231.16/42.42  | | 
% 231.16/42.42  | End of split
% 231.16/42.42  | 
% 231.16/42.42  End of proof
% 231.16/42.42  
% 231.16/42.42  Sub-proof #1382 shows that the following formulas are inconsistent:
% 231.16/42.42  ----------------------------------------------------------------
% 231.16/42.42    (1)   ~ (all_10_2 = e2)
% 231.16/42.42    (2)  all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 231.16/42.42    (3)  op(e3, e3) = all_10_2
% 231.16/42.42    (4)  op(e0, e1) = all_53_11
% 231.16/42.42    (5)  op(e1, e3) = e0
% 231.16/42.42    (6)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 231.16/42.42    (7)   ~ (all_53_6 = all_53_14)
% 231.16/42.42    (8)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 231.16/42.42    (9)  all_57_15 = e0
% 231.16/42.42    (10)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.16/42.42          (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.16/42.42    (11)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.16/42.42          (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.16/42.42    (12)   ~ (all_53_8 = all_53_12)
% 231.16/42.42    (13)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.16/42.42          (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.16/42.42    (14)   ~ (all_53_8 = all_53_11)
% 231.16/42.42    (15)   ~ (e3 = e1)
% 231.16/42.42    (16)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 231.16/42.42          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.16/42.42    (17)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.16/42.42            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.16/42.42    (18)  all_55_0 = all_10_2
% 231.16/42.42    (19)   ~ (all_10_2 = e0)
% 231.16/42.42    (20)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.16/42.42          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.16/42.42    (21)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 231.16/42.42            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 231.16/42.42              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 231.16/42.42    (22)   ~ (all_6_2 = e3)
% 231.16/42.42    (23)  op(e1, e1) = all_6_2
% 231.16/42.42    (24)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 231.16/42.42    (25)  all_55_0 = e3 | all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 231.16/42.42    (26)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 231.16/42.42    (27)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.16/42.42          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.16/42.42    (28)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0)
% 231.16/42.42    (29)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 231.16/42.42    (30)  all_55_9 = all_53_6
% 231.16/42.42    (31)   ~ (all_53_11 = all_6_2)
% 231.16/42.42    (32)   ~ (all_53_4 = all_53_12)
% 231.16/42.42    (33)   ~ (all_53_8 = e3)
% 231.16/42.42    (34)   ~ (all_53_8 = all_53_9)
% 231.16/42.42    (35)  all_42_2 = all_6_2
% 231.16/42.42    (36)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.16/42.42          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.16/42.42    (37)  op(e2, e2) = e0
% 231.16/42.42    (38)   ~ (all_53_9 = all_53_11)
% 231.16/42.42    (39)   ~ (all_53_9 = all_6_2)
% 231.16/42.42    (40)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.16/42.42          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.16/42.42    (41)   ~ (all_53_14 = all_6_2)
% 231.16/42.42    (42)  all_57_3 = e0
% 231.16/42.42    (43)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.16/42.42          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.16/42.42    (44)   ~ (e3 = e2)
% 231.16/42.42    (45)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 231.16/42.42    (46)  all_55_1 = all_53_4
% 231.16/42.42    (47)  op(e1, e0) = all_53_14
% 231.16/42.42    (48)   ~ (all_53_6 = all_53_7)
% 231.16/42.42    (49)   ~ (e3 = e0)
% 231.16/42.42    (50)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.16/42.42          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.16/42.42    (51)  op(e3, e3) = e3
% 231.16/42.42    (52)  all_57_6 = e0
% 231.16/42.42    (53)   ~ (all_53_8 = all_6_2)
% 231.16/42.42    (54)  all_55_2 = all_53_8
% 231.16/42.42    (55)   ~ (all_53_4 = all_53_7)
% 231.16/42.42    (56)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 231.16/42.42    (57)   ~ (all_53_7 = e0)
% 231.16/42.42    (58)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.16/42.42          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.16/42.42            e1)
% 231.16/42.42    (59)   ~ (all_53_4 = all_53_8)
% 231.16/42.42    (60)  all_55_6 = all_53_9
% 231.16/42.42    (61)  op(e3, e2) = all_53_4
% 231.16/42.42    (62)   ~ (e2 = e0)
% 231.16/42.42    (63)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 231.16/42.42            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 231.16/42.42            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 231.16/42.42            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 231.16/42.42              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 231.16/42.42            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 231.16/42.42            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 231.16/42.42              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 231.16/42.42              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 231.16/42.42            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 231.16/42.42            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 231.16/42.42            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 231.16/42.42              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 231.16/42.42              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 231.16/42.42            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 231.16/42.42              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 231.16/42.42            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 231.16/42.42            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 231.16/42.42              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 231.16/42.42              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 231.16/42.42            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 231.16/42.42            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 231.16/42.42    (64)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 231.16/42.42          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.16/42.42    (65)   ~ (all_53_2 = all_53_14)
% 231.16/42.42    (66)   ~ (e1 = e0)
% 231.16/42.42    (67)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 231.16/42.42            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 231.16/42.42              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 231.16/42.42    (68)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.16/42.42          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.16/42.42    (69)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.16/42.42          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.16/42.42    (70)   ~ (all_10_2 = e1)
% 231.16/42.42    (71)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 231.16/42.42    (72)  op(e0, e0) = e0
% 231.16/42.42    (73)  all_57_10 = e3
% 231.16/42.42    (74)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.16/42.42          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 231.16/42.42            e3)
% 231.16/42.42    (75)   ~ (all_53_4 = all_53_6)
% 231.16/42.42    (76)  op(e0, e2) = all_53_7
% 231.16/42.42    (77)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.16/42.42          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.16/42.42            e2)
% 231.16/42.42    (78)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.16/42.42              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.16/42.42                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.16/42.42                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.16/42.42    (79)  all_55_10 = all_6_2
% 231.16/42.42    (80)   ~ (all_53_6 = all_6_2)
% 231.16/42.42    (81)  all_55_13 = all_53_7
% 231.16/42.42    (82)  op(e2, e0) = all_53_13
% 231.16/42.42    (83)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.16/42.42          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.16/42.42    (84)  all_38_2 = all_6_2
% 231.16/42.42    (85)  all_55_11 = all_53_14
% 231.16/42.42    (86)  all_55_3 = all_53_12
% 231.16/42.42    (87)   ~ (all_53_12 = e3)
% 231.16/42.42    (88)  all_57_0 = e3
% 231.16/42.42    (89)  op(e1, e3) = all_53_2
% 231.16/42.42    (90)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 231.16/42.42            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 231.16/42.42              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 231.16/42.42    (91)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.16/42.42          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.16/42.42    (92)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 231.16/42.42          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 231.16/42.42    (93)   ~ (all_53_12 = all_10_2)
% 231.16/42.42    (94)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 231.16/42.42          (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 231.16/42.42    (95)   ~ (all_53_13 = all_53_14)
% 231.16/42.42    (96)   ~ (e2 = e1)
% 231.16/42.42    (97)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.16/42.42          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.16/42.42    (98)  op(e2, e1) = all_53_9
% 231.16/42.42    (99)  op(e1, e2) = all_53_6
% 231.16/42.42    (100)   ~ (all_53_2 = all_53_6)
% 231.16/42.42    (101)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.16/42.42           (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.16/42.42    (102)  all_24_2 = all_6_2
% 231.16/42.42    (103)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.16/42.42           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.16/42.42    (104)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.16/42.42           (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.16/42.42    (105)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.16/42.42           | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.16/42.42             e1)
% 231.16/42.42    (106)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 231.16/42.42           (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 231.16/42.42    (107)   ~ (all_53_12 = all_53_14)
% 231.16/42.42    (108)  all_55_14 = all_53_11
% 231.16/42.42    (109)  op(e3, e1) = all_53_8
% 231.16/42.42    (110)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.16/42.42           (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.16/42.42    (111)   ~ (all_53_4 = e3)
% 231.16/42.42    (112)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 231.16/42.42           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 231.16/42.42    (113)  op(e3, e0) = all_53_12
% 231.16/42.42  
% 231.16/42.42  Begin of proof
% 231.16/42.42  | 
% 231.16/42.42  | BETA: splitting (28) gives:
% 231.16/42.42  | 
% 231.16/42.42  | Case 1:
% 231.16/42.42  | | 
% 231.16/42.42  | |   (114)  all_57_4 = e0 & op(e3, e1) = e0
% 231.16/42.42  | | 
% 231.16/42.42  | | ALPHA: (114) implies:
% 231.16/42.42  | |   (115)  all_57_4 = e0
% 231.16/42.42  | |   (116)  op(e3, e1) = e0
% 231.16/42.42  | | 
% 231.16/42.42  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 231.16/42.42  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 231.16/42.42  | |            (24), (25), (26), (27), (29), (30), (31), (32), (33), (34), (35),
% 231.16/42.42  | |            (36), (37), (38), (39), (40), (41), (42), (43), (45), (46), (47),
% 231.16/42.42  | |            (48), (50), (51), (52), (53), (54), (55), (56), (57), (58), (59),
% 231.16/42.42  | |            (60), (61), (62), (63), (64), (65), (66), (67), (68), (69), (70),
% 231.16/42.42  | |            (71), (72), (74), (75), (76), (77), (78), (79), (80), (81), (82),
% 231.16/42.42  | |            (83), (84), (85), (86), (87), (88), (89), (90), (91), (92), (93),
% 231.16/42.42  | |            (94), (95), (96), (97), (98), (99), (100), (101), (102), (103),
% 231.16/42.42  | |            (104), (105), (106), (107), (108), (109), (110), (111), (112),
% 231.16/42.42  | |            (113), (115), (116) are inconsistent by sub-proof #1410.
% 231.16/42.42  | | 
% 231.16/42.42  | Case 2:
% 231.16/42.42  | | 
% 231.16/42.42  | |   (117)  all_57_5 = e0 & op(e2, e1) = e0
% 231.16/42.42  | | 
% 231.16/42.42  | | ALPHA: (117) implies:
% 231.16/42.42  | |   (118)  all_57_5 = e0
% 231.16/42.42  | | 
% 231.16/42.42  | | REF_CLOSE: (10), (15), (17), (37), (42), (44), (49), (62), (66), (73), (83),
% 231.16/42.42  | |            (91), (96), (118) are inconsistent by sub-proof #2348.
% 231.16/42.42  | | 
% 231.16/42.42  | End of split
% 231.16/42.42  | 
% 231.16/42.42  End of proof
% 231.16/42.42  
% 231.16/42.42  Sub-proof #1383 shows that the following formulas are inconsistent:
% 231.16/42.42  ----------------------------------------------------------------
% 231.16/42.42    (1)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3)
% 231.16/42.42    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.16/42.42         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.16/42.42    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.16/42.42         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.16/42.42    (4)   ~ (e3 = e1)
% 231.16/42.42    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.16/42.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.16/42.42    (6)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.16/42.42         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.16/42.42    (7)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.16/42.42         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.16/42.42    (8)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.16/42.42         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.16/42.42    (9)  all_57_3 = e0
% 231.16/42.42    (10)   ~ (e3 = e2)
% 231.16/42.42    (11)   ~ (e3 = e0)
% 231.16/42.42    (12)  op(e3, e3) = e3
% 231.16/42.42    (13)   ~ (e2 = e0)
% 231.16/42.42    (14)   ~ (e1 = e0)
% 231.16/42.42    (15)  all_57_10 = e3
% 231.16/42.42    (16)  all_57_7 = e3
% 231.16/42.42    (17)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.16/42.42          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.16/42.42    (18)   ~ (e2 = e1)
% 231.16/42.42    (19)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.16/42.42          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.16/42.42  
% 231.16/42.42  Begin of proof
% 231.16/42.42  | 
% 231.16/42.42  | BETA: splitting (1) gives:
% 231.16/42.42  | 
% 231.16/42.42  | Case 1:
% 231.16/42.42  | | 
% 231.16/42.42  | |   (20)  all_57_4 = e3 & op(e3, e1) = e3
% 231.16/42.42  | | 
% 231.16/42.42  | | ALPHA: (20) implies:
% 231.16/42.42  | |   (21)  all_57_4 = e3
% 231.16/42.42  | | 
% 231.16/42.42  | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), (14),
% 231.16/42.42  | |            (16), (18), (19), (21) are inconsistent by sub-proof #1539.
% 231.16/42.42  | | 
% 231.16/42.42  | Case 2:
% 231.16/42.42  | | 
% 231.16/42.42  | |   (22)  all_57_5 = e3 & op(e2, e1) = e3
% 231.16/42.42  | | 
% 231.16/42.42  | | ALPHA: (22) implies:
% 231.16/42.43  | |   (23)  all_57_5 = e3
% 231.16/42.43  | | 
% 231.16/42.43  | | REF_CLOSE: (2), (4), (9), (10), (13), (14), (15), (17), (18), (23) are
% 231.16/42.43  | |            inconsistent by sub-proof #1693.
% 231.16/42.43  | | 
% 231.16/42.43  | End of split
% 231.16/42.43  | 
% 231.16/42.43  End of proof
% 231.16/42.43  
% 231.16/42.43  Sub-proof #1384 shows that the following formulas are inconsistent:
% 231.16/42.43  ----------------------------------------------------------------
% 231.16/42.43    (1)   ~ (all_10_2 = e2)
% 231.16/42.43    (2)  all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 231.16/42.43    (3)  op(e3, e3) = all_10_2
% 231.16/42.43    (4)  op(e0, e1) = all_53_11
% 231.16/42.43    (5)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 231.16/42.43    (6)   ~ (all_53_6 = all_53_14)
% 231.16/42.43    (7)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 231.16/42.43    (8)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.16/42.43         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.16/42.43    (9)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.16/42.43         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.16/42.43    (10)   ~ (all_53_8 = all_53_12)
% 231.16/42.43    (11)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.16/42.43          (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.16/42.43    (12)   ~ (all_53_8 = all_53_11)
% 231.16/42.43    (13)   ~ (e3 = e1)
% 231.16/42.43    (14)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 231.16/42.43          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.16/42.43    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.16/42.43            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.16/42.43    (16)  all_55_0 = all_10_2
% 231.16/42.43    (17)   ~ (all_10_2 = e0)
% 231.16/42.43    (18)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.16/42.43          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.16/42.43    (19)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 231.16/42.43            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 231.16/42.43              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 231.16/42.43    (20)   ~ (all_6_2 = e3)
% 231.16/42.43    (21)  op(e1, e1) = all_6_2
% 231.16/42.43    (22)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 231.16/42.43    (23)   ~ (all_53_9 = e0)
% 231.16/42.43    (24)  all_55_0 = e3 | all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 231.16/42.43    (25)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 231.16/42.43    (26)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.16/42.43          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.16/42.43    (27)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 231.16/42.43    (28)  all_55_9 = all_53_6
% 231.16/42.43    (29)   ~ (all_53_11 = all_6_2)
% 231.16/42.43    (30)  all_57_9 = e1
% 231.16/42.43    (31)   ~ (all_53_4 = all_53_12)
% 231.16/42.43    (32)   ~ (all_53_8 = e3)
% 231.16/42.43    (33)   ~ (all_53_8 = all_53_9)
% 231.16/42.43    (34)  all_42_2 = all_6_2
% 231.16/42.43    (35)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.16/42.43          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.16/42.43    (36)  op(e2, e2) = e0
% 231.16/42.43    (37)   ~ (all_53_9 = all_53_11)
% 231.16/42.43    (38)   ~ (all_53_9 = all_6_2)
% 231.16/42.43    (39)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.16/42.43          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.16/42.43    (40)   ~ (all_53_14 = all_6_2)
% 231.16/42.43    (41)  all_57_3 = e0
% 231.16/42.43    (42)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.16/42.43          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.16/42.43    (43)   ~ (e3 = e2)
% 231.16/42.43    (44)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 231.16/42.43    (45)  all_55_1 = all_53_4
% 231.16/42.43    (46)  op(e1, e0) = all_53_14
% 231.16/42.43    (47)   ~ (all_53_6 = all_53_7)
% 231.16/42.43    (48)   ~ (e3 = e0)
% 231.16/42.43    (49)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.16/42.43          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.16/42.43    (50)  op(e3, e3) = e3
% 231.16/42.43    (51)   ~ (all_53_8 = all_6_2)
% 231.16/42.43    (52)  all_55_2 = all_53_8
% 231.16/42.43    (53)   ~ (all_53_4 = all_53_7)
% 231.16/42.43    (54)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 231.16/42.43    (55)   ~ (all_53_7 = e0)
% 231.16/42.43    (56)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.16/42.43          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.16/42.43            e1)
% 231.16/42.43    (57)   ~ (all_53_4 = all_53_8)
% 231.16/42.43    (58)  all_55_6 = all_53_9
% 231.16/42.43    (59)  op(e3, e2) = all_53_4
% 231.16/42.43    (60)   ~ (e2 = e0)
% 231.16/42.43    (61)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 231.16/42.43            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 231.16/42.43            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 231.16/42.43            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 231.16/42.43              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 231.16/42.43            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 231.16/42.43            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 231.16/42.43              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 231.16/42.43              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 231.16/42.43            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 231.16/42.43            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 231.16/42.43            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 231.16/42.43              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 231.16/42.43              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 231.16/42.43            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 231.16/42.43              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 231.16/42.43            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 231.16/42.43            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 231.16/42.43              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 231.16/42.43              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 231.16/42.43            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 231.16/42.43            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 231.16/42.43    (62)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 231.16/42.43          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.16/42.43    (63)   ~ (all_53_2 = all_53_14)
% 231.16/42.43    (64)   ~ (e1 = e0)
% 231.16/42.43    (65)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 231.16/42.43            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 231.16/42.43              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 231.16/42.43    (66)   ~ (all_53_4 = e0)
% 231.16/42.43    (67)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.16/42.43          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.16/42.43    (68)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.16/42.43          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.16/42.43    (69)   ~ (all_10_2 = e1)
% 231.16/42.43    (70)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 231.16/42.43    (71)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.16/42.43          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 231.16/42.43            e3)
% 231.16/42.43    (72)   ~ (all_53_4 = all_53_6)
% 231.16/42.43    (73)  op(e0, e2) = all_53_7
% 231.16/42.43    (74)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.16/42.43          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.16/42.43            e2)
% 231.16/42.43    (75)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.16/42.43              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.16/42.43                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.16/42.43                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.16/42.43    (76)  all_55_10 = all_6_2
% 231.16/42.43    (77)   ~ (all_53_6 = all_6_2)
% 231.16/42.43    (78)   ~ (all_53_13 = e0)
% 231.16/42.43    (79)  all_55_13 = all_53_7
% 231.16/42.43    (80)  op(e0, e0) = e1
% 231.16/42.43    (81)  op(e2, e0) = all_53_13
% 231.16/42.43    (82)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.16/42.43          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.16/42.43    (83)  all_38_2 = all_6_2
% 231.16/42.43    (84)  all_55_11 = all_53_14
% 231.16/42.43    (85)  all_55_3 = all_53_12
% 231.16/42.43    (86)   ~ (all_53_12 = e3)
% 231.16/42.43    (87)  all_57_0 = e3
% 231.16/42.43    (88)  op(e1, e3) = all_53_2
% 231.16/42.43    (89)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 231.16/42.43            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 231.16/42.43              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 231.16/42.43    (90)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.16/42.43          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.16/42.43    (91)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 231.16/42.43          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 231.16/42.43    (92)   ~ (all_53_12 = all_10_2)
% 231.16/42.43    (93)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 231.16/42.43          (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 231.16/42.43    (94)   ~ (all_53_13 = all_53_14)
% 231.16/42.43    (95)   ~ (e2 = e1)
% 231.16/42.43    (96)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.16/42.43          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.16/42.43    (97)  op(e2, e1) = all_53_9
% 231.16/42.43    (98)  op(e1, e2) = all_53_6
% 231.16/42.43    (99)   ~ (all_53_2 = all_53_6)
% 231.16/42.43    (100)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.16/42.43           (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.16/42.43    (101)  all_24_2 = all_6_2
% 231.16/42.43    (102)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.16/42.43           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.16/42.43    (103)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.16/42.43           (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.16/42.43    (104)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.16/42.43           | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.16/42.43             e1)
% 231.16/42.43    (105)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 231.16/42.43           (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 231.16/42.43    (106)   ~ (all_53_12 = all_53_14)
% 231.16/42.43    (107)  all_55_14 = all_53_11
% 231.16/42.43    (108)  op(e3, e1) = all_53_8
% 231.16/42.43    (109)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.16/42.43           (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.16/42.43    (110)   ~ (all_53_4 = e3)
% 231.16/42.43    (111)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 231.16/42.43           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 231.16/42.43    (112)  op(e3, e0) = all_53_12
% 231.16/42.43  
% 231.16/42.43  Begin of proof
% 231.16/42.43  | 
% 231.16/42.43  | BETA: splitting (39) gives:
% 231.16/42.43  | 
% 231.16/42.43  | Case 1:
% 231.16/42.43  | | 
% 231.16/42.43  | |   (113)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) =
% 231.16/42.43  | |            e0)
% 231.16/42.43  | | 
% 231.16/42.43  | | REF_CLOSE: (15), (48), (50), (59), (66), (113) are inconsistent by sub-proof
% 231.16/42.43  | |            #1543.
% 231.16/42.43  | | 
% 231.16/42.43  | Case 2:
% 231.16/42.43  | | 
% 231.16/42.43  | |   (114)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) =
% 231.16/42.43  | |            e0)
% 231.16/42.43  | | 
% 231.16/42.43  | | BETA: splitting (114) gives:
% 231.16/42.43  | | 
% 231.16/42.43  | | Case 1:
% 231.16/42.43  | | | 
% 231.16/42.43  | | |   (115)  all_57_4 = e0 & op(e3, e1) = e0
% 231.16/42.43  | | | 
% 231.16/42.43  | | | ALPHA: (115) implies:
% 231.16/42.43  | | |   (116)  all_57_4 = e0
% 231.16/42.43  | | |   (117)  op(e3, e1) = e0
% 231.16/42.43  | | | 
% 231.16/42.43  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 231.16/42.43  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 231.16/42.43  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 231.16/42.43  | | |            (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 231.16/42.43  | | |            (43), (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 231.16/42.43  | | |            (53), (54), (55), (56), (57), (58), (59), (60), (61), (62),
% 231.16/42.43  | | |            (63), (64), (65), (66), (67), (68), (69), (70), (71), (72),
% 231.16/42.43  | | |            (73), (74), (75), (76), (77), (78), (79), (80), (81), (82),
% 231.16/42.43  | | |            (83), (84), (85), (86), (87), (88), (89), (90), (91), (92),
% 231.16/42.43  | | |            (93), (94), (95), (96), (97), (98), (99), (100), (101), (102),
% 231.16/42.43  | | |            (103), (104), (105), (106), (107), (108), (109), (110), (111),
% 231.16/42.43  | | |            (112), (116), (117) are inconsistent by sub-proof #1385.
% 231.16/42.43  | | | 
% 231.16/42.43  | | Case 2:
% 231.16/42.43  | | | 
% 231.16/42.43  | | |   (118)  all_57_9 = e0 & op(e3, e0) = e0
% 231.16/42.43  | | | 
% 231.16/42.43  | | | REF_CLOSE: (30), (64), (118) are inconsistent by sub-proof #1990.
% 231.16/42.43  | | | 
% 231.16/42.43  | | End of split
% 231.16/42.43  | | 
% 231.16/42.43  | End of split
% 231.16/42.43  | 
% 231.16/42.43  End of proof
% 231.16/42.43  
% 231.16/42.43  Sub-proof #1385 shows that the following formulas are inconsistent:
% 231.16/42.43  ----------------------------------------------------------------
% 231.16/42.43    (1)   ~ (all_10_2 = e2)
% 231.16/42.43    (2)  all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 231.16/42.43    (3)  op(e3, e3) = all_10_2
% 231.16/42.43    (4)  op(e0, e1) = all_53_11
% 231.16/42.43    (5)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 231.16/42.43    (6)   ~ (all_53_6 = all_53_14)
% 231.16/42.43    (7)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 231.16/42.43    (8)  op(e3, e1) = e0
% 231.16/42.43    (9)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.16/42.43         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.16/42.43    (10)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.16/42.43          (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.16/42.43    (11)   ~ (all_53_8 = all_53_12)
% 231.16/42.43    (12)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.16/42.43          (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.16/42.43    (13)   ~ (all_53_8 = all_53_11)
% 231.16/42.43    (14)   ~ (e3 = e1)
% 231.16/42.43    (15)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 231.16/42.43          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.16/42.43    (16)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.16/42.43            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.16/42.43    (17)  all_55_0 = all_10_2
% 231.16/42.43    (18)   ~ (all_10_2 = e0)
% 231.16/42.43    (19)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.16/42.43          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.16/42.43    (20)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 231.16/42.43            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 231.16/42.43              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 231.16/42.43    (21)   ~ (all_6_2 = e3)
% 231.16/42.43    (22)  op(e1, e1) = all_6_2
% 231.16/42.43    (23)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 231.16/42.43    (24)   ~ (all_53_9 = e0)
% 231.16/42.43    (25)  all_55_0 = e3 | all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 231.16/42.43    (26)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 231.16/42.43    (27)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.16/42.43          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.16/42.43    (28)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 231.16/42.43    (29)  all_55_9 = all_53_6
% 231.16/42.43    (30)   ~ (all_53_11 = all_6_2)
% 231.16/42.43    (31)  all_57_9 = e1
% 231.16/42.43    (32)   ~ (all_53_4 = all_53_12)
% 231.16/42.43    (33)  all_57_4 = e0
% 231.16/42.43    (34)   ~ (all_53_8 = e3)
% 231.16/42.43    (35)   ~ (all_53_8 = all_53_9)
% 231.16/42.43    (36)  all_42_2 = all_6_2
% 231.16/42.43    (37)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.16/42.43          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.16/42.43    (38)  op(e2, e2) = e0
% 231.16/42.43    (39)   ~ (all_53_9 = all_53_11)
% 231.16/42.43    (40)   ~ (all_53_9 = all_6_2)
% 231.16/42.43    (41)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.16/42.43          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.16/42.43    (42)   ~ (all_53_14 = all_6_2)
% 231.16/42.43    (43)  all_57_3 = e0
% 231.16/42.43    (44)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.16/42.43          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.16/42.43    (45)   ~ (e3 = e2)
% 231.16/42.43    (46)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 231.16/42.43    (47)  all_55_1 = all_53_4
% 231.16/42.43    (48)  op(e1, e0) = all_53_14
% 231.16/42.43    (49)   ~ (all_53_6 = all_53_7)
% 231.26/42.43    (50)   ~ (e3 = e0)
% 231.26/42.43    (51)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.26/42.43          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.26/42.43    (52)  op(e3, e3) = e3
% 231.26/42.43    (53)   ~ (all_53_8 = all_6_2)
% 231.26/42.43    (54)  all_55_2 = all_53_8
% 231.26/42.43    (55)   ~ (all_53_4 = all_53_7)
% 231.26/42.43    (56)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 231.26/42.43    (57)   ~ (all_53_7 = e0)
% 231.26/42.43    (58)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.26/42.43          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.26/42.43            e1)
% 231.26/42.43    (59)   ~ (all_53_4 = all_53_8)
% 231.26/42.43    (60)  all_55_6 = all_53_9
% 231.26/42.43    (61)  op(e3, e2) = all_53_4
% 231.26/42.43    (62)   ~ (e2 = e0)
% 231.26/42.43    (63)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 231.26/42.43            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 231.26/42.43            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 231.26/42.43            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 231.26/42.43              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 231.26/42.43            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 231.26/42.43            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 231.26/42.43              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 231.26/42.43              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 231.26/42.43            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 231.26/42.43            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 231.26/42.43            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 231.26/42.43              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 231.26/42.43              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 231.26/42.43            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 231.26/42.43              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 231.26/42.43            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 231.26/42.43            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 231.26/42.43              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 231.26/42.43              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 231.26/42.43            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 231.26/42.43            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 231.26/42.43    (64)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 231.26/42.43          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.26/42.43    (65)   ~ (all_53_2 = all_53_14)
% 231.26/42.43    (66)   ~ (e1 = e0)
% 231.26/42.43    (67)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 231.26/42.43            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 231.26/42.43              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 231.26/42.43    (68)   ~ (all_53_4 = e0)
% 231.26/42.43    (69)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.26/42.43          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.26/42.43    (70)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.26/42.43          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.26/42.43    (71)   ~ (all_10_2 = e1)
% 231.26/42.43    (72)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 231.26/42.43    (73)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.26/42.44          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 231.26/42.44            e3)
% 231.26/42.44    (74)   ~ (all_53_4 = all_53_6)
% 231.26/42.44    (75)  op(e0, e2) = all_53_7
% 231.26/42.44    (76)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.26/42.44          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.26/42.44            e2)
% 231.26/42.44    (77)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.26/42.44              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.26/42.44                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.26/42.44                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.26/42.44    (78)  all_55_10 = all_6_2
% 231.26/42.44    (79)   ~ (all_53_6 = all_6_2)
% 231.26/42.44    (80)   ~ (all_53_13 = e0)
% 231.26/42.44    (81)  all_55_13 = all_53_7
% 231.26/42.44    (82)  op(e0, e0) = e1
% 231.26/42.44    (83)  op(e2, e0) = all_53_13
% 231.26/42.44    (84)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.26/42.44          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.26/42.44    (85)  all_38_2 = all_6_2
% 231.26/42.44    (86)  all_55_11 = all_53_14
% 231.26/42.44    (87)  all_55_3 = all_53_12
% 231.26/42.44    (88)   ~ (all_53_12 = e3)
% 231.26/42.44    (89)  all_57_0 = e3
% 231.26/42.44    (90)  op(e1, e3) = all_53_2
% 231.26/42.44    (91)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 231.26/42.44            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 231.26/42.44              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 231.26/42.44    (92)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.26/42.44          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.26/42.44    (93)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 231.26/42.44          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 231.26/42.44    (94)   ~ (all_53_12 = all_10_2)
% 231.26/42.44    (95)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 231.26/42.44          (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 231.26/42.44    (96)   ~ (all_53_13 = all_53_14)
% 231.26/42.44    (97)   ~ (e2 = e1)
% 231.26/42.44    (98)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.26/42.44          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.26/42.44    (99)  op(e2, e1) = all_53_9
% 231.26/42.44    (100)  op(e1, e2) = all_53_6
% 231.26/42.44    (101)   ~ (all_53_2 = all_53_6)
% 231.26/42.44    (102)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.26/42.44           (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.26/42.44    (103)  all_24_2 = all_6_2
% 231.26/42.44    (104)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.26/42.44           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.26/42.44    (105)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.26/42.44           (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.26/42.44    (106)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.26/42.44           | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.26/42.44             e1)
% 231.26/42.44    (107)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 231.26/42.44           (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 231.26/42.44    (108)   ~ (all_53_12 = all_53_14)
% 231.26/42.44    (109)  all_55_14 = all_53_11
% 231.26/42.44    (110)  op(e3, e1) = all_53_8
% 231.26/42.44    (111)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.26/42.44           (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.26/42.44    (112)   ~ (all_53_4 = e3)
% 231.26/42.44    (113)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 231.26/42.44           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 231.26/42.44    (114)  op(e3, e0) = all_53_12
% 231.26/42.44  
% 231.26/42.44  Begin of proof
% 231.26/42.44  | 
% 231.26/42.44  | BETA: splitting (58) gives:
% 231.26/42.44  | 
% 231.26/42.44  | Case 1:
% 231.26/42.44  | | 
% 231.26/42.44  | |   (115)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 231.26/42.44  | |            e1)
% 231.26/42.44  | | 
% 231.26/42.44  | | BETA: splitting (115) gives:
% 231.26/42.44  | | 
% 231.26/42.44  | | Case 1:
% 231.26/42.44  | | | 
% 231.26/42.44  | | |   (116)  all_57_12 = e1 & op(e0, e3) = e1
% 231.26/42.44  | | | 
% 231.26/42.44  | | | ALPHA: (116) implies:
% 231.26/42.44  | | |   (117)  all_57_12 = e1
% 231.26/42.44  | | | 
% 231.26/42.44  | | | BETA: splitting (77) gives:
% 231.26/42.44  | | | 
% 231.26/42.44  | | | Case 1:
% 231.26/42.44  | | | | 
% 231.26/42.44  | | | |   (118)  all_57_15 = e0 & op(e0, e0) = e0
% 231.26/42.44  | | | | 
% 231.26/42.44  | | | | ALPHA: (118) implies:
% 231.26/42.44  | | | |   (119)  all_57_15 = e0
% 231.26/42.44  | | | |   (120)  op(e0, e0) = e0
% 231.26/42.44  | | | | 
% 231.26/42.44  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 231.26/42.44  | | | |            (12), (13), (14), (15), (16), (17), (18), (19), (20), (21),
% 231.26/42.44  | | | |            (22), (23), (25), (26), (27), (28), (29), (30), (31), (32),
% 231.26/42.44  | | | |            (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 231.26/42.44  | | | |            (43), (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 231.26/42.44  | | | |            (53), (54), (55), (56), (57), (58), (59), (60), (61), (62),
% 231.26/42.44  | | | |            (63), (64), (65), (66), (67), (69), (70), (71), (72), (73),
% 231.26/42.44  | | | |            (74), (75), (76), (77), (78), (79), (81), (83), (84), (85),
% 231.26/42.44  | | | |            (86), (87), (88), (89), (90), (91), (92), (93), (94), (95),
% 231.26/42.44  | | | |            (96), (97), (98), (99), (100), (101), (102), (103), (104),
% 231.26/42.44  | | | |            (105), (106), (107), (108), (109), (110), (111), (112),
% 231.26/42.44  | | | |            (113), (114), (117), (119), (120) are inconsistent by
% 231.26/42.44  | | | |            sub-proof #1400.
% 231.26/42.44  | | | | 
% 231.26/42.44  | | | Case 2:
% 231.26/42.44  | | | | 
% 231.26/42.44  | | | |   (121)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2,
% 231.26/42.44  | | | |                e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) &
% 231.26/42.44  | | | |          ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0,
% 231.26/42.44  | | | |                e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 231.26/42.44  | | | | 
% 231.26/42.44  | | | | ALPHA: (121) implies:
% 231.26/42.44  | | | |   (122)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0,
% 231.26/42.44  | | | |              e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.26/42.44  | | | | 
% 231.26/42.44  | | | | BETA: splitting (122) gives:
% 231.26/42.44  | | | | 
% 231.26/42.44  | | | | Case 1:
% 231.26/42.44  | | | | | 
% 231.26/42.44  | | | | |   (123)  all_57_12 = e0 & op(e0, e3) = e0
% 231.26/42.44  | | | | | 
% 231.26/42.44  | | | | | REF_CLOSE: (14), (16), (27), (31), (33), (37), (45), (52), (62), (66),
% 231.26/42.44  | | | | |            (97), (117), (123) are inconsistent by sub-proof #1401.
% 231.26/42.44  | | | | | 
% 231.26/42.44  | | | | Case 2:
% 231.26/42.44  | | | | | 
% 231.26/42.44  | | | | |   (124)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 231.26/42.44  | | | | |              e1) = e0)
% 231.26/42.44  | | | | | 
% 231.26/42.44  | | | | | REF_CLOSE: (14), (16), (21), (22), (33), (45), (50), (51), (57), (62),
% 231.26/42.44  | | | | |            (66), (69), (75), (97), (104), (124) are inconsistent by
% 231.26/42.44  | | | | |            sub-proof #1399.
% 231.26/42.44  | | | | | 
% 231.26/42.44  | | | | End of split
% 231.26/42.44  | | | | 
% 231.26/42.44  | | | End of split
% 231.26/42.44  | | | 
% 231.26/42.44  | | Case 2:
% 231.26/42.44  | | | 
% 231.26/42.44  | | |   (125)  all_57_13 = e1 & op(e0, e2) = e1
% 231.26/42.44  | | | 
% 231.26/42.44  | | | ALPHA: (125) implies:
% 231.26/42.44  | | |   (126)  all_57_13 = e1
% 231.26/42.44  | | | 
% 231.26/42.44  | | | BETA: splitting (77) gives:
% 231.26/42.44  | | | 
% 231.26/42.44  | | | Case 1:
% 231.26/42.44  | | | | 
% 231.26/42.44  | | | |   (127)  all_57_15 = e0 & op(e0, e0) = e0
% 231.26/42.44  | | | | 
% 231.26/42.44  | | | | ALPHA: (127) implies:
% 231.26/42.44  | | | |   (128)  all_57_15 = e0
% 231.26/42.44  | | | |   (129)  op(e0, e0) = e0
% 231.26/42.44  | | | | 
% 231.26/42.44  | | | | BETA: splitting (73) gives:
% 231.26/42.44  | | | | 
% 231.26/42.44  | | | | Case 1:
% 231.26/42.44  | | | | | 
% 231.26/42.44  | | | | |   (130)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0,
% 231.26/42.44  | | | | |              e2) = e3)
% 231.26/42.44  | | | | | 
% 231.26/42.44  | | | | | BETA: splitting (130) gives:
% 231.26/42.44  | | | | | 
% 231.26/42.44  | | | | | Case 1:
% 231.26/42.44  | | | | | | 
% 231.26/42.44  | | | | | |   (131)  all_57_12 = e3 & op(e0, e3) = e3
% 231.26/42.44  | | | | | | 
% 231.26/42.44  | | | | | | ALPHA: (131) implies:
% 231.26/42.44  | | | | | |   (132)  all_57_12 = e3
% 231.26/42.44  | | | | | | 
% 231.26/42.44  | | | | | | BETA: splitting (37) gives:
% 231.26/42.44  | | | | | | 
% 231.26/42.44  | | | | | | Case 1:
% 231.26/42.44  | | | | | | | 
% 231.26/42.44  | | | | | | |   (133)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 &
% 231.26/42.44  | | | | | | |            op(e3, e2) = e2)
% 231.26/42.44  | | | | | | | 
% 231.26/42.44  | | | | | | | BETA: splitting (133) gives:
% 231.26/42.44  | | | | | | | 
% 231.26/42.44  | | | | | | | Case 1:
% 231.26/42.44  | | | | | | | | 
% 231.26/42.44  | | | | | | | |   (134)  all_57_0 = e2 & op(e3, e3) = e2
% 231.26/42.44  | | | | | | | | 
% 231.26/42.44  | | | | | | | | ALPHA: (134) implies:
% 231.26/42.44  | | | | | | | |   (135)  op(e3, e3) = e2
% 231.26/42.44  | | | | | | | | 
% 231.26/42.44  | | | | | | | | REF_CLOSE: (16), (45), (52), (135) are inconsistent by sub-proof
% 231.26/42.44  | | | | | | | |            #2490.
% 231.26/42.44  | | | | | | | | 
% 231.26/42.44  | | | | | | | Case 2:
% 231.26/42.44  | | | | | | | | 
% 231.26/42.44  | | | | | | | |   (136)  all_57_1 = e2 & op(e3, e2) = e2
% 231.26/42.44  | | | | | | | | 
% 231.26/42.44  | | | | | | | | ALPHA: (136) implies:
% 231.26/42.44  | | | | | | | |   (137)  all_57_1 = e2
% 231.26/42.44  | | | | | | | | 
% 231.26/42.44  | | | | | | | | BETA: splitting (76) gives:
% 231.26/42.44  | | | | | | | | 
% 231.26/42.44  | | | | | | | | Case 1:
% 231.26/42.44  | | | | | | | | | 
% 231.26/42.44  | | | | | | | | |   (138)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2
% 231.26/42.44  | | | | | | | | |            & op(e0, e2) = e2)
% 231.26/42.44  | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | BETA: splitting (138) gives:
% 231.26/42.44  | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | Case 1:
% 231.26/42.44  | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | |   (139)  all_57_12 = e2 & op(e0, e3) = e2
% 231.26/42.44  | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | | REF_CLOSE: (45), (132), (139) are inconsistent by sub-proof
% 231.26/42.44  | | | | | | | | | |            #2232.
% 231.26/42.44  | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | Case 2:
% 231.26/42.44  | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | |   (140)  all_57_13 = e2 & op(e0, e2) = e2
% 231.26/42.44  | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | | REF_CLOSE: (16), (31), (33), (37), (45), (52), (62), (97),
% 231.26/42.44  | | | | | | | | | |            (126), (137), (140) are inconsistent by sub-proof
% 231.26/42.44  | | | | | | | | | |            #1398.
% 231.26/42.44  | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | End of split
% 231.26/42.44  | | | | | | | | | 
% 231.26/42.44  | | | | | | | | Case 2:
% 231.26/42.44  | | | | | | | | | 
% 231.26/42.44  | | | | | | | | |   (141)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2
% 231.26/42.44  | | | | | | | | |            & op(e0, e0) = e2)
% 231.26/42.44  | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | BETA: splitting (141) gives:
% 231.26/42.44  | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | Case 1:
% 231.26/42.44  | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | |   (142)  all_57_14 = e2 & op(e0, e1) = e2
% 231.26/42.44  | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | | ALPHA: (142) implies:
% 231.26/42.44  | | | | | | | | | |   (143)  all_57_14 = e2
% 231.26/42.44  | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | | BETA: splitting (69) gives:
% 231.26/42.44  | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | | Case 1:
% 231.26/42.44  | | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | | |   (144)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 231.26/42.44  | | | | | | | | | | |            & op(e2, e1) = e3)
% 231.26/42.44  | | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | | | BETA: splitting (144) gives:
% 231.26/42.44  | | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | | | Case 1:
% 231.26/42.44  | | | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | | | |   (145)  all_57_4 = e3 & op(e3, e1) = e3
% 231.26/42.44  | | | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | | | | REF_CLOSE: (14), (16), (27), (37), (41), (45), (50), (52),
% 231.26/42.44  | | | | | | | | | | | |            (62), (66), (97), (137), (145) are inconsistent by
% 231.26/42.44  | | | | | | | | | | | |            sub-proof #1829.
% 231.26/42.44  | | | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | | | Case 2:
% 231.26/42.44  | | | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | | | |   (146)  all_57_5 = e3 & op(e2, e1) = e3
% 231.26/42.44  | | | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | | | | ALPHA: (146) implies:
% 231.26/42.44  | | | | | | | | | | | |   (147)  all_57_5 = e3
% 231.26/42.44  | | | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | | | | BETA: splitting (70) gives:
% 231.26/42.44  | | | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | | | | Case 1:
% 231.26/42.44  | | | | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | | | | |   (148)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 231.26/42.44  | | | | | | | | | | | | |            & op(e2, e2) = e3)
% 231.26/42.44  | | | | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | | | | | BETA: splitting (148) gives:
% 231.26/42.44  | | | | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | | | | | Case 1:
% 231.26/42.44  | | | | | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | | | | | |   (149)  all_57_1 = e3 & op(e3, e2) = e3
% 231.26/42.44  | | | | | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | | | | | | ALPHA: (149) implies:
% 231.26/42.44  | | | | | | | | | | | | | |   (150)  all_57_1 = e3
% 231.26/42.44  | | | | | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | | | | | | COMBINE_EQS: (137), (150) imply:
% 231.26/42.44  | | | | | | | | | | | | | |   (151)  e3 = e2
% 231.26/42.44  | | | | | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | | | | | | SIMP: (151) implies:
% 231.26/42.44  | | | | | | | | | | | | | |   (152)  e3 = e2
% 231.26/42.44  | | | | | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | | | | | | COMBINE_EQS: (147), (152) imply:
% 231.26/42.44  | | | | | | | | | | | | | |   (153)  all_57_5 = e2
% 231.26/42.44  | | | | | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | | | | | | REF_CLOSE: (16), (21), (22), (33), (45), (50), (69), (143),
% 231.26/42.44  | | | | | | | | | | | | | |            (153) are inconsistent by sub-proof #2188.
% 231.26/42.44  | | | | | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | | | | | Case 2:
% 231.26/42.44  | | | | | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | | | | | |   (154)  all_57_3 = e3 & op(e2, e2) = e3
% 231.26/42.44  | | | | | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | | | | | | REF_CLOSE: (9), (14), (16), (21), (22), (33), (38), (43),
% 231.26/42.44  | | | | | | | | | | | | | |            (45), (50), (51), (62), (66), (69), (84), (92),
% 231.26/42.44  | | | | | | | | | | | | | |            (97), (104), (147), (154) are inconsistent by
% 231.26/42.44  | | | | | | | | | | | | | |            sub-proof #1397.
% 231.26/42.44  | | | | | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | | | | | End of split
% 231.26/42.44  | | | | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | | | | Case 2:
% 231.26/42.44  | | | | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | | | | |   (155)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 231.26/42.44  | | | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 231.26/42.44  | | | | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | | | | | BETA: splitting (155) gives:
% 231.26/42.44  | | | | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | | | | | Case 1:
% 231.26/42.44  | | | | | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | | | | | |   (156)  all_57_7 = e3 & op(e1, e2) = e3
% 231.26/42.44  | | | | | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | | | | | | ALPHA: (156) implies:
% 231.26/42.44  | | | | | | | | | | | | | |   (157)  all_57_7 = e3
% 231.26/42.44  | | | | | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | | | | | | REF_CLOSE: (9), (10), (12), (14), (16), (21), (22), (27),
% 231.26/42.44  | | | | | | | | | | | | | |            (31), (33), (37), (38), (41), (43), (45), (50),
% 231.26/42.44  | | | | | | | | | | | | | |            (51), (52), (62), (64), (66), (69), (70), (84),
% 231.26/42.44  | | | | | | | | | | | | | |            (88), (92), (97), (102), (104), (105), (111),
% 231.26/42.44  | | | | | | | | | | | | | |            (114), (132), (147), (157) are inconsistent by
% 231.26/42.44  | | | | | | | | | | | | | |            sub-proof #1395.
% 231.26/42.44  | | | | | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | | | | | Case 2:
% 231.26/42.44  | | | | | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | | | | | |   (158)  all_57_13 = e3 & op(e0, e2) = e3
% 231.26/42.44  | | | | | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | | | | | | ALPHA: (158) implies:
% 231.26/42.44  | | | | | | | | | | | | | |   (159)  all_57_13 = e3
% 231.26/42.44  | | | | | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | | | | | | COMBINE_EQS: (126), (159) imply:
% 231.26/42.44  | | | | | | | | | | | | | |   (160)  e3 = e1
% 231.26/42.44  | | | | | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | | | | | | SIMP: (160) implies:
% 231.26/42.44  | | | | | | | | | | | | | |   (161)  e3 = e1
% 231.26/42.44  | | | | | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | | | | | | COMBINE_EQS: (132), (161) imply:
% 231.26/42.44  | | | | | | | | | | | | | |   (162)  all_57_12 = e1
% 231.26/42.44  | | | | | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 231.26/42.44  | | | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 231.26/42.44  | | | | | | | | | | | | | |            (19), (20), (21), (22), (23), (25), (26), (27),
% 231.26/42.44  | | | | | | | | | | | | | |            (28), (29), (30), (31), (32), (33), (34), (35),
% 231.26/42.44  | | | | | | | | | | | | | |            (36), (37), (38), (39), (40), (41), (42), (43),
% 231.26/42.44  | | | | | | | | | | | | | |            (44), (45), (46), (47), (48), (49), (50), (51),
% 231.26/42.44  | | | | | | | | | | | | | |            (52), (53), (54), (55), (56), (57), (58), (59),
% 231.26/42.44  | | | | | | | | | | | | | |            (60), (61), (62), (63), (64), (65), (66), (67),
% 231.26/42.44  | | | | | | | | | | | | | |            (69), (70), (71), (72), (73), (74), (75), (76),
% 231.26/42.44  | | | | | | | | | | | | | |            (77), (78), (79), (81), (83), (84), (85), (86),
% 231.26/42.44  | | | | | | | | | | | | | |            (87), (88), (89), (90), (91), (92), (93), (94),
% 231.26/42.44  | | | | | | | | | | | | | |            (95), (96), (97), (98), (99), (100), (101), (102),
% 231.26/42.44  | | | | | | | | | | | | | |            (103), (104), (105), (106), (107), (108), (109),
% 231.26/42.44  | | | | | | | | | | | | | |            (110), (111), (112), (113), (114), (128), (129),
% 231.26/42.44  | | | | | | | | | | | | | |            (162) are inconsistent by sub-proof #1400.
% 231.26/42.44  | | | | | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | | | | | End of split
% 231.26/42.44  | | | | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | | | | End of split
% 231.26/42.44  | | | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | | | End of split
% 231.26/42.44  | | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | | Case 2:
% 231.26/42.44  | | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | | |   (163)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 231.26/42.44  | | | | | | | | | | |            e3 & op(e0, e1) = e3)
% 231.26/42.44  | | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | | | REF_CLOSE: (16), (21), (22), (45), (143), (163) are
% 231.26/42.44  | | | | | | | | | | |            inconsistent by sub-proof #2409.
% 231.26/42.44  | | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | | End of split
% 231.26/42.44  | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | Case 2:
% 231.26/42.44  | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | |   (164)  all_57_15 = e2 & op(e0, e0) = e2
% 231.26/42.44  | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | | ALPHA: (164) implies:
% 231.26/42.44  | | | | | | | | | |   (165)  op(e0, e0) = e2
% 231.26/42.44  | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | | REF_CLOSE: (16), (82), (97), (165) are inconsistent by
% 231.26/42.44  | | | | | | | | | |            sub-proof #2177.
% 231.26/42.44  | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | End of split
% 231.26/42.44  | | | | | | | | | 
% 231.26/42.44  | | | | | | | | End of split
% 231.26/42.44  | | | | | | | | 
% 231.26/42.44  | | | | | | | End of split
% 231.26/42.44  | | | | | | | 
% 231.26/42.44  | | | | | | Case 2:
% 231.26/42.44  | | | | | | | 
% 231.26/42.44  | | | | | | |   (166)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 &
% 231.26/42.44  | | | | | | |            op(e3, e0) = e2)
% 231.26/42.44  | | | | | | | 
% 231.26/42.44  | | | | | | | REF_CLOSE: (31), (33), (62), (97), (166) are inconsistent by
% 231.26/42.44  | | | | | | |            sub-proof #2221.
% 231.26/42.44  | | | | | | | 
% 231.26/42.44  | | | | | | End of split
% 231.26/42.44  | | | | | | 
% 231.26/42.44  | | | | | Case 2:
% 231.26/42.44  | | | | | | 
% 231.26/42.44  | | | | | |   (167)  all_57_13 = e3 & op(e0, e2) = e3
% 231.26/42.44  | | | | | | 
% 231.26/42.44  | | | | | | ALPHA: (167) implies:
% 231.26/42.44  | | | | | |   (168)  all_57_13 = e3
% 231.26/42.44  | | | | | | 
% 231.26/42.44  | | | | | | REF_CLOSE: (14), (126), (168) are inconsistent by sub-proof #2268.
% 231.26/42.44  | | | | | | 
% 231.26/42.44  | | | | | End of split
% 231.26/42.44  | | | | | 
% 231.26/42.44  | | | | Case 2:
% 231.26/42.44  | | | | | 
% 231.26/42.44  | | | | |   (169)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0,
% 231.26/42.44  | | | | |              e0) = e3)
% 231.26/42.44  | | | | | 
% 231.26/42.44  | | | | | BETA: splitting (169) gives:
% 231.26/42.44  | | | | | 
% 231.26/42.44  | | | | | Case 1:
% 231.26/42.44  | | | | | | 
% 231.26/42.44  | | | | | |   (170)  all_57_14 = e3 & op(e0, e1) = e3
% 231.26/42.44  | | | | | | 
% 231.26/42.44  | | | | | | ALPHA: (170) implies:
% 231.26/42.44  | | | | | |   (171)  all_57_14 = e3
% 231.26/42.44  | | | | | | 
% 231.26/42.44  | | | | | | BETA: splitting (37) gives:
% 231.26/42.44  | | | | | | 
% 231.26/42.44  | | | | | | Case 1:
% 231.26/42.44  | | | | | | | 
% 231.26/42.44  | | | | | | |   (172)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 &
% 231.26/42.44  | | | | | | |            op(e3, e2) = e2)
% 231.26/42.44  | | | | | | | 
% 231.26/42.44  | | | | | | | BETA: splitting (172) gives:
% 231.26/42.44  | | | | | | | 
% 231.26/42.44  | | | | | | | Case 1:
% 231.26/42.44  | | | | | | | | 
% 231.26/42.44  | | | | | | | |   (173)  all_57_0 = e2 & op(e3, e3) = e2
% 231.26/42.44  | | | | | | | | 
% 231.26/42.44  | | | | | | | | ALPHA: (173) implies:
% 231.26/42.44  | | | | | | | |   (174)  op(e3, e3) = e2
% 231.26/42.44  | | | | | | | | 
% 231.26/42.44  | | | | | | | | REF_CLOSE: (16), (45), (52), (174) are inconsistent by sub-proof
% 231.26/42.44  | | | | | | | |            #2490.
% 231.26/42.44  | | | | | | | | 
% 231.26/42.44  | | | | | | | Case 2:
% 231.26/42.44  | | | | | | | | 
% 231.26/42.44  | | | | | | | |   (175)  all_57_1 = e2 & op(e3, e2) = e2
% 231.26/42.44  | | | | | | | | 
% 231.26/42.44  | | | | | | | | ALPHA: (175) implies:
% 231.26/42.44  | | | | | | | |   (176)  all_57_1 = e2
% 231.26/42.44  | | | | | | | | 
% 231.26/42.44  | | | | | | | | BETA: splitting (76) gives:
% 231.26/42.44  | | | | | | | | 
% 231.26/42.44  | | | | | | | | Case 1:
% 231.26/42.44  | | | | | | | | | 
% 231.26/42.44  | | | | | | | | |   (177)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2
% 231.26/42.44  | | | | | | | | |            & op(e0, e2) = e2)
% 231.26/42.44  | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | BETA: splitting (177) gives:
% 231.26/42.44  | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | Case 1:
% 231.26/42.44  | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | |   (178)  all_57_12 = e2 & op(e0, e3) = e2
% 231.26/42.44  | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | | ALPHA: (178) implies:
% 231.26/42.44  | | | | | | | | | |   (179)  all_57_12 = e2
% 231.26/42.44  | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | | BETA: splitting (105) gives:
% 231.26/42.44  | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | | Case 1:
% 231.26/42.44  | | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | | |   (180)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 231.26/42.44  | | | | | | | | | | |            & op(e2, e3) = e0)
% 231.26/42.44  | | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | | | REF_CLOSE: (9), (14), (16), (31), (33), (37), (43), (45),
% 231.26/42.44  | | | | | | | | | | |            (50), (62), (64), (66), (84), (88), (92), (97),
% 231.26/42.44  | | | | | | | | | | |            (114), (180) are inconsistent by sub-proof #1402.
% 231.26/42.44  | | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | | Case 2:
% 231.26/42.44  | | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | | |   (181)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 231.26/42.44  | | | | | | | | | | |            e0 & op(e0, e3) = e0)
% 231.26/42.44  | | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 231.26/42.44  | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 231.26/42.44  | | | | | | | | | | |            (19), (20), (21), (22), (23), (25), (26), (27),
% 231.26/42.44  | | | | | | | | | | |            (28), (29), (30), (32), (33), (34), (35), (36),
% 231.26/42.44  | | | | | | | | | | |            (37), (38), (39), (40), (41), (42), (43), (44),
% 231.26/42.44  | | | | | | | | | | |            (46), (47), (48), (49), (51), (52), (53), (54),
% 231.26/42.44  | | | | | | | | | | |            (55), (56), (57), (58), (59), (60), (61), (62),
% 231.26/42.44  | | | | | | | | | | |            (63), (64), (65), (66), (67), (69), (70), (71),
% 231.26/42.44  | | | | | | | | | | |            (72), (73), (74), (75), (76), (77), (78), (79),
% 231.26/42.44  | | | | | | | | | | |            (81), (83), (84), (85), (86), (87), (88), (89),
% 231.26/42.44  | | | | | | | | | | |            (90), (91), (92), (93), (94), (95), (96), (97),
% 231.26/42.44  | | | | | | | | | | |            (98), (99), (100), (101), (102), (103), (104),
% 231.26/42.44  | | | | | | | | | | |            (105), (106), (107), (108), (109), (110), (111),
% 231.26/42.44  | | | | | | | | | | |            (112), (113), (114), (128), (129), (179), (181)
% 231.26/42.44  | | | | | | | | | | |            are inconsistent by sub-proof #1394.
% 231.26/42.44  | | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | | End of split
% 231.26/42.44  | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | Case 2:
% 231.26/42.44  | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | |   (182)  all_57_13 = e2 & op(e0, e2) = e2
% 231.26/42.44  | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | | REF_CLOSE: (16), (31), (33), (37), (45), (52), (62), (97),
% 231.26/42.44  | | | | | | | | | |            (126), (176), (182) are inconsistent by sub-proof
% 231.26/42.44  | | | | | | | | | |            #1398.
% 231.26/42.44  | | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | End of split
% 231.26/42.44  | | | | | | | | | 
% 231.26/42.44  | | | | | | | | Case 2:
% 231.26/42.44  | | | | | | | | | 
% 231.26/42.44  | | | | | | | | |   (183)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2
% 231.26/42.44  | | | | | | | | |            & op(e0, e0) = e2)
% 231.26/42.44  | | | | | | | | | 
% 231.26/42.44  | | | | | | | | | REF_CLOSE: (16), (45), (82), (97), (171), (183) are
% 231.26/42.44  | | | | | | | | |            inconsistent by sub-proof #1393.
% 231.26/42.44  | | | | | | | | | 
% 231.26/42.44  | | | | | | | | End of split
% 231.26/42.44  | | | | | | | | 
% 231.26/42.44  | | | | | | | End of split
% 231.26/42.44  | | | | | | | 
% 231.26/42.44  | | | | | | Case 2:
% 231.26/42.44  | | | | | | | 
% 231.26/42.44  | | | | | | |   (184)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 &
% 231.26/42.44  | | | | | | |            op(e3, e0) = e2)
% 231.26/42.44  | | | | | | | 
% 231.26/42.44  | | | | | | | REF_CLOSE: (31), (33), (62), (97), (184) are inconsistent by
% 231.26/42.44  | | | | | | |            sub-proof #2221.
% 231.26/42.44  | | | | | | | 
% 231.26/42.44  | | | | | | End of split
% 231.26/42.44  | | | | | | 
% 231.26/42.44  | | | | | Case 2:
% 231.26/42.44  | | | | | | 
% 231.26/42.44  | | | | | |   (185)  all_57_15 = e3 & op(e0, e0) = e3
% 231.26/42.44  | | | | | | 
% 231.26/42.44  | | | | | | ALPHA: (185) implies:
% 231.26/42.44  | | | | | |   (186)  all_57_15 = e3
% 231.26/42.44  | | | | | |   (187)  op(e0, e0) = e3
% 231.26/42.44  | | | | | | 
% 231.26/42.44  | | | | | | REF_CLOSE: (1), (3), (5), (7), (9), (10), (11), (12), (15), (16),
% 231.26/42.44  | | | | | |            (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 231.26/42.44  | | | | | |            (27), (32), (35), (36), (37), (40), (41), (43), (44),
% 231.26/42.44  | | | | | |            (47), (51), (53), (54), (56), (58), (59), (61), (62),
% 231.26/42.44  | | | | | |            (63), (64), (66), (67), (68), (69), (70), (71), (74),
% 231.26/42.44  | | | | | |            (76), (77), (78), (84), (85), (87), (91), (92), (93),
% 231.26/42.44  | | | | | |            (94), (97), (98), (99), (100), (102), (103), (104),
% 231.26/42.44  | | | | | |            (105), (106), (107), (110), (111), (113), (114), (186),
% 231.26/42.44  | | | | | |            (187) are inconsistent by sub-proof #1414.
% 231.26/42.44  | | | | | | 
% 231.26/42.44  | | | | | End of split
% 231.26/42.44  | | | | | 
% 231.26/42.44  | | | | End of split
% 231.26/42.44  | | | | 
% 231.26/42.44  | | | Case 2:
% 231.26/42.44  | | | | 
% 231.26/42.44  | | | |   (188)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2,
% 231.26/42.44  | | | |                e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) &
% 231.26/42.44  | | | |          ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0,
% 231.26/42.44  | | | |                e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 231.26/42.44  | | | | 
% 231.26/42.44  | | | | ALPHA: (188) implies:
% 231.26/42.44  | | | |   (189)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2,
% 231.26/42.44  | | | |              e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.26/42.44  | | | | 
% 231.26/42.44  | | | | REF_CLOSE: (1), (3), (5), (7), (9), (10), (11), (12), (14), (15), (16),
% 231.26/42.44  | | | |            (17), (18), (19), (20), (21), (22), (23), (24), (25), (27),
% 231.26/42.44  | | | |            (31), (32), (33), (35), (36), (37), (38), (40), (41), (43),
% 231.26/42.44  | | | |            (44), (45), (47), (50), (51), (52), (53), (54), (56), (58),
% 231.26/42.44  | | | |            (59), (61), (62), (63), (64), (66), (67), (68), (69), (70),
% 231.26/42.44  | | | |            (71), (74), (76), (77), (78), (80), (82), (83), (84), (85),
% 231.26/42.44  | | | |            (87), (88), (89), (91), (92), (93), (94), (95), (97), (98),
% 231.26/42.44  | | | |            (99), (100), (102), (103), (104), (105), (106), (107), (110),
% 231.26/42.44  | | | |            (111), (113), (114), (189) are inconsistent by sub-proof
% 231.26/42.44  | | | |            #1390.
% 231.26/42.44  | | | | 
% 231.26/42.44  | | | End of split
% 231.26/42.44  | | | 
% 231.26/42.44  | | End of split
% 231.26/42.44  | | 
% 231.26/42.44  | Case 2:
% 231.26/42.44  | | 
% 231.26/42.44  | |   (190)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.26/42.44  | |            e1)
% 231.26/42.44  | | 
% 231.26/42.44  | | BETA: splitting (190) gives:
% 231.26/42.44  | | 
% 231.26/42.44  | | Case 1:
% 231.26/42.44  | | | 
% 231.26/42.44  | | |   (191)  all_57_14 = e1 & op(e0, e1) = e1
% 231.26/42.44  | | | 
% 231.26/42.44  | | | ALPHA: (191) implies:
% 231.26/42.44  | | |   (192)  all_57_14 = e1
% 231.26/42.44  | | | 
% 231.26/42.44  | | | BETA: splitting (77) gives:
% 231.26/42.44  | | | 
% 231.26/42.44  | | | Case 1:
% 231.26/42.44  | | | | 
% 231.26/42.44  | | | |   (193)  all_57_15 = e0 & op(e0, e0) = e0
% 231.26/42.44  | | | | 
% 231.26/42.44  | | | | ALPHA: (193) implies:
% 231.26/42.44  | | | |   (194)  all_57_15 = e0
% 231.26/42.44  | | | |   (195)  op(e0, e0) = e0
% 231.26/42.44  | | | | 
% 231.26/42.44  | | | | BETA: splitting (73) gives:
% 231.26/42.44  | | | | 
% 231.26/42.44  | | | | Case 1:
% 231.26/42.44  | | | | | 
% 231.26/42.44  | | | | |   (196)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0,
% 231.26/42.44  | | | | |              e2) = e3)
% 231.26/42.44  | | | | | 
% 231.26/42.44  | | | | | BETA: splitting (196) gives:
% 231.26/42.44  | | | | | 
% 231.26/42.44  | | | | | Case 1:
% 231.26/42.44  | | | | | | 
% 231.26/42.44  | | | | | |   (197)  all_57_12 = e3 & op(e0, e3) = e3
% 231.26/42.44  | | | | | | 
% 231.26/42.44  | | | | | | ALPHA: (197) implies:
% 231.26/42.44  | | | | | |   (198)  all_57_12 = e3
% 231.26/42.44  | | | | | | 
% 231.26/42.44  | | | | | | BETA: splitting (37) gives:
% 231.26/42.44  | | | | | | 
% 231.26/42.44  | | | | | | Case 1:
% 231.26/42.44  | | | | | | | 
% 231.26/42.44  | | | | | | |   (199)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 &
% 231.26/42.44  | | | | | | |            op(e3, e2) = e2)
% 231.26/42.44  | | | | | | | 
% 231.26/42.44  | | | | | | | BETA: splitting (199) gives:
% 231.26/42.44  | | | | | | | 
% 231.26/42.44  | | | | | | | Case 1:
% 231.26/42.44  | | | | | | | | 
% 231.26/42.44  | | | | | | | |   (200)  all_57_0 = e2 & op(e3, e3) = e2
% 231.26/42.44  | | | | | | | | 
% 231.26/42.44  | | | | | | | | ALPHA: (200) implies:
% 231.26/42.44  | | | | | | | |   (201)  op(e3, e3) = e2
% 231.26/42.44  | | | | | | | | 
% 231.26/42.44  | | | | | | | | REF_CLOSE: (16), (45), (52), (201) are inconsistent by sub-proof
% 231.26/42.44  | | | | | | | |            #2490.
% 231.26/42.44  | | | | | | | | 
% 231.26/42.44  | | | | | | | Case 2:
% 231.26/42.44  | | | | | | | | 
% 231.26/42.44  | | | | | | | |   (202)  all_57_1 = e2 & op(e3, e2) = e2
% 231.26/42.44  | | | | | | | | 
% 231.26/42.44  | | | | | | | | ALPHA: (202) implies:
% 231.26/42.44  | | | | | | | |   (203)  all_57_1 = e2
% 231.26/42.44  | | | | | | | | 
% 231.26/42.44  | | | | | | | | BETA: splitting (76) gives:
% 231.26/42.44  | | | | | | | | 
% 231.26/42.44  | | | | | | | | Case 1:
% 231.26/42.44  | | | | | | | | | 
% 231.26/42.45  | | | | | | | | |   (204)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2
% 231.26/42.45  | | | | | | | | |            & op(e0, e2) = e2)
% 231.26/42.45  | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | BETA: splitting (204) gives:
% 231.26/42.45  | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | Case 1:
% 231.26/42.45  | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | |   (205)  all_57_12 = e2 & op(e0, e3) = e2
% 231.26/42.45  | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | REF_CLOSE: (45), (198), (205) are inconsistent by sub-proof
% 231.26/42.45  | | | | | | | | | |            #2232.
% 231.26/42.45  | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | Case 2:
% 231.26/42.45  | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | |   (206)  all_57_13 = e2 & op(e0, e2) = e2
% 231.26/42.45  | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | ALPHA: (206) implies:
% 231.26/42.45  | | | | | | | | | |   (207)  all_57_13 = e2
% 231.26/42.45  | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | BETA: splitting (69) gives:
% 231.26/42.45  | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | Case 1:
% 231.26/42.45  | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | |   (208)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 231.26/42.45  | | | | | | | | | | |            & op(e2, e1) = e3)
% 231.26/42.45  | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | | BETA: splitting (208) gives:
% 231.26/42.45  | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | | Case 1:
% 231.26/42.45  | | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | | |   (209)  all_57_4 = e3 & op(e3, e1) = e3
% 231.26/42.45  | | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | | | REF_CLOSE: (14), (16), (27), (37), (41), (45), (50), (52),
% 231.26/42.45  | | | | | | | | | | | |            (62), (66), (97), (203), (209) are inconsistent by
% 231.26/42.45  | | | | | | | | | | | |            sub-proof #1829.
% 231.26/42.45  | | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | | Case 2:
% 231.26/42.45  | | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | | |   (210)  all_57_5 = e3 & op(e2, e1) = e3
% 231.26/42.45  | | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | | | ALPHA: (210) implies:
% 231.26/42.45  | | | | | | | | | | | |   (211)  all_57_5 = e3
% 231.26/42.45  | | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | | | BETA: splitting (70) gives:
% 231.26/42.45  | | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | | | Case 1:
% 231.26/42.45  | | | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | | | |   (212)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 231.26/42.45  | | | | | | | | | | | | |            & op(e2, e2) = e3)
% 231.26/42.45  | | | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | | | | BETA: splitting (212) gives:
% 231.26/42.45  | | | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | | | | Case 1:
% 231.26/42.45  | | | | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | | | | |   (213)  all_57_1 = e3 & op(e3, e2) = e3
% 231.26/42.45  | | | | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | | | | | REF_CLOSE: (45), (203), (213) are inconsistent by sub-proof
% 231.26/42.45  | | | | | | | | | | | | | |            #1664.
% 231.26/42.45  | | | | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | | | | Case 2:
% 231.26/42.45  | | | | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | | | | |   (214)  all_57_3 = e3 & op(e2, e2) = e3
% 231.26/42.45  | | | | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | | | | | REF_CLOSE: (9), (14), (16), (21), (22), (33), (38), (43),
% 231.26/42.45  | | | | | | | | | | | | | |            (45), (50), (51), (62), (66), (69), (84), (92),
% 231.26/42.45  | | | | | | | | | | | | | |            (97), (104), (211), (214) are inconsistent by
% 231.26/42.45  | | | | | | | | | | | | | |            sub-proof #1397.
% 231.26/42.45  | | | | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | | | | End of split
% 231.26/42.45  | | | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | | | Case 2:
% 231.26/42.45  | | | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | | | |   (215)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 231.26/42.45  | | | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 231.26/42.45  | | | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | | | | BETA: splitting (215) gives:
% 231.26/42.45  | | | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | | | | Case 1:
% 231.26/42.45  | | | | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | | | | |   (216)  all_57_7 = e3 & op(e1, e2) = e3
% 231.26/42.45  | | | | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | | | | | ALPHA: (216) implies:
% 231.26/42.45  | | | | | | | | | | | | | |   (217)  all_57_7 = e3
% 231.26/42.45  | | | | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | | | | | REF_CLOSE: (9), (10), (12), (14), (16), (21), (22), (27),
% 231.26/42.45  | | | | | | | | | | | | | |            (31), (33), (37), (38), (41), (43), (45), (50),
% 231.26/42.45  | | | | | | | | | | | | | |            (51), (52), (62), (64), (66), (69), (70), (84),
% 231.26/42.45  | | | | | | | | | | | | | |            (88), (92), (97), (102), (104), (105), (111),
% 231.26/42.45  | | | | | | | | | | | | | |            (114), (198), (211), (217) are inconsistent by
% 231.26/42.45  | | | | | | | | | | | | | |            sub-proof #1395.
% 231.26/42.45  | | | | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | | | | Case 2:
% 231.26/42.45  | | | | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | | | | |   (218)  all_57_13 = e3 & op(e0, e2) = e3
% 231.26/42.45  | | | | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | | | | | ALPHA: (218) implies:
% 231.26/42.45  | | | | | | | | | | | | | |   (219)  all_57_13 = e3
% 231.26/42.45  | | | | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | | | | | REF_CLOSE: (45), (207), (219) are inconsistent by sub-proof
% 231.26/42.45  | | | | | | | | | | | | | |            #2203.
% 231.26/42.45  | | | | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | | | | End of split
% 231.26/42.45  | | | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | | | End of split
% 231.26/42.45  | | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | | End of split
% 231.26/42.45  | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | Case 2:
% 231.26/42.45  | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | |   (220)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 231.26/42.45  | | | | | | | | | | |            e3 & op(e0, e1) = e3)
% 231.26/42.45  | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | | BETA: splitting (220) gives:
% 231.26/42.45  | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | | Case 1:
% 231.26/42.45  | | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | | |   (221)  all_57_8 = e3 & op(e1, e1) = e3
% 231.26/42.45  | | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | | | ALPHA: (221) implies:
% 231.26/42.45  | | | | | | | | | | | |   (222)  op(e1, e1) = e3
% 231.26/42.45  | | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | | | REF_CLOSE: (16), (21), (22), (222) are inconsistent by
% 231.26/42.45  | | | | | | | | | | | |            sub-proof #2468.
% 231.26/42.45  | | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | | Case 2:
% 231.26/42.45  | | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | | |   (223)  all_57_14 = e3 & op(e0, e1) = e3
% 231.26/42.45  | | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | | | ALPHA: (223) implies:
% 231.26/42.45  | | | | | | | | | | | |   (224)  all_57_14 = e3
% 231.26/42.45  | | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | | | COMBINE_EQS: (192), (224) imply:
% 231.26/42.45  | | | | | | | | | | | |   (225)  e3 = e1
% 231.26/42.45  | | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | | | SIMP: (225) implies:
% 231.26/42.45  | | | | | | | | | | | |   (226)  e3 = e1
% 231.26/42.45  | | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | | | COMBINE_EQS: (198), (226) imply:
% 231.26/42.45  | | | | | | | | | | | |   (227)  all_57_12 = e1
% 231.26/42.45  | | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 231.26/42.45  | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 231.26/42.45  | | | | | | | | | | | |            (19), (20), (21), (22), (23), (25), (26), (27),
% 231.26/42.45  | | | | | | | | | | | |            (28), (29), (30), (31), (32), (33), (34), (35),
% 231.26/42.45  | | | | | | | | | | | |            (36), (37), (38), (39), (40), (41), (42), (43),
% 231.26/42.45  | | | | | | | | | | | |            (44), (45), (46), (47), (48), (49), (50), (51),
% 231.26/42.45  | | | | | | | | | | | |            (52), (53), (54), (55), (56), (57), (58), (59),
% 231.26/42.45  | | | | | | | | | | | |            (60), (61), (62), (63), (64), (65), (66), (67),
% 231.26/42.45  | | | | | | | | | | | |            (69), (70), (71), (72), (73), (74), (75), (76),
% 231.26/42.45  | | | | | | | | | | | |            (77), (78), (79), (81), (83), (84), (85), (86),
% 231.26/42.45  | | | | | | | | | | | |            (87), (88), (89), (90), (91), (92), (93), (94),
% 231.26/42.45  | | | | | | | | | | | |            (95), (96), (97), (98), (99), (100), (101), (102),
% 231.26/42.45  | | | | | | | | | | | |            (103), (104), (105), (106), (107), (108), (109),
% 231.26/42.45  | | | | | | | | | | | |            (110), (111), (112), (113), (114), (194), (195),
% 231.26/42.45  | | | | | | | | | | | |            (227) are inconsistent by sub-proof #1400.
% 231.26/42.45  | | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | | End of split
% 231.26/42.45  | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | End of split
% 231.26/42.45  | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | End of split
% 231.26/42.45  | | | | | | | | | 
% 231.26/42.45  | | | | | | | | Case 2:
% 231.26/42.45  | | | | | | | | | 
% 231.26/42.45  | | | | | | | | |   (228)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2
% 231.26/42.45  | | | | | | | | |            & op(e0, e0) = e2)
% 231.26/42.45  | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | REF_CLOSE: (16), (31), (33), (37), (45), (52), (62), (82),
% 231.26/42.45  | | | | | | | | |            (97), (192), (203), (228) are inconsistent by
% 231.26/42.45  | | | | | | | | |            sub-proof #1389.
% 231.26/42.45  | | | | | | | | | 
% 231.26/42.45  | | | | | | | | End of split
% 231.26/42.45  | | | | | | | | 
% 231.26/42.45  | | | | | | | End of split
% 231.26/42.45  | | | | | | | 
% 231.26/42.45  | | | | | | Case 2:
% 231.26/42.45  | | | | | | | 
% 231.26/42.45  | | | | | | |   (229)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 &
% 231.26/42.45  | | | | | | |            op(e3, e0) = e2)
% 231.26/42.45  | | | | | | | 
% 231.26/42.45  | | | | | | | REF_CLOSE: (31), (33), (62), (97), (229) are inconsistent by
% 231.26/42.45  | | | | | | |            sub-proof #2221.
% 231.26/42.45  | | | | | | | 
% 231.26/42.45  | | | | | | End of split
% 231.26/42.45  | | | | | | 
% 231.26/42.45  | | | | | Case 2:
% 231.26/42.45  | | | | | | 
% 231.26/42.45  | | | | | |   (230)  all_57_13 = e3 & op(e0, e2) = e3
% 231.26/42.45  | | | | | | 
% 231.26/42.45  | | | | | | ALPHA: (230) implies:
% 231.26/42.45  | | | | | |   (231)  all_57_13 = e3
% 231.26/42.45  | | | | | | 
% 231.26/42.45  | | | | | | BETA: splitting (37) gives:
% 231.26/42.45  | | | | | | 
% 231.26/42.45  | | | | | | Case 1:
% 231.26/42.45  | | | | | | | 
% 231.26/42.45  | | | | | | |   (232)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 &
% 231.26/42.45  | | | | | | |            op(e3, e2) = e2)
% 231.26/42.45  | | | | | | | 
% 231.26/42.45  | | | | | | | BETA: splitting (232) gives:
% 231.26/42.45  | | | | | | | 
% 231.26/42.45  | | | | | | | Case 1:
% 231.26/42.45  | | | | | | | | 
% 231.26/42.45  | | | | | | | |   (233)  all_57_0 = e2 & op(e3, e3) = e2
% 231.26/42.45  | | | | | | | | 
% 231.26/42.45  | | | | | | | | ALPHA: (233) implies:
% 231.26/42.45  | | | | | | | |   (234)  op(e3, e3) = e2
% 231.26/42.45  | | | | | | | | 
% 231.26/42.45  | | | | | | | | REF_CLOSE: (12), (14), (16), (27), (33), (38), (41), (43), (45),
% 231.26/42.45  | | | | | | | |            (50), (62), (64), (66), (70), (88), (97), (111),
% 231.26/42.45  | | | | | | | |            (114), (231), (234) are inconsistent by sub-proof
% 231.26/42.45  | | | | | | | |            #1616.
% 231.26/42.45  | | | | | | | | 
% 231.26/42.45  | | | | | | | Case 2:
% 231.26/42.45  | | | | | | | | 
% 231.26/42.45  | | | | | | | |   (235)  all_57_1 = e2 & op(e3, e2) = e2
% 231.26/42.45  | | | | | | | | 
% 231.26/42.45  | | | | | | | | ALPHA: (235) implies:
% 231.26/42.45  | | | | | | | |   (236)  all_57_1 = e2
% 231.26/42.45  | | | | | | | | 
% 231.26/42.45  | | | | | | | | BETA: splitting (76) gives:
% 231.26/42.45  | | | | | | | | 
% 231.26/42.45  | | | | | | | | Case 1:
% 231.26/42.45  | | | | | | | | | 
% 231.26/42.45  | | | | | | | | |   (237)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2
% 231.26/42.45  | | | | | | | | |            & op(e0, e2) = e2)
% 231.26/42.45  | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | BETA: splitting (237) gives:
% 231.26/42.45  | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | Case 1:
% 231.26/42.45  | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | |   (238)  all_57_12 = e2 & op(e0, e3) = e2
% 231.26/42.45  | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | ALPHA: (238) implies:
% 231.26/42.45  | | | | | | | | | |   (239)  all_57_12 = e2
% 231.26/42.45  | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | BETA: splitting (69) gives:
% 231.26/42.45  | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | Case 1:
% 231.26/42.45  | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | |   (240)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 231.26/42.45  | | | | | | | | | | |            & op(e2, e1) = e3)
% 231.26/42.45  | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | | BETA: splitting (240) gives:
% 231.26/42.45  | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | | Case 1:
% 231.26/42.45  | | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | | |   (241)  all_57_4 = e3 & op(e3, e1) = e3
% 231.26/42.45  | | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | | | REF_CLOSE: (14), (16), (27), (37), (41), (45), (50), (52),
% 231.26/42.45  | | | | | | | | | | | |            (62), (66), (97), (236), (241) are inconsistent by
% 231.26/42.45  | | | | | | | | | | | |            sub-proof #1829.
% 231.26/42.45  | | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | | Case 2:
% 231.26/42.45  | | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | | |   (242)  all_57_5 = e3 & op(e2, e1) = e3
% 231.26/42.45  | | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | | | ALPHA: (242) implies:
% 231.26/42.45  | | | | | | | | | | | |   (243)  all_57_5 = e3
% 231.26/42.45  | | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | | | BETA: splitting (105) gives:
% 231.26/42.45  | | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | | | Case 1:
% 231.26/42.45  | | | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | | | |   (244)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 231.26/42.45  | | | | | | | | | | | | |            & op(e2, e3) = e0)
% 231.26/42.45  | | | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | | | | REF_CLOSE: (9), (14), (16), (31), (33), (37), (43), (45),
% 231.26/42.45  | | | | | | | | | | | | |            (50), (62), (64), (66), (88), (92), (97), (114),
% 231.26/42.45  | | | | | | | | | | | | |            (243), (244) are inconsistent by sub-proof #1396.
% 231.26/42.45  | | | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | | | Case 2:
% 231.26/42.45  | | | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | | | |   (245)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 231.26/42.45  | | | | | | | | | | | | |            e0 & op(e0, e3) = e0)
% 231.26/42.45  | | | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 231.26/42.45  | | | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 231.26/42.45  | | | | | | | | | | | | |            (19), (20), (21), (22), (23), (25), (26), (27),
% 231.26/42.45  | | | | | | | | | | | | |            (28), (29), (30), (32), (33), (34), (35), (36),
% 231.26/42.45  | | | | | | | | | | | | |            (37), (38), (39), (40), (41), (42), (43), (44),
% 231.26/42.45  | | | | | | | | | | | | |            (46), (47), (48), (49), (51), (52), (53), (54),
% 231.26/42.45  | | | | | | | | | | | | |            (55), (56), (57), (58), (59), (60), (61), (62),
% 231.26/42.45  | | | | | | | | | | | | |            (63), (64), (65), (66), (67), (69), (70), (71),
% 231.26/42.45  | | | | | | | | | | | | |            (72), (73), (74), (75), (76), (77), (78), (79),
% 231.26/42.45  | | | | | | | | | | | | |            (81), (83), (84), (85), (86), (87), (88), (89),
% 231.26/42.45  | | | | | | | | | | | | |            (90), (91), (92), (93), (94), (95), (96), (97),
% 231.26/42.45  | | | | | | | | | | | | |            (98), (99), (100), (101), (102), (103), (104),
% 231.26/42.45  | | | | | | | | | | | | |            (105), (106), (107), (108), (109), (110), (111),
% 231.26/42.45  | | | | | | | | | | | | |            (112), (113), (114), (194), (195), (239), (245)
% 231.26/42.45  | | | | | | | | | | | | |            are inconsistent by sub-proof #1394.
% 231.26/42.45  | | | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | | | End of split
% 231.26/42.45  | | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | | End of split
% 231.26/42.45  | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | Case 2:
% 231.26/42.45  | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | |   (246)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 231.26/42.45  | | | | | | | | | | |            e3 & op(e0, e1) = e3)
% 231.26/42.45  | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | | REF_CLOSE: (14), (16), (21), (22), (192), (246) are
% 231.26/42.45  | | | | | | | | | | |            inconsistent by sub-proof #2263.
% 231.26/42.45  | | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | End of split
% 231.26/42.45  | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | Case 2:
% 231.26/42.45  | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | |   (247)  all_57_13 = e2 & op(e0, e2) = e2
% 231.26/42.45  | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | | REF_CLOSE: (45), (231), (247) are inconsistent by sub-proof
% 231.26/42.45  | | | | | | | | | |            #2146.
% 231.26/42.45  | | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | End of split
% 231.26/42.45  | | | | | | | | | 
% 231.26/42.45  | | | | | | | | Case 2:
% 231.26/42.45  | | | | | | | | | 
% 231.26/42.45  | | | | | | | | |   (248)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2
% 231.26/42.45  | | | | | | | | |            & op(e0, e0) = e2)
% 231.26/42.45  | | | | | | | | | 
% 231.26/42.45  | | | | | | | | | REF_CLOSE: (16), (31), (33), (37), (45), (52), (62), (82),
% 231.26/42.45  | | | | | | | | |            (97), (192), (236), (248) are inconsistent by
% 231.26/42.45  | | | | | | | | |            sub-proof #1389.
% 231.26/42.45  | | | | | | | | | 
% 231.26/42.45  | | | | | | | | End of split
% 231.26/42.45  | | | | | | | | 
% 231.26/42.45  | | | | | | | End of split
% 231.26/42.45  | | | | | | | 
% 231.26/42.45  | | | | | | Case 2:
% 231.26/42.45  | | | | | | | 
% 231.26/42.45  | | | | | | |   (249)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 &
% 231.26/42.45  | | | | | | |            op(e3, e0) = e2)
% 231.26/42.45  | | | | | | | 
% 231.26/42.45  | | | | | | | REF_CLOSE: (31), (33), (62), (97), (249) are inconsistent by
% 231.26/42.45  | | | | | | |            sub-proof #2221.
% 231.26/42.45  | | | | | | | 
% 231.26/42.45  | | | | | | End of split
% 231.26/42.45  | | | | | | 
% 231.26/42.45  | | | | | End of split
% 231.26/42.45  | | | | | 
% 231.26/42.45  | | | | Case 2:
% 231.26/42.45  | | | | | 
% 231.26/42.45  | | | | |   (250)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0,
% 231.26/42.45  | | | | |              e0) = e3)
% 231.26/42.45  | | | | | 
% 231.26/42.45  | | | | | REF_CLOSE: (1), (3), (5), (7), (9), (10), (11), (12), (14), (15),
% 231.26/42.45  | | | | |            (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 231.26/42.45  | | | | |            (27), (32), (35), (36), (37), (40), (41), (43), (44), (47),
% 231.26/42.45  | | | | |            (51), (53), (54), (56), (58), (59), (61), (62), (63), (64),
% 231.26/42.45  | | | | |            (66), (67), (68), (69), (70), (71), (74), (76), (77), (78),
% 231.26/42.45  | | | | |            (84), (85), (87), (91), (92), (93), (94), (97), (98), (99),
% 231.26/42.45  | | | | |            (100), (102), (103), (104), (105), (106), (107), (110),
% 231.26/42.45  | | | | |            (111), (113), (114), (192), (250) are inconsistent by
% 231.26/42.45  | | | | |            sub-proof #1388.
% 231.26/42.45  | | | | | 
% 231.26/42.45  | | | | End of split
% 231.26/42.45  | | | | 
% 231.26/42.45  | | | Case 2:
% 231.26/42.45  | | | | 
% 231.26/42.45  | | | |   (251)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2,
% 231.26/42.45  | | | |                e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) &
% 231.26/42.45  | | | |          ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0,
% 231.26/42.45  | | | |                e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 231.26/42.45  | | | | 
% 231.26/42.45  | | | | ALPHA: (251) implies:
% 231.26/42.45  | | | |   (252)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0,
% 231.26/42.45  | | | |              e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.26/42.45  | | | |   (253)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2,
% 231.26/42.45  | | | |              e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.26/42.45  | | | | 
% 231.26/42.45  | | | | REF_CLOSE: (1), (3), (5), (7), (9), (10), (11), (12), (14), (15), (16),
% 231.26/42.45  | | | |            (17), (18), (19), (20), (21), (22), (23), (24), (25), (27),
% 231.26/42.45  | | | |            (32), (33), (35), (36), (37), (40), (41), (43), (44), (45),
% 231.26/42.45  | | | |            (47), (50), (51), (52), (53), (54), (56), (57), (58), (59),
% 231.26/42.45  | | | |            (61), (62), (63), (64), (66), (67), (68), (69), (70), (71),
% 231.26/42.45  | | | |            (73), (74), (75), (76), (77), (78), (80), (83), (84), (85),
% 231.26/42.45  | | | |            (87), (88), (91), (92), (93), (94), (95), (97), (98), (99),
% 231.26/42.45  | | | |            (100), (102), (103), (104), (105), (106), (107), (110),
% 231.26/42.45  | | | |            (111), (113), (114), (192), (252), (253) are inconsistent by
% 231.26/42.45  | | | |            sub-proof #1386.
% 231.26/42.45  | | | | 
% 231.26/42.45  | | | End of split
% 231.26/42.45  | | | 
% 231.26/42.45  | | Case 2:
% 231.26/42.45  | | | 
% 231.26/42.45  | | |   (254)  all_57_15 = e1 & op(e0, e0) = e1
% 231.26/42.45  | | | 
% 231.26/42.45  | | | ALPHA: (254) implies:
% 231.26/42.45  | | |   (255)  all_57_15 = e1
% 231.26/42.45  | | | 
% 231.26/42.45  | | | BETA: splitting (77) gives:
% 231.26/42.45  | | | 
% 231.26/42.45  | | | Case 1:
% 231.26/42.45  | | | | 
% 231.26/42.45  | | | |   (256)  all_57_15 = e0 & op(e0, e0) = e0
% 231.26/42.45  | | | | 
% 231.26/42.45  | | | | ALPHA: (256) implies:
% 231.26/42.45  | | | |   (257)  all_57_15 = e0
% 231.26/42.45  | | | | 
% 231.26/42.45  | | | | COMBINE_EQS: (255), (257) imply:
% 231.26/42.45  | | | |   (258)  e1 = e0
% 231.26/42.45  | | | | 
% 231.26/42.45  | | | | COMBINE_EQS: (31), (258) imply:
% 231.26/42.45  | | | |   (259)  all_57_9 = e0
% 231.26/42.45  | | | | 
% 231.26/42.45  | | | | REF_CLOSE: (14), (16), (27), (33), (37), (45), (52), (62), (66), (97),
% 231.26/42.45  | | | |            (259) are inconsistent by sub-proof #2436.
% 231.26/42.45  | | | | 
% 231.26/42.45  | | | Case 2:
% 231.26/42.45  | | | | 
% 231.26/42.45  | | | |   (260)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2,
% 231.26/42.45  | | | |                e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) &
% 231.26/42.45  | | | |          ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0,
% 231.26/42.45  | | | |                e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 231.26/42.45  | | | | 
% 231.26/42.45  | | | | ALPHA: (260) implies:
% 231.26/42.45  | | | |   (261)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2,
% 231.26/42.45  | | | |              e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.26/42.45  | | | | 
% 231.26/42.45  | | | | REF_CLOSE: (1), (3), (5), (7), (9), (10), (11), (12), (14), (15), (16),
% 231.26/42.45  | | | |            (17), (18), (19), (20), (21), (22), (23), (24), (25), (27),
% 231.26/42.45  | | | |            (31), (32), (33), (35), (36), (37), (38), (40), (41), (43),
% 231.26/42.45  | | | |            (44), (45), (47), (50), (51), (52), (53), (54), (56), (58),
% 231.26/42.45  | | | |            (59), (61), (62), (63), (64), (66), (67), (68), (69), (70),
% 231.26/42.45  | | | |            (71), (74), (76), (77), (78), (80), (82), (83), (84), (85),
% 231.26/42.45  | | | |            (87), (88), (89), (91), (92), (93), (94), (95), (97), (98),
% 231.26/42.45  | | | |            (99), (100), (102), (103), (104), (105), (106), (107), (110),
% 231.26/42.45  | | | |            (111), (113), (114), (261) are inconsistent by sub-proof
% 231.26/42.45  | | | |            #1390.
% 231.26/42.45  | | | | 
% 231.26/42.45  | | | End of split
% 231.26/42.45  | | | 
% 231.26/42.45  | | End of split
% 231.26/42.45  | | 
% 231.26/42.45  | End of split
% 231.26/42.45  | 
% 231.26/42.45  End of proof
% 231.26/42.45  
% 231.26/42.45  Sub-proof #1386 shows that the following formulas are inconsistent:
% 231.26/42.45  ----------------------------------------------------------------
% 231.26/42.45    (1)   ~ (all_10_2 = e2)
% 231.26/42.45    (2)  op(e3, e3) = all_10_2
% 231.26/42.45    (3)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 231.26/42.45    (4)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 231.26/42.45    (5)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.26/42.45         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.26/42.45    (6)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.26/42.45         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.26/42.45    (7)   ~ (all_53_8 = all_53_12)
% 231.26/42.45    (8)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.26/42.45         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.26/42.45    (9)   ~ (e3 = e1)
% 231.26/42.45    (10)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 231.26/42.45          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.26/42.45    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.26/42.45            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.26/42.45    (12)  all_55_0 = all_10_2
% 231.26/42.45    (13)   ~ (all_10_2 = e0)
% 231.26/42.45    (14)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.26/42.45          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.26/42.45    (15)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 231.26/42.45            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 231.26/42.45              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 231.26/42.45    (16)   ~ (all_6_2 = e3)
% 231.26/42.45    (17)  op(e1, e1) = all_6_2
% 231.26/42.45    (18)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 231.26/42.45    (19)   ~ (all_53_9 = e0)
% 231.26/42.45    (20)  all_55_0 = e3 | all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 231.26/42.45    (21)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.26/42.45          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.26/42.45    (22)   ~ (all_53_4 = all_53_12)
% 231.26/42.45    (23)  all_57_4 = e0
% 231.26/42.45    (24)   ~ (all_53_8 = all_53_9)
% 231.26/42.45    (25)  all_42_2 = all_6_2
% 231.26/42.45    (26)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.26/42.45          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.26/42.45    (27)   ~ (all_53_9 = all_6_2)
% 231.26/42.45    (28)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.26/42.45          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.26/42.45    (29)  all_57_3 = e0
% 231.26/42.45    (30)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.26/42.45          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.26/42.45    (31)   ~ (e3 = e2)
% 231.26/42.45    (32)  all_55_1 = all_53_4
% 231.26/42.45    (33)   ~ (e3 = e0)
% 231.26/42.45    (34)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.26/42.45          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.26/42.45    (35)  op(e3, e3) = e3
% 231.26/42.45    (36)   ~ (all_53_8 = all_6_2)
% 231.26/42.45    (37)  all_55_2 = all_53_8
% 231.26/42.45    (38)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 231.26/42.45          | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.26/42.45    (39)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 231.26/42.45    (40)   ~ (all_53_7 = e0)
% 231.26/42.45    (41)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.26/42.45          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.26/42.45            e1)
% 231.26/42.45    (42)   ~ (all_53_4 = all_53_8)
% 231.26/42.45    (43)  op(e3, e2) = all_53_4
% 231.26/42.45    (44)   ~ (e2 = e0)
% 231.26/42.45    (45)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 231.26/42.45            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 231.26/42.45            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 231.26/42.45            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 231.26/42.45              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 231.26/42.45            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 231.26/42.45            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 231.26/42.45              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 231.26/42.45              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 231.26/42.45            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 231.26/42.45            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 231.26/42.45            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 231.26/42.45              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 231.26/42.45              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 231.26/42.45            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 231.26/42.45              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 231.26/42.45            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 231.26/42.45            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 231.26/42.45              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 231.26/42.45              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 231.26/42.45            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 231.26/42.45            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 231.26/42.45    (46)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 231.26/42.45          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.26/42.45    (47)   ~ (e1 = e0)
% 231.26/42.45    (48)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 231.26/42.45            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 231.26/42.45              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 231.26/42.45    (49)   ~ (all_53_4 = e0)
% 231.26/42.45    (50)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.26/42.45          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.26/42.45    (51)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.26/42.45          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.26/42.45    (52)   ~ (all_10_2 = e1)
% 231.26/42.45    (53)  all_57_14 = e1
% 231.26/42.45    (54)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.26/42.45          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 231.26/42.45            e3)
% 231.26/42.45    (55)   ~ (all_53_4 = all_53_6)
% 231.26/42.45    (56)  op(e0, e2) = all_53_7
% 231.26/42.45    (57)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.26/42.45          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.26/42.45            e2)
% 231.26/42.45    (58)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.26/42.45              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.26/42.45                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.26/42.45                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.26/42.45    (59)  all_55_10 = all_6_2
% 231.26/42.45    (60)   ~ (all_53_13 = e0)
% 231.26/42.45    (61)  op(e2, e0) = all_53_13
% 231.26/42.45    (62)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.26/42.45          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.26/42.45    (63)  all_38_2 = all_6_2
% 231.26/42.45    (64)  all_55_3 = all_53_12
% 231.26/42.45    (65)   ~ (all_53_12 = e3)
% 231.26/42.45    (66)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 231.26/42.45            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 231.26/42.45              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 231.26/42.46    (67)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.26/42.46          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.26/42.46    (68)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 231.26/42.46          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 231.26/42.46    (69)   ~ (all_53_12 = all_10_2)
% 231.26/42.46    (70)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 231.26/42.46          (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 231.26/42.46    (71)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) |
% 231.26/42.46          (all_57_11 = e0 & op(e1, e0) = e0)
% 231.26/42.46    (72)   ~ (e2 = e1)
% 231.26/42.46    (73)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.26/42.46          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.26/42.46    (74)  op(e2, e1) = all_53_9
% 231.26/42.46    (75)  op(e1, e2) = all_53_6
% 231.26/42.46    (76)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.26/42.46          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.26/42.46    (77)  all_24_2 = all_6_2
% 231.26/42.46    (78)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.26/42.46          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.26/42.46    (79)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.26/42.46          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.26/42.46    (80)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.26/42.46          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.26/42.46    (81)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 231.26/42.46          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 231.26/42.46    (82)  op(e3, e1) = all_53_8
% 231.26/42.46    (83)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.26/42.46          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.26/42.46    (84)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 231.26/42.46          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 231.26/42.46    (85)  op(e3, e0) = all_53_12
% 231.26/42.46  
% 231.26/42.46  Begin of proof
% 231.26/42.46  | 
% 231.26/42.46  | BETA: splitting (38) gives:
% 231.26/42.46  | 
% 231.26/42.46  | Case 1:
% 231.26/42.46  | | 
% 231.26/42.46  | |   (86)  all_57_12 = e0 & op(e0, e3) = e0
% 231.26/42.46  | | 
% 231.26/42.46  | | ALPHA: (86) implies:
% 231.26/42.46  | |   (87)  all_57_12 = e0
% 231.26/42.46  | | 
% 231.26/42.46  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 231.26/42.46  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 231.26/42.46  | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 231.26/42.46  | |            (35), (36), (37), (39), (41), (42), (43), (44), (45), (46), (47),
% 231.26/42.46  | |            (48), (49), (50), (51), (52), (53), (54), (55), (57), (58), (59),
% 231.26/42.46  | |            (60), (61), (62), (63), (64), (65), (66), (67), (68), (69), (70),
% 231.26/42.46  | |            (71), (72), (73), (74), (75), (76), (77), (78), (79), (80), (81),
% 231.26/42.46  | |            (82), (83), (84), (85), (87) are inconsistent by sub-proof #1387.
% 231.26/42.46  | | 
% 231.26/42.46  | Case 2:
% 231.26/42.46  | | 
% 231.26/42.46  | |   (88)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 231.26/42.46  | |           e0)
% 231.26/42.46  | | 
% 231.26/42.46  | | REF_CLOSE: (9), (11), (16), (17), (23), (31), (33), (34), (40), (44), (47),
% 231.26/42.46  | |            (50), (56), (72), (78), (88) are inconsistent by sub-proof #1399.
% 231.26/42.46  | | 
% 231.26/42.46  | End of split
% 231.26/42.46  | 
% 231.26/42.46  End of proof
% 231.26/42.46  
% 231.26/42.46  Sub-proof #1387 shows that the following formulas are inconsistent:
% 231.26/42.46  ----------------------------------------------------------------
% 231.26/42.46    (1)   ~ (all_10_2 = e2)
% 231.26/42.46    (2)  op(e3, e3) = all_10_2
% 231.26/42.46    (3)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 231.26/42.46    (4)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 231.26/42.46    (5)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.26/42.46         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.26/42.46    (6)  all_57_12 = e0
% 231.26/42.46    (7)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.26/42.46         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.26/42.46    (8)   ~ (all_53_8 = all_53_12)
% 231.26/42.46    (9)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.26/42.46         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.26/42.46    (10)   ~ (e3 = e1)
% 231.26/42.46    (11)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 231.26/42.46          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.26/42.46    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.26/42.46            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.26/42.46    (13)  all_55_0 = all_10_2
% 231.26/42.46    (14)   ~ (all_10_2 = e0)
% 231.26/42.46    (15)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.26/42.46          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.26/42.46    (16)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 231.26/42.46            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 231.26/42.46              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 231.26/42.46    (17)   ~ (all_6_2 = e3)
% 231.26/42.46    (18)  op(e1, e1) = all_6_2
% 231.26/42.46    (19)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 231.26/42.46    (20)   ~ (all_53_9 = e0)
% 231.26/42.46    (21)  all_55_0 = e3 | all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 231.26/42.46    (22)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.26/42.46          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.26/42.46    (23)   ~ (all_53_4 = all_53_12)
% 231.26/42.46    (24)  all_57_4 = e0
% 231.26/42.46    (25)   ~ (all_53_8 = all_53_9)
% 231.26/42.46    (26)  all_42_2 = all_6_2
% 231.26/42.46    (27)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.26/42.46          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.26/42.46    (28)   ~ (all_53_9 = all_6_2)
% 231.26/42.46    (29)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.26/42.46          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.26/42.46    (30)  all_57_3 = e0
% 231.26/42.46    (31)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.26/42.46          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.26/42.46    (32)   ~ (e3 = e2)
% 231.26/42.46    (33)  all_55_1 = all_53_4
% 231.26/42.46    (34)   ~ (e3 = e0)
% 231.26/42.46    (35)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.26/42.46          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.26/42.46    (36)  op(e3, e3) = e3
% 231.26/42.46    (37)   ~ (all_53_8 = all_6_2)
% 231.26/42.46    (38)  all_55_2 = all_53_8
% 231.26/42.46    (39)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 231.26/42.46    (40)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.26/42.46          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.26/42.46            e1)
% 231.26/42.46    (41)   ~ (all_53_4 = all_53_8)
% 231.26/42.46    (42)  op(e3, e2) = all_53_4
% 231.26/42.46    (43)   ~ (e2 = e0)
% 231.26/42.46    (44)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 231.26/42.46            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 231.26/42.46            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 231.26/42.46            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 231.26/42.46              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 231.26/42.46            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 231.26/42.46            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 231.26/42.46              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 231.26/42.46              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 231.26/42.46            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 231.26/42.46            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 231.26/42.46            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 231.26/42.46              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 231.26/42.46              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 231.26/42.46            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 231.26/42.46              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 231.26/42.46            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 231.26/42.46            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 231.26/42.46              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 231.26/42.46              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 231.26/42.46            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 231.26/42.46            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 231.26/42.46    (45)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 231.26/42.46          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.26/42.46    (46)   ~ (e1 = e0)
% 231.26/42.46    (47)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 231.26/42.46            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 231.26/42.46              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 231.26/42.46    (48)   ~ (all_53_4 = e0)
% 231.26/42.46    (49)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.26/42.46          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.26/42.46    (50)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.26/42.46          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.26/42.46    (51)   ~ (all_10_2 = e1)
% 231.26/42.46    (52)  all_57_14 = e1
% 231.26/42.46    (53)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.26/42.46          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 231.26/42.46            e3)
% 231.26/42.46    (54)   ~ (all_53_4 = all_53_6)
% 231.26/42.46    (55)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.26/42.46          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.26/42.46            e2)
% 231.26/42.46    (56)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.26/42.46              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.26/42.46                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.26/42.46                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.26/42.46    (57)  all_55_10 = all_6_2
% 231.26/42.46    (58)   ~ (all_53_13 = e0)
% 231.26/42.46    (59)  op(e2, e0) = all_53_13
% 231.26/42.46    (60)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.26/42.46          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.26/42.46    (61)  all_38_2 = all_6_2
% 231.26/42.46    (62)  all_55_3 = all_53_12
% 231.26/42.46    (63)   ~ (all_53_12 = e3)
% 231.26/42.46    (64)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 231.26/42.46            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 231.26/42.46              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 231.26/42.46    (65)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.26/42.46          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.26/42.46    (66)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 231.26/42.46          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 231.26/42.46    (67)   ~ (all_53_12 = all_10_2)
% 231.26/42.46    (68)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 231.26/42.46          (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 231.26/42.46    (69)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) |
% 231.26/42.46          (all_57_11 = e0 & op(e1, e0) = e0)
% 231.26/42.46    (70)   ~ (e2 = e1)
% 231.26/42.46    (71)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.26/42.46          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.26/42.46    (72)  op(e2, e1) = all_53_9
% 231.26/42.46    (73)  op(e1, e2) = all_53_6
% 231.26/42.46    (74)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.26/42.46          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.26/42.46    (75)  all_24_2 = all_6_2
% 231.26/42.46    (76)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.26/42.46          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.26/42.46    (77)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.26/42.46          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.26/42.46    (78)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.26/42.46          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.26/42.46    (79)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 231.26/42.46          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 231.26/42.46    (80)  op(e3, e1) = all_53_8
% 231.26/42.46    (81)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.26/42.46          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.26/42.46    (82)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 231.26/42.46          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 231.26/42.46    (83)  op(e3, e0) = all_53_12
% 231.26/42.46  
% 231.26/42.46  Begin of proof
% 231.26/42.46  | 
% 231.26/42.46  | BETA: splitting (53) gives:
% 231.26/42.46  | 
% 231.26/42.46  | Case 1:
% 231.26/42.46  | | 
% 231.26/42.46  | |   (84)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 231.26/42.46  | |           e3)
% 231.26/42.46  | | 
% 231.26/42.46  | | BETA: splitting (84) gives:
% 231.26/42.46  | | 
% 231.26/42.46  | | Case 1:
% 231.26/42.46  | | | 
% 231.26/42.46  | | |   (85)  all_57_12 = e3 & op(e0, e3) = e3
% 231.26/42.46  | | | 
% 231.26/42.46  | | | ALPHA: (85) implies:
% 231.26/42.46  | | |   (86)  all_57_12 = e3
% 231.26/42.46  | | | 
% 231.26/42.46  | | | REF_CLOSE: (6), (34), (86) are inconsistent by sub-proof #2153.
% 231.26/42.46  | | | 
% 231.26/42.46  | | Case 2:
% 231.26/42.46  | | | 
% 231.26/42.46  | | |   (87)  all_57_13 = e3 & op(e0, e2) = e3
% 231.26/42.46  | | | 
% 231.26/42.46  | | | ALPHA: (87) implies:
% 231.26/42.46  | | |   (88)  all_57_13 = e3
% 231.26/42.46  | | | 
% 231.26/42.46  | | | BETA: splitting (69) gives:
% 231.26/42.46  | | | 
% 231.26/42.46  | | | Case 1:
% 231.26/42.46  | | | | 
% 231.26/42.46  | | | |   (89)  all_57_9 = e0 & op(e3, e0) = e0
% 231.26/42.46  | | | | 
% 231.26/42.46  | | | | ALPHA: (89) implies:
% 231.26/42.46  | | | |   (90)  all_57_9 = e0
% 231.26/42.46  | | | | 
% 231.26/42.46  | | | | REF_CLOSE: (10), (12), (22), (24), (27), (32), (36), (43), (46), (70),
% 231.26/42.46  | | | |            (90) are inconsistent by sub-proof #2436.
% 231.26/42.46  | | | | 
% 231.26/42.46  | | | Case 2:
% 231.26/42.46  | | | | 
% 231.26/42.46  | | | |   (91)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 231.26/42.46  | | | |             e0) = e0)
% 231.26/42.46  | | | | 
% 231.26/42.46  | | | | BETA: splitting (91) gives:
% 231.26/42.46  | | | | 
% 231.26/42.46  | | | | Case 1:
% 231.26/42.46  | | | | | 
% 231.26/42.46  | | | | |   (92)  all_57_10 = e0 & op(e2, e0) = e0
% 231.26/42.46  | | | | | 
% 231.26/42.46  | | | | | ALPHA: (92) implies:
% 231.26/42.46  | | | | |   (93)  op(e2, e0) = e0
% 231.26/42.46  | | | | | 
% 231.26/42.46  | | | | | REF_CLOSE: (12), (58), (59), (93) are inconsistent by sub-proof #2470.
% 231.26/42.46  | | | | | 
% 231.26/42.46  | | | | Case 2:
% 231.26/42.46  | | | | | 
% 231.26/42.46  | | | | |   (94)  all_57_11 = e0 & op(e1, e0) = e0
% 231.26/42.46  | | | | | 
% 231.26/42.46  | | | | | ALPHA: (94) implies:
% 231.26/42.46  | | | | |   (95)  all_57_11 = e0
% 231.26/42.46  | | | | | 
% 231.26/42.46  | | | | | BETA: splitting (68) gives:
% 231.26/42.46  | | | | | 
% 231.26/42.46  | | | | | Case 1:
% 231.26/42.46  | | | | | | 
% 231.26/42.46  | | | | | |   (96)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2,
% 231.26/42.46  | | | | | |             e0) = e3)
% 231.26/42.46  | | | | | | 
% 231.26/42.46  | | | | | | BETA: splitting (96) gives:
% 231.26/42.46  | | | | | | 
% 231.26/42.46  | | | | | | Case 1:
% 231.26/42.46  | | | | | | | 
% 231.26/42.46  | | | | | | |   (97)  all_57_9 = e3 & op(e3, e0) = e3
% 231.26/42.46  | | | | | | | 
% 231.26/42.46  | | | | | | | ALPHA: (97) implies:
% 231.26/42.46  | | | | | | |   (98)  op(e3, e0) = e3
% 231.26/42.46  | | | | | | | 
% 231.26/42.46  | | | | | | | REF_CLOSE: (12), (63), (83), (98) are inconsistent by sub-proof
% 231.26/42.46  | | | | | | |            #2458.
% 231.26/42.46  | | | | | | | 
% 231.26/42.46  | | | | | | Case 2:
% 231.26/42.46  | | | | | | | 
% 231.26/42.46  | | | | | | |   (99)  all_57_10 = e3 & op(e2, e0) = e3
% 231.26/42.46  | | | | | | | 
% 231.26/42.46  | | | | | | | ALPHA: (99) implies:
% 231.26/42.46  | | | | | | |   (100)  all_57_10 = e3
% 231.26/42.46  | | | | | | | 
% 231.26/42.46  | | | | | | | REF_CLOSE: (5), (10), (12), (17), (18), (22), (27), (29), (30),
% 231.26/42.46  | | | | | | |            (32), (34), (36), (43), (46), (49), (52), (65), (70),
% 231.26/42.46  | | | | | | |            (100) are inconsistent by sub-proof #1692.
% 231.26/42.46  | | | | | | | 
% 231.26/42.46  | | | | | | End of split
% 231.26/42.46  | | | | | | 
% 231.26/42.46  | | | | | Case 2:
% 231.26/42.46  | | | | | | 
% 231.26/42.46  | | | | | |   (101)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 &
% 231.26/42.46  | | | | | |            op(e0, e0) = e3)
% 231.26/42.46  | | | | | | 
% 231.26/42.46  | | | | | | BETA: splitting (101) gives:
% 231.26/42.46  | | | | | | 
% 231.26/42.46  | | | | | | Case 1:
% 231.26/42.46  | | | | | | | 
% 231.26/42.46  | | | | | | |   (102)  all_57_11 = e3 & op(e1, e0) = e3
% 231.26/42.46  | | | | | | | 
% 231.26/42.46  | | | | | | | ALPHA: (102) implies:
% 231.26/42.46  | | | | | | |   (103)  all_57_11 = e3
% 231.26/42.46  | | | | | | | 
% 231.26/42.46  | | | | | | | REF_CLOSE: (34), (95), (103) are inconsistent by sub-proof #1595.
% 231.26/42.46  | | | | | | | 
% 231.26/42.46  | | | | | | Case 2:
% 231.26/42.46  | | | | | | | 
% 231.26/42.46  | | | | | | |   (104)  all_57_15 = e3 & op(e0, e0) = e3
% 231.26/42.46  | | | | | | | 
% 231.26/42.46  | | | | | | | ALPHA: (104) implies:
% 231.26/42.46  | | | | | | |   (105)  all_57_15 = e3
% 231.26/42.46  | | | | | | | 
% 231.26/42.46  | | | | | | | REF_CLOSE: (6), (10), (32), (40), (43), (46), (55), (70), (88),
% 231.26/42.46  | | | | | | |            (105) are inconsistent by sub-proof #2059.
% 231.26/42.46  | | | | | | | 
% 231.26/42.46  | | | | | | End of split
% 231.26/42.46  | | | | | | 
% 231.26/42.46  | | | | | End of split
% 231.26/42.46  | | | | | 
% 231.26/42.46  | | | | End of split
% 231.26/42.46  | | | | 
% 231.26/42.46  | | | End of split
% 231.26/42.46  | | | 
% 231.26/42.46  | | End of split
% 231.26/42.46  | | 
% 231.26/42.46  | Case 2:
% 231.26/42.46  | | 
% 231.26/42.46  | |   (106)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 231.26/42.46  | |            e3)
% 231.26/42.46  | | 
% 231.26/42.46  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 231.26/42.46  | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (25),
% 231.26/42.46  | |            (26), (27), (28), (29), (30), (31), (33), (35), (37), (38), (39),
% 231.26/42.46  | |            (40), (41), (42), (43), (44), (45), (46), (47), (48), (49), (50),
% 231.26/42.46  | |            (51), (52), (54), (55), (56), (57), (60), (61), (62), (64), (65),
% 231.26/42.46  | |            (66), (67), (70), (71), (72), (73), (74), (75), (76), (77), (78),
% 231.26/42.46  | |            (79), (80), (81), (82), (83), (106) are inconsistent by sub-proof
% 231.26/42.46  | |            #1388.
% 231.26/42.46  | | 
% 231.26/42.46  | End of split
% 231.26/42.46  | 
% 231.26/42.46  End of proof
% 231.26/42.46  
% 231.26/42.46  Sub-proof #1388 shows that the following formulas are inconsistent:
% 231.26/42.46  ----------------------------------------------------------------
% 231.26/42.46    (1)   ~ (all_10_2 = e2)
% 231.26/42.46    (2)  op(e3, e3) = all_10_2
% 231.26/42.46    (3)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 231.26/42.46    (4)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 231.26/42.46    (5)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.26/42.46         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.26/42.46    (6)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.26/42.46         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.26/42.46    (7)   ~ (all_53_8 = all_53_12)
% 231.26/42.46    (8)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.26/42.46         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.26/42.46    (9)   ~ (e3 = e1)
% 231.26/42.46    (10)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 231.26/42.46          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.26/42.46    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.26/42.46            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.26/42.46    (12)  all_55_0 = all_10_2
% 231.26/42.46    (13)   ~ (all_10_2 = e0)
% 231.26/42.46    (14)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.26/42.46          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.26/42.46    (15)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 231.26/42.46            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 231.26/42.46              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 231.26/42.46    (16)   ~ (all_6_2 = e3)
% 231.26/42.46    (17)  op(e1, e1) = all_6_2
% 231.26/42.46    (18)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 231.26/42.46    (19)   ~ (all_53_9 = e0)
% 231.26/42.46    (20)  all_55_0 = e3 | all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 231.26/42.46    (21)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.26/42.46          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.26/42.46    (22)   ~ (all_53_4 = all_53_12)
% 231.26/42.46    (23)   ~ (all_53_8 = all_53_9)
% 231.26/42.46    (24)  all_42_2 = all_6_2
% 231.26/42.46    (25)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.26/42.46          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.26/42.46    (26)   ~ (all_53_9 = all_6_2)
% 231.26/42.46    (27)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.26/42.46          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.26/42.46    (28)  all_57_3 = e0
% 231.26/42.46    (29)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.26/42.46          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.26/42.46    (30)  all_55_1 = all_53_4
% 231.26/42.46    (31)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.26/42.46          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.26/42.46    (32)   ~ (all_53_8 = all_6_2)
% 231.26/42.46    (33)  all_55_2 = all_53_8
% 231.26/42.46    (34)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 231.26/42.46    (35)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.26/42.46          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.26/42.46            e1)
% 231.26/42.46    (36)   ~ (all_53_4 = all_53_8)
% 231.26/42.46    (37)  op(e3, e2) = all_53_4
% 231.26/42.46    (38)   ~ (e2 = e0)
% 231.26/42.46    (39)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 231.26/42.46            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 231.26/42.46            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 231.26/42.46            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 231.26/42.46              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 231.26/42.46            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 231.26/42.46            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 231.26/42.46              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 231.26/42.46              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 231.26/42.46            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 231.26/42.46            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 231.26/42.46            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 231.26/42.46              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 231.26/42.46              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 231.26/42.46            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 231.26/42.46              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 231.26/42.46            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 231.26/42.46            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 231.26/42.46              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 231.26/42.46              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 231.26/42.46            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 231.26/42.46            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 231.26/42.46    (40)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 231.26/42.46          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.26/42.46    (41)   ~ (e1 = e0)
% 231.26/42.46    (42)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 231.26/42.46            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 231.26/42.46              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 231.26/42.46    (43)   ~ (all_53_4 = e0)
% 231.26/42.46    (44)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.26/42.46          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.26/42.46    (45)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.26/42.46          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.26/42.46    (46)   ~ (all_10_2 = e1)
% 231.26/42.46    (47)  all_57_14 = e1
% 231.26/42.46    (48)   ~ (all_53_4 = all_53_6)
% 231.26/42.46    (49)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.26/42.46          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.26/42.46            e2)
% 231.26/42.46    (50)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.26/42.46              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.26/42.46                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.26/42.46                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.26/42.46    (51)  all_55_10 = all_6_2
% 231.26/42.47    (52)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.26/42.47          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.26/42.47    (53)  all_38_2 = all_6_2
% 231.26/42.47    (54)  all_55_3 = all_53_12
% 231.26/42.47    (55)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 231.26/42.47            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 231.26/42.47              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 231.26/42.47    (56)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.26/42.47          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.26/42.47    (57)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 231.26/42.47          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 231.26/42.47    (58)   ~ (all_53_12 = all_10_2)
% 231.26/42.47    (59)   ~ (e2 = e1)
% 231.26/42.47    (60)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.26/42.47          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.26/42.47    (61)  op(e2, e1) = all_53_9
% 231.26/42.47    (62)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 231.26/42.47    (63)  op(e1, e2) = all_53_6
% 231.26/42.47    (64)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.26/42.47          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.26/42.47    (65)  all_24_2 = all_6_2
% 231.26/42.47    (66)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.26/42.47          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.26/42.47    (67)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.26/42.47          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.26/42.47    (68)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.26/42.47          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.26/42.47    (69)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 231.26/42.47          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 231.26/42.47    (70)  op(e3, e1) = all_53_8
% 231.26/42.47    (71)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.26/42.47          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.26/42.47    (72)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 231.26/42.47          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 231.26/42.47    (73)  op(e3, e0) = all_53_12
% 231.26/42.47  
% 231.26/42.47  Begin of proof
% 231.26/42.47  | 
% 231.26/42.47  | BETA: splitting (62) gives:
% 231.26/42.47  | 
% 231.26/42.47  | Case 1:
% 231.26/42.47  | | 
% 231.26/42.47  | |   (74)  all_57_14 = e3 & op(e0, e1) = e3
% 231.26/42.47  | | 
% 231.26/42.47  | | ALPHA: (74) implies:
% 231.26/42.47  | |   (75)  all_57_14 = e3
% 231.26/42.47  | | 
% 231.26/42.47  | | REF_CLOSE: (9), (47), (75) are inconsistent by sub-proof #2326.
% 231.26/42.47  | | 
% 231.26/42.47  | Case 2:
% 231.26/42.47  | | 
% 231.26/42.47  | |   (76)  all_57_15 = e3 & op(e0, e0) = e3
% 231.26/42.47  | | 
% 231.26/42.47  | | ALPHA: (76) implies:
% 231.26/42.47  | |   (77)  all_57_15 = e3
% 231.26/42.47  | |   (78)  op(e0, e0) = e3
% 231.26/42.47  | | 
% 231.26/42.47  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13),
% 231.26/42.47  | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 231.26/42.47  | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 231.26/42.47  | |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 231.26/42.47  | |            (48), (49), (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 231.26/42.47  | |            (59), (60), (61), (63), (64), (65), (66), (67), (68), (69), (70),
% 231.26/42.47  | |            (71), (72), (73), (77), (78) are inconsistent by sub-proof #1414.
% 231.26/42.47  | | 
% 231.26/42.47  | End of split
% 231.26/42.47  | 
% 231.26/42.47  End of proof
% 231.26/42.47  
% 231.26/42.47  Sub-proof #1389 shows that the following formulas are inconsistent:
% 231.26/42.47  ----------------------------------------------------------------
% 231.26/42.47    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.26/42.47           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.26/42.47    (2)  all_57_9 = e1
% 231.26/42.47    (3)  all_57_4 = e0
% 231.26/42.47    (4)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.26/42.47         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.26/42.47    (5)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.26/42.47    (6)   ~ (e3 = e2)
% 231.26/42.47    (7)  all_57_1 = e2
% 231.26/42.47    (8)  op(e3, e3) = e3
% 231.26/42.47    (9)   ~ (e2 = e0)
% 231.26/42.47    (10)  all_57_14 = e1
% 231.26/42.47    (11)  op(e0, e0) = e1
% 231.26/42.47    (12)   ~ (e2 = e1)
% 231.26/42.47  
% 231.26/42.47  Begin of proof
% 231.26/42.47  | 
% 231.26/42.47  | BETA: splitting (5) gives:
% 231.26/42.47  | 
% 231.26/42.47  | Case 1:
% 231.26/42.47  | | 
% 231.26/42.47  | |   (13)  all_57_14 = e2 & op(e0, e1) = e2
% 231.26/42.47  | | 
% 231.26/42.47  | | ALPHA: (13) implies:
% 231.26/42.47  | |   (14)  all_57_14 = e2
% 231.26/42.47  | | 
% 231.26/42.47  | | COMBINE_EQS: (10), (14) imply:
% 231.26/42.47  | |   (15)  e2 = e1
% 231.26/42.47  | | 
% 231.26/42.47  | | SIMP: (15) implies:
% 231.26/42.47  | |   (16)  e2 = e1
% 231.26/42.47  | | 
% 231.26/42.47  | | COMBINE_EQS: (7), (16) imply:
% 231.26/42.47  | |   (17)  all_57_1 = e1
% 231.26/42.47  | | 
% 231.26/42.47  | | REF_CLOSE: (1), (2), (3), (4), (6), (8), (9), (12), (17) are inconsistent by
% 231.26/42.47  | |            sub-proof #2220.
% 231.26/42.47  | | 
% 231.26/42.47  | Case 2:
% 231.26/42.47  | | 
% 231.26/42.47  | |   (18)  all_57_15 = e2 & op(e0, e0) = e2
% 231.26/42.47  | | 
% 231.26/42.47  | | ALPHA: (18) implies:
% 231.26/42.47  | |   (19)  op(e0, e0) = e2
% 231.26/42.47  | | 
% 231.26/42.47  | | REF_CLOSE: (1), (11), (12), (19) are inconsistent by sub-proof #2177.
% 231.26/42.47  | | 
% 231.26/42.47  | End of split
% 231.26/42.47  | 
% 231.26/42.47  End of proof
% 231.26/42.47  
% 231.26/42.47  Sub-proof #1390 shows that the following formulas are inconsistent:
% 231.26/42.47  ----------------------------------------------------------------
% 231.26/42.47    (1)   ~ (all_10_2 = e2)
% 231.26/42.47    (2)  op(e3, e3) = all_10_2
% 231.26/42.47    (3)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 231.26/42.47    (4)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 231.26/42.47    (5)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.26/42.47         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.26/42.47    (6)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.26/42.47         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.26/42.47    (7)   ~ (all_53_8 = all_53_12)
% 231.26/42.47    (8)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.26/42.47         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.26/42.47    (9)   ~ (e3 = e1)
% 231.26/42.47    (10)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 231.26/42.47          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.26/42.47    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.26/42.47            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.26/42.47    (12)  all_55_0 = all_10_2
% 231.26/42.47    (13)   ~ (all_10_2 = e0)
% 231.26/42.47    (14)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.26/42.47          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.26/42.47    (15)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 231.26/42.47            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 231.26/42.47              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 231.26/42.47    (16)   ~ (all_6_2 = e3)
% 231.26/42.47    (17)  op(e1, e1) = all_6_2
% 231.26/42.47    (18)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 231.26/42.47    (19)   ~ (all_53_9 = e0)
% 231.26/42.47    (20)  all_55_0 = e3 | all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 231.26/42.47    (21)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.26/42.47          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.26/42.47    (22)  all_57_9 = e1
% 231.26/42.47    (23)   ~ (all_53_4 = all_53_12)
% 231.26/42.47    (24)  all_57_4 = e0
% 231.26/42.47    (25)   ~ (all_53_8 = all_53_9)
% 231.26/42.47    (26)  all_42_2 = all_6_2
% 231.26/42.47    (27)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.26/42.47          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.26/42.47    (28)  op(e2, e2) = e0
% 231.26/42.47    (29)   ~ (all_53_9 = all_6_2)
% 231.26/42.47    (30)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.26/42.47          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.26/42.47    (31)  all_57_3 = e0
% 231.26/42.47    (32)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.26/42.47          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.26/42.47    (33)   ~ (e3 = e2)
% 231.26/42.47    (34)  all_55_1 = all_53_4
% 231.26/42.47    (35)   ~ (e3 = e0)
% 231.26/42.47    (36)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.26/42.47          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.26/42.47    (37)  op(e3, e3) = e3
% 231.26/42.47    (38)   ~ (all_53_8 = all_6_2)
% 231.26/42.47    (39)  all_55_2 = all_53_8
% 231.26/42.47    (40)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 231.26/42.47    (41)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.26/42.47          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.26/42.47            e1)
% 231.26/42.47    (42)   ~ (all_53_4 = all_53_8)
% 231.26/42.47    (43)  op(e3, e2) = all_53_4
% 231.26/42.47    (44)   ~ (e2 = e0)
% 231.26/42.47    (45)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 231.26/42.47            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 231.26/42.47            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 231.26/42.47            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 231.26/42.47              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 231.26/42.47            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 231.26/42.47            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 231.26/42.47              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 231.26/42.47              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 231.26/42.47            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 231.26/42.47            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 231.26/42.47            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 231.26/42.47              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 231.26/42.47              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 231.26/42.47            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 231.26/42.47              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 231.26/42.47            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 231.26/42.47            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 231.26/42.47              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 231.26/42.47              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 231.26/42.47            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 231.26/42.47            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 231.26/42.47    (46)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 231.26/42.47          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.26/42.47    (47)   ~ (e1 = e0)
% 231.26/42.47    (48)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 231.26/42.47            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 231.26/42.47              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 231.26/42.47    (49)   ~ (all_53_4 = e0)
% 231.26/42.47    (50)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.26/42.47          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.26/42.47    (51)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.26/42.47          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.26/42.47    (52)   ~ (all_10_2 = e1)
% 231.26/42.47    (53)   ~ (all_53_4 = all_53_6)
% 231.26/42.47    (54)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.26/42.47          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.26/42.47            e2)
% 231.26/42.47    (55)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.26/42.47              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.26/42.47                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.26/42.47                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.26/42.47    (56)  all_55_10 = all_6_2
% 231.26/42.47    (57)   ~ (all_53_13 = e0)
% 231.26/42.47    (58)  op(e0, e0) = e1
% 231.26/42.47    (59)  op(e2, e0) = all_53_13
% 231.26/42.47    (60)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.26/42.47          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.26/42.47    (61)  all_38_2 = all_6_2
% 231.26/42.47    (62)  all_55_3 = all_53_12
% 231.26/42.47    (63)   ~ (all_53_12 = e3)
% 231.26/42.47    (64)  all_57_0 = e3
% 231.26/42.47    (65)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 231.26/42.47            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 231.26/42.47              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 231.26/42.47    (66)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.26/42.47          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.26/42.47    (67)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 231.26/42.47          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 231.26/42.47    (68)   ~ (all_53_12 = all_10_2)
% 231.26/42.47    (69)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 231.26/42.47          (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 231.26/42.47    (70)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) |
% 231.26/42.47          (all_57_11 = e0 & op(e1, e0) = e0)
% 231.26/42.47    (71)   ~ (e2 = e1)
% 231.26/42.47    (72)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.26/42.47          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.26/42.47    (73)  op(e2, e1) = all_53_9
% 231.26/42.47    (74)  op(e1, e2) = all_53_6
% 231.26/42.47    (75)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.26/42.47          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.26/42.47    (76)  all_24_2 = all_6_2
% 231.26/42.47    (77)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.26/42.47          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.26/42.47    (78)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.26/42.47          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.26/42.47    (79)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.26/42.47          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.26/42.47    (80)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 231.26/42.47          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 231.26/42.47    (81)  op(e3, e1) = all_53_8
% 231.26/42.47    (82)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.26/42.47          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.26/42.47    (83)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 231.26/42.47          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 231.26/42.47    (84)  op(e3, e0) = all_53_12
% 231.26/42.47  
% 231.26/42.47  Begin of proof
% 231.26/42.47  | 
% 231.26/42.47  | BETA: splitting (70) gives:
% 231.26/42.47  | 
% 231.26/42.47  | Case 1:
% 231.26/42.47  | | 
% 231.26/42.47  | |   (85)  all_57_9 = e0 & op(e3, e0) = e0
% 231.26/42.47  | | 
% 231.26/42.47  | | ALPHA: (85) implies:
% 231.26/42.47  | |   (86)  all_57_9 = e0
% 231.26/42.47  | | 
% 231.26/42.47  | | REF_CLOSE: (9), (11), (21), (24), (27), (33), (37), (44), (47), (71), (86)
% 231.26/42.47  | |            are inconsistent by sub-proof #2436.
% 231.26/42.47  | | 
% 231.26/42.47  | Case 2:
% 231.26/42.47  | | 
% 231.26/42.47  | |   (87)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 231.26/42.47  | |           e0)
% 231.26/42.47  | | 
% 231.26/42.47  | | BETA: splitting (87) gives:
% 231.26/42.47  | | 
% 231.26/42.47  | | Case 1:
% 231.26/42.47  | | | 
% 231.26/42.47  | | |   (88)  all_57_10 = e0 & op(e2, e0) = e0
% 231.26/42.47  | | | 
% 231.26/42.47  | | | ALPHA: (88) implies:
% 231.26/42.47  | | |   (89)  op(e2, e0) = e0
% 231.26/42.47  | | | 
% 231.26/42.47  | | | REF_CLOSE: (11), (57), (59), (89) are inconsistent by sub-proof #2470.
% 231.26/42.47  | | | 
% 231.26/42.47  | | Case 2:
% 231.26/42.47  | | | 
% 231.26/42.47  | | |   (90)  all_57_11 = e0 & op(e1, e0) = e0
% 231.26/42.47  | | | 
% 231.26/42.47  | | | ALPHA: (90) implies:
% 231.26/42.47  | | |   (91)  all_57_11 = e0
% 231.26/42.47  | | | 
% 231.26/42.47  | | | BETA: splitting (14) gives:
% 231.26/42.47  | | | 
% 231.26/42.47  | | | Case 1:
% 231.26/42.47  | | | | 
% 231.26/42.47  | | | |   (92)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2)
% 231.26/42.47  | | | |           = e3)
% 231.26/42.47  | | | | 
% 231.26/42.47  | | | | BETA: splitting (92) gives:
% 231.26/42.47  | | | | 
% 231.26/42.47  | | | | Case 1:
% 231.26/42.47  | | | | | 
% 231.26/42.47  | | | | |   (93)  all_57_6 = e3 & op(e1, e3) = e3
% 231.26/42.47  | | | | | 
% 231.26/42.47  | | | | | ALPHA: (93) implies:
% 231.26/42.47  | | | | |   (94)  all_57_6 = e3
% 231.26/42.47  | | | | | 
% 231.26/42.47  | | | | | REF_CLOSE: (6), (9), (33), (35), (44), (47), (64), (71), (75), (78),
% 231.26/42.47  | | | | |            (94) are inconsistent by sub-proof #2010.
% 231.26/42.47  | | | | | 
% 231.26/42.47  | | | | Case 2:
% 231.26/42.47  | | | | | 
% 231.26/42.47  | | | | |   (95)  all_57_7 = e3 & op(e1, e2) = e3
% 231.26/42.47  | | | | | 
% 231.26/42.47  | | | | | ALPHA: (95) implies:
% 231.26/42.47  | | | | |   (96)  all_57_7 = e3
% 231.26/42.47  | | | | | 
% 231.26/42.47  | | | | | BETA: splitting (27) gives:
% 231.26/42.47  | | | | | 
% 231.26/42.47  | | | | | Case 1:
% 231.26/42.47  | | | | | | 
% 231.26/42.47  | | | | | |   (97)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3,
% 231.26/42.47  | | | | | |             e2) = e2)
% 231.26/42.47  | | | | | | 
% 231.26/42.47  | | | | | | BETA: splitting (97) gives:
% 231.26/42.47  | | | | | | 
% 231.26/42.47  | | | | | | Case 1:
% 231.26/42.47  | | | | | | | 
% 231.26/42.47  | | | | | | |   (98)  all_57_0 = e2 & op(e3, e3) = e2
% 231.26/42.47  | | | | | | | 
% 231.26/42.47  | | | | | | | ALPHA: (98) implies:
% 231.26/42.47  | | | | | | |   (99)  op(e3, e3) = e2
% 231.26/42.47  | | | | | | | 
% 231.26/42.47  | | | | | | | REF_CLOSE: (8), (9), (11), (21), (24), (28), (30), (31), (33),
% 231.26/42.47  | | | | | | |            (35), (44), (46), (47), (51), (63), (71), (82), (84),
% 231.26/42.47  | | | | | | |            (96), (99) are inconsistent by sub-proof #1619.
% 231.26/42.47  | | | | | | | 
% 231.26/42.47  | | | | | | Case 2:
% 231.26/42.47  | | | | | | | 
% 231.26/42.47  | | | | | | |   (100)  all_57_1 = e2 & op(e3, e2) = e2
% 231.26/42.47  | | | | | | | 
% 231.26/42.47  | | | | | | | ALPHA: (100) implies:
% 231.26/42.47  | | | | | | |   (101)  all_57_1 = e2
% 231.26/42.47  | | | | | | | 
% 231.26/42.47  | | | | | | | BETA: splitting (69) gives:
% 231.26/42.47  | | | | | | | 
% 231.26/42.47  | | | | | | | Case 1:
% 231.26/42.47  | | | | | | | | 
% 231.26/42.47  | | | | | | | |   (102)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 &
% 231.26/42.47  | | | | | | | |            op(e2, e0) = e3)
% 231.26/42.47  | | | | | | | | 
% 231.26/42.47  | | | | | | | | BETA: splitting (102) gives:
% 231.26/42.47  | | | | | | | | 
% 231.26/42.47  | | | | | | | | Case 1:
% 231.26/42.47  | | | | | | | | | 
% 231.26/42.47  | | | | | | | | |   (103)  all_57_9 = e3 & op(e3, e0) = e3
% 231.26/42.47  | | | | | | | | | 
% 231.26/42.47  | | | | | | | | | ALPHA: (103) implies:
% 231.26/42.47  | | | | | | | | |   (104)  op(e3, e0) = e3
% 231.26/42.47  | | | | | | | | | 
% 231.26/42.47  | | | | | | | | | REF_CLOSE: (11), (63), (84), (104) are inconsistent by
% 231.26/42.47  | | | | | | | | |            sub-proof #2458.
% 231.26/42.47  | | | | | | | | | 
% 231.26/42.47  | | | | | | | | Case 2:
% 231.26/42.47  | | | | | | | | | 
% 231.26/42.47  | | | | | | | | |   (105)  all_57_10 = e3 & op(e2, e0) = e3
% 231.26/42.47  | | | | | | | | | 
% 231.26/42.47  | | | | | | | | | ALPHA: (105) implies:
% 231.26/42.47  | | | | | | | | |   (106)  all_57_10 = e3
% 231.26/42.47  | | | | | | | | | 
% 231.26/42.47  | | | | | | | | | BETA: splitting (72) gives:
% 231.26/42.47  | | | | | | | | | 
% 231.26/42.47  | | | | | | | | | Case 1:
% 231.26/42.47  | | | | | | | | | | 
% 231.26/42.47  | | | | | | | | | |   (107)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2
% 231.26/42.47  | | | | | | | | | |            & op(e2, e0) = e2)
% 231.26/42.47  | | | | | | | | | | 
% 231.26/42.47  | | | | | | | | | | BETA: splitting (107) gives:
% 231.26/42.47  | | | | | | | | | | 
% 231.26/42.47  | | | | | | | | | | Case 1:
% 231.26/42.47  | | | | | | | | | | | 
% 231.26/42.47  | | | | | | | | | | |   (108)  all_57_9 = e2 & op(e3, e0) = e2
% 231.26/42.47  | | | | | | | | | | | 
% 231.26/42.47  | | | | | | | | | | | ALPHA: (108) implies:
% 231.26/42.47  | | | | | | | | | | |   (109)  all_57_9 = e2
% 231.26/42.47  | | | | | | | | | | | 
% 231.26/42.47  | | | | | | | | | | | COMBINE_EQS: (22), (109) imply:
% 231.26/42.47  | | | | | | | | | | |   (110)  e2 = e1
% 231.26/42.47  | | | | | | | | | | | 
% 231.26/42.47  | | | | | | | | | | | SIMP: (110) implies:
% 231.26/42.47  | | | | | | | | | | |   (111)  e2 = e1
% 231.26/42.47  | | | | | | | | | | | 
% 231.26/42.47  | | | | | | | | | | | COMBINE_EQS: (101), (111) imply:
% 231.26/42.47  | | | | | | | | | | |   (112)  all_57_1 = e1
% 231.26/42.47  | | | | | | | | | | | 
% 231.26/42.47  | | | | | | | | | | | BETA: splitting (27) gives:
% 231.26/42.47  | | | | | | | | | | | 
% 231.26/42.47  | | | | | | | | | | | Case 1:
% 231.26/42.47  | | | | | | | | | | | | 
% 231.26/42.47  | | | | | | | | | | | | 
% 231.26/42.47  | | | | | | | | | | | | BETA: splitting (97) gives:
% 231.26/42.47  | | | | | | | | | | | | 
% 231.26/42.47  | | | | | | | | | | | | Case 1:
% 231.26/42.47  | | | | | | | | | | | | | 
% 231.26/42.47  | | | | | | | | | | | | |   (113)  all_57_0 = e2 & op(e3, e3) = e2
% 231.26/42.47  | | | | | | | | | | | | | 
% 231.26/42.47  | | | | | | | | | | | | | ALPHA: (113) implies:
% 231.26/42.47  | | | | | | | | | | | | |   (114)  op(e3, e3) = e2
% 231.26/42.47  | | | | | | | | | | | | | 
% 231.26/42.47  | | | | | | | | | | | | | REF_CLOSE: (8), (9), (11), (21), (24), (28), (30), (31),
% 231.26/42.47  | | | | | | | | | | | | |            (33), (35), (44), (46), (47), (51), (63), (71),
% 231.26/42.47  | | | | | | | | | | | | |            (82), (84), (96), (114) are inconsistent by
% 231.26/42.47  | | | | | | | | | | | | |            sub-proof #1619.
% 231.26/42.47  | | | | | | | | | | | | | 
% 231.26/42.47  | | | | | | | | | | | | Case 2:
% 231.26/42.47  | | | | | | | | | | | | | 
% 231.26/42.47  | | | | | | | | | | | | | 
% 231.26/42.47  | | | | | | | | | | | | | REF_CLOSE: (71), (100), (112) are inconsistent by sub-proof
% 231.26/42.47  | | | | | | | | | | | | |            #2489.
% 231.26/42.47  | | | | | | | | | | | | | 
% 231.26/42.47  | | | | | | | | | | | | End of split
% 231.26/42.47  | | | | | | | | | | | | 
% 231.26/42.47  | | | | | | | | | | | Case 2:
% 231.26/42.47  | | | | | | | | | | | | 
% 231.26/42.47  | | | | | | | | | | | |   (115)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 231.26/42.47  | | | | | | | | | | | |            & op(e3, e0) = e2)
% 231.26/42.47  | | | | | | | | | | | | 
% 231.26/42.47  | | | | | | | | | | | | REF_CLOSE: (22), (24), (44), (71), (115) are inconsistent by
% 231.26/42.47  | | | | | | | | | | | |            sub-proof #2221.
% 231.26/42.47  | | | | | | | | | | | | 
% 231.26/42.47  | | | | | | | | | | | End of split
% 231.26/42.47  | | | | | | | | | | | 
% 231.26/42.47  | | | | | | | | | | Case 2:
% 231.26/42.47  | | | | | | | | | | | 
% 231.26/42.47  | | | | | | | | | | |   (116)  all_57_10 = e2 & op(e2, e0) = e2
% 231.26/42.47  | | | | | | | | | | | 
% 231.26/42.47  | | | | | | | | | | | REF_CLOSE: (33), (106), (116) are inconsistent by sub-proof
% 231.26/42.47  | | | | | | | | | | |            #2250.
% 231.26/42.47  | | | | | | | | | | | 
% 231.26/42.47  | | | | | | | | | | End of split
% 231.26/42.47  | | | | | | | | | | 
% 231.26/42.47  | | | | | | | | | Case 2:
% 231.26/42.47  | | | | | | | | | | 
% 231.26/42.47  | | | | | | | | | |   (117)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 231.26/42.47  | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 231.26/42.47  | | | | | | | | | | 
% 231.26/42.47  | | | | | | | | | | BETA: splitting (117) gives:
% 231.26/42.47  | | | | | | | | | | 
% 231.26/42.47  | | | | | | | | | | Case 1:
% 231.26/42.47  | | | | | | | | | | | 
% 231.26/42.47  | | | | | | | | | | |   (118)  all_57_11 = e2 & op(e1, e0) = e2
% 231.26/42.47  | | | | | | | | | | | 
% 231.26/42.47  | | | | | | | | | | | ALPHA: (118) implies:
% 231.26/42.47  | | | | | | | | | | |   (119)  all_57_11 = e2
% 231.26/42.47  | | | | | | | | | | | 
% 231.26/42.47  | | | | | | | | | | | COMBINE_EQS: (91), (119) imply:
% 231.26/42.47  | | | | | | | | | | |   (120)  e2 = e0
% 231.26/42.47  | | | | | | | | | | | 
% 231.26/42.47  | | | | | | | | | | | REF_CLOSE: (8), (9), (31), (33), (44), (47), (71), (82),
% 231.26/42.47  | | | | | | | | | | |            (96), (101), (120) are inconsistent by sub-proof
% 231.26/42.47  | | | | | | | | | | |            #1392.
% 231.26/42.47  | | | | | | | | | | | 
% 231.26/42.47  | | | | | | | | | | Case 2:
% 231.26/42.47  | | | | | | | | | | | 
% 231.26/42.47  | | | | | | | | | | |   (121)  all_57_15 = e2 & op(e0, e0) = e2
% 231.26/42.47  | | | | | | | | | | | 
% 231.26/42.47  | | | | | | | | | | | ALPHA: (121) implies:
% 231.26/42.47  | | | | | | | | | | |   (122)  op(e0, e0) = e2
% 231.26/42.47  | | | | | | | | | | | 
% 231.26/42.47  | | | | | | | | | | | REF_CLOSE: (11), (58), (71), (122) are inconsistent by
% 231.26/42.47  | | | | | | | | | | |            sub-proof #2177.
% 231.26/42.47  | | | | | | | | | | | 
% 231.26/42.47  | | | | | | | | | | End of split
% 231.26/42.47  | | | | | | | | | | 
% 231.26/42.47  | | | | | | | | | End of split
% 231.26/42.47  | | | | | | | | | 
% 231.26/42.47  | | | | | | | | End of split
% 231.26/42.47  | | | | | | | | 
% 231.26/42.47  | | | | | | | Case 2:
% 231.26/42.47  | | | | | | | | 
% 231.26/42.47  | | | | | | | |   (123)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 &
% 231.26/42.47  | | | | | | | |            op(e0, e0) = e3)
% 231.26/42.47  | | | | | | | | 
% 231.26/42.47  | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11),
% 231.26/42.47  | | | | | | | |            (12), (13), (14), (15), (16), (17), (18), (19), (20),
% 231.26/42.47  | | | | | | | |            (21), (23), (25), (26), (27), (29), (30), (31), (32),
% 231.26/42.47  | | | | | | | |            (34), (35), (36), (38), (39), (40), (41), (42), (43),
% 231.26/42.47  | | | | | | | |            (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 231.26/42.47  | | | | | | | |            (53), (54), (55), (56), (60), (61), (62), (65), (66),
% 231.26/42.47  | | | | | | | |            (67), (68), (71), (72), (73), (74), (75), (76), (77),
% 231.26/42.47  | | | | | | | |            (78), (79), (80), (81), (82), (83), (84), (91), (123)
% 231.26/42.47  | | | | | | | |            are inconsistent by sub-proof #1391.
% 231.26/42.47  | | | | | | | | 
% 231.26/42.47  | | | | | | | End of split
% 231.26/42.47  | | | | | | | 
% 231.26/42.47  | | | | | | End of split
% 231.26/42.47  | | | | | | 
% 231.26/42.47  | | | | | Case 2:
% 231.26/42.47  | | | | | | 
% 231.26/42.47  | | | | | |   (124)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3,
% 231.26/42.47  | | | | | |              e0) = e2)
% 231.26/42.47  | | | | | | 
% 231.26/42.47  | | | | | | REF_CLOSE: (22), (24), (44), (71), (124) are inconsistent by
% 231.26/42.47  | | | | | |            sub-proof #2221.
% 231.26/42.47  | | | | | | 
% 231.26/42.47  | | | | | End of split
% 231.26/42.47  | | | | | 
% 231.26/42.47  | | | | End of split
% 231.26/42.47  | | | | 
% 231.26/42.47  | | | Case 2:
% 231.26/42.47  | | | | 
% 231.26/42.47  | | | |   (125)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1,
% 231.26/42.47  | | | |              e0) = e3)
% 231.26/42.47  | | | | 
% 231.26/42.47  | | | | REF_CLOSE: (11), (16), (17), (35), (91), (125) are inconsistent by
% 231.26/42.47  | | | |            sub-proof #1594.
% 231.26/42.47  | | | | 
% 231.26/42.47  | | | End of split
% 231.26/42.47  | | | 
% 231.26/42.47  | | End of split
% 231.26/42.47  | | 
% 231.26/42.47  | End of split
% 231.26/42.47  | 
% 231.26/42.47  End of proof
% 231.26/42.47  
% 231.26/42.47  Sub-proof #1391 shows that the following formulas are inconsistent:
% 231.26/42.47  ----------------------------------------------------------------
% 231.26/42.47    (1)   ~ (all_10_2 = e2)
% 231.26/42.47    (2)  op(e3, e3) = all_10_2
% 231.26/42.47    (3)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 231.26/42.47    (4)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 231.26/42.47    (5)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.26/42.47         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.26/42.47    (6)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.26/42.47         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.26/42.47    (7)   ~ (all_53_8 = all_53_12)
% 231.26/42.47    (8)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.26/42.47         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.26/42.47    (9)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 231.26/42.47         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.26/42.47    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.26/42.47            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.26/42.47    (11)  all_55_0 = all_10_2
% 231.26/42.47    (12)   ~ (all_10_2 = e0)
% 231.26/42.47    (13)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.26/42.47          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.26/42.47    (14)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 231.26/42.47            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 231.26/42.47              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 231.26/42.47    (15)   ~ (all_6_2 = e3)
% 231.26/42.47    (16)  op(e1, e1) = all_6_2
% 231.26/42.47    (17)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 231.26/42.47    (18)   ~ (all_53_9 = e0)
% 231.26/42.47    (19)  all_55_0 = e3 | all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 231.26/42.47    (20)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.26/42.47          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.26/42.47    (21)   ~ (all_53_4 = all_53_12)
% 231.26/42.47    (22)   ~ (all_53_8 = all_53_9)
% 231.26/42.47    (23)  all_42_2 = all_6_2
% 231.26/42.47    (24)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.26/42.47          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.26/42.47    (25)   ~ (all_53_9 = all_6_2)
% 231.26/42.48    (26)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.26/42.48          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.26/42.48    (27)  all_57_3 = e0
% 231.26/42.48    (28)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.26/42.48          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.26/42.48    (29)  all_55_1 = all_53_4
% 231.26/42.48    (30)   ~ (e3 = e0)
% 231.26/42.48    (31)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.26/42.48          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.26/42.48    (32)   ~ (all_53_8 = all_6_2)
% 231.26/42.48    (33)  all_55_2 = all_53_8
% 231.26/42.48    (34)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 231.26/42.48    (35)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.26/42.48          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.26/42.48            e1)
% 231.26/42.48    (36)  all_57_11 = e0
% 231.26/42.48    (37)   ~ (all_53_4 = all_53_8)
% 231.26/42.48    (38)  op(e3, e2) = all_53_4
% 231.26/42.48    (39)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 231.26/42.48    (40)   ~ (e2 = e0)
% 231.26/42.48    (41)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 231.26/42.48            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 231.26/42.48            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 231.26/42.48            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 231.26/42.48              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 231.26/42.48            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 231.26/42.48            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 231.26/42.48              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 231.26/42.48              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 231.26/42.48            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 231.26/42.48            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 231.26/42.48            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 231.26/42.48              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 231.26/42.48              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 231.26/42.48            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 231.26/42.48              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 231.26/42.48            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 231.26/42.48            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 231.26/42.48              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 231.26/42.48              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 231.26/42.48            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 231.26/42.48            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 231.26/42.48    (42)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 231.26/42.48          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.26/42.48    (43)   ~ (e1 = e0)
% 231.26/42.48    (44)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 231.26/42.48            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 231.26/42.48              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 231.26/42.48    (45)   ~ (all_53_4 = e0)
% 231.26/42.48    (46)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.26/42.48          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.26/42.48    (47)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.26/42.48          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.26/42.48    (48)   ~ (all_10_2 = e1)
% 231.26/42.48    (49)   ~ (all_53_4 = all_53_6)
% 231.26/42.48    (50)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.26/42.48          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.26/42.48            e2)
% 231.26/42.48    (51)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.26/42.48              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.26/42.48                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.26/42.48                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.26/42.48    (52)  all_55_10 = all_6_2
% 231.26/42.48    (53)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.26/42.48          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.26/42.48    (54)  all_38_2 = all_6_2
% 231.26/42.48    (55)  all_55_3 = all_53_12
% 231.26/42.48    (56)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 231.26/42.48            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 231.26/42.48              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 231.26/42.48    (57)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.26/42.48          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.26/42.48    (58)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 231.26/42.48          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 231.26/42.48    (59)   ~ (all_53_12 = all_10_2)
% 231.26/42.48    (60)   ~ (e2 = e1)
% 231.26/42.48    (61)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.26/42.48          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.26/42.48    (62)  op(e2, e1) = all_53_9
% 231.26/42.48    (63)  op(e1, e2) = all_53_6
% 231.26/42.48    (64)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.26/42.48          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.26/42.48    (65)  all_24_2 = all_6_2
% 231.26/42.48    (66)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.26/42.48          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.26/42.48    (67)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.26/42.48          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.26/42.48    (68)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.26/42.48          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.26/42.48    (69)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 231.26/42.48          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 231.26/42.48    (70)  op(e3, e1) = all_53_8
% 231.26/42.48    (71)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.26/42.48          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.26/42.48    (72)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 231.26/42.48          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 231.26/42.48    (73)  op(e3, e0) = all_53_12
% 231.26/42.48  
% 231.26/42.48  Begin of proof
% 231.26/42.48  | 
% 231.26/42.48  | BETA: splitting (39) gives:
% 231.26/42.48  | 
% 231.26/42.48  | Case 1:
% 231.26/42.48  | | 
% 231.26/42.48  | |   (74)  all_57_11 = e3 & op(e1, e0) = e3
% 231.26/42.48  | | 
% 231.26/42.48  | | ALPHA: (74) implies:
% 231.26/42.48  | |   (75)  all_57_11 = e3
% 231.26/42.48  | | 
% 231.26/42.48  | | REF_CLOSE: (30), (36), (75) are inconsistent by sub-proof #1595.
% 231.26/42.48  | | 
% 231.26/42.48  | Case 2:
% 231.26/42.48  | | 
% 231.26/42.48  | |   (76)  all_57_15 = e3 & op(e0, e0) = e3
% 231.26/42.48  | | 
% 231.26/42.48  | | ALPHA: (76) implies:
% 231.26/42.48  | |   (77)  all_57_15 = e3
% 231.26/42.48  | |   (78)  op(e0, e0) = e3
% 231.26/42.48  | | 
% 231.26/42.48  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 231.26/42.48  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 231.26/42.48  | |            (24), (25), (26), (27), (28), (29), (31), (32), (33), (34), (35),
% 231.26/42.48  | |            (37), (38), (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 231.26/42.48  | |            (49), (50), (51), (52), (53), (54), (55), (56), (57), (58), (59),
% 231.26/42.48  | |            (60), (61), (62), (63), (64), (65), (66), (67), (68), (69), (70),
% 231.26/42.48  | |            (71), (72), (73), (77), (78) are inconsistent by sub-proof #1414.
% 231.26/42.48  | | 
% 231.26/42.48  | End of split
% 231.26/42.48  | 
% 231.26/42.48  End of proof
% 231.26/42.48  
% 231.26/42.48  Sub-proof #1392 shows that the following formulas are inconsistent:
% 231.26/42.48  ----------------------------------------------------------------
% 231.26/42.48    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.26/42.48         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.26/42.48    (2)   ~ (e3 = e1)
% 231.26/42.48    (3)  all_57_3 = e0
% 231.26/42.48    (4)   ~ (e3 = e2)
% 231.26/42.48    (5)  all_57_1 = e2
% 231.26/42.48    (6)  e2 = e0
% 231.26/42.48    (7)   ~ (e2 = e0)
% 231.26/42.48    (8)   ~ (e1 = e0)
% 231.26/42.48    (9)  all_57_7 = e3
% 231.26/42.48    (10)   ~ (e2 = e1)
% 231.26/42.48    (11)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.26/42.48          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.26/42.48  
% 231.26/42.48  Begin of proof
% 231.26/42.48  | 
% 231.26/42.48  | SIMP: (6) implies:
% 231.26/42.48  |   (12)  e2 = e0
% 231.26/42.48  | 
% 231.26/42.48  | COMBINE_EQS: (5), (12) imply:
% 231.26/42.48  |   (13)  all_57_1 = e0
% 231.26/42.48  | 
% 231.26/42.48  | REF_CLOSE: (1), (2), (3), (4), (7), (8), (9), (10), (11), (13) are
% 231.26/42.48  |            inconsistent by sub-proof #2098.
% 231.26/42.48  | 
% 231.26/42.48  End of proof
% 231.26/42.48  
% 231.26/42.48  Sub-proof #1393 shows that the following formulas are inconsistent:
% 231.26/42.48  ----------------------------------------------------------------
% 231.26/42.48    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.26/42.48           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.26/42.48    (2)  all_57_14 = e3
% 231.26/42.48    (3)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.26/42.48    (4)   ~ (e3 = e2)
% 231.26/42.48    (5)  op(e0, e0) = e1
% 231.26/42.48    (6)   ~ (e2 = e1)
% 231.26/42.48  
% 231.26/42.48  Begin of proof
% 231.26/42.48  | 
% 231.26/42.48  | BETA: splitting (3) gives:
% 231.26/42.48  | 
% 231.26/42.48  | Case 1:
% 231.26/42.48  | | 
% 231.26/42.48  | |   (7)  all_57_14 = e2 & op(e0, e1) = e2
% 231.26/42.48  | | 
% 231.26/42.48  | | REF_CLOSE: (2), (4), (7) are inconsistent by sub-proof #2324.
% 231.26/42.48  | | 
% 231.26/42.48  | Case 2:
% 231.26/42.48  | | 
% 231.26/42.48  | |   (8)  all_57_15 = e2 & op(e0, e0) = e2
% 231.26/42.48  | | 
% 231.26/42.48  | | ALPHA: (8) implies:
% 231.26/42.48  | |   (9)  op(e0, e0) = e2
% 231.26/42.48  | | 
% 231.26/42.48  | | REF_CLOSE: (1), (5), (6), (9) are inconsistent by sub-proof #2177.
% 231.26/42.48  | | 
% 231.26/42.48  | End of split
% 231.26/42.48  | 
% 231.26/42.48  End of proof
% 231.26/42.48  
% 231.26/42.48  Sub-proof #1394 shows that the following formulas are inconsistent:
% 231.26/42.48  ----------------------------------------------------------------
% 231.26/42.48    (1)   ~ (all_10_2 = e2)
% 231.26/42.48    (2)  all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 231.26/42.48    (3)  op(e3, e3) = all_10_2
% 231.26/42.48    (4)  op(e0, e1) = all_53_11
% 231.26/42.48    (5)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 231.26/42.48    (6)   ~ (all_53_6 = all_53_14)
% 231.26/42.48    (7)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 231.26/42.48    (8)  op(e3, e1) = e0
% 231.26/42.48    (9)  all_57_15 = e0
% 231.26/42.48    (10)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.26/42.48          (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.26/42.48    (11)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.26/42.48          (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.26/42.48    (12)   ~ (all_53_8 = all_53_12)
% 231.26/42.48    (13)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.26/42.48          (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.26/42.48    (14)   ~ (all_53_8 = all_53_11)
% 231.26/42.48    (15)   ~ (e3 = e1)
% 231.26/42.48    (16)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 231.26/42.48          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.26/42.48    (17)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.26/42.48            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.26/42.48    (18)  all_55_0 = all_10_2
% 231.26/42.48    (19)   ~ (all_10_2 = e0)
% 231.26/42.48    (20)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.26/42.48    (21)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.26/42.48          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.26/42.48    (22)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 231.26/42.48            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 231.26/42.48              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 231.26/42.48    (23)   ~ (all_6_2 = e3)
% 231.26/42.48    (24)  op(e1, e1) = all_6_2
% 231.26/42.48    (25)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 231.26/42.48    (26)  all_55_0 = e3 | all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 231.26/42.48    (27)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 231.26/42.48    (28)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.26/42.48          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.26/42.48    (29)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 231.26/42.48    (30)  all_55_9 = all_53_6
% 231.26/42.48    (31)   ~ (all_53_11 = all_6_2)
% 231.26/42.48    (32)   ~ (all_53_4 = all_53_12)
% 231.26/42.48    (33)  all_57_4 = e0
% 231.26/42.48    (34)   ~ (all_53_8 = e3)
% 231.26/42.48    (35)   ~ (all_53_8 = all_53_9)
% 231.26/42.48    (36)  all_57_12 = e2
% 231.26/42.48    (37)  all_42_2 = all_6_2
% 231.26/42.48    (38)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.26/42.48          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.26/42.48    (39)  op(e2, e2) = e0
% 231.26/42.48    (40)   ~ (all_53_9 = all_53_11)
% 231.26/42.48    (41)   ~ (all_53_9 = all_6_2)
% 231.26/42.48    (42)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.26/42.48          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.26/42.48    (43)   ~ (all_53_14 = all_6_2)
% 231.26/42.48    (44)  all_57_3 = e0
% 231.26/42.48    (45)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.26/42.48          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.26/42.48    (46)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 231.26/42.48    (47)  all_55_1 = all_53_4
% 231.26/42.48    (48)  op(e1, e0) = all_53_14
% 231.26/42.48    (49)   ~ (all_53_6 = all_53_7)
% 231.26/42.48    (50)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.26/42.48          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.26/42.48    (51)  op(e3, e3) = e3
% 231.26/42.48    (52)   ~ (all_53_8 = all_6_2)
% 231.26/42.48    (53)  all_55_2 = all_53_8
% 231.26/42.48    (54)   ~ (all_53_4 = all_53_7)
% 231.26/42.48    (55)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 231.26/42.48    (56)   ~ (all_53_7 = e0)
% 231.26/42.48    (57)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.26/42.48          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.26/42.48            e1)
% 231.26/42.48    (58)   ~ (all_53_4 = all_53_8)
% 231.26/42.48    (59)  all_55_6 = all_53_9
% 231.26/42.48    (60)  op(e3, e2) = all_53_4
% 231.26/42.48    (61)   ~ (e2 = e0)
% 231.26/42.48    (62)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 231.26/42.48            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 231.26/42.48            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 231.26/42.48            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 231.26/42.48              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 231.26/42.48            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 231.26/42.48            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 231.26/42.48              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 231.26/42.48              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 231.26/42.48            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 231.26/42.48            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 231.26/42.48            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 231.26/42.48              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 231.26/42.48              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 231.26/42.48            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 231.26/42.48              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 231.26/42.48            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 231.26/42.48            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 231.26/42.48              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 231.26/42.48              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 231.26/42.48            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 231.26/42.48            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 231.26/42.48    (63)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 231.26/42.48          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.26/42.48    (64)   ~ (all_53_2 = all_53_14)
% 231.26/42.48    (65)   ~ (e1 = e0)
% 231.26/42.48    (66)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 231.26/42.48            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 231.26/42.48              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 231.26/42.48    (67)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.26/42.48          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.26/42.48    (68)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.26/42.48          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.26/42.48    (69)   ~ (all_10_2 = e1)
% 231.26/42.48    (70)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 231.26/42.48    (71)  op(e0, e0) = e0
% 231.26/42.48    (72)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.26/42.48          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 231.26/42.48            e3)
% 231.26/42.48    (73)   ~ (all_53_4 = all_53_6)
% 231.26/42.48    (74)  op(e0, e2) = all_53_7
% 231.26/42.48    (75)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.26/42.48          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.26/42.48            e2)
% 231.26/42.48    (76)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.26/42.48              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.26/42.48                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.26/42.48                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.26/42.48    (77)  all_55_10 = all_6_2
% 231.26/42.48    (78)   ~ (all_53_6 = all_6_2)
% 231.26/42.48    (79)  all_55_13 = all_53_7
% 231.26/42.48    (80)  op(e2, e0) = all_53_13
% 231.26/42.48    (81)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.26/42.48          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.26/42.48    (82)  all_38_2 = all_6_2
% 231.26/42.48    (83)  all_55_11 = all_53_14
% 231.26/42.48    (84)  all_55_3 = all_53_12
% 231.26/42.48    (85)   ~ (all_53_12 = e3)
% 231.26/42.48    (86)  all_57_0 = e3
% 231.26/42.48    (87)  op(e1, e3) = all_53_2
% 231.26/42.48    (88)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 231.26/42.48            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 231.26/42.48              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 231.26/42.48    (89)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.26/42.48          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.26/42.48    (90)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 231.26/42.48          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 231.26/42.48    (91)   ~ (all_53_12 = all_10_2)
% 231.26/42.48    (92)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 231.26/42.48          (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 231.26/42.48    (93)   ~ (all_53_13 = all_53_14)
% 231.26/42.48    (94)   ~ (e2 = e1)
% 231.26/42.48    (95)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.26/42.48          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.26/42.48    (96)  op(e2, e1) = all_53_9
% 231.26/42.48    (97)  op(e1, e2) = all_53_6
% 231.26/42.48    (98)   ~ (all_53_2 = all_53_6)
% 231.26/42.48    (99)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.26/42.48          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.26/42.48    (100)  all_24_2 = all_6_2
% 231.26/42.48    (101)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.26/42.48           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.26/42.48    (102)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.26/42.48           (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.26/42.48    (103)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.26/42.48           | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.26/42.48             e1)
% 231.26/42.48    (104)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 231.26/42.48           (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 231.26/42.48    (105)   ~ (all_53_12 = all_53_14)
% 231.26/42.48    (106)  all_55_14 = all_53_11
% 231.26/42.48    (107)  op(e3, e1) = all_53_8
% 231.26/42.48    (108)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.26/42.48           (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.26/42.48    (109)   ~ (all_53_4 = e3)
% 231.26/42.48    (110)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 231.26/42.48           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 231.26/42.48    (111)  op(e3, e0) = all_53_12
% 231.26/42.48  
% 231.26/42.48  Begin of proof
% 231.26/42.48  | 
% 231.26/42.48  | BETA: splitting (20) gives:
% 231.26/42.48  | 
% 231.26/42.48  | Case 1:
% 231.26/42.48  | | 
% 231.26/42.48  | |   (112)  all_57_6 = e0 & op(e1, e3) = e0
% 231.26/42.48  | | 
% 231.26/42.48  | | ALPHA: (112) implies:
% 231.26/42.48  | |   (113)  all_57_6 = e0
% 231.26/42.48  | |   (114)  op(e1, e3) = e0
% 231.26/42.48  | | 
% 231.26/42.48  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 231.26/42.48  | |            (13), (14), (15), (16), (17), (18), (19), (21), (22), (23), (24),
% 231.26/42.48  | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 231.26/42.48  | |            (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 231.26/42.48  | |            (48), (49), (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 231.26/42.48  | |            (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), (69),
% 231.26/42.48  | |            (70), (71), (72), (73), (74), (75), (76), (77), (78), (79), (80),
% 231.26/42.48  | |            (81), (82), (83), (84), (85), (86), (87), (88), (89), (90), (91),
% 231.26/42.48  | |            (92), (93), (94), (95), (96), (97), (98), (99), (100), (101),
% 231.26/42.48  | |            (102), (103), (104), (105), (106), (107), (108), (109), (110),
% 231.26/42.48  | |            (111), (113), (114) are inconsistent by sub-proof #1410.
% 231.26/42.48  | | 
% 231.26/42.48  | Case 2:
% 231.26/42.48  | | 
% 231.26/42.48  | |   (115)  all_57_12 = e0 & op(e0, e3) = e0
% 231.26/42.48  | | 
% 231.26/42.48  | | REF_CLOSE: (36), (61), (115) are inconsistent by sub-proof #2185.
% 231.26/42.48  | | 
% 231.26/42.48  | End of split
% 231.26/42.48  | 
% 231.26/42.48  End of proof
% 231.26/42.48  
% 231.26/42.48  Sub-proof #1395 shows that the following formulas are inconsistent:
% 231.26/42.48  ----------------------------------------------------------------
% 231.26/42.48    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.26/42.48         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.26/42.48    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.26/42.48         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.26/42.48    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.26/42.48         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.26/42.48    (4)   ~ (e3 = e1)
% 231.26/42.48    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.26/42.48           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.26/42.48    (6)   ~ (all_6_2 = e3)
% 231.26/42.48    (7)  op(e1, e1) = all_6_2
% 231.26/42.48    (8)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.26/42.48         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.26/42.48    (9)  all_57_9 = e1
% 231.26/42.48    (10)  all_57_4 = e0
% 231.26/42.48    (11)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.26/42.48          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.26/42.48    (12)  op(e2, e2) = e0
% 231.26/42.48    (13)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.26/42.48          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.26/42.48    (14)  all_57_3 = e0
% 231.26/42.48    (15)   ~ (e3 = e2)
% 231.26/42.48    (16)   ~ (e3 = e0)
% 231.26/42.48    (17)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.26/42.48          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.26/42.48    (18)  op(e3, e3) = e3
% 231.26/42.48    (19)  all_57_5 = e3
% 231.26/42.48    (20)   ~ (e2 = e0)
% 231.26/42.48    (21)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 231.26/42.48          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.26/42.48    (22)   ~ (e1 = e0)
% 231.26/42.48    (23)  all_57_12 = e3
% 231.26/42.48    (24)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.26/42.48          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.26/42.48    (25)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.26/42.48          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.26/42.48    (26)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.26/42.48          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.26/42.48    (27)   ~ (all_53_12 = e3)
% 231.26/42.48    (28)  all_57_7 = e3
% 231.26/42.49    (29)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.26/42.49          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.26/42.49    (30)   ~ (e2 = e1)
% 231.26/42.49    (31)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.26/42.49          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.26/42.49    (32)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.26/42.49          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.26/42.49    (33)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.26/42.49          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.26/42.49    (34)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.26/42.49          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.26/42.49    (35)  op(e3, e0) = all_53_12
% 231.26/42.49  
% 231.26/42.49  Begin of proof
% 231.26/42.49  | 
% 231.26/42.49  | BETA: splitting (33) gives:
% 231.26/42.49  | 
% 231.26/42.49  | Case 1:
% 231.26/42.49  | | 
% 231.26/42.49  | |   (36)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) =
% 231.26/42.49  | |           e0)
% 231.26/42.49  | | 
% 231.26/42.49  | | REF_CLOSE: (1), (4), (5), (9), (10), (11), (14), (15), (16), (19), (20),
% 231.26/42.49  | |            (21), (22), (27), (29), (30), (35), (36) are inconsistent by
% 231.26/42.49  | |            sub-proof #1396.
% 231.26/42.49  | | 
% 231.26/42.49  | Case 2:
% 231.26/42.49  | | 
% 231.26/42.49  | |   (37)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) =
% 231.26/42.49  | |           e0)
% 231.26/42.49  | | 
% 231.26/42.49  | | BETA: splitting (37) gives:
% 231.26/42.49  | | 
% 231.26/42.49  | | Case 1:
% 231.26/42.49  | | | 
% 231.26/42.49  | | |   (38)  all_57_6 = e0 & op(e1, e3) = e0
% 231.26/42.49  | | | 
% 231.26/42.49  | | | ALPHA: (38) implies:
% 231.26/42.49  | | |   (39)  all_57_6 = e0
% 231.26/42.49  | | | 
% 231.26/42.49  | | | BETA: splitting (2) gives:
% 231.26/42.49  | | | 
% 231.26/42.49  | | | Case 1:
% 231.26/42.49  | | | | 
% 231.26/42.49  | | | |   (40)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3)
% 231.26/42.49  | | | |           = e1)
% 231.26/42.49  | | | | 
% 231.26/42.49  | | | | BETA: splitting (40) gives:
% 231.26/42.49  | | | | 
% 231.26/42.49  | | | | Case 1:
% 231.26/42.49  | | | | | 
% 231.26/42.49  | | | | |   (41)  all_57_0 = e1 & op(e3, e3) = e1
% 231.26/42.49  | | | | | 
% 231.26/42.49  | | | | | ALPHA: (41) implies:
% 231.26/42.49  | | | | |   (42)  op(e3, e3) = e1
% 231.26/42.49  | | | | | 
% 231.26/42.49  | | | | | REF_CLOSE: (4), (5), (18), (42) are inconsistent by sub-proof #2495.
% 231.26/42.49  | | | | | 
% 231.26/42.49  | | | | Case 2:
% 231.26/42.49  | | | | | 
% 231.26/42.49  | | | | |   (43)  all_57_2 = e1 & op(e2, e3) = e1
% 231.26/42.49  | | | | | 
% 231.26/42.49  | | | | | ALPHA: (43) implies:
% 231.26/42.49  | | | | |   (44)  all_57_2 = e1
% 231.26/42.49  | | | | | 
% 231.26/42.49  | | | | | BETA: splitting (31) gives:
% 231.26/42.49  | | | | | 
% 231.26/42.49  | | | | | Case 1:
% 231.26/42.49  | | | | | | 
% 231.26/42.49  | | | | | |   (45)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2,
% 231.26/42.49  | | | | | |             e3) = e2)
% 231.26/42.49  | | | | | | 
% 231.26/42.49  | | | | | | BETA: splitting (45) gives:
% 231.26/42.49  | | | | | | 
% 231.26/42.49  | | | | | | Case 1:
% 231.26/42.49  | | | | | | | 
% 231.26/42.49  | | | | | | |   (46)  all_57_0 = e2 & op(e3, e3) = e2
% 231.26/42.49  | | | | | | | 
% 231.26/42.49  | | | | | | | ALPHA: (46) implies:
% 231.26/42.49  | | | | | | |   (47)  op(e3, e3) = e2
% 231.26/42.49  | | | | | | | 
% 231.26/42.49  | | | | | | | REF_CLOSE: (3), (4), (5), (8), (10), (12), (13), (14), (15), (16),
% 231.26/42.49  | | | | | | |            (20), (21), (22), (25), (27), (28), (30), (34), (35),
% 231.26/42.49  | | | | | | |            (47) are inconsistent by sub-proof #1619.
% 231.26/42.49  | | | | | | | 
% 231.26/42.49  | | | | | | Case 2:
% 231.26/42.49  | | | | | | | 
% 231.26/42.49  | | | | | | |   (48)  all_57_2 = e2 & op(e2, e3) = e2
% 231.26/42.49  | | | | | | | 
% 231.26/42.49  | | | | | | | ALPHA: (48) implies:
% 231.26/42.49  | | | | | | |   (49)  all_57_2 = e2
% 231.26/42.49  | | | | | | | 
% 231.26/42.49  | | | | | | | REF_CLOSE: (30), (44), (49) are inconsistent by sub-proof #2464.
% 231.26/42.49  | | | | | | | 
% 231.26/42.49  | | | | | | End of split
% 231.26/42.49  | | | | | | 
% 231.26/42.49  | | | | | Case 2:
% 231.26/42.49  | | | | | | 
% 231.26/42.49  | | | | | |   (50)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0,
% 231.26/42.49  | | | | | |             e3) = e2)
% 231.26/42.49  | | | | | | 
% 231.26/42.49  | | | | | | BETA: splitting (50) gives:
% 231.26/42.49  | | | | | | 
% 231.26/42.49  | | | | | | Case 1:
% 231.26/42.49  | | | | | | | 
% 231.26/42.49  | | | | | | |   (51)  all_57_6 = e2 & op(e1, e3) = e2
% 231.26/42.49  | | | | | | | 
% 231.26/42.49  | | | | | | | ALPHA: (51) implies:
% 231.26/42.49  | | | | | | |   (52)  all_57_6 = e2
% 231.26/42.49  | | | | | | | 
% 231.26/42.49  | | | | | | | REF_CLOSE: (5), (16), (18), (20), (22), (23), (33), (44), (52) are
% 231.26/42.49  | | | | | | |            inconsistent by sub-proof #2236.
% 231.26/42.49  | | | | | | | 
% 231.26/42.49  | | | | | | Case 2:
% 231.26/42.49  | | | | | | | 
% 231.26/42.49  | | | | | | |   (53)  all_57_12 = e2 & op(e0, e3) = e2
% 231.26/42.49  | | | | | | | 
% 231.26/42.49  | | | | | | | REF_CLOSE: (15), (23), (53) are inconsistent by sub-proof #2232.
% 231.26/42.49  | | | | | | | 
% 231.26/42.49  | | | | | | End of split
% 231.26/42.49  | | | | | | 
% 231.26/42.49  | | | | | End of split
% 231.26/42.49  | | | | | 
% 231.26/42.49  | | | | End of split
% 231.26/42.49  | | | | 
% 231.26/42.49  | | | Case 2:
% 231.26/42.49  | | | | 
% 231.26/42.49  | | | |   (54)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3)
% 231.26/42.49  | | | |           = e1)
% 231.26/42.49  | | | | 
% 231.26/42.49  | | | | BETA: splitting (54) gives:
% 231.26/42.49  | | | | 
% 231.26/42.49  | | | | Case 1:
% 231.26/42.49  | | | | | 
% 231.26/42.49  | | | | |   (55)  all_57_6 = e1 & op(e1, e3) = e1
% 231.26/42.49  | | | | | 
% 231.26/42.49  | | | | | ALPHA: (55) implies:
% 231.26/42.49  | | | | |   (56)  all_57_6 = e1
% 231.26/42.49  | | | | | 
% 231.26/42.49  | | | | | REF_CLOSE: (4), (5), (8), (9), (10), (11), (15), (18), (20), (22),
% 231.26/42.49  | | | | |            (30), (39), (56) are inconsistent by sub-proof #1483.
% 231.26/42.49  | | | | | 
% 231.26/42.49  | | | | Case 2:
% 231.26/42.49  | | | | | 
% 231.26/42.49  | | | | |   (57)  all_57_12 = e1 & op(e0, e3) = e1
% 231.26/42.49  | | | | | 
% 231.26/42.49  | | | | | REF_CLOSE: (4), (23), (57) are inconsistent by sub-proof #2230.
% 231.26/42.49  | | | | | 
% 231.26/42.49  | | | | End of split
% 231.26/42.49  | | | | 
% 231.26/42.49  | | | End of split
% 231.26/42.49  | | | 
% 231.26/42.49  | | Case 2:
% 231.26/42.49  | | | 
% 231.26/42.49  | | |   (58)  all_57_12 = e0 & op(e0, e3) = e0
% 231.26/42.49  | | | 
% 231.26/42.49  | | | ALPHA: (58) implies:
% 231.26/42.49  | | |   (59)  all_57_12 = e0
% 231.26/42.49  | | | 
% 231.26/42.49  | | | COMBINE_EQS: (23), (59) imply:
% 231.26/42.49  | | |   (60)  e3 = e0
% 231.26/42.49  | | | 
% 231.26/42.49  | | | COMBINE_EQS: (19), (60) imply:
% 231.26/42.49  | | |   (61)  all_57_5 = e0
% 231.26/42.49  | | | 
% 231.26/42.49  | | | REF_CLOSE: (1), (4), (5), (6), (7), (10), (12), (14), (15), (16), (17),
% 231.26/42.49  | | |            (20), (22), (24), (26), (29), (30), (32), (61) are inconsistent
% 231.26/42.49  | | |            by sub-proof #1624.
% 231.26/42.49  | | | 
% 231.26/42.49  | | End of split
% 231.26/42.49  | | 
% 231.26/42.49  | End of split
% 231.26/42.49  | 
% 231.26/42.49  End of proof
% 231.26/42.49  
% 231.26/42.49  Sub-proof #1396 shows that the following formulas are inconsistent:
% 231.26/42.49  ----------------------------------------------------------------
% 231.26/42.49    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.26/42.49         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.26/42.49    (2)   ~ (e3 = e1)
% 231.26/42.49    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.26/42.49           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.26/42.49    (4)  all_57_9 = e1
% 231.26/42.49    (5)  all_57_4 = e0
% 231.26/42.49    (6)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.26/42.49         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.26/42.49    (7)  all_57_3 = e0
% 231.26/42.49    (8)   ~ (e3 = e2)
% 231.26/42.49    (9)   ~ (e3 = e0)
% 231.26/42.49    (10)  all_57_5 = e3
% 231.26/42.49    (11)   ~ (e2 = e0)
% 231.26/42.49    (12)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 231.26/42.49          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.26/42.49    (13)   ~ (e1 = e0)
% 231.26/42.49    (14)   ~ (all_53_12 = e3)
% 231.26/42.49    (15)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.26/42.49          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.26/42.49    (16)   ~ (e2 = e1)
% 231.26/42.49    (17)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0)
% 231.26/42.49    (18)  op(e3, e0) = all_53_12
% 231.26/42.49  
% 231.26/42.49  Begin of proof
% 231.26/42.49  | 
% 231.26/42.49  | BETA: splitting (17) gives:
% 231.26/42.49  | 
% 231.26/42.49  | Case 1:
% 231.26/42.49  | | 
% 231.26/42.49  | |   (19)  all_57_0 = e0 & op(e3, e3) = e0
% 231.26/42.49  | | 
% 231.26/42.49  | | ALPHA: (19) implies:
% 231.26/42.49  | |   (20)  op(e3, e3) = e0
% 231.26/42.49  | | 
% 231.26/42.49  | | REF_CLOSE: (3), (4), (5), (6), (8), (9), (11), (12), (14), (16), (18), (20)
% 231.26/42.49  | |            are inconsistent by sub-proof #1403.
% 231.26/42.49  | | 
% 231.26/42.49  | Case 2:
% 231.26/42.49  | | 
% 231.26/42.49  | |   (21)  all_57_2 = e0 & op(e2, e3) = e0
% 231.26/42.49  | | 
% 231.26/42.49  | | ALPHA: (21) implies:
% 231.26/42.49  | |   (22)  all_57_2 = e0
% 231.26/42.49  | | 
% 231.26/42.49  | | REF_CLOSE: (1), (2), (7), (8), (10), (11), (13), (15), (16), (22) are
% 231.26/42.49  | |            inconsistent by sub-proof #2253.
% 231.26/42.49  | | 
% 231.26/42.49  | End of split
% 231.26/42.49  | 
% 231.26/42.49  End of proof
% 231.26/42.49  
% 231.26/42.49  Sub-proof #1397 shows that the following formulas are inconsistent:
% 231.26/42.49  ----------------------------------------------------------------
% 231.26/42.49    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.26/42.49         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.26/42.49    (2)   ~ (e3 = e1)
% 231.26/42.49    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.26/42.49           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.26/42.49    (4)   ~ (all_6_2 = e3)
% 231.26/42.49    (5)  op(e1, e1) = all_6_2
% 231.26/42.49    (6)  all_57_4 = e0
% 231.26/42.49    (7)  op(e2, e2) = e0
% 231.26/42.49    (8)  all_57_3 = e0
% 231.26/42.49    (9)   ~ (e3 = e2)
% 231.26/42.49    (10)   ~ (e3 = e0)
% 231.26/42.49    (11)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.26/42.49          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.26/42.49    (12)  all_57_5 = e3
% 231.26/42.49    (13)   ~ (e2 = e0)
% 231.26/42.49    (14)  all_57_3 = e3 & op(e2, e2) = e3
% 231.26/42.49    (15)   ~ (e1 = e0)
% 231.26/42.49    (16)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.26/42.49          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.26/42.49    (17)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.26/42.49          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.26/42.49    (18)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.26/42.49          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.26/42.49    (19)   ~ (e2 = e1)
% 231.26/42.49    (20)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.26/42.49          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.26/42.49  
% 231.26/42.49  Begin of proof
% 231.26/42.49  | 
% 231.26/42.49  | ALPHA: (14) implies:
% 231.26/42.49  |   (21)  all_57_3 = e3
% 231.26/42.49  | 
% 231.26/42.49  | COMBINE_EQS: (8), (21) imply:
% 231.26/42.49  |   (22)  e3 = e0
% 231.26/42.49  | 
% 231.26/42.49  | SIMP: (22) implies:
% 231.26/42.49  |   (23)  e3 = e0
% 231.26/42.49  | 
% 231.26/42.49  | COMBINE_EQS: (12), (23) imply:
% 231.26/42.49  |   (24)  all_57_5 = e0
% 231.26/42.49  | 
% 231.26/42.49  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 231.26/42.49  |            (15), (16), (17), (18), (19), (20), (24) are inconsistent by
% 231.26/42.49  |            sub-proof #1624.
% 231.26/42.49  | 
% 231.26/42.49  End of proof
% 231.26/42.49  
% 231.26/42.49  Sub-proof #1398 shows that the following formulas are inconsistent:
% 231.26/42.49  ----------------------------------------------------------------
% 231.26/42.49    (1)  all_57_13 = e1
% 231.26/42.49    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.26/42.49           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.26/42.49    (3)  all_57_9 = e1
% 231.26/42.49    (4)  all_57_4 = e0
% 231.26/42.49    (5)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.26/42.49         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.26/42.49    (6)   ~ (e3 = e2)
% 231.26/42.49    (7)  all_57_1 = e2
% 231.26/42.49    (8)  op(e3, e3) = e3
% 231.26/42.49    (9)   ~ (e2 = e0)
% 231.26/42.49    (10)   ~ (e2 = e1)
% 231.26/42.49    (11)  all_57_13 = e2 & op(e0, e2) = e2
% 231.26/42.49  
% 231.26/42.49  Begin of proof
% 231.26/42.49  | 
% 231.26/42.49  | ALPHA: (11) implies:
% 231.26/42.49  |   (12)  all_57_13 = e2
% 231.26/42.49  | 
% 231.26/42.49  | COMBINE_EQS: (1), (12) imply:
% 231.26/42.49  |   (13)  e2 = e1
% 231.26/42.49  | 
% 231.26/42.49  | SIMP: (13) implies:
% 231.26/42.49  |   (14)  e2 = e1
% 231.26/42.49  | 
% 231.26/42.49  | COMBINE_EQS: (7), (14) imply:
% 231.26/42.49  |   (15)  all_57_1 = e1
% 231.26/42.49  | 
% 231.26/42.49  | REF_CLOSE: (2), (3), (4), (5), (6), (8), (9), (10), (15) are inconsistent by
% 231.26/42.49  |            sub-proof #2220.
% 231.26/42.49  | 
% 231.26/42.49  End of proof
% 231.26/42.49  
% 231.26/42.49  Sub-proof #1399 shows that the following formulas are inconsistent:
% 231.26/42.49  ----------------------------------------------------------------
% 231.26/42.49    (1)   ~ (e3 = e1)
% 231.26/42.49    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.26/42.49           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.26/42.49    (3)   ~ (all_6_2 = e3)
% 231.26/42.49    (4)  op(e1, e1) = all_6_2
% 231.26/42.49    (5)  all_57_4 = e0
% 231.26/42.49    (6)   ~ (e3 = e2)
% 231.26/42.49    (7)   ~ (e3 = e0)
% 231.26/42.49    (8)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.26/42.49         (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.26/42.49    (9)   ~ (all_53_7 = e0)
% 231.26/42.49    (10)   ~ (e2 = e0)
% 231.26/42.49    (11)   ~ (e1 = e0)
% 231.26/42.49    (12)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.26/42.49          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.26/42.49    (13)  op(e0, e2) = all_53_7
% 231.26/42.49    (14)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.26/42.49    (15)   ~ (e2 = e1)
% 231.26/42.49    (16)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.26/42.49          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.26/42.49  
% 231.26/42.49  Begin of proof
% 231.26/42.49  | 
% 231.26/42.49  | BETA: splitting (14) gives:
% 231.26/42.49  | 
% 231.26/42.49  | Case 1:
% 231.26/42.49  | | 
% 231.26/42.49  | |   (17)  all_57_13 = e0 & op(e0, e2) = e0
% 231.26/42.49  | | 
% 231.26/42.49  | | ALPHA: (17) implies:
% 231.26/42.49  | |   (18)  op(e0, e2) = e0
% 231.26/42.49  | | 
% 231.26/42.49  | | REF_CLOSE: (2), (9), (13), (18) are inconsistent by sub-proof #2332.
% 231.26/42.49  | | 
% 231.26/42.49  | Case 2:
% 231.26/42.49  | | 
% 231.26/42.49  | |   (19)  all_57_14 = e0 & op(e0, e1) = e0
% 231.26/42.49  | | 
% 231.26/42.49  | | ALPHA: (19) implies:
% 231.26/42.49  | |   (20)  all_57_14 = e0
% 231.26/42.49  | | 
% 231.26/42.49  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (15),
% 231.26/42.49  | |            (16), (20) are inconsistent by sub-proof #2371.
% 231.26/42.49  | | 
% 231.26/42.49  | End of split
% 231.26/42.49  | 
% 231.26/42.49  End of proof
% 231.26/42.49  
% 231.26/42.49  Sub-proof #1400 shows that the following formulas are inconsistent:
% 231.26/42.49  ----------------------------------------------------------------
% 231.26/42.49    (1)   ~ (all_10_2 = e2)
% 231.26/42.49    (2)  all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 231.26/42.49    (3)  op(e3, e3) = all_10_2
% 231.26/42.49    (4)  op(e0, e1) = all_53_11
% 231.26/42.49    (5)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 231.26/42.49    (6)   ~ (all_53_6 = all_53_14)
% 231.26/42.49    (7)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 231.26/42.49    (8)  op(e3, e1) = e0
% 231.26/42.49    (9)  all_57_15 = e0
% 231.26/42.49    (10)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.26/42.49          (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.26/42.49    (11)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.26/42.49          (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.26/42.49    (12)   ~ (all_53_8 = all_53_12)
% 231.26/42.49    (13)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.26/42.49          (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.26/42.49    (14)   ~ (all_53_8 = all_53_11)
% 231.26/42.49    (15)   ~ (e3 = e1)
% 231.26/42.49    (16)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 231.26/42.49          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.26/42.49    (17)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.26/42.49            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.26/42.49    (18)  all_55_0 = all_10_2
% 231.26/42.49    (19)   ~ (all_10_2 = e0)
% 231.26/42.49    (20)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.26/42.49          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.26/42.49    (21)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 231.26/42.49            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 231.26/42.49              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 231.26/42.49    (22)   ~ (all_6_2 = e3)
% 231.26/42.49    (23)  op(e1, e1) = all_6_2
% 231.26/42.49    (24)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 231.26/42.49    (25)  all_55_0 = e3 | all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 231.26/42.49    (26)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 231.26/42.49    (27)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.26/42.49          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.26/42.49    (28)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 231.26/42.49    (29)  all_55_9 = all_53_6
% 231.26/42.49    (30)   ~ (all_53_11 = all_6_2)
% 231.26/42.49    (31)  all_57_9 = e1
% 231.26/42.49    (32)   ~ (all_53_4 = all_53_12)
% 231.26/42.49    (33)  all_57_4 = e0
% 231.26/42.49    (34)   ~ (all_53_8 = e3)
% 231.26/42.49    (35)   ~ (all_53_8 = all_53_9)
% 231.26/42.49    (36)  all_42_2 = all_6_2
% 231.26/42.49    (37)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.26/42.49          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.26/42.49    (38)  op(e2, e2) = e0
% 231.26/42.49    (39)   ~ (all_53_9 = all_53_11)
% 231.26/42.49    (40)   ~ (all_53_9 = all_6_2)
% 231.26/42.49    (41)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.26/42.49          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.26/42.49    (42)   ~ (all_53_14 = all_6_2)
% 231.26/42.49    (43)  all_57_3 = e0
% 231.26/42.49    (44)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.26/42.49          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.26/42.49    (45)   ~ (e3 = e2)
% 231.26/42.49    (46)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 231.26/42.49    (47)  all_55_1 = all_53_4
% 231.26/42.49    (48)  op(e1, e0) = all_53_14
% 231.26/42.49    (49)   ~ (all_53_6 = all_53_7)
% 231.26/42.49    (50)   ~ (e3 = e0)
% 231.26/42.49    (51)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.26/42.49          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.26/42.49    (52)  op(e3, e3) = e3
% 231.26/42.49    (53)   ~ (all_53_8 = all_6_2)
% 231.26/42.49    (54)  all_55_2 = all_53_8
% 231.26/42.49    (55)   ~ (all_53_4 = all_53_7)
% 231.26/42.49    (56)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 231.26/42.49    (57)   ~ (all_53_7 = e0)
% 231.26/42.49    (58)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.26/42.49          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.26/42.49            e1)
% 231.26/42.49    (59)  all_57_12 = e1
% 231.26/42.49    (60)   ~ (all_53_4 = all_53_8)
% 231.26/42.49    (61)  all_55_6 = all_53_9
% 231.26/42.49    (62)  op(e3, e2) = all_53_4
% 231.26/42.49    (63)   ~ (e2 = e0)
% 231.26/42.49    (64)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 231.26/42.49            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 231.26/42.49            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 231.26/42.49            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 231.26/42.49              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 231.26/42.49            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 231.26/42.49            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 231.26/42.49              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 231.26/42.49              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 231.26/42.49            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 231.26/42.49            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 231.26/42.49            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 231.26/42.49              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 231.26/42.49              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 231.26/42.49            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 231.26/42.49              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 231.26/42.49            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 231.26/42.49            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 231.26/42.49              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 231.26/42.49              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 231.26/42.49            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 231.26/42.49            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 231.26/42.49    (65)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 231.26/42.49          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.26/42.49    (66)   ~ (all_53_2 = all_53_14)
% 231.26/42.49    (67)   ~ (e1 = e0)
% 231.26/42.49    (68)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 231.26/42.49            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 231.26/42.49              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 231.26/42.49    (69)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.26/42.49          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.26/42.49    (70)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.26/42.49          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.26/42.49    (71)   ~ (all_10_2 = e1)
% 231.26/42.49    (72)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 231.26/42.49    (73)  op(e0, e0) = e0
% 231.26/42.49    (74)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.26/42.49          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 231.26/42.49            e3)
% 231.26/42.49    (75)   ~ (all_53_4 = all_53_6)
% 231.26/42.49    (76)  op(e0, e2) = all_53_7
% 231.26/42.49    (77)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.26/42.49          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.26/42.49            e2)
% 231.26/42.49    (78)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.26/42.49              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.26/42.49                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.26/42.49                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.26/42.49    (79)  all_55_10 = all_6_2
% 231.26/42.49    (80)   ~ (all_53_6 = all_6_2)
% 231.26/42.49    (81)  all_55_13 = all_53_7
% 231.26/42.49    (82)  op(e2, e0) = all_53_13
% 231.26/42.49    (83)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.26/42.49          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.26/42.49    (84)  all_38_2 = all_6_2
% 231.26/42.49    (85)  all_55_11 = all_53_14
% 231.26/42.49    (86)  all_55_3 = all_53_12
% 231.26/42.49    (87)   ~ (all_53_12 = e3)
% 231.26/42.49    (88)  all_57_0 = e3
% 231.26/42.49    (89)  op(e1, e3) = all_53_2
% 231.26/42.49    (90)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 231.26/42.49            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 231.26/42.49              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 231.26/42.49    (91)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.26/42.49          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.26/42.49    (92)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 231.26/42.49          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 231.26/42.49    (93)   ~ (all_53_12 = all_10_2)
% 231.26/42.49    (94)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 231.26/42.49          (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 231.26/42.49    (95)   ~ (all_53_13 = all_53_14)
% 231.26/42.49    (96)   ~ (e2 = e1)
% 231.26/42.49    (97)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.26/42.49          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.26/42.49    (98)  op(e2, e1) = all_53_9
% 231.26/42.49    (99)  op(e1, e2) = all_53_6
% 231.26/42.49    (100)   ~ (all_53_2 = all_53_6)
% 231.26/42.49    (101)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.26/42.49           (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.26/42.49    (102)  all_24_2 = all_6_2
% 231.26/42.49    (103)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.26/42.49           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.26/42.49    (104)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.26/42.49           (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.26/42.49    (105)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.26/42.49           | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.26/42.49             e1)
% 231.26/42.49    (106)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 231.26/42.49           (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 231.26/42.49    (107)   ~ (all_53_12 = all_53_14)
% 231.26/42.49    (108)  all_55_14 = all_53_11
% 231.26/42.49    (109)  op(e3, e1) = all_53_8
% 231.26/42.49    (110)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.26/42.49           (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.26/42.49    (111)   ~ (all_53_4 = e3)
% 231.26/42.49    (112)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 231.26/42.49           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 231.26/42.49    (113)  op(e3, e0) = all_53_12
% 231.26/42.49  
% 231.26/42.49  Begin of proof
% 231.26/42.49  | 
% 231.26/42.49  | BETA: splitting (104) gives:
% 231.26/42.49  | 
% 231.26/42.49  | Case 1:
% 231.26/42.49  | | 
% 231.26/42.49  | |   (114)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) =
% 231.26/42.49  | |            e0)
% 231.26/42.49  | | 
% 231.26/42.49  | | REF_CLOSE: (10), (15), (17), (31), (33), (37), (43), (45), (50), (63), (65),
% 231.26/42.49  | |            (67), (83), (87), (91), (96), (113), (114) are inconsistent by
% 231.26/42.49  | |            sub-proof #1402.
% 231.26/42.49  | | 
% 231.26/42.49  | Case 2:
% 231.26/42.49  | | 
% 231.26/42.49  | |   (115)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) =
% 231.26/42.49  | |            e0)
% 231.26/42.49  | | 
% 231.26/42.49  | | BETA: splitting (115) gives:
% 231.26/42.49  | | 
% 231.26/42.49  | | Case 1:
% 231.26/42.49  | | | 
% 231.26/42.49  | | |   (116)  all_57_6 = e0 & op(e1, e3) = e0
% 231.26/42.49  | | | 
% 231.26/42.49  | | | ALPHA: (116) implies:
% 231.26/42.49  | | |   (117)  all_57_6 = e0
% 231.26/42.49  | | |   (118)  op(e1, e3) = e0
% 231.26/42.49  | | | 
% 231.26/42.50  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 231.26/42.50  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 231.26/42.50  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (32), (33),
% 231.26/42.50  | | |            (34), (35), (36), (37), (38), (39), (40), (41), (42), (43),
% 231.26/42.50  | | |            (44), (46), (47), (48), (49), (51), (52), (53), (54), (55),
% 231.26/42.50  | | |            (56), (57), (58), (60), (61), (62), (63), (64), (65), (66),
% 231.26/42.50  | | |            (67), (68), (69), (70), (71), (72), (73), (74), (75), (76),
% 231.26/42.50  | | |            (77), (78), (79), (80), (81), (82), (83), (84), (85), (86),
% 231.26/42.50  | | |            (87), (88), (89), (90), (91), (92), (93), (94), (95), (96),
% 231.26/42.50  | | |            (97), (98), (99), (100), (101), (102), (103), (104), (105),
% 231.26/42.50  | | |            (106), (107), (108), (109), (110), (111), (112), (113), (117),
% 231.26/42.50  | | |            (118) are inconsistent by sub-proof #1410.
% 231.26/42.50  | | | 
% 231.26/42.50  | | Case 2:
% 231.26/42.50  | | | 
% 231.26/42.50  | | |   (119)  all_57_12 = e0 & op(e0, e3) = e0
% 231.26/42.50  | | | 
% 231.26/42.50  | | | REF_CLOSE: (15), (17), (27), (31), (33), (37), (45), (52), (59), (63),
% 231.26/42.50  | | |            (67), (96), (119) are inconsistent by sub-proof #1401.
% 231.26/42.50  | | | 
% 231.26/42.50  | | End of split
% 231.26/42.50  | | 
% 231.26/42.50  | End of split
% 231.26/42.50  | 
% 231.26/42.50  End of proof
% 231.26/42.50  
% 231.26/42.50  Sub-proof #1401 shows that the following formulas are inconsistent:
% 231.26/42.50  ----------------------------------------------------------------
% 231.26/42.50    (1)   ~ (e3 = e1)
% 231.26/42.50    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.26/42.50           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.26/42.50    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.26/42.50         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.26/42.50    (4)  all_57_9 = e1
% 231.26/42.50    (5)  all_57_4 = e0
% 231.26/42.50    (6)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.26/42.50         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.26/42.50    (7)   ~ (e3 = e2)
% 231.26/42.50    (8)  op(e3, e3) = e3
% 231.26/42.50    (9)  all_57_12 = e1
% 231.26/42.50    (10)   ~ (e2 = e0)
% 231.26/42.50    (11)   ~ (e1 = e0)
% 231.26/42.50    (12)   ~ (e2 = e1)
% 231.26/42.50    (13)  all_57_12 = e0 & op(e0, e3) = e0
% 231.26/42.50  
% 231.26/42.50  Begin of proof
% 231.26/42.50  | 
% 231.26/42.50  | ALPHA: (13) implies:
% 231.26/42.50  |   (14)  all_57_12 = e0
% 231.26/42.50  | 
% 231.26/42.50  | COMBINE_EQS: (9), (14) imply:
% 231.26/42.50  |   (15)  e1 = e0
% 231.26/42.50  | 
% 231.26/42.50  | COMBINE_EQS: (4), (15) imply:
% 231.26/42.50  |   (16)  all_57_9 = e0
% 231.26/42.50  | 
% 231.26/42.50  | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (10), (11), (12), (16) are
% 231.26/42.50  |            inconsistent by sub-proof #2436.
% 231.26/42.50  | 
% 231.26/42.50  End of proof
% 231.33/42.50  
% 231.33/42.50  Sub-proof #1402 shows that the following formulas are inconsistent:
% 231.33/42.50  ----------------------------------------------------------------
% 231.33/42.50    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.33/42.50         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.33/42.50    (2)   ~ (e3 = e1)
% 231.33/42.50    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.33/42.50           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.33/42.50    (4)  all_57_9 = e1
% 231.33/42.50    (5)  all_57_4 = e0
% 231.33/42.50    (6)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.33/42.50         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.33/42.50    (7)  all_57_3 = e0
% 231.33/42.50    (8)   ~ (e3 = e2)
% 231.33/42.50    (9)   ~ (e3 = e0)
% 231.33/42.50    (10)   ~ (e2 = e0)
% 231.33/42.50    (11)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 231.33/42.50          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.33/42.50    (12)   ~ (e1 = e0)
% 231.33/42.50    (13)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.33/42.50          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.33/42.50    (14)   ~ (all_53_12 = e3)
% 231.33/42.50    (15)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.33/42.50          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.33/42.50    (16)   ~ (e2 = e1)
% 231.33/42.50    (17)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0)
% 231.33/42.50    (18)  op(e3, e0) = all_53_12
% 231.33/42.50  
% 231.33/42.50  Begin of proof
% 231.33/42.50  | 
% 231.33/42.50  | BETA: splitting (17) gives:
% 231.33/42.50  | 
% 231.33/42.50  | Case 1:
% 231.33/42.50  | | 
% 231.33/42.50  | |   (19)  all_57_0 = e0 & op(e3, e3) = e0
% 231.33/42.50  | | 
% 231.33/42.50  | | ALPHA: (19) implies:
% 231.33/42.50  | |   (20)  op(e3, e3) = e0
% 231.33/42.50  | | 
% 231.33/42.50  | | REF_CLOSE: (3), (4), (5), (6), (8), (9), (10), (11), (14), (16), (18), (20)
% 231.33/42.50  | |            are inconsistent by sub-proof #1403.
% 231.33/42.50  | | 
% 231.33/42.50  | Case 2:
% 231.33/42.50  | | 
% 231.33/42.50  | |   (21)  all_57_2 = e0 & op(e2, e3) = e0
% 231.33/42.50  | | 
% 231.33/42.50  | | ALPHA: (21) implies:
% 231.33/42.50  | |   (22)  all_57_2 = e0
% 231.33/42.50  | | 
% 231.33/42.50  | | REF_CLOSE: (1), (2), (7), (8), (9), (10), (12), (13), (15), (16), (22) are
% 231.33/42.50  | |            inconsistent by sub-proof #2246.
% 231.33/42.50  | | 
% 231.33/42.50  | End of split
% 231.33/42.50  | 
% 231.33/42.50  End of proof
% 231.33/42.50  
% 231.33/42.50  Sub-proof #1403 shows that the following formulas are inconsistent:
% 231.33/42.50  ----------------------------------------------------------------
% 231.33/42.50    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.33/42.50           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.33/42.50    (2)  all_57_9 = e1
% 231.33/42.50    (3)  all_57_4 = e0
% 231.33/42.50    (4)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.33/42.50         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.33/42.50    (5)   ~ (e3 = e2)
% 231.33/42.50    (6)   ~ (e3 = e0)
% 231.33/42.50    (7)  op(e3, e3) = e0
% 231.33/42.50    (8)   ~ (e2 = e0)
% 231.33/42.50    (9)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 231.33/42.50         (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.33/42.50    (10)   ~ (all_53_12 = e3)
% 231.33/42.50    (11)   ~ (e2 = e1)
% 231.33/42.50    (12)  op(e3, e0) = all_53_12
% 231.33/42.50  
% 231.33/42.50  Begin of proof
% 231.33/42.50  | 
% 231.33/42.50  | BETA: splitting (4) gives:
% 231.33/42.50  | 
% 231.33/42.50  | Case 1:
% 231.33/42.50  | | 
% 231.33/42.50  | |   (13)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) =
% 231.33/42.50  | |           e2)
% 231.33/42.50  | | 
% 231.33/42.50  | | BETA: splitting (13) gives:
% 231.33/42.50  | | 
% 231.33/42.50  | | Case 1:
% 231.33/42.50  | | | 
% 231.33/42.50  | | |   (14)  all_57_0 = e2 & op(e3, e3) = e2
% 231.33/42.50  | | | 
% 231.33/42.50  | | | ALPHA: (14) implies:
% 231.33/42.50  | | |   (15)  op(e3, e3) = e2
% 231.33/42.50  | | | 
% 231.33/42.50  | | | REF_CLOSE: (1), (7), (8), (15) are inconsistent by sub-proof #2403.
% 231.33/42.50  | | | 
% 231.33/42.50  | | Case 2:
% 231.33/42.50  | | | 
% 231.33/42.50  | | |   (16)  all_57_1 = e2 & op(e3, e2) = e2
% 231.33/42.50  | | | 
% 231.33/42.50  | | | ALPHA: (16) implies:
% 231.33/42.50  | | |   (17)  all_57_1 = e2
% 231.33/42.50  | | | 
% 231.33/42.50  | | | REF_CLOSE: (1), (3), (5), (6), (7), (9), (10), (12), (17) are inconsistent
% 231.33/42.50  | | |            by sub-proof #1405.
% 231.33/42.50  | | | 
% 231.33/42.50  | | End of split
% 231.33/42.50  | | 
% 231.33/42.50  | Case 2:
% 231.33/42.50  | | 
% 231.33/42.50  | |   (18)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) =
% 231.33/42.50  | |           e2)
% 231.33/42.50  | | 
% 231.33/42.50  | | BETA: splitting (18) gives:
% 231.33/42.50  | | 
% 231.33/42.50  | | Case 1:
% 231.33/42.50  | | | 
% 231.33/42.50  | | |   (19)  all_57_4 = e2 & op(e3, e1) = e2
% 231.33/42.50  | | | 
% 231.33/42.50  | | | REF_CLOSE: (3), (8), (19) are inconsistent by sub-proof #1404.
% 231.33/42.50  | | | 
% 231.33/42.50  | | Case 2:
% 231.33/42.50  | | | 
% 231.33/42.50  | | |   (20)  all_57_9 = e2 & op(e3, e0) = e2
% 231.33/42.50  | | | 
% 231.33/42.50  | | | REF_CLOSE: (2), (11), (20) are inconsistent by sub-proof #2481.
% 231.33/42.50  | | | 
% 231.33/42.50  | | End of split
% 231.33/42.50  | | 
% 231.33/42.50  | End of split
% 231.33/42.50  | 
% 231.33/42.50  End of proof
% 231.33/42.50  
% 231.33/42.50  Sub-proof #1404 shows that the following formulas are inconsistent:
% 231.33/42.50  ----------------------------------------------------------------
% 231.33/42.50    (1)  all_57_4 = e2 & op(e3, e1) = e2
% 231.33/42.50    (2)  all_57_4 = e0
% 231.33/42.50    (3)   ~ (e2 = e0)
% 231.33/42.50  
% 231.33/42.50  Begin of proof
% 231.33/42.50  | 
% 231.33/42.50  | ALPHA: (1) implies:
% 231.33/42.50  |   (4)  all_57_4 = e2
% 231.33/42.50  | 
% 231.33/42.50  | COMBINE_EQS: (2), (4) imply:
% 231.33/42.50  |   (5)  e2 = e0
% 231.33/42.50  | 
% 231.33/42.50  | REDUCE: (3), (5) imply:
% 231.33/42.50  |   (6)  $false
% 231.33/42.50  | 
% 231.33/42.50  | CLOSE: (6) is inconsistent.
% 231.33/42.50  | 
% 231.33/42.50  End of proof
% 231.33/42.50  
% 231.33/42.50  Sub-proof #1405 shows that the following formulas are inconsistent:
% 231.33/42.50  ----------------------------------------------------------------
% 231.33/42.50    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.33/42.50           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.33/42.50    (2)  all_57_4 = e0
% 231.33/42.50    (3)   ~ (e3 = e2)
% 231.33/42.50    (4)   ~ (e3 = e0)
% 231.33/42.50    (5)  all_57_1 = e2
% 231.33/42.50    (6)  op(e3, e3) = e0
% 231.33/42.50    (7)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 231.33/42.50         (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.33/42.50    (8)   ~ (all_53_12 = e3)
% 231.33/42.50    (9)  op(e3, e0) = all_53_12
% 231.33/42.50  
% 231.33/42.50  Begin of proof
% 231.33/42.50  | 
% 231.33/42.50  | BETA: splitting (7) gives:
% 231.33/42.50  | 
% 231.33/42.50  | Case 1:
% 231.33/42.50  | | 
% 231.33/42.50  | |   (10)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) =
% 231.33/42.50  | |           e3)
% 231.33/42.50  | | 
% 231.33/42.50  | | REF_CLOSE: (1), (3), (4), (5), (6), (10) are inconsistent by sub-proof
% 231.33/42.50  | |            #1407.
% 231.33/42.50  | | 
% 231.33/42.50  | Case 2:
% 231.33/42.50  | | 
% 231.33/42.50  | |   (11)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) =
% 231.33/42.50  | |           e3)
% 231.33/42.50  | | 
% 231.33/42.50  | | REF_CLOSE: (1), (2), (4), (8), (9), (11) are inconsistent by sub-proof
% 231.33/42.50  | |            #1406.
% 231.33/42.50  | | 
% 231.33/42.50  | End of split
% 231.33/42.50  | 
% 231.33/42.50  End of proof
% 231.33/42.50  
% 231.33/42.50  Sub-proof #1406 shows that the following formulas are inconsistent:
% 231.33/42.50  ----------------------------------------------------------------
% 231.33/42.50    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.33/42.50           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.33/42.50    (2)  all_57_4 = e0
% 231.33/42.50    (3)   ~ (e3 = e0)
% 231.33/42.50    (4)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.33/42.50    (5)   ~ (all_53_12 = e3)
% 231.33/42.50    (6)  op(e3, e0) = all_53_12
% 231.33/42.50  
% 231.33/42.50  Begin of proof
% 231.33/42.50  | 
% 231.33/42.50  | BETA: splitting (4) gives:
% 231.33/42.50  | 
% 231.33/42.50  | Case 1:
% 231.33/42.50  | | 
% 231.33/42.50  | |   (7)  all_57_4 = e3 & op(e3, e1) = e3
% 231.33/42.50  | | 
% 231.33/42.50  | | ALPHA: (7) implies:
% 231.33/42.50  | |   (8)  all_57_4 = e3
% 231.33/42.50  | | 
% 231.33/42.50  | | REF_CLOSE: (2), (3), (8) are inconsistent by sub-proof #2372.
% 231.33/42.50  | | 
% 231.33/42.50  | Case 2:
% 231.33/42.50  | | 
% 231.33/42.50  | |   (9)  all_57_9 = e3 & op(e3, e0) = e3
% 231.33/42.50  | | 
% 231.33/42.50  | | ALPHA: (9) implies:
% 231.33/42.50  | |   (10)  op(e3, e0) = e3
% 231.33/42.50  | | 
% 231.33/42.50  | | REF_CLOSE: (1), (5), (6), (10) are inconsistent by sub-proof #2458.
% 231.33/42.50  | | 
% 231.33/42.50  | End of split
% 231.33/42.50  | 
% 231.33/42.50  End of proof
% 231.33/42.50  
% 231.33/42.50  Sub-proof #1407 shows that the following formulas are inconsistent:
% 231.33/42.50  ----------------------------------------------------------------
% 231.33/42.50    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.33/42.50           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.33/42.50    (2)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3)
% 231.33/42.50    (3)   ~ (e3 = e2)
% 231.33/42.50    (4)   ~ (e3 = e0)
% 231.33/42.50    (5)  all_57_1 = e2
% 231.33/42.50    (6)  op(e3, e3) = e0
% 231.33/42.50  
% 231.33/42.50  Begin of proof
% 231.33/42.50  | 
% 231.33/42.50  | BETA: splitting (2) gives:
% 231.33/42.50  | 
% 231.33/42.50  | Case 1:
% 231.33/42.50  | | 
% 231.33/42.50  | |   (7)  all_57_0 = e3 & op(e3, e3) = e3
% 231.33/42.50  | | 
% 231.33/42.50  | | ALPHA: (7) implies:
% 231.33/42.50  | |   (8)  op(e3, e3) = e3
% 231.33/42.50  | | 
% 231.33/42.50  | | REF_CLOSE: (1), (4), (6), (8) are inconsistent by sub-proof #2494.
% 231.33/42.50  | | 
% 231.33/42.50  | Case 2:
% 231.33/42.50  | | 
% 231.33/42.50  | |   (9)  all_57_1 = e3 & op(e3, e2) = e3
% 231.33/42.50  | | 
% 231.33/42.50  | | REF_CLOSE: (3), (5), (9) are inconsistent by sub-proof #1664.
% 231.33/42.50  | | 
% 231.33/42.50  | End of split
% 231.33/42.50  | 
% 231.33/42.50  End of proof
% 231.33/42.50  
% 231.33/42.50  Sub-proof #1408 shows that the following formulas are inconsistent:
% 231.33/42.50  ----------------------------------------------------------------
% 231.33/42.50    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 231.33/42.50    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 231.33/42.50    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.33/42.50         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.33/42.50    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.33/42.50         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.33/42.50    (5)  op(e2, e1) = e3
% 231.33/42.50    (6)   ~ (all_53_8 = all_53_12)
% 231.33/42.50    (7)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.33/42.50         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.33/42.50    (8)   ~ (e3 = e1)
% 231.33/42.50    (9)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 231.33/42.50         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.33/42.50    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.33/42.50            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.33/42.50    (11)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.33/42.50          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.33/42.50    (12)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 231.33/42.50            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 231.33/42.50              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 231.33/42.50    (13)   ~ (all_6_2 = e3)
% 231.33/42.50    (14)  op(e1, e1) = all_6_2
% 231.33/42.50    (15)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 231.33/42.50    (16)   ~ (all_53_9 = e0)
% 231.33/42.50    (17)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.33/42.50          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.33/42.50    (18)   ~ (all_53_4 = all_53_12)
% 231.33/42.50    (19)   ~ (all_53_8 = all_53_9)
% 231.33/42.50    (20)  all_42_2 = all_6_2
% 231.33/42.50    (21)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.33/42.50          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.33/42.50    (22)  op(e2, e2) = e0
% 231.33/42.50    (23)   ~ (all_53_9 = all_6_2)
% 231.33/42.50    (24)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.33/42.50          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.33/42.50    (25)  all_57_3 = e0
% 231.33/42.50    (26)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.33/42.50          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.33/42.50    (27)   ~ (e3 = e2)
% 231.33/42.50    (28)  all_55_1 = all_53_4
% 231.33/42.50    (29)   ~ (e3 = e0)
% 231.33/42.50    (30)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.33/42.50          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.33/42.50    (31)  op(e3, e3) = e3
% 231.33/42.50    (32)   ~ (all_53_8 = all_6_2)
% 231.33/42.50    (33)  all_55_2 = all_53_8
% 231.33/42.50    (34)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 231.33/42.50    (35)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.33/42.50          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.33/42.50            e1)
% 231.33/42.50    (36)  all_57_5 = e3
% 231.33/42.50    (37)  all_57_11 = e0
% 231.33/42.50    (38)   ~ (all_53_4 = all_53_8)
% 231.33/42.50    (39)  op(e3, e2) = all_53_4
% 231.33/42.50    (40)   ~ (e2 = e0)
% 231.33/42.50    (41)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 231.33/42.50            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 231.33/42.50            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 231.33/42.50            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 231.33/42.50              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 231.33/42.50            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 231.33/42.50            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 231.33/42.50              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 231.33/42.50              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 231.33/42.50            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 231.33/42.50            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 231.33/42.50            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 231.33/42.50              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 231.33/42.50              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 231.33/42.50            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 231.33/42.50              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 231.33/42.50            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 231.33/42.50            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 231.33/42.50              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 231.33/42.50              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 231.33/42.50            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 231.33/42.50            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 231.33/42.50    (42)   ~ (e1 = e0)
% 231.33/42.50    (43)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 231.33/42.50            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 231.33/42.50              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 231.33/42.50    (44)   ~ (all_53_4 = e0)
% 231.33/42.50    (45)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.33/42.50          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.33/42.50    (46)  all_57_13 = e3
% 231.33/42.50    (47)   ~ (all_53_4 = all_53_6)
% 231.33/42.50    (48)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.33/42.50          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.33/42.50            e2)
% 231.33/42.50    (49)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.33/42.50              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.33/42.50                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.33/42.50                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.33/42.50    (50)  all_55_10 = all_6_2
% 231.33/42.50    (51)  all_38_2 = all_6_2
% 231.33/42.50    (52)  all_55_3 = all_53_12
% 231.33/42.50    (53)   ~ (all_53_12 = e3)
% 231.33/42.50    (54)  all_57_0 = e3
% 231.33/42.50    (55)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 231.33/42.50            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 231.33/42.50              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 231.33/42.50    (56)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.33/42.50          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.33/42.50    (57)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 231.33/42.50          (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 231.33/42.50    (58)   ~ (e2 = e1)
% 231.33/42.50    (59)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.33/42.50          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.33/42.50    (60)  op(e2, e1) = all_53_9
% 231.33/42.50    (61)  op(e1, e2) = all_53_6
% 231.33/42.50    (62)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.33/42.50          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.33/42.50    (63)  all_24_2 = all_6_2
% 231.33/42.50    (64)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.33/42.50          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.33/42.50    (65)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.33/42.50          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.33/42.50    (66)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.33/42.50          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.33/42.50    (67)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 231.33/42.50          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 231.33/42.50    (68)  op(e3, e1) = all_53_8
% 231.33/42.50    (69)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.33/42.50          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.33/42.50    (70)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 231.33/42.50          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 231.33/42.50    (71)  op(e3, e0) = all_53_12
% 231.33/42.50  
% 231.33/42.50  Begin of proof
% 231.33/42.50  | 
% 231.33/42.50  | BETA: splitting (11) gives:
% 231.33/42.50  | 
% 231.33/42.50  | Case 1:
% 231.33/42.50  | | 
% 231.33/42.50  | |   (72)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 231.33/42.50  | |           e3)
% 231.33/42.50  | | 
% 231.33/42.50  | | BETA: splitting (72) gives:
% 231.33/42.50  | | 
% 231.33/42.50  | | Case 1:
% 231.33/42.50  | | | 
% 231.33/42.50  | | |   (73)  all_57_6 = e3 & op(e1, e3) = e3
% 231.33/42.50  | | | 
% 231.33/42.50  | | | ALPHA: (73) implies:
% 231.33/42.50  | | |   (74)  all_57_6 = e3
% 231.33/42.50  | | | 
% 231.33/42.50  | | | REF_CLOSE: (3), (4), (8), (10), (25), (27), (29), (31), (36), (40), (42),
% 231.33/42.50  | | |            (56), (58), (62), (65), (74) are inconsistent by sub-proof
% 231.33/42.50  | | |            #1781.
% 231.33/42.50  | | | 
% 231.33/42.50  | | Case 2:
% 231.33/42.50  | | | 
% 231.33/42.50  | | |   (75)  all_57_7 = e3 & op(e1, e2) = e3
% 231.33/42.50  | | | 
% 231.33/42.50  | | | ALPHA: (75) implies:
% 231.33/42.50  | | |   (76)  all_57_7 = e3
% 231.33/42.50  | | | 
% 231.33/42.50  | | | BETA: splitting (57) gives:
% 231.33/42.50  | | | 
% 231.33/42.50  | | | Case 1:
% 231.33/42.50  | | | | 
% 231.33/42.50  | | | |   (77)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0)
% 231.33/42.50  | | | |           = e3)
% 231.33/42.50  | | | | 
% 231.33/42.50  | | | | REF_CLOSE: (3), (8), (10), (25), (27), (36), (40), (42), (53), (56),
% 231.33/42.50  | | | |            (58), (71), (77) are inconsistent by sub-proof #1409.
% 231.33/42.50  | | | | 
% 231.33/42.50  | | | Case 2:
% 231.33/42.50  | | | | 
% 231.33/42.50  | | | |   (78)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0,
% 231.33/42.50  | | | |             e0) = e3)
% 231.33/42.50  | | | | 
% 231.33/42.50  | | | | BETA: splitting (78) gives:
% 231.33/42.50  | | | | 
% 231.33/42.50  | | | | Case 1:
% 231.33/42.50  | | | | | 
% 231.33/42.50  | | | | |   (79)  all_57_11 = e3 & op(e1, e0) = e3
% 231.33/42.50  | | | | | 
% 231.33/42.50  | | | | | ALPHA: (79) implies:
% 231.33/42.50  | | | | |   (80)  all_57_11 = e3
% 231.33/42.50  | | | | | 
% 231.33/42.50  | | | | | COMBINE_EQS: (37), (80) imply:
% 231.33/42.50  | | | | |   (81)  e3 = e0
% 231.33/42.50  | | | | | 
% 231.33/42.50  | | | | | SIMP: (81) implies:
% 231.33/42.50  | | | | |   (82)  e3 = e0
% 231.33/42.50  | | | | | 
% 231.33/42.50  | | | | | COMBINE_EQS: (76), (82) imply:
% 231.33/42.50  | | | | |   (83)  all_57_7 = e0
% 231.33/42.50  | | | | | 
% 231.33/42.50  | | | | | REF_CLOSE: (7), (8), (10), (22), (25), (27), (29), (40), (42), (45),
% 231.33/42.50  | | | | |            (46), (58), (69), (83) are inconsistent by sub-proof #2199.
% 231.33/42.50  | | | | | 
% 231.33/42.50  | | | | Case 2:
% 231.33/42.50  | | | | | 
% 231.33/42.50  | | | | |   (84)  all_57_15 = e3 & op(e0, e0) = e3
% 231.33/42.50  | | | | | 
% 231.33/42.50  | | | | | ALPHA: (84) implies:
% 231.33/42.50  | | | | |   (85)  all_57_15 = e3
% 231.33/42.50  | | | | |   (86)  op(e0, e0) = e3
% 231.33/42.50  | | | | | 
% 231.33/42.50  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 231.33/42.50  | | | | |            (12), (13), (14), (15), (16), (17), (18), (19), (20), (21),
% 231.33/42.50  | | | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 231.33/42.50  | | | | |            (33), (34), (35), (36), (38), (39), (40), (41), (42), (43),
% 231.33/42.50  | | | | |            (44), (47), (48), (49), (50), (51), (52), (53), (54), (55),
% 231.33/42.50  | | | | |            (56), (58), (59), (60), (61), (62), (63), (64), (65), (66),
% 231.33/42.50  | | | | |            (67), (68), (69), (70), (71), (85), (86) are inconsistent
% 231.33/42.50  | | | | |            by sub-proof #1440.
% 231.33/42.50  | | | | | 
% 231.33/42.50  | | | | End of split
% 231.33/42.50  | | | | 
% 231.33/42.50  | | | End of split
% 231.33/42.50  | | | 
% 231.33/42.50  | | End of split
% 231.33/42.50  | | 
% 231.33/42.50  | Case 2:
% 231.33/42.50  | | 
% 231.33/42.50  | |   (87)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 231.33/42.50  | |           e3)
% 231.33/42.50  | | 
% 231.33/42.50  | | REF_CLOSE: (10), (13), (14), (29), (37), (87) are inconsistent by sub-proof
% 231.33/42.50  | |            #1594.
% 231.33/42.50  | | 
% 231.33/42.50  | End of split
% 231.33/42.50  | 
% 231.33/42.50  End of proof
% 231.33/42.50  
% 231.33/42.50  Sub-proof #1409 shows that the following formulas are inconsistent:
% 231.33/42.50  ----------------------------------------------------------------
% 231.33/42.50    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.33/42.50         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.33/42.50    (2)   ~ (e3 = e1)
% 231.33/42.50    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.33/42.50           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.33/42.50    (4)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.33/42.50    (5)  all_57_3 = e0
% 231.33/42.50    (6)   ~ (e3 = e2)
% 231.33/42.50    (7)  all_57_5 = e3
% 231.33/42.50    (8)   ~ (e2 = e0)
% 231.33/42.50    (9)   ~ (e1 = e0)
% 231.33/42.50    (10)   ~ (all_53_12 = e3)
% 231.33/42.50    (11)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.33/42.50          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.33/42.50    (12)   ~ (e2 = e1)
% 231.33/42.50    (13)  op(e3, e0) = all_53_12
% 231.33/42.50  
% 231.33/42.50  Begin of proof
% 231.33/42.50  | 
% 231.33/42.50  | BETA: splitting (4) gives:
% 231.33/42.50  | 
% 231.33/42.50  | Case 1:
% 231.33/42.50  | | 
% 231.33/42.50  | |   (14)  all_57_9 = e3 & op(e3, e0) = e3
% 231.33/42.50  | | 
% 231.33/42.50  | | ALPHA: (14) implies:
% 231.33/42.50  | |   (15)  op(e3, e0) = e3
% 231.33/42.50  | | 
% 231.33/42.50  | | REF_CLOSE: (3), (10), (13), (15) are inconsistent by sub-proof #2458.
% 231.33/42.50  | | 
% 231.33/42.50  | Case 2:
% 231.33/42.50  | | 
% 231.33/42.50  | |   (16)  all_57_10 = e3 & op(e2, e0) = e3
% 231.33/42.50  | | 
% 231.33/42.50  | | ALPHA: (16) implies:
% 231.33/42.50  | |   (17)  all_57_10 = e3
% 231.33/42.50  | | 
% 231.33/42.50  | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (9), (11), (12), (17) are
% 231.33/42.50  | |            inconsistent by sub-proof #1693.
% 231.33/42.50  | | 
% 231.33/42.50  | End of split
% 231.33/42.50  | 
% 231.33/42.50  End of proof
% 231.33/42.50  
% 231.33/42.50  Sub-proof #1410 shows that the following formulas are inconsistent:
% 231.33/42.50  ----------------------------------------------------------------
% 231.33/42.50    (1)   ~ (all_10_2 = e2)
% 231.33/42.50    (2)  all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 231.33/42.50    (3)  op(e3, e3) = all_10_2
% 231.33/42.50    (4)  op(e0, e1) = all_53_11
% 231.33/42.50    (5)  op(e1, e3) = e0
% 231.33/42.50    (6)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 231.33/42.50    (7)   ~ (all_53_6 = all_53_14)
% 231.33/42.50    (8)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 231.33/42.50    (9)  op(e3, e1) = e0
% 231.33/42.50    (10)  all_57_15 = e0
% 231.33/42.50    (11)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.33/42.50          (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.33/42.50    (12)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.33/42.50          (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.33/42.50    (13)   ~ (all_53_8 = all_53_12)
% 231.33/42.50    (14)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.33/42.50          (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.33/42.50    (15)   ~ (all_53_8 = all_53_11)
% 231.33/42.50    (16)   ~ (e3 = e1)
% 231.33/42.50    (17)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 231.33/42.50          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.33/42.50    (18)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.33/42.50            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.33/42.50    (19)  all_55_0 = all_10_2
% 231.33/42.50    (20)   ~ (all_10_2 = e0)
% 231.33/42.50    (21)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.33/42.50          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.33/42.51    (22)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 231.33/42.51            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 231.33/42.51              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 231.33/42.51    (23)   ~ (all_6_2 = e3)
% 231.33/42.51    (24)  op(e1, e1) = all_6_2
% 231.33/42.51    (25)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 231.33/42.51    (26)  all_55_0 = e3 | all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 231.33/42.51    (27)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 231.33/42.51    (28)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.33/42.51          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.33/42.51    (29)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 231.33/42.51    (30)  all_55_9 = all_53_6
% 231.33/42.51    (31)   ~ (all_53_11 = all_6_2)
% 231.33/42.51    (32)   ~ (all_53_4 = all_53_12)
% 231.33/42.51    (33)  all_57_4 = e0
% 231.33/42.51    (34)   ~ (all_53_8 = e3)
% 231.33/42.51    (35)   ~ (all_53_8 = all_53_9)
% 231.33/42.51    (36)  all_42_2 = all_6_2
% 231.33/42.51    (37)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.33/42.51          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.33/42.51    (38)  op(e2, e2) = e0
% 231.33/42.51    (39)   ~ (all_53_9 = all_53_11)
% 231.33/42.51    (40)   ~ (all_53_9 = all_6_2)
% 231.33/42.51    (41)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.33/42.51          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.33/42.51    (42)   ~ (all_53_14 = all_6_2)
% 231.33/42.51    (43)  all_57_3 = e0
% 231.33/42.51    (44)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.33/42.51          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.33/42.51    (45)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 231.33/42.51    (46)  all_55_1 = all_53_4
% 231.33/42.51    (47)  op(e1, e0) = all_53_14
% 231.33/42.51    (48)   ~ (all_53_6 = all_53_7)
% 231.33/42.51    (49)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.33/42.51          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.33/42.51    (50)  op(e3, e3) = e3
% 231.33/42.51    (51)  all_57_6 = e0
% 231.33/42.51    (52)   ~ (all_53_8 = all_6_2)
% 231.33/42.51    (53)  all_55_2 = all_53_8
% 231.33/42.51    (54)   ~ (all_53_4 = all_53_7)
% 231.33/42.51    (55)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 231.33/42.51    (56)   ~ (all_53_7 = e0)
% 231.33/42.51    (57)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.33/42.51          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.33/42.51            e1)
% 231.33/42.51    (58)   ~ (all_53_4 = all_53_8)
% 231.33/42.51    (59)  all_55_6 = all_53_9
% 231.33/42.51    (60)  op(e3, e2) = all_53_4
% 231.33/42.51    (61)   ~ (e2 = e0)
% 231.33/42.51    (62)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 231.33/42.51            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 231.33/42.51            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 231.33/42.51            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 231.33/42.51              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 231.33/42.51            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 231.33/42.51            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 231.33/42.51              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 231.33/42.51              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 231.33/42.51            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 231.33/42.51            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 231.33/42.51            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 231.33/42.51              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 231.33/42.51              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 231.33/42.51            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 231.33/42.51              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 231.33/42.51            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 231.33/42.51            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 231.33/42.51              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 231.33/42.51              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 231.33/42.51            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 231.33/42.51            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 231.33/42.51    (63)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 231.33/42.51          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.33/42.51    (64)   ~ (all_53_2 = all_53_14)
% 231.33/42.51    (65)   ~ (e1 = e0)
% 231.33/42.51    (66)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 231.33/42.51            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 231.33/42.51              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 231.33/42.51    (67)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.33/42.51          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.33/42.51    (68)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.33/42.51          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.33/42.51    (69)   ~ (all_10_2 = e1)
% 231.33/42.51    (70)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 231.33/42.51    (71)  op(e0, e0) = e0
% 231.33/42.51    (72)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.33/42.51          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 231.33/42.51            e3)
% 231.33/42.51    (73)   ~ (all_53_4 = all_53_6)
% 231.33/42.51    (74)  op(e0, e2) = all_53_7
% 231.33/42.51    (75)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.33/42.51          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.33/42.51            e2)
% 231.33/42.51    (76)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.33/42.51              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.33/42.51                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.33/42.51                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.33/42.51    (77)  all_55_10 = all_6_2
% 231.33/42.51    (78)   ~ (all_53_6 = all_6_2)
% 231.33/42.51    (79)  all_55_13 = all_53_7
% 231.33/42.51    (80)  op(e2, e0) = all_53_13
% 231.33/42.51    (81)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.33/42.51          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.33/42.51    (82)  all_38_2 = all_6_2
% 231.33/42.51    (83)  all_55_11 = all_53_14
% 231.33/42.51    (84)  all_55_3 = all_53_12
% 231.33/42.51    (85)   ~ (all_53_12 = e3)
% 231.33/42.51    (86)  all_57_0 = e3
% 231.33/42.51    (87)  op(e1, e3) = all_53_2
% 231.33/42.51    (88)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 231.33/42.51            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 231.33/42.51              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 231.33/42.51    (89)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.33/42.51          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.33/42.51    (90)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 231.33/42.51          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 231.33/42.51    (91)   ~ (all_53_12 = all_10_2)
% 231.33/42.51    (92)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 231.33/42.51          (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 231.33/42.51    (93)   ~ (all_53_13 = all_53_14)
% 231.33/42.51    (94)   ~ (e2 = e1)
% 231.33/42.51    (95)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.33/42.51          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.33/42.51    (96)  op(e2, e1) = all_53_9
% 231.33/42.51    (97)  op(e1, e2) = all_53_6
% 231.33/42.51    (98)   ~ (all_53_2 = all_53_6)
% 231.33/42.51    (99)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.33/42.51          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.33/42.51    (100)  all_24_2 = all_6_2
% 231.33/42.51    (101)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.33/42.51           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.33/42.51    (102)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.33/42.51           (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.33/42.51    (103)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.33/42.51           | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.33/42.51             e1)
% 231.33/42.51    (104)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 231.33/42.51           (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 231.33/42.51    (105)   ~ (all_53_12 = all_53_14)
% 231.33/42.51    (106)  all_55_14 = all_53_11
% 231.33/42.51    (107)  op(e3, e1) = all_53_8
% 231.33/42.51    (108)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.33/42.51           (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.33/42.51    (109)   ~ (all_53_4 = e3)
% 231.33/42.51    (110)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 231.33/42.51           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 231.33/42.51    (111)  op(e3, e0) = all_53_12
% 231.33/42.51  
% 231.33/42.51  Begin of proof
% 231.33/42.51  | 
% 231.33/42.51  | GROUND_INST: instantiating (18) with all_53_2, e0, e3, e1, simplifying with
% 231.33/42.51  |              (5), (87) gives:
% 231.33/42.51  |   (112)  all_53_2 = e0
% 231.33/42.51  | 
% 231.33/42.51  | GROUND_INST: instantiating (18) with all_53_8, e0, e1, e3, simplifying with
% 231.33/42.51  |              (9), (107) gives:
% 231.33/42.51  |   (113)  all_53_8 = e0
% 231.33/42.51  | 
% 231.33/42.51  | REDUCE: (98), (112) imply:
% 231.33/42.51  |   (114)   ~ (all_53_6 = e0)
% 231.33/42.51  | 
% 231.33/42.51  | SIMP: (114) implies:
% 231.33/42.51  |   (115)   ~ (all_53_6 = e0)
% 231.33/42.51  | 
% 231.33/42.51  | REDUCE: (64), (112) imply:
% 231.33/42.51  |   (116)   ~ (all_53_14 = e0)
% 231.33/42.51  | 
% 231.33/42.51  | SIMP: (116) implies:
% 231.33/42.51  |   (117)   ~ (all_53_14 = e0)
% 231.33/42.51  | 
% 231.33/42.51  | REDUCE: (58), (113) imply:
% 231.33/42.51  |   (118)   ~ (all_53_4 = e0)
% 231.33/42.51  | 
% 231.33/42.51  | REDUCE: (35), (113) imply:
% 231.33/42.51  |   (119)   ~ (all_53_9 = e0)
% 231.33/42.51  | 
% 231.33/42.51  | SIMP: (119) implies:
% 231.33/42.51  |   (120)   ~ (all_53_9 = e0)
% 231.33/42.51  | 
% 231.33/42.51  | REDUCE: (15), (113) imply:
% 231.33/42.51  |   (121)   ~ (all_53_11 = e0)
% 231.33/42.51  | 
% 231.33/42.51  | SIMP: (121) implies:
% 231.33/42.51  |   (122)   ~ (all_53_11 = e0)
% 231.33/42.51  | 
% 231.33/42.51  | REDUCE: (13), (113) imply:
% 231.33/42.51  |   (123)   ~ (all_53_12 = e0)
% 231.33/42.51  | 
% 231.33/42.51  | SIMP: (123) implies:
% 231.33/42.51  |   (124)   ~ (all_53_12 = e0)
% 231.33/42.51  | 
% 231.33/42.51  | REDUCE: (52), (113) imply:
% 231.33/42.51  |   (125)   ~ (all_6_2 = e0)
% 231.33/42.51  | 
% 231.33/42.51  | SIMP: (125) implies:
% 231.33/42.51  |   (126)   ~ (all_6_2 = e0)
% 231.33/42.51  | 
% 231.33/42.51  | REDUCE: (34), (113) imply:
% 231.33/42.51  |   (127)   ~ (e3 = e0)
% 231.33/42.51  | 
% 231.33/42.51  | SIMP: (127) implies:
% 231.33/42.51  |   (128)   ~ (e3 = e0)
% 231.33/42.51  | 
% 231.33/42.51  | BETA: splitting (62) gives:
% 231.33/42.51  | 
% 231.33/42.51  | Case 1:
% 231.33/42.51  | | 
% 231.33/42.51  | |   (129)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 231.33/42.51  | |            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 231.33/42.51  | |            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 231.33/42.51  | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) =
% 231.33/42.51  | |            all_52_5 & op(e3, e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) &
% 231.33/42.51  | |            $i(all_52_5) & $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 &
% 231.33/42.51  | |            all_52_12 = e1 & all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 231.33/42.51  | |            op(all_52_11, all_52_11) = e2 & op(all_52_13, all_52_13) = e1 &
% 231.33/42.51  | |            op(all_52_15, all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2,
% 231.33/42.51  | |              e2) = all_52_11 & op(e2, e1) = all_52_13 & op(e2, e0) =
% 231.33/42.51  | |            all_52_15 & $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 231.33/42.51  | |            $i(all_52_15))
% 231.33/42.51  | | 
% 231.33/42.51  | | BETA: splitting (129) gives:
% 231.33/42.51  | | 
% 231.33/42.51  | | Case 1:
% 231.33/42.51  | | | 
% 231.33/42.51  | | |   (130)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 231.33/42.51  | | |          op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 231.33/42.51  | | |          op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 231.33/42.51  | | |          op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) =
% 231.33/42.51  | | |          all_52_5 & op(e3, e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) &
% 231.33/42.51  | | |          $i(all_52_5) & $i(all_52_7)
% 231.33/42.51  | | | 
% 231.33/42.51  | | | ALPHA: (130) implies:
% 231.33/42.51  | | |   (131)  op(e3, e1) = all_52_5
% 231.33/42.51  | | |   (132)  op(all_52_5, all_52_5) = e1
% 231.33/42.51  | | | 
% 231.33/42.51  | | | REF_CLOSE: (9), (18), (65), (71), (131), (132) are inconsistent by
% 231.33/42.51  | | |            sub-proof #2167.
% 231.33/42.51  | | | 
% 231.33/42.51  | | Case 2:
% 231.33/42.51  | | | 
% 231.33/42.51  | | |   (133)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 231.33/42.51  | | |          & op(all_52_9, all_52_9) = e3 & op(all_52_11, all_52_11) = e2 &
% 231.33/42.51  | | |          op(all_52_13, all_52_13) = e1 & op(all_52_15, all_52_15) = e0 &
% 231.33/42.51  | | |          op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 & op(e2, e1) =
% 231.33/42.51  | | |          all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) & $i(all_52_11)
% 231.33/42.51  | | |          & $i(all_52_13) & $i(all_52_15)
% 231.33/42.51  | | | 
% 231.33/42.51  | | | ALPHA: (133) implies:
% 231.33/42.51  | | |   (134)  op(e2, e2) = all_52_11
% 231.33/42.51  | | |   (135)  op(all_52_11, all_52_11) = e2
% 231.33/42.51  | | | 
% 231.33/42.51  | | | REF_CLOSE: (18), (38), (61), (71), (134), (135) are inconsistent by
% 231.33/42.51  | | |            sub-proof #2270.
% 231.33/42.51  | | | 
% 231.33/42.51  | | End of split
% 231.33/42.51  | | 
% 231.33/42.51  | Case 2:
% 231.33/42.51  | | 
% 231.33/42.51  | |   (136)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 231.33/42.51  | |            & op(all_52_17, all_52_17) = e3 & op(all_52_19, all_52_19) = e2 &
% 231.33/42.51  | |            op(all_52_21, all_52_21) = e1 & op(all_52_23, all_52_23) = e0 &
% 231.33/42.51  | |            op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) =
% 231.33/42.51  | |            all_52_21 & op(e1, e0) = all_52_23 & $i(all_52_17) &
% 231.33/42.51  | |            $i(all_52_19) & $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 231.33/42.51  | |            & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0 &
% 231.33/42.51  | |            op(all_52_25, all_52_25) = e3 & op(all_52_27, all_52_27) = e2 &
% 231.33/42.51  | |            op(all_52_29, all_52_29) = e1 & op(all_52_31, all_52_31) = e0 &
% 231.33/42.51  | |            op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 & op(e0, e1) =
% 231.33/42.51  | |            all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 231.33/42.51  | |            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 231.33/42.51  | | 
% 231.33/42.51  | | BETA: splitting (136) gives:
% 231.33/42.51  | | 
% 231.33/42.51  | | Case 1:
% 231.33/42.51  | | | 
% 231.33/42.51  | | |   (137)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 231.33/42.51  | | |          & op(all_52_17, all_52_17) = e3 & op(all_52_19, all_52_19) = e2 &
% 231.33/42.51  | | |          op(all_52_21, all_52_21) = e1 & op(all_52_23, all_52_23) = e0 &
% 231.33/42.51  | | |          op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) =
% 231.33/42.51  | | |          all_52_21 & op(e1, e0) = all_52_23 & $i(all_52_17) &
% 231.33/42.51  | | |          $i(all_52_19) & $i(all_52_21) & $i(all_52_23)
% 231.33/42.51  | | | 
% 231.33/42.51  | | | REF_CLOSE: (5), (18), (71), (128), (137) are inconsistent by sub-proof
% 231.33/42.51  | | |            #1652.
% 231.33/42.51  | | | 
% 231.33/42.51  | | Case 2:
% 231.33/42.51  | | | 
% 231.33/42.51  | | |   (138)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 231.33/42.51  | | |          & op(all_52_25, all_52_25) = e3 & op(all_52_27, all_52_27) = e2 &
% 231.33/42.51  | | |          op(all_52_29, all_52_29) = e1 & op(all_52_31, all_52_31) = e0 &
% 231.33/42.51  | | |          op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 & op(e0, e1) =
% 231.33/42.51  | | |          all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 231.33/42.51  | | |          $i(all_52_27) & $i(all_52_29) & $i(all_52_31)
% 231.33/42.51  | | | 
% 231.33/42.51  | | | ALPHA: (138) implies:
% 231.33/42.51  | | |   (139)  op(e0, e1) = all_52_29
% 231.33/42.51  | | |   (140)  op(e0, e2) = all_52_27
% 231.33/42.51  | | |   (141)  op(all_52_29, all_52_29) = e1
% 231.33/42.51  | | |   (142)  op(all_52_27, all_52_27) = e2
% 231.33/42.51  | | | 
% 231.33/42.51  | | | GROUND_INST: instantiating (18) with all_53_11, all_52_29, e1, e0,
% 231.33/42.51  | | |              simplifying with (4), (139) gives:
% 231.33/42.51  | | |   (143)  all_53_11 = all_52_29
% 231.33/42.51  | | | 
% 231.33/42.51  | | | GROUND_INST: instantiating (18) with all_53_7, all_52_27, e2, e0,
% 231.33/42.51  | | |              simplifying with (74), (140) gives:
% 231.33/42.51  | | |   (144)  all_53_7 = all_52_27
% 231.33/42.51  | | | 
% 231.33/42.51  | | | COMBINE_EQS: (106), (143) imply:
% 231.33/42.51  | | |   (145)  all_55_14 = all_52_29
% 231.33/42.51  | | | 
% 231.33/42.51  | | | COMBINE_EQS: (79), (144) imply:
% 231.33/42.51  | | |   (146)  all_55_13 = all_52_27
% 231.33/42.51  | | | 
% 231.33/42.51  | | | REDUCE: (54), (144) imply:
% 231.33/42.51  | | |   (147)   ~ (all_53_4 = all_52_27)
% 231.33/42.51  | | | 
% 231.33/42.51  | | | REDUCE: (48), (144) imply:
% 231.33/42.51  | | |   (148)   ~ (all_53_6 = all_52_27)
% 231.33/42.51  | | | 
% 231.33/42.51  | | | REDUCE: (56), (144) imply:
% 231.33/42.51  | | |   (149)   ~ (all_52_27 = e0)
% 231.33/42.51  | | | 
% 231.33/42.51  | | | REDUCE: (39), (143) imply:
% 231.33/42.51  | | |   (150)   ~ (all_53_9 = all_52_29)
% 231.33/42.51  | | | 
% 231.33/42.51  | | | REDUCE: (31), (143) imply:
% 231.33/42.51  | | |   (151)   ~ (all_52_29 = all_6_2)
% 231.33/42.51  | | | 
% 231.33/42.51  | | | REDUCE: (122), (143) imply:
% 231.33/42.51  | | |   (152)   ~ (all_52_29 = e0)
% 231.33/42.51  | | | 
% 231.33/42.51  | | | BETA: splitting (66) gives:
% 231.33/42.51  | | | 
% 231.33/42.51  | | | Case 1:
% 231.33/42.51  | | | | 
% 231.33/42.51  | | | |   (153)   ~ (all_38_2 = e2)
% 231.33/42.51  | | | | 
% 231.33/42.51  | | | | REDUCE: (82), (153) imply:
% 231.33/42.51  | | | |   (154)   ~ (all_6_2 = e2)
% 231.33/42.51  | | | | 
% 231.33/42.51  | | | | BETA: splitting (8) gives:
% 231.33/42.51  | | | | 
% 231.33/42.51  | | | | Case 1:
% 231.33/42.51  | | | | | 
% 231.33/42.51  | | | | |   (155)  all_55_10 = e3
% 231.33/42.51  | | | | | 
% 231.33/42.51  | | | | | REF_CLOSE: (23), (77), (155) are inconsistent by sub-proof #2500.
% 231.33/42.51  | | | | | 
% 231.33/42.51  | | | | Case 2:
% 231.33/42.51  | | | | | 
% 231.33/42.51  | | | | |   (156)  all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 231.33/42.51  | | | | | 
% 231.33/42.51  | | | | | BETA: splitting (156) gives:
% 231.33/42.51  | | | | | 
% 231.33/42.51  | | | | | Case 1:
% 231.33/42.51  | | | | | | 
% 231.33/42.51  | | | | | |   (157)  all_55_10 = e2
% 231.33/42.51  | | | | | | 
% 231.33/42.51  | | | | | | REF_CLOSE: (77), (154), (157) are inconsistent by sub-proof #2499.
% 231.33/42.51  | | | | | | 
% 231.33/42.51  | | | | | Case 2:
% 231.33/42.51  | | | | | | 
% 231.33/42.51  | | | | | |   (158)  all_55_10 = e1 | all_55_10 = e0
% 231.33/42.51  | | | | | | 
% 231.33/42.51  | | | | | | BETA: splitting (158) gives:
% 231.33/42.51  | | | | | | 
% 231.33/42.51  | | | | | | Case 1:
% 231.33/42.51  | | | | | | | 
% 231.33/42.51  | | | | | | |   (159)  all_55_10 = e1
% 231.33/42.51  | | | | | | | 
% 231.33/42.51  | | | | | | | COMBINE_EQS: (77), (159) imply:
% 231.33/42.51  | | | | | | |   (160)  all_6_2 = e1
% 231.33/42.51  | | | | | | | 
% 231.33/42.51  | | | | | | | SIMP: (160) implies:
% 231.33/42.51  | | | | | | |   (161)  all_6_2 = e1
% 231.33/42.51  | | | | | | | 
% 231.33/42.51  | | | | | | | REDUCE: (40), (161) imply:
% 231.33/42.51  | | | | | | |   (162)   ~ (all_53_9 = e1)
% 231.33/42.51  | | | | | | | 
% 231.33/42.51  | | | | | | | REDUCE: (151), (161) imply:
% 231.33/42.51  | | | | | | |   (163)   ~ (all_52_29 = e1)
% 231.33/42.51  | | | | | | | 
% 231.33/42.51  | | | | | | | BETA: splitting (45) gives:
% 231.33/42.51  | | | | | | | 
% 231.33/42.51  | | | | | | | Case 1:
% 231.33/42.51  | | | | | | | | 
% 231.33/42.51  | | | | | | | |   (164)  all_55_6 = e3
% 231.33/42.51  | | | | | | | | 
% 231.33/42.51  | | | | | | | | COMBINE_EQS: (59), (164) imply:
% 231.33/42.51  | | | | | | | |   (165)  all_53_9 = e3
% 231.33/42.51  | | | | | | | | 
% 231.33/42.51  | | | | | | | | SIMP: (165) implies:
% 231.33/42.51  | | | | | | | |   (166)  all_53_9 = e3
% 231.33/42.51  | | | | | | | | 
% 231.33/42.51  | | | | | | | | REDUCE: (150), (166) imply:
% 231.33/42.51  | | | | | | | |   (167)   ~ (all_52_29 = e3)
% 231.33/42.51  | | | | | | | | 
% 231.33/42.51  | | | | | | | | SIMP: (167) implies:
% 231.33/42.51  | | | | | | | |   (168)   ~ (all_52_29 = e3)
% 231.33/42.51  | | | | | | | | 
% 231.33/42.51  | | | | | | | | REF_CLOSE: (18), (38), (65), (70), (141), (145), (152), (163),
% 231.33/42.51  | | | | | | | |            (168) are inconsistent by sub-proof #1542.
% 231.33/42.51  | | | | | | | | 
% 231.33/42.51  | | | | | | | Case 2:
% 231.33/42.51  | | | | | | | | 
% 231.33/42.51  | | | | | | | |   (169)  all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 231.33/42.51  | | | | | | | | 
% 231.33/42.51  | | | | | | | | REF_CLOSE: (18), (50), (59), (70), (120), (141), (145), (150),
% 231.33/42.51  | | | | | | | |            (152), (162), (163), (169) are inconsistent by
% 231.33/42.51  | | | | | | | |            sub-proof #1680.
% 231.33/42.51  | | | | | | | | 
% 231.33/42.51  | | | | | | | End of split
% 231.33/42.51  | | | | | | | 
% 231.33/42.51  | | | | | | Case 2:
% 231.33/42.51  | | | | | | | 
% 231.33/42.51  | | | | | | |   (170)  all_55_10 = e0
% 231.33/42.51  | | | | | | | 
% 231.33/42.51  | | | | | | | REF_CLOSE: (77), (126), (170) are inconsistent by sub-proof #2118.
% 231.33/42.51  | | | | | | | 
% 231.33/42.51  | | | | | | End of split
% 231.33/42.51  | | | | | | 
% 231.33/42.51  | | | | | End of split
% 231.33/42.51  | | | | | 
% 231.33/42.51  | | | | End of split
% 231.33/42.51  | | | | 
% 231.33/42.52  | | | Case 2:
% 231.33/42.52  | | | | 
% 231.33/42.52  | | | |   (171)  all_38_2 = e2
% 231.33/42.52  | | | | 
% 231.33/42.52  | | | | COMBINE_EQS: (82), (171) imply:
% 231.33/42.52  | | | |   (172)  all_6_2 = e2
% 231.33/42.52  | | | | 
% 231.33/42.52  | | | | REDUCE: (78), (172) imply:
% 231.33/42.52  | | | |   (173)   ~ (all_53_6 = e2)
% 231.33/42.52  | | | | 
% 231.33/42.52  | | | | REDUCE: (42), (172) imply:
% 231.33/42.52  | | | |   (174)   ~ (all_53_14 = e2)
% 231.33/42.52  | | | | 
% 231.33/42.52  | | | | REDUCE: (23), (172) imply:
% 231.33/42.52  | | | |   (175)   ~ (e3 = e2)
% 231.33/42.52  | | | | 
% 231.33/42.52  | | | | SIMP: (175) implies:
% 231.33/42.52  | | | |   (176)   ~ (e3 = e2)
% 231.33/42.52  | | | | 
% 231.33/42.52  | | | | REDUCE: (24), (172) imply:
% 231.33/42.52  | | | |   (177)  op(e1, e1) = e2
% 231.33/42.52  | | | | 
% 231.33/42.52  | | | | BETA: splitting (29) gives:
% 231.33/42.52  | | | | 
% 231.33/42.52  | | | | Case 1:
% 231.33/42.52  | | | | | 
% 231.33/42.52  | | | | |   (178)  all_55_9 = e3
% 231.33/42.52  | | | | | 
% 231.33/42.52  | | | | | COMBINE_EQS: (30), (178) imply:
% 231.33/42.52  | | | | |   (179)  all_53_6 = e3
% 231.33/42.52  | | | | | 
% 231.33/42.52  | | | | | SIMP: (179) implies:
% 231.33/42.52  | | | | |   (180)  all_53_6 = e3
% 231.33/42.52  | | | | | 
% 231.33/42.52  | | | | | REDUCE: (7), (180) imply:
% 231.33/42.52  | | | | |   (181)   ~ (all_53_14 = e3)
% 231.33/42.52  | | | | | 
% 231.33/42.52  | | | | | SIMP: (181) implies:
% 231.33/42.52  | | | | |   (182)   ~ (all_53_14 = e3)
% 231.33/42.52  | | | | | 
% 231.33/42.52  | | | | | REDUCE: (148), (180) imply:
% 231.33/42.52  | | | | |   (183)   ~ (all_52_27 = e3)
% 231.33/42.52  | | | | | 
% 231.33/42.52  | | | | | SIMP: (183) implies:
% 231.33/42.52  | | | | |   (184)   ~ (all_52_27 = e3)
% 231.33/42.52  | | | | | 
% 231.33/42.52  | | | | | BETA: splitting (27) gives:
% 231.33/42.52  | | | | | 
% 231.33/42.52  | | | | | Case 1:
% 231.33/42.52  | | | | | | 
% 231.33/42.52  | | | | | |   (185)  all_55_11 = e3
% 231.33/42.52  | | | | | | 
% 231.33/42.52  | | | | | | REF_CLOSE: (83), (182), (185) are inconsistent by sub-proof #2497.
% 231.33/42.52  | | | | | | 
% 231.33/42.52  | | | | | Case 2:
% 231.33/42.52  | | | | | | 
% 231.33/42.52  | | | | | |   (186)  all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 231.33/42.52  | | | | | | 
% 231.33/42.52  | | | | | | BETA: splitting (186) gives:
% 231.33/42.52  | | | | | | 
% 231.33/42.52  | | | | | | Case 1:
% 231.33/42.52  | | | | | | | 
% 231.33/42.52  | | | | | | |   (187)  all_55_11 = e2
% 231.33/42.52  | | | | | | | 
% 231.33/42.52  | | | | | | | REF_CLOSE: (83), (174), (187) are inconsistent by sub-proof #2282.
% 231.33/42.52  | | | | | | | 
% 231.33/42.52  | | | | | | Case 2:
% 231.33/42.52  | | | | | | | 
% 231.33/42.52  | | | | | | |   (188)  all_55_11 = e1 | all_55_11 = e0
% 231.33/42.52  | | | | | | | 
% 231.33/42.52  | | | | | | | BETA: splitting (188) gives:
% 231.33/42.52  | | | | | | | 
% 231.33/42.52  | | | | | | | Case 1:
% 231.33/42.52  | | | | | | | | 
% 231.33/42.52  | | | | | | | |   (189)  all_55_11 = e1
% 231.33/42.52  | | | | | | | | 
% 231.33/42.52  | | | | | | | | COMBINE_EQS: (83), (189) imply:
% 231.33/42.52  | | | | | | | |   (190)  all_53_14 = e1
% 231.33/42.52  | | | | | | | | 
% 231.33/42.52  | | | | | | | | SIMP: (190) implies:
% 231.33/42.52  | | | | | | | |   (191)  all_53_14 = e1
% 231.33/42.52  | | | | | | | | 
% 231.33/42.52  | | | | | | | | REDUCE: (105), (191) imply:
% 231.33/42.52  | | | | | | | |   (192)   ~ (all_53_12 = e1)
% 231.33/42.52  | | | | | | | | 
% 231.33/42.52  | | | | | | | | BETA: splitting (25) gives:
% 231.33/42.52  | | | | | | | | 
% 231.33/42.52  | | | | | | | | Case 1:
% 231.33/42.52  | | | | | | | | | 
% 231.33/42.52  | | | | | | | | |   (193)  all_55_3 = e3
% 231.33/42.52  | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | REF_CLOSE: (84), (85), (193) are inconsistent by sub-proof
% 231.33/42.52  | | | | | | | | |            #2169.
% 231.33/42.52  | | | | | | | | | 
% 231.33/42.52  | | | | | | | | Case 2:
% 231.33/42.52  | | | | | | | | | 
% 231.33/42.52  | | | | | | | | |   (194)  all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 231.33/42.52  | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | BETA: splitting (194) gives:
% 231.33/42.52  | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | Case 1:
% 231.33/42.52  | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | |   (195)  all_55_3 = e2
% 231.33/42.52  | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | COMBINE_EQS: (84), (195) imply:
% 231.33/42.52  | | | | | | | | | |   (196)  all_53_12 = e2
% 231.33/42.52  | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | SIMP: (196) implies:
% 231.33/42.52  | | | | | | | | | |   (197)  all_53_12 = e2
% 231.33/42.52  | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | REDUCE: (32), (197) imply:
% 231.33/42.52  | | | | | | | | | |   (198)   ~ (all_53_4 = e2)
% 231.33/42.52  | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | BETA: splitting (6) gives:
% 231.33/42.52  | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | Case 1:
% 231.33/42.52  | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | |   (199)  all_55_1 = e3
% 231.33/42.52  | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | REF_CLOSE: (46), (109), (199) are inconsistent by sub-proof
% 231.33/42.52  | | | | | | | | | | |            #2295.
% 231.33/42.52  | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | Case 2:
% 231.33/42.52  | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | |   (200)  all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 231.33/42.52  | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | REF_CLOSE: (2), (18), (38), (46), (118), (142), (146), (147),
% 231.33/42.52  | | | | | | | | | | |            (149), (184), (198), (200) are inconsistent by
% 231.33/42.52  | | | | | | | | | | |            sub-proof #1541.
% 231.33/42.52  | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | End of split
% 231.33/42.52  | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | Case 2:
% 231.33/42.52  | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | |   (201)  all_55_3 = e1 | all_55_3 = e0
% 231.33/42.52  | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | REF_CLOSE: (84), (124), (192), (201) are inconsistent by
% 231.33/42.52  | | | | | | | | | |            sub-proof #2132.
% 231.33/42.52  | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | End of split
% 231.33/42.52  | | | | | | | | | 
% 231.33/42.52  | | | | | | | | End of split
% 231.33/42.52  | | | | | | | | 
% 231.33/42.52  | | | | | | | Case 2:
% 231.33/42.52  | | | | | | | | 
% 231.33/42.52  | | | | | | | |   (202)  all_55_11 = e0
% 231.33/42.52  | | | | | | | | 
% 231.33/42.52  | | | | | | | | REF_CLOSE: (83), (117), (202) are inconsistent by sub-proof
% 231.33/42.52  | | | | | | | |            #2308.
% 231.33/42.52  | | | | | | | | 
% 231.33/42.52  | | | | | | | End of split
% 231.33/42.52  | | | | | | | 
% 231.33/42.52  | | | | | | End of split
% 231.33/42.52  | | | | | | 
% 231.33/42.52  | | | | | End of split
% 231.33/42.52  | | | | | 
% 231.33/42.52  | | | | Case 2:
% 231.33/42.52  | | | | | 
% 231.33/42.52  | | | | |   (203)   ~ (all_55_9 = e3)
% 231.33/42.52  | | | | |   (204)  all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 231.33/42.52  | | | | | 
% 231.33/42.52  | | | | | REDUCE: (30), (203) imply:
% 231.33/42.52  | | | | |   (205)   ~ (all_53_6 = e3)
% 231.33/42.52  | | | | | 
% 231.33/42.52  | | | | | BETA: splitting (204) gives:
% 231.33/42.52  | | | | | 
% 231.33/42.52  | | | | | Case 1:
% 231.33/42.52  | | | | | | 
% 231.33/42.52  | | | | | |   (206)  all_55_9 = e2
% 231.33/42.52  | | | | | | 
% 231.33/42.52  | | | | | | REF_CLOSE: (30), (173), (206) are inconsistent by sub-proof #2274.
% 231.33/42.52  | | | | | | 
% 231.33/42.52  | | | | | Case 2:
% 231.33/42.52  | | | | | | 
% 231.33/42.52  | | | | | |   (207)   ~ (all_55_9 = e2)
% 231.33/42.52  | | | | | |   (208)  all_55_9 = e1 | all_55_9 = e0
% 231.33/42.52  | | | | | | 
% 231.33/42.52  | | | | | | BETA: splitting (21) gives:
% 231.33/42.52  | | | | | | 
% 231.33/42.52  | | | | | | Case 1:
% 231.33/42.52  | | | | | | | 
% 231.33/42.52  | | | | | | |   (209)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 &
% 231.33/42.52  | | | | | | |            op(e1, e2) = e3)
% 231.33/42.52  | | | | | | | 
% 231.33/42.52  | | | | | | | BETA: splitting (209) gives:
% 231.33/42.52  | | | | | | | 
% 231.33/42.52  | | | | | | | Case 1:
% 231.33/42.52  | | | | | | | | 
% 231.33/42.52  | | | | | | | |   (210)  all_57_6 = e3 & op(e1, e3) = e3
% 231.33/42.52  | | | | | | | | 
% 231.33/42.52  | | | | | | | | ALPHA: (210) implies:
% 231.33/42.52  | | | | | | | |   (211)  all_57_6 = e3
% 231.33/42.52  | | | | | | | | 
% 231.33/42.52  | | | | | | | | REF_CLOSE: (12), (16), (61), (65), (86), (94), (99), (102),
% 231.33/42.52  | | | | | | | |            (128), (176), (211) are inconsistent by sub-proof
% 231.33/42.52  | | | | | | | |            #2010.
% 231.33/42.52  | | | | | | | | 
% 231.33/42.52  | | | | | | | Case 2:
% 231.33/42.52  | | | | | | | | 
% 231.33/42.52  | | | | | | | |   (212)  all_57_7 = e3 & op(e1, e2) = e3
% 231.33/42.52  | | | | | | | | 
% 231.33/42.52  | | | | | | | | ALPHA: (212) implies:
% 231.33/42.52  | | | | | | | |   (213)  all_57_7 = e3
% 231.33/42.52  | | | | | | | | 
% 231.33/42.52  | | | | | | | | BETA: splitting (104) gives:
% 231.33/42.52  | | | | | | | | 
% 231.33/42.52  | | | | | | | | Case 1:
% 231.33/42.52  | | | | | | | | | 
% 231.33/42.52  | | | | | | | | |   (214)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 &
% 231.33/42.52  | | | | | | | | |            op(e1, e2) = e1)
% 231.33/42.52  | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | BETA: splitting (214) gives:
% 231.33/42.52  | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | Case 1:
% 231.33/42.52  | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | |   (215)  all_57_6 = e1 & op(e1, e3) = e1
% 231.33/42.52  | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | ALPHA: (215) implies:
% 231.33/42.52  | | | | | | | | | |   (216)  all_57_6 = e1
% 231.33/42.52  | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | REF_CLOSE: (51), (65), (216) are inconsistent by sub-proof
% 231.33/42.52  | | | | | | | | | |            #2227.
% 231.33/42.52  | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | Case 2:
% 231.33/42.52  | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | |   (217)  all_57_7 = e1 & op(e1, e2) = e1
% 231.33/42.52  | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | ALPHA: (217) implies:
% 231.33/42.52  | | | | | | | | | |   (218)  all_57_7 = e1
% 231.33/42.52  | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | REF_CLOSE: (16), (213), (218) are inconsistent by sub-proof
% 231.33/42.52  | | | | | | | | | |            #2115.
% 231.33/42.52  | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | End of split
% 231.33/42.52  | | | | | | | | | 
% 231.33/42.52  | | | | | | | | Case 2:
% 231.33/42.52  | | | | | | | | | 
% 231.33/42.52  | | | | | | | | |   (219)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 &
% 231.33/42.52  | | | | | | | | |            op(e1, e0) = e1)
% 231.33/42.52  | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | BETA: splitting (219) gives:
% 231.33/42.52  | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | Case 1:
% 231.33/42.52  | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | |   (220)  all_57_8 = e1 & op(e1, e1) = e1
% 231.33/42.52  | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | ALPHA: (220) implies:
% 231.33/42.52  | | | | | | | | | |   (221)  op(e1, e1) = e1
% 231.33/42.52  | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | REF_CLOSE: (18), (94), (177), (221) are inconsistent by
% 231.33/42.52  | | | | | | | | | |            sub-proof #2423.
% 231.33/42.52  | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | Case 2:
% 231.33/42.52  | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | |   (222)  all_57_11 = e1 & op(e1, e0) = e1
% 231.33/42.52  | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | ALPHA: (222) implies:
% 231.33/42.52  | | | | | | | | | |   (223)  all_57_11 = e1
% 231.33/42.52  | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | BETA: splitting (92) gives:
% 231.33/42.52  | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | Case 1:
% 231.33/42.52  | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | |   (224)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 231.33/42.52  | | | | | | | | | | |            e3 & op(e2, e0) = e3)
% 231.33/42.52  | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | BETA: splitting (224) gives:
% 231.33/42.52  | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | Case 1:
% 231.33/42.52  | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | |   (225)  all_57_9 = e3 & op(e3, e0) = e3
% 231.33/42.52  | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | ALPHA: (225) implies:
% 231.33/42.52  | | | | | | | | | | | |   (226)  op(e3, e0) = e3
% 231.33/42.52  | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | REF_CLOSE: (18), (85), (111), (226) are inconsistent by
% 231.33/42.52  | | | | | | | | | | | |            sub-proof #2458.
% 231.33/42.52  | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | Case 2:
% 231.33/42.52  | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | |   (227)  all_57_10 = e3 & op(e2, e0) = e3
% 231.33/42.52  | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | ALPHA: (227) implies:
% 231.33/42.52  | | | | | | | | | | | |   (228)  all_57_10 = e3
% 231.33/42.52  | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | BETA: splitting (89) gives:
% 231.33/42.52  | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | Case 1:
% 231.33/42.52  | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | |   (229)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 231.33/42.52  | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 231.33/42.52  | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | BETA: splitting (229) gives:
% 231.33/42.52  | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | Case 1:
% 231.33/42.52  | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | |   (230)  all_57_2 = e2 & op(e2, e3) = e2
% 231.33/42.52  | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | ALPHA: (230) implies:
% 231.33/42.52  | | | | | | | | | | | | | |   (231)  all_57_2 = e2
% 231.33/42.52  | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | BETA: splitting (11) gives:
% 231.33/42.52  | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | Case 1:
% 231.33/42.52  | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | |   (232)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 231.33/42.52  | | | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 231.33/42.52  | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | REF_CLOSE: (18), (38), (65), (94), (231), (232) are
% 231.33/42.52  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1540.
% 231.33/42.52  | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | Case 2:
% 231.33/42.52  | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | |   (233)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 231.33/42.52  | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 231.33/42.52  | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 231.33/42.52  | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | Case 1:
% 231.33/42.52  | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | |   (234)  all_57_5 = e1 & op(e2, e1) = e1
% 231.33/42.52  | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | ALPHA: (234) implies:
% 231.33/42.52  | | | | | | | | | | | | | | | |   (235)  all_57_5 = e1
% 231.33/42.52  | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 231.33/42.52  | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | Case 1:
% 231.33/42.52  | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | |   (236)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 231.33/42.52  | | | | | | | | | | | | | | | | |            & op(e2, e1) = e3)
% 231.33/42.52  | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 231.33/42.52  | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | Case 1:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | |   (237)  all_57_4 = e3 & op(e3, e1) = e3
% 231.33/42.52  | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | ALPHA: (237) implies:
% 231.33/42.52  | | | | | | | | | | | | | | | | | |   (238)  all_57_4 = e3
% 231.33/42.52  | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (16), (18), (28), (37), (41), (43), (50),
% 231.33/42.52  | | | | | | | | | | | | | | | | | |            (61), (65), (94), (108), (128), (176), (213),
% 231.33/42.52  | | | | | | | | | | | | | | | | | |            (238) are inconsistent by sub-proof #1539.
% 231.33/42.52  | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | Case 2:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | |   (239)  all_57_5 = e3 & op(e2, e1) = e3
% 231.33/42.52  | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | ALPHA: (239) implies:
% 231.33/42.52  | | | | | | | | | | | | | | | | | |   (240)  all_57_5 = e3
% 231.33/42.52  | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (16), (43), (65), (94), (228), (231), (240)
% 231.33/42.52  | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1694.
% 231.33/42.52  | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | End of split
% 231.33/42.52  | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | Case 2:
% 231.33/42.52  | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | |   (241)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 231.33/42.52  | | | | | | | | | | | | | | | | |            e3 & op(e0, e1) = e3)
% 231.33/42.52  | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 231.33/42.52  | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | Case 1:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | |   (242)  all_57_8 = e3 & op(e1, e1) = e3
% 231.33/42.52  | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | ALPHA: (242) implies:
% 231.33/42.52  | | | | | | | | | | | | | | | | | |   (243)  op(e1, e1) = e3
% 231.33/42.52  | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (23), (24), (243) are inconsistent by
% 231.33/42.52  | | | | | | | | | | | | | | | | | |            sub-proof #2468.
% 231.33/42.52  | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | Case 2:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | |   (244)  all_57_14 = e3 & op(e0, e1) = e3
% 231.33/42.52  | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | ALPHA: (244) implies:
% 231.33/42.52  | | | | | | | | | | | | | | | | | |   (245)  all_57_14 = e3
% 231.33/42.52  | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | Case 1:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | |   (246)  all_55_9 = e1
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (30), (246) imply:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | |   (247)  all_53_6 = e1
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | SIMP: (247) implies:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | |   (248)  all_53_6 = e1
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | REDUCE: (73), (248) imply:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | |   (249)   ~ (all_53_4 = e1)
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | REDUCE: (205), (248) imply:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | |   (250)   ~ (e3 = e1)
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | REDUCE: (173), (248) imply:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | |   (251)   ~ (e2 = e1)
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | BETA: splitting (6) gives:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | Case 1:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | |   (252)  all_55_1 = e3
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (46), (109), (252) are inconsistent by sub-proof
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | |            #2295.
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | Case 2:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | |   (253)  all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | BETA: splitting (95) gives:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | |   (254)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (254) gives:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | |   (255)  all_57_9 = e2 & op(e3, e0) = e2
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (32), (46), (111), (118), (249), (253),
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | |            (255) are inconsistent by sub-proof #1538.
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | |   (256)  all_57_10 = e2 & op(e2, e0) = e2
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (256) implies:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | |   (257)  all_57_10 = e2
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (228), (257) imply:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | |   (258)  e3 = e2
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (258) imply:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | |   (259)  all_57_14 = e2
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (72) gives:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | |   (260)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (260) gives:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | |   (261)  all_57_12 = e3 & op(e0, e3) = e3
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (261) implies:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | |   (262)  all_57_12 = e3
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | |   (263)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e3)
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (263) gives:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | |   (264)  all_57_4 = e3 & op(e3, e1) = e3
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (264) implies:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | |   (265)  all_57_4 = e3
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (18), (28), (37), (41), (50), (61), (65),
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | |            (94), (128), (176), (265) are inconsistent by
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2474.
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | |   (266)  all_57_5 = e3 & op(e2, e1) = e3
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (266) implies:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | |   (267)  all_57_5 = e3
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12) gives:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (268)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e1)
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (268) gives:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (269)  all_57_0 = e1 & op(e3, e3) = e1
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (269) implies:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (270)  op(e3, e3) = e1
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (18), (50), (270) are inconsistent by
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2495.
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (271)  all_57_2 = e1 & op(e2, e3) = e1
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (271) implies:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (272)  all_57_2 = e1
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (49) gives:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (273)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e1)
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (273) gives:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (274)  all_57_4 = e1 & op(e3, e1) = e1
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (274) implies:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (275)  all_57_4 = e1
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (16), (33), (43), (61), (65), (89), (94),
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (176), (267), (272), (275) are inconsistent by
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1537.
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (18), (38), (43), (61), (81), (89), (94),
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (128), (176), (235), (272) are inconsistent by
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1536.
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (276)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e1) = e1)
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (94), (177), (259), (276) are inconsistent
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2198.
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (277)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e3) = e1)
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (51), (65), (262), (277) are inconsistent by
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2226.
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (23), (24), (176), (241), (259) are
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1890.
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | |   (278)  all_57_13 = e3 & op(e0, e2) = e3
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (278) implies:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | |   (279)  all_57_13 = e3
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | |   (280)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e3)
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (280) gives:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | |   (281)  all_57_4 = e3 & op(e3, e1) = e3
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (281) implies:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | |   (282)  all_57_4 = e3
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (18), (28), (37), (41), (50), (61), (65),
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | |            (94), (128), (176), (282) are inconsistent by
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2474.
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | |   (283)  all_57_5 = e3 & op(e2, e1) = e3
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (283) implies:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | |   (284)  all_57_5 = e3
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (16), (18), (23), (24), (33), (38), (43),
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | |            (49), (61), (65), (67), (68), (94), (108), (128),
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | |            (176), (177), (259), (279), (284) are inconsistent
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2187.
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (23), (24), (176), (241), (259) are
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1890.
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | |   (285)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e0) = e3)
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (6), (8), (11), (12), (13), (14), (17),
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | |            (18), (19), (20), (21), (22), (23), (24), (25),
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | |            (26), (28), (32), (35), (36), (37), (40), (41),
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | |            (43), (44), (46), (49), (52), (53), (55), (57),
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | |            (58), (60), (61), (62), (63), (65), (66), (67),
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | |            (68), (69), (73), (75), (76), (77), (81), (82),
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | |            (84), (88), (89), (90), (91), (94), (95), (96),
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | |            (97), (99), (100), (101), (102), (103), (104),
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | |            (107), (108), (110), (111), (118), (120), (176),
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | |            (259), (285) are inconsistent by sub-proof #1413.
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | End of split
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | |   (286)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (286) gives:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | |   (287)  all_57_11 = e2 & op(e1, e0) = e2
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (287) implies:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | |   (288)  all_57_11 = e2
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (223), (288) imply:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | |   (289)  e2 = e1
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | SIMP: (289) implies:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | |   (290)  e2 = e1
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (231), (290) imply:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | |   (291)  all_57_2 = e1
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (18), (38), (43), (61), (81), (89), (94),
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | |            (128), (176), (235), (291) are inconsistent by
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1536.
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | |   (292)  all_57_15 = e2 & op(e0, e0) = e2
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (43), (61), (89), (94), (176), (228), (231),
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | |            (235), (292) are inconsistent by sub-proof #1412.
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | End of split
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | End of split
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | End of split
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | Case 2:
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | |   (293)  all_55_9 = e0
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (115), (293) are inconsistent by sub-proof
% 231.33/42.52  | | | | | | | | | | | | | | | | | | |            #2272.
% 231.33/42.52  | | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | | End of split
% 231.33/42.52  | | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | | End of split
% 231.33/42.52  | | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | End of split
% 231.33/42.52  | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | Case 2:
% 231.33/42.52  | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | |   (294)  all_57_10 = e1 & op(e2, e0) = e1
% 231.33/42.52  | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | REF_CLOSE: (16), (228), (294) are inconsistent by sub-proof
% 231.33/42.52  | | | | | | | | | | | | | | | |            #2349.
% 231.33/42.52  | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | End of split
% 231.33/42.52  | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | End of split
% 231.33/42.52  | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | Case 2:
% 231.33/42.52  | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | |   (295)  all_57_3 = e2 & op(e2, e2) = e2
% 231.33/42.52  | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | ALPHA: (295) implies:
% 231.33/42.52  | | | | | | | | | | | | | |   (296)  op(e2, e2) = e2
% 231.33/42.52  | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | REF_CLOSE: (18), (38), (61), (296) are inconsistent by
% 231.33/42.52  | | | | | | | | | | | | | |            sub-proof #2472.
% 231.33/42.52  | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | End of split
% 231.33/42.52  | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | Case 2:
% 231.33/42.52  | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | |   (297)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 231.33/42.52  | | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 231.33/42.52  | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | BETA: splitting (297) gives:
% 231.33/42.52  | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | Case 1:
% 231.33/42.52  | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | |   (298)  all_57_5 = e2 & op(e2, e1) = e2
% 231.33/42.52  | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | ALPHA: (298) implies:
% 231.33/42.52  | | | | | | | | | | | | | |   (299)  all_57_5 = e2
% 231.33/42.52  | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | REF_CLOSE: (11), (16), (18), (23), (24), (28), (33), (37),
% 231.33/42.52  | | | | | | | | | | | | | |            (41), (43), (49), (50), (61), (65), (67), (89),
% 231.33/42.52  | | | | | | | | | | | | | |            (94), (128), (176), (177), (228), (299) are
% 231.33/42.52  | | | | | | | | | | | | | |            inconsistent by sub-proof #1691.
% 231.33/42.52  | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | Case 2:
% 231.33/42.52  | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | |   (300)  all_57_10 = e2 & op(e2, e0) = e2
% 231.33/42.52  | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | ALPHA: (300) implies:
% 231.33/42.52  | | | | | | | | | | | | | |   (301)  all_57_10 = e2
% 231.33/42.52  | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | REF_CLOSE: (176), (228), (301) are inconsistent by sub-proof
% 231.33/42.52  | | | | | | | | | | | | | |            #2356.
% 231.33/42.52  | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | End of split
% 231.33/42.52  | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | End of split
% 231.33/42.52  | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | End of split
% 231.33/42.52  | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | Case 2:
% 231.33/42.52  | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | |   (302)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 231.33/42.52  | | | | | | | | | | |            e3 & op(e0, e0) = e3)
% 231.33/42.52  | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | BETA: splitting (302) gives:
% 231.33/42.52  | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | Case 1:
% 231.33/42.52  | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | |   (303)  all_57_11 = e3 & op(e1, e0) = e3
% 231.33/42.52  | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | REF_CLOSE: (16), (223), (303) are inconsistent by sub-proof
% 231.33/42.52  | | | | | | | | | | | |            #1820.
% 231.33/42.52  | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | Case 2:
% 231.33/42.52  | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | |   (304)  all_57_15 = e3 & op(e0, e0) = e3
% 231.33/42.52  | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | ALPHA: (304) implies:
% 231.33/42.52  | | | | | | | | | | | |   (305)  all_57_15 = e3
% 231.33/42.52  | | | | | | | | | | | |   (306)  op(e0, e0) = e3
% 231.33/42.52  | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | REF_CLOSE: (1), (3), (6), (8), (11), (12), (13), (14), (17),
% 231.33/42.52  | | | | | | | | | | | |            (18), (19), (20), (21), (22), (23), (24), (25),
% 231.33/42.52  | | | | | | | | | | | |            (26), (28), (32), (35), (36), (37), (40), (41),
% 231.33/42.52  | | | | | | | | | | | |            (43), (44), (46), (49), (52), (53), (55), (57),
% 231.33/42.52  | | | | | | | | | | | |            (58), (60), (61), (62), (63), (65), (66), (67),
% 231.33/42.52  | | | | | | | | | | | |            (68), (69), (73), (75), (76), (77), (81), (82),
% 231.33/42.52  | | | | | | | | | | | |            (84), (88), (89), (90), (91), (94), (95), (96),
% 231.33/42.52  | | | | | | | | | | | |            (97), (99), (100), (101), (102), (103), (104),
% 231.33/42.52  | | | | | | | | | | | |            (107), (108), (110), (111), (118), (120), (305),
% 231.33/42.52  | | | | | | | | | | | |            (306) are inconsistent by sub-proof #1414.
% 231.33/42.52  | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | End of split
% 231.33/42.52  | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | End of split
% 231.33/42.52  | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | End of split
% 231.33/42.52  | | | | | | | | | 
% 231.33/42.52  | | | | | | | | End of split
% 231.33/42.52  | | | | | | | | 
% 231.33/42.52  | | | | | | | End of split
% 231.33/42.52  | | | | | | | 
% 231.33/42.52  | | | | | | Case 2:
% 231.33/42.52  | | | | | | | 
% 231.33/42.52  | | | | | | |   (307)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 &
% 231.33/42.52  | | | | | | |            op(e1, e0) = e3)
% 231.33/42.52  | | | | | | | 
% 231.33/42.52  | | | | | | | BETA: splitting (307) gives:
% 231.33/42.52  | | | | | | | 
% 231.33/42.52  | | | | | | | Case 1:
% 231.33/42.52  | | | | | | | | 
% 231.33/42.52  | | | | | | | |   (308)  all_57_8 = e3 & op(e1, e1) = e3
% 231.33/42.52  | | | | | | | | 
% 231.33/42.52  | | | | | | | | ALPHA: (308) implies:
% 231.33/42.52  | | | | | | | |   (309)  op(e1, e1) = e3
% 231.33/42.52  | | | | | | | | 
% 231.33/42.52  | | | | | | | | REF_CLOSE: (18), (23), (24), (309) are inconsistent by sub-proof
% 231.33/42.52  | | | | | | | |            #2468.
% 231.33/42.52  | | | | | | | | 
% 231.33/42.52  | | | | | | | Case 2:
% 231.33/42.52  | | | | | | | | 
% 231.33/42.52  | | | | | | | |   (310)  all_57_11 = e3 & op(e1, e0) = e3
% 231.33/42.52  | | | | | | | | 
% 231.33/42.52  | | | | | | | | ALPHA: (310) implies:
% 231.33/42.52  | | | | | | | |   (311)  all_57_11 = e3
% 231.33/42.52  | | | | | | | |   (312)  op(e1, e0) = e3
% 231.33/42.52  | | | | | | | | 
% 231.33/42.52  | | | | | | | | BETA: splitting (104) gives:
% 231.33/42.52  | | | | | | | | 
% 231.33/42.52  | | | | | | | | Case 1:
% 231.33/42.52  | | | | | | | | | 
% 231.33/42.52  | | | | | | | | |   (313)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 &
% 231.33/42.52  | | | | | | | | |            op(e1, e2) = e1)
% 231.33/42.52  | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | BETA: splitting (313) gives:
% 231.33/42.52  | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | Case 1:
% 231.33/42.52  | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | |   (314)  all_57_6 = e1 & op(e1, e3) = e1
% 231.33/42.52  | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | ALPHA: (314) implies:
% 231.33/42.52  | | | | | | | | | |   (315)  all_57_6 = e1
% 231.33/42.52  | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | REF_CLOSE: (51), (65), (315) are inconsistent by sub-proof
% 231.33/42.52  | | | | | | | | | |            #2227.
% 231.33/42.52  | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | Case 2:
% 231.33/42.52  | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | |   (316)  all_57_7 = e1 & op(e1, e2) = e1
% 231.33/42.52  | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | ALPHA: (316) implies:
% 231.33/42.52  | | | | | | | | | |   (317)  all_57_7 = e1
% 231.33/42.52  | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | BETA: splitting (208) gives:
% 231.33/42.52  | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | Case 1:
% 231.33/42.52  | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | |   (318)  all_55_9 = e1
% 231.33/42.52  | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | COMBINE_EQS: (30), (318) imply:
% 231.33/42.52  | | | | | | | | | | |   (319)  all_53_6 = e1
% 231.33/42.52  | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | SIMP: (319) implies:
% 231.33/42.52  | | | | | | | | | | |   (320)  all_53_6 = e1
% 231.33/42.52  | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | REDUCE: (73), (320) imply:
% 231.33/42.52  | | | | | | | | | | |   (321)   ~ (all_53_4 = e1)
% 231.33/42.52  | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | REDUCE: (7), (320) imply:
% 231.33/42.52  | | | | | | | | | | |   (322)   ~ (all_53_14 = e1)
% 231.33/42.52  | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | SIMP: (322) implies:
% 231.33/42.52  | | | | | | | | | | |   (323)   ~ (all_53_14 = e1)
% 231.33/42.52  | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | REDUCE: (205), (320) imply:
% 231.33/42.52  | | | | | | | | | | |   (324)   ~ (e3 = e1)
% 231.33/42.52  | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | REDUCE: (173), (320) imply:
% 231.33/42.52  | | | | | | | | | | |   (325)   ~ (e2 = e1)
% 231.33/42.52  | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | BETA: splitting (28) gives:
% 231.33/42.52  | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | Case 1:
% 231.33/42.52  | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | |   (326)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 231.33/42.52  | | | | | | | | | | | |            & op(e3, e2) = e1)
% 231.33/42.52  | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | BETA: splitting (326) gives:
% 231.33/42.52  | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | Case 1:
% 231.33/42.52  | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | |   (327)  all_57_0 = e1 & op(e3, e3) = e1
% 231.33/42.52  | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | ALPHA: (327) implies:
% 231.33/42.52  | | | | | | | | | | | | |   (328)  op(e3, e3) = e1
% 231.33/42.52  | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | REF_CLOSE: (16), (18), (50), (328) are inconsistent by
% 231.33/42.52  | | | | | | | | | | | | |            sub-proof #2495.
% 231.33/42.52  | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | Case 2:
% 231.33/42.52  | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | |   (329)  all_57_1 = e1 & op(e3, e2) = e1
% 231.33/42.52  | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | ALPHA: (329) implies:
% 231.33/42.52  | | | | | | | | | | | | |   (330)  all_57_1 = e1
% 231.33/42.52  | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | BETA: splitting (6) gives:
% 231.33/42.52  | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | Case 1:
% 231.33/42.52  | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | |   (331)  all_55_1 = e3
% 231.33/42.52  | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | COMBINE_EQS: (46), (331) imply:
% 231.33/42.52  | | | | | | | | | | | | | |   (332)  all_53_4 = e3
% 231.33/42.52  | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | REDUCE: (109), (332) imply:
% 231.33/42.52  | | | | | | | | | | | | | |   (333)  $false
% 231.33/42.52  | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | CLOSE: (333) is inconsistent.
% 231.33/42.52  | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | Case 2:
% 231.33/42.52  | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | |   (334)  all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 231.33/42.52  | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | BETA: splitting (37) gives:
% 231.33/42.52  | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | Case 1:
% 231.33/42.52  | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | |   (335)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 231.33/42.52  | | | | | | | | | | | | | | |            & op(e3, e2) = e2)
% 231.33/42.52  | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | REF_CLOSE: (18), (50), (94), (176), (330), (335) are
% 231.33/42.52  | | | | | | | | | | | | | | |            inconsistent by sub-proof #2488.
% 231.33/42.52  | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | Case 2:
% 231.33/42.52  | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | |   (336)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 231.33/42.52  | | | | | | | | | | | | | | |            & op(e3, e0) = e2)
% 231.33/42.52  | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | BETA: splitting (336) gives:
% 231.33/42.52  | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | Case 1:
% 231.33/42.52  | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | |   (337)  all_57_4 = e2 & op(e3, e1) = e2
% 231.33/42.52  | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | ALPHA: (337) implies:
% 231.33/42.52  | | | | | | | | | | | | | | | |   (338)  all_57_4 = e2
% 231.33/42.52  | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | REF_CLOSE: (33), (61), (338) are inconsistent by sub-proof
% 231.33/42.52  | | | | | | | | | | | | | | | |            #2441.
% 231.33/42.52  | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | Case 2:
% 231.33/42.52  | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | |   (339)  all_57_9 = e2 & op(e3, e0) = e2
% 231.33/42.52  | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | | REF_CLOSE: (18), (32), (46), (111), (118), (321), (334),
% 231.33/42.52  | | | | | | | | | | | | | | | |            (339) are inconsistent by sub-proof #1538.
% 231.33/42.52  | | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | | End of split
% 231.33/42.52  | | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | End of split
% 231.33/42.52  | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | End of split
% 231.33/42.52  | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | End of split
% 231.33/42.52  | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | Case 2:
% 231.33/42.52  | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | |   (340)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 231.33/42.52  | | | | | | | | | | | |            & op(e3, e0) = e1)
% 231.33/42.52  | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | BETA: splitting (340) gives:
% 231.33/42.52  | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | Case 1:
% 231.33/42.52  | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | |   (341)  all_57_4 = e1 & op(e3, e1) = e1
% 231.33/42.52  | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | REF_CLOSE: (33), (65), (341) are inconsistent by sub-proof
% 231.33/42.52  | | | | | | | | | | | | |            #1411.
% 231.33/42.52  | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | Case 2:
% 231.33/42.52  | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | |   (342)  all_57_9 = e1 & op(e3, e0) = e1
% 231.33/42.52  | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | ALPHA: (342) implies:
% 231.33/42.52  | | | | | | | | | | | | |   (343)  all_57_9 = e1
% 231.33/42.52  | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | BETA: splitting (27) gives:
% 231.33/42.52  | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | Case 1:
% 231.33/42.52  | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | |   (344)  all_55_11 = e3
% 231.33/42.52  | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | COMBINE_EQS: (83), (344) imply:
% 231.33/42.52  | | | | | | | | | | | | | |   (345)  all_53_14 = e3
% 231.33/42.52  | | | | | | | | | | | | | | 
% 231.33/42.52  | | | | | | | | | | | | | | SIMP: (345) implies:
% 231.33/42.52  | | | | | | | | | | | | | |   (346)  all_53_14 = e3
% 231.33/42.52  | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | REDUCE: (93), (346) imply:
% 231.33/42.53  | | | | | | | | | | | | | |   (347)   ~ (all_53_13 = e3)
% 231.33/42.53  | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | BETA: splitting (81) gives:
% 231.33/42.53  | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | Case 1:
% 231.33/42.53  | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | |   (348)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 231.33/42.53  | | | | | | | | | | | | | | |            & op(e2, e2) = e3)
% 231.33/42.53  | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | BETA: splitting (348) gives:
% 231.33/42.53  | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | Case 1:
% 231.33/42.53  | | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | |   (349)  all_57_2 = e3 & op(e2, e3) = e3
% 231.33/42.53  | | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | | ALPHA: (349) implies:
% 231.33/42.53  | | | | | | | | | | | | | | | |   (350)  all_57_2 = e3
% 231.33/42.53  | | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | | BETA: splitting (99) gives:
% 231.33/42.53  | | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | | Case 1:
% 231.33/42.53  | | | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | | |   (351)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 231.33/42.53  | | | | | | | | | | | | | | | | |            & op(e2, e3) = e2)
% 231.33/42.53  | | | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | | | BETA: splitting (351) gives:
% 231.33/42.53  | | | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | | | Case 1:
% 231.33/42.53  | | | | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | | | |   (352)  all_57_0 = e2 & op(e3, e3) = e2
% 231.33/42.53  | | | | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | | | | ALPHA: (352) implies:
% 231.33/42.53  | | | | | | | | | | | | | | | | | |   (353)  op(e3, e3) = e2
% 231.33/42.53  | | | | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (50), (176), (353) are inconsistent by
% 231.33/42.53  | | | | | | | | | | | | | | | | | |            sub-proof #2490.
% 231.33/42.53  | | | | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | | | Case 2:
% 231.33/42.53  | | | | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | | | |   (354)  all_57_2 = e2 & op(e2, e3) = e2
% 231.33/42.53  | | | | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | | | | ALPHA: (354) implies:
% 231.33/42.53  | | | | | | | | | | | | | | | | | |   (355)  all_57_2 = e2
% 231.33/42.53  | | | | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (350), (355) imply:
% 231.33/42.53  | | | | | | | | | | | | | | | | | |   (356)  e3 = e2
% 231.33/42.53  | | | | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (311), (356) imply:
% 231.33/42.53  | | | | | | | | | | | | | | | | | |   (357)  all_57_11 = e2
% 231.33/42.53  | | | | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (18), (21), (23), (24), (51), (128), (176),
% 231.33/42.53  | | | | | | | | | | | | | | | | | |            (317), (357) are inconsistent by sub-proof #2114.
% 231.33/42.53  | | | | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | | | End of split
% 231.33/42.53  | | | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | | Case 2:
% 231.33/42.53  | | | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | | |   (358)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 231.33/42.53  | | | | | | | | | | | | | | | | |            e2 & op(e0, e3) = e2)
% 231.33/42.53  | | | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | | | BETA: splitting (358) gives:
% 231.33/42.53  | | | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | | | Case 1:
% 231.33/42.53  | | | | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | | | |   (359)  all_57_6 = e2 & op(e1, e3) = e2
% 231.33/42.53  | | | | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | | | | ALPHA: (359) implies:
% 231.33/42.53  | | | | | | | | | | | | | | | | | |   (360)  all_57_6 = e2
% 231.33/42.53  | | | | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (61), (360) are inconsistent by sub-proof
% 231.33/42.53  | | | | | | | | | | | | | | | | | |            #1846.
% 231.33/42.53  | | | | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | | | Case 2:
% 231.33/42.53  | | | | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | | | |   (361)  all_57_12 = e2 & op(e0, e3) = e2
% 231.33/42.53  | | | | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | | | | ALPHA: (361) implies:
% 231.33/42.53  | | | | | | | | | | | | | | | | | |   (362)  all_57_12 = e2
% 231.33/42.53  | | | | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | | | | BETA: splitting (12) gives:
% 231.33/42.53  | | | | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | | | | Case 1:
% 231.33/42.53  | | | | | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | | | | |   (363)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 231.33/42.53  | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e1)
% 231.33/42.53  | | | | | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | | | | | BETA: splitting (363) gives:
% 231.33/42.53  | | | | | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | | | | | Case 1:
% 231.33/42.53  | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | | | | | |   (364)  all_57_0 = e1 & op(e3, e3) = e1
% 231.33/42.53  | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | | | | | | ALPHA: (364) implies:
% 231.33/42.53  | | | | | | | | | | | | | | | | | | | |   (365)  op(e3, e3) = e1
% 231.33/42.53  | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (18), (50), (365) are inconsistent by
% 231.33/42.53  | | | | | | | | | | | | | | | | | | | |            sub-proof #2495.
% 231.33/42.53  | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | | | | | Case 2:
% 231.33/42.53  | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | | | | | |   (366)  all_57_2 = e1 & op(e2, e3) = e1
% 231.33/42.53  | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (350), (366) are inconsistent by sub-proof
% 231.33/42.53  | | | | | | | | | | | | | | | | | | | |            #1928.
% 231.33/42.53  | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | | | | | End of split
% 231.33/42.53  | | | | | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | | | | Case 2:
% 231.33/42.53  | | | | | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | | | | |   (367)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 231.33/42.53  | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e3) = e1)
% 231.33/42.53  | | | | | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | | | | | BETA: splitting (367) gives:
% 231.33/42.53  | | | | | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | | | | | Case 1:
% 231.33/42.53  | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | | | | | |   (368)  all_57_6 = e1 & op(e1, e3) = e1
% 231.33/42.53  | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | | | | | | ALPHA: (368) implies:
% 231.33/42.53  | | | | | | | | | | | | | | | | | | | |   (369)  all_57_6 = e1
% 231.33/42.53  | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (18), (28), (33), (37), (50), (51), (61),
% 231.33/42.53  | | | | | | | | | | | | | | | | | | | |            (65), (94), (176), (343), (369) are inconsistent
% 231.33/42.53  | | | | | | | | | | | | | | | | | | | |            by sub-proof #1483.
% 231.33/42.53  | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | | | | | Case 2:
% 231.33/42.53  | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | | | | | |   (370)  all_57_12 = e1 & op(e0, e3) = e1
% 231.33/42.53  | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (94), (362), (370) are inconsistent by sub-proof
% 231.33/42.53  | | | | | | | | | | | | | | | | | | | |            #2388.
% 231.33/42.53  | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | | | | | End of split
% 231.33/42.53  | | | | | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | | | | End of split
% 231.33/42.53  | | | | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | | | End of split
% 231.33/42.53  | | | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | | End of split
% 231.33/42.53  | | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | Case 2:
% 231.33/42.53  | | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | |   (371)  all_57_3 = e3 & op(e2, e2) = e3
% 231.33/42.53  | | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | | ALPHA: (371) implies:
% 231.33/42.53  | | | | | | | | | | | | | | | |   (372)  all_57_3 = e3
% 231.33/42.53  | | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | | REF_CLOSE: (43), (128), (372) are inconsistent by sub-proof
% 231.33/42.53  | | | | | | | | | | | | | | | |            #2358.
% 231.33/42.53  | | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | End of split
% 231.33/42.53  | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | Case 2:
% 231.33/42.53  | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | |   (373)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 231.33/42.53  | | | | | | | | | | | | | | |            e3 & op(e2, e0) = e3)
% 231.33/42.53  | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | BETA: splitting (373) gives:
% 231.33/42.53  | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | Case 1:
% 231.33/42.53  | | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | |   (374)  all_57_5 = e3 & op(e2, e1) = e3
% 231.33/42.53  | | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | | ALPHA: (374) implies:
% 231.33/42.53  | | | | | | | | | | | | | | | |   (375)  all_57_5 = e3
% 231.33/42.53  | | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (16), (18), (28), (33), (37), (46), (49),
% 231.33/42.53  | | | | | | | | | | | | | | | |            (50), (61), (65), (94), (109), (118), (139),
% 231.33/42.53  | | | | | | | | | | | | | | | |            (141), (176), (177), (321), (343), (375) are
% 231.33/42.53  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1728.
% 231.33/42.53  | | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | Case 2:
% 231.33/42.53  | | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | |   (376)  all_57_10 = e3 & op(e2, e0) = e3
% 231.33/42.53  | | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | | ALPHA: (376) implies:
% 231.33/42.53  | | | | | | | | | | | | | | | |   (377)  op(e2, e0) = e3
% 231.33/42.53  | | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | | REF_CLOSE: (18), (80), (347), (377) are inconsistent by
% 231.33/42.53  | | | | | | | | | | | | | | | |            sub-proof #2301.
% 231.33/42.53  | | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | | End of split
% 231.33/42.53  | | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | End of split
% 231.33/42.53  | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | Case 2:
% 231.33/42.53  | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | |   (378)   ~ (all_55_11 = e3)
% 231.33/42.53  | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | REDUCE: (83), (378) imply:
% 231.33/42.53  | | | | | | | | | | | | | |   (379)   ~ (all_53_14 = e3)
% 231.33/42.53  | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | | REF_CLOSE: (18), (47), (312), (379) are inconsistent by
% 231.33/42.53  | | | | | | | | | | | | | |            sub-proof #2330.
% 231.33/42.53  | | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | | End of split
% 231.33/42.53  | | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | | End of split
% 231.33/42.53  | | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | End of split
% 231.33/42.53  | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | Case 2:
% 231.33/42.53  | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | |   (380)  all_55_9 = e0
% 231.33/42.53  | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | | REF_CLOSE: (30), (115), (380) are inconsistent by sub-proof
% 231.33/42.53  | | | | | | | | | | |            #2272.
% 231.33/42.53  | | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | | End of split
% 231.33/42.53  | | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | End of split
% 231.33/42.53  | | | | | | | | | 
% 231.33/42.53  | | | | | | | | Case 2:
% 231.33/42.53  | | | | | | | | | 
% 231.33/42.53  | | | | | | | | |   (381)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 &
% 231.33/42.53  | | | | | | | | |            op(e1, e0) = e1)
% 231.33/42.53  | | | | | | | | | 
% 231.33/42.53  | | | | | | | | | REF_CLOSE: (16), (18), (94), (177), (311), (381) are
% 231.33/42.53  | | | | | | | | |            inconsistent by sub-proof #2217.
% 231.33/42.53  | | | | | | | | | 
% 231.33/42.53  | | | | | | | | End of split
% 231.33/42.53  | | | | | | | | 
% 231.33/42.53  | | | | | | | End of split
% 231.33/42.53  | | | | | | | 
% 231.33/42.53  | | | | | | End of split
% 231.33/42.53  | | | | | | 
% 231.33/42.53  | | | | | End of split
% 231.33/42.53  | | | | | 
% 231.33/42.53  | | | | End of split
% 231.33/42.53  | | | | 
% 231.33/42.53  | | | End of split
% 231.33/42.53  | | | 
% 231.33/42.53  | | End of split
% 231.33/42.53  | | 
% 231.33/42.53  | End of split
% 231.33/42.53  | 
% 231.33/42.53  End of proof
% 231.33/42.53  
% 231.33/42.53  Sub-proof #1411 shows that the following formulas are inconsistent:
% 231.33/42.53  ----------------------------------------------------------------
% 231.33/42.53    (1)  all_57_4 = e1 & op(e3, e1) = e1
% 231.33/42.53    (2)  all_57_4 = e0
% 231.33/42.53    (3)   ~ (e1 = e0)
% 231.33/42.53  
% 231.33/42.53  Begin of proof
% 231.33/42.53  | 
% 231.33/42.53  | ALPHA: (1) implies:
% 231.33/42.53  |   (4)  all_57_4 = e1
% 231.33/42.53  | 
% 231.33/42.53  | COMBINE_EQS: (2), (4) imply:
% 231.33/42.53  |   (5)  e1 = e0
% 231.33/42.53  | 
% 231.33/42.53  | REDUCE: (3), (5) imply:
% 231.33/42.53  |   (6)  $false
% 231.33/42.53  | 
% 231.33/42.53  | CLOSE: (6) is inconsistent.
% 231.33/42.53  | 
% 231.33/42.53  End of proof
% 231.33/42.53  
% 231.33/42.53  Sub-proof #1412 shows that the following formulas are inconsistent:
% 231.33/42.53  ----------------------------------------------------------------
% 231.33/42.53    (1)  all_57_15 = e0
% 231.33/42.53    (2)  all_57_2 = e2
% 231.33/42.53    (3)  all_57_3 = e0
% 231.33/42.53    (4)   ~ (e3 = e2)
% 231.33/42.53    (5)   ~ (e2 = e0)
% 231.33/42.53    (6)  all_57_10 = e3
% 231.33/42.53    (7)  all_57_5 = e1
% 231.33/42.53    (8)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.33/42.53         (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.33/42.53    (9)   ~ (e2 = e1)
% 231.33/42.53    (10)  all_57_15 = e2 & op(e0, e0) = e2
% 231.33/42.53  
% 231.33/42.53  Begin of proof
% 231.33/42.53  | 
% 231.33/42.53  | ALPHA: (10) implies:
% 231.33/42.53  |   (11)  all_57_15 = e2
% 231.33/42.53  | 
% 231.33/42.53  | COMBINE_EQS: (1), (11) imply:
% 231.33/42.53  |   (12)  e2 = e0
% 231.33/42.53  | 
% 231.33/42.53  | COMBINE_EQS: (2), (12) imply:
% 231.33/42.53  |   (13)  all_57_2 = e0
% 231.33/42.53  | 
% 231.33/42.53  | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (13) are inconsistent by
% 231.33/42.53  |            sub-proof #2249.
% 231.33/42.53  | 
% 231.33/42.53  End of proof
% 231.33/42.53  
% 231.33/42.53  Sub-proof #1413 shows that the following formulas are inconsistent:
% 231.33/42.53  ----------------------------------------------------------------
% 231.33/42.53    (1)   ~ (all_10_2 = e2)
% 231.33/42.53    (2)  op(e3, e3) = all_10_2
% 231.33/42.53    (3)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 231.33/42.53    (4)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 231.33/42.53    (5)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.33/42.53         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.33/42.53    (6)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.33/42.53         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.33/42.53    (7)   ~ (all_53_8 = all_53_12)
% 231.33/42.53    (8)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.33/42.53         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.33/42.53    (9)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 231.33/42.53         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.33/42.53    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.33/42.53            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.33/42.53    (11)  all_55_0 = all_10_2
% 231.33/42.53    (12)   ~ (all_10_2 = e0)
% 231.33/42.53    (13)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.33/42.53          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.33/42.53    (14)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 231.33/42.53            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 231.33/42.53              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 231.33/42.53    (15)   ~ (all_6_2 = e3)
% 231.33/42.53    (16)  op(e1, e1) = all_6_2
% 231.33/42.53    (17)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 231.33/42.53    (18)   ~ (all_53_9 = e0)
% 231.33/42.53    (19)  all_55_0 = e3 | all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 231.33/42.53    (20)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.33/42.53          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.33/42.53    (21)   ~ (all_53_4 = all_53_12)
% 231.33/42.53    (22)   ~ (all_53_8 = all_53_9)
% 231.33/42.53    (23)  all_42_2 = all_6_2
% 231.33/42.53    (24)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.33/42.53          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.33/42.53    (25)   ~ (all_53_9 = all_6_2)
% 231.33/42.53    (26)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.33/42.53          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.33/42.53    (27)  all_57_3 = e0
% 231.33/42.53    (28)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.33/42.53          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.33/42.53    (29)   ~ (e3 = e2)
% 231.33/42.53    (30)  all_55_1 = all_53_4
% 231.33/42.53    (31)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.33/42.53          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.33/42.53    (32)   ~ (all_53_8 = all_6_2)
% 231.33/42.53    (33)  all_55_2 = all_53_8
% 231.33/42.53    (34)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 231.33/42.53    (35)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.33/42.53          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.33/42.53            e1)
% 231.33/42.53    (36)   ~ (all_53_4 = all_53_8)
% 231.33/42.53    (37)  op(e3, e2) = all_53_4
% 231.33/42.53    (38)   ~ (e2 = e0)
% 231.33/42.53    (39)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 231.33/42.53            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 231.33/42.53            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 231.33/42.53            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 231.33/42.53              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 231.33/42.53            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 231.33/42.53            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 231.33/42.53              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 231.33/42.53              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 231.33/42.53            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 231.33/42.53            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 231.33/42.53            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 231.33/42.53              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 231.33/42.53              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 231.33/42.53            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 231.33/42.53              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 231.33/42.53            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 231.33/42.53            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 231.33/42.53              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 231.33/42.53              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 231.33/42.53            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 231.33/42.53            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 231.33/42.53    (40)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 231.33/42.53          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.33/42.53    (41)   ~ (e1 = e0)
% 231.33/42.53    (42)  all_57_14 = e2
% 231.33/42.53    (43)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 231.33/42.53            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 231.33/42.53              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 231.33/42.53    (44)   ~ (all_53_4 = e0)
% 231.33/42.53    (45)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.33/42.53          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.33/42.53    (46)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.33/42.53          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.33/42.53    (47)   ~ (all_10_2 = e1)
% 231.33/42.53    (48)   ~ (all_53_4 = all_53_6)
% 231.33/42.53    (49)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.33/42.53          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.33/42.53            e2)
% 231.33/42.53    (50)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.33/42.53              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.33/42.53                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.33/42.53                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.33/42.53    (51)  all_55_10 = all_6_2
% 231.33/42.53    (52)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.33/42.53          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.33/42.53    (53)  all_38_2 = all_6_2
% 231.33/42.53    (54)  all_55_3 = all_53_12
% 231.33/42.53    (55)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 231.33/42.53            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 231.33/42.53              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 231.33/42.53    (56)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.33/42.53          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.33/42.53    (57)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 231.33/42.53          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 231.33/42.53    (58)   ~ (all_53_12 = all_10_2)
% 231.33/42.53    (59)   ~ (e2 = e1)
% 231.33/42.53    (60)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.33/42.53          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.33/42.53    (61)  op(e2, e1) = all_53_9
% 231.33/42.53    (62)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 231.33/42.53    (63)  op(e1, e2) = all_53_6
% 231.33/42.53    (64)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.33/42.53          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.33/42.53    (65)  all_24_2 = all_6_2
% 231.33/42.53    (66)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.33/42.53          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.33/42.53    (67)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.33/42.53          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.33/42.53    (68)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.33/42.53          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.33/42.53    (69)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 231.33/42.53          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 231.33/42.53    (70)  op(e3, e1) = all_53_8
% 231.33/42.53    (71)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.33/42.53          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.33/42.53    (72)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 231.33/42.53          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 231.33/42.53    (73)  op(e3, e0) = all_53_12
% 231.33/42.53  
% 231.33/42.53  Begin of proof
% 231.33/42.53  | 
% 231.33/42.53  | BETA: splitting (62) gives:
% 231.33/42.53  | 
% 231.33/42.53  | Case 1:
% 231.33/42.53  | | 
% 231.33/42.53  | |   (74)  all_57_14 = e3 & op(e0, e1) = e3
% 231.33/42.53  | | 
% 231.33/42.53  | | ALPHA: (74) implies:
% 231.33/42.53  | |   (75)  all_57_14 = e3
% 231.33/42.53  | | 
% 231.33/42.53  | | REF_CLOSE: (29), (42), (75) are inconsistent by sub-proof #2410.
% 231.33/42.53  | | 
% 231.33/42.53  | Case 2:
% 231.33/42.53  | | 
% 231.33/42.53  | |   (76)  all_57_15 = e3 & op(e0, e0) = e3
% 231.33/42.53  | | 
% 231.33/42.53  | | ALPHA: (76) implies:
% 231.33/42.53  | |   (77)  all_57_15 = e3
% 231.33/42.53  | |   (78)  op(e0, e0) = e3
% 231.33/42.53  | | 
% 231.33/42.53  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 231.33/42.53  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 231.33/42.53  | |            (24), (25), (26), (27), (28), (30), (31), (32), (33), (34), (35),
% 231.33/42.53  | |            (36), (37), (38), (39), (40), (41), (43), (44), (45), (46), (47),
% 231.33/42.53  | |            (48), (49), (50), (51), (52), (53), (54), (55), (56), (57), (58),
% 231.33/42.53  | |            (59), (60), (61), (63), (64), (65), (66), (67), (68), (69), (70),
% 231.33/42.53  | |            (71), (72), (73), (77), (78) are inconsistent by sub-proof #1414.
% 231.33/42.53  | | 
% 231.33/42.53  | End of split
% 231.33/42.53  | 
% 231.33/42.53  End of proof
% 231.33/42.53  
% 231.33/42.53  Sub-proof #1414 shows that the following formulas are inconsistent:
% 231.33/42.53  ----------------------------------------------------------------
% 231.33/42.53    (1)   ~ (all_10_2 = e2)
% 231.33/42.53    (2)  op(e3, e3) = all_10_2
% 231.33/42.53    (3)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 231.33/42.53    (4)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 231.33/42.53    (5)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.33/42.53         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.33/42.53    (6)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.33/42.53         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.33/42.53    (7)   ~ (all_53_8 = all_53_12)
% 231.33/42.53    (8)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.33/42.53         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.33/42.53    (9)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 231.33/42.53         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.33/42.53    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.33/42.53            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.33/42.53    (11)  all_55_0 = all_10_2
% 231.33/42.53    (12)   ~ (all_10_2 = e0)
% 231.33/42.53    (13)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.33/42.53          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.33/42.53    (14)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 231.33/42.53            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 231.33/42.53              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 231.33/42.53    (15)   ~ (all_6_2 = e3)
% 231.33/42.53    (16)  op(e1, e1) = all_6_2
% 231.33/42.53    (17)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 231.33/42.53    (18)   ~ (all_53_9 = e0)
% 231.33/42.53    (19)  all_55_0 = e3 | all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 231.33/42.53    (20)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.33/42.53          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.33/42.53    (21)   ~ (all_53_4 = all_53_12)
% 231.33/42.53    (22)   ~ (all_53_8 = all_53_9)
% 231.33/42.53    (23)  all_42_2 = all_6_2
% 231.33/42.53    (24)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.33/42.53          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.33/42.53    (25)   ~ (all_53_9 = all_6_2)
% 231.33/42.53    (26)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.33/42.53          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.33/42.53    (27)  all_57_3 = e0
% 231.33/42.53    (28)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.33/42.53          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.33/42.53    (29)  all_55_1 = all_53_4
% 231.33/42.53    (30)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.33/42.53          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.33/42.53    (31)   ~ (all_53_8 = all_6_2)
% 231.33/42.53    (32)  all_55_2 = all_53_8
% 231.33/42.53    (33)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 231.33/42.53    (34)  all_57_15 = e3
% 231.33/42.53    (35)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.33/42.53          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.33/42.53            e1)
% 231.33/42.53    (36)   ~ (all_53_4 = all_53_8)
% 231.33/42.53    (37)  op(e3, e2) = all_53_4
% 231.33/42.53    (38)   ~ (e2 = e0)
% 231.33/42.53    (39)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 231.33/42.53            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 231.33/42.53            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 231.33/42.53            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 231.33/42.53              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 231.33/42.53            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 231.33/42.53            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 231.33/42.53              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 231.33/42.53              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 231.33/42.53            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 231.33/42.53            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 231.33/42.53            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 231.33/42.53              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 231.33/42.53              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 231.33/42.53            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 231.33/42.53              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 231.33/42.53            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 231.33/42.53            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 231.33/42.53              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 231.33/42.53              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 231.33/42.53            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 231.33/42.53            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 231.33/42.53    (40)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 231.33/42.53          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.33/42.53    (41)   ~ (e1 = e0)
% 231.33/42.53    (42)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 231.33/42.53            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 231.33/42.53              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 231.33/42.53    (43)   ~ (all_53_4 = e0)
% 231.33/42.53    (44)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.33/42.53          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.33/42.53    (45)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.33/42.53          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.33/42.53    (46)   ~ (all_10_2 = e1)
% 231.33/42.53    (47)  op(e0, e0) = e3
% 231.33/42.53    (48)   ~ (all_53_4 = all_53_6)
% 231.33/42.53    (49)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.33/42.53          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.33/42.53            e2)
% 231.33/42.53    (50)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.33/42.53              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.33/42.53                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.33/42.53                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.33/42.53    (51)  all_55_10 = all_6_2
% 231.33/42.53    (52)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.33/42.53          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.33/42.53    (53)  all_38_2 = all_6_2
% 231.33/42.53    (54)  all_55_3 = all_53_12
% 231.33/42.53    (55)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 231.33/42.53            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 231.33/42.53              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 231.33/42.53    (56)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.33/42.53          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.33/42.53    (57)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 231.33/42.53          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 231.33/42.53    (58)   ~ (all_53_12 = all_10_2)
% 231.33/42.53    (59)   ~ (e2 = e1)
% 231.33/42.53    (60)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.33/42.53          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.33/42.53    (61)  op(e2, e1) = all_53_9
% 231.33/42.53    (62)  op(e1, e2) = all_53_6
% 231.33/42.54    (63)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.33/42.54          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.33/42.54    (64)  all_24_2 = all_6_2
% 231.33/42.54    (65)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.33/42.54          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.33/42.54    (66)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.33/42.54          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.33/42.54    (67)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.33/42.54          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.33/42.54    (68)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 231.33/42.54          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 231.33/42.54    (69)  op(e3, e1) = all_53_8
% 231.33/42.54    (70)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.33/42.54          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.33/42.54    (71)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 231.33/42.54          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 231.33/42.54    (72)  op(e3, e0) = all_53_12
% 231.33/42.54  
% 231.33/42.54  Begin of proof
% 231.33/42.54  | 
% 231.33/42.54  | BETA: splitting (19) gives:
% 231.33/42.54  | 
% 231.33/42.54  | Case 1:
% 231.33/42.54  | | 
% 231.33/42.54  | |   (73)  all_55_0 = e3
% 231.33/42.54  | | 
% 231.33/42.54  | | COMBINE_EQS: (11), (73) imply:
% 231.33/42.54  | |   (74)  all_10_2 = e3
% 231.33/42.54  | | 
% 231.33/42.54  | | REDUCE: (58), (74) imply:
% 231.33/42.54  | |   (75)   ~ (all_53_12 = e3)
% 231.33/42.54  | | 
% 231.33/42.54  | | REDUCE: (1), (74) imply:
% 231.33/42.54  | |   (76)   ~ (e3 = e2)
% 231.33/42.54  | | 
% 231.33/42.54  | | REDUCE: (46), (74) imply:
% 231.33/42.54  | |   (77)   ~ (e3 = e1)
% 231.33/42.54  | | 
% 231.33/42.54  | | REDUCE: (12), (74) imply:
% 231.33/42.54  | |   (78)   ~ (e3 = e0)
% 231.33/42.54  | | 
% 231.33/42.54  | | REDUCE: (2), (74) imply:
% 231.33/42.54  | |   (79)  op(e3, e3) = e3
% 231.33/42.54  | | 
% 231.33/42.54  | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (10), (13), (14), (15), (16),
% 231.33/42.54  | |            (17), (18), (20), (21), (22), (23), (24), (25), (26), (27), (28),
% 231.33/42.54  | |            (29), (30), (31), (32), (33), (34), (35), (36), (37), (38), (39),
% 231.33/42.54  | |            (40), (41), (42), (43), (44), (45), (47), (48), (49), (50), (51),
% 231.33/42.54  | |            (52), (53), (54), (55), (56), (57), (59), (60), (61), (62), (63),
% 231.33/42.54  | |            (64), (65), (66), (67), (68), (69), (70), (71), (72), (75), (76),
% 231.33/42.54  | |            (77), (78), (79) are inconsistent by sub-proof #1415.
% 231.33/42.54  | | 
% 231.33/42.54  | Case 2:
% 231.33/42.54  | | 
% 231.33/42.54  | |   (80)  all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 231.33/42.54  | | 
% 231.33/42.54  | | REF_CLOSE: (1), (11), (12), (46), (80) are inconsistent by sub-proof #1953.
% 231.33/42.54  | | 
% 231.33/42.54  | End of split
% 231.33/42.54  | 
% 231.33/42.54  End of proof
% 231.33/42.54  
% 231.33/42.54  Sub-proof #1415 shows that the following formulas are inconsistent:
% 231.33/42.54  ----------------------------------------------------------------
% 231.33/42.54    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 231.33/42.54    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 231.33/42.54    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.33/42.54         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.33/42.54    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.33/42.54         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.33/42.54    (5)   ~ (all_53_8 = all_53_12)
% 231.33/42.54    (6)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.33/42.54         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.33/42.54    (7)   ~ (e3 = e1)
% 231.33/42.54    (8)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 231.33/42.54         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.33/42.54    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.33/42.54           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.33/42.54    (10)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.33/42.54          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.33/42.54    (11)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 231.33/42.54            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 231.33/42.54              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 231.33/42.54    (12)   ~ (all_6_2 = e3)
% 231.33/42.54    (13)  op(e1, e1) = all_6_2
% 231.33/42.54    (14)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 231.33/42.54    (15)   ~ (all_53_9 = e0)
% 231.33/42.54    (16)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.33/42.54          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.33/42.54    (17)   ~ (all_53_4 = all_53_12)
% 231.33/42.54    (18)   ~ (all_53_8 = all_53_9)
% 231.33/42.54    (19)  all_42_2 = all_6_2
% 231.33/42.54    (20)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.33/42.54          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.33/42.54    (21)   ~ (all_53_9 = all_6_2)
% 231.33/42.54    (22)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.33/42.54          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.33/42.54    (23)  all_57_3 = e0
% 231.33/42.54    (24)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.33/42.54          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.33/42.54    (25)   ~ (e3 = e2)
% 231.33/42.54    (26)  all_55_1 = all_53_4
% 231.33/42.54    (27)   ~ (e3 = e0)
% 231.33/42.54    (28)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.33/42.54          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.33/42.54    (29)  op(e3, e3) = e3
% 231.33/42.54    (30)   ~ (all_53_8 = all_6_2)
% 231.33/42.54    (31)  all_55_2 = all_53_8
% 231.33/42.54    (32)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 231.33/42.54    (33)  all_57_15 = e3
% 231.33/42.54    (34)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.33/42.54          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.33/42.54            e1)
% 231.33/42.54    (35)   ~ (all_53_4 = all_53_8)
% 231.33/42.54    (36)  op(e3, e2) = all_53_4
% 231.33/42.54    (37)   ~ (e2 = e0)
% 231.33/42.54    (38)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 231.33/42.54            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 231.33/42.54            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 231.33/42.54            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 231.33/42.54              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 231.33/42.54            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 231.33/42.54            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 231.33/42.54              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 231.33/42.54              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 231.33/42.54            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 231.33/42.54            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 231.33/42.54            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 231.33/42.54              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 231.33/42.54              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 231.33/42.54            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 231.33/42.54              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 231.33/42.54            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 231.33/42.54            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 231.33/42.54              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 231.33/42.54              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 231.33/42.54            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 231.33/42.54            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 231.33/42.54    (39)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 231.33/42.54          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.33/42.54    (40)   ~ (e1 = e0)
% 231.33/42.54    (41)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 231.33/42.54            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 231.33/42.54              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 231.33/42.54    (42)   ~ (all_53_4 = e0)
% 231.33/42.54    (43)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.33/42.54          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.33/42.54    (44)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.33/42.54          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.33/42.54    (45)  op(e0, e0) = e3
% 231.33/42.54    (46)   ~ (all_53_4 = all_53_6)
% 231.33/42.54    (47)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.33/42.54          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.33/42.54            e2)
% 231.33/42.54    (48)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.33/42.54              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.33/42.54                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.33/42.54                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.33/42.54    (49)  all_55_10 = all_6_2
% 231.33/42.54    (50)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.33/42.54          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.33/42.54    (51)  all_38_2 = all_6_2
% 231.33/42.54    (52)  all_55_3 = all_53_12
% 231.33/42.54    (53)   ~ (all_53_12 = e3)
% 231.33/42.54    (54)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 231.33/42.54            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 231.33/42.54              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 231.33/42.54    (55)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.33/42.54          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.33/42.54    (56)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 231.33/42.54          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 231.33/42.54    (57)   ~ (e2 = e1)
% 231.33/42.54    (58)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.33/42.54          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.33/42.54    (59)  op(e2, e1) = all_53_9
% 231.33/42.54    (60)  op(e1, e2) = all_53_6
% 231.33/42.54    (61)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.33/42.54          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.33/42.54    (62)  all_24_2 = all_6_2
% 231.33/42.54    (63)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.33/42.54          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.33/42.54    (64)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.33/42.54          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.33/42.54    (65)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.33/42.54          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.33/42.54    (66)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 231.33/42.54          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 231.33/42.54    (67)  op(e3, e1) = all_53_8
% 231.33/42.54    (68)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.33/42.54          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.33/42.54    (69)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 231.33/42.54          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 231.33/42.54    (70)  op(e3, e0) = all_53_12
% 231.33/42.54  
% 231.33/42.54  Begin of proof
% 231.33/42.54  | 
% 231.33/42.54  | BETA: splitting (50) gives:
% 231.33/42.54  | 
% 231.33/42.54  | Case 1:
% 231.33/42.54  | | 
% 231.33/42.54  | |   (71)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 231.33/42.54  | |           e3)
% 231.33/42.54  | | 
% 231.33/42.54  | | BETA: splitting (71) gives:
% 231.33/42.54  | | 
% 231.33/42.54  | | Case 1:
% 231.33/42.54  | | | 
% 231.33/42.54  | | |   (72)  all_57_2 = e3 & op(e2, e3) = e3
% 231.33/42.54  | | | 
% 231.33/42.54  | | | ALPHA: (72) implies:
% 231.33/42.54  | | |   (73)  all_57_2 = e3
% 231.33/42.54  | | | 
% 231.33/42.54  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 231.33/42.54  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 231.33/42.54  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 231.33/42.54  | | |            (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 231.33/42.54  | | |            (43), (45), (46), (47), (48), (49), (51), (52), (53), (54),
% 231.33/42.54  | | |            (55), (57), (58), (59), (60), (61), (62), (63), (64), (65),
% 231.33/42.54  | | |            (66), (67), (68), (69), (70), (73) are inconsistent by
% 231.33/42.54  | | |            sub-proof #1437.
% 231.33/42.54  | | | 
% 231.33/42.54  | | Case 2:
% 231.33/42.54  | | | 
% 231.33/42.54  | | |   (74)  all_57_3 = e3 & op(e2, e2) = e3
% 231.33/42.54  | | | 
% 231.33/42.54  | | | ALPHA: (74) implies:
% 231.33/42.54  | | |   (75)  all_57_3 = e3
% 231.33/42.54  | | | 
% 231.33/42.54  | | | REF_CLOSE: (23), (27), (75) are inconsistent by sub-proof #2358.
% 231.33/42.54  | | | 
% 231.33/42.54  | | End of split
% 231.33/42.54  | | 
% 231.33/42.54  | Case 2:
% 231.33/42.54  | | 
% 231.33/42.54  | |   (76)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 231.33/42.54  | |           e3)
% 231.33/42.54  | | 
% 231.33/42.54  | | BETA: splitting (76) gives:
% 231.33/42.54  | | 
% 231.33/42.54  | | Case 1:
% 231.33/42.54  | | | 
% 231.33/42.54  | | |   (77)  all_57_5 = e3 & op(e2, e1) = e3
% 231.33/42.54  | | | 
% 231.33/42.54  | | | ALPHA: (77) implies:
% 231.33/42.54  | | |   (78)  all_57_5 = e3
% 231.33/42.54  | | |   (79)  op(e2, e1) = e3
% 231.33/42.54  | | | 
% 231.33/42.54  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 231.33/42.54  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 231.33/42.54  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 231.33/42.54  | | |            (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 231.33/42.54  | | |            (45), (46), (47), (48), (49), (51), (52), (53), (54), (55),
% 231.33/42.54  | | |            (57), (58), (59), (60), (61), (62), (63), (64), (65), (66),
% 231.33/42.54  | | |            (67), (68), (69), (70), (78), (79) are inconsistent by
% 231.33/42.54  | | |            sub-proof #1438.
% 231.33/42.54  | | | 
% 231.33/42.54  | | Case 2:
% 231.33/42.54  | | | 
% 231.33/42.54  | | |   (80)  all_57_10 = e3 & op(e2, e0) = e3
% 231.33/42.54  | | | 
% 231.33/42.54  | | | ALPHA: (80) implies:
% 231.33/42.54  | | |   (81)  all_57_10 = e3
% 231.33/42.54  | | | 
% 231.33/42.54  | | | REF_CLOSE: (3), (4), (6), (7), (8), (9), (10), (12), (13), (16), (20),
% 231.33/42.54  | | |            (22), (23), (24), (25), (27), (29), (33), (34), (37), (40),
% 231.33/42.54  | | |            (43), (44), (47), (48), (55), (56), (57), (58), (61), (63),
% 231.33/42.54  | | |            (64), (65), (68), (81) are inconsistent by sub-proof #1416.
% 231.33/42.54  | | | 
% 231.33/42.54  | | End of split
% 231.33/42.54  | | 
% 231.33/42.54  | End of split
% 231.33/42.54  | 
% 231.33/42.54  End of proof
% 231.33/42.54  
% 231.33/42.54  Sub-proof #1416 shows that the following formulas are inconsistent:
% 231.33/42.54  ----------------------------------------------------------------
% 231.33/42.54    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.33/42.54         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.33/42.54    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.33/42.54         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.33/42.54    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.33/42.54         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.33/42.54    (4)   ~ (e3 = e1)
% 231.33/42.54    (5)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 231.33/42.54         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.33/42.54    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.33/42.54           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.33/42.54    (7)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.33/42.54         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.33/42.54    (8)   ~ (all_6_2 = e3)
% 231.33/42.54    (9)  op(e1, e1) = all_6_2
% 231.33/42.54    (10)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.33/42.54          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.33/42.54    (11)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.33/42.54          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.33/42.54    (12)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.33/42.54          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.33/42.54    (13)  all_57_3 = e0
% 231.33/42.54    (14)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.33/42.54          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.33/42.54    (15)   ~ (e3 = e2)
% 231.33/42.54    (16)   ~ (e3 = e0)
% 231.33/42.54    (17)  op(e3, e3) = e3
% 231.33/42.54    (18)  all_57_15 = e3
% 231.33/42.54    (19)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.33/42.54          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.33/42.54            e1)
% 231.33/42.54    (20)   ~ (e2 = e0)
% 231.33/42.54    (21)   ~ (e1 = e0)
% 231.33/42.54    (22)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.33/42.54          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.33/42.54    (23)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.33/42.54          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.33/42.54    (24)  all_57_10 = e3
% 231.33/42.54    (25)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.33/42.54          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.33/42.54            e2)
% 231.33/42.54    (26)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.33/42.54              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.33/42.54                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.33/42.54                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.33/42.54    (27)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.33/42.54          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.33/42.54    (28)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 231.33/42.54          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 231.33/42.54    (29)   ~ (e2 = e1)
% 231.33/42.54    (30)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.33/42.54          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.33/42.54    (31)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.33/42.54          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.33/42.54    (32)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.33/42.54          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.33/42.54    (33)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.33/42.54          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.33/42.54    (34)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.33/42.54          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.33/42.54    (35)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.33/42.54          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.33/42.54  
% 231.33/42.54  Begin of proof
% 231.33/42.54  | 
% 231.33/42.54  | BETA: splitting (22) gives:
% 231.33/42.54  | 
% 231.33/42.54  | Case 1:
% 231.33/42.54  | | 
% 231.33/42.54  | |   (36)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) =
% 231.33/42.54  | |           e3)
% 231.33/42.54  | | 
% 231.33/42.54  | | BETA: splitting (36) gives:
% 231.33/42.54  | | 
% 231.33/42.54  | | Case 1:
% 231.33/42.54  | | | 
% 231.33/42.54  | | |   (37)  all_57_4 = e3 & op(e3, e1) = e3
% 231.33/42.54  | | | 
% 231.33/42.54  | | | ALPHA: (37) implies:
% 231.33/42.54  | | |   (38)  all_57_4 = e3
% 231.33/42.54  | | | 
% 231.33/42.54  | | | BETA: splitting (23) gives:
% 231.33/42.54  | | | 
% 231.33/42.54  | | | Case 1:
% 231.33/42.54  | | | | 
% 231.33/42.54  | | | |   (39)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2)
% 231.33/42.54  | | | |           = e3)
% 231.33/42.54  | | | | 
% 231.33/42.54  | | | | REF_CLOSE: (4), (10), (11), (12), (13), (15), (16), (18), (20), (21),
% 231.33/42.54  | | | |            (24), (26), (29), (30), (38), (39) are inconsistent by
% 231.33/42.54  | | | |            sub-proof #1435.
% 231.33/42.54  | | | | 
% 231.33/42.54  | | | Case 2:
% 231.33/42.54  | | | | 
% 231.33/42.54  | | | |   (40)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2)
% 231.33/42.54  | | | |           = e3)
% 231.33/42.54  | | | | 
% 231.33/42.54  | | | | BETA: splitting (40) gives:
% 231.33/42.54  | | | | 
% 231.33/42.54  | | | | Case 1:
% 231.33/42.54  | | | | | 
% 231.33/42.54  | | | | |   (41)  all_57_7 = e3 & op(e1, e2) = e3
% 231.33/42.54  | | | | | 
% 231.33/42.54  | | | | | ALPHA: (41) implies:
% 231.33/42.54  | | | | |   (42)  all_57_7 = e3
% 231.33/42.54  | | | | | 
% 231.33/42.54  | | | | | BETA: splitting (12) gives:
% 231.33/42.54  | | | | | 
% 231.33/42.54  | | | | | Case 1:
% 231.33/42.54  | | | | | | 
% 231.33/42.54  | | | | | |   (43)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3,
% 231.33/42.54  | | | | | |             e2) = e0)
% 231.33/42.54  | | | | | | 
% 231.33/42.54  | | | | | | BETA: splitting (43) gives:
% 231.33/42.54  | | | | | | 
% 231.33/42.54  | | | | | | Case 1:
% 231.33/42.54  | | | | | | | 
% 231.33/42.54  | | | | | | |   (44)  all_57_0 = e0 & op(e3, e3) = e0
% 231.33/42.54  | | | | | | | 
% 231.33/42.54  | | | | | | | ALPHA: (44) implies:
% 231.33/42.54  | | | | | | |   (45)  op(e3, e3) = e0
% 231.33/42.54  | | | | | | | 
% 231.33/42.54  | | | | | | | REF_CLOSE: (6), (16), (17), (45) are inconsistent by sub-proof
% 231.33/42.54  | | | | | | |            #2494.
% 231.33/42.54  | | | | | | | 
% 231.33/42.54  | | | | | | Case 2:
% 231.33/42.54  | | | | | | | 
% 231.33/42.54  | | | | | | |   (46)  all_57_1 = e0 & op(e3, e2) = e0
% 231.33/42.54  | | | | | | | 
% 231.33/42.54  | | | | | | | ALPHA: (46) implies:
% 231.33/42.54  | | | | | | |   (47)  all_57_1 = e0
% 231.33/42.54  | | | | | | | 
% 231.33/42.54  | | | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (10), (11), (13), (15), (16),
% 231.33/42.54  | | | | | | |            (17), (18), (19), (20), (21), (24), (25), (26), (27),
% 231.33/42.54  | | | | | | |            (28), (29), (30), (33), (34), (35), (38), (42), (47)
% 231.33/42.54  | | | | | | |            are inconsistent by sub-proof #1428.
% 231.33/42.54  | | | | | | | 
% 231.33/42.54  | | | | | | End of split
% 231.33/42.54  | | | | | | 
% 231.33/42.54  | | | | | Case 2:
% 231.33/42.54  | | | | | | 
% 231.33/42.54  | | | | | |   (48)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3,
% 231.33/42.54  | | | | | |             e0) = e0)
% 231.33/42.54  | | | | | | 
% 231.33/42.54  | | | | | | REF_CLOSE: (4), (15), (16), (18), (20), (21), (24), (26), (29),
% 231.33/42.54  | | | | | |            (30), (34), (38), (48) are inconsistent by sub-proof
% 231.33/42.54  | | | | | |            #1427.
% 231.33/42.54  | | | | | | 
% 231.33/42.54  | | | | | End of split
% 231.33/42.54  | | | | | 
% 231.33/42.54  | | | | Case 2:
% 231.33/42.54  | | | | | 
% 231.33/42.54  | | | | |   (49)  all_57_13 = e3 & op(e0, e2) = e3
% 231.33/42.54  | | | | | 
% 231.33/42.54  | | | | | ALPHA: (49) implies:
% 231.33/42.54  | | | | |   (50)  all_57_13 = e3
% 231.33/42.54  | | | | | 
% 231.33/42.54  | | | | | BETA: splitting (12) gives:
% 231.33/42.54  | | | | | 
% 231.33/42.54  | | | | | Case 1:
% 231.33/42.54  | | | | | | 
% 231.33/42.54  | | | | | |   (51)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3,
% 231.33/42.54  | | | | | |             e2) = e0)
% 231.33/42.54  | | | | | | 
% 231.33/42.54  | | | | | | BETA: splitting (51) gives:
% 231.33/42.54  | | | | | | 
% 231.33/42.54  | | | | | | Case 1:
% 231.33/42.54  | | | | | | | 
% 231.33/42.54  | | | | | | |   (52)  all_57_0 = e0 & op(e3, e3) = e0
% 231.33/42.54  | | | | | | | 
% 231.33/42.54  | | | | | | | ALPHA: (52) implies:
% 231.33/42.54  | | | | | | |   (53)  op(e3, e3) = e0
% 231.33/42.54  | | | | | | | 
% 231.33/42.54  | | | | | | | REF_CLOSE: (6), (16), (17), (53) are inconsistent by sub-proof
% 231.33/42.54  | | | | | | |            #2494.
% 231.33/42.54  | | | | | | | 
% 231.33/42.54  | | | | | | Case 2:
% 231.33/42.54  | | | | | | | 
% 231.33/42.54  | | | | | | |   (54)  all_57_1 = e0 & op(e3, e2) = e0
% 231.33/42.54  | | | | | | | 
% 231.33/42.54  | | | | | | | ALPHA: (54) implies:
% 231.33/42.54  | | | | | | |   (55)  all_57_1 = e0
% 231.33/42.54  | | | | | | | 
% 231.33/42.54  | | | | | | | BETA: splitting (35) gives:
% 231.33/42.54  | | | | | | | 
% 231.33/42.54  | | | | | | | Case 1:
% 231.33/42.54  | | | | | | | | 
% 231.33/42.54  | | | | | | | |   (56)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 &
% 231.33/42.54  | | | | | | | |           op(e2, e2) = e1)
% 231.33/42.54  | | | | | | | | 
% 231.33/42.54  | | | | | | | | BETA: splitting (56) gives:
% 231.33/42.54  | | | | | | | | 
% 231.33/42.54  | | | | | | | | Case 1:
% 231.33/42.54  | | | | | | | | | 
% 231.33/42.54  | | | | | | | | |   (57)  all_57_1 = e1 & op(e3, e2) = e1
% 231.33/42.54  | | | | | | | | | 
% 231.33/42.54  | | | | | | | | | REF_CLOSE: (21), (55), (57) are inconsistent by sub-proof
% 231.33/42.54  | | | | | | | | |            #2446.
% 231.33/42.54  | | | | | | | | | 
% 231.33/42.54  | | | | | | | | Case 2:
% 231.33/42.54  | | | | | | | | | 
% 231.33/42.54  | | | | | | | | |   (58)  all_57_3 = e1 & op(e2, e2) = e1
% 231.33/42.54  | | | | | | | | | 
% 231.33/42.54  | | | | | | | | | REF_CLOSE: (13), (21), (58) are inconsistent by sub-proof
% 231.33/42.54  | | | | | | | | |            #2362.
% 231.33/42.54  | | | | | | | | | 
% 231.33/42.54  | | | | | | | | End of split
% 231.33/42.54  | | | | | | | | 
% 231.33/42.54  | | | | | | | Case 2:
% 231.33/42.54  | | | | | | | | 
% 231.33/42.54  | | | | | | | |   (59)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 &
% 231.33/42.54  | | | | | | | |           op(e0, e2) = e1)
% 231.33/42.54  | | | | | | | | 
% 231.33/42.54  | | | | | | | | BETA: splitting (59) gives:
% 231.33/42.54  | | | | | | | | 
% 231.33/42.54  | | | | | | | | Case 1:
% 231.33/42.54  | | | | | | | | | 
% 231.33/42.54  | | | | | | | | |   (60)  all_57_7 = e1 & op(e1, e2) = e1
% 231.33/42.54  | | | | | | | | | 
% 231.33/42.54  | | | | | | | | | ALPHA: (60) implies:
% 231.33/42.54  | | | | | | | | |   (61)  all_57_7 = e1
% 231.33/42.54  | | | | | | | | | 
% 231.33/42.54  | | | | | | | | | BETA: splitting (7) gives:
% 231.33/42.54  | | | | | | | | | 
% 231.33/42.54  | | | | | | | | | Case 1:
% 231.33/42.54  | | | | | | | | | | 
% 231.33/42.54  | | | | | | | | | |   (62)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 &
% 231.33/42.54  | | | | | | | | | |           op(e1, e2) = e3)
% 231.33/42.54  | | | | | | | | | | 
% 231.33/42.54  | | | | | | | | | | BETA: splitting (62) gives:
% 231.33/42.54  | | | | | | | | | | 
% 231.33/42.54  | | | | | | | | | | Case 1:
% 231.33/42.54  | | | | | | | | | | | 
% 231.33/42.54  | | | | | | | | | | |   (63)  all_57_6 = e3 & op(e1, e3) = e3
% 231.33/42.54  | | | | | | | | | | | 
% 231.33/42.54  | | | | | | | | | | | ALPHA: (63) implies:
% 231.33/42.54  | | | | | | | | | | |   (64)  all_57_6 = e3
% 231.33/42.54  | | | | | | | | | | | 
% 231.33/42.54  | | | | | | | | | | | BETA: splitting (33) gives:
% 231.33/42.54  | | | | | | | | | | | 
% 231.33/42.54  | | | | | | | | | | | Case 1:
% 231.33/42.54  | | | | | | | | | | | | 
% 231.33/42.54  | | | | | | | | | | | |   (65)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 231.33/42.54  | | | | | | | | | | | |           & op(e2, e3) = e0)
% 231.33/42.54  | | | | | | | | | | | | 
% 231.33/42.54  | | | | | | | | | | | | REF_CLOSE: (1), (4), (6), (13), (15), (16), (17), (20), (21),
% 231.33/42.54  | | | | | | | | | | | |            (24), (27), (29), (65) are inconsistent by
% 231.33/42.54  | | | | | | | | | | | |            sub-proof #1432.
% 231.33/42.54  | | | | | | | | | | | | 
% 231.33/42.54  | | | | | | | | | | | Case 2:
% 231.33/42.54  | | | | | | | | | | | | 
% 231.33/42.54  | | | | | | | | | | | |   (66)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 231.33/42.54  | | | | | | | | | | | |           e0 & op(e0, e3) = e0)
% 231.33/42.54  | | | | | | | | | | | | 
% 231.33/42.54  | | | | | | | | | | | | BETA: splitting (66) gives:
% 231.33/42.54  | | | | | | | | | | | | 
% 231.33/42.54  | | | | | | | | | | | | Case 1:
% 231.33/42.54  | | | | | | | | | | | | | 
% 231.33/42.54  | | | | | | | | | | | | |   (67)  all_57_6 = e0 & op(e1, e3) = e0
% 231.33/42.54  | | | | | | | | | | | | | 
% 231.33/42.54  | | | | | | | | | | | | | REF_CLOSE: (16), (64), (67) are inconsistent by sub-proof
% 231.33/42.54  | | | | | | | | | | | | |            #2465.
% 231.33/42.54  | | | | | | | | | | | | | 
% 231.33/42.54  | | | | | | | | | | | | Case 2:
% 231.33/42.54  | | | | | | | | | | | | | 
% 231.33/42.54  | | | | | | | | | | | | |   (68)  all_57_12 = e0 & op(e0, e3) = e0
% 231.33/42.54  | | | | | | | | | | | | | 
% 231.33/42.54  | | | | | | | | | | | | | ALPHA: (68) implies:
% 231.33/42.54  | | | | | | | | | | | | |   (69)  all_57_12 = e0
% 231.33/42.54  | | | | | | | | | | | | | 
% 231.33/42.54  | | | | | | | | | | | | | BETA: splitting (2) gives:
% 231.33/42.54  | | | | | | | | | | | | | 
% 231.33/42.54  | | | | | | | | | | | | | Case 1:
% 231.33/42.54  | | | | | | | | | | | | | | 
% 231.33/42.54  | | | | | | | | | | | | | |   (70)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 231.33/42.54  | | | | | | | | | | | | | |           & op(e2, e3) = e1)
% 231.33/42.54  | | | | | | | | | | | | | | 
% 231.33/42.54  | | | | | | | | | | | | | | BETA: splitting (70) gives:
% 231.33/42.54  | | | | | | | | | | | | | | 
% 231.33/42.54  | | | | | | | | | | | | | | Case 1:
% 231.33/42.54  | | | | | | | | | | | | | | | 
% 231.33/42.54  | | | | | | | | | | | | | | |   (71)  all_57_0 = e1 & op(e3, e3) = e1
% 231.33/42.54  | | | | | | | | | | | | | | | 
% 231.33/42.54  | | | | | | | | | | | | | | | ALPHA: (71) implies:
% 231.33/42.54  | | | | | | | | | | | | | | |   (72)  all_57_0 = e1
% 231.33/42.54  | | | | | | | | | | | | | | | 
% 231.33/42.54  | | | | | | | | | | | | | | | BETA: splitting (19) gives:
% 231.33/42.54  | | | | | | | | | | | | | | | 
% 231.33/42.54  | | | | | | | | | | | | | | | Case 1:
% 231.33/42.54  | | | | | | | | | | | | | | | | 
% 231.33/42.54  | | | | | | | | | | | | | | | |   (73)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 231.33/42.54  | | | | | | | | | | | | | | | |           e1 & op(e0, e2) = e1)
% 231.33/42.54  | | | | | | | | | | | | | | | | 
% 231.33/42.54  | | | | | | | | | | | | | | | | BETA: splitting (73) gives:
% 231.33/42.54  | | | | | | | | | | | | | | | | 
% 231.33/42.54  | | | | | | | | | | | | | | | | Case 1:
% 231.33/42.54  | | | | | | | | | | | | | | | | | 
% 231.33/42.54  | | | | | | | | | | | | | | | | |   (74)  all_57_12 = e1 & op(e0, e3) = e1
% 231.33/42.54  | | | | | | | | | | | | | | | | | 
% 231.33/42.54  | | | | | | | | | | | | | | | | | ALPHA: (74) implies:
% 231.33/42.54  | | | | | | | | | | | | | | | | |   (75)  all_57_12 = e1
% 231.33/42.54  | | | | | | | | | | | | | | | | | 
% 231.33/42.54  | | | | | | | | | | | | | | | | | COMBINE_EQS: (69), (75) imply:
% 231.33/42.54  | | | | | | | | | | | | | | | | |   (76)  e1 = e0
% 231.33/42.54  | | | | | | | | | | | | | | | | | 
% 231.33/42.54  | | | | | | | | | | | | | | | | | SIMP: (76) implies:
% 231.33/42.55  | | | | | | | | | | | | | | | | |   (77)  e1 = e0
% 231.33/42.55  | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | COMBINE_EQS: (72), (77) imply:
% 231.33/42.55  | | | | | | | | | | | | | | | | |   (78)  all_57_0 = e0
% 231.33/42.55  | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (15), (20), (21), (29), (31), (64),
% 231.33/42.55  | | | | | | | | | | | | | | | | |            (69), (78) are inconsistent by sub-proof #1425.
% 231.33/42.55  | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | Case 2:
% 231.33/42.55  | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | |   (79)  all_57_13 = e1 & op(e0, e2) = e1
% 231.33/42.55  | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | ALPHA: (79) implies:
% 231.33/42.55  | | | | | | | | | | | | | | | | |   (80)  all_57_13 = e1
% 231.33/42.55  | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (50), (80) are inconsistent by sub-proof
% 231.33/42.55  | | | | | | | | | | | | | | | | |            #2268.
% 231.33/42.55  | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | End of split
% 231.33/42.55  | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | Case 2:
% 231.33/42.55  | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | |   (81)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 231.33/42.55  | | | | | | | | | | | | | | | |           e1 & op(e0, e0) = e1)
% 231.33/42.55  | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | BETA: splitting (81) gives:
% 231.33/42.55  | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | Case 1:
% 231.33/42.55  | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | |   (82)  all_57_14 = e1 & op(e0, e1) = e1
% 231.33/42.55  | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | ALPHA: (82) implies:
% 231.33/42.55  | | | | | | | | | | | | | | | | |   (83)  all_57_14 = e1
% 231.33/42.55  | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | BETA: splitting (11) gives:
% 231.33/42.55  | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | Case 1:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | |   (84)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 231.33/42.55  | | | | | | | | | | | | | | | | | |           & op(e3, e2) = e2)
% 231.33/42.55  | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | BETA: splitting (84) gives:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | Case 1:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | |   (85)  all_57_0 = e2 & op(e3, e3) = e2
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (29), (72), (85) are inconsistent by sub-proof
% 231.33/42.55  | | | | | | | | | | | | | | | | | | |            #1810.
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | Case 2:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | |   (86)  all_57_1 = e2 & op(e3, e2) = e2
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (55), (86) are inconsistent by sub-proof
% 231.33/42.55  | | | | | | | | | | | | | | | | | | |            #2483.
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | End of split
% 231.33/42.55  | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | Case 2:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | |   (87)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 231.33/42.55  | | | | | | | | | | | | | | | | | |           & op(e3, e0) = e2)
% 231.33/42.55  | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | BETA: splitting (87) gives:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | Case 1:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | |   (88)  all_57_4 = e2 & op(e3, e1) = e2
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (38), (88) are inconsistent by sub-proof
% 231.33/42.55  | | | | | | | | | | | | | | | | | | |            #2487.
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | Case 2:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | |   (89)  all_57_9 = e2 & op(e3, e0) = e2
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | ALPHA: (89) implies:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | |   (90)  all_57_9 = e2
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | BETA: splitting (14) gives:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | Case 1:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | |   (91)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | |           & op(e2, e1) = e0)
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | BETA: splitting (91) gives:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | |   (92)  all_57_4 = e0 & op(e3, e1) = e0
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (38), (92) are inconsistent by sub-proof
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | |            #2491.
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | |   (93)  all_57_5 = e0 & op(e2, e1) = e0
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | ALPHA: (93) implies:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | |   (94)  all_57_5 = e0
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (34) gives:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | |   (95)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | |           e1 & op(e2, e0) = e1)
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (15), (16), (18), (20), (21), (24), (26),
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | |            (29), (30), (95) are inconsistent by sub-proof
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | |            #1984.
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | |   (96)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | |           e1 & op(e0, e0) = e1)
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (96) gives:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | |   (97)  all_57_11 = e1 & op(e1, e0) = e1
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (97) implies:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | |   (98)  all_57_11 = e1
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5) gives:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | |   (99)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | |           & op(e1, e2) = e0)
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (99) gives:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | |   (100)  all_57_6 = e0 & op(e1, e3) = e0
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (100) implies:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | |   (101)  all_57_6 = e0
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (64), (101) are inconsistent by sub-proof
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | |            #1822.
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | |   (102)  all_57_7 = e0 & op(e1, e2) = e0
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (102) implies:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | |   (103)  all_57_7 = e0
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (61), (103) imply:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | |   (104)  e1 = e0
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (104) implies:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | |   (105)  e1 = e0
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (72), (105) imply:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | |   (106)  all_57_0 = e0
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (15), (20), (21), (29), (31), (64),
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | |            (69), (106) are inconsistent by sub-proof #1425.
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | |   (107)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | |   (108)  all_57_8 = e0 & op(e1, e1) = e0
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (15), (16), (18), (20), (21), (24), (26),
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | |            (29), (30), (32), (34), (38), (83), (90), (94),
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | |            (108) are inconsistent by sub-proof #1421.
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | |   (109)  all_57_11 = e0 & op(e1, e0) = e0
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (109) implies:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | |   (110)  all_57_11 = e0
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (98), (110) imply:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | |   (111)  e1 = e0
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (111) implies:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | |   (112)  e1 = e0
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (72), (112) imply:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | |   (113)  all_57_0 = e0
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (15), (20), (21), (29), (31), (64),
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | |            (69), (113) are inconsistent by sub-proof #1425.
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | |   (114)  all_57_15 = e1 & op(e0, e0) = e1
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (18), (114) are inconsistent by sub-proof
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | |            #2318.
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | End of split
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | End of split
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | Case 2:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | |   (115)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | BETA: splitting (115) gives:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | |   (116)  all_57_8 = e0 & op(e1, e1) = e0
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (15), (16), (18), (20), (21), (24), (25),
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | |            (26), (29), (30), (32), (34), (38), (50), (69),
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | |            (83), (90), (116) are inconsistent by sub-proof
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | |            #1420.
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | |   (117)  all_57_14 = e0 & op(e0, e1) = e0
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | ALPHA: (117) implies:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | |   (118)  all_57_14 = e0
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (83), (118) imply:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | |   (119)  e1 = e0
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | SIMP: (119) implies:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | |   (120)  e1 = e0
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (72), (120) imply:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | |   (121)  all_57_0 = e0
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (15), (20), (21), (29), (31), (64),
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | |            (69), (121) are inconsistent by sub-proof #1425.
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | End of split
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | End of split
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | End of split
% 231.33/42.55  | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | End of split
% 231.33/42.55  | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | Case 2:
% 231.33/42.55  | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | |   (122)  all_57_15 = e1 & op(e0, e0) = e1
% 231.33/42.55  | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (18), (122) are inconsistent by sub-proof
% 231.33/42.55  | | | | | | | | | | | | | | | | |            #2318.
% 231.33/42.55  | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | End of split
% 231.33/42.55  | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | End of split
% 231.33/42.55  | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | Case 2:
% 231.33/42.55  | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | |   (123)  all_57_2 = e1 & op(e2, e3) = e1
% 231.33/42.55  | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | ALPHA: (123) implies:
% 231.33/42.55  | | | | | | | | | | | | | | |   (124)  all_57_2 = e1
% 231.33/42.55  | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | BETA: splitting (19) gives:
% 231.33/42.55  | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | Case 1:
% 231.33/42.55  | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | |   (125)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 231.33/42.55  | | | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 231.33/42.55  | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | BETA: splitting (125) gives:
% 231.33/42.55  | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | Case 1:
% 231.33/42.55  | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | |   (126)  all_57_12 = e1 & op(e0, e3) = e1
% 231.33/42.55  | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | ALPHA: (126) implies:
% 231.33/42.55  | | | | | | | | | | | | | | | | |   (127)  all_57_12 = e1
% 231.33/42.55  | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | COMBINE_EQS: (69), (127) imply:
% 231.33/42.55  | | | | | | | | | | | | | | | | |   (128)  e1 = e0
% 231.33/42.55  | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | SIMP: (128) implies:
% 231.33/42.55  | | | | | | | | | | | | | | | | |   (129)  e1 = e0
% 231.33/42.55  | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | COMBINE_EQS: (124), (129) imply:
% 231.33/42.55  | | | | | | | | | | | | | | | | |   (130)  all_57_2 = e0
% 231.33/42.55  | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (13), (15), (20), (21), (24), (27),
% 231.33/42.55  | | | | | | | | | | | | | | | | |            (29), (130) are inconsistent by sub-proof #2247.
% 231.33/42.55  | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | Case 2:
% 231.33/42.55  | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | |   (131)  all_57_13 = e1 & op(e0, e2) = e1
% 231.33/42.55  | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | ALPHA: (131) implies:
% 231.33/42.55  | | | | | | | | | | | | | | | | |   (132)  all_57_13 = e1
% 231.33/42.55  | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (50), (132) are inconsistent by sub-proof
% 231.33/42.55  | | | | | | | | | | | | | | | | |            #2268.
% 231.33/42.55  | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | End of split
% 231.33/42.55  | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | Case 2:
% 231.33/42.55  | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | |   (133)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 231.33/42.55  | | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 231.33/42.55  | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | BETA: splitting (133) gives:
% 231.33/42.55  | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | Case 1:
% 231.33/42.55  | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | |   (134)  all_57_14 = e1 & op(e0, e1) = e1
% 231.33/42.55  | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | ALPHA: (134) implies:
% 231.33/42.55  | | | | | | | | | | | | | | | | |   (135)  all_57_14 = e1
% 231.33/42.55  | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | BETA: splitting (11) gives:
% 231.33/42.55  | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | Case 1:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | |   (136)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 231.33/42.55  | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e2)
% 231.33/42.55  | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | BETA: splitting (136) gives:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | Case 1:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | |   (137)  all_57_0 = e2 & op(e3, e3) = e2
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | ALPHA: (137) implies:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | |   (138)  all_57_0 = e2
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | BETA: splitting (25) gives:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | Case 1:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | |   (139)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | BETA: splitting (139) gives:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | |   (140)  all_57_12 = e2 & op(e0, e3) = e2
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | ALPHA: (140) implies:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | |   (141)  all_57_12 = e2
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (20), (29), (31), (64), (69), (124), (138),
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | |            (141) are inconsistent by sub-proof #1419.
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | |   (142)  all_57_13 = e2 & op(e0, e2) = e2
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | ALPHA: (142) implies:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | |   (143)  all_57_13 = e2
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (50), (143) are inconsistent by sub-proof
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | |            #2203.
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | End of split
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | Case 2:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | |   (144)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (18), (29), (135), (144) are inconsistent by
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | |            sub-proof #1418.
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | End of split
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | Case 2:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | |   (145)  all_57_1 = e2 & op(e3, e2) = e2
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (55), (145) are inconsistent by sub-proof
% 231.33/42.55  | | | | | | | | | | | | | | | | | | |            #2483.
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | End of split
% 231.33/42.55  | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | Case 2:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | |   (146)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 231.33/42.55  | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e2)
% 231.33/42.55  | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | BETA: splitting (146) gives:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | Case 1:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | |   (147)  all_57_4 = e2 & op(e3, e1) = e2
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (38), (147) are inconsistent by sub-proof
% 231.33/42.55  | | | | | | | | | | | | | | | | | | |            #2487.
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | Case 2:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | |   (148)  all_57_9 = e2 & op(e3, e0) = e2
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | ALPHA: (148) implies:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | |   (149)  all_57_9 = e2
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | BETA: splitting (14) gives:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | Case 1:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | |   (150)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e0)
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | BETA: splitting (150) gives:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | |   (151)  all_57_4 = e0 & op(e3, e1) = e0
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (38), (151) are inconsistent by sub-proof
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | |            #2491.
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | |   (152)  all_57_5 = e0 & op(e2, e1) = e0
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | ALPHA: (152) implies:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | |   (153)  all_57_5 = e0
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (34) gives:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | |   (154)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (15), (16), (18), (20), (21), (24), (26),
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | |            (29), (30), (154) are inconsistent by sub-proof
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | |            #1984.
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | |   (155)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (155) gives:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | |   (156)  all_57_11 = e1 & op(e1, e0) = e1
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (156) implies:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | |   (157)  all_57_11 = e1
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5) gives:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | |   (158)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e0)
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (158) gives:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | |   (159)  all_57_6 = e0 & op(e1, e3) = e0
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (159) implies:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | |   (160)  all_57_6 = e0
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (64), (160) are inconsistent by sub-proof
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | |            #1822.
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | |   (161)  all_57_7 = e0 & op(e1, e2) = e0
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (161) implies:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | |   (162)  all_57_7 = e0
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (61), (162) imply:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | |   (163)  e1 = e0
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (163) implies:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | |   (164)  e1 = e0
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (124), (164) imply:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | |   (165)  all_57_2 = e0
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (13), (15), (20), (21), (24), (27),
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | |            (29), (165) are inconsistent by sub-proof #2247.
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | |   (166)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (166) gives:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | |   (167)  all_57_8 = e0 & op(e1, e1) = e0
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (15), (16), (18), (20), (21), (24), (26),
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | |            (29), (30), (32), (34), (38), (135), (149), (153),
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | |            (167) are inconsistent by sub-proof #1421.
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | |   (168)  all_57_11 = e0 & op(e1, e0) = e0
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (168) implies:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | |   (169)  all_57_11 = e0
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (157), (169) imply:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | |   (170)  e1 = e0
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (170) implies:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | |   (171)  e1 = e0
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (124), (171) imply:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | |   (172)  all_57_2 = e0
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (13), (15), (20), (21), (24), (27),
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | |            (29), (172) are inconsistent by sub-proof #2247.
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | |   (173)  all_57_15 = e1 & op(e0, e0) = e1
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (18), (173) are inconsistent by sub-proof
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | |            #2318.
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | End of split
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | End of split
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | Case 2:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | |   (174)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | BETA: splitting (174) gives:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | |   (175)  all_57_8 = e0 & op(e1, e1) = e0
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (15), (16), (18), (20), (21), (24), (25),
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | |            (26), (29), (30), (32), (34), (38), (50), (69),
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | |            (135), (149), (175) are inconsistent by sub-proof
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | |            #1420.
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | |   (176)  all_57_14 = e0 & op(e0, e1) = e0
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | ALPHA: (176) implies:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | |   (177)  all_57_14 = e0
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (135), (177) imply:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | |   (178)  e1 = e0
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | SIMP: (178) implies:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | |   (179)  e1 = e0
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (124), (179) imply:
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | |   (180)  all_57_2 = e0
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (13), (15), (20), (21), (24), (27),
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | |            (29), (180) are inconsistent by sub-proof #2247.
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | End of split
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | End of split
% 231.33/42.55  | | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | | End of split
% 231.33/42.55  | | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | End of split
% 231.33/42.55  | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | Case 2:
% 231.33/42.55  | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | |   (181)  all_57_15 = e1 & op(e0, e0) = e1
% 231.33/42.55  | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (18), (181) are inconsistent by sub-proof
% 231.33/42.55  | | | | | | | | | | | | | | | | |            #2318.
% 231.33/42.55  | | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | | End of split
% 231.33/42.55  | | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | End of split
% 231.33/42.55  | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | End of split
% 231.33/42.55  | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | Case 2:
% 231.33/42.55  | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | |   (182)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 231.33/42.55  | | | | | | | | | | | | | |            e1 & op(e0, e3) = e1)
% 231.33/42.55  | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | BETA: splitting (182) gives:
% 231.33/42.55  | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | Case 1:
% 231.33/42.55  | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | |   (183)  all_57_6 = e1 & op(e1, e3) = e1
% 231.33/42.55  | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | REF_CLOSE: (4), (64), (183) are inconsistent by sub-proof
% 231.33/42.55  | | | | | | | | | | | | | | |            #2117.
% 231.33/42.55  | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | Case 2:
% 231.33/42.55  | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | |   (184)  all_57_12 = e1 & op(e0, e3) = e1
% 231.33/42.55  | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | | REF_CLOSE: (21), (69), (184) are inconsistent by sub-proof
% 231.33/42.55  | | | | | | | | | | | | | | |            #2328.
% 231.33/42.55  | | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | | End of split
% 231.33/42.55  | | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | | End of split
% 231.33/42.55  | | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | | End of split
% 231.33/42.55  | | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | End of split
% 231.33/42.55  | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | Case 2:
% 231.33/42.55  | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | |   (185)  all_57_7 = e3 & op(e1, e2) = e3
% 231.33/42.55  | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | ALPHA: (185) implies:
% 231.33/42.55  | | | | | | | | | | |   (186)  all_57_7 = e3
% 231.33/42.55  | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (10), (11), (13), (15),
% 231.33/42.55  | | | | | | | | | | |            (16), (17), (18), (19), (20), (21), (24), (25),
% 231.33/42.55  | | | | | | | | | | |            (26), (27), (28), (29), (30), (33), (34), (35),
% 231.33/42.55  | | | | | | | | | | |            (38), (55), (186) are inconsistent by sub-proof
% 231.33/42.55  | | | | | | | | | | |            #1428.
% 231.33/42.55  | | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | End of split
% 231.33/42.55  | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | Case 2:
% 231.33/42.55  | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | |   (187)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3
% 231.33/42.55  | | | | | | | | | |            & op(e1, e0) = e3)
% 231.33/42.55  | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | | REF_CLOSE: (4), (6), (8), (9), (15), (16), (18), (20), (21),
% 231.33/42.55  | | | | | | | | | |            (24), (26), (29), (30), (34), (187) are
% 231.33/42.55  | | | | | | | | | |            inconsistent by sub-proof #1417.
% 231.33/42.55  | | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | End of split
% 231.33/42.55  | | | | | | | | | 
% 231.33/42.55  | | | | | | | | Case 2:
% 231.33/42.55  | | | | | | | | | 
% 231.33/42.55  | | | | | | | | |   (188)  all_57_13 = e1 & op(e0, e2) = e1
% 231.33/42.55  | | | | | | | | | 
% 231.33/42.55  | | | | | | | | | REF_CLOSE: (4), (50), (188) are inconsistent by sub-proof
% 231.33/42.55  | | | | | | | | |            #2264.
% 231.33/42.55  | | | | | | | | | 
% 231.33/42.55  | | | | | | | | End of split
% 231.33/42.55  | | | | | | | | 
% 231.33/42.55  | | | | | | | End of split
% 231.33/42.55  | | | | | | | 
% 231.33/42.55  | | | | | | End of split
% 231.33/42.55  | | | | | | 
% 231.33/42.55  | | | | | Case 2:
% 231.33/42.55  | | | | | | 
% 231.33/42.55  | | | | | |   (189)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3,
% 231.33/42.55  | | | | | |              e0) = e0)
% 231.33/42.55  | | | | | | 
% 231.33/42.55  | | | | | | REF_CLOSE: (4), (15), (16), (18), (20), (21), (24), (26), (29),
% 231.33/42.55  | | | | | |            (30), (34), (38), (189) are inconsistent by sub-proof
% 231.33/42.55  | | | | | |            #1427.
% 231.33/42.55  | | | | | | 
% 231.33/42.55  | | | | | End of split
% 231.33/42.55  | | | | | 
% 231.33/42.55  | | | | End of split
% 231.33/42.55  | | | | 
% 231.33/42.55  | | | End of split
% 231.33/42.55  | | | 
% 231.33/42.55  | | Case 2:
% 231.33/42.55  | | | 
% 231.33/42.55  | | |   (190)  all_57_5 = e3 & op(e2, e1) = e3
% 231.33/42.55  | | | 
% 231.33/42.55  | | | ALPHA: (190) implies:
% 231.33/42.55  | | |   (191)  all_57_5 = e3
% 231.33/42.55  | | | 
% 231.33/42.55  | | | REF_CLOSE: (1), (4), (13), (15), (20), (21), (24), (27), (29), (191) are
% 231.33/42.55  | | |            inconsistent by sub-proof #1693.
% 231.33/42.55  | | | 
% 231.33/42.55  | | End of split
% 231.33/42.55  | | 
% 231.33/42.55  | Case 2:
% 231.33/42.55  | | 
% 231.33/42.55  | |   (192)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) =
% 231.33/42.55  | |            e3)
% 231.33/42.55  | | 
% 231.33/42.55  | | REF_CLOSE: (4), (6), (8), (9), (15), (16), (18), (19), (20), (21), (25),
% 231.33/42.55  | |            (26), (29), (192) are inconsistent by sub-proof #1794.
% 231.33/42.55  | | 
% 231.33/42.55  | End of split
% 231.33/42.55  | 
% 231.33/42.55  End of proof
% 231.33/42.55  
% 231.33/42.55  Sub-proof #1417 shows that the following formulas are inconsistent:
% 231.33/42.55  ----------------------------------------------------------------
% 231.33/42.55    (1)   ~ (e3 = e1)
% 231.33/42.55    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.33/42.55           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.33/42.55    (3)   ~ (all_6_2 = e3)
% 231.33/42.55    (4)  op(e1, e1) = all_6_2
% 231.33/42.55    (5)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.33/42.55    (6)   ~ (e3 = e2)
% 231.33/42.55    (7)   ~ (e3 = e0)
% 231.33/42.55    (8)  all_57_15 = e3
% 231.33/42.55    (9)   ~ (e2 = e0)
% 231.33/42.55    (10)   ~ (e1 = e0)
% 231.33/42.55    (11)  all_57_10 = e3
% 231.33/42.55    (12)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.33/42.55              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.33/42.55                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.33/42.55                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.33/42.55    (13)   ~ (e2 = e1)
% 231.33/42.55    (14)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.33/42.55          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.33/42.55    (15)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.33/42.55          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.33/42.55  
% 231.33/42.55  Begin of proof
% 231.33/42.55  | 
% 231.33/42.55  | BETA: splitting (5) gives:
% 231.33/42.55  | 
% 231.33/42.55  | Case 1:
% 231.33/42.55  | | 
% 231.33/42.55  | |   (16)  all_57_8 = e3 & op(e1, e1) = e3
% 231.33/42.55  | | 
% 231.33/42.55  | | ALPHA: (16) implies:
% 231.33/42.55  | |   (17)  op(e1, e1) = e3
% 231.33/42.55  | | 
% 231.33/42.55  | | REF_CLOSE: (2), (3), (4), (17) are inconsistent by sub-proof #2468.
% 231.33/42.55  | | 
% 231.33/42.55  | Case 2:
% 231.33/42.55  | | 
% 231.33/42.55  | |   (18)  all_57_11 = e3 & op(e1, e0) = e3
% 231.33/42.55  | | 
% 231.33/42.55  | | ALPHA: (18) implies:
% 231.33/42.55  | |   (19)  all_57_11 = e3
% 231.33/42.55  | | 
% 231.33/42.55  | | BETA: splitting (12) gives:
% 231.33/42.55  | | 
% 231.33/42.55  | | Case 1:
% 231.33/42.55  | | | 
% 231.33/42.55  | | |   (20)  all_57_15 = e0 & op(e0, e0) = e0
% 231.33/42.55  | | | 
% 231.33/42.55  | | | REF_CLOSE: (7), (8), (20) are inconsistent by sub-proof #2329.
% 231.33/42.55  | | | 
% 231.33/42.55  | | Case 2:
% 231.33/42.55  | | | 
% 231.33/42.55  | | |   (21)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0)
% 231.33/42.55  | | |             = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0
% 231.33/42.55  | | |             & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 231.33/42.55  | | |           (all_57_14 = e0 & op(e0, e1) = e0))
% 231.33/42.55  | | | 
% 231.33/42.55  | | | ALPHA: (21) implies:
% 231.33/42.55  | | |   (22)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 231.33/42.55  | | |           e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.33/42.55  | | | 
% 231.33/42.55  | | | BETA: splitting (15) gives:
% 231.33/42.55  | | | 
% 231.33/42.55  | | | Case 1:
% 231.33/42.55  | | | | 
% 231.33/42.55  | | | |   (23)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0)
% 231.33/42.55  | | | |           = e1)
% 231.33/42.55  | | | | 
% 231.33/42.55  | | | | BETA: splitting (23) gives:
% 231.33/42.55  | | | | 
% 231.33/42.55  | | | | Case 1:
% 231.33/42.55  | | | | | 
% 231.33/42.55  | | | | |   (24)  all_57_9 = e1 & op(e3, e0) = e1
% 231.33/42.55  | | | | | 
% 231.33/42.55  | | | | | ALPHA: (24) implies:
% 231.33/42.55  | | | | |   (25)  all_57_9 = e1
% 231.33/42.55  | | | | | 
% 231.33/42.55  | | | | | REF_CLOSE: (6), (7), (8), (9), (10), (11), (13), (14), (22), (25) are
% 231.33/42.55  | | | | |            inconsistent by sub-proof #1986.
% 231.33/42.55  | | | | | 
% 231.33/42.55  | | | | Case 2:
% 231.33/42.55  | | | | | 
% 231.33/42.55  | | | | |   (26)  all_57_10 = e1 & op(e2, e0) = e1
% 231.33/42.55  | | | | | 
% 231.33/42.55  | | | | | REF_CLOSE: (1), (11), (26) are inconsistent by sub-proof #2349.
% 231.33/42.55  | | | | | 
% 231.33/42.55  | | | | End of split
% 231.33/42.55  | | | | 
% 231.33/42.55  | | | Case 2:
% 231.33/42.55  | | | | 
% 231.33/42.55  | | | |   (27)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0,
% 231.33/42.55  | | | |             e0) = e1)
% 231.33/42.55  | | | | 
% 231.33/42.55  | | | | BETA: splitting (27) gives:
% 231.33/42.55  | | | | 
% 231.33/42.55  | | | | Case 1:
% 231.33/42.55  | | | | | 
% 231.33/42.55  | | | | |   (28)  all_57_11 = e1 & op(e1, e0) = e1
% 231.33/42.55  | | | | | 
% 231.33/42.55  | | | | | REF_CLOSE: (1), (19), (28) are inconsistent by sub-proof #2143.
% 231.33/42.55  | | | | | 
% 231.33/42.55  | | | | Case 2:
% 231.33/42.55  | | | | | 
% 231.33/42.55  | | | | |   (29)  all_57_15 = e1 & op(e0, e0) = e1
% 231.33/42.55  | | | | | 
% 231.33/42.55  | | | | | REF_CLOSE: (1), (8), (29) are inconsistent by sub-proof #2325.
% 231.33/42.55  | | | | | 
% 231.33/42.55  | | | | End of split
% 231.33/42.55  | | | | 
% 231.33/42.55  | | | End of split
% 231.33/42.55  | | | 
% 231.33/42.55  | | End of split
% 231.33/42.55  | | 
% 231.33/42.55  | End of split
% 231.33/42.55  | 
% 231.33/42.55  End of proof
% 231.33/42.55  
% 231.33/42.55  Sub-proof #1418 shows that the following formulas are inconsistent:
% 231.33/42.55  ----------------------------------------------------------------
% 231.33/42.55    (1)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.33/42.55    (2)   ~ (e3 = e2)
% 231.33/42.55    (3)  all_57_15 = e3
% 231.33/42.55    (4)  all_57_14 = e1
% 231.33/42.55    (5)   ~ (e2 = e1)
% 231.33/42.55  
% 231.33/42.55  Begin of proof
% 231.33/42.55  | 
% 231.33/42.55  | BETA: splitting (1) gives:
% 231.33/42.55  | 
% 231.33/42.55  | Case 1:
% 231.33/42.55  | | 
% 231.33/42.55  | |   (6)  all_57_14 = e2 & op(e0, e1) = e2
% 231.33/42.55  | | 
% 231.33/42.55  | | REF_CLOSE: (4), (5), (6) are inconsistent by sub-proof #1968.
% 231.33/42.55  | | 
% 231.33/42.55  | Case 2:
% 231.33/42.55  | | 
% 231.33/42.55  | |   (7)  all_57_15 = e2 & op(e0, e0) = e2
% 231.33/42.55  | | 
% 231.33/42.55  | | ALPHA: (7) implies:
% 231.33/42.55  | |   (8)  all_57_15 = e2
% 231.33/42.55  | | 
% 231.33/42.55  | | REF_CLOSE: (2), (3), (8) are inconsistent by sub-proof #2058.
% 231.33/42.55  | | 
% 231.33/42.55  | End of split
% 231.33/42.55  | 
% 231.33/42.55  End of proof
% 231.33/42.55  
% 231.33/42.55  Sub-proof #1419 shows that the following formulas are inconsistent:
% 231.33/42.55  ----------------------------------------------------------------
% 231.33/42.55    (1)  all_57_0 = e2
% 231.33/42.55    (2)  all_57_12 = e0
% 231.33/42.55    (3)  all_57_12 = e2
% 231.33/42.55    (4)   ~ (e3 = e2)
% 231.33/42.55    (5)   ~ (e2 = e0)
% 231.33/42.55    (6)  all_57_6 = e3
% 231.33/42.55    (7)  all_57_2 = e1
% 231.33/42.55    (8)   ~ (e2 = e1)
% 231.33/42.55    (9)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.33/42.55         (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.33/42.55  
% 231.33/42.55  Begin of proof
% 231.33/42.55  | 
% 231.33/42.55  | COMBINE_EQS: (2), (3) imply:
% 231.33/42.55  |   (10)  e2 = e0
% 231.33/42.55  | 
% 231.33/42.55  | COMBINE_EQS: (1), (10) imply:
% 231.33/42.55  |   (11)  all_57_0 = e0
% 231.33/42.55  | 
% 231.33/42.55  | REF_CLOSE: (2), (4), (5), (6), (7), (8), (9), (11) are inconsistent by
% 231.33/42.55  |            sub-proof #1426.
% 231.33/42.55  | 
% 231.33/42.55  End of proof
% 231.33/42.55  
% 231.33/42.55  Sub-proof #1420 shows that the following formulas are inconsistent:
% 231.33/42.55  ----------------------------------------------------------------
% 231.33/42.55    (1)  all_57_9 = e2
% 231.33/42.55    (2)  all_57_12 = e0
% 231.33/42.55    (3)   ~ (e3 = e1)
% 231.33/42.55    (4)  all_57_8 = e0 & op(e1, e1) = e0
% 231.33/42.55    (5)  all_57_4 = e3
% 231.33/42.55    (6)   ~ (e3 = e2)
% 231.33/42.55    (7)   ~ (e3 = e0)
% 231.33/42.55    (8)  all_57_15 = e3
% 231.33/42.55    (9)   ~ (e2 = e0)
% 231.33/42.55    (10)   ~ (e1 = e0)
% 231.33/42.55    (11)  all_57_14 = e1
% 231.33/42.55    (12)  all_57_13 = e3
% 231.33/42.55    (13)  all_57_10 = e3
% 231.33/42.55    (14)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.33/42.55          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.33/42.55            e2)
% 231.33/42.55    (15)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.33/42.55              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.33/42.55                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.33/42.55                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.33/42.55    (16)   ~ (e2 = e1)
% 231.33/42.55    (17)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.33/42.55          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.33/42.55    (18)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.33/42.55          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.33/42.55    (19)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.33/42.55          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.33/42.55  
% 231.33/42.55  Begin of proof
% 231.33/42.55  | 
% 231.33/42.55  | ALPHA: (4) implies:
% 231.33/42.55  |   (20)  all_57_8 = e0
% 231.33/42.55  | 
% 231.33/42.55  | BETA: splitting (15) gives:
% 231.33/42.55  | 
% 231.33/42.55  | Case 1:
% 231.33/42.55  | | 
% 231.33/42.55  | |   (21)  all_57_15 = e0 & op(e0, e0) = e0
% 231.33/42.55  | | 
% 231.33/42.55  | | ALPHA: (21) implies:
% 231.33/42.55  | |   (22)  all_57_15 = e0
% 231.33/42.55  | | 
% 231.33/42.55  | | COMBINE_EQS: (8), (22) imply:
% 231.33/42.55  | |   (23)  e3 = e0
% 231.33/42.55  | | 
% 231.33/42.55  | | SIMP: (23) implies:
% 231.33/42.55  | |   (24)  e3 = e0
% 231.33/42.55  | | 
% 231.33/42.55  | | REDUCE: (7), (24) imply:
% 231.33/42.55  | |   (25)  $false
% 231.33/42.55  | | 
% 231.33/42.55  | | CLOSE: (25) is inconsistent.
% 231.33/42.55  | | 
% 231.33/42.55  | Case 2:
% 231.33/42.55  | | 
% 231.33/42.55  | |   (26)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 231.33/42.55  | |             e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0 &
% 231.33/42.55  | |             op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 231.33/42.55  | |           (all_57_14 = e0 & op(e0, e1) = e0))
% 231.33/42.55  | | 
% 231.33/42.55  | | ALPHA: (26) implies:
% 231.33/42.55  | |   (27)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 231.33/42.55  | |           e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.33/42.55  | | 
% 231.33/42.55  | | BETA: splitting (18) gives:
% 231.33/42.55  | | 
% 231.33/42.55  | | Case 1:
% 231.33/42.55  | | | 
% 231.33/42.55  | | |   (28)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) =
% 231.33/42.55  | | |           e2)
% 231.33/42.55  | | | 
% 231.33/42.55  | | | BETA: splitting (28) gives:
% 231.33/42.55  | | | 
% 231.33/42.55  | | | Case 1:
% 231.33/42.55  | | | | 
% 231.33/42.55  | | | |   (29)  all_57_4 = e2 & op(e3, e1) = e2
% 231.33/42.55  | | | | 
% 231.33/42.55  | | | | ALPHA: (29) implies:
% 231.33/42.55  | | | |   (30)  all_57_4 = e2
% 231.33/42.55  | | | | 
% 231.33/42.55  | | | | REF_CLOSE: (5), (6), (30) are inconsistent by sub-proof #2482.
% 231.33/42.55  | | | | 
% 231.33/42.55  | | | Case 2:
% 231.33/42.55  | | | | 
% 231.33/42.55  | | | |   (31)  all_57_5 = e2 & op(e2, e1) = e2
% 231.33/42.55  | | | | 
% 231.33/42.55  | | | | ALPHA: (31) implies:
% 231.33/42.55  | | | |   (32)  all_57_5 = e2
% 231.33/42.55  | | | | 
% 231.33/42.55  | | | | BETA: splitting (14) gives:
% 231.33/42.55  | | | | 
% 231.33/42.55  | | | | Case 1:
% 231.33/42.55  | | | | | 
% 231.33/42.55  | | | | |   (33)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0,
% 231.33/42.55  | | | | |             e2) = e2)
% 231.33/42.55  | | | | | 
% 231.33/42.55  | | | | | BETA: splitting (33) gives:
% 231.33/42.55  | | | | | 
% 231.33/42.55  | | | | | Case 1:
% 231.33/42.55  | | | | | | 
% 231.33/42.55  | | | | | |   (34)  all_57_12 = e2 & op(e0, e3) = e2
% 231.33/42.55  | | | | | | 
% 231.33/42.55  | | | | | | ALPHA: (34) implies:
% 231.33/42.56  | | | | | |   (35)  all_57_12 = e2
% 231.33/42.56  | | | | | | 
% 231.33/42.56  | | | | | | COMBINE_EQS: (2), (35) imply:
% 231.33/42.56  | | | | | |   (36)  e2 = e0
% 231.33/42.56  | | | | | | 
% 231.33/42.56  | | | | | | COMBINE_EQS: (32), (36) imply:
% 231.33/42.56  | | | | | |   (37)  all_57_5 = e0
% 231.33/42.56  | | | | | | 
% 231.33/42.56  | | | | | | REF_CLOSE: (1), (3), (5), (6), (7), (8), (9), (10), (11), (13),
% 231.33/42.56  | | | | | |            (15), (16), (17), (18), (19), (20), (27), (37) are
% 231.33/42.56  | | | | | |            inconsistent by sub-proof #1422.
% 231.33/42.56  | | | | | | 
% 231.33/42.56  | | | | | Case 2:
% 231.33/42.56  | | | | | | 
% 231.33/42.56  | | | | | |   (38)  all_57_13 = e2 & op(e0, e2) = e2
% 231.33/42.56  | | | | | | 
% 231.33/42.56  | | | | | | ALPHA: (38) implies:
% 231.33/42.56  | | | | | |   (39)  all_57_13 = e2
% 231.33/42.56  | | | | | | 
% 231.33/42.56  | | | | | | REF_CLOSE: (6), (12), (39) are inconsistent by sub-proof #2203.
% 231.33/42.56  | | | | | | 
% 231.33/42.56  | | | | | End of split
% 231.33/42.56  | | | | | 
% 231.33/42.56  | | | | Case 2:
% 231.33/42.56  | | | | | 
% 231.33/42.56  | | | | |   (40)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0,
% 231.33/42.56  | | | | |             e0) = e2)
% 231.33/42.56  | | | | | 
% 231.33/42.56  | | | | | BETA: splitting (40) gives:
% 231.33/42.56  | | | | | 
% 231.33/42.56  | | | | | Case 1:
% 231.33/42.56  | | | | | | 
% 231.33/42.56  | | | | | |   (41)  all_57_14 = e2 & op(e0, e1) = e2
% 231.33/42.56  | | | | | | 
% 231.33/42.56  | | | | | | REF_CLOSE: (1), (6), (7), (8), (9), (10), (11), (13), (16), (17),
% 231.33/42.56  | | | | | |            (27), (41) are inconsistent by sub-proof #1424.
% 231.33/42.56  | | | | | | 
% 231.33/42.56  | | | | | Case 2:
% 231.33/42.56  | | | | | | 
% 231.33/42.56  | | | | | |   (42)  all_57_15 = e2 & op(e0, e0) = e2
% 231.33/42.56  | | | | | | 
% 231.33/42.56  | | | | | | REF_CLOSE: (6), (8), (42) are inconsistent by sub-proof #2323.
% 231.33/42.56  | | | | | | 
% 231.33/42.56  | | | | | End of split
% 231.33/42.56  | | | | | 
% 231.33/42.56  | | | | End of split
% 231.33/42.56  | | | | 
% 231.33/42.56  | | | End of split
% 231.33/42.56  | | | 
% 231.33/42.56  | | Case 2:
% 231.33/42.56  | | | 
% 231.33/42.56  | | |   (43)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) =
% 231.33/42.56  | | |           e2)
% 231.33/42.56  | | | 
% 231.33/42.56  | | | REF_CLOSE: (1), (3), (6), (7), (8), (9), (10), (11), (13), (15), (16),
% 231.33/42.56  | | |            (17), (19), (20), (27), (43) are inconsistent by sub-proof
% 231.33/42.56  | | |            #1423.
% 231.33/42.56  | | | 
% 231.33/42.56  | | End of split
% 231.33/42.56  | | 
% 231.33/42.56  | End of split
% 231.33/42.56  | 
% 231.33/42.56  End of proof
% 231.33/42.56  
% 231.33/42.56  Sub-proof #1421 shows that the following formulas are inconsistent:
% 231.33/42.56  ----------------------------------------------------------------
% 231.33/42.56    (1)  all_57_9 = e2
% 231.33/42.56    (2)   ~ (e3 = e1)
% 231.33/42.56    (3)  all_57_8 = e0 & op(e1, e1) = e0
% 231.33/42.56    (4)  all_57_4 = e3
% 231.33/42.56    (5)   ~ (e3 = e2)
% 231.33/42.56    (6)   ~ (e3 = e0)
% 231.33/42.56    (7)  all_57_15 = e3
% 231.33/42.56    (8)   ~ (e2 = e0)
% 231.33/42.56    (9)   ~ (e1 = e0)
% 231.33/42.56    (10)  all_57_14 = e1
% 231.33/42.56    (11)  all_57_10 = e3
% 231.33/42.56    (12)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.33/42.56              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.33/42.56                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.33/42.56                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.33/42.56    (13)   ~ (e2 = e1)
% 231.33/42.56    (14)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.33/42.56          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.33/42.56    (15)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.33/42.56          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.33/42.56    (16)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.33/42.56          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.33/42.56    (17)  all_57_5 = e0
% 231.33/42.56  
% 231.33/42.56  Begin of proof
% 231.33/42.56  | 
% 231.33/42.56  | ALPHA: (3) implies:
% 231.33/42.56  |   (18)  all_57_8 = e0
% 231.33/42.56  | 
% 231.33/42.56  | BETA: splitting (12) gives:
% 231.33/42.56  | 
% 231.33/42.56  | Case 1:
% 231.33/42.56  | | 
% 231.33/42.56  | |   (19)  all_57_15 = e0 & op(e0, e0) = e0
% 231.33/42.56  | | 
% 231.33/42.56  | | REF_CLOSE: (6), (7), (19) are inconsistent by sub-proof #2329.
% 231.33/42.56  | | 
% 231.33/42.56  | Case 2:
% 231.33/42.56  | | 
% 231.33/42.56  | |   (20)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 231.33/42.56  | |             e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0 &
% 231.33/42.56  | |             op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 231.33/42.56  | |           (all_57_14 = e0 & op(e0, e1) = e0))
% 231.33/42.56  | | 
% 231.33/42.56  | | ALPHA: (20) implies:
% 231.33/42.56  | |   (21)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 231.33/42.56  | |           e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.33/42.56  | | 
% 231.33/42.56  | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 231.33/42.56  | |            (14), (15), (16), (17), (18), (21) are inconsistent by sub-proof
% 231.33/42.56  | |            #1422.
% 231.33/42.56  | | 
% 231.33/42.56  | End of split
% 231.33/42.56  | 
% 231.33/42.56  End of proof
% 231.33/42.56  
% 231.33/42.56  Sub-proof #1422 shows that the following formulas are inconsistent:
% 231.33/42.56  ----------------------------------------------------------------
% 231.33/42.56    (1)  all_57_9 = e2
% 231.33/42.56    (2)   ~ (e3 = e1)
% 231.33/42.56    (3)  all_57_4 = e3
% 231.33/42.56    (4)   ~ (e3 = e2)
% 231.33/42.56    (5)   ~ (e3 = e0)
% 231.33/42.56    (6)  all_57_15 = e3
% 231.33/42.56    (7)   ~ (e2 = e0)
% 231.33/42.56    (8)   ~ (e1 = e0)
% 231.33/42.56    (9)  all_57_14 = e1
% 231.33/42.56    (10)  all_57_10 = e3
% 231.33/42.56    (11)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.33/42.56              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.33/42.56                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.33/42.56                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.33/42.56    (12)  all_57_8 = e0
% 231.33/42.56    (13)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) |
% 231.33/42.56          (all_57_11 = e0 & op(e1, e0) = e0)
% 231.33/42.56    (14)   ~ (e2 = e1)
% 231.33/42.56    (15)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.33/42.56          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.33/42.56    (16)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.33/42.56          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.33/42.56    (17)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.33/42.56          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.33/42.56    (18)  all_57_5 = e0
% 231.33/42.56  
% 231.33/42.56  Begin of proof
% 231.33/42.56  | 
% 231.33/42.56  | BETA: splitting (16) gives:
% 231.33/42.56  | 
% 231.33/42.56  | Case 1:
% 231.33/42.56  | | 
% 231.33/42.56  | |   (19)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) =
% 231.33/42.56  | |           e2)
% 231.33/42.56  | | 
% 231.33/42.56  | | BETA: splitting (19) gives:
% 231.33/42.56  | | 
% 231.33/42.56  | | Case 1:
% 231.33/42.56  | | | 
% 231.33/42.56  | | |   (20)  all_57_4 = e2 & op(e3, e1) = e2
% 231.33/42.56  | | | 
% 231.33/42.56  | | | REF_CLOSE: (3), (4), (20) are inconsistent by sub-proof #2487.
% 231.33/42.56  | | | 
% 231.33/42.56  | | Case 2:
% 231.33/42.56  | | | 
% 231.33/42.56  | | |   (21)  all_57_5 = e2 & op(e2, e1) = e2
% 231.33/42.56  | | | 
% 231.33/42.56  | | | ALPHA: (21) implies:
% 231.33/42.56  | | |   (22)  all_57_5 = e2
% 231.33/42.56  | | | 
% 231.33/42.56  | | | COMBINE_EQS: (18), (22) imply:
% 231.33/42.56  | | |   (23)  e2 = e0
% 231.33/42.56  | | | 
% 231.33/42.56  | | | COMBINE_EQS: (1), (23) imply:
% 231.33/42.56  | | |   (24)  all_57_9 = e0
% 231.33/42.56  | | | 
% 231.33/42.56  | | | REF_CLOSE: (2), (4), (5), (6), (7), (8), (10), (11), (14), (15), (17),
% 231.33/42.56  | | |            (24) are inconsistent by sub-proof #1982.
% 231.33/42.56  | | | 
% 231.33/42.56  | | End of split
% 231.33/42.56  | | 
% 231.33/42.56  | Case 2:
% 231.33/42.56  | | 
% 231.33/42.56  | |   (25)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) =
% 231.33/42.56  | |           e2)
% 231.33/42.56  | | 
% 231.33/42.56  | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 231.33/42.56  | |            (14), (15), (17), (25) are inconsistent by sub-proof #1423.
% 231.33/42.56  | | 
% 231.33/42.56  | End of split
% 231.33/42.56  | 
% 231.33/42.56  End of proof
% 231.33/42.56  
% 231.33/42.56  Sub-proof #1423 shows that the following formulas are inconsistent:
% 231.33/42.56  ----------------------------------------------------------------
% 231.33/42.56    (1)  all_57_9 = e2
% 231.33/42.56    (2)   ~ (e3 = e1)
% 231.33/42.56    (3)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.33/42.56    (4)   ~ (e3 = e2)
% 231.33/42.56    (5)   ~ (e3 = e0)
% 231.33/42.56    (6)  all_57_15 = e3
% 231.33/42.56    (7)   ~ (e2 = e0)
% 231.33/42.56    (8)   ~ (e1 = e0)
% 231.33/42.56    (9)  all_57_14 = e1
% 231.33/42.56    (10)  all_57_10 = e3
% 231.33/42.56    (11)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.33/42.56              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.33/42.56                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.33/42.56                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.33/42.56    (12)  all_57_8 = e0
% 231.33/42.56    (13)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) |
% 231.33/42.56          (all_57_11 = e0 & op(e1, e0) = e0)
% 231.33/42.56    (14)   ~ (e2 = e1)
% 231.33/42.56    (15)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.33/42.56          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.33/42.56    (16)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.33/42.56          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.33/42.56  
% 231.33/42.56  Begin of proof
% 231.33/42.56  | 
% 231.33/42.56  | BETA: splitting (3) gives:
% 231.33/42.56  | 
% 231.33/42.56  | Case 1:
% 231.33/42.56  | | 
% 231.33/42.56  | |   (17)  all_57_8 = e2 & op(e1, e1) = e2
% 231.33/42.56  | | 
% 231.33/42.56  | | ALPHA: (17) implies:
% 231.33/42.56  | |   (18)  all_57_8 = e2
% 231.33/42.56  | | 
% 231.33/42.56  | | COMBINE_EQS: (12), (18) imply:
% 231.33/42.56  | |   (19)  e2 = e0
% 231.33/42.56  | | 
% 231.33/42.56  | | SIMP: (19) implies:
% 231.33/42.56  | |   (20)  e2 = e0
% 231.33/42.56  | | 
% 231.33/42.56  | | COMBINE_EQS: (1), (20) imply:
% 231.33/42.56  | |   (21)  all_57_9 = e0
% 231.33/42.56  | | 
% 231.33/42.56  | | REF_CLOSE: (2), (4), (5), (6), (7), (8), (10), (11), (14), (15), (16), (21)
% 231.33/42.56  | |            are inconsistent by sub-proof #1982.
% 231.33/42.56  | | 
% 231.33/42.56  | Case 2:
% 231.33/42.56  | | 
% 231.33/42.56  | |   (22)  all_57_14 = e2 & op(e0, e1) = e2
% 231.33/42.56  | | 
% 231.33/42.56  | | REF_CLOSE: (1), (4), (5), (6), (7), (8), (9), (10), (13), (14), (15), (22)
% 231.33/42.56  | |            are inconsistent by sub-proof #1424.
% 231.33/42.56  | | 
% 231.33/42.56  | End of split
% 231.33/42.56  | 
% 231.33/42.56  End of proof
% 231.33/42.56  
% 231.33/42.56  Sub-proof #1424 shows that the following formulas are inconsistent:
% 231.33/42.56  ----------------------------------------------------------------
% 231.33/42.56    (1)  all_57_9 = e2
% 231.33/42.56    (2)   ~ (e3 = e2)
% 231.33/42.56    (3)   ~ (e3 = e0)
% 231.33/42.56    (4)  all_57_15 = e3
% 231.33/42.56    (5)   ~ (e2 = e0)
% 231.33/42.56    (6)   ~ (e1 = e0)
% 231.33/42.56    (7)  all_57_14 = e1
% 231.33/42.56    (8)  all_57_10 = e3
% 231.33/42.56    (9)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) |
% 231.33/42.56         (all_57_11 = e0 & op(e1, e0) = e0)
% 231.33/42.56    (10)   ~ (e2 = e1)
% 231.33/42.56    (11)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.33/42.56          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.33/42.56    (12)  all_57_14 = e2 & op(e0, e1) = e2
% 231.33/42.56  
% 231.33/42.56  Begin of proof
% 231.33/42.56  | 
% 231.33/42.56  | ALPHA: (12) implies:
% 231.33/42.56  |   (13)  all_57_14 = e2
% 231.33/42.56  | 
% 231.33/42.56  | COMBINE_EQS: (7), (13) imply:
% 231.33/42.56  |   (14)  e2 = e1
% 231.33/42.56  | 
% 231.33/42.56  | COMBINE_EQS: (1), (14) imply:
% 231.33/42.56  |   (15)  all_57_9 = e1
% 231.33/42.56  | 
% 231.33/42.56  | REF_CLOSE: (2), (3), (4), (5), (6), (8), (9), (10), (11), (15) are
% 231.33/42.56  |            inconsistent by sub-proof #1986.
% 231.33/42.56  | 
% 231.33/42.56  End of proof
% 231.33/42.56  
% 231.33/42.56  Sub-proof #1425 shows that the following formulas are inconsistent:
% 231.33/42.56  ----------------------------------------------------------------
% 231.33/42.56    (1)  all_57_12 = e0
% 231.33/42.56    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.33/42.56         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.33/42.56    (3)   ~ (e3 = e1)
% 231.33/42.56    (4)   ~ (e3 = e2)
% 231.33/42.56    (5)  all_57_0 = e0
% 231.33/42.56    (6)   ~ (e2 = e0)
% 231.33/42.56    (7)   ~ (e1 = e0)
% 231.33/42.56    (8)  all_57_6 = e3
% 231.33/42.56    (9)   ~ (e2 = e1)
% 231.33/42.56    (10)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.33/42.56          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.33/42.56  
% 231.33/42.56  Begin of proof
% 231.33/42.56  | 
% 231.33/42.56  | BETA: splitting (2) gives:
% 231.33/42.56  | 
% 231.33/42.56  | Case 1:
% 231.33/42.56  | | 
% 231.33/42.56  | |   (11)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) =
% 231.33/42.56  | |           e1)
% 231.33/42.56  | | 
% 231.33/42.56  | | BETA: splitting (11) gives:
% 231.33/42.56  | | 
% 231.33/42.56  | | Case 1:
% 231.33/42.56  | | | 
% 231.33/42.56  | | |   (12)  all_57_0 = e1 & op(e3, e3) = e1
% 231.33/42.56  | | | 
% 231.33/42.56  | | | REF_CLOSE: (5), (7), (12) are inconsistent by sub-proof #2454.
% 231.33/42.56  | | | 
% 231.33/42.56  | | Case 2:
% 231.33/42.56  | | | 
% 231.33/42.56  | | |   (13)  all_57_2 = e1 & op(e2, e3) = e1
% 231.33/42.56  | | | 
% 231.33/42.56  | | | ALPHA: (13) implies:
% 231.33/42.56  | | |   (14)  all_57_2 = e1
% 231.33/42.56  | | | 
% 231.33/42.56  | | | REF_CLOSE: (1), (4), (5), (6), (8), (9), (10), (14) are inconsistent by
% 231.33/42.56  | | |            sub-proof #1426.
% 231.33/42.56  | | | 
% 231.33/42.56  | | End of split
% 231.33/42.56  | | 
% 231.33/42.56  | Case 2:
% 231.33/42.56  | | 
% 231.33/42.56  | |   (15)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) =
% 231.33/42.56  | |           e1)
% 231.33/42.56  | | 
% 231.33/42.56  | | BETA: splitting (15) gives:
% 231.33/42.56  | | 
% 231.33/42.56  | | Case 1:
% 231.33/42.56  | | | 
% 231.33/42.56  | | |   (16)  all_57_6 = e1 & op(e1, e3) = e1
% 231.33/42.56  | | | 
% 231.33/42.56  | | | REF_CLOSE: (3), (8), (16) are inconsistent by sub-proof #2117.
% 231.33/42.56  | | | 
% 231.33/42.56  | | Case 2:
% 231.40/42.56  | | | 
% 231.40/42.56  | | |   (17)  all_57_12 = e1 & op(e0, e3) = e1
% 231.40/42.56  | | | 
% 231.40/42.56  | | | REF_CLOSE: (1), (7), (17) are inconsistent by sub-proof #2328.
% 231.40/42.56  | | | 
% 231.40/42.56  | | End of split
% 231.40/42.56  | | 
% 231.40/42.56  | End of split
% 231.40/42.56  | 
% 231.40/42.56  End of proof
% 231.40/42.56  
% 231.40/42.56  Sub-proof #1426 shows that the following formulas are inconsistent:
% 231.40/42.56  ----------------------------------------------------------------
% 231.40/42.56    (1)  all_57_12 = e0
% 231.40/42.56    (2)   ~ (e3 = e2)
% 231.40/42.56    (3)  all_57_0 = e0
% 231.40/42.56    (4)   ~ (e2 = e0)
% 231.40/42.56    (5)  all_57_6 = e3
% 231.40/42.56    (6)  all_57_2 = e1
% 231.40/42.56    (7)   ~ (e2 = e1)
% 231.40/42.56    (8)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.40/42.56         (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.40/42.56  
% 231.40/42.56  Begin of proof
% 231.40/42.56  | 
% 231.40/42.56  | BETA: splitting (8) gives:
% 231.40/42.56  | 
% 231.40/42.56  | Case 1:
% 231.40/42.56  | | 
% 231.40/42.56  | |   (9)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2)
% 231.40/42.56  | | 
% 231.40/42.56  | | BETA: splitting (9) gives:
% 231.40/42.56  | | 
% 231.40/42.56  | | Case 1:
% 231.40/42.56  | | | 
% 231.40/42.56  | | |   (10)  all_57_0 = e2 & op(e3, e3) = e2
% 231.40/42.56  | | | 
% 231.40/42.56  | | | REF_CLOSE: (3), (4), (10) are inconsistent by sub-proof #1429.
% 231.40/42.56  | | | 
% 231.40/42.56  | | Case 2:
% 231.40/42.56  | | | 
% 231.40/42.56  | | |   (11)  all_57_2 = e2 & op(e2, e3) = e2
% 231.40/42.56  | | | 
% 231.40/42.56  | | | ALPHA: (11) implies:
% 231.40/42.56  | | |   (12)  all_57_2 = e2
% 231.40/42.56  | | | 
% 231.40/42.56  | | | REF_CLOSE: (6), (7), (12) are inconsistent by sub-proof #2464.
% 231.40/42.56  | | | 
% 231.40/42.56  | | End of split
% 231.40/42.56  | | 
% 231.40/42.56  | Case 2:
% 231.40/42.56  | | 
% 231.40/42.56  | |   (13)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) =
% 231.40/42.56  | |           e2)
% 231.40/42.56  | | 
% 231.40/42.56  | | REF_CLOSE: (1), (2), (4), (5), (13) are inconsistent by sub-proof #2461.
% 231.40/42.56  | | 
% 231.40/42.56  | End of split
% 231.40/42.56  | 
% 231.40/42.56  End of proof
% 231.40/42.56  
% 231.40/42.56  Sub-proof #1427 shows that the following formulas are inconsistent:
% 231.40/42.56  ----------------------------------------------------------------
% 231.40/42.56    (1)   ~ (e3 = e1)
% 231.40/42.56    (2)  all_57_4 = e3
% 231.40/42.56    (3)   ~ (e3 = e2)
% 231.40/42.56    (4)   ~ (e3 = e0)
% 231.40/42.56    (5)  all_57_15 = e3
% 231.40/42.56    (6)   ~ (e2 = e0)
% 231.40/42.56    (7)   ~ (e1 = e0)
% 231.40/42.56    (8)  all_57_10 = e3
% 231.40/42.56    (9)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.40/42.56             | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 231.40/42.56               e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.40/42.56               op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.40/42.56    (10)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.40/42.56    (11)   ~ (e2 = e1)
% 231.40/42.56    (12)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.40/42.56          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.40/42.56    (13)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.40/42.56          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.40/42.56  
% 231.40/42.56  Begin of proof
% 231.40/42.56  | 
% 231.40/42.56  | BETA: splitting (10) gives:
% 231.40/42.56  | 
% 231.40/42.56  | Case 1:
% 231.40/42.56  | | 
% 231.40/42.56  | |   (14)  all_57_4 = e0 & op(e3, e1) = e0
% 231.40/42.56  | | 
% 231.40/42.56  | | REF_CLOSE: (2), (4), (14) are inconsistent by sub-proof #2491.
% 231.40/42.56  | | 
% 231.40/42.56  | Case 2:
% 231.40/42.56  | | 
% 231.40/42.56  | |   (15)  all_57_9 = e0 & op(e3, e0) = e0
% 231.40/42.56  | | 
% 231.40/42.56  | | ALPHA: (15) implies:
% 231.40/42.56  | |   (16)  all_57_9 = e0
% 231.40/42.56  | | 
% 231.40/42.56  | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13), (16)
% 231.40/42.56  | |            are inconsistent by sub-proof #1982.
% 231.40/42.56  | | 
% 231.40/42.56  | End of split
% 231.40/42.56  | 
% 231.40/42.56  End of proof
% 231.40/42.56  
% 231.40/42.56  Sub-proof #1428 shows that the following formulas are inconsistent:
% 231.40/42.56  ----------------------------------------------------------------
% 231.40/42.56    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.40/42.56         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.40/42.56    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.40/42.56         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.40/42.56    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.40/42.56         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.40/42.56    (4)   ~ (e3 = e1)
% 231.40/42.56    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.40/42.56           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.40/42.56    (6)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.40/42.56         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.40/42.56    (7)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.40/42.56         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.40/42.56    (8)  all_57_3 = e0
% 231.40/42.56    (9)  all_57_4 = e3
% 231.40/42.56    (10)   ~ (e3 = e2)
% 231.40/42.56    (11)   ~ (e3 = e0)
% 231.40/42.56    (12)  op(e3, e3) = e3
% 231.40/42.56    (13)  all_57_1 = e0
% 231.40/42.56    (14)  all_57_15 = e3
% 231.40/42.56    (15)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.40/42.56          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.40/42.56            e1)
% 231.40/42.56    (16)   ~ (e2 = e0)
% 231.40/42.56    (17)   ~ (e1 = e0)
% 231.40/42.56    (18)  all_57_10 = e3
% 231.40/42.56    (19)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.40/42.56          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.40/42.56            e2)
% 231.40/42.56    (20)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.40/42.56              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.40/42.56                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.40/42.56                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.40/42.56    (21)  all_57_7 = e3
% 231.40/42.56    (22)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.40/42.56          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.40/42.56    (23)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 231.40/42.56          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 231.40/42.56    (24)   ~ (e2 = e1)
% 231.40/42.56    (25)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.40/42.56          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.40/42.56    (26)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.40/42.56          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.40/42.56    (27)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.40/42.56          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.40/42.56    (28)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.40/42.56          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.40/42.56  
% 231.40/42.56  Begin of proof
% 231.40/42.56  | 
% 231.40/42.56  | BETA: splitting (28) gives:
% 231.40/42.56  | 
% 231.40/42.56  | Case 1:
% 231.40/42.56  | | 
% 231.40/42.56  | |   (29)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) =
% 231.40/42.56  | |           e1)
% 231.40/42.56  | | 
% 231.40/42.56  | | BETA: splitting (29) gives:
% 231.40/42.56  | | 
% 231.40/42.56  | | Case 1:
% 231.40/42.56  | | | 
% 231.40/42.56  | | |   (30)  all_57_1 = e1 & op(e3, e2) = e1
% 231.40/42.56  | | | 
% 231.40/42.56  | | | REF_CLOSE: (13), (17), (30) are inconsistent by sub-proof #2446.
% 231.40/42.56  | | | 
% 231.40/42.56  | | Case 2:
% 231.40/42.56  | | | 
% 231.40/42.56  | | |   (31)  all_57_3 = e1 & op(e2, e2) = e1
% 231.40/42.56  | | | 
% 231.40/42.56  | | | REF_CLOSE: (8), (17), (31) are inconsistent by sub-proof #2362.
% 231.40/42.56  | | | 
% 231.40/42.56  | | End of split
% 231.40/42.56  | | 
% 231.40/42.56  | Case 2:
% 231.40/42.56  | | 
% 231.40/42.56  | |   (32)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 231.40/42.56  | |           e1)
% 231.40/42.56  | | 
% 231.40/42.56  | | BETA: splitting (32) gives:
% 231.40/42.56  | | 
% 231.40/42.56  | | Case 1:
% 231.40/42.56  | | | 
% 231.40/42.56  | | |   (33)  all_57_7 = e1 & op(e1, e2) = e1
% 231.40/42.56  | | | 
% 231.40/42.56  | | | REF_CLOSE: (4), (21), (33) are inconsistent by sub-proof #2104.
% 231.40/42.56  | | | 
% 231.40/42.56  | | Case 2:
% 231.40/42.56  | | | 
% 231.40/42.56  | | |   (34)  all_57_13 = e1 & op(e0, e2) = e1
% 231.40/42.56  | | | 
% 231.40/42.56  | | | ALPHA: (34) implies:
% 231.40/42.56  | | |   (35)  all_57_13 = e1
% 231.40/42.56  | | | 
% 231.40/42.56  | | | BETA: splitting (23) gives:
% 231.40/42.56  | | | 
% 231.40/42.56  | | | Case 1:
% 231.40/42.56  | | | | 
% 231.40/42.56  | | | |   (36)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3)
% 231.40/42.56  | | | |           = e3)
% 231.40/42.56  | | | | 
% 231.40/42.56  | | | | BETA: splitting (36) gives:
% 231.40/42.56  | | | | 
% 231.40/42.56  | | | | Case 1:
% 231.40/42.56  | | | | | 
% 231.40/42.56  | | | | |   (37)  all_57_0 = e3 & op(e3, e3) = e3
% 231.40/42.56  | | | | | 
% 231.40/42.56  | | | | | ALPHA: (37) implies:
% 231.40/42.56  | | | | |   (38)  all_57_0 = e3
% 231.40/42.56  | | | | | 
% 231.40/42.56  | | | | | BETA: splitting (7) gives:
% 231.40/42.56  | | | | | 
% 231.40/42.56  | | | | | Case 1:
% 231.40/42.56  | | | | | | 
% 231.40/42.56  | | | | | |   (39)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3,
% 231.40/42.56  | | | | | |             e2) = e2)
% 231.40/42.56  | | | | | | 
% 231.40/42.56  | | | | | | BETA: splitting (39) gives:
% 231.40/42.56  | | | | | | 
% 231.40/42.56  | | | | | | Case 1:
% 231.40/42.56  | | | | | | | 
% 231.40/42.56  | | | | | | |   (40)  all_57_0 = e2 & op(e3, e3) = e2
% 231.40/42.56  | | | | | | | 
% 231.40/42.56  | | | | | | | REF_CLOSE: (10), (38), (40) are inconsistent by sub-proof #2021.
% 231.40/42.56  | | | | | | | 
% 231.40/42.56  | | | | | | Case 2:
% 231.40/42.56  | | | | | | | 
% 231.40/42.56  | | | | | | |   (41)  all_57_1 = e2 & op(e3, e2) = e2
% 231.40/42.56  | | | | | | | 
% 231.40/42.56  | | | | | | | REF_CLOSE: (13), (16), (41) are inconsistent by sub-proof #2483.
% 231.40/42.56  | | | | | | | 
% 231.40/42.56  | | | | | | End of split
% 231.40/42.56  | | | | | | 
% 231.40/42.56  | | | | | Case 2:
% 231.40/42.56  | | | | | | 
% 231.40/42.56  | | | | | |   (42)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3,
% 231.40/42.56  | | | | | |             e0) = e2)
% 231.40/42.56  | | | | | | 
% 231.40/42.56  | | | | | | REF_CLOSE: (3), (4), (8), (9), (10), (11), (13), (14), (16), (17),
% 231.40/42.56  | | | | | |            (18), (20), (21), (24), (25), (27), (35), (42) are
% 231.40/42.56  | | | | | |            inconsistent by sub-proof #1434.
% 231.40/42.56  | | | | | | 
% 231.40/42.56  | | | | | End of split
% 231.40/42.56  | | | | | 
% 231.40/42.56  | | | | Case 2:
% 231.40/42.56  | | | | | 
% 231.40/42.56  | | | | |   (43)  all_57_2 = e3 & op(e2, e3) = e3
% 231.40/42.56  | | | | | 
% 231.40/42.56  | | | | | ALPHA: (43) implies:
% 231.40/42.56  | | | | |   (44)  all_57_2 = e3
% 231.40/42.56  | | | | | 
% 231.40/42.56  | | | | | REF_CLOSE: (1), (4), (8), (10), (16), (17), (18), (22), (24), (44) are
% 231.40/42.56  | | | | |            inconsistent by sub-proof #1433.
% 231.40/42.56  | | | | | 
% 231.40/42.56  | | | | End of split
% 231.40/42.56  | | | | 
% 231.40/42.56  | | | Case 2:
% 231.40/42.56  | | | | 
% 231.40/42.56  | | | |   (45)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3)
% 231.40/42.56  | | | |           = e3)
% 231.40/42.56  | | | | 
% 231.40/42.56  | | | | BETA: splitting (45) gives:
% 231.40/42.56  | | | | 
% 231.40/42.56  | | | | Case 1:
% 231.40/42.56  | | | | | 
% 231.40/42.56  | | | | |   (46)  all_57_6 = e3 & op(e1, e3) = e3
% 231.40/42.56  | | | | | 
% 231.40/42.56  | | | | | ALPHA: (46) implies:
% 231.40/42.56  | | | | |   (47)  all_57_6 = e3
% 231.40/42.56  | | | | | 
% 231.40/42.56  | | | | | BETA: splitting (26) gives:
% 231.40/42.56  | | | | | 
% 231.40/42.56  | | | | | Case 1:
% 231.40/42.56  | | | | | | 
% 231.40/42.56  | | | | | |   (48)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2,
% 231.40/42.56  | | | | | |             e3) = e0)
% 231.40/42.56  | | | | | | 
% 231.40/42.56  | | | | | | REF_CLOSE: (1), (4), (5), (8), (10), (11), (12), (16), (17), (18),
% 231.40/42.56  | | | | | |            (22), (24), (48) are inconsistent by sub-proof #1432.
% 231.40/42.56  | | | | | | 
% 231.40/42.56  | | | | | Case 2:
% 231.40/42.56  | | | | | | 
% 231.40/42.56  | | | | | |   (49)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0,
% 231.40/42.56  | | | | | |             e3) = e0)
% 231.40/42.56  | | | | | | 
% 231.40/42.56  | | | | | | BETA: splitting (49) gives:
% 231.40/42.56  | | | | | | 
% 231.40/42.56  | | | | | | Case 1:
% 231.40/42.56  | | | | | | | 
% 231.40/42.56  | | | | | | |   (50)  all_57_6 = e0 & op(e1, e3) = e0
% 231.40/42.56  | | | | | | | 
% 231.40/42.56  | | | | | | | REF_CLOSE: (11), (47), (50) are inconsistent by sub-proof #2465.
% 231.40/42.56  | | | | | | | 
% 231.40/42.56  | | | | | | Case 2:
% 231.40/42.56  | | | | | | | 
% 231.40/42.56  | | | | | | |   (51)  all_57_12 = e0 & op(e0, e3) = e0
% 231.40/42.56  | | | | | | | 
% 231.40/42.56  | | | | | | | ALPHA: (51) implies:
% 231.40/42.56  | | | | | | |   (52)  all_57_12 = e0
% 231.40/42.56  | | | | | | | 
% 231.40/42.56  | | | | | | | BETA: splitting (2) gives:
% 231.40/42.56  | | | | | | | 
% 231.40/42.56  | | | | | | | Case 1:
% 231.40/42.56  | | | | | | | | 
% 231.40/42.56  | | | | | | | |   (53)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 &
% 231.40/42.56  | | | | | | | |           op(e2, e3) = e1)
% 231.40/42.56  | | | | | | | | 
% 231.40/42.56  | | | | | | | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (10), (11), (13),
% 231.40/42.56  | | | | | | | |            (14), (16), (17), (18), (20), (21), (22), (24), (25),
% 231.40/42.56  | | | | | | | |            (27), (35), (53) are inconsistent by sub-proof #1430.
% 231.40/42.56  | | | | | | | | 
% 231.40/42.56  | | | | | | | Case 2:
% 231.40/42.56  | | | | | | | | 
% 231.40/42.56  | | | | | | | |   (54)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 &
% 231.40/42.56  | | | | | | | |           op(e0, e3) = e1)
% 231.40/42.56  | | | | | | | | 
% 231.40/42.56  | | | | | | | | BETA: splitting (54) gives:
% 231.40/42.56  | | | | | | | | 
% 231.40/42.56  | | | | | | | | Case 1:
% 231.40/42.56  | | | | | | | | | 
% 231.40/42.56  | | | | | | | | |   (55)  all_57_6 = e1 & op(e1, e3) = e1
% 231.40/42.56  | | | | | | | | | 
% 231.40/42.56  | | | | | | | | | REF_CLOSE: (4), (47), (55) are inconsistent by sub-proof
% 231.40/42.56  | | | | | | | | |            #2117.
% 231.40/42.56  | | | | | | | | | 
% 231.40/42.56  | | | | | | | | Case 2:
% 231.40/42.56  | | | | | | | | | 
% 231.40/42.56  | | | | | | | | |   (56)  all_57_12 = e1 & op(e0, e3) = e1
% 231.40/42.56  | | | | | | | | | 
% 231.40/42.56  | | | | | | | | | REF_CLOSE: (17), (52), (56) are inconsistent by sub-proof
% 231.40/42.56  | | | | | | | | |            #2328.
% 231.40/42.56  | | | | | | | | | 
% 231.40/42.56  | | | | | | | | End of split
% 231.40/42.56  | | | | | | | | 
% 231.40/42.56  | | | | | | | End of split
% 231.40/42.56  | | | | | | | 
% 231.40/42.56  | | | | | | End of split
% 231.40/42.56  | | | | | | 
% 231.40/42.56  | | | | | End of split
% 231.40/42.56  | | | | | 
% 231.40/42.56  | | | | Case 2:
% 231.40/42.56  | | | | | 
% 231.40/42.56  | | | | |   (57)  all_57_12 = e3 & op(e0, e3) = e3
% 231.40/42.56  | | | | | 
% 231.40/42.56  | | | | | ALPHA: (57) implies:
% 231.40/42.56  | | | | |   (58)  all_57_12 = e3
% 231.40/42.56  | | | | | 
% 231.40/42.56  | | | | | BETA: splitting (26) gives:
% 231.40/42.56  | | | | | 
% 231.40/42.56  | | | | | Case 1:
% 231.40/42.56  | | | | | | 
% 231.40/42.56  | | | | | |   (59)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2,
% 231.40/42.56  | | | | | |             e3) = e0)
% 231.40/42.56  | | | | | | 
% 231.40/42.56  | | | | | | BETA: splitting (59) gives:
% 231.40/42.56  | | | | | | 
% 231.40/42.56  | | | | | | Case 1:
% 231.40/42.56  | | | | | | | 
% 231.40/42.56  | | | | | | |   (60)  all_57_0 = e0 & op(e3, e3) = e0
% 231.40/42.56  | | | | | | | 
% 231.40/42.56  | | | | | | | ALPHA: (60) implies:
% 231.40/42.56  | | | | | | |   (61)  all_57_0 = e0
% 231.40/42.56  | | | | | | | 
% 231.40/42.56  | | | | | | | BETA: splitting (20) gives:
% 231.40/42.56  | | | | | | | 
% 231.40/42.56  | | | | | | | Case 1:
% 231.40/42.56  | | | | | | | | 
% 231.40/42.56  | | | | | | | |   (62)  all_57_15 = e0 & op(e0, e0) = e0
% 231.40/42.56  | | | | | | | | 
% 231.40/42.56  | | | | | | | | REF_CLOSE: (11), (14), (62) are inconsistent by sub-proof #2329.
% 231.40/42.56  | | | | | | | | 
% 231.40/42.56  | | | | | | | Case 2:
% 231.40/42.56  | | | | | | | | 
% 231.40/42.56  | | | | | | | |   (63)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 &
% 231.40/42.56  | | | | | | | |             op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 231.40/42.56  | | | | | | | |             e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) |
% 231.40/42.56  | | | | | | | |           (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 &
% 231.40/42.56  | | | | | | | |             op(e0, e1) = e0))
% 231.40/42.56  | | | | | | | | 
% 231.40/42.56  | | | | | | | | ALPHA: (63) implies:
% 231.40/42.56  | | | | | | | |   (64)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.40/42.56  | | | | | | | |           op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.40/42.56  | | | | | | | |   (65)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 &
% 231.40/42.56  | | | | | | | |           op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.40/42.56  | | | | | | | | 
% 231.40/42.56  | | | | | | | | BETA: splitting (64) gives:
% 231.40/42.56  | | | | | | | | 
% 231.40/42.56  | | | | | | | | Case 1:
% 231.40/42.56  | | | | | | | | | 
% 231.40/42.56  | | | | | | | | |   (66)  all_57_12 = e0 & op(e0, e3) = e0
% 231.40/42.56  | | | | | | | | | 
% 231.40/42.56  | | | | | | | | | REF_CLOSE: (11), (58), (66) are inconsistent by sub-proof
% 231.40/42.56  | | | | | | | | |            #2237.
% 231.40/42.56  | | | | | | | | | 
% 231.40/42.56  | | | | | | | | Case 2:
% 231.40/42.56  | | | | | | | | | 
% 231.40/42.56  | | | | | | | | |   (67)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 &
% 231.40/42.56  | | | | | | | | |           op(e0, e1) = e0)
% 231.40/42.56  | | | | | | | | | 
% 231.40/42.56  | | | | | | | | | BETA: splitting (67) gives:
% 231.40/42.56  | | | | | | | | | 
% 231.40/42.56  | | | | | | | | | Case 1:
% 231.40/42.56  | | | | | | | | | | 
% 231.40/42.56  | | | | | | | | | |   (68)  all_57_13 = e0 & op(e0, e2) = e0
% 231.40/42.56  | | | | | | | | | | 
% 231.40/42.56  | | | | | | | | | | ALPHA: (68) implies:
% 231.40/42.56  | | | | | | | | | |   (69)  all_57_13 = e0
% 231.40/42.56  | | | | | | | | | | 
% 231.40/42.56  | | | | | | | | | | BETA: splitting (28) gives:
% 231.40/42.56  | | | | | | | | | | 
% 231.40/42.56  | | | | | | | | | | Case 1:
% 231.40/42.56  | | | | | | | | | | | 
% 231.40/42.56  | | | | | | | | | | |   (70)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 231.40/42.56  | | | | | | | | | | |           & op(e2, e2) = e1)
% 231.40/42.56  | | | | | | | | | | | 
% 231.40/42.56  | | | | | | | | | | | BETA: splitting (70) gives:
% 231.40/42.56  | | | | | | | | | | | 
% 231.40/42.56  | | | | | | | | | | | Case 1:
% 231.40/42.56  | | | | | | | | | | | | 
% 231.40/42.56  | | | | | | | | | | | |   (71)  all_57_1 = e1 & op(e3, e2) = e1
% 231.40/42.56  | | | | | | | | | | | | 
% 231.40/42.56  | | | | | | | | | | | | ALPHA: (71) implies:
% 231.40/42.56  | | | | | | | | | | | |   (72)  all_57_1 = e1
% 231.40/42.56  | | | | | | | | | | | | 
% 231.40/42.56  | | | | | | | | | | | | BETA: splitting (7) gives:
% 231.40/42.56  | | | | | | | | | | | | 
% 231.40/42.56  | | | | | | | | | | | | Case 1:
% 231.40/42.56  | | | | | | | | | | | | | 
% 231.40/42.56  | | | | | | | | | | | | |   (73)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 231.40/42.56  | | | | | | | | | | | | |           & op(e3, e2) = e2)
% 231.40/42.56  | | | | | | | | | | | | | 
% 231.40/42.56  | | | | | | | | | | | | | BETA: splitting (73) gives:
% 231.40/42.56  | | | | | | | | | | | | | 
% 231.40/42.56  | | | | | | | | | | | | | Case 1:
% 231.40/42.56  | | | | | | | | | | | | | | 
% 231.40/42.56  | | | | | | | | | | | | | |   (74)  all_57_0 = e2 & op(e3, e3) = e2
% 231.40/42.56  | | | | | | | | | | | | | | 
% 231.40/42.56  | | | | | | | | | | | | | | REF_CLOSE: (16), (61), (74) are inconsistent by sub-proof
% 231.40/42.56  | | | | | | | | | | | | | |            #1429.
% 231.40/42.56  | | | | | | | | | | | | | | 
% 231.40/42.56  | | | | | | | | | | | | | Case 2:
% 231.40/42.56  | | | | | | | | | | | | | | 
% 231.40/42.56  | | | | | | | | | | | | | |   (75)  all_57_1 = e2 & op(e3, e2) = e2
% 231.40/42.56  | | | | | | | | | | | | | | 
% 231.40/42.56  | | | | | | | | | | | | | | REF_CLOSE: (24), (72), (75) are inconsistent by sub-proof
% 231.40/42.56  | | | | | | | | | | | | | |            #2489.
% 231.40/42.56  | | | | | | | | | | | | | | 
% 231.40/42.56  | | | | | | | | | | | | | End of split
% 231.40/42.56  | | | | | | | | | | | | | 
% 231.40/42.56  | | | | | | | | | | | | Case 2:
% 231.40/42.56  | | | | | | | | | | | | | 
% 231.40/42.56  | | | | | | | | | | | | |   (76)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 231.40/42.56  | | | | | | | | | | | | |           & op(e3, e0) = e2)
% 231.40/42.56  | | | | | | | | | | | | | 
% 231.40/42.56  | | | | | | | | | | | | | BETA: splitting (76) gives:
% 231.40/42.56  | | | | | | | | | | | | | 
% 231.40/42.56  | | | | | | | | | | | | | Case 1:
% 231.40/42.56  | | | | | | | | | | | | | | 
% 231.40/42.56  | | | | | | | | | | | | | |   (77)  all_57_4 = e2 & op(e3, e1) = e2
% 231.40/42.56  | | | | | | | | | | | | | | 
% 231.40/42.56  | | | | | | | | | | | | | | REF_CLOSE: (9), (10), (77) are inconsistent by sub-proof
% 231.40/42.56  | | | | | | | | | | | | | |            #2487.
% 231.40/42.56  | | | | | | | | | | | | | | 
% 231.40/42.56  | | | | | | | | | | | | | Case 2:
% 231.40/42.56  | | | | | | | | | | | | | | 
% 231.40/42.56  | | | | | | | | | | | | | |   (78)  all_57_9 = e2 & op(e3, e0) = e2
% 231.40/42.56  | | | | | | | | | | | | | | 
% 231.40/42.56  | | | | | | | | | | | | | | ALPHA: (78) implies:
% 231.40/42.56  | | | | | | | | | | | | | |   (79)  all_57_9 = e2
% 231.40/42.56  | | | | | | | | | | | | | | 
% 231.40/42.56  | | | | | | | | | | | | | | BETA: splitting (3) gives:
% 231.40/42.56  | | | | | | | | | | | | | | 
% 231.40/42.56  | | | | | | | | | | | | | | Case 1:
% 231.40/42.56  | | | | | | | | | | | | | | | 
% 231.40/42.57  | | | | | | | | | | | | | | |   (80)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 231.40/42.57  | | | | | | | | | | | | | | |           & op(e2, e2) = e2)
% 231.40/42.57  | | | | | | | | | | | | | | | 
% 231.40/42.57  | | | | | | | | | | | | | | | BETA: splitting (80) gives:
% 231.40/42.57  | | | | | | | | | | | | | | | 
% 231.40/42.57  | | | | | | | | | | | | | | | Case 1:
% 231.40/42.57  | | | | | | | | | | | | | | | | 
% 231.40/42.57  | | | | | | | | | | | | | | | |   (81)  all_57_1 = e2 & op(e3, e2) = e2
% 231.40/42.57  | | | | | | | | | | | | | | | | 
% 231.40/42.57  | | | | | | | | | | | | | | | | ALPHA: (81) implies:
% 231.40/42.57  | | | | | | | | | | | | | | | |   (82)  all_57_1 = e2
% 231.40/42.57  | | | | | | | | | | | | | | | | 
% 231.40/42.57  | | | | | | | | | | | | | | | | COMBINE_EQS: (72), (82) imply:
% 231.40/42.57  | | | | | | | | | | | | | | | |   (83)  e2 = e1
% 231.40/42.57  | | | | | | | | | | | | | | | | 
% 231.40/42.57  | | | | | | | | | | | | | | | | SIMP: (83) implies:
% 231.40/42.57  | | | | | | | | | | | | | | | |   (84)  e2 = e1
% 231.40/42.57  | | | | | | | | | | | | | | | | 
% 231.40/42.57  | | | | | | | | | | | | | | | | COMBINE_EQS: (79), (84) imply:
% 231.40/42.57  | | | | | | | | | | | | | | | |   (85)  all_57_9 = e1
% 231.40/42.57  | | | | | | | | | | | | | | | | 
% 231.40/42.57  | | | | | | | | | | | | | | | | REF_CLOSE: (10), (11), (14), (16), (17), (18), (24), (25),
% 231.40/42.57  | | | | | | | | | | | | | | | |            (65), (85) are inconsistent by sub-proof #1986.
% 231.40/42.57  | | | | | | | | | | | | | | | | 
% 231.40/42.57  | | | | | | | | | | | | | | | Case 2:
% 231.40/42.57  | | | | | | | | | | | | | | | | 
% 231.40/42.57  | | | | | | | | | | | | | | | |   (86)  all_57_3 = e2 & op(e2, e2) = e2
% 231.40/42.57  | | | | | | | | | | | | | | | | 
% 231.40/42.57  | | | | | | | | | | | | | | | | REF_CLOSE: (8), (16), (86) are inconsistent by sub-proof
% 231.40/42.57  | | | | | | | | | | | | | | | |            #2256.
% 231.40/42.57  | | | | | | | | | | | | | | | | 
% 231.40/42.57  | | | | | | | | | | | | | | | End of split
% 231.40/42.57  | | | | | | | | | | | | | | | 
% 231.40/42.57  | | | | | | | | | | | | | | Case 2:
% 231.40/42.57  | | | | | | | | | | | | | | | 
% 231.40/42.57  | | | | | | | | | | | | | | |   (87)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 231.40/42.57  | | | | | | | | | | | | | | |           e2 & op(e0, e2) = e2)
% 231.40/42.57  | | | | | | | | | | | | | | | 
% 231.40/42.57  | | | | | | | | | | | | | | | BETA: splitting (87) gives:
% 231.40/42.57  | | | | | | | | | | | | | | | 
% 231.40/42.57  | | | | | | | | | | | | | | | Case 1:
% 231.40/42.57  | | | | | | | | | | | | | | | | 
% 231.40/42.57  | | | | | | | | | | | | | | | |   (88)  all_57_7 = e2 & op(e1, e2) = e2
% 231.40/42.57  | | | | | | | | | | | | | | | | 
% 231.40/42.57  | | | | | | | | | | | | | | | | ALPHA: (88) implies:
% 231.40/42.57  | | | | | | | | | | | | | | | |   (89)  all_57_7 = e2
% 231.40/42.57  | | | | | | | | | | | | | | | | 
% 231.40/42.57  | | | | | | | | | | | | | | | | REF_CLOSE: (10), (21), (89) are inconsistent by sub-proof
% 231.40/42.57  | | | | | | | | | | | | | | | |            #2102.
% 231.40/42.57  | | | | | | | | | | | | | | | | 
% 231.40/42.57  | | | | | | | | | | | | | | | Case 2:
% 231.40/42.57  | | | | | | | | | | | | | | | | 
% 231.40/42.57  | | | | | | | | | | | | | | | |   (90)  all_57_13 = e2 & op(e0, e2) = e2
% 231.40/42.57  | | | | | | | | | | | | | | | | 
% 231.40/42.57  | | | | | | | | | | | | | | | | REF_CLOSE: (16), (69), (90) are inconsistent by sub-proof
% 231.40/42.57  | | | | | | | | | | | | | | | |            #2316.
% 231.40/42.57  | | | | | | | | | | | | | | | | 
% 231.40/42.57  | | | | | | | | | | | | | | | End of split
% 231.40/42.57  | | | | | | | | | | | | | | | 
% 231.40/42.57  | | | | | | | | | | | | | | End of split
% 231.40/42.57  | | | | | | | | | | | | | | 
% 231.40/42.57  | | | | | | | | | | | | | End of split
% 231.40/42.57  | | | | | | | | | | | | | 
% 231.40/42.57  | | | | | | | | | | | | End of split
% 231.40/42.57  | | | | | | | | | | | | 
% 231.40/42.57  | | | | | | | | | | | Case 2:
% 231.40/42.57  | | | | | | | | | | | | 
% 231.40/42.57  | | | | | | | | | | | |   (91)  all_57_3 = e1 & op(e2, e2) = e1
% 231.40/42.57  | | | | | | | | | | | | 
% 231.40/42.57  | | | | | | | | | | | | REF_CLOSE: (8), (17), (91) are inconsistent by sub-proof
% 231.40/42.57  | | | | | | | | | | | |            #2362.
% 231.40/42.57  | | | | | | | | | | | | 
% 231.40/42.57  | | | | | | | | | | | End of split
% 231.40/42.57  | | | | | | | | | | | 
% 231.40/42.57  | | | | | | | | | | Case 2:
% 231.40/42.57  | | | | | | | | | | | 
% 231.40/42.57  | | | | | | | | | | | 
% 231.40/42.57  | | | | | | | | | | | BETA: splitting (32) gives:
% 231.40/42.57  | | | | | | | | | | | 
% 231.40/42.57  | | | | | | | | | | | Case 1:
% 231.40/42.57  | | | | | | | | | | | | 
% 231.40/42.57  | | | | | | | | | | | |   (92)  all_57_7 = e1 & op(e1, e2) = e1
% 231.40/42.57  | | | | | | | | | | | | 
% 231.40/42.57  | | | | | | | | | | | | REF_CLOSE: (4), (21), (92) are inconsistent by sub-proof
% 231.40/42.57  | | | | | | | | | | | |            #2104.
% 231.40/42.57  | | | | | | | | | | | | 
% 231.40/42.57  | | | | | | | | | | | Case 2:
% 231.40/42.57  | | | | | | | | | | | | 
% 231.40/42.57  | | | | | | | | | | | | 
% 231.40/42.57  | | | | | | | | | | | | REF_CLOSE: (17), (34), (69) are inconsistent by sub-proof
% 231.40/42.57  | | | | | | | | | | | |            #2320.
% 231.40/42.57  | | | | | | | | | | | | 
% 231.40/42.57  | | | | | | | | | | | End of split
% 231.40/42.57  | | | | | | | | | | | 
% 231.40/42.57  | | | | | | | | | | End of split
% 231.40/42.57  | | | | | | | | | | 
% 231.40/42.57  | | | | | | | | | Case 2:
% 231.40/42.57  | | | | | | | | | | 
% 231.40/42.57  | | | | | | | | | |   (93)  all_57_14 = e0 & op(e0, e1) = e0
% 231.40/42.57  | | | | | | | | | | 
% 231.40/42.57  | | | | | | | | | | ALPHA: (93) implies:
% 231.40/42.57  | | | | | | | | | |   (94)  all_57_14 = e0
% 231.40/42.57  | | | | | | | | | | 
% 231.40/42.57  | | | | | | | | | | REF_CLOSE: (4), (10), (14), (15), (16), (17), (19), (24),
% 231.40/42.57  | | | | | | | | | |            (58), (94) are inconsistent by sub-proof #1763.
% 231.40/42.57  | | | | | | | | | | 
% 231.40/42.57  | | | | | | | | | End of split
% 231.40/42.57  | | | | | | | | | 
% 231.40/42.57  | | | | | | | | End of split
% 231.40/42.57  | | | | | | | | 
% 231.40/42.57  | | | | | | | End of split
% 231.40/42.57  | | | | | | | 
% 231.40/42.57  | | | | | | Case 2:
% 231.40/42.57  | | | | | | | 
% 231.40/42.57  | | | | | | |   (95)  all_57_2 = e0 & op(e2, e3) = e0
% 231.40/42.57  | | | | | | | 
% 231.40/42.57  | | | | | | | ALPHA: (95) implies:
% 231.40/42.57  | | | | | | |   (96)  all_57_2 = e0
% 231.40/42.57  | | | | | | | 
% 231.40/42.57  | | | | | | | REF_CLOSE: (1), (4), (8), (10), (16), (17), (18), (22), (24), (96)
% 231.40/42.57  | | | | | | |            are inconsistent by sub-proof #2247.
% 231.40/42.57  | | | | | | | 
% 231.40/42.57  | | | | | | End of split
% 231.40/42.57  | | | | | | 
% 231.40/42.57  | | | | | Case 2:
% 231.40/42.57  | | | | | | 
% 231.40/42.57  | | | | | |   (97)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0,
% 231.40/42.57  | | | | | |             e3) = e0)
% 231.40/42.57  | | | | | | 
% 231.40/42.57  | | | | | | BETA: splitting (97) gives:
% 231.40/42.57  | | | | | | 
% 231.40/42.57  | | | | | | Case 1:
% 231.40/42.57  | | | | | | | 
% 231.40/42.57  | | | | | | |   (98)  all_57_6 = e0 & op(e1, e3) = e0
% 231.40/42.57  | | | | | | | 
% 231.40/42.57  | | | | | | | ALPHA: (98) implies:
% 231.40/42.57  | | | | | | |   (99)  all_57_6 = e0
% 231.40/42.57  | | | | | | | 
% 231.40/42.57  | | | | | | | BETA: splitting (2) gives:
% 231.40/42.57  | | | | | | | 
% 231.40/42.57  | | | | | | | Case 1:
% 231.40/42.57  | | | | | | | | 
% 231.40/42.57  | | | | | | | |   (100)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 &
% 231.40/42.57  | | | | | | | |            op(e2, e3) = e1)
% 231.40/42.57  | | | | | | | | 
% 231.40/42.57  | | | | | | | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (10), (11), (13),
% 231.40/42.57  | | | | | | | |            (14), (16), (17), (18), (20), (21), (22), (24), (25),
% 231.40/42.57  | | | | | | | |            (27), (35), (100) are inconsistent by sub-proof
% 231.40/42.57  | | | | | | | |            #1430.
% 231.40/42.57  | | | | | | | | 
% 231.40/42.57  | | | | | | | Case 2:
% 231.40/42.57  | | | | | | | | 
% 231.40/42.57  | | | | | | | |   (101)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 &
% 231.40/42.57  | | | | | | | |            op(e0, e3) = e1)
% 231.40/42.57  | | | | | | | | 
% 231.40/42.57  | | | | | | | | BETA: splitting (101) gives:
% 231.40/42.57  | | | | | | | | 
% 231.40/42.57  | | | | | | | | Case 1:
% 231.40/42.57  | | | | | | | | | 
% 231.40/42.57  | | | | | | | | |   (102)  all_57_6 = e1 & op(e1, e3) = e1
% 231.40/42.57  | | | | | | | | | 
% 231.40/42.57  | | | | | | | | | ALPHA: (102) implies:
% 231.40/42.57  | | | | | | | | |   (103)  all_57_6 = e1
% 231.40/42.57  | | | | | | | | | 
% 231.40/42.57  | | | | | | | | | REF_CLOSE: (17), (99), (103) are inconsistent by sub-proof
% 231.40/42.57  | | | | | | | | |            #2227.
% 231.40/42.57  | | | | | | | | | 
% 231.40/42.57  | | | | | | | | Case 2:
% 231.40/42.57  | | | | | | | | | 
% 231.40/42.57  | | | | | | | | |   (104)  all_57_12 = e1 & op(e0, e3) = e1
% 231.40/42.57  | | | | | | | | | 
% 231.40/42.57  | | | | | | | | | ALPHA: (104) implies:
% 231.40/42.57  | | | | | | | | |   (105)  all_57_12 = e1
% 231.40/42.57  | | | | | | | | | 
% 231.40/42.57  | | | | | | | | | REF_CLOSE: (4), (58), (105) are inconsistent by sub-proof
% 231.40/42.57  | | | | | | | | |            #2151.
% 231.40/42.57  | | | | | | | | | 
% 231.40/42.57  | | | | | | | | End of split
% 231.40/42.57  | | | | | | | | 
% 231.40/42.57  | | | | | | | End of split
% 231.40/42.57  | | | | | | | 
% 231.40/42.57  | | | | | | Case 2:
% 231.40/42.57  | | | | | | | 
% 231.40/42.57  | | | | | | |   (106)  all_57_12 = e0 & op(e0, e3) = e0
% 231.40/42.57  | | | | | | | 
% 231.40/42.57  | | | | | | | ALPHA: (106) implies:
% 231.40/42.57  | | | | | | |   (107)  all_57_12 = e0
% 231.40/42.57  | | | | | | | 
% 231.40/42.57  | | | | | | | REF_CLOSE: (11), (58), (107) are inconsistent by sub-proof #2153.
% 231.40/42.57  | | | | | | | 
% 231.40/42.57  | | | | | | End of split
% 231.40/42.57  | | | | | | 
% 231.40/42.57  | | | | | End of split
% 231.40/42.57  | | | | | 
% 231.40/42.57  | | | | End of split
% 231.40/42.57  | | | | 
% 231.40/42.57  | | | End of split
% 231.40/42.57  | | | 
% 231.40/42.57  | | End of split
% 231.40/42.57  | | 
% 231.40/42.57  | End of split
% 231.40/42.57  | 
% 231.40/42.57  End of proof
% 231.40/42.57  
% 231.40/42.57  Sub-proof #1429 shows that the following formulas are inconsistent:
% 231.40/42.57  ----------------------------------------------------------------
% 231.40/42.57    (1)  all_57_0 = e2 & op(e3, e3) = e2
% 231.40/42.57    (2)  all_57_0 = e0
% 231.40/42.57    (3)   ~ (e2 = e0)
% 231.40/42.57  
% 231.40/42.57  Begin of proof
% 231.40/42.57  | 
% 231.40/42.57  | ALPHA: (1) implies:
% 231.40/42.57  |   (4)  all_57_0 = e2
% 231.40/42.57  | 
% 231.40/42.57  | COMBINE_EQS: (2), (4) imply:
% 231.40/42.57  |   (5)  e2 = e0
% 231.40/42.57  | 
% 231.40/42.57  | SIMP: (5) implies:
% 231.40/42.57  |   (6)  e2 = e0
% 231.40/42.57  | 
% 231.40/42.57  | REDUCE: (3), (6) imply:
% 231.40/42.57  |   (7)  $false
% 231.40/42.57  | 
% 231.40/42.57  | CLOSE: (7) is inconsistent.
% 231.40/42.57  | 
% 231.40/42.57  End of proof
% 231.40/42.57  
% 231.40/42.57  Sub-proof #1430 shows that the following formulas are inconsistent:
% 231.40/42.57  ----------------------------------------------------------------
% 231.40/42.57    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.40/42.57         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.40/42.57    (2)  all_57_13 = e1
% 231.40/42.57    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.40/42.57         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.40/42.57    (4)   ~ (e3 = e1)
% 231.40/42.57    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.40/42.57         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.40/42.57    (6)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1)
% 231.40/42.57    (7)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.40/42.57         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.40/42.57    (8)  all_57_3 = e0
% 231.40/42.57    (9)  all_57_4 = e3
% 231.40/42.57    (10)   ~ (e3 = e2)
% 231.40/42.57    (11)   ~ (e3 = e0)
% 231.40/42.57    (12)  all_57_1 = e0
% 231.40/42.57    (13)  all_57_15 = e3
% 231.40/42.57    (14)   ~ (e2 = e0)
% 231.40/42.57    (15)   ~ (e1 = e0)
% 231.40/42.57    (16)  all_57_10 = e3
% 231.40/42.57    (17)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.40/42.57              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.40/42.57                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.40/42.57                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.40/42.57    (18)  all_57_7 = e3
% 231.40/42.57    (19)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.40/42.57          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.40/42.57    (20)   ~ (e2 = e1)
% 231.40/42.57    (21)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.40/42.57          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.40/42.57    (22)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.40/42.57          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.40/42.57  
% 231.40/42.57  Begin of proof
% 231.40/42.57  | 
% 231.40/42.57  | BETA: splitting (6) gives:
% 231.40/42.57  | 
% 231.40/42.57  | Case 1:
% 231.40/42.57  | | 
% 231.40/42.57  | |   (23)  all_57_0 = e1 & op(e3, e3) = e1
% 231.40/42.57  | | 
% 231.40/42.57  | | REF_CLOSE: (2), (3), (4), (7), (8), (9), (10), (11), (12), (13), (14), (15),
% 231.40/42.57  | |            (16), (17), (18), (20), (21), (22), (23) are inconsistent by
% 231.40/42.57  | |            sub-proof #1431.
% 231.40/42.57  | | 
% 231.40/42.57  | Case 2:
% 231.40/42.57  | | 
% 231.40/42.57  | |   (24)  all_57_2 = e1 & op(e2, e3) = e1
% 231.40/42.57  | | 
% 231.40/42.57  | | ALPHA: (24) implies:
% 231.40/42.57  | |   (25)  all_57_2 = e1
% 231.40/42.57  | | 
% 231.40/42.57  | | BETA: splitting (5) gives:
% 231.40/42.57  | | 
% 231.40/42.57  | | Case 1:
% 231.40/42.57  | | | 
% 231.40/42.57  | | |   (26)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) =
% 231.40/42.57  | | |           e1)
% 231.40/42.57  | | | 
% 231.40/42.57  | | | BETA: splitting (26) gives:
% 231.40/42.57  | | | 
% 231.40/42.57  | | | Case 1:
% 231.40/42.57  | | | | 
% 231.40/42.57  | | | |   (27)  all_57_0 = e1 & op(e3, e3) = e1
% 231.40/42.57  | | | | 
% 231.40/42.57  | | | | REF_CLOSE: (2), (3), (4), (7), (8), (9), (10), (11), (12), (13), (14),
% 231.40/42.57  | | | |            (15), (16), (17), (18), (20), (21), (22), (27) are
% 231.40/42.57  | | | |            inconsistent by sub-proof #1431.
% 231.40/42.57  | | | | 
% 231.40/42.57  | | | Case 2:
% 231.40/42.57  | | | | 
% 231.40/42.57  | | | |   (28)  all_57_1 = e1 & op(e3, e2) = e1
% 231.40/42.57  | | | | 
% 231.40/42.57  | | | | ALPHA: (28) implies:
% 231.40/42.57  | | | |   (29)  all_57_1 = e1
% 231.40/42.57  | | | | 
% 231.40/42.57  | | | | COMBINE_EQS: (12), (29) imply:
% 231.40/42.57  | | | |   (30)  e1 = e0
% 231.40/42.57  | | | | 
% 231.40/42.57  | | | | SIMP: (30) implies:
% 231.40/42.57  | | | |   (31)  e1 = e0
% 231.40/42.57  | | | | 
% 231.40/42.57  | | | | COMBINE_EQS: (25), (31) imply:
% 231.40/42.57  | | | |   (32)  all_57_2 = e0
% 231.40/42.57  | | | | 
% 231.40/42.57  | | | | REF_CLOSE: (1), (4), (8), (10), (14), (15), (16), (19), (20), (32) are
% 231.40/42.57  | | | |            inconsistent by sub-proof #2247.
% 231.40/42.57  | | | | 
% 231.40/42.57  | | | End of split
% 231.40/42.57  | | | 
% 231.40/42.57  | | Case 2:
% 231.40/42.57  | | | 
% 231.40/42.57  | | |   (33)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) =
% 231.40/42.57  | | |           e1)
% 231.40/42.57  | | | 
% 231.40/42.57  | | | BETA: splitting (33) gives:
% 231.40/42.57  | | | 
% 231.40/42.57  | | | Case 1:
% 231.40/42.57  | | | | 
% 231.40/42.57  | | | |   (34)  all_57_4 = e1 & op(e3, e1) = e1
% 231.40/42.57  | | | | 
% 231.40/42.57  | | | | ALPHA: (34) implies:
% 231.40/42.57  | | | |   (35)  all_57_4 = e1
% 231.40/42.57  | | | | 
% 231.40/42.57  | | | | REF_CLOSE: (4), (9), (35) are inconsistent by sub-proof #2426.
% 231.40/42.57  | | | | 
% 231.40/42.57  | | | Case 2:
% 231.40/42.57  | | | | 
% 231.40/42.57  | | | |   (36)  all_57_9 = e1 & op(e3, e0) = e1
% 231.40/42.57  | | | | 
% 231.40/42.57  | | | | ALPHA: (36) implies:
% 231.40/42.57  | | | |   (37)  all_57_9 = e1
% 231.40/42.57  | | | | 
% 231.40/42.57  | | | | REF_CLOSE: (10), (11), (13), (14), (15), (16), (17), (20), (21), (37)
% 231.40/42.57  | | | |            are inconsistent by sub-proof #1985.
% 231.40/42.57  | | | | 
% 231.40/42.57  | | | End of split
% 231.40/42.57  | | | 
% 231.40/42.57  | | End of split
% 231.40/42.57  | | 
% 231.40/42.57  | End of split
% 231.40/42.57  | 
% 231.40/42.57  End of proof
% 231.40/42.57  
% 231.40/42.57  Sub-proof #1431 shows that the following formulas are inconsistent:
% 231.40/42.57  ----------------------------------------------------------------
% 231.40/42.57    (1)  all_57_13 = e1
% 231.40/42.57    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.40/42.57         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.40/42.57    (3)   ~ (e3 = e1)
% 231.40/42.57    (4)  all_57_0 = e1 & op(e3, e3) = e1
% 231.40/42.57    (5)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.40/42.57         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.40/42.57    (6)  all_57_3 = e0
% 231.40/42.57    (7)  all_57_4 = e3
% 231.40/42.57    (8)   ~ (e3 = e2)
% 231.40/42.57    (9)   ~ (e3 = e0)
% 231.40/42.57    (10)  all_57_1 = e0
% 231.40/42.57    (11)  all_57_15 = e3
% 231.40/42.57    (12)   ~ (e2 = e0)
% 231.40/42.57    (13)   ~ (e1 = e0)
% 231.40/42.57    (14)  all_57_10 = e3
% 231.40/42.57    (15)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.40/42.57              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.40/42.57                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.40/42.57                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.40/42.57    (16)  all_57_7 = e3
% 231.40/42.57    (17)   ~ (e2 = e1)
% 231.40/42.57    (18)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.40/42.57          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.40/42.57    (19)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.40/42.57          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.40/42.57  
% 231.40/42.57  Begin of proof
% 231.40/42.57  | 
% 231.40/42.57  | ALPHA: (4) implies:
% 231.40/42.57  |   (20)  all_57_0 = e1
% 231.40/42.57  | 
% 231.40/42.57  | BETA: splitting (5) gives:
% 231.40/42.57  | 
% 231.40/42.57  | Case 1:
% 231.40/42.57  | | 
% 231.40/42.57  | |   (21)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) =
% 231.40/42.57  | |           e2)
% 231.40/42.57  | | 
% 231.40/42.57  | | BETA: splitting (21) gives:
% 231.40/42.57  | | 
% 231.40/42.57  | | Case 1:
% 231.40/42.57  | | | 
% 231.40/42.57  | | |   (22)  all_57_0 = e2 & op(e3, e3) = e2
% 231.40/42.57  | | | 
% 231.40/42.57  | | | REF_CLOSE: (17), (20), (22) are inconsistent by sub-proof #1810.
% 231.40/42.57  | | | 
% 231.40/42.57  | | Case 2:
% 231.40/42.57  | | | 
% 231.40/42.57  | | |   (23)  all_57_1 = e2 & op(e3, e2) = e2
% 231.40/42.57  | | | 
% 231.40/42.57  | | | REF_CLOSE: (10), (12), (23) are inconsistent by sub-proof #2483.
% 231.40/42.57  | | | 
% 231.40/42.57  | | End of split
% 231.40/42.57  | | 
% 231.40/42.57  | Case 2:
% 231.40/42.57  | | 
% 231.40/42.57  | |   (24)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) =
% 231.40/42.57  | |           e2)
% 231.40/42.57  | | 
% 231.40/42.57  | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (9), (10), (11), (12), (13), (14),
% 231.40/42.57  | |            (15), (16), (17), (18), (19), (24) are inconsistent by sub-proof
% 231.40/42.57  | |            #1434.
% 231.40/42.57  | | 
% 231.40/42.57  | End of split
% 231.40/42.57  | 
% 231.40/42.57  End of proof
% 231.40/42.57  
% 231.40/42.57  Sub-proof #1432 shows that the following formulas are inconsistent:
% 231.40/42.57  ----------------------------------------------------------------
% 231.40/42.57    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.40/42.57         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.40/42.57    (2)   ~ (e3 = e1)
% 231.40/42.57    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.40/42.57           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.40/42.57    (4)  all_57_3 = e0
% 231.40/42.57    (5)   ~ (e3 = e2)
% 231.40/42.57    (6)   ~ (e3 = e0)
% 231.40/42.57    (7)  op(e3, e3) = e3
% 231.40/42.57    (8)   ~ (e2 = e0)
% 231.40/42.57    (9)   ~ (e1 = e0)
% 231.40/42.57    (10)  all_57_10 = e3
% 231.40/42.57    (11)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.40/42.57          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.40/42.57    (12)   ~ (e2 = e1)
% 231.40/42.57    (13)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0)
% 231.40/42.57  
% 231.40/42.57  Begin of proof
% 231.40/42.57  | 
% 231.40/42.57  | BETA: splitting (13) gives:
% 231.40/42.57  | 
% 231.40/42.57  | Case 1:
% 231.40/42.57  | | 
% 231.40/42.57  | |   (14)  all_57_0 = e0 & op(e3, e3) = e0
% 231.40/42.57  | | 
% 231.40/42.57  | | ALPHA: (14) implies:
% 231.40/42.57  | |   (15)  op(e3, e3) = e0
% 231.40/42.57  | | 
% 231.40/42.57  | | REF_CLOSE: (3), (6), (7), (15) are inconsistent by sub-proof #2494.
% 231.40/42.57  | | 
% 231.40/42.57  | Case 2:
% 231.40/42.57  | | 
% 231.40/42.57  | |   (16)  all_57_2 = e0 & op(e2, e3) = e0
% 231.40/42.57  | | 
% 231.40/42.57  | | ALPHA: (16) implies:
% 231.40/42.57  | |   (17)  all_57_2 = e0
% 231.40/42.57  | | 
% 231.40/42.57  | | REF_CLOSE: (1), (2), (4), (5), (8), (9), (10), (11), (12), (17) are
% 231.40/42.57  | |            inconsistent by sub-proof #2247.
% 231.40/42.57  | | 
% 231.40/42.57  | End of split
% 231.40/42.57  | 
% 231.40/42.57  End of proof
% 231.40/42.57  
% 231.40/42.57  Sub-proof #1433 shows that the following formulas are inconsistent:
% 231.40/42.57  ----------------------------------------------------------------
% 231.40/42.57    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.40/42.57         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.40/42.57    (2)   ~ (e3 = e1)
% 231.40/42.57    (3)  all_57_3 = e0
% 231.40/42.57    (4)   ~ (e3 = e2)
% 231.40/42.57    (5)   ~ (e2 = e0)
% 231.40/42.57    (6)  all_57_2 = e3
% 231.40/42.57    (7)   ~ (e1 = e0)
% 231.40/42.57    (8)  all_57_10 = e3
% 231.40/42.57    (9)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.40/42.57         (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.40/42.57    (10)   ~ (e2 = e1)
% 231.40/42.57  
% 231.40/42.57  Begin of proof
% 231.40/42.57  | 
% 231.40/42.57  | BETA: splitting (9) gives:
% 231.40/42.57  | 
% 231.40/42.57  | Case 1:
% 231.40/42.57  | | 
% 231.40/42.57  | |   (11)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 231.40/42.57  | |           e2)
% 231.40/42.57  | | 
% 231.40/42.57  | | BETA: splitting (11) gives:
% 231.40/42.57  | | 
% 231.40/42.57  | | Case 1:
% 231.40/42.57  | | | 
% 231.40/42.57  | | |   (12)  all_57_2 = e2 & op(e2, e3) = e2
% 231.40/42.57  | | | 
% 231.40/42.57  | | | REF_CLOSE: (4), (6), (12) are inconsistent by sub-proof #1925.
% 231.40/42.57  | | | 
% 231.40/42.57  | | Case 2:
% 231.40/42.57  | | | 
% 231.40/42.57  | | |   (13)  all_57_3 = e2 & op(e2, e2) = e2
% 231.40/42.57  | | | 
% 231.40/42.57  | | | REF_CLOSE: (3), (5), (13) are inconsistent by sub-proof #2103.
% 231.40/42.57  | | | 
% 231.40/42.57  | | End of split
% 231.40/42.57  | | 
% 231.40/42.57  | Case 2:
% 231.40/42.57  | | 
% 231.40/42.57  | |   (14)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 231.40/42.57  | |           e2)
% 231.40/42.57  | | 
% 231.40/42.57  | | BETA: splitting (14) gives:
% 231.40/42.57  | | 
% 231.40/42.57  | | Case 1:
% 231.40/42.57  | | | 
% 231.40/42.57  | | |   (15)  all_57_5 = e2 & op(e2, e1) = e2
% 231.40/42.57  | | | 
% 231.40/42.57  | | | ALPHA: (15) implies:
% 231.40/42.57  | | |   (16)  all_57_5 = e2
% 231.40/42.57  | | | 
% 231.40/42.57  | | | BETA: splitting (1) gives:
% 231.40/42.57  | | | 
% 231.40/42.57  | | | Case 1:
% 231.40/42.57  | | | | 
% 231.40/42.57  | | | |   (17)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2)
% 231.40/42.57  | | | |           = e1)
% 231.40/42.57  | | | | 
% 231.40/42.57  | | | | BETA: splitting (17) gives:
% 231.40/42.57  | | | | 
% 231.40/42.57  | | | | Case 1:
% 231.40/42.57  | | | | | 
% 231.40/42.57  | | | | |   (18)  all_57_2 = e1 & op(e2, e3) = e1
% 231.40/42.57  | | | | | 
% 231.40/42.57  | | | | | REF_CLOSE: (2), (6), (18) are inconsistent by sub-proof #1928.
% 231.40/42.57  | | | | | 
% 231.40/42.57  | | | | Case 2:
% 231.40/42.57  | | | | | 
% 231.40/42.57  | | | | |   (19)  all_57_3 = e1 & op(e2, e2) = e1
% 231.40/42.57  | | | | | 
% 231.40/42.57  | | | | | REF_CLOSE: (3), (7), (19) are inconsistent by sub-proof #2252.
% 231.40/42.57  | | | | | 
% 231.40/42.57  | | | | End of split
% 231.40/42.57  | | | | 
% 231.40/42.57  | | | Case 2:
% 231.40/42.57  | | | | 
% 231.40/42.57  | | | |   (20)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0)
% 231.40/42.57  | | | |           = e1)
% 231.40/42.57  | | | | 
% 231.40/42.57  | | | | BETA: splitting (20) gives:
% 231.40/42.57  | | | | 
% 231.40/42.57  | | | | Case 1:
% 231.40/42.57  | | | | | 
% 231.40/42.57  | | | | |   (21)  all_57_5 = e1 & op(e2, e1) = e1
% 231.40/42.57  | | | | | 
% 231.40/42.57  | | | | | ALPHA: (21) implies:
% 231.40/42.57  | | | | |   (22)  all_57_5 = e1
% 231.40/42.57  | | | | | 
% 231.40/42.57  | | | | | REF_CLOSE: (10), (16), (22) are inconsistent by sub-proof #1885.
% 231.40/42.57  | | | | | 
% 231.40/42.57  | | | | Case 2:
% 231.40/42.57  | | | | | 
% 231.40/42.57  | | | | |   (23)  all_57_10 = e1 & op(e2, e0) = e1
% 231.40/42.57  | | | | | 
% 231.40/42.57  | | | | | ALPHA: (23) implies:
% 231.40/42.57  | | | | |   (24)  all_57_10 = e1
% 231.40/42.57  | | | | | 
% 231.40/42.57  | | | | | REF_CLOSE: (2), (8), (24) are inconsistent by sub-proof #2248.
% 231.40/42.57  | | | | | 
% 231.40/42.57  | | | | End of split
% 231.40/42.57  | | | | 
% 231.40/42.57  | | | End of split
% 231.40/42.57  | | | 
% 231.40/42.57  | | Case 2:
% 231.40/42.57  | | | 
% 231.40/42.57  | | |   (25)  all_57_10 = e2 & op(e2, e0) = e2
% 231.40/42.57  | | | 
% 231.40/42.57  | | | REF_CLOSE: (4), (8), (25) are inconsistent by sub-proof #2250.
% 231.40/42.57  | | | 
% 231.40/42.57  | | End of split
% 231.40/42.57  | | 
% 231.40/42.57  | End of split
% 231.40/42.57  | 
% 231.40/42.57  End of proof
% 231.40/42.57  
% 231.40/42.57  Sub-proof #1434 shows that the following formulas are inconsistent:
% 231.40/42.57  ----------------------------------------------------------------
% 231.40/42.57    (1)  all_57_13 = e1
% 231.40/42.57    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.40/42.57         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.40/42.57    (3)   ~ (e3 = e1)
% 231.40/42.57    (4)  all_57_3 = e0
% 231.40/42.57    (5)  all_57_4 = e3
% 231.40/42.57    (6)   ~ (e3 = e2)
% 231.40/42.57    (7)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.40/42.57    (8)   ~ (e3 = e0)
% 231.40/42.57    (9)  all_57_1 = e0
% 231.40/42.57    (10)  all_57_15 = e3
% 231.40/42.57    (11)   ~ (e2 = e0)
% 231.40/42.57    (12)   ~ (e1 = e0)
% 231.40/42.57    (13)  all_57_10 = e3
% 231.40/42.57    (14)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.40/42.57              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.40/42.57                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.40/42.57                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.40/42.57    (15)  all_57_7 = e3
% 231.40/42.57    (16)   ~ (e2 = e1)
% 231.40/42.57    (17)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.40/42.57          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.40/42.57    (18)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.40/42.57          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.40/42.57  
% 231.40/42.57  Begin of proof
% 231.40/42.57  | 
% 231.40/42.57  | BETA: splitting (7) gives:
% 231.40/42.57  | 
% 231.40/42.57  | Case 1:
% 231.40/42.57  | | 
% 231.40/42.57  | |   (19)  all_57_4 = e2 & op(e3, e1) = e2
% 231.40/42.57  | | 
% 231.40/42.57  | | REF_CLOSE: (5), (6), (19) are inconsistent by sub-proof #2487.
% 231.40/42.57  | | 
% 231.40/42.57  | Case 2:
% 231.40/42.57  | | 
% 231.40/42.57  | |   (20)  all_57_9 = e2 & op(e3, e0) = e2
% 231.40/42.57  | | 
% 231.40/42.57  | | ALPHA: (20) implies:
% 231.40/42.57  | |   (21)  all_57_9 = e2
% 231.40/42.57  | | 
% 231.40/42.57  | | BETA: splitting (2) gives:
% 231.40/42.57  | | 
% 231.40/42.57  | | Case 1:
% 231.40/42.57  | | | 
% 231.40/42.57  | | |   (22)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 231.40/42.57  | | |           e2)
% 231.40/42.57  | | | 
% 231.40/42.57  | | | BETA: splitting (22) gives:
% 231.40/42.57  | | | 
% 231.40/42.57  | | | Case 1:
% 231.40/42.57  | | | | 
% 231.40/42.57  | | | |   (23)  all_57_1 = e2 & op(e3, e2) = e2
% 231.40/42.57  | | | | 
% 231.40/42.57  | | | | ALPHA: (23) implies:
% 231.40/42.57  | | | |   (24)  all_57_1 = e2
% 231.40/42.57  | | | | 
% 231.40/42.57  | | | | COMBINE_EQS: (9), (24) imply:
% 231.40/42.57  | | | |   (25)  e2 = e0
% 231.40/42.57  | | | | 
% 231.40/42.57  | | | | SIMP: (25) implies:
% 231.40/42.57  | | | |   (26)  e2 = e0
% 231.40/42.57  | | | | 
% 231.40/42.57  | | | | COMBINE_EQS: (21), (26) imply:
% 231.40/42.57  | | | |   (27)  all_57_9 = e0
% 231.40/42.57  | | | | 
% 231.40/42.57  | | | | REF_CLOSE: (3), (6), (8), (10), (11), (12), (13), (14), (16), (17),
% 231.40/42.57  | | | |            (18), (27) are inconsistent by sub-proof #1982.
% 231.40/42.57  | | | | 
% 231.40/42.57  | | | Case 2:
% 231.40/42.57  | | | | 
% 231.40/42.57  | | | |   (28)  all_57_3 = e2 & op(e2, e2) = e2
% 231.40/42.57  | | | | 
% 231.40/42.57  | | | | ALPHA: (28) implies:
% 231.40/42.57  | | | |   (29)  all_57_3 = e2
% 231.40/42.57  | | | | 
% 231.40/42.57  | | | | COMBINE_EQS: (4), (29) imply:
% 231.40/42.57  | | | |   (30)  e2 = e0
% 231.40/42.57  | | | | 
% 231.40/42.57  | | | | COMBINE_EQS: (21), (30) imply:
% 231.40/42.57  | | | |   (31)  all_57_9 = e0
% 231.40/42.57  | | | | 
% 231.40/42.57  | | | | REF_CLOSE: (3), (6), (8), (10), (11), (12), (13), (14), (16), (17),
% 231.40/42.57  | | | |            (18), (31) are inconsistent by sub-proof #1982.
% 231.40/42.57  | | | | 
% 231.40/42.57  | | | End of split
% 231.40/42.57  | | | 
% 231.40/42.57  | | Case 2:
% 231.40/42.57  | | | 
% 231.40/42.57  | | |   (32)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 231.40/42.57  | | |           e2)
% 231.40/42.57  | | | 
% 231.40/42.57  | | | BETA: splitting (32) gives:
% 231.40/42.57  | | | 
% 231.40/42.57  | | | Case 1:
% 231.40/42.57  | | | | 
% 231.40/42.57  | | | |   (33)  all_57_7 = e2 & op(e1, e2) = e2
% 231.40/42.57  | | | | 
% 231.40/42.57  | | | | ALPHA: (33) implies:
% 231.40/42.57  | | | |   (34)  all_57_7 = e2
% 231.40/42.57  | | | | 
% 231.40/42.57  | | | | REF_CLOSE: (6), (15), (34) are inconsistent by sub-proof #2102.
% 231.40/42.57  | | | | 
% 231.40/42.57  | | | Case 2:
% 231.40/42.57  | | | | 
% 231.40/42.57  | | | |   (35)  all_57_13 = e2 & op(e0, e2) = e2
% 231.40/42.57  | | | | 
% 231.40/42.57  | | | | ALPHA: (35) implies:
% 231.40/42.57  | | | |   (36)  all_57_13 = e2
% 231.40/42.57  | | | | 
% 231.40/42.57  | | | | COMBINE_EQS: (1), (36) imply:
% 231.40/42.57  | | | |   (37)  e2 = e1
% 231.40/42.57  | | | | 
% 231.40/42.57  | | | | COMBINE_EQS: (21), (37) imply:
% 231.40/42.57  | | | |   (38)  all_57_9 = e1
% 231.40/42.57  | | | | 
% 231.40/42.57  | | | | REF_CLOSE: (6), (8), (10), (11), (12), (13), (14), (16), (17), (38) are
% 231.40/42.57  | | | |            inconsistent by sub-proof #1985.
% 231.40/42.57  | | | | 
% 231.40/42.57  | | | End of split
% 231.40/42.57  | | | 
% 231.40/42.57  | | End of split
% 231.40/42.57  | | 
% 231.40/42.57  | End of split
% 231.40/42.57  | 
% 231.40/42.57  End of proof
% 231.40/42.57  
% 231.40/42.57  Sub-proof #1435 shows that the following formulas are inconsistent:
% 231.40/42.57  ----------------------------------------------------------------
% 231.40/42.57    (1)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3)
% 231.40/42.57    (2)   ~ (e3 = e1)
% 231.40/42.57    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.40/42.57         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.40/42.57    (4)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.40/42.57         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.40/42.57    (5)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.40/42.57         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.40/42.57    (6)  all_57_3 = e0
% 231.40/42.57    (7)  all_57_4 = e3
% 231.40/42.57    (8)   ~ (e3 = e2)
% 231.40/42.57    (9)   ~ (e3 = e0)
% 231.40/42.57    (10)  all_57_15 = e3
% 231.40/42.57    (11)   ~ (e2 = e0)
% 231.40/42.57    (12)   ~ (e1 = e0)
% 231.40/42.57    (13)  all_57_10 = e3
% 231.40/42.57    (14)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.40/42.57              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.40/42.57                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.40/42.57                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.40/42.57    (15)   ~ (e2 = e1)
% 231.40/42.57    (16)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.40/42.57          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.40/42.57  
% 231.40/42.57  Begin of proof
% 231.40/42.57  | 
% 231.40/42.57  | BETA: splitting (1) gives:
% 231.40/42.57  | 
% 231.40/42.57  | Case 1:
% 231.40/42.57  | | 
% 231.40/42.57  | |   (17)  all_57_1 = e3 & op(e3, e2) = e3
% 231.40/42.57  | | 
% 231.40/42.57  | | ALPHA: (17) implies:
% 231.40/42.57  | |   (18)  all_57_1 = e3
% 231.40/42.57  | | 
% 231.40/42.57  | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13), (14),
% 231.40/42.57  | |            (15), (16), (18) are inconsistent by sub-proof #1436.
% 231.40/42.57  | | 
% 231.40/42.57  | Case 2:
% 231.40/42.57  | | 
% 231.40/42.57  | |   (19)  all_57_3 = e3 & op(e2, e2) = e3
% 231.40/42.57  | | 
% 231.40/42.57  | | ALPHA: (19) implies:
% 231.40/42.57  | |   (20)  all_57_3 = e3
% 231.40/42.57  | | 
% 231.40/42.57  | | REF_CLOSE: (6), (9), (20) are inconsistent by sub-proof #2358.
% 231.40/42.57  | | 
% 231.40/42.57  | End of split
% 231.40/42.57  | 
% 231.40/42.57  End of proof
% 231.40/42.57  
% 231.40/42.57  Sub-proof #1436 shows that the following formulas are inconsistent:
% 231.40/42.57  ----------------------------------------------------------------
% 231.40/42.57    (1)   ~ (e3 = e1)
% 231.40/42.57    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.40/42.57         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.40/42.57    (3)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.40/42.57         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.40/42.57    (4)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.40/42.57         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.40/42.57    (5)  all_57_4 = e3
% 231.40/42.57    (6)   ~ (e3 = e2)
% 231.40/42.57    (7)   ~ (e3 = e0)
% 231.40/42.57    (8)  all_57_15 = e3
% 231.40/42.57    (9)   ~ (e2 = e0)
% 231.40/42.57    (10)   ~ (e1 = e0)
% 231.40/42.57    (11)  all_57_10 = e3
% 231.40/42.57    (12)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.40/42.57              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.40/42.57                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.40/42.57                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.40/42.57    (13)  all_57_1 = e3
% 231.40/42.57    (14)   ~ (e2 = e1)
% 231.40/42.57    (15)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.40/42.57          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.40/42.57  
% 231.40/42.57  Begin of proof
% 231.40/42.57  | 
% 231.40/42.57  | BETA: splitting (2) gives:
% 231.40/42.57  | 
% 231.40/42.57  | Case 1:
% 231.40/42.57  | | 
% 231.40/42.57  | |   (16)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) =
% 231.40/42.57  | |           e1)
% 231.40/42.57  | | 
% 231.40/42.57  | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (9), (10), (13), (14), (16) are
% 231.40/42.57  | |            inconsistent by sub-proof #1807.
% 231.40/42.57  | | 
% 231.40/42.57  | Case 2:
% 231.40/42.57  | | 
% 231.40/42.57  | |   (17)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) =
% 231.40/42.57  | |           e1)
% 231.40/42.57  | | 
% 231.40/42.57  | | BETA: splitting (17) gives:
% 231.40/42.57  | | 
% 231.40/42.57  | | Case 1:
% 231.40/42.57  | | | 
% 231.40/42.57  | | |   (18)  all_57_4 = e1 & op(e3, e1) = e1
% 231.40/42.57  | | | 
% 231.40/42.57  | | | REF_CLOSE: (1), (5), (18) are inconsistent by sub-proof #2484.
% 231.40/42.57  | | | 
% 231.40/42.57  | | Case 2:
% 231.40/42.57  | | | 
% 231.40/42.57  | | |   (19)  all_57_9 = e1 & op(e3, e0) = e1
% 231.40/42.57  | | | 
% 231.40/42.57  | | | ALPHA: (19) implies:
% 231.40/42.57  | | |   (20)  all_57_9 = e1
% 231.40/42.57  | | | 
% 231.40/42.57  | | | REF_CLOSE: (6), (7), (8), (9), (10), (11), (12), (14), (15), (20) are
% 231.40/42.57  | | |            inconsistent by sub-proof #1985.
% 231.40/42.57  | | | 
% 231.40/42.57  | | End of split
% 231.40/42.57  | | 
% 231.40/42.57  | End of split
% 231.40/42.57  | 
% 231.40/42.57  End of proof
% 231.40/42.57  
% 231.40/42.57  Sub-proof #1437 shows that the following formulas are inconsistent:
% 231.40/42.57  ----------------------------------------------------------------
% 231.40/42.57    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 231.40/42.57    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 231.40/42.57    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.40/42.57         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.40/42.57    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.40/42.57         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.40/42.58    (5)   ~ (all_53_8 = all_53_12)
% 231.40/42.58    (6)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.40/42.58         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.40/42.58    (7)   ~ (e3 = e1)
% 231.40/42.58    (8)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 231.40/42.58         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.40/42.58    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.40/42.58           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.40/42.58    (10)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.40/42.58          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.40/42.58    (11)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 231.40/42.58            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 231.40/42.58              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 231.40/42.58    (12)   ~ (all_6_2 = e3)
% 231.40/42.58    (13)  op(e1, e1) = all_6_2
% 231.40/42.58    (14)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 231.40/42.58    (15)   ~ (all_53_9 = e0)
% 231.40/42.58    (16)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.40/42.58          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.40/42.58    (17)   ~ (all_53_4 = all_53_12)
% 231.40/42.58    (18)   ~ (all_53_8 = all_53_9)
% 231.40/42.58    (19)  all_42_2 = all_6_2
% 231.40/42.58    (20)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.40/42.58          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.40/42.58    (21)   ~ (all_53_9 = all_6_2)
% 231.40/42.58    (22)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.40/42.58          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.40/42.58    (23)  all_57_3 = e0
% 231.40/42.58    (24)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.40/42.58          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.40/42.58    (25)   ~ (e3 = e2)
% 231.40/42.58    (26)  all_55_1 = all_53_4
% 231.40/42.58    (27)   ~ (e3 = e0)
% 231.40/42.58    (28)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.40/42.58          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.40/42.58    (29)  op(e3, e3) = e3
% 231.40/42.58    (30)   ~ (all_53_8 = all_6_2)
% 231.40/42.58    (31)  all_55_2 = all_53_8
% 231.40/42.58    (32)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 231.40/42.58    (33)  all_57_15 = e3
% 231.40/42.58    (34)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.40/42.58          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.40/42.58            e1)
% 231.40/42.58    (35)   ~ (all_53_4 = all_53_8)
% 231.40/42.58    (36)  op(e3, e2) = all_53_4
% 231.40/42.58    (37)   ~ (e2 = e0)
% 231.40/42.58    (38)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 231.40/42.58            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 231.40/42.58            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 231.40/42.58            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 231.40/42.58              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 231.40/42.58            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 231.40/42.58            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 231.40/42.58              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 231.40/42.58              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 231.40/42.58            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 231.40/42.58            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 231.40/42.58            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 231.40/42.58              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 231.40/42.58              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 231.40/42.58            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 231.40/42.58              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 231.40/42.58            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 231.40/42.58            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 231.40/42.58              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 231.40/42.58              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 231.40/42.58            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 231.40/42.58            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 231.40/42.58    (39)  all_57_2 = e3
% 231.40/42.58    (40)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 231.40/42.58          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.40/42.58    (41)   ~ (e1 = e0)
% 231.40/42.58    (42)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 231.40/42.58            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 231.40/42.58              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 231.40/42.58    (43)   ~ (all_53_4 = e0)
% 231.40/42.58    (44)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.40/42.58          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.40/42.58    (45)  op(e0, e0) = e3
% 231.40/42.58    (46)   ~ (all_53_4 = all_53_6)
% 231.40/42.58    (47)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.40/42.58          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.40/42.58            e2)
% 231.40/42.58    (48)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.40/42.58              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.40/42.58                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.40/42.58                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.40/42.58    (49)  all_55_10 = all_6_2
% 231.40/42.58    (50)  all_38_2 = all_6_2
% 231.40/42.58    (51)  all_55_3 = all_53_12
% 231.40/42.58    (52)   ~ (all_53_12 = e3)
% 231.40/42.58    (53)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 231.40/42.58            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 231.40/42.58              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 231.40/42.58    (54)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.40/42.58          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.40/42.58    (55)   ~ (e2 = e1)
% 231.40/42.58    (56)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.40/42.58          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.40/42.58    (57)  op(e2, e1) = all_53_9
% 231.40/42.58    (58)  op(e1, e2) = all_53_6
% 231.40/42.58    (59)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.40/42.58          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.40/42.58    (60)  all_24_2 = all_6_2
% 231.40/42.58    (61)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.40/42.58          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.40/42.58    (62)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.40/42.58          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.40/42.58    (63)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.40/42.58          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.40/42.58    (64)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 231.40/42.58          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 231.40/42.58    (65)  op(e3, e1) = all_53_8
% 231.40/42.58    (66)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.40/42.58          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.40/42.58    (67)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 231.40/42.58          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 231.40/42.58    (68)  op(e3, e0) = all_53_12
% 231.40/42.58  
% 231.40/42.58  Begin of proof
% 231.40/42.58  | 
% 231.40/42.58  | BETA: splitting (44) gives:
% 231.40/42.58  | 
% 231.40/42.58  | Case 1:
% 231.40/42.58  | | 
% 231.40/42.58  | |   (69)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) =
% 231.40/42.58  | |           e3)
% 231.40/42.58  | | 
% 231.40/42.58  | | BETA: splitting (69) gives:
% 231.40/42.58  | | 
% 231.40/42.58  | | Case 1:
% 231.40/42.58  | | | 
% 231.40/42.58  | | |   (70)  all_57_4 = e3 & op(e3, e1) = e3
% 231.40/42.58  | | | 
% 231.40/42.58  | | | ALPHA: (70) implies:
% 231.40/42.58  | | |   (71)  all_57_4 = e3
% 231.40/42.58  | | | 
% 231.40/42.58  | | | BETA: splitting (22) gives:
% 231.40/42.58  | | | 
% 231.40/42.58  | | | Case 1:
% 231.40/42.58  | | | | 
% 231.40/42.58  | | | |   (72)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2)
% 231.40/42.58  | | | |           = e0)
% 231.40/42.58  | | | | 
% 231.40/42.58  | | | | BETA: splitting (72) gives:
% 231.40/42.58  | | | | 
% 231.40/42.58  | | | | Case 1:
% 231.40/42.58  | | | | | 
% 231.40/42.58  | | | | |   (73)  all_57_0 = e0 & op(e3, e3) = e0
% 231.40/42.58  | | | | | 
% 231.40/42.58  | | | | | ALPHA: (73) implies:
% 231.40/42.58  | | | | |   (74)  op(e3, e3) = e0
% 231.40/42.58  | | | | | 
% 231.40/42.58  | | | | | REF_CLOSE: (9), (27), (29), (74) are inconsistent by sub-proof #2494.
% 231.40/42.58  | | | | | 
% 231.40/42.58  | | | | Case 2:
% 231.40/42.58  | | | | | 
% 231.40/42.58  | | | | |   (75)  all_57_1 = e0 & op(e3, e2) = e0
% 231.40/42.58  | | | | | 
% 231.40/42.58  | | | | | ALPHA: (75) implies:
% 231.40/42.58  | | | | |   (76)  all_57_1 = e0
% 231.40/42.58  | | | | | 
% 231.40/42.58  | | | | | BETA: splitting (10) gives:
% 231.40/42.58  | | | | | 
% 231.40/42.58  | | | | | Case 1:
% 231.40/42.58  | | | | | | 
% 231.40/42.58  | | | | | |   (77)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1,
% 231.40/42.58  | | | | | |             e2) = e3)
% 231.40/42.58  | | | | | | 
% 231.40/42.58  | | | | | | BETA: splitting (77) gives:
% 231.40/42.58  | | | | | | 
% 231.40/42.58  | | | | | | Case 1:
% 231.40/42.58  | | | | | | | 
% 231.40/42.58  | | | | | | |   (78)  all_57_6 = e3 & op(e1, e3) = e3
% 231.40/42.58  | | | | | | | 
% 231.40/42.58  | | | | | | | REF_CLOSE: (4), (7), (9), (25), (27), (29), (37), (39), (41),
% 231.40/42.58  | | | | | | |            (55), (59), (62), (78) are inconsistent by sub-proof
% 231.40/42.58  | | | | | | |            #1534.
% 231.40/42.58  | | | | | | | 
% 231.40/42.58  | | | | | | Case 2:
% 231.40/42.58  | | | | | | | 
% 231.40/42.58  | | | | | | |   (79)  all_57_7 = e3 & op(e1, e2) = e3
% 231.40/42.58  | | | | | | | 
% 231.40/42.58  | | | | | | | ALPHA: (79) implies:
% 231.40/42.58  | | | | | | |   (80)  all_57_7 = e3
% 231.40/42.58  | | | | | | | 
% 231.40/42.58  | | | | | | | REF_CLOSE: (6), (7), (23), (25), (37), (41), (55), (66), (76),
% 231.40/42.58  | | | | | | |            (80) are inconsistent by sub-proof #2098.
% 231.40/42.58  | | | | | | | 
% 231.40/42.58  | | | | | | End of split
% 231.40/42.58  | | | | | | 
% 231.40/42.58  | | | | | Case 2:
% 231.40/42.58  | | | | | | 
% 231.40/42.58  | | | | | |   (81)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1,
% 231.40/42.58  | | | | | |             e0) = e3)
% 231.40/42.58  | | | | | | 
% 231.40/42.58  | | | | | | REF_CLOSE: (7), (9), (12), (13), (25), (27), (33), (37), (41), (48),
% 231.40/42.58  | | | | | |            (55), (56), (63), (81) are inconsistent by sub-proof
% 231.40/42.58  | | | | | |            #1786.
% 231.40/42.58  | | | | | | 
% 231.40/42.58  | | | | | End of split
% 231.40/42.58  | | | | | 
% 231.40/42.58  | | | | End of split
% 231.40/42.58  | | | | 
% 231.40/42.58  | | | Case 2:
% 231.40/42.58  | | | | 
% 231.40/42.58  | | | |   (82)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0)
% 231.40/42.58  | | | |           = e0)
% 231.40/42.58  | | | | 
% 231.40/42.58  | | | | REF_CLOSE: (7), (9), (16), (20), (25), (27), (29), (37), (41), (55),
% 231.40/42.58  | | | |            (71), (82) are inconsistent by sub-proof #2476.
% 231.40/42.58  | | | | 
% 231.40/42.58  | | | End of split
% 231.40/42.58  | | | 
% 231.40/42.58  | | Case 2:
% 231.40/42.58  | | | 
% 231.40/42.58  | | |   (83)  all_57_5 = e3 & op(e2, e1) = e3
% 231.40/42.58  | | | 
% 231.40/42.58  | | | ALPHA: (83) implies:
% 231.40/42.58  | | |   (84)  all_57_5 = e3
% 231.40/42.58  | | |   (85)  op(e2, e1) = e3
% 231.40/42.58  | | | 
% 231.40/42.58  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 231.40/42.58  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 231.40/42.58  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 231.40/42.58  | | |            (33), (34), (35), (36), (37), (38), (40), (41), (42), (43),
% 231.40/42.58  | | |            (45), (46), (47), (48), (49), (50), (51), (52), (53), (54),
% 231.40/42.58  | | |            (55), (56), (57), (58), (59), (60), (61), (62), (63), (64),
% 231.40/42.58  | | |            (65), (66), (67), (68), (84), (85) are inconsistent by
% 231.40/42.58  | | |            sub-proof #1438.
% 231.40/42.58  | | | 
% 231.40/42.58  | | End of split
% 231.40/42.58  | | 
% 231.40/42.58  | Case 2:
% 231.40/42.58  | | 
% 231.40/42.58  | |   (86)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) =
% 231.40/42.58  | |           e3)
% 231.40/42.58  | | 
% 231.40/42.58  | | REF_CLOSE: (7), (9), (12), (13), (25), (27), (33), (34), (37), (41), (47),
% 231.40/42.58  | |            (48), (55), (86) are inconsistent by sub-proof #1794.
% 231.40/42.58  | | 
% 231.40/42.58  | End of split
% 231.40/42.58  | 
% 231.40/42.58  End of proof
% 231.40/42.58  
% 231.40/42.58  Sub-proof #1438 shows that the following formulas are inconsistent:
% 231.40/42.58  ----------------------------------------------------------------
% 231.40/42.58    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 231.40/42.58    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 231.40/42.58    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.40/42.58         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.40/42.58    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.40/42.58         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.40/42.58    (5)  op(e2, e1) = e3
% 231.40/42.58    (6)   ~ (all_53_8 = all_53_12)
% 231.40/42.58    (7)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.40/42.58         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.40/42.58    (8)   ~ (e3 = e1)
% 231.40/42.58    (9)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 231.40/42.58         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.40/42.58    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.40/42.58            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.40/42.58    (11)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.40/42.58          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.40/42.58    (12)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 231.40/42.58            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 231.40/42.58              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 231.40/42.58    (13)   ~ (all_6_2 = e3)
% 231.40/42.58    (14)  op(e1, e1) = all_6_2
% 231.40/42.58    (15)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 231.40/42.58    (16)   ~ (all_53_9 = e0)
% 231.40/42.58    (17)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.40/42.58          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.40/42.58    (18)   ~ (all_53_4 = all_53_12)
% 231.40/42.58    (19)   ~ (all_53_8 = all_53_9)
% 231.40/42.58    (20)  all_42_2 = all_6_2
% 231.40/42.58    (21)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.40/42.58          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.40/42.58    (22)   ~ (all_53_9 = all_6_2)
% 231.40/42.58    (23)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.40/42.58          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.40/42.58    (24)  all_57_3 = e0
% 231.40/42.58    (25)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.40/42.58          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.40/42.58    (26)   ~ (e3 = e2)
% 231.40/42.58    (27)  all_55_1 = all_53_4
% 231.40/42.58    (28)   ~ (e3 = e0)
% 231.40/42.58    (29)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.40/42.58          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.40/42.58    (30)  op(e3, e3) = e3
% 231.40/42.58    (31)   ~ (all_53_8 = all_6_2)
% 231.40/42.58    (32)  all_55_2 = all_53_8
% 231.40/42.58    (33)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 231.40/42.58    (34)  all_57_15 = e3
% 231.40/42.58    (35)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.40/42.58          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.40/42.58            e1)
% 231.40/42.58    (36)  all_57_5 = e3
% 231.40/42.58    (37)   ~ (all_53_4 = all_53_8)
% 231.40/42.58    (38)  op(e3, e2) = all_53_4
% 231.40/42.58    (39)   ~ (e2 = e0)
% 231.40/42.58    (40)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 231.40/42.58            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 231.40/42.58            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 231.40/42.58            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 231.40/42.58              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 231.40/42.58            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 231.40/42.58            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 231.40/42.58              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 231.40/42.58              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 231.40/42.58            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 231.40/42.58            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 231.40/42.58            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 231.40/42.58              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 231.40/42.58              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 231.40/42.58            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 231.40/42.58              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 231.40/42.58            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 231.40/42.58            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 231.40/42.58              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 231.40/42.58              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 231.40/42.58            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 231.40/42.58            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 231.40/42.58    (41)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 231.40/42.58          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.40/42.58    (42)   ~ (e1 = e0)
% 231.40/42.58    (43)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 231.40/42.58            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 231.40/42.58              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 231.40/42.58    (44)   ~ (all_53_4 = e0)
% 231.40/42.58    (45)  op(e0, e0) = e3
% 231.40/42.58    (46)   ~ (all_53_4 = all_53_6)
% 231.40/42.58    (47)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.40/42.58          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.40/42.58            e2)
% 231.40/42.58    (48)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.40/42.58              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.40/42.58                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.40/42.58                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.40/42.58    (49)  all_55_10 = all_6_2
% 231.40/42.58    (50)  all_38_2 = all_6_2
% 231.40/42.58    (51)  all_55_3 = all_53_12
% 231.40/42.58    (52)   ~ (all_53_12 = e3)
% 231.40/42.58    (53)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 231.40/42.58            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 231.40/42.58              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 231.40/42.58    (54)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.40/42.58          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.40/42.58    (55)   ~ (e2 = e1)
% 231.40/42.58    (56)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.40/42.58          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.40/42.58    (57)  op(e2, e1) = all_53_9
% 231.40/42.58    (58)  op(e1, e2) = all_53_6
% 231.40/42.58    (59)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.40/42.58          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.40/42.58    (60)  all_24_2 = all_6_2
% 231.40/42.58    (61)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.40/42.58          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.40/42.58    (62)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.40/42.58          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.40/42.58    (63)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.40/42.58          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.40/42.58    (64)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 231.40/42.58          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 231.40/42.58    (65)  op(e3, e1) = all_53_8
% 231.40/42.58    (66)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.40/42.58          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.40/42.58    (67)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 231.40/42.58          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 231.40/42.58    (68)  op(e3, e0) = all_53_12
% 231.40/42.58  
% 231.40/42.58  Begin of proof
% 231.40/42.58  | 
% 231.40/42.58  | BETA: splitting (41) gives:
% 231.40/42.58  | 
% 231.40/42.58  | Case 1:
% 231.40/42.58  | | 
% 231.40/42.58  | |   (69)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) =
% 231.40/42.58  | |           e3)
% 231.40/42.58  | | 
% 231.40/42.58  | | BETA: splitting (69) gives:
% 231.40/42.58  | | 
% 231.40/42.58  | | Case 1:
% 231.40/42.58  | | | 
% 231.40/42.58  | | |   (70)  all_57_0 = e3 & op(e3, e3) = e3
% 231.40/42.58  | | | 
% 231.40/42.58  | | | ALPHA: (70) implies:
% 231.40/42.58  | | |   (71)  all_57_0 = e3
% 231.40/42.58  | | | 
% 231.40/42.58  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 231.40/42.58  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 231.40/42.58  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 231.40/42.58  | | |            (33), (34), (35), (36), (37), (38), (39), (40), (42), (43),
% 231.40/42.58  | | |            (44), (45), (46), (47), (48), (49), (50), (51), (52), (53),
% 231.40/42.58  | | |            (54), (55), (56), (57), (58), (59), (60), (61), (62), (63),
% 231.40/42.58  | | |            (64), (65), (66), (67), (68), (71) are inconsistent by
% 231.40/42.58  | | |            sub-proof #1440.
% 231.40/42.58  | | | 
% 231.40/42.58  | | Case 2:
% 231.40/42.58  | | | 
% 231.40/42.58  | | |   (72)  all_57_1 = e3 & op(e3, e2) = e3
% 231.40/42.58  | | | 
% 231.40/42.58  | | | ALPHA: (72) implies:
% 231.40/42.58  | | |   (73)  all_57_1 = e3
% 231.40/42.58  | | | 
% 231.40/42.58  | | | REF_CLOSE: (3), (4), (7), (8), (10), (11), (13), (14), (24), (26), (28),
% 231.40/42.58  | | |            (30), (34), (36), (39), (42), (48), (54), (55), (56), (59),
% 231.40/42.58  | | |            (62), (63), (66), (73) are inconsistent by sub-proof #1777.
% 231.40/42.58  | | | 
% 231.40/42.58  | | End of split
% 231.40/42.58  | | 
% 231.40/42.58  | Case 2:
% 231.40/42.58  | | 
% 231.40/42.58  | |   (74)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) =
% 231.40/42.58  | |           e3)
% 231.40/42.58  | | 
% 231.40/42.58  | | BETA: splitting (74) gives:
% 231.40/42.58  | | 
% 231.40/42.58  | | Case 1:
% 231.40/42.58  | | | 
% 231.40/42.58  | | |   (75)  all_57_4 = e3 & op(e3, e1) = e3
% 231.40/42.58  | | | 
% 231.40/42.58  | | | ALPHA: (75) implies:
% 231.40/42.58  | | |   (76)  all_57_4 = e3
% 231.40/42.58  | | | 
% 231.40/42.58  | | | BETA: splitting (23) gives:
% 231.40/42.58  | | | 
% 231.40/42.58  | | | Case 1:
% 231.40/42.58  | | | | 
% 231.40/42.58  | | | |   (77)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2)
% 231.40/42.58  | | | |           = e0)
% 231.40/42.58  | | | | 
% 231.40/42.58  | | | | BETA: splitting (77) gives:
% 231.40/42.58  | | | | 
% 231.40/42.58  | | | | Case 1:
% 231.40/42.58  | | | | | 
% 231.40/42.58  | | | | |   (78)  all_57_0 = e0 & op(e3, e3) = e0
% 231.40/42.58  | | | | | 
% 231.40/42.58  | | | | | ALPHA: (78) implies:
% 231.40/42.58  | | | | |   (79)  op(e3, e3) = e0
% 231.40/42.58  | | | | | 
% 231.40/42.58  | | | | | REF_CLOSE: (10), (28), (30), (79) are inconsistent by sub-proof #2494.
% 231.40/42.58  | | | | | 
% 231.40/42.58  | | | | Case 2:
% 231.40/42.58  | | | | | 
% 231.40/42.58  | | | | |   (80)  all_57_1 = e0 & op(e3, e2) = e0
% 231.40/42.58  | | | | | 
% 231.40/42.58  | | | | | ALPHA: (80) implies:
% 231.40/42.58  | | | | |   (81)  all_57_1 = e0
% 231.40/42.58  | | | | | 
% 231.40/42.58  | | | | | REF_CLOSE: (3), (4), (7), (8), (10), (11), (13), (14), (24), (26),
% 231.40/42.58  | | | | |            (28), (30), (34), (36), (39), (42), (48), (54), (55), (56),
% 231.40/42.58  | | | | |            (59), (62), (63), (66), (81) are inconsistent by sub-proof
% 231.40/42.58  | | | | |            #1439.
% 231.40/42.58  | | | | | 
% 231.40/42.58  | | | | End of split
% 231.40/42.58  | | | | 
% 231.40/42.58  | | | Case 2:
% 231.40/42.58  | | | | 
% 231.40/42.58  | | | |   (82)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0)
% 231.40/42.58  | | | |           = e0)
% 231.40/42.58  | | | | 
% 231.40/42.58  | | | | REF_CLOSE: (8), (10), (17), (21), (26), (28), (30), (39), (42), (55),
% 231.40/42.58  | | | |            (76), (82) are inconsistent by sub-proof #2476.
% 231.40/42.58  | | | | 
% 231.40/42.58  | | | End of split
% 231.40/42.58  | | | 
% 231.40/42.58  | | Case 2:
% 231.40/42.58  | | | 
% 231.40/42.58  | | |   (83)  all_57_9 = e3 & op(e3, e0) = e3
% 231.40/42.58  | | | 
% 231.40/42.58  | | | ALPHA: (83) implies:
% 231.40/42.58  | | |   (84)  op(e3, e0) = e3
% 231.40/42.58  | | | 
% 231.40/42.58  | | | REF_CLOSE: (10), (52), (68), (84) are inconsistent by sub-proof #2458.
% 231.40/42.58  | | | 
% 231.40/42.58  | | End of split
% 231.40/42.58  | | 
% 231.40/42.58  | End of split
% 231.40/42.58  | 
% 231.40/42.58  End of proof
% 231.40/42.58  
% 231.40/42.58  Sub-proof #1439 shows that the following formulas are inconsistent:
% 231.40/42.58  ----------------------------------------------------------------
% 231.40/42.58    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.40/42.58         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.40/42.58    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.40/42.58         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.40/42.58    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.40/42.58         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.40/42.58    (4)   ~ (e3 = e1)
% 231.40/42.58    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.40/42.58           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.40/42.58    (6)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.40/42.58         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.40/42.58    (7)   ~ (all_6_2 = e3)
% 231.40/42.58    (8)  op(e1, e1) = all_6_2
% 231.40/42.58    (9)  all_57_3 = e0
% 231.40/42.58    (10)   ~ (e3 = e2)
% 231.40/42.58    (11)   ~ (e3 = e0)
% 231.40/42.58    (12)  op(e3, e3) = e3
% 231.40/42.58    (13)  all_57_1 = e0
% 231.40/42.58    (14)  all_57_15 = e3
% 231.40/42.58    (15)  all_57_5 = e3
% 231.40/42.58    (16)   ~ (e2 = e0)
% 231.40/42.58    (17)   ~ (e1 = e0)
% 231.40/42.58    (18)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.40/42.58              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.40/42.58                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.40/42.58                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.40/42.58    (19)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.40/42.58          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.40/42.58    (20)   ~ (e2 = e1)
% 231.40/42.58    (21)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.40/42.58          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.40/42.58    (22)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.40/42.58          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.40/42.58    (23)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.40/42.58          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.40/42.58    (24)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.40/42.58          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.40/42.58    (25)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.40/42.58          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.40/42.58  
% 231.40/42.58  Begin of proof
% 231.40/42.58  | 
% 231.40/42.58  | BETA: splitting (6) gives:
% 231.40/42.58  | 
% 231.40/42.58  | Case 1:
% 231.40/42.58  | | 
% 231.40/42.58  | |   (26)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 231.40/42.58  | |           e3)
% 231.40/42.58  | | 
% 231.40/42.58  | | BETA: splitting (26) gives:
% 231.40/42.58  | | 
% 231.40/42.58  | | Case 1:
% 231.40/42.58  | | | 
% 231.40/42.58  | | |   (27)  all_57_6 = e3 & op(e1, e3) = e3
% 231.40/42.58  | | | 
% 231.40/42.58  | | | ALPHA: (27) implies:
% 231.40/42.58  | | |   (28)  all_57_6 = e3
% 231.40/42.58  | | | 
% 231.40/42.58  | | | REF_CLOSE: (1), (2), (4), (5), (9), (10), (11), (12), (15), (16), (17),
% 231.40/42.58  | | |            (19), (20), (22), (23), (28) are inconsistent by sub-proof
% 231.40/42.58  | | |            #1781.
% 231.40/42.58  | | | 
% 231.40/42.58  | | Case 2:
% 231.40/42.58  | | | 
% 231.40/42.58  | | |   (29)  all_57_7 = e3 & op(e1, e2) = e3
% 231.40/42.58  | | | 
% 231.40/42.58  | | | ALPHA: (29) implies:
% 231.40/42.58  | | |   (30)  all_57_7 = e3
% 231.40/42.58  | | | 
% 231.40/42.59  | | | REF_CLOSE: (3), (4), (9), (10), (13), (16), (17), (20), (25), (30) are
% 231.40/42.59  | | |            inconsistent by sub-proof #2098.
% 231.40/42.59  | | | 
% 231.40/42.59  | | End of split
% 231.40/42.59  | | 
% 231.40/42.59  | Case 2:
% 231.40/42.59  | | 
% 231.40/42.59  | |   (31)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 231.40/42.59  | |           e3)
% 231.40/42.59  | | 
% 231.40/42.59  | | REF_CLOSE: (4), (5), (7), (8), (10), (11), (14), (16), (17), (18), (20),
% 231.40/42.59  | |            (21), (24), (31) are inconsistent by sub-proof #1786.
% 231.40/42.59  | | 
% 231.40/42.59  | End of split
% 231.40/42.59  | 
% 231.40/42.59  End of proof
% 231.40/42.59  
% 231.40/42.59  Sub-proof #1440 shows that the following formulas are inconsistent:
% 231.40/42.59  ----------------------------------------------------------------
% 231.40/42.59    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 231.40/42.59    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 231.40/42.59    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.40/42.59         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.40/42.59    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.40/42.59         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.40/42.59    (5)  op(e2, e1) = e3
% 231.40/42.59    (6)   ~ (all_53_8 = all_53_12)
% 231.40/42.59    (7)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.40/42.59         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.40/42.59    (8)   ~ (e3 = e1)
% 231.40/42.59    (9)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 231.40/42.59         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.40/42.59    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.40/42.59            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.40/42.59    (11)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.40/42.59          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.40/42.59    (12)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 231.40/42.59            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 231.40/42.59              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 231.40/42.59    (13)   ~ (all_6_2 = e3)
% 231.40/42.59    (14)  op(e1, e1) = all_6_2
% 231.40/42.59    (15)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 231.40/42.59    (16)   ~ (all_53_9 = e0)
% 231.40/42.59    (17)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.40/42.59          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.40/42.59    (18)   ~ (all_53_4 = all_53_12)
% 231.40/42.59    (19)   ~ (all_53_8 = all_53_9)
% 231.40/42.59    (20)  all_42_2 = all_6_2
% 231.40/42.59    (21)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.40/42.59          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.40/42.59    (22)   ~ (all_53_9 = all_6_2)
% 231.40/42.59    (23)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.40/42.59          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.40/42.59    (24)  all_57_3 = e0
% 231.40/42.59    (25)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.40/42.59          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.40/42.59    (26)   ~ (e3 = e2)
% 231.40/42.59    (27)  all_55_1 = all_53_4
% 231.40/42.59    (28)   ~ (e3 = e0)
% 231.40/42.59    (29)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.40/42.59          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.40/42.59    (30)  op(e3, e3) = e3
% 231.40/42.59    (31)   ~ (all_53_8 = all_6_2)
% 231.40/42.59    (32)  all_55_2 = all_53_8
% 231.40/42.59    (33)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 231.40/42.59    (34)  all_57_15 = e3
% 231.40/42.59    (35)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.40/42.59          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.40/42.59            e1)
% 231.40/42.59    (36)  all_57_5 = e3
% 231.40/42.59    (37)   ~ (all_53_4 = all_53_8)
% 231.40/42.59    (38)  op(e3, e2) = all_53_4
% 231.40/42.59    (39)   ~ (e2 = e0)
% 231.40/42.59    (40)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 231.40/42.59            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 231.40/42.59            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 231.40/42.59            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 231.40/42.59              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 231.40/42.59            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 231.40/42.59            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 231.40/42.59              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 231.40/42.59              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 231.40/42.59            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 231.40/42.59            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 231.40/42.59            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 231.40/42.59              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 231.40/42.59              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 231.40/42.59            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 231.40/42.59              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 231.40/42.59            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 231.40/42.59            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 231.40/42.59              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 231.40/42.59              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 231.40/42.59            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 231.40/42.59            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 231.40/42.59    (41)   ~ (e1 = e0)
% 231.40/42.59    (42)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 231.40/42.59            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 231.40/42.59              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 231.40/42.59    (43)   ~ (all_53_4 = e0)
% 231.40/42.59    (44)  op(e0, e0) = e3
% 231.40/42.59    (45)   ~ (all_53_4 = all_53_6)
% 231.40/42.59    (46)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.40/42.59          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.40/42.59            e2)
% 231.40/42.59    (47)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.40/42.59              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.40/42.59                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.40/42.59                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.40/42.59    (48)  all_55_10 = all_6_2
% 231.40/42.59    (49)  all_38_2 = all_6_2
% 231.40/42.59    (50)  all_55_3 = all_53_12
% 231.40/42.59    (51)   ~ (all_53_12 = e3)
% 231.40/42.59    (52)  all_57_0 = e3
% 231.40/42.59    (53)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 231.40/42.59            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 231.40/42.59              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 231.40/42.59    (54)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.40/42.59          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.40/42.59    (55)   ~ (e2 = e1)
% 231.40/42.59    (56)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.40/42.59          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.40/42.59    (57)  op(e2, e1) = all_53_9
% 231.40/42.59    (58)  op(e1, e2) = all_53_6
% 231.40/42.59    (59)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.40/42.59          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.40/42.59    (60)  all_24_2 = all_6_2
% 231.40/42.59    (61)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.40/42.59          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.40/42.59    (62)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.40/42.59          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.40/42.59    (63)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.40/42.59          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.40/42.59    (64)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 231.40/42.59          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 231.40/42.59    (65)  op(e3, e1) = all_53_8
% 231.40/42.59    (66)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.40/42.59          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.40/42.59    (67)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 231.40/42.59          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 231.40/42.59    (68)  op(e3, e0) = all_53_12
% 231.40/42.59  
% 231.40/42.59  Begin of proof
% 231.40/42.59  | 
% 231.40/42.59  | BETA: splitting (11) gives:
% 231.40/42.59  | 
% 231.40/42.59  | Case 1:
% 231.40/42.59  | | 
% 231.40/42.59  | |   (69)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 231.40/42.59  | |           e3)
% 231.40/42.59  | | 
% 231.40/42.59  | | BETA: splitting (69) gives:
% 231.40/42.59  | | 
% 231.40/42.59  | | Case 1:
% 231.40/42.59  | | | 
% 231.40/42.59  | | |   (70)  all_57_6 = e3 & op(e1, e3) = e3
% 231.40/42.59  | | | 
% 231.40/42.59  | | | ALPHA: (70) implies:
% 231.40/42.59  | | |   (71)  all_57_6 = e3
% 231.40/42.59  | | | 
% 231.40/42.59  | | | REF_CLOSE: (4), (8), (26), (28), (39), (41), (52), (55), (59), (62), (71)
% 231.40/42.59  | | |            are inconsistent by sub-proof #2010.
% 231.40/42.59  | | | 
% 231.40/42.59  | | Case 2:
% 231.40/42.59  | | | 
% 231.40/42.59  | | |   (72)  all_57_7 = e3 & op(e1, e2) = e3
% 231.40/42.59  | | | 
% 231.40/42.59  | | | ALPHA: (72) implies:
% 231.40/42.59  | | |   (73)  all_57_7 = e3
% 231.40/42.59  | | |   (74)  op(e1, e2) = e3
% 231.40/42.59  | | | 
% 231.40/42.59  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (14),
% 231.40/42.59  | | |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 231.40/42.59  | | |            (25), (26), (27), (29), (30), (31), (32), (33), (34), (35),
% 231.40/42.59  | | |            (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 231.40/42.59  | | |            (46), (47), (48), (49), (50), (51), (53), (54), (55), (56),
% 231.40/42.59  | | |            (57), (58), (59), (60), (61), (62), (63), (64), (65), (66),
% 231.40/42.59  | | |            (67), (68), (73), (74) are inconsistent by sub-proof #1441.
% 231.40/42.59  | | | 
% 231.40/42.59  | | End of split
% 231.40/42.59  | | 
% 231.40/42.59  | Case 2:
% 231.40/42.59  | | 
% 231.40/42.59  | |   (75)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 231.40/42.59  | |           e3)
% 231.40/42.59  | | 
% 231.40/42.59  | | REF_CLOSE: (8), (10), (13), (14), (26), (28), (34), (39), (41), (47), (55),
% 231.40/42.59  | |            (56), (63), (75) are inconsistent by sub-proof #1786.
% 231.40/42.59  | | 
% 231.40/42.59  | End of split
% 231.40/42.59  | 
% 231.40/42.59  End of proof
% 231.40/42.59  
% 231.40/42.59  Sub-proof #1441 shows that the following formulas are inconsistent:
% 231.40/42.59  ----------------------------------------------------------------
% 231.40/42.59    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 231.40/42.59    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 231.40/42.59    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.40/42.59         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.40/42.59    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.40/42.59         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.40/42.59    (5)  op(e2, e1) = e3
% 231.40/42.59    (6)   ~ (all_53_8 = all_53_12)
% 231.40/42.59    (7)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.40/42.59         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.40/42.59    (8)   ~ (e3 = e1)
% 231.40/42.59    (9)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 231.40/42.59         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.40/42.59    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.40/42.59            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.40/42.59    (11)  op(e1, e2) = e3
% 231.40/42.59    (12)   ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 &
% 231.40/42.59            op(e1, e0) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 231.40/42.59              e3) & op(e1, e0) = all_24_1 & $i(all_24_1))
% 231.40/42.59    (13)  op(e1, e1) = all_6_2
% 231.40/42.59    (14)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 231.40/42.59    (15)   ~ (all_53_9 = e0)
% 231.40/42.59    (16)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.40/42.59          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.40/42.59    (17)   ~ (all_53_4 = all_53_12)
% 231.40/42.59    (18)   ~ (all_53_8 = all_53_9)
% 231.40/42.59    (19)  all_42_2 = all_6_2
% 231.40/42.59    (20)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.40/42.59          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.40/42.59    (21)   ~ (all_53_9 = all_6_2)
% 231.40/42.59    (22)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.40/42.59          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.40/42.59    (23)  all_57_3 = e0
% 231.40/42.59    (24)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.40/42.59          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.40/42.59    (25)   ~ (e3 = e2)
% 231.40/42.59    (26)  all_55_1 = all_53_4
% 231.40/42.59    (27)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.40/42.59          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.40/42.59    (28)  op(e3, e3) = e3
% 231.40/42.59    (29)   ~ (all_53_8 = all_6_2)
% 231.40/42.59    (30)  all_55_2 = all_53_8
% 231.40/42.59    (31)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 231.40/42.59    (32)  all_57_15 = e3
% 231.40/42.59    (33)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.40/42.59          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.40/42.59            e1)
% 231.40/42.59    (34)  all_57_5 = e3
% 231.40/42.59    (35)   ~ (all_53_4 = all_53_8)
% 231.40/42.59    (36)  op(e3, e2) = all_53_4
% 231.40/42.59    (37)   ~ (e2 = e0)
% 231.40/42.59    (38)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 231.40/42.59            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 231.40/42.59            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 231.40/42.59            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 231.40/42.59              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 231.40/42.59            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 231.40/42.59            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 231.40/42.59              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 231.40/42.59              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 231.40/42.59            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 231.40/42.59            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 231.40/42.59            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 231.40/42.59              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 231.40/42.59              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 231.40/42.59            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 231.40/42.59              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 231.40/42.59            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 231.40/42.59            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 231.40/42.59              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 231.40/42.59              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 231.40/42.59            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 231.40/42.59            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 231.40/42.59    (39)   ~ (e1 = e0)
% 231.40/42.59    (40)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 231.40/42.59            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 231.40/42.59              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 231.40/42.59    (41)   ~ (all_53_4 = e0)
% 231.40/42.59    (42)  op(e0, e0) = e3
% 231.40/42.59    (43)   ~ (all_53_4 = all_53_6)
% 231.40/42.59    (44)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.40/42.59          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.40/42.59            e2)
% 231.40/42.59    (45)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.40/42.59              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.40/42.59                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.40/42.59                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.40/42.59    (46)  all_55_10 = all_6_2
% 231.40/42.59    (47)  all_38_2 = all_6_2
% 231.40/42.59    (48)  all_55_3 = all_53_12
% 231.40/42.59    (49)   ~ (all_53_12 = e3)
% 231.40/42.59    (50)  all_57_7 = e3
% 231.40/42.59    (51)   ~ (all_42_2 = e2) | ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 &
% 231.40/42.59            op(e1, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 231.40/42.59              e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 231.40/42.59    (52)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.40/42.59          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.40/42.59    (53)   ~ (e2 = e1)
% 231.40/42.59    (54)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.40/42.59          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.40/42.59    (55)  op(e2, e1) = all_53_9
% 231.40/42.59    (56)  op(e1, e2) = all_53_6
% 231.40/42.59    (57)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.40/42.59          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.40/42.59    (58)  all_24_2 = all_6_2
% 231.40/42.59    (59)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.40/42.59          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.40/42.59    (60)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.40/42.59          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.40/42.59    (61)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.40/42.59          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.40/42.59    (62)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 231.40/42.59          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 231.40/42.59    (63)  op(e3, e1) = all_53_8
% 231.40/42.59    (64)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.40/42.59          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.40/42.59    (65)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 231.40/42.59          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 231.40/42.59    (66)  op(e3, e0) = all_53_12
% 231.40/42.59  
% 231.40/42.59  Begin of proof
% 231.40/42.59  | 
% 231.40/42.59  | GROUND_INST: instantiating (10) with all_53_6, e3, e2, e1, simplifying with
% 231.40/42.59  |              (11), (56) gives:
% 231.40/42.59  |   (67)  all_53_6 = e3
% 231.40/42.59  | 
% 231.40/42.59  | GROUND_INST: instantiating (10) with all_53_9, e3, e1, e2, simplifying with
% 231.40/42.59  |              (5), (55) gives:
% 231.40/42.59  |   (68)  all_53_9 = e3
% 231.40/42.59  | 
% 231.40/42.59  | REDUCE: (43), (67) imply:
% 231.40/42.59  |   (69)   ~ (all_53_4 = e3)
% 231.40/42.59  | 
% 231.40/42.59  | REDUCE: (18), (68) imply:
% 231.40/42.59  |   (70)   ~ (all_53_8 = e3)
% 231.40/42.59  | 
% 231.40/42.59  | REDUCE: (21), (68) imply:
% 231.40/42.59  |   (71)   ~ (all_6_2 = e3)
% 231.40/42.59  | 
% 231.40/42.59  | SIMP: (71) implies:
% 231.40/42.59  |   (72)   ~ (all_6_2 = e3)
% 231.40/42.59  | 
% 231.40/42.59  | REDUCE: (15), (68) imply:
% 231.40/42.59  |   (73)   ~ (e3 = e0)
% 231.40/42.59  | 
% 231.40/42.59  | BETA: splitting (38) gives:
% 231.40/42.59  | 
% 231.40/42.59  | Case 1:
% 231.40/42.59  | | 
% 231.40/42.59  | |   (74)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 231.40/42.59  | |           op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 231.40/42.59  | |           op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3,
% 231.40/42.59  | |             e3) = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 &
% 231.40/42.59  | |           op(e3, e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5)
% 231.40/42.59  | |           & $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1
% 231.40/42.59  | |           & all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 231.40/42.59  | |             all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 231.40/42.59  | |             all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11
% 231.40/42.59  | |           & op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 231.40/42.59  | |           $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 231.40/42.59  | | 
% 231.40/42.59  | | BETA: splitting (74) gives:
% 231.40/42.59  | | 
% 231.40/42.59  | | Case 1:
% 231.40/42.59  | | | 
% 231.40/42.59  | | |   (75)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 231.40/42.59  | | |         op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 231.40/42.59  | | |         op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3,
% 231.40/42.59  | | |           e3) = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 &
% 231.40/42.59  | | |         op(e3, e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5)
% 231.40/42.59  | | |         & $i(all_52_7)
% 231.40/42.59  | | | 
% 231.40/42.59  | | | ALPHA: (75) implies:
% 231.40/42.59  | | |   (76)  op(e3, e0) = all_52_7
% 231.40/42.59  | | |   (77)  op(e3, e1) = all_52_5
% 231.40/42.59  | | |   (78)  op(e3, e2) = all_52_3
% 231.40/42.59  | | |   (79)  op(e3, e3) = all_52_1
% 231.40/42.59  | | |   (80)  op(all_52_7, all_52_7) = e0
% 231.40/42.59  | | | 
% 231.40/42.59  | | | GROUND_INST: instantiating (10) with all_53_12, all_52_7, e0, e3,
% 231.40/42.59  | | |              simplifying with (66), (76) gives:
% 231.40/42.59  | | |   (81)  all_53_12 = all_52_7
% 231.40/42.59  | | | 
% 231.40/42.59  | | | GROUND_INST: instantiating (10) with all_53_8, all_52_5, e1, e3,
% 231.40/42.59  | | |              simplifying with (63), (77) gives:
% 231.40/42.59  | | |   (82)  all_53_8 = all_52_5
% 231.40/42.59  | | | 
% 231.40/42.59  | | | GROUND_INST: instantiating (10) with all_53_4, all_52_3, e2, e3,
% 231.40/42.59  | | |              simplifying with (36), (78) gives:
% 231.40/42.59  | | |   (83)  all_53_4 = all_52_3
% 231.40/42.59  | | | 
% 231.40/42.59  | | | GROUND_INST: instantiating (10) with e3, all_52_1, e3, e3, simplifying
% 231.40/42.59  | | |              with (28), (79) gives:
% 231.40/42.59  | | |   (84)  all_52_1 = e3
% 231.40/42.59  | | | 
% 231.40/42.59  | | | COMBINE_EQS: (48), (81) imply:
% 231.40/42.59  | | |   (85)  all_55_3 = all_52_7
% 231.40/42.59  | | | 
% 231.40/42.59  | | | COMBINE_EQS: (30), (82) imply:
% 231.40/42.59  | | |   (86)  all_55_2 = all_52_5
% 231.40/42.59  | | | 
% 231.40/42.59  | | | COMBINE_EQS: (26), (83) imply:
% 231.40/42.59  | | |   (87)  all_55_1 = all_52_3
% 231.40/42.59  | | | 
% 231.40/42.59  | | | REDUCE: (35), (82), (83) imply:
% 231.40/42.59  | | |   (88)   ~ (all_52_3 = all_52_5)
% 231.40/42.59  | | | 
% 231.40/42.59  | | | REDUCE: (17), (81), (83) imply:
% 231.40/42.59  | | |   (89)   ~ (all_52_3 = all_52_7)
% 231.40/42.59  | | | 
% 231.40/42.59  | | | REDUCE: (69), (83) imply:
% 231.40/42.59  | | |   (90)   ~ (all_52_3 = e3)
% 231.40/42.59  | | | 
% 231.40/42.59  | | | REDUCE: (41), (83) imply:
% 231.40/42.59  | | |   (91)   ~ (all_52_3 = e0)
% 231.40/42.59  | | | 
% 231.40/42.59  | | | REDUCE: (6), (81), (82) imply:
% 231.40/42.59  | | |   (92)   ~ (all_52_5 = all_52_7)
% 231.40/42.59  | | | 
% 231.40/42.59  | | | REDUCE: (29), (82) imply:
% 231.40/42.59  | | |   (93)   ~ (all_52_5 = all_6_2)
% 231.40/42.59  | | | 
% 231.40/42.59  | | | REDUCE: (70), (82) imply:
% 231.40/42.59  | | |   (94)   ~ (all_52_5 = e3)
% 231.40/42.59  | | | 
% 231.40/42.59  | | | REDUCE: (49), (81) imply:
% 231.40/42.59  | | |   (95)   ~ (all_52_7 = e3)
% 231.40/42.59  | | | 
% 231.40/42.59  | | | BETA: splitting (12) gives:
% 231.40/42.59  | | | 
% 231.40/42.59  | | | Case 1:
% 231.40/42.59  | | | | 
% 231.40/42.59  | | | |   (96)   ~ (all_24_2 = e0)
% 231.40/42.59  | | | | 
% 231.40/42.59  | | | | REDUCE: (58), (96) imply:
% 231.40/42.59  | | | |   (97)   ~ (all_6_2 = e0)
% 231.40/42.59  | | | | 
% 231.40/42.59  | | | | BETA: splitting (40) gives:
% 231.40/42.59  | | | | 
% 231.40/42.59  | | | | Case 1:
% 231.40/42.59  | | | | | 
% 231.40/42.59  | | | | |   (98)   ~ (all_38_2 = e2)
% 231.40/42.59  | | | | | 
% 231.40/42.59  | | | | | REDUCE: (47), (98) imply:
% 231.40/42.59  | | | | |   (99)   ~ (all_6_2 = e2)
% 231.40/42.59  | | | | | 
% 231.40/42.59  | | | | | BETA: splitting (2) gives:
% 231.40/42.59  | | | | | 
% 231.40/42.59  | | | | | Case 1:
% 231.40/42.59  | | | | | | 
% 231.40/42.59  | | | | | |   (100)  all_55_10 = e3
% 231.40/42.59  | | | | | | 
% 231.40/42.59  | | | | | | REF_CLOSE: (46), (72), (100) are inconsistent by sub-proof #2500.
% 231.40/42.59  | | | | | | 
% 231.40/42.59  | | | | | Case 2:
% 231.40/42.59  | | | | | | 
% 231.40/42.59  | | | | | |   (101)   ~ (all_55_10 = e3)
% 231.40/42.59  | | | | | |   (102)  all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 231.40/42.59  | | | | | | 
% 231.40/42.59  | | | | | | REF_CLOSE: (3), (4), (7), (9), (10), (13), (16), (20), (22), (23),
% 231.40/42.59  | | | | | |            (24), (25), (27), (28), (32), (33), (34), (37), (42),
% 231.40/42.59  | | | | | |            (44), (45), (46), (50), (52), (54), (57), (59), (60),
% 231.40/42.59  | | | | | |            (61), (62), (64), (65), (72), (73), (76), (77), (78),
% 231.40/42.59  | | | | | |            (80), (89), (90), (91), (93), (95), (97), (99), (102) are
% 231.40/42.59  | | | | | |            inconsistent by sub-proof #1453.
% 231.40/42.59  | | | | | | 
% 231.40/42.59  | | | | | End of split
% 231.40/42.59  | | | | | 
% 231.40/42.59  | | | | Case 2:
% 231.40/42.59  | | | | | 
% 231.40/42.59  | | | | |   (103)  all_38_2 = e2
% 231.40/42.59  | | | | |   (104)  ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 & op(e1,
% 231.40/42.59  | | | | |              e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~
% 231.40/42.59  | | | | |            (all_38_1 = e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 231.40/42.59  | | | | | 
% 231.40/42.59  | | | | | COMBINE_EQS: (47), (103) imply:
% 231.40/42.59  | | | | |   (105)  all_6_2 = e2
% 231.40/42.59  | | | | | 
% 231.40/42.59  | | | | | COMBINE_EQS: (19), (105) imply:
% 231.40/42.59  | | | | |   (106)  all_42_2 = e2
% 231.40/42.59  | | | | | 
% 231.40/42.59  | | | | | REDUCE: (93), (105) imply:
% 231.40/42.59  | | | | |   (107)   ~ (all_52_5 = e2)
% 231.40/42.59  | | | | | 
% 231.40/42.59  | | | | | BETA: splitting (51) gives:
% 231.40/42.59  | | | | | 
% 231.40/42.59  | | | | | Case 1:
% 231.40/42.59  | | | | | | 
% 231.40/42.59  | | | | | |   (108)   ~ (all_42_2 = e2)
% 231.40/42.59  | | | | | | 
% 231.40/42.59  | | | | | | REDUCE: (106), (108) imply:
% 231.40/42.59  | | | | | |   (109)  $false
% 231.40/42.59  | | | | | | 
% 231.40/42.59  | | | | | | CLOSE: (109) is inconsistent.
% 231.40/42.59  | | | | | | 
% 231.40/42.59  | | | | | Case 2:
% 231.40/42.59  | | | | | | 
% 231.40/42.59  | | | | | |   (110)  ( ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 & op(e1,
% 231.40/42.59  | | | | | |              e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~
% 231.40/42.59  | | | | | |            (all_42_1 = e0) & op(e1, e2) = all_42_1 & $i(all_42_1))
% 231.40/42.59  | | | | | | 
% 231.40/42.59  | | | | | | BETA: splitting (110) gives:
% 231.40/42.59  | | | | | | 
% 231.40/42.59  | | | | | | Case 1:
% 231.40/42.59  | | | | | | | 
% 231.40/42.59  | | | | | | |   (111)   ~ (all_42_0 = e3) & op(all_42_1, e1) = all_42_0 & op(e1,
% 231.40/42.59  | | | | | | |            e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)
% 231.40/42.59  | | | | | | | 
% 231.40/42.59  | | | | | | | ALPHA: (111) implies:
% 231.40/42.59  | | | | | | |   (112)  op(e1, e2) = all_42_1
% 231.40/42.59  | | | | | | |   (113)  op(all_42_1, e1) = all_42_0
% 231.40/42.59  | | | | | | | 
% 231.40/42.59  | | | | | | | GROUND_INST: instantiating (10) with e3, all_42_1, e2, e1,
% 231.40/42.59  | | | | | | |              simplifying with (11), (112) gives:
% 231.40/42.59  | | | | | | |   (114)  all_42_1 = e3
% 231.40/42.59  | | | | | | | 
% 231.40/42.59  | | | | | | | REDUCE: (113), (114) imply:
% 231.40/42.59  | | | | | | |   (115)  op(e3, e1) = all_42_0
% 231.40/42.59  | | | | | | | 
% 231.40/42.59  | | | | | | | BETA: splitting (104) gives:
% 231.40/42.59  | | | | | | | 
% 231.40/42.59  | | | | | | | Case 1:
% 231.40/42.59  | | | | | | | | 
% 231.40/42.59  | | | | | | | |   (116)   ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 231.40/42.59  | | | | | | | |          op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)
% 231.40/42.59  | | | | | | | | 
% 231.40/42.59  | | | | | | | | ALPHA: (116) implies:
% 231.40/42.59  | | | | | | | |   (117)   ~ (all_38_0 = e0)
% 231.40/42.59  | | | | | | | |   (118)  op(e1, e2) = all_38_1
% 231.40/42.59  | | | | | | | |   (119)  op(all_38_1, e1) = all_38_0
% 231.40/42.59  | | | | | | | | 
% 231.40/42.60  | | | | | | | | GROUND_INST: instantiating (10) with e3, all_38_1, e2, e1,
% 231.40/42.60  | | | | | | | |              simplifying with (11), (118) gives:
% 231.40/42.60  | | | | | | | |   (120)  all_38_1 = e3
% 231.40/42.60  | | | | | | | | 
% 231.40/42.60  | | | | | | | | GROUND_INST: instantiating (10) with all_52_5, all_42_0, e1, e3,
% 231.40/42.60  | | | | | | | |              simplifying with (77), (115) gives:
% 231.40/42.60  | | | | | | | |   (121)  all_52_5 = all_42_0
% 231.40/42.60  | | | | | | | | 
% 231.40/42.60  | | | | | | | | COMBINE_EQS: (86), (121) imply:
% 231.40/42.60  | | | | | | | |   (122)  all_55_2 = all_42_0
% 231.40/42.60  | | | | | | | | 
% 231.40/42.60  | | | | | | | | REDUCE: (88), (121) imply:
% 231.40/42.60  | | | | | | | |   (123)   ~ (all_52_3 = all_42_0)
% 231.40/42.60  | | | | | | | | 
% 231.40/42.60  | | | | | | | | REDUCE: (92), (121) imply:
% 231.40/42.60  | | | | | | | |   (124)   ~ (all_52_7 = all_42_0)
% 231.40/42.60  | | | | | | | | 
% 231.40/42.60  | | | | | | | | SIMP: (124) implies:
% 231.40/42.60  | | | | | | | |   (125)   ~ (all_52_7 = all_42_0)
% 231.40/42.60  | | | | | | | | 
% 231.40/42.60  | | | | | | | | REDUCE: (94), (121) imply:
% 231.40/42.60  | | | | | | | |   (126)   ~ (all_42_0 = e3)
% 231.40/42.60  | | | | | | | | 
% 231.40/42.60  | | | | | | | | REDUCE: (107), (121) imply:
% 231.40/42.60  | | | | | | | |   (127)   ~ (all_42_0 = e2)
% 231.40/42.60  | | | | | | | | 
% 231.40/42.60  | | | | | | | | REDUCE: (119), (120) imply:
% 231.40/42.60  | | | | | | | |   (128)  op(e3, e1) = all_38_0
% 231.40/42.60  | | | | | | | | 
% 231.40/42.60  | | | | | | | | GROUND_INST: instantiating (10) with all_42_0, all_38_0, e1, e3,
% 231.40/42.60  | | | | | | | |              simplifying with (115), (128) gives:
% 231.40/42.60  | | | | | | | |   (129)  all_42_0 = all_38_0
% 231.40/42.60  | | | | | | | | 
% 231.40/42.60  | | | | | | | | COMBINE_EQS: (122), (129) imply:
% 231.40/42.60  | | | | | | | |   (130)  all_55_2 = all_38_0
% 231.40/42.60  | | | | | | | | 
% 231.40/42.60  | | | | | | | | REDUCE: (123), (129) imply:
% 231.40/42.60  | | | | | | | |   (131)   ~ (all_52_3 = all_38_0)
% 231.40/42.60  | | | | | | | | 
% 231.40/42.60  | | | | | | | | REDUCE: (125), (129) imply:
% 231.40/42.60  | | | | | | | |   (132)   ~ (all_52_7 = all_38_0)
% 231.40/42.60  | | | | | | | | 
% 231.40/42.60  | | | | | | | | REDUCE: (126), (129) imply:
% 231.40/42.60  | | | | | | | |   (133)   ~ (all_38_0 = e3)
% 231.40/42.60  | | | | | | | | 
% 231.40/42.60  | | | | | | | | REDUCE: (127), (129) imply:
% 231.40/42.60  | | | | | | | |   (134)   ~ (all_38_0 = e2)
% 231.40/42.60  | | | | | | | | 
% 231.40/42.60  | | | | | | | | REF_CLOSE: (1), (10), (14), (31), (42), (80), (85), (87), (89),
% 231.40/42.60  | | | | | | | |            (90), (91), (95), (117), (130), (131), (132), (133),
% 231.40/42.60  | | | | | | | |            (134) are inconsistent by sub-proof #1445.
% 231.40/42.60  | | | | | | | | 
% 231.40/42.60  | | | | | | | Case 2:
% 231.40/42.60  | | | | | | | | 
% 231.40/42.60  | | | | | | | |   (135)   ~ (all_38_1 = e3) & op(e1, e2) = all_38_1 &
% 231.40/42.60  | | | | | | | |          $i(all_38_1)
% 231.40/42.60  | | | | | | | | 
% 231.40/42.60  | | | | | | | | ALPHA: (135) implies:
% 231.40/42.60  | | | | | | | |   (136)   ~ (all_38_1 = e3)
% 231.40/42.60  | | | | | | | |   (137)  op(e1, e2) = all_38_1
% 231.40/42.60  | | | | | | | | 
% 231.40/42.60  | | | | | | | | GROUND_INST: instantiating (10) with e3, all_38_1, e2, e1,
% 231.40/42.60  | | | | | | | |              simplifying with (11), (137) gives:
% 231.40/42.60  | | | | | | | |   (138)  all_38_1 = e3
% 231.40/42.60  | | | | | | | | 
% 231.40/42.60  | | | | | | | | REDUCE: (136), (138) imply:
% 231.40/42.60  | | | | | | | |   (139)  $false
% 231.40/42.60  | | | | | | | | 
% 231.40/42.60  | | | | | | | | CLOSE: (139) is inconsistent.
% 231.40/42.60  | | | | | | | | 
% 231.40/42.60  | | | | | | | End of split
% 231.40/42.60  | | | | | | | 
% 231.40/42.60  | | | | | | Case 2:
% 231.40/42.60  | | | | | | | 
% 231.40/42.60  | | | | | | |   (140)   ~ (all_42_1 = e0) & op(e1, e2) = all_42_1 & $i(all_42_1)
% 231.40/42.60  | | | | | | | 
% 231.40/42.60  | | | | | | | ALPHA: (140) implies:
% 231.40/42.60  | | | | | | |   (141)  op(e1, e2) = all_42_1
% 231.40/42.60  | | | | | | | 
% 231.40/42.60  | | | | | | | GROUND_INST: instantiating (10) with e3, all_42_1, e2, e1,
% 231.40/42.60  | | | | | | |              simplifying with (11), (141) gives:
% 231.40/42.60  | | | | | | |   (142)  all_42_1 = e3
% 231.40/42.60  | | | | | | | 
% 231.40/42.60  | | | | | | | BETA: splitting (104) gives:
% 231.40/42.60  | | | | | | | 
% 231.40/42.60  | | | | | | | Case 1:
% 231.40/42.60  | | | | | | | | 
% 231.40/42.60  | | | | | | | |   (143)   ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 231.40/42.60  | | | | | | | |          op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)
% 231.40/42.60  | | | | | | | | 
% 231.40/42.60  | | | | | | | | ALPHA: (143) implies:
% 231.40/42.60  | | | | | | | |   (144)   ~ (all_38_0 = e0)
% 231.40/42.60  | | | | | | | |   (145)  op(e1, e2) = all_38_1
% 231.40/42.60  | | | | | | | |   (146)  op(all_38_1, e1) = all_38_0
% 231.40/42.60  | | | | | | | | 
% 231.40/42.60  | | | | | | | | GROUND_INST: instantiating (10) with e3, all_38_1, e2, e1,
% 231.40/42.60  | | | | | | | |              simplifying with (11), (145) gives:
% 231.40/42.60  | | | | | | | |   (147)  all_38_1 = e3
% 231.40/42.60  | | | | | | | | 
% 231.40/42.60  | | | | | | | | REDUCE: (146), (147) imply:
% 231.40/42.60  | | | | | | | |   (148)  op(e3, e1) = all_38_0
% 231.40/42.60  | | | | | | | | 
% 231.40/42.60  | | | | | | | | GROUND_INST: instantiating (10) with all_52_5, all_38_0, e1, e3,
% 231.40/42.60  | | | | | | | |              simplifying with (77), (148) gives:
% 231.40/42.60  | | | | | | | |   (149)  all_52_5 = all_38_0
% 231.40/42.60  | | | | | | | | 
% 231.40/42.60  | | | | | | | | COMBINE_EQS: (86), (149) imply:
% 231.40/42.60  | | | | | | | |   (150)  all_55_2 = all_38_0
% 231.40/42.60  | | | | | | | | 
% 231.40/42.60  | | | | | | | | REDUCE: (88), (149) imply:
% 231.40/42.60  | | | | | | | |   (151)   ~ (all_52_3 = all_38_0)
% 231.40/42.60  | | | | | | | | 
% 231.40/42.60  | | | | | | | | REDUCE: (92), (149) imply:
% 231.40/42.60  | | | | | | | |   (152)   ~ (all_52_7 = all_38_0)
% 231.40/42.60  | | | | | | | | 
% 231.40/42.60  | | | | | | | | SIMP: (152) implies:
% 231.40/42.60  | | | | | | | |   (153)   ~ (all_52_7 = all_38_0)
% 231.40/42.60  | | | | | | | | 
% 231.40/42.60  | | | | | | | | REDUCE: (94), (149) imply:
% 231.40/42.60  | | | | | | | |   (154)   ~ (all_38_0 = e3)
% 231.40/42.60  | | | | | | | | 
% 231.40/42.60  | | | | | | | | REDUCE: (107), (149) imply:
% 231.40/42.60  | | | | | | | |   (155)   ~ (all_38_0 = e2)
% 231.40/42.60  | | | | | | | | 
% 231.40/42.60  | | | | | | | | REF_CLOSE: (1), (10), (14), (31), (42), (80), (85), (87), (89),
% 231.40/42.60  | | | | | | | |            (90), (91), (95), (144), (150), (151), (153), (154),
% 231.40/42.60  | | | | | | | |            (155) are inconsistent by sub-proof #1445.
% 231.40/42.60  | | | | | | | | 
% 231.40/42.60  | | | | | | | Case 2:
% 231.40/42.60  | | | | | | | | 
% 231.40/42.60  | | | | | | | |   (156)   ~ (all_38_1 = e3) & op(e1, e2) = all_38_1 &
% 231.40/42.60  | | | | | | | |          $i(all_38_1)
% 231.40/42.60  | | | | | | | | 
% 231.40/42.60  | | | | | | | | REF_CLOSE: (10), (11), (156) are inconsistent by sub-proof
% 231.40/42.60  | | | | | | | |            #1444.
% 231.40/42.60  | | | | | | | | 
% 231.40/42.60  | | | | | | | End of split
% 231.40/42.60  | | | | | | | 
% 231.40/42.60  | | | | | | End of split
% 231.40/42.60  | | | | | | 
% 231.40/42.60  | | | | | End of split
% 231.40/42.60  | | | | | 
% 231.40/42.60  | | | | End of split
% 231.40/42.60  | | | | 
% 231.40/42.60  | | | Case 2:
% 231.40/42.60  | | | | 
% 231.40/42.60  | | | |   (157)  all_24_2 = e0
% 231.40/42.60  | | | | 
% 231.40/42.60  | | | | COMBINE_EQS: (58), (157) imply:
% 231.40/42.60  | | | |   (158)  all_6_2 = e0
% 231.40/42.60  | | | | 
% 231.40/42.60  | | | | SIMP: (158) implies:
% 231.40/42.60  | | | |   (159)  all_6_2 = e0
% 231.40/42.60  | | | | 
% 231.40/42.60  | | | | REDUCE: (72), (159) imply:
% 231.40/42.60  | | | |   (160)   ~ (e3 = e0)
% 231.40/42.60  | | | | 
% 231.40/42.60  | | | | REDUCE: (13), (159) imply:
% 231.40/42.60  | | | |   (161)  op(e1, e1) = e0
% 231.40/42.60  | | | | 
% 231.40/42.60  | | | | REF_CLOSE: (3), (4), (7), (8), (9), (10), (16), (20), (22), (23), (24),
% 231.40/42.60  | | | |            (25), (27), (28), (32), (34), (37), (39), (42), (44), (45),
% 231.40/42.60  | | | |            (50), (52), (53), (54), (57), (59), (60), (61), (62), (64),
% 231.40/42.60  | | | |            (65), (73), (76), (80), (95), (161) are inconsistent by
% 231.40/42.60  | | | |            sub-proof #1486.
% 231.40/42.60  | | | | 
% 231.40/42.60  | | | End of split
% 231.40/42.60  | | | 
% 231.40/42.60  | | Case 2:
% 231.40/42.60  | | | 
% 231.40/42.60  | | |   (162)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 231.40/42.60  | | |          & op(all_52_9, all_52_9) = e3 & op(all_52_11, all_52_11) = e2 &
% 231.40/42.60  | | |          op(all_52_13, all_52_13) = e1 & op(all_52_15, all_52_15) = e0 &
% 231.40/42.60  | | |          op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 & op(e2, e1) =
% 231.40/42.60  | | |          all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) & $i(all_52_11)
% 231.40/42.60  | | |          & $i(all_52_13) & $i(all_52_15)
% 231.40/42.60  | | | 
% 231.40/42.60  | | | REF_CLOSE: (5), (8), (10), (28), (162) are inconsistent by sub-proof
% 231.40/42.60  | | |            #1443.
% 231.40/42.60  | | | 
% 231.40/42.60  | | End of split
% 231.40/42.60  | | 
% 231.40/42.60  | Case 2:
% 231.40/42.60  | | 
% 231.40/42.60  | |   (163)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 231.40/42.60  | |            & op(all_52_17, all_52_17) = e3 & op(all_52_19, all_52_19) = e2 &
% 231.40/42.60  | |            op(all_52_21, all_52_21) = e1 & op(all_52_23, all_52_23) = e0 &
% 231.40/42.60  | |            op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) =
% 231.40/42.60  | |            all_52_21 & op(e1, e0) = all_52_23 & $i(all_52_17) &
% 231.40/42.60  | |            $i(all_52_19) & $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 231.40/42.60  | |            & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0 &
% 231.40/42.60  | |            op(all_52_25, all_52_25) = e3 & op(all_52_27, all_52_27) = e2 &
% 231.40/42.60  | |            op(all_52_29, all_52_29) = e1 & op(all_52_31, all_52_31) = e0 &
% 231.40/42.60  | |            op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 & op(e0, e1) =
% 231.40/42.60  | |            all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 231.40/42.60  | |            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 231.40/42.60  | | 
% 231.40/42.60  | | BETA: splitting (163) gives:
% 231.40/42.60  | | 
% 231.40/42.60  | | Case 1:
% 231.40/42.60  | | | 
% 231.40/42.60  | | |   (164)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 231.40/42.60  | | |          & op(all_52_17, all_52_17) = e3 & op(all_52_19, all_52_19) = e2 &
% 231.40/42.60  | | |          op(all_52_21, all_52_21) = e1 & op(all_52_23, all_52_23) = e0 &
% 231.40/42.60  | | |          op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) =
% 231.40/42.60  | | |          all_52_21 & op(e1, e0) = all_52_23 & $i(all_52_17) &
% 231.40/42.60  | | |          $i(all_52_19) & $i(all_52_21) & $i(all_52_23)
% 231.40/42.60  | | | 
% 231.40/42.60  | | | REF_CLOSE: (10), (11), (25), (28), (164) are inconsistent by sub-proof
% 231.40/42.60  | | |            #1790.
% 231.40/42.60  | | | 
% 231.40/42.60  | | Case 2:
% 231.40/42.60  | | | 
% 231.40/42.60  | | |   (165)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 231.40/42.60  | | |          & op(all_52_25, all_52_25) = e3 & op(all_52_27, all_52_27) = e2 &
% 231.40/42.60  | | |          op(all_52_29, all_52_29) = e1 & op(all_52_31, all_52_31) = e0 &
% 231.40/42.60  | | |          op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 & op(e0, e1) =
% 231.40/42.60  | | |          all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 231.40/42.60  | | |          $i(all_52_27) & $i(all_52_29) & $i(all_52_31)
% 231.40/42.60  | | | 
% 231.40/42.60  | | | REF_CLOSE: (10), (28), (42), (73), (165) are inconsistent by sub-proof
% 231.40/42.60  | | |            #1442.
% 231.40/42.60  | | | 
% 231.40/42.60  | | End of split
% 231.40/42.60  | | 
% 231.40/42.60  | End of split
% 231.40/42.60  | 
% 231.40/42.60  End of proof
% 231.40/42.60  
% 231.40/42.60  Sub-proof #1442 shows that the following formulas are inconsistent:
% 231.40/42.60  ----------------------------------------------------------------
% 231.40/42.60    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.40/42.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.40/42.60    (2)   ~ (e3 = e0)
% 231.40/42.60    (3)  op(e3, e3) = e3
% 231.40/42.60    (4)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0 &
% 231.40/42.60         op(all_52_25, all_52_25) = e3 & op(all_52_27, all_52_27) = e2 &
% 231.40/42.60         op(all_52_29, all_52_29) = e1 & op(all_52_31, all_52_31) = e0 & op(e0,
% 231.40/42.60           e3) = all_52_25 & op(e0, e2) = all_52_27 & op(e0, e1) = all_52_29 &
% 231.40/42.60         op(e0, e0) = all_52_31 & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 231.40/42.60         $i(all_52_31)
% 231.40/42.60    (5)  op(e0, e0) = e3
% 231.40/42.60  
% 231.40/42.60  Begin of proof
% 231.40/42.60  | 
% 231.40/42.60  | ALPHA: (4) implies:
% 231.40/42.60  |   (6)  op(e0, e0) = all_52_31
% 231.40/42.60  |   (7)  op(all_52_31, all_52_31) = e0
% 231.40/42.60  | 
% 231.40/42.60  | GROUND_INST: instantiating (1) with e3, all_52_31, e0, e0, simplifying with
% 231.40/42.60  |              (5), (6) gives:
% 231.40/42.60  |   (8)  all_52_31 = e3
% 231.40/42.60  | 
% 231.40/42.60  | REDUCE: (7), (8) imply:
% 231.40/42.60  |   (9)  op(e3, e3) = e0
% 231.40/42.60  | 
% 231.40/42.60  | REF_CLOSE: (1), (2), (3), (9) are inconsistent by sub-proof #2494.
% 231.40/42.60  | 
% 231.40/42.60  End of proof
% 231.40/42.60  
% 231.40/42.60  Sub-proof #1443 shows that the following formulas are inconsistent:
% 231.40/42.60  ----------------------------------------------------------------
% 231.40/42.60    (1)  op(e2, e1) = e3
% 231.40/42.60    (2)   ~ (e3 = e1)
% 231.40/42.60    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.40/42.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.40/42.60    (4)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0 &
% 231.40/42.60         op(all_52_9, all_52_9) = e3 & op(all_52_11, all_52_11) = e2 &
% 231.40/42.60         op(all_52_13, all_52_13) = e1 & op(all_52_15, all_52_15) = e0 & op(e2,
% 231.40/42.60           e3) = all_52_9 & op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13 &
% 231.40/42.60         op(e2, e0) = all_52_15 & $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 231.40/42.60         $i(all_52_15)
% 231.40/42.60    (5)  op(e3, e3) = e3
% 231.40/42.60  
% 231.40/42.60  Begin of proof
% 231.40/42.60  | 
% 231.40/42.60  | ALPHA: (4) implies:
% 231.40/42.60  |   (6)  op(e2, e1) = all_52_13
% 231.40/42.60  |   (7)  op(all_52_13, all_52_13) = e1
% 231.40/42.60  | 
% 231.40/42.60  | GROUND_INST: instantiating (3) with e3, all_52_13, e1, e2, simplifying with
% 231.40/42.60  |              (1), (6) gives:
% 231.40/42.60  |   (8)  all_52_13 = e3
% 231.40/42.60  | 
% 231.40/42.60  | REDUCE: (7), (8) imply:
% 231.40/42.60  |   (9)  op(e3, e3) = e1
% 231.40/42.60  | 
% 231.40/42.60  | REF_CLOSE: (2), (3), (5), (9) are inconsistent by sub-proof #2495.
% 231.40/42.60  | 
% 231.40/42.60  End of proof
% 231.40/42.60  
% 231.40/42.60  Sub-proof #1444 shows that the following formulas are inconsistent:
% 231.40/42.60  ----------------------------------------------------------------
% 231.40/42.60    (1)   ~ (all_38_1 = e3) & op(e1, e2) = all_38_1 & $i(all_38_1)
% 231.40/42.60    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.40/42.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.40/42.60    (3)  op(e1, e2) = e3
% 231.40/42.60  
% 231.40/42.60  Begin of proof
% 231.40/42.60  | 
% 231.40/42.60  | ALPHA: (1) implies:
% 231.40/42.60  |   (4)   ~ (all_38_1 = e3)
% 231.40/42.60  |   (5)  op(e1, e2) = all_38_1
% 231.40/42.60  | 
% 231.40/42.60  | GROUND_INST: instantiating (2) with e3, all_38_1, e2, e1, simplifying with
% 231.40/42.60  |              (3), (5) gives:
% 231.40/42.60  |   (6)  all_38_1 = e3
% 231.40/42.60  | 
% 231.40/42.60  | REDUCE: (4), (6) imply:
% 231.40/42.60  |   (7)  $false
% 231.40/42.60  | 
% 231.40/42.60  | CLOSE: (7) is inconsistent.
% 231.40/42.60  | 
% 231.40/42.60  End of proof
% 231.40/42.60  
% 231.40/42.60  Sub-proof #1445 shows that the following formulas are inconsistent:
% 231.40/42.60  ----------------------------------------------------------------
% 231.40/42.60    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 231.40/42.60    (2)   ~ (all_52_7 = e3)
% 231.40/42.60    (3)   ~ (all_38_0 = e0)
% 231.40/42.60    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.40/42.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.40/42.60    (5)   ~ (all_52_3 = e0)
% 231.40/42.60    (6)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 231.40/42.60    (7)  op(all_52_7, all_52_7) = e0
% 231.40/42.60    (8)   ~ (all_52_3 = all_38_0)
% 231.40/42.60    (9)  all_55_3 = all_52_7
% 231.40/42.60    (10)   ~ (all_38_0 = e3)
% 231.40/42.60    (11)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 231.40/42.60    (12)   ~ (all_52_3 = e3)
% 231.40/42.60    (13)   ~ (all_52_3 = all_52_7)
% 231.40/42.60    (14)  op(e0, e0) = e3
% 231.40/42.60    (15)  all_55_2 = all_38_0
% 231.40/42.60    (16)   ~ (all_52_7 = all_38_0)
% 231.40/42.60    (17)  all_55_1 = all_52_3
% 231.40/42.60    (18)   ~ (all_38_0 = e2)
% 231.40/42.60  
% 231.40/42.60  Begin of proof
% 231.40/42.60  | 
% 231.40/42.60  | BETA: splitting (11) gives:
% 231.40/42.60  | 
% 231.40/42.60  | Case 1:
% 231.40/42.60  | | 
% 231.40/42.60  | |   (19)  all_55_2 = e3
% 231.40/42.60  | | 
% 231.40/42.60  | | COMBINE_EQS: (15), (19) imply:
% 231.40/42.60  | |   (20)  all_38_0 = e3
% 231.40/42.60  | | 
% 231.40/42.60  | | REDUCE: (10), (20) imply:
% 231.40/42.60  | |   (21)  $false
% 231.40/42.60  | | 
% 231.40/42.60  | | CLOSE: (21) is inconsistent.
% 231.40/42.60  | | 
% 231.40/42.60  | Case 2:
% 231.40/42.60  | | 
% 231.40/42.60  | |   (22)  all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 231.40/42.60  | | 
% 231.40/42.60  | | BETA: splitting (22) gives:
% 231.40/42.60  | | 
% 231.40/42.60  | | Case 1:
% 231.40/42.60  | | | 
% 231.40/42.60  | | |   (23)  all_55_2 = e2
% 231.40/42.60  | | | 
% 231.40/42.60  | | | REF_CLOSE: (15), (18), (23) are inconsistent by sub-proof #1452.
% 231.40/42.60  | | | 
% 231.40/42.60  | | Case 2:
% 231.40/42.60  | | | 
% 231.40/42.60  | | |   (24)  all_55_2 = e1 | all_55_2 = e0
% 231.40/42.60  | | | 
% 231.40/42.60  | | | BETA: splitting (24) gives:
% 231.40/42.60  | | | 
% 231.40/42.60  | | | Case 1:
% 231.40/42.60  | | | | 
% 231.40/42.60  | | | |   (25)  all_55_2 = e1
% 231.40/42.60  | | | | 
% 231.40/42.60  | | | | COMBINE_EQS: (15), (25) imply:
% 231.40/42.60  | | | |   (26)  all_38_0 = e1
% 231.40/42.60  | | | | 
% 231.40/42.60  | | | | SIMP: (26) implies:
% 231.40/42.60  | | | |   (27)  all_38_0 = e1
% 231.40/42.60  | | | | 
% 231.40/42.60  | | | | REDUCE: (8), (27) imply:
% 231.40/42.60  | | | |   (28)   ~ (all_52_3 = e1)
% 231.40/42.60  | | | | 
% 231.40/42.60  | | | | REDUCE: (16), (27) imply:
% 231.40/42.60  | | | |   (29)   ~ (all_52_7 = e1)
% 231.40/42.60  | | | | 
% 231.40/42.60  | | | | BETA: splitting (1) gives:
% 231.40/42.60  | | | | 
% 231.40/42.60  | | | | Case 1:
% 231.40/42.60  | | | | | 
% 231.40/42.60  | | | | |   (30)  all_55_1 = e3
% 231.40/42.60  | | | | | 
% 231.40/42.60  | | | | | COMBINE_EQS: (17), (30) imply:
% 231.40/42.60  | | | | |   (31)  all_52_3 = e3
% 231.40/42.60  | | | | | 
% 231.40/42.60  | | | | | REDUCE: (12), (31) imply:
% 231.40/42.60  | | | | |   (32)  $false
% 231.40/42.60  | | | | | 
% 231.40/42.60  | | | | | CLOSE: (32) is inconsistent.
% 231.40/42.60  | | | | | 
% 231.40/42.60  | | | | Case 2:
% 231.40/42.60  | | | | | 
% 231.40/42.60  | | | | |   (33)  all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 231.40/42.60  | | | | | 
% 231.40/42.60  | | | | | BETA: splitting (33) gives:
% 231.40/42.60  | | | | | 
% 231.40/42.60  | | | | | Case 1:
% 231.40/42.60  | | | | | | 
% 231.40/42.60  | | | | | |   (34)  all_55_1 = e2
% 231.40/42.60  | | | | | | 
% 231.40/42.60  | | | | | | COMBINE_EQS: (17), (34) imply:
% 231.40/42.60  | | | | | |   (35)  all_52_3 = e2
% 231.40/42.60  | | | | | | 
% 231.40/42.60  | | | | | | REDUCE: (13), (35) imply:
% 231.40/42.60  | | | | | |   (36)   ~ (all_52_7 = e2)
% 231.40/42.60  | | | | | | 
% 231.40/42.60  | | | | | | SIMP: (36) implies:
% 231.40/42.60  | | | | | |   (37)   ~ (all_52_7 = e2)
% 231.40/42.60  | | | | | | 
% 231.40/42.60  | | | | | | BETA: splitting (6) gives:
% 231.40/42.60  | | | | | | 
% 231.40/42.60  | | | | | | Case 1:
% 231.40/42.60  | | | | | | | 
% 231.40/42.60  | | | | | | |   (38)  all_55_3 = e3
% 231.40/42.60  | | | | | | | 
% 231.40/42.60  | | | | | | | REF_CLOSE: (2), (9), (38) are inconsistent by sub-proof #1451.
% 231.40/42.60  | | | | | | | 
% 231.40/42.60  | | | | | | Case 2:
% 231.40/42.60  | | | | | | | 
% 231.40/42.60  | | | | | | |   (39)   ~ (all_55_3 = e3)
% 231.40/42.60  | | | | | | |   (40)  all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 231.40/42.60  | | | | | | | 
% 231.40/42.60  | | | | | | | BETA: splitting (40) gives:
% 231.40/42.60  | | | | | | | 
% 231.40/42.60  | | | | | | | Case 1:
% 231.40/42.60  | | | | | | | | 
% 231.40/42.60  | | | | | | | |   (41)  all_55_3 = e2
% 231.40/42.60  | | | | | | | | 
% 231.40/42.60  | | | | | | | | REF_CLOSE: (9), (37), (41) are inconsistent by sub-proof #1450.
% 231.40/42.60  | | | | | | | | 
% 231.40/42.60  | | | | | | | Case 2:
% 231.40/42.60  | | | | | | | | 
% 231.40/42.60  | | | | | | | |   (42)  all_55_3 = e1 | all_55_3 = e0
% 231.40/42.60  | | | | | | | | 
% 231.40/42.60  | | | | | | | | REF_CLOSE: (2), (4), (7), (9), (14), (29), (42) are inconsistent
% 231.40/42.60  | | | | | | | |            by sub-proof #1448.
% 231.40/42.60  | | | | | | | | 
% 231.40/42.60  | | | | | | | End of split
% 231.40/42.60  | | | | | | | 
% 231.40/42.60  | | | | | | End of split
% 231.40/42.60  | | | | | | 
% 231.40/42.60  | | | | | Case 2:
% 231.40/42.60  | | | | | | 
% 231.40/42.60  | | | | | |   (43)  all_55_1 = e1 | all_55_1 = e0
% 231.40/42.60  | | | | | | 
% 231.40/42.60  | | | | | | REF_CLOSE: (5), (17), (28), (43) are inconsistent by sub-proof
% 231.40/42.60  | | | | | |            #1447.
% 231.40/42.60  | | | | | | 
% 231.40/42.60  | | | | | End of split
% 231.40/42.60  | | | | | 
% 231.40/42.60  | | | | End of split
% 231.40/42.60  | | | | 
% 231.40/42.60  | | | Case 2:
% 231.40/42.60  | | | | 
% 231.40/42.60  | | | |   (44)  all_55_2 = e0
% 231.40/42.60  | | | | 
% 231.40/42.60  | | | | REF_CLOSE: (3), (15), (44) are inconsistent by sub-proof #1446.
% 231.40/42.60  | | | | 
% 231.40/42.60  | | | End of split
% 231.40/42.60  | | | 
% 231.40/42.60  | | End of split
% 231.40/42.60  | | 
% 231.40/42.60  | End of split
% 231.40/42.60  | 
% 231.40/42.60  End of proof
% 231.40/42.60  
% 231.40/42.60  Sub-proof #1446 shows that the following formulas are inconsistent:
% 231.40/42.60  ----------------------------------------------------------------
% 231.40/42.60    (1)  all_55_2 = all_38_0
% 231.40/42.60    (2)  all_55_2 = e0
% 231.40/42.60    (3)   ~ (all_38_0 = e0)
% 231.40/42.60  
% 231.40/42.60  Begin of proof
% 231.40/42.60  | 
% 231.40/42.60  | COMBINE_EQS: (1), (2) imply:
% 231.40/42.60  |   (4)  all_38_0 = e0
% 231.40/42.60  | 
% 231.40/42.60  | SIMP: (4) implies:
% 231.40/42.60  |   (5)  all_38_0 = e0
% 231.40/42.60  | 
% 231.40/42.60  | REDUCE: (3), (5) imply:
% 231.40/42.60  |   (6)  $false
% 231.40/42.60  | 
% 231.40/42.60  | CLOSE: (6) is inconsistent.
% 231.40/42.60  | 
% 231.40/42.60  End of proof
% 231.40/42.60  
% 231.40/42.60  Sub-proof #1447 shows that the following formulas are inconsistent:
% 231.40/42.60  ----------------------------------------------------------------
% 231.40/42.60    (1)  all_55_1 = e1 | all_55_1 = e0
% 231.40/42.60    (2)  all_55_1 = all_52_3
% 231.40/42.60    (3)   ~ (all_52_3 = e1)
% 231.40/42.60    (4)   ~ (all_52_3 = e0)
% 231.40/42.60  
% 231.40/42.60  Begin of proof
% 231.40/42.60  | 
% 231.40/42.60  | BETA: splitting (1) gives:
% 231.40/42.60  | 
% 231.40/42.60  | Case 1:
% 231.40/42.60  | | 
% 231.40/42.60  | |   (5)  all_55_1 = e1
% 231.40/42.60  | | 
% 231.40/42.60  | | COMBINE_EQS: (2), (5) imply:
% 231.40/42.60  | |   (6)  all_52_3 = e1
% 231.40/42.60  | | 
% 231.40/42.60  | | REDUCE: (3), (6) imply:
% 231.40/42.60  | |   (7)  $false
% 231.40/42.60  | | 
% 231.40/42.60  | | CLOSE: (7) is inconsistent.
% 231.40/42.60  | | 
% 231.40/42.60  | Case 2:
% 231.40/42.60  | | 
% 231.40/42.60  | |   (8)  all_55_1 = e0
% 231.40/42.60  | | 
% 231.40/42.60  | | COMBINE_EQS: (2), (8) imply:
% 231.40/42.60  | |   (9)  all_52_3 = e0
% 231.40/42.60  | | 
% 231.40/42.60  | | REDUCE: (4), (9) imply:
% 231.40/42.60  | |   (10)  $false
% 231.40/42.60  | | 
% 231.40/42.60  | | CLOSE: (10) is inconsistent.
% 231.40/42.60  | | 
% 231.40/42.60  | End of split
% 231.40/42.60  | 
% 231.40/42.60  End of proof
% 231.40/42.60  
% 231.40/42.60  Sub-proof #1448 shows that the following formulas are inconsistent:
% 231.40/42.60  ----------------------------------------------------------------
% 231.40/42.60    (1)   ~ (all_52_7 = e3)
% 231.40/42.60    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.40/42.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.40/42.60    (3)  op(all_52_7, all_52_7) = e0
% 231.40/42.60    (4)  all_55_3 = all_52_7
% 231.40/42.60    (5)   ~ (all_52_7 = e1)
% 231.40/42.60    (6)  op(e0, e0) = e3
% 231.40/42.60    (7)  all_55_3 = e1 | all_55_3 = e0
% 231.40/42.60  
% 231.40/42.60  Begin of proof
% 231.40/42.60  | 
% 231.40/42.60  | BETA: splitting (7) gives:
% 231.40/42.60  | 
% 231.40/42.60  | Case 1:
% 231.40/42.60  | | 
% 231.40/42.60  | |   (8)  all_55_3 = e1
% 231.40/42.60  | | 
% 231.40/42.60  | | REF_CLOSE: (4), (5), (8) are inconsistent by sub-proof #1449.
% 231.40/42.60  | | 
% 231.40/42.60  | Case 2:
% 231.40/42.60  | | 
% 231.40/42.60  | |   (9)  all_55_3 = e0
% 231.40/42.60  | | 
% 231.40/42.60  | | COMBINE_EQS: (4), (9) imply:
% 231.40/42.60  | |   (10)  all_52_7 = e0
% 231.40/42.60  | | 
% 231.40/42.60  | | SIMP: (10) implies:
% 231.40/42.60  | |   (11)  all_52_7 = e0
% 231.40/42.60  | | 
% 231.40/42.60  | | REF_CLOSE: (1), (2), (3), (6), (11) are inconsistent by sub-proof #1505.
% 231.40/42.60  | | 
% 231.40/42.60  | End of split
% 231.40/42.60  | 
% 231.40/42.60  End of proof
% 231.40/42.60  
% 231.40/42.60  Sub-proof #1449 shows that the following formulas are inconsistent:
% 231.40/42.60  ----------------------------------------------------------------
% 231.40/42.60    (1)  all_55_3 = all_52_7
% 231.40/42.60    (2)  all_55_3 = e1
% 231.40/42.60    (3)   ~ (all_52_7 = e1)
% 231.40/42.60  
% 231.40/42.60  Begin of proof
% 231.40/42.60  | 
% 231.40/42.60  | COMBINE_EQS: (1), (2) imply:
% 231.40/42.60  |   (4)  all_52_7 = e1
% 231.40/42.60  | 
% 231.40/42.60  | SIMP: (4) implies:
% 231.40/42.60  |   (5)  all_52_7 = e1
% 231.40/42.60  | 
% 231.40/42.60  | REDUCE: (3), (5) imply:
% 231.40/42.60  |   (6)  $false
% 231.40/42.60  | 
% 231.40/42.60  | CLOSE: (6) is inconsistent.
% 231.40/42.60  | 
% 231.40/42.60  End of proof
% 231.40/42.60  
% 231.40/42.60  Sub-proof #1450 shows that the following formulas are inconsistent:
% 231.40/42.60  ----------------------------------------------------------------
% 231.40/42.60    (1)  all_55_3 = all_52_7
% 231.40/42.60    (2)  all_55_3 = e2
% 231.40/42.60    (3)   ~ (all_52_7 = e2)
% 231.40/42.60  
% 231.40/42.60  Begin of proof
% 231.40/42.60  | 
% 231.40/42.60  | COMBINE_EQS: (1), (2) imply:
% 231.40/42.60  |   (4)  all_52_7 = e2
% 231.40/42.60  | 
% 231.40/42.60  | SIMP: (4) implies:
% 231.40/42.60  |   (5)  all_52_7 = e2
% 231.40/42.60  | 
% 231.40/42.60  | REDUCE: (3), (5) imply:
% 231.40/42.60  |   (6)  $false
% 231.40/42.60  | 
% 231.40/42.60  | CLOSE: (6) is inconsistent.
% 231.40/42.60  | 
% 231.40/42.60  End of proof
% 231.40/42.60  
% 231.40/42.60  Sub-proof #1451 shows that the following formulas are inconsistent:
% 231.40/42.60  ----------------------------------------------------------------
% 231.40/42.60    (1)  all_55_3 = all_52_7
% 231.40/42.60    (2)  all_55_3 = e3
% 231.40/42.60    (3)   ~ (all_52_7 = e3)
% 231.40/42.60  
% 231.40/42.60  Begin of proof
% 231.40/42.60  | 
% 231.40/42.60  | COMBINE_EQS: (1), (2) imply:
% 231.40/42.60  |   (4)  all_52_7 = e3
% 231.40/42.60  | 
% 231.40/42.60  | SIMP: (4) implies:
% 231.40/42.60  |   (5)  all_52_7 = e3
% 231.40/42.60  | 
% 231.40/42.60  | REDUCE: (3), (5) imply:
% 231.40/42.60  |   (6)  $false
% 231.40/42.60  | 
% 231.40/42.60  | CLOSE: (6) is inconsistent.
% 231.40/42.60  | 
% 231.40/42.60  End of proof
% 231.40/42.60  
% 231.40/42.60  Sub-proof #1452 shows that the following formulas are inconsistent:
% 231.40/42.60  ----------------------------------------------------------------
% 231.40/42.60    (1)  all_55_2 = all_38_0
% 231.40/42.60    (2)  all_55_2 = e2
% 231.40/42.60    (3)   ~ (all_38_0 = e2)
% 231.40/42.60  
% 231.40/42.60  Begin of proof
% 231.40/42.60  | 
% 231.40/42.60  | COMBINE_EQS: (1), (2) imply:
% 231.40/42.60  |   (4)  all_38_0 = e2
% 231.40/42.60  | 
% 231.40/42.60  | SIMP: (4) implies:
% 231.40/42.60  |   (5)  all_38_0 = e2
% 231.40/42.60  | 
% 231.40/42.60  | REDUCE: (3), (5) imply:
% 231.40/42.60  |   (6)  $false
% 231.40/42.60  | 
% 231.40/42.60  | CLOSE: (6) is inconsistent.
% 231.40/42.60  | 
% 231.40/42.60  End of proof
% 231.40/42.60  
% 231.40/42.60  Sub-proof #1453 shows that the following formulas are inconsistent:
% 231.40/42.60  ----------------------------------------------------------------
% 231.40/42.60    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.40/42.60         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.40/42.60    (2)  op(e3, e1) = all_52_5
% 231.40/42.60    (3)   ~ (all_52_7 = e3)
% 231.40/42.60    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.40/42.60         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.40/42.60    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.40/42.60         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.40/42.60    (6)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 231.40/42.60         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.40/42.60    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.40/42.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.40/42.60    (8)   ~ (all_6_2 = e3)
% 231.40/42.60    (9)   ~ (all_52_3 = e0)
% 231.40/42.60    (10)  op(e1, e1) = all_6_2
% 231.40/42.60    (11)  op(all_52_7, all_52_7) = e0
% 231.40/42.60    (12)  op(e3, e2) = all_52_3
% 231.40/42.60    (13)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.40/42.60          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.40/42.60    (14)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.40/42.60          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.40/42.60    (15)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.40/42.60          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.40/42.60    (16)  all_57_3 = e0
% 231.40/42.60    (17)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.40/42.60          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.40/42.60    (18)   ~ (e3 = e2)
% 231.40/42.60    (19)  all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 231.40/42.60    (20)   ~ (e3 = e0)
% 231.40/42.60    (21)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.40/42.60          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.40/42.60    (22)  op(e3, e3) = e3
% 231.40/42.60    (23)   ~ (all_6_2 = e2)
% 231.40/42.60    (24)  all_57_15 = e3
% 231.40/42.60    (25)   ~ (all_52_3 = e3)
% 231.40/42.60    (26)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.40/42.60          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.40/42.60            e1)
% 231.40/42.60    (27)  all_57_5 = e3
% 231.40/42.60    (28)   ~ (e2 = e0)
% 231.40/42.60    (29)   ~ (all_52_3 = all_52_7)
% 231.40/42.60    (30)  op(e0, e0) = e3
% 231.40/42.60    (31)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.40/42.60          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.40/42.60            e2)
% 231.40/42.60    (32)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.40/42.60              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.40/42.60                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.40/42.60                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.40/42.60    (33)  all_55_10 = all_6_2
% 231.40/42.60    (34)  all_57_7 = e3
% 231.40/42.60    (35)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.40/42.60          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.40/42.60    (36)   ~ (all_52_5 = all_6_2)
% 231.40/42.60    (37)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.40/42.60          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.40/42.60    (38)   ~ (all_6_2 = e0)
% 231.40/42.60    (39)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.40/42.60          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.40/42.60    (40)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.40/42.60          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.40/42.60    (41)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.40/42.60          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.40/42.60    (42)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.40/42.60          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.40/42.60    (43)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 231.40/42.60          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 231.40/42.60    (44)  op(e3, e0) = all_52_7
% 231.40/42.60    (45)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.40/42.60          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.40/42.60    (46)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 231.40/42.60          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 231.40/42.60  
% 231.40/42.60  Begin of proof
% 231.40/42.60  | 
% 231.40/42.60  | BETA: splitting (19) gives:
% 231.40/42.60  | 
% 231.40/42.60  | Case 1:
% 231.40/42.60  | | 
% 231.40/42.60  | |   (47)  all_55_10 = e2
% 231.40/42.60  | | 
% 231.40/42.60  | | REF_CLOSE: (23), (33), (47) are inconsistent by sub-proof #2499.
% 231.40/42.60  | | 
% 231.40/42.60  | Case 2:
% 231.40/42.60  | | 
% 231.40/42.60  | |   (48)   ~ (all_55_10 = e2)
% 231.40/42.60  | |   (49)  all_55_10 = e1 | all_55_10 = e0
% 231.40/42.60  | | 
% 231.40/42.60  | | BETA: splitting (49) gives:
% 231.40/42.60  | | 
% 231.40/42.60  | | Case 1:
% 231.40/42.60  | | | 
% 231.40/42.60  | | |   (50)  all_55_10 = e1
% 231.40/42.60  | | | 
% 231.40/42.60  | | | COMBINE_EQS: (33), (50) imply:
% 231.40/42.60  | | |   (51)  all_6_2 = e1
% 231.40/42.60  | | | 
% 231.40/42.60  | | | SIMP: (51) implies:
% 231.40/42.60  | | |   (52)  all_6_2 = e1
% 231.40/42.60  | | | 
% 231.40/42.60  | | | REDUCE: (36), (52) imply:
% 231.40/42.60  | | |   (53)   ~ (all_52_5 = e1)
% 231.40/42.60  | | | 
% 231.40/42.60  | | | REDUCE: (8), (52) imply:
% 231.40/42.60  | | |   (54)   ~ (e3 = e1)
% 231.40/42.60  | | | 
% 231.40/42.60  | | | SIMP: (54) implies:
% 231.40/42.60  | | |   (55)   ~ (e3 = e1)
% 231.40/42.60  | | | 
% 231.40/42.60  | | | REDUCE: (23), (52) imply:
% 231.40/42.60  | | |   (56)   ~ (e2 = e1)
% 231.40/42.60  | | | 
% 231.40/42.60  | | | SIMP: (56) implies:
% 231.40/42.60  | | |   (57)   ~ (e2 = e1)
% 231.40/42.60  | | | 
% 231.40/42.60  | | | REDUCE: (38), (52) imply:
% 231.40/42.60  | | |   (58)   ~ (e1 = e0)
% 231.40/42.60  | | | 
% 231.40/42.60  | | | REDUCE: (10), (52) imply:
% 231.40/42.60  | | |   (59)  op(e1, e1) = e1
% 231.40/42.60  | | | 
% 231.40/42.60  | | | BETA: splitting (43) gives:
% 231.40/42.60  | | | 
% 231.40/42.60  | | | Case 1:
% 231.40/42.60  | | | | 
% 231.40/42.60  | | | |   (60)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2)
% 231.40/42.60  | | | |           = e1)
% 231.40/42.60  | | | | 
% 231.40/42.60  | | | | BETA: splitting (60) gives:
% 231.40/42.60  | | | | 
% 231.40/42.60  | | | | Case 1:
% 231.40/42.60  | | | | | 
% 231.40/42.60  | | | | |   (61)  all_57_6 = e1 & op(e1, e3) = e1
% 231.40/42.60  | | | | | 
% 231.40/42.60  | | | | | ALPHA: (61) implies:
% 231.40/42.60  | | | | |   (62)  all_57_6 = e1
% 231.40/42.60  | | | | | 
% 231.40/42.60  | | | | | BETA: splitting (41) gives:
% 231.40/42.60  | | | | | 
% 231.40/42.60  | | | | | Case 1:
% 231.40/42.60  | | | | | | 
% 231.40/42.60  | | | | | |   (63)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2,
% 231.40/42.60  | | | | | |             e3) = e0)
% 231.40/42.60  | | | | | | 
% 231.40/42.60  | | | | | | REF_CLOSE: (1), (7), (16), (18), (20), (22), (27), (28), (35), (55),
% 231.40/42.60  | | | | | |            (57), (58), (63) are inconsistent by sub-proof #1784.
% 231.40/42.60  | | | | | | 
% 231.40/42.60  | | | | | Case 2:
% 231.40/42.60  | | | | | | 
% 231.40/42.60  | | | | | |   (64)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0,
% 231.40/42.60  | | | | | |             e3) = e0)
% 231.40/42.60  | | | | | | 
% 231.40/42.60  | | | | | | BETA: splitting (64) gives:
% 231.40/42.60  | | | | | | 
% 231.40/42.60  | | | | | | Case 1:
% 231.40/42.60  | | | | | | | 
% 231.40/42.60  | | | | | | |   (65)  all_57_6 = e0 & op(e1, e3) = e0
% 231.40/42.60  | | | | | | | 
% 231.40/42.60  | | | | | | | REF_CLOSE: (58), (62), (65) are inconsistent by sub-proof #2347.
% 231.40/42.60  | | | | | | | 
% 231.40/42.60  | | | | | | Case 2:
% 231.40/42.60  | | | | | | | 
% 231.40/42.60  | | | | | | |   (66)  all_57_12 = e0 & op(e0, e3) = e0
% 231.40/42.60  | | | | | | | 
% 231.40/42.60  | | | | | | | ALPHA: (66) implies:
% 231.40/42.60  | | | | | | |   (67)  all_57_12 = e0
% 231.40/42.60  | | | | | | | 
% 231.40/42.61  | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (11), (12),
% 231.40/42.61  | | | | | | |            (13), (14), (15), (16), (17), (18), (20), (21), (22),
% 231.40/42.61  | | | | | | |            (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 231.40/42.61  | | | | | | |            (34), (35), (37), (39), (40), (41), (42), (43), (44),
% 231.40/42.61  | | | | | | |            (45), (46), (53), (55), (57), (58), (59), (62), (67)
% 231.40/42.61  | | | | | | |            are inconsistent by sub-proof #1457.
% 231.40/42.61  | | | | | | | 
% 231.40/42.61  | | | | | | End of split
% 231.40/42.61  | | | | | | 
% 231.40/42.61  | | | | | End of split
% 231.40/42.61  | | | | | 
% 231.40/42.61  | | | | Case 2:
% 231.40/42.61  | | | | | 
% 231.40/42.61  | | | | |   (68)  all_57_7 = e1 & op(e1, e2) = e1
% 231.40/42.61  | | | | | 
% 231.40/42.61  | | | | | REF_CLOSE: (34), (55), (68) are inconsistent by sub-proof #2104.
% 231.40/42.61  | | | | | 
% 231.40/42.61  | | | | End of split
% 231.40/42.61  | | | | 
% 231.40/42.61  | | | Case 2:
% 231.40/42.61  | | | | 
% 231.40/42.61  | | | |   (69)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0)
% 231.40/42.61  | | | |           = e1)
% 231.40/42.61  | | | | 
% 231.40/42.61  | | | | BETA: splitting (69) gives:
% 231.40/42.61  | | | | 
% 231.40/42.61  | | | | Case 1:
% 231.40/42.61  | | | | | 
% 231.40/42.61  | | | | |   (70)  all_57_8 = e1 & op(e1, e1) = e1
% 231.40/42.61  | | | | | 
% 231.40/42.61  | | | | | ALPHA: (70) implies:
% 231.40/42.61  | | | | |   (71)  all_57_8 = e1
% 231.40/42.61  | | | | | 
% 231.40/42.61  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (11), (12), (13),
% 231.40/42.61  | | | | |            (14), (15), (16), (17), (18), (20), (21), (22), (24), (25),
% 231.40/42.61  | | | | |            (26), (27), (28), (29), (30), (31), (32), (34), (35), (37),
% 231.40/42.61  | | | | |            (39), (40), (41), (42), (43), (44), (45), (46), (53), (55),
% 231.40/42.61  | | | | |            (57), (58), (59), (71) are inconsistent by sub-proof #1459.
% 231.40/42.61  | | | | | 
% 231.40/42.61  | | | | Case 2:
% 231.40/42.61  | | | | | 
% 231.40/42.61  | | | | |   (72)  all_57_11 = e1 & op(e1, e0) = e1
% 231.40/42.61  | | | | | 
% 231.40/42.61  | | | | | ALPHA: (72) implies:
% 231.40/42.61  | | | | |   (73)  all_57_11 = e1
% 231.40/42.61  | | | | | 
% 231.40/42.61  | | | | | BETA: splitting (21) gives:
% 231.40/42.61  | | | | | 
% 231.40/42.61  | | | | | Case 1:
% 231.40/42.61  | | | | | | 
% 231.40/42.61  | | | | | |   (74)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2,
% 231.40/42.61  | | | | | |             e1) = e1)
% 231.40/42.61  | | | | | | 
% 231.40/42.61  | | | | | | BETA: splitting (74) gives:
% 231.40/42.61  | | | | | | 
% 231.40/42.61  | | | | | | Case 1:
% 231.40/42.61  | | | | | | | 
% 231.40/42.61  | | | | | | |   (75)  all_57_4 = e1 & op(e3, e1) = e1
% 231.40/42.61  | | | | | | | 
% 231.40/42.61  | | | | | | | ALPHA: (75) implies:
% 231.40/42.61  | | | | | | |   (76)  all_57_4 = e1
% 231.40/42.61  | | | | | | | 
% 231.40/42.61  | | | | | | | BETA: splitting (17) gives:
% 231.40/42.61  | | | | | | | 
% 231.40/42.61  | | | | | | | Case 1:
% 231.40/42.61  | | | | | | | | 
% 231.40/42.61  | | | | | | | |   (77)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 &
% 231.40/42.61  | | | | | | | |           op(e2, e1) = e0)
% 231.40/42.61  | | | | | | | | 
% 231.40/42.61  | | | | | | | | REF_CLOSE: (20), (27), (58), (76), (77) are inconsistent by
% 231.40/42.61  | | | | | | | |            sub-proof #2413.
% 231.40/42.61  | | | | | | | | 
% 231.40/42.61  | | | | | | | Case 2:
% 231.40/42.61  | | | | | | | | 
% 231.40/42.61  | | | | | | | |   (78)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 &
% 231.40/42.61  | | | | | | | |           op(e0, e1) = e0)
% 231.40/42.61  | | | | | | | | 
% 231.40/42.61  | | | | | | | | BETA: splitting (78) gives:
% 231.40/42.61  | | | | | | | | 
% 231.40/42.61  | | | | | | | | Case 1:
% 231.40/42.61  | | | | | | | | | 
% 231.40/42.61  | | | | | | | | |   (79)  all_57_8 = e0 & op(e1, e1) = e0
% 231.40/42.61  | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | ALPHA: (79) implies:
% 231.40/42.61  | | | | | | | | |   (80)  op(e1, e1) = e0
% 231.40/42.61  | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (11), (13), (14),
% 231.40/42.61  | | | | | | | | |            (15), (16), (17), (18), (20), (21), (22), (24),
% 231.40/42.61  | | | | | | | | |            (27), (28), (30), (31), (32), (34), (35), (37),
% 231.40/42.61  | | | | | | | | |            (39), (40), (41), (42), (43), (44), (45), (46),
% 231.40/42.61  | | | | | | | | |            (55), (57), (58), (80) are inconsistent by
% 231.40/42.61  | | | | | | | | |            sub-proof #1486.
% 231.40/42.61  | | | | | | | | | 
% 231.40/42.61  | | | | | | | | Case 2:
% 231.40/42.61  | | | | | | | | | 
% 231.40/42.61  | | | | | | | | |   (81)  all_57_14 = e0 & op(e0, e1) = e0
% 231.40/42.61  | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | ALPHA: (81) implies:
% 231.40/42.61  | | | | | | | | |   (82)  all_57_14 = e0
% 231.40/42.61  | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | BETA: splitting (15) gives:
% 231.40/42.61  | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | Case 1:
% 231.40/42.61  | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | |   (83)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 &
% 231.40/42.61  | | | | | | | | | |           op(e3, e2) = e0)
% 231.40/42.61  | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | REF_CLOSE: (5), (7), (16), (18), (20), (22), (28), (34),
% 231.40/42.61  | | | | | | | | | |            (45), (55), (57), (58), (83) are inconsistent by
% 231.40/42.61  | | | | | | | | | |            sub-proof #2097.
% 231.40/42.61  | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | Case 2:
% 231.40/42.61  | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | |   (84)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 &
% 231.40/42.61  | | | | | | | | | |           op(e3, e0) = e0)
% 231.40/42.61  | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | BETA: splitting (84) gives:
% 231.40/42.61  | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | Case 1:
% 231.40/42.61  | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | |   (85)  all_57_4 = e0 & op(e3, e1) = e0
% 231.40/42.61  | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | REF_CLOSE: (58), (76), (85) are inconsistent by sub-proof
% 231.40/42.61  | | | | | | | | | | |            #2429.
% 231.40/42.61  | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | Case 2:
% 231.40/42.61  | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | |   (86)  all_57_9 = e0 & op(e3, e0) = e0
% 231.40/42.61  | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | ALPHA: (86) implies:
% 231.40/42.61  | | | | | | | | | | |   (87)  all_57_9 = e0
% 231.40/42.61  | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | BETA: splitting (46) gives:
% 231.40/42.61  | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | Case 1:
% 231.40/42.61  | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | |   (88)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 231.40/42.61  | | | | | | | | | | | |           & op(e1, e2) = e2)
% 231.40/42.61  | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | BETA: splitting (88) gives:
% 231.40/42.61  | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | Case 1:
% 231.40/42.61  | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | |   (89)  all_57_6 = e2 & op(e1, e3) = e2
% 231.40/42.61  | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | ALPHA: (89) implies:
% 231.40/42.61  | | | | | | | | | | | | |   (90)  all_57_6 = e2
% 231.40/42.61  | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | BETA: splitting (6) gives:
% 231.40/42.61  | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | Case 1:
% 231.40/42.61  | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | |   (91)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 231.40/42.61  | | | | | | | | | | | | | |           & op(e1, e2) = e0)
% 231.40/42.61  | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | BETA: splitting (91) gives:
% 231.40/42.61  | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | Case 1:
% 231.40/42.61  | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | |   (92)  all_57_6 = e0 & op(e1, e3) = e0
% 231.40/42.61  | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | REF_CLOSE: (28), (90), (92) are inconsistent by sub-proof
% 231.40/42.61  | | | | | | | | | | | | | | |            #2386.
% 231.40/42.61  | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | Case 2:
% 231.40/42.61  | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | |   (93)  all_57_7 = e0 & op(e1, e2) = e0
% 231.40/42.61  | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | REF_CLOSE: (20), (34), (93) are inconsistent by sub-proof
% 231.40/42.61  | | | | | | | | | | | | | | |            #2042.
% 231.40/42.61  | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | End of split
% 231.40/42.61  | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | Case 2:
% 231.40/42.61  | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | |   (94)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 231.40/42.61  | | | | | | | | | | | | | |           e0 & op(e1, e0) = e0)
% 231.40/42.61  | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | BETA: splitting (94) gives:
% 231.40/42.61  | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | Case 1:
% 231.40/42.61  | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | |   (95)  all_57_8 = e0 & op(e1, e1) = e0
% 231.40/42.61  | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | ALPHA: (95) implies:
% 231.40/42.61  | | | | | | | | | | | | | | |   (96)  op(e1, e1) = e0
% 231.40/42.61  | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | REF_CLOSE: (1), (5), (6), (7), (13), (14), (16), (17), (18),
% 231.40/42.61  | | | | | | | | | | | | | | |            (20), (21), (22), (24), (27), (28), (34), (35),
% 231.40/42.61  | | | | | | | | | | | | | | |            (37), (40), (42), (45), (46), (55), (57), (58),
% 231.40/42.61  | | | | | | | | | | | | | | |            (82), (87), (96) are inconsistent by sub-proof
% 231.40/42.61  | | | | | | | | | | | | | | |            #1491.
% 231.40/42.61  | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | Case 2:
% 231.40/42.61  | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | |   (97)  all_57_11 = e0 & op(e1, e0) = e0
% 231.40/42.61  | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | ALPHA: (97) implies:
% 231.40/42.61  | | | | | | | | | | | | | | |   (98)  all_57_11 = e0
% 231.40/42.61  | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | COMBINE_EQS: (73), (98) imply:
% 231.40/42.61  | | | | | | | | | | | | | | |   (99)  e1 = e0
% 231.40/42.61  | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | COMBINE_EQS: (76), (99) imply:
% 231.40/42.61  | | | | | | | | | | | | | | |   (100)  all_57_4 = e0
% 231.40/42.61  | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | REF_CLOSE: (7), (13), (14), (18), (22), (28), (55), (57),
% 231.40/42.61  | | | | | | | | | | | | | | |            (58), (87), (100) are inconsistent by sub-proof
% 231.40/42.61  | | | | | | | | | | | | | | |            #2436.
% 231.40/42.61  | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | End of split
% 231.40/42.61  | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | End of split
% 231.40/42.61  | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | Case 2:
% 231.40/42.61  | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | |   (101)  all_57_7 = e2 & op(e1, e2) = e2
% 231.40/42.61  | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | REF_CLOSE: (18), (34), (101) are inconsistent by sub-proof
% 231.40/42.61  | | | | | | | | | | | | |            #2092.
% 231.40/42.61  | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | End of split
% 231.40/42.61  | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | Case 2:
% 231.40/42.61  | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | |   (102)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 231.40/42.61  | | | | | | | | | | | |            e2 & op(e1, e0) = e2)
% 231.40/42.61  | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | BETA: splitting (102) gives:
% 231.40/42.61  | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | Case 1:
% 231.40/42.61  | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | |   (103)  all_57_8 = e2 & op(e1, e1) = e2
% 231.40/42.61  | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | ALPHA: (103) implies:
% 231.40/42.61  | | | | | | | | | | | | |   (104)  all_57_8 = e2
% 231.40/42.61  | | | | | | | | | | | | |   (105)  op(e1, e1) = e2
% 231.40/42.61  | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | BETA: splitting (37) gives:
% 231.40/42.61  | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | Case 1:
% 231.40/42.61  | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | |   (106)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 231.40/42.61  | | | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 231.40/42.61  | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | BETA: splitting (106) gives:
% 231.40/42.61  | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | Case 1:
% 231.40/42.61  | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | |   (107)  all_57_9 = e2 & op(e3, e0) = e2
% 231.40/42.61  | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | ALPHA: (107) implies:
% 231.40/42.61  | | | | | | | | | | | | | | |   (108)  all_57_9 = e2
% 231.40/42.61  | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | REF_CLOSE: (28), (87), (108) are inconsistent by sub-proof
% 231.40/42.61  | | | | | | | | | | | | | | |            #2440.
% 231.40/42.61  | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | Case 2:
% 231.40/42.61  | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | |   (109)  all_57_10 = e2 & op(e2, e0) = e2
% 231.40/42.61  | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | ALPHA: (109) implies:
% 231.40/42.61  | | | | | | | | | | | | | | |   (110)  all_57_10 = e2
% 231.40/42.61  | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | BETA: splitting (14) gives:
% 231.40/42.61  | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | Case 1:
% 231.40/42.61  | | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | |   (111)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 231.40/42.61  | | | | | | | | | | | | | | | |            & op(e3, e2) = e2)
% 231.40/42.61  | | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | | BETA: splitting (111) gives:
% 231.40/42.61  | | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | | Case 1:
% 231.40/42.61  | | | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | | |   (112)  all_57_0 = e2 & op(e3, e3) = e2
% 231.40/42.61  | | | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | | | ALPHA: (112) implies:
% 231.40/42.61  | | | | | | | | | | | | | | | | |   (113)  op(e3, e3) = e2
% 231.40/42.61  | | | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (18), (22), (113) are inconsistent by
% 231.40/42.61  | | | | | | | | | | | | | | | | |            sub-proof #2490.
% 231.40/42.61  | | | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | | Case 2:
% 231.40/42.61  | | | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | | |   (114)  all_57_1 = e2 & op(e3, e2) = e2
% 231.40/42.61  | | | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | | | ALPHA: (114) implies:
% 231.40/42.61  | | | | | | | | | | | | | | | | |   (115)  all_57_1 = e2
% 231.40/42.61  | | | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | | | BETA: splitting (1) gives:
% 231.40/42.61  | | | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | | | Case 1:
% 231.40/42.61  | | | | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | | | |   (116)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 231.40/42.61  | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 231.40/42.61  | | | | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | | | | BETA: splitting (116) gives:
% 231.40/42.61  | | | | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | | | | Case 1:
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | | | | |   (117)  all_57_2 = e1 & op(e2, e3) = e1
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | ALPHA: (117) implies:
% 231.40/42.61  | | | | | | | | | | | | | | | | | | |   (118)  all_57_2 = e1
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | BETA: splitting (39) gives:
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | Case 1:
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | |   (119)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e2)
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | | BETA: splitting (119) gives:
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | | |   (120)  all_57_0 = e2 & op(e3, e3) = e2
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | | | ALPHA: (120) implies:
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | | |   (121)  op(e3, e3) = e2
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (18), (22), (121) are inconsistent by
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | | |            sub-proof #2490.
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | | |   (122)  all_57_2 = e2 & op(e2, e3) = e2
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | | | ALPHA: (122) implies:
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | | |   (123)  all_57_2 = e2
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (118), (123) imply:
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | | |   (124)  e2 = e1
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (11), (13), (14),
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | | |            (15), (16), (17), (18), (20), (21), (22), (24),
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | | |            (26), (27), (28), (30), (31), (32), (34), (35),
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | | |            (37), (39), (40), (41), (42), (43), (44), (45),
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | | |            (46), (55), (57), (58), (59), (73), (82), (87),
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | | |            (104), (110), (115), (124) are inconsistent by
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | | |            sub-proof #1454.
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | | End of split
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | Case 2:
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | |   (125)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e3) = e2)
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | | BETA: splitting (125) gives:
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | | |   (126)  all_57_6 = e2 & op(e1, e3) = e2
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | | | ALPHA: (126) implies:
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | | |   (127)  all_57_6 = e2
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (11), (13), (14),
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | | |            (15), (16), (17), (18), (20), (21), (22), (24),
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | | |            (26), (27), (28), (30), (31), (32), (34), (35),
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | | |            (37), (39), (40), (41), (42), (43), (44), (45),
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | | |            (46), (55), (57), (58), (105), (127) are
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1461.
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with e1, e2, e1, e1, simplifying
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | | |              with (59), (105) gives:
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | | |   (128)  e2 = e1
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (11), (13), (14),
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | | |            (15), (16), (17), (18), (20), (21), (22), (24),
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | | |            (26), (27), (28), (30), (31), (32), (34), (35),
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | | |            (37), (39), (40), (41), (42), (43), (44), (45),
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | | |            (46), (55), (57), (58), (59), (73), (82), (87),
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | | |            (104), (110), (115), (128) are inconsistent by
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | | |            sub-proof #1454.
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | | End of split
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | End of split
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | | | | Case 2:
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | | | | |   (129)  all_57_3 = e1 & op(e2, e2) = e1
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (13), (14), (16), (18), (22), (28), (55),
% 231.40/42.61  | | | | | | | | | | | | | | | | | | |            (57), (58), (76), (87), (129) are inconsistent by
% 231.40/42.61  | | | | | | | | | | | | | | | | | | |            sub-proof #2095.
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | | | | End of split
% 231.40/42.61  | | | | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | | | Case 2:
% 231.40/42.61  | | | | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | | | |   (130)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 231.40/42.61  | | | | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 231.40/42.61  | | | | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | | | | BETA: splitting (130) gives:
% 231.40/42.61  | | | | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | | | | Case 1:
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | | | | |   (131)  all_57_5 = e1 & op(e2, e1) = e1
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (55), (131) are inconsistent by sub-proof
% 231.40/42.61  | | | | | | | | | | | | | | | | | | |            #2376.
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | | | | Case 2:
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | | | | |   (132)  all_57_10 = e1 & op(e2, e0) = e1
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | ALPHA: (132) implies:
% 231.40/42.61  | | | | | | | | | | | | | | | | | | |   (133)  all_57_10 = e1
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (110), (133) imply:
% 231.40/42.61  | | | | | | | | | | | | | | | | | | |   (134)  e2 = e1
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (11), (13), (14),
% 231.40/42.61  | | | | | | | | | | | | | | | | | | |            (15), (16), (17), (18), (20), (21), (22), (24),
% 231.40/42.61  | | | | | | | | | | | | | | | | | | |            (26), (27), (28), (30), (31), (32), (34), (35),
% 231.40/42.61  | | | | | | | | | | | | | | | | | | |            (37), (39), (40), (41), (42), (43), (44), (45),
% 231.40/42.61  | | | | | | | | | | | | | | | | | | |            (46), (55), (57), (58), (59), (73), (82), (87),
% 231.40/42.61  | | | | | | | | | | | | | | | | | | |            (104), (110), (115), (134) are inconsistent by
% 231.40/42.61  | | | | | | | | | | | | | | | | | | |            sub-proof #1454.
% 231.40/42.61  | | | | | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | | | | End of split
% 231.40/42.61  | | | | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | | | End of split
% 231.40/42.61  | | | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | | End of split
% 231.40/42.61  | | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | Case 2:
% 231.40/42.61  | | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | |   (135)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 231.40/42.61  | | | | | | | | | | | | | | | |            & op(e3, e0) = e2)
% 231.40/42.61  | | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | | REF_CLOSE: (1), (16), (18), (21), (27), (28), (35), (55),
% 231.40/42.61  | | | | | | | | | | | | | | | |            (57), (58), (82), (87), (104), (110), (135) are
% 231.40/42.61  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1455.
% 231.40/42.61  | | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | End of split
% 231.40/42.61  | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | End of split
% 231.40/42.61  | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | Case 2:
% 231.40/42.61  | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | |   (136)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 231.40/42.61  | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 231.40/42.61  | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | BETA: splitting (136) gives:
% 231.40/42.61  | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | Case 1:
% 231.40/42.61  | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | |   (137)  all_57_11 = e2 & op(e1, e0) = e2
% 231.40/42.61  | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | ALPHA: (137) implies:
% 231.40/42.61  | | | | | | | | | | | | | | |   (138)  all_57_11 = e2
% 231.40/42.61  | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | COMBINE_EQS: (73), (138) imply:
% 231.40/42.61  | | | | | | | | | | | | | | |   (139)  e2 = e1
% 231.40/42.61  | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | SIMP: (139) implies:
% 231.40/42.61  | | | | | | | | | | | | | | |   (140)  e2 = e1
% 231.40/42.61  | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | COMBINE_EQS: (104), (140) imply:
% 231.40/42.61  | | | | | | | | | | | | | | |   (141)  all_57_8 = e1
% 231.40/42.61  | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (11),
% 231.40/42.61  | | | | | | | | | | | | | | |            (12), (13), (14), (15), (16), (17), (18), (20),
% 231.40/42.61  | | | | | | | | | | | | | | |            (21), (22), (24), (25), (26), (27), (28), (29),
% 231.40/42.61  | | | | | | | | | | | | | | |            (30), (31), (32), (34), (35), (37), (39), (40),
% 231.40/42.61  | | | | | | | | | | | | | | |            (41), (42), (43), (44), (45), (46), (53), (55),
% 231.40/42.61  | | | | | | | | | | | | | | |            (57), (58), (59), (141) are inconsistent by
% 231.40/42.61  | | | | | | | | | | | | | | |            sub-proof #1459.
% 231.40/42.61  | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | Case 2:
% 231.40/42.61  | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | |   (142)  all_57_15 = e2 & op(e0, e0) = e2
% 231.40/42.61  | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | REF_CLOSE: (18), (24), (142) are inconsistent by sub-proof
% 231.40/42.61  | | | | | | | | | | | | | | |            #2323.
% 231.40/42.61  | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | End of split
% 231.40/42.61  | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | End of split
% 231.40/42.61  | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | Case 2:
% 231.40/42.61  | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | |   (143)  all_57_11 = e2 & op(e1, e0) = e2
% 231.40/42.61  | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | REF_CLOSE: (57), (73), (143) are inconsistent by sub-proof
% 231.40/42.61  | | | | | | | | | | | | |            #2048.
% 231.40/42.61  | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | End of split
% 231.40/42.61  | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | End of split
% 231.40/42.61  | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | End of split
% 231.40/42.61  | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | End of split
% 231.40/42.61  | | | | | | | | | 
% 231.40/42.61  | | | | | | | | End of split
% 231.40/42.61  | | | | | | | | 
% 231.40/42.61  | | | | | | | End of split
% 231.40/42.61  | | | | | | | 
% 231.40/42.61  | | | | | | Case 2:
% 231.40/42.61  | | | | | | | 
% 231.40/42.61  | | | | | | |   (144)  all_57_5 = e1 & op(e2, e1) = e1
% 231.40/42.61  | | | | | | | 
% 231.40/42.61  | | | | | | | ALPHA: (144) implies:
% 231.40/42.61  | | | | | | |   (145)  all_57_5 = e1
% 231.40/42.61  | | | | | | | 
% 231.40/42.61  | | | | | | | REF_CLOSE: (27), (55), (145) are inconsistent by sub-proof #2382.
% 231.40/42.61  | | | | | | | 
% 231.40/42.61  | | | | | | End of split
% 231.40/42.61  | | | | | | 
% 231.40/42.61  | | | | | Case 2:
% 231.40/42.61  | | | | | | 
% 231.40/42.61  | | | | | |   (146)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 &
% 231.40/42.61  | | | | | |            op(e0, e1) = e1)
% 231.40/42.61  | | | | | | 
% 231.40/42.61  | | | | | | BETA: splitting (146) gives:
% 231.40/42.61  | | | | | | 
% 231.40/42.61  | | | | | | Case 1:
% 231.40/42.61  | | | | | | | 
% 231.40/42.61  | | | | | | |   (147)  all_57_8 = e1 & op(e1, e1) = e1
% 231.40/42.61  | | | | | | | 
% 231.40/42.61  | | | | | | | ALPHA: (147) implies:
% 231.40/42.61  | | | | | | |   (148)  all_57_8 = e1
% 231.40/42.61  | | | | | | | 
% 231.40/42.61  | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (11), (12),
% 231.40/42.61  | | | | | | |            (13), (14), (15), (16), (17), (18), (20), (21), (22),
% 231.40/42.61  | | | | | | |            (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 231.40/42.61  | | | | | | |            (34), (35), (37), (39), (40), (41), (42), (43), (44),
% 231.40/42.61  | | | | | | |            (45), (46), (53), (55), (57), (58), (59), (148) are
% 231.40/42.61  | | | | | | |            inconsistent by sub-proof #1459.
% 231.40/42.61  | | | | | | | 
% 231.40/42.61  | | | | | | Case 2:
% 231.40/42.61  | | | | | | | 
% 231.40/42.61  | | | | | | |   (149)  all_57_14 = e1 & op(e0, e1) = e1
% 231.40/42.61  | | | | | | | 
% 231.40/42.61  | | | | | | | ALPHA: (149) implies:
% 231.40/42.61  | | | | | | |   (150)  all_57_14 = e1
% 231.40/42.61  | | | | | | | 
% 231.40/42.61  | | | | | | | BETA: splitting (17) gives:
% 231.40/42.61  | | | | | | | 
% 231.40/42.61  | | | | | | | Case 1:
% 231.40/42.61  | | | | | | | | 
% 231.40/42.61  | | | | | | | |   (151)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 &
% 231.40/42.61  | | | | | | | |            op(e2, e1) = e0)
% 231.40/42.61  | | | | | | | | 
% 231.40/42.61  | | | | | | | | BETA: splitting (151) gives:
% 231.40/42.61  | | | | | | | | 
% 231.40/42.61  | | | | | | | | Case 1:
% 231.40/42.61  | | | | | | | | | 
% 231.40/42.61  | | | | | | | | |   (152)  all_57_4 = e0 & op(e3, e1) = e0
% 231.40/42.61  | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | ALPHA: (152) implies:
% 231.40/42.61  | | | | | | | | |   (153)  all_57_4 = e0
% 231.40/42.61  | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | BETA: splitting (32) gives:
% 231.40/42.61  | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | Case 1:
% 231.40/42.61  | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | |   (154)  all_57_15 = e0 & op(e0, e0) = e0
% 231.40/42.61  | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | ALPHA: (154) implies:
% 231.40/42.61  | | | | | | | | | |   (155)  op(e0, e0) = e0
% 231.40/42.61  | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | REF_CLOSE: (7), (20), (30), (155) are inconsistent by
% 231.40/42.61  | | | | | | | | | |            sub-proof #2304.
% 231.40/42.61  | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | Case 2:
% 231.40/42.61  | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | |   (156)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 231.40/42.61  | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 231.40/42.61  | | | | | | | | | |              op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 231.40/42.61  | | | | | | | | | |                e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 231.40/42.61  | | | | | | | | | |              e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 231.40/42.61  | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | ALPHA: (156) implies:
% 231.40/42.61  | | | | | | | | | |   (157)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 231.40/42.61  | | | | | | | | | |            e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 231.40/42.61  | | | | | | | | | |              e1) = e0)
% 231.40/42.61  | | | | | | | | | |   (158)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0
% 231.40/42.61  | | | | | | | | | |            & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.40/42.61  | | | | | | | | | |            = e0)
% 231.40/42.61  | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | BETA: splitting (157) gives:
% 231.40/42.61  | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | Case 1:
% 231.40/42.61  | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | |   (159)  all_57_12 = e0 & op(e0, e3) = e0
% 231.40/42.61  | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | ALPHA: (159) implies:
% 231.40/42.61  | | | | | | | | | | |   (160)  all_57_12 = e0
% 231.40/42.61  | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | BETA: splitting (4) gives:
% 231.40/42.61  | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | Case 1:
% 231.40/42.61  | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | |   (161)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 231.40/42.61  | | | | | | | | | | | |            & op(e2, e3) = e1)
% 231.40/42.61  | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | BETA: splitting (161) gives:
% 231.40/42.61  | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | Case 1:
% 231.40/42.61  | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | |   (162)  all_57_0 = e1 & op(e3, e3) = e1
% 231.40/42.61  | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | ALPHA: (162) implies:
% 231.40/42.61  | | | | | | | | | | | | |   (163)  op(e3, e3) = e1
% 231.40/42.61  | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | REF_CLOSE: (7), (22), (55), (163) are inconsistent by
% 231.40/42.61  | | | | | | | | | | | | |            sub-proof #2495.
% 231.40/42.61  | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | Case 2:
% 231.40/42.61  | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | |   (164)  all_57_2 = e1 & op(e2, e3) = e1
% 231.40/42.61  | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | ALPHA: (164) implies:
% 231.40/42.61  | | | | | | | | | | | | |   (165)  all_57_2 = e1
% 231.40/42.61  | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | BETA: splitting (158) gives:
% 231.40/42.61  | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | Case 1:
% 231.40/42.61  | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | |   (166)  all_57_9 = e0 & op(e3, e0) = e0
% 231.40/42.61  | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | ALPHA: (166) implies:
% 231.40/42.61  | | | | | | | | | | | | | |   (167)  all_57_9 = e0
% 231.40/42.61  | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | REF_CLOSE: (7), (13), (14), (18), (22), (28), (55), (57),
% 231.40/42.61  | | | | | | | | | | | | | |            (58), (153), (167) are inconsistent by sub-proof
% 231.40/42.61  | | | | | | | | | | | | | |            #2436.
% 231.40/42.61  | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | Case 2:
% 231.40/42.61  | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | |   (168)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 =
% 231.40/42.61  | | | | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 231.40/42.61  | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | BETA: splitting (168) gives:
% 231.40/42.61  | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | Case 1:
% 231.40/42.61  | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | |   (169)  all_57_10 = e0 & op(e2, e0) = e0
% 231.40/42.61  | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | ALPHA: (169) implies:
% 231.40/42.61  | | | | | | | | | | | | | | |   (170)  all_57_10 = e0
% 231.40/42.61  | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | REF_CLOSE: (1), (16), (18), (27), (28), (35), (55), (57),
% 231.40/42.61  | | | | | | | | | | | | | | |            (58), (170) are inconsistent by sub-proof #1518.
% 231.40/42.61  | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | Case 2:
% 231.40/42.61  | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | |   (171)  all_57_11 = e0 & op(e1, e0) = e0
% 231.40/42.61  | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | | REF_CLOSE: (1), (16), (18), (27), (28), (35), (55), (57),
% 231.40/42.61  | | | | | | | | | | | | | | |            (58), (73), (165), (171) are inconsistent by
% 231.40/42.61  | | | | | | | | | | | | | | |            sub-proof #1465.
% 231.40/42.61  | | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | | End of split
% 231.40/42.61  | | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | End of split
% 231.40/42.61  | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | End of split
% 231.40/42.61  | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | Case 2:
% 231.40/42.61  | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | |   (172)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 231.40/42.61  | | | | | | | | | | | |            e1 & op(e0, e3) = e1)
% 231.40/42.61  | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | BETA: splitting (172) gives:
% 231.40/42.61  | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | Case 1:
% 231.40/42.61  | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | |   (173)  all_57_6 = e1 & op(e1, e3) = e1
% 231.40/42.61  | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | ALPHA: (173) implies:
% 231.40/42.61  | | | | | | | | | | | | |   (174)  all_57_6 = e1
% 231.40/42.61  | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (11),
% 231.40/42.61  | | | | | | | | | | | | |            (12), (13), (14), (15), (16), (17), (18), (20),
% 231.40/42.61  | | | | | | | | | | | | |            (21), (22), (24), (25), (26), (27), (28), (29),
% 231.40/42.61  | | | | | | | | | | | | |            (30), (31), (32), (34), (35), (37), (39), (40),
% 231.40/42.61  | | | | | | | | | | | | |            (41), (42), (43), (44), (45), (46), (53), (55),
% 231.40/42.61  | | | | | | | | | | | | |            (57), (58), (59), (160), (174) are inconsistent by
% 231.40/42.61  | | | | | | | | | | | | |            sub-proof #1457.
% 231.40/42.61  | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | Case 2:
% 231.40/42.61  | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | |   (175)  all_57_12 = e1 & op(e0, e3) = e1
% 231.40/42.61  | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | ALPHA: (175) implies:
% 231.40/42.61  | | | | | | | | | | | | |   (176)  all_57_12 = e1
% 231.40/42.61  | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | | REF_CLOSE: (58), (160), (176) are inconsistent by sub-proof
% 231.40/42.61  | | | | | | | | | | | | |            #2014.
% 231.40/42.61  | | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | End of split
% 231.40/42.61  | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | End of split
% 231.40/42.61  | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | Case 2:
% 231.40/42.61  | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | |   (177)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 231.40/42.61  | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 231.40/42.61  | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | BETA: splitting (177) gives:
% 231.40/42.61  | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | Case 1:
% 231.40/42.61  | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | |   (178)  all_57_13 = e0 & op(e0, e2) = e0
% 231.40/42.61  | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | ALPHA: (178) implies:
% 231.40/42.61  | | | | | | | | | | | |   (179)  all_57_13 = e0
% 231.40/42.61  | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | REF_CLOSE: (5), (7), (13), (14), (15), (16), (18), (20),
% 231.40/42.61  | | | | | | | | | | | |            (22), (28), (34), (45), (55), (57), (58), (179)
% 231.40/42.61  | | | | | | | | | | | |            are inconsistent by sub-proof #2091.
% 231.40/42.61  | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | Case 2:
% 231.40/42.61  | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | |   (180)  all_57_14 = e0 & op(e0, e1) = e0
% 231.40/42.61  | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | ALPHA: (180) implies:
% 231.40/42.61  | | | | | | | | | | | |   (181)  all_57_14 = e0
% 231.40/42.61  | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | | REF_CLOSE: (58), (150), (181) are inconsistent by sub-proof
% 231.40/42.61  | | | | | | | | | | | |            #2122.
% 231.40/42.61  | | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | | End of split
% 231.40/42.61  | | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | | End of split
% 231.40/42.61  | | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | End of split
% 231.40/42.61  | | | | | | | | | 
% 231.40/42.61  | | | | | | | | Case 2:
% 231.40/42.61  | | | | | | | | | 
% 231.40/42.61  | | | | | | | | |   (182)  all_57_5 = e0 & op(e2, e1) = e0
% 231.40/42.61  | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | ALPHA: (182) implies:
% 231.40/42.61  | | | | | | | | |   (183)  all_57_5 = e0
% 231.40/42.61  | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | REF_CLOSE: (20), (27), (183) are inconsistent by sub-proof
% 231.40/42.61  | | | | | | | | |            #2471.
% 231.40/42.61  | | | | | | | | | 
% 231.40/42.61  | | | | | | | | End of split
% 231.40/42.61  | | | | | | | | 
% 231.40/42.61  | | | | | | | Case 2:
% 231.40/42.61  | | | | | | | | 
% 231.40/42.61  | | | | | | | |   (184)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 &
% 231.40/42.61  | | | | | | | |            op(e0, e1) = e0)
% 231.40/42.61  | | | | | | | | 
% 231.40/42.61  | | | | | | | | BETA: splitting (184) gives:
% 231.40/42.61  | | | | | | | | 
% 231.40/42.61  | | | | | | | | Case 1:
% 231.40/42.61  | | | | | | | | | 
% 231.40/42.61  | | | | | | | | |   (185)  all_57_8 = e0 & op(e1, e1) = e0
% 231.40/42.61  | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | ALPHA: (185) implies:
% 231.40/42.61  | | | | | | | | |   (186)  op(e1, e1) = e0
% 231.40/42.61  | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (11), (13), (14),
% 231.40/42.61  | | | | | | | | |            (15), (16), (17), (18), (20), (21), (22), (24),
% 231.40/42.61  | | | | | | | | |            (27), (28), (30), (31), (32), (34), (35), (37),
% 231.40/42.61  | | | | | | | | |            (39), (40), (41), (42), (43), (44), (45), (46),
% 231.40/42.61  | | | | | | | | |            (55), (57), (58), (186) are inconsistent by
% 231.40/42.61  | | | | | | | | |            sub-proof #1486.
% 231.40/42.61  | | | | | | | | | 
% 231.40/42.61  | | | | | | | | Case 2:
% 231.40/42.61  | | | | | | | | | 
% 231.40/42.61  | | | | | | | | |   (187)  all_57_14 = e0 & op(e0, e1) = e0
% 231.40/42.61  | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | ALPHA: (187) implies:
% 231.40/42.61  | | | | | | | | |   (188)  all_57_14 = e0
% 231.40/42.61  | | | | | | | | | 
% 231.40/42.61  | | | | | | | | | REF_CLOSE: (58), (150), (188) are inconsistent by sub-proof
% 231.40/42.61  | | | | | | | | |            #2122.
% 231.40/42.61  | | | | | | | | | 
% 231.40/42.61  | | | | | | | | End of split
% 231.40/42.61  | | | | | | | | 
% 231.40/42.61  | | | | | | | End of split
% 231.40/42.61  | | | | | | | 
% 231.40/42.61  | | | | | | End of split
% 231.40/42.61  | | | | | | 
% 231.40/42.61  | | | | | End of split
% 231.40/42.61  | | | | | 
% 231.40/42.61  | | | | End of split
% 231.40/42.61  | | | | 
% 231.40/42.61  | | | End of split
% 231.40/42.61  | | | 
% 231.40/42.61  | | Case 2:
% 231.40/42.61  | | | 
% 231.40/42.61  | | |   (189)  all_55_10 = e0
% 231.40/42.61  | | | 
% 231.40/42.61  | | | REF_CLOSE: (33), (38), (189) are inconsistent by sub-proof #2118.
% 231.40/42.61  | | | 
% 231.40/42.61  | | End of split
% 231.40/42.61  | | 
% 231.40/42.61  | End of split
% 231.40/42.61  | 
% 231.40/42.61  End of proof
% 231.40/42.61  
% 231.40/42.61  Sub-proof #1454 shows that the following formulas are inconsistent:
% 231.40/42.61  ----------------------------------------------------------------
% 231.40/42.61    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.40/42.61         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.40/42.61    (2)   ~ (all_52_7 = e3)
% 231.40/42.61    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.40/42.61         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.40/42.61    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.40/42.61         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.40/42.61    (5)   ~ (e3 = e1)
% 231.40/42.61    (6)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 231.40/42.61         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.40/42.61    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.40/42.61           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.40/42.61    (8)  op(all_52_7, all_52_7) = e0
% 231.40/42.61    (9)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.40/42.61         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.40/42.61    (10)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.40/42.61          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.40/42.61    (11)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.40/42.61          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.40/42.61    (12)  all_57_3 = e0
% 231.40/42.61    (13)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.40/42.61          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.40/42.61    (14)   ~ (e3 = e2)
% 231.40/42.61    (15)   ~ (e3 = e0)
% 231.40/42.61    (16)  all_57_1 = e2
% 231.40/42.61    (17)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.40/42.61          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.40/42.61    (18)  op(e3, e3) = e3
% 231.40/42.61    (19)  all_57_15 = e3
% 231.40/42.61    (20)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.40/42.61          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.40/42.61            e1)
% 231.40/42.61    (21)  all_57_10 = e2
% 231.40/42.61    (22)  all_57_5 = e3
% 231.40/42.61    (23)  all_57_9 = e0
% 231.40/42.61    (24)  op(e1, e1) = e1
% 231.40/42.61    (25)   ~ (e2 = e0)
% 231.40/42.61    (26)   ~ (e1 = e0)
% 231.40/42.61    (27)  all_57_8 = e2
% 231.40/42.61    (28)  op(e0, e0) = e3
% 231.40/42.61    (29)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.40/42.61          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.40/42.61            e2)
% 231.40/42.61    (30)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.40/42.61              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.40/42.61                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.40/42.61                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.40/42.61    (31)  all_57_7 = e3
% 231.40/42.61    (32)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.40/42.61          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.40/42.61    (33)  all_57_11 = e1
% 231.40/42.61    (34)   ~ (e2 = e1)
% 231.40/42.61    (35)  e2 = e1
% 231.40/42.61    (36)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.40/42.61          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.40/42.62    (37)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.40/42.62          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.40/42.62    (38)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.40/42.62          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.40/42.62    (39)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.40/42.62          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.40/42.62    (40)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.40/42.62          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.40/42.62    (41)  all_57_14 = e0
% 231.40/42.62    (42)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 231.40/42.62          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 231.40/42.62    (43)  op(e3, e0) = all_52_7
% 231.40/42.62    (44)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.40/42.62          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.40/42.62    (45)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 231.40/42.62          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 231.40/42.62  
% 231.40/42.62  Begin of proof
% 231.40/42.62  | 
% 231.40/42.62  | COMBINE_EQS: (16), (35) imply:
% 231.40/42.62  |   (46)  all_57_1 = e1
% 231.40/42.62  | 
% 231.40/42.62  | BETA: splitting (10) gives:
% 231.40/42.62  | 
% 231.40/42.62  | Case 1:
% 231.40/42.62  | | 
% 231.40/42.62  | |   (47)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) =
% 231.40/42.62  | |           e2)
% 231.40/42.62  | | 
% 231.40/42.62  | | BETA: splitting (47) gives:
% 231.40/42.62  | | 
% 231.40/42.62  | | Case 1:
% 231.40/42.62  | | | 
% 231.40/42.62  | | |   (48)  all_57_0 = e2 & op(e3, e3) = e2
% 231.40/42.62  | | | 
% 231.40/42.62  | | | ALPHA: (48) implies:
% 231.40/42.62  | | |   (49)  op(e3, e3) = e2
% 231.40/42.62  | | | 
% 231.40/42.62  | | | REF_CLOSE: (7), (14), (18), (49) are inconsistent by sub-proof #2490.
% 231.40/42.62  | | | 
% 231.40/42.62  | | Case 2:
% 231.40/42.62  | | | 
% 231.40/42.62  | | |   (50)  all_57_1 = e2 & op(e3, e2) = e2
% 231.40/42.62  | | | 
% 231.40/42.62  | | | COMBINE_EQS: (16), (46) imply:
% 231.40/42.62  | | |   (51)  e2 = e1
% 231.40/42.62  | | | 
% 231.40/42.62  | | | COMBINE_EQS: (27), (35) imply:
% 231.40/42.62  | | |   (52)  all_57_8 = e1
% 231.40/42.62  | | | 
% 231.40/42.62  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 231.40/42.62  | | |            (13), (14), (15), (17), (18), (19), (20), (21), (22), (24),
% 231.40/42.62  | | |            (25), (26), (28), (29), (30), (31), (32), (33), (34), (36),
% 231.40/42.62  | | |            (37), (38), (39), (40), (42), (43), (44), (45), (52) are
% 231.40/42.62  | | |            inconsistent by sub-proof #1460.
% 231.40/42.62  | | | 
% 231.40/42.62  | | End of split
% 231.40/42.62  | | 
% 231.40/42.62  | Case 2:
% 231.40/42.62  | | 
% 231.40/42.62  | |   (53)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) =
% 231.40/42.62  | |           e2)
% 231.40/42.62  | | 
% 231.40/42.62  | | REF_CLOSE: (1), (5), (12), (14), (17), (21), (22), (23), (25), (26), (27),
% 231.40/42.62  | |            (32), (34), (41), (53) are inconsistent by sub-proof #1455.
% 231.40/42.62  | | 
% 231.40/42.62  | End of split
% 231.40/42.62  | 
% 231.40/42.62  End of proof
% 231.40/42.62  
% 231.40/42.62  Sub-proof #1455 shows that the following formulas are inconsistent:
% 231.40/42.62  ----------------------------------------------------------------
% 231.40/42.62    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.40/42.62         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.40/42.62    (2)   ~ (e3 = e1)
% 231.40/42.62    (3)  all_57_3 = e0
% 231.40/42.62    (4)   ~ (e3 = e2)
% 231.40/42.62    (5)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.40/42.62    (6)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.40/42.62         (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.40/42.62    (7)  all_57_10 = e2
% 231.40/42.62    (8)  all_57_5 = e3
% 231.40/42.62    (9)  all_57_9 = e0
% 231.40/42.62    (10)   ~ (e2 = e0)
% 231.40/42.62    (11)   ~ (e1 = e0)
% 231.40/42.62    (12)  all_57_8 = e2
% 231.40/42.62    (13)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.40/42.62          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.40/42.62    (14)   ~ (e2 = e1)
% 231.40/42.62    (15)  all_57_14 = e0
% 231.40/42.62  
% 231.40/42.62  Begin of proof
% 231.40/42.62  | 
% 231.40/42.62  | BETA: splitting (5) gives:
% 231.40/42.62  | 
% 231.40/42.62  | Case 1:
% 231.40/42.62  | | 
% 231.40/42.62  | |   (16)  all_57_4 = e2 & op(e3, e1) = e2
% 231.40/42.62  | | 
% 231.40/42.62  | | ALPHA: (16) implies:
% 231.40/42.62  | |   (17)  all_57_4 = e2
% 231.40/42.62  | | 
% 231.40/42.62  | | REF_CLOSE: (2), (6), (8), (11), (12), (14), (15), (17) are inconsistent by
% 231.40/42.62  | |            sub-proof #1456.
% 231.40/42.62  | | 
% 231.40/42.62  | Case 2:
% 231.40/42.62  | | 
% 231.40/42.62  | |   (18)  all_57_9 = e2 & op(e3, e0) = e2
% 231.40/42.62  | | 
% 231.40/42.62  | | ALPHA: (18) implies:
% 231.40/42.62  | |   (19)  all_57_9 = e2
% 231.40/42.62  | | 
% 231.40/42.62  | | COMBINE_EQS: (9), (19) imply:
% 231.40/42.62  | |   (20)  e2 = e0
% 231.40/42.62  | | 
% 231.40/42.62  | | REF_CLOSE: (1), (2), (3), (4), (7), (8), (10), (11), (13), (14), (20) are
% 231.40/42.62  | |            inconsistent by sub-proof #1517.
% 231.40/42.62  | | 
% 231.40/42.62  | End of split
% 231.40/42.62  | 
% 231.40/42.62  End of proof
% 231.40/42.62  
% 231.40/42.62  Sub-proof #1456 shows that the following formulas are inconsistent:
% 231.40/42.62  ----------------------------------------------------------------
% 231.40/42.62    (1)   ~ (e3 = e1)
% 231.40/42.62    (2)  all_57_4 = e2
% 231.40/42.62    (3)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.40/42.62         (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.40/42.62    (4)  all_57_5 = e3
% 231.40/42.62    (5)   ~ (e1 = e0)
% 231.40/42.62    (6)  all_57_8 = e2
% 231.40/42.62    (7)   ~ (e2 = e1)
% 231.40/42.62    (8)  all_57_14 = e0
% 231.40/42.62  
% 231.40/42.62  Begin of proof
% 231.40/42.62  | 
% 231.40/42.62  | BETA: splitting (3) gives:
% 231.40/42.62  | 
% 231.40/42.62  | Case 1:
% 231.40/42.62  | | 
% 231.40/42.62  | |   (9)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1)
% 231.40/42.62  | | 
% 231.40/42.62  | | BETA: splitting (9) gives:
% 231.40/42.62  | | 
% 231.40/42.62  | | Case 1:
% 231.40/42.62  | | | 
% 231.40/42.62  | | |   (10)  all_57_4 = e1 & op(e3, e1) = e1
% 231.40/42.62  | | | 
% 231.40/42.62  | | | REF_CLOSE: (2), (7), (10) are inconsistent by sub-proof #2452.
% 231.40/42.62  | | | 
% 231.40/42.62  | | Case 2:
% 231.40/42.62  | | | 
% 231.40/42.62  | | |   (11)  all_57_5 = e1 & op(e2, e1) = e1
% 231.40/42.62  | | | 
% 231.40/42.62  | | | REF_CLOSE: (1), (4), (11) are inconsistent by sub-proof #2376.
% 231.40/42.62  | | | 
% 231.40/42.62  | | End of split
% 231.40/42.62  | | 
% 231.40/42.62  | Case 2:
% 231.40/42.62  | | 
% 231.40/42.62  | |   (12)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) =
% 231.40/42.62  | |           e1)
% 231.40/42.62  | | 
% 231.40/42.62  | | REF_CLOSE: (5), (6), (7), (8), (12) are inconsistent by sub-proof #1490.
% 231.40/42.62  | | 
% 231.40/42.62  | End of split
% 231.40/42.62  | 
% 231.40/42.62  End of proof
% 231.40/42.62  
% 231.40/42.62  Sub-proof #1457 shows that the following formulas are inconsistent:
% 231.40/42.62  ----------------------------------------------------------------
% 231.40/42.62    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.40/42.62         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.40/42.62    (2)  all_57_12 = e0
% 231.40/42.62    (3)  op(e3, e1) = all_52_5
% 231.40/42.62    (4)   ~ (all_52_7 = e3)
% 231.40/42.62    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.40/42.62         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.40/42.62    (6)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.40/42.62         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.40/42.62    (7)   ~ (e3 = e1)
% 231.40/42.62    (8)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 231.40/42.62         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.40/42.62    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.40/42.62           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.40/42.62    (10)   ~ (all_52_3 = e0)
% 231.40/42.62    (11)  op(all_52_7, all_52_7) = e0
% 231.40/42.62    (12)  op(e3, e2) = all_52_3
% 231.40/42.62    (13)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.40/42.62          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.40/42.62    (14)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.40/42.62          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.40/42.62    (15)  all_57_6 = e1
% 231.40/42.62    (16)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.40/42.62          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.40/42.62    (17)  all_57_3 = e0
% 231.40/42.62    (18)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.40/42.62          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.40/42.62    (19)   ~ (e3 = e2)
% 231.40/42.62    (20)   ~ (e3 = e0)
% 231.40/42.62    (21)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.40/42.62          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.40/42.62    (22)  op(e3, e3) = e3
% 231.40/42.62    (23)  all_57_15 = e3
% 231.40/42.62    (24)   ~ (all_52_3 = e3)
% 231.40/42.62    (25)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.40/42.62          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.40/42.62            e1)
% 231.40/42.62    (26)  all_57_5 = e3
% 231.40/42.62    (27)  op(e1, e1) = e1
% 231.40/42.62    (28)   ~ (e2 = e0)
% 231.40/42.62    (29)   ~ (e1 = e0)
% 231.40/42.62    (30)   ~ (all_52_3 = all_52_7)
% 231.40/42.62    (31)  op(e0, e0) = e3
% 231.40/42.62    (32)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.40/42.62          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.40/42.62            e2)
% 231.40/42.62    (33)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.40/42.62              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.40/42.62                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.40/42.62                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.40/42.62    (34)  all_57_7 = e3
% 231.40/42.62    (35)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.40/42.62          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.40/42.62    (36)   ~ (all_52_5 = e1)
% 231.40/42.62    (37)   ~ (e2 = e1)
% 231.40/42.62    (38)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.40/42.62          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.40/42.62    (39)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.40/42.62          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.40/42.62    (40)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.40/42.62          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.40/42.62    (41)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.40/42.62          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.40/42.62    (42)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.40/42.62          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.40/42.62    (43)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 231.40/42.62          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 231.40/42.62    (44)  op(e3, e0) = all_52_7
% 231.40/42.62    (45)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.40/42.62          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.40/42.62    (46)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 231.40/42.62          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 231.40/42.62  
% 231.40/42.62  Begin of proof
% 231.40/42.62  | 
% 231.40/42.62  | BETA: splitting (21) gives:
% 231.40/42.62  | 
% 231.40/42.62  | Case 1:
% 231.40/42.62  | | 
% 231.40/42.62  | |   (47)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) =
% 231.40/42.62  | |           e1)
% 231.40/42.62  | | 
% 231.40/42.62  | | BETA: splitting (47) gives:
% 231.40/42.62  | | 
% 231.40/42.62  | | Case 1:
% 231.40/42.62  | | | 
% 231.40/42.62  | | |   (48)  all_57_4 = e1 & op(e3, e1) = e1
% 231.40/42.62  | | | 
% 231.40/42.62  | | | ALPHA: (48) implies:
% 231.40/42.62  | | |   (49)  all_57_4 = e1
% 231.40/42.62  | | | 
% 231.40/42.62  | | | BETA: splitting (16) gives:
% 231.40/42.62  | | | 
% 231.40/42.62  | | | Case 1:
% 231.40/42.62  | | | | 
% 231.40/42.62  | | | |   (50)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2)
% 231.40/42.62  | | | |           = e0)
% 231.40/42.62  | | | | 
% 231.40/42.62  | | | | REF_CLOSE: (6), (7), (9), (17), (19), (20), (22), (28), (29), (34),
% 231.40/42.62  | | | |            (37), (45), (50) are inconsistent by sub-proof #2097.
% 231.40/42.62  | | | | 
% 231.40/42.62  | | | Case 2:
% 231.40/42.62  | | | | 
% 231.40/42.62  | | | |   (51)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0)
% 231.40/42.62  | | | |           = e0)
% 231.40/42.62  | | | | 
% 231.40/42.62  | | | | BETA: splitting (51) gives:
% 231.40/42.62  | | | | 
% 231.40/42.62  | | | | Case 1:
% 231.40/42.62  | | | | | 
% 231.40/42.62  | | | | |   (52)  all_57_4 = e0 & op(e3, e1) = e0
% 231.40/42.62  | | | | | 
% 231.40/42.62  | | | | | REF_CLOSE: (29), (49), (52) are inconsistent by sub-proof #2429.
% 231.40/42.62  | | | | | 
% 231.40/42.62  | | | | Case 2:
% 231.40/42.62  | | | | | 
% 231.40/42.62  | | | | |   (53)  all_57_9 = e0 & op(e3, e0) = e0
% 231.40/42.62  | | | | | 
% 231.40/42.62  | | | | | ALPHA: (53) implies:
% 231.40/42.62  | | | | |   (54)  all_57_9 = e0
% 231.40/42.62  | | | | |   (55)  op(e3, e0) = e0
% 231.40/42.62  | | | | | 
% 231.40/42.62  | | | | | BETA: splitting (8) gives:
% 231.40/42.62  | | | | | 
% 231.40/42.62  | | | | | Case 1:
% 231.40/42.62  | | | | | | 
% 231.40/42.62  | | | | | |   (56)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1,
% 231.40/42.62  | | | | | |             e2) = e0)
% 231.40/42.62  | | | | | | 
% 231.40/42.62  | | | | | | BETA: splitting (56) gives:
% 231.40/42.62  | | | | | | 
% 231.40/42.62  | | | | | | Case 1:
% 231.40/42.62  | | | | | | | 
% 231.40/42.62  | | | | | | |   (57)  all_57_6 = e0 & op(e1, e3) = e0
% 231.40/42.62  | | | | | | | 
% 231.40/42.62  | | | | | | | ALPHA: (57) implies:
% 231.40/42.62  | | | | | | |   (58)  all_57_6 = e0
% 231.40/42.62  | | | | | | | 
% 231.40/42.62  | | | | | | | COMBINE_EQS: (15), (58) imply:
% 231.40/42.62  | | | | | | |   (59)  e1 = e0
% 231.40/42.62  | | | | | | | 
% 231.40/42.62  | | | | | | | COMBINE_EQS: (49), (59) imply:
% 231.40/42.62  | | | | | | |   (60)  all_57_4 = e0
% 231.40/42.62  | | | | | | | 
% 231.40/42.62  | | | | | | | REF_CLOSE: (7), (9), (13), (14), (19), (22), (28), (29), (37),
% 231.40/42.62  | | | | | | |            (54), (60) are inconsistent by sub-proof #2436.
% 231.40/42.62  | | | | | | | 
% 231.40/42.62  | | | | | | Case 2:
% 231.40/42.62  | | | | | | | 
% 231.40/42.62  | | | | | | |   (61)  all_57_7 = e0 & op(e1, e2) = e0
% 231.40/42.62  | | | | | | | 
% 231.40/42.62  | | | | | | | REF_CLOSE: (20), (34), (61) are inconsistent by sub-proof #2042.
% 231.40/42.62  | | | | | | | 
% 231.40/42.62  | | | | | | End of split
% 231.40/42.62  | | | | | | 
% 231.40/42.62  | | | | | Case 2:
% 231.40/42.62  | | | | | | 
% 231.40/42.62  | | | | | |   (62)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1,
% 231.40/42.62  | | | | | |             e0) = e0)
% 231.40/42.62  | | | | | | 
% 231.40/42.62  | | | | | | BETA: splitting (62) gives:
% 231.40/42.62  | | | | | | 
% 231.40/42.62  | | | | | | Case 1:
% 231.40/42.62  | | | | | | | 
% 231.40/42.62  | | | | | | |   (63)  all_57_8 = e0 & op(e1, e1) = e0
% 231.40/42.62  | | | | | | | 
% 231.40/42.62  | | | | | | | ALPHA: (63) implies:
% 231.40/42.62  | | | | | | |   (64)  op(e1, e1) = e0
% 231.40/42.62  | | | | | | | 
% 231.40/42.62  | | | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (9), (11), (14), (16),
% 231.40/42.62  | | | | | | |            (17), (19), (20), (21), (22), (23), (26), (28), (29),
% 231.40/42.62  | | | | | | |            (31), (32), (34), (35), (37), (38), (39), (41), (42),
% 231.40/42.62  | | | | | | |            (43), (44), (45), (46), (54), (55), (64) are
% 231.40/42.62  | | | | | | |            inconsistent by sub-proof #1504.
% 231.40/42.62  | | | | | | | 
% 231.40/42.62  | | | | | | Case 2:
% 231.40/42.62  | | | | | | | 
% 231.40/42.62  | | | | | | |   (65)  all_57_11 = e0 & op(e1, e0) = e0
% 231.40/42.62  | | | | | | | 
% 231.40/42.62  | | | | | | | ALPHA: (65) implies:
% 231.40/42.62  | | | | | | |   (66)  all_57_11 = e0
% 231.40/42.62  | | | | | | | 
% 231.40/42.62  | | | | | | | BETA: splitting (18) gives:
% 231.40/42.62  | | | | | | | 
% 231.40/42.62  | | | | | | | Case 1:
% 231.40/42.62  | | | | | | | | 
% 231.40/42.62  | | | | | | | |   (67)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 &
% 231.40/42.62  | | | | | | | |           op(e2, e1) = e0)
% 231.40/42.62  | | | | | | | | 
% 231.40/42.62  | | | | | | | | BETA: splitting (67) gives:
% 231.40/42.62  | | | | | | | | 
% 231.40/42.62  | | | | | | | | Case 1:
% 231.40/42.62  | | | | | | | | | 
% 231.40/42.62  | | | | | | | | |   (68)  all_57_4 = e0 & op(e3, e1) = e0
% 231.40/42.62  | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | ALPHA: (68) implies:
% 231.40/42.62  | | | | | | | | |   (69)  all_57_4 = e0
% 231.40/42.62  | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | REF_CLOSE: (7), (9), (13), (14), (19), (22), (28), (29), (37),
% 231.40/42.62  | | | | | | | | |            (54), (69) are inconsistent by sub-proof #2436.
% 231.40/42.62  | | | | | | | | | 
% 231.40/42.62  | | | | | | | | Case 2:
% 231.40/42.62  | | | | | | | | | 
% 231.40/42.62  | | | | | | | | |   (70)  all_57_5 = e0 & op(e2, e1) = e0
% 231.40/42.62  | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | REF_CLOSE: (20), (26), (70) are inconsistent by sub-proof
% 231.40/42.62  | | | | | | | | |            #2414.
% 231.40/42.62  | | | | | | | | | 
% 231.40/42.62  | | | | | | | | End of split
% 231.40/42.62  | | | | | | | | 
% 231.40/42.62  | | | | | | | Case 2:
% 231.40/42.62  | | | | | | | | 
% 231.40/42.62  | | | | | | | |   (71)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 &
% 231.40/42.62  | | | | | | | |           op(e0, e1) = e0)
% 231.40/42.62  | | | | | | | | 
% 231.40/42.62  | | | | | | | | BETA: splitting (71) gives:
% 231.40/42.62  | | | | | | | | 
% 231.40/42.62  | | | | | | | | Case 1:
% 231.40/42.62  | | | | | | | | | 
% 231.40/42.62  | | | | | | | | |   (72)  all_57_8 = e0 & op(e1, e1) = e0
% 231.40/42.62  | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | ALPHA: (72) implies:
% 231.40/42.62  | | | | | | | | |   (73)  op(e1, e1) = e0
% 231.40/42.62  | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (9), (11), (14),
% 231.40/42.62  | | | | | | | | |            (16), (17), (19), (20), (21), (22), (23), (26),
% 231.40/42.62  | | | | | | | | |            (28), (29), (31), (32), (34), (35), (37), (38),
% 231.40/42.62  | | | | | | | | |            (39), (41), (42), (43), (44), (45), (46), (54),
% 231.40/42.62  | | | | | | | | |            (55), (73) are inconsistent by sub-proof #1504.
% 231.40/42.62  | | | | | | | | | 
% 231.40/42.62  | | | | | | | | Case 2:
% 231.40/42.62  | | | | | | | | | 
% 231.40/42.62  | | | | | | | | |   (74)  all_57_14 = e0 & op(e0, e1) = e0
% 231.40/42.62  | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | ALPHA: (74) implies:
% 231.40/42.62  | | | | | | | | |   (75)  all_57_14 = e0
% 231.40/42.62  | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | BETA: splitting (25) gives:
% 231.40/42.62  | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | Case 1:
% 231.40/42.62  | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | |   (76)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1
% 231.40/42.62  | | | | | | | | | |           & op(e0, e2) = e1)
% 231.40/42.62  | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | BETA: splitting (76) gives:
% 231.40/42.62  | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | Case 1:
% 231.40/42.62  | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | |   (77)  all_57_12 = e1 & op(e0, e3) = e1
% 231.40/42.62  | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | ALPHA: (77) implies:
% 231.40/42.62  | | | | | | | | | | |   (78)  all_57_12 = e1
% 231.40/42.62  | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | COMBINE_EQS: (2), (78) imply:
% 231.40/42.62  | | | | | | | | | | |   (79)  e1 = e0
% 231.40/42.62  | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | SIMP: (79) implies:
% 231.40/42.62  | | | | | | | | | | |   (80)  e1 = e0
% 231.40/42.62  | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | COMBINE_EQS: (49), (80) imply:
% 231.40/42.62  | | | | | | | | | | |   (81)  all_57_4 = e0
% 231.40/42.62  | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | REF_CLOSE: (7), (9), (13), (14), (19), (22), (28), (29),
% 231.40/42.62  | | | | | | | | | | |            (37), (54), (81) are inconsistent by sub-proof
% 231.40/42.62  | | | | | | | | | | |            #2436.
% 231.40/42.62  | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | Case 2:
% 231.40/42.62  | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | |   (82)  all_57_13 = e1 & op(e0, e2) = e1
% 231.40/42.62  | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | ALPHA: (82) implies:
% 231.40/42.62  | | | | | | | | | | |   (83)  all_57_13 = e1
% 231.40/42.62  | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | BETA: splitting (46) gives:
% 231.40/42.62  | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | Case 1:
% 231.40/42.62  | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | |   (84)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 231.40/42.62  | | | | | | | | | | | |           & op(e1, e2) = e2)
% 231.40/42.62  | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | BETA: splitting (84) gives:
% 231.40/42.62  | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | Case 1:
% 231.40/42.62  | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | |   (85)  all_57_6 = e2 & op(e1, e3) = e2
% 231.40/42.62  | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | ALPHA: (85) implies:
% 231.40/42.62  | | | | | | | | | | | | |   (86)  all_57_6 = e2
% 231.40/42.62  | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | REF_CLOSE: (1), (2), (5), (7), (9), (17), (19), (22), (23),
% 231.40/42.62  | | | | | | | | | | | | |            (26), (28), (29), (35), (37), (42), (54), (66),
% 231.40/42.62  | | | | | | | | | | | | |            (86) are inconsistent by sub-proof #1511.
% 231.40/42.62  | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | Case 2:
% 231.40/42.62  | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | |   (87)  all_57_7 = e2 & op(e1, e2) = e2
% 231.40/42.62  | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | REF_CLOSE: (19), (34), (87) are inconsistent by sub-proof
% 231.40/42.62  | | | | | | | | | | | | |            #2092.
% 231.40/42.62  | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | End of split
% 231.40/42.62  | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | Case 2:
% 231.40/42.62  | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | |   (88)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 231.40/42.62  | | | | | | | | | | | |           e2 & op(e1, e0) = e2)
% 231.40/42.62  | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | BETA: splitting (88) gives:
% 231.40/42.62  | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | Case 1:
% 231.40/42.62  | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | |   (89)  all_57_8 = e2 & op(e1, e1) = e2
% 231.40/42.62  | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | ALPHA: (89) implies:
% 231.40/42.62  | | | | | | | | | | | | |   (90)  all_57_8 = e2
% 231.40/42.62  | | | | | | | | | | | | |   (91)  op(e1, e1) = e2
% 231.40/42.62  | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | BETA: splitting (14) gives:
% 231.40/42.62  | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | Case 1:
% 231.40/42.62  | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | |   (92)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 231.40/42.62  | | | | | | | | | | | | | |           & op(e3, e2) = e2)
% 231.40/42.62  | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | BETA: splitting (92) gives:
% 231.40/42.62  | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | Case 1:
% 231.40/42.62  | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | |   (93)  all_57_0 = e2 & op(e3, e3) = e2
% 231.40/42.62  | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | ALPHA: (93) implies:
% 231.40/42.62  | | | | | | | | | | | | | | |   (94)  op(e3, e3) = e2
% 231.40/42.62  | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | REF_CLOSE: (9), (19), (22), (94) are inconsistent by
% 231.40/42.62  | | | | | | | | | | | | | | |            sub-proof #2490.
% 231.40/42.62  | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | Case 2:
% 231.40/42.62  | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | |   (95)  all_57_1 = e2 & op(e3, e2) = e2
% 231.40/42.62  | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | ALPHA: (95) implies:
% 231.40/42.62  | | | | | | | | | | | | | | |   (96)  all_57_1 = e2
% 231.40/42.62  | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | BETA: splitting (42) gives:
% 231.40/42.62  | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | Case 1:
% 231.40/42.62  | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | |   (97)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 231.40/42.62  | | | | | | | | | | | | | | | |           e1 & op(e2, e0) = e1)
% 231.40/42.62  | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | BETA: splitting (97) gives:
% 231.40/42.62  | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | Case 1:
% 231.40/42.62  | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | |   (98)  all_57_9 = e1 & op(e3, e0) = e1
% 231.40/42.62  | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | | ALPHA: (98) implies:
% 231.40/42.62  | | | | | | | | | | | | | | | | |   (99)  all_57_9 = e1
% 231.40/42.62  | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | | COMBINE_EQS: (54), (99) imply:
% 231.40/42.62  | | | | | | | | | | | | | | | | |   (100)  e1 = e0
% 231.40/42.62  | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | | SIMP: (100) implies:
% 231.40/42.62  | | | | | | | | | | | | | | | | |   (101)  e1 = e0
% 231.40/42.62  | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | | COMBINE_EQS: (49), (101) imply:
% 231.40/42.62  | | | | | | | | | | | | | | | | |   (102)  all_57_4 = e0
% 231.40/42.62  | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (13), (14), (19), (22), (28), (29),
% 231.40/42.62  | | | | | | | | | | | | | | | | |            (37), (54), (102) are inconsistent by sub-proof
% 231.40/42.62  | | | | | | | | | | | | | | | | |            #2436.
% 231.40/42.62  | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | Case 2:
% 231.40/42.62  | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | |   (103)  all_57_10 = e1 & op(e2, e0) = e1
% 231.40/42.62  | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | | ALPHA: (103) implies:
% 231.40/42.62  | | | | | | | | | | | | | | | | |   (104)  all_57_10 = e1
% 231.40/42.62  | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | | BETA: splitting (35) gives:
% 231.40/42.62  | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | | Case 1:
% 231.40/42.62  | | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | | |   (105)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 231.40/42.62  | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 231.40/42.62  | | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | | | BETA: splitting (105) gives:
% 231.40/42.62  | | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | | | Case 1:
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | | | |   (106)  all_57_2 = e2 & op(e2, e3) = e2
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | ALPHA: (106) implies:
% 231.40/42.62  | | | | | | | | | | | | | | | | | | |   (107)  all_57_2 = e2
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (11),
% 231.40/42.62  | | | | | | | | | | | | | | | | | | |            (13), (14), (15), (16), (17), (18), (19), (20),
% 231.40/42.62  | | | | | | | | | | | | | | | | | | |            (21), (22), (23), (25), (26), (27), (28), (29),
% 231.40/42.62  | | | | | | | | | | | | | | | | | | |            (31), (32), (33), (34), (35), (37), (38), (39),
% 231.40/42.62  | | | | | | | | | | | | | | | | | | |            (40), (41), (42), (43), (44), (45), (46), (90),
% 231.40/42.62  | | | | | | | | | | | | | | | | | | |            (91), (104), (107) are inconsistent by sub-proof
% 231.40/42.62  | | | | | | | | | | | | | | | | | | |            #1476.
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | | | Case 2:
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | | | |   (108)  all_57_3 = e2 & op(e2, e2) = e2
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (17), (19), (28), (34), (37), (83), (96),
% 231.40/42.62  | | | | | | | | | | | | | | | | | | |            (108) are inconsistent by sub-proof #1475.
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | | | End of split
% 231.40/42.62  | | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | | Case 2:
% 231.40/42.62  | | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | | |   (109)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 231.40/42.62  | | | | | | | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 231.40/42.62  | | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | | | BETA: splitting (109) gives:
% 231.40/42.62  | | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | | | Case 1:
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | | | |   (110)  all_57_5 = e2 & op(e2, e1) = e2
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (26), (110) are inconsistent by sub-proof
% 231.40/42.62  | | | | | | | | | | | | | | | | | | |            #2425.
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | | | Case 2:
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | | | |   (111)  all_57_10 = e2 & op(e2, e0) = e2
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | ALPHA: (111) implies:
% 231.40/42.62  | | | | | | | | | | | | | | | | | | |   (112)  all_57_10 = e2
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (104), (112) imply:
% 231.40/42.62  | | | | | | | | | | | | | | | | | | |   (113)  e2 = e1
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | SIMP: (113) implies:
% 231.40/42.62  | | | | | | | | | | | | | | | | | | |   (114)  e2 = e1
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (96), (114) imply:
% 231.40/42.62  | | | | | | | | | | | | | | | | | | |   (115)  all_57_1 = e1
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | BETA: splitting (14) gives:
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | Case 1:
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | | BETA: splitting (92) gives:
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | | |   (116)  all_57_0 = e2 & op(e3, e3) = e2
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | | | ALPHA: (116) implies:
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | | |   (117)  op(e3, e3) = e2
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (19), (22), (117) are inconsistent by
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | | |            sub-proof #2490.
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (90), (114) imply:
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | | |   (118)  all_57_8 = e1
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (17), (19), (26), (28), (34), (37), (40),
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | | |            (49), (75), (83), (96), (118) are inconsistent by
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | | |            sub-proof #1484.
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | | End of split
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | Case 2:
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | |   (119)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e2)
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | | BETA: splitting (119) gives:
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | | |   (120)  all_57_4 = e2 & op(e3, e1) = e2
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | | | ALPHA: (120) implies:
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | | |   (121)  all_57_4 = e2
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (9), (14), (17), (19), (22), (23), (26),
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | | |            (28), (29), (34), (35), (37), (38), (42), (45),
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | | |            (54), (66), (115), (121) are inconsistent by
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | | |            sub-proof #1493.
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | | |   (122)  all_57_9 = e2 & op(e3, e0) = e2
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | | | ALPHA: (122) implies:
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | | |   (123)  all_57_9 = e2
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (28), (54), (123) are inconsistent by sub-proof
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | | |            #2440.
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | | End of split
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | End of split
% 231.40/42.62  | | | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | | | End of split
% 231.40/42.62  | | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | | End of split
% 231.40/42.62  | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | End of split
% 231.40/42.62  | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | Case 2:
% 231.40/42.62  | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | |   (124)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 231.40/42.62  | | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 231.40/42.62  | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | BETA: splitting (124) gives:
% 231.40/42.62  | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | Case 1:
% 231.40/42.62  | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | |   (125)  all_57_11 = e1 & op(e1, e0) = e1
% 231.40/42.62  | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | | ALPHA: (125) implies:
% 231.40/42.62  | | | | | | | | | | | | | | | | |   (126)  all_57_11 = e1
% 231.40/42.62  | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | | COMBINE_EQS: (66), (126) imply:
% 231.40/42.62  | | | | | | | | | | | | | | | | |   (127)  e1 = e0
% 231.40/42.62  | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | | SIMP: (127) implies:
% 231.40/42.62  | | | | | | | | | | | | | | | | |   (128)  e1 = e0
% 231.40/42.62  | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | | COMBINE_EQS: (49), (128) imply:
% 231.40/42.62  | | | | | | | | | | | | | | | | |   (129)  all_57_4 = e0
% 231.40/42.62  | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (13), (14), (19), (22), (28), (29),
% 231.40/42.62  | | | | | | | | | | | | | | | | |            (37), (54), (129) are inconsistent by sub-proof
% 231.40/42.62  | | | | | | | | | | | | | | | | |            #2436.
% 231.40/42.62  | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | Case 2:
% 231.40/42.62  | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | |   (130)  all_57_15 = e1 & op(e0, e0) = e1
% 231.40/42.62  | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (23), (130) are inconsistent by sub-proof
% 231.40/42.62  | | | | | | | | | | | | | | | | |            #2325.
% 231.40/42.62  | | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | | End of split
% 231.40/42.62  | | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | End of split
% 231.40/42.62  | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | End of split
% 231.40/42.62  | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | Case 2:
% 231.40/42.62  | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | |   (131)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 231.40/42.62  | | | | | | | | | | | | | |            & op(e3, e0) = e2)
% 231.40/42.62  | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | BETA: splitting (131) gives:
% 231.40/42.62  | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | Case 1:
% 231.40/42.62  | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | |   (132)  all_57_4 = e2 & op(e3, e1) = e2
% 231.40/42.62  | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | ALPHA: (132) implies:
% 231.40/42.62  | | | | | | | | | | | | | | |   (133)  all_57_4 = e2
% 231.40/42.62  | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (9), (13), (14), (17), (19), (22), (23),
% 231.40/42.62  | | | | | | | | | | | | | | |            (26), (28), (29), (34), (35), (37), (38), (42),
% 231.40/42.62  | | | | | | | | | | | | | | |            (45), (54), (66), (133) are inconsistent by
% 231.40/42.62  | | | | | | | | | | | | | | |            sub-proof #1481.
% 231.40/42.62  | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | Case 2:
% 231.40/42.62  | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | |   (134)  all_57_9 = e2 & op(e3, e0) = e2
% 231.40/42.62  | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | ALPHA: (134) implies:
% 231.40/42.62  | | | | | | | | | | | | | | |   (135)  all_57_9 = e2
% 231.40/42.62  | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | | REF_CLOSE: (28), (54), (135) are inconsistent by sub-proof
% 231.40/42.62  | | | | | | | | | | | | | | |            #2440.
% 231.40/42.62  | | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | | End of split
% 231.40/42.62  | | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | End of split
% 231.40/42.62  | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | Case 2:
% 231.40/42.62  | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | |   (136)  all_57_11 = e2 & op(e1, e0) = e2
% 231.40/42.62  | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | ALPHA: (136) implies:
% 231.40/42.62  | | | | | | | | | | | | |   (137)  all_57_11 = e2
% 231.40/42.62  | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | | REF_CLOSE: (28), (66), (137) are inconsistent by sub-proof
% 231.40/42.62  | | | | | | | | | | | | |            #1949.
% 231.40/42.62  | | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | | End of split
% 231.40/42.62  | | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | End of split
% 231.40/42.62  | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | End of split
% 231.40/42.62  | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | Case 2:
% 231.40/42.62  | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | |   (138)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 231.40/42.62  | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 231.40/42.62  | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | BETA: splitting (138) gives:
% 231.40/42.62  | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | Case 1:
% 231.40/42.62  | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | |   (139)  all_57_14 = e1 & op(e0, e1) = e1
% 231.40/42.62  | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | ALPHA: (139) implies:
% 231.40/42.62  | | | | | | | | | | |   (140)  all_57_14 = e1
% 231.40/42.62  | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 231.40/42.62  | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 231.40/42.62  | | | | | | | | | | |            (19), (20), (21), (22), (23), (24), (25), (26),
% 231.40/42.62  | | | | | | | | | | |            (27), (28), (29), (30), (31), (32), (33), (34),
% 231.40/42.62  | | | | | | | | | | |            (35), (36), (37), (38), (39), (40), (41), (42),
% 231.40/42.62  | | | | | | | | | | |            (43), (44), (45), (46), (140) are inconsistent by
% 231.40/42.62  | | | | | | | | | | |            sub-proof #1458.
% 231.40/42.62  | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | Case 2:
% 231.40/42.62  | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | |   (141)  all_57_15 = e1 & op(e0, e0) = e1
% 231.40/42.62  | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | | REF_CLOSE: (7), (23), (141) are inconsistent by sub-proof
% 231.40/42.62  | | | | | | | | | | |            #2325.
% 231.40/42.62  | | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | | End of split
% 231.40/42.62  | | | | | | | | | | 
% 231.40/42.62  | | | | | | | | | End of split
% 231.40/42.62  | | | | | | | | | 
% 231.40/42.62  | | | | | | | | End of split
% 231.40/42.62  | | | | | | | | 
% 231.40/42.62  | | | | | | | End of split
% 231.40/42.62  | | | | | | | 
% 231.40/42.62  | | | | | | End of split
% 231.40/42.62  | | | | | | 
% 231.40/42.62  | | | | | End of split
% 231.40/42.62  | | | | | 
% 231.40/42.62  | | | | End of split
% 231.40/42.62  | | | | 
% 231.40/42.62  | | | End of split
% 231.40/42.62  | | | 
% 231.40/42.62  | | Case 2:
% 231.40/42.62  | | | 
% 231.40/42.62  | | |   (142)  all_57_5 = e1 & op(e2, e1) = e1
% 231.40/42.62  | | | 
% 231.40/42.62  | | | ALPHA: (142) implies:
% 231.40/42.62  | | |   (143)  all_57_5 = e1
% 231.40/42.62  | | | 
% 231.40/42.62  | | | REF_CLOSE: (7), (26), (143) are inconsistent by sub-proof #2382.
% 231.40/42.62  | | | 
% 231.40/42.62  | | End of split
% 231.40/42.62  | | 
% 231.40/42.62  | Case 2:
% 231.40/42.62  | | 
% 231.40/42.62  | |   (144)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) =
% 231.40/42.62  | |            e1)
% 231.40/42.62  | | 
% 231.40/42.63  | | BETA: splitting (144) gives:
% 231.40/42.63  | | 
% 231.40/42.63  | | Case 1:
% 231.40/42.63  | | | 
% 231.40/42.63  | | |   (145)  all_57_8 = e1 & op(e1, e1) = e1
% 231.40/42.63  | | | 
% 231.40/42.63  | | | ALPHA: (145) implies:
% 231.40/42.63  | | |   (146)  all_57_8 = e1
% 231.40/42.63  | | | 
% 231.40/42.63  | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 231.40/42.63  | | |            (14), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 231.40/42.63  | | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 231.40/42.63  | | |            (35), (36), (37), (38), (39), (40), (41), (42), (43), (44),
% 231.40/42.63  | | |            (45), (46), (146) are inconsistent by sub-proof #1459.
% 231.40/42.63  | | | 
% 231.40/42.63  | | Case 2:
% 231.40/42.63  | | | 
% 231.40/42.63  | | |   (147)  all_57_14 = e1 & op(e0, e1) = e1
% 231.40/42.63  | | | 
% 231.40/42.63  | | | ALPHA: (147) implies:
% 231.40/42.63  | | |   (148)  all_57_14 = e1
% 231.40/42.63  | | | 
% 231.40/42.63  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 231.40/42.63  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 231.40/42.63  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 231.40/42.63  | | |            (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 231.40/42.63  | | |            (43), (44), (45), (46), (148) are inconsistent by sub-proof
% 231.40/42.63  | | |            #1458.
% 231.40/42.63  | | | 
% 231.40/42.63  | | End of split
% 231.40/42.63  | | 
% 231.40/42.63  | End of split
% 231.40/42.63  | 
% 231.40/42.63  End of proof
% 231.40/42.63  
% 231.40/42.63  Sub-proof #1458 shows that the following formulas are inconsistent:
% 231.40/42.63  ----------------------------------------------------------------
% 231.40/42.63    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.40/42.63         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.40/42.63    (2)  all_57_12 = e0
% 231.40/42.63    (3)  op(e3, e1) = all_52_5
% 231.40/42.63    (4)   ~ (all_52_7 = e3)
% 231.40/42.63    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.40/42.63         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.40/42.63    (6)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.40/42.63         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.40/42.63    (7)   ~ (e3 = e1)
% 231.40/42.63    (8)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 231.40/42.63         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.40/42.63    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.40/42.63           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.40/42.63    (10)   ~ (all_52_3 = e0)
% 231.40/42.63    (11)  op(all_52_7, all_52_7) = e0
% 231.40/42.63    (12)  op(e3, e2) = all_52_3
% 231.40/42.63    (13)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.40/42.63          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.40/42.63    (14)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.40/42.63          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.40/42.63    (15)  all_57_6 = e1
% 231.40/42.63    (16)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.40/42.63          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.40/42.63    (17)  all_57_3 = e0
% 231.40/42.63    (18)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.40/42.63          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.40/42.63    (19)   ~ (e3 = e2)
% 231.40/42.63    (20)   ~ (e3 = e0)
% 231.40/42.63    (21)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.40/42.63          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.40/42.63    (22)  op(e3, e3) = e3
% 231.40/42.63    (23)  all_57_15 = e3
% 231.40/42.63    (24)   ~ (all_52_3 = e3)
% 231.40/42.63    (25)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.40/42.63          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.40/42.63            e1)
% 231.40/42.63    (26)  all_57_5 = e3
% 231.40/42.63    (27)  op(e1, e1) = e1
% 231.40/42.63    (28)   ~ (e2 = e0)
% 231.40/42.63    (29)   ~ (e1 = e0)
% 231.40/42.63    (30)   ~ (all_52_3 = all_52_7)
% 231.40/42.63    (31)  all_57_14 = e1
% 231.40/42.63    (32)  op(e0, e0) = e3
% 231.40/42.63    (33)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.40/42.63          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.40/42.63            e2)
% 231.40/42.63    (34)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.40/42.63              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.40/42.63                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.40/42.63                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.40/42.63    (35)  all_57_7 = e3
% 231.40/42.63    (36)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.40/42.63          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.40/42.63    (37)   ~ (all_52_5 = e1)
% 231.40/42.63    (38)   ~ (e2 = e1)
% 231.40/42.63    (39)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.40/42.63          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.40/42.63    (40)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.40/42.63          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.40/42.63    (41)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.40/42.63          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.40/42.63    (42)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.40/42.63          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.40/42.63    (43)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.40/42.63          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.40/42.63    (44)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 231.40/42.63          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 231.40/42.63    (45)  op(e3, e0) = all_52_7
% 231.40/42.63    (46)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.40/42.63          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.40/42.63    (47)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 231.40/42.63          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 231.40/42.63  
% 231.40/42.63  Begin of proof
% 231.40/42.63  | 
% 231.40/42.63  | BETA: splitting (33) gives:
% 231.40/42.63  | 
% 231.40/42.63  | Case 1:
% 231.40/42.63  | | 
% 231.40/42.63  | |   (48)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 231.40/42.63  | |           e2)
% 231.40/42.63  | | 
% 231.40/42.63  | | BETA: splitting (48) gives:
% 231.40/42.63  | | 
% 231.40/42.63  | | Case 1:
% 231.40/42.63  | | | 
% 231.40/42.63  | | |   (49)  all_57_12 = e2 & op(e0, e3) = e2
% 231.40/42.63  | | | 
% 231.40/42.63  | | | ALPHA: (49) implies:
% 231.40/42.63  | | |   (50)  all_57_12 = e2
% 231.40/42.63  | | | 
% 231.40/42.63  | | | REF_CLOSE: (2), (28), (50) are inconsistent by sub-proof #2385.
% 231.40/42.63  | | | 
% 231.40/42.63  | | Case 2:
% 231.40/42.63  | | | 
% 231.40/42.63  | | |   (51)  all_57_13 = e2 & op(e0, e2) = e2
% 231.40/42.63  | | | 
% 231.40/42.63  | | | ALPHA: (51) implies:
% 231.40/42.63  | | |   (52)  all_57_13 = e2
% 231.40/42.63  | | | 
% 231.40/42.63  | | | BETA: splitting (46) gives:
% 231.40/42.63  | | | 
% 231.40/42.63  | | | Case 1:
% 231.40/42.63  | | | | 
% 231.40/42.63  | | | |   (53)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2)
% 231.40/42.63  | | | |           = e1)
% 231.40/42.63  | | | | 
% 231.40/42.63  | | | | BETA: splitting (53) gives:
% 231.40/42.63  | | | | 
% 231.40/42.63  | | | | Case 1:
% 231.40/42.63  | | | | | 
% 231.40/42.63  | | | | |   (54)  all_57_1 = e1 & op(e3, e2) = e1
% 231.40/42.63  | | | | | 
% 231.40/42.63  | | | | | ALPHA: (54) implies:
% 231.40/42.63  | | | | |   (55)  all_57_1 = e1
% 231.40/42.63  | | | | | 
% 231.40/42.63  | | | | | BETA: splitting (34) gives:
% 231.40/42.63  | | | | | 
% 231.40/42.63  | | | | | Case 1:
% 231.40/42.63  | | | | | | 
% 231.40/42.63  | | | | | |   (56)  all_57_15 = e0 & op(e0, e0) = e0
% 231.40/42.63  | | | | | | 
% 231.40/42.63  | | | | | | ALPHA: (56) implies:
% 231.40/42.63  | | | | | |   (57)  op(e0, e0) = e0
% 231.40/42.63  | | | | | | 
% 231.40/42.63  | | | | | | REF_CLOSE: (9), (20), (32), (57) are inconsistent by sub-proof
% 231.40/42.63  | | | | | |            #2304.
% 231.40/42.63  | | | | | | 
% 231.40/42.63  | | | | | Case 2:
% 231.40/42.63  | | | | | | 
% 231.40/42.63  | | | | | |   (58)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 &
% 231.40/42.63  | | | | | |             op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) &
% 231.40/42.63  | | | | | |         ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.40/42.63  | | | | | |             op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 231.40/42.63  | | | | | | 
% 231.40/42.63  | | | | | | ALPHA: (58) implies:
% 231.40/42.63  | | | | | |   (59)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.40/42.63  | | | | | |           op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.40/42.63  | | | | | |   (60)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2,
% 231.40/42.63  | | | | | |             e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.40/42.63  | | | | | | 
% 231.40/42.63  | | | | | | BETA: splitting (8) gives:
% 231.40/42.63  | | | | | | 
% 231.40/42.63  | | | | | | Case 1:
% 231.40/42.63  | | | | | | | 
% 231.40/42.63  | | | | | | |   (61)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 &
% 231.40/42.63  | | | | | | |           op(e1, e2) = e0)
% 231.40/42.63  | | | | | | | 
% 231.40/42.63  | | | | | | | BETA: splitting (61) gives:
% 231.40/42.63  | | | | | | | 
% 231.40/42.63  | | | | | | | Case 1:
% 231.40/42.63  | | | | | | | | 
% 231.40/42.63  | | | | | | | |   (62)  all_57_6 = e0 & op(e1, e3) = e0
% 231.40/42.63  | | | | | | | | 
% 231.40/42.63  | | | | | | | | ALPHA: (62) implies:
% 231.40/42.63  | | | | | | | |   (63)  all_57_6 = e0
% 231.40/42.63  | | | | | | | | 
% 231.40/42.63  | | | | | | | | COMBINE_EQS: (15), (63) imply:
% 231.40/42.63  | | | | | | | |   (64)  e1 = e0
% 231.40/42.63  | | | | | | | | 
% 231.40/42.63  | | | | | | | | COMBINE_EQS: (55), (64) imply:
% 231.40/42.63  | | | | | | | |   (65)  all_57_1 = e0
% 231.40/42.63  | | | | | | | | 
% 231.40/42.63  | | | | | | | | REF_CLOSE: (6), (7), (17), (19), (28), (29), (35), (38), (46),
% 231.40/42.63  | | | | | | | |            (65) are inconsistent by sub-proof #2098.
% 231.40/42.63  | | | | | | | | 
% 231.40/42.63  | | | | | | | Case 2:
% 231.40/42.63  | | | | | | | | 
% 231.40/42.63  | | | | | | | |   (66)  all_57_7 = e0 & op(e1, e2) = e0
% 231.40/42.63  | | | | | | | | 
% 231.40/42.63  | | | | | | | | REF_CLOSE: (20), (35), (66) are inconsistent by sub-proof #2042.
% 231.40/42.63  | | | | | | | | 
% 231.40/42.63  | | | | | | | End of split
% 231.40/42.63  | | | | | | | 
% 231.40/42.63  | | | | | | Case 2:
% 231.40/42.63  | | | | | | | 
% 231.40/42.63  | | | | | | |   (67)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 &
% 231.40/42.63  | | | | | | |           op(e1, e0) = e0)
% 231.40/42.63  | | | | | | | 
% 231.40/42.63  | | | | | | | BETA: splitting (67) gives:
% 231.40/42.63  | | | | | | | 
% 231.40/42.63  | | | | | | | Case 1:
% 231.40/42.63  | | | | | | | | 
% 231.40/42.63  | | | | | | | |   (68)  all_57_8 = e0 & op(e1, e1) = e0
% 231.40/42.63  | | | | | | | | 
% 231.40/42.63  | | | | | | | | ALPHA: (68) implies:
% 231.40/42.63  | | | | | | | |   (69)  op(e1, e1) = e0
% 231.40/42.63  | | | | | | | | 
% 231.40/42.63  | | | | | | | | REF_CLOSE: (1), (4), (5), (6), (7), (8), (9), (11), (13), (14),
% 231.40/42.63  | | | | | | | |            (16), (17), (18), (19), (20), (21), (22), (23), (26),
% 231.40/42.63  | | | | | | | |            (28), (29), (32), (33), (35), (36), (38), (39), (40),
% 231.40/42.63  | | | | | | | |            (41), (42), (43), (44), (45), (46), (47), (59), (60),
% 231.40/42.63  | | | | | | | |            (69) are inconsistent by sub-proof #1487.
% 231.40/42.63  | | | | | | | | 
% 231.40/42.63  | | | | | | | Case 2:
% 231.40/42.63  | | | | | | | | 
% 231.40/42.63  | | | | | | | |   (70)  all_57_11 = e0 & op(e1, e0) = e0
% 231.40/42.63  | | | | | | | | 
% 231.40/42.63  | | | | | | | | ALPHA: (70) implies:
% 231.40/42.63  | | | | | | | |   (71)  all_57_11 = e0
% 231.40/42.63  | | | | | | | | 
% 231.40/42.63  | | | | | | | | BETA: splitting (47) gives:
% 231.40/42.63  | | | | | | | | 
% 231.40/42.63  | | | | | | | | Case 1:
% 231.40/42.63  | | | | | | | | | 
% 231.40/42.63  | | | | | | | | |   (72)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 &
% 231.40/42.63  | | | | | | | | |           op(e1, e2) = e2)
% 231.40/42.63  | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | BETA: splitting (72) gives:
% 231.40/42.63  | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | Case 1:
% 231.40/42.63  | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | |   (73)  all_57_6 = e2 & op(e1, e3) = e2
% 231.40/42.63  | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | ALPHA: (73) implies:
% 231.40/42.63  | | | | | | | | | |   (74)  all_57_6 = e2
% 231.40/42.63  | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | BETA: splitting (5) gives:
% 231.40/42.63  | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | Case 1:
% 231.40/42.63  | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | |   (75)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 231.40/42.63  | | | | | | | | | | |           & op(e2, e3) = e1)
% 231.40/42.63  | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | BETA: splitting (75) gives:
% 231.40/42.63  | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | Case 1:
% 231.40/42.63  | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | |   (76)  all_57_0 = e1 & op(e3, e3) = e1
% 231.40/42.63  | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | ALPHA: (76) implies:
% 231.40/42.63  | | | | | | | | | | | |   (77)  op(e3, e3) = e1
% 231.40/42.63  | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | REF_CLOSE: (7), (9), (22), (77) are inconsistent by sub-proof
% 231.40/42.63  | | | | | | | | | | | |            #2495.
% 231.40/42.63  | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | Case 2:
% 231.40/42.63  | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | |   (78)  all_57_2 = e1 & op(e2, e3) = e1
% 231.40/42.63  | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | ALPHA: (78) implies:
% 231.40/42.63  | | | | | | | | | | | |   (79)  all_57_2 = e1
% 231.40/42.63  | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | REF_CLOSE: (1), (2), (5), (6), (7), (9), (13), (14), (16),
% 231.40/42.63  | | | | | | | | | | | |            (17), (19), (20), (22), (23), (26), (28), (29),
% 231.40/42.63  | | | | | | | | | | | |            (35), (36), (38), (39), (43), (46), (52), (71),
% 231.40/42.63  | | | | | | | | | | | |            (74), (79) are inconsistent by sub-proof #1472.
% 231.40/42.63  | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | End of split
% 231.40/42.63  | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | Case 2:
% 231.40/42.63  | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | |   (80)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 231.40/42.63  | | | | | | | | | | |           e1 & op(e0, e3) = e1)
% 231.40/42.63  | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | REF_CLOSE: (2), (29), (38), (74), (80) are inconsistent by
% 231.40/42.63  | | | | | | | | | | |            sub-proof #1513.
% 231.40/42.63  | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | End of split
% 231.40/42.63  | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | Case 2:
% 231.40/42.63  | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | |   (81)  all_57_7 = e2 & op(e1, e2) = e2
% 231.40/42.63  | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | REF_CLOSE: (19), (35), (81) are inconsistent by sub-proof
% 231.40/42.63  | | | | | | | | | |            #2092.
% 231.40/42.63  | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | End of split
% 231.40/42.63  | | | | | | | | | 
% 231.40/42.63  | | | | | | | | Case 2:
% 231.40/42.63  | | | | | | | | | 
% 231.40/42.63  | | | | | | | | |   (82)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 &
% 231.40/42.63  | | | | | | | | |           op(e1, e0) = e2)
% 231.40/42.63  | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | BETA: splitting (82) gives:
% 231.40/42.63  | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | Case 1:
% 231.40/42.63  | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | |   (83)  all_57_8 = e2 & op(e1, e1) = e2
% 231.40/42.63  | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | ALPHA: (83) implies:
% 231.40/42.63  | | | | | | | | | |   (84)  all_57_8 = e2
% 231.40/42.63  | | | | | | | | | |   (85)  op(e1, e1) = e2
% 231.40/42.63  | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | BETA: splitting (18) gives:
% 231.40/42.63  | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | Case 1:
% 231.40/42.63  | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | |   (86)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 231.40/42.63  | | | | | | | | | | |           & op(e2, e1) = e0)
% 231.40/42.63  | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | BETA: splitting (86) gives:
% 231.40/42.63  | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | Case 1:
% 231.40/42.63  | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | |   (87)  all_57_4 = e0 & op(e3, e1) = e0
% 231.40/42.63  | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | ALPHA: (87) implies:
% 231.40/42.63  | | | | | | | | | | | |   (88)  all_57_4 = e0
% 231.40/42.63  | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | BETA: splitting (14) gives:
% 231.40/42.63  | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | Case 1:
% 231.40/42.63  | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | |   (89)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 231.40/42.63  | | | | | | | | | | | | |           & op(e3, e2) = e2)
% 231.40/42.63  | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | BETA: splitting (89) gives:
% 231.40/42.63  | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | Case 1:
% 231.40/42.63  | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | |   (90)  all_57_0 = e2 & op(e3, e3) = e2
% 231.40/42.63  | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | | ALPHA: (90) implies:
% 231.40/42.63  | | | | | | | | | | | | | |   (91)  op(e3, e3) = e2
% 231.40/42.63  | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | | REF_CLOSE: (9), (19), (22), (91) are inconsistent by
% 231.40/42.63  | | | | | | | | | | | | | |            sub-proof #2490.
% 231.40/42.63  | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | Case 2:
% 231.40/42.63  | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | |   (92)  all_57_1 = e2 & op(e3, e2) = e2
% 231.40/42.63  | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | | ALPHA: (92) implies:
% 231.40/42.63  | | | | | | | | | | | | | |   (93)  all_57_1 = e2
% 231.40/42.63  | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | | COMBINE_EQS: (55), (93) imply:
% 231.40/42.63  | | | | | | | | | | | | | |   (94)  e2 = e1
% 231.40/42.63  | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | | SIMP: (94) implies:
% 231.40/42.63  | | | | | | | | | | | | | |   (95)  e2 = e1
% 231.40/42.63  | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | | COMBINE_EQS: (84), (95) imply:
% 231.40/42.63  | | | | | | | | | | | | | |   (96)  all_57_8 = e1
% 231.40/42.63  | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10),
% 231.40/42.63  | | | | | | | | | | | | | |            (11), (12), (13), (14), (16), (17), (18), (19),
% 231.40/42.63  | | | | | | | | | | | | | |            (20), (21), (22), (23), (24), (25), (26), (27),
% 231.40/42.63  | | | | | | | | | | | | | |            (28), (29), (30), (32), (33), (34), (35), (36),
% 231.40/42.63  | | | | | | | | | | | | | |            (37), (38), (39), (40), (41), (42), (43), (44),
% 231.40/42.63  | | | | | | | | | | | | | |            (45), (46), (47), (96) are inconsistent by
% 231.40/42.63  | | | | | | | | | | | | | |            sub-proof #1459.
% 231.40/42.63  | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | End of split
% 231.40/42.63  | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | Case 2:
% 231.40/42.63  | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | |   (97)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 231.40/42.63  | | | | | | | | | | | | |           & op(e3, e0) = e2)
% 231.40/42.63  | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | BETA: splitting (97) gives:
% 231.40/42.63  | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | Case 1:
% 231.40/42.63  | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | |   (98)  all_57_4 = e2 & op(e3, e1) = e2
% 231.40/42.63  | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | | ALPHA: (98) implies:
% 231.40/42.63  | | | | | | | | | | | | | |   (99)  all_57_4 = e2
% 231.40/42.63  | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (9), (13), (14), (16), (17), (19), (20),
% 231.40/42.63  | | | | | | | | | | | | | |            (22), (23), (26), (28), (29), (35), (36), (38),
% 231.40/42.63  | | | | | | | | | | | | | |            (39), (43), (46), (71), (99) are inconsistent by
% 231.40/42.63  | | | | | | | | | | | | | |            sub-proof #1480.
% 231.40/42.63  | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | Case 2:
% 231.40/42.63  | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | |   (100)  all_57_9 = e2 & op(e3, e0) = e2
% 231.40/42.63  | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | | ALPHA: (100) implies:
% 231.40/42.63  | | | | | | | | | | | | | |   (101)  all_57_9 = e2
% 231.40/42.63  | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | | BETA: splitting (40) gives:
% 231.40/42.63  | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | | Case 1:
% 231.40/42.63  | | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | | |   (102)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 231.40/42.63  | | | | | | | | | | | | | | |            & op(e2, e3) = e2)
% 231.40/42.63  | | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | | | BETA: splitting (102) gives:
% 231.40/42.63  | | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | | | Case 1:
% 231.40/42.63  | | | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | | | |   (103)  all_57_0 = e2 & op(e3, e3) = e2
% 231.40/42.63  | | | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | | | | ALPHA: (103) implies:
% 231.40/42.63  | | | | | | | | | | | | | | | |   (104)  op(e3, e3) = e2
% 231.40/42.63  | | | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | | | | REF_CLOSE: (9), (19), (22), (104) are inconsistent by
% 231.40/42.63  | | | | | | | | | | | | | | | |            sub-proof #2490.
% 231.40/42.63  | | | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | | | Case 2:
% 231.40/42.63  | | | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | | | |   (105)  all_57_2 = e2 & op(e2, e3) = e2
% 231.40/42.63  | | | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | | | | ALPHA: (105) implies:
% 231.40/42.63  | | | | | | | | | | | | | | | |   (106)  all_57_2 = e2
% 231.40/42.63  | | | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | | | | BETA: splitting (1) gives:
% 231.40/42.63  | | | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | | | | Case 1:
% 231.40/42.63  | | | | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | | | | |   (107)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 231.40/42.63  | | | | | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 231.40/42.63  | | | | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 231.40/42.63  | | | | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | | | | | Case 1:
% 231.40/42.63  | | | | | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | | | | | |   (108)  all_57_2 = e1 & op(e2, e3) = e1
% 231.40/42.63  | | | | | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | | | | | | ALPHA: (108) implies:
% 231.40/42.63  | | | | | | | | | | | | | | | | | |   (109)  all_57_2 = e1
% 231.40/42.63  | | | | | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (106), (109) imply:
% 231.40/42.63  | | | | | | | | | | | | | | | | | |   (110)  e2 = e1
% 231.40/42.63  | | | | | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (84), (110) imply:
% 231.40/42.63  | | | | | | | | | | | | | | | | | |   (111)  all_57_8 = e1
% 231.40/42.63  | | | | | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (5), (6), (7), (8), (9), (11), (13),
% 231.40/42.63  | | | | | | | | | | | | | | | | | |            (14), (16), (17), (18), (19), (20), (21), (22),
% 231.40/42.63  | | | | | | | | | | | | | | | | | |            (23), (25), (26), (28), (29), (32), (33), (34),
% 231.40/42.63  | | | | | | | | | | | | | | | | | |            (35), (36), (38), (39), (40), (41), (42), (43),
% 231.40/42.63  | | | | | | | | | | | | | | | | | |            (44), (45), (46), (47), (106), (111) are
% 231.40/42.63  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1471.
% 231.40/42.63  | | | | | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | | | | | Case 2:
% 231.40/42.63  | | | | | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | | | | | |   (112)  all_57_3 = e1 & op(e2, e2) = e1
% 231.40/42.63  | | | | | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | | | | | | ALPHA: (112) implies:
% 231.40/42.63  | | | | | | | | | | | | | | | | | |   (113)  all_57_3 = e1
% 231.40/42.63  | | | | | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (17), (113) imply:
% 231.40/42.63  | | | | | | | | | | | | | | | | | |   (114)  e1 = e0
% 231.40/42.63  | | | | | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (17), (19), (28), (29), (35), (38),
% 231.40/42.63  | | | | | | | | | | | | | | | | | |            (46), (55), (114) are inconsistent by sub-proof
% 231.40/42.63  | | | | | | | | | | | | | | | | | |            #1626.
% 231.40/42.63  | | | | | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | | | | | End of split
% 231.40/42.63  | | | | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | | | | Case 2:
% 231.40/42.63  | | | | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | | | | |   (115)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 231.40/42.63  | | | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 231.40/42.63  | | | | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | | | | | BETA: splitting (115) gives:
% 231.40/42.63  | | | | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | | | | | Case 1:
% 231.40/42.63  | | | | | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | | | | | |   (116)  all_57_5 = e1 & op(e2, e1) = e1
% 231.40/42.63  | | | | | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (26), (116) are inconsistent by sub-proof
% 231.40/42.63  | | | | | | | | | | | | | | | | | |            #2376.
% 231.40/42.63  | | | | | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | | | | | Case 2:
% 231.40/42.63  | | | | | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | | | | | |   (117)  all_57_10 = e1 & op(e2, e0) = e1
% 231.40/42.63  | | | | | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | | | | | | ALPHA: (117) implies:
% 231.40/42.63  | | | | | | | | | | | | | | | | | |   (118)  all_57_10 = e1
% 231.40/42.63  | | | | | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (11),
% 231.40/42.63  | | | | | | | | | | | | | | | | | |            (13), (14), (15), (16), (17), (18), (19), (20),
% 231.40/42.63  | | | | | | | | | | | | | | | | | |            (21), (22), (23), (25), (26), (27), (28), (29),
% 231.40/42.63  | | | | | | | | | | | | | | | | | |            (32), (33), (34), (35), (36), (38), (39), (40),
% 231.40/42.63  | | | | | | | | | | | | | | | | | |            (41), (42), (43), (44), (45), (46), (47), (84),
% 231.40/42.63  | | | | | | | | | | | | | | | | | |            (85), (106), (118) are inconsistent by sub-proof
% 231.40/42.63  | | | | | | | | | | | | | | | | | |            #1476.
% 231.40/42.63  | | | | | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | | | | | End of split
% 231.40/42.63  | | | | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | | | | End of split
% 231.40/42.63  | | | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | | | End of split
% 231.40/42.63  | | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | | Case 2:
% 231.40/42.63  | | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | | |   (119)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 231.40/42.63  | | | | | | | | | | | | | | |            e2 & op(e0, e3) = e2)
% 231.40/42.63  | | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | | | BETA: splitting (119) gives:
% 231.40/42.63  | | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | | | Case 1:
% 231.40/42.63  | | | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | | | |   (120)  all_57_6 = e2 & op(e1, e3) = e2
% 231.40/42.63  | | | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | | | | ALPHA: (120) implies:
% 231.40/42.63  | | | | | | | | | | | | | | | |   (121)  all_57_6 = e2
% 231.40/42.63  | | | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | | | | REF_CLOSE: (1), (5), (6), (7), (9), (13), (14), (16), (17),
% 231.40/42.63  | | | | | | | | | | | | | | | |            (19), (20), (22), (23), (25), (26), (28), (29),
% 231.40/42.63  | | | | | | | | | | | | | | | |            (35), (36), (38), (39), (41), (42), (43), (44),
% 231.40/42.63  | | | | | | | | | | | | | | | |            (46), (71), (85), (121) are inconsistent by
% 231.40/42.63  | | | | | | | | | | | | | | | |            sub-proof #1462.
% 231.40/42.63  | | | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | | | Case 2:
% 231.40/42.63  | | | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | | | |   (122)  all_57_12 = e2 & op(e0, e3) = e2
% 231.40/42.63  | | | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | | | | ALPHA: (122) implies:
% 231.40/42.63  | | | | | | | | | | | | | | | |   (123)  all_57_12 = e2
% 231.40/42.63  | | | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | | | | COMBINE_EQS: (2), (123) imply:
% 231.40/42.63  | | | | | | | | | | | | | | | |   (124)  e2 = e0
% 231.40/42.63  | | | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | | | | SIMP: (124) implies:
% 231.40/42.63  | | | | | | | | | | | | | | | |   (125)  e2 = e0
% 231.40/42.63  | | | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | | | | COMBINE_EQS: (101), (125) imply:
% 231.40/42.63  | | | | | | | | | | | | | | | |   (126)  all_57_9 = e0
% 231.40/42.63  | | | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (13), (14), (19), (22), (28), (29),
% 231.40/42.63  | | | | | | | | | | | | | | | |            (38), (88), (126) are inconsistent by sub-proof
% 231.40/42.63  | | | | | | | | | | | | | | | |            #2436.
% 231.40/42.63  | | | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | | | End of split
% 231.40/42.63  | | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | | End of split
% 231.40/42.63  | | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | | End of split
% 231.40/42.63  | | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | End of split
% 231.40/42.63  | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | Case 2:
% 231.40/42.63  | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | |   (127)  all_57_5 = e0 & op(e2, e1) = e0
% 231.40/42.63  | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | REF_CLOSE: (20), (26), (127) are inconsistent by sub-proof
% 231.40/42.63  | | | | | | | | | | | |            #2414.
% 231.40/42.63  | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | End of split
% 231.40/42.63  | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | Case 2:
% 231.40/42.63  | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | |   (128)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 231.40/42.63  | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 231.40/42.63  | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | BETA: splitting (128) gives:
% 231.40/42.63  | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | Case 1:
% 231.40/42.63  | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | |   (129)  all_57_8 = e0 & op(e1, e1) = e0
% 231.40/42.63  | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | ALPHA: (129) implies:
% 231.40/42.63  | | | | | | | | | | | |   (130)  op(e1, e1) = e0
% 231.40/42.63  | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | REF_CLOSE: (1), (2), (5), (6), (7), (9), (14), (16), (17),
% 231.40/42.63  | | | | | | | | | | | |            (19), (20), (21), (22), (23), (26), (28), (29),
% 231.40/42.63  | | | | | | | | | | | |            (33), (35), (36), (38), (39), (40), (43), (44),
% 231.40/42.63  | | | | | | | | | | | |            (46), (71), (84), (85), (130) are inconsistent by
% 231.40/42.63  | | | | | | | | | | | |            sub-proof #1508.
% 231.40/42.63  | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | Case 2:
% 231.40/42.63  | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | |   (131)  all_57_14 = e0 & op(e0, e1) = e0
% 231.40/42.63  | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | ALPHA: (131) implies:
% 231.40/42.63  | | | | | | | | | | | |   (132)  all_57_14 = e0
% 231.40/42.63  | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | COMBINE_EQS: (31), (132) imply:
% 231.40/42.63  | | | | | | | | | | | |   (133)  e1 = e0
% 231.40/42.63  | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | COMBINE_EQS: (55), (133) imply:
% 231.40/42.63  | | | | | | | | | | | |   (134)  all_57_1 = e0
% 231.40/42.63  | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | | REF_CLOSE: (6), (7), (17), (19), (28), (29), (35), (38),
% 231.40/42.63  | | | | | | | | | | | |            (46), (134) are inconsistent by sub-proof #2098.
% 231.40/42.63  | | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | | End of split
% 231.40/42.63  | | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | End of split
% 231.40/42.63  | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | Case 2:
% 231.40/42.63  | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | |   (135)  all_57_11 = e2 & op(e1, e0) = e2
% 231.40/42.63  | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | ALPHA: (135) implies:
% 231.40/42.63  | | | | | | | | | |   (136)  all_57_11 = e2
% 231.40/42.63  | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | COMBINE_EQS: (71), (136) imply:
% 231.40/42.63  | | | | | | | | | |   (137)  e2 = e0
% 231.40/42.63  | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | COMBINE_EQS: (52), (137) imply:
% 231.40/42.63  | | | | | | | | | |   (138)  all_57_13 = e0
% 231.40/42.63  | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | | REF_CLOSE: (6), (7), (9), (13), (14), (16), (17), (19), (20),
% 231.40/42.63  | | | | | | | | | |            (22), (28), (29), (35), (38), (46), (138) are
% 231.40/42.63  | | | | | | | | | |            inconsistent by sub-proof #2091.
% 231.40/42.63  | | | | | | | | | | 
% 231.40/42.63  | | | | | | | | | End of split
% 231.40/42.63  | | | | | | | | | 
% 231.40/42.63  | | | | | | | | End of split
% 231.40/42.63  | | | | | | | | 
% 231.40/42.63  | | | | | | | End of split
% 231.40/42.63  | | | | | | | 
% 231.40/42.63  | | | | | | End of split
% 231.40/42.63  | | | | | | 
% 231.40/42.63  | | | | | End of split
% 231.40/42.63  | | | | | 
% 231.40/42.63  | | | | Case 2:
% 231.40/42.63  | | | | | 
% 231.40/42.63  | | | | |   (139)  all_57_3 = e1 & op(e2, e2) = e1
% 231.40/42.63  | | | | | 
% 231.40/42.63  | | | | | REF_CLOSE: (17), (29), (139) are inconsistent by sub-proof #2362.
% 231.40/42.63  | | | | | 
% 231.40/42.63  | | | | End of split
% 231.40/42.63  | | | | 
% 231.40/42.63  | | | Case 2:
% 231.40/42.63  | | | | 
% 231.40/42.63  | | | |   (140)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0,
% 231.40/42.63  | | | |              e2) = e1)
% 231.40/42.63  | | | | 
% 231.40/42.63  | | | | REF_CLOSE: (7), (35), (38), (52), (140) are inconsistent by sub-proof
% 231.40/42.63  | | | |            #1780.
% 231.40/42.63  | | | | 
% 231.40/42.63  | | | End of split
% 231.40/42.63  | | | 
% 231.40/42.63  | | End of split
% 231.40/42.63  | | 
% 231.40/42.63  | Case 2:
% 231.40/42.63  | | 
% 231.40/42.63  | |   (141)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.40/42.63  | |            e2)
% 231.40/42.63  | | 
% 231.40/42.63  | | BETA: splitting (141) gives:
% 231.40/42.63  | | 
% 231.40/42.63  | | Case 1:
% 231.40/42.63  | | | 
% 231.40/42.63  | | |   (142)  all_57_14 = e2 & op(e0, e1) = e2
% 231.40/42.63  | | | 
% 231.40/42.63  | | | REF_CLOSE: (31), (38), (142) are inconsistent by sub-proof #1968.
% 231.40/42.63  | | | 
% 231.40/42.63  | | Case 2:
% 231.40/42.63  | | | 
% 231.40/42.63  | | |   (143)  all_57_15 = e2 & op(e0, e0) = e2
% 231.40/42.63  | | | 
% 231.40/42.63  | | | REF_CLOSE: (19), (23), (143) are inconsistent by sub-proof #2323.
% 231.40/42.63  | | | 
% 231.40/42.63  | | End of split
% 231.40/42.63  | | 
% 231.40/42.63  | End of split
% 231.40/42.63  | 
% 231.40/42.63  End of proof
% 231.40/42.63  
% 231.40/42.63  Sub-proof #1459 shows that the following formulas are inconsistent:
% 231.40/42.63  ----------------------------------------------------------------
% 231.40/42.63    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.40/42.63         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.40/42.63    (2)  op(e3, e1) = all_52_5
% 231.40/42.63    (3)   ~ (all_52_7 = e3)
% 231.40/42.63    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.40/42.63         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.40/42.63    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.40/42.63         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.40/42.63    (6)   ~ (e3 = e1)
% 231.40/42.63    (7)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 231.40/42.63         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.40/42.63    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.40/42.63           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.40/42.63    (9)   ~ (all_52_3 = e0)
% 231.40/42.63    (10)  op(all_52_7, all_52_7) = e0
% 231.40/42.63    (11)  op(e3, e2) = all_52_3
% 231.40/42.63    (12)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.40/42.63          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.40/42.63    (13)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.40/42.63          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.40/42.63    (14)  all_57_8 = e1
% 231.40/42.63    (15)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.40/42.63          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.40/42.63    (16)  all_57_3 = e0
% 231.40/42.63    (17)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.40/42.63          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.40/42.63    (18)   ~ (e3 = e2)
% 231.40/42.63    (19)   ~ (e3 = e0)
% 231.40/42.63    (20)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.40/42.63          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.40/42.63    (21)  op(e3, e3) = e3
% 231.40/42.63    (22)  all_57_15 = e3
% 231.40/42.63    (23)   ~ (all_52_3 = e3)
% 231.40/42.63    (24)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.40/42.63          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.40/42.63            e1)
% 231.40/42.63    (25)  all_57_5 = e3
% 231.40/42.63    (26)  op(e1, e1) = e1
% 231.40/42.63    (27)   ~ (e2 = e0)
% 231.40/42.63    (28)   ~ (e1 = e0)
% 231.40/42.63    (29)   ~ (all_52_3 = all_52_7)
% 231.40/42.63    (30)  op(e0, e0) = e3
% 231.40/42.63    (31)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.40/42.63          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.40/42.63            e2)
% 231.40/42.63    (32)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.40/42.63              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.40/42.63                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.40/42.63                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.40/42.63    (33)  all_57_7 = e3
% 231.40/42.63    (34)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.40/42.63          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.40/42.63    (35)   ~ (all_52_5 = e1)
% 231.40/42.63    (36)   ~ (e2 = e1)
% 231.40/42.63    (37)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.40/42.63          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.40/42.63    (38)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.40/42.63          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.40/42.63    (39)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.40/42.63          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.40/42.63    (40)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.40/42.63          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.40/42.63    (41)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.40/42.63          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.40/42.64    (42)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 231.40/42.64          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 231.40/42.64    (43)  op(e3, e0) = all_52_7
% 231.40/42.64    (44)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.40/42.64          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.40/42.64    (45)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 231.40/42.64          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 231.40/42.64  
% 231.40/42.64  Begin of proof
% 231.40/42.64  | 
% 231.40/42.64  | BETA: splitting (34) gives:
% 231.40/42.64  | 
% 231.40/42.64  | Case 1:
% 231.40/42.64  | | 
% 231.40/42.64  | |   (46)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 231.40/42.64  | |           e2)
% 231.40/42.64  | | 
% 231.40/42.64  | | BETA: splitting (46) gives:
% 231.40/42.64  | | 
% 231.40/42.64  | | Case 1:
% 231.40/42.64  | | | 
% 231.40/42.64  | | |   (47)  all_57_2 = e2 & op(e2, e3) = e2
% 231.40/42.64  | | | 
% 231.40/42.64  | | | ALPHA: (47) implies:
% 231.40/42.64  | | |   (48)  all_57_2 = e2
% 231.40/42.64  | | | 
% 231.40/42.64  | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (10), (12), (13), (14),
% 231.40/42.64  | | |            (15), (16), (17), (18), (19), (20), (21), (22), (24), (25),
% 231.40/42.64  | | |            (27), (28), (30), (31), (32), (33), (34), (36), (37), (38),
% 231.40/42.64  | | |            (39), (40), (41), (42), (43), (44), (45), (48) are inconsistent
% 231.40/42.64  | | |            by sub-proof #1471.
% 231.40/42.64  | | | 
% 231.40/42.64  | | Case 2:
% 231.40/42.64  | | | 
% 231.40/42.64  | | |   (49)  all_57_3 = e2 & op(e2, e2) = e2
% 231.40/42.64  | | | 
% 231.40/42.64  | | | REF_CLOSE: (16), (27), (49) are inconsistent by sub-proof #2103.
% 231.40/42.64  | | | 
% 231.40/42.64  | | End of split
% 231.40/42.64  | | 
% 231.40/42.64  | Case 2:
% 231.40/42.64  | | 
% 231.40/42.64  | |   (50)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 231.40/42.64  | |           e2)
% 231.40/42.64  | | 
% 231.40/42.64  | | BETA: splitting (50) gives:
% 231.40/42.64  | | 
% 231.40/42.64  | | Case 1:
% 231.40/42.64  | | | 
% 231.40/42.64  | | |   (51)  all_57_5 = e2 & op(e2, e1) = e2
% 231.40/42.64  | | | 
% 231.40/42.64  | | | ALPHA: (51) implies:
% 231.40/42.64  | | |   (52)  all_57_5 = e2
% 231.40/42.64  | | | 
% 231.40/42.64  | | | REF_CLOSE: (18), (25), (52) are inconsistent by sub-proof #2189.
% 231.40/42.64  | | | 
% 231.40/42.64  | | Case 2:
% 231.40/42.64  | | | 
% 231.40/42.64  | | |   (53)  all_57_10 = e2 & op(e2, e0) = e2
% 231.40/42.64  | | | 
% 231.40/42.64  | | | ALPHA: (53) implies:
% 231.40/42.64  | | |   (54)  all_57_10 = e2
% 231.40/42.64  | | | 
% 231.40/42.64  | | | BETA: splitting (41) gives:
% 231.40/42.64  | | | 
% 231.40/42.64  | | | Case 1:
% 231.40/42.64  | | | | 
% 231.40/42.64  | | | |   (55)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0)
% 231.40/42.64  | | | |           = e1)
% 231.40/42.64  | | | | 
% 231.40/42.64  | | | | BETA: splitting (55) gives:
% 231.40/42.64  | | | | 
% 231.40/42.64  | | | | Case 1:
% 231.40/42.64  | | | | | 
% 231.40/42.64  | | | | |   (56)  all_57_9 = e1 & op(e3, e0) = e1
% 231.40/42.64  | | | | | 
% 231.40/42.64  | | | | | ALPHA: (56) implies:
% 231.40/42.64  | | | | |   (57)  all_57_9 = e1
% 231.40/42.64  | | | | | 
% 231.40/42.64  | | | | | BETA: splitting (1) gives:
% 231.40/42.64  | | | | | 
% 231.40/42.64  | | | | | Case 1:
% 231.40/42.64  | | | | | | 
% 231.40/42.64  | | | | | |   (58)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2,
% 231.40/42.64  | | | | | |             e2) = e1)
% 231.40/42.64  | | | | | | 
% 231.40/42.64  | | | | | | BETA: splitting (58) gives:
% 231.40/42.64  | | | | | | 
% 231.40/42.64  | | | | | | Case 1:
% 231.40/42.64  | | | | | | | 
% 231.40/42.64  | | | | | | |   (59)  all_57_2 = e1 & op(e2, e3) = e1
% 231.40/42.64  | | | | | | | 
% 231.40/42.64  | | | | | | | ALPHA: (59) implies:
% 231.40/42.64  | | | | | | |   (60)  all_57_2 = e1
% 231.40/42.64  | | | | | | | 
% 231.40/42.64  | | | | | | | BETA: splitting (32) gives:
% 231.40/42.64  | | | | | | | 
% 231.40/42.64  | | | | | | | Case 1:
% 231.40/42.64  | | | | | | | | 
% 231.40/42.64  | | | | | | | |   (61)  all_57_15 = e0 & op(e0, e0) = e0
% 231.40/42.64  | | | | | | | | 
% 231.40/42.64  | | | | | | | | ALPHA: (61) implies:
% 231.40/42.64  | | | | | | | |   (62)  op(e0, e0) = e0
% 231.40/42.64  | | | | | | | | 
% 231.40/42.64  | | | | | | | | REF_CLOSE: (8), (19), (30), (62) are inconsistent by sub-proof
% 231.40/42.64  | | | | | | | |            #2304.
% 231.40/42.64  | | | | | | | | 
% 231.40/42.64  | | | | | | | Case 2:
% 231.40/42.64  | | | | | | | | 
% 231.40/42.64  | | | | | | | |   (63)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 &
% 231.40/42.64  | | | | | | | |             op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 231.40/42.64  | | | | | | | |             e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) |
% 231.40/42.64  | | | | | | | |           (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 &
% 231.40/42.64  | | | | | | | |             op(e0, e1) = e0))
% 231.40/42.64  | | | | | | | | 
% 231.40/42.64  | | | | | | | | ALPHA: (63) implies:
% 231.40/42.64  | | | | | | | |   (64)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.40/42.64  | | | | | | | |           op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.40/42.64  | | | | | | | | 
% 231.40/42.64  | | | | | | | | BETA: splitting (15) gives:
% 231.40/42.64  | | | | | | | | 
% 231.40/42.64  | | | | | | | | Case 1:
% 231.40/42.64  | | | | | | | | | 
% 231.40/42.64  | | | | | | | | |   (65)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 &
% 231.40/42.64  | | | | | | | | |           op(e3, e2) = e0)
% 231.40/42.64  | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | REF_CLOSE: (5), (6), (8), (16), (18), (19), (21), (27), (28),
% 231.40/42.64  | | | | | | | | |            (33), (36), (44), (65) are inconsistent by
% 231.40/42.64  | | | | | | | | |            sub-proof #2097.
% 231.40/42.64  | | | | | | | | | 
% 231.40/42.64  | | | | | | | | Case 2:
% 231.40/42.64  | | | | | | | | | 
% 231.40/42.64  | | | | | | | | |   (66)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 &
% 231.40/42.64  | | | | | | | | |           op(e3, e0) = e0)
% 231.40/42.64  | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | BETA: splitting (66) gives:
% 231.40/42.64  | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | Case 1:
% 231.40/42.64  | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | |   (67)  all_57_4 = e0 & op(e3, e1) = e0
% 231.40/42.64  | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | ALPHA: (67) implies:
% 231.40/42.64  | | | | | | | | | |   (68)  all_57_4 = e0
% 231.40/42.64  | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | BETA: splitting (39) gives:
% 231.40/42.64  | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | Case 1:
% 231.40/42.64  | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | |   (69)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 231.40/42.64  | | | | | | | | | | |           & op(e2, e1) = e2)
% 231.40/42.64  | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | BETA: splitting (69) gives:
% 231.40/42.64  | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | Case 1:
% 231.40/42.64  | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | |   (70)  all_57_4 = e2 & op(e3, e1) = e2
% 231.40/42.64  | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | ALPHA: (70) implies:
% 231.40/42.64  | | | | | | | | | | | |   (71)  all_57_4 = e2
% 231.40/42.64  | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | COMBINE_EQS: (68), (71) imply:
% 231.40/42.64  | | | | | | | | | | | |   (72)  e2 = e0
% 231.40/42.64  | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | REF_CLOSE: (1), (6), (16), (18), (25), (27), (28), (34),
% 231.40/42.64  | | | | | | | | | | | |            (36), (54), (72) are inconsistent by sub-proof
% 231.40/42.64  | | | | | | | | | | | |            #1517.
% 231.40/42.64  | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | Case 2:
% 231.40/42.64  | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | |   (73)  all_57_5 = e2 & op(e2, e1) = e2
% 231.40/42.64  | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | REF_CLOSE: (18), (25), (73) are inconsistent by sub-proof
% 231.40/42.64  | | | | | | | | | | | |            #2425.
% 231.40/42.64  | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | End of split
% 231.40/42.64  | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | Case 2:
% 231.40/42.64  | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | |   (74)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 231.40/42.64  | | | | | | | | | | |           e2 & op(e0, e1) = e2)
% 231.40/42.64  | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | BETA: splitting (74) gives:
% 231.40/42.64  | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | Case 1:
% 231.40/42.64  | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | |   (75)  all_57_8 = e2 & op(e1, e1) = e2
% 231.40/42.64  | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | REF_CLOSE: (14), (36), (75) are inconsistent by sub-proof
% 231.40/42.64  | | | | | | | | | | | |            #1501.
% 231.40/42.64  | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | Case 2:
% 231.40/42.64  | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | |   (76)  all_57_14 = e2 & op(e0, e1) = e2
% 231.40/42.64  | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | ALPHA: (76) implies:
% 231.40/42.64  | | | | | | | | | | | |   (77)  all_57_14 = e2
% 231.40/42.64  | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | BETA: splitting (64) gives:
% 231.40/42.64  | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | Case 1:
% 231.40/42.64  | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | |   (78)  all_57_12 = e0 & op(e0, e3) = e0
% 231.40/42.64  | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | ALPHA: (78) implies:
% 231.40/42.64  | | | | | | | | | | | | |   (79)  all_57_12 = e0
% 231.40/42.64  | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | BETA: splitting (24) gives:
% 231.40/42.64  | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | Case 1:
% 231.40/42.64  | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | |   (80)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 231.40/42.64  | | | | | | | | | | | | | |           e1 & op(e0, e2) = e1)
% 231.40/42.64  | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | BETA: splitting (80) gives:
% 231.40/42.64  | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | Case 1:
% 231.40/42.64  | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | |   (81)  all_57_12 = e1 & op(e0, e3) = e1
% 231.40/42.64  | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | REF_CLOSE: (1), (6), (16), (18), (25), (27), (28), (34),
% 231.40/42.64  | | | | | | | | | | | | | | |            (36), (60), (79), (81) are inconsistent by
% 231.40/42.64  | | | | | | | | | | | | | | |            sub-proof #1470.
% 231.40/42.64  | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | Case 2:
% 231.40/42.64  | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | |   (82)  all_57_13 = e1 & op(e0, e2) = e1
% 231.40/42.64  | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | ALPHA: (82) implies:
% 231.40/42.64  | | | | | | | | | | | | | | |   (83)  all_57_13 = e1
% 231.40/42.64  | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | BETA: splitting (38) gives:
% 231.40/42.64  | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | Case 1:
% 231.40/42.64  | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | |   (84)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 231.40/42.64  | | | | | | | | | | | | | | | |           & op(e2, e3) = e2)
% 231.40/42.64  | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | REF_CLOSE: (8), (18), (21), (36), (60), (84) are inconsistent
% 231.40/42.64  | | | | | | | | | | | | | | | |            by sub-proof #1526.
% 231.40/42.64  | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | Case 2:
% 231.40/42.64  | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | |   (85)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 231.40/42.64  | | | | | | | | | | | | | | | |           e2 & op(e0, e3) = e2)
% 231.40/42.64  | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | BETA: splitting (85) gives:
% 231.40/42.64  | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | Case 1:
% 231.40/42.64  | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | |   (86)  all_57_6 = e2 & op(e1, e3) = e2
% 231.40/42.64  | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | ALPHA: (86) implies:
% 231.40/42.64  | | | | | | | | | | | | | | | | |   (87)  all_57_6 = e2
% 231.40/42.64  | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | BETA: splitting (7) gives:
% 231.40/42.64  | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | Case 1:
% 231.40/42.64  | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | |   (88)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 231.40/42.64  | | | | | | | | | | | | | | | | | |           & op(e1, e2) = e0)
% 231.40/42.64  | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | BETA: splitting (88) gives:
% 231.40/42.64  | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | Case 1:
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | |   (89)  all_57_6 = e0 & op(e1, e3) = e0
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | ALPHA: (89) implies:
% 231.40/42.64  | | | | | | | | | | | | | | | | | | |   (90)  all_57_6 = e0
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (6), (16), (18), (25), (27), (28), (34),
% 231.40/42.64  | | | | | | | | | | | | | | | | | | |            (36), (54), (87), (90) are inconsistent by
% 231.40/42.64  | | | | | | | | | | | | | | | | | | |            sub-proof #1469.
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | Case 2:
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | |   (91)  all_57_7 = e0 & op(e1, e2) = e0
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | ALPHA: (91) implies:
% 231.40/42.64  | | | | | | | | | | | | | | | | | | |   (92)  all_57_7 = e0
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (33), (92) are inconsistent by sub-proof
% 231.40/42.64  | | | | | | | | | | | | | | | | | | |            #2269.
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | End of split
% 231.40/42.64  | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | Case 2:
% 231.40/42.64  | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | |   (93)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 231.40/42.64  | | | | | | | | | | | | | | | | | |           e0 & op(e1, e0) = e0)
% 231.40/42.64  | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | BETA: splitting (93) gives:
% 231.40/42.64  | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | Case 1:
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | |   (94)  all_57_8 = e0 & op(e1, e1) = e0
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | ALPHA: (94) implies:
% 231.40/42.64  | | | | | | | | | | | | | | | | | | |   (95)  op(e1, e1) = e0
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (6), (8), (13), (16), (18), (21), (25),
% 231.40/42.64  | | | | | | | | | | | | | | | | | | |            (26), (27), (28), (33), (34), (36), (44), (54),
% 231.40/42.64  | | | | | | | | | | | | | | | | | | |            (57), (60), (68), (79), (87), (95) are
% 231.40/42.64  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1516.
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | Case 2:
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | |   (96)  all_57_11 = e0 & op(e1, e0) = e0
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | ALPHA: (96) implies:
% 231.40/42.64  | | | | | | | | | | | | | | | | | | |   (97)  all_57_11 = e0
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | BETA: splitting (13) gives:
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | Case 1:
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | |   (98)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | |           & op(e3, e2) = e2)
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | BETA: splitting (98) gives:
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | |   (99)  all_57_0 = e2 & op(e3, e3) = e2
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | ALPHA: (99) implies:
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | |   (100)  op(e3, e3) = e2
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (18), (21), (100) are inconsistent by
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | |            sub-proof #2490.
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | |   (101)  all_57_1 = e2 & op(e3, e2) = e2
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | ALPHA: (101) implies:
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | |   (102)  all_57_1 = e2
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (45) gives:
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | |   (103)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e2)
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (103) gives:
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (101) implies:
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | |   (104)  op(e3, e2) = e2
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (56) implies:
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | |   (105)  op(e3, e0) = e1
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (67) implies:
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | |   (106)  op(e3, e1) = e0
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_52_7, e1, e0, e3,
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (43), (105) gives:
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | |   (107)  all_52_7 = e1
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_52_5, e0, e1, e3,
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (2), (106) gives:
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | |   (108)  all_52_5 = e0
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_52_3, e2, e2, e3,
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (11), (104) gives:
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | |   (109)  all_52_3 = e2
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (23), (109) imply:
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | |   (110)   ~ (e3 = e2)
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (35), (108) imply:
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | |   (111)   ~ (e1 = e0)
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3), (107) imply:
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | |   (112)   ~ (e3 = e1)
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10), (107) imply:
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | |   (113)  op(e1, e1) = e0
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (6), (8), (13), (16), (18), (21), (22),
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | |            (25), (26), (27), (28), (33), (34), (36), (41),
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | |            (44), (54), (60), (68), (79), (87), (97), (113)
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1514.
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | |   (114)  all_57_7 = e2 & op(e1, e2) = e2
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (33), (114) are inconsistent by sub-proof
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | |            #2092.
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | |   (115)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e1, e0) = e2)
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (115) gives:
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | |   (116)  all_57_8 = e2 & op(e1, e1) = e2
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (116) implies:
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | |   (117)  op(e1, e1) = e2
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (5), (6), (8), (12), (13), (15), (16),
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | |            (18), (19), (21), (22), (24), (25), (26), (27),
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | |            (28), (33), (34), (36), (37), (41), (44), (77),
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | |            (79), (87), (97), (117) are inconsistent by
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1468.
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | |   (118)  all_57_11 = e2 & op(e1, e0) = e2
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (118) implies:
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | |   (119)  all_57_11 = e2
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (97), (119) imply:
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | |   (120)  e2 = e0
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (120) implies:
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | |   (121)  e2 = e0
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (102), (121) imply:
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | |   (122)  all_57_1 = e0
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (16), (18), (27), (33), (36), (83), (122) are
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2099.
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | End of split
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | End of split
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | End of split
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | Case 2:
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | |   (123)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e2)
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | BETA: splitting (123) gives:
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | Case 1:
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | |   (124)  all_57_4 = e2 & op(e3, e1) = e2
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | ALPHA: (124) implies:
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | |   (125)  all_57_4 = e2
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (8), (12), (13), (15), (16), (18), (19),
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | |            (21), (22), (25), (27), (28), (33), (34), (36),
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | |            (37), (41), (44), (97), (125) are inconsistent by
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | |            sub-proof #1480.
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | Case 2:
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | |   (126)  all_57_9 = e2 & op(e3, e0) = e2
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | ALPHA: (126) implies:
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | |   (127)  all_57_9 = e2
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (57), (127) imply:
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | |   (128)  e2 = e1
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | SIMP: (128) implies:
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | |   (129)  e2 = e1
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (87), (129) imply:
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | |   (130)  all_57_6 = e1
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (6), (8), (16), (18), (21), (25), (27),
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | |            (28), (34), (36), (38), (54), (60), (79), (130)
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1477.
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | End of split
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | End of split
% 231.40/42.64  | | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | | End of split
% 231.40/42.64  | | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | End of split
% 231.40/42.64  | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | Case 2:
% 231.40/42.64  | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | |   (131)  all_57_12 = e2 & op(e0, e3) = e2
% 231.40/42.64  | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | ALPHA: (131) implies:
% 231.40/42.64  | | | | | | | | | | | | | | | | |   (132)  all_57_12 = e2
% 231.40/42.64  | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | COMBINE_EQS: (79), (132) imply:
% 231.40/42.64  | | | | | | | | | | | | | | | | |   (133)  e2 = e0
% 231.40/42.64  | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (6), (16), (18), (25), (27), (28), (34),
% 231.40/42.64  | | | | | | | | | | | | | | | | |            (36), (54), (133) are inconsistent by sub-proof
% 231.40/42.64  | | | | | | | | | | | | | | | | |            #1517.
% 231.40/42.64  | | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | | End of split
% 231.40/42.64  | | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | End of split
% 231.40/42.64  | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | End of split
% 231.40/42.64  | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | Case 2:
% 231.40/42.64  | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | |   (134)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 231.40/42.64  | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 231.40/42.64  | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | BETA: splitting (134) gives:
% 231.40/42.64  | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | Case 1:
% 231.40/42.64  | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | |   (135)  all_57_14 = e1 & op(e0, e1) = e1
% 231.40/42.64  | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | ALPHA: (135) implies:
% 231.40/42.64  | | | | | | | | | | | | | | |   (136)  all_57_14 = e1
% 231.40/42.64  | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | REF_CLOSE: (36), (77), (136) are inconsistent by sub-proof
% 231.40/42.64  | | | | | | | | | | | | | | |            #2178.
% 231.40/42.64  | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | Case 2:
% 231.40/42.64  | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | |   (137)  all_57_15 = e1 & op(e0, e0) = e1
% 231.40/42.64  | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | | REF_CLOSE: (6), (22), (137) are inconsistent by sub-proof
% 231.40/42.64  | | | | | | | | | | | | | | |            #2318.
% 231.40/42.64  | | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | End of split
% 231.40/42.64  | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | End of split
% 231.40/42.64  | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | Case 2:
% 231.40/42.64  | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | |   (138)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 231.40/42.64  | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 231.40/42.64  | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | BETA: splitting (138) gives:
% 231.40/42.64  | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | Case 1:
% 231.40/42.64  | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | |   (139)  all_57_13 = e0 & op(e0, e2) = e0
% 231.40/42.64  | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | ALPHA: (139) implies:
% 231.40/42.64  | | | | | | | | | | | | | |   (140)  all_57_13 = e0
% 231.40/42.64  | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (8), (12), (13), (15), (16), (18), (19),
% 231.40/42.64  | | | | | | | | | | | | | |            (21), (27), (28), (33), (36), (44), (140) are
% 231.40/42.64  | | | | | | | | | | | | | |            inconsistent by sub-proof #2091.
% 231.40/42.64  | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | Case 2:
% 231.40/42.64  | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | |   (141)  all_57_14 = e0 & op(e0, e1) = e0
% 231.40/42.64  | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | ALPHA: (141) implies:
% 231.40/42.64  | | | | | | | | | | | | | |   (142)  all_57_14 = e0
% 231.40/42.64  | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | COMBINE_EQS: (77), (142) imply:
% 231.40/42.64  | | | | | | | | | | | | | |   (143)  e2 = e0
% 231.40/42.64  | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | COMBINE_EQS: (54), (143) imply:
% 231.40/42.64  | | | | | | | | | | | | | |   (144)  all_57_10 = e0
% 231.40/42.64  | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | REF_CLOSE: (1), (6), (16), (18), (25), (27), (28), (34),
% 231.40/42.64  | | | | | | | | | | | | | |            (36), (144) are inconsistent by sub-proof #1518.
% 231.40/42.64  | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | End of split
% 231.40/42.64  | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | End of split
% 231.40/42.64  | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | End of split
% 231.40/42.64  | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | End of split
% 231.40/42.64  | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | Case 2:
% 231.40/42.64  | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | |   (145)  all_57_9 = e0 & op(e3, e0) = e0
% 231.40/42.64  | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | ALPHA: (145) implies:
% 231.40/42.64  | | | | | | | | | |   (146)  all_57_9 = e0
% 231.40/42.64  | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | REF_CLOSE: (1), (6), (16), (18), (25), (27), (28), (34),
% 231.40/42.64  | | | | | | | | | |            (36), (57), (60), (146) are inconsistent by
% 231.40/42.64  | | | | | | | | | |            sub-proof #1467.
% 231.40/42.64  | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | End of split
% 231.40/42.64  | | | | | | | | | 
% 231.40/42.64  | | | | | | | | End of split
% 231.40/42.64  | | | | | | | | 
% 231.40/42.64  | | | | | | | End of split
% 231.40/42.64  | | | | | | | 
% 231.40/42.64  | | | | | | Case 2:
% 231.40/42.64  | | | | | | | 
% 231.40/42.64  | | | | | | |   (147)  all_57_3 = e1 & op(e2, e2) = e1
% 231.40/42.64  | | | | | | | 
% 231.40/42.64  | | | | | | | REF_CLOSE: (16), (28), (147) are inconsistent by sub-proof #2362.
% 231.40/42.64  | | | | | | | 
% 231.40/42.64  | | | | | | End of split
% 231.40/42.64  | | | | | | 
% 231.40/42.64  | | | | | Case 2:
% 231.40/42.64  | | | | | | 
% 231.40/42.64  | | | | | |   (148)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 &
% 231.40/42.64  | | | | | |            op(e2, e0) = e1)
% 231.40/42.64  | | | | | | 
% 231.40/42.64  | | | | | | REF_CLOSE: (6), (25), (36), (54), (148) are inconsistent by
% 231.40/42.64  | | | | | |            sub-proof #1466.
% 231.40/42.64  | | | | | | 
% 231.40/42.64  | | | | | End of split
% 231.40/42.64  | | | | | 
% 231.40/42.64  | | | | Case 2:
% 231.40/42.64  | | | | | 
% 231.40/42.64  | | | | |   (149)  all_57_10 = e1 & op(e2, e0) = e1
% 231.40/42.64  | | | | | 
% 231.40/42.64  | | | | | ALPHA: (149) implies:
% 231.40/42.64  | | | | |   (150)  all_57_10 = e1
% 231.40/42.64  | | | | | 
% 231.40/42.64  | | | | | REF_CLOSE: (36), (54), (150) are inconsistent by sub-proof #2144.
% 231.40/42.64  | | | | | 
% 231.40/42.64  | | | | End of split
% 231.40/42.64  | | | | 
% 231.40/42.64  | | | Case 2:
% 231.40/42.64  | | | | 
% 231.40/42.64  | | | |   (151)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0,
% 231.40/42.64  | | | |              e0) = e1)
% 231.40/42.64  | | | | 
% 231.40/42.64  | | | | BETA: splitting (151) gives:
% 231.40/42.64  | | | | 
% 231.40/42.64  | | | | Case 1:
% 231.40/42.64  | | | | | 
% 231.40/42.64  | | | | |   (152)  all_57_11 = e1 & op(e1, e0) = e1
% 231.40/42.64  | | | | | 
% 231.40/42.64  | | | | | ALPHA: (152) implies:
% 231.40/42.64  | | | | |   (153)  all_57_11 = e1
% 231.40/42.64  | | | | | 
% 231.40/42.64  | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (10), (12), (13), (14),
% 231.40/42.64  | | | | |            (15), (16), (17), (18), (19), (20), (21), (22), (24), (25),
% 231.40/42.64  | | | | |            (26), (27), (28), (30), (31), (32), (33), (34), (36), (37),
% 231.40/42.64  | | | | |            (38), (39), (40), (41), (42), (43), (44), (45), (54), (153)
% 231.40/42.64  | | | | |            are inconsistent by sub-proof #1460.
% 231.40/42.64  | | | | | 
% 231.40/42.64  | | | | Case 2:
% 231.40/42.64  | | | | | 
% 231.40/42.64  | | | | |   (154)  all_57_15 = e1 & op(e0, e0) = e1
% 231.40/42.64  | | | | | 
% 231.40/42.64  | | | | | REF_CLOSE: (6), (22), (154) are inconsistent by sub-proof #2318.
% 231.40/42.64  | | | | | 
% 231.40/42.64  | | | | End of split
% 231.40/42.64  | | | | 
% 231.40/42.64  | | | End of split
% 231.40/42.64  | | | 
% 231.40/42.64  | | End of split
% 231.40/42.64  | | 
% 231.40/42.64  | End of split
% 231.40/42.64  | 
% 231.40/42.64  End of proof
% 231.40/42.64  
% 231.40/42.64  Sub-proof #1460 shows that the following formulas are inconsistent:
% 231.40/42.64  ----------------------------------------------------------------
% 231.40/42.64    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.40/42.64         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.40/42.64    (2)   ~ (all_52_7 = e3)
% 231.40/42.64    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.40/42.64         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.40/42.64    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.40/42.64         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.40/42.64    (5)   ~ (e3 = e1)
% 231.40/42.64    (6)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 231.40/42.64         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.40/42.64    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.40/42.64           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.40/42.64    (8)  op(all_52_7, all_52_7) = e0
% 231.40/42.64    (9)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.40/42.64         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.40/42.64    (10)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.40/42.64          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.40/42.64    (11)  all_57_8 = e1
% 231.40/42.64    (12)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.40/42.64          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.40/42.64    (13)  all_57_3 = e0
% 231.40/42.64    (14)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.40/42.64          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.40/42.64    (15)   ~ (e3 = e2)
% 231.40/42.64    (16)   ~ (e3 = e0)
% 231.40/42.64    (17)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.40/42.64          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.40/42.64    (18)  op(e3, e3) = e3
% 231.40/42.64    (19)  all_57_15 = e3
% 231.40/42.64    (20)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.40/42.64          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.40/42.64            e1)
% 231.40/42.64    (21)  all_57_10 = e2
% 231.40/42.64    (22)  all_57_5 = e3
% 231.40/42.64    (23)  op(e1, e1) = e1
% 231.40/42.64    (24)   ~ (e2 = e0)
% 231.40/42.64    (25)   ~ (e1 = e0)
% 231.40/42.64    (26)  op(e0, e0) = e3
% 231.40/42.64    (27)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.40/42.64          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.40/42.64            e2)
% 231.40/42.64    (28)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.40/42.64              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.40/42.64                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.40/42.64                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.40/42.64    (29)  all_57_7 = e3
% 231.40/42.64    (30)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.40/42.64          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.40/42.64    (31)  all_57_11 = e1
% 231.40/42.64    (32)   ~ (e2 = e1)
% 231.40/42.64    (33)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.40/42.64          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.40/42.64    (34)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.40/42.64          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.40/42.64    (35)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.40/42.64          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.40/42.64    (36)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.40/42.64          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.40/42.64    (37)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.40/42.64          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.40/42.64    (38)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 231.40/42.64          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 231.40/42.64    (39)  op(e3, e0) = all_52_7
% 231.40/42.64    (40)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.40/42.64          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.40/42.64    (41)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 231.40/42.64          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 231.40/42.64  
% 231.40/42.64  Begin of proof
% 231.40/42.64  | 
% 231.40/42.64  | BETA: splitting (1) gives:
% 231.40/42.64  | 
% 231.40/42.64  | Case 1:
% 231.40/42.64  | | 
% 231.40/42.64  | |   (42)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) =
% 231.40/42.64  | |           e1)
% 231.40/42.64  | | 
% 231.40/42.64  | | BETA: splitting (42) gives:
% 231.40/42.64  | | 
% 231.40/42.64  | | Case 1:
% 231.40/42.64  | | | 
% 231.40/42.64  | | |   (43)  all_57_2 = e1 & op(e2, e3) = e1
% 231.40/42.64  | | | 
% 231.40/42.64  | | | ALPHA: (43) implies:
% 231.40/42.64  | | |   (44)  all_57_2 = e1
% 231.40/42.64  | | | 
% 231.40/42.64  | | | BETA: splitting (41) gives:
% 231.40/42.64  | | | 
% 231.40/42.64  | | | Case 1:
% 231.40/42.64  | | | | 
% 231.40/42.64  | | | |   (45)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2)
% 231.40/42.64  | | | |           = e2)
% 231.40/42.64  | | | | 
% 231.40/42.64  | | | | BETA: splitting (45) gives:
% 231.40/42.64  | | | | 
% 231.40/42.64  | | | | Case 1:
% 231.40/42.64  | | | | | 
% 231.40/42.64  | | | | |   (46)  all_57_6 = e2 & op(e1, e3) = e2
% 231.40/42.64  | | | | | 
% 231.40/42.64  | | | | | ALPHA: (46) implies:
% 231.40/42.64  | | | | |   (47)  all_57_6 = e2
% 231.40/42.64  | | | | | 
% 231.40/42.64  | | | | | BETA: splitting (28) gives:
% 231.40/42.64  | | | | | 
% 231.40/42.64  | | | | | Case 1:
% 231.40/42.64  | | | | | | 
% 231.40/42.64  | | | | | |   (48)  all_57_15 = e0 & op(e0, e0) = e0
% 231.40/42.64  | | | | | | 
% 231.40/42.64  | | | | | | ALPHA: (48) implies:
% 231.40/42.64  | | | | | |   (49)  op(e0, e0) = e0
% 231.40/42.64  | | | | | | 
% 231.40/42.64  | | | | | | REF_CLOSE: (7), (16), (26), (49) are inconsistent by sub-proof
% 231.40/42.64  | | | | | |            #2304.
% 231.40/42.64  | | | | | | 
% 231.40/42.64  | | | | | Case 2:
% 231.40/42.64  | | | | | | 
% 231.40/42.64  | | | | | |   (50)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 &
% 231.40/42.64  | | | | | |             op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) &
% 231.40/42.64  | | | | | |         ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.40/42.64  | | | | | |             op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 231.40/42.64  | | | | | | 
% 231.40/42.64  | | | | | | ALPHA: (50) implies:
% 231.40/42.64  | | | | | |   (51)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2,
% 231.40/42.64  | | | | | |             e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.40/42.64  | | | | | | 
% 231.40/42.64  | | | | | | BETA: splitting (36) gives:
% 231.40/42.64  | | | | | | 
% 231.40/42.64  | | | | | | Case 1:
% 231.40/42.64  | | | | | | | 
% 231.40/42.64  | | | | | | |   (52)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 &
% 231.40/42.64  | | | | | | |           op(e2, e3) = e0)
% 231.40/42.64  | | | | | | | 
% 231.40/42.64  | | | | | | | REF_CLOSE: (1), (5), (7), (13), (15), (16), (18), (22), (24),
% 231.40/42.64  | | | | | | |            (25), (30), (32), (52) are inconsistent by sub-proof
% 231.40/42.64  | | | | | | |            #1784.
% 231.40/42.64  | | | | | | | 
% 231.40/42.64  | | | | | | Case 2:
% 231.40/42.64  | | | | | | | 
% 231.40/42.64  | | | | | | |   (53)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 &
% 231.40/42.64  | | | | | | |           op(e0, e3) = e0)
% 231.40/42.64  | | | | | | | 
% 231.40/42.64  | | | | | | | BETA: splitting (53) gives:
% 231.40/42.64  | | | | | | | 
% 231.40/42.64  | | | | | | | Case 1:
% 231.40/42.64  | | | | | | | | 
% 231.40/42.64  | | | | | | | |   (54)  all_57_6 = e0 & op(e1, e3) = e0
% 231.40/42.64  | | | | | | | | 
% 231.40/42.64  | | | | | | | | ALPHA: (54) implies:
% 231.40/42.64  | | | | | | | |   (55)  all_57_6 = e0
% 231.40/42.64  | | | | | | | | 
% 231.40/42.64  | | | | | | | | REF_CLOSE: (1), (5), (13), (15), (21), (22), (24), (25), (30),
% 231.40/42.64  | | | | | | | |            (32), (47), (55) are inconsistent by sub-proof #1469.
% 231.40/42.64  | | | | | | | | 
% 231.40/42.64  | | | | | | | Case 2:
% 231.40/42.64  | | | | | | | | 
% 231.40/42.64  | | | | | | | |   (56)  all_57_12 = e0 & op(e0, e3) = e0
% 231.40/42.64  | | | | | | | | 
% 231.40/42.64  | | | | | | | | ALPHA: (56) implies:
% 231.40/42.64  | | | | | | | |   (57)  all_57_12 = e0
% 231.40/42.64  | | | | | | | | 
% 231.40/42.64  | | | | | | | | BETA: splitting (20) gives:
% 231.40/42.64  | | | | | | | | 
% 231.40/42.64  | | | | | | | | Case 1:
% 231.40/42.64  | | | | | | | | | 
% 231.40/42.64  | | | | | | | | |   (58)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 &
% 231.40/42.64  | | | | | | | | |           op(e0, e2) = e1)
% 231.40/42.64  | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | BETA: splitting (58) gives:
% 231.40/42.64  | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | Case 1:
% 231.40/42.64  | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | |   (59)  all_57_12 = e1 & op(e0, e3) = e1
% 231.40/42.64  | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | REF_CLOSE: (1), (5), (13), (15), (22), (24), (25), (30),
% 231.40/42.64  | | | | | | | | | |            (32), (44), (57), (59) are inconsistent by
% 231.40/42.64  | | | | | | | | | |            sub-proof #1470.
% 231.40/42.64  | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | Case 2:
% 231.40/42.64  | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | |   (60)  all_57_13 = e1 & op(e0, e2) = e1
% 231.40/42.64  | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | ALPHA: (60) implies:
% 231.40/42.64  | | | | | | | | | |   (61)  all_57_13 = e1
% 231.40/42.64  | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | BETA: splitting (4) gives:
% 231.40/42.64  | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | Case 1:
% 231.40/42.64  | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | |   (62)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 231.40/42.64  | | | | | | | | | | |           & op(e2, e2) = e2)
% 231.40/42.64  | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | BETA: splitting (62) gives:
% 231.40/42.64  | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | Case 1:
% 231.40/42.64  | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | |   (63)  all_57_1 = e2 & op(e3, e2) = e2
% 231.40/42.64  | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | ALPHA: (63) implies:
% 231.40/42.64  | | | | | | | | | | | |   (64)  all_57_1 = e2
% 231.40/42.64  | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | BETA: splitting (6) gives:
% 231.40/42.64  | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | Case 1:
% 231.40/42.64  | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | |   (65)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 231.40/42.64  | | | | | | | | | | | | |           & op(e1, e2) = e0)
% 231.40/42.64  | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | BETA: splitting (65) gives:
% 231.40/42.64  | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | Case 1:
% 231.40/42.64  | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | |   (66)  all_57_6 = e0 & op(e1, e3) = e0
% 231.40/42.64  | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | ALPHA: (66) implies:
% 231.40/42.64  | | | | | | | | | | | | | |   (67)  all_57_6 = e0
% 231.40/42.64  | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | COMBINE_EQS: (47), (67) imply:
% 231.40/42.64  | | | | | | | | | | | | | |   (68)  e2 = e0
% 231.40/42.64  | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | COMBINE_EQS: (64), (68) imply:
% 231.40/42.64  | | | | | | | | | | | | | |   (69)  all_57_1 = e0
% 231.40/42.64  | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | REF_CLOSE: (4), (13), (15), (24), (29), (32), (61), (69) are
% 231.40/42.64  | | | | | | | | | | | | | |            inconsistent by sub-proof #2099.
% 231.40/42.64  | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | Case 2:
% 231.40/42.64  | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | |   (70)  all_57_7 = e0 & op(e1, e2) = e0
% 231.40/42.64  | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | ALPHA: (70) implies:
% 231.40/42.64  | | | | | | | | | | | | | |   (71)  all_57_7 = e0
% 231.40/42.64  | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | REF_CLOSE: (16), (29), (71) are inconsistent by sub-proof
% 231.40/42.64  | | | | | | | | | | | | | |            #2269.
% 231.40/42.64  | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | End of split
% 231.40/42.64  | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | Case 2:
% 231.40/42.64  | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | |   (72)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 231.40/42.64  | | | | | | | | | | | | |           e0 & op(e1, e0) = e0)
% 231.40/42.64  | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | BETA: splitting (72) gives:
% 231.40/42.64  | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | Case 1:
% 231.40/42.64  | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | |   (73)  all_57_8 = e0 & op(e1, e1) = e0
% 231.40/42.64  | | | | | | | | | | | | | | 
% 231.40/42.64  | | | | | | | | | | | | | | ALPHA: (73) implies:
% 231.40/42.65  | | | | | | | | | | | | | |   (74)  op(e1, e1) = e0
% 231.40/42.65  | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (5), (7), (13), (15), (18), (21), (22),
% 231.40/42.65  | | | | | | | | | | | | | |            (23), (24), (25), (29), (30), (32), (40), (44),
% 231.40/42.65  | | | | | | | | | | | | | |            (47), (57), (64), (74) are inconsistent by
% 231.40/42.65  | | | | | | | | | | | | | |            sub-proof #1519.
% 231.40/42.65  | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | Case 2:
% 231.40/42.65  | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | |   (75)  all_57_11 = e0 & op(e1, e0) = e0
% 231.40/42.65  | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | | REF_CLOSE: (1), (5), (13), (15), (22), (24), (25), (30),
% 231.40/42.65  | | | | | | | | | | | | | |            (31), (32), (44), (75) are inconsistent by
% 231.40/42.65  | | | | | | | | | | | | | |            sub-proof #1465.
% 231.40/42.65  | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | End of split
% 231.40/42.65  | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | End of split
% 231.40/42.65  | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | Case 2:
% 231.40/42.65  | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | |   (76)  all_57_3 = e2 & op(e2, e2) = e2
% 231.40/42.65  | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | ALPHA: (76) implies:
% 231.40/42.65  | | | | | | | | | | | |   (77)  all_57_3 = e2
% 231.40/42.65  | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | COMBINE_EQS: (13), (77) imply:
% 231.40/42.65  | | | | | | | | | | | |   (78)  e2 = e0
% 231.40/42.65  | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | COMBINE_EQS: (21), (78) imply:
% 231.40/42.65  | | | | | | | | | | | |   (79)  all_57_10 = e0
% 231.40/42.65  | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | REF_CLOSE: (1), (5), (13), (15), (22), (24), (25), (30),
% 231.40/42.65  | | | | | | | | | | | |            (32), (79) are inconsistent by sub-proof #1518.
% 231.40/42.65  | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | End of split
% 231.40/42.65  | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | Case 2:
% 231.40/42.65  | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | |   (80)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 231.40/42.65  | | | | | | | | | | |           e2 & op(e0, e2) = e2)
% 231.40/42.65  | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | BETA: splitting (80) gives:
% 231.40/42.65  | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | Case 1:
% 231.40/42.65  | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | |   (81)  all_57_7 = e2 & op(e1, e2) = e2
% 231.40/42.65  | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | ALPHA: (81) implies:
% 231.40/42.65  | | | | | | | | | | | |   (82)  all_57_7 = e2
% 231.40/42.65  | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | REF_CLOSE: (15), (29), (82) are inconsistent by sub-proof
% 231.40/42.65  | | | | | | | | | | | |            #2102.
% 231.40/42.65  | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | Case 2:
% 231.40/42.65  | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | |   (83)  all_57_13 = e2 & op(e0, e2) = e2
% 231.40/42.65  | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | ALPHA: (83) implies:
% 231.40/42.65  | | | | | | | | | | | |   (84)  all_57_13 = e2
% 231.40/42.65  | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | COMBINE_EQS: (61), (84) imply:
% 231.40/42.65  | | | | | | | | | | | |   (85)  e2 = e1
% 231.40/42.65  | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | COMBINE_EQS: (47), (85) imply:
% 231.40/42.65  | | | | | | | | | | | |   (86)  all_57_6 = e1
% 231.40/42.65  | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | REF_CLOSE: (1), (3), (5), (7), (13), (15), (18), (21), (22),
% 231.40/42.65  | | | | | | | | | | | |            (24), (25), (30), (32), (34), (44), (57), (86) are
% 231.40/42.65  | | | | | | | | | | | |            inconsistent by sub-proof #1477.
% 231.40/42.65  | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | End of split
% 231.40/42.65  | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | End of split
% 231.40/42.65  | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | End of split
% 231.40/42.65  | | | | | | | | | 
% 231.40/42.65  | | | | | | | | Case 2:
% 231.40/42.65  | | | | | | | | | 
% 231.40/42.65  | | | | | | | | |   (87)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 &
% 231.40/42.65  | | | | | | | | |           op(e0, e0) = e1)
% 231.40/42.65  | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | BETA: splitting (87) gives:
% 231.40/42.65  | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | Case 1:
% 231.40/42.65  | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | |   (88)  all_57_14 = e1 & op(e0, e1) = e1
% 231.40/42.65  | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | ALPHA: (88) implies:
% 231.40/42.65  | | | | | | | | | |   (89)  all_57_14 = e1
% 231.40/42.65  | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | BETA: splitting (35) gives:
% 231.40/42.65  | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | Case 1:
% 231.40/42.65  | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | |   (90)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 231.40/42.65  | | | | | | | | | | |           & op(e2, e1) = e2)
% 231.40/42.65  | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | BETA: splitting (90) gives:
% 231.40/42.65  | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | Case 1:
% 231.40/42.65  | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | |   (91)  all_57_4 = e2 & op(e3, e1) = e2
% 231.40/42.65  | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | ALPHA: (91) implies:
% 231.40/42.65  | | | | | | | | | | | |   (92)  all_57_4 = e2
% 231.40/42.65  | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | BETA: splitting (27) gives:
% 231.40/42.65  | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | Case 1:
% 231.40/42.65  | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | |   (93)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 231.40/42.65  | | | | | | | | | | | | |           e2 & op(e0, e2) = e2)
% 231.40/42.65  | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | BETA: splitting (93) gives:
% 231.40/42.65  | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | Case 1:
% 231.40/42.65  | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | |   (94)  all_57_12 = e2 & op(e0, e3) = e2
% 231.40/42.65  | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | | ALPHA: (94) implies:
% 231.40/42.65  | | | | | | | | | | | | | |   (95)  all_57_12 = e2
% 231.40/42.65  | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | | COMBINE_EQS: (57), (95) imply:
% 231.40/42.65  | | | | | | | | | | | | | |   (96)  e2 = e0
% 231.40/42.65  | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (5), (7), (11), (13), (15), (18), (21),
% 231.40/42.65  | | | | | | | | | | | | | |            (22), (24), (25), (30), (32), (35), (47), (57),
% 231.40/42.65  | | | | | | | | | | | | | |            (89), (92), (96) are inconsistent by sub-proof
% 231.40/42.65  | | | | | | | | | | | | | |            #1464.
% 231.40/42.65  | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | Case 2:
% 231.40/42.65  | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | |   (97)  all_57_13 = e2 & op(e0, e2) = e2
% 231.40/42.65  | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | | ALPHA: (97) implies:
% 231.40/42.65  | | | | | | | | | | | | | |   (98)  all_57_13 = e2
% 231.40/42.65  | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | | BETA: splitting (40) gives:
% 231.40/42.65  | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | | Case 1:
% 231.40/42.65  | | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | | |   (99)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 231.40/42.65  | | | | | | | | | | | | | | |           & op(e2, e2) = e1)
% 231.40/42.65  | | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | | | BETA: splitting (99) gives:
% 231.40/42.65  | | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | | | Case 1:
% 231.40/42.65  | | | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | | | |   (100)  all_57_1 = e1 & op(e3, e2) = e1
% 231.40/42.65  | | | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | | | | ALPHA: (100) implies:
% 231.40/42.65  | | | | | | | | | | | | | | | |   (101)  all_57_1 = e1
% 231.40/42.65  | | | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | | | | BETA: splitting (6) gives:
% 231.40/42.65  | | | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | | | | Case 1:
% 231.40/42.65  | | | | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | | | | |   (102)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 231.40/42.65  | | | | | | | | | | | | | | | | |            & op(e1, e2) = e0)
% 231.40/42.65  | | | | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | | | | | BETA: splitting (102) gives:
% 231.40/42.65  | | | | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | | | | | Case 1:
% 231.40/42.65  | | | | | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | | | | | |   (103)  all_57_6 = e0 & op(e1, e3) = e0
% 231.40/42.65  | | | | | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | | | | | | ALPHA: (103) implies:
% 231.40/42.65  | | | | | | | | | | | | | | | | | |   (104)  all_57_6 = e0
% 231.40/42.65  | | | | | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (47), (104) imply:
% 231.40/42.65  | | | | | | | | | | | | | | | | | |   (105)  e2 = e0
% 231.40/42.65  | | | | | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (5), (7), (11), (13), (15), (18), (21),
% 231.40/42.65  | | | | | | | | | | | | | | | | | |            (22), (24), (25), (30), (32), (35), (47), (57),
% 231.40/42.65  | | | | | | | | | | | | | | | | | |            (89), (92), (105) are inconsistent by sub-proof
% 231.40/42.65  | | | | | | | | | | | | | | | | | |            #1464.
% 231.40/42.65  | | | | | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | | | | | Case 2:
% 231.40/42.65  | | | | | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | | | | | |   (106)  all_57_7 = e0 & op(e1, e2) = e0
% 231.40/42.65  | | | | | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (29), (106) are inconsistent by sub-proof
% 231.40/42.65  | | | | | | | | | | | | | | | | | |            #2042.
% 231.40/42.65  | | | | | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | | | | | End of split
% 231.40/42.65  | | | | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | | | | Case 2:
% 231.40/42.65  | | | | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | | | | |   (107)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 231.40/42.65  | | | | | | | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 231.40/42.65  | | | | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 231.40/42.65  | | | | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | | | | | Case 1:
% 231.40/42.65  | | | | | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | | | | | |   (108)  all_57_8 = e0 & op(e1, e1) = e0
% 231.40/42.65  | | | | | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | | | | | | ALPHA: (108) implies:
% 231.40/42.65  | | | | | | | | | | | | | | | | | |   (109)  op(e1, e1) = e0
% 231.40/42.65  | | | | | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (10), (12),
% 231.40/42.65  | | | | | | | | | | | | | | | | | |            (13), (15), (16), (17), (18), (19), (22), (24),
% 231.40/42.65  | | | | | | | | | | | | | | | | | |            (25), (26), (27), (29), (30), (32), (33), (34),
% 231.40/42.65  | | | | | | | | | | | | | | | | | |            (36), (37), (38), (39), (40), (41), (51), (57),
% 231.40/42.65  | | | | | | | | | | | | | | | | | |            (109) are inconsistent by sub-proof #1500.
% 231.40/42.65  | | | | | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | | | | | Case 2:
% 231.40/42.65  | | | | | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | | | | | |   (110)  all_57_11 = e0 & op(e1, e0) = e0
% 231.40/42.65  | | | | | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | | | | | | ALPHA: (110) implies:
% 231.40/42.65  | | | | | | | | | | | | | | | | | |   (111)  all_57_11 = e0
% 231.40/42.65  | | | | | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (7), (9), (10), (12), (13),
% 231.40/42.65  | | | | | | | | | | | | | | | | | |            (15), (16), (18), (19), (22), (24), (25), (29),
% 231.40/42.65  | | | | | | | | | | | | | | | | | |            (30), (32), (33), (37), (40), (44), (47), (57),
% 231.40/42.65  | | | | | | | | | | | | | | | | | |            (98), (101), (111) are inconsistent by sub-proof
% 231.40/42.65  | | | | | | | | | | | | | | | | | |            #1473.
% 231.40/42.65  | | | | | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | | | | | End of split
% 231.40/42.65  | | | | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | | | | End of split
% 231.40/42.65  | | | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | | | Case 2:
% 231.40/42.65  | | | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | | | |   (112)  all_57_3 = e1 & op(e2, e2) = e1
% 231.40/42.65  | | | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | | | | REF_CLOSE: (1), (5), (13), (15), (22), (24), (25), (30),
% 231.40/42.65  | | | | | | | | | | | | | | | |            (32), (44), (112) are inconsistent by sub-proof
% 231.40/42.65  | | | | | | | | | | | | | | | |            #1520.
% 231.40/42.65  | | | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | | | End of split
% 231.40/42.65  | | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | | Case 2:
% 231.40/42.65  | | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | | |   (113)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 231.40/42.65  | | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 231.40/42.65  | | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | | | BETA: splitting (113) gives:
% 231.40/42.65  | | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | | | Case 1:
% 231.40/42.65  | | | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | | | |   (114)  all_57_7 = e1 & op(e1, e2) = e1
% 231.40/42.65  | | | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | | | | ALPHA: (114) implies:
% 231.40/42.65  | | | | | | | | | | | | | | | |   (115)  all_57_7 = e1
% 231.40/42.65  | | | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | | | | REF_CLOSE: (5), (29), (115) are inconsistent by sub-proof
% 231.40/42.65  | | | | | | | | | | | | | | | |            #2115.
% 231.40/42.65  | | | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | | | Case 2:
% 231.40/42.65  | | | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | | | |   (116)  all_57_13 = e1 & op(e0, e2) = e1
% 231.40/42.65  | | | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | | | | ALPHA: (116) implies:
% 231.40/42.65  | | | | | | | | | | | | | | | |   (117)  all_57_13 = e1
% 231.40/42.65  | | | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | | | | COMBINE_EQS: (98), (117) imply:
% 231.40/42.65  | | | | | | | | | | | | | | | |   (118)  e2 = e1
% 231.40/42.65  | | | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | | | | SIMP: (118) implies:
% 231.40/42.65  | | | | | | | | | | | | | | | |   (119)  e2 = e1
% 231.40/42.65  | | | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | | | | COMBINE_EQS: (47), (119) imply:
% 231.40/42.65  | | | | | | | | | | | | | | | |   (120)  all_57_6 = e1
% 231.40/42.65  | | | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (5), (7), (13), (15), (18), (21), (22),
% 231.40/42.65  | | | | | | | | | | | | | | | |            (24), (25), (30), (32), (34), (44), (57), (120)
% 231.40/42.65  | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1477.
% 231.40/42.65  | | | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | | | End of split
% 231.40/42.65  | | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | | End of split
% 231.40/42.65  | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | End of split
% 231.40/42.65  | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | Case 2:
% 231.40/42.65  | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | |   (121)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 231.40/42.65  | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 231.40/42.65  | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | BETA: splitting (121) gives:
% 231.40/42.65  | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | Case 1:
% 231.40/42.65  | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | |   (122)  all_57_14 = e2 & op(e0, e1) = e2
% 231.40/42.65  | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (5), (7), (13), (15), (18), (21), (22),
% 231.40/42.65  | | | | | | | | | | | | | |            (24), (25), (30), (32), (34), (44), (47), (57),
% 231.40/42.65  | | | | | | | | | | | | | |            (89), (122) are inconsistent by sub-proof #1463.
% 231.40/42.65  | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | Case 2:
% 231.40/42.65  | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | |   (123)  all_57_15 = e2 & op(e0, e0) = e2
% 231.40/42.65  | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | | ALPHA: (123) implies:
% 231.40/42.65  | | | | | | | | | | | | | |   (124)  all_57_15 = e2
% 231.40/42.65  | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | | REF_CLOSE: (15), (19), (124) are inconsistent by sub-proof
% 231.40/42.65  | | | | | | | | | | | | | |            #2058.
% 231.40/42.65  | | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | | End of split
% 231.40/42.65  | | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | End of split
% 231.40/42.65  | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | Case 2:
% 231.40/42.65  | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | |   (125)  all_57_5 = e2 & op(e2, e1) = e2
% 231.40/42.65  | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | REF_CLOSE: (15), (22), (125) are inconsistent by sub-proof
% 231.40/42.65  | | | | | | | | | | | |            #2425.
% 231.40/42.65  | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | End of split
% 231.40/42.65  | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | Case 2:
% 231.40/42.65  | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | |   (126)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 231.40/42.65  | | | | | | | | | | |            e2 & op(e0, e1) = e2)
% 231.40/42.65  | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | BETA: splitting (126) gives:
% 231.40/42.65  | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | Case 1:
% 231.40/42.65  | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | |   (127)  all_57_8 = e2 & op(e1, e1) = e2
% 231.40/42.65  | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | ALPHA: (127) implies:
% 231.40/42.65  | | | | | | | | | | | |   (128)  op(e1, e1) = e2
% 231.40/42.65  | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 231.40/42.65  | | | | | | | | | | | |            (12), (13), (14), (15), (16), (17), (18), (19),
% 231.40/42.65  | | | | | | | | | | | |            (20), (22), (24), (25), (26), (27), (28), (29),
% 231.40/42.65  | | | | | | | | | | | |            (30), (32), (33), (34), (35), (36), (37), (38),
% 231.40/42.65  | | | | | | | | | | | |            (39), (40), (41), (47), (128) are inconsistent by
% 231.40/42.65  | | | | | | | | | | | |            sub-proof #1461.
% 231.40/42.65  | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | Case 2:
% 231.40/42.65  | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | |   (129)  all_57_14 = e2 & op(e0, e1) = e2
% 231.40/42.65  | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | | REF_CLOSE: (1), (3), (5), (7), (13), (15), (18), (21), (22),
% 231.40/42.65  | | | | | | | | | | | |            (24), (25), (30), (32), (34), (44), (47), (57),
% 231.40/42.65  | | | | | | | | | | | |            (89), (129) are inconsistent by sub-proof #1463.
% 231.40/42.65  | | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | | End of split
% 231.40/42.65  | | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | End of split
% 231.40/42.65  | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | Case 2:
% 231.40/42.65  | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | |   (130)  all_57_15 = e1 & op(e0, e0) = e1
% 231.40/42.65  | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | | REF_CLOSE: (5), (19), (130) are inconsistent by sub-proof
% 231.40/42.65  | | | | | | | | | |            #2318.
% 231.40/42.65  | | | | | | | | | | 
% 231.40/42.65  | | | | | | | | | End of split
% 231.40/42.65  | | | | | | | | | 
% 231.40/42.65  | | | | | | | | End of split
% 231.40/42.65  | | | | | | | | 
% 231.40/42.65  | | | | | | | End of split
% 231.40/42.65  | | | | | | | 
% 231.40/42.65  | | | | | | End of split
% 231.40/42.65  | | | | | | 
% 231.40/42.65  | | | | | End of split
% 231.40/42.65  | | | | | 
% 231.40/42.65  | | | | Case 2:
% 231.40/42.65  | | | | | 
% 231.40/42.65  | | | | |   (131)  all_57_7 = e2 & op(e1, e2) = e2
% 231.40/42.65  | | | | | 
% 231.40/42.65  | | | | | REF_CLOSE: (15), (29), (131) are inconsistent by sub-proof #2092.
% 231.40/42.65  | | | | | 
% 231.40/42.65  | | | | End of split
% 231.40/42.65  | | | | 
% 231.40/42.65  | | | Case 2:
% 231.40/42.65  | | | | 
% 231.40/42.65  | | | |   (132)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1,
% 231.40/42.65  | | | |              e0) = e2)
% 231.40/42.65  | | | | 
% 231.40/42.65  | | | | BETA: splitting (132) gives:
% 231.40/42.65  | | | | 
% 231.40/42.65  | | | | Case 1:
% 231.40/42.65  | | | | | 
% 231.40/42.65  | | | | |   (133)  all_57_8 = e2 & op(e1, e1) = e2
% 231.40/42.65  | | | | | 
% 231.40/42.65  | | | | | REF_CLOSE: (11), (32), (133) are inconsistent by sub-proof #1501.
% 231.40/42.65  | | | | | 
% 231.40/42.65  | | | | Case 2:
% 231.40/42.65  | | | | | 
% 231.40/42.65  | | | | |   (134)  all_57_11 = e2 & op(e1, e0) = e2
% 231.40/42.65  | | | | | 
% 231.40/42.65  | | | | | ALPHA: (134) implies:
% 231.40/42.65  | | | | |   (135)  all_57_11 = e2
% 231.40/42.65  | | | | | 
% 231.40/42.65  | | | | | REF_CLOSE: (31), (32), (135) are inconsistent by sub-proof #2113.
% 231.40/42.65  | | | | | 
% 231.40/42.65  | | | | End of split
% 231.40/42.65  | | | | 
% 231.40/42.65  | | | End of split
% 231.40/42.65  | | | 
% 231.40/42.65  | | Case 2:
% 231.40/42.65  | | | 
% 231.40/42.65  | | |   (136)  all_57_3 = e1 & op(e2, e2) = e1
% 231.40/42.65  | | | 
% 231.40/42.65  | | | REF_CLOSE: (13), (25), (136) are inconsistent by sub-proof #2362.
% 231.40/42.65  | | | 
% 231.40/42.65  | | End of split
% 231.40/42.65  | | 
% 231.40/42.65  | Case 2:
% 231.40/42.65  | | 
% 231.40/42.65  | |   (137)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) =
% 231.40/42.65  | |            e1)
% 231.40/42.65  | | 
% 231.40/42.65  | | REF_CLOSE: (5), (21), (22), (32), (137) are inconsistent by sub-proof #1466.
% 231.40/42.65  | | 
% 231.40/42.65  | End of split
% 231.40/42.65  | 
% 231.40/42.65  End of proof
% 231.40/42.65  
% 231.40/42.65  Sub-proof #1461 shows that the following formulas are inconsistent:
% 231.40/42.65  ----------------------------------------------------------------
% 231.40/42.65    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.40/42.65         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.40/42.65    (2)   ~ (all_52_7 = e3)
% 231.40/42.65    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.40/42.65         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.40/42.65    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.40/42.65         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.40/42.65    (5)   ~ (e3 = e1)
% 231.40/42.65    (6)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 231.40/42.65         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.40/42.65    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.40/42.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.40/42.65    (8)  op(all_52_7, all_52_7) = e0
% 231.40/42.65    (9)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.40/42.65         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.40/42.65    (10)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.40/42.65          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.40/42.65    (11)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.40/42.65          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.40/42.65    (12)  all_57_3 = e0
% 231.40/42.65    (13)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.40/42.65          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.40/42.65    (14)   ~ (e3 = e2)
% 231.40/42.65    (15)   ~ (e3 = e0)
% 231.40/42.65    (16)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.40/42.65          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.40/42.65    (17)  op(e3, e3) = e3
% 231.40/42.65    (18)  all_57_15 = e3
% 231.40/42.65    (19)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.40/42.65          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.40/42.65            e1)
% 231.40/42.65    (20)  all_57_5 = e3
% 231.40/42.65    (21)  all_57_6 = e2
% 231.40/42.65    (22)   ~ (e2 = e0)
% 231.40/42.65    (23)   ~ (e1 = e0)
% 231.40/42.65    (24)  op(e0, e0) = e3
% 231.40/42.65    (25)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.40/42.65          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.40/42.65            e2)
% 231.40/42.65    (26)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.40/42.65              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.40/42.65                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.40/42.65                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.40/42.65    (27)  op(e1, e1) = e2
% 231.40/42.65    (28)  all_57_7 = e3
% 231.40/42.65    (29)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.40/42.65          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.40/42.65    (30)   ~ (e2 = e1)
% 231.40/42.65    (31)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.40/42.65          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.40/42.65    (32)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.40/42.65          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.40/42.65    (33)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.40/42.65          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.40/42.65    (34)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.40/42.65          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.40/42.65    (35)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.40/42.65          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.40/42.65    (36)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 231.40/42.65          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 231.40/42.65    (37)  op(e3, e0) = all_52_7
% 231.40/42.65    (38)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.40/42.65          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.40/42.65    (39)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 231.40/42.65          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 231.40/42.65  
% 231.40/42.65  Begin of proof
% 231.40/42.65  | 
% 231.40/42.65  | BETA: splitting (6) gives:
% 231.40/42.65  | 
% 231.40/42.65  | Case 1:
% 231.40/42.65  | | 
% 231.40/42.65  | |   (40)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) =
% 231.40/42.65  | |           e0)
% 231.40/42.65  | | 
% 231.40/42.65  | | BETA: splitting (40) gives:
% 231.40/42.65  | | 
% 231.40/42.65  | | Case 1:
% 231.40/42.65  | | | 
% 231.40/42.65  | | |   (41)  all_57_6 = e0 & op(e1, e3) = e0
% 231.40/42.65  | | | 
% 231.40/42.65  | | | REF_CLOSE: (21), (22), (41) are inconsistent by sub-proof #2386.
% 231.40/42.65  | | | 
% 231.40/42.65  | | Case 2:
% 231.40/42.65  | | | 
% 231.40/42.65  | | |   (42)  all_57_7 = e0 & op(e1, e2) = e0
% 231.40/42.65  | | | 
% 231.40/42.65  | | | REF_CLOSE: (15), (28), (42) are inconsistent by sub-proof #2042.
% 231.40/42.65  | | | 
% 231.40/42.65  | | End of split
% 231.40/42.65  | | 
% 231.40/42.65  | Case 2:
% 231.40/42.65  | | 
% 231.40/42.65  | |   (43)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 231.40/42.65  | |           e0)
% 231.40/42.65  | | 
% 231.40/42.65  | | BETA: splitting (43) gives:
% 231.40/42.65  | | 
% 231.40/42.65  | | Case 1:
% 231.40/42.65  | | | 
% 231.40/42.65  | | |   (44)  all_57_8 = e0 & op(e1, e1) = e0
% 231.40/42.65  | | | 
% 231.40/42.65  | | | ALPHA: (44) implies:
% 231.40/42.65  | | |   (45)  op(e1, e1) = e0
% 231.40/42.65  | | | 
% 231.40/42.65  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 231.40/42.65  | | |            (13), (14), (15), (16), (17), (18), (20), (22), (23), (24),
% 231.40/42.65  | | |            (25), (26), (28), (29), (30), (31), (32), (33), (34), (35),
% 231.40/42.65  | | |            (36), (37), (38), (39), (45) are inconsistent by sub-proof
% 231.40/42.65  | | |            #1486.
% 231.40/42.65  | | | 
% 231.40/42.65  | | Case 2:
% 231.40/42.65  | | | 
% 231.40/42.65  | | |   (46)  all_57_11 = e0 & op(e1, e0) = e0
% 231.40/42.65  | | | 
% 231.40/42.65  | | | ALPHA: (46) implies:
% 231.40/42.65  | | |   (47)  all_57_11 = e0
% 231.40/42.65  | | | 
% 231.40/42.65  | | | REF_CLOSE: (1), (3), (4), (5), (7), (9), (10), (11), (12), (14), (15),
% 231.40/42.65  | | |            (17), (18), (19), (20), (21), (22), (23), (27), (28), (29),
% 231.40/42.65  | | |            (30), (31), (33), (34), (35), (36), (38), (47) are inconsistent
% 231.40/42.65  | | |            by sub-proof #1462.
% 231.40/42.65  | | | 
% 231.40/42.65  | | End of split
% 231.40/42.65  | | 
% 231.40/42.65  | End of split
% 231.40/42.65  | 
% 231.40/42.65  End of proof
% 231.40/42.65  
% 231.40/42.65  Sub-proof #1462 shows that the following formulas are inconsistent:
% 231.40/42.65  ----------------------------------------------------------------
% 231.40/42.65    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.40/42.65         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.40/42.65    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.40/42.65         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.40/42.65    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.40/42.65         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.40/42.65    (4)   ~ (e3 = e1)
% 231.40/42.65    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.40/42.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.40/42.65    (6)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.40/42.65         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.40/42.65    (7)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.40/42.65         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.40/42.65    (8)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.40/42.65         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.40/42.65    (9)  all_57_3 = e0
% 231.40/42.65    (10)   ~ (e3 = e2)
% 231.40/42.65    (11)   ~ (e3 = e0)
% 231.40/42.65    (12)  op(e3, e3) = e3
% 231.40/42.65    (13)  all_57_15 = e3
% 231.40/42.65    (14)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.40/42.65          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.40/42.65            e1)
% 231.40/42.65    (15)  all_57_5 = e3
% 231.40/42.65    (16)  all_57_6 = e2
% 231.40/42.65    (17)  all_57_11 = e0
% 231.40/42.65    (18)   ~ (e2 = e0)
% 231.40/42.65    (19)   ~ (e1 = e0)
% 231.40/42.65    (20)  op(e1, e1) = e2
% 231.40/42.65    (21)  all_57_7 = e3
% 231.40/42.65    (22)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.40/42.65          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.40/42.65    (23)   ~ (e2 = e1)
% 231.40/42.65    (24)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.40/42.65          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.40/42.65    (25)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.40/42.65          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.40/42.65    (26)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.40/42.65          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.40/42.65    (27)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.40/42.65          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.40/42.65    (28)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 231.40/42.65          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 231.40/42.65    (29)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.40/42.65          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.40/42.65  
% 231.40/42.65  Begin of proof
% 231.40/42.65  | 
% 231.40/42.65  | BETA: splitting (28) gives:
% 231.40/42.65  | 
% 231.40/42.65  | Case 1:
% 231.40/42.65  | | 
% 231.40/42.65  | |   (30)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) =
% 231.40/42.65  | |           e1)
% 231.40/42.65  | | 
% 231.40/42.65  | | BETA: splitting (30) gives:
% 231.40/42.65  | | 
% 231.40/42.65  | | Case 1:
% 231.40/42.65  | | | 
% 231.40/42.65  | | |   (31)  all_57_6 = e1 & op(e1, e3) = e1
% 231.40/42.65  | | | 
% 231.40/42.65  | | | REF_CLOSE: (16), (23), (31) are inconsistent by sub-proof #2389.
% 231.40/42.65  | | | 
% 231.40/42.65  | | Case 2:
% 231.40/42.65  | | | 
% 231.40/42.65  | | |   (32)  all_57_7 = e1 & op(e1, e2) = e1
% 231.40/42.65  | | | 
% 231.40/42.65  | | | REF_CLOSE: (4), (21), (32) are inconsistent by sub-proof #2104.
% 231.40/42.65  | | | 
% 231.40/42.65  | | End of split
% 231.40/42.65  | | 
% 231.40/42.65  | Case 2:
% 231.40/42.65  | | 
% 231.40/42.65  | |   (33)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) =
% 231.40/42.65  | |           e1)
% 231.40/42.65  | | 
% 231.40/42.65  | | BETA: splitting (33) gives:
% 231.40/42.65  | | 
% 231.40/42.65  | | Case 1:
% 231.40/42.65  | | | 
% 231.40/42.65  | | |   (34)  all_57_8 = e1 & op(e1, e1) = e1
% 231.40/42.65  | | | 
% 231.40/42.65  | | | ALPHA: (34) implies:
% 231.40/42.65  | | |   (35)  all_57_8 = e1
% 231.40/42.65  | | |   (36)  op(e1, e1) = e1
% 231.40/42.65  | | | 
% 231.40/42.65  | | | BETA: splitting (25) gives:
% 231.40/42.65  | | | 
% 231.40/42.65  | | | Case 1:
% 231.40/42.65  | | | | 
% 231.40/42.65  | | | |   (37)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1)
% 231.40/42.65  | | | |           = e2)
% 231.40/42.65  | | | | 
% 231.40/42.65  | | | | BETA: splitting (37) gives:
% 231.40/42.65  | | | | 
% 231.40/42.65  | | | | Case 1:
% 231.40/42.65  | | | | | 
% 231.40/42.65  | | | | |   (38)  all_57_4 = e2 & op(e3, e1) = e2
% 231.40/42.65  | | | | | 
% 231.40/42.65  | | | | | ALPHA: (38) implies:
% 231.40/42.65  | | | | |   (39)  all_57_4 = e2
% 231.40/42.65  | | | | | 
% 231.40/42.65  | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 231.40/42.65  | | | | |            (15), (17), (18), (19), (21), (22), (23), (24), (27), (29),
% 231.40/42.65  | | | | |            (39) are inconsistent by sub-proof #1480.
% 231.40/42.65  | | | | | 
% 231.40/42.65  | | | | Case 2:
% 231.40/42.65  | | | | | 
% 231.40/42.65  | | | | |   (40)  all_57_5 = e2 & op(e2, e1) = e2
% 231.40/42.65  | | | | | 
% 231.40/42.65  | | | | | REF_CLOSE: (10), (15), (40) are inconsistent by sub-proof #2425.
% 231.40/42.65  | | | | | 
% 231.40/42.65  | | | | End of split
% 231.40/42.65  | | | | 
% 231.40/42.65  | | | Case 2:
% 231.40/42.65  | | | | 
% 231.40/42.65  | | | |   (41)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1)
% 231.40/42.65  | | | |           = e2)
% 231.40/42.65  | | | | 
% 231.40/42.65  | | | | BETA: splitting (41) gives:
% 231.40/42.65  | | | | 
% 231.40/42.65  | | | | Case 1:
% 231.40/42.65  | | | | | 
% 231.40/42.65  | | | | |   (42)  all_57_8 = e2 & op(e1, e1) = e2
% 231.40/42.65  | | | | | 
% 231.40/42.65  | | | | | ALPHA: (42) implies:
% 231.40/42.65  | | | | |   (43)  all_57_8 = e2
% 231.40/42.65  | | | | | 
% 231.40/42.65  | | | | | REF_CLOSE: (23), (35), (43) are inconsistent by sub-proof #1485.
% 231.40/42.65  | | | | | 
% 231.40/42.65  | | | | Case 2:
% 231.40/42.65  | | | | | 
% 231.40/42.65  | | | | |   (44)  all_57_14 = e2 & op(e0, e1) = e2
% 231.40/42.65  | | | | | 
% 231.40/42.65  | | | | | ALPHA: (44) implies:
% 231.40/42.65  | | | | |   (45)  all_57_14 = e2
% 231.40/42.65  | | | | | 
% 231.40/42.65  | | | | | BETA: splitting (26) gives:
% 231.40/42.65  | | | | | 
% 231.40/42.65  | | | | | Case 1:
% 231.40/42.65  | | | | | | 
% 231.40/42.65  | | | | | |   (46)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2,
% 231.40/42.65  | | | | | |             e3) = e0)
% 231.40/42.65  | | | | | | 
% 231.40/42.65  | | | | | | REF_CLOSE: (1), (4), (5), (9), (10), (11), (12), (15), (18), (19),
% 231.40/42.65  | | | | | |            (22), (23), (46) are inconsistent by sub-proof #1784.
% 231.40/42.65  | | | | | | 
% 231.40/42.65  | | | | | Case 2:
% 231.40/42.65  | | | | | | 
% 231.40/42.65  | | | | | |   (47)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0,
% 231.40/42.65  | | | | | |             e3) = e0)
% 231.40/42.65  | | | | | | 
% 231.40/42.65  | | | | | | BETA: splitting (47) gives:
% 231.40/42.65  | | | | | | 
% 231.40/42.65  | | | | | | Case 1:
% 231.40/42.65  | | | | | | | 
% 231.40/42.65  | | | | | | |   (48)  all_57_6 = e0 & op(e1, e3) = e0
% 231.40/42.65  | | | | | | | 
% 231.40/42.65  | | | | | | | REF_CLOSE: (16), (18), (48) are inconsistent by sub-proof #2386.
% 231.40/42.65  | | | | | | | 
% 231.40/42.65  | | | | | | Case 2:
% 231.40/42.65  | | | | | | | 
% 231.40/42.65  | | | | | | |   (49)  all_57_12 = e0 & op(e0, e3) = e0
% 231.40/42.65  | | | | | | | 
% 231.40/42.65  | | | | | | | ALPHA: (49) implies:
% 231.40/42.65  | | | | | | |   (50)  all_57_12 = e0
% 231.40/42.65  | | | | | | | 
% 231.40/42.65  | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 231.40/42.65  | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18), (19),
% 231.40/42.65  | | | | | | |            (20), (21), (22), (23), (24), (27), (29), (36), (45),
% 231.40/42.65  | | | | | | |            (50) are inconsistent by sub-proof #1468.
% 231.40/42.65  | | | | | | | 
% 231.40/42.65  | | | | | | End of split
% 231.40/42.65  | | | | | | 
% 231.40/42.65  | | | | | End of split
% 231.40/42.65  | | | | | 
% 231.40/42.65  | | | | End of split
% 231.40/42.65  | | | | 
% 231.40/42.65  | | | End of split
% 231.40/42.65  | | | 
% 231.40/42.65  | | Case 2:
% 231.40/42.65  | | | 
% 231.40/42.65  | | |   (51)  all_57_11 = e1 & op(e1, e0) = e1
% 231.40/42.65  | | | 
% 231.40/42.65  | | | REF_CLOSE: (17), (19), (51) are inconsistent by sub-proof #1750.
% 231.40/42.65  | | | 
% 231.40/42.65  | | End of split
% 231.40/42.65  | | 
% 231.40/42.65  | End of split
% 231.40/42.65  | 
% 231.40/42.65  End of proof
% 231.40/42.65  
% 231.40/42.65  Sub-proof #1463 shows that the following formulas are inconsistent:
% 231.40/42.65  ----------------------------------------------------------------
% 231.40/42.65    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.40/42.65         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.40/42.65    (2)  all_57_12 = e0
% 231.40/42.65    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.40/42.65         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.40/42.65    (4)   ~ (e3 = e1)
% 231.40/42.65    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.40/42.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.40/42.65    (6)  all_57_3 = e0
% 231.40/42.65    (7)   ~ (e3 = e2)
% 231.40/42.65    (8)  op(e3, e3) = e3
% 231.40/42.65    (9)  all_57_10 = e2
% 231.40/42.65    (10)  all_57_5 = e3
% 231.40/42.65    (11)  all_57_6 = e2
% 231.40/42.65    (12)   ~ (e2 = e0)
% 231.40/42.65    (13)   ~ (e1 = e0)
% 231.40/42.65    (14)  all_57_14 = e1
% 231.40/42.65    (15)  all_57_2 = e1
% 231.40/42.65    (16)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.40/42.65          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.40/42.65    (17)   ~ (e2 = e1)
% 231.40/42.65    (18)  all_57_14 = e2 & op(e0, e1) = e2
% 231.40/42.65    (19)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.40/42.65          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.40/42.65  
% 231.40/42.65  Begin of proof
% 231.40/42.65  | 
% 231.40/42.65  | ALPHA: (18) implies:
% 231.40/42.65  |   (20)  all_57_14 = e2
% 231.40/42.65  | 
% 231.40/42.65  | COMBINE_EQS: (14), (20) imply:
% 231.40/42.65  |   (21)  e2 = e1
% 231.40/42.65  | 
% 231.40/42.65  | COMBINE_EQS: (11), (21) imply:
% 231.40/42.65  |   (22)  all_57_6 = e1
% 231.40/42.65  | 
% 231.40/42.65  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 231.40/42.65  |            (15), (16), (17), (19), (22) are inconsistent by sub-proof #1477.
% 231.40/42.65  | 
% 231.40/42.65  End of proof
% 231.40/42.65  
% 231.40/42.65  Sub-proof #1464 shows that the following formulas are inconsistent:
% 231.40/42.65  ----------------------------------------------------------------
% 231.40/42.65    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.40/42.65         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.40/42.65    (2)  all_57_12 = e0
% 231.40/42.65    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.40/42.65         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.40/42.65    (4)   ~ (e3 = e1)
% 231.40/42.66    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.40/42.66           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.40/42.66    (6)  all_57_4 = e2
% 231.40/42.66    (7)  all_57_8 = e1
% 231.40/42.66    (8)  all_57_3 = e0
% 231.40/42.66    (9)   ~ (e3 = e2)
% 231.40/42.66    (10)  op(e3, e3) = e3
% 231.40/42.66    (11)  all_57_10 = e2
% 231.40/42.66    (12)  all_57_5 = e3
% 231.40/42.66    (13)  all_57_6 = e2
% 231.40/42.66    (14)  e2 = e0
% 231.40/42.66    (15)   ~ (e2 = e0)
% 231.40/42.66    (16)   ~ (e1 = e0)
% 231.40/42.66    (17)  all_57_14 = e1
% 231.40/42.66    (18)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.40/42.66          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.40/42.66    (19)   ~ (e2 = e1)
% 231.40/42.66    (20)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.40/42.66          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.40/42.66  
% 231.40/42.66  Begin of proof
% 231.40/42.66  | 
% 231.40/42.66  | SIMP: (14) implies:
% 231.40/42.66  |   (21)  e2 = e0
% 231.40/42.66  | 
% 231.40/42.66  | COMBINE_EQS: (6), (21) imply:
% 231.40/42.66  |   (22)  all_57_4 = e0
% 231.40/42.66  | 
% 231.40/42.66  | BETA: splitting (20) gives:
% 231.40/42.66  | 
% 231.40/42.66  | Case 1:
% 231.40/42.66  | | 
% 231.40/42.66  | |   (23)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) =
% 231.40/42.66  | |           e2)
% 231.40/42.66  | | 
% 231.40/42.66  | | BETA: splitting (23) gives:
% 231.40/42.66  | | 
% 231.40/42.66  | | Case 1:
% 231.40/42.66  | | | 
% 231.40/42.66  | | |   (24)  all_57_4 = e2 & op(e3, e1) = e2
% 231.40/42.66  | | | 
% 231.40/42.66  | | | REF_CLOSE: (1), (4), (8), (9), (11), (12), (14), (15), (16), (18), (19)
% 231.40/42.66  | | |            are inconsistent by sub-proof #1517.
% 231.40/42.66  | | | 
% 231.40/42.66  | | Case 2:
% 231.40/42.66  | | | 
% 231.40/42.66  | | |   (25)  all_57_5 = e2 & op(e2, e1) = e2
% 231.40/42.66  | | | 
% 231.40/42.66  | | | ALPHA: (25) implies:
% 231.40/42.66  | | |   (26)  all_57_5 = e2
% 231.40/42.66  | | | 
% 231.40/42.66  | | | REF_CLOSE: (9), (12), (26) are inconsistent by sub-proof #2189.
% 231.40/42.66  | | | 
% 231.40/42.66  | | End of split
% 231.40/42.66  | | 
% 231.40/42.66  | Case 2:
% 231.40/42.66  | | 
% 231.40/42.66  | |   (27)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) =
% 231.40/42.66  | |           e2)
% 231.40/42.66  | | 
% 231.40/42.66  | | BETA: splitting (27) gives:
% 231.40/42.66  | | 
% 231.40/42.66  | | Case 1:
% 231.40/42.66  | | | 
% 231.40/42.66  | | |   (28)  all_57_8 = e2 & op(e1, e1) = e2
% 231.40/42.66  | | | 
% 231.40/42.66  | | | ALPHA: (28) implies:
% 231.40/42.66  | | |   (29)  all_57_8 = e2
% 231.40/42.66  | | | 
% 231.40/42.66  | | | COMBINE_EQS: (7), (29) imply:
% 231.40/42.66  | | |   (30)  e2 = e1
% 231.40/42.66  | | | 
% 231.40/42.66  | | | SIMP: (30) implies:
% 231.40/42.66  | | |   (31)  e2 = e1
% 231.40/42.66  | | | 
% 231.40/42.66  | | | COMBINE_EQS: (11), (31) imply:
% 231.40/42.66  | | |   (32)  all_57_10 = e1
% 231.40/42.66  | | | 
% 231.40/42.66  | | | REF_CLOSE: (1), (2), (3), (4), (5), (8), (9), (10), (12), (13), (15),
% 231.40/42.66  | | |            (16), (18), (19), (32) are inconsistent by sub-proof #1522.
% 231.40/42.66  | | | 
% 231.40/42.66  | | Case 2:
% 231.40/42.66  | | | 
% 231.40/42.66  | | |   (33)  all_57_14 = e2 & op(e0, e1) = e2
% 231.40/42.66  | | | 
% 231.40/42.66  | | | ALPHA: (33) implies:
% 231.40/42.66  | | |   (34)  all_57_14 = e2
% 231.40/42.66  | | | 
% 231.40/42.66  | | | COMBINE_EQS: (17), (34) imply:
% 231.40/42.66  | | |   (35)  e2 = e1
% 231.40/42.66  | | | 
% 231.40/42.66  | | | COMBINE_EQS: (11), (35) imply:
% 231.40/42.66  | | |   (36)  all_57_10 = e1
% 231.40/42.66  | | | 
% 231.40/42.66  | | | REF_CLOSE: (1), (2), (3), (4), (5), (8), (9), (10), (12), (13), (15),
% 231.40/42.66  | | |            (16), (18), (19), (36) are inconsistent by sub-proof #1522.
% 231.40/42.66  | | | 
% 231.40/42.66  | | End of split
% 231.40/42.66  | | 
% 231.40/42.66  | End of split
% 231.40/42.66  | 
% 231.40/42.66  End of proof
% 231.40/42.66  
% 231.40/42.66  Sub-proof #1465 shows that the following formulas are inconsistent:
% 231.40/42.66  ----------------------------------------------------------------
% 231.40/42.66    (1)  all_57_11 = e0 & op(e1, e0) = e0
% 231.40/42.66    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.40/42.66         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.40/42.66    (3)   ~ (e3 = e1)
% 231.40/42.66    (4)  all_57_3 = e0
% 231.40/42.66    (5)   ~ (e3 = e2)
% 231.40/42.66    (6)  all_57_5 = e3
% 231.40/42.66    (7)   ~ (e2 = e0)
% 231.40/42.66    (8)   ~ (e1 = e0)
% 231.40/42.66    (9)  all_57_2 = e1
% 231.40/42.66    (10)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.40/42.66          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.40/42.66    (11)  all_57_11 = e1
% 231.40/42.66    (12)   ~ (e2 = e1)
% 231.40/42.66  
% 231.40/42.66  Begin of proof
% 231.40/42.66  | 
% 231.40/42.66  | ALPHA: (1) implies:
% 231.40/42.66  |   (13)  all_57_11 = e0
% 231.40/42.66  | 
% 231.40/42.66  | COMBINE_EQS: (11), (13) imply:
% 231.40/42.66  |   (14)  e1 = e0
% 231.40/42.66  | 
% 231.40/42.66  | COMBINE_EQS: (9), (14) imply:
% 231.40/42.66  |   (15)  all_57_2 = e0
% 231.40/42.66  | 
% 231.40/42.66  | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (10), (12), (15) are
% 231.40/42.66  |            inconsistent by sub-proof #2253.
% 231.40/42.66  | 
% 231.40/42.66  End of proof
% 231.40/42.66  
% 231.40/42.66  Sub-proof #1466 shows that the following formulas are inconsistent:
% 231.40/42.66  ----------------------------------------------------------------
% 231.40/42.66    (1)   ~ (e3 = e1)
% 231.40/42.66    (2)  all_57_10 = e2
% 231.40/42.66    (3)  all_57_5 = e3
% 231.40/42.66    (4)   ~ (e2 = e1)
% 231.40/42.66    (5)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.40/42.66  
% 231.40/42.66  Begin of proof
% 231.40/42.66  | 
% 231.40/42.66  | BETA: splitting (5) gives:
% 231.40/42.66  | 
% 231.40/42.66  | Case 1:
% 231.40/42.66  | | 
% 231.40/42.66  | |   (6)  all_57_5 = e1 & op(e2, e1) = e1
% 231.40/42.66  | | 
% 231.40/42.66  | | ALPHA: (6) implies:
% 231.40/42.66  | |   (7)  all_57_5 = e1
% 231.40/42.66  | | 
% 231.40/42.66  | | REF_CLOSE: (1), (3), (7) are inconsistent by sub-proof #2382.
% 231.40/42.66  | | 
% 231.40/42.66  | Case 2:
% 231.40/42.66  | | 
% 231.40/42.66  | |   (8)  all_57_10 = e1 & op(e2, e0) = e1
% 231.40/42.66  | | 
% 231.40/42.66  | | ALPHA: (8) implies:
% 231.40/42.66  | |   (9)  all_57_10 = e1
% 231.40/42.66  | | 
% 231.40/42.66  | | REF_CLOSE: (2), (4), (9) are inconsistent by sub-proof #2144.
% 231.40/42.66  | | 
% 231.40/42.66  | End of split
% 231.40/42.66  | 
% 231.40/42.66  End of proof
% 231.40/42.66  
% 231.40/42.66  Sub-proof #1467 shows that the following formulas are inconsistent:
% 231.40/42.66  ----------------------------------------------------------------
% 231.40/42.66    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.40/42.66         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.40/42.66    (2)   ~ (e3 = e1)
% 231.40/42.66    (3)  all_57_9 = e1
% 231.40/42.66    (4)  all_57_3 = e0
% 231.40/42.66    (5)   ~ (e3 = e2)
% 231.40/42.66    (6)  all_57_5 = e3
% 231.40/42.66    (7)  all_57_9 = e0
% 231.40/42.66    (8)   ~ (e2 = e0)
% 231.40/42.66    (9)   ~ (e1 = e0)
% 231.40/42.66    (10)  all_57_2 = e1
% 231.40/42.66    (11)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.40/42.66          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.40/42.66    (12)   ~ (e2 = e1)
% 231.40/42.66  
% 231.40/42.66  Begin of proof
% 231.40/42.66  | 
% 231.40/42.66  | COMBINE_EQS: (3), (7) imply:
% 231.40/42.66  |   (13)  e1 = e0
% 231.40/42.66  | 
% 231.40/42.66  | SIMP: (13) implies:
% 231.40/42.66  |   (14)  e1 = e0
% 231.40/42.66  | 
% 231.40/42.66  | COMBINE_EQS: (10), (14) imply:
% 231.40/42.66  |   (15)  all_57_2 = e0
% 231.40/42.66  | 
% 231.40/42.66  | REF_CLOSE: (1), (2), (4), (5), (6), (8), (9), (11), (12), (15) are
% 231.40/42.66  |            inconsistent by sub-proof #2253.
% 231.40/42.66  | 
% 231.40/42.66  End of proof
% 231.40/42.66  
% 231.40/42.66  Sub-proof #1468 shows that the following formulas are inconsistent:
% 231.40/42.66  ----------------------------------------------------------------
% 231.40/42.66    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.40/42.66         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.40/42.66    (2)  all_57_12 = e0
% 231.40/42.66    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.40/42.66         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.40/42.66    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.40/42.66         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.40/42.66    (5)   ~ (e3 = e1)
% 231.40/42.66    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.40/42.66           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.40/42.66    (7)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.40/42.66         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.40/42.66    (8)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.40/42.66         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.40/42.66    (9)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.40/42.66         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.40/42.66    (10)  all_57_3 = e0
% 231.40/42.66    (11)   ~ (e3 = e2)
% 231.40/42.66    (12)   ~ (e3 = e0)
% 231.40/42.66    (13)  op(e3, e3) = e3
% 231.40/42.66    (14)  all_57_15 = e3
% 231.40/42.66    (15)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.40/42.66          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.40/42.66            e1)
% 231.40/42.66    (16)  all_57_5 = e3
% 231.40/42.66    (17)  all_57_6 = e2
% 231.40/42.66    (18)  all_57_11 = e0
% 231.40/42.66    (19)  op(e1, e1) = e1
% 231.40/42.66    (20)   ~ (e2 = e0)
% 231.40/42.66    (21)   ~ (e1 = e0)
% 231.40/42.66    (22)  all_57_14 = e2
% 231.40/42.66    (23)  op(e1, e1) = e2
% 231.40/42.66    (24)  all_57_7 = e3
% 231.40/42.66    (25)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.40/42.66          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.40/42.66    (26)   ~ (e2 = e1)
% 231.40/42.66    (27)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.40/42.66          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.40/42.66    (28)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.40/42.66          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.40/42.66    (29)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.40/42.66          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.40/42.66  
% 231.40/42.66  Begin of proof
% 231.40/42.66  | 
% 231.40/42.66  | BETA: splitting (3) gives:
% 231.40/42.66  | 
% 231.40/42.66  | Case 1:
% 231.40/42.66  | | 
% 231.40/42.66  | |   (30)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) =
% 231.40/42.66  | |           e1)
% 231.40/42.66  | | 
% 231.40/42.66  | | BETA: splitting (30) gives:
% 231.40/42.66  | | 
% 231.40/42.66  | | Case 1:
% 231.40/42.66  | | | 
% 231.40/42.66  | | |   (31)  all_57_0 = e1 & op(e3, e3) = e1
% 231.40/42.66  | | | 
% 231.40/42.66  | | | ALPHA: (31) implies:
% 231.40/42.66  | | |   (32)  op(e3, e3) = e1
% 231.40/42.66  | | | 
% 231.40/42.66  | | | REF_CLOSE: (5), (6), (13), (32) are inconsistent by sub-proof #2495.
% 231.40/42.66  | | | 
% 231.40/42.66  | | Case 2:
% 231.40/42.66  | | | 
% 231.40/42.66  | | |   (33)  all_57_2 = e1 & op(e2, e3) = e1
% 231.40/42.66  | | | 
% 231.40/42.66  | | | ALPHA: (33) implies:
% 231.40/42.66  | | |   (34)  all_57_2 = e1
% 231.40/42.66  | | | 
% 231.40/42.66  | | | BETA: splitting (25) gives:
% 231.40/42.66  | | | 
% 231.40/42.66  | | | Case 1:
% 231.40/42.66  | | | | 
% 231.40/42.66  | | | |   (35)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2)
% 231.40/42.66  | | | |           = e2)
% 231.40/42.66  | | | | 
% 231.40/42.66  | | | | REF_CLOSE: (10), (20), (26), (34), (35) are inconsistent by sub-proof
% 231.40/42.66  | | | |            #1521.
% 231.40/42.66  | | | | 
% 231.40/42.66  | | | Case 2:
% 231.40/42.66  | | | | 
% 231.40/42.66  | | | |   (36)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0)
% 231.40/42.66  | | | |           = e2)
% 231.40/42.66  | | | | 
% 231.40/42.66  | | | | BETA: splitting (36) gives:
% 231.40/42.66  | | | | 
% 231.40/42.66  | | | | Case 1:
% 231.40/42.66  | | | | | 
% 231.40/42.66  | | | | |   (37)  all_57_5 = e2 & op(e2, e1) = e2
% 231.40/42.66  | | | | | 
% 231.40/42.66  | | | | | REF_CLOSE: (11), (16), (37) are inconsistent by sub-proof #2425.
% 231.40/42.66  | | | | | 
% 231.40/42.66  | | | | Case 2:
% 231.40/42.66  | | | | | 
% 231.40/42.66  | | | | |   (38)  all_57_10 = e2 & op(e2, e0) = e2
% 231.40/42.66  | | | | | 
% 231.40/42.66  | | | | | ALPHA: (38) implies:
% 231.40/42.66  | | | | |   (39)  all_57_10 = e2
% 231.40/42.66  | | | | | 
% 231.40/42.66  | | | | | BETA: splitting (15) gives:
% 231.40/42.66  | | | | | 
% 231.40/42.66  | | | | | Case 1:
% 231.40/42.66  | | | | | | 
% 231.40/42.66  | | | | | |   (40)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 &
% 231.40/42.66  | | | | | |           op(e0, e2) = e1)
% 231.40/42.66  | | | | | | 
% 231.40/42.66  | | | | | | BETA: splitting (40) gives:
% 231.40/42.66  | | | | | | 
% 231.40/42.66  | | | | | | Case 1:
% 231.40/42.66  | | | | | | | 
% 231.40/42.66  | | | | | | |   (41)  all_57_12 = e1 & op(e0, e3) = e1
% 231.40/42.66  | | | | | | | 
% 231.40/42.66  | | | | | | | REF_CLOSE: (1), (2), (5), (10), (11), (16), (20), (21), (25),
% 231.40/42.66  | | | | | | |            (26), (34), (41) are inconsistent by sub-proof #1470.
% 231.40/42.66  | | | | | | | 
% 231.40/42.66  | | | | | | Case 2:
% 231.40/42.66  | | | | | | | 
% 231.40/42.66  | | | | | | |   (42)  all_57_13 = e1 & op(e0, e2) = e1
% 231.40/42.66  | | | | | | | 
% 231.40/42.66  | | | | | | | ALPHA: (42) implies:
% 231.40/42.66  | | | | | | |   (43)  all_57_13 = e1
% 231.40/42.66  | | | | | | | 
% 231.40/42.66  | | | | | | | BETA: splitting (28) gives:
% 231.40/42.66  | | | | | | | 
% 231.40/42.66  | | | | | | | Case 1:
% 231.40/42.66  | | | | | | | | 
% 231.40/42.66  | | | | | | | |   (44)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 &
% 231.40/42.66  | | | | | | | |           op(e2, e0) = e1)
% 231.40/42.66  | | | | | | | | 
% 231.40/42.66  | | | | | | | | BETA: splitting (44) gives:
% 231.40/42.66  | | | | | | | | 
% 231.40/42.66  | | | | | | | | Case 1:
% 231.40/42.66  | | | | | | | | | 
% 231.40/42.66  | | | | | | | | |   (45)  all_57_9 = e1 & op(e3, e0) = e1
% 231.40/42.66  | | | | | | | | | 
% 231.40/42.66  | | | | | | | | | ALPHA: (45) implies:
% 231.40/42.66  | | | | | | | | |   (46)  all_57_9 = e1
% 231.40/42.66  | | | | | | | | | 
% 231.40/42.66  | | | | | | | | | BETA: splitting (8) gives:
% 231.40/42.66  | | | | | | | | | 
% 231.40/42.66  | | | | | | | | | Case 1:
% 231.40/42.66  | | | | | | | | | | 
% 231.40/42.66  | | | | | | | | | |   (47)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 &
% 231.40/42.66  | | | | | | | | | |           op(e3, e2) = e2)
% 231.40/42.66  | | | | | | | | | | 
% 231.40/42.66  | | | | | | | | | | BETA: splitting (47) gives:
% 231.40/42.66  | | | | | | | | | | 
% 231.40/42.66  | | | | | | | | | | Case 1:
% 231.40/42.66  | | | | | | | | | | | 
% 231.40/42.66  | | | | | | | | | | |   (48)  all_57_0 = e2 & op(e3, e3) = e2
% 231.40/42.66  | | | | | | | | | | | 
% 231.40/42.66  | | | | | | | | | | | ALPHA: (48) implies:
% 231.40/42.66  | | | | | | | | | | |   (49)  op(e3, e3) = e2
% 231.40/42.66  | | | | | | | | | | | 
% 231.40/42.66  | | | | | | | | | | | REF_CLOSE: (6), (11), (13), (49) are inconsistent by
% 231.40/42.66  | | | | | | | | | | |            sub-proof #2490.
% 231.40/42.66  | | | | | | | | | | | 
% 231.40/42.66  | | | | | | | | | | Case 2:
% 231.40/42.66  | | | | | | | | | | | 
% 231.40/42.66  | | | | | | | | | | |   (50)  all_57_1 = e2 & op(e3, e2) = e2
% 231.40/42.66  | | | | | | | | | | | 
% 231.40/42.66  | | | | | | | | | | | ALPHA: (50) implies:
% 231.40/42.66  | | | | | | | | | | |   (51)  all_57_1 = e2
% 231.40/42.66  | | | | | | | | | | | 
% 231.40/42.66  | | | | | | | | | | | BETA: splitting (4) gives:
% 231.40/42.66  | | | | | | | | | | | 
% 231.40/42.66  | | | | | | | | | | | Case 1:
% 231.40/42.66  | | | | | | | | | | | | 
% 231.40/42.66  | | | | | | | | | | | |   (52)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 231.40/42.66  | | | | | | | | | | | |           & op(e2, e2) = e2)
% 231.40/42.66  | | | | | | | | | | | | 
% 231.40/42.66  | | | | | | | | | | | | BETA: splitting (52) gives:
% 231.40/42.66  | | | | | | | | | | | | 
% 231.40/42.66  | | | | | | | | | | | | Case 1:
% 231.40/42.66  | | | | | | | | | | | | | 
% 231.40/42.66  | | | | | | | | | | | | | 
% 231.40/42.66  | | | | | | | | | | | | | GROUND_INST: instantiating (6) with e1, e2, e1, e1, simplifying
% 231.40/42.66  | | | | | | | | | | | | |              with (19), (23) gives:
% 231.40/42.66  | | | | | | | | | | | | |   (53)  e2 = e1
% 231.40/42.66  | | | | | | | | | | | | | 
% 231.40/42.66  | | | | | | | | | | | | | COMBINE_EQS: (51), (53) imply:
% 231.40/42.66  | | | | | | | | | | | | |   (54)  all_57_1 = e1
% 231.40/42.66  | | | | | | | | | | | | | 
% 231.40/42.66  | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 231.40/42.66  | | | | | | | | | | | | |            (11), (12), (13), (14), (16), (17), (18), (20),
% 231.40/42.66  | | | | | | | | | | | | |            (21), (24), (25), (26), (27), (28), (29), (39),
% 231.40/42.66  | | | | | | | | | | | | |            (54) are inconsistent by sub-proof #1474.
% 231.40/42.66  | | | | | | | | | | | | | 
% 231.40/42.66  | | | | | | | | | | | | Case 2:
% 231.40/42.66  | | | | | | | | | | | | | 
% 231.40/42.66  | | | | | | | | | | | | |   (55)  all_57_3 = e2 & op(e2, e2) = e2
% 231.40/42.66  | | | | | | | | | | | | | 
% 231.40/42.66  | | | | | | | | | | | | | REF_CLOSE: (4), (10), (11), (20), (24), (26), (43), (51),
% 231.40/42.66  | | | | | | | | | | | | |            (55) are inconsistent by sub-proof #1475.
% 231.40/42.66  | | | | | | | | | | | | | 
% 231.40/42.66  | | | | | | | | | | | | End of split
% 231.40/42.66  | | | | | | | | | | | | 
% 231.40/42.66  | | | | | | | | | | | Case 2:
% 231.40/42.66  | | | | | | | | | | | | 
% 231.40/42.66  | | | | | | | | | | | |   (56)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 231.40/42.66  | | | | | | | | | | | |           e2 & op(e0, e2) = e2)
% 231.40/42.66  | | | | | | | | | | | | 
% 231.40/42.66  | | | | | | | | | | | | BETA: splitting (56) gives:
% 231.40/42.66  | | | | | | | | | | | | 
% 231.40/42.66  | | | | | | | | | | | | Case 1:
% 231.40/42.66  | | | | | | | | | | | | | 
% 231.40/42.66  | | | | | | | | | | | | |   (57)  all_57_7 = e2 & op(e1, e2) = e2
% 231.40/42.66  | | | | | | | | | | | | | 
% 231.40/42.66  | | | | | | | | | | | | | REF_CLOSE: (11), (24), (57) are inconsistent by sub-proof
% 231.40/42.66  | | | | | | | | | | | | |            #2092.
% 231.40/42.66  | | | | | | | | | | | | | 
% 231.40/42.66  | | | | | | | | | | | | Case 2:
% 231.40/42.66  | | | | | | | | | | | | | 
% 231.40/42.66  | | | | | | | | | | | | |   (58)  all_57_13 = e2 & op(e0, e2) = e2
% 231.40/42.66  | | | | | | | | | | | | | 
% 231.40/42.66  | | | | | | | | | | | | | ALPHA: (58) implies:
% 231.40/42.66  | | | | | | | | | | | | |   (59)  all_57_13 = e2
% 231.40/42.66  | | | | | | | | | | | | | 
% 231.51/42.66  | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 231.51/42.66  | | | | | | | | | | | | |            (11), (12), (13), (14), (16), (17), (18), (20),
% 231.51/42.66  | | | | | | | | | | | | |            (21), (24), (25), (26), (27), (28), (29), (34),
% 231.51/42.66  | | | | | | | | | | | | |            (59) are inconsistent by sub-proof #1472.
% 231.51/42.66  | | | | | | | | | | | | | 
% 231.51/42.66  | | | | | | | | | | | | End of split
% 231.51/42.66  | | | | | | | | | | | | 
% 231.51/42.66  | | | | | | | | | | | End of split
% 231.51/42.66  | | | | | | | | | | | 
% 231.51/42.66  | | | | | | | | | | End of split
% 231.51/42.66  | | | | | | | | | | 
% 231.51/42.66  | | | | | | | | | Case 2:
% 231.51/42.66  | | | | | | | | | | 
% 231.51/42.66  | | | | | | | | | |   (60)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 &
% 231.51/42.66  | | | | | | | | | |           op(e3, e0) = e2)
% 231.51/42.66  | | | | | | | | | | 
% 231.51/42.66  | | | | | | | | | | BETA: splitting (60) gives:
% 231.51/42.66  | | | | | | | | | | 
% 231.51/42.66  | | | | | | | | | | Case 1:
% 231.51/42.66  | | | | | | | | | | | 
% 231.51/42.66  | | | | | | | | | | |   (61)  all_57_4 = e2 & op(e3, e1) = e2
% 231.51/42.66  | | | | | | | | | | | 
% 231.51/42.66  | | | | | | | | | | | ALPHA: (61) implies:
% 231.51/42.66  | | | | | | | | | | |   (62)  all_57_4 = e2
% 231.51/42.66  | | | | | | | | | | | 
% 231.51/42.66  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 231.51/42.66  | | | | | | | | | | |            (13), (14), (16), (18), (20), (21), (24), (25),
% 231.51/42.66  | | | | | | | | | | |            (26), (27), (28), (29), (62) are inconsistent by
% 231.51/42.66  | | | | | | | | | | |            sub-proof #1480.
% 231.51/42.66  | | | | | | | | | | | 
% 231.51/42.66  | | | | | | | | | | Case 2:
% 231.51/42.66  | | | | | | | | | | | 
% 231.51/42.66  | | | | | | | | | | |   (63)  all_57_9 = e2 & op(e3, e0) = e2
% 231.51/42.66  | | | | | | | | | | | 
% 231.51/42.66  | | | | | | | | | | | ALPHA: (63) implies:
% 231.51/42.66  | | | | | | | | | | |   (64)  all_57_9 = e2
% 231.51/42.66  | | | | | | | | | | | 
% 231.51/42.66  | | | | | | | | | | | COMBINE_EQS: (46), (64) imply:
% 231.51/42.66  | | | | | | | | | | |   (65)  e2 = e1
% 231.51/42.66  | | | | | | | | | | | 
% 231.51/42.66  | | | | | | | | | | | SIMP: (65) implies:
% 231.51/42.66  | | | | | | | | | | |   (66)  e2 = e1
% 231.51/42.66  | | | | | | | | | | | 
% 231.51/42.66  | | | | | | | | | | | COMBINE_EQS: (39), (66) imply:
% 231.51/42.66  | | | | | | | | | | |   (67)  all_57_10 = e1
% 231.51/42.66  | | | | | | | | | | | 
% 231.51/42.66  | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (5), (6), (10), (11), (13), (16),
% 231.51/42.66  | | | | | | | | | | |            (17), (20), (21), (25), (26), (67) are
% 231.51/42.66  | | | | | | | | | | |            inconsistent by sub-proof #1522.
% 231.51/42.66  | | | | | | | | | | | 
% 231.51/42.66  | | | | | | | | | | End of split
% 231.51/42.66  | | | | | | | | | | 
% 231.51/42.66  | | | | | | | | | End of split
% 231.51/42.66  | | | | | | | | | 
% 231.51/42.66  | | | | | | | | Case 2:
% 231.51/42.66  | | | | | | | | | 
% 231.51/42.66  | | | | | | | | |   (68)  all_57_10 = e1 & op(e2, e0) = e1
% 231.51/42.66  | | | | | | | | | 
% 231.51/42.66  | | | | | | | | | ALPHA: (68) implies:
% 231.51/42.66  | | | | | | | | |   (69)  all_57_10 = e1
% 231.51/42.66  | | | | | | | | | 
% 231.51/42.66  | | | | | | | | | REF_CLOSE: (1), (2), (3), (5), (6), (10), (11), (13), (16),
% 231.51/42.66  | | | | | | | | |            (17), (20), (21), (25), (26), (69) are inconsistent
% 231.51/42.66  | | | | | | | | |            by sub-proof #1522.
% 231.51/42.66  | | | | | | | | | 
% 231.51/42.66  | | | | | | | | End of split
% 231.51/42.66  | | | | | | | | 
% 231.51/42.66  | | | | | | | Case 2:
% 231.51/42.66  | | | | | | | | 
% 231.51/42.66  | | | | | | | |   (70)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 &
% 231.51/42.66  | | | | | | | |           op(e0, e0) = e1)
% 231.51/42.66  | | | | | | | | 
% 231.51/42.66  | | | | | | | | BETA: splitting (70) gives:
% 231.51/42.66  | | | | | | | | 
% 231.51/42.66  | | | | | | | | Case 1:
% 231.51/42.66  | | | | | | | | | 
% 231.51/42.66  | | | | | | | | |   (71)  all_57_11 = e1 & op(e1, e0) = e1
% 231.51/42.66  | | | | | | | | | 
% 231.51/42.66  | | | | | | | | | REF_CLOSE: (1), (5), (10), (11), (16), (18), (20), (21), (25),
% 231.51/42.66  | | | | | | | | |            (26), (34), (71) are inconsistent by sub-proof
% 231.51/42.66  | | | | | | | | |            #1515.
% 231.51/42.66  | | | | | | | | | 
% 231.51/42.66  | | | | | | | | Case 2:
% 231.51/42.66  | | | | | | | | | 
% 231.51/42.66  | | | | | | | | |   (72)  all_57_15 = e1 & op(e0, e0) = e1
% 231.51/42.66  | | | | | | | | | 
% 231.51/42.66  | | | | | | | | | REF_CLOSE: (5), (14), (72) are inconsistent by sub-proof
% 231.51/42.66  | | | | | | | | |            #2325.
% 231.51/42.66  | | | | | | | | | 
% 231.51/42.66  | | | | | | | | End of split
% 231.51/42.66  | | | | | | | | 
% 231.51/42.66  | | | | | | | End of split
% 231.51/42.66  | | | | | | | 
% 231.51/42.66  | | | | | | End of split
% 231.51/42.66  | | | | | | 
% 231.51/42.66  | | | | | Case 2:
% 231.51/42.66  | | | | | | 
% 231.51/42.66  | | | | | |   (73)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 &
% 231.51/42.66  | | | | | |           op(e0, e0) = e1)
% 231.51/42.66  | | | | | | 
% 231.51/42.66  | | | | | | BETA: splitting (73) gives:
% 231.51/42.66  | | | | | | 
% 231.51/42.66  | | | | | | Case 1:
% 231.51/42.66  | | | | | | | 
% 231.51/42.66  | | | | | | |   (74)  all_57_14 = e1 & op(e0, e1) = e1
% 231.51/42.66  | | | | | | | 
% 231.51/42.66  | | | | | | | ALPHA: (74) implies:
% 231.51/42.66  | | | | | | |   (75)  all_57_14 = e1
% 231.51/42.66  | | | | | | | 
% 231.51/42.66  | | | | | | | COMBINE_EQS: (22), (75) imply:
% 231.51/42.66  | | | | | | |   (76)  e2 = e1
% 231.51/42.66  | | | | | | | 
% 231.51/42.66  | | | | | | | COMBINE_EQS: (39), (76) imply:
% 231.51/42.66  | | | | | | |   (77)  all_57_10 = e1
% 231.51/42.66  | | | | | | | 
% 231.51/42.66  | | | | | | | REF_CLOSE: (1), (2), (3), (5), (6), (10), (11), (13), (16), (17),
% 231.51/42.66  | | | | | | |            (20), (21), (25), (26), (77) are inconsistent by
% 231.51/42.66  | | | | | | |            sub-proof #1522.
% 231.51/42.66  | | | | | | | 
% 231.51/42.66  | | | | | | Case 2:
% 231.51/42.66  | | | | | | | 
% 231.51/42.66  | | | | | | |   (78)  all_57_15 = e1 & op(e0, e0) = e1
% 231.51/42.66  | | | | | | | 
% 231.51/42.66  | | | | | | | REF_CLOSE: (5), (14), (78) are inconsistent by sub-proof #2325.
% 231.51/42.66  | | | | | | | 
% 231.51/42.66  | | | | | | End of split
% 231.51/42.66  | | | | | | 
% 231.51/42.66  | | | | | End of split
% 231.51/42.66  | | | | | 
% 231.51/42.66  | | | | End of split
% 231.51/42.66  | | | | 
% 231.51/42.66  | | | End of split
% 231.51/42.66  | | | 
% 231.51/42.66  | | End of split
% 231.51/42.66  | | 
% 231.51/42.66  | Case 2:
% 231.51/42.66  | | 
% 231.51/42.66  | |   (79)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) =
% 231.51/42.66  | |           e1)
% 231.51/42.66  | | 
% 231.51/42.66  | | REF_CLOSE: (2), (17), (21), (26), (79) are inconsistent by sub-proof #1513.
% 231.51/42.66  | | 
% 231.51/42.66  | End of split
% 231.51/42.66  | 
% 231.51/42.66  End of proof
% 231.51/42.66  
% 231.51/42.66  Sub-proof #1469 shows that the following formulas are inconsistent:
% 231.51/42.66  ----------------------------------------------------------------
% 231.51/42.66    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.51/42.66         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.51/42.66    (2)   ~ (e3 = e1)
% 231.51/42.66    (3)  all_57_3 = e0
% 231.51/42.66    (4)   ~ (e3 = e2)
% 231.51/42.66    (5)  all_57_6 = e0
% 231.51/42.66    (6)  all_57_10 = e2
% 231.51/42.66    (7)  all_57_5 = e3
% 231.51/42.66    (8)  all_57_6 = e2
% 231.51/42.66    (9)   ~ (e2 = e0)
% 231.51/42.66    (10)   ~ (e1 = e0)
% 231.51/42.66    (11)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.51/42.66          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.51/42.66    (12)   ~ (e2 = e1)
% 231.51/42.66  
% 231.51/42.66  Begin of proof
% 231.51/42.66  | 
% 231.51/42.66  | COMBINE_EQS: (5), (8) imply:
% 231.51/42.66  |   (13)  e2 = e0
% 231.51/42.66  | 
% 231.51/42.66  | COMBINE_EQS: (6), (13) imply:
% 231.51/42.66  |   (14)  all_57_10 = e0
% 231.51/42.66  | 
% 231.51/42.66  | REF_CLOSE: (1), (2), (3), (4), (7), (9), (10), (11), (12), (14) are
% 231.51/42.66  |            inconsistent by sub-proof #1518.
% 231.51/42.66  | 
% 231.51/42.66  End of proof
% 231.51/42.66  
% 231.51/42.66  Sub-proof #1470 shows that the following formulas are inconsistent:
% 231.51/42.66  ----------------------------------------------------------------
% 231.51/42.66    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.51/42.66         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.51/42.66    (2)  all_57_12 = e0
% 231.51/42.66    (3)   ~ (e3 = e1)
% 231.51/42.66    (4)  all_57_3 = e0
% 231.51/42.66    (5)   ~ (e3 = e2)
% 231.51/42.66    (6)  all_57_5 = e3
% 231.51/42.66    (7)   ~ (e2 = e0)
% 231.51/42.66    (8)   ~ (e1 = e0)
% 231.51/42.66    (9)  all_57_2 = e1
% 231.51/42.66    (10)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.51/42.66          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.51/42.66    (11)   ~ (e2 = e1)
% 231.51/42.66    (12)  all_57_12 = e1 & op(e0, e3) = e1
% 231.51/42.66  
% 231.51/42.66  Begin of proof
% 231.51/42.66  | 
% 231.51/42.66  | ALPHA: (12) implies:
% 231.51/42.66  |   (13)  all_57_12 = e1
% 231.51/42.66  | 
% 231.51/42.66  | COMBINE_EQS: (2), (13) imply:
% 231.51/42.66  |   (14)  e1 = e0
% 231.51/42.66  | 
% 231.51/42.66  | SIMP: (14) implies:
% 231.51/42.66  |   (15)  e1 = e0
% 231.51/42.66  | 
% 231.51/42.66  | COMBINE_EQS: (9), (15) imply:
% 231.51/42.66  |   (16)  all_57_2 = e0
% 231.51/42.66  | 
% 231.51/42.66  | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (10), (11), (16) are
% 231.51/42.66  |            inconsistent by sub-proof #2253.
% 231.51/42.66  | 
% 231.51/42.66  End of proof
% 231.51/42.66  
% 231.51/42.66  Sub-proof #1471 shows that the following formulas are inconsistent:
% 231.51/42.66  ----------------------------------------------------------------
% 231.51/42.66    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.51/42.66         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.51/42.66    (2)   ~ (all_52_7 = e3)
% 231.51/42.66    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.51/42.66         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.51/42.66    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.51/42.66         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.51/42.66    (5)   ~ (e3 = e1)
% 231.51/42.66    (6)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 231.51/42.66         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.51/42.66    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.51/42.66           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.51/42.66    (8)  op(all_52_7, all_52_7) = e0
% 231.51/42.66    (9)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.51/42.66         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.51/42.66    (10)  all_57_2 = e2
% 231.51/42.66    (11)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.51/42.66          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.51/42.66    (12)  all_57_8 = e1
% 231.51/42.66    (13)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.51/42.66          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.51/42.66    (14)  all_57_3 = e0
% 231.51/42.66    (15)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.51/42.66          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.51/42.66    (16)   ~ (e3 = e2)
% 231.51/42.66    (17)   ~ (e3 = e0)
% 231.51/42.66    (18)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.51/42.66          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.51/42.66    (19)  op(e3, e3) = e3
% 231.51/42.66    (20)  all_57_15 = e3
% 231.51/42.66    (21)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.51/42.66          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.51/42.66            e1)
% 231.51/42.66    (22)  all_57_5 = e3
% 231.51/42.66    (23)   ~ (e2 = e0)
% 231.51/42.66    (24)   ~ (e1 = e0)
% 231.51/42.66    (25)  op(e0, e0) = e3
% 231.51/42.66    (26)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.51/42.66          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.51/42.66            e2)
% 231.51/42.66    (27)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.51/42.66              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.51/42.66                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.51/42.66                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.51/42.66    (28)  all_57_7 = e3
% 231.51/42.66    (29)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.51/42.66          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.51/42.66    (30)   ~ (e2 = e1)
% 231.51/42.66    (31)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.51/42.66          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.51/42.66    (32)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.51/42.66          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.51/42.66    (33)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.51/42.66          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.51/42.66    (34)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.51/42.66          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.51/42.66    (35)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.51/42.66          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.51/42.66    (36)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 231.51/42.66          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 231.51/42.66    (37)  op(e3, e0) = all_52_7
% 231.51/42.66    (38)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.51/42.66          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.51/42.66    (39)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 231.51/42.66          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 231.51/42.66  
% 231.51/42.66  Begin of proof
% 231.51/42.66  | 
% 231.51/42.66  | BETA: splitting (1) gives:
% 231.51/42.66  | 
% 231.51/42.66  | Case 1:
% 231.51/42.66  | | 
% 231.51/42.66  | |   (40)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) =
% 231.51/42.66  | |           e1)
% 231.51/42.66  | | 
% 231.51/42.66  | | BETA: splitting (40) gives:
% 231.51/42.66  | | 
% 231.51/42.66  | | Case 1:
% 231.51/42.66  | | | 
% 231.51/42.66  | | |   (41)  all_57_2 = e1 & op(e2, e3) = e1
% 231.51/42.66  | | | 
% 231.51/42.66  | | | REF_CLOSE: (10), (30), (41) are inconsistent by sub-proof #2244.
% 231.51/42.66  | | | 
% 231.51/42.66  | | Case 2:
% 231.51/42.66  | | | 
% 231.51/42.66  | | |   (42)  all_57_3 = e1 & op(e2, e2) = e1
% 231.51/42.66  | | | 
% 231.51/42.66  | | | REF_CLOSE: (14), (24), (42) are inconsistent by sub-proof #2252.
% 231.51/42.66  | | | 
% 231.51/42.66  | | End of split
% 231.51/42.66  | | 
% 231.51/42.66  | Case 2:
% 231.51/42.66  | | 
% 231.51/42.66  | |   (43)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) =
% 231.51/42.66  | |           e1)
% 231.51/42.66  | | 
% 231.51/42.66  | | BETA: splitting (43) gives:
% 231.51/42.66  | | 
% 231.51/42.66  | | Case 1:
% 231.51/42.66  | | | 
% 231.51/42.66  | | |   (44)  all_57_5 = e1 & op(e2, e1) = e1
% 231.51/42.66  | | | 
% 231.51/42.66  | | | REF_CLOSE: (5), (22), (44) are inconsistent by sub-proof #2376.
% 231.51/42.66  | | | 
% 231.51/42.66  | | Case 2:
% 231.51/42.66  | | | 
% 231.51/42.66  | | |   (45)  all_57_10 = e1 & op(e2, e0) = e1
% 231.51/42.66  | | | 
% 231.51/42.66  | | | ALPHA: (45) implies:
% 231.51/42.66  | | |   (46)  all_57_10 = e1
% 231.51/42.66  | | | 
% 231.51/42.66  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 231.51/42.66  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 231.51/42.66  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 231.51/42.66  | | |            (33), (34), (35), (36), (37), (38), (39), (46) are inconsistent
% 231.51/42.66  | | |            by sub-proof #1478.
% 231.51/42.66  | | | 
% 231.51/42.66  | | End of split
% 231.51/42.66  | | 
% 231.51/42.66  | End of split
% 231.51/42.66  | 
% 231.51/42.66  End of proof
% 231.51/42.66  
% 231.51/42.66  Sub-proof #1472 shows that the following formulas are inconsistent:
% 231.51/42.66  ----------------------------------------------------------------
% 231.51/42.66    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.51/42.66         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.51/42.66    (2)  all_57_12 = e0
% 231.51/42.67    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.51/42.67         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.51/42.67    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.51/42.67         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.51/42.67    (5)   ~ (e3 = e1)
% 231.51/42.67    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.51/42.67           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.51/42.67    (7)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.51/42.67         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.51/42.67    (8)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.51/42.67         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.51/42.67    (9)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.51/42.67         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.51/42.67    (10)  all_57_3 = e0
% 231.51/42.67    (11)   ~ (e3 = e2)
% 231.51/42.67    (12)   ~ (e3 = e0)
% 231.51/42.67    (13)  op(e3, e3) = e3
% 231.51/42.67    (14)  all_57_15 = e3
% 231.51/42.67    (15)  all_57_5 = e3
% 231.51/42.67    (16)  all_57_6 = e2
% 231.51/42.67    (17)  all_57_11 = e0
% 231.51/42.67    (18)   ~ (e2 = e0)
% 231.51/42.67    (19)  all_57_13 = e2
% 231.51/42.67    (20)   ~ (e1 = e0)
% 231.51/42.67    (21)  all_57_2 = e1
% 231.51/42.67    (22)  all_57_7 = e3
% 231.51/42.67    (23)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.51/42.67          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.51/42.67    (24)   ~ (e2 = e1)
% 231.51/42.67    (25)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.51/42.67          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.51/42.67    (26)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.51/42.67          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.51/42.67    (27)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.51/42.67          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.51/42.67  
% 231.51/42.67  Begin of proof
% 231.51/42.67  | 
% 231.51/42.67  | BETA: splitting (27) gives:
% 231.51/42.67  | 
% 231.51/42.67  | Case 1:
% 231.51/42.67  | | 
% 231.51/42.67  | |   (28)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) =
% 231.51/42.67  | |           e1)
% 231.51/42.67  | | 
% 231.51/42.67  | | BETA: splitting (28) gives:
% 231.51/42.67  | | 
% 231.51/42.67  | | Case 1:
% 231.51/42.67  | | | 
% 231.51/42.67  | | |   (29)  all_57_1 = e1 & op(e3, e2) = e1
% 231.51/42.67  | | | 
% 231.51/42.67  | | | ALPHA: (29) implies:
% 231.51/42.67  | | |   (30)  all_57_1 = e1
% 231.51/42.67  | | | 
% 231.51/42.67  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 231.51/42.67  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 231.51/42.67  | | |            (23), (24), (25), (26), (27), (30) are inconsistent by
% 231.51/42.67  | | |            sub-proof #1473.
% 231.51/42.67  | | | 
% 231.51/42.67  | | Case 2:
% 231.51/42.67  | | | 
% 231.51/42.67  | | |   (31)  all_57_3 = e1 & op(e2, e2) = e1
% 231.51/42.67  | | | 
% 231.51/42.67  | | | REF_CLOSE: (1), (5), (10), (11), (15), (18), (20), (21), (23), (24), (31)
% 231.51/42.67  | | |            are inconsistent by sub-proof #1520.
% 231.51/42.67  | | | 
% 231.51/42.67  | | End of split
% 231.51/42.67  | | 
% 231.51/42.67  | Case 2:
% 231.51/42.67  | | 
% 231.51/42.67  | |   (32)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 231.51/42.67  | |           e1)
% 231.51/42.67  | | 
% 231.51/42.67  | | BETA: splitting (32) gives:
% 231.51/42.67  | | 
% 231.51/42.67  | | Case 1:
% 231.51/42.67  | | | 
% 231.51/42.67  | | |   (33)  all_57_7 = e1 & op(e1, e2) = e1
% 231.51/42.67  | | | 
% 231.51/42.67  | | | REF_CLOSE: (5), (22), (33) are inconsistent by sub-proof #2104.
% 231.51/42.67  | | | 
% 231.51/42.67  | | Case 2:
% 231.51/42.67  | | | 
% 231.51/42.67  | | |   (34)  all_57_13 = e1 & op(e0, e2) = e1
% 231.51/42.67  | | | 
% 231.51/42.67  | | | REF_CLOSE: (19), (24), (34) are inconsistent by sub-proof #2205.
% 231.51/42.67  | | | 
% 231.51/42.67  | | End of split
% 231.51/42.67  | | 
% 231.51/42.67  | End of split
% 231.51/42.67  | 
% 231.51/42.67  End of proof
% 231.51/42.67  
% 231.51/42.67  Sub-proof #1473 shows that the following formulas are inconsistent:
% 231.51/42.67  ----------------------------------------------------------------
% 231.51/42.67    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.51/42.67         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.51/42.67    (2)  all_57_12 = e0
% 231.51/42.67    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.51/42.67         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.51/42.67    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.51/42.67         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.51/42.67    (5)   ~ (e3 = e1)
% 231.51/42.67    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.51/42.67           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.51/42.67    (7)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.51/42.67         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.51/42.67    (8)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.51/42.67         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.51/42.67    (9)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.51/42.67         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.51/42.67    (10)  all_57_3 = e0
% 231.51/42.67    (11)   ~ (e3 = e2)
% 231.51/42.67    (12)   ~ (e3 = e0)
% 231.51/42.67    (13)  op(e3, e3) = e3
% 231.51/42.67    (14)  all_57_15 = e3
% 231.51/42.67    (15)  all_57_1 = e1
% 231.51/42.67    (16)  all_57_5 = e3
% 231.51/42.67    (17)  all_57_6 = e2
% 231.51/42.67    (18)  all_57_11 = e0
% 231.51/42.67    (19)   ~ (e2 = e0)
% 231.51/42.67    (20)  all_57_13 = e2
% 231.51/42.67    (21)   ~ (e1 = e0)
% 231.51/42.67    (22)  all_57_2 = e1
% 231.51/42.67    (23)  all_57_7 = e3
% 231.51/42.67    (24)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.51/42.67          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.51/42.67    (25)   ~ (e2 = e1)
% 231.51/42.67    (26)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.51/42.67          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.51/42.67    (27)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.51/42.67          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.51/42.67    (28)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.51/42.67          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.51/42.67  
% 231.51/42.67  Begin of proof
% 231.51/42.67  | 
% 231.51/42.67  | BETA: splitting (24) gives:
% 231.51/42.67  | 
% 231.51/42.67  | Case 1:
% 231.51/42.67  | | 
% 231.51/42.67  | |   (29)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 231.51/42.67  | |           e2)
% 231.51/42.67  | | 
% 231.51/42.67  | | BETA: splitting (29) gives:
% 231.51/42.67  | | 
% 231.51/42.67  | | Case 1:
% 231.51/42.67  | | | 
% 231.51/42.67  | | |   (30)  all_57_2 = e2 & op(e2, e3) = e2
% 231.51/42.67  | | | 
% 231.51/42.67  | | | ALPHA: (30) implies:
% 231.51/42.67  | | |   (31)  all_57_2 = e2
% 231.51/42.67  | | | 
% 231.51/42.67  | | | REF_CLOSE: (22), (25), (31) are inconsistent by sub-proof #2464.
% 231.51/42.67  | | | 
% 231.51/42.67  | | Case 2:
% 231.51/42.67  | | | 
% 231.51/42.67  | | |   (32)  all_57_3 = e2 & op(e2, e2) = e2
% 231.51/42.67  | | | 
% 231.51/42.67  | | | ALPHA: (32) implies:
% 231.51/42.67  | | |   (33)  all_57_3 = e2
% 231.51/42.67  | | | 
% 231.51/42.67  | | | COMBINE_EQS: (10), (33) imply:
% 231.51/42.67  | | |   (34)  e2 = e0
% 231.51/42.67  | | | 
% 231.51/42.67  | | | SIMP: (34) implies:
% 231.51/42.67  | | |   (35)  e2 = e0
% 231.51/42.67  | | | 
% 231.51/42.67  | | | COMBINE_EQS: (20), (35) imply:
% 231.51/42.67  | | |   (36)  all_57_13 = e0
% 231.51/42.67  | | | 
% 231.51/42.67  | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), (19),
% 231.51/42.67  | | |            (21), (23), (25), (28), (36) are inconsistent by sub-proof
% 231.51/42.67  | | |            #2091.
% 231.51/42.67  | | | 
% 231.51/42.67  | | End of split
% 231.51/42.67  | | 
% 231.51/42.67  | Case 2:
% 231.51/42.67  | | 
% 231.51/42.67  | |   (37)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 231.51/42.67  | |           e2)
% 231.51/42.67  | | 
% 231.51/42.67  | | BETA: splitting (37) gives:
% 231.51/42.67  | | 
% 231.51/42.67  | | Case 1:
% 231.51/42.67  | | | 
% 231.51/42.67  | | |   (38)  all_57_5 = e2 & op(e2, e1) = e2
% 231.51/42.67  | | | 
% 231.51/42.67  | | | REF_CLOSE: (11), (16), (38) are inconsistent by sub-proof #2425.
% 231.51/42.67  | | | 
% 231.51/42.67  | | Case 2:
% 231.51/42.67  | | | 
% 231.51/42.67  | | |   (39)  all_57_10 = e2 & op(e2, e0) = e2
% 231.51/42.67  | | | 
% 231.51/42.67  | | | ALPHA: (39) implies:
% 231.51/42.67  | | |   (40)  all_57_10 = e2
% 231.51/42.67  | | | 
% 231.51/42.67  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 231.51/42.67  | | |            (13), (14), (15), (16), (17), (18), (19), (21), (23), (24),
% 231.51/42.67  | | |            (25), (26), (27), (28), (40) are inconsistent by sub-proof
% 231.51/42.67  | | |            #1474.
% 231.51/42.67  | | | 
% 231.51/42.67  | | End of split
% 231.51/42.67  | | 
% 231.51/42.67  | End of split
% 231.51/42.67  | 
% 231.51/42.67  End of proof
% 231.51/42.67  
% 231.51/42.67  Sub-proof #1474 shows that the following formulas are inconsistent:
% 231.51/42.67  ----------------------------------------------------------------
% 231.51/42.67    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.51/42.67         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.51/42.67    (2)  all_57_12 = e0
% 231.51/42.67    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.51/42.67         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.51/42.67    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.51/42.67         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.51/42.67    (5)   ~ (e3 = e1)
% 231.51/42.67    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.51/42.67           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.51/42.67    (7)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.51/42.67         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.51/42.67    (8)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.51/42.67         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.51/42.67    (9)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.51/42.67         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.51/42.67    (10)  all_57_3 = e0
% 231.51/42.67    (11)   ~ (e3 = e2)
% 231.51/42.67    (12)   ~ (e3 = e0)
% 231.51/42.67    (13)  op(e3, e3) = e3
% 231.51/42.67    (14)  all_57_15 = e3
% 231.51/42.67    (15)  all_57_1 = e1
% 231.51/42.67    (16)  all_57_10 = e2
% 231.51/42.67    (17)  all_57_5 = e3
% 231.51/42.67    (18)  all_57_6 = e2
% 231.51/42.67    (19)  all_57_11 = e0
% 231.51/42.67    (20)   ~ (e2 = e0)
% 231.51/42.67    (21)   ~ (e1 = e0)
% 231.51/42.67    (22)  all_57_7 = e3
% 231.51/42.67    (23)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.51/42.67          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.51/42.67    (24)   ~ (e2 = e1)
% 231.51/42.67    (25)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.51/42.67          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.51/42.67    (26)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.51/42.67          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.51/42.67    (27)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.51/42.67          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.51/42.67  
% 231.51/42.67  Begin of proof
% 231.51/42.67  | 
% 231.51/42.67  | BETA: splitting (8) gives:
% 231.51/42.67  | 
% 231.51/42.67  | Case 1:
% 231.51/42.67  | | 
% 231.51/42.67  | |   (28)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) =
% 231.51/42.67  | |           e2)
% 231.51/42.67  | | 
% 231.51/42.67  | | BETA: splitting (28) gives:
% 231.51/42.67  | | 
% 231.51/42.67  | | Case 1:
% 231.51/42.67  | | | 
% 231.51/42.67  | | |   (29)  all_57_0 = e2 & op(e3, e3) = e2
% 231.51/42.67  | | | 
% 231.51/42.67  | | | ALPHA: (29) implies:
% 231.51/42.67  | | |   (30)  op(e3, e3) = e2
% 231.51/42.67  | | | 
% 231.51/42.67  | | | REF_CLOSE: (6), (11), (13), (30) are inconsistent by sub-proof #2490.
% 231.51/42.67  | | | 
% 231.51/42.67  | | Case 2:
% 231.51/42.67  | | | 
% 231.51/42.67  | | |   (31)  all_57_1 = e2 & op(e3, e2) = e2
% 231.51/42.67  | | | 
% 231.51/42.67  | | | ALPHA: (31) implies:
% 231.51/42.67  | | |   (32)  all_57_1 = e2
% 231.51/42.67  | | | 
% 231.51/42.67  | | | COMBINE_EQS: (15), (32) imply:
% 231.51/42.67  | | |   (33)  e2 = e1
% 231.51/42.67  | | | 
% 231.51/42.67  | | | SIMP: (33) implies:
% 231.51/42.67  | | |   (34)  e2 = e1
% 231.51/42.67  | | | 
% 231.51/42.67  | | | COMBINE_EQS: (16), (34) imply:
% 231.51/42.67  | | |   (35)  all_57_10 = e1
% 231.51/42.67  | | | 
% 231.51/42.67  | | | REF_CLOSE: (1), (2), (3), (5), (6), (10), (11), (13), (17), (18), (20),
% 231.51/42.67  | | |            (21), (23), (24), (35) are inconsistent by sub-proof #1522.
% 231.51/42.67  | | | 
% 231.51/42.67  | | End of split
% 231.51/42.67  | | 
% 231.51/42.67  | Case 2:
% 231.51/42.67  | | 
% 231.51/42.67  | |   (36)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) =
% 231.51/42.67  | |           e2)
% 231.51/42.67  | | 
% 231.51/42.67  | | BETA: splitting (36) gives:
% 231.51/42.67  | | 
% 231.51/42.67  | | Case 1:
% 231.51/42.67  | | | 
% 231.51/42.67  | | |   (37)  all_57_4 = e2 & op(e3, e1) = e2
% 231.51/42.67  | | | 
% 231.51/42.67  | | | ALPHA: (37) implies:
% 231.51/42.67  | | |   (38)  all_57_4 = e2
% 231.51/42.67  | | | 
% 231.51/42.67  | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), (14),
% 231.51/42.67  | | |            (17), (19), (20), (21), (22), (23), (24), (25), (26), (27),
% 231.51/42.67  | | |            (38) are inconsistent by sub-proof #1480.
% 231.51/42.67  | | | 
% 231.51/42.67  | | Case 2:
% 231.51/42.67  | | | 
% 231.51/42.67  | | |   (39)  all_57_9 = e2 & op(e3, e0) = e2
% 231.51/42.67  | | | 
% 231.51/42.67  | | | ALPHA: (39) implies:
% 231.51/42.67  | | |   (40)  all_57_9 = e2
% 231.51/42.67  | | | 
% 231.51/42.67  | | | BETA: splitting (26) gives:
% 231.51/42.67  | | | 
% 231.51/42.67  | | | Case 1:
% 231.51/42.67  | | | | 
% 231.51/42.67  | | | |   (41)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0)
% 231.51/42.67  | | | |           = e1)
% 231.51/42.67  | | | | 
% 231.51/42.67  | | | | BETA: splitting (41) gives:
% 231.51/42.67  | | | | 
% 231.51/42.67  | | | | Case 1:
% 231.51/42.67  | | | | | 
% 231.51/42.67  | | | | |   (42)  all_57_9 = e1 & op(e3, e0) = e1
% 231.51/42.67  | | | | | 
% 231.51/42.67  | | | | | ALPHA: (42) implies:
% 231.51/42.67  | | | | |   (43)  all_57_9 = e1
% 231.51/42.67  | | | | | 
% 231.51/42.67  | | | | | COMBINE_EQS: (40), (43) imply:
% 231.51/42.67  | | | | |   (44)  e2 = e1
% 231.51/42.67  | | | | | 
% 231.51/42.67  | | | | | COMBINE_EQS: (16), (44) imply:
% 231.51/42.67  | | | | |   (45)  all_57_10 = e1
% 231.51/42.67  | | | | | 
% 231.51/42.67  | | | | | REF_CLOSE: (1), (2), (3), (5), (6), (10), (11), (13), (17), (18),
% 231.51/42.67  | | | | |            (20), (21), (23), (24), (45) are inconsistent by sub-proof
% 231.51/42.67  | | | | |            #1522.
% 231.51/42.67  | | | | | 
% 231.51/42.67  | | | | Case 2:
% 231.51/42.67  | | | | | 
% 231.51/42.67  | | | | |   (46)  all_57_10 = e1 & op(e2, e0) = e1
% 231.51/42.67  | | | | | 
% 231.51/42.67  | | | | | ALPHA: (46) implies:
% 231.51/42.67  | | | | |   (47)  all_57_10 = e1
% 231.51/42.67  | | | | | 
% 231.51/42.67  | | | | | REF_CLOSE: (1), (2), (3), (5), (6), (10), (11), (13), (17), (18),
% 231.51/42.67  | | | | |            (20), (21), (23), (24), (47) are inconsistent by sub-proof
% 231.51/42.67  | | | | |            #1522.
% 231.51/42.67  | | | | | 
% 231.51/42.67  | | | | End of split
% 231.51/42.67  | | | | 
% 231.51/42.67  | | | Case 2:
% 231.51/42.67  | | | | 
% 231.51/42.67  | | | |   (48)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0,
% 231.51/42.67  | | | |             e0) = e1)
% 231.51/42.67  | | | | 
% 231.51/42.67  | | | | BETA: splitting (48) gives:
% 231.51/42.67  | | | | 
% 231.51/42.67  | | | | Case 1:
% 231.51/42.67  | | | | | 
% 231.51/42.67  | | | | |   (49)  all_57_11 = e1 & op(e1, e0) = e1
% 231.51/42.67  | | | | | 
% 231.51/42.67  | | | | | ALPHA: (49) implies:
% 231.51/42.67  | | | | |   (50)  all_57_11 = e1
% 231.51/42.67  | | | | | 
% 231.51/42.67  | | | | | COMBINE_EQS: (19), (50) imply:
% 231.51/42.67  | | | | |   (51)  e1 = e0
% 231.51/42.67  | | | | | 
% 231.51/42.67  | | | | | REF_CLOSE: (4), (5), (10), (11), (15), (20), (21), (22), (24), (27),
% 231.51/42.67  | | | | |            (51) are inconsistent by sub-proof #1626.
% 231.51/42.67  | | | | | 
% 231.51/42.67  | | | | Case 2:
% 231.51/42.67  | | | | | 
% 231.51/42.67  | | | | |   (52)  all_57_15 = e1 & op(e0, e0) = e1
% 231.51/42.67  | | | | | 
% 231.51/42.67  | | | | | REF_CLOSE: (5), (14), (52) are inconsistent by sub-proof #2318.
% 231.51/42.67  | | | | | 
% 231.51/42.67  | | | | End of split
% 231.51/42.67  | | | | 
% 231.51/42.67  | | | End of split
% 231.51/42.67  | | | 
% 231.51/42.67  | | End of split
% 231.51/42.67  | | 
% 231.51/42.67  | End of split
% 231.51/42.67  | 
% 231.51/42.67  End of proof
% 231.51/42.67  
% 231.51/42.67  Sub-proof #1475 shows that the following formulas are inconsistent:
% 231.51/42.67  ----------------------------------------------------------------
% 231.51/42.67    (1)  all_57_3 = e2 & op(e2, e2) = e2
% 231.51/42.67    (2)  all_57_13 = e1
% 231.51/42.67    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.51/42.67         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.51/42.67    (4)  all_57_3 = e0
% 231.51/42.67    (5)   ~ (e3 = e2)
% 231.51/42.67    (6)  all_57_1 = e2
% 231.51/42.67    (7)   ~ (e2 = e0)
% 231.51/42.67    (8)  all_57_7 = e3
% 231.51/42.67    (9)   ~ (e2 = e1)
% 231.51/42.67  
% 231.51/42.67  Begin of proof
% 231.51/42.67  | 
% 231.51/42.67  | ALPHA: (1) implies:
% 231.51/42.67  |   (10)  all_57_3 = e2
% 231.51/42.67  | 
% 231.51/42.67  | COMBINE_EQS: (4), (10) imply:
% 231.51/42.67  |   (11)  e2 = e0
% 231.51/42.67  | 
% 231.51/42.67  | SIMP: (11) implies:
% 231.51/42.67  |   (12)  e2 = e0
% 231.51/42.67  | 
% 231.51/42.67  | COMBINE_EQS: (6), (12) imply:
% 231.51/42.67  |   (13)  all_57_1 = e0
% 231.51/42.67  | 
% 231.51/42.67  | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (13) are inconsistent by
% 231.51/42.67  |            sub-proof #2099.
% 231.51/42.67  | 
% 231.51/42.67  End of proof
% 231.51/42.67  
% 231.51/42.67  Sub-proof #1476 shows that the following formulas are inconsistent:
% 231.51/42.67  ----------------------------------------------------------------
% 231.51/42.67    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.51/42.67         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.51/42.67    (2)  all_57_12 = e0
% 231.51/42.67    (3)   ~ (all_52_7 = e3)
% 231.51/42.67    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.51/42.67         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.51/42.67    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.51/42.67         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.51/42.67    (6)   ~ (e3 = e1)
% 231.51/42.67    (7)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 231.51/42.67         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.51/42.67    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.51/42.67           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.51/42.67    (9)  all_57_10 = e1
% 231.51/42.67    (10)  op(all_52_7, all_52_7) = e0
% 231.51/42.67    (11)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.51/42.67          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.51/42.67    (12)  all_57_2 = e2
% 231.51/42.67    (13)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.51/42.67          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.51/42.67    (14)  all_57_6 = e1
% 231.51/42.67    (15)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.51/42.67          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.51/42.67    (16)  all_57_3 = e0
% 231.51/42.67    (17)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.51/42.67          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.51/42.67    (18)   ~ (e3 = e2)
% 231.51/42.67    (19)   ~ (e3 = e0)
% 231.51/42.67    (20)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.51/42.67          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.51/42.67    (21)  op(e3, e3) = e3
% 231.51/42.67    (22)  all_57_15 = e3
% 231.51/42.67    (23)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.51/42.67          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.51/42.67            e1)
% 231.51/42.67    (24)  all_57_5 = e3
% 231.51/42.67    (25)  op(e1, e1) = e1
% 231.51/42.67    (26)   ~ (e2 = e0)
% 231.51/42.67    (27)   ~ (e1 = e0)
% 231.51/42.67    (28)  all_57_8 = e2
% 231.51/42.67    (29)  op(e0, e0) = e3
% 231.51/42.67    (30)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.51/42.67          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.51/42.67            e2)
% 231.51/42.67    (31)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.51/42.67              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.51/42.67                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.51/42.67                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.51/42.67    (32)  op(e1, e1) = e2
% 231.51/42.67    (33)  all_57_7 = e3
% 231.51/42.67    (34)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.51/42.67          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.51/42.67    (35)   ~ (e2 = e1)
% 231.51/42.67    (36)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.51/42.67          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.51/42.67    (37)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.51/42.67          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.51/42.67    (38)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.51/42.67          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.51/42.67    (39)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.51/42.67          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.51/42.67    (40)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.51/42.67          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.51/42.67    (41)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 231.51/42.67          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 231.51/42.67    (42)  op(e3, e0) = all_52_7
% 231.51/42.67    (43)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.51/42.67          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.51/42.67    (44)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 231.51/42.67          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 231.51/42.67  
% 231.51/42.67  Begin of proof
% 231.51/42.67  | 
% 231.51/42.67  | BETA: splitting (34) gives:
% 231.51/42.67  | 
% 231.51/42.67  | Case 1:
% 231.51/42.67  | | 
% 231.51/42.67  | |   (45)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 231.51/42.67  | |           e2)
% 231.51/42.67  | | 
% 231.51/42.67  | | BETA: splitting (45) gives:
% 231.51/42.67  | | 
% 231.51/42.67  | | Case 1:
% 231.51/42.67  | | | 
% 231.51/42.67  | | |   (46)  all_57_2 = e2 & op(e2, e3) = e2
% 231.51/42.67  | | | 
% 231.51/42.67  | | | GROUND_INST: instantiating (8) with e1, e2, e1, e1, simplifying with (25),
% 231.51/42.67  | | |              (32) gives:
% 231.51/42.67  | | |   (47)  e2 = e1
% 231.51/42.67  | | | 
% 231.51/42.67  | | | COMBINE_EQS: (28), (47) imply:
% 231.51/42.67  | | |   (48)  all_57_8 = e1
% 231.51/42.67  | | | 
% 231.51/42.67  | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 231.51/42.67  | | |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 231.51/42.67  | | |            (26), (27), (29), (30), (31), (33), (34), (35), (36), (37),
% 231.51/42.67  | | |            (38), (39), (40), (41), (42), (43), (44), (48) are inconsistent
% 231.51/42.67  | | |            by sub-proof #1478.
% 231.51/42.67  | | | 
% 231.51/42.67  | | Case 2:
% 231.51/42.67  | | | 
% 231.51/42.67  | | |   (49)  all_57_3 = e2 & op(e2, e2) = e2
% 231.51/42.67  | | | 
% 231.51/42.67  | | | ALPHA: (49) implies:
% 231.51/42.67  | | |   (50)  all_57_3 = e2
% 231.51/42.67  | | | 
% 231.51/42.67  | | | COMBINE_EQS: (16), (50) imply:
% 231.51/42.67  | | |   (51)  e2 = e0
% 231.51/42.67  | | | 
% 231.51/42.67  | | | REF_CLOSE: (9), (12), (16), (18), (24), (26), (34), (35), (51) are
% 231.51/42.67  | | |            inconsistent by sub-proof #1532.
% 231.51/42.67  | | | 
% 231.51/42.67  | | End of split
% 231.51/42.67  | | 
% 231.51/42.67  | Case 2:
% 231.51/42.67  | | 
% 231.51/42.67  | |   (52)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 231.51/42.67  | |           e2)
% 231.51/42.67  | | 
% 231.51/42.67  | | BETA: splitting (52) gives:
% 231.51/42.67  | | 
% 231.51/42.67  | | Case 1:
% 231.51/42.67  | | | 
% 231.51/42.67  | | |   (53)  all_57_5 = e2 & op(e2, e1) = e2
% 231.51/42.67  | | | 
% 231.51/42.67  | | | ALPHA: (53) implies:
% 231.51/42.67  | | |   (54)  all_57_5 = e2
% 231.51/42.67  | | | 
% 231.51/42.67  | | | REF_CLOSE: (18), (24), (54) are inconsistent by sub-proof #2189.
% 231.51/42.67  | | | 
% 231.51/42.67  | | Case 2:
% 231.51/42.67  | | | 
% 231.51/42.67  | | |   (55)  all_57_10 = e2 & op(e2, e0) = e2
% 231.51/42.67  | | | 
% 231.51/42.67  | | | ALPHA: (55) implies:
% 231.51/42.67  | | |   (56)  all_57_10 = e2
% 231.51/42.67  | | | 
% 231.51/42.67  | | | COMBINE_EQS: (9), (56) imply:
% 231.51/42.67  | | |   (57)  e2 = e1
% 231.51/42.67  | | | 
% 231.51/42.67  | | | COMBINE_EQS: (12), (57) imply:
% 231.51/42.67  | | |   (58)  all_57_2 = e1
% 231.51/42.67  | | | 
% 231.51/42.67  | | | REF_CLOSE: (1), (2), (4), (6), (8), (14), (16), (18), (21), (24), (26),
% 231.51/42.67  | | |            (27), (34), (35), (37), (56), (58) are inconsistent by
% 231.51/42.67  | | |            sub-proof #1477.
% 231.51/42.67  | | | 
% 231.51/42.67  | | End of split
% 231.51/42.67  | | 
% 231.51/42.67  | End of split
% 231.51/42.67  | 
% 231.51/42.67  End of proof
% 231.51/42.67  
% 231.51/42.67  Sub-proof #1477 shows that the following formulas are inconsistent:
% 231.51/42.67  ----------------------------------------------------------------
% 231.51/42.67    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.51/42.67         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.51/42.67    (2)  all_57_12 = e0
% 231.51/42.67    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.51/42.67         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.51/42.67    (4)   ~ (e3 = e1)
% 231.51/42.67    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.51/42.67           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.51/42.67    (6)  all_57_6 = e1
% 231.51/42.67    (7)  all_57_3 = e0
% 231.51/42.67    (8)   ~ (e3 = e2)
% 231.51/42.67    (9)  op(e3, e3) = e3
% 231.51/42.67    (10)  all_57_10 = e2
% 231.51/42.67    (11)  all_57_5 = e3
% 231.51/42.67    (12)   ~ (e2 = e0)
% 231.51/42.67    (13)   ~ (e1 = e0)
% 231.51/42.67    (14)  all_57_2 = e1
% 231.51/42.67    (15)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.51/42.67          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.51/42.67    (16)   ~ (e2 = e1)
% 231.51/42.67    (17)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.51/42.67          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.51/42.67  
% 231.51/42.67  Begin of proof
% 231.51/42.67  | 
% 231.51/42.67  | BETA: splitting (17) gives:
% 231.51/42.67  | 
% 231.51/42.67  | Case 1:
% 231.51/42.67  | | 
% 231.51/42.67  | |   (18)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) =
% 231.51/42.67  | |           e2)
% 231.51/42.67  | | 
% 231.51/42.67  | | REF_CLOSE: (5), (8), (9), (14), (16), (18) are inconsistent by sub-proof
% 231.51/42.67  | |            #1526.
% 231.51/42.67  | | 
% 231.51/42.67  | Case 2:
% 231.51/42.67  | | 
% 231.51/42.67  | |   (19)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) =
% 231.51/42.67  | |           e2)
% 231.51/42.67  | | 
% 231.51/42.67  | | BETA: splitting (19) gives:
% 231.51/42.67  | | 
% 231.51/42.67  | | Case 1:
% 231.51/42.67  | | | 
% 231.51/42.67  | | |   (20)  all_57_6 = e2 & op(e1, e3) = e2
% 231.51/42.67  | | | 
% 231.51/42.67  | | | ALPHA: (20) implies:
% 231.51/42.67  | | |   (21)  all_57_6 = e2
% 231.51/42.67  | | | 
% 231.51/42.67  | | | COMBINE_EQS: (6), (21) imply:
% 231.51/42.67  | | |   (22)  e2 = e1
% 231.51/42.67  | | | 
% 231.51/42.67  | | | SIMP: (22) implies:
% 231.51/42.67  | | |   (23)  e2 = e1
% 231.51/42.67  | | | 
% 231.51/42.67  | | | COMBINE_EQS: (10), (23) imply:
% 231.51/42.67  | | |   (24)  all_57_10 = e1
% 231.51/42.67  | | | 
% 231.51/42.67  | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (11), (12), (13), (15),
% 231.51/42.67  | | |            (16), (21), (24) are inconsistent by sub-proof #1522.
% 231.51/42.67  | | | 
% 231.51/42.67  | | Case 2:
% 231.51/42.67  | | | 
% 231.51/42.67  | | |   (25)  all_57_12 = e2 & op(e0, e3) = e2
% 231.51/42.67  | | | 
% 231.51/42.67  | | | ALPHA: (25) implies:
% 231.51/42.68  | | |   (26)  all_57_12 = e2
% 231.51/42.68  | | | 
% 231.51/42.68  | | | COMBINE_EQS: (2), (26) imply:
% 231.51/42.68  | | |   (27)  e2 = e0
% 231.51/42.68  | | | 
% 231.51/42.68  | | | COMBINE_EQS: (10), (27) imply:
% 231.51/42.68  | | |   (28)  all_57_10 = e0
% 231.51/42.68  | | | 
% 231.51/42.68  | | | REF_CLOSE: (1), (4), (7), (8), (11), (12), (13), (15), (16), (28) are
% 231.51/42.68  | | |            inconsistent by sub-proof #1518.
% 231.51/42.68  | | | 
% 231.51/42.68  | | End of split
% 231.51/42.68  | | 
% 231.51/42.68  | End of split
% 231.51/42.68  | 
% 231.51/42.68  End of proof
% 231.51/42.68  
% 231.51/42.68  Sub-proof #1478 shows that the following formulas are inconsistent:
% 231.51/42.68  ----------------------------------------------------------------
% 231.51/42.68    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.51/42.68         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.51/42.68    (2)   ~ (all_52_7 = e3)
% 231.51/42.68    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.51/42.68         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.51/42.68    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.51/42.68         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.51/42.68    (5)   ~ (e3 = e1)
% 231.51/42.68    (6)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 231.51/42.68         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.51/42.68    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.51/42.68           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.51/42.68    (8)  all_57_10 = e1
% 231.51/42.68    (9)  op(all_52_7, all_52_7) = e0
% 231.51/42.68    (10)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.51/42.68          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.51/42.68    (11)  all_57_2 = e2
% 231.51/42.68    (12)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.51/42.68          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.51/42.68    (13)  all_57_8 = e1
% 231.51/42.68    (14)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.51/42.68          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.51/42.68    (15)  all_57_3 = e0
% 231.51/42.68    (16)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.51/42.68          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.51/42.68    (17)   ~ (e3 = e2)
% 231.51/42.68    (18)   ~ (e3 = e0)
% 231.51/42.68    (19)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.51/42.68          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.51/42.68    (20)  op(e3, e3) = e3
% 231.51/42.68    (21)  all_57_15 = e3
% 231.51/42.68    (22)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.51/42.68          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.51/42.68            e1)
% 231.51/42.68    (23)  all_57_5 = e3
% 231.51/42.68    (24)   ~ (e2 = e0)
% 231.51/42.68    (25)   ~ (e1 = e0)
% 231.51/42.68    (26)  op(e0, e0) = e3
% 231.51/42.68    (27)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.51/42.68          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.51/42.68            e2)
% 231.51/42.68    (28)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.51/42.68              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.51/42.68                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.51/42.68                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.51/42.68    (29)  all_57_7 = e3
% 231.51/42.68    (30)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.51/42.68          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.51/42.68    (31)   ~ (e2 = e1)
% 231.51/42.68    (32)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.51/42.68          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.51/42.68    (33)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.51/42.68          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.51/42.68    (34)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.51/42.68          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.51/42.68    (35)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.51/42.68          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.51/42.68    (36)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.51/42.68          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.51/42.68    (37)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 231.51/42.68          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 231.51/42.68    (38)  op(e3, e0) = all_52_7
% 231.51/42.68    (39)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.51/42.68          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.51/42.68    (40)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 231.51/42.68          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 231.51/42.68  
% 231.51/42.68  Begin of proof
% 231.51/42.68  | 
% 231.51/42.68  | BETA: splitting (3) gives:
% 231.51/42.68  | 
% 231.51/42.68  | Case 1:
% 231.51/42.68  | | 
% 231.51/42.68  | |   (41)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) =
% 231.51/42.68  | |           e1)
% 231.51/42.68  | | 
% 231.51/42.68  | | REF_CLOSE: (5), (7), (11), (20), (31), (41) are inconsistent by sub-proof
% 231.51/42.68  | |            #2228.
% 231.51/42.68  | | 
% 231.51/42.68  | Case 2:
% 231.51/42.68  | | 
% 231.51/42.68  | |   (42)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) =
% 231.51/42.68  | |           e1)
% 231.51/42.68  | | 
% 231.51/42.68  | | BETA: splitting (42) gives:
% 231.51/42.68  | | 
% 231.51/42.68  | | Case 1:
% 231.51/42.68  | | | 
% 231.51/42.68  | | |   (43)  all_57_6 = e1 & op(e1, e3) = e1
% 231.51/42.68  | | | 
% 231.51/42.68  | | | ALPHA: (43) implies:
% 231.51/42.68  | | |   (44)  all_57_6 = e1
% 231.51/42.68  | | | 
% 231.51/42.68  | | | BETA: splitting (35) gives:
% 231.51/42.68  | | | 
% 231.51/42.68  | | | Case 1:
% 231.51/42.68  | | | | 
% 231.51/42.68  | | | |   (45)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3)
% 231.51/42.68  | | | |           = e0)
% 231.51/42.68  | | | | 
% 231.51/42.68  | | | | REF_CLOSE: (7), (8), (15), (17), (18), (20), (23), (24), (30), (31),
% 231.51/42.68  | | | |            (45) are inconsistent by sub-proof #1503.
% 231.51/42.68  | | | | 
% 231.51/42.68  | | | Case 2:
% 231.51/42.68  | | | | 
% 231.51/42.68  | | | |   (46)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3)
% 231.51/42.68  | | | |           = e0)
% 231.51/42.68  | | | | 
% 231.51/42.68  | | | | BETA: splitting (46) gives:
% 231.51/42.68  | | | | 
% 231.51/42.68  | | | | Case 1:
% 231.51/42.68  | | | | | 
% 231.51/42.68  | | | | |   (47)  all_57_6 = e0 & op(e1, e3) = e0
% 231.51/42.68  | | | | | 
% 231.51/42.68  | | | | | REF_CLOSE: (1), (5), (8), (11), (15), (23), (25), (31), (44), (47) are
% 231.51/42.68  | | | | |            inconsistent by sub-proof #1502.
% 231.51/42.68  | | | | | 
% 231.51/42.68  | | | | Case 2:
% 231.51/42.68  | | | | | 
% 231.51/42.68  | | | | |   (48)  all_57_12 = e0 & op(e0, e3) = e0
% 231.51/42.68  | | | | | 
% 231.51/42.68  | | | | | ALPHA: (48) implies:
% 231.51/42.68  | | | | |   (49)  all_57_12 = e0
% 231.51/42.68  | | | | | 
% 231.51/42.68  | | | | | BETA: splitting (22) gives:
% 231.51/42.68  | | | | | 
% 231.51/42.68  | | | | | Case 1:
% 231.51/42.68  | | | | | | 
% 231.51/42.68  | | | | | |   (50)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 &
% 231.51/42.68  | | | | | |           op(e0, e2) = e1)
% 231.51/42.68  | | | | | | 
% 231.51/42.68  | | | | | | BETA: splitting (50) gives:
% 231.51/42.68  | | | | | | 
% 231.51/42.68  | | | | | | Case 1:
% 231.51/42.68  | | | | | | | 
% 231.51/42.68  | | | | | | |   (51)  all_57_12 = e1 & op(e0, e3) = e1
% 231.51/42.68  | | | | | | | 
% 231.51/42.68  | | | | | | | REF_CLOSE: (1), (5), (8), (11), (15), (23), (25), (31), (49), (51)
% 231.51/42.68  | | | | | | |            are inconsistent by sub-proof #1525.
% 231.51/42.68  | | | | | | | 
% 231.51/42.68  | | | | | | Case 2:
% 231.51/42.68  | | | | | | | 
% 231.51/42.68  | | | | | | |   (52)  all_57_13 = e1 & op(e0, e2) = e1
% 231.51/42.68  | | | | | | | 
% 231.51/42.68  | | | | | | | ALPHA: (52) implies:
% 231.51/42.68  | | | | | | |   (53)  all_57_13 = e1
% 231.51/42.68  | | | | | | | 
% 231.51/42.68  | | | | | | | BETA: splitting (40) gives:
% 231.51/42.68  | | | | | | | 
% 231.51/42.68  | | | | | | | Case 1:
% 231.51/42.68  | | | | | | | | 
% 231.51/42.68  | | | | | | | |   (54)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 &
% 231.51/42.68  | | | | | | | |           op(e1, e2) = e2)
% 231.51/42.68  | | | | | | | | 
% 231.51/42.68  | | | | | | | | BETA: splitting (54) gives:
% 231.51/42.68  | | | | | | | | 
% 231.51/42.68  | | | | | | | | Case 1:
% 231.51/42.68  | | | | | | | | | 
% 231.51/42.68  | | | | | | | | |   (55)  all_57_6 = e2 & op(e1, e3) = e2
% 231.51/42.68  | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | ALPHA: (55) implies:
% 231.51/42.68  | | | | | | | | |   (56)  all_57_6 = e2
% 231.51/42.68  | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | REF_CLOSE: (1), (3), (5), (7), (8), (11), (15), (20), (23),
% 231.51/42.68  | | | | | | | | |            (25), (31), (49), (56) are inconsistent by
% 231.51/42.68  | | | | | | | | |            sub-proof #1524.
% 231.51/42.68  | | | | | | | | | 
% 231.51/42.68  | | | | | | | | Case 2:
% 231.51/42.68  | | | | | | | | | 
% 231.51/42.68  | | | | | | | | |   (57)  all_57_7 = e2 & op(e1, e2) = e2
% 231.51/42.68  | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | ALPHA: (57) implies:
% 231.51/42.68  | | | | | | | | |   (58)  all_57_7 = e2
% 231.51/42.68  | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | REF_CLOSE: (17), (29), (58) are inconsistent by sub-proof
% 231.51/42.68  | | | | | | | | |            #2102.
% 231.51/42.68  | | | | | | | | | 
% 231.51/42.68  | | | | | | | | End of split
% 231.51/42.68  | | | | | | | | 
% 231.51/42.68  | | | | | | | Case 2:
% 231.51/42.68  | | | | | | | | 
% 231.51/42.68  | | | | | | | |   (59)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 &
% 231.51/42.68  | | | | | | | |           op(e1, e0) = e2)
% 231.51/42.68  | | | | | | | | 
% 231.51/42.68  | | | | | | | | BETA: splitting (59) gives:
% 231.51/42.68  | | | | | | | | 
% 231.51/42.68  | | | | | | | | Case 1:
% 231.51/42.68  | | | | | | | | | 
% 231.51/42.68  | | | | | | | | |   (60)  all_57_8 = e2 & op(e1, e1) = e2
% 231.51/42.68  | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | REF_CLOSE: (13), (31), (60) are inconsistent by sub-proof
% 231.51/42.68  | | | | | | | | |            #1501.
% 231.51/42.68  | | | | | | | | | 
% 231.51/42.68  | | | | | | | | Case 2:
% 231.51/42.68  | | | | | | | | | 
% 231.51/42.68  | | | | | | | | |   (61)  all_57_11 = e2 & op(e1, e0) = e2
% 231.51/42.68  | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | ALPHA: (61) implies:
% 231.51/42.68  | | | | | | | | |   (62)  all_57_11 = e2
% 231.51/42.68  | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | BETA: splitting (4) gives:
% 231.51/42.68  | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | Case 1:
% 231.51/42.68  | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | |   (63)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 &
% 231.51/42.68  | | | | | | | | | |           op(e2, e2) = e2)
% 231.51/42.68  | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | BETA: splitting (63) gives:
% 231.51/42.68  | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | Case 1:
% 231.51/42.68  | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | |   (64)  all_57_1 = e2 & op(e3, e2) = e2
% 231.51/42.68  | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | ALPHA: (64) implies:
% 231.51/42.68  | | | | | | | | | | |   (65)  all_57_1 = e2
% 231.51/42.68  | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | BETA: splitting (10) gives:
% 231.51/42.68  | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | Case 1:
% 231.51/42.68  | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | |   (66)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 231.51/42.68  | | | | | | | | | | | |           & op(e3, e2) = e1)
% 231.51/42.68  | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | REF_CLOSE: (5), (7), (20), (31), (65), (66) are inconsistent
% 231.51/42.68  | | | | | | | | | | | |            by sub-proof #2096.
% 231.51/42.68  | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | Case 2:
% 231.51/42.68  | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | |   (67)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 231.51/42.68  | | | | | | | | | | | |           & op(e3, e0) = e1)
% 231.51/42.68  | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | BETA: splitting (67) gives:
% 231.51/42.68  | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | Case 1:
% 231.51/42.68  | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | |   (68)  all_57_4 = e1 & op(e3, e1) = e1
% 231.51/42.68  | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | ALPHA: (68) implies:
% 231.51/42.68  | | | | | | | | | | | | |   (69)  all_57_4 = e1
% 231.51/42.68  | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | BETA: splitting (16) gives:
% 231.51/42.68  | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | Case 1:
% 231.51/42.68  | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | |   (70)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 231.51/42.68  | | | | | | | | | | | | | |           & op(e2, e1) = e0)
% 231.51/42.68  | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | BETA: splitting (70) gives:
% 231.51/42.68  | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | Case 1:
% 231.51/42.68  | | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | |   (71)  all_57_4 = e0 & op(e3, e1) = e0
% 231.51/42.68  | | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | | ALPHA: (71) implies:
% 231.51/42.68  | | | | | | | | | | | | | | |   (72)  all_57_4 = e0
% 231.51/42.68  | | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | | COMBINE_EQS: (69), (72) imply:
% 231.51/42.68  | | | | | | | | | | | | | | |   (73)  e1 = e0
% 231.51/42.68  | | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | | COMBINE_EQS: (8), (73) imply:
% 231.51/42.68  | | | | | | | | | | | | | | |   (74)  all_57_10 = e0
% 231.51/42.68  | | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | | REF_CLOSE: (1), (5), (11), (15), (23), (25), (31), (74) are
% 231.51/42.68  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1530.
% 231.51/42.68  | | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | Case 2:
% 231.51/42.68  | | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | |   (75)  all_57_5 = e0 & op(e2, e1) = e0
% 231.51/42.68  | | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | | REF_CLOSE: (18), (23), (75) are inconsistent by sub-proof
% 231.51/42.68  | | | | | | | | | | | | | | |            #2414.
% 231.51/42.68  | | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | End of split
% 231.51/42.68  | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | Case 2:
% 231.51/42.68  | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | |   (76)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 231.51/42.68  | | | | | | | | | | | | | |           e0 & op(e0, e1) = e0)
% 231.51/42.68  | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | BETA: splitting (76) gives:
% 231.51/42.68  | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | Case 1:
% 231.51/42.68  | | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | |   (77)  all_57_8 = e0 & op(e1, e1) = e0
% 231.51/42.68  | | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | | ALPHA: (77) implies:
% 231.51/42.68  | | | | | | | | | | | | | | |   (78)  op(e1, e1) = e0
% 231.51/42.68  | | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10),
% 231.51/42.68  | | | | | | | | | | | | | | |            (12), (14), (15), (16), (17), (18), (19), (20),
% 231.51/42.68  | | | | | | | | | | | | | | |            (21), (23), (24), (25), (26), (27), (28), (29),
% 231.51/42.68  | | | | | | | | | | | | | | |            (30), (31), (32), (33), (34), (35), (36), (37),
% 231.51/42.68  | | | | | | | | | | | | | | |            (38), (39), (40), (78) are inconsistent by
% 231.51/42.68  | | | | | | | | | | | | | | |            sub-proof #1486.
% 231.51/42.68  | | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | Case 2:
% 231.51/42.68  | | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | |   (79)  all_57_14 = e0 & op(e0, e1) = e0
% 231.51/42.68  | | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | | ALPHA: (79) implies:
% 231.51/42.68  | | | | | | | | | | | | | | |   (80)  all_57_14 = e0
% 231.51/42.68  | | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | | REF_CLOSE: (4), (13), (15), (17), (23), (24), (29), (31),
% 231.51/42.68  | | | | | | | | | | | | | | |            (34), (53), (65), (69), (80) are inconsistent by
% 231.51/42.68  | | | | | | | | | | | | | | |            sub-proof #1484.
% 231.51/42.68  | | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | End of split
% 231.51/42.68  | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | End of split
% 231.51/42.68  | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | Case 2:
% 231.51/42.68  | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | |   (81)  all_57_9 = e1 & op(e3, e0) = e1
% 231.51/42.68  | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | ALPHA: (81) implies:
% 231.51/42.68  | | | | | | | | | | | | |   (82)  all_57_9 = e1
% 231.51/42.68  | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | BETA: splitting (14) gives:
% 231.51/42.68  | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | Case 1:
% 231.51/42.68  | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | |   (83)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 231.51/42.68  | | | | | | | | | | | | | |           & op(e3, e2) = e0)
% 231.51/42.68  | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | BETA: splitting (83) gives:
% 231.51/42.68  | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | Case 1:
% 231.51/42.68  | | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | |   (84)  all_57_0 = e0 & op(e3, e3) = e0
% 231.51/42.68  | | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | | ALPHA: (84) implies:
% 231.51/42.68  | | | | | | | | | | | | | | |   (85)  op(e3, e3) = e0
% 231.51/42.68  | | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | | REF_CLOSE: (7), (18), (20), (85) are inconsistent by
% 231.51/42.68  | | | | | | | | | | | | | | |            sub-proof #2494.
% 231.51/42.68  | | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | Case 2:
% 231.51/42.68  | | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | |   (86)  all_57_1 = e0 & op(e3, e2) = e0
% 231.51/42.68  | | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | | ALPHA: (86) implies:
% 231.51/42.68  | | | | | | | | | | | | | | |   (87)  all_57_1 = e0
% 231.51/42.68  | | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | | REF_CLOSE: (4), (15), (17), (24), (29), (31), (53), (87) are
% 231.51/42.68  | | | | | | | | | | | | | | |            inconsistent by sub-proof #2099.
% 231.51/42.68  | | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | End of split
% 231.51/42.68  | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | Case 2:
% 231.51/42.68  | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | |   (88)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 231.51/42.68  | | | | | | | | | | | | | |           & op(e3, e0) = e0)
% 231.51/42.68  | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | BETA: splitting (88) gives:
% 231.51/42.68  | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | Case 1:
% 231.51/42.68  | | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | |   (89)  all_57_4 = e0 & op(e3, e1) = e0
% 231.51/42.68  | | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | | ALPHA: (89) implies:
% 231.51/42.68  | | | | | | | | | | | | | | |   (90)  all_57_4 = e0
% 231.51/42.68  | | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | | BETA: splitting (6) gives:
% 231.51/42.68  | | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | | Case 1:
% 231.51/42.68  | | | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | | |   (91)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 231.51/42.68  | | | | | | | | | | | | | | | |           & op(e1, e2) = e0)
% 231.51/42.68  | | | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | | | BETA: splitting (91) gives:
% 231.51/42.68  | | | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | | | Case 1:
% 231.51/42.68  | | | | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | | | |   (92)  all_57_6 = e0 & op(e1, e3) = e0
% 231.51/42.68  | | | | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | | | | ALPHA: (92) implies:
% 231.51/42.68  | | | | | | | | | | | | | | | | |   (93)  all_57_6 = e0
% 231.51/42.68  | | | | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (10), (12), (17), (20), (24), (25),
% 231.51/42.68  | | | | | | | | | | | | | | | | |            (31), (44), (82), (90), (93) are inconsistent by
% 231.51/42.68  | | | | | | | | | | | | | | | | |            sub-proof #1483.
% 231.51/42.68  | | | | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | | | Case 2:
% 231.51/42.68  | | | | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | | | |   (94)  all_57_7 = e0 & op(e1, e2) = e0
% 231.51/42.68  | | | | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (29), (94) are inconsistent by sub-proof
% 231.51/42.68  | | | | | | | | | | | | | | | | |            #2042.
% 231.51/42.68  | | | | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | | | End of split
% 231.51/42.68  | | | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | | Case 2:
% 231.51/42.68  | | | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | | |   (95)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 231.51/42.68  | | | | | | | | | | | | | | | |           e0 & op(e1, e0) = e0)
% 231.51/42.68  | | | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | | | BETA: splitting (95) gives:
% 231.51/42.68  | | | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | | | Case 1:
% 231.51/42.68  | | | | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | | | |   (96)  all_57_8 = e0 & op(e1, e1) = e0
% 231.51/42.68  | | | | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | | | | ALPHA: (96) implies:
% 231.51/42.68  | | | | | | | | | | | | | | | | |   (97)  op(e1, e1) = e0
% 231.51/42.68  | | | | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10),
% 231.51/42.68  | | | | | | | | | | | | | | | | |            (12), (14), (15), (16), (17), (18), (19), (20),
% 231.51/42.68  | | | | | | | | | | | | | | | | |            (21), (23), (24), (25), (26), (27), (28), (29),
% 231.51/42.68  | | | | | | | | | | | | | | | | |            (30), (31), (32), (33), (34), (35), (36), (37),
% 231.51/42.68  | | | | | | | | | | | | | | | | |            (38), (39), (40), (97) are inconsistent by
% 231.51/42.68  | | | | | | | | | | | | | | | | |            sub-proof #1486.
% 231.51/42.68  | | | | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | | | Case 2:
% 231.51/42.68  | | | | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | | | |   (98)  all_57_11 = e0 & op(e1, e0) = e0
% 231.51/42.68  | | | | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | | | | ALPHA: (98) implies:
% 231.51/42.68  | | | | | | | | | | | | | | | | |   (99)  all_57_11 = e0
% 231.51/42.68  | | | | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | | | | COMBINE_EQS: (62), (99) imply:
% 231.51/42.68  | | | | | | | | | | | | | | | | |   (100)  e2 = e0
% 231.51/42.68  | | | | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | | | | COMBINE_EQS: (65), (100) imply:
% 231.51/42.68  | | | | | | | | | | | | | | | | |   (101)  all_57_1 = e0
% 231.51/42.68  | | | | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (15), (17), (24), (29), (31), (53), (101) are
% 231.51/42.68  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2099.
% 231.51/42.68  | | | | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | | | End of split
% 231.51/42.68  | | | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | | End of split
% 231.51/42.68  | | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | Case 2:
% 231.51/42.68  | | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | |   (102)  all_57_9 = e0 & op(e3, e0) = e0
% 231.51/42.68  | | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | | ALPHA: (102) implies:
% 231.51/42.68  | | | | | | | | | | | | | | |   (103)  all_57_9 = e0
% 231.51/42.68  | | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | | COMBINE_EQS: (82), (103) imply:
% 231.51/42.68  | | | | | | | | | | | | | | |   (104)  e1 = e0
% 231.51/42.68  | | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | | COMBINE_EQS: (8), (104) imply:
% 231.51/42.68  | | | | | | | | | | | | | | |   (105)  all_57_10 = e0
% 231.51/42.68  | | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | | REF_CLOSE: (1), (5), (11), (15), (23), (25), (31), (105) are
% 231.51/42.68  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1530.
% 231.51/42.68  | | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | End of split
% 231.51/42.68  | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | End of split
% 231.51/42.68  | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | End of split
% 231.51/42.68  | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | End of split
% 231.51/42.68  | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | Case 2:
% 231.51/42.68  | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | |   (106)  all_57_3 = e2 & op(e2, e2) = e2
% 231.51/42.68  | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | ALPHA: (106) implies:
% 231.51/42.68  | | | | | | | | | | |   (107)  all_57_3 = e2
% 231.51/42.68  | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | COMBINE_EQS: (15), (107) imply:
% 231.51/42.68  | | | | | | | | | | |   (108)  e2 = e0
% 231.51/42.68  | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | REF_CLOSE: (8), (11), (17), (23), (24), (30), (31), (107),
% 231.51/42.68  | | | | | | | | | | |            (108) are inconsistent by sub-proof #1482.
% 231.51/42.68  | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | End of split
% 231.51/42.68  | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | Case 2:
% 231.51/42.68  | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | |   (109)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2
% 231.51/42.68  | | | | | | | | | |            & op(e0, e2) = e2)
% 231.51/42.68  | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | REF_CLOSE: (17), (29), (31), (53), (109) are inconsistent by
% 231.51/42.68  | | | | | | | | | |            sub-proof #2100.
% 231.51/42.68  | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | End of split
% 231.51/42.68  | | | | | | | | | 
% 231.51/42.68  | | | | | | | | End of split
% 231.51/42.68  | | | | | | | | 
% 231.51/42.68  | | | | | | | End of split
% 231.51/42.68  | | | | | | | 
% 231.51/42.68  | | | | | | End of split
% 231.51/42.68  | | | | | | 
% 231.51/42.68  | | | | | Case 2:
% 231.51/42.68  | | | | | | 
% 231.51/42.68  | | | | | |   (110)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 &
% 231.51/42.68  | | | | | |            op(e0, e0) = e1)
% 231.51/42.68  | | | | | | 
% 231.51/42.68  | | | | | | BETA: splitting (110) gives:
% 231.51/42.68  | | | | | | 
% 231.51/42.68  | | | | | | Case 1:
% 231.51/42.68  | | | | | | | 
% 231.51/42.68  | | | | | | |   (111)  all_57_14 = e1 & op(e0, e1) = e1
% 231.51/42.68  | | | | | | | 
% 231.51/42.68  | | | | | | | ALPHA: (111) implies:
% 231.51/42.68  | | | | | | |   (112)  all_57_14 = e1
% 231.51/42.68  | | | | | | | 
% 231.51/42.68  | | | | | | | BETA: splitting (34) gives:
% 231.51/42.68  | | | | | | | 
% 231.51/42.68  | | | | | | | Case 1:
% 231.51/42.68  | | | | | | | | 
% 231.51/42.68  | | | | | | | |   (113)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 &
% 231.51/42.68  | | | | | | | |            op(e2, e1) = e2)
% 231.51/42.68  | | | | | | | | 
% 231.51/42.68  | | | | | | | | BETA: splitting (113) gives:
% 231.51/42.68  | | | | | | | | 
% 231.51/42.68  | | | | | | | | Case 1:
% 231.51/42.68  | | | | | | | | | 
% 231.51/42.68  | | | | | | | | |   (114)  all_57_4 = e2 & op(e3, e1) = e2
% 231.51/42.68  | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | ALPHA: (114) implies:
% 231.51/42.68  | | | | | | | | |   (115)  all_57_4 = e2
% 231.51/42.68  | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | BETA: splitting (6) gives:
% 231.51/42.68  | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | Case 1:
% 231.51/42.68  | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | |   (116)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 231.51/42.68  | | | | | | | | | |            & op(e1, e2) = e0)
% 231.51/42.68  | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | BETA: splitting (116) gives:
% 231.51/42.68  | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | Case 1:
% 231.51/42.68  | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | |   (117)  all_57_6 = e0 & op(e1, e3) = e0
% 231.51/42.68  | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | REF_CLOSE: (1), (5), (8), (11), (15), (23), (25), (31), (44),
% 231.51/42.68  | | | | | | | | | | |            (117) are inconsistent by sub-proof #1502.
% 231.51/42.68  | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | Case 2:
% 231.51/42.68  | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | |   (118)  all_57_7 = e0 & op(e1, e2) = e0
% 231.51/42.68  | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | ALPHA: (118) implies:
% 231.51/42.68  | | | | | | | | | | |   (119)  all_57_7 = e0
% 231.51/42.68  | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | REF_CLOSE: (18), (29), (119) are inconsistent by sub-proof
% 231.51/42.68  | | | | | | | | | | |            #2269.
% 231.51/42.68  | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | End of split
% 231.51/42.68  | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | Case 2:
% 231.51/42.68  | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | |   (120)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0
% 231.51/42.68  | | | | | | | | | |            & op(e1, e0) = e0)
% 231.51/42.68  | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | BETA: splitting (120) gives:
% 231.51/42.68  | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | Case 1:
% 231.51/42.68  | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | |   (121)  all_57_8 = e0 & op(e1, e1) = e0
% 231.51/42.68  | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | ALPHA: (121) implies:
% 231.51/42.68  | | | | | | | | | | |   (122)  op(e1, e1) = e0
% 231.51/42.68  | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10),
% 231.51/42.68  | | | | | | | | | | |            (12), (14), (15), (16), (17), (18), (19), (20),
% 231.51/42.68  | | | | | | | | | | |            (21), (23), (24), (25), (26), (27), (28), (29),
% 231.51/42.68  | | | | | | | | | | |            (30), (31), (32), (33), (34), (35), (36), (37),
% 231.51/42.68  | | | | | | | | | | |            (38), (39), (40), (122) are inconsistent by
% 231.51/42.68  | | | | | | | | | | |            sub-proof #1486.
% 231.51/42.68  | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | Case 2:
% 231.51/42.68  | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | |   (123)  all_57_11 = e0 & op(e1, e0) = e0
% 231.51/42.68  | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | ALPHA: (123) implies:
% 231.51/42.68  | | | | | | | | | | |   (124)  all_57_11 = e0
% 231.51/42.68  | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (10), (12), (14), (15), (17), (18),
% 231.51/42.68  | | | | | | | | | | |            (20), (21), (23), (24), (25), (29), (30), (31),
% 231.51/42.68  | | | | | | | | | | |            (32), (36), (39), (115), (124) are inconsistent by
% 231.51/42.68  | | | | | | | | | | |            sub-proof #1480.
% 231.51/42.68  | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | End of split
% 231.51/42.68  | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | End of split
% 231.51/42.68  | | | | | | | | | 
% 231.51/42.68  | | | | | | | | Case 2:
% 231.51/42.68  | | | | | | | | | 
% 231.51/42.68  | | | | | | | | |   (125)  all_57_5 = e2 & op(e2, e1) = e2
% 231.51/42.68  | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | REF_CLOSE: (17), (23), (125) are inconsistent by sub-proof
% 231.51/42.68  | | | | | | | | |            #2425.
% 231.51/42.68  | | | | | | | | | 
% 231.51/42.68  | | | | | | | | End of split
% 231.51/42.68  | | | | | | | | 
% 231.51/42.68  | | | | | | | Case 2:
% 231.51/42.68  | | | | | | | | 
% 231.51/42.68  | | | | | | | |   (126)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 &
% 231.51/42.68  | | | | | | | |            op(e0, e1) = e2)
% 231.51/42.68  | | | | | | | | 
% 231.51/42.68  | | | | | | | | BETA: splitting (126) gives:
% 231.51/42.68  | | | | | | | | 
% 231.51/42.68  | | | | | | | | Case 1:
% 231.51/42.68  | | | | | | | | | 
% 231.51/42.68  | | | | | | | | |   (127)  all_57_8 = e2 & op(e1, e1) = e2
% 231.51/42.68  | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | REF_CLOSE: (13), (31), (127) are inconsistent by sub-proof
% 231.51/42.68  | | | | | | | | |            #1501.
% 231.51/42.68  | | | | | | | | | 
% 231.51/42.68  | | | | | | | | Case 2:
% 231.51/42.68  | | | | | | | | | 
% 231.51/42.68  | | | | | | | | |   (128)  all_57_14 = e2 & op(e0, e1) = e2
% 231.51/42.68  | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | REF_CLOSE: (31), (112), (128) are inconsistent by sub-proof
% 231.51/42.68  | | | | | | | | |            #1968.
% 231.51/42.68  | | | | | | | | | 
% 231.51/42.68  | | | | | | | | End of split
% 231.51/42.68  | | | | | | | | 
% 231.51/42.68  | | | | | | | End of split
% 231.51/42.68  | | | | | | | 
% 231.51/42.68  | | | | | | Case 2:
% 231.51/42.68  | | | | | | | 
% 231.51/42.68  | | | | | | |   (129)  all_57_15 = e1 & op(e0, e0) = e1
% 231.51/42.68  | | | | | | | 
% 231.51/42.68  | | | | | | | REF_CLOSE: (5), (21), (129) are inconsistent by sub-proof #2318.
% 231.51/42.68  | | | | | | | 
% 231.51/42.68  | | | | | | End of split
% 231.51/42.68  | | | | | | 
% 231.51/42.68  | | | | | End of split
% 231.51/42.68  | | | | | 
% 231.51/42.68  | | | | End of split
% 231.51/42.68  | | | | 
% 231.51/42.68  | | | End of split
% 231.51/42.68  | | | 
% 231.51/42.68  | | Case 2:
% 231.51/42.68  | | | 
% 231.51/42.68  | | |   (130)  all_57_12 = e1 & op(e0, e3) = e1
% 231.51/42.68  | | | 
% 231.51/42.68  | | | ALPHA: (130) implies:
% 231.51/42.68  | | |   (131)  all_57_12 = e1
% 231.51/42.68  | | | 
% 231.51/42.68  | | | BETA: splitting (35) gives:
% 231.51/42.68  | | | 
% 231.51/42.68  | | | Case 1:
% 231.51/42.68  | | | | 
% 231.51/42.68  | | | |   (132)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3)
% 231.51/42.68  | | | |            = e0)
% 231.51/42.68  | | | | 
% 231.51/42.68  | | | | REF_CLOSE: (7), (8), (15), (17), (18), (20), (23), (24), (30), (31),
% 231.51/42.68  | | | |            (132) are inconsistent by sub-proof #1503.
% 231.51/42.68  | | | | 
% 231.51/42.68  | | | Case 2:
% 231.51/42.68  | | | | 
% 231.51/42.68  | | | |   (133)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0,
% 231.51/42.68  | | | |              e3) = e0)
% 231.51/42.68  | | | | 
% 231.51/42.68  | | | | BETA: splitting (133) gives:
% 231.51/42.68  | | | | 
% 231.51/42.68  | | | | Case 1:
% 231.51/42.68  | | | | | 
% 231.51/42.68  | | | | |   (134)  all_57_6 = e0 & op(e1, e3) = e0
% 231.51/42.68  | | | | | 
% 231.51/42.68  | | | | | ALPHA: (134) implies:
% 231.51/42.68  | | | | |   (135)  all_57_6 = e0
% 231.51/42.68  | | | | | 
% 231.51/42.68  | | | | | BETA: splitting (28) gives:
% 231.51/42.68  | | | | | 
% 231.51/42.68  | | | | | Case 1:
% 231.51/42.68  | | | | | | 
% 231.51/42.68  | | | | | |   (136)  all_57_15 = e0 & op(e0, e0) = e0
% 231.51/42.68  | | | | | | 
% 231.51/42.68  | | | | | | ALPHA: (136) implies:
% 231.51/42.68  | | | | | |   (137)  op(e0, e0) = e0
% 231.51/42.68  | | | | | | 
% 231.51/42.68  | | | | | | REF_CLOSE: (7), (18), (26), (137) are inconsistent by sub-proof
% 231.51/42.68  | | | | | |            #2304.
% 231.51/42.68  | | | | | | 
% 231.51/42.68  | | | | | Case 2:
% 231.51/42.68  | | | | | | 
% 231.51/42.68  | | | | | |   (138)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 &
% 231.51/42.68  | | | | | |              op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0))
% 231.51/42.68  | | | | | |          & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.51/42.68  | | | | | |              op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 231.51/42.68  | | | | | | 
% 231.51/42.68  | | | | | | ALPHA: (138) implies:
% 231.51/42.68  | | | | | |   (139)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.51/42.68  | | | | | |            op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.51/42.68  | | | | | | 
% 231.51/42.68  | | | | | | BETA: splitting (139) gives:
% 231.51/42.68  | | | | | | 
% 231.51/42.68  | | | | | | Case 1:
% 231.51/42.68  | | | | | | | 
% 231.51/42.68  | | | | | | |   (140)  all_57_12 = e0 & op(e0, e3) = e0
% 231.51/42.68  | | | | | | | 
% 231.51/42.68  | | | | | | | REF_CLOSE: (1), (5), (8), (11), (15), (23), (25), (31), (131),
% 231.51/42.68  | | | | | | |            (140) are inconsistent by sub-proof #1479.
% 231.51/42.68  | | | | | | | 
% 231.51/42.68  | | | | | | Case 2:
% 231.51/42.68  | | | | | | | 
% 231.51/42.68  | | | | | | |   (141)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 &
% 231.51/42.68  | | | | | | |            op(e0, e1) = e0)
% 231.51/42.68  | | | | | | | 
% 231.51/42.68  | | | | | | | BETA: splitting (141) gives:
% 231.51/42.68  | | | | | | | 
% 231.51/42.68  | | | | | | | Case 1:
% 231.51/42.68  | | | | | | | | 
% 231.51/42.68  | | | | | | | |   (142)  all_57_13 = e0 & op(e0, e2) = e0
% 231.51/42.68  | | | | | | | | 
% 231.51/42.68  | | | | | | | | ALPHA: (142) implies:
% 231.51/42.68  | | | | | | | |   (143)  all_57_13 = e0
% 231.51/42.68  | | | | | | | | 
% 231.51/42.68  | | | | | | | | REF_CLOSE: (4), (5), (7), (10), (12), (14), (15), (17), (18),
% 231.51/42.68  | | | | | | | |            (20), (24), (25), (29), (31), (39), (143) are
% 231.51/42.68  | | | | | | | |            inconsistent by sub-proof #2091.
% 231.51/42.68  | | | | | | | | 
% 231.51/42.68  | | | | | | | Case 2:
% 231.51/42.68  | | | | | | | | 
% 231.51/42.68  | | | | | | | |   (144)  all_57_14 = e0 & op(e0, e1) = e0
% 231.51/42.68  | | | | | | | | 
% 231.51/42.68  | | | | | | | | ALPHA: (144) implies:
% 231.51/42.68  | | | | | | | |   (145)  all_57_14 = e0
% 231.51/42.68  | | | | | | | | 
% 231.51/42.68  | | | | | | | | BETA: splitting (34) gives:
% 231.51/42.68  | | | | | | | | 
% 231.51/42.68  | | | | | | | | Case 1:
% 231.51/42.68  | | | | | | | | | 
% 231.51/42.68  | | | | | | | | |   (146)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 &
% 231.51/42.68  | | | | | | | | |            op(e2, e1) = e2)
% 231.51/42.68  | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | BETA: splitting (146) gives:
% 231.51/42.68  | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | Case 1:
% 231.51/42.68  | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | |   (147)  all_57_4 = e2 & op(e3, e1) = e2
% 231.51/42.68  | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | ALPHA: (147) implies:
% 231.51/42.68  | | | | | | | | | |   (148)  all_57_4 = e2
% 231.51/42.68  | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | BETA: splitting (14) gives:
% 231.51/42.68  | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | Case 1:
% 231.51/42.68  | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | |   (149)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 231.51/42.68  | | | | | | | | | | |            & op(e3, e2) = e0)
% 231.51/42.68  | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (15), (17), (18), (20), (24), (25),
% 231.51/42.68  | | | | | | | | | | |            (29), (31), (39), (149) are inconsistent by
% 231.51/42.68  | | | | | | | | | | |            sub-proof #2097.
% 231.51/42.68  | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | Case 2:
% 231.51/42.68  | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | |   (150)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 231.51/42.68  | | | | | | | | | | |            & op(e3, e0) = e0)
% 231.51/42.68  | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | BETA: splitting (150) gives:
% 231.51/42.68  | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | Case 1:
% 231.51/42.68  | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | |   (151)  all_57_4 = e0 & op(e3, e1) = e0
% 231.51/42.68  | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | ALPHA: (151) implies:
% 231.51/42.68  | | | | | | | | | | | |   (152)  all_57_4 = e0
% 231.51/42.68  | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | COMBINE_EQS: (148), (152) imply:
% 231.51/42.68  | | | | | | | | | | | |   (153)  e2 = e0
% 231.51/42.68  | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | COMBINE_EQS: (11), (153) imply:
% 231.51/42.68  | | | | | | | | | | | |   (154)  all_57_2 = e0
% 231.51/42.68  | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | REF_CLOSE: (8), (15), (17), (23), (24), (30), (31), (154) are
% 231.51/42.68  | | | | | | | | | | | |            inconsistent by sub-proof #2254.
% 231.51/42.68  | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | Case 2:
% 231.51/42.68  | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | |   (155)  all_57_9 = e0 & op(e3, e0) = e0
% 231.51/42.68  | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | ALPHA: (155) implies:
% 231.51/42.68  | | | | | | | | | | | |   (156)  op(e3, e0) = e0
% 231.51/42.68  | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | BETA: splitting (33) gives:
% 231.51/42.68  | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | Case 1:
% 231.51/42.68  | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | |   (157)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 231.51/42.68  | | | | | | | | | | | | |            & op(e2, e3) = e2)
% 231.51/42.68  | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | BETA: splitting (157) gives:
% 231.51/42.68  | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | Case 1:
% 231.51/42.68  | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | |   (158)  all_57_0 = e2 & op(e3, e3) = e2
% 231.51/42.68  | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | ALPHA: (158) implies:
% 231.51/42.68  | | | | | | | | | | | | | |   (159)  op(e3, e3) = e2
% 231.51/42.68  | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | REF_CLOSE: (7), (17), (20), (159) are inconsistent by
% 231.51/42.68  | | | | | | | | | | | | | |            sub-proof #2490.
% 231.51/42.68  | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | Case 2:
% 231.51/42.68  | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_52_7, e0, e0, e3,
% 231.51/42.68  | | | | | | | | | | | | | |              simplifying with (38), (156) gives:
% 231.51/42.68  | | | | | | | | | | | | | |   (160)  all_52_7 = e0
% 231.51/42.68  | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | REF_CLOSE: (2), (7), (9), (26), (160) are inconsistent by
% 231.51/42.68  | | | | | | | | | | | | | |            sub-proof #1505.
% 231.51/42.68  | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | End of split
% 231.51/42.68  | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | Case 2:
% 231.51/42.68  | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | |   (161)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 231.51/42.68  | | | | | | | | | | | | |            e2 & op(e0, e3) = e2)
% 231.51/42.68  | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | BETA: splitting (161) gives:
% 231.51/42.68  | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | Case 1:
% 231.51/42.68  | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | |   (162)  all_57_6 = e2 & op(e1, e3) = e2
% 231.51/42.68  | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | ALPHA: (162) implies:
% 231.51/42.68  | | | | | | | | | | | | | |   (163)  all_57_6 = e2
% 231.51/42.68  | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | COMBINE_EQS: (135), (163) imply:
% 231.51/42.68  | | | | | | | | | | | | | |   (164)  e2 = e0
% 231.51/42.68  | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | COMBINE_EQS: (11), (164) imply:
% 231.51/42.68  | | | | | | | | | | | | | |   (165)  all_57_2 = e0
% 231.51/42.68  | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | REF_CLOSE: (8), (15), (17), (23), (24), (30), (31), (165) are
% 231.51/42.68  | | | | | | | | | | | | | |            inconsistent by sub-proof #2254.
% 231.51/42.68  | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | Case 2:
% 231.51/42.68  | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | |   (166)  all_57_12 = e2 & op(e0, e3) = e2
% 231.51/42.68  | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | | REF_CLOSE: (31), (131), (166) are inconsistent by sub-proof
% 231.51/42.68  | | | | | | | | | | | | | |            #1922.
% 231.51/42.68  | | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | | End of split
% 231.51/42.68  | | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | | End of split
% 231.51/42.68  | | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | | End of split
% 231.51/42.68  | | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | End of split
% 231.51/42.68  | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | Case 2:
% 231.51/42.68  | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | |   (167)  all_57_5 = e2 & op(e2, e1) = e2
% 231.51/42.68  | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | REF_CLOSE: (17), (23), (167) are inconsistent by sub-proof
% 231.51/42.68  | | | | | | | | | |            #2425.
% 231.51/42.68  | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | End of split
% 231.51/42.68  | | | | | | | | | 
% 231.51/42.68  | | | | | | | | Case 2:
% 231.51/42.68  | | | | | | | | | 
% 231.51/42.68  | | | | | | | | |   (168)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 &
% 231.51/42.68  | | | | | | | | |            op(e0, e1) = e2)
% 231.51/42.68  | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | BETA: splitting (168) gives:
% 231.51/42.68  | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | Case 1:
% 231.51/42.68  | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | |   (169)  all_57_8 = e2 & op(e1, e1) = e2
% 231.51/42.68  | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | REF_CLOSE: (13), (31), (169) are inconsistent by sub-proof
% 231.51/42.68  | | | | | | | | | |            #1501.
% 231.51/42.68  | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | Case 2:
% 231.51/42.68  | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | |   (170)  all_57_14 = e2 & op(e0, e1) = e2
% 231.51/42.68  | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | ALPHA: (170) implies:
% 231.51/42.68  | | | | | | | | | |   (171)  all_57_14 = e2
% 231.51/42.68  | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | COMBINE_EQS: (145), (171) imply:
% 231.51/42.68  | | | | | | | | | |   (172)  e2 = e0
% 231.51/42.68  | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | COMBINE_EQS: (11), (172) imply:
% 231.51/42.68  | | | | | | | | | |   (173)  all_57_2 = e0
% 231.51/42.68  | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | | REF_CLOSE: (8), (15), (17), (23), (24), (30), (31), (173) are
% 231.51/42.68  | | | | | | | | | |            inconsistent by sub-proof #2254.
% 231.51/42.68  | | | | | | | | | | 
% 231.51/42.68  | | | | | | | | | End of split
% 231.51/42.68  | | | | | | | | | 
% 231.51/42.68  | | | | | | | | End of split
% 231.51/42.68  | | | | | | | | 
% 231.51/42.68  | | | | | | | End of split
% 231.51/42.68  | | | | | | | 
% 231.51/42.68  | | | | | | End of split
% 231.51/42.68  | | | | | | 
% 231.51/42.68  | | | | | End of split
% 231.51/42.68  | | | | | 
% 231.51/42.68  | | | | Case 2:
% 231.51/42.68  | | | | | 
% 231.51/42.68  | | | | |   (174)  all_57_12 = e0 & op(e0, e3) = e0
% 231.51/42.68  | | | | | 
% 231.51/42.68  | | | | | REF_CLOSE: (1), (5), (8), (11), (15), (23), (25), (31), (131), (174)
% 231.51/42.68  | | | | |            are inconsistent by sub-proof #1479.
% 231.51/42.68  | | | | | 
% 231.51/42.68  | | | | End of split
% 231.51/42.68  | | | | 
% 231.51/42.68  | | | End of split
% 231.51/42.68  | | | 
% 231.51/42.68  | | End of split
% 231.51/42.68  | | 
% 231.51/42.68  | End of split
% 231.51/42.68  | 
% 231.51/42.68  End of proof
% 231.51/42.68  
% 231.51/42.68  Sub-proof #1479 shows that the following formulas are inconsistent:
% 231.51/42.68  ----------------------------------------------------------------
% 231.51/42.68    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.51/42.68         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.51/42.68    (2)   ~ (e3 = e1)
% 231.51/42.68    (3)  all_57_10 = e1
% 231.51/42.68    (4)  all_57_2 = e2
% 231.51/42.68    (5)  all_57_3 = e0
% 231.51/42.68    (6)  all_57_5 = e3
% 231.51/42.68    (7)  all_57_12 = e1
% 231.51/42.68    (8)   ~ (e1 = e0)
% 231.51/42.68    (9)   ~ (e2 = e1)
% 231.51/42.68    (10)  all_57_12 = e0 & op(e0, e3) = e0
% 231.51/42.68  
% 231.51/42.68  Begin of proof
% 231.51/42.68  | 
% 231.51/42.68  | ALPHA: (10) implies:
% 231.51/42.68  |   (11)  all_57_12 = e0
% 231.51/42.68  | 
% 231.51/42.68  | COMBINE_EQS: (7), (11) imply:
% 231.51/42.68  |   (12)  e1 = e0
% 231.51/42.68  | 
% 231.51/42.68  | COMBINE_EQS: (3), (12) imply:
% 231.51/42.68  |   (13)  all_57_10 = e0
% 231.51/42.68  | 
% 231.51/42.68  | REF_CLOSE: (1), (2), (4), (5), (6), (8), (9), (13) are inconsistent by
% 231.51/42.68  |            sub-proof #1530.
% 231.51/42.68  | 
% 231.51/42.68  End of proof
% 231.51/42.68  
% 231.51/42.68  Sub-proof #1480 shows that the following formulas are inconsistent:
% 231.51/42.68  ----------------------------------------------------------------
% 231.51/42.69    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.51/42.69         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.51/42.69    (2)   ~ (e3 = e1)
% 231.51/42.69    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.51/42.69           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.51/42.69    (4)  all_57_4 = e2
% 231.51/42.69    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.51/42.69         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.51/42.69    (6)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.51/42.69         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.51/42.69    (7)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.51/42.69         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.51/42.69    (8)  all_57_3 = e0
% 231.51/42.69    (9)   ~ (e3 = e2)
% 231.51/42.69    (10)   ~ (e3 = e0)
% 231.51/42.69    (11)  op(e3, e3) = e3
% 231.51/42.69    (12)  all_57_15 = e3
% 231.51/42.69    (13)  all_57_5 = e3
% 231.51/42.69    (14)  all_57_11 = e0
% 231.51/42.69    (15)   ~ (e2 = e0)
% 231.51/42.69    (16)   ~ (e1 = e0)
% 231.51/42.69    (17)  all_57_7 = e3
% 231.51/42.69    (18)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.51/42.69          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.51/42.69    (19)   ~ (e2 = e1)
% 231.51/42.69    (20)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.51/42.69          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.51/42.69    (21)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.51/42.69          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.51/42.69    (22)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.51/42.69          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.51/42.69  
% 231.51/42.69  Begin of proof
% 231.51/42.69  | 
% 231.51/42.69  | BETA: splitting (7) gives:
% 231.51/42.69  | 
% 231.51/42.69  | Case 1:
% 231.51/42.69  | | 
% 231.51/42.69  | |   (23)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) =
% 231.51/42.69  | |           e0)
% 231.51/42.69  | | 
% 231.51/42.69  | | REF_CLOSE: (1), (2), (3), (8), (9), (10), (11), (15), (16), (17), (19),
% 231.51/42.69  | |            (22), (23) are inconsistent by sub-proof #2097.
% 231.51/42.69  | | 
% 231.51/42.69  | Case 2:
% 231.51/42.69  | | 
% 231.51/42.69  | |   (24)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) =
% 231.51/42.69  | |           e0)
% 231.51/42.69  | | 
% 231.51/42.69  | | BETA: splitting (24) gives:
% 231.51/42.69  | | 
% 231.51/42.69  | | Case 1:
% 231.51/42.69  | | | 
% 231.51/42.69  | | |   (25)  all_57_4 = e0 & op(e3, e1) = e0
% 231.51/42.69  | | | 
% 231.51/42.69  | | | REF_CLOSE: (4), (15), (25) are inconsistent by sub-proof #2045.
% 231.51/42.69  | | | 
% 231.51/42.69  | | Case 2:
% 231.51/42.69  | | | 
% 231.51/42.69  | | |   (26)  all_57_9 = e0 & op(e3, e0) = e0
% 231.51/42.69  | | | 
% 231.51/42.69  | | | ALPHA: (26) implies:
% 231.51/42.69  | | |   (27)  all_57_9 = e0
% 231.51/42.69  | | | 
% 231.51/42.69  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (11), (12), (13), (14),
% 231.51/42.69  | | |            (15), (16), (17), (18), (19), (20), (21), (22), (27) are
% 231.51/42.69  | | |            inconsistent by sub-proof #1481.
% 231.51/42.69  | | | 
% 231.51/42.69  | | End of split
% 231.51/42.69  | | 
% 231.51/42.69  | End of split
% 231.51/42.69  | 
% 231.51/42.69  End of proof
% 231.51/42.69  
% 231.51/42.69  Sub-proof #1481 shows that the following formulas are inconsistent:
% 231.51/42.69  ----------------------------------------------------------------
% 231.51/42.69    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.51/42.69         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.51/42.69    (2)   ~ (e3 = e1)
% 231.51/42.69    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.51/42.69           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.51/42.69    (4)  all_57_4 = e2
% 231.51/42.69    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.51/42.69         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.51/42.69    (6)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.51/42.69         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.51/42.69    (7)  all_57_3 = e0
% 231.51/42.69    (8)   ~ (e3 = e2)
% 231.51/42.69    (9)  op(e3, e3) = e3
% 231.51/42.69    (10)  all_57_15 = e3
% 231.51/42.69    (11)  all_57_5 = e3
% 231.51/42.69    (12)  all_57_9 = e0
% 231.51/42.69    (13)  all_57_11 = e0
% 231.51/42.69    (14)   ~ (e2 = e0)
% 231.51/42.69    (15)   ~ (e1 = e0)
% 231.51/42.69    (16)  all_57_7 = e3
% 231.51/42.69    (17)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.51/42.69          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.51/42.69    (18)   ~ (e2 = e1)
% 231.51/42.69    (19)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.51/42.69          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.51/42.69    (20)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.51/42.69          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.51/42.69    (21)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.51/42.69          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.51/42.69  
% 231.51/42.69  Begin of proof
% 231.51/42.69  | 
% 231.51/42.69  | BETA: splitting (5) gives:
% 231.51/42.69  | 
% 231.51/42.69  | Case 1:
% 231.51/42.69  | | 
% 231.51/42.69  | |   (22)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) =
% 231.51/42.69  | |           e1)
% 231.51/42.69  | | 
% 231.51/42.69  | | BETA: splitting (22) gives:
% 231.51/42.69  | | 
% 231.51/42.69  | | Case 1:
% 231.51/42.69  | | | 
% 231.51/42.69  | | |   (23)  all_57_0 = e1 & op(e3, e3) = e1
% 231.51/42.69  | | | 
% 231.51/42.69  | | | ALPHA: (23) implies:
% 231.51/42.69  | | |   (24)  op(e3, e3) = e1
% 231.51/42.69  | | | 
% 231.51/42.69  | | | REF_CLOSE: (2), (3), (9), (24) are inconsistent by sub-proof #2495.
% 231.51/42.69  | | | 
% 231.51/42.69  | | Case 2:
% 231.51/42.69  | | | 
% 231.51/42.69  | | |   (25)  all_57_1 = e1 & op(e3, e2) = e1
% 231.51/42.69  | | | 
% 231.51/42.69  | | | ALPHA: (25) implies:
% 231.51/42.69  | | |   (26)  all_57_1 = e1
% 231.51/42.69  | | | 
% 231.51/42.69  | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13),
% 231.51/42.69  | | |            (14), (15), (16), (17), (18), (19), (20), (21), (26) are
% 231.51/42.69  | | |            inconsistent by sub-proof #1493.
% 231.51/42.69  | | | 
% 231.51/42.69  | | End of split
% 231.51/42.69  | | 
% 231.51/42.69  | Case 2:
% 231.51/42.69  | | 
% 231.51/42.69  | |   (27)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) =
% 231.51/42.69  | |           e1)
% 231.51/42.69  | | 
% 231.51/42.69  | | REF_CLOSE: (4), (12), (15), (18), (27) are inconsistent by sub-proof #1606.
% 231.51/42.69  | | 
% 231.51/42.69  | End of split
% 231.51/42.69  | 
% 231.51/42.69  End of proof
% 231.51/42.69  
% 231.51/42.69  Sub-proof #1482 shows that the following formulas are inconsistent:
% 231.51/42.69  ----------------------------------------------------------------
% 231.51/42.69    (1)  all_57_10 = e1
% 231.51/42.69    (2)  all_57_2 = e2
% 231.51/42.69    (3)   ~ (e3 = e2)
% 231.51/42.69    (4)  all_57_5 = e3
% 231.51/42.69    (5)   ~ (e2 = e0)
% 231.51/42.69    (6)  e2 = e0
% 231.51/42.69    (7)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.51/42.69         (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.51/42.69    (8)   ~ (e2 = e1)
% 231.51/42.69    (9)  all_57_3 = e2
% 231.51/42.69  
% 231.51/42.69  Begin of proof
% 231.51/42.69  | 
% 231.51/42.69  | COMBINE_EQS: (6), (9) imply:
% 231.51/42.69  |   (10)  all_57_3 = e0
% 231.51/42.69  | 
% 231.51/42.69  | COMBINE_EQS: (2), (6) imply:
% 231.51/42.69  |   (11)  all_57_2 = e0
% 231.51/42.69  | 
% 231.51/42.69  | REF_CLOSE: (1), (3), (4), (5), (7), (8), (10), (11) are inconsistent by
% 231.51/42.69  |            sub-proof #2254.
% 231.51/42.69  | 
% 231.51/42.69  End of proof
% 231.51/42.69  
% 231.51/42.69  Sub-proof #1483 shows that the following formulas are inconsistent:
% 231.51/42.69  ----------------------------------------------------------------
% 231.51/42.69    (1)   ~ (e3 = e1)
% 231.51/42.69    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.51/42.69           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.51/42.69    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.51/42.69         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.51/42.69    (4)  all_57_9 = e1
% 231.51/42.69    (5)  all_57_4 = e0
% 231.51/42.69    (6)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.51/42.69         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.51/42.69    (7)  all_57_6 = e1
% 231.51/42.69    (8)   ~ (e3 = e2)
% 231.51/42.69    (9)  op(e3, e3) = e3
% 231.51/42.69    (10)  all_57_6 = e0
% 231.51/42.69    (11)   ~ (e2 = e0)
% 231.51/42.69    (12)   ~ (e1 = e0)
% 231.51/42.69    (13)   ~ (e2 = e1)
% 231.51/42.69  
% 231.51/42.69  Begin of proof
% 231.51/42.69  | 
% 231.51/42.69  | COMBINE_EQS: (7), (10) imply:
% 231.51/42.69  |   (14)  e1 = e0
% 231.51/42.69  | 
% 231.51/42.69  | SIMP: (14) implies:
% 231.51/42.69  |   (15)  e1 = e0
% 231.51/42.69  | 
% 231.51/42.69  | COMBINE_EQS: (4), (15) imply:
% 231.51/42.69  |   (16)  all_57_9 = e0
% 231.51/42.69  | 
% 231.51/42.69  | REF_CLOSE: (1), (2), (3), (5), (6), (8), (9), (11), (12), (13), (16) are
% 231.51/42.69  |            inconsistent by sub-proof #2436.
% 231.51/42.69  | 
% 231.51/42.69  End of proof
% 231.51/42.69  
% 231.51/42.69  Sub-proof #1484 shows that the following formulas are inconsistent:
% 231.51/42.69  ----------------------------------------------------------------
% 231.51/42.69    (1)  all_57_13 = e1
% 231.51/42.69    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.51/42.69         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.51/42.69    (3)  all_57_8 = e1
% 231.51/42.69    (4)  all_57_3 = e0
% 231.51/42.69    (5)   ~ (e3 = e2)
% 231.51/42.69    (6)  all_57_1 = e2
% 231.51/42.69    (7)  all_57_4 = e1
% 231.51/42.69    (8)  all_57_5 = e3
% 231.51/42.69    (9)   ~ (e2 = e0)
% 231.51/42.69    (10)  all_57_7 = e3
% 231.51/42.69    (11)   ~ (e2 = e1)
% 231.51/42.69    (12)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.51/42.69          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.51/42.69    (13)  all_57_14 = e0
% 231.51/42.69  
% 231.51/42.69  Begin of proof
% 231.51/42.69  | 
% 231.51/42.69  | BETA: splitting (12) gives:
% 231.51/42.69  | 
% 231.51/42.69  | Case 1:
% 231.51/42.69  | | 
% 231.51/42.69  | |   (14)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) =
% 231.51/42.69  | |           e2)
% 231.51/42.69  | | 
% 231.51/42.69  | | REF_CLOSE: (5), (7), (8), (11), (14) are inconsistent by sub-proof #2424.
% 231.51/42.69  | | 
% 231.51/42.69  | Case 2:
% 231.51/42.69  | | 
% 231.51/42.69  | |   (15)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) =
% 231.51/42.69  | |           e2)
% 231.51/42.69  | | 
% 231.51/42.69  | | BETA: splitting (15) gives:
% 231.51/42.69  | | 
% 231.51/42.69  | | Case 1:
% 231.51/42.69  | | | 
% 231.51/42.69  | | |   (16)  all_57_8 = e2 & op(e1, e1) = e2
% 231.51/42.69  | | | 
% 231.51/42.69  | | | ALPHA: (16) implies:
% 231.51/42.69  | | |   (17)  all_57_8 = e2
% 231.51/42.69  | | | 
% 231.51/42.69  | | | REF_CLOSE: (3), (11), (17) are inconsistent by sub-proof #1485.
% 231.51/42.69  | | | 
% 231.51/42.69  | | Case 2:
% 231.51/42.69  | | | 
% 231.51/42.69  | | |   (18)  all_57_14 = e2 & op(e0, e1) = e2
% 231.51/42.69  | | | 
% 231.51/42.69  | | | ALPHA: (18) implies:
% 231.51/42.69  | | |   (19)  all_57_14 = e2
% 231.51/42.69  | | | 
% 231.51/42.69  | | | COMBINE_EQS: (13), (19) imply:
% 231.51/42.69  | | |   (20)  e2 = e0
% 231.51/42.69  | | | 
% 231.51/42.69  | | | COMBINE_EQS: (6), (20) imply:
% 231.51/42.69  | | |   (21)  all_57_1 = e0
% 231.51/42.69  | | | 
% 231.51/42.69  | | | REF_CLOSE: (1), (2), (4), (5), (9), (10), (11), (21) are inconsistent by
% 231.51/42.69  | | |            sub-proof #2099.
% 231.51/42.69  | | | 
% 231.51/42.69  | | End of split
% 231.51/42.69  | | 
% 231.51/42.69  | End of split
% 231.51/42.69  | 
% 231.51/42.69  End of proof
% 231.51/42.69  
% 231.51/42.69  Sub-proof #1485 shows that the following formulas are inconsistent:
% 231.51/42.69  ----------------------------------------------------------------
% 231.51/42.69    (1)  all_57_8 = e2
% 231.51/42.69    (2)  all_57_8 = e1
% 231.51/42.69    (3)   ~ (e2 = e1)
% 231.51/42.69  
% 231.51/42.69  Begin of proof
% 231.51/42.69  | 
% 231.51/42.69  | COMBINE_EQS: (1), (2) imply:
% 231.51/42.69  |   (4)  e2 = e1
% 231.51/42.69  | 
% 231.51/42.69  | SIMP: (4) implies:
% 231.51/42.69  |   (5)  e2 = e1
% 231.51/42.69  | 
% 231.51/42.69  | REDUCE: (3), (5) imply:
% 231.51/42.69  |   (6)  $false
% 231.51/42.69  | 
% 231.51/42.69  | CLOSE: (6) is inconsistent.
% 231.51/42.69  | 
% 231.51/42.69  End of proof
% 231.51/42.69  
% 231.51/42.69  Sub-proof #1486 shows that the following formulas are inconsistent:
% 231.51/42.69  ----------------------------------------------------------------
% 231.51/42.69    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.51/42.69         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.51/42.69    (2)   ~ (all_52_7 = e3)
% 231.51/42.69    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.51/42.69         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.51/42.69    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.51/42.69         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.51/42.69    (5)   ~ (e3 = e1)
% 231.51/42.69    (6)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 231.51/42.69         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.51/42.69    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.51/42.69           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.51/42.69    (8)  op(all_52_7, all_52_7) = e0
% 231.51/42.69    (9)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.51/42.69         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.51/42.69    (10)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.51/42.69          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.51/42.69    (11)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.51/42.69          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.51/42.69    (12)  all_57_3 = e0
% 231.51/42.69    (13)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.51/42.69          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.51/42.69    (14)   ~ (e3 = e2)
% 231.51/42.69    (15)   ~ (e3 = e0)
% 231.51/42.69    (16)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.51/42.69          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.51/42.69    (17)  op(e3, e3) = e3
% 231.51/42.69    (18)  all_57_15 = e3
% 231.51/42.69    (19)  all_57_5 = e3
% 231.51/42.69    (20)   ~ (e2 = e0)
% 231.51/42.69    (21)   ~ (e1 = e0)
% 231.51/42.69    (22)  op(e0, e0) = e3
% 231.51/42.69    (23)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.51/42.69          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.51/42.69            e2)
% 231.51/42.69    (24)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.51/42.69              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.51/42.69                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.51/42.69                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.51/42.69    (25)  op(e1, e1) = e0
% 231.51/42.69    (26)  all_57_7 = e3
% 231.51/42.69    (27)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.51/42.69          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.51/42.69    (28)   ~ (e2 = e1)
% 231.51/42.69    (29)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.51/42.69          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.51/42.69    (30)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.51/42.69          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.51/42.69    (31)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.51/42.69          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.51/42.69    (32)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.51/42.69          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.51/42.69    (33)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.51/42.69          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.51/42.69    (34)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 231.51/42.69          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 231.51/42.69    (35)  op(e3, e0) = all_52_7
% 231.51/42.69    (36)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.51/42.69          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.51/42.69    (37)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 231.51/42.69          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 231.51/42.69  
% 231.51/42.69  Begin of proof
% 231.51/42.69  | 
% 231.51/42.69  | BETA: splitting (24) gives:
% 231.51/42.69  | 
% 231.51/42.69  | Case 1:
% 231.51/42.69  | | 
% 231.51/42.69  | |   (38)  all_57_15 = e0 & op(e0, e0) = e0
% 231.51/42.69  | | 
% 231.51/42.69  | | REF_CLOSE: (15), (18), (38) are inconsistent by sub-proof #2329.
% 231.51/42.69  | | 
% 231.51/42.69  | Case 2:
% 231.51/42.69  | | 
% 231.51/42.69  | |   (39)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 231.51/42.69  | |             e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0 &
% 231.51/42.69  | |             op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 231.51/42.69  | |           (all_57_14 = e0 & op(e0, e1) = e0))
% 231.51/42.69  | | 
% 231.51/42.69  | | ALPHA: (39) implies:
% 231.51/42.69  | |   (40)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 231.51/42.69  | |           e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.51/42.69  | |   (41)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 231.51/42.69  | |           e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.51/42.69  | | 
% 231.51/42.69  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 231.51/42.69  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 231.51/42.69  | |            (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 231.51/42.69  | |            (36), (37), (40), (41) are inconsistent by sub-proof #1487.
% 231.51/42.69  | | 
% 231.51/42.69  | End of split
% 231.51/42.69  | 
% 231.51/42.69  End of proof
% 231.51/42.69  
% 231.51/42.69  Sub-proof #1487 shows that the following formulas are inconsistent:
% 231.51/42.69  ----------------------------------------------------------------
% 231.51/42.69    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.51/42.69         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.51/42.69    (2)   ~ (all_52_7 = e3)
% 231.51/42.69    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.51/42.69         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.51/42.69    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.51/42.69         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.51/42.69    (5)   ~ (e3 = e1)
% 231.51/42.69    (6)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 231.51/42.69         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.51/42.69    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.51/42.69           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.51/42.69    (8)  op(all_52_7, all_52_7) = e0
% 231.51/42.69    (9)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.51/42.69         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.51/42.69    (10)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.51/42.69          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.51/42.69    (11)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.51/42.69          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.51/42.69    (12)  all_57_3 = e0
% 231.51/42.69    (13)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.51/42.69          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.51/42.69    (14)   ~ (e3 = e2)
% 231.51/42.69    (15)   ~ (e3 = e0)
% 231.51/42.69    (16)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.51/42.69          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.51/42.69    (17)  op(e3, e3) = e3
% 231.51/42.69    (18)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 231.51/42.69          | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.51/42.69    (19)  all_57_15 = e3
% 231.51/42.69    (20)  all_57_5 = e3
% 231.51/42.69    (21)   ~ (e2 = e0)
% 231.51/42.69    (22)   ~ (e1 = e0)
% 231.51/42.69    (23)  op(e0, e0) = e3
% 231.51/42.69    (24)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.51/42.69          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.51/42.69            e2)
% 231.51/42.69    (25)  op(e1, e1) = e0
% 231.51/42.69    (26)  all_57_7 = e3
% 231.51/42.69    (27)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.51/42.69          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.51/42.69    (28)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) |
% 231.51/42.69          (all_57_11 = e0 & op(e1, e0) = e0)
% 231.51/42.69    (29)   ~ (e2 = e1)
% 231.51/42.69    (30)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.51/42.69          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.51/42.69    (31)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.51/42.69          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.51/42.69    (32)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.51/42.69          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.51/42.69    (33)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.51/42.69          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.51/42.69    (34)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.51/42.69          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.51/42.69    (35)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 231.51/42.69          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 231.51/42.69    (36)  op(e3, e0) = all_52_7
% 231.51/42.69    (37)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.51/42.69          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.51/42.69    (38)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 231.51/42.69          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 231.51/42.69  
% 231.51/42.69  Begin of proof
% 231.51/42.69  | 
% 231.51/42.69  | BETA: splitting (18) gives:
% 231.51/42.69  | 
% 231.51/42.69  | Case 1:
% 231.51/42.69  | | 
% 231.51/42.69  | |   (39)  all_57_12 = e0 & op(e0, e3) = e0
% 231.51/42.69  | | 
% 231.51/42.69  | | ALPHA: (39) implies:
% 231.51/42.69  | |   (40)  all_57_12 = e0
% 231.51/42.69  | | 
% 231.51/42.69  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (10), (11), (12), (14), (15),
% 231.51/42.69  | |            (16), (17), (19), (20), (21), (22), (23), (24), (25), (26), (27),
% 231.51/42.69  | |            (28), (29), (30), (31), (33), (34), (35), (36), (37), (38), (40)
% 231.51/42.69  | |            are inconsistent by sub-proof #1500.
% 231.51/42.69  | | 
% 231.51/42.69  | Case 2:
% 231.51/42.69  | | 
% 231.51/42.69  | |   (41)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 231.51/42.69  | |           e0)
% 231.51/42.69  | | 
% 231.51/42.69  | | BETA: splitting (41) gives:
% 231.51/42.69  | | 
% 231.51/42.69  | | Case 1:
% 231.51/42.69  | | | 
% 231.51/42.69  | | |   (42)  all_57_13 = e0 & op(e0, e2) = e0
% 231.51/42.69  | | | 
% 231.51/42.69  | | | ALPHA: (42) implies:
% 231.51/42.69  | | |   (43)  all_57_13 = e0
% 231.51/42.69  | | | 
% 231.51/42.69  | | | REF_CLOSE: (4), (5), (7), (9), (10), (11), (12), (14), (15), (17), (21),
% 231.51/42.69  | | |            (22), (26), (29), (37), (43) are inconsistent by sub-proof
% 231.51/42.69  | | |            #2091.
% 231.51/42.69  | | | 
% 231.51/42.69  | | Case 2:
% 231.51/42.69  | | | 
% 231.51/42.69  | | |   (44)  all_57_14 = e0 & op(e0, e1) = e0
% 231.51/42.69  | | | 
% 231.51/42.69  | | | ALPHA: (44) implies:
% 231.51/42.69  | | |   (45)  all_57_14 = e0
% 231.51/42.69  | | | 
% 231.51/42.69  | | | REF_CLOSE: (1), (4), (5), (6), (7), (9), (10), (11), (12), (13), (14),
% 231.51/42.69  | | |            (15), (16), (17), (19), (20), (21), (22), (25), (26), (27),
% 231.51/42.69  | | |            (28), (29), (30), (32), (34), (35), (37), (38), (45) are
% 231.51/42.69  | | |            inconsistent by sub-proof #1488.
% 231.51/42.69  | | | 
% 231.51/42.69  | | End of split
% 231.51/42.69  | | 
% 231.51/42.69  | End of split
% 231.51/42.69  | 
% 231.51/42.69  End of proof
% 231.51/42.69  
% 231.51/42.69  Sub-proof #1488 shows that the following formulas are inconsistent:
% 231.51/42.69  ----------------------------------------------------------------
% 231.51/42.69    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.51/42.69         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.51/42.69    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.51/42.69         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.51/42.69    (3)   ~ (e3 = e1)
% 231.51/42.69    (4)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 231.51/42.69         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.51/42.69    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.51/42.69           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.51/42.69    (6)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.51/42.69         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.51/42.69    (7)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.51/42.69         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.51/42.69    (8)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.51/42.69         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.51/42.69    (9)  all_57_3 = e0
% 231.51/42.69    (10)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.51/42.69          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.51/42.69    (11)   ~ (e3 = e2)
% 231.51/42.69    (12)   ~ (e3 = e0)
% 231.51/42.69    (13)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.51/42.69          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.51/42.69    (14)  op(e3, e3) = e3
% 231.51/42.69    (15)  all_57_15 = e3
% 231.51/42.69    (16)  all_57_5 = e3
% 231.51/42.69    (17)   ~ (e2 = e0)
% 231.51/42.69    (18)   ~ (e1 = e0)
% 231.51/42.69    (19)  op(e1, e1) = e0
% 231.51/42.69    (20)  all_57_7 = e3
% 231.51/42.69    (21)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.51/42.69          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.51/42.69    (22)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) |
% 231.51/42.69          (all_57_11 = e0 & op(e1, e0) = e0)
% 231.51/42.69    (23)   ~ (e2 = e1)
% 231.51/42.69    (24)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.51/42.69          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.51/42.69    (25)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.51/42.69          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.51/42.69    (26)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.51/42.69          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.51/42.69    (27)  all_57_14 = e0
% 231.51/42.69    (28)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 231.51/42.69          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 231.51/42.69    (29)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.51/42.69          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.51/42.69    (30)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 231.51/42.70          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 231.51/42.70  
% 231.51/42.70  Begin of proof
% 231.51/42.70  | 
% 231.51/42.70  | BETA: splitting (22) gives:
% 231.51/42.70  | 
% 231.51/42.70  | Case 1:
% 231.51/42.70  | | 
% 231.51/42.70  | |   (31)  all_57_9 = e0 & op(e3, e0) = e0
% 231.51/42.70  | | 
% 231.51/42.70  | | ALPHA: (31) implies:
% 231.51/42.70  | |   (32)  all_57_9 = e0
% 231.51/42.70  | | 
% 231.51/42.70  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13),
% 231.51/42.70  | |            (14), (15), (16), (17), (18), (19), (20), (21), (23), (24), (25),
% 231.51/42.70  | |            (26), (27), (29), (30), (32) are inconsistent by sub-proof #1491.
% 231.51/42.70  | | 
% 231.51/42.70  | Case 2:
% 231.51/42.70  | | 
% 231.51/42.70  | |   (33)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 231.51/42.70  | |           e0)
% 231.51/42.70  | | 
% 231.51/42.70  | | BETA: splitting (33) gives:
% 231.51/42.70  | | 
% 231.51/42.70  | | Case 1:
% 231.51/42.70  | | | 
% 231.51/42.70  | | |   (34)  all_57_10 = e0 & op(e2, e0) = e0
% 231.51/42.70  | | | 
% 231.51/42.70  | | | ALPHA: (34) implies:
% 231.51/42.70  | | |   (35)  all_57_10 = e0
% 231.51/42.70  | | | 
% 231.51/42.70  | | | REF_CLOSE: (1), (3), (9), (11), (16), (17), (18), (21), (23), (35) are
% 231.51/42.70  | | |            inconsistent by sub-proof #1518.
% 231.51/42.70  | | | 
% 231.51/42.70  | | Case 2:
% 231.51/42.70  | | | 
% 231.51/42.70  | | |   (36)  all_57_11 = e0 & op(e1, e0) = e0
% 231.51/42.70  | | | 
% 231.51/42.70  | | | ALPHA: (36) implies:
% 231.51/42.70  | | |   (37)  all_57_11 = e0
% 231.51/42.70  | | | 
% 231.51/42.70  | | | BETA: splitting (30) gives:
% 231.51/42.70  | | | 
% 231.51/42.70  | | | Case 1:
% 231.51/42.70  | | | | 
% 231.51/42.70  | | | |   (38)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2)
% 231.51/42.70  | | | |           = e2)
% 231.51/42.70  | | | | 
% 231.51/42.70  | | | | BETA: splitting (38) gives:
% 231.51/42.70  | | | | 
% 231.51/42.70  | | | | Case 1:
% 231.51/42.70  | | | | | 
% 231.51/42.70  | | | | |   (39)  all_57_6 = e2 & op(e1, e3) = e2
% 231.51/42.70  | | | | | 
% 231.51/42.70  | | | | | ALPHA: (39) implies:
% 231.51/42.70  | | | | |   (40)  all_57_6 = e2
% 231.51/42.70  | | | | | 
% 231.51/42.70  | | | | | BETA: splitting (28) gives:
% 231.51/42.70  | | | | | 
% 231.51/42.70  | | | | | Case 1:
% 231.51/42.70  | | | | | | 
% 231.51/42.70  | | | | | |   (41)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1,
% 231.51/42.70  | | | | | |             e2) = e1)
% 231.51/42.70  | | | | | | 
% 231.51/42.70  | | | | | | BETA: splitting (41) gives:
% 231.51/42.70  | | | | | | 
% 231.51/42.70  | | | | | | Case 1:
% 231.51/42.70  | | | | | | | 
% 231.51/42.70  | | | | | | |   (42)  all_57_6 = e1 & op(e1, e3) = e1
% 231.51/42.70  | | | | | | | 
% 231.51/42.70  | | | | | | | REF_CLOSE: (23), (40), (42) are inconsistent by sub-proof #2389.
% 231.51/42.70  | | | | | | | 
% 231.51/42.70  | | | | | | Case 2:
% 231.51/42.70  | | | | | | | 
% 231.51/42.70  | | | | | | |   (43)  all_57_7 = e1 & op(e1, e2) = e1
% 231.51/42.70  | | | | | | | 
% 231.51/42.70  | | | | | | | REF_CLOSE: (3), (20), (43) are inconsistent by sub-proof #2104.
% 231.51/42.70  | | | | | | | 
% 231.51/42.70  | | | | | | End of split
% 231.51/42.70  | | | | | | 
% 231.51/42.70  | | | | | Case 2:
% 231.51/42.70  | | | | | | 
% 231.51/42.70  | | | | | |   (44)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1,
% 231.51/42.70  | | | | | |             e0) = e1)
% 231.51/42.70  | | | | | | 
% 231.51/42.70  | | | | | | BETA: splitting (44) gives:
% 231.51/42.70  | | | | | | 
% 231.51/42.70  | | | | | | Case 1:
% 231.51/42.70  | | | | | | | 
% 231.51/42.70  | | | | | | |   (45)  all_57_8 = e1 & op(e1, e1) = e1
% 231.51/42.70  | | | | | | | 
% 231.51/42.70  | | | | | | | ALPHA: (45) implies:
% 231.51/42.70  | | | | | | |   (46)  all_57_8 = e1
% 231.51/42.70  | | | | | | |   (47)  op(e1, e1) = e1
% 231.51/42.70  | | | | | | | 
% 231.51/42.70  | | | | | | | BETA: splitting (25) gives:
% 231.51/42.70  | | | | | | | 
% 231.51/42.70  | | | | | | | Case 1:
% 231.51/42.70  | | | | | | | | 
% 231.51/42.70  | | | | | | | |   (48)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 &
% 231.51/42.70  | | | | | | | |           op(e2, e1) = e2)
% 231.51/42.70  | | | | | | | | 
% 231.51/42.70  | | | | | | | | BETA: splitting (48) gives:
% 231.51/42.70  | | | | | | | | 
% 231.51/42.70  | | | | | | | | Case 1:
% 231.51/42.70  | | | | | | | | | 
% 231.51/42.70  | | | | | | | | |   (49)  all_57_4 = e2 & op(e3, e1) = e2
% 231.51/42.70  | | | | | | | | | 
% 231.51/42.70  | | | | | | | | | ALPHA: (49) implies:
% 231.51/42.70  | | | | | | | | |   (50)  all_57_4 = e2
% 231.51/42.70  | | | | | | | | | 
% 231.51/42.70  | | | | | | | | | BETA: splitting (8) gives:
% 231.51/42.70  | | | | | | | | | 
% 231.51/42.70  | | | | | | | | | Case 1:
% 231.51/42.70  | | | | | | | | | | 
% 231.51/42.70  | | | | | | | | | |   (51)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 &
% 231.51/42.70  | | | | | | | | | |           op(e3, e2) = e0)
% 231.51/42.70  | | | | | | | | | | 
% 231.51/42.70  | | | | | | | | | | REF_CLOSE: (2), (3), (5), (9), (11), (12), (14), (17), (18),
% 231.51/42.70  | | | | | | | | | |            (20), (23), (29), (51) are inconsistent by
% 231.51/42.70  | | | | | | | | | |            sub-proof #2097.
% 231.51/42.70  | | | | | | | | | | 
% 231.51/42.70  | | | | | | | | | Case 2:
% 231.51/42.70  | | | | | | | | | | 
% 231.51/42.70  | | | | | | | | | |   (52)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 &
% 231.51/42.70  | | | | | | | | | |           op(e3, e0) = e0)
% 231.51/42.70  | | | | | | | | | | 
% 231.51/42.70  | | | | | | | | | | BETA: splitting (52) gives:
% 231.51/42.70  | | | | | | | | | | 
% 231.51/42.70  | | | | | | | | | | Case 1:
% 231.51/42.70  | | | | | | | | | | | 
% 231.51/42.70  | | | | | | | | | | |   (53)  all_57_4 = e0 & op(e3, e1) = e0
% 231.51/42.70  | | | | | | | | | | | 
% 231.51/42.70  | | | | | | | | | | | REF_CLOSE: (17), (50), (53) are inconsistent by sub-proof
% 231.51/42.70  | | | | | | | | | | |            #2045.
% 231.51/42.70  | | | | | | | | | | | 
% 231.51/42.70  | | | | | | | | | | Case 2:
% 231.51/42.70  | | | | | | | | | | | 
% 231.51/42.70  | | | | | | | | | | |   (54)  all_57_9 = e0 & op(e3, e0) = e0
% 231.51/42.70  | | | | | | | | | | | 
% 231.51/42.70  | | | | | | | | | | | ALPHA: (54) implies:
% 231.51/42.70  | | | | | | | | | | |   (55)  all_57_9 = e0
% 231.51/42.70  | | | | | | | | | | | 
% 231.51/42.70  | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10),
% 231.51/42.70  | | | | | | | | | | |            (11), (12), (13), (14), (15), (16), (17), (18),
% 231.51/42.70  | | | | | | | | | | |            (19), (20), (21), (23), (24), (26), (27), (29),
% 231.51/42.70  | | | | | | | | | | |            (30), (46), (47), (50), (55) are inconsistent by
% 231.51/42.70  | | | | | | | | | | |            sub-proof #1492.
% 231.51/42.70  | | | | | | | | | | | 
% 231.51/42.70  | | | | | | | | | | End of split
% 231.51/42.70  | | | | | | | | | | 
% 231.51/42.70  | | | | | | | | | End of split
% 231.51/42.70  | | | | | | | | | 
% 231.51/42.70  | | | | | | | | Case 2:
% 231.51/42.70  | | | | | | | | | 
% 231.51/42.70  | | | | | | | | |   (56)  all_57_5 = e2 & op(e2, e1) = e2
% 231.51/42.70  | | | | | | | | | 
% 231.51/42.70  | | | | | | | | | REF_CLOSE: (11), (16), (56) are inconsistent by sub-proof
% 231.51/42.70  | | | | | | | | |            #2425.
% 231.51/42.70  | | | | | | | | | 
% 231.51/42.70  | | | | | | | | End of split
% 231.51/42.70  | | | | | | | | 
% 231.51/42.70  | | | | | | | Case 2:
% 231.51/42.70  | | | | | | | | 
% 231.51/42.70  | | | | | | | |   (57)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 &
% 231.51/42.70  | | | | | | | |           op(e0, e1) = e2)
% 231.51/42.70  | | | | | | | | 
% 231.51/42.70  | | | | | | | | BETA: splitting (57) gives:
% 231.51/42.70  | | | | | | | | 
% 231.51/42.70  | | | | | | | | Case 1:
% 231.51/42.70  | | | | | | | | | 
% 231.51/42.70  | | | | | | | | |   (58)  all_57_8 = e2 & op(e1, e1) = e2
% 231.51/42.70  | | | | | | | | | 
% 231.51/42.70  | | | | | | | | | ALPHA: (58) implies:
% 231.51/42.70  | | | | | | | | |   (59)  all_57_8 = e2
% 231.51/42.70  | | | | | | | | |   (60)  op(e1, e1) = e2
% 231.51/42.70  | | | | | | | | | 
% 231.51/42.70  | | | | | | | | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (9), (10), (11),
% 231.51/42.70  | | | | | | | | |            (12), (13), (14), (16), (17), (18), (19), (20),
% 231.51/42.70  | | | | | | | | |            (23), (27), (29), (59), (60) are inconsistent by
% 231.51/42.70  | | | | | | | | |            sub-proof #1489.
% 231.51/42.70  | | | | | | | | | 
% 231.51/42.70  | | | | | | | | Case 2:
% 231.51/42.70  | | | | | | | | | 
% 231.51/42.70  | | | | | | | | |   (61)  all_57_14 = e2 & op(e0, e1) = e2
% 231.51/42.70  | | | | | | | | | 
% 231.51/42.70  | | | | | | | | | ALPHA: (61) implies:
% 231.51/42.70  | | | | | | | | |   (62)  all_57_14 = e2
% 231.51/42.70  | | | | | | | | | 
% 231.51/42.70  | | | | | | | | | REF_CLOSE: (17), (27), (62) are inconsistent by sub-proof
% 231.51/42.70  | | | | | | | | |            #2422.
% 231.51/42.70  | | | | | | | | | 
% 231.51/42.70  | | | | | | | | End of split
% 231.51/42.70  | | | | | | | | 
% 231.51/42.70  | | | | | | | End of split
% 231.51/42.70  | | | | | | | 
% 231.51/42.70  | | | | | | Case 2:
% 231.51/42.70  | | | | | | | 
% 231.51/42.70  | | | | | | |   (63)  all_57_11 = e1 & op(e1, e0) = e1
% 231.51/42.70  | | | | | | | 
% 231.51/42.70  | | | | | | | ALPHA: (63) implies:
% 231.51/42.70  | | | | | | |   (64)  all_57_11 = e1
% 231.51/42.70  | | | | | | | 
% 231.51/42.70  | | | | | | | REF_CLOSE: (18), (37), (64) are inconsistent by sub-proof #1862.
% 231.51/42.70  | | | | | | | 
% 231.51/42.70  | | | | | | End of split
% 231.51/42.70  | | | | | | 
% 231.51/42.70  | | | | | End of split
% 231.51/42.70  | | | | | 
% 231.51/42.70  | | | | Case 2:
% 231.51/42.70  | | | | | 
% 231.51/42.70  | | | | |   (65)  all_57_7 = e2 & op(e1, e2) = e2
% 231.51/42.70  | | | | | 
% 231.51/42.70  | | | | | REF_CLOSE: (11), (20), (65) are inconsistent by sub-proof #2092.
% 231.51/42.70  | | | | | 
% 231.51/42.70  | | | | End of split
% 231.51/42.70  | | | | 
% 231.51/42.70  | | | Case 2:
% 231.51/42.70  | | | | 
% 231.51/42.70  | | | |   (66)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0)
% 231.51/42.70  | | | |           = e2)
% 231.51/42.70  | | | | 
% 231.51/42.70  | | | | BETA: splitting (66) gives:
% 231.51/42.70  | | | | 
% 231.51/42.70  | | | | Case 1:
% 231.51/42.70  | | | | | 
% 231.51/42.70  | | | | |   (67)  all_57_8 = e2 & op(e1, e1) = e2
% 231.51/42.70  | | | | | 
% 231.51/42.70  | | | | | ALPHA: (67) implies:
% 231.51/42.70  | | | | |   (68)  all_57_8 = e2
% 231.51/42.70  | | | | |   (69)  op(e1, e1) = e2
% 231.51/42.70  | | | | | 
% 231.51/42.70  | | | | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 231.51/42.70  | | | | |            (14), (16), (17), (18), (19), (20), (23), (27), (29), (68),
% 231.51/42.70  | | | | |            (69) are inconsistent by sub-proof #1489.
% 231.51/42.70  | | | | | 
% 231.51/42.70  | | | | Case 2:
% 231.51/42.70  | | | | | 
% 231.51/42.70  | | | | |   (70)  all_57_11 = e2 & op(e1, e0) = e2
% 231.51/42.70  | | | | | 
% 231.51/42.70  | | | | | ALPHA: (70) implies:
% 231.51/42.70  | | | | |   (71)  all_57_11 = e2
% 231.51/42.70  | | | | | 
% 231.51/42.70  | | | | | REF_CLOSE: (17), (37), (71) are inconsistent by sub-proof #1949.
% 231.51/42.70  | | | | | 
% 231.51/42.70  | | | | End of split
% 231.51/42.70  | | | | 
% 231.51/42.70  | | | End of split
% 231.51/42.70  | | | 
% 231.51/42.70  | | End of split
% 231.51/42.70  | | 
% 231.51/42.70  | End of split
% 231.51/42.70  | 
% 231.51/42.70  End of proof
% 231.51/42.70  
% 231.51/42.70  Sub-proof #1489 shows that the following formulas are inconsistent:
% 231.51/42.70  ----------------------------------------------------------------
% 231.51/42.70    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.51/42.70         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.51/42.70    (2)   ~ (e3 = e1)
% 231.51/42.70    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.51/42.70           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.51/42.70    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.51/42.70         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.54/42.70    (5)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.54/42.70         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.54/42.70    (6)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.54/42.70         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.54/42.70    (7)  all_57_3 = e0
% 231.54/42.70    (8)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.54/42.70         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.54/42.70    (9)   ~ (e3 = e2)
% 231.54/42.70    (10)   ~ (e3 = e0)
% 231.54/42.70    (11)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.54/42.70          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.54/42.70    (12)  op(e3, e3) = e3
% 231.54/42.70    (13)  all_57_5 = e3
% 231.54/42.70    (14)   ~ (e2 = e0)
% 231.54/42.70    (15)   ~ (e1 = e0)
% 231.54/42.70    (16)  all_57_8 = e2
% 231.54/42.70    (17)  op(e1, e1) = e0
% 231.54/42.70    (18)  op(e1, e1) = e2
% 231.54/42.70    (19)  all_57_7 = e3
% 231.54/42.70    (20)   ~ (e2 = e1)
% 231.54/42.70    (21)  all_57_14 = e0
% 231.54/42.70    (22)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.70          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.54/42.70  
% 231.54/42.70  Begin of proof
% 231.54/42.70  | 
% 231.54/42.70  | BETA: splitting (11) gives:
% 231.54/42.70  | 
% 231.54/42.70  | Case 1:
% 231.54/42.70  | | 
% 231.54/42.70  | |   (23)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) =
% 231.54/42.70  | |           e1)
% 231.54/42.70  | | 
% 231.54/42.70  | | BETA: splitting (23) gives:
% 231.54/42.70  | | 
% 231.54/42.70  | | Case 1:
% 231.54/42.70  | | | 
% 231.54/42.70  | | |   (24)  all_57_4 = e1 & op(e3, e1) = e1
% 231.54/42.70  | | | 
% 231.54/42.70  | | | ALPHA: (24) implies:
% 231.54/42.70  | | |   (25)  all_57_4 = e1
% 231.54/42.70  | | | 
% 231.54/42.70  | | | BETA: splitting (6) gives:
% 231.54/42.70  | | | 
% 231.54/42.70  | | | Case 1:
% 231.54/42.70  | | | | 
% 231.54/42.70  | | | |   (26)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2)
% 231.54/42.70  | | | |           = e0)
% 231.54/42.70  | | | | 
% 231.54/42.70  | | | | REF_CLOSE: (1), (2), (3), (7), (9), (10), (12), (14), (15), (19), (20),
% 231.54/42.70  | | | |            (22), (26) are inconsistent by sub-proof #2097.
% 231.54/42.70  | | | | 
% 231.54/42.70  | | | Case 2:
% 231.54/42.70  | | | | 
% 231.54/42.70  | | | |   (27)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0)
% 231.54/42.70  | | | |           = e0)
% 231.54/42.70  | | | | 
% 231.54/42.70  | | | | BETA: splitting (27) gives:
% 231.54/42.70  | | | | 
% 231.54/42.70  | | | | Case 1:
% 231.54/42.70  | | | | | 
% 231.54/42.70  | | | | |   (28)  all_57_4 = e0 & op(e3, e1) = e0
% 231.54/42.70  | | | | | 
% 231.54/42.70  | | | | | REF_CLOSE: (15), (25), (28) are inconsistent by sub-proof #2429.
% 231.54/42.70  | | | | | 
% 231.54/42.70  | | | | Case 2:
% 231.54/42.70  | | | | | 
% 231.54/42.70  | | | | |   (29)  all_57_9 = e0 & op(e3, e0) = e0
% 231.54/42.70  | | | | | 
% 231.54/42.70  | | | | | ALPHA: (29) implies:
% 231.54/42.70  | | | | |   (30)  all_57_9 = e0
% 231.54/42.70  | | | | | 
% 231.54/42.70  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (12), (13),
% 231.54/42.70  | | | | |            (14), (15), (16), (17), (18), (19), (20), (22), (25), (30)
% 231.54/42.70  | | | | |            are inconsistent by sub-proof #1496.
% 231.54/42.70  | | | | | 
% 231.54/42.70  | | | | End of split
% 231.54/42.70  | | | | 
% 231.54/42.70  | | | End of split
% 231.54/42.70  | | | 
% 231.54/42.70  | | Case 2:
% 231.54/42.70  | | | 
% 231.54/42.70  | | |   (31)  all_57_5 = e1 & op(e2, e1) = e1
% 231.54/42.70  | | | 
% 231.54/42.70  | | | REF_CLOSE: (2), (13), (31) are inconsistent by sub-proof #2376.
% 231.54/42.70  | | | 
% 231.54/42.70  | | End of split
% 231.54/42.70  | | 
% 231.54/42.70  | Case 2:
% 231.54/42.70  | | 
% 231.54/42.70  | |   (32)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) =
% 231.54/42.70  | |           e1)
% 231.54/42.70  | | 
% 231.54/42.70  | | REF_CLOSE: (15), (16), (20), (21), (32) are inconsistent by sub-proof #1490.
% 231.54/42.70  | | 
% 231.54/42.70  | End of split
% 231.54/42.70  | 
% 231.54/42.70  End of proof
% 231.54/42.70  
% 231.54/42.70  Sub-proof #1490 shows that the following formulas are inconsistent:
% 231.54/42.70  ----------------------------------------------------------------
% 231.54/42.70    (1)   ~ (e1 = e0)
% 231.54/42.70    (2)  all_57_8 = e2
% 231.54/42.70    (3)   ~ (e2 = e1)
% 231.54/42.70    (4)  all_57_14 = e0
% 231.54/42.70    (5)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.54/42.70  
% 231.54/42.70  Begin of proof
% 231.54/42.70  | 
% 231.54/42.70  | BETA: splitting (5) gives:
% 231.54/42.70  | 
% 231.54/42.70  | Case 1:
% 231.54/42.70  | | 
% 231.54/42.70  | |   (6)  all_57_8 = e1 & op(e1, e1) = e1
% 231.54/42.70  | | 
% 231.54/42.70  | | REF_CLOSE: (2), (3), (6) are inconsistent by sub-proof #1533.
% 231.54/42.70  | | 
% 231.54/42.70  | Case 2:
% 231.54/42.70  | | 
% 231.54/42.70  | |   (7)  all_57_14 = e1 & op(e0, e1) = e1
% 231.54/42.70  | | 
% 231.54/42.70  | | ALPHA: (7) implies:
% 231.54/42.70  | |   (8)  all_57_14 = e1
% 231.54/42.70  | | 
% 231.54/42.70  | | REF_CLOSE: (1), (4), (8) are inconsistent by sub-proof #2122.
% 231.54/42.70  | | 
% 231.54/42.70  | End of split
% 231.54/42.70  | 
% 231.54/42.70  End of proof
% 231.54/42.70  
% 231.54/42.70  Sub-proof #1491 shows that the following formulas are inconsistent:
% 231.54/42.70  ----------------------------------------------------------------
% 231.54/42.70    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.70         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.54/42.70    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.70         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.54/42.70    (3)   ~ (e3 = e1)
% 231.54/42.70    (4)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 231.54/42.70         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.54/42.70    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.70           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.70    (6)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.54/42.70         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.54/42.70    (7)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.54/42.70         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.54/42.70    (8)  all_57_3 = e0
% 231.54/42.70    (9)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.54/42.70         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.54/42.70    (10)   ~ (e3 = e2)
% 231.54/42.70    (11)   ~ (e3 = e0)
% 231.54/42.70    (12)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.54/42.70          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.54/42.70    (13)  op(e3, e3) = e3
% 231.54/42.70    (14)  all_57_15 = e3
% 231.54/42.70    (15)  all_57_5 = e3
% 231.54/42.70    (16)  all_57_9 = e0
% 231.54/42.70    (17)   ~ (e2 = e0)
% 231.54/42.70    (18)   ~ (e1 = e0)
% 231.54/42.70    (19)  op(e1, e1) = e0
% 231.54/42.70    (20)  all_57_7 = e3
% 231.54/42.70    (21)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.70          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.54/42.70    (22)   ~ (e2 = e1)
% 231.54/42.70    (23)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.54/42.70          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.54/42.70    (24)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.54/42.70          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.54/42.70    (25)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.54/42.70          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.54/42.70    (26)  all_57_14 = e0
% 231.54/42.70    (27)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.70          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.54/42.70    (28)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 231.54/42.70          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 231.54/42.70  
% 231.54/42.70  Begin of proof
% 231.54/42.70  | 
% 231.54/42.70  | BETA: splitting (24) gives:
% 231.54/42.70  | 
% 231.54/42.70  | Case 1:
% 231.54/42.70  | | 
% 231.54/42.70  | |   (29)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) =
% 231.54/42.70  | |           e2)
% 231.54/42.70  | | 
% 231.54/42.70  | | BETA: splitting (29) gives:
% 231.54/42.70  | | 
% 231.54/42.70  | | Case 1:
% 231.54/42.70  | | | 
% 231.54/42.70  | | |   (30)  all_57_4 = e2 & op(e3, e1) = e2
% 231.54/42.70  | | | 
% 231.54/42.70  | | | ALPHA: (30) implies:
% 231.54/42.70  | | |   (31)  all_57_4 = e2
% 231.54/42.70  | | | 
% 231.54/42.70  | | | BETA: splitting (12) gives:
% 231.54/42.70  | | | 
% 231.54/42.70  | | | Case 1:
% 231.54/42.70  | | | | 
% 231.54/42.70  | | | |   (32)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1)
% 231.54/42.70  | | | |           = e1)
% 231.54/42.70  | | | | 
% 231.54/42.70  | | | | BETA: splitting (32) gives:
% 231.54/42.70  | | | | 
% 231.54/42.70  | | | | Case 1:
% 231.54/42.70  | | | | | 
% 231.54/42.70  | | | | |   (33)  all_57_4 = e1 & op(e3, e1) = e1
% 231.54/42.70  | | | | | 
% 231.54/42.70  | | | | | REF_CLOSE: (22), (31), (33) are inconsistent by sub-proof #2452.
% 231.54/42.70  | | | | | 
% 231.54/42.70  | | | | Case 2:
% 231.54/42.70  | | | | | 
% 231.54/42.70  | | | | |   (34)  all_57_5 = e1 & op(e2, e1) = e1
% 231.54/42.70  | | | | | 
% 231.54/42.70  | | | | | REF_CLOSE: (3), (15), (34) are inconsistent by sub-proof #2376.
% 231.54/42.70  | | | | | 
% 231.54/42.70  | | | | End of split
% 231.54/42.70  | | | | 
% 231.54/42.70  | | | Case 2:
% 231.54/42.70  | | | | 
% 231.54/42.70  | | | |   (35)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1)
% 231.54/42.70  | | | |           = e1)
% 231.54/42.70  | | | | 
% 231.54/42.70  | | | | BETA: splitting (35) gives:
% 231.54/42.70  | | | | 
% 231.54/42.70  | | | | Case 1:
% 231.54/42.70  | | | | | 
% 231.54/42.70  | | | | |   (36)  all_57_8 = e1 & op(e1, e1) = e1
% 231.54/42.70  | | | | | 
% 231.54/42.70  | | | | | ALPHA: (36) implies:
% 231.54/42.70  | | | | |   (37)  all_57_8 = e1
% 231.54/42.70  | | | | |   (38)  op(e1, e1) = e1
% 231.54/42.70  | | | | | 
% 231.54/42.70  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 231.54/42.70  | | | | |            (12), (13), (14), (15), (16), (17), (18), (19), (20), (21),
% 231.54/42.70  | | | | |            (22), (23), (25), (26), (27), (28), (31), (37), (38) are
% 231.54/42.70  | | | | |            inconsistent by sub-proof #1492.
% 231.54/42.70  | | | | | 
% 231.54/42.70  | | | | Case 2:
% 231.54/42.70  | | | | | 
% 231.54/42.70  | | | | |   (39)  all_57_14 = e1 & op(e0, e1) = e1
% 231.54/42.70  | | | | | 
% 231.54/42.70  | | | | | REF_CLOSE: (18), (26), (39) are inconsistent by sub-proof #2381.
% 231.54/42.70  | | | | | 
% 231.54/42.70  | | | | End of split
% 231.54/42.70  | | | | 
% 231.54/42.70  | | | End of split
% 231.54/42.70  | | | 
% 231.54/42.70  | | Case 2:
% 231.54/42.70  | | | 
% 231.54/42.70  | | |   (40)  all_57_5 = e2 & op(e2, e1) = e2
% 231.54/42.70  | | | 
% 231.54/42.70  | | | REF_CLOSE: (10), (15), (40) are inconsistent by sub-proof #2425.
% 231.54/42.70  | | | 
% 231.54/42.70  | | End of split
% 231.54/42.70  | | 
% 231.54/42.70  | Case 2:
% 231.54/42.70  | | 
% 231.54/42.70  | |   (41)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) =
% 231.54/42.70  | |           e2)
% 231.54/42.70  | | 
% 231.54/42.70  | | BETA: splitting (41) gives:
% 231.54/42.70  | | 
% 231.54/42.70  | | Case 1:
% 231.54/42.70  | | | 
% 231.54/42.70  | | |   (42)  all_57_8 = e2 & op(e1, e1) = e2
% 231.54/42.70  | | | 
% 231.54/42.70  | | | ALPHA: (42) implies:
% 231.54/42.70  | | |   (43)  all_57_8 = e2
% 231.54/42.70  | | |   (44)  op(e1, e1) = e2
% 231.54/42.70  | | | 
% 231.54/42.70  | | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 231.54/42.70  | | |            (15), (16), (17), (18), (19), (20), (22), (26), (27), (43),
% 231.54/42.70  | | |            (44) are inconsistent by sub-proof #1495.
% 231.54/42.70  | | | 
% 231.54/42.70  | | Case 2:
% 231.54/42.70  | | | 
% 231.54/42.70  | | |   (45)  all_57_14 = e2 & op(e0, e1) = e2
% 231.54/42.70  | | | 
% 231.54/42.70  | | | ALPHA: (45) implies:
% 231.54/42.70  | | |   (46)  all_57_14 = e2
% 231.54/42.70  | | | 
% 231.54/42.70  | | | REF_CLOSE: (17), (26), (46) are inconsistent by sub-proof #2422.
% 231.54/42.70  | | | 
% 231.54/42.70  | | End of split
% 231.54/42.70  | | 
% 231.54/42.70  | End of split
% 231.54/42.70  | 
% 231.54/42.70  End of proof
% 231.54/42.70  
% 231.54/42.70  Sub-proof #1492 shows that the following formulas are inconsistent:
% 231.54/42.70  ----------------------------------------------------------------
% 231.54/42.70    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.70         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.54/42.70    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.70         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.54/42.70    (3)   ~ (e3 = e1)
% 231.54/42.70    (4)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 231.54/42.70         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.54/42.70    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.70           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.70    (6)  all_57_4 = e2
% 231.54/42.70    (7)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.54/42.70         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.54/42.70    (8)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.54/42.70         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.54/42.70    (9)  all_57_8 = e1
% 231.54/42.70    (10)  all_57_3 = e0
% 231.54/42.70    (11)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.54/42.70          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.54/42.70    (12)   ~ (e3 = e2)
% 231.54/42.70    (13)   ~ (e3 = e0)
% 231.54/42.70    (14)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.54/42.70          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.54/42.70    (15)  op(e3, e3) = e3
% 231.54/42.70    (16)  all_57_15 = e3
% 231.54/42.70    (17)  all_57_5 = e3
% 231.54/42.70    (18)  all_57_9 = e0
% 231.54/42.70    (19)  op(e1, e1) = e1
% 231.54/42.70    (20)   ~ (e2 = e0)
% 231.54/42.70    (21)   ~ (e1 = e0)
% 231.54/42.70    (22)  op(e1, e1) = e0
% 231.54/42.70    (23)  all_57_7 = e3
% 231.54/42.70    (24)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.70          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.54/42.70    (25)   ~ (e2 = e1)
% 231.54/42.70    (26)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.54/42.70          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.54/42.70    (27)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.54/42.70          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.54/42.70    (28)  all_57_14 = e0
% 231.54/42.70    (29)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.70          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.54/42.70    (30)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 231.54/42.70          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 231.54/42.70  
% 231.54/42.70  Begin of proof
% 231.54/42.70  | 
% 231.54/42.70  | BETA: splitting (7) gives:
% 231.54/42.70  | 
% 231.54/42.70  | Case 1:
% 231.54/42.70  | | 
% 231.54/42.70  | |   (31)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) =
% 231.54/42.70  | |           e1)
% 231.54/42.70  | | 
% 231.54/42.70  | | BETA: splitting (31) gives:
% 231.54/42.70  | | 
% 231.54/42.70  | | Case 1:
% 231.54/42.70  | | | 
% 231.54/42.70  | | |   (32)  all_57_0 = e1 & op(e3, e3) = e1
% 231.54/42.70  | | | 
% 231.54/42.70  | | | ALPHA: (32) implies:
% 231.54/42.70  | | |   (33)  op(e3, e3) = e1
% 231.54/42.70  | | | 
% 231.54/42.70  | | | REF_CLOSE: (3), (5), (15), (33) are inconsistent by sub-proof #2495.
% 231.54/42.70  | | | 
% 231.54/42.70  | | Case 2:
% 231.54/42.70  | | | 
% 231.54/42.70  | | |   (34)  all_57_1 = e1 & op(e3, e2) = e1
% 231.54/42.70  | | | 
% 231.54/42.70  | | | ALPHA: (34) implies:
% 231.54/42.70  | | |   (35)  all_57_1 = e1
% 231.54/42.70  | | | 
% 231.54/42.70  | | | BETA: splitting (4) gives:
% 231.54/42.70  | | | 
% 231.54/42.70  | | | Case 1:
% 231.54/42.70  | | | | 
% 231.54/42.70  | | | |   (36)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2)
% 231.54/42.70  | | | |           = e0)
% 231.54/42.70  | | | | 
% 231.54/42.70  | | | | BETA: splitting (36) gives:
% 231.54/42.70  | | | | 
% 231.54/42.70  | | | | Case 1:
% 231.54/42.70  | | | | | 
% 231.54/42.70  | | | | |   (37)  all_57_6 = e0 & op(e1, e3) = e0
% 231.54/42.70  | | | | | 
% 231.54/42.70  | | | | | ALPHA: (37) implies:
% 231.54/42.70  | | | | |   (38)  all_57_6 = e0
% 231.54/42.70  | | | | | 
% 231.54/42.70  | | | | | BETA: splitting (2) gives:
% 231.54/42.70  | | | | | 
% 231.54/42.70  | | | | | Case 1:
% 231.54/42.70  | | | | | | 
% 231.54/42.70  | | | | | |   (39)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2,
% 231.54/42.70  | | | | | |             e2) = e2)
% 231.54/42.70  | | | | | | 
% 231.54/42.70  | | | | | | REF_CLOSE: (5), (6), (8), (10), (12), (15), (18), (20), (25), (35),
% 231.54/42.70  | | | | | |            (39) are inconsistent by sub-proof #1499.
% 231.54/42.70  | | | | | | 
% 231.54/42.70  | | | | | Case 2:
% 231.54/42.70  | | | | | | 
% 231.54/42.70  | | | | | |   (40)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0,
% 231.54/42.70  | | | | | |             e2) = e2)
% 231.54/42.70  | | | | | | 
% 231.54/42.70  | | | | | | BETA: splitting (40) gives:
% 231.54/42.70  | | | | | | 
% 231.54/42.70  | | | | | | Case 1:
% 231.54/42.70  | | | | | | | 
% 231.54/42.70  | | | | | | |   (41)  all_57_7 = e2 & op(e1, e2) = e2
% 231.54/42.70  | | | | | | | 
% 231.54/42.70  | | | | | | | REF_CLOSE: (12), (23), (41) are inconsistent by sub-proof #2092.
% 231.54/42.70  | | | | | | | 
% 231.54/42.70  | | | | | | Case 2:
% 231.54/42.70  | | | | | | | 
% 231.54/42.70  | | | | | | |   (42)  all_57_13 = e2 & op(e0, e2) = e2
% 231.54/42.70  | | | | | | | 
% 231.54/42.70  | | | | | | | ALPHA: (42) implies:
% 231.54/42.70  | | | | | | |   (43)  all_57_13 = e2
% 231.54/42.70  | | | | | | | 
% 231.54/42.70  | | | | | | | BETA: splitting (30) gives:
% 231.54/42.70  | | | | | | | 
% 231.54/42.70  | | | | | | | Case 1:
% 231.54/42.70  | | | | | | | | 
% 231.54/42.70  | | | | | | | |   (44)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 &
% 231.54/42.70  | | | | | | | |           op(e1, e2) = e2)
% 231.54/42.70  | | | | | | | | 
% 231.54/42.70  | | | | | | | | REF_CLOSE: (3), (5), (6), (8), (10), (12), (15), (18), (20),
% 231.54/42.70  | | | | | | | |            (21), (23), (25), (29), (38), (43), (44) are
% 231.54/42.70  | | | | | | | |            inconsistent by sub-proof #1497.
% 231.54/42.70  | | | | | | | | 
% 231.54/42.70  | | | | | | | Case 2:
% 231.54/42.70  | | | | | | | | 
% 231.54/42.70  | | | | | | | |   (45)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 &
% 231.54/42.70  | | | | | | | |           op(e1, e0) = e2)
% 231.54/42.70  | | | | | | | | 
% 231.54/42.70  | | | | | | | | BETA: splitting (45) gives:
% 231.54/42.70  | | | | | | | | 
% 231.54/42.70  | | | | | | | | Case 1:
% 231.54/42.70  | | | | | | | | | 
% 231.54/42.70  | | | | | | | | |   (46)  all_57_8 = e2 & op(e1, e1) = e2
% 231.54/42.70  | | | | | | | | | 
% 231.54/42.70  | | | | | | | | | ALPHA: (46) implies:
% 231.54/42.70  | | | | | | | | |   (47)  all_57_8 = e2
% 231.54/42.70  | | | | | | | | |   (48)  op(e1, e1) = e2
% 231.54/42.70  | | | | | | | | | 
% 231.54/42.70  | | | | | | | | | REF_CLOSE: (2), (3), (5), (7), (8), (10), (11), (12), (13),
% 231.54/42.70  | | | | | | | | |            (14), (15), (17), (18), (20), (21), (22), (23),
% 231.54/42.70  | | | | | | | | |            (25), (28), (29), (47), (48) are inconsistent by
% 231.54/42.70  | | | | | | | | |            sub-proof #1495.
% 231.54/42.70  | | | | | | | | | 
% 231.54/42.70  | | | | | | | | Case 2:
% 231.54/42.70  | | | | | | | | | 
% 231.54/42.70  | | | | | | | | |   (49)  all_57_11 = e2 & op(e1, e0) = e2
% 231.54/42.70  | | | | | | | | | 
% 231.54/42.70  | | | | | | | | | ALPHA: (49) implies:
% 231.54/42.70  | | | | | | | | |   (50)  all_57_11 = e2
% 231.54/42.70  | | | | | | | | | 
% 231.54/42.70  | | | | | | | | | BETA: splitting (27) gives:
% 231.54/42.70  | | | | | | | | | 
% 231.54/42.70  | | | | | | | | | Case 1:
% 231.54/42.70  | | | | | | | | | | 
% 231.54/42.70  | | | | | | | | | |   (51)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1
% 231.54/42.70  | | | | | | | | | |           & op(e2, e0) = e1)
% 231.54/42.70  | | | | | | | | | | 
% 231.54/42.70  | | | | | | | | | | BETA: splitting (51) gives:
% 231.54/42.70  | | | | | | | | | | 
% 231.54/42.70  | | | | | | | | | | Case 1:
% 231.54/42.70  | | | | | | | | | | | 
% 231.54/42.70  | | | | | | | | | | |   (52)  all_57_9 = e1 & op(e3, e0) = e1
% 231.54/42.70  | | | | | | | | | | | 
% 231.54/42.70  | | | | | | | | | | | ALPHA: (52) implies:
% 231.54/42.70  | | | | | | | | | | |   (53)  all_57_9 = e1
% 231.54/42.70  | | | | | | | | | | | 
% 231.54/42.70  | | | | | | | | | | | COMBINE_EQS: (18), (53) imply:
% 231.54/42.70  | | | | | | | | | | |   (54)  e1 = e0
% 231.54/42.70  | | | | | | | | | | | 
% 231.54/42.70  | | | | | | | | | | | REF_CLOSE: (2), (3), (10), (12), (20), (21), (23), (25),
% 231.54/42.70  | | | | | | | | | | |            (29), (35), (54) are inconsistent by sub-proof
% 231.54/42.70  | | | | | | | | | | |            #1626.
% 231.54/42.70  | | | | | | | | | | | 
% 231.54/42.70  | | | | | | | | | | Case 2:
% 231.54/42.70  | | | | | | | | | | | 
% 231.54/42.70  | | | | | | | | | | |   (55)  all_57_10 = e1 & op(e2, e0) = e1
% 231.54/42.70  | | | | | | | | | | | 
% 231.54/42.70  | | | | | | | | | | | ALPHA: (55) implies:
% 231.54/42.70  | | | | | | | | | | |   (56)  all_57_10 = e1
% 231.54/42.70  | | | | | | | | | | | 
% 231.54/42.70  | | | | | | | | | | | BETA: splitting (24) gives:
% 231.54/42.70  | | | | | | | | | | | 
% 231.54/42.70  | | | | | | | | | | | Case 1:
% 231.54/42.70  | | | | | | | | | | | | 
% 231.54/42.70  | | | | | | | | | | | |   (57)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 231.54/42.70  | | | | | | | | | | | |           & op(e2, e2) = e2)
% 231.54/42.70  | | | | | | | | | | | | 
% 231.54/42.70  | | | | | | | | | | | | BETA: splitting (57) gives:
% 231.54/42.70  | | | | | | | | | | | | 
% 231.54/42.70  | | | | | | | | | | | | Case 1:
% 231.54/42.70  | | | | | | | | | | | | | 
% 231.54/42.70  | | | | | | | | | | | | |   (58)  all_57_2 = e2 & op(e2, e3) = e2
% 231.54/42.70  | | | | | | | | | | | | | 
% 231.54/42.70  | | | | | | | | | | | | | ALPHA: (58) implies:
% 231.54/42.70  | | | | | | | | | | | | |   (59)  all_57_2 = e2
% 231.54/42.70  | | | | | | | | | | | | | 
% 231.54/42.70  | | | | | | | | | | | | | BETA: splitting (1) gives:
% 231.54/42.70  | | | | | | | | | | | | | 
% 231.54/42.70  | | | | | | | | | | | | | Case 1:
% 231.54/42.70  | | | | | | | | | | | | | | 
% 231.54/42.70  | | | | | | | | | | | | | |   (60)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 231.54/42.70  | | | | | | | | | | | | | |           & op(e2, e2) = e1)
% 231.54/42.70  | | | | | | | | | | | | | | 
% 231.54/42.70  | | | | | | | | | | | | | | BETA: splitting (60) gives:
% 231.54/42.70  | | | | | | | | | | | | | | 
% 231.54/42.70  | | | | | | | | | | | | | | Case 1:
% 231.54/42.70  | | | | | | | | | | | | | | | 
% 231.54/42.70  | | | | | | | | | | | | | | |   (61)  all_57_2 = e1 & op(e2, e3) = e1
% 231.54/42.70  | | | | | | | | | | | | | | | 
% 231.54/42.70  | | | | | | | | | | | | | | | ALPHA: (61) implies:
% 231.54/42.70  | | | | | | | | | | | | | | |   (62)  all_57_2 = e1
% 231.54/42.70  | | | | | | | | | | | | | | | 
% 231.54/42.70  | | | | | | | | | | | | | | | COMBINE_EQS: (59), (62) imply:
% 231.54/42.70  | | | | | | | | | | | | | | |   (63)  e2 = e1
% 231.54/42.70  | | | | | | | | | | | | | | | 
% 231.54/42.70  | | | | | | | | | | | | | | | SIMP: (63) implies:
% 231.54/42.70  | | | | | | | | | | | | | | |   (64)  e2 = e1
% 231.54/42.70  | | | | | | | | | | | | | | | 
% 231.54/42.70  | | | | | | | | | | | | | | | COMBINE_EQS: (50), (64) imply:
% 231.54/42.70  | | | | | | | | | | | | | | |   (65)  all_57_11 = e1
% 231.54/42.70  | | | | | | | | | | | | | | | 
% 231.54/42.70  | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (10), (11), (12),
% 231.54/42.70  | | | | | | | | | | | | | | |            (13), (14), (15), (17), (18), (20), (21), (22),
% 231.54/42.70  | | | | | | | | | | | | | | |            (23), (25), (28), (29), (30), (38), (43), (65) are
% 231.54/42.70  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1494.
% 231.54/42.70  | | | | | | | | | | | | | | | 
% 231.54/42.70  | | | | | | | | | | | | | | Case 2:
% 231.54/42.70  | | | | | | | | | | | | | | | 
% 231.54/42.70  | | | | | | | | | | | | | | |   (66)  all_57_3 = e1 & op(e2, e2) = e1
% 231.54/42.70  | | | | | | | | | | | | | | | 
% 231.54/42.70  | | | | | | | | | | | | | | | ALPHA: (66) implies:
% 231.54/42.70  | | | | | | | | | | | | | | |   (67)  all_57_3 = e1
% 231.54/42.70  | | | | | | | | | | | | | | | 
% 231.54/42.70  | | | | | | | | | | | | | | | COMBINE_EQS: (10), (67) imply:
% 231.54/42.70  | | | | | | | | | | | | | | |   (68)  e1 = e0
% 231.54/42.70  | | | | | | | | | | | | | | | 
% 231.54/42.70  | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (10), (12), (20), (21), (23), (25),
% 231.54/42.71  | | | | | | | | | | | | | | |            (29), (35), (68) are inconsistent by sub-proof
% 231.54/42.71  | | | | | | | | | | | | | | |            #1626.
% 231.54/42.71  | | | | | | | | | | | | | | | 
% 231.54/42.71  | | | | | | | | | | | | | | End of split
% 231.54/42.71  | | | | | | | | | | | | | | 
% 231.54/42.71  | | | | | | | | | | | | | Case 2:
% 231.54/42.71  | | | | | | | | | | | | | | 
% 231.54/42.71  | | | | | | | | | | | | | |   (69)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 231.54/42.71  | | | | | | | | | | | | | |           e1 & op(e2, e0) = e1)
% 231.54/42.71  | | | | | | | | | | | | | | 
% 231.54/42.71  | | | | | | | | | | | | | | BETA: splitting (69) gives:
% 231.54/42.71  | | | | | | | | | | | | | | 
% 231.54/42.71  | | | | | | | | | | | | | | Case 1:
% 231.54/42.71  | | | | | | | | | | | | | | | 
% 231.54/42.71  | | | | | | | | | | | | | | |   (70)  all_57_5 = e1 & op(e2, e1) = e1
% 231.54/42.71  | | | | | | | | | | | | | | | 
% 231.54/42.71  | | | | | | | | | | | | | | | ALPHA: (70) implies:
% 231.54/42.71  | | | | | | | | | | | | | | |   (71)  all_57_5 = e1
% 231.54/42.71  | | | | | | | | | | | | | | | 
% 231.54/42.71  | | | | | | | | | | | | | | | REF_CLOSE: (3), (17), (71) are inconsistent by sub-proof
% 231.54/42.71  | | | | | | | | | | | | | | |            #2382.
% 231.54/42.71  | | | | | | | | | | | | | | | 
% 231.54/42.71  | | | | | | | | | | | | | | Case 2:
% 231.54/42.71  | | | | | | | | | | | | | | | 
% 231.54/42.71  | | | | | | | | | | | | | | | 
% 231.54/42.71  | | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with e0, e1, e1, e1, simplifying
% 231.54/42.71  | | | | | | | | | | | | | | |              with (19), (22) gives:
% 231.54/42.71  | | | | | | | | | | | | | | |   (72)  e1 = e0
% 231.54/42.71  | | | | | | | | | | | | | | | 
% 231.54/42.71  | | | | | | | | | | | | | | | COMBINE_EQS: (35), (72) imply:
% 231.54/42.71  | | | | | | | | | | | | | | |   (73)  all_57_1 = e0
% 231.54/42.71  | | | | | | | | | | | | | | | 
% 231.54/42.71  | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (10), (12), (20), (21), (23), (25),
% 231.54/42.71  | | | | | | | | | | | | | | |            (29), (73) are inconsistent by sub-proof #2098.
% 231.54/42.71  | | | | | | | | | | | | | | | 
% 231.54/42.71  | | | | | | | | | | | | | | End of split
% 231.54/42.71  | | | | | | | | | | | | | | 
% 231.54/42.71  | | | | | | | | | | | | | End of split
% 231.54/42.71  | | | | | | | | | | | | | 
% 231.54/42.71  | | | | | | | | | | | | Case 2:
% 231.54/42.71  | | | | | | | | | | | | | 
% 231.54/42.71  | | | | | | | | | | | | |   (74)  all_57_3 = e2 & op(e2, e2) = e2
% 231.54/42.71  | | | | | | | | | | | | | 
% 231.54/42.71  | | | | | | | | | | | | | ALPHA: (74) implies:
% 231.54/42.71  | | | | | | | | | | | | |   (75)  all_57_3 = e2
% 231.54/42.71  | | | | | | | | | | | | | 
% 231.54/42.71  | | | | | | | | | | | | | COMBINE_EQS: (10), (75) imply:
% 231.54/42.71  | | | | | | | | | | | | |   (76)  e2 = e0
% 231.54/42.71  | | | | | | | | | | | | | 
% 231.54/42.71  | | | | | | | | | | | | | COMBINE_EQS: (6), (76) imply:
% 231.54/42.71  | | | | | | | | | | | | |   (77)  all_57_4 = e0
% 231.54/42.71  | | | | | | | | | | | | | 
% 231.54/42.71  | | | | | | | | | | | | | REF_CLOSE: (3), (5), (8), (10), (12), (15), (18), (20), (21),
% 231.54/42.71  | | | | | | | | | | | | |            (23), (25), (29), (43), (77) are inconsistent by
% 231.54/42.71  | | | | | | | | | | | | |            sub-proof #1498.
% 231.54/42.71  | | | | | | | | | | | | | 
% 231.54/42.71  | | | | | | | | | | | | End of split
% 231.54/42.71  | | | | | | | | | | | | 
% 231.54/42.71  | | | | | | | | | | | Case 2:
% 231.54/42.71  | | | | | | | | | | | | 
% 231.54/42.71  | | | | | | | | | | | |   (78)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 231.54/42.71  | | | | | | | | | | | |           e2 & op(e2, e0) = e2)
% 231.54/42.71  | | | | | | | | | | | | 
% 231.54/42.71  | | | | | | | | | | | | BETA: splitting (78) gives:
% 231.54/42.71  | | | | | | | | | | | | 
% 231.54/42.71  | | | | | | | | | | | | Case 1:
% 231.54/42.71  | | | | | | | | | | | | | 
% 231.54/42.71  | | | | | | | | | | | | |   (79)  all_57_5 = e2 & op(e2, e1) = e2
% 231.54/42.71  | | | | | | | | | | | | | 
% 231.54/42.71  | | | | | | | | | | | | | ALPHA: (79) implies:
% 231.54/42.71  | | | | | | | | | | | | |   (80)  all_57_5 = e2
% 231.54/42.71  | | | | | | | | | | | | | 
% 231.54/42.71  | | | | | | | | | | | | | REF_CLOSE: (12), (17), (80) are inconsistent by sub-proof
% 231.54/42.71  | | | | | | | | | | | | |            #2189.
% 231.54/42.71  | | | | | | | | | | | | | 
% 231.54/42.71  | | | | | | | | | | | | Case 2:
% 231.54/42.71  | | | | | | | | | | | | | 
% 231.54/42.71  | | | | | | | | | | | | |   (81)  all_57_10 = e2 & op(e2, e0) = e2
% 231.54/42.71  | | | | | | | | | | | | | 
% 231.54/42.71  | | | | | | | | | | | | | ALPHA: (81) implies:
% 231.54/42.71  | | | | | | | | | | | | |   (82)  all_57_10 = e2
% 231.54/42.71  | | | | | | | | | | | | | 
% 231.54/42.71  | | | | | | | | | | | | | COMBINE_EQS: (56), (82) imply:
% 231.54/42.71  | | | | | | | | | | | | |   (83)  e2 = e1
% 231.54/42.71  | | | | | | | | | | | | | 
% 231.54/42.71  | | | | | | | | | | | | | COMBINE_EQS: (50), (83) imply:
% 231.54/42.71  | | | | | | | | | | | | |   (84)  all_57_11 = e1
% 231.54/42.71  | | | | | | | | | | | | | 
% 231.54/42.71  | | | | | | | | | | | | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (10), (11), (12),
% 231.54/42.71  | | | | | | | | | | | | |            (13), (14), (15), (17), (18), (20), (21), (22),
% 231.54/42.71  | | | | | | | | | | | | |            (23), (25), (28), (29), (30), (38), (43), (84) are
% 231.54/42.71  | | | | | | | | | | | | |            inconsistent by sub-proof #1494.
% 231.54/42.71  | | | | | | | | | | | | | 
% 231.54/42.71  | | | | | | | | | | | | End of split
% 231.54/42.71  | | | | | | | | | | | | 
% 231.54/42.71  | | | | | | | | | | | End of split
% 231.54/42.71  | | | | | | | | | | | 
% 231.54/42.71  | | | | | | | | | | End of split
% 231.54/42.71  | | | | | | | | | | 
% 231.54/42.71  | | | | | | | | | Case 2:
% 231.54/42.71  | | | | | | | | | | 
% 231.54/42.71  | | | | | | | | | |   (85)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1
% 231.54/42.71  | | | | | | | | | |           & op(e0, e0) = e1)
% 231.54/42.71  | | | | | | | | | | 
% 231.54/42.71  | | | | | | | | | | BETA: splitting (85) gives:
% 231.54/42.71  | | | | | | | | | | 
% 231.54/42.71  | | | | | | | | | | Case 1:
% 231.54/42.71  | | | | | | | | | | | 
% 231.54/42.71  | | | | | | | | | | |   (86)  all_57_11 = e1 & op(e1, e0) = e1
% 231.54/42.71  | | | | | | | | | | | 
% 231.54/42.71  | | | | | | | | | | | ALPHA: (86) implies:
% 231.54/42.71  | | | | | | | | | | |   (87)  all_57_11 = e1
% 231.54/42.71  | | | | | | | | | | | 
% 231.54/42.71  | | | | | | | | | | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (10), (11), (12),
% 231.54/42.71  | | | | | | | | | | |            (13), (14), (15), (17), (18), (20), (21), (22),
% 231.54/42.71  | | | | | | | | | | |            (23), (25), (28), (29), (30), (38), (43), (87) are
% 231.54/42.71  | | | | | | | | | | |            inconsistent by sub-proof #1494.
% 231.54/42.71  | | | | | | | | | | | 
% 231.54/42.71  | | | | | | | | | | Case 2:
% 231.54/42.71  | | | | | | | | | | | 
% 231.54/42.71  | | | | | | | | | | |   (88)  all_57_15 = e1 & op(e0, e0) = e1
% 231.54/42.71  | | | | | | | | | | | 
% 231.54/42.71  | | | | | | | | | | | REF_CLOSE: (3), (16), (88) are inconsistent by sub-proof
% 231.54/42.71  | | | | | | | | | | |            #2325.
% 231.54/42.71  | | | | | | | | | | | 
% 231.54/42.71  | | | | | | | | | | End of split
% 231.54/42.71  | | | | | | | | | | 
% 231.54/42.71  | | | | | | | | | End of split
% 231.54/42.71  | | | | | | | | | 
% 231.54/42.71  | | | | | | | | End of split
% 231.54/42.71  | | | | | | | | 
% 231.54/42.71  | | | | | | | End of split
% 231.54/42.71  | | | | | | | 
% 231.54/42.71  | | | | | | End of split
% 231.54/42.71  | | | | | | 
% 231.54/42.71  | | | | | End of split
% 231.54/42.71  | | | | | 
% 231.54/42.71  | | | | Case 2:
% 231.54/42.71  | | | | | 
% 231.54/42.71  | | | | |   (89)  all_57_7 = e0 & op(e1, e2) = e0
% 231.54/42.71  | | | | | 
% 231.54/42.71  | | | | | REF_CLOSE: (13), (23), (89) are inconsistent by sub-proof #2042.
% 231.54/42.71  | | | | | 
% 231.54/42.71  | | | | End of split
% 231.54/42.71  | | | | 
% 231.54/42.71  | | | Case 2:
% 231.54/42.71  | | | | 
% 231.54/42.71  | | | |   (90)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.54/42.71  | | | |           = e0)
% 231.54/42.71  | | | | 
% 231.54/42.71  | | | | BETA: splitting (90) gives:
% 231.54/42.71  | | | | 
% 231.54/42.71  | | | | Case 1:
% 231.54/42.71  | | | | | 
% 231.54/42.71  | | | | |   (91)  all_57_8 = e0 & op(e1, e1) = e0
% 231.54/42.71  | | | | | 
% 231.54/42.71  | | | | | ALPHA: (91) implies:
% 231.54/42.71  | | | | |   (92)  all_57_8 = e0
% 231.54/42.71  | | | | | 
% 231.54/42.71  | | | | | COMBINE_EQS: (9), (92) imply:
% 231.54/42.71  | | | | |   (93)  e1 = e0
% 231.54/42.71  | | | | | 
% 231.54/42.71  | | | | | COMBINE_EQS: (35), (93) imply:
% 231.54/42.71  | | | | |   (94)  all_57_1 = e0
% 231.54/42.71  | | | | | 
% 231.54/42.71  | | | | | REF_CLOSE: (2), (3), (10), (12), (20), (21), (23), (25), (29), (94)
% 231.54/42.71  | | | | |            are inconsistent by sub-proof #2098.
% 231.54/42.71  | | | | | 
% 231.54/42.71  | | | | Case 2:
% 231.54/42.71  | | | | | 
% 231.54/42.71  | | | | |   (95)  all_57_11 = e0 & op(e1, e0) = e0
% 231.54/42.71  | | | | | 
% 231.54/42.71  | | | | | ALPHA: (95) implies:
% 231.54/42.71  | | | | |   (96)  all_57_11 = e0
% 231.54/42.71  | | | | | 
% 231.54/42.71  | | | | | REF_CLOSE: (2), (3), (5), (6), (8), (10), (12), (15), (16), (17),
% 231.54/42.71  | | | | |            (18), (20), (21), (23), (24), (25), (26), (27), (29), (35),
% 231.54/42.71  | | | | |            (96) are inconsistent by sub-proof #1493.
% 231.54/42.71  | | | | | 
% 231.54/42.71  | | | | End of split
% 231.54/42.71  | | | | 
% 231.54/42.71  | | | End of split
% 231.54/42.71  | | | 
% 231.54/42.71  | | End of split
% 231.54/42.71  | | 
% 231.54/42.71  | Case 2:
% 231.54/42.71  | | 
% 231.54/42.71  | |   (97)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) =
% 231.54/42.71  | |           e1)
% 231.54/42.71  | | 
% 231.54/42.71  | | BETA: splitting (97) gives:
% 231.54/42.71  | | 
% 231.54/42.71  | | Case 1:
% 231.54/42.71  | | | 
% 231.54/42.71  | | |   (98)  all_57_4 = e1 & op(e3, e1) = e1
% 231.54/42.71  | | | 
% 231.54/42.71  | | | REF_CLOSE: (6), (25), (98) are inconsistent by sub-proof #2452.
% 231.54/42.71  | | | 
% 231.54/42.71  | | Case 2:
% 231.54/42.71  | | | 
% 231.54/42.71  | | |   (99)  all_57_9 = e1 & op(e3, e0) = e1
% 231.54/42.71  | | | 
% 231.54/42.71  | | | REF_CLOSE: (18), (21), (99) are inconsistent by sub-proof #2437.
% 231.54/42.71  | | | 
% 231.54/42.71  | | End of split
% 231.54/42.71  | | 
% 231.54/42.71  | End of split
% 231.54/42.71  | 
% 231.54/42.71  End of proof
% 231.54/42.71  
% 231.54/42.71  Sub-proof #1493 shows that the following formulas are inconsistent:
% 231.54/42.71  ----------------------------------------------------------------
% 231.54/42.71    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.71         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.54/42.71    (2)   ~ (e3 = e1)
% 231.54/42.71    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.71           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.71    (4)  all_57_4 = e2
% 231.54/42.71    (5)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.54/42.71         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.54/42.71    (6)  all_57_3 = e0
% 231.54/42.71    (7)   ~ (e3 = e2)
% 231.54/42.71    (8)  op(e3, e3) = e3
% 231.54/42.71    (9)  all_57_15 = e3
% 231.54/42.71    (10)  all_57_1 = e1
% 231.54/42.71    (11)  all_57_5 = e3
% 231.54/42.71    (12)  all_57_9 = e0
% 231.54/42.71    (13)  all_57_11 = e0
% 231.54/42.71    (14)   ~ (e2 = e0)
% 231.54/42.71    (15)   ~ (e1 = e0)
% 231.54/42.71    (16)  all_57_7 = e3
% 231.54/42.71    (17)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.71          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.54/42.71    (18)   ~ (e2 = e1)
% 231.54/42.71    (19)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.54/42.71          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.54/42.71    (20)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.54/42.71          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.54/42.71    (21)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.71          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.54/42.71  
% 231.54/42.71  Begin of proof
% 231.54/42.71  | 
% 231.54/42.71  | BETA: splitting (1) gives:
% 231.54/42.71  | 
% 231.54/42.71  | Case 1:
% 231.54/42.71  | | 
% 231.54/42.71  | |   (22)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 231.54/42.71  | |           e2)
% 231.54/42.71  | | 
% 231.54/42.71  | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (10), (12), (14), (18), (22) are
% 231.54/42.71  | |            inconsistent by sub-proof #1499.
% 231.54/42.71  | | 
% 231.54/42.71  | Case 2:
% 231.54/42.71  | | 
% 231.54/42.71  | |   (23)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 231.54/42.71  | |           e2)
% 231.54/42.71  | | 
% 231.54/42.71  | | BETA: splitting (23) gives:
% 231.54/42.71  | | 
% 231.54/42.71  | | Case 1:
% 231.54/42.71  | | | 
% 231.54/42.71  | | |   (24)  all_57_7 = e2 & op(e1, e2) = e2
% 231.54/42.71  | | | 
% 231.54/42.71  | | | REF_CLOSE: (7), (16), (24) are inconsistent by sub-proof #2092.
% 231.54/42.71  | | | 
% 231.54/42.71  | | Case 2:
% 231.54/42.71  | | | 
% 231.54/42.71  | | |   (25)  all_57_13 = e2 & op(e0, e2) = e2
% 231.54/42.71  | | | 
% 231.54/42.71  | | | ALPHA: (25) implies:
% 231.54/42.71  | | |   (26)  all_57_13 = e2
% 231.54/42.71  | | | 
% 231.54/42.71  | | | BETA: splitting (20) gives:
% 231.54/42.71  | | | 
% 231.54/42.71  | | | Case 1:
% 231.54/42.71  | | | | 
% 231.54/42.71  | | | |   (27)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0)
% 231.54/42.71  | | | |           = e1)
% 231.54/42.71  | | | | 
% 231.54/42.71  | | | | BETA: splitting (27) gives:
% 231.54/42.71  | | | | 
% 231.54/42.71  | | | | Case 1:
% 231.54/42.71  | | | | | 
% 231.54/42.71  | | | | |   (28)  all_57_9 = e1 & op(e3, e0) = e1
% 231.54/42.71  | | | | | 
% 231.54/42.71  | | | | | ALPHA: (28) implies:
% 231.54/42.71  | | | | |   (29)  all_57_9 = e1
% 231.54/42.71  | | | | | 
% 231.54/42.71  | | | | | COMBINE_EQS: (12), (29) imply:
% 231.54/42.71  | | | | |   (30)  e1 = e0
% 231.54/42.71  | | | | | 
% 231.54/42.71  | | | | | REF_CLOSE: (1), (2), (6), (7), (10), (14), (15), (16), (18), (21),
% 231.54/42.71  | | | | |            (30) are inconsistent by sub-proof #1626.
% 231.54/42.71  | | | | | 
% 231.54/42.71  | | | | Case 2:
% 231.54/42.71  | | | | | 
% 231.54/42.71  | | | | |   (31)  all_57_10 = e1 & op(e2, e0) = e1
% 231.54/42.71  | | | | | 
% 231.54/42.71  | | | | | ALPHA: (31) implies:
% 231.54/42.71  | | | | |   (32)  all_57_10 = e1
% 231.54/42.71  | | | | | 
% 231.54/42.71  | | | | | BETA: splitting (17) gives:
% 231.54/42.71  | | | | | 
% 231.54/42.71  | | | | | Case 1:
% 231.54/42.71  | | | | | | 
% 231.54/42.71  | | | | | |   (33)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2,
% 231.54/42.71  | | | | | |             e2) = e2)
% 231.54/42.71  | | | | | | 
% 231.54/42.71  | | | | | | BETA: splitting (33) gives:
% 231.54/42.71  | | | | | | 
% 231.54/42.71  | | | | | | Case 1:
% 231.54/42.71  | | | | | | | 
% 231.54/42.71  | | | | | | |   (34)  all_57_2 = e2 & op(e2, e3) = e2
% 231.54/42.71  | | | | | | | 
% 231.54/42.71  | | | | | | | ALPHA: (34) implies:
% 231.54/42.71  | | | | | | |   (35)  all_57_2 = e2
% 231.54/42.71  | | | | | | | 
% 231.54/42.71  | | | | | | | REF_CLOSE: (6), (7), (9), (11), (12), (13), (14), (17), (18),
% 231.54/42.71  | | | | | | |            (19), (32), (35) are inconsistent by sub-proof #1509.
% 231.54/42.71  | | | | | | | 
% 231.54/42.71  | | | | | | Case 2:
% 231.54/42.71  | | | | | | | 
% 231.54/42.71  | | | | | | |   (36)  all_57_3 = e2 & op(e2, e2) = e2
% 231.54/42.71  | | | | | | | 
% 231.54/42.71  | | | | | | | ALPHA: (36) implies:
% 231.54/42.71  | | | | | | |   (37)  all_57_3 = e2
% 231.54/42.71  | | | | | | | 
% 231.54/42.71  | | | | | | | COMBINE_EQS: (6), (37) imply:
% 231.54/42.71  | | | | | | |   (38)  e2 = e0
% 231.54/42.71  | | | | | | | 
% 231.54/42.71  | | | | | | | SIMP: (38) implies:
% 231.54/42.71  | | | | | | |   (39)  e2 = e0
% 231.54/42.71  | | | | | | | 
% 231.54/42.71  | | | | | | | COMBINE_EQS: (4), (39) imply:
% 231.54/42.71  | | | | | | |   (40)  all_57_4 = e0
% 231.54/42.71  | | | | | | | 
% 231.54/42.71  | | | | | | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (12), (14), (15), (16),
% 231.54/42.71  | | | | | | |            (18), (21), (26), (40) are inconsistent by sub-proof
% 231.54/42.71  | | | | | | |            #1498.
% 231.54/42.71  | | | | | | | 
% 231.54/42.71  | | | | | | End of split
% 231.54/42.71  | | | | | | 
% 231.54/42.71  | | | | | Case 2:
% 231.54/42.71  | | | | | | 
% 231.54/42.71  | | | | | |   (41)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2,
% 231.54/42.71  | | | | | |             e0) = e2)
% 231.54/42.71  | | | | | | 
% 231.54/42.71  | | | | | | REF_CLOSE: (7), (11), (18), (32), (41) are inconsistent by sub-proof
% 231.54/42.71  | | | | | |            #1523.
% 231.54/42.71  | | | | | | 
% 231.54/42.71  | | | | | End of split
% 231.54/42.71  | | | | | 
% 231.54/42.71  | | | | End of split
% 231.54/42.71  | | | | 
% 231.54/42.71  | | | Case 2:
% 231.54/42.71  | | | | 
% 231.54/42.71  | | | |   (42)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0,
% 231.54/42.71  | | | |             e0) = e1)
% 231.54/42.71  | | | | 
% 231.54/42.71  | | | | BETA: splitting (42) gives:
% 231.54/42.71  | | | | 
% 231.54/42.71  | | | | Case 1:
% 231.54/42.71  | | | | | 
% 231.54/42.71  | | | | |   (43)  all_57_11 = e1 & op(e1, e0) = e1
% 231.54/42.71  | | | | | 
% 231.54/42.71  | | | | | ALPHA: (43) implies:
% 231.54/42.71  | | | | |   (44)  all_57_11 = e1
% 231.54/42.71  | | | | | 
% 231.54/42.71  | | | | | COMBINE_EQS: (13), (44) imply:
% 231.54/42.71  | | | | |   (45)  e1 = e0
% 231.54/42.71  | | | | | 
% 231.54/42.71  | | | | | REF_CLOSE: (1), (2), (6), (7), (10), (14), (15), (16), (18), (21),
% 231.54/42.71  | | | | |            (45) are inconsistent by sub-proof #1626.
% 231.54/42.71  | | | | | 
% 231.54/42.71  | | | | Case 2:
% 231.54/42.71  | | | | | 
% 231.54/42.71  | | | | |   (46)  all_57_15 = e1 & op(e0, e0) = e1
% 231.54/42.71  | | | | | 
% 231.54/42.71  | | | | | REF_CLOSE: (2), (9), (46) are inconsistent by sub-proof #2325.
% 231.54/42.71  | | | | | 
% 231.54/42.71  | | | | End of split
% 231.54/42.71  | | | | 
% 231.54/42.71  | | | End of split
% 231.54/42.71  | | | 
% 231.54/42.71  | | End of split
% 231.54/42.71  | | 
% 231.54/42.71  | End of split
% 231.54/42.71  | 
% 231.54/42.71  End of proof
% 231.54/42.71  
% 231.54/42.71  Sub-proof #1494 shows that the following formulas are inconsistent:
% 231.54/42.71  ----------------------------------------------------------------
% 231.54/42.71    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.71         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.54/42.71    (2)   ~ (e3 = e1)
% 231.54/42.71    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.71           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.71    (4)  all_57_4 = e2
% 231.54/42.71    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.54/42.71         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.54/42.71    (6)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.54/42.71         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.54/42.71    (7)  all_57_3 = e0
% 231.54/42.71    (8)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.54/42.71         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.54/42.71    (9)   ~ (e3 = e2)
% 231.54/42.71    (10)   ~ (e3 = e0)
% 231.54/42.71    (11)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.54/42.71          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.54/42.71    (12)  op(e3, e3) = e3
% 231.54/42.71    (13)  all_57_6 = e0
% 231.54/42.71    (14)  all_57_5 = e3
% 231.54/42.71    (15)  all_57_9 = e0
% 231.54/42.71    (16)   ~ (e2 = e0)
% 231.54/42.71    (17)  all_57_13 = e2
% 231.54/42.71    (18)   ~ (e1 = e0)
% 231.54/42.71    (19)  op(e1, e1) = e0
% 231.54/42.71    (20)  all_57_7 = e3
% 231.54/42.71    (21)  all_57_11 = e1
% 231.54/42.71    (22)   ~ (e2 = e1)
% 231.54/42.71    (23)  all_57_14 = e0
% 231.54/42.71    (24)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.71          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.54/42.71    (25)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 231.54/42.71          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 231.54/42.71  
% 231.54/42.71  Begin of proof
% 231.54/42.71  | 
% 231.54/42.71  | BETA: splitting (25) gives:
% 231.54/42.71  | 
% 231.54/42.71  | Case 1:
% 231.54/42.71  | | 
% 231.54/42.71  | |   (26)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) =
% 231.54/42.71  | |           e2)
% 231.54/42.71  | | 
% 231.54/42.71  | | REF_CLOSE: (2), (3), (4), (6), (7), (9), (12), (13), (15), (16), (17), (18),
% 231.54/42.71  | |            (20), (22), (24), (26) are inconsistent by sub-proof #1497.
% 231.54/42.71  | | 
% 231.54/42.71  | Case 2:
% 231.54/42.71  | | 
% 231.54/42.71  | |   (27)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) =
% 231.54/42.71  | |           e2)
% 231.54/42.71  | | 
% 231.54/42.71  | | BETA: splitting (27) gives:
% 231.54/42.71  | | 
% 231.54/42.71  | | Case 1:
% 231.54/42.71  | | | 
% 231.54/42.71  | | |   (28)  all_57_8 = e2 & op(e1, e1) = e2
% 231.54/42.71  | | | 
% 231.54/42.71  | | | ALPHA: (28) implies:
% 231.54/42.71  | | |   (29)  all_57_8 = e2
% 231.54/42.71  | | |   (30)  op(e1, e1) = e2
% 231.54/42.71  | | | 
% 231.54/42.71  | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (14),
% 231.54/42.71  | | |            (15), (16), (18), (19), (20), (22), (23), (24), (29), (30) are
% 231.54/42.71  | | |            inconsistent by sub-proof #1495.
% 231.54/42.71  | | | 
% 231.54/42.71  | | Case 2:
% 231.54/42.71  | | | 
% 231.54/42.71  | | |   (31)  all_57_11 = e2 & op(e1, e0) = e2
% 231.54/42.71  | | | 
% 231.54/42.71  | | | ALPHA: (31) implies:
% 231.54/42.71  | | |   (32)  all_57_11 = e2
% 231.54/42.71  | | | 
% 231.54/42.71  | | | REF_CLOSE: (21), (22), (32) are inconsistent by sub-proof #2113.
% 231.54/42.71  | | | 
% 231.54/42.71  | | End of split
% 231.54/42.71  | | 
% 231.54/42.71  | End of split
% 231.54/42.71  | 
% 231.54/42.71  End of proof
% 231.54/42.71  
% 231.54/42.71  Sub-proof #1495 shows that the following formulas are inconsistent:
% 231.54/42.71  ----------------------------------------------------------------
% 231.54/42.71    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.71         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.54/42.71    (2)   ~ (e3 = e1)
% 231.54/42.71    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.71           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.71    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.54/42.71         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.54/42.71    (5)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.54/42.71         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.54/42.71    (6)  all_57_3 = e0
% 231.54/42.71    (7)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.54/42.71         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.54/42.71    (8)   ~ (e3 = e2)
% 231.54/42.71    (9)   ~ (e3 = e0)
% 231.54/42.71    (10)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.54/42.71          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.54/42.71    (11)  op(e3, e3) = e3
% 231.54/42.71    (12)  all_57_5 = e3
% 231.54/42.71    (13)  all_57_9 = e0
% 231.54/42.71    (14)   ~ (e2 = e0)
% 231.54/42.71    (15)   ~ (e1 = e0)
% 231.54/42.71    (16)  all_57_8 = e2
% 231.54/42.71    (17)  op(e1, e1) = e0
% 231.54/42.71    (18)  op(e1, e1) = e2
% 231.54/42.71    (19)  all_57_7 = e3
% 231.54/42.71    (20)   ~ (e2 = e1)
% 231.54/42.71    (21)  all_57_14 = e0
% 231.54/42.71    (22)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.71          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.54/42.71  
% 231.54/42.71  Begin of proof
% 231.54/42.71  | 
% 231.54/42.71  | BETA: splitting (10) gives:
% 231.54/42.71  | 
% 231.54/42.71  | Case 1:
% 231.54/42.71  | | 
% 231.54/42.71  | |   (23)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) =
% 231.54/42.71  | |           e1)
% 231.54/42.71  | | 
% 231.54/42.71  | | BETA: splitting (23) gives:
% 231.54/42.71  | | 
% 231.54/42.71  | | Case 1:
% 231.54/42.71  | | | 
% 231.54/42.71  | | |   (24)  all_57_4 = e1 & op(e3, e1) = e1
% 231.54/42.71  | | | 
% 231.54/42.71  | | | ALPHA: (24) implies:
% 231.54/42.71  | | |   (25)  all_57_4 = e1
% 231.54/42.71  | | | 
% 231.54/42.71  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13),
% 231.54/42.71  | | |            (14), (15), (16), (17), (18), (19), (20), (22), (25) are
% 231.54/42.71  | | |            inconsistent by sub-proof #1496.
% 231.54/42.71  | | | 
% 231.54/42.71  | | Case 2:
% 231.54/42.71  | | | 
% 231.54/42.71  | | |   (26)  all_57_5 = e1 & op(e2, e1) = e1
% 231.54/42.71  | | | 
% 231.54/42.71  | | | REF_CLOSE: (2), (12), (26) are inconsistent by sub-proof #2376.
% 231.54/42.71  | | | 
% 231.54/42.71  | | End of split
% 231.54/42.71  | | 
% 231.54/42.71  | Case 2:
% 231.54/42.71  | | 
% 231.54/42.71  | |   (27)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) =
% 231.54/42.71  | |           e1)
% 231.54/42.71  | | 
% 231.54/42.71  | | BETA: splitting (27) gives:
% 231.54/42.71  | | 
% 231.54/42.71  | | Case 1:
% 231.54/42.71  | | | 
% 231.54/42.71  | | |   (28)  all_57_8 = e1 & op(e1, e1) = e1
% 231.54/42.71  | | | 
% 231.54/42.71  | | | REF_CLOSE: (16), (20), (28) are inconsistent by sub-proof #1533.
% 231.54/42.71  | | | 
% 231.54/42.71  | | Case 2:
% 231.54/42.71  | | | 
% 231.54/42.71  | | |   (29)  all_57_14 = e1 & op(e0, e1) = e1
% 231.54/42.71  | | | 
% 231.54/42.71  | | | REF_CLOSE: (15), (21), (29) are inconsistent by sub-proof #2381.
% 231.54/42.71  | | | 
% 231.54/42.71  | | End of split
% 231.54/42.71  | | 
% 231.54/42.71  | End of split
% 231.54/42.71  | 
% 231.54/42.71  End of proof
% 231.54/42.71  
% 231.54/42.71  Sub-proof #1496 shows that the following formulas are inconsistent:
% 231.54/42.71  ----------------------------------------------------------------
% 231.54/42.71    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.71         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.54/42.71    (2)   ~ (e3 = e1)
% 231.54/42.71    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.71           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.71    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.54/42.71         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.54/42.71    (5)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.54/42.71         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.54/42.71    (6)  all_57_3 = e0
% 231.54/42.71    (7)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.54/42.71         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.54/42.71    (8)   ~ (e3 = e2)
% 231.54/42.71    (9)   ~ (e3 = e0)
% 231.54/42.71    (10)  op(e3, e3) = e3
% 231.54/42.71    (11)  all_57_4 = e1
% 231.54/42.71    (12)  all_57_5 = e3
% 231.54/42.71    (13)  all_57_9 = e0
% 231.54/42.71    (14)   ~ (e2 = e0)
% 231.54/42.71    (15)   ~ (e1 = e0)
% 231.54/42.71    (16)  all_57_8 = e2
% 231.54/42.71    (17)  op(e1, e1) = e0
% 231.54/42.71    (18)  op(e1, e1) = e2
% 231.54/42.71    (19)  all_57_7 = e3
% 231.54/42.71    (20)   ~ (e2 = e1)
% 231.54/42.71    (21)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.71          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.54/42.71  
% 231.54/42.71  Begin of proof
% 231.54/42.71  | 
% 231.54/42.71  | BETA: splitting (5) gives:
% 231.54/42.71  | 
% 231.54/42.71  | Case 1:
% 231.54/42.71  | | 
% 231.54/42.71  | |   (22)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) =
% 231.54/42.71  | |           e2)
% 231.54/42.71  | | 
% 231.54/42.71  | | BETA: splitting (22) gives:
% 231.54/42.71  | | 
% 231.54/42.71  | | Case 1:
% 231.54/42.71  | | | 
% 231.54/42.71  | | |   (23)  all_57_0 = e2 & op(e3, e3) = e2
% 231.54/42.71  | | | 
% 231.54/42.71  | | | ALPHA: (23) implies:
% 231.54/42.71  | | |   (24)  op(e3, e3) = e2
% 231.54/42.71  | | | 
% 231.54/42.71  | | | REF_CLOSE: (3), (8), (10), (24) are inconsistent by sub-proof #2490.
% 231.54/42.71  | | | 
% 231.54/42.71  | | Case 2:
% 231.54/42.71  | | | 
% 231.54/42.71  | | |   (25)  all_57_1 = e2 & op(e3, e2) = e2
% 231.54/42.71  | | | 
% 231.54/42.71  | | | ALPHA: (25) implies:
% 231.54/42.71  | | |   (26)  all_57_1 = e2
% 231.54/42.71  | | | 
% 231.54/42.71  | | | BETA: splitting (21) gives:
% 231.54/42.71  | | | 
% 231.54/42.71  | | | Case 1:
% 231.54/42.71  | | | | 
% 231.54/42.71  | | | |   (27)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2)
% 231.54/42.71  | | | |           = e1)
% 231.54/42.71  | | | | 
% 231.54/42.71  | | | | BETA: splitting (27) gives:
% 231.54/42.71  | | | | 
% 231.54/42.71  | | | | Case 1:
% 231.54/42.71  | | | | | 
% 231.54/42.71  | | | | |   (28)  all_57_1 = e1 & op(e3, e2) = e1
% 231.54/42.71  | | | | | 
% 231.54/42.71  | | | | | REF_CLOSE: (20), (26), (28) are inconsistent by sub-proof #2210.
% 231.54/42.71  | | | | | 
% 231.54/42.71  | | | | Case 2:
% 231.54/42.71  | | | | | 
% 231.54/42.71  | | | | |   (29)  all_57_3 = e1 & op(e2, e2) = e1
% 231.54/42.71  | | | | | 
% 231.54/42.71  | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (10), (11), (13), (14), (15),
% 231.54/42.71  | | | | |            (20), (29) are inconsistent by sub-proof #2095.
% 231.54/42.71  | | | | | 
% 231.54/42.71  | | | | End of split
% 231.54/42.71  | | | | 
% 231.54/42.71  | | | Case 2:
% 231.54/42.71  | | | | 
% 231.54/42.71  | | | |   (30)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2)
% 231.54/42.71  | | | |           = e1)
% 231.54/42.71  | | | | 
% 231.54/42.71  | | | | BETA: splitting (30) gives:
% 231.54/42.71  | | | | 
% 231.54/42.71  | | | | Case 1:
% 231.54/42.71  | | | | | 
% 231.54/42.71  | | | | |   (31)  all_57_7 = e1 & op(e1, e2) = e1
% 231.54/42.71  | | | | | 
% 231.54/42.71  | | | | | REF_CLOSE: (2), (19), (31) are inconsistent by sub-proof #2104.
% 231.54/42.71  | | | | | 
% 231.54/42.71  | | | | Case 2:
% 231.54/42.71  | | | | | 
% 231.54/42.71  | | | | |   (32)  all_57_13 = e1 & op(e0, e2) = e1
% 231.54/42.71  | | | | | 
% 231.54/42.71  | | | | | ALPHA: (32) implies:
% 231.54/42.71  | | | | |   (33)  all_57_13 = e1
% 231.54/42.71  | | | | | 
% 231.54/42.71  | | | | | BETA: splitting (7) gives:
% 231.54/42.71  | | | | | 
% 231.54/42.71  | | | | | Case 1:
% 231.54/42.71  | | | | | | 
% 231.54/42.71  | | | | | |   (34)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2,
% 231.54/42.71  | | | | | |             e1) = e0)
% 231.54/42.71  | | | | | | 
% 231.54/42.71  | | | | | | BETA: splitting (34) gives:
% 231.54/42.71  | | | | | | 
% 231.54/42.71  | | | | | | Case 1:
% 231.54/42.71  | | | | | | | 
% 231.54/42.71  | | | | | | |   (35)  all_57_4 = e0 & op(e3, e1) = e0
% 231.54/42.71  | | | | | | | 
% 231.54/42.71  | | | | | | | ALPHA: (35) implies:
% 231.54/42.71  | | | | | | |   (36)  all_57_4 = e0
% 231.54/42.71  | | | | | | | 
% 231.54/42.71  | | | | | | | REF_CLOSE: (2), (3), (4), (5), (8), (10), (13), (14), (15), (20),
% 231.54/42.71  | | | | | | |            (36) are inconsistent by sub-proof #2436.
% 231.54/42.71  | | | | | | | 
% 231.54/42.71  | | | | | | Case 2:
% 231.54/42.71  | | | | | | | 
% 231.54/42.71  | | | | | | |   (37)  all_57_5 = e0 & op(e2, e1) = e0
% 231.54/42.71  | | | | | | | 
% 231.54/42.71  | | | | | | | ALPHA: (37) implies:
% 231.54/42.71  | | | | | | |   (38)  all_57_5 = e0
% 231.54/42.71  | | | | | | | 
% 231.54/42.71  | | | | | | | REF_CLOSE: (9), (12), (38) are inconsistent by sub-proof #2471.
% 231.54/42.71  | | | | | | | 
% 231.54/42.71  | | | | | | End of split
% 231.54/42.71  | | | | | | 
% 231.54/42.71  | | | | | Case 2:
% 231.54/42.71  | | | | | | 
% 231.54/42.71  | | | | | |   (39)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0,
% 231.54/42.71  | | | | | |             e1) = e0)
% 231.54/42.71  | | | | | | 
% 231.54/42.71  | | | | | | BETA: splitting (39) gives:
% 231.54/42.71  | | | | | | 
% 231.54/42.71  | | | | | | Case 1:
% 231.54/42.71  | | | | | | | 
% 231.54/42.71  | | | | | | |   (40)  all_57_8 = e0 & op(e1, e1) = e0
% 231.54/42.71  | | | | | | | 
% 231.54/42.71  | | | | | | | ALPHA: (40) implies:
% 231.54/42.71  | | | | | | |   (41)  all_57_8 = e0
% 231.54/42.71  | | | | | | | 
% 231.54/42.71  | | | | | | | COMBINE_EQS: (16), (41) imply:
% 231.54/42.71  | | | | | | |   (42)  e2 = e0
% 231.54/42.71  | | | | | | | 
% 231.54/42.71  | | | | | | | COMBINE_EQS: (26), (42) imply:
% 231.54/42.71  | | | | | | |   (43)  all_57_1 = e0
% 231.54/42.71  | | | | | | | 
% 231.54/42.71  | | | | | | | REF_CLOSE: (1), (6), (8), (14), (19), (20), (33), (43) are
% 231.54/42.71  | | | | | | |            inconsistent by sub-proof #2099.
% 231.54/42.71  | | | | | | | 
% 231.54/42.71  | | | | | | Case 2:
% 231.54/42.71  | | | | | | | 
% 231.54/42.71  | | | | | | | 
% 231.54/42.71  | | | | | | | GROUND_INST: instantiating (3) with e0, e2, e1, e1, simplifying
% 231.54/42.71  | | | | | | |              with (17), (18) gives:
% 231.54/42.71  | | | | | | |   (44)  e2 = e0
% 231.54/42.71  | | | | | | | 
% 231.54/42.71  | | | | | | | COMBINE_EQS: (26), (44) imply:
% 231.54/42.71  | | | | | | |   (45)  all_57_1 = e0
% 231.54/42.71  | | | | | | | 
% 231.54/42.71  | | | | | | | REF_CLOSE: (1), (6), (8), (14), (19), (20), (33), (45) are
% 231.54/42.71  | | | | | | |            inconsistent by sub-proof #2099.
% 231.54/42.71  | | | | | | | 
% 231.54/42.71  | | | | | | End of split
% 231.54/42.71  | | | | | | 
% 231.54/42.71  | | | | | End of split
% 231.54/42.71  | | | | | 
% 231.54/42.71  | | | | End of split
% 231.54/42.71  | | | | 
% 231.54/42.71  | | | End of split
% 231.54/42.71  | | | 
% 231.54/42.71  | | End of split
% 231.54/42.71  | | 
% 231.54/42.71  | Case 2:
% 231.54/42.71  | | 
% 231.54/42.71  | |   (46)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) =
% 231.54/42.71  | |           e2)
% 231.54/42.71  | | 
% 231.54/42.71  | | BETA: splitting (46) gives:
% 231.54/42.71  | | 
% 231.54/42.71  | | Case 1:
% 231.54/42.71  | | | 
% 231.54/42.71  | | |   (47)  all_57_4 = e2 & op(e3, e1) = e2
% 231.54/42.71  | | | 
% 231.54/42.71  | | | ALPHA: (47) implies:
% 231.54/42.71  | | |   (48)  all_57_4 = e2
% 231.54/42.71  | | | 
% 231.54/42.71  | | | REF_CLOSE: (11), (20), (48) are inconsistent by sub-proof #2430.
% 231.54/42.71  | | | 
% 231.54/42.71  | | Case 2:
% 231.54/42.71  | | | 
% 231.54/42.71  | | |   (49)  all_57_9 = e2 & op(e3, e0) = e2
% 231.54/42.71  | | | 
% 231.54/42.71  | | | ALPHA: (49) implies:
% 231.54/42.71  | | |   (50)  all_57_9 = e2
% 231.54/42.71  | | | 
% 231.54/42.71  | | | REF_CLOSE: (13), (14), (50) are inconsistent by sub-proof #2440.
% 231.54/42.71  | | | 
% 231.54/42.71  | | End of split
% 231.54/42.71  | | 
% 231.54/42.71  | End of split
% 231.54/42.71  | 
% 231.54/42.71  End of proof
% 231.54/42.71  
% 231.54/42.71  Sub-proof #1497 shows that the following formulas are inconsistent:
% 231.54/42.71  ----------------------------------------------------------------
% 231.54/42.71    (1)   ~ (e3 = e1)
% 231.54/42.71    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.71           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.71    (3)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2)
% 231.54/42.71    (4)  all_57_4 = e2
% 231.54/42.71    (5)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.54/42.71         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.54/42.71    (6)  all_57_3 = e0
% 231.54/42.71    (7)   ~ (e3 = e2)
% 231.54/42.71    (8)  op(e3, e3) = e3
% 231.54/42.71    (9)  all_57_6 = e0
% 231.54/42.71    (10)  all_57_9 = e0
% 231.54/42.71    (11)   ~ (e2 = e0)
% 231.54/42.71    (12)  all_57_13 = e2
% 231.54/42.71    (13)   ~ (e1 = e0)
% 231.54/42.71    (14)  all_57_7 = e3
% 231.54/42.71    (15)   ~ (e2 = e1)
% 231.54/42.71    (16)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.71          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.54/42.71  
% 231.54/42.71  Begin of proof
% 231.54/42.71  | 
% 231.54/42.71  | BETA: splitting (3) gives:
% 231.54/42.71  | 
% 231.54/42.71  | Case 1:
% 231.54/42.71  | | 
% 231.54/42.71  | |   (17)  all_57_6 = e2 & op(e1, e3) = e2
% 231.54/42.71  | | 
% 231.54/42.71  | | ALPHA: (17) implies:
% 231.54/42.71  | |   (18)  all_57_6 = e2
% 231.54/42.71  | | 
% 231.54/42.71  | | COMBINE_EQS: (9), (18) imply:
% 231.54/42.71  | |   (19)  e2 = e0
% 231.54/42.71  | | 
% 231.54/42.71  | | SIMP: (19) implies:
% 231.54/42.71  | |   (20)  e2 = e0
% 231.54/42.71  | | 
% 231.54/42.71  | | COMBINE_EQS: (4), (20) imply:
% 231.54/42.71  | |   (21)  all_57_4 = e0
% 231.54/42.71  | | 
% 231.54/42.71  | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (10), (11), (12), (13), (14), (15),
% 231.54/42.71  | |            (16), (21) are inconsistent by sub-proof #1498.
% 231.54/42.71  | | 
% 231.54/42.71  | Case 2:
% 231.54/42.71  | | 
% 231.54/42.71  | |   (22)  all_57_7 = e2 & op(e1, e2) = e2
% 231.54/42.71  | | 
% 231.54/42.72  | | REF_CLOSE: (7), (14), (22) are inconsistent by sub-proof #2092.
% 231.54/42.72  | | 
% 231.54/42.72  | End of split
% 231.54/42.72  | 
% 231.54/42.72  End of proof
% 231.54/42.72  
% 231.54/42.72  Sub-proof #1498 shows that the following formulas are inconsistent:
% 231.54/42.72  ----------------------------------------------------------------
% 231.54/42.72    (1)   ~ (e3 = e1)
% 231.54/42.72    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.72           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.72    (3)  all_57_4 = e0
% 231.54/42.72    (4)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.54/42.72         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.54/42.72    (5)  all_57_3 = e0
% 231.54/42.72    (6)   ~ (e3 = e2)
% 231.54/42.72    (7)  op(e3, e3) = e3
% 231.54/42.72    (8)  all_57_9 = e0
% 231.54/42.72    (9)   ~ (e2 = e0)
% 231.54/42.72    (10)  all_57_13 = e2
% 231.54/42.72    (11)   ~ (e1 = e0)
% 231.54/42.72    (12)  all_57_7 = e3
% 231.54/42.72    (13)   ~ (e2 = e1)
% 231.54/42.72    (14)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.72          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.54/42.72  
% 231.54/42.72  Begin of proof
% 231.54/42.72  | 
% 231.54/42.72  | BETA: splitting (14) gives:
% 231.54/42.72  | 
% 231.54/42.72  | Case 1:
% 231.54/42.72  | | 
% 231.54/42.72  | |   (15)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) =
% 231.54/42.72  | |           e1)
% 231.54/42.72  | | 
% 231.54/42.72  | | BETA: splitting (15) gives:
% 231.54/42.72  | | 
% 231.54/42.72  | | Case 1:
% 231.54/42.72  | | | 
% 231.54/42.72  | | |   (16)  all_57_1 = e1 & op(e3, e2) = e1
% 231.54/42.72  | | | 
% 231.54/42.72  | | | ALPHA: (16) implies:
% 231.54/42.72  | | |   (17)  all_57_1 = e1
% 231.54/42.72  | | | 
% 231.54/42.72  | | | REF_CLOSE: (2), (3), (4), (6), (7), (8), (9), (13), (17) are inconsistent
% 231.54/42.72  | | |            by sub-proof #2439.
% 231.54/42.72  | | | 
% 231.54/42.72  | | Case 2:
% 231.54/42.72  | | | 
% 231.54/42.72  | | |   (18)  all_57_3 = e1 & op(e2, e2) = e1
% 231.54/42.72  | | | 
% 231.54/42.72  | | | REF_CLOSE: (5), (11), (18) are inconsistent by sub-proof #2362.
% 231.54/42.72  | | | 
% 231.54/42.72  | | End of split
% 231.54/42.72  | | 
% 231.54/42.72  | Case 2:
% 231.54/42.72  | | 
% 231.54/42.72  | |   (19)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 231.54/42.72  | |           e1)
% 231.54/42.72  | | 
% 231.54/42.72  | | BETA: splitting (19) gives:
% 231.54/42.72  | | 
% 231.54/42.72  | | Case 1:
% 231.54/42.72  | | | 
% 231.54/42.72  | | |   (20)  all_57_7 = e1 & op(e1, e2) = e1
% 231.54/42.72  | | | 
% 231.54/42.72  | | | REF_CLOSE: (1), (12), (20) are inconsistent by sub-proof #2104.
% 231.54/42.72  | | | 
% 231.54/42.72  | | Case 2:
% 231.54/42.72  | | | 
% 231.54/42.72  | | |   (21)  all_57_13 = e1 & op(e0, e2) = e1
% 231.54/42.72  | | | 
% 231.54/42.72  | | | REF_CLOSE: (10), (13), (21) are inconsistent by sub-proof #2205.
% 231.54/42.72  | | | 
% 231.54/42.72  | | End of split
% 231.54/42.72  | | 
% 231.54/42.72  | End of split
% 231.54/42.72  | 
% 231.54/42.72  End of proof
% 231.54/42.72  
% 231.54/42.72  Sub-proof #1499 shows that the following formulas are inconsistent:
% 231.54/42.72  ----------------------------------------------------------------
% 231.54/42.72    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.72           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.72    (2)  all_57_4 = e2
% 231.54/42.72    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2)
% 231.54/42.72    (4)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.54/42.72         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.54/42.72    (5)  all_57_3 = e0
% 231.54/42.72    (6)   ~ (e3 = e2)
% 231.54/42.72    (7)  op(e3, e3) = e3
% 231.54/42.72    (8)  all_57_1 = e1
% 231.54/42.72    (9)  all_57_9 = e0
% 231.54/42.72    (10)   ~ (e2 = e0)
% 231.54/42.72    (11)   ~ (e2 = e1)
% 231.54/42.72  
% 231.54/42.72  Begin of proof
% 231.54/42.72  | 
% 231.54/42.72  | BETA: splitting (3) gives:
% 231.54/42.72  | 
% 231.54/42.72  | Case 1:
% 231.54/42.72  | | 
% 231.54/42.72  | |   (12)  all_57_1 = e2 & op(e3, e2) = e2
% 231.54/42.72  | | 
% 231.54/42.72  | | REF_CLOSE: (8), (11), (12) are inconsistent by sub-proof #2489.
% 231.54/42.72  | | 
% 231.54/42.72  | Case 2:
% 231.54/42.72  | | 
% 231.54/42.72  | |   (13)  all_57_3 = e2 & op(e2, e2) = e2
% 231.54/42.72  | | 
% 231.54/42.72  | | ALPHA: (13) implies:
% 231.54/42.72  | |   (14)  all_57_3 = e2
% 231.54/42.72  | | 
% 231.54/42.72  | | COMBINE_EQS: (5), (14) imply:
% 231.54/42.72  | |   (15)  e2 = e0
% 231.54/42.72  | | 
% 231.54/42.72  | | SIMP: (15) implies:
% 231.54/42.72  | |   (16)  e2 = e0
% 231.54/42.72  | | 
% 231.54/42.72  | | COMBINE_EQS: (2), (16) imply:
% 231.54/42.72  | |   (17)  all_57_4 = e0
% 231.54/42.72  | | 
% 231.54/42.72  | | REF_CLOSE: (1), (4), (6), (7), (8), (9), (10), (11), (17) are inconsistent
% 231.54/42.72  | |            by sub-proof #2439.
% 231.54/42.72  | | 
% 231.54/42.72  | End of split
% 231.54/42.72  | 
% 231.54/42.72  End of proof
% 231.54/42.72  
% 231.54/42.72  Sub-proof #1500 shows that the following formulas are inconsistent:
% 231.54/42.72  ----------------------------------------------------------------
% 231.54/42.72    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.72         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.54/42.72    (2)  all_57_12 = e0
% 231.54/42.72    (3)   ~ (all_52_7 = e3)
% 231.54/42.72    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.54/42.72         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.54/42.72    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.72         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.54/42.72    (6)   ~ (e3 = e1)
% 231.54/42.72    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.72           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.72    (8)  op(all_52_7, all_52_7) = e0
% 231.54/42.72    (9)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.54/42.72         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.54/42.72    (10)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.54/42.72          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.54/42.72    (11)  all_57_3 = e0
% 231.54/42.72    (12)   ~ (e3 = e2)
% 231.54/42.72    (13)   ~ (e3 = e0)
% 231.54/42.72    (14)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.54/42.72          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.54/42.72    (15)  op(e3, e3) = e3
% 231.54/42.72    (16)  all_57_15 = e3
% 231.54/42.72    (17)  all_57_5 = e3
% 231.54/42.72    (18)   ~ (e2 = e0)
% 231.54/42.72    (19)   ~ (e1 = e0)
% 231.54/42.72    (20)  op(e0, e0) = e3
% 231.54/42.72    (21)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.54/42.72          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.54/42.72            e2)
% 231.54/42.72    (22)  op(e1, e1) = e0
% 231.54/42.72    (23)  all_57_7 = e3
% 231.54/42.72    (24)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.72          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.54/42.72    (25)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) |
% 231.54/42.72          (all_57_11 = e0 & op(e1, e0) = e0)
% 231.54/42.72    (26)   ~ (e2 = e1)
% 231.54/42.72    (27)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.54/42.72          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.54/42.72    (28)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.54/42.72          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.54/42.72    (29)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.54/42.72          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.54/42.72    (30)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.54/42.72          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.54/42.72    (31)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 231.54/42.72          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 231.54/42.72    (32)  op(e3, e0) = all_52_7
% 231.54/42.72    (33)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.72          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.54/42.72    (34)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 231.54/42.72          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 231.54/42.72  
% 231.54/42.72  Begin of proof
% 231.54/42.72  | 
% 231.54/42.72  | BETA: splitting (25) gives:
% 231.54/42.72  | 
% 231.54/42.72  | Case 1:
% 231.54/42.72  | | 
% 231.54/42.72  | |   (35)  all_57_9 = e0 & op(e3, e0) = e0
% 231.54/42.72  | | 
% 231.54/42.72  | | ALPHA: (35) implies:
% 231.54/42.72  | |   (36)  all_57_9 = e0
% 231.54/42.72  | |   (37)  op(e3, e0) = e0
% 231.54/42.72  | | 
% 231.54/42.72  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 231.54/42.72  | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 231.54/42.72  | |            (24), (26), (27), (28), (29), (30), (31), (32), (33), (34), (36),
% 231.54/42.72  | |            (37) are inconsistent by sub-proof #1504.
% 231.54/42.72  | | 
% 231.54/42.72  | Case 2:
% 231.54/42.72  | | 
% 231.54/42.72  | |   (38)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 231.54/42.72  | |           e0)
% 231.54/42.72  | | 
% 231.54/42.72  | | BETA: splitting (38) gives:
% 231.54/42.72  | | 
% 231.54/42.72  | | Case 1:
% 231.54/42.72  | | | 
% 231.54/42.72  | | |   (39)  all_57_10 = e0 & op(e2, e0) = e0
% 231.54/42.72  | | | 
% 231.54/42.72  | | | ALPHA: (39) implies:
% 231.54/42.72  | | |   (40)  all_57_10 = e0
% 231.54/42.72  | | | 
% 231.54/42.72  | | | REF_CLOSE: (1), (6), (11), (12), (17), (18), (19), (24), (26), (40) are
% 231.54/42.72  | | |            inconsistent by sub-proof #1518.
% 231.54/42.72  | | | 
% 231.54/42.72  | | Case 2:
% 231.54/42.72  | | | 
% 231.54/42.72  | | |   (41)  all_57_11 = e0 & op(e1, e0) = e0
% 231.54/42.72  | | | 
% 231.54/42.72  | | | ALPHA: (41) implies:
% 231.54/42.72  | | |   (42)  all_57_11 = e0
% 231.54/42.72  | | | 
% 231.54/42.72  | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (9), (10), (11), (12), (13),
% 231.54/42.72  | | |            (14), (15), (16), (17), (18), (19), (21), (22), (23), (24),
% 231.54/42.72  | | |            (26), (27), (28), (30), (31), (33), (34), (42) are inconsistent
% 231.54/42.72  | | |            by sub-proof #1507.
% 231.54/42.72  | | | 
% 231.54/42.72  | | End of split
% 231.54/42.72  | | 
% 231.54/42.72  | End of split
% 231.54/42.72  | 
% 231.54/42.72  End of proof
% 231.54/42.72  
% 231.54/42.72  Sub-proof #1501 shows that the following formulas are inconsistent:
% 231.54/42.72  ----------------------------------------------------------------
% 231.54/42.72    (1)  all_57_8 = e2 & op(e1, e1) = e2
% 231.54/42.72    (2)  all_57_8 = e1
% 231.54/42.72    (3)   ~ (e2 = e1)
% 231.54/42.72  
% 231.54/42.72  Begin of proof
% 231.54/42.72  | 
% 231.54/42.72  | ALPHA: (1) implies:
% 231.54/42.72  |   (4)  all_57_8 = e2
% 231.54/42.72  | 
% 231.54/42.72  | COMBINE_EQS: (2), (4) imply:
% 231.54/42.72  |   (5)  e2 = e1
% 231.54/42.72  | 
% 231.54/42.72  | REDUCE: (3), (5) imply:
% 231.54/42.72  |   (6)  $false
% 231.54/42.72  | 
% 231.54/42.72  | CLOSE: (6) is inconsistent.
% 231.54/42.72  | 
% 231.54/42.72  End of proof
% 231.54/42.72  
% 231.54/42.72  Sub-proof #1502 shows that the following formulas are inconsistent:
% 231.54/42.72  ----------------------------------------------------------------
% 231.54/42.72    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.72         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.54/42.72    (2)   ~ (e3 = e1)
% 231.54/42.72    (3)  all_57_10 = e1
% 231.54/42.72    (4)  all_57_2 = e2
% 231.54/42.72    (5)  all_57_6 = e1
% 231.54/42.72    (6)  all_57_3 = e0
% 231.54/42.72    (7)  all_57_5 = e3
% 231.54/42.72    (8)   ~ (e1 = e0)
% 231.54/42.72    (9)  all_57_6 = e0 & op(e1, e3) = e0
% 231.54/42.72    (10)   ~ (e2 = e1)
% 231.54/42.72  
% 231.54/42.72  Begin of proof
% 231.54/42.72  | 
% 231.54/42.72  | ALPHA: (9) implies:
% 231.54/42.72  |   (11)  all_57_6 = e0
% 231.54/42.72  | 
% 231.54/42.72  | COMBINE_EQS: (5), (11) imply:
% 231.54/42.72  |   (12)  e1 = e0
% 231.54/42.72  | 
% 231.54/42.72  | COMBINE_EQS: (3), (12) imply:
% 231.54/42.72  |   (13)  all_57_10 = e0
% 231.54/42.72  | 
% 231.54/42.72  | REF_CLOSE: (1), (2), (4), (6), (7), (8), (10), (13) are inconsistent by
% 231.54/42.72  |            sub-proof #1530.
% 231.54/42.72  | 
% 231.54/42.72  End of proof
% 231.54/42.72  
% 231.54/42.72  Sub-proof #1503 shows that the following formulas are inconsistent:
% 231.54/42.72  ----------------------------------------------------------------
% 231.54/42.72    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.72           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.72    (2)  all_57_10 = e1
% 231.54/42.72    (3)  all_57_3 = e0
% 231.54/42.72    (4)   ~ (e3 = e2)
% 231.54/42.72    (5)   ~ (e3 = e0)
% 231.54/42.72    (6)  op(e3, e3) = e3
% 231.54/42.72    (7)  all_57_5 = e3
% 231.54/42.72    (8)   ~ (e2 = e0)
% 231.54/42.72    (9)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.72         (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.54/42.72    (10)   ~ (e2 = e1)
% 231.54/42.72    (11)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0)
% 231.54/42.72  
% 231.54/42.72  Begin of proof
% 231.54/42.72  | 
% 231.54/42.72  | BETA: splitting (11) gives:
% 231.54/42.72  | 
% 231.54/42.72  | Case 1:
% 231.54/42.72  | | 
% 231.54/42.72  | |   (12)  all_57_0 = e0 & op(e3, e3) = e0
% 231.54/42.72  | | 
% 231.54/42.72  | | ALPHA: (12) implies:
% 231.54/42.72  | |   (13)  op(e3, e3) = e0
% 231.54/42.72  | | 
% 231.54/42.72  | | REF_CLOSE: (1), (5), (6), (13) are inconsistent by sub-proof #2494.
% 231.54/42.72  | | 
% 231.54/42.72  | Case 2:
% 231.54/42.72  | | 
% 231.54/42.72  | |   (14)  all_57_2 = e0 & op(e2, e3) = e0
% 231.54/42.72  | | 
% 231.54/42.72  | | ALPHA: (14) implies:
% 231.54/42.72  | |   (15)  all_57_2 = e0
% 231.54/42.72  | | 
% 231.54/42.72  | | REF_CLOSE: (2), (3), (4), (7), (8), (9), (10), (15) are inconsistent by
% 231.54/42.72  | |            sub-proof #2254.
% 231.54/42.72  | | 
% 231.54/42.72  | End of split
% 231.54/42.72  | 
% 231.54/42.72  End of proof
% 231.54/42.72  
% 231.54/42.72  Sub-proof #1504 shows that the following formulas are inconsistent:
% 231.54/42.72  ----------------------------------------------------------------
% 231.54/42.72    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.72         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.54/42.72    (2)  all_57_12 = e0
% 231.54/42.72    (3)   ~ (all_52_7 = e3)
% 231.54/42.72    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.54/42.72         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.54/42.72    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.72         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.54/42.72    (6)   ~ (e3 = e1)
% 231.54/42.72    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.72           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.72    (8)  op(all_52_7, all_52_7) = e0
% 231.54/42.72    (9)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.54/42.72         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.54/42.72    (10)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.54/42.72          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.54/42.72    (11)  all_57_3 = e0
% 231.54/42.72    (12)   ~ (e3 = e2)
% 231.54/42.72    (13)   ~ (e3 = e0)
% 231.54/42.72    (14)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.54/42.72          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.54/42.72    (15)  op(e3, e3) = e3
% 231.54/42.72    (16)  op(e3, e0) = e0
% 231.54/42.72    (17)  all_57_15 = e3
% 231.54/42.72    (18)  all_57_5 = e3
% 231.54/42.72    (19)  all_57_9 = e0
% 231.54/42.72    (20)   ~ (e2 = e0)
% 231.54/42.72    (21)   ~ (e1 = e0)
% 231.54/42.72    (22)  op(e0, e0) = e3
% 231.54/42.72    (23)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.54/42.72          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.54/42.72            e2)
% 231.54/42.72    (24)  op(e1, e1) = e0
% 231.54/42.72    (25)  all_57_7 = e3
% 231.54/42.72    (26)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.72          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.54/42.72    (27)   ~ (e2 = e1)
% 231.54/42.72    (28)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.54/42.72          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.54/42.72    (29)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.54/42.72          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.54/42.72    (30)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.54/42.72          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.54/42.72    (31)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.54/42.72          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.54/42.72    (32)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 231.54/42.72          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 231.54/42.72    (33)  op(e3, e0) = all_52_7
% 231.54/42.72    (34)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.72          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.54/42.72    (35)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 231.54/42.72          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 231.54/42.72  
% 231.54/42.72  Begin of proof
% 231.54/42.72  | 
% 231.54/42.72  | BETA: splitting (30) gives:
% 231.54/42.72  | 
% 231.54/42.72  | Case 1:
% 231.54/42.72  | | 
% 231.54/42.72  | |   (36)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) =
% 231.54/42.72  | |           e0)
% 231.54/42.72  | | 
% 231.54/42.72  | | REF_CLOSE: (1), (6), (7), (11), (12), (13), (15), (18), (20), (21), (26),
% 231.54/42.72  | |            (27), (36) are inconsistent by sub-proof #1784.
% 231.54/42.72  | | 
% 231.54/42.72  | Case 2:
% 231.54/42.72  | | 
% 231.54/42.72  | |   (37)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) =
% 231.54/42.72  | |           e0)
% 231.54/42.72  | | 
% 231.54/42.72  | | BETA: splitting (37) gives:
% 231.54/42.72  | | 
% 231.54/42.72  | | Case 1:
% 231.54/42.72  | | | 
% 231.54/42.72  | | |   (38)  all_57_6 = e0 & op(e1, e3) = e0
% 231.54/42.72  | | | 
% 231.54/42.72  | | | ALPHA: (38) implies:
% 231.54/42.72  | | |   (39)  all_57_6 = e0
% 231.54/42.72  | | | 
% 231.54/42.72  | | | BETA: splitting (35) gives:
% 231.54/42.72  | | | 
% 231.54/42.72  | | | Case 1:
% 231.54/42.72  | | | | 
% 231.54/42.72  | | | |   (40)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2)
% 231.54/42.72  | | | |           = e2)
% 231.54/42.72  | | | | 
% 231.54/42.72  | | | | REF_CLOSE: (12), (20), (25), (39), (40) are inconsistent by sub-proof
% 231.54/42.72  | | | |            #1845.
% 231.54/42.72  | | | | 
% 231.54/42.72  | | | Case 2:
% 231.54/42.72  | | | | 
% 231.54/42.72  | | | |   (41)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0)
% 231.54/42.72  | | | |           = e2)
% 231.54/42.72  | | | | 
% 231.54/42.72  | | | | BETA: splitting (41) gives:
% 231.54/42.72  | | | | 
% 231.54/42.72  | | | | Case 1:
% 231.54/42.72  | | | | | 
% 231.54/42.72  | | | | |   (42)  all_57_8 = e2 & op(e1, e1) = e2
% 231.54/42.72  | | | | | 
% 231.54/42.72  | | | | | ALPHA: (42) implies:
% 231.54/42.72  | | | | |   (43)  all_57_8 = e2
% 231.54/42.72  | | | | |   (44)  op(e1, e1) = e2
% 231.54/42.72  | | | | | 
% 231.54/42.72  | | | | | BETA: splitting (29) gives:
% 231.54/42.72  | | | | | 
% 231.54/42.72  | | | | | Case 1:
% 231.54/42.72  | | | | | | 
% 231.54/42.72  | | | | | |   (45)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2,
% 231.54/42.72  | | | | | |             e3) = e2)
% 231.54/42.72  | | | | | | 
% 231.54/42.72  | | | | | | BETA: splitting (45) gives:
% 231.54/42.72  | | | | | | 
% 231.54/42.72  | | | | | | Case 1:
% 231.54/42.72  | | | | | | | 
% 231.54/42.72  | | | | | | |   (46)  all_57_0 = e2 & op(e3, e3) = e2
% 231.54/42.72  | | | | | | | 
% 231.54/42.72  | | | | | | | ALPHA: (46) implies:
% 231.54/42.72  | | | | | | |   (47)  op(e3, e3) = e2
% 231.54/42.72  | | | | | | | 
% 231.54/42.72  | | | | | | | REF_CLOSE: (7), (12), (15), (47) are inconsistent by sub-proof
% 231.54/42.72  | | | | | | |            #2490.
% 231.54/42.72  | | | | | | | 
% 231.54/42.72  | | | | | | Case 2:
% 231.54/42.72  | | | | | | | 
% 231.54/42.72  | | | | | | |   (48)  all_57_2 = e2 & op(e2, e3) = e2
% 231.54/42.72  | | | | | | | 
% 231.54/42.72  | | | | | | | ALPHA: (48) implies:
% 231.54/42.72  | | | | | | |   (49)  all_57_2 = e2
% 231.54/42.72  | | | | | | | 
% 231.54/42.72  | | | | | | | BETA: splitting (14) gives:
% 231.54/42.72  | | | | | | | 
% 231.54/42.72  | | | | | | | Case 1:
% 231.54/42.72  | | | | | | | | 
% 231.54/42.72  | | | | | | | |   (50)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 &
% 231.54/42.72  | | | | | | | |           op(e2, e1) = e1)
% 231.54/42.72  | | | | | | | | 
% 231.54/42.72  | | | | | | | | BETA: splitting (50) gives:
% 231.54/42.72  | | | | | | | | 
% 231.54/42.72  | | | | | | | | Case 1:
% 231.54/42.72  | | | | | | | | | 
% 231.54/42.72  | | | | | | | | |   (51)  all_57_4 = e1 & op(e3, e1) = e1
% 231.54/42.72  | | | | | | | | | 
% 231.54/42.72  | | | | | | | | | ALPHA: (51) implies:
% 231.54/42.72  | | | | | | | | |   (52)  all_57_4 = e1
% 231.54/42.72  | | | | | | | | | 
% 231.54/42.72  | | | | | | | | | BETA: splitting (4) gives:
% 231.54/42.72  | | | | | | | | | 
% 231.54/42.72  | | | | | | | | | Case 1:
% 231.54/42.72  | | | | | | | | | | 
% 231.54/42.72  | | | | | | | | | |   (53)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 &
% 231.54/42.72  | | | | | | | | | |           op(e2, e3) = e1)
% 231.54/42.72  | | | | | | | | | | 
% 231.54/42.72  | | | | | | | | | | REF_CLOSE: (6), (7), (15), (27), (49), (53) are inconsistent
% 231.54/42.72  | | | | | | | | | |            by sub-proof #2228.
% 231.54/42.72  | | | | | | | | | | 
% 231.54/42.72  | | | | | | | | | Case 2:
% 231.54/42.72  | | | | | | | | | | 
% 231.54/42.72  | | | | | | | | | |   (54)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1
% 231.54/42.72  | | | | | | | | | |           & op(e0, e3) = e1)
% 231.54/42.72  | | | | | | | | | | 
% 231.54/42.72  | | | | | | | | | | BETA: splitting (54) gives:
% 231.54/42.72  | | | | | | | | | | 
% 231.54/42.72  | | | | | | | | | | Case 1:
% 231.54/42.72  | | | | | | | | | | | 
% 231.54/42.72  | | | | | | | | | | |   (55)  all_57_6 = e1 & op(e1, e3) = e1
% 231.54/42.72  | | | | | | | | | | | 
% 231.54/42.72  | | | | | | | | | | | ALPHA: (55) implies:
% 231.54/42.72  | | | | | | | | | | |   (56)  all_57_6 = e1
% 231.54/42.72  | | | | | | | | | | | 
% 231.54/42.72  | | | | | | | | | | | COMBINE_EQS: (39), (56) imply:
% 231.54/42.72  | | | | | | | | | | |   (57)  e1 = e0
% 231.54/42.72  | | | | | | | | | | | 
% 231.54/42.72  | | | | | | | | | | | COMBINE_EQS: (52), (57) imply:
% 231.54/42.72  | | | | | | | | | | |   (58)  all_57_4 = e0
% 231.54/42.72  | | | | | | | | | | | 
% 231.54/42.72  | | | | | | | | | | | REF_CLOSE: (1), (2), (5), (6), (7), (11), (12), (14), (17),
% 231.54/42.72  | | | | | | | | | | |            (18), (20), (21), (23), (24), (25), (26), (27),
% 231.54/42.72  | | | | | | | | | | |            (34), (43), (44), (49), (58) are inconsistent by
% 231.54/42.72  | | | | | | | | | | |            sub-proof #1527.
% 231.54/42.72  | | | | | | | | | | | 
% 231.54/42.72  | | | | | | | | | | Case 2:
% 231.54/42.72  | | | | | | | | | | | 
% 231.54/42.72  | | | | | | | | | | |   (59)  all_57_12 = e1 & op(e0, e3) = e1
% 231.54/42.72  | | | | | | | | | | | 
% 231.54/42.72  | | | | | | | | | | | ALPHA: (59) implies:
% 231.54/42.72  | | | | | | | | | | |   (60)  all_57_12 = e1
% 231.54/42.72  | | | | | | | | | | | 
% 231.54/42.72  | | | | | | | | | | | COMBINE_EQS: (2), (60) imply:
% 231.54/42.72  | | | | | | | | | | |   (61)  e1 = e0
% 231.54/42.72  | | | | | | | | | | | 
% 231.54/42.72  | | | | | | | | | | | COMBINE_EQS: (52), (61) imply:
% 231.54/42.72  | | | | | | | | | | |   (62)  all_57_4 = e0
% 231.54/42.72  | | | | | | | | | | | 
% 231.54/42.72  | | | | | | | | | | | REF_CLOSE: (1), (2), (5), (6), (7), (11), (12), (14), (17),
% 231.54/42.72  | | | | | | | | | | |            (18), (20), (21), (23), (24), (25), (26), (27),
% 231.54/42.72  | | | | | | | | | | |            (34), (43), (44), (49), (62) are inconsistent by
% 231.54/42.72  | | | | | | | | | | |            sub-proof #1527.
% 231.54/42.72  | | | | | | | | | | | 
% 231.54/42.72  | | | | | | | | | | End of split
% 231.54/42.72  | | | | | | | | | | 
% 231.54/42.72  | | | | | | | | | End of split
% 231.54/42.72  | | | | | | | | | 
% 231.54/42.72  | | | | | | | | Case 2:
% 231.54/42.72  | | | | | | | | | 
% 231.54/42.72  | | | | | | | | |   (63)  all_57_5 = e1 & op(e2, e1) = e1
% 231.54/42.72  | | | | | | | | | 
% 231.54/42.72  | | | | | | | | | REF_CLOSE: (6), (18), (63) are inconsistent by sub-proof
% 231.54/42.72  | | | | | | | | |            #2376.
% 231.54/42.72  | | | | | | | | | 
% 231.54/42.72  | | | | | | | | End of split
% 231.54/42.72  | | | | | | | | 
% 231.54/42.72  | | | | | | | Case 2:
% 231.54/42.72  | | | | | | | | 
% 231.54/42.72  | | | | | | | |   (64)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 &
% 231.54/42.72  | | | | | | | |           op(e0, e1) = e1)
% 231.54/42.72  | | | | | | | | 
% 231.54/42.72  | | | | | | | | BETA: splitting (64) gives:
% 231.54/42.72  | | | | | | | | 
% 231.54/42.72  | | | | | | | | Case 1:
% 231.54/42.72  | | | | | | | | | 
% 231.54/42.72  | | | | | | | | |   (65)  all_57_8 = e1 & op(e1, e1) = e1
% 231.54/42.72  | | | | | | | | | 
% 231.54/42.72  | | | | | | | | | REF_CLOSE: (27), (43), (65) are inconsistent by sub-proof
% 231.54/42.72  | | | | | | | | |            #1533.
% 231.54/42.72  | | | | | | | | | 
% 231.54/42.72  | | | | | | | | Case 2:
% 231.54/42.72  | | | | | | | | | 
% 231.54/42.72  | | | | | | | | |   (66)  all_57_14 = e1 & op(e0, e1) = e1
% 231.54/42.72  | | | | | | | | | 
% 231.54/42.72  | | | | | | | | | ALPHA: (66) implies:
% 231.54/42.72  | | | | | | | | |   (67)  all_57_14 = e1
% 231.54/42.72  | | | | | | | | | 
% 231.54/42.72  | | | | | | | | | REF_CLOSE: (1), (2), (5), (6), (7), (11), (12), (17), (18),
% 231.54/42.72  | | | | | | | | |            (20), (21), (23), (24), (25), (26), (27), (34),
% 231.54/42.72  | | | | | | | | |            (44), (49), (67) are inconsistent by sub-proof
% 231.54/42.72  | | | | | | | | |            #1528.
% 231.54/42.72  | | | | | | | | | 
% 231.54/42.72  | | | | | | | | End of split
% 231.54/42.72  | | | | | | | | 
% 231.54/42.72  | | | | | | | End of split
% 231.54/42.72  | | | | | | | 
% 231.54/42.72  | | | | | | End of split
% 231.54/42.72  | | | | | | 
% 231.54/42.72  | | | | | Case 2:
% 231.54/42.72  | | | | | | 
% 231.54/42.72  | | | | | |   (68)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0,
% 231.54/42.72  | | | | | |             e3) = e2)
% 231.54/42.72  | | | | | | 
% 231.54/42.72  | | | | | | BETA: splitting (68) gives:
% 231.54/42.72  | | | | | | 
% 231.54/42.72  | | | | | | Case 1:
% 231.54/42.72  | | | | | | | 
% 231.54/42.72  | | | | | | |   (69)  all_57_6 = e2 & op(e1, e3) = e2
% 231.54/42.72  | | | | | | | 
% 231.54/42.72  | | | | | | | ALPHA: (69) implies:
% 231.54/42.72  | | | | | | |   (70)  all_57_6 = e2
% 231.54/42.72  | | | | | | | 
% 231.54/42.72  | | | | | | | REF_CLOSE: (20), (39), (70) are inconsistent by sub-proof #1846.
% 231.54/42.72  | | | | | | | 
% 231.54/42.72  | | | | | | Case 2:
% 231.54/42.72  | | | | | | | 
% 231.54/42.72  | | | | | | |   (71)  all_57_12 = e2 & op(e0, e3) = e2
% 231.54/42.72  | | | | | | | 
% 231.54/42.72  | | | | | | | ALPHA: (71) implies:
% 231.54/42.72  | | | | | | |   (72)  all_57_12 = e2
% 231.54/42.72  | | | | | | | 
% 231.54/42.72  | | | | | | | REF_CLOSE: (2), (20), (72) are inconsistent by sub-proof #2385.
% 231.54/42.72  | | | | | | | 
% 231.54/42.72  | | | | | | End of split
% 231.54/42.72  | | | | | | 
% 231.54/42.72  | | | | | End of split
% 231.54/42.72  | | | | | 
% 231.54/42.72  | | | | Case 2:
% 231.54/42.72  | | | | | 
% 231.54/42.72  | | | | |   (73)  all_57_11 = e2 & op(e1, e0) = e2
% 231.54/42.72  | | | | | 
% 231.54/42.72  | | | | | ALPHA: (73) implies:
% 231.54/42.72  | | | | |   (74)  all_57_11 = e2
% 231.54/42.72  | | | | | 
% 231.54/42.72  | | | | | BETA: splitting (31) gives:
% 231.54/42.72  | | | | | 
% 231.54/42.72  | | | | | Case 1:
% 231.54/42.72  | | | | | | 
% 231.54/42.72  | | | | | |   (75)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2,
% 231.54/42.72  | | | | | |             e0) = e1)
% 231.54/42.72  | | | | | | 
% 231.54/42.72  | | | | | | BETA: splitting (75) gives:
% 231.54/42.72  | | | | | | 
% 231.54/42.72  | | | | | | Case 1:
% 231.54/42.72  | | | | | | | 
% 231.54/42.72  | | | | | | |   (76)  all_57_9 = e1 & op(e3, e0) = e1
% 231.54/42.72  | | | | | | | 
% 231.54/42.72  | | | | | | | ALPHA: (76) implies:
% 231.54/42.72  | | | | | | |   (77)  all_57_9 = e1
% 231.54/42.72  | | | | | | | 
% 231.54/42.72  | | | | | | | REF_CLOSE: (19), (21), (77) are inconsistent by sub-proof #2479.
% 231.54/42.72  | | | | | | | 
% 231.54/42.72  | | | | | | Case 2:
% 231.54/42.72  | | | | | | | 
% 231.54/42.72  | | | | | | |   (78)  all_57_10 = e1 & op(e2, e0) = e1
% 231.54/42.72  | | | | | | | 
% 231.54/42.72  | | | | | | | ALPHA: (78) implies:
% 231.54/42.72  | | | | | | |   (79)  all_57_10 = e1
% 231.54/42.72  | | | | | | | 
% 231.54/42.72  | | | | | | | BETA: splitting (4) gives:
% 231.54/42.72  | | | | | | | 
% 231.54/42.72  | | | | | | | Case 1:
% 231.54/42.72  | | | | | | | | 
% 231.54/42.72  | | | | | | | |   (80)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 &
% 231.54/42.72  | | | | | | | |           op(e2, e3) = e1)
% 231.54/42.72  | | | | | | | | 
% 231.54/42.72  | | | | | | | | BETA: splitting (80) gives:
% 231.54/42.72  | | | | | | | | 
% 231.54/42.72  | | | | | | | | Case 1:
% 231.54/42.72  | | | | | | | | | 
% 231.54/42.72  | | | | | | | | |   (81)  all_57_0 = e1 & op(e3, e3) = e1
% 231.54/42.72  | | | | | | | | | 
% 231.54/42.72  | | | | | | | | | ALPHA: (81) implies:
% 231.54/42.72  | | | | | | | | |   (82)  op(e3, e3) = e1
% 231.54/42.72  | | | | | | | | | 
% 231.54/42.72  | | | | | | | | | REF_CLOSE: (6), (7), (15), (82) are inconsistent by sub-proof
% 231.54/42.72  | | | | | | | | |            #2495.
% 231.54/42.72  | | | | | | | | | 
% 231.54/42.72  | | | | | | | | Case 2:
% 231.54/42.72  | | | | | | | | | 
% 231.54/42.72  | | | | | | | | |   (83)  all_57_2 = e1 & op(e2, e3) = e1
% 231.54/42.72  | | | | | | | | | 
% 231.54/42.72  | | | | | | | | | ALPHA: (83) implies:
% 231.54/42.72  | | | | | | | | |   (84)  all_57_2 = e1
% 231.54/42.72  | | | | | | | | | 
% 231.54/42.72  | | | | | | | | | BETA: splitting (29) gives:
% 231.54/42.72  | | | | | | | | | 
% 231.54/42.72  | | | | | | | | | Case 1:
% 231.54/42.72  | | | | | | | | | | 
% 231.54/42.72  | | | | | | | | | |   (85)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 &
% 231.54/42.72  | | | | | | | | | |           op(e2, e3) = e2)
% 231.54/42.72  | | | | | | | | | | 
% 231.54/42.72  | | | | | | | | | | REF_CLOSE: (7), (12), (15), (27), (84), (85) are inconsistent
% 231.54/42.72  | | | | | | | | | |            by sub-proof #1526.
% 231.54/42.72  | | | | | | | | | | 
% 231.54/42.72  | | | | | | | | | Case 2:
% 231.54/42.72  | | | | | | | | | | 
% 231.54/42.72  | | | | | | | | | |   (86)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2
% 231.54/42.72  | | | | | | | | | |           & op(e0, e3) = e2)
% 231.54/42.72  | | | | | | | | | | 
% 231.54/42.72  | | | | | | | | | | BETA: splitting (86) gives:
% 231.54/42.72  | | | | | | | | | | 
% 231.54/42.72  | | | | | | | | | | Case 1:
% 231.54/42.72  | | | | | | | | | | | 
% 231.54/42.72  | | | | | | | | | | |   (87)  all_57_6 = e2 & op(e1, e3) = e2
% 231.54/42.72  | | | | | | | | | | | 
% 231.54/42.72  | | | | | | | | | | | ALPHA: (87) implies:
% 231.54/42.72  | | | | | | | | | | |   (88)  all_57_6 = e2
% 231.54/42.72  | | | | | | | | | | | 
% 231.54/42.72  | | | | | | | | | | | REF_CLOSE: (1), (2), (4), (6), (7), (11), (12), (15), (18),
% 231.54/42.72  | | | | | | | | | | |            (20), (21), (26), (27), (79), (88) are
% 231.54/42.72  | | | | | | | | | | |            inconsistent by sub-proof #1522.
% 231.54/42.72  | | | | | | | | | | | 
% 231.54/42.72  | | | | | | | | | | Case 2:
% 231.54/42.72  | | | | | | | | | | | 
% 231.54/42.72  | | | | | | | | | | |   (89)  all_57_12 = e2 & op(e0, e3) = e2
% 231.54/42.72  | | | | | | | | | | | 
% 231.54/42.72  | | | | | | | | | | | ALPHA: (89) implies:
% 231.54/42.72  | | | | | | | | | | |   (90)  all_57_12 = e2
% 231.54/42.72  | | | | | | | | | | | 
% 231.54/42.72  | | | | | | | | | | | COMBINE_EQS: (2), (90) imply:
% 231.54/42.72  | | | | | | | | | | |   (91)  e2 = e0
% 231.54/42.72  | | | | | | | | | | | 
% 231.54/42.72  | | | | | | | | | | | SIMP: (91) implies:
% 231.54/42.72  | | | | | | | | | | |   (92)  e2 = e0
% 231.54/42.72  | | | | | | | | | | | 
% 231.54/42.72  | | | | | | | | | | | COMBINE_EQS: (74), (92) imply:
% 231.54/42.72  | | | | | | | | | | |   (93)  all_57_11 = e0
% 231.54/42.72  | | | | | | | | | | | 
% 231.54/42.72  | | | | | | | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (9), (10), (11),
% 231.54/42.72  | | | | | | | | | | |            (12), (13), (14), (15), (17), (18), (20), (21),
% 231.54/42.72  | | | | | | | | | | |            (23), (24), (25), (26), (27), (28), (29), (31),
% 231.54/42.72  | | | | | | | | | | |            (32), (34), (35), (93) are inconsistent by
% 231.54/42.72  | | | | | | | | | | |            sub-proof #1507.
% 231.54/42.72  | | | | | | | | | | | 
% 231.54/42.72  | | | | | | | | | | End of split
% 231.54/42.72  | | | | | | | | | | 
% 231.54/42.72  | | | | | | | | | End of split
% 231.54/42.72  | | | | | | | | | 
% 231.54/42.72  | | | | | | | | End of split
% 231.54/42.72  | | | | | | | | 
% 231.54/42.72  | | | | | | | Case 2:
% 231.54/42.72  | | | | | | | | 
% 231.54/42.72  | | | | | | | |   (94)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 &
% 231.54/42.72  | | | | | | | |           op(e0, e3) = e1)
% 231.54/42.72  | | | | | | | | 
% 231.54/42.72  | | | | | | | | BETA: splitting (94) gives:
% 231.54/42.72  | | | | | | | | 
% 231.54/42.72  | | | | | | | | Case 1:
% 231.54/42.72  | | | | | | | | | 
% 231.54/42.73  | | | | | | | | |   (95)  all_57_6 = e1 & op(e1, e3) = e1
% 231.54/42.73  | | | | | | | | | 
% 231.54/42.73  | | | | | | | | | ALPHA: (95) implies:
% 231.54/42.73  | | | | | | | | |   (96)  all_57_6 = e1
% 231.54/42.73  | | | | | | | | | 
% 231.54/42.73  | | | | | | | | | COMBINE_EQS: (39), (96) imply:
% 231.54/42.73  | | | | | | | | |   (97)  e1 = e0
% 231.54/42.73  | | | | | | | | | 
% 231.54/42.73  | | | | | | | | | REF_CLOSE: (1), (6), (11), (12), (18), (20), (21), (26), (27),
% 231.54/42.73  | | | | | | | | |            (79), (97) are inconsistent by sub-proof #1506.
% 231.54/42.73  | | | | | | | | | 
% 231.54/42.73  | | | | | | | | Case 2:
% 231.54/42.73  | | | | | | | | | 
% 231.54/42.73  | | | | | | | | |   (98)  all_57_12 = e1 & op(e0, e3) = e1
% 231.54/42.73  | | | | | | | | | 
% 231.54/42.73  | | | | | | | | | ALPHA: (98) implies:
% 231.54/42.73  | | | | | | | | |   (99)  all_57_12 = e1
% 231.54/42.73  | | | | | | | | | 
% 231.54/42.73  | | | | | | | | | COMBINE_EQS: (2), (99) imply:
% 231.54/42.73  | | | | | | | | |   (100)  e1 = e0
% 231.54/42.73  | | | | | | | | | 
% 231.54/42.73  | | | | | | | | | REF_CLOSE: (1), (6), (11), (12), (18), (20), (21), (26), (27),
% 231.54/42.73  | | | | | | | | |            (79), (100) are inconsistent by sub-proof #1506.
% 231.54/42.73  | | | | | | | | | 
% 231.54/42.73  | | | | | | | | End of split
% 231.54/42.73  | | | | | | | | 
% 231.54/42.73  | | | | | | | End of split
% 231.54/42.73  | | | | | | | 
% 231.54/42.73  | | | | | | End of split
% 231.54/42.73  | | | | | | 
% 231.54/42.73  | | | | | Case 2:
% 231.54/42.73  | | | | | | 
% 231.54/42.73  | | | | | |   (101)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 &
% 231.54/42.73  | | | | | |            op(e0, e0) = e1)
% 231.54/42.73  | | | | | | 
% 231.54/42.73  | | | | | | BETA: splitting (101) gives:
% 231.54/42.73  | | | | | | 
% 231.54/42.73  | | | | | | Case 1:
% 231.54/42.73  | | | | | | | 
% 231.54/42.73  | | | | | | |   (102)  all_57_11 = e1 & op(e1, e0) = e1
% 231.54/42.73  | | | | | | | 
% 231.54/42.73  | | | | | | | REF_CLOSE: (27), (74), (102) are inconsistent by sub-proof #1726.
% 231.54/42.73  | | | | | | | 
% 231.54/42.73  | | | | | | Case 2:
% 231.54/42.73  | | | | | | | 
% 231.54/42.73  | | | | | | |   (103)  all_57_15 = e1 & op(e0, e0) = e1
% 231.54/42.73  | | | | | | | 
% 231.54/42.73  | | | | | | | REF_CLOSE: (6), (17), (103) are inconsistent by sub-proof #2325.
% 231.54/42.73  | | | | | | | 
% 231.54/42.73  | | | | | | End of split
% 231.54/42.73  | | | | | | 
% 231.54/42.73  | | | | | End of split
% 231.54/42.73  | | | | | 
% 231.54/42.73  | | | | End of split
% 231.54/42.73  | | | | 
% 231.54/42.73  | | | End of split
% 231.54/42.73  | | | 
% 231.54/42.73  | | Case 2:
% 231.54/42.73  | | | 
% 231.54/42.73  | | | 
% 231.54/42.73  | | | GROUND_INST: instantiating (7) with all_52_7, e0, e0, e3, simplifying with
% 231.54/42.73  | | |              (16), (33) gives:
% 231.54/42.73  | | |   (104)  all_52_7 = e0
% 231.54/42.73  | | | 
% 231.54/42.73  | | | REF_CLOSE: (3), (7), (8), (22), (104) are inconsistent by sub-proof #1505.
% 231.54/42.73  | | | 
% 231.54/42.73  | | End of split
% 231.54/42.73  | | 
% 231.54/42.73  | End of split
% 231.54/42.73  | 
% 231.54/42.73  End of proof
% 231.54/42.73  
% 231.54/42.73  Sub-proof #1505 shows that the following formulas are inconsistent:
% 231.54/42.73  ----------------------------------------------------------------
% 231.54/42.73    (1)   ~ (all_52_7 = e3)
% 231.54/42.73    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.73           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.73    (3)  op(all_52_7, all_52_7) = e0
% 231.54/42.73    (4)  op(e0, e0) = e3
% 231.54/42.73    (5)  all_52_7 = e0
% 231.54/42.73  
% 231.54/42.73  Begin of proof
% 231.54/42.73  | 
% 231.54/42.73  | REDUCE: (1), (5) imply:
% 231.54/42.73  |   (6)   ~ (e3 = e0)
% 231.54/42.73  | 
% 231.54/42.73  | SIMP: (6) implies:
% 231.54/42.73  |   (7)   ~ (e3 = e0)
% 231.54/42.73  | 
% 231.54/42.73  | REDUCE: (3), (5) imply:
% 231.54/42.73  |   (8)  op(e0, e0) = e0
% 231.54/42.73  | 
% 231.54/42.73  | REF_CLOSE: (2), (4), (7), (8) are inconsistent by sub-proof #2304.
% 231.54/42.73  | 
% 231.54/42.73  End of proof
% 231.54/42.73  
% 231.54/42.73  Sub-proof #1506 shows that the following formulas are inconsistent:
% 231.54/42.73  ----------------------------------------------------------------
% 231.54/42.73    (1)  e1 = e0
% 231.54/42.73    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.73         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.54/42.73    (3)   ~ (e3 = e1)
% 231.54/42.73    (4)  all_57_10 = e1
% 231.54/42.73    (5)  all_57_3 = e0
% 231.54/42.73    (6)   ~ (e3 = e2)
% 231.54/42.73    (7)  all_57_5 = e3
% 231.54/42.73    (8)   ~ (e2 = e0)
% 231.54/42.73    (9)   ~ (e1 = e0)
% 231.54/42.73    (10)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.73          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.54/42.73    (11)   ~ (e2 = e1)
% 231.54/42.73  
% 231.54/42.73  Begin of proof
% 231.54/42.73  | 
% 231.54/42.73  | SIMP: (1) implies:
% 231.54/42.73  |   (12)  e1 = e0
% 231.54/42.73  | 
% 231.54/42.73  | COMBINE_EQS: (4), (12) imply:
% 231.54/42.73  |   (13)  all_57_10 = e0
% 231.54/42.73  | 
% 231.54/42.73  | REF_CLOSE: (2), (3), (5), (6), (7), (8), (9), (10), (11), (13) are
% 231.54/42.73  |            inconsistent by sub-proof #1518.
% 231.54/42.73  | 
% 231.54/42.73  End of proof
% 231.54/42.73  
% 231.54/42.73  Sub-proof #1507 shows that the following formulas are inconsistent:
% 231.54/42.73  ----------------------------------------------------------------
% 231.54/42.73    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.73         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.54/42.73    (2)  all_57_12 = e0
% 231.54/42.73    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.54/42.73         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.54/42.73    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.73         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.54/42.73    (5)   ~ (e3 = e1)
% 231.54/42.73    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.73           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.73    (7)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.54/42.73         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.54/42.73    (8)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.54/42.73         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.54/42.73    (9)  all_57_3 = e0
% 231.54/42.73    (10)   ~ (e3 = e2)
% 231.54/42.73    (11)   ~ (e3 = e0)
% 231.54/42.73    (12)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.54/42.73          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.54/42.73    (13)  op(e3, e3) = e3
% 231.54/42.73    (14)  all_57_15 = e3
% 231.54/42.73    (15)  all_57_5 = e3
% 231.54/42.73    (16)  all_57_11 = e0
% 231.54/42.73    (17)   ~ (e2 = e0)
% 231.54/42.73    (18)   ~ (e1 = e0)
% 231.54/42.73    (19)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.54/42.73          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.54/42.73            e2)
% 231.54/42.73    (20)  op(e1, e1) = e0
% 231.54/42.73    (21)  all_57_7 = e3
% 231.54/42.73    (22)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.73          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.54/42.73    (23)   ~ (e2 = e1)
% 231.54/42.73    (24)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.54/42.73          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.54/42.73    (25)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.54/42.73          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.54/42.73    (26)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.54/42.73          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.54/42.73    (27)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 231.54/42.73          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 231.54/42.73    (28)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.73          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.54/42.73    (29)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 231.54/42.73          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 231.54/42.73  
% 231.54/42.73  Begin of proof
% 231.54/42.73  | 
% 231.54/42.73  | BETA: splitting (29) gives:
% 231.54/42.73  | 
% 231.54/42.73  | Case 1:
% 231.54/42.73  | | 
% 231.54/42.73  | |   (30)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) =
% 231.54/42.73  | |           e2)
% 231.54/42.73  | | 
% 231.54/42.73  | | BETA: splitting (30) gives:
% 231.54/42.73  | | 
% 231.54/42.73  | | Case 1:
% 231.54/42.73  | | | 
% 231.54/42.73  | | |   (31)  all_57_6 = e2 & op(e1, e3) = e2
% 231.54/42.73  | | | 
% 231.54/42.73  | | | ALPHA: (31) implies:
% 231.54/42.73  | | |   (32)  all_57_6 = e2
% 231.54/42.73  | | | 
% 231.54/42.73  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 231.54/42.73  | | |            (14), (15), (16), (17), (18), (20), (21), (22), (23), (26),
% 231.54/42.73  | | |            (27), (28), (32) are inconsistent by sub-proof #1510.
% 231.54/42.73  | | | 
% 231.54/42.73  | | Case 2:
% 231.54/42.73  | | | 
% 231.54/42.73  | | |   (33)  all_57_7 = e2 & op(e1, e2) = e2
% 231.54/42.73  | | | 
% 231.54/42.73  | | | REF_CLOSE: (10), (21), (33) are inconsistent by sub-proof #2092.
% 231.54/42.73  | | | 
% 231.54/42.73  | | End of split
% 231.54/42.73  | | 
% 231.54/42.73  | Case 2:
% 231.54/42.73  | | 
% 231.54/42.73  | |   (34)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) =
% 231.54/42.73  | |           e2)
% 231.54/42.73  | | 
% 231.54/42.73  | | BETA: splitting (34) gives:
% 231.54/42.73  | | 
% 231.54/42.73  | | Case 1:
% 231.54/42.73  | | | 
% 231.54/42.73  | | |   (35)  all_57_8 = e2 & op(e1, e1) = e2
% 231.54/42.73  | | | 
% 231.54/42.73  | | | ALPHA: (35) implies:
% 231.54/42.73  | | |   (36)  all_57_8 = e2
% 231.54/42.73  | | |   (37)  op(e1, e1) = e2
% 231.54/42.73  | | | 
% 231.54/42.73  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 231.54/42.73  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 231.54/42.73  | | |            (23), (24), (25), (26), (27), (28), (36), (37) are inconsistent
% 231.54/42.73  | | |            by sub-proof #1508.
% 231.54/42.73  | | | 
% 231.54/42.73  | | Case 2:
% 231.54/42.73  | | | 
% 231.54/42.73  | | |   (38)  all_57_11 = e2 & op(e1, e0) = e2
% 231.54/42.73  | | | 
% 231.54/42.73  | | | ALPHA: (38) implies:
% 231.54/42.73  | | |   (39)  all_57_11 = e2
% 231.54/42.73  | | | 
% 231.54/42.73  | | | REF_CLOSE: (16), (17), (39) are inconsistent by sub-proof #1949.
% 231.54/42.73  | | | 
% 231.54/42.73  | | End of split
% 231.54/42.73  | | 
% 231.54/42.73  | End of split
% 231.54/42.73  | 
% 231.54/42.73  End of proof
% 231.54/42.73  
% 231.54/42.73  Sub-proof #1508 shows that the following formulas are inconsistent:
% 231.54/42.73  ----------------------------------------------------------------
% 231.54/42.73    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.73         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.54/42.73    (2)  all_57_12 = e0
% 231.54/42.73    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.54/42.73         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.54/42.73    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.73         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.54/42.73    (5)   ~ (e3 = e1)
% 231.54/42.73    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.73           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.73    (7)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.54/42.73         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.54/42.73    (8)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.54/42.73         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.54/42.73    (9)  all_57_3 = e0
% 231.54/42.73    (10)   ~ (e3 = e2)
% 231.54/42.73    (11)   ~ (e3 = e0)
% 231.54/42.73    (12)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.54/42.73          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.54/42.73    (13)  op(e3, e3) = e3
% 231.54/42.73    (14)  all_57_15 = e3
% 231.54/42.73    (15)  all_57_5 = e3
% 231.54/42.73    (16)  all_57_11 = e0
% 231.54/42.73    (17)   ~ (e2 = e0)
% 231.54/42.73    (18)   ~ (e1 = e0)
% 231.54/42.73    (19)  all_57_8 = e2
% 231.54/42.73    (20)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.54/42.73          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.54/42.73            e2)
% 231.54/42.73    (21)  op(e1, e1) = e0
% 231.54/42.73    (22)  op(e1, e1) = e2
% 231.54/42.73    (23)  all_57_7 = e3
% 231.54/42.73    (24)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.73          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.54/42.73    (25)   ~ (e2 = e1)
% 231.54/42.73    (26)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.54/42.73          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.54/42.73    (27)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.54/42.73          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.54/42.73    (28)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.54/42.73          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.54/42.73    (29)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 231.54/42.73          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 231.54/42.73    (30)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.73          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.54/42.73  
% 231.54/42.73  Begin of proof
% 231.54/42.73  | 
% 231.54/42.73  | BETA: splitting (27) gives:
% 231.54/42.73  | 
% 231.54/42.73  | Case 1:
% 231.54/42.73  | | 
% 231.54/42.73  | |   (31)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) =
% 231.54/42.73  | |           e2)
% 231.54/42.73  | | 
% 231.54/42.73  | | BETA: splitting (31) gives:
% 231.54/42.73  | | 
% 231.54/42.73  | | Case 1:
% 231.54/42.73  | | | 
% 231.54/42.73  | | |   (32)  all_57_0 = e2 & op(e3, e3) = e2
% 231.54/42.73  | | | 
% 231.54/42.73  | | | ALPHA: (32) implies:
% 231.54/42.73  | | |   (33)  op(e3, e3) = e2
% 231.54/42.73  | | | 
% 231.54/42.73  | | | REF_CLOSE: (6), (10), (13), (33) are inconsistent by sub-proof #2490.
% 231.54/42.73  | | | 
% 231.54/42.73  | | Case 2:
% 231.54/42.73  | | | 
% 231.54/42.73  | | |   (34)  all_57_2 = e2 & op(e2, e3) = e2
% 231.54/42.73  | | | 
% 231.54/42.73  | | | ALPHA: (34) implies:
% 231.54/42.73  | | |   (35)  all_57_2 = e2
% 231.54/42.73  | | | 
% 231.54/42.73  | | | BETA: splitting (8) gives:
% 231.54/42.73  | | | 
% 231.54/42.73  | | | Case 1:
% 231.54/42.73  | | | | 
% 231.54/42.73  | | | |   (36)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2)
% 231.54/42.73  | | | |           = e0)
% 231.54/42.73  | | | | 
% 231.54/42.73  | | | | REF_CLOSE: (4), (5), (6), (9), (10), (11), (13), (17), (18), (23), (25),
% 231.54/42.73  | | | |            (30), (36) are inconsistent by sub-proof #2097.
% 231.54/42.73  | | | | 
% 231.54/42.73  | | | Case 2:
% 231.54/42.73  | | | | 
% 231.54/42.73  | | | |   (37)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0)
% 231.54/42.73  | | | |           = e0)
% 231.54/42.73  | | | | 
% 231.54/42.73  | | | | BETA: splitting (37) gives:
% 231.54/42.73  | | | | 
% 231.54/42.73  | | | | Case 1:
% 231.54/42.73  | | | | | 
% 231.54/42.73  | | | | |   (38)  all_57_4 = e0 & op(e3, e1) = e0
% 231.54/42.73  | | | | | 
% 231.54/42.73  | | | | | ALPHA: (38) implies:
% 231.54/42.73  | | | | |   (39)  all_57_4 = e0
% 231.54/42.73  | | | | | 
% 231.54/42.73  | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (9), (10), (12), (14), (15), (17),
% 231.54/42.73  | | | | |            (18), (19), (20), (21), (22), (23), (24), (25), (30), (35),
% 231.54/42.73  | | | | |            (39) are inconsistent by sub-proof #1527.
% 231.54/42.73  | | | | | 
% 231.54/42.73  | | | | Case 2:
% 231.54/42.73  | | | | | 
% 231.54/42.73  | | | | |   (40)  all_57_9 = e0 & op(e3, e0) = e0
% 231.54/42.73  | | | | | 
% 231.54/42.73  | | | | | ALPHA: (40) implies:
% 231.54/42.73  | | | | |   (41)  all_57_9 = e0
% 231.54/42.73  | | | | | 
% 231.54/42.73  | | | | | BETA: splitting (28) gives:
% 231.54/42.73  | | | | | 
% 231.54/42.73  | | | | | Case 1:
% 231.54/42.73  | | | | | | 
% 231.54/42.73  | | | | | |   (42)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2,
% 231.54/42.73  | | | | | |             e0) = e1)
% 231.54/42.73  | | | | | | 
% 231.54/42.73  | | | | | | BETA: splitting (42) gives:
% 231.54/42.73  | | | | | | 
% 231.54/42.73  | | | | | | Case 1:
% 231.54/42.73  | | | | | | | 
% 231.54/42.73  | | | | | | |   (43)  all_57_9 = e1 & op(e3, e0) = e1
% 231.54/42.73  | | | | | | | 
% 231.54/42.73  | | | | | | | ALPHA: (43) implies:
% 231.54/42.73  | | | | | | |   (44)  all_57_9 = e1
% 231.54/42.73  | | | | | | | 
% 231.54/42.73  | | | | | | | REF_CLOSE: (18), (41), (44) are inconsistent by sub-proof #2479.
% 231.54/42.73  | | | | | | | 
% 231.54/42.73  | | | | | | Case 2:
% 231.54/42.73  | | | | | | | 
% 231.54/42.73  | | | | | | |   (45)  all_57_10 = e1 & op(e2, e0) = e1
% 231.54/42.73  | | | | | | | 
% 231.54/42.73  | | | | | | | ALPHA: (45) implies:
% 231.54/42.73  | | | | | | |   (46)  all_57_10 = e1
% 231.54/42.73  | | | | | | | 
% 231.54/42.73  | | | | | | | REF_CLOSE: (9), (10), (14), (15), (16), (17), (24), (25), (26),
% 231.54/42.73  | | | | | | |            (35), (41), (46) are inconsistent by sub-proof #1509.
% 231.54/42.73  | | | | | | | 
% 231.54/42.73  | | | | | | End of split
% 231.54/42.73  | | | | | | 
% 231.54/42.73  | | | | | Case 2:
% 231.54/42.73  | | | | | | 
% 231.54/42.73  | | | | | |   (47)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 &
% 231.54/42.73  | | | | | |           op(e0, e0) = e1)
% 231.54/42.73  | | | | | | 
% 231.54/42.73  | | | | | | REF_CLOSE: (5), (14), (16), (18), (47) are inconsistent by sub-proof
% 231.54/42.73  | | | | | |            #1512.
% 231.54/42.73  | | | | | | 
% 231.54/42.73  | | | | | End of split
% 231.54/42.73  | | | | | 
% 231.54/42.73  | | | | End of split
% 231.54/42.73  | | | | 
% 231.54/42.73  | | | End of split
% 231.54/42.73  | | | 
% 231.54/42.73  | | End of split
% 231.54/42.73  | | 
% 231.54/42.73  | Case 2:
% 231.54/42.73  | | 
% 231.54/42.73  | |   (48)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) =
% 231.54/42.73  | |           e2)
% 231.54/42.73  | | 
% 231.54/42.73  | | BETA: splitting (48) gives:
% 231.54/42.73  | | 
% 231.54/42.73  | | Case 1:
% 231.54/42.73  | | | 
% 231.54/42.73  | | |   (49)  all_57_6 = e2 & op(e1, e3) = e2
% 231.54/42.73  | | | 
% 231.54/42.73  | | | ALPHA: (49) implies:
% 231.54/42.73  | | |   (50)  all_57_6 = e2
% 231.54/42.73  | | | 
% 231.54/42.73  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 231.54/42.73  | | |            (14), (15), (16), (17), (18), (21), (23), (24), (25), (28),
% 231.54/42.73  | | |            (29), (30), (50) are inconsistent by sub-proof #1510.
% 231.54/42.73  | | | 
% 231.54/42.73  | | Case 2:
% 231.54/42.73  | | | 
% 231.54/42.73  | | |   (51)  all_57_12 = e2 & op(e0, e3) = e2
% 231.54/42.73  | | | 
% 231.54/42.73  | | | ALPHA: (51) implies:
% 231.54/42.73  | | |   (52)  all_57_12 = e2
% 231.54/42.73  | | | 
% 231.54/42.73  | | | REF_CLOSE: (2), (17), (52) are inconsistent by sub-proof #2385.
% 231.54/42.73  | | | 
% 231.54/42.73  | | End of split
% 231.54/42.73  | | 
% 231.54/42.73  | End of split
% 231.54/42.73  | 
% 231.54/42.73  End of proof
% 231.54/42.73  
% 231.54/42.73  Sub-proof #1509 shows that the following formulas are inconsistent:
% 231.54/42.73  ----------------------------------------------------------------
% 231.54/42.73    (1)  all_57_10 = e1
% 231.54/42.73    (2)  all_57_2 = e2
% 231.54/42.73    (3)  all_57_3 = e0
% 231.54/42.73    (4)   ~ (e3 = e2)
% 231.54/42.73    (5)  all_57_15 = e3
% 231.54/42.73    (6)  all_57_5 = e3
% 231.54/42.73    (7)  all_57_9 = e0
% 231.54/42.73    (8)  all_57_11 = e0
% 231.54/42.73    (9)   ~ (e2 = e0)
% 231.54/42.73    (10)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.73          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.54/42.73    (11)   ~ (e2 = e1)
% 231.54/42.73    (12)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.54/42.73          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.54/42.73  
% 231.54/42.73  Begin of proof
% 231.54/42.73  | 
% 231.54/42.73  | BETA: splitting (12) gives:
% 231.54/42.73  | 
% 231.54/42.73  | Case 1:
% 231.54/42.73  | | 
% 231.54/42.73  | |   (13)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 231.54/42.73  | |           e2)
% 231.54/42.73  | | 
% 231.54/42.73  | | BETA: splitting (13) gives:
% 231.54/42.73  | | 
% 231.54/42.73  | | Case 1:
% 231.54/42.73  | | | 
% 231.54/42.73  | | |   (14)  all_57_9 = e2 & op(e3, e0) = e2
% 231.54/42.73  | | | 
% 231.54/42.73  | | | ALPHA: (14) implies:
% 231.54/42.73  | | |   (15)  all_57_9 = e2
% 231.54/42.73  | | | 
% 231.54/42.73  | | | COMBINE_EQS: (7), (15) imply:
% 231.54/42.73  | | |   (16)  e2 = e0
% 231.54/42.73  | | | 
% 231.54/42.73  | | | REF_CLOSE: (1), (2), (3), (4), (6), (9), (10), (11), (16) are inconsistent
% 231.54/42.73  | | |            by sub-proof #1532.
% 231.54/42.73  | | | 
% 231.54/42.73  | | Case 2:
% 231.54/42.73  | | | 
% 231.54/42.73  | | |   (17)  all_57_10 = e2 & op(e2, e0) = e2
% 231.54/42.73  | | | 
% 231.54/42.73  | | | ALPHA: (17) implies:
% 231.54/42.73  | | |   (18)  all_57_10 = e2
% 231.54/42.73  | | | 
% 231.54/42.73  | | | REF_CLOSE: (1), (11), (18) are inconsistent by sub-proof #2144.
% 231.54/42.73  | | | 
% 231.54/42.73  | | End of split
% 231.54/42.73  | | 
% 231.54/42.73  | Case 2:
% 231.54/42.73  | | 
% 231.54/42.73  | |   (19)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.54/42.73  | |           e2)
% 231.54/42.73  | | 
% 231.54/42.73  | | BETA: splitting (19) gives:
% 231.54/42.73  | | 
% 231.54/42.73  | | Case 1:
% 231.54/42.73  | | | 
% 231.54/42.73  | | |   (20)  all_57_11 = e2 & op(e1, e0) = e2
% 231.54/42.73  | | | 
% 231.54/42.73  | | | ALPHA: (20) implies:
% 231.54/42.73  | | |   (21)  all_57_11 = e2
% 231.54/42.73  | | | 
% 231.54/42.73  | | | COMBINE_EQS: (8), (21) imply:
% 231.54/42.73  | | |   (22)  e2 = e0
% 231.54/42.73  | | | 
% 231.54/42.73  | | | REF_CLOSE: (1), (2), (3), (4), (6), (9), (10), (11), (22) are inconsistent
% 231.54/42.73  | | |            by sub-proof #1532.
% 231.54/42.73  | | | 
% 231.54/42.73  | | Case 2:
% 231.54/42.73  | | | 
% 231.54/42.73  | | |   (23)  all_57_15 = e2 & op(e0, e0) = e2
% 231.54/42.73  | | | 
% 231.54/42.73  | | | REF_CLOSE: (4), (5), (23) are inconsistent by sub-proof #2323.
% 231.54/42.73  | | | 
% 231.54/42.73  | | End of split
% 231.54/42.73  | | 
% 231.54/42.73  | End of split
% 231.54/42.73  | 
% 231.54/42.73  End of proof
% 231.54/42.73  
% 231.54/42.73  Sub-proof #1510 shows that the following formulas are inconsistent:
% 231.54/42.73  ----------------------------------------------------------------
% 231.54/42.73    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.73         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.54/42.73    (2)  all_57_12 = e0
% 231.54/42.73    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.54/42.73         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.54/42.73    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.73         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.54/42.73    (5)   ~ (e3 = e1)
% 231.54/42.73    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.73           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.73    (7)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.54/42.73         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.54/42.73    (8)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.54/42.73         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.54/42.73    (9)  all_57_3 = e0
% 231.54/42.73    (10)   ~ (e3 = e2)
% 231.54/42.73    (11)   ~ (e3 = e0)
% 231.54/42.73    (12)  op(e3, e3) = e3
% 231.54/42.73    (13)  all_57_15 = e3
% 231.54/42.73    (14)  all_57_5 = e3
% 231.54/42.73    (15)  all_57_6 = e2
% 231.54/42.73    (16)  all_57_11 = e0
% 231.54/42.73    (17)   ~ (e2 = e0)
% 231.54/42.73    (18)   ~ (e1 = e0)
% 231.54/42.73    (19)  op(e1, e1) = e0
% 231.54/42.73    (20)  all_57_7 = e3
% 231.54/42.73    (21)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.73          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.54/42.73    (22)   ~ (e2 = e1)
% 231.54/42.73    (23)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.54/42.73          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.54/42.73    (24)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 231.54/42.73          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 231.54/42.73    (25)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.73          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.54/42.73  
% 231.54/42.73  Begin of proof
% 231.54/42.73  | 
% 231.54/42.73  | BETA: splitting (24) gives:
% 231.54/42.73  | 
% 231.54/42.73  | Case 1:
% 231.54/42.73  | | 
% 231.54/42.73  | |   (26)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) =
% 231.54/42.73  | |           e1)
% 231.54/42.73  | | 
% 231.54/42.73  | | BETA: splitting (26) gives:
% 231.54/42.73  | | 
% 231.54/42.73  | | Case 1:
% 231.54/42.73  | | | 
% 231.54/42.73  | | |   (27)  all_57_6 = e1 & op(e1, e3) = e1
% 231.54/42.73  | | | 
% 231.54/42.73  | | | REF_CLOSE: (15), (22), (27) are inconsistent by sub-proof #2389.
% 231.54/42.73  | | | 
% 231.54/42.73  | | Case 2:
% 231.54/42.73  | | | 
% 231.54/42.73  | | |   (28)  all_57_7 = e1 & op(e1, e2) = e1
% 231.54/42.73  | | | 
% 231.54/42.73  | | | REF_CLOSE: (5), (20), (28) are inconsistent by sub-proof #2104.
% 231.54/42.73  | | | 
% 231.54/42.73  | | End of split
% 231.54/42.73  | | 
% 231.54/42.73  | Case 2:
% 231.54/42.73  | | 
% 231.54/42.73  | |   (29)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) =
% 231.54/42.73  | |           e1)
% 231.54/42.73  | | 
% 231.54/42.73  | | BETA: splitting (29) gives:
% 231.54/42.73  | | 
% 231.54/42.73  | | Case 1:
% 231.54/42.73  | | | 
% 231.54/42.73  | | |   (30)  all_57_8 = e1 & op(e1, e1) = e1
% 231.54/42.73  | | | 
% 231.54/42.73  | | | ALPHA: (30) implies:
% 231.54/42.73  | | |   (31)  op(e1, e1) = e1
% 231.54/42.73  | | | 
% 231.54/42.73  | | | BETA: splitting (8) gives:
% 231.54/42.73  | | | 
% 231.54/42.73  | | | Case 1:
% 231.54/42.73  | | | | 
% 231.54/42.73  | | | |   (32)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2)
% 231.54/42.73  | | | |           = e0)
% 231.54/42.73  | | | | 
% 231.54/42.73  | | | | REF_CLOSE: (4), (5), (6), (9), (10), (11), (12), (17), (18), (20), (22),
% 231.54/42.73  | | | |            (25), (32) are inconsistent by sub-proof #2097.
% 231.54/42.73  | | | | 
% 231.54/42.73  | | | Case 2:
% 231.54/42.73  | | | | 
% 231.54/42.73  | | | |   (33)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0)
% 231.54/42.73  | | | |           = e0)
% 231.54/42.73  | | | | 
% 231.54/42.73  | | | | BETA: splitting (33) gives:
% 231.54/42.73  | | | | 
% 231.54/42.73  | | | | Case 1:
% 231.54/42.73  | | | | | 
% 231.54/42.73  | | | | |   (34)  all_57_4 = e0 & op(e3, e1) = e0
% 231.54/42.73  | | | | | 
% 231.54/42.73  | | | | | ALPHA: (34) implies:
% 231.54/42.73  | | | | |   (35)  all_57_4 = e0
% 231.54/42.73  | | | | | 
% 231.54/42.73  | | | | | BETA: splitting (3) gives:
% 231.54/42.73  | | | | | 
% 231.54/42.73  | | | | | Case 1:
% 231.54/42.73  | | | | | | 
% 231.54/42.73  | | | | | |   (36)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2,
% 231.54/42.73  | | | | | |             e3) = e1)
% 231.54/42.73  | | | | | | 
% 231.54/42.73  | | | | | | BETA: splitting (36) gives:
% 231.54/42.73  | | | | | | 
% 231.54/42.73  | | | | | | Case 1:
% 231.54/42.73  | | | | | | | 
% 231.54/42.73  | | | | | | |   (37)  all_57_0 = e1 & op(e3, e3) = e1
% 231.54/42.73  | | | | | | | 
% 231.54/42.73  | | | | | | | ALPHA: (37) implies:
% 231.54/42.73  | | | | | | |   (38)  op(e3, e3) = e1
% 231.54/42.73  | | | | | | | 
% 231.54/42.73  | | | | | | | REF_CLOSE: (5), (6), (12), (38) are inconsistent by sub-proof
% 231.54/42.73  | | | | | | |            #2495.
% 231.54/42.73  | | | | | | | 
% 231.54/42.73  | | | | | | Case 2:
% 231.54/42.73  | | | | | | | 
% 231.54/42.73  | | | | | | |   (39)  all_57_2 = e1 & op(e2, e3) = e1
% 231.54/42.73  | | | | | | | 
% 231.54/42.73  | | | | | | | ALPHA: (39) implies:
% 231.54/42.73  | | | | | | |   (40)  all_57_2 = e1
% 231.54/42.73  | | | | | | | 
% 231.54/42.73  | | | | | | | BETA: splitting (21) gives:
% 231.54/42.73  | | | | | | | 
% 231.54/42.73  | | | | | | | Case 1:
% 231.54/42.73  | | | | | | | | 
% 231.54/42.73  | | | | | | | |   (41)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 &
% 231.54/42.73  | | | | | | | |           op(e2, e2) = e2)
% 231.54/42.73  | | | | | | | | 
% 231.54/42.73  | | | | | | | | REF_CLOSE: (9), (17), (22), (40), (41) are inconsistent by
% 231.54/42.73  | | | | | | | |            sub-proof #1521.
% 231.54/42.73  | | | | | | | | 
% 231.54/42.73  | | | | | | | Case 2:
% 231.54/42.73  | | | | | | | | 
% 231.54/42.73  | | | | | | | |   (42)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 &
% 231.54/42.73  | | | | | | | |           op(e2, e0) = e2)
% 231.54/42.73  | | | | | | | | 
% 231.54/42.73  | | | | | | | | BETA: splitting (42) gives:
% 231.54/42.73  | | | | | | | | 
% 231.54/42.73  | | | | | | | | Case 1:
% 231.54/42.73  | | | | | | | | | 
% 231.54/42.73  | | | | | | | | |   (43)  all_57_5 = e2 & op(e2, e1) = e2
% 231.54/42.73  | | | | | | | | | 
% 231.54/42.73  | | | | | | | | | REF_CLOSE: (10), (14), (43) are inconsistent by sub-proof
% 231.54/42.73  | | | | | | | | |            #2425.
% 231.54/42.73  | | | | | | | | | 
% 231.54/42.73  | | | | | | | | Case 2:
% 231.54/42.73  | | | | | | | | | 
% 231.54/42.73  | | | | | | | | |   (44)  all_57_10 = e2 & op(e2, e0) = e2
% 231.54/42.73  | | | | | | | | | 
% 231.54/42.73  | | | | | | | | | ALPHA: (44) implies:
% 231.54/42.73  | | | | | | | | |   (45)  all_57_10 = e2
% 231.54/42.73  | | | | | | | | | 
% 231.54/42.73  | | | | | | | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (9), (10), (12),
% 231.54/42.73  | | | | | | | | |            (13), (14), (15), (16), (17), (18), (19), (20),
% 231.54/42.73  | | | | | | | | |            (21), (22), (23), (25), (31), (35), (40), (45) are
% 231.54/42.73  | | | | | | | | |            inconsistent by sub-proof #1514.
% 231.54/42.73  | | | | | | | | | 
% 231.54/42.73  | | | | | | | | End of split
% 231.54/42.73  | | | | | | | | 
% 231.54/42.73  | | | | | | | End of split
% 231.54/42.73  | | | | | | | 
% 231.54/42.73  | | | | | | End of split
% 231.54/42.73  | | | | | | 
% 231.54/42.73  | | | | | Case 2:
% 231.54/42.73  | | | | | | 
% 231.54/42.73  | | | | | |   (46)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0,
% 231.54/42.73  | | | | | |             e3) = e1)
% 231.54/42.73  | | | | | | 
% 231.54/42.73  | | | | | | REF_CLOSE: (2), (15), (18), (22), (46) are inconsistent by sub-proof
% 231.54/42.73  | | | | | |            #1513.
% 231.54/42.73  | | | | | | 
% 231.54/42.73  | | | | | End of split
% 231.54/42.74  | | | | | 
% 231.54/42.74  | | | | Case 2:
% 231.54/42.74  | | | | | 
% 231.54/42.74  | | | | |   (47)  all_57_9 = e0 & op(e3, e0) = e0
% 231.54/42.74  | | | | | 
% 231.54/42.74  | | | | | ALPHA: (47) implies:
% 231.54/42.74  | | | | |   (48)  all_57_9 = e0
% 231.54/42.74  | | | | | 
% 231.54/42.74  | | | | | REF_CLOSE: (1), (2), (3), (5), (6), (9), (10), (12), (13), (14), (15),
% 231.54/42.74  | | | | |            (16), (17), (18), (21), (22), (23), (48) are inconsistent
% 231.54/42.74  | | | | |            by sub-proof #1511.
% 231.54/42.74  | | | | | 
% 231.54/42.74  | | | | End of split
% 231.54/42.74  | | | | 
% 231.54/42.74  | | | End of split
% 231.54/42.74  | | | 
% 231.54/42.74  | | Case 2:
% 231.54/42.74  | | | 
% 231.54/42.74  | | |   (49)  all_57_11 = e1 & op(e1, e0) = e1
% 231.54/42.74  | | | 
% 231.54/42.74  | | | ALPHA: (49) implies:
% 231.54/42.74  | | |   (50)  all_57_11 = e1
% 231.54/42.74  | | | 
% 231.54/42.74  | | | REF_CLOSE: (16), (18), (50) are inconsistent by sub-proof #1862.
% 231.54/42.74  | | | 
% 231.54/42.74  | | End of split
% 231.54/42.74  | | 
% 231.54/42.74  | End of split
% 231.54/42.74  | 
% 231.54/42.74  End of proof
% 231.54/42.74  
% 231.54/42.74  Sub-proof #1511 shows that the following formulas are inconsistent:
% 231.54/42.74  ----------------------------------------------------------------
% 231.54/42.74    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.74         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.54/42.74    (2)  all_57_12 = e0
% 231.54/42.74    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.54/42.74         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.54/42.74    (4)   ~ (e3 = e1)
% 231.54/42.74    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.74           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.74    (6)  all_57_3 = e0
% 231.54/42.74    (7)   ~ (e3 = e2)
% 231.54/42.74    (8)  op(e3, e3) = e3
% 231.54/42.74    (9)  all_57_15 = e3
% 231.54/42.74    (10)  all_57_5 = e3
% 231.54/42.74    (11)  all_57_6 = e2
% 231.54/42.74    (12)  all_57_9 = e0
% 231.54/42.74    (13)  all_57_11 = e0
% 231.54/42.74    (14)   ~ (e2 = e0)
% 231.54/42.74    (15)   ~ (e1 = e0)
% 231.54/42.74    (16)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.74          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.54/42.74    (17)   ~ (e2 = e1)
% 231.54/42.74    (18)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.54/42.74          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.54/42.74  
% 231.54/42.74  Begin of proof
% 231.54/42.74  | 
% 231.54/42.74  | BETA: splitting (18) gives:
% 231.54/42.74  | 
% 231.54/42.74  | Case 1:
% 231.54/42.74  | | 
% 231.54/42.74  | |   (19)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) =
% 231.54/42.74  | |           e1)
% 231.54/42.74  | | 
% 231.54/42.74  | | BETA: splitting (19) gives:
% 231.54/42.74  | | 
% 231.54/42.74  | | Case 1:
% 231.54/42.74  | | | 
% 231.54/42.74  | | |   (20)  all_57_9 = e1 & op(e3, e0) = e1
% 231.54/42.74  | | | 
% 231.54/42.74  | | | ALPHA: (20) implies:
% 231.54/42.74  | | |   (21)  all_57_9 = e1
% 231.54/42.74  | | | 
% 231.54/42.74  | | | REF_CLOSE: (12), (15), (21) are inconsistent by sub-proof #2479.
% 231.54/42.74  | | | 
% 231.54/42.74  | | Case 2:
% 231.54/42.74  | | | 
% 231.54/42.74  | | |   (22)  all_57_10 = e1 & op(e2, e0) = e1
% 231.54/42.74  | | | 
% 231.54/42.74  | | | ALPHA: (22) implies:
% 231.54/42.74  | | |   (23)  all_57_10 = e1
% 231.54/42.74  | | | 
% 231.54/42.74  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (14), (15),
% 231.54/42.74  | | |            (16), (17), (23) are inconsistent by sub-proof #1522.
% 231.54/42.74  | | | 
% 231.54/42.74  | | End of split
% 231.54/42.74  | | 
% 231.54/42.74  | Case 2:
% 231.54/42.74  | | 
% 231.54/42.74  | |   (24)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.54/42.74  | |           e1)
% 231.54/42.74  | | 
% 231.54/42.74  | | REF_CLOSE: (4), (9), (13), (15), (24) are inconsistent by sub-proof #1512.
% 231.54/42.74  | | 
% 231.54/42.74  | End of split
% 231.54/42.74  | 
% 231.54/42.74  End of proof
% 231.54/42.74  
% 231.54/42.74  Sub-proof #1512 shows that the following formulas are inconsistent:
% 231.54/42.74  ----------------------------------------------------------------
% 231.54/42.74    (1)   ~ (e3 = e1)
% 231.54/42.74    (2)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.54/42.74    (3)  all_57_15 = e3
% 231.54/42.74    (4)  all_57_11 = e0
% 231.54/42.74    (5)   ~ (e1 = e0)
% 231.54/42.74  
% 231.54/42.74  Begin of proof
% 231.54/42.74  | 
% 231.54/42.74  | BETA: splitting (2) gives:
% 231.54/42.74  | 
% 231.54/42.74  | Case 1:
% 231.54/42.74  | | 
% 231.54/42.74  | |   (6)  all_57_11 = e1 & op(e1, e0) = e1
% 231.54/42.74  | | 
% 231.54/42.74  | | ALPHA: (6) implies:
% 231.54/42.74  | |   (7)  all_57_11 = e1
% 231.54/42.74  | | 
% 231.54/42.74  | | REF_CLOSE: (4), (5), (7) are inconsistent by sub-proof #1862.
% 231.54/42.74  | | 
% 231.54/42.74  | Case 2:
% 231.54/42.74  | | 
% 231.54/42.74  | |   (8)  all_57_15 = e1 & op(e0, e0) = e1
% 231.54/42.74  | | 
% 231.54/42.74  | | REF_CLOSE: (1), (3), (8) are inconsistent by sub-proof #2325.
% 231.54/42.74  | | 
% 231.54/42.74  | End of split
% 231.54/42.74  | 
% 231.54/42.74  End of proof
% 231.54/42.74  
% 231.54/42.74  Sub-proof #1513 shows that the following formulas are inconsistent:
% 231.54/42.74  ----------------------------------------------------------------
% 231.54/42.74    (1)  all_57_12 = e0
% 231.54/42.74    (2)  all_57_6 = e2
% 231.54/42.74    (3)   ~ (e1 = e0)
% 231.54/42.74    (4)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.54/42.74    (5)   ~ (e2 = e1)
% 231.54/42.74  
% 231.54/42.74  Begin of proof
% 231.54/42.74  | 
% 231.54/42.74  | BETA: splitting (4) gives:
% 231.54/42.74  | 
% 231.54/42.74  | Case 1:
% 231.54/42.74  | | 
% 231.54/42.74  | |   (6)  all_57_6 = e1 & op(e1, e3) = e1
% 231.54/42.74  | | 
% 231.54/42.74  | | REF_CLOSE: (2), (5), (6) are inconsistent by sub-proof #2389.
% 231.54/42.74  | | 
% 231.54/42.74  | Case 2:
% 231.54/42.74  | | 
% 231.54/42.74  | |   (7)  all_57_12 = e1 & op(e0, e3) = e1
% 231.54/42.74  | | 
% 231.54/42.74  | | ALPHA: (7) implies:
% 231.54/42.74  | |   (8)  all_57_12 = e1
% 231.54/42.74  | | 
% 231.54/42.74  | | REF_CLOSE: (1), (3), (8) are inconsistent by sub-proof #2014.
% 231.54/42.74  | | 
% 231.54/42.74  | End of split
% 231.54/42.74  | 
% 231.54/42.74  End of proof
% 231.54/42.74  
% 231.54/42.74  Sub-proof #1514 shows that the following formulas are inconsistent:
% 231.54/42.74  ----------------------------------------------------------------
% 231.54/42.74    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.74         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.54/42.74    (2)  all_57_12 = e0
% 231.54/42.74    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.54/42.74         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.54/42.74    (4)   ~ (e3 = e1)
% 231.54/42.74    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.74           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.74    (6)  all_57_4 = e0
% 231.54/42.74    (7)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.54/42.74         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.54/42.74    (8)  all_57_3 = e0
% 231.54/42.74    (9)   ~ (e3 = e2)
% 231.54/42.74    (10)  op(e3, e3) = e3
% 231.54/42.74    (11)  all_57_15 = e3
% 231.54/42.74    (12)  all_57_10 = e2
% 231.54/42.74    (13)  all_57_5 = e3
% 231.54/42.74    (14)  all_57_6 = e2
% 231.54/42.74    (15)  all_57_11 = e0
% 231.54/42.74    (16)  op(e1, e1) = e1
% 231.54/42.74    (17)   ~ (e2 = e0)
% 231.54/42.74    (18)   ~ (e1 = e0)
% 231.54/42.74    (19)  all_57_2 = e1
% 231.54/42.74    (20)  op(e1, e1) = e0
% 231.54/42.74    (21)  all_57_7 = e3
% 231.54/42.74    (22)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.74          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.54/42.74    (23)   ~ (e2 = e1)
% 231.54/42.74    (24)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.54/42.74          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.54/42.74    (25)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.74          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.54/42.74  
% 231.54/42.74  Begin of proof
% 231.54/42.74  | 
% 231.54/42.74  | BETA: splitting (24) gives:
% 231.54/42.74  | 
% 231.54/42.74  | Case 1:
% 231.54/42.74  | | 
% 231.54/42.74  | |   (26)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) =
% 231.54/42.74  | |           e1)
% 231.54/42.74  | | 
% 231.54/42.74  | | BETA: splitting (26) gives:
% 231.54/42.74  | | 
% 231.54/42.74  | | Case 1:
% 231.54/42.74  | | | 
% 231.54/42.74  | | |   (27)  all_57_9 = e1 & op(e3, e0) = e1
% 231.54/42.74  | | | 
% 231.54/42.74  | | | ALPHA: (27) implies:
% 231.54/42.74  | | |   (28)  all_57_9 = e1
% 231.54/42.74  | | | 
% 231.54/42.74  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 231.54/42.74  | | |            (14), (16), (17), (18), (19), (20), (21), (22), (23), (25),
% 231.54/42.74  | | |            (28) are inconsistent by sub-proof #1516.
% 231.54/42.74  | | | 
% 231.54/42.74  | | Case 2:
% 231.54/42.74  | | | 
% 231.54/42.74  | | |   (29)  all_57_10 = e1 & op(e2, e0) = e1
% 231.54/42.74  | | | 
% 231.54/42.74  | | | ALPHA: (29) implies:
% 231.54/42.74  | | |   (30)  all_57_10 = e1
% 231.54/42.74  | | | 
% 231.54/42.74  | | | REF_CLOSE: (1), (2), (3), (4), (5), (8), (9), (10), (13), (14), (17),
% 231.54/42.74  | | |            (18), (22), (23), (30) are inconsistent by sub-proof #1522.
% 231.54/42.74  | | | 
% 231.54/42.74  | | End of split
% 231.54/42.74  | | 
% 231.54/42.74  | Case 2:
% 231.54/42.74  | | 
% 231.54/42.74  | |   (31)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.54/42.74  | |           e1)
% 231.54/42.74  | | 
% 231.54/42.74  | | BETA: splitting (31) gives:
% 231.54/42.74  | | 
% 231.54/42.74  | | Case 1:
% 231.54/42.74  | | | 
% 231.54/42.74  | | |   (32)  all_57_11 = e1 & op(e1, e0) = e1
% 231.54/42.74  | | | 
% 231.54/42.74  | | | REF_CLOSE: (1), (4), (8), (9), (13), (15), (17), (18), (19), (22), (23),
% 231.54/42.74  | | |            (32) are inconsistent by sub-proof #1515.
% 231.54/42.74  | | | 
% 231.54/42.74  | | Case 2:
% 231.54/42.74  | | | 
% 231.54/42.74  | | |   (33)  all_57_15 = e1 & op(e0, e0) = e1
% 231.54/42.74  | | | 
% 231.54/42.74  | | | REF_CLOSE: (4), (11), (33) are inconsistent by sub-proof #2325.
% 231.54/42.74  | | | 
% 231.54/42.74  | | End of split
% 231.54/42.74  | | 
% 231.54/42.74  | End of split
% 231.54/42.74  | 
% 231.54/42.74  End of proof
% 231.54/42.74  
% 231.54/42.74  Sub-proof #1515 shows that the following formulas are inconsistent:
% 231.54/42.74  ----------------------------------------------------------------
% 231.54/42.74    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.74         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.54/42.74    (2)   ~ (e3 = e1)
% 231.54/42.74    (3)  all_57_3 = e0
% 231.54/42.74    (4)   ~ (e3 = e2)
% 231.54/42.74    (5)  all_57_11 = e1 & op(e1, e0) = e1
% 231.54/42.74    (6)  all_57_5 = e3
% 231.54/42.74    (7)  all_57_11 = e0
% 231.54/42.74    (8)   ~ (e2 = e0)
% 231.54/42.74    (9)   ~ (e1 = e0)
% 231.54/42.74    (10)  all_57_2 = e1
% 231.54/42.74    (11)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.74          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.54/42.74    (12)   ~ (e2 = e1)
% 231.54/42.74  
% 231.54/42.74  Begin of proof
% 231.54/42.74  | 
% 231.54/42.74  | ALPHA: (5) implies:
% 231.54/42.74  |   (13)  all_57_11 = e1
% 231.54/42.74  | 
% 231.54/42.74  | COMBINE_EQS: (7), (13) imply:
% 231.54/42.74  |   (14)  e1 = e0
% 231.54/42.74  | 
% 231.54/42.74  | SIMP: (14) implies:
% 231.54/42.74  |   (15)  e1 = e0
% 231.54/42.74  | 
% 231.54/42.74  | COMBINE_EQS: (10), (15) imply:
% 231.54/42.74  |   (16)  all_57_2 = e0
% 231.54/42.74  | 
% 231.54/42.74  | REF_CLOSE: (1), (2), (3), (4), (6), (8), (9), (11), (12), (16) are
% 231.54/42.74  |            inconsistent by sub-proof #2253.
% 231.54/42.74  | 
% 231.54/42.74  End of proof
% 231.54/42.74  
% 231.54/42.74  Sub-proof #1516 shows that the following formulas are inconsistent:
% 231.54/42.74  ----------------------------------------------------------------
% 231.54/42.74    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.74         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.54/42.74    (2)  all_57_12 = e0
% 231.54/42.74    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.54/42.74         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.54/42.74    (4)   ~ (e3 = e1)
% 231.54/42.74    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.74           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.74    (6)  all_57_9 = e1
% 231.54/42.74    (7)  all_57_4 = e0
% 231.54/42.74    (8)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.54/42.74         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.54/42.74    (9)  all_57_3 = e0
% 231.54/42.74    (10)   ~ (e3 = e2)
% 231.54/42.74    (11)  op(e3, e3) = e3
% 231.54/42.74    (12)  all_57_10 = e2
% 231.54/42.74    (13)  all_57_5 = e3
% 231.54/42.74    (14)  all_57_6 = e2
% 231.54/42.74    (15)  op(e1, e1) = e1
% 231.54/42.74    (16)   ~ (e2 = e0)
% 231.54/42.74    (17)   ~ (e1 = e0)
% 231.54/42.74    (18)  all_57_2 = e1
% 231.54/42.74    (19)  op(e1, e1) = e0
% 231.54/42.74    (20)  all_57_7 = e3
% 231.54/42.74    (21)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.74          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.54/42.74    (22)   ~ (e2 = e1)
% 231.54/42.74    (23)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.74          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.54/42.74  
% 231.54/42.74  Begin of proof
% 231.54/42.74  | 
% 231.54/42.74  | BETA: splitting (8) gives:
% 231.54/42.74  | 
% 231.54/42.74  | Case 1:
% 231.54/42.74  | | 
% 231.54/42.74  | |   (24)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) =
% 231.54/42.74  | |           e2)
% 231.54/42.74  | | 
% 231.54/42.74  | | BETA: splitting (24) gives:
% 231.54/42.74  | | 
% 231.54/42.74  | | Case 1:
% 231.54/42.74  | | | 
% 231.54/42.74  | | |   (25)  all_57_0 = e2 & op(e3, e3) = e2
% 231.54/42.74  | | | 
% 231.54/42.74  | | | ALPHA: (25) implies:
% 231.54/42.74  | | |   (26)  op(e3, e3) = e2
% 231.54/42.74  | | | 
% 231.54/42.74  | | | REF_CLOSE: (5), (10), (11), (26) are inconsistent by sub-proof #2490.
% 231.54/42.74  | | | 
% 231.54/42.74  | | Case 2:
% 231.54/42.74  | | | 
% 231.54/42.74  | | |   (27)  all_57_1 = e2 & op(e3, e2) = e2
% 231.54/42.74  | | | 
% 231.54/42.74  | | | ALPHA: (27) implies:
% 231.54/42.74  | | |   (28)  all_57_1 = e2
% 231.54/42.74  | | | 
% 231.54/42.74  | | | REF_CLOSE: (1), (2), (3), (4), (5), (9), (10), (11), (12), (13), (14),
% 231.54/42.74  | | |            (15), (16), (17), (18), (19), (20), (21), (22), (23), (28) are
% 231.54/42.74  | | |            inconsistent by sub-proof #1519.
% 231.54/42.74  | | | 
% 231.54/42.74  | | End of split
% 231.54/42.74  | | 
% 231.54/42.74  | Case 2:
% 231.54/42.74  | | 
% 231.54/42.74  | |   (29)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) =
% 231.54/42.74  | |           e2)
% 231.54/42.74  | | 
% 231.54/42.74  | | BETA: splitting (29) gives:
% 231.54/42.74  | | 
% 231.54/42.74  | | Case 1:
% 231.54/42.74  | | | 
% 231.54/42.74  | | |   (30)  all_57_4 = e2 & op(e3, e1) = e2
% 231.54/42.74  | | | 
% 231.54/42.74  | | | ALPHA: (30) implies:
% 231.54/42.74  | | |   (31)  all_57_4 = e2
% 231.54/42.74  | | | 
% 231.54/42.74  | | | COMBINE_EQS: (7), (31) imply:
% 231.54/42.74  | | |   (32)  e2 = e0
% 231.54/42.74  | | | 
% 231.54/42.74  | | | REF_CLOSE: (1), (4), (9), (10), (12), (13), (16), (17), (21), (22), (32)
% 231.54/42.74  | | |            are inconsistent by sub-proof #1517.
% 231.54/42.74  | | | 
% 231.54/42.74  | | Case 2:
% 231.54/42.74  | | | 
% 231.54/42.74  | | |   (33)  all_57_9 = e2 & op(e3, e0) = e2
% 231.54/42.74  | | | 
% 231.54/42.74  | | | ALPHA: (33) implies:
% 231.54/42.74  | | |   (34)  all_57_9 = e2
% 231.54/42.74  | | | 
% 231.54/42.74  | | | COMBINE_EQS: (6), (34) imply:
% 231.54/42.74  | | |   (35)  e2 = e1
% 231.54/42.74  | | | 
% 231.54/42.74  | | | COMBINE_EQS: (12), (35) imply:
% 231.54/42.74  | | |   (36)  all_57_10 = e1
% 231.54/42.74  | | | 
% 231.54/42.74  | | | REF_CLOSE: (1), (2), (3), (4), (5), (9), (10), (11), (13), (14), (16),
% 231.54/42.74  | | |            (17), (21), (22), (36) are inconsistent by sub-proof #1522.
% 231.54/42.74  | | | 
% 231.54/42.74  | | End of split
% 231.54/42.74  | | 
% 231.54/42.74  | End of split
% 231.54/42.74  | 
% 231.54/42.74  End of proof
% 231.54/42.74  
% 231.54/42.74  Sub-proof #1517 shows that the following formulas are inconsistent:
% 231.54/42.74  ----------------------------------------------------------------
% 231.54/42.74    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.74         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.54/42.74    (2)   ~ (e3 = e1)
% 231.54/42.74    (3)  all_57_3 = e0
% 231.54/42.74    (4)   ~ (e3 = e2)
% 231.54/42.74    (5)  all_57_10 = e2
% 231.54/42.74    (6)  all_57_5 = e3
% 231.54/42.74    (7)  e2 = e0
% 231.54/42.74    (8)   ~ (e2 = e0)
% 231.54/42.74    (9)   ~ (e1 = e0)
% 231.54/42.74    (10)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.74          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.54/42.74    (11)   ~ (e2 = e1)
% 231.54/42.74  
% 231.54/42.74  Begin of proof
% 231.54/42.74  | 
% 231.54/42.74  | SIMP: (7) implies:
% 231.54/42.74  |   (12)  e2 = e0
% 231.54/42.74  | 
% 231.54/42.74  | COMBINE_EQS: (5), (12) imply:
% 231.54/42.74  |   (13)  all_57_10 = e0
% 231.54/42.74  | 
% 231.54/42.74  | REF_CLOSE: (1), (2), (3), (4), (6), (8), (9), (10), (11), (13) are
% 231.54/42.74  |            inconsistent by sub-proof #1518.
% 231.54/42.74  | 
% 231.54/42.74  End of proof
% 231.54/42.74  
% 231.54/42.74  Sub-proof #1518 shows that the following formulas are inconsistent:
% 231.54/42.74  ----------------------------------------------------------------
% 231.54/42.74    (1)  all_57_10 = e0
% 231.54/42.74    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.74         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.54/42.74    (3)   ~ (e3 = e1)
% 231.54/42.74    (4)  all_57_3 = e0
% 231.54/42.74    (5)   ~ (e3 = e2)
% 231.54/42.74    (6)  all_57_5 = e3
% 231.54/42.74    (7)   ~ (e2 = e0)
% 231.54/42.74    (8)   ~ (e1 = e0)
% 231.54/42.74    (9)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.74         (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.54/42.74    (10)   ~ (e2 = e1)
% 231.54/42.74  
% 231.54/42.74  Begin of proof
% 231.54/42.74  | 
% 231.54/42.74  | BETA: splitting (9) gives:
% 231.54/42.74  | 
% 231.54/42.74  | Case 1:
% 231.54/42.74  | | 
% 231.54/42.74  | |   (11)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 231.54/42.74  | |           e2)
% 231.54/42.74  | | 
% 231.54/42.74  | | BETA: splitting (11) gives:
% 231.54/42.74  | | 
% 231.54/42.74  | | Case 1:
% 231.54/42.74  | | | 
% 231.54/42.74  | | |   (12)  all_57_2 = e2 & op(e2, e3) = e2
% 231.54/42.74  | | | 
% 231.54/42.74  | | | ALPHA: (12) implies:
% 231.54/42.74  | | |   (13)  all_57_2 = e2
% 231.54/42.74  | | | 
% 231.54/42.74  | | | REF_CLOSE: (1), (2), (3), (4), (6), (8), (10), (13) are inconsistent by
% 231.54/42.74  | | |            sub-proof #1530.
% 231.54/42.74  | | | 
% 231.54/42.74  | | Case 2:
% 231.54/42.74  | | | 
% 231.54/42.74  | | |   (14)  all_57_3 = e2 & op(e2, e2) = e2
% 231.54/42.74  | | | 
% 231.54/42.74  | | | REF_CLOSE: (4), (7), (14) are inconsistent by sub-proof #2103.
% 231.54/42.74  | | | 
% 231.54/42.74  | | End of split
% 231.54/42.74  | | 
% 231.54/42.74  | Case 2:
% 231.54/42.74  | | 
% 231.54/42.74  | |   (15)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 231.54/42.74  | |           e2)
% 231.54/42.74  | | 
% 231.54/42.74  | | REF_CLOSE: (1), (5), (6), (7), (15) are inconsistent by sub-proof #1827.
% 231.54/42.74  | | 
% 231.54/42.74  | End of split
% 231.54/42.74  | 
% 231.54/42.74  End of proof
% 231.54/42.74  
% 231.54/42.74  Sub-proof #1519 shows that the following formulas are inconsistent:
% 231.54/42.74  ----------------------------------------------------------------
% 231.54/42.74    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.74         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.54/42.74    (2)  all_57_12 = e0
% 231.54/42.74    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.54/42.74         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.54/42.74    (4)   ~ (e3 = e1)
% 231.54/42.74    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.74           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.74    (6)  all_57_3 = e0
% 231.54/42.74    (7)   ~ (e3 = e2)
% 231.54/42.74    (8)  all_57_1 = e2
% 231.54/42.74    (9)  op(e3, e3) = e3
% 231.54/42.74    (10)  all_57_10 = e2
% 231.54/42.74    (11)  all_57_5 = e3
% 231.54/42.74    (12)  all_57_6 = e2
% 231.54/42.74    (13)  op(e1, e1) = e1
% 231.54/42.74    (14)   ~ (e2 = e0)
% 231.54/42.74    (15)   ~ (e1 = e0)
% 231.54/42.74    (16)  all_57_2 = e1
% 231.54/42.74    (17)  op(e1, e1) = e0
% 231.54/42.74    (18)  all_57_7 = e3
% 231.54/42.74    (19)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.74          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.54/42.74    (20)   ~ (e2 = e1)
% 231.54/42.74    (21)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.74          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.54/42.74  
% 231.54/42.74  Begin of proof
% 231.54/42.74  | 
% 231.54/42.74  | BETA: splitting (21) gives:
% 231.54/42.74  | 
% 231.54/42.74  | Case 1:
% 231.54/42.74  | | 
% 231.54/42.74  | |   (22)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) =
% 231.54/42.74  | |           e1)
% 231.54/42.74  | | 
% 231.54/42.74  | | BETA: splitting (22) gives:
% 231.54/42.74  | | 
% 231.54/42.74  | | Case 1:
% 231.54/42.74  | | | 
% 231.54/42.74  | | |   (23)  all_57_1 = e1 & op(e3, e2) = e1
% 231.54/42.74  | | | 
% 231.54/42.74  | | | ALPHA: (23) implies:
% 231.54/42.74  | | |   (24)  all_57_1 = e1
% 231.54/42.74  | | | 
% 231.54/42.74  | | | COMBINE_EQS: (8), (24) imply:
% 231.54/42.74  | | |   (25)  e2 = e1
% 231.54/42.74  | | | 
% 231.54/42.74  | | | COMBINE_EQS: (10), (25) imply:
% 231.54/42.74  | | |   (26)  all_57_10 = e1
% 231.54/42.74  | | | 
% 231.54/42.74  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (11), (12), (14), (15),
% 231.54/42.74  | | |            (19), (20), (26) are inconsistent by sub-proof #1522.
% 231.54/42.74  | | | 
% 231.54/42.74  | | Case 2:
% 231.54/42.74  | | | 
% 231.54/42.74  | | |   (27)  all_57_3 = e1 & op(e2, e2) = e1
% 231.54/42.74  | | | 
% 231.54/42.74  | | | REF_CLOSE: (1), (4), (6), (7), (11), (14), (15), (16), (19), (20), (27)
% 231.54/42.74  | | |            are inconsistent by sub-proof #1520.
% 231.54/42.74  | | | 
% 231.54/42.74  | | End of split
% 231.54/42.74  | | 
% 231.54/42.74  | Case 2:
% 231.54/42.74  | | 
% 231.54/42.74  | |   (28)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 231.54/42.74  | |           e1)
% 231.54/42.74  | | 
% 231.54/42.74  | | BETA: splitting (28) gives:
% 231.54/42.74  | | 
% 231.54/42.74  | | Case 1:
% 231.54/42.74  | | | 
% 231.54/42.74  | | |   (29)  all_57_7 = e1 & op(e1, e2) = e1
% 231.54/42.74  | | | 
% 231.54/42.74  | | | REF_CLOSE: (4), (18), (29) are inconsistent by sub-proof #2104.
% 231.54/42.74  | | | 
% 231.54/42.74  | | Case 2:
% 231.54/42.74  | | | 
% 231.54/42.74  | | | 
% 231.54/42.74  | | | GROUND_INST: instantiating (5) with e0, e1, e1, e1, simplifying with (13),
% 231.54/42.74  | | |              (17) gives:
% 231.54/42.74  | | |   (30)  e1 = e0
% 231.54/42.74  | | | 
% 231.54/42.74  | | | COMBINE_EQS: (16), (30) imply:
% 231.54/42.74  | | |   (31)  all_57_2 = e0
% 231.54/42.74  | | | 
% 231.54/42.74  | | | REF_CLOSE: (1), (4), (6), (7), (11), (14), (15), (19), (20), (31) are
% 231.54/42.74  | | |            inconsistent by sub-proof #2253.
% 231.54/42.74  | | | 
% 231.54/42.74  | | End of split
% 231.54/42.74  | | 
% 231.54/42.74  | End of split
% 231.54/42.74  | 
% 231.54/42.74  End of proof
% 231.54/42.74  
% 231.54/42.74  Sub-proof #1520 shows that the following formulas are inconsistent:
% 231.54/42.74  ----------------------------------------------------------------
% 231.54/42.74    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.74         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.54/42.74    (2)   ~ (e3 = e1)
% 231.54/42.74    (3)  all_57_3 = e0
% 231.54/42.74    (4)   ~ (e3 = e2)
% 231.54/42.74    (5)  all_57_5 = e3
% 231.54/42.74    (6)   ~ (e2 = e0)
% 231.54/42.74    (7)   ~ (e1 = e0)
% 231.54/42.74    (8)  all_57_2 = e1
% 231.54/42.74    (9)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.74         (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.54/42.74    (10)  all_57_3 = e1 & op(e2, e2) = e1
% 231.54/42.74    (11)   ~ (e2 = e1)
% 231.54/42.74  
% 231.54/42.74  Begin of proof
% 231.54/42.74  | 
% 231.54/42.74  | ALPHA: (10) implies:
% 231.54/42.74  |   (12)  all_57_3 = e1
% 231.54/42.74  | 
% 231.54/42.74  | COMBINE_EQS: (3), (12) imply:
% 231.54/42.74  |   (13)  e1 = e0
% 231.54/42.74  | 
% 231.54/42.74  | SIMP: (13) implies:
% 231.54/42.74  |   (14)  e1 = e0
% 231.54/42.74  | 
% 231.54/42.74  | COMBINE_EQS: (8), (14) imply:
% 231.54/42.74  |   (15)  all_57_2 = e0
% 231.54/42.74  | 
% 231.54/42.74  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (11), (15) are inconsistent
% 231.54/42.74  |            by sub-proof #2253.
% 231.54/42.74  | 
% 231.54/42.74  End of proof
% 231.54/42.74  
% 231.54/42.74  Sub-proof #1521 shows that the following formulas are inconsistent:
% 231.54/42.74  ----------------------------------------------------------------
% 231.54/42.74    (1)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2)
% 231.54/42.74    (2)  all_57_3 = e0
% 231.54/42.74    (3)   ~ (e2 = e0)
% 231.54/42.74    (4)  all_57_2 = e1
% 231.54/42.74    (5)   ~ (e2 = e1)
% 231.54/42.74  
% 231.54/42.74  Begin of proof
% 231.54/42.74  | 
% 231.54/42.74  | BETA: splitting (1) gives:
% 231.54/42.74  | 
% 231.54/42.74  | Case 1:
% 231.54/42.74  | | 
% 231.54/42.74  | |   (6)  all_57_2 = e2 & op(e2, e3) = e2
% 231.54/42.74  | | 
% 231.54/42.74  | | ALPHA: (6) implies:
% 231.54/42.74  | |   (7)  all_57_2 = e2
% 231.54/42.74  | | 
% 231.54/42.74  | | REF_CLOSE: (4), (5), (7) are inconsistent by sub-proof #2464.
% 231.54/42.74  | | 
% 231.54/42.74  | Case 2:
% 231.54/42.74  | | 
% 231.54/42.74  | |   (8)  all_57_3 = e2 & op(e2, e2) = e2
% 231.54/42.74  | | 
% 231.54/42.74  | | REF_CLOSE: (2), (3), (8) are inconsistent by sub-proof #2103.
% 231.54/42.74  | | 
% 231.54/42.74  | End of split
% 231.54/42.74  | 
% 231.54/42.74  End of proof
% 231.54/42.74  
% 231.54/42.74  Sub-proof #1522 shows that the following formulas are inconsistent:
% 231.54/42.74  ----------------------------------------------------------------
% 231.54/42.74    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.74         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.54/42.74    (2)  all_57_12 = e0
% 231.54/42.74    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.54/42.74         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.54/42.74    (4)   ~ (e3 = e1)
% 231.54/42.74    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.74           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.74    (6)  all_57_10 = e1
% 231.54/42.74    (7)  all_57_3 = e0
% 231.54/42.74    (8)   ~ (e3 = e2)
% 231.54/42.74    (9)  op(e3, e3) = e3
% 231.54/42.74    (10)  all_57_5 = e3
% 231.54/42.74    (11)  all_57_6 = e2
% 231.54/42.74    (12)   ~ (e2 = e0)
% 231.54/42.74    (13)   ~ (e1 = e0)
% 231.54/42.74    (14)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.74          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.54/42.74    (15)   ~ (e2 = e1)
% 231.54/42.74  
% 231.54/42.74  Begin of proof
% 231.54/42.74  | 
% 231.54/42.74  | BETA: splitting (14) gives:
% 231.54/42.74  | 
% 231.54/42.74  | Case 1:
% 231.54/42.74  | | 
% 231.54/42.74  | |   (16)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 231.54/42.74  | |           e2)
% 231.54/42.74  | | 
% 231.54/42.74  | | BETA: splitting (16) gives:
% 231.54/42.74  | | 
% 231.54/42.74  | | Case 1:
% 231.54/42.74  | | | 
% 231.54/42.74  | | |   (17)  all_57_2 = e2 & op(e2, e3) = e2
% 231.54/42.74  | | | 
% 231.54/42.74  | | | ALPHA: (17) implies:
% 231.54/42.74  | | |   (18)  all_57_2 = e2
% 231.54/42.74  | | | 
% 231.54/42.74  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (13), (15),
% 231.54/42.74  | | |            (18) are inconsistent by sub-proof #1524.
% 231.54/42.74  | | | 
% 231.54/42.74  | | Case 2:
% 231.54/42.74  | | | 
% 231.54/42.74  | | |   (19)  all_57_3 = e2 & op(e2, e2) = e2
% 231.54/42.74  | | | 
% 231.54/42.74  | | | REF_CLOSE: (7), (12), (19) are inconsistent by sub-proof #2103.
% 231.54/42.74  | | | 
% 231.54/42.74  | | End of split
% 231.54/42.74  | | 
% 231.54/42.74  | Case 2:
% 231.54/42.74  | | 
% 231.54/42.74  | |   (20)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 231.54/42.74  | |           e2)
% 231.54/42.74  | | 
% 231.54/42.74  | | REF_CLOSE: (6), (8), (10), (15), (20) are inconsistent by sub-proof #1523.
% 231.54/42.74  | | 
% 231.54/42.74  | End of split
% 231.54/42.74  | 
% 231.54/42.74  End of proof
% 231.54/42.74  
% 231.54/42.74  Sub-proof #1523 shows that the following formulas are inconsistent:
% 231.54/42.74  ----------------------------------------------------------------
% 231.54/42.74    (1)  all_57_10 = e1
% 231.54/42.74    (2)   ~ (e3 = e2)
% 231.54/42.74    (3)  all_57_5 = e3
% 231.54/42.74    (4)   ~ (e2 = e1)
% 231.54/42.74    (5)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.54/42.74  
% 231.54/42.74  Begin of proof
% 231.54/42.74  | 
% 231.54/42.74  | BETA: splitting (5) gives:
% 231.54/42.74  | 
% 231.54/42.74  | Case 1:
% 231.54/42.74  | | 
% 231.54/42.74  | |   (6)  all_57_5 = e2 & op(e2, e1) = e2
% 231.54/42.74  | | 
% 231.54/42.74  | | REF_CLOSE: (2), (3), (6) are inconsistent by sub-proof #2425.
% 231.54/42.74  | | 
% 231.54/42.74  | Case 2:
% 231.54/42.74  | | 
% 231.54/42.74  | |   (7)  all_57_10 = e2 & op(e2, e0) = e2
% 231.54/42.74  | | 
% 231.54/42.74  | | ALPHA: (7) implies:
% 231.54/42.74  | |   (8)  all_57_10 = e2
% 231.54/42.74  | | 
% 231.54/42.74  | | REF_CLOSE: (1), (4), (8) are inconsistent by sub-proof #2144.
% 231.54/42.74  | | 
% 231.54/42.74  | End of split
% 231.54/42.74  | 
% 231.54/42.74  End of proof
% 231.54/42.74  
% 231.54/42.74  Sub-proof #1524 shows that the following formulas are inconsistent:
% 231.54/42.74  ----------------------------------------------------------------
% 231.54/42.74    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.74         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.54/42.74    (2)  all_57_12 = e0
% 231.54/42.75    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.54/42.75         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.54/42.75    (4)   ~ (e3 = e1)
% 231.54/42.75    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.75           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.75    (6)  all_57_10 = e1
% 231.54/42.75    (7)  all_57_2 = e2
% 231.54/42.75    (8)  all_57_3 = e0
% 231.54/42.75    (9)  op(e3, e3) = e3
% 231.54/42.75    (10)  all_57_5 = e3
% 231.54/42.75    (11)  all_57_6 = e2
% 231.54/42.75    (12)   ~ (e1 = e0)
% 231.54/42.75    (13)   ~ (e2 = e1)
% 231.54/42.75  
% 231.54/42.75  Begin of proof
% 231.54/42.75  | 
% 231.54/42.75  | BETA: splitting (3) gives:
% 231.54/42.75  | 
% 231.54/42.75  | Case 1:
% 231.54/42.75  | | 
% 231.54/42.75  | |   (14)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) =
% 231.54/42.75  | |           e1)
% 231.54/42.75  | | 
% 231.54/42.75  | | REF_CLOSE: (4), (5), (7), (9), (13), (14) are inconsistent by sub-proof
% 231.54/42.75  | |            #2228.
% 231.54/42.75  | | 
% 231.54/42.75  | Case 2:
% 231.54/42.75  | | 
% 231.54/42.75  | |   (15)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) =
% 231.54/42.75  | |           e1)
% 231.54/42.75  | | 
% 231.54/42.75  | | BETA: splitting (15) gives:
% 231.54/42.75  | | 
% 231.54/42.75  | | Case 1:
% 231.54/42.75  | | | 
% 231.54/42.75  | | |   (16)  all_57_6 = e1 & op(e1, e3) = e1
% 231.54/42.75  | | | 
% 231.54/42.75  | | | REF_CLOSE: (11), (13), (16) are inconsistent by sub-proof #2389.
% 231.54/42.75  | | | 
% 231.54/42.75  | | Case 2:
% 231.54/42.75  | | | 
% 231.54/42.75  | | |   (17)  all_57_12 = e1 & op(e0, e3) = e1
% 231.54/42.75  | | | 
% 231.54/42.75  | | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (10), (12), (13), (17) are
% 231.54/42.75  | | |            inconsistent by sub-proof #1525.
% 231.54/42.75  | | | 
% 231.54/42.75  | | End of split
% 231.54/42.75  | | 
% 231.54/42.75  | End of split
% 231.54/42.75  | 
% 231.54/42.75  End of proof
% 231.54/42.75  
% 231.54/42.75  Sub-proof #1525 shows that the following formulas are inconsistent:
% 231.54/42.75  ----------------------------------------------------------------
% 231.54/42.75    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.75         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.54/42.75    (2)  all_57_12 = e0
% 231.54/42.75    (3)   ~ (e3 = e1)
% 231.54/42.75    (4)  all_57_10 = e1
% 231.54/42.75    (5)  all_57_2 = e2
% 231.54/42.75    (6)  all_57_3 = e0
% 231.54/42.75    (7)  all_57_5 = e3
% 231.54/42.75    (8)   ~ (e1 = e0)
% 231.54/42.75    (9)   ~ (e2 = e1)
% 231.54/42.75    (10)  all_57_12 = e1 & op(e0, e3) = e1
% 231.54/42.75  
% 231.54/42.75  Begin of proof
% 231.54/42.75  | 
% 231.54/42.75  | ALPHA: (10) implies:
% 231.54/42.75  |   (11)  all_57_12 = e1
% 231.54/42.75  | 
% 231.54/42.75  | COMBINE_EQS: (2), (11) imply:
% 231.54/42.75  |   (12)  e1 = e0
% 231.54/42.75  | 
% 231.54/42.75  | SIMP: (12) implies:
% 231.54/42.75  |   (13)  e1 = e0
% 231.54/42.75  | 
% 231.54/42.75  | COMBINE_EQS: (4), (13) imply:
% 231.54/42.75  |   (14)  all_57_10 = e0
% 231.54/42.75  | 
% 231.54/42.75  | REF_CLOSE: (1), (3), (5), (6), (7), (8), (9), (14) are inconsistent by
% 231.54/42.75  |            sub-proof #1530.
% 231.54/42.75  | 
% 231.54/42.75  End of proof
% 231.54/42.75  
% 231.54/42.75  Sub-proof #1526 shows that the following formulas are inconsistent:
% 231.54/42.75  ----------------------------------------------------------------
% 231.54/42.75    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.75           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.75    (2)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2)
% 231.54/42.75    (3)   ~ (e3 = e2)
% 231.54/42.75    (4)  op(e3, e3) = e3
% 231.54/42.75    (5)  all_57_2 = e1
% 231.54/42.75    (6)   ~ (e2 = e1)
% 231.54/42.75  
% 231.54/42.75  Begin of proof
% 231.54/42.75  | 
% 231.54/42.75  | BETA: splitting (2) gives:
% 231.54/42.75  | 
% 231.54/42.75  | Case 1:
% 231.54/42.75  | | 
% 231.54/42.75  | |   (7)  all_57_0 = e2 & op(e3, e3) = e2
% 231.54/42.75  | | 
% 231.54/42.75  | | ALPHA: (7) implies:
% 231.54/42.75  | |   (8)  op(e3, e3) = e2
% 231.54/42.75  | | 
% 231.54/42.75  | | REF_CLOSE: (1), (3), (4), (8) are inconsistent by sub-proof #2490.
% 231.54/42.75  | | 
% 231.54/42.75  | Case 2:
% 231.54/42.75  | | 
% 231.54/42.75  | |   (9)  all_57_2 = e2 & op(e2, e3) = e2
% 231.54/42.75  | | 
% 231.54/42.75  | | ALPHA: (9) implies:
% 231.54/42.75  | |   (10)  all_57_2 = e2
% 231.54/42.75  | | 
% 231.54/42.75  | | REF_CLOSE: (5), (6), (10) are inconsistent by sub-proof #2464.
% 231.54/42.75  | | 
% 231.54/42.75  | End of split
% 231.54/42.75  | 
% 231.54/42.75  End of proof
% 231.54/42.75  
% 231.54/42.75  Sub-proof #1527 shows that the following formulas are inconsistent:
% 231.54/42.75  ----------------------------------------------------------------
% 231.54/42.75    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.75         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.54/42.75    (2)  all_57_12 = e0
% 231.54/42.75    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.75         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.54/42.75    (4)   ~ (e3 = e1)
% 231.54/42.75    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.75           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.75    (6)  all_57_4 = e0
% 231.54/42.75    (7)  all_57_2 = e2
% 231.54/42.75    (8)  all_57_3 = e0
% 231.54/42.75    (9)   ~ (e3 = e2)
% 231.54/42.75    (10)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.54/42.75          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.54/42.75    (11)  all_57_15 = e3
% 231.54/42.75    (12)  all_57_5 = e3
% 231.54/42.75    (13)   ~ (e2 = e0)
% 231.54/42.75    (14)   ~ (e1 = e0)
% 231.54/42.75    (15)  all_57_8 = e2
% 231.54/42.75    (16)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.54/42.75          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.54/42.75            e2)
% 231.54/42.75    (17)  op(e1, e1) = e0
% 231.54/42.75    (18)  op(e1, e1) = e2
% 231.54/42.75    (19)  all_57_7 = e3
% 231.54/42.75    (20)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.75          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.54/42.75    (21)   ~ (e2 = e1)
% 231.54/42.75    (22)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.75          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.54/42.75  
% 231.54/42.75  Begin of proof
% 231.54/42.75  | 
% 231.54/42.75  | BETA: splitting (10) gives:
% 231.54/42.75  | 
% 231.54/42.75  | Case 1:
% 231.54/42.75  | | 
% 231.54/42.75  | |   (23)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) =
% 231.54/42.75  | |           e1)
% 231.54/42.75  | | 
% 231.54/42.75  | | BETA: splitting (23) gives:
% 231.54/42.75  | | 
% 231.54/42.75  | | Case 1:
% 231.54/42.75  | | | 
% 231.54/42.75  | | |   (24)  all_57_4 = e1 & op(e3, e1) = e1
% 231.54/42.75  | | | 
% 231.54/42.75  | | | ALPHA: (24) implies:
% 231.54/42.75  | | |   (25)  all_57_4 = e1
% 231.54/42.75  | | | 
% 231.54/42.75  | | | REF_CLOSE: (6), (14), (25) are inconsistent by sub-proof #2438.
% 231.54/42.75  | | | 
% 231.54/42.75  | | Case 2:
% 231.54/42.75  | | | 
% 231.54/42.75  | | |   (26)  all_57_5 = e1 & op(e2, e1) = e1
% 231.54/42.75  | | | 
% 231.54/42.75  | | | REF_CLOSE: (4), (12), (26) are inconsistent by sub-proof #2376.
% 231.54/42.75  | | | 
% 231.54/42.75  | | End of split
% 231.54/42.75  | | 
% 231.54/42.75  | Case 2:
% 231.54/42.75  | | 
% 231.54/42.75  | |   (27)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) =
% 231.54/42.75  | |           e1)
% 231.54/42.75  | | 
% 231.54/42.75  | | BETA: splitting (27) gives:
% 231.54/42.75  | | 
% 231.54/42.75  | | Case 1:
% 231.54/42.75  | | | 
% 231.54/42.75  | | |   (28)  all_57_8 = e1 & op(e1, e1) = e1
% 231.54/42.75  | | | 
% 231.54/42.75  | | | REF_CLOSE: (15), (21), (28) are inconsistent by sub-proof #1533.
% 231.54/42.75  | | | 
% 231.54/42.75  | | Case 2:
% 231.54/42.75  | | | 
% 231.54/42.75  | | |   (29)  all_57_14 = e1 & op(e0, e1) = e1
% 231.54/42.75  | | | 
% 231.54/42.75  | | | ALPHA: (29) implies:
% 231.54/42.75  | | |   (30)  all_57_14 = e1
% 231.54/42.75  | | | 
% 231.54/42.75  | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (11), (12), (13), (14),
% 231.54/42.75  | | |            (16), (17), (18), (19), (20), (21), (22), (30) are inconsistent
% 231.54/42.75  | | |            by sub-proof #1528.
% 231.54/42.75  | | | 
% 231.54/42.75  | | End of split
% 231.54/42.75  | | 
% 231.54/42.75  | End of split
% 231.54/42.75  | 
% 231.54/42.75  End of proof
% 231.54/42.75  
% 231.54/42.75  Sub-proof #1528 shows that the following formulas are inconsistent:
% 231.54/42.75  ----------------------------------------------------------------
% 231.54/42.75    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.75         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.54/42.75    (2)  all_57_12 = e0
% 231.54/42.75    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.75         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.54/42.75    (4)   ~ (e3 = e1)
% 231.54/42.75    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.75           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.75    (6)  all_57_2 = e2
% 231.54/42.75    (7)  all_57_3 = e0
% 231.54/42.75    (8)   ~ (e3 = e2)
% 231.54/42.75    (9)  all_57_15 = e3
% 231.54/42.75    (10)  all_57_5 = e3
% 231.54/42.75    (11)   ~ (e2 = e0)
% 231.54/42.75    (12)   ~ (e1 = e0)
% 231.54/42.75    (13)  all_57_14 = e1
% 231.54/42.75    (14)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.54/42.75          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.54/42.75            e2)
% 231.54/42.75    (15)  op(e1, e1) = e0
% 231.54/42.75    (16)  op(e1, e1) = e2
% 231.54/42.75    (17)  all_57_7 = e3
% 231.54/42.75    (18)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.75          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.54/42.75    (19)   ~ (e2 = e1)
% 231.54/42.75    (20)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.75          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.54/42.75  
% 231.54/42.75  Begin of proof
% 231.54/42.75  | 
% 231.54/42.75  | BETA: splitting (1) gives:
% 231.54/42.75  | 
% 231.54/42.75  | Case 1:
% 231.54/42.75  | | 
% 231.54/42.75  | |   (21)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) =
% 231.54/42.75  | |           e1)
% 231.54/42.75  | | 
% 231.54/42.75  | | BETA: splitting (21) gives:
% 231.54/42.75  | | 
% 231.54/42.75  | | Case 1:
% 231.54/42.75  | | | 
% 231.54/42.75  | | |   (22)  all_57_2 = e1 & op(e2, e3) = e1
% 231.54/42.75  | | | 
% 231.54/42.75  | | | REF_CLOSE: (6), (19), (22) are inconsistent by sub-proof #2244.
% 231.54/42.75  | | | 
% 231.54/42.75  | | Case 2:
% 231.54/42.75  | | | 
% 231.54/42.75  | | |   (23)  all_57_3 = e1 & op(e2, e2) = e1
% 231.54/42.75  | | | 
% 231.54/42.75  | | | REF_CLOSE: (7), (12), (23) are inconsistent by sub-proof #2362.
% 231.54/42.75  | | | 
% 231.54/42.75  | | End of split
% 231.54/42.75  | | 
% 231.54/42.75  | Case 2:
% 231.54/42.75  | | 
% 231.54/42.75  | |   (24)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) =
% 231.54/42.75  | |           e1)
% 231.54/42.75  | | 
% 231.54/42.75  | | BETA: splitting (24) gives:
% 231.54/42.75  | | 
% 231.54/42.75  | | Case 1:
% 231.54/42.75  | | | 
% 231.54/42.75  | | |   (25)  all_57_5 = e1 & op(e2, e1) = e1
% 231.54/42.75  | | | 
% 231.54/42.75  | | | REF_CLOSE: (4), (10), (25) are inconsistent by sub-proof #2376.
% 231.54/42.75  | | | 
% 231.54/42.75  | | Case 2:
% 231.54/42.75  | | | 
% 231.54/42.75  | | |   (26)  all_57_10 = e1 & op(e2, e0) = e1
% 231.54/42.75  | | | 
% 231.54/42.75  | | | ALPHA: (26) implies:
% 231.54/42.75  | | |   (27)  all_57_10 = e1
% 231.54/42.75  | | | 
% 231.54/42.75  | | | BETA: splitting (14) gives:
% 231.54/42.75  | | | 
% 231.54/42.75  | | | Case 1:
% 231.54/42.75  | | | | 
% 231.54/42.75  | | | |   (28)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0,
% 231.54/42.75  | | | |             e2) = e2)
% 231.54/42.75  | | | | 
% 231.54/42.75  | | | | BETA: splitting (28) gives:
% 231.54/42.75  | | | | 
% 231.54/42.75  | | | | Case 1:
% 231.54/42.75  | | | | | 
% 231.54/42.75  | | | | |   (29)  all_57_12 = e2 & op(e0, e3) = e2
% 231.54/42.75  | | | | | 
% 231.54/42.75  | | | | | ALPHA: (29) implies:
% 231.54/42.75  | | | | |   (30)  all_57_12 = e2
% 231.54/42.75  | | | | | 
% 231.54/42.75  | | | | | COMBINE_EQS: (2), (30) imply:
% 231.54/42.75  | | | | |   (31)  e2 = e0
% 231.54/42.75  | | | | | 
% 231.54/42.75  | | | | | REF_CLOSE: (6), (7), (8), (10), (11), (18), (19), (27), (31) are
% 231.54/42.75  | | | | |            inconsistent by sub-proof #1532.
% 231.54/42.75  | | | | | 
% 231.54/42.75  | | | | Case 2:
% 231.54/42.75  | | | | | 
% 231.54/42.75  | | | | |   (32)  all_57_13 = e2 & op(e0, e2) = e2
% 231.54/42.75  | | | | | 
% 231.54/42.75  | | | | | ALPHA: (32) implies:
% 231.54/42.75  | | | | |   (33)  all_57_13 = e2
% 231.54/42.75  | | | | | 
% 231.54/42.75  | | | | | BETA: splitting (20) gives:
% 231.54/42.75  | | | | | 
% 231.54/42.75  | | | | | Case 1:
% 231.54/42.75  | | | | | | 
% 231.54/42.75  | | | | | |   (34)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2,
% 231.54/42.75  | | | | | |             e2) = e1)
% 231.54/42.75  | | | | | | 
% 231.54/42.75  | | | | | | BETA: splitting (34) gives:
% 231.54/42.75  | | | | | | 
% 231.54/42.75  | | | | | | Case 1:
% 231.54/42.75  | | | | | | | 
% 231.54/42.75  | | | | | | |   (35)  all_57_1 = e1 & op(e3, e2) = e1
% 231.54/42.75  | | | | | | | 
% 231.54/42.75  | | | | | | | ALPHA: (35) implies:
% 231.54/42.75  | | | | | | |   (36)  all_57_1 = e1
% 231.54/42.75  | | | | | | | 
% 231.54/42.75  | | | | | | | BETA: splitting (3) gives:
% 231.54/42.75  | | | | | | | 
% 231.54/42.75  | | | | | | | Case 1:
% 231.54/42.75  | | | | | | | | 
% 231.54/42.75  | | | | | | | |   (37)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 &
% 231.54/42.75  | | | | | | | |           op(e2, e2) = e2)
% 231.54/42.75  | | | | | | | | 
% 231.54/42.75  | | | | | | | | BETA: splitting (37) gives:
% 231.54/42.75  | | | | | | | | 
% 231.54/42.75  | | | | | | | | Case 1:
% 231.54/42.75  | | | | | | | | | 
% 231.54/42.75  | | | | | | | | |   (38)  all_57_1 = e2 & op(e3, e2) = e2
% 231.54/42.75  | | | | | | | | | 
% 231.54/42.75  | | | | | | | | | REF_CLOSE: (19), (36), (38) are inconsistent by sub-proof
% 231.54/42.75  | | | | | | | | |            #2489.
% 231.54/42.75  | | | | | | | | | 
% 231.54/42.75  | | | | | | | | Case 2:
% 231.54/42.75  | | | | | | | | | 
% 231.54/42.75  | | | | | | | | |   (39)  all_57_3 = e2 & op(e2, e2) = e2
% 231.54/42.75  | | | | | | | | | 
% 231.54/42.75  | | | | | | | | | ALPHA: (39) implies:
% 231.54/42.75  | | | | | | | | |   (40)  all_57_3 = e2
% 231.54/42.75  | | | | | | | | | 
% 231.54/42.75  | | | | | | | | | COMBINE_EQS: (7), (40) imply:
% 231.54/42.75  | | | | | | | | |   (41)  e2 = e0
% 231.54/42.75  | | | | | | | | | 
% 231.54/42.75  | | | | | | | | | REF_CLOSE: (6), (7), (8), (10), (11), (18), (19), (27), (41)
% 231.54/42.75  | | | | | | | | |            are inconsistent by sub-proof #1532.
% 231.54/42.75  | | | | | | | | | 
% 231.54/42.75  | | | | | | | | End of split
% 231.54/42.75  | | | | | | | | 
% 231.54/42.75  | | | | | | | Case 2:
% 231.54/42.75  | | | | | | | | 
% 231.54/42.75  | | | | | | | |   (42)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 &
% 231.54/42.75  | | | | | | | |           op(e0, e2) = e2)
% 231.54/42.75  | | | | | | | | 
% 231.54/42.75  | | | | | | | | BETA: splitting (42) gives:
% 231.54/42.75  | | | | | | | | 
% 231.54/42.75  | | | | | | | | Case 1:
% 231.54/42.75  | | | | | | | | | 
% 231.54/42.75  | | | | | | | | |   (43)  all_57_7 = e2 & op(e1, e2) = e2
% 231.54/42.75  | | | | | | | | | 
% 231.54/42.75  | | | | | | | | | REF_CLOSE: (8), (17), (43) are inconsistent by sub-proof
% 231.54/42.75  | | | | | | | | |            #2092.
% 231.54/42.75  | | | | | | | | | 
% 231.54/42.75  | | | | | | | | Case 2:
% 231.54/42.75  | | | | | | | | | 
% 231.54/42.75  | | | | | | | | | 
% 231.54/42.75  | | | | | | | | | GROUND_INST: instantiating (5) with e0, e2, e1, e1, simplifying
% 231.54/42.75  | | | | | | | | |              with (15), (16) gives:
% 231.54/42.75  | | | | | | | | |   (44)  e2 = e0
% 231.54/42.75  | | | | | | | | | 
% 231.54/42.75  | | | | | | | | | COMBINE_EQS: (6), (44) imply:
% 231.54/42.75  | | | | | | | | |   (45)  all_57_2 = e0
% 231.54/42.75  | | | | | | | | | 
% 231.54/42.75  | | | | | | | | | REF_CLOSE: (7), (8), (10), (11), (18), (19), (27), (45) are
% 231.54/42.75  | | | | | | | | |            inconsistent by sub-proof #2254.
% 231.54/42.75  | | | | | | | | | 
% 231.54/42.75  | | | | | | | | End of split
% 231.54/42.75  | | | | | | | | 
% 231.54/42.75  | | | | | | | End of split
% 231.54/42.75  | | | | | | | 
% 231.54/42.75  | | | | | | Case 2:
% 231.54/42.75  | | | | | | | 
% 231.54/42.75  | | | | | | |   (46)  all_57_3 = e1 & op(e2, e2) = e1
% 231.54/42.75  | | | | | | | 
% 231.54/42.75  | | | | | | | ALPHA: (46) implies:
% 231.54/42.75  | | | | | | |   (47)  all_57_3 = e1
% 231.54/42.75  | | | | | | | 
% 231.54/42.75  | | | | | | | COMBINE_EQS: (7), (47) imply:
% 231.54/42.75  | | | | | | |   (48)  e1 = e0
% 231.54/42.75  | | | | | | | 
% 231.54/42.75  | | | | | | | COMBINE_EQS: (27), (48) imply:
% 231.54/42.75  | | | | | | |   (49)  all_57_10 = e0
% 231.54/42.75  | | | | | | | 
% 231.54/42.75  | | | | | | | REF_CLOSE: (1), (4), (6), (7), (10), (12), (19), (49) are
% 231.54/42.75  | | | | | | |            inconsistent by sub-proof #1530.
% 231.54/42.75  | | | | | | | 
% 231.54/42.75  | | | | | | End of split
% 231.54/42.75  | | | | | | 
% 231.54/42.75  | | | | | Case 2:
% 231.54/42.75  | | | | | | 
% 231.54/42.75  | | | | | |   (50)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0,
% 231.54/42.75  | | | | | |             e2) = e1)
% 231.54/42.75  | | | | | | 
% 231.54/42.75  | | | | | | BETA: splitting (50) gives:
% 231.54/42.75  | | | | | | 
% 231.54/42.75  | | | | | | Case 1:
% 231.54/42.75  | | | | | | | 
% 231.54/42.75  | | | | | | |   (51)  all_57_7 = e1 & op(e1, e2) = e1
% 231.54/42.75  | | | | | | | 
% 231.54/42.75  | | | | | | | ALPHA: (51) implies:
% 231.54/42.75  | | | | | | |   (52)  all_57_7 = e1
% 231.54/42.75  | | | | | | | 
% 231.54/42.75  | | | | | | | REF_CLOSE: (4), (17), (52) are inconsistent by sub-proof #2115.
% 231.54/42.75  | | | | | | | 
% 231.54/42.75  | | | | | | Case 2:
% 231.54/42.75  | | | | | | | 
% 231.54/42.75  | | | | | | |   (53)  all_57_13 = e1 & op(e0, e2) = e1
% 231.54/42.75  | | | | | | | 
% 231.54/42.75  | | | | | | | ALPHA: (53) implies:
% 231.54/42.75  | | | | | | |   (54)  all_57_13 = e1
% 231.54/42.75  | | | | | | | 
% 231.54/42.75  | | | | | | | REF_CLOSE: (19), (33), (54) are inconsistent by sub-proof #2327.
% 231.54/42.75  | | | | | | | 
% 231.54/42.75  | | | | | | End of split
% 231.54/42.75  | | | | | | 
% 231.54/42.75  | | | | | End of split
% 231.54/42.75  | | | | | 
% 231.54/42.75  | | | | End of split
% 231.54/42.75  | | | | 
% 231.54/42.75  | | | Case 2:
% 231.54/42.75  | | | | 
% 231.54/42.75  | | | |   (55)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0,
% 231.54/42.75  | | | |             e0) = e2)
% 231.54/42.75  | | | | 
% 231.54/42.75  | | | | REF_CLOSE: (8), (9), (13), (19), (55) are inconsistent by sub-proof
% 231.54/42.75  | | | |            #1529.
% 231.54/42.75  | | | | 
% 231.54/42.75  | | | End of split
% 231.54/42.75  | | | 
% 231.54/42.75  | | End of split
% 231.54/42.75  | | 
% 231.54/42.75  | End of split
% 231.54/42.75  | 
% 231.54/42.75  End of proof
% 231.54/42.75  
% 231.54/42.75  Sub-proof #1529 shows that the following formulas are inconsistent:
% 231.54/42.75  ----------------------------------------------------------------
% 231.54/42.75    (1)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.54/42.75    (2)   ~ (e3 = e2)
% 231.54/42.75    (3)  all_57_15 = e3
% 231.54/42.75    (4)  all_57_14 = e1
% 231.54/42.75    (5)   ~ (e2 = e1)
% 231.54/42.75  
% 231.54/42.75  Begin of proof
% 231.54/42.75  | 
% 231.54/42.75  | BETA: splitting (1) gives:
% 231.54/42.75  | 
% 231.54/42.75  | Case 1:
% 231.54/42.75  | | 
% 231.54/42.75  | |   (6)  all_57_14 = e2 & op(e0, e1) = e2
% 231.54/42.75  | | 
% 231.54/42.75  | | ALPHA: (6) implies:
% 231.54/42.75  | |   (7)  all_57_14 = e2
% 231.54/42.75  | | 
% 231.54/42.75  | | REF_CLOSE: (4), (5), (7) are inconsistent by sub-proof #2178.
% 231.54/42.75  | | 
% 231.54/42.75  | Case 2:
% 231.54/42.75  | | 
% 231.54/42.75  | |   (8)  all_57_15 = e2 & op(e0, e0) = e2
% 231.54/42.75  | | 
% 231.54/42.75  | | REF_CLOSE: (2), (3), (8) are inconsistent by sub-proof #2323.
% 231.54/42.75  | | 
% 231.54/42.75  | End of split
% 231.54/42.75  | 
% 231.54/42.75  End of proof
% 231.54/42.75  
% 231.54/42.75  Sub-proof #1530 shows that the following formulas are inconsistent:
% 231.54/42.75  ----------------------------------------------------------------
% 231.54/42.75    (1)  all_57_10 = e0
% 231.54/42.75    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.75         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.54/42.75    (3)   ~ (e3 = e1)
% 231.54/42.75    (4)  all_57_2 = e2
% 231.54/42.75    (5)  all_57_3 = e0
% 231.54/42.75    (6)  all_57_5 = e3
% 231.54/42.75    (7)   ~ (e1 = e0)
% 231.54/42.75    (8)   ~ (e2 = e1)
% 231.54/42.75  
% 231.54/42.75  Begin of proof
% 231.54/42.75  | 
% 231.54/42.75  | BETA: splitting (2) gives:
% 231.54/42.75  | 
% 231.54/42.75  | Case 1:
% 231.54/42.75  | | 
% 231.54/42.75  | |   (9)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1)
% 231.54/42.75  | | 
% 231.54/42.75  | | BETA: splitting (9) gives:
% 231.54/42.75  | | 
% 231.54/42.75  | | Case 1:
% 231.54/42.75  | | | 
% 231.54/42.75  | | |   (10)  all_57_2 = e1 & op(e2, e3) = e1
% 231.54/42.75  | | | 
% 231.54/42.75  | | | REF_CLOSE: (4), (8), (10) are inconsistent by sub-proof #2244.
% 231.54/42.75  | | | 
% 231.54/42.75  | | Case 2:
% 231.54/42.75  | | | 
% 231.54/42.75  | | |   (11)  all_57_3 = e1 & op(e2, e2) = e1
% 231.54/42.75  | | | 
% 231.54/42.75  | | | REF_CLOSE: (5), (7), (11) are inconsistent by sub-proof #2362.
% 231.54/42.75  | | | 
% 231.54/42.75  | | End of split
% 231.54/42.75  | | 
% 231.54/42.75  | Case 2:
% 231.54/42.75  | | 
% 231.54/42.75  | |   (12)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) =
% 231.54/42.75  | |           e1)
% 231.54/42.75  | | 
% 231.54/42.75  | | BETA: splitting (12) gives:
% 231.54/42.75  | | 
% 231.54/42.75  | | Case 1:
% 231.54/42.75  | | | 
% 231.54/42.75  | | |   (13)  all_57_5 = e1 & op(e2, e1) = e1
% 231.54/42.75  | | | 
% 231.54/42.75  | | | REF_CLOSE: (3), (6), (13) are inconsistent by sub-proof #2376.
% 231.54/42.75  | | | 
% 231.54/42.75  | | Case 2:
% 231.54/42.75  | | | 
% 231.54/42.75  | | |   (14)  all_57_10 = e1 & op(e2, e0) = e1
% 231.54/42.75  | | | 
% 231.54/42.75  | | | ALPHA: (14) implies:
% 231.54/42.75  | | |   (15)  all_57_10 = e1
% 231.54/42.75  | | | 
% 231.54/42.75  | | | REF_CLOSE: (1), (7), (15) are inconsistent by sub-proof #1531.
% 231.54/42.75  | | | 
% 231.54/42.75  | | End of split
% 231.54/42.75  | | 
% 231.54/42.75  | End of split
% 231.54/42.75  | 
% 231.54/42.75  End of proof
% 231.54/42.75  
% 231.54/42.75  Sub-proof #1531 shows that the following formulas are inconsistent:
% 231.54/42.75  ----------------------------------------------------------------
% 231.54/42.75    (1)  all_57_10 = e1
% 231.54/42.75    (2)  all_57_10 = e0
% 231.54/42.75    (3)   ~ (e1 = e0)
% 231.54/42.75  
% 231.54/42.75  Begin of proof
% 231.54/42.75  | 
% 231.54/42.75  | COMBINE_EQS: (1), (2) imply:
% 231.54/42.75  |   (4)  e1 = e0
% 231.54/42.75  | 
% 231.54/42.75  | SIMP: (4) implies:
% 231.54/42.75  |   (5)  e1 = e0
% 231.54/42.75  | 
% 231.54/42.75  | REDUCE: (3), (5) imply:
% 231.54/42.75  |   (6)  $false
% 231.54/42.75  | 
% 231.54/42.75  | CLOSE: (6) is inconsistent.
% 231.54/42.75  | 
% 231.54/42.75  End of proof
% 231.54/42.75  
% 231.54/42.75  Sub-proof #1532 shows that the following formulas are inconsistent:
% 231.54/42.75  ----------------------------------------------------------------
% 231.54/42.75    (1)  all_57_10 = e1
% 231.54/42.75    (2)  all_57_2 = e2
% 231.54/42.75    (3)  all_57_3 = e0
% 231.54/42.75    (4)   ~ (e3 = e2)
% 231.54/42.75    (5)  all_57_5 = e3
% 231.54/42.75    (6)  e2 = e0
% 231.54/42.75    (7)   ~ (e2 = e0)
% 231.54/42.75    (8)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.75         (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.54/42.75    (9)   ~ (e2 = e1)
% 231.54/42.75  
% 231.54/42.75  Begin of proof
% 231.54/42.75  | 
% 231.54/42.75  | SIMP: (6) implies:
% 231.54/42.75  |   (10)  e2 = e0
% 231.54/42.75  | 
% 231.54/42.75  | COMBINE_EQS: (2), (10) imply:
% 231.54/42.75  |   (11)  all_57_2 = e0
% 231.54/42.75  | 
% 231.54/42.75  | REF_CLOSE: (1), (3), (4), (5), (7), (8), (9), (11) are inconsistent by
% 231.54/42.75  |            sub-proof #2254.
% 231.54/42.75  | 
% 231.54/42.75  End of proof
% 231.54/42.75  
% 231.54/42.75  Sub-proof #1533 shows that the following formulas are inconsistent:
% 231.54/42.75  ----------------------------------------------------------------
% 231.54/42.75    (1)  all_57_8 = e1 & op(e1, e1) = e1
% 231.54/42.75    (2)  all_57_8 = e2
% 231.54/42.75    (3)   ~ (e2 = e1)
% 231.54/42.75  
% 231.54/42.75  Begin of proof
% 231.54/42.75  | 
% 231.54/42.75  | ALPHA: (1) implies:
% 231.54/42.75  |   (4)  all_57_8 = e1
% 231.54/42.75  | 
% 231.54/42.75  | COMBINE_EQS: (2), (4) imply:
% 231.54/42.75  |   (5)  e2 = e1
% 231.54/42.75  | 
% 231.54/42.75  | REDUCE: (3), (5) imply:
% 231.54/42.75  |   (6)  $false
% 231.54/42.75  | 
% 231.54/42.75  | CLOSE: (6) is inconsistent.
% 231.54/42.75  | 
% 231.54/42.75  End of proof
% 231.54/42.75  
% 231.54/42.75  Sub-proof #1534 shows that the following formulas are inconsistent:
% 231.54/42.75  ----------------------------------------------------------------
% 231.54/42.75    (1)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.54/42.75         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.54/42.75    (2)   ~ (e3 = e1)
% 231.54/42.75    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.75           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.75    (4)   ~ (e3 = e2)
% 231.54/42.75    (5)   ~ (e3 = e0)
% 231.54/42.75    (6)  op(e3, e3) = e3
% 231.54/42.75    (7)   ~ (e2 = e0)
% 231.54/42.75    (8)  all_57_2 = e3
% 231.54/42.75    (9)   ~ (e1 = e0)
% 231.54/42.75    (10)   ~ (e2 = e1)
% 231.54/42.75    (11)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.54/42.75          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.54/42.75    (12)  all_57_6 = e3 & op(e1, e3) = e3
% 231.54/42.75    (13)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.54/42.75          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.54/42.75  
% 231.54/42.75  Begin of proof
% 231.54/42.75  | 
% 231.54/42.75  | ALPHA: (12) implies:
% 231.54/42.75  |   (14)  all_57_6 = e3
% 231.54/42.75  | 
% 231.54/42.75  | BETA: splitting (11) gives:
% 231.54/42.75  | 
% 231.54/42.75  | Case 1:
% 231.54/42.75  | | 
% 231.54/42.75  | |   (15)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) =
% 231.54/42.75  | |           e2)
% 231.54/42.75  | | 
% 231.54/42.75  | | BETA: splitting (15) gives:
% 231.54/42.75  | | 
% 231.54/42.75  | | Case 1:
% 231.54/42.75  | | | 
% 231.54/42.75  | | |   (16)  all_57_0 = e2 & op(e3, e3) = e2
% 231.54/42.75  | | | 
% 231.54/42.75  | | | ALPHA: (16) implies:
% 231.54/42.75  | | |   (17)  all_57_0 = e2
% 231.54/42.75  | | | 
% 231.54/42.75  | | | BETA: splitting (13) gives:
% 231.54/42.75  | | | 
% 231.54/42.75  | | | Case 1:
% 231.54/42.75  | | | | 
% 231.54/42.75  | | | |   (18)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3)
% 231.54/42.75  | | | |           = e0)
% 231.54/42.75  | | | | 
% 231.54/42.75  | | | | BETA: splitting (18) gives:
% 231.54/42.75  | | | | 
% 231.54/42.75  | | | | Case 1:
% 231.54/42.75  | | | | | 
% 231.54/42.75  | | | | |   (19)  all_57_0 = e0 & op(e3, e3) = e0
% 231.54/42.75  | | | | | 
% 231.54/42.75  | | | | | ALPHA: (19) implies:
% 231.54/42.75  | | | | |   (20)  op(e3, e3) = e0
% 231.54/42.75  | | | | | 
% 231.54/42.75  | | | | | REF_CLOSE: (3), (5), (6), (20) are inconsistent by sub-proof #2494.
% 231.54/42.75  | | | | | 
% 231.54/42.75  | | | | Case 2:
% 231.54/42.75  | | | | | 
% 231.54/42.75  | | | | |   (21)  all_57_2 = e0 & op(e2, e3) = e0
% 231.54/42.75  | | | | | 
% 231.54/42.75  | | | | | ALPHA: (21) implies:
% 231.54/42.75  | | | | |   (22)  all_57_2 = e0
% 231.54/42.75  | | | | | 
% 231.54/42.75  | | | | | REF_CLOSE: (5), (8), (22) are inconsistent by sub-proof #2258.
% 231.54/42.75  | | | | | 
% 231.54/42.75  | | | | End of split
% 231.54/42.75  | | | | 
% 231.54/42.75  | | | Case 2:
% 231.54/42.75  | | | | 
% 231.54/42.75  | | | |   (23)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3)
% 231.54/42.75  | | | |           = e0)
% 231.54/42.75  | | | | 
% 231.54/42.75  | | | | BETA: splitting (23) gives:
% 231.54/42.75  | | | | 
% 231.54/42.75  | | | | Case 1:
% 231.54/42.75  | | | | | 
% 231.54/42.75  | | | | |   (24)  all_57_6 = e0 & op(e1, e3) = e0
% 231.54/42.75  | | | | | 
% 231.54/42.75  | | | | | ALPHA: (24) implies:
% 231.54/42.75  | | | | |   (25)  all_57_6 = e0
% 231.54/42.75  | | | | | 
% 231.54/42.75  | | | | | REF_CLOSE: (5), (14), (25) are inconsistent by sub-proof #1822.
% 231.54/42.75  | | | | | 
% 231.54/42.75  | | | | Case 2:
% 231.54/42.75  | | | | | 
% 231.54/42.75  | | | | |   (26)  all_57_12 = e0 & op(e0, e3) = e0
% 231.54/42.75  | | | | | 
% 231.54/42.75  | | | | | ALPHA: (26) implies:
% 231.54/42.75  | | | | |   (27)  all_57_12 = e0
% 231.54/42.75  | | | | | 
% 231.54/42.75  | | | | | REF_CLOSE: (1), (2), (8), (9), (10), (14), (17), (27) are inconsistent
% 231.54/42.75  | | | | |            by sub-proof #1535.
% 231.54/42.75  | | | | | 
% 231.54/42.75  | | | | End of split
% 231.54/42.75  | | | | 
% 231.54/42.75  | | | End of split
% 231.54/42.75  | | | 
% 231.54/42.75  | | Case 2:
% 231.54/42.75  | | | 
% 231.54/42.75  | | |   (28)  all_57_2 = e2 & op(e2, e3) = e2
% 231.54/42.75  | | | 
% 231.54/42.75  | | | REF_CLOSE: (4), (8), (28) are inconsistent by sub-proof #1925.
% 231.54/42.75  | | | 
% 231.54/42.75  | | End of split
% 231.54/42.75  | | 
% 231.54/42.75  | Case 2:
% 231.54/42.75  | | 
% 231.54/42.75  | |   (29)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) =
% 231.54/42.75  | |           e2)
% 231.54/42.75  | | 
% 231.54/42.75  | | BETA: splitting (29) gives:
% 231.54/42.75  | | 
% 231.54/42.75  | | Case 1:
% 231.54/42.75  | | | 
% 231.54/42.75  | | |   (30)  all_57_6 = e2 & op(e1, e3) = e2
% 231.54/42.75  | | | 
% 231.54/42.75  | | | REF_CLOSE: (4), (14), (30) are inconsistent by sub-proof #2012.
% 231.54/42.75  | | | 
% 231.54/42.75  | | Case 2:
% 231.54/42.75  | | | 
% 231.54/42.75  | | |   (31)  all_57_12 = e2 & op(e0, e3) = e2
% 231.54/42.75  | | | 
% 231.54/42.75  | | | ALPHA: (31) implies:
% 231.54/42.75  | | |   (32)  all_57_12 = e2
% 231.54/42.75  | | | 
% 231.54/42.75  | | | BETA: splitting (13) gives:
% 231.54/42.75  | | | 
% 231.54/42.75  | | | Case 1:
% 231.54/42.75  | | | | 
% 231.54/42.75  | | | |   (33)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3)
% 231.54/42.75  | | | |           = e0)
% 231.54/42.75  | | | | 
% 231.54/42.75  | | | | BETA: splitting (33) gives:
% 231.54/42.75  | | | | 
% 231.54/42.75  | | | | Case 1:
% 231.54/42.75  | | | | | 
% 231.54/42.75  | | | | |   (34)  all_57_0 = e0 & op(e3, e3) = e0
% 231.54/42.75  | | | | | 
% 231.54/42.75  | | | | | ALPHA: (34) implies:
% 231.54/42.75  | | | | |   (35)  op(e3, e3) = e0
% 231.54/42.75  | | | | | 
% 231.54/42.75  | | | | | REF_CLOSE: (3), (5), (6), (35) are inconsistent by sub-proof #2494.
% 231.54/42.75  | | | | | 
% 231.54/42.75  | | | | Case 2:
% 231.54/42.75  | | | | | 
% 231.54/42.75  | | | | |   (36)  all_57_2 = e0 & op(e2, e3) = e0
% 231.54/42.75  | | | | | 
% 231.54/42.75  | | | | | REF_CLOSE: (5), (8), (36) are inconsistent by sub-proof #1805.
% 231.54/42.75  | | | | | 
% 231.54/42.75  | | | | End of split
% 231.54/42.75  | | | | 
% 231.54/42.75  | | | Case 2:
% 231.54/42.75  | | | | 
% 231.54/42.75  | | | |   (37)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3)
% 231.54/42.75  | | | |           = e0)
% 231.54/42.75  | | | | 
% 231.54/42.75  | | | | BETA: splitting (37) gives:
% 231.54/42.75  | | | | 
% 231.54/42.75  | | | | Case 1:
% 231.54/42.75  | | | | | 
% 231.54/42.75  | | | | |   (38)  all_57_6 = e0 & op(e1, e3) = e0
% 231.54/42.75  | | | | | 
% 231.54/42.75  | | | | | ALPHA: (38) implies:
% 231.54/42.75  | | | | |   (39)  all_57_6 = e0
% 231.54/42.75  | | | | | 
% 231.54/42.75  | | | | | REF_CLOSE: (5), (14), (39) are inconsistent by sub-proof #1822.
% 231.54/42.75  | | | | | 
% 231.54/42.75  | | | | Case 2:
% 231.54/42.75  | | | | | 
% 231.54/42.75  | | | | |   (40)  all_57_12 = e0 & op(e0, e3) = e0
% 231.54/42.75  | | | | | 
% 231.54/42.75  | | | | | ALPHA: (40) implies:
% 231.54/42.75  | | | | |   (41)  all_57_12 = e0
% 231.54/42.75  | | | | | 
% 231.54/42.75  | | | | | REF_CLOSE: (7), (32), (41) are inconsistent by sub-proof #2385.
% 231.54/42.75  | | | | | 
% 231.54/42.75  | | | | End of split
% 231.54/42.75  | | | | 
% 231.54/42.75  | | | End of split
% 231.54/42.75  | | | 
% 231.54/42.75  | | End of split
% 231.54/42.75  | | 
% 231.54/42.75  | End of split
% 231.54/42.75  | 
% 231.54/42.75  End of proof
% 231.54/42.75  
% 231.54/42.75  Sub-proof #1535 shows that the following formulas are inconsistent:
% 231.54/42.75  ----------------------------------------------------------------
% 231.54/42.75    (1)  all_57_0 = e2
% 231.54/42.75    (2)  all_57_12 = e0
% 231.54/42.75    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.54/42.75         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.54/42.75    (4)   ~ (e3 = e1)
% 231.54/42.75    (5)  all_57_2 = e3
% 231.54/42.75    (6)   ~ (e1 = e0)
% 231.54/42.75    (7)  all_57_6 = e3
% 231.54/42.75    (8)   ~ (e2 = e1)
% 231.54/42.75  
% 231.54/42.75  Begin of proof
% 231.54/42.75  | 
% 231.54/42.75  | BETA: splitting (3) gives:
% 231.54/42.75  | 
% 231.54/42.75  | Case 1:
% 231.54/42.75  | | 
% 231.54/42.75  | |   (9)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1)
% 231.54/42.75  | | 
% 231.54/42.75  | | BETA: splitting (9) gives:
% 231.54/42.75  | | 
% 231.54/42.75  | | Case 1:
% 231.54/42.75  | | | 
% 231.54/42.75  | | |   (10)  all_57_0 = e1 & op(e3, e3) = e1
% 231.54/42.75  | | | 
% 231.54/42.75  | | | ALPHA: (10) implies:
% 231.54/42.75  | | |   (11)  all_57_0 = e1
% 231.54/42.75  | | | 
% 231.54/42.75  | | | COMBINE_EQS: (1), (11) imply:
% 231.54/42.75  | | |   (12)  e2 = e1
% 231.54/42.75  | | | 
% 231.54/42.75  | | | REDUCE: (8), (12) imply:
% 231.54/42.75  | | |   (13)  $false
% 231.54/42.75  | | | 
% 231.54/42.75  | | | CLOSE: (13) is inconsistent.
% 231.54/42.75  | | | 
% 231.54/42.75  | | Case 2:
% 231.54/42.75  | | | 
% 231.54/42.75  | | |   (14)  all_57_2 = e1 & op(e2, e3) = e1
% 231.54/42.75  | | | 
% 231.54/42.75  | | | ALPHA: (14) implies:
% 231.54/42.75  | | |   (15)  all_57_2 = e1
% 231.54/42.75  | | | 
% 231.54/42.75  | | | REF_CLOSE: (4), (5), (15) are inconsistent by sub-proof #2397.
% 231.54/42.75  | | | 
% 231.54/42.75  | | End of split
% 231.54/42.75  | | 
% 231.54/42.75  | Case 2:
% 231.54/42.75  | | 
% 231.54/42.75  | |   (16)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) =
% 231.54/42.75  | |           e1)
% 231.54/42.75  | | 
% 231.54/42.75  | | REF_CLOSE: (2), (4), (6), (7), (16) are inconsistent by sub-proof #2013.
% 231.54/42.75  | | 
% 231.54/42.75  | End of split
% 231.54/42.75  | 
% 231.54/42.75  End of proof
% 231.54/42.75  
% 231.54/42.75  Sub-proof #1536 shows that the following formulas are inconsistent:
% 231.54/42.75  ----------------------------------------------------------------
% 231.54/42.75    (1)   ~ (e3 = e1)
% 231.54/42.75    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.75           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.75    (3)  op(e2, e2) = e0
% 231.54/42.75    (4)  all_57_3 = e0
% 231.54/42.75    (5)   ~ (e3 = e2)
% 231.54/42.75    (6)   ~ (e3 = e0)
% 231.54/42.75    (7)   ~ (e2 = e0)
% 231.54/42.75    (8)  all_57_2 = e1
% 231.54/42.75    (9)  all_57_5 = e1
% 231.54/42.75    (10)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.54/42.75          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.54/42.75    (11)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.75          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.54/42.75    (12)   ~ (e2 = e1)
% 231.54/42.75  
% 231.54/42.75  Begin of proof
% 231.54/42.75  | 
% 231.54/42.75  | BETA: splitting (11) gives:
% 231.54/42.75  | 
% 231.54/42.75  | Case 1:
% 231.54/42.75  | | 
% 231.54/42.75  | |   (13)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 231.54/42.75  | |           e2)
% 231.54/42.75  | | 
% 231.54/42.75  | | REF_CLOSE: (2), (3), (7), (8), (12), (13) are inconsistent by sub-proof
% 231.54/42.75  | |            #2364.
% 231.54/42.75  | | 
% 231.54/42.75  | Case 2:
% 231.54/42.75  | | 
% 231.54/42.75  | |   (14)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 231.54/42.75  | |           e2)
% 231.54/42.75  | | 
% 231.54/42.75  | | BETA: splitting (14) gives:
% 231.54/42.75  | | 
% 231.54/42.75  | | Case 1:
% 231.54/42.75  | | | 
% 231.54/42.75  | | |   (15)  all_57_5 = e2 & op(e2, e1) = e2
% 231.54/42.75  | | | 
% 231.54/42.75  | | | ALPHA: (15) implies:
% 231.54/42.75  | | |   (16)  all_57_5 = e2
% 231.54/42.75  | | | 
% 231.54/42.76  | | | REF_CLOSE: (9), (12), (16) are inconsistent by sub-proof #1885.
% 231.54/42.76  | | | 
% 231.54/42.76  | | Case 2:
% 231.54/42.76  | | | 
% 231.54/42.76  | | |   (17)  all_57_10 = e2 & op(e2, e0) = e2
% 231.54/42.76  | | | 
% 231.54/42.76  | | | ALPHA: (17) implies:
% 231.54/42.76  | | |   (18)  all_57_10 = e2
% 231.54/42.76  | | | 
% 231.54/42.76  | | | REF_CLOSE: (1), (4), (5), (6), (8), (9), (10), (18) are inconsistent by
% 231.54/42.76  | | |            sub-proof #1645.
% 231.54/42.76  | | | 
% 231.54/42.76  | | End of split
% 231.54/42.76  | | 
% 231.54/42.76  | End of split
% 231.54/42.76  | 
% 231.54/42.76  End of proof
% 231.54/42.76  
% 231.54/42.76  Sub-proof #1537 shows that the following formulas are inconsistent:
% 231.54/42.76  ----------------------------------------------------------------
% 231.54/42.76    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.76         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.54/42.76    (2)   ~ (e3 = e1)
% 231.54/42.76    (3)  all_57_4 = e0
% 231.54/42.76    (4)  all_57_3 = e0
% 231.54/42.76    (5)   ~ (e3 = e2)
% 231.54/42.76    (6)  all_57_4 = e1
% 231.54/42.76    (7)  all_57_5 = e3
% 231.54/42.76    (8)   ~ (e2 = e0)
% 231.54/42.76    (9)   ~ (e1 = e0)
% 231.54/42.76    (10)  all_57_2 = e1
% 231.54/42.76    (11)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.76          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.54/42.76    (12)   ~ (e2 = e1)
% 231.54/42.76  
% 231.54/42.76  Begin of proof
% 231.54/42.76  | 
% 231.54/42.76  | COMBINE_EQS: (3), (6) imply:
% 231.54/42.76  |   (13)  e1 = e0
% 231.54/42.76  | 
% 231.54/42.76  | SIMP: (13) implies:
% 231.54/42.76  |   (14)  e1 = e0
% 231.54/42.76  | 
% 231.54/42.76  | COMBINE_EQS: (10), (14) imply:
% 231.54/42.76  |   (15)  all_57_2 = e0
% 231.54/42.76  | 
% 231.54/42.76  | REF_CLOSE: (1), (2), (4), (5), (7), (8), (9), (11), (12), (15) are
% 231.54/42.76  |            inconsistent by sub-proof #2253.
% 231.54/42.76  | 
% 231.54/42.76  End of proof
% 231.54/42.76  
% 231.54/42.76  Sub-proof #1538 shows that the following formulas are inconsistent:
% 231.54/42.76  ----------------------------------------------------------------
% 231.54/42.76    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.76           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.76    (2)  all_57_9 = e2 & op(e3, e0) = e2
% 231.54/42.76    (3)   ~ (all_53_4 = all_53_12)
% 231.54/42.76    (4)   ~ (all_53_4 = e1)
% 231.54/42.76    (5)  all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 231.54/42.76    (6)  all_55_1 = all_53_4
% 231.54/42.76    (7)   ~ (all_53_4 = e0)
% 231.54/42.76    (8)  op(e3, e0) = all_53_12
% 231.54/42.76  
% 231.54/42.76  Begin of proof
% 231.54/42.76  | 
% 231.54/42.76  | ALPHA: (2) implies:
% 231.54/42.76  |   (9)  op(e3, e0) = e2
% 231.54/42.76  | 
% 231.54/42.76  | BETA: splitting (5) gives:
% 231.54/42.76  | 
% 231.54/42.76  | Case 1:
% 231.54/42.76  | | 
% 231.54/42.76  | |   (10)  all_55_1 = e2
% 231.54/42.76  | | 
% 231.54/42.76  | | COMBINE_EQS: (6), (10) imply:
% 231.54/42.76  | |   (11)  all_53_4 = e2
% 231.54/42.76  | | 
% 231.54/42.76  | | SIMP: (11) implies:
% 231.54/42.76  | |   (12)  all_53_4 = e2
% 231.54/42.76  | | 
% 231.54/42.76  | | REDUCE: (3), (12) imply:
% 231.54/42.76  | |   (13)   ~ (all_53_12 = e2)
% 231.54/42.76  | | 
% 231.54/42.76  | | SIMP: (13) implies:
% 231.54/42.76  | |   (14)   ~ (all_53_12 = e2)
% 231.54/42.76  | | 
% 231.54/42.76  | | REF_CLOSE: (1), (8), (9), (14) are inconsistent by sub-proof #2331.
% 231.54/42.76  | | 
% 231.54/42.76  | Case 2:
% 231.54/42.76  | | 
% 231.54/42.76  | |   (15)  all_55_1 = e1 | all_55_1 = e0
% 231.54/42.76  | | 
% 231.54/42.76  | | REF_CLOSE: (4), (6), (7), (15) are inconsistent by sub-proof #1730.
% 231.54/42.76  | | 
% 231.54/42.76  | End of split
% 231.54/42.76  | 
% 231.54/42.76  End of proof
% 231.54/42.76  
% 231.54/42.76  Sub-proof #1539 shows that the following formulas are inconsistent:
% 231.54/42.76  ----------------------------------------------------------------
% 231.54/42.76    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.76         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.54/42.76    (2)   ~ (e3 = e1)
% 231.54/42.76    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.76           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.76    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.54/42.76         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.54/42.76    (5)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.54/42.76         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.54/42.76    (6)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.54/42.76         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.54/42.76    (7)  all_57_3 = e0
% 231.54/42.76    (8)  all_57_4 = e3
% 231.54/42.76    (9)   ~ (e3 = e2)
% 231.54/42.76    (10)   ~ (e3 = e0)
% 231.54/42.76    (11)  op(e3, e3) = e3
% 231.54/42.76    (12)   ~ (e2 = e0)
% 231.54/42.76    (13)   ~ (e1 = e0)
% 231.54/42.76    (14)  all_57_7 = e3
% 231.54/42.76    (15)   ~ (e2 = e1)
% 231.54/42.76    (16)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.76          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.54/42.76  
% 231.54/42.76  Begin of proof
% 231.54/42.76  | 
% 231.54/42.76  | BETA: splitting (6) gives:
% 231.54/42.76  | 
% 231.54/42.76  | Case 1:
% 231.54/42.76  | | 
% 231.54/42.76  | |   (17)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) =
% 231.54/42.76  | |           e0)
% 231.54/42.76  | | 
% 231.54/42.76  | | BETA: splitting (17) gives:
% 231.54/42.76  | | 
% 231.54/42.76  | | Case 1:
% 231.54/42.76  | | | 
% 231.54/42.76  | | |   (18)  all_57_0 = e0 & op(e3, e3) = e0
% 231.54/42.76  | | | 
% 231.54/42.76  | | | ALPHA: (18) implies:
% 231.54/42.76  | | |   (19)  op(e3, e3) = e0
% 231.54/42.76  | | | 
% 231.54/42.76  | | | REF_CLOSE: (3), (10), (11), (19) are inconsistent by sub-proof #2494.
% 231.54/42.76  | | | 
% 231.54/42.76  | | Case 2:
% 231.54/42.76  | | | 
% 231.54/42.76  | | |   (20)  all_57_1 = e0 & op(e3, e2) = e0
% 231.54/42.76  | | | 
% 231.54/42.76  | | | ALPHA: (20) implies:
% 231.54/42.76  | | |   (21)  all_57_1 = e0
% 231.54/42.76  | | | 
% 231.54/42.76  | | | REF_CLOSE: (1), (2), (7), (9), (12), (13), (14), (15), (16), (21) are
% 231.54/42.76  | | |            inconsistent by sub-proof #2098.
% 231.54/42.76  | | | 
% 231.54/42.76  | | End of split
% 231.54/42.76  | | 
% 231.54/42.76  | Case 2:
% 231.54/42.76  | | 
% 231.54/42.76  | |   (22)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) =
% 231.54/42.76  | |           e0)
% 231.54/42.76  | | 
% 231.54/42.76  | | BETA: splitting (22) gives:
% 231.54/42.76  | | 
% 231.54/42.76  | | Case 1:
% 231.54/42.76  | | | 
% 231.54/42.76  | | |   (23)  all_57_4 = e0 & op(e3, e1) = e0
% 231.54/42.76  | | | 
% 231.54/42.76  | | | REF_CLOSE: (8), (10), (23) are inconsistent by sub-proof #2491.
% 231.54/42.76  | | | 
% 231.54/42.76  | | Case 2:
% 231.54/42.76  | | | 
% 231.54/42.76  | | |   (24)  all_57_9 = e0 & op(e3, e0) = e0
% 231.54/42.76  | | | 
% 231.54/42.76  | | | ALPHA: (24) implies:
% 231.54/42.76  | | |   (25)  all_57_9 = e0
% 231.54/42.76  | | | 
% 231.54/42.76  | | | REF_CLOSE: (2), (3), (4), (5), (8), (9), (11), (12), (13), (15), (25) are
% 231.54/42.76  | | |            inconsistent by sub-proof #2477.
% 231.54/42.76  | | | 
% 231.54/42.76  | | End of split
% 231.54/42.76  | | 
% 231.54/42.76  | End of split
% 231.54/42.76  | 
% 231.54/42.76  End of proof
% 231.54/42.76  
% 231.54/42.76  Sub-proof #1540 shows that the following formulas are inconsistent:
% 231.54/42.76  ----------------------------------------------------------------
% 231.54/42.76    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.76           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.76    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1)
% 231.54/42.76    (3)  all_57_2 = e2
% 231.54/42.76    (4)  op(e2, e2) = e0
% 231.54/42.76    (5)   ~ (e1 = e0)
% 231.54/42.76    (6)   ~ (e2 = e1)
% 231.54/42.76  
% 231.54/42.76  Begin of proof
% 231.54/42.76  | 
% 231.54/42.76  | BETA: splitting (2) gives:
% 231.54/42.76  | 
% 231.54/42.76  | Case 1:
% 231.54/42.76  | | 
% 231.54/42.76  | |   (7)  all_57_2 = e1 & op(e2, e3) = e1
% 231.54/42.76  | | 
% 231.54/42.76  | | REF_CLOSE: (3), (6), (7) are inconsistent by sub-proof #2244.
% 231.54/42.76  | | 
% 231.54/42.76  | Case 2:
% 231.54/42.76  | | 
% 231.54/42.76  | |   (8)  all_57_3 = e1 & op(e2, e2) = e1
% 231.54/42.76  | | 
% 231.54/42.76  | | ALPHA: (8) implies:
% 231.54/42.76  | |   (9)  op(e2, e2) = e1
% 231.54/42.76  | | 
% 231.54/42.76  | | REF_CLOSE: (1), (4), (5), (9) are inconsistent by sub-proof #2352.
% 231.54/42.76  | | 
% 231.54/42.76  | End of split
% 231.54/42.76  | 
% 231.54/42.76  End of proof
% 231.54/42.76  
% 231.54/42.76  Sub-proof #1541 shows that the following formulas are inconsistent:
% 231.54/42.76  ----------------------------------------------------------------
% 231.54/42.76    (1)  all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 231.54/42.76    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.76           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.76    (3)  op(e2, e2) = e0
% 231.54/42.76    (4)  all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 231.54/42.76    (5)  all_55_1 = all_53_4
% 231.54/42.76    (6)  all_55_13 = all_52_27
% 231.54/42.76    (7)   ~ (all_53_4 = e0)
% 231.54/42.76    (8)   ~ (all_52_27 = e0)
% 231.54/42.76    (9)   ~ (all_53_4 = all_52_27)
% 231.54/42.76    (10)   ~ (all_53_4 = e2)
% 231.54/42.76    (11)  op(all_52_27, all_52_27) = e2
% 231.54/42.76    (12)   ~ (all_52_27 = e3)
% 231.54/42.76  
% 231.54/42.76  Begin of proof
% 231.54/42.76  | 
% 231.54/42.76  | BETA: splitting (4) gives:
% 231.54/42.76  | 
% 231.54/42.76  | Case 1:
% 231.54/42.76  | | 
% 231.54/42.76  | |   (13)  all_55_1 = e2
% 231.54/42.76  | | 
% 231.54/42.76  | | REF_CLOSE: (5), (10), (13) are inconsistent by sub-proof #2284.
% 231.54/42.76  | | 
% 231.54/42.76  | Case 2:
% 231.54/42.76  | | 
% 231.54/42.76  | |   (14)  all_55_1 = e1 | all_55_1 = e0
% 231.54/42.76  | | 
% 231.54/42.76  | | BETA: splitting (14) gives:
% 231.54/42.76  | | 
% 231.54/42.76  | | Case 1:
% 231.54/42.76  | | | 
% 231.54/42.76  | | |   (15)  all_55_1 = e1
% 231.54/42.76  | | | 
% 231.54/42.76  | | | COMBINE_EQS: (5), (15) imply:
% 231.54/42.76  | | |   (16)  all_53_4 = e1
% 231.54/42.76  | | | 
% 231.54/42.76  | | | SIMP: (16) implies:
% 231.54/42.76  | | |   (17)  all_53_4 = e1
% 231.54/42.76  | | | 
% 231.54/42.76  | | | REDUCE: (9), (17) imply:
% 231.54/42.76  | | |   (18)   ~ (all_52_27 = e1)
% 231.54/42.76  | | | 
% 231.54/42.76  | | | SIMP: (18) implies:
% 231.54/42.76  | | |   (19)   ~ (all_52_27 = e1)
% 231.54/42.76  | | | 
% 231.54/42.76  | | | REF_CLOSE: (1), (2), (3), (6), (8), (11), (12), (19) are inconsistent by
% 231.54/42.76  | | |            sub-proof #1613.
% 231.54/42.76  | | | 
% 231.54/42.76  | | Case 2:
% 231.54/42.76  | | | 
% 231.54/42.76  | | |   (20)  all_55_1 = e0
% 231.54/42.76  | | | 
% 231.54/42.76  | | | REF_CLOSE: (5), (7), (20) are inconsistent by sub-proof #2076.
% 231.54/42.76  | | | 
% 231.54/42.76  | | End of split
% 231.54/42.76  | | 
% 231.54/42.76  | End of split
% 231.54/42.76  | 
% 231.54/42.76  End of proof
% 231.54/42.76  
% 231.54/42.76  Sub-proof #1542 shows that the following formulas are inconsistent:
% 231.54/42.76  ----------------------------------------------------------------
% 231.54/42.76    (1)   ~ (all_52_29 = e0)
% 231.54/42.76    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.76           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.76    (3)  op(e2, e2) = e0
% 231.54/42.76    (4)  all_55_14 = all_52_29
% 231.54/42.76    (5)   ~ (all_52_29 = e3)
% 231.54/42.76    (6)   ~ (all_52_29 = e1)
% 231.54/42.76    (7)   ~ (e1 = e0)
% 231.54/42.76    (8)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 231.54/42.76    (9)  op(all_52_29, all_52_29) = e1
% 231.54/42.76  
% 231.54/42.76  Begin of proof
% 231.54/42.76  | 
% 231.54/42.76  | BETA: splitting (8) gives:
% 231.54/42.76  | 
% 231.54/42.76  | Case 1:
% 231.54/42.76  | | 
% 231.54/42.76  | |   (10)  all_55_14 = e3
% 231.54/42.76  | | 
% 231.54/42.76  | | COMBINE_EQS: (4), (10) imply:
% 231.54/42.76  | |   (11)  all_52_29 = e3
% 231.54/42.76  | | 
% 231.54/42.76  | | REDUCE: (5), (11) imply:
% 231.54/42.76  | |   (12)  $false
% 231.54/42.76  | | 
% 231.54/42.76  | | CLOSE: (12) is inconsistent.
% 231.54/42.76  | | 
% 231.54/42.76  | Case 2:
% 231.54/42.76  | | 
% 231.54/42.76  | |   (13)  all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 231.54/42.76  | | 
% 231.54/42.76  | | BETA: splitting (13) gives:
% 231.54/42.76  | | 
% 231.54/42.76  | | Case 1:
% 231.54/42.76  | | | 
% 231.54/42.76  | | |   (14)  all_55_14 = e2
% 231.54/42.76  | | | 
% 231.54/42.76  | | | COMBINE_EQS: (4), (14) imply:
% 231.54/42.76  | | |   (15)  all_52_29 = e2
% 231.54/42.76  | | | 
% 231.54/42.76  | | | SIMP: (15) implies:
% 231.54/42.76  | | |   (16)  all_52_29 = e2
% 231.54/42.76  | | | 
% 231.54/42.76  | | | REDUCE: (9), (16) imply:
% 231.54/42.76  | | |   (17)  op(e2, e2) = e1
% 231.54/42.76  | | | 
% 231.54/42.76  | | | REF_CLOSE: (2), (3), (7), (17) are inconsistent by sub-proof #2352.
% 231.54/42.76  | | | 
% 231.54/42.76  | | Case 2:
% 231.54/42.76  | | | 
% 231.54/42.76  | | |   (18)  all_55_14 = e1 | all_55_14 = e0
% 231.54/42.76  | | | 
% 231.54/42.76  | | | REF_CLOSE: (1), (4), (6), (18) are inconsistent by sub-proof #2035.
% 231.54/42.76  | | | 
% 231.54/42.76  | | End of split
% 231.54/42.76  | | 
% 231.54/42.76  | End of split
% 231.54/42.76  | 
% 231.54/42.76  End of proof
% 231.54/42.76  
% 231.54/42.76  Sub-proof #1543 shows that the following formulas are inconsistent:
% 231.54/42.76  ----------------------------------------------------------------
% 231.54/42.76    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.76           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.76    (2)   ~ (e3 = e0)
% 231.54/42.76    (3)  op(e3, e3) = e3
% 231.54/42.76    (4)  op(e3, e2) = all_53_4
% 231.54/42.76    (5)   ~ (all_53_4 = e0)
% 231.54/42.76    (6)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0)
% 231.54/42.76  
% 231.54/42.76  Begin of proof
% 231.54/42.76  | 
% 231.54/42.76  | BETA: splitting (6) gives:
% 231.54/42.76  | 
% 231.54/42.76  | Case 1:
% 231.54/42.76  | | 
% 231.54/42.76  | |   (7)  all_57_0 = e0 & op(e3, e3) = e0
% 231.54/42.76  | | 
% 231.54/42.76  | | ALPHA: (7) implies:
% 231.54/42.76  | |   (8)  op(e3, e3) = e0
% 231.54/42.76  | | 
% 231.54/42.76  | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #2494.
% 231.54/42.76  | | 
% 231.54/42.76  | Case 2:
% 231.54/42.76  | | 
% 231.54/42.76  | |   (9)  all_57_1 = e0 & op(e3, e2) = e0
% 231.54/42.76  | | 
% 231.54/42.76  | | ALPHA: (9) implies:
% 231.54/42.76  | |   (10)  op(e3, e2) = e0
% 231.54/42.76  | | 
% 231.54/42.76  | | REF_CLOSE: (1), (4), (5), (10) are inconsistent by sub-proof #1941.
% 231.54/42.76  | | 
% 231.54/42.76  | End of split
% 231.54/42.76  | 
% 231.54/42.76  End of proof
% 231.54/42.76  
% 231.54/42.76  Sub-proof #1544 shows that the following formulas are inconsistent:
% 231.54/42.76  ----------------------------------------------------------------
% 231.54/42.76    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.76           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.76    (2)   ~ (all_53_12 = e0)
% 231.54/42.76    (3)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.54/42.76    (4)   ~ (all_53_8 = e0)
% 231.54/42.76    (5)  op(e3, e1) = all_53_8
% 231.54/42.76    (6)  op(e3, e0) = all_53_12
% 231.54/42.76  
% 231.54/42.76  Begin of proof
% 231.54/42.76  | 
% 231.54/42.76  | BETA: splitting (3) gives:
% 231.54/42.76  | 
% 231.54/42.76  | Case 1:
% 231.54/42.76  | | 
% 231.54/42.76  | |   (7)  all_57_4 = e0 & op(e3, e1) = e0
% 231.54/42.76  | | 
% 231.54/42.76  | | ALPHA: (7) implies:
% 231.54/42.76  | |   (8)  op(e3, e1) = e0
% 231.54/42.76  | | 
% 231.54/42.76  | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #2267.
% 231.54/42.76  | | 
% 231.54/42.76  | Case 2:
% 231.54/42.76  | | 
% 231.54/42.76  | |   (9)  all_57_9 = e0 & op(e3, e0) = e0
% 231.54/42.76  | | 
% 231.54/42.76  | | REF_CLOSE: (1), (2), (6), (9) are inconsistent by sub-proof #2434.
% 231.54/42.76  | | 
% 231.54/42.76  | End of split
% 231.54/42.76  | 
% 231.54/42.76  End of proof
% 231.54/42.76  
% 231.54/42.76  Sub-proof #1545 shows that the following formulas are inconsistent:
% 231.54/42.76  ----------------------------------------------------------------
% 231.54/42.76    (1)  op(e1, e3) = all_52_17
% 231.54/42.76    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 231.54/42.76    (3)  op(e2, e3) = all_53_1
% 231.54/42.76    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.54/42.76         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.54/42.76    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.76           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.76    (6)   ~ (all_6_2 = e3)
% 231.54/42.76    (7)  op(e1, e1) = all_6_2
% 231.54/42.76    (8)  op(all_52_17, all_52_17) = e3
% 231.54/42.76    (9)  op(e0, e3) = all_53_3
% 231.54/42.76    (10)  all_57_0 = e0
% 231.54/42.76    (11)   ~ (all_53_1 = e1)
% 231.54/42.76    (12)   ~ (e1 = e0)
% 231.54/42.76    (13)  all_55_10 = all_6_2
% 231.54/42.76    (14)   ~ (all_53_3 = e1)
% 231.54/42.76  
% 231.54/42.76  Begin of proof
% 231.54/42.76  | 
% 231.54/42.76  | BETA: splitting (4) gives:
% 231.54/42.76  | 
% 231.54/42.76  | Case 1:
% 231.54/42.76  | | 
% 231.54/42.76  | |   (15)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) =
% 231.54/42.76  | |           e1)
% 231.54/42.76  | | 
% 231.54/42.76  | | BETA: splitting (15) gives:
% 231.54/42.76  | | 
% 231.54/42.76  | | Case 1:
% 231.54/42.76  | | | 
% 231.54/42.76  | | |   (16)  all_57_0 = e1 & op(e3, e3) = e1
% 231.54/42.76  | | | 
% 231.54/42.76  | | | REF_CLOSE: (10), (12), (16) are inconsistent by sub-proof #2454.
% 231.54/42.76  | | | 
% 231.54/42.76  | | Case 2:
% 231.54/42.76  | | | 
% 231.54/42.76  | | |   (17)  all_57_2 = e1 & op(e2, e3) = e1
% 231.54/42.76  | | | 
% 231.54/42.76  | | | REF_CLOSE: (3), (5), (11), (17) are inconsistent by sub-proof #2156.
% 231.54/42.76  | | | 
% 231.54/42.76  | | End of split
% 231.54/42.76  | | 
% 231.54/42.76  | Case 2:
% 231.54/42.76  | | 
% 231.54/42.76  | |   (18)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) =
% 231.54/42.76  | |           e1)
% 231.54/42.76  | | 
% 231.54/42.76  | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (9), (13), (14), (18) are
% 231.54/42.76  | |            inconsistent by sub-proof #1860.
% 231.54/42.76  | | 
% 231.54/42.76  | End of split
% 231.54/42.76  | 
% 231.54/42.76  End of proof
% 231.54/42.76  
% 231.54/42.76  Sub-proof #1546 shows that the following formulas are inconsistent:
% 231.54/42.76  ----------------------------------------------------------------
% 231.54/42.76    (1)  all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 231.54/42.76    (2)   ~ (all_53_12 = e1)
% 231.54/42.76    (3)  all_55_3 = all_53_12
% 231.54/42.76    (4)   ~ (all_53_12 = e0)
% 231.54/42.76    (5)   ~ (all_53_12 = e2)
% 231.54/42.76  
% 231.54/42.76  Begin of proof
% 231.54/42.76  | 
% 231.54/42.76  | BETA: splitting (1) gives:
% 231.54/42.76  | 
% 231.54/42.76  | Case 1:
% 231.54/42.76  | | 
% 231.54/42.76  | |   (6)  all_55_3 = e2
% 231.54/42.76  | | 
% 231.54/42.76  | | REF_CLOSE: (3), (5), (6) are inconsistent by sub-proof #1612.
% 231.54/42.76  | | 
% 231.54/42.76  | Case 2:
% 231.54/42.76  | | 
% 231.54/42.76  | |   (7)  all_55_3 = e1 | all_55_3 = e0
% 231.54/42.76  | | 
% 231.54/42.76  | | REF_CLOSE: (2), (3), (4), (7) are inconsistent by sub-proof #2132.
% 231.54/42.76  | | 
% 231.54/42.76  | End of split
% 231.54/42.76  | 
% 231.54/42.76  End of proof
% 231.54/42.76  
% 231.54/42.76  Sub-proof #1547 shows that the following formulas are inconsistent:
% 231.54/42.76  ----------------------------------------------------------------
% 231.54/42.76    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.76         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.54/42.76    (2)   ~ (e3 = e1)
% 231.54/42.76    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.76           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.76    (4)  op(e2, e2) = e1
% 231.54/42.76    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.54/42.76         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.54/42.76    (6)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.54/42.76         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.54/42.76    (7)   ~ (e3 = e2)
% 231.54/42.76    (8)   ~ (e3 = e0)
% 231.54/42.76    (9)  all_57_0 = e0
% 231.54/42.76    (10)  op(e3, e3) = e0
% 231.54/42.76    (11)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 231.54/42.76          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 231.54/42.76    (12)   ~ (e2 = e0)
% 231.54/42.76    (13)  all_57_13 = e2
% 231.54/42.76    (14)  all_57_3 = e1
% 231.54/42.76    (15)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 231.54/42.76          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.54/42.76    (16)   ~ (e1 = e0)
% 231.54/42.76    (17)   ~ (all_53_12 = e3)
% 231.54/42.76    (18)  all_57_7 = e3
% 231.54/42.76    (19)  all_57_1 = e3
% 231.54/42.76    (20)   ~ (e2 = e1)
% 231.54/42.76    (21)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.76          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.54/42.76    (22)  all_57_7 = e0
% 231.54/42.76    (23)  op(e3, e0) = all_53_12
% 231.54/42.76  
% 231.54/42.76  Begin of proof
% 231.54/42.76  | 
% 231.54/42.76  | COMBINE_EQS: (18), (22) imply:
% 231.54/42.76  |   (24)  e3 = e0
% 231.54/42.76  | 
% 231.54/42.76  | SIMP: (24) implies:
% 231.54/42.76  |   (25)  e3 = e0
% 231.54/42.76  | 
% 231.54/42.76  | COMBINE_EQS: (19), (25) imply:
% 231.54/42.76  |   (26)  all_57_1 = e0
% 231.54/42.76  | 
% 231.54/42.76  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 231.54/42.76  |            (13), (14), (15), (16), (17), (18), (20), (21), (23), (26) are
% 231.54/42.76  |            inconsistent by sub-proof #1707.
% 231.54/42.76  | 
% 231.54/42.76  End of proof
% 231.54/42.76  
% 231.54/42.76  Sub-proof #1548 shows that the following formulas are inconsistent:
% 231.54/42.76  ----------------------------------------------------------------
% 231.54/42.76    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.76         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.54/42.76    (2)   ~ (e3 = e1)
% 231.54/42.76    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.76           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.76    (4)  op(e2, e2) = e1
% 231.54/42.76    (5)  all_57_6 = e1
% 231.54/42.76    (6)   ~ (e3 = e2)
% 231.54/42.76    (7)   ~ (e3 = e0)
% 231.54/42.76    (8)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 231.54/42.76         (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 231.54/42.76    (9)   ~ (e2 = e0)
% 231.54/42.76    (10)   ~ (e1 = e0)
% 231.54/42.76    (11)  all_57_6 = e3
% 231.54/42.76    (12)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.54/42.76          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.54/42.76    (13)  all_57_1 = e3
% 231.54/42.76    (14)   ~ (e2 = e1)
% 231.54/42.76  
% 231.54/42.76  Begin of proof
% 231.54/42.76  | 
% 231.54/42.76  | COMBINE_EQS: (5), (11) imply:
% 231.54/42.76  |   (15)  e3 = e1
% 231.54/42.76  | 
% 231.54/42.76  | SIMP: (15) implies:
% 231.54/42.76  |   (16)  e3 = e1
% 231.54/42.76  | 
% 231.54/42.76  | COMBINE_EQS: (13), (16) imply:
% 231.54/42.76  |   (17)  all_57_1 = e1
% 231.54/42.76  | 
% 231.54/42.76  | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (12), (14), (17) are
% 231.54/42.76  |            inconsistent by sub-proof #1908.
% 231.54/42.76  | 
% 231.54/42.76  End of proof
% 231.54/42.76  
% 231.54/42.76  Sub-proof #1549 shows that the following formulas are inconsistent:
% 231.54/42.76  ----------------------------------------------------------------
% 231.54/42.76    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.76           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.76    (2)  op(e3, e2) = e3
% 231.54/42.76    (3)  op(e3, e2) = e2
% 231.54/42.76    (4)   ~ (e3 = e2)
% 231.54/42.76  
% 231.54/42.76  Begin of proof
% 231.54/42.76  | 
% 231.54/42.76  | GROUND_INST: instantiating (1) with e2, e3, e2, e3, simplifying with (2), (3)
% 231.54/42.76  |              gives:
% 231.54/42.76  |   (5)  e3 = e2
% 231.54/42.76  | 
% 231.54/42.76  | REDUCE: (4), (5) imply:
% 231.54/42.76  |   (6)  $false
% 231.54/42.76  | 
% 231.54/42.76  | CLOSE: (6) is inconsistent.
% 231.54/42.76  | 
% 231.54/42.76  End of proof
% 231.54/42.76  
% 231.54/42.76  Sub-proof #1550 shows that the following formulas are inconsistent:
% 231.54/42.76  ----------------------------------------------------------------
% 231.54/42.76    (1)   ~ (e3 = e1)
% 231.54/42.76    (2)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 231.54/42.76         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.54/42.76    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.76           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.76    (4)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.54/42.76         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.54/42.76    (5)   ~ (all_6_2 = e3)
% 231.54/42.76    (6)  op(e1, e1) = all_6_2
% 231.54/42.76    (7)  all_57_7 = e2
% 231.54/42.76    (8)  all_57_6 = e1
% 231.54/42.76    (9)   ~ (e3 = e2)
% 231.54/42.76    (10)   ~ (e3 = e0)
% 231.54/42.76    (11)   ~ (all_53_2 = e0)
% 231.54/42.76    (12)   ~ (e2 = e0)
% 231.54/42.76    (13)  op(e1, e3) = all_53_2
% 231.54/42.76    (14)   ~ (all_6_2 = e0)
% 231.54/42.76  
% 231.54/42.76  Begin of proof
% 231.54/42.76  | 
% 231.54/42.76  | BETA: splitting (2) gives:
% 231.54/42.76  | 
% 231.54/42.76  | Case 1:
% 231.54/42.76  | | 
% 231.54/42.76  | |   (15)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) =
% 231.54/42.76  | |           e0)
% 231.54/42.76  | | 
% 231.54/42.76  | | BETA: splitting (15) gives:
% 231.54/42.76  | | 
% 231.54/42.76  | | Case 1:
% 231.54/42.76  | | | 
% 231.54/42.76  | | |   (16)  all_57_6 = e0 & op(e1, e3) = e0
% 231.54/42.76  | | | 
% 231.54/42.76  | | | ALPHA: (16) implies:
% 231.54/42.76  | | |   (17)  op(e1, e3) = e0
% 231.54/42.76  | | | 
% 231.54/42.76  | | | REF_CLOSE: (3), (11), (13), (17) are inconsistent by sub-proof #2154.
% 231.54/42.76  | | | 
% 231.54/42.76  | | Case 2:
% 231.54/42.76  | | | 
% 231.54/42.76  | | |   (18)  all_57_7 = e0 & op(e1, e2) = e0
% 231.54/42.76  | | | 
% 231.54/42.76  | | | ALPHA: (18) implies:
% 231.54/42.76  | | |   (19)  all_57_7 = e0
% 231.54/42.76  | | | 
% 231.54/42.76  | | | REF_CLOSE: (7), (12), (19) are inconsistent by sub-proof #2207.
% 231.54/42.76  | | | 
% 231.54/42.76  | | End of split
% 231.54/42.76  | | 
% 231.54/42.76  | Case 2:
% 231.54/42.76  | | 
% 231.54/42.76  | |   (20)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 231.54/42.76  | |           e0)
% 231.54/42.76  | | 
% 231.54/42.76  | | BETA: splitting (20) gives:
% 231.54/42.76  | | 
% 231.54/42.76  | | Case 1:
% 231.54/42.76  | | | 
% 231.54/42.76  | | |   (21)  all_57_8 = e0 & op(e1, e1) = e0
% 231.54/42.76  | | | 
% 231.54/42.76  | | | REF_CLOSE: (3), (6), (14), (21) are inconsistent by sub-proof #2412.
% 231.54/42.76  | | | 
% 231.54/42.76  | | Case 2:
% 231.54/42.76  | | | 
% 231.54/42.76  | | |   (22)  all_57_11 = e0 & op(e1, e0) = e0
% 231.54/42.76  | | | 
% 231.54/42.76  | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (22) are
% 231.54/42.76  | | |            inconsistent by sub-proof #1586.
% 231.54/42.76  | | | 
% 231.54/42.76  | | End of split
% 231.54/42.76  | | 
% 231.54/42.76  | End of split
% 231.54/42.76  | 
% 231.54/42.76  End of proof
% 231.54/42.76  
% 231.54/42.76  Sub-proof #1551 shows that the following formulas are inconsistent:
% 231.54/42.76  ----------------------------------------------------------------
% 231.54/42.76    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.76         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.54/42.76    (2)   ~ (e3 = e1)
% 231.54/42.76    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.76           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.76    (4)  op(e2, e2) = e1
% 231.54/42.76    (5)   ~ (e3 = e2)
% 231.54/42.76    (6)   ~ (e3 = e0)
% 231.54/42.76    (7)  all_57_0 = e0
% 231.54/42.76    (8)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 231.54/42.76         (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 231.54/42.76    (9)   ~ (e2 = e0)
% 231.54/42.76    (10)   ~ (e1 = e0)
% 231.54/42.76    (11)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.54/42.76          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.54/42.76    (12)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1)
% 231.54/42.76    (13)   ~ (e2 = e1)
% 231.54/42.76  
% 231.54/42.76  Begin of proof
% 231.54/42.76  | 
% 231.54/42.76  | BETA: splitting (12) gives:
% 231.54/42.76  | 
% 231.54/42.76  | Case 1:
% 231.54/42.76  | | 
% 231.54/42.76  | |   (14)  all_57_0 = e1 & op(e3, e3) = e1
% 231.54/42.76  | | 
% 231.54/42.76  | | REF_CLOSE: (7), (10), (14) are inconsistent by sub-proof #2454.
% 231.54/42.76  | | 
% 231.54/42.76  | Case 2:
% 231.54/42.76  | | 
% 231.54/42.76  | |   (15)  all_57_1 = e1 & op(e3, e2) = e1
% 231.54/42.76  | | 
% 231.54/42.76  | | ALPHA: (15) implies:
% 231.54/42.76  | |   (16)  all_57_1 = e1
% 231.54/42.76  | | 
% 231.54/42.76  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (13), (16)
% 231.54/42.76  | |            are inconsistent by sub-proof #1908.
% 231.54/42.76  | | 
% 231.54/42.76  | End of split
% 231.54/42.76  | 
% 231.54/42.76  End of proof
% 231.54/42.76  
% 231.54/42.76  Sub-proof #1552 shows that the following formulas are inconsistent:
% 231.54/42.76  ----------------------------------------------------------------
% 231.54/42.76    (1)  all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 231.54/42.76    (2)  ( ~ (all_26_0 = e3) & op(all_26_1, e2) = all_26_0 & op(e2, e1) = all_26_1
% 231.54/42.76           & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 = e0) & op(e2, e1) =
% 231.54/42.76           all_26_1 & $i(all_26_1))
% 231.54/42.76    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.76           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.76    (4)   ~ (all_53_7 = e1)
% 231.54/42.76    (5)   ~ (all_53_9 = e1)
% 231.54/42.76    (6)  op(e2, e2) = e1
% 231.54/42.76    (7)   ~ (all_53_6 = all_53_7)
% 231.54/42.76    (8)   ~ (e3 = e0)
% 231.54/42.76    (9)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 231.54/42.76    (10)  op(e3, e3) = e0
% 231.54/42.76    (11)  op(e1, e2) = e0
% 231.54/42.76    (12)   ~ (e2 = e0)
% 231.54/42.77    (13)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 231.54/42.77            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 231.54/42.77            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 231.54/42.77            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 231.54/42.77              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 231.54/42.77            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 231.54/42.77            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 231.54/42.77              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 231.54/42.77              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 231.54/42.77            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 231.54/42.77            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 231.54/42.77            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 231.54/42.77              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 231.54/42.77              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 231.54/42.77            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 231.54/42.77              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 231.54/42.77            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 231.54/42.77            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 231.54/42.77              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 231.54/42.77              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 231.54/42.77            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 231.54/42.77            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 231.54/42.77    (14)  op(e0, e0) = e0
% 231.54/42.77    (15)  op(e0, e2) = all_53_7
% 231.54/42.77    (16)   ~ (all_53_13 = e0)
% 231.54/42.77    (17)  ( ~ (all_16_0 = e0) & op(all_16_1, e2) = all_16_0 & op(e2, e1) =
% 231.54/42.77            all_16_1 & $i(all_16_0) & $i(all_16_1)) | ( ~ (all_16_1 = e3) & op(e2,
% 231.54/42.77              e1) = all_16_1 & $i(all_16_1))
% 231.54/42.77    (18)  all_55_13 = all_53_7
% 231.54/42.77    (19)  op(e2, e0) = all_53_13
% 231.54/42.77    (20)  op(e2, e1) = all_53_9
% 231.54/42.77    (21)  op(e1, e2) = all_53_6
% 231.54/42.77  
% 231.54/42.77  Begin of proof
% 231.54/42.77  | 
% 231.54/42.77  | BETA: splitting (9) gives:
% 231.54/42.77  | 
% 231.54/42.77  | Case 1:
% 231.54/42.77  | | 
% 231.54/42.77  | |   (22)  all_57_5 = e0 & op(e2, e1) = e0
% 231.54/42.77  | | 
% 231.54/42.77  | | ALPHA: (22) implies:
% 231.54/42.77  | |   (23)  op(e2, e1) = e0
% 231.54/42.77  | | 
% 231.54/42.77  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13),
% 231.54/42.77  | |            (14), (15), (17), (18), (20), (21), (23) are inconsistent by
% 231.54/42.77  | |            sub-proof #1553.
% 231.54/42.77  | | 
% 231.54/42.77  | Case 2:
% 231.54/42.77  | | 
% 231.54/42.77  | |   (24)  all_57_10 = e0 & op(e2, e0) = e0
% 231.54/42.77  | | 
% 231.54/42.77  | | ALPHA: (24) implies:
% 231.54/42.77  | |   (25)  op(e2, e0) = e0
% 231.54/42.77  | | 
% 231.54/42.77  | | REF_CLOSE: (3), (16), (19), (25) are inconsistent by sub-proof #2470.
% 231.54/42.77  | | 
% 231.54/42.77  | End of split
% 231.54/42.77  | 
% 231.54/42.77  End of proof
% 231.54/42.77  
% 231.54/42.77  Sub-proof #1553 shows that the following formulas are inconsistent:
% 231.54/42.77  ----------------------------------------------------------------
% 231.54/42.77    (1)  all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 231.54/42.77    (2)  ( ~ (all_26_0 = e3) & op(all_26_1, e2) = all_26_0 & op(e2, e1) = all_26_1
% 231.54/42.77           & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 = e0) & op(e2, e1) =
% 231.54/42.77           all_26_1 & $i(all_26_1))
% 231.54/42.77    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.77           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.77    (4)   ~ (all_53_7 = e1)
% 231.54/42.77    (5)   ~ (all_53_9 = e1)
% 231.54/42.77    (6)  op(e2, e2) = e1
% 231.54/42.77    (7)   ~ (all_53_6 = all_53_7)
% 231.54/42.77    (8)   ~ (e3 = e0)
% 231.54/42.77    (9)  op(e3, e3) = e0
% 231.54/42.77    (10)  op(e1, e2) = e0
% 231.54/42.77    (11)   ~ (e2 = e0)
% 231.54/42.77    (12)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 231.54/42.77            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 231.54/42.77            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 231.54/42.77            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 231.54/42.77              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 231.54/42.77            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 231.54/42.77            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 231.54/42.77              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 231.54/42.77              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 231.54/42.77            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 231.54/42.77            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 231.54/42.77            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 231.54/42.77              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 231.54/42.77              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 231.54/42.77            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 231.54/42.77              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 231.54/42.77            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 231.54/42.77            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 231.54/42.77              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 231.54/42.77              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 231.54/42.77            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 231.54/42.77            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 231.54/42.77    (13)  op(e0, e0) = e0
% 231.54/42.77    (14)  op(e0, e2) = all_53_7
% 231.54/42.77    (15)  ( ~ (all_16_0 = e0) & op(all_16_1, e2) = all_16_0 & op(e2, e1) =
% 231.54/42.77            all_16_1 & $i(all_16_0) & $i(all_16_1)) | ( ~ (all_16_1 = e3) & op(e2,
% 231.54/42.77              e1) = all_16_1 & $i(all_16_1))
% 231.54/42.77    (16)  all_55_13 = all_53_7
% 231.54/42.77    (17)  op(e2, e1) = e0
% 231.54/42.77    (18)  op(e2, e1) = all_53_9
% 231.54/42.77    (19)  op(e1, e2) = all_53_6
% 231.54/42.77  
% 231.54/42.77  Begin of proof
% 231.54/42.77  | 
% 231.54/42.77  | GROUND_INST: instantiating (3) with all_53_6, e0, e2, e1, simplifying with
% 231.54/42.77  |              (10), (19) gives:
% 231.54/42.77  |   (20)  all_53_6 = e0
% 231.54/42.77  | 
% 231.54/42.77  | GROUND_INST: instantiating (3) with all_53_9, e0, e1, e2, simplifying with
% 231.54/42.77  |              (17), (18) gives:
% 231.54/42.77  |   (21)  all_53_9 = e0
% 231.54/42.77  | 
% 231.54/42.77  | REDUCE: (7), (20) imply:
% 231.54/42.77  |   (22)   ~ (all_53_7 = e0)
% 231.54/42.77  | 
% 231.54/42.77  | SIMP: (22) implies:
% 231.54/42.77  |   (23)   ~ (all_53_7 = e0)
% 231.54/42.77  | 
% 231.54/42.77  | REDUCE: (5), (21) imply:
% 231.54/42.77  |   (24)   ~ (e1 = e0)
% 231.54/42.77  | 
% 231.54/42.77  | SIMP: (24) implies:
% 231.54/42.77  |   (25)   ~ (e1 = e0)
% 231.54/42.77  | 
% 231.54/42.77  | BETA: splitting (2) gives:
% 231.54/42.77  | 
% 231.54/42.77  | Case 1:
% 231.54/42.77  | | 
% 231.54/42.77  | |   (26)   ~ (all_26_0 = e3) & op(all_26_1, e2) = all_26_0 & op(e2, e1) =
% 231.54/42.77  | |         all_26_1 & $i(all_26_0) & $i(all_26_1)
% 231.54/42.77  | | 
% 231.54/42.77  | | ALPHA: (26) implies:
% 231.54/42.77  | |   (27)   ~ (all_26_0 = e3)
% 231.54/42.77  | |   (28)  op(e2, e1) = all_26_1
% 231.54/42.77  | |   (29)  op(all_26_1, e2) = all_26_0
% 231.54/42.77  | | 
% 231.54/42.77  | | BETA: splitting (12) gives:
% 231.54/42.77  | | 
% 231.54/42.77  | | Case 1:
% 231.54/42.77  | | | 
% 231.54/42.77  | | |   (30)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 231.54/42.77  | | |           op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 231.54/42.77  | | |           op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 231.54/42.77  | | |           op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) =
% 231.54/42.77  | | |           all_52_5 & op(e3, e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) &
% 231.54/42.77  | | |           $i(all_52_5) & $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 &
% 231.54/42.77  | | |           all_52_12 = e1 & all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 231.54/42.77  | | |           op(all_52_11, all_52_11) = e2 & op(all_52_13, all_52_13) = e1 &
% 231.54/42.77  | | |           op(all_52_15, all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2,
% 231.54/42.77  | | |             e2) = all_52_11 & op(e2, e1) = all_52_13 & op(e2, e0) =
% 231.54/42.77  | | |           all_52_15 & $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 231.54/42.77  | | |           $i(all_52_15))
% 231.54/42.77  | | | 
% 231.54/42.77  | | | BETA: splitting (30) gives:
% 231.54/42.77  | | | 
% 231.54/42.77  | | | Case 1:
% 231.54/42.77  | | | | 
% 231.54/42.77  | | | |   (31)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 231.54/42.77  | | | |         op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 231.54/42.77  | | | |         op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 231.54/42.77  | | | |         op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) =
% 231.54/42.77  | | | |         all_52_5 & op(e3, e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) &
% 231.54/42.77  | | | |         $i(all_52_5) & $i(all_52_7)
% 231.54/42.77  | | | | 
% 231.54/42.77  | | | | REF_CLOSE: (3), (8), (9), (13), (31) are inconsistent by sub-proof
% 231.54/42.77  | | | |            #1939.
% 231.54/42.77  | | | | 
% 231.54/42.77  | | | Case 2:
% 231.54/42.77  | | | | 
% 231.54/42.77  | | | |   (32)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 231.54/42.77  | | | |         & op(all_52_9, all_52_9) = e3 & op(all_52_11, all_52_11) = e2 &
% 231.54/42.77  | | | |         op(all_52_13, all_52_13) = e1 & op(all_52_15, all_52_15) = e0 &
% 231.54/42.77  | | | |         op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 & op(e2, e1) =
% 231.54/42.77  | | | |         all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 231.54/42.77  | | | |         $i(all_52_11) & $i(all_52_13) & $i(all_52_15)
% 231.54/42.77  | | | | 
% 231.54/42.77  | | | | ALPHA: (32) implies:
% 231.54/42.77  | | | |   (33)  op(e2, e1) = all_52_13
% 231.54/42.77  | | | |   (34)  op(all_52_13, all_52_13) = e1
% 231.54/42.77  | | | | 
% 231.54/42.77  | | | | REF_CLOSE: (3), (13), (15), (17), (25), (28), (33), (34) are
% 231.54/42.77  | | | |            inconsistent by sub-proof #1713.
% 231.54/42.77  | | | | 
% 231.54/42.77  | | | End of split
% 231.54/42.77  | | | 
% 231.54/42.77  | | Case 2:
% 231.54/42.77  | | | 
% 231.54/42.77  | | |   (35)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 231.54/42.77  | | |           & op(all_52_17, all_52_17) = e3 & op(all_52_19, all_52_19) = e2
% 231.54/42.77  | | |           & op(all_52_21, all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 231.54/42.77  | | |           & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) =
% 231.54/42.77  | | |           all_52_21 & op(e1, e0) = all_52_23 & $i(all_52_17) &
% 231.54/42.77  | | |           $i(all_52_19) & $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 231.54/42.77  | | |           & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0 &
% 231.54/42.77  | | |           op(all_52_25, all_52_25) = e3 & op(all_52_27, all_52_27) = e2 &
% 231.54/42.77  | | |           op(all_52_29, all_52_29) = e1 & op(all_52_31, all_52_31) = e0 &
% 231.54/42.77  | | |           op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 & op(e0, e1) =
% 231.54/42.77  | | |           all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 231.54/42.77  | | |           $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 231.54/42.77  | | | 
% 231.54/42.77  | | | BETA: splitting (35) gives:
% 231.54/42.77  | | | 
% 231.54/42.77  | | | Case 1:
% 231.54/42.77  | | | | 
% 231.54/42.77  | | | |   (36)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 231.54/42.77  | | | |         e0 & op(all_52_17, all_52_17) = e3 & op(all_52_19, all_52_19) =
% 231.54/42.77  | | | |         e2 & op(all_52_21, all_52_21) = e1 & op(all_52_23, all_52_23) =
% 231.54/42.77  | | | |         e0 & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19 & op(e1,
% 231.54/42.77  | | | |           e1) = all_52_21 & op(e1, e0) = all_52_23 & $i(all_52_17) &
% 231.54/42.77  | | | |         $i(all_52_19) & $i(all_52_21) & $i(all_52_23)
% 231.54/42.77  | | | | 
% 231.54/42.77  | | | | ALPHA: (36) implies:
% 231.54/42.77  | | | |   (37)  op(e1, e2) = all_52_19
% 231.54/42.77  | | | |   (38)  op(all_52_19, all_52_19) = e2
% 231.54/42.77  | | | | 
% 231.54/42.77  | | | | REF_CLOSE: (3), (10), (11), (13), (37), (38) are inconsistent by
% 231.54/42.77  | | | |            sub-proof #2158.
% 231.54/42.77  | | | | 
% 231.54/42.77  | | | Case 2:
% 231.54/42.77  | | | | 
% 231.54/42.77  | | | |   (39)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 231.54/42.77  | | | |         e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27, all_52_27) =
% 231.54/42.77  | | | |         e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31, all_52_31) =
% 231.54/42.77  | | | |         e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 & op(e0,
% 231.54/42.77  | | | |           e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 231.54/42.77  | | | |         $i(all_52_27) & $i(all_52_29) & $i(all_52_31)
% 231.54/42.77  | | | | 
% 231.54/42.77  | | | | ALPHA: (39) implies:
% 231.54/42.77  | | | |   (40)  op(e0, e2) = all_52_27
% 231.54/42.77  | | | |   (41)  op(all_52_27, all_52_27) = e2
% 231.54/42.77  | | | | 
% 231.54/42.77  | | | | REF_CLOSE: (1), (3), (4), (6), (14), (16), (17), (23), (27), (28), (29),
% 231.54/42.77  | | | |            (40), (41) are inconsistent by sub-proof #1712.
% 231.54/42.77  | | | | 
% 231.54/42.77  | | | End of split
% 231.54/42.77  | | | 
% 231.54/42.77  | | End of split
% 231.54/42.77  | | 
% 231.54/42.77  | Case 2:
% 231.54/42.77  | | 
% 231.54/42.77  | |   (42)   ~ (all_26_1 = e0) & op(e2, e1) = all_26_1 & $i(all_26_1)
% 231.54/42.77  | | 
% 231.54/42.77  | | REF_CLOSE: (3), (15), (17), (42) are inconsistent by sub-proof #1710.
% 231.54/42.77  | | 
% 231.54/42.77  | End of split
% 231.54/42.77  | 
% 231.54/42.77  End of proof
% 231.54/42.77  
% 231.54/42.77  Sub-proof #1554 shows that the following formulas are inconsistent:
% 231.54/42.77  ----------------------------------------------------------------
% 231.54/42.77    (1)  all_57_15 = e0
% 231.54/42.77    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.77         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.54/42.77    (3)   ~ (e3 = e1)
% 231.54/42.77    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.77           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.77    (5)  op(e2, e2) = e1
% 231.54/42.77    (6)   ~ (e3 = e2)
% 231.54/42.77    (7)   ~ (e3 = e0)
% 231.54/42.77    (8)  op(e3, e3) = e0
% 231.54/42.77    (9)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 231.54/42.77         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.54/42.77    (10)  all_57_12 = e1
% 231.54/42.77    (11)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 231.54/42.77          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 231.54/42.77    (12)   ~ (e2 = e0)
% 231.54/42.77    (13)   ~ (e1 = e0)
% 231.54/42.77    (14)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.54/42.77          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.54/42.77    (15)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.54/42.77          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 231.54/42.77            e3)
% 231.54/42.77    (16)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.54/42.77          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.54/42.77            e2)
% 231.54/42.77    (17)  all_57_2 = e0
% 231.54/42.77    (18)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 231.54/42.77          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 231.54/42.77    (19)   ~ (e2 = e1)
% 231.54/42.77    (20)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.54/42.77          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.54/42.77    (21)  all_57_14 = e0
% 231.54/42.77    (22)  all_57_7 = e0
% 231.54/42.77  
% 231.54/42.77  Begin of proof
% 231.54/42.77  | 
% 231.54/42.77  | BETA: splitting (15) gives:
% 231.54/42.77  | 
% 231.54/42.77  | Case 1:
% 231.54/42.77  | | 
% 231.54/42.77  | |   (23)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 231.54/42.77  | |           e3)
% 231.54/42.77  | | 
% 231.54/42.77  | | BETA: splitting (23) gives:
% 231.54/42.77  | | 
% 231.54/42.77  | | Case 1:
% 231.54/42.77  | | | 
% 231.54/42.77  | | |   (24)  all_57_12 = e3 & op(e0, e3) = e3
% 231.54/42.77  | | | 
% 231.54/42.77  | | | ALPHA: (24) implies:
% 231.54/42.77  | | |   (25)  all_57_12 = e3
% 231.54/42.77  | | | 
% 231.54/42.77  | | | REF_CLOSE: (3), (10), (25) are inconsistent by sub-proof #2151.
% 231.54/42.77  | | | 
% 231.54/42.77  | | Case 2:
% 231.54/42.77  | | | 
% 231.54/42.77  | | |   (26)  all_57_13 = e3 & op(e0, e2) = e3
% 231.54/42.77  | | | 
% 231.54/42.77  | | | ALPHA: (26) implies:
% 231.54/42.77  | | |   (27)  all_57_13 = e3
% 231.54/42.77  | | | 
% 231.54/42.77  | | | BETA: splitting (2) gives:
% 231.54/42.77  | | | 
% 231.54/42.77  | | | Case 1:
% 231.54/42.77  | | | | 
% 231.54/42.77  | | | |   (28)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2)
% 231.54/42.77  | | | |           = e2)
% 231.54/42.77  | | | | 
% 231.54/42.77  | | | | BETA: splitting (28) gives:
% 231.54/42.77  | | | | 
% 231.54/42.77  | | | | Case 1:
% 231.54/42.77  | | | | | 
% 231.54/42.77  | | | | |   (29)  all_57_1 = e2 & op(e3, e2) = e2
% 231.54/42.77  | | | | | 
% 231.54/42.77  | | | | | ALPHA: (29) implies:
% 231.54/42.77  | | | | |   (30)  all_57_1 = e2
% 231.54/42.77  | | | | | 
% 231.54/42.77  | | | | | BETA: splitting (16) gives:
% 231.54/42.77  | | | | | 
% 231.54/42.77  | | | | | Case 1:
% 231.54/42.77  | | | | | | 
% 231.54/42.77  | | | | | |   (31)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 &
% 231.54/42.77  | | | | | |           op(e0, e2) = e2)
% 231.54/42.77  | | | | | | 
% 231.54/42.77  | | | | | | BETA: splitting (31) gives:
% 231.54/42.77  | | | | | | 
% 231.54/42.77  | | | | | | Case 1:
% 231.54/42.77  | | | | | | | 
% 231.54/42.77  | | | | | | |   (32)  all_57_12 = e2 & op(e0, e3) = e2
% 231.54/42.77  | | | | | | | 
% 231.54/42.77  | | | | | | | ALPHA: (32) implies:
% 231.54/42.77  | | | | | | |   (33)  all_57_12 = e2
% 231.54/42.77  | | | | | | | 
% 231.54/42.77  | | | | | | | COMBINE_EQS: (10), (33) imply:
% 231.54/42.77  | | | | | | |   (34)  e2 = e1
% 231.54/42.77  | | | | | | | 
% 231.54/42.77  | | | | | | | SIMP: (34) implies:
% 231.54/42.77  | | | | | | |   (35)  e2 = e1
% 231.54/42.77  | | | | | | | 
% 231.54/42.77  | | | | | | | COMBINE_EQS: (30), (35) imply:
% 231.54/42.77  | | | | | | |   (36)  all_57_1 = e1
% 231.54/42.77  | | | | | | | 
% 231.54/42.77  | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (11), (12), (13), (14),
% 231.54/42.77  | | | | | | |            (19), (36) are inconsistent by sub-proof #1908.
% 231.54/42.77  | | | | | | | 
% 231.54/42.77  | | | | | | Case 2:
% 231.54/42.77  | | | | | | | 
% 231.54/42.77  | | | | | | |   (37)  all_57_13 = e2 & op(e0, e2) = e2
% 231.54/42.77  | | | | | | | 
% 231.54/42.77  | | | | | | | REF_CLOSE: (6), (27), (37) are inconsistent by sub-proof #2146.
% 231.54/42.77  | | | | | | | 
% 231.54/42.77  | | | | | | End of split
% 231.54/42.77  | | | | | | 
% 231.54/42.77  | | | | | Case 2:
% 231.54/42.77  | | | | | | 
% 231.54/42.77  | | | | | |   (38)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 &
% 231.54/42.77  | | | | | |           op(e0, e0) = e2)
% 231.54/42.77  | | | | | | 
% 231.54/42.77  | | | | | | REF_CLOSE: (1), (12), (21), (38) are inconsistent by sub-proof
% 231.54/42.77  | | | | | |            #2125.
% 231.54/42.77  | | | | | | 
% 231.54/42.77  | | | | | End of split
% 231.54/42.77  | | | | | 
% 231.54/42.77  | | | | Case 2:
% 231.54/42.77  | | | | | 
% 231.54/42.77  | | | | |   (39)  all_57_3 = e2 & op(e2, e2) = e2
% 231.54/42.77  | | | | | 
% 231.54/42.77  | | | | | ALPHA: (39) implies:
% 231.54/42.77  | | | | |   (40)  op(e2, e2) = e2
% 231.54/42.77  | | | | | 
% 231.54/42.77  | | | | | REF_CLOSE: (4), (5), (19), (40) are inconsistent by sub-proof #2306.
% 231.54/42.77  | | | | | 
% 231.54/42.77  | | | | End of split
% 231.54/42.77  | | | | 
% 231.54/42.77  | | | Case 2:
% 231.54/42.77  | | | | 
% 231.54/42.77  | | | |   (41)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2)
% 231.54/42.77  | | | |           = e2)
% 231.54/42.77  | | | | 
% 231.54/42.77  | | | | BETA: splitting (41) gives:
% 231.54/42.77  | | | | 
% 231.54/42.77  | | | | Case 1:
% 231.54/42.77  | | | | | 
% 231.54/42.77  | | | | |   (42)  all_57_7 = e2 & op(e1, e2) = e2
% 231.54/42.77  | | | | | 
% 231.54/42.77  | | | | | ALPHA: (42) implies:
% 231.54/42.77  | | | | |   (43)  all_57_7 = e2
% 231.54/42.77  | | | | | 
% 231.54/42.77  | | | | | REF_CLOSE: (12), (22), (43) are inconsistent by sub-proof #2207.
% 231.54/42.77  | | | | | 
% 231.54/42.77  | | | | Case 2:
% 231.54/42.77  | | | | | 
% 231.54/42.77  | | | | |   (44)  all_57_13 = e2 & op(e0, e2) = e2
% 231.54/42.77  | | | | | 
% 231.54/42.77  | | | | | REF_CLOSE: (6), (27), (44) are inconsistent by sub-proof #2146.
% 231.54/42.77  | | | | | 
% 231.54/42.77  | | | | End of split
% 231.54/42.77  | | | | 
% 231.54/42.77  | | | End of split
% 231.54/42.77  | | | 
% 231.54/42.77  | | End of split
% 231.54/42.77  | | 
% 231.54/42.77  | Case 2:
% 231.54/42.77  | | 
% 231.54/42.77  | |   (45)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 231.54/42.77  | |           e3)
% 231.54/42.77  | | 
% 231.54/42.77  | | BETA: splitting (45) gives:
% 231.54/42.77  | | 
% 231.54/42.77  | | Case 1:
% 231.54/42.77  | | | 
% 231.54/42.77  | | |   (46)  all_57_14 = e3 & op(e0, e1) = e3
% 231.54/42.77  | | | 
% 231.54/42.77  | | | ALPHA: (46) implies:
% 231.54/42.77  | | |   (47)  all_57_14 = e3
% 231.54/42.77  | | | 
% 231.54/42.77  | | | REF_CLOSE: (7), (21), (47) are inconsistent by sub-proof #2420.
% 231.54/42.77  | | | 
% 231.54/42.77  | | Case 2:
% 231.54/42.77  | | | 
% 231.54/42.77  | | |   (48)  all_57_15 = e3 & op(e0, e0) = e3
% 231.54/42.77  | | | 
% 231.54/42.77  | | | ALPHA: (48) implies:
% 231.54/42.77  | | |   (49)  all_57_15 = e3
% 231.54/42.77  | | | 
% 231.54/42.77  | | | REF_CLOSE: (3), (4), (6), (7), (8), (9), (10), (12), (13), (16), (17),
% 231.54/42.77  | | |            (18), (19), (20), (21), (49) are inconsistent by sub-proof
% 231.54/42.77  | | |            #1555.
% 231.54/42.77  | | | 
% 231.54/42.77  | | End of split
% 231.54/42.77  | | 
% 231.54/42.77  | End of split
% 231.54/42.77  | 
% 231.54/42.77  End of proof
% 231.54/42.77  
% 231.54/42.77  Sub-proof #1555 shows that the following formulas are inconsistent:
% 231.54/42.77  ----------------------------------------------------------------
% 231.54/42.77    (1)   ~ (e3 = e1)
% 231.54/42.77    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.77           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.77    (3)   ~ (e3 = e2)
% 231.54/42.77    (4)   ~ (e3 = e0)
% 231.54/42.77    (5)  all_57_15 = e3
% 231.54/42.77    (6)  op(e3, e3) = e0
% 231.54/42.77    (7)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 231.54/42.77         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.54/42.77    (8)  all_57_12 = e1
% 231.54/42.77    (9)   ~ (e2 = e0)
% 231.54/42.77    (10)   ~ (e1 = e0)
% 231.54/42.77    (11)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.54/42.77          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.54/42.77            e2)
% 231.54/42.77    (12)  all_57_2 = e0
% 231.54/42.77    (13)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 231.54/42.77          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 231.54/42.77    (14)   ~ (e2 = e1)
% 231.54/42.77    (15)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.54/42.77          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.54/42.77    (16)  all_57_14 = e0
% 231.54/42.77  
% 231.54/42.77  Begin of proof
% 231.54/42.77  | 
% 231.54/42.77  | BETA: splitting (15) gives:
% 231.54/42.77  | 
% 231.54/42.77  | Case 1:
% 231.54/42.77  | | 
% 231.54/42.77  | |   (17)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) =
% 231.54/42.77  | |           e2)
% 231.54/42.77  | | 
% 231.54/42.77  | | REF_CLOSE: (2), (6), (9), (12), (17) are inconsistent by sub-proof #1560.
% 231.54/42.77  | | 
% 231.54/42.77  | Case 2:
% 231.54/42.77  | | 
% 231.54/42.77  | |   (18)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) =
% 231.54/42.77  | |           e2)
% 231.54/42.77  | | 
% 231.54/42.77  | | BETA: splitting (18) gives:
% 231.54/42.77  | | 
% 231.54/42.77  | | Case 1:
% 231.54/42.77  | | | 
% 231.54/42.77  | | |   (19)  all_57_6 = e2 & op(e1, e3) = e2
% 231.54/42.77  | | | 
% 231.54/42.77  | | | ALPHA: (19) implies:
% 231.54/42.77  | | |   (20)  all_57_6 = e2
% 231.54/42.77  | | | 
% 231.54/42.77  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13),
% 231.54/42.77  | | |            (14), (16), (20) are inconsistent by sub-proof #1556.
% 231.54/42.77  | | | 
% 231.54/42.77  | | Case 2:
% 231.54/42.77  | | | 
% 231.54/42.77  | | |   (21)  all_57_12 = e2 & op(e0, e3) = e2
% 231.54/42.77  | | | 
% 231.54/42.77  | | | REF_CLOSE: (8), (14), (21) are inconsistent by sub-proof #1922.
% 231.54/42.77  | | | 
% 231.54/42.77  | | End of split
% 231.54/42.77  | | 
% 231.54/42.77  | End of split
% 231.54/42.77  | 
% 231.54/42.77  End of proof
% 231.54/42.77  
% 231.54/42.77  Sub-proof #1556 shows that the following formulas are inconsistent:
% 231.54/42.77  ----------------------------------------------------------------
% 231.54/42.77    (1)   ~ (e3 = e1)
% 231.54/42.77    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.77           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.77    (3)   ~ (e3 = e2)
% 231.54/42.77    (4)   ~ (e3 = e0)
% 231.54/42.77    (5)  all_57_15 = e3
% 231.54/42.77    (6)  op(e3, e3) = e0
% 231.54/42.77    (7)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 231.54/42.77         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.54/42.77    (8)  all_57_6 = e2
% 231.54/42.77    (9)   ~ (e2 = e0)
% 231.54/42.77    (10)   ~ (e1 = e0)
% 231.54/42.77    (11)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.54/42.77          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.54/42.77            e2)
% 231.54/42.77    (12)  all_57_2 = e0
% 231.54/42.77    (13)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 231.54/42.77          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 231.54/42.77    (14)   ~ (e2 = e1)
% 231.54/42.77    (15)  all_57_14 = e0
% 231.54/42.77  
% 231.54/42.77  Begin of proof
% 231.54/42.77  | 
% 231.54/42.77  | BETA: splitting (13) gives:
% 231.54/42.77  | 
% 231.54/42.77  | Case 1:
% 231.54/42.77  | | 
% 231.54/42.77  | |   (16)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) =
% 231.54/42.77  | |           e3)
% 231.54/42.77  | | 
% 231.54/42.77  | | REF_CLOSE: (2), (4), (6), (12), (16) are inconsistent by sub-proof #1559.
% 231.54/42.77  | | 
% 231.54/42.77  | Case 2:
% 231.54/42.77  | | 
% 231.54/42.77  | |   (17)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) =
% 231.54/42.77  | |           e3)
% 231.54/42.77  | | 
% 231.54/42.77  | | REF_CLOSE: (1), (3), (5), (7), (8), (9), (10), (11), (14), (15), (17) are
% 231.54/42.77  | |            inconsistent by sub-proof #1557.
% 231.54/42.77  | | 
% 231.54/42.77  | End of split
% 231.54/42.77  | 
% 231.54/42.77  End of proof
% 231.54/42.77  
% 231.54/42.77  Sub-proof #1557 shows that the following formulas are inconsistent:
% 231.54/42.77  ----------------------------------------------------------------
% 231.54/42.77    (1)   ~ (e3 = e1)
% 231.54/42.77    (2)   ~ (e3 = e2)
% 231.54/42.77    (3)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 231.54/42.77    (4)  all_57_15 = e3
% 231.54/42.77    (5)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 231.54/42.77         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.54/42.77    (6)  all_57_6 = e2
% 231.54/42.77    (7)   ~ (e2 = e0)
% 231.54/42.77    (8)   ~ (e1 = e0)
% 231.54/42.77    (9)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2) |
% 231.54/42.77         (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.54/42.77    (10)   ~ (e2 = e1)
% 231.54/42.77    (11)  all_57_14 = e0
% 231.54/42.77  
% 231.54/42.77  Begin of proof
% 231.54/42.77  | 
% 231.54/42.77  | BETA: splitting (3) gives:
% 231.54/42.77  | 
% 231.54/42.77  | Case 1:
% 231.54/42.77  | | 
% 231.54/42.77  | |   (12)  all_57_6 = e3 & op(e1, e3) = e3
% 231.54/42.77  | | 
% 231.54/42.77  | | REF_CLOSE: (2), (6), (12) are inconsistent by sub-proof #1558.
% 231.54/42.77  | | 
% 231.54/42.77  | Case 2:
% 231.54/42.77  | | 
% 231.54/42.77  | |   (13)  all_57_12 = e3 & op(e0, e3) = e3
% 231.54/42.77  | | 
% 231.54/42.77  | | ALPHA: (13) implies:
% 231.54/42.77  | |   (14)  all_57_12 = e3
% 231.54/42.77  | | 
% 231.54/42.77  | | REF_CLOSE: (1), (2), (4), (5), (7), (8), (9), (10), (11), (14) are
% 231.54/42.77  | |            inconsistent by sub-proof #1763.
% 231.54/42.77  | | 
% 231.54/42.77  | End of split
% 231.54/42.77  | 
% 231.54/42.77  End of proof
% 231.54/42.77  
% 231.54/42.77  Sub-proof #1558 shows that the following formulas are inconsistent:
% 231.54/42.77  ----------------------------------------------------------------
% 231.54/42.77    (1)  all_57_6 = e3 & op(e1, e3) = e3
% 231.54/42.77    (2)  all_57_6 = e2
% 231.54/42.77    (3)   ~ (e3 = e2)
% 231.54/42.77  
% 231.54/42.77  Begin of proof
% 231.54/42.77  | 
% 231.54/42.77  | ALPHA: (1) implies:
% 231.54/42.77  |   (4)  all_57_6 = e3
% 231.54/42.77  | 
% 231.54/42.77  | COMBINE_EQS: (2), (4) imply:
% 231.54/42.77  |   (5)  e3 = e2
% 231.54/42.77  | 
% 231.54/42.77  | REDUCE: (3), (5) imply:
% 231.54/42.77  |   (6)  $false
% 231.54/42.77  | 
% 231.54/42.77  | CLOSE: (6) is inconsistent.
% 231.54/42.77  | 
% 231.54/42.77  End of proof
% 231.54/42.77  
% 231.54/42.77  Sub-proof #1559 shows that the following formulas are inconsistent:
% 231.54/42.77  ----------------------------------------------------------------
% 231.54/42.77    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.77           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.77    (2)   ~ (e3 = e0)
% 231.54/42.77    (3)  op(e3, e3) = e0
% 231.54/42.77    (4)  all_57_2 = e0
% 231.54/42.77    (5)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3)
% 231.54/42.77  
% 231.54/42.77  Begin of proof
% 231.54/42.77  | 
% 231.54/42.77  | BETA: splitting (5) gives:
% 231.54/42.77  | 
% 231.54/42.77  | Case 1:
% 231.54/42.77  | | 
% 231.54/42.77  | |   (6)  all_57_0 = e3 & op(e3, e3) = e3
% 231.54/42.77  | | 
% 231.54/42.77  | | ALPHA: (6) implies:
% 231.54/42.77  | |   (7)  op(e3, e3) = e3
% 231.54/42.77  | | 
% 231.54/42.77  | | REF_CLOSE: (1), (2), (3), (7) are inconsistent by sub-proof #2494.
% 231.54/42.77  | | 
% 231.54/42.77  | Case 2:
% 231.54/42.77  | | 
% 231.54/42.77  | |   (8)  all_57_2 = e3 & op(e2, e3) = e3
% 231.54/42.77  | | 
% 231.54/42.77  | | ALPHA: (8) implies:
% 231.54/42.77  | |   (9)  all_57_2 = e3
% 231.54/42.77  | | 
% 231.54/42.77  | | REF_CLOSE: (2), (4), (9) are inconsistent by sub-proof #2258.
% 231.54/42.77  | | 
% 231.54/42.77  | End of split
% 231.54/42.77  | 
% 231.54/42.77  End of proof
% 231.54/42.77  
% 231.54/42.77  Sub-proof #1560 shows that the following formulas are inconsistent:
% 231.54/42.77  ----------------------------------------------------------------
% 231.54/42.77    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.77           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.77    (2)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2)
% 231.54/42.77    (3)  op(e3, e3) = e0
% 231.54/42.77    (4)   ~ (e2 = e0)
% 231.54/42.77    (5)  all_57_2 = e0
% 231.54/42.77  
% 231.54/42.77  Begin of proof
% 231.54/42.77  | 
% 231.54/42.77  | BETA: splitting (2) gives:
% 231.54/42.77  | 
% 231.54/42.77  | Case 1:
% 231.54/42.77  | | 
% 231.54/42.77  | |   (6)  all_57_0 = e2 & op(e3, e3) = e2
% 231.54/42.77  | | 
% 231.54/42.77  | | ALPHA: (6) implies:
% 231.54/42.77  | |   (7)  op(e3, e3) = e2
% 231.54/42.77  | | 
% 231.54/42.77  | | REF_CLOSE: (1), (3), (4), (7) are inconsistent by sub-proof #2403.
% 231.54/42.77  | | 
% 231.54/42.77  | Case 2:
% 231.54/42.77  | | 
% 231.54/42.77  | |   (8)  all_57_2 = e2 & op(e2, e3) = e2
% 231.54/42.77  | | 
% 231.54/42.77  | | REF_CLOSE: (4), (5), (8) are inconsistent by sub-proof #2257.
% 231.54/42.77  | | 
% 231.54/42.77  | End of split
% 231.54/42.77  | 
% 231.54/42.77  End of proof
% 231.54/42.77  
% 231.54/42.77  Sub-proof #1561 shows that the following formulas are inconsistent:
% 231.54/42.77  ----------------------------------------------------------------
% 231.54/42.77    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.77           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.77    (2)  op(e2, e2) = e1
% 231.54/42.77    (3)  op(e3, e2) = all_53_4
% 231.54/42.77    (4)   ~ (e1 = e0)
% 231.54/42.77    (5)   ~ (all_53_4 = e0)
% 231.54/42.77    (6)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0)
% 231.54/42.77  
% 231.54/42.77  Begin of proof
% 231.54/42.77  | 
% 231.54/42.77  | BETA: splitting (6) gives:
% 231.54/42.77  | 
% 231.54/42.77  | Case 1:
% 231.54/42.77  | | 
% 231.54/42.77  | |   (7)  all_57_1 = e0 & op(e3, e2) = e0
% 231.54/42.77  | | 
% 231.54/42.77  | | ALPHA: (7) implies:
% 231.54/42.77  | |   (8)  op(e3, e2) = e0
% 231.54/42.77  | | 
% 231.54/42.77  | | REF_CLOSE: (1), (3), (5), (8) are inconsistent by sub-proof #1941.
% 231.54/42.77  | | 
% 231.54/42.77  | Case 2:
% 231.54/42.78  | | 
% 231.54/42.78  | |   (9)  all_57_3 = e0 & op(e2, e2) = e0
% 231.54/42.78  | | 
% 231.54/42.78  | | ALPHA: (9) implies:
% 231.54/42.78  | |   (10)  op(e2, e2) = e0
% 231.54/42.78  | | 
% 231.54/42.78  | | REF_CLOSE: (1), (2), (4), (10) are inconsistent by sub-proof #2352.
% 231.54/42.78  | | 
% 231.54/42.78  | End of split
% 231.54/42.78  | 
% 231.54/42.78  End of proof
% 231.54/42.78  
% 231.54/42.78  Sub-proof #1562 shows that the following formulas are inconsistent:
% 231.54/42.78  ----------------------------------------------------------------
% 231.54/42.78    (1)   ~ (all_52_25 = e1)
% 231.54/42.78    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.78           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.78    (3)   ~ (all_52_25 = e2)
% 231.54/42.78    (4)  all_55_12 = all_52_25
% 231.54/42.78    (5)  op(e3, e3) = e2
% 231.54/42.78    (6)  op(all_52_25, all_52_25) = e3
% 231.54/42.78    (7)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 231.54/42.78    (8)   ~ (all_52_25 = e0)
% 231.54/42.78  
% 231.54/42.78  Begin of proof
% 231.54/42.78  | 
% 231.54/42.78  | BETA: splitting (7) gives:
% 231.54/42.78  | 
% 231.54/42.78  | Case 1:
% 231.54/42.78  | | 
% 231.54/42.78  | |   (9)  all_55_12 = e3
% 231.54/42.78  | | 
% 231.54/42.78  | | COMBINE_EQS: (4), (9) imply:
% 231.54/42.78  | |   (10)  all_52_25 = e3
% 231.54/42.78  | | 
% 231.54/42.78  | | SIMP: (10) implies:
% 231.54/42.78  | |   (11)  all_52_25 = e3
% 231.54/42.78  | | 
% 231.54/42.78  | | REDUCE: (3), (11) imply:
% 231.54/42.78  | |   (12)   ~ (e3 = e2)
% 231.54/42.78  | | 
% 231.54/42.78  | | REDUCE: (6), (11) imply:
% 231.54/42.78  | |   (13)  op(e3, e3) = e3
% 231.54/42.78  | | 
% 231.54/42.78  | | REF_CLOSE: (2), (5), (12), (13) are inconsistent by sub-proof #2490.
% 231.54/42.78  | | 
% 231.54/42.78  | Case 2:
% 231.54/42.78  | | 
% 231.54/42.78  | |   (14)  all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 231.54/42.78  | | 
% 231.54/42.78  | | REF_CLOSE: (1), (3), (4), (8), (14) are inconsistent by sub-proof #1563.
% 231.54/42.78  | | 
% 231.54/42.78  | End of split
% 231.54/42.78  | 
% 231.54/42.78  End of proof
% 231.54/42.78  
% 231.54/42.78  Sub-proof #1563 shows that the following formulas are inconsistent:
% 231.54/42.78  ----------------------------------------------------------------
% 231.54/42.78    (1)   ~ (all_52_25 = e1)
% 231.54/42.78    (2)   ~ (all_52_25 = e2)
% 231.54/42.78    (3)  all_55_12 = all_52_25
% 231.54/42.78    (4)  all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 231.54/42.78    (5)   ~ (all_52_25 = e0)
% 231.54/42.78  
% 231.54/42.78  Begin of proof
% 231.54/42.78  | 
% 231.54/42.78  | BETA: splitting (4) gives:
% 231.54/42.78  | 
% 231.54/42.78  | Case 1:
% 231.54/42.78  | | 
% 231.54/42.78  | |   (6)  all_55_12 = e2
% 231.54/42.78  | | 
% 231.54/42.78  | | REF_CLOSE: (2), (3), (6) are inconsistent by sub-proof #1682.
% 231.54/42.78  | | 
% 231.54/42.78  | Case 2:
% 231.54/42.78  | | 
% 231.54/42.78  | |   (7)  all_55_12 = e1 | all_55_12 = e0
% 231.54/42.78  | | 
% 231.54/42.78  | | BETA: splitting (7) gives:
% 231.54/42.78  | | 
% 231.54/42.78  | | Case 1:
% 231.54/42.78  | | | 
% 231.54/42.78  | | |   (8)  all_55_12 = e1
% 231.54/42.78  | | | 
% 231.54/42.78  | | | REF_CLOSE: (1), (3), (8) are inconsistent by sub-proof #1681.
% 231.54/42.78  | | | 
% 231.54/42.78  | | Case 2:
% 231.54/42.78  | | | 
% 231.54/42.78  | | |   (9)  all_55_12 = e0
% 231.54/42.78  | | | 
% 231.54/42.78  | | | REF_CLOSE: (3), (5), (9) are inconsistent by sub-proof #1564.
% 231.54/42.78  | | | 
% 231.54/42.78  | | End of split
% 231.54/42.78  | | 
% 231.54/42.78  | End of split
% 231.54/42.78  | 
% 231.54/42.78  End of proof
% 231.54/42.78  
% 231.54/42.78  Sub-proof #1564 shows that the following formulas are inconsistent:
% 231.54/42.78  ----------------------------------------------------------------
% 231.54/42.78    (1)  all_55_12 = all_52_25
% 231.54/42.78    (2)  all_55_12 = e0
% 231.54/42.78    (3)   ~ (all_52_25 = e0)
% 231.54/42.78  
% 231.54/42.78  Begin of proof
% 231.54/42.78  | 
% 231.54/42.78  | COMBINE_EQS: (1), (2) imply:
% 231.54/42.78  |   (4)  all_52_25 = e0
% 231.54/42.78  | 
% 231.54/42.78  | SIMP: (4) implies:
% 231.54/42.78  |   (5)  all_52_25 = e0
% 231.54/42.78  | 
% 231.54/42.78  | REDUCE: (3), (5) imply:
% 231.54/42.78  |   (6)  $false
% 231.54/42.78  | 
% 231.54/42.78  | CLOSE: (6) is inconsistent.
% 231.54/42.78  | 
% 231.54/42.78  End of proof
% 231.54/42.78  
% 231.54/42.78  Sub-proof #1565 shows that the following formulas are inconsistent:
% 231.54/42.78  ----------------------------------------------------------------
% 231.54/42.78    (1)   ~ (all_52_29 = e0)
% 231.54/42.78    (2)   ~ (all_52_29 = e2)
% 231.54/42.78    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.78           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.78    (4)  all_55_14 = all_52_29
% 231.54/42.78    (5)  op(e3, e3) = e2
% 231.54/42.78    (6)   ~ (all_52_29 = e1)
% 231.54/42.78    (7)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 231.54/42.78    (8)  op(all_52_29, all_52_29) = e1
% 231.54/42.78    (9)   ~ (e2 = e1)
% 231.54/42.78  
% 231.54/42.78  Begin of proof
% 231.54/42.78  | 
% 231.54/42.78  | BETA: splitting (7) gives:
% 231.54/42.78  | 
% 231.54/42.78  | Case 1:
% 231.54/42.78  | | 
% 231.54/42.78  | |   (10)  all_55_14 = e3
% 231.54/42.78  | | 
% 231.54/42.78  | | COMBINE_EQS: (4), (10) imply:
% 231.54/42.78  | |   (11)  all_52_29 = e3
% 231.54/42.78  | | 
% 231.54/42.78  | | REDUCE: (8), (11) imply:
% 231.54/42.78  | |   (12)  op(e3, e3) = e1
% 231.54/42.78  | | 
% 231.54/42.78  | | REF_CLOSE: (3), (5), (9), (12) are inconsistent by sub-proof #1950.
% 231.54/42.78  | | 
% 231.54/42.78  | Case 2:
% 231.54/42.78  | | 
% 231.54/42.78  | |   (13)  all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 231.54/42.78  | | 
% 231.54/42.78  | | REF_CLOSE: (1), (2), (4), (6), (13) are inconsistent by sub-proof #2034.
% 231.54/42.78  | | 
% 231.54/42.78  | End of split
% 231.54/42.78  | 
% 231.54/42.78  End of proof
% 231.54/42.78  
% 231.54/42.78  Sub-proof #1566 shows that the following formulas are inconsistent:
% 231.54/42.78  ----------------------------------------------------------------
% 231.54/42.78    (1)  all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 231.54/42.78    (2)   ~ (all_53_6 = e0)
% 231.54/42.78    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.78           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.78    (4)  all_55_15 = all_4_2
% 231.54/42.78    (5)  ( ~ (all_28_0 = e0) & op(all_28_1, e3) = all_28_0 & op(e3, e2) = all_28_1
% 231.54/42.78           & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 = e1) & op(e3, e2) =
% 231.54/42.78           all_28_1 & $i(all_28_1))
% 231.54/42.78    (6)  op(e2, e2) = e1
% 231.54/42.78    (7)  op(e0, e3) = all_52_25
% 231.54/42.78    (8)   ~ (all_4_2 = e2)
% 231.54/42.78    (9)  op(e0, e3) = all_53_3
% 231.54/42.78    (10)   ~ (all_53_7 = all_4_2)
% 231.54/42.78    (11)  op(e3, e3) = e2
% 231.54/42.78    (12)   ~ (all_53_3 = e2)
% 231.54/42.78    (13)  op(all_52_25, all_52_25) = e3
% 231.54/42.78    (14)  op(e3, e2) = all_53_4
% 231.54/42.78    (15)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 231.54/42.78          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 231.54/42.78    (16)  all_55_12 = all_53_3
% 231.54/42.78    (17)  op(e0, e2) = all_53_7
% 231.54/42.78    (18)  ( ~ (all_20_0 = e1) & op(all_20_1, e3) = all_20_0 & op(e3, e2) =
% 231.54/42.78            all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e0) & op(e3,
% 231.54/42.78              e2) = all_20_1 & $i(all_20_1))
% 231.54/42.78    (19)   ~ (all_53_3 = all_4_2)
% 231.54/42.78    (20)   ~ (all_4_2 = e1)
% 231.54/42.78    (21)  op(e1, e2) = all_53_6
% 231.54/42.78    (22)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 231.54/42.78  
% 231.54/42.78  Begin of proof
% 231.54/42.78  | 
% 231.54/42.78  | BETA: splitting (1) gives:
% 231.54/42.78  | 
% 231.54/42.78  | Case 1:
% 231.54/42.78  | | 
% 231.54/42.78  | |   (23)  all_55_15 = e2
% 231.54/42.78  | | 
% 231.54/42.78  | | REF_CLOSE: (4), (8), (23) are inconsistent by sub-proof #2502.
% 231.54/42.78  | | 
% 231.54/42.78  | Case 2:
% 231.54/42.78  | | 
% 231.54/42.78  | |   (24)  all_55_15 = e1 | all_55_15 = e0
% 231.54/42.78  | | 
% 231.54/42.78  | | BETA: splitting (24) gives:
% 231.54/42.78  | | 
% 231.54/42.78  | | Case 1:
% 231.54/42.78  | | | 
% 231.54/42.78  | | |   (25)  all_55_15 = e1
% 231.54/42.78  | | | 
% 231.54/42.78  | | | REF_CLOSE: (4), (20), (25) are inconsistent by sub-proof #2501.
% 231.54/42.78  | | | 
% 231.54/42.78  | | Case 2:
% 231.54/42.78  | | | 
% 231.54/42.78  | | |   (26)  all_55_15 = e0
% 231.54/42.78  | | | 
% 231.54/42.78  | | | COMBINE_EQS: (4), (26) imply:
% 231.54/42.78  | | |   (27)  all_4_2 = e0
% 231.54/42.78  | | | 
% 231.54/42.78  | | | SIMP: (27) implies:
% 231.54/42.78  | | |   (28)  all_4_2 = e0
% 231.54/42.78  | | | 
% 231.54/42.78  | | | REDUCE: (19), (28) imply:
% 231.54/42.78  | | |   (29)   ~ (all_53_3 = e0)
% 231.54/42.78  | | | 
% 231.54/42.78  | | | REDUCE: (10), (28) imply:
% 231.54/42.78  | | |   (30)   ~ (all_53_7 = e0)
% 231.54/42.78  | | | 
% 231.54/42.78  | | | REDUCE: (20), (28) imply:
% 231.54/42.78  | | |   (31)   ~ (e1 = e0)
% 231.54/42.78  | | | 
% 231.54/42.78  | | | SIMP: (31) implies:
% 231.54/42.78  | | |   (32)   ~ (e1 = e0)
% 231.54/42.78  | | | 
% 231.54/42.78  | | | BETA: splitting (15) gives:
% 231.54/42.78  | | | 
% 231.54/42.78  | | | Case 1:
% 231.54/42.78  | | | | 
% 231.54/42.78  | | | |   (33)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2)
% 231.54/42.78  | | | |           = e0)
% 231.54/42.78  | | | | 
% 231.54/42.78  | | | | BETA: splitting (33) gives:
% 231.54/42.78  | | | | 
% 231.54/42.78  | | | | Case 1:
% 231.54/42.78  | | | | | 
% 231.54/42.78  | | | | |   (34)  all_57_1 = e0 & op(e3, e2) = e0
% 231.54/42.78  | | | | | 
% 231.54/42.78  | | | | | ALPHA: (34) implies:
% 231.54/42.78  | | | | |   (35)  op(e3, e2) = e0
% 231.54/42.78  | | | | | 
% 231.54/42.78  | | | | | REF_CLOSE: (3), (5), (7), (9), (11), (12), (13), (14), (16), (18),
% 231.54/42.78  | | | | |            (22), (29), (35) are inconsistent by sub-proof #1567.
% 231.54/42.78  | | | | | 
% 231.54/42.78  | | | | Case 2:
% 231.54/42.78  | | | | | 
% 231.54/42.78  | | | | |   (36)  all_57_3 = e0 & op(e2, e2) = e0
% 231.54/42.78  | | | | | 
% 231.54/42.78  | | | | | ALPHA: (36) implies:
% 231.54/42.78  | | | | |   (37)  op(e2, e2) = e0
% 231.54/42.78  | | | | | 
% 231.54/42.78  | | | | | REF_CLOSE: (3), (6), (32), (37) are inconsistent by sub-proof #2352.
% 231.54/42.78  | | | | | 
% 231.54/42.78  | | | | End of split
% 231.54/42.78  | | | | 
% 231.54/42.78  | | | Case 2:
% 231.54/42.78  | | | | 
% 231.54/42.78  | | | |   (38)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2)
% 231.54/42.78  | | | |           = e0)
% 231.54/42.78  | | | | 
% 231.54/42.78  | | | | REF_CLOSE: (2), (3), (17), (21), (30), (38) are inconsistent by
% 231.54/42.78  | | | |            sub-proof #2024.
% 231.54/42.78  | | | | 
% 231.54/42.78  | | | End of split
% 231.54/42.78  | | | 
% 231.54/42.78  | | End of split
% 231.54/42.78  | | 
% 231.54/42.78  | End of split
% 231.54/42.78  | 
% 231.54/42.78  End of proof
% 231.54/42.78  
% 231.54/42.78  Sub-proof #1567 shows that the following formulas are inconsistent:
% 231.54/42.78  ----------------------------------------------------------------
% 231.54/42.78    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.78           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.78    (2)  ( ~ (all_28_0 = e0) & op(all_28_1, e3) = all_28_0 & op(e3, e2) = all_28_1
% 231.54/42.78           & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 = e1) & op(e3, e2) =
% 231.54/42.78           all_28_1 & $i(all_28_1))
% 231.54/42.78    (3)  op(e0, e3) = all_52_25
% 231.54/42.78    (4)  op(e0, e3) = all_53_3
% 231.54/42.78    (5)  op(e3, e3) = e2
% 231.54/42.78    (6)   ~ (all_53_3 = e2)
% 231.54/42.78    (7)  op(all_52_25, all_52_25) = e3
% 231.54/42.78    (8)  op(e3, e2) = all_53_4
% 231.54/42.78    (9)  all_55_12 = all_53_3
% 231.54/42.78    (10)  ( ~ (all_20_0 = e1) & op(all_20_1, e3) = all_20_0 & op(e3, e2) =
% 231.54/42.78            all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e0) & op(e3,
% 231.54/42.78              e2) = all_20_1 & $i(all_20_1))
% 231.54/42.78    (11)   ~ (all_53_3 = e0)
% 231.54/42.78    (12)  op(e3, e2) = e0
% 231.54/42.78    (13)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 231.54/42.78  
% 231.54/42.78  Begin of proof
% 231.54/42.78  | 
% 231.54/42.78  | GROUND_INST: instantiating (1) with all_53_3, all_52_25, e3, e0, simplifying
% 231.54/42.78  |              with (3), (4) gives:
% 231.54/42.78  |   (14)  all_53_3 = all_52_25
% 231.54/42.78  | 
% 231.54/42.78  | GROUND_INST: instantiating (1) with all_53_4, e0, e2, e3, simplifying with
% 231.54/42.78  |              (8), (12) gives:
% 231.54/42.78  |   (15)  all_53_4 = e0
% 231.54/42.78  | 
% 231.54/42.78  | COMBINE_EQS: (9), (14) imply:
% 231.54/42.78  |   (16)  all_55_12 = all_52_25
% 231.54/42.78  | 
% 231.54/42.78  | REDUCE: (6), (14) imply:
% 231.54/42.78  |   (17)   ~ (all_52_25 = e2)
% 231.54/42.78  | 
% 231.54/42.78  | REDUCE: (11), (14) imply:
% 231.54/42.78  |   (18)   ~ (all_52_25 = e0)
% 231.54/42.78  | 
% 231.54/42.78  | BETA: splitting (10) gives:
% 231.54/42.78  | 
% 231.54/42.78  | Case 1:
% 231.54/42.78  | | 
% 231.54/42.78  | |   (19)   ~ (all_20_0 = e1) & op(all_20_1, e3) = all_20_0 & op(e3, e2) =
% 231.54/42.78  | |         all_20_1 & $i(all_20_0) & $i(all_20_1)
% 231.54/42.78  | | 
% 231.54/42.78  | | ALPHA: (19) implies:
% 231.54/42.78  | |   (20)   ~ (all_20_0 = e1)
% 231.54/42.78  | |   (21)  op(e3, e2) = all_20_1
% 231.54/42.78  | |   (22)  op(all_20_1, e3) = all_20_0
% 231.54/42.78  | | 
% 231.54/42.78  | | BETA: splitting (2) gives:
% 231.54/42.78  | | 
% 231.54/42.78  | | Case 1:
% 231.54/42.78  | | | 
% 231.54/42.78  | | |   (23)   ~ (all_28_0 = e0) & op(all_28_1, e3) = all_28_0 & op(e3, e2) =
% 231.54/42.78  | | |         all_28_1 & $i(all_28_0) & $i(all_28_1)
% 231.54/42.78  | | | 
% 231.54/42.78  | | | ALPHA: (23) implies:
% 231.54/42.78  | | |   (24)   ~ (all_28_0 = e0)
% 231.54/42.78  | | |   (25)  op(e3, e2) = all_28_1
% 231.54/42.78  | | |   (26)  op(all_28_1, e3) = all_28_0
% 231.54/42.78  | | | 
% 231.54/42.78  | | | GROUND_INST: instantiating (1) with e0, all_28_1, e2, e3, simplifying with
% 231.54/42.78  | | |              (12), (25) gives:
% 231.54/42.78  | | |   (27)  all_28_1 = e0
% 231.54/42.78  | | | 
% 231.54/42.78  | | | GROUND_INST: instantiating (1) with all_20_1, all_28_1, e2, e3,
% 231.54/42.78  | | |              simplifying with (21), (25) gives:
% 231.54/42.78  | | |   (28)  all_28_1 = all_20_1
% 231.54/42.78  | | | 
% 231.54/42.78  | | | COMBINE_EQS: (27), (28) imply:
% 231.54/42.78  | | |   (29)  all_20_1 = e0
% 231.54/42.78  | | | 
% 231.54/42.78  | | | REDUCE: (26), (27) imply:
% 231.54/42.78  | | |   (30)  op(e0, e3) = all_28_0
% 231.54/42.78  | | | 
% 231.54/42.78  | | | REDUCE: (22), (29) imply:
% 231.54/42.78  | | |   (31)  op(e0, e3) = all_20_0
% 231.54/42.78  | | | 
% 231.54/42.78  | | | GROUND_INST: instantiating (1) with all_52_25, all_20_0, e3, e0,
% 231.54/42.78  | | |              simplifying with (3), (31) gives:
% 231.54/42.78  | | |   (32)  all_52_25 = all_20_0
% 231.54/42.78  | | | 
% 231.54/42.78  | | | GROUND_INST: instantiating (1) with all_52_25, all_28_0, e3, e0,
% 231.54/42.78  | | |              simplifying with (3), (30) gives:
% 231.54/42.78  | | |   (33)  all_52_25 = all_28_0
% 231.54/42.78  | | | 
% 231.54/42.78  | | | COMBINE_EQS: (32), (33) imply:
% 231.54/42.78  | | |   (34)  all_28_0 = all_20_0
% 231.54/42.78  | | | 
% 231.54/42.78  | | | SIMP: (34) implies:
% 231.54/42.78  | | |   (35)  all_28_0 = all_20_0
% 231.54/42.78  | | | 
% 231.54/42.78  | | | COMBINE_EQS: (16), (32) imply:
% 231.54/42.78  | | |   (36)  all_55_12 = all_20_0
% 231.54/42.78  | | | 
% 231.54/42.78  | | | REDUCE: (17), (32) imply:
% 231.54/42.78  | | |   (37)   ~ (all_20_0 = e2)
% 231.54/42.78  | | | 
% 231.54/42.78  | | | REDUCE: (24), (35) imply:
% 231.54/42.78  | | |   (38)   ~ (all_20_0 = e0)
% 231.54/42.78  | | | 
% 231.54/42.78  | | | REF_CLOSE: (1), (5), (7), (13), (20), (32), (36), (37), (38) are
% 231.54/42.78  | | |            inconsistent by sub-proof #1569.
% 231.54/42.78  | | | 
% 231.54/42.78  | | Case 2:
% 231.54/42.78  | | | 
% 231.54/42.78  | | |   (39)   ~ (all_28_1 = e1) & op(e3, e2) = all_28_1 & $i(all_28_1)
% 231.54/42.78  | | | 
% 231.54/42.78  | | | ALPHA: (39) implies:
% 231.54/42.78  | | |   (40)  op(e3, e2) = all_28_1
% 231.54/42.78  | | | 
% 231.54/42.78  | | | GROUND_INST: instantiating (1) with e0, all_28_1, e2, e3, simplifying with
% 231.54/42.78  | | |              (12), (40) gives:
% 231.54/42.78  | | |   (41)  all_28_1 = e0
% 231.54/42.78  | | | 
% 231.54/42.78  | | | GROUND_INST: instantiating (1) with all_20_1, all_28_1, e2, e3,
% 231.54/42.78  | | |              simplifying with (21), (40) gives:
% 231.54/42.78  | | |   (42)  all_28_1 = all_20_1
% 231.54/42.78  | | | 
% 231.54/42.78  | | | COMBINE_EQS: (41), (42) imply:
% 231.54/42.78  | | |   (43)  all_20_1 = e0
% 231.54/42.78  | | | 
% 231.54/42.78  | | | REDUCE: (22), (43) imply:
% 231.54/42.78  | | |   (44)  op(e0, e3) = all_20_0
% 231.54/42.78  | | | 
% 231.54/42.78  | | | GROUND_INST: instantiating (1) with all_52_25, all_20_0, e3, e0,
% 231.54/42.78  | | |              simplifying with (3), (44) gives:
% 231.54/42.78  | | |   (45)  all_52_25 = all_20_0
% 231.54/42.78  | | | 
% 231.54/42.78  | | | COMBINE_EQS: (16), (45) imply:
% 231.54/42.78  | | |   (46)  all_55_12 = all_20_0
% 231.54/42.78  | | | 
% 231.54/42.78  | | | REDUCE: (17), (45) imply:
% 231.54/42.78  | | |   (47)   ~ (all_20_0 = e2)
% 231.54/42.78  | | | 
% 231.54/42.78  | | | REDUCE: (18), (45) imply:
% 231.54/42.78  | | |   (48)   ~ (all_20_0 = e0)
% 231.54/42.78  | | | 
% 231.54/42.78  | | | REF_CLOSE: (1), (5), (7), (13), (20), (45), (46), (47), (48) are
% 231.54/42.78  | | |            inconsistent by sub-proof #1569.
% 231.54/42.78  | | | 
% 231.54/42.78  | | End of split
% 231.54/42.78  | | 
% 231.54/42.78  | Case 2:
% 231.54/42.78  | | 
% 231.54/42.78  | |   (49)   ~ (all_20_1 = e0) & op(e3, e2) = all_20_1 & $i(all_20_1)
% 231.54/42.78  | | 
% 231.54/42.78  | | ALPHA: (49) implies:
% 231.54/42.78  | |   (50)   ~ (all_20_1 = e0)
% 231.54/42.78  | |   (51)  op(e3, e2) = all_20_1
% 231.54/42.78  | | 
% 231.54/42.78  | | BETA: splitting (2) gives:
% 231.54/42.78  | | 
% 231.54/42.78  | | Case 1:
% 231.54/42.78  | | | 
% 231.54/42.78  | | |   (52)   ~ (all_28_0 = e0) & op(all_28_1, e3) = all_28_0 & op(e3, e2) =
% 231.54/42.78  | | |         all_28_1 & $i(all_28_0) & $i(all_28_1)
% 231.54/42.78  | | | 
% 231.54/42.78  | | | ALPHA: (52) implies:
% 231.54/42.78  | | |   (53)  op(e3, e2) = all_28_1
% 231.54/42.78  | | | 
% 231.54/42.78  | | | REF_CLOSE: (1), (12), (50), (51), (53) are inconsistent by sub-proof
% 231.54/42.78  | | |            #1568.
% 231.54/42.78  | | | 
% 231.54/42.78  | | Case 2:
% 231.54/42.78  | | | 
% 231.54/42.78  | | |   (54)   ~ (all_28_1 = e1) & op(e3, e2) = all_28_1 & $i(all_28_1)
% 231.54/42.78  | | | 
% 231.54/42.78  | | | ALPHA: (54) implies:
% 231.54/42.78  | | |   (55)  op(e3, e2) = all_28_1
% 231.54/42.78  | | | 
% 231.54/42.78  | | | REF_CLOSE: (1), (12), (50), (51), (55) are inconsistent by sub-proof
% 231.54/42.78  | | |            #1568.
% 231.54/42.78  | | | 
% 231.54/42.78  | | End of split
% 231.54/42.78  | | 
% 231.54/42.78  | End of split
% 231.54/42.78  | 
% 231.54/42.78  End of proof
% 231.54/42.78  
% 231.54/42.78  Sub-proof #1568 shows that the following formulas are inconsistent:
% 231.54/42.78  ----------------------------------------------------------------
% 231.54/42.78    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.78           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.78    (2)  op(e3, e2) = all_20_1
% 231.54/42.78    (3)  op(e3, e2) = all_28_1
% 231.54/42.78    (4)   ~ (all_20_1 = e0)
% 231.54/42.78    (5)  op(e3, e2) = e0
% 231.54/42.78  
% 231.54/42.78  Begin of proof
% 231.54/42.78  | 
% 231.54/42.78  | GROUND_INST: instantiating (1) with e0, all_28_1, e2, e3, simplifying with
% 231.54/42.78  |              (3), (5) gives:
% 231.54/42.78  |   (6)  all_28_1 = e0
% 231.54/42.78  | 
% 231.54/42.78  | GROUND_INST: instantiating (1) with all_20_1, all_28_1, e2, e3, simplifying
% 231.54/42.78  |              with (2), (3) gives:
% 231.54/42.78  |   (7)  all_28_1 = all_20_1
% 231.54/42.78  | 
% 231.54/42.78  | COMBINE_EQS: (6), (7) imply:
% 231.54/42.78  |   (8)  all_20_1 = e0
% 231.54/42.78  | 
% 231.54/42.78  | REDUCE: (4), (8) imply:
% 231.54/42.78  |   (9)  $false
% 231.54/42.78  | 
% 231.54/42.78  | CLOSE: (9) is inconsistent.
% 231.54/42.78  | 
% 231.54/42.78  End of proof
% 231.54/42.78  
% 231.54/42.78  Sub-proof #1569 shows that the following formulas are inconsistent:
% 231.54/42.78  ----------------------------------------------------------------
% 231.54/42.78    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.78           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.78    (2)   ~ (all_20_0 = e1)
% 231.54/42.78    (3)  all_55_12 = all_20_0
% 231.54/42.78    (4)  op(e3, e3) = e2
% 231.54/42.78    (5)  op(all_52_25, all_52_25) = e3
% 231.54/42.78    (6)  all_52_25 = all_20_0
% 231.54/42.78    (7)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 231.54/42.78    (8)   ~ (all_20_0 = e0)
% 231.54/42.78    (9)   ~ (all_20_0 = e2)
% 231.54/42.78  
% 231.54/42.78  Begin of proof
% 231.54/42.78  | 
% 231.54/42.78  | REDUCE: (5), (6) imply:
% 231.54/42.78  |   (10)  op(all_20_0, all_20_0) = e3
% 231.54/42.78  | 
% 231.54/42.78  | BETA: splitting (7) gives:
% 231.54/42.78  | 
% 231.54/42.78  | Case 1:
% 231.54/42.78  | | 
% 231.54/42.78  | |   (11)  all_55_12 = e3
% 231.54/42.78  | | 
% 231.54/42.78  | | COMBINE_EQS: (3), (11) imply:
% 231.54/42.78  | |   (12)  all_20_0 = e3
% 231.54/42.78  | | 
% 231.54/42.78  | | REDUCE: (9), (12) imply:
% 231.54/42.78  | |   (13)   ~ (e3 = e2)
% 231.54/42.78  | | 
% 231.54/42.78  | | REDUCE: (10), (12) imply:
% 231.54/42.78  | |   (14)  op(e3, e3) = e3
% 231.54/42.78  | | 
% 231.54/42.78  | | REF_CLOSE: (1), (4), (13), (14) are inconsistent by sub-proof #2490.
% 231.54/42.78  | | 
% 231.54/42.78  | Case 2:
% 231.54/42.78  | | 
% 231.54/42.78  | |   (15)  all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 231.54/42.78  | | 
% 231.54/42.78  | | BETA: splitting (15) gives:
% 231.54/42.78  | | 
% 231.54/42.78  | | Case 1:
% 231.54/42.78  | | | 
% 231.54/42.78  | | |   (16)  all_55_12 = e2
% 231.54/42.78  | | | 
% 231.54/42.78  | | | COMBINE_EQS: (3), (16) imply:
% 231.54/42.78  | | |   (17)  all_20_0 = e2
% 231.54/42.78  | | | 
% 231.54/42.78  | | | REDUCE: (9), (17) imply:
% 231.54/42.78  | | |   (18)  $false
% 231.54/42.78  | | | 
% 231.54/42.78  | | | CLOSE: (18) is inconsistent.
% 231.54/42.78  | | | 
% 231.54/42.78  | | Case 2:
% 231.54/42.78  | | | 
% 231.54/42.78  | | |   (19)  all_55_12 = e1 | all_55_12 = e0
% 231.54/42.78  | | | 
% 231.54/42.78  | | | BETA: splitting (19) gives:
% 231.54/42.78  | | | 
% 231.54/42.78  | | | Case 1:
% 231.54/42.78  | | | | 
% 231.54/42.78  | | | |   (20)  all_55_12 = e1
% 231.54/42.78  | | | | 
% 231.54/42.78  | | | | COMBINE_EQS: (3), (20) imply:
% 231.54/42.78  | | | |   (21)  all_20_0 = e1
% 231.54/42.78  | | | | 
% 231.54/42.78  | | | | REDUCE: (2), (21) imply:
% 231.54/42.78  | | | |   (22)  $false
% 231.54/42.78  | | | | 
% 231.54/42.78  | | | | CLOSE: (22) is inconsistent.
% 231.54/42.78  | | | | 
% 231.54/42.78  | | | Case 2:
% 231.54/42.78  | | | | 
% 231.54/42.78  | | | |   (23)  all_55_12 = e0
% 231.54/42.78  | | | | 
% 231.54/42.78  | | | | COMBINE_EQS: (3), (23) imply:
% 231.54/42.78  | | | |   (24)  all_20_0 = e0
% 231.54/42.78  | | | | 
% 231.54/42.78  | | | | REDUCE: (8), (24) imply:
% 231.54/42.78  | | | |   (25)  $false
% 231.54/42.78  | | | | 
% 231.54/42.78  | | | | CLOSE: (25) is inconsistent.
% 231.54/42.78  | | | | 
% 231.54/42.78  | | | End of split
% 231.54/42.78  | | | 
% 231.54/42.78  | | End of split
% 231.54/42.78  | | 
% 231.54/42.78  | End of split
% 231.54/42.78  | 
% 231.54/42.78  End of proof
% 231.54/42.78  
% 231.54/42.78  Sub-proof #1570 shows that the following formulas are inconsistent:
% 231.54/42.78  ----------------------------------------------------------------
% 231.54/42.78    (1)  op(e0, e0) = all_4_2
% 231.54/42.78    (2)  op(e2, e3) = all_53_1
% 231.54/42.78    (3)  all_55_15 = e3 | all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 231.54/42.78    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.78           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.78    (5)  all_55_15 = all_4_2
% 231.54/42.78    (6)  op(e2, e3) = all_52_9
% 231.54/42.78    (7)   ~ (all_4_2 = e2)
% 231.54/42.78    (8)  op(e0, e3) = all_53_3
% 231.54/42.78    (9)   ~ (all_53_2 = e0)
% 231.54/42.78    (10)  op(e3, e3) = e2
% 231.54/42.78    (11)  op(all_52_9, all_52_9) = e3
% 231.54/42.78    (12)   ~ (all_53_3 = all_4_2)
% 231.54/42.78    (13)  op(e1, e3) = all_53_2
% 231.54/42.78    (14)   ~ (all_4_2 = e3)
% 231.54/42.78    (15)   ~ (all_4_2 = e1)
% 231.54/42.78    (16)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.54/42.78          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.54/42.78  
% 231.54/42.78  Begin of proof
% 231.54/42.78  | 
% 231.54/42.78  | BETA: splitting (3) gives:
% 231.54/42.78  | 
% 231.54/42.78  | Case 1:
% 231.54/42.78  | | 
% 231.54/42.78  | |   (17)  all_55_15 = e3
% 231.54/42.78  | | 
% 231.54/42.78  | | REF_CLOSE: (5), (14), (17) are inconsistent by sub-proof #2503.
% 231.54/42.78  | | 
% 231.54/42.78  | Case 2:
% 231.54/42.78  | | 
% 231.54/42.78  | |   (18)   ~ (all_55_15 = e3)
% 231.54/42.78  | |   (19)  all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 231.54/42.78  | | 
% 231.54/42.78  | | BETA: splitting (19) gives:
% 231.54/42.78  | | 
% 231.54/42.78  | | Case 1:
% 231.54/42.78  | | | 
% 231.54/42.78  | | |   (20)  all_55_15 = e2
% 231.54/42.78  | | | 
% 231.54/42.78  | | | REF_CLOSE: (5), (7), (20) are inconsistent by sub-proof #2502.
% 231.54/42.78  | | | 
% 231.54/42.78  | | Case 2:
% 231.54/42.78  | | | 
% 231.54/42.78  | | |   (21)   ~ (all_55_15 = e2)
% 231.54/42.78  | | |   (22)  all_55_15 = e1 | all_55_15 = e0
% 231.54/42.78  | | | 
% 231.54/42.78  | | | BETA: splitting (22) gives:
% 231.54/42.78  | | | 
% 231.54/42.78  | | | Case 1:
% 231.54/42.78  | | | | 
% 231.54/42.78  | | | |   (23)  all_55_15 = e1
% 231.54/42.78  | | | | 
% 231.54/42.78  | | | | REF_CLOSE: (5), (15), (23) are inconsistent by sub-proof #2501.
% 231.54/42.78  | | | | 
% 231.54/42.78  | | | Case 2:
% 231.54/42.78  | | | | 
% 231.54/42.78  | | | |   (24)  all_55_15 = e0
% 231.54/42.78  | | | | 
% 231.54/42.78  | | | | COMBINE_EQS: (5), (24) imply:
% 231.54/42.78  | | | |   (25)  all_4_2 = e0
% 231.54/42.78  | | | | 
% 231.54/42.78  | | | | SIMP: (25) implies:
% 231.54/42.78  | | | |   (26)  all_4_2 = e0
% 231.54/42.78  | | | | 
% 231.54/42.78  | | | | REDUCE: (12), (26) imply:
% 231.54/42.78  | | | |   (27)   ~ (all_53_3 = e0)
% 231.54/42.78  | | | | 
% 231.54/42.78  | | | | REDUCE: (14), (26) imply:
% 231.54/42.78  | | | |   (28)   ~ (e3 = e0)
% 231.54/42.78  | | | | 
% 231.54/42.78  | | | | SIMP: (28) implies:
% 231.54/42.78  | | | |   (29)   ~ (e3 = e0)
% 231.54/42.78  | | | | 
% 231.54/42.78  | | | | REDUCE: (7), (26) imply:
% 231.54/42.78  | | | |   (30)   ~ (e2 = e0)
% 231.54/42.78  | | | | 
% 231.54/42.78  | | | | SIMP: (30) implies:
% 231.54/42.78  | | | |   (31)   ~ (e2 = e0)
% 231.54/42.78  | | | | 
% 231.54/42.78  | | | | REDUCE: (1), (26) imply:
% 231.54/42.78  | | | |   (32)  op(e0, e0) = e0
% 231.54/42.78  | | | | 
% 231.54/42.78  | | | | REF_CLOSE: (2), (4), (6), (8), (9), (10), (11), (13), (16), (27), (29),
% 231.54/42.78  | | | |            (31), (32) are inconsistent by sub-proof #1571.
% 231.54/42.78  | | | | 
% 231.54/42.78  | | | End of split
% 231.54/42.78  | | | 
% 231.54/42.78  | | End of split
% 231.54/42.78  | | 
% 231.54/42.78  | End of split
% 231.54/42.78  | 
% 231.54/42.78  End of proof
% 231.54/42.78  
% 231.54/42.78  Sub-proof #1571 shows that the following formulas are inconsistent:
% 231.54/42.78  ----------------------------------------------------------------
% 231.54/42.78    (1)  op(e2, e3) = all_53_1
% 231.54/42.78    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.78           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.78    (3)  op(e2, e3) = all_52_9
% 231.54/42.78    (4)   ~ (e3 = e0)
% 231.54/42.78    (5)  op(e0, e3) = all_53_3
% 231.54/42.78    (6)   ~ (all_53_2 = e0)
% 231.54/42.78    (7)  op(e3, e3) = e2
% 231.54/42.78    (8)   ~ (e2 = e0)
% 231.54/42.78    (9)  op(e0, e0) = e0
% 231.54/42.78    (10)   ~ (all_53_3 = e0)
% 231.54/42.78    (11)  op(all_52_9, all_52_9) = e3
% 231.54/42.78    (12)  op(e1, e3) = all_53_2
% 231.54/42.78    (13)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.54/42.78          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.54/42.78  
% 231.54/42.78  Begin of proof
% 231.54/42.78  | 
% 231.54/42.78  | BETA: splitting (13) gives:
% 231.54/42.78  | 
% 231.54/42.78  | Case 1:
% 231.54/42.78  | | 
% 231.54/42.78  | |   (14)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) =
% 231.54/42.78  | |           e0)
% 231.54/42.78  | | 
% 231.54/42.78  | | BETA: splitting (14) gives:
% 231.54/42.78  | | 
% 231.54/42.78  | | Case 1:
% 231.54/42.78  | | | 
% 231.54/42.78  | | |   (15)  all_57_0 = e0 & op(e3, e3) = e0
% 231.54/42.78  | | | 
% 231.54/42.78  | | | ALPHA: (15) implies:
% 231.54/42.78  | | |   (16)  op(e3, e3) = e0
% 231.54/42.78  | | | 
% 231.54/42.78  | | | REF_CLOSE: (2), (7), (8), (16) are inconsistent by sub-proof #2403.
% 231.54/42.78  | | | 
% 231.54/42.78  | | Case 2:
% 231.54/42.78  | | | 
% 231.54/42.78  | | |   (17)  all_57_2 = e0 & op(e2, e3) = e0
% 231.54/42.78  | | | 
% 231.54/42.78  | | | ALPHA: (17) implies:
% 231.54/42.78  | | |   (18)  op(e2, e3) = e0
% 231.54/42.78  | | | 
% 231.54/42.78  | | | GROUND_INST: instantiating (2) with all_53_1, e0, e3, e2, simplifying with
% 231.54/42.78  | | |              (1), (18) gives:
% 231.54/42.78  | | |   (19)  all_53_1 = e0
% 231.54/42.78  | | | 
% 231.54/42.78  | | | GROUND_INST: instantiating (2) with all_53_1, all_52_9, e3, e2,
% 231.54/42.78  | | |              simplifying with (1), (3) gives:
% 231.54/42.78  | | |   (20)  all_53_1 = all_52_9
% 231.54/42.78  | | | 
% 231.54/42.78  | | | COMBINE_EQS: (19), (20) imply:
% 231.54/42.78  | | |   (21)  all_52_9 = e0
% 231.54/42.78  | | | 
% 231.54/42.78  | | | SIMP: (21) implies:
% 231.54/42.78  | | |   (22)  all_52_9 = e0
% 231.54/42.78  | | | 
% 231.54/42.78  | | | REDUCE: (11), (22) imply:
% 231.54/42.78  | | |   (23)  op(e0, e0) = e3
% 231.54/42.78  | | | 
% 231.54/42.78  | | | REF_CLOSE: (2), (4), (9), (23) are inconsistent by sub-proof #2304.
% 231.54/42.78  | | | 
% 231.54/42.78  | | End of split
% 231.54/42.78  | | 
% 231.54/42.78  | Case 2:
% 231.54/42.78  | | 
% 231.54/42.78  | |   (24)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) =
% 231.54/42.78  | |           e0)
% 231.54/42.78  | | 
% 231.54/42.78  | | REF_CLOSE: (2), (5), (6), (10), (12), (24) are inconsistent by sub-proof
% 231.54/42.78  | |            #1859.
% 231.54/42.78  | | 
% 231.54/42.78  | End of split
% 231.54/42.78  | 
% 231.54/42.78  End of proof
% 231.54/42.78  
% 231.54/42.78  Sub-proof #1572 shows that the following formulas are inconsistent:
% 231.54/42.78  ----------------------------------------------------------------
% 231.54/42.78    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.78         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.54/42.78    (2)   ~ (e3 = e1)
% 231.54/42.78    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.78           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.78    (4)   ~ (all_6_2 = e3)
% 231.54/42.78    (5)  op(e1, e1) = all_6_2
% 231.54/42.78    (6)  op(e2, e2) = e1
% 231.54/42.78    (7)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.54/42.78         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.54/42.78    (8)  op(e2, e0) = all_52_15
% 231.54/42.78    (9)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.54/42.78         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.54/42.79    (10)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.54/42.79          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.54/42.79    (11)   ~ (e3 = e2)
% 231.54/42.79    (12)   ~ (e3 = e0)
% 231.54/42.79    (13)  all_57_10 = e2 & op(e2, e0) = e2
% 231.54/42.79    (14)  op(e0, e3) = all_53_3
% 231.54/42.79    (15)  op(e2, e2) = all_52_11
% 231.54/42.79    (16)  op(e3, e3) = e2
% 231.54/42.79    (17)   ~ (all_53_3 = e2)
% 231.54/42.79    (18)  all_57_4 = e1
% 231.54/42.79    (19)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 231.54/42.79          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 231.54/42.79    (20)   ~ (e2 = e0)
% 231.54/42.79    (21)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 231.54/42.79          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.54/42.79    (22)   ~ (e1 = e0)
% 231.54/42.79    (23)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.54/42.79          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.54/42.79    (24)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.54/42.79          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.54/42.79    (25)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.54/42.79          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.54/42.79            e2)
% 231.54/42.79    (26)  op(e0, e0) = e1
% 231.54/42.79    (27)  op(e2, e0) = all_53_13
% 231.54/42.79    (28)  op(all_52_15, all_52_15) = e0
% 231.54/42.79    (29)   ~ (e2 = e1)
% 231.54/42.79    (30)   ~ (all_6_2 = e0)
% 231.54/42.79    (31)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.79          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.54/42.79  
% 231.54/42.79  Begin of proof
% 231.54/42.79  | 
% 231.54/42.79  | BETA: splitting (1) gives:
% 231.54/42.79  | 
% 231.54/42.79  | Case 1:
% 231.54/42.79  | | 
% 231.54/42.79  | |   (32)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 231.54/42.79  | |           e2)
% 231.54/42.79  | | 
% 231.54/42.79  | | REF_CLOSE: (2), (3), (6), (7), (9), (11), (12), (16), (20), (21), (22),
% 231.54/42.79  | |            (29), (32) are inconsistent by sub-proof #1591.
% 231.54/42.79  | | 
% 231.54/42.79  | Case 2:
% 231.54/42.79  | | 
% 231.54/42.79  | |   (33)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 231.54/42.79  | |           e2)
% 231.54/42.79  | | 
% 231.54/42.79  | | BETA: splitting (33) gives:
% 231.54/42.79  | | 
% 231.54/42.79  | | Case 1:
% 231.54/42.79  | | | 
% 231.54/42.79  | | |   (34)  all_57_7 = e2 & op(e1, e2) = e2
% 231.54/42.79  | | | 
% 231.54/42.79  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (10), (11), (12), (14), (17),
% 231.54/42.79  | | |            (18), (19), (20), (22), (23), (24), (25), (26), (29), (30),
% 231.54/42.79  | | |            (31), (34) are inconsistent by sub-proof #1579.
% 231.54/42.79  | | | 
% 231.54/42.79  | | Case 2:
% 231.54/42.79  | | | 
% 231.54/42.79  | | | 
% 231.54/42.79  | | | ALPHA: (13) implies:
% 231.54/42.79  | | |   (35)  op(e2, e0) = e2
% 231.54/42.79  | | | 
% 231.54/42.79  | | | GROUND_INST: instantiating (3) with all_53_13, e2, e0, e2, simplifying
% 231.54/42.79  | | |              with (27), (35) gives:
% 231.54/42.79  | | |   (36)  all_53_13 = e2
% 231.54/42.79  | | | 
% 231.54/42.79  | | | GROUND_INST: instantiating (3) with all_53_13, all_52_15, e0, e2,
% 231.54/42.79  | | |              simplifying with (8), (27) gives:
% 231.54/42.79  | | |   (37)  all_53_13 = all_52_15
% 231.54/42.79  | | | 
% 231.54/42.79  | | | GROUND_INST: instantiating (3) with e1, all_52_11, e2, e2, simplifying
% 231.54/42.79  | | |              with (6), (15) gives:
% 231.54/42.79  | | |   (38)  all_52_11 = e1
% 231.54/42.79  | | | 
% 231.54/42.79  | | | COMBINE_EQS: (36), (37) imply:
% 231.54/42.79  | | |   (39)  all_52_15 = e2
% 231.54/42.79  | | | 
% 231.54/42.79  | | | REDUCE: (28), (39) imply:
% 231.54/42.79  | | |   (40)  op(e2, e2) = e0
% 231.54/42.79  | | | 
% 231.54/42.79  | | | REF_CLOSE: (3), (6), (22), (40) are inconsistent by sub-proof #2352.
% 231.54/42.79  | | | 
% 231.54/42.79  | | End of split
% 231.54/42.79  | | 
% 231.54/42.79  | End of split
% 231.54/42.79  | 
% 231.54/42.79  End of proof
% 231.54/42.79  
% 231.54/42.79  Sub-proof #1573 shows that the following formulas are inconsistent:
% 231.54/42.79  ----------------------------------------------------------------
% 231.54/42.79    (1)   ~ (e3 = e1)
% 231.54/42.79    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.79           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.79    (3)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.54/42.79         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.54/42.79    (4)   ~ (all_6_2 = e3)
% 231.54/42.79    (5)  op(e1, e1) = all_6_2
% 231.54/42.79    (6)  all_57_6 = e1
% 231.54/42.79    (7)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.54/42.79         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.54/42.79    (8)   ~ (e3 = e2)
% 231.54/42.79    (9)   ~ (e3 = e0)
% 231.54/42.79    (10)  all_57_4 = e1
% 231.54/42.79    (11)  all_57_11 = e2
% 231.54/42.79    (12)   ~ (e2 = e0)
% 231.54/42.79    (13)   ~ (e1 = e0)
% 231.54/42.79    (14)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.54/42.79          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.54/42.79    (15)  all_57_5 = e2 & op(e2, e1) = e2
% 231.54/42.79    (16)   ~ (all_6_2 = e0)
% 231.54/42.79  
% 231.54/42.79  Begin of proof
% 231.54/42.79  | 
% 231.54/42.79  | ALPHA: (15) implies:
% 231.54/42.79  |   (17)  all_57_5 = e2
% 231.54/42.79  | 
% 231.54/42.79  | BETA: splitting (14) gives:
% 231.54/42.79  | 
% 231.54/42.79  | Case 1:
% 231.54/42.79  | | 
% 231.54/42.79  | |   (18)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) =
% 231.54/42.79  | |           e3)
% 231.54/42.79  | | 
% 231.54/42.79  | | BETA: splitting (18) gives:
% 231.54/42.79  | | 
% 231.54/42.79  | | Case 1:
% 231.54/42.79  | | | 
% 231.54/42.79  | | |   (19)  all_57_4 = e3 & op(e3, e1) = e3
% 231.54/42.79  | | | 
% 231.54/42.79  | | | REF_CLOSE: (1), (10), (19) are inconsistent by sub-proof #2415.
% 231.54/42.79  | | | 
% 231.54/42.79  | | Case 2:
% 231.54/42.79  | | | 
% 231.54/42.79  | | |   (20)  all_57_5 = e3 & op(e2, e1) = e3
% 231.54/42.79  | | | 
% 231.54/42.79  | | | ALPHA: (20) implies:
% 231.54/42.79  | | |   (21)  all_57_5 = e3
% 231.54/42.79  | | | 
% 231.54/42.79  | | | REF_CLOSE: (8), (17), (21) are inconsistent by sub-proof #2189.
% 231.54/42.79  | | | 
% 231.54/42.79  | | End of split
% 231.54/42.79  | | 
% 231.54/42.79  | Case 2:
% 231.54/42.79  | | 
% 231.54/42.79  | |   (22)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) =
% 231.54/42.79  | |           e3)
% 231.54/42.79  | | 
% 231.54/42.79  | | BETA: splitting (22) gives:
% 231.54/42.79  | | 
% 231.54/42.79  | | Case 1:
% 231.54/42.79  | | | 
% 231.54/42.79  | | |   (23)  all_57_8 = e3 & op(e1, e1) = e3
% 231.54/42.79  | | | 
% 231.54/42.79  | | | ALPHA: (23) implies:
% 231.54/42.79  | | |   (24)  op(e1, e1) = e3
% 231.54/42.79  | | | 
% 231.54/42.79  | | | REF_CLOSE: (2), (4), (5), (24) are inconsistent by sub-proof #2468.
% 231.54/42.79  | | | 
% 231.54/42.79  | | Case 2:
% 231.54/42.79  | | | 
% 231.54/42.79  | | |   (25)  all_57_14 = e3 & op(e0, e1) = e3
% 231.54/42.79  | | | 
% 231.54/42.79  | | | ALPHA: (25) implies:
% 231.54/42.79  | | |   (26)  all_57_14 = e3
% 231.54/42.79  | | | 
% 231.54/42.79  | | | BETA: splitting (3) gives:
% 231.54/42.79  | | | 
% 231.54/42.79  | | | Case 1:
% 231.54/42.79  | | | | 
% 231.54/42.79  | | | |   (27)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2)
% 231.54/42.79  | | | |           = e3)
% 231.54/42.79  | | | | 
% 231.54/42.79  | | | | BETA: splitting (27) gives:
% 231.54/42.79  | | | | 
% 231.54/42.79  | | | | Case 1:
% 231.54/42.79  | | | | | 
% 231.54/42.79  | | | | |   (28)  all_57_6 = e3 & op(e1, e3) = e3
% 231.54/42.79  | | | | | 
% 231.54/42.79  | | | | | REF_CLOSE: (1), (6), (28) are inconsistent by sub-proof #2346.
% 231.54/42.79  | | | | | 
% 231.54/42.79  | | | | Case 2:
% 231.54/42.79  | | | | | 
% 231.54/42.79  | | | | |   (29)  all_57_7 = e3 & op(e1, e2) = e3
% 231.54/42.79  | | | | | 
% 231.54/42.79  | | | | | ALPHA: (29) implies:
% 231.54/42.79  | | | | |   (30)  all_57_7 = e3
% 231.54/42.79  | | | | | 
% 231.54/42.79  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 231.54/42.79  | | | | |            (12), (13), (16), (17), (26), (30) are inconsistent by
% 231.54/42.79  | | | | |            sub-proof #1690.
% 231.54/42.79  | | | | | 
% 231.54/42.79  | | | | End of split
% 231.54/42.79  | | | | 
% 231.54/42.79  | | | Case 2:
% 231.54/42.79  | | | | 
% 231.54/42.79  | | | |   (31)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0)
% 231.54/42.79  | | | |           = e3)
% 231.54/42.79  | | | | 
% 231.54/42.79  | | | | BETA: splitting (31) gives:
% 231.54/42.79  | | | | 
% 231.54/42.79  | | | | Case 1:
% 231.54/42.79  | | | | | 
% 231.54/42.79  | | | | |   (32)  all_57_8 = e3 & op(e1, e1) = e3
% 231.54/42.79  | | | | | 
% 231.54/42.79  | | | | | ALPHA: (32) implies:
% 231.54/42.79  | | | | |   (33)  op(e1, e1) = e3
% 231.54/42.79  | | | | | 
% 231.54/42.79  | | | | | REF_CLOSE: (2), (4), (5), (33) are inconsistent by sub-proof #2468.
% 231.54/42.79  | | | | | 
% 231.54/42.79  | | | | Case 2:
% 231.54/42.79  | | | | | 
% 231.54/42.79  | | | | |   (34)  all_57_11 = e3 & op(e1, e0) = e3
% 231.54/42.79  | | | | | 
% 231.54/42.79  | | | | | ALPHA: (34) implies:
% 231.54/42.79  | | | | |   (35)  all_57_11 = e3
% 231.54/42.79  | | | | | 
% 231.54/42.79  | | | | | COMBINE_EQS: (11), (35) imply:
% 231.54/42.79  | | | | |   (36)  e3 = e2
% 231.54/42.79  | | | | | 
% 231.54/42.79  | | | | | COMBINE_EQS: (26), (36) imply:
% 231.54/42.79  | | | | |   (37)  all_57_14 = e2
% 231.54/42.79  | | | | | 
% 231.54/42.79  | | | | | REF_CLOSE: (1), (2), (4), (5), (8), (10), (14), (17), (37) are
% 231.54/42.79  | | | | |            inconsistent by sub-proof #1889.
% 231.54/42.79  | | | | | 
% 231.54/42.79  | | | | End of split
% 231.54/42.79  | | | | 
% 231.54/42.79  | | | End of split
% 231.54/42.79  | | | 
% 231.54/42.79  | | End of split
% 231.54/42.79  | | 
% 231.54/42.79  | End of split
% 231.54/42.79  | 
% 231.54/42.79  End of proof
% 231.54/42.79  
% 231.54/42.79  Sub-proof #1574 shows that the following formulas are inconsistent:
% 231.54/42.79  ----------------------------------------------------------------
% 231.54/42.79    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.79         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.54/42.79    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.54/42.79         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.54/42.79    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.79         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.54/42.79    (4)   ~ (e3 = e1)
% 231.54/42.79    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.79           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.79    (6)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.54/42.79         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.54/42.79    (7)   ~ (all_6_2 = e3)
% 231.54/42.79    (8)  op(e1, e1) = all_6_2
% 231.54/42.79    (9)  op(e2, e2) = e1
% 231.54/42.79    (10)  all_57_6 = e1
% 231.54/42.79    (11)   ~ (e3 = e2)
% 231.54/42.79    (12)   ~ (e3 = e0)
% 231.54/42.79    (13)  all_57_2 = e2 & op(e2, e3) = e2
% 231.54/42.79    (14)  op(e3, e3) = e2
% 231.54/42.79    (15)  all_57_4 = e1
% 231.54/42.79    (16)  all_57_11 = e2
% 231.54/42.79    (17)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 231.54/42.79          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 231.54/42.79    (18)   ~ (e2 = e0)
% 231.54/42.79    (19)  all_57_13 = e2
% 231.54/42.79    (20)  all_57_3 = e1
% 231.54/42.79    (21)   ~ (e1 = e0)
% 231.54/42.79    (22)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.54/42.79          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.54/42.79    (23)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.54/42.79          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.54/42.79    (24)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.54/42.79          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 231.54/42.79            e3)
% 231.54/42.79    (25)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.54/42.79          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.54/42.79            e2)
% 231.54/42.79    (26)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.54/42.79              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.54/42.79                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.54/42.79                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.54/42.79    (27)  op(e0, e0) = e1
% 231.54/42.79    (28)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.79          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.54/42.79    (29)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 231.54/42.79          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 231.54/42.79    (30)   ~ (e2 = e1)
% 231.54/42.79    (31)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.54/42.79          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.54/42.79    (32)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.79          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.54/42.79  
% 231.54/42.79  Begin of proof
% 231.54/42.79  | 
% 231.54/42.79  | ALPHA: (13) implies:
% 231.54/42.79  |   (33)  all_57_2 = e2
% 231.54/42.79  | 
% 231.54/42.79  | BETA: splitting (6) gives:
% 231.54/42.79  | 
% 231.54/42.79  | Case 1:
% 231.54/42.79  | | 
% 231.54/42.79  | |   (34)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 231.54/42.79  | |           e3)
% 231.54/42.79  | | 
% 231.54/42.79  | | BETA: splitting (34) gives:
% 231.54/42.79  | | 
% 231.54/42.79  | | Case 1:
% 231.54/42.79  | | | 
% 231.54/42.79  | | |   (35)  all_57_6 = e3 & op(e1, e3) = e3
% 231.54/42.79  | | | 
% 231.54/42.79  | | | REF_CLOSE: (4), (10), (35) are inconsistent by sub-proof #2346.
% 231.54/42.79  | | | 
% 231.54/42.79  | | Case 2:
% 231.54/42.79  | | | 
% 231.54/42.79  | | |   (36)  all_57_7 = e3 & op(e1, e2) = e3
% 231.54/42.79  | | | 
% 231.54/42.79  | | | ALPHA: (36) implies:
% 231.54/42.79  | | |   (37)  all_57_7 = e3
% 231.54/42.79  | | | 
% 231.54/42.79  | | | BETA: splitting (29) gives:
% 231.54/42.79  | | | 
% 231.54/42.79  | | | Case 1:
% 231.54/42.79  | | | | 
% 231.54/42.79  | | | |   (38)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3)
% 231.54/42.79  | | | |           = e3)
% 231.54/42.79  | | | | 
% 231.54/42.79  | | | | BETA: splitting (38) gives:
% 231.54/42.79  | | | | 
% 231.54/42.79  | | | | Case 1:
% 231.54/42.79  | | | | | 
% 231.54/42.79  | | | | |   (39)  all_57_0 = e3 & op(e3, e3) = e3
% 231.54/42.79  | | | | | 
% 231.54/42.79  | | | | | ALPHA: (39) implies:
% 231.54/42.79  | | | | |   (40)  op(e3, e3) = e3
% 231.54/42.79  | | | | | 
% 231.54/42.79  | | | | | REF_CLOSE: (5), (11), (14), (40) are inconsistent by sub-proof #2490.
% 231.54/42.79  | | | | | 
% 231.54/42.79  | | | | Case 2:
% 231.54/42.79  | | | | | 
% 231.54/42.79  | | | | |   (41)  all_57_2 = e3 & op(e2, e3) = e3
% 231.54/42.79  | | | | | 
% 231.54/42.79  | | | | | ALPHA: (41) implies:
% 231.54/42.79  | | | | |   (42)  all_57_2 = e3
% 231.54/42.79  | | | | | 
% 231.54/42.79  | | | | | COMBINE_EQS: (33), (42) imply:
% 231.54/42.79  | | | | |   (43)  e3 = e2
% 231.54/42.79  | | | | | 
% 231.54/42.79  | | | | | SIMP: (43) implies:
% 231.54/42.79  | | | | |   (44)  e3 = e2
% 231.54/42.79  | | | | | 
% 231.54/42.79  | | | | | COMBINE_EQS: (37), (44) imply:
% 231.54/42.79  | | | | |   (45)  all_57_7 = e2
% 231.54/42.79  | | | | | 
% 231.54/42.79  | | | | | REF_CLOSE: (3), (4), (5), (9), (11), (12), (17), (18), (19), (21),
% 231.54/42.79  | | | | |            (23), (30), (32), (45) are inconsistent by sub-proof #1696.
% 231.54/42.79  | | | | | 
% 231.54/42.79  | | | | End of split
% 231.54/42.79  | | | | 
% 231.54/42.79  | | | Case 2:
% 231.54/42.79  | | | | 
% 231.54/42.79  | | | |   (46)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3)
% 231.54/42.79  | | | |           = e3)
% 231.54/42.79  | | | | 
% 231.54/42.79  | | | | BETA: splitting (46) gives:
% 231.54/42.79  | | | | 
% 231.54/42.79  | | | | Case 1:
% 231.54/42.79  | | | | | 
% 231.54/42.79  | | | | |   (47)  all_57_6 = e3 & op(e1, e3) = e3
% 231.54/42.79  | | | | | 
% 231.54/42.79  | | | | | REF_CLOSE: (4), (10), (47) are inconsistent by sub-proof #2346.
% 231.54/42.79  | | | | | 
% 231.54/42.79  | | | | Case 2:
% 231.54/42.79  | | | | | 
% 231.54/42.79  | | | | |   (48)  all_57_12 = e3 & op(e0, e3) = e3
% 231.54/42.79  | | | | | 
% 231.54/42.79  | | | | | ALPHA: (48) implies:
% 231.54/42.79  | | | | |   (49)  all_57_12 = e3
% 231.54/42.79  | | | | | 
% 231.54/42.79  | | | | | BETA: splitting (26) gives:
% 231.54/42.79  | | | | | 
% 231.54/42.79  | | | | | Case 1:
% 231.54/42.79  | | | | | | 
% 231.54/42.79  | | | | | |   (50)  all_57_15 = e0 & op(e0, e0) = e0
% 231.54/42.79  | | | | | | 
% 231.54/42.79  | | | | | | ALPHA: (50) implies:
% 231.54/42.79  | | | | | |   (51)  op(e0, e0) = e0
% 231.54/42.79  | | | | | | 
% 231.54/42.79  | | | | | | REF_CLOSE: (5), (21), (27), (51) are inconsistent by sub-proof
% 231.54/42.79  | | | | | |            #2290.
% 231.54/42.79  | | | | | | 
% 231.54/42.79  | | | | | Case 2:
% 231.54/42.79  | | | | | | 
% 231.54/42.79  | | | | | |   (52)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 &
% 231.54/42.79  | | | | | |             op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) &
% 231.54/42.79  | | | | | |         ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.54/42.79  | | | | | |             op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 231.54/42.79  | | | | | | 
% 231.54/42.79  | | | | | | ALPHA: (52) implies:
% 231.54/42.79  | | | | | |   (53)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.54/42.79  | | | | | |           op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.54/42.79  | | | | | | 
% 231.54/42.79  | | | | | | BETA: splitting (53) gives:
% 231.54/42.79  | | | | | | 
% 231.54/42.79  | | | | | | Case 1:
% 231.54/42.79  | | | | | | | 
% 231.54/42.79  | | | | | | |   (54)  all_57_12 = e0 & op(e0, e3) = e0
% 231.54/42.79  | | | | | | | 
% 231.54/42.79  | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (10), (11), (12), (16), (37),
% 231.54/42.79  | | | | | | |            (49), (54) are inconsistent by sub-proof #1702.
% 231.54/42.79  | | | | | | | 
% 231.54/42.79  | | | | | | Case 2:
% 231.54/42.79  | | | | | | | 
% 231.54/42.79  | | | | | | |   (55)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 &
% 231.54/42.79  | | | | | | |           op(e0, e1) = e0)
% 231.54/42.79  | | | | | | | 
% 231.54/42.79  | | | | | | | BETA: splitting (55) gives:
% 231.54/42.79  | | | | | | | 
% 231.54/42.79  | | | | | | | Case 1:
% 231.54/42.79  | | | | | | | | 
% 231.54/42.79  | | | | | | | |   (56)  all_57_13 = e0 & op(e0, e2) = e0
% 231.54/42.79  | | | | | | | | 
% 231.54/42.79  | | | | | | | | ALPHA: (56) implies:
% 231.54/42.79  | | | | | | | |   (57)  all_57_13 = e0
% 231.54/42.79  | | | | | | | | 
% 231.54/42.79  | | | | | | | | REF_CLOSE: (18), (19), (57) are inconsistent by sub-proof #1911.
% 231.54/42.79  | | | | | | | | 
% 231.54/42.79  | | | | | | | Case 2:
% 231.54/42.79  | | | | | | | | 
% 231.54/42.79  | | | | | | | |   (58)  all_57_14 = e0 & op(e0, e1) = e0
% 231.54/42.79  | | | | | | | | 
% 231.54/42.79  | | | | | | | | ALPHA: (58) implies:
% 231.54/42.79  | | | | | | | |   (59)  all_57_14 = e0
% 231.54/42.79  | | | | | | | | 
% 231.54/42.79  | | | | | | | | BETA: splitting (22) gives:
% 231.54/42.79  | | | | | | | | 
% 231.54/42.79  | | | | | | | | Case 1:
% 231.54/42.79  | | | | | | | | | 
% 231.54/42.79  | | | | | | | | |   (60)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 &
% 231.54/42.79  | | | | | | | | |           op(e2, e1) = e3)
% 231.54/42.79  | | | | | | | | | 
% 231.54/42.79  | | | | | | | | | BETA: splitting (60) gives:
% 231.54/42.79  | | | | | | | | | 
% 231.54/42.79  | | | | | | | | | Case 1:
% 231.54/42.79  | | | | | | | | | | 
% 231.54/42.79  | | | | | | | | | |   (61)  all_57_4 = e3 & op(e3, e1) = e3
% 231.54/42.79  | | | | | | | | | | 
% 231.54/42.79  | | | | | | | | | | ALPHA: (61) implies:
% 231.54/42.79  | | | | | | | | | |   (62)  all_57_4 = e3
% 231.54/42.79  | | | | | | | | | | 
% 231.54/42.79  | | | | | | | | | | COMBINE_EQS: (15), (62) imply:
% 231.54/42.79  | | | | | | | | | |   (63)  e3 = e1
% 231.54/42.79  | | | | | | | | | | 
% 231.54/42.79  | | | | | | | | | | SIMP: (63) implies:
% 231.54/42.79  | | | | | | | | | |   (64)  e3 = e1
% 231.54/42.79  | | | | | | | | | | 
% 231.54/42.79  | | | | | | | | | | COMBINE_EQS: (49), (64) imply:
% 231.54/42.79  | | | | | | | | | |   (65)  all_57_12 = e1
% 231.54/42.79  | | | | | | | | | | 
% 231.54/42.79  | | | | | | | | | | REF_CLOSE: (4), (5), (11), (12), (18), (24), (25), (27),
% 231.54/42.79  | | | | | | | | | |            (30), (59), (65) are inconsistent by sub-proof
% 231.54/42.79  | | | | | | | | | |            #2070.
% 231.54/42.79  | | | | | | | | | | 
% 231.54/42.79  | | | | | | | | | Case 2:
% 231.54/42.79  | | | | | | | | | | 
% 231.54/42.79  | | | | | | | | | |   (66)  all_57_5 = e3 & op(e2, e1) = e3
% 231.54/42.79  | | | | | | | | | | 
% 231.54/42.79  | | | | | | | | | | ALPHA: (66) implies:
% 231.54/42.79  | | | | | | | | | |   (67)  all_57_5 = e3
% 231.54/42.79  | | | | | | | | | | 
% 231.54/42.79  | | | | | | | | | | REF_CLOSE: (1), (2), (4), (5), (11), (12), (14), (18), (20),
% 231.54/42.79  | | | | | | | | | |            (21), (28), (30), (31), (33), (49), (67) are
% 231.54/42.79  | | | | | | | | | |            inconsistent by sub-proof #1575.
% 231.54/42.79  | | | | | | | | | | 
% 231.54/42.79  | | | | | | | | | End of split
% 231.54/42.79  | | | | | | | | | 
% 231.54/42.79  | | | | | | | | Case 2:
% 231.54/42.79  | | | | | | | | | 
% 231.54/42.79  | | | | | | | | |   (68)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 &
% 231.54/42.79  | | | | | | | | |           op(e0, e1) = e3)
% 231.54/42.79  | | | | | | | | | 
% 231.54/42.79  | | | | | | | | | BETA: splitting (68) gives:
% 231.54/42.79  | | | | | | | | | 
% 231.54/42.79  | | | | | | | | | Case 1:
% 231.54/42.79  | | | | | | | | | | 
% 231.54/42.79  | | | | | | | | | |   (69)  all_57_8 = e3 & op(e1, e1) = e3
% 231.54/42.79  | | | | | | | | | | 
% 231.54/42.79  | | | | | | | | | | ALPHA: (69) implies:
% 231.54/42.79  | | | | | | | | | |   (70)  op(e1, e1) = e3
% 231.54/42.79  | | | | | | | | | | 
% 231.54/42.79  | | | | | | | | | | REF_CLOSE: (5), (7), (8), (70) are inconsistent by sub-proof
% 231.54/42.79  | | | | | | | | | |            #2468.
% 231.54/42.79  | | | | | | | | | | 
% 231.54/42.79  | | | | | | | | | Case 2:
% 231.54/42.79  | | | | | | | | | | 
% 231.54/42.79  | | | | | | | | | |   (71)  all_57_14 = e3 & op(e0, e1) = e3
% 231.54/42.79  | | | | | | | | | | 
% 231.54/42.79  | | | | | | | | | | ALPHA: (71) implies:
% 231.54/42.79  | | | | | | | | | |   (72)  all_57_14 = e3
% 231.54/42.79  | | | | | | | | | | 
% 231.54/42.79  | | | | | | | | | | COMBINE_EQS: (59), (72) imply:
% 231.54/42.79  | | | | | | | | | |   (73)  e3 = e0
% 231.54/42.79  | | | | | | | | | | 
% 231.54/42.79  | | | | | | | | | | COMBINE_EQS: (37), (73) imply:
% 231.54/42.79  | | | | | | | | | |   (74)  all_57_7 = e0
% 231.54/42.79  | | | | | | | | | | 
% 231.54/42.79  | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (10), (11), (12), (16),
% 231.54/42.79  | | | | | | | | | |            (74) are inconsistent by sub-proof #2343.
% 231.54/42.79  | | | | | | | | | | 
% 231.54/42.79  | | | | | | | | | End of split
% 231.54/42.79  | | | | | | | | | 
% 231.54/42.79  | | | | | | | | End of split
% 231.54/42.79  | | | | | | | | 
% 231.54/42.79  | | | | | | | End of split
% 231.54/42.79  | | | | | | | 
% 231.54/42.79  | | | | | | End of split
% 231.54/42.79  | | | | | | 
% 231.54/42.79  | | | | | End of split
% 231.54/42.79  | | | | | 
% 231.54/42.79  | | | | End of split
% 231.54/42.79  | | | | 
% 231.54/42.79  | | | End of split
% 231.54/42.79  | | | 
% 231.54/42.79  | | End of split
% 231.54/42.79  | | 
% 231.54/42.79  | Case 2:
% 231.54/42.79  | | 
% 231.54/42.79  | |   (75)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 231.54/42.79  | |           e3)
% 231.54/42.79  | | 
% 231.54/42.79  | | REF_CLOSE: (5), (7), (8), (11), (16), (75) are inconsistent by sub-proof
% 231.54/42.79  | |            #2344.
% 231.54/42.79  | | 
% 231.54/42.79  | End of split
% 231.54/42.79  | 
% 231.54/42.79  End of proof
% 231.54/42.79  
% 231.54/42.79  Sub-proof #1575 shows that the following formulas are inconsistent:
% 231.54/42.79  ----------------------------------------------------------------
% 231.54/42.79    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.79         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.54/42.79    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.54/42.79         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.54/42.79    (3)   ~ (e3 = e1)
% 231.54/42.79    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.79           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.79    (5)  all_57_2 = e2
% 231.54/42.79    (6)   ~ (e3 = e2)
% 231.54/42.79    (7)   ~ (e3 = e0)
% 231.54/42.79    (8)  op(e3, e3) = e2
% 231.54/42.79    (9)  all_57_5 = e3
% 231.54/42.79    (10)   ~ (e2 = e0)
% 231.54/42.79    (11)  all_57_3 = e1
% 231.54/42.79    (12)   ~ (e1 = e0)
% 231.54/42.79    (13)  all_57_12 = e3
% 231.54/42.79    (14)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.79          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.54/42.79    (15)   ~ (e2 = e1)
% 231.54/42.79    (16)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.54/42.79          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.54/42.79  
% 231.54/42.79  Begin of proof
% 231.54/42.79  | 
% 231.54/42.79  | BETA: splitting (16) gives:
% 231.54/42.79  | 
% 231.54/42.79  | Case 1:
% 231.54/42.79  | | 
% 231.54/42.79  | |   (17)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) =
% 231.54/42.79  | |           e0)
% 231.54/42.79  | | 
% 231.54/42.79  | | REF_CLOSE: (4), (5), (8), (10), (17) are inconsistent by sub-proof #1577.
% 231.54/42.79  | | 
% 231.54/42.79  | Case 2:
% 231.54/42.79  | | 
% 231.54/42.79  | |   (18)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) =
% 231.54/42.79  | |           e0)
% 231.54/42.79  | | 
% 231.54/42.79  | | BETA: splitting (18) gives:
% 231.54/42.79  | | 
% 231.54/42.79  | | Case 1:
% 231.54/42.79  | | | 
% 231.54/42.79  | | |   (19)  all_57_6 = e0 & op(e1, e3) = e0
% 231.54/42.79  | | | 
% 231.54/42.79  | | | ALPHA: (19) implies:
% 231.54/42.79  | | |   (20)  all_57_6 = e0
% 231.54/42.79  | | | 
% 231.54/42.79  | | | BETA: splitting (2) gives:
% 231.54/42.79  | | | 
% 231.54/42.79  | | | Case 1:
% 231.54/42.79  | | | | 
% 231.54/42.79  | | | |   (21)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3)
% 231.54/42.79  | | | |           = e1)
% 231.54/42.79  | | | | 
% 231.54/42.79  | | | | REF_CLOSE: (4), (5), (8), (15), (21) are inconsistent by sub-proof
% 231.54/42.79  | | | |            #1633.
% 231.54/42.79  | | | | 
% 231.54/42.79  | | | Case 2:
% 231.54/42.79  | | | | 
% 231.54/42.79  | | | |   (22)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3)
% 231.54/42.79  | | | |           = e1)
% 231.54/42.79  | | | | 
% 231.54/42.79  | | | | BETA: splitting (22) gives:
% 231.54/42.79  | | | | 
% 231.54/42.79  | | | | Case 1:
% 231.54/42.79  | | | | | 
% 231.54/42.79  | | | | |   (23)  all_57_6 = e1 & op(e1, e3) = e1
% 231.54/42.79  | | | | | 
% 231.54/42.79  | | | | | ALPHA: (23) implies:
% 231.54/42.79  | | | | |   (24)  all_57_6 = e1
% 231.54/42.79  | | | | | 
% 231.54/42.79  | | | | | COMBINE_EQS: (20), (24) imply:
% 231.54/42.79  | | | | |   (25)  e1 = e0
% 231.54/42.79  | | | | | 
% 231.54/42.79  | | | | | SIMP: (25) implies:
% 231.54/42.79  | | | | |   (26)  e1 = e0
% 231.54/42.79  | | | | | 
% 231.54/42.79  | | | | | COMBINE_EQS: (11), (26) imply:
% 231.54/42.79  | | | | |   (27)  all_57_3 = e0
% 231.54/42.79  | | | | | 
% 231.54/42.79  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12),
% 231.54/42.79  | | | | |            (13), (14), (15), (16), (27) are inconsistent by sub-proof
% 231.54/42.79  | | | | |            #1576.
% 231.54/42.79  | | | | | 
% 231.54/42.79  | | | | Case 2:
% 231.54/42.79  | | | | | 
% 231.54/42.79  | | | | |   (28)  all_57_12 = e1 & op(e0, e3) = e1
% 231.54/42.79  | | | | | 
% 231.54/42.79  | | | | | REF_CLOSE: (3), (13), (28) are inconsistent by sub-proof #2230.
% 231.54/42.79  | | | | | 
% 231.54/42.79  | | | | End of split
% 231.54/42.79  | | | | 
% 231.54/42.79  | | | End of split
% 231.54/42.79  | | | 
% 231.54/42.79  | | Case 2:
% 231.54/42.79  | | | 
% 231.54/42.79  | | |   (29)  all_57_12 = e0 & op(e0, e3) = e0
% 231.54/42.79  | | | 
% 231.54/42.79  | | | REF_CLOSE: (7), (13), (29) are inconsistent by sub-proof #2237.
% 231.54/42.79  | | | 
% 231.54/42.79  | | End of split
% 231.54/42.79  | | 
% 231.54/42.79  | End of split
% 231.54/42.79  | 
% 231.54/42.79  End of proof
% 231.54/42.79  
% 231.54/42.79  Sub-proof #1576 shows that the following formulas are inconsistent:
% 231.54/42.79  ----------------------------------------------------------------
% 231.54/42.79    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.79         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.54/42.79    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.54/42.79         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.54/42.79    (3)   ~ (e3 = e1)
% 231.54/42.79    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.79           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.79    (5)  all_57_2 = e2
% 231.54/42.79    (6)  all_57_3 = e0
% 231.54/42.79    (7)   ~ (e3 = e2)
% 231.54/42.79    (8)   ~ (e3 = e0)
% 231.54/42.79    (9)  op(e3, e3) = e2
% 231.54/42.79    (10)  all_57_5 = e3
% 231.54/42.79    (11)   ~ (e2 = e0)
% 231.54/42.79    (12)   ~ (e1 = e0)
% 231.54/42.79    (13)  all_57_12 = e3
% 231.54/42.79    (14)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.79          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.54/42.79    (15)   ~ (e2 = e1)
% 231.54/42.79    (16)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.54/42.79          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.54/42.79  
% 231.54/42.79  Begin of proof
% 231.54/42.79  | 
% 231.54/42.79  | BETA: splitting (2) gives:
% 231.54/42.79  | 
% 231.54/42.79  | Case 1:
% 231.54/42.79  | | 
% 231.54/42.79  | |   (17)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) =
% 231.54/42.79  | |           e1)
% 231.54/42.79  | | 
% 231.54/42.79  | | REF_CLOSE: (4), (5), (9), (15), (17) are inconsistent by sub-proof #1633.
% 231.54/42.79  | | 
% 231.54/42.79  | Case 2:
% 231.54/42.79  | | 
% 231.54/42.79  | |   (18)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) =
% 231.54/42.79  | |           e1)
% 231.54/42.79  | | 
% 231.54/42.79  | | BETA: splitting (18) gives:
% 231.54/42.79  | | 
% 231.54/42.79  | | Case 1:
% 231.54/42.79  | | | 
% 231.54/42.79  | | |   (19)  all_57_6 = e1 & op(e1, e3) = e1
% 231.54/42.79  | | | 
% 231.54/42.79  | | | ALPHA: (19) implies:
% 231.54/42.79  | | |   (20)  all_57_6 = e1
% 231.54/42.79  | | | 
% 231.54/42.79  | | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13),
% 231.54/42.79  | | |            (14), (15), (16), (20) are inconsistent by sub-proof #1643.
% 231.54/42.79  | | | 
% 231.54/42.79  | | Case 2:
% 231.54/42.79  | | | 
% 231.54/42.79  | | |   (21)  all_57_12 = e1 & op(e0, e3) = e1
% 231.54/42.79  | | | 
% 231.54/42.79  | | | REF_CLOSE: (3), (13), (21) are inconsistent by sub-proof #2230.
% 231.54/42.79  | | | 
% 231.54/42.79  | | End of split
% 231.54/42.79  | | 
% 231.54/42.79  | End of split
% 231.54/42.79  | 
% 231.54/42.79  End of proof
% 231.54/42.79  
% 231.54/42.79  Sub-proof #1577 shows that the following formulas are inconsistent:
% 231.54/42.79  ----------------------------------------------------------------
% 231.54/42.79    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.79           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.79    (2)  all_57_2 = e2
% 231.54/42.79    (3)  op(e3, e3) = e2
% 231.54/42.79    (4)   ~ (e2 = e0)
% 231.54/42.79    (5)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0)
% 231.54/42.79  
% 231.54/42.79  Begin of proof
% 231.54/42.79  | 
% 231.54/42.79  | BETA: splitting (5) gives:
% 231.54/42.79  | 
% 231.54/42.79  | Case 1:
% 231.54/42.79  | | 
% 231.54/42.79  | |   (6)  all_57_0 = e0 & op(e3, e3) = e0
% 231.54/42.79  | | 
% 231.54/42.79  | | ALPHA: (6) implies:
% 231.54/42.79  | |   (7)  op(e3, e3) = e0
% 231.54/42.79  | | 
% 231.54/42.79  | | REF_CLOSE: (1), (3), (4), (7) are inconsistent by sub-proof #2403.
% 231.54/42.79  | | 
% 231.54/42.79  | Case 2:
% 231.54/42.79  | | 
% 231.54/42.79  | |   (8)  all_57_2 = e0 & op(e2, e3) = e0
% 231.54/42.79  | | 
% 231.54/42.79  | | REF_CLOSE: (2), (4), (8) are inconsistent by sub-proof #1700.
% 231.54/42.79  | | 
% 231.54/42.79  | End of split
% 231.54/42.79  | 
% 231.54/42.79  End of proof
% 231.54/42.79  
% 231.54/42.79  Sub-proof #1578 shows that the following formulas are inconsistent:
% 231.54/42.79  ----------------------------------------------------------------
% 231.54/42.79    (1)  op(e3, e1) = all_52_5
% 231.54/42.79    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.79         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.54/42.79    (3)   ~ (e3 = e1)
% 231.54/42.79    (4)   ~ (all_53_13 = e1)
% 231.54/42.79    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.79           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.79    (6)  op(all_52_5, all_52_5) = e1
% 231.54/42.80    (7)   ~ (all_6_2 = e3)
% 231.54/42.80    (8)  op(e1, e1) = all_6_2
% 231.54/42.80    (9)  op(e2, e2) = e1
% 231.54/42.80    (10)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.54/42.80          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.54/42.80    (11)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.54/42.80          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.54/42.80    (12)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.54/42.80          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.54/42.80    (13)   ~ (e3 = e2)
% 231.54/42.80    (14)   ~ (e3 = e0)
% 231.54/42.80    (15)  all_57_10 = e2 & op(e2, e0) = e2
% 231.54/42.80    (16)  op(e0, e3) = all_53_3
% 231.54/42.80    (17)  op(e3, e3) = e2
% 231.54/42.80    (18)   ~ (all_53_3 = e2)
% 231.54/42.80    (19)  all_57_4 = e1
% 231.54/42.80    (20)  op(e3, e3) = all_52_1
% 231.54/42.80    (21)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 231.54/42.80          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 231.54/42.80    (22)  op(all_52_1, all_52_1) = e3
% 231.54/42.80    (23)   ~ (e2 = e0)
% 231.54/42.80    (24)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 231.54/42.80          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.54/42.80    (25)   ~ (e1 = e0)
% 231.54/42.80    (26)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.54/42.80          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.54/42.80    (27)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.54/42.80          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.54/42.80    (28)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.54/42.80          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.54/42.80            e2)
% 231.54/42.80    (29)  op(e1, e1) = e2
% 231.54/42.80    (30)  op(e0, e0) = e1
% 231.54/42.80    (31)  op(e2, e0) = all_53_13
% 231.54/42.80    (32)  op(e3, e1) = e1
% 231.54/42.80    (33)   ~ (e2 = e1)
% 231.54/42.80    (34)   ~ (all_6_2 = e0)
% 231.54/42.80    (35)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.80          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.54/42.80  
% 231.54/42.80  Begin of proof
% 231.54/42.80  | 
% 231.54/42.80  | BETA: splitting (2) gives:
% 231.54/42.80  | 
% 231.54/42.80  | Case 1:
% 231.54/42.80  | | 
% 231.54/42.80  | |   (36)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 231.54/42.80  | |           e2)
% 231.54/42.80  | | 
% 231.54/42.80  | | REF_CLOSE: (3), (5), (10), (11), (13), (14), (17), (20), (22), (23), (24),
% 231.54/42.80  | |            (25), (33), (36) are inconsistent by sub-proof #1580.
% 231.54/42.80  | | 
% 231.54/42.80  | Case 2:
% 231.54/42.80  | | 
% 231.54/42.80  | |   (37)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 231.54/42.80  | |           e2)
% 231.54/42.80  | | 
% 231.54/42.80  | | BETA: splitting (37) gives:
% 231.54/42.80  | | 
% 231.54/42.80  | | Case 1:
% 231.54/42.80  | | | 
% 231.54/42.80  | | |   (38)  all_57_7 = e2 & op(e1, e2) = e2
% 231.54/42.80  | | | 
% 231.54/42.80  | | | REF_CLOSE: (2), (3), (5), (7), (8), (9), (12), (13), (14), (16), (18),
% 231.54/42.80  | | |            (19), (21), (23), (25), (26), (27), (28), (30), (33), (34),
% 231.54/42.80  | | |            (35), (38) are inconsistent by sub-proof #1579.
% 231.54/42.80  | | | 
% 231.54/42.80  | | Case 2:
% 231.54/42.80  | | | 
% 231.54/42.80  | | | 
% 231.54/42.80  | | | ALPHA: (15) implies:
% 231.54/42.80  | | |   (39)  op(e2, e0) = e2
% 231.54/42.80  | | | 
% 231.54/42.80  | | | GROUND_INST: instantiating (5) with all_53_13, e2, e0, e2, simplifying
% 231.54/42.80  | | |              with (31), (39) gives:
% 231.54/42.80  | | |   (40)  all_53_13 = e2
% 231.54/42.80  | | | 
% 231.54/42.80  | | | GROUND_INST: instantiating (5) with e1, all_52_5, e1, e3, simplifying with
% 231.54/42.80  | | |              (1), (32) gives:
% 231.54/42.80  | | |   (41)  all_52_5 = e1
% 231.54/42.80  | | | 
% 231.54/42.80  | | | REDUCE: (6), (41) imply:
% 231.54/42.80  | | |   (42)  op(e1, e1) = e1
% 231.54/42.80  | | | 
% 231.54/42.80  | | | REF_CLOSE: (5), (29), (33), (42) are inconsistent by sub-proof #2423.
% 231.54/42.80  | | | 
% 231.54/42.80  | | End of split
% 231.54/42.80  | | 
% 231.54/42.80  | End of split
% 231.54/42.80  | 
% 231.54/42.80  End of proof
% 231.54/42.80  
% 231.54/42.80  Sub-proof #1579 shows that the following formulas are inconsistent:
% 231.54/42.80  ----------------------------------------------------------------
% 231.54/42.80    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.80         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.54/42.80    (2)   ~ (e3 = e1)
% 231.54/42.80    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.80           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.80    (4)   ~ (all_6_2 = e3)
% 231.54/42.80    (5)  op(e1, e1) = all_6_2
% 231.54/42.80    (6)  op(e2, e2) = e1
% 231.54/42.80    (7)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.54/42.80         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.54/42.80    (8)   ~ (e3 = e2)
% 231.54/42.80    (9)   ~ (e3 = e0)
% 231.54/42.80    (10)  op(e0, e3) = all_53_3
% 231.54/42.80    (11)   ~ (all_53_3 = e2)
% 231.54/42.80    (12)  all_57_4 = e1
% 231.54/42.80    (13)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 231.54/42.80          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 231.54/42.80    (14)   ~ (e2 = e0)
% 231.54/42.80    (15)   ~ (e1 = e0)
% 231.54/42.80    (16)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.54/42.80          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.54/42.80    (17)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.54/42.80          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.54/42.80    (18)  all_57_7 = e2 & op(e1, e2) = e2
% 231.54/42.80    (19)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.54/42.80          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.54/42.80            e2)
% 231.54/42.80    (20)  op(e0, e0) = e1
% 231.54/42.80    (21)   ~ (e2 = e1)
% 231.54/42.80    (22)   ~ (all_6_2 = e0)
% 231.54/42.80    (23)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.80          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.54/42.80  
% 231.54/42.80  Begin of proof
% 231.54/42.80  | 
% 231.54/42.80  | ALPHA: (18) implies:
% 231.54/42.80  |   (24)  all_57_7 = e2
% 231.54/42.80  | 
% 231.54/42.80  | BETA: splitting (19) gives:
% 231.54/42.80  | 
% 231.54/42.80  | Case 1:
% 231.54/42.80  | | 
% 231.54/42.80  | |   (25)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 231.54/42.80  | |           e2)
% 231.54/42.80  | | 
% 231.54/42.80  | | BETA: splitting (25) gives:
% 231.54/42.80  | | 
% 231.54/42.80  | | Case 1:
% 231.54/42.80  | | | 
% 231.54/42.80  | | |   (26)  all_57_12 = e2 & op(e0, e3) = e2
% 231.54/42.80  | | | 
% 231.54/42.80  | | | ALPHA: (26) implies:
% 231.54/42.80  | | |   (27)  op(e0, e3) = e2
% 231.54/42.80  | | | 
% 231.54/42.80  | | | REF_CLOSE: (3), (10), (11), (27) are inconsistent by sub-proof #1980.
% 231.54/42.80  | | | 
% 231.54/42.80  | | Case 2:
% 231.54/42.80  | | | 
% 231.54/42.80  | | |   (28)  all_57_13 = e2 & op(e0, e2) = e2
% 231.54/42.80  | | | 
% 231.54/42.80  | | | ALPHA: (28) implies:
% 231.54/42.80  | | |   (29)  all_57_13 = e2
% 231.54/42.80  | | | 
% 231.54/42.80  | | | REF_CLOSE: (1), (2), (3), (6), (8), (9), (13), (14), (15), (17), (21),
% 231.54/42.80  | | |            (23), (24), (29) are inconsistent by sub-proof #1696.
% 231.54/42.80  | | | 
% 231.54/42.80  | | End of split
% 231.54/42.80  | | 
% 231.54/42.80  | Case 2:
% 231.54/42.80  | | 
% 231.54/42.80  | |   (30)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.54/42.80  | |           e2)
% 231.54/42.80  | | 
% 231.54/42.80  | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (12), (14), (15), (16), (20),
% 231.54/42.80  | |            (21), (22), (30) are inconsistent by sub-proof #1695.
% 231.54/42.80  | | 
% 231.54/42.80  | End of split
% 231.54/42.80  | 
% 231.54/42.80  End of proof
% 231.54/42.80  
% 231.54/42.80  Sub-proof #1580 shows that the following formulas are inconsistent:
% 231.54/42.80  ----------------------------------------------------------------
% 231.54/42.80    (1)   ~ (e3 = e1)
% 231.54/42.80    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.80           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.80    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.54/42.80         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.54/42.80    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2)
% 231.54/42.80    (5)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.54/42.80         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.54/42.80    (6)   ~ (e3 = e2)
% 231.54/42.80    (7)   ~ (e3 = e0)
% 231.54/42.80    (8)  op(e3, e3) = e2
% 231.54/42.80    (9)  op(e3, e3) = all_52_1
% 231.54/42.80    (10)  op(all_52_1, all_52_1) = e3
% 231.54/42.80    (11)   ~ (e2 = e0)
% 231.54/42.80    (12)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 231.54/42.80          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.54/42.80    (13)   ~ (e1 = e0)
% 231.54/42.80    (14)   ~ (e2 = e1)
% 231.54/42.80  
% 231.54/42.80  Begin of proof
% 231.54/42.80  | 
% 231.54/42.80  | BETA: splitting (4) gives:
% 231.54/42.80  | 
% 231.54/42.80  | Case 1:
% 231.54/42.80  | | 
% 231.54/42.80  | |   (15)  all_57_1 = e2 & op(e3, e2) = e2
% 231.54/42.80  | | 
% 231.54/42.80  | | ALPHA: (15) implies:
% 231.54/42.80  | |   (16)  all_57_1 = e2
% 231.54/42.80  | | 
% 231.54/42.80  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (11), (12), (13), (14), (16)
% 231.54/42.80  | |            are inconsistent by sub-proof #1655.
% 231.54/42.80  | | 
% 231.54/42.80  | Case 2:
% 231.54/42.80  | | 
% 231.54/42.80  | |   (17)  all_57_3 = e2 & op(e2, e2) = e2
% 231.54/42.80  | | 
% 231.54/42.80  | | ALPHA: (17) implies:
% 231.54/42.80  | |   (18)  op(e2, e2) = e2
% 231.54/42.80  | | 
% 231.54/42.80  | | REF_CLOSE: (2), (6), (8), (9), (10), (18) are inconsistent by sub-proof
% 231.54/42.80  | |            #1951.
% 231.54/42.80  | | 
% 231.54/42.80  | End of split
% 231.54/42.80  | 
% 231.54/42.80  End of proof
% 231.54/42.80  
% 231.54/42.80  Sub-proof #1581 shows that the following formulas are inconsistent:
% 231.54/42.80  ----------------------------------------------------------------
% 231.54/42.80    (1)   ~ (e3 = e1)
% 231.54/42.80    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.80           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.80    (3)   ~ (e3 = e2)
% 231.54/42.80    (4)   ~ (e3 = e0)
% 231.54/42.80    (5)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 231.54/42.80         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.54/42.80    (6)   ~ (e2 = e0)
% 231.54/42.80    (7)  all_57_13 = e2
% 231.54/42.80    (8)   ~ (e1 = e0)
% 231.54/42.80    (9)  all_57_14 = e2
% 231.54/42.80    (10)  op(e0, e0) = e0
% 231.54/42.80    (11)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.54/42.80          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 231.54/42.80            e3)
% 231.54/42.80    (12)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.54/42.80              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.54/42.80                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.54/42.80                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.54/42.80    (13)   ~ (e2 = e1)
% 231.54/42.80  
% 231.54/42.80  Begin of proof
% 231.54/42.80  | 
% 231.54/42.80  | BETA: splitting (5) gives:
% 231.54/42.80  | 
% 231.54/42.80  | Case 1:
% 231.54/42.80  | | 
% 231.54/42.80  | |   (14)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 231.54/42.80  | |           e1)
% 231.54/42.80  | | 
% 231.54/42.80  | | BETA: splitting (14) gives:
% 231.54/42.80  | | 
% 231.54/42.80  | | Case 1:
% 231.54/42.80  | | | 
% 231.54/42.80  | | |   (15)  all_57_12 = e1 & op(e0, e3) = e1
% 231.54/42.80  | | | 
% 231.54/42.80  | | | ALPHA: (15) implies:
% 231.54/42.80  | | |   (16)  all_57_12 = e1
% 231.54/42.80  | | | 
% 231.54/42.80  | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (11), (12), (16) are
% 231.54/42.80  | | |            inconsistent by sub-proof #1582.
% 231.54/42.80  | | | 
% 231.54/42.80  | | Case 2:
% 231.54/42.80  | | | 
% 231.54/42.80  | | |   (17)  all_57_13 = e1 & op(e0, e2) = e1
% 231.54/42.80  | | | 
% 231.54/42.80  | | | REF_CLOSE: (7), (13), (17) are inconsistent by sub-proof #2205.
% 231.54/42.80  | | | 
% 231.54/42.80  | | End of split
% 231.54/42.80  | | 
% 231.54/42.80  | Case 2:
% 231.54/42.80  | | 
% 231.54/42.80  | |   (18)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.54/42.80  | |           e1)
% 231.54/42.80  | | 
% 231.54/42.80  | | BETA: splitting (18) gives:
% 231.54/42.80  | | 
% 231.54/42.80  | | Case 1:
% 231.54/42.80  | | | 
% 231.54/42.80  | | |   (19)  all_57_14 = e1 & op(e0, e1) = e1
% 231.54/42.80  | | | 
% 231.54/42.80  | | | REF_CLOSE: (9), (13), (19) are inconsistent by sub-proof #2375.
% 231.54/42.80  | | | 
% 231.54/42.80  | | Case 2:
% 231.54/42.80  | | | 
% 231.54/42.80  | | |   (20)  all_57_15 = e1 & op(e0, e0) = e1
% 231.54/42.80  | | | 
% 231.54/42.80  | | | ALPHA: (20) implies:
% 231.54/42.80  | | |   (21)  op(e0, e0) = e1
% 231.54/42.80  | | | 
% 231.54/42.80  | | | REF_CLOSE: (2), (8), (10), (21) are inconsistent by sub-proof #2290.
% 231.54/42.80  | | | 
% 231.54/42.80  | | End of split
% 231.54/42.80  | | 
% 231.54/42.80  | End of split
% 231.54/42.80  | 
% 231.54/42.80  End of proof
% 231.54/42.80  
% 231.54/42.80  Sub-proof #1582 shows that the following formulas are inconsistent:
% 231.54/42.80  ----------------------------------------------------------------
% 231.54/42.80    (1)   ~ (e3 = e1)
% 231.54/42.80    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.80           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.80    (3)   ~ (e3 = e2)
% 231.54/42.80    (4)   ~ (e3 = e0)
% 231.54/42.80    (5)  all_57_12 = e1
% 231.54/42.80    (6)   ~ (e2 = e0)
% 231.54/42.80    (7)  all_57_13 = e2
% 231.54/42.80    (8)   ~ (e1 = e0)
% 231.54/42.80    (9)  all_57_14 = e2
% 231.54/42.80    (10)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.54/42.80          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 231.54/42.80            e3)
% 231.54/42.80    (11)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.54/42.80              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.54/42.80                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.54/42.80                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.54/42.80  
% 231.54/42.80  Begin of proof
% 231.54/42.80  | 
% 231.54/42.80  | BETA: splitting (10) gives:
% 231.54/42.80  | 
% 231.54/42.80  | Case 1:
% 231.54/42.80  | | 
% 231.54/42.80  | |   (12)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 231.54/42.80  | |           e3)
% 231.54/42.80  | | 
% 231.54/42.80  | | REF_CLOSE: (1), (3), (5), (7), (12) are inconsistent by sub-proof #1585.
% 231.54/42.80  | | 
% 231.54/42.80  | Case 2:
% 231.54/42.80  | | 
% 231.54/42.80  | |   (13)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 231.54/42.80  | |           e3)
% 231.54/42.80  | | 
% 231.54/42.80  | | BETA: splitting (13) gives:
% 231.54/42.80  | | 
% 231.54/42.80  | | Case 1:
% 231.54/42.80  | | | 
% 231.54/42.80  | | |   (14)  all_57_14 = e3 & op(e0, e1) = e3
% 231.54/42.80  | | | 
% 231.54/42.80  | | | REF_CLOSE: (3), (9), (14) are inconsistent by sub-proof #1891.
% 231.54/42.80  | | | 
% 231.54/42.80  | | Case 2:
% 231.54/42.80  | | | 
% 231.54/42.80  | | |   (15)  all_57_15 = e3 & op(e0, e0) = e3
% 231.54/42.80  | | | 
% 231.54/42.80  | | | ALPHA: (15) implies:
% 231.54/42.80  | | |   (16)  op(e0, e0) = e3
% 231.54/42.80  | | | 
% 231.54/42.80  | | | REF_CLOSE: (2), (4), (5), (6), (7), (8), (9), (11), (16) are inconsistent
% 231.54/42.80  | | |            by sub-proof #1583.
% 231.54/42.80  | | | 
% 231.54/42.80  | | End of split
% 231.54/42.80  | | 
% 231.54/42.80  | End of split
% 231.54/42.80  | 
% 231.54/42.80  End of proof
% 231.54/42.80  
% 231.54/42.80  Sub-proof #1583 shows that the following formulas are inconsistent:
% 231.54/42.80  ----------------------------------------------------------------
% 231.54/42.80    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.80           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.80    (2)   ~ (e3 = e0)
% 231.54/42.80    (3)  all_57_12 = e1
% 231.54/42.80    (4)   ~ (e2 = e0)
% 231.54/42.80    (5)  all_57_13 = e2
% 231.54/42.80    (6)   ~ (e1 = e0)
% 231.54/42.80    (7)  all_57_14 = e2
% 231.54/42.80    (8)  op(e0, e0) = e3
% 231.54/42.80    (9)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.54/42.80             | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 231.54/42.80               e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.54/42.80               op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.54/42.80  
% 231.54/42.80  Begin of proof
% 231.54/42.80  | 
% 231.54/42.80  | BETA: splitting (9) gives:
% 231.54/42.80  | 
% 231.54/42.80  | Case 1:
% 231.54/42.80  | | 
% 231.54/42.80  | |   (10)  all_57_15 = e0 & op(e0, e0) = e0
% 231.54/42.80  | | 
% 231.54/42.80  | | ALPHA: (10) implies:
% 231.54/42.80  | |   (11)  op(e0, e0) = e0
% 231.54/42.80  | | 
% 231.54/42.80  | | REF_CLOSE: (1), (2), (8), (11) are inconsistent by sub-proof #2304.
% 231.54/42.80  | | 
% 231.54/42.80  | Case 2:
% 231.54/42.80  | | 
% 231.54/42.80  | |   (12)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 231.54/42.80  | |             e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0 &
% 231.54/42.80  | |             op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 231.54/42.80  | |           (all_57_14 = e0 & op(e0, e1) = e0))
% 231.54/42.80  | | 
% 231.54/42.80  | | ALPHA: (12) implies:
% 231.54/42.80  | |   (13)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 231.54/42.80  | |           e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.54/42.80  | | 
% 231.54/42.80  | | REF_CLOSE: (3), (4), (5), (6), (7), (13) are inconsistent by sub-proof
% 231.54/42.80  | |            #1584.
% 231.54/42.80  | | 
% 231.54/42.80  | End of split
% 231.54/42.80  | 
% 231.54/42.80  End of proof
% 231.54/42.80  
% 231.54/42.80  Sub-proof #1584 shows that the following formulas are inconsistent:
% 231.54/42.80  ----------------------------------------------------------------
% 231.54/42.80    (1)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 231.54/42.80         (all_57_14 = e0 & op(e0, e1) = e0)
% 231.54/42.80    (2)  all_57_12 = e1
% 231.54/42.80    (3)   ~ (e2 = e0)
% 231.54/42.80    (4)  all_57_13 = e2
% 231.54/42.80    (5)   ~ (e1 = e0)
% 231.54/42.80    (6)  all_57_14 = e2
% 231.54/42.80  
% 231.54/42.80  Begin of proof
% 231.54/42.80  | 
% 231.54/42.80  | BETA: splitting (1) gives:
% 231.54/42.80  | 
% 231.54/42.80  | Case 1:
% 231.54/42.80  | | 
% 231.54/42.80  | |   (7)  all_57_12 = e0 & op(e0, e3) = e0
% 231.54/42.80  | | 
% 231.54/42.80  | | ALPHA: (7) implies:
% 231.54/42.80  | |   (8)  all_57_12 = e0
% 231.54/42.80  | | 
% 231.54/42.80  | | REF_CLOSE: (2), (5), (8) are inconsistent by sub-proof #2014.
% 231.54/42.80  | | 
% 231.54/42.80  | Case 2:
% 231.54/42.80  | | 
% 231.54/42.80  | |   (9)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 231.54/42.80  | |          e0)
% 231.54/42.80  | | 
% 231.54/42.80  | | BETA: splitting (9) gives:
% 231.54/42.80  | | 
% 231.54/42.80  | | Case 1:
% 231.54/42.80  | | | 
% 231.54/42.80  | | |   (10)  all_57_13 = e0 & op(e0, e2) = e0
% 231.54/42.80  | | | 
% 231.54/42.80  | | | REF_CLOSE: (3), (4), (10) are inconsistent by sub-proof #1743.
% 231.54/42.80  | | | 
% 231.54/42.80  | | Case 2:
% 231.54/42.80  | | | 
% 231.54/42.80  | | |   (11)  all_57_14 = e0 & op(e0, e1) = e0
% 231.54/42.80  | | | 
% 231.54/42.80  | | | REF_CLOSE: (3), (6), (11) are inconsistent by sub-proof #2173.
% 231.54/42.80  | | | 
% 231.54/42.80  | | End of split
% 231.54/42.80  | | 
% 231.54/42.80  | End of split
% 231.54/42.80  | 
% 231.54/42.80  End of proof
% 231.54/42.80  
% 231.54/42.80  Sub-proof #1585 shows that the following formulas are inconsistent:
% 231.54/42.80  ----------------------------------------------------------------
% 231.54/42.80    (1)   ~ (e3 = e1)
% 231.54/42.80    (2)   ~ (e3 = e2)
% 231.54/42.80    (3)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.54/42.80    (4)  all_57_12 = e1
% 231.54/42.80    (5)  all_57_13 = e2
% 231.54/42.80  
% 231.54/42.80  Begin of proof
% 231.54/42.80  | 
% 231.54/42.80  | BETA: splitting (3) gives:
% 231.54/42.80  | 
% 231.54/42.80  | Case 1:
% 231.54/42.80  | | 
% 231.54/42.80  | |   (6)  all_57_12 = e3 & op(e0, e3) = e3
% 231.54/42.80  | | 
% 231.54/42.80  | | ALPHA: (6) implies:
% 231.54/42.80  | |   (7)  all_57_12 = e3
% 231.54/42.80  | | 
% 231.54/42.80  | | REF_CLOSE: (1), (4), (7) are inconsistent by sub-proof #2151.
% 231.54/42.80  | | 
% 231.54/42.80  | Case 2:
% 231.54/42.80  | | 
% 231.54/42.80  | |   (8)  all_57_13 = e3 & op(e0, e2) = e3
% 231.54/42.80  | | 
% 231.54/42.80  | | ALPHA: (8) implies:
% 231.54/42.80  | |   (9)  all_57_13 = e3
% 231.54/42.80  | | 
% 231.54/42.80  | | REF_CLOSE: (2), (5), (9) are inconsistent by sub-proof #2203.
% 231.54/42.80  | | 
% 231.54/42.80  | End of split
% 231.54/42.80  | 
% 231.54/42.80  End of proof
% 231.54/42.80  
% 231.54/42.80  Sub-proof #1586 shows that the following formulas are inconsistent:
% 231.54/42.80  ----------------------------------------------------------------
% 231.54/42.80    (1)  all_57_11 = e0 & op(e1, e0) = e0
% 231.54/42.80    (2)   ~ (e3 = e1)
% 231.54/42.80    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.80           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.80    (4)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.54/42.80         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.54/42.80    (5)   ~ (all_6_2 = e3)
% 231.54/42.80    (6)  op(e1, e1) = all_6_2
% 231.54/42.80    (7)  all_57_7 = e2
% 231.54/42.80    (8)  all_57_6 = e1
% 231.54/42.80    (9)   ~ (e3 = e2)
% 231.54/42.80    (10)   ~ (e3 = e0)
% 231.54/42.80  
% 231.54/42.80  Begin of proof
% 231.54/42.80  | 
% 231.54/42.80  | ALPHA: (1) implies:
% 231.54/42.80  |   (11)  all_57_11 = e0
% 231.54/42.80  | 
% 231.54/42.80  | BETA: splitting (4) gives:
% 231.54/42.80  | 
% 231.54/42.80  | Case 1:
% 231.54/42.80  | | 
% 231.54/42.80  | |   (12)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 231.54/42.80  | |           e3)
% 231.54/42.80  | | 
% 231.54/42.80  | | BETA: splitting (12) gives:
% 231.54/42.80  | | 
% 231.54/42.80  | | Case 1:
% 231.54/42.80  | | | 
% 231.54/42.80  | | |   (13)  all_57_6 = e3 & op(e1, e3) = e3
% 231.54/42.80  | | | 
% 231.54/42.80  | | | ALPHA: (13) implies:
% 231.54/42.80  | | |   (14)  all_57_6 = e3
% 231.54/42.80  | | | 
% 231.54/42.80  | | | REF_CLOSE: (2), (8), (14) are inconsistent by sub-proof #2017.
% 231.54/42.80  | | | 
% 231.54/42.80  | | Case 2:
% 231.54/42.80  | | | 
% 231.54/42.80  | | |   (15)  all_57_7 = e3 & op(e1, e2) = e3
% 231.54/42.80  | | | 
% 231.54/42.80  | | | REF_CLOSE: (7), (9), (15) are inconsistent by sub-proof #2194.
% 231.54/42.80  | | | 
% 231.54/42.80  | | End of split
% 231.54/42.80  | | 
% 231.54/42.80  | Case 2:
% 231.54/42.80  | | 
% 231.54/42.80  | |   (16)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 231.54/42.80  | |           e3)
% 231.54/42.80  | | 
% 231.54/42.80  | | REF_CLOSE: (3), (5), (6), (10), (11), (16) are inconsistent by sub-proof
% 231.54/42.80  | |            #1863.
% 231.54/42.80  | | 
% 231.54/42.80  | End of split
% 231.54/42.80  | 
% 231.54/42.80  End of proof
% 231.54/42.80  
% 231.54/42.80  Sub-proof #1587 shows that the following formulas are inconsistent:
% 231.54/42.80  ----------------------------------------------------------------
% 231.54/42.80    (1)  all_57_13 = e1
% 231.54/42.80    (2)   ~ (e3 = e1)
% 231.54/42.80    (3)  all_57_7 = e2
% 231.54/42.80    (4)  all_57_3 = e1
% 231.54/42.80    (5)   ~ (e1 = e0)
% 231.54/42.80    (6)  e1 = e0
% 231.54/42.80    (7)  all_57_1 = e3
% 231.54/42.80    (8)   ~ (e2 = e1)
% 231.54/42.80    (9)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.80         (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.54/42.80  
% 231.54/42.80  Begin of proof
% 231.54/42.80  | 
% 231.54/42.80  | COMBINE_EQS: (1), (6) imply:
% 231.54/42.80  |   (10)  all_57_13 = e0
% 231.54/42.80  | 
% 231.54/42.80  | COMBINE_EQS: (4), (6) imply:
% 231.54/42.80  |   (11)  all_57_3 = e0
% 231.54/42.80  | 
% 231.54/42.80  | REF_CLOSE: (2), (3), (5), (7), (8), (9), (10), (11) are inconsistent by
% 231.54/42.80  |            sub-proof #1759.
% 231.54/42.80  | 
% 231.54/42.80  End of proof
% 231.54/42.80  
% 231.54/42.80  Sub-proof #1588 shows that the following formulas are inconsistent:
% 231.54/42.80  ----------------------------------------------------------------
% 231.54/42.80    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.80         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.54/42.80    (2)  all_57_13 = e1
% 231.54/42.80    (3)   ~ (e3 = e1)
% 231.54/42.80    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.80           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.80    (5)  op(e2, e2) = e1
% 231.54/42.80    (6)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1)
% 231.54/42.80    (7)  all_57_7 = e2
% 231.54/42.80    (8)   ~ (e3 = e2)
% 231.54/42.80    (9)   ~ (e3 = e0)
% 231.54/42.80    (10)  op(e3, e3) = e2
% 231.54/42.80    (11)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 231.54/42.80          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 231.54/42.80    (12)   ~ (e2 = e0)
% 231.54/42.80    (13)  all_57_3 = e1
% 231.54/42.80    (14)   ~ (e1 = e0)
% 231.54/42.80    (15)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.54/42.80          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.54/42.80    (16)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.80          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.54/42.80    (17)  all_57_1 = e3
% 231.54/42.80    (18)   ~ (e2 = e1)
% 231.54/42.80  
% 231.54/42.80  Begin of proof
% 231.54/42.80  | 
% 231.54/42.80  | BETA: splitting (6) gives:
% 231.54/42.80  | 
% 231.54/42.80  | Case 1:
% 231.54/42.80  | | 
% 231.54/42.80  | |   (19)  all_57_0 = e1 & op(e3, e3) = e1
% 231.54/42.80  | | 
% 231.54/42.80  | | ALPHA: (19) implies:
% 231.54/42.80  | |   (20)  op(e3, e3) = e1
% 231.54/42.80  | | 
% 231.54/42.80  | | REF_CLOSE: (4), (10), (18), (20) are inconsistent by sub-proof #1950.
% 231.54/42.80  | | 
% 231.54/42.80  | Case 2:
% 231.54/42.80  | | 
% 231.54/42.80  | |   (21)  all_57_2 = e1 & op(e2, e3) = e1
% 231.54/42.80  | | 
% 231.54/42.80  | | ALPHA: (21) implies:
% 231.54/42.80  | |   (22)  all_57_2 = e1
% 231.54/42.80  | | 
% 231.54/42.80  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (11), (12), (13), (14),
% 231.54/42.80  | |            (15), (16), (17), (18), (22) are inconsistent by sub-proof #1589.
% 231.54/42.80  | | 
% 231.54/42.80  | End of split
% 231.54/42.80  | 
% 231.54/42.80  End of proof
% 231.54/42.80  
% 231.54/42.80  Sub-proof #1589 shows that the following formulas are inconsistent:
% 231.54/42.80  ----------------------------------------------------------------
% 231.54/42.80    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.80         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.54/42.80    (2)  all_57_13 = e1
% 231.54/42.80    (3)   ~ (e3 = e1)
% 231.54/42.80    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.80           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.80    (5)  op(e2, e2) = e1
% 231.54/42.80    (6)  all_57_7 = e2
% 231.54/42.80    (7)   ~ (e3 = e2)
% 231.54/42.80    (8)   ~ (e3 = e0)
% 231.54/42.80    (9)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 231.54/42.80         (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 231.54/42.80    (10)   ~ (e2 = e0)
% 231.54/42.80    (11)  all_57_3 = e1
% 231.54/42.80    (12)   ~ (e1 = e0)
% 231.54/42.80    (13)  all_57_2 = e1
% 231.54/42.80    (14)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.54/42.80          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.54/42.80    (15)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.80          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.54/42.80    (16)  all_57_1 = e3
% 231.54/42.80    (17)   ~ (e2 = e1)
% 231.54/42.80  
% 231.54/42.80  Begin of proof
% 231.54/42.80  | 
% 231.54/42.80  | BETA: splitting (9) gives:
% 231.54/42.80  | 
% 231.54/42.80  | Case 1:
% 231.54/42.80  | | 
% 231.54/42.80  | |   (18)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) =
% 231.54/42.80  | |           e0)
% 231.54/42.80  | | 
% 231.54/42.80  | | BETA: splitting (18) gives:
% 231.54/42.80  | | 
% 231.54/42.80  | | Case 1:
% 231.54/42.80  | | | 
% 231.54/42.80  | | |   (19)  all_57_1 = e0 & op(e3, e2) = e0
% 231.54/42.80  | | | 
% 231.54/42.80  | | | REF_CLOSE: (8), (16), (19) are inconsistent by sub-proof #1811.
% 231.54/42.80  | | | 
% 231.54/42.80  | | Case 2:
% 231.54/42.80  | | | 
% 231.54/42.80  | | |   (20)  all_57_3 = e0 & op(e2, e2) = e0
% 231.54/42.80  | | | 
% 231.54/42.80  | | | ALPHA: (20) implies:
% 231.54/42.80  | | |   (21)  op(e2, e2) = e0
% 231.54/42.80  | | | 
% 231.54/42.80  | | | REF_CLOSE: (4), (5), (12), (21) are inconsistent by sub-proof #2352.
% 231.54/42.80  | | | 
% 231.54/42.80  | | End of split
% 231.54/42.80  | | 
% 231.54/42.80  | Case 2:
% 231.54/42.80  | | 
% 231.54/42.80  | |   (22)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 231.54/42.80  | |           e0)
% 231.54/42.80  | | 
% 231.54/42.80  | | BETA: splitting (22) gives:
% 231.54/42.80  | | 
% 231.54/42.80  | | Case 1:
% 231.54/42.80  | | | 
% 231.54/42.80  | | |   (23)  all_57_7 = e0 & op(e1, e2) = e0
% 231.54/42.80  | | | 
% 231.54/42.80  | | | REF_CLOSE: (6), (10), (23) are inconsistent by sub-proof #2148.
% 231.54/42.80  | | | 
% 231.54/42.80  | | Case 2:
% 231.54/42.80  | | | 
% 231.54/42.81  | | |   (24)  all_57_13 = e0 & op(e0, e2) = e0
% 231.54/42.81  | | | 
% 231.54/42.81  | | | ALPHA: (24) implies:
% 231.54/42.81  | | |   (25)  all_57_13 = e0
% 231.54/42.81  | | | 
% 231.54/42.81  | | | COMBINE_EQS: (2), (25) imply:
% 231.54/42.81  | | |   (26)  e1 = e0
% 231.54/42.81  | | | 
% 231.54/42.81  | | | REF_CLOSE: (1), (3), (7), (8), (10), (11), (12), (13), (14), (15), (17),
% 231.54/42.81  | | |            (26) are inconsistent by sub-proof #1590.
% 231.54/42.81  | | | 
% 231.54/42.81  | | End of split
% 231.54/42.81  | | 
% 231.54/42.81  | End of split
% 231.54/42.81  | 
% 231.54/42.81  End of proof
% 231.54/42.81  
% 231.54/42.81  Sub-proof #1590 shows that the following formulas are inconsistent:
% 231.54/42.81  ----------------------------------------------------------------
% 231.54/42.81    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.81         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.54/42.81    (2)   ~ (e3 = e1)
% 231.54/42.81    (3)   ~ (e3 = e2)
% 231.54/42.81    (4)   ~ (e3 = e0)
% 231.54/42.81    (5)   ~ (e2 = e0)
% 231.54/42.81    (6)  all_57_3 = e1
% 231.54/42.81    (7)   ~ (e1 = e0)
% 231.54/42.81    (8)  e1 = e0
% 231.54/42.81    (9)  all_57_2 = e1
% 231.54/42.81    (10)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.54/42.81          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.54/42.81    (11)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.81          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.54/42.81    (12)   ~ (e2 = e1)
% 231.54/42.81  
% 231.54/42.81  Begin of proof
% 231.54/42.81  | 
% 231.54/42.81  | COMBINE_EQS: (6), (8) imply:
% 231.54/42.81  |   (13)  all_57_3 = e0
% 231.54/42.81  | 
% 231.54/42.81  | COMBINE_EQS: (8), (9) imply:
% 231.54/42.81  |   (14)  all_57_2 = e0
% 231.54/42.81  | 
% 231.54/42.81  | REF_CLOSE: (1), (2), (3), (4), (5), (7), (10), (11), (12), (13), (14) are
% 231.54/42.81  |            inconsistent by sub-proof #2246.
% 231.54/42.81  | 
% 231.54/42.81  End of proof
% 231.54/42.81  
% 231.54/42.81  Sub-proof #1591 shows that the following formulas are inconsistent:
% 231.54/42.81  ----------------------------------------------------------------
% 231.54/42.81    (1)   ~ (e3 = e1)
% 231.54/42.81    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.81           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.81    (3)  op(e2, e2) = e1
% 231.54/42.81    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.54/42.81         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.54/42.81    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2)
% 231.54/42.81    (6)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.54/42.81         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.54/42.81    (7)   ~ (e3 = e2)
% 231.54/42.81    (8)   ~ (e3 = e0)
% 231.54/42.81    (9)  op(e3, e3) = e2
% 231.54/42.81    (10)   ~ (e2 = e0)
% 231.54/42.81    (11)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 231.54/42.81          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.54/42.81    (12)   ~ (e1 = e0)
% 231.54/42.81    (13)   ~ (e2 = e1)
% 231.54/42.81  
% 231.54/42.81  Begin of proof
% 231.54/42.81  | 
% 231.54/42.81  | BETA: splitting (5) gives:
% 231.54/42.81  | 
% 231.54/42.81  | Case 1:
% 231.54/42.81  | | 
% 231.54/42.81  | |   (14)  all_57_1 = e2 & op(e3, e2) = e2
% 231.54/42.81  | | 
% 231.54/42.81  | | ALPHA: (14) implies:
% 231.54/42.81  | |   (15)  all_57_1 = e2
% 231.54/42.81  | | 
% 231.54/42.81  | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (9), (10), (11), (12), (13), (15)
% 231.54/42.81  | |            are inconsistent by sub-proof #1655.
% 231.54/42.81  | | 
% 231.54/42.81  | Case 2:
% 231.54/42.81  | | 
% 231.54/42.81  | |   (16)  all_57_3 = e2 & op(e2, e2) = e2
% 231.54/42.81  | | 
% 231.54/42.81  | | ALPHA: (16) implies:
% 231.54/42.81  | |   (17)  op(e2, e2) = e2
% 231.54/42.81  | | 
% 231.54/42.81  | | REF_CLOSE: (2), (3), (13), (17) are inconsistent by sub-proof #2306.
% 231.54/42.81  | | 
% 231.54/42.81  | End of split
% 231.54/42.81  | 
% 231.54/42.81  End of proof
% 231.54/42.81  
% 231.54/42.81  Sub-proof #1592 shows that the following formulas are inconsistent:
% 231.54/42.81  ----------------------------------------------------------------
% 231.54/42.81    (1)  all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 231.54/42.81    (2)  op(e0, e0) = all_4_2
% 231.54/42.81    (3)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 231.54/42.81    (4)   ~ (all_53_12 = all_4_2)
% 231.54/42.81    (5)   ~ (all_53_6 = all_53_14)
% 231.54/42.81    (6)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 231.54/42.81    (7)  all_57_15 = e0
% 231.54/42.81    (8)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.81         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.54/42.81    (9)  op(e2, e3) = all_53_1
% 231.54/42.81    (10)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.54/42.81          (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.54/42.81    (11)   ~ (all_53_8 = all_53_12)
% 231.54/42.81    (12)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.81          (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.54/42.81    (13)   ~ (all_53_8 = all_53_11)
% 231.54/42.81    (14)   ~ (e3 = e1)
% 231.54/42.81    (15)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 231.54/42.81          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.54/42.81    (16)   ~ (all_53_13 = e1)
% 231.54/42.81    (17)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.81            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.81    (18)  all_55_15 = all_4_2
% 231.54/42.81    (19)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.54/42.81          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.54/42.81    (20)   ~ (all_53_3 = all_53_7)
% 231.54/42.81    (21)   ~ (all_6_2 = e3)
% 231.54/42.81    (22)  op(e1, e1) = all_6_2
% 231.54/42.81    (23)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 231.54/42.81    (24)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 231.54/42.81    (25)  op(e2, e2) = e1
% 231.54/42.81    (26)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.54/42.81          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.54/42.81    (27)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 231.54/42.81    (28)  all_55_9 = all_53_6
% 231.54/42.81    (29)  all_57_9 = e1
% 231.54/42.81    (30)   ~ (all_53_4 = all_53_12)
% 231.54/42.81    (31)   ~ (all_53_4 = e1)
% 231.54/42.81    (32)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.54/42.81    (33)   ~ (all_53_8 = all_53_9)
% 231.54/42.81    (34)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.54/42.81          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.54/42.81    (35)   ~ (all_53_14 = all_6_2)
% 231.54/42.81    (36)   ~ (all_53_14 = all_4_2)
% 231.54/42.81    (37)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.54/42.81          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.54/42.81    (38)   ~ (e3 = e2)
% 231.54/42.81    (39)  op(e3, e0) = e1
% 231.54/42.81    (40)  all_55_1 = all_53_4
% 231.54/42.81    (41)  op(e1, e0) = all_53_14
% 231.54/42.81    (42)   ~ (all_53_6 = all_53_7)
% 231.54/42.81    (43)   ~ (e3 = e0)
% 231.54/42.81    (44)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.54/42.81          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.54/42.81    (45)   ~ (all_53_8 = all_6_2)
% 231.54/42.81    (46)   ~ (all_4_2 = e2)
% 231.54/42.81    (47)  op(e0, e3) = all_53_3
% 231.54/42.81    (48)   ~ (all_53_7 = all_4_2)
% 231.54/42.81    (49)   ~ (all_53_11 = e0)
% 231.54/42.81    (50)  all_55_2 = all_53_8
% 231.54/42.81    (51)   ~ (all_53_4 = all_53_7)
% 231.54/42.81    (52)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 231.54/42.81    (53)  op(e3, e3) = e2
% 231.54/42.81    (54)   ~ (all_53_3 = e2)
% 231.54/42.81    (55)   ~ (all_53_7 = e0)
% 231.54/42.81    (56)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.54/42.81          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.54/42.81            e1)
% 231.54/42.81    (57)   ~ (all_53_1 = e1)
% 231.54/42.81    (58)   ~ (all_53_4 = all_53_8)
% 231.54/42.81    (59)  op(e3, e2) = all_53_4
% 231.54/42.81    (60)  op(e1, e1) = e1
% 231.54/42.81    (61)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 231.54/42.81          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 231.54/42.81    (62)   ~ (e2 = e0)
% 231.54/42.81    (63)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 231.54/42.81            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 231.54/42.81            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 231.54/42.81            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 231.54/42.81              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 231.54/42.81            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 231.54/42.81            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 231.54/42.81              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 231.54/42.81              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 231.54/42.81            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 231.54/42.81            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 231.54/42.81            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 231.54/42.81              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 231.54/42.81              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 231.54/42.81            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 231.54/42.81              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 231.54/42.81            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 231.54/42.81            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 231.54/42.81              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 231.54/42.81              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 231.54/42.81            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 231.54/42.81            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 231.54/42.81    (64)   ~ (all_53_6 = e1)
% 231.54/42.81    (65)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 231.54/42.81          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.54/42.81    (66)   ~ (all_53_2 = all_53_14)
% 231.54/42.81    (67)   ~ (e1 = e0)
% 231.54/42.81    (68)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 231.54/42.81            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 231.54/42.81              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 231.54/42.81    (69)   ~ (all_53_3 = all_53_11)
% 231.54/42.81    (70)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.54/42.81          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.54/42.81    (71)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.54/42.81          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.54/42.81    (72)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 231.54/42.81    (73)  op(e0, e0) = e0
% 231.54/42.81    (74)   ~ (all_53_7 = all_53_11)
% 231.54/42.81    (75)   ~ (all_53_14 = e0)
% 231.54/42.81    (76)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.54/42.81          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 231.54/42.81            e3)
% 231.54/42.81    (77)   ~ (all_53_13 = all_4_2)
% 231.54/42.81    (78)   ~ (all_53_4 = all_53_6)
% 231.54/42.81    (79)  op(e0, e2) = all_53_7
% 231.54/42.81    (80)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.54/42.81          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.54/42.81            e2)
% 231.54/42.81    (81)   ~ (all_53_8 = e2)
% 231.54/42.81    (82)   ~ (all_53_3 = e0)
% 231.54/42.81    (83)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.54/42.81              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.54/42.81                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.54/42.81                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.54/42.81    (84)  all_55_10 = all_6_2
% 231.54/42.81    (85)   ~ (all_53_6 = all_6_2)
% 231.54/42.81    (86)   ~ (all_53_13 = e0)
% 231.54/42.81    (87)  all_55_13 = all_53_7
% 231.54/42.81    (88)  op(e2, e0) = all_53_13
% 231.54/42.81    (89)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.54/42.81          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.54/42.81    (90)  all_38_2 = all_6_2
% 231.54/42.81    (91)  all_55_11 = all_53_14
% 231.54/42.81    (92)  all_55_3 = all_53_12
% 231.54/42.81    (93)  all_55_15 = e1 | all_55_15 = e0
% 231.54/42.81    (94)   ~ (all_53_4 = e2)
% 231.54/42.81    (95)  op(e1, e3) = all_53_2
% 231.54/42.81    (96)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.81          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.54/42.81    (97)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 231.54/42.81          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 231.54/42.81    (98)   ~ (all_53_12 = e0)
% 231.54/42.81    (99)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 231.54/42.81          (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 231.54/42.81    (100)   ~ (all_53_13 = all_53_14)
% 231.54/42.81    (101)   ~ (all_4_2 = e1)
% 231.54/42.81    (102)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 231.54/42.81           (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 231.54/42.81    (103)   ~ (e2 = e1)
% 231.54/42.81    (104)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.54/42.81           | (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.54/42.81             e2)
% 231.54/42.81    (105)  op(e2, e1) = all_53_9
% 231.54/42.81    (106)  op(e1, e2) = all_53_6
% 231.54/42.81    (107)   ~ (all_6_2 = e0)
% 231.54/42.81    (108)   ~ (all_53_2 = all_53_6)
% 231.54/42.81    (109)   ~ (all_53_12 = e2)
% 231.54/42.81    (110)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.54/42.81           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.54/42.81    (111)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.54/42.81           (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.54/42.81    (112)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.54/42.81           | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.54/42.81             e1)
% 231.54/42.81    (113)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 231.54/42.81           (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 231.54/42.81    (114)   ~ (all_53_12 = all_53_14)
% 231.54/42.81    (115)  all_55_14 = all_53_11
% 231.54/42.81    (116)  op(e3, e1) = all_53_8
% 231.54/42.81    (117)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.81           (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.54/42.81    (118)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 231.54/42.81           (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 231.54/42.81    (119)  op(e3, e0) = all_53_12
% 231.54/42.81  
% 231.54/42.81  Begin of proof
% 231.54/42.81  | 
% 231.54/42.81  | BETA: splitting (32) gives:
% 231.54/42.81  | 
% 231.54/42.81  | Case 1:
% 231.54/42.81  | | 
% 231.54/42.81  | |   (120)  all_57_12 = e2 & op(e0, e3) = e2
% 231.54/42.81  | | 
% 231.54/42.81  | | ALPHA: (120) implies:
% 231.54/42.81  | |   (121)  op(e0, e3) = e2
% 231.54/42.81  | | 
% 231.54/42.81  | | REF_CLOSE: (17), (47), (54), (121) are inconsistent by sub-proof #1980.
% 231.54/42.81  | | 
% 231.54/42.81  | Case 2:
% 231.54/42.81  | | 
% 231.54/42.81  | |   (122)  all_57_13 = e2 & op(e0, e2) = e2
% 231.54/42.81  | | 
% 231.54/42.81  | | ALPHA: (122) implies:
% 231.54/42.81  | |   (123)  op(e0, e2) = e2
% 231.54/42.81  | | 
% 231.54/42.81  | | BETA: splitting (10) gives:
% 231.54/42.81  | | 
% 231.54/42.81  | | Case 1:
% 231.54/42.81  | | | 
% 231.54/42.81  | | |   (124)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) =
% 231.54/42.81  | | |            e1)
% 231.54/42.81  | | | 
% 231.54/42.81  | | | REF_CLOSE: (9), (17), (53), (57), (103), (124) are inconsistent by
% 231.54/42.81  | | |            sub-proof #1598.
% 231.54/42.81  | | | 
% 231.54/42.81  | | Case 2:
% 231.54/42.81  | | | 
% 231.54/42.81  | | |   (125)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3)
% 231.54/42.81  | | |            = e1)
% 231.54/42.81  | | | 
% 231.54/42.81  | | | BETA: splitting (125) gives:
% 231.54/42.81  | | | 
% 231.54/42.81  | | | Case 1:
% 231.54/42.81  | | | | 
% 231.54/42.81  | | | |   (126)  all_57_6 = e1 & op(e1, e3) = e1
% 231.54/42.81  | | | | 
% 231.54/42.81  | | | | ALPHA: (126) implies:
% 231.54/42.81  | | | |   (127)  all_57_6 = e1
% 231.54/42.81  | | | | 
% 231.54/42.81  | | | | BETA: splitting (15) gives:
% 231.54/42.81  | | | | 
% 231.54/42.81  | | | | Case 1:
% 231.54/42.81  | | | | | 
% 231.54/42.81  | | | | |   (128)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1,
% 231.54/42.81  | | | | |              e2) = e0)
% 231.54/42.81  | | | | | 
% 231.54/42.81  | | | | | BETA: splitting (128) gives:
% 231.54/42.81  | | | | | 
% 231.54/42.81  | | | | | Case 1:
% 231.54/42.81  | | | | | | 
% 231.54/42.81  | | | | | |   (129)  all_57_6 = e0 & op(e1, e3) = e0
% 231.54/42.81  | | | | | | 
% 231.54/42.81  | | | | | | REF_CLOSE: (67), (127), (129) are inconsistent by sub-proof #2347.
% 231.54/42.81  | | | | | | 
% 231.54/42.81  | | | | | Case 2:
% 231.54/42.81  | | | | | | 
% 231.54/42.81  | | | | | |   (130)  all_57_7 = e0 & op(e1, e2) = e0
% 231.54/42.81  | | | | | | 
% 231.54/42.81  | | | | | | ALPHA: (130) implies:
% 231.54/42.81  | | | | | |   (131)  all_57_7 = e0
% 231.54/42.81  | | | | | | 
% 231.54/42.81  | | | | | | BETA: splitting (118) gives:
% 231.54/42.81  | | | | | | 
% 231.54/42.81  | | | | | | Case 1:
% 231.54/42.81  | | | | | | | 
% 231.54/42.81  | | | | | | |   (132)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 &
% 231.54/42.81  | | | | | | |            op(e1, e2) = e2)
% 231.54/42.81  | | | | | | | 
% 231.54/42.81  | | | | | | | BETA: splitting (132) gives:
% 231.54/42.81  | | | | | | | 
% 231.54/42.81  | | | | | | | Case 1:
% 231.54/42.81  | | | | | | | | 
% 231.54/42.81  | | | | | | | |   (133)  all_57_6 = e2 & op(e1, e3) = e2
% 231.54/42.81  | | | | | | | | 
% 231.54/42.81  | | | | | | | | ALPHA: (133) implies:
% 231.54/42.81  | | | | | | | |   (134)  all_57_6 = e2
% 231.54/42.81  | | | | | | | | 
% 231.54/42.81  | | | | | | | | REF_CLOSE: (103), (127), (134) are inconsistent by sub-proof
% 231.54/42.81  | | | | | | | |            #2233.
% 231.54/42.81  | | | | | | | | 
% 231.54/42.81  | | | | | | | Case 2:
% 231.54/42.81  | | | | | | | | 
% 231.54/42.81  | | | | | | | |   (135)  all_57_7 = e2 & op(e1, e2) = e2
% 231.54/42.81  | | | | | | | | 
% 231.54/42.81  | | | | | | | | ALPHA: (135) implies:
% 231.54/42.81  | | | | | | | |   (136)  all_57_7 = e2
% 231.54/42.81  | | | | | | | | 
% 231.54/42.81  | | | | | | | | REF_CLOSE: (62), (131), (136) are inconsistent by sub-proof
% 231.54/42.81  | | | | | | | |            #2207.
% 231.54/42.81  | | | | | | | | 
% 231.54/42.81  | | | | | | | End of split
% 231.54/42.81  | | | | | | | 
% 231.54/42.81  | | | | | | Case 2:
% 231.54/42.81  | | | | | | | 
% 231.54/42.81  | | | | | | |   (137)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 &
% 231.54/42.81  | | | | | | |            op(e1, e0) = e2)
% 231.54/42.81  | | | | | | | 
% 231.54/42.81  | | | | | | | BETA: splitting (137) gives:
% 231.54/42.81  | | | | | | | 
% 231.54/42.81  | | | | | | | Case 1:
% 231.54/42.81  | | | | | | | | 
% 231.54/42.81  | | | | | | | |   (138)  all_57_8 = e2 & op(e1, e1) = e2
% 231.54/42.81  | | | | | | | | 
% 231.54/42.81  | | | | | | | | ALPHA: (138) implies:
% 231.54/42.81  | | | | | | | |   (139)  op(e1, e1) = e2
% 231.54/42.81  | | | | | | | | 
% 231.54/42.81  | | | | | | | | REF_CLOSE: (2), (4), (6), (7), (14), (15), (16), (17), (18),
% 231.54/42.81  | | | | | | | |            (19), (21), (22), (23), (24), (25), (31), (36), (38),
% 231.54/42.81  | | | | | | | |            (41), (43), (46), (48), (53), (59), (61), (62), (63),
% 231.54/42.81  | | | | | | | |            (64), (67), (73), (75), (77), (79), (83), (84), (86),
% 231.54/42.81  | | | | | | | |            (88), (91), (92), (93), (95), (99), (100), (101),
% 231.54/42.81  | | | | | | | |            (103), (104), (106), (107), (109), (113), (114),
% 231.54/42.81  | | | | | | | |            (119), (123), (139) are inconsistent by sub-proof
% 231.54/42.81  | | | | | | | |            #1596.
% 231.54/42.81  | | | | | | | | 
% 231.54/42.81  | | | | | | | Case 2:
% 231.54/42.81  | | | | | | | | 
% 231.54/42.81  | | | | | | | |   (140)  all_57_11 = e2 & op(e1, e0) = e2
% 231.54/42.81  | | | | | | | | 
% 231.54/42.81  | | | | | | | | ALPHA: (140) implies:
% 231.54/42.81  | | | | | | | |   (141)  all_57_11 = e2
% 231.54/42.81  | | | | | | | | 
% 231.54/42.81  | | | | | | | | REF_CLOSE: (14), (15), (17), (19), (21), (22), (38), (41), (43),
% 231.54/42.81  | | | | | | | |            (67), (75), (107), (127), (141) are inconsistent by
% 231.54/42.81  | | | | | | | |            sub-proof #2340.
% 231.54/42.81  | | | | | | | | 
% 231.54/42.81  | | | | | | | End of split
% 231.54/42.81  | | | | | | | 
% 231.54/42.81  | | | | | | End of split
% 231.54/42.81  | | | | | | 
% 231.54/42.81  | | | | | End of split
% 231.54/42.81  | | | | | 
% 231.54/42.81  | | | | Case 2:
% 231.54/42.81  | | | | | 
% 231.54/42.81  | | | | |   (142)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1,
% 231.54/42.81  | | | | |              e0) = e0)
% 231.54/42.81  | | | | | 
% 231.54/42.81  | | | | | REF_CLOSE: (14), (17), (19), (21), (22), (38), (43), (60), (62), (67),
% 231.54/42.81  | | | | |            (103), (118), (127), (142) are inconsistent by sub-proof
% 231.54/42.81  | | | | |            #1593.
% 231.54/42.81  | | | | | 
% 231.54/42.81  | | | | End of split
% 231.54/42.81  | | | | 
% 231.54/42.81  | | | Case 2:
% 231.54/42.81  | | | | 
% 231.54/42.81  | | | |   (143)  all_57_12 = e1 & op(e0, e3) = e1
% 231.54/42.81  | | | | 
% 231.54/42.81  | | | | REF_CLOSE: (1), (3), (5), (6), (7), (8), (10), (11), (12), (13), (15),
% 231.54/42.81  | | | |            (17), (19), (20), (21), (22), (23), (24), (25), (26), (27),
% 231.54/42.81  | | | |            (28), (29), (30), (33), (34), (35), (37), (39), (40), (41),
% 231.54/42.81  | | | |            (42), (44), (45), (47), (49), (50), (51), (52), (53), (54),
% 231.54/42.81  | | | |            (55), (56), (58), (59), (60), (61), (63), (64), (65), (66),
% 231.54/42.81  | | | |            (68), (69), (70), (71), (72), (73), (74), (75), (76), (78),
% 231.54/42.81  | | | |            (79), (80), (81), (82), (83), (84), (85), (86), (87), (88),
% 231.54/42.81  | | | |            (89), (90), (91), (92), (94), (95), (96), (97), (98), (102),
% 231.54/42.81  | | | |            (104), (105), (106), (108), (109), (110), (111), (112),
% 231.54/42.81  | | | |            (113), (114), (115), (116), (117), (118), (119), (143) are
% 231.54/42.81  | | | |            inconsistent by sub-proof #1599.
% 231.54/42.81  | | | | 
% 231.54/42.81  | | | End of split
% 231.54/42.81  | | | 
% 231.54/42.81  | | End of split
% 231.54/42.81  | | 
% 231.54/42.81  | End of split
% 231.54/42.81  | 
% 231.54/42.81  End of proof
% 231.54/42.81  
% 231.54/42.81  Sub-proof #1593 shows that the following formulas are inconsistent:
% 231.54/42.81  ----------------------------------------------------------------
% 231.54/42.81    (1)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.54/42.81    (2)   ~ (e3 = e1)
% 231.54/42.81    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.81           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.81    (4)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.54/42.81         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.54/42.81    (5)   ~ (all_6_2 = e3)
% 231.54/42.81    (6)  op(e1, e1) = all_6_2
% 231.54/42.81    (7)  all_57_6 = e1
% 231.54/42.81    (8)   ~ (e3 = e2)
% 231.54/42.81    (9)   ~ (e3 = e0)
% 231.54/42.81    (10)  op(e1, e1) = e1
% 231.54/42.81    (11)   ~ (e2 = e0)
% 231.54/42.81    (12)   ~ (e1 = e0)
% 231.54/42.81    (13)   ~ (e2 = e1)
% 231.54/42.81    (14)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 231.54/42.81          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 231.54/42.81  
% 231.54/42.81  Begin of proof
% 231.54/42.81  | 
% 231.54/42.81  | BETA: splitting (1) gives:
% 231.54/42.81  | 
% 231.54/42.81  | Case 1:
% 231.54/42.81  | | 
% 231.54/42.81  | |   (15)  all_57_8 = e0 & op(e1, e1) = e0
% 231.54/42.81  | | 
% 231.54/42.81  | | ALPHA: (15) implies:
% 231.54/42.81  | |   (16)  op(e1, e1) = e0
% 231.54/42.81  | | 
% 231.54/42.81  | | REF_CLOSE: (3), (10), (12), (16) are inconsistent by sub-proof #2427.
% 231.54/42.81  | | 
% 231.54/42.81  | Case 2:
% 231.54/42.81  | | 
% 231.54/42.81  | |   (17)  all_57_11 = e0 & op(e1, e0) = e0
% 231.54/42.81  | | 
% 231.54/42.81  | | ALPHA: (17) implies:
% 231.54/42.81  | |   (18)  all_57_11 = e0
% 231.54/42.81  | | 
% 231.54/42.81  | | BETA: splitting (4) gives:
% 231.54/42.81  | | 
% 231.54/42.81  | | Case 1:
% 231.54/42.81  | | | 
% 231.54/42.81  | | |   (19)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 231.54/42.81  | | |           e3)
% 231.54/42.81  | | | 
% 231.54/42.81  | | | BETA: splitting (19) gives:
% 231.54/42.81  | | | 
% 231.54/42.81  | | | Case 1:
% 231.54/42.81  | | | | 
% 231.54/42.81  | | | |   (20)  all_57_6 = e3 & op(e1, e3) = e3
% 231.54/42.81  | | | | 
% 231.54/42.81  | | | | ALPHA: (20) implies:
% 231.54/42.81  | | | |   (21)  all_57_6 = e3
% 231.54/42.81  | | | | 
% 231.54/42.81  | | | | REF_CLOSE: (2), (7), (21) are inconsistent by sub-proof #2017.
% 231.54/42.81  | | | | 
% 231.54/42.81  | | | Case 2:
% 231.54/42.81  | | | | 
% 231.54/42.81  | | | |   (22)  all_57_7 = e3 & op(e1, e2) = e3
% 231.54/42.81  | | | | 
% 231.54/42.81  | | | | ALPHA: (22) implies:
% 231.54/42.81  | | | |   (23)  all_57_7 = e3
% 231.54/42.81  | | | | 
% 231.54/42.81  | | | | REF_CLOSE: (3), (7), (8), (10), (11), (13), (14), (18), (23) are
% 231.54/42.81  | | | |            inconsistent by sub-proof #1948.
% 231.54/42.81  | | | | 
% 231.54/42.81  | | | End of split
% 231.54/42.81  | | | 
% 231.54/42.81  | | Case 2:
% 231.54/42.81  | | | 
% 231.54/42.81  | | |   (24)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 231.54/42.81  | | |           e3)
% 231.54/42.81  | | | 
% 231.54/42.81  | | | REF_CLOSE: (3), (5), (6), (9), (18), (24) are inconsistent by sub-proof
% 231.54/42.81  | | |            #1594.
% 231.54/42.81  | | | 
% 231.54/42.81  | | End of split
% 231.54/42.81  | | 
% 231.54/42.81  | End of split
% 231.54/42.81  | 
% 231.54/42.81  End of proof
% 231.54/42.81  
% 231.54/42.81  Sub-proof #1594 shows that the following formulas are inconsistent:
% 231.54/42.81  ----------------------------------------------------------------
% 231.54/42.81    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.81           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.81    (2)   ~ (all_6_2 = e3)
% 231.54/42.81    (3)  op(e1, e1) = all_6_2
% 231.54/42.81    (4)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.54/42.81    (5)   ~ (e3 = e0)
% 231.54/42.81    (6)  all_57_11 = e0
% 231.54/42.81  
% 231.54/42.81  Begin of proof
% 231.54/42.81  | 
% 231.54/42.81  | BETA: splitting (4) gives:
% 231.54/42.81  | 
% 231.54/42.81  | Case 1:
% 231.54/42.81  | | 
% 231.54/42.81  | |   (7)  all_57_8 = e3 & op(e1, e1) = e3
% 231.54/42.81  | | 
% 231.54/42.81  | | ALPHA: (7) implies:
% 231.54/42.81  | |   (8)  op(e1, e1) = e3
% 231.54/42.81  | | 
% 231.54/42.81  | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #2468.
% 231.54/42.81  | | 
% 231.54/42.81  | Case 2:
% 231.54/42.81  | | 
% 231.54/42.81  | |   (9)  all_57_11 = e3 & op(e1, e0) = e3
% 231.54/42.81  | | 
% 231.54/42.81  | | ALPHA: (9) implies:
% 231.54/42.81  | |   (10)  all_57_11 = e3
% 231.54/42.81  | | 
% 231.54/42.81  | | REF_CLOSE: (5), (6), (10) are inconsistent by sub-proof #1595.
% 231.54/42.81  | | 
% 231.54/42.81  | End of split
% 231.54/42.81  | 
% 231.54/42.81  End of proof
% 231.54/42.81  
% 231.54/42.81  Sub-proof #1595 shows that the following formulas are inconsistent:
% 231.54/42.81  ----------------------------------------------------------------
% 231.54/42.81    (1)  all_57_11 = e3
% 231.54/42.81    (2)  all_57_11 = e0
% 231.54/42.81    (3)   ~ (e3 = e0)
% 231.54/42.81  
% 231.54/42.81  Begin of proof
% 231.54/42.81  | 
% 231.54/42.81  | COMBINE_EQS: (1), (2) imply:
% 231.54/42.81  |   (4)  e3 = e0
% 231.54/42.81  | 
% 231.54/42.81  | SIMP: (4) implies:
% 231.54/42.81  |   (5)  e3 = e0
% 231.54/42.81  | 
% 231.54/42.81  | REDUCE: (3), (5) imply:
% 231.54/42.81  |   (6)  $false
% 231.54/42.81  | 
% 231.54/42.81  | CLOSE: (6) is inconsistent.
% 231.54/42.81  | 
% 231.54/42.81  End of proof
% 231.54/42.81  
% 231.54/42.81  Sub-proof #1596 shows that the following formulas are inconsistent:
% 231.54/42.81  ----------------------------------------------------------------
% 231.54/42.81    (1)  op(e0, e0) = all_4_2
% 231.54/42.81    (2)   ~ (all_53_12 = all_4_2)
% 231.54/42.81    (3)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 231.54/42.81    (4)  all_57_15 = e0
% 231.54/42.81    (5)   ~ (e3 = e1)
% 231.54/42.81    (6)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 231.54/42.81         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.54/42.81    (7)   ~ (all_53_13 = e1)
% 231.54/42.81    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.81           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.81    (9)  all_55_15 = all_4_2
% 231.54/42.81    (10)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.54/42.81          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.54/42.81    (11)   ~ (all_6_2 = e3)
% 231.54/42.81    (12)  op(e1, e1) = all_6_2
% 231.54/42.81    (13)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 231.54/42.81    (14)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 231.54/42.81    (15)  op(e2, e2) = e1
% 231.54/42.81    (16)   ~ (all_53_4 = e1)
% 231.54/42.82    (17)   ~ (all_53_14 = all_4_2)
% 231.54/42.82    (18)   ~ (e3 = e2)
% 231.54/42.82    (19)  op(e1, e0) = all_53_14
% 231.54/42.82    (20)   ~ (e3 = e0)
% 231.54/42.82    (21)   ~ (all_4_2 = e2)
% 231.54/42.82    (22)   ~ (all_53_7 = all_4_2)
% 231.54/42.82    (23)  op(e3, e3) = e2
% 231.54/42.82    (24)  op(e3, e2) = all_53_4
% 231.54/42.82    (25)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 231.54/42.82          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 231.54/42.82    (26)   ~ (e2 = e0)
% 231.54/42.82    (27)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 231.54/42.82            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 231.54/42.82            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 231.54/42.82            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 231.54/42.82              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 231.54/42.82            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 231.54/42.82            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 231.54/42.82              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 231.54/42.82              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 231.54/42.82            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 231.54/42.82            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 231.54/42.82            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 231.54/42.82              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 231.54/42.82              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 231.54/42.82            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 231.54/42.82              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 231.54/42.82            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 231.54/42.82            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 231.54/42.82              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 231.54/42.82              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 231.54/42.82            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 231.54/42.82            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 231.54/42.82    (28)   ~ (all_53_6 = e1)
% 231.54/42.82    (29)   ~ (e1 = e0)
% 231.54/42.82    (30)  op(e0, e0) = e0
% 231.54/42.82    (31)   ~ (all_53_14 = e0)
% 231.54/42.82    (32)   ~ (all_53_13 = all_4_2)
% 231.54/42.82    (33)  op(e0, e2) = all_53_7
% 231.54/42.82    (34)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.54/42.82              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.54/42.82                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.54/42.82                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.54/42.82    (35)  all_55_10 = all_6_2
% 231.54/42.82    (36)   ~ (all_53_13 = e0)
% 231.54/42.82    (37)  op(e1, e1) = e2
% 231.54/42.82    (38)  op(e2, e0) = all_53_13
% 231.54/42.82    (39)  all_55_11 = all_53_14
% 231.54/42.82    (40)  all_55_3 = all_53_12
% 231.54/42.82    (41)  all_55_15 = e1 | all_55_15 = e0
% 231.54/42.82    (42)  op(e1, e3) = all_53_2
% 231.54/42.82    (43)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 231.54/42.82          (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 231.54/42.82    (44)   ~ (all_53_13 = all_53_14)
% 231.54/42.82    (45)   ~ (all_4_2 = e1)
% 231.54/42.82    (46)   ~ (e2 = e1)
% 231.54/42.82    (47)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.54/42.82          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.54/42.82    (48)  op(e1, e2) = all_53_6
% 231.54/42.82    (49)   ~ (all_6_2 = e0)
% 231.54/42.82    (50)   ~ (all_53_12 = e2)
% 231.54/42.82    (51)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 231.54/42.82          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 231.54/42.82    (52)   ~ (all_53_12 = all_53_14)
% 231.54/42.82    (53)  op(e0, e2) = e2
% 231.54/42.82    (54)  op(e3, e0) = all_53_12
% 231.54/42.82  
% 231.54/42.82  Begin of proof
% 231.54/42.82  | 
% 231.54/42.82  | BETA: splitting (47) gives:
% 231.54/42.82  | 
% 231.54/42.82  | Case 1:
% 231.54/42.82  | | 
% 231.54/42.82  | |   (55)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 231.54/42.82  | |           e2)
% 231.54/42.82  | | 
% 231.54/42.82  | | BETA: splitting (55) gives:
% 231.54/42.82  | | 
% 231.54/42.82  | | Case 1:
% 231.54/42.82  | | | 
% 231.54/42.82  | | |   (56)  all_57_9 = e2 & op(e3, e0) = e2
% 231.54/42.82  | | | 
% 231.54/42.82  | | | ALPHA: (56) implies:
% 231.54/42.82  | | |   (57)  op(e3, e0) = e2
% 231.54/42.82  | | | 
% 231.54/42.82  | | | REF_CLOSE: (8), (50), (54), (57) are inconsistent by sub-proof #2331.
% 231.54/42.82  | | | 
% 231.54/42.82  | | Case 2:
% 231.54/42.82  | | | 
% 231.54/42.82  | | |   (58)  all_57_10 = e2 & op(e2, e0) = e2
% 231.54/42.82  | | | 
% 231.54/42.82  | | | ALPHA: (58) implies:
% 231.54/42.82  | | |   (59)  all_57_10 = e2
% 231.54/42.82  | | |   (60)  op(e2, e0) = e2
% 231.54/42.82  | | | 
% 231.54/42.82  | | | GROUND_INST: instantiating (8) with all_53_7, e2, e2, e0, simplifying with
% 231.54/42.82  | | |              (33), (53) gives:
% 231.54/42.82  | | |   (61)  all_53_7 = e2
% 231.54/42.82  | | | 
% 231.54/42.82  | | | GROUND_INST: instantiating (8) with all_53_13, e2, e0, e2, simplifying
% 231.54/42.82  | | |              with (38), (60) gives:
% 231.54/42.82  | | |   (62)  all_53_13 = e2
% 231.54/42.82  | | | 
% 231.54/42.82  | | | REDUCE: (44), (62) imply:
% 231.54/42.82  | | |   (63)   ~ (all_53_14 = e2)
% 231.54/42.82  | | | 
% 231.54/42.82  | | | SIMP: (63) implies:
% 231.54/42.82  | | |   (64)   ~ (all_53_14 = e2)
% 231.54/42.82  | | | 
% 231.54/42.82  | | | BETA: splitting (27) gives:
% 231.54/42.82  | | | 
% 231.54/42.82  | | | Case 1:
% 231.54/42.82  | | | | 
% 231.54/42.82  | | | |   (65)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 231.54/42.82  | | | |           op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 231.54/42.82  | | | |           op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 231.54/42.82  | | | |           op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) =
% 231.54/42.82  | | | |           all_52_5 & op(e3, e0) = all_52_7 & $i(all_52_1) & $i(all_52_3)
% 231.54/42.82  | | | |           & $i(all_52_5) & $i(all_52_7)) | (all_52_8 = e3 & all_52_10 =
% 231.54/42.82  | | | |           e2 & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9, all_52_9)
% 231.54/42.82  | | | |           = e3 & op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 231.54/42.82  | | | |             all_52_13) = e1 & op(all_52_15, all_52_15) = e0 & op(e2, e3)
% 231.54/42.82  | | | |           = all_52_9 & op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13 &
% 231.54/42.82  | | | |           op(e2, e0) = all_52_15 & $i(all_52_9) & $i(all_52_11) &
% 231.54/42.82  | | | |           $i(all_52_13) & $i(all_52_15))
% 231.54/42.82  | | | | 
% 231.54/42.82  | | | | BETA: splitting (65) gives:
% 231.54/42.82  | | | | 
% 231.54/42.82  | | | | Case 1:
% 231.54/42.82  | | | | | 
% 231.54/42.82  | | | | |   (66)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 231.54/42.82  | | | | |         & op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 231.54/42.82  | | | | |         op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 231.54/42.82  | | | | |         op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) =
% 231.54/42.82  | | | | |         all_52_5 & op(e3, e0) = all_52_7 & $i(all_52_1) & $i(all_52_3)
% 231.54/42.82  | | | | |         & $i(all_52_5) & $i(all_52_7)
% 231.54/42.82  | | | | | 
% 231.54/42.82  | | | | | REF_CLOSE: (5), (8), (15), (23), (66) are inconsistent by sub-proof
% 231.54/42.82  | | | | |            #1597.
% 231.54/42.82  | | | | | 
% 231.54/42.82  | | | | Case 2:
% 231.54/42.82  | | | | | 
% 231.54/42.82  | | | | |   (67)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 231.54/42.82  | | | | |         e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11, all_52_11) =
% 231.54/42.82  | | | | |         e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15, all_52_15)
% 231.54/42.82  | | | | |         = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 & op(e2,
% 231.54/42.82  | | | | |           e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 231.54/42.82  | | | | |         $i(all_52_11) & $i(all_52_13) & $i(all_52_15)
% 231.54/42.82  | | | | | 
% 231.54/42.82  | | | | | ALPHA: (67) implies:
% 231.54/42.82  | | | | |   (68)  op(e2, e0) = all_52_15
% 231.54/42.82  | | | | |   (69)  op(e2, e2) = all_52_11
% 231.54/42.82  | | | | |   (70)  op(all_52_15, all_52_15) = e0
% 231.54/42.82  | | | | |   (71)  op(all_52_11, all_52_11) = e2
% 231.54/42.82  | | | | | 
% 231.54/42.82  | | | | | GROUND_INST: instantiating (8) with e2, all_52_15, e0, e2, simplifying
% 231.54/42.82  | | | | |              with (60), (68) gives:
% 231.54/42.82  | | | | |   (72)  all_52_15 = e2
% 231.54/42.82  | | | | | 
% 231.54/42.82  | | | | | REDUCE: (70), (72) imply:
% 231.54/42.82  | | | | |   (73)  op(e2, e2) = e0
% 231.54/42.82  | | | | | 
% 231.54/42.82  | | | | | REF_CLOSE: (8), (26), (30), (69), (71), (73) are inconsistent by
% 231.54/42.82  | | | | |            sub-proof #2270.
% 231.54/42.82  | | | | | 
% 231.54/42.82  | | | | End of split
% 231.54/42.82  | | | | 
% 231.54/42.82  | | | Case 2:
% 231.54/42.82  | | | | 
% 231.54/42.82  | | | |   (74)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 231.54/42.82  | | | |           e0 & op(all_52_17, all_52_17) = e3 & op(all_52_19, all_52_19)
% 231.54/42.82  | | | |           = e2 & op(all_52_21, all_52_21) = e1 & op(all_52_23,
% 231.54/42.82  | | | |             all_52_23) = e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 231.54/42.82  | | | |           all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23 &
% 231.54/42.82  | | | |           $i(all_52_17) & $i(all_52_19) & $i(all_52_21) & $i(all_52_23))
% 231.54/42.82  | | | |         | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30
% 231.54/42.82  | | | |           = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 231.54/42.82  | | | |             all_52_27) = e2 & op(all_52_29, all_52_29) = e1 &
% 231.54/42.82  | | | |           op(all_52_31, all_52_31) = e0 & op(e0, e3) = all_52_25 &
% 231.54/42.82  | | | |           op(e0, e2) = all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0) =
% 231.54/42.82  | | | |           all_52_31 & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 231.54/42.82  | | | |           $i(all_52_31))
% 231.54/42.82  | | | | 
% 231.54/42.82  | | | | BETA: splitting (74) gives:
% 231.54/42.82  | | | | 
% 231.54/42.82  | | | | Case 1:
% 231.54/42.82  | | | | | 
% 231.54/42.82  | | | | |   (75)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 231.54/42.82  | | | | |         e0 & op(all_52_17, all_52_17) = e3 & op(all_52_19, all_52_19)
% 231.54/42.82  | | | | |         = e2 & op(all_52_21, all_52_21) = e1 & op(all_52_23,
% 231.54/42.82  | | | | |           all_52_23) = e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 231.54/42.82  | | | | |         all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23 &
% 231.54/42.82  | | | | |         $i(all_52_17) & $i(all_52_19) & $i(all_52_21) & $i(all_52_23)
% 231.54/42.82  | | | | | 
% 231.54/42.82  | | | | | ALPHA: (75) implies:
% 231.54/42.82  | | | | |   (76)  op(e1, e0) = all_52_23
% 231.54/42.82  | | | | |   (77)  op(e1, e1) = all_52_21
% 231.54/42.82  | | | | |   (78)  op(e1, e2) = all_52_19
% 231.54/42.82  | | | | |   (79)  op(e1, e3) = all_52_17
% 231.54/42.82  | | | | |   (80)  op(all_52_23, all_52_23) = e0
% 231.54/42.82  | | | | |   (81)  op(all_52_21, all_52_21) = e1
% 231.54/42.82  | | | | |   (82)  op(all_52_19, all_52_19) = e2
% 231.54/42.82  | | | | |   (83)  op(all_52_17, all_52_17) = e3
% 231.54/42.82  | | | | | 
% 231.54/42.82  | | | | | GROUND_INST: instantiating (8) with all_53_14, all_52_23, e0, e1,
% 231.54/42.82  | | | | |              simplifying with (19), (76) gives:
% 231.54/42.82  | | | | |   (84)  all_53_14 = all_52_23
% 231.54/42.82  | | | | | 
% 231.54/42.82  | | | | | GROUND_INST: instantiating (8) with e2, all_52_21, e1, e1, simplifying
% 231.54/42.82  | | | | |              with (37), (77) gives:
% 231.54/42.82  | | | | |   (85)  all_52_21 = e2
% 231.54/42.82  | | | | | 
% 231.54/42.82  | | | | | GROUND_INST: instantiating (8) with all_53_6, all_52_19, e2, e1,
% 231.54/42.82  | | | | |              simplifying with (48), (78) gives:
% 231.54/42.82  | | | | |   (86)  all_53_6 = all_52_19
% 231.54/42.82  | | | | | 
% 231.54/42.82  | | | | | GROUND_INST: instantiating (8) with all_53_2, all_52_17, e3, e1,
% 231.54/42.82  | | | | |              simplifying with (42), (79) gives:
% 231.54/42.82  | | | | |   (87)  all_53_2 = all_52_17
% 231.54/42.82  | | | | | 
% 231.54/42.82  | | | | | COMBINE_EQS: (39), (84) imply:
% 231.54/42.82  | | | | |   (88)  all_55_11 = all_52_23
% 231.54/42.82  | | | | | 
% 231.54/42.82  | | | | | REDUCE: (52), (84) imply:
% 231.54/42.82  | | | | |   (89)   ~ (all_53_12 = all_52_23)
% 231.54/42.82  | | | | | 
% 231.54/42.82  | | | | | REDUCE: (64), (84) imply:
% 231.54/42.82  | | | | |   (90)   ~ (all_52_23 = e2)
% 231.54/42.82  | | | | | 
% 231.54/42.82  | | | | | REDUCE: (31), (84) imply:
% 231.54/42.82  | | | | |   (91)   ~ (all_52_23 = e0)
% 231.54/42.82  | | | | | 
% 231.54/42.82  | | | | | BETA: splitting (13) gives:
% 231.54/42.82  | | | | | 
% 231.54/42.82  | | | | | Case 1:
% 231.54/42.82  | | | | | | 
% 231.54/42.82  | | | | | |   (92)  all_55_3 = e3
% 231.54/42.82  | | | | | | 
% 231.54/42.82  | | | | | | COMBINE_EQS: (40), (92) imply:
% 231.54/42.82  | | | | | |   (93)  all_53_12 = e3
% 231.54/42.82  | | | | | | 
% 231.54/42.82  | | | | | | SIMP: (93) implies:
% 231.54/42.82  | | | | | |   (94)  all_53_12 = e3
% 231.54/42.82  | | | | | | 
% 231.54/42.82  | | | | | | REDUCE: (89), (94) imply:
% 231.54/42.82  | | | | | |   (95)   ~ (all_52_23 = e3)
% 231.54/42.82  | | | | | | 
% 231.54/42.82  | | | | | | SIMP: (95) implies:
% 231.54/42.82  | | | | | |   (96)   ~ (all_52_23 = e3)
% 231.54/42.82  | | | | | | 
% 231.54/42.82  | | | | | | BETA: splitting (14) gives:
% 231.54/42.82  | | | | | | 
% 231.54/42.82  | | | | | | Case 1:
% 231.54/42.82  | | | | | | | 
% 231.54/42.82  | | | | | | |   (97)  all_55_11 = e3
% 231.54/42.82  | | | | | | | 
% 231.54/42.82  | | | | | | | COMBINE_EQS: (88), (97) imply:
% 231.54/42.82  | | | | | | |   (98)  all_52_23 = e3
% 231.54/42.82  | | | | | | | 
% 231.54/42.82  | | | | | | | REDUCE: (96), (98) imply:
% 231.54/42.82  | | | | | | |   (99)  $false
% 231.54/42.82  | | | | | | | 
% 231.54/42.82  | | | | | | | CLOSE: (99) is inconsistent.
% 231.54/42.82  | | | | | | | 
% 231.54/42.82  | | | | | | Case 2:
% 231.54/42.82  | | | | | | | 
% 231.54/42.82  | | | | | | |   (100)  all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 231.54/42.82  | | | | | | | 
% 231.54/42.82  | | | | | | | BETA: splitting (100) gives:
% 231.54/42.82  | | | | | | | 
% 231.54/42.82  | | | | | | | Case 1:
% 231.54/42.82  | | | | | | | | 
% 231.54/42.82  | | | | | | | |   (101)  all_55_11 = e2
% 231.54/42.82  | | | | | | | | 
% 231.54/42.82  | | | | | | | | COMBINE_EQS: (88), (101) imply:
% 231.54/42.82  | | | | | | | |   (102)  all_52_23 = e2
% 231.54/42.82  | | | | | | | | 
% 231.54/42.82  | | | | | | | | REDUCE: (90), (102) imply:
% 231.54/42.82  | | | | | | | |   (103)  $false
% 231.54/42.82  | | | | | | | | 
% 231.54/42.82  | | | | | | | | CLOSE: (103) is inconsistent.
% 231.54/42.82  | | | | | | | | 
% 231.54/42.82  | | | | | | | Case 2:
% 231.54/42.82  | | | | | | | | 
% 231.54/42.82  | | | | | | | |   (104)  all_55_11 = e1 | all_55_11 = e0
% 231.54/42.82  | | | | | | | | 
% 231.54/42.82  | | | | | | | | BETA: splitting (104) gives:
% 231.54/42.82  | | | | | | | | 
% 231.54/42.82  | | | | | | | | Case 1:
% 231.54/42.82  | | | | | | | | | 
% 231.54/42.82  | | | | | | | | |   (105)  all_55_11 = e1
% 231.54/42.82  | | | | | | | | | 
% 231.54/42.82  | | | | | | | | | COMBINE_EQS: (88), (105) imply:
% 231.54/42.82  | | | | | | | | |   (106)  all_52_23 = e1
% 231.54/42.82  | | | | | | | | | 
% 231.54/42.82  | | | | | | | | | REDUCE: (80), (106) imply:
% 231.54/42.82  | | | | | | | | |   (107)  op(e1, e1) = e0
% 231.54/42.82  | | | | | | | | | 
% 231.54/42.82  | | | | | | | | | REF_CLOSE: (1), (2), (8), (9), (15), (16), (17), (19), (21),
% 231.54/42.82  | | | | | | | | |            (22), (24), (25), (32), (33), (34), (38), (41),
% 231.54/42.82  | | | | | | | | |            (45), (54), (77), (78), (81), (82), (107) are
% 231.54/42.82  | | | | | | | | |            inconsistent by sub-proof #1839.
% 231.54/42.82  | | | | | | | | | 
% 231.54/42.82  | | | | | | | | Case 2:
% 231.54/42.82  | | | | | | | | | 
% 231.54/42.82  | | | | | | | | |   (108)  all_55_11 = e0
% 231.54/42.82  | | | | | | | | | 
% 231.54/42.82  | | | | | | | | | COMBINE_EQS: (88), (108) imply:
% 231.54/42.82  | | | | | | | | |   (109)  all_52_23 = e0
% 231.54/42.82  | | | | | | | | | 
% 231.54/42.82  | | | | | | | | | REDUCE: (91), (109) imply:
% 231.54/42.82  | | | | | | | | |   (110)  $false
% 231.54/42.82  | | | | | | | | | 
% 231.54/42.82  | | | | | | | | | CLOSE: (110) is inconsistent.
% 231.54/42.82  | | | | | | | | | 
% 231.54/42.82  | | | | | | | | End of split
% 231.54/42.82  | | | | | | | | 
% 231.54/42.82  | | | | | | | End of split
% 231.54/42.82  | | | | | | | 
% 231.54/42.82  | | | | | | End of split
% 231.54/42.82  | | | | | | 
% 231.54/42.82  | | | | | Case 2:
% 231.54/42.82  | | | | | | 
% 231.54/42.82  | | | | | |   (111)   ~ (all_55_3 = e3)
% 231.54/42.82  | | | | | | 
% 231.54/42.82  | | | | | | REDUCE: (40), (111) imply:
% 231.54/42.82  | | | | | |   (112)   ~ (all_53_12 = e3)
% 231.54/42.82  | | | | | | 
% 231.54/42.82  | | | | | | BETA: splitting (43) gives:
% 231.54/42.82  | | | | | | 
% 231.54/42.82  | | | | | | Case 1:
% 231.54/42.82  | | | | | | | 
% 231.54/42.82  | | | | | | |   (113)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 &
% 231.54/42.82  | | | | | | |            op(e2, e0) = e3)
% 231.54/42.82  | | | | | | | 
% 231.54/42.82  | | | | | | | BETA: splitting (113) gives:
% 231.54/42.82  | | | | | | | 
% 231.54/42.82  | | | | | | | Case 1:
% 231.54/42.82  | | | | | | | | 
% 231.54/42.82  | | | | | | | |   (114)  all_57_9 = e3 & op(e3, e0) = e3
% 231.54/42.82  | | | | | | | | 
% 231.54/42.82  | | | | | | | | ALPHA: (114) implies:
% 231.54/42.82  | | | | | | | |   (115)  op(e3, e0) = e3
% 231.54/42.82  | | | | | | | | 
% 231.54/42.82  | | | | | | | | REF_CLOSE: (8), (54), (112), (115) are inconsistent by sub-proof
% 231.54/42.82  | | | | | | | |            #2458.
% 231.54/42.82  | | | | | | | | 
% 231.54/42.82  | | | | | | | Case 2:
% 231.54/42.82  | | | | | | | | 
% 231.54/42.82  | | | | | | | |   (116)  all_57_10 = e3 & op(e2, e0) = e3
% 231.54/42.82  | | | | | | | | 
% 231.54/42.82  | | | | | | | | ALPHA: (116) implies:
% 231.54/42.82  | | | | | | | |   (117)  all_57_10 = e3
% 231.54/42.82  | | | | | | | | 
% 231.54/42.82  | | | | | | | | REF_CLOSE: (18), (59), (117) are inconsistent by sub-proof
% 231.54/42.82  | | | | | | | |            #2356.
% 231.54/42.82  | | | | | | | | 
% 231.54/42.82  | | | | | | | End of split
% 231.54/42.82  | | | | | | | 
% 231.54/42.82  | | | | | | Case 2:
% 231.54/42.82  | | | | | | | 
% 231.54/42.82  | | | | | | |   (118)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 &
% 231.54/42.82  | | | | | | |            op(e0, e0) = e3)
% 231.54/42.82  | | | | | | | 
% 231.54/42.82  | | | | | | | BETA: splitting (118) gives:
% 231.54/42.82  | | | | | | | 
% 231.54/42.82  | | | | | | | Case 1:
% 231.54/42.82  | | | | | | | | 
% 231.54/42.82  | | | | | | | |   (119)  all_57_11 = e3 & op(e1, e0) = e3
% 231.54/42.82  | | | | | | | | 
% 231.54/42.82  | | | | | | | | ALPHA: (119) implies:
% 231.54/42.82  | | | | | | | |   (120)  all_57_11 = e3
% 231.54/42.82  | | | | | | | | 
% 231.54/42.82  | | | | | | | | REF_CLOSE: (3), (5), (8), (11), (12), (28), (35), (37), (46),
% 231.54/42.82  | | | | | | | |            (48), (51), (79), (83), (120) are inconsistent by
% 231.54/42.82  | | | | | | | |            sub-proof #1731.
% 231.54/42.82  | | | | | | | | 
% 231.54/42.82  | | | | | | | Case 2:
% 231.54/42.82  | | | | | | | | 
% 231.54/42.82  | | | | | | | |   (121)  all_57_15 = e3 & op(e0, e0) = e3
% 231.54/42.82  | | | | | | | | 
% 231.54/42.82  | | | | | | | | ALPHA: (121) implies:
% 231.54/42.82  | | | | | | | |   (122)  op(e0, e0) = e3
% 231.54/42.82  | | | | | | | | 
% 231.54/42.82  | | | | | | | | REF_CLOSE: (8), (20), (30), (122) are inconsistent by sub-proof
% 231.54/42.82  | | | | | | | |            #2304.
% 231.54/42.82  | | | | | | | | 
% 231.54/42.82  | | | | | | | End of split
% 231.54/42.82  | | | | | | | 
% 231.54/42.82  | | | | | | End of split
% 231.54/42.82  | | | | | | 
% 231.54/42.82  | | | | | End of split
% 231.54/42.82  | | | | | 
% 231.54/42.82  | | | | Case 2:
% 231.54/42.82  | | | | | 
% 231.54/42.82  | | | | |   (123)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30
% 231.54/42.82  | | | | |          = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 231.54/42.82  | | | | |            all_52_27) = e2 & op(all_52_29, all_52_29) = e1 &
% 231.54/42.82  | | | | |          op(all_52_31, all_52_31) = e0 & op(e0, e3) = all_52_25 &
% 231.54/42.82  | | | | |          op(e0, e2) = all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 231.54/42.82  | | | | |          = all_52_31 & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 231.54/42.82  | | | | |          $i(all_52_31)
% 231.54/42.82  | | | | | 
% 231.54/42.82  | | | | | ALPHA: (123) implies:
% 231.54/42.82  | | | | |   (124)  op(e0, e2) = all_52_27
% 231.54/42.82  | | | | |   (125)  op(all_52_27, all_52_27) = e2
% 231.54/42.82  | | | | | 
% 231.54/42.82  | | | | | GROUND_INST: instantiating (8) with e2, all_52_27, e2, e0, simplifying
% 231.54/42.82  | | | | |              with (53), (124) gives:
% 231.54/42.82  | | | | |   (126)  all_52_27 = e2
% 231.54/42.82  | | | | | 
% 231.54/42.82  | | | | | REDUCE: (125), (126) imply:
% 231.54/42.82  | | | | |   (127)  op(e2, e2) = e2
% 231.54/42.82  | | | | | 
% 231.54/42.82  | | | | | REF_CLOSE: (8), (15), (46), (127) are inconsistent by sub-proof #2306.
% 231.54/42.82  | | | | | 
% 231.54/42.82  | | | | End of split
% 231.54/42.82  | | | | 
% 231.54/42.82  | | | End of split
% 231.54/42.82  | | | 
% 231.54/42.82  | | End of split
% 231.54/42.82  | | 
% 231.54/42.82  | Case 2:
% 231.54/42.82  | | 
% 231.54/42.82  | |   (128)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.54/42.82  | |            e2)
% 231.54/42.82  | | 
% 231.54/42.82  | | BETA: splitting (128) gives:
% 231.54/42.82  | | 
% 231.54/42.82  | | Case 1:
% 231.54/42.82  | | | 
% 231.54/42.82  | | |   (129)  all_57_11 = e2 & op(e1, e0) = e2
% 231.54/42.82  | | | 
% 231.54/42.82  | | | ALPHA: (129) implies:
% 231.54/42.82  | | |   (130)  all_57_11 = e2
% 231.54/42.82  | | | 
% 231.54/42.82  | | | REF_CLOSE: (5), (6), (8), (10), (11), (12), (18), (19), (20), (28), (29),
% 231.54/42.82  | | |            (31), (37), (46), (48), (49), (51), (130) are inconsistent by
% 231.54/42.82  | | |            sub-proof #1724.
% 231.54/42.82  | | | 
% 231.54/42.82  | | Case 2:
% 231.54/42.82  | | | 
% 231.54/42.82  | | |   (131)  all_57_15 = e2 & op(e0, e0) = e2
% 231.54/42.82  | | | 
% 231.54/42.82  | | | ALPHA: (131) implies:
% 231.54/42.82  | | |   (132)  all_57_15 = e2
% 231.54/42.82  | | | 
% 231.54/42.82  | | | REF_CLOSE: (4), (26), (132) are inconsistent by sub-proof #2126.
% 231.54/42.82  | | | 
% 231.54/42.82  | | End of split
% 231.54/42.82  | | 
% 231.54/42.82  | End of split
% 231.54/42.82  | 
% 231.54/42.82  End of proof
% 231.54/42.82  
% 231.54/42.82  Sub-proof #1597 shows that the following formulas are inconsistent:
% 231.54/42.82  ----------------------------------------------------------------
% 231.54/42.82    (1)   ~ (e3 = e1)
% 231.54/42.82    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.82           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.82    (3)  op(e2, e2) = e1
% 231.54/42.82    (4)  op(e3, e3) = e2
% 231.54/42.82    (5)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 231.54/42.82         op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 231.54/42.82           all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3) = all_52_1 &
% 231.54/42.82         op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 231.54/42.82         $i(all_52_1) & $i(all_52_3) & $i(all_52_5) & $i(all_52_7)
% 231.54/42.82  
% 231.54/42.82  Begin of proof
% 231.54/42.82  | 
% 231.54/42.82  | ALPHA: (5) implies:
% 231.54/42.82  |   (6)  op(e3, e3) = all_52_1
% 231.54/42.82  |   (7)  op(all_52_1, all_52_1) = e3
% 231.54/42.82  | 
% 231.54/42.82  | GROUND_INST: instantiating (2) with e2, all_52_1, e3, e3, simplifying with
% 231.54/42.82  |              (4), (6) gives:
% 231.54/42.82  |   (8)  all_52_1 = e2
% 231.54/42.82  | 
% 231.54/42.82  | REDUCE: (7), (8) imply:
% 231.54/42.82  |   (9)  op(e2, e2) = e3
% 231.54/42.82  | 
% 231.54/42.82  | REF_CLOSE: (1), (2), (3), (9) are inconsistent by sub-proof #1912.
% 231.54/42.82  | 
% 231.54/42.82  End of proof
% 231.54/42.82  
% 231.54/42.82  Sub-proof #1598 shows that the following formulas are inconsistent:
% 231.54/42.82  ----------------------------------------------------------------
% 231.54/42.82    (1)  op(e2, e3) = all_53_1
% 231.54/42.82    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.82           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.82    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1)
% 231.54/42.82    (4)  op(e3, e3) = e2
% 231.54/42.82    (5)   ~ (all_53_1 = e1)
% 231.54/42.82    (6)   ~ (e2 = e1)
% 231.54/42.82  
% 231.54/42.82  Begin of proof
% 231.54/42.82  | 
% 231.54/42.82  | BETA: splitting (3) gives:
% 231.54/42.82  | 
% 231.54/42.82  | Case 1:
% 231.54/42.82  | | 
% 231.54/42.82  | |   (7)  all_57_0 = e1 & op(e3, e3) = e1
% 231.54/42.82  | | 
% 231.54/42.82  | | ALPHA: (7) implies:
% 231.54/42.82  | |   (8)  op(e3, e3) = e1
% 231.54/42.82  | | 
% 231.54/42.82  | | REF_CLOSE: (2), (4), (6), (8) are inconsistent by sub-proof #1950.
% 231.54/42.82  | | 
% 231.54/42.82  | Case 2:
% 231.54/42.82  | | 
% 231.54/42.82  | |   (9)  all_57_2 = e1 & op(e2, e3) = e1
% 231.54/42.82  | | 
% 231.54/42.82  | | REF_CLOSE: (1), (2), (5), (9) are inconsistent by sub-proof #2156.
% 231.54/42.82  | | 
% 231.54/42.82  | End of split
% 231.54/42.82  | 
% 231.54/42.82  End of proof
% 231.54/42.82  
% 231.54/42.82  Sub-proof #1599 shows that the following formulas are inconsistent:
% 231.54/42.82  ----------------------------------------------------------------
% 231.54/42.82    (1)  all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 231.54/42.82    (2)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 231.54/42.82    (3)   ~ (all_53_6 = all_53_14)
% 231.54/42.82    (4)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 231.54/42.82    (5)  all_57_15 = e0
% 231.54/42.82    (6)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.82         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.54/42.82    (7)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.54/42.82         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.54/42.82    (8)   ~ (all_53_8 = all_53_12)
% 231.54/42.82    (9)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.82         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.54/42.82    (10)   ~ (all_53_8 = all_53_11)
% 231.54/42.82    (11)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 231.54/42.82          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.54/42.82    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.82            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.82    (13)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.54/42.82          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.54/42.82    (14)   ~ (all_53_3 = all_53_7)
% 231.54/42.82    (15)   ~ (all_6_2 = e3)
% 231.54/42.82    (16)  op(e1, e1) = all_6_2
% 231.54/42.82    (17)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 231.54/42.82    (18)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 231.54/42.82    (19)  op(e2, e2) = e1
% 231.54/42.82    (20)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.54/42.82          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.54/42.82    (21)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 231.54/42.82    (22)  all_55_9 = all_53_6
% 231.54/42.82    (23)  all_57_9 = e1
% 231.54/42.82    (24)   ~ (all_53_4 = all_53_12)
% 231.54/42.82    (25)   ~ (all_53_8 = all_53_9)
% 231.54/42.82    (26)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.54/42.82          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.54/42.82    (27)   ~ (all_53_14 = all_6_2)
% 231.54/42.82    (28)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.54/42.82          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.54/42.82    (29)  op(e3, e0) = e1
% 231.54/42.82    (30)  all_55_1 = all_53_4
% 231.54/42.82    (31)  op(e1, e0) = all_53_14
% 231.54/42.82    (32)   ~ (all_53_6 = all_53_7)
% 231.54/42.82    (33)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.54/42.82          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.54/42.82    (34)   ~ (all_53_8 = all_6_2)
% 231.54/42.82    (35)  op(e0, e3) = all_53_3
% 231.54/42.82    (36)   ~ (all_53_11 = e0)
% 231.54/42.82    (37)  all_55_2 = all_53_8
% 231.54/42.82    (38)   ~ (all_53_4 = all_53_7)
% 231.54/42.82    (39)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 231.54/42.82    (40)  op(e3, e3) = e2
% 231.54/42.82    (41)   ~ (all_53_3 = e2)
% 231.54/42.82    (42)   ~ (all_53_7 = e0)
% 231.54/42.82    (43)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.54/42.82          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.54/42.82            e1)
% 231.54/42.82    (44)   ~ (all_53_4 = all_53_8)
% 231.54/42.82    (45)  op(e3, e2) = all_53_4
% 231.54/42.82    (46)  op(e1, e1) = e1
% 231.54/42.82    (47)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 231.54/42.82          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 231.54/42.82    (48)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 231.54/42.82            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 231.54/42.82            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 231.54/42.82            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 231.54/42.82              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 231.54/42.82            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 231.54/42.82            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 231.54/42.82              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 231.54/42.82              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 231.54/42.82            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 231.54/42.82            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 231.54/42.82            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 231.54/42.82              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 231.54/42.82              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 231.54/42.82            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 231.54/42.82              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 231.54/42.82            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 231.54/42.82            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 231.54/42.82              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 231.54/42.82              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 231.54/42.82            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 231.54/42.82            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 231.54/42.82    (49)   ~ (all_53_6 = e1)
% 231.54/42.82    (50)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 231.54/42.82          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.54/42.82    (51)   ~ (all_53_2 = all_53_14)
% 231.54/42.82    (52)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 231.54/42.82            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 231.54/42.82              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 231.54/42.82    (53)   ~ (all_53_3 = all_53_11)
% 231.54/42.82    (54)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.54/42.82          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.54/42.82    (55)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.54/42.82          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.54/42.82    (56)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 231.54/42.82    (57)  op(e0, e0) = e0
% 231.54/42.82    (58)   ~ (all_53_7 = all_53_11)
% 231.54/42.82    (59)   ~ (all_53_14 = e0)
% 231.54/42.82    (60)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.54/42.82          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 231.54/42.82            e3)
% 231.54/42.83    (61)   ~ (all_53_4 = all_53_6)
% 231.54/42.83    (62)  op(e0, e2) = all_53_7
% 231.54/42.83    (63)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.54/42.83          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.54/42.83            e2)
% 231.54/42.83    (64)   ~ (all_53_8 = e2)
% 231.54/42.83    (65)   ~ (all_53_3 = e0)
% 231.54/42.83    (66)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.54/42.83              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.54/42.83                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.54/42.83                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.54/42.83    (67)  all_55_10 = all_6_2
% 231.54/42.83    (68)   ~ (all_53_6 = all_6_2)
% 231.54/42.83    (69)   ~ (all_53_13 = e0)
% 231.54/42.83    (70)  all_55_13 = all_53_7
% 231.54/42.83    (71)  op(e2, e0) = all_53_13
% 231.54/42.83    (72)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.54/42.83          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.54/42.83    (73)  all_38_2 = all_6_2
% 231.54/42.83    (74)  all_55_11 = all_53_14
% 231.54/42.83    (75)  all_55_3 = all_53_12
% 231.54/42.83    (76)   ~ (all_53_4 = e2)
% 231.54/42.83    (77)  op(e1, e3) = all_53_2
% 231.54/42.83    (78)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.83          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.54/42.83    (79)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 231.54/42.83          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 231.54/42.83    (80)   ~ (all_53_12 = e0)
% 231.54/42.83    (81)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 231.54/42.83          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 231.54/42.83    (82)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.54/42.83          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.54/42.83    (83)  op(e2, e1) = all_53_9
% 231.54/42.83    (84)  op(e1, e2) = all_53_6
% 231.54/42.83    (85)  all_57_12 = e1 & op(e0, e3) = e1
% 231.54/42.83    (86)   ~ (all_53_2 = all_53_6)
% 231.54/42.83    (87)   ~ (all_53_12 = e2)
% 231.54/42.83    (88)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.54/42.83          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.54/42.83    (89)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.54/42.83          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.54/42.83    (90)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.54/42.83          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.54/42.83    (91)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 231.54/42.83          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 231.54/42.83    (92)   ~ (all_53_12 = all_53_14)
% 231.54/42.83    (93)  all_55_14 = all_53_11
% 231.54/42.83    (94)  op(e3, e1) = all_53_8
% 231.54/42.83    (95)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.83          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.54/42.83    (96)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 231.54/42.83          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 231.54/42.83    (97)  op(e3, e0) = all_53_12
% 231.54/42.83  
% 231.54/42.83  Begin of proof
% 231.54/42.83  | 
% 231.54/42.83  | ALPHA: (85) implies:
% 231.54/42.83  |   (98)  all_57_12 = e1
% 231.54/42.83  |   (99)  op(e0, e3) = e1
% 231.54/42.83  | 
% 231.54/42.83  | GROUND_INST: instantiating (12) with all_53_3, e1, e3, e0, simplifying with
% 231.54/42.83  |              (35), (99) gives:
% 231.54/42.83  |   (100)  all_53_3 = e1
% 231.54/42.83  | 
% 231.54/42.83  | GROUND_INST: instantiating (12) with all_53_12, e1, e0, e3, simplifying with
% 231.54/42.83  |              (29), (97) gives:
% 231.54/42.83  |   (101)  all_53_12 = e1
% 231.54/42.83  | 
% 231.54/42.83  | REDUCE: (14), (100) imply:
% 231.54/42.83  |   (102)   ~ (all_53_7 = e1)
% 231.54/42.83  | 
% 231.54/42.83  | SIMP: (102) implies:
% 231.54/42.83  |   (103)   ~ (all_53_7 = e1)
% 231.54/42.83  | 
% 231.54/42.83  | REDUCE: (53), (100) imply:
% 231.54/42.83  |   (104)   ~ (all_53_11 = e1)
% 231.54/42.83  | 
% 231.54/42.83  | SIMP: (104) implies:
% 231.54/42.83  |   (105)   ~ (all_53_11 = e1)
% 231.54/42.83  | 
% 231.54/42.83  | REDUCE: (24), (101) imply:
% 231.54/42.83  |   (106)   ~ (all_53_4 = e1)
% 231.54/42.83  | 
% 231.54/42.83  | REDUCE: (8), (101) imply:
% 231.54/42.83  |   (107)   ~ (all_53_8 = e1)
% 231.54/42.83  | 
% 231.54/42.83  | REDUCE: (87), (101) imply:
% 231.54/42.83  |   (108)   ~ (e2 = e1)
% 231.54/42.83  | 
% 231.54/42.83  | SIMP: (108) implies:
% 231.54/42.83  |   (109)   ~ (e2 = e1)
% 231.54/42.83  | 
% 231.54/42.83  | REDUCE: (80), (101) imply:
% 231.54/42.83  |   (110)   ~ (e1 = e0)
% 231.54/42.83  | 
% 231.54/42.83  | BETA: splitting (48) gives:
% 231.54/42.83  | 
% 231.54/42.83  | Case 1:
% 231.54/42.83  | | 
% 231.54/42.83  | |   (111)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 231.54/42.83  | |            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 231.54/42.83  | |            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 231.54/42.83  | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) =
% 231.54/42.83  | |            all_52_5 & op(e3, e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) &
% 231.54/42.83  | |            $i(all_52_5) & $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 &
% 231.54/42.83  | |            all_52_12 = e1 & all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 231.54/42.83  | |            op(all_52_11, all_52_11) = e2 & op(all_52_13, all_52_13) = e1 &
% 231.54/42.83  | |            op(all_52_15, all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2,
% 231.54/42.83  | |              e2) = all_52_11 & op(e2, e1) = all_52_13 & op(e2, e0) =
% 231.54/42.83  | |            all_52_15 & $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 231.54/42.83  | |            $i(all_52_15))
% 231.54/42.83  | | 
% 231.54/42.83  | | REF_CLOSE: (12), (19), (29), (46), (109), (110), (111) are inconsistent by
% 231.54/42.83  | |            sub-proof #1854.
% 231.54/42.83  | | 
% 231.54/42.83  | Case 2:
% 231.54/42.83  | | 
% 231.54/42.83  | |   (112)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 231.54/42.83  | |            & op(all_52_17, all_52_17) = e3 & op(all_52_19, all_52_19) = e2 &
% 231.54/42.83  | |            op(all_52_21, all_52_21) = e1 & op(all_52_23, all_52_23) = e0 &
% 231.54/42.83  | |            op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) =
% 231.54/42.83  | |            all_52_21 & op(e1, e0) = all_52_23 & $i(all_52_17) &
% 231.54/42.83  | |            $i(all_52_19) & $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 231.54/42.83  | |            & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0 &
% 231.54/42.83  | |            op(all_52_25, all_52_25) = e3 & op(all_52_27, all_52_27) = e2 &
% 231.54/42.83  | |            op(all_52_29, all_52_29) = e1 & op(all_52_31, all_52_31) = e0 &
% 231.54/42.83  | |            op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 & op(e0, e1) =
% 231.54/42.83  | |            all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 231.54/42.83  | |            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 231.54/42.83  | | 
% 231.54/42.83  | | BETA: splitting (112) gives:
% 231.54/42.83  | | 
% 231.54/42.83  | | Case 1:
% 231.54/42.83  | | | 
% 231.54/42.83  | | |   (113)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 231.54/42.83  | | |          & op(all_52_17, all_52_17) = e3 & op(all_52_19, all_52_19) = e2 &
% 231.54/42.83  | | |          op(all_52_21, all_52_21) = e1 & op(all_52_23, all_52_23) = e0 &
% 231.54/42.83  | | |          op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) =
% 231.54/42.83  | | |          all_52_21 & op(e1, e0) = all_52_23 & $i(all_52_17) &
% 231.54/42.83  | | |          $i(all_52_19) & $i(all_52_21) & $i(all_52_23)
% 231.54/42.83  | | | 
% 231.54/42.83  | | | ALPHA: (113) implies:
% 231.54/42.83  | | |   (114)  op(e1, e1) = all_52_21
% 231.54/42.83  | | |   (115)  op(e1, e2) = all_52_19
% 231.54/42.83  | | |   (116)  op(all_52_21, all_52_21) = e1
% 231.54/42.83  | | |   (117)  op(all_52_19, all_52_19) = e2
% 231.54/42.83  | | | 
% 231.54/42.83  | | | GROUND_INST: instantiating (12) with e1, all_52_21, e1, e1, simplifying
% 231.54/42.83  | | |              with (46), (114) gives:
% 231.54/42.83  | | |   (118)  all_52_21 = e1
% 231.54/42.83  | | | 
% 231.54/42.83  | | | GROUND_INST: instantiating (12) with all_53_6, all_52_19, e2, e1,
% 231.54/42.83  | | |              simplifying with (84), (115) gives:
% 231.54/42.83  | | |   (119)  all_53_6 = all_52_19
% 231.54/42.83  | | | 
% 231.54/42.83  | | | COMBINE_EQS: (22), (119) imply:
% 231.54/42.83  | | |   (120)  all_55_9 = all_52_19
% 231.54/42.83  | | | 
% 231.54/42.83  | | | REDUCE: (61), (119) imply:
% 231.54/42.83  | | |   (121)   ~ (all_53_4 = all_52_19)
% 231.54/42.83  | | | 
% 231.54/42.83  | | | REDUCE: (32), (119) imply:
% 231.54/42.83  | | |   (122)   ~ (all_53_7 = all_52_19)
% 231.54/42.83  | | | 
% 231.54/42.83  | | | SIMP: (122) implies:
% 231.54/42.83  | | |   (123)   ~ (all_53_7 = all_52_19)
% 231.54/42.83  | | | 
% 231.54/42.83  | | | REDUCE: (49), (119) imply:
% 231.54/42.83  | | |   (124)   ~ (all_52_19 = e1)
% 231.54/42.83  | | | 
% 231.54/42.83  | | | BETA: splitting (2) gives:
% 231.54/42.83  | | | 
% 231.54/42.83  | | | Case 1:
% 231.54/42.83  | | | | 
% 231.54/42.83  | | | |   (125)  all_55_1 = e3
% 231.54/42.83  | | | | 
% 231.54/42.83  | | | | COMBINE_EQS: (30), (125) imply:
% 231.54/42.83  | | | |   (126)  all_53_4 = e3
% 231.54/42.83  | | | | 
% 231.54/42.83  | | | | SIMP: (126) implies:
% 231.54/42.83  | | | |   (127)  all_53_4 = e3
% 231.54/42.83  | | | | 
% 231.54/42.83  | | | | REDUCE: (44), (127) imply:
% 231.54/42.83  | | | |   (128)   ~ (all_53_8 = e3)
% 231.54/42.83  | | | | 
% 231.54/42.83  | | | | SIMP: (128) implies:
% 231.54/42.83  | | | |   (129)   ~ (all_53_8 = e3)
% 231.54/42.83  | | | | 
% 231.54/42.83  | | | | REDUCE: (76), (127) imply:
% 231.54/42.83  | | | |   (130)   ~ (e3 = e2)
% 231.54/42.83  | | | | 
% 231.54/42.83  | | | | REDUCE: (106), (127) imply:
% 231.54/42.83  | | | |   (131)   ~ (e3 = e1)
% 231.54/42.83  | | | | 
% 231.54/42.83  | | | | BETA: splitting (39) gives:
% 231.54/42.83  | | | | 
% 231.54/42.83  | | | | Case 1:
% 231.54/42.83  | | | | | 
% 231.54/42.83  | | | | |   (132)  all_55_2 = e3
% 231.54/42.83  | | | | | 
% 231.54/42.83  | | | | | COMBINE_EQS: (37), (132) imply:
% 231.54/42.83  | | | | |   (133)  all_53_8 = e3
% 231.54/42.83  | | | | | 
% 231.54/42.83  | | | | | REDUCE: (129), (133) imply:
% 231.54/42.83  | | | | |   (134)  $false
% 231.54/42.83  | | | | | 
% 231.54/42.83  | | | | | CLOSE: (134) is inconsistent.
% 231.54/42.83  | | | | | 
% 231.54/42.83  | | | | Case 2:
% 231.54/42.83  | | | | | 
% 231.54/42.83  | | | | |   (135)   ~ (all_55_2 = e3)
% 231.54/42.83  | | | | |   (136)  all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 231.54/42.83  | | | | | 
% 231.54/42.83  | | | | | BETA: splitting (136) gives:
% 231.54/42.83  | | | | | 
% 231.54/42.83  | | | | | Case 1:
% 231.54/42.83  | | | | | | 
% 231.54/42.83  | | | | | |   (137)  all_55_2 = e2
% 231.54/42.83  | | | | | | 
% 231.54/42.83  | | | | | | COMBINE_EQS: (37), (137) imply:
% 231.54/42.83  | | | | | |   (138)  all_53_8 = e2
% 231.54/42.83  | | | | | | 
% 231.54/42.83  | | | | | | REDUCE: (64), (138) imply:
% 231.54/42.83  | | | | | |   (139)  $false
% 231.54/42.83  | | | | | | 
% 231.54/42.83  | | | | | | CLOSE: (139) is inconsistent.
% 231.54/42.83  | | | | | | 
% 231.54/42.83  | | | | | Case 2:
% 231.54/42.83  | | | | | | 
% 231.54/42.83  | | | | | |   (140)   ~ (all_55_2 = e2)
% 231.54/42.83  | | | | | |   (141)  all_55_2 = e1 | all_55_2 = e0
% 231.54/42.83  | | | | | | 
% 231.54/42.83  | | | | | | BETA: splitting (50) gives:
% 231.54/42.83  | | | | | | 
% 231.54/42.83  | | | | | | Case 1:
% 231.54/42.83  | | | | | | | 
% 231.54/42.83  | | | | | | |   (142)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 &
% 231.54/42.83  | | | | | | |            op(e3, e2) = e3)
% 231.54/42.83  | | | | | | | 
% 231.54/42.83  | | | | | | | BETA: splitting (142) gives:
% 231.54/42.83  | | | | | | | 
% 231.54/42.83  | | | | | | | Case 1:
% 231.54/42.83  | | | | | | | | 
% 231.54/42.83  | | | | | | | |   (143)  all_57_0 = e3 & op(e3, e3) = e3
% 231.54/42.83  | | | | | | | | 
% 231.54/42.83  | | | | | | | | ALPHA: (143) implies:
% 231.54/42.83  | | | | | | | |   (144)  op(e3, e3) = e3
% 231.54/42.83  | | | | | | | | 
% 231.54/42.83  | | | | | | | | REF_CLOSE: (12), (40), (130), (144) are inconsistent by
% 231.54/42.83  | | | | | | | |            sub-proof #2490.
% 231.54/42.83  | | | | | | | | 
% 231.54/42.83  | | | | | | | Case 2:
% 231.54/42.83  | | | | | | | | 
% 231.54/42.83  | | | | | | | |   (145)  all_57_1 = e3 & op(e3, e2) = e3
% 231.54/42.83  | | | | | | | | 
% 231.54/42.83  | | | | | | | | ALPHA: (145) implies:
% 231.54/42.83  | | | | | | | |   (146)  all_57_1 = e3
% 231.54/42.83  | | | | | | | | 
% 231.54/42.83  | | | | | | | | BETA: splitting (141) gives:
% 231.54/42.83  | | | | | | | | 
% 231.54/42.83  | | | | | | | | Case 1:
% 231.54/42.83  | | | | | | | | | 
% 231.54/42.83  | | | | | | | | |   (147)  all_55_2 = e1
% 231.54/42.83  | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | REF_CLOSE: (37), (107), (147) are inconsistent by sub-proof
% 231.54/42.83  | | | | | | | | |            #2032.
% 231.54/42.83  | | | | | | | | | 
% 231.54/42.83  | | | | | | | | Case 2:
% 231.54/42.83  | | | | | | | | | 
% 231.54/42.83  | | | | | | | | |   (148)  all_55_2 = e0
% 231.54/42.83  | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | COMBINE_EQS: (37), (148) imply:
% 231.54/42.83  | | | | | | | | |   (149)  all_53_8 = e0
% 231.54/42.83  | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | SIMP: (149) implies:
% 231.54/42.83  | | | | | | | | |   (150)  all_53_8 = e0
% 231.54/42.83  | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | REDUCE: (25), (150) imply:
% 231.54/42.83  | | | | | | | | |   (151)   ~ (all_53_9 = e0)
% 231.54/42.83  | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | SIMP: (151) implies:
% 231.54/42.83  | | | | | | | | |   (152)   ~ (all_53_9 = e0)
% 231.54/42.83  | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | REDUCE: (129), (150) imply:
% 231.54/42.83  | | | | | | | | |   (153)   ~ (e3 = e0)
% 231.54/42.83  | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | SIMP: (153) implies:
% 231.54/42.83  | | | | | | | | |   (154)   ~ (e3 = e0)
% 231.54/42.83  | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | REDUCE: (64), (150) imply:
% 231.54/42.83  | | | | | | | | |   (155)   ~ (e2 = e0)
% 231.54/42.83  | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | SIMP: (155) implies:
% 231.54/42.83  | | | | | | | | |   (156)   ~ (e2 = e0)
% 231.54/42.83  | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | REDUCE: (107), (150) imply:
% 231.54/42.83  | | | | | | | | |   (157)   ~ (e1 = e0)
% 231.54/42.83  | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | BETA: splitting (60) gives:
% 231.54/42.83  | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | Case 1:
% 231.54/42.83  | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | |   (158)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 231.54/42.83  | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 231.54/42.83  | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | BETA: splitting (158) gives:
% 231.54/42.83  | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | Case 1:
% 231.54/42.83  | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | |   (159)  all_57_12 = e3 & op(e0, e3) = e3
% 231.54/42.83  | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | ALPHA: (159) implies:
% 231.54/42.83  | | | | | | | | | | |   (160)  all_57_12 = e3
% 231.54/42.83  | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | COMBINE_EQS: (98), (160) imply:
% 231.54/42.83  | | | | | | | | | | |   (161)  e3 = e1
% 231.54/42.83  | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | COMBINE_EQS: (146), (161) imply:
% 231.54/42.83  | | | | | | | | | | |   (162)  all_57_1 = e1
% 231.54/42.83  | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | REF_CLOSE: (9), (12), (19), (47), (55), (109), (110), (130),
% 231.54/42.83  | | | | | | | | | | |            (131), (154), (156), (162) are inconsistent by
% 231.54/42.83  | | | | | | | | | | |            sub-proof #1908.
% 231.54/42.83  | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | Case 2:
% 231.54/42.83  | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | |   (163)  all_57_13 = e3 & op(e0, e2) = e3
% 231.54/42.83  | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | ALPHA: (163) implies:
% 231.54/42.83  | | | | | | | | | | |   (164)  all_57_13 = e3
% 231.54/42.83  | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | BETA: splitting (63) gives:
% 231.54/42.83  | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | Case 1:
% 231.54/42.83  | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | |   (165)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 231.54/42.83  | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 231.54/42.83  | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | BETA: splitting (165) gives:
% 231.54/42.83  | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | Case 1:
% 231.54/42.83  | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | |   (166)  all_57_12 = e2 & op(e0, e3) = e2
% 231.54/42.83  | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | ALPHA: (166) implies:
% 231.54/42.83  | | | | | | | | | | | | |   (167)  op(e0, e3) = e2
% 231.54/42.83  | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | REF_CLOSE: (12), (35), (41), (167) are inconsistent by
% 231.54/42.83  | | | | | | | | | | | | |            sub-proof #1980.
% 231.54/42.83  | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | Case 2:
% 231.54/42.83  | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | |   (168)  all_57_13 = e2 & op(e0, e2) = e2
% 231.54/42.83  | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | ALPHA: (168) implies:
% 231.54/42.83  | | | | | | | | | | | | |   (169)  all_57_13 = e2
% 231.54/42.83  | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | COMBINE_EQS: (164), (169) imply:
% 231.54/42.83  | | | | | | | | | | | | |   (170)  e3 = e2
% 231.54/42.83  | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | SIMP: (170) implies:
% 231.54/42.83  | | | | | | | | | | | | |   (171)  e3 = e2
% 231.54/42.83  | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | COMBINE_EQS: (146), (171) imply:
% 231.54/42.83  | | | | | | | | | | | | |   (172)  all_57_1 = e2
% 231.54/42.83  | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | REF_CLOSE: (12), (20), (26), (40), (50), (109), (110), (130),
% 231.54/42.83  | | | | | | | | | | | | |            (131), (154), (156), (172) are inconsistent by
% 231.54/42.83  | | | | | | | | | | | | |            sub-proof #1655.
% 231.54/42.83  | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | End of split
% 231.54/42.83  | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | Case 2:
% 231.54/42.83  | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | |   (173)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 231.54/42.83  | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 231.54/42.83  | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | BETA: splitting (173) gives:
% 231.54/42.83  | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | Case 1:
% 231.54/42.83  | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | |   (174)  all_57_14 = e2 & op(e0, e1) = e2
% 231.54/42.83  | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | ALPHA: (174) implies:
% 231.54/42.83  | | | | | | | | | | | | |   (175)  all_57_14 = e2
% 231.54/42.83  | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | BETA: splitting (28) gives:
% 231.54/42.83  | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | Case 1:
% 231.54/42.83  | | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | |   (176)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 231.54/42.83  | | | | | | | | | | | | | |            & op(e2, e1) = e0)
% 231.54/42.83  | | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | | BETA: splitting (176) gives:
% 231.54/42.83  | | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | | Case 1:
% 231.54/42.83  | | | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | | |   (177)  all_57_4 = e0 & op(e3, e1) = e0
% 231.54/42.83  | | | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | | | ALPHA: (177) implies:
% 231.54/42.83  | | | | | | | | | | | | | | |   (178)  all_57_4 = e0
% 231.54/42.83  | | | | | | | | | | | | | | |   (179)  op(e3, e1) = e0
% 231.54/42.83  | | | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | | | BETA: splitting (47) gives:
% 231.54/42.83  | | | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | | | Case 1:
% 231.54/42.83  | | | | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | | | |   (180)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 231.54/42.83  | | | | | | | | | | | | | | | |            & op(e2, e2) = e0)
% 231.54/42.83  | | | | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | | | | BETA: splitting (180) gives:
% 231.54/42.83  | | | | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.83  | | | | | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | | | | |   (181)  all_57_1 = e0 & op(e3, e2) = e0
% 231.54/42.83  | | | | | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | | | | | REF_CLOSE: (146), (154), (181) are inconsistent by sub-proof
% 231.54/42.83  | | | | | | | | | | | | | | | | |            #1811.
% 231.54/42.83  | | | | | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.83  | | | | | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | | | | |   (182)  all_57_3 = e0 & op(e2, e2) = e0
% 231.54/42.83  | | | | | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | | | | | ALPHA: (182) implies:
% 231.54/42.83  | | | | | | | | | | | | | | | | |   (183)  all_57_3 = e0
% 231.54/42.83  | | | | | | | | | | | | | | | | |   (184)  op(e2, e2) = e0
% 231.54/42.83  | | | | | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11),
% 231.54/42.83  | | | | | | | | | | | | | | | | |            (12), (13), (15), (16), (17), (18), (20), (21),
% 231.54/42.83  | | | | | | | | | | | | | | | | |            (22), (24), (26), (27), (30), (32), (33), (34),
% 231.54/42.83  | | | | | | | | | | | | | | | | |            (35), (38), (40), (41), (42), (43), (44), (48),
% 231.54/42.83  | | | | | | | | | | | | | | | | |            (50), (51), (52), (54), (55), (57), (60), (61),
% 231.54/42.83  | | | | | | | | | | | | | | | | |            (62), (63), (64), (65), (66), (67), (68), (70),
% 231.54/42.83  | | | | | | | | | | | | | | | | |            (72), (73), (74), (75), (76), (77), (78), (79),
% 231.54/42.83  | | | | | | | | | | | | | | | | |            (81), (82), (86), (87), (88), (89), (90), (91),
% 231.54/42.83  | | | | | | | | | | | | | | | | |            (92), (94), (95), (96), (97), (109), (110), (130),
% 231.54/42.83  | | | | | | | | | | | | | | | | |            (131), (154), (156), (178), (179), (183), (184)
% 231.54/42.83  | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1611.
% 231.54/42.83  | | | | | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | | | | End of split
% 231.54/42.83  | | | | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | | | Case 2:
% 231.54/42.83  | | | | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | | | |   (185)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 231.54/42.83  | | | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0)
% 231.54/42.83  | | | | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | | | | REF_CLOSE: (12), (42), (57), (62), (115), (117), (156), (185)
% 231.54/42.83  | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1841.
% 231.54/42.83  | | | | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | | | End of split
% 231.54/42.83  | | | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | | Case 2:
% 231.54/42.83  | | | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | | |   (186)  all_57_5 = e0 & op(e2, e1) = e0
% 231.54/42.83  | | | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | | | REF_CLOSE: (12), (83), (152), (186) are inconsistent by
% 231.54/42.83  | | | | | | | | | | | | | | |            sub-proof #2023.
% 231.54/42.83  | | | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | | End of split
% 231.54/42.83  | | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | Case 2:
% 231.54/42.83  | | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | |   (187)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 231.54/42.83  | | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 231.54/42.83  | | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 231.54/42.83  | | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | | Case 1:
% 231.54/42.83  | | | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | | |   (188)  all_57_8 = e0 & op(e1, e1) = e0
% 231.54/42.83  | | | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | | | ALPHA: (188) implies:
% 231.54/42.83  | | | | | | | | | | | | | | |   (189)  op(e1, e1) = e0
% 231.54/42.83  | | | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | | | REF_CLOSE: (12), (19), (31), (42), (45), (47), (57), (59),
% 231.54/42.83  | | | | | | | | | | | | | | |            (62), (66), (69), (71), (80), (97), (106), (110),
% 231.54/42.83  | | | | | | | | | | | | | | |            (114), (115), (116), (117), (156), (189) are
% 231.54/42.83  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1840.
% 231.54/42.83  | | | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | | Case 2:
% 231.54/42.83  | | | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | | |   (190)  all_57_14 = e0 & op(e0, e1) = e0
% 231.54/42.83  | | | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | | | REF_CLOSE: (156), (175), (190) are inconsistent by sub-proof
% 231.54/42.83  | | | | | | | | | | | | | | |            #2173.
% 231.54/42.83  | | | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | | End of split
% 231.54/42.83  | | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | End of split
% 231.54/42.83  | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | Case 2:
% 231.54/42.83  | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | |   (191)  all_57_15 = e2 & op(e0, e0) = e2
% 231.54/42.83  | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | ALPHA: (191) implies:
% 231.54/42.83  | | | | | | | | | | | | |   (192)  all_57_15 = e2
% 231.54/42.83  | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | REF_CLOSE: (5), (156), (192) are inconsistent by sub-proof
% 231.54/42.83  | | | | | | | | | | | | |            #2126.
% 231.54/42.83  | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | End of split
% 231.54/42.83  | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | End of split
% 231.54/42.83  | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | End of split
% 231.54/42.83  | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | Case 2:
% 231.54/42.83  | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | |   (193)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 231.54/42.83  | | | | | | | | | |            e3 & op(e0, e0) = e3)
% 231.54/42.83  | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | BETA: splitting (193) gives:
% 231.54/42.83  | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | Case 1:
% 231.54/42.83  | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | |   (194)  all_57_14 = e3 & op(e0, e1) = e3
% 231.54/42.83  | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | ALPHA: (194) implies:
% 231.54/42.83  | | | | | | | | | | |   (195)  all_57_14 = e3
% 231.54/42.83  | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | BETA: splitting (28) gives:
% 231.54/42.83  | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | Case 1:
% 231.54/42.83  | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | |   (196)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 231.54/42.83  | | | | | | | | | | | |            & op(e2, e1) = e0)
% 231.54/42.83  | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | BETA: splitting (196) gives:
% 231.54/42.83  | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | Case 1:
% 231.54/42.83  | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | |   (197)  all_57_4 = e0 & op(e3, e1) = e0
% 231.54/42.83  | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | ALPHA: (197) implies:
% 231.54/42.83  | | | | | | | | | | | | |   (198)  all_57_4 = e0
% 231.54/42.83  | | | | | | | | | | | | |   (199)  op(e3, e1) = e0
% 231.54/42.83  | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | BETA: splitting (47) gives:
% 231.54/42.83  | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | Case 1:
% 231.54/42.83  | | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | |   (200)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 231.54/42.83  | | | | | | | | | | | | | |            & op(e2, e2) = e0)
% 231.54/42.83  | | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 231.54/42.83  | | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | | Case 1:
% 231.54/42.83  | | | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | | |   (201)  all_57_1 = e0 & op(e3, e2) = e0
% 231.54/42.83  | | | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | | | ALPHA: (201) implies:
% 231.54/42.83  | | | | | | | | | | | | | | |   (202)  all_57_1 = e0
% 231.54/42.83  | | | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | | | COMBINE_EQS: (146), (202) imply:
% 231.54/42.83  | | | | | | | | | | | | | | |   (203)  e3 = e0
% 231.54/42.83  | | | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | | | COMBINE_EQS: (195), (203) imply:
% 231.54/42.83  | | | | | | | | | | | | | | |   (204)  all_57_14 = e0
% 231.54/42.83  | | | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | | | REF_CLOSE: (12), (15), (16), (33), (54), (88), (109), (110),
% 231.54/42.83  | | | | | | | | | | | | | | |            (130), (131), (154), (156), (198), (204) are
% 231.54/42.83  | | | | | | | | | | | | | | |            inconsistent by sub-proof #2371.
% 231.54/42.83  | | | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | | Case 2:
% 231.54/42.83  | | | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | | |   (205)  all_57_3 = e0 & op(e2, e2) = e0
% 231.54/42.83  | | | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | | | ALPHA: (205) implies:
% 231.54/42.83  | | | | | | | | | | | | | | |   (206)  all_57_3 = e0
% 231.54/42.83  | | | | | | | | | | | | | | |   (207)  op(e2, e2) = e0
% 231.54/42.83  | | | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11),
% 231.54/42.83  | | | | | | | | | | | | | | |            (12), (13), (15), (16), (17), (18), (20), (21),
% 231.54/42.83  | | | | | | | | | | | | | | |            (22), (24), (26), (27), (30), (32), (33), (34),
% 231.54/42.83  | | | | | | | | | | | | | | |            (35), (38), (40), (41), (42), (43), (44), (48),
% 231.54/42.83  | | | | | | | | | | | | | | |            (50), (51), (52), (54), (55), (57), (60), (61),
% 231.54/42.83  | | | | | | | | | | | | | | |            (62), (63), (64), (65), (66), (67), (68), (70),
% 231.54/42.83  | | | | | | | | | | | | | | |            (72), (73), (74), (75), (76), (77), (78), (79),
% 231.54/42.83  | | | | | | | | | | | | | | |            (81), (82), (86), (87), (88), (89), (90), (91),
% 231.54/42.83  | | | | | | | | | | | | | | |            (92), (94), (95), (96), (97), (109), (110), (130),
% 231.54/42.83  | | | | | | | | | | | | | | |            (131), (154), (156), (198), (199), (206), (207)
% 231.54/42.83  | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1611.
% 231.54/42.83  | | | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | | End of split
% 231.54/42.83  | | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | Case 2:
% 231.54/42.83  | | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | |   (208)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 231.54/42.83  | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0)
% 231.54/42.83  | | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | | REF_CLOSE: (12), (42), (57), (62), (115), (117), (156), (208)
% 231.54/42.83  | | | | | | | | | | | | | |            are inconsistent by sub-proof #1841.
% 231.54/42.83  | | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | End of split
% 231.54/42.83  | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | Case 2:
% 231.54/42.83  | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | |   (209)  all_57_5 = e0 & op(e2, e1) = e0
% 231.54/42.83  | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | REF_CLOSE: (12), (83), (152), (209) are inconsistent by
% 231.54/42.83  | | | | | | | | | | | | |            sub-proof #2023.
% 231.54/42.83  | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | End of split
% 231.54/42.83  | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | Case 2:
% 231.54/42.83  | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | |   (210)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 231.54/42.83  | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 231.54/42.83  | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | BETA: splitting (210) gives:
% 231.54/42.83  | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | Case 1:
% 231.54/42.83  | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | |   (211)  all_57_8 = e0 & op(e1, e1) = e0
% 231.54/42.83  | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | ALPHA: (211) implies:
% 231.54/42.83  | | | | | | | | | | | | |   (212)  op(e1, e1) = e0
% 231.54/42.83  | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | REF_CLOSE: (12), (19), (31), (42), (45), (47), (57), (59),
% 231.54/42.83  | | | | | | | | | | | | |            (62), (66), (69), (71), (80), (97), (106), (110),
% 231.54/42.83  | | | | | | | | | | | | |            (114), (115), (116), (117), (156), (212) are
% 231.54/42.83  | | | | | | | | | | | | |            inconsistent by sub-proof #1840.
% 231.54/42.83  | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | Case 2:
% 231.54/42.83  | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | |   (213)  all_57_14 = e0 & op(e0, e1) = e0
% 231.54/42.83  | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | | REF_CLOSE: (154), (195), (213) are inconsistent by sub-proof
% 231.54/42.83  | | | | | | | | | | | | |            #2314.
% 231.54/42.83  | | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | | End of split
% 231.54/42.83  | | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | End of split
% 231.54/42.83  | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | Case 2:
% 231.54/42.83  | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | |   (214)  all_57_15 = e3 & op(e0, e0) = e3
% 231.54/42.83  | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | ALPHA: (214) implies:
% 231.54/42.83  | | | | | | | | | | |   (215)  op(e0, e0) = e3
% 231.54/42.83  | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | REF_CLOSE: (12), (57), (154), (215) are inconsistent by
% 231.54/42.83  | | | | | | | | | | |            sub-proof #2304.
% 231.54/42.83  | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | End of split
% 231.54/42.83  | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | End of split
% 231.54/42.83  | | | | | | | | | 
% 231.54/42.83  | | | | | | | | End of split
% 231.54/42.83  | | | | | | | | 
% 231.54/42.83  | | | | | | | End of split
% 231.54/42.83  | | | | | | | 
% 231.54/42.83  | | | | | | Case 2:
% 231.54/42.83  | | | | | | | 
% 231.54/42.83  | | | | | | |   (216)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 &
% 231.54/42.83  | | | | | | |            op(e3, e0) = e3)
% 231.54/42.83  | | | | | | | 
% 231.54/42.83  | | | | | | | BETA: splitting (216) gives:
% 231.54/42.83  | | | | | | | 
% 231.54/42.83  | | | | | | | Case 1:
% 231.54/42.83  | | | | | | | | 
% 231.54/42.83  | | | | | | | |   (217)  all_57_4 = e3 & op(e3, e1) = e3
% 231.54/42.83  | | | | | | | | 
% 231.54/42.83  | | | | | | | | ALPHA: (217) implies:
% 231.54/42.83  | | | | | | | |   (218)  all_57_4 = e3
% 231.54/42.83  | | | | | | | | 
% 231.54/42.83  | | | | | | | | BETA: splitting (141) gives:
% 231.54/42.83  | | | | | | | | 
% 231.54/42.83  | | | | | | | | Case 1:
% 231.54/42.83  | | | | | | | | | 
% 231.54/42.83  | | | | | | | | |   (219)  all_55_2 = e1
% 231.54/42.83  | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | REF_CLOSE: (37), (107), (219) are inconsistent by sub-proof
% 231.54/42.83  | | | | | | | | |            #2032.
% 231.54/42.83  | | | | | | | | | 
% 231.54/42.83  | | | | | | | | Case 2:
% 231.54/42.83  | | | | | | | | | 
% 231.54/42.83  | | | | | | | | |   (220)  all_55_2 = e0
% 231.54/42.83  | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | COMBINE_EQS: (37), (220) imply:
% 231.54/42.83  | | | | | | | | |   (221)  all_53_8 = e0
% 231.54/42.83  | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | SIMP: (221) implies:
% 231.54/42.83  | | | | | | | | |   (222)  all_53_8 = e0
% 231.54/42.83  | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | REDUCE: (25), (222) imply:
% 231.54/42.83  | | | | | | | | |   (223)   ~ (all_53_9 = e0)
% 231.54/42.83  | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | SIMP: (223) implies:
% 231.54/42.83  | | | | | | | | |   (224)   ~ (all_53_9 = e0)
% 231.54/42.83  | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | REDUCE: (129), (222) imply:
% 231.54/42.83  | | | | | | | | |   (225)   ~ (e3 = e0)
% 231.54/42.83  | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | SIMP: (225) implies:
% 231.54/42.83  | | | | | | | | |   (226)   ~ (e3 = e0)
% 231.54/42.83  | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | REDUCE: (64), (222) imply:
% 231.54/42.83  | | | | | | | | |   (227)   ~ (e2 = e0)
% 231.54/42.83  | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | SIMP: (227) implies:
% 231.54/42.83  | | | | | | | | |   (228)   ~ (e2 = e0)
% 231.54/42.83  | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | REDUCE: (107), (222) imply:
% 231.54/42.83  | | | | | | | | |   (229)   ~ (e1 = e0)
% 231.54/42.83  | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | BETA: splitting (28) gives:
% 231.54/42.83  | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | Case 1:
% 231.54/42.83  | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | |   (230)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 231.54/42.83  | | | | | | | | | |            & op(e2, e1) = e0)
% 231.54/42.83  | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | BETA: splitting (230) gives:
% 231.54/42.83  | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | Case 1:
% 231.54/42.83  | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | |   (231)  all_57_4 = e0 & op(e3, e1) = e0
% 231.54/42.83  | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | ALPHA: (231) implies:
% 231.54/42.83  | | | | | | | | | | |   (232)  all_57_4 = e0
% 231.54/42.83  | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | REF_CLOSE: (218), (226), (232) are inconsistent by sub-proof
% 231.54/42.83  | | | | | | | | | | |            #2372.
% 231.54/42.83  | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | Case 2:
% 231.54/42.83  | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | |   (233)  all_57_5 = e0 & op(e2, e1) = e0
% 231.54/42.83  | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | REF_CLOSE: (12), (83), (224), (233) are inconsistent by
% 231.54/42.83  | | | | | | | | | | |            sub-proof #2023.
% 231.54/42.83  | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | End of split
% 231.54/42.83  | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | Case 2:
% 231.54/42.83  | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | |   (234)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0
% 231.54/42.83  | | | | | | | | | |            & op(e0, e1) = e0)
% 231.54/42.83  | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | BETA: splitting (234) gives:
% 231.54/42.83  | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | Case 1:
% 231.54/42.83  | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | |   (235)  all_57_8 = e0 & op(e1, e1) = e0
% 231.54/42.83  | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | ALPHA: (235) implies:
% 231.54/42.83  | | | | | | | | | | |   (236)  op(e1, e1) = e0
% 231.54/42.83  | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | REF_CLOSE: (12), (19), (31), (42), (45), (47), (57), (59),
% 231.54/42.83  | | | | | | | | | | |            (62), (66), (69), (71), (80), (97), (106), (110),
% 231.54/42.83  | | | | | | | | | | |            (114), (115), (116), (117), (228), (236) are
% 231.54/42.83  | | | | | | | | | | |            inconsistent by sub-proof #1840.
% 231.54/42.83  | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | Case 2:
% 231.54/42.83  | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | |   (237)  all_57_14 = e0 & op(e0, e1) = e0
% 231.54/42.83  | | | | | | | | | | | 
% 231.54/42.83  | | | | | | | | | | | ALPHA: (237) implies:
% 231.54/42.83  | | | | | | | | | | |   (238)  all_57_14 = e0
% 231.54/42.83  | | | | | | | | | | | 
% 231.54/42.84  | | | | | | | | | | | BETA: splitting (63) gives:
% 231.54/42.84  | | | | | | | | | | | 
% 231.54/42.84  | | | | | | | | | | | Case 1:
% 231.54/42.84  | | | | | | | | | | | | 
% 231.54/42.84  | | | | | | | | | | | |   (239)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 231.54/42.84  | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 231.54/42.84  | | | | | | | | | | | | 
% 231.54/42.84  | | | | | | | | | | | | BETA: splitting (239) gives:
% 231.54/42.84  | | | | | | | | | | | | 
% 231.54/42.84  | | | | | | | | | | | | Case 1:
% 231.54/42.84  | | | | | | | | | | | | | 
% 231.54/42.84  | | | | | | | | | | | | |   (240)  all_57_12 = e2 & op(e0, e3) = e2
% 231.54/42.84  | | | | | | | | | | | | | 
% 231.54/42.84  | | | | | | | | | | | | | ALPHA: (240) implies:
% 231.54/42.84  | | | | | | | | | | | | |   (241)  op(e0, e3) = e2
% 231.54/42.84  | | | | | | | | | | | | | 
% 231.54/42.84  | | | | | | | | | | | | | REF_CLOSE: (12), (35), (41), (241) are inconsistent by
% 231.54/42.84  | | | | | | | | | | | | |            sub-proof #1980.
% 231.54/42.84  | | | | | | | | | | | | | 
% 231.54/42.84  | | | | | | | | | | | | Case 2:
% 231.54/42.84  | | | | | | | | | | | | | 
% 231.54/42.84  | | | | | | | | | | | | |   (242)  all_57_13 = e2 & op(e0, e2) = e2
% 231.54/42.84  | | | | | | | | | | | | | 
% 231.54/42.84  | | | | | | | | | | | | | ALPHA: (242) implies:
% 231.54/42.84  | | | | | | | | | | | | |   (243)  all_57_13 = e2
% 231.54/42.84  | | | | | | | | | | | | | 
% 231.54/42.84  | | | | | | | | | | | | | BETA: splitting (60) gives:
% 231.54/42.84  | | | | | | | | | | | | | 
% 231.54/42.84  | | | | | | | | | | | | | Case 1:
% 231.54/42.84  | | | | | | | | | | | | | | 
% 231.54/42.84  | | | | | | | | | | | | | |   (244)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 231.54/42.84  | | | | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 231.54/42.84  | | | | | | | | | | | | | | 
% 231.54/42.84  | | | | | | | | | | | | | | BETA: splitting (244) gives:
% 231.54/42.84  | | | | | | | | | | | | | | 
% 231.54/42.84  | | | | | | | | | | | | | | Case 1:
% 231.54/42.84  | | | | | | | | | | | | | | | 
% 231.54/42.84  | | | | | | | | | | | | | | |   (245)  all_57_12 = e3 & op(e0, e3) = e3
% 231.54/42.84  | | | | | | | | | | | | | | | 
% 231.54/42.84  | | | | | | | | | | | | | | | ALPHA: (245) implies:
% 231.54/42.84  | | | | | | | | | | | | | | |   (246)  all_57_12 = e3
% 231.54/42.84  | | | | | | | | | | | | | | | 
% 231.54/42.84  | | | | | | | | | | | | | | | COMBINE_EQS: (98), (246) imply:
% 231.54/42.84  | | | | | | | | | | | | | | |   (247)  e3 = e1
% 231.54/42.84  | | | | | | | | | | | | | | | 
% 231.54/42.84  | | | | | | | | | | | | | | | SIMP: (247) implies:
% 231.54/42.84  | | | | | | | | | | | | | | |   (248)  e3 = e1
% 231.54/42.84  | | | | | | | | | | | | | | | 
% 231.54/42.84  | | | | | | | | | | | | | | | COMBINE_EQS: (218), (248) imply:
% 231.54/42.84  | | | | | | | | | | | | | | |   (249)  all_57_4 = e1
% 231.54/42.84  | | | | | | | | | | | | | | | 
% 231.54/42.84  | | | | | | | | | | | | | | | REF_CLOSE: (12), (15), (16), (46), (54), (88), (109), (130),
% 231.54/42.84  | | | | | | | | | | | | | | |            (131), (226), (228), (238), (249) are inconsistent
% 231.54/42.84  | | | | | | | | | | | | | | |            by sub-proof #2418.
% 231.54/42.84  | | | | | | | | | | | | | | | 
% 231.54/42.84  | | | | | | | | | | | | | | Case 2:
% 231.54/42.84  | | | | | | | | | | | | | | | 
% 231.54/42.84  | | | | | | | | | | | | | | |   (250)  all_57_13 = e3 & op(e0, e2) = e3
% 231.54/42.84  | | | | | | | | | | | | | | | 
% 231.54/42.84  | | | | | | | | | | | | | | | ALPHA: (250) implies:
% 231.54/42.84  | | | | | | | | | | | | | | |   (251)  all_57_13 = e3
% 231.54/42.84  | | | | | | | | | | | | | | | 
% 231.54/42.84  | | | | | | | | | | | | | | | COMBINE_EQS: (243), (251) imply:
% 231.54/42.84  | | | | | | | | | | | | | | |   (252)  e3 = e2
% 231.54/42.84  | | | | | | | | | | | | | | | 
% 231.54/42.84  | | | | | | | | | | | | | | | SIMP: (252) implies:
% 231.54/42.84  | | | | | | | | | | | | | | |   (253)  e3 = e2
% 231.54/42.84  | | | | | | | | | | | | | | | 
% 231.54/42.84  | | | | | | | | | | | | | | | COMBINE_EQS: (218), (253) imply:
% 231.54/42.84  | | | | | | | | | | | | | | |   (254)  all_57_4 = e2
% 231.54/42.84  | | | | | | | | | | | | | | | 
% 231.54/42.84  | | | | | | | | | | | | | | | REF_CLOSE: (12), (20), (23), (26), (40), (50), (109), (110),
% 231.54/42.84  | | | | | | | | | | | | | | |            (130), (131), (226), (228), (254) are inconsistent
% 231.54/42.84  | | | | | | | | | | | | | | |            by sub-proof #1604.
% 231.54/42.84  | | | | | | | | | | | | | | | 
% 231.54/42.84  | | | | | | | | | | | | | | End of split
% 231.54/42.84  | | | | | | | | | | | | | | 
% 231.54/42.84  | | | | | | | | | | | | | Case 2:
% 231.54/42.84  | | | | | | | | | | | | | | 
% 231.54/42.84  | | | | | | | | | | | | | |   (255)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 231.54/42.84  | | | | | | | | | | | | | |            e3 & op(e0, e0) = e3)
% 231.54/42.84  | | | | | | | | | | | | | | 
% 231.54/42.84  | | | | | | | | | | | | | | BETA: splitting (255) gives:
% 231.54/42.84  | | | | | | | | | | | | | | 
% 231.54/42.84  | | | | | | | | | | | | | | Case 1:
% 231.54/42.84  | | | | | | | | | | | | | | | 
% 231.54/42.84  | | | | | | | | | | | | | | |   (256)  all_57_14 = e3 & op(e0, e1) = e3
% 231.54/42.84  | | | | | | | | | | | | | | | 
% 231.54/42.84  | | | | | | | | | | | | | | | ALPHA: (256) implies:
% 231.54/42.84  | | | | | | | | | | | | | | |   (257)  all_57_14 = e3
% 231.54/42.84  | | | | | | | | | | | | | | | 
% 231.54/42.84  | | | | | | | | | | | | | | | COMBINE_EQS: (238), (257) imply:
% 231.54/42.84  | | | | | | | | | | | | | | |   (258)  e3 = e0
% 231.54/42.84  | | | | | | | | | | | | | | | 
% 231.54/42.84  | | | | | | | | | | | | | | | SIMP: (258) implies:
% 231.54/42.84  | | | | | | | | | | | | | | |   (259)  e3 = e0
% 231.54/42.84  | | | | | | | | | | | | | | | 
% 231.54/42.84  | | | | | | | | | | | | | | | COMBINE_EQS: (218), (259) imply:
% 231.54/42.84  | | | | | | | | | | | | | | |   (260)  all_57_4 = e0
% 231.54/42.84  | | | | | | | | | | | | | | | 
% 231.54/42.84  | | | | | | | | | | | | | | | REF_CLOSE: (12), (15), (16), (33), (54), (88), (109), (110),
% 231.54/42.84  | | | | | | | | | | | | | | |            (130), (131), (226), (228), (238), (260) are
% 231.54/42.84  | | | | | | | | | | | | | | |            inconsistent by sub-proof #2371.
% 231.54/42.84  | | | | | | | | | | | | | | | 
% 231.54/42.84  | | | | | | | | | | | | | | Case 2:
% 231.54/42.84  | | | | | | | | | | | | | | | 
% 231.54/42.84  | | | | | | | | | | | | | | |   (261)  all_57_15 = e3 & op(e0, e0) = e3
% 231.54/42.84  | | | | | | | | | | | | | | | 
% 231.54/42.84  | | | | | | | | | | | | | | | ALPHA: (261) implies:
% 231.54/42.84  | | | | | | | | | | | | | | |   (262)  op(e0, e0) = e3
% 231.54/42.84  | | | | | | | | | | | | | | | 
% 231.54/42.84  | | | | | | | | | | | | | | | REF_CLOSE: (12), (57), (226), (262) are inconsistent by
% 231.54/42.84  | | | | | | | | | | | | | | |            sub-proof #2304.
% 231.54/42.84  | | | | | | | | | | | | | | | 
% 231.54/42.84  | | | | | | | | | | | | | | End of split
% 231.54/42.84  | | | | | | | | | | | | | | 
% 231.54/42.84  | | | | | | | | | | | | | End of split
% 231.54/42.84  | | | | | | | | | | | | | 
% 231.54/42.84  | | | | | | | | | | | | End of split
% 231.54/42.84  | | | | | | | | | | | | 
% 231.54/42.84  | | | | | | | | | | | Case 2:
% 231.54/42.84  | | | | | | | | | | | | 
% 231.54/42.84  | | | | | | | | | | | |   (263)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 231.54/42.84  | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 231.54/42.84  | | | | | | | | | | | | 
% 231.54/42.84  | | | | | | | | | | | | REF_CLOSE: (5), (228), (238), (263) are inconsistent by
% 231.54/42.84  | | | | | | | | | | | |            sub-proof #2125.
% 231.54/42.84  | | | | | | | | | | | | 
% 231.54/42.84  | | | | | | | | | | | End of split
% 231.54/42.84  | | | | | | | | | | | 
% 231.54/42.84  | | | | | | | | | | End of split
% 231.54/42.84  | | | | | | | | | | 
% 231.54/42.84  | | | | | | | | | End of split
% 231.54/42.84  | | | | | | | | | 
% 231.54/42.84  | | | | | | | | End of split
% 231.54/42.84  | | | | | | | | 
% 231.54/42.84  | | | | | | | Case 2:
% 231.54/42.84  | | | | | | | | 
% 231.54/42.84  | | | | | | | |   (264)  all_57_9 = e3 & op(e3, e0) = e3
% 231.54/42.84  | | | | | | | | 
% 231.54/42.84  | | | | | | | | ALPHA: (264) implies:
% 231.54/42.84  | | | | | | | |   (265)  all_57_9 = e3
% 231.54/42.84  | | | | | | | | 
% 231.54/42.84  | | | | | | | | REF_CLOSE: (23), (131), (265) are inconsistent by sub-proof
% 231.54/42.84  | | | | | | | |            #1673.
% 231.54/42.84  | | | | | | | | 
% 231.54/42.84  | | | | | | | End of split
% 231.54/42.84  | | | | | | | 
% 231.54/42.84  | | | | | | End of split
% 231.54/42.84  | | | | | | 
% 231.54/42.84  | | | | | End of split
% 231.54/42.84  | | | | | 
% 231.54/42.84  | | | | End of split
% 231.54/42.84  | | | | 
% 231.54/42.84  | | | Case 2:
% 231.54/42.84  | | | | 
% 231.54/42.84  | | | |   (266)  all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 231.54/42.84  | | | | 
% 231.54/42.84  | | | | BETA: splitting (266) gives:
% 231.54/42.84  | | | | 
% 231.54/42.84  | | | | Case 1:
% 231.54/42.84  | | | | | 
% 231.54/42.84  | | | | |   (267)  all_55_1 = e2
% 231.54/42.84  | | | | | 
% 231.54/42.84  | | | | | REF_CLOSE: (30), (76), (267) are inconsistent by sub-proof #2284.
% 231.54/42.84  | | | | | 
% 231.54/42.84  | | | | Case 2:
% 231.54/42.84  | | | | | 
% 231.54/42.84  | | | | |   (268)  all_55_1 = e1 | all_55_1 = e0
% 231.54/42.84  | | | | | 
% 231.54/42.84  | | | | | BETA: splitting (268) gives:
% 231.54/42.84  | | | | | 
% 231.54/42.84  | | | | | Case 1:
% 231.54/42.84  | | | | | | 
% 231.54/42.84  | | | | | |   (269)  all_55_1 = e1
% 231.54/42.84  | | | | | | 
% 231.54/42.84  | | | | | | REF_CLOSE: (30), (106), (269) are inconsistent by sub-proof #2283.
% 231.54/42.84  | | | | | | 
% 231.54/42.84  | | | | | Case 2:
% 231.54/42.84  | | | | | | 
% 231.54/42.84  | | | | | |   (270)  all_55_1 = e0
% 231.54/42.84  | | | | | | 
% 231.54/42.84  | | | | | | COMBINE_EQS: (30), (270) imply:
% 231.54/42.84  | | | | | |   (271)  all_53_4 = e0
% 231.54/42.84  | | | | | | 
% 231.54/42.84  | | | | | | SIMP: (271) implies:
% 231.54/42.84  | | | | | |   (272)  all_53_4 = e0
% 231.54/42.84  | | | | | | 
% 231.54/42.84  | | | | | | REDUCE: (38), (272) imply:
% 231.54/42.84  | | | | | |   (273)   ~ (all_53_7 = e0)
% 231.54/42.84  | | | | | | 
% 231.54/42.84  | | | | | | REDUCE: (44), (272) imply:
% 231.54/42.84  | | | | | |   (274)   ~ (all_53_8 = e0)
% 231.54/42.84  | | | | | | 
% 231.54/42.84  | | | | | | SIMP: (274) implies:
% 231.54/42.84  | | | | | |   (275)   ~ (all_53_8 = e0)
% 231.54/42.84  | | | | | | 
% 231.54/42.84  | | | | | | REDUCE: (121), (272) imply:
% 231.54/42.84  | | | | | |   (276)   ~ (all_52_19 = e0)
% 231.54/42.84  | | | | | | 
% 231.54/42.84  | | | | | | SIMP: (276) implies:
% 231.54/42.84  | | | | | |   (277)   ~ (all_52_19 = e0)
% 231.54/42.84  | | | | | | 
% 231.54/42.84  | | | | | | BETA: splitting (39) gives:
% 231.54/42.84  | | | | | | 
% 231.54/42.84  | | | | | | Case 1:
% 231.54/42.84  | | | | | | | 
% 231.54/42.84  | | | | | | |   (278)  all_55_2 = e3
% 231.54/42.84  | | | | | | | 
% 231.54/42.84  | | | | | | | COMBINE_EQS: (37), (278) imply:
% 231.54/42.84  | | | | | | |   (279)  all_53_8 = e3
% 231.54/42.84  | | | | | | | 
% 231.54/42.84  | | | | | | | SIMP: (279) implies:
% 231.54/42.84  | | | | | | |   (280)  all_53_8 = e3
% 231.54/42.84  | | | | | | | 
% 231.54/42.84  | | | | | | | REDUCE: (10), (280) imply:
% 231.54/42.84  | | | | | | |   (281)   ~ (all_53_11 = e3)
% 231.54/42.84  | | | | | | | 
% 231.54/42.84  | | | | | | | SIMP: (281) implies:
% 231.54/42.84  | | | | | | |   (282)   ~ (all_53_11 = e3)
% 231.54/42.84  | | | | | | | 
% 231.54/42.84  | | | | | | | BETA: splitting (56) gives:
% 231.54/42.84  | | | | | | | 
% 231.54/42.84  | | | | | | | Case 1:
% 231.54/42.84  | | | | | | | | 
% 231.54/42.84  | | | | | | | |   (283)  all_55_14 = e3
% 231.54/42.84  | | | | | | | | 
% 231.54/42.84  | | | | | | | | COMBINE_EQS: (93), (283) imply:
% 231.54/42.84  | | | | | | | |   (284)  all_53_11 = e3
% 231.54/42.84  | | | | | | | | 
% 231.54/42.84  | | | | | | | | REDUCE: (282), (284) imply:
% 231.54/42.84  | | | | | | | |   (285)  $false
% 231.54/42.84  | | | | | | | | 
% 231.54/42.84  | | | | | | | | CLOSE: (285) is inconsistent.
% 231.54/42.84  | | | | | | | | 
% 231.54/42.84  | | | | | | | Case 2:
% 231.54/42.84  | | | | | | | | 
% 231.54/42.84  | | | | | | | |   (286)  all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 231.54/42.84  | | | | | | | | 
% 231.54/42.84  | | | | | | | | REF_CLOSE: (1), (12), (19), (21), (36), (42), (58), (70), (93),
% 231.54/42.84  | | | | | | | |            (103), (105), (117), (120), (123), (124), (277),
% 231.54/42.84  | | | | | | | |            (286) are inconsistent by sub-proof #1600.
% 231.54/42.84  | | | | | | | | 
% 231.54/42.84  | | | | | | | End of split
% 231.54/42.84  | | | | | | | 
% 231.54/42.84  | | | | | | Case 2:
% 231.54/42.84  | | | | | | | 
% 231.54/42.84  | | | | | | |   (287)  all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 231.54/42.84  | | | | | | | 
% 231.54/42.84  | | | | | | | REF_CLOSE: (37), (64), (107), (275), (287) are inconsistent by
% 231.54/42.84  | | | | | | |            sub-proof #1937.
% 231.54/42.84  | | | | | | | 
% 231.54/42.84  | | | | | | End of split
% 231.54/42.84  | | | | | | 
% 231.54/42.84  | | | | | End of split
% 231.54/42.84  | | | | | 
% 231.54/42.84  | | | | End of split
% 231.54/42.84  | | | | 
% 231.54/42.84  | | | End of split
% 231.54/42.84  | | | 
% 231.54/42.84  | | Case 2:
% 231.54/42.84  | | | 
% 231.54/42.84  | | |   (288)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 231.54/42.84  | | |          & op(all_52_25, all_52_25) = e3 & op(all_52_27, all_52_27) = e2 &
% 231.54/42.84  | | |          op(all_52_29, all_52_29) = e1 & op(all_52_31, all_52_31) = e0 &
% 231.54/42.84  | | |          op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 & op(e0, e1) =
% 231.54/42.84  | | |          all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 231.54/42.84  | | |          $i(all_52_27) & $i(all_52_29) & $i(all_52_31)
% 231.54/42.84  | | | 
% 231.54/42.84  | | | REF_CLOSE: (12), (15), (16), (99), (288) are inconsistent by sub-proof
% 231.54/42.84  | | |            #1853.
% 231.54/42.84  | | | 
% 231.54/42.84  | | End of split
% 231.54/42.84  | | 
% 231.54/42.84  | End of split
% 231.54/42.84  | 
% 231.54/42.84  End of proof
% 231.54/42.84  
% 231.54/42.84  Sub-proof #1600 shows that the following formulas are inconsistent:
% 231.54/42.84  ----------------------------------------------------------------
% 231.54/42.84    (1)  all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 231.54/42.84    (2)   ~ (all_53_7 = all_52_19)
% 231.54/42.84    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.84           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.84    (4)   ~ (all_53_7 = e1)
% 231.54/42.84    (5)  all_55_9 = all_52_19
% 231.54/42.84    (6)  op(e2, e2) = e1
% 231.54/42.84    (7)  all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 231.54/42.84    (8)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 231.54/42.84    (9)   ~ (all_53_11 = e0)
% 231.54/42.84    (10)   ~ (all_53_7 = e0)
% 231.54/42.84    (11)   ~ (all_53_7 = all_53_11)
% 231.54/42.84    (12)   ~ (all_52_19 = e0)
% 231.54/42.84    (13)   ~ (all_53_11 = e1)
% 231.54/42.84    (14)  all_55_13 = all_53_7
% 231.54/42.84    (15)  op(all_52_19, all_52_19) = e2
% 231.54/42.84    (16)   ~ (all_52_19 = e1)
% 231.54/42.84    (17)  all_55_14 = all_53_11
% 231.54/42.84  
% 231.54/42.84  Begin of proof
% 231.54/42.84  | 
% 231.54/42.84  | BETA: splitting (7) gives:
% 231.54/42.84  | 
% 231.54/42.84  | Case 1:
% 231.54/42.84  | | 
% 231.54/42.84  | |   (18)  all_55_14 = e2
% 231.54/42.84  | | 
% 231.54/42.84  | | COMBINE_EQS: (17), (18) imply:
% 231.54/42.84  | |   (19)  all_53_11 = e2
% 231.54/42.84  | | 
% 231.54/42.84  | | SIMP: (19) implies:
% 231.54/42.84  | |   (20)  all_53_11 = e2
% 231.54/42.84  | | 
% 231.54/42.84  | | REDUCE: (11), (20) imply:
% 231.54/42.84  | |   (21)   ~ (all_53_7 = e2)
% 231.54/42.84  | | 
% 231.54/42.84  | | BETA: splitting (1) gives:
% 231.54/42.84  | | 
% 231.54/42.84  | | Case 1:
% 231.54/42.84  | | | 
% 231.54/42.84  | | |   (22)  all_55_13 = e3
% 231.54/42.84  | | | 
% 231.54/42.84  | | | COMBINE_EQS: (14), (22) imply:
% 231.54/42.84  | | |   (23)  all_53_7 = e3
% 231.54/42.84  | | | 
% 231.54/42.84  | | | SIMP: (23) implies:
% 231.54/42.84  | | |   (24)  all_53_7 = e3
% 231.54/42.84  | | | 
% 231.54/42.84  | | | REDUCE: (2), (24) imply:
% 231.54/42.84  | | |   (25)   ~ (all_52_19 = e3)
% 231.54/42.84  | | | 
% 231.54/42.84  | | | SIMP: (25) implies:
% 231.54/42.84  | | |   (26)   ~ (all_52_19 = e3)
% 231.54/42.84  | | | 
% 231.54/42.84  | | | BETA: splitting (8) gives:
% 231.54/42.84  | | | 
% 231.54/42.84  | | | Case 1:
% 231.54/42.84  | | | | 
% 231.54/42.84  | | | |   (27)  all_55_9 = e3
% 231.54/42.84  | | | | 
% 231.54/42.84  | | | | REF_CLOSE: (5), (26), (27) are inconsistent by sub-proof #1603.
% 231.54/42.84  | | | | 
% 231.54/42.84  | | | Case 2:
% 231.54/42.84  | | | | 
% 231.54/42.84  | | | |   (28)  all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 231.54/42.84  | | | | 
% 231.54/42.84  | | | | REF_CLOSE: (3), (5), (6), (12), (15), (16), (28) are inconsistent by
% 231.54/42.84  | | | |            sub-proof #1602.
% 231.54/42.84  | | | | 
% 231.54/42.84  | | | End of split
% 231.54/42.84  | | | 
% 231.54/42.84  | | Case 2:
% 231.54/42.84  | | | 
% 231.54/42.84  | | |   (29)  all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 231.54/42.84  | | | 
% 231.54/42.84  | | | REF_CLOSE: (4), (10), (14), (21), (29) are inconsistent by sub-proof
% 231.54/42.84  | | |            #1601.
% 231.54/42.84  | | | 
% 231.54/42.84  | | End of split
% 231.54/42.84  | | 
% 231.54/42.84  | Case 2:
% 231.54/42.84  | | 
% 231.54/42.84  | |   (30)  all_55_14 = e1 | all_55_14 = e0
% 231.54/42.84  | | 
% 231.54/42.84  | | REF_CLOSE: (9), (13), (17), (30) are inconsistent by sub-proof #1720.
% 231.54/42.84  | | 
% 231.54/42.84  | End of split
% 231.54/42.84  | 
% 231.54/42.84  End of proof
% 231.54/42.84  
% 231.54/42.84  Sub-proof #1601 shows that the following formulas are inconsistent:
% 231.54/42.84  ----------------------------------------------------------------
% 231.54/42.84    (1)   ~ (all_53_7 = e1)
% 231.54/42.84    (2)   ~ (all_53_7 = e2)
% 231.54/42.84    (3)  all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 231.54/42.84    (4)   ~ (all_53_7 = e0)
% 231.54/42.84    (5)  all_55_13 = all_53_7
% 231.54/42.84  
% 231.54/42.84  Begin of proof
% 231.54/42.84  | 
% 231.54/42.84  | BETA: splitting (3) gives:
% 231.54/42.84  | 
% 231.54/42.84  | Case 1:
% 231.54/42.84  | | 
% 231.54/42.84  | |   (6)  all_55_13 = e2
% 231.54/42.84  | | 
% 231.54/42.84  | | REF_CLOSE: (2), (5), (6) are inconsistent by sub-proof #2287.
% 231.54/42.84  | | 
% 231.54/42.84  | Case 2:
% 231.54/42.84  | | 
% 231.54/42.84  | |   (7)  all_55_13 = e1 | all_55_13 = e0
% 231.54/42.84  | | 
% 231.54/42.84  | | REF_CLOSE: (1), (4), (5), (7) are inconsistent by sub-proof #1837.
% 231.54/42.84  | | 
% 231.54/42.84  | End of split
% 231.54/42.84  | 
% 231.54/42.84  End of proof
% 231.54/42.84  
% 231.54/42.84  Sub-proof #1602 shows that the following formulas are inconsistent:
% 231.54/42.84  ----------------------------------------------------------------
% 231.54/42.84    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.84           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.84    (2)  all_55_9 = all_52_19
% 231.54/42.84    (3)  op(e2, e2) = e1
% 231.54/42.84    (4)  all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 231.54/42.84    (5)   ~ (all_52_19 = e0)
% 231.54/42.84    (6)  op(all_52_19, all_52_19) = e2
% 231.54/42.84    (7)   ~ (all_52_19 = e1)
% 231.54/42.84  
% 231.54/42.84  Begin of proof
% 231.54/42.84  | 
% 231.54/42.84  | BETA: splitting (4) gives:
% 231.54/42.84  | 
% 231.54/42.84  | Case 1:
% 231.54/42.84  | | 
% 231.54/42.84  | |   (8)  all_55_9 = e2
% 231.54/42.84  | | 
% 231.54/42.84  | | COMBINE_EQS: (2), (8) imply:
% 231.54/42.84  | |   (9)  all_52_19 = e2
% 231.54/42.84  | | 
% 231.54/42.84  | | SIMP: (9) implies:
% 231.54/42.84  | |   (10)  all_52_19 = e2
% 231.54/42.84  | | 
% 231.54/42.84  | | REDUCE: (7), (10) imply:
% 231.54/42.84  | |   (11)   ~ (e2 = e1)
% 231.54/42.84  | | 
% 231.54/42.84  | | REDUCE: (6), (10) imply:
% 231.54/42.84  | |   (12)  op(e2, e2) = e2
% 231.54/42.84  | | 
% 231.54/42.84  | | REF_CLOSE: (1), (3), (11), (12) are inconsistent by sub-proof #2306.
% 231.54/42.84  | | 
% 231.54/42.84  | Case 2:
% 231.54/42.84  | | 
% 231.54/42.84  | |   (13)  all_55_9 = e1 | all_55_9 = e0
% 231.54/42.84  | | 
% 231.54/42.84  | | REF_CLOSE: (2), (5), (7), (13) are inconsistent by sub-proof #1883.
% 231.54/42.84  | | 
% 231.54/42.84  | End of split
% 231.54/42.84  | 
% 231.54/42.84  End of proof
% 231.54/42.84  
% 231.54/42.84  Sub-proof #1603 shows that the following formulas are inconsistent:
% 231.54/42.84  ----------------------------------------------------------------
% 231.54/42.84    (1)  all_55_9 = all_52_19
% 231.54/42.84    (2)  all_55_9 = e3
% 231.54/42.84    (3)   ~ (all_52_19 = e3)
% 231.54/42.84  
% 231.54/42.84  Begin of proof
% 231.54/42.84  | 
% 231.54/42.84  | COMBINE_EQS: (1), (2) imply:
% 231.54/42.84  |   (4)  all_52_19 = e3
% 231.54/42.84  | 
% 231.54/42.84  | SIMP: (4) implies:
% 231.54/42.84  |   (5)  all_52_19 = e3
% 231.54/42.84  | 
% 231.54/42.84  | REDUCE: (3), (5) imply:
% 231.54/42.84  |   (6)  $false
% 231.54/42.84  | 
% 231.54/42.84  | CLOSE: (6) is inconsistent.
% 231.54/42.84  | 
% 231.54/42.84  End of proof
% 231.54/42.84  
% 231.54/42.84  Sub-proof #1604 shows that the following formulas are inconsistent:
% 231.54/42.84  ----------------------------------------------------------------
% 231.54/42.84    (1)   ~ (e3 = e1)
% 231.54/42.84    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.84           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.84    (3)  all_57_4 = e2
% 231.54/42.84    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.54/42.84         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.54/42.84    (5)  all_57_9 = e1
% 231.54/42.84    (6)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.54/42.84         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.54/42.84    (7)   ~ (e3 = e2)
% 231.54/42.84    (8)   ~ (e3 = e0)
% 231.54/42.84    (9)  op(e3, e3) = e2
% 231.54/42.84    (10)   ~ (e2 = e0)
% 231.54/42.84    (11)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 231.54/42.84          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.54/42.84    (12)   ~ (e1 = e0)
% 231.54/42.84    (13)   ~ (e2 = e1)
% 231.54/42.84  
% 231.54/42.84  Begin of proof
% 231.54/42.84  | 
% 231.54/42.84  | BETA: splitting (6) gives:
% 231.54/42.84  | 
% 231.54/42.84  | Case 1:
% 231.54/42.84  | | 
% 231.54/42.84  | |   (14)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) =
% 231.54/42.84  | |           e0)
% 231.54/42.84  | | 
% 231.54/42.84  | | BETA: splitting (14) gives:
% 231.54/42.84  | | 
% 231.54/42.84  | | Case 1:
% 231.54/42.84  | | | 
% 231.54/42.84  | | |   (15)  all_57_0 = e0 & op(e3, e3) = e0
% 231.54/42.84  | | | 
% 231.54/42.84  | | | ALPHA: (15) implies:
% 231.54/42.84  | | |   (16)  op(e3, e3) = e0
% 231.54/42.84  | | | 
% 231.54/42.84  | | | REF_CLOSE: (2), (9), (10), (16) are inconsistent by sub-proof #2403.
% 231.54/42.84  | | | 
% 231.54/42.84  | | Case 2:
% 231.54/42.84  | | | 
% 231.54/42.84  | | |   (17)  all_57_1 = e0 & op(e3, e2) = e0
% 231.54/42.84  | | | 
% 231.54/42.84  | | | ALPHA: (17) implies:
% 231.54/42.84  | | |   (18)  all_57_1 = e0
% 231.54/42.84  | | | 
% 231.54/42.84  | | | REF_CLOSE: (1), (2), (3), (5), (7), (8), (9), (11), (18) are inconsistent
% 231.54/42.84  | | |            by sub-proof #1608.
% 231.54/42.84  | | | 
% 231.54/42.84  | | End of split
% 231.54/42.84  | | 
% 231.54/42.84  | Case 2:
% 231.54/42.84  | | 
% 231.54/42.84  | |   (19)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) =
% 231.54/42.84  | |           e0)
% 231.54/42.84  | | 
% 231.54/42.84  | | REF_CLOSE: (1), (2), (3), (4), (7), (8), (9), (10), (11), (12), (13), (19)
% 231.54/42.84  | |            are inconsistent by sub-proof #1605.
% 231.54/42.84  | | 
% 231.54/42.84  | End of split
% 231.54/42.84  | 
% 231.54/42.84  End of proof
% 231.54/42.84  
% 231.54/42.84  Sub-proof #1605 shows that the following formulas are inconsistent:
% 231.54/42.84  ----------------------------------------------------------------
% 231.54/42.84    (1)   ~ (e3 = e1)
% 231.54/42.84    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.84           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.84    (3)  all_57_4 = e2
% 231.54/42.84    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.54/42.84         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.54/42.84    (5)   ~ (e3 = e2)
% 231.54/42.84    (6)   ~ (e3 = e0)
% 231.54/42.84    (7)  op(e3, e3) = e2
% 231.54/42.84    (8)   ~ (e2 = e0)
% 231.54/42.84    (9)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 231.54/42.84         (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.54/42.84    (10)   ~ (e1 = e0)
% 231.54/42.84    (11)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.54/42.84    (12)   ~ (e2 = e1)
% 231.54/42.84  
% 231.54/42.84  Begin of proof
% 231.54/42.84  | 
% 231.54/42.84  | BETA: splitting (11) gives:
% 231.54/42.84  | 
% 231.54/42.84  | Case 1:
% 231.54/42.84  | | 
% 231.54/42.84  | |   (13)  all_57_4 = e0 & op(e3, e1) = e0
% 231.54/42.84  | | 
% 231.54/42.84  | | REF_CLOSE: (3), (8), (13) are inconsistent by sub-proof #2045.
% 231.54/42.84  | | 
% 231.54/42.84  | Case 2:
% 231.54/42.84  | | 
% 231.54/42.84  | |   (14)  all_57_9 = e0 & op(e3, e0) = e0
% 231.54/42.84  | | 
% 231.54/42.84  | | ALPHA: (14) implies:
% 231.54/42.84  | |   (15)  all_57_9 = e0
% 231.54/42.84  | | 
% 231.54/42.84  | | BETA: splitting (9) gives:
% 231.54/42.84  | | 
% 231.54/42.84  | | Case 1:
% 231.54/42.84  | | | 
% 231.54/42.84  | | |   (16)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) =
% 231.54/42.84  | | |           e3)
% 231.54/42.84  | | | 
% 231.54/42.84  | | | BETA: splitting (16) gives:
% 231.54/42.84  | | | 
% 231.54/42.84  | | | Case 1:
% 231.54/42.84  | | | | 
% 231.54/42.84  | | | |   (17)  all_57_0 = e3 & op(e3, e3) = e3
% 231.54/42.84  | | | | 
% 231.54/42.84  | | | | ALPHA: (17) implies:
% 231.54/42.84  | | | |   (18)  op(e3, e3) = e3
% 231.54/42.84  | | | | 
% 231.54/42.84  | | | | REF_CLOSE: (2), (5), (7), (18) are inconsistent by sub-proof #2490.
% 231.54/42.84  | | | | 
% 231.54/42.84  | | | Case 2:
% 231.54/42.84  | | | | 
% 231.54/42.84  | | | |   (19)  all_57_1 = e3 & op(e3, e2) = e3
% 231.54/42.84  | | | | 
% 231.54/42.84  | | | | ALPHA: (19) implies:
% 231.54/42.84  | | | |   (20)  all_57_1 = e3
% 231.54/42.84  | | | | 
% 231.54/42.84  | | | | BETA: splitting (4) gives:
% 231.54/42.84  | | | | 
% 231.54/42.84  | | | | Case 1:
% 231.54/42.84  | | | | | 
% 231.54/42.84  | | | | |   (21)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3,
% 231.54/42.84  | | | | |             e2) = e1)
% 231.54/42.84  | | | | | 
% 231.54/42.84  | | | | | REF_CLOSE: (1), (2), (7), (12), (20), (21) are inconsistent by
% 231.54/42.84  | | | | |            sub-proof #1607.
% 231.54/42.84  | | | | | 
% 231.54/42.84  | | | | Case 2:
% 231.54/42.84  | | | | | 
% 231.54/42.84  | | | | |   (22)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3,
% 231.54/42.84  | | | | |             e0) = e1)
% 231.54/42.84  | | | | | 
% 231.54/42.84  | | | | | REF_CLOSE: (3), (10), (12), (15), (22) are inconsistent by sub-proof
% 231.54/42.84  | | | | |            #1606.
% 231.54/42.84  | | | | | 
% 231.54/42.84  | | | | End of split
% 231.54/42.84  | | | | 
% 231.54/42.84  | | | End of split
% 231.54/42.84  | | | 
% 231.54/42.84  | | Case 2:
% 231.54/42.84  | | | 
% 231.54/42.84  | | |   (23)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) =
% 231.54/42.84  | | |           e3)
% 231.54/42.84  | | | 
% 231.54/42.84  | | | BETA: splitting (23) gives:
% 231.54/42.84  | | | 
% 231.54/42.84  | | | Case 1:
% 231.54/42.84  | | | | 
% 231.54/42.84  | | | |   (24)  all_57_4 = e3 & op(e3, e1) = e3
% 231.54/42.84  | | | | 
% 231.54/42.84  | | | | ALPHA: (24) implies:
% 231.54/42.84  | | | |   (25)  all_57_4 = e3
% 231.54/42.84  | | | | 
% 231.54/42.84  | | | | REF_CLOSE: (3), (5), (25) are inconsistent by sub-proof #2482.
% 231.54/42.84  | | | | 
% 231.54/42.84  | | | Case 2:
% 231.54/42.84  | | | | 
% 231.54/42.84  | | | |   (26)  all_57_9 = e3 & op(e3, e0) = e3
% 231.54/42.84  | | | | 
% 231.54/42.84  | | | | ALPHA: (26) implies:
% 231.54/42.84  | | | |   (27)  all_57_9 = e3
% 231.54/42.84  | | | | 
% 231.54/42.84  | | | | REF_CLOSE: (6), (15), (27) are inconsistent by sub-proof #1657.
% 231.54/42.84  | | | | 
% 231.54/42.84  | | | End of split
% 231.54/42.84  | | | 
% 231.54/42.84  | | End of split
% 231.54/42.84  | | 
% 231.54/42.84  | End of split
% 231.54/42.84  | 
% 231.54/42.84  End of proof
% 231.54/42.84  
% 231.54/42.84  Sub-proof #1606 shows that the following formulas are inconsistent:
% 231.54/42.84  ----------------------------------------------------------------
% 231.54/42.84    (1)  all_57_4 = e2
% 231.54/42.84    (2)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.54/42.84    (3)  all_57_9 = e0
% 231.54/42.84    (4)   ~ (e1 = e0)
% 231.54/42.84    (5)   ~ (e2 = e1)
% 231.54/42.84  
% 231.54/42.84  Begin of proof
% 231.54/42.84  | 
% 231.54/42.84  | BETA: splitting (2) gives:
% 231.54/42.84  | 
% 231.54/42.84  | Case 1:
% 231.54/42.84  | | 
% 231.54/42.84  | |   (6)  all_57_4 = e1 & op(e3, e1) = e1
% 231.54/42.84  | | 
% 231.54/42.84  | | REF_CLOSE: (1), (5), (6) are inconsistent by sub-proof #2452.
% 231.54/42.84  | | 
% 231.54/42.84  | Case 2:
% 231.54/42.84  | | 
% 231.54/42.84  | |   (7)  all_57_9 = e1 & op(e3, e0) = e1
% 231.54/42.84  | | 
% 231.54/42.84  | | ALPHA: (7) implies:
% 231.54/42.84  | |   (8)  all_57_9 = e1
% 231.54/42.84  | | 
% 231.54/42.84  | | REF_CLOSE: (3), (4), (8) are inconsistent by sub-proof #2479.
% 231.54/42.84  | | 
% 231.54/42.84  | End of split
% 231.54/42.84  | 
% 231.54/42.84  End of proof
% 231.54/42.84  
% 231.54/42.84  Sub-proof #1607 shows that the following formulas are inconsistent:
% 231.54/42.84  ----------------------------------------------------------------
% 231.54/42.84    (1)   ~ (e3 = e1)
% 231.54/42.84    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.84           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.84    (3)  op(e3, e3) = e2
% 231.54/42.84    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1)
% 231.54/42.84    (5)  all_57_1 = e3
% 231.54/42.84    (6)   ~ (e2 = e1)
% 231.54/42.84  
% 231.54/42.84  Begin of proof
% 231.54/42.84  | 
% 231.54/42.84  | BETA: splitting (4) gives:
% 231.54/42.84  | 
% 231.54/42.84  | Case 1:
% 231.54/42.84  | | 
% 231.54/42.84  | |   (7)  all_57_0 = e1 & op(e3, e3) = e1
% 231.54/42.84  | | 
% 231.54/42.84  | | ALPHA: (7) implies:
% 231.54/42.84  | |   (8)  op(e3, e3) = e1
% 231.54/42.84  | | 
% 231.54/42.84  | | REF_CLOSE: (2), (3), (6), (8) are inconsistent by sub-proof #1950.
% 231.54/42.84  | | 
% 231.54/42.84  | Case 2:
% 231.54/42.84  | | 
% 231.54/42.84  | |   (9)  all_57_1 = e1 & op(e3, e2) = e1
% 231.54/42.84  | | 
% 231.54/42.84  | | REF_CLOSE: (1), (5), (9) are inconsistent by sub-proof #2453.
% 231.54/42.84  | | 
% 231.54/42.84  | End of split
% 231.54/42.84  | 
% 231.54/42.84  End of proof
% 231.54/42.84  
% 231.54/42.84  Sub-proof #1608 shows that the following formulas are inconsistent:
% 231.54/42.84  ----------------------------------------------------------------
% 231.54/42.84    (1)   ~ (e3 = e1)
% 231.54/42.84    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.84           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.84    (3)  all_57_4 = e2
% 231.54/42.84    (4)  all_57_9 = e1
% 231.54/42.84    (5)   ~ (e3 = e2)
% 231.54/42.84    (6)   ~ (e3 = e0)
% 231.54/42.84    (7)  all_57_1 = e0
% 231.54/42.84    (8)  op(e3, e3) = e2
% 231.54/42.84    (9)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 231.54/42.84         (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.54/42.84  
% 231.54/42.84  Begin of proof
% 231.54/42.84  | 
% 231.54/42.84  | BETA: splitting (9) gives:
% 231.54/42.84  | 
% 231.54/42.84  | Case 1:
% 231.54/42.84  | | 
% 231.54/42.84  | |   (10)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) =
% 231.54/42.84  | |           e3)
% 231.54/42.84  | | 
% 231.54/42.84  | | REF_CLOSE: (2), (5), (6), (7), (8), (10) are inconsistent by sub-proof
% 231.54/42.84  | |            #1610.
% 231.54/42.84  | | 
% 231.54/42.84  | Case 2:
% 231.54/42.84  | | 
% 231.54/42.84  | |   (11)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) =
% 231.54/42.84  | |           e3)
% 231.54/42.84  | | 
% 231.54/42.84  | | REF_CLOSE: (1), (3), (4), (5), (11) are inconsistent by sub-proof #1609.
% 231.54/42.84  | | 
% 231.54/42.84  | End of split
% 231.54/42.84  | 
% 231.54/42.84  End of proof
% 231.54/42.84  
% 231.54/42.84  Sub-proof #1609 shows that the following formulas are inconsistent:
% 231.54/42.84  ----------------------------------------------------------------
% 231.54/42.84    (1)   ~ (e3 = e1)
% 231.54/42.84    (2)  all_57_4 = e2
% 231.54/42.84    (3)  all_57_9 = e1
% 231.54/42.84    (4)   ~ (e3 = e2)
% 231.54/42.84    (5)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.54/42.84  
% 231.54/42.84  Begin of proof
% 231.54/42.84  | 
% 231.54/42.84  | BETA: splitting (5) gives:
% 231.54/42.84  | 
% 231.54/42.84  | Case 1:
% 231.54/42.84  | | 
% 231.54/42.84  | |   (6)  all_57_4 = e3 & op(e3, e1) = e3
% 231.54/42.84  | | 
% 231.54/42.84  | | ALPHA: (6) implies:
% 231.54/42.84  | |   (7)  all_57_4 = e3
% 231.54/42.84  | | 
% 231.54/42.84  | | REF_CLOSE: (2), (4), (7) are inconsistent by sub-proof #2482.
% 231.54/42.84  | | 
% 231.54/42.84  | Case 2:
% 231.54/42.84  | | 
% 231.54/42.84  | |   (8)  all_57_9 = e3 & op(e3, e0) = e3
% 231.54/42.84  | | 
% 231.54/42.84  | | ALPHA: (8) implies:
% 231.54/42.84  | |   (9)  all_57_9 = e3
% 231.54/42.84  | | 
% 231.54/42.84  | | REF_CLOSE: (1), (3), (9) are inconsistent by sub-proof #1673.
% 231.54/42.84  | | 
% 231.54/42.84  | End of split
% 231.54/42.84  | 
% 231.54/42.84  End of proof
% 231.54/42.84  
% 231.54/42.84  Sub-proof #1610 shows that the following formulas are inconsistent:
% 231.54/42.84  ----------------------------------------------------------------
% 231.54/42.84    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.84           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.84    (2)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3)
% 231.54/42.84    (3)   ~ (e3 = e2)
% 231.54/42.84    (4)   ~ (e3 = e0)
% 231.54/42.84    (5)  all_57_1 = e0
% 231.54/42.84    (6)  op(e3, e3) = e2
% 231.54/42.84  
% 231.54/42.84  Begin of proof
% 231.54/42.84  | 
% 231.54/42.84  | BETA: splitting (2) gives:
% 231.54/42.84  | 
% 231.54/42.84  | Case 1:
% 231.54/42.84  | | 
% 231.54/42.84  | |   (7)  all_57_0 = e3 & op(e3, e3) = e3
% 231.54/42.84  | | 
% 231.54/42.84  | | ALPHA: (7) implies:
% 231.54/42.84  | |   (8)  op(e3, e3) = e3
% 231.54/42.84  | | 
% 231.54/42.84  | | REF_CLOSE: (1), (3), (6), (8) are inconsistent by sub-proof #2490.
% 231.54/42.84  | | 
% 231.54/42.84  | Case 2:
% 231.54/42.84  | | 
% 231.54/42.84  | |   (9)  all_57_1 = e3 & op(e3, e2) = e3
% 231.54/42.84  | | 
% 231.54/42.84  | | REF_CLOSE: (4), (5), (9) are inconsistent by sub-proof #2405.
% 231.54/42.84  | | 
% 231.54/42.84  | End of split
% 231.54/42.84  | 
% 231.54/42.84  End of proof
% 231.54/42.84  
% 231.54/42.84  Sub-proof #1611 shows that the following formulas are inconsistent:
% 231.54/42.84  ----------------------------------------------------------------
% 231.54/42.84    (1)  all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 231.54/42.84    (2)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 231.54/42.84    (3)   ~ (all_53_6 = all_53_14)
% 231.54/42.84    (4)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 231.54/42.84    (5)  op(e3, e1) = e0
% 231.54/42.84    (6)  all_57_15 = e0
% 231.54/42.84    (7)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.84         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.54/42.84    (8)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.54/42.84         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.54/42.84    (9)   ~ (all_53_8 = all_53_12)
% 231.54/42.84    (10)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.84          (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.54/42.84    (11)   ~ (e3 = e1)
% 231.54/42.84    (12)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 231.54/42.84          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.54/42.84    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.84            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.84    (14)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.54/42.84          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.54/42.84    (15)   ~ (all_6_2 = e3)
% 231.54/42.84    (16)  op(e1, e1) = all_6_2
% 231.54/42.84    (17)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 231.54/42.84    (18)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 231.54/42.84    (19)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.54/42.84          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.54/42.84    (20)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 231.54/42.84    (21)  all_55_9 = all_53_6
% 231.54/42.84    (22)   ~ (all_53_4 = all_53_12)
% 231.54/42.84    (23)  all_57_4 = e0
% 231.54/42.84    (24)  op(e2, e2) = e0
% 231.54/42.84    (25)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.54/42.84          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.54/42.84    (26)   ~ (all_53_14 = all_6_2)
% 231.54/42.84    (27)  all_57_3 = e0
% 231.54/42.84    (28)   ~ (e3 = e2)
% 231.54/42.84    (29)  all_55_1 = all_53_4
% 231.54/42.84    (30)   ~ (all_53_6 = all_53_7)
% 231.54/42.84    (31)   ~ (e3 = e0)
% 231.54/42.85    (32)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.54/42.85          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.54/42.85    (33)   ~ (all_53_8 = all_6_2)
% 231.54/42.85    (34)  op(e0, e3) = all_53_3
% 231.54/42.85    (35)   ~ (all_53_4 = all_53_7)
% 231.54/42.85    (36)  op(e3, e3) = e2
% 231.54/42.85    (37)   ~ (all_53_3 = e2)
% 231.54/42.85    (38)   ~ (all_53_7 = e0)
% 231.54/42.85    (39)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.54/42.85          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.54/42.85            e1)
% 231.54/42.85    (40)   ~ (all_53_4 = all_53_8)
% 231.54/42.85    (41)   ~ (e2 = e0)
% 231.54/42.85    (42)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 231.54/42.85            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 231.54/42.85            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 231.54/42.85            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 231.54/42.85              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 231.54/42.85            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 231.54/42.85            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 231.54/42.85              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 231.54/42.85              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 231.54/42.85            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 231.54/42.85            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 231.54/42.85            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 231.54/42.85              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 231.54/42.85              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 231.54/42.85            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 231.54/42.85              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 231.54/42.85            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 231.54/42.85            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 231.54/42.85              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 231.54/42.85              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 231.54/42.85            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 231.54/42.85            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 231.54/42.85    (43)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 231.54/42.85          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.54/42.85    (44)   ~ (all_53_2 = all_53_14)
% 231.54/42.85    (45)   ~ (e1 = e0)
% 231.54/42.85    (46)   ~ (all_38_2 = e2) | ( ~ (all_38_0 = e0) & op(all_38_1, e1) = all_38_0 &
% 231.54/42.85            op(e1, e2) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 231.54/42.85              e3) & op(e1, e2) = all_38_1 & $i(all_38_1))
% 231.54/42.85    (47)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.54/42.85          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.54/42.85    (48)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.54/42.85          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.54/42.85    (49)  op(e0, e0) = e0
% 231.54/42.85    (50)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.54/42.85          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 231.54/42.85            e3)
% 231.54/42.85    (51)   ~ (all_53_4 = all_53_6)
% 231.54/42.85    (52)  op(e0, e2) = all_53_7
% 231.54/42.85    (53)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.54/42.85          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.54/42.85            e2)
% 231.54/42.85    (54)   ~ (all_53_8 = e2)
% 231.54/42.85    (55)   ~ (all_53_3 = e0)
% 231.54/42.85    (56)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.54/42.85              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.54/42.85                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.54/42.85                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.54/42.85    (57)  all_55_10 = all_6_2
% 231.54/42.85    (58)   ~ (all_53_6 = all_6_2)
% 231.54/42.85    (59)  all_55_13 = all_53_7
% 231.54/42.85    (60)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.54/42.85          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.54/42.85    (61)  all_38_2 = all_6_2
% 231.54/42.85    (62)  all_55_11 = all_53_14
% 231.54/42.85    (63)  all_55_3 = all_53_12
% 231.54/42.85    (64)   ~ (all_53_4 = e2)
% 231.54/42.85    (65)  op(e1, e3) = all_53_2
% 231.54/42.85    (66)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.85          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.54/42.85    (67)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 231.54/42.85          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 231.54/42.85    (68)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 231.54/42.85          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 231.54/42.85    (69)   ~ (e2 = e1)
% 231.54/42.85    (70)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.54/42.85          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.54/42.85    (71)   ~ (all_53_2 = all_53_6)
% 231.54/42.85    (72)   ~ (all_53_12 = e2)
% 231.54/42.85    (73)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.54/42.85          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.54/42.85    (74)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.54/42.85          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.54/42.85    (75)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.54/42.85          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.54/42.85    (76)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 231.54/42.85          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 231.54/42.85    (77)   ~ (all_53_12 = all_53_14)
% 231.54/42.85    (78)  op(e3, e1) = all_53_8
% 231.54/42.85    (79)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.85          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.54/42.85    (80)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 231.54/42.85          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 231.54/42.85    (81)  op(e3, e0) = all_53_12
% 231.54/42.85  
% 231.54/42.85  Begin of proof
% 231.54/42.85  | 
% 231.54/42.85  | BETA: splitting (74) gives:
% 231.54/42.85  | 
% 231.54/42.85  | Case 1:
% 231.54/42.85  | | 
% 231.54/42.85  | |   (82)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) =
% 231.54/42.85  | |           e0)
% 231.54/42.85  | | 
% 231.54/42.85  | | REF_CLOSE: (7), (11), (13), (27), (28), (31), (36), (41), (45), (60), (66),
% 231.54/42.85  | |            (69), (82) are inconsistent by sub-proof #1654.
% 231.54/42.85  | | 
% 231.54/42.85  | Case 2:
% 231.54/42.85  | | 
% 231.54/42.85  | |   (83)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) =
% 231.54/42.85  | |           e0)
% 231.54/42.85  | | 
% 231.54/42.85  | | BETA: splitting (83) gives:
% 231.54/42.85  | | 
% 231.54/42.85  | | Case 1:
% 231.54/42.85  | | | 
% 231.54/42.85  | | |   (84)  all_57_6 = e0 & op(e1, e3) = e0
% 231.54/42.85  | | | 
% 231.54/42.85  | | | ALPHA: (84) implies:
% 231.54/42.85  | | |   (85)  all_57_6 = e0
% 231.54/42.85  | | |   (86)  op(e1, e3) = e0
% 231.54/42.85  | | | 
% 231.54/42.85  | | | GROUND_INST: instantiating (13) with all_53_2, e0, e3, e1, simplifying
% 231.54/42.85  | | |              with (65), (86) gives:
% 231.54/42.85  | | |   (87)  all_53_2 = e0
% 231.54/42.85  | | | 
% 231.54/42.85  | | | GROUND_INST: instantiating (13) with all_53_8, e0, e1, e3, simplifying
% 231.54/42.85  | | |              with (5), (78) gives:
% 231.54/42.85  | | |   (88)  all_53_8 = e0
% 231.54/42.85  | | | 
% 231.54/42.85  | | | REDUCE: (71), (87) imply:
% 231.54/42.85  | | |   (89)   ~ (all_53_6 = e0)
% 231.54/42.85  | | | 
% 231.54/42.85  | | | SIMP: (89) implies:
% 231.54/42.85  | | |   (90)   ~ (all_53_6 = e0)
% 231.54/42.85  | | | 
% 231.54/42.85  | | | REDUCE: (44), (87) imply:
% 231.54/42.85  | | |   (91)   ~ (all_53_14 = e0)
% 231.54/42.85  | | | 
% 231.54/42.85  | | | SIMP: (91) implies:
% 231.54/42.85  | | |   (92)   ~ (all_53_14 = e0)
% 231.54/42.85  | | | 
% 231.54/42.85  | | | REDUCE: (40), (88) imply:
% 231.54/42.85  | | |   (93)   ~ (all_53_4 = e0)
% 231.54/42.85  | | | 
% 231.54/42.85  | | | REDUCE: (9), (88) imply:
% 231.54/42.85  | | |   (94)   ~ (all_53_12 = e0)
% 231.54/42.85  | | | 
% 231.54/42.85  | | | SIMP: (94) implies:
% 231.54/42.85  | | |   (95)   ~ (all_53_12 = e0)
% 231.54/42.85  | | | 
% 231.54/42.85  | | | REDUCE: (33), (88) imply:
% 231.54/42.85  | | |   (96)   ~ (all_6_2 = e0)
% 231.54/42.85  | | | 
% 231.54/42.85  | | | SIMP: (96) implies:
% 231.54/42.85  | | |   (97)   ~ (all_6_2 = e0)
% 231.54/42.85  | | | 
% 231.54/42.85  | | | REDUCE: (54), (88) imply:
% 231.54/42.85  | | |   (98)   ~ (e2 = e0)
% 231.54/42.85  | | | 
% 231.54/42.85  | | | BETA: splitting (42) gives:
% 231.54/42.85  | | | 
% 231.54/42.85  | | | Case 1:
% 231.54/42.85  | | | | 
% 231.54/42.85  | | | |   (99)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 231.54/42.85  | | | |           op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 231.54/42.85  | | | |           op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 231.54/42.85  | | | |           op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) =
% 231.54/42.85  | | | |           all_52_5 & op(e3, e0) = all_52_7 & $i(all_52_1) & $i(all_52_3)
% 231.54/42.85  | | | |           & $i(all_52_5) & $i(all_52_7)) | (all_52_8 = e3 & all_52_10 =
% 231.54/42.85  | | | |           e2 & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9, all_52_9)
% 231.54/42.85  | | | |           = e3 & op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 231.54/42.85  | | | |             all_52_13) = e1 & op(all_52_15, all_52_15) = e0 & op(e2, e3)
% 231.54/42.85  | | | |           = all_52_9 & op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13 &
% 231.54/42.85  | | | |           op(e2, e0) = all_52_15 & $i(all_52_9) & $i(all_52_11) &
% 231.54/42.85  | | | |           $i(all_52_13) & $i(all_52_15))
% 231.54/42.85  | | | | 
% 231.54/42.85  | | | | BETA: splitting (99) gives:
% 231.54/42.85  | | | | 
% 231.54/42.85  | | | | Case 1:
% 231.54/42.85  | | | | | 
% 231.54/42.85  | | | | |   (100)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 231.54/42.85  | | | | |          & op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 231.54/42.85  | | | | |          op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 231.54/42.85  | | | | |          op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) =
% 231.54/42.85  | | | | |          all_52_5 & op(e3, e0) = all_52_7 & $i(all_52_1) &
% 231.54/42.85  | | | | |          $i(all_52_3) & $i(all_52_5) & $i(all_52_7)
% 231.54/42.85  | | | | | 
% 231.54/42.85  | | | | | ALPHA: (100) implies:
% 231.54/42.85  | | | | |   (101)  op(e3, e3) = all_52_1
% 231.54/42.85  | | | | |   (102)  op(all_52_1, all_52_1) = e3
% 231.54/42.85  | | | | | 
% 231.54/42.85  | | | | | REF_CLOSE: (13), (24), (31), (36), (101), (102) are inconsistent by
% 231.54/42.85  | | | | |            sub-proof #1653.
% 231.54/42.85  | | | | | 
% 231.54/42.85  | | | | Case 2:
% 231.54/42.85  | | | | | 
% 231.54/42.85  | | | | |   (103)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 231.54/42.85  | | | | |          e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11, all_52_11) =
% 231.54/42.85  | | | | |          e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15, all_52_15)
% 231.54/42.85  | | | | |          = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 231.54/42.85  | | | | |          op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 231.54/42.85  | | | | |          $i(all_52_9) & $i(all_52_11) & $i(all_52_13) & $i(all_52_15)
% 231.54/42.85  | | | | | 
% 231.54/42.85  | | | | | ALPHA: (103) implies:
% 231.54/42.85  | | | | |   (104)  op(e2, e2) = all_52_11
% 231.54/42.85  | | | | |   (105)  op(all_52_11, all_52_11) = e2
% 231.54/42.85  | | | | | 
% 231.54/42.85  | | | | | REF_CLOSE: (13), (24), (41), (49), (104), (105) are inconsistent by
% 231.54/42.85  | | | | |            sub-proof #2270.
% 231.54/42.85  | | | | | 
% 231.54/42.85  | | | | End of split
% 231.54/42.85  | | | | 
% 231.54/42.85  | | | Case 2:
% 231.54/42.85  | | | | 
% 231.54/42.85  | | | |   (106)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 231.54/42.85  | | | |            e0 & op(all_52_17, all_52_17) = e3 & op(all_52_19, all_52_19)
% 231.54/42.85  | | | |            = e2 & op(all_52_21, all_52_21) = e1 & op(all_52_23,
% 231.54/42.85  | | | |              all_52_23) = e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 231.54/42.85  | | | |            all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23 &
% 231.54/42.85  | | | |            $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 231.54/42.85  | | | |            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28
% 231.54/42.85  | | | |            = e1 & all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 231.54/42.85  | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29, all_52_29) = e1
% 231.54/42.85  | | | |            & op(all_52_31, all_52_31) = e0 & op(e0, e3) = all_52_25 &
% 231.54/42.85  | | | |            op(e0, e2) = all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 231.54/42.85  | | | |            = all_52_31 & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 231.54/42.85  | | | |            $i(all_52_31))
% 231.54/42.85  | | | | 
% 231.54/42.85  | | | | BETA: splitting (106) gives:
% 231.54/42.85  | | | | 
% 231.54/42.85  | | | | Case 1:
% 231.54/42.85  | | | | | 
% 231.54/42.85  | | | | |   (107)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22
% 231.54/42.85  | | | | |          = e0 & op(all_52_17, all_52_17) = e3 & op(all_52_19,
% 231.54/42.85  | | | | |            all_52_19) = e2 & op(all_52_21, all_52_21) = e1 &
% 231.54/42.85  | | | | |          op(all_52_23, all_52_23) = e0 & op(e1, e3) = all_52_17 &
% 231.54/42.85  | | | | |          op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 231.54/42.85  | | | | |          = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 231.54/42.85  | | | | |          $i(all_52_23)
% 231.54/42.85  | | | | | 
% 231.54/42.85  | | | | | REF_CLOSE: (13), (31), (49), (86), (107) are inconsistent by sub-proof
% 231.54/42.85  | | | | |            #1652.
% 231.54/42.85  | | | | | 
% 231.54/42.85  | | | | Case 2:
% 231.54/42.85  | | | | | 
% 231.54/42.85  | | | | |   (108)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30
% 231.54/42.85  | | | | |          = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 231.54/42.85  | | | | |            all_52_27) = e2 & op(all_52_29, all_52_29) = e1 &
% 231.54/42.85  | | | | |          op(all_52_31, all_52_31) = e0 & op(e0, e3) = all_52_25 &
% 231.54/42.85  | | | | |          op(e0, e2) = all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 231.54/42.85  | | | | |          = all_52_31 & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 231.54/42.85  | | | | |          $i(all_52_31)
% 231.54/42.85  | | | | | 
% 231.54/42.85  | | | | | ALPHA: (108) implies:
% 231.54/42.85  | | | | |   (109)  op(e0, e0) = all_52_31
% 231.54/42.85  | | | | |   (110)  op(e0, e2) = all_52_27
% 231.54/42.85  | | | | |   (111)  op(all_52_31, all_52_31) = e0
% 231.54/42.85  | | | | |   (112)  op(all_52_27, all_52_27) = e2
% 231.54/42.85  | | | | | 
% 231.54/42.85  | | | | | GROUND_INST: instantiating (13) with e0, all_52_31, e0, e0,
% 231.54/42.85  | | | | |              simplifying with (49), (109) gives:
% 231.54/42.85  | | | | |   (113)  all_52_31 = e0
% 231.54/42.85  | | | | | 
% 231.54/42.85  | | | | | GROUND_INST: instantiating (13) with all_53_7, all_52_27, e2, e0,
% 231.54/42.85  | | | | |              simplifying with (52), (110) gives:
% 231.54/42.85  | | | | |   (114)  all_53_7 = all_52_27
% 231.54/42.85  | | | | | 
% 231.54/42.85  | | | | | COMBINE_EQS: (59), (114) imply:
% 231.54/42.85  | | | | |   (115)  all_55_13 = all_52_27
% 231.54/42.85  | | | | | 
% 231.54/42.85  | | | | | REDUCE: (35), (114) imply:
% 231.54/42.85  | | | | |   (116)   ~ (all_53_4 = all_52_27)
% 231.54/42.85  | | | | | 
% 231.54/42.85  | | | | | REDUCE: (30), (114) imply:
% 231.54/42.85  | | | | |   (117)   ~ (all_53_6 = all_52_27)
% 231.54/42.85  | | | | | 
% 231.54/42.85  | | | | | REDUCE: (38), (114) imply:
% 231.54/42.85  | | | | |   (118)   ~ (all_52_27 = e0)
% 231.54/42.85  | | | | | 
% 231.54/42.85  | | | | | BETA: splitting (46) gives:
% 231.54/42.85  | | | | | 
% 231.54/42.85  | | | | | Case 1:
% 231.54/42.85  | | | | | | 
% 231.54/42.85  | | | | | |   (119)   ~ (all_38_2 = e2)
% 231.54/42.85  | | | | | | 
% 231.54/42.85  | | | | | | REDUCE: (61), (119) imply:
% 231.54/42.85  | | | | | |   (120)   ~ (all_6_2 = e2)
% 231.54/42.85  | | | | | | 
% 231.54/42.85  | | | | | | BETA: splitting (4) gives:
% 231.54/42.85  | | | | | | 
% 231.54/42.85  | | | | | | Case 1:
% 231.54/42.85  | | | | | | | 
% 231.54/42.85  | | | | | | |   (121)  all_55_10 = e3
% 231.54/42.85  | | | | | | | 
% 231.54/42.85  | | | | | | | REF_CLOSE: (15), (57), (121) are inconsistent by sub-proof #2500.
% 231.54/42.85  | | | | | | | 
% 231.54/42.85  | | | | | | Case 2:
% 231.54/42.85  | | | | | | | 
% 231.54/42.85  | | | | | | |   (122)   ~ (all_55_10 = e3)
% 231.54/42.85  | | | | | | |   (123)  all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 231.54/42.85  | | | | | | | 
% 231.54/42.85  | | | | | | | BETA: splitting (123) gives:
% 231.54/42.85  | | | | | | | 
% 231.54/42.85  | | | | | | | Case 1:
% 231.54/42.85  | | | | | | | | 
% 231.54/42.85  | | | | | | | |   (124)  all_55_10 = e2
% 231.54/42.85  | | | | | | | | 
% 231.54/42.85  | | | | | | | | REF_CLOSE: (57), (120), (124) are inconsistent by sub-proof
% 231.54/42.85  | | | | | | | |            #2499.
% 231.54/42.85  | | | | | | | | 
% 231.54/42.85  | | | | | | | Case 2:
% 231.54/42.85  | | | | | | | | 
% 231.54/42.85  | | | | | | | |   (125)   ~ (all_55_10 = e2)
% 231.54/42.85  | | | | | | | |   (126)  all_55_10 = e1 | all_55_10 = e0
% 231.54/42.85  | | | | | | | | 
% 231.54/42.85  | | | | | | | | BETA: splitting (126) gives:
% 231.54/42.85  | | | | | | | | 
% 231.54/42.85  | | | | | | | | Case 1:
% 231.54/42.85  | | | | | | | | | 
% 231.54/42.85  | | | | | | | | |   (127)  all_55_10 = e1
% 231.54/42.85  | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | COMBINE_EQS: (57), (127) imply:
% 231.54/42.85  | | | | | | | | |   (128)  all_6_2 = e1
% 231.54/42.85  | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | SIMP: (128) implies:
% 231.54/42.85  | | | | | | | | |   (129)  all_6_2 = e1
% 231.54/42.85  | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | REDUCE: (58), (129) imply:
% 231.54/42.85  | | | | | | | | |   (130)   ~ (all_53_6 = e1)
% 231.54/42.85  | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | REDUCE: (26), (129) imply:
% 231.54/42.85  | | | | | | | | |   (131)   ~ (all_53_14 = e1)
% 231.54/42.85  | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | REDUCE: (15), (129) imply:
% 231.54/42.85  | | | | | | | | |   (132)   ~ (e3 = e1)
% 231.54/42.85  | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | REDUCE: (120), (129) imply:
% 231.54/42.85  | | | | | | | | |   (133)   ~ (e2 = e1)
% 231.54/42.85  | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | REDUCE: (16), (129) imply:
% 231.54/42.85  | | | | | | | | |   (134)  op(e1, e1) = e1
% 231.54/42.85  | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | BETA: splitting (2) gives:
% 231.54/42.85  | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | Case 1:
% 231.54/42.85  | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | |   (135)  all_55_1 = e3
% 231.54/42.85  | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | COMBINE_EQS: (29), (135) imply:
% 231.54/42.85  | | | | | | | | | |   (136)  all_53_4 = e3
% 231.54/42.85  | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | SIMP: (136) implies:
% 231.54/42.85  | | | | | | | | | |   (137)  all_53_4 = e3
% 231.54/42.85  | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | REDUCE: (51), (137) imply:
% 231.54/42.85  | | | | | | | | | |   (138)   ~ (all_53_6 = e3)
% 231.54/42.85  | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | SIMP: (138) implies:
% 231.54/42.85  | | | | | | | | | |   (139)   ~ (all_53_6 = e3)
% 231.54/42.85  | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | REDUCE: (22), (137) imply:
% 231.54/42.85  | | | | | | | | | |   (140)   ~ (all_53_12 = e3)
% 231.54/42.85  | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | SIMP: (140) implies:
% 231.54/42.85  | | | | | | | | | |   (141)   ~ (all_53_12 = e3)
% 231.54/42.85  | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | REDUCE: (116), (137) imply:
% 231.54/42.85  | | | | | | | | | |   (142)   ~ (all_52_27 = e3)
% 231.54/42.85  | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | SIMP: (142) implies:
% 231.54/42.85  | | | | | | | | | |   (143)   ~ (all_52_27 = e3)
% 231.54/42.85  | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | BETA: splitting (48) gives:
% 231.54/42.85  | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | Case 1:
% 231.54/42.85  | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | |   (144)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 231.54/42.85  | | | | | | | | | | |            & op(e2, e2) = e3)
% 231.54/42.85  | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | BETA: splitting (144) gives:
% 231.54/42.85  | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | Case 1:
% 231.54/42.85  | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | |   (145)  all_57_1 = e3 & op(e3, e2) = e3
% 231.54/42.85  | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | ALPHA: (145) implies:
% 231.54/42.85  | | | | | | | | | | | |   (146)  all_57_1 = e3
% 231.54/42.85  | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | BETA: splitting (79) gives:
% 231.54/42.85  | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | Case 1:
% 231.54/42.85  | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | |   (147)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 231.54/42.85  | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 231.54/42.85  | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | REF_CLOSE: (11), (13), (24), (45), (146), (147) are
% 231.54/42.85  | | | | | | | | | | | | |            inconsistent by sub-proof #2206.
% 231.54/42.85  | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | Case 2:
% 231.54/42.85  | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | |   (148)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 231.54/42.85  | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 231.54/42.85  | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | BETA: splitting (148) gives:
% 231.54/42.85  | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | Case 1:
% 231.54/42.85  | | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | |   (149)  all_57_7 = e1 & op(e1, e2) = e1
% 231.54/42.85  | | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | | ALPHA: (149) implies:
% 231.54/42.85  | | | | | | | | | | | | | |   (150)  all_57_7 = e1
% 231.54/42.85  | | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | | BETA: splitting (10) gives:
% 231.54/42.85  | | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | | Case 1:
% 231.54/42.85  | | | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | | |   (151)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 231.54/42.85  | | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 231.54/42.85  | | | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | | | REF_CLOSE: (11), (13), (19), (24), (25), (28), (31), (36),
% 231.54/42.85  | | | | | | | | | | | | | | |            (41), (43), (45), (69), (81), (141), (151) are
% 231.54/42.85  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1649.
% 231.54/42.85  | | | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | | Case 2:
% 231.54/42.85  | | | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | | |   (152)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 231.54/42.85  | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 231.54/42.85  | | | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | | | BETA: splitting (152) gives:
% 231.54/42.85  | | | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | | | Case 1:
% 231.54/42.85  | | | | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | | | |   (153)  all_57_7 = e2 & op(e1, e2) = e2
% 231.54/42.85  | | | | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | | | | ALPHA: (153) implies:
% 231.54/42.85  | | | | | | | | | | | | | | | |   (154)  all_57_7 = e2
% 231.54/42.85  | | | | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | | | | REF_CLOSE: (1), (6), (7), (10), (11), (13), (14), (15), (16),
% 231.54/42.85  | | | | | | | | | | | | | | | |            (19), (20), (21), (23), (24), (25), (27), (28),
% 231.54/42.85  | | | | | | | | | | | | | | | |            (31), (34), (36), (37), (41), (43), (45), (47),
% 231.54/42.85  | | | | | | | | | | | | | | | |            (48), (50), (53), (56), (60), (66), (68), (69),
% 231.54/42.85  | | | | | | | | | | | | | | | |            (70), (72), (74), (75), (76), (79), (81), (85),
% 231.54/42.85  | | | | | | | | | | | | | | | |            (90), (97), (109), (111), (112), (115), (117),
% 231.54/42.85  | | | | | | | | | | | | | | | |            (118), (130), (139), (143), (146), (154) are
% 231.54/42.85  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1635.
% 231.54/42.85  | | | | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | | | Case 2:
% 231.54/42.85  | | | | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | | | |   (155)  all_57_13 = e2 & op(e0, e2) = e2
% 231.54/42.85  | | | | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | | | | ALPHA: (155) implies:
% 231.54/42.85  | | | | | | | | | | | | | | | |   (156)  all_57_13 = e2
% 231.54/42.85  | | | | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | | | | BETA: splitting (80) gives:
% 231.54/42.85  | | | | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.85  | | | | | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | | | | |   (157)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 231.54/42.85  | | | | | | | | | | | | | | | | |            & op(e1, e2) = e2)
% 231.54/42.85  | | | | | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | | | | | BETA: splitting (157) gives:
% 231.54/42.85  | | | | | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.85  | | | | | | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | | | | | |   (158)  all_57_6 = e2 & op(e1, e3) = e2
% 231.54/42.85  | | | | | | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | | | | | | ALPHA: (158) implies:
% 231.54/42.85  | | | | | | | | | | | | | | | | | |   (159)  all_57_6 = e2
% 231.54/42.85  | | | | | | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (85), (159) imply:
% 231.54/42.85  | | | | | | | | | | | | | | | | | |   (160)  e2 = e0
% 231.54/42.85  | | | | | | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | | | | | | SIMP: (160) implies:
% 231.54/42.85  | | | | | | | | | | | | | | | | | |   (161)  e2 = e0
% 231.54/42.85  | | | | | | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (156), (161) imply:
% 231.54/42.85  | | | | | | | | | | | | | | | | | |   (162)  all_57_13 = e0
% 231.54/42.85  | | | | | | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (11), (27), (28), (41), (45), (69), (79),
% 231.54/42.85  | | | | | | | | | | | | | | | | | |            (146), (162) are inconsistent by sub-proof #1758.
% 231.54/42.85  | | | | | | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.85  | | | | | | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | | | | | |   (163)  all_57_7 = e2 & op(e1, e2) = e2
% 231.54/42.85  | | | | | | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | | | | | | ALPHA: (163) implies:
% 231.54/42.85  | | | | | | | | | | | | | | | | | |   (164)  all_57_7 = e2
% 231.54/42.85  | | | | | | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (27), (45), (69), (79), (146), (156), (164)
% 231.54/42.85  | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1698.
% 231.54/42.85  | | | | | | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | | | | | End of split
% 231.54/42.85  | | | | | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.85  | | | | | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | | | | |   (165)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 231.54/42.85  | | | | | | | | | | | | | | | | |            e2 & op(e1, e0) = e2)
% 231.54/42.85  | | | | | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | | | | | BETA: splitting (165) gives:
% 231.54/42.85  | | | | | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.85  | | | | | | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | | | | | |   (166)  all_57_8 = e2 & op(e1, e1) = e2
% 231.54/42.85  | | | | | | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | | | | | | ALPHA: (166) implies:
% 231.54/42.85  | | | | | | | | | | | | | | | | | |   (167)  op(e1, e1) = e2
% 231.54/42.85  | | | | | | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (8), (10), (11), (13), (14), (15), (16),
% 231.54/42.85  | | | | | | | | | | | | | | | | | |            (19), (23), (24), (25), (27), (28), (31), (32),
% 231.54/42.85  | | | | | | | | | | | | | | | | | |            (36), (41), (43), (45), (47), (48), (60), (66),
% 231.54/42.85  | | | | | | | | | | | | | | | | | |            (67), (69), (70), (72), (73), (74), (75), (76),
% 231.54/42.85  | | | | | | | | | | | | | | | | | |            (79), (81), (85), (110), (112), (118), (155),
% 231.54/42.85  | | | | | | | | | | | | | | | | | |            (156), (167) are inconsistent by sub-proof #1623.
% 231.54/42.85  | | | | | | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.85  | | | | | | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | | | | | |   (168)  all_57_11 = e2 & op(e1, e0) = e2
% 231.54/42.85  | | | | | | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | | | | | | ALPHA: (168) implies:
% 231.54/42.85  | | | | | | | | | | | | | | | | | |   (169)  all_57_11 = e2
% 231.54/42.85  | | | | | | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (12), (13), (14), (15), (16), (24), (27),
% 231.54/42.85  | | | | | | | | | | | | | | | | | |            (28), (31), (41), (45), (48), (69), (79), (134),
% 231.54/42.85  | | | | | | | | | | | | | | | | | |            (150), (156), (169) are inconsistent by sub-proof
% 231.54/42.85  | | | | | | | | | | | | | | | | | |            #1621.
% 231.54/42.85  | | | | | | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | | | | | End of split
% 231.54/42.85  | | | | | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | | | | End of split
% 231.54/42.85  | | | | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | | | End of split
% 231.54/42.85  | | | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | | End of split
% 231.54/42.85  | | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | Case 2:
% 231.54/42.85  | | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | |   (170)  all_57_13 = e1 & op(e0, e2) = e1
% 231.54/42.85  | | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | | ALPHA: (170) implies:
% 231.54/42.85  | | | | | | | | | | | | | |   (171)  all_57_13 = e1
% 231.54/42.85  | | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | | BETA: splitting (10) gives:
% 231.54/42.85  | | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | | Case 1:
% 231.54/42.85  | | | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | | |   (172)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 231.54/42.85  | | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 231.54/42.85  | | | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | | | REF_CLOSE: (11), (13), (19), (24), (25), (28), (31), (36),
% 231.54/42.85  | | | | | | | | | | | | | | |            (41), (43), (45), (69), (81), (141), (172) are
% 231.54/42.85  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1649.
% 231.54/42.85  | | | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | | Case 2:
% 231.54/42.85  | | | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | | |   (173)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 231.54/42.85  | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 231.54/42.85  | | | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | | | BETA: splitting (173) gives:
% 231.54/42.85  | | | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | | | Case 1:
% 231.54/42.85  | | | | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | | | |   (174)  all_57_7 = e2 & op(e1, e2) = e2
% 231.54/42.85  | | | | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | | | | ALPHA: (174) implies:
% 231.54/42.85  | | | | | | | | | | | | | | | |   (175)  all_57_7 = e2
% 231.54/42.85  | | | | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | | | | REF_CLOSE: (1), (6), (7), (10), (11), (13), (14), (15), (16),
% 231.54/42.85  | | | | | | | | | | | | | | | |            (19), (20), (21), (23), (24), (25), (27), (28),
% 231.54/42.85  | | | | | | | | | | | | | | | |            (31), (34), (36), (37), (41), (43), (45), (47),
% 231.54/42.85  | | | | | | | | | | | | | | | |            (48), (50), (53), (56), (60), (66), (68), (69),
% 231.54/42.85  | | | | | | | | | | | | | | | |            (70), (72), (74), (75), (76), (79), (81), (85),
% 231.54/42.85  | | | | | | | | | | | | | | | |            (90), (97), (109), (111), (112), (115), (117),
% 231.54/42.85  | | | | | | | | | | | | | | | |            (118), (130), (139), (143), (146), (175) are
% 231.54/42.85  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1635.
% 231.54/42.85  | | | | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | | | Case 2:
% 231.54/42.85  | | | | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | | | |   (176)  all_57_13 = e2 & op(e0, e2) = e2
% 231.54/42.85  | | | | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | | | | ALPHA: (176) implies:
% 231.54/42.85  | | | | | | | | | | | | | | | |   (177)  all_57_13 = e2
% 231.54/42.85  | | | | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | | | | REF_CLOSE: (69), (171), (177) are inconsistent by sub-proof
% 231.54/42.85  | | | | | | | | | | | | | | | |            #2327.
% 231.54/42.85  | | | | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | | | End of split
% 231.54/42.85  | | | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | | End of split
% 231.54/42.85  | | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | | End of split
% 231.54/42.85  | | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | End of split
% 231.54/42.85  | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | Case 2:
% 231.54/42.85  | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | |   (178)  all_57_3 = e3 & op(e2, e2) = e3
% 231.54/42.85  | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | ALPHA: (178) implies:
% 231.54/42.85  | | | | | | | | | | | |   (179)  all_57_3 = e3
% 231.54/42.85  | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | REF_CLOSE: (27), (31), (179) are inconsistent by sub-proof
% 231.54/42.85  | | | | | | | | | | | |            #2358.
% 231.54/42.85  | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | End of split
% 231.54/42.85  | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | Case 2:
% 231.54/42.85  | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | |   (180)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 231.54/42.85  | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 231.54/42.85  | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | BETA: splitting (180) gives:
% 231.54/42.85  | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | Case 1:
% 231.54/42.85  | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | |   (181)  all_57_7 = e3 & op(e1, e2) = e3
% 231.54/42.85  | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | ALPHA: (181) implies:
% 231.54/42.85  | | | | | | | | | | | |   (182)  all_57_7 = e3
% 231.54/42.85  | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | REF_CLOSE: (10), (11), (13), (19), (23), (24), (25), (27),
% 231.54/42.85  | | | | | | | | | | | |            (28), (31), (36), (41), (43), (45), (48), (69),
% 231.54/42.85  | | | | | | | | | | | |            (79), (81), (141), (182) are inconsistent by
% 231.54/42.85  | | | | | | | | | | | |            sub-proof #1619.
% 231.54/42.85  | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | Case 2:
% 231.54/42.85  | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | |   (183)  all_57_13 = e3 & op(e0, e2) = e3
% 231.54/42.85  | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | ALPHA: (183) implies:
% 231.54/42.85  | | | | | | | | | | | |   (184)  all_57_13 = e3
% 231.54/42.85  | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | REF_CLOSE: (10), (11), (13), (19), (23), (24), (25), (27),
% 231.54/42.85  | | | | | | | | | | | |            (28), (31), (36), (41), (43), (45), (48), (69),
% 231.54/42.85  | | | | | | | | | | | |            (79), (81), (141), (184) are inconsistent by
% 231.54/42.85  | | | | | | | | | | | |            sub-proof #1616.
% 231.54/42.85  | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | End of split
% 231.54/42.85  | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | End of split
% 231.54/42.85  | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | Case 2:
% 231.54/42.85  | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | |   (185)  all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 231.54/42.85  | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | BETA: splitting (185) gives:
% 231.54/42.85  | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | Case 1:
% 231.54/42.85  | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | |   (186)  all_55_1 = e2
% 231.54/42.85  | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | REF_CLOSE: (29), (64), (186) are inconsistent by sub-proof
% 231.54/42.85  | | | | | | | | | | |            #2284.
% 231.54/42.85  | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | Case 2:
% 231.54/42.85  | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | |   (187)  all_55_1 = e1 | all_55_1 = e0
% 231.54/42.85  | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | BETA: splitting (187) gives:
% 231.54/42.85  | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | Case 1:
% 231.54/42.85  | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | |   (188)  all_55_1 = e1
% 231.54/42.85  | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | COMBINE_EQS: (29), (188) imply:
% 231.54/42.85  | | | | | | | | | | | |   (189)  all_53_4 = e1
% 231.54/42.85  | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | SIMP: (189) implies:
% 231.54/42.85  | | | | | | | | | | | |   (190)  all_53_4 = e1
% 231.54/42.85  | | | | | | | | | | | | 
% 231.54/42.85  | | | | | | | | | | | | REDUCE: (51), (190) imply:
% 231.54/42.86  | | | | | | | | | | | |   (191)   ~ (all_53_6 = e1)
% 231.54/42.86  | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | REDUCE: (22), (190) imply:
% 231.54/42.86  | | | | | | | | | | | |   (192)   ~ (all_53_12 = e1)
% 231.54/42.86  | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | SIMP: (192) implies:
% 231.54/42.86  | | | | | | | | | | | |   (193)   ~ (all_53_12 = e1)
% 231.54/42.86  | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | REDUCE: (116), (190) imply:
% 231.54/42.86  | | | | | | | | | | | |   (194)   ~ (all_52_27 = e1)
% 231.54/42.86  | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | SIMP: (194) implies:
% 231.54/42.86  | | | | | | | | | | | |   (195)   ~ (all_52_27 = e1)
% 231.54/42.86  | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | BETA: splitting (17) gives:
% 231.54/42.86  | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | Case 1:
% 231.54/42.86  | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | |   (196)  all_55_3 = e3
% 231.54/42.86  | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | COMBINE_EQS: (63), (196) imply:
% 231.54/42.86  | | | | | | | | | | | | |   (197)  all_53_12 = e3
% 231.54/42.86  | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | SIMP: (197) implies:
% 231.54/42.86  | | | | | | | | | | | | |   (198)  all_53_12 = e3
% 231.54/42.86  | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | REDUCE: (81), (198) imply:
% 231.54/42.86  | | | | | | | | | | | | |   (199)  op(e3, e0) = e3
% 231.54/42.86  | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | BETA: splitting (17) gives:
% 231.54/42.86  | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | Case 1:
% 231.54/42.86  | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | REDUCE: (77), (198) imply:
% 231.54/42.86  | | | | | | | | | | | | | |   (200)   ~ (all_53_14 = e3)
% 231.54/42.86  | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | SIMP: (200) implies:
% 231.54/42.86  | | | | | | | | | | | | | |   (201)   ~ (all_53_14 = e3)
% 231.54/42.86  | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | BETA: splitting (18) gives:
% 231.54/42.86  | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | Case 1:
% 231.54/42.86  | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | |   (202)  all_55_11 = e3
% 231.54/42.86  | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | COMBINE_EQS: (62), (202) imply:
% 231.54/42.86  | | | | | | | | | | | | | | |   (203)  all_53_14 = e3
% 231.54/42.86  | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | REDUCE: (201), (203) imply:
% 231.54/42.86  | | | | | | | | | | | | | | |   (204)  $false
% 231.54/42.86  | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | CLOSE: (204) is inconsistent.
% 231.54/42.86  | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | Case 2:
% 231.54/42.86  | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | |   (205)  all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 231.54/42.86  | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | BETA: splitting (205) gives:
% 231.54/42.86  | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | Case 1:
% 231.54/42.86  | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | |   (206)  all_55_11 = e2
% 231.54/42.86  | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | | COMBINE_EQS: (62), (206) imply:
% 231.54/42.86  | | | | | | | | | | | | | | | |   (207)  all_53_14 = e2
% 231.54/42.86  | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | | REDUCE: (3), (207) imply:
% 231.54/42.86  | | | | | | | | | | | | | | | |   (208)   ~ (all_53_6 = e2)
% 231.54/42.86  | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | | BETA: splitting (20) gives:
% 231.54/42.86  | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.86  | | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | | |   (209)  all_55_9 = e3
% 231.54/42.86  | | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | | | COMBINE_EQS: (21), (209) imply:
% 231.54/42.86  | | | | | | | | | | | | | | | | |   (210)  all_53_6 = e3
% 231.54/42.86  | | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | | | SIMP: (210) implies:
% 231.54/42.86  | | | | | | | | | | | | | | | | |   (211)  all_53_6 = e3
% 231.54/42.86  | | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | | | REDUCE: (117), (211) imply:
% 231.54/42.86  | | | | | | | | | | | | | | | | |   (212)   ~ (all_52_27 = e3)
% 231.54/42.86  | | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | | | SIMP: (212) implies:
% 231.54/42.86  | | | | | | | | | | | | | | | | |   (213)   ~ (all_52_27 = e3)
% 231.54/42.86  | | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (13), (24), (112), (115), (118), (195), (213)
% 231.54/42.86  | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1613.
% 231.54/42.86  | | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.86  | | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | | |   (214)  all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 231.54/42.86  | | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (90), (130), (208), (214) are inconsistent
% 231.54/42.86  | | | | | | | | | | | | | | | | |            by sub-proof #2271.
% 231.54/42.86  | | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | | End of split
% 231.54/42.86  | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | Case 2:
% 231.54/42.86  | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | |   (215)  all_55_11 = e1 | all_55_11 = e0
% 231.54/42.86  | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | | REF_CLOSE: (62), (92), (131), (215) are inconsistent by
% 231.54/42.86  | | | | | | | | | | | | | | | |            sub-proof #2307.
% 231.54/42.86  | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | End of split
% 231.54/42.86  | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | End of split
% 231.54/42.86  | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | Case 2:
% 231.54/42.86  | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | |   (216)   ~ (all_55_3 = e3)
% 231.54/42.86  | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | REDUCE: (63), (216) imply:
% 231.54/42.86  | | | | | | | | | | | | | |   (217)   ~ (all_53_12 = e3)
% 231.54/42.86  | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | REF_CLOSE: (13), (81), (199), (217) are inconsistent by
% 231.54/42.86  | | | | | | | | | | | | | |            sub-proof #2458.
% 231.54/42.86  | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | End of split
% 231.54/42.86  | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | Case 2:
% 231.54/42.86  | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | |   (218)  all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 231.54/42.86  | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | BETA: splitting (218) gives:
% 231.54/42.86  | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | Case 1:
% 231.54/42.86  | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | |   (219)  all_55_3 = e2
% 231.54/42.86  | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | REF_CLOSE: (63), (72), (219) are inconsistent by sub-proof
% 231.54/42.86  | | | | | | | | | | | | | |            #1612.
% 231.54/42.86  | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | Case 2:
% 231.54/42.86  | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | |   (220)  all_55_3 = e1 | all_55_3 = e0
% 231.54/42.86  | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | REF_CLOSE: (63), (95), (193), (220) are inconsistent by
% 231.54/42.86  | | | | | | | | | | | | | |            sub-proof #2132.
% 231.54/42.86  | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | End of split
% 231.54/42.86  | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | End of split
% 231.54/42.86  | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | Case 2:
% 231.54/42.86  | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | |   (221)  all_55_1 = e0
% 231.54/42.86  | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | REF_CLOSE: (29), (93), (221) are inconsistent by sub-proof
% 231.54/42.86  | | | | | | | | | | | |            #2076.
% 231.54/42.86  | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | End of split
% 231.54/42.86  | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | End of split
% 231.54/42.86  | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | End of split
% 231.54/42.86  | | | | | | | | | 
% 231.54/42.86  | | | | | | | | Case 2:
% 231.54/42.86  | | | | | | | | | 
% 231.54/42.86  | | | | | | | | |   (222)  all_55_10 = e0
% 231.54/42.86  | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | REF_CLOSE: (57), (97), (222) are inconsistent by sub-proof
% 231.54/42.86  | | | | | | | | |            #2118.
% 231.54/42.86  | | | | | | | | | 
% 231.54/42.86  | | | | | | | | End of split
% 231.54/42.86  | | | | | | | | 
% 231.54/42.86  | | | | | | | End of split
% 231.54/42.86  | | | | | | | 
% 231.54/42.86  | | | | | | End of split
% 231.54/42.86  | | | | | | 
% 231.54/42.86  | | | | | Case 2:
% 231.54/42.86  | | | | | | 
% 231.54/42.86  | | | | | |   (223)  all_38_2 = e2
% 231.54/42.86  | | | | | | 
% 231.54/42.86  | | | | | | COMBINE_EQS: (61), (223) imply:
% 231.54/42.86  | | | | | |   (224)  all_6_2 = e2
% 231.54/42.86  | | | | | | 
% 231.54/42.86  | | | | | | REDUCE: (15), (224) imply:
% 231.54/42.86  | | | | | |   (225)   ~ (e3 = e2)
% 231.54/42.86  | | | | | | 
% 231.54/42.86  | | | | | | REDUCE: (16), (224) imply:
% 231.54/42.86  | | | | | |   (226)  op(e1, e1) = e2
% 231.54/42.86  | | | | | | 
% 231.54/42.86  | | | | | | BETA: splitting (53) gives:
% 231.54/42.86  | | | | | | 
% 231.54/42.86  | | | | | | Case 1:
% 231.54/42.86  | | | | | | | 
% 231.54/42.86  | | | | | | |   (227)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 &
% 231.54/42.86  | | | | | | |            op(e0, e2) = e2)
% 231.54/42.86  | | | | | | | 
% 231.54/42.86  | | | | | | | BETA: splitting (227) gives:
% 231.54/42.86  | | | | | | | 
% 231.54/42.86  | | | | | | | Case 1:
% 231.54/42.86  | | | | | | | | 
% 231.54/42.86  | | | | | | | |   (228)  all_57_12 = e2 & op(e0, e3) = e2
% 231.54/42.86  | | | | | | | | 
% 231.54/42.86  | | | | | | | | ALPHA: (228) implies:
% 231.54/42.86  | | | | | | | |   (229)  op(e0, e3) = e2
% 231.54/42.86  | | | | | | | | 
% 231.54/42.86  | | | | | | | | REF_CLOSE: (13), (34), (37), (229) are inconsistent by sub-proof
% 231.54/42.86  | | | | | | | |            #1980.
% 231.54/42.86  | | | | | | | | 
% 231.54/42.86  | | | | | | | Case 2:
% 231.54/42.86  | | | | | | | | 
% 231.54/42.86  | | | | | | | |   (230)  all_57_13 = e2 & op(e0, e2) = e2
% 231.54/42.86  | | | | | | | | 
% 231.54/42.86  | | | | | | | | ALPHA: (230) implies:
% 231.54/42.86  | | | | | | | |   (231)  all_57_13 = e2
% 231.54/42.86  | | | | | | | | 
% 231.54/42.86  | | | | | | | | REF_CLOSE: (6), (7), (8), (10), (11), (13), (14), (15), (16),
% 231.54/42.86  | | | | | | | |            (19), (23), (24), (25), (27), (28), (31), (32), (36),
% 231.54/42.86  | | | | | | | |            (41), (43), (45), (47), (48), (60), (66), (67), (69),
% 231.54/42.86  | | | | | | | |            (70), (72), (73), (74), (75), (76), (79), (81), (85),
% 231.54/42.86  | | | | | | | |            (110), (112), (118), (226), (230), (231) are
% 231.54/42.86  | | | | | | | |            inconsistent by sub-proof #1623.
% 231.54/42.86  | | | | | | | | 
% 231.54/42.86  | | | | | | | End of split
% 231.54/42.86  | | | | | | | 
% 231.54/42.86  | | | | | | Case 2:
% 231.54/42.86  | | | | | | | 
% 231.54/42.86  | | | | | | |   (232)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 &
% 231.54/42.86  | | | | | | |            op(e0, e0) = e2)
% 231.54/42.86  | | | | | | | 
% 231.54/42.86  | | | | | | | BETA: splitting (232) gives:
% 231.54/42.86  | | | | | | | 
% 231.54/42.86  | | | | | | | Case 1:
% 231.54/42.86  | | | | | | | | 
% 231.54/42.86  | | | | | | | |   (233)  all_57_14 = e2 & op(e0, e1) = e2
% 231.54/42.86  | | | | | | | | 
% 231.54/42.86  | | | | | | | | ALPHA: (233) implies:
% 231.54/42.86  | | | | | | | |   (234)  all_57_14 = e2
% 231.54/42.86  | | | | | | | | 
% 231.54/42.86  | | | | | | | | BETA: splitting (66) gives:
% 231.54/42.86  | | | | | | | | 
% 231.54/42.86  | | | | | | | | Case 1:
% 231.54/42.86  | | | | | | | | | 
% 231.54/42.86  | | | | | | | | |   (235)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 &
% 231.54/42.86  | | | | | | | | |            op(e2, e2) = e2)
% 231.54/42.86  | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | BETA: splitting (235) gives:
% 231.54/42.86  | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | Case 1:
% 231.54/42.86  | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | |   (236)  all_57_2 = e2 & op(e2, e3) = e2
% 231.54/42.86  | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | ALPHA: (236) implies:
% 231.54/42.86  | | | | | | | | | |   (237)  all_57_2 = e2
% 231.54/42.86  | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | REF_CLOSE: (7), (8), (11), (13), (27), (28), (31), (36),
% 231.54/42.86  | | | | | | | | | |            (41), (45), (60), (66), (67), (69), (74), (85),
% 231.54/42.86  | | | | | | | | | |            (237) are inconsistent by sub-proof #1628.
% 231.54/42.86  | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | Case 2:
% 231.54/42.86  | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | |   (238)  all_57_3 = e2 & op(e2, e2) = e2
% 231.54/42.86  | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | ALPHA: (238) implies:
% 231.54/42.86  | | | | | | | | | |   (239)  op(e2, e2) = e2
% 231.54/42.86  | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | REF_CLOSE: (13), (24), (41), (239) are inconsistent by
% 231.54/42.86  | | | | | | | | | |            sub-proof #2472.
% 231.54/42.86  | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | End of split
% 231.54/42.86  | | | | | | | | | 
% 231.54/42.86  | | | | | | | | Case 2:
% 231.54/42.86  | | | | | | | | | 
% 231.54/42.86  | | | | | | | | |   (240)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 &
% 231.54/42.86  | | | | | | | | |            op(e2, e0) = e2)
% 231.54/42.86  | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | BETA: splitting (240) gives:
% 231.54/42.86  | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | Case 1:
% 231.54/42.86  | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | |   (241)  all_57_5 = e2 & op(e2, e1) = e2
% 231.54/42.86  | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | ALPHA: (241) implies:
% 231.54/42.86  | | | | | | | | | |   (242)  all_57_5 = e2
% 231.54/42.86  | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | REF_CLOSE: (13), (15), (16), (23), (28), (31), (47), (234),
% 231.54/42.86  | | | | | | | | | |            (242) are inconsistent by sub-proof #2188.
% 231.54/42.86  | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | Case 2:
% 231.54/42.86  | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | |   (243)  all_57_10 = e2 & op(e2, e0) = e2
% 231.54/42.86  | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | ALPHA: (243) implies:
% 231.54/42.86  | | | | | | | | | |   (244)  all_57_10 = e2
% 231.54/42.86  | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | BETA: splitting (10) gives:
% 231.54/42.86  | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | Case 1:
% 231.54/42.86  | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | |   (245)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 231.54/42.86  | | | | | | | | | | |            & op(e2, e2) = e2)
% 231.54/42.86  | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | REF_CLOSE: (11), (13), (19), (23), (24), (25), (28), (31),
% 231.54/42.86  | | | | | | | | | | |            (36), (41), (43), (45), (69), (245) are
% 231.54/42.86  | | | | | | | | | | |            inconsistent by sub-proof #1637.
% 231.54/42.86  | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | Case 2:
% 231.54/42.86  | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | |   (246)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 231.54/42.86  | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 231.54/42.86  | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | BETA: splitting (246) gives:
% 231.54/42.86  | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | Case 1:
% 231.54/42.86  | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | |   (247)  all_57_7 = e2 & op(e1, e2) = e2
% 231.54/42.86  | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | ALPHA: (247) implies:
% 231.54/42.86  | | | | | | | | | | | |   (248)  all_57_7 = e2
% 231.54/42.86  | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | REF_CLOSE: (7), (11), (13), (14), (15), (16), (19), (23),
% 231.54/42.86  | | | | | | | | | | | |            (24), (25), (27), (28), (31), (36), (41), (43),
% 231.54/42.86  | | | | | | | | | | | |            (45), (47), (48), (50), (56), (60), (66), (68),
% 231.54/42.86  | | | | | | | | | | | |            (69), (70), (74), (75), (76), (79), (85), (97),
% 231.54/42.86  | | | | | | | | | | | |            (109), (111), (226), (234), (244), (248) are
% 231.54/42.86  | | | | | | | | | | | |            inconsistent by sub-proof #1640.
% 231.54/42.86  | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | Case 2:
% 231.54/42.86  | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | |   (249)  all_57_13 = e2 & op(e0, e2) = e2
% 231.54/42.86  | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | ALPHA: (249) implies:
% 231.54/42.86  | | | | | | | | | | | |   (250)  all_57_13 = e2
% 231.54/42.86  | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | BETA: splitting (50) gives:
% 231.54/42.86  | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | Case 1:
% 231.54/42.86  | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | |   (251)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 231.54/42.86  | | | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 231.54/42.86  | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | BETA: splitting (251) gives:
% 231.54/42.86  | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | Case 1:
% 231.54/42.86  | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | |   (252)  all_57_12 = e3 & op(e0, e3) = e3
% 231.54/42.86  | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | ALPHA: (252) implies:
% 231.54/42.86  | | | | | | | | | | | | | |   (253)  all_57_12 = e3
% 231.54/42.86  | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | BETA: splitting (8) gives:
% 231.54/42.86  | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | Case 1:
% 231.54/42.86  | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | |   (254)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 231.54/42.86  | | | | | | | | | | | | | | |            & op(e2, e3) = e1)
% 231.54/42.86  | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | BETA: splitting (254) gives:
% 231.54/42.86  | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | Case 1:
% 231.54/42.86  | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | |   (255)  all_57_0 = e1 & op(e3, e3) = e1
% 231.54/42.86  | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | | ALPHA: (255) implies:
% 231.54/42.86  | | | | | | | | | | | | | | | |   (256)  op(e3, e3) = e1
% 231.54/42.86  | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | | REF_CLOSE: (13), (36), (69), (256) are inconsistent by
% 231.54/42.86  | | | | | | | | | | | | | | | |            sub-proof #1950.
% 231.54/42.86  | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | Case 2:
% 231.54/42.86  | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | |   (257)  all_57_2 = e1 & op(e2, e3) = e1
% 231.54/42.86  | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | | ALPHA: (257) implies:
% 231.54/42.86  | | | | | | | | | | | | | | | |   (258)  all_57_2 = e1
% 231.54/42.86  | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | | BETA: splitting (47) gives:
% 231.54/42.86  | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.86  | | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | | |   (259)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 231.54/42.86  | | | | | | | | | | | | | | | | |            & op(e2, e1) = e3)
% 231.54/42.86  | | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | | | BETA: splitting (259) gives:
% 231.54/42.86  | | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.86  | | | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | | | |   (260)  all_57_4 = e3 & op(e3, e1) = e3
% 231.54/42.86  | | | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | | | | ALPHA: (260) implies:
% 231.54/42.86  | | | | | | | | | | | | | | | | | |   (261)  all_57_4 = e3
% 231.54/42.86  | | | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | | | | REF_CLOSE: (23), (31), (261) are inconsistent by sub-proof
% 231.54/42.86  | | | | | | | | | | | | | | | | | |            #2372.
% 231.54/42.86  | | | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.86  | | | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | | | |   (262)  all_57_5 = e3 & op(e2, e1) = e3
% 231.54/42.86  | | | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | | | | ALPHA: (262) implies:
% 231.54/42.86  | | | | | | | | | | | | | | | | | |   (263)  all_57_5 = e3
% 231.54/42.86  | | | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | | | | BETA: splitting (39) gives:
% 231.54/42.86  | | | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.86  | | | | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | | | | |   (264)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 231.54/42.86  | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 231.54/42.86  | | | | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | | | | | BETA: splitting (264) gives:
% 231.54/42.86  | | | | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.86  | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | | | | | |   (265)  all_57_12 = e1 & op(e0, e3) = e1
% 231.54/42.86  | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | | | | | | ALPHA: (265) implies:
% 231.54/42.86  | | | | | | | | | | | | | | | | | | | |   (266)  all_57_12 = e1
% 231.54/42.86  | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (253), (266) imply:
% 231.54/42.86  | | | | | | | | | | | | | | | | | | | |   (267)  e3 = e1
% 231.54/42.86  | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (263), (267) imply:
% 231.54/42.86  | | | | | | | | | | | | | | | | | | | |   (268)  all_57_5 = e1
% 231.54/42.86  | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (27), (28), (31), (60), (244), (258), (268)
% 231.54/42.86  | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1645.
% 231.54/42.86  | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.86  | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | | | | | |   (269)  all_57_13 = e1 & op(e0, e2) = e1
% 231.54/42.86  | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (69), (250), (269) are inconsistent by sub-proof
% 231.54/42.86  | | | | | | | | | | | | | | | | | | | |            #2205.
% 231.54/42.86  | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.86  | | | | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.86  | | | | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | | | | |   (270)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 231.54/42.86  | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 231.54/42.86  | | | | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | | | | | BETA: splitting (270) gives:
% 231.54/42.86  | | | | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.86  | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | | | | | |   (271)  all_57_14 = e1 & op(e0, e1) = e1
% 231.54/42.86  | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (69), (234), (271) are inconsistent by sub-proof
% 231.54/42.86  | | | | | | | | | | | | | | | | | | | |            #2375.
% 231.54/42.86  | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.86  | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | | | | | |   (272)  all_57_15 = e1 & op(e0, e0) = e1
% 231.54/42.86  | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | | | | | | ALPHA: (272) implies:
% 231.54/42.86  | | | | | | | | | | | | | | | | | | | |   (273)  op(e0, e0) = e1
% 231.54/42.86  | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (16), (97), (109), (111), (273) are
% 231.54/42.86  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2086.
% 231.54/42.86  | | | | | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.86  | | | | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | | | | End of split
% 231.54/42.86  | | | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | | | End of split
% 231.54/42.86  | | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.86  | | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | | |   (274)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 231.54/42.86  | | | | | | | | | | | | | | | | |            e3 & op(e0, e1) = e3)
% 231.54/42.86  | | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (15), (16), (28), (234), (274) are
% 231.54/42.86  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2409.
% 231.54/42.86  | | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | | End of split
% 231.54/42.86  | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | End of split
% 231.54/42.86  | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | Case 2:
% 231.54/42.86  | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | |   (275)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 231.54/42.86  | | | | | | | | | | | | | | |            e1 & op(e0, e3) = e1)
% 231.54/42.86  | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | BETA: splitting (275) gives:
% 231.54/42.86  | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | Case 1:
% 231.54/42.86  | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | |   (276)  all_57_6 = e1 & op(e1, e3) = e1
% 231.54/42.86  | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | | ALPHA: (276) implies:
% 231.54/42.86  | | | | | | | | | | | | | | | |   (277)  all_57_6 = e1
% 231.54/42.86  | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | | REF_CLOSE: (7), (11), (13), (27), (28), (31), (36), (41),
% 231.54/42.86  | | | | | | | | | | | | | | | |            (45), (60), (66), (69), (74), (253), (277) are
% 231.54/42.86  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1632.
% 231.54/42.86  | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | Case 2:
% 231.54/42.86  | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | |   (278)  all_57_12 = e1 & op(e0, e3) = e1
% 231.54/42.86  | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | | REF_CLOSE: (11), (253), (278) are inconsistent by sub-proof
% 231.54/42.86  | | | | | | | | | | | | | | | |            #2230.
% 231.54/42.86  | | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | | End of split
% 231.54/42.86  | | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | End of split
% 231.54/42.86  | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | Case 2:
% 231.54/42.86  | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | |   (279)  all_57_13 = e3 & op(e0, e2) = e3
% 231.54/42.86  | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | ALPHA: (279) implies:
% 231.54/42.86  | | | | | | | | | | | | | |   (280)  all_57_13 = e3
% 231.54/42.86  | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | REF_CLOSE: (28), (250), (280) are inconsistent by sub-proof
% 231.54/42.86  | | | | | | | | | | | | | |            #2203.
% 231.54/42.86  | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | End of split
% 231.54/42.86  | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | Case 2:
% 231.54/42.86  | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | |   (281)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 231.54/42.86  | | | | | | | | | | | | |            e3 & op(e0, e0) = e3)
% 231.54/42.86  | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | BETA: splitting (281) gives:
% 231.54/42.86  | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | Case 1:
% 231.54/42.86  | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | |   (282)  all_57_14 = e3 & op(e0, e1) = e3
% 231.54/42.86  | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | REF_CLOSE: (28), (234), (282) are inconsistent by sub-proof
% 231.54/42.86  | | | | | | | | | | | | | |            #1891.
% 231.54/42.86  | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | Case 2:
% 231.54/42.86  | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | |   (283)  all_57_15 = e3 & op(e0, e0) = e3
% 231.54/42.86  | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | ALPHA: (283) implies:
% 231.54/42.86  | | | | | | | | | | | | | |   (284)  op(e0, e0) = e3
% 231.54/42.86  | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | | REF_CLOSE: (13), (31), (49), (284) are inconsistent by
% 231.54/42.86  | | | | | | | | | | | | | |            sub-proof #2304.
% 231.54/42.86  | | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | | End of split
% 231.54/42.86  | | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | | End of split
% 231.54/42.86  | | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | | End of split
% 231.54/42.86  | | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | | End of split
% 231.54/42.86  | | | | | | | | | | 
% 231.54/42.86  | | | | | | | | | End of split
% 231.54/42.86  | | | | | | | | | 
% 231.54/42.86  | | | | | | | | End of split
% 231.54/42.86  | | | | | | | | 
% 231.54/42.86  | | | | | | | Case 2:
% 231.54/42.86  | | | | | | | | 
% 231.54/42.86  | | | | | | | |   (285)  all_57_15 = e2 & op(e0, e0) = e2
% 231.54/42.86  | | | | | | | | 
% 231.54/42.86  | | | | | | | | ALPHA: (285) implies:
% 231.54/42.86  | | | | | | | |   (286)  all_57_15 = e2
% 231.54/42.86  | | | | | | | | 
% 231.54/42.86  | | | | | | | | REF_CLOSE: (6), (41), (286) are inconsistent by sub-proof #2126.
% 231.54/42.86  | | | | | | | | 
% 231.54/42.86  | | | | | | | End of split
% 231.54/42.86  | | | | | | | 
% 231.54/42.86  | | | | | | End of split
% 231.54/42.86  | | | | | | 
% 231.54/42.86  | | | | | End of split
% 231.54/42.86  | | | | | 
% 231.54/42.86  | | | | End of split
% 231.54/42.86  | | | | 
% 231.54/42.86  | | | End of split
% 231.54/42.86  | | | 
% 231.54/42.86  | | Case 2:
% 231.54/42.86  | | | 
% 231.54/42.86  | | |   (287)  all_57_12 = e0 & op(e0, e3) = e0
% 231.54/42.86  | | | 
% 231.54/42.86  | | | ALPHA: (287) implies:
% 231.54/42.86  | | |   (288)  op(e0, e3) = e0
% 231.54/42.86  | | | 
% 231.54/42.86  | | | REF_CLOSE: (13), (34), (55), (288) are inconsistent by sub-proof #2366.
% 231.54/42.86  | | | 
% 231.54/42.86  | | End of split
% 231.54/42.86  | | 
% 231.54/42.86  | End of split
% 231.54/42.86  | 
% 231.54/42.86  End of proof
% 231.54/42.86  
% 231.54/42.86  Sub-proof #1612 shows that the following formulas are inconsistent:
% 231.54/42.86  ----------------------------------------------------------------
% 231.54/42.86    (1)  all_55_3 = all_53_12
% 231.54/42.86    (2)  all_55_3 = e2
% 231.54/42.86    (3)   ~ (all_53_12 = e2)
% 231.54/42.86  
% 231.54/42.86  Begin of proof
% 231.54/42.86  | 
% 231.54/42.86  | COMBINE_EQS: (1), (2) imply:
% 231.54/42.86  |   (4)  all_53_12 = e2
% 231.54/42.86  | 
% 231.54/42.86  | SIMP: (4) implies:
% 231.54/42.86  |   (5)  all_53_12 = e2
% 231.54/42.86  | 
% 231.54/42.86  | REDUCE: (3), (5) imply:
% 231.54/42.86  |   (6)  $false
% 231.54/42.86  | 
% 231.54/42.86  | CLOSE: (6) is inconsistent.
% 231.54/42.86  | 
% 231.54/42.86  End of proof
% 231.54/42.86  
% 231.54/42.86  Sub-proof #1613 shows that the following formulas are inconsistent:
% 231.54/42.86  ----------------------------------------------------------------
% 231.54/42.86    (1)  all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 231.54/42.86    (2)   ~ (all_52_27 = e1)
% 231.54/42.86    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.86           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.86    (4)  op(e2, e2) = e0
% 231.54/42.86    (5)  all_55_13 = all_52_27
% 231.54/42.86    (6)   ~ (all_52_27 = e0)
% 231.54/42.86    (7)  op(all_52_27, all_52_27) = e2
% 231.54/42.86    (8)   ~ (all_52_27 = e3)
% 231.54/42.86  
% 231.54/42.86  Begin of proof
% 231.54/42.86  | 
% 231.54/42.86  | BETA: splitting (1) gives:
% 231.54/42.86  | 
% 231.54/42.86  | Case 1:
% 231.54/42.86  | | 
% 231.54/42.86  | |   (9)  all_55_13 = e3
% 231.54/42.86  | | 
% 231.54/42.86  | | REF_CLOSE: (5), (8), (9) are inconsistent by sub-proof #1648.
% 231.54/42.86  | | 
% 231.54/42.86  | Case 2:
% 231.54/42.86  | | 
% 231.54/42.86  | |   (10)  all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 231.54/42.86  | | 
% 231.54/42.86  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (10) are inconsistent by sub-proof
% 231.54/42.86  | |            #1614.
% 231.54/42.86  | | 
% 231.54/42.86  | End of split
% 231.54/42.86  | 
% 231.54/42.86  End of proof
% 231.54/42.86  
% 231.54/42.86  Sub-proof #1614 shows that the following formulas are inconsistent:
% 231.54/42.86  ----------------------------------------------------------------
% 231.54/42.86    (1)   ~ (all_52_27 = e1)
% 231.54/42.86    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.86           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.86    (3)  op(e2, e2) = e0
% 231.54/42.86    (4)  all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 231.54/42.86    (5)  all_55_13 = all_52_27
% 231.54/42.86    (6)   ~ (all_52_27 = e0)
% 231.54/42.86    (7)  op(all_52_27, all_52_27) = e2
% 231.54/42.86  
% 231.54/42.86  Begin of proof
% 231.54/42.86  | 
% 231.54/42.86  | BETA: splitting (4) gives:
% 231.54/42.86  | 
% 231.54/42.86  | Case 1:
% 231.54/42.86  | | 
% 231.54/42.86  | |   (8)  all_55_13 = e2
% 231.54/42.86  | | 
% 231.54/42.86  | | COMBINE_EQS: (5), (8) imply:
% 231.54/42.86  | |   (9)  all_52_27 = e2
% 231.54/42.86  | | 
% 231.54/42.86  | | SIMP: (9) implies:
% 231.54/42.86  | |   (10)  all_52_27 = e2
% 231.54/42.86  | | 
% 231.54/42.86  | | REDUCE: (6), (10) imply:
% 231.54/42.86  | |   (11)   ~ (e2 = e0)
% 231.54/42.86  | | 
% 231.54/42.86  | | REDUCE: (7), (10) imply:
% 231.54/42.86  | |   (12)  op(e2, e2) = e2
% 231.54/42.86  | | 
% 231.54/42.86  | | REF_CLOSE: (2), (3), (11), (12) are inconsistent by sub-proof #2472.
% 231.54/42.86  | | 
% 231.54/42.86  | Case 2:
% 231.54/42.86  | | 
% 231.54/42.86  | |   (13)  all_55_13 = e1 | all_55_13 = e0
% 231.54/42.86  | | 
% 231.54/42.86  | | REF_CLOSE: (1), (5), (6), (13) are inconsistent by sub-proof #1615.
% 231.54/42.86  | | 
% 231.54/42.86  | End of split
% 231.54/42.86  | 
% 231.54/42.86  End of proof
% 231.54/42.86  
% 231.54/42.86  Sub-proof #1615 shows that the following formulas are inconsistent:
% 231.54/42.86  ----------------------------------------------------------------
% 231.54/42.86    (1)  all_55_13 = e1 | all_55_13 = e0
% 231.54/42.86    (2)  all_55_13 = all_52_27
% 231.54/42.86    (3)   ~ (all_52_27 = e1)
% 231.54/42.86    (4)   ~ (all_52_27 = e0)
% 231.54/42.86  
% 231.54/42.86  Begin of proof
% 231.54/42.86  | 
% 231.54/42.86  | BETA: splitting (1) gives:
% 231.54/42.86  | 
% 231.54/42.86  | Case 1:
% 231.54/42.86  | | 
% 231.54/42.86  | |   (5)  all_55_13 = e1
% 231.54/42.86  | | 
% 231.54/42.86  | | COMBINE_EQS: (2), (5) imply:
% 231.54/42.86  | |   (6)  all_52_27 = e1
% 231.54/42.86  | | 
% 231.54/42.86  | | SIMP: (6) implies:
% 231.54/42.86  | |   (7)  all_52_27 = e1
% 231.54/42.86  | | 
% 231.54/42.86  | | REDUCE: (3), (7) imply:
% 231.54/42.86  | |   (8)  $false
% 231.54/42.86  | | 
% 231.54/42.86  | | CLOSE: (8) is inconsistent.
% 231.54/42.86  | | 
% 231.54/42.86  | Case 2:
% 231.54/42.86  | | 
% 231.54/42.86  | |   (9)  all_55_13 = e0
% 231.54/42.86  | | 
% 231.54/42.86  | | REF_CLOSE: (2), (4), (9) are inconsistent by sub-proof #1639.
% 231.54/42.86  | | 
% 231.54/42.86  | End of split
% 231.54/42.86  | 
% 231.54/42.86  End of proof
% 231.54/42.86  
% 231.54/42.86  Sub-proof #1616 shows that the following formulas are inconsistent:
% 231.54/42.86  ----------------------------------------------------------------
% 231.54/42.86    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.86         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.54/42.86    (2)   ~ (e3 = e1)
% 231.54/42.86    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.86           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.86    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.54/42.86         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.54/42.86    (5)  all_57_4 = e0
% 231.54/42.86    (6)  op(e2, e2) = e0
% 231.54/42.86    (7)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.54/42.86         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.54/42.86    (8)  all_57_3 = e0
% 231.54/42.86    (9)   ~ (e3 = e2)
% 231.54/42.86    (10)   ~ (e3 = e0)
% 231.54/42.86    (11)  op(e3, e3) = e2
% 231.54/42.86    (12)   ~ (e2 = e0)
% 231.54/42.86    (13)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 231.54/42.86          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.54/42.86    (14)   ~ (e1 = e0)
% 231.54/42.86    (15)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.54/42.86          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.54/42.86    (16)  all_57_13 = e3
% 231.54/42.86    (17)   ~ (all_53_12 = e3)
% 231.54/42.86    (18)   ~ (e2 = e1)
% 231.54/42.86    (19)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.86          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.54/42.86    (20)  op(e3, e0) = all_53_12
% 231.54/42.86  
% 231.54/42.86  Begin of proof
% 231.54/42.86  | 
% 231.54/42.86  | BETA: splitting (13) gives:
% 231.54/42.86  | 
% 231.54/42.86  | Case 1:
% 231.54/42.86  | | 
% 231.54/42.86  | |   (21)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) =
% 231.54/42.86  | |           e3)
% 231.54/42.86  | | 
% 231.54/42.86  | | BETA: splitting (21) gives:
% 231.54/42.86  | | 
% 231.54/42.86  | | Case 1:
% 231.54/42.86  | | | 
% 231.54/42.86  | | |   (22)  all_57_0 = e3 & op(e3, e3) = e3
% 231.54/42.86  | | | 
% 231.54/42.86  | | | ALPHA: (22) implies:
% 231.54/42.86  | | |   (23)  op(e3, e3) = e3
% 231.54/42.86  | | | 
% 231.54/42.86  | | | REF_CLOSE: (3), (9), (11), (23) are inconsistent by sub-proof #2490.
% 231.54/42.86  | | | 
% 231.54/42.86  | | Case 2:
% 231.54/42.86  | | | 
% 231.54/42.86  | | |   (24)  all_57_1 = e3 & op(e3, e2) = e3
% 231.54/42.86  | | | 
% 231.54/42.86  | | | ALPHA: (24) implies:
% 231.54/42.86  | | |   (25)  all_57_1 = e3
% 231.54/42.86  | | | 
% 231.54/42.86  | | | BETA: splitting (1) gives:
% 231.54/42.86  | | | 
% 231.54/42.86  | | | Case 1:
% 231.54/42.86  | | | | 
% 231.54/42.86  | | | |   (26)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2)
% 231.54/42.86  | | | |           = e2)
% 231.54/42.86  | | | | 
% 231.54/42.86  | | | | REF_CLOSE: (2), (3), (4), (6), (7), (9), (10), (11), (12), (13), (14),
% 231.54/42.86  | | | |            (17), (18), (20), (26) are inconsistent by sub-proof #1649.
% 231.54/42.86  | | | | 
% 231.54/42.86  | | | Case 2:
% 231.54/42.86  | | | | 
% 231.54/42.86  | | | |   (27)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2)
% 231.54/42.86  | | | |           = e2)
% 231.54/42.86  | | | | 
% 231.54/42.86  | | | | BETA: splitting (27) gives:
% 231.54/42.86  | | | | 
% 231.54/42.86  | | | | Case 1:
% 231.54/42.86  | | | | | 
% 231.54/42.86  | | | | |   (28)  all_57_7 = e2 & op(e1, e2) = e2
% 231.54/42.86  | | | | | 
% 231.54/42.86  | | | | | ALPHA: (28) implies:
% 231.54/42.86  | | | | |   (29)  all_57_7 = e2
% 231.54/42.86  | | | | | 
% 231.54/42.86  | | | | | BETA: splitting (19) gives:
% 231.54/42.86  | | | | | 
% 231.54/42.86  | | | | | Case 1:
% 231.54/42.86  | | | | | | 
% 231.54/42.86  | | | | | |   (30)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2,
% 231.54/42.86  | | | | | |             e2) = e1)
% 231.54/42.86  | | | | | | 
% 231.54/42.86  | | | | | | BETA: splitting (30) gives:
% 231.54/42.86  | | | | | | 
% 231.54/42.86  | | | | | | Case 1:
% 231.54/42.86  | | | | | | | 
% 231.54/42.86  | | | | | | |   (31)  all_57_1 = e1 & op(e3, e2) = e1
% 231.54/42.86  | | | | | | | 
% 231.54/42.86  | | | | | | | ALPHA: (31) implies:
% 231.54/42.86  | | | | | | |   (32)  all_57_1 = e1
% 231.54/42.86  | | | | | | | 
% 231.54/42.86  | | | | | | | COMBINE_EQS: (25), (32) imply:
% 231.54/42.86  | | | | | | |   (33)  e3 = e1
% 231.54/42.86  | | | | | | | 
% 231.54/42.86  | | | | | | | COMBINE_EQS: (16), (33) imply:
% 231.54/42.86  | | | | | | |   (34)  all_57_13 = e1
% 231.54/42.86  | | | | | | | 
% 231.54/42.86  | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 231.54/42.86  | | | | | | |            (11), (12), (13), (14), (15), (18), (32), (34) are
% 231.54/42.86  | | | | | | |            inconsistent by sub-proof #1625.
% 231.54/42.86  | | | | | | | 
% 231.54/42.86  | | | | | | Case 2:
% 231.54/42.86  | | | | | | | 
% 231.54/42.86  | | | | | | |   (35)  all_57_3 = e1 & op(e2, e2) = e1
% 231.54/42.86  | | | | | | | 
% 231.54/42.86  | | | | | | | ALPHA: (35) implies:
% 231.54/42.86  | | | | | | |   (36)  op(e2, e2) = e1
% 231.54/42.86  | | | | | | | 
% 231.54/42.86  | | | | | | | REF_CLOSE: (3), (6), (14), (36) are inconsistent by sub-proof
% 231.54/42.86  | | | | | | |            #2352.
% 231.54/42.86  | | | | | | | 
% 231.54/42.86  | | | | | | End of split
% 231.54/42.86  | | | | | | 
% 231.54/42.86  | | | | | Case 2:
% 231.54/42.86  | | | | | | 
% 231.54/42.86  | | | | | |   (37)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0,
% 231.54/42.86  | | | | | |             e2) = e1)
% 231.54/42.86  | | | | | | 
% 231.54/42.86  | | | | | | BETA: splitting (37) gives:
% 231.54/42.86  | | | | | | 
% 231.54/42.86  | | | | | | Case 1:
% 231.54/42.86  | | | | | | | 
% 231.54/42.86  | | | | | | |   (38)  all_57_7 = e1 & op(e1, e2) = e1
% 231.54/42.86  | | | | | | | 
% 231.54/42.86  | | | | | | | ALPHA: (38) implies:
% 231.54/42.86  | | | | | | |   (39)  all_57_7 = e1
% 231.54/42.86  | | | | | | | 
% 231.54/42.86  | | | | | | | REF_CLOSE: (18), (29), (39) are inconsistent by sub-proof #1761.
% 231.54/42.86  | | | | | | | 
% 231.54/42.86  | | | | | | Case 2:
% 231.54/42.86  | | | | | | | 
% 231.54/42.86  | | | | | | |   (40)  all_57_13 = e1 & op(e0, e2) = e1
% 231.54/42.86  | | | | | | | 
% 231.54/42.86  | | | | | | | ALPHA: (40) implies:
% 231.54/42.86  | | | | | | |   (41)  all_57_13 = e1
% 231.54/42.86  | | | | | | | 
% 231.54/42.86  | | | | | | | COMBINE_EQS: (16), (41) imply:
% 231.54/42.86  | | | | | | |   (42)  e3 = e1
% 231.54/42.86  | | | | | | | 
% 231.54/42.86  | | | | | | | COMBINE_EQS: (25), (42) imply:
% 231.54/42.86  | | | | | | |   (43)  all_57_1 = e1
% 231.54/42.86  | | | | | | | 
% 231.54/42.86  | | | | | | | REF_CLOSE: (2), (8), (9), (10), (15), (29), (41), (43) are
% 231.54/42.86  | | | | | | |            inconsistent by sub-proof #2193.
% 231.54/42.86  | | | | | | | 
% 231.54/42.86  | | | | | | End of split
% 231.54/42.86  | | | | | | 
% 231.54/42.86  | | | | | End of split
% 231.54/42.86  | | | | | 
% 231.54/42.86  | | | | Case 2:
% 231.54/42.86  | | | | | 
% 231.54/42.86  | | | | |   (44)  all_57_13 = e2 & op(e0, e2) = e2
% 231.54/42.86  | | | | | 
% 231.54/42.86  | | | | | ALPHA: (44) implies:
% 231.54/42.86  | | | | |   (45)  all_57_13 = e2
% 231.54/42.86  | | | | | 
% 231.54/42.86  | | | | | COMBINE_EQS: (16), (45) imply:
% 231.54/42.86  | | | | |   (46)  e3 = e2
% 231.54/42.86  | | | | | 
% 231.54/42.86  | | | | | SIMP: (46) implies:
% 231.54/42.86  | | | | |   (47)  e3 = e2
% 231.54/42.86  | | | | | 
% 231.54/42.86  | | | | | COMBINE_EQS: (25), (47) imply:
% 231.54/42.86  | | | | |   (48)  all_57_1 = e2
% 231.54/42.86  | | | | | 
% 231.54/42.86  | | | | | REF_CLOSE: (2), (3), (4), (7), (9), (10), (11), (12), (13), (14),
% 231.54/42.86  | | | | |            (17), (18), (20), (48) are inconsistent by sub-proof #1650.
% 231.54/42.86  | | | | | 
% 231.54/42.86  | | | | End of split
% 231.54/42.86  | | | | 
% 231.54/42.86  | | | End of split
% 231.54/42.86  | | | 
% 231.54/42.86  | | End of split
% 231.54/42.86  | | 
% 231.54/42.86  | Case 2:
% 231.54/42.86  | | 
% 231.54/42.86  | |   (49)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) =
% 231.54/42.86  | |           e3)
% 231.54/42.86  | | 
% 231.54/42.86  | | REF_CLOSE: (3), (5), (10), (17), (20), (49) are inconsistent by sub-proof
% 231.54/42.86  | |            #1617.
% 231.54/42.86  | | 
% 231.54/42.86  | End of split
% 231.54/42.86  | 
% 231.54/42.86  End of proof
% 231.54/42.86  
% 231.54/42.86  Sub-proof #1617 shows that the following formulas are inconsistent:
% 231.54/42.86  ----------------------------------------------------------------
% 231.54/42.86    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.86           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.86    (2)  all_57_4 = e0
% 231.54/42.86    (3)   ~ (e3 = e0)
% 231.54/42.86    (4)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.54/42.86    (5)   ~ (all_53_12 = e3)
% 231.54/42.86    (6)  op(e3, e0) = all_53_12
% 231.54/42.86  
% 231.54/42.86  Begin of proof
% 231.54/42.86  | 
% 231.54/42.86  | BETA: splitting (4) gives:
% 231.54/42.86  | 
% 231.54/42.86  | Case 1:
% 231.54/42.86  | | 
% 231.54/42.86  | |   (7)  all_57_4 = e3 & op(e3, e1) = e3
% 231.54/42.86  | | 
% 231.54/42.86  | | REF_CLOSE: (2), (3), (7) are inconsistent by sub-proof #1618.
% 231.54/42.86  | | 
% 231.54/42.86  | Case 2:
% 231.54/42.86  | | 
% 231.54/42.86  | |   (8)  all_57_9 = e3 & op(e3, e0) = e3
% 231.54/42.86  | | 
% 231.54/42.86  | | ALPHA: (8) implies:
% 231.54/42.86  | |   (9)  op(e3, e0) = e3
% 231.54/42.86  | | 
% 231.54/42.86  | | REF_CLOSE: (1), (5), (6), (9) are inconsistent by sub-proof #2458.
% 231.54/42.86  | | 
% 231.54/42.86  | End of split
% 231.54/42.86  | 
% 231.54/42.86  End of proof
% 231.54/42.86  
% 231.54/42.86  Sub-proof #1618 shows that the following formulas are inconsistent:
% 231.54/42.86  ----------------------------------------------------------------
% 231.54/42.86    (1)  all_57_4 = e3 & op(e3, e1) = e3
% 231.54/42.86    (2)  all_57_4 = e0
% 231.54/42.87    (3)   ~ (e3 = e0)
% 231.54/42.87  
% 231.54/42.87  Begin of proof
% 231.54/42.87  | 
% 231.54/42.87  | ALPHA: (1) implies:
% 231.54/42.87  |   (4)  all_57_4 = e3
% 231.54/42.87  | 
% 231.54/42.87  | COMBINE_EQS: (2), (4) imply:
% 231.54/42.87  |   (5)  e3 = e0
% 231.54/42.87  | 
% 231.54/42.87  | REDUCE: (3), (5) imply:
% 231.54/42.87  |   (6)  $false
% 231.54/42.87  | 
% 231.54/42.87  | CLOSE: (6) is inconsistent.
% 231.54/42.87  | 
% 231.54/42.87  End of proof
% 231.54/42.87  
% 231.54/42.87  Sub-proof #1619 shows that the following formulas are inconsistent:
% 231.54/42.87  ----------------------------------------------------------------
% 231.54/42.87    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.87         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.54/42.87    (2)   ~ (e3 = e1)
% 231.54/42.87    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.87           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.87    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.54/42.87         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.54/42.87    (5)  all_57_4 = e0
% 231.54/42.87    (6)  op(e2, e2) = e0
% 231.54/42.87    (7)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.54/42.87         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.54/42.87    (8)  all_57_3 = e0
% 231.54/42.87    (9)   ~ (e3 = e2)
% 231.54/42.87    (10)   ~ (e3 = e0)
% 231.54/42.87    (11)  op(e3, e3) = e2
% 231.54/42.87    (12)   ~ (e2 = e0)
% 231.54/42.87    (13)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 231.54/42.87          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.54/42.87    (14)   ~ (e1 = e0)
% 231.54/42.87    (15)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.54/42.87          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.54/42.87    (16)   ~ (all_53_12 = e3)
% 231.54/42.87    (17)  all_57_7 = e3
% 231.54/42.87    (18)   ~ (e2 = e1)
% 231.54/42.87    (19)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.87          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.54/42.87    (20)  op(e3, e0) = all_53_12
% 231.54/42.87  
% 231.54/42.87  Begin of proof
% 231.54/42.87  | 
% 231.54/42.87  | BETA: splitting (13) gives:
% 231.54/42.87  | 
% 231.54/42.87  | Case 1:
% 231.54/42.87  | | 
% 231.54/42.87  | |   (21)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) =
% 231.54/42.87  | |           e3)
% 231.54/42.87  | | 
% 231.54/42.87  | | REF_CLOSE: (1), (2), (3), (8), (9), (11), (12), (14), (17), (18), (19), (21)
% 231.54/42.87  | |            are inconsistent by sub-proof #1620.
% 231.54/42.87  | | 
% 231.54/42.87  | Case 2:
% 231.54/42.87  | | 
% 231.54/42.87  | |   (22)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) =
% 231.54/42.87  | |           e3)
% 231.54/42.87  | | 
% 231.54/42.87  | | BETA: splitting (22) gives:
% 231.54/42.87  | | 
% 231.54/42.87  | | Case 1:
% 231.54/42.87  | | | 
% 231.54/42.87  | | |   (23)  all_57_4 = e3 & op(e3, e1) = e3
% 231.54/42.87  | | | 
% 231.54/42.87  | | | ALPHA: (23) implies:
% 231.54/42.87  | | |   (24)  all_57_4 = e3
% 231.54/42.87  | | | 
% 231.54/42.87  | | | COMBINE_EQS: (5), (24) imply:
% 231.54/42.87  | | |   (25)  e3 = e0
% 231.54/42.87  | | | 
% 231.54/42.87  | | | COMBINE_EQS: (17), (25) imply:
% 231.54/42.87  | | |   (26)  all_57_7 = e0
% 231.54/42.87  | | | 
% 231.54/42.87  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 231.54/42.87  | | |            (13), (14), (15), (18), (19), (26) are inconsistent by
% 231.54/42.87  | | |            sub-proof #1636.
% 231.54/42.87  | | | 
% 231.54/42.87  | | Case 2:
% 231.54/42.87  | | | 
% 231.54/42.87  | | |   (27)  all_57_9 = e3 & op(e3, e0) = e3
% 231.54/42.87  | | | 
% 231.54/42.87  | | | ALPHA: (27) implies:
% 231.54/42.87  | | |   (28)  op(e3, e0) = e3
% 231.54/42.87  | | | 
% 231.54/42.87  | | | REF_CLOSE: (3), (16), (20), (28) are inconsistent by sub-proof #2458.
% 231.54/42.87  | | | 
% 231.54/42.87  | | End of split
% 231.54/42.87  | | 
% 231.54/42.87  | End of split
% 231.54/42.87  | 
% 231.54/42.87  End of proof
% 231.54/42.87  
% 231.54/42.87  Sub-proof #1620 shows that the following formulas are inconsistent:
% 231.54/42.87  ----------------------------------------------------------------
% 231.54/42.87    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.87         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.54/42.87    (2)   ~ (e3 = e1)
% 231.54/42.87    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.87           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.87    (4)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3)
% 231.54/42.87    (5)  all_57_3 = e0
% 231.54/42.87    (6)   ~ (e3 = e2)
% 231.54/42.87    (7)  op(e3, e3) = e2
% 231.54/42.87    (8)   ~ (e2 = e0)
% 231.54/42.87    (9)   ~ (e1 = e0)
% 231.54/42.87    (10)  all_57_7 = e3
% 231.54/42.87    (11)   ~ (e2 = e1)
% 231.54/42.87    (12)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.87          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.54/42.87  
% 231.54/42.87  Begin of proof
% 231.54/42.87  | 
% 231.54/42.87  | BETA: splitting (4) gives:
% 231.54/42.87  | 
% 231.54/42.87  | Case 1:
% 231.54/42.87  | | 
% 231.54/42.87  | |   (13)  all_57_0 = e3 & op(e3, e3) = e3
% 231.54/42.87  | | 
% 231.54/42.87  | | ALPHA: (13) implies:
% 231.54/42.87  | |   (14)  op(e3, e3) = e3
% 231.54/42.87  | | 
% 231.54/42.87  | | REF_CLOSE: (3), (6), (7), (14) are inconsistent by sub-proof #2490.
% 231.54/42.87  | | 
% 231.54/42.87  | Case 2:
% 231.54/42.87  | | 
% 231.54/42.87  | |   (15)  all_57_1 = e3 & op(e3, e2) = e3
% 231.54/42.87  | | 
% 231.54/42.87  | | ALPHA: (15) implies:
% 231.54/42.87  | |   (16)  all_57_1 = e3
% 231.54/42.87  | | 
% 231.54/42.87  | | REF_CLOSE: (1), (2), (5), (6), (8), (9), (10), (11), (12), (16) are
% 231.54/42.87  | |            inconsistent by sub-proof #1778.
% 231.54/42.87  | | 
% 231.54/42.87  | End of split
% 231.54/42.87  | 
% 231.54/42.87  End of proof
% 231.54/42.87  
% 231.54/42.87  Sub-proof #1621 shows that the following formulas are inconsistent:
% 231.54/42.87  ----------------------------------------------------------------
% 231.54/42.87    (1)   ~ (e3 = e1)
% 231.54/42.87    (2)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 231.54/42.87         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.54/42.87    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.87           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.87    (4)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.54/42.87         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.54/42.87    (5)   ~ (all_6_2 = e3)
% 231.54/42.87    (6)  op(e1, e1) = all_6_2
% 231.54/42.87    (7)  all_57_7 = e1
% 231.54/42.87    (8)  op(e2, e2) = e0
% 231.54/42.87    (9)  all_57_3 = e0
% 231.54/42.87    (10)   ~ (e3 = e2)
% 231.54/42.87    (11)   ~ (e3 = e0)
% 231.54/42.87    (12)  all_57_11 = e2
% 231.54/42.87    (13)  op(e1, e1) = e1
% 231.54/42.87    (14)   ~ (e2 = e0)
% 231.54/42.87    (15)  all_57_13 = e2
% 231.54/42.87    (16)   ~ (e1 = e0)
% 231.54/42.87    (17)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.54/42.87          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.54/42.87    (18)   ~ (e2 = e1)
% 231.54/42.87    (19)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.87          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.54/42.87  
% 231.54/42.87  Begin of proof
% 231.54/42.87  | 
% 231.54/42.87  | BETA: splitting (2) gives:
% 231.54/42.87  | 
% 231.54/42.87  | Case 1:
% 231.54/42.87  | | 
% 231.54/42.87  | |   (20)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) =
% 231.54/42.87  | |           e0)
% 231.54/42.87  | | 
% 231.54/42.87  | | BETA: splitting (20) gives:
% 231.54/42.87  | | 
% 231.54/42.87  | | Case 1:
% 231.54/42.87  | | | 
% 231.54/42.87  | | |   (21)  all_57_6 = e0 & op(e1, e3) = e0
% 231.54/42.87  | | | 
% 231.54/42.87  | | | ALPHA: (21) implies:
% 231.54/42.87  | | |   (22)  all_57_6 = e0
% 231.54/42.87  | | | 
% 231.54/42.87  | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (10), (11), (12), (22) are
% 231.54/42.87  | | |            inconsistent by sub-proof #2114.
% 231.54/42.87  | | | 
% 231.54/42.87  | | Case 2:
% 231.54/42.87  | | | 
% 231.54/42.87  | | |   (23)  all_57_7 = e0 & op(e1, e2) = e0
% 231.54/42.87  | | | 
% 231.54/42.87  | | | ALPHA: (23) implies:
% 231.54/42.87  | | |   (24)  all_57_7 = e0
% 231.54/42.87  | | | 
% 231.54/42.87  | | | REF_CLOSE: (1), (3), (8), (9), (10), (11), (15), (16), (17), (18), (19),
% 231.54/42.87  | | |            (24) are inconsistent by sub-proof #2202.
% 231.54/42.87  | | | 
% 231.54/42.87  | | End of split
% 231.54/42.87  | | 
% 231.54/42.87  | Case 2:
% 231.54/42.87  | | 
% 231.54/42.87  | |   (25)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 231.54/42.87  | |           e0)
% 231.54/42.87  | | 
% 231.54/42.87  | | REF_CLOSE: (3), (12), (13), (14), (16), (25) are inconsistent by sub-proof
% 231.54/42.87  | |            #1622.
% 231.54/42.87  | | 
% 231.54/42.87  | End of split
% 231.54/42.87  | 
% 231.54/42.87  End of proof
% 231.54/42.87  
% 231.54/42.87  Sub-proof #1622 shows that the following formulas are inconsistent:
% 231.54/42.87  ----------------------------------------------------------------
% 231.54/42.87    (1)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.54/42.87    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.87           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.87    (3)  all_57_11 = e2
% 231.54/42.87    (4)  op(e1, e1) = e1
% 231.54/42.87    (5)   ~ (e2 = e0)
% 231.54/42.87    (6)   ~ (e1 = e0)
% 231.54/42.87  
% 231.54/42.87  Begin of proof
% 231.54/42.87  | 
% 231.54/42.87  | BETA: splitting (1) gives:
% 231.54/42.87  | 
% 231.54/42.87  | Case 1:
% 231.54/42.87  | | 
% 231.54/42.87  | |   (7)  all_57_8 = e0 & op(e1, e1) = e0
% 231.54/42.87  | | 
% 231.54/42.87  | | ALPHA: (7) implies:
% 231.54/42.87  | |   (8)  op(e1, e1) = e0
% 231.54/42.87  | | 
% 231.54/42.87  | | REF_CLOSE: (2), (4), (6), (8) are inconsistent by sub-proof #2427.
% 231.54/42.87  | | 
% 231.54/42.87  | Case 2:
% 231.54/42.87  | | 
% 231.54/42.87  | |   (9)  all_57_11 = e0 & op(e1, e0) = e0
% 231.54/42.87  | | 
% 231.54/42.87  | | REF_CLOSE: (3), (5), (9) are inconsistent by sub-proof #2041.
% 231.54/42.87  | | 
% 231.54/42.87  | End of split
% 231.54/42.87  | 
% 231.54/42.87  End of proof
% 231.54/42.87  
% 231.54/42.87  Sub-proof #1623 shows that the following formulas are inconsistent:
% 231.54/42.87  ----------------------------------------------------------------
% 231.54/42.87    (1)  all_57_15 = e0
% 231.54/42.87    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.87         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.54/42.87    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.54/42.87         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.54/42.87    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.87         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.54/42.87    (5)   ~ (e3 = e1)
% 231.54/42.87    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.87           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.87    (7)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.54/42.87         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.54/42.87    (8)   ~ (all_6_2 = e3)
% 231.54/42.87    (9)  op(e1, e1) = all_6_2
% 231.54/42.87    (10)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.54/42.87          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.54/42.87    (11)  all_57_4 = e0
% 231.54/42.87    (12)  op(e2, e2) = e0
% 231.54/42.87    (13)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.54/42.87          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.54/42.87    (14)  all_57_3 = e0
% 231.54/42.87    (15)   ~ (e3 = e2)
% 231.54/42.87    (16)   ~ (e3 = e0)
% 231.54/42.87    (17)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.54/42.87          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.54/42.87    (18)  all_57_6 = e0
% 231.54/42.87    (19)  op(e3, e3) = e2
% 231.54/42.87    (20)   ~ (e2 = e0)
% 231.54/42.87    (21)  all_57_13 = e2
% 231.54/42.87    (22)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 231.54/42.87          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.54/42.87    (23)   ~ (e1 = e0)
% 231.54/42.87    (24)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.54/42.87          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.54/42.87    (25)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.54/42.87          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.54/42.87    (26)  op(e1, e1) = e2
% 231.54/42.87    (27)   ~ (all_52_27 = e0)
% 231.54/42.87    (28)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.54/42.87          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.54/42.87    (29)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.87          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.54/42.87    (30)  op(e0, e2) = all_52_27
% 231.54/42.87    (31)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 231.54/42.87          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 231.54/42.87    (32)   ~ (e2 = e1)
% 231.54/42.87    (33)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.54/42.87          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.54/42.87    (34)   ~ (all_53_12 = e2)
% 231.54/42.87    (35)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.54/42.87          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.54/42.87    (36)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.54/42.87          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.54/42.87    (37)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.54/42.87          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.54/42.87    (38)  op(all_52_27, all_52_27) = e2
% 231.54/42.87    (39)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 231.54/42.87          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 231.54/42.87    (40)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.87          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.54/42.87    (41)  all_57_13 = e2 & op(e0, e2) = e2
% 231.54/42.87    (42)  op(e3, e0) = all_53_12
% 231.54/42.87  
% 231.54/42.87  Begin of proof
% 231.54/42.87  | 
% 231.54/42.87  | BETA: splitting (29) gives:
% 231.54/42.87  | 
% 231.54/42.87  | Case 1:
% 231.54/42.87  | | 
% 231.54/42.87  | |   (43)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 231.54/42.87  | |           e2)
% 231.54/42.87  | | 
% 231.54/42.87  | | BETA: splitting (43) gives:
% 231.54/42.87  | | 
% 231.54/42.87  | | Case 1:
% 231.54/42.87  | | | 
% 231.54/42.87  | | |   (44)  all_57_2 = e2 & op(e2, e3) = e2
% 231.54/42.87  | | | 
% 231.54/42.87  | | | ALPHA: (44) implies:
% 231.54/42.87  | | |   (45)  all_57_2 = e2
% 231.54/42.87  | | | 
% 231.54/42.87  | | | REF_CLOSE: (2), (3), (5), (6), (14), (15), (16), (18), (19), (20), (23),
% 231.54/42.87  | | |            (28), (29), (31), (32), (36), (45) are inconsistent by
% 231.54/42.87  | | |            sub-proof #1628.
% 231.54/42.87  | | | 
% 231.54/42.87  | | Case 2:
% 231.54/42.87  | | | 
% 231.54/42.87  | | |   (46)  all_57_3 = e2 & op(e2, e2) = e2
% 231.54/42.87  | | | 
% 231.54/42.87  | | | ALPHA: (46) implies:
% 231.54/42.87  | | |   (47)  op(e2, e2) = e2
% 231.54/42.87  | | | 
% 231.54/42.87  | | | REF_CLOSE: (6), (12), (20), (47) are inconsistent by sub-proof #2472.
% 231.54/42.87  | | | 
% 231.54/42.87  | | End of split
% 231.54/42.87  | | 
% 231.54/42.87  | Case 2:
% 231.54/42.87  | | 
% 231.54/42.87  | |   (48)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 231.54/42.87  | |           e2)
% 231.54/42.87  | | 
% 231.54/42.87  | | BETA: splitting (48) gives:
% 231.54/42.87  | | 
% 231.54/42.87  | | Case 1:
% 231.54/42.87  | | | 
% 231.54/42.87  | | |   (49)  all_57_5 = e2 & op(e2, e1) = e2
% 231.54/42.87  | | | 
% 231.54/42.87  | | | ALPHA: (49) implies:
% 231.54/42.87  | | |   (50)  all_57_5 = e2
% 231.54/42.87  | | | 
% 231.54/42.87  | | | BETA: splitting (33) gives:
% 231.54/42.87  | | | 
% 231.54/42.87  | | | Case 1:
% 231.54/42.87  | | | | 
% 231.54/42.87  | | | |   (51)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0)
% 231.54/42.87  | | | |           = e2)
% 231.54/42.87  | | | | 
% 231.54/42.87  | | | | BETA: splitting (51) gives:
% 231.54/42.87  | | | | 
% 231.54/42.87  | | | | Case 1:
% 231.54/42.87  | | | | | 
% 231.54/42.87  | | | | |   (52)  all_57_9 = e2 & op(e3, e0) = e2
% 231.54/42.87  | | | | | 
% 231.54/42.87  | | | | | ALPHA: (52) implies:
% 231.54/42.87  | | | | |   (53)  op(e3, e0) = e2
% 231.54/42.87  | | | | | 
% 231.54/42.87  | | | | | REF_CLOSE: (6), (34), (42), (53) are inconsistent by sub-proof #2331.
% 231.54/42.87  | | | | | 
% 231.54/42.87  | | | | Case 2:
% 231.54/42.87  | | | | | 
% 231.54/42.87  | | | | |   (54)  all_57_10 = e2 & op(e2, e0) = e2
% 231.54/42.87  | | | | | 
% 231.54/42.87  | | | | | ALPHA: (54) implies:
% 231.54/42.87  | | | | |   (55)  all_57_10 = e2
% 231.54/42.87  | | | | | 
% 231.54/42.87  | | | | | REF_CLOSE: (1), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 231.54/42.87  | | | | |            (14), (15), (16), (18), (19), (20), (22), (23), (27), (30),
% 231.54/42.87  | | | | |            (32), (33), (34), (37), (38), (40), (41), (42), (55) are
% 231.54/42.87  | | | | |            inconsistent by sub-proof #1627.
% 231.54/42.87  | | | | | 
% 231.54/42.87  | | | | End of split
% 231.54/42.87  | | | | 
% 231.54/42.87  | | | Case 2:
% 231.54/42.87  | | | | 
% 231.54/42.87  | | | |   (56)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0,
% 231.54/42.87  | | | |             e0) = e2)
% 231.54/42.87  | | | | 
% 231.54/42.87  | | | | BETA: splitting (56) gives:
% 231.54/42.87  | | | | 
% 231.54/42.87  | | | | Case 1:
% 231.54/42.87  | | | | | 
% 231.54/42.87  | | | | |   (57)  all_57_11 = e2 & op(e1, e0) = e2
% 231.54/42.87  | | | | | 
% 231.54/42.87  | | | | | ALPHA: (57) implies:
% 231.54/42.87  | | | | |   (58)  all_57_11 = e2
% 231.54/42.87  | | | | | 
% 231.54/42.87  | | | | | BETA: splitting (7) gives:
% 231.54/42.87  | | | | | 
% 231.54/42.87  | | | | | Case 1:
% 231.54/42.87  | | | | | | 
% 231.54/42.87  | | | | | |   (59)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1,
% 231.54/42.87  | | | | | |             e2) = e3)
% 231.54/42.87  | | | | | | 
% 231.54/42.87  | | | | | | BETA: splitting (59) gives:
% 231.54/42.87  | | | | | | 
% 231.54/42.87  | | | | | | Case 1:
% 231.54/42.87  | | | | | | | 
% 231.54/42.87  | | | | | | |   (60)  all_57_6 = e3 & op(e1, e3) = e3
% 231.54/42.87  | | | | | | | 
% 231.54/42.87  | | | | | | | ALPHA: (60) implies:
% 231.54/42.87  | | | | | | |   (61)  all_57_6 = e3
% 231.54/42.87  | | | | | | | 
% 231.54/42.87  | | | | | | | REF_CLOSE: (16), (18), (61) are inconsistent by sub-proof #1822.
% 231.54/42.87  | | | | | | | 
% 231.54/42.87  | | | | | | Case 2:
% 231.54/42.87  | | | | | | | 
% 231.54/42.87  | | | | | | |   (62)  all_57_7 = e3 & op(e1, e2) = e3
% 231.54/42.87  | | | | | | | 
% 231.54/42.87  | | | | | | | ALPHA: (62) implies:
% 231.54/42.87  | | | | | | |   (63)  all_57_7 = e3
% 231.54/42.87  | | | | | | | 
% 231.54/42.87  | | | | | | | BETA: splitting (40) gives:
% 231.54/42.87  | | | | | | | 
% 231.54/42.87  | | | | | | | Case 1:
% 231.54/42.87  | | | | | | | | 
% 231.54/42.87  | | | | | | | |   (64)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 &
% 231.54/42.87  | | | | | | | |           op(e2, e2) = e1)
% 231.54/42.87  | | | | | | | | 
% 231.54/42.87  | | | | | | | | BETA: splitting (64) gives:
% 231.54/42.87  | | | | | | | | 
% 231.54/42.87  | | | | | | | | Case 1:
% 231.54/42.87  | | | | | | | | | 
% 231.54/42.87  | | | | | | | | |   (65)  all_57_1 = e1 & op(e3, e2) = e1
% 231.54/42.87  | | | | | | | | | 
% 231.54/42.87  | | | | | | | | | ALPHA: (65) implies:
% 231.54/42.87  | | | | | | | | |   (66)  all_57_1 = e1
% 231.54/42.87  | | | | | | | | | 
% 231.54/42.87  | | | | | | | | | BETA: splitting (39) gives:
% 231.54/42.87  | | | | | | | | | 
% 231.54/42.87  | | | | | | | | | Case 1:
% 231.54/42.87  | | | | | | | | | | 
% 231.54/42.87  | | | | | | | | | |   (67)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 &
% 231.54/42.87  | | | | | | | | | |           op(e1, e2) = e1)
% 231.54/42.87  | | | | | | | | | | 
% 231.54/42.87  | | | | | | | | | | BETA: splitting (67) gives:
% 231.54/42.87  | | | | | | | | | | 
% 231.54/42.87  | | | | | | | | | | Case 1:
% 231.54/42.87  | | | | | | | | | | | 
% 231.54/42.87  | | | | | | | | | | |   (68)  all_57_6 = e1 & op(e1, e3) = e1
% 231.54/42.87  | | | | | | | | | | | 
% 231.54/42.87  | | | | | | | | | | | ALPHA: (68) implies:
% 231.54/42.87  | | | | | | | | | | |   (69)  all_57_6 = e1
% 231.54/42.87  | | | | | | | | | | | 
% 231.54/42.87  | | | | | | | | | | | COMBINE_EQS: (18), (69) imply:
% 231.54/42.87  | | | | | | | | | | |   (70)  e1 = e0
% 231.54/42.87  | | | | | | | | | | | 
% 231.54/42.87  | | | | | | | | | | | REF_CLOSE: (4), (5), (14), (15), (20), (23), (32), (40),
% 231.54/42.87  | | | | | | | | | | |            (63), (66), (70) are inconsistent by sub-proof
% 231.54/42.87  | | | | | | | | | | |            #1626.
% 231.54/42.87  | | | | | | | | | | | 
% 231.54/42.87  | | | | | | | | | | Case 2:
% 231.54/42.87  | | | | | | | | | | | 
% 231.54/42.87  | | | | | | | | | | |   (71)  all_57_7 = e1 & op(e1, e2) = e1
% 231.54/42.87  | | | | | | | | | | | 
% 231.54/42.87  | | | | | | | | | | | ALPHA: (71) implies:
% 231.54/42.87  | | | | | | | | | | |   (72)  all_57_7 = e1
% 231.54/42.87  | | | | | | | | | | | 
% 231.54/42.87  | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (15), (16), (18), (58),
% 231.54/42.87  | | | | | | | | | | |            (72) are inconsistent by sub-proof #2114.
% 231.54/42.87  | | | | | | | | | | | 
% 231.54/42.87  | | | | | | | | | | End of split
% 231.54/42.87  | | | | | | | | | | 
% 231.54/42.87  | | | | | | | | | Case 2:
% 231.54/42.87  | | | | | | | | | | 
% 231.54/42.87  | | | | | | | | | |   (73)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1
% 231.54/42.87  | | | | | | | | | |           & op(e1, e0) = e1)
% 231.54/42.87  | | | | | | | | | | 
% 231.54/42.87  | | | | | | | | | | BETA: splitting (73) gives:
% 231.54/42.87  | | | | | | | | | | 
% 231.54/42.87  | | | | | | | | | | Case 1:
% 231.54/42.87  | | | | | | | | | | | 
% 231.54/42.87  | | | | | | | | | | |   (74)  all_57_8 = e1 & op(e1, e1) = e1
% 231.54/42.87  | | | | | | | | | | | 
% 231.54/42.87  | | | | | | | | | | | ALPHA: (74) implies:
% 231.54/42.87  | | | | | | | | | | |   (75)  op(e1, e1) = e1
% 231.54/42.87  | | | | | | | | | | | 
% 231.54/42.87  | | | | | | | | | | | REF_CLOSE: (6), (26), (32), (75) are inconsistent by
% 231.54/42.87  | | | | | | | | | | |            sub-proof #2423.
% 231.54/42.87  | | | | | | | | | | | 
% 231.54/42.87  | | | | | | | | | | Case 2:
% 231.54/42.87  | | | | | | | | | | | 
% 231.54/42.87  | | | | | | | | | | |   (76)  all_57_11 = e1 & op(e1, e0) = e1
% 231.54/42.87  | | | | | | | | | | | 
% 231.54/42.87  | | | | | | | | | | | ALPHA: (76) implies:
% 231.54/42.87  | | | | | | | | | | |   (77)  all_57_11 = e1
% 231.54/42.87  | | | | | | | | | | | 
% 231.54/42.87  | | | | | | | | | | | COMBINE_EQS: (58), (77) imply:
% 231.54/42.87  | | | | | | | | | | |   (78)  e2 = e1
% 231.54/42.87  | | | | | | | | | | | 
% 231.54/42.87  | | | | | | | | | | | COMBINE_EQS: (21), (78) imply:
% 231.54/42.87  | | | | | | | | | | |   (79)  all_57_13 = e1
% 231.54/42.87  | | | | | | | | | | | 
% 231.54/42.87  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (10), (11), (12), (13), (14), (15),
% 231.54/42.87  | | | | | | | | | | |            (16), (19), (20), (22), (23), (25), (32), (66),
% 231.54/42.87  | | | | | | | | | | |            (79) are inconsistent by sub-proof #1625.
% 231.54/42.87  | | | | | | | | | | | 
% 231.54/42.87  | | | | | | | | | | End of split
% 231.54/42.87  | | | | | | | | | | 
% 231.54/42.87  | | | | | | | | | End of split
% 231.54/42.87  | | | | | | | | | 
% 231.54/42.87  | | | | | | | | Case 2:
% 231.54/42.87  | | | | | | | | | 
% 231.54/42.87  | | | | | | | | |   (80)  all_57_3 = e1 & op(e2, e2) = e1
% 231.54/42.87  | | | | | | | | | 
% 231.54/42.87  | | | | | | | | | ALPHA: (80) implies:
% 231.54/42.87  | | | | | | | | |   (81)  op(e2, e2) = e1
% 231.54/42.87  | | | | | | | | | 
% 231.54/42.87  | | | | | | | | | REF_CLOSE: (6), (12), (23), (81) are inconsistent by sub-proof
% 231.54/42.87  | | | | | | | | |            #2352.
% 231.54/42.87  | | | | | | | | | 
% 231.54/42.87  | | | | | | | | End of split
% 231.54/42.87  | | | | | | | | 
% 231.54/42.87  | | | | | | | Case 2:
% 231.54/42.87  | | | | | | | | 
% 231.54/42.87  | | | | | | | |   (82)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 &
% 231.54/42.87  | | | | | | | |           op(e0, e2) = e1)
% 231.54/42.87  | | | | | | | | 
% 231.54/42.87  | | | | | | | | BETA: splitting (82) gives:
% 231.54/42.87  | | | | | | | | 
% 231.54/42.87  | | | | | | | | Case 1:
% 231.54/42.87  | | | | | | | | | 
% 231.54/42.87  | | | | | | | | |   (83)  all_57_7 = e1 & op(e1, e2) = e1
% 231.54/42.87  | | | | | | | | | 
% 231.54/42.87  | | | | | | | | | ALPHA: (83) implies:
% 231.54/42.87  | | | | | | | | |   (84)  all_57_7 = e1
% 231.54/42.87  | | | | | | | | | 
% 231.54/42.87  | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (15), (16), (18), (58),
% 231.54/42.87  | | | | | | | | |            (84) are inconsistent by sub-proof #2114.
% 231.54/42.87  | | | | | | | | | 
% 231.54/42.87  | | | | | | | | Case 2:
% 231.54/42.87  | | | | | | | | | 
% 231.54/42.87  | | | | | | | | |   (85)  all_57_13 = e1 & op(e0, e2) = e1
% 231.54/42.87  | | | | | | | | | 
% 231.54/42.87  | | | | | | | | | REF_CLOSE: (21), (32), (85) are inconsistent by sub-proof
% 231.54/42.87  | | | | | | | | |            #2205.
% 231.54/42.87  | | | | | | | | | 
% 231.54/42.87  | | | | | | | | End of split
% 231.54/42.87  | | | | | | | | 
% 231.54/42.87  | | | | | | | End of split
% 231.54/42.87  | | | | | | | 
% 231.54/42.87  | | | | | | End of split
% 231.54/42.87  | | | | | | 
% 231.54/42.87  | | | | | Case 2:
% 231.54/42.87  | | | | | | 
% 231.54/42.87  | | | | | |   (86)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1,
% 231.54/42.87  | | | | | |             e0) = e3)
% 231.54/42.87  | | | | | | 
% 231.54/42.87  | | | | | | REF_CLOSE: (6), (8), (9), (15), (58), (86) are inconsistent by
% 231.54/42.87  | | | | | |            sub-proof #2040.
% 231.54/42.87  | | | | | | 
% 231.54/42.87  | | | | | End of split
% 231.54/42.87  | | | | | 
% 231.54/42.87  | | | | Case 2:
% 231.54/42.87  | | | | | 
% 231.54/42.87  | | | | |   (87)  all_57_15 = e2 & op(e0, e0) = e2
% 231.54/42.87  | | | | | 
% 231.54/42.87  | | | | | ALPHA: (87) implies:
% 231.54/42.87  | | | | |   (88)  all_57_15 = e2
% 231.54/42.87  | | | | | 
% 231.54/42.87  | | | | | COMBINE_EQS: (1), (88) imply:
% 231.54/42.87  | | | | |   (89)  e2 = e0
% 231.54/42.87  | | | | | 
% 231.54/42.87  | | | | | COMBINE_EQS: (50), (89) imply:
% 231.54/42.87  | | | | |   (90)  all_57_5 = e0
% 231.54/42.87  | | | | | 
% 231.54/42.87  | | | | | REF_CLOSE: (2), (5), (6), (8), (9), (11), (12), (14), (15), (16),
% 231.54/42.87  | | | | |            (17), (20), (23), (24), (28), (29), (32), (35), (90) are
% 231.54/42.87  | | | | |            inconsistent by sub-proof #1624.
% 231.54/42.87  | | | | | 
% 231.54/42.87  | | | | End of split
% 231.54/42.87  | | | | 
% 231.54/42.87  | | | End of split
% 231.54/42.87  | | | 
% 231.54/42.87  | | Case 2:
% 231.54/42.87  | | | 
% 231.54/42.87  | | |   (91)  all_57_10 = e2 & op(e2, e0) = e2
% 231.54/42.87  | | | 
% 231.54/42.87  | | | ALPHA: (91) implies:
% 231.54/42.87  | | |   (92)  all_57_10 = e2
% 231.54/42.87  | | | 
% 231.54/42.87  | | | REF_CLOSE: (1), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 231.54/42.87  | | |            (14), (15), (16), (18), (19), (20), (22), (23), (27), (30),
% 231.54/42.87  | | |            (32), (33), (34), (37), (38), (40), (41), (42), (92) are
% 231.54/42.87  | | |            inconsistent by sub-proof #1627.
% 231.54/42.87  | | | 
% 231.54/42.87  | | End of split
% 231.54/42.87  | | 
% 231.54/42.87  | End of split
% 231.54/42.87  | 
% 231.54/42.87  End of proof
% 231.54/42.87  
% 231.54/42.87  Sub-proof #1624 shows that the following formulas are inconsistent:
% 231.54/42.87  ----------------------------------------------------------------
% 231.54/42.87    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.87         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.54/42.87    (2)   ~ (e3 = e1)
% 231.54/42.87    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.87           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.87    (4)   ~ (all_6_2 = e3)
% 231.54/42.87    (5)  op(e1, e1) = all_6_2
% 231.54/42.87    (6)  all_57_4 = e0
% 231.54/42.87    (7)  op(e2, e2) = e0
% 231.54/42.87    (8)  all_57_3 = e0
% 231.54/42.87    (9)   ~ (e3 = e2)
% 231.54/42.87    (10)   ~ (e3 = e0)
% 231.54/42.87    (11)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.54/42.87          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.54/42.87    (12)   ~ (e2 = e0)
% 231.54/42.87    (13)   ~ (e1 = e0)
% 231.54/42.87    (14)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.54/42.87          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.54/42.87    (15)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.54/42.87          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.54/42.87    (16)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.87          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.54/42.87    (17)   ~ (e2 = e1)
% 231.54/42.87    (18)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.54/42.87          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.54/42.87    (19)  all_57_5 = e0
% 231.54/42.87  
% 231.54/42.87  Begin of proof
% 231.54/42.87  | 
% 231.54/42.87  | BETA: splitting (16) gives:
% 231.54/42.87  | 
% 231.54/42.87  | Case 1:
% 231.54/42.87  | | 
% 231.54/42.87  | |   (20)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 231.54/42.87  | |           e2)
% 231.54/42.87  | | 
% 231.54/42.87  | | BETA: splitting (20) gives:
% 231.54/42.87  | | 
% 231.54/42.87  | | Case 1:
% 231.54/42.87  | | | 
% 231.54/42.87  | | |   (21)  all_57_2 = e2 & op(e2, e3) = e2
% 231.54/42.87  | | | 
% 231.54/42.87  | | | ALPHA: (21) implies:
% 231.54/42.87  | | |   (22)  all_57_2 = e2
% 231.54/42.87  | | | 
% 231.54/42.87  | | | BETA: splitting (1) gives:
% 231.54/42.87  | | | 
% 231.54/42.87  | | | Case 1:
% 231.54/42.87  | | | | 
% 231.54/42.87  | | | |   (23)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2)
% 231.54/42.87  | | | |           = e1)
% 231.54/42.87  | | | | 
% 231.54/42.87  | | | | REF_CLOSE: (1), (2), (3), (7), (8), (9), (10), (12), (13), (15), (16),
% 231.54/42.87  | | | |            (17), (19), (23) are inconsistent by sub-proof #2351.
% 231.54/42.87  | | | | 
% 231.54/42.87  | | | Case 2:
% 231.54/42.87  | | | | 
% 231.54/42.87  | | | |   (24)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0)
% 231.54/42.87  | | | |           = e1)
% 231.54/42.87  | | | | 
% 231.54/42.87  | | | | BETA: splitting (24) gives:
% 231.54/42.87  | | | | 
% 231.54/42.87  | | | | Case 1:
% 231.54/42.87  | | | | | 
% 231.54/42.87  | | | | |   (25)  all_57_5 = e1 & op(e2, e1) = e1
% 231.54/42.87  | | | | | 
% 231.54/42.87  | | | | | ALPHA: (25) implies:
% 231.54/42.87  | | | | |   (26)  all_57_5 = e1
% 231.54/42.87  | | | | | 
% 231.54/42.87  | | | | | REF_CLOSE: (13), (19), (26) are inconsistent by sub-proof #2350.
% 231.54/42.87  | | | | | 
% 231.54/42.87  | | | | Case 2:
% 231.54/42.87  | | | | | 
% 231.54/42.87  | | | | |   (27)  all_57_10 = e1 & op(e2, e0) = e1
% 231.54/42.87  | | | | | 
% 231.54/42.87  | | | | | ALPHA: (27) implies:
% 231.54/42.87  | | | | |   (28)  all_57_10 = e1
% 231.54/42.87  | | | | | 
% 231.54/42.87  | | | | | BETA: splitting (14) gives:
% 231.54/42.87  | | | | | 
% 231.54/42.87  | | | | | Case 1:
% 231.54/42.87  | | | | | | 
% 231.54/42.87  | | | | | |   (29)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2,
% 231.54/42.87  | | | | | |             e1) = e3)
% 231.54/42.87  | | | | | | 
% 231.54/42.87  | | | | | | BETA: splitting (29) gives:
% 231.54/42.87  | | | | | | 
% 231.54/42.87  | | | | | | Case 1:
% 231.54/42.87  | | | | | | | 
% 231.54/42.87  | | | | | | |   (30)  all_57_4 = e3 & op(e3, e1) = e3
% 231.54/42.87  | | | | | | | 
% 231.54/42.87  | | | | | | | ALPHA: (30) implies:
% 231.54/42.87  | | | | | | |   (31)  all_57_4 = e3
% 231.54/42.87  | | | | | | | 
% 231.54/42.88  | | | | | | | REF_CLOSE: (6), (10), (31) are inconsistent by sub-proof #2372.
% 231.54/42.88  | | | | | | | 
% 231.54/42.88  | | | | | | Case 2:
% 231.54/42.88  | | | | | | | 
% 231.54/42.88  | | | | | | |   (32)  all_57_5 = e3 & op(e2, e1) = e3
% 231.54/42.88  | | | | | | | 
% 231.54/42.88  | | | | | | | ALPHA: (32) implies:
% 231.54/42.88  | | | | | | |   (33)  all_57_5 = e3
% 231.54/42.88  | | | | | | | 
% 231.54/42.88  | | | | | | | REF_CLOSE: (10), (19), (33) are inconsistent by sub-proof #2471.
% 231.54/42.88  | | | | | | | 
% 231.54/42.88  | | | | | | End of split
% 231.54/42.88  | | | | | | 
% 231.54/42.88  | | | | | Case 2:
% 231.54/42.88  | | | | | | 
% 231.54/42.88  | | | | | |   (34)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0,
% 231.54/42.88  | | | | | |             e1) = e3)
% 231.54/42.88  | | | | | | 
% 231.54/42.88  | | | | | | BETA: splitting (34) gives:
% 231.54/42.88  | | | | | | 
% 231.54/42.88  | | | | | | Case 1:
% 231.54/42.88  | | | | | | | 
% 231.54/42.88  | | | | | | |   (35)  all_57_8 = e3 & op(e1, e1) = e3
% 231.54/42.88  | | | | | | | 
% 231.54/42.88  | | | | | | | ALPHA: (35) implies:
% 231.54/42.88  | | | | | | |   (36)  op(e1, e1) = e3
% 231.54/42.88  | | | | | | | 
% 231.54/42.88  | | | | | | | REF_CLOSE: (3), (4), (5), (36) are inconsistent by sub-proof
% 231.54/42.88  | | | | | | |            #2468.
% 231.54/42.88  | | | | | | | 
% 231.54/42.88  | | | | | | Case 2:
% 231.54/42.88  | | | | | | | 
% 231.54/42.88  | | | | | | |   (37)  all_57_14 = e3 & op(e0, e1) = e3
% 231.54/42.88  | | | | | | | 
% 231.54/42.88  | | | | | | | ALPHA: (37) implies:
% 231.54/42.88  | | | | | | |   (38)  all_57_14 = e3
% 231.54/42.88  | | | | | | | 
% 231.54/42.88  | | | | | | | BETA: splitting (15) gives:
% 231.54/42.88  | | | | | | | 
% 231.54/42.88  | | | | | | | Case 1:
% 231.54/42.88  | | | | | | | | 
% 231.54/42.88  | | | | | | | |   (39)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 &
% 231.54/42.88  | | | | | | | |           op(e2, e2) = e3)
% 231.54/42.88  | | | | | | | | 
% 231.54/42.88  | | | | | | | | BETA: splitting (39) gives:
% 231.54/42.88  | | | | | | | | 
% 231.54/42.88  | | | | | | | | Case 1:
% 231.54/42.88  | | | | | | | | | 
% 231.54/42.88  | | | | | | | | |   (40)  all_57_2 = e3 & op(e2, e3) = e3
% 231.54/42.88  | | | | | | | | | 
% 231.54/42.88  | | | | | | | | | ALPHA: (40) implies:
% 231.54/42.88  | | | | | | | | |   (41)  all_57_2 = e3
% 231.54/42.88  | | | | | | | | | 
% 231.54/42.88  | | | | | | | | | REF_CLOSE: (9), (22), (41) are inconsistent by sub-proof
% 231.54/42.88  | | | | | | | | |            #1800.
% 231.54/42.88  | | | | | | | | | 
% 231.54/42.88  | | | | | | | | Case 2:
% 231.54/42.88  | | | | | | | | | 
% 231.54/42.88  | | | | | | | | |   (42)  all_57_3 = e3 & op(e2, e2) = e3
% 231.54/42.88  | | | | | | | | | 
% 231.54/42.88  | | | | | | | | | ALPHA: (42) implies:
% 231.54/42.88  | | | | | | | | |   (43)  all_57_3 = e3
% 231.54/42.88  | | | | | | | | | 
% 231.54/42.88  | | | | | | | | | COMBINE_EQS: (8), (43) imply:
% 231.54/42.88  | | | | | | | | |   (44)  e3 = e0
% 231.54/42.88  | | | | | | | | | 
% 231.54/42.88  | | | | | | | | | SIMP: (44) implies:
% 231.54/42.88  | | | | | | | | |   (45)  e3 = e0
% 231.54/42.88  | | | | | | | | | 
% 231.54/42.88  | | | | | | | | | COMBINE_EQS: (38), (45) imply:
% 231.54/42.88  | | | | | | | | |   (46)  all_57_14 = e0
% 231.54/42.88  | | | | | | | | | 
% 231.54/42.88  | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (9), (10), (11), (12),
% 231.54/42.88  | | | | | | | | |            (13), (14), (17), (18), (46) are inconsistent by
% 231.54/42.88  | | | | | | | | |            sub-proof #2371.
% 231.54/42.88  | | | | | | | | | 
% 231.54/42.88  | | | | | | | | End of split
% 231.54/42.88  | | | | | | | | 
% 231.54/42.88  | | | | | | | Case 2:
% 231.54/42.88  | | | | | | | | 
% 231.54/42.88  | | | | | | | |   (47)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 &
% 231.54/42.88  | | | | | | | |           op(e2, e0) = e3)
% 231.54/42.88  | | | | | | | | 
% 231.54/42.88  | | | | | | | | BETA: splitting (47) gives:
% 231.54/42.88  | | | | | | | | 
% 231.54/42.88  | | | | | | | | Case 1:
% 231.54/42.88  | | | | | | | | | 
% 231.54/42.88  | | | | | | | | |   (48)  all_57_5 = e3 & op(e2, e1) = e3
% 231.54/42.88  | | | | | | | | | 
% 231.54/42.88  | | | | | | | | | ALPHA: (48) implies:
% 231.54/42.88  | | | | | | | | |   (49)  all_57_5 = e3
% 231.54/42.88  | | | | | | | | | 
% 231.54/42.88  | | | | | | | | | COMBINE_EQS: (19), (49) imply:
% 231.54/42.88  | | | | | | | | |   (50)  e3 = e0
% 231.54/42.88  | | | | | | | | | 
% 231.54/42.88  | | | | | | | | | SIMP: (50) implies:
% 231.54/42.88  | | | | | | | | |   (51)  e3 = e0
% 231.54/42.88  | | | | | | | | | 
% 231.54/42.88  | | | | | | | | | COMBINE_EQS: (38), (51) imply:
% 231.54/42.88  | | | | | | | | |   (52)  all_57_14 = e0
% 231.54/42.88  | | | | | | | | | 
% 231.54/42.88  | | | | | | | | | REF_CLOSE: (2), (3), (6), (9), (11), (12), (13), (17), (18),
% 231.54/42.88  | | | | | | | | |            (49), (52) are inconsistent by sub-proof #2378.
% 231.54/42.88  | | | | | | | | | 
% 231.54/42.88  | | | | | | | | Case 2:
% 231.54/42.88  | | | | | | | | | 
% 231.54/42.88  | | | | | | | | |   (53)  all_57_10 = e3 & op(e2, e0) = e3
% 231.54/42.88  | | | | | | | | | 
% 231.54/42.88  | | | | | | | | | ALPHA: (53) implies:
% 231.54/42.88  | | | | | | | | |   (54)  all_57_10 = e3
% 231.54/42.88  | | | | | | | | | 
% 231.54/42.88  | | | | | | | | | REF_CLOSE: (2), (28), (54) are inconsistent by sub-proof
% 231.54/42.88  | | | | | | | | |            #2248.
% 231.54/42.88  | | | | | | | | | 
% 231.54/42.88  | | | | | | | | End of split
% 231.54/42.88  | | | | | | | | 
% 231.54/42.88  | | | | | | | End of split
% 231.54/42.88  | | | | | | | 
% 231.54/42.88  | | | | | | End of split
% 231.54/42.88  | | | | | | 
% 231.54/42.88  | | | | | End of split
% 231.54/42.88  | | | | | 
% 231.54/42.88  | | | | End of split
% 231.54/42.88  | | | | 
% 231.54/42.88  | | | End of split
% 231.54/42.88  | | | 
% 231.54/42.88  | | Case 2:
% 231.54/42.88  | | | 
% 231.54/42.88  | | |   (55)  all_57_3 = e2 & op(e2, e2) = e2
% 231.54/42.88  | | | 
% 231.54/42.88  | | | ALPHA: (55) implies:
% 231.54/42.88  | | |   (56)  op(e2, e2) = e2
% 231.54/42.88  | | | 
% 231.54/42.88  | | | REF_CLOSE: (3), (7), (12), (56) are inconsistent by sub-proof #2472.
% 231.54/42.88  | | | 
% 231.54/42.88  | | End of split
% 231.54/42.88  | | 
% 231.54/42.88  | Case 2:
% 231.54/42.88  | | 
% 231.54/42.88  | |   (57)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 231.54/42.88  | |           e2)
% 231.54/42.88  | | 
% 231.54/42.88  | | REF_CLOSE: (1), (2), (8), (9), (10), (12), (13), (15), (17), (19), (57) are
% 231.54/42.88  | |            inconsistent by sub-proof #2354.
% 231.54/42.88  | | 
% 231.54/42.88  | End of split
% 231.54/42.88  | 
% 231.54/42.88  End of proof
% 231.54/42.88  
% 231.54/42.88  Sub-proof #1625 shows that the following formulas are inconsistent:
% 231.54/42.88  ----------------------------------------------------------------
% 231.54/42.88    (1)  all_57_13 = e1
% 231.54/42.88    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.88         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.54/42.88    (3)   ~ (e3 = e1)
% 231.54/42.88    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.88           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.88    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.54/42.88         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.54/42.88    (6)  all_57_4 = e0
% 231.54/42.88    (7)  op(e2, e2) = e0
% 231.54/42.88    (8)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.54/42.88         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.54/42.88    (9)  all_57_3 = e0
% 231.54/42.88    (10)   ~ (e3 = e2)
% 231.54/42.88    (11)   ~ (e3 = e0)
% 231.54/42.88    (12)  all_57_1 = e1
% 231.54/42.88    (13)  op(e3, e3) = e2
% 231.54/42.88    (14)   ~ (e2 = e0)
% 231.54/42.88    (15)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 231.54/42.88          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.54/42.88    (16)   ~ (e1 = e0)
% 231.54/42.88    (17)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.54/42.88          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.54/42.88    (18)   ~ (e2 = e1)
% 231.54/42.88  
% 231.54/42.88  Begin of proof
% 231.54/42.88  | 
% 231.54/42.88  | BETA: splitting (2) gives:
% 231.54/42.88  | 
% 231.54/42.88  | Case 1:
% 231.54/42.88  | | 
% 231.54/42.88  | |   (19)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 231.54/42.88  | |           e2)
% 231.54/42.88  | | 
% 231.54/42.88  | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (10), (11), (13), (14), (15), (16),
% 231.54/42.88  | |            (18), (19) are inconsistent by sub-proof #1637.
% 231.54/42.88  | | 
% 231.54/42.88  | Case 2:
% 231.54/42.88  | | 
% 231.54/42.88  | |   (20)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 231.54/42.88  | |           e2)
% 231.54/42.88  | | 
% 231.54/42.88  | | BETA: splitting (20) gives:
% 231.54/42.88  | | 
% 231.54/42.88  | | Case 1:
% 231.54/42.88  | | | 
% 231.54/42.88  | | |   (21)  all_57_7 = e2 & op(e1, e2) = e2
% 231.54/42.88  | | | 
% 231.54/42.88  | | | ALPHA: (21) implies:
% 231.54/42.88  | | |   (22)  all_57_7 = e2
% 231.54/42.88  | | | 
% 231.54/42.88  | | | REF_CLOSE: (1), (3), (9), (10), (11), (12), (17), (22) are inconsistent by
% 231.54/42.88  | | |            sub-proof #2193.
% 231.54/42.88  | | | 
% 231.54/42.88  | | Case 2:
% 231.54/42.88  | | | 
% 231.54/42.88  | | |   (23)  all_57_13 = e2 & op(e0, e2) = e2
% 231.54/42.88  | | | 
% 231.54/42.88  | | | REF_CLOSE: (1), (18), (23) are inconsistent by sub-proof #2101.
% 231.54/42.88  | | | 
% 231.54/42.88  | | End of split
% 231.54/42.88  | | 
% 231.54/42.88  | End of split
% 231.54/42.88  | 
% 231.54/42.88  End of proof
% 231.54/42.88  
% 231.54/42.88  Sub-proof #1626 shows that the following formulas are inconsistent:
% 231.54/42.88  ----------------------------------------------------------------
% 231.54/42.88    (1)  e1 = e0
% 231.54/42.88    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.88         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.54/42.88    (3)   ~ (e3 = e1)
% 231.54/42.88    (4)  all_57_3 = e0
% 231.54/42.88    (5)   ~ (e3 = e2)
% 231.54/42.88    (6)  all_57_1 = e1
% 231.54/42.88    (7)   ~ (e2 = e0)
% 231.54/42.88    (8)   ~ (e1 = e0)
% 231.54/42.88    (9)  all_57_7 = e3
% 231.54/42.88    (10)   ~ (e2 = e1)
% 231.54/42.88    (11)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.88          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.54/42.88  
% 231.54/42.88  Begin of proof
% 231.54/42.88  | 
% 231.54/42.88  | SIMP: (1) implies:
% 231.54/42.88  |   (12)  e1 = e0
% 231.54/42.88  | 
% 231.54/42.88  | COMBINE_EQS: (6), (12) imply:
% 231.54/42.88  |   (13)  all_57_1 = e0
% 231.54/42.88  | 
% 231.54/42.88  | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (10), (11), (13) are
% 231.54/42.88  |            inconsistent by sub-proof #2098.
% 231.54/42.88  | 
% 231.54/42.88  End of proof
% 231.54/42.88  
% 231.54/42.88  Sub-proof #1627 shows that the following formulas are inconsistent:
% 231.54/42.88  ----------------------------------------------------------------
% 231.54/42.88    (1)  all_57_15 = e0
% 231.54/42.88    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.88         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.54/42.88    (3)   ~ (e3 = e1)
% 231.54/42.88    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.88           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.88    (5)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.54/42.88         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.54/42.88    (6)   ~ (all_6_2 = e3)
% 231.54/42.88    (7)  op(e1, e1) = all_6_2
% 231.54/42.88    (8)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.54/42.88         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.54/42.88    (9)  all_57_4 = e0
% 231.54/42.88    (10)  op(e2, e2) = e0
% 231.54/42.88    (11)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.54/42.88          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.54/42.88    (12)  all_57_3 = e0
% 231.54/42.88    (13)   ~ (e3 = e2)
% 231.54/42.88    (14)   ~ (e3 = e0)
% 231.54/42.88    (15)  all_57_6 = e0
% 231.54/42.88    (16)  op(e3, e3) = e2
% 231.54/42.88    (17)  all_57_10 = e2
% 231.54/42.88    (18)   ~ (e2 = e0)
% 231.54/42.88    (19)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 231.54/42.88          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.54/42.88    (20)   ~ (e1 = e0)
% 231.54/42.88    (21)   ~ (all_52_27 = e0)
% 231.54/42.88    (22)  op(e0, e2) = all_52_27
% 231.54/42.88    (23)   ~ (e2 = e1)
% 231.54/42.88    (24)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.54/42.88          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.54/42.88    (25)   ~ (all_53_12 = e2)
% 231.54/42.88    (26)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.54/42.88          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.54/42.88    (27)  op(all_52_27, all_52_27) = e2
% 231.54/42.88    (28)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.88          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.54/42.88    (29)  all_57_13 = e2 & op(e0, e2) = e2
% 231.54/42.88    (30)  op(e3, e0) = all_53_12
% 231.54/42.88  
% 231.54/42.88  Begin of proof
% 231.54/42.88  | 
% 231.54/42.88  | BETA: splitting (24) gives:
% 231.54/42.88  | 
% 231.54/42.88  | Case 1:
% 231.54/42.88  | | 
% 231.54/42.88  | |   (31)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 231.54/42.88  | |           e2)
% 231.54/42.88  | | 
% 231.54/42.88  | | BETA: splitting (31) gives:
% 231.54/42.88  | | 
% 231.54/42.88  | | Case 1:
% 231.54/42.88  | | | 
% 231.54/42.88  | | |   (32)  all_57_9 = e2 & op(e3, e0) = e2
% 231.54/42.88  | | | 
% 231.54/42.88  | | | ALPHA: (32) implies:
% 231.54/42.88  | | |   (33)  op(e3, e0) = e2
% 231.54/42.88  | | | 
% 231.54/42.88  | | | REF_CLOSE: (4), (25), (30), (33) are inconsistent by sub-proof #2331.
% 231.54/42.88  | | | 
% 231.54/42.88  | | Case 2:
% 231.54/42.88  | | | 
% 231.54/42.88  | | | 
% 231.54/42.88  | | | ALPHA: (29) implies:
% 231.54/42.88  | | |   (34)  op(e0, e2) = e2
% 231.54/42.88  | | | 
% 231.54/42.88  | | | GROUND_INST: instantiating (4) with all_52_27, e2, e2, e0, simplifying
% 231.54/42.88  | | |              with (22), (34) gives:
% 231.54/42.88  | | |   (35)  all_52_27 = e2
% 231.54/42.88  | | | 
% 231.54/42.88  | | | REDUCE: (27), (35) imply:
% 231.54/42.88  | | |   (36)  op(e2, e2) = e2
% 231.54/42.88  | | | 
% 231.54/42.88  | | | REF_CLOSE: (4), (10), (18), (36) are inconsistent by sub-proof #2472.
% 231.54/42.88  | | | 
% 231.54/42.88  | | End of split
% 231.54/42.88  | | 
% 231.54/42.88  | Case 2:
% 231.54/42.88  | | 
% 231.54/42.88  | |   (37)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.54/42.88  | |           e2)
% 231.54/42.88  | | 
% 231.54/42.88  | | BETA: splitting (37) gives:
% 231.54/42.88  | | 
% 231.54/42.88  | | Case 1:
% 231.54/42.88  | | | 
% 231.54/42.88  | | |   (38)  all_57_11 = e2 & op(e1, e0) = e2
% 231.54/42.88  | | | 
% 231.54/42.88  | | | ALPHA: (38) implies:
% 231.54/42.88  | | |   (39)  all_57_11 = e2
% 231.54/42.88  | | | 
% 231.54/42.88  | | | BETA: splitting (19) gives:
% 231.54/42.88  | | | 
% 231.54/42.88  | | | Case 1:
% 231.54/42.88  | | | | 
% 231.54/42.88  | | | |   (40)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2)
% 231.54/42.88  | | | |           = e3)
% 231.54/42.88  | | | | 
% 231.54/42.88  | | | | BETA: splitting (40) gives:
% 231.54/42.88  | | | | 
% 231.54/42.88  | | | | Case 1:
% 231.54/42.88  | | | | | 
% 231.54/42.88  | | | | |   (41)  all_57_0 = e3 & op(e3, e3) = e3
% 231.54/42.88  | | | | | 
% 231.54/42.88  | | | | | ALPHA: (41) implies:
% 231.54/42.88  | | | | |   (42)  op(e3, e3) = e3
% 231.54/42.88  | | | | | 
% 231.54/42.88  | | | | | REF_CLOSE: (4), (13), (16), (42) are inconsistent by sub-proof #2490.
% 231.54/42.88  | | | | | 
% 231.54/42.88  | | | | Case 2:
% 231.54/42.88  | | | | | 
% 231.54/42.88  | | | | |   (43)  all_57_1 = e3 & op(e3, e2) = e3
% 231.54/42.88  | | | | | 
% 231.54/42.88  | | | | | ALPHA: (43) implies:
% 231.54/42.88  | | | | |   (44)  all_57_1 = e3
% 231.54/42.88  | | | | | 
% 231.54/42.88  | | | | | BETA: splitting (5) gives:
% 231.54/42.88  | | | | | 
% 231.54/42.88  | | | | | Case 1:
% 231.54/42.88  | | | | | | 
% 231.54/42.88  | | | | | |   (45)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1,
% 231.54/42.88  | | | | | |             e2) = e3)
% 231.54/42.88  | | | | | | 
% 231.54/42.88  | | | | | | BETA: splitting (45) gives:
% 231.54/42.88  | | | | | | 
% 231.54/42.88  | | | | | | Case 1:
% 231.54/42.88  | | | | | | | 
% 231.54/42.88  | | | | | | |   (46)  all_57_6 = e3 & op(e1, e3) = e3
% 231.54/42.88  | | | | | | | 
% 231.54/42.88  | | | | | | | ALPHA: (46) implies:
% 231.54/42.88  | | | | | | |   (47)  all_57_6 = e3
% 231.54/42.88  | | | | | | | 
% 231.54/42.88  | | | | | | | REF_CLOSE: (14), (15), (47) are inconsistent by sub-proof #1822.
% 231.54/42.88  | | | | | | | 
% 231.54/42.88  | | | | | | Case 2:
% 231.54/42.88  | | | | | | | 
% 231.54/42.88  | | | | | | |   (48)  all_57_7 = e3 & op(e1, e2) = e3
% 231.54/42.88  | | | | | | | 
% 231.54/42.88  | | | | | | | ALPHA: (48) implies:
% 231.54/42.88  | | | | | | |   (49)  all_57_7 = e3
% 231.54/42.88  | | | | | | | 
% 231.54/42.88  | | | | | | | REF_CLOSE: (2), (3), (12), (13), (18), (20), (23), (28), (44),
% 231.54/42.88  | | | | | | |            (49) are inconsistent by sub-proof #1778.
% 231.54/42.88  | | | | | | | 
% 231.54/42.88  | | | | | | End of split
% 231.54/42.88  | | | | | | 
% 231.54/42.88  | | | | | Case 2:
% 231.54/42.88  | | | | | | 
% 231.54/42.88  | | | | | |   (50)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1,
% 231.54/42.88  | | | | | |             e0) = e3)
% 231.54/42.88  | | | | | | 
% 231.54/42.88  | | | | | | BETA: splitting (50) gives:
% 231.54/42.88  | | | | | | 
% 231.54/42.88  | | | | | | Case 1:
% 231.54/42.88  | | | | | | | 
% 231.54/42.88  | | | | | | |   (51)  all_57_8 = e3 & op(e1, e1) = e3
% 231.54/42.88  | | | | | | | 
% 231.54/42.88  | | | | | | | ALPHA: (51) implies:
% 231.54/42.88  | | | | | | |   (52)  op(e1, e1) = e3
% 231.54/42.88  | | | | | | | 
% 231.54/42.88  | | | | | | | REF_CLOSE: (4), (6), (7), (52) are inconsistent by sub-proof
% 231.54/42.88  | | | | | | |            #2468.
% 231.54/42.88  | | | | | | | 
% 231.54/42.88  | | | | | | Case 2:
% 231.54/42.88  | | | | | | | 
% 231.54/42.88  | | | | | | |   (53)  all_57_11 = e3 & op(e1, e0) = e3
% 231.54/42.88  | | | | | | | 
% 231.54/42.88  | | | | | | | ALPHA: (53) implies:
% 231.54/42.88  | | | | | | |   (54)  all_57_11 = e3
% 231.54/42.88  | | | | | | | 
% 231.54/42.88  | | | | | | | COMBINE_EQS: (39), (54) imply:
% 231.54/42.88  | | | | | | |   (55)  e3 = e2
% 231.54/42.88  | | | | | | | 
% 231.54/42.88  | | | | | | | SIMP: (55) implies:
% 231.54/42.88  | | | | | | |   (56)  e3 = e2
% 231.54/42.88  | | | | | | | 
% 231.54/42.88  | | | | | | | COMBINE_EQS: (44), (56) imply:
% 231.54/42.88  | | | | | | |   (57)  all_57_1 = e2
% 231.54/42.88  | | | | | | | 
% 231.54/42.88  | | | | | | | REF_CLOSE: (3), (4), (8), (9), (11), (13), (14), (16), (18), (19),
% 231.54/42.88  | | | | | | |            (20), (23), (57) are inconsistent by sub-proof #1658.
% 231.54/42.88  | | | | | | | 
% 231.54/42.88  | | | | | | End of split
% 231.54/42.88  | | | | | | 
% 231.54/42.88  | | | | | End of split
% 231.54/42.88  | | | | | 
% 231.54/42.88  | | | | End of split
% 231.54/42.88  | | | | 
% 231.54/42.88  | | | Case 2:
% 231.54/42.88  | | | | 
% 231.54/42.88  | | | |   (58)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0)
% 231.54/42.88  | | | |           = e3)
% 231.54/42.88  | | | | 
% 231.54/42.88  | | | | BETA: splitting (58) gives:
% 231.54/42.88  | | | | 
% 231.54/42.88  | | | | Case 1:
% 231.54/42.88  | | | | | 
% 231.54/42.88  | | | | |   (59)  all_57_4 = e3 & op(e3, e1) = e3
% 231.54/42.88  | | | | | 
% 231.54/42.88  | | | | | ALPHA: (59) implies:
% 231.54/42.88  | | | | |   (60)  all_57_4 = e3
% 231.54/42.88  | | | | | 
% 231.54/42.88  | | | | | REF_CLOSE: (9), (14), (60) are inconsistent by sub-proof #2372.
% 231.54/42.88  | | | | | 
% 231.54/42.88  | | | | Case 2:
% 231.54/42.88  | | | | | 
% 231.54/42.88  | | | | |   (61)  all_57_9 = e3 & op(e3, e0) = e3
% 231.54/42.88  | | | | | 
% 231.54/42.88  | | | | | ALPHA: (61) implies:
% 231.54/42.88  | | | | |   (62)  all_57_9 = e3
% 231.54/42.88  | | | | | 
% 231.54/42.88  | | | | | REF_CLOSE: (1), (3), (17), (20), (23), (26), (39), (62) are
% 231.54/42.88  | | | | |            inconsistent by sub-proof #1668.
% 231.54/42.88  | | | | | 
% 231.54/42.88  | | | | End of split
% 231.54/42.88  | | | | 
% 231.54/42.88  | | | End of split
% 231.54/42.88  | | | 
% 231.54/42.88  | | Case 2:
% 231.54/42.88  | | | 
% 231.54/42.88  | | |   (63)  all_57_15 = e2 & op(e0, e0) = e2
% 231.54/42.88  | | | 
% 231.54/42.88  | | | ALPHA: (63) implies:
% 231.54/42.88  | | |   (64)  all_57_15 = e2
% 231.54/42.88  | | | 
% 231.54/42.88  | | | COMBINE_EQS: (1), (64) imply:
% 231.54/42.88  | | |   (65)  e2 = e0
% 231.54/42.88  | | | 
% 231.54/42.88  | | | REDUCE: (18), (65) imply:
% 231.54/42.88  | | |   (66)  $false
% 231.54/42.88  | | | 
% 231.54/42.88  | | | CLOSE: (66) is inconsistent.
% 231.54/42.88  | | | 
% 231.54/42.88  | | End of split
% 231.54/42.88  | | 
% 231.54/42.88  | End of split
% 231.54/42.88  | 
% 231.54/42.88  End of proof
% 231.54/42.88  
% 231.54/42.88  Sub-proof #1628 shows that the following formulas are inconsistent:
% 231.54/42.88  ----------------------------------------------------------------
% 231.54/42.88    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.88         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.54/42.88    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.54/42.88         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.54/42.88    (3)   ~ (e3 = e1)
% 231.54/42.88    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.88           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.88    (5)  all_57_2 = e2
% 231.54/42.88    (6)  all_57_3 = e0
% 231.54/42.88    (7)   ~ (e3 = e2)
% 231.54/42.88    (8)   ~ (e3 = e0)
% 231.54/42.88    (9)  all_57_6 = e0
% 231.54/42.88    (10)  op(e3, e3) = e2
% 231.54/42.88    (11)   ~ (e2 = e0)
% 231.54/42.88    (12)   ~ (e1 = e0)
% 231.54/42.88    (13)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.54/42.88          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.54/42.88    (14)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.88          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.54/42.88    (15)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 231.54/42.88          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 231.54/42.88    (16)   ~ (e2 = e1)
% 231.54/42.88    (17)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.54/42.88          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.54/42.88  
% 231.54/42.88  Begin of proof
% 231.54/42.88  | 
% 231.54/42.88  | BETA: splitting (15) gives:
% 231.54/42.88  | 
% 231.54/42.88  | Case 1:
% 231.54/42.88  | | 
% 231.54/42.88  | |   (18)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) =
% 231.54/42.88  | |           e3)
% 231.54/42.88  | | 
% 231.54/42.88  | | REF_CLOSE: (4), (5), (7), (10), (18) are inconsistent by sub-proof #1634.
% 231.54/42.88  | | 
% 231.54/42.88  | Case 2:
% 231.54/42.88  | | 
% 231.54/42.88  | |   (19)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) =
% 231.54/42.88  | |           e3)
% 231.54/42.88  | | 
% 231.54/42.88  | | BETA: splitting (19) gives:
% 231.54/42.88  | | 
% 231.54/42.88  | | Case 1:
% 231.54/42.88  | | | 
% 231.54/42.88  | | |   (20)  all_57_6 = e3 & op(e1, e3) = e3
% 231.54/42.88  | | | 
% 231.54/42.88  | | | ALPHA: (20) implies:
% 231.54/42.88  | | |   (21)  all_57_6 = e3
% 231.54/42.88  | | | 
% 231.54/42.88  | | | REF_CLOSE: (8), (9), (21) are inconsistent by sub-proof #1822.
% 231.54/42.88  | | | 
% 231.54/42.88  | | Case 2:
% 231.54/42.88  | | | 
% 231.54/42.88  | | |   (22)  all_57_12 = e3 & op(e0, e3) = e3
% 231.54/42.88  | | | 
% 231.54/42.88  | | | ALPHA: (22) implies:
% 231.54/42.88  | | |   (23)  all_57_12 = e3
% 231.54/42.88  | | | 
% 231.54/42.88  | | | BETA: splitting (2) gives:
% 231.54/42.88  | | | 
% 231.54/42.88  | | | Case 1:
% 231.54/42.88  | | | | 
% 231.54/42.88  | | | |   (24)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3)
% 231.54/42.88  | | | |           = e1)
% 231.54/42.88  | | | | 
% 231.54/42.88  | | | | REF_CLOSE: (4), (5), (10), (16), (24) are inconsistent by sub-proof
% 231.54/42.88  | | | |            #1633.
% 231.54/42.88  | | | | 
% 231.54/42.88  | | | Case 2:
% 231.54/42.88  | | | | 
% 231.54/42.88  | | | |   (25)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3)
% 231.54/42.88  | | | |           = e1)
% 231.54/42.88  | | | | 
% 231.54/42.88  | | | | BETA: splitting (25) gives:
% 231.54/42.88  | | | | 
% 231.54/42.88  | | | | Case 1:
% 231.54/42.88  | | | | | 
% 231.54/42.88  | | | | |   (26)  all_57_6 = e1 & op(e1, e3) = e1
% 231.54/42.88  | | | | | 
% 231.54/42.88  | | | | | ALPHA: (26) implies:
% 231.54/42.88  | | | | |   (27)  all_57_6 = e1
% 231.54/42.88  | | | | | 
% 231.54/42.88  | | | | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (10), (11), (12), (13), (14),
% 231.54/42.88  | | | | |            (16), (17), (23), (27) are inconsistent by sub-proof #1632.
% 231.54/42.88  | | | | | 
% 231.54/42.88  | | | | Case 2:
% 231.54/42.88  | | | | | 
% 231.54/42.88  | | | | |   (28)  all_57_12 = e1 & op(e0, e3) = e1
% 231.54/42.88  | | | | | 
% 231.54/42.88  | | | | | ALPHA: (28) implies:
% 231.54/42.88  | | | | |   (29)  all_57_12 = e1
% 231.54/42.88  | | | | | 
% 231.54/42.88  | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13),
% 231.54/42.88  | | | | |            (14), (15), (16), (17), (29) are inconsistent by sub-proof
% 231.54/42.88  | | | | |            #1629.
% 231.54/42.88  | | | | | 
% 231.54/42.88  | | | | End of split
% 231.54/42.88  | | | | 
% 231.54/42.88  | | | End of split
% 231.54/42.88  | | | 
% 231.54/42.88  | | End of split
% 231.54/42.88  | | 
% 231.54/42.88  | End of split
% 231.54/42.88  | 
% 231.54/42.88  End of proof
% 231.54/42.88  
% 231.54/42.88  Sub-proof #1629 shows that the following formulas are inconsistent:
% 231.54/42.88  ----------------------------------------------------------------
% 231.54/42.88    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.88         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.54/42.88    (2)   ~ (e3 = e1)
% 231.54/42.88    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.88           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.88    (4)  all_57_2 = e2
% 231.54/42.88    (5)  all_57_3 = e0
% 231.54/42.88    (6)   ~ (e3 = e2)
% 231.54/42.88    (7)   ~ (e3 = e0)
% 231.54/42.88    (8)  op(e3, e3) = e2
% 231.54/42.88    (9)  all_57_12 = e1
% 231.54/42.88    (10)   ~ (e2 = e0)
% 231.54/42.88    (11)   ~ (e1 = e0)
% 231.54/42.88    (12)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.54/42.88          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.54/42.88    (13)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.88          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.54/42.88    (14)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 231.54/42.88          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 231.54/42.88    (15)   ~ (e2 = e1)
% 231.54/42.88    (16)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.54/42.88          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.54/42.88  
% 231.54/42.88  Begin of proof
% 231.54/42.88  | 
% 231.54/42.88  | BETA: splitting (16) gives:
% 231.54/42.88  | 
% 231.54/42.88  | Case 1:
% 231.54/42.88  | | 
% 231.54/42.88  | |   (17)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) =
% 231.54/42.88  | |           e0)
% 231.54/42.88  | | 
% 231.54/42.88  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (10), (11), (12), (13), (15),
% 231.54/42.88  | |            (17) are inconsistent by sub-proof #1654.
% 231.54/42.88  | | 
% 231.54/42.88  | Case 2:
% 231.54/42.88  | | 
% 231.54/42.88  | |   (18)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) =
% 231.54/42.88  | |           e0)
% 231.54/42.88  | | 
% 231.54/42.88  | | BETA: splitting (18) gives:
% 231.54/42.88  | | 
% 231.54/42.88  | | Case 1:
% 231.54/42.88  | | | 
% 231.54/42.88  | | |   (19)  all_57_6 = e0 & op(e1, e3) = e0
% 231.54/42.88  | | | 
% 231.54/42.88  | | | ALPHA: (19) implies:
% 231.54/42.88  | | |   (20)  all_57_6 = e0
% 231.54/42.88  | | | 
% 231.54/42.88  | | | REF_CLOSE: (2), (3), (4), (6), (7), (8), (9), (14), (20) are inconsistent
% 231.54/42.88  | | |            by sub-proof #1630.
% 231.54/42.88  | | | 
% 231.54/42.88  | | Case 2:
% 231.54/42.88  | | | 
% 231.54/42.88  | | |   (21)  all_57_12 = e0 & op(e0, e3) = e0
% 231.54/42.88  | | | 
% 231.54/42.88  | | | ALPHA: (21) implies:
% 231.54/42.88  | | |   (22)  all_57_12 = e0
% 231.54/42.88  | | | 
% 231.54/42.88  | | | REF_CLOSE: (9), (11), (22) are inconsistent by sub-proof #2014.
% 231.54/42.88  | | | 
% 231.54/42.88  | | End of split
% 231.54/42.88  | | 
% 231.54/42.88  | End of split
% 231.54/42.88  | 
% 231.54/42.88  End of proof
% 231.54/42.88  
% 231.54/42.88  Sub-proof #1630 shows that the following formulas are inconsistent:
% 231.54/42.88  ----------------------------------------------------------------
% 231.54/42.88    (1)   ~ (e3 = e1)
% 231.54/42.88    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.88           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.88    (3)  all_57_2 = e2
% 231.54/42.88    (4)   ~ (e3 = e2)
% 231.54/42.88    (5)   ~ (e3 = e0)
% 231.54/42.88    (6)  all_57_6 = e0
% 231.54/42.88    (7)  op(e3, e3) = e2
% 231.54/42.88    (8)  all_57_12 = e1
% 231.54/42.88    (9)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 231.54/42.88         (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 231.54/42.88  
% 231.54/42.88  Begin of proof
% 231.54/42.88  | 
% 231.54/42.88  | BETA: splitting (9) gives:
% 231.54/42.88  | 
% 231.54/42.88  | Case 1:
% 231.54/42.88  | | 
% 231.54/42.88  | |   (10)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) =
% 231.54/42.88  | |           e3)
% 231.54/42.88  | | 
% 231.54/42.88  | | REF_CLOSE: (2), (3), (4), (7), (10) are inconsistent by sub-proof #1634.
% 231.54/42.88  | | 
% 231.54/42.88  | Case 2:
% 231.54/42.88  | | 
% 231.54/42.88  | |   (11)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) =
% 231.54/42.88  | |           e3)
% 231.54/42.88  | | 
% 231.54/42.88  | | REF_CLOSE: (1), (5), (6), (8), (11) are inconsistent by sub-proof #1631.
% 231.54/42.88  | | 
% 231.54/42.88  | End of split
% 231.54/42.88  | 
% 231.54/42.88  End of proof
% 231.54/42.88  
% 231.54/42.88  Sub-proof #1631 shows that the following formulas are inconsistent:
% 231.54/42.88  ----------------------------------------------------------------
% 231.54/42.88    (1)   ~ (e3 = e1)
% 231.54/42.88    (2)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 231.54/42.88    (3)   ~ (e3 = e0)
% 231.54/42.88    (4)  all_57_6 = e0
% 231.54/42.88    (5)  all_57_12 = e1
% 231.54/42.88  
% 231.54/42.88  Begin of proof
% 231.54/42.88  | 
% 231.54/42.88  | BETA: splitting (2) gives:
% 231.54/42.88  | 
% 231.54/42.88  | Case 1:
% 231.54/42.88  | | 
% 231.54/42.88  | |   (6)  all_57_6 = e3 & op(e1, e3) = e3
% 231.54/42.88  | | 
% 231.54/42.88  | | ALPHA: (6) implies:
% 231.54/42.88  | |   (7)  all_57_6 = e3
% 231.54/42.88  | | 
% 231.54/42.88  | | REF_CLOSE: (3), (4), (7) are inconsistent by sub-proof #1822.
% 231.54/42.88  | | 
% 231.54/42.88  | Case 2:
% 231.54/42.88  | | 
% 231.54/42.88  | |   (8)  all_57_12 = e3 & op(e0, e3) = e3
% 231.54/42.88  | | 
% 231.54/42.88  | | ALPHA: (8) implies:
% 231.54/42.88  | |   (9)  all_57_12 = e3
% 231.54/42.88  | | 
% 231.54/42.88  | | REF_CLOSE: (1), (5), (9) are inconsistent by sub-proof #2151.
% 231.54/42.88  | | 
% 231.54/42.88  | End of split
% 231.54/42.88  | 
% 231.54/42.88  End of proof
% 231.54/42.88  
% 231.54/42.88  Sub-proof #1632 shows that the following formulas are inconsistent:
% 231.54/42.88  ----------------------------------------------------------------
% 231.54/42.88    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.88         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.54/42.88    (2)   ~ (e3 = e1)
% 231.54/42.88    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.88           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.88    (4)  all_57_6 = e1
% 231.54/42.88    (5)  all_57_3 = e0
% 231.54/42.88    (6)   ~ (e3 = e2)
% 231.54/42.88    (7)   ~ (e3 = e0)
% 231.54/42.88    (8)  op(e3, e3) = e2
% 231.54/42.88    (9)   ~ (e2 = e0)
% 231.54/42.88    (10)   ~ (e1 = e0)
% 231.54/42.88    (11)  all_57_12 = e3
% 231.54/42.88    (12)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.54/42.88          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.54/42.88    (13)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.88          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.54/42.88    (14)   ~ (e2 = e1)
% 231.54/42.88    (15)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.54/42.88          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.54/42.88  
% 231.54/42.88  Begin of proof
% 231.54/42.88  | 
% 231.54/42.88  | BETA: splitting (15) gives:
% 231.54/42.88  | 
% 231.54/42.88  | Case 1:
% 231.54/42.88  | | 
% 231.54/42.88  | |   (16)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) =
% 231.54/42.88  | |           e0)
% 231.54/42.88  | | 
% 231.54/42.88  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (12), (13), (14),
% 231.54/42.88  | |            (16) are inconsistent by sub-proof #1654.
% 231.54/42.88  | | 
% 231.54/42.88  | Case 2:
% 231.54/42.88  | | 
% 231.54/42.88  | |   (17)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) =
% 231.54/42.88  | |           e0)
% 231.54/42.88  | | 
% 231.54/42.88  | | BETA: splitting (17) gives:
% 231.54/42.88  | | 
% 231.54/42.88  | | Case 1:
% 231.54/42.88  | | | 
% 231.54/42.88  | | |   (18)  all_57_6 = e0 & op(e1, e3) = e0
% 231.54/42.88  | | | 
% 231.54/42.88  | | | ALPHA: (18) implies:
% 231.54/42.88  | | |   (19)  all_57_6 = e0
% 231.54/42.88  | | | 
% 231.54/42.88  | | | REF_CLOSE: (4), (10), (19) are inconsistent by sub-proof #2227.
% 231.54/42.88  | | | 
% 231.54/42.88  | | Case 2:
% 231.54/42.88  | | | 
% 231.54/42.88  | | |   (20)  all_57_12 = e0 & op(e0, e3) = e0
% 231.54/42.88  | | | 
% 231.54/42.88  | | | REF_CLOSE: (7), (11), (20) are inconsistent by sub-proof #2237.
% 231.54/42.88  | | | 
% 231.54/42.88  | | End of split
% 231.54/42.88  | | 
% 231.54/42.88  | End of split
% 231.54/42.88  | 
% 231.54/42.88  End of proof
% 231.54/42.88  
% 231.54/42.88  Sub-proof #1633 shows that the following formulas are inconsistent:
% 231.54/42.88  ----------------------------------------------------------------
% 231.54/42.88    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.88           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.88    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1)
% 231.54/42.88    (3)  all_57_2 = e2
% 231.54/42.88    (4)  op(e3, e3) = e2
% 231.54/42.88    (5)   ~ (e2 = e1)
% 231.54/42.88  
% 231.54/42.88  Begin of proof
% 231.54/42.88  | 
% 231.54/42.88  | BETA: splitting (2) gives:
% 231.54/42.88  | 
% 231.54/42.89  | Case 1:
% 231.54/42.89  | | 
% 231.54/42.89  | |   (6)  all_57_0 = e1 & op(e3, e3) = e1
% 231.54/42.89  | | 
% 231.54/42.89  | | ALPHA: (6) implies:
% 231.54/42.89  | |   (7)  op(e3, e3) = e1
% 231.54/42.89  | | 
% 231.54/42.89  | | REF_CLOSE: (1), (4), (5), (7) are inconsistent by sub-proof #1950.
% 231.54/42.89  | | 
% 231.54/42.89  | Case 2:
% 231.54/42.89  | | 
% 231.54/42.89  | |   (8)  all_57_2 = e1 & op(e2, e3) = e1
% 231.54/42.89  | | 
% 231.54/42.89  | | REF_CLOSE: (3), (5), (8) are inconsistent by sub-proof #2244.
% 231.54/42.89  | | 
% 231.54/42.89  | End of split
% 231.54/42.89  | 
% 231.54/42.89  End of proof
% 231.54/42.89  
% 231.54/42.89  Sub-proof #1634 shows that the following formulas are inconsistent:
% 231.54/42.89  ----------------------------------------------------------------
% 231.54/42.89    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.89           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.89    (2)  all_57_2 = e2
% 231.54/42.89    (3)   ~ (e3 = e2)
% 231.54/42.89    (4)  op(e3, e3) = e2
% 231.54/42.89    (5)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3)
% 231.54/42.89  
% 231.54/42.89  Begin of proof
% 231.54/42.89  | 
% 231.54/42.89  | BETA: splitting (5) gives:
% 231.54/42.89  | 
% 231.54/42.89  | Case 1:
% 231.54/42.89  | | 
% 231.54/42.89  | |   (6)  all_57_0 = e3 & op(e3, e3) = e3
% 231.54/42.89  | | 
% 231.54/42.89  | | ALPHA: (6) implies:
% 231.54/42.89  | |   (7)  op(e3, e3) = e3
% 231.54/42.89  | | 
% 231.54/42.89  | | REF_CLOSE: (1), (3), (4), (7) are inconsistent by sub-proof #2490.
% 231.54/42.89  | | 
% 231.54/42.89  | Case 2:
% 231.54/42.89  | | 
% 231.54/42.89  | |   (8)  all_57_2 = e3 & op(e2, e3) = e3
% 231.54/42.89  | | 
% 231.54/42.89  | | ALPHA: (8) implies:
% 231.54/42.89  | |   (9)  all_57_2 = e3
% 231.54/42.89  | | 
% 231.54/42.89  | | REF_CLOSE: (2), (3), (9) are inconsistent by sub-proof #1800.
% 231.54/42.89  | | 
% 231.54/42.89  | End of split
% 231.54/42.89  | 
% 231.54/42.89  End of proof
% 231.54/42.89  
% 231.54/42.89  Sub-proof #1635 shows that the following formulas are inconsistent:
% 231.54/42.89  ----------------------------------------------------------------
% 231.54/42.89    (1)  all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 231.54/42.89    (2)  all_57_15 = e0
% 231.54/42.89    (3)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.89         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.54/42.89    (4)   ~ (all_53_6 = e0)
% 231.54/42.89    (5)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.89         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.54/42.89    (6)   ~ (e3 = e1)
% 231.54/42.89    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.89           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.89    (8)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.54/42.89         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.54/42.89    (9)   ~ (all_6_2 = e3)
% 231.54/42.89    (10)  op(e1, e1) = all_6_2
% 231.54/42.89    (11)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.54/42.89          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.54/42.89    (12)  all_57_7 = e2
% 231.54/42.89    (13)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 231.54/42.89    (14)  all_55_9 = all_53_6
% 231.54/42.89    (15)  all_57_4 = e0
% 231.54/42.89    (16)  op(e2, e2) = e0
% 231.54/42.89    (17)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.54/42.89          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.54/42.89    (18)  all_57_3 = e0
% 231.54/42.89    (19)   ~ (e3 = e2)
% 231.54/42.89    (20)   ~ (e3 = e0)
% 231.54/42.89    (21)  all_57_6 = e0
% 231.54/42.89    (22)  op(e0, e3) = all_53_3
% 231.54/42.89    (23)  op(e3, e3) = e2
% 231.54/42.89    (24)   ~ (all_53_3 = e2)
% 231.54/42.89    (25)  op(e0, e0) = all_52_31
% 231.54/42.89    (26)   ~ (e2 = e0)
% 231.54/42.89    (27)   ~ (all_53_6 = e1)
% 231.54/42.89    (28)  all_55_13 = all_52_27
% 231.54/42.89    (29)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 231.54/42.89          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.54/42.89    (30)   ~ (e1 = e0)
% 231.54/42.89    (31)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.54/42.89          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.54/42.89    (32)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.54/42.89          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.54/42.89    (33)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.54/42.89          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 231.54/42.89            e3)
% 231.54/42.89    (34)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.54/42.89          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.54/42.89            e2)
% 231.54/42.89    (35)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.54/42.89              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.54/42.89                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.54/42.89                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.54/42.89    (36)   ~ (all_52_27 = e0)
% 231.54/42.89    (37)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.54/42.89          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.54/42.89    (38)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.89          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.54/42.89    (39)  all_57_1 = e3
% 231.54/42.89    (40)   ~ (all_53_6 = e3)
% 231.54/42.89    (41)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 231.54/42.89          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 231.54/42.89    (42)   ~ (e2 = e1)
% 231.54/42.89    (43)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.54/42.89          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.54/42.89    (44)   ~ (all_6_2 = e0)
% 231.54/42.89    (45)   ~ (all_53_12 = e2)
% 231.54/42.89    (46)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.54/42.89          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.54/42.89    (47)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.54/42.89          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.54/42.89    (48)  op(all_52_31, all_52_31) = e0
% 231.54/42.89    (49)  op(all_52_27, all_52_27) = e2
% 231.54/42.89    (50)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 231.54/42.89          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 231.54/42.89    (51)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.89          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.54/42.89    (52)   ~ (all_52_27 = e3)
% 231.54/42.89    (53)   ~ (all_53_6 = all_52_27)
% 231.54/42.89    (54)  op(e3, e0) = all_53_12
% 231.54/42.89  
% 231.54/42.89  Begin of proof
% 231.54/42.89  | 
% 231.54/42.89  | BETA: splitting (34) gives:
% 231.54/42.89  | 
% 231.54/42.89  | Case 1:
% 231.54/42.89  | | 
% 231.54/42.89  | |   (55)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 231.54/42.89  | |           e2)
% 231.54/42.89  | | 
% 231.54/42.89  | | BETA: splitting (55) gives:
% 231.54/42.89  | | 
% 231.54/42.89  | | Case 1:
% 231.54/42.89  | | | 
% 231.54/42.89  | | |   (56)  all_57_12 = e2 & op(e0, e3) = e2
% 231.54/42.89  | | | 
% 231.54/42.89  | | | ALPHA: (56) implies:
% 231.54/42.89  | | |   (57)  op(e0, e3) = e2
% 231.54/42.89  | | | 
% 231.54/42.89  | | | REF_CLOSE: (7), (22), (24), (57) are inconsistent by sub-proof #1980.
% 231.54/42.89  | | | 
% 231.54/42.89  | | Case 2:
% 231.54/42.89  | | | 
% 231.54/42.89  | | |   (58)  all_57_13 = e2 & op(e0, e2) = e2
% 231.54/42.89  | | | 
% 231.54/42.89  | | | ALPHA: (58) implies:
% 231.54/42.89  | | |   (59)  all_57_13 = e2
% 231.54/42.89  | | | 
% 231.54/42.89  | | | REF_CLOSE: (6), (12), (18), (30), (39), (42), (51), (59) are inconsistent
% 231.54/42.89  | | |            by sub-proof #1698.
% 231.54/42.89  | | | 
% 231.54/42.89  | | End of split
% 231.54/42.89  | | 
% 231.54/42.89  | Case 2:
% 231.54/42.89  | | 
% 231.54/42.89  | |   (60)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.54/42.89  | |           e2)
% 231.54/42.89  | | 
% 231.54/42.89  | | BETA: splitting (60) gives:
% 231.54/42.89  | | 
% 231.54/42.89  | | Case 1:
% 231.54/42.89  | | | 
% 231.54/42.89  | | |   (61)  all_57_14 = e2 & op(e0, e1) = e2
% 231.54/42.89  | | | 
% 231.54/42.89  | | | ALPHA: (61) implies:
% 231.54/42.89  | | |   (62)  all_57_14 = e2
% 231.54/42.89  | | | 
% 231.54/42.89  | | | BETA: splitting (43) gives:
% 231.54/42.89  | | | 
% 231.54/42.89  | | | Case 1:
% 231.54/42.89  | | | | 
% 231.54/42.89  | | | |   (63)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0)
% 231.54/42.89  | | | |           = e2)
% 231.54/42.89  | | | | 
% 231.54/42.89  | | | | BETA: splitting (63) gives:
% 231.54/42.89  | | | | 
% 231.54/42.89  | | | | Case 1:
% 231.54/42.89  | | | | | 
% 231.54/42.89  | | | | |   (64)  all_57_9 = e2 & op(e3, e0) = e2
% 231.54/42.89  | | | | | 
% 231.54/42.89  | | | | | ALPHA: (64) implies:
% 231.54/42.89  | | | | |   (65)  op(e3, e0) = e2
% 231.54/42.89  | | | | | 
% 231.54/42.89  | | | | | REF_CLOSE: (7), (45), (54), (65) are inconsistent by sub-proof #2331.
% 231.54/42.89  | | | | | 
% 231.54/42.89  | | | | Case 2:
% 231.54/42.89  | | | | | 
% 231.54/42.89  | | | | |   (66)  all_57_10 = e2 & op(e2, e0) = e2
% 231.54/42.89  | | | | | 
% 231.54/42.89  | | | | | ALPHA: (66) implies:
% 231.54/42.89  | | | | |   (67)  all_57_10 = e2
% 231.54/42.89  | | | | | 
% 231.54/42.89  | | | | | BETA: splitting (13) gives:
% 231.54/42.89  | | | | | 
% 231.54/42.89  | | | | | Case 1:
% 231.54/42.89  | | | | | | 
% 231.54/42.89  | | | | | |   (68)  all_55_9 = e3
% 231.54/42.89  | | | | | | 
% 231.54/42.89  | | | | | | REF_CLOSE: (14), (40), (68) are inconsistent by sub-proof #2159.
% 231.54/42.89  | | | | | | 
% 231.54/42.89  | | | | | Case 2:
% 231.54/42.89  | | | | | | 
% 231.54/42.89  | | | | | |   (69)   ~ (all_55_9 = e3)
% 231.54/42.89  | | | | | |   (70)  all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 231.54/42.89  | | | | | | 
% 231.54/42.89  | | | | | | BETA: splitting (70) gives:
% 231.54/42.89  | | | | | | 
% 231.54/42.89  | | | | | | Case 1:
% 231.54/42.89  | | | | | | | 
% 231.54/42.89  | | | | | | |   (71)  all_55_9 = e2
% 231.54/42.89  | | | | | | | 
% 231.54/42.89  | | | | | | | COMBINE_EQS: (14), (71) imply:
% 231.54/42.89  | | | | | | |   (72)  all_53_6 = e2
% 231.54/42.89  | | | | | | | 
% 231.54/42.89  | | | | | | | SIMP: (72) implies:
% 231.54/42.89  | | | | | | |   (73)  all_53_6 = e2
% 231.54/42.89  | | | | | | | 
% 231.54/42.89  | | | | | | | REDUCE: (53), (73) imply:
% 231.54/42.89  | | | | | | |   (74)   ~ (all_52_27 = e2)
% 231.54/42.89  | | | | | | | 
% 231.54/42.89  | | | | | | | SIMP: (74) implies:
% 231.54/42.89  | | | | | | |   (75)   ~ (all_52_27 = e2)
% 231.54/42.89  | | | | | | | 
% 231.54/42.89  | | | | | | | REDUCE: (40), (73) imply:
% 231.54/42.89  | | | | | | |   (76)   ~ (e3 = e2)
% 231.54/42.89  | | | | | | | 
% 231.54/42.89  | | | | | | | BETA: splitting (1) gives:
% 231.54/42.89  | | | | | | | 
% 231.54/42.89  | | | | | | | Case 1:
% 231.54/42.89  | | | | | | | | 
% 231.54/42.89  | | | | | | | |   (77)  all_55_13 = e3
% 231.54/42.89  | | | | | | | | 
% 231.54/42.89  | | | | | | | | REF_CLOSE: (28), (52), (77) are inconsistent by sub-proof #1648.
% 231.54/42.89  | | | | | | | | 
% 231.54/42.89  | | | | | | | Case 2:
% 231.54/42.89  | | | | | | | | 
% 231.54/42.89  | | | | | | | |   (78)   ~ (all_55_13 = e3)
% 231.54/42.89  | | | | | | | |   (79)  all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 231.54/42.89  | | | | | | | | 
% 231.54/42.89  | | | | | | | | BETA: splitting (79) gives:
% 231.54/42.89  | | | | | | | | 
% 231.54/42.89  | | | | | | | | Case 1:
% 231.54/42.89  | | | | | | | | | 
% 231.54/42.89  | | | | | | | | |   (80)  all_55_13 = e2
% 231.54/42.89  | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | REF_CLOSE: (28), (75), (80) are inconsistent by sub-proof
% 231.54/42.89  | | | | | | | | |            #1647.
% 231.54/42.89  | | | | | | | | | 
% 231.54/42.89  | | | | | | | | Case 2:
% 231.54/42.89  | | | | | | | | | 
% 231.54/42.89  | | | | | | | | |   (81)   ~ (all_55_13 = e2)
% 231.54/42.89  | | | | | | | | |   (82)  all_55_13 = e1 | all_55_13 = e0
% 231.54/42.89  | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | BETA: splitting (82) gives:
% 231.54/42.89  | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | Case 1:
% 231.54/42.89  | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | |   (83)  all_55_13 = e1
% 231.54/42.89  | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | COMBINE_EQS: (28), (83) imply:
% 231.54/42.89  | | | | | | | | | |   (84)  all_52_27 = e1
% 231.54/42.89  | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | SIMP: (84) implies:
% 231.54/42.89  | | | | | | | | | |   (85)  all_52_27 = e1
% 231.54/42.89  | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | REDUCE: (52), (85) imply:
% 231.54/42.89  | | | | | | | | | |   (86)   ~ (e3 = e1)
% 231.54/42.89  | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | REDUCE: (75), (85) imply:
% 231.54/42.89  | | | | | | | | | |   (87)   ~ (e2 = e1)
% 231.54/42.89  | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | REDUCE: (49), (85) imply:
% 231.54/42.89  | | | | | | | | | |   (88)  op(e1, e1) = e2
% 231.54/42.89  | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | REF_CLOSE: (3), (6), (7), (8), (9), (10), (11), (12), (15),
% 231.54/42.89  | | | | | | | | | |            (16), (17), (18), (19), (20), (21), (23), (25),
% 231.54/42.89  | | | | | | | | | |            (26), (29), (30), (31), (32), (33), (35), (37),
% 231.54/42.89  | | | | | | | | | |            (38), (41), (42), (43), (44), (46), (47), (48),
% 231.54/42.89  | | | | | | | | | |            (50), (51), (62), (67), (88) are inconsistent by
% 231.54/42.89  | | | | | | | | | |            sub-proof #1640.
% 231.54/42.89  | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | Case 2:
% 231.54/42.89  | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | |   (89)  all_55_13 = e0
% 231.54/42.89  | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | | REF_CLOSE: (28), (36), (89) are inconsistent by sub-proof
% 231.54/42.89  | | | | | | | | | |            #1639.
% 231.54/42.89  | | | | | | | | | | 
% 231.54/42.89  | | | | | | | | | End of split
% 231.54/42.89  | | | | | | | | | 
% 231.54/42.89  | | | | | | | | End of split
% 231.54/42.89  | | | | | | | | 
% 231.54/42.89  | | | | | | | End of split
% 231.54/42.89  | | | | | | | 
% 231.54/42.89  | | | | | | Case 2:
% 231.54/42.89  | | | | | | | 
% 231.54/42.89  | | | | | | |   (90)  all_55_9 = e1 | all_55_9 = e0
% 231.54/42.89  | | | | | | | 
% 231.54/42.89  | | | | | | | REF_CLOSE: (4), (14), (27), (90) are inconsistent by sub-proof
% 231.54/42.89  | | | | | | |            #1835.
% 231.54/42.89  | | | | | | | 
% 231.54/42.89  | | | | | | End of split
% 231.54/42.89  | | | | | | 
% 231.54/42.89  | | | | | End of split
% 231.54/42.89  | | | | | 
% 231.54/42.89  | | | | End of split
% 231.54/42.89  | | | | 
% 231.54/42.89  | | | Case 2:
% 231.54/42.89  | | | | 
% 231.54/42.89  | | | |   (91)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0,
% 231.54/42.89  | | | |             e0) = e2)
% 231.54/42.89  | | | | 
% 231.54/42.89  | | | | BETA: splitting (91) gives:
% 231.54/42.89  | | | | 
% 231.54/42.89  | | | | Case 1:
% 231.54/42.89  | | | | | 
% 231.54/42.89  | | | | |   (92)  all_57_11 = e2 & op(e1, e0) = e2
% 231.54/42.89  | | | | | 
% 231.54/42.89  | | | | | ALPHA: (92) implies:
% 231.54/42.89  | | | | |   (93)  all_57_11 = e2
% 231.54/42.89  | | | | | 
% 231.54/42.89  | | | | | REF_CLOSE: (7), (8), (9), (10), (12), (19), (20), (21), (93) are
% 231.54/42.89  | | | | |            inconsistent by sub-proof #1638.
% 231.54/42.89  | | | | | 
% 231.54/42.89  | | | | Case 2:
% 231.54/42.89  | | | | | 
% 231.54/42.89  | | | | |   (94)  all_57_15 = e2 & op(e0, e0) = e2
% 231.54/42.89  | | | | | 
% 231.54/42.89  | | | | | ALPHA: (94) implies:
% 231.54/42.89  | | | | |   (95)  all_57_15 = e2
% 231.54/42.89  | | | | | 
% 231.54/42.89  | | | | | COMBINE_EQS: (2), (95) imply:
% 231.54/42.89  | | | | |   (96)  e2 = e0
% 231.54/42.89  | | | | | 
% 231.54/42.89  | | | | | COMBINE_EQS: (12), (96) imply:
% 231.54/42.89  | | | | |   (97)  all_57_7 = e0
% 231.54/42.89  | | | | | 
% 231.54/42.89  | | | | | REF_CLOSE: (5), (6), (7), (11), (15), (16), (17), (18), (19), (20),
% 231.54/42.89  | | | | |            (23), (26), (29), (30), (32), (42), (51), (97) are
% 231.54/42.89  | | | | |            inconsistent by sub-proof #1636.
% 231.54/42.89  | | | | | 
% 231.54/42.89  | | | | End of split
% 231.54/42.89  | | | | 
% 231.54/42.89  | | | End of split
% 231.54/42.89  | | | 
% 231.54/42.89  | | Case 2:
% 231.54/42.89  | | | 
% 231.54/42.89  | | |   (98)  all_57_15 = e2 & op(e0, e0) = e2
% 231.54/42.89  | | | 
% 231.54/42.89  | | | ALPHA: (98) implies:
% 231.54/42.89  | | |   (99)  all_57_15 = e2
% 231.54/42.89  | | | 
% 231.54/42.89  | | | COMBINE_EQS: (2), (99) imply:
% 231.54/42.89  | | |   (100)  e2 = e0
% 231.54/42.89  | | | 
% 231.54/42.89  | | | SIMP: (100) implies:
% 231.54/42.89  | | |   (101)  e2 = e0
% 231.54/42.89  | | | 
% 231.54/42.89  | | | COMBINE_EQS: (12), (101) imply:
% 231.54/42.89  | | |   (102)  all_57_7 = e0
% 231.54/42.89  | | | 
% 231.54/42.89  | | | REF_CLOSE: (5), (6), (7), (11), (15), (16), (17), (18), (19), (20), (23),
% 231.54/42.89  | | |            (26), (29), (30), (32), (42), (51), (102) are inconsistent by
% 231.54/42.89  | | |            sub-proof #1636.
% 231.54/42.89  | | | 
% 231.54/42.89  | | End of split
% 231.54/42.89  | | 
% 231.54/42.89  | End of split
% 231.54/42.89  | 
% 231.54/42.89  End of proof
% 231.54/42.89  
% 231.54/42.89  Sub-proof #1636 shows that the following formulas are inconsistent:
% 231.54/42.89  ----------------------------------------------------------------
% 231.54/42.89    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.89         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.54/42.89    (2)   ~ (e3 = e1)
% 231.54/42.89    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.89           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.89    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.54/42.89         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.54/42.89    (5)  all_57_4 = e0
% 231.54/42.89    (6)  op(e2, e2) = e0
% 231.54/42.89    (7)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.54/42.89         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.54/42.89    (8)  all_57_3 = e0
% 231.54/42.89    (9)   ~ (e3 = e2)
% 231.54/42.89    (10)   ~ (e3 = e0)
% 231.54/42.89    (11)  op(e3, e3) = e2
% 231.54/42.89    (12)   ~ (e2 = e0)
% 231.54/42.89    (13)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 231.54/42.89          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.54/42.89    (14)   ~ (e1 = e0)
% 231.54/42.89    (15)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.54/42.89          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.54/42.89    (16)   ~ (e2 = e1)
% 231.54/42.89    (17)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.89          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.54/42.89    (18)  all_57_7 = e0
% 231.54/42.89  
% 231.54/42.89  Begin of proof
% 231.54/42.89  | 
% 231.54/42.89  | BETA: splitting (1) gives:
% 231.54/42.89  | 
% 231.54/42.89  | Case 1:
% 231.54/42.89  | | 
% 231.54/42.89  | |   (19)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 231.54/42.89  | |           e2)
% 231.54/42.89  | | 
% 231.54/42.89  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13), (14),
% 231.54/42.89  | |            (16), (19) are inconsistent by sub-proof #1637.
% 231.54/42.89  | | 
% 231.54/42.89  | Case 2:
% 231.54/42.89  | | 
% 231.54/42.89  | |   (20)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 231.54/42.89  | |           e2)
% 231.54/42.89  | | 
% 231.54/42.89  | | REF_CLOSE: (2), (3), (6), (8), (9), (10), (12), (14), (15), (16), (17),
% 231.54/42.89  | |            (18), (20) are inconsistent by sub-proof #2201.
% 231.54/42.89  | | 
% 231.54/42.89  | End of split
% 231.54/42.89  | 
% 231.54/42.89  End of proof
% 231.54/42.89  
% 231.54/42.89  Sub-proof #1637 shows that the following formulas are inconsistent:
% 231.54/42.89  ----------------------------------------------------------------
% 231.54/42.89    (1)   ~ (e3 = e1)
% 231.54/42.89    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.89           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.89    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.54/42.89         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.54/42.89    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2)
% 231.54/42.89    (5)  all_57_4 = e0
% 231.54/42.89    (6)  op(e2, e2) = e0
% 231.54/42.89    (7)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.54/42.89         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.54/42.89    (8)   ~ (e3 = e2)
% 231.54/42.89    (9)   ~ (e3 = e0)
% 231.54/42.89    (10)  op(e3, e3) = e2
% 231.54/42.89    (11)   ~ (e2 = e0)
% 231.54/42.89    (12)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 231.54/42.89          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.54/42.89    (13)   ~ (e1 = e0)
% 231.54/42.89    (14)   ~ (e2 = e1)
% 231.54/42.89  
% 231.54/42.89  Begin of proof
% 231.54/42.89  | 
% 231.54/42.89  | BETA: splitting (4) gives:
% 231.54/42.89  | 
% 231.54/42.89  | Case 1:
% 231.54/42.89  | | 
% 231.54/42.89  | |   (15)  all_57_1 = e2 & op(e3, e2) = e2
% 231.54/42.89  | | 
% 231.54/42.89  | | ALPHA: (15) implies:
% 231.54/42.89  | |   (16)  all_57_1 = e2
% 231.54/42.89  | | 
% 231.54/42.89  | | REF_CLOSE: (1), (2), (3), (5), (7), (8), (9), (10), (11), (12), (13), (14),
% 231.54/42.89  | |            (16) are inconsistent by sub-proof #1658.
% 231.54/42.89  | | 
% 231.54/42.89  | Case 2:
% 231.54/42.89  | | 
% 231.54/42.89  | |   (17)  all_57_3 = e2 & op(e2, e2) = e2
% 231.54/42.89  | | 
% 231.54/42.89  | | ALPHA: (17) implies:
% 231.54/42.89  | |   (18)  op(e2, e2) = e2
% 231.54/42.89  | | 
% 231.54/42.89  | | REF_CLOSE: (2), (6), (11), (18) are inconsistent by sub-proof #2472.
% 231.54/42.89  | | 
% 231.54/42.89  | End of split
% 231.54/42.89  | 
% 231.54/42.89  End of proof
% 231.54/42.89  
% 231.54/42.89  Sub-proof #1638 shows that the following formulas are inconsistent:
% 231.54/42.89  ----------------------------------------------------------------
% 231.54/42.89    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.89           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.89    (2)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.54/42.89         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.54/42.89    (3)   ~ (all_6_2 = e3)
% 231.54/42.89    (4)  op(e1, e1) = all_6_2
% 231.54/42.89    (5)  all_57_7 = e2
% 231.54/42.89    (6)   ~ (e3 = e2)
% 231.54/42.89    (7)   ~ (e3 = e0)
% 231.54/42.89    (8)  all_57_6 = e0
% 231.54/42.89    (9)  all_57_11 = e2
% 231.54/42.89  
% 231.54/42.89  Begin of proof
% 231.54/42.89  | 
% 231.54/42.89  | BETA: splitting (2) gives:
% 231.54/42.89  | 
% 231.54/42.89  | Case 1:
% 231.54/42.89  | | 
% 231.54/42.89  | |   (10)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 231.54/42.89  | |           e3)
% 231.54/42.89  | | 
% 231.54/42.89  | | BETA: splitting (10) gives:
% 231.54/42.89  | | 
% 231.54/42.89  | | Case 1:
% 231.54/42.89  | | | 
% 231.54/42.89  | | |   (11)  all_57_6 = e3 & op(e1, e3) = e3
% 231.54/42.89  | | | 
% 231.54/42.89  | | | ALPHA: (11) implies:
% 231.54/42.89  | | |   (12)  all_57_6 = e3
% 231.54/42.89  | | | 
% 231.54/42.89  | | | REF_CLOSE: (7), (8), (12) are inconsistent by sub-proof #1822.
% 231.54/42.89  | | | 
% 231.54/42.89  | | Case 2:
% 231.54/42.89  | | | 
% 231.54/42.89  | | |   (13)  all_57_7 = e3 & op(e1, e2) = e3
% 231.54/42.89  | | | 
% 231.54/42.89  | | | REF_CLOSE: (5), (6), (13) are inconsistent by sub-proof #2194.
% 231.54/42.89  | | | 
% 231.54/42.89  | | End of split
% 231.54/42.89  | | 
% 231.54/42.89  | Case 2:
% 231.54/42.89  | | 
% 231.54/42.89  | |   (14)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 231.54/42.89  | |           e3)
% 231.54/42.89  | | 
% 231.54/42.89  | | REF_CLOSE: (1), (3), (4), (6), (9), (14) are inconsistent by sub-proof
% 231.54/42.89  | |            #2040.
% 231.54/42.89  | | 
% 231.54/42.89  | End of split
% 231.54/42.89  | 
% 231.54/42.89  End of proof
% 231.54/42.89  
% 231.54/42.89  Sub-proof #1639 shows that the following formulas are inconsistent:
% 231.54/42.89  ----------------------------------------------------------------
% 231.54/42.89    (1)  all_55_13 = all_52_27
% 231.54/42.89    (2)  all_55_13 = e0
% 231.54/42.89    (3)   ~ (all_52_27 = e0)
% 231.54/42.89  
% 231.54/42.89  Begin of proof
% 231.54/42.89  | 
% 231.54/42.89  | COMBINE_EQS: (1), (2) imply:
% 231.54/42.89  |   (4)  all_52_27 = e0
% 231.54/42.89  | 
% 231.54/42.89  | SIMP: (4) implies:
% 231.54/42.89  |   (5)  all_52_27 = e0
% 231.54/42.89  | 
% 231.54/42.89  | REDUCE: (3), (5) imply:
% 231.54/42.89  |   (6)  $false
% 231.54/42.89  | 
% 231.54/42.89  | CLOSE: (6) is inconsistent.
% 231.54/42.89  | 
% 231.54/42.89  End of proof
% 231.54/42.89  
% 231.54/42.89  Sub-proof #1640 shows that the following formulas are inconsistent:
% 231.54/42.89  ----------------------------------------------------------------
% 231.54/42.89    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.89         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.54/42.89    (2)   ~ (e3 = e1)
% 231.54/42.89    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.89           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.89    (4)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.54/42.89         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.54/42.89    (5)   ~ (all_6_2 = e3)
% 231.54/42.89    (6)  op(e1, e1) = all_6_2
% 231.54/42.89    (7)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.54/42.89         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.54/42.89    (8)  all_57_7 = e2
% 231.54/42.89    (9)  all_57_4 = e0
% 231.54/42.89    (10)  op(e2, e2) = e0
% 231.54/42.89    (11)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.54/42.89          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.54/42.89    (12)  all_57_3 = e0
% 231.54/42.89    (13)   ~ (e3 = e2)
% 231.54/42.89    (14)   ~ (e3 = e0)
% 231.54/42.89    (15)  all_57_6 = e0
% 231.54/42.89    (16)  op(e3, e3) = e2
% 231.54/42.89    (17)  all_57_10 = e2
% 231.54/42.89    (18)  op(e0, e0) = all_52_31
% 231.54/42.89    (19)   ~ (e2 = e0)
% 231.54/42.89    (20)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 231.54/42.89          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.54/42.89    (21)   ~ (e1 = e0)
% 231.54/42.89    (22)  all_57_14 = e2
% 231.54/42.89    (23)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.54/42.89          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.54/42.89    (24)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.54/42.89          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.54/42.89    (25)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.54/42.89          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 231.54/42.89            e3)
% 231.54/42.89    (26)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.54/42.89              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.54/42.89                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.54/42.89                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.54/42.89    (27)  op(e1, e1) = e2
% 231.54/42.89    (28)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.54/42.89          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.54/42.89    (29)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.89          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.54/42.89    (30)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 231.54/42.89          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 231.54/42.89    (31)   ~ (e2 = e1)
% 231.54/42.89    (32)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.54/42.89          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.54/42.89    (33)   ~ (all_6_2 = e0)
% 231.54/42.89    (34)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.54/42.89          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.54/42.89    (35)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.54/42.89          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.54/42.89    (36)  op(all_52_31, all_52_31) = e0
% 231.54/42.89    (37)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 231.54/42.89          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 231.54/42.90    (38)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.90          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.54/42.90  
% 231.54/42.90  Begin of proof
% 231.54/42.90  | 
% 231.54/42.90  | BETA: splitting (4) gives:
% 231.54/42.90  | 
% 231.54/42.90  | Case 1:
% 231.54/42.90  | | 
% 231.54/42.90  | |   (39)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 231.54/42.90  | |           e3)
% 231.54/42.90  | | 
% 231.54/42.90  | | REF_CLOSE: (8), (13), (14), (15), (39) are inconsistent by sub-proof #1821.
% 231.54/42.90  | | 
% 231.54/42.90  | Case 2:
% 231.54/42.90  | | 
% 231.54/42.90  | |   (40)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 231.54/42.90  | |           e3)
% 231.54/42.90  | | 
% 231.54/42.90  | | BETA: splitting (40) gives:
% 231.54/42.90  | | 
% 231.54/42.90  | | Case 1:
% 231.54/42.90  | | | 
% 231.54/42.90  | | |   (41)  all_57_8 = e3 & op(e1, e1) = e3
% 231.54/42.90  | | | 
% 231.54/42.90  | | | ALPHA: (41) implies:
% 231.54/42.90  | | |   (42)  op(e1, e1) = e3
% 231.54/42.90  | | | 
% 231.54/42.90  | | | REF_CLOSE: (3), (5), (6), (42) are inconsistent by sub-proof #2468.
% 231.54/42.90  | | | 
% 231.54/42.90  | | Case 2:
% 231.54/42.90  | | | 
% 231.54/42.90  | | |   (43)  all_57_11 = e3 & op(e1, e0) = e3
% 231.54/42.90  | | | 
% 231.54/42.90  | | | ALPHA: (43) implies:
% 231.54/42.90  | | |   (44)  all_57_11 = e3
% 231.54/42.90  | | | 
% 231.54/42.90  | | | BETA: splitting (35) gives:
% 231.54/42.90  | | | 
% 231.54/42.90  | | | Case 1:
% 231.54/42.90  | | | | 
% 231.54/42.90  | | | |   (45)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0)
% 231.54/42.90  | | | |           = e1)
% 231.54/42.90  | | | | 
% 231.54/42.90  | | | | BETA: splitting (45) gives:
% 231.54/42.90  | | | | 
% 231.54/42.90  | | | | Case 1:
% 231.54/42.90  | | | | | 
% 231.54/42.90  | | | | |   (46)  all_57_9 = e1 & op(e3, e0) = e1
% 231.54/42.90  | | | | | 
% 231.54/42.90  | | | | | ALPHA: (46) implies:
% 231.54/42.90  | | | | |   (47)  all_57_9 = e1
% 231.54/42.90  | | | | | 
% 231.54/42.90  | | | | | BETA: splitting (20) gives:
% 231.54/42.90  | | | | | 
% 231.54/42.90  | | | | | Case 1:
% 231.54/42.90  | | | | | | 
% 231.54/42.90  | | | | | |   (48)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3,
% 231.54/42.90  | | | | | |             e2) = e3)
% 231.54/42.90  | | | | | | 
% 231.54/42.90  | | | | | | BETA: splitting (48) gives:
% 231.54/42.90  | | | | | | 
% 231.54/42.90  | | | | | | Case 1:
% 231.54/42.90  | | | | | | | 
% 231.54/42.90  | | | | | | |   (49)  all_57_0 = e3 & op(e3, e3) = e3
% 231.54/42.90  | | | | | | | 
% 231.54/42.90  | | | | | | | ALPHA: (49) implies:
% 231.54/42.90  | | | | | | |   (50)  op(e3, e3) = e3
% 231.54/42.90  | | | | | | | 
% 231.54/42.90  | | | | | | | REF_CLOSE: (3), (13), (16), (50) are inconsistent by sub-proof
% 231.54/42.90  | | | | | | |            #2490.
% 231.54/42.90  | | | | | | | 
% 231.54/42.90  | | | | | | Case 2:
% 231.54/42.90  | | | | | | | 
% 231.54/42.90  | | | | | | |   (51)  all_57_1 = e3 & op(e3, e2) = e3
% 231.54/42.90  | | | | | | | 
% 231.54/42.90  | | | | | | | ALPHA: (51) implies:
% 231.54/42.90  | | | | | | |   (52)  all_57_1 = e3
% 231.54/42.90  | | | | | | | 
% 231.54/42.90  | | | | | | | BETA: splitting (23) gives:
% 231.54/42.90  | | | | | | | 
% 231.54/42.90  | | | | | | | Case 1:
% 231.54/42.90  | | | | | | | | 
% 231.54/42.90  | | | | | | | |   (53)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 &
% 231.54/42.90  | | | | | | | |           op(e2, e1) = e3)
% 231.54/42.90  | | | | | | | | 
% 231.54/42.90  | | | | | | | | BETA: splitting (53) gives:
% 231.54/42.90  | | | | | | | | 
% 231.54/42.90  | | | | | | | | Case 1:
% 231.54/42.90  | | | | | | | | | 
% 231.54/42.90  | | | | | | | | |   (54)  all_57_4 = e3 & op(e3, e1) = e3
% 231.54/42.90  | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | ALPHA: (54) implies:
% 231.54/42.90  | | | | | | | | |   (55)  all_57_4 = e3
% 231.54/42.90  | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | REF_CLOSE: (9), (14), (55) are inconsistent by sub-proof
% 231.54/42.90  | | | | | | | | |            #2372.
% 231.54/42.90  | | | | | | | | | 
% 231.54/42.90  | | | | | | | | Case 2:
% 231.54/42.90  | | | | | | | | | 
% 231.54/42.90  | | | | | | | | |   (56)  all_57_5 = e3 & op(e2, e1) = e3
% 231.54/42.90  | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | ALPHA: (56) implies:
% 231.54/42.90  | | | | | | | | |   (57)  all_57_5 = e3
% 231.54/42.90  | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | BETA: splitting (1) gives:
% 231.54/42.90  | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | Case 1:
% 231.54/42.90  | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | |   (58)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 &
% 231.54/42.90  | | | | | | | | | |           op(e2, e2) = e1)
% 231.54/42.90  | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | BETA: splitting (58) gives:
% 231.54/42.90  | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | Case 1:
% 231.54/42.90  | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | |   (59)  all_57_2 = e1 & op(e2, e3) = e1
% 231.54/42.90  | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | ALPHA: (59) implies:
% 231.54/42.90  | | | | | | | | | | |   (60)  all_57_2 = e1
% 231.54/42.90  | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | BETA: splitting (38) gives:
% 231.54/42.90  | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | Case 1:
% 231.54/42.90  | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | |   (61)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 231.54/42.90  | | | | | | | | | | | |           & op(e2, e2) = e1)
% 231.54/42.90  | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | BETA: splitting (61) gives:
% 231.54/42.90  | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | Case 1:
% 231.54/42.90  | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | |   (62)  all_57_1 = e1 & op(e3, e2) = e1
% 231.54/42.90  | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | ALPHA: (62) implies:
% 231.54/42.90  | | | | | | | | | | | | |   (63)  all_57_1 = e1
% 231.54/42.90  | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | COMBINE_EQS: (52), (63) imply:
% 231.54/42.90  | | | | | | | | | | | | |   (64)  e3 = e1
% 231.54/42.90  | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | COMBINE_EQS: (57), (64) imply:
% 231.54/42.90  | | | | | | | | | | | | |   (65)  all_57_5 = e1
% 231.54/42.90  | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | REF_CLOSE: (2), (12), (13), (14), (17), (28), (60), (65) are
% 231.54/42.90  | | | | | | | | | | | | |            inconsistent by sub-proof #1645.
% 231.54/42.90  | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | Case 2:
% 231.54/42.90  | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | |   (66)  all_57_3 = e1 & op(e2, e2) = e1
% 231.54/42.90  | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | ALPHA: (66) implies:
% 231.54/42.90  | | | | | | | | | | | | |   (67)  op(e2, e2) = e1
% 231.54/42.90  | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | REF_CLOSE: (3), (13), (14), (19), (21), (29), (30), (31),
% 231.54/42.90  | | | | | | | | | | | | |            (57), (60), (67) are inconsistent by sub-proof
% 231.54/42.90  | | | | | | | | | | | | |            #1825.
% 231.54/42.90  | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | End of split
% 231.54/42.90  | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | Case 2:
% 231.54/42.90  | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | |   (68)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 231.54/42.90  | | | | | | | | | | | |           e1 & op(e0, e2) = e1)
% 231.54/42.90  | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | BETA: splitting (68) gives:
% 231.54/42.90  | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | Case 1:
% 231.54/42.90  | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | |   (69)  all_57_7 = e1 & op(e1, e2) = e1
% 231.54/42.90  | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | REF_CLOSE: (8), (31), (69) are inconsistent by sub-proof
% 231.54/42.90  | | | | | | | | | | | | |            #2190.
% 231.54/42.90  | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | Case 2:
% 231.54/42.90  | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | |   (70)  all_57_13 = e1 & op(e0, e2) = e1
% 231.54/42.90  | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | ALPHA: (70) implies:
% 231.54/42.90  | | | | | | | | | | | | |   (71)  all_57_13 = e1
% 231.54/42.90  | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | BETA: splitting (25) gives:
% 231.54/42.90  | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | Case 1:
% 231.54/42.90  | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | |   (72)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 231.54/42.90  | | | | | | | | | | | | | |           e3 & op(e0, e2) = e3)
% 231.54/42.90  | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | BETA: splitting (72) gives:
% 231.54/42.90  | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | Case 1:
% 231.54/42.90  | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | |   (73)  all_57_12 = e3 & op(e0, e3) = e3
% 231.54/42.90  | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | ALPHA: (73) implies:
% 231.54/42.90  | | | | | | | | | | | | | | |   (74)  all_57_12 = e3
% 231.54/42.90  | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | BETA: splitting (37) gives:
% 231.54/42.90  | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | Case 1:
% 231.54/42.90  | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | |   (75)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 231.54/42.90  | | | | | | | | | | | | | | | |           & op(e1, e2) = e1)
% 231.54/42.90  | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | BETA: splitting (75) gives:
% 231.54/42.90  | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.90  | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | |   (76)  all_57_6 = e1 & op(e1, e3) = e1
% 231.54/42.90  | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | ALPHA: (76) implies:
% 231.54/42.90  | | | | | | | | | | | | | | | | |   (77)  all_57_6 = e1
% 231.54/42.90  | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (12), (13), (14), (16), (19), (21),
% 231.54/42.90  | | | | | | | | | | | | | | | | |            (29), (31), (34), (57), (74), (77) are
% 231.54/42.90  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1643.
% 231.54/42.90  | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.90  | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | |   (78)  all_57_7 = e1 & op(e1, e2) = e1
% 231.54/42.90  | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (31), (78) are inconsistent by sub-proof
% 231.54/42.90  | | | | | | | | | | | | | | | | |            #2190.
% 231.54/42.90  | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | End of split
% 231.54/42.90  | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | Case 2:
% 231.54/42.90  | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | |   (79)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 231.54/42.90  | | | | | | | | | | | | | | | |           e1 & op(e1, e0) = e1)
% 231.54/42.90  | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | BETA: splitting (79) gives:
% 231.54/42.90  | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | Case 1:
% 231.54/42.90  | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | |   (80)  all_57_8 = e1 & op(e1, e1) = e1
% 231.54/42.90  | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | ALPHA: (80) implies:
% 231.54/42.90  | | | | | | | | | | | | | | | | |   (81)  op(e1, e1) = e1
% 231.54/42.90  | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (27), (31), (81) are inconsistent by
% 231.54/42.90  | | | | | | | | | | | | | | | | |            sub-proof #2423.
% 231.54/42.90  | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | Case 2:
% 231.54/42.90  | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | |   (82)  all_57_11 = e1 & op(e1, e0) = e1
% 231.54/42.90  | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | ALPHA: (82) implies:
% 231.54/42.90  | | | | | | | | | | | | | | | | |   (83)  all_57_11 = e1
% 231.54/42.90  | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | COMBINE_EQS: (44), (83) imply:
% 231.54/42.90  | | | | | | | | | | | | | | | | |   (84)  e3 = e1
% 231.54/42.90  | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | SIMP: (84) implies:
% 231.54/42.90  | | | | | | | | | | | | | | | | |   (85)  e3 = e1
% 231.54/42.90  | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | COMBINE_EQS: (52), (85) imply:
% 231.54/42.90  | | | | | | | | | | | | | | | | |   (86)  all_57_1 = e1
% 231.54/42.90  | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (8), (12), (13), (14), (24), (71), (86) are
% 231.54/42.90  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2193.
% 231.54/42.90  | | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | | End of split
% 231.54/42.90  | | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | End of split
% 231.54/42.90  | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | Case 2:
% 231.54/42.90  | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | |   (87)  all_57_13 = e3 & op(e0, e2) = e3
% 231.54/42.90  | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | ALPHA: (87) implies:
% 231.54/42.90  | | | | | | | | | | | | | | |   (88)  all_57_13 = e3
% 231.54/42.90  | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | COMBINE_EQS: (71), (88) imply:
% 231.54/42.90  | | | | | | | | | | | | | | |   (89)  e3 = e1
% 231.54/42.90  | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | SIMP: (89) implies:
% 231.54/42.90  | | | | | | | | | | | | | | |   (90)  e3 = e1
% 231.54/42.90  | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | COMBINE_EQS: (52), (90) imply:
% 231.54/42.90  | | | | | | | | | | | | | | |   (91)  all_57_1 = e1
% 231.54/42.90  | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | REF_CLOSE: (2), (8), (12), (13), (14), (24), (71), (91) are
% 231.54/42.90  | | | | | | | | | | | | | | |            inconsistent by sub-proof #2193.
% 231.54/42.90  | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | End of split
% 231.54/42.90  | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | Case 2:
% 231.54/42.90  | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | |   (92)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 231.54/42.90  | | | | | | | | | | | | | |           e3 & op(e0, e0) = e3)
% 231.54/42.90  | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | BETA: splitting (92) gives:
% 231.54/42.90  | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | Case 1:
% 231.54/42.90  | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | |   (93)  all_57_14 = e3 & op(e0, e1) = e3
% 231.54/42.90  | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | ALPHA: (93) implies:
% 231.54/42.90  | | | | | | | | | | | | | | |   (94)  all_57_14 = e3
% 231.54/42.90  | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (7), (9), (11), (13), (14), (16), (19),
% 231.54/42.90  | | | | | | | | | | | | | | |            (20), (21), (22), (31), (52), (94) are
% 231.54/42.90  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1642.
% 231.54/42.90  | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | Case 2:
% 231.54/42.90  | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | |   (95)  all_57_15 = e3 & op(e0, e0) = e3
% 231.54/42.90  | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | ALPHA: (95) implies:
% 231.54/42.90  | | | | | | | | | | | | | | |   (96)  all_57_15 = e3
% 231.54/42.90  | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | | REF_CLOSE: (2), (13), (14), (19), (21), (26), (31), (32),
% 231.54/42.90  | | | | | | | | | | | | | | |            (35), (44), (96) are inconsistent by sub-proof
% 231.54/42.90  | | | | | | | | | | | | | | |            #2134.
% 231.54/42.90  | | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | | End of split
% 231.54/42.90  | | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | | End of split
% 231.54/42.90  | | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | | End of split
% 231.54/42.90  | | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | End of split
% 231.54/42.90  | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | Case 2:
% 231.54/42.90  | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | |   (97)  all_57_3 = e1 & op(e2, e2) = e1
% 231.54/42.90  | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | ALPHA: (97) implies:
% 231.54/42.90  | | | | | | | | | | |   (98)  op(e2, e2) = e1
% 231.54/42.90  | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | REF_CLOSE: (3), (10), (21), (98) are inconsistent by
% 231.54/42.90  | | | | | | | | | | |            sub-proof #2352.
% 231.54/42.90  | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | End of split
% 231.54/42.90  | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | Case 2:
% 231.54/42.90  | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | |   (99)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1
% 231.54/42.90  | | | | | | | | | |           & op(e2, e0) = e1)
% 231.54/42.90  | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | BETA: splitting (99) gives:
% 231.54/42.90  | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | Case 1:
% 231.54/42.90  | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | |   (100)  all_57_5 = e1 & op(e2, e1) = e1
% 231.54/42.90  | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | REF_CLOSE: (2), (57), (100) are inconsistent by sub-proof
% 231.54/42.90  | | | | | | | | | | |            #2376.
% 231.54/42.90  | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | Case 2:
% 231.54/42.90  | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | |   (101)  all_57_10 = e1 & op(e2, e0) = e1
% 231.54/42.90  | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | | REF_CLOSE: (17), (31), (101) are inconsistent by sub-proof
% 231.54/42.90  | | | | | | | | | | |            #2360.
% 231.54/42.90  | | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | | End of split
% 231.54/42.90  | | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | End of split
% 231.54/42.90  | | | | | | | | | 
% 231.54/42.90  | | | | | | | | End of split
% 231.54/42.90  | | | | | | | | 
% 231.54/42.90  | | | | | | | Case 2:
% 231.54/42.90  | | | | | | | | 
% 231.54/42.90  | | | | | | | |   (102)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 &
% 231.54/42.90  | | | | | | | |            op(e0, e1) = e3)
% 231.54/42.90  | | | | | | | | 
% 231.54/42.90  | | | | | | | | BETA: splitting (102) gives:
% 231.54/42.90  | | | | | | | | 
% 231.54/42.90  | | | | | | | | Case 1:
% 231.54/42.90  | | | | | | | | | 
% 231.54/42.90  | | | | | | | | |   (103)  all_57_8 = e3 & op(e1, e1) = e3
% 231.54/42.90  | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | ALPHA: (103) implies:
% 231.54/42.90  | | | | | | | | |   (104)  op(e1, e1) = e3
% 231.54/42.90  | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | REF_CLOSE: (3), (5), (6), (104) are inconsistent by sub-proof
% 231.54/42.90  | | | | | | | | |            #2468.
% 231.54/42.90  | | | | | | | | | 
% 231.54/42.90  | | | | | | | | Case 2:
% 231.54/42.90  | | | | | | | | | 
% 231.54/42.90  | | | | | | | | |   (105)  all_57_14 = e3 & op(e0, e1) = e3
% 231.54/42.90  | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | ALPHA: (105) implies:
% 231.54/42.90  | | | | | | | | |   (106)  all_57_14 = e3
% 231.54/42.90  | | | | | | | | | 
% 231.54/42.90  | | | | | | | | | REF_CLOSE: (2), (3), (7), (9), (11), (13), (14), (16), (19),
% 231.54/42.90  | | | | | | | | |            (20), (21), (22), (31), (52), (106) are
% 231.54/42.90  | | | | | | | | |            inconsistent by sub-proof #1642.
% 231.54/42.90  | | | | | | | | | 
% 231.54/42.90  | | | | | | | | End of split
% 231.54/42.90  | | | | | | | | 
% 231.54/42.90  | | | | | | | End of split
% 231.54/42.90  | | | | | | | 
% 231.54/42.90  | | | | | | End of split
% 231.54/42.90  | | | | | | 
% 231.54/42.90  | | | | | Case 2:
% 231.54/42.90  | | | | | | 
% 231.54/42.90  | | | | | |   (107)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3,
% 231.54/42.90  | | | | | |              e0) = e3)
% 231.54/42.90  | | | | | | 
% 231.54/42.90  | | | | | | REF_CLOSE: (2), (9), (14), (47), (107) are inconsistent by sub-proof
% 231.54/42.90  | | | | | |            #1641.
% 231.54/42.90  | | | | | | 
% 231.54/42.90  | | | | | End of split
% 231.54/42.90  | | | | | 
% 231.54/42.90  | | | | Case 2:
% 231.54/42.90  | | | | | 
% 231.54/42.90  | | | | |   (108)  all_57_10 = e1 & op(e2, e0) = e1
% 231.54/42.90  | | | | | 
% 231.54/42.90  | | | | | REF_CLOSE: (17), (31), (108) are inconsistent by sub-proof #2360.
% 231.54/42.90  | | | | | 
% 231.54/42.90  | | | | End of split
% 231.54/42.90  | | | | 
% 231.54/42.90  | | | Case 2:
% 231.54/42.90  | | | | 
% 231.54/42.90  | | | |   (109)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0,
% 231.54/42.90  | | | |              e0) = e1)
% 231.54/42.90  | | | | 
% 231.54/42.90  | | | | BETA: splitting (109) gives:
% 231.54/42.90  | | | | 
% 231.54/42.90  | | | | Case 1:
% 231.54/42.90  | | | | | 
% 231.54/42.90  | | | | |   (110)  all_57_11 = e1 & op(e1, e0) = e1
% 231.54/42.90  | | | | | 
% 231.54/42.90  | | | | | ALPHA: (110) implies:
% 231.54/42.90  | | | | |   (111)  all_57_11 = e1
% 231.54/42.90  | | | | | 
% 231.54/42.90  | | | | | REF_CLOSE: (2), (44), (111) are inconsistent by sub-proof #2218.
% 231.54/42.90  | | | | | 
% 231.54/42.90  | | | | Case 2:
% 231.54/42.90  | | | | | 
% 231.54/42.90  | | | | |   (112)  all_57_15 = e1 & op(e0, e0) = e1
% 231.54/42.90  | | | | | 
% 231.54/42.90  | | | | | ALPHA: (112) implies:
% 231.54/42.90  | | | | |   (113)  op(e0, e0) = e1
% 231.54/42.90  | | | | | 
% 231.54/42.90  | | | | | REF_CLOSE: (3), (6), (18), (33), (36), (113) are inconsistent by
% 231.54/42.90  | | | | |            sub-proof #2086.
% 231.54/42.90  | | | | | 
% 231.54/42.90  | | | | End of split
% 231.54/42.90  | | | | 
% 231.54/42.90  | | | End of split
% 231.54/42.90  | | | 
% 231.54/42.90  | | End of split
% 231.54/42.90  | | 
% 231.54/42.90  | End of split
% 231.54/42.90  | 
% 231.54/42.90  End of proof
% 231.54/42.90  
% 231.54/42.90  Sub-proof #1641 shows that the following formulas are inconsistent:
% 231.54/42.90  ----------------------------------------------------------------
% 231.54/42.90    (1)   ~ (e3 = e1)
% 231.54/42.90    (2)  all_57_9 = e1
% 231.54/42.90    (3)  all_57_4 = e0
% 231.54/42.90    (4)   ~ (e3 = e0)
% 231.54/42.90    (5)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.54/42.90  
% 231.54/42.90  Begin of proof
% 231.54/42.90  | 
% 231.54/42.90  | BETA: splitting (5) gives:
% 231.54/42.90  | 
% 231.54/42.90  | Case 1:
% 231.54/42.90  | | 
% 231.54/42.90  | |   (6)  all_57_4 = e3 & op(e3, e1) = e3
% 231.54/42.90  | | 
% 231.54/42.90  | | ALPHA: (6) implies:
% 231.54/42.90  | |   (7)  all_57_4 = e3
% 231.54/42.90  | | 
% 231.54/42.90  | | REF_CLOSE: (3), (4), (7) are inconsistent by sub-proof #2372.
% 231.54/42.90  | | 
% 231.54/42.90  | Case 2:
% 231.54/42.90  | | 
% 231.54/42.90  | |   (8)  all_57_9 = e3 & op(e3, e0) = e3
% 231.54/42.90  | | 
% 231.54/42.90  | | ALPHA: (8) implies:
% 231.54/42.90  | |   (9)  all_57_9 = e3
% 231.54/42.90  | | 
% 231.54/42.90  | | REF_CLOSE: (1), (2), (9) are inconsistent by sub-proof #1673.
% 231.54/42.90  | | 
% 231.54/42.90  | End of split
% 231.54/42.90  | 
% 231.54/42.90  End of proof
% 231.54/42.90  
% 231.54/42.90  Sub-proof #1642 shows that the following formulas are inconsistent:
% 231.54/42.90  ----------------------------------------------------------------
% 231.54/42.90    (1)   ~ (e3 = e1)
% 231.54/42.90    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.90           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.90    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.54/42.90         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.54/42.90    (4)  all_57_14 = e3
% 231.54/42.90    (5)  all_57_4 = e0
% 231.54/42.90    (6)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.54/42.90         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.54/42.90    (7)   ~ (e3 = e2)
% 231.54/42.90    (8)   ~ (e3 = e0)
% 231.54/42.90    (9)  op(e3, e3) = e2
% 231.54/42.90    (10)   ~ (e2 = e0)
% 231.54/42.90    (11)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 231.54/42.90          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.54/42.90    (12)   ~ (e1 = e0)
% 231.54/42.90    (13)  all_57_14 = e2
% 231.54/42.90    (14)  all_57_1 = e3
% 231.54/42.90    (15)   ~ (e2 = e1)
% 231.54/42.90  
% 231.54/42.90  Begin of proof
% 231.54/42.90  | 
% 231.54/42.90  | COMBINE_EQS: (4), (13) imply:
% 231.54/42.90  |   (16)  e3 = e2
% 231.54/42.90  | 
% 231.54/42.90  | SIMP: (16) implies:
% 231.54/42.90  |   (17)  e3 = e2
% 231.54/42.90  | 
% 231.54/42.90  | COMBINE_EQS: (14), (17) imply:
% 231.54/42.90  |   (18)  all_57_1 = e2
% 231.54/42.90  | 
% 231.54/42.90  | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (15),
% 231.54/42.90  |            (18) are inconsistent by sub-proof #1658.
% 231.54/42.90  | 
% 231.54/42.90  End of proof
% 231.54/42.90  
% 231.54/42.90  Sub-proof #1643 shows that the following formulas are inconsistent:
% 231.54/42.90  ----------------------------------------------------------------
% 231.54/42.90    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.90         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.54/42.90    (2)   ~ (e3 = e1)
% 231.54/42.90    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.90           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.90    (4)  all_57_6 = e1
% 231.54/42.90    (5)  all_57_3 = e0
% 231.54/42.90    (6)   ~ (e3 = e2)
% 231.54/42.90    (7)   ~ (e3 = e0)
% 231.54/42.90    (8)  op(e3, e3) = e2
% 231.54/42.90    (9)  all_57_5 = e3
% 231.54/42.90    (10)   ~ (e2 = e0)
% 231.54/42.90    (11)   ~ (e1 = e0)
% 231.54/42.90    (12)  all_57_12 = e3
% 231.54/42.90    (13)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.90          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.54/42.90    (14)   ~ (e2 = e1)
% 231.54/42.90    (15)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.54/42.90          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.54/42.90  
% 231.54/42.90  Begin of proof
% 231.54/42.90  | 
% 231.54/42.90  | BETA: splitting (15) gives:
% 231.54/42.90  | 
% 231.54/42.90  | Case 1:
% 231.54/42.90  | | 
% 231.54/42.90  | |   (16)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) =
% 231.54/42.90  | |           e0)
% 231.54/42.90  | | 
% 231.54/42.90  | | REF_CLOSE: (1), (2), (3), (5), (6), (8), (9), (10), (11), (13), (14), (16)
% 231.54/42.90  | |            are inconsistent by sub-proof #1644.
% 231.54/42.90  | | 
% 231.54/42.90  | Case 2:
% 231.54/42.90  | | 
% 231.54/42.90  | |   (17)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) =
% 231.54/42.90  | |           e0)
% 231.54/42.90  | | 
% 231.54/42.90  | | BETA: splitting (17) gives:
% 231.54/42.90  | | 
% 231.54/42.90  | | Case 1:
% 231.54/42.90  | | | 
% 231.54/42.90  | | |   (18)  all_57_6 = e0 & op(e1, e3) = e0
% 231.54/42.90  | | | 
% 231.54/42.90  | | | ALPHA: (18) implies:
% 231.54/42.90  | | |   (19)  all_57_6 = e0
% 231.54/42.90  | | | 
% 231.54/42.90  | | | REF_CLOSE: (4), (11), (19) are inconsistent by sub-proof #2227.
% 231.54/42.90  | | | 
% 231.54/42.90  | | Case 2:
% 231.54/42.90  | | | 
% 231.54/42.90  | | |   (20)  all_57_12 = e0 & op(e0, e3) = e0
% 231.54/42.90  | | | 
% 231.54/42.90  | | | ALPHA: (20) implies:
% 231.54/42.90  | | |   (21)  all_57_12 = e0
% 231.54/42.90  | | | 
% 231.54/42.90  | | | REF_CLOSE: (7), (12), (21) are inconsistent by sub-proof #2153.
% 231.54/42.90  | | | 
% 231.54/42.90  | | End of split
% 231.54/42.90  | | 
% 231.54/42.90  | End of split
% 231.54/42.90  | 
% 231.54/42.90  End of proof
% 231.54/42.90  
% 231.54/42.90  Sub-proof #1644 shows that the following formulas are inconsistent:
% 231.54/42.90  ----------------------------------------------------------------
% 231.54/42.90    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.90         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.54/42.90    (2)   ~ (e3 = e1)
% 231.54/42.90    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.90           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.90    (4)  all_57_3 = e0
% 231.54/42.90    (5)   ~ (e3 = e2)
% 231.54/42.90    (6)  op(e3, e3) = e2
% 231.54/42.90    (7)  all_57_5 = e3
% 231.54/42.90    (8)   ~ (e2 = e0)
% 231.54/42.90    (9)   ~ (e1 = e0)
% 231.54/42.90    (10)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.90          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.54/42.90    (11)   ~ (e2 = e1)
% 231.54/42.90    (12)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0)
% 231.54/42.90  
% 231.54/42.90  Begin of proof
% 231.54/42.90  | 
% 231.54/42.90  | BETA: splitting (12) gives:
% 231.54/42.90  | 
% 231.54/42.90  | Case 1:
% 231.54/42.90  | | 
% 231.54/42.90  | |   (13)  all_57_0 = e0 & op(e3, e3) = e0
% 231.54/42.90  | | 
% 231.54/42.90  | | ALPHA: (13) implies:
% 231.54/42.90  | |   (14)  op(e3, e3) = e0
% 231.54/42.90  | | 
% 231.54/42.90  | | REF_CLOSE: (3), (6), (8), (14) are inconsistent by sub-proof #2403.
% 231.54/42.90  | | 
% 231.54/42.90  | Case 2:
% 231.54/42.90  | | 
% 231.54/42.90  | |   (15)  all_57_2 = e0 & op(e2, e3) = e0
% 231.54/42.90  | | 
% 231.54/42.90  | | ALPHA: (15) implies:
% 231.54/42.90  | |   (16)  all_57_2 = e0
% 231.54/42.90  | | 
% 231.54/42.90  | | REF_CLOSE: (1), (2), (4), (5), (7), (8), (9), (10), (11), (16) are
% 231.54/42.90  | |            inconsistent by sub-proof #2253.
% 231.54/42.90  | | 
% 231.54/42.90  | End of split
% 231.54/42.90  | 
% 231.54/42.90  End of proof
% 231.54/42.90  
% 231.54/42.90  Sub-proof #1645 shows that the following formulas are inconsistent:
% 231.54/42.90  ----------------------------------------------------------------
% 231.54/42.90    (1)   ~ (e3 = e1)
% 231.54/42.90    (2)  all_57_3 = e0
% 231.54/42.90    (3)   ~ (e3 = e2)
% 231.54/42.90    (4)   ~ (e3 = e0)
% 231.54/42.90    (5)  all_57_10 = e2
% 231.54/42.90    (6)  all_57_2 = e1
% 231.54/42.90    (7)  all_57_5 = e1
% 231.54/42.90    (8)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.54/42.90         (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.54/42.90  
% 231.54/42.90  Begin of proof
% 231.54/42.90  | 
% 231.54/42.90  | BETA: splitting (8) gives:
% 231.54/42.90  | 
% 231.54/42.90  | Case 1:
% 231.54/42.90  | | 
% 231.54/42.90  | |   (9)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3)
% 231.54/42.90  | | 
% 231.54/42.90  | | REF_CLOSE: (1), (2), (4), (6), (9) are inconsistent by sub-proof #1646.
% 231.54/42.90  | | 
% 231.54/42.90  | Case 2:
% 231.54/42.90  | | 
% 231.54/42.90  | |   (10)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 231.54/42.90  | |           e3)
% 231.54/42.90  | | 
% 231.54/42.90  | | BETA: splitting (10) gives:
% 231.54/42.90  | | 
% 231.54/42.90  | | Case 1:
% 231.54/42.90  | | | 
% 231.54/42.90  | | |   (11)  all_57_5 = e3 & op(e2, e1) = e3
% 231.54/42.90  | | | 
% 231.54/42.90  | | | ALPHA: (11) implies:
% 231.54/42.90  | | |   (12)  all_57_5 = e3
% 231.54/42.90  | | | 
% 231.54/42.90  | | | REF_CLOSE: (1), (7), (12) are inconsistent by sub-proof #2382.
% 231.54/42.90  | | | 
% 231.54/42.90  | | Case 2:
% 231.54/42.90  | | | 
% 231.54/42.90  | | |   (13)  all_57_10 = e3 & op(e2, e0) = e3
% 231.54/42.90  | | | 
% 231.54/42.90  | | | REF_CLOSE: (3), (5), (13) are inconsistent by sub-proof #2051.
% 231.54/42.90  | | | 
% 231.54/42.90  | | End of split
% 231.54/42.90  | | 
% 231.54/42.90  | End of split
% 231.54/42.90  | 
% 231.54/42.90  End of proof
% 231.54/42.90  
% 231.54/42.90  Sub-proof #1646 shows that the following formulas are inconsistent:
% 231.54/42.90  ----------------------------------------------------------------
% 231.54/42.90    (1)   ~ (e3 = e1)
% 231.54/42.90    (2)  all_57_3 = e0
% 231.54/42.90    (3)   ~ (e3 = e0)
% 231.54/42.90    (4)  all_57_2 = e1
% 231.54/42.90    (5)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3)
% 231.54/42.90  
% 231.54/42.90  Begin of proof
% 231.54/42.90  | 
% 231.54/42.90  | BETA: splitting (5) gives:
% 231.54/42.90  | 
% 231.54/42.90  | Case 1:
% 231.54/42.90  | | 
% 231.54/42.90  | |   (6)  all_57_2 = e3 & op(e2, e3) = e3
% 231.54/42.90  | | 
% 231.54/42.90  | | ALPHA: (6) implies:
% 231.54/42.90  | |   (7)  all_57_2 = e3
% 231.54/42.90  | | 
% 231.54/42.90  | | REF_CLOSE: (1), (4), (7) are inconsistent by sub-proof #2397.
% 231.54/42.90  | | 
% 231.54/42.90  | Case 2:
% 231.54/42.90  | | 
% 231.54/42.90  | |   (8)  all_57_3 = e3 & op(e2, e2) = e3
% 231.54/42.90  | | 
% 231.54/42.90  | | ALPHA: (8) implies:
% 231.54/42.90  | |   (9)  all_57_3 = e3
% 231.54/42.90  | | 
% 231.54/42.90  | | REF_CLOSE: (2), (3), (9) are inconsistent by sub-proof #2358.
% 231.54/42.90  | | 
% 231.54/42.90  | End of split
% 231.54/42.90  | 
% 231.54/42.90  End of proof
% 231.54/42.90  
% 231.54/42.90  Sub-proof #1647 shows that the following formulas are inconsistent:
% 231.54/42.90  ----------------------------------------------------------------
% 231.54/42.90    (1)  all_55_13 = all_52_27
% 231.54/42.90    (2)  all_55_13 = e2
% 231.54/42.90    (3)   ~ (all_52_27 = e2)
% 231.54/42.90  
% 231.54/42.90  Begin of proof
% 231.54/42.90  | 
% 231.54/42.90  | COMBINE_EQS: (1), (2) imply:
% 231.54/42.90  |   (4)  all_52_27 = e2
% 231.54/42.90  | 
% 231.54/42.90  | SIMP: (4) implies:
% 231.54/42.90  |   (5)  all_52_27 = e2
% 231.54/42.90  | 
% 231.54/42.90  | REDUCE: (3), (5) imply:
% 231.54/42.90  |   (6)  $false
% 231.54/42.90  | 
% 231.54/42.90  | CLOSE: (6) is inconsistent.
% 231.54/42.90  | 
% 231.54/42.90  End of proof
% 231.54/42.90  
% 231.54/42.90  Sub-proof #1648 shows that the following formulas are inconsistent:
% 231.54/42.90  ----------------------------------------------------------------
% 231.54/42.90    (1)  all_55_13 = all_52_27
% 231.54/42.90    (2)  all_55_13 = e3
% 231.54/42.90    (3)   ~ (all_52_27 = e3)
% 231.54/42.90  
% 231.54/42.90  Begin of proof
% 231.54/42.90  | 
% 231.54/42.90  | COMBINE_EQS: (1), (2) imply:
% 231.54/42.90  |   (4)  all_52_27 = e3
% 231.54/42.90  | 
% 231.54/42.90  | SIMP: (4) implies:
% 231.54/42.90  |   (5)  all_52_27 = e3
% 231.54/42.90  | 
% 231.54/42.90  | REDUCE: (3), (5) imply:
% 231.54/42.90  |   (6)  $false
% 231.54/42.90  | 
% 231.54/42.90  | CLOSE: (6) is inconsistent.
% 231.54/42.90  | 
% 231.54/42.90  End of proof
% 231.54/42.90  
% 231.54/42.90  Sub-proof #1649 shows that the following formulas are inconsistent:
% 231.54/42.90  ----------------------------------------------------------------
% 231.54/42.90    (1)   ~ (e3 = e1)
% 231.54/42.90    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.90           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.90    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.54/42.90         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.54/42.90    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2)
% 231.54/42.90    (5)  op(e2, e2) = e0
% 231.54/42.90    (6)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.54/42.90         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.54/42.90    (7)   ~ (e3 = e2)
% 231.54/42.90    (8)   ~ (e3 = e0)
% 231.54/42.90    (9)  op(e3, e3) = e2
% 231.54/42.90    (10)   ~ (e2 = e0)
% 231.54/42.90    (11)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 231.54/42.90          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.54/42.90    (12)   ~ (e1 = e0)
% 231.54/42.90    (13)   ~ (all_53_12 = e3)
% 231.54/42.90    (14)   ~ (e2 = e1)
% 231.54/42.90    (15)  op(e3, e0) = all_53_12
% 231.54/42.90  
% 231.54/42.90  Begin of proof
% 231.54/42.90  | 
% 231.54/42.90  | BETA: splitting (4) gives:
% 231.54/42.90  | 
% 231.54/42.90  | Case 1:
% 231.54/42.90  | | 
% 231.54/42.90  | |   (16)  all_57_1 = e2 & op(e3, e2) = e2
% 231.54/42.90  | | 
% 231.54/42.90  | | ALPHA: (16) implies:
% 231.54/42.90  | |   (17)  all_57_1 = e2
% 231.54/42.90  | | 
% 231.54/42.90  | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (9), (10), (11), (12), (13), (14),
% 231.54/42.90  | |            (15), (17) are inconsistent by sub-proof #1650.
% 231.54/42.90  | | 
% 231.54/42.90  | Case 2:
% 231.54/42.90  | | 
% 231.54/42.90  | |   (18)  all_57_3 = e2 & op(e2, e2) = e2
% 231.54/42.90  | | 
% 231.54/42.90  | | ALPHA: (18) implies:
% 231.54/42.90  | |   (19)  op(e2, e2) = e2
% 231.54/42.90  | | 
% 231.54/42.90  | | REF_CLOSE: (2), (5), (10), (19) are inconsistent by sub-proof #2472.
% 231.54/42.90  | | 
% 231.54/42.90  | End of split
% 231.54/42.90  | 
% 231.54/42.90  End of proof
% 231.54/42.90  
% 231.54/42.90  Sub-proof #1650 shows that the following formulas are inconsistent:
% 231.54/42.90  ----------------------------------------------------------------
% 231.54/42.90    (1)   ~ (e3 = e1)
% 231.54/42.90    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.90           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.90    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.54/42.90         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.54/42.90    (4)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.54/42.90         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.54/42.90    (5)   ~ (e3 = e2)
% 231.54/42.90    (6)   ~ (e3 = e0)
% 231.54/42.90    (7)  all_57_1 = e2
% 231.54/42.90    (8)  op(e3, e3) = e2
% 231.54/42.90    (9)   ~ (e2 = e0)
% 231.54/42.90    (10)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 231.54/42.90          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.54/42.90    (11)   ~ (e1 = e0)
% 231.54/42.90    (12)   ~ (all_53_12 = e3)
% 231.54/42.90    (13)   ~ (e2 = e1)
% 231.54/42.90    (14)  op(e3, e0) = all_53_12
% 231.54/42.90  
% 231.54/42.90  Begin of proof
% 231.54/42.90  | 
% 231.54/42.90  | BETA: splitting (10) gives:
% 231.54/42.90  | 
% 231.54/42.90  | Case 1:
% 231.54/42.90  | | 
% 231.54/42.90  | |   (15)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) =
% 231.54/42.90  | |           e3)
% 231.54/42.90  | | 
% 231.54/42.90  | | REF_CLOSE: (2), (5), (7), (8), (15) are inconsistent by sub-proof #1663.
% 231.54/42.90  | | 
% 231.54/42.90  | Case 2:
% 231.54/42.90  | | 
% 231.54/42.90  | |   (16)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) =
% 231.54/42.90  | |           e3)
% 231.54/42.90  | | 
% 231.54/42.90  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (11), (12), (13), (14),
% 231.54/42.90  | |            (16) are inconsistent by sub-proof #1651.
% 231.54/42.90  | | 
% 231.54/42.90  | End of split
% 231.54/42.90  | 
% 231.54/42.90  End of proof
% 231.54/42.90  
% 231.54/42.90  Sub-proof #1651 shows that the following formulas are inconsistent:
% 231.54/42.90  ----------------------------------------------------------------
% 231.54/42.90    (1)   ~ (e3 = e1)
% 231.54/42.90    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.90           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.90    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.54/42.90         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.54/42.90    (4)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.54/42.90         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.54/42.90    (5)   ~ (e3 = e0)
% 231.54/42.90    (6)  all_57_1 = e2
% 231.54/42.90    (7)  op(e3, e3) = e2
% 231.54/42.90    (8)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.54/42.90    (9)   ~ (e2 = e0)
% 231.54/42.90    (10)   ~ (e1 = e0)
% 231.54/42.90    (11)   ~ (all_53_12 = e3)
% 231.54/42.90    (12)   ~ (e2 = e1)
% 231.54/42.90    (13)  op(e3, e0) = all_53_12
% 231.54/42.90  
% 231.54/42.90  Begin of proof
% 231.54/42.90  | 
% 231.54/42.90  | BETA: splitting (8) gives:
% 231.54/42.90  | 
% 231.54/42.90  | Case 1:
% 231.54/42.90  | | 
% 231.54/42.90  | |   (14)  all_57_4 = e3 & op(e3, e1) = e3
% 231.54/42.90  | | 
% 231.54/42.90  | | ALPHA: (14) implies:
% 231.54/42.91  | |   (15)  all_57_4 = e3
% 231.54/42.91  | | 
% 231.54/42.91  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (12), (15) are
% 231.54/42.91  | |            inconsistent by sub-proof #1659.
% 231.54/42.91  | | 
% 231.54/42.91  | Case 2:
% 231.54/42.91  | | 
% 231.54/42.91  | |   (16)  all_57_9 = e3 & op(e3, e0) = e3
% 231.54/42.91  | | 
% 231.54/42.91  | | ALPHA: (16) implies:
% 231.54/42.91  | |   (17)  op(e3, e0) = e3
% 231.54/42.91  | | 
% 231.54/42.91  | | REF_CLOSE: (2), (11), (13), (17) are inconsistent by sub-proof #2458.
% 231.54/42.91  | | 
% 231.54/42.91  | End of split
% 231.54/42.91  | 
% 231.54/42.91  End of proof
% 231.54/42.91  
% 231.54/42.91  Sub-proof #1652 shows that the following formulas are inconsistent:
% 231.54/42.91  ----------------------------------------------------------------
% 231.54/42.91    (1)  op(e1, e3) = e0
% 231.54/42.91    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.91           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.91    (3)   ~ (e3 = e0)
% 231.54/42.91    (4)  op(e0, e0) = e0
% 231.54/42.91    (5)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 &
% 231.54/42.91         op(all_52_17, all_52_17) = e3 & op(all_52_19, all_52_19) = e2 &
% 231.54/42.91         op(all_52_21, all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1,
% 231.54/42.91           e3) = all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 &
% 231.54/42.91         op(e1, e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 231.54/42.91         $i(all_52_23)
% 231.54/42.91  
% 231.54/42.91  Begin of proof
% 231.54/42.91  | 
% 231.54/42.91  | ALPHA: (5) implies:
% 231.54/42.91  |   (6)  op(e1, e3) = all_52_17
% 231.54/42.91  |   (7)  op(all_52_17, all_52_17) = e3
% 231.54/42.91  | 
% 231.54/42.91  | GROUND_INST: instantiating (2) with e0, all_52_17, e3, e1, simplifying with
% 231.54/42.91  |              (1), (6) gives:
% 231.54/42.91  |   (8)  all_52_17 = e0
% 231.54/42.91  | 
% 231.54/42.91  | REDUCE: (7), (8) imply:
% 231.54/42.91  |   (9)  op(e0, e0) = e3
% 231.54/42.91  | 
% 231.54/42.91  | REF_CLOSE: (2), (3), (4), (9) are inconsistent by sub-proof #2304.
% 231.54/42.91  | 
% 231.54/42.91  End of proof
% 231.54/42.91  
% 231.54/42.91  Sub-proof #1653 shows that the following formulas are inconsistent:
% 231.54/42.91  ----------------------------------------------------------------
% 231.54/42.91    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.91           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.91    (2)  op(e2, e2) = e0
% 231.54/42.91    (3)   ~ (e3 = e0)
% 231.54/42.91    (4)  op(e3, e3) = e2
% 231.54/42.91    (5)  op(e3, e3) = all_52_1
% 231.54/42.91    (6)  op(all_52_1, all_52_1) = e3
% 231.54/42.91  
% 231.54/42.91  Begin of proof
% 231.54/42.91  | 
% 231.54/42.91  | GROUND_INST: instantiating (1) with e2, all_52_1, e3, e3, simplifying with
% 231.54/42.91  |              (4), (5) gives:
% 231.54/42.91  |   (7)  all_52_1 = e2
% 231.54/42.91  | 
% 231.54/42.91  | REDUCE: (6), (7) imply:
% 231.54/42.91  |   (8)  op(e2, e2) = e3
% 231.54/42.91  | 
% 231.54/42.91  | GROUND_INST: instantiating (1) with e0, e3, e2, e2, simplifying with (2), (8)
% 231.54/42.91  |              gives:
% 231.54/42.91  |   (9)  e3 = e0
% 231.54/42.91  | 
% 231.54/42.91  | REDUCE: (3), (9) imply:
% 231.54/42.91  |   (10)  $false
% 231.54/42.91  | 
% 231.54/42.91  | CLOSE: (10) is inconsistent.
% 231.54/42.91  | 
% 231.54/42.91  End of proof
% 231.54/42.91  
% 231.54/42.91  Sub-proof #1654 shows that the following formulas are inconsistent:
% 231.54/42.91  ----------------------------------------------------------------
% 231.54/42.91    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.91         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.54/42.91    (2)   ~ (e3 = e1)
% 231.54/42.91    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.91           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.91    (4)  all_57_3 = e0
% 231.54/42.91    (5)   ~ (e3 = e2)
% 231.54/42.91    (6)   ~ (e3 = e0)
% 231.54/42.91    (7)  op(e3, e3) = e2
% 231.54/42.91    (8)   ~ (e2 = e0)
% 231.54/42.91    (9)   ~ (e1 = e0)
% 231.54/42.91    (10)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.54/42.91          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.54/42.91    (11)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.91          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.54/42.91    (12)   ~ (e2 = e1)
% 231.54/42.91    (13)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0)
% 231.54/42.91  
% 231.54/42.91  Begin of proof
% 231.54/42.91  | 
% 231.54/42.91  | BETA: splitting (13) gives:
% 231.54/42.91  | 
% 231.54/42.91  | Case 1:
% 231.54/42.91  | | 
% 231.54/42.91  | |   (14)  all_57_0 = e0 & op(e3, e3) = e0
% 231.54/42.91  | | 
% 231.54/42.91  | | ALPHA: (14) implies:
% 231.54/42.91  | |   (15)  op(e3, e3) = e0
% 231.54/42.91  | | 
% 231.54/42.91  | | REF_CLOSE: (3), (7), (8), (15) are inconsistent by sub-proof #2403.
% 231.54/42.91  | | 
% 231.54/42.91  | Case 2:
% 231.54/42.91  | | 
% 231.54/42.91  | |   (16)  all_57_2 = e0 & op(e2, e3) = e0
% 231.54/42.91  | | 
% 231.54/42.91  | | ALPHA: (16) implies:
% 231.54/42.91  | |   (17)  all_57_2 = e0
% 231.54/42.91  | | 
% 231.54/42.91  | | REF_CLOSE: (1), (2), (4), (5), (6), (8), (9), (10), (11), (12), (17) are
% 231.54/42.91  | |            inconsistent by sub-proof #2246.
% 231.54/42.91  | | 
% 231.54/42.91  | End of split
% 231.54/42.91  | 
% 231.54/42.91  End of proof
% 231.54/42.91  
% 231.54/42.91  Sub-proof #1655 shows that the following formulas are inconsistent:
% 231.54/42.91  ----------------------------------------------------------------
% 231.54/42.91    (1)   ~ (e3 = e1)
% 231.54/42.91    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.91           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.91    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.54/42.91         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.54/42.91    (4)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.54/42.91         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.54/42.91    (5)   ~ (e3 = e2)
% 231.54/42.91    (6)   ~ (e3 = e0)
% 231.54/42.91    (7)  all_57_1 = e2
% 231.54/42.91    (8)  op(e3, e3) = e2
% 231.54/42.91    (9)   ~ (e2 = e0)
% 231.54/42.91    (10)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 231.54/42.91          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.54/42.91    (11)   ~ (e1 = e0)
% 231.54/42.91    (12)   ~ (e2 = e1)
% 231.54/42.91  
% 231.54/42.91  Begin of proof
% 231.54/42.91  | 
% 231.54/42.91  | BETA: splitting (4) gives:
% 231.54/42.91  | 
% 231.54/42.91  | Case 1:
% 231.54/42.91  | | 
% 231.54/42.91  | |   (13)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) =
% 231.54/42.91  | |           e0)
% 231.54/42.91  | | 
% 231.54/42.91  | | REF_CLOSE: (2), (7), (8), (9), (13) are inconsistent by sub-proof #1665.
% 231.54/42.91  | | 
% 231.54/42.91  | Case 2:
% 231.54/42.91  | | 
% 231.54/42.91  | |   (14)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) =
% 231.54/42.91  | |           e0)
% 231.54/42.91  | | 
% 231.54/42.91  | | BETA: splitting (14) gives:
% 231.54/42.91  | | 
% 231.54/42.91  | | Case 1:
% 231.54/42.91  | | | 
% 231.54/42.91  | | |   (15)  all_57_4 = e0 & op(e3, e1) = e0
% 231.54/42.91  | | | 
% 231.54/42.91  | | | ALPHA: (15) implies:
% 231.54/42.91  | | |   (16)  all_57_4 = e0
% 231.54/42.91  | | | 
% 231.54/42.91  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 231.54/42.91  | | |            (16) are inconsistent by sub-proof #1658.
% 231.54/42.91  | | | 
% 231.54/42.91  | | Case 2:
% 231.54/42.91  | | | 
% 231.54/42.91  | | |   (17)  all_57_9 = e0 & op(e3, e0) = e0
% 231.54/42.91  | | | 
% 231.54/42.91  | | | ALPHA: (17) implies:
% 231.54/42.91  | | |   (18)  all_57_9 = e0
% 231.54/42.91  | | | 
% 231.54/42.91  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 231.54/42.91  | | |            (18) are inconsistent by sub-proof #1656.
% 231.54/42.91  | | | 
% 231.54/42.91  | | End of split
% 231.54/42.91  | | 
% 231.54/42.91  | End of split
% 231.54/42.91  | 
% 231.54/42.91  End of proof
% 231.54/42.91  
% 231.54/42.91  Sub-proof #1656 shows that the following formulas are inconsistent:
% 231.54/42.91  ----------------------------------------------------------------
% 231.54/42.91    (1)   ~ (e3 = e1)
% 231.54/42.91    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.91           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.91    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.54/42.91         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.54/42.91    (4)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.54/42.91         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.54/42.91    (5)   ~ (e3 = e2)
% 231.54/42.91    (6)   ~ (e3 = e0)
% 231.54/42.91    (7)  all_57_1 = e2
% 231.54/42.91    (8)  op(e3, e3) = e2
% 231.54/42.91    (9)  all_57_9 = e0
% 231.54/42.91    (10)   ~ (e2 = e0)
% 231.54/42.91    (11)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 231.54/42.91          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.54/42.91    (12)   ~ (e1 = e0)
% 231.54/42.91    (13)   ~ (e2 = e1)
% 231.54/42.91  
% 231.54/42.91  Begin of proof
% 231.54/42.91  | 
% 231.54/42.91  | BETA: splitting (11) gives:
% 231.54/42.91  | 
% 231.54/42.91  | Case 1:
% 231.54/42.91  | | 
% 231.54/42.91  | |   (14)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) =
% 231.54/42.91  | |           e3)
% 231.54/42.91  | | 
% 231.54/42.91  | | REF_CLOSE: (2), (5), (7), (8), (14) are inconsistent by sub-proof #1663.
% 231.54/42.91  | | 
% 231.54/42.91  | Case 2:
% 231.54/42.91  | | 
% 231.54/42.91  | |   (15)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) =
% 231.54/42.91  | |           e3)
% 231.54/42.91  | | 
% 231.54/42.91  | | BETA: splitting (15) gives:
% 231.54/42.91  | | 
% 231.54/42.91  | | Case 1:
% 231.54/42.91  | | | 
% 231.54/42.91  | | |   (16)  all_57_4 = e3 & op(e3, e1) = e3
% 231.54/42.91  | | | 
% 231.54/42.91  | | | ALPHA: (16) implies:
% 231.54/42.91  | | |   (17)  all_57_4 = e3
% 231.54/42.91  | | | 
% 231.54/42.91  | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (10), (12), (13), (17) are
% 231.54/42.91  | | |            inconsistent by sub-proof #1659.
% 231.54/42.91  | | | 
% 231.54/42.91  | | Case 2:
% 231.54/42.91  | | | 
% 231.54/42.91  | | |   (18)  all_57_9 = e3 & op(e3, e0) = e3
% 231.54/42.91  | | | 
% 231.54/42.91  | | | ALPHA: (18) implies:
% 231.54/42.91  | | |   (19)  all_57_9 = e3
% 231.54/42.91  | | | 
% 231.54/42.91  | | | REF_CLOSE: (6), (9), (19) are inconsistent by sub-proof #1657.
% 231.54/42.91  | | | 
% 231.54/42.91  | | End of split
% 231.54/42.91  | | 
% 231.54/42.91  | End of split
% 231.54/42.91  | 
% 231.54/42.91  End of proof
% 231.54/42.91  
% 231.54/42.91  Sub-proof #1657 shows that the following formulas are inconsistent:
% 231.54/42.91  ----------------------------------------------------------------
% 231.54/42.91    (1)  all_57_9 = e3
% 231.54/42.91    (2)  all_57_9 = e0
% 231.54/42.91    (3)   ~ (e3 = e0)
% 231.54/42.91  
% 231.54/42.91  Begin of proof
% 231.54/42.91  | 
% 231.54/42.91  | COMBINE_EQS: (1), (2) imply:
% 231.54/42.91  |   (4)  e3 = e0
% 231.54/42.91  | 
% 231.54/42.91  | SIMP: (4) implies:
% 231.54/42.91  |   (5)  e3 = e0
% 231.54/42.91  | 
% 231.54/42.91  | REDUCE: (3), (5) imply:
% 231.54/42.91  |   (6)  $false
% 231.54/42.91  | 
% 231.54/42.91  | CLOSE: (6) is inconsistent.
% 231.54/42.91  | 
% 231.54/42.91  End of proof
% 231.54/42.91  
% 231.54/42.91  Sub-proof #1658 shows that the following formulas are inconsistent:
% 231.54/42.91  ----------------------------------------------------------------
% 231.54/42.91    (1)   ~ (e3 = e1)
% 231.54/42.91    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.91           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.91    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.54/42.91         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.54/42.91    (4)  all_57_4 = e0
% 231.54/42.91    (5)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.54/42.91         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.54/42.91    (6)   ~ (e3 = e2)
% 231.54/42.91    (7)   ~ (e3 = e0)
% 231.54/42.91    (8)  all_57_1 = e2
% 231.54/42.91    (9)  op(e3, e3) = e2
% 231.54/42.91    (10)   ~ (e2 = e0)
% 231.54/42.91    (11)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 231.54/42.91          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.54/42.91    (12)   ~ (e1 = e0)
% 231.54/42.91    (13)   ~ (e2 = e1)
% 231.54/42.91  
% 231.54/42.91  Begin of proof
% 231.54/42.91  | 
% 231.54/42.91  | BETA: splitting (11) gives:
% 231.54/42.91  | 
% 231.54/42.91  | Case 1:
% 231.54/42.91  | | 
% 231.54/42.91  | |   (14)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) =
% 231.54/42.91  | |           e3)
% 231.54/42.91  | | 
% 231.54/42.91  | | REF_CLOSE: (2), (6), (8), (9), (14) are inconsistent by sub-proof #1663.
% 231.54/42.91  | | 
% 231.54/42.91  | Case 2:
% 231.54/42.91  | | 
% 231.54/42.91  | |   (15)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) =
% 231.54/42.91  | |           e3)
% 231.54/42.91  | | 
% 231.54/42.91  | | BETA: splitting (15) gives:
% 231.54/42.91  | | 
% 231.54/42.91  | | Case 1:
% 231.54/42.91  | | | 
% 231.54/42.91  | | |   (16)  all_57_4 = e3 & op(e3, e1) = e3
% 231.54/42.91  | | | 
% 231.54/42.91  | | | ALPHA: (16) implies:
% 231.54/42.91  | | |   (17)  all_57_4 = e3
% 231.54/42.91  | | | 
% 231.54/42.91  | | | REF_CLOSE: (1), (2), (3), (5), (7), (8), (9), (10), (12), (13), (17) are
% 231.54/42.91  | | |            inconsistent by sub-proof #1659.
% 231.54/42.91  | | | 
% 231.54/42.91  | | Case 2:
% 231.54/42.91  | | | 
% 231.54/42.91  | | |   (18)  all_57_9 = e3 & op(e3, e0) = e3
% 231.54/42.91  | | | 
% 231.54/42.91  | | | ALPHA: (18) implies:
% 231.54/42.91  | | |   (19)  all_57_9 = e3
% 231.54/42.91  | | | 
% 231.54/42.91  | | | BETA: splitting (3) gives:
% 231.54/42.91  | | | 
% 231.54/42.91  | | | Case 1:
% 231.54/42.91  | | | | 
% 231.54/42.91  | | | |   (20)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2)
% 231.54/42.91  | | | |           = e1)
% 231.54/42.91  | | | | 
% 231.54/42.91  | | | | REF_CLOSE: (2), (8), (9), (13), (20) are inconsistent by sub-proof
% 231.54/42.91  | | | |            #1662.
% 231.54/42.91  | | | | 
% 231.54/42.91  | | | Case 2:
% 231.54/42.91  | | | | 
% 231.54/42.91  | | | |   (21)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0)
% 231.54/42.91  | | | |           = e1)
% 231.54/42.91  | | | | 
% 231.54/42.91  | | | | BETA: splitting (21) gives:
% 231.54/42.91  | | | | 
% 231.54/42.91  | | | | Case 1:
% 231.54/42.91  | | | | | 
% 231.54/42.91  | | | | |   (22)  all_57_4 = e1 & op(e3, e1) = e1
% 231.54/42.91  | | | | | 
% 231.54/42.91  | | | | | ALPHA: (22) implies:
% 231.54/42.91  | | | | |   (23)  all_57_4 = e1
% 231.54/42.91  | | | | | 
% 231.54/42.91  | | | | | REF_CLOSE: (4), (12), (23) are inconsistent by sub-proof #2438.
% 231.54/42.91  | | | | | 
% 231.54/42.91  | | | | Case 2:
% 231.54/42.91  | | | | | 
% 231.54/42.91  | | | | |   (24)  all_57_9 = e1 & op(e3, e0) = e1
% 231.54/42.91  | | | | | 
% 231.54/42.91  | | | | | ALPHA: (24) implies:
% 231.54/42.91  | | | | |   (25)  all_57_9 = e1
% 231.54/42.91  | | | | | 
% 231.54/42.91  | | | | | REF_CLOSE: (1), (19), (25) are inconsistent by sub-proof #1673.
% 231.54/42.91  | | | | | 
% 231.54/42.91  | | | | End of split
% 231.54/42.91  | | | | 
% 231.54/42.91  | | | End of split
% 231.54/42.91  | | | 
% 231.54/42.91  | | End of split
% 231.54/42.91  | | 
% 231.54/42.91  | End of split
% 231.54/42.91  | 
% 231.54/42.91  End of proof
% 231.54/42.91  
% 231.54/42.91  Sub-proof #1659 shows that the following formulas are inconsistent:
% 231.54/42.91  ----------------------------------------------------------------
% 231.54/42.91    (1)   ~ (e3 = e1)
% 231.54/42.91    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.91           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.91    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.54/42.91         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.54/42.91    (4)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.54/42.91         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.54/42.91    (5)  all_57_4 = e3
% 231.54/42.91    (6)   ~ (e3 = e0)
% 231.54/42.91    (7)  all_57_1 = e2
% 231.54/42.91    (8)  op(e3, e3) = e2
% 231.54/42.91    (9)   ~ (e2 = e0)
% 231.54/42.91    (10)   ~ (e1 = e0)
% 231.54/42.91    (11)   ~ (e2 = e1)
% 231.54/42.91  
% 231.54/42.91  Begin of proof
% 231.54/42.91  | 
% 231.54/42.91  | BETA: splitting (4) gives:
% 231.54/42.91  | 
% 231.54/42.91  | Case 1:
% 231.54/42.91  | | 
% 231.54/42.91  | |   (12)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) =
% 231.54/42.91  | |           e0)
% 231.54/42.91  | | 
% 231.54/42.91  | | REF_CLOSE: (2), (7), (8), (9), (12) are inconsistent by sub-proof #1665.
% 231.54/42.91  | | 
% 231.54/42.91  | Case 2:
% 231.54/42.91  | | 
% 231.54/42.91  | |   (13)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) =
% 231.54/42.91  | |           e0)
% 231.54/42.91  | | 
% 231.54/42.91  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (10), (11), (13) are
% 231.54/42.91  | |            inconsistent by sub-proof #1660.
% 231.54/42.91  | | 
% 231.54/42.91  | End of split
% 231.54/42.91  | 
% 231.54/42.91  End of proof
% 231.54/42.91  
% 231.54/42.91  Sub-proof #1660 shows that the following formulas are inconsistent:
% 231.54/42.91  ----------------------------------------------------------------
% 231.54/42.91    (1)   ~ (e3 = e1)
% 231.54/42.91    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.91           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.91    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.54/42.91         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.54/42.91    (4)  all_57_4 = e3
% 231.54/42.91    (5)   ~ (e3 = e0)
% 231.54/42.91    (6)  all_57_1 = e2
% 231.54/42.91    (7)  op(e3, e3) = e2
% 231.54/42.91    (8)   ~ (e1 = e0)
% 231.54/42.91    (9)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.54/42.91    (10)   ~ (e2 = e1)
% 231.54/42.91  
% 231.54/42.91  Begin of proof
% 231.54/42.91  | 
% 231.54/42.91  | BETA: splitting (9) gives:
% 231.54/42.91  | 
% 231.54/42.91  | Case 1:
% 231.54/42.91  | | 
% 231.54/42.91  | |   (11)  all_57_4 = e0 & op(e3, e1) = e0
% 231.54/42.91  | | 
% 231.54/42.91  | | REF_CLOSE: (4), (5), (11) are inconsistent by sub-proof #2491.
% 231.54/42.91  | | 
% 231.54/42.91  | Case 2:
% 231.54/42.91  | | 
% 231.54/42.91  | |   (12)  all_57_9 = e0 & op(e3, e0) = e0
% 231.54/42.91  | | 
% 231.54/42.91  | | ALPHA: (12) implies:
% 231.54/42.91  | |   (13)  all_57_9 = e0
% 231.54/42.91  | | 
% 231.54/42.91  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (10), (13) are inconsistent by
% 231.54/42.91  | |            sub-proof #1661.
% 231.54/42.91  | | 
% 231.54/42.91  | End of split
% 231.54/42.91  | 
% 231.54/42.91  End of proof
% 231.54/42.91  
% 231.54/42.91  Sub-proof #1661 shows that the following formulas are inconsistent:
% 231.54/42.91  ----------------------------------------------------------------
% 231.54/42.91    (1)   ~ (e3 = e1)
% 231.54/42.91    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.91           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.91    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.54/42.91         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.54/42.91    (4)  all_57_4 = e3
% 231.54/42.91    (5)  all_57_1 = e2
% 231.54/42.91    (6)  op(e3, e3) = e2
% 231.54/42.91    (7)  all_57_9 = e0
% 231.54/42.91    (8)   ~ (e1 = e0)
% 231.54/42.91    (9)   ~ (e2 = e1)
% 231.54/42.91  
% 231.54/42.91  Begin of proof
% 231.54/42.91  | 
% 231.54/42.91  | BETA: splitting (3) gives:
% 231.54/42.91  | 
% 231.54/42.91  | Case 1:
% 231.54/42.91  | | 
% 231.54/42.91  | |   (10)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) =
% 231.54/42.91  | |           e1)
% 231.54/42.91  | | 
% 231.54/42.91  | | REF_CLOSE: (2), (5), (6), (9), (10) are inconsistent by sub-proof #1662.
% 231.54/42.91  | | 
% 231.54/42.91  | Case 2:
% 231.54/42.91  | | 
% 231.54/42.91  | |   (11)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) =
% 231.54/42.91  | |           e1)
% 231.54/42.91  | | 
% 231.54/42.91  | | BETA: splitting (11) gives:
% 231.54/42.91  | | 
% 231.54/42.91  | | Case 1:
% 231.54/42.91  | | | 
% 231.54/42.91  | | |   (12)  all_57_4 = e1 & op(e3, e1) = e1
% 231.54/42.91  | | | 
% 231.54/42.91  | | | REF_CLOSE: (1), (4), (12) are inconsistent by sub-proof #2484.
% 231.54/42.91  | | | 
% 231.54/42.91  | | Case 2:
% 231.54/42.91  | | | 
% 231.54/42.91  | | |   (13)  all_57_9 = e1 & op(e3, e0) = e1
% 231.54/42.91  | | | 
% 231.54/42.91  | | | REF_CLOSE: (7), (8), (13) are inconsistent by sub-proof #2437.
% 231.54/42.91  | | | 
% 231.54/42.91  | | End of split
% 231.54/42.91  | | 
% 231.54/42.91  | End of split
% 231.54/42.91  | 
% 231.54/42.91  End of proof
% 231.54/42.91  
% 231.54/42.91  Sub-proof #1662 shows that the following formulas are inconsistent:
% 231.54/42.91  ----------------------------------------------------------------
% 231.54/42.91    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.91           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.91    (2)  all_57_1 = e2
% 231.54/42.91    (3)  op(e3, e3) = e2
% 231.54/42.91    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1)
% 231.54/42.91    (5)   ~ (e2 = e1)
% 231.54/42.91  
% 231.54/42.91  Begin of proof
% 231.54/42.91  | 
% 231.54/42.91  | BETA: splitting (4) gives:
% 231.54/42.91  | 
% 231.54/42.91  | Case 1:
% 231.54/42.91  | | 
% 231.54/42.91  | |   (6)  all_57_0 = e1 & op(e3, e3) = e1
% 231.54/42.91  | | 
% 231.54/42.91  | | ALPHA: (6) implies:
% 231.54/42.91  | |   (7)  op(e3, e3) = e1
% 231.54/42.91  | | 
% 231.54/42.91  | | REF_CLOSE: (1), (3), (5), (7) are inconsistent by sub-proof #1950.
% 231.54/42.91  | | 
% 231.54/42.91  | Case 2:
% 231.54/42.91  | | 
% 231.54/42.91  | |   (8)  all_57_1 = e1 & op(e3, e2) = e1
% 231.54/42.91  | | 
% 231.54/42.91  | | REF_CLOSE: (2), (5), (8) are inconsistent by sub-proof #2210.
% 231.54/42.91  | | 
% 231.54/42.91  | End of split
% 231.54/42.91  | 
% 231.54/42.91  End of proof
% 231.54/42.91  
% 231.54/42.91  Sub-proof #1663 shows that the following formulas are inconsistent:
% 231.54/42.91  ----------------------------------------------------------------
% 231.54/42.91    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.91           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.91    (2)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3)
% 231.54/42.91    (3)   ~ (e3 = e2)
% 231.54/42.91    (4)  all_57_1 = e2
% 231.54/42.91    (5)  op(e3, e3) = e2
% 231.54/42.91  
% 231.54/42.91  Begin of proof
% 231.54/42.91  | 
% 231.54/42.91  | BETA: splitting (2) gives:
% 231.54/42.91  | 
% 231.54/42.91  | Case 1:
% 231.54/42.91  | | 
% 231.54/42.91  | |   (6)  all_57_0 = e3 & op(e3, e3) = e3
% 231.54/42.91  | | 
% 231.54/42.91  | | ALPHA: (6) implies:
% 231.54/42.91  | |   (7)  op(e3, e3) = e3
% 231.54/42.91  | | 
% 231.54/42.91  | | REF_CLOSE: (1), (3), (5), (7) are inconsistent by sub-proof #2490.
% 231.54/42.91  | | 
% 231.54/42.91  | Case 2:
% 231.54/42.91  | | 
% 231.54/42.91  | |   (8)  all_57_1 = e3 & op(e3, e2) = e3
% 231.54/42.91  | | 
% 231.54/42.91  | | REF_CLOSE: (3), (4), (8) are inconsistent by sub-proof #1664.
% 231.54/42.91  | | 
% 231.54/42.91  | End of split
% 231.54/42.91  | 
% 231.54/42.91  End of proof
% 231.54/42.91  
% 231.54/42.91  Sub-proof #1664 shows that the following formulas are inconsistent:
% 231.54/42.91  ----------------------------------------------------------------
% 231.54/42.91    (1)  all_57_1 = e3 & op(e3, e2) = e3
% 231.54/42.91    (2)  all_57_1 = e2
% 231.54/42.91    (3)   ~ (e3 = e2)
% 231.54/42.91  
% 231.54/42.91  Begin of proof
% 231.54/42.91  | 
% 231.54/42.91  | ALPHA: (1) implies:
% 231.54/42.91  |   (4)  all_57_1 = e3
% 231.54/42.91  | 
% 231.54/42.91  | COMBINE_EQS: (2), (4) imply:
% 231.54/42.91  |   (5)  e3 = e2
% 231.54/42.91  | 
% 231.54/42.91  | SIMP: (5) implies:
% 231.54/42.91  |   (6)  e3 = e2
% 231.54/42.91  | 
% 231.54/42.91  | REDUCE: (3), (6) imply:
% 231.54/42.91  |   (7)  $false
% 231.54/42.91  | 
% 231.54/42.91  | CLOSE: (7) is inconsistent.
% 231.54/42.91  | 
% 231.54/42.91  End of proof
% 231.54/42.91  
% 231.54/42.91  Sub-proof #1665 shows that the following formulas are inconsistent:
% 231.54/42.91  ----------------------------------------------------------------
% 231.54/42.91    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.91           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.91    (2)  all_57_1 = e2
% 231.54/42.91    (3)  op(e3, e3) = e2
% 231.54/42.91    (4)   ~ (e2 = e0)
% 231.54/42.91    (5)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0)
% 231.54/42.91  
% 231.54/42.91  Begin of proof
% 231.54/42.91  | 
% 231.54/42.91  | BETA: splitting (5) gives:
% 231.54/42.91  | 
% 231.54/42.91  | Case 1:
% 231.54/42.91  | | 
% 231.54/42.91  | |   (6)  all_57_0 = e0 & op(e3, e3) = e0
% 231.54/42.91  | | 
% 231.54/42.91  | | ALPHA: (6) implies:
% 231.54/42.91  | |   (7)  op(e3, e3) = e0
% 231.54/42.91  | | 
% 231.54/42.91  | | REF_CLOSE: (1), (3), (4), (7) are inconsistent by sub-proof #2403.
% 231.54/42.91  | | 
% 231.54/42.91  | Case 2:
% 231.54/42.91  | | 
% 231.54/42.91  | |   (8)  all_57_1 = e0 & op(e3, e2) = e0
% 231.54/42.91  | | 
% 231.54/42.91  | | REF_CLOSE: (2), (4), (8) are inconsistent by sub-proof #1723.
% 231.54/42.91  | | 
% 231.54/42.91  | End of split
% 231.54/42.91  | 
% 231.54/42.91  End of proof
% 231.54/42.91  
% 231.54/42.91  Sub-proof #1666 shows that the following formulas are inconsistent:
% 231.54/42.91  ----------------------------------------------------------------
% 231.54/42.91    (1)  all_57_15 = e0
% 231.54/42.91    (2)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.54/42.91    (3)   ~ (e2 = e0)
% 231.54/42.91    (4)  all_57_11 = e1
% 231.54/42.91    (5)   ~ (e2 = e1)
% 231.54/42.91  
% 231.54/42.91  Begin of proof
% 231.54/42.91  | 
% 231.54/42.91  | BETA: splitting (2) gives:
% 231.54/42.91  | 
% 231.54/42.91  | Case 1:
% 231.54/42.91  | | 
% 231.54/42.91  | |   (6)  all_57_11 = e2 & op(e1, e0) = e2
% 231.54/42.91  | | 
% 231.54/42.91  | | ALPHA: (6) implies:
% 231.54/42.91  | |   (7)  all_57_11 = e2
% 231.54/42.91  | | 
% 231.54/42.91  | | REF_CLOSE: (4), (5), (7) are inconsistent by sub-proof #2113.
% 231.54/42.91  | | 
% 231.54/42.91  | Case 2:
% 231.54/42.91  | | 
% 231.54/42.91  | |   (8)  all_57_15 = e2 & op(e0, e0) = e2
% 231.54/42.91  | | 
% 231.54/42.91  | | ALPHA: (8) implies:
% 231.54/42.91  | |   (9)  all_57_15 = e2
% 231.54/42.91  | | 
% 231.54/42.91  | | REF_CLOSE: (1), (3), (9) are inconsistent by sub-proof #2126.
% 231.54/42.91  | | 
% 231.54/42.91  | End of split
% 231.54/42.91  | 
% 231.54/42.91  End of proof
% 231.54/42.91  
% 231.54/42.91  Sub-proof #1667 shows that the following formulas are inconsistent:
% 231.54/42.91  ----------------------------------------------------------------
% 231.54/42.91    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.91           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.91    (2)   ~ (e3 = e2)
% 231.54/42.91    (3)   ~ (e3 = e0)
% 231.54/42.91    (4)  all_57_11 = e2
% 231.54/42.91    (5)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 231.54/42.91    (6)  op(e0, e0) = e0
% 231.54/42.91  
% 231.54/42.91  Begin of proof
% 231.54/42.91  | 
% 231.54/42.91  | BETA: splitting (5) gives:
% 231.54/42.91  | 
% 231.54/42.91  | Case 1:
% 231.54/42.91  | | 
% 231.54/42.91  | |   (7)  all_57_11 = e3 & op(e1, e0) = e3
% 231.54/42.91  | | 
% 231.54/42.91  | | ALPHA: (7) implies:
% 231.54/42.91  | |   (8)  all_57_11 = e3
% 231.54/42.91  | | 
% 231.54/42.91  | | REF_CLOSE: (2), (4), (8) are inconsistent by sub-proof #2119.
% 231.54/42.91  | | 
% 231.54/42.91  | Case 2:
% 231.54/42.91  | | 
% 231.54/42.91  | |   (9)  all_57_15 = e3 & op(e0, e0) = e3
% 231.54/42.91  | | 
% 231.54/42.91  | | ALPHA: (9) implies:
% 231.54/42.91  | |   (10)  op(e0, e0) = e3
% 231.54/42.91  | | 
% 231.54/42.91  | | REF_CLOSE: (1), (3), (6), (10) are inconsistent by sub-proof #2304.
% 231.54/42.91  | | 
% 231.54/42.91  | End of split
% 231.54/42.91  | 
% 231.54/42.91  End of proof
% 231.54/42.91  
% 231.54/42.91  Sub-proof #1668 shows that the following formulas are inconsistent:
% 231.54/42.91  ----------------------------------------------------------------
% 231.54/42.91    (1)  all_57_15 = e0
% 231.54/42.91    (2)   ~ (e3 = e1)
% 231.54/42.91    (3)  all_57_10 = e2
% 231.54/42.91    (4)  all_57_11 = e2
% 231.54/42.91    (5)  all_57_9 = e3
% 231.54/42.91    (6)   ~ (e1 = e0)
% 231.54/42.91    (7)   ~ (e2 = e1)
% 231.54/42.91    (8)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.54/42.91         (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.54/42.91  
% 231.54/42.91  Begin of proof
% 231.54/42.91  | 
% 231.54/42.91  | BETA: splitting (8) gives:
% 231.54/42.91  | 
% 231.54/42.91  | Case 1:
% 231.54/42.91  | | 
% 231.54/42.91  | |   (9)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) =
% 231.54/42.91  | |          e1)
% 231.54/42.91  | | 
% 231.54/42.91  | | BETA: splitting (9) gives:
% 231.54/42.91  | | 
% 231.54/42.91  | | Case 1:
% 231.54/42.91  | | | 
% 231.54/42.91  | | |   (10)  all_57_9 = e1 & op(e3, e0) = e1
% 231.54/42.91  | | | 
% 231.54/42.91  | | | REF_CLOSE: (2), (5), (10) are inconsistent by sub-proof #1669.
% 231.54/42.91  | | | 
% 231.54/42.91  | | Case 2:
% 231.54/42.91  | | | 
% 231.54/42.91  | | |   (11)  all_57_10 = e1 & op(e2, e0) = e1
% 231.54/42.91  | | | 
% 231.54/42.91  | | | ALPHA: (11) implies:
% 231.54/42.91  | | |   (12)  all_57_10 = e1
% 231.54/42.91  | | | 
% 231.54/42.91  | | | REF_CLOSE: (3), (7), (12) are inconsistent by sub-proof #2144.
% 231.54/42.91  | | | 
% 231.54/42.91  | | End of split
% 231.54/42.91  | | 
% 231.54/42.91  | Case 2:
% 231.54/42.91  | | 
% 231.54/42.91  | |   (13)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.54/42.91  | |           e1)
% 231.54/42.91  | | 
% 231.54/42.91  | | BETA: splitting (13) gives:
% 231.54/42.91  | | 
% 231.54/42.91  | | Case 1:
% 231.54/42.91  | | | 
% 231.54/42.91  | | |   (14)  all_57_11 = e1 & op(e1, e0) = e1
% 231.54/42.91  | | | 
% 231.54/42.91  | | | ALPHA: (14) implies:
% 231.54/42.91  | | |   (15)  all_57_11 = e1
% 231.54/42.91  | | | 
% 231.54/42.91  | | | REF_CLOSE: (4), (7), (15) are inconsistent by sub-proof #2113.
% 231.54/42.91  | | | 
% 231.54/42.91  | | Case 2:
% 231.54/42.91  | | | 
% 231.54/42.91  | | |   (16)  all_57_15 = e1 & op(e0, e0) = e1
% 231.54/42.91  | | | 
% 231.54/42.91  | | | ALPHA: (16) implies:
% 231.54/42.91  | | |   (17)  all_57_15 = e1
% 231.54/42.91  | | | 
% 231.54/42.91  | | | COMBINE_EQS: (1), (17) imply:
% 231.54/42.91  | | |   (18)  e1 = e0
% 231.54/42.91  | | | 
% 231.54/42.91  | | | REDUCE: (6), (18) imply:
% 231.54/42.91  | | |   (19)  $false
% 231.54/42.91  | | | 
% 231.54/42.91  | | | CLOSE: (19) is inconsistent.
% 231.54/42.91  | | | 
% 231.54/42.91  | | End of split
% 231.54/42.91  | | 
% 231.54/42.91  | End of split
% 231.54/42.91  | 
% 231.54/42.91  End of proof
% 231.54/42.91  
% 231.54/42.91  Sub-proof #1669 shows that the following formulas are inconsistent:
% 231.54/42.91  ----------------------------------------------------------------
% 231.54/42.91    (1)  all_57_9 = e1 & op(e3, e0) = e1
% 231.54/42.91    (2)  all_57_9 = e3
% 231.54/42.91    (3)   ~ (e3 = e1)
% 231.54/42.91  
% 231.54/42.91  Begin of proof
% 231.54/42.91  | 
% 231.54/42.91  | ALPHA: (1) implies:
% 231.54/42.91  |   (4)  all_57_9 = e1
% 231.54/42.91  | 
% 231.54/42.91  | COMBINE_EQS: (2), (4) imply:
% 231.54/42.91  |   (5)  e3 = e1
% 231.54/42.91  | 
% 231.54/42.91  | REDUCE: (3), (5) imply:
% 231.54/42.91  |   (6)  $false
% 231.54/42.91  | 
% 231.54/42.91  | CLOSE: (6) is inconsistent.
% 231.54/42.91  | 
% 231.54/42.91  End of proof
% 231.54/42.91  
% 231.54/42.91  Sub-proof #1670 shows that the following formulas are inconsistent:
% 231.54/42.91  ----------------------------------------------------------------
% 231.54/42.91    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.91           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.91    (2)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.54/42.91    (3)  op(e0, e3) = all_53_3
% 231.54/42.91    (4)  all_57_6 = e2
% 231.54/42.91    (5)   ~ (e2 = e0)
% 231.54/42.91    (6)   ~ (all_53_3 = e0)
% 231.54/42.91  
% 231.54/42.91  Begin of proof
% 231.54/42.91  | 
% 231.54/42.91  | BETA: splitting (2) gives:
% 231.54/42.91  | 
% 231.54/42.91  | Case 1:
% 231.54/42.91  | | 
% 231.54/42.91  | |   (7)  all_57_6 = e0 & op(e1, e3) = e0
% 231.54/42.91  | | 
% 231.54/42.91  | | REF_CLOSE: (4), (5), (7) are inconsistent by sub-proof #2386.
% 231.54/42.91  | | 
% 231.54/42.91  | Case 2:
% 231.54/42.91  | | 
% 231.54/42.91  | |   (8)  all_57_12 = e0 & op(e0, e3) = e0
% 231.54/42.91  | | 
% 231.54/42.91  | | ALPHA: (8) implies:
% 231.54/42.91  | |   (9)  op(e0, e3) = e0
% 231.54/42.92  | | 
% 231.54/42.92  | | REF_CLOSE: (1), (3), (6), (9) are inconsistent by sub-proof #2366.
% 231.54/42.92  | | 
% 231.54/42.92  | End of split
% 231.54/42.92  | 
% 231.54/42.92  End of proof
% 231.54/42.92  
% 231.54/42.92  Sub-proof #1671 shows that the following formulas are inconsistent:
% 231.54/42.92  ----------------------------------------------------------------
% 231.54/42.92    (1)   ~ (e3 = e1)
% 231.54/42.92    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.92           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.92    (3)  op(e2, e2) = e1
% 231.54/42.92    (4)   ~ (e3 = e2)
% 231.54/42.92    (5)   ~ (e3 = e0)
% 231.54/42.92    (6)  op(e3, e3) = e2
% 231.54/42.92    (7)   ~ (e2 = e0)
% 231.54/42.92    (8)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.54/42.92         (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.54/42.92    (9)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.92         (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.54/42.92    (10)   ~ (e2 = e1)
% 231.54/42.92    (11)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0)
% 231.54/42.92    (12)  all_57_5 = e0
% 231.54/42.92  
% 231.54/42.92  Begin of proof
% 231.54/42.92  | 
% 231.54/42.92  | BETA: splitting (11) gives:
% 231.54/42.92  | 
% 231.54/42.92  | Case 1:
% 231.54/42.92  | | 
% 231.54/42.92  | |   (13)  all_57_0 = e0 & op(e3, e3) = e0
% 231.54/42.92  | | 
% 231.54/42.92  | | ALPHA: (13) implies:
% 231.54/42.92  | |   (14)  op(e3, e3) = e0
% 231.54/42.92  | | 
% 231.54/42.92  | | REF_CLOSE: (2), (6), (7), (14) are inconsistent by sub-proof #2403.
% 231.54/42.92  | | 
% 231.54/42.92  | Case 2:
% 231.54/42.92  | | 
% 231.54/42.92  | |   (15)  all_57_2 = e0 & op(e2, e3) = e0
% 231.54/42.92  | | 
% 231.54/42.92  | | ALPHA: (15) implies:
% 231.54/42.92  | |   (16)  all_57_2 = e0
% 231.54/42.92  | | 
% 231.54/42.92  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (12), (16) are
% 231.54/42.92  | |            inconsistent by sub-proof #1848.
% 231.54/42.92  | | 
% 231.54/42.92  | End of split
% 231.54/42.92  | 
% 231.54/42.92  End of proof
% 231.54/42.92  
% 231.54/42.92  Sub-proof #1672 shows that the following formulas are inconsistent:
% 231.54/42.92  ----------------------------------------------------------------
% 231.54/42.92    (1)   ~ (e3 = e1)
% 231.54/42.92    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.92           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.92    (3)  all_57_9 = e1
% 231.54/42.92    (4)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.54/42.92         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.54/42.92    (5)   ~ (e3 = e2)
% 231.54/42.92    (6)   ~ (e3 = e0)
% 231.54/42.92    (7)  op(e3, e3) = e2
% 231.54/42.92    (8)  all_57_4 = e1
% 231.54/42.92    (9)   ~ (e2 = e0)
% 231.54/42.92    (10)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 231.54/42.92          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.54/42.92    (11)   ~ (e1 = e0)
% 231.54/42.92  
% 231.54/42.92  Begin of proof
% 231.54/42.92  | 
% 231.54/42.92  | BETA: splitting (10) gives:
% 231.54/42.92  | 
% 231.54/42.92  | Case 1:
% 231.54/42.92  | | 
% 231.54/42.92  | |   (12)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) =
% 231.54/42.92  | |           e3)
% 231.54/42.92  | | 
% 231.54/42.92  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (11), (12) are
% 231.54/42.92  | |            inconsistent by sub-proof #1674.
% 231.54/42.92  | | 
% 231.54/42.92  | Case 2:
% 231.54/42.92  | | 
% 231.54/42.92  | |   (13)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) =
% 231.54/42.92  | |           e3)
% 231.54/42.92  | | 
% 231.54/42.92  | | BETA: splitting (13) gives:
% 231.54/42.92  | | 
% 231.54/42.92  | | Case 1:
% 231.54/42.92  | | | 
% 231.54/42.92  | | |   (14)  all_57_4 = e3 & op(e3, e1) = e3
% 231.54/42.92  | | | 
% 231.54/42.92  | | | ALPHA: (14) implies:
% 231.54/42.92  | | |   (15)  all_57_4 = e3
% 231.54/42.92  | | | 
% 231.54/42.92  | | | REF_CLOSE: (1), (8), (15) are inconsistent by sub-proof #2426.
% 231.54/42.92  | | | 
% 231.54/42.92  | | Case 2:
% 231.54/42.92  | | | 
% 231.54/42.92  | | |   (16)  all_57_9 = e3 & op(e3, e0) = e3
% 231.54/42.92  | | | 
% 231.54/42.92  | | | ALPHA: (16) implies:
% 231.54/42.92  | | |   (17)  all_57_9 = e3
% 231.54/42.92  | | | 
% 231.54/42.92  | | | REF_CLOSE: (1), (3), (17) are inconsistent by sub-proof #1673.
% 231.54/42.92  | | | 
% 231.54/42.92  | | End of split
% 231.54/42.92  | | 
% 231.54/42.92  | End of split
% 231.54/42.92  | 
% 231.54/42.92  End of proof
% 231.54/42.92  
% 231.54/42.92  Sub-proof #1673 shows that the following formulas are inconsistent:
% 231.54/42.92  ----------------------------------------------------------------
% 231.54/42.92    (1)  all_57_9 = e3
% 231.54/42.92    (2)  all_57_9 = e1
% 231.54/42.92    (3)   ~ (e3 = e1)
% 231.54/42.92  
% 231.54/42.92  Begin of proof
% 231.54/42.92  | 
% 231.54/42.92  | COMBINE_EQS: (1), (2) imply:
% 231.54/42.92  |   (4)  e3 = e1
% 231.54/42.92  | 
% 231.54/42.92  | SIMP: (4) implies:
% 231.54/42.92  |   (5)  e3 = e1
% 231.54/42.92  | 
% 231.54/42.92  | REDUCE: (3), (5) imply:
% 231.54/42.92  |   (6)  $false
% 231.54/42.92  | 
% 231.54/42.92  | CLOSE: (6) is inconsistent.
% 231.54/42.92  | 
% 231.54/42.92  End of proof
% 231.54/42.92  
% 231.54/42.92  Sub-proof #1674 shows that the following formulas are inconsistent:
% 231.54/42.92  ----------------------------------------------------------------
% 231.54/42.92    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.92           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.92    (2)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3)
% 231.54/42.92    (3)  all_57_9 = e1
% 231.54/42.92    (4)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.54/42.92         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.54/42.92    (5)   ~ (e3 = e2)
% 231.54/42.92    (6)   ~ (e3 = e0)
% 231.54/42.92    (7)  op(e3, e3) = e2
% 231.54/42.92    (8)  all_57_4 = e1
% 231.54/42.92    (9)   ~ (e2 = e0)
% 231.54/42.92    (10)   ~ (e1 = e0)
% 231.54/42.92  
% 231.54/42.92  Begin of proof
% 231.54/42.92  | 
% 231.54/42.92  | BETA: splitting (2) gives:
% 231.54/42.92  | 
% 231.54/42.92  | Case 1:
% 231.54/42.92  | | 
% 231.54/42.92  | |   (11)  all_57_0 = e3 & op(e3, e3) = e3
% 231.54/42.92  | | 
% 231.54/42.92  | | ALPHA: (11) implies:
% 231.54/42.92  | |   (12)  op(e3, e3) = e3
% 231.54/42.92  | | 
% 231.54/42.92  | | REF_CLOSE: (1), (5), (7), (12) are inconsistent by sub-proof #2490.
% 231.54/42.92  | | 
% 231.54/42.92  | Case 2:
% 231.54/42.92  | | 
% 231.54/42.92  | |   (13)  all_57_1 = e3 & op(e3, e2) = e3
% 231.54/42.92  | | 
% 231.54/42.92  | | ALPHA: (13) implies:
% 231.54/42.92  | |   (14)  all_57_1 = e3
% 231.54/42.92  | | 
% 231.54/42.92  | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (10), (14) are inconsistent by
% 231.54/42.92  | |            sub-proof #1675.
% 231.54/42.92  | | 
% 231.54/42.92  | End of split
% 231.54/42.92  | 
% 231.54/42.92  End of proof
% 231.54/42.92  
% 231.54/42.92  Sub-proof #1675 shows that the following formulas are inconsistent:
% 231.54/42.92  ----------------------------------------------------------------
% 231.54/42.92    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.92           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.92    (2)  all_57_9 = e1
% 231.54/42.92    (3)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.54/42.92         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.54/42.92    (4)   ~ (e3 = e0)
% 231.54/42.92    (5)  op(e3, e3) = e2
% 231.54/42.92    (6)  all_57_4 = e1
% 231.54/42.92    (7)   ~ (e2 = e0)
% 231.54/42.92    (8)   ~ (e1 = e0)
% 231.54/42.92    (9)  all_57_1 = e3
% 231.54/42.92  
% 231.54/42.92  Begin of proof
% 231.54/42.92  | 
% 231.54/42.92  | BETA: splitting (3) gives:
% 231.54/42.92  | 
% 231.54/42.92  | Case 1:
% 231.54/42.92  | | 
% 231.54/42.92  | |   (10)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) =
% 231.54/42.92  | |           e0)
% 231.54/42.92  | | 
% 231.54/42.92  | | REF_CLOSE: (1), (4), (5), (7), (9), (10) are inconsistent by sub-proof
% 231.54/42.92  | |            #1676.
% 231.54/42.92  | | 
% 231.54/42.92  | Case 2:
% 231.54/42.92  | | 
% 231.54/42.92  | |   (11)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) =
% 231.54/42.92  | |           e0)
% 231.54/42.92  | | 
% 231.54/42.92  | | BETA: splitting (11) gives:
% 231.54/42.92  | | 
% 231.54/42.92  | | Case 1:
% 231.54/42.92  | | | 
% 231.54/42.92  | | |   (12)  all_57_4 = e0 & op(e3, e1) = e0
% 231.54/42.92  | | | 
% 231.54/42.92  | | | REF_CLOSE: (6), (8), (12) are inconsistent by sub-proof #2429.
% 231.54/42.92  | | | 
% 231.54/42.92  | | Case 2:
% 231.54/42.92  | | | 
% 231.54/42.92  | | |   (13)  all_57_9 = e0 & op(e3, e0) = e0
% 231.54/42.92  | | | 
% 231.54/42.92  | | | REF_CLOSE: (2), (8), (13) are inconsistent by sub-proof #1990.
% 231.54/42.92  | | | 
% 231.54/42.92  | | End of split
% 231.54/42.92  | | 
% 231.54/42.92  | End of split
% 231.54/42.92  | 
% 231.54/42.92  End of proof
% 231.54/42.92  
% 231.54/42.92  Sub-proof #1676 shows that the following formulas are inconsistent:
% 231.54/42.92  ----------------------------------------------------------------
% 231.54/42.92    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.92           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.92    (2)   ~ (e3 = e0)
% 231.54/42.92    (3)  op(e3, e3) = e2
% 231.54/42.92    (4)   ~ (e2 = e0)
% 231.54/42.92    (5)  all_57_1 = e3
% 231.54/42.92    (6)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0)
% 231.54/42.92  
% 231.54/42.92  Begin of proof
% 231.54/42.92  | 
% 231.54/42.92  | BETA: splitting (6) gives:
% 231.54/42.92  | 
% 231.54/42.92  | Case 1:
% 231.54/42.92  | | 
% 231.54/42.92  | |   (7)  all_57_0 = e0 & op(e3, e3) = e0
% 231.54/42.92  | | 
% 231.54/42.92  | | ALPHA: (7) implies:
% 231.54/42.92  | |   (8)  op(e3, e3) = e0
% 231.54/42.92  | | 
% 231.54/42.92  | | REF_CLOSE: (1), (3), (4), (8) are inconsistent by sub-proof #2403.
% 231.54/42.92  | | 
% 231.54/42.92  | Case 2:
% 231.54/42.92  | | 
% 231.54/42.92  | |   (9)  all_57_1 = e0 & op(e3, e2) = e0
% 231.54/42.92  | | 
% 231.54/42.92  | | REF_CLOSE: (2), (5), (9) are inconsistent by sub-proof #1811.
% 231.54/42.92  | | 
% 231.54/42.92  | End of split
% 231.54/42.92  | 
% 231.54/42.92  End of proof
% 231.54/42.92  
% 231.54/42.92  Sub-proof #1677 shows that the following formulas are inconsistent:
% 231.54/42.92  ----------------------------------------------------------------
% 231.54/42.92    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.92         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.54/42.92    (2)   ~ (e3 = e1)
% 231.54/42.92    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.92           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.92    (4)  op(e2, e2) = e1
% 231.54/42.92    (5)   ~ (e3 = e2)
% 231.54/42.92    (6)   ~ (e3 = e0)
% 231.54/42.92    (7)  op(e3, e3) = e2
% 231.54/42.92    (8)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 231.54/42.92         (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 231.54/42.92    (9)   ~ (e2 = e0)
% 231.54/42.92    (10)   ~ (e1 = e0)
% 231.54/42.92    (11)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.54/42.92          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.54/42.92    (12)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1)
% 231.54/42.92    (13)   ~ (e2 = e1)
% 231.54/42.92  
% 231.54/42.92  Begin of proof
% 231.54/42.92  | 
% 231.54/42.92  | BETA: splitting (12) gives:
% 231.54/42.92  | 
% 231.54/42.92  | Case 1:
% 231.54/42.92  | | 
% 231.54/42.92  | |   (14)  all_57_0 = e1 & op(e3, e3) = e1
% 231.54/42.92  | | 
% 231.54/42.92  | | ALPHA: (14) implies:
% 231.54/42.92  | |   (15)  op(e3, e3) = e1
% 231.54/42.92  | | 
% 231.54/42.92  | | REF_CLOSE: (3), (7), (13), (15) are inconsistent by sub-proof #1950.
% 231.54/42.92  | | 
% 231.54/42.92  | Case 2:
% 231.54/42.92  | | 
% 231.54/42.92  | |   (16)  all_57_1 = e1 & op(e3, e2) = e1
% 231.54/42.92  | | 
% 231.54/42.92  | | ALPHA: (16) implies:
% 231.54/42.92  | |   (17)  all_57_1 = e1
% 231.54/42.92  | | 
% 231.54/42.92  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (13), (17)
% 231.54/42.92  | |            are inconsistent by sub-proof #1908.
% 231.54/42.92  | | 
% 231.54/42.92  | End of split
% 231.54/42.92  | 
% 231.54/42.92  End of proof
% 231.54/42.92  
% 231.54/42.92  Sub-proof #1678 shows that the following formulas are inconsistent:
% 231.54/42.92  ----------------------------------------------------------------
% 231.54/42.92    (1)  op(e2, e3) = all_53_1
% 231.54/42.92    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.54/42.92         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.54/42.92    (3)   ~ (e3 = e1)
% 231.54/42.92    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.92           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.92    (5)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.54/42.92         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.54/42.92    (6)   ~ (all_6_2 = e3)
% 231.54/42.92    (7)  op(e1, e1) = all_6_2
% 231.54/42.92    (8)   ~ (e3 = e2)
% 231.54/42.92    (9)  op(e0, e3) = all_53_3
% 231.54/42.92    (10)  all_57_0 = e0
% 231.54/42.92    (11)   ~ (all_53_1 = e1)
% 231.54/42.92    (12)   ~ (e2 = e0)
% 231.54/42.92    (13)   ~ (e1 = e0)
% 231.54/42.92    (14)   ~ (all_53_3 = e1)
% 231.54/42.92    (15)  all_57_8 = e0
% 231.54/42.92    (16)  all_57_11 = e1
% 231.54/42.92    (17)   ~ (e2 = e1)
% 231.54/42.92    (18)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 231.54/42.92          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 231.54/42.92  
% 231.54/42.92  Begin of proof
% 231.54/42.92  | 
% 231.54/42.92  | BETA: splitting (2) gives:
% 231.54/42.92  | 
% 231.54/42.92  | Case 1:
% 231.54/42.92  | | 
% 231.54/42.92  | |   (19)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) =
% 231.54/42.92  | |           e1)
% 231.54/42.92  | | 
% 231.54/42.92  | | BETA: splitting (19) gives:
% 231.54/42.92  | | 
% 231.54/42.92  | | Case 1:
% 231.54/42.92  | | | 
% 231.54/42.92  | | |   (20)  all_57_0 = e1 & op(e3, e3) = e1
% 231.54/42.92  | | | 
% 231.54/42.92  | | | REF_CLOSE: (10), (13), (20) are inconsistent by sub-proof #2454.
% 231.54/42.92  | | | 
% 231.54/42.92  | | Case 2:
% 231.54/42.92  | | | 
% 231.54/42.92  | | |   (21)  all_57_2 = e1 & op(e2, e3) = e1
% 231.54/42.92  | | | 
% 231.54/42.92  | | | REF_CLOSE: (1), (4), (11), (21) are inconsistent by sub-proof #2156.
% 231.54/42.92  | | | 
% 231.54/42.92  | | End of split
% 231.54/42.92  | | 
% 231.54/42.92  | Case 2:
% 231.54/42.92  | | 
% 231.54/42.92  | |   (22)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) =
% 231.54/42.92  | |           e1)
% 231.54/42.92  | | 
% 231.54/42.92  | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (12), (14), (15), (16), (17),
% 231.54/42.92  | |            (18), (22) are inconsistent by sub-proof #1679.
% 231.54/42.92  | | 
% 231.54/42.92  | End of split
% 231.54/42.92  | 
% 231.54/42.92  End of proof
% 231.54/42.92  
% 231.54/42.92  Sub-proof #1679 shows that the following formulas are inconsistent:
% 231.54/42.92  ----------------------------------------------------------------
% 231.54/42.92    (1)   ~ (e3 = e1)
% 231.54/42.92    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.92           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.92    (3)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.54/42.92         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.54/42.92    (4)   ~ (all_6_2 = e3)
% 231.54/42.92    (5)  op(e1, e1) = all_6_2
% 231.54/42.92    (6)   ~ (e3 = e2)
% 231.54/42.92    (7)  op(e0, e3) = all_53_3
% 231.54/42.92    (8)   ~ (e2 = e0)
% 231.54/42.92    (9)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.54/42.92    (10)   ~ (all_53_3 = e1)
% 231.54/42.92    (11)  all_57_8 = e0
% 231.54/42.92    (12)  all_57_11 = e1
% 231.54/42.92    (13)   ~ (e2 = e1)
% 231.54/42.92    (14)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 231.54/42.92          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 231.54/42.92  
% 231.54/42.92  Begin of proof
% 231.54/42.92  | 
% 231.54/42.92  | BETA: splitting (9) gives:
% 231.54/42.92  | 
% 231.54/42.92  | Case 1:
% 231.54/42.92  | | 
% 231.54/42.92  | |   (15)  all_57_6 = e1 & op(e1, e3) = e1
% 231.54/42.92  | | 
% 231.54/42.92  | | ALPHA: (15) implies:
% 231.54/42.92  | |   (16)  all_57_6 = e1
% 231.54/42.92  | | 
% 231.54/42.92  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (11), (12), (13), (14), (16)
% 231.54/42.92  | |            are inconsistent by sub-proof #2003.
% 231.54/42.92  | | 
% 231.54/42.92  | Case 2:
% 231.54/42.92  | | 
% 231.54/42.92  | |   (17)  all_57_12 = e1 & op(e0, e3) = e1
% 231.54/42.92  | | 
% 231.54/42.92  | | REF_CLOSE: (2), (7), (10), (17) are inconsistent by sub-proof #1947.
% 231.54/42.92  | | 
% 231.54/42.92  | End of split
% 231.54/42.92  | 
% 231.54/42.92  End of proof
% 231.54/42.92  
% 231.54/42.92  Sub-proof #1680 shows that the following formulas are inconsistent:
% 231.54/42.92  ----------------------------------------------------------------
% 231.54/42.92    (1)   ~ (all_52_29 = e0)
% 231.54/42.92    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.92           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.92    (3)   ~ (all_53_9 = e1)
% 231.54/42.92    (4)   ~ (all_53_9 = e0)
% 231.54/42.92    (5)  op(e3, e3) = e3
% 231.54/42.92    (6)  all_55_14 = all_52_29
% 231.54/42.92    (7)  all_55_6 = all_53_9
% 231.54/42.92    (8)   ~ (all_52_29 = e1)
% 231.54/42.92    (9)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 231.54/42.92    (10)   ~ (all_53_9 = all_52_29)
% 231.54/42.92    (11)  op(all_52_29, all_52_29) = e1
% 231.54/42.92    (12)  all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 231.54/42.92  
% 231.54/42.92  Begin of proof
% 231.54/42.92  | 
% 231.54/42.92  | BETA: splitting (12) gives:
% 231.54/42.92  | 
% 231.54/42.92  | Case 1:
% 231.54/42.92  | | 
% 231.54/42.92  | |   (13)  all_55_6 = e2
% 231.54/42.92  | | 
% 231.54/42.92  | | COMBINE_EQS: (7), (13) imply:
% 231.54/42.92  | |   (14)  all_53_9 = e2
% 231.54/42.92  | | 
% 231.54/42.92  | | SIMP: (14) implies:
% 231.54/42.92  | |   (15)  all_53_9 = e2
% 231.54/42.92  | | 
% 231.54/42.92  | | REDUCE: (10), (15) imply:
% 231.54/42.92  | |   (16)   ~ (all_52_29 = e2)
% 231.54/42.92  | | 
% 231.54/42.92  | | REF_CLOSE: (1), (2), (5), (6), (8), (9), (11), (16) are inconsistent by
% 231.54/42.92  | |            sub-proof #2033.
% 231.54/42.92  | | 
% 231.54/42.92  | Case 2:
% 231.54/42.92  | | 
% 231.54/42.92  | |   (17)  all_55_6 = e1 | all_55_6 = e0
% 231.54/42.92  | | 
% 231.54/42.92  | | REF_CLOSE: (3), (4), (7), (17) are inconsistent by sub-proof #2161.
% 231.54/42.92  | | 
% 231.54/42.92  | End of split
% 231.54/42.92  | 
% 231.54/42.92  End of proof
% 231.54/42.92  
% 231.54/42.92  Sub-proof #1681 shows that the following formulas are inconsistent:
% 231.54/42.92  ----------------------------------------------------------------
% 231.54/42.92    (1)  all_55_12 = all_52_25
% 231.54/42.92    (2)  all_55_12 = e1
% 231.54/42.92    (3)   ~ (all_52_25 = e1)
% 231.54/42.92  
% 231.54/42.92  Begin of proof
% 231.54/42.92  | 
% 231.54/42.92  | COMBINE_EQS: (1), (2) imply:
% 231.54/42.92  |   (4)  all_52_25 = e1
% 231.54/42.92  | 
% 231.54/42.92  | SIMP: (4) implies:
% 231.54/42.92  |   (5)  all_52_25 = e1
% 231.54/42.92  | 
% 231.54/42.92  | REDUCE: (3), (5) imply:
% 231.54/42.92  |   (6)  $false
% 231.54/42.92  | 
% 231.54/42.92  | CLOSE: (6) is inconsistent.
% 231.54/42.92  | 
% 231.54/42.92  End of proof
% 231.54/42.92  
% 231.54/42.92  Sub-proof #1682 shows that the following formulas are inconsistent:
% 231.54/42.92  ----------------------------------------------------------------
% 231.54/42.92    (1)  all_55_12 = all_52_25
% 231.54/42.92    (2)  all_55_12 = e2
% 231.54/42.92    (3)   ~ (all_52_25 = e2)
% 231.54/42.92  
% 231.54/42.92  Begin of proof
% 231.54/42.92  | 
% 231.54/42.92  | COMBINE_EQS: (1), (2) imply:
% 231.54/42.92  |   (4)  all_52_25 = e2
% 231.54/42.92  | 
% 231.54/42.92  | SIMP: (4) implies:
% 231.54/42.92  |   (5)  all_52_25 = e2
% 231.54/42.92  | 
% 231.54/42.92  | REDUCE: (3), (5) imply:
% 231.54/42.92  |   (6)  $false
% 231.54/42.92  | 
% 231.54/42.92  | CLOSE: (6) is inconsistent.
% 231.54/42.92  | 
% 231.54/42.92  End of proof
% 231.54/42.92  
% 231.54/42.92  Sub-proof #1683 shows that the following formulas are inconsistent:
% 231.54/42.92  ----------------------------------------------------------------
% 231.54/42.92    (1)  all_55_12 = all_52_25
% 231.54/42.92    (2)  all_55_12 = e3
% 231.54/42.92    (3)   ~ (all_52_25 = e3)
% 231.54/42.92  
% 231.54/42.92  Begin of proof
% 231.54/42.92  | 
% 231.54/42.92  | COMBINE_EQS: (1), (2) imply:
% 231.54/42.92  |   (4)  all_52_25 = e3
% 231.54/42.92  | 
% 231.54/42.92  | SIMP: (4) implies:
% 231.54/42.92  |   (5)  all_52_25 = e3
% 231.54/42.92  | 
% 231.54/42.92  | REDUCE: (3), (5) imply:
% 231.54/42.92  |   (6)  $false
% 231.54/42.92  | 
% 231.54/42.92  | CLOSE: (6) is inconsistent.
% 231.54/42.92  | 
% 231.54/42.92  End of proof
% 231.54/42.92  
% 231.54/42.92  Sub-proof #1684 shows that the following formulas are inconsistent:
% 231.54/42.92  ----------------------------------------------------------------
% 231.54/42.92    (1)  op(e3, e1) = all_52_5
% 231.54/42.92    (2)   ~ (e3 = e1)
% 231.54/42.92    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.92           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.92    (4)  op(all_52_5, all_52_5) = e1
% 231.54/42.92    (5)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.54/42.92         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.54/42.92    (6)   ~ (all_6_2 = e3)
% 231.54/42.92    (7)  op(e1, e1) = all_6_2
% 231.54/42.92    (8)  all_57_6 = e1
% 231.54/42.92    (9)  all_57_4 = e1 & op(e3, e1) = e1
% 231.54/42.92    (10)   ~ (e3 = e2)
% 231.54/42.92    (11)   ~ (e2 = e0)
% 231.54/42.92    (12)   ~ (all_53_6 = e1)
% 231.54/42.92    (13)   ~ (e1 = e0)
% 231.54/42.92    (14)  op(e1, e1) = e0
% 231.54/42.92    (15)  all_57_8 = e0
% 231.54/42.92    (16)   ~ (all_53_8 = e0)
% 231.54/42.92    (17)   ~ (e2 = e1)
% 231.54/42.92    (18)  op(e1, e2) = all_53_6
% 231.54/42.92    (19)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 231.54/42.92          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 231.54/42.92    (20)  op(e3, e1) = all_53_8
% 231.54/42.92    (21)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 231.54/42.92          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 231.54/42.92  
% 231.54/42.92  Begin of proof
% 231.54/42.92  | 
% 231.54/42.92  | BETA: splitting (19) gives:
% 231.54/42.92  | 
% 231.54/42.92  | Case 1:
% 231.54/42.92  | | 
% 231.54/42.92  | |   (22)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) =
% 231.54/42.92  | |           e1)
% 231.54/42.92  | | 
% 231.54/42.92  | | BETA: splitting (22) gives:
% 231.54/42.92  | | 
% 231.54/42.92  | | Case 1:
% 231.54/42.92  | | | 
% 231.54/42.92  | | | 
% 231.54/42.92  | | | ALPHA: (9) implies:
% 231.54/42.92  | | |   (23)  op(e3, e1) = e1
% 231.54/42.92  | | | 
% 231.54/42.92  | | | GROUND_INST: instantiating (3) with all_53_8, e1, e1, e3, simplifying with
% 231.54/42.92  | | |              (20), (23) gives:
% 231.54/42.92  | | |   (24)  all_53_8 = e1
% 231.54/42.92  | | | 
% 231.54/42.92  | | | GROUND_INST: instantiating (3) with all_53_8, all_52_5, e1, e3,
% 231.54/42.92  | | |              simplifying with (1), (20) gives:
% 231.54/42.92  | | |   (25)  all_53_8 = all_52_5
% 231.54/42.92  | | | 
% 231.54/42.92  | | | COMBINE_EQS: (24), (25) imply:
% 231.54/42.92  | | |   (26)  all_52_5 = e1
% 231.54/42.92  | | | 
% 231.54/42.92  | | | REDUCE: (4), (26) imply:
% 231.54/42.92  | | |   (27)  op(e1, e1) = e1
% 231.54/42.92  | | | 
% 231.54/42.92  | | | REF_CLOSE: (3), (13), (14), (27) are inconsistent by sub-proof #2427.
% 231.54/42.92  | | | 
% 231.54/42.92  | | Case 2:
% 231.54/42.92  | | | 
% 231.54/42.92  | | |   (28)  all_57_7 = e1 & op(e1, e2) = e1
% 231.54/42.92  | | | 
% 231.54/42.92  | | | REF_CLOSE: (3), (12), (18), (28) are inconsistent by sub-proof #2265.
% 231.54/42.92  | | | 
% 231.54/42.92  | | End of split
% 231.54/42.92  | | 
% 231.54/42.92  | Case 2:
% 231.54/42.92  | | 
% 231.54/42.92  | |   (29)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) =
% 231.54/42.92  | |           e1)
% 231.54/42.92  | | 
% 231.54/42.92  | | BETA: splitting (29) gives:
% 231.54/42.92  | | 
% 231.54/42.92  | | Case 1:
% 231.54/42.92  | | | 
% 231.54/42.92  | | |   (30)  all_57_8 = e1 & op(e1, e1) = e1
% 231.54/42.92  | | | 
% 231.54/42.92  | | | ALPHA: (30) implies:
% 231.54/42.92  | | |   (31)  op(e1, e1) = e1
% 231.54/42.92  | | | 
% 231.54/42.92  | | | REF_CLOSE: (3), (13), (14), (31) are inconsistent by sub-proof #2427.
% 231.54/42.92  | | | 
% 231.54/42.92  | | Case 2:
% 231.54/42.92  | | | 
% 231.54/42.92  | | |   (32)  all_57_11 = e1 & op(e1, e0) = e1
% 231.54/42.92  | | | 
% 231.54/42.92  | | | ALPHA: (32) implies:
% 231.54/42.92  | | |   (33)  all_57_11 = e1
% 231.54/42.92  | | | 
% 231.54/42.92  | | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (10), (11), (15), (17), (21),
% 231.54/42.92  | | |            (33) are inconsistent by sub-proof #2003.
% 231.54/42.92  | | | 
% 231.54/42.92  | | End of split
% 231.54/42.92  | | 
% 231.54/42.92  | End of split
% 231.54/42.92  | 
% 231.54/42.92  End of proof
% 231.54/42.92  
% 231.54/42.92  Sub-proof #1685 shows that the following formulas are inconsistent:
% 231.54/42.92  ----------------------------------------------------------------
% 231.54/42.92    (1)  all_55_10 = e1 | all_55_10 = e0
% 231.54/42.92    (2)  all_55_10 = all_6_2
% 231.54/42.92    (3)   ~ (all_6_2 = e1)
% 231.54/42.92    (4)   ~ (all_6_2 = e0)
% 231.54/42.92  
% 231.54/42.92  Begin of proof
% 231.54/42.92  | 
% 231.54/42.92  | BETA: splitting (1) gives:
% 231.54/42.92  | 
% 231.54/42.92  | Case 1:
% 231.54/42.92  | | 
% 231.54/42.92  | |   (5)  all_55_10 = e1
% 231.54/42.92  | | 
% 231.54/42.92  | | COMBINE_EQS: (2), (5) imply:
% 231.54/42.92  | |   (6)  all_6_2 = e1
% 231.54/42.92  | | 
% 231.54/42.92  | | SIMP: (6) implies:
% 231.54/42.92  | |   (7)  all_6_2 = e1
% 231.54/42.92  | | 
% 231.54/42.92  | | REDUCE: (3), (7) imply:
% 231.54/42.92  | |   (8)  $false
% 231.54/42.92  | | 
% 231.54/42.92  | | CLOSE: (8) is inconsistent.
% 231.54/42.92  | | 
% 231.54/42.92  | Case 2:
% 231.54/42.92  | | 
% 231.54/42.92  | |   (9)  all_55_10 = e0
% 231.54/42.92  | | 
% 231.54/42.92  | | REF_CLOSE: (2), (4), (9) are inconsistent by sub-proof #2118.
% 231.54/42.92  | | 
% 231.54/42.92  | End of split
% 231.54/42.92  | 
% 231.54/42.92  End of proof
% 231.54/42.92  
% 231.54/42.92  Sub-proof #1686 shows that the following formulas are inconsistent:
% 231.54/42.92  ----------------------------------------------------------------
% 231.54/42.92    (1)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 &
% 231.54/42.92           op(all_52_17, all_52_17) = e3 & op(all_52_19, all_52_19) = e2 &
% 231.54/42.92           op(all_52_21, all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1,
% 231.54/42.92             e3) = all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 &
% 231.54/42.92           op(e1, e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21)
% 231.54/42.92           & $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 231.54/42.92           all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 231.54/42.92             all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 231.54/42.92             all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 231.54/42.92           op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 231.54/42.92           $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 231.54/42.92    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 231.54/42.92    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.92           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.92    (4)   ~ (all_6_2 = e3)
% 231.54/42.92    (5)  op(e1, e1) = all_6_2
% 231.54/42.92    (6)  op(e1, e3) = e1
% 231.54/42.92    (7)  all_55_10 = all_6_2
% 231.54/42.92    (8)  op(e0, e0) = e1
% 231.54/42.92    (9)   ~ (all_6_2 = e0)
% 231.54/42.92  
% 231.54/42.92  Begin of proof
% 231.54/42.92  | 
% 231.54/42.92  | BETA: splitting (1) gives:
% 231.54/42.92  | 
% 231.54/42.92  | Case 1:
% 231.54/42.92  | | 
% 231.54/42.92  | |   (10)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 &
% 231.54/42.92  | |         op(all_52_17, all_52_17) = e3 & op(all_52_19, all_52_19) = e2 &
% 231.54/42.92  | |         op(all_52_21, all_52_21) = e1 & op(all_52_23, all_52_23) = e0 &
% 231.54/42.92  | |         op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) =
% 231.54/42.92  | |         all_52_21 & op(e1, e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 231.54/42.92  | |         $i(all_52_21) & $i(all_52_23)
% 231.54/42.92  | | 
% 231.54/42.92  | | ALPHA: (10) implies:
% 231.54/42.92  | |   (11)  op(e1, e3) = all_52_17
% 231.54/42.92  | |   (12)  op(all_52_17, all_52_17) = e3
% 231.54/42.92  | | 
% 231.54/42.92  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (11), (12) are inconsistent by
% 231.54/42.92  | |            sub-proof #1998.
% 231.54/42.92  | | 
% 231.54/42.92  | Case 2:
% 231.54/42.92  | | 
% 231.54/42.92  | |   (13)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0 &
% 231.54/42.92  | |         op(all_52_25, all_52_25) = e3 & op(all_52_27, all_52_27) = e2 &
% 231.54/42.92  | |         op(all_52_29, all_52_29) = e1 & op(all_52_31, all_52_31) = e0 &
% 231.54/42.92  | |         op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 & op(e0, e1) =
% 231.54/42.92  | |         all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 231.54/42.92  | |         $i(all_52_29) & $i(all_52_31)
% 231.54/42.92  | | 
% 231.54/42.92  | | ALPHA: (13) implies:
% 231.54/42.92  | |   (14)  op(e0, e0) = all_52_31
% 231.54/42.92  | |   (15)  op(all_52_31, all_52_31) = e0
% 231.54/42.92  | | 
% 231.54/42.92  | | REF_CLOSE: (3), (5), (8), (9), (14), (15) are inconsistent by sub-proof
% 231.54/42.92  | |            #2086.
% 231.54/42.92  | | 
% 231.54/42.92  | End of split
% 231.54/42.92  | 
% 231.54/42.92  End of proof
% 231.54/42.92  
% 231.54/42.92  Sub-proof #1687 shows that the following formulas are inconsistent:
% 231.54/42.92  ----------------------------------------------------------------
% 231.54/42.92    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.92           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.92    (2)   ~ (all_52_15 = e3)
% 231.54/42.92    (3)  op(e2, e2) = e1
% 231.54/42.92    (4)  all_55_7 = all_52_15
% 231.54/42.92    (5)   ~ (all_52_15 = e1)
% 231.54/42.92    (6)  all_55_7 = e3 | all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 231.54/42.92    (7)   ~ (e1 = e0)
% 231.54/42.92    (8)  op(e0, e0) = e1
% 231.54/42.92    (9)  op(all_52_15, all_52_15) = e0
% 231.54/42.92  
% 231.54/42.92  Begin of proof
% 231.54/42.92  | 
% 231.54/42.92  | SIMP: (2) implies:
% 231.54/42.92  |   (10)   ~ (all_52_15 = e3)
% 231.54/42.92  | 
% 231.54/42.92  | BETA: splitting (6) gives:
% 231.54/42.92  | 
% 231.54/42.92  | Case 1:
% 231.54/42.92  | | 
% 231.54/42.92  | |   (11)  all_55_7 = e3
% 231.54/42.92  | | 
% 231.54/42.92  | | REF_CLOSE: (4), (10), (11) are inconsistent by sub-proof #2063.
% 231.54/42.92  | | 
% 231.54/42.92  | Case 2:
% 231.54/42.92  | | 
% 231.54/42.92  | |   (12)  all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 231.54/42.92  | | 
% 231.54/42.92  | | REF_CLOSE: (1), (3), (4), (5), (7), (8), (9), (12) are inconsistent by
% 231.54/42.92  | |            sub-proof #1688.
% 231.54/42.92  | | 
% 231.54/42.92  | End of split
% 231.54/42.92  | 
% 231.54/42.92  End of proof
% 231.54/42.92  
% 231.54/42.92  Sub-proof #1688 shows that the following formulas are inconsistent:
% 231.54/42.92  ----------------------------------------------------------------
% 231.54/42.92    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.92           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.92    (2)  all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 231.54/42.92    (3)  op(e2, e2) = e1
% 231.54/42.92    (4)  all_55_7 = all_52_15
% 231.54/42.92    (5)   ~ (all_52_15 = e1)
% 231.54/42.92    (6)   ~ (e1 = e0)
% 231.54/42.92    (7)  op(e0, e0) = e1
% 231.54/42.92    (8)  op(all_52_15, all_52_15) = e0
% 231.54/42.92  
% 231.54/42.92  Begin of proof
% 231.54/42.92  | 
% 231.54/42.92  | BETA: splitting (2) gives:
% 231.54/42.92  | 
% 231.54/42.92  | Case 1:
% 231.54/42.92  | | 
% 231.54/42.92  | |   (9)  all_55_7 = e2
% 231.54/42.92  | | 
% 231.54/42.92  | | COMBINE_EQS: (4), (9) imply:
% 231.54/42.92  | |   (10)  all_52_15 = e2
% 231.54/42.92  | | 
% 231.54/42.92  | | SIMP: (10) implies:
% 231.54/42.92  | |   (11)  all_52_15 = e2
% 231.54/42.92  | | 
% 231.54/42.92  | | REDUCE: (8), (11) imply:
% 231.54/42.92  | |   (12)  op(e2, e2) = e0
% 231.54/42.92  | | 
% 231.54/42.92  | | REF_CLOSE: (1), (3), (6), (12) are inconsistent by sub-proof #2352.
% 231.54/42.92  | | 
% 231.54/42.92  | Case 2:
% 231.54/42.92  | | 
% 231.54/42.92  | |   (13)  all_55_7 = e1 | all_55_7 = e0
% 231.54/42.92  | | 
% 231.54/42.92  | | REF_CLOSE: (1), (4), (5), (7), (8), (13) are inconsistent by sub-proof
% 231.54/42.93  | |            #2079.
% 231.54/42.93  | | 
% 231.54/42.93  | End of split
% 231.54/42.93  | 
% 231.54/42.93  End of proof
% 231.54/42.93  
% 231.54/42.93  Sub-proof #1689 shows that the following formulas are inconsistent:
% 231.54/42.93  ----------------------------------------------------------------
% 231.54/42.93    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.93         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.54/42.93    (2)   ~ (e3 = e1)
% 231.54/42.93    (3)   ~ (all_53_13 = e1)
% 231.54/42.93    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.93           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.93    (5)  op(e2, e2) = e0
% 231.54/42.93    (6)  all_57_3 = e0
% 231.54/42.93    (7)   ~ (e3 = e2)
% 231.54/42.93    (8)   ~ (e3 = e0)
% 231.54/42.93    (9)   ~ (e2 = e0)
% 231.54/42.93    (10)   ~ (e1 = e0)
% 231.54/42.93    (11)  op(e2, e0) = all_53_13
% 231.54/42.93    (12)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.54/42.93          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.54/42.93    (13)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.93          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.54/42.93    (14)   ~ (e2 = e1)
% 231.54/42.93    (15)  all_57_5 = e0
% 231.54/42.93  
% 231.54/42.93  Begin of proof
% 231.54/42.93  | 
% 231.54/42.93  | BETA: splitting (1) gives:
% 231.54/42.93  | 
% 231.54/42.93  | Case 1:
% 231.54/42.93  | | 
% 231.54/42.93  | |   (16)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) =
% 231.54/42.93  | |           e1)
% 231.54/42.93  | | 
% 231.54/42.93  | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (12), (13), (14),
% 231.54/42.93  | |            (15), (16) are inconsistent by sub-proof #2351.
% 231.54/42.93  | | 
% 231.54/42.93  | Case 2:
% 231.54/42.93  | | 
% 231.54/42.93  | |   (17)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) =
% 231.54/42.93  | |           e1)
% 231.54/42.93  | | 
% 231.54/42.93  | | BETA: splitting (17) gives:
% 231.54/42.93  | | 
% 231.54/42.93  | | Case 1:
% 231.54/42.93  | | | 
% 231.54/42.93  | | |   (18)  all_57_5 = e1 & op(e2, e1) = e1
% 231.54/42.93  | | | 
% 231.54/42.93  | | | ALPHA: (18) implies:
% 231.54/42.93  | | |   (19)  all_57_5 = e1
% 231.54/42.93  | | | 
% 231.54/42.93  | | | REF_CLOSE: (10), (15), (19) are inconsistent by sub-proof #2350.
% 231.54/42.93  | | | 
% 231.54/42.93  | | Case 2:
% 231.54/42.93  | | | 
% 231.54/42.93  | | |   (20)  all_57_10 = e1 & op(e2, e0) = e1
% 231.54/42.93  | | | 
% 231.54/42.93  | | | REF_CLOSE: (3), (4), (11), (20) are inconsistent by sub-proof #2084.
% 231.54/42.93  | | | 
% 231.54/42.93  | | End of split
% 231.54/42.93  | | 
% 231.54/42.93  | End of split
% 231.54/42.93  | 
% 231.54/42.93  End of proof
% 231.54/42.93  
% 231.54/42.93  Sub-proof #1690 shows that the following formulas are inconsistent:
% 231.54/42.93  ----------------------------------------------------------------
% 231.54/42.93    (1)   ~ (e3 = e1)
% 231.54/42.93    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.93           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.93    (3)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.54/42.93         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.54/42.93    (4)   ~ (all_6_2 = e3)
% 231.54/42.93    (5)  op(e1, e1) = all_6_2
% 231.54/42.93    (6)  all_57_14 = e3
% 231.54/42.93    (7)  all_57_6 = e1
% 231.54/42.93    (8)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.54/42.93         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.54/42.93    (9)   ~ (e3 = e2)
% 231.54/42.93    (10)   ~ (e3 = e0)
% 231.54/42.93    (11)  all_57_4 = e1
% 231.54/42.93    (12)  all_57_11 = e2
% 231.54/42.93    (13)   ~ (e2 = e0)
% 231.54/42.93    (14)   ~ (e1 = e0)
% 231.54/42.93    (15)  all_57_5 = e2
% 231.54/42.93    (16)  all_57_7 = e3
% 231.54/42.93    (17)   ~ (all_6_2 = e0)
% 231.54/42.93  
% 231.54/42.93  Begin of proof
% 231.54/42.93  | 
% 231.54/42.93  | BETA: splitting (8) gives:
% 231.54/42.93  | 
% 231.54/42.93  | Case 1:
% 231.54/42.93  | | 
% 231.54/42.93  | |   (18)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) =
% 231.54/42.93  | |           e0)
% 231.54/42.93  | | 
% 231.54/42.93  | | BETA: splitting (18) gives:
% 231.54/42.93  | | 
% 231.54/42.93  | | Case 1:
% 231.54/42.93  | | | 
% 231.54/42.93  | | |   (19)  all_57_4 = e0 & op(e3, e1) = e0
% 231.54/42.93  | | | 
% 231.54/42.93  | | | ALPHA: (19) implies:
% 231.54/42.93  | | |   (20)  all_57_4 = e0
% 231.54/42.93  | | | 
% 231.54/42.93  | | | REF_CLOSE: (11), (14), (20) are inconsistent by sub-proof #2438.
% 231.54/42.93  | | | 
% 231.54/42.93  | | Case 2:
% 231.54/42.93  | | | 
% 231.54/42.93  | | |   (21)  all_57_5 = e0 & op(e2, e1) = e0
% 231.54/42.93  | | | 
% 231.54/42.93  | | | REF_CLOSE: (13), (15), (21) are inconsistent by sub-proof #2428.
% 231.54/42.93  | | | 
% 231.54/42.93  | | End of split
% 231.54/42.93  | | 
% 231.54/42.93  | Case 2:
% 231.54/42.93  | | 
% 231.54/42.93  | |   (22)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 231.54/42.93  | |           e0)
% 231.54/42.93  | | 
% 231.54/42.93  | | BETA: splitting (22) gives:
% 231.54/42.93  | | 
% 231.54/42.93  | | Case 1:
% 231.54/42.93  | | | 
% 231.54/42.93  | | |   (23)  all_57_8 = e0 & op(e1, e1) = e0
% 231.54/42.93  | | | 
% 231.54/42.93  | | | REF_CLOSE: (2), (5), (17), (23) are inconsistent by sub-proof #2412.
% 231.54/42.93  | | | 
% 231.54/42.93  | | Case 2:
% 231.54/42.93  | | | 
% 231.54/42.93  | | |   (24)  all_57_14 = e0 & op(e0, e1) = e0
% 231.54/42.93  | | | 
% 231.54/42.93  | | | ALPHA: (24) implies:
% 231.54/42.93  | | |   (25)  all_57_14 = e0
% 231.54/42.93  | | | 
% 231.54/42.93  | | | COMBINE_EQS: (6), (25) imply:
% 231.54/42.93  | | |   (26)  e3 = e0
% 231.54/42.93  | | | 
% 231.54/42.93  | | | SIMP: (26) implies:
% 231.54/42.93  | | |   (27)  e3 = e0
% 231.54/42.93  | | | 
% 231.54/42.93  | | | COMBINE_EQS: (16), (27) imply:
% 231.54/42.93  | | |   (28)  all_57_7 = e0
% 231.54/42.93  | | | 
% 231.54/42.93  | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (9), (10), (12), (28) are
% 231.54/42.93  | | |            inconsistent by sub-proof #2343.
% 231.54/42.93  | | | 
% 231.54/42.93  | | End of split
% 231.54/42.93  | | 
% 231.54/42.93  | End of split
% 231.54/42.93  | 
% 231.54/42.93  End of proof
% 231.54/42.93  
% 231.54/42.93  Sub-proof #1691 shows that the following formulas are inconsistent:
% 231.54/42.93  ----------------------------------------------------------------
% 231.54/42.93    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.93         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.54/42.93    (2)   ~ (e3 = e1)
% 231.54/42.93    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.93           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.93    (4)   ~ (all_6_2 = e3)
% 231.54/42.93    (5)  op(e1, e1) = all_6_2
% 231.54/42.93    (6)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.54/42.93         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.54/42.93    (7)  all_57_4 = e0
% 231.54/42.93    (8)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.54/42.93         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.54/42.93    (9)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.54/42.93         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.54/42.93    (10)  all_57_3 = e0
% 231.54/42.93    (11)   ~ (e3 = e2)
% 231.54/42.93    (12)   ~ (e3 = e0)
% 231.54/42.93    (13)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.54/42.93          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.54/42.93    (14)  op(e3, e3) = e3
% 231.54/42.93    (15)   ~ (e2 = e0)
% 231.54/42.93    (16)   ~ (e1 = e0)
% 231.54/42.93    (17)  all_57_5 = e2
% 231.54/42.93    (18)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.54/42.93          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.54/42.93    (19)  all_57_10 = e3
% 231.54/42.93    (20)  op(e1, e1) = e2
% 231.54/42.93    (21)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.93          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.54/42.93    (22)   ~ (e2 = e1)
% 231.54/42.93  
% 231.54/42.93  Begin of proof
% 231.54/42.93  | 
% 231.54/42.93  | BETA: splitting (13) gives:
% 231.54/42.93  | 
% 231.54/42.93  | Case 1:
% 231.54/42.93  | | 
% 231.54/42.93  | |   (23)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) =
% 231.54/42.93  | |           e1)
% 231.54/42.93  | | 
% 231.54/42.93  | | BETA: splitting (23) gives:
% 231.54/42.93  | | 
% 231.54/42.93  | | Case 1:
% 231.54/42.93  | | | 
% 231.54/42.93  | | |   (24)  all_57_4 = e1 & op(e3, e1) = e1
% 231.54/42.93  | | | 
% 231.54/42.93  | | | ALPHA: (24) implies:
% 231.54/42.93  | | |   (25)  all_57_4 = e1
% 231.54/42.93  | | | 
% 231.54/42.93  | | | REF_CLOSE: (7), (16), (25) are inconsistent by sub-proof #2438.
% 231.54/42.93  | | | 
% 231.54/42.93  | | Case 2:
% 231.54/42.93  | | | 
% 231.54/42.93  | | |   (26)  all_57_5 = e1 & op(e2, e1) = e1
% 231.54/42.93  | | | 
% 231.54/42.93  | | | REF_CLOSE: (17), (22), (26) are inconsistent by sub-proof #1886.
% 231.54/42.93  | | | 
% 231.54/42.93  | | End of split
% 231.54/42.93  | | 
% 231.54/42.93  | Case 2:
% 231.54/42.93  | | 
% 231.54/42.93  | |   (27)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) =
% 231.54/42.93  | |           e1)
% 231.54/42.93  | | 
% 231.54/42.93  | | BETA: splitting (27) gives:
% 231.54/42.93  | | 
% 231.54/42.93  | | Case 1:
% 231.54/42.93  | | | 
% 231.54/42.93  | | |   (28)  all_57_8 = e1 & op(e1, e1) = e1
% 231.54/42.93  | | | 
% 231.54/42.93  | | | ALPHA: (28) implies:
% 231.54/42.93  | | |   (29)  op(e1, e1) = e1
% 231.54/42.93  | | | 
% 231.54/42.93  | | | REF_CLOSE: (3), (20), (22), (29) are inconsistent by sub-proof #2423.
% 231.54/42.93  | | | 
% 231.54/42.93  | | Case 2:
% 231.54/42.93  | | | 
% 231.54/42.93  | | |   (30)  all_57_14 = e1 & op(e0, e1) = e1
% 231.54/42.93  | | | 
% 231.54/42.93  | | | ALPHA: (30) implies:
% 231.54/42.93  | | |   (31)  all_57_14 = e1
% 231.54/42.93  | | | 
% 231.54/42.93  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (14),
% 231.54/42.93  | | |            (15), (16), (18), (19), (21), (22), (31) are inconsistent by
% 231.54/42.93  | | |            sub-proof #1692.
% 231.54/42.93  | | | 
% 231.54/42.93  | | End of split
% 231.54/42.93  | | 
% 231.54/42.93  | End of split
% 231.54/42.93  | 
% 231.54/42.93  End of proof
% 231.54/42.93  
% 231.54/42.93  Sub-proof #1692 shows that the following formulas are inconsistent:
% 231.54/42.93  ----------------------------------------------------------------
% 231.54/42.93    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.93         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.54/42.93    (2)   ~ (e3 = e1)
% 231.54/42.93    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.93           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.93    (4)   ~ (all_6_2 = e3)
% 231.54/42.93    (5)  op(e1, e1) = all_6_2
% 231.54/42.93    (6)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.54/42.93         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.54/42.93    (7)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.54/42.93         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.54/42.93    (8)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.54/42.93         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.54/42.93    (9)  all_57_3 = e0
% 231.54/42.93    (10)   ~ (e3 = e2)
% 231.54/42.93    (11)   ~ (e3 = e0)
% 231.54/42.93    (12)  op(e3, e3) = e3
% 231.54/42.93    (13)   ~ (e2 = e0)
% 231.54/42.93    (14)   ~ (e1 = e0)
% 231.54/42.93    (15)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.54/42.93          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.54/42.93    (16)  all_57_14 = e1
% 231.54/42.93    (17)  all_57_10 = e3
% 231.54/42.93    (18)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.93          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.54/42.93    (19)   ~ (e2 = e1)
% 231.54/42.93  
% 231.54/42.93  Begin of proof
% 231.54/42.93  | 
% 231.54/42.93  | BETA: splitting (15) gives:
% 231.54/42.93  | 
% 231.54/42.93  | Case 1:
% 231.54/42.93  | | 
% 231.54/42.93  | |   (20)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) =
% 231.54/42.93  | |           e3)
% 231.54/42.93  | | 
% 231.54/42.93  | | BETA: splitting (20) gives:
% 231.54/42.93  | | 
% 231.54/42.93  | | Case 1:
% 231.54/42.93  | | | 
% 231.54/42.93  | | |   (21)  all_57_4 = e3 & op(e3, e1) = e3
% 231.54/42.93  | | | 
% 231.54/42.93  | | | ALPHA: (21) implies:
% 231.54/42.93  | | |   (22)  all_57_4 = e3
% 231.54/42.93  | | | 
% 231.54/42.93  | | | REF_CLOSE: (2), (3), (6), (7), (8), (10), (11), (12), (13), (14), (19),
% 231.54/42.93  | | |            (22) are inconsistent by sub-proof #2474.
% 231.54/42.93  | | | 
% 231.54/42.93  | | Case 2:
% 231.54/42.93  | | | 
% 231.54/42.93  | | |   (23)  all_57_5 = e3 & op(e2, e1) = e3
% 231.54/42.93  | | | 
% 231.54/42.93  | | | ALPHA: (23) implies:
% 231.54/42.93  | | |   (24)  all_57_5 = e3
% 231.54/42.93  | | | 
% 231.54/42.93  | | | REF_CLOSE: (1), (2), (9), (10), (13), (14), (17), (18), (19), (24) are
% 231.54/42.93  | | |            inconsistent by sub-proof #1693.
% 231.54/42.93  | | | 
% 231.54/42.93  | | End of split
% 231.54/42.93  | | 
% 231.54/42.93  | Case 2:
% 231.54/42.93  | | 
% 231.54/42.93  | |   (25)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) =
% 231.54/42.93  | |           e3)
% 231.54/42.93  | | 
% 231.54/42.93  | | REF_CLOSE: (2), (3), (4), (5), (16), (25) are inconsistent by sub-proof
% 231.54/42.93  | |            #2263.
% 231.54/42.93  | | 
% 231.54/42.93  | End of split
% 231.54/42.93  | 
% 231.54/42.93  End of proof
% 231.54/42.93  
% 231.54/42.93  Sub-proof #1693 shows that the following formulas are inconsistent:
% 231.54/42.93  ----------------------------------------------------------------
% 231.54/42.93    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.93         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.54/42.93    (2)   ~ (e3 = e1)
% 231.54/42.93    (3)  all_57_3 = e0
% 231.54/42.93    (4)   ~ (e3 = e2)
% 231.54/42.93    (5)  all_57_5 = e3
% 231.54/42.93    (6)   ~ (e2 = e0)
% 231.54/42.93    (7)   ~ (e1 = e0)
% 231.54/42.93    (8)  all_57_10 = e3
% 231.54/42.93    (9)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.93         (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.54/42.93    (10)   ~ (e2 = e1)
% 231.54/42.93  
% 231.54/42.93  Begin of proof
% 231.54/42.93  | 
% 231.54/42.93  | BETA: splitting (9) gives:
% 231.54/42.93  | 
% 231.54/42.93  | Case 1:
% 231.54/42.93  | | 
% 231.54/42.93  | |   (11)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 231.54/42.93  | |           e2)
% 231.54/42.93  | | 
% 231.54/42.93  | | BETA: splitting (11) gives:
% 231.54/42.93  | | 
% 231.54/42.93  | | Case 1:
% 231.54/42.93  | | | 
% 231.54/42.93  | | |   (12)  all_57_2 = e2 & op(e2, e3) = e2
% 231.54/42.93  | | | 
% 231.54/42.93  | | | ALPHA: (12) implies:
% 231.54/42.93  | | |   (13)  all_57_2 = e2
% 231.54/42.93  | | | 
% 231.54/42.93  | | | REF_CLOSE: (1), (2), (3), (5), (7), (8), (10), (13) are inconsistent by
% 231.54/42.93  | | |            sub-proof #1694.
% 231.54/42.93  | | | 
% 231.54/42.93  | | Case 2:
% 231.54/42.93  | | | 
% 231.54/42.93  | | |   (14)  all_57_3 = e2 & op(e2, e2) = e2
% 231.54/42.93  | | | 
% 231.54/42.93  | | | REF_CLOSE: (3), (6), (14) are inconsistent by sub-proof #2103.
% 231.54/42.93  | | | 
% 231.54/42.93  | | End of split
% 231.54/42.93  | | 
% 231.54/42.93  | Case 2:
% 231.54/42.93  | | 
% 231.54/42.93  | |   (15)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 231.54/42.93  | |           e2)
% 231.54/42.93  | | 
% 231.54/42.93  | | BETA: splitting (15) gives:
% 231.54/42.93  | | 
% 231.54/42.93  | | Case 1:
% 231.54/42.93  | | | 
% 231.54/42.93  | | |   (16)  all_57_5 = e2 & op(e2, e1) = e2
% 231.54/42.93  | | | 
% 231.54/42.93  | | | REF_CLOSE: (4), (5), (16) are inconsistent by sub-proof #2425.
% 231.54/42.93  | | | 
% 231.54/42.93  | | Case 2:
% 231.54/42.93  | | | 
% 231.54/42.93  | | |   (17)  all_57_10 = e2 & op(e2, e0) = e2
% 231.54/42.93  | | | 
% 231.54/42.93  | | | REF_CLOSE: (4), (8), (17) are inconsistent by sub-proof #2250.
% 231.54/42.93  | | | 
% 231.54/42.93  | | End of split
% 231.54/42.93  | | 
% 231.54/42.93  | End of split
% 231.54/42.93  | 
% 231.54/42.93  End of proof
% 231.54/42.93  
% 231.54/42.93  Sub-proof #1694 shows that the following formulas are inconsistent:
% 231.54/42.93  ----------------------------------------------------------------
% 231.54/42.93    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.54/42.93         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.54/42.93    (2)   ~ (e3 = e1)
% 231.54/42.93    (3)  all_57_2 = e2
% 231.54/42.93    (4)  all_57_3 = e0
% 231.54/42.93    (5)  all_57_5 = e3
% 231.54/42.93    (6)   ~ (e1 = e0)
% 231.54/42.93    (7)  all_57_10 = e3
% 231.54/42.93    (8)   ~ (e2 = e1)
% 231.54/42.93  
% 231.54/42.93  Begin of proof
% 231.54/42.93  | 
% 231.54/42.93  | BETA: splitting (1) gives:
% 231.54/42.93  | 
% 231.54/42.93  | Case 1:
% 231.54/42.93  | | 
% 231.54/42.93  | |   (9)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1)
% 231.54/42.93  | | 
% 231.54/42.93  | | BETA: splitting (9) gives:
% 231.54/42.93  | | 
% 231.54/42.93  | | Case 1:
% 231.54/42.93  | | | 
% 231.54/42.93  | | |   (10)  all_57_2 = e1 & op(e2, e3) = e1
% 231.54/42.93  | | | 
% 231.54/42.93  | | | REF_CLOSE: (3), (8), (10) are inconsistent by sub-proof #2244.
% 231.54/42.93  | | | 
% 231.54/42.93  | | Case 2:
% 231.54/42.93  | | | 
% 231.54/42.93  | | |   (11)  all_57_3 = e1 & op(e2, e2) = e1
% 231.54/42.93  | | | 
% 231.54/42.93  | | | REF_CLOSE: (4), (6), (11) are inconsistent by sub-proof #2362.
% 231.54/42.93  | | | 
% 231.54/42.93  | | End of split
% 231.54/42.93  | | 
% 231.54/42.93  | Case 2:
% 231.54/42.93  | | 
% 231.54/42.93  | |   (12)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) =
% 231.54/42.93  | |           e1)
% 231.54/42.93  | | 
% 231.54/42.93  | | BETA: splitting (12) gives:
% 231.54/42.93  | | 
% 231.54/42.93  | | Case 1:
% 231.54/42.93  | | | 
% 231.54/42.93  | | |   (13)  all_57_5 = e1 & op(e2, e1) = e1
% 231.54/42.93  | | | 
% 231.54/42.93  | | | REF_CLOSE: (2), (5), (13) are inconsistent by sub-proof #2376.
% 231.54/42.93  | | | 
% 231.54/42.93  | | Case 2:
% 231.54/42.93  | | | 
% 231.54/42.93  | | |   (14)  all_57_10 = e1 & op(e2, e0) = e1
% 231.54/42.93  | | | 
% 231.54/42.93  | | | REF_CLOSE: (2), (7), (14) are inconsistent by sub-proof #2349.
% 231.54/42.93  | | | 
% 231.54/42.93  | | End of split
% 231.54/42.93  | | 
% 231.54/42.93  | End of split
% 231.54/42.93  | 
% 231.54/42.93  End of proof
% 231.54/42.93  
% 231.54/42.93  Sub-proof #1695 shows that the following formulas are inconsistent:
% 231.54/42.93  ----------------------------------------------------------------
% 231.54/42.93    (1)   ~ (e3 = e1)
% 231.54/42.93    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.93           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.93    (3)   ~ (all_6_2 = e3)
% 231.54/42.93    (4)  op(e1, e1) = all_6_2
% 231.54/42.93    (5)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.54/42.93    (6)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.54/42.93         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.54/42.93    (7)   ~ (e3 = e2)
% 231.54/42.93    (8)   ~ (e3 = e0)
% 231.54/42.93    (9)  all_57_4 = e1
% 231.54/42.93    (10)   ~ (e2 = e0)
% 231.54/42.93    (11)   ~ (e1 = e0)
% 231.54/42.93    (12)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.54/42.93          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.54/42.93    (13)  op(e0, e0) = e1
% 231.54/42.93    (14)   ~ (e2 = e1)
% 231.54/42.93    (15)   ~ (all_6_2 = e0)
% 231.54/42.93  
% 231.54/42.93  Begin of proof
% 231.54/42.93  | 
% 231.54/42.93  | BETA: splitting (5) gives:
% 231.54/42.93  | 
% 231.54/42.93  | Case 1:
% 231.54/42.93  | | 
% 231.54/42.93  | |   (16)  all_57_14 = e2 & op(e0, e1) = e2
% 231.54/42.93  | | 
% 231.54/42.93  | | ALPHA: (16) implies:
% 231.54/42.93  | |   (17)  all_57_14 = e2
% 231.54/42.93  | | 
% 231.54/42.93  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (15),
% 231.54/42.93  | |            (17) are inconsistent by sub-proof #2408.
% 231.54/42.93  | | 
% 231.54/42.93  | Case 2:
% 231.54/42.93  | | 
% 231.54/42.93  | |   (18)  all_57_15 = e2 & op(e0, e0) = e2
% 231.54/42.93  | | 
% 231.54/42.93  | | ALPHA: (18) implies:
% 231.54/42.93  | |   (19)  op(e0, e0) = e2
% 231.54/42.93  | | 
% 231.54/42.93  | | REF_CLOSE: (2), (13), (14), (19) are inconsistent by sub-proof #2177.
% 231.54/42.93  | | 
% 231.54/42.93  | End of split
% 231.54/42.93  | 
% 231.54/42.93  End of proof
% 231.54/42.93  
% 231.54/42.93  Sub-proof #1696 shows that the following formulas are inconsistent:
% 231.54/42.93  ----------------------------------------------------------------
% 231.54/42.93    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.54/42.93         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.54/42.93    (2)   ~ (e3 = e1)
% 231.54/42.93    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.54/42.93           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.54/42.93    (4)  op(e2, e2) = e1
% 231.54/42.93    (5)  all_57_7 = e2
% 231.54/42.93    (6)   ~ (e3 = e2)
% 231.54/42.93    (7)   ~ (e3 = e0)
% 231.54/42.93    (8)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 231.54/42.93         (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 231.54/42.93    (9)   ~ (e2 = e0)
% 231.54/42.93    (10)  all_57_13 = e2
% 231.54/42.93    (11)   ~ (e1 = e0)
% 231.54/42.93    (12)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.54/42.93          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.54/42.93    (13)   ~ (e2 = e1)
% 231.83/42.93    (14)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.83/42.93          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.83/42.93  
% 231.83/42.93  Begin of proof
% 231.83/42.93  | 
% 231.83/42.93  | BETA: splitting (12) gives:
% 231.83/42.93  | 
% 231.83/42.93  | Case 1:
% 231.83/42.93  | | 
% 231.83/42.93  | |   (15)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 231.83/42.93  | |           e3)
% 231.83/42.93  | | 
% 231.83/42.93  | | BETA: splitting (15) gives:
% 231.83/42.93  | | 
% 231.83/42.93  | | Case 1:
% 231.83/42.93  | | | 
% 231.83/42.93  | | |   (16)  all_57_1 = e3 & op(e3, e2) = e3
% 231.83/42.93  | | | 
% 231.83/42.93  | | | ALPHA: (16) implies:
% 231.83/42.93  | | |   (17)  all_57_1 = e3
% 231.83/42.93  | | | 
% 231.83/42.93  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 231.83/42.93  | | |            (14), (17) are inconsistent by sub-proof #1697.
% 231.83/42.93  | | | 
% 231.83/42.93  | | Case 2:
% 231.83/42.93  | | | 
% 231.83/42.93  | | |   (18)  all_57_3 = e3 & op(e2, e2) = e3
% 231.83/42.93  | | | 
% 231.83/42.93  | | | ALPHA: (18) implies:
% 231.83/42.93  | | |   (19)  op(e2, e2) = e3
% 231.83/42.93  | | | 
% 231.83/42.93  | | | REF_CLOSE: (2), (3), (4), (19) are inconsistent by sub-proof #1912.
% 231.83/42.93  | | | 
% 231.83/42.93  | | End of split
% 231.83/42.93  | | 
% 231.83/42.93  | Case 2:
% 231.83/42.93  | | 
% 231.83/42.93  | |   (20)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 231.83/42.93  | |           e3)
% 231.83/42.93  | | 
% 231.83/42.93  | | BETA: splitting (20) gives:
% 231.83/42.93  | | 
% 231.83/42.93  | | Case 1:
% 231.83/42.93  | | | 
% 231.83/42.93  | | |   (21)  all_57_7 = e3 & op(e1, e2) = e3
% 231.83/42.93  | | | 
% 231.83/42.93  | | | REF_CLOSE: (5), (6), (21) are inconsistent by sub-proof #2194.
% 231.83/42.93  | | | 
% 231.83/42.93  | | Case 2:
% 231.83/42.93  | | | 
% 231.83/42.93  | | |   (22)  all_57_13 = e3 & op(e0, e2) = e3
% 231.83/42.93  | | | 
% 231.83/42.93  | | | ALPHA: (22) implies:
% 231.83/42.93  | | |   (23)  all_57_13 = e3
% 231.83/42.93  | | | 
% 231.83/42.93  | | | REF_CLOSE: (6), (10), (23) are inconsistent by sub-proof #2203.
% 231.83/42.93  | | | 
% 231.83/42.93  | | End of split
% 231.83/42.93  | | 
% 231.83/42.93  | End of split
% 231.83/42.93  | 
% 231.83/42.93  End of proof
% 231.83/42.93  
% 231.83/42.93  Sub-proof #1697 shows that the following formulas are inconsistent:
% 231.83/42.93  ----------------------------------------------------------------
% 231.83/42.93    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.83/42.93         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.83/42.93    (2)   ~ (e3 = e1)
% 231.83/42.93    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/42.93           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/42.93    (4)  op(e2, e2) = e1
% 231.83/42.93    (5)  all_57_7 = e2
% 231.83/42.93    (6)   ~ (e3 = e2)
% 231.83/42.93    (7)   ~ (e3 = e0)
% 231.83/42.93    (8)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 231.83/42.93         (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 231.83/42.93    (9)   ~ (e2 = e0)
% 231.83/42.93    (10)  all_57_13 = e2
% 231.83/42.93    (11)   ~ (e1 = e0)
% 231.83/42.93    (12)  all_57_1 = e3
% 231.83/42.93    (13)   ~ (e2 = e1)
% 231.83/42.93    (14)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.83/42.93          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.83/42.93  
% 231.83/42.93  Begin of proof
% 231.83/42.93  | 
% 231.83/42.93  | BETA: splitting (8) gives:
% 231.83/42.93  | 
% 231.83/42.93  | Case 1:
% 231.83/42.93  | | 
% 231.83/42.93  | |   (15)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) =
% 231.83/42.93  | |           e0)
% 231.83/42.93  | | 
% 231.83/42.93  | | BETA: splitting (15) gives:
% 231.83/42.93  | | 
% 231.83/42.93  | | Case 1:
% 231.83/42.93  | | | 
% 231.83/42.93  | | |   (16)  all_57_1 = e0 & op(e3, e2) = e0
% 231.83/42.93  | | | 
% 231.83/42.93  | | | REF_CLOSE: (7), (12), (16) are inconsistent by sub-proof #1811.
% 231.83/42.93  | | | 
% 231.83/42.93  | | Case 2:
% 231.83/42.93  | | | 
% 231.83/42.93  | | |   (17)  all_57_3 = e0 & op(e2, e2) = e0
% 231.83/42.93  | | | 
% 231.83/42.93  | | | ALPHA: (17) implies:
% 231.83/42.93  | | |   (18)  all_57_3 = e0
% 231.83/42.93  | | | 
% 231.83/42.93  | | | REF_CLOSE: (2), (5), (10), (11), (12), (13), (14), (18) are inconsistent
% 231.83/42.93  | | |            by sub-proof #1698.
% 231.83/42.93  | | | 
% 231.83/42.93  | | End of split
% 231.83/42.93  | | 
% 231.83/42.93  | Case 2:
% 231.83/42.93  | | 
% 231.83/42.93  | |   (19)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 231.83/42.93  | |           e0)
% 231.83/42.93  | | 
% 231.83/42.93  | | BETA: splitting (19) gives:
% 231.83/42.93  | | 
% 231.83/42.93  | | Case 1:
% 231.83/42.93  | | | 
% 231.83/42.93  | | |   (20)  all_57_7 = e0 & op(e1, e2) = e0
% 231.83/42.93  | | | 
% 231.83/42.93  | | | ALPHA: (20) implies:
% 231.83/42.93  | | |   (21)  all_57_7 = e0
% 231.83/42.93  | | | 
% 231.83/42.93  | | | COMBINE_EQS: (5), (21) imply:
% 231.83/42.93  | | |   (22)  e2 = e0
% 231.83/42.93  | | | 
% 231.83/42.93  | | | COMBINE_EQS: (10), (22) imply:
% 231.83/42.93  | | |   (23)  all_57_13 = e0
% 231.83/42.93  | | | 
% 231.83/42.93  | | | REF_CLOSE: (1), (3), (4), (6), (9), (12), (13), (21), (23) are
% 231.83/42.93  | | |            inconsistent by sub-proof #1767.
% 231.83/42.93  | | | 
% 231.83/42.93  | | Case 2:
% 231.83/42.93  | | | 
% 231.83/42.93  | | |   (24)  all_57_13 = e0 & op(e0, e2) = e0
% 231.83/42.93  | | | 
% 231.83/42.93  | | | ALPHA: (24) implies:
% 231.83/42.93  | | |   (25)  all_57_13 = e0
% 231.83/42.93  | | | 
% 231.83/42.93  | | | COMBINE_EQS: (10), (25) imply:
% 231.83/42.93  | | |   (26)  e2 = e0
% 231.83/42.93  | | | 
% 231.83/42.93  | | | COMBINE_EQS: (5), (26) imply:
% 231.83/42.93  | | |   (27)  all_57_7 = e0
% 231.83/42.93  | | | 
% 231.83/42.93  | | | REF_CLOSE: (1), (3), (4), (6), (9), (12), (13), (25), (27) are
% 231.83/42.93  | | |            inconsistent by sub-proof #1767.
% 231.83/42.93  | | | 
% 231.83/42.93  | | End of split
% 231.83/42.93  | | 
% 231.83/42.93  | End of split
% 231.83/42.93  | 
% 231.83/42.93  End of proof
% 231.83/42.93  
% 231.83/42.93  Sub-proof #1698 shows that the following formulas are inconsistent:
% 231.83/42.93  ----------------------------------------------------------------
% 231.83/42.93    (1)   ~ (e3 = e1)
% 231.83/42.93    (2)  all_57_7 = e2
% 231.83/42.93    (3)  all_57_3 = e0
% 231.83/42.93    (4)  all_57_13 = e2
% 231.83/42.93    (5)   ~ (e1 = e0)
% 231.83/42.93    (6)  all_57_1 = e3
% 231.83/42.93    (7)   ~ (e2 = e1)
% 231.83/42.93    (8)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.83/42.93         (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.83/42.93  
% 231.83/42.93  Begin of proof
% 231.83/42.93  | 
% 231.83/42.93  | BETA: splitting (8) gives:
% 231.83/42.93  | 
% 231.83/42.93  | Case 1:
% 231.83/42.93  | | 
% 231.83/42.93  | |   (9)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1)
% 231.83/42.93  | | 
% 231.83/42.93  | | BETA: splitting (9) gives:
% 231.83/42.93  | | 
% 231.83/42.93  | | Case 1:
% 231.83/42.93  | | | 
% 231.83/42.93  | | |   (10)  all_57_1 = e1 & op(e3, e2) = e1
% 231.83/42.93  | | | 
% 231.83/42.93  | | | REF_CLOSE: (1), (6), (10) are inconsistent by sub-proof #2453.
% 231.83/42.93  | | | 
% 231.83/42.93  | | Case 2:
% 231.83/42.93  | | | 
% 231.83/42.93  | | |   (11)  all_57_3 = e1 & op(e2, e2) = e1
% 231.83/42.93  | | | 
% 231.83/42.93  | | | REF_CLOSE: (3), (5), (11) are inconsistent by sub-proof #2362.
% 231.83/42.93  | | | 
% 231.83/42.93  | | End of split
% 231.83/42.93  | | 
% 231.83/42.93  | Case 2:
% 231.83/42.93  | | 
% 231.83/42.93  | |   (12)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 231.83/42.93  | |           e1)
% 231.83/42.93  | | 
% 231.83/42.93  | | BETA: splitting (12) gives:
% 231.83/42.93  | | 
% 231.83/42.93  | | Case 1:
% 231.83/42.93  | | | 
% 231.83/42.93  | | |   (13)  all_57_7 = e1 & op(e1, e2) = e1
% 231.83/42.93  | | | 
% 231.83/42.93  | | | REF_CLOSE: (2), (7), (13) are inconsistent by sub-proof #2190.
% 231.83/42.93  | | | 
% 231.83/42.93  | | Case 2:
% 231.83/42.93  | | | 
% 231.83/42.93  | | |   (14)  all_57_13 = e1 & op(e0, e2) = e1
% 231.83/42.93  | | | 
% 231.83/42.93  | | | REF_CLOSE: (4), (7), (14) are inconsistent by sub-proof #2205.
% 231.83/42.93  | | | 
% 231.83/42.93  | | End of split
% 231.83/42.93  | | 
% 231.83/42.93  | End of split
% 231.83/42.93  | 
% 231.83/42.93  End of proof
% 231.83/42.93  
% 231.83/42.93  Sub-proof #1699 shows that the following formulas are inconsistent:
% 231.83/42.93  ----------------------------------------------------------------
% 231.83/42.93    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.83/42.93         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.83/42.93    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.83/42.93         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.83/42.93    (3)   ~ (e3 = e1)
% 231.83/42.93    (4)  all_57_2 = e2
% 231.83/42.93    (5)  all_57_3 = e0
% 231.83/42.93    (6)   ~ (e3 = e2)
% 231.83/42.93    (7)   ~ (e2 = e0)
% 231.83/42.93    (8)   ~ (e1 = e0)
% 231.83/42.93    (9)  all_57_13 = e3
% 231.83/42.93    (10)  all_57_10 = e3
% 231.83/42.93    (11)  all_57_7 = e3
% 231.83/42.93    (12)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.83/42.93          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.83/42.93    (13)   ~ (e2 = e1)
% 231.83/42.93    (14)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.83/42.93          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.83/42.93  
% 231.83/42.93  Begin of proof
% 231.83/42.93  | 
% 231.83/42.93  | BETA: splitting (2) gives:
% 231.83/42.93  | 
% 231.83/42.93  | Case 1:
% 231.83/42.93  | | 
% 231.83/42.93  | |   (15)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 231.83/42.93  | |           e2)
% 231.83/42.93  | | 
% 231.83/42.93  | | BETA: splitting (15) gives:
% 231.83/42.93  | | 
% 231.83/42.93  | | Case 1:
% 231.83/42.93  | | | 
% 231.83/42.93  | | |   (16)  all_57_1 = e2 & op(e3, e2) = e2
% 231.83/42.93  | | | 
% 231.83/42.93  | | | ALPHA: (16) implies:
% 231.83/42.93  | | |   (17)  all_57_1 = e2
% 231.83/42.93  | | | 
% 231.83/42.93  | | | REF_CLOSE: (3), (5), (8), (9), (11), (13), (14), (17) are inconsistent by
% 231.83/42.93  | | |            sub-proof #2008.
% 231.83/42.93  | | | 
% 231.83/42.93  | | Case 2:
% 231.83/42.93  | | | 
% 231.83/42.93  | | |   (18)  all_57_3 = e2 & op(e2, e2) = e2
% 231.83/42.93  | | | 
% 231.83/42.93  | | | ALPHA: (18) implies:
% 231.83/42.93  | | |   (19)  all_57_3 = e2
% 231.83/42.93  | | | 
% 231.83/42.93  | | | COMBINE_EQS: (5), (19) imply:
% 231.83/42.93  | | |   (20)  e2 = e0
% 231.83/42.93  | | | 
% 231.83/42.93  | | | COMBINE_EQS: (4), (20) imply:
% 231.83/42.93  | | |   (21)  all_57_2 = e0
% 231.83/42.93  | | | 
% 231.83/42.93  | | | REF_CLOSE: (1), (3), (5), (6), (7), (8), (10), (12), (13), (21) are
% 231.83/42.93  | | |            inconsistent by sub-proof #2247.
% 231.83/42.93  | | | 
% 231.83/42.93  | | End of split
% 231.83/42.93  | | 
% 231.83/42.93  | Case 2:
% 231.83/42.93  | | 
% 231.83/42.94  | |   (22)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 231.83/42.94  | |           e2)
% 231.83/42.94  | | 
% 231.83/42.94  | | BETA: splitting (22) gives:
% 231.83/42.94  | | 
% 231.83/42.94  | | Case 1:
% 231.83/42.94  | | | 
% 231.83/42.94  | | |   (23)  all_57_7 = e2 & op(e1, e2) = e2
% 231.83/42.94  | | | 
% 231.83/42.94  | | | ALPHA: (23) implies:
% 231.83/42.94  | | |   (24)  all_57_7 = e2
% 231.83/42.94  | | | 
% 231.83/42.94  | | | REF_CLOSE: (6), (11), (24) are inconsistent by sub-proof #2102.
% 231.83/42.94  | | | 
% 231.83/42.94  | | Case 2:
% 231.83/42.94  | | | 
% 231.83/42.94  | | |   (25)  all_57_13 = e2 & op(e0, e2) = e2
% 231.83/42.94  | | | 
% 231.83/42.94  | | | ALPHA: (25) implies:
% 231.83/42.94  | | |   (26)  all_57_13 = e2
% 231.83/42.94  | | | 
% 231.83/42.94  | | | REF_CLOSE: (6), (9), (26) are inconsistent by sub-proof #2203.
% 231.83/42.94  | | | 
% 231.83/42.94  | | End of split
% 231.83/42.94  | | 
% 231.83/42.94  | End of split
% 231.83/42.94  | 
% 231.83/42.94  End of proof
% 231.83/42.94  
% 231.83/42.94  Sub-proof #1700 shows that the following formulas are inconsistent:
% 231.83/42.94  ----------------------------------------------------------------
% 231.83/42.94    (1)  all_57_2 = e0 & op(e2, e3) = e0
% 231.83/42.94    (2)  all_57_2 = e2
% 231.83/42.94    (3)   ~ (e2 = e0)
% 231.83/42.94  
% 231.83/42.94  Begin of proof
% 231.83/42.94  | 
% 231.83/42.94  | ALPHA: (1) implies:
% 231.83/42.94  |   (4)  all_57_2 = e0
% 231.83/42.94  | 
% 231.83/42.94  | COMBINE_EQS: (2), (4) imply:
% 231.83/42.94  |   (5)  e2 = e0
% 231.83/42.94  | 
% 231.83/42.94  | REDUCE: (3), (5) imply:
% 231.83/42.94  |   (6)  $false
% 231.83/42.94  | 
% 231.83/42.94  | CLOSE: (6) is inconsistent.
% 231.83/42.94  | 
% 231.83/42.94  End of proof
% 231.83/42.94  
% 231.83/42.94  Sub-proof #1701 shows that the following formulas are inconsistent:
% 231.83/42.94  ----------------------------------------------------------------
% 231.83/42.94    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.83/42.94         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.83/42.94    (2)   ~ (e3 = e1)
% 231.83/42.94    (3)  all_57_2 = e0 & op(e2, e3) = e0
% 231.83/42.94    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/42.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/42.94    (5)   ~ (all_6_2 = e3)
% 231.83/42.94    (6)  op(e1, e1) = all_6_2
% 231.83/42.94    (7)  op(e2, e2) = e1
% 231.83/42.94    (8)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.83/42.94         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.83/42.94    (9)   ~ (e3 = e2)
% 231.83/42.94    (10)   ~ (e3 = e0)
% 231.83/42.94    (11)  all_57_4 = e1
% 231.83/42.94    (12)   ~ (e2 = e0)
% 231.83/42.94    (13)  all_57_3 = e1
% 231.83/42.94    (14)   ~ (e1 = e0)
% 231.83/42.94    (15)  all_57_5 = e2
% 231.83/42.94    (16)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.83/42.94          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.83/42.94    (17)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.83/42.94          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.83/42.94    (18)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.83/42.94          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.83/42.94    (19)   ~ (e2 = e1)
% 231.83/42.94    (20)   ~ (all_6_2 = e0)
% 231.83/42.94  
% 231.83/42.94  Begin of proof
% 231.83/42.94  | 
% 231.83/42.94  | ALPHA: (3) implies:
% 231.83/42.94  |   (21)  all_57_2 = e0
% 231.83/42.94  | 
% 231.83/42.94  | BETA: splitting (16) gives:
% 231.83/42.94  | 
% 231.83/42.94  | Case 1:
% 231.83/42.94  | | 
% 231.83/42.94  | |   (22)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) =
% 231.83/42.94  | |           e3)
% 231.83/42.94  | | 
% 231.83/42.94  | | REF_CLOSE: (2), (9), (11), (15), (22) are inconsistent by sub-proof #1892.
% 231.83/42.94  | | 
% 231.83/42.94  | Case 2:
% 231.83/42.94  | | 
% 231.83/42.94  | |   (23)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) =
% 231.83/42.94  | |           e3)
% 231.83/42.94  | | 
% 231.83/42.94  | | BETA: splitting (23) gives:
% 231.83/42.94  | | 
% 231.83/42.94  | | Case 1:
% 231.83/42.94  | | | 
% 231.83/42.94  | | |   (24)  all_57_8 = e3 & op(e1, e1) = e3
% 231.83/42.94  | | | 
% 231.83/42.94  | | | ALPHA: (24) implies:
% 231.83/42.94  | | |   (25)  op(e1, e1) = e3
% 231.83/42.94  | | | 
% 231.83/42.94  | | | REF_CLOSE: (4), (5), (6), (25) are inconsistent by sub-proof #2468.
% 231.83/42.94  | | | 
% 231.83/42.94  | | Case 2:
% 231.83/42.94  | | | 
% 231.83/42.94  | | |   (26)  all_57_14 = e3 & op(e0, e1) = e3
% 231.83/42.94  | | | 
% 231.83/42.94  | | | ALPHA: (26) implies:
% 231.83/42.94  | | |   (27)  all_57_14 = e3
% 231.83/42.94  | | | 
% 231.83/42.94  | | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (9), (10), (11), (12), (13),
% 231.83/42.94  | | |            (14), (17), (18), (19), (20), (21), (27) are inconsistent by
% 231.83/42.94  | | |            sub-proof #1716.
% 231.83/42.94  | | | 
% 231.83/42.94  | | End of split
% 231.83/42.94  | | 
% 231.83/42.94  | End of split
% 231.83/42.94  | 
% 231.83/42.94  End of proof
% 231.83/42.94  
% 231.83/42.94  Sub-proof #1702 shows that the following formulas are inconsistent:
% 231.83/42.94  ----------------------------------------------------------------
% 231.83/42.94    (1)   ~ (e3 = e1)
% 231.83/42.94    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/42.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/42.94    (3)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.83/42.94         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.83/42.94    (4)   ~ (all_6_2 = e3)
% 231.83/42.94    (5)  op(e1, e1) = all_6_2
% 231.83/42.94    (6)  all_57_6 = e1
% 231.83/42.94    (7)   ~ (e3 = e2)
% 231.83/42.94    (8)   ~ (e3 = e0)
% 231.83/42.94    (9)  all_57_11 = e2
% 231.83/42.94    (10)  all_57_12 = e3
% 231.83/42.94    (11)  all_57_7 = e3
% 231.83/42.94    (12)  all_57_12 = e0 & op(e0, e3) = e0
% 231.83/42.94  
% 231.83/42.94  Begin of proof
% 231.83/42.94  | 
% 231.83/42.94  | ALPHA: (12) implies:
% 231.83/42.94  |   (13)  all_57_12 = e0
% 231.83/42.94  | 
% 231.83/42.94  | COMBINE_EQS: (10), (13) imply:
% 231.83/42.94  |   (14)  e3 = e0
% 231.83/42.94  | 
% 231.83/42.94  | COMBINE_EQS: (11), (14) imply:
% 231.83/42.94  |   (15)  all_57_7 = e0
% 231.83/42.94  | 
% 231.83/42.94  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (15) are inconsistent
% 231.83/42.94  |            by sub-proof #2343.
% 231.83/42.94  | 
% 231.83/42.94  End of proof
% 231.83/42.94  
% 231.83/42.94  Sub-proof #1703 shows that the following formulas are inconsistent:
% 231.83/42.94  ----------------------------------------------------------------
% 231.83/42.94    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.83/42.94         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.83/42.94    (2)   ~ (e3 = e1)
% 231.83/42.94    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/42.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/42.94    (4)  op(e1, e1) = all_6_2
% 231.83/42.94    (5)  op(e2, e2) = e1
% 231.83/42.94    (6)  all_57_14 = e3
% 231.83/42.94    (7)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.83/42.94         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.83/42.94    (8)   ~ (e3 = e2)
% 231.83/42.94    (9)   ~ (e3 = e0)
% 231.83/42.94    (10)  op(e3, e3) = e3
% 231.83/42.94    (11)  all_57_4 = e1
% 231.83/42.94    (12)   ~ (e2 = e0)
% 231.83/42.94    (13)  all_57_3 = e1
% 231.83/42.94    (14)   ~ (e1 = e0)
% 231.83/42.94    (15)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.83/42.94          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.83/42.94    (16)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.83/42.94          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.83/42.94    (17)   ~ (e2 = e1)
% 231.83/42.94    (18)   ~ (all_6_2 = e0)
% 231.83/42.94    (19)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0)
% 231.83/42.94  
% 231.83/42.94  Begin of proof
% 231.83/42.94  | 
% 231.83/42.94  | BETA: splitting (19) gives:
% 231.83/42.94  | 
% 231.83/42.94  | Case 1:
% 231.83/42.94  | | 
% 231.83/42.94  | |   (20)  all_57_0 = e0 & op(e3, e3) = e0
% 231.83/42.94  | | 
% 231.83/42.94  | | ALPHA: (20) implies:
% 231.83/42.94  | |   (21)  op(e3, e3) = e0
% 231.83/42.94  | | 
% 231.83/42.94  | | REF_CLOSE: (3), (9), (10), (21) are inconsistent by sub-proof #2494.
% 231.83/42.94  | | 
% 231.83/42.94  | Case 2:
% 231.83/42.94  | | 
% 231.83/42.94  | |   (22)  all_57_2 = e0 & op(e2, e3) = e0
% 231.83/42.94  | | 
% 231.83/42.94  | | ALPHA: (22) implies:
% 231.83/42.94  | |   (23)  all_57_2 = e0
% 231.83/42.94  | | 
% 231.83/42.94  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13),
% 231.83/42.94  | |            (14), (15), (16), (17), (18), (23) are inconsistent by sub-proof
% 231.83/42.94  | |            #1716.
% 231.83/42.94  | | 
% 231.83/42.94  | End of split
% 231.83/42.94  | 
% 231.83/42.94  End of proof
% 231.83/42.94  
% 231.83/42.94  Sub-proof #1704 shows that the following formulas are inconsistent:
% 231.83/42.94  ----------------------------------------------------------------
% 231.83/42.94    (1)   ~ (e3 = e1)
% 231.83/42.94    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/42.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/42.94    (3)   ~ (all_6_2 = e3)
% 231.83/42.94    (4)  op(e1, e1) = all_6_2
% 231.83/42.94    (5)  all_57_14 = e3
% 231.83/42.94    (6)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.83/42.94         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.83/42.94    (7)   ~ (e3 = e2)
% 231.83/42.94    (8)   ~ (e3 = e0)
% 231.83/42.94    (9)  all_57_10 = e2 & op(e2, e0) = e2
% 231.83/42.94    (10)  all_57_4 = e1
% 231.83/42.94    (11)   ~ (e2 = e0)
% 231.83/42.94    (12)   ~ (e1 = e0)
% 231.83/42.94    (13)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.83/42.94          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.83/42.94    (14)  all_57_10 = e3
% 231.83/42.94    (15)   ~ (all_6_2 = e0)
% 231.83/42.94  
% 231.83/42.94  Begin of proof
% 231.83/42.94  | 
% 231.83/42.94  | ALPHA: (9) implies:
% 231.83/42.94  |   (16)  all_57_10 = e2
% 231.83/42.94  | 
% 231.83/42.94  | COMBINE_EQS: (14), (16) imply:
% 231.83/42.94  |   (17)  e3 = e2
% 231.83/42.94  | 
% 231.83/42.94  | COMBINE_EQS: (5), (17) imply:
% 231.83/42.94  |   (18)  all_57_14 = e2
% 231.83/42.94  | 
% 231.83/42.94  | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (10), (11), (12), (13), (15),
% 231.83/42.94  |            (18) are inconsistent by sub-proof #2408.
% 231.83/42.94  | 
% 231.83/42.94  End of proof
% 231.83/42.94  
% 231.83/42.94  Sub-proof #1705 shows that the following formulas are inconsistent:
% 231.83/42.94  ----------------------------------------------------------------
% 231.83/42.94    (1)  all_57_9 = e2
% 231.83/42.94    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.83/42.94         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.83/42.94    (3)   ~ (e3 = e1)
% 231.83/42.94    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/42.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/42.94    (5)  op(e1, e1) = all_6_2
% 231.83/42.94    (6)  all_57_9 = e0 & op(e3, e0) = e0
% 231.83/42.94    (7)  op(e2, e2) = e1
% 231.83/42.94    (8)  all_57_14 = e3
% 231.83/42.94    (9)  all_57_2 = e2
% 231.83/42.94    (10)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.83/42.94          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.83/42.94    (11)   ~ (e3 = e2)
% 231.83/42.94    (12)   ~ (e3 = e0)
% 231.83/42.94    (13)  all_57_4 = e1
% 231.83/42.94    (14)   ~ (e2 = e0)
% 231.83/42.94    (15)  all_57_3 = e1
% 231.83/42.94    (16)   ~ (e1 = e0)
% 231.83/42.94    (17)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.83/42.94          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.83/42.94    (18)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.83/42.94          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.83/42.94    (19)   ~ (e2 = e1)
% 231.83/42.94    (20)   ~ (all_6_2 = e0)
% 231.83/42.94  
% 231.83/42.94  Begin of proof
% 231.83/42.94  | 
% 231.83/42.94  | ALPHA: (6) implies:
% 231.83/42.94  |   (21)  all_57_9 = e0
% 231.83/42.94  | 
% 231.83/42.94  | COMBINE_EQS: (1), (21) imply:
% 231.83/42.94  |   (22)  e2 = e0
% 231.83/42.94  | 
% 231.83/42.94  | COMBINE_EQS: (9), (22) imply:
% 231.83/42.94  |   (23)  all_57_2 = e0
% 231.83/42.94  | 
% 231.83/42.94  | REF_CLOSE: (2), (3), (4), (5), (7), (8), (10), (11), (12), (13), (14), (15),
% 231.83/42.94  |            (16), (17), (18), (19), (20), (23) are inconsistent by sub-proof
% 231.83/42.94  |            #1716.
% 231.83/42.94  | 
% 231.83/42.94  End of proof
% 231.83/42.94  
% 231.83/42.94  Sub-proof #1706 shows that the following formulas are inconsistent:
% 231.83/42.94  ----------------------------------------------------------------
% 231.83/42.94    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.83/42.94         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.83/42.94    (2)   ~ (e3 = e1)
% 231.83/42.94    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/42.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/42.94    (4)  op(e2, e2) = e1
% 231.83/42.94    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.83/42.94         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.83/42.94    (6)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.83/42.94         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.83/42.94    (7)   ~ (e3 = e2)
% 231.83/42.94    (8)   ~ (e3 = e0)
% 231.83/42.94    (9)  all_57_1 = e0
% 231.83/42.94    (10)  all_57_0 = e0
% 231.83/42.94    (11)  op(e3, e3) = e0
% 231.83/42.94    (12)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 231.83/42.94          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 231.83/42.94    (13)   ~ (e2 = e0)
% 231.83/42.94    (14)  all_57_3 = e1
% 231.83/42.94    (15)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 231.83/42.94          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.83/42.94    (16)   ~ (e1 = e0)
% 231.83/42.94    (17)   ~ (all_53_12 = e3)
% 231.83/42.94    (18)  all_57_7 = e3
% 231.83/42.94    (19)   ~ (e2 = e1)
% 231.83/42.94    (20)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.83/42.94          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.83/42.94    (21)  op(e3, e0) = all_53_12
% 231.83/42.94  
% 231.83/42.94  Begin of proof
% 231.83/42.94  | 
% 231.83/42.94  | BETA: splitting (1) gives:
% 231.83/42.94  | 
% 231.83/42.94  | Case 1:
% 231.83/42.94  | | 
% 231.83/42.94  | |   (22)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 231.83/42.94  | |           e2)
% 231.83/42.94  | | 
% 231.83/42.94  | | REF_CLOSE: (3), (4), (9), (13), (19), (22) are inconsistent by sub-proof
% 231.83/42.94  | |            #1738.
% 231.83/42.94  | | 
% 231.83/42.94  | Case 2:
% 231.83/42.94  | | 
% 231.83/42.94  | |   (23)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 231.83/42.94  | |           e2)
% 231.83/42.94  | | 
% 231.83/42.94  | | BETA: splitting (23) gives:
% 231.83/42.94  | | 
% 231.83/42.94  | | Case 1:
% 231.83/42.94  | | | 
% 231.83/42.94  | | |   (24)  all_57_7 = e2 & op(e1, e2) = e2
% 231.83/42.94  | | | 
% 231.83/42.94  | | | REF_CLOSE: (7), (18), (24) are inconsistent by sub-proof #2092.
% 231.83/42.94  | | | 
% 231.83/42.94  | | Case 2:
% 231.83/42.94  | | | 
% 231.83/42.94  | | |   (25)  all_57_13 = e2 & op(e0, e2) = e2
% 231.83/42.94  | | | 
% 231.83/42.94  | | | ALPHA: (25) implies:
% 231.83/42.94  | | |   (26)  all_57_13 = e2
% 231.83/42.94  | | | 
% 231.83/42.94  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 231.83/42.94  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (26) are
% 231.83/42.94  | | |            inconsistent by sub-proof #1707.
% 231.83/42.94  | | | 
% 231.83/42.94  | | End of split
% 231.83/42.94  | | 
% 231.83/42.94  | End of split
% 231.83/42.94  | 
% 231.83/42.94  End of proof
% 231.83/42.94  
% 231.83/42.94  Sub-proof #1707 shows that the following formulas are inconsistent:
% 231.83/42.94  ----------------------------------------------------------------
% 231.83/42.94    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.83/42.94         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.83/42.94    (2)   ~ (e3 = e1)
% 231.83/42.94    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/42.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/42.94    (4)  op(e2, e2) = e1
% 231.83/42.94    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.83/42.94         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.83/42.94    (6)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.83/42.94         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.83/42.94    (7)   ~ (e3 = e2)
% 231.83/42.94    (8)   ~ (e3 = e0)
% 231.83/42.94    (9)  all_57_1 = e0
% 231.83/42.94    (10)  all_57_0 = e0
% 231.83/42.94    (11)  op(e3, e3) = e0
% 231.83/42.94    (12)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 231.83/42.94          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 231.83/42.94    (13)   ~ (e2 = e0)
% 231.83/42.94    (14)  all_57_13 = e2
% 231.83/42.94    (15)  all_57_3 = e1
% 231.83/42.94    (16)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 231.83/42.94          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 231.83/42.94    (17)   ~ (e1 = e0)
% 231.83/42.94    (18)   ~ (all_53_12 = e3)
% 231.83/42.94    (19)  all_57_7 = e3
% 231.83/42.94    (20)   ~ (e2 = e1)
% 231.83/42.94    (21)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.83/42.94          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.83/42.94    (22)  op(e3, e0) = all_53_12
% 231.83/42.94  
% 231.83/42.94  Begin of proof
% 231.83/42.94  | 
% 231.83/42.94  | BETA: splitting (5) gives:
% 231.83/42.94  | 
% 231.83/42.94  | Case 1:
% 231.83/42.94  | | 
% 231.83/42.94  | |   (23)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) =
% 231.83/42.94  | |           e1)
% 231.83/42.94  | | 
% 231.83/42.94  | | BETA: splitting (23) gives:
% 231.83/42.94  | | 
% 231.83/42.94  | | Case 1:
% 231.83/42.94  | | | 
% 231.83/42.94  | | |   (24)  all_57_0 = e1 & op(e3, e3) = e1
% 231.83/42.94  | | | 
% 231.83/42.94  | | | ALPHA: (24) implies:
% 231.83/42.94  | | |   (25)  all_57_0 = e1
% 231.83/42.94  | | | 
% 231.83/42.94  | | | COMBINE_EQS: (10), (25) imply:
% 231.83/42.94  | | |   (26)  e1 = e0
% 231.83/42.94  | | | 
% 231.83/42.94  | | | REF_CLOSE: (1), (2), (7), (9), (13), (15), (17), (19), (20), (21), (26)
% 231.83/42.94  | | |            are inconsistent by sub-proof #1708.
% 231.83/42.94  | | | 
% 231.83/42.94  | | Case 2:
% 231.83/42.94  | | | 
% 231.83/42.94  | | |   (27)  all_57_1 = e1 & op(e3, e2) = e1
% 231.83/42.94  | | | 
% 231.83/42.94  | | | ALPHA: (27) implies:
% 231.83/42.94  | | |   (28)  all_57_1 = e1
% 231.83/42.94  | | | 
% 231.83/42.94  | | | REF_CLOSE: (3), (4), (8), (12), (13), (14), (17), (19), (28) are
% 231.83/42.94  | | |            inconsistent by sub-proof #1910.
% 231.83/42.94  | | | 
% 231.83/42.94  | | End of split
% 231.83/42.94  | | 
% 231.83/42.94  | Case 2:
% 231.83/42.94  | | 
% 231.83/42.94  | |   (29)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) =
% 231.83/42.94  | |           e1)
% 231.83/42.94  | | 
% 231.83/42.94  | | BETA: splitting (29) gives:
% 231.83/42.94  | | 
% 231.83/42.94  | | Case 1:
% 231.83/42.94  | | | 
% 231.83/42.94  | | |   (30)  all_57_4 = e1 & op(e3, e1) = e1
% 231.83/42.94  | | | 
% 231.83/42.94  | | | ALPHA: (30) implies:
% 231.83/42.94  | | |   (31)  all_57_4 = e1
% 231.83/42.94  | | | 
% 231.83/42.94  | | | REF_CLOSE: (2), (3), (8), (9), (11), (16), (18), (22), (31) are
% 231.83/42.94  | | |            inconsistent by sub-proof #2280.
% 231.83/42.94  | | | 
% 231.83/42.94  | | Case 2:
% 231.83/42.94  | | | 
% 231.83/42.94  | | |   (32)  all_57_9 = e1 & op(e3, e0) = e1
% 231.83/42.94  | | | 
% 231.83/42.94  | | | ALPHA: (32) implies:
% 231.83/42.94  | | |   (33)  all_57_9 = e1
% 231.83/42.94  | | | 
% 231.83/42.94  | | | REF_CLOSE: (3), (6), (7), (8), (9), (11), (13), (16), (18), (20), (22),
% 231.83/42.94  | | |            (33) are inconsistent by sub-proof #2400.
% 231.83/42.94  | | | 
% 231.83/42.94  | | End of split
% 231.83/42.94  | | 
% 231.83/42.94  | End of split
% 231.83/42.94  | 
% 231.83/42.94  End of proof
% 231.83/42.94  
% 231.83/42.94  Sub-proof #1708 shows that the following formulas are inconsistent:
% 231.83/42.94  ----------------------------------------------------------------
% 231.83/42.94    (1)  e1 = e0
% 231.83/42.94    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.83/42.94         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.83/42.94    (3)   ~ (e3 = e1)
% 231.83/42.94    (4)   ~ (e3 = e2)
% 231.83/42.94    (5)  all_57_1 = e0
% 231.83/42.94    (6)   ~ (e2 = e0)
% 231.83/42.94    (7)  all_57_3 = e1
% 231.83/42.94    (8)   ~ (e1 = e0)
% 231.83/42.94    (9)  all_57_7 = e3
% 231.83/42.94    (10)   ~ (e2 = e1)
% 231.83/42.94    (11)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.83/42.94          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.83/42.94  
% 231.83/42.94  Begin of proof
% 231.83/42.94  | 
% 231.83/42.94  | SIMP: (1) implies:
% 231.83/42.94  |   (12)  e1 = e0
% 231.83/42.94  | 
% 231.83/42.94  | COMBINE_EQS: (7), (12) imply:
% 231.83/42.94  |   (13)  all_57_3 = e0
% 231.83/42.94  | 
% 231.83/42.94  | REF_CLOSE: (2), (3), (4), (5), (6), (8), (9), (10), (11), (13) are
% 231.83/42.94  |            inconsistent by sub-proof #2098.
% 231.83/42.94  | 
% 231.83/42.94  End of proof
% 231.83/42.94  
% 231.83/42.94  Sub-proof #1709 shows that the following formulas are inconsistent:
% 231.83/42.94  ----------------------------------------------------------------
% 231.83/42.94    (1)  all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 231.83/42.94    (2)  ( ~ (all_26_0 = e3) & op(all_26_1, e2) = all_26_0 & op(e2, e1) = all_26_1
% 231.83/42.94           & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 = e0) & op(e2, e1) =
% 231.83/42.94           all_26_1 & $i(all_26_1))
% 231.83/42.94    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/42.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/42.94    (4)   ~ (all_53_7 = e1)
% 231.83/42.94    (5)  op(e2, e2) = e1
% 231.83/42.94    (6)   ~ (all_53_7 = e0)
% 231.83/42.94    (7)  op(e0, e2) = all_53_7
% 231.83/42.94    (8)  ( ~ (all_16_0 = e0) & op(all_16_1, e2) = all_16_0 & op(e2, e1) = all_16_1
% 231.83/42.94           & $i(all_16_0) & $i(all_16_1)) | ( ~ (all_16_1 = e3) & op(e2, e1) =
% 231.83/42.94           all_16_1 & $i(all_16_1))
% 231.83/42.94    (9)  all_55_13 = all_53_7
% 231.83/42.94    (10)  op(e0, e2) = all_52_27
% 231.83/42.94    (11)  op(e2, e1) = e0
% 231.83/42.94    (12)  op(all_52_27, all_52_27) = e2
% 231.83/42.94  
% 231.83/42.94  Begin of proof
% 231.83/42.94  | 
% 231.83/42.94  | BETA: splitting (2) gives:
% 231.83/42.94  | 
% 231.83/42.94  | Case 1:
% 231.83/42.94  | | 
% 231.83/42.94  | |   (13)   ~ (all_26_0 = e3) & op(all_26_1, e2) = all_26_0 & op(e2, e1) =
% 231.83/42.94  | |         all_26_1 & $i(all_26_0) & $i(all_26_1)
% 231.83/42.94  | | 
% 231.83/42.94  | | ALPHA: (13) implies:
% 231.83/42.94  | |   (14)   ~ (all_26_0 = e3)
% 231.83/42.94  | |   (15)  op(e2, e1) = all_26_1
% 231.83/42.94  | |   (16)  op(all_26_1, e2) = all_26_0
% 231.83/42.94  | | 
% 231.83/42.94  | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (9), (10), (11), (12), (14), (15),
% 231.83/42.94  | |            (16) are inconsistent by sub-proof #1712.
% 231.83/42.94  | | 
% 231.83/42.94  | Case 2:
% 231.83/42.94  | | 
% 231.83/42.94  | |   (17)   ~ (all_26_1 = e0) & op(e2, e1) = all_26_1 & $i(all_26_1)
% 231.83/42.94  | | 
% 231.83/42.94  | | REF_CLOSE: (3), (8), (11), (17) are inconsistent by sub-proof #1710.
% 231.83/42.94  | | 
% 231.83/42.94  | End of split
% 231.83/42.94  | 
% 231.83/42.94  End of proof
% 231.83/42.94  
% 231.83/42.94  Sub-proof #1710 shows that the following formulas are inconsistent:
% 231.83/42.94  ----------------------------------------------------------------
% 231.83/42.94    (1)   ~ (all_26_1 = e0) & op(e2, e1) = all_26_1 & $i(all_26_1)
% 231.83/42.94    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/42.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/42.94    (3)  ( ~ (all_16_0 = e0) & op(all_16_1, e2) = all_16_0 & op(e2, e1) = all_16_1
% 231.83/42.94           & $i(all_16_0) & $i(all_16_1)) | ( ~ (all_16_1 = e3) & op(e2, e1) =
% 231.83/42.94           all_16_1 & $i(all_16_1))
% 231.83/42.94    (4)  op(e2, e1) = e0
% 231.83/42.94  
% 231.83/42.94  Begin of proof
% 231.83/42.94  | 
% 231.83/42.94  | ALPHA: (1) implies:
% 231.83/42.94  |   (5)   ~ (all_26_1 = e0)
% 231.83/42.94  |   (6)  op(e2, e1) = all_26_1
% 231.83/42.94  | 
% 231.83/42.94  | BETA: splitting (3) gives:
% 231.83/42.94  | 
% 231.83/42.94  | Case 1:
% 231.83/42.94  | | 
% 231.83/42.94  | |   (7)   ~ (all_16_0 = e0) & op(all_16_1, e2) = all_16_0 & op(e2, e1) =
% 231.83/42.94  | |        all_16_1 & $i(all_16_0) & $i(all_16_1)
% 231.83/42.94  | | 
% 231.83/42.94  | | ALPHA: (7) implies:
% 231.83/42.94  | |   (8)  op(e2, e1) = all_16_1
% 231.83/42.94  | | 
% 231.83/42.94  | | REF_CLOSE: (2), (4), (5), (6), (8) are inconsistent by sub-proof #1711.
% 231.83/42.94  | | 
% 231.83/42.94  | Case 2:
% 231.83/42.94  | | 
% 231.83/42.94  | |   (9)   ~ (all_16_1 = e3) & op(e2, e1) = all_16_1 & $i(all_16_1)
% 231.83/42.94  | | 
% 231.83/42.94  | | ALPHA: (9) implies:
% 231.83/42.94  | |   (10)  op(e2, e1) = all_16_1
% 231.83/42.94  | | 
% 231.83/42.94  | | REF_CLOSE: (2), (4), (5), (6), (10) are inconsistent by sub-proof #1711.
% 231.83/42.94  | | 
% 231.83/42.94  | End of split
% 231.83/42.94  | 
% 231.83/42.94  End of proof
% 231.83/42.94  
% 231.83/42.94  Sub-proof #1711 shows that the following formulas are inconsistent:
% 231.83/42.94  ----------------------------------------------------------------
% 231.83/42.94    (1)  op(e2, e1) = all_26_1
% 231.83/42.94    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/42.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/42.94    (3)   ~ (all_26_1 = e0)
% 231.83/42.94    (4)  op(e2, e1) = all_16_1
% 231.83/42.94    (5)  op(e2, e1) = e0
% 231.83/42.94  
% 231.83/42.94  Begin of proof
% 231.83/42.94  | 
% 231.83/42.94  | GROUND_INST: instantiating (2) with all_16_1, all_26_1, e1, e2, simplifying
% 231.83/42.94  |              with (1), (4) gives:
% 231.83/42.94  |   (6)  all_26_1 = all_16_1
% 231.83/42.94  | 
% 231.83/42.94  | GROUND_INST: instantiating (2) with e0, all_26_1, e1, e2, simplifying with
% 231.83/42.94  |              (1), (5) gives:
% 231.83/42.94  |   (7)  all_26_1 = e0
% 231.83/42.94  | 
% 231.83/42.94  | COMBINE_EQS: (6), (7) imply:
% 231.83/42.94  |   (8)  all_16_1 = e0
% 231.83/42.94  | 
% 231.83/42.94  | REDUCE: (3), (7) imply:
% 231.83/42.94  |   (9)  $false
% 231.83/42.94  | 
% 231.83/42.94  | CLOSE: (9) is inconsistent.
% 231.83/42.94  | 
% 231.83/42.94  End of proof
% 231.83/42.94  
% 231.83/42.94  Sub-proof #1712 shows that the following formulas are inconsistent:
% 231.83/42.94  ----------------------------------------------------------------
% 231.83/42.94    (1)  all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 231.83/42.94    (2)  op(e2, e1) = all_26_1
% 231.83/42.94    (3)  op(all_26_1, e2) = all_26_0
% 231.83/42.94    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/42.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/42.94    (5)   ~ (all_53_7 = e1)
% 231.83/42.94    (6)  op(e2, e2) = e1
% 231.83/42.94    (7)   ~ (all_26_0 = e3)
% 231.83/42.94    (8)   ~ (all_53_7 = e0)
% 231.83/42.94    (9)  op(e0, e2) = all_53_7
% 231.83/42.94    (10)  all_55_13 = all_53_7
% 231.83/42.94    (11)  op(e0, e2) = all_52_27
% 231.83/42.94    (12)  op(e2, e1) = e0
% 231.83/42.94    (13)  op(all_52_27, all_52_27) = e2
% 231.83/42.94  
% 231.83/42.94  Begin of proof
% 231.83/42.94  | 
% 231.83/42.94  | GROUND_INST: instantiating (4) with all_53_7, all_52_27, e2, e0, simplifying
% 231.83/42.94  |              with (9), (11) gives:
% 231.83/42.94  |   (14)  all_53_7 = all_52_27
% 231.83/42.94  | 
% 231.83/42.94  | GROUND_INST: instantiating (4) with e0, all_26_1, e1, e2, simplifying with
% 231.83/42.94  |              (2), (12) gives:
% 231.83/42.94  |   (15)  all_26_1 = e0
% 231.83/42.94  | 
% 231.83/42.94  | COMBINE_EQS: (10), (14) imply:
% 231.83/42.94  |   (16)  all_55_13 = all_52_27
% 231.83/42.94  | 
% 231.83/42.94  | REDUCE: (5), (14) imply:
% 231.83/42.94  |   (17)   ~ (all_52_27 = e1)
% 231.83/42.94  | 
% 231.83/42.94  | REDUCE: (3), (15) imply:
% 231.83/42.94  |   (18)  op(e0, e2) = all_26_0
% 231.83/42.94  | 
% 231.83/42.94  | GROUND_INST: instantiating (4) with all_52_27, all_26_0, e2, e0, simplifying
% 231.83/42.94  |              with (11), (18) gives:
% 231.83/42.94  |   (19)  all_52_27 = all_26_0
% 231.83/42.94  | 
% 231.83/42.94  | COMBINE_EQS: (16), (19) imply:
% 231.83/42.94  |   (20)  all_55_13 = all_26_0
% 231.83/42.94  | 
% 231.83/42.94  | REDUCE: (17), (19) imply:
% 231.83/42.94  |   (21)   ~ (all_26_0 = e1)
% 231.83/42.94  | 
% 231.83/42.94  | REDUCE: (13), (19) imply:
% 231.83/42.94  |   (22)  op(all_26_0, all_26_0) = e2
% 231.83/42.94  | 
% 231.83/42.94  | BETA: splitting (1) gives:
% 231.83/42.94  | 
% 231.83/42.94  | Case 1:
% 231.83/42.94  | | 
% 231.83/42.94  | |   (23)  all_55_13 = e3
% 231.83/42.94  | | 
% 231.83/42.94  | | COMBINE_EQS: (20), (23) imply:
% 231.83/42.94  | |   (24)  all_26_0 = e3
% 231.83/42.94  | | 
% 231.83/42.94  | | REDUCE: (7), (24) imply:
% 231.83/42.94  | |   (25)  $false
% 231.83/42.95  | | 
% 231.83/42.95  | | CLOSE: (25) is inconsistent.
% 231.83/42.95  | | 
% 231.83/42.95  | Case 2:
% 231.83/42.95  | | 
% 231.83/42.95  | |   (26)  all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 231.83/42.95  | | 
% 231.83/42.95  | | BETA: splitting (26) gives:
% 231.83/42.95  | | 
% 231.83/42.95  | | Case 1:
% 231.83/42.95  | | | 
% 231.83/42.95  | | |   (27)  all_55_13 = e2
% 231.83/42.95  | | | 
% 231.83/42.95  | | | COMBINE_EQS: (20), (27) imply:
% 231.83/42.95  | | |   (28)  all_26_0 = e2
% 231.83/42.95  | | | 
% 231.83/42.95  | | | REDUCE: (21), (28) imply:
% 231.83/42.95  | | |   (29)   ~ (e2 = e1)
% 231.83/42.95  | | | 
% 231.83/42.95  | | | REDUCE: (22), (28) imply:
% 231.83/42.95  | | |   (30)  op(e2, e2) = e2
% 231.83/42.95  | | | 
% 231.83/42.95  | | | REF_CLOSE: (4), (6), (29), (30) are inconsistent by sub-proof #2306.
% 231.83/42.95  | | | 
% 231.83/42.95  | | Case 2:
% 231.83/42.95  | | | 
% 231.83/42.95  | | |   (31)  all_55_13 = e1 | all_55_13 = e0
% 231.83/42.95  | | | 
% 231.83/42.95  | | | REF_CLOSE: (5), (8), (10), (31) are inconsistent by sub-proof #1837.
% 231.83/42.95  | | | 
% 231.83/42.95  | | End of split
% 231.83/42.95  | | 
% 231.83/42.95  | End of split
% 231.83/42.95  | 
% 231.83/42.95  End of proof
% 231.83/42.95  
% 231.83/42.95  Sub-proof #1713 shows that the following formulas are inconsistent:
% 231.83/42.95  ----------------------------------------------------------------
% 231.83/42.95    (1)  op(e2, e1) = all_26_1
% 231.83/42.95    (2)  op(e2, e1) = all_52_13
% 231.83/42.95    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/42.95           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/42.95    (4)  op(all_52_13, all_52_13) = e1
% 231.83/42.95    (5)   ~ (e1 = e0)
% 231.83/42.95    (6)  op(e0, e0) = e0
% 231.83/42.95    (7)  ( ~ (all_16_0 = e0) & op(all_16_1, e2) = all_16_0 & op(e2, e1) = all_16_1
% 231.83/42.95           & $i(all_16_0) & $i(all_16_1)) | ( ~ (all_16_1 = e3) & op(e2, e1) =
% 231.83/42.95           all_16_1 & $i(all_16_1))
% 231.83/42.95    (8)  op(e2, e1) = e0
% 231.83/42.95  
% 231.83/42.95  Begin of proof
% 231.83/42.95  | 
% 231.83/42.95  | BETA: splitting (7) gives:
% 231.83/42.95  | 
% 231.83/42.95  | Case 1:
% 231.83/42.95  | | 
% 231.83/42.95  | |   (9)   ~ (all_16_0 = e0) & op(all_16_1, e2) = all_16_0 & op(e2, e1) =
% 231.83/42.95  | |        all_16_1 & $i(all_16_0) & $i(all_16_1)
% 231.83/42.95  | | 
% 231.83/42.95  | | ALPHA: (9) implies:
% 231.83/42.95  | |   (10)  op(e2, e1) = all_16_1
% 231.83/42.95  | | 
% 231.83/42.95  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (10) are inconsistent by
% 231.83/42.95  | |            sub-proof #1714.
% 231.83/42.95  | | 
% 231.83/42.95  | Case 2:
% 231.83/42.95  | | 
% 231.83/42.95  | |   (11)   ~ (all_16_1 = e3) & op(e2, e1) = all_16_1 & $i(all_16_1)
% 231.83/42.95  | | 
% 231.83/42.95  | | ALPHA: (11) implies:
% 231.83/42.95  | |   (12)  op(e2, e1) = all_16_1
% 231.83/42.95  | | 
% 231.83/42.95  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (12) are inconsistent by
% 231.83/42.95  | |            sub-proof #1714.
% 231.83/42.95  | | 
% 231.83/42.95  | End of split
% 231.83/42.95  | 
% 231.83/42.95  End of proof
% 231.83/42.95  
% 231.83/42.95  Sub-proof #1714 shows that the following formulas are inconsistent:
% 231.83/42.95  ----------------------------------------------------------------
% 231.83/42.95    (1)  op(e2, e1) = all_26_1
% 231.83/42.95    (2)  op(e2, e1) = all_52_13
% 231.83/42.95    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/42.95           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/42.95    (4)  op(all_52_13, all_52_13) = e1
% 231.83/42.95    (5)   ~ (e1 = e0)
% 231.83/42.95    (6)  op(e0, e0) = e0
% 231.83/42.95    (7)  op(e2, e1) = all_16_1
% 231.83/42.95    (8)  op(e2, e1) = e0
% 231.83/42.95  
% 231.83/42.95  Begin of proof
% 231.83/42.95  | 
% 231.83/42.95  | GROUND_INST: instantiating (3) with e0, all_52_13, e1, e2, simplifying with
% 231.83/42.95  |              (2), (8) gives:
% 231.83/42.95  |   (9)  all_52_13 = e0
% 231.83/42.95  | 
% 231.83/42.95  | GROUND_INST: instantiating (3) with all_26_1, all_52_13, e1, e2, simplifying
% 231.83/42.95  |              with (1), (2) gives:
% 231.83/42.95  |   (10)  all_52_13 = all_26_1
% 231.83/42.95  | 
% 231.83/42.95  | GROUND_INST: instantiating (3) with all_16_1, all_52_13, e1, e2, simplifying
% 231.83/42.95  |              with (2), (7) gives:
% 231.83/42.95  |   (11)  all_52_13 = all_16_1
% 231.83/42.95  | 
% 231.83/42.95  | COMBINE_EQS: (10), (11) imply:
% 231.83/42.95  |   (12)  all_26_1 = all_16_1
% 231.83/42.95  | 
% 231.83/42.95  | COMBINE_EQS: (9), (10) imply:
% 231.83/42.95  |   (13)  all_26_1 = e0
% 231.83/42.95  | 
% 231.83/42.95  | COMBINE_EQS: (12), (13) imply:
% 231.83/42.95  |   (14)  all_16_1 = e0
% 231.83/42.95  | 
% 231.83/42.95  | REDUCE: (4), (9) imply:
% 231.83/42.95  |   (15)  op(e0, e0) = e1
% 231.83/42.95  | 
% 231.83/42.95  | REF_CLOSE: (3), (5), (6), (15) are inconsistent by sub-proof #2290.
% 231.83/42.95  | 
% 231.83/42.95  End of proof
% 231.83/42.95  
% 231.83/42.95  Sub-proof #1715 shows that the following formulas are inconsistent:
% 231.83/42.95  ----------------------------------------------------------------
% 231.83/42.95    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.83/42.95         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.83/42.95    (2)   ~ (e3 = e1)
% 231.83/42.95    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/42.95           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/42.95    (4)  op(e1, e1) = all_6_2
% 231.83/42.95    (5)  op(e2, e2) = e1
% 231.83/42.95    (6)  all_57_14 = e3
% 231.83/42.95    (7)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.83/42.95         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.83/42.95    (8)   ~ (e3 = e2)
% 231.83/42.95    (9)   ~ (e3 = e0)
% 231.83/42.95    (10)  all_57_4 = e1
% 231.83/42.95    (11)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0)
% 231.83/42.95    (12)   ~ (e2 = e0)
% 231.83/42.95    (13)  all_57_3 = e1
% 231.83/42.95    (14)   ~ (e1 = e0)
% 231.83/42.95    (15)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.83/42.95          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.83/42.95    (16)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.83/42.95          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.83/42.95    (17)   ~ (e2 = e1)
% 231.83/42.95    (18)   ~ (all_6_2 = e0)
% 231.83/42.95  
% 231.83/42.95  Begin of proof
% 231.83/42.95  | 
% 231.83/42.95  | BETA: splitting (11) gives:
% 231.83/42.95  | 
% 231.83/42.95  | Case 1:
% 231.83/42.95  | | 
% 231.83/42.95  | |   (19)  all_57_2 = e0 & op(e2, e3) = e0
% 231.83/42.95  | | 
% 231.83/42.95  | | ALPHA: (19) implies:
% 231.83/42.95  | |   (20)  all_57_2 = e0
% 231.83/42.95  | | 
% 231.83/42.95  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 231.83/42.95  | |            (14), (15), (16), (17), (18), (20) are inconsistent by sub-proof
% 231.83/42.95  | |            #1716.
% 231.83/42.95  | | 
% 231.83/42.95  | Case 2:
% 231.83/42.95  | | 
% 231.83/42.95  | |   (21)  all_57_3 = e0 & op(e2, e2) = e0
% 231.83/42.95  | | 
% 231.83/42.95  | | ALPHA: (21) implies:
% 231.83/42.95  | |   (22)  op(e2, e2) = e0
% 231.83/42.95  | | 
% 231.83/42.95  | | REF_CLOSE: (3), (5), (14), (22) are inconsistent by sub-proof #2352.
% 231.83/42.95  | | 
% 231.83/42.95  | End of split
% 231.83/42.95  | 
% 231.83/42.95  End of proof
% 231.83/42.95  
% 231.83/42.95  Sub-proof #1716 shows that the following formulas are inconsistent:
% 231.83/42.95  ----------------------------------------------------------------
% 231.83/42.95    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.83/42.95         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.83/42.95    (2)   ~ (e3 = e1)
% 231.83/42.95    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/42.95           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/42.95    (4)  op(e1, e1) = all_6_2
% 231.83/42.95    (5)  op(e2, e2) = e1
% 231.83/42.95    (6)  all_57_14 = e3
% 231.83/42.95    (7)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.83/42.95         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.83/42.95    (8)   ~ (e3 = e2)
% 231.83/42.95    (9)   ~ (e3 = e0)
% 231.83/42.95    (10)  all_57_4 = e1
% 231.83/42.95    (11)   ~ (e2 = e0)
% 231.83/42.95    (12)  all_57_3 = e1
% 231.83/42.95    (13)   ~ (e1 = e0)
% 231.83/42.95    (14)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.83/42.95          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.83/42.95    (15)  all_57_2 = e0
% 231.83/42.95    (16)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.83/42.95          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.83/42.95    (17)   ~ (e2 = e1)
% 231.83/42.95    (18)   ~ (all_6_2 = e0)
% 231.83/42.95  
% 231.83/42.95  Begin of proof
% 231.83/42.95  | 
% 231.83/42.95  | BETA: splitting (7) gives:
% 231.83/42.95  | 
% 231.83/42.95  | Case 1:
% 231.83/42.95  | | 
% 231.83/42.95  | |   (19)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) =
% 231.83/42.95  | |           e0)
% 231.83/42.95  | | 
% 231.83/42.95  | | BETA: splitting (19) gives:
% 231.83/42.95  | | 
% 231.83/42.95  | | Case 1:
% 231.83/42.95  | | | 
% 231.83/42.95  | | |   (20)  all_57_4 = e0 & op(e3, e1) = e0
% 231.83/42.95  | | | 
% 231.83/42.95  | | | ALPHA: (20) implies:
% 231.83/42.95  | | |   (21)  all_57_4 = e0
% 231.83/42.95  | | | 
% 231.83/42.95  | | | COMBINE_EQS: (10), (21) imply:
% 231.83/42.95  | | |   (22)  e1 = e0
% 231.83/42.95  | | | 
% 231.83/42.95  | | | COMBINE_EQS: (12), (22) imply:
% 231.83/42.95  | | |   (23)  all_57_3 = e0
% 231.83/42.95  | | | 
% 231.83/42.95  | | | REF_CLOSE: (1), (2), (8), (9), (11), (13), (14), (15), (16), (17), (23)
% 231.83/42.95  | | |            are inconsistent by sub-proof #2246.
% 231.83/42.95  | | | 
% 231.83/42.95  | | Case 2:
% 231.83/42.95  | | | 
% 231.83/42.95  | | |   (24)  all_57_5 = e0 & op(e2, e1) = e0
% 231.83/42.95  | | | 
% 231.83/42.95  | | | ALPHA: (24) implies:
% 231.83/42.95  | | |   (25)  all_57_5 = e0
% 231.83/42.95  | | | 
% 231.83/42.95  | | | REF_CLOSE: (2), (3), (5), (8), (9), (11), (14), (15), (16), (17), (25) are
% 231.83/42.95  | | |            inconsistent by sub-proof #1848.
% 231.83/42.95  | | | 
% 231.83/42.95  | | End of split
% 231.83/42.95  | | 
% 231.83/42.95  | Case 2:
% 231.83/42.95  | | 
% 231.83/42.95  | |   (26)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 231.83/42.95  | |           e0)
% 231.83/42.95  | | 
% 231.83/42.95  | | REF_CLOSE: (3), (4), (6), (9), (18), (26) are inconsistent by sub-proof
% 231.83/42.95  | |            #1717.
% 231.83/42.95  | | 
% 231.83/42.95  | End of split
% 231.83/42.95  | 
% 231.83/42.95  End of proof
% 231.83/42.95  
% 231.83/42.95  Sub-proof #1717 shows that the following formulas are inconsistent:
% 231.83/42.95  ----------------------------------------------------------------
% 231.83/42.95    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/42.95           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/42.95    (2)  op(e1, e1) = all_6_2
% 231.83/42.95    (3)  all_57_14 = e3
% 231.83/42.95    (4)   ~ (e3 = e0)
% 231.83/42.95    (5)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.83/42.95    (6)   ~ (all_6_2 = e0)
% 231.83/42.95  
% 231.83/42.95  Begin of proof
% 231.83/42.95  | 
% 231.83/42.95  | BETA: splitting (5) gives:
% 231.83/42.95  | 
% 231.83/42.95  | Case 1:
% 231.83/42.95  | | 
% 231.83/42.95  | |   (7)  all_57_8 = e0 & op(e1, e1) = e0
% 231.83/42.95  | | 
% 231.83/42.95  | | REF_CLOSE: (1), (2), (6), (7) are inconsistent by sub-proof #2412.
% 231.83/42.95  | | 
% 231.83/42.95  | Case 2:
% 231.83/42.95  | | 
% 231.83/42.95  | |   (8)  all_57_14 = e0 & op(e0, e1) = e0
% 231.83/42.95  | | 
% 231.83/42.95  | | ALPHA: (8) implies:
% 231.83/42.95  | |   (9)  all_57_14 = e0
% 231.83/42.95  | | 
% 231.83/42.95  | | REF_CLOSE: (3), (4), (9) are inconsistent by sub-proof #2420.
% 231.83/42.95  | | 
% 231.83/42.95  | End of split
% 231.83/42.95  | 
% 231.83/42.95  End of proof
% 231.83/42.95  
% 231.83/42.95  Sub-proof #1718 shows that the following formulas are inconsistent:
% 231.83/42.95  ----------------------------------------------------------------
% 231.83/42.95    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/42.95           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/42.95    (2)   ~ (all_53_7 = e1)
% 231.83/42.95    (3)   ~ (all_53_3 = e3)
% 231.83/42.95    (4)   ~ (all_53_3 = all_53_7)
% 231.83/42.95    (5)   ~ (all_53_9 = e1)
% 231.83/42.95    (6)   ~ (all_53_8 = all_53_9)
% 231.83/42.95    (7)   ~ (all_53_9 = all_53_11)
% 231.83/42.95    (8)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 231.83/42.95    (9)   ~ (all_53_11 = e0)
% 231.83/42.95    (10)  all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 231.83/42.95    (11)   ~ (all_53_7 = e0)
% 231.83/42.95    (12)  all_55_6 = all_53_9
% 231.83/42.95    (13)   ~ (all_53_9 = e2)
% 231.83/42.95    (14)  all_55_12 = all_53_3
% 231.83/42.95    (15)   ~ (all_53_3 = all_53_11)
% 231.83/42.95    (16)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 231.83/42.95    (17)   ~ (all_53_7 = all_53_11)
% 231.83/42.95    (18)   ~ (all_53_3 = e0)
% 231.83/42.95    (19)  all_55_13 = all_53_7
% 231.83/42.95    (20)   ~ (all_53_12 = e0)
% 231.83/42.95    (21)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.83/42.95    (22)  all_55_12 = e3 | all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 231.83/42.95    (23)  all_55_14 = all_53_11
% 231.83/42.95    (24)  op(e3, e1) = all_53_8
% 231.83/42.95    (25)  op(e3, e0) = all_53_12
% 231.83/42.95  
% 231.83/42.95  Begin of proof
% 231.83/42.95  | 
% 231.83/42.95  | BETA: splitting (21) gives:
% 231.83/42.95  | 
% 231.83/42.95  | Case 1:
% 231.83/42.95  | | 
% 231.83/42.95  | |   (26)  all_57_4 = e0 & op(e3, e1) = e0
% 231.83/42.95  | | 
% 231.83/42.95  | | ALPHA: (26) implies:
% 231.83/42.95  | |   (27)  op(e3, e1) = e0
% 231.83/42.95  | | 
% 231.83/42.95  | | BETA: splitting (10) gives:
% 231.83/42.95  | | 
% 231.83/42.95  | | Case 1:
% 231.83/42.95  | | | 
% 231.83/42.95  | | |   (28)  all_55_13 = e2
% 231.83/42.95  | | | 
% 231.83/42.95  | | | COMBINE_EQS: (19), (28) imply:
% 231.83/42.95  | | |   (29)  all_53_7 = e2
% 231.83/42.95  | | | 
% 231.83/42.95  | | | REDUCE: (4), (29) imply:
% 231.83/42.95  | | |   (30)   ~ (all_53_3 = e2)
% 231.83/42.95  | | | 
% 231.83/42.95  | | | REDUCE: (17), (29) imply:
% 231.83/42.95  | | |   (31)   ~ (all_53_11 = e2)
% 231.83/42.95  | | | 
% 231.83/42.95  | | | SIMP: (31) implies:
% 231.83/42.95  | | |   (32)   ~ (all_53_11 = e2)
% 231.83/42.95  | | | 
% 231.83/42.95  | | | BETA: splitting (22) gives:
% 231.83/42.95  | | | 
% 231.83/42.95  | | | Case 1:
% 231.83/42.95  | | | | 
% 231.83/42.95  | | | |   (33)  all_55_12 = e3
% 231.83/42.95  | | | | 
% 231.83/42.95  | | | | COMBINE_EQS: (14), (33) imply:
% 231.83/42.95  | | | |   (34)  all_53_3 = e3
% 231.83/42.95  | | | | 
% 231.83/42.95  | | | | REDUCE: (3), (34) imply:
% 231.83/42.95  | | | |   (35)  $false
% 231.83/42.95  | | | | 
% 231.83/42.95  | | | | CLOSE: (35) is inconsistent.
% 231.83/42.95  | | | | 
% 231.83/42.95  | | | Case 2:
% 231.83/42.95  | | | | 
% 231.83/42.95  | | | |   (36)  all_55_12 = e2 | all_55_12 = e1 | all_55_12 = e0
% 231.83/42.95  | | | | 
% 231.83/42.95  | | | | BETA: splitting (36) gives:
% 231.83/42.95  | | | | 
% 231.83/42.95  | | | | Case 1:
% 231.83/42.95  | | | | | 
% 231.83/42.95  | | | | |   (37)  all_55_12 = e2
% 231.83/42.95  | | | | | 
% 231.83/42.95  | | | | | COMBINE_EQS: (14), (37) imply:
% 231.83/42.95  | | | | |   (38)  all_53_3 = e2
% 231.83/42.95  | | | | | 
% 231.83/42.95  | | | | | REDUCE: (30), (38) imply:
% 231.83/42.95  | | | | |   (39)  $false
% 231.83/42.95  | | | | | 
% 231.83/42.95  | | | | | CLOSE: (39) is inconsistent.
% 231.83/42.95  | | | | | 
% 231.83/42.95  | | | | Case 2:
% 231.83/42.95  | | | | | 
% 231.83/42.95  | | | | |   (40)  all_55_12 = e1 | all_55_12 = e0
% 231.83/42.95  | | | | | 
% 231.83/42.95  | | | | | BETA: splitting (40) gives:
% 231.83/42.95  | | | | | 
% 231.83/42.95  | | | | | Case 1:
% 231.83/42.95  | | | | | | 
% 231.83/42.95  | | | | | |   (41)  all_55_12 = e1
% 231.83/42.95  | | | | | | 
% 231.83/42.95  | | | | | | COMBINE_EQS: (14), (41) imply:
% 231.83/42.95  | | | | | |   (42)  all_53_3 = e1
% 231.83/42.95  | | | | | | 
% 231.83/42.95  | | | | | | REDUCE: (15), (42) imply:
% 231.83/42.95  | | | | | |   (43)   ~ (all_53_11 = e1)
% 231.83/42.95  | | | | | | 
% 231.83/42.95  | | | | | | SIMP: (43) implies:
% 231.83/42.95  | | | | | |   (44)   ~ (all_53_11 = e1)
% 231.83/42.95  | | | | | | 
% 231.83/42.95  | | | | | | BETA: splitting (16) gives:
% 231.83/42.95  | | | | | | 
% 231.83/42.95  | | | | | | Case 1:
% 231.83/42.95  | | | | | | | 
% 231.83/42.95  | | | | | | |   (45)  all_55_14 = e3
% 231.83/42.95  | | | | | | | 
% 231.83/42.95  | | | | | | | COMBINE_EQS: (23), (45) imply:
% 231.83/42.95  | | | | | | |   (46)  all_53_11 = e3
% 231.83/42.95  | | | | | | | 
% 231.83/42.95  | | | | | | | REDUCE: (7), (46) imply:
% 231.83/42.95  | | | | | | |   (47)   ~ (all_53_9 = e3)
% 231.83/42.95  | | | | | | | 
% 231.83/42.95  | | | | | | | BETA: splitting (8) gives:
% 231.83/42.95  | | | | | | | 
% 231.83/42.95  | | | | | | | Case 1:
% 231.83/42.95  | | | | | | | | 
% 231.83/42.95  | | | | | | | |   (48)  all_55_6 = e3
% 231.83/42.95  | | | | | | | | 
% 231.83/42.95  | | | | | | | | REF_CLOSE: (12), (47), (48) are inconsistent by sub-proof #2498.
% 231.83/42.95  | | | | | | | | 
% 231.83/42.95  | | | | | | | Case 2:
% 231.83/42.95  | | | | | | | | 
% 231.83/42.95  | | | | | | | |   (49)  all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 231.83/42.95  | | | | | | | | 
% 231.83/42.95  | | | | | | | | REF_CLOSE: (1), (5), (6), (12), (13), (24), (27), (49) are
% 231.83/42.95  | | | | | | | |            inconsistent by sub-proof #1721.
% 231.83/42.95  | | | | | | | | 
% 231.83/42.95  | | | | | | | End of split
% 231.83/42.95  | | | | | | | 
% 231.83/42.95  | | | | | | Case 2:
% 231.83/42.95  | | | | | | | 
% 231.83/42.95  | | | | | | |   (50)  all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 231.83/42.95  | | | | | | | 
% 231.83/42.95  | | | | | | | REF_CLOSE: (9), (23), (32), (44), (50) are inconsistent by
% 231.83/42.95  | | | | | | |            sub-proof #1719.
% 231.83/42.95  | | | | | | | 
% 231.83/42.95  | | | | | | End of split
% 231.83/42.95  | | | | | | 
% 231.83/42.95  | | | | | Case 2:
% 231.83/42.95  | | | | | | 
% 231.83/42.95  | | | | | |   (51)  all_55_12 = e0
% 231.83/42.95  | | | | | | 
% 231.83/42.95  | | | | | | COMBINE_EQS: (14), (51) imply:
% 231.83/42.95  | | | | | |   (52)  all_53_3 = e0
% 231.83/42.95  | | | | | | 
% 231.83/42.95  | | | | | | REDUCE: (18), (52) imply:
% 231.83/42.95  | | | | | |   (53)  $false
% 231.83/42.95  | | | | | | 
% 231.83/42.95  | | | | | | CLOSE: (53) is inconsistent.
% 231.83/42.95  | | | | | | 
% 231.83/42.95  | | | | | End of split
% 231.83/42.95  | | | | | 
% 231.83/42.95  | | | | End of split
% 231.83/42.95  | | | | 
% 231.83/42.95  | | | End of split
% 231.83/42.95  | | | 
% 231.83/42.95  | | Case 2:
% 231.83/42.95  | | | 
% 231.83/42.95  | | |   (54)  all_55_13 = e1 | all_55_13 = e0
% 231.83/42.95  | | | 
% 231.83/42.95  | | | REF_CLOSE: (2), (11), (19), (54) are inconsistent by sub-proof #1837.
% 231.83/42.95  | | | 
% 231.83/42.95  | | End of split
% 231.83/42.95  | | 
% 231.83/42.95  | Case 2:
% 231.83/42.95  | | 
% 231.83/42.95  | |   (55)  all_57_9 = e0 & op(e3, e0) = e0
% 231.83/42.95  | | 
% 231.83/42.95  | | REF_CLOSE: (1), (20), (25), (55) are inconsistent by sub-proof #2434.
% 231.83/42.95  | | 
% 231.83/42.95  | End of split
% 231.83/42.95  | 
% 231.83/42.95  End of proof
% 231.83/42.95  
% 231.83/42.95  Sub-proof #1719 shows that the following formulas are inconsistent:
% 231.83/42.95  ----------------------------------------------------------------
% 231.83/42.95    (1)  all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 231.83/42.95    (2)   ~ (all_53_11 = e0)
% 231.83/42.95    (3)   ~ (all_53_11 = e2)
% 231.83/42.95    (4)   ~ (all_53_11 = e1)
% 231.83/42.95    (5)  all_55_14 = all_53_11
% 231.83/42.95  
% 231.83/42.95  Begin of proof
% 231.83/42.95  | 
% 231.83/42.95  | BETA: splitting (1) gives:
% 231.83/42.95  | 
% 231.83/42.95  | Case 1:
% 231.83/42.95  | | 
% 231.83/42.95  | |   (6)  all_55_14 = e2
% 231.83/42.95  | | 
% 231.83/42.95  | | REF_CLOSE: (3), (5), (6) are inconsistent by sub-proof #2293.
% 231.83/42.95  | | 
% 231.83/42.95  | Case 2:
% 231.83/42.95  | | 
% 231.83/42.95  | |   (7)  all_55_14 = e1 | all_55_14 = e0
% 231.83/42.95  | | 
% 231.83/42.95  | | REF_CLOSE: (2), (4), (5), (7) are inconsistent by sub-proof #1720.
% 231.83/42.95  | | 
% 231.83/42.95  | End of split
% 231.83/42.95  | 
% 231.83/42.95  End of proof
% 231.83/42.95  
% 231.83/42.95  Sub-proof #1720 shows that the following formulas are inconsistent:
% 231.83/42.95  ----------------------------------------------------------------
% 231.83/42.95    (1)  all_55_14 = e1 | all_55_14 = e0
% 231.83/42.95    (2)  all_55_14 = all_53_11
% 231.83/42.95    (3)   ~ (all_53_11 = e1)
% 231.83/42.95    (4)   ~ (all_53_11 = e0)
% 231.83/42.95  
% 231.83/42.95  Begin of proof
% 231.83/42.95  | 
% 231.83/42.95  | BETA: splitting (1) gives:
% 231.83/42.95  | 
% 231.83/42.95  | Case 1:
% 231.83/42.95  | | 
% 231.83/42.95  | |   (5)  all_55_14 = e1
% 231.83/42.95  | | 
% 231.83/42.95  | | COMBINE_EQS: (2), (5) imply:
% 231.83/42.95  | |   (6)  all_53_11 = e1
% 231.83/42.95  | | 
% 231.83/42.95  | | REDUCE: (3), (6) imply:
% 231.83/42.95  | |   (7)  $false
% 231.83/42.95  | | 
% 231.83/42.95  | | CLOSE: (7) is inconsistent.
% 231.83/42.95  | | 
% 231.83/42.95  | Case 2:
% 231.83/42.95  | | 
% 231.83/42.95  | |   (8)  all_55_14 = e0
% 231.83/42.95  | | 
% 231.83/42.95  | | COMBINE_EQS: (2), (8) imply:
% 231.83/42.95  | |   (9)  all_53_11 = e0
% 231.83/42.95  | | 
% 231.83/42.95  | | REDUCE: (4), (9) imply:
% 231.83/42.95  | |   (10)  $false
% 231.83/42.95  | | 
% 231.83/42.95  | | CLOSE: (10) is inconsistent.
% 231.83/42.95  | | 
% 231.83/42.95  | End of split
% 231.83/42.95  | 
% 231.83/42.95  End of proof
% 231.83/42.95  
% 231.83/42.95  Sub-proof #1721 shows that the following formulas are inconsistent:
% 231.83/42.95  ----------------------------------------------------------------
% 231.83/42.95    (1)  op(e3, e1) = e0
% 231.83/42.95    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/42.95           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/42.95    (3)   ~ (all_53_9 = e1)
% 231.83/42.95    (4)   ~ (all_53_8 = all_53_9)
% 231.83/42.95    (5)  all_55_6 = all_53_9
% 231.83/42.95    (6)   ~ (all_53_9 = e2)
% 231.83/42.95    (7)  all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 231.83/42.95    (8)  op(e3, e1) = all_53_8
% 231.83/42.95  
% 231.83/42.95  Begin of proof
% 231.83/42.95  | 
% 231.83/42.95  | BETA: splitting (7) gives:
% 231.83/42.95  | 
% 231.83/42.95  | Case 1:
% 231.83/42.95  | | 
% 231.83/42.95  | |   (9)  all_55_6 = e2
% 231.83/42.95  | | 
% 231.83/42.95  | | REF_CLOSE: (5), (6), (9) are inconsistent by sub-proof #2398.
% 231.83/42.95  | | 
% 231.83/42.95  | Case 2:
% 231.83/42.95  | | 
% 231.83/42.95  | |   (10)  all_55_6 = e1 | all_55_6 = e0
% 231.83/42.95  | | 
% 231.83/42.95  | | BETA: splitting (10) gives:
% 231.83/42.95  | | 
% 231.83/42.95  | | Case 1:
% 231.83/42.95  | | | 
% 231.83/42.95  | | |   (11)  all_55_6 = e1
% 231.83/42.95  | | | 
% 231.83/42.95  | | | REF_CLOSE: (3), (5), (11) are inconsistent by sub-proof #2163.
% 231.83/42.95  | | | 
% 231.83/42.95  | | Case 2:
% 231.83/42.95  | | | 
% 231.83/42.96  | | |   (12)  all_55_6 = e0
% 231.83/42.96  | | | 
% 231.83/42.96  | | | COMBINE_EQS: (5), (12) imply:
% 231.83/42.96  | | |   (13)  all_53_9 = e0
% 231.83/42.96  | | | 
% 231.83/42.96  | | | SIMP: (13) implies:
% 231.83/42.96  | | |   (14)  all_53_9 = e0
% 231.83/42.96  | | | 
% 231.83/42.96  | | | REDUCE: (4), (14) imply:
% 231.83/42.96  | | |   (15)   ~ (all_53_8 = e0)
% 231.83/42.96  | | | 
% 231.83/42.96  | | | REF_CLOSE: (1), (2), (8), (15) are inconsistent by sub-proof #2267.
% 231.83/42.96  | | | 
% 231.83/42.96  | | End of split
% 231.83/42.96  | | 
% 231.83/42.96  | End of split
% 231.83/42.96  | 
% 231.83/42.96  End of proof
% 231.83/42.96  
% 231.83/42.96  Sub-proof #1722 shows that the following formulas are inconsistent:
% 231.83/42.96  ----------------------------------------------------------------
% 231.83/42.96    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/42.96           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/42.96    (2)   ~ (e3 = e0)
% 231.83/42.96    (3)  all_57_1 = e2
% 231.83/42.96    (4)  op(e3, e3) = e3
% 231.83/42.96    (5)   ~ (e2 = e0)
% 231.83/42.96    (6)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0)
% 231.83/42.96  
% 231.83/42.96  Begin of proof
% 231.83/42.96  | 
% 231.83/42.96  | BETA: splitting (6) gives:
% 231.83/42.96  | 
% 231.83/42.96  | Case 1:
% 231.83/42.96  | | 
% 231.83/42.96  | |   (7)  all_57_0 = e0 & op(e3, e3) = e0
% 231.83/42.96  | | 
% 231.83/42.96  | | ALPHA: (7) implies:
% 231.83/42.96  | |   (8)  op(e3, e3) = e0
% 231.83/42.96  | | 
% 231.83/42.96  | | REF_CLOSE: (1), (2), (4), (8) are inconsistent by sub-proof #2494.
% 231.83/42.96  | | 
% 231.83/42.96  | Case 2:
% 231.83/42.96  | | 
% 231.83/42.96  | |   (9)  all_57_1 = e0 & op(e3, e2) = e0
% 231.83/42.96  | | 
% 231.83/42.96  | | REF_CLOSE: (3), (5), (9) are inconsistent by sub-proof #1723.
% 231.83/42.96  | | 
% 231.83/42.96  | End of split
% 231.83/42.96  | 
% 231.83/42.96  End of proof
% 231.83/42.96  
% 231.83/42.96  Sub-proof #1723 shows that the following formulas are inconsistent:
% 231.83/42.96  ----------------------------------------------------------------
% 231.83/42.96    (1)  all_57_1 = e0 & op(e3, e2) = e0
% 231.83/42.96    (2)  all_57_1 = e2
% 231.83/42.96    (3)   ~ (e2 = e0)
% 231.83/42.96  
% 231.83/42.96  Begin of proof
% 231.83/42.96  | 
% 231.83/42.96  | ALPHA: (1) implies:
% 231.83/42.96  |   (4)  all_57_1 = e0
% 231.83/42.96  | 
% 231.83/42.96  | COMBINE_EQS: (2), (4) imply:
% 231.83/42.96  |   (5)  e2 = e0
% 231.83/42.96  | 
% 231.83/42.96  | REDUCE: (3), (5) imply:
% 231.83/42.96  |   (6)  $false
% 231.83/42.96  | 
% 231.83/42.96  | CLOSE: (6) is inconsistent.
% 231.83/42.96  | 
% 231.83/42.96  End of proof
% 231.83/42.96  
% 231.83/42.96  Sub-proof #1724 shows that the following formulas are inconsistent:
% 231.83/42.96  ----------------------------------------------------------------
% 231.83/42.96    (1)   ~ (e3 = e1)
% 231.83/42.96    (2)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 231.83/42.96         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.83/42.96    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/42.96           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/42.96    (4)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.83/42.96         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.83/42.96    (5)   ~ (all_6_2 = e3)
% 231.83/42.96    (6)  op(e1, e1) = all_6_2
% 231.83/42.96    (7)   ~ (e3 = e2)
% 231.83/42.96    (8)  op(e1, e0) = all_53_14
% 231.83/42.96    (9)   ~ (e3 = e0)
% 231.83/42.96    (10)  all_57_11 = e2
% 231.83/42.96    (11)   ~ (all_53_6 = e1)
% 231.83/42.96    (12)   ~ (e1 = e0)
% 231.83/42.96    (13)   ~ (all_53_14 = e0)
% 231.83/42.96    (14)  op(e1, e1) = e2
% 231.83/42.96    (15)   ~ (e2 = e1)
% 231.83/42.96    (16)  op(e1, e2) = all_53_6
% 231.83/42.96    (17)   ~ (all_6_2 = e0)
% 231.83/42.96    (18)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 231.83/42.96          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 231.83/42.96  
% 231.83/42.96  Begin of proof
% 231.83/42.96  | 
% 231.83/42.96  | BETA: splitting (18) gives:
% 231.83/42.96  | 
% 231.83/42.96  | Case 1:
% 231.83/42.96  | | 
% 231.83/42.96  | |   (19)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) =
% 231.83/42.96  | |           e1)
% 231.83/42.96  | | 
% 231.83/42.96  | | BETA: splitting (19) gives:
% 231.83/42.96  | | 
% 231.83/42.96  | | Case 1:
% 231.83/42.96  | | | 
% 231.83/42.96  | | |   (20)  all_57_6 = e1 & op(e1, e3) = e1
% 231.83/42.96  | | | 
% 231.83/42.96  | | | ALPHA: (20) implies:
% 231.83/42.96  | | |   (21)  all_57_6 = e1
% 231.83/42.96  | | | 
% 231.83/42.96  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 231.83/42.96  | | |            (17), (21) are inconsistent by sub-proof #2340.
% 231.83/42.96  | | | 
% 231.83/42.96  | | Case 2:
% 231.83/42.96  | | | 
% 231.83/42.96  | | |   (22)  all_57_7 = e1 & op(e1, e2) = e1
% 231.83/42.96  | | | 
% 231.83/42.96  | | | REF_CLOSE: (3), (11), (16), (22) are inconsistent by sub-proof #2265.
% 231.83/42.96  | | | 
% 231.83/42.96  | | End of split
% 231.83/42.96  | | 
% 231.83/42.96  | Case 2:
% 231.83/42.96  | | 
% 231.83/42.96  | |   (23)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) =
% 231.83/42.96  | |           e1)
% 231.83/42.96  | | 
% 231.83/42.96  | | REF_CLOSE: (3), (10), (14), (15), (23) are inconsistent by sub-proof #1725.
% 231.83/42.96  | | 
% 231.83/42.96  | End of split
% 231.83/42.96  | 
% 231.83/42.96  End of proof
% 231.83/42.96  
% 231.83/42.96  Sub-proof #1725 shows that the following formulas are inconsistent:
% 231.83/42.96  ----------------------------------------------------------------
% 231.83/42.96    (1)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 231.83/42.96    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/42.96           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/42.96    (3)  all_57_11 = e2
% 231.83/42.96    (4)  op(e1, e1) = e2
% 231.83/42.96    (5)   ~ (e2 = e1)
% 231.83/42.96  
% 231.83/42.96  Begin of proof
% 231.83/42.96  | 
% 231.83/42.96  | BETA: splitting (1) gives:
% 231.83/42.96  | 
% 231.83/42.96  | Case 1:
% 231.83/42.96  | | 
% 231.83/42.96  | |   (6)  all_57_8 = e1 & op(e1, e1) = e1
% 231.83/42.96  | | 
% 231.83/42.96  | | ALPHA: (6) implies:
% 231.83/42.96  | |   (7)  op(e1, e1) = e1
% 231.83/42.96  | | 
% 231.83/42.96  | | REF_CLOSE: (2), (4), (5), (7) are inconsistent by sub-proof #2423.
% 231.83/42.96  | | 
% 231.83/42.96  | Case 2:
% 231.83/42.96  | | 
% 231.83/42.96  | |   (8)  all_57_11 = e1 & op(e1, e0) = e1
% 231.83/42.96  | | 
% 231.83/42.96  | | REF_CLOSE: (3), (5), (8) are inconsistent by sub-proof #1726.
% 231.83/42.96  | | 
% 231.83/42.96  | End of split
% 231.83/42.96  | 
% 231.83/42.96  End of proof
% 231.83/42.96  
% 231.83/42.96  Sub-proof #1726 shows that the following formulas are inconsistent:
% 231.83/42.96  ----------------------------------------------------------------
% 231.83/42.96    (1)  all_57_11 = e1 & op(e1, e0) = e1
% 231.83/42.96    (2)  all_57_11 = e2
% 231.83/42.96    (3)   ~ (e2 = e1)
% 231.83/42.96  
% 231.83/42.96  Begin of proof
% 231.83/42.96  | 
% 231.83/42.96  | ALPHA: (1) implies:
% 231.83/42.96  |   (4)  all_57_11 = e1
% 231.83/42.96  | 
% 231.83/42.96  | COMBINE_EQS: (2), (4) imply:
% 231.83/42.96  |   (5)  e2 = e1
% 231.83/42.96  | 
% 231.83/42.96  | REDUCE: (3), (5) imply:
% 231.83/42.96  |   (6)  $false
% 231.83/42.96  | 
% 231.83/42.96  | CLOSE: (6) is inconsistent.
% 231.83/42.96  | 
% 231.83/42.96  End of proof
% 231.83/42.96  
% 231.83/42.96  Sub-proof #1727 shows that the following formulas are inconsistent:
% 231.83/42.96  ----------------------------------------------------------------
% 231.83/42.96    (1)   ~ (e3 = e1)
% 231.83/42.96    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/42.96           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/42.96    (3)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.83/42.96    (4)   ~ (e1 = e0)
% 231.83/42.96    (5)  op(e0, e0) = e0
% 231.83/42.96    (6)  all_57_11 = e3
% 231.83/42.96  
% 231.83/42.96  Begin of proof
% 231.83/42.96  | 
% 231.83/42.96  | BETA: splitting (3) gives:
% 231.83/42.96  | 
% 231.83/42.96  | Case 1:
% 231.83/42.96  | | 
% 231.83/42.96  | |   (7)  all_57_11 = e1 & op(e1, e0) = e1
% 231.83/42.96  | | 
% 231.83/42.96  | | REF_CLOSE: (1), (6), (7) are inconsistent by sub-proof #2143.
% 231.83/42.96  | | 
% 231.83/42.96  | Case 2:
% 231.83/42.96  | | 
% 231.83/42.96  | |   (8)  all_57_15 = e1 & op(e0, e0) = e1
% 231.83/42.96  | | 
% 231.83/42.96  | | ALPHA: (8) implies:
% 231.83/42.96  | |   (9)  op(e0, e0) = e1
% 231.83/42.96  | | 
% 231.83/42.96  | | REF_CLOSE: (2), (4), (5), (9) are inconsistent by sub-proof #2290.
% 231.83/42.96  | | 
% 231.83/42.96  | End of split
% 231.83/42.96  | 
% 231.83/42.96  End of proof
% 231.83/42.96  
% 231.83/42.96  Sub-proof #1728 shows that the following formulas are inconsistent:
% 231.83/42.96  ----------------------------------------------------------------
% 231.83/42.96    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 231.83/42.96    (2)   ~ (e3 = e1)
% 231.83/42.96    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/42.96           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/42.96    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.83/42.96         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.83/42.96    (5)  all_57_9 = e1
% 231.83/42.96    (6)   ~ (all_53_4 = e1)
% 231.83/42.96    (7)  all_57_4 = e0
% 231.83/42.96    (8)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.83/42.96         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.83/42.96    (9)   ~ (e3 = e2)
% 231.83/42.96    (10)  all_55_1 = all_53_4
% 231.83/42.96    (11)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.83/42.96          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.83/42.96    (12)  op(e3, e3) = e3
% 231.83/42.96    (13)  all_57_5 = e3
% 231.83/42.96    (14)   ~ (e2 = e0)
% 231.83/42.96    (15)   ~ (e1 = e0)
% 231.83/42.96    (16)  op(e0, e1) = all_52_29
% 231.83/42.96    (17)   ~ (all_53_4 = e0)
% 231.83/42.96    (18)  op(all_52_29, all_52_29) = e1
% 231.83/42.96    (19)  op(e1, e1) = e2
% 231.83/42.96    (20)   ~ (e2 = e1)
% 231.83/42.96    (21)   ~ (all_53_4 = e3)
% 231.83/42.96  
% 231.83/42.96  Begin of proof
% 231.83/42.96  | 
% 231.83/42.96  | BETA: splitting (11) gives:
% 231.83/42.96  | 
% 231.83/42.96  | Case 1:
% 231.83/42.96  | | 
% 231.83/42.96  | |   (22)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) =
% 231.83/42.96  | |           e1)
% 231.83/42.96  | | 
% 231.83/42.96  | | BETA: splitting (22) gives:
% 231.83/42.96  | | 
% 231.83/42.96  | | Case 1:
% 231.83/42.96  | | | 
% 231.83/42.96  | | |   (23)  all_57_4 = e1 & op(e3, e1) = e1
% 231.83/42.96  | | | 
% 231.83/42.96  | | | ALPHA: (23) implies:
% 231.83/42.96  | | |   (24)  all_57_4 = e1
% 231.83/42.96  | | | 
% 231.83/42.96  | | | COMBINE_EQS: (7), (24) imply:
% 231.83/42.96  | | |   (25)  e1 = e0
% 231.83/42.96  | | | 
% 231.83/42.96  | | | SIMP: (25) implies:
% 231.83/42.96  | | |   (26)  e1 = e0
% 231.83/42.96  | | | 
% 231.83/42.96  | | | COMBINE_EQS: (5), (26) imply:
% 231.83/42.96  | | |   (27)  all_57_9 = e0
% 231.83/42.96  | | | 
% 231.83/42.96  | | | REF_CLOSE: (2), (3), (4), (7), (8), (9), (12), (14), (15), (20), (27) are
% 231.83/42.96  | | |            inconsistent by sub-proof #2436.
% 231.83/42.96  | | | 
% 231.83/42.96  | | Case 2:
% 231.83/42.96  | | | 
% 231.83/42.96  | | |   (28)  all_57_5 = e1 & op(e2, e1) = e1
% 231.83/42.96  | | | 
% 231.83/42.96  | | | REF_CLOSE: (2), (13), (28) are inconsistent by sub-proof #2376.
% 231.83/42.96  | | | 
% 231.83/42.96  | | End of split
% 231.83/42.96  | | 
% 231.83/42.96  | Case 2:
% 231.83/42.96  | | 
% 231.83/42.96  | |   (29)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) =
% 231.83/42.96  | |           e1)
% 231.83/42.96  | | 
% 231.83/42.96  | | BETA: splitting (29) gives:
% 231.83/42.96  | | 
% 231.83/42.96  | | Case 1:
% 231.83/42.96  | | | 
% 231.83/42.96  | | |   (30)  all_57_8 = e1 & op(e1, e1) = e1
% 231.83/42.96  | | | 
% 231.83/42.96  | | | ALPHA: (30) implies:
% 231.83/42.96  | | |   (31)  op(e1, e1) = e1
% 231.83/42.96  | | | 
% 231.83/42.96  | | | REF_CLOSE: (3), (19), (20), (31) are inconsistent by sub-proof #2423.
% 231.83/42.96  | | | 
% 231.83/42.96  | | Case 2:
% 231.83/42.96  | | | 
% 231.83/42.96  | | |   (32)  all_57_14 = e1 & op(e0, e1) = e1
% 231.83/42.96  | | | 
% 231.83/42.96  | | | ALPHA: (32) implies:
% 231.83/42.96  | | |   (33)  op(e0, e1) = e1
% 231.83/42.96  | | | 
% 231.83/42.96  | | | REF_CLOSE: (1), (3), (6), (10), (16), (17), (18), (19), (21), (33) are
% 231.83/42.96  | | |            inconsistent by sub-proof #1729.
% 231.83/42.96  | | | 
% 231.83/42.96  | | End of split
% 231.83/42.96  | | 
% 231.83/42.96  | End of split
% 231.83/42.96  | 
% 231.83/42.96  End of proof
% 231.83/42.96  
% 231.83/42.96  Sub-proof #1729 shows that the following formulas are inconsistent:
% 231.83/42.96  ----------------------------------------------------------------
% 231.83/42.96    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 231.83/42.96    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/42.96           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/42.96    (3)   ~ (all_53_4 = e1)
% 231.83/42.96    (4)  all_55_1 = all_53_4
% 231.83/42.96    (5)  op(e0, e1) = all_52_29
% 231.83/42.96    (6)   ~ (all_53_4 = e0)
% 231.83/42.96    (7)  op(all_52_29, all_52_29) = e1
% 231.83/42.96    (8)  op(e1, e1) = e2
% 231.83/42.96    (9)  op(e0, e1) = e1
% 231.83/42.96    (10)   ~ (all_53_4 = e3)
% 231.83/42.96  
% 231.83/42.96  Begin of proof
% 231.83/42.96  | 
% 231.83/42.96  | BETA: splitting (1) gives:
% 231.83/42.96  | 
% 231.83/42.96  | Case 1:
% 231.83/42.96  | | 
% 231.83/42.96  | |   (11)  all_55_1 = e3
% 231.83/42.96  | | 
% 231.83/42.96  | | COMBINE_EQS: (4), (11) imply:
% 231.83/42.96  | |   (12)  all_53_4 = e3
% 231.83/42.96  | | 
% 231.83/42.96  | | REDUCE: (10), (12) imply:
% 231.83/42.96  | |   (13)  $false
% 231.83/42.96  | | 
% 231.83/42.96  | | CLOSE: (13) is inconsistent.
% 231.83/42.96  | | 
% 231.83/42.96  | Case 2:
% 231.83/42.96  | | 
% 231.83/42.96  | |   (14)  all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 231.83/42.96  | | 
% 231.83/42.96  | | BETA: splitting (14) gives:
% 231.83/42.96  | | 
% 231.83/42.96  | | Case 1:
% 231.83/42.96  | | | 
% 231.83/42.96  | | |   (15)  all_55_1 = e2
% 231.83/42.96  | | | 
% 231.83/42.96  | | | COMBINE_EQS: (4), (15) imply:
% 231.83/42.96  | | |   (16)  all_53_4 = e2
% 231.83/42.96  | | | 
% 231.83/42.96  | | | REDUCE: (3), (16) imply:
% 231.83/42.96  | | |   (17)   ~ (e2 = e1)
% 231.83/42.96  | | | 
% 231.83/42.96  | | | GROUND_INST: instantiating (2) with e1, all_52_29, e1, e0, simplifying
% 231.83/42.96  | | |              with (5), (9) gives:
% 231.83/42.96  | | |   (18)  all_52_29 = e1
% 231.83/42.96  | | | 
% 231.83/42.96  | | | REDUCE: (7), (18) imply:
% 231.83/42.96  | | |   (19)  op(e1, e1) = e1
% 231.83/42.96  | | | 
% 231.83/42.96  | | | REF_CLOSE: (2), (8), (17), (19) are inconsistent by sub-proof #2423.
% 231.83/42.96  | | | 
% 231.83/42.96  | | Case 2:
% 231.83/42.96  | | | 
% 231.83/42.96  | | |   (20)  all_55_1 = e1 | all_55_1 = e0
% 231.83/42.96  | | | 
% 231.83/42.96  | | | REF_CLOSE: (3), (4), (6), (20) are inconsistent by sub-proof #1730.
% 231.83/42.96  | | | 
% 231.83/42.96  | | End of split
% 231.83/42.96  | | 
% 231.83/42.96  | End of split
% 231.83/42.96  | 
% 231.83/42.96  End of proof
% 231.83/42.96  
% 231.83/42.96  Sub-proof #1730 shows that the following formulas are inconsistent:
% 231.83/42.96  ----------------------------------------------------------------
% 231.83/42.96    (1)  all_55_1 = e1 | all_55_1 = e0
% 231.83/42.96    (2)  all_55_1 = all_53_4
% 231.83/42.96    (3)   ~ (all_53_4 = e1)
% 231.83/42.96    (4)   ~ (all_53_4 = e0)
% 231.83/42.96  
% 231.83/42.96  Begin of proof
% 231.83/42.96  | 
% 231.83/42.96  | BETA: splitting (1) gives:
% 231.83/42.96  | 
% 231.83/42.96  | Case 1:
% 231.83/42.96  | | 
% 231.83/42.96  | |   (5)  all_55_1 = e1
% 231.83/42.96  | | 
% 231.83/42.96  | | COMBINE_EQS: (2), (5) imply:
% 231.83/42.96  | |   (6)  all_53_4 = e1
% 231.83/42.96  | | 
% 231.83/42.96  | | REDUCE: (3), (6) imply:
% 231.83/42.96  | |   (7)  $false
% 231.83/42.96  | | 
% 231.83/42.96  | | CLOSE: (7) is inconsistent.
% 231.83/42.96  | | 
% 231.83/42.96  | Case 2:
% 231.83/42.96  | | 
% 231.83/42.96  | |   (8)  all_55_1 = e0
% 231.83/42.96  | | 
% 231.83/42.96  | | COMBINE_EQS: (2), (8) imply:
% 231.83/42.96  | |   (9)  all_53_4 = e0
% 231.83/42.96  | | 
% 231.83/42.96  | | REDUCE: (4), (9) imply:
% 231.83/42.96  | |   (10)  $false
% 231.83/42.96  | | 
% 231.83/42.96  | | CLOSE: (10) is inconsistent.
% 231.83/42.96  | | 
% 231.83/42.96  | End of split
% 231.83/42.96  | 
% 231.83/42.96  End of proof
% 231.83/42.96  
% 231.83/42.96  Sub-proof #1731 shows that the following formulas are inconsistent:
% 231.83/42.96  ----------------------------------------------------------------
% 231.83/42.96    (1)  op(e1, e3) = all_52_17
% 231.83/42.96    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 231.83/42.96    (3)   ~ (e3 = e1)
% 231.83/42.96    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/42.96           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/42.96    (5)   ~ (all_6_2 = e3)
% 231.83/42.96    (6)  op(e1, e1) = all_6_2
% 231.83/42.96    (7)  op(all_52_17, all_52_17) = e3
% 231.83/42.96    (8)   ~ (all_53_6 = e1)
% 231.83/42.96    (9)  all_55_10 = all_6_2
% 231.83/42.96    (10)  op(e1, e1) = e2
% 231.83/42.96    (11)  all_57_11 = e3
% 231.83/42.96    (12)   ~ (e2 = e1)
% 231.83/42.96    (13)  op(e1, e2) = all_53_6
% 231.83/42.96    (14)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 231.83/42.96          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 231.83/42.96  
% 231.83/42.96  Begin of proof
% 231.83/42.96  | 
% 231.83/42.96  | BETA: splitting (14) gives:
% 231.83/42.96  | 
% 231.83/42.96  | Case 1:
% 231.83/42.96  | | 
% 231.83/42.96  | |   (15)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) =
% 231.83/42.96  | |           e1)
% 231.83/42.96  | | 
% 231.83/42.96  | | BETA: splitting (15) gives:
% 231.83/42.96  | | 
% 231.83/42.96  | | Case 1:
% 231.83/42.96  | | | 
% 231.83/42.96  | | |   (16)  all_57_6 = e1 & op(e1, e3) = e1
% 231.83/42.96  | | | 
% 231.83/42.96  | | | ALPHA: (16) implies:
% 231.83/42.96  | | |   (17)  op(e1, e3) = e1
% 231.83/42.96  | | | 
% 231.83/42.96  | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (9), (17) are inconsistent by
% 231.83/42.96  | | |            sub-proof #1998.
% 231.83/42.96  | | | 
% 231.83/42.96  | | Case 2:
% 231.83/42.96  | | | 
% 231.83/42.96  | | |   (18)  all_57_7 = e1 & op(e1, e2) = e1
% 231.83/42.96  | | | 
% 231.83/42.96  | | | REF_CLOSE: (4), (8), (13), (18) are inconsistent by sub-proof #2265.
% 231.83/42.96  | | | 
% 231.83/42.96  | | End of split
% 231.83/42.96  | | 
% 231.83/42.96  | Case 2:
% 231.83/42.96  | | 
% 231.83/42.96  | |   (19)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) =
% 231.83/42.96  | |           e1)
% 231.83/42.96  | | 
% 231.83/42.96  | | REF_CLOSE: (3), (4), (10), (11), (12), (19) are inconsistent by sub-proof
% 231.83/42.96  | |            #2217.
% 231.83/42.96  | | 
% 231.83/42.96  | End of split
% 231.83/42.96  | 
% 231.83/42.96  End of proof
% 231.83/42.96  
% 231.83/42.96  Sub-proof #1732 shows that the following formulas are inconsistent:
% 231.83/42.96  ----------------------------------------------------------------
% 231.83/42.96    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 231.83/42.96    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.83/42.96         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.83/42.96    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.83/42.96         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.83/42.96    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.83/42.96         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.83/42.96    (5)   ~ (e3 = e1)
% 231.83/42.96    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/42.96           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/42.96    (7)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.83/42.96         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.83/42.96    (8)   ~ (all_6_2 = e3)
% 231.83/42.96    (9)   ~ (all_53_9 = e1)
% 231.83/42.96    (10)  op(e1, e1) = all_6_2
% 231.83/42.96    (11)  op(e2, e2) = e1
% 231.83/42.96    (12)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.83/42.96          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.83/42.96    (13)   ~ (all_53_4 = e1)
% 231.83/42.96    (14)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.83/42.96          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.83/42.96    (15)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.83/42.96          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.83/42.96    (16)   ~ (e3 = e2)
% 231.83/42.96    (17)  all_55_1 = all_53_4
% 231.83/42.96    (18)   ~ (e3 = e0)
% 231.83/42.96    (19)  op(e3, e3) = e3
% 231.83/42.96    (20)  all_57_15 = e3
% 231.83/42.96    (21)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.83/42.96          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.83/42.96            e1)
% 231.83/42.96    (22)  op(e3, e2) = all_53_4
% 231.83/42.96    (23)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 231.83/42.96          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 231.83/42.96    (24)   ~ (e2 = e0)
% 231.83/42.96    (25)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 231.83/42.96            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 231.83/42.96            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 231.83/42.96            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 231.83/42.96              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 231.83/42.96            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 231.83/42.96            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 231.83/42.96              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 231.83/42.96              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 231.83/42.96            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 231.83/42.96            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 231.83/42.96            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 231.83/42.96              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 231.83/42.96              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 231.83/42.96            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 231.83/42.96              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 231.83/42.96            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 231.83/42.96            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 231.83/42.96              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 231.83/42.96              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 231.83/42.96            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 231.83/42.96            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 231.83/42.96    (26)  all_57_3 = e1
% 231.83/42.96    (27)   ~ (e1 = e0)
% 231.83/42.96    (28)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.83/42.96          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.83/42.96    (29)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.83/42.96          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.83/42.96    (30)  op(e0, e0) = e3
% 231.83/42.96    (31)   ~ (all_53_4 = all_53_6)
% 231.83/42.96    (32)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.83/42.96          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.83/42.96            e2)
% 231.83/42.96    (33)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.83/42.96              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.83/42.96                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.83/42.96                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.83/42.96    (34)  ( ~ (all_16_0 = e0) & op(all_16_1, e2) = all_16_0 & op(e2, e1) =
% 231.83/42.96            all_16_1 & $i(all_16_0) & $i(all_16_1)) | ( ~ (all_16_1 = e3) & op(e2,
% 231.83/42.96              e1) = all_16_1 & $i(all_16_1))
% 231.83/42.96    (35)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.83/42.96          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.83/42.96    (36)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.83/42.96          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.83/42.96    (37)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 231.83/42.96          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 231.83/42.96    (38)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 231.83/42.96          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 231.83/42.96    (39)   ~ (e2 = e1)
% 231.83/42.96    (40)   ~ (all_26_2 = e1) | ( ~ (all_26_0 = e3) & op(all_26_1, e2) = all_26_0 &
% 231.83/42.96            op(e2, e1) = all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 =
% 231.83/42.96              e0) & op(e2, e1) = all_26_1 & $i(all_26_1))
% 231.83/42.96    (41)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.83/42.96          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.83/42.96    (42)  op(e2, e1) = all_53_9
% 231.83/42.96    (43)  op(e1, e2) = all_53_6
% 231.83/42.96    (44)  all_26_2 = e1
% 231.83/42.96    (45)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.83/42.96          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.83/42.96    (46)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.83/42.96          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.83/42.96    (47)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.83/42.96          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.83/42.96    (48)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.83/42.96          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.83/42.96  
% 231.83/42.96  Begin of proof
% 231.83/42.96  | 
% 231.83/42.96  | BETA: splitting (35) gives:
% 231.83/42.96  | 
% 231.83/42.96  | Case 1:
% 231.83/42.96  | | 
% 231.83/42.96  | |   (49)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 231.83/42.96  | |           e3)
% 231.83/42.96  | | 
% 231.83/42.96  | | BETA: splitting (49) gives:
% 231.83/42.96  | | 
% 231.83/42.96  | | Case 1:
% 231.83/42.96  | | | 
% 231.83/42.96  | | |   (50)  all_57_2 = e3 & op(e2, e3) = e3
% 231.83/42.96  | | | 
% 231.83/42.96  | | | ALPHA: (50) implies:
% 231.83/42.96  | | |   (51)  all_57_2 = e3
% 231.83/42.96  | | | 
% 231.83/42.96  | | | BETA: splitting (29) gives:
% 231.83/42.96  | | | 
% 231.83/42.96  | | | Case 1:
% 231.83/42.96  | | | | 
% 231.83/42.96  | | | |   (52)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2)
% 231.83/42.96  | | | |           = e3)
% 231.83/42.96  | | | | 
% 231.83/42.96  | | | | BETA: splitting (52) gives:
% 231.83/42.96  | | | | 
% 231.83/42.96  | | | | Case 1:
% 231.83/42.96  | | | | | 
% 231.83/42.96  | | | | |   (53)  all_57_1 = e3 & op(e3, e2) = e3
% 231.83/42.96  | | | | | 
% 231.83/42.96  | | | | | ALPHA: (53) implies:
% 231.83/42.96  | | | | |   (54)  all_57_1 = e3
% 231.83/42.96  | | | | | 
% 231.83/42.96  | | | | | BETA: splitting (28) gives:
% 231.83/42.96  | | | | | 
% 231.83/42.96  | | | | | Case 1:
% 231.83/42.96  | | | | | | 
% 231.83/42.96  | | | | | |   (55)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2,
% 231.83/42.96  | | | | | |             e1) = e3)
% 231.83/42.96  | | | | | | 
% 231.83/42.96  | | | | | | BETA: splitting (55) gives:
% 231.83/42.96  | | | | | | 
% 231.83/42.96  | | | | | | Case 1:
% 231.83/42.96  | | | | | | | 
% 231.83/42.96  | | | | | | |   (56)  all_57_4 = e3 & op(e3, e1) = e3
% 231.83/42.96  | | | | | | | 
% 231.83/42.96  | | | | | | | ALPHA: (56) implies:
% 231.83/42.96  | | | | | | |   (57)  all_57_4 = e3
% 231.83/42.96  | | | | | | | 
% 231.83/42.96  | | | | | | | REF_CLOSE: (5), (6), (12), (14), (15), (16), (18), (19), (24),
% 231.83/42.96  | | | | | | |            (27), (39), (54), (57) are inconsistent by sub-proof
% 231.83/42.96  | | | | | | |            #1806.
% 231.83/42.96  | | | | | | | 
% 231.83/42.96  | | | | | | Case 2:
% 231.83/42.96  | | | | | | | 
% 231.83/42.96  | | | | | | |   (58)  all_57_5 = e3 & op(e2, e1) = e3
% 231.83/42.96  | | | | | | | 
% 231.83/42.96  | | | | | | | ALPHA: (58) implies:
% 231.83/42.96  | | | | | | |   (59)  all_57_5 = e3
% 231.83/42.96  | | | | | | | 
% 231.83/42.96  | | | | | | | REF_CLOSE: (2), (5), (6), (11), (16), (18), (24), (27), (36),
% 231.83/42.96  | | | | | | |            (38), (39), (51), (59) are inconsistent by sub-proof
% 231.83/42.96  | | | | | | |            #1795.
% 231.83/42.96  | | | | | | | 
% 231.83/42.96  | | | | | | End of split
% 231.83/42.96  | | | | | | 
% 231.83/42.96  | | | | | Case 2:
% 231.83/42.96  | | | | | | 
% 231.83/42.96  | | | | | |   (60)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0,
% 231.83/42.96  | | | | | |             e1) = e3)
% 231.83/42.96  | | | | | | 
% 231.83/42.96  | | | | | | REF_CLOSE: (5), (6), (8), (10), (16), (18), (20), (21), (24), (27),
% 231.83/42.96  | | | | | |            (32), (33), (39), (60) are inconsistent by sub-proof
% 231.83/42.96  | | | | | |            #1794.
% 231.83/42.96  | | | | | | 
% 231.83/42.96  | | | | | End of split
% 231.83/42.96  | | | | | 
% 231.83/42.96  | | | | Case 2:
% 231.83/42.96  | | | | | 
% 231.83/42.96  | | | | |   (61)  all_57_3 = e3 & op(e2, e2) = e3
% 231.83/42.96  | | | | | 
% 231.83/42.96  | | | | | ALPHA: (61) implies:
% 231.83/42.96  | | | | |   (62)  op(e2, e2) = e3
% 231.83/42.96  | | | | | 
% 231.83/42.96  | | | | | REF_CLOSE: (5), (6), (11), (62) are inconsistent by sub-proof #1912.
% 231.83/42.96  | | | | | 
% 231.83/42.96  | | | | End of split
% 231.83/42.96  | | | | 
% 231.83/42.96  | | | Case 2:
% 231.83/42.96  | | | | 
% 231.83/42.96  | | | |   (63)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2)
% 231.83/42.96  | | | |           = e3)
% 231.83/42.96  | | | | 
% 231.83/42.96  | | | | BETA: splitting (63) gives:
% 231.83/42.96  | | | | 
% 231.83/42.96  | | | | Case 1:
% 231.83/42.96  | | | | | 
% 231.83/42.96  | | | | |   (64)  all_57_7 = e3 & op(e1, e2) = e3
% 231.83/42.96  | | | | | 
% 231.83/42.96  | | | | | ALPHA: (64) implies:
% 231.83/42.96  | | | | |   (65)  all_57_7 = e3
% 231.83/42.96  | | | | | 
% 231.83/42.96  | | | | | REF_CLOSE: (2), (4), (5), (6), (8), (10), (11), (12), (14), (15),
% 231.83/42.96  | | | | |            (16), (18), (19), (20), (21), (23), (24), (27), (28), (32),
% 231.83/42.96  | | | | |            (33), (36), (38), (39), (51), (65) are inconsistent by
% 231.83/42.96  | | | | |            sub-proof #1793.
% 231.83/42.96  | | | | | 
% 231.83/42.96  | | | | Case 2:
% 231.83/42.96  | | | | | 
% 231.83/42.96  | | | | |   (66)  all_57_13 = e3 & op(e0, e2) = e3
% 231.83/42.96  | | | | | 
% 231.83/42.96  | | | | | ALPHA: (66) implies:
% 231.83/42.96  | | | | |   (67)  all_57_13 = e3
% 231.83/42.96  | | | | | 
% 231.83/42.96  | | | | | REF_CLOSE: (5), (6), (16), (18), (20), (21), (24), (27), (30), (32),
% 231.83/42.96  | | | | |            (33), (39), (67) are inconsistent by sub-proof #1792.
% 231.83/42.96  | | | | | 
% 231.83/42.96  | | | | End of split
% 231.83/42.96  | | | | 
% 231.83/42.96  | | | End of split
% 231.83/42.96  | | | 
% 231.83/42.96  | | Case 2:
% 231.83/42.96  | | | 
% 231.83/42.96  | | |   (68)  all_57_3 = e3 & op(e2, e2) = e3
% 231.83/42.96  | | | 
% 231.83/42.96  | | | ALPHA: (68) implies:
% 231.83/42.96  | | |   (69)  op(e2, e2) = e3
% 231.83/42.96  | | | 
% 231.83/42.96  | | | REF_CLOSE: (5), (6), (11), (69) are inconsistent by sub-proof #1912.
% 231.83/42.96  | | | 
% 231.83/42.96  | | End of split
% 231.83/42.96  | | 
% 231.83/42.96  | Case 2:
% 231.83/42.96  | | 
% 231.83/42.96  | |   (70)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 231.83/42.96  | |           e3)
% 231.83/42.96  | | 
% 231.83/42.96  | | BETA: splitting (70) gives:
% 231.83/42.96  | | 
% 231.83/42.96  | | Case 1:
% 231.83/42.96  | | | 
% 231.83/42.96  | | |   (71)  all_57_5 = e3 & op(e2, e1) = e3
% 231.83/42.97  | | | 
% 231.83/42.97  | | | ALPHA: (71) implies:
% 231.83/42.97  | | |   (72)  all_57_5 = e3
% 231.83/42.97  | | |   (73)  op(e2, e1) = e3
% 231.83/42.97  | | | 
% 231.83/42.97  | | | BETA: splitting (37) gives:
% 231.83/42.97  | | | 
% 231.83/42.97  | | | Case 1:
% 231.83/42.97  | | | | 
% 231.83/42.97  | | | |   (74)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3)
% 231.83/42.97  | | | |           = e3)
% 231.83/42.97  | | | | 
% 231.83/42.97  | | | | BETA: splitting (74) gives:
% 231.83/42.97  | | | | 
% 231.83/42.97  | | | | Case 1:
% 231.83/42.97  | | | | | 
% 231.83/42.97  | | | | |   (75)  all_57_0 = e3 & op(e3, e3) = e3
% 231.83/42.97  | | | | | 
% 231.83/42.97  | | | | | ALPHA: (75) implies:
% 231.83/42.97  | | | | |   (76)  all_57_0 = e3
% 231.83/42.97  | | | | | 
% 231.83/42.97  | | | | | REF_CLOSE: (1), (3), (5), (6), (7), (8), (9), (10), (11), (13), (16),
% 231.83/42.97  | | | | |            (17), (18), (19), (20), (22), (24), (25), (27), (30), (31),
% 231.83/42.97  | | | | |            (33), (34), (39), (40), (41), (42), (43), (44), (45), (46),
% 231.83/42.97  | | | | |            (47), (73), (76) are inconsistent by sub-proof #1785.
% 231.83/42.97  | | | | | 
% 231.83/42.97  | | | | Case 2:
% 231.83/42.97  | | | | | 
% 231.83/42.97  | | | | |   (77)  all_57_2 = e3 & op(e2, e3) = e3
% 231.83/42.97  | | | | | 
% 231.83/42.97  | | | | | ALPHA: (77) implies:
% 231.83/42.97  | | | | |   (78)  all_57_2 = e3
% 231.83/42.97  | | | | | 
% 231.83/42.97  | | | | | REF_CLOSE: (2), (5), (6), (11), (16), (18), (24), (27), (36), (38),
% 231.83/42.97  | | | | |            (39), (72), (78) are inconsistent by sub-proof #1795.
% 231.83/42.97  | | | | | 
% 231.83/42.97  | | | | End of split
% 231.83/42.97  | | | | 
% 231.83/42.97  | | | Case 2:
% 231.83/42.97  | | | | 
% 231.83/42.97  | | | |   (79)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3)
% 231.83/42.97  | | | |           = e3)
% 231.83/42.97  | | | | 
% 231.83/42.97  | | | | BETA: splitting (79) gives:
% 231.83/42.97  | | | | 
% 231.83/42.97  | | | | Case 1:
% 231.83/42.97  | | | | | 
% 231.83/42.97  | | | | |   (80)  all_57_6 = e3 & op(e1, e3) = e3
% 231.83/42.97  | | | | | 
% 231.83/42.97  | | | | | ALPHA: (80) implies:
% 231.83/42.97  | | | | |   (81)  all_57_6 = e3
% 231.83/42.97  | | | | | 
% 231.83/42.97  | | | | | BETA: splitting (29) gives:
% 231.83/42.97  | | | | | 
% 231.83/42.97  | | | | | Case 1:
% 231.83/42.97  | | | | | | 
% 231.83/42.97  | | | | | |   (82)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2,
% 231.83/42.97  | | | | | |             e2) = e3)
% 231.83/42.97  | | | | | | 
% 231.83/42.97  | | | | | | BETA: splitting (82) gives:
% 231.83/42.97  | | | | | | 
% 231.83/42.97  | | | | | | Case 1:
% 231.83/42.97  | | | | | | | 
% 231.83/42.97  | | | | | | |   (83)  all_57_1 = e3 & op(e3, e2) = e3
% 231.83/42.97  | | | | | | | 
% 231.83/42.97  | | | | | | | ALPHA: (83) implies:
% 231.83/42.97  | | | | | | |   (84)  all_57_1 = e3
% 231.83/42.97  | | | | | | | 
% 231.83/42.97  | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (10), (11), (16),
% 231.83/42.97  | | | | | | |            (18), (19), (20), (23), (24), (26), (27), (29), (33),
% 231.83/42.97  | | | | | | |            (36), (38), (39), (41), (45), (46), (47), (48), (72),
% 231.83/42.97  | | | | | | |            (81), (84) are inconsistent by sub-proof #1770.
% 231.83/42.97  | | | | | | | 
% 231.83/42.97  | | | | | | Case 2:
% 231.83/42.97  | | | | | | | 
% 231.83/42.97  | | | | | | |   (85)  all_57_3 = e3 & op(e2, e2) = e3
% 231.83/42.97  | | | | | | | 
% 231.83/42.97  | | | | | | | ALPHA: (85) implies:
% 231.83/42.97  | | | | | | |   (86)  op(e2, e2) = e3
% 231.83/42.97  | | | | | | | 
% 231.83/42.97  | | | | | | | REF_CLOSE: (5), (6), (11), (86) are inconsistent by sub-proof
% 231.83/42.97  | | | | | | |            #1912.
% 231.83/42.97  | | | | | | | 
% 231.83/42.97  | | | | | | End of split
% 231.83/42.97  | | | | | | 
% 231.83/42.97  | | | | | Case 2:
% 231.83/42.97  | | | | | | 
% 231.83/42.97  | | | | | |   (87)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0,
% 231.83/42.97  | | | | | |             e2) = e3)
% 231.83/42.97  | | | | | | 
% 231.83/42.97  | | | | | | BETA: splitting (87) gives:
% 231.83/42.97  | | | | | | 
% 231.83/42.97  | | | | | | Case 1:
% 231.83/42.97  | | | | | | | 
% 231.83/42.97  | | | | | | |   (88)  all_57_7 = e3 & op(e1, e2) = e3
% 231.83/42.97  | | | | | | | 
% 231.83/42.97  | | | | | | | REF_CLOSE: (1), (6), (9), (11), (13), (16), (17), (18), (19),
% 231.83/42.97  | | | | | | |            (22), (25), (30), (31), (34), (40), (42), (43), (44),
% 231.83/42.97  | | | | | | |            (73), (88) are inconsistent by sub-proof #1787.
% 231.83/42.97  | | | | | | | 
% 231.83/42.97  | | | | | | Case 2:
% 231.83/42.97  | | | | | | | 
% 231.83/42.97  | | | | | | |   (89)  all_57_13 = e3 & op(e0, e2) = e3
% 231.83/42.97  | | | | | | | 
% 231.83/42.97  | | | | | | | ALPHA: (89) implies:
% 231.83/42.97  | | | | | | |   (90)  all_57_13 = e3
% 231.83/42.97  | | | | | | | 
% 231.83/42.97  | | | | | | | REF_CLOSE: (5), (6), (16), (18), (20), (21), (24), (27), (30),
% 231.83/42.97  | | | | | | |            (32), (33), (39), (90) are inconsistent by sub-proof
% 231.83/42.97  | | | | | | |            #1792.
% 231.83/42.97  | | | | | | | 
% 231.83/42.97  | | | | | | End of split
% 231.83/42.97  | | | | | | 
% 231.83/42.97  | | | | | End of split
% 231.83/42.97  | | | | | 
% 231.83/42.97  | | | | Case 2:
% 231.83/42.97  | | | | | 
% 231.83/42.97  | | | | |   (91)  all_57_12 = e3 & op(e0, e3) = e3
% 231.83/42.97  | | | | | 
% 231.83/42.97  | | | | | ALPHA: (91) implies:
% 231.83/42.97  | | | | |   (92)  all_57_12 = e3
% 231.83/42.97  | | | | | 
% 231.83/42.97  | | | | | BETA: splitting (29) gives:
% 231.83/42.97  | | | | | 
% 231.83/42.97  | | | | | Case 1:
% 231.83/42.97  | | | | | | 
% 231.83/42.97  | | | | | |   (93)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2,
% 231.83/42.97  | | | | | |             e2) = e3)
% 231.83/42.97  | | | | | | 
% 231.83/42.97  | | | | | | BETA: splitting (93) gives:
% 231.83/42.97  | | | | | | 
% 231.83/42.97  | | | | | | Case 1:
% 231.83/42.97  | | | | | | | 
% 231.83/42.97  | | | | | | |   (94)  all_57_1 = e3 & op(e3, e2) = e3
% 231.83/42.97  | | | | | | | 
% 231.83/42.97  | | | | | | | ALPHA: (94) implies:
% 231.83/42.97  | | | | | | |   (95)  all_57_1 = e3
% 231.83/42.97  | | | | | | | 
% 231.83/42.97  | | | | | | | BETA: splitting (21) gives:
% 231.83/42.97  | | | | | | | 
% 231.83/42.97  | | | | | | | Case 1:
% 231.83/42.97  | | | | | | | | 
% 231.83/42.97  | | | | | | | |   (96)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 &
% 231.83/42.97  | | | | | | | |           op(e0, e2) = e1)
% 231.83/42.97  | | | | | | | | 
% 231.83/42.97  | | | | | | | | BETA: splitting (96) gives:
% 231.83/42.97  | | | | | | | | 
% 231.83/42.97  | | | | | | | | Case 1:
% 231.83/42.97  | | | | | | | | | 
% 231.83/42.97  | | | | | | | | |   (97)  all_57_12 = e1 & op(e0, e3) = e1
% 231.83/42.97  | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | REF_CLOSE: (4), (5), (6), (11), (16), (18), (23), (24), (27),
% 231.83/42.97  | | | | | | | | |            (29), (39), (92), (95), (97) are inconsistent by
% 231.83/42.97  | | | | | | | | |            sub-proof #1769.
% 231.83/42.97  | | | | | | | | | 
% 231.83/42.97  | | | | | | | | Case 2:
% 231.83/42.97  | | | | | | | | | 
% 231.83/42.97  | | | | | | | | |   (98)  all_57_13 = e1 & op(e0, e2) = e1
% 231.83/42.97  | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | ALPHA: (98) implies:
% 231.83/42.97  | | | | | | | | |   (99)  all_57_13 = e1
% 231.83/42.97  | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | BETA: splitting (23) gives:
% 231.83/42.97  | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | Case 1:
% 231.83/42.97  | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | |   (100)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 231.83/42.97  | | | | | | | | | |            & op(e2, e2) = e0)
% 231.83/42.97  | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | BETA: splitting (100) gives:
% 231.83/42.97  | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | Case 1:
% 231.83/42.97  | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | |   (101)  all_57_1 = e0 & op(e3, e2) = e0
% 231.83/42.97  | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | REF_CLOSE: (18), (95), (101) are inconsistent by sub-proof
% 231.83/42.97  | | | | | | | | | | |            #1811.
% 231.83/42.97  | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | Case 2:
% 231.83/42.97  | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | |   (102)  all_57_3 = e0 & op(e2, e2) = e0
% 231.83/42.97  | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | ALPHA: (102) implies:
% 231.83/42.97  | | | | | | | | | | |   (103)  all_57_3 = e0
% 231.83/42.97  | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (10), (16),
% 231.83/42.97  | | | | | | | | | | |            (18), (19), (20), (24), (27), (33), (36), (39),
% 231.83/42.97  | | | | | | | | | | |            (41), (45), (46), (47), (48), (72), (95), (103)
% 231.83/42.97  | | | | | | | | | | |            are inconsistent by sub-proof #1777.
% 231.83/42.97  | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | End of split
% 231.83/42.97  | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | Case 2:
% 231.83/42.97  | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | |   (104)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0
% 231.83/42.97  | | | | | | | | | |            & op(e0, e2) = e0)
% 231.83/42.97  | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | BETA: splitting (104) gives:
% 231.83/42.97  | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | Case 1:
% 231.83/42.97  | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | |   (105)  all_57_7 = e0 & op(e1, e2) = e0
% 231.83/42.97  | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | ALPHA: (105) implies:
% 231.83/42.97  | | | | | | | | | | |   (106)  all_57_7 = e0
% 231.83/42.97  | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (10), (11), (16),
% 231.83/42.97  | | | | | | | | | | |            (18), (19), (20), (21), (24), (27), (29), (30),
% 231.83/42.97  | | | | | | | | | | |            (32), (33), (39), (41), (45), (47), (92), (106)
% 231.83/42.97  | | | | | | | | | | |            are inconsistent by sub-proof #1762.
% 231.83/42.97  | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | Case 2:
% 231.83/42.97  | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | |   (107)  all_57_13 = e0 & op(e0, e2) = e0
% 231.83/42.97  | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | REF_CLOSE: (4), (5), (16), (24), (26), (27), (39), (48),
% 231.83/42.97  | | | | | | | | | | |            (95), (99), (107) are inconsistent by sub-proof
% 231.83/42.97  | | | | | | | | | | |            #1757.
% 231.83/42.97  | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | End of split
% 231.83/42.97  | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | End of split
% 231.83/42.97  | | | | | | | | | 
% 231.83/42.97  | | | | | | | | End of split
% 231.83/42.97  | | | | | | | | 
% 231.83/42.97  | | | | | | | Case 2:
% 231.83/42.97  | | | | | | | | 
% 231.83/42.97  | | | | | | | |   (108)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 &
% 231.83/42.97  | | | | | | | |            op(e0, e0) = e1)
% 231.83/42.97  | | | | | | | | 
% 231.83/42.97  | | | | | | | | BETA: splitting (108) gives:
% 231.83/42.97  | | | | | | | | 
% 231.83/42.97  | | | | | | | | Case 1:
% 231.83/42.97  | | | | | | | | | 
% 231.83/42.97  | | | | | | | | |   (109)  all_57_14 = e1 & op(e0, e1) = e1
% 231.83/42.97  | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | ALPHA: (109) implies:
% 231.83/42.97  | | | | | | | | |   (110)  all_57_14 = e1
% 231.83/42.97  | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | BETA: splitting (46) gives:
% 231.83/42.97  | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | Case 1:
% 231.83/42.97  | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | |   (111)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 231.83/42.97  | | | | | | | | | |            & op(e2, e3) = e0)
% 231.83/42.97  | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | BETA: splitting (111) gives:
% 231.83/42.97  | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | Case 1:
% 231.83/42.97  | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | |   (112)  all_57_0 = e0 & op(e3, e3) = e0
% 231.83/42.97  | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | ALPHA: (112) implies:
% 231.83/42.97  | | | | | | | | | | |   (113)  op(e3, e3) = e0
% 231.83/42.97  | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | REF_CLOSE: (6), (18), (19), (113) are inconsistent by
% 231.83/42.97  | | | | | | | | | | |            sub-proof #2494.
% 231.83/42.97  | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | Case 2:
% 231.83/42.97  | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | |   (114)  all_57_2 = e0 & op(e2, e3) = e0
% 231.83/42.97  | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | ALPHA: (114) implies:
% 231.83/42.97  | | | | | | | | | | |   (115)  all_57_2 = e0
% 231.83/42.97  | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | REF_CLOSE: (2), (5), (6), (8), (10), (11), (16), (18), (20),
% 231.83/42.97  | | | | | | | | | | |            (21), (24), (27), (28), (30), (32), (33), (35),
% 231.83/42.97  | | | | | | | | | | |            (36), (38), (39), (41), (47), (72), (92), (110),
% 231.83/42.97  | | | | | | | | | | |            (115) are inconsistent by sub-proof #1739.
% 231.83/42.97  | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | End of split
% 231.83/42.97  | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | Case 2:
% 231.83/42.97  | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | |   (116)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0
% 231.83/42.97  | | | | | | | | | |            & op(e0, e3) = e0)
% 231.83/42.97  | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | BETA: splitting (116) gives:
% 231.83/42.97  | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | Case 1:
% 231.83/42.97  | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | |   (117)  all_57_6 = e0 & op(e1, e3) = e0
% 231.83/42.97  | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | ALPHA: (117) implies:
% 231.83/42.97  | | | | | | | | | | |   (118)  all_57_6 = e0
% 231.83/42.97  | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (10), (11), (16), (18),
% 231.83/42.97  | | | | | | | | | | |            (20), (23), (24), (27), (33), (39), (41), (47),
% 231.83/42.97  | | | | | | | | | | |            (48), (95), (118) are inconsistent by sub-proof
% 231.83/42.97  | | | | | | | | | | |            #1773.
% 231.83/42.97  | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | Case 2:
% 231.83/42.97  | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | |   (119)  all_57_12 = e0 & op(e0, e3) = e0
% 231.83/42.97  | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | ALPHA: (119) implies:
% 231.83/42.97  | | | | | | | | | | |   (120)  all_57_12 = e0
% 231.83/42.97  | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | REF_CLOSE: (18), (92), (120) are inconsistent by sub-proof
% 231.83/42.97  | | | | | | | | | | |            #2153.
% 231.83/42.97  | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | End of split
% 231.83/42.97  | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | End of split
% 231.83/42.97  | | | | | | | | | 
% 231.83/42.97  | | | | | | | | Case 2:
% 231.83/42.97  | | | | | | | | | 
% 231.83/42.97  | | | | | | | | |   (121)  all_57_15 = e1 & op(e0, e0) = e1
% 231.83/42.97  | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | ALPHA: (121) implies:
% 231.83/42.97  | | | | | | | | |   (122)  op(e0, e0) = e1
% 231.83/42.97  | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | REF_CLOSE: (5), (6), (30), (122) are inconsistent by sub-proof
% 231.83/42.97  | | | | | | | | |            #2183.
% 231.83/42.97  | | | | | | | | | 
% 231.83/42.97  | | | | | | | | End of split
% 231.83/42.97  | | | | | | | | 
% 231.83/42.97  | | | | | | | End of split
% 231.83/42.97  | | | | | | | 
% 231.83/42.97  | | | | | | Case 2:
% 231.83/42.97  | | | | | | | 
% 231.83/42.97  | | | | | | |   (123)  all_57_3 = e3 & op(e2, e2) = e3
% 231.83/42.97  | | | | | | | 
% 231.83/42.97  | | | | | | | ALPHA: (123) implies:
% 231.83/42.97  | | | | | | |   (124)  op(e2, e2) = e3
% 231.83/42.97  | | | | | | | 
% 231.83/42.97  | | | | | | | REF_CLOSE: (5), (6), (11), (124) are inconsistent by sub-proof
% 231.83/42.97  | | | | | | |            #1912.
% 231.83/42.97  | | | | | | | 
% 231.83/42.97  | | | | | | End of split
% 231.83/42.97  | | | | | | 
% 231.83/42.97  | | | | | Case 2:
% 231.83/42.97  | | | | | | 
% 231.83/42.97  | | | | | |   (125)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 &
% 231.83/42.97  | | | | | |            op(e0, e2) = e3)
% 231.83/42.97  | | | | | | 
% 231.83/42.97  | | | | | | BETA: splitting (125) gives:
% 231.83/42.97  | | | | | | 
% 231.83/42.97  | | | | | | Case 1:
% 231.83/42.97  | | | | | | | 
% 231.83/42.97  | | | | | | |   (126)  all_57_7 = e3 & op(e1, e2) = e3
% 231.83/42.97  | | | | | | | 
% 231.83/42.97  | | | | | | | ALPHA: (126) implies:
% 231.83/42.97  | | | | | | |   (127)  all_57_7 = e3
% 231.83/42.97  | | | | | | | 
% 231.83/42.97  | | | | | | | BETA: splitting (21) gives:
% 231.83/42.97  | | | | | | | 
% 231.83/42.97  | | | | | | | Case 1:
% 231.83/42.97  | | | | | | | | 
% 231.83/42.97  | | | | | | | |   (128)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 &
% 231.83/42.97  | | | | | | | |            op(e0, e2) = e1)
% 231.83/42.97  | | | | | | | | 
% 231.83/42.97  | | | | | | | | BETA: splitting (128) gives:
% 231.83/42.97  | | | | | | | | 
% 231.83/42.97  | | | | | | | | Case 1:
% 231.83/42.97  | | | | | | | | | 
% 231.83/42.97  | | | | | | | | |   (129)  all_57_12 = e1 & op(e0, e3) = e1
% 231.83/42.97  | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | REF_CLOSE: (5), (92), (129) are inconsistent by sub-proof
% 231.83/42.97  | | | | | | | | |            #2230.
% 231.83/42.97  | | | | | | | | | 
% 231.83/42.97  | | | | | | | | Case 2:
% 231.83/42.97  | | | | | | | | | 
% 231.83/42.97  | | | | | | | | |   (130)  all_57_13 = e1 & op(e0, e2) = e1
% 231.83/42.97  | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | ALPHA: (130) implies:
% 231.83/42.97  | | | | | | | | |   (131)  all_57_13 = e1
% 231.83/42.97  | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | BETA: splitting (23) gives:
% 231.83/42.97  | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | Case 1:
% 231.83/42.97  | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | |   (132)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 231.83/42.97  | | | | | | | | | |            & op(e2, e2) = e0)
% 231.83/42.97  | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | BETA: splitting (132) gives:
% 231.83/42.97  | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | Case 1:
% 231.83/42.97  | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | |   (133)  all_57_1 = e0 & op(e3, e2) = e0
% 231.83/42.97  | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | ALPHA: (133) implies:
% 231.83/42.97  | | | | | | | | | | |   (134)  all_57_1 = e0
% 231.83/42.97  | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | BETA: splitting (3) gives:
% 231.83/42.97  | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | Case 1:
% 231.83/42.97  | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | |   (135)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 231.83/42.97  | | | | | | | | | | | |            & op(e2, e3) = e1)
% 231.83/42.97  | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | BETA: splitting (135) gives:
% 231.83/42.97  | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | Case 1:
% 231.83/42.97  | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | |   (136)  all_57_0 = e1 & op(e3, e3) = e1
% 231.83/42.97  | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | ALPHA: (136) implies:
% 231.83/42.97  | | | | | | | | | | | | |   (137)  op(e3, e3) = e1
% 231.83/42.97  | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | REF_CLOSE: (5), (6), (19), (137) are inconsistent by
% 231.83/42.97  | | | | | | | | | | | | |            sub-proof #2495.
% 231.83/42.97  | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | Case 2:
% 231.83/42.97  | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | |   (138)  all_57_2 = e1 & op(e2, e3) = e1
% 231.83/42.97  | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | ALPHA: (138) implies:
% 231.83/42.97  | | | | | | | | | | | | |   (139)  all_57_2 = e1
% 231.83/42.97  | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | BETA: splitting (33) gives:
% 231.83/42.97  | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | Case 1:
% 231.83/42.97  | | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | |   (140)  all_57_15 = e0 & op(e0, e0) = e0
% 231.83/42.97  | | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | | ALPHA: (140) implies:
% 231.83/42.97  | | | | | | | | | | | | | |   (141)  op(e0, e0) = e0
% 231.83/42.97  | | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | | REF_CLOSE: (6), (18), (30), (141) are inconsistent by
% 231.83/42.97  | | | | | | | | | | | | | |            sub-proof #2304.
% 231.83/42.97  | | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | Case 2:
% 231.83/42.97  | | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | |   (142)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 231.83/42.97  | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 231.83/42.97  | | | | | | | | | | | | | |              op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 231.83/42.97  | | | | | | | | | | | | | |                e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 231.83/42.97  | | | | | | | | | | | | | |              e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 231.83/42.97  | | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | | ALPHA: (142) implies:
% 231.83/42.97  | | | | | | | | | | | | | |   (143)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 231.83/42.97  | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 231.83/42.97  | | | | | | | | | | | | | |              e1) = e0)
% 231.83/42.97  | | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | | BETA: splitting (143) gives:
% 231.83/42.97  | | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | | Case 1:
% 231.83/42.97  | | | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | | |   (144)  all_57_12 = e0 & op(e0, e3) = e0
% 231.83/42.97  | | | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | | | ALPHA: (144) implies:
% 231.83/42.97  | | | | | | | | | | | | | | |   (145)  all_57_12 = e0
% 231.83/42.97  | | | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | | | COMBINE_EQS: (92), (145) imply:
% 231.83/42.97  | | | | | | | | | | | | | | |   (146)  e3 = e0
% 231.83/42.97  | | | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | | | SIMP: (146) implies:
% 231.83/42.97  | | | | | | | | | | | | | | |   (147)  e3 = e0
% 231.83/42.97  | | | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | | | COMBINE_EQS: (127), (147) imply:
% 231.83/42.97  | | | | | | | | | | | | | | |   (148)  all_57_7 = e0
% 231.83/42.97  | | | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (10), (11), (16),
% 231.83/42.97  | | | | | | | | | | | | | | |            (18), (19), (20), (21), (24), (27), (29), (30),
% 231.83/42.97  | | | | | | | | | | | | | | |            (32), (33), (39), (41), (45), (47), (92), (148)
% 231.83/42.97  | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1762.
% 231.83/42.97  | | | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | | Case 2:
% 231.83/42.97  | | | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | | |   (149)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 231.83/42.97  | | | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 231.83/42.97  | | | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | | | BETA: splitting (149) gives:
% 231.83/42.97  | | | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | | | Case 1:
% 231.83/42.97  | | | | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | | | |   (150)  all_57_13 = e0 & op(e0, e2) = e0
% 231.83/42.97  | | | | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | | | | ALPHA: (150) implies:
% 231.83/42.97  | | | | | | | | | | | | | | | |   (151)  all_57_13 = e0
% 231.83/42.97  | | | | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | | | | COMBINE_EQS: (131), (151) imply:
% 231.83/42.97  | | | | | | | | | | | | | | | |   (152)  e1 = e0
% 231.83/42.97  | | | | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | | | | COMBINE_EQS: (26), (152) imply:
% 231.83/42.97  | | | | | | | | | | | | | | | |   (153)  all_57_3 = e0
% 231.83/42.97  | | | | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | | | | COMBINE_EQS: (139), (152) imply:
% 231.83/42.97  | | | | | | | | | | | | | | | |   (154)  all_57_2 = e0
% 231.83/42.97  | | | | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | | | | REF_CLOSE: (2), (5), (16), (24), (27), (36), (39), (72),
% 231.83/42.97  | | | | | | | | | | | | | | | |            (153), (154) are inconsistent by sub-proof #2253.
% 231.83/42.97  | | | | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | | | Case 2:
% 231.83/42.97  | | | | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | | | |   (155)  all_57_14 = e0 & op(e0, e1) = e0
% 231.83/42.97  | | | | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | | | | ALPHA: (155) implies:
% 231.83/42.97  | | | | | | | | | | | | | | | |   (156)  all_57_14 = e0
% 231.83/42.97  | | | | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (11), (16), (18), (20), (21), (24),
% 231.83/42.97  | | | | | | | | | | | | | | | |            (27), (29), (30), (32), (39), (131), (134), (143),
% 231.83/42.97  | | | | | | | | | | | | | | | |            (156) are inconsistent by sub-proof #1736.
% 231.83/42.97  | | | | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | | | End of split
% 231.83/42.97  | | | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | | End of split
% 231.83/42.97  | | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | End of split
% 231.83/42.97  | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | End of split
% 231.83/42.97  | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | Case 2:
% 231.83/42.97  | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | |   (157)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 231.83/42.97  | | | | | | | | | | | |            e1 & op(e0, e3) = e1)
% 231.83/42.97  | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | BETA: splitting (157) gives:
% 231.83/42.97  | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | Case 1:
% 231.83/42.97  | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | |   (158)  all_57_6 = e1 & op(e1, e3) = e1
% 231.83/42.97  | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | ALPHA: (158) implies:
% 231.83/42.97  | | | | | | | | | | | | |   (159)  all_57_6 = e1
% 231.83/42.97  | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | BETA: splitting (33) gives:
% 231.83/42.97  | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | Case 1:
% 231.83/42.97  | | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | |   (160)  all_57_15 = e0 & op(e0, e0) = e0
% 231.83/42.97  | | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | | ALPHA: (160) implies:
% 231.83/42.97  | | | | | | | | | | | | | |   (161)  op(e0, e0) = e0
% 231.83/42.97  | | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | | REF_CLOSE: (6), (18), (30), (161) are inconsistent by
% 231.83/42.97  | | | | | | | | | | | | | |            sub-proof #2304.
% 231.83/42.97  | | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | Case 2:
% 231.83/42.97  | | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | |   (162)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 231.83/42.97  | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 231.83/42.97  | | | | | | | | | | | | | |              op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 231.83/42.97  | | | | | | | | | | | | | |                e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 231.83/42.97  | | | | | | | | | | | | | |              e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 231.83/42.97  | | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | | ALPHA: (162) implies:
% 231.83/42.97  | | | | | | | | | | | | | |   (163)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 231.83/42.97  | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 231.83/42.97  | | | | | | | | | | | | | |              e1) = e0)
% 231.83/42.97  | | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | | BETA: splitting (163) gives:
% 231.83/42.97  | | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | | Case 1:
% 231.83/42.97  | | | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | | |   (164)  all_57_12 = e0 & op(e0, e3) = e0
% 231.83/42.97  | | | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | | | ALPHA: (164) implies:
% 231.83/42.97  | | | | | | | | | | | | | | |   (165)  all_57_12 = e0
% 231.83/42.97  | | | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | | | COMBINE_EQS: (92), (165) imply:
% 231.83/42.97  | | | | | | | | | | | | | | |   (166)  e3 = e0
% 231.83/42.97  | | | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | | | COMBINE_EQS: (127), (166) imply:
% 231.83/42.97  | | | | | | | | | | | | | | |   (167)  all_57_7 = e0
% 231.83/42.97  | | | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (10), (16), (18), (20), (24),
% 231.83/42.97  | | | | | | | | | | | | | | |            (27), (33), (39), (41), (47), (159), (167) are
% 231.83/42.97  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1735.
% 231.83/42.97  | | | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | | Case 2:
% 231.83/42.97  | | | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | | |   (168)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 231.83/42.97  | | | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 231.83/42.97  | | | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | | | BETA: splitting (168) gives:
% 231.83/42.97  | | | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | | | Case 1:
% 231.83/42.97  | | | | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | | | |   (169)  all_57_13 = e0 & op(e0, e2) = e0
% 231.83/42.97  | | | | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | | | | ALPHA: (169) implies:
% 231.83/42.97  | | | | | | | | | | | | | | | |   (170)  all_57_13 = e0
% 231.83/42.97  | | | | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | | | | COMBINE_EQS: (131), (170) imply:
% 231.83/42.97  | | | | | | | | | | | | | | | |   (171)  e1 = e0
% 231.83/42.97  | | | | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | | | | SIMP: (171) implies:
% 231.83/42.97  | | | | | | | | | | | | | | | |   (172)  e1 = e0
% 231.83/42.97  | | | | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | | | | COMBINE_EQS: (26), (172) imply:
% 231.83/42.97  | | | | | | | | | | | | | | | |   (173)  all_57_3 = e0
% 231.83/42.97  | | | | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (12), (14), (15), (16), (18), (19),
% 231.83/42.97  | | | | | | | | | | | | | | | |            (24), (27), (39), (48), (127), (170), (173) are
% 231.83/42.97  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2091.
% 231.83/42.97  | | | | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | | | Case 2:
% 231.83/42.97  | | | | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | | | |   (174)  all_57_14 = e0 & op(e0, e1) = e0
% 231.83/42.97  | | | | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | | | | ALPHA: (174) implies:
% 231.83/42.97  | | | | | | | | | | | | | | | |   (175)  all_57_14 = e0
% 231.83/42.97  | | | | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (11), (16), (18), (20), (21), (24),
% 231.83/42.97  | | | | | | | | | | | | | | | |            (27), (29), (30), (32), (39), (131), (134), (163),
% 231.83/42.97  | | | | | | | | | | | | | | | |            (175) are inconsistent by sub-proof #1736.
% 231.83/42.97  | | | | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | | | End of split
% 231.83/42.97  | | | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | | End of split
% 231.83/42.97  | | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | End of split
% 231.83/42.97  | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | Case 2:
% 231.83/42.97  | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | |   (176)  all_57_12 = e1 & op(e0, e3) = e1
% 231.83/42.97  | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | REF_CLOSE: (5), (92), (176) are inconsistent by sub-proof
% 231.83/42.97  | | | | | | | | | | | | |            #2230.
% 231.83/42.97  | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | End of split
% 231.83/42.97  | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | End of split
% 231.83/42.97  | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | Case 2:
% 231.83/42.97  | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | |   (177)  all_57_3 = e0 & op(e2, e2) = e0
% 231.83/42.97  | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | ALPHA: (177) implies:
% 231.83/42.97  | | | | | | | | | | |   (178)  op(e2, e2) = e0
% 231.83/42.97  | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | REF_CLOSE: (6), (11), (27), (178) are inconsistent by
% 231.83/42.97  | | | | | | | | | | |            sub-proof #2352.
% 231.83/42.97  | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | End of split
% 231.83/42.97  | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | Case 2:
% 231.83/42.97  | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | |   (179)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0
% 231.83/42.97  | | | | | | | | | |            & op(e0, e2) = e0)
% 231.83/42.97  | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | BETA: splitting (179) gives:
% 231.83/42.97  | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | Case 1:
% 231.83/42.97  | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | |   (180)  all_57_7 = e0 & op(e1, e2) = e0
% 231.83/42.97  | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | ALPHA: (180) implies:
% 231.83/42.97  | | | | | | | | | | |   (181)  all_57_7 = e0
% 231.83/42.97  | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (10), (11), (16),
% 231.83/42.97  | | | | | | | | | | |            (18), (19), (20), (21), (24), (27), (29), (30),
% 231.83/42.97  | | | | | | | | | | |            (32), (33), (39), (41), (45), (47), (92), (181)
% 231.83/42.97  | | | | | | | | | | |            are inconsistent by sub-proof #1762.
% 231.83/42.97  | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | Case 2:
% 231.83/42.97  | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | |   (182)  all_57_13 = e0 & op(e0, e2) = e0
% 231.83/42.97  | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | ALPHA: (182) implies:
% 231.83/42.97  | | | | | | | | | | |   (183)  all_57_13 = e0
% 231.83/42.97  | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | COMBINE_EQS: (131), (183) imply:
% 231.83/42.97  | | | | | | | | | | |   (184)  e1 = e0
% 231.83/42.97  | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | COMBINE_EQS: (26), (184) imply:
% 231.83/42.97  | | | | | | | | | | |   (185)  all_57_3 = e0
% 231.83/42.97  | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (12), (14), (15), (16), (18), (19),
% 231.83/42.97  | | | | | | | | | | |            (24), (27), (39), (48), (127), (183), (185) are
% 231.83/42.97  | | | | | | | | | | |            inconsistent by sub-proof #2091.
% 231.83/42.97  | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | End of split
% 231.83/42.97  | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | End of split
% 231.83/42.97  | | | | | | | | | 
% 231.83/42.97  | | | | | | | | End of split
% 231.83/42.97  | | | | | | | | 
% 231.83/42.97  | | | | | | | Case 2:
% 231.83/42.97  | | | | | | | | 
% 231.83/42.97  | | | | | | | |   (186)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 &
% 231.83/42.97  | | | | | | | |            op(e0, e0) = e1)
% 231.83/42.97  | | | | | | | | 
% 231.83/42.97  | | | | | | | | BETA: splitting (186) gives:
% 231.83/42.97  | | | | | | | | 
% 231.83/42.97  | | | | | | | | Case 1:
% 231.83/42.97  | | | | | | | | | 
% 231.83/42.97  | | | | | | | | |   (187)  all_57_14 = e1 & op(e0, e1) = e1
% 231.83/42.97  | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | ALPHA: (187) implies:
% 231.83/42.97  | | | | | | | | |   (188)  all_57_14 = e1
% 231.83/42.97  | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | BETA: splitting (3) gives:
% 231.83/42.97  | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | Case 1:
% 231.83/42.97  | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | |   (189)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 231.83/42.97  | | | | | | | | | |            & op(e2, e3) = e1)
% 231.83/42.97  | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | BETA: splitting (189) gives:
% 231.83/42.97  | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | Case 1:
% 231.83/42.97  | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | |   (190)  all_57_0 = e1 & op(e3, e3) = e1
% 231.83/42.97  | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | ALPHA: (190) implies:
% 231.83/42.97  | | | | | | | | | | |   (191)  op(e3, e3) = e1
% 231.83/42.97  | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | REF_CLOSE: (5), (6), (19), (191) are inconsistent by
% 231.83/42.97  | | | | | | | | | | |            sub-proof #2495.
% 231.83/42.97  | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | Case 2:
% 231.83/42.97  | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | |   (192)  all_57_2 = e1 & op(e2, e3) = e1
% 231.83/42.97  | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | ALPHA: (192) implies:
% 231.83/42.97  | | | | | | | | | | |   (193)  all_57_2 = e1
% 231.83/42.97  | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | BETA: splitting (36) gives:
% 231.83/42.97  | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | Case 1:
% 231.83/42.97  | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | |   (194)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 231.83/42.97  | | | | | | | | | | | |            & op(e2, e2) = e2)
% 231.83/42.97  | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | REF_CLOSE: (6), (11), (39), (193), (194) are inconsistent by
% 231.83/42.97  | | | | | | | | | | | |            sub-proof #1828.
% 231.83/42.97  | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | Case 2:
% 231.83/42.97  | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | |   (195)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 231.83/42.97  | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 231.83/42.97  | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | BETA: splitting (195) gives:
% 231.83/42.97  | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | Case 1:
% 231.83/42.97  | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | |   (196)  all_57_5 = e2 & op(e2, e1) = e2
% 231.83/42.97  | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | REF_CLOSE: (16), (72), (196) are inconsistent by sub-proof
% 231.83/42.97  | | | | | | | | | | | | |            #2425.
% 231.83/42.97  | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | Case 2:
% 231.83/42.97  | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | |   (197)  all_57_10 = e2 & op(e2, e0) = e2
% 231.83/42.97  | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | ALPHA: (197) implies:
% 231.83/42.97  | | | | | | | | | | | | |   (198)  all_57_10 = e2
% 231.83/42.97  | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | REF_CLOSE: (2), (5), (6), (8), (10), (11), (16), (18), (20),
% 231.83/42.97  | | | | | | | | | | | | |            (21), (24), (27), (28), (30), (32), (33), (35),
% 231.83/42.97  | | | | | | | | | | | | |            (38), (39), (41), (47), (72), (92), (188), (198)
% 231.83/42.97  | | | | | | | | | | | | |            are inconsistent by sub-proof #1740.
% 231.83/42.97  | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | End of split
% 231.83/42.97  | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | End of split
% 231.83/42.97  | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | End of split
% 231.83/42.97  | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | Case 2:
% 231.83/42.97  | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | |   (199)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1
% 231.83/42.97  | | | | | | | | | |            & op(e0, e3) = e1)
% 231.83/42.97  | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | BETA: splitting (199) gives:
% 231.83/42.97  | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | Case 1:
% 231.83/42.97  | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | |   (200)  all_57_6 = e1 & op(e1, e3) = e1
% 231.83/42.97  | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | ALPHA: (200) implies:
% 231.83/42.97  | | | | | | | | | | |   (201)  all_57_6 = e1
% 231.83/42.97  | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | BETA: splitting (46) gives:
% 231.83/42.97  | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | Case 1:
% 231.83/42.97  | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | |   (202)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 231.83/42.97  | | | | | | | | | | | |            & op(e2, e3) = e0)
% 231.83/42.97  | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | BETA: splitting (202) gives:
% 231.83/42.97  | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | Case 1:
% 231.83/42.97  | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | |   (203)  all_57_0 = e0 & op(e3, e3) = e0
% 231.83/42.97  | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | ALPHA: (203) implies:
% 231.83/42.97  | | | | | | | | | | | | |   (204)  op(e3, e3) = e0
% 231.83/42.97  | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | REF_CLOSE: (6), (18), (19), (204) are inconsistent by
% 231.83/42.97  | | | | | | | | | | | | |            sub-proof #2494.
% 231.83/42.97  | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | Case 2:
% 231.83/42.97  | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | |   (205)  all_57_2 = e0 & op(e2, e3) = e0
% 231.83/42.97  | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | ALPHA: (205) implies:
% 231.83/42.97  | | | | | | | | | | | | |   (206)  all_57_2 = e0
% 231.83/42.97  | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | REF_CLOSE: (2), (5), (6), (8), (10), (11), (16), (18), (20),
% 231.83/42.97  | | | | | | | | | | | | |            (21), (24), (27), (28), (30), (32), (33), (35),
% 231.83/42.97  | | | | | | | | | | | | |            (36), (38), (39), (41), (47), (72), (92), (188),
% 231.83/42.97  | | | | | | | | | | | | |            (206) are inconsistent by sub-proof #1739.
% 231.83/42.97  | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | End of split
% 231.83/42.97  | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | Case 2:
% 231.83/42.97  | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | |   (207)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 231.83/42.97  | | | | | | | | | | | |            e0 & op(e0, e3) = e0)
% 231.83/42.97  | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | BETA: splitting (207) gives:
% 231.83/42.97  | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | Case 1:
% 231.83/42.97  | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | |   (208)  all_57_6 = e0 & op(e1, e3) = e0
% 231.83/42.97  | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | ALPHA: (208) implies:
% 231.83/42.97  | | | | | | | | | | | | |   (209)  all_57_6 = e0
% 231.83/42.97  | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | COMBINE_EQS: (201), (209) imply:
% 231.83/42.97  | | | | | | | | | | | | |   (210)  e1 = e0
% 231.83/42.97  | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | COMBINE_EQS: (188), (210) imply:
% 231.83/42.97  | | | | | | | | | | | | |   (211)  all_57_14 = e0
% 231.83/42.97  | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | REF_CLOSE: (5), (16), (20), (21), (24), (27), (32), (39),
% 231.83/42.97  | | | | | | | | | | | | |            (92), (211) are inconsistent by sub-proof #1763.
% 231.83/42.97  | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | Case 2:
% 231.83/42.97  | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | |   (212)  all_57_12 = e0 & op(e0, e3) = e0
% 231.83/42.97  | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | ALPHA: (212) implies:
% 231.83/42.97  | | | | | | | | | | | | |   (213)  all_57_12 = e0
% 231.83/42.97  | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | COMBINE_EQS: (92), (213) imply:
% 231.83/42.97  | | | | | | | | | | | | |   (214)  e3 = e0
% 231.83/42.97  | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | SIMP: (214) implies:
% 231.83/42.97  | | | | | | | | | | | | |   (215)  e3 = e0
% 231.83/42.97  | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | COMBINE_EQS: (127), (215) imply:
% 231.83/42.97  | | | | | | | | | | | | |   (216)  all_57_7 = e0
% 231.83/42.97  | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (10), (16), (18), (20), (24),
% 231.83/42.97  | | | | | | | | | | | | |            (27), (33), (39), (41), (47), (201), (216) are
% 231.83/42.97  | | | | | | | | | | | | |            inconsistent by sub-proof #1735.
% 231.83/42.97  | | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | | End of split
% 231.83/42.97  | | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | End of split
% 231.83/42.97  | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | Case 2:
% 231.83/42.97  | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | |   (217)  all_57_12 = e1 & op(e0, e3) = e1
% 231.83/42.97  | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | | REF_CLOSE: (5), (92), (217) are inconsistent by sub-proof
% 231.83/42.97  | | | | | | | | | | |            #2230.
% 231.83/42.97  | | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | | End of split
% 231.83/42.97  | | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | End of split
% 231.83/42.97  | | | | | | | | | 
% 231.83/42.97  | | | | | | | | Case 2:
% 231.83/42.97  | | | | | | | | | 
% 231.83/42.97  | | | | | | | | |   (218)  all_57_15 = e1 & op(e0, e0) = e1
% 231.83/42.97  | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | ALPHA: (218) implies:
% 231.83/42.97  | | | | | | | | |   (219)  op(e0, e0) = e1
% 231.83/42.97  | | | | | | | | | 
% 231.83/42.97  | | | | | | | | | REF_CLOSE: (5), (6), (30), (219) are inconsistent by sub-proof
% 231.83/42.97  | | | | | | | | |            #2183.
% 231.83/42.97  | | | | | | | | | 
% 231.83/42.97  | | | | | | | | End of split
% 231.83/42.97  | | | | | | | | 
% 231.83/42.97  | | | | | | | End of split
% 231.83/42.97  | | | | | | | 
% 231.83/42.97  | | | | | | Case 2:
% 231.83/42.97  | | | | | | | 
% 231.83/42.97  | | | | | | |   (220)  all_57_13 = e3 & op(e0, e2) = e3
% 231.83/42.97  | | | | | | | 
% 231.83/42.97  | | | | | | | ALPHA: (220) implies:
% 231.83/42.97  | | | | | | |   (221)  all_57_13 = e3
% 231.83/42.97  | | | | | | | 
% 231.83/42.97  | | | | | | | REF_CLOSE: (5), (16), (20), (21), (24), (27), (32), (33), (39),
% 231.83/42.97  | | | | | | |            (92), (221) are inconsistent by sub-proof #1733.
% 231.83/42.97  | | | | | | | 
% 231.83/42.97  | | | | | | End of split
% 231.83/42.97  | | | | | | 
% 231.83/42.97  | | | | | End of split
% 231.83/42.97  | | | | | 
% 231.83/42.97  | | | | End of split
% 231.83/42.97  | | | | 
% 231.83/42.97  | | | End of split
% 231.83/42.97  | | | 
% 231.83/42.97  | | Case 2:
% 231.83/42.97  | | | 
% 231.83/42.97  | | |   (222)  all_57_10 = e3 & op(e2, e0) = e3
% 231.83/42.97  | | | 
% 231.83/42.97  | | | ALPHA: (222) implies:
% 231.83/42.97  | | |   (223)  all_57_10 = e3
% 231.83/42.97  | | | 
% 231.83/42.97  | | | REF_CLOSE: (5), (6), (16), (18), (20), (24), (27), (30), (33), (39), (41),
% 231.83/42.97  | | |            (47), (223) are inconsistent by sub-proof #1746.
% 231.83/42.97  | | | 
% 231.83/42.97  | | End of split
% 231.83/42.97  | | 
% 231.83/42.97  | End of split
% 231.83/42.97  | 
% 231.83/42.97  End of proof
% 231.83/42.97  
% 231.83/42.97  Sub-proof #1733 shows that the following formulas are inconsistent:
% 231.83/42.97  ----------------------------------------------------------------
% 231.83/42.97    (1)   ~ (e3 = e1)
% 231.83/42.97    (2)   ~ (e3 = e2)
% 231.83/42.97    (3)  all_57_15 = e3
% 231.83/42.97    (4)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 231.83/42.97         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.83/42.97    (5)   ~ (e2 = e0)
% 231.83/42.97    (6)   ~ (e1 = e0)
% 231.83/42.97    (7)  all_57_12 = e3
% 231.83/42.97    (8)  all_57_13 = e3
% 231.83/42.97    (9)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2) |
% 231.83/42.97         (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.83/42.97    (10)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.83/42.97              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.83/42.97                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.83/42.97                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.83/42.97    (11)   ~ (e2 = e1)
% 231.83/42.97  
% 231.83/42.97  Begin of proof
% 231.83/42.97  | 
% 231.83/42.97  | BETA: splitting (9) gives:
% 231.83/42.97  | 
% 231.83/42.97  | Case 1:
% 231.83/42.97  | | 
% 231.83/42.97  | |   (12)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 231.83/42.97  | |           e2)
% 231.83/42.97  | | 
% 231.83/42.97  | | BETA: splitting (12) gives:
% 231.83/42.97  | | 
% 231.83/42.97  | | Case 1:
% 231.83/42.97  | | | 
% 231.83/42.97  | | |   (13)  all_57_12 = e2 & op(e0, e3) = e2
% 231.83/42.97  | | | 
% 231.83/42.97  | | | ALPHA: (13) implies:
% 231.83/42.97  | | |   (14)  all_57_12 = e2
% 231.83/42.97  | | | 
% 231.83/42.97  | | | REF_CLOSE: (2), (7), (14) are inconsistent by sub-proof #2392.
% 231.83/42.97  | | | 
% 231.83/42.97  | | Case 2:
% 231.83/42.97  | | | 
% 231.83/42.97  | | |   (15)  all_57_13 = e2 & op(e0, e2) = e2
% 231.83/42.97  | | | 
% 231.83/42.97  | | | ALPHA: (15) implies:
% 231.83/42.97  | | |   (16)  all_57_13 = e2
% 231.83/42.97  | | | 
% 231.83/42.97  | | | REF_CLOSE: (2), (8), (16) are inconsistent by sub-proof #2203.
% 231.83/42.97  | | | 
% 231.83/42.97  | | End of split
% 231.83/42.97  | | 
% 231.83/42.98  | Case 2:
% 231.83/42.98  | | 
% 231.83/42.98  | |   (17)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.83/42.98  | |           e2)
% 231.83/42.98  | | 
% 231.83/42.98  | | BETA: splitting (17) gives:
% 231.83/42.98  | | 
% 231.83/42.98  | | Case 1:
% 231.83/42.98  | | | 
% 231.83/42.98  | | |   (18)  all_57_14 = e2 & op(e0, e1) = e2
% 231.83/42.98  | | | 
% 231.83/42.98  | | | ALPHA: (18) implies:
% 231.83/42.98  | | |   (19)  all_57_14 = e2
% 231.83/42.98  | | | 
% 231.83/42.98  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (19)
% 231.83/42.98  | | |            are inconsistent by sub-proof #1734.
% 231.83/42.98  | | | 
% 231.83/42.98  | | Case 2:
% 231.83/42.98  | | | 
% 231.83/42.98  | | |   (20)  all_57_15 = e2 & op(e0, e0) = e2
% 231.83/42.98  | | | 
% 231.83/42.98  | | | REF_CLOSE: (2), (3), (20) are inconsistent by sub-proof #2323.
% 231.83/42.98  | | | 
% 231.83/42.98  | | End of split
% 231.83/42.98  | | 
% 231.83/42.98  | End of split
% 231.83/42.98  | 
% 231.83/42.98  End of proof
% 231.83/42.98  
% 231.83/42.98  Sub-proof #1734 shows that the following formulas are inconsistent:
% 231.83/42.98  ----------------------------------------------------------------
% 231.83/42.98    (1)   ~ (e3 = e1)
% 231.83/42.98    (2)   ~ (e3 = e2)
% 231.83/42.98    (3)  all_57_15 = e3
% 231.83/42.98    (4)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 231.83/42.98         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.83/42.98    (5)   ~ (e2 = e0)
% 231.83/42.98    (6)   ~ (e1 = e0)
% 231.83/42.98    (7)  all_57_12 = e3
% 231.83/42.98    (8)  all_57_14 = e2
% 231.83/42.98    (9)  all_57_13 = e3
% 231.83/42.98    (10)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.83/42.98          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.83/42.98            e2)
% 231.83/42.98    (11)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.83/42.98              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.83/42.98                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.83/42.98                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.83/42.98    (12)   ~ (e2 = e1)
% 231.83/42.98  
% 231.83/42.98  Begin of proof
% 231.83/42.98  | 
% 231.83/42.98  | BETA: splitting (11) gives:
% 231.83/42.98  | 
% 231.83/42.98  | Case 1:
% 231.83/42.98  | | 
% 231.83/42.98  | |   (13)  all_57_15 = e0 & op(e0, e0) = e0
% 231.83/42.98  | | 
% 231.83/42.98  | | ALPHA: (13) implies:
% 231.83/42.98  | |   (14)  all_57_15 = e0
% 231.83/42.98  | | 
% 231.83/42.98  | | COMBINE_EQS: (3), (14) imply:
% 231.83/42.98  | |   (15)  e3 = e0
% 231.83/42.98  | | 
% 231.83/42.98  | | SIMP: (15) implies:
% 231.83/42.98  | |   (16)  e3 = e0
% 231.83/42.98  | | 
% 231.83/42.98  | | COMBINE_EQS: (7), (16) imply:
% 231.83/42.98  | |   (17)  all_57_12 = e0
% 231.83/42.98  | | 
% 231.83/42.98  | | REF_CLOSE: (1), (3), (4), (6), (8), (9), (12), (17) are inconsistent by
% 231.83/42.98  | |            sub-proof #2215.
% 231.83/42.98  | | 
% 231.83/42.98  | Case 2:
% 231.83/42.98  | | 
% 231.83/42.98  | |   (18)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 231.83/42.98  | |             e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0 &
% 231.83/42.98  | |             op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 231.83/42.98  | |           (all_57_14 = e0 & op(e0, e1) = e0))
% 231.83/42.98  | | 
% 231.83/42.98  | | ALPHA: (18) implies:
% 231.83/42.98  | |   (19)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 231.83/42.98  | |           e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.83/42.98  | | 
% 231.83/42.98  | | BETA: splitting (19) gives:
% 231.83/42.98  | | 
% 231.83/42.98  | | Case 1:
% 231.83/42.98  | | | 
% 231.83/42.98  | | |   (20)  all_57_12 = e0 & op(e0, e3) = e0
% 231.83/42.98  | | | 
% 231.83/42.98  | | | ALPHA: (20) implies:
% 231.83/42.98  | | |   (21)  all_57_12 = e0
% 231.83/42.98  | | | 
% 231.83/42.98  | | | REF_CLOSE: (1), (3), (4), (6), (8), (9), (12), (21) are inconsistent by
% 231.83/42.98  | | |            sub-proof #2215.
% 231.83/42.98  | | | 
% 231.83/42.98  | | Case 2:
% 231.83/42.98  | | | 
% 231.83/42.98  | | |   (22)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1)
% 231.83/42.98  | | |           = e0)
% 231.83/42.98  | | | 
% 231.83/42.98  | | | BETA: splitting (22) gives:
% 231.83/42.98  | | | 
% 231.83/42.98  | | | Case 1:
% 231.83/42.98  | | | | 
% 231.83/42.98  | | | |   (23)  all_57_13 = e0 & op(e0, e2) = e0
% 231.83/42.98  | | | | 
% 231.83/42.98  | | | | ALPHA: (23) implies:
% 231.83/42.98  | | | |   (24)  all_57_13 = e0
% 231.83/42.98  | | | | 
% 231.83/42.98  | | | | COMBINE_EQS: (9), (24) imply:
% 231.83/42.98  | | | |   (25)  e3 = e0
% 231.83/42.98  | | | | 
% 231.83/42.98  | | | | SIMP: (25) implies:
% 231.83/42.98  | | | |   (26)  e3 = e0
% 231.83/42.98  | | | | 
% 231.83/42.98  | | | | COMBINE_EQS: (7), (26) imply:
% 231.83/42.98  | | | |   (27)  all_57_12 = e0
% 231.83/42.98  | | | | 
% 231.83/42.98  | | | | REF_CLOSE: (1), (3), (4), (6), (8), (9), (12), (27) are inconsistent by
% 231.83/42.98  | | | |            sub-proof #2215.
% 231.83/42.98  | | | | 
% 231.83/42.98  | | | Case 2:
% 231.83/42.98  | | | | 
% 231.83/42.98  | | | |   (28)  all_57_14 = e0 & op(e0, e1) = e0
% 231.83/42.98  | | | | 
% 231.83/42.98  | | | | ALPHA: (28) implies:
% 231.83/42.98  | | | |   (29)  all_57_14 = e0
% 231.83/42.98  | | | | 
% 231.83/42.98  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (10), (12), (29) are
% 231.83/42.98  | | | |            inconsistent by sub-proof #1763.
% 231.83/42.98  | | | | 
% 231.83/42.98  | | | End of split
% 231.83/42.98  | | | 
% 231.83/42.98  | | End of split
% 231.83/42.98  | | 
% 231.83/42.98  | End of split
% 231.83/42.98  | 
% 231.83/42.98  End of proof
% 231.83/42.98  
% 231.83/42.98  Sub-proof #1735 shows that the following formulas are inconsistent:
% 231.83/42.98  ----------------------------------------------------------------
% 231.83/42.98    (1)   ~ (e3 = e1)
% 231.83/42.98    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/42.98           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/42.98    (3)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.83/42.98         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.83/42.98    (4)   ~ (all_6_2 = e3)
% 231.83/42.98    (5)  op(e1, e1) = all_6_2
% 231.83/42.98    (6)  all_57_6 = e1
% 231.83/42.98    (7)   ~ (e3 = e2)
% 231.83/42.98    (8)   ~ (e3 = e0)
% 231.83/42.98    (9)  all_57_15 = e3
% 231.83/42.98    (10)   ~ (e2 = e0)
% 231.83/42.98    (11)   ~ (e1 = e0)
% 231.83/42.98    (12)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.83/42.98              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.83/42.98                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.83/42.98                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.83/42.98    (13)   ~ (e2 = e1)
% 231.83/42.98    (14)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.83/42.98          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.83/42.98    (15)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.83/42.98          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.83/42.98    (16)  all_57_7 = e0
% 231.83/42.98  
% 231.83/42.98  Begin of proof
% 231.83/42.98  | 
% 231.83/42.98  | BETA: splitting (3) gives:
% 231.83/42.98  | 
% 231.83/42.98  | Case 1:
% 231.83/42.98  | | 
% 231.83/42.98  | |   (17)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 231.83/42.98  | |           e3)
% 231.83/42.98  | | 
% 231.83/42.98  | | BETA: splitting (17) gives:
% 231.83/42.98  | | 
% 231.83/42.98  | | Case 1:
% 231.83/42.98  | | | 
% 231.83/42.98  | | |   (18)  all_57_6 = e3 & op(e1, e3) = e3
% 231.83/42.98  | | | 
% 231.83/42.98  | | | ALPHA: (18) implies:
% 231.83/42.98  | | |   (19)  all_57_6 = e3
% 231.83/42.98  | | | 
% 231.83/42.98  | | | REF_CLOSE: (1), (6), (19) are inconsistent by sub-proof #2017.
% 231.83/42.98  | | | 
% 231.83/42.98  | | Case 2:
% 231.83/42.98  | | | 
% 231.83/42.98  | | |   (20)  all_57_7 = e3 & op(e1, e2) = e3
% 231.83/42.98  | | | 
% 231.83/42.98  | | | REF_CLOSE: (8), (16), (20) are inconsistent by sub-proof #2345.
% 231.83/42.98  | | | 
% 231.83/42.98  | | End of split
% 231.83/42.98  | | 
% 231.83/42.98  | Case 2:
% 231.83/42.98  | | 
% 231.83/42.98  | |   (21)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 231.83/42.98  | |           e3)
% 231.83/42.98  | | 
% 231.83/42.98  | | REF_CLOSE: (1), (2), (4), (5), (7), (8), (9), (10), (11), (12), (13), (14),
% 231.83/42.98  | |            (15), (21) are inconsistent by sub-proof #1786.
% 231.83/42.98  | | 
% 231.83/42.98  | End of split
% 231.83/42.98  | 
% 231.83/42.98  End of proof
% 231.83/42.98  
% 231.83/42.98  Sub-proof #1736 shows that the following formulas are inconsistent:
% 231.83/42.98  ----------------------------------------------------------------
% 231.83/42.98    (1)  all_57_13 = e1
% 231.83/42.98    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.83/42.98         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.83/42.98    (3)   ~ (e3 = e1)
% 231.83/42.98    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/42.98           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/42.98    (5)  op(e2, e2) = e1
% 231.83/42.98    (6)   ~ (e3 = e2)
% 231.83/42.98    (7)   ~ (e3 = e0)
% 231.83/42.98    (8)  all_57_1 = e0
% 231.83/42.98    (9)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 231.83/42.98         (all_57_14 = e0 & op(e0, e1) = e0)
% 231.83/42.98    (10)  all_57_15 = e3
% 231.83/42.98    (11)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.83/42.98          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.83/42.98            e1)
% 231.83/42.98    (12)   ~ (e2 = e0)
% 231.83/42.98    (13)   ~ (e1 = e0)
% 231.83/42.98    (14)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.83/42.98          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.83/42.98    (15)  op(e0, e0) = e3
% 231.83/42.98    (16)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.83/42.98          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.83/42.98            e2)
% 231.83/42.98    (17)   ~ (e2 = e1)
% 231.83/42.98    (18)  all_57_14 = e0
% 231.83/42.98  
% 231.83/42.98  Begin of proof
% 231.83/42.98  | 
% 231.83/42.98  | BETA: splitting (2) gives:
% 231.83/42.98  | 
% 231.83/42.98  | Case 1:
% 231.83/42.98  | | 
% 231.83/42.98  | |   (19)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 231.83/42.98  | |           e2)
% 231.83/42.98  | | 
% 231.83/42.98  | | REF_CLOSE: (4), (5), (8), (12), (17), (19) are inconsistent by sub-proof
% 231.83/42.98  | |            #1738.
% 231.83/42.98  | | 
% 231.83/42.98  | Case 2:
% 231.83/42.98  | | 
% 231.83/42.98  | |   (20)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 231.83/42.98  | |           e2)
% 231.83/42.98  | | 
% 231.83/42.98  | | BETA: splitting (20) gives:
% 231.83/42.98  | | 
% 231.83/42.98  | | Case 1:
% 231.83/42.98  | | | 
% 231.83/42.98  | | |   (21)  all_57_7 = e2 & op(e1, e2) = e2
% 231.83/42.98  | | | 
% 231.83/42.98  | | | ALPHA: (21) implies:
% 231.83/42.98  | | |   (22)  all_57_7 = e2
% 231.83/42.98  | | | 
% 231.83/42.98  | | | BETA: splitting (14) gives:
% 231.83/42.98  | | | 
% 231.83/42.98  | | | Case 1:
% 231.83/42.98  | | | | 
% 231.83/42.98  | | | |   (23)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2)
% 231.83/42.98  | | | |           = e3)
% 231.83/42.98  | | | | 
% 231.83/42.98  | | | | REF_CLOSE: (3), (4), (5), (7), (8), (23) are inconsistent by sub-proof
% 231.83/42.98  | | | |            #1737.
% 231.83/42.98  | | | | 
% 231.83/42.98  | | | Case 2:
% 231.83/42.98  | | | | 
% 231.83/42.98  | | | |   (24)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2)
% 231.83/42.98  | | | |           = e3)
% 231.83/42.98  | | | | 
% 231.83/42.98  | | | | BETA: splitting (24) gives:
% 231.83/42.98  | | | | 
% 231.83/42.98  | | | | Case 1:
% 231.83/42.98  | | | | | 
% 231.83/42.98  | | | | |   (25)  all_57_7 = e3 & op(e1, e2) = e3
% 231.83/42.98  | | | | | 
% 231.83/42.98  | | | | | REF_CLOSE: (6), (22), (25) are inconsistent by sub-proof #2194.
% 231.83/42.98  | | | | | 
% 231.83/42.98  | | | | Case 2:
% 231.83/42.98  | | | | | 
% 231.83/42.98  | | | | |   (26)  all_57_13 = e3 & op(e0, e2) = e3
% 231.83/42.98  | | | | | 
% 231.83/42.98  | | | | | ALPHA: (26) implies:
% 231.83/42.98  | | | | |   (27)  all_57_13 = e3
% 231.83/42.98  | | | | | 
% 231.83/42.98  | | | | | REF_CLOSE: (3), (4), (6), (7), (9), (10), (11), (12), (13), (15),
% 231.83/42.98  | | | | |            (16), (17), (18), (27) are inconsistent by sub-proof #2055.
% 231.83/42.98  | | | | | 
% 231.83/42.98  | | | | End of split
% 231.83/42.98  | | | | 
% 231.83/42.98  | | | End of split
% 231.83/42.98  | | | 
% 231.83/42.98  | | Case 2:
% 231.83/42.98  | | | 
% 231.83/42.98  | | |   (28)  all_57_13 = e2 & op(e0, e2) = e2
% 231.83/42.98  | | | 
% 231.83/42.98  | | | ALPHA: (28) implies:
% 231.83/42.98  | | |   (29)  all_57_13 = e2
% 231.83/42.98  | | | 
% 231.83/42.98  | | | REF_CLOSE: (1), (17), (29) are inconsistent by sub-proof #2327.
% 231.83/42.98  | | | 
% 231.83/42.98  | | End of split
% 231.83/42.98  | | 
% 231.83/42.98  | End of split
% 231.83/42.98  | 
% 231.83/42.98  End of proof
% 231.83/42.98  
% 231.83/42.98  Sub-proof #1737 shows that the following formulas are inconsistent:
% 231.83/42.98  ----------------------------------------------------------------
% 231.83/42.98    (1)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3)
% 231.83/42.98    (2)   ~ (e3 = e1)
% 231.83/42.98    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/42.98           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/42.98    (4)  op(e2, e2) = e1
% 231.83/42.98    (5)   ~ (e3 = e0)
% 231.83/42.98    (6)  all_57_1 = e0
% 231.83/42.98  
% 231.83/42.98  Begin of proof
% 231.83/42.98  | 
% 231.83/42.98  | BETA: splitting (1) gives:
% 231.83/42.98  | 
% 231.83/42.98  | Case 1:
% 231.83/42.98  | | 
% 231.83/42.98  | |   (7)  all_57_1 = e3 & op(e3, e2) = e3
% 231.83/42.98  | | 
% 231.83/42.98  | | REF_CLOSE: (5), (6), (7) are inconsistent by sub-proof #2405.
% 231.83/42.98  | | 
% 231.83/42.98  | Case 2:
% 231.83/42.98  | | 
% 231.83/42.98  | |   (8)  all_57_3 = e3 & op(e2, e2) = e3
% 231.83/42.98  | | 
% 231.83/42.98  | | ALPHA: (8) implies:
% 231.83/42.98  | |   (9)  op(e2, e2) = e3
% 231.83/42.98  | | 
% 231.83/42.98  | | REF_CLOSE: (2), (3), (4), (9) are inconsistent by sub-proof #1912.
% 231.83/42.98  | | 
% 231.83/42.98  | End of split
% 231.83/42.98  | 
% 231.83/42.98  End of proof
% 231.83/42.98  
% 231.83/42.98  Sub-proof #1738 shows that the following formulas are inconsistent:
% 231.83/42.98  ----------------------------------------------------------------
% 231.83/42.98    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/42.98           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/42.98    (2)  op(e2, e2) = e1
% 231.83/42.98    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2)
% 231.83/42.98    (4)  all_57_1 = e0
% 231.83/42.98    (5)   ~ (e2 = e0)
% 231.83/42.98    (6)   ~ (e2 = e1)
% 231.83/42.98  
% 231.83/42.98  Begin of proof
% 231.83/42.98  | 
% 231.83/42.98  | BETA: splitting (3) gives:
% 231.83/42.98  | 
% 231.83/42.98  | Case 1:
% 231.83/42.98  | | 
% 231.83/42.98  | |   (7)  all_57_1 = e2 & op(e3, e2) = e2
% 231.83/42.98  | | 
% 231.83/42.98  | | REF_CLOSE: (4), (5), (7) are inconsistent by sub-proof #2483.
% 231.83/42.98  | | 
% 231.83/42.98  | Case 2:
% 231.83/42.98  | | 
% 231.83/42.98  | |   (8)  all_57_3 = e2 & op(e2, e2) = e2
% 231.83/42.98  | | 
% 231.83/42.98  | | ALPHA: (8) implies:
% 231.83/42.98  | |   (9)  op(e2, e2) = e2
% 231.83/42.98  | | 
% 231.83/42.98  | | REF_CLOSE: (1), (2), (6), (9) are inconsistent by sub-proof #2306.
% 231.83/42.98  | | 
% 231.83/42.98  | End of split
% 231.83/42.98  | 
% 231.83/42.98  End of proof
% 231.83/42.98  
% 231.83/42.98  Sub-proof #1739 shows that the following formulas are inconsistent:
% 231.83/42.98  ----------------------------------------------------------------
% 231.83/42.98    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.83/42.98         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.83/42.98    (2)   ~ (e3 = e1)
% 231.83/42.98    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/42.98           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/42.98    (4)   ~ (all_6_2 = e3)
% 231.83/42.98    (5)  op(e1, e1) = all_6_2
% 231.83/42.98    (6)  op(e2, e2) = e1
% 231.83/42.98    (7)   ~ (e3 = e2)
% 231.83/42.98    (8)   ~ (e3 = e0)
% 231.83/42.98    (9)  all_57_15 = e3
% 231.83/42.98    (10)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.83/42.98          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.83/42.98            e1)
% 231.83/42.98    (11)  all_57_5 = e3
% 231.83/42.98    (12)   ~ (e2 = e0)
% 231.83/42.98    (13)   ~ (e1 = e0)
% 231.83/42.98    (14)  all_57_12 = e3
% 231.83/42.98    (15)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.83/42.98          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.83/42.98    (16)  all_57_14 = e1
% 231.83/42.98    (17)  op(e0, e0) = e3
% 231.83/42.98    (18)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.83/42.98          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.83/42.98            e2)
% 231.83/42.98    (19)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.83/42.98              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.83/42.98                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.83/42.98                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.83/42.98    (20)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.83/42.98          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.83/42.98    (21)  all_57_2 = e0
% 231.83/42.98    (22)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.83/42.98          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.83/42.98    (23)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 231.83/42.98          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 231.83/42.98    (24)   ~ (e2 = e1)
% 231.83/42.98    (25)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.83/42.98          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.83/42.98    (26)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.83/42.98          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.83/42.98  
% 231.83/42.98  Begin of proof
% 231.83/42.98  | 
% 231.83/42.98  | BETA: splitting (22) gives:
% 231.83/42.98  | 
% 231.83/42.98  | Case 1:
% 231.83/42.98  | | 
% 231.83/42.98  | |   (27)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 231.83/42.98  | |           e2)
% 231.83/42.98  | | 
% 231.83/42.98  | | BETA: splitting (27) gives:
% 231.83/42.98  | | 
% 231.83/42.98  | | Case 1:
% 231.83/42.98  | | | 
% 231.83/42.98  | | |   (28)  all_57_2 = e2 & op(e2, e3) = e2
% 231.83/42.98  | | | 
% 231.83/42.98  | | | REF_CLOSE: (12), (21), (28) are inconsistent by sub-proof #2020.
% 231.83/42.98  | | | 
% 231.83/42.98  | | Case 2:
% 231.83/42.98  | | | 
% 231.83/42.98  | | |   (29)  all_57_3 = e2 & op(e2, e2) = e2
% 231.83/42.98  | | | 
% 231.83/42.98  | | | ALPHA: (29) implies:
% 231.83/42.98  | | |   (30)  op(e2, e2) = e2
% 231.83/42.98  | | | 
% 231.83/42.98  | | | REF_CLOSE: (3), (6), (24), (30) are inconsistent by sub-proof #2306.
% 231.83/42.98  | | | 
% 231.83/42.98  | | End of split
% 231.83/42.98  | | 
% 231.83/42.98  | Case 2:
% 231.83/42.98  | | 
% 231.83/42.98  | |   (31)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 231.83/42.98  | |           e2)
% 231.83/42.98  | | 
% 231.83/42.98  | | BETA: splitting (31) gives:
% 231.83/42.98  | | 
% 231.83/42.98  | | Case 1:
% 231.83/42.98  | | | 
% 231.83/42.98  | | |   (32)  all_57_5 = e2 & op(e2, e1) = e2
% 231.83/42.98  | | | 
% 231.83/42.98  | | | ALPHA: (32) implies:
% 231.83/42.98  | | |   (33)  all_57_5 = e2
% 231.83/42.98  | | | 
% 231.83/42.98  | | | REF_CLOSE: (7), (11), (33) are inconsistent by sub-proof #2189.
% 231.83/42.98  | | | 
% 231.83/42.98  | | Case 2:
% 231.83/42.98  | | | 
% 231.83/42.98  | | |   (34)  all_57_10 = e2 & op(e2, e0) = e2
% 231.83/42.98  | | | 
% 231.83/42.98  | | | ALPHA: (34) implies:
% 231.83/42.98  | | |   (35)  all_57_10 = e2
% 231.83/42.98  | | | 
% 231.83/42.98  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 231.83/42.98  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (23), (24),
% 231.83/42.98  | | |            (25), (26), (35) are inconsistent by sub-proof #1740.
% 231.83/42.98  | | | 
% 231.83/42.98  | | End of split
% 231.83/42.98  | | 
% 231.83/42.98  | End of split
% 231.83/42.98  | 
% 231.83/42.98  End of proof
% 231.83/42.98  
% 231.83/42.98  Sub-proof #1740 shows that the following formulas are inconsistent:
% 231.83/42.98  ----------------------------------------------------------------
% 231.83/42.98    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.83/42.98         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.83/42.98    (2)   ~ (e3 = e1)
% 231.83/42.98    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/42.98           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/42.98    (4)   ~ (all_6_2 = e3)
% 231.83/42.98    (5)  op(e1, e1) = all_6_2
% 231.83/42.98    (6)  op(e2, e2) = e1
% 231.83/42.98    (7)   ~ (e3 = e2)
% 231.83/42.98    (8)   ~ (e3 = e0)
% 231.83/42.98    (9)  all_57_15 = e3
% 231.83/42.98    (10)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.83/42.98          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.83/42.98            e1)
% 231.83/42.98    (11)  all_57_10 = e2
% 231.83/42.98    (12)  all_57_5 = e3
% 231.83/42.98    (13)   ~ (e2 = e0)
% 231.83/42.98    (14)   ~ (e1 = e0)
% 231.83/42.98    (15)  all_57_12 = e3
% 231.83/42.98    (16)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.83/42.98          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.83/42.98    (17)  all_57_14 = e1
% 231.83/42.98    (18)  op(e0, e0) = e3
% 231.83/42.98    (19)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.83/42.98          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.83/42.98            e2)
% 231.83/42.98    (20)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.83/42.98              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.83/42.98                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.83/42.98                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.83/42.98    (21)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.83/42.98          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.83/42.98    (22)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 231.83/42.98          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 231.83/42.98    (23)   ~ (e2 = e1)
% 231.83/42.98    (24)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.83/42.98          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.83/42.98    (25)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.83/42.98          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.83/42.98  
% 231.83/42.98  Begin of proof
% 231.83/42.98  | 
% 231.83/42.98  | BETA: splitting (19) gives:
% 231.83/42.98  | 
% 231.83/42.98  | Case 1:
% 231.83/42.98  | | 
% 231.83/42.98  | |   (26)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 231.83/42.98  | |           e2)
% 231.83/42.98  | | 
% 231.83/42.98  | | BETA: splitting (26) gives:
% 231.83/42.98  | | 
% 231.83/42.98  | | Case 1:
% 231.83/42.98  | | | 
% 231.83/42.98  | | |   (27)  all_57_12 = e2 & op(e0, e3) = e2
% 231.83/42.98  | | | 
% 231.83/42.98  | | | ALPHA: (27) implies:
% 231.83/42.98  | | |   (28)  all_57_12 = e2
% 231.83/42.98  | | | 
% 231.83/42.98  | | | COMBINE_EQS: (15), (28) imply:
% 231.83/42.98  | | |   (29)  e3 = e2
% 231.83/42.98  | | | 
% 231.83/42.98  | | | SIMP: (29) implies:
% 231.83/42.98  | | |   (30)  e3 = e2
% 231.83/42.98  | | | 
% 231.83/42.98  | | | COMBINE_EQS: (12), (30) imply:
% 231.83/42.98  | | |   (31)  all_57_5 = e2
% 231.83/42.98  | | | 
% 231.83/42.98  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 231.83/42.98  | | |            (14), (16), (18), (19), (20), (21), (22), (23), (24), (25),
% 231.83/42.98  | | |            (31) are inconsistent by sub-proof #1744.
% 231.83/42.98  | | | 
% 231.83/42.98  | | Case 2:
% 231.83/42.98  | | | 
% 231.83/42.98  | | |   (32)  all_57_13 = e2 & op(e0, e2) = e2
% 231.83/42.98  | | | 
% 231.83/42.98  | | | ALPHA: (32) implies:
% 231.83/42.98  | | |   (33)  all_57_13 = e2
% 231.83/42.98  | | | 
% 231.83/42.98  | | | REF_CLOSE: (2), (3), (8), (9), (10), (13), (14), (15), (18), (20), (23),
% 231.83/42.98  | | |            (33) are inconsistent by sub-proof #1742.
% 231.83/42.98  | | | 
% 231.83/42.98  | | End of split
% 231.83/42.98  | | 
% 231.83/42.98  | Case 2:
% 231.83/42.98  | | 
% 231.83/42.98  | |   (34)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.83/42.98  | |           e2)
% 231.83/42.98  | | 
% 231.83/42.98  | | BETA: splitting (34) gives:
% 231.83/42.98  | | 
% 231.83/42.98  | | Case 1:
% 231.83/42.98  | | | 
% 231.83/42.98  | | |   (35)  all_57_14 = e2 & op(e0, e1) = e2
% 231.83/42.98  | | | 
% 231.83/42.98  | | | REF_CLOSE: (17), (23), (35) are inconsistent by sub-proof #1968.
% 231.83/42.98  | | | 
% 231.83/42.98  | | Case 2:
% 231.83/42.98  | | | 
% 231.83/42.98  | | |   (36)  all_57_15 = e2 & op(e0, e0) = e2
% 231.83/42.98  | | | 
% 231.83/42.98  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 231.83/42.98  | | |            (13), (14), (16), (18), (19), (20), (21), (22), (23), (24),
% 231.83/42.98  | | |            (25), (36) are inconsistent by sub-proof #1741.
% 231.83/42.98  | | | 
% 231.83/42.98  | | End of split
% 231.83/42.98  | | 
% 231.83/42.98  | End of split
% 231.83/42.98  | 
% 231.83/42.98  End of proof
% 231.83/42.98  
% 231.83/42.98  Sub-proof #1741 shows that the following formulas are inconsistent:
% 231.83/42.98  ----------------------------------------------------------------
% 231.83/42.98    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.83/42.98         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.83/42.98    (2)   ~ (e3 = e1)
% 231.83/42.98    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/42.98           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/42.98    (4)   ~ (all_6_2 = e3)
% 231.83/42.98    (5)  op(e1, e1) = all_6_2
% 231.83/42.98    (6)  op(e2, e2) = e1
% 231.83/42.98    (7)   ~ (e3 = e2)
% 231.83/42.98    (8)   ~ (e3 = e0)
% 231.83/42.98    (9)  all_57_15 = e3
% 231.83/42.98    (10)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.83/42.98          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.83/42.98            e1)
% 231.83/42.98    (11)  all_57_10 = e2
% 231.83/42.98    (12)  all_57_5 = e3
% 231.83/42.98    (13)   ~ (e2 = e0)
% 231.83/42.98    (14)   ~ (e1 = e0)
% 231.83/42.98    (15)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.83/42.98          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.83/42.98    (16)  op(e0, e0) = e3
% 231.83/42.98    (17)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.83/42.98          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.83/42.98            e2)
% 231.83/42.98    (18)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.83/42.98              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.83/42.98                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.83/42.98                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.83/42.98    (19)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.83/42.98          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.83/42.98    (20)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 231.83/42.98          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 231.83/42.98    (21)   ~ (e2 = e1)
% 231.83/42.98    (22)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.83/42.98          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.83/42.98    (23)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.83/42.98          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.83/42.98    (24)  all_57_15 = e2 & op(e0, e0) = e2
% 231.83/42.98  
% 231.83/42.98  Begin of proof
% 231.83/42.98  | 
% 231.83/42.98  | ALPHA: (24) implies:
% 231.83/42.98  |   (25)  all_57_15 = e2
% 231.83/42.98  | 
% 231.83/42.98  | COMBINE_EQS: (9), (25) imply:
% 231.83/42.98  |   (26)  e3 = e2
% 231.83/42.98  | 
% 231.83/42.98  | SIMP: (26) implies:
% 231.83/42.98  |   (27)  e3 = e2
% 231.83/42.98  | 
% 231.83/42.98  | COMBINE_EQS: (12), (27) imply:
% 231.83/42.98  |   (28)  all_57_5 = e2
% 231.83/42.98  | 
% 231.83/42.98  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 231.83/42.98  |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (28)
% 231.83/42.98  |            are inconsistent by sub-proof #1744.
% 231.83/42.98  | 
% 231.83/42.98  End of proof
% 231.83/42.98  
% 231.83/42.98  Sub-proof #1742 shows that the following formulas are inconsistent:
% 231.83/42.98  ----------------------------------------------------------------
% 231.83/42.98    (1)   ~ (e3 = e1)
% 231.83/42.98    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/42.98           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/42.98    (3)   ~ (e3 = e0)
% 231.83/42.98    (4)  all_57_15 = e3
% 231.83/42.98    (5)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 231.83/42.98         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.83/42.98    (6)   ~ (e2 = e0)
% 231.83/42.98    (7)  all_57_13 = e2
% 231.83/42.98    (8)   ~ (e1 = e0)
% 231.83/42.98    (9)  all_57_12 = e3
% 231.83/42.98    (10)  op(e0, e0) = e3
% 231.83/42.98    (11)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.83/42.98              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.83/42.98                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.83/42.98                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.83/42.98    (12)   ~ (e2 = e1)
% 231.83/42.98  
% 231.83/42.98  Begin of proof
% 231.83/42.98  | 
% 231.83/42.98  | BETA: splitting (11) gives:
% 231.83/42.98  | 
% 231.83/42.98  | Case 1:
% 231.83/42.98  | | 
% 231.83/42.98  | |   (13)  all_57_15 = e0 & op(e0, e0) = e0
% 231.83/42.98  | | 
% 231.83/42.98  | | ALPHA: (13) implies:
% 231.83/42.98  | |   (14)  op(e0, e0) = e0
% 231.83/42.98  | | 
% 231.83/42.98  | | REF_CLOSE: (2), (3), (10), (14) are inconsistent by sub-proof #2304.
% 231.83/42.98  | | 
% 231.83/42.98  | Case 2:
% 231.83/42.98  | | 
% 231.83/42.98  | |   (15)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 231.83/42.98  | |             e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0 &
% 231.83/42.98  | |             op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 231.83/42.98  | |           (all_57_14 = e0 & op(e0, e1) = e0))
% 231.83/42.98  | | 
% 231.83/42.98  | | ALPHA: (15) implies:
% 231.83/42.98  | |   (16)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 231.83/42.98  | |           e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.83/42.98  | | 
% 231.83/42.98  | | BETA: splitting (16) gives:
% 231.83/42.98  | | 
% 231.83/42.98  | | Case 1:
% 231.83/42.98  | | | 
% 231.83/42.98  | | |   (17)  all_57_12 = e0 & op(e0, e3) = e0
% 231.83/42.98  | | | 
% 231.83/42.98  | | | REF_CLOSE: (3), (9), (17) are inconsistent by sub-proof #2237.
% 231.83/42.98  | | | 
% 231.83/42.98  | | Case 2:
% 231.83/42.98  | | | 
% 231.83/42.99  | | |   (18)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1)
% 231.83/42.99  | | |           = e0)
% 231.83/42.99  | | | 
% 231.83/42.99  | | | BETA: splitting (18) gives:
% 231.83/42.99  | | | 
% 231.83/42.99  | | | Case 1:
% 231.83/42.99  | | | | 
% 231.83/42.99  | | | |   (19)  all_57_13 = e0 & op(e0, e2) = e0
% 231.83/42.99  | | | | 
% 231.83/42.99  | | | | REF_CLOSE: (6), (7), (19) are inconsistent by sub-proof #1743.
% 231.83/42.99  | | | | 
% 231.83/42.99  | | | Case 2:
% 231.83/42.99  | | | | 
% 231.83/42.99  | | | |   (20)  all_57_14 = e0 & op(e0, e1) = e0
% 231.83/42.99  | | | | 
% 231.83/42.99  | | | | ALPHA: (20) implies:
% 231.83/42.99  | | | |   (21)  all_57_14 = e0
% 231.83/42.99  | | | | 
% 231.83/42.99  | | | | REF_CLOSE: (1), (4), (5), (7), (8), (9), (12), (21) are inconsistent by
% 231.83/42.99  | | | |            sub-proof #1764.
% 231.83/42.99  | | | | 
% 231.83/42.99  | | | End of split
% 231.83/42.99  | | | 
% 231.83/42.99  | | End of split
% 231.83/42.99  | | 
% 231.83/42.99  | End of split
% 231.83/42.99  | 
% 231.83/42.99  End of proof
% 231.83/42.99  
% 231.83/42.99  Sub-proof #1743 shows that the following formulas are inconsistent:
% 231.83/42.99  ----------------------------------------------------------------
% 231.83/42.99    (1)  all_57_13 = e0 & op(e0, e2) = e0
% 231.83/42.99    (2)  all_57_13 = e2
% 231.83/42.99    (3)   ~ (e2 = e0)
% 231.83/42.99  
% 231.83/42.99  Begin of proof
% 231.83/42.99  | 
% 231.83/42.99  | ALPHA: (1) implies:
% 231.83/42.99  |   (4)  all_57_13 = e0
% 231.83/42.99  | 
% 231.83/42.99  | COMBINE_EQS: (2), (4) imply:
% 231.83/42.99  |   (5)  e2 = e0
% 231.83/42.99  | 
% 231.83/42.99  | REDUCE: (3), (5) imply:
% 231.83/42.99  |   (6)  $false
% 231.83/42.99  | 
% 231.83/42.99  | CLOSE: (6) is inconsistent.
% 231.83/42.99  | 
% 231.83/42.99  End of proof
% 231.83/42.99  
% 231.83/42.99  Sub-proof #1744 shows that the following formulas are inconsistent:
% 231.83/42.99  ----------------------------------------------------------------
% 231.83/42.99    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.83/42.99         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.83/42.99    (2)   ~ (e3 = e1)
% 231.83/42.99    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/42.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/42.99    (4)   ~ (all_6_2 = e3)
% 231.83/42.99    (5)  op(e1, e1) = all_6_2
% 231.83/42.99    (6)  op(e2, e2) = e1
% 231.83/42.99    (7)   ~ (e3 = e2)
% 231.83/42.99    (8)   ~ (e3 = e0)
% 231.83/42.99    (9)  all_57_15 = e3
% 231.83/42.99    (10)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.83/42.99          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.83/42.99            e1)
% 231.83/42.99    (11)  all_57_10 = e2
% 231.83/42.99    (12)   ~ (e2 = e0)
% 231.83/42.99    (13)   ~ (e1 = e0)
% 231.83/42.99    (14)  all_57_5 = e2
% 231.83/42.99    (15)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.83/42.99          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.83/42.99    (16)  op(e0, e0) = e3
% 231.83/42.99    (17)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.83/42.99          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.83/42.99            e2)
% 231.83/42.99    (18)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.83/42.99              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.83/42.99                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.83/42.99                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.83/42.99    (19)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.83/42.99          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.83/42.99    (20)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 231.83/42.99          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 231.83/42.99    (21)   ~ (e2 = e1)
% 231.83/42.99    (22)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.83/42.99          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.83/42.99    (23)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.83/42.99          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.83/42.99  
% 231.83/42.99  Begin of proof
% 231.83/42.99  | 
% 231.83/42.99  | BETA: splitting (19) gives:
% 231.83/42.99  | 
% 231.83/42.99  | Case 1:
% 231.83/42.99  | | 
% 231.83/42.99  | |   (24)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 231.83/42.99  | |           e3)
% 231.83/42.99  | | 
% 231.83/42.99  | | BETA: splitting (24) gives:
% 231.83/42.99  | | 
% 231.83/42.99  | | Case 1:
% 231.83/42.99  | | | 
% 231.83/42.99  | | |   (25)  all_57_2 = e3 & op(e2, e3) = e3
% 231.83/42.99  | | | 
% 231.83/42.99  | | | ALPHA: (25) implies:
% 231.83/42.99  | | |   (26)  all_57_2 = e3
% 231.83/42.99  | | | 
% 231.83/42.99  | | | BETA: splitting (20) gives:
% 231.83/42.99  | | | 
% 231.83/42.99  | | | Case 1:
% 231.83/42.99  | | | | 
% 231.83/42.99  | | | |   (27)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2)
% 231.83/42.99  | | | |           = e0)
% 231.83/42.99  | | | | 
% 231.83/42.99  | | | | BETA: splitting (27) gives:
% 231.83/42.99  | | | | 
% 231.83/42.99  | | | | Case 1:
% 231.83/42.99  | | | | | 
% 231.83/42.99  | | | | |   (28)  all_57_2 = e0 & op(e2, e3) = e0
% 231.83/42.99  | | | | | 
% 231.83/42.99  | | | | | REF_CLOSE: (8), (26), (28) are inconsistent by sub-proof #1805.
% 231.83/42.99  | | | | | 
% 231.83/42.99  | | | | Case 2:
% 231.83/42.99  | | | | | 
% 231.83/42.99  | | | | |   (29)  all_57_3 = e0 & op(e2, e2) = e0
% 231.83/42.99  | | | | | 
% 231.83/42.99  | | | | | ALPHA: (29) implies:
% 231.83/42.99  | | | | |   (30)  all_57_3 = e0
% 231.83/42.99  | | | | | 
% 231.83/42.99  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12),
% 231.83/42.99  | | | | |            (13), (14), (15), (17), (18), (21), (26), (30) are
% 231.83/42.99  | | | | |            inconsistent by sub-proof #1752.
% 231.83/42.99  | | | | | 
% 231.83/42.99  | | | | End of split
% 231.83/42.99  | | | | 
% 231.83/42.99  | | | Case 2:
% 231.83/42.99  | | | | 
% 231.83/42.99  | | | |   (31)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0)
% 231.83/42.99  | | | |           = e0)
% 231.83/42.99  | | | | 
% 231.83/42.99  | | | | BETA: splitting (31) gives:
% 231.83/42.99  | | | | 
% 231.83/42.99  | | | | Case 1:
% 231.83/42.99  | | | | | 
% 231.83/42.99  | | | | |   (32)  all_57_5 = e0 & op(e2, e1) = e0
% 231.83/42.99  | | | | | 
% 231.83/42.99  | | | | | REF_CLOSE: (12), (14), (32) are inconsistent by sub-proof #2428.
% 231.83/42.99  | | | | | 
% 231.83/42.99  | | | | Case 2:
% 231.83/42.99  | | | | | 
% 231.83/42.99  | | | | |   (33)  all_57_10 = e0 & op(e2, e0) = e0
% 231.83/42.99  | | | | | 
% 231.83/42.99  | | | | | REF_CLOSE: (11), (12), (33) are inconsistent by sub-proof #1751.
% 231.83/42.99  | | | | | 
% 231.83/42.99  | | | | End of split
% 231.83/42.99  | | | | 
% 231.83/42.99  | | | End of split
% 231.83/42.99  | | | 
% 231.83/42.99  | | Case 2:
% 231.83/42.99  | | | 
% 231.83/42.99  | | |   (34)  all_57_3 = e3 & op(e2, e2) = e3
% 231.83/42.99  | | | 
% 231.83/42.99  | | | ALPHA: (34) implies:
% 231.83/42.99  | | |   (35)  op(e2, e2) = e3
% 231.83/42.99  | | | 
% 231.83/42.99  | | | REF_CLOSE: (2), (3), (6), (35) are inconsistent by sub-proof #1912.
% 231.83/42.99  | | | 
% 231.83/42.99  | | End of split
% 231.83/42.99  | | 
% 231.83/42.99  | Case 2:
% 231.83/42.99  | | 
% 231.83/42.99  | |   (36)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 231.83/42.99  | |           e3)
% 231.83/42.99  | | 
% 231.83/42.99  | | REF_CLOSE: (2), (3), (7), (8), (9), (12), (13), (14), (16), (18), (21),
% 231.83/42.99  | |            (22), (23), (36) are inconsistent by sub-proof #1745.
% 231.83/42.99  | | 
% 231.83/42.99  | End of split
% 231.83/42.99  | 
% 231.83/42.99  End of proof
% 231.83/42.99  
% 231.83/42.99  Sub-proof #1745 shows that the following formulas are inconsistent:
% 231.83/42.99  ----------------------------------------------------------------
% 231.83/42.99    (1)   ~ (e3 = e1)
% 231.83/42.99    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/42.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/42.99    (3)   ~ (e3 = e2)
% 231.83/42.99    (4)   ~ (e3 = e0)
% 231.83/42.99    (5)  all_57_15 = e3
% 231.83/42.99    (6)   ~ (e2 = e0)
% 231.83/42.99    (7)   ~ (e1 = e0)
% 231.83/42.99    (8)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.83/42.99    (9)  all_57_5 = e2
% 231.83/42.99    (10)  op(e0, e0) = e3
% 231.83/42.99    (11)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.83/42.99              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.83/42.99                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.83/42.99                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.83/42.99    (12)   ~ (e2 = e1)
% 231.83/42.99    (13)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.83/42.99          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.83/42.99    (14)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.83/42.99          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.83/42.99  
% 231.83/42.99  Begin of proof
% 231.83/42.99  | 
% 231.83/42.99  | BETA: splitting (8) gives:
% 231.83/42.99  | 
% 231.83/42.99  | Case 1:
% 231.83/42.99  | | 
% 231.83/42.99  | |   (15)  all_57_5 = e3 & op(e2, e1) = e3
% 231.83/42.99  | | 
% 231.83/42.99  | | ALPHA: (15) implies:
% 231.83/42.99  | |   (16)  all_57_5 = e3
% 231.83/42.99  | | 
% 231.83/42.99  | | REF_CLOSE: (3), (9), (16) are inconsistent by sub-proof #2189.
% 231.83/42.99  | | 
% 231.83/42.99  | Case 2:
% 231.83/42.99  | | 
% 231.83/42.99  | |   (17)  all_57_10 = e3 & op(e2, e0) = e3
% 231.83/42.99  | | 
% 231.83/42.99  | | ALPHA: (17) implies:
% 231.83/42.99  | |   (18)  all_57_10 = e3
% 231.83/42.99  | | 
% 231.83/42.99  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (10), (11), (12), (13), (14),
% 231.83/42.99  | |            (18) are inconsistent by sub-proof #1746.
% 231.83/42.99  | | 
% 231.83/42.99  | End of split
% 231.83/42.99  | 
% 231.83/42.99  End of proof
% 231.83/42.99  
% 231.83/42.99  Sub-proof #1746 shows that the following formulas are inconsistent:
% 231.83/42.99  ----------------------------------------------------------------
% 231.83/42.99    (1)   ~ (e3 = e1)
% 231.83/42.99    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/42.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/42.99    (3)   ~ (e3 = e2)
% 231.83/42.99    (4)   ~ (e3 = e0)
% 231.83/42.99    (5)  all_57_15 = e3
% 231.83/42.99    (6)   ~ (e2 = e0)
% 231.83/42.99    (7)   ~ (e1 = e0)
% 231.83/42.99    (8)  all_57_10 = e3
% 231.83/42.99    (9)  op(e0, e0) = e3
% 231.83/42.99    (10)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.83/42.99              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.83/42.99                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.83/42.99                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.83/42.99    (11)   ~ (e2 = e1)
% 231.83/42.99    (12)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.83/42.99          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.83/42.99    (13)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.83/42.99          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.83/42.99  
% 231.83/42.99  Begin of proof
% 231.83/42.99  | 
% 231.83/42.99  | BETA: splitting (10) gives:
% 231.83/42.99  | 
% 231.83/42.99  | Case 1:
% 231.83/42.99  | | 
% 231.83/42.99  | |   (14)  all_57_15 = e0 & op(e0, e0) = e0
% 231.83/42.99  | | 
% 231.83/42.99  | | ALPHA: (14) implies:
% 231.83/42.99  | |   (15)  op(e0, e0) = e0
% 231.83/42.99  | | 
% 231.83/42.99  | | REF_CLOSE: (2), (4), (9), (15) are inconsistent by sub-proof #2304.
% 231.83/42.99  | | 
% 231.83/42.99  | Case 2:
% 231.83/42.99  | | 
% 231.83/42.99  | |   (16)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 231.83/42.99  | |             e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0 &
% 231.83/42.99  | |             op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 231.83/42.99  | |           (all_57_14 = e0 & op(e0, e1) = e0))
% 231.83/42.99  | | 
% 231.83/42.99  | | ALPHA: (16) implies:
% 231.83/42.99  | |   (17)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 231.83/42.99  | |           e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.83/42.99  | | 
% 231.83/42.99  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 231.83/42.99  | |            (13), (17) are inconsistent by sub-proof #1747.
% 231.83/42.99  | | 
% 231.83/42.99  | End of split
% 231.83/42.99  | 
% 231.83/42.99  End of proof
% 231.83/42.99  
% 231.83/42.99  Sub-proof #1747 shows that the following formulas are inconsistent:
% 231.83/42.99  ----------------------------------------------------------------
% 231.83/42.99    (1)   ~ (e3 = e1)
% 231.83/42.99    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/42.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/42.99    (3)   ~ (e3 = e2)
% 231.83/42.99    (4)   ~ (e3 = e0)
% 231.83/42.99    (5)  all_57_15 = e3
% 231.83/42.99    (6)   ~ (e2 = e0)
% 231.83/42.99    (7)   ~ (e1 = e0)
% 231.83/42.99    (8)  all_57_10 = e3
% 231.83/42.99    (9)  op(e0, e0) = e3
% 231.83/42.99    (10)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.83/42.99              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.83/42.99                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.83/42.99                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.83/42.99    (11)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) |
% 231.83/42.99          (all_57_11 = e0 & op(e1, e0) = e0)
% 231.83/42.99    (12)   ~ (e2 = e1)
% 231.83/42.99    (13)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.83/42.99          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.83/42.99    (14)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.83/42.99          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.83/42.99  
% 231.83/42.99  Begin of proof
% 231.83/42.99  | 
% 231.83/42.99  | BETA: splitting (11) gives:
% 231.83/42.99  | 
% 231.83/42.99  | Case 1:
% 231.83/42.99  | | 
% 231.83/42.99  | |   (15)  all_57_9 = e0 & op(e3, e0) = e0
% 231.83/42.99  | | 
% 231.83/42.99  | | ALPHA: (15) implies:
% 231.83/42.99  | |   (16)  all_57_9 = e0
% 231.83/42.99  | | 
% 231.83/42.99  | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (10), (12), (13), (14), (16)
% 231.83/42.99  | |            are inconsistent by sub-proof #1982.
% 231.83/42.99  | | 
% 231.83/42.99  | Case 2:
% 231.83/42.99  | | 
% 231.83/42.99  | |   (17)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 231.83/42.99  | |           e0)
% 231.83/42.99  | | 
% 231.83/42.99  | | BETA: splitting (17) gives:
% 231.83/42.99  | | 
% 231.83/42.99  | | Case 1:
% 231.83/42.99  | | | 
% 231.83/42.99  | | |   (18)  all_57_10 = e0 & op(e2, e0) = e0
% 231.83/42.99  | | | 
% 231.83/42.99  | | | REF_CLOSE: (4), (8), (18) are inconsistent by sub-proof #1981.
% 231.83/42.99  | | | 
% 231.83/42.99  | | Case 2:
% 231.83/42.99  | | | 
% 231.83/42.99  | | |   (19)  all_57_11 = e0 & op(e1, e0) = e0
% 231.83/42.99  | | | 
% 231.83/42.99  | | | ALPHA: (19) implies:
% 231.83/42.99  | | |   (20)  all_57_11 = e0
% 231.83/42.99  | | | 
% 231.83/42.99  | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (12), (13), (14), (20)
% 231.83/42.99  | | |            are inconsistent by sub-proof #1748.
% 231.83/42.99  | | | 
% 231.83/42.99  | | End of split
% 231.83/42.99  | | 
% 231.83/42.99  | End of split
% 231.83/42.99  | 
% 231.83/42.99  End of proof
% 231.83/42.99  
% 231.83/42.99  Sub-proof #1748 shows that the following formulas are inconsistent:
% 231.83/42.99  ----------------------------------------------------------------
% 231.83/42.99    (1)   ~ (e3 = e1)
% 231.83/42.99    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/42.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/42.99    (3)   ~ (e3 = e2)
% 231.83/42.99    (4)  all_57_15 = e3
% 231.83/42.99    (5)  all_57_11 = e0
% 231.83/42.99    (6)   ~ (e2 = e0)
% 231.83/42.99    (7)   ~ (e1 = e0)
% 231.83/42.99    (8)  all_57_10 = e3
% 231.83/42.99    (9)  op(e0, e0) = e3
% 231.83/42.99    (10)   ~ (e2 = e1)
% 231.83/42.99    (11)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.83/42.99          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.83/42.99    (12)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.83/42.99          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.83/42.99  
% 231.83/42.99  Begin of proof
% 231.83/42.99  | 
% 231.83/42.99  | BETA: splitting (12) gives:
% 231.83/42.99  | 
% 231.83/42.99  | Case 1:
% 231.83/42.99  | | 
% 231.83/42.99  | |   (13)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) =
% 231.83/42.99  | |           e1)
% 231.83/42.99  | | 
% 231.83/42.99  | | BETA: splitting (13) gives:
% 231.83/42.99  | | 
% 231.83/42.99  | | Case 1:
% 231.83/42.99  | | | 
% 231.83/42.99  | | |   (14)  all_57_9 = e1 & op(e3, e0) = e1
% 231.83/42.99  | | | 
% 231.83/42.99  | | | ALPHA: (14) implies:
% 231.83/42.99  | | |   (15)  all_57_9 = e1
% 231.83/42.99  | | | 
% 231.83/42.99  | | | REF_CLOSE: (3), (4), (5), (6), (8), (10), (11), (15) are inconsistent by
% 231.83/42.99  | | |            sub-proof #1987.
% 231.83/42.99  | | | 
% 231.83/42.99  | | Case 2:
% 231.83/42.99  | | | 
% 231.83/42.99  | | |   (16)  all_57_10 = e1 & op(e2, e0) = e1
% 231.83/42.99  | | | 
% 231.83/42.99  | | | ALPHA: (16) implies:
% 231.83/42.99  | | |   (17)  all_57_10 = e1
% 231.83/42.99  | | | 
% 231.83/42.99  | | | REF_CLOSE: (1), (8), (17) are inconsistent by sub-proof #2248.
% 231.83/42.99  | | | 
% 231.83/42.99  | | End of split
% 231.83/42.99  | | 
% 231.83/42.99  | Case 2:
% 231.83/42.99  | | 
% 231.83/42.99  | |   (18)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.83/42.99  | |           e1)
% 231.83/42.99  | | 
% 231.83/42.99  | | REF_CLOSE: (1), (2), (5), (7), (9), (18) are inconsistent by sub-proof
% 231.83/42.99  | |            #1749.
% 231.83/42.99  | | 
% 231.83/42.99  | End of split
% 231.83/42.99  | 
% 231.83/42.99  End of proof
% 231.83/42.99  
% 231.83/42.99  Sub-proof #1749 shows that the following formulas are inconsistent:
% 231.83/42.99  ----------------------------------------------------------------
% 231.83/42.99    (1)   ~ (e3 = e1)
% 231.83/42.99    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/42.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/42.99    (3)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.83/42.99    (4)  all_57_11 = e0
% 231.83/42.99    (5)   ~ (e1 = e0)
% 231.83/42.99    (6)  op(e0, e0) = e3
% 231.83/42.99  
% 231.83/42.99  Begin of proof
% 231.83/42.99  | 
% 231.83/42.99  | BETA: splitting (3) gives:
% 231.83/42.99  | 
% 231.83/42.99  | Case 1:
% 231.83/42.99  | | 
% 231.83/42.99  | |   (7)  all_57_11 = e1 & op(e1, e0) = e1
% 231.83/42.99  | | 
% 231.83/42.99  | | REF_CLOSE: (4), (5), (7) are inconsistent by sub-proof #1750.
% 231.83/42.99  | | 
% 231.83/42.99  | Case 2:
% 231.83/42.99  | | 
% 231.83/42.99  | |   (8)  all_57_15 = e1 & op(e0, e0) = e1
% 231.83/42.99  | | 
% 231.83/42.99  | | ALPHA: (8) implies:
% 231.83/42.99  | |   (9)  op(e0, e0) = e1
% 231.83/42.99  | | 
% 231.83/42.99  | | REF_CLOSE: (1), (2), (6), (9) are inconsistent by sub-proof #2183.
% 231.83/42.99  | | 
% 231.83/42.99  | End of split
% 231.83/42.99  | 
% 231.83/42.99  End of proof
% 231.83/42.99  
% 231.83/42.99  Sub-proof #1750 shows that the following formulas are inconsistent:
% 231.83/42.99  ----------------------------------------------------------------
% 231.83/42.99    (1)  all_57_11 = e1 & op(e1, e0) = e1
% 231.83/42.99    (2)  all_57_11 = e0
% 231.83/42.99    (3)   ~ (e1 = e0)
% 231.83/42.99  
% 231.83/42.99  Begin of proof
% 231.83/42.99  | 
% 231.83/42.99  | ALPHA: (1) implies:
% 231.83/42.99  |   (4)  all_57_11 = e1
% 231.83/42.99  | 
% 231.83/42.99  | COMBINE_EQS: (2), (4) imply:
% 231.83/42.99  |   (5)  e1 = e0
% 231.83/42.99  | 
% 231.83/42.99  | REDUCE: (3), (5) imply:
% 231.83/42.99  |   (6)  $false
% 231.83/42.99  | 
% 231.83/42.99  | CLOSE: (6) is inconsistent.
% 231.83/42.99  | 
% 231.83/42.99  End of proof
% 231.83/42.99  
% 231.83/42.99  Sub-proof #1751 shows that the following formulas are inconsistent:
% 231.83/42.99  ----------------------------------------------------------------
% 231.83/42.99    (1)  all_57_10 = e0 & op(e2, e0) = e0
% 231.83/42.99    (2)  all_57_10 = e2
% 231.83/42.99    (3)   ~ (e2 = e0)
% 231.83/42.99  
% 231.83/42.99  Begin of proof
% 231.83/42.99  | 
% 231.83/42.99  | ALPHA: (1) implies:
% 231.83/42.99  |   (4)  all_57_10 = e0
% 231.83/42.99  | 
% 231.83/42.99  | COMBINE_EQS: (2), (4) imply:
% 231.83/42.99  |   (5)  e2 = e0
% 231.83/42.99  | 
% 231.83/42.99  | REDUCE: (3), (5) imply:
% 231.83/42.99  |   (6)  $false
% 231.83/42.99  | 
% 231.83/42.99  | CLOSE: (6) is inconsistent.
% 231.83/42.99  | 
% 231.83/42.99  End of proof
% 231.83/42.99  
% 231.83/42.99  Sub-proof #1752 shows that the following formulas are inconsistent:
% 231.83/42.99  ----------------------------------------------------------------
% 231.83/42.99    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.83/42.99         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.83/42.99    (2)   ~ (e3 = e1)
% 231.83/42.99    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/42.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/42.99    (4)   ~ (all_6_2 = e3)
% 231.83/42.99    (5)  op(e1, e1) = all_6_2
% 231.83/42.99    (6)  all_57_3 = e0
% 231.83/42.99    (7)   ~ (e3 = e2)
% 231.83/42.99    (8)   ~ (e3 = e0)
% 231.83/42.99    (9)  all_57_15 = e3
% 231.83/42.99    (10)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.83/42.99          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.83/42.99            e1)
% 231.83/42.99    (11)  all_57_10 = e2
% 231.83/42.99    (12)   ~ (e2 = e0)
% 231.83/42.99    (13)  all_57_2 = e3
% 231.83/42.99    (14)   ~ (e1 = e0)
% 231.83/42.99    (15)  all_57_5 = e2
% 231.83/42.99    (16)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.83/42.99          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.83/42.99    (17)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.83/42.99          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.83/42.99            e2)
% 231.83/42.99    (18)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.83/42.99              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.83/42.99                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.83/42.99                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.83/42.99    (19)   ~ (e2 = e1)
% 231.83/42.99  
% 231.83/42.99  Begin of proof
% 231.83/42.99  | 
% 231.83/42.99  | BETA: splitting (16) gives:
% 231.83/42.99  | 
% 231.83/42.99  | Case 1:
% 231.83/42.99  | | 
% 231.83/42.99  | |   (20)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) =
% 231.83/42.99  | |           e3)
% 231.83/42.99  | | 
% 231.83/42.99  | | BETA: splitting (20) gives:
% 231.83/42.99  | | 
% 231.83/42.99  | | Case 1:
% 231.83/42.99  | | | 
% 231.83/42.99  | | |   (21)  all_57_4 = e3 & op(e3, e1) = e3
% 231.83/42.99  | | | 
% 231.83/42.99  | | | ALPHA: (21) implies:
% 231.83/42.99  | | |   (22)  all_57_4 = e3
% 231.83/42.99  | | | 
% 231.83/42.99  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 231.83/42.99  | | |            (13), (14), (15), (16), (17), (18), (19), (22) are inconsistent
% 231.83/42.99  | | |            by sub-proof #1753.
% 231.83/42.99  | | | 
% 231.83/42.99  | | Case 2:
% 231.83/42.99  | | | 
% 231.83/42.99  | | |   (23)  all_57_5 = e3 & op(e2, e1) = e3
% 231.83/42.99  | | | 
% 231.83/42.99  | | | ALPHA: (23) implies:
% 231.83/42.99  | | |   (24)  all_57_5 = e3
% 231.83/42.99  | | | 
% 231.83/42.99  | | | REF_CLOSE: (1), (2), (6), (11), (13), (14), (19), (24) are inconsistent by
% 231.83/42.99  | | |            sub-proof #1804.
% 231.83/42.99  | | | 
% 231.83/42.99  | | End of split
% 231.83/42.99  | | 
% 231.83/42.99  | Case 2:
% 231.83/42.99  | | 
% 231.83/42.99  | |   (25)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) =
% 231.83/42.99  | |           e3)
% 231.83/42.99  | | 
% 231.83/42.99  | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (10), (12), (14), (17), (18),
% 231.83/42.99  | |            (19), (25) are inconsistent by sub-proof #1794.
% 231.83/42.99  | | 
% 231.83/42.99  | End of split
% 231.83/42.99  | 
% 231.83/42.99  End of proof
% 231.83/42.99  
% 231.83/42.99  Sub-proof #1753 shows that the following formulas are inconsistent:
% 231.83/42.99  ----------------------------------------------------------------
% 231.83/42.99    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.83/42.99         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.83/42.99    (2)   ~ (e3 = e1)
% 231.83/42.99    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/42.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/42.99    (4)   ~ (all_6_2 = e3)
% 231.83/42.99    (5)  op(e1, e1) = all_6_2
% 231.83/42.99    (6)  all_57_3 = e0
% 231.83/42.99    (7)  all_57_4 = e3
% 231.83/42.99    (8)   ~ (e3 = e2)
% 231.83/42.99    (9)   ~ (e3 = e0)
% 231.83/42.99    (10)  all_57_15 = e3
% 231.83/42.99    (11)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.83/42.99          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.83/42.99            e1)
% 231.83/42.99    (12)  all_57_10 = e2
% 231.83/42.99    (13)   ~ (e2 = e0)
% 231.83/42.99    (14)  all_57_2 = e3
% 231.83/42.99    (15)   ~ (e1 = e0)
% 231.83/42.99    (16)  all_57_5 = e2
% 231.83/42.99    (17)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.83/42.99          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.83/42.99    (18)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.83/42.99          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.83/42.99            e2)
% 231.83/42.99    (19)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.83/42.99              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.83/42.99                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.83/42.99                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.83/42.99    (20)   ~ (e2 = e1)
% 231.83/42.99  
% 231.83/42.99  Begin of proof
% 231.83/42.99  | 
% 231.83/42.99  | BETA: splitting (1) gives:
% 231.83/42.99  | 
% 231.83/42.99  | Case 1:
% 231.83/42.99  | | 
% 231.83/42.99  | |   (21)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) =
% 231.83/42.99  | |           e1)
% 231.83/42.99  | | 
% 231.83/42.99  | | BETA: splitting (21) gives:
% 231.83/42.99  | | 
% 231.83/42.99  | | Case 1:
% 231.83/42.99  | | | 
% 231.83/42.99  | | |   (22)  all_57_2 = e1 & op(e2, e3) = e1
% 231.83/42.99  | | | 
% 231.83/42.99  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 231.83/42.99  | | |            (13), (14), (15), (17), (18), (19), (20), (22) are inconsistent
% 231.83/42.99  | | |            by sub-proof #1754.
% 231.83/42.99  | | | 
% 231.83/42.99  | | Case 2:
% 231.83/42.99  | | | 
% 231.83/42.99  | | |   (23)  all_57_3 = e1 & op(e2, e2) = e1
% 231.83/42.99  | | | 
% 231.83/42.99  | | | REF_CLOSE: (6), (15), (23) are inconsistent by sub-proof #2362.
% 231.83/42.99  | | | 
% 231.83/42.99  | | End of split
% 231.83/42.99  | | 
% 231.83/42.99  | Case 2:
% 231.83/42.99  | | 
% 231.83/42.99  | |   (24)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) =
% 231.83/42.99  | |           e1)
% 231.83/42.99  | | 
% 231.83/42.99  | | BETA: splitting (24) gives:
% 231.83/42.99  | | 
% 231.83/42.99  | | Case 1:
% 231.83/42.99  | | | 
% 231.83/42.99  | | |   (25)  all_57_5 = e1 & op(e2, e1) = e1
% 231.83/42.99  | | | 
% 231.83/42.99  | | | REF_CLOSE: (16), (20), (25) are inconsistent by sub-proof #1886.
% 231.83/42.99  | | | 
% 231.83/42.99  | | Case 2:
% 231.83/42.99  | | | 
% 231.83/42.99  | | |   (26)  all_57_10 = e1 & op(e2, e0) = e1
% 231.83/42.99  | | | 
% 231.83/42.99  | | | REF_CLOSE: (12), (20), (26) are inconsistent by sub-proof #2360.
% 231.83/42.99  | | | 
% 231.83/42.99  | | End of split
% 231.83/42.99  | | 
% 231.83/42.99  | End of split
% 231.83/42.99  | 
% 231.83/42.99  End of proof
% 231.83/42.99  
% 231.83/42.99  Sub-proof #1754 shows that the following formulas are inconsistent:
% 231.83/42.99  ----------------------------------------------------------------
% 231.83/42.99    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.83/42.99         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.83/42.99    (2)   ~ (e3 = e1)
% 231.83/42.99    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/42.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/42.99    (4)   ~ (all_6_2 = e3)
% 231.83/42.99    (5)  op(e1, e1) = all_6_2
% 231.83/42.99    (6)  all_57_3 = e0
% 231.83/42.99    (7)  all_57_4 = e3
% 231.83/42.99    (8)   ~ (e3 = e2)
% 231.83/42.99    (9)   ~ (e3 = e0)
% 231.83/42.99    (10)  all_57_15 = e3
% 231.83/42.99    (11)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.83/42.99          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.83/42.99            e1)
% 231.83/42.99    (12)  all_57_10 = e2
% 231.83/42.99    (13)  all_57_2 = e1 & op(e2, e3) = e1
% 231.83/42.99    (14)   ~ (e2 = e0)
% 231.83/42.99    (15)  all_57_2 = e3
% 231.83/42.99    (16)   ~ (e1 = e0)
% 231.83/42.99    (17)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.83/42.99          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.83/42.99    (18)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.83/42.99          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.83/42.99            e2)
% 231.83/42.99    (19)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.83/42.99              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.83/42.99                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.83/42.99                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.83/42.99    (20)   ~ (e2 = e1)
% 231.83/42.99  
% 231.83/42.99  Begin of proof
% 231.83/42.99  | 
% 231.83/42.99  | ALPHA: (13) implies:
% 231.83/42.99  |   (21)  all_57_2 = e1
% 231.83/42.99  | 
% 231.83/42.99  | COMBINE_EQS: (15), (21) imply:
% 231.83/42.99  |   (22)  e3 = e1
% 231.83/42.99  | 
% 231.83/42.99  | COMBINE_EQS: (7), (22) imply:
% 231.83/42.99  |   (23)  all_57_4 = e1
% 231.83/42.99  | 
% 231.83/42.99  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (14),
% 231.83/42.99  |            (15), (16), (17), (18), (19), (20), (23) are inconsistent by
% 231.83/42.99  |            sub-proof #1755.
% 231.83/42.99  | 
% 231.83/42.99  End of proof
% 231.83/42.99  
% 231.83/42.99  Sub-proof #1755 shows that the following formulas are inconsistent:
% 231.83/42.99  ----------------------------------------------------------------
% 231.83/42.99    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.83/42.99         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.83/42.99    (2)   ~ (e3 = e1)
% 231.83/42.99    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/42.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/42.99    (4)   ~ (all_6_2 = e3)
% 231.83/42.99    (5)  op(e1, e1) = all_6_2
% 231.83/42.99    (6)  all_57_3 = e0
% 231.83/42.99    (7)   ~ (e3 = e2)
% 231.83/42.99    (8)   ~ (e3 = e0)
% 231.83/42.99    (9)  all_57_15 = e3
% 231.83/42.99    (10)  all_57_4 = e1
% 231.83/42.99    (11)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.83/42.99          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.83/42.99            e1)
% 231.83/42.99    (12)  all_57_10 = e2
% 231.83/42.99    (13)   ~ (e2 = e0)
% 231.83/42.99    (14)  all_57_2 = e3
% 231.83/42.99    (15)   ~ (e1 = e0)
% 231.83/42.99    (16)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.83/42.99          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.83/42.99    (17)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.83/42.99          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.83/42.99            e2)
% 231.83/42.99    (18)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.83/42.99              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.83/42.99                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.83/43.00                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.83/43.00    (19)   ~ (e2 = e1)
% 231.83/43.00  
% 231.83/43.00  Begin of proof
% 231.83/43.00  | 
% 231.83/43.00  | BETA: splitting (16) gives:
% 231.83/43.00  | 
% 231.83/43.00  | Case 1:
% 231.83/43.00  | | 
% 231.83/43.00  | |   (20)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) =
% 231.83/43.00  | |           e3)
% 231.83/43.00  | | 
% 231.83/43.00  | | REF_CLOSE: (1), (2), (6), (10), (12), (14), (15), (19), (20) are
% 231.83/43.00  | |            inconsistent by sub-proof #1756.
% 231.83/43.00  | | 
% 231.83/43.00  | Case 2:
% 231.83/43.00  | | 
% 231.83/43.00  | |   (21)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) =
% 231.83/43.00  | |           e3)
% 231.83/43.00  | | 
% 231.83/43.00  | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (11), (13), (15), (17), (18),
% 231.83/43.00  | |            (19), (21) are inconsistent by sub-proof #1794.
% 231.83/43.00  | | 
% 231.83/43.00  | End of split
% 231.83/43.00  | 
% 231.83/43.00  End of proof
% 231.83/43.00  
% 231.83/43.00  Sub-proof #1756 shows that the following formulas are inconsistent:
% 231.83/43.00  ----------------------------------------------------------------
% 231.83/43.00    (1)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3)
% 231.83/43.00    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.83/43.00         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.83/43.00    (3)   ~ (e3 = e1)
% 231.83/43.00    (4)  all_57_3 = e0
% 231.83/43.00    (5)  all_57_4 = e1
% 231.83/43.00    (6)  all_57_10 = e2
% 231.83/43.00    (7)  all_57_2 = e3
% 231.83/43.00    (8)   ~ (e1 = e0)
% 231.83/43.00    (9)   ~ (e2 = e1)
% 231.83/43.00  
% 231.83/43.00  Begin of proof
% 231.83/43.00  | 
% 231.83/43.00  | BETA: splitting (1) gives:
% 231.83/43.00  | 
% 231.83/43.00  | Case 1:
% 231.83/43.00  | | 
% 231.83/43.00  | |   (10)  all_57_4 = e3 & op(e3, e1) = e3
% 231.83/43.00  | | 
% 231.83/43.00  | | ALPHA: (10) implies:
% 231.83/43.00  | |   (11)  all_57_4 = e3
% 231.83/43.00  | | 
% 231.83/43.00  | | REF_CLOSE: (3), (5), (11) are inconsistent by sub-proof #2426.
% 231.83/43.00  | | 
% 231.83/43.00  | Case 2:
% 231.83/43.00  | | 
% 231.83/43.00  | |   (12)  all_57_5 = e3 & op(e2, e1) = e3
% 231.83/43.00  | | 
% 231.83/43.00  | | ALPHA: (12) implies:
% 231.83/43.00  | |   (13)  all_57_5 = e3
% 231.83/43.00  | | 
% 231.83/43.00  | | REF_CLOSE: (2), (3), (4), (6), (7), (8), (9), (13) are inconsistent by
% 231.83/43.00  | |            sub-proof #1804.
% 231.83/43.00  | | 
% 231.83/43.00  | End of split
% 231.83/43.00  | 
% 231.83/43.00  End of proof
% 231.83/43.00  
% 231.83/43.00  Sub-proof #1757 shows that the following formulas are inconsistent:
% 231.83/43.00  ----------------------------------------------------------------
% 231.83/43.00    (1)  all_57_13 = e1
% 231.83/43.00    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.83/43.00         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.83/43.00    (3)   ~ (e3 = e1)
% 231.83/43.00    (4)  all_57_13 = e0 & op(e0, e2) = e0
% 231.83/43.00    (5)   ~ (e3 = e2)
% 231.83/43.00    (6)   ~ (e2 = e0)
% 231.83/43.00    (7)  all_57_3 = e1
% 231.83/43.00    (8)   ~ (e1 = e0)
% 231.83/43.00    (9)  all_57_1 = e3
% 231.83/43.00    (10)   ~ (e2 = e1)
% 231.83/43.00    (11)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.83/43.00          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.83/43.00  
% 231.83/43.00  Begin of proof
% 231.83/43.00  | 
% 231.83/43.00  | ALPHA: (4) implies:
% 231.83/43.00  |   (12)  all_57_13 = e0
% 231.83/43.00  | 
% 231.83/43.00  | COMBINE_EQS: (1), (12) imply:
% 231.83/43.00  |   (13)  e1 = e0
% 231.83/43.00  | 
% 231.83/43.00  | COMBINE_EQS: (7), (13) imply:
% 231.83/43.00  |   (14)  all_57_3 = e0
% 231.83/43.00  | 
% 231.83/43.00  | REF_CLOSE: (2), (3), (5), (6), (8), (9), (10), (11), (12), (14) are
% 231.83/43.00  |            inconsistent by sub-proof #1758.
% 231.83/43.00  | 
% 231.83/43.00  End of proof
% 231.83/43.00  
% 231.83/43.00  Sub-proof #1758 shows that the following formulas are inconsistent:
% 231.83/43.00  ----------------------------------------------------------------
% 231.83/43.00    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.83/43.00         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.83/43.00    (2)   ~ (e3 = e1)
% 231.83/43.00    (3)  all_57_3 = e0
% 231.83/43.00    (4)   ~ (e3 = e2)
% 231.83/43.00    (5)   ~ (e2 = e0)
% 231.83/43.00    (6)   ~ (e1 = e0)
% 231.83/43.00    (7)  all_57_13 = e0
% 231.83/43.00    (8)  all_57_1 = e3
% 231.83/43.00    (9)   ~ (e2 = e1)
% 231.83/43.00    (10)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.83/43.00          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.83/43.00  
% 231.83/43.00  Begin of proof
% 231.83/43.00  | 
% 231.83/43.00  | BETA: splitting (1) gives:
% 231.83/43.00  | 
% 231.83/43.00  | Case 1:
% 231.83/43.00  | | 
% 231.83/43.00  | |   (11)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 231.83/43.00  | |           e2)
% 231.83/43.00  | | 
% 231.83/43.00  | | BETA: splitting (11) gives:
% 231.83/43.00  | | 
% 231.83/43.00  | | Case 1:
% 231.83/43.00  | | | 
% 231.83/43.00  | | |   (12)  all_57_1 = e2 & op(e3, e2) = e2
% 231.83/43.00  | | | 
% 231.83/43.00  | | | REF_CLOSE: (4), (8), (12) are inconsistent by sub-proof #1809.
% 231.83/43.00  | | | 
% 231.83/43.00  | | Case 2:
% 231.83/43.00  | | | 
% 231.83/43.00  | | |   (13)  all_57_3 = e2 & op(e2, e2) = e2
% 231.83/43.00  | | | 
% 231.83/43.00  | | | REF_CLOSE: (3), (5), (13) are inconsistent by sub-proof #2256.
% 231.83/43.00  | | | 
% 231.83/43.00  | | End of split
% 231.83/43.00  | | 
% 231.83/43.00  | Case 2:
% 231.83/43.00  | | 
% 231.83/43.00  | |   (14)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 231.83/43.00  | |           e2)
% 231.83/43.00  | | 
% 231.83/43.00  | | BETA: splitting (14) gives:
% 231.83/43.00  | | 
% 231.83/43.00  | | Case 1:
% 231.83/43.00  | | | 
% 231.83/43.00  | | |   (15)  all_57_7 = e2 & op(e1, e2) = e2
% 231.83/43.00  | | | 
% 231.83/43.00  | | | ALPHA: (15) implies:
% 231.83/43.00  | | |   (16)  all_57_7 = e2
% 231.83/43.00  | | | 
% 231.83/43.00  | | | REF_CLOSE: (2), (3), (6), (7), (8), (9), (10), (16) are inconsistent by
% 231.83/43.00  | | |            sub-proof #1759.
% 231.83/43.00  | | | 
% 231.83/43.00  | | Case 2:
% 231.83/43.00  | | | 
% 231.83/43.00  | | |   (17)  all_57_13 = e2 & op(e0, e2) = e2
% 231.83/43.00  | | | 
% 231.83/43.00  | | | REF_CLOSE: (5), (7), (17) are inconsistent by sub-proof #2316.
% 231.83/43.00  | | | 
% 231.83/43.00  | | End of split
% 231.83/43.00  | | 
% 231.83/43.00  | End of split
% 231.83/43.00  | 
% 231.83/43.00  End of proof
% 231.83/43.00  
% 231.83/43.00  Sub-proof #1759 shows that the following formulas are inconsistent:
% 231.83/43.00  ----------------------------------------------------------------
% 231.83/43.00    (1)   ~ (e3 = e1)
% 231.83/43.00    (2)  all_57_7 = e2
% 231.83/43.00    (3)  all_57_3 = e0
% 231.83/43.00    (4)   ~ (e1 = e0)
% 231.83/43.00    (5)  all_57_13 = e0
% 231.83/43.00    (6)  all_57_1 = e3
% 231.83/43.00    (7)   ~ (e2 = e1)
% 231.83/43.00    (8)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.83/43.00         (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.83/43.00  
% 231.83/43.00  Begin of proof
% 231.83/43.00  | 
% 231.83/43.00  | BETA: splitting (8) gives:
% 231.83/43.00  | 
% 231.83/43.00  | Case 1:
% 231.83/43.00  | | 
% 231.83/43.00  | |   (9)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1)
% 231.83/43.00  | | 
% 231.83/43.00  | | BETA: splitting (9) gives:
% 231.83/43.00  | | 
% 231.83/43.00  | | Case 1:
% 231.83/43.00  | | | 
% 231.83/43.00  | | |   (10)  all_57_1 = e1 & op(e3, e2) = e1
% 231.83/43.00  | | | 
% 231.83/43.00  | | | REF_CLOSE: (1), (6), (10) are inconsistent by sub-proof #2453.
% 231.83/43.00  | | | 
% 231.83/43.00  | | Case 2:
% 231.83/43.00  | | | 
% 231.83/43.00  | | |   (11)  all_57_3 = e1 & op(e2, e2) = e1
% 231.83/43.00  | | | 
% 231.83/43.00  | | | REF_CLOSE: (3), (4), (11) are inconsistent by sub-proof #2252.
% 231.83/43.00  | | | 
% 231.83/43.00  | | End of split
% 231.83/43.00  | | 
% 231.83/43.00  | Case 2:
% 231.83/43.00  | | 
% 231.83/43.00  | |   (12)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 231.83/43.00  | |           e1)
% 231.83/43.00  | | 
% 231.83/43.00  | | BETA: splitting (12) gives:
% 231.83/43.00  | | 
% 231.83/43.00  | | Case 1:
% 231.83/43.00  | | | 
% 231.83/43.00  | | |   (13)  all_57_7 = e1 & op(e1, e2) = e1
% 231.83/43.00  | | | 
% 231.83/43.00  | | | ALPHA: (13) implies:
% 231.83/43.00  | | |   (14)  all_57_7 = e1
% 231.83/43.00  | | | 
% 231.83/43.00  | | | REF_CLOSE: (2), (7), (14) are inconsistent by sub-proof #1761.
% 231.83/43.00  | | | 
% 231.83/43.00  | | Case 2:
% 231.83/43.00  | | | 
% 231.83/43.00  | | |   (15)  all_57_13 = e1 & op(e0, e2) = e1
% 231.83/43.00  | | | 
% 231.83/43.00  | | | ALPHA: (15) implies:
% 231.83/43.00  | | |   (16)  all_57_13 = e1
% 231.83/43.00  | | | 
% 231.83/43.00  | | | REF_CLOSE: (4), (5), (16) are inconsistent by sub-proof #1760.
% 231.83/43.00  | | | 
% 231.83/43.00  | | End of split
% 231.83/43.00  | | 
% 231.83/43.00  | End of split
% 231.83/43.00  | 
% 231.83/43.00  End of proof
% 231.83/43.00  
% 231.83/43.00  Sub-proof #1760 shows that the following formulas are inconsistent:
% 231.83/43.00  ----------------------------------------------------------------
% 231.83/43.00    (1)  all_57_13 = e1
% 231.83/43.00    (2)  all_57_13 = e0
% 231.83/43.00    (3)   ~ (e1 = e0)
% 231.83/43.00  
% 231.83/43.00  Begin of proof
% 231.83/43.00  | 
% 231.83/43.00  | COMBINE_EQS: (1), (2) imply:
% 231.83/43.00  |   (4)  e1 = e0
% 231.83/43.00  | 
% 231.83/43.00  | SIMP: (4) implies:
% 231.83/43.00  |   (5)  e1 = e0
% 231.83/43.00  | 
% 231.83/43.00  | REDUCE: (3), (5) imply:
% 231.83/43.00  |   (6)  $false
% 231.83/43.00  | 
% 231.83/43.00  | CLOSE: (6) is inconsistent.
% 231.83/43.00  | 
% 231.83/43.00  End of proof
% 231.83/43.00  
% 231.83/43.00  Sub-proof #1761 shows that the following formulas are inconsistent:
% 231.83/43.00  ----------------------------------------------------------------
% 231.83/43.00    (1)  all_57_7 = e2
% 231.83/43.00    (2)  all_57_7 = e1
% 231.83/43.00    (3)   ~ (e2 = e1)
% 231.83/43.00  
% 231.83/43.00  Begin of proof
% 231.83/43.00  | 
% 231.83/43.00  | COMBINE_EQS: (1), (2) imply:
% 231.83/43.00  |   (4)  e2 = e1
% 231.83/43.00  | 
% 231.83/43.00  | SIMP: (4) implies:
% 231.83/43.00  |   (5)  e2 = e1
% 231.83/43.00  | 
% 231.83/43.00  | REDUCE: (3), (5) imply:
% 231.83/43.00  |   (6)  $false
% 231.83/43.00  | 
% 231.83/43.00  | CLOSE: (6) is inconsistent.
% 231.83/43.00  | 
% 231.83/43.00  End of proof
% 231.83/43.00  
% 231.83/43.00  Sub-proof #1762 shows that the following formulas are inconsistent:
% 231.83/43.00  ----------------------------------------------------------------
% 231.83/43.00    (1)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.83/43.00         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.83/43.00    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.83/43.00         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.83/43.00    (3)   ~ (e3 = e1)
% 231.83/43.00    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/43.00           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/43.00    (5)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.83/43.00         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.83/43.00    (6)   ~ (all_6_2 = e3)
% 231.83/43.00    (7)  op(e1, e1) = all_6_2
% 231.83/43.00    (8)  op(e2, e2) = e1
% 231.83/43.00    (9)   ~ (e3 = e2)
% 231.83/43.00    (10)   ~ (e3 = e0)
% 231.83/43.00    (11)  op(e3, e3) = e3
% 231.83/43.00    (12)  all_57_15 = e3
% 231.83/43.00    (13)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.83/43.00          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.83/43.00            e1)
% 231.83/43.00    (14)   ~ (e2 = e0)
% 231.83/43.00    (15)   ~ (e1 = e0)
% 231.83/43.00    (16)  all_57_12 = e3
% 231.83/43.00    (17)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.83/43.00          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.83/43.00    (18)  op(e0, e0) = e3
% 231.83/43.00    (19)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.83/43.00          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.83/43.00            e2)
% 231.83/43.00    (20)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.83/43.00              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.83/43.00                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.83/43.00                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.83/43.00    (21)   ~ (e2 = e1)
% 231.83/43.00    (22)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.83/43.00          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.83/43.00    (23)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.83/43.00          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.83/43.00    (24)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.83/43.00          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.83/43.00    (25)  all_57_7 = e0
% 231.83/43.00  
% 231.83/43.00  Begin of proof
% 231.83/43.00  | 
% 231.83/43.00  | BETA: splitting (5) gives:
% 231.83/43.00  | 
% 231.83/43.00  | Case 1:
% 231.83/43.00  | | 
% 231.83/43.00  | |   (26)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 231.83/43.00  | |           e3)
% 231.83/43.00  | | 
% 231.83/43.00  | | BETA: splitting (26) gives:
% 231.83/43.00  | | 
% 231.83/43.00  | | Case 1:
% 231.83/43.00  | | | 
% 231.83/43.00  | | |   (27)  all_57_6 = e3 & op(e1, e3) = e3
% 231.83/43.00  | | | 
% 231.83/43.00  | | | ALPHA: (27) implies:
% 231.83/43.00  | | |   (28)  all_57_6 = e3
% 231.83/43.00  | | | 
% 231.83/43.00  | | | BETA: splitting (20) gives:
% 231.83/43.00  | | | 
% 231.83/43.00  | | | Case 1:
% 231.83/43.00  | | | | 
% 231.83/43.00  | | | |   (29)  all_57_15 = e0 & op(e0, e0) = e0
% 231.83/43.00  | | | | 
% 231.83/43.00  | | | | ALPHA: (29) implies:
% 231.83/43.00  | | | |   (30)  op(e0, e0) = e0
% 231.83/43.00  | | | | 
% 231.83/43.00  | | | | REF_CLOSE: (4), (10), (18), (30) are inconsistent by sub-proof #2304.
% 231.83/43.00  | | | | 
% 231.83/43.00  | | | Case 2:
% 231.83/43.00  | | | | 
% 231.83/43.00  | | | |   (31)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2,
% 231.83/43.00  | | | |               e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) &
% 231.83/43.00  | | | |         ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0,
% 231.83/43.00  | | | |               e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 231.83/43.00  | | | | 
% 231.83/43.00  | | | | ALPHA: (31) implies:
% 231.83/43.00  | | | |   (32)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0,
% 231.83/43.00  | | | |             e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.83/43.00  | | | | 
% 231.83/43.00  | | | | BETA: splitting (32) gives:
% 231.83/43.00  | | | | 
% 231.83/43.00  | | | | Case 1:
% 231.83/43.00  | | | | | 
% 231.83/43.00  | | | | |   (33)  all_57_12 = e0 & op(e0, e3) = e0
% 231.83/43.00  | | | | | 
% 231.83/43.00  | | | | | ALPHA: (33) implies:
% 231.83/43.00  | | | | |   (34)  all_57_12 = e0
% 231.83/43.00  | | | | | 
% 231.83/43.00  | | | | | REF_CLOSE: (1), (3), (4), (9), (11), (14), (15), (21), (23), (28),
% 231.83/43.00  | | | | |            (34) are inconsistent by sub-proof #1782.
% 231.83/43.00  | | | | | 
% 231.83/43.00  | | | | Case 2:
% 231.83/43.00  | | | | | 
% 231.83/43.00  | | | | |   (35)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 231.83/43.00  | | | | |             e1) = e0)
% 231.83/43.00  | | | | | 
% 231.83/43.00  | | | | | BETA: splitting (35) gives:
% 231.83/43.00  | | | | | 
% 231.83/43.00  | | | | | Case 1:
% 231.83/43.00  | | | | | | 
% 231.83/43.00  | | | | | |   (36)  all_57_13 = e0 & op(e0, e2) = e0
% 231.83/43.00  | | | | | | 
% 231.83/43.00  | | | | | | ALPHA: (36) implies:
% 231.83/43.00  | | | | | |   (37)  all_57_13 = e0
% 231.83/43.00  | | | | | | 
% 231.83/43.00  | | | | | | REF_CLOSE: (2), (3), (4), (8), (9), (10), (12), (13), (14), (15),
% 231.83/43.00  | | | | | |            (17), (18), (19), (21), (25), (32), (37) are inconsistent
% 231.83/43.00  | | | | | |            by sub-proof #1765.
% 231.83/43.00  | | | | | | 
% 231.83/43.00  | | | | | Case 2:
% 231.83/43.00  | | | | | | 
% 231.83/43.00  | | | | | |   (38)  all_57_14 = e0 & op(e0, e1) = e0
% 231.83/43.00  | | | | | | 
% 231.83/43.00  | | | | | | ALPHA: (38) implies:
% 231.83/43.00  | | | | | |   (39)  all_57_14 = e0
% 231.83/43.00  | | | | | | 
% 231.83/43.00  | | | | | | REF_CLOSE: (3), (9), (12), (13), (14), (15), (16), (19), (21), (39)
% 231.83/43.00  | | | | | |            are inconsistent by sub-proof #1763.
% 231.83/43.00  | | | | | | 
% 231.83/43.00  | | | | | End of split
% 231.83/43.00  | | | | | 
% 231.83/43.00  | | | | End of split
% 231.83/43.00  | | | | 
% 231.83/43.00  | | | End of split
% 231.83/43.00  | | | 
% 231.83/43.00  | | Case 2:
% 231.83/43.00  | | | 
% 231.83/43.00  | | |   (40)  all_57_7 = e3 & op(e1, e2) = e3
% 231.83/43.00  | | | 
% 231.83/43.00  | | | REF_CLOSE: (10), (25), (40) are inconsistent by sub-proof #2345.
% 231.83/43.00  | | | 
% 231.83/43.00  | | End of split
% 231.83/43.00  | | 
% 231.83/43.00  | Case 2:
% 231.83/43.00  | | 
% 231.83/43.00  | |   (41)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 231.83/43.00  | |           e3)
% 231.83/43.00  | | 
% 231.83/43.00  | | REF_CLOSE: (3), (4), (6), (7), (9), (10), (12), (14), (15), (20), (21),
% 231.83/43.00  | |            (22), (24), (41) are inconsistent by sub-proof #1786.
% 231.83/43.00  | | 
% 231.83/43.00  | End of split
% 231.83/43.00  | 
% 231.83/43.00  End of proof
% 231.83/43.00  
% 231.83/43.00  Sub-proof #1763 shows that the following formulas are inconsistent:
% 231.83/43.00  ----------------------------------------------------------------
% 231.83/43.00    (1)   ~ (e3 = e1)
% 231.83/43.00    (2)   ~ (e3 = e2)
% 231.83/43.00    (3)  all_57_15 = e3
% 231.83/43.00    (4)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 231.83/43.00         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.83/43.00    (5)   ~ (e2 = e0)
% 231.83/43.00    (6)   ~ (e1 = e0)
% 231.83/43.00    (7)  all_57_12 = e3
% 231.83/43.00    (8)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2) |
% 231.83/43.00         (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.83/43.00    (9)   ~ (e2 = e1)
% 231.83/43.00    (10)  all_57_14 = e0
% 231.83/43.00  
% 231.83/43.00  Begin of proof
% 231.83/43.00  | 
% 231.83/43.00  | BETA: splitting (8) gives:
% 231.83/43.00  | 
% 231.83/43.00  | Case 1:
% 231.83/43.00  | | 
% 231.83/43.00  | |   (11)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 231.83/43.00  | |           e2)
% 231.83/43.00  | | 
% 231.83/43.00  | | BETA: splitting (11) gives:
% 231.83/43.00  | | 
% 231.83/43.00  | | Case 1:
% 231.83/43.00  | | | 
% 231.83/43.00  | | |   (12)  all_57_12 = e2 & op(e0, e3) = e2
% 231.83/43.00  | | | 
% 231.83/43.00  | | | ALPHA: (12) implies:
% 231.83/43.00  | | |   (13)  all_57_12 = e2
% 231.83/43.00  | | | 
% 231.83/43.00  | | | REF_CLOSE: (2), (7), (13) are inconsistent by sub-proof #2392.
% 231.83/43.00  | | | 
% 231.83/43.00  | | Case 2:
% 231.83/43.00  | | | 
% 231.83/43.00  | | |   (14)  all_57_13 = e2 & op(e0, e2) = e2
% 231.83/43.00  | | | 
% 231.83/43.00  | | | ALPHA: (14) implies:
% 231.83/43.00  | | |   (15)  all_57_13 = e2
% 231.83/43.00  | | | 
% 231.83/43.00  | | | REF_CLOSE: (1), (3), (4), (6), (7), (9), (10), (15) are inconsistent by
% 231.83/43.00  | | |            sub-proof #1764.
% 231.83/43.00  | | | 
% 231.83/43.00  | | End of split
% 231.83/43.00  | | 
% 231.83/43.00  | Case 2:
% 231.83/43.00  | | 
% 231.83/43.00  | |   (16)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.83/43.00  | |           e2)
% 231.83/43.00  | | 
% 231.83/43.00  | | BETA: splitting (16) gives:
% 231.83/43.00  | | 
% 231.83/43.00  | | Case 1:
% 231.83/43.00  | | | 
% 231.83/43.00  | | |   (17)  all_57_14 = e2 & op(e0, e1) = e2
% 231.83/43.00  | | | 
% 231.83/43.00  | | | REF_CLOSE: (5), (10), (17) are inconsistent by sub-proof #2074.
% 231.83/43.00  | | | 
% 231.83/43.00  | | Case 2:
% 231.83/43.00  | | | 
% 231.83/43.00  | | |   (18)  all_57_15 = e2 & op(e0, e0) = e2
% 231.83/43.00  | | | 
% 231.83/43.00  | | | REF_CLOSE: (2), (3), (18) are inconsistent by sub-proof #2323.
% 231.83/43.00  | | | 
% 231.83/43.00  | | End of split
% 231.83/43.00  | | 
% 231.83/43.00  | End of split
% 231.83/43.00  | 
% 231.83/43.00  End of proof
% 231.83/43.00  
% 231.83/43.00  Sub-proof #1764 shows that the following formulas are inconsistent:
% 231.83/43.00  ----------------------------------------------------------------
% 231.83/43.00    (1)   ~ (e3 = e1)
% 231.83/43.00    (2)  all_57_15 = e3
% 231.83/43.00    (3)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 231.83/43.00         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.83/43.00    (4)  all_57_13 = e2
% 231.83/43.00    (5)   ~ (e1 = e0)
% 231.83/43.00    (6)  all_57_12 = e3
% 231.83/43.00    (7)   ~ (e2 = e1)
% 231.83/43.00    (8)  all_57_14 = e0
% 231.83/43.00  
% 231.83/43.00  Begin of proof
% 231.83/43.00  | 
% 231.83/43.00  | BETA: splitting (3) gives:
% 231.83/43.00  | 
% 231.83/43.00  | Case 1:
% 231.83/43.00  | | 
% 231.83/43.00  | |   (9)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 231.83/43.00  | |          e1)
% 231.83/43.00  | | 
% 231.83/43.00  | | BETA: splitting (9) gives:
% 231.83/43.00  | | 
% 231.83/43.00  | | Case 1:
% 231.83/43.00  | | | 
% 231.83/43.00  | | |   (10)  all_57_12 = e1 & op(e0, e3) = e1
% 231.83/43.00  | | | 
% 231.83/43.00  | | | ALPHA: (10) implies:
% 231.83/43.00  | | |   (11)  all_57_12 = e1
% 231.83/43.00  | | | 
% 231.83/43.00  | | | REF_CLOSE: (1), (6), (11) are inconsistent by sub-proof #2151.
% 231.83/43.00  | | | 
% 231.83/43.00  | | Case 2:
% 231.83/43.00  | | | 
% 231.83/43.00  | | |   (12)  all_57_13 = e1 & op(e0, e2) = e1
% 231.83/43.00  | | | 
% 231.83/43.00  | | | ALPHA: (12) implies:
% 231.83/43.00  | | |   (13)  all_57_13 = e1
% 231.83/43.00  | | | 
% 231.83/43.00  | | | REF_CLOSE: (4), (7), (13) are inconsistent by sub-proof #2327.
% 231.83/43.00  | | | 
% 231.83/43.00  | | End of split
% 231.83/43.00  | | 
% 231.83/43.00  | Case 2:
% 231.83/43.00  | | 
% 231.83/43.00  | |   (14)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.83/43.00  | |           e1)
% 231.83/43.00  | | 
% 231.83/43.00  | | BETA: splitting (14) gives:
% 231.83/43.00  | | 
% 231.83/43.00  | | Case 1:
% 231.83/43.00  | | | 
% 231.83/43.00  | | |   (15)  all_57_14 = e1 & op(e0, e1) = e1
% 231.83/43.00  | | | 
% 231.83/43.00  | | | ALPHA: (15) implies:
% 231.83/43.00  | | |   (16)  all_57_14 = e1
% 231.83/43.00  | | | 
% 231.83/43.00  | | | REF_CLOSE: (5), (8), (16) are inconsistent by sub-proof #2122.
% 231.83/43.00  | | | 
% 231.83/43.00  | | Case 2:
% 231.83/43.00  | | | 
% 231.83/43.00  | | |   (17)  all_57_15 = e1 & op(e0, e0) = e1
% 231.83/43.00  | | | 
% 231.83/43.00  | | | REF_CLOSE: (1), (2), (17) are inconsistent by sub-proof #2318.
% 231.83/43.00  | | | 
% 231.83/43.00  | | End of split
% 231.83/43.00  | | 
% 231.83/43.00  | End of split
% 231.83/43.00  | 
% 231.83/43.00  End of proof
% 231.83/43.00  
% 231.83/43.00  Sub-proof #1765 shows that the following formulas are inconsistent:
% 231.83/43.00  ----------------------------------------------------------------
% 231.83/43.00    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.83/43.00         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.83/43.00    (2)   ~ (e3 = e1)
% 231.83/43.00    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/43.00           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/43.00    (4)  op(e2, e2) = e1
% 231.83/43.00    (5)   ~ (e3 = e2)
% 231.83/43.00    (6)   ~ (e3 = e0)
% 231.83/43.00    (7)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 231.83/43.00         (all_57_14 = e0 & op(e0, e1) = e0)
% 231.83/43.00    (8)  all_57_15 = e3
% 231.83/43.00    (9)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 231.83/43.00         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.83/43.00    (10)   ~ (e2 = e0)
% 231.83/43.00    (11)   ~ (e1 = e0)
% 231.83/43.00    (12)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.83/43.00          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.83/43.00    (13)  op(e0, e0) = e3
% 231.83/43.00    (14)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.83/43.00          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.83/43.00            e2)
% 231.83/43.00    (15)  all_57_13 = e0
% 231.83/43.00    (16)   ~ (e2 = e1)
% 231.83/43.00    (17)  all_57_7 = e0
% 231.83/43.00  
% 231.83/43.00  Begin of proof
% 231.83/43.00  | 
% 231.83/43.00  | BETA: splitting (12) gives:
% 231.83/43.00  | 
% 231.83/43.00  | Case 1:
% 231.83/43.00  | | 
% 231.83/43.00  | |   (18)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 231.83/43.00  | |           e3)
% 231.83/43.00  | | 
% 231.83/43.00  | | BETA: splitting (18) gives:
% 231.83/43.00  | | 
% 231.83/43.00  | | Case 1:
% 231.83/43.00  | | | 
% 231.83/43.00  | | |   (19)  all_57_1 = e3 & op(e3, e2) = e3
% 231.83/43.00  | | | 
% 231.83/43.00  | | | ALPHA: (19) implies:
% 231.83/43.00  | | |   (20)  all_57_1 = e3
% 231.83/43.00  | | | 
% 231.83/43.00  | | | REF_CLOSE: (1), (3), (4), (5), (10), (15), (16), (17), (20) are
% 231.83/43.00  | | |            inconsistent by sub-proof #1767.
% 231.83/43.00  | | | 
% 231.83/43.00  | | Case 2:
% 231.83/43.00  | | | 
% 231.83/43.00  | | |   (21)  all_57_3 = e3 & op(e2, e2) = e3
% 231.83/43.00  | | | 
% 231.83/43.00  | | | ALPHA: (21) implies:
% 231.83/43.00  | | |   (22)  op(e2, e2) = e3
% 231.83/43.00  | | | 
% 231.83/43.00  | | | REF_CLOSE: (2), (3), (4), (22) are inconsistent by sub-proof #1912.
% 231.83/43.00  | | | 
% 231.83/43.00  | | End of split
% 231.83/43.00  | | 
% 231.83/43.00  | Case 2:
% 231.83/43.00  | | 
% 231.83/43.00  | |   (23)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 231.83/43.00  | |           e3)
% 231.83/43.00  | | 
% 231.83/43.00  | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (9), (10), (11), (13), (14), (16),
% 231.83/43.00  | |            (17), (23) are inconsistent by sub-proof #1766.
% 231.83/43.00  | | 
% 231.83/43.00  | End of split
% 231.83/43.00  | 
% 231.83/43.00  End of proof
% 231.83/43.00  
% 231.83/43.00  Sub-proof #1766 shows that the following formulas are inconsistent:
% 231.83/43.00  ----------------------------------------------------------------
% 231.83/43.00    (1)   ~ (e3 = e1)
% 231.83/43.00    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/43.00           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/43.00    (3)   ~ (e3 = e2)
% 231.83/43.00    (4)   ~ (e3 = e0)
% 231.83/43.00    (5)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 231.83/43.00         (all_57_14 = e0 & op(e0, e1) = e0)
% 231.83/43.00    (6)  all_57_15 = e3
% 231.83/43.00    (7)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 231.83/43.00         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.83/43.00    (8)   ~ (e2 = e0)
% 231.83/43.00    (9)   ~ (e1 = e0)
% 231.83/43.00    (10)  op(e0, e0) = e3
% 231.83/43.00    (11)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.83/43.00          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.83/43.00            e2)
% 231.83/43.00    (12)   ~ (e2 = e1)
% 231.83/43.00    (13)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.83/43.00    (14)  all_57_7 = e0
% 231.83/43.00  
% 231.83/43.00  Begin of proof
% 231.83/43.00  | 
% 231.83/43.00  | BETA: splitting (13) gives:
% 231.83/43.00  | 
% 231.83/43.00  | Case 1:
% 231.83/43.00  | | 
% 231.83/43.00  | |   (15)  all_57_7 = e3 & op(e1, e2) = e3
% 231.83/43.00  | | 
% 231.83/43.00  | | ALPHA: (15) implies:
% 231.83/43.00  | |   (16)  all_57_7 = e3
% 231.83/43.00  | | 
% 231.83/43.00  | | REF_CLOSE: (4), (14), (16) are inconsistent by sub-proof #2269.
% 231.83/43.00  | | 
% 231.83/43.00  | Case 2:
% 231.83/43.00  | | 
% 231.83/43.00  | |   (17)  all_57_13 = e3 & op(e0, e2) = e3
% 231.83/43.00  | | 
% 231.83/43.00  | | ALPHA: (17) implies:
% 231.83/43.00  | |   (18)  all_57_13 = e3
% 231.83/43.00  | | 
% 231.83/43.00  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 231.83/43.00  | |            (18) are inconsistent by sub-proof #2054.
% 231.83/43.00  | | 
% 231.83/43.00  | End of split
% 231.83/43.00  | 
% 231.83/43.00  End of proof
% 231.83/43.00  
% 231.83/43.00  Sub-proof #1767 shows that the following formulas are inconsistent:
% 231.83/43.00  ----------------------------------------------------------------
% 231.83/43.00    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.83/43.00         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.83/43.00    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/43.00           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/43.00    (3)  op(e2, e2) = e1
% 231.83/43.00    (4)   ~ (e3 = e2)
% 231.83/43.00    (5)   ~ (e2 = e0)
% 231.83/43.00    (6)  all_57_13 = e0
% 231.83/43.00    (7)  all_57_1 = e3
% 231.83/43.00    (8)   ~ (e2 = e1)
% 231.83/43.00    (9)  all_57_7 = e0
% 231.83/43.00  
% 231.83/43.00  Begin of proof
% 231.83/43.00  | 
% 231.83/43.00  | BETA: splitting (1) gives:
% 231.83/43.00  | 
% 231.83/43.00  | Case 1:
% 231.83/43.00  | | 
% 231.83/43.00  | |   (10)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 231.83/43.00  | |           e2)
% 231.83/43.00  | | 
% 231.83/43.00  | | REF_CLOSE: (2), (3), (4), (7), (8), (10) are inconsistent by sub-proof
% 231.83/43.00  | |            #1768.
% 231.83/43.00  | | 
% 231.83/43.00  | Case 2:
% 231.83/43.00  | | 
% 231.83/43.00  | |   (11)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 231.83/43.00  | |           e2)
% 231.83/43.00  | | 
% 231.83/43.00  | | BETA: splitting (11) gives:
% 231.83/43.00  | | 
% 231.83/43.00  | | Case 1:
% 231.83/43.00  | | | 
% 231.83/43.00  | | |   (12)  all_57_7 = e2 & op(e1, e2) = e2
% 231.83/43.00  | | | 
% 231.83/43.00  | | | ALPHA: (12) implies:
% 231.83/43.00  | | |   (13)  all_57_7 = e2
% 231.83/43.00  | | | 
% 231.83/43.00  | | | REF_CLOSE: (5), (9), (13) are inconsistent by sub-proof #2207.
% 231.83/43.00  | | | 
% 231.83/43.00  | | Case 2:
% 231.83/43.00  | | | 
% 231.83/43.00  | | |   (14)  all_57_13 = e2 & op(e0, e2) = e2
% 231.83/43.00  | | | 
% 231.83/43.00  | | | ALPHA: (14) implies:
% 231.83/43.00  | | |   (15)  all_57_13 = e2
% 231.83/43.00  | | | 
% 231.83/43.00  | | | REF_CLOSE: (5), (6), (15) are inconsistent by sub-proof #1911.
% 231.83/43.00  | | | 
% 231.83/43.00  | | End of split
% 231.83/43.00  | | 
% 231.83/43.00  | End of split
% 231.83/43.00  | 
% 231.83/43.00  End of proof
% 231.83/43.00  
% 231.83/43.00  Sub-proof #1768 shows that the following formulas are inconsistent:
% 231.83/43.00  ----------------------------------------------------------------
% 231.83/43.00    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/43.00           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/43.00    (2)  op(e2, e2) = e1
% 231.83/43.00    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2)
% 231.83/43.00    (4)   ~ (e3 = e2)
% 231.83/43.00    (5)  all_57_1 = e3
% 231.83/43.00    (6)   ~ (e2 = e1)
% 231.83/43.00  
% 231.83/43.00  Begin of proof
% 231.83/43.00  | 
% 231.83/43.00  | BETA: splitting (3) gives:
% 231.83/43.00  | 
% 231.83/43.00  | Case 1:
% 231.83/43.00  | | 
% 231.83/43.00  | |   (7)  all_57_1 = e2 & op(e3, e2) = e2
% 231.83/43.00  | | 
% 231.83/43.00  | | REF_CLOSE: (4), (5), (7) are inconsistent by sub-proof #1809.
% 231.83/43.00  | | 
% 231.83/43.00  | Case 2:
% 231.83/43.00  | | 
% 231.83/43.00  | |   (8)  all_57_3 = e2 & op(e2, e2) = e2
% 231.83/43.00  | | 
% 231.83/43.00  | | ALPHA: (8) implies:
% 231.83/43.00  | |   (9)  op(e2, e2) = e2
% 231.83/43.00  | | 
% 231.83/43.00  | | REF_CLOSE: (1), (2), (6), (9) are inconsistent by sub-proof #2306.
% 231.83/43.00  | | 
% 231.83/43.00  | End of split
% 231.83/43.00  | 
% 231.83/43.00  End of proof
% 231.83/43.00  
% 231.83/43.00  Sub-proof #1769 shows that the following formulas are inconsistent:
% 231.83/43.00  ----------------------------------------------------------------
% 231.83/43.00    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.83/43.00         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.83/43.00    (2)   ~ (e3 = e1)
% 231.83/43.00    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/43.00           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/43.00    (4)  op(e2, e2) = e1
% 231.83/43.00    (5)   ~ (e3 = e2)
% 231.83/43.00    (6)   ~ (e3 = e0)
% 231.83/43.00    (7)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 231.83/43.00         (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 231.83/43.00    (8)   ~ (e2 = e0)
% 231.83/43.00    (9)   ~ (e1 = e0)
% 231.83/43.00    (10)  all_57_12 = e3
% 231.83/43.00    (11)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.83/43.00          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.83/43.00    (12)  all_57_1 = e3
% 231.83/43.00    (13)   ~ (e2 = e1)
% 231.83/43.00    (14)  all_57_12 = e1 & op(e0, e3) = e1
% 231.83/43.00  
% 231.83/43.00  Begin of proof
% 231.83/43.00  | 
% 231.83/43.00  | ALPHA: (14) implies:
% 231.83/43.00  |   (15)  all_57_12 = e1
% 231.83/43.00  | 
% 231.83/43.00  | COMBINE_EQS: (10), (15) imply:
% 231.83/43.00  |   (16)  e3 = e1
% 231.83/43.00  | 
% 231.83/43.00  | COMBINE_EQS: (12), (16) imply:
% 231.83/43.00  |   (17)  all_57_1 = e1
% 231.83/43.00  | 
% 231.83/43.00  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (13), (17) are
% 231.83/43.00  |            inconsistent by sub-proof #1908.
% 231.83/43.00  | 
% 231.83/43.00  End of proof
% 231.83/43.00  
% 231.83/43.00  Sub-proof #1770 shows that the following formulas are inconsistent:
% 231.83/43.00  ----------------------------------------------------------------
% 231.83/43.00    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.83/43.00         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.83/43.00    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.83/43.00         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.83/43.00    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.83/43.00         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.83/43.00    (4)   ~ (e3 = e1)
% 231.83/43.00    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/43.00           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/43.00    (6)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.83/43.00         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.83/43.00    (7)   ~ (all_6_2 = e3)
% 231.83/43.00    (8)  op(e1, e1) = all_6_2
% 231.83/43.00    (9)  op(e2, e2) = e1
% 231.83/43.00    (10)   ~ (e3 = e2)
% 231.83/43.00    (11)   ~ (e3 = e0)
% 231.83/43.00    (12)  op(e3, e3) = e3
% 231.83/43.00    (13)  all_57_15 = e3
% 231.83/43.00    (14)  all_57_5 = e3
% 231.83/43.00    (15)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 231.83/43.00          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 231.83/43.00    (16)   ~ (e2 = e0)
% 231.83/43.00    (17)  all_57_3 = e1
% 231.83/43.00    (18)   ~ (e1 = e0)
% 231.83/43.00    (19)  all_57_6 = e3
% 231.83/43.01    (20)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.83/43.01          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.83/43.01    (21)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.83/43.01              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.83/43.01                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.83/43.01                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.83/43.01    (22)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.83/43.01          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.83/43.01    (23)  all_57_1 = e3
% 231.83/43.01    (24)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 231.83/43.01          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 231.83/43.01    (25)   ~ (e2 = e1)
% 231.83/43.01    (26)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.83/43.01          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.83/43.01    (27)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.83/43.01          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.83/43.01    (28)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.83/43.01          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.83/43.01    (29)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.83/43.01          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.83/43.01    (30)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.83/43.01          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.83/43.01  
% 231.83/43.01  Begin of proof
% 231.83/43.01  | 
% 231.83/43.01  | BETA: splitting (2) gives:
% 231.83/43.01  | 
% 231.83/43.01  | Case 1:
% 231.83/43.01  | | 
% 231.83/43.01  | |   (31)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) =
% 231.83/43.01  | |           e1)
% 231.83/43.01  | | 
% 231.83/43.01  | | BETA: splitting (31) gives:
% 231.83/43.01  | | 
% 231.83/43.01  | | Case 1:
% 231.83/43.01  | | | 
% 231.83/43.01  | | |   (32)  all_57_0 = e1 & op(e3, e3) = e1
% 231.83/43.01  | | | 
% 231.83/43.01  | | | ALPHA: (32) implies:
% 231.83/43.01  | | |   (33)  op(e3, e3) = e1
% 231.83/43.01  | | | 
% 231.83/43.01  | | | REF_CLOSE: (4), (5), (12), (33) are inconsistent by sub-proof #2495.
% 231.83/43.01  | | | 
% 231.83/43.01  | | Case 2:
% 231.83/43.01  | | | 
% 231.83/43.01  | | |   (34)  all_57_2 = e1 & op(e2, e3) = e1
% 231.83/43.01  | | | 
% 231.83/43.01  | | | ALPHA: (34) implies:
% 231.83/43.01  | | |   (35)  all_57_2 = e1
% 231.83/43.01  | | | 
% 231.83/43.01  | | | BETA: splitting (24) gives:
% 231.83/43.01  | | | 
% 231.83/43.01  | | | Case 1:
% 231.83/43.01  | | | | 
% 231.83/43.01  | | | |   (36)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2)
% 231.83/43.01  | | | |           = e0)
% 231.83/43.01  | | | | 
% 231.83/43.01  | | | | BETA: splitting (36) gives:
% 231.83/43.01  | | | | 
% 231.83/43.01  | | | | Case 1:
% 231.83/43.01  | | | | | 
% 231.83/43.01  | | | | |   (37)  all_57_2 = e0 & op(e2, e3) = e0
% 231.83/43.01  | | | | | 
% 231.83/43.01  | | | | | ALPHA: (37) implies:
% 231.83/43.01  | | | | |   (38)  all_57_2 = e0
% 231.83/43.01  | | | | | 
% 231.83/43.01  | | | | | COMBINE_EQS: (35), (38) imply:
% 231.83/43.01  | | | | |   (39)  e1 = e0
% 231.83/43.01  | | | | | 
% 231.83/43.01  | | | | | COMBINE_EQS: (17), (39) imply:
% 231.83/43.01  | | | | |   (40)  all_57_3 = e0
% 231.83/43.01  | | | | | 
% 231.83/43.01  | | | | | REF_CLOSE: (1), (4), (10), (14), (16), (18), (22), (25), (38), (40)
% 231.83/43.01  | | | | |            are inconsistent by sub-proof #2253.
% 231.83/43.01  | | | | | 
% 231.83/43.01  | | | | Case 2:
% 231.83/43.01  | | | | | 
% 231.83/43.01  | | | | |   (41)  all_57_3 = e0 & op(e2, e2) = e0
% 231.83/43.01  | | | | | 
% 231.83/43.01  | | | | | ALPHA: (41) implies:
% 231.83/43.01  | | | | |   (42)  all_57_3 = e0
% 231.83/43.01  | | | | | 
% 231.83/43.01  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12),
% 231.83/43.01  | | | | |            (13), (14), (16), (18), (21), (22), (23), (25), (26), (27),
% 231.83/43.01  | | | | |            (28), (29), (30), (42) are inconsistent by sub-proof #1777.
% 231.83/43.01  | | | | | 
% 231.83/43.01  | | | | End of split
% 231.83/43.01  | | | | 
% 231.83/43.01  | | | Case 2:
% 231.83/43.01  | | | | 
% 231.83/43.01  | | | |   (43)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0)
% 231.83/43.01  | | | |           = e0)
% 231.83/43.01  | | | | 
% 231.83/43.01  | | | | BETA: splitting (43) gives:
% 231.83/43.01  | | | | 
% 231.83/43.01  | | | | Case 1:
% 231.83/43.01  | | | | | 
% 231.83/43.01  | | | | |   (44)  all_57_5 = e0 & op(e2, e1) = e0
% 231.83/43.01  | | | | | 
% 231.83/43.01  | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (10), (11), (13), (14),
% 231.83/43.01  | | | | |            (15), (16), (18), (19), (21), (23), (25), (26), (29), (30),
% 231.83/43.01  | | | | |            (44) are inconsistent by sub-proof #1772.
% 231.83/43.01  | | | | | 
% 231.83/43.01  | | | | Case 2:
% 231.83/43.01  | | | | | 
% 231.83/43.01  | | | | |   (45)  all_57_10 = e0 & op(e2, e0) = e0
% 231.83/43.01  | | | | | 
% 231.83/43.01  | | | | | REF_CLOSE: (5), (9), (10), (14), (16), (22), (25), (35), (45) are
% 231.83/43.01  | | | | |            inconsistent by sub-proof #1826.
% 231.83/43.01  | | | | | 
% 231.83/43.01  | | | | End of split
% 231.83/43.01  | | | | 
% 231.83/43.01  | | | End of split
% 231.83/43.01  | | | 
% 231.83/43.01  | | End of split
% 231.83/43.01  | | 
% 231.83/43.01  | Case 2:
% 231.83/43.01  | | 
% 231.83/43.01  | |   (46)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) =
% 231.83/43.01  | |           e1)
% 231.83/43.01  | | 
% 231.83/43.01  | | BETA: splitting (46) gives:
% 231.83/43.01  | | 
% 231.83/43.01  | | Case 1:
% 231.83/43.01  | | | 
% 231.83/43.01  | | |   (47)  all_57_6 = e1 & op(e1, e3) = e1
% 231.83/43.01  | | | 
% 231.83/43.01  | | | REF_CLOSE: (3), (4), (5), (9), (10), (11), (15), (16), (18), (19), (20),
% 231.83/43.01  | | |            (23), (25), (47) are inconsistent by sub-proof #1771.
% 231.83/43.01  | | | 
% 231.83/43.01  | | Case 2:
% 231.83/43.01  | | | 
% 231.83/43.01  | | |   (48)  all_57_12 = e1 & op(e0, e3) = e1
% 231.83/43.01  | | | 
% 231.83/43.01  | | | ALPHA: (48) implies:
% 231.83/43.01  | | |   (49)  all_57_12 = e1
% 231.83/43.01  | | | 
% 231.83/43.01  | | | BETA: splitting (28) gives:
% 231.83/43.01  | | | 
% 231.83/43.01  | | | Case 1:
% 231.83/43.01  | | | | 
% 231.83/43.01  | | | |   (50)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3)
% 231.83/43.01  | | | |           = e0)
% 231.83/43.01  | | | | 
% 231.83/43.01  | | | | BETA: splitting (50) gives:
% 231.83/43.01  | | | | 
% 231.83/43.01  | | | | Case 1:
% 231.83/43.01  | | | | | 
% 231.83/43.01  | | | | |   (51)  all_57_0 = e0 & op(e3, e3) = e0
% 231.83/43.01  | | | | | 
% 231.83/43.01  | | | | | ALPHA: (51) implies:
% 231.83/43.01  | | | | |   (52)  op(e3, e3) = e0
% 231.83/43.01  | | | | | 
% 231.83/43.01  | | | | | REF_CLOSE: (5), (11), (12), (52) are inconsistent by sub-proof #2494.
% 231.83/43.01  | | | | | 
% 231.83/43.01  | | | | Case 2:
% 231.83/43.01  | | | | | 
% 231.83/43.01  | | | | |   (53)  all_57_2 = e0 & op(e2, e3) = e0
% 231.83/43.01  | | | | | 
% 231.83/43.01  | | | | | ALPHA: (53) implies:
% 231.83/43.01  | | | | |   (54)  all_57_2 = e0
% 231.83/43.01  | | | | | 
% 231.83/43.01  | | | | | BETA: splitting (27) gives:
% 231.83/43.01  | | | | | 
% 231.83/43.01  | | | | | Case 1:
% 231.83/43.01  | | | | | | 
% 231.83/43.01  | | | | | |   (55)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2,
% 231.83/43.01  | | | | | |             e3) = e2)
% 231.83/43.01  | | | | | | 
% 231.83/43.01  | | | | | | REF_CLOSE: (5), (10), (12), (16), (54), (55) are inconsistent by
% 231.83/43.01  | | | | | |            sub-proof #2234.
% 231.83/43.01  | | | | | | 
% 231.83/43.01  | | | | | Case 2:
% 231.83/43.01  | | | | | | 
% 231.83/43.01  | | | | | |   (56)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0,
% 231.83/43.01  | | | | | |             e3) = e2)
% 231.83/43.01  | | | | | | 
% 231.83/43.01  | | | | | | BETA: splitting (56) gives:
% 231.83/43.01  | | | | | | 
% 231.83/43.01  | | | | | | Case 1:
% 231.83/43.01  | | | | | | | 
% 231.83/43.01  | | | | | | |   (57)  all_57_6 = e2 & op(e1, e3) = e2
% 231.83/43.01  | | | | | | | 
% 231.83/43.01  | | | | | | | REF_CLOSE: (10), (19), (57) are inconsistent by sub-proof #2012.
% 231.83/43.01  | | | | | | | 
% 231.83/43.01  | | | | | | Case 2:
% 231.83/43.01  | | | | | | | 
% 231.83/43.01  | | | | | | |   (58)  all_57_12 = e2 & op(e0, e3) = e2
% 231.83/43.01  | | | | | | | 
% 231.83/43.01  | | | | | | | ALPHA: (58) implies:
% 231.83/43.01  | | | | | | |   (59)  all_57_12 = e2
% 231.83/43.01  | | | | | | | 
% 231.83/43.01  | | | | | | | REF_CLOSE: (25), (49), (59) are inconsistent by sub-proof #2321.
% 231.83/43.01  | | | | | | | 
% 231.83/43.01  | | | | | | End of split
% 231.83/43.01  | | | | | | 
% 231.83/43.01  | | | | | End of split
% 231.83/43.01  | | | | | 
% 231.83/43.01  | | | | End of split
% 231.83/43.01  | | | | 
% 231.83/43.01  | | | Case 2:
% 231.83/43.01  | | | | 
% 231.83/43.01  | | | |   (60)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3)
% 231.83/43.01  | | | |           = e0)
% 231.83/43.01  | | | | 
% 231.83/43.01  | | | | BETA: splitting (60) gives:
% 231.83/43.01  | | | | 
% 231.83/43.01  | | | | Case 1:
% 231.83/43.01  | | | | | 
% 231.83/43.01  | | | | |   (61)  all_57_6 = e0 & op(e1, e3) = e0
% 231.83/43.01  | | | | | 
% 231.83/43.01  | | | | | ALPHA: (61) implies:
% 231.83/43.01  | | | | |   (62)  all_57_6 = e0
% 231.83/43.01  | | | | | 
% 231.83/43.01  | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (10), (11), (13), (15),
% 231.83/43.01  | | | | |            (16), (18), (21), (23), (25), (26), (29), (30), (62) are
% 231.83/43.01  | | | | |            inconsistent by sub-proof #1773.
% 231.83/43.01  | | | | | 
% 231.83/43.01  | | | | Case 2:
% 231.83/43.01  | | | | | 
% 231.83/43.01  | | | | |   (63)  all_57_12 = e0 & op(e0, e3) = e0
% 231.83/43.01  | | | | | 
% 231.83/43.01  | | | | | ALPHA: (63) implies:
% 231.83/43.01  | | | | |   (64)  all_57_12 = e0
% 231.83/43.01  | | | | | 
% 231.83/43.01  | | | | | REF_CLOSE: (2), (4), (5), (10), (12), (16), (18), (19), (25), (27),
% 231.83/43.01  | | | | |            (64) are inconsistent by sub-proof #1782.
% 231.83/43.01  | | | | | 
% 231.83/43.01  | | | | End of split
% 231.83/43.01  | | | | 
% 231.83/43.01  | | | End of split
% 231.83/43.01  | | | 
% 231.83/43.01  | | End of split
% 231.83/43.01  | | 
% 231.83/43.01  | End of split
% 231.83/43.01  | 
% 231.83/43.01  End of proof
% 231.83/43.01  
% 231.83/43.01  Sub-proof #1771 shows that the following formulas are inconsistent:
% 231.83/43.01  ----------------------------------------------------------------
% 231.83/43.01    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.83/43.01         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.83/43.01    (2)   ~ (e3 = e1)
% 231.83/43.01    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/43.01           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/43.01    (4)  op(e2, e2) = e1
% 231.83/43.01    (5)   ~ (e3 = e2)
% 231.83/43.01    (6)   ~ (e3 = e0)
% 231.83/43.01    (7)  all_57_6 = e1 & op(e1, e3) = e1
% 231.83/43.01    (8)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 231.83/43.01         (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 231.83/43.01    (9)   ~ (e2 = e0)
% 231.83/43.01    (10)   ~ (e1 = e0)
% 231.83/43.01    (11)  all_57_6 = e3
% 231.83/43.01    (12)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.83/43.01          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.83/43.01    (13)  all_57_1 = e3
% 231.83/43.01    (14)   ~ (e2 = e1)
% 231.83/43.01  
% 231.83/43.01  Begin of proof
% 231.83/43.01  | 
% 231.83/43.01  | ALPHA: (7) implies:
% 231.83/43.01  |   (15)  all_57_6 = e1
% 231.83/43.01  | 
% 231.83/43.01  | COMBINE_EQS: (11), (15) imply:
% 231.83/43.01  |   (16)  e3 = e1
% 231.83/43.01  | 
% 231.83/43.01  | COMBINE_EQS: (13), (16) imply:
% 231.83/43.01  |   (17)  all_57_1 = e1
% 231.83/43.01  | 
% 231.83/43.01  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (12), (14), (17) are
% 231.83/43.01  |            inconsistent by sub-proof #1908.
% 231.83/43.01  | 
% 231.83/43.01  End of proof
% 231.83/43.01  
% 231.83/43.01  Sub-proof #1772 shows that the following formulas are inconsistent:
% 231.83/43.01  ----------------------------------------------------------------
% 231.83/43.01    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.83/43.01         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.83/43.01    (2)   ~ (e3 = e1)
% 231.83/43.01    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/43.01           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/43.01    (4)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.83/43.01         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.83/43.01    (5)   ~ (all_6_2 = e3)
% 231.83/43.01    (6)  op(e1, e1) = all_6_2
% 231.83/43.01    (7)  op(e2, e2) = e1
% 231.83/43.01    (8)   ~ (e3 = e2)
% 231.83/43.01    (9)   ~ (e3 = e0)
% 231.83/43.01    (10)  all_57_15 = e3
% 231.83/43.01    (11)  all_57_5 = e3
% 231.83/43.01    (12)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 231.83/43.01          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 231.83/43.01    (13)   ~ (e2 = e0)
% 231.83/43.01    (14)   ~ (e1 = e0)
% 231.83/43.01    (15)  all_57_6 = e3
% 231.83/43.01    (16)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.83/43.01              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.83/43.01                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.83/43.01                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.83/43.01    (17)  all_57_5 = e0 & op(e2, e1) = e0
% 231.83/43.01    (18)  all_57_1 = e3
% 231.83/43.01    (19)   ~ (e2 = e1)
% 231.83/43.01    (20)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.83/43.01          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.83/43.01    (21)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.83/43.01          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.83/43.01    (22)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.83/43.01          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.83/43.01  
% 231.83/43.01  Begin of proof
% 231.83/43.01  | 
% 231.83/43.01  | ALPHA: (17) implies:
% 231.83/43.01  |   (23)  all_57_5 = e0
% 231.83/43.01  | 
% 231.83/43.01  | COMBINE_EQS: (11), (23) imply:
% 231.83/43.01  |   (24)  e3 = e0
% 231.83/43.01  | 
% 231.83/43.01  | COMBINE_EQS: (15), (24) imply:
% 231.83/43.01  |   (25)  all_57_6 = e0
% 231.83/43.01  | 
% 231.83/43.01  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 231.83/43.01  |            (14), (16), (18), (19), (20), (21), (22), (25) are inconsistent by
% 231.83/43.01  |            sub-proof #1773.
% 231.83/43.01  | 
% 231.83/43.01  End of proof
% 231.83/43.01  
% 231.83/43.01  Sub-proof #1773 shows that the following formulas are inconsistent:
% 231.83/43.01  ----------------------------------------------------------------
% 231.83/43.01    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.83/43.01         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.83/43.01    (2)   ~ (e3 = e1)
% 231.83/43.01    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/43.01           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/43.01    (4)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.83/43.01         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.83/43.01    (5)   ~ (all_6_2 = e3)
% 231.83/43.01    (6)  op(e1, e1) = all_6_2
% 231.83/43.01    (7)  op(e2, e2) = e1
% 231.83/43.01    (8)   ~ (e3 = e2)
% 231.83/43.01    (9)   ~ (e3 = e0)
% 231.83/43.01    (10)  all_57_6 = e0
% 231.83/43.01    (11)  all_57_15 = e3
% 231.83/43.01    (12)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 231.83/43.01          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 231.83/43.01    (13)   ~ (e2 = e0)
% 231.83/43.01    (14)   ~ (e1 = e0)
% 231.83/43.01    (15)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.83/43.01              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.83/43.01                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.83/43.01                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.83/43.01    (16)  all_57_1 = e3
% 231.83/43.01    (17)   ~ (e2 = e1)
% 231.83/43.01    (18)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.83/43.01          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.83/43.01    (19)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.83/43.01          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.83/43.01    (20)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.83/43.01          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.83/43.01  
% 231.83/43.01  Begin of proof
% 231.83/43.01  | 
% 231.83/43.01  | BETA: splitting (4) gives:
% 231.83/43.01  | 
% 231.83/43.01  | Case 1:
% 231.83/43.01  | | 
% 231.83/43.01  | |   (21)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 231.83/43.01  | |           e3)
% 231.83/43.01  | | 
% 231.83/43.01  | | BETA: splitting (21) gives:
% 231.83/43.01  | | 
% 231.83/43.01  | | Case 1:
% 231.83/43.01  | | | 
% 231.83/43.01  | | |   (22)  all_57_6 = e3 & op(e1, e3) = e3
% 231.83/43.01  | | | 
% 231.83/43.01  | | | REF_CLOSE: (9), (10), (22) are inconsistent by sub-proof #2395.
% 231.83/43.01  | | | 
% 231.83/43.01  | | Case 2:
% 231.83/43.01  | | | 
% 231.83/43.01  | | |   (23)  all_57_7 = e3 & op(e1, e2) = e3
% 231.83/43.01  | | | 
% 231.83/43.01  | | | ALPHA: (23) implies:
% 231.83/43.01  | | |   (24)  all_57_7 = e3
% 231.83/43.01  | | | 
% 231.83/43.01  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 231.83/43.01  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (24) are
% 231.83/43.01  | | |            inconsistent by sub-proof #1774.
% 231.83/43.01  | | | 
% 231.83/43.01  | | End of split
% 231.83/43.01  | | 
% 231.83/43.01  | Case 2:
% 231.83/43.01  | | 
% 231.83/43.01  | |   (25)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 231.83/43.01  | |           e3)
% 231.83/43.01  | | 
% 231.83/43.01  | | REF_CLOSE: (2), (3), (5), (6), (8), (9), (11), (13), (14), (15), (17), (18),
% 231.83/43.01  | |            (19), (25) are inconsistent by sub-proof #1786.
% 231.83/43.01  | | 
% 231.83/43.01  | End of split
% 231.83/43.01  | 
% 231.83/43.01  End of proof
% 231.83/43.01  
% 231.83/43.01  Sub-proof #1774 shows that the following formulas are inconsistent:
% 231.83/43.01  ----------------------------------------------------------------
% 231.83/43.01    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.83/43.01         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.83/43.01    (2)   ~ (e3 = e1)
% 231.83/43.01    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/43.01           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/43.01    (4)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.83/43.01         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.83/43.01    (5)   ~ (all_6_2 = e3)
% 231.83/43.01    (6)  op(e1, e1) = all_6_2
% 231.83/43.01    (7)  op(e2, e2) = e1
% 231.83/43.01    (8)   ~ (e3 = e2)
% 231.83/43.01    (9)   ~ (e3 = e0)
% 231.83/43.01    (10)  all_57_6 = e0
% 231.83/43.01    (11)  all_57_15 = e3
% 231.83/43.01    (12)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 231.83/43.01          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 231.83/43.01    (13)   ~ (e2 = e0)
% 231.83/43.01    (14)   ~ (e1 = e0)
% 231.83/43.01    (15)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.83/43.01              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.83/43.01                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.83/43.01                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.83/43.01    (16)  all_57_7 = e3
% 231.83/43.01    (17)  all_57_1 = e3
% 231.83/43.01    (18)   ~ (e2 = e1)
% 231.83/43.01    (19)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.83/43.01          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.83/43.01    (20)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.83/43.01          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.83/43.01    (21)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.83/43.01          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.83/43.01  
% 231.83/43.01  Begin of proof
% 231.83/43.01  | 
% 231.83/43.01  | BETA: splitting (12) gives:
% 231.83/43.01  | 
% 231.83/43.01  | Case 1:
% 231.83/43.01  | | 
% 231.83/43.01  | |   (22)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) =
% 231.83/43.01  | |           e0)
% 231.83/43.01  | | 
% 231.83/43.01  | | REF_CLOSE: (1), (2), (8), (9), (13), (14), (16), (17), (18), (21), (22) are
% 231.83/43.01  | |            inconsistent by sub-proof #1776.
% 231.83/43.01  | | 
% 231.83/43.01  | Case 2:
% 231.83/43.01  | | 
% 231.83/43.01  | |   (23)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 231.83/43.01  | |           e0)
% 231.83/43.01  | | 
% 231.83/43.01  | | BETA: splitting (23) gives:
% 231.83/43.01  | | 
% 231.83/43.01  | | Case 1:
% 231.83/43.01  | | | 
% 231.83/43.01  | | |   (24)  all_57_7 = e0 & op(e1, e2) = e0
% 231.83/43.01  | | | 
% 231.83/43.01  | | | REF_CLOSE: (9), (16), (24) are inconsistent by sub-proof #2042.
% 231.83/43.01  | | | 
% 231.83/43.01  | | Case 2:
% 231.83/43.01  | | | 
% 231.83/43.01  | | |   (25)  all_57_13 = e0 & op(e0, e2) = e0
% 231.83/43.01  | | | 
% 231.83/43.01  | | | ALPHA: (25) implies:
% 231.83/43.01  | | |   (26)  all_57_13 = e0
% 231.83/43.01  | | | 
% 231.83/43.01  | | | BETA: splitting (1) gives:
% 231.83/43.01  | | | 
% 231.83/43.01  | | | Case 1:
% 231.83/43.01  | | | | 
% 231.83/43.01  | | | |   (27)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2)
% 231.83/43.01  | | | |           = e2)
% 231.83/43.01  | | | | 
% 231.83/43.01  | | | | BETA: splitting (27) gives:
% 231.83/43.01  | | | | 
% 231.83/43.01  | | | | Case 1:
% 231.83/43.01  | | | | | 
% 231.83/43.01  | | | | |   (28)  all_57_1 = e2 & op(e3, e2) = e2
% 231.83/43.01  | | | | | 
% 231.83/43.01  | | | | | ALPHA: (28) implies:
% 231.83/43.01  | | | | |   (29)  all_57_1 = e2
% 231.83/43.01  | | | | | 
% 231.83/43.01  | | | | | COMBINE_EQS: (17), (29) imply:
% 231.83/43.01  | | | | |   (30)  e3 = e2
% 231.83/43.01  | | | | | 
% 231.83/43.01  | | | | | COMBINE_EQS: (16), (30) imply:
% 231.83/43.01  | | | | |   (31)  all_57_7 = e2
% 231.83/43.01  | | | | | 
% 231.83/43.01  | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (9), (10), (11), (13), (14),
% 231.83/43.01  | | | | |            (15), (18), (19), (20), (31) are inconsistent by sub-proof
% 231.83/43.01  | | | | |            #1775.
% 231.83/43.01  | | | | | 
% 231.83/43.01  | | | | Case 2:
% 231.83/43.01  | | | | | 
% 231.83/43.01  | | | | |   (32)  all_57_3 = e2 & op(e2, e2) = e2
% 231.83/43.01  | | | | | 
% 231.83/43.01  | | | | | ALPHA: (32) implies:
% 231.83/43.01  | | | | |   (33)  op(e2, e2) = e2
% 231.83/43.01  | | | | | 
% 231.83/43.01  | | | | | REF_CLOSE: (3), (7), (18), (33) are inconsistent by sub-proof #2306.
% 231.83/43.01  | | | | | 
% 231.83/43.01  | | | | End of split
% 231.83/43.01  | | | | 
% 231.83/43.01  | | | Case 2:
% 231.83/43.01  | | | | 
% 231.83/43.01  | | | |   (34)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2)
% 231.83/43.01  | | | |           = e2)
% 231.83/43.01  | | | | 
% 231.83/43.01  | | | | BETA: splitting (34) gives:
% 231.83/43.01  | | | | 
% 231.83/43.01  | | | | Case 1:
% 231.83/43.01  | | | | | 
% 231.83/43.01  | | | | |   (35)  all_57_7 = e2 & op(e1, e2) = e2
% 231.83/43.01  | | | | | 
% 231.83/43.01  | | | | | ALPHA: (35) implies:
% 231.83/43.01  | | | | |   (36)  all_57_7 = e2
% 231.83/43.01  | | | | | 
% 231.83/43.01  | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (9), (10), (11), (13), (14),
% 231.83/43.01  | | | | |            (15), (18), (19), (20), (36) are inconsistent by sub-proof
% 231.83/43.01  | | | | |            #1775.
% 231.83/43.01  | | | | | 
% 231.83/43.01  | | | | Case 2:
% 231.83/43.01  | | | | | 
% 231.83/43.01  | | | | |   (37)  all_57_13 = e2 & op(e0, e2) = e2
% 231.83/43.01  | | | | | 
% 231.83/43.01  | | | | | REF_CLOSE: (13), (26), (37) are inconsistent by sub-proof #2316.
% 231.83/43.01  | | | | | 
% 231.83/43.01  | | | | End of split
% 231.83/43.01  | | | | 
% 231.83/43.01  | | | End of split
% 231.83/43.01  | | | 
% 231.83/43.01  | | End of split
% 231.83/43.01  | | 
% 231.83/43.01  | End of split
% 231.83/43.01  | 
% 231.83/43.01  End of proof
% 231.83/43.01  
% 231.83/43.01  Sub-proof #1775 shows that the following formulas are inconsistent:
% 231.83/43.01  ----------------------------------------------------------------
% 231.83/43.01    (1)   ~ (e3 = e1)
% 231.83/43.01    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/43.01           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/43.01    (3)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.83/43.01         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.83/43.01    (4)   ~ (all_6_2 = e3)
% 231.83/43.01    (5)  op(e1, e1) = all_6_2
% 231.83/43.01    (6)  all_57_7 = e2
% 231.83/43.01    (7)   ~ (e3 = e2)
% 231.83/43.01    (8)   ~ (e3 = e0)
% 231.83/43.01    (9)  all_57_6 = e0
% 231.83/43.01    (10)  all_57_15 = e3
% 231.83/43.01    (11)   ~ (e2 = e0)
% 231.83/43.01    (12)   ~ (e1 = e0)
% 231.83/43.01    (13)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.83/43.01              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.83/43.01                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.83/43.01                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.83/43.01    (14)   ~ (e2 = e1)
% 231.83/43.01    (15)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.83/43.01          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.83/43.01    (16)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.83/43.01          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.83/43.01  
% 231.83/43.01  Begin of proof
% 231.83/43.01  | 
% 231.83/43.01  | BETA: splitting (3) gives:
% 231.83/43.01  | 
% 231.83/43.01  | Case 1:
% 231.83/43.01  | | 
% 231.83/43.01  | |   (17)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 231.83/43.01  | |           e3)
% 231.83/43.01  | | 
% 231.83/43.01  | | BETA: splitting (17) gives:
% 231.83/43.01  | | 
% 231.83/43.01  | | Case 1:
% 231.83/43.01  | | | 
% 231.83/43.01  | | |   (18)  all_57_6 = e3 & op(e1, e3) = e3
% 231.83/43.01  | | | 
% 231.83/43.01  | | | REF_CLOSE: (8), (9), (18) are inconsistent by sub-proof #2395.
% 231.83/43.01  | | | 
% 231.83/43.01  | | Case 2:
% 231.83/43.01  | | | 
% 231.83/43.01  | | |   (19)  all_57_7 = e3 & op(e1, e2) = e3
% 231.83/43.01  | | | 
% 231.83/43.01  | | | REF_CLOSE: (6), (7), (19) are inconsistent by sub-proof #2194.
% 231.83/43.01  | | | 
% 231.83/43.01  | | End of split
% 231.83/43.01  | | 
% 231.83/43.01  | Case 2:
% 231.83/43.01  | | 
% 231.83/43.01  | |   (20)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 231.83/43.01  | |           e3)
% 231.83/43.01  | | 
% 231.83/43.01  | | REF_CLOSE: (1), (2), (4), (5), (7), (8), (10), (11), (12), (13), (14), (15),
% 231.83/43.01  | |            (16), (20) are inconsistent by sub-proof #1786.
% 231.83/43.01  | | 
% 231.83/43.01  | End of split
% 231.83/43.01  | 
% 231.83/43.01  End of proof
% 231.83/43.01  
% 231.83/43.01  Sub-proof #1776 shows that the following formulas are inconsistent:
% 231.83/43.01  ----------------------------------------------------------------
% 231.83/43.01    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.83/43.01         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.83/43.01    (2)   ~ (e3 = e1)
% 231.83/43.01    (3)   ~ (e3 = e2)
% 231.83/43.01    (4)   ~ (e3 = e0)
% 231.83/43.01    (5)   ~ (e2 = e0)
% 231.83/43.01    (6)   ~ (e1 = e0)
% 231.83/43.01    (7)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0)
% 231.83/43.01    (8)  all_57_7 = e3
% 231.83/43.01    (9)  all_57_1 = e3
% 231.83/43.01    (10)   ~ (e2 = e1)
% 231.83/43.01    (11)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.83/43.01          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.83/43.01  
% 231.83/43.01  Begin of proof
% 231.83/43.01  | 
% 231.83/43.01  | BETA: splitting (7) gives:
% 231.83/43.01  | 
% 231.83/43.01  | Case 1:
% 231.83/43.01  | | 
% 231.83/43.01  | |   (12)  all_57_1 = e0 & op(e3, e2) = e0
% 231.83/43.01  | | 
% 231.83/43.01  | | REF_CLOSE: (4), (9), (12) are inconsistent by sub-proof #1811.
% 231.83/43.01  | | 
% 231.83/43.01  | Case 2:
% 231.83/43.01  | | 
% 231.83/43.01  | |   (13)  all_57_3 = e0 & op(e2, e2) = e0
% 231.83/43.01  | | 
% 231.83/43.01  | | ALPHA: (13) implies:
% 231.83/43.01  | |   (14)  all_57_3 = e0
% 231.83/43.01  | | 
% 231.83/43.01  | | REF_CLOSE: (1), (2), (3), (5), (6), (8), (9), (10), (11), (14) are
% 231.83/43.01  | |            inconsistent by sub-proof #1778.
% 231.83/43.01  | | 
% 231.83/43.01  | End of split
% 231.83/43.01  | 
% 231.83/43.01  End of proof
% 231.83/43.01  
% 231.83/43.01  Sub-proof #1777 shows that the following formulas are inconsistent:
% 231.83/43.01  ----------------------------------------------------------------
% 231.83/43.01    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.83/43.01         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.83/43.01    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.83/43.01         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.83/43.01    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.83/43.01         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.83/43.01    (4)   ~ (e3 = e1)
% 231.83/43.01    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/43.01           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/43.01    (6)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.83/43.01         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.83/43.01    (7)   ~ (all_6_2 = e3)
% 231.83/43.01    (8)  op(e1, e1) = all_6_2
% 231.83/43.01    (9)  all_57_3 = e0
% 231.83/43.01    (10)   ~ (e3 = e2)
% 231.83/43.01    (11)   ~ (e3 = e0)
% 231.83/43.01    (12)  op(e3, e3) = e3
% 231.83/43.01    (13)  all_57_15 = e3
% 231.83/43.01    (14)  all_57_5 = e3
% 231.83/43.01    (15)   ~ (e2 = e0)
% 231.83/43.01    (16)   ~ (e1 = e0)
% 231.83/43.01    (17)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.83/43.01              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.83/43.01                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.83/43.01                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.83/43.01    (18)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.83/43.01          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.83/43.01    (19)  all_57_1 = e3
% 231.83/43.01    (20)   ~ (e2 = e1)
% 231.83/43.01    (21)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.83/43.01          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.83/43.01    (22)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.83/43.01          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.83/43.01    (23)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.83/43.01          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.83/43.01    (24)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.83/43.01          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.83/43.01    (25)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.83/43.01          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.83/43.01  
% 231.83/43.01  Begin of proof
% 231.83/43.01  | 
% 231.83/43.01  | BETA: splitting (6) gives:
% 231.83/43.01  | 
% 231.83/43.01  | Case 1:
% 231.83/43.01  | | 
% 231.83/43.01  | |   (26)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 231.83/43.01  | |           e3)
% 231.83/43.01  | | 
% 231.83/43.01  | | BETA: splitting (26) gives:
% 231.83/43.01  | | 
% 231.83/43.01  | | Case 1:
% 231.83/43.01  | | | 
% 231.83/43.01  | | |   (27)  all_57_6 = e3 & op(e1, e3) = e3
% 231.83/43.01  | | | 
% 231.83/43.01  | | | ALPHA: (27) implies:
% 231.83/43.01  | | |   (28)  all_57_6 = e3
% 231.83/43.01  | | | 
% 231.83/43.01  | | | REF_CLOSE: (1), (2), (4), (5), (9), (10), (11), (12), (14), (15), (16),
% 231.83/43.01  | | |            (18), (20), (22), (23), (28) are inconsistent by sub-proof
% 231.83/43.01  | | |            #1781.
% 231.83/43.01  | | | 
% 231.83/43.01  | | Case 2:
% 231.83/43.01  | | | 
% 231.83/43.01  | | |   (29)  all_57_7 = e3 & op(e1, e2) = e3
% 231.83/43.01  | | | 
% 231.83/43.01  | | | ALPHA: (29) implies:
% 231.83/43.01  | | |   (30)  all_57_7 = e3
% 231.83/43.01  | | | 
% 231.83/43.01  | | | REF_CLOSE: (3), (4), (9), (10), (15), (16), (19), (20), (25), (30) are
% 231.83/43.01  | | |            inconsistent by sub-proof #1778.
% 231.83/43.01  | | | 
% 231.83/43.01  | | End of split
% 231.83/43.01  | | 
% 231.83/43.01  | Case 2:
% 231.83/43.01  | | 
% 231.83/43.02  | |   (31)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 231.83/43.02  | |           e3)
% 231.83/43.02  | | 
% 231.83/43.02  | | REF_CLOSE: (4), (5), (7), (8), (10), (11), (13), (15), (16), (17), (20),
% 231.83/43.02  | |            (21), (24), (31) are inconsistent by sub-proof #1786.
% 231.83/43.02  | | 
% 231.83/43.02  | End of split
% 231.83/43.02  | 
% 231.83/43.02  End of proof
% 231.83/43.02  
% 231.83/43.02  Sub-proof #1778 shows that the following formulas are inconsistent:
% 231.83/43.02  ----------------------------------------------------------------
% 231.83/43.02    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.83/43.02         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.83/43.02    (2)   ~ (e3 = e1)
% 231.83/43.02    (3)  all_57_3 = e0
% 231.83/43.02    (4)   ~ (e3 = e2)
% 231.83/43.02    (5)   ~ (e2 = e0)
% 231.83/43.02    (6)   ~ (e1 = e0)
% 231.83/43.02    (7)  all_57_7 = e3
% 231.83/43.02    (8)  all_57_1 = e3
% 231.83/43.02    (9)   ~ (e2 = e1)
% 231.83/43.02    (10)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.83/43.02          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.83/43.02  
% 231.83/43.02  Begin of proof
% 231.83/43.02  | 
% 231.83/43.02  | BETA: splitting (1) gives:
% 231.83/43.02  | 
% 231.83/43.02  | Case 1:
% 231.83/43.02  | | 
% 231.83/43.02  | |   (11)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 231.83/43.02  | |           e2)
% 231.83/43.02  | | 
% 231.83/43.02  | | BETA: splitting (11) gives:
% 231.83/43.02  | | 
% 231.83/43.02  | | Case 1:
% 231.83/43.02  | | | 
% 231.83/43.02  | | |   (12)  all_57_1 = e2 & op(e3, e2) = e2
% 231.83/43.02  | | | 
% 231.83/43.02  | | | REF_CLOSE: (4), (8), (12) are inconsistent by sub-proof #1809.
% 231.83/43.02  | | | 
% 231.83/43.02  | | Case 2:
% 231.83/43.02  | | | 
% 231.83/43.02  | | |   (13)  all_57_3 = e2 & op(e2, e2) = e2
% 231.83/43.02  | | | 
% 231.83/43.02  | | | REF_CLOSE: (3), (5), (13) are inconsistent by sub-proof #2103.
% 231.83/43.02  | | | 
% 231.83/43.02  | | End of split
% 231.83/43.02  | | 
% 231.83/43.02  | Case 2:
% 231.83/43.02  | | 
% 231.83/43.02  | |   (14)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 231.83/43.02  | |           e2)
% 231.83/43.02  | | 
% 231.83/43.02  | | BETA: splitting (14) gives:
% 231.83/43.02  | | 
% 231.83/43.02  | | Case 1:
% 231.83/43.02  | | | 
% 231.83/43.02  | | |   (15)  all_57_7 = e2 & op(e1, e2) = e2
% 231.83/43.02  | | | 
% 231.83/43.02  | | | REF_CLOSE: (4), (7), (15) are inconsistent by sub-proof #2092.
% 231.83/43.02  | | | 
% 231.83/43.02  | | Case 2:
% 231.83/43.02  | | | 
% 231.83/43.02  | | |   (16)  all_57_13 = e2 & op(e0, e2) = e2
% 231.83/43.02  | | | 
% 231.83/43.02  | | | ALPHA: (16) implies:
% 231.83/43.02  | | |   (17)  all_57_13 = e2
% 231.83/43.02  | | | 
% 231.83/43.02  | | | REF_CLOSE: (2), (3), (6), (7), (8), (9), (10), (17) are inconsistent by
% 231.83/43.02  | | |            sub-proof #1779.
% 231.83/43.02  | | | 
% 231.83/43.02  | | End of split
% 231.83/43.02  | | 
% 231.83/43.02  | End of split
% 231.83/43.02  | 
% 231.83/43.02  End of proof
% 231.83/43.02  
% 231.83/43.02  Sub-proof #1779 shows that the following formulas are inconsistent:
% 231.83/43.02  ----------------------------------------------------------------
% 231.83/43.02    (1)   ~ (e3 = e1)
% 231.83/43.02    (2)  all_57_3 = e0
% 231.83/43.02    (3)  all_57_13 = e2
% 231.83/43.02    (4)   ~ (e1 = e0)
% 231.83/43.02    (5)  all_57_7 = e3
% 231.83/43.02    (6)  all_57_1 = e3
% 231.83/43.02    (7)   ~ (e2 = e1)
% 231.83/43.02    (8)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.83/43.02         (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.83/43.02  
% 231.83/43.02  Begin of proof
% 231.83/43.02  | 
% 231.83/43.02  | BETA: splitting (8) gives:
% 231.83/43.02  | 
% 231.83/43.02  | Case 1:
% 231.83/43.02  | | 
% 231.83/43.02  | |   (9)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1)
% 231.83/43.02  | | 
% 231.83/43.02  | | BETA: splitting (9) gives:
% 231.83/43.02  | | 
% 231.83/43.02  | | Case 1:
% 231.83/43.02  | | | 
% 231.83/43.02  | | |   (10)  all_57_1 = e1 & op(e3, e2) = e1
% 231.83/43.02  | | | 
% 231.83/43.02  | | | REF_CLOSE: (1), (6), (10) are inconsistent by sub-proof #2453.
% 231.83/43.02  | | | 
% 231.83/43.02  | | Case 2:
% 231.83/43.02  | | | 
% 231.83/43.02  | | |   (11)  all_57_3 = e1 & op(e2, e2) = e1
% 231.83/43.02  | | | 
% 231.83/43.02  | | | REF_CLOSE: (2), (4), (11) are inconsistent by sub-proof #2252.
% 231.83/43.02  | | | 
% 231.83/43.02  | | End of split
% 231.83/43.02  | | 
% 231.83/43.02  | Case 2:
% 231.83/43.02  | | 
% 231.83/43.02  | |   (12)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 231.83/43.02  | |           e1)
% 231.83/43.02  | | 
% 231.83/43.02  | | REF_CLOSE: (1), (3), (5), (7), (12) are inconsistent by sub-proof #1780.
% 231.83/43.02  | | 
% 231.83/43.02  | End of split
% 231.83/43.02  | 
% 231.83/43.02  End of proof
% 231.83/43.02  
% 231.83/43.02  Sub-proof #1780 shows that the following formulas are inconsistent:
% 231.83/43.02  ----------------------------------------------------------------
% 231.83/43.02    (1)   ~ (e3 = e1)
% 231.83/43.02    (2)  all_57_13 = e2
% 231.83/43.02    (3)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.83/43.02    (4)  all_57_7 = e3
% 231.83/43.02    (5)   ~ (e2 = e1)
% 231.83/43.02  
% 231.83/43.02  Begin of proof
% 231.83/43.02  | 
% 231.83/43.02  | BETA: splitting (3) gives:
% 231.83/43.02  | 
% 231.83/43.02  | Case 1:
% 231.83/43.02  | | 
% 231.83/43.02  | |   (6)  all_57_7 = e1 & op(e1, e2) = e1
% 231.83/43.02  | | 
% 231.83/43.02  | | REF_CLOSE: (1), (4), (6) are inconsistent by sub-proof #2104.
% 231.83/43.02  | | 
% 231.83/43.02  | Case 2:
% 231.83/43.02  | | 
% 231.83/43.02  | |   (7)  all_57_13 = e1 & op(e0, e2) = e1
% 231.83/43.02  | | 
% 231.83/43.02  | | ALPHA: (7) implies:
% 231.83/43.02  | |   (8)  all_57_13 = e1
% 231.83/43.02  | | 
% 231.83/43.02  | | REF_CLOSE: (2), (5), (8) are inconsistent by sub-proof #2327.
% 231.83/43.02  | | 
% 231.83/43.02  | End of split
% 231.83/43.02  | 
% 231.83/43.02  End of proof
% 231.83/43.02  
% 231.83/43.02  Sub-proof #1781 shows that the following formulas are inconsistent:
% 231.83/43.02  ----------------------------------------------------------------
% 231.83/43.02    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.83/43.02         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.83/43.02    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.83/43.02         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.83/43.02    (3)   ~ (e3 = e1)
% 231.83/43.02    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/43.02           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/43.02    (5)  all_57_3 = e0
% 231.83/43.02    (6)   ~ (e3 = e2)
% 231.83/43.02    (7)   ~ (e3 = e0)
% 231.83/43.02    (8)  op(e3, e3) = e3
% 231.83/43.02    (9)  all_57_5 = e3
% 231.83/43.02    (10)   ~ (e2 = e0)
% 231.83/43.02    (11)   ~ (e1 = e0)
% 231.83/43.02    (12)  all_57_6 = e3
% 231.83/43.02    (13)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.83/43.02          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.83/43.02    (14)   ~ (e2 = e1)
% 231.83/43.02    (15)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.83/43.02          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.83/43.02    (16)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.83/43.02          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.83/43.02  
% 231.83/43.02  Begin of proof
% 231.83/43.02  | 
% 231.83/43.02  | BETA: splitting (16) gives:
% 231.83/43.02  | 
% 231.83/43.02  | Case 1:
% 231.83/43.02  | | 
% 231.83/43.02  | |   (17)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) =
% 231.83/43.02  | |           e0)
% 231.83/43.02  | | 
% 231.83/43.02  | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13), (14),
% 231.83/43.02  | |            (17) are inconsistent by sub-proof #1784.
% 231.83/43.02  | | 
% 231.83/43.02  | Case 2:
% 231.83/43.02  | | 
% 231.83/43.02  | |   (18)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) =
% 231.83/43.02  | |           e0)
% 231.83/43.02  | | 
% 231.83/43.02  | | BETA: splitting (18) gives:
% 231.83/43.02  | | 
% 231.83/43.02  | | Case 1:
% 231.83/43.02  | | | 
% 231.83/43.02  | | |   (19)  all_57_6 = e0 & op(e1, e3) = e0
% 231.83/43.02  | | | 
% 231.83/43.02  | | | REF_CLOSE: (7), (12), (19) are inconsistent by sub-proof #2465.
% 231.83/43.02  | | | 
% 231.83/43.02  | | Case 2:
% 231.83/43.02  | | | 
% 231.83/43.02  | | |   (20)  all_57_12 = e0 & op(e0, e3) = e0
% 231.83/43.02  | | | 
% 231.83/43.02  | | | ALPHA: (20) implies:
% 231.83/43.02  | | |   (21)  all_57_12 = e0
% 231.83/43.02  | | | 
% 231.83/43.02  | | | REF_CLOSE: (2), (3), (4), (6), (8), (10), (11), (12), (14), (15), (21) are
% 231.83/43.02  | | |            inconsistent by sub-proof #1782.
% 231.83/43.02  | | | 
% 231.83/43.02  | | End of split
% 231.83/43.02  | | 
% 231.83/43.02  | End of split
% 231.83/43.02  | 
% 231.83/43.02  End of proof
% 231.83/43.02  
% 231.83/43.02  Sub-proof #1782 shows that the following formulas are inconsistent:
% 231.83/43.02  ----------------------------------------------------------------
% 231.83/43.02    (1)  all_57_12 = e0
% 231.83/43.02    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.83/43.02         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.83/43.02    (3)   ~ (e3 = e1)
% 231.83/43.02    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/43.02           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/43.02    (5)   ~ (e3 = e2)
% 231.83/43.02    (6)  op(e3, e3) = e3
% 231.83/43.02    (7)   ~ (e2 = e0)
% 231.83/43.02    (8)   ~ (e1 = e0)
% 231.83/43.02    (9)  all_57_6 = e3
% 231.83/43.02    (10)   ~ (e2 = e1)
% 231.83/43.02    (11)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.83/43.02          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.83/43.02  
% 231.83/43.02  Begin of proof
% 231.83/43.02  | 
% 231.83/43.02  | BETA: splitting (2) gives:
% 231.83/43.02  | 
% 231.83/43.02  | Case 1:
% 231.83/43.02  | | 
% 231.83/43.02  | |   (12)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) =
% 231.83/43.02  | |           e1)
% 231.83/43.02  | | 
% 231.83/43.02  | | BETA: splitting (12) gives:
% 231.83/43.02  | | 
% 231.83/43.02  | | Case 1:
% 231.83/43.02  | | | 
% 231.83/43.02  | | |   (13)  all_57_0 = e1 & op(e3, e3) = e1
% 231.83/43.02  | | | 
% 231.83/43.02  | | | ALPHA: (13) implies:
% 231.83/43.02  | | |   (14)  op(e3, e3) = e1
% 231.83/43.02  | | | 
% 231.83/43.02  | | | REF_CLOSE: (3), (4), (6), (14) are inconsistent by sub-proof #2495.
% 231.83/43.02  | | | 
% 231.83/43.02  | | Case 2:
% 231.83/43.02  | | | 
% 231.83/43.02  | | |   (15)  all_57_2 = e1 & op(e2, e3) = e1
% 231.83/43.02  | | | 
% 231.83/43.02  | | | ALPHA: (15) implies:
% 231.83/43.02  | | |   (16)  all_57_2 = e1
% 231.83/43.02  | | | 
% 231.83/43.02  | | | REF_CLOSE: (1), (4), (5), (6), (7), (9), (10), (11), (16) are inconsistent
% 231.83/43.02  | | |            by sub-proof #2460.
% 231.83/43.02  | | | 
% 231.83/43.02  | | End of split
% 231.83/43.02  | | 
% 231.83/43.02  | Case 2:
% 231.83/43.02  | | 
% 231.83/43.02  | |   (17)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) =
% 231.83/43.02  | |           e1)
% 231.83/43.02  | | 
% 231.83/43.02  | | REF_CLOSE: (1), (3), (8), (9), (17) are inconsistent by sub-proof #1783.
% 231.83/43.02  | | 
% 231.83/43.02  | End of split
% 231.83/43.02  | 
% 231.83/43.02  End of proof
% 231.83/43.02  
% 231.83/43.02  Sub-proof #1783 shows that the following formulas are inconsistent:
% 231.83/43.02  ----------------------------------------------------------------
% 231.83/43.02    (1)  all_57_12 = e0
% 231.83/43.02    (2)   ~ (e3 = e1)
% 231.83/43.02    (3)   ~ (e1 = e0)
% 231.83/43.02    (4)  all_57_6 = e3
% 231.83/43.02    (5)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.83/43.02  
% 231.83/43.02  Begin of proof
% 231.83/43.02  | 
% 231.83/43.02  | BETA: splitting (5) gives:
% 231.83/43.02  | 
% 231.83/43.02  | Case 1:
% 231.83/43.02  | | 
% 231.83/43.02  | |   (6)  all_57_6 = e1 & op(e1, e3) = e1
% 231.83/43.02  | | 
% 231.83/43.02  | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #2117.
% 231.83/43.02  | | 
% 231.83/43.02  | Case 2:
% 231.83/43.02  | | 
% 231.83/43.02  | |   (7)  all_57_12 = e1 & op(e0, e3) = e1
% 231.83/43.02  | | 
% 231.83/43.02  | | ALPHA: (7) implies:
% 231.83/43.02  | |   (8)  all_57_12 = e1
% 231.83/43.02  | | 
% 231.83/43.02  | | REF_CLOSE: (1), (3), (8) are inconsistent by sub-proof #2014.
% 231.83/43.02  | | 
% 231.83/43.02  | End of split
% 231.83/43.02  | 
% 231.83/43.02  End of proof
% 231.83/43.02  
% 231.83/43.02  Sub-proof #1784 shows that the following formulas are inconsistent:
% 231.83/43.02  ----------------------------------------------------------------
% 231.83/43.02    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.83/43.02         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.83/43.02    (2)   ~ (e3 = e1)
% 231.83/43.02    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/43.02           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/43.02    (4)  all_57_3 = e0
% 231.83/43.02    (5)   ~ (e3 = e2)
% 231.83/43.02    (6)   ~ (e3 = e0)
% 231.83/43.02    (7)  op(e3, e3) = e3
% 231.83/43.02    (8)  all_57_5 = e3
% 231.83/43.02    (9)   ~ (e2 = e0)
% 231.83/43.02    (10)   ~ (e1 = e0)
% 231.83/43.02    (11)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.83/43.02          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.83/43.02    (12)   ~ (e2 = e1)
% 231.83/43.02    (13)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0)
% 231.83/43.02  
% 231.83/43.02  Begin of proof
% 231.83/43.02  | 
% 231.83/43.02  | BETA: splitting (13) gives:
% 231.83/43.02  | 
% 231.83/43.02  | Case 1:
% 231.83/43.02  | | 
% 231.83/43.02  | |   (14)  all_57_0 = e0 & op(e3, e3) = e0
% 231.83/43.02  | | 
% 231.83/43.02  | | ALPHA: (14) implies:
% 231.83/43.02  | |   (15)  op(e3, e3) = e0
% 231.83/43.02  | | 
% 231.83/43.02  | | REF_CLOSE: (3), (6), (7), (15) are inconsistent by sub-proof #2494.
% 231.83/43.02  | | 
% 231.83/43.02  | Case 2:
% 231.83/43.02  | | 
% 231.83/43.02  | |   (16)  all_57_2 = e0 & op(e2, e3) = e0
% 231.83/43.02  | | 
% 231.83/43.02  | | ALPHA: (16) implies:
% 231.83/43.02  | |   (17)  all_57_2 = e0
% 231.83/43.02  | | 
% 231.83/43.02  | | REF_CLOSE: (1), (2), (4), (5), (8), (9), (10), (11), (12), (17) are
% 231.83/43.02  | |            inconsistent by sub-proof #2253.
% 231.83/43.02  | | 
% 231.83/43.02  | End of split
% 231.83/43.02  | 
% 231.83/43.02  End of proof
% 231.83/43.02  
% 231.83/43.02  Sub-proof #1785 shows that the following formulas are inconsistent:
% 231.83/43.02  ----------------------------------------------------------------
% 231.83/43.02    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 231.83/43.02    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.83/43.02         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.83/43.02    (3)  op(e2, e1) = e3
% 231.83/43.02    (4)   ~ (e3 = e1)
% 231.83/43.02    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/43.02           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/43.02    (6)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.83/43.02         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.83/43.02    (7)   ~ (all_6_2 = e3)
% 231.83/43.02    (8)   ~ (all_53_9 = e1)
% 231.83/43.02    (9)  op(e1, e1) = all_6_2
% 231.83/43.02    (10)  op(e2, e2) = e1
% 231.83/43.02    (11)   ~ (all_53_4 = e1)
% 231.83/43.02    (12)   ~ (e3 = e2)
% 231.83/43.02    (13)  all_55_1 = all_53_4
% 231.83/43.02    (14)   ~ (e3 = e0)
% 231.83/43.02    (15)  op(e3, e3) = e3
% 231.83/43.02    (16)  all_57_15 = e3
% 231.83/43.02    (17)  op(e3, e2) = all_53_4
% 231.83/43.02    (18)   ~ (e2 = e0)
% 231.83/43.02    (19)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 231.83/43.02            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 231.83/43.02            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 231.83/43.02            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 231.83/43.02              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 231.83/43.02            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 231.83/43.02            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 231.83/43.02              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 231.83/43.02              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 231.83/43.02            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 231.83/43.02            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 231.83/43.02            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 231.83/43.02              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 231.83/43.02              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 231.83/43.02            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 231.83/43.02              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 231.83/43.02            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 231.83/43.02            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 231.83/43.02              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 231.83/43.02              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 231.83/43.02            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 231.83/43.02            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 231.83/43.02    (20)   ~ (e1 = e0)
% 231.83/43.02    (21)  op(e0, e0) = e3
% 231.83/43.02    (22)   ~ (all_53_4 = all_53_6)
% 231.83/43.02    (23)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.83/43.02              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.83/43.02                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.83/43.02                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.83/43.02    (24)  ( ~ (all_16_0 = e0) & op(all_16_1, e2) = all_16_0 & op(e2, e1) =
% 231.83/43.02            all_16_1 & $i(all_16_0) & $i(all_16_1)) | ( ~ (all_16_1 = e3) & op(e2,
% 231.83/43.02              e1) = all_16_1 & $i(all_16_1))
% 231.83/43.02    (25)  all_57_0 = e3
% 231.83/43.02    (26)   ~ (e2 = e1)
% 231.83/43.02    (27)   ~ (all_26_2 = e1) | ( ~ (all_26_0 = e3) & op(all_26_1, e2) = all_26_0 &
% 231.83/43.02            op(e2, e1) = all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 =
% 231.83/43.02              e0) & op(e2, e1) = all_26_1 & $i(all_26_1))
% 231.83/43.02    (28)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.83/43.02          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.83/43.02    (29)  op(e2, e1) = all_53_9
% 231.83/43.02    (30)  op(e1, e2) = all_53_6
% 231.83/43.02    (31)  all_26_2 = e1
% 231.83/43.02    (32)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.83/43.02          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.83/43.02    (33)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.83/43.02          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.83/43.02    (34)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.83/43.02          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.83/43.02  
% 231.83/43.02  Begin of proof
% 231.83/43.02  | 
% 231.83/43.02  | BETA: splitting (6) gives:
% 231.83/43.02  | 
% 231.83/43.02  | Case 1:
% 231.83/43.02  | | 
% 231.83/43.02  | |   (35)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 231.83/43.02  | |           e3)
% 231.83/43.02  | | 
% 231.83/43.02  | | BETA: splitting (35) gives:
% 231.83/43.02  | | 
% 231.83/43.02  | | Case 1:
% 231.83/43.02  | | | 
% 231.83/43.02  | | |   (36)  all_57_6 = e3 & op(e1, e3) = e3
% 231.83/43.02  | | | 
% 231.83/43.02  | | | ALPHA: (36) implies:
% 231.83/43.02  | | |   (37)  all_57_6 = e3
% 231.83/43.02  | | | 
% 231.83/43.02  | | | REF_CLOSE: (2), (4), (12), (14), (18), (20), (25), (26), (32), (33), (37)
% 231.83/43.02  | | |            are inconsistent by sub-proof #2010.
% 231.83/43.02  | | | 
% 231.83/43.02  | | Case 2:
% 231.83/43.02  | | | 
% 231.83/43.02  | | |   (38)  all_57_7 = e3 & op(e1, e2) = e3
% 231.83/43.02  | | | 
% 231.83/43.02  | | | REF_CLOSE: (1), (3), (5), (8), (10), (11), (12), (13), (14), (15), (17),
% 231.83/43.02  | | |            (19), (21), (22), (24), (27), (29), (30), (31), (38) are
% 231.83/43.02  | | |            inconsistent by sub-proof #1787.
% 231.83/43.02  | | | 
% 231.83/43.02  | | End of split
% 231.83/43.02  | | 
% 231.83/43.02  | Case 2:
% 231.83/43.02  | | 
% 231.83/43.02  | |   (39)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 231.83/43.02  | |           e3)
% 231.83/43.02  | | 
% 231.83/43.02  | | REF_CLOSE: (4), (5), (7), (9), (12), (14), (16), (18), (20), (23), (26),
% 231.83/43.02  | |            (28), (34), (39) are inconsistent by sub-proof #1786.
% 231.83/43.02  | | 
% 231.83/43.02  | End of split
% 231.83/43.02  | 
% 231.83/43.02  End of proof
% 231.83/43.02  
% 231.83/43.02  Sub-proof #1786 shows that the following formulas are inconsistent:
% 231.83/43.02  ----------------------------------------------------------------
% 231.83/43.02    (1)   ~ (e3 = e1)
% 231.83/43.02    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/43.02           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/43.02    (3)   ~ (all_6_2 = e3)
% 231.83/43.02    (4)  op(e1, e1) = all_6_2
% 231.83/43.02    (5)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.83/43.02    (6)   ~ (e3 = e2)
% 231.83/43.02    (7)   ~ (e3 = e0)
% 231.83/43.02    (8)  all_57_15 = e3
% 231.83/43.02    (9)   ~ (e2 = e0)
% 231.83/43.02    (10)   ~ (e1 = e0)
% 231.83/43.02    (11)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.83/43.02              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.83/43.02                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.83/43.02                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.83/43.02    (12)   ~ (e2 = e1)
% 231.83/43.02    (13)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 231.83/43.02          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 231.83/43.02    (14)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 231.83/43.02          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.83/43.02  
% 231.83/43.02  Begin of proof
% 231.83/43.02  | 
% 231.83/43.02  | BETA: splitting (5) gives:
% 231.83/43.02  | 
% 231.83/43.02  | Case 1:
% 231.83/43.02  | | 
% 231.83/43.02  | |   (15)  all_57_8 = e3 & op(e1, e1) = e3
% 231.83/43.02  | | 
% 231.83/43.02  | | ALPHA: (15) implies:
% 231.83/43.02  | |   (16)  op(e1, e1) = e3
% 231.83/43.02  | | 
% 231.83/43.02  | | REF_CLOSE: (2), (3), (4), (16) are inconsistent by sub-proof #2468.
% 231.83/43.02  | | 
% 231.83/43.02  | Case 2:
% 231.83/43.02  | | 
% 231.83/43.02  | |   (17)  all_57_11 = e3 & op(e1, e0) = e3
% 231.83/43.02  | | 
% 231.83/43.02  | | ALPHA: (17) implies:
% 231.83/43.02  | |   (18)  all_57_11 = e3
% 231.83/43.02  | | 
% 231.83/43.02  | | REF_CLOSE: (1), (6), (7), (8), (9), (10), (11), (12), (13), (14), (18) are
% 231.83/43.02  | |            inconsistent by sub-proof #2134.
% 231.83/43.02  | | 
% 231.83/43.02  | End of split
% 231.83/43.02  | 
% 231.83/43.02  End of proof
% 231.83/43.02  
% 231.83/43.02  Sub-proof #1787 shows that the following formulas are inconsistent:
% 231.83/43.02  ----------------------------------------------------------------
% 231.83/43.02    (1)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 231.83/43.02    (2)  all_57_7 = e3 & op(e1, e2) = e3
% 231.83/43.02    (3)  op(e2, e1) = e3
% 231.83/43.02    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/43.02           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/43.02    (5)   ~ (all_53_9 = e1)
% 231.83/43.02    (6)  op(e2, e2) = e1
% 231.83/43.02    (7)   ~ (all_53_4 = e1)
% 231.83/43.02    (8)   ~ (e3 = e2)
% 231.83/43.02    (9)  all_55_1 = all_53_4
% 231.83/43.02    (10)   ~ (e3 = e0)
% 231.83/43.02    (11)  op(e3, e3) = e3
% 231.83/43.02    (12)  op(e3, e2) = all_53_4
% 231.83/43.02    (13)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 231.83/43.02            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 231.83/43.02            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 231.83/43.02            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 231.83/43.02              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 231.83/43.02            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 231.83/43.02            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 231.83/43.02              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 231.83/43.02              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 231.83/43.02            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 231.83/43.02            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 231.83/43.02            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 231.83/43.02              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 231.83/43.02              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 231.83/43.02            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 231.83/43.02              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 231.83/43.02            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 231.83/43.02            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 231.83/43.02              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 231.83/43.02              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 231.83/43.02            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 231.83/43.02            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 231.83/43.02    (14)  op(e0, e0) = e3
% 231.83/43.02    (15)   ~ (all_53_4 = all_53_6)
% 231.83/43.02    (16)  ( ~ (all_16_0 = e0) & op(all_16_1, e2) = all_16_0 & op(e2, e1) =
% 231.83/43.02            all_16_1 & $i(all_16_0) & $i(all_16_1)) | ( ~ (all_16_1 = e3) & op(e2,
% 231.83/43.02              e1) = all_16_1 & $i(all_16_1))
% 231.83/43.02    (17)   ~ (all_26_2 = e1) | ( ~ (all_26_0 = e3) & op(all_26_1, e2) = all_26_0 &
% 231.83/43.02            op(e2, e1) = all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 =
% 231.83/43.02              e0) & op(e2, e1) = all_26_1 & $i(all_26_1))
% 231.83/43.02    (18)  op(e2, e1) = all_53_9
% 231.83/43.02    (19)  op(e1, e2) = all_53_6
% 231.83/43.02    (20)  all_26_2 = e1
% 231.83/43.02  
% 231.83/43.02  Begin of proof
% 231.83/43.02  | 
% 231.83/43.02  | ALPHA: (2) implies:
% 231.83/43.02  |   (21)  op(e1, e2) = e3
% 231.83/43.02  | 
% 231.83/43.02  | GROUND_INST: instantiating (4) with all_53_6, e3, e2, e1, simplifying with
% 231.83/43.02  |              (19), (21) gives:
% 231.83/43.02  |   (22)  all_53_6 = e3
% 231.83/43.02  | 
% 231.83/43.02  | GROUND_INST: instantiating (4) with all_53_9, e3, e1, e2, simplifying with
% 231.83/43.02  |              (3), (18) gives:
% 231.83/43.02  |   (23)  all_53_9 = e3
% 231.83/43.02  | 
% 231.83/43.02  | REDUCE: (15), (22) imply:
% 231.83/43.02  |   (24)   ~ (all_53_4 = e3)
% 231.83/43.02  | 
% 231.83/43.02  | REDUCE: (5), (23) imply:
% 231.83/43.02  |   (25)   ~ (e3 = e1)
% 231.83/43.02  | 
% 231.83/43.02  | BETA: splitting (16) gives:
% 231.83/43.02  | 
% 231.83/43.02  | Case 1:
% 231.83/43.02  | | 
% 231.83/43.02  | |   (26)   ~ (all_16_0 = e0) & op(all_16_1, e2) = all_16_0 & op(e2, e1) =
% 231.83/43.02  | |         all_16_1 & $i(all_16_0) & $i(all_16_1)
% 231.83/43.02  | | 
% 231.83/43.02  | | ALPHA: (26) implies:
% 231.83/43.02  | |   (27)   ~ (all_16_0 = e0)
% 231.83/43.02  | |   (28)  op(e2, e1) = all_16_1
% 231.83/43.02  | |   (29)  op(all_16_1, e2) = all_16_0
% 231.83/43.02  | | 
% 231.83/43.02  | | BETA: splitting (13) gives:
% 231.83/43.02  | | 
% 231.83/43.02  | | Case 1:
% 231.83/43.02  | | | 
% 231.83/43.02  | | |   (30)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 231.83/43.02  | | |           op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 231.83/43.02  | | |           op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 231.83/43.02  | | |           op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) =
% 231.83/43.02  | | |           all_52_5 & op(e3, e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) &
% 231.83/43.02  | | |           $i(all_52_5) & $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 &
% 231.83/43.02  | | |           all_52_12 = e1 & all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 231.83/43.02  | | |           op(all_52_11, all_52_11) = e2 & op(all_52_13, all_52_13) = e1 &
% 231.83/43.02  | | |           op(all_52_15, all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2,
% 231.83/43.02  | | |             e2) = all_52_11 & op(e2, e1) = all_52_13 & op(e2, e0) =
% 231.83/43.02  | | |           all_52_15 & $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 231.83/43.02  | | |           $i(all_52_15))
% 231.83/43.02  | | | 
% 231.83/43.02  | | | BETA: splitting (30) gives:
% 231.83/43.02  | | | 
% 231.83/43.02  | | | Case 1:
% 231.83/43.02  | | | | 
% 231.83/43.02  | | | |   (31)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 231.83/43.02  | | | |         op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 231.83/43.02  | | | |         op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 231.83/43.02  | | | |         op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) =
% 231.83/43.02  | | | |         all_52_5 & op(e3, e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) &
% 231.83/43.02  | | | |         $i(all_52_5) & $i(all_52_7)
% 231.83/43.02  | | | | 
% 231.83/43.02  | | | | ALPHA: (31) implies:
% 231.83/43.02  | | | |   (32)  op(e3, e2) = all_52_3
% 231.83/43.02  | | | |   (33)  op(all_52_3, all_52_3) = e2
% 231.83/43.02  | | | | 
% 231.83/43.02  | | | | BETA: splitting (17) gives:
% 231.83/43.02  | | | | 
% 231.83/43.02  | | | | Case 1:
% 231.83/43.02  | | | | | 
% 231.83/43.02  | | | | |   (34)   ~ (all_26_2 = e1)
% 231.83/43.02  | | | | | 
% 231.83/43.02  | | | | | REDUCE: (20), (34) imply:
% 231.83/43.02  | | | | |   (35)  $false
% 231.83/43.02  | | | | | 
% 231.83/43.02  | | | | | CLOSE: (35) is inconsistent.
% 231.83/43.02  | | | | | 
% 231.83/43.02  | | | | Case 2:
% 231.83/43.02  | | | | | 
% 231.83/43.02  | | | | | 
% 231.83/43.02  | | | | | GROUND_INST: instantiating (4) with e3, all_16_1, e1, e2, simplifying
% 231.83/43.02  | | | | |              with (3), (28) gives:
% 231.83/43.02  | | | | |   (36)  all_16_1 = e3
% 231.83/43.02  | | | | | 
% 231.83/43.02  | | | | | GROUND_INST: instantiating (4) with all_53_4, all_52_3, e2, e3,
% 231.83/43.02  | | | | |              simplifying with (12), (32) gives:
% 231.83/43.02  | | | | |   (37)  all_53_4 = all_52_3
% 231.83/43.02  | | | | | 
% 231.83/43.02  | | | | | COMBINE_EQS: (9), (37) imply:
% 231.83/43.02  | | | | |   (38)  all_55_1 = all_52_3
% 231.83/43.02  | | | | | 
% 231.83/43.02  | | | | | REDUCE: (24), (37) imply:
% 231.83/43.02  | | | | |   (39)   ~ (all_52_3 = e3)
% 231.83/43.02  | | | | | 
% 231.83/43.02  | | | | | REDUCE: (7), (37) imply:
% 231.83/43.02  | | | | |   (40)   ~ (all_52_3 = e1)
% 231.83/43.02  | | | | | 
% 231.83/43.02  | | | | | REDUCE: (29), (36) imply:
% 231.83/43.02  | | | | |   (41)  op(e3, e2) = all_16_0
% 231.83/43.02  | | | | | 
% 231.83/43.02  | | | | | GROUND_INST: instantiating (4) with all_52_3, all_16_0, e2, e3,
% 231.83/43.02  | | | | |              simplifying with (32), (41) gives:
% 231.83/43.02  | | | | |   (42)  all_52_3 = all_16_0
% 231.83/43.02  | | | | | 
% 231.83/43.02  | | | | | COMBINE_EQS: (38), (42) imply:
% 231.83/43.02  | | | | |   (43)  all_55_1 = all_16_0
% 231.83/43.02  | | | | | 
% 231.83/43.02  | | | | | REDUCE: (39), (42) imply:
% 231.83/43.02  | | | | |   (44)   ~ (all_16_0 = e3)
% 231.83/43.02  | | | | | 
% 231.83/43.02  | | | | | REDUCE: (40), (42) imply:
% 231.83/43.02  | | | | |   (45)   ~ (all_16_0 = e1)
% 231.83/43.02  | | | | | 
% 231.83/43.02  | | | | | REDUCE: (33), (42) imply:
% 231.83/43.02  | | | | |   (46)  op(all_16_0, all_16_0) = e2
% 231.83/43.02  | | | | | 
% 231.83/43.02  | | | | | BETA: splitting (1) gives:
% 231.83/43.02  | | | | | 
% 231.83/43.02  | | | | | Case 1:
% 231.83/43.02  | | | | | | 
% 231.83/43.02  | | | | | |   (47)  all_55_1 = e3
% 231.83/43.02  | | | | | | 
% 231.83/43.02  | | | | | | COMBINE_EQS: (43), (47) imply:
% 231.83/43.02  | | | | | |   (48)  all_16_0 = e3
% 231.83/43.02  | | | | | | 
% 231.83/43.02  | | | | | | SIMP: (48) implies:
% 231.83/43.02  | | | | | |   (49)  all_16_0 = e3
% 231.83/43.02  | | | | | | 
% 231.83/43.02  | | | | | | REDUCE: (44), (49) imply:
% 231.83/43.02  | | | | | |   (50)  $false
% 231.83/43.02  | | | | | | 
% 231.83/43.02  | | | | | | CLOSE: (50) is inconsistent.
% 231.83/43.02  | | | | | | 
% 231.83/43.02  | | | | | Case 2:
% 231.83/43.02  | | | | | | 
% 231.83/43.02  | | | | | |   (51)  all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 231.83/43.02  | | | | | | 
% 231.83/43.02  | | | | | | BETA: splitting (51) gives:
% 231.83/43.02  | | | | | | 
% 231.83/43.02  | | | | | | Case 1:
% 231.83/43.02  | | | | | | | 
% 231.83/43.02  | | | | | | |   (52)  all_55_1 = e2
% 231.83/43.02  | | | | | | | 
% 231.83/43.02  | | | | | | | COMBINE_EQS: (43), (52) imply:
% 231.83/43.02  | | | | | | |   (53)  all_16_0 = e2
% 231.83/43.02  | | | | | | | 
% 231.83/43.02  | | | | | | | SIMP: (53) implies:
% 231.83/43.02  | | | | | | |   (54)  all_16_0 = e2
% 231.83/43.02  | | | | | | | 
% 231.83/43.02  | | | | | | | REDUCE: (45), (54) imply:
% 231.83/43.02  | | | | | | |   (55)   ~ (e2 = e1)
% 231.83/43.02  | | | | | | | 
% 231.83/43.02  | | | | | | | REDUCE: (46), (54) imply:
% 231.83/43.02  | | | | | | |   (56)  op(e2, e2) = e2
% 231.83/43.02  | | | | | | | 
% 231.83/43.02  | | | | | | | REF_CLOSE: (4), (6), (55), (56) are inconsistent by sub-proof
% 231.83/43.02  | | | | | | |            #2306.
% 231.83/43.02  | | | | | | | 
% 231.83/43.02  | | | | | | Case 2:
% 231.83/43.02  | | | | | | | 
% 231.83/43.02  | | | | | | |   (57)  all_55_1 = e1 | all_55_1 = e0
% 231.83/43.02  | | | | | | | 
% 231.83/43.02  | | | | | | | BETA: splitting (57) gives:
% 231.83/43.02  | | | | | | | 
% 231.83/43.02  | | | | | | | Case 1:
% 231.83/43.02  | | | | | | | | 
% 231.83/43.02  | | | | | | | |   (58)  all_55_1 = e1
% 231.83/43.02  | | | | | | | | 
% 231.83/43.02  | | | | | | | | COMBINE_EQS: (43), (58) imply:
% 231.83/43.02  | | | | | | | |   (59)  all_16_0 = e1
% 231.83/43.02  | | | | | | | | 
% 231.83/43.02  | | | | | | | | REDUCE: (45), (59) imply:
% 231.83/43.02  | | | | | | | |   (60)  $false
% 231.83/43.02  | | | | | | | | 
% 231.83/43.02  | | | | | | | | CLOSE: (60) is inconsistent.
% 231.83/43.02  | | | | | | | | 
% 231.83/43.02  | | | | | | | Case 2:
% 231.83/43.02  | | | | | | | | 
% 231.83/43.03  | | | | | | | |   (61)  all_55_1 = e0
% 231.83/43.03  | | | | | | | | 
% 231.83/43.03  | | | | | | | | COMBINE_EQS: (43), (61) imply:
% 231.83/43.03  | | | | | | | |   (62)  all_16_0 = e0
% 231.83/43.03  | | | | | | | | 
% 231.83/43.03  | | | | | | | | REDUCE: (27), (62) imply:
% 231.83/43.03  | | | | | | | |   (63)  $false
% 231.83/43.03  | | | | | | | | 
% 231.83/43.03  | | | | | | | | CLOSE: (63) is inconsistent.
% 231.83/43.03  | | | | | | | | 
% 231.83/43.03  | | | | | | | End of split
% 231.83/43.03  | | | | | | | 
% 231.83/43.03  | | | | | | End of split
% 231.83/43.03  | | | | | | 
% 231.83/43.03  | | | | | End of split
% 231.83/43.03  | | | | | 
% 231.83/43.03  | | | | End of split
% 231.83/43.03  | | | | 
% 231.83/43.03  | | | Case 2:
% 231.83/43.03  | | | | 
% 231.83/43.03  | | | |   (64)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0
% 231.83/43.03  | | | |         & op(all_52_9, all_52_9) = e3 & op(all_52_11, all_52_11) = e2 &
% 231.83/43.03  | | | |         op(all_52_13, all_52_13) = e1 & op(all_52_15, all_52_15) = e0 &
% 231.83/43.03  | | | |         op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 & op(e2, e1) =
% 231.83/43.03  | | | |         all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 231.83/43.03  | | | |         $i(all_52_11) & $i(all_52_13) & $i(all_52_15)
% 231.83/43.03  | | | | 
% 231.83/43.03  | | | | ALPHA: (64) implies:
% 231.83/43.03  | | | |   (65)  op(e2, e1) = all_52_13
% 231.83/43.03  | | | |   (66)  op(all_52_13, all_52_13) = e1
% 231.83/43.03  | | | | 
% 231.83/43.03  | | | | REF_CLOSE: (3), (4), (11), (17), (20), (25), (65), (66) are inconsistent
% 231.83/43.03  | | | |            by sub-proof #1791.
% 231.83/43.03  | | | | 
% 231.83/43.03  | | | End of split
% 231.83/43.03  | | | 
% 231.83/43.03  | | Case 2:
% 231.83/43.03  | | | 
% 231.83/43.03  | | |   (67)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 231.83/43.03  | | |           & op(all_52_17, all_52_17) = e3 & op(all_52_19, all_52_19) = e2
% 231.83/43.03  | | |           & op(all_52_21, all_52_21) = e1 & op(all_52_23, all_52_23) = e0
% 231.83/43.03  | | |           & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) =
% 231.83/43.03  | | |           all_52_21 & op(e1, e0) = all_52_23 & $i(all_52_17) &
% 231.83/43.03  | | |           $i(all_52_19) & $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 231.83/43.03  | | |           & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0 &
% 231.83/43.03  | | |           op(all_52_25, all_52_25) = e3 & op(all_52_27, all_52_27) = e2 &
% 231.83/43.03  | | |           op(all_52_29, all_52_29) = e1 & op(all_52_31, all_52_31) = e0 &
% 231.83/43.03  | | |           op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 & op(e0, e1) =
% 231.83/43.03  | | |           all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 231.83/43.03  | | |           $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 231.83/43.03  | | | 
% 231.83/43.03  | | | BETA: splitting (67) gives:
% 231.83/43.03  | | | 
% 231.83/43.03  | | | Case 1:
% 231.83/43.03  | | | | 
% 231.83/43.03  | | | |   (68)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 231.83/43.03  | | | |         e0 & op(all_52_17, all_52_17) = e3 & op(all_52_19, all_52_19) =
% 231.83/43.03  | | | |         e2 & op(all_52_21, all_52_21) = e1 & op(all_52_23, all_52_23) =
% 231.83/43.03  | | | |         e0 & op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19 & op(e1,
% 231.83/43.03  | | | |           e1) = all_52_21 & op(e1, e0) = all_52_23 & $i(all_52_17) &
% 231.83/43.03  | | | |         $i(all_52_19) & $i(all_52_21) & $i(all_52_23)
% 231.83/43.03  | | | | 
% 231.83/43.03  | | | | REF_CLOSE: (4), (8), (11), (21), (68) are inconsistent by sub-proof
% 231.83/43.03  | | | |            #1790.
% 231.83/43.03  | | | | 
% 231.83/43.03  | | | Case 2:
% 231.83/43.03  | | | | 
% 231.83/43.03  | | | |   (69)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 =
% 231.83/43.03  | | | |         e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27, all_52_27) =
% 231.83/43.03  | | | |         e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31, all_52_31) =
% 231.83/43.03  | | | |         e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 & op(e0,
% 231.83/43.03  | | | |           e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 231.83/43.03  | | | |         $i(all_52_27) & $i(all_52_29) & $i(all_52_31)
% 231.83/43.03  | | | | 
% 231.83/43.03  | | | | ALPHA: (69) implies:
% 231.83/43.03  | | | |   (70)  op(e0, e0) = all_52_31
% 231.83/43.03  | | | |   (71)  op(all_52_31, all_52_31) = e0
% 231.83/43.03  | | | | 
% 231.83/43.03  | | | | REF_CLOSE: (4), (10), (11), (14), (17), (20), (70), (71) are
% 231.83/43.03  | | | |            inconsistent by sub-proof #1789.
% 231.83/43.03  | | | | 
% 231.83/43.03  | | | End of split
% 231.83/43.03  | | | 
% 231.83/43.03  | | End of split
% 231.83/43.03  | | 
% 231.83/43.03  | Case 2:
% 231.83/43.03  | | 
% 231.83/43.03  | |   (72)   ~ (all_16_1 = e3) & op(e2, e1) = all_16_1 & $i(all_16_1)
% 231.83/43.03  | | 
% 231.83/43.03  | | ALPHA: (72) implies:
% 231.83/43.03  | |   (73)   ~ (all_16_1 = e3)
% 231.83/43.03  | |   (74)  op(e2, e1) = all_16_1
% 231.83/43.03  | | 
% 231.83/43.03  | | BETA: splitting (17) gives:
% 231.83/43.03  | | 
% 231.83/43.03  | | Case 1:
% 231.83/43.03  | | | 
% 231.83/43.03  | | |   (75)   ~ (all_26_2 = e1)
% 231.83/43.03  | | | 
% 231.83/43.03  | | | REDUCE: (20), (75) imply:
% 231.83/43.03  | | |   (76)  $false
% 231.83/43.03  | | | 
% 231.83/43.03  | | | CLOSE: (76) is inconsistent.
% 231.83/43.03  | | | 
% 231.83/43.03  | | Case 2:
% 231.83/43.03  | | | 
% 231.83/43.03  | | |   (77)  ( ~ (all_26_0 = e3) & op(all_26_1, e2) = all_26_0 & op(e2, e1) =
% 231.83/43.03  | | |           all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 = e0) &
% 231.83/43.03  | | |           op(e2, e1) = all_26_1 & $i(all_26_1))
% 231.83/43.03  | | | 
% 231.83/43.03  | | | BETA: splitting (77) gives:
% 231.83/43.03  | | | 
% 231.83/43.03  | | | Case 1:
% 231.83/43.03  | | | | 
% 231.83/43.03  | | | |   (78)   ~ (all_26_0 = e3) & op(all_26_1, e2) = all_26_0 & op(e2, e1) =
% 231.83/43.03  | | | |         all_26_1 & $i(all_26_0) & $i(all_26_1)
% 231.83/43.03  | | | | 
% 231.83/43.03  | | | | ALPHA: (78) implies:
% 231.83/43.03  | | | |   (79)  op(e2, e1) = all_26_1
% 231.83/43.03  | | | | 
% 231.83/43.03  | | | | REF_CLOSE: (3), (4), (73), (74), (79) are inconsistent by sub-proof
% 231.83/43.03  | | | |            #1788.
% 231.83/43.03  | | | | 
% 231.83/43.03  | | | Case 2:
% 231.83/43.03  | | | | 
% 231.83/43.03  | | | |   (80)   ~ (all_26_1 = e0) & op(e2, e1) = all_26_1 & $i(all_26_1)
% 231.83/43.03  | | | | 
% 231.83/43.03  | | | | ALPHA: (80) implies:
% 231.83/43.03  | | | |   (81)  op(e2, e1) = all_26_1
% 231.83/43.03  | | | | 
% 231.83/43.03  | | | | REF_CLOSE: (3), (4), (73), (74), (81) are inconsistent by sub-proof
% 231.83/43.03  | | | |            #1788.
% 231.83/43.03  | | | | 
% 231.83/43.03  | | | End of split
% 231.83/43.03  | | | 
% 231.83/43.03  | | End of split
% 231.83/43.03  | | 
% 231.83/43.03  | End of split
% 231.83/43.03  | 
% 231.83/43.03  End of proof
% 231.83/43.03  
% 231.83/43.03  Sub-proof #1788 shows that the following formulas are inconsistent:
% 231.83/43.03  ----------------------------------------------------------------
% 231.83/43.03    (1)  op(e2, e1) = all_26_1
% 231.83/43.03    (2)  op(e2, e1) = e3
% 231.83/43.03    (3)   ~ (all_16_1 = e3)
% 231.83/43.03    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/43.03           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/43.03    (5)  op(e2, e1) = all_16_1
% 231.83/43.03  
% 231.83/43.03  Begin of proof
% 231.83/43.03  | 
% 231.83/43.03  | GROUND_INST: instantiating (4) with all_16_1, all_26_1, e1, e2, simplifying
% 231.83/43.03  |              with (1), (5) gives:
% 231.83/43.03  |   (6)  all_26_1 = all_16_1
% 231.83/43.03  | 
% 231.83/43.03  | GROUND_INST: instantiating (4) with e3, all_26_1, e1, e2, simplifying with
% 231.83/43.03  |              (1), (2) gives:
% 231.83/43.03  |   (7)  all_26_1 = e3
% 231.83/43.03  | 
% 231.83/43.03  | COMBINE_EQS: (6), (7) imply:
% 231.83/43.03  |   (8)  all_16_1 = e3
% 231.83/43.03  | 
% 231.83/43.03  | SIMP: (8) implies:
% 231.83/43.03  |   (9)  all_16_1 = e3
% 231.83/43.03  | 
% 231.83/43.03  | REDUCE: (3), (9) imply:
% 231.83/43.03  |   (10)  $false
% 231.83/43.03  | 
% 231.83/43.03  | CLOSE: (10) is inconsistent.
% 231.83/43.03  | 
% 231.83/43.03  End of proof
% 231.83/43.03  
% 231.83/43.03  Sub-proof #1789 shows that the following formulas are inconsistent:
% 231.83/43.03  ----------------------------------------------------------------
% 231.83/43.03    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/43.03           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/43.03    (2)   ~ (e3 = e0)
% 231.83/43.03    (3)  op(e3, e3) = e3
% 231.83/43.03    (4)  op(e0, e0) = all_52_31
% 231.83/43.03    (5)  op(e0, e0) = e3
% 231.83/43.03    (6)   ~ (all_26_2 = e1) | ( ~ (all_26_0 = e3) & op(all_26_1, e2) = all_26_0 &
% 231.83/43.03           op(e2, e1) = all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 =
% 231.83/43.03             e0) & op(e2, e1) = all_26_1 & $i(all_26_1))
% 231.83/43.03    (7)  all_26_2 = e1
% 231.83/43.03    (8)  op(all_52_31, all_52_31) = e0
% 231.83/43.03  
% 231.83/43.03  Begin of proof
% 231.83/43.03  | 
% 231.83/43.03  | BETA: splitting (6) gives:
% 231.83/43.03  | 
% 231.83/43.03  | Case 1:
% 231.83/43.03  | | 
% 231.83/43.03  | |   (9)   ~ (all_26_2 = e1)
% 231.83/43.03  | | 
% 231.83/43.03  | | REDUCE: (7), (9) imply:
% 231.83/43.03  | |   (10)  $false
% 231.83/43.03  | | 
% 231.83/43.03  | | CLOSE: (10) is inconsistent.
% 231.83/43.03  | | 
% 231.83/43.03  | Case 2:
% 231.83/43.03  | | 
% 231.83/43.03  | | 
% 231.83/43.03  | | GROUND_INST: instantiating (1) with e3, all_52_31, e0, e0, simplifying with
% 231.83/43.03  | |              (4), (5) gives:
% 231.83/43.03  | |   (11)  all_52_31 = e3
% 231.83/43.03  | | 
% 231.83/43.03  | | REDUCE: (8), (11) imply:
% 231.83/43.03  | |   (12)  op(e3, e3) = e0
% 231.83/43.03  | | 
% 231.83/43.03  | | REF_CLOSE: (1), (2), (3), (12) are inconsistent by sub-proof #2494.
% 231.83/43.03  | | 
% 231.83/43.03  | End of split
% 231.83/43.03  | 
% 231.83/43.03  End of proof
% 231.83/43.03  
% 231.83/43.03  Sub-proof #1790 shows that the following formulas are inconsistent:
% 231.83/43.03  ----------------------------------------------------------------
% 231.83/43.03    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/43.03           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/43.03    (2)  op(e1, e2) = e3
% 231.83/43.03    (3)   ~ (e3 = e2)
% 231.83/43.03    (4)  op(e3, e3) = e3
% 231.83/43.03    (5)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 &
% 231.83/43.03         op(all_52_17, all_52_17) = e3 & op(all_52_19, all_52_19) = e2 &
% 231.83/43.03         op(all_52_21, all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1,
% 231.83/43.03           e3) = all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 &
% 231.83/43.03         op(e1, e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 231.83/43.03         $i(all_52_23)
% 231.83/43.03  
% 231.83/43.03  Begin of proof
% 231.83/43.03  | 
% 231.83/43.03  | ALPHA: (5) implies:
% 231.83/43.03  |   (6)  op(e1, e2) = all_52_19
% 231.83/43.03  |   (7)  op(all_52_19, all_52_19) = e2
% 231.83/43.03  | 
% 231.83/43.03  | GROUND_INST: instantiating (1) with e3, all_52_19, e2, e1, simplifying with
% 231.83/43.03  |              (2), (6) gives:
% 231.83/43.03  |   (8)  all_52_19 = e3
% 231.83/43.03  | 
% 231.83/43.03  | REDUCE: (7), (8) imply:
% 231.83/43.03  |   (9)  op(e3, e3) = e2
% 231.83/43.03  | 
% 231.83/43.03  | REF_CLOSE: (1), (3), (4), (9) are inconsistent by sub-proof #2490.
% 231.83/43.03  | 
% 231.83/43.03  End of proof
% 231.83/43.03  
% 231.83/43.03  Sub-proof #1791 shows that the following formulas are inconsistent:
% 231.83/43.03  ----------------------------------------------------------------
% 231.83/43.03    (1)  op(e2, e1) = all_52_13
% 231.83/43.03    (2)  op(e2, e1) = e3
% 231.83/43.03    (3)   ~ (e3 = e1)
% 231.83/43.03    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/43.03           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/43.03    (5)  op(e3, e3) = e3
% 231.83/43.03    (6)  op(all_52_13, all_52_13) = e1
% 231.83/43.03    (7)   ~ (all_26_2 = e1) | ( ~ (all_26_0 = e3) & op(all_26_1, e2) = all_26_0 &
% 231.83/43.03           op(e2, e1) = all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 =
% 231.83/43.03             e0) & op(e2, e1) = all_26_1 & $i(all_26_1))
% 231.83/43.03    (8)  all_26_2 = e1
% 231.83/43.03  
% 231.83/43.03  Begin of proof
% 231.83/43.03  | 
% 231.83/43.03  | BETA: splitting (7) gives:
% 231.83/43.03  | 
% 231.83/43.03  | Case 1:
% 231.83/43.03  | | 
% 231.83/43.03  | |   (9)   ~ (all_26_2 = e1)
% 231.83/43.03  | | 
% 231.83/43.03  | | REDUCE: (8), (9) imply:
% 231.83/43.03  | |   (10)  $false
% 231.83/43.03  | | 
% 231.83/43.03  | | CLOSE: (10) is inconsistent.
% 231.83/43.03  | | 
% 231.83/43.03  | Case 2:
% 231.83/43.03  | | 
% 231.83/43.03  | | 
% 231.83/43.03  | | GROUND_INST: instantiating (4) with e3, all_52_13, e1, e2, simplifying with
% 231.83/43.03  | |              (1), (2) gives:
% 231.83/43.03  | |   (11)  all_52_13 = e3
% 231.83/43.03  | | 
% 231.83/43.03  | | REDUCE: (6), (11) imply:
% 231.83/43.03  | |   (12)  op(e3, e3) = e1
% 231.83/43.03  | | 
% 231.83/43.03  | | REF_CLOSE: (3), (4), (5), (12) are inconsistent by sub-proof #2495.
% 231.83/43.03  | | 
% 231.83/43.03  | End of split
% 231.83/43.03  | 
% 231.83/43.03  End of proof
% 231.83/43.03  
% 231.83/43.03  Sub-proof #1792 shows that the following formulas are inconsistent:
% 231.83/43.03  ----------------------------------------------------------------
% 231.83/43.03    (1)   ~ (e3 = e1)
% 231.83/43.03    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/43.03           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/43.03    (3)   ~ (e3 = e2)
% 231.83/43.03    (4)   ~ (e3 = e0)
% 231.83/43.03    (5)  all_57_15 = e3
% 231.83/43.03    (6)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 231.83/43.03         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.83/43.03    (7)   ~ (e2 = e0)
% 231.83/43.03    (8)   ~ (e1 = e0)
% 231.83/43.03    (9)  all_57_13 = e3
% 231.83/43.03    (10)  op(e0, e0) = e3
% 231.83/43.03    (11)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.83/43.03          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.83/43.03            e2)
% 231.83/43.03    (12)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.83/43.03              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.83/43.03                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.83/43.03                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.83/43.03    (13)   ~ (e2 = e1)
% 231.83/43.03  
% 231.83/43.03  Begin of proof
% 231.83/43.03  | 
% 231.83/43.03  | BETA: splitting (12) gives:
% 231.83/43.03  | 
% 231.83/43.03  | Case 1:
% 231.83/43.03  | | 
% 231.83/43.03  | |   (14)  all_57_15 = e0 & op(e0, e0) = e0
% 231.83/43.03  | | 
% 231.83/43.03  | | ALPHA: (14) implies:
% 231.83/43.03  | |   (15)  op(e0, e0) = e0
% 231.83/43.03  | | 
% 231.83/43.03  | | REF_CLOSE: (2), (4), (10), (15) are inconsistent by sub-proof #2304.
% 231.83/43.03  | | 
% 231.83/43.03  | Case 2:
% 231.83/43.03  | | 
% 231.83/43.03  | |   (16)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 231.83/43.03  | |             e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0 &
% 231.83/43.03  | |             op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 231.83/43.03  | |           (all_57_14 = e0 & op(e0, e1) = e0))
% 231.83/43.03  | | 
% 231.83/43.03  | | ALPHA: (16) implies:
% 231.83/43.03  | |   (17)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 231.83/43.03  | |           e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.83/43.03  | | 
% 231.83/43.03  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 231.83/43.03  | |            (17) are inconsistent by sub-proof #2054.
% 231.83/43.03  | | 
% 231.83/43.03  | End of split
% 231.83/43.03  | 
% 231.83/43.03  End of proof
% 231.83/43.03  
% 231.83/43.03  Sub-proof #1793 shows that the following formulas are inconsistent:
% 231.83/43.03  ----------------------------------------------------------------
% 231.83/43.03    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.83/43.03         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.83/43.03    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.83/43.03         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.83/43.03    (3)   ~ (e3 = e1)
% 231.83/43.03    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.83/43.03           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.83/43.03    (5)   ~ (all_6_2 = e3)
% 231.83/43.03    (6)  op(e1, e1) = all_6_2
% 231.83/43.03    (7)  op(e2, e2) = e1
% 231.83/43.03    (8)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.83/43.03         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.83/43.03    (9)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.83/43.03         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.83/43.03    (10)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.83/43.03          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.83/43.03    (11)   ~ (e3 = e2)
% 231.83/43.03    (12)   ~ (e3 = e0)
% 231.83/43.03    (13)  op(e3, e3) = e3
% 231.83/43.03    (14)  all_57_15 = e3
% 231.83/43.03    (15)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.83/43.03          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.83/43.03            e1)
% 231.83/43.03    (16)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 231.83/43.03          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 231.83/43.03    (17)   ~ (e2 = e0)
% 231.83/43.03    (18)  all_57_2 = e3
% 231.83/43.03    (19)   ~ (e1 = e0)
% 231.83/43.03    (20)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.83/43.03          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.83/43.03    (21)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.83/43.03          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.83/43.03            e2)
% 231.83/43.03    (22)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.83/43.03              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.83/43.03                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.83/43.03                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.83/43.03    (23)  all_57_7 = e3
% 231.83/43.03    (24)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.83/43.03          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.83/43.03    (25)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 231.83/43.03          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 231.95/43.03    (26)   ~ (e2 = e1)
% 231.95/43.03  
% 231.95/43.03  Begin of proof
% 231.95/43.03  | 
% 231.95/43.03  | BETA: splitting (20) gives:
% 231.95/43.03  | 
% 231.95/43.03  | Case 1:
% 231.95/43.03  | | 
% 231.95/43.03  | |   (27)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) =
% 231.95/43.03  | |           e3)
% 231.95/43.03  | | 
% 231.95/43.03  | | BETA: splitting (27) gives:
% 231.95/43.03  | | 
% 231.95/43.03  | | Case 1:
% 231.95/43.03  | | | 
% 231.95/43.03  | | |   (28)  all_57_4 = e3 & op(e3, e1) = e3
% 231.95/43.03  | | | 
% 231.95/43.03  | | | ALPHA: (28) implies:
% 231.95/43.03  | | |   (29)  all_57_4 = e3
% 231.95/43.03  | | | 
% 231.95/43.03  | | | BETA: splitting (8) gives:
% 231.95/43.03  | | | 
% 231.95/43.03  | | | Case 1:
% 231.95/43.03  | | | | 
% 231.95/43.03  | | | |   (30)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2)
% 231.95/43.03  | | | |           = e1)
% 231.95/43.03  | | | | 
% 231.95/43.03  | | | | BETA: splitting (30) gives:
% 231.95/43.03  | | | | 
% 231.95/43.03  | | | | Case 1:
% 231.95/43.03  | | | | | 
% 231.95/43.03  | | | | |   (31)  all_57_0 = e1 & op(e3, e3) = e1
% 231.95/43.03  | | | | | 
% 231.95/43.03  | | | | | ALPHA: (31) implies:
% 231.95/43.03  | | | | |   (32)  op(e3, e3) = e1
% 231.95/43.03  | | | | | 
% 231.95/43.03  | | | | | REF_CLOSE: (3), (4), (13), (32) are inconsistent by sub-proof #2495.
% 231.95/43.03  | | | | | 
% 231.95/43.03  | | | | Case 2:
% 231.95/43.03  | | | | | 
% 231.95/43.03  | | | | |   (33)  all_57_1 = e1 & op(e3, e2) = e1
% 231.95/43.03  | | | | | 
% 231.95/43.03  | | | | | ALPHA: (33) implies:
% 231.95/43.03  | | | | |   (34)  all_57_1 = e1
% 231.95/43.03  | | | | | 
% 231.95/43.03  | | | | | REF_CLOSE: (2), (4), (7), (11), (12), (16), (17), (19), (23), (26),
% 231.95/43.03  | | | | |            (34) are inconsistent by sub-proof #1909.
% 231.95/43.03  | | | | | 
% 231.95/43.03  | | | | End of split
% 231.95/43.03  | | | | 
% 231.95/43.03  | | | Case 2:
% 231.95/43.03  | | | | 
% 231.95/43.03  | | | |   (35)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0)
% 231.95/43.03  | | | |           = e1)
% 231.95/43.03  | | | | 
% 231.95/43.03  | | | | REF_CLOSE: (3), (4), (8), (9), (10), (11), (12), (13), (17), (19), (26),
% 231.95/43.03  | | | |            (29), (35) are inconsistent by sub-proof #2475.
% 231.95/43.03  | | | | 
% 231.95/43.03  | | | End of split
% 231.95/43.03  | | | 
% 231.95/43.03  | | Case 2:
% 231.95/43.03  | | | 
% 231.95/43.03  | | |   (36)  all_57_5 = e3 & op(e2, e1) = e3
% 231.95/43.03  | | | 
% 231.95/43.03  | | | ALPHA: (36) implies:
% 231.95/43.03  | | |   (37)  all_57_5 = e3
% 231.95/43.03  | | | 
% 231.95/43.03  | | | REF_CLOSE: (1), (3), (4), (7), (11), (12), (17), (18), (19), (24), (25),
% 231.95/43.03  | | |            (26), (37) are inconsistent by sub-proof #1795.
% 231.95/43.03  | | | 
% 231.95/43.03  | | End of split
% 231.95/43.03  | | 
% 231.95/43.03  | Case 2:
% 231.95/43.03  | | 
% 231.95/43.03  | |   (38)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) =
% 231.95/43.03  | |           e3)
% 231.95/43.03  | | 
% 231.95/43.03  | | REF_CLOSE: (3), (4), (5), (6), (11), (12), (14), (15), (17), (19), (21),
% 231.95/43.03  | |            (22), (26), (38) are inconsistent by sub-proof #1794.
% 231.95/43.03  | | 
% 231.95/43.03  | End of split
% 231.95/43.03  | 
% 231.95/43.03  End of proof
% 231.95/43.03  
% 231.95/43.03  Sub-proof #1794 shows that the following formulas are inconsistent:
% 231.95/43.03  ----------------------------------------------------------------
% 231.95/43.03    (1)   ~ (e3 = e1)
% 231.95/43.03    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.95/43.03           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.95/43.03    (3)   ~ (all_6_2 = e3)
% 231.95/43.03    (4)  op(e1, e1) = all_6_2
% 231.95/43.03    (5)   ~ (e3 = e2)
% 231.95/43.03    (6)   ~ (e3 = e0)
% 231.95/43.03    (7)  all_57_15 = e3
% 231.95/43.03    (8)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 231.95/43.03         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 231.95/43.03    (9)   ~ (e2 = e0)
% 231.95/43.03    (10)   ~ (e1 = e0)
% 231.95/43.03    (11)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.95/43.03          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.95/43.03            e2)
% 231.95/43.03    (12)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.95/43.03              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.95/43.03                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.95/43.03                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.95/43.03    (13)   ~ (e2 = e1)
% 231.95/43.03    (14)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.95/43.03  
% 231.95/43.03  Begin of proof
% 231.95/43.03  | 
% 231.95/43.03  | BETA: splitting (14) gives:
% 231.95/43.03  | 
% 231.95/43.03  | Case 1:
% 231.95/43.03  | | 
% 231.95/43.03  | |   (15)  all_57_8 = e3 & op(e1, e1) = e3
% 231.95/43.03  | | 
% 231.95/43.03  | | ALPHA: (15) implies:
% 231.95/43.03  | |   (16)  op(e1, e1) = e3
% 231.95/43.03  | | 
% 231.95/43.03  | | REF_CLOSE: (2), (3), (4), (16) are inconsistent by sub-proof #2468.
% 231.95/43.03  | | 
% 231.95/43.03  | Case 2:
% 231.95/43.03  | | 
% 231.95/43.03  | |   (17)  all_57_14 = e3 & op(e0, e1) = e3
% 231.95/43.03  | | 
% 231.95/43.03  | | ALPHA: (17) implies:
% 231.95/43.03  | |   (18)  all_57_14 = e3
% 231.95/43.03  | | 
% 231.95/43.03  | | REF_CLOSE: (1), (5), (6), (7), (8), (9), (10), (11), (12), (13), (18) are
% 231.95/43.03  | |            inconsistent by sub-proof #2312.
% 231.95/43.03  | | 
% 231.95/43.03  | End of split
% 231.95/43.03  | 
% 231.95/43.03  End of proof
% 231.95/43.03  
% 231.95/43.03  Sub-proof #1795 shows that the following formulas are inconsistent:
% 231.95/43.03  ----------------------------------------------------------------
% 231.95/43.03    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.95/43.03         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.95/43.03    (2)   ~ (e3 = e1)
% 231.95/43.03    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.95/43.03           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.95/43.03    (4)  op(e2, e2) = e1
% 231.95/43.03    (5)   ~ (e3 = e2)
% 231.95/43.03    (6)   ~ (e3 = e0)
% 231.95/43.03    (7)  all_57_5 = e3
% 231.95/43.03    (8)   ~ (e2 = e0)
% 231.95/43.03    (9)  all_57_2 = e3
% 231.95/43.03    (10)   ~ (e1 = e0)
% 231.95/43.03    (11)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.95/43.03          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.95/43.03    (12)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 231.95/43.03          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 231.95/43.03    (13)   ~ (e2 = e1)
% 231.95/43.03  
% 231.95/43.03  Begin of proof
% 231.95/43.03  | 
% 231.95/43.03  | BETA: splitting (12) gives:
% 231.95/43.03  | 
% 231.95/43.03  | Case 1:
% 231.95/43.03  | | 
% 231.95/43.03  | |   (14)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) =
% 231.95/43.03  | |           e0)
% 231.95/43.03  | | 
% 231.95/43.03  | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (9), (10), (11), (13), (14) are
% 231.95/43.03  | |            inconsistent by sub-proof #1801.
% 231.95/43.03  | | 
% 231.95/43.03  | Case 2:
% 231.95/43.03  | | 
% 231.95/43.03  | |   (15)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 231.95/43.03  | |           e0)
% 231.95/43.03  | | 
% 231.95/43.03  | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (11), (13), (15) are
% 231.95/43.03  | |            inconsistent by sub-proof #1796.
% 231.95/43.03  | | 
% 231.95/43.03  | End of split
% 231.95/43.03  | 
% 231.95/43.03  End of proof
% 231.95/43.03  
% 231.95/43.03  Sub-proof #1796 shows that the following formulas are inconsistent:
% 231.95/43.03  ----------------------------------------------------------------
% 231.95/43.03    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.95/43.03           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.95/43.03    (2)  op(e2, e2) = e1
% 231.95/43.03    (3)   ~ (e3 = e2)
% 231.95/43.03    (4)   ~ (e3 = e0)
% 231.95/43.03    (5)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 231.95/43.03    (6)  all_57_5 = e3
% 231.95/43.03    (7)   ~ (e2 = e0)
% 231.95/43.03    (8)  all_57_2 = e3
% 231.95/43.03    (9)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.95/43.03         (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.95/43.03    (10)   ~ (e2 = e1)
% 231.95/43.03  
% 231.95/43.03  Begin of proof
% 231.95/43.03  | 
% 231.95/43.03  | BETA: splitting (5) gives:
% 231.95/43.03  | 
% 231.95/43.03  | Case 1:
% 231.95/43.03  | | 
% 231.95/43.03  | |   (11)  all_57_5 = e0 & op(e2, e1) = e0
% 231.95/43.03  | | 
% 231.95/43.03  | | REF_CLOSE: (4), (6), (11) are inconsistent by sub-proof #2414.
% 231.95/43.03  | | 
% 231.95/43.03  | Case 2:
% 231.95/43.03  | | 
% 231.95/43.03  | |   (12)  all_57_10 = e0 & op(e2, e0) = e0
% 231.95/43.03  | | 
% 231.95/43.03  | | ALPHA: (12) implies:
% 231.95/43.03  | |   (13)  all_57_10 = e0
% 231.95/43.03  | | 
% 231.95/43.03  | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (9), (10), (13) are inconsistent by
% 231.95/43.03  | |            sub-proof #1797.
% 231.95/43.03  | | 
% 231.95/43.03  | End of split
% 231.95/43.03  | 
% 231.95/43.03  End of proof
% 231.95/43.03  
% 231.95/43.03  Sub-proof #1797 shows that the following formulas are inconsistent:
% 231.95/43.03  ----------------------------------------------------------------
% 231.95/43.03    (1)  all_57_10 = e0
% 231.95/43.03    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.95/43.03           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.95/43.03    (3)  op(e2, e2) = e1
% 231.95/43.03    (4)   ~ (e3 = e2)
% 231.95/43.03    (5)  all_57_5 = e3
% 231.95/43.03    (6)   ~ (e2 = e0)
% 231.95/43.03    (7)  all_57_2 = e3
% 231.95/43.03    (8)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.95/43.03         (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.95/43.03    (9)   ~ (e2 = e1)
% 231.95/43.03  
% 231.95/43.03  Begin of proof
% 231.95/43.03  | 
% 231.95/43.03  | BETA: splitting (8) gives:
% 231.95/43.03  | 
% 231.95/43.03  | Case 1:
% 231.95/43.03  | | 
% 231.95/43.03  | |   (10)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 231.95/43.03  | |           e2)
% 231.95/43.03  | | 
% 231.95/43.03  | | REF_CLOSE: (2), (3), (4), (7), (9), (10) are inconsistent by sub-proof
% 231.95/43.03  | |            #1799.
% 231.95/43.03  | | 
% 231.95/43.03  | Case 2:
% 231.95/43.03  | | 
% 231.95/43.03  | |   (11)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 231.95/43.03  | |           e2)
% 231.95/43.03  | | 
% 231.95/43.03  | | BETA: splitting (11) gives:
% 231.95/43.03  | | 
% 231.95/43.03  | | Case 1:
% 231.95/43.03  | | | 
% 231.95/43.03  | | |   (12)  all_57_5 = e2 & op(e2, e1) = e2
% 231.95/43.03  | | | 
% 231.95/43.03  | | | ALPHA: (12) implies:
% 231.95/43.03  | | |   (13)  all_57_5 = e2
% 231.95/43.03  | | | 
% 231.95/43.03  | | | REF_CLOSE: (4), (5), (13) are inconsistent by sub-proof #2189.
% 231.95/43.03  | | | 
% 231.95/43.03  | | Case 2:
% 231.95/43.03  | | | 
% 231.95/43.03  | | |   (14)  all_57_10 = e2 & op(e2, e0) = e2
% 231.95/43.03  | | | 
% 231.95/43.03  | | | REF_CLOSE: (1), (6), (14) are inconsistent by sub-proof #1798.
% 231.95/43.03  | | | 
% 231.95/43.03  | | End of split
% 231.95/43.03  | | 
% 231.95/43.03  | End of split
% 231.95/43.03  | 
% 231.95/43.03  End of proof
% 231.95/43.03  
% 231.95/43.03  Sub-proof #1798 shows that the following formulas are inconsistent:
% 231.95/43.03  ----------------------------------------------------------------
% 231.95/43.03    (1)  all_57_10 = e2 & op(e2, e0) = e2
% 231.95/43.03    (2)  all_57_10 = e0
% 231.95/43.03    (3)   ~ (e2 = e0)
% 231.95/43.03  
% 231.95/43.03  Begin of proof
% 231.95/43.03  | 
% 231.95/43.03  | ALPHA: (1) implies:
% 231.95/43.03  |   (4)  all_57_10 = e2
% 231.95/43.03  | 
% 231.95/43.03  | COMBINE_EQS: (2), (4) imply:
% 231.95/43.03  |   (5)  e2 = e0
% 231.95/43.03  | 
% 231.95/43.03  | REDUCE: (3), (5) imply:
% 231.95/43.03  |   (6)  $false
% 231.95/43.03  | 
% 231.95/43.03  | CLOSE: (6) is inconsistent.
% 231.95/43.03  | 
% 231.95/43.03  End of proof
% 231.95/43.03  
% 231.95/43.03  Sub-proof #1799 shows that the following formulas are inconsistent:
% 231.95/43.03  ----------------------------------------------------------------
% 231.95/43.03    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.95/43.03           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.95/43.03    (2)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2)
% 231.95/43.03    (3)  op(e2, e2) = e1
% 231.95/43.03    (4)   ~ (e3 = e2)
% 231.95/43.03    (5)  all_57_2 = e3
% 231.95/43.03    (6)   ~ (e2 = e1)
% 231.95/43.03  
% 231.95/43.03  Begin of proof
% 231.95/43.03  | 
% 231.95/43.03  | BETA: splitting (2) gives:
% 231.95/43.03  | 
% 231.95/43.03  | Case 1:
% 231.95/43.03  | | 
% 231.95/43.03  | |   (7)  all_57_2 = e2 & op(e2, e3) = e2
% 231.95/43.03  | | 
% 231.95/43.03  | | ALPHA: (7) implies:
% 231.95/43.03  | |   (8)  all_57_2 = e2
% 231.95/43.03  | | 
% 231.95/43.03  | | REF_CLOSE: (4), (5), (8) are inconsistent by sub-proof #1800.
% 231.95/43.03  | | 
% 231.95/43.03  | Case 2:
% 231.95/43.03  | | 
% 231.95/43.03  | |   (9)  all_57_3 = e2 & op(e2, e2) = e2
% 231.95/43.03  | | 
% 231.95/43.03  | | ALPHA: (9) implies:
% 231.95/43.03  | |   (10)  op(e2, e2) = e2
% 231.95/43.03  | | 
% 231.95/43.03  | | REF_CLOSE: (1), (3), (6), (10) are inconsistent by sub-proof #2306.
% 231.95/43.03  | | 
% 231.95/43.03  | End of split
% 231.95/43.03  | 
% 231.95/43.03  End of proof
% 231.95/43.03  
% 231.95/43.03  Sub-proof #1800 shows that the following formulas are inconsistent:
% 231.95/43.03  ----------------------------------------------------------------
% 231.95/43.03    (1)  all_57_2 = e3
% 231.95/43.03    (2)  all_57_2 = e2
% 231.95/43.03    (3)   ~ (e3 = e2)
% 231.95/43.03  
% 231.95/43.03  Begin of proof
% 231.95/43.03  | 
% 231.95/43.03  | COMBINE_EQS: (1), (2) imply:
% 231.95/43.03  |   (4)  e3 = e2
% 231.95/43.03  | 
% 231.95/43.03  | SIMP: (4) implies:
% 231.95/43.03  |   (5)  e3 = e2
% 231.95/43.03  | 
% 231.95/43.03  | REDUCE: (3), (5) imply:
% 231.95/43.03  |   (6)  $false
% 231.95/43.03  | 
% 231.95/43.03  | CLOSE: (6) is inconsistent.
% 231.95/43.03  | 
% 231.95/43.03  End of proof
% 231.95/43.03  
% 231.95/43.03  Sub-proof #1801 shows that the following formulas are inconsistent:
% 231.95/43.03  ----------------------------------------------------------------
% 231.95/43.03    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.95/43.03         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.95/43.03    (2)   ~ (e3 = e1)
% 231.95/43.03    (3)   ~ (e3 = e2)
% 231.95/43.04    (4)   ~ (e3 = e0)
% 231.95/43.04    (5)  all_57_5 = e3
% 231.95/43.04    (6)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0)
% 231.95/43.04    (7)   ~ (e2 = e0)
% 231.95/43.04    (8)  all_57_2 = e3
% 231.95/43.04    (9)   ~ (e1 = e0)
% 231.95/43.04    (10)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.95/43.04          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.95/43.04    (11)   ~ (e2 = e1)
% 231.95/43.04  
% 231.95/43.04  Begin of proof
% 231.95/43.04  | 
% 231.95/43.04  | BETA: splitting (6) gives:
% 231.95/43.04  | 
% 231.95/43.04  | Case 1:
% 231.95/43.04  | | 
% 231.95/43.04  | |   (12)  all_57_2 = e0 & op(e2, e3) = e0
% 231.95/43.04  | | 
% 231.95/43.04  | | REF_CLOSE: (4), (8), (12) are inconsistent by sub-proof #1805.
% 231.95/43.04  | | 
% 231.95/43.04  | Case 2:
% 231.95/43.04  | | 
% 231.95/43.04  | |   (13)  all_57_3 = e0 & op(e2, e2) = e0
% 231.95/43.04  | | 
% 231.95/43.04  | | ALPHA: (13) implies:
% 231.95/43.04  | |   (14)  all_57_3 = e0
% 231.95/43.04  | | 
% 231.95/43.04  | | REF_CLOSE: (1), (2), (3), (5), (7), (8), (9), (10), (11), (14) are
% 231.95/43.04  | |            inconsistent by sub-proof #1802.
% 231.95/43.04  | | 
% 231.95/43.04  | End of split
% 231.95/43.04  | 
% 231.95/43.04  End of proof
% 231.95/43.04  
% 231.95/43.04  Sub-proof #1802 shows that the following formulas are inconsistent:
% 231.95/43.04  ----------------------------------------------------------------
% 231.95/43.04    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.95/43.04         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.95/43.04    (2)   ~ (e3 = e1)
% 231.95/43.04    (3)  all_57_3 = e0
% 231.95/43.04    (4)   ~ (e3 = e2)
% 231.95/43.04    (5)  all_57_5 = e3
% 231.95/43.04    (6)   ~ (e2 = e0)
% 231.95/43.04    (7)  all_57_2 = e3
% 231.95/43.04    (8)   ~ (e1 = e0)
% 231.95/43.04    (9)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.95/43.04         (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.95/43.04    (10)   ~ (e2 = e1)
% 231.95/43.04  
% 231.95/43.04  Begin of proof
% 231.95/43.04  | 
% 231.95/43.04  | BETA: splitting (9) gives:
% 231.95/43.04  | 
% 231.95/43.04  | Case 1:
% 231.95/43.04  | | 
% 231.95/43.04  | |   (11)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 231.95/43.04  | |           e2)
% 231.95/43.04  | | 
% 231.95/43.04  | | BETA: splitting (11) gives:
% 231.95/43.04  | | 
% 231.95/43.04  | | Case 1:
% 231.95/43.04  | | | 
% 231.95/43.04  | | |   (12)  all_57_2 = e2 & op(e2, e3) = e2
% 231.95/43.04  | | | 
% 231.95/43.04  | | | REF_CLOSE: (4), (7), (12) are inconsistent by sub-proof #1925.
% 231.95/43.04  | | | 
% 231.95/43.04  | | Case 2:
% 231.95/43.04  | | | 
% 231.95/43.04  | | |   (13)  all_57_3 = e2 & op(e2, e2) = e2
% 231.95/43.04  | | | 
% 231.95/43.04  | | | REF_CLOSE: (3), (6), (13) are inconsistent by sub-proof #2103.
% 231.95/43.04  | | | 
% 231.95/43.04  | | End of split
% 231.95/43.04  | | 
% 231.95/43.04  | Case 2:
% 231.95/43.04  | | 
% 231.95/43.04  | |   (14)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 231.95/43.04  | |           e2)
% 231.95/43.04  | | 
% 231.95/43.04  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (10), (14) are inconsistent by
% 231.95/43.04  | |            sub-proof #1803.
% 231.95/43.04  | | 
% 231.95/43.04  | End of split
% 231.95/43.04  | 
% 231.95/43.04  End of proof
% 231.95/43.04  
% 231.95/43.04  Sub-proof #1803 shows that the following formulas are inconsistent:
% 231.95/43.04  ----------------------------------------------------------------
% 231.95/43.04    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.95/43.04         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.95/43.04    (2)   ~ (e3 = e1)
% 231.95/43.04    (3)  all_57_3 = e0
% 231.95/43.04    (4)   ~ (e3 = e2)
% 231.95/43.04    (5)  all_57_5 = e3
% 231.95/43.04    (6)  all_57_2 = e3
% 231.95/43.04    (7)   ~ (e1 = e0)
% 231.95/43.04    (8)   ~ (e2 = e1)
% 231.95/43.04    (9)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.95/43.04  
% 231.95/43.04  Begin of proof
% 231.95/43.04  | 
% 231.95/43.04  | BETA: splitting (9) gives:
% 231.95/43.04  | 
% 231.95/43.04  | Case 1:
% 231.95/43.04  | | 
% 231.95/43.04  | |   (10)  all_57_5 = e2 & op(e2, e1) = e2
% 231.95/43.04  | | 
% 231.95/43.04  | | REF_CLOSE: (4), (5), (10) are inconsistent by sub-proof #2425.
% 231.95/43.04  | | 
% 231.95/43.04  | Case 2:
% 231.95/43.04  | | 
% 231.95/43.04  | |   (11)  all_57_10 = e2 & op(e2, e0) = e2
% 231.95/43.04  | | 
% 231.95/43.04  | | ALPHA: (11) implies:
% 231.95/43.04  | |   (12)  all_57_10 = e2
% 231.95/43.04  | | 
% 231.95/43.04  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (12) are inconsistent by
% 231.95/43.04  | |            sub-proof #1804.
% 231.95/43.04  | | 
% 231.95/43.04  | End of split
% 231.95/43.04  | 
% 231.95/43.04  End of proof
% 231.95/43.04  
% 231.95/43.04  Sub-proof #1804 shows that the following formulas are inconsistent:
% 231.95/43.04  ----------------------------------------------------------------
% 231.95/43.04    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.95/43.04         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.95/43.04    (2)   ~ (e3 = e1)
% 231.95/43.04    (3)  all_57_3 = e0
% 231.95/43.04    (4)  all_57_10 = e2
% 231.95/43.04    (5)  all_57_5 = e3
% 231.95/43.04    (6)  all_57_2 = e3
% 231.95/43.04    (7)   ~ (e1 = e0)
% 231.95/43.04    (8)   ~ (e2 = e1)
% 231.95/43.04  
% 231.95/43.04  Begin of proof
% 231.95/43.04  | 
% 231.95/43.04  | BETA: splitting (1) gives:
% 231.95/43.04  | 
% 231.95/43.04  | Case 1:
% 231.95/43.04  | | 
% 231.95/43.04  | |   (9)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1)
% 231.95/43.04  | | 
% 231.95/43.04  | | BETA: splitting (9) gives:
% 231.95/43.04  | | 
% 231.95/43.04  | | Case 1:
% 231.95/43.04  | | | 
% 231.95/43.04  | | |   (10)  all_57_2 = e1 & op(e2, e3) = e1
% 231.95/43.04  | | | 
% 231.95/43.04  | | | REF_CLOSE: (2), (6), (10) are inconsistent by sub-proof #1928.
% 231.95/43.04  | | | 
% 231.95/43.04  | | Case 2:
% 231.95/43.04  | | | 
% 231.95/43.04  | | |   (11)  all_57_3 = e1 & op(e2, e2) = e1
% 231.95/43.04  | | | 
% 231.95/43.04  | | | REF_CLOSE: (3), (7), (11) are inconsistent by sub-proof #2362.
% 231.95/43.04  | | | 
% 231.95/43.04  | | End of split
% 231.95/43.04  | | 
% 231.95/43.04  | Case 2:
% 231.95/43.04  | | 
% 231.95/43.04  | |   (12)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) =
% 231.95/43.04  | |           e1)
% 231.95/43.04  | | 
% 231.95/43.04  | | BETA: splitting (12) gives:
% 231.95/43.04  | | 
% 231.95/43.04  | | Case 1:
% 231.95/43.04  | | | 
% 231.95/43.04  | | |   (13)  all_57_5 = e1 & op(e2, e1) = e1
% 231.95/43.04  | | | 
% 231.95/43.04  | | | REF_CLOSE: (2), (5), (13) are inconsistent by sub-proof #2376.
% 231.95/43.04  | | | 
% 231.95/43.04  | | Case 2:
% 231.95/43.04  | | | 
% 231.95/43.04  | | |   (14)  all_57_10 = e1 & op(e2, e0) = e1
% 231.95/43.04  | | | 
% 231.95/43.04  | | | REF_CLOSE: (4), (8), (14) are inconsistent by sub-proof #2360.
% 231.95/43.04  | | | 
% 231.95/43.04  | | End of split
% 231.95/43.04  | | 
% 231.95/43.04  | End of split
% 231.95/43.04  | 
% 231.95/43.04  End of proof
% 231.95/43.04  
% 231.95/43.04  Sub-proof #1805 shows that the following formulas are inconsistent:
% 231.95/43.04  ----------------------------------------------------------------
% 231.95/43.04    (1)  all_57_2 = e0 & op(e2, e3) = e0
% 231.95/43.04    (2)  all_57_2 = e3
% 231.95/43.04    (3)   ~ (e3 = e0)
% 231.95/43.04  
% 231.95/43.04  Begin of proof
% 231.95/43.04  | 
% 231.95/43.04  | ALPHA: (1) implies:
% 231.95/43.04  |   (4)  all_57_2 = e0
% 231.95/43.04  | 
% 231.95/43.04  | COMBINE_EQS: (2), (4) imply:
% 231.95/43.04  |   (5)  e3 = e0
% 231.95/43.04  | 
% 231.95/43.04  | REDUCE: (3), (5) imply:
% 231.95/43.04  |   (6)  $false
% 231.95/43.04  | 
% 231.95/43.04  | CLOSE: (6) is inconsistent.
% 231.95/43.04  | 
% 231.95/43.04  End of proof
% 231.95/43.04  
% 231.95/43.04  Sub-proof #1806 shows that the following formulas are inconsistent:
% 231.95/43.04  ----------------------------------------------------------------
% 231.95/43.04    (1)   ~ (e3 = e1)
% 231.95/43.04    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.95/43.04           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.95/43.04    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.95/43.04         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.95/43.04    (4)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.95/43.04         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.95/43.04    (5)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.95/43.04         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.95/43.04    (6)  all_57_4 = e3
% 231.95/43.04    (7)   ~ (e3 = e2)
% 231.95/43.04    (8)   ~ (e3 = e0)
% 231.95/43.04    (9)  op(e3, e3) = e3
% 231.95/43.04    (10)   ~ (e2 = e0)
% 231.95/43.04    (11)   ~ (e1 = e0)
% 231.95/43.04    (12)  all_57_1 = e3
% 231.95/43.04    (13)   ~ (e2 = e1)
% 231.95/43.04  
% 231.95/43.04  Begin of proof
% 231.95/43.04  | 
% 231.95/43.04  | BETA: splitting (3) gives:
% 231.95/43.04  | 
% 231.95/43.04  | Case 1:
% 231.95/43.04  | | 
% 231.95/43.04  | |   (14)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) =
% 231.95/43.04  | |           e1)
% 231.95/43.04  | | 
% 231.95/43.04  | | REF_CLOSE: (1), (4), (5), (6), (7), (8), (10), (11), (12), (13), (14) are
% 231.95/43.04  | |            inconsistent by sub-proof #1807.
% 231.95/43.04  | | 
% 231.95/43.04  | Case 2:
% 231.95/43.04  | | 
% 231.95/43.04  | |   (15)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) =
% 231.95/43.04  | |           e1)
% 231.95/43.04  | | 
% 231.95/43.04  | | BETA: splitting (15) gives:
% 231.95/43.04  | | 
% 231.95/43.04  | | Case 1:
% 231.95/43.04  | | | 
% 231.95/43.04  | | |   (16)  all_57_4 = e1 & op(e3, e1) = e1
% 231.95/43.04  | | | 
% 231.95/43.04  | | | REF_CLOSE: (1), (6), (16) are inconsistent by sub-proof #2484.
% 231.95/43.04  | | | 
% 231.95/43.04  | | Case 2:
% 231.95/43.04  | | | 
% 231.95/43.04  | | |   (17)  all_57_9 = e1 & op(e3, e0) = e1
% 231.95/43.04  | | | 
% 231.95/43.04  | | | ALPHA: (17) implies:
% 231.95/43.04  | | |   (18)  all_57_9 = e1
% 231.95/43.04  | | | 
% 231.95/43.04  | | | BETA: splitting (5) gives:
% 231.95/43.04  | | | 
% 231.95/43.04  | | | Case 1:
% 231.95/43.04  | | | | 
% 231.95/43.04  | | | |   (19)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2)
% 231.95/43.04  | | | |           = e0)
% 231.95/43.04  | | | | 
% 231.95/43.04  | | | | BETA: splitting (19) gives:
% 231.95/43.04  | | | | 
% 231.95/43.04  | | | | Case 1:
% 231.95/43.04  | | | | | 
% 231.95/43.04  | | | | |   (20)  all_57_0 = e0 & op(e3, e3) = e0
% 231.95/43.04  | | | | | 
% 231.95/43.04  | | | | | ALPHA: (20) implies:
% 231.95/43.04  | | | | |   (21)  op(e3, e3) = e0
% 231.95/43.04  | | | | | 
% 231.95/43.04  | | | | | REF_CLOSE: (2), (8), (9), (21) are inconsistent by sub-proof #2494.
% 231.95/43.04  | | | | | 
% 231.95/43.04  | | | | Case 2:
% 231.95/43.04  | | | | | 
% 231.95/43.04  | | | | |   (22)  all_57_1 = e0 & op(e3, e2) = e0
% 231.95/43.04  | | | | | 
% 231.95/43.04  | | | | | REF_CLOSE: (8), (12), (22) are inconsistent by sub-proof #1811.
% 231.95/43.04  | | | | | 
% 231.95/43.04  | | | | End of split
% 231.95/43.04  | | | | 
% 231.95/43.04  | | | Case 2:
% 231.95/43.04  | | | | 
% 231.95/43.04  | | | |   (23)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0)
% 231.95/43.04  | | | |           = e0)
% 231.95/43.04  | | | | 
% 231.95/43.04  | | | | BETA: splitting (23) gives:
% 231.95/43.04  | | | | 
% 231.95/43.04  | | | | Case 1:
% 231.95/43.04  | | | | | 
% 231.95/43.04  | | | | |   (24)  all_57_4 = e0 & op(e3, e1) = e0
% 231.95/43.04  | | | | | 
% 231.95/43.04  | | | | | REF_CLOSE: (6), (8), (24) are inconsistent by sub-proof #2491.
% 231.95/43.04  | | | | | 
% 231.95/43.04  | | | | Case 2:
% 231.95/43.04  | | | | | 
% 231.95/43.04  | | | | |   (25)  all_57_9 = e0 & op(e3, e0) = e0
% 231.95/43.04  | | | | | 
% 231.95/43.04  | | | | | ALPHA: (25) implies:
% 231.95/43.04  | | | | |   (26)  all_57_9 = e0
% 231.95/43.04  | | | | | 
% 231.95/43.04  | | | | | REF_CLOSE: (11), (18), (26) are inconsistent by sub-proof #2479.
% 231.95/43.04  | | | | | 
% 231.95/43.04  | | | | End of split
% 231.95/43.04  | | | | 
% 231.95/43.04  | | | End of split
% 231.95/43.04  | | | 
% 231.95/43.04  | | End of split
% 231.95/43.04  | | 
% 231.95/43.04  | End of split
% 231.95/43.04  | 
% 231.95/43.04  End of proof
% 231.95/43.04  
% 231.95/43.04  Sub-proof #1807 shows that the following formulas are inconsistent:
% 231.95/43.04  ----------------------------------------------------------------
% 231.95/43.04    (1)   ~ (e3 = e1)
% 231.95/43.04    (2)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.95/43.04         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.95/43.04    (3)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.95/43.04         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.95/43.04    (4)  all_57_4 = e3
% 231.95/43.04    (5)   ~ (e3 = e2)
% 231.95/43.04    (6)   ~ (e3 = e0)
% 231.95/43.04    (7)   ~ (e2 = e0)
% 231.95/43.04    (8)   ~ (e1 = e0)
% 231.95/43.04    (9)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1)
% 231.95/43.04    (10)  all_57_1 = e3
% 231.95/43.04    (11)   ~ (e2 = e1)
% 231.95/43.04  
% 231.95/43.04  Begin of proof
% 231.95/43.04  | 
% 231.95/43.04  | BETA: splitting (9) gives:
% 231.95/43.04  | 
% 231.95/43.04  | Case 1:
% 231.95/43.04  | | 
% 231.95/43.04  | |   (12)  all_57_0 = e1 & op(e3, e3) = e1
% 231.95/43.04  | | 
% 231.95/43.04  | | ALPHA: (12) implies:
% 231.95/43.04  | |   (13)  all_57_0 = e1
% 231.95/43.04  | | 
% 231.95/43.04  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (10), (11), (13) are
% 231.95/43.04  | |            inconsistent by sub-proof #1808.
% 231.95/43.04  | | 
% 231.95/43.04  | Case 2:
% 231.95/43.04  | | 
% 231.95/43.04  | |   (14)  all_57_1 = e1 & op(e3, e2) = e1
% 231.95/43.04  | | 
% 231.95/43.04  | | REF_CLOSE: (1), (10), (14) are inconsistent by sub-proof #2453.
% 231.95/43.04  | | 
% 231.95/43.04  | End of split
% 231.95/43.04  | 
% 231.95/43.04  End of proof
% 231.95/43.04  
% 231.95/43.04  Sub-proof #1808 shows that the following formulas are inconsistent:
% 231.95/43.04  ----------------------------------------------------------------
% 231.95/43.04    (1)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.95/43.04         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.95/43.04    (2)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.95/43.04         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.95/43.04    (3)  all_57_4 = e3
% 231.95/43.04    (4)   ~ (e3 = e2)
% 231.95/43.04    (5)   ~ (e3 = e0)
% 231.95/43.04    (6)  all_57_0 = e1
% 231.95/43.04    (7)   ~ (e2 = e0)
% 231.95/43.04    (8)   ~ (e1 = e0)
% 231.95/43.04    (9)  all_57_1 = e3
% 231.95/43.04    (10)   ~ (e2 = e1)
% 231.95/43.04  
% 231.95/43.04  Begin of proof
% 231.95/43.04  | 
% 231.95/43.04  | BETA: splitting (2) gives:
% 231.95/43.04  | 
% 231.95/43.04  | Case 1:
% 231.95/43.04  | | 
% 231.95/43.04  | |   (11)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) =
% 231.95/43.04  | |           e0)
% 231.95/43.04  | | 
% 231.95/43.04  | | BETA: splitting (11) gives:
% 231.95/43.04  | | 
% 231.95/43.04  | | Case 1:
% 231.95/43.04  | | | 
% 231.95/43.04  | | |   (12)  all_57_0 = e0 & op(e3, e3) = e0
% 231.95/43.04  | | | 
% 231.95/43.04  | | | REF_CLOSE: (6), (8), (12) are inconsistent by sub-proof #1812.
% 231.95/43.04  | | | 
% 231.95/43.04  | | Case 2:
% 231.95/43.04  | | | 
% 231.95/43.04  | | |   (13)  all_57_1 = e0 & op(e3, e2) = e0
% 231.95/43.04  | | | 
% 231.95/43.04  | | | REF_CLOSE: (5), (9), (13) are inconsistent by sub-proof #1811.
% 231.95/43.04  | | | 
% 231.95/43.04  | | End of split
% 231.95/43.04  | | 
% 231.95/43.04  | Case 2:
% 231.95/43.04  | | 
% 231.95/43.04  | |   (14)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) =
% 231.95/43.04  | |           e0)
% 231.95/43.04  | | 
% 231.95/43.04  | | BETA: splitting (14) gives:
% 231.95/43.04  | | 
% 231.95/43.04  | | Case 1:
% 231.95/43.04  | | | 
% 231.95/43.04  | | |   (15)  all_57_4 = e0 & op(e3, e1) = e0
% 231.95/43.04  | | | 
% 231.95/43.04  | | | REF_CLOSE: (3), (5), (15) are inconsistent by sub-proof #2491.
% 231.95/43.04  | | | 
% 231.95/43.04  | | Case 2:
% 231.95/43.04  | | | 
% 231.95/43.04  | | |   (16)  all_57_9 = e0 & op(e3, e0) = e0
% 231.95/43.04  | | | 
% 231.95/43.04  | | | ALPHA: (16) implies:
% 231.95/43.04  | | |   (17)  all_57_9 = e0
% 231.95/43.04  | | | 
% 231.95/43.04  | | | BETA: splitting (1) gives:
% 231.95/43.04  | | | 
% 231.95/43.04  | | | Case 1:
% 231.95/43.04  | | | | 
% 231.95/43.04  | | | |   (18)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2)
% 231.95/43.04  | | | |           = e2)
% 231.95/43.04  | | | | 
% 231.95/43.04  | | | | BETA: splitting (18) gives:
% 231.95/43.04  | | | | 
% 231.95/43.04  | | | | Case 1:
% 231.95/43.04  | | | | | 
% 231.95/43.04  | | | | |   (19)  all_57_0 = e2 & op(e3, e3) = e2
% 231.95/43.04  | | | | | 
% 231.95/43.04  | | | | | REF_CLOSE: (6), (10), (19) are inconsistent by sub-proof #1810.
% 231.95/43.04  | | | | | 
% 231.95/43.04  | | | | Case 2:
% 231.95/43.04  | | | | | 
% 231.95/43.04  | | | | |   (20)  all_57_1 = e2 & op(e3, e2) = e2
% 231.95/43.04  | | | | | 
% 231.95/43.04  | | | | | REF_CLOSE: (4), (9), (20) are inconsistent by sub-proof #1809.
% 231.95/43.04  | | | | | 
% 231.95/43.04  | | | | End of split
% 231.95/43.04  | | | | 
% 231.95/43.04  | | | Case 2:
% 231.95/43.04  | | | | 
% 231.95/43.04  | | | |   (21)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0)
% 231.95/43.04  | | | |           = e2)
% 231.95/43.04  | | | | 
% 231.95/43.04  | | | | BETA: splitting (21) gives:
% 231.95/43.04  | | | | 
% 231.95/43.04  | | | | Case 1:
% 231.95/43.04  | | | | | 
% 231.95/43.04  | | | | |   (22)  all_57_4 = e2 & op(e3, e1) = e2
% 231.95/43.04  | | | | | 
% 231.95/43.04  | | | | | REF_CLOSE: (3), (4), (22) are inconsistent by sub-proof #2487.
% 231.95/43.04  | | | | | 
% 231.95/43.04  | | | | Case 2:
% 231.95/43.04  | | | | | 
% 231.95/43.04  | | | | |   (23)  all_57_9 = e2 & op(e3, e0) = e2
% 231.95/43.04  | | | | | 
% 231.95/43.04  | | | | | REF_CLOSE: (7), (17), (23) are inconsistent by sub-proof #2486.
% 231.95/43.04  | | | | | 
% 231.95/43.04  | | | | End of split
% 231.95/43.04  | | | | 
% 231.95/43.04  | | | End of split
% 231.95/43.04  | | | 
% 231.95/43.04  | | End of split
% 231.95/43.04  | | 
% 231.95/43.04  | End of split
% 231.95/43.04  | 
% 231.95/43.04  End of proof
% 231.95/43.04  
% 231.95/43.04  Sub-proof #1809 shows that the following formulas are inconsistent:
% 231.95/43.04  ----------------------------------------------------------------
% 231.95/43.04    (1)  all_57_1 = e2 & op(e3, e2) = e2
% 231.95/43.04    (2)  all_57_1 = e3
% 231.95/43.04    (3)   ~ (e3 = e2)
% 231.95/43.04  
% 231.95/43.04  Begin of proof
% 231.95/43.04  | 
% 231.95/43.04  | ALPHA: (1) implies:
% 231.95/43.04  |   (4)  all_57_1 = e2
% 231.95/43.04  | 
% 231.95/43.04  | COMBINE_EQS: (2), (4) imply:
% 231.95/43.04  |   (5)  e3 = e2
% 231.95/43.04  | 
% 231.95/43.04  | REDUCE: (3), (5) imply:
% 231.95/43.04  |   (6)  $false
% 231.95/43.04  | 
% 231.95/43.04  | CLOSE: (6) is inconsistent.
% 231.95/43.04  | 
% 231.95/43.04  End of proof
% 231.95/43.04  
% 231.95/43.04  Sub-proof #1810 shows that the following formulas are inconsistent:
% 231.95/43.04  ----------------------------------------------------------------
% 231.95/43.04    (1)  all_57_0 = e2 & op(e3, e3) = e2
% 231.95/43.04    (2)  all_57_0 = e1
% 231.95/43.04    (3)   ~ (e2 = e1)
% 231.95/43.04  
% 231.95/43.04  Begin of proof
% 231.95/43.04  | 
% 231.95/43.04  | ALPHA: (1) implies:
% 231.95/43.04  |   (4)  all_57_0 = e2
% 231.95/43.04  | 
% 231.95/43.04  | COMBINE_EQS: (2), (4) imply:
% 231.95/43.04  |   (5)  e2 = e1
% 231.95/43.04  | 
% 231.95/43.04  | SIMP: (5) implies:
% 231.95/43.04  |   (6)  e2 = e1
% 231.95/43.04  | 
% 231.95/43.04  | REDUCE: (3), (6) imply:
% 231.95/43.04  |   (7)  $false
% 231.95/43.04  | 
% 231.95/43.04  | CLOSE: (7) is inconsistent.
% 231.95/43.04  | 
% 231.95/43.04  End of proof
% 231.95/43.04  
% 231.95/43.04  Sub-proof #1811 shows that the following formulas are inconsistent:
% 231.95/43.04  ----------------------------------------------------------------
% 231.95/43.04    (1)  all_57_1 = e0 & op(e3, e2) = e0
% 231.95/43.04    (2)  all_57_1 = e3
% 231.95/43.04    (3)   ~ (e3 = e0)
% 231.95/43.04  
% 231.95/43.04  Begin of proof
% 231.95/43.04  | 
% 231.95/43.04  | ALPHA: (1) implies:
% 231.95/43.04  |   (4)  all_57_1 = e0
% 231.95/43.04  | 
% 231.95/43.04  | COMBINE_EQS: (2), (4) imply:
% 231.95/43.04  |   (5)  e3 = e0
% 231.95/43.04  | 
% 231.95/43.04  | REDUCE: (3), (5) imply:
% 231.95/43.04  |   (6)  $false
% 231.95/43.04  | 
% 231.95/43.04  | CLOSE: (6) is inconsistent.
% 231.95/43.04  | 
% 231.95/43.04  End of proof
% 231.95/43.04  
% 231.95/43.04  Sub-proof #1812 shows that the following formulas are inconsistent:
% 231.95/43.04  ----------------------------------------------------------------
% 231.95/43.04    (1)  all_57_0 = e0 & op(e3, e3) = e0
% 231.95/43.04    (2)  all_57_0 = e1
% 231.95/43.04    (3)   ~ (e1 = e0)
% 231.95/43.04  
% 231.95/43.04  Begin of proof
% 231.95/43.04  | 
% 231.95/43.04  | ALPHA: (1) implies:
% 231.95/43.04  |   (4)  all_57_0 = e0
% 231.95/43.04  | 
% 231.95/43.04  | COMBINE_EQS: (2), (4) imply:
% 231.95/43.04  |   (5)  e1 = e0
% 231.95/43.04  | 
% 231.95/43.04  | REDUCE: (3), (5) imply:
% 231.95/43.04  |   (6)  $false
% 231.95/43.04  | 
% 231.95/43.04  | CLOSE: (6) is inconsistent.
% 231.95/43.04  | 
% 231.95/43.04  End of proof
% 231.95/43.04  
% 231.95/43.04  Sub-proof #1813 shows that the following formulas are inconsistent:
% 231.95/43.04  ----------------------------------------------------------------
% 231.95/43.04    (1)   ~ (all_53_6 = e2)
% 231.95/43.04    (2)   ~ (e3 = e1)
% 231.95/43.04    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.95/43.04           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.95/43.04    (4)   ~ (all_6_2 = e3)
% 231.95/43.04    (5)   ~ (all_53_9 = e1)
% 231.95/43.04    (6)  op(e1, e1) = all_6_2
% 231.95/43.04    (7)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 231.95/43.04    (8)  all_55_9 = all_53_6
% 231.95/43.04    (9)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.95/43.04         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.95/43.04    (10)   ~ (e3 = e0)
% 231.95/43.04    (11)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.95/43.04          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.95/43.04    (12)  op(e3, e3) = e3
% 231.95/43.04    (13)  op(e3, e2) = all_53_4
% 231.95/43.04    (14)   ~ (all_53_6 = e1)
% 231.95/43.04    (15)   ~ (e1 = e0)
% 231.95/43.04    (16)   ~ (all_53_4 = all_53_6)
% 231.95/43.04    (17)  op(e1, e1) = e2
% 231.95/43.04    (18)   ~ (all_53_12 = e0)
% 231.95/43.04    (19)   ~ (all_53_6 = e3)
% 231.95/43.04    (20)   ~ (e2 = e1)
% 231.95/43.04    (21)  op(e2, e1) = all_53_9
% 231.95/43.04    (22)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.95/43.04    (23)  op(e3, e0) = all_53_12
% 231.95/43.04  
% 231.95/43.04  Begin of proof
% 231.95/43.04  | 
% 231.95/43.04  | BETA: splitting (22) gives:
% 231.95/43.04  | 
% 231.95/43.04  | Case 1:
% 231.95/43.04  | | 
% 231.95/43.04  | |   (24)  all_57_8 = e3 & op(e1, e1) = e3
% 231.95/43.04  | | 
% 231.95/43.04  | | ALPHA: (24) implies:
% 231.95/43.04  | |   (25)  op(e1, e1) = e3
% 231.95/43.04  | | 
% 231.95/43.04  | | REF_CLOSE: (3), (4), (6), (25) are inconsistent by sub-proof #2468.
% 231.95/43.04  | | 
% 231.95/43.04  | Case 2:
% 231.95/43.04  | | 
% 231.95/43.04  | |   (26)  all_57_14 = e3 & op(e0, e1) = e3
% 231.95/43.04  | | 
% 231.95/43.04  | | REF_CLOSE: (1), (2), (3), (5), (7), (8), (9), (10), (11), (12), (13), (14),
% 231.95/43.04  | |            (15), (16), (17), (18), (19), (20), (21), (23), (26) are
% 231.95/43.04  | |            inconsistent by sub-proof #1814.
% 231.95/43.04  | | 
% 231.95/43.04  | End of split
% 231.95/43.04  | 
% 231.95/43.04  End of proof
% 231.95/43.04  
% 231.95/43.04  Sub-proof #1814 shows that the following formulas are inconsistent:
% 231.95/43.04  ----------------------------------------------------------------
% 231.95/43.04    (1)   ~ (all_53_6 = e2)
% 231.95/43.04    (2)   ~ (e3 = e1)
% 231.95/43.04    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.95/43.04           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.95/43.04    (4)   ~ (all_53_9 = e1)
% 231.95/43.04    (5)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 231.95/43.04    (6)  all_55_9 = all_53_6
% 231.95/43.04    (7)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.95/43.04         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.95/43.04    (8)   ~ (e3 = e0)
% 231.95/43.04    (9)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.95/43.04         (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.95/43.04    (10)  op(e3, e3) = e3
% 231.95/43.04    (11)  op(e3, e2) = all_53_4
% 231.95/43.04    (12)   ~ (all_53_6 = e1)
% 231.95/43.04    (13)   ~ (e1 = e0)
% 231.95/43.04    (14)   ~ (all_53_4 = all_53_6)
% 231.95/43.04    (15)  op(e1, e1) = e2
% 231.95/43.04    (16)   ~ (all_53_12 = e0)
% 231.95/43.04    (17)   ~ (all_53_6 = e3)
% 231.95/43.04    (18)   ~ (e2 = e1)
% 231.95/43.04    (19)  all_57_14 = e3 & op(e0, e1) = e3
% 231.95/43.04    (20)  op(e2, e1) = all_53_9
% 231.95/43.04    (21)  op(e3, e0) = all_53_12
% 231.95/43.04  
% 231.95/43.04  Begin of proof
% 231.95/43.04  | 
% 231.95/43.04  | ALPHA: (19) implies:
% 231.95/43.04  |   (22)  all_57_14 = e3
% 231.95/43.04  | 
% 231.95/43.04  | BETA: splitting (9) gives:
% 231.95/43.04  | 
% 231.95/43.04  | Case 1:
% 231.95/43.04  | | 
% 231.95/43.04  | |   (23)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) =
% 231.95/43.04  | |           e1)
% 231.95/43.04  | | 
% 231.95/43.04  | | BETA: splitting (23) gives:
% 231.95/43.04  | | 
% 231.95/43.04  | | Case 1:
% 231.95/43.04  | | | 
% 231.95/43.04  | | |   (24)  all_57_4 = e1 & op(e3, e1) = e1
% 231.95/43.04  | | | 
% 231.95/43.04  | | | ALPHA: (24) implies:
% 231.95/43.04  | | |   (25)  all_57_4 = e1
% 231.95/43.04  | | | 
% 231.95/43.04  | | | REF_CLOSE: (1), (3), (5), (6), (7), (8), (10), (11), (12), (13), (14),
% 231.95/43.04  | | |            (16), (17), (21), (25) are inconsistent by sub-proof #1830.
% 231.95/43.04  | | | 
% 231.95/43.04  | | Case 2:
% 231.95/43.04  | | | 
% 231.95/43.04  | | |   (26)  all_57_5 = e1 & op(e2, e1) = e1
% 231.95/43.04  | | | 
% 231.95/43.04  | | | REF_CLOSE: (3), (4), (20), (26) are inconsistent by sub-proof #2305.
% 231.95/43.04  | | | 
% 231.95/43.04  | | End of split
% 231.95/43.04  | | 
% 231.95/43.04  | Case 2:
% 231.95/43.04  | | 
% 231.95/43.04  | |   (27)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) =
% 231.95/43.04  | |           e1)
% 231.95/43.04  | | 
% 231.95/43.04  | | REF_CLOSE: (2), (3), (15), (18), (22), (27) are inconsistent by sub-proof
% 231.95/43.04  | |            #1815.
% 231.95/43.04  | | 
% 231.95/43.04  | End of split
% 231.95/43.04  | 
% 231.95/43.04  End of proof
% 231.95/43.04  
% 231.95/43.04  Sub-proof #1815 shows that the following formulas are inconsistent:
% 231.95/43.04  ----------------------------------------------------------------
% 231.95/43.04    (1)   ~ (e3 = e1)
% 231.95/43.04    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.95/43.04           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.95/43.04    (3)  all_57_14 = e3
% 231.95/43.04    (4)  op(e1, e1) = e2
% 231.95/43.04    (5)   ~ (e2 = e1)
% 231.95/43.04    (6)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.95/43.04  
% 231.95/43.04  Begin of proof
% 231.95/43.04  | 
% 231.95/43.04  | BETA: splitting (6) gives:
% 231.95/43.04  | 
% 231.95/43.04  | Case 1:
% 231.95/43.04  | | 
% 231.95/43.04  | |   (7)  all_57_8 = e1 & op(e1, e1) = e1
% 231.95/43.04  | | 
% 231.95/43.04  | | ALPHA: (7) implies:
% 231.95/43.04  | |   (8)  op(e1, e1) = e1
% 231.95/43.04  | | 
% 231.95/43.04  | | REF_CLOSE: (2), (4), (5), (8) are inconsistent by sub-proof #2423.
% 231.95/43.04  | | 
% 231.95/43.04  | Case 2:
% 231.95/43.04  | | 
% 231.95/43.04  | |   (9)  all_57_14 = e1 & op(e0, e1) = e1
% 231.95/43.04  | | 
% 231.95/43.04  | | ALPHA: (9) implies:
% 231.95/43.04  | |   (10)  all_57_14 = e1
% 231.95/43.04  | | 
% 231.95/43.04  | | REF_CLOSE: (1), (3), (10) are inconsistent by sub-proof #2326.
% 231.95/43.04  | | 
% 231.95/43.04  | End of split
% 231.95/43.04  | 
% 231.95/43.04  End of proof
% 231.95/43.04  
% 231.95/43.04  Sub-proof #1816 shows that the following formulas are inconsistent:
% 231.95/43.04  ----------------------------------------------------------------
% 231.95/43.04    (1)   ~ (e3 = e1)
% 231.95/43.04    (2)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 231.95/43.04         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.95/43.04    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.95/43.04           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.95/43.04    (4)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.95/43.04         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.95/43.04    (5)   ~ (all_6_2 = e3)
% 231.95/43.04    (6)  op(e1, e1) = all_6_2
% 231.95/43.04    (7)   ~ (e3 = e2)
% 231.95/43.04    (8)  op(e1, e0) = all_53_14
% 231.95/43.04    (9)   ~ (e3 = e0)
% 231.95/43.04    (10)   ~ (e2 = e0)
% 231.95/43.04    (11)   ~ (all_53_6 = e1)
% 231.95/43.04    (12)   ~ (e1 = e0)
% 231.95/43.04    (13)  all_57_13 = e3
% 231.95/43.04    (14)   ~ (all_53_14 = e0)
% 231.95/43.04    (15)  op(e1, e1) = e2
% 231.95/43.04    (16)  all_57_7 = e3
% 231.95/43.04    (17)   ~ (e2 = e1)
% 231.95/43.04    (18)  op(e1, e2) = all_53_6
% 231.95/43.04    (19)   ~ (all_6_2 = e0)
% 231.95/43.04    (20)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 231.95/43.04          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 231.95/43.04    (21)  all_57_13 = e2 & op(e0, e2) = e2
% 231.95/43.04  
% 231.95/43.04  Begin of proof
% 231.95/43.04  | 
% 231.95/43.04  | ALPHA: (21) implies:
% 231.95/43.04  |   (22)  all_57_13 = e2
% 231.95/43.04  | 
% 231.95/43.04  | COMBINE_EQS: (13), (22) imply:
% 231.95/43.04  |   (23)  e3 = e2
% 231.95/43.04  | 
% 231.95/43.04  | COMBINE_EQS: (16), (23) imply:
% 231.95/43.04  |   (24)  all_57_7 = e2
% 231.95/43.04  | 
% 231.95/43.04  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 231.95/43.04  |            (14), (15), (17), (18), (19), (20), (24) are inconsistent by
% 231.95/43.04  |            sub-proof #1817.
% 231.95/43.04  | 
% 231.95/43.04  End of proof
% 231.95/43.04  
% 231.95/43.04  Sub-proof #1817 shows that the following formulas are inconsistent:
% 231.95/43.04  ----------------------------------------------------------------
% 231.95/43.04    (1)   ~ (e3 = e1)
% 231.95/43.04    (2)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 231.95/43.04         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.95/43.04    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.95/43.04           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.95/43.04    (4)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.95/43.04         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.95/43.04    (5)   ~ (all_6_2 = e3)
% 231.95/43.04    (6)  op(e1, e1) = all_6_2
% 231.95/43.04    (7)  all_57_7 = e2
% 231.95/43.04    (8)   ~ (e3 = e2)
% 231.95/43.04    (9)  op(e1, e0) = all_53_14
% 231.95/43.04    (10)   ~ (e3 = e0)
% 231.95/43.04    (11)   ~ (e2 = e0)
% 231.95/43.04    (12)   ~ (all_53_6 = e1)
% 231.95/43.04    (13)   ~ (e1 = e0)
% 231.95/43.04    (14)   ~ (all_53_14 = e0)
% 231.95/43.04    (15)  op(e1, e1) = e2
% 231.95/43.04    (16)   ~ (e2 = e1)
% 231.95/43.04    (17)  op(e1, e2) = all_53_6
% 231.95/43.04    (18)   ~ (all_6_2 = e0)
% 231.95/43.04    (19)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 231.95/43.04          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 231.95/43.04  
% 231.95/43.04  Begin of proof
% 231.95/43.04  | 
% 231.95/43.04  | BETA: splitting (2) gives:
% 231.95/43.04  | 
% 231.95/43.04  | Case 1:
% 231.95/43.04  | | 
% 231.95/43.04  | |   (20)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) =
% 231.95/43.04  | |           e0)
% 231.95/43.04  | | 
% 231.95/43.04  | | BETA: splitting (20) gives:
% 231.95/43.04  | | 
% 231.95/43.04  | | Case 1:
% 231.95/43.04  | | | 
% 231.95/43.04  | | |   (21)  all_57_6 = e0 & op(e1, e3) = e0
% 231.95/43.04  | | | 
% 231.95/43.04  | | | ALPHA: (21) implies:
% 231.95/43.04  | | |   (22)  all_57_6 = e0
% 231.95/43.04  | | | 
% 231.95/43.04  | | | BETA: splitting (19) gives:
% 231.95/43.04  | | | 
% 231.95/43.04  | | | Case 1:
% 231.95/43.04  | | | | 
% 231.95/43.04  | | | |   (23)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2)
% 231.95/43.04  | | | |           = e1)
% 231.95/43.04  | | | | 
% 231.95/43.04  | | | | BETA: splitting (23) gives:
% 231.95/43.04  | | | | 
% 231.95/43.04  | | | | Case 1:
% 231.95/43.04  | | | | | 
% 231.95/43.04  | | | | |   (24)  all_57_6 = e1 & op(e1, e3) = e1
% 231.95/43.04  | | | | | 
% 231.95/43.04  | | | | | ALPHA: (24) implies:
% 231.95/43.04  | | | | |   (25)  all_57_6 = e1
% 231.95/43.04  | | | | | 
% 231.95/43.04  | | | | | REF_CLOSE: (13), (22), (25) are inconsistent by sub-proof #2227.
% 231.95/43.04  | | | | | 
% 231.95/43.04  | | | | Case 2:
% 231.95/43.04  | | | | | 
% 231.95/43.04  | | | | |   (26)  all_57_7 = e1 & op(e1, e2) = e1
% 231.95/43.04  | | | | | 
% 231.95/43.04  | | | | | REF_CLOSE: (3), (12), (17), (26) are inconsistent by sub-proof #2265.
% 231.95/43.04  | | | | | 
% 231.95/43.04  | | | | End of split
% 231.95/43.04  | | | | 
% 231.95/43.04  | | | Case 2:
% 231.95/43.04  | | | | 
% 231.95/43.04  | | | |   (27)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0)
% 231.95/43.04  | | | |           = e1)
% 231.95/43.04  | | | | 
% 231.95/43.04  | | | | BETA: splitting (27) gives:
% 231.95/43.04  | | | | 
% 231.95/43.04  | | | | Case 1:
% 231.95/43.04  | | | | | 
% 231.95/43.04  | | | | |   (28)  all_57_8 = e1 & op(e1, e1) = e1
% 231.95/43.04  | | | | | 
% 231.95/43.04  | | | | | ALPHA: (28) implies:
% 231.95/43.04  | | | | |   (29)  op(e1, e1) = e1
% 231.95/43.04  | | | | | 
% 231.95/43.04  | | | | | REF_CLOSE: (3), (15), (16), (29) are inconsistent by sub-proof #2423.
% 231.95/43.04  | | | | | 
% 231.95/43.04  | | | | Case 2:
% 231.95/43.04  | | | | | 
% 231.95/43.04  | | | | |   (30)  all_57_11 = e1 & op(e1, e0) = e1
% 231.95/43.04  | | | | | 
% 231.95/43.04  | | | | | ALPHA: (30) implies:
% 231.95/43.04  | | | | |   (31)  all_57_11 = e1
% 231.95/43.04  | | | | | 
% 231.95/43.04  | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (10), (22), (31) are
% 231.95/43.04  | | | | |            inconsistent by sub-proof #1818.
% 231.95/43.04  | | | | | 
% 231.95/43.04  | | | | End of split
% 231.95/43.04  | | | | 
% 231.95/43.04  | | | End of split
% 231.95/43.04  | | | 
% 231.95/43.04  | | Case 2:
% 231.95/43.04  | | | 
% 231.95/43.04  | | |   (32)  all_57_7 = e0 & op(e1, e2) = e0
% 231.95/43.04  | | | 
% 231.95/43.04  | | | ALPHA: (32) implies:
% 231.95/43.04  | | |   (33)  all_57_7 = e0
% 231.95/43.04  | | | 
% 231.95/43.04  | | | REF_CLOSE: (7), (11), (33) are inconsistent by sub-proof #2207.
% 231.95/43.04  | | | 
% 231.95/43.04  | | End of split
% 231.95/43.04  | | 
% 231.95/43.04  | Case 2:
% 231.95/43.04  | | 
% 231.95/43.04  | |   (34)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 231.95/43.04  | |           e0)
% 231.95/43.04  | | 
% 231.95/43.04  | | BETA: splitting (34) gives:
% 231.95/43.04  | | 
% 231.95/43.04  | | Case 1:
% 231.95/43.04  | | | 
% 231.95/43.04  | | |   (35)  all_57_8 = e0 & op(e1, e1) = e0
% 231.95/43.04  | | | 
% 231.95/43.04  | | | REF_CLOSE: (3), (6), (18), (35) are inconsistent by sub-proof #2412.
% 231.95/43.04  | | | 
% 231.95/43.04  | | Case 2:
% 231.95/43.05  | | | 
% 231.95/43.05  | | |   (36)  all_57_11 = e0 & op(e1, e0) = e0
% 231.95/43.05  | | | 
% 231.95/43.05  | | | REF_CLOSE: (3), (9), (14), (36) are inconsistent by sub-proof #2341.
% 231.95/43.05  | | | 
% 231.95/43.05  | | End of split
% 231.95/43.05  | | 
% 231.95/43.05  | End of split
% 231.95/43.05  | 
% 231.95/43.05  End of proof
% 231.95/43.05  
% 231.95/43.05  Sub-proof #1818 shows that the following formulas are inconsistent:
% 231.95/43.05  ----------------------------------------------------------------
% 231.95/43.05    (1)   ~ (e3 = e1)
% 231.95/43.05    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.95/43.05           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.95/43.05    (3)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.95/43.05         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.95/43.05    (4)   ~ (all_6_2 = e3)
% 231.95/43.05    (5)  op(e1, e1) = all_6_2
% 231.95/43.05    (6)  all_57_7 = e2
% 231.95/43.05    (7)   ~ (e3 = e2)
% 231.95/43.05    (8)   ~ (e3 = e0)
% 231.95/43.05    (9)  all_57_6 = e0
% 231.95/43.05    (10)  all_57_11 = e1
% 231.95/43.05  
% 231.95/43.05  Begin of proof
% 231.95/43.05  | 
% 231.95/43.05  | BETA: splitting (3) gives:
% 231.95/43.05  | 
% 231.95/43.05  | Case 1:
% 231.95/43.05  | | 
% 231.95/43.05  | |   (11)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 231.95/43.05  | |           e3)
% 231.95/43.05  | | 
% 231.95/43.05  | | REF_CLOSE: (6), (7), (8), (9), (11) are inconsistent by sub-proof #1821.
% 231.95/43.05  | | 
% 231.95/43.05  | Case 2:
% 231.95/43.05  | | 
% 231.95/43.05  | |   (12)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 231.95/43.05  | |           e3)
% 231.95/43.05  | | 
% 231.95/43.05  | | REF_CLOSE: (1), (2), (4), (5), (10), (12) are inconsistent by sub-proof
% 231.95/43.05  | |            #1819.
% 231.95/43.05  | | 
% 231.95/43.05  | End of split
% 231.95/43.05  | 
% 231.95/43.05  End of proof
% 231.95/43.05  
% 231.95/43.05  Sub-proof #1819 shows that the following formulas are inconsistent:
% 231.95/43.05  ----------------------------------------------------------------
% 231.95/43.05    (1)   ~ (e3 = e1)
% 231.95/43.05    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.95/43.05           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.95/43.05    (3)   ~ (all_6_2 = e3)
% 231.95/43.05    (4)  op(e1, e1) = all_6_2
% 231.95/43.05    (5)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.95/43.05    (6)  all_57_11 = e1
% 231.95/43.05  
% 231.95/43.05  Begin of proof
% 231.95/43.05  | 
% 231.95/43.05  | BETA: splitting (5) gives:
% 231.95/43.05  | 
% 231.95/43.05  | Case 1:
% 231.95/43.05  | | 
% 231.95/43.05  | |   (7)  all_57_8 = e3 & op(e1, e1) = e3
% 231.95/43.05  | | 
% 231.95/43.05  | | ALPHA: (7) implies:
% 231.95/43.05  | |   (8)  op(e1, e1) = e3
% 231.95/43.05  | | 
% 231.95/43.05  | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #2468.
% 231.95/43.05  | | 
% 231.95/43.05  | Case 2:
% 231.95/43.05  | | 
% 231.95/43.05  | |   (9)  all_57_11 = e3 & op(e1, e0) = e3
% 231.95/43.05  | | 
% 231.95/43.05  | | REF_CLOSE: (1), (6), (9) are inconsistent by sub-proof #1820.
% 231.95/43.05  | | 
% 231.95/43.05  | End of split
% 231.95/43.05  | 
% 231.95/43.05  End of proof
% 231.95/43.05  
% 231.95/43.05  Sub-proof #1820 shows that the following formulas are inconsistent:
% 231.95/43.05  ----------------------------------------------------------------
% 231.95/43.05    (1)  all_57_11 = e3 & op(e1, e0) = e3
% 231.95/43.05    (2)  all_57_11 = e1
% 231.95/43.05    (3)   ~ (e3 = e1)
% 231.95/43.05  
% 231.95/43.05  Begin of proof
% 231.95/43.05  | 
% 231.95/43.05  | ALPHA: (1) implies:
% 231.95/43.05  |   (4)  all_57_11 = e3
% 231.95/43.05  | 
% 231.95/43.05  | COMBINE_EQS: (2), (4) imply:
% 231.95/43.05  |   (5)  e3 = e1
% 231.95/43.05  | 
% 231.95/43.05  | REDUCE: (3), (5) imply:
% 231.95/43.05  |   (6)  $false
% 231.95/43.05  | 
% 231.95/43.05  | CLOSE: (6) is inconsistent.
% 231.95/43.05  | 
% 231.95/43.05  End of proof
% 231.95/43.05  
% 231.95/43.05  Sub-proof #1821 shows that the following formulas are inconsistent:
% 231.95/43.05  ----------------------------------------------------------------
% 231.95/43.05    (1)  all_57_7 = e2
% 231.95/43.05    (2)   ~ (e3 = e2)
% 231.95/43.05    (3)   ~ (e3 = e0)
% 231.95/43.05    (4)  all_57_6 = e0
% 231.95/43.05    (5)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3)
% 231.95/43.05  
% 231.95/43.05  Begin of proof
% 231.95/43.05  | 
% 231.95/43.05  | BETA: splitting (5) gives:
% 231.95/43.05  | 
% 231.95/43.05  | Case 1:
% 231.95/43.05  | | 
% 231.95/43.05  | |   (6)  all_57_6 = e3 & op(e1, e3) = e3
% 231.95/43.05  | | 
% 231.95/43.05  | | ALPHA: (6) implies:
% 231.95/43.05  | |   (7)  all_57_6 = e3
% 231.95/43.05  | | 
% 231.95/43.05  | | REF_CLOSE: (3), (4), (7) are inconsistent by sub-proof #1822.
% 231.95/43.05  | | 
% 231.95/43.05  | Case 2:
% 231.95/43.05  | | 
% 231.95/43.05  | |   (8)  all_57_7 = e3 & op(e1, e2) = e3
% 231.95/43.05  | | 
% 231.95/43.05  | | ALPHA: (8) implies:
% 231.95/43.05  | |   (9)  all_57_7 = e3
% 231.95/43.05  | | 
% 231.95/43.05  | | REF_CLOSE: (1), (2), (9) are inconsistent by sub-proof #2102.
% 231.95/43.05  | | 
% 231.95/43.05  | End of split
% 231.95/43.05  | 
% 231.95/43.05  End of proof
% 231.95/43.05  
% 231.95/43.05  Sub-proof #1822 shows that the following formulas are inconsistent:
% 231.95/43.05  ----------------------------------------------------------------
% 231.95/43.05    (1)  all_57_6 = e3
% 231.95/43.05    (2)  all_57_6 = e0
% 231.95/43.05    (3)   ~ (e3 = e0)
% 231.95/43.05  
% 231.95/43.05  Begin of proof
% 231.95/43.05  | 
% 231.95/43.05  | COMBINE_EQS: (1), (2) imply:
% 231.95/43.05  |   (4)  e3 = e0
% 231.95/43.05  | 
% 231.95/43.05  | SIMP: (4) implies:
% 231.95/43.05  |   (5)  e3 = e0
% 231.95/43.05  | 
% 231.95/43.05  | REDUCE: (3), (5) imply:
% 231.95/43.05  |   (6)  $false
% 231.95/43.05  | 
% 231.95/43.05  | CLOSE: (6) is inconsistent.
% 231.95/43.05  | 
% 231.95/43.05  End of proof
% 231.95/43.05  
% 231.95/43.05  Sub-proof #1823 shows that the following formulas are inconsistent:
% 231.95/43.05  ----------------------------------------------------------------
% 231.95/43.05    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.95/43.05         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.95/43.05    (2)   ~ (e3 = e1)
% 231.95/43.05    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.95/43.05           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.95/43.05    (4)  op(e2, e2) = e1
% 231.95/43.05    (5)  all_57_12 = e2
% 231.95/43.05    (6)   ~ (e3 = e2)
% 231.95/43.05    (7)   ~ (e3 = e0)
% 231.95/43.05    (8)  all_57_1 = e2
% 231.95/43.05    (9)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 231.95/43.05         (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 231.95/43.05    (10)   ~ (e2 = e0)
% 231.95/43.05    (11)   ~ (e1 = e0)
% 231.95/43.05    (12)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.95/43.05          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.95/43.05    (13)   ~ (e2 = e1)
% 231.95/43.05    (14)  all_57_12 = e1 & op(e0, e3) = e1
% 231.95/43.05  
% 231.95/43.05  Begin of proof
% 231.95/43.05  | 
% 231.95/43.05  | ALPHA: (14) implies:
% 231.95/43.05  |   (15)  all_57_12 = e1
% 231.95/43.05  | 
% 231.95/43.05  | COMBINE_EQS: (5), (15) imply:
% 231.95/43.05  |   (16)  e2 = e1
% 231.95/43.05  | 
% 231.95/43.05  | COMBINE_EQS: (8), (16) imply:
% 231.95/43.05  |   (17)  all_57_1 = e1
% 231.95/43.05  | 
% 231.95/43.05  | REF_CLOSE: (1), (2), (3), (4), (6), (7), (9), (10), (11), (12), (13), (17) are
% 231.95/43.05  |            inconsistent by sub-proof #1908.
% 231.95/43.05  | 
% 231.95/43.05  End of proof
% 231.95/43.05  
% 231.95/43.05  Sub-proof #1824 shows that the following formulas are inconsistent:
% 231.95/43.05  ----------------------------------------------------------------
% 231.95/43.05    (1)  e1 = e0
% 231.95/43.05    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.95/43.05         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.95/43.05    (3)   ~ (e3 = e1)
% 231.95/43.05    (4)   ~ (e3 = e2)
% 231.95/43.05    (5)   ~ (e3 = e0)
% 231.95/43.05    (6)   ~ (e2 = e0)
% 231.95/43.05    (7)  all_57_3 = e1
% 231.95/43.05    (8)   ~ (e1 = e0)
% 231.95/43.05    (9)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.95/43.05         (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.95/43.05    (10)  all_57_2 = e0
% 231.95/43.05    (11)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.95/43.05          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.95/43.05    (12)   ~ (e2 = e1)
% 231.95/43.05  
% 231.95/43.05  Begin of proof
% 231.95/43.05  | 
% 231.95/43.05  | SIMP: (1) implies:
% 231.95/43.05  |   (13)  e1 = e0
% 231.95/43.05  | 
% 231.95/43.05  | COMBINE_EQS: (7), (13) imply:
% 231.95/43.05  |   (14)  all_57_3 = e0
% 231.95/43.05  | 
% 231.95/43.05  | REF_CLOSE: (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (14) are
% 231.95/43.05  |            inconsistent by sub-proof #2246.
% 231.95/43.05  | 
% 231.95/43.05  End of proof
% 231.95/43.05  
% 231.95/43.05  Sub-proof #1825 shows that the following formulas are inconsistent:
% 231.95/43.05  ----------------------------------------------------------------
% 231.95/43.05    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.95/43.05           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.95/43.05    (2)  op(e2, e2) = e1
% 231.95/43.05    (3)   ~ (e3 = e2)
% 231.95/43.05    (4)   ~ (e3 = e0)
% 231.95/43.05    (5)  all_57_5 = e3
% 231.95/43.05    (6)   ~ (e2 = e0)
% 231.95/43.05    (7)   ~ (e1 = e0)
% 231.95/43.05    (8)  all_57_2 = e1
% 231.95/43.05    (9)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.95/43.05         (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.95/43.05    (10)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 231.95/43.05          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 231.95/43.05    (11)   ~ (e2 = e1)
% 231.95/43.05  
% 231.95/43.05  Begin of proof
% 231.95/43.05  | 
% 231.95/43.05  | BETA: splitting (10) gives:
% 231.95/43.05  | 
% 231.95/43.05  | Case 1:
% 231.95/43.05  | | 
% 231.95/43.05  | |   (12)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) =
% 231.95/43.05  | |           e0)
% 231.95/43.05  | | 
% 231.95/43.05  | | BETA: splitting (12) gives:
% 231.95/43.05  | | 
% 231.95/43.05  | | Case 1:
% 231.95/43.05  | | | 
% 231.95/43.05  | | |   (13)  all_57_2 = e0 & op(e2, e3) = e0
% 231.95/43.05  | | | 
% 231.95/43.05  | | | REF_CLOSE: (7), (8), (13) are inconsistent by sub-proof #2467.
% 231.95/43.05  | | | 
% 231.95/43.05  | | Case 2:
% 231.95/43.05  | | | 
% 231.95/43.05  | | |   (14)  all_57_3 = e0 & op(e2, e2) = e0
% 231.95/43.05  | | | 
% 231.95/43.05  | | | ALPHA: (14) implies:
% 231.95/43.05  | | |   (15)  op(e2, e2) = e0
% 231.95/43.05  | | | 
% 231.95/43.05  | | | REF_CLOSE: (1), (2), (7), (15) are inconsistent by sub-proof #2352.
% 231.95/43.05  | | | 
% 231.95/43.05  | | End of split
% 231.95/43.05  | | 
% 231.95/43.05  | Case 2:
% 231.95/43.05  | | 
% 231.95/43.05  | |   (16)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 231.95/43.05  | |           e0)
% 231.95/43.05  | | 
% 231.95/43.05  | | BETA: splitting (16) gives:
% 231.95/43.05  | | 
% 231.95/43.05  | | Case 1:
% 231.95/43.05  | | | 
% 231.95/43.05  | | |   (17)  all_57_5 = e0 & op(e2, e1) = e0
% 231.95/43.05  | | | 
% 231.95/43.05  | | | REF_CLOSE: (4), (5), (17) are inconsistent by sub-proof #2414.
% 231.95/43.05  | | | 
% 231.95/43.05  | | Case 2:
% 231.95/43.05  | | | 
% 231.95/43.05  | | |   (18)  all_57_10 = e0 & op(e2, e0) = e0
% 231.95/43.05  | | | 
% 231.95/43.05  | | | REF_CLOSE: (1), (2), (3), (5), (6), (8), (9), (11), (18) are inconsistent
% 231.95/43.05  | | |            by sub-proof #1826.
% 231.95/43.05  | | | 
% 231.95/43.05  | | End of split
% 231.95/43.05  | | 
% 231.95/43.05  | End of split
% 231.95/43.05  | 
% 231.95/43.05  End of proof
% 231.95/43.05  
% 231.95/43.05  Sub-proof #1826 shows that the following formulas are inconsistent:
% 231.95/43.05  ----------------------------------------------------------------
% 231.95/43.05    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.95/43.05           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.95/43.05    (2)  op(e2, e2) = e1
% 231.95/43.05    (3)   ~ (e3 = e2)
% 231.95/43.05    (4)  all_57_10 = e0 & op(e2, e0) = e0
% 231.95/43.05    (5)  all_57_5 = e3
% 231.95/43.05    (6)   ~ (e2 = e0)
% 231.95/43.05    (7)  all_57_2 = e1
% 231.95/43.05    (8)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.95/43.05         (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.95/43.05    (9)   ~ (e2 = e1)
% 231.95/43.05  
% 231.95/43.05  Begin of proof
% 231.95/43.05  | 
% 231.95/43.05  | ALPHA: (4) implies:
% 231.95/43.05  |   (10)  all_57_10 = e0
% 231.95/43.05  | 
% 231.95/43.05  | BETA: splitting (8) gives:
% 231.95/43.05  | 
% 231.95/43.05  | Case 1:
% 231.95/43.05  | | 
% 231.95/43.05  | |   (11)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 231.95/43.05  | |           e2)
% 231.95/43.05  | | 
% 231.95/43.05  | | REF_CLOSE: (1), (2), (7), (9), (11) are inconsistent by sub-proof #1828.
% 231.95/43.05  | | 
% 231.95/43.05  | Case 2:
% 231.95/43.05  | | 
% 231.95/43.05  | |   (12)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 231.95/43.05  | |           e2)
% 231.95/43.05  | | 
% 231.95/43.05  | | REF_CLOSE: (3), (5), (6), (10), (12) are inconsistent by sub-proof #1827.
% 231.95/43.05  | | 
% 231.95/43.05  | End of split
% 231.95/43.05  | 
% 231.95/43.05  End of proof
% 231.95/43.05  
% 231.95/43.05  Sub-proof #1827 shows that the following formulas are inconsistent:
% 231.95/43.05  ----------------------------------------------------------------
% 231.95/43.05    (1)  all_57_10 = e0
% 231.95/43.05    (2)   ~ (e3 = e2)
% 231.95/43.05    (3)  all_57_5 = e3
% 231.95/43.05    (4)   ~ (e2 = e0)
% 231.95/43.05    (5)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.95/43.05  
% 231.95/43.05  Begin of proof
% 231.95/43.05  | 
% 231.95/43.05  | BETA: splitting (5) gives:
% 231.95/43.05  | 
% 231.95/43.05  | Case 1:
% 231.95/43.05  | | 
% 231.95/43.05  | |   (6)  all_57_5 = e2 & op(e2, e1) = e2
% 231.95/43.05  | | 
% 231.95/43.05  | | REF_CLOSE: (2), (3), (6) are inconsistent by sub-proof #2425.
% 231.95/43.05  | | 
% 231.95/43.05  | Case 2:
% 231.95/43.05  | | 
% 231.95/43.05  | |   (7)  all_57_10 = e2 & op(e2, e0) = e2
% 231.95/43.05  | | 
% 231.95/43.05  | | ALPHA: (7) implies:
% 231.95/43.05  | |   (8)  all_57_10 = e2
% 231.95/43.05  | | 
% 231.95/43.05  | | REF_CLOSE: (1), (4), (8) are inconsistent by sub-proof #2138.
% 231.95/43.05  | | 
% 231.95/43.05  | End of split
% 231.95/43.05  | 
% 231.95/43.05  End of proof
% 231.95/43.05  
% 231.95/43.05  Sub-proof #1828 shows that the following formulas are inconsistent:
% 231.95/43.05  ----------------------------------------------------------------
% 231.95/43.05    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.95/43.05           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.95/43.05    (2)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2)
% 231.95/43.05    (3)  op(e2, e2) = e1
% 231.95/43.05    (4)  all_57_2 = e1
% 231.95/43.05    (5)   ~ (e2 = e1)
% 231.95/43.05  
% 231.95/43.05  Begin of proof
% 231.95/43.05  | 
% 231.95/43.05  | BETA: splitting (2) gives:
% 231.95/43.05  | 
% 231.95/43.05  | Case 1:
% 231.95/43.05  | | 
% 231.95/43.05  | |   (6)  all_57_2 = e2 & op(e2, e3) = e2
% 231.95/43.05  | | 
% 231.95/43.05  | | ALPHA: (6) implies:
% 231.95/43.05  | |   (7)  all_57_2 = e2
% 231.95/43.05  | | 
% 231.95/43.05  | | REF_CLOSE: (4), (5), (7) are inconsistent by sub-proof #2464.
% 231.95/43.05  | | 
% 231.95/43.05  | Case 2:
% 231.95/43.05  | | 
% 231.95/43.05  | |   (8)  all_57_3 = e2 & op(e2, e2) = e2
% 231.95/43.05  | | 
% 231.95/43.05  | | ALPHA: (8) implies:
% 231.95/43.05  | |   (9)  op(e2, e2) = e2
% 231.95/43.05  | | 
% 231.95/43.05  | | REF_CLOSE: (1), (3), (5), (9) are inconsistent by sub-proof #2306.
% 231.95/43.05  | | 
% 231.95/43.05  | End of split
% 231.95/43.05  | 
% 231.95/43.05  End of proof
% 231.95/43.05  
% 231.95/43.05  Sub-proof #1829 shows that the following formulas are inconsistent:
% 231.95/43.05  ----------------------------------------------------------------
% 231.95/43.05    (1)   ~ (e3 = e1)
% 231.95/43.05    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.95/43.05           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.95/43.05    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.95/43.05         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.95/43.05    (4)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.95/43.05         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.95/43.05    (5)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.95/43.05         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.95/43.05    (6)   ~ (e3 = e2)
% 231.95/43.05    (7)   ~ (e3 = e0)
% 231.95/43.05    (8)  all_57_1 = e2
% 231.95/43.05    (9)  op(e3, e3) = e3
% 231.95/43.05    (10)   ~ (e2 = e0)
% 231.95/43.05    (11)   ~ (e1 = e0)
% 231.95/43.05    (12)   ~ (e2 = e1)
% 231.95/43.05    (13)  all_57_4 = e3 & op(e3, e1) = e3
% 231.95/43.05  
% 231.95/43.05  Begin of proof
% 231.95/43.05  | 
% 231.95/43.05  | ALPHA: (13) implies:
% 231.95/43.05  |   (14)  all_57_4 = e3
% 231.95/43.05  | 
% 231.95/43.05  | BETA: splitting (3) gives:
% 231.95/43.05  | 
% 231.95/43.05  | Case 1:
% 231.95/43.05  | | 
% 231.95/43.05  | |   (15)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) =
% 231.95/43.05  | |           e1)
% 231.95/43.05  | | 
% 231.95/43.05  | | REF_CLOSE: (1), (2), (8), (9), (12), (15) are inconsistent by sub-proof
% 231.95/43.05  | |            #2096.
% 231.95/43.05  | | 
% 231.95/43.05  | Case 2:
% 231.95/43.05  | | 
% 231.95/43.05  | |   (16)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) =
% 231.95/43.05  | |           e1)
% 231.95/43.05  | | 
% 231.95/43.05  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (14),
% 231.95/43.05  | |            (16) are inconsistent by sub-proof #2475.
% 231.95/43.05  | | 
% 231.95/43.05  | End of split
% 231.95/43.05  | 
% 231.95/43.05  End of proof
% 231.95/43.05  
% 231.95/43.05  Sub-proof #1830 shows that the following formulas are inconsistent:
% 231.95/43.05  ----------------------------------------------------------------
% 231.95/43.05    (1)   ~ (all_53_6 = e2)
% 231.95/43.05    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.95/43.05           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.95/43.05    (3)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 231.95/43.05    (4)  all_55_9 = all_53_6
% 231.95/43.05    (5)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.95/43.05         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.95/43.05    (6)   ~ (e3 = e0)
% 231.95/43.05    (7)  op(e3, e3) = e3
% 231.95/43.05    (8)  all_57_4 = e1
% 231.95/43.05    (9)  op(e3, e2) = all_53_4
% 231.95/43.05    (10)   ~ (all_53_6 = e1)
% 231.95/43.05    (11)   ~ (e1 = e0)
% 231.95/43.05    (12)   ~ (all_53_4 = all_53_6)
% 231.95/43.05    (13)   ~ (all_53_12 = e0)
% 231.95/43.05    (14)   ~ (all_53_6 = e3)
% 231.95/43.05    (15)  op(e3, e0) = all_53_12
% 231.95/43.05  
% 231.95/43.05  Begin of proof
% 231.95/43.05  | 
% 231.95/43.05  | BETA: splitting (5) gives:
% 231.95/43.05  | 
% 231.95/43.05  | Case 1:
% 231.95/43.05  | | 
% 231.95/43.05  | |   (16)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) =
% 231.95/43.05  | |           e0)
% 231.95/43.05  | | 
% 231.95/43.05  | | BETA: splitting (16) gives:
% 231.95/43.05  | | 
% 231.95/43.05  | | Case 1:
% 231.95/43.05  | | | 
% 231.95/43.05  | | |   (17)  all_57_0 = e0 & op(e3, e3) = e0
% 231.95/43.05  | | | 
% 231.95/43.05  | | | ALPHA: (17) implies:
% 231.95/43.05  | | |   (18)  op(e3, e3) = e0
% 231.95/43.05  | | | 
% 231.95/43.05  | | | REF_CLOSE: (2), (6), (7), (18) are inconsistent by sub-proof #2494.
% 231.95/43.05  | | | 
% 231.95/43.05  | | Case 2:
% 231.95/43.05  | | | 
% 231.95/43.05  | | |   (19)  all_57_1 = e0 & op(e3, e2) = e0
% 231.95/43.05  | | | 
% 231.95/43.05  | | | ALPHA: (19) implies:
% 231.95/43.05  | | |   (20)  op(e3, e2) = e0
% 231.95/43.05  | | | 
% 231.95/43.05  | | | BETA: splitting (3) gives:
% 231.95/43.05  | | | 
% 231.95/43.05  | | | Case 1:
% 231.95/43.05  | | | | 
% 231.95/43.05  | | | |   (21)  all_55_9 = e3
% 231.95/43.05  | | | | 
% 231.95/43.05  | | | | REF_CLOSE: (4), (14), (21) are inconsistent by sub-proof #2159.
% 231.95/43.05  | | | | 
% 231.95/43.05  | | | Case 2:
% 231.95/43.05  | | | | 
% 231.95/43.05  | | | |   (22)  all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 231.95/43.05  | | | | 
% 231.95/43.05  | | | | REF_CLOSE: (1), (2), (4), (9), (10), (12), (20), (22) are inconsistent
% 231.95/43.05  | | | |            by sub-proof #1831.
% 231.95/43.05  | | | | 
% 231.95/43.05  | | | End of split
% 231.95/43.05  | | | 
% 231.95/43.05  | | End of split
% 231.95/43.05  | | 
% 231.95/43.05  | Case 2:
% 231.95/43.05  | | 
% 231.95/43.05  | |   (23)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) =
% 231.95/43.05  | |           e0)
% 231.95/43.05  | | 
% 231.95/43.05  | | BETA: splitting (23) gives:
% 231.95/43.05  | | 
% 231.95/43.05  | | Case 1:
% 231.95/43.05  | | | 
% 231.95/43.05  | | |   (24)  all_57_4 = e0 & op(e3, e1) = e0
% 231.95/43.05  | | | 
% 231.95/43.05  | | | ALPHA: (24) implies:
% 231.95/43.05  | | |   (25)  all_57_4 = e0
% 231.95/43.05  | | | 
% 231.95/43.05  | | | REF_CLOSE: (8), (11), (25) are inconsistent by sub-proof #2438.
% 231.95/43.05  | | | 
% 231.95/43.05  | | Case 2:
% 231.95/43.05  | | | 
% 231.95/43.05  | | |   (26)  all_57_9 = e0 & op(e3, e0) = e0
% 231.95/43.05  | | | 
% 231.95/43.05  | | | REF_CLOSE: (2), (13), (15), (26) are inconsistent by sub-proof #2434.
% 231.95/43.05  | | | 
% 231.95/43.05  | | End of split
% 231.95/43.05  | | 
% 231.95/43.05  | End of split
% 231.95/43.05  | 
% 231.95/43.05  End of proof
% 231.95/43.05  
% 231.95/43.05  Sub-proof #1831 shows that the following formulas are inconsistent:
% 231.95/43.05  ----------------------------------------------------------------
% 231.95/43.05    (1)   ~ (all_53_6 = e2)
% 231.95/43.05    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.95/43.05           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.95/43.05    (3)  all_55_9 = all_53_6
% 231.95/43.05    (4)  all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 231.95/43.05    (5)  op(e3, e2) = all_53_4
% 231.95/43.05    (6)   ~ (all_53_6 = e1)
% 231.95/43.05    (7)   ~ (all_53_4 = all_53_6)
% 231.95/43.05    (8)  op(e3, e2) = e0
% 231.95/43.05  
% 231.95/43.05  Begin of proof
% 231.95/43.05  | 
% 231.95/43.05  | BETA: splitting (4) gives:
% 231.95/43.05  | 
% 231.95/43.05  | Case 1:
% 231.95/43.05  | | 
% 231.95/43.05  | |   (9)  all_55_9 = e2
% 231.95/43.05  | | 
% 231.95/43.05  | | REF_CLOSE: (1), (3), (9) are inconsistent by sub-proof #2274.
% 231.95/43.05  | | 
% 231.95/43.05  | Case 2:
% 231.95/43.05  | | 
% 231.95/43.05  | |   (10)  all_55_9 = e1 | all_55_9 = e0
% 231.95/43.05  | | 
% 231.95/43.05  | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (10) are inconsistent by sub-proof
% 231.95/43.05  | |            #1832.
% 231.95/43.05  | | 
% 231.95/43.05  | End of split
% 231.95/43.05  | 
% 231.95/43.05  End of proof
% 231.95/43.05  
% 231.95/43.05  Sub-proof #1832 shows that the following formulas are inconsistent:
% 231.95/43.05  ----------------------------------------------------------------
% 231.95/43.05    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.95/43.05           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.95/43.05    (2)  all_55_9 = e1 | all_55_9 = e0
% 231.95/43.05    (3)  all_55_9 = all_53_6
% 231.95/43.05    (4)  op(e3, e2) = all_53_4
% 231.95/43.05    (5)   ~ (all_53_6 = e1)
% 231.95/43.05    (6)   ~ (all_53_4 = all_53_6)
% 231.95/43.05    (7)  op(e3, e2) = e0
% 231.95/43.05  
% 231.95/43.05  Begin of proof
% 231.95/43.05  | 
% 231.95/43.05  | BETA: splitting (2) gives:
% 231.95/43.05  | 
% 231.95/43.05  | Case 1:
% 231.95/43.05  | | 
% 231.95/43.05  | |   (8)  all_55_9 = e1
% 231.95/43.05  | | 
% 231.95/43.05  | | REF_CLOSE: (3), (5), (8) are inconsistent by sub-proof #2273.
% 231.95/43.05  | | 
% 231.95/43.05  | Case 2:
% 231.95/43.05  | | 
% 231.95/43.05  | |   (9)  all_55_9 = e0
% 231.95/43.05  | | 
% 231.95/43.05  | | COMBINE_EQS: (3), (9) imply:
% 231.95/43.05  | |   (10)  all_53_6 = e0
% 231.95/43.05  | | 
% 231.95/43.05  | | SIMP: (10) implies:
% 231.95/43.05  | |   (11)  all_53_6 = e0
% 231.95/43.05  | | 
% 231.95/43.05  | | REDUCE: (6), (11) imply:
% 231.95/43.05  | |   (12)   ~ (all_53_4 = e0)
% 231.95/43.05  | | 
% 231.95/43.05  | | REF_CLOSE: (1), (4), (7), (12) are inconsistent by sub-proof #1941.
% 231.95/43.05  | | 
% 231.95/43.05  | End of split
% 231.95/43.05  | 
% 231.95/43.05  End of proof
% 231.95/43.05  
% 231.95/43.05  Sub-proof #1833 shows that the following formulas are inconsistent:
% 231.95/43.05  ----------------------------------------------------------------
% 231.95/43.05    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.95/43.05         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.95/43.05    (2)  op(e2, e3) = all_53_1
% 231.95/43.05    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.95/43.05         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.95/43.05    (4)   ~ (e3 = e1)
% 231.95/43.05    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.95/43.05           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.95/43.05    (6)   ~ (e3 = e2)
% 231.95/43.05    (7)   ~ (e3 = e0)
% 231.95/43.05    (8)  op(e3, e3) = e3
% 231.95/43.05    (9)  op(e0, e3) = all_53_3
% 231.95/43.05    (10)   ~ (all_53_1 = e1)
% 231.95/43.05    (11)   ~ (e2 = e0)
% 231.95/43.05    (12)  all_57_3 = e1
% 231.95/43.05    (13)   ~ (e1 = e0)
% 231.95/43.05    (14)   ~ (all_53_3 = e0)
% 231.95/43.05    (15)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.95/43.05          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.95/43.05    (16)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.95/43.05          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.95/43.05    (17)   ~ (e2 = e1)
% 231.95/43.05    (18)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 231.95/43.05          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 231.95/43.05    (19)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 231.95/43.05          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.95/43.05    (20)  all_57_12 = e3 & op(e0, e3) = e3
% 231.95/43.05  
% 231.95/43.05  Begin of proof
% 231.95/43.05  | 
% 231.95/43.05  | ALPHA: (20) implies:
% 231.95/43.05  |   (21)  all_57_12 = e3
% 231.95/43.05  | 
% 231.95/43.05  | BETA: splitting (3) gives:
% 231.95/43.05  | 
% 231.95/43.05  | Case 1:
% 231.95/43.05  | | 
% 231.95/43.05  | |   (22)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) =
% 231.95/43.05  | |           e1)
% 231.95/43.05  | | 
% 231.95/43.05  | | REF_CLOSE: (2), (4), (5), (8), (10), (22) are inconsistent by sub-proof
% 231.95/43.05  | |            #2155.
% 231.95/43.05  | | 
% 231.95/43.05  | Case 2:
% 231.95/43.05  | | 
% 231.95/43.05  | |   (23)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) =
% 231.95/43.05  | |           e1)
% 231.95/43.05  | | 
% 231.95/43.05  | | BETA: splitting (23) gives:
% 231.95/43.05  | | 
% 231.95/43.05  | | Case 1:
% 231.95/43.05  | | | 
% 231.95/43.05  | | |   (24)  all_57_6 = e1 & op(e1, e3) = e1
% 231.95/43.05  | | | 
% 231.95/43.05  | | | ALPHA: (24) implies:
% 231.95/43.05  | | |   (25)  all_57_6 = e1
% 231.95/43.05  | | | 
% 231.95/43.05  | | | BETA: splitting (19) gives:
% 231.95/43.05  | | | 
% 231.95/43.05  | | | Case 1:
% 231.95/43.05  | | | | 
% 231.95/43.05  | | | |   (26)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3)
% 231.95/43.05  | | | |           = e0)
% 231.95/43.05  | | | | 
% 231.95/43.05  | | | | BETA: splitting (26) gives:
% 231.95/43.05  | | | | 
% 231.95/43.05  | | | | Case 1:
% 231.95/43.05  | | | | | 
% 231.95/43.05  | | | | |   (27)  all_57_0 = e0 & op(e3, e3) = e0
% 231.95/43.05  | | | | | 
% 231.95/43.05  | | | | | ALPHA: (27) implies:
% 231.95/43.05  | | | | |   (28)  op(e3, e3) = e0
% 231.95/43.05  | | | | | 
% 231.95/43.05  | | | | | REF_CLOSE: (5), (7), (8), (28) are inconsistent by sub-proof #2494.
% 231.95/43.05  | | | | | 
% 231.95/43.05  | | | | Case 2:
% 231.95/43.05  | | | | | 
% 231.95/43.05  | | | | |   (29)  all_57_2 = e0 & op(e2, e3) = e0
% 231.95/43.05  | | | | | 
% 231.95/43.05  | | | | | ALPHA: (29) implies:
% 231.95/43.05  | | | | |   (30)  all_57_2 = e0
% 231.95/43.05  | | | | | 
% 231.95/43.05  | | | | | REF_CLOSE: (5), (6), (8), (11), (17), (18), (21), (25), (30) are
% 231.95/43.05  | | | | |            inconsistent by sub-proof #2231.
% 231.95/43.05  | | | | | 
% 231.95/43.05  | | | | End of split
% 231.95/43.05  | | | | 
% 231.95/43.05  | | | Case 2:
% 231.95/43.05  | | | | 
% 231.95/43.05  | | | |   (31)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3)
% 231.95/43.05  | | | |           = e0)
% 231.95/43.05  | | | | 
% 231.95/43.05  | | | | BETA: splitting (31) gives:
% 231.95/43.05  | | | | 
% 231.95/43.05  | | | | Case 1:
% 231.95/43.05  | | | | | 
% 231.95/43.05  | | | | |   (32)  all_57_6 = e0 & op(e1, e3) = e0
% 231.95/43.05  | | | | | 
% 231.95/43.05  | | | | | ALPHA: (32) implies:
% 231.95/43.05  | | | | |   (33)  all_57_6 = e0
% 231.95/43.05  | | | | | 
% 231.95/43.05  | | | | | COMBINE_EQS: (25), (33) imply:
% 231.95/43.05  | | | | |   (34)  e1 = e0
% 231.95/43.05  | | | | | 
% 231.95/43.05  | | | | | SIMP: (34) implies:
% 231.95/43.05  | | | | |   (35)  e1 = e0
% 231.95/43.05  | | | | | 
% 231.95/43.05  | | | | | COMBINE_EQS: (12), (35) imply:
% 231.95/43.05  | | | | |   (36)  all_57_3 = e0
% 231.95/43.05  | | | | | 
% 231.95/43.05  | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (11), (13), (15), (16),
% 231.95/43.05  | | | | |            (17), (18), (19), (21), (36) are inconsistent by sub-proof
% 231.95/43.05  | | | | |            #2223.
% 231.95/43.05  | | | | | 
% 231.95/43.05  | | | | Case 2:
% 231.95/43.05  | | | | | 
% 231.95/43.05  | | | | |   (37)  all_57_12 = e0 & op(e0, e3) = e0
% 231.95/43.05  | | | | | 
% 231.95/43.05  | | | | | ALPHA: (37) implies:
% 231.95/43.05  | | | | |   (38)  op(e0, e3) = e0
% 231.95/43.05  | | | | | 
% 231.95/43.05  | | | | | REF_CLOSE: (5), (9), (14), (38) are inconsistent by sub-proof #2366.
% 231.95/43.05  | | | | | 
% 231.95/43.05  | | | | End of split
% 231.95/43.05  | | | | 
% 231.95/43.05  | | | End of split
% 231.95/43.05  | | | 
% 231.95/43.05  | | Case 2:
% 231.95/43.05  | | | 
% 231.95/43.05  | | |   (39)  all_57_12 = e1 & op(e0, e3) = e1
% 231.95/43.05  | | | 
% 231.95/43.05  | | | REF_CLOSE: (4), (21), (39) are inconsistent by sub-proof #2230.
% 231.95/43.05  | | | 
% 231.95/43.05  | | End of split
% 231.95/43.05  | | 
% 231.95/43.05  | End of split
% 231.95/43.05  | 
% 231.95/43.05  End of proof
% 231.95/43.05  
% 231.95/43.05  Sub-proof #1834 shows that the following formulas are inconsistent:
% 231.95/43.05  ----------------------------------------------------------------
% 231.95/43.05    (1)  all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 231.95/43.05    (2)  op(e0, e0) = all_4_2
% 231.95/43.05    (3)   ~ (all_53_12 = all_4_2)
% 231.95/43.05    (4)  all_55_15 = e3 | all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 231.95/43.05    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.95/43.05           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.95/43.05    (6)   ~ (all_53_7 = e1)
% 231.95/43.05    (7)  all_55_15 = all_4_2
% 231.95/43.05    (8)  op(e2, e2) = e1
% 231.95/43.05    (9)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 231.95/43.05    (10)  all_55_9 = all_53_6
% 231.95/43.05    (11)   ~ (all_53_4 = e1)
% 231.95/43.05    (12)   ~ (all_53_14 = all_4_2)
% 231.95/43.05    (13)  op(e1, e0) = all_53_14
% 231.95/43.05    (14)   ~ (all_53_6 = all_53_7)
% 231.95/43.05    (15)  op(e3, e3) = e3
% 231.95/43.05    (16)   ~ (all_4_2 = e2)
% 231.95/43.05    (17)   ~ (all_53_7 = all_4_2)
% 231.95/43.05    (18)   ~ (all_53_4 = all_53_7)
% 231.95/43.05    (19)  op(e3, e2) = all_53_4
% 231.95/43.05    (20)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 231.95/43.05          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 231.95/43.05    (21)   ~ (e2 = e0)
% 231.95/43.06    (22)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 231.95/43.06            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 231.95/43.06            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 231.95/43.06            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 231.95/43.06              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 231.95/43.06            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 231.95/43.06            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 231.95/43.06              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 231.95/43.06              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 231.95/43.06            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 231.95/43.06            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 231.95/43.06            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 231.95/43.06              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 231.95/43.06              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 231.95/43.06            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 231.95/43.06              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 231.95/43.06            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 231.95/43.06            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 231.95/43.06              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 231.95/43.06              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 231.95/43.06            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 231.95/43.06            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 231.95/43.06    (23)   ~ (all_53_6 = e1)
% 231.95/43.06    (24)  op(e0, e0) = e0
% 231.95/43.06    (25)   ~ (all_53_13 = all_4_2)
% 231.95/43.06    (26)   ~ (all_53_4 = all_53_6)
% 231.95/43.06    (27)  op(e0, e2) = all_53_7
% 231.95/43.06    (28)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.95/43.06              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.95/43.06                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.95/43.06                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.95/43.06    (29)  op(e1, e1) = e0
% 231.95/43.06    (30)  all_55_13 = all_53_7
% 231.95/43.06    (31)  op(e2, e0) = all_53_13
% 231.95/43.06    (32)   ~ (all_4_2 = e3)
% 231.95/43.06    (33)   ~ (all_4_2 = e1)
% 231.95/43.06    (34)  op(e3, e2) = e0
% 231.95/43.06    (35)  op(e3, e0) = all_53_12
% 231.95/43.06  
% 231.95/43.06  Begin of proof
% 231.95/43.06  | 
% 231.95/43.06  | GROUND_INST: instantiating (5) with all_53_4, e0, e2, e3, simplifying with
% 231.95/43.06  |              (19), (34) gives:
% 231.95/43.06  |   (36)  all_53_4 = e0
% 231.95/43.06  | 
% 231.95/43.06  | REDUCE: (26), (36) imply:
% 231.95/43.06  |   (37)   ~ (all_53_6 = e0)
% 231.95/43.06  | 
% 231.95/43.06  | SIMP: (37) implies:
% 231.95/43.06  |   (38)   ~ (all_53_6 = e0)
% 231.95/43.06  | 
% 231.95/43.06  | REDUCE: (18), (36) imply:
% 231.95/43.06  |   (39)   ~ (all_53_7 = e0)
% 231.95/43.06  | 
% 231.95/43.06  | SIMP: (39) implies:
% 231.95/43.06  |   (40)   ~ (all_53_7 = e0)
% 231.95/43.06  | 
% 231.95/43.06  | BETA: splitting (22) gives:
% 231.95/43.06  | 
% 231.95/43.06  | Case 1:
% 231.95/43.06  | | 
% 231.95/43.06  | |   (41)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 231.95/43.06  | |           op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 231.95/43.06  | |           op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3,
% 231.95/43.06  | |             e3) = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 &
% 231.95/43.06  | |           op(e3, e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5)
% 231.95/43.06  | |           & $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1
% 231.95/43.06  | |           & all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 231.95/43.06  | |             all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 231.95/43.06  | |             all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11
% 231.95/43.06  | |           & op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 231.95/43.06  | |           $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 231.95/43.06  | | 
% 231.95/43.06  | | BETA: splitting (41) gives:
% 231.95/43.06  | | 
% 231.95/43.06  | | Case 1:
% 231.95/43.06  | | | 
% 231.95/43.06  | | |   (42)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 231.95/43.06  | | |         op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 231.95/43.06  | | |         op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3,
% 231.95/43.06  | | |           e3) = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 &
% 231.95/43.06  | | |         op(e3, e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5)
% 231.95/43.06  | | |         & $i(all_52_7)
% 231.95/43.06  | | | 
% 231.95/43.06  | | | ALPHA: (42) implies:
% 231.95/43.06  | | |   (43)  op(e3, e2) = all_52_3
% 231.95/43.06  | | |   (44)  op(all_52_3, all_52_3) = e2
% 231.95/43.06  | | | 
% 231.95/43.06  | | | REF_CLOSE: (5), (21), (24), (34), (43), (44) are inconsistent by sub-proof
% 231.95/43.06  | | |            #2399.
% 231.95/43.06  | | | 
% 231.95/43.06  | | Case 2:
% 231.95/43.06  | | | 
% 231.95/43.06  | | |   (45)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0 &
% 231.95/43.06  | | |         op(all_52_9, all_52_9) = e3 & op(all_52_11, all_52_11) = e2 &
% 231.95/43.06  | | |         op(all_52_13, all_52_13) = e1 & op(all_52_15, all_52_15) = e0 &
% 231.95/43.06  | | |         op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 & op(e2, e1) =
% 231.95/43.06  | | |         all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) & $i(all_52_11)
% 231.95/43.06  | | |         & $i(all_52_13) & $i(all_52_15)
% 231.95/43.06  | | | 
% 231.95/43.06  | | | ALPHA: (45) implies:
% 231.95/43.06  | | |   (46)  op(e2, e2) = all_52_11
% 231.95/43.06  | | |   (47)  op(all_52_11, all_52_11) = e2
% 231.95/43.06  | | | 
% 231.95/43.06  | | | REF_CLOSE: (5), (8), (21), (29), (46), (47) are inconsistent by sub-proof
% 231.95/43.06  | | |            #1843.
% 231.95/43.06  | | | 
% 231.95/43.06  | | End of split
% 231.95/43.06  | | 
% 231.95/43.06  | Case 2:
% 231.95/43.06  | | 
% 231.95/43.06  | |   (48)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 &
% 231.95/43.06  | |           op(all_52_17, all_52_17) = e3 & op(all_52_19, all_52_19) = e2 &
% 231.95/43.06  | |           op(all_52_21, all_52_21) = e1 & op(all_52_23, all_52_23) = e0 &
% 231.95/43.06  | |           op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) =
% 231.95/43.06  | |           all_52_21 & op(e1, e0) = all_52_23 & $i(all_52_17) & $i(all_52_19)
% 231.95/43.06  | |           & $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3 & all_52_26 =
% 231.95/43.06  | |           e2 & all_52_28 = e1 & all_52_30 = e0 & op(all_52_25, all_52_25) =
% 231.95/43.06  | |           e3 & op(all_52_27, all_52_27) = e2 & op(all_52_29, all_52_29) = e1
% 231.95/43.06  | |           & op(all_52_31, all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0,
% 231.95/43.06  | |             e2) = all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0) =
% 231.95/43.06  | |           all_52_31 & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 231.95/43.06  | |           $i(all_52_31))
% 231.95/43.06  | | 
% 231.95/43.06  | | BETA: splitting (48) gives:
% 231.95/43.06  | | 
% 231.95/43.06  | | Case 1:
% 231.95/43.06  | | | 
% 231.95/43.06  | | |   (49)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 231.95/43.06  | | |         & op(all_52_17, all_52_17) = e3 & op(all_52_19, all_52_19) = e2 &
% 231.95/43.06  | | |         op(all_52_21, all_52_21) = e1 & op(all_52_23, all_52_23) = e0 &
% 231.95/43.06  | | |         op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) =
% 231.95/43.06  | | |         all_52_21 & op(e1, e0) = all_52_23 & $i(all_52_17) & $i(all_52_19)
% 231.95/43.06  | | |         & $i(all_52_21) & $i(all_52_23)
% 231.95/43.06  | | | 
% 231.95/43.06  | | | ALPHA: (49) implies:
% 231.95/43.06  | | |   (50)  op(e1, e1) = all_52_21
% 231.95/43.06  | | |   (51)  op(e1, e2) = all_52_19
% 231.95/43.06  | | |   (52)  op(all_52_21, all_52_21) = e1
% 231.95/43.06  | | |   (53)  op(all_52_19, all_52_19) = e2
% 231.95/43.06  | | | 
% 231.95/43.06  | | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (11), (12), (13), (16), (17),
% 231.95/43.06  | | |            (19), (20), (25), (27), (28), (29), (31), (32), (33), (35),
% 231.95/43.06  | | |            (50), (51), (52), (53) are inconsistent by sub-proof #1838.
% 231.95/43.06  | | | 
% 231.95/43.06  | | Case 2:
% 231.95/43.06  | | | 
% 231.95/43.06  | | |   (54)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 231.95/43.06  | | |         & op(all_52_25, all_52_25) = e3 & op(all_52_27, all_52_27) = e2 &
% 231.95/43.06  | | |         op(all_52_29, all_52_29) = e1 & op(all_52_31, all_52_31) = e0 &
% 231.95/43.06  | | |         op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 & op(e0, e1) =
% 231.95/43.06  | | |         all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) & $i(all_52_27)
% 231.95/43.06  | | |         & $i(all_52_29) & $i(all_52_31)
% 231.95/43.06  | | | 
% 231.95/43.06  | | | ALPHA: (54) implies:
% 231.95/43.06  | | |   (55)  op(e0, e2) = all_52_27
% 231.95/43.06  | | |   (56)  op(all_52_27, all_52_27) = e2
% 231.95/43.06  | | | 
% 231.95/43.06  | | | GROUND_INST: instantiating (5) with all_53_7, all_52_27, e2, e0,
% 231.95/43.06  | | |              simplifying with (27), (55) gives:
% 231.95/43.06  | | |   (57)  all_53_7 = all_52_27
% 231.95/43.06  | | | 
% 231.95/43.06  | | | COMBINE_EQS: (30), (57) imply:
% 231.95/43.06  | | |   (58)  all_55_13 = all_52_27
% 231.95/43.06  | | | 
% 231.95/43.06  | | | REDUCE: (14), (57) imply:
% 231.95/43.06  | | |   (59)   ~ (all_53_6 = all_52_27)
% 231.95/43.06  | | | 
% 231.95/43.06  | | | REDUCE: (6), (57) imply:
% 231.95/43.06  | | |   (60)   ~ (all_52_27 = e1)
% 231.95/43.06  | | | 
% 231.95/43.06  | | | BETA: splitting (9) gives:
% 231.95/43.06  | | | 
% 231.95/43.06  | | | Case 1:
% 231.95/43.06  | | | | 
% 231.95/43.06  | | | |   (61)  all_55_9 = e3
% 231.95/43.06  | | | | 
% 231.95/43.06  | | | | COMBINE_EQS: (10), (61) imply:
% 231.95/43.06  | | | |   (62)  all_53_6 = e3
% 231.95/43.06  | | | | 
% 231.95/43.06  | | | | SIMP: (62) implies:
% 231.95/43.06  | | | |   (63)  all_53_6 = e3
% 231.95/43.06  | | | | 
% 231.95/43.06  | | | | REDUCE: (59), (63) imply:
% 231.95/43.06  | | | |   (64)   ~ (all_52_27 = e3)
% 231.95/43.06  | | | | 
% 231.95/43.06  | | | | SIMP: (64) implies:
% 231.95/43.06  | | | |   (65)   ~ (all_52_27 = e3)
% 231.95/43.06  | | | | 
% 231.95/43.06  | | | | BETA: splitting (1) gives:
% 231.95/43.06  | | | | 
% 231.95/43.06  | | | | Case 1:
% 231.95/43.06  | | | | | 
% 231.95/43.06  | | | | |   (66)  all_55_13 = e3
% 231.95/43.06  | | | | | 
% 231.95/43.06  | | | | | COMBINE_EQS: (58), (66) imply:
% 231.95/43.06  | | | | |   (67)  all_52_27 = e3
% 231.95/43.06  | | | | | 
% 231.95/43.06  | | | | | REDUCE: (65), (67) imply:
% 231.95/43.06  | | | | |   (68)  $false
% 231.95/43.06  | | | | | 
% 231.95/43.06  | | | | | CLOSE: (68) is inconsistent.
% 231.95/43.06  | | | | | 
% 231.95/43.06  | | | | Case 2:
% 231.95/43.06  | | | | | 
% 231.95/43.06  | | | | |   (69)  all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 231.95/43.06  | | | | | 
% 231.95/43.06  | | | | | REF_CLOSE: (5), (6), (8), (30), (40), (56), (58), (60), (69) are
% 231.95/43.06  | | | | |            inconsistent by sub-proof #1836.
% 231.95/43.06  | | | | | 
% 231.95/43.06  | | | | End of split
% 231.95/43.06  | | | | 
% 231.95/43.06  | | | Case 2:
% 231.95/43.06  | | | | 
% 231.95/43.06  | | | |   (70)  all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 231.95/43.06  | | | | 
% 231.95/43.06  | | | | BETA: splitting (70) gives:
% 231.95/43.06  | | | | 
% 231.95/43.06  | | | | Case 1:
% 231.95/43.06  | | | | | 
% 231.95/43.06  | | | | |   (71)  all_55_9 = e2
% 231.95/43.06  | | | | | 
% 231.95/43.06  | | | | | COMBINE_EQS: (10), (71) imply:
% 231.95/43.06  | | | | |   (72)  all_53_6 = e2
% 231.95/43.06  | | | | | 
% 231.95/43.06  | | | | | SIMP: (72) implies:
% 231.95/43.06  | | | | |   (73)  all_53_6 = e2
% 231.95/43.06  | | | | | 
% 231.95/43.06  | | | | | REDUCE: (59), (73) imply:
% 231.95/43.06  | | | | |   (74)   ~ (all_52_27 = e2)
% 231.95/43.06  | | | | | 
% 231.95/43.06  | | | | | SIMP: (74) implies:
% 231.95/43.06  | | | | |   (75)   ~ (all_52_27 = e2)
% 231.95/43.06  | | | | | 
% 231.95/43.06  | | | | | BETA: splitting (1) gives:
% 231.95/43.06  | | | | | 
% 231.95/43.06  | | | | | Case 1:
% 231.95/43.06  | | | | | | 
% 231.95/43.06  | | | | | |   (76)  all_55_13 = e3
% 231.95/43.06  | | | | | | 
% 231.95/43.06  | | | | | | COMBINE_EQS: (58), (76) imply:
% 231.95/43.06  | | | | | |   (77)  all_52_27 = e3
% 231.95/43.06  | | | | | | 
% 231.95/43.06  | | | | | | REDUCE: (75), (77) imply:
% 231.95/43.06  | | | | | |   (78)   ~ (e3 = e2)
% 231.95/43.06  | | | | | | 
% 231.95/43.06  | | | | | | REDUCE: (56), (77) imply:
% 231.95/43.06  | | | | | |   (79)  op(e3, e3) = e2
% 231.95/43.06  | | | | | | 
% 231.95/43.06  | | | | | | REF_CLOSE: (5), (15), (78), (79) are inconsistent by sub-proof
% 231.95/43.06  | | | | | |            #2490.
% 231.95/43.06  | | | | | | 
% 231.95/43.06  | | | | | Case 2:
% 231.95/43.06  | | | | | | 
% 231.95/43.06  | | | | | |   (80)  all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 231.95/43.06  | | | | | | 
% 231.95/43.06  | | | | | | REF_CLOSE: (5), (6), (8), (30), (40), (56), (58), (60), (80) are
% 231.95/43.06  | | | | | |            inconsistent by sub-proof #1836.
% 231.95/43.06  | | | | | | 
% 231.95/43.06  | | | | | End of split
% 231.95/43.06  | | | | | 
% 231.95/43.06  | | | | Case 2:
% 231.95/43.06  | | | | | 
% 231.95/43.06  | | | | |   (81)  all_55_9 = e1 | all_55_9 = e0
% 231.95/43.06  | | | | | 
% 231.95/43.06  | | | | | REF_CLOSE: (10), (23), (38), (81) are inconsistent by sub-proof #1835.
% 231.95/43.06  | | | | | 
% 231.95/43.06  | | | | End of split
% 231.95/43.06  | | | | 
% 231.95/43.06  | | | End of split
% 231.95/43.06  | | | 
% 231.95/43.06  | | End of split
% 231.95/43.06  | | 
% 231.95/43.06  | End of split
% 231.95/43.06  | 
% 231.95/43.06  End of proof
% 231.95/43.06  
% 231.95/43.06  Sub-proof #1835 shows that the following formulas are inconsistent:
% 231.95/43.06  ----------------------------------------------------------------
% 231.95/43.06    (1)  all_55_9 = e1 | all_55_9 = e0
% 231.95/43.06    (2)  all_55_9 = all_53_6
% 231.95/43.06    (3)   ~ (all_53_6 = e1)
% 231.95/43.06    (4)   ~ (all_53_6 = e0)
% 231.95/43.06  
% 231.95/43.06  Begin of proof
% 231.95/43.06  | 
% 231.95/43.06  | BETA: splitting (1) gives:
% 231.95/43.06  | 
% 231.95/43.06  | Case 1:
% 231.95/43.06  | | 
% 231.95/43.06  | |   (5)  all_55_9 = e1
% 231.95/43.06  | | 
% 231.95/43.06  | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #2273.
% 231.95/43.06  | | 
% 231.95/43.06  | Case 2:
% 231.95/43.06  | | 
% 231.95/43.06  | |   (6)  all_55_9 = e0
% 231.95/43.06  | | 
% 231.95/43.06  | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #2272.
% 231.95/43.06  | | 
% 231.95/43.06  | End of split
% 231.95/43.06  | 
% 231.95/43.06  End of proof
% 231.95/43.06  
% 231.95/43.06  Sub-proof #1836 shows that the following formulas are inconsistent:
% 231.95/43.06  ----------------------------------------------------------------
% 231.95/43.06    (1)   ~ (all_52_27 = e1)
% 231.95/43.06    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.95/43.06           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.95/43.06    (3)   ~ (all_53_7 = e1)
% 231.95/43.06    (4)  op(e2, e2) = e1
% 231.95/43.06    (5)  all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 231.95/43.06    (6)   ~ (all_53_7 = e0)
% 231.95/43.06    (7)  all_55_13 = all_52_27
% 231.95/43.06    (8)  all_55_13 = all_53_7
% 231.95/43.06    (9)  op(all_52_27, all_52_27) = e2
% 231.95/43.06  
% 231.95/43.06  Begin of proof
% 231.95/43.06  | 
% 231.95/43.06  | BETA: splitting (5) gives:
% 231.95/43.06  | 
% 231.95/43.06  | Case 1:
% 231.95/43.06  | | 
% 231.95/43.06  | |   (10)  all_55_13 = e2
% 231.95/43.06  | | 
% 231.95/43.06  | | COMBINE_EQS: (7), (10) imply:
% 231.95/43.06  | |   (11)  all_52_27 = e2
% 231.95/43.06  | | 
% 231.95/43.06  | | REDUCE: (1), (11) imply:
% 231.95/43.06  | |   (12)   ~ (e2 = e1)
% 231.95/43.06  | | 
% 231.95/43.06  | | REDUCE: (9), (11) imply:
% 231.95/43.06  | |   (13)  op(e2, e2) = e2
% 231.95/43.06  | | 
% 231.95/43.06  | | REF_CLOSE: (2), (4), (12), (13) are inconsistent by sub-proof #2306.
% 231.95/43.06  | | 
% 231.95/43.06  | Case 2:
% 231.95/43.06  | | 
% 231.95/43.06  | |   (14)  all_55_13 = e1 | all_55_13 = e0
% 231.95/43.06  | | 
% 231.95/43.06  | | REF_CLOSE: (3), (6), (8), (14) are inconsistent by sub-proof #1837.
% 231.95/43.06  | | 
% 231.95/43.06  | End of split
% 231.95/43.06  | 
% 231.95/43.06  End of proof
% 231.95/43.06  
% 231.95/43.06  Sub-proof #1837 shows that the following formulas are inconsistent:
% 231.95/43.06  ----------------------------------------------------------------
% 231.95/43.06    (1)  all_55_13 = e1 | all_55_13 = e0
% 231.95/43.06    (2)  all_55_13 = all_53_7
% 231.95/43.06    (3)   ~ (all_53_7 = e1)
% 231.95/43.06    (4)   ~ (all_53_7 = e0)
% 231.95/43.06  
% 231.95/43.06  Begin of proof
% 231.95/43.06  | 
% 231.95/43.06  | BETA: splitting (1) gives:
% 231.95/43.06  | 
% 231.95/43.06  | Case 1:
% 231.95/43.06  | | 
% 231.95/43.06  | |   (5)  all_55_13 = e1
% 231.95/43.06  | | 
% 231.95/43.06  | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #2002.
% 231.95/43.06  | | 
% 231.95/43.06  | Case 2:
% 231.95/43.06  | | 
% 231.95/43.06  | |   (6)  all_55_13 = e0
% 231.95/43.06  | | 
% 231.95/43.06  | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #2261.
% 231.95/43.06  | | 
% 231.95/43.06  | End of split
% 231.95/43.06  | 
% 231.95/43.06  End of proof
% 231.95/43.06  
% 231.95/43.06  Sub-proof #1838 shows that the following formulas are inconsistent:
% 231.95/43.06  ----------------------------------------------------------------
% 231.95/43.06    (1)  op(e0, e0) = all_4_2
% 231.95/43.06    (2)   ~ (all_53_12 = all_4_2)
% 231.95/43.06    (3)  all_55_15 = e3 | all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 231.95/43.06    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.95/43.06           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.95/43.06    (5)  all_55_15 = all_4_2
% 231.95/43.06    (6)  op(e2, e2) = e1
% 231.95/43.06    (7)   ~ (all_53_4 = e1)
% 231.95/43.06    (8)   ~ (all_53_14 = all_4_2)
% 231.95/43.06    (9)  op(e1, e0) = all_53_14
% 231.95/43.06    (10)   ~ (all_4_2 = e2)
% 231.95/43.06    (11)   ~ (all_53_7 = all_4_2)
% 231.95/43.06    (12)  op(e3, e2) = all_53_4
% 231.95/43.06    (13)  op(e1, e1) = all_52_21
% 231.95/43.06    (14)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 231.95/43.06          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 231.95/43.06    (15)   ~ (all_53_13 = all_4_2)
% 231.95/43.06    (16)  op(e0, e2) = all_53_7
% 231.95/43.06    (17)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.95/43.06              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.95/43.06                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.95/43.06                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.95/43.06    (18)  op(e1, e1) = e0
% 231.95/43.06    (19)  op(e2, e0) = all_53_13
% 231.95/43.06    (20)  op(e1, e2) = all_52_19
% 231.95/43.06    (21)   ~ (all_4_2 = e3)
% 231.95/43.06    (22)  op(all_52_19, all_52_19) = e2
% 231.95/43.06    (23)   ~ (all_4_2 = e1)
% 231.95/43.06    (24)  op(all_52_21, all_52_21) = e1
% 231.95/43.06    (25)  op(e3, e0) = all_53_12
% 231.95/43.06  
% 231.95/43.06  Begin of proof
% 231.95/43.06  | 
% 231.95/43.06  | BETA: splitting (3) gives:
% 231.95/43.06  | 
% 231.95/43.06  | Case 1:
% 231.95/43.06  | | 
% 231.95/43.06  | |   (26)  all_55_15 = e3
% 231.95/43.06  | | 
% 231.95/43.06  | | REF_CLOSE: (5), (21), (26) are inconsistent by sub-proof #2503.
% 231.95/43.06  | | 
% 231.95/43.06  | Case 2:
% 231.95/43.06  | | 
% 231.95/43.06  | |   (27)  all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 231.95/43.06  | | 
% 231.95/43.06  | | BETA: splitting (27) gives:
% 231.95/43.06  | | 
% 231.95/43.06  | | Case 1:
% 231.95/43.06  | | | 
% 231.95/43.06  | | |   (28)  all_55_15 = e2
% 231.95/43.06  | | | 
% 231.95/43.06  | | | REF_CLOSE: (5), (10), (28) are inconsistent by sub-proof #2502.
% 231.95/43.06  | | | 
% 231.95/43.06  | | Case 2:
% 231.95/43.06  | | | 
% 231.95/43.06  | | |   (29)   ~ (all_55_15 = e2)
% 231.95/43.06  | | |   (30)  all_55_15 = e1 | all_55_15 = e0
% 231.95/43.06  | | | 
% 231.95/43.06  | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 231.95/43.06  | | |            (14), (15), (16), (17), (18), (19), (20), (22), (23), (24),
% 231.95/43.06  | | |            (25), (30) are inconsistent by sub-proof #1839.
% 231.95/43.06  | | | 
% 231.95/43.06  | | End of split
% 231.95/43.06  | | 
% 231.95/43.06  | End of split
% 231.95/43.06  | 
% 231.95/43.06  End of proof
% 231.95/43.06  
% 231.95/43.06  Sub-proof #1839 shows that the following formulas are inconsistent:
% 231.95/43.06  ----------------------------------------------------------------
% 231.95/43.06    (1)  op(e0, e0) = all_4_2
% 231.95/43.06    (2)   ~ (all_53_12 = all_4_2)
% 231.95/43.06    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.95/43.06           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.95/43.06    (4)  all_55_15 = all_4_2
% 231.95/43.06    (5)  op(e2, e2) = e1
% 231.95/43.06    (6)   ~ (all_53_4 = e1)
% 231.95/43.06    (7)   ~ (all_53_14 = all_4_2)
% 231.95/43.06    (8)  op(e1, e0) = all_53_14
% 231.95/43.06    (9)   ~ (all_4_2 = e2)
% 231.95/43.06    (10)   ~ (all_53_7 = all_4_2)
% 231.95/43.06    (11)  op(e3, e2) = all_53_4
% 231.95/43.06    (12)  op(e1, e1) = all_52_21
% 231.95/43.06    (13)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 231.95/43.06          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 231.95/43.06    (14)   ~ (all_53_13 = all_4_2)
% 231.95/43.06    (15)  op(e0, e2) = all_53_7
% 231.95/43.06    (16)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.95/43.06              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.95/43.06                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.95/43.06                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.95/43.06    (17)  op(e1, e1) = e0
% 231.95/43.06    (18)  op(e2, e0) = all_53_13
% 231.95/43.06    (19)  op(e1, e2) = all_52_19
% 231.95/43.06    (20)  all_55_15 = e1 | all_55_15 = e0
% 231.95/43.06    (21)  op(all_52_19, all_52_19) = e2
% 231.95/43.06    (22)   ~ (all_4_2 = e1)
% 231.95/43.06    (23)  op(all_52_21, all_52_21) = e1
% 231.95/43.06    (24)  op(e3, e0) = all_53_12
% 231.95/43.06  
% 231.95/43.06  Begin of proof
% 231.95/43.06  | 
% 231.95/43.06  | BETA: splitting (20) gives:
% 231.95/43.06  | 
% 231.95/43.06  | Case 1:
% 231.95/43.06  | | 
% 231.95/43.06  | |   (25)  all_55_15 = e1
% 231.95/43.06  | | 
% 231.95/43.06  | | REF_CLOSE: (4), (22), (25) are inconsistent by sub-proof #2501.
% 231.95/43.06  | | 
% 231.95/43.06  | Case 2:
% 231.95/43.06  | | 
% 231.95/43.06  | |   (26)  all_55_15 = e0
% 231.95/43.06  | | 
% 231.95/43.06  | | COMBINE_EQS: (4), (26) imply:
% 231.95/43.06  | |   (27)  all_4_2 = e0
% 231.95/43.06  | | 
% 231.95/43.06  | | SIMP: (27) implies:
% 231.95/43.06  | |   (28)  all_4_2 = e0
% 231.95/43.06  | | 
% 231.95/43.06  | | REDUCE: (10), (28) imply:
% 231.95/43.06  | |   (29)   ~ (all_53_7 = e0)
% 231.95/43.06  | | 
% 231.95/43.06  | | REDUCE: (2), (28) imply:
% 231.95/43.06  | |   (30)   ~ (all_53_12 = e0)
% 231.95/43.06  | | 
% 231.95/43.06  | | REDUCE: (14), (28) imply:
% 231.95/43.06  | |   (31)   ~ (all_53_13 = e0)
% 231.95/43.06  | | 
% 231.95/43.06  | | REDUCE: (7), (28) imply:
% 231.95/43.06  | |   (32)   ~ (all_53_14 = e0)
% 231.95/43.06  | | 
% 231.95/43.06  | | REDUCE: (9), (28) imply:
% 231.95/43.06  | |   (33)   ~ (e2 = e0)
% 231.95/43.06  | | 
% 231.95/43.06  | | SIMP: (33) implies:
% 231.95/43.06  | |   (34)   ~ (e2 = e0)
% 231.95/43.06  | | 
% 231.95/43.06  | | REDUCE: (22), (28) imply:
% 231.95/43.06  | |   (35)   ~ (e1 = e0)
% 231.95/43.06  | | 
% 231.95/43.06  | | SIMP: (35) implies:
% 231.95/43.06  | |   (36)   ~ (e1 = e0)
% 231.95/43.06  | | 
% 231.95/43.06  | | REDUCE: (1), (28) imply:
% 231.95/43.06  | |   (37)  op(e0, e0) = e0
% 231.95/43.06  | | 
% 231.95/43.06  | | REF_CLOSE: (3), (5), (6), (8), (11), (12), (13), (15), (16), (17), (18),
% 231.95/43.06  | |            (19), (21), (23), (24), (29), (30), (31), (32), (34), (36), (37)
% 231.95/43.06  | |            are inconsistent by sub-proof #1840.
% 231.95/43.06  | | 
% 231.95/43.06  | End of split
% 231.95/43.06  | 
% 231.95/43.06  End of proof
% 231.95/43.06  
% 231.95/43.06  Sub-proof #1840 shows that the following formulas are inconsistent:
% 231.95/43.06  ----------------------------------------------------------------
% 231.95/43.06    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.95/43.06           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.95/43.06    (2)  op(e2, e2) = e1
% 231.95/43.06    (3)   ~ (all_53_4 = e1)
% 231.95/43.06    (4)  op(e1, e0) = all_53_14
% 231.95/43.06    (5)   ~ (all_53_7 = e0)
% 231.95/43.06    (6)  op(e3, e2) = all_53_4
% 231.95/43.06    (7)  op(e1, e1) = all_52_21
% 231.95/43.06    (8)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 231.95/43.06         (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 231.95/43.06    (9)   ~ (e2 = e0)
% 231.95/43.06    (10)   ~ (e1 = e0)
% 231.95/43.06    (11)  op(e0, e0) = e0
% 231.95/43.06    (12)   ~ (all_53_14 = e0)
% 231.95/43.06    (13)  op(e0, e2) = all_53_7
% 231.95/43.06    (14)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.95/43.06              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.95/43.06                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.95/43.06                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.95/43.06    (15)  op(e1, e1) = e0
% 231.95/43.06    (16)   ~ (all_53_13 = e0)
% 231.95/43.06    (17)  op(e2, e0) = all_53_13
% 231.95/43.06    (18)  op(e1, e2) = all_52_19
% 231.95/43.06    (19)  op(all_52_19, all_52_19) = e2
% 231.95/43.06    (20)   ~ (all_53_12 = e0)
% 231.95/43.06    (21)  op(all_52_21, all_52_21) = e1
% 231.95/43.06    (22)  op(e3, e0) = all_53_12
% 231.95/43.06  
% 231.95/43.06  Begin of proof
% 231.95/43.06  | 
% 231.95/43.06  | BETA: splitting (8) gives:
% 231.95/43.06  | 
% 231.95/43.06  | Case 1:
% 231.95/43.06  | | 
% 231.95/43.06  | |   (23)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) =
% 231.95/43.06  | |           e0)
% 231.95/43.06  | | 
% 231.95/43.06  | | BETA: splitting (23) gives:
% 231.95/43.06  | | 
% 231.95/43.06  | | Case 1:
% 231.95/43.06  | | | 
% 231.95/43.06  | | |   (24)  all_57_1 = e0 & op(e3, e2) = e0
% 231.95/43.06  | | | 
% 231.95/43.06  | | | REF_CLOSE: (1), (3), (4), (6), (7), (12), (14), (15), (16), (17), (20),
% 231.95/43.06  | | |            (21), (22), (24) are inconsistent by sub-proof #1842.
% 231.95/43.06  | | | 
% 231.95/43.06  | | Case 2:
% 231.95/43.06  | | | 
% 231.95/43.06  | | |   (25)  all_57_3 = e0 & op(e2, e2) = e0
% 231.95/43.06  | | | 
% 231.95/43.06  | | | ALPHA: (25) implies:
% 231.95/43.06  | | |   (26)  op(e2, e2) = e0
% 231.95/43.06  | | | 
% 231.95/43.06  | | | REF_CLOSE: (1), (2), (10), (26) are inconsistent by sub-proof #2352.
% 231.95/43.06  | | | 
% 231.95/43.06  | | End of split
% 231.95/43.06  | | 
% 231.95/43.06  | Case 2:
% 231.95/43.06  | | 
% 231.95/43.06  | |   (27)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 231.95/43.06  | |           e0)
% 231.95/43.06  | | 
% 231.95/43.06  | | REF_CLOSE: (1), (5), (9), (11), (13), (18), (19), (27) are inconsistent by
% 231.95/43.06  | |            sub-proof #1841.
% 231.95/43.06  | | 
% 231.95/43.06  | End of split
% 231.95/43.06  | 
% 231.95/43.06  End of proof
% 231.95/43.06  
% 231.95/43.06  Sub-proof #1841 shows that the following formulas are inconsistent:
% 231.95/43.06  ----------------------------------------------------------------
% 231.95/43.06    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.95/43.06           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.95/43.06    (2)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 231.95/43.06    (3)   ~ (all_53_7 = e0)
% 231.95/43.06    (4)   ~ (e2 = e0)
% 231.95/43.06    (5)  op(e0, e0) = e0
% 231.95/43.06    (6)  op(e0, e2) = all_53_7
% 231.95/43.06    (7)  op(e1, e2) = all_52_19
% 231.95/43.06    (8)  op(all_52_19, all_52_19) = e2
% 231.95/43.06  
% 231.95/43.06  Begin of proof
% 231.95/43.06  | 
% 231.95/43.06  | BETA: splitting (2) gives:
% 231.95/43.06  | 
% 231.95/43.06  | Case 1:
% 231.95/43.06  | | 
% 231.95/43.06  | |   (9)  all_57_7 = e0 & op(e1, e2) = e0
% 231.95/43.06  | | 
% 231.95/43.06  | | ALPHA: (9) implies:
% 231.95/43.06  | |   (10)  op(e1, e2) = e0
% 231.95/43.06  | | 
% 231.95/43.06  | | REF_CLOSE: (1), (4), (5), (7), (8), (10) are inconsistent by sub-proof
% 231.95/43.06  | |            #2158.
% 231.95/43.06  | | 
% 231.95/43.06  | Case 2:
% 231.95/43.06  | | 
% 231.95/43.06  | |   (11)  all_57_13 = e0 & op(e0, e2) = e0
% 231.95/43.06  | | 
% 231.95/43.06  | | ALPHA: (11) implies:
% 231.95/43.06  | |   (12)  op(e0, e2) = e0
% 231.95/43.06  | | 
% 231.95/43.06  | | REF_CLOSE: (1), (3), (6), (12) are inconsistent by sub-proof #2332.
% 231.95/43.06  | | 
% 231.95/43.06  | End of split
% 231.95/43.06  | 
% 231.95/43.06  End of proof
% 231.95/43.06  
% 231.95/43.06  Sub-proof #1842 shows that the following formulas are inconsistent:
% 231.95/43.06  ----------------------------------------------------------------
% 231.95/43.06    (1)  all_57_1 = e0 & op(e3, e2) = e0
% 231.95/43.06    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.95/43.06           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.95/43.06    (3)   ~ (all_53_4 = e1)
% 231.95/43.06    (4)  op(e1, e0) = all_53_14
% 231.95/43.06    (5)  op(e3, e2) = all_53_4
% 231.95/43.06    (6)  op(e1, e1) = all_52_21
% 231.95/43.06    (7)   ~ (all_53_14 = e0)
% 231.95/43.06    (8)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.95/43.06             | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 231.95/43.06               e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.95/43.06               op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.95/43.06    (9)  op(e1, e1) = e0
% 231.95/43.06    (10)   ~ (all_53_13 = e0)
% 231.95/43.06    (11)  op(e2, e0) = all_53_13
% 231.95/43.06    (12)   ~ (all_53_12 = e0)
% 231.95/43.06    (13)  op(all_52_21, all_52_21) = e1
% 231.95/43.06    (14)  op(e3, e0) = all_53_12
% 231.95/43.06  
% 231.95/43.06  Begin of proof
% 231.95/43.06  | 
% 231.95/43.06  | BETA: splitting (8) gives:
% 231.95/43.06  | 
% 231.95/43.06  | Case 1:
% 231.95/43.06  | | 
% 231.95/43.06  | |   (15)  all_57_15 = e0 & op(e0, e0) = e0
% 231.95/43.06  | | 
% 231.95/43.06  | | ALPHA: (15) implies:
% 231.95/43.06  | |   (16)  op(e0, e0) = e0
% 231.95/43.06  | | 
% 231.95/43.06  | | ALPHA: (1) implies:
% 231.95/43.06  | |   (17)  op(e3, e2) = e0
% 231.95/43.06  | | 
% 231.95/43.06  | | GROUND_INST: instantiating (2) with e0, all_52_21, e1, e1, simplifying with
% 231.95/43.06  | |              (6), (9) gives:
% 231.95/43.06  | |   (18)  all_52_21 = e0
% 231.95/43.06  | | 
% 231.95/43.06  | | GROUND_INST: instantiating (2) with all_53_4, e0, e2, e3, simplifying with
% 231.95/43.06  | |              (5), (17) gives:
% 231.95/43.06  | |   (19)  all_53_4 = e0
% 231.95/43.06  | | 
% 231.95/43.06  | | REDUCE: (3), (19) imply:
% 231.95/43.06  | |   (20)   ~ (e1 = e0)
% 231.95/43.06  | | 
% 231.95/43.06  | | SIMP: (20) implies:
% 231.95/43.06  | |   (21)   ~ (e1 = e0)
% 231.95/43.06  | | 
% 231.95/43.06  | | REDUCE: (13), (18) imply:
% 231.95/43.06  | |   (22)  op(e0, e0) = e1
% 231.95/43.06  | | 
% 231.95/43.06  | | REF_CLOSE: (2), (16), (21), (22) are inconsistent by sub-proof #2290.
% 231.95/43.06  | | 
% 231.95/43.06  | Case 2:
% 231.95/43.06  | | 
% 231.95/43.06  | |   (23)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 231.95/43.06  | |             e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0 &
% 231.95/43.06  | |             op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 231.95/43.06  | |           (all_57_14 = e0 & op(e0, e1) = e0))
% 231.95/43.06  | | 
% 231.95/43.06  | | REF_CLOSE: (2), (4), (7), (10), (11), (12), (14), (23) are inconsistent by
% 231.95/43.06  | |            sub-proof #2112.
% 231.95/43.06  | | 
% 231.95/43.06  | End of split
% 231.95/43.06  | 
% 231.95/43.06  End of proof
% 231.95/43.06  
% 231.95/43.06  Sub-proof #1843 shows that the following formulas are inconsistent:
% 231.95/43.06  ----------------------------------------------------------------
% 231.95/43.06    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.95/43.06           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.95/43.06    (2)  op(e2, e2) = e1
% 231.95/43.06    (3)  op(e2, e2) = all_52_11
% 231.95/43.06    (4)   ~ (e2 = e0)
% 231.95/43.06    (5)  op(e1, e1) = e0
% 231.95/43.06    (6)  op(all_52_11, all_52_11) = e2
% 231.95/43.06  
% 231.95/43.06  Begin of proof
% 231.95/43.06  | 
% 231.95/43.06  | GROUND_INST: instantiating (1) with e1, all_52_11, e2, e2, simplifying with
% 231.95/43.06  |              (2), (3) gives:
% 231.95/43.06  |   (7)  all_52_11 = e1
% 231.95/43.06  | 
% 231.95/43.06  | REDUCE: (6), (7) imply:
% 231.95/43.06  |   (8)  op(e1, e1) = e2
% 231.95/43.06  | 
% 231.95/43.07  | GROUND_INST: instantiating (1) with e0, e2, e1, e1, simplifying with (5), (8)
% 231.95/43.07  |              gives:
% 231.95/43.07  |   (9)  e2 = e0
% 231.95/43.07  | 
% 231.95/43.07  | REDUCE: (4), (9) imply:
% 231.95/43.07  |   (10)  $false
% 231.95/43.07  | 
% 231.95/43.07  | CLOSE: (10) is inconsistent.
% 231.95/43.07  | 
% 231.95/43.07  End of proof
% 231.95/43.07  
% 231.95/43.07  Sub-proof #1844 shows that the following formulas are inconsistent:
% 231.95/43.07  ----------------------------------------------------------------
% 231.95/43.07    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.95/43.07           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.95/43.07    (2)   ~ (e3 = e2)
% 231.95/43.07    (3)  all_57_6 = e0
% 231.95/43.07    (4)  op(e1, e1) = e1
% 231.95/43.07    (5)   ~ (e2 = e0)
% 231.95/43.07    (6)  all_57_7 = e3
% 231.95/43.07    (7)  all_57_11 = e1
% 231.95/43.07    (8)   ~ (e2 = e1)
% 231.95/43.07    (9)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 231.95/43.07         (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 231.95/43.07  
% 231.95/43.07  Begin of proof
% 231.95/43.07  | 
% 231.95/43.07  | BETA: splitting (9) gives:
% 231.95/43.07  | 
% 231.95/43.07  | Case 1:
% 231.95/43.07  | | 
% 231.95/43.07  | |   (10)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) =
% 231.95/43.07  | |           e2)
% 231.95/43.07  | | 
% 231.95/43.07  | | REF_CLOSE: (2), (3), (5), (6), (10) are inconsistent by sub-proof #1845.
% 231.95/43.07  | | 
% 231.95/43.07  | Case 2:
% 231.95/43.07  | | 
% 231.95/43.07  | |   (11)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) =
% 231.95/43.07  | |           e2)
% 231.95/43.07  | | 
% 231.95/43.07  | | REF_CLOSE: (1), (4), (7), (8), (11) are inconsistent by sub-proof #1932.
% 231.95/43.07  | | 
% 231.95/43.07  | End of split
% 231.95/43.07  | 
% 231.95/43.07  End of proof
% 231.95/43.07  
% 231.95/43.07  Sub-proof #1845 shows that the following formulas are inconsistent:
% 231.95/43.07  ----------------------------------------------------------------
% 231.95/43.07    (1)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2)
% 231.95/43.07    (2)   ~ (e3 = e2)
% 231.95/43.07    (3)  all_57_6 = e0
% 231.95/43.07    (4)   ~ (e2 = e0)
% 231.95/43.07    (5)  all_57_7 = e3
% 231.95/43.07  
% 231.95/43.07  Begin of proof
% 231.95/43.07  | 
% 231.95/43.07  | BETA: splitting (1) gives:
% 231.95/43.07  | 
% 231.95/43.07  | Case 1:
% 231.95/43.07  | | 
% 231.95/43.07  | |   (6)  all_57_6 = e2 & op(e1, e3) = e2
% 231.95/43.07  | | 
% 231.95/43.07  | | ALPHA: (6) implies:
% 231.95/43.07  | |   (7)  all_57_6 = e2
% 231.95/43.07  | | 
% 231.95/43.07  | | REF_CLOSE: (3), (4), (7) are inconsistent by sub-proof #1846.
% 231.95/43.07  | | 
% 231.95/43.07  | Case 2:
% 231.95/43.07  | | 
% 231.95/43.07  | |   (8)  all_57_7 = e2 & op(e1, e2) = e2
% 231.95/43.07  | | 
% 231.95/43.07  | | REF_CLOSE: (2), (5), (8) are inconsistent by sub-proof #2092.
% 231.95/43.07  | | 
% 231.95/43.07  | End of split
% 231.95/43.07  | 
% 231.95/43.07  End of proof
% 231.95/43.07  
% 231.95/43.07  Sub-proof #1846 shows that the following formulas are inconsistent:
% 231.95/43.07  ----------------------------------------------------------------
% 231.95/43.07    (1)  all_57_6 = e2
% 231.95/43.07    (2)  all_57_6 = e0
% 231.95/43.07    (3)   ~ (e2 = e0)
% 231.95/43.07  
% 231.95/43.07  Begin of proof
% 231.95/43.07  | 
% 231.95/43.07  | COMBINE_EQS: (1), (2) imply:
% 231.95/43.07  |   (4)  e2 = e0
% 231.95/43.07  | 
% 231.95/43.07  | SIMP: (4) implies:
% 231.95/43.07  |   (5)  e2 = e0
% 231.95/43.07  | 
% 231.95/43.07  | REDUCE: (3), (5) imply:
% 231.95/43.07  |   (6)  $false
% 231.95/43.07  | 
% 231.95/43.07  | CLOSE: (6) is inconsistent.
% 231.95/43.07  | 
% 231.95/43.07  End of proof
% 231.95/43.07  
% 231.95/43.07  Sub-proof #1847 shows that the following formulas are inconsistent:
% 231.95/43.07  ----------------------------------------------------------------
% 231.95/43.07    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 231.95/43.07         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 231.95/43.07    (2)  op(e2, e3) = all_53_1
% 231.95/43.07    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 231.95/43.07         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.95/43.07    (4)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.95/43.07         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.95/43.07    (5)   ~ (e3 = e1)
% 231.95/43.07    (6)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 231.95/43.07         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 231.95/43.07    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.95/43.07           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.95/43.07    (8)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 231.95/43.07         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.95/43.07    (9)   ~ (all_6_2 = e3)
% 231.95/43.07    (10)  op(e1, e1) = all_6_2
% 231.95/43.07    (11)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 231.95/43.07    (12)  op(e2, e2) = e1
% 231.95/43.07    (13)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 231.95/43.07          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 231.95/43.07    (14)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 231.95/43.07          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 231.95/43.07    (15)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 231.95/43.07          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 231.95/43.07    (16)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.95/43.07          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.95/43.07    (17)   ~ (e3 = e2)
% 231.95/43.07    (18)  op(e1, e0) = all_53_14
% 231.95/43.07    (19)   ~ (e3 = e0)
% 231.95/43.07    (20)  op(e3, e3) = e3
% 231.95/43.07    (21)  op(e0, e3) = all_53_3
% 231.95/43.07    (22)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.95/43.07          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.95/43.07            e1)
% 231.95/43.07    (23)   ~ (all_53_1 = e1)
% 231.95/43.07    (24)  op(e3, e2) = all_53_4
% 231.95/43.07    (25)  op(e1, e1) = e1
% 231.95/43.07    (26)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 231.95/43.07          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 231.95/43.07    (27)   ~ (e2 = e0)
% 231.95/43.07    (28)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 231.95/43.07            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 231.95/43.07            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 231.95/43.07            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 231.95/43.07              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 231.95/43.07            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 231.95/43.07            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 231.95/43.07              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 231.95/43.07              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 231.95/43.07            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 231.95/43.07            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 231.95/43.07            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 231.95/43.07              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 231.95/43.07              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 231.95/43.07            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 231.95/43.07              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 231.95/43.07            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 231.95/43.07            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 231.95/43.07              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 231.95/43.07              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 231.95/43.07            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 231.95/43.07            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 231.95/43.07    (29)  all_57_3 = e1
% 231.95/43.07    (30)   ~ (e1 = e0)
% 231.95/43.07    (31)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.95/43.07          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.95/43.07    (32)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.95/43.07          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.95/43.07    (33)  op(e0, e0) = e0
% 231.95/43.07    (34)   ~ (all_53_14 = e0)
% 231.95/43.07    (35)   ~ (all_53_13 = e0)
% 231.95/43.07    (36)  op(e2, e0) = all_53_13
% 231.95/43.07    (37)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.95/43.07          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.95/43.07    (38)  all_55_11 = all_53_14
% 231.95/43.07    (39)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.95/43.07          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.95/43.07    (40)   ~ (all_53_12 = e0)
% 231.95/43.07    (41)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 231.95/43.07          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 231.95/43.07    (42)   ~ (e2 = e1)
% 231.95/43.07    (43)   ~ (all_6_2 = e0)
% 231.95/43.07    (44)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.95/43.07          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.95/43.07    (45)  all_57_9 = e1 & op(e3, e0) = e1
% 231.95/43.07    (46)   ~ (all_53_12 = all_53_14)
% 231.95/43.07    (47)   ~ (all_53_4 = e3)
% 231.95/43.07    (48)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 231.95/43.07          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 231.95/43.07    (49)  op(e3, e0) = all_53_12
% 231.95/43.07  
% 231.95/43.07  Begin of proof
% 231.95/43.07  | 
% 231.95/43.07  | ALPHA: (45) implies:
% 231.95/43.07  |   (50)  all_57_9 = e1
% 231.95/43.07  |   (51)  op(e3, e0) = e1
% 231.95/43.07  | 
% 231.95/43.07  | BETA: splitting (22) gives:
% 231.95/43.07  | 
% 231.95/43.07  | Case 1:
% 231.95/43.07  | | 
% 231.95/43.07  | |   (52)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 231.95/43.07  | |           e1)
% 231.95/43.07  | | 
% 231.95/43.07  | | BETA: splitting (52) gives:
% 231.95/43.07  | | 
% 231.95/43.07  | | Case 1:
% 231.95/43.07  | | | 
% 231.95/43.07  | | |   (53)  all_57_12 = e1 & op(e0, e3) = e1
% 231.95/43.07  | | | 
% 231.95/43.07  | | | REF_CLOSE: (7), (9), (10), (11), (12), (18), (20), (21), (25), (28), (34),
% 231.95/43.07  | | |            (38), (40), (42), (46), (49), (51), (53) are inconsistent by
% 231.95/43.07  | | |            sub-proof #1852.
% 231.95/43.07  | | | 
% 231.95/43.07  | | Case 2:
% 231.95/43.07  | | | 
% 231.95/43.07  | | |   (54)  all_57_13 = e1 & op(e0, e2) = e1
% 231.95/43.07  | | | 
% 231.95/43.07  | | | ALPHA: (54) implies:
% 231.95/43.07  | | |   (55)  all_57_13 = e1
% 231.95/43.07  | | | 
% 231.95/43.07  | | | BETA: splitting (32) gives:
% 231.95/43.07  | | | 
% 231.95/43.07  | | | Case 1:
% 231.95/43.07  | | | | 
% 231.95/43.07  | | | |   (56)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2)
% 231.95/43.07  | | | |           = e3)
% 231.95/43.07  | | | | 
% 231.95/43.07  | | | | REF_CLOSE: (5), (7), (12), (24), (47), (56) are inconsistent by
% 231.95/43.07  | | | |            sub-proof #1851.
% 231.95/43.07  | | | | 
% 231.95/43.07  | | | Case 2:
% 231.95/43.07  | | | | 
% 231.95/43.07  | | | |   (57)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2)
% 231.95/43.07  | | | |           = e3)
% 231.95/43.07  | | | | 
% 231.95/43.07  | | | | BETA: splitting (57) gives:
% 231.95/43.07  | | | | 
% 231.95/43.07  | | | | Case 1:
% 231.95/43.07  | | | | | 
% 231.95/43.07  | | | | |   (58)  all_57_7 = e3 & op(e1, e2) = e3
% 231.95/43.07  | | | | | 
% 231.95/43.07  | | | | | ALPHA: (58) implies:
% 231.95/43.07  | | | | |   (59)  all_57_7 = e3
% 231.95/43.07  | | | | | 
% 231.95/43.07  | | | | | BETA: splitting (3) gives:
% 231.95/43.07  | | | | | 
% 231.95/43.07  | | | | | Case 1:
% 231.95/43.07  | | | | | | 
% 231.95/43.07  | | | | | |   (60)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2,
% 231.95/43.07  | | | | | |             e3) = e1)
% 231.95/43.07  | | | | | | 
% 231.95/43.07  | | | | | | REF_CLOSE: (2), (5), (7), (20), (23), (60) are inconsistent by
% 231.95/43.07  | | | | | |            sub-proof #2155.
% 231.95/43.07  | | | | | | 
% 231.95/43.07  | | | | | Case 2:
% 231.95/43.07  | | | | | | 
% 231.95/43.07  | | | | | |   (61)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0,
% 231.95/43.07  | | | | | |             e3) = e1)
% 231.95/43.07  | | | | | | 
% 231.95/43.07  | | | | | | BETA: splitting (61) gives:
% 231.95/43.07  | | | | | | 
% 231.95/43.07  | | | | | | Case 1:
% 231.95/43.07  | | | | | | | 
% 231.95/43.07  | | | | | | |   (62)  all_57_6 = e1 & op(e1, e3) = e1
% 231.95/43.07  | | | | | | | 
% 231.95/43.07  | | | | | | | ALPHA: (62) implies:
% 231.95/43.07  | | | | | | |   (63)  all_57_6 = e1
% 231.95/43.07  | | | | | | | 
% 231.95/43.07  | | | | | | | BETA: splitting (48) gives:
% 231.95/43.07  | | | | | | | 
% 231.95/43.07  | | | | | | | Case 1:
% 231.95/43.07  | | | | | | | | 
% 231.95/43.07  | | | | | | | |   (64)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 &
% 231.95/43.07  | | | | | | | |           op(e1, e2) = e2)
% 231.95/43.07  | | | | | | | | 
% 231.95/43.07  | | | | | | | | REF_CLOSE: (17), (42), (59), (63), (64) are inconsistent by
% 231.95/43.07  | | | | | | | |            sub-proof #2006.
% 231.95/43.07  | | | | | | | | 
% 231.95/43.07  | | | | | | | Case 2:
% 231.95/43.07  | | | | | | | | 
% 231.95/43.07  | | | | | | | |   (65)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 &
% 231.95/43.07  | | | | | | | |           op(e1, e0) = e2)
% 231.95/43.07  | | | | | | | | 
% 231.95/43.07  | | | | | | | | BETA: splitting (65) gives:
% 231.95/43.07  | | | | | | | | 
% 231.95/43.07  | | | | | | | | Case 1:
% 231.95/43.07  | | | | | | | | | 
% 231.95/43.07  | | | | | | | | |   (66)  all_57_8 = e2 & op(e1, e1) = e2
% 231.95/43.07  | | | | | | | | | 
% 231.95/43.07  | | | | | | | | | ALPHA: (66) implies:
% 231.95/43.07  | | | | | | | | |   (67)  op(e1, e1) = e2
% 231.95/43.07  | | | | | | | | | 
% 231.95/43.07  | | | | | | | | | REF_CLOSE: (7), (25), (42), (67) are inconsistent by sub-proof
% 231.95/43.07  | | | | | | | | |            #2423.
% 231.95/43.07  | | | | | | | | | 
% 231.95/43.07  | | | | | | | | Case 2:
% 231.95/43.07  | | | | | | | | | 
% 231.95/43.07  | | | | | | | | |   (68)  all_57_11 = e2 & op(e1, e0) = e2
% 231.95/43.07  | | | | | | | | | 
% 231.95/43.07  | | | | | | | | | ALPHA: (68) implies:
% 231.95/43.07  | | | | | | | | |   (69)  all_57_11 = e2
% 231.95/43.07  | | | | | | | | | 
% 231.95/43.07  | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (10), (17), (18), (19),
% 231.95/43.07  | | | | | | | | |            (30), (34), (43), (63), (69) are inconsistent by
% 231.95/43.07  | | | | | | | | |            sub-proof #2340.
% 231.95/43.07  | | | | | | | | | 
% 231.95/43.07  | | | | | | | | End of split
% 231.95/43.07  | | | | | | | | 
% 231.95/43.07  | | | | | | | End of split
% 231.95/43.07  | | | | | | | 
% 231.95/43.07  | | | | | | Case 2:
% 231.95/43.07  | | | | | | | 
% 231.95/43.07  | | | | | | |   (70)  all_57_12 = e1 & op(e0, e3) = e1
% 231.95/43.07  | | | | | | | 
% 231.95/43.07  | | | | | | | REF_CLOSE: (7), (9), (10), (11), (12), (18), (20), (21), (25),
% 231.95/43.07  | | | | | | |            (28), (34), (38), (40), (42), (46), (49), (51), (70)
% 231.95/43.07  | | | | | | |            are inconsistent by sub-proof #1852.
% 231.95/43.07  | | | | | | | 
% 231.95/43.07  | | | | | | End of split
% 231.95/43.07  | | | | | | 
% 231.95/43.07  | | | | | End of split
% 231.95/43.07  | | | | | 
% 231.95/43.07  | | | | Case 2:
% 231.95/43.07  | | | | | 
% 231.95/43.07  | | | | |   (71)  all_57_13 = e3 & op(e0, e2) = e3
% 231.95/43.07  | | | | | 
% 231.95/43.07  | | | | | ALPHA: (71) implies:
% 231.95/43.07  | | | | |   (72)  all_57_13 = e3
% 231.95/43.07  | | | | | 
% 231.95/43.07  | | | | | REF_CLOSE: (5), (55), (72) are inconsistent by sub-proof #2268.
% 231.95/43.07  | | | | | 
% 231.95/43.07  | | | | End of split
% 231.95/43.07  | | | | 
% 231.95/43.07  | | | End of split
% 231.95/43.07  | | | 
% 231.95/43.07  | | End of split
% 231.95/43.07  | | 
% 231.95/43.07  | Case 2:
% 231.95/43.07  | | 
% 231.95/43.07  | |   (73)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.95/43.07  | |           e1)
% 231.95/43.07  | | 
% 231.95/43.07  | | BETA: splitting (73) gives:
% 231.95/43.07  | | 
% 231.95/43.07  | | Case 1:
% 231.95/43.07  | | | 
% 231.95/43.07  | | |   (74)  all_57_14 = e1 & op(e0, e1) = e1
% 231.95/43.07  | | | 
% 231.95/43.07  | | | ALPHA: (74) implies:
% 231.95/43.07  | | |   (75)  all_57_14 = e1
% 231.95/43.07  | | | 
% 231.95/43.07  | | | BETA: splitting (31) gives:
% 231.95/43.07  | | | 
% 231.95/43.07  | | | Case 1:
% 231.95/43.07  | | | | 
% 231.95/43.07  | | | |   (76)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1)
% 231.95/43.07  | | | |           = e3)
% 231.95/43.07  | | | | 
% 231.95/43.07  | | | | BETA: splitting (76) gives:
% 231.95/43.07  | | | | 
% 231.95/43.07  | | | | Case 1:
% 231.95/43.07  | | | | | 
% 231.95/43.07  | | | | |   (77)  all_57_4 = e3 & op(e3, e1) = e3
% 231.95/43.07  | | | | | 
% 231.95/43.07  | | | | | ALPHA: (77) implies:
% 231.95/43.07  | | | | |   (78)  all_57_4 = e3
% 231.95/43.07  | | | | | 
% 231.95/43.07  | | | | | REF_CLOSE: (5), (7), (13), (14), (15), (17), (19), (20), (27), (30),
% 231.95/43.07  | | | | |            (42), (78) are inconsistent by sub-proof #2474.
% 231.95/43.07  | | | | | 
% 231.95/43.07  | | | | Case 2:
% 231.95/43.07  | | | | | 
% 231.95/43.07  | | | | |   (79)  all_57_5 = e3 & op(e2, e1) = e3
% 231.95/43.07  | | | | | 
% 231.95/43.07  | | | | | ALPHA: (79) implies:
% 231.95/43.07  | | | | |   (80)  all_57_5 = e3
% 231.95/43.07  | | | | | 
% 231.95/43.07  | | | | | BETA: splitting (41) gives:
% 231.95/43.07  | | | | | 
% 231.95/43.07  | | | | | Case 1:
% 231.95/43.07  | | | | | | 
% 231.95/43.07  | | | | | |   (81)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2,
% 231.95/43.07  | | | | | |             e2) = e0)
% 231.95/43.07  | | | | | | 
% 231.95/43.07  | | | | | | BETA: splitting (81) gives:
% 231.95/43.07  | | | | | | 
% 231.95/43.07  | | | | | | Case 1:
% 231.95/43.07  | | | | | | | 
% 231.95/43.07  | | | | | | |   (82)  all_57_2 = e0 & op(e2, e3) = e0
% 231.95/43.07  | | | | | | | 
% 231.95/43.07  | | | | | | | ALPHA: (82) implies:
% 231.95/43.07  | | | | | | |   (83)  all_57_2 = e0
% 231.95/43.07  | | | | | | | 
% 231.95/43.07  | | | | | | | BETA: splitting (16) gives:
% 231.95/43.07  | | | | | | | 
% 231.95/43.07  | | | | | | | Case 1:
% 231.95/43.07  | | | | | | | | 
% 231.95/43.07  | | | | | | | |   (84)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 &
% 231.95/43.07  | | | | | | | |           op(e2, e1) = e0)
% 231.95/43.07  | | | | | | | | 
% 231.95/43.07  | | | | | | | | BETA: splitting (84) gives:
% 231.95/43.07  | | | | | | | | 
% 231.95/43.07  | | | | | | | | Case 1:
% 231.95/43.07  | | | | | | | | | 
% 231.95/43.07  | | | | | | | | |   (85)  all_57_4 = e0 & op(e3, e1) = e0
% 231.95/43.07  | | | | | | | | | 
% 231.95/43.07  | | | | | | | | | ALPHA: (85) implies:
% 231.95/43.07  | | | | | | | | |   (86)  all_57_4 = e0
% 231.95/43.07  | | | | | | | | | 
% 231.95/43.07  | | | | | | | | | BETA: splitting (14) gives:
% 231.95/43.07  | | | | | | | | | 
% 231.95/43.07  | | | | | | | | | Case 1:
% 231.95/43.07  | | | | | | | | | | 
% 231.95/43.07  | | | | | | | | | |   (87)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 &
% 231.95/43.07  | | | | | | | | | |           op(e3, e2) = e2)
% 231.95/43.07  | | | | | | | | | | 
% 231.95/43.07  | | | | | | | | | | BETA: splitting (87) gives:
% 231.95/43.07  | | | | | | | | | | 
% 231.95/43.07  | | | | | | | | | | Case 1:
% 231.95/43.07  | | | | | | | | | | | 
% 231.95/43.07  | | | | | | | | | | |   (88)  all_57_0 = e2 & op(e3, e3) = e2
% 231.95/43.07  | | | | | | | | | | | 
% 231.95/43.07  | | | | | | | | | | | ALPHA: (88) implies:
% 231.95/43.07  | | | | | | | | | | |   (89)  op(e3, e3) = e2
% 231.95/43.07  | | | | | | | | | | | 
% 231.95/43.07  | | | | | | | | | | | REF_CLOSE: (7), (17), (20), (89) are inconsistent by
% 231.95/43.07  | | | | | | | | | | |            sub-proof #2490.
% 231.95/43.07  | | | | | | | | | | | 
% 231.95/43.07  | | | | | | | | | | Case 2:
% 231.95/43.07  | | | | | | | | | | | 
% 231.95/43.07  | | | | | | | | | | |   (90)  all_57_1 = e2 & op(e3, e2) = e2
% 231.95/43.07  | | | | | | | | | | | 
% 231.95/43.07  | | | | | | | | | | | ALPHA: (90) implies:
% 231.95/43.07  | | | | | | | | | | |   (91)  all_57_1 = e2
% 231.95/43.07  | | | | | | | | | | | 
% 231.95/43.07  | | | | | | | | | | | BETA: splitting (44) gives:
% 231.95/43.07  | | | | | | | | | | | 
% 231.95/43.07  | | | | | | | | | | | Case 1:
% 231.95/43.07  | | | | | | | | | | | | 
% 231.95/43.07  | | | | | | | | | | | |   (92)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 231.95/43.07  | | | | | | | | | | | |           & op(e2, e1) = e2)
% 231.95/43.07  | | | | | | | | | | | | 
% 231.95/43.07  | | | | | | | | | | | | REF_CLOSE: (17), (27), (80), (86), (92) are inconsistent by
% 231.95/43.07  | | | | | | | | | | | |            sub-proof #2383.
% 231.95/43.07  | | | | | | | | | | | | 
% 231.95/43.07  | | | | | | | | | | | Case 2:
% 231.95/43.07  | | | | | | | | | | | | 
% 231.95/43.07  | | | | | | | | | | | |   (93)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 231.95/43.07  | | | | | | | | | | | |           e2 & op(e0, e1) = e2)
% 231.95/43.07  | | | | | | | | | | | | 
% 231.95/43.07  | | | | | | | | | | | | BETA: splitting (93) gives:
% 231.95/43.07  | | | | | | | | | | | | 
% 231.95/43.07  | | | | | | | | | | | | Case 1:
% 231.95/43.07  | | | | | | | | | | | | | 
% 231.95/43.07  | | | | | | | | | | | | |   (94)  all_57_8 = e2 & op(e1, e1) = e2
% 231.95/43.07  | | | | | | | | | | | | | 
% 231.95/43.07  | | | | | | | | | | | | | ALPHA: (94) implies:
% 231.95/43.07  | | | | | | | | | | | | |   (95)  op(e1, e1) = e2
% 231.95/43.07  | | | | | | | | | | | | | 
% 231.95/43.07  | | | | | | | | | | | | | REF_CLOSE: (7), (25), (42), (95) are inconsistent by
% 231.95/43.07  | | | | | | | | | | | | |            sub-proof #2423.
% 231.95/43.07  | | | | | | | | | | | | | 
% 231.95/43.07  | | | | | | | | | | | | Case 2:
% 231.95/43.07  | | | | | | | | | | | | | 
% 231.95/43.07  | | | | | | | | | | | | |   (96)  all_57_14 = e2 & op(e0, e1) = e2
% 231.95/43.07  | | | | | | | | | | | | | 
% 231.95/43.07  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (12), (17), (19), (26), (27), (30),
% 231.95/43.07  | | | | | | | | | | | | |            (32), (42), (75), (91), (96) are inconsistent by
% 231.95/43.07  | | | | | | | | | | | | |            sub-proof #1850.
% 231.95/43.07  | | | | | | | | | | | | | 
% 231.95/43.07  | | | | | | | | | | | | End of split
% 231.95/43.07  | | | | | | | | | | | | 
% 231.95/43.07  | | | | | | | | | | | End of split
% 231.95/43.07  | | | | | | | | | | | 
% 231.95/43.07  | | | | | | | | | | End of split
% 231.95/43.07  | | | | | | | | | | 
% 231.95/43.07  | | | | | | | | | Case 2:
% 231.95/43.07  | | | | | | | | | | 
% 231.95/43.07  | | | | | | | | | |   (97)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 &
% 231.95/43.07  | | | | | | | | | |           op(e3, e0) = e2)
% 231.95/43.07  | | | | | | | | | | 
% 231.95/43.07  | | | | | | | | | | BETA: splitting (97) gives:
% 231.95/43.07  | | | | | | | | | | 
% 231.95/43.07  | | | | | | | | | | Case 1:
% 231.95/43.07  | | | | | | | | | | | 
% 231.95/43.07  | | | | | | | | | | |   (98)  all_57_4 = e2 & op(e3, e1) = e2
% 231.95/43.07  | | | | | | | | | | | 
% 231.95/43.07  | | | | | | | | | | | ALPHA: (98) implies:
% 231.95/43.07  | | | | | | | | | | |   (99)  all_57_4 = e2
% 231.95/43.07  | | | | | | | | | | | 
% 231.95/43.07  | | | | | | | | | | | REF_CLOSE: (27), (86), (99) are inconsistent by sub-proof
% 231.95/43.07  | | | | | | | | | | |            #2441.
% 231.95/43.07  | | | | | | | | | | | 
% 231.95/43.07  | | | | | | | | | | Case 2:
% 231.95/43.07  | | | | | | | | | | | 
% 231.95/43.07  | | | | | | | | | | |   (100)  all_57_9 = e2 & op(e3, e0) = e2
% 231.95/43.07  | | | | | | | | | | | 
% 231.95/43.07  | | | | | | | | | | | REF_CLOSE: (42), (50), (100) are inconsistent by sub-proof
% 231.95/43.07  | | | | | | | | | | |            #2481.
% 231.95/43.07  | | | | | | | | | | | 
% 231.95/43.07  | | | | | | | | | | End of split
% 231.95/43.07  | | | | | | | | | | 
% 231.95/43.07  | | | | | | | | | End of split
% 231.95/43.07  | | | | | | | | | 
% 231.95/43.07  | | | | | | | | Case 2:
% 231.95/43.07  | | | | | | | | | 
% 231.95/43.07  | | | | | | | | |   (101)  all_57_5 = e0 & op(e2, e1) = e0
% 231.95/43.07  | | | | | | | | | 
% 231.95/43.07  | | | | | | | | | ALPHA: (101) implies:
% 231.95/43.07  | | | | | | | | |   (102)  all_57_5 = e0
% 231.95/43.07  | | | | | | | | | 
% 231.95/43.07  | | | | | | | | | REF_CLOSE: (5), (7), (12), (17), (19), (27), (37), (39), (42),
% 231.95/43.07  | | | | | | | | |            (83), (102) are inconsistent by sub-proof #1848.
% 231.95/43.07  | | | | | | | | | 
% 231.95/43.07  | | | | | | | | End of split
% 231.95/43.07  | | | | | | | | 
% 231.95/43.07  | | | | | | | Case 2:
% 231.95/43.07  | | | | | | | | 
% 231.95/43.07  | | | | | | | |   (103)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 &
% 231.95/43.07  | | | | | | | |            op(e0, e1) = e0)
% 231.95/43.07  | | | | | | | | 
% 231.95/43.07  | | | | | | | | BETA: splitting (103) gives:
% 231.95/43.07  | | | | | | | | 
% 231.95/43.07  | | | | | | | | Case 1:
% 231.95/43.07  | | | | | | | | | 
% 231.95/43.07  | | | | | | | | |   (104)  all_57_8 = e0 & op(e1, e1) = e0
% 231.95/43.07  | | | | | | | | | 
% 231.95/43.07  | | | | | | | | | ALPHA: (104) implies:
% 231.95/43.07  | | | | | | | | |   (105)  op(e1, e1) = e0
% 231.95/43.07  | | | | | | | | | 
% 231.95/43.07  | | | | | | | | | REF_CLOSE: (7), (25), (30), (105) are inconsistent by
% 231.95/43.07  | | | | | | | | |            sub-proof #2427.
% 231.95/43.07  | | | | | | | | | 
% 231.95/43.07  | | | | | | | | Case 2:
% 231.95/43.07  | | | | | | | | | 
% 231.95/43.07  | | | | | | | | |   (106)  all_57_14 = e0 & op(e0, e1) = e0
% 231.95/43.07  | | | | | | | | | 
% 231.95/43.07  | | | | | | | | | ALPHA: (106) implies:
% 231.95/43.07  | | | | | | | | |   (107)  all_57_14 = e0
% 231.95/43.07  | | | | | | | | | 
% 231.95/43.07  | | | | | | | | | COMBINE_EQS: (75), (107) imply:
% 231.95/43.07  | | | | | | | | |   (108)  e1 = e0
% 231.95/43.07  | | | | | | | | | 
% 231.95/43.07  | | | | | | | | | SIMP: (108) implies:
% 231.95/43.07  | | | | | | | | |   (109)  e1 = e0
% 231.95/43.07  | | | | | | | | | 
% 231.95/43.07  | | | | | | | | | COMBINE_EQS: (29), (109) imply:
% 231.95/43.07  | | | | | | | | |   (110)  all_57_3 = e0
% 231.95/43.07  | | | | | | | | | 
% 231.95/43.07  | | | | | | | | | REF_CLOSE: (1), (5), (17), (27), (30), (39), (42), (80), (83),
% 231.95/43.07  | | | | | | | | |            (110) are inconsistent by sub-proof #2253.
% 231.95/43.07  | | | | | | | | | 
% 231.95/43.07  | | | | | | | | End of split
% 231.95/43.07  | | | | | | | | 
% 231.95/43.07  | | | | | | | End of split
% 231.95/43.07  | | | | | | | 
% 231.95/43.07  | | | | | | Case 2:
% 231.95/43.07  | | | | | | | 
% 231.95/43.07  | | | | | | |   (111)  all_57_3 = e0 & op(e2, e2) = e0
% 231.95/43.07  | | | | | | | 
% 231.95/43.07  | | | | | | | ALPHA: (111) implies:
% 231.95/43.07  | | | | | | |   (112)  op(e2, e2) = e0
% 231.95/43.07  | | | | | | | 
% 231.95/43.07  | | | | | | | REF_CLOSE: (7), (12), (30), (112) are inconsistent by sub-proof
% 231.95/43.07  | | | | | | |            #2352.
% 231.95/43.07  | | | | | | | 
% 231.95/43.07  | | | | | | End of split
% 231.95/43.07  | | | | | | 
% 231.95/43.07  | | | | | Case 2:
% 231.95/43.07  | | | | | | 
% 231.95/43.07  | | | | | |   (113)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 &
% 231.95/43.07  | | | | | |            op(e2, e0) = e0)
% 231.95/43.07  | | | | | | 
% 231.95/43.07  | | | | | | REF_CLOSE: (7), (19), (35), (36), (80), (113) are inconsistent by
% 231.95/43.07  | | | | | |            sub-proof #2222.
% 231.95/43.07  | | | | | | 
% 231.95/43.07  | | | | | End of split
% 231.95/43.07  | | | | | 
% 231.95/43.07  | | | | End of split
% 231.95/43.07  | | | | 
% 231.95/43.07  | | | Case 2:
% 231.95/43.07  | | | | 
% 231.95/43.07  | | | |   (114)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0,
% 231.95/43.07  | | | |              e1) = e3)
% 231.95/43.07  | | | | 
% 231.95/43.07  | | | | REF_CLOSE: (5), (7), (9), (10), (75), (114) are inconsistent by
% 231.95/43.07  | | | |            sub-proof #2263.
% 231.95/43.07  | | | | 
% 231.95/43.07  | | | End of split
% 231.95/43.07  | | | 
% 231.95/43.07  | | Case 2:
% 231.95/43.07  | | | 
% 231.95/43.07  | | |   (115)  all_57_15 = e1 & op(e0, e0) = e1
% 231.95/43.07  | | | 
% 231.95/43.07  | | | ALPHA: (115) implies:
% 231.95/43.07  | | |   (116)  op(e0, e0) = e1
% 231.95/43.07  | | | 
% 231.95/43.07  | | | REF_CLOSE: (7), (30), (33), (116) are inconsistent by sub-proof #2290.
% 231.95/43.07  | | | 
% 231.95/43.07  | | End of split
% 231.95/43.07  | | 
% 231.95/43.07  | End of split
% 231.95/43.07  | 
% 231.95/43.07  End of proof
% 231.95/43.07  
% 231.95/43.07  Sub-proof #1848 shows that the following formulas are inconsistent:
% 231.95/43.07  ----------------------------------------------------------------
% 231.95/43.07    (1)   ~ (e3 = e1)
% 231.95/43.07    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.95/43.07           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.95/43.07    (3)  op(e2, e2) = e1
% 231.95/43.07    (4)   ~ (e3 = e2)
% 231.95/43.07    (5)   ~ (e3 = e0)
% 231.95/43.07    (6)   ~ (e2 = e0)
% 231.95/43.07    (7)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.95/43.07         (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 231.95/43.07    (8)  all_57_2 = e0
% 231.95/43.07    (9)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.95/43.07         (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 231.95/43.07    (10)   ~ (e2 = e1)
% 231.95/43.07    (11)  all_57_5 = e0
% 231.95/43.07  
% 231.95/43.07  Begin of proof
% 231.95/43.07  | 
% 231.95/43.07  | BETA: splitting (7) gives:
% 231.95/43.07  | 
% 231.95/43.07  | Case 1:
% 231.95/43.07  | | 
% 231.95/43.07  | |   (12)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 231.95/43.07  | |           e3)
% 231.95/43.07  | | 
% 231.95/43.07  | | REF_CLOSE: (1), (2), (3), (5), (8), (12) are inconsistent by sub-proof
% 231.95/43.07  | |            #1849.
% 231.95/43.07  | | 
% 231.95/43.07  | Case 2:
% 231.95/43.07  | | 
% 231.95/43.07  | |   (13)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 231.95/43.07  | |           e3)
% 231.95/43.07  | | 
% 231.95/43.07  | | BETA: splitting (13) gives:
% 231.95/43.07  | | 
% 231.95/43.07  | | Case 1:
% 231.95/43.07  | | | 
% 231.95/43.07  | | |   (14)  all_57_5 = e3 & op(e2, e1) = e3
% 231.95/43.07  | | | 
% 231.95/43.07  | | | ALPHA: (14) implies:
% 231.95/43.07  | | |   (15)  all_57_5 = e3
% 231.95/43.07  | | | 
% 231.95/43.07  | | | REF_CLOSE: (5), (11), (15) are inconsistent by sub-proof #2471.
% 231.95/43.07  | | | 
% 231.95/43.07  | | Case 2:
% 231.95/43.07  | | | 
% 231.95/43.07  | | |   (16)  all_57_10 = e3 & op(e2, e0) = e3
% 231.95/43.07  | | | 
% 231.95/43.07  | | | ALPHA: (16) implies:
% 231.95/43.07  | | |   (17)  all_57_10 = e3
% 231.95/43.07  | | | 
% 231.95/43.07  | | | BETA: splitting (9) gives:
% 231.95/43.07  | | | 
% 231.95/43.07  | | | Case 1:
% 231.95/43.07  | | | | 
% 231.95/43.07  | | | |   (18)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2)
% 231.95/43.07  | | | |           = e2)
% 231.95/43.07  | | | | 
% 231.95/43.07  | | | | BETA: splitting (18) gives:
% 231.95/43.07  | | | | 
% 231.95/43.07  | | | | Case 1:
% 231.95/43.07  | | | | | 
% 231.95/43.07  | | | | |   (19)  all_57_2 = e2 & op(e2, e3) = e2
% 231.95/43.07  | | | | | 
% 231.95/43.07  | | | | | REF_CLOSE: (6), (8), (19) are inconsistent by sub-proof #2257.
% 231.95/43.07  | | | | | 
% 231.95/43.07  | | | | Case 2:
% 231.95/43.07  | | | | | 
% 231.95/43.07  | | | | |   (20)  all_57_3 = e2 & op(e2, e2) = e2
% 231.95/43.07  | | | | | 
% 231.95/43.07  | | | | | ALPHA: (20) implies:
% 231.95/43.07  | | | | |   (21)  op(e2, e2) = e2
% 231.95/43.07  | | | | | 
% 231.95/43.07  | | | | | REF_CLOSE: (2), (3), (10), (21) are inconsistent by sub-proof #2306.
% 231.95/43.07  | | | | | 
% 231.95/43.07  | | | | End of split
% 231.95/43.07  | | | | 
% 231.95/43.07  | | | Case 2:
% 231.95/43.07  | | | | 
% 231.95/43.07  | | | |   (22)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0)
% 231.95/43.07  | | | |           = e2)
% 231.95/43.07  | | | | 
% 231.95/43.07  | | | | BETA: splitting (22) gives:
% 231.95/43.07  | | | | 
% 231.95/43.07  | | | | Case 1:
% 231.95/43.07  | | | | | 
% 231.95/43.07  | | | | |   (23)  all_57_5 = e2 & op(e2, e1) = e2
% 231.95/43.07  | | | | | 
% 231.95/43.07  | | | | | ALPHA: (23) implies:
% 231.95/43.07  | | | | |   (24)  all_57_5 = e2
% 231.95/43.07  | | | | | 
% 231.95/43.07  | | | | | REF_CLOSE: (6), (11), (24) are inconsistent by sub-proof #2363.
% 231.95/43.07  | | | | | 
% 231.95/43.07  | | | | Case 2:
% 231.95/43.07  | | | | | 
% 231.95/43.07  | | | | |   (25)  all_57_10 = e2 & op(e2, e0) = e2
% 231.95/43.07  | | | | | 
% 231.95/43.07  | | | | | REF_CLOSE: (4), (17), (25) are inconsistent by sub-proof #2250.
% 231.95/43.07  | | | | | 
% 231.95/43.07  | | | | End of split
% 231.95/43.07  | | | | 
% 231.95/43.07  | | | End of split
% 231.95/43.07  | | | 
% 231.95/43.07  | | End of split
% 231.95/43.07  | | 
% 231.95/43.07  | End of split
% 231.95/43.07  | 
% 231.95/43.07  End of proof
% 231.95/43.07  
% 231.95/43.07  Sub-proof #1849 shows that the following formulas are inconsistent:
% 231.95/43.07  ----------------------------------------------------------------
% 231.95/43.07    (1)   ~ (e3 = e1)
% 231.95/43.07    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.95/43.07           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.95/43.07    (3)  op(e2, e2) = e1
% 231.95/43.07    (4)   ~ (e3 = e0)
% 231.95/43.07    (5)  all_57_2 = e0
% 231.95/43.07    (6)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3)
% 231.95/43.07  
% 231.95/43.07  Begin of proof
% 231.95/43.07  | 
% 231.95/43.07  | BETA: splitting (6) gives:
% 231.95/43.07  | 
% 231.95/43.07  | Case 1:
% 231.95/43.07  | | 
% 231.95/43.07  | |   (7)  all_57_2 = e3 & op(e2, e3) = e3
% 231.95/43.07  | | 
% 231.95/43.07  | | ALPHA: (7) implies:
% 231.95/43.07  | |   (8)  all_57_2 = e3
% 231.95/43.07  | | 
% 231.95/43.07  | | REF_CLOSE: (4), (5), (8) are inconsistent by sub-proof #2258.
% 231.95/43.07  | | 
% 231.95/43.07  | Case 2:
% 231.95/43.07  | | 
% 231.95/43.07  | |   (9)  all_57_3 = e3 & op(e2, e2) = e3
% 231.95/43.07  | | 
% 231.95/43.07  | | ALPHA: (9) implies:
% 231.95/43.07  | |   (10)  op(e2, e2) = e3
% 231.95/43.07  | | 
% 231.95/43.07  | | REF_CLOSE: (1), (2), (3), (10) are inconsistent by sub-proof #1912.
% 231.95/43.07  | | 
% 231.95/43.07  | End of split
% 231.95/43.07  | 
% 231.95/43.07  End of proof
% 231.95/43.07  
% 231.95/43.07  Sub-proof #1850 shows that the following formulas are inconsistent:
% 231.95/43.07  ----------------------------------------------------------------
% 231.95/43.07    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.95/43.07         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.95/43.07    (2)   ~ (e3 = e1)
% 231.95/43.07    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.95/43.07           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.95/43.07    (4)  op(e2, e2) = e1
% 231.95/43.07    (5)   ~ (e3 = e2)
% 231.95/43.07    (6)   ~ (e3 = e0)
% 231.95/43.07    (7)  all_57_1 = e2
% 231.95/43.07    (8)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 231.95/43.07         (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 231.95/43.07    (9)   ~ (e2 = e0)
% 231.95/43.07    (10)   ~ (e1 = e0)
% 231.95/43.07    (11)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.95/43.07          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.95/43.07    (12)  all_57_14 = e1
% 231.95/43.07    (13)   ~ (e2 = e1)
% 231.95/43.07    (14)  all_57_14 = e2 & op(e0, e1) = e2
% 231.95/43.07  
% 231.95/43.07  Begin of proof
% 231.95/43.07  | 
% 231.95/43.07  | ALPHA: (14) implies:
% 231.95/43.07  |   (15)  all_57_14 = e2
% 231.95/43.07  | 
% 231.95/43.07  | COMBINE_EQS: (12), (15) imply:
% 231.95/43.07  |   (16)  e2 = e1
% 231.95/43.07  | 
% 231.95/43.07  | SIMP: (16) implies:
% 231.95/43.07  |   (17)  e2 = e1
% 231.95/43.07  | 
% 231.95/43.07  | COMBINE_EQS: (7), (17) imply:
% 231.95/43.07  |   (18)  all_57_1 = e1
% 231.95/43.07  | 
% 231.95/43.07  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (13), (18) are
% 231.95/43.07  |            inconsistent by sub-proof #1908.
% 231.95/43.07  | 
% 231.95/43.07  End of proof
% 231.95/43.07  
% 231.95/43.07  Sub-proof #1851 shows that the following formulas are inconsistent:
% 231.95/43.07  ----------------------------------------------------------------
% 231.95/43.07    (1)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3)
% 231.95/43.07    (2)   ~ (e3 = e1)
% 231.95/43.08    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.95/43.08           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.95/43.08    (4)  op(e2, e2) = e1
% 231.95/43.08    (5)  op(e3, e2) = all_53_4
% 231.95/43.08    (6)   ~ (all_53_4 = e3)
% 231.95/43.08  
% 231.95/43.08  Begin of proof
% 231.95/43.08  | 
% 231.95/43.08  | BETA: splitting (1) gives:
% 231.95/43.08  | 
% 231.95/43.08  | Case 1:
% 231.95/43.08  | | 
% 231.95/43.08  | |   (7)  all_57_1 = e3 & op(e3, e2) = e3
% 231.95/43.08  | | 
% 231.95/43.08  | | REF_CLOSE: (3), (5), (6), (7) are inconsistent by sub-proof #2286.
% 231.95/43.08  | | 
% 231.95/43.08  | Case 2:
% 231.95/43.08  | | 
% 231.95/43.08  | |   (8)  all_57_3 = e3 & op(e2, e2) = e3
% 231.95/43.08  | | 
% 231.95/43.08  | | ALPHA: (8) implies:
% 231.95/43.08  | |   (9)  op(e2, e2) = e3
% 231.95/43.08  | | 
% 231.95/43.08  | | REF_CLOSE: (2), (3), (4), (9) are inconsistent by sub-proof #1912.
% 231.95/43.08  | | 
% 231.95/43.08  | End of split
% 231.95/43.08  | 
% 231.95/43.08  End of proof
% 231.95/43.08  
% 231.95/43.08  Sub-proof #1852 shows that the following formulas are inconsistent:
% 231.95/43.08  ----------------------------------------------------------------
% 231.95/43.08    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.95/43.08           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.95/43.08    (2)   ~ (all_6_2 = e3)
% 231.95/43.08    (3)  op(e1, e1) = all_6_2
% 231.95/43.08    (4)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 231.95/43.08    (5)  op(e2, e2) = e1
% 231.95/43.08    (6)  op(e3, e0) = e1
% 231.95/43.08    (7)  op(e1, e0) = all_53_14
% 231.95/43.08    (8)  op(e3, e3) = e3
% 231.95/43.08    (9)  op(e0, e3) = all_53_3
% 231.95/43.08    (10)  op(e1, e1) = e1
% 231.95/43.08    (11)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 231.95/43.08            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 231.95/43.08            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 231.95/43.08            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 231.95/43.08              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 231.95/43.08            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 231.95/43.08            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 231.95/43.08              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 231.95/43.08              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 231.95/43.08            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 231.95/43.08            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 231.95/43.08            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 231.95/43.08              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 231.95/43.08              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 231.95/43.08            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 231.95/43.08              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 231.95/43.08            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 231.95/43.08            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 231.95/43.08              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 231.95/43.08              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 231.95/43.08            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 231.95/43.08            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 231.95/43.08    (12)   ~ (all_53_14 = e0)
% 231.95/43.08    (13)  all_55_11 = all_53_14
% 231.95/43.08    (14)   ~ (all_53_12 = e0)
% 231.95/43.08    (15)   ~ (e2 = e1)
% 231.95/43.08    (16)  all_57_12 = e1 & op(e0, e3) = e1
% 231.95/43.08    (17)   ~ (all_53_12 = all_53_14)
% 231.95/43.08    (18)  op(e3, e0) = all_53_12
% 231.95/43.08  
% 231.95/43.08  Begin of proof
% 231.95/43.08  | 
% 231.95/43.08  | ALPHA: (16) implies:
% 231.95/43.08  |   (19)  op(e0, e3) = e1
% 231.95/43.08  | 
% 231.95/43.08  | GROUND_INST: instantiating (1) with all_53_3, e1, e3, e0, simplifying with
% 231.95/43.08  |              (9), (19) gives:
% 231.95/43.08  |   (20)  all_53_3 = e1
% 231.95/43.08  | 
% 231.95/43.08  | GROUND_INST: instantiating (1) with all_53_12, e1, e0, e3, simplifying with
% 231.95/43.08  |              (6), (18) gives:
% 231.95/43.08  |   (21)  all_53_12 = e1
% 231.95/43.08  | 
% 231.95/43.08  | REDUCE: (17), (21) imply:
% 231.95/43.08  |   (22)   ~ (all_53_14 = e1)
% 231.95/43.08  | 
% 231.95/43.08  | SIMP: (22) implies:
% 231.95/43.08  |   (23)   ~ (all_53_14 = e1)
% 231.95/43.08  | 
% 231.95/43.08  | REDUCE: (14), (21) imply:
% 231.95/43.08  |   (24)   ~ (e1 = e0)
% 231.95/43.08  | 
% 231.95/43.08  | BETA: splitting (11) gives:
% 231.95/43.08  | 
% 231.95/43.08  | Case 1:
% 231.95/43.08  | | 
% 231.95/43.08  | |   (25)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 231.95/43.08  | |           op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 231.95/43.08  | |           op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3,
% 231.95/43.08  | |             e3) = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 &
% 231.95/43.08  | |           op(e3, e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5)
% 231.95/43.08  | |           & $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1
% 231.95/43.08  | |           & all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 231.95/43.08  | |             all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 231.95/43.08  | |             all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11
% 231.95/43.08  | |           & op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 231.95/43.08  | |           $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 231.95/43.08  | | 
% 231.95/43.08  | | REF_CLOSE: (1), (5), (6), (10), (15), (24), (25) are inconsistent by
% 231.95/43.08  | |            sub-proof #1854.
% 231.95/43.08  | | 
% 231.95/43.08  | Case 2:
% 231.95/43.08  | | 
% 231.95/43.08  | |   (26)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 &
% 231.95/43.08  | |           op(all_52_17, all_52_17) = e3 & op(all_52_19, all_52_19) = e2 &
% 231.95/43.08  | |           op(all_52_21, all_52_21) = e1 & op(all_52_23, all_52_23) = e0 &
% 231.95/43.08  | |           op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) =
% 231.95/43.08  | |           all_52_21 & op(e1, e0) = all_52_23 & $i(all_52_17) & $i(all_52_19)
% 231.95/43.08  | |           & $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3 & all_52_26 =
% 231.95/43.08  | |           e2 & all_52_28 = e1 & all_52_30 = e0 & op(all_52_25, all_52_25) =
% 231.95/43.08  | |           e3 & op(all_52_27, all_52_27) = e2 & op(all_52_29, all_52_29) = e1
% 231.95/43.08  | |           & op(all_52_31, all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0,
% 231.95/43.08  | |             e2) = all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0) =
% 231.95/43.08  | |           all_52_31 & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 231.95/43.08  | |           $i(all_52_31))
% 231.95/43.08  | | 
% 231.95/43.08  | | BETA: splitting (26) gives:
% 231.95/43.08  | | 
% 231.95/43.08  | | Case 1:
% 231.95/43.08  | | | 
% 231.95/43.08  | | |   (27)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 231.95/43.08  | | |         & op(all_52_17, all_52_17) = e3 & op(all_52_19, all_52_19) = e2 &
% 231.95/43.08  | | |         op(all_52_21, all_52_21) = e1 & op(all_52_23, all_52_23) = e0 &
% 231.95/43.08  | | |         op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) =
% 231.95/43.08  | | |         all_52_21 & op(e1, e0) = all_52_23 & $i(all_52_17) & $i(all_52_19)
% 231.95/43.08  | | |         & $i(all_52_21) & $i(all_52_23)
% 231.95/43.08  | | | 
% 231.95/43.08  | | | ALPHA: (27) implies:
% 231.95/43.08  | | |   (28)  op(e1, e0) = all_52_23
% 231.95/43.08  | | |   (29)  op(all_52_23, all_52_23) = e0
% 231.95/43.08  | | | 
% 231.95/43.08  | | | GROUND_INST: instantiating (1) with all_53_14, all_52_23, e0, e1,
% 231.95/43.08  | | |              simplifying with (7), (28) gives:
% 231.95/43.08  | | |   (30)  all_53_14 = all_52_23
% 231.95/43.08  | | | 
% 231.95/43.08  | | | COMBINE_EQS: (13), (30) imply:
% 231.95/43.08  | | |   (31)  all_55_11 = all_52_23
% 231.95/43.08  | | | 
% 231.95/43.08  | | | REDUCE: (23), (30) imply:
% 231.95/43.08  | | |   (32)   ~ (all_52_23 = e1)
% 231.95/43.08  | | | 
% 231.95/43.08  | | | REDUCE: (12), (30) imply:
% 231.95/43.08  | | |   (33)   ~ (all_52_23 = e0)
% 231.95/43.08  | | | 
% 231.95/43.08  | | | BETA: splitting (4) gives:
% 231.95/43.08  | | | 
% 231.95/43.08  | | | Case 1:
% 231.95/43.08  | | | | 
% 231.95/43.08  | | | |   (34)  all_55_11 = e3
% 231.95/43.08  | | | | 
% 231.95/43.08  | | | | REF_CLOSE: (1), (8), (29), (31), (33), (34) are inconsistent by
% 231.95/43.08  | | | |            sub-proof #2108.
% 231.95/43.08  | | | | 
% 231.95/43.08  | | | Case 2:
% 231.95/43.08  | | | | 
% 231.95/43.08  | | | |   (35)  all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 231.95/43.08  | | | | 
% 231.95/43.08  | | | | BETA: splitting (35) gives:
% 231.95/43.08  | | | | 
% 231.95/43.08  | | | | Case 1:
% 231.95/43.08  | | | | | 
% 231.95/43.08  | | | | |   (36)  all_55_11 = e2
% 231.95/43.08  | | | | | 
% 231.95/43.08  | | | | | COMBINE_EQS: (31), (36) imply:
% 231.95/43.08  | | | | |   (37)  all_52_23 = e2
% 231.95/43.08  | | | | | 
% 231.95/43.08  | | | | | SIMP: (37) implies:
% 231.95/43.08  | | | | |   (38)  all_52_23 = e2
% 231.95/43.08  | | | | | 
% 231.95/43.08  | | | | | REDUCE: (29), (38) imply:
% 231.95/43.08  | | | | |   (39)  op(e2, e2) = e0
% 231.95/43.08  | | | | | 
% 231.95/43.08  | | | | | REF_CLOSE: (1), (5), (24), (39) are inconsistent by sub-proof #2352.
% 231.95/43.08  | | | | | 
% 231.95/43.08  | | | | Case 2:
% 231.95/43.08  | | | | | 
% 231.95/43.08  | | | | |   (40)  all_55_11 = e1 | all_55_11 = e0
% 231.95/43.08  | | | | | 
% 231.95/43.08  | | | | | REF_CLOSE: (31), (32), (33), (40) are inconsistent by sub-proof #2107.
% 231.95/43.08  | | | | | 
% 231.95/43.08  | | | | End of split
% 231.95/43.08  | | | | 
% 231.95/43.08  | | | End of split
% 231.95/43.08  | | | 
% 231.95/43.08  | | Case 2:
% 231.95/43.08  | | | 
% 231.95/43.08  | | |   (41)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 231.95/43.08  | | |         & op(all_52_25, all_52_25) = e3 & op(all_52_27, all_52_27) = e2 &
% 231.95/43.08  | | |         op(all_52_29, all_52_29) = e1 & op(all_52_31, all_52_31) = e0 &
% 231.95/43.08  | | |         op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 & op(e0, e1) =
% 231.95/43.08  | | |         all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) & $i(all_52_27)
% 231.95/43.08  | | |         & $i(all_52_29) & $i(all_52_31)
% 231.95/43.08  | | | 
% 231.95/43.08  | | | REF_CLOSE: (1), (2), (3), (19), (41) are inconsistent by sub-proof #1853.
% 231.95/43.08  | | | 
% 231.95/43.08  | | End of split
% 231.95/43.08  | | 
% 231.95/43.08  | End of split
% 231.95/43.08  | 
% 231.95/43.08  End of proof
% 231.95/43.08  
% 231.95/43.08  Sub-proof #1853 shows that the following formulas are inconsistent:
% 231.95/43.08  ----------------------------------------------------------------
% 231.95/43.08    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.95/43.08           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.95/43.08    (2)   ~ (all_6_2 = e3)
% 231.95/43.08    (3)  op(e1, e1) = all_6_2
% 231.95/43.08    (4)  op(e0, e3) = e1
% 231.95/43.08    (5)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0 &
% 231.95/43.08         op(all_52_25, all_52_25) = e3 & op(all_52_27, all_52_27) = e2 &
% 231.95/43.08         op(all_52_29, all_52_29) = e1 & op(all_52_31, all_52_31) = e0 & op(e0,
% 231.95/43.08           e3) = all_52_25 & op(e0, e2) = all_52_27 & op(e0, e1) = all_52_29 &
% 231.95/43.08         op(e0, e0) = all_52_31 & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 231.95/43.08         $i(all_52_31)
% 231.95/43.08  
% 231.95/43.08  Begin of proof
% 231.95/43.08  | 
% 231.95/43.08  | ALPHA: (5) implies:
% 231.95/43.08  |   (6)  op(e0, e3) = all_52_25
% 231.95/43.08  |   (7)  op(all_52_25, all_52_25) = e3
% 231.95/43.08  | 
% 231.95/43.08  | GROUND_INST: instantiating (1) with e1, all_52_25, e3, e0, simplifying with
% 231.95/43.08  |              (4), (6) gives:
% 231.95/43.08  |   (8)  all_52_25 = e1
% 231.95/43.08  | 
% 231.95/43.08  | REDUCE: (7), (8) imply:
% 231.95/43.08  |   (9)  op(e1, e1) = e3
% 231.95/43.08  | 
% 231.95/43.08  | REF_CLOSE: (1), (2), (3), (9) are inconsistent by sub-proof #2468.
% 231.95/43.08  | 
% 231.95/43.08  End of proof
% 231.95/43.08  
% 231.95/43.08  Sub-proof #1854 shows that the following formulas are inconsistent:
% 231.95/43.08  ----------------------------------------------------------------
% 231.95/43.08    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.95/43.08           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.95/43.08    (2)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 231.95/43.08           op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 231.95/43.08           op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 231.95/43.08           = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3, e0)
% 231.95/43.08           = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) & $i(all_52_7))
% 231.95/43.08         | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0 &
% 231.95/43.08           op(all_52_9, all_52_9) = e3 & op(all_52_11, all_52_11) = e2 &
% 231.95/43.08           op(all_52_13, all_52_13) = e1 & op(all_52_15, all_52_15) = e0 & op(e2,
% 231.95/43.08             e3) = all_52_9 & op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13 &
% 231.95/43.08           op(e2, e0) = all_52_15 & $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 231.95/43.08           $i(all_52_15))
% 231.95/43.08    (3)  op(e2, e2) = e1
% 231.95/43.08    (4)  op(e3, e0) = e1
% 231.95/43.08    (5)  op(e1, e1) = e1
% 231.95/43.08    (6)   ~ (e1 = e0)
% 231.95/43.08    (7)   ~ (e2 = e1)
% 231.95/43.08  
% 231.95/43.08  Begin of proof
% 231.95/43.08  | 
% 231.95/43.08  | BETA: splitting (2) gives:
% 231.95/43.08  | 
% 231.95/43.08  | Case 1:
% 231.95/43.08  | | 
% 231.95/43.08  | |   (8)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 231.95/43.08  | |        op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 231.95/43.08  | |        op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3,
% 231.95/43.08  | |          e3) = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 &
% 231.95/43.08  | |        op(e3, e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 231.95/43.08  | |        $i(all_52_7)
% 231.95/43.08  | | 
% 231.95/43.08  | | ALPHA: (8) implies:
% 231.95/43.08  | |   (9)  op(e3, e0) = all_52_7
% 231.95/43.08  | |   (10)  op(all_52_7, all_52_7) = e0
% 231.95/43.08  | | 
% 231.95/43.08  | | GROUND_INST: instantiating (1) with e1, all_52_7, e0, e3, simplifying with
% 231.95/43.08  | |              (4), (9) gives:
% 231.95/43.08  | |   (11)  all_52_7 = e1
% 231.95/43.08  | | 
% 231.95/43.08  | | REDUCE: (10), (11) imply:
% 231.95/43.08  | |   (12)  op(e1, e1) = e0
% 231.95/43.08  | | 
% 231.95/43.08  | | REF_CLOSE: (1), (5), (6), (12) are inconsistent by sub-proof #2427.
% 231.95/43.08  | | 
% 231.95/43.08  | Case 2:
% 231.95/43.08  | | 
% 231.95/43.08  | |   (13)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0 &
% 231.95/43.08  | |         op(all_52_9, all_52_9) = e3 & op(all_52_11, all_52_11) = e2 &
% 231.95/43.08  | |         op(all_52_13, all_52_13) = e1 & op(all_52_15, all_52_15) = e0 &
% 231.95/43.08  | |         op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 & op(e2, e1) =
% 231.95/43.08  | |         all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) & $i(all_52_11) &
% 231.95/43.08  | |         $i(all_52_13) & $i(all_52_15)
% 231.95/43.08  | | 
% 231.95/43.08  | | REF_CLOSE: (1), (3), (5), (7), (13) are inconsistent by sub-proof #1855.
% 231.95/43.08  | | 
% 231.95/43.08  | End of split
% 231.95/43.08  | 
% 231.95/43.08  End of proof
% 231.95/43.08  
% 231.95/43.08  Sub-proof #1855 shows that the following formulas are inconsistent:
% 231.95/43.08  ----------------------------------------------------------------
% 231.95/43.08    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.95/43.08           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.95/43.08    (2)  op(e2, e2) = e1
% 231.95/43.08    (3)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0 &
% 231.95/43.08         op(all_52_9, all_52_9) = e3 & op(all_52_11, all_52_11) = e2 &
% 231.95/43.08         op(all_52_13, all_52_13) = e1 & op(all_52_15, all_52_15) = e0 & op(e2,
% 231.95/43.08           e3) = all_52_9 & op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13 &
% 231.95/43.08         op(e2, e0) = all_52_15 & $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 231.95/43.08         $i(all_52_15)
% 231.95/43.08    (4)  op(e1, e1) = e1
% 231.95/43.08    (5)   ~ (e2 = e1)
% 231.95/43.08  
% 231.95/43.08  Begin of proof
% 231.95/43.08  | 
% 231.95/43.08  | ALPHA: (3) implies:
% 231.95/43.08  |   (6)  op(e2, e2) = all_52_11
% 231.95/43.08  |   (7)  op(all_52_11, all_52_11) = e2
% 231.95/43.08  | 
% 231.95/43.08  | GROUND_INST: instantiating (1) with e1, all_52_11, e2, e2, simplifying with
% 231.95/43.08  |              (2), (6) gives:
% 231.95/43.08  |   (8)  all_52_11 = e1
% 231.95/43.08  | 
% 231.95/43.08  | REDUCE: (7), (8) imply:
% 231.95/43.08  |   (9)  op(e1, e1) = e2
% 231.95/43.08  | 
% 231.95/43.08  | REF_CLOSE: (1), (4), (5), (9) are inconsistent by sub-proof #2423.
% 231.95/43.08  | 
% 231.95/43.08  End of proof
% 231.95/43.08  
% 231.95/43.08  Sub-proof #1856 shows that the following formulas are inconsistent:
% 231.95/43.08  ----------------------------------------------------------------
% 231.95/43.08    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 231.95/43.08         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.95/43.08    (2)   ~ (e3 = e1)
% 231.95/43.08    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.95/43.08           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.95/43.08    (4)  op(e2, e2) = e1
% 231.95/43.08    (5)   ~ (e3 = e2)
% 231.95/43.08    (6)   ~ (e3 = e0)
% 231.95/43.08    (7)  op(e3, e3) = e3
% 231.95/43.08    (8)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 231.95/43.08         (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 231.95/43.08    (9)   ~ (e2 = e0)
% 231.95/43.08    (10)   ~ (e1 = e0)
% 231.95/43.08    (11)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 231.95/43.08          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.95/43.08    (12)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1)
% 231.95/43.08    (13)   ~ (e2 = e1)
% 231.95/43.08  
% 231.95/43.08  Begin of proof
% 231.95/43.08  | 
% 231.95/43.08  | BETA: splitting (12) gives:
% 231.95/43.08  | 
% 231.95/43.08  | Case 1:
% 231.95/43.08  | | 
% 231.95/43.08  | |   (14)  all_57_0 = e1 & op(e3, e3) = e1
% 231.95/43.08  | | 
% 231.95/43.08  | | ALPHA: (14) implies:
% 231.95/43.08  | |   (15)  op(e3, e3) = e1
% 231.95/43.08  | | 
% 231.95/43.08  | | REF_CLOSE: (2), (3), (7), (15) are inconsistent by sub-proof #2495.
% 231.95/43.08  | | 
% 231.95/43.08  | Case 2:
% 231.95/43.08  | | 
% 231.95/43.08  | |   (16)  all_57_1 = e1 & op(e3, e2) = e1
% 231.95/43.08  | | 
% 231.95/43.08  | | ALPHA: (16) implies:
% 231.95/43.08  | |   (17)  all_57_1 = e1
% 231.95/43.08  | | 
% 231.95/43.08  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (13), (17)
% 231.95/43.08  | |            are inconsistent by sub-proof #1908.
% 231.95/43.08  | | 
% 231.95/43.08  | End of split
% 231.95/43.08  | 
% 231.95/43.08  End of proof
% 231.95/43.08  
% 231.95/43.08  Sub-proof #1857 shows that the following formulas are inconsistent:
% 231.95/43.08  ----------------------------------------------------------------
% 231.95/43.08    (1)  all_55_5 = e1 | all_55_5 = e0
% 231.95/43.08    (2)  all_55_5 = all_8_2
% 231.95/43.08    (3)   ~ (all_8_2 = e1)
% 231.95/43.08    (4)   ~ (all_8_2 = e0)
% 231.95/43.08  
% 231.95/43.08  Begin of proof
% 231.95/43.08  | 
% 231.95/43.08  | BETA: splitting (1) gives:
% 231.95/43.08  | 
% 231.95/43.08  | Case 1:
% 231.95/43.08  | | 
% 231.95/43.08  | |   (5)  all_55_5 = e1
% 231.95/43.08  | | 
% 231.95/43.08  | | COMBINE_EQS: (2), (5) imply:
% 231.95/43.08  | |   (6)  all_8_2 = e1
% 231.95/43.08  | | 
% 231.95/43.08  | | REDUCE: (3), (6) imply:
% 231.95/43.08  | |   (7)  $false
% 231.95/43.08  | | 
% 231.95/43.08  | | CLOSE: (7) is inconsistent.
% 231.95/43.08  | | 
% 231.95/43.08  | Case 2:
% 231.95/43.08  | | 
% 231.95/43.08  | |   (8)  all_55_5 = e0
% 231.95/43.08  | | 
% 231.95/43.08  | | COMBINE_EQS: (2), (8) imply:
% 231.95/43.08  | |   (9)  all_8_2 = e0
% 231.95/43.08  | | 
% 231.95/43.08  | | REDUCE: (4), (9) imply:
% 231.95/43.08  | |   (10)  $false
% 231.95/43.08  | | 
% 231.95/43.08  | | CLOSE: (10) is inconsistent.
% 231.95/43.08  | | 
% 231.95/43.08  | End of split
% 231.95/43.08  | 
% 231.95/43.08  End of proof
% 231.95/43.08  
% 231.95/43.08  Sub-proof #1858 shows that the following formulas are inconsistent:
% 231.95/43.08  ----------------------------------------------------------------
% 231.95/43.08    (1)  all_57_5 = e2 & op(e2, e1) = e2
% 231.95/43.08    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.95/43.08           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.95/43.08    (3)  op(e2, e1) = all_53_9
% 231.95/43.08    (4)   ~ (all_53_9 = e2)
% 231.95/43.08  
% 231.95/43.08  Begin of proof
% 231.95/43.08  | 
% 231.95/43.08  | ALPHA: (1) implies:
% 231.95/43.08  |   (5)  op(e2, e1) = e2
% 231.95/43.08  | 
% 231.95/43.08  | GROUND_INST: instantiating (2) with all_53_9, e2, e1, e2, simplifying with
% 231.95/43.08  |              (3), (5) gives:
% 231.95/43.08  |   (6)  all_53_9 = e2
% 231.95/43.08  | 
% 231.95/43.08  | REDUCE: (4), (6) imply:
% 231.95/43.08  |   (7)  $false
% 231.95/43.08  | 
% 231.95/43.08  | CLOSE: (7) is inconsistent.
% 231.95/43.08  | 
% 231.95/43.08  End of proof
% 231.95/43.08  
% 231.95/43.08  Sub-proof #1859 shows that the following formulas are inconsistent:
% 231.95/43.08  ----------------------------------------------------------------
% 231.95/43.08    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.95/43.08           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.95/43.08    (2)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 231.95/43.08    (3)  op(e0, e3) = all_53_3
% 231.95/43.08    (4)   ~ (all_53_2 = e0)
% 231.95/43.08    (5)   ~ (all_53_3 = e0)
% 231.95/43.08    (6)  op(e1, e3) = all_53_2
% 231.95/43.08  
% 231.95/43.08  Begin of proof
% 231.95/43.08  | 
% 231.95/43.08  | BETA: splitting (2) gives:
% 231.95/43.08  | 
% 231.95/43.08  | Case 1:
% 231.95/43.08  | | 
% 231.95/43.08  | |   (7)  all_57_6 = e0 & op(e1, e3) = e0
% 231.95/43.08  | | 
% 231.95/43.08  | | ALPHA: (7) implies:
% 231.95/43.08  | |   (8)  op(e1, e3) = e0
% 231.95/43.08  | | 
% 231.95/43.08  | | REF_CLOSE: (1), (4), (6), (8) are inconsistent by sub-proof #2154.
% 231.95/43.08  | | 
% 231.95/43.08  | Case 2:
% 231.95/43.08  | | 
% 231.95/43.08  | |   (9)  all_57_12 = e0 & op(e0, e3) = e0
% 231.95/43.08  | | 
% 231.95/43.08  | | ALPHA: (9) implies:
% 231.95/43.08  | |   (10)  op(e0, e3) = e0
% 231.95/43.08  | | 
% 231.95/43.08  | | REF_CLOSE: (1), (3), (5), (10) are inconsistent by sub-proof #2366.
% 231.95/43.08  | | 
% 231.95/43.08  | End of split
% 231.95/43.08  | 
% 231.95/43.08  End of proof
% 231.95/43.08  
% 231.95/43.08  Sub-proof #1860 shows that the following formulas are inconsistent:
% 231.95/43.08  ----------------------------------------------------------------
% 231.95/43.08    (1)  op(e1, e3) = all_52_17
% 231.95/43.08    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 231.95/43.08    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.95/43.08           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.95/43.08    (4)   ~ (all_6_2 = e3)
% 231.95/43.08    (5)  op(e1, e1) = all_6_2
% 231.95/43.08    (6)  op(all_52_17, all_52_17) = e3
% 231.95/43.08    (7)  op(e0, e3) = all_53_3
% 231.95/43.08    (8)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 231.95/43.08    (9)  all_55_10 = all_6_2
% 231.95/43.08    (10)   ~ (all_53_3 = e1)
% 231.95/43.08  
% 231.95/43.08  Begin of proof
% 231.95/43.08  | 
% 231.95/43.08  | BETA: splitting (8) gives:
% 231.95/43.08  | 
% 231.95/43.08  | Case 1:
% 231.95/43.08  | | 
% 231.95/43.08  | |   (11)  all_57_6 = e1 & op(e1, e3) = e1
% 231.95/43.08  | | 
% 231.95/43.08  | | ALPHA: (11) implies:
% 231.95/43.08  | |   (12)  op(e1, e3) = e1
% 231.95/43.08  | | 
% 231.95/43.08  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (9), (12) are inconsistent by
% 231.95/43.08  | |            sub-proof #1998.
% 231.95/43.08  | | 
% 231.95/43.08  | Case 2:
% 231.95/43.08  | | 
% 231.95/43.08  | |   (13)  all_57_12 = e1 & op(e0, e3) = e1
% 231.95/43.08  | | 
% 231.95/43.08  | | REF_CLOSE: (3), (7), (10), (13) are inconsistent by sub-proof #1947.
% 231.95/43.08  | | 
% 231.95/43.08  | End of split
% 231.95/43.08  | 
% 231.95/43.08  End of proof
% 231.95/43.08  
% 231.95/43.08  Sub-proof #1861 shows that the following formulas are inconsistent:
% 231.95/43.08  ----------------------------------------------------------------
% 231.95/43.08    (1)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 231.95/43.08    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.95/43.08           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.95/43.08    (3)  all_57_11 = e0
% 231.95/43.08    (4)   ~ (e1 = e0)
% 231.95/43.08    (5)  op(e1, e1) = e2
% 231.95/43.08    (6)   ~ (e2 = e1)
% 231.95/43.08  
% 231.95/43.08  Begin of proof
% 231.95/43.08  | 
% 231.95/43.08  | BETA: splitting (1) gives:
% 231.95/43.08  | 
% 231.95/43.08  | Case 1:
% 231.95/43.08  | | 
% 231.95/43.08  | |   (7)  all_57_8 = e1 & op(e1, e1) = e1
% 231.95/43.08  | | 
% 231.95/43.08  | | ALPHA: (7) implies:
% 231.95/43.08  | |   (8)  op(e1, e1) = e1
% 231.95/43.08  | | 
% 231.95/43.08  | | REF_CLOSE: (2), (5), (6), (8) are inconsistent by sub-proof #2423.
% 231.95/43.08  | | 
% 231.95/43.08  | Case 2:
% 231.95/43.08  | | 
% 231.95/43.08  | |   (9)  all_57_11 = e1 & op(e1, e0) = e1
% 231.95/43.08  | | 
% 231.95/43.08  | | ALPHA: (9) implies:
% 231.95/43.08  | |   (10)  all_57_11 = e1
% 231.95/43.08  | | 
% 231.95/43.08  | | REF_CLOSE: (3), (4), (10) are inconsistent by sub-proof #1862.
% 231.95/43.08  | | 
% 231.95/43.08  | End of split
% 231.95/43.08  | 
% 231.95/43.08  End of proof
% 231.95/43.08  
% 231.95/43.08  Sub-proof #1862 shows that the following formulas are inconsistent:
% 231.95/43.08  ----------------------------------------------------------------
% 231.95/43.08    (1)  all_57_11 = e1
% 231.95/43.08    (2)  all_57_11 = e0
% 231.95/43.08    (3)   ~ (e1 = e0)
% 231.95/43.08  
% 231.95/43.08  Begin of proof
% 231.95/43.08  | 
% 231.95/43.08  | COMBINE_EQS: (1), (2) imply:
% 231.95/43.08  |   (4)  e1 = e0
% 231.95/43.08  | 
% 231.95/43.08  | SIMP: (4) implies:
% 231.95/43.08  |   (5)  e1 = e0
% 231.95/43.08  | 
% 231.95/43.08  | REDUCE: (3), (5) imply:
% 231.95/43.08  |   (6)  $false
% 231.95/43.08  | 
% 231.95/43.08  | CLOSE: (6) is inconsistent.
% 231.95/43.08  | 
% 231.95/43.08  End of proof
% 231.95/43.08  
% 231.95/43.08  Sub-proof #1863 shows that the following formulas are inconsistent:
% 231.95/43.08  ----------------------------------------------------------------
% 231.95/43.08    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.95/43.08           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.95/43.08    (2)   ~ (all_6_2 = e3)
% 231.95/43.08    (3)  op(e1, e1) = all_6_2
% 231.95/43.08    (4)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 231.95/43.08    (5)   ~ (e3 = e0)
% 231.95/43.08    (6)  all_57_11 = e0
% 231.95/43.08  
% 231.95/43.08  Begin of proof
% 231.95/43.08  | 
% 231.95/43.08  | BETA: splitting (4) gives:
% 231.95/43.08  | 
% 231.95/43.08  | Case 1:
% 231.95/43.08  | | 
% 231.95/43.08  | |   (7)  all_57_8 = e3 & op(e1, e1) = e3
% 231.95/43.08  | | 
% 231.95/43.08  | | ALPHA: (7) implies:
% 231.95/43.08  | |   (8)  op(e1, e1) = e3
% 231.95/43.08  | | 
% 231.95/43.08  | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #2468.
% 231.95/43.08  | | 
% 231.95/43.08  | Case 2:
% 231.95/43.08  | | 
% 231.95/43.08  | |   (9)  all_57_11 = e3 & op(e1, e0) = e3
% 231.95/43.08  | | 
% 231.95/43.08  | | ALPHA: (9) implies:
% 231.95/43.08  | |   (10)  all_57_11 = e3
% 231.95/43.08  | | 
% 231.95/43.08  | | COMBINE_EQS: (6), (10) imply:
% 231.95/43.08  | |   (11)  e3 = e0
% 231.95/43.08  | | 
% 231.95/43.08  | | REDUCE: (5), (11) imply:
% 231.95/43.08  | |   (12)  $false
% 231.95/43.08  | | 
% 231.95/43.08  | | CLOSE: (12) is inconsistent.
% 231.95/43.08  | | 
% 231.95/43.08  | End of split
% 231.95/43.08  | 
% 231.95/43.08  End of proof
% 231.95/43.08  
% 231.95/43.08  Sub-proof #1864 shows that the following formulas are inconsistent:
% 231.95/43.08  ----------------------------------------------------------------
% 231.95/43.08    (1)   ~ (all_53_2 = e2)
% 231.95/43.08    (2)  op(e1, e3) = all_52_17
% 231.95/43.08    (3)  all_55_15 = e3 | all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 231.95/43.08    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.95/43.08           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.95/43.08    (5)  all_55_15 = all_4_2
% 231.95/43.08    (6)   ~ (all_6_2 = e3)
% 231.95/43.08    (7)  op(e1, e1) = all_6_2
% 231.95/43.08    (8)  op(all_52_17, all_52_17) = e3
% 231.95/43.08    (9)  all_55_4 = all_53_1
% 231.95/43.08    (10)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 231.95/43.08    (11)   ~ (all_53_2 = e0)
% 231.95/43.08    (12)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 231.95/43.08    (13)  op(e3, e3) = e2
% 231.95/43.08    (14)   ~ (all_53_1 = all_53_2)
% 231.95/43.08    (15)   ~ (all_53_1 = e0)
% 231.95/43.08    (16)  all_55_8 = all_53_2
% 231.95/43.08    (17)  op(e1, e3) = all_53_2
% 231.95/43.08    (18)   ~ (all_4_2 = e3)
% 231.95/43.08    (19)   ~ (all_53_1 = e2)
% 231.95/43.08  
% 231.95/43.08  Begin of proof
% 231.95/43.08  | 
% 231.95/43.08  | BETA: splitting (3) gives:
% 231.95/43.08  | 
% 231.95/43.08  | Case 1:
% 231.95/43.08  | | 
% 231.95/43.08  | |   (20)  all_55_15 = e3
% 231.95/43.08  | | 
% 231.95/43.08  | | REF_CLOSE: (5), (18), (20) are inconsistent by sub-proof #2503.
% 231.95/43.08  | | 
% 231.95/43.08  | Case 2:
% 231.95/43.08  | | 
% 231.95/43.08  | | 
% 231.95/43.08  | | GROUND_INST: instantiating (4) with all_53_2, all_52_17, e3, e1, simplifying
% 231.95/43.08  | |              with (2), (17) gives:
% 231.95/43.08  | |   (21)  all_53_2 = all_52_17
% 231.95/43.08  | | 
% 231.95/43.08  | | COMBINE_EQS: (16), (21) imply:
% 231.95/43.08  | |   (22)  all_55_8 = all_52_17
% 231.95/43.08  | | 
% 231.95/43.08  | | REDUCE: (14), (21) imply:
% 231.95/43.08  | |   (23)   ~ (all_53_1 = all_52_17)
% 231.95/43.08  | | 
% 231.95/43.08  | | REDUCE: (1), (21) imply:
% 231.95/43.08  | |   (24)   ~ (all_52_17 = e2)
% 231.95/43.08  | | 
% 231.95/43.08  | | REDUCE: (11), (21) imply:
% 231.95/43.08  | |   (25)   ~ (all_52_17 = e0)
% 231.95/43.08  | | 
% 231.95/43.08  | | BETA: splitting (12) gives:
% 231.95/43.08  | | 
% 231.95/43.08  | | Case 1:
% 231.95/43.08  | | | 
% 231.95/43.08  | | |   (26)  all_55_4 = e3
% 231.95/43.08  | | | 
% 231.95/43.08  | | | COMBINE_EQS: (9), (26) imply:
% 231.95/43.08  | | |   (27)  all_53_1 = e3
% 231.95/43.08  | | | 
% 231.95/43.08  | | | SIMP: (27) implies:
% 231.95/43.08  | | |   (28)  all_53_1 = e3
% 231.95/43.08  | | | 
% 231.95/43.08  | | | REDUCE: (23), (28) imply:
% 231.95/43.08  | | |   (29)   ~ (all_52_17 = e3)
% 231.95/43.08  | | | 
% 231.95/43.08  | | | SIMP: (29) implies:
% 231.95/43.08  | | |   (30)   ~ (all_52_17 = e3)
% 231.95/43.08  | | | 
% 231.95/43.08  | | | REF_CLOSE: (4), (6), (7), (8), (10), (22), (24), (25), (30) are
% 231.95/43.08  | | |            inconsistent by sub-proof #1868.
% 231.95/43.08  | | | 
% 231.95/43.08  | | Case 2:
% 231.95/43.08  | | | 
% 231.95/43.08  | | |   (31)  all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 231.95/43.08  | | | 
% 231.95/43.08  | | | BETA: splitting (31) gives:
% 231.95/43.08  | | | 
% 231.95/43.08  | | | Case 1:
% 231.95/43.08  | | | | 
% 231.95/43.08  | | | |   (32)  all_55_4 = e2
% 231.95/43.08  | | | | 
% 231.95/43.08  | | | | REF_CLOSE: (9), (19), (32) are inconsistent by sub-proof #2168.
% 231.95/43.08  | | | | 
% 231.95/43.08  | | | Case 2:
% 231.95/43.08  | | | | 
% 231.95/43.08  | | | |   (33)  all_55_4 = e1 | all_55_4 = e0
% 231.95/43.08  | | | | 
% 231.95/43.08  | | | | BETA: splitting (33) gives:
% 231.95/43.08  | | | | 
% 231.95/43.08  | | | | Case 1:
% 231.95/43.08  | | | | | 
% 231.95/43.08  | | | | |   (34)  all_55_4 = e1
% 231.95/43.08  | | | | | 
% 231.95/43.08  | | | | | COMBINE_EQS: (9), (34) imply:
% 231.95/43.08  | | | | |   (35)  all_53_1 = e1
% 231.95/43.08  | | | | | 
% 231.95/43.08  | | | | | SIMP: (35) implies:
% 231.95/43.08  | | | | |   (36)  all_53_1 = e1
% 231.95/43.08  | | | | | 
% 231.95/43.08  | | | | | REDUCE: (23), (36) imply:
% 231.95/43.08  | | | | |   (37)   ~ (all_52_17 = e1)
% 231.95/43.08  | | | | | 
% 231.95/43.08  | | | | | SIMP: (37) implies:
% 231.95/43.08  | | | | |   (38)   ~ (all_52_17 = e1)
% 231.95/43.08  | | | | | 
% 231.95/43.08  | | | | | REF_CLOSE: (4), (8), (10), (13), (22), (24), (25), (38) are
% 231.95/43.08  | | | | |            inconsistent by sub-proof #1866.
% 231.95/43.08  | | | | | 
% 231.95/43.08  | | | | Case 2:
% 231.95/43.08  | | | | | 
% 231.95/43.08  | | | | |   (39)  all_55_4 = e0
% 231.95/43.08  | | | | | 
% 231.95/43.08  | | | | | REF_CLOSE: (9), (15), (39) are inconsistent by sub-proof #1865.
% 231.95/43.08  | | | | | 
% 231.95/43.08  | | | | End of split
% 231.95/43.08  | | | | 
% 231.95/43.08  | | | End of split
% 231.95/43.08  | | | 
% 231.95/43.08  | | End of split
% 231.95/43.08  | | 
% 231.95/43.08  | End of split
% 231.95/43.08  | 
% 231.95/43.08  End of proof
% 231.95/43.08  
% 231.95/43.08  Sub-proof #1865 shows that the following formulas are inconsistent:
% 231.95/43.08  ----------------------------------------------------------------
% 231.95/43.08    (1)  all_55_4 = all_53_1
% 231.95/43.08    (2)  all_55_4 = e0
% 231.95/43.08    (3)   ~ (all_53_1 = e0)
% 231.95/43.08  
% 231.95/43.08  Begin of proof
% 231.95/43.08  | 
% 231.95/43.08  | COMBINE_EQS: (1), (2) imply:
% 231.95/43.08  |   (4)  all_53_1 = e0
% 231.95/43.08  | 
% 231.95/43.08  | SIMP: (4) implies:
% 231.95/43.08  |   (5)  all_53_1 = e0
% 231.95/43.08  | 
% 231.95/43.08  | REDUCE: (3), (5) imply:
% 231.95/43.08  |   (6)  $false
% 231.95/43.08  | 
% 231.95/43.08  | CLOSE: (6) is inconsistent.
% 231.95/43.08  | 
% 231.95/43.08  End of proof
% 231.95/43.08  
% 231.95/43.08  Sub-proof #1866 shows that the following formulas are inconsistent:
% 231.95/43.08  ----------------------------------------------------------------
% 231.95/43.08    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.95/43.08           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.95/43.08    (2)   ~ (all_52_17 = e2)
% 231.95/43.08    (3)  op(all_52_17, all_52_17) = e3
% 231.95/43.08    (4)   ~ (all_52_17 = e1)
% 231.95/43.08    (5)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 231.95/43.09    (6)  op(e3, e3) = e2
% 231.95/43.09    (7)   ~ (all_52_17 = e0)
% 231.95/43.09    (8)  all_55_8 = all_52_17
% 231.95/43.09  
% 231.95/43.09  Begin of proof
% 231.95/43.09  | 
% 231.95/43.09  | BETA: splitting (5) gives:
% 231.95/43.09  | 
% 231.95/43.09  | Case 1:
% 231.95/43.09  | | 
% 231.95/43.09  | |   (9)  all_55_8 = e3
% 231.95/43.09  | | 
% 231.95/43.09  | | COMBINE_EQS: (8), (9) imply:
% 231.95/43.09  | |   (10)  all_52_17 = e3
% 231.95/43.09  | | 
% 231.95/43.09  | | SIMP: (10) implies:
% 231.95/43.09  | |   (11)  all_52_17 = e3
% 231.95/43.09  | | 
% 231.95/43.09  | | REDUCE: (2), (11) imply:
% 231.95/43.09  | |   (12)   ~ (e3 = e2)
% 231.95/43.09  | | 
% 231.95/43.09  | | REDUCE: (3), (11) imply:
% 231.95/43.09  | |   (13)  op(e3, e3) = e3
% 231.95/43.09  | | 
% 231.95/43.09  | | REF_CLOSE: (1), (6), (12), (13) are inconsistent by sub-proof #2490.
% 231.95/43.09  | | 
% 231.95/43.09  | Case 2:
% 231.95/43.09  | | 
% 231.95/43.09  | |   (14)  all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 231.95/43.09  | | 
% 231.95/43.09  | | REF_CLOSE: (2), (4), (7), (8), (14) are inconsistent by sub-proof #1867.
% 231.95/43.09  | | 
% 231.95/43.09  | End of split
% 231.95/43.09  | 
% 231.95/43.09  End of proof
% 231.95/43.09  
% 231.95/43.09  Sub-proof #1867 shows that the following formulas are inconsistent:
% 231.95/43.09  ----------------------------------------------------------------
% 231.95/43.09    (1)  all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 231.95/43.09    (2)   ~ (all_52_17 = e2)
% 231.95/43.09    (3)   ~ (all_52_17 = e1)
% 231.95/43.09    (4)   ~ (all_52_17 = e0)
% 231.95/43.09    (5)  all_55_8 = all_52_17
% 231.95/43.09  
% 231.95/43.09  Begin of proof
% 231.95/43.09  | 
% 231.95/43.09  | BETA: splitting (1) gives:
% 231.95/43.09  | 
% 231.95/43.09  | Case 1:
% 231.95/43.09  | | 
% 231.95/43.09  | |   (6)  all_55_8 = e2
% 231.95/43.09  | | 
% 231.95/43.09  | | REF_CLOSE: (2), (5), (6) are inconsistent by sub-proof #1869.
% 231.95/43.09  | | 
% 231.95/43.09  | Case 2:
% 231.95/43.09  | | 
% 231.95/43.09  | |   (7)  all_55_8 = e1 | all_55_8 = e0
% 231.95/43.09  | | 
% 231.95/43.09  | | REF_CLOSE: (3), (4), (5), (7) are inconsistent by sub-proof #1878.
% 231.95/43.09  | | 
% 231.95/43.09  | End of split
% 231.95/43.09  | 
% 231.95/43.09  End of proof
% 231.95/43.09  
% 231.95/43.09  Sub-proof #1868 shows that the following formulas are inconsistent:
% 231.95/43.09  ----------------------------------------------------------------
% 231.95/43.09    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.95/43.09           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.95/43.09    (2)   ~ (all_6_2 = e3)
% 231.95/43.09    (3)  op(e1, e1) = all_6_2
% 231.95/43.09    (4)   ~ (all_52_17 = e3)
% 231.95/43.09    (5)   ~ (all_52_17 = e2)
% 231.95/43.09    (6)  op(all_52_17, all_52_17) = e3
% 231.95/43.09    (7)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 231.95/43.09    (8)   ~ (all_52_17 = e0)
% 231.95/43.09    (9)  all_55_8 = all_52_17
% 231.95/43.09  
% 231.95/43.09  Begin of proof
% 231.95/43.09  | 
% 231.95/43.09  | BETA: splitting (7) gives:
% 231.95/43.09  | 
% 231.95/43.09  | Case 1:
% 231.95/43.09  | | 
% 231.95/43.09  | |   (10)  all_55_8 = e3
% 231.95/43.09  | | 
% 231.95/43.09  | | REF_CLOSE: (4), (9), (10) are inconsistent by sub-proof #1881.
% 231.95/43.09  | | 
% 231.95/43.09  | Case 2:
% 231.95/43.09  | | 
% 231.95/43.09  | |   (11)  all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 231.95/43.09  | | 
% 231.95/43.09  | | BETA: splitting (11) gives:
% 231.95/43.09  | | 
% 231.95/43.09  | | Case 1:
% 231.95/43.09  | | | 
% 231.95/43.09  | | |   (12)  all_55_8 = e2
% 231.95/43.09  | | | 
% 231.95/43.09  | | | REF_CLOSE: (5), (9), (12) are inconsistent by sub-proof #1869.
% 231.95/43.09  | | | 
% 231.95/43.09  | | Case 2:
% 231.95/43.09  | | | 
% 231.95/43.09  | | |   (13)  all_55_8 = e1 | all_55_8 = e0
% 231.95/43.09  | | | 
% 231.95/43.09  | | | BETA: splitting (13) gives:
% 231.95/43.09  | | | 
% 231.95/43.09  | | | Case 1:
% 231.95/43.09  | | | | 
% 231.95/43.09  | | | |   (14)  all_55_8 = e1
% 231.95/43.09  | | | | 
% 231.95/43.09  | | | | COMBINE_EQS: (9), (14) imply:
% 231.95/43.09  | | | |   (15)  all_52_17 = e1
% 231.95/43.09  | | | | 
% 231.95/43.09  | | | | SIMP: (15) implies:
% 231.95/43.09  | | | |   (16)  all_52_17 = e1
% 231.95/43.09  | | | | 
% 231.95/43.09  | | | | REDUCE: (6), (16) imply:
% 231.95/43.09  | | | |   (17)  op(e1, e1) = e3
% 231.95/43.09  | | | | 
% 231.95/43.09  | | | | REF_CLOSE: (1), (2), (3), (17) are inconsistent by sub-proof #2468.
% 231.95/43.09  | | | | 
% 231.95/43.09  | | | Case 2:
% 231.95/43.09  | | | | 
% 231.95/43.09  | | | |   (18)  all_55_8 = e0
% 231.95/43.09  | | | | 
% 231.95/43.09  | | | | REF_CLOSE: (8), (9), (18) are inconsistent by sub-proof #1879.
% 231.95/43.09  | | | | 
% 231.95/43.09  | | | End of split
% 231.95/43.09  | | | 
% 231.95/43.09  | | End of split
% 231.95/43.09  | | 
% 231.95/43.09  | End of split
% 231.95/43.09  | 
% 231.95/43.09  End of proof
% 231.95/43.09  
% 231.95/43.09  Sub-proof #1869 shows that the following formulas are inconsistent:
% 231.95/43.09  ----------------------------------------------------------------
% 231.95/43.09    (1)  all_55_8 = all_52_17
% 231.95/43.09    (2)  all_55_8 = e2
% 231.95/43.09    (3)   ~ (all_52_17 = e2)
% 231.95/43.09  
% 231.95/43.09  Begin of proof
% 231.95/43.09  | 
% 231.95/43.09  | COMBINE_EQS: (1), (2) imply:
% 231.95/43.09  |   (4)  all_52_17 = e2
% 231.95/43.09  | 
% 231.95/43.09  | SIMP: (4) implies:
% 231.95/43.09  |   (5)  all_52_17 = e2
% 231.95/43.09  | 
% 231.95/43.09  | REDUCE: (3), (5) imply:
% 231.95/43.09  |   (6)  $false
% 231.95/43.09  | 
% 231.95/43.09  | CLOSE: (6) is inconsistent.
% 231.95/43.09  | 
% 231.95/43.09  End of proof
% 231.95/43.09  
% 231.95/43.09  Sub-proof #1870 shows that the following formulas are inconsistent:
% 231.95/43.09  ----------------------------------------------------------------
% 231.95/43.09    (1)   ~ (e3 = e1)
% 231.95/43.09    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.95/43.09           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.95/43.09    (3)   ~ (all_6_2 = e3)
% 231.95/43.09    (4)  op(e1, e1) = all_6_2
% 231.95/43.09    (5)   ~ (all_53_7 = e2)
% 231.95/43.09    (6)  all_57_12 = e2
% 231.95/43.09    (7)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.95/43.09         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.95/43.09    (8)   ~ (e3 = e2)
% 231.95/43.09    (9)   ~ (e3 = e0)
% 231.95/43.09    (10)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.95/43.09          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.95/43.09    (11)  op(e0, e3) = all_53_3
% 231.95/43.09    (12)   ~ (e2 = e0)
% 231.95/43.09    (13)   ~ (e1 = e0)
% 231.95/43.09    (14)  all_57_14 = e2
% 231.95/43.09    (15)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.95/43.09          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.95/43.09    (16)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.95/43.09          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 231.95/43.09            e3)
% 231.95/43.09    (17)  op(e0, e2) = all_53_7
% 231.95/43.09    (18)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 231.95/43.09          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 231.95/43.09            e2)
% 231.95/43.09    (19)   ~ (all_53_3 = e0)
% 231.95/43.09    (20)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 231.95/43.09              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 231.95/43.09                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 231.95/43.09                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 231.95/43.09    (21)  op(e1, e1) = e2
% 231.95/43.09    (22)  op(e0, e0) = e1
% 231.95/43.09    (23)   ~ (e2 = e1)
% 231.95/43.09    (24)   ~ (all_6_2 = e0)
% 231.95/43.09    (25)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.95/43.09          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.95/43.09  
% 231.95/43.09  Begin of proof
% 231.95/43.09  | 
% 231.95/43.09  | BETA: splitting (20) gives:
% 231.95/43.09  | 
% 231.95/43.09  | Case 1:
% 231.95/43.09  | | 
% 231.95/43.09  | |   (26)  all_57_15 = e0 & op(e0, e0) = e0
% 231.95/43.09  | | 
% 231.95/43.09  | | ALPHA: (26) implies:
% 231.95/43.09  | |   (27)  op(e0, e0) = e0
% 231.95/43.09  | | 
% 231.95/43.09  | | REF_CLOSE: (2), (13), (22), (27) are inconsistent by sub-proof #2290.
% 231.95/43.09  | | 
% 231.95/43.09  | Case 2:
% 231.95/43.09  | | 
% 231.95/43.09  | |   (28)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 231.95/43.09  | |             e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0 &
% 231.95/43.09  | |             op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 231.95/43.09  | |           (all_57_14 = e0 & op(e0, e1) = e0))
% 231.95/43.09  | | 
% 231.95/43.09  | | ALPHA: (28) implies:
% 231.95/43.09  | |   (29)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 231.95/43.09  | |           e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.95/43.09  | | 
% 231.95/43.09  | | BETA: splitting (29) gives:
% 231.95/43.09  | | 
% 231.95/43.09  | | Case 1:
% 231.95/43.09  | | | 
% 231.95/43.09  | | |   (30)  all_57_12 = e0 & op(e0, e3) = e0
% 231.95/43.09  | | | 
% 231.95/43.09  | | | ALPHA: (30) implies:
% 231.95/43.09  | | |   (31)  op(e0, e3) = e0
% 231.95/43.09  | | | 
% 231.95/43.09  | | | REF_CLOSE: (2), (11), (19), (31) are inconsistent by sub-proof #2366.
% 231.95/43.09  | | | 
% 231.95/43.09  | | Case 2:
% 231.95/43.09  | | | 
% 231.95/43.09  | | |   (32)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1)
% 231.95/43.09  | | |           = e0)
% 231.95/43.09  | | | 
% 231.95/43.09  | | | BETA: splitting (32) gives:
% 231.95/43.09  | | | 
% 231.95/43.09  | | | Case 1:
% 231.95/43.09  | | | | 
% 231.95/43.09  | | | |   (33)  all_57_13 = e0 & op(e0, e2) = e0
% 231.95/43.09  | | | | 
% 231.95/43.09  | | | | ALPHA: (33) implies:
% 231.95/43.09  | | | |   (34)  all_57_13 = e0
% 231.95/43.09  | | | | 
% 231.95/43.09  | | | | BETA: splitting (15) gives:
% 231.95/43.09  | | | | 
% 231.95/43.09  | | | | Case 1:
% 231.95/43.09  | | | | | 
% 231.95/43.09  | | | | |   (35)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2,
% 231.95/43.09  | | | | |             e1) = e3)
% 231.95/43.09  | | | | | 
% 231.95/43.09  | | | | | BETA: splitting (35) gives:
% 231.95/43.09  | | | | | 
% 231.95/43.09  | | | | | Case 1:
% 231.95/43.09  | | | | | | 
% 231.95/43.09  | | | | | |   (36)  all_57_4 = e3 & op(e3, e1) = e3
% 231.95/43.09  | | | | | | 
% 231.95/43.09  | | | | | | ALPHA: (36) implies:
% 231.95/43.09  | | | | | |   (37)  all_57_4 = e3
% 231.95/43.09  | | | | | | 
% 231.95/43.09  | | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (12), (13),
% 231.95/43.09  | | | | | |            (14), (15), (16), (22), (23), (25), (34), (37) are
% 231.95/43.09  | | | | | |            inconsistent by sub-proof #1871.
% 231.95/43.09  | | | | | | 
% 231.95/43.09  | | | | | Case 2:
% 231.95/43.09  | | | | | | 
% 231.95/43.09  | | | | | |   (38)  all_57_5 = e3 & op(e2, e1) = e3
% 231.95/43.09  | | | | | | 
% 231.95/43.09  | | | | | | ALPHA: (38) implies:
% 231.95/43.09  | | | | | |   (39)  all_57_5 = e3
% 231.95/43.09  | | | | | | 
% 231.95/43.09  | | | | | | REF_CLOSE: (1), (2), (4), (5), (7), (8), (9), (10), (12), (13),
% 231.95/43.09  | | | | | |            (14), (16), (17), (18), (20), (21), (22), (23), (24),
% 231.95/43.09  | | | | | |            (39) are inconsistent by sub-proof #2174.
% 231.95/43.09  | | | | | | 
% 231.95/43.09  | | | | | End of split
% 231.95/43.09  | | | | | 
% 231.95/43.09  | | | | Case 2:
% 231.95/43.09  | | | | | 
% 231.95/43.09  | | | | |   (40)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0,
% 231.95/43.09  | | | | |             e1) = e3)
% 231.95/43.09  | | | | | 
% 231.95/43.09  | | | | | REF_CLOSE: (2), (3), (4), (8), (14), (40) are inconsistent by
% 231.95/43.09  | | | | |            sub-proof #2409.
% 231.95/43.09  | | | | | 
% 231.95/43.09  | | | | End of split
% 231.95/43.09  | | | | 
% 231.95/43.09  | | | Case 2:
% 231.95/43.09  | | | | 
% 231.95/43.09  | | | |   (41)  all_57_14 = e0 & op(e0, e1) = e0
% 231.95/43.09  | | | | 
% 231.95/43.09  | | | | REF_CLOSE: (12), (14), (41) are inconsistent by sub-proof #2173.
% 231.95/43.09  | | | | 
% 231.95/43.09  | | | End of split
% 231.95/43.09  | | | 
% 231.95/43.09  | | End of split
% 231.95/43.09  | | 
% 231.95/43.09  | End of split
% 231.95/43.09  | 
% 231.95/43.09  End of proof
% 231.95/43.09  
% 231.95/43.09  Sub-proof #1871 shows that the following formulas are inconsistent:
% 231.95/43.09  ----------------------------------------------------------------
% 231.95/43.09    (1)   ~ (e3 = e1)
% 231.95/43.09    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.95/43.09           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.95/43.09    (3)   ~ (all_6_2 = e3)
% 231.95/43.09    (4)  op(e1, e1) = all_6_2
% 231.95/43.09    (5)  all_57_12 = e2
% 231.95/43.09    (6)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.95/43.09         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.95/43.09    (7)  all_57_4 = e3
% 231.95/43.09    (8)   ~ (e3 = e2)
% 231.95/43.09    (9)   ~ (e3 = e0)
% 231.95/43.09    (10)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.95/43.09          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.95/43.09    (11)   ~ (e2 = e0)
% 231.95/43.09    (12)   ~ (e1 = e0)
% 231.95/43.09    (13)  all_57_14 = e2
% 231.95/43.09    (14)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.95/43.09          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.95/43.09    (15)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 231.95/43.09          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 231.95/43.09            e3)
% 231.95/43.09    (16)  op(e0, e0) = e1
% 231.95/43.09    (17)  all_57_13 = e0
% 231.95/43.09    (18)   ~ (e2 = e1)
% 231.95/43.09    (19)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.95/43.09          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.95/43.09  
% 231.95/43.09  Begin of proof
% 231.95/43.09  | 
% 231.95/43.09  | BETA: splitting (15) gives:
% 231.95/43.09  | 
% 231.95/43.09  | Case 1:
% 231.95/43.09  | | 
% 231.95/43.09  | |   (20)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 231.95/43.09  | |           e3)
% 231.95/43.09  | | 
% 231.95/43.09  | | BETA: splitting (20) gives:
% 231.95/43.09  | | 
% 231.95/43.09  | | Case 1:
% 231.95/43.09  | | | 
% 231.95/43.09  | | |   (21)  all_57_12 = e3 & op(e0, e3) = e3
% 231.95/43.09  | | | 
% 231.95/43.09  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 231.95/43.09  | | |            (13), (14), (18), (19), (21) are inconsistent by sub-proof
% 231.95/43.09  | | |            #1873.
% 231.95/43.09  | | | 
% 231.95/43.09  | | Case 2:
% 231.95/43.09  | | | 
% 231.95/43.09  | | |   (22)  all_57_13 = e3 & op(e0, e2) = e3
% 231.95/43.09  | | | 
% 231.95/43.09  | | | ALPHA: (22) implies:
% 231.95/43.09  | | |   (23)  all_57_13 = e3
% 231.95/43.09  | | | 
% 231.95/43.09  | | | REF_CLOSE: (9), (17), (23) are inconsistent by sub-proof #2184.
% 231.95/43.09  | | | 
% 231.95/43.09  | | End of split
% 231.95/43.09  | | 
% 231.95/43.09  | Case 2:
% 231.95/43.09  | | 
% 231.95/43.09  | |   (24)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 231.95/43.09  | |           e3)
% 231.95/43.09  | | 
% 231.95/43.09  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13),
% 231.95/43.09  | |            (14), (16), (18), (19), (24) are inconsistent by sub-proof #1872.
% 231.95/43.09  | | 
% 231.95/43.09  | End of split
% 231.95/43.09  | 
% 231.95/43.09  End of proof
% 231.95/43.09  
% 231.95/43.09  Sub-proof #1872 shows that the following formulas are inconsistent:
% 231.95/43.09  ----------------------------------------------------------------
% 231.95/43.09    (1)   ~ (e3 = e1)
% 231.95/43.09    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.95/43.09           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.95/43.09    (3)   ~ (all_6_2 = e3)
% 231.95/43.09    (4)  op(e1, e1) = all_6_2
% 231.95/43.09    (5)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.95/43.09         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.95/43.09    (6)  all_57_4 = e3
% 231.95/43.09    (7)   ~ (e3 = e2)
% 231.95/43.09    (8)   ~ (e3 = e0)
% 231.95/43.09    (9)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.95/43.09         (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.95/43.09    (10)   ~ (e2 = e0)
% 231.95/43.09    (11)   ~ (e1 = e0)
% 231.95/43.09    (12)  all_57_14 = e2
% 231.95/43.09    (13)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.95/43.09          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.95/43.09    (14)  op(e0, e0) = e1
% 231.95/43.09    (15)   ~ (e2 = e1)
% 231.95/43.09    (16)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 231.95/43.09    (17)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.95/43.09          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.95/43.09  
% 231.95/43.09  Begin of proof
% 231.95/43.09  | 
% 231.95/43.09  | BETA: splitting (16) gives:
% 231.95/43.09  | 
% 231.95/43.09  | Case 1:
% 231.95/43.09  | | 
% 231.95/43.09  | |   (18)  all_57_14 = e3 & op(e0, e1) = e3
% 231.95/43.09  | | 
% 231.95/43.09  | | ALPHA: (18) implies:
% 231.95/43.09  | |   (19)  all_57_14 = e3
% 231.95/43.09  | | 
% 231.95/43.09  | | COMBINE_EQS: (12), (19) imply:
% 231.95/43.09  | |   (20)  e3 = e2
% 231.95/43.09  | | 
% 231.95/43.09  | | COMBINE_EQS: (6), (20) imply:
% 231.95/43.09  | |   (21)  all_57_4 = e2
% 231.95/43.09  | | 
% 231.95/43.09  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 231.95/43.09  | |            (15), (17), (21) are inconsistent by sub-proof #2370.
% 231.95/43.09  | | 
% 231.95/43.09  | Case 2:
% 231.95/43.09  | | 
% 231.95/43.09  | |   (22)  all_57_15 = e3 & op(e0, e0) = e3
% 231.95/43.09  | | 
% 231.95/43.09  | | ALPHA: (22) implies:
% 231.95/43.09  | |   (23)  op(e0, e0) = e3
% 231.95/43.09  | | 
% 231.95/43.09  | | REF_CLOSE: (1), (2), (14), (23) are inconsistent by sub-proof #2183.
% 231.95/43.09  | | 
% 231.95/43.09  | End of split
% 231.95/43.09  | 
% 231.95/43.09  End of proof
% 231.95/43.09  
% 231.95/43.09  Sub-proof #1873 shows that the following formulas are inconsistent:
% 231.95/43.09  ----------------------------------------------------------------
% 231.95/43.09    (1)   ~ (e3 = e1)
% 231.95/43.09    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.95/43.09           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.95/43.09    (3)   ~ (all_6_2 = e3)
% 231.95/43.09    (4)  op(e1, e1) = all_6_2
% 231.95/43.09    (5)  all_57_12 = e2
% 231.95/43.09    (6)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 231.95/43.09         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 231.95/43.09    (7)  all_57_4 = e3
% 231.95/43.09    (8)   ~ (e3 = e2)
% 231.95/43.09    (9)   ~ (e3 = e0)
% 231.95/43.09    (10)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 231.95/43.09          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 231.95/43.09    (11)   ~ (e2 = e0)
% 231.95/43.09    (12)   ~ (e1 = e0)
% 231.95/43.09    (13)  all_57_14 = e2
% 231.95/43.09    (14)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 231.95/43.09          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 231.95/43.09    (15)   ~ (e2 = e1)
% 231.95/43.09    (16)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 231.95/43.09          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 231.95/43.09    (17)  all_57_12 = e3 & op(e0, e3) = e3
% 231.95/43.09  
% 231.95/43.09  Begin of proof
% 231.95/43.09  | 
% 231.95/43.09  | ALPHA: (17) implies:
% 231.95/43.09  |   (18)  all_57_12 = e3
% 231.95/43.09  | 
% 231.95/43.09  | COMBINE_EQS: (5), (18) imply:
% 231.95/43.09  |   (19)  e3 = e2
% 231.95/43.09  | 
% 231.95/43.09  | COMBINE_EQS: (7), (19) imply:
% 231.95/43.09  |   (20)  all_57_4 = e2
% 231.95/43.09  | 
% 231.95/43.09  | REF_CLOSE: (1), (2), (3), (4), (6), (8), (9), (10), (11), (12), (13), (14),
% 231.95/43.09  |            (15), (16), (20) are inconsistent by sub-proof #2370.
% 231.95/43.09  | 
% 231.95/43.09  End of proof
% 231.95/43.09  
% 231.95/43.09  Sub-proof #1874 shows that the following formulas are inconsistent:
% 231.95/43.09  ----------------------------------------------------------------
% 231.95/43.09    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.95/43.09           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.95/43.09    (2)  op(e3, e0) = e2
% 231.95/43.09    (3)  op(e1, e1) = all_52_21
% 231.95/43.09    (4)  op(e2, e2) = e2
% 231.95/43.09    (5)   ~ (all_53_12 = e1)
% 231.95/43.09    (6)  op(e1, e1) = e2
% 231.95/43.09    (7)  op(all_52_21, all_52_21) = e1
% 231.95/43.09    (8)  op(e3, e0) = all_53_12
% 231.95/43.09  
% 231.95/43.09  Begin of proof
% 231.95/43.09  | 
% 231.95/43.09  | GROUND_INST: instantiating (1) with e2, all_52_21, e1, e1, simplifying with
% 231.95/43.09  |              (3), (6) gives:
% 231.95/43.09  |   (9)  all_52_21 = e2
% 231.95/43.09  | 
% 231.95/43.09  | GROUND_INST: instantiating (1) with all_53_12, e2, e0, e3, simplifying with
% 231.95/43.09  |              (2), (8) gives:
% 231.95/43.09  |   (10)  all_53_12 = e2
% 231.95/43.09  | 
% 231.95/43.09  | REDUCE: (5), (10) imply:
% 231.95/43.09  |   (11)   ~ (e2 = e1)
% 231.95/43.09  | 
% 231.95/43.09  | REDUCE: (7), (9) imply:
% 231.95/43.09  |   (12)  op(e2, e2) = e1
% 231.95/43.09  | 
% 231.95/43.09  | REF_CLOSE: (1), (4), (11), (12) are inconsistent by sub-proof #2306.
% 231.95/43.09  | 
% 231.95/43.09  End of proof
% 231.95/43.09  
% 231.95/43.09  Sub-proof #1875 shows that the following formulas are inconsistent:
% 231.95/43.09  ----------------------------------------------------------------
% 231.95/43.09    (1)  op(e0, e0) = all_4_2
% 231.95/43.09    (2)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 231.95/43.09    (3)  op(e0, e2) = e0
% 231.95/43.09    (4)   ~ (all_53_12 = all_4_2)
% 231.95/43.09    (5)   ~ (all_53_6 = all_53_14)
% 231.95/43.09    (6)   ~ (all_53_6 = e2)
% 231.95/43.09    (7)  op(e2, e0) = e0
% 231.95/43.09    (8)  all_55_15 = e3 | all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 231.95/43.09    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 231.95/43.09           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 231.95/43.09    (10)  all_55_15 = all_4_2
% 231.95/43.09    (11)   ~ (all_53_3 = all_53_7)
% 231.95/43.09    (12)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 231.95/43.09    (13)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 231.95/43.09    (14)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 231.95/43.09    (15)  all_55_9 = all_53_6
% 231.95/43.09    (16)   ~ (all_53_13 = e2)
% 231.95/43.09    (17)   ~ (all_53_4 = all_53_12)
% 231.95/43.09    (18)   ~ (all_53_7 = e2)
% 231.95/43.09    (19)   ~ (all_53_12 = all_53_13)
% 231.95/43.09    (20)   ~ (all_53_14 = all_4_2)
% 231.95/43.09    (21)   ~ (e3 = e2)
% 231.95/43.09    (22)  all_55_1 = all_53_4
% 231.95/43.09    (23)  op(e1, e0) = all_53_14
% 231.95/43.09    (24)   ~ (all_53_6 = all_53_7)
% 231.95/43.09    (25)   ~ (e3 = e0)
% 231.95/43.09    (26)   ~ (all_4_2 = e2)
% 231.95/43.09    (27)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 231.95/43.09    (28)  op(e0, e3) = all_53_3
% 231.95/43.09    (29)   ~ (all_53_2 = e0)
% 231.95/43.09    (30)   ~ (all_53_4 = all_53_7)
% 231.95/43.09    (31)  op(e3, e3) = e0
% 231.95/43.09    (32)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 231.95/43.09          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 231.95/43.09            e1)
% 231.95/43.09    (33)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 231.95/43.09            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 231.95/43.09            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 231.95/43.09            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 231.95/43.09              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 231.95/43.09            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 231.95/43.09            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 231.95/43.09              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 231.95/43.09              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 231.95/43.09            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 231.95/43.09            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 231.95/43.09            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 231.95/43.09              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 231.95/43.09              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 231.95/43.09            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 231.95/43.09              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 231.95/43.09            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 231.95/43.09            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 231.95/43.09              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 231.95/43.09              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 231.95/43.09            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 231.95/43.09            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 231.95/43.09    (34)   ~ (all_53_2 = all_53_14)
% 231.95/43.09    (35)  op(e2, e2) = e2
% 231.95/43.09    (36)  all_55_8 = all_53_2
% 231.95/43.09    (37)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 232.00/43.09          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 232.00/43.09            e3)
% 232.00/43.09    (38)   ~ (all_53_13 = all_4_2)
% 232.00/43.09    (39)   ~ (all_53_4 = all_53_6)
% 232.00/43.09    (40)  op(e0, e2) = all_53_7
% 232.00/43.09    (41)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 232.00/43.09          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 232.00/43.09            e2)
% 232.00/43.09    (42)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 232.00/43.09              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 232.00/43.09                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 232.00/43.09                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 232.00/43.09    (43)  op(e2, e0) = all_53_13
% 232.00/43.09    (44)   ~ (all_53_3 = all_4_2)
% 232.00/43.09    (45)  all_55_11 = all_53_14
% 232.00/43.09    (46)  all_55_3 = all_53_12
% 232.00/43.09    (47)   ~ (all_53_4 = e2)
% 232.00/43.09    (48)  op(e1, e3) = all_53_2
% 232.00/43.09    (49)   ~ (all_4_2 = e3)
% 232.00/43.09    (50)   ~ (all_53_13 = all_53_14)
% 232.00/43.09    (51)  op(e1, e2) = all_53_6
% 232.00/43.09    (52)   ~ (all_53_2 = all_53_6)
% 232.00/43.09    (53)   ~ (all_53_12 = all_53_14)
% 232.00/43.09  
% 232.00/43.09  Begin of proof
% 232.00/43.09  | 
% 232.00/43.09  | GROUND_INST: instantiating (9) with all_53_7, e0, e2, e0, simplifying with
% 232.00/43.09  |              (3), (40) gives:
% 232.00/43.09  |   (54)  all_53_7 = e0
% 232.00/43.09  | 
% 232.00/43.09  | GROUND_INST: instantiating (9) with all_53_13, e0, e0, e2, simplifying with
% 232.00/43.09  |              (7), (43) gives:
% 232.00/43.09  |   (55)  all_53_13 = e0
% 232.00/43.09  | 
% 232.00/43.09  | REDUCE: (11), (54) imply:
% 232.00/43.09  |   (56)   ~ (all_53_3 = e0)
% 232.00/43.09  | 
% 232.00/43.09  | REDUCE: (30), (54) imply:
% 232.00/43.09  |   (57)   ~ (all_53_4 = e0)
% 232.00/43.09  | 
% 232.00/43.09  | REDUCE: (24), (54) imply:
% 232.00/43.09  |   (58)   ~ (all_53_6 = e0)
% 232.00/43.09  | 
% 232.00/43.09  | REDUCE: (19), (55) imply:
% 232.00/43.09  |   (59)   ~ (all_53_12 = e0)
% 232.00/43.09  | 
% 232.00/43.09  | REDUCE: (50), (55) imply:
% 232.00/43.09  |   (60)   ~ (all_53_14 = e0)
% 232.00/43.09  | 
% 232.00/43.09  | SIMP: (60) implies:
% 232.00/43.09  |   (61)   ~ (all_53_14 = e0)
% 232.00/43.09  | 
% 232.00/43.09  | REDUCE: (38), (55) imply:
% 232.00/43.09  |   (62)   ~ (all_4_2 = e0)
% 232.00/43.09  | 
% 232.00/43.09  | SIMP: (62) implies:
% 232.00/43.09  |   (63)   ~ (all_4_2 = e0)
% 232.00/43.09  | 
% 232.00/43.09  | REDUCE: (16), (55) imply:
% 232.00/43.09  |   (64)   ~ (e2 = e0)
% 232.00/43.09  | 
% 232.00/43.09  | SIMP: (64) implies:
% 232.00/43.09  |   (65)   ~ (e2 = e0)
% 232.00/43.09  | 
% 232.00/43.09  | BETA: splitting (8) gives:
% 232.00/43.09  | 
% 232.00/43.09  | Case 1:
% 232.00/43.09  | | 
% 232.00/43.09  | |   (66)  all_55_15 = e3
% 232.00/43.09  | | 
% 232.00/43.09  | | REF_CLOSE: (10), (49), (66) are inconsistent by sub-proof #2503.
% 232.00/43.09  | | 
% 232.00/43.09  | Case 2:
% 232.00/43.09  | | 
% 232.00/43.09  | |   (67)   ~ (all_55_15 = e3)
% 232.00/43.09  | |   (68)  all_55_15 = e2 | all_55_15 = e1 | all_55_15 = e0
% 232.00/43.09  | | 
% 232.00/43.09  | | BETA: splitting (68) gives:
% 232.00/43.09  | | 
% 232.00/43.09  | | Case 1:
% 232.00/43.09  | | | 
% 232.00/43.09  | | |   (69)  all_55_15 = e2
% 232.00/43.09  | | | 
% 232.00/43.09  | | | REF_CLOSE: (10), (26), (69) are inconsistent by sub-proof #2502.
% 232.00/43.09  | | | 
% 232.00/43.09  | | Case 2:
% 232.00/43.09  | | | 
% 232.00/43.09  | | |   (70)   ~ (all_55_15 = e2)
% 232.00/43.09  | | |   (71)  all_55_15 = e1 | all_55_15 = e0
% 232.00/43.09  | | | 
% 232.00/43.09  | | | BETA: splitting (33) gives:
% 232.00/43.09  | | | 
% 232.00/43.09  | | | Case 1:
% 232.00/43.09  | | | | 
% 232.00/43.09  | | | |   (72)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 232.00/43.09  | | | |           op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 232.00/43.09  | | | |           op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 232.00/43.09  | | | |           op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) =
% 232.00/43.09  | | | |           all_52_5 & op(e3, e0) = all_52_7 & $i(all_52_1) & $i(all_52_3)
% 232.00/43.09  | | | |           & $i(all_52_5) & $i(all_52_7)) | (all_52_8 = e3 & all_52_10 =
% 232.00/43.09  | | | |           e2 & all_52_12 = e1 & all_52_14 = e0 & op(all_52_9, all_52_9)
% 232.00/43.09  | | | |           = e3 & op(all_52_11, all_52_11) = e2 & op(all_52_13,
% 232.00/43.09  | | | |             all_52_13) = e1 & op(all_52_15, all_52_15) = e0 & op(e2, e3)
% 232.00/43.09  | | | |           = all_52_9 & op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13 &
% 232.00/43.09  | | | |           op(e2, e0) = all_52_15 & $i(all_52_9) & $i(all_52_11) &
% 232.00/43.09  | | | |           $i(all_52_13) & $i(all_52_15))
% 232.00/43.09  | | | | 
% 232.00/43.09  | | | | BETA: splitting (72) gives:
% 232.00/43.09  | | | | 
% 232.00/43.09  | | | | Case 1:
% 232.00/43.09  | | | | | 
% 232.00/43.09  | | | | |   (73)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 232.00/43.09  | | | | |         & op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 232.00/43.09  | | | | |         op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 232.00/43.09  | | | | |         op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) =
% 232.00/43.09  | | | | |         all_52_5 & op(e3, e0) = all_52_7 & $i(all_52_1) & $i(all_52_3)
% 232.00/43.09  | | | | |         & $i(all_52_5) & $i(all_52_7)
% 232.00/43.09  | | | | | 
% 232.00/43.09  | | | | | ALPHA: (73) implies:
% 232.00/43.09  | | | | |   (74)  op(e3, e3) = all_52_1
% 232.00/43.10  | | | | |   (75)  op(all_52_1, all_52_1) = e3
% 232.00/43.10  | | | | | 
% 232.00/43.10  | | | | | BETA: splitting (71) gives:
% 232.00/43.10  | | | | | 
% 232.00/43.10  | | | | | Case 1:
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | |   (76)  all_55_15 = e1
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | | COMBINE_EQS: (10), (76) imply:
% 232.00/43.10  | | | | | |   (77)  all_4_2 = e1
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | | SIMP: (77) implies:
% 232.00/43.10  | | | | | |   (78)  all_4_2 = e1
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | | REDUCE: (44), (78) imply:
% 232.00/43.10  | | | | | |   (79)   ~ (all_53_3 = e1)
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | | REDUCE: (49), (78) imply:
% 232.00/43.10  | | | | | |   (80)   ~ (e3 = e1)
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | | SIMP: (80) implies:
% 232.00/43.10  | | | | | |   (81)   ~ (e3 = e1)
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | | REDUCE: (26), (78) imply:
% 232.00/43.10  | | | | | |   (82)   ~ (e2 = e1)
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | | SIMP: (82) implies:
% 232.00/43.10  | | | | | |   (83)   ~ (e2 = e1)
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | | REDUCE: (63), (78) imply:
% 232.00/43.10  | | | | | |   (84)   ~ (e1 = e0)
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | | REDUCE: (1), (78) imply:
% 232.00/43.10  | | | | | |   (85)  op(e0, e0) = e1
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | | REF_CLOSE: (9), (18), (21), (25), (28), (31), (32), (37), (40),
% 232.00/43.10  | | | | | |            (41), (42), (56), (65), (74), (75), (79), (81), (83),
% 232.00/43.10  | | | | | |            (84), (85) are inconsistent by sub-proof #1915.
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | Case 2:
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | |   (86)  all_55_15 = e0
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | | REF_CLOSE: (10), (63), (86) are inconsistent by sub-proof #1884.
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | End of split
% 232.00/43.10  | | | | | 
% 232.00/43.10  | | | | Case 2:
% 232.00/43.10  | | | | | 
% 232.00/43.10  | | | | |   (87)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 232.00/43.10  | | | | |         e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11, all_52_11) =
% 232.00/43.10  | | | | |         e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15, all_52_15)
% 232.00/43.10  | | | | |         = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 & op(e2,
% 232.00/43.10  | | | | |           e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 232.00/43.10  | | | | |         $i(all_52_11) & $i(all_52_13) & $i(all_52_15)
% 232.00/43.10  | | | | | 
% 232.00/43.10  | | | | | ALPHA: (87) implies:
% 232.00/43.10  | | | | |   (88)  op(e2, e0) = all_52_15
% 232.00/43.10  | | | | |   (89)  op(all_52_15, all_52_15) = e0
% 232.00/43.10  | | | | | 
% 232.00/43.10  | | | | | BETA: splitting (71) gives:
% 232.00/43.10  | | | | | 
% 232.00/43.10  | | | | | Case 1:
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | |   (90)  all_55_15 = e1
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | | COMBINE_EQS: (10), (90) imply:
% 232.00/43.10  | | | | | |   (91)  all_4_2 = e1
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | | SIMP: (91) implies:
% 232.00/43.10  | | | | | |   (92)  all_4_2 = e1
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | | REDUCE: (44), (92) imply:
% 232.00/43.10  | | | | | |   (93)   ~ (all_53_3 = e1)
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | | REDUCE: (49), (92) imply:
% 232.00/43.10  | | | | | |   (94)   ~ (e3 = e1)
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | | SIMP: (94) implies:
% 232.00/43.10  | | | | | |   (95)   ~ (e3 = e1)
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | | REDUCE: (26), (92) imply:
% 232.00/43.10  | | | | | |   (96)   ~ (e2 = e1)
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | | SIMP: (96) implies:
% 232.00/43.10  | | | | | |   (97)   ~ (e2 = e1)
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | | REDUCE: (63), (92) imply:
% 232.00/43.10  | | | | | |   (98)   ~ (e1 = e0)
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | | REDUCE: (1), (92) imply:
% 232.00/43.10  | | | | | |   (99)  op(e0, e0) = e1
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | | REF_CLOSE: (7), (9), (18), (21), (25), (28), (32), (37), (40), (41),
% 232.00/43.10  | | | | | |            (42), (56), (65), (88), (89), (93), (95), (97), (98),
% 232.00/43.10  | | | | | |            (99) are inconsistent by sub-proof #1896.
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | Case 2:
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | |   (100)  all_55_15 = e0
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | | REF_CLOSE: (10), (63), (100) are inconsistent by sub-proof #1884.
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | End of split
% 232.00/43.10  | | | | | 
% 232.00/43.10  | | | | End of split
% 232.00/43.10  | | | | 
% 232.00/43.10  | | | Case 2:
% 232.00/43.10  | | | | 
% 232.00/43.10  | | | |   (101)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 232.00/43.10  | | | |            e0 & op(all_52_17, all_52_17) = e3 & op(all_52_19, all_52_19)
% 232.00/43.10  | | | |            = e2 & op(all_52_21, all_52_21) = e1 & op(all_52_23,
% 232.00/43.10  | | | |              all_52_23) = e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 232.00/43.10  | | | |            all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23 &
% 232.00/43.10  | | | |            $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 232.00/43.10  | | | |            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28
% 232.00/43.10  | | | |            = e1 & all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 232.00/43.10  | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29, all_52_29) = e1
% 232.00/43.10  | | | |            & op(all_52_31, all_52_31) = e0 & op(e0, e3) = all_52_25 &
% 232.00/43.10  | | | |            op(e0, e2) = all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 232.00/43.10  | | | |            = all_52_31 & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 232.00/43.10  | | | |            $i(all_52_31))
% 232.00/43.10  | | | | 
% 232.00/43.10  | | | | BETA: splitting (101) gives:
% 232.00/43.10  | | | | 
% 232.00/43.10  | | | | Case 1:
% 232.00/43.10  | | | | | 
% 232.00/43.10  | | | | |   (102)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22
% 232.00/43.10  | | | | |          = e0 & op(all_52_17, all_52_17) = e3 & op(all_52_19,
% 232.00/43.10  | | | | |            all_52_19) = e2 & op(all_52_21, all_52_21) = e1 &
% 232.00/43.10  | | | | |          op(all_52_23, all_52_23) = e0 & op(e1, e3) = all_52_17 &
% 232.00/43.10  | | | | |          op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0)
% 232.00/43.10  | | | | |          = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 232.00/43.10  | | | | |          $i(all_52_23)
% 232.00/43.10  | | | | | 
% 232.00/43.10  | | | | | ALPHA: (102) implies:
% 232.00/43.10  | | | | |   (103)  op(e1, e0) = all_52_23
% 232.00/43.10  | | | | |   (104)  op(e1, e2) = all_52_19
% 232.00/43.10  | | | | |   (105)  op(e1, e3) = all_52_17
% 232.00/43.10  | | | | |   (106)  op(all_52_19, all_52_19) = e2
% 232.00/43.10  | | | | |   (107)  op(all_52_17, all_52_17) = e3
% 232.00/43.10  | | | | | 
% 232.00/43.10  | | | | | BETA: splitting (71) gives:
% 232.00/43.10  | | | | | 
% 232.00/43.10  | | | | | Case 1:
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | |   (108)  all_55_15 = e1
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | | COMBINE_EQS: (10), (108) imply:
% 232.00/43.10  | | | | | |   (109)  all_4_2 = e1
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | | SIMP: (109) implies:
% 232.00/43.10  | | | | | |   (110)  all_4_2 = e1
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | | REDUCE: (4), (110) imply:
% 232.00/43.10  | | | | | |   (111)   ~ (all_53_12 = e1)
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | | REDUCE: (20), (110) imply:
% 232.00/43.10  | | | | | |   (112)   ~ (all_53_14 = e1)
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | | GROUND_INST: instantiating (9) with all_53_14, all_52_23, e0, e1,
% 232.00/43.10  | | | | | |              simplifying with (23), (103) gives:
% 232.00/43.10  | | | | | |   (113)  all_53_14 = all_52_23
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | | GROUND_INST: instantiating (9) with all_53_6, all_52_19, e2, e1,
% 232.00/43.10  | | | | | |              simplifying with (51), (104) gives:
% 232.00/43.10  | | | | | |   (114)  all_53_6 = all_52_19
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | | GROUND_INST: instantiating (9) with all_53_2, all_52_17, e3, e1,
% 232.00/43.10  | | | | | |              simplifying with (48), (105) gives:
% 232.00/43.10  | | | | | |   (115)  all_53_2 = all_52_17
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | | COMBINE_EQS: (45), (113) imply:
% 232.00/43.10  | | | | | |   (116)  all_55_11 = all_52_23
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | | COMBINE_EQS: (15), (114) imply:
% 232.00/43.10  | | | | | |   (117)  all_55_9 = all_52_19
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | | COMBINE_EQS: (36), (115) imply:
% 232.00/43.10  | | | | | |   (118)  all_55_8 = all_52_17
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | | REDUCE: (52), (114), (115) imply:
% 232.00/43.10  | | | | | |   (119)   ~ (all_52_17 = all_52_19)
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | | REDUCE: (34), (113), (115) imply:
% 232.00/43.10  | | | | | |   (120)   ~ (all_52_17 = all_52_23)
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | | REDUCE: (29), (115) imply:
% 232.00/43.10  | | | | | |   (121)   ~ (all_52_17 = e0)
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | | REDUCE: (39), (114) imply:
% 232.00/43.10  | | | | | |   (122)   ~ (all_53_4 = all_52_19)
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | | REDUCE: (5), (113), (114) imply:
% 232.00/43.10  | | | | | |   (123)   ~ (all_52_19 = all_52_23)
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | | REDUCE: (6), (114) imply:
% 232.00/43.10  | | | | | |   (124)   ~ (all_52_19 = e2)
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | | REDUCE: (58), (114) imply:
% 232.00/43.10  | | | | | |   (125)   ~ (all_52_19 = e0)
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | | REDUCE: (53), (113) imply:
% 232.00/43.10  | | | | | |   (126)   ~ (all_53_12 = all_52_23)
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | | REDUCE: (112), (113) imply:
% 232.00/43.10  | | | | | |   (127)   ~ (all_52_23 = e1)
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | | REDUCE: (61), (113) imply:
% 232.00/43.10  | | | | | |   (128)   ~ (all_52_23 = e0)
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | | BETA: splitting (12) gives:
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | | Case 1:
% 232.00/43.10  | | | | | | | 
% 232.00/43.10  | | | | | | |   (129)  all_55_3 = e3
% 232.00/43.10  | | | | | | | 
% 232.00/43.10  | | | | | | | COMBINE_EQS: (46), (129) imply:
% 232.00/43.10  | | | | | | |   (130)  all_53_12 = e3
% 232.00/43.10  | | | | | | | 
% 232.00/43.10  | | | | | | | SIMP: (130) implies:
% 232.00/43.10  | | | | | | |   (131)  all_53_12 = e3
% 232.00/43.10  | | | | | | | 
% 232.00/43.10  | | | | | | | REDUCE: (17), (131) imply:
% 232.00/43.10  | | | | | | |   (132)   ~ (all_53_4 = e3)
% 232.00/43.10  | | | | | | | 
% 232.00/43.10  | | | | | | | BETA: splitting (2) gives:
% 232.00/43.10  | | | | | | | 
% 232.00/43.10  | | | | | | | Case 1:
% 232.00/43.10  | | | | | | | | 
% 232.00/43.10  | | | | | | | |   (133)  all_55_1 = e3
% 232.00/43.10  | | | | | | | | 
% 232.00/43.10  | | | | | | | | COMBINE_EQS: (22), (133) imply:
% 232.00/43.10  | | | | | | | |   (134)  all_53_4 = e3
% 232.00/43.10  | | | | | | | | 
% 232.00/43.10  | | | | | | | | REDUCE: (132), (134) imply:
% 232.00/43.10  | | | | | | | |   (135)  $false
% 232.00/43.10  | | | | | | | | 
% 232.00/43.10  | | | | | | | | CLOSE: (135) is inconsistent.
% 232.00/43.10  | | | | | | | | 
% 232.00/43.10  | | | | | | | Case 2:
% 232.00/43.10  | | | | | | | | 
% 232.00/43.10  | | | | | | | |   (136)  all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 232.00/43.10  | | | | | | | | 
% 232.00/43.10  | | | | | | | | BETA: splitting (136) gives:
% 232.00/43.10  | | | | | | | | 
% 232.00/43.10  | | | | | | | | Case 1:
% 232.00/43.10  | | | | | | | | | 
% 232.00/43.10  | | | | | | | | |   (137)  all_55_1 = e2
% 232.00/43.10  | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | COMBINE_EQS: (22), (137) imply:
% 232.00/43.10  | | | | | | | | |   (138)  all_53_4 = e2
% 232.00/43.10  | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | REDUCE: (47), (138) imply:
% 232.00/43.10  | | | | | | | | |   (139)  $false
% 232.00/43.10  | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | CLOSE: (139) is inconsistent.
% 232.00/43.10  | | | | | | | | | 
% 232.00/43.10  | | | | | | | | Case 2:
% 232.00/43.10  | | | | | | | | | 
% 232.00/43.10  | | | | | | | | |   (140)  all_55_1 = e1 | all_55_1 = e0
% 232.00/43.10  | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | BETA: splitting (140) gives:
% 232.00/43.10  | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | Case 1:
% 232.00/43.10  | | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | |   (141)  all_55_1 = e1
% 232.00/43.10  | | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | | COMBINE_EQS: (22), (141) imply:
% 232.00/43.10  | | | | | | | | | |   (142)  all_53_4 = e1
% 232.00/43.10  | | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | | REDUCE: (122), (142) imply:
% 232.00/43.10  | | | | | | | | | |   (143)   ~ (all_52_19 = e1)
% 232.00/43.10  | | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | | SIMP: (143) implies:
% 232.00/43.10  | | | | | | | | | |   (144)   ~ (all_52_19 = e1)
% 232.00/43.10  | | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | | BETA: splitting (14) gives:
% 232.00/43.10  | | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | | Case 1:
% 232.00/43.10  | | | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | | |   (145)  all_55_9 = e3
% 232.00/43.10  | | | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | | | COMBINE_EQS: (117), (145) imply:
% 232.00/43.10  | | | | | | | | | | |   (146)  all_52_19 = e3
% 232.00/43.10  | | | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | | | REDUCE: (106), (146) imply:
% 232.00/43.10  | | | | | | | | | | |   (147)  op(e3, e3) = e2
% 232.00/43.10  | | | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | | | REF_CLOSE: (9), (31), (65), (147) are inconsistent by
% 232.00/43.10  | | | | | | | | | | |            sub-proof #2403.
% 232.00/43.10  | | | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | | Case 2:
% 232.00/43.10  | | | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | | |   (148)  all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 232.00/43.10  | | | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | | | REF_CLOSE: (117), (124), (125), (144), (148) are inconsistent
% 232.00/43.10  | | | | | | | | | | |            by sub-proof #1882.
% 232.00/43.10  | | | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | | End of split
% 232.00/43.10  | | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | Case 2:
% 232.00/43.10  | | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | |   (149)  all_55_1 = e0
% 232.00/43.10  | | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | | COMBINE_EQS: (22), (149) imply:
% 232.00/43.10  | | | | | | | | | |   (150)  all_53_4 = e0
% 232.00/43.10  | | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | | REDUCE: (57), (150) imply:
% 232.00/43.10  | | | | | | | | | |   (151)  $false
% 232.00/43.10  | | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | | CLOSE: (151) is inconsistent.
% 232.00/43.10  | | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | End of split
% 232.00/43.10  | | | | | | | | | 
% 232.00/43.10  | | | | | | | | End of split
% 232.00/43.10  | | | | | | | | 
% 232.00/43.10  | | | | | | | End of split
% 232.00/43.10  | | | | | | | 
% 232.00/43.10  | | | | | | Case 2:
% 232.00/43.10  | | | | | | | 
% 232.00/43.10  | | | | | | |   (152)  all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 232.00/43.10  | | | | | | | 
% 232.00/43.10  | | | | | | | BETA: splitting (152) gives:
% 232.00/43.10  | | | | | | | 
% 232.00/43.10  | | | | | | | Case 1:
% 232.00/43.10  | | | | | | | | 
% 232.00/43.10  | | | | | | | |   (153)  all_55_3 = e2
% 232.00/43.10  | | | | | | | | 
% 232.00/43.10  | | | | | | | | COMBINE_EQS: (46), (153) imply:
% 232.00/43.10  | | | | | | | |   (154)  all_53_12 = e2
% 232.00/43.10  | | | | | | | | 
% 232.00/43.10  | | | | | | | | SIMP: (154) implies:
% 232.00/43.10  | | | | | | | |   (155)  all_53_12 = e2
% 232.00/43.10  | | | | | | | | 
% 232.00/43.10  | | | | | | | | REDUCE: (126), (155) imply:
% 232.00/43.10  | | | | | | | |   (156)   ~ (all_52_23 = e2)
% 232.00/43.10  | | | | | | | | 
% 232.00/43.10  | | | | | | | | SIMP: (156) implies:
% 232.00/43.10  | | | | | | | |   (157)   ~ (all_52_23 = e2)
% 232.00/43.10  | | | | | | | | 
% 232.00/43.10  | | | | | | | | BETA: splitting (13) gives:
% 232.00/43.10  | | | | | | | | 
% 232.00/43.10  | | | | | | | | Case 1:
% 232.00/43.10  | | | | | | | | | 
% 232.00/43.10  | | | | | | | | |   (158)  all_55_11 = e3
% 232.00/43.10  | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | COMBINE_EQS: (116), (158) imply:
% 232.00/43.10  | | | | | | | | |   (159)  all_52_23 = e3
% 232.00/43.10  | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | SIMP: (159) implies:
% 232.00/43.10  | | | | | | | | |   (160)  all_52_23 = e3
% 232.00/43.10  | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | REDUCE: (120), (160) imply:
% 232.00/43.10  | | | | | | | | |   (161)   ~ (all_52_17 = e3)
% 232.00/43.10  | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | REDUCE: (123), (160) imply:
% 232.00/43.10  | | | | | | | | |   (162)   ~ (all_52_19 = e3)
% 232.00/43.10  | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | BETA: splitting (14) gives:
% 232.00/43.10  | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | Case 1:
% 232.00/43.10  | | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | |   (163)  all_55_9 = e3
% 232.00/43.10  | | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | | COMBINE_EQS: (117), (163) imply:
% 232.00/43.10  | | | | | | | | | |   (164)  all_52_19 = e3
% 232.00/43.10  | | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | | REDUCE: (162), (164) imply:
% 232.00/43.10  | | | | | | | | | |   (165)  $false
% 232.00/43.10  | | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | | CLOSE: (165) is inconsistent.
% 232.00/43.10  | | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | Case 2:
% 232.00/43.10  | | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | |   (166)  all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 232.00/43.10  | | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | | BETA: splitting (166) gives:
% 232.00/43.10  | | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | | Case 1:
% 232.00/43.10  | | | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | | |   (167)  all_55_9 = e2
% 232.00/43.10  | | | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | | | COMBINE_EQS: (117), (167) imply:
% 232.00/43.10  | | | | | | | | | | |   (168)  all_52_19 = e2
% 232.00/43.10  | | | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | | | REDUCE: (124), (168) imply:
% 232.00/43.10  | | | | | | | | | | |   (169)  $false
% 232.00/43.10  | | | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | | | CLOSE: (169) is inconsistent.
% 232.00/43.10  | | | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | | Case 2:
% 232.00/43.10  | | | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | | |   (170)  all_55_9 = e1 | all_55_9 = e0
% 232.00/43.10  | | | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | | | BETA: splitting (170) gives:
% 232.00/43.10  | | | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | | | Case 1:
% 232.00/43.10  | | | | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | | | |   (171)  all_55_9 = e1
% 232.00/43.10  | | | | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | | | | COMBINE_EQS: (117), (171) imply:
% 232.00/43.10  | | | | | | | | | | | |   (172)  all_52_19 = e1
% 232.00/43.10  | | | | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | | | | SIMP: (172) implies:
% 232.00/43.10  | | | | | | | | | | | |   (173)  all_52_19 = e1
% 232.00/43.10  | | | | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | | | | REDUCE: (119), (173) imply:
% 232.00/43.10  | | | | | | | | | | | |   (174)   ~ (all_52_17 = e1)
% 232.00/43.10  | | | | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | | | | BETA: splitting (27) gives:
% 232.00/43.10  | | | | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | | | | Case 1:
% 232.00/43.10  | | | | | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | | | | |   (175)  all_55_8 = e3
% 232.00/43.10  | | | | | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | | | | | REF_CLOSE: (118), (161), (175) are inconsistent by sub-proof
% 232.00/43.10  | | | | | | | | | | | | |            #1881.
% 232.00/43.10  | | | | | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | | | | Case 2:
% 232.00/43.10  | | | | | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | | | | |   (176)   ~ (all_55_8 = e3)
% 232.00/43.10  | | | | | | | | | | | | |   (177)  all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 232.00/43.10  | | | | | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | | | | | BETA: splitting (177) gives:
% 232.00/43.10  | | | | | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | | | | | Case 1:
% 232.00/43.10  | | | | | | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | | | | | |   (178)  all_55_8 = e2
% 232.00/43.10  | | | | | | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | | | | | | COMBINE_EQS: (118), (178) imply:
% 232.00/43.10  | | | | | | | | | | | | | |   (179)  all_52_17 = e2
% 232.00/43.10  | | | | | | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | | | | | | SIMP: (179) implies:
% 232.00/43.10  | | | | | | | | | | | | | |   (180)  all_52_17 = e2
% 232.00/43.10  | | | | | | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | | | | | | REDUCE: (161), (180) imply:
% 232.00/43.10  | | | | | | | | | | | | | |   (181)   ~ (e3 = e2)
% 232.00/43.10  | | | | | | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | | | | | | REDUCE: (107), (180) imply:
% 232.00/43.10  | | | | | | | | | | | | | |   (182)  op(e2, e2) = e3
% 232.00/43.10  | | | | | | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | | | | | | REF_CLOSE: (9), (21), (35), (182) are inconsistent by
% 232.00/43.10  | | | | | | | | | | | | | |            sub-proof #2298.
% 232.00/43.10  | | | | | | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | | | | | Case 2:
% 232.00/43.10  | | | | | | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | | | | | |   (183)  all_55_8 = e1 | all_55_8 = e0
% 232.00/43.10  | | | | | | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | | | | | | REF_CLOSE: (118), (121), (174), (183) are inconsistent by
% 232.00/43.10  | | | | | | | | | | | | | |            sub-proof #1878.
% 232.00/43.10  | | | | | | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | | | | | End of split
% 232.00/43.10  | | | | | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | | | | End of split
% 232.00/43.10  | | | | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | | | Case 2:
% 232.00/43.10  | | | | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | | | |   (184)  all_55_9 = e0
% 232.00/43.10  | | | | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | | | | COMBINE_EQS: (117), (184) imply:
% 232.00/43.10  | | | | | | | | | | | |   (185)  all_52_19 = e0
% 232.00/43.10  | | | | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | | | | SIMP: (185) implies:
% 232.00/43.10  | | | | | | | | | | | |   (186)  all_52_19 = e0
% 232.00/43.10  | | | | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | | | | REDUCE: (125), (186) imply:
% 232.00/43.10  | | | | | | | | | | | |   (187)  $false
% 232.00/43.10  | | | | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | | | | CLOSE: (187) is inconsistent.
% 232.00/43.10  | | | | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | | | End of split
% 232.00/43.10  | | | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | | End of split
% 232.00/43.10  | | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | End of split
% 232.00/43.10  | | | | | | | | | 
% 232.00/43.10  | | | | | | | | Case 2:
% 232.00/43.10  | | | | | | | | | 
% 232.00/43.10  | | | | | | | | |   (188)  all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 232.00/43.10  | | | | | | | | | 
% 232.00/43.10  | | | | | | | | | REF_CLOSE: (116), (127), (128), (157), (188) are inconsistent
% 232.00/43.10  | | | | | | | | |            by sub-proof #2106.
% 232.00/43.10  | | | | | | | | | 
% 232.00/43.10  | | | | | | | | End of split
% 232.00/43.10  | | | | | | | | 
% 232.00/43.10  | | | | | | | Case 2:
% 232.00/43.10  | | | | | | | | 
% 232.00/43.10  | | | | | | | |   (189)  all_55_3 = e1 | all_55_3 = e0
% 232.00/43.10  | | | | | | | | 
% 232.00/43.10  | | | | | | | | REF_CLOSE: (46), (59), (111), (189) are inconsistent by
% 232.00/43.10  | | | | | | | |            sub-proof #2132.
% 232.00/43.10  | | | | | | | | 
% 232.00/43.10  | | | | | | | End of split
% 232.00/43.10  | | | | | | | 
% 232.00/43.10  | | | | | | End of split
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | Case 2:
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | |   (190)  all_55_15 = e0
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | | REF_CLOSE: (10), (63), (190) are inconsistent by sub-proof #1884.
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | End of split
% 232.00/43.10  | | | | | 
% 232.00/43.10  | | | | Case 2:
% 232.00/43.10  | | | | | 
% 232.00/43.10  | | | | |   (191)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30
% 232.00/43.10  | | | | |          = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 232.00/43.10  | | | | |            all_52_27) = e2 & op(all_52_29, all_52_29) = e1 &
% 232.00/43.10  | | | | |          op(all_52_31, all_52_31) = e0 & op(e0, e3) = all_52_25 &
% 232.00/43.10  | | | | |          op(e0, e2) = all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 232.00/43.10  | | | | |          = all_52_31 & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 232.00/43.10  | | | | |          $i(all_52_31)
% 232.00/43.10  | | | | | 
% 232.00/43.10  | | | | | ALPHA: (191) implies:
% 232.00/43.10  | | | | |   (192)  op(e0, e0) = all_52_31
% 232.00/43.10  | | | | |   (193)  op(e0, e2) = all_52_27
% 232.00/43.10  | | | | |   (194)  op(all_52_27, all_52_27) = e2
% 232.00/43.10  | | | | | 
% 232.00/43.10  | | | | | BETA: splitting (71) gives:
% 232.00/43.10  | | | | | 
% 232.00/43.10  | | | | | Case 1:
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | |   (195)  all_55_15 = e1
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | | COMBINE_EQS: (10), (195) imply:
% 232.00/43.10  | | | | | |   (196)  all_4_2 = e1
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | | SIMP: (196) implies:
% 232.00/43.10  | | | | | |   (197)  all_4_2 = e1
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | | REDUCE: (44), (197) imply:
% 232.00/43.10  | | | | | |   (198)   ~ (all_53_3 = e1)
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | | REDUCE: (49), (197) imply:
% 232.00/43.10  | | | | | |   (199)   ~ (e3 = e1)
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | | SIMP: (199) implies:
% 232.00/43.10  | | | | | |   (200)   ~ (e3 = e1)
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | | REDUCE: (26), (197) imply:
% 232.00/43.10  | | | | | |   (201)   ~ (e2 = e1)
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | | SIMP: (201) implies:
% 232.00/43.10  | | | | | |   (202)   ~ (e2 = e1)
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | | REDUCE: (63), (197) imply:
% 232.00/43.10  | | | | | |   (203)   ~ (e1 = e0)
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | | REDUCE: (1), (197) imply:
% 232.00/43.10  | | | | | |   (204)  op(e0, e0) = e1
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | | REF_CLOSE: (3), (9), (18), (21), (25), (28), (32), (37), (40), (41),
% 232.00/43.10  | | | | | |            (42), (56), (65), (192), (193), (194), (198), (200),
% 232.00/43.10  | | | | | |            (202), (203), (204) are inconsistent by sub-proof #1876.
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | Case 2:
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | |   (205)  all_55_15 = e0
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | | REF_CLOSE: (10), (63), (205) are inconsistent by sub-proof #1884.
% 232.00/43.10  | | | | | | 
% 232.00/43.10  | | | | | End of split
% 232.00/43.10  | | | | | 
% 232.00/43.10  | | | | End of split
% 232.00/43.10  | | | | 
% 232.00/43.10  | | | End of split
% 232.00/43.10  | | | 
% 232.00/43.10  | | End of split
% 232.00/43.10  | | 
% 232.00/43.10  | End of split
% 232.00/43.10  | 
% 232.00/43.10  End of proof
% 232.00/43.10  
% 232.00/43.10  Sub-proof #1876 shows that the following formulas are inconsistent:
% 232.00/43.10  ----------------------------------------------------------------
% 232.00/43.10    (1)  op(e0, e2) = e0
% 232.00/43.10    (2)   ~ (e3 = e1)
% 232.00/43.10    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.00/43.10           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.00/43.10    (4)   ~ (all_53_7 = e2)
% 232.00/43.10    (5)   ~ (e3 = e2)
% 232.00/43.10    (6)   ~ (e3 = e0)
% 232.00/43.10    (7)  op(e0, e3) = all_53_3
% 232.00/43.10    (8)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 232.00/43.10         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 232.00/43.10    (9)  op(e0, e0) = all_52_31
% 232.00/43.10    (10)   ~ (e2 = e0)
% 232.00/43.10    (11)   ~ (e1 = e0)
% 232.00/43.10    (12)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 232.00/43.10          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 232.00/43.10            e3)
% 232.00/43.10    (13)  op(e0, e2) = all_53_7
% 232.00/43.10    (14)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 232.00/43.10          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 232.00/43.10            e2)
% 232.00/43.10    (15)   ~ (all_53_3 = e0)
% 232.00/43.10    (16)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 232.00/43.10              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 232.00/43.10                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 232.00/43.10                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 232.00/43.10    (17)   ~ (all_53_3 = e1)
% 232.00/43.10    (18)  op(e0, e0) = e1
% 232.00/43.10    (19)  op(e0, e2) = all_52_27
% 232.00/43.10    (20)   ~ (e2 = e1)
% 232.00/43.10    (21)  op(all_52_27, all_52_27) = e2
% 232.00/43.10  
% 232.00/43.10  Begin of proof
% 232.00/43.10  | 
% 232.00/43.10  | BETA: splitting (8) gives:
% 232.00/43.10  | 
% 232.00/43.10  | Case 1:
% 232.00/43.10  | | 
% 232.00/43.10  | |   (22)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 232.00/43.10  | |           e1)
% 232.00/43.10  | | 
% 232.00/43.10  | | REF_CLOSE: (2), (3), (5), (6), (7), (10), (11), (12), (14), (15), (16),
% 232.00/43.10  | |            (17), (18), (20), (22) are inconsistent by sub-proof #1917.
% 232.00/43.10  | | 
% 232.00/43.10  | Case 2:
% 232.00/43.10  | | 
% 232.00/43.10  | |   (23)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 232.00/43.10  | |           e1)
% 232.00/43.10  | | 
% 232.00/43.10  | | BETA: splitting (23) gives:
% 232.00/43.10  | | 
% 232.00/43.10  | | Case 1:
% 232.00/43.10  | | | 
% 232.00/43.10  | | |   (24)  all_57_14 = e1 & op(e0, e1) = e1
% 232.00/43.10  | | | 
% 232.00/43.10  | | | ALPHA: (24) implies:
% 232.00/43.10  | | |   (25)  all_57_14 = e1
% 232.00/43.10  | | | 
% 232.00/43.10  | | | REF_CLOSE: (2), (3), (4), (5), (6), (10), (11), (12), (13), (14), (16),
% 232.00/43.10  | | |            (18), (20), (25) are inconsistent by sub-proof #2175.
% 232.00/43.10  | | | 
% 232.00/43.10  | | Case 2:
% 232.00/43.10  | | | 
% 232.00/43.10  | | |   (26)  all_57_15 = e1 & op(e0, e0) = e1
% 232.00/43.10  | | | 
% 232.00/43.10  | | | REF_CLOSE: (1), (3), (9), (19), (20), (21), (26) are inconsistent by
% 232.00/43.10  | | |            sub-proof #1877.
% 232.00/43.10  | | | 
% 232.00/43.10  | | End of split
% 232.00/43.10  | | 
% 232.00/43.10  | End of split
% 232.00/43.10  | 
% 232.00/43.10  End of proof
% 232.00/43.10  
% 232.00/43.10  Sub-proof #1877 shows that the following formulas are inconsistent:
% 232.00/43.10  ----------------------------------------------------------------
% 232.00/43.10    (1)  op(e0, e2) = e0
% 232.00/43.10    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.00/43.10           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.00/43.10    (3)  all_57_15 = e1 & op(e0, e0) = e1
% 232.00/43.10    (4)  op(e0, e0) = all_52_31
% 232.00/43.10    (5)  op(e0, e2) = all_52_27
% 232.00/43.10    (6)   ~ (e2 = e1)
% 232.00/43.10    (7)  op(all_52_27, all_52_27) = e2
% 232.00/43.10  
% 232.00/43.10  Begin of proof
% 232.00/43.10  | 
% 232.00/43.10  | ALPHA: (3) implies:
% 232.00/43.10  |   (8)  op(e0, e0) = e1
% 232.00/43.10  | 
% 232.00/43.10  | GROUND_INST: instantiating (2) with e1, all_52_31, e0, e0, simplifying with
% 232.00/43.10  |              (4), (8) gives:
% 232.00/43.10  |   (9)  all_52_31 = e1
% 232.00/43.10  | 
% 232.00/43.10  | GROUND_INST: instantiating (2) with e0, all_52_27, e2, e0, simplifying with
% 232.00/43.10  |              (1), (5) gives:
% 232.00/43.10  |   (10)  all_52_27 = e0
% 232.00/43.10  | 
% 232.00/43.10  | REDUCE: (7), (10) imply:
% 232.00/43.10  |   (11)  op(e0, e0) = e2
% 232.00/43.10  | 
% 232.00/43.10  | REF_CLOSE: (2), (6), (8), (11) are inconsistent by sub-proof #2177.
% 232.00/43.10  | 
% 232.00/43.10  End of proof
% 232.00/43.10  
% 232.00/43.10  Sub-proof #1878 shows that the following formulas are inconsistent:
% 232.00/43.10  ----------------------------------------------------------------
% 232.00/43.10    (1)  all_55_8 = e1 | all_55_8 = e0
% 232.00/43.10    (2)  all_55_8 = all_52_17
% 232.00/43.10    (3)   ~ (all_52_17 = e1)
% 232.00/43.10    (4)   ~ (all_52_17 = e0)
% 232.00/43.10  
% 232.00/43.10  Begin of proof
% 232.00/43.10  | 
% 232.00/43.10  | BETA: splitting (1) gives:
% 232.00/43.10  | 
% 232.00/43.10  | Case 1:
% 232.00/43.10  | | 
% 232.00/43.10  | |   (5)  all_55_8 = e1
% 232.00/43.10  | | 
% 232.00/43.10  | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #1880.
% 232.00/43.10  | | 
% 232.00/43.10  | Case 2:
% 232.00/43.10  | | 
% 232.00/43.10  | |   (6)  all_55_8 = e0
% 232.00/43.10  | | 
% 232.00/43.10  | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #1879.
% 232.00/43.10  | | 
% 232.00/43.10  | End of split
% 232.00/43.10  | 
% 232.00/43.10  End of proof
% 232.00/43.10  
% 232.00/43.10  Sub-proof #1879 shows that the following formulas are inconsistent:
% 232.00/43.10  ----------------------------------------------------------------
% 232.00/43.10    (1)  all_55_8 = all_52_17
% 232.00/43.10    (2)  all_55_8 = e0
% 232.00/43.10    (3)   ~ (all_52_17 = e0)
% 232.00/43.10  
% 232.00/43.10  Begin of proof
% 232.00/43.10  | 
% 232.00/43.10  | COMBINE_EQS: (1), (2) imply:
% 232.00/43.10  |   (4)  all_52_17 = e0
% 232.00/43.10  | 
% 232.00/43.10  | SIMP: (4) implies:
% 232.00/43.10  |   (5)  all_52_17 = e0
% 232.00/43.10  | 
% 232.00/43.10  | REDUCE: (3), (5) imply:
% 232.00/43.10  |   (6)  $false
% 232.00/43.10  | 
% 232.00/43.10  | CLOSE: (6) is inconsistent.
% 232.00/43.10  | 
% 232.00/43.10  End of proof
% 232.00/43.10  
% 232.00/43.10  Sub-proof #1880 shows that the following formulas are inconsistent:
% 232.00/43.10  ----------------------------------------------------------------
% 232.00/43.10    (1)  all_55_8 = all_52_17
% 232.00/43.10    (2)  all_55_8 = e1
% 232.00/43.10    (3)   ~ (all_52_17 = e1)
% 232.00/43.10  
% 232.00/43.10  Begin of proof
% 232.00/43.10  | 
% 232.00/43.10  | COMBINE_EQS: (1), (2) imply:
% 232.00/43.10  |   (4)  all_52_17 = e1
% 232.00/43.10  | 
% 232.00/43.10  | SIMP: (4) implies:
% 232.00/43.10  |   (5)  all_52_17 = e1
% 232.00/43.10  | 
% 232.00/43.10  | REDUCE: (3), (5) imply:
% 232.00/43.10  |   (6)  $false
% 232.00/43.10  | 
% 232.00/43.10  | CLOSE: (6) is inconsistent.
% 232.00/43.10  | 
% 232.00/43.10  End of proof
% 232.00/43.10  
% 232.00/43.10  Sub-proof #1881 shows that the following formulas are inconsistent:
% 232.00/43.10  ----------------------------------------------------------------
% 232.00/43.10    (1)  all_55_8 = all_52_17
% 232.00/43.10    (2)  all_55_8 = e3
% 232.00/43.10    (3)   ~ (all_52_17 = e3)
% 232.00/43.10  
% 232.00/43.10  Begin of proof
% 232.00/43.10  | 
% 232.00/43.10  | COMBINE_EQS: (1), (2) imply:
% 232.00/43.10  |   (4)  all_52_17 = e3
% 232.00/43.10  | 
% 232.00/43.10  | SIMP: (4) implies:
% 232.00/43.10  |   (5)  all_52_17 = e3
% 232.00/43.10  | 
% 232.00/43.10  | REDUCE: (3), (5) imply:
% 232.00/43.10  |   (6)  $false
% 232.00/43.10  | 
% 232.00/43.10  | CLOSE: (6) is inconsistent.
% 232.00/43.10  | 
% 232.00/43.10  End of proof
% 232.00/43.10  
% 232.00/43.10  Sub-proof #1882 shows that the following formulas are inconsistent:
% 232.00/43.10  ----------------------------------------------------------------
% 232.00/43.10    (1)  all_55_9 = all_52_19
% 232.00/43.10    (2)  all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 232.00/43.10    (3)   ~ (all_52_19 = e0)
% 232.00/43.10    (4)   ~ (all_52_19 = e2)
% 232.00/43.10    (5)   ~ (all_52_19 = e1)
% 232.00/43.10  
% 232.00/43.10  Begin of proof
% 232.00/43.10  | 
% 232.00/43.10  | BETA: splitting (2) gives:
% 232.00/43.10  | 
% 232.00/43.10  | Case 1:
% 232.00/43.10  | | 
% 232.00/43.10  | |   (6)  all_55_9 = e2
% 232.00/43.10  | | 
% 232.00/43.10  | | COMBINE_EQS: (1), (6) imply:
% 232.00/43.10  | |   (7)  all_52_19 = e2
% 232.00/43.10  | | 
% 232.00/43.10  | | REDUCE: (4), (7) imply:
% 232.00/43.10  | |   (8)  $false
% 232.00/43.10  | | 
% 232.00/43.10  | | CLOSE: (8) is inconsistent.
% 232.00/43.10  | | 
% 232.00/43.10  | Case 2:
% 232.00/43.10  | | 
% 232.00/43.10  | |   (9)  all_55_9 = e1 | all_55_9 = e0
% 232.00/43.10  | | 
% 232.00/43.10  | | REF_CLOSE: (1), (3), (5), (9) are inconsistent by sub-proof #1883.
% 232.00/43.10  | | 
% 232.00/43.10  | End of split
% 232.00/43.10  | 
% 232.00/43.10  End of proof
% 232.00/43.10  
% 232.00/43.10  Sub-proof #1883 shows that the following formulas are inconsistent:
% 232.00/43.10  ----------------------------------------------------------------
% 232.00/43.10    (1)  all_55_9 = e1 | all_55_9 = e0
% 232.00/43.10    (2)  all_55_9 = all_52_19
% 232.00/43.10    (3)   ~ (all_52_19 = e1)
% 232.00/43.10    (4)   ~ (all_52_19 = e0)
% 232.00/43.10  
% 232.00/43.10  Begin of proof
% 232.00/43.10  | 
% 232.00/43.10  | BETA: splitting (1) gives:
% 232.00/43.10  | 
% 232.00/43.10  | Case 1:
% 232.00/43.10  | | 
% 232.00/43.10  | |   (5)  all_55_9 = e1
% 232.00/43.10  | | 
% 232.00/43.10  | | COMBINE_EQS: (2), (5) imply:
% 232.00/43.10  | |   (6)  all_52_19 = e1
% 232.00/43.10  | | 
% 232.00/43.10  | | REDUCE: (3), (6) imply:
% 232.00/43.10  | |   (7)  $false
% 232.00/43.10  | | 
% 232.00/43.10  | | CLOSE: (7) is inconsistent.
% 232.00/43.10  | | 
% 232.00/43.10  | Case 2:
% 232.00/43.10  | | 
% 232.00/43.10  | |   (8)  all_55_9 = e0
% 232.00/43.10  | | 
% 232.00/43.10  | | COMBINE_EQS: (2), (8) imply:
% 232.00/43.10  | |   (9)  all_52_19 = e0
% 232.00/43.10  | | 
% 232.00/43.10  | | REDUCE: (4), (9) imply:
% 232.00/43.10  | |   (10)  $false
% 232.00/43.10  | | 
% 232.00/43.10  | | CLOSE: (10) is inconsistent.
% 232.00/43.10  | | 
% 232.00/43.10  | End of split
% 232.00/43.10  | 
% 232.00/43.10  End of proof
% 232.00/43.10  
% 232.00/43.10  Sub-proof #1884 shows that the following formulas are inconsistent:
% 232.00/43.10  ----------------------------------------------------------------
% 232.00/43.10    (1)  all_55_15 = all_4_2
% 232.00/43.10    (2)  all_55_15 = e0
% 232.00/43.10    (3)   ~ (all_4_2 = e0)
% 232.00/43.10  
% 232.00/43.10  Begin of proof
% 232.00/43.10  | 
% 232.00/43.10  | COMBINE_EQS: (1), (2) imply:
% 232.00/43.10  |   (4)  all_4_2 = e0
% 232.00/43.10  | 
% 232.00/43.10  | SIMP: (4) implies:
% 232.00/43.10  |   (5)  all_4_2 = e0
% 232.00/43.10  | 
% 232.00/43.10  | REDUCE: (3), (5) imply:
% 232.00/43.10  |   (6)  $false
% 232.00/43.10  | 
% 232.00/43.10  | CLOSE: (6) is inconsistent.
% 232.00/43.10  | 
% 232.00/43.10  End of proof
% 232.00/43.10  
% 232.00/43.10  Sub-proof #1885 shows that the following formulas are inconsistent:
% 232.00/43.10  ----------------------------------------------------------------
% 232.00/43.10    (1)  all_57_5 = e2
% 232.00/43.10    (2)  all_57_5 = e1
% 232.00/43.10    (3)   ~ (e2 = e1)
% 232.00/43.10  
% 232.00/43.10  Begin of proof
% 232.00/43.10  | 
% 232.00/43.10  | COMBINE_EQS: (1), (2) imply:
% 232.00/43.10  |   (4)  e2 = e1
% 232.00/43.10  | 
% 232.00/43.10  | SIMP: (4) implies:
% 232.00/43.10  |   (5)  e2 = e1
% 232.00/43.10  | 
% 232.00/43.10  | REDUCE: (3), (5) imply:
% 232.00/43.10  |   (6)  $false
% 232.00/43.10  | 
% 232.00/43.10  | CLOSE: (6) is inconsistent.
% 232.00/43.10  | 
% 232.00/43.10  End of proof
% 232.00/43.10  
% 232.00/43.10  Sub-proof #1886 shows that the following formulas are inconsistent:
% 232.00/43.10  ----------------------------------------------------------------
% 232.00/43.10    (1)  all_57_5 = e1 & op(e2, e1) = e1
% 232.00/43.10    (2)  all_57_5 = e2
% 232.00/43.10    (3)   ~ (e2 = e1)
% 232.00/43.10  
% 232.00/43.10  Begin of proof
% 232.00/43.10  | 
% 232.00/43.10  | ALPHA: (1) implies:
% 232.00/43.10  |   (4)  all_57_5 = e1
% 232.00/43.10  | 
% 232.00/43.10  | COMBINE_EQS: (2), (4) imply:
% 232.00/43.10  |   (5)  e2 = e1
% 232.00/43.10  | 
% 232.00/43.10  | REDUCE: (3), (5) imply:
% 232.00/43.10  |   (6)  $false
% 232.00/43.10  | 
% 232.00/43.10  | CLOSE: (6) is inconsistent.
% 232.00/43.10  | 
% 232.00/43.10  End of proof
% 232.00/43.10  
% 232.00/43.10  Sub-proof #1887 shows that the following formulas are inconsistent:
% 232.00/43.10  ----------------------------------------------------------------
% 232.00/43.10    (1)  all_57_10 = e0
% 232.00/43.10    (2)   ~ (e3 = e1)
% 232.00/43.10    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.00/43.10           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.00/43.10    (4)   ~ (all_6_2 = e3)
% 232.00/43.10    (5)  op(e1, e1) = all_6_2
% 232.00/43.10    (6)   ~ (all_53_7 = e2)
% 232.00/43.10    (7)   ~ (e3 = e2)
% 232.00/43.10    (8)   ~ (e3 = e0)
% 232.00/43.10    (9)  all_57_4 = e1
% 232.00/43.11    (10)   ~ (e2 = e0)
% 232.00/43.11    (11)  op(e2, e2) = e2
% 232.00/43.11    (12)   ~ (e1 = e0)
% 232.00/43.11    (13)  all_57_5 = e2
% 232.00/43.11    (14)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 232.00/43.11          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 232.00/43.11    (15)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 232.00/43.11          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 232.00/43.11            e3)
% 232.00/43.11    (16)  op(e0, e2) = all_53_7
% 232.00/43.11    (17)  all_57_2 = e1
% 232.00/43.11    (18)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 232.00/43.11          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 232.00/43.11            e2)
% 232.00/43.11    (19)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 232.00/43.11              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 232.00/43.11                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 232.00/43.11                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 232.00/43.11    (20)  op(e0, e0) = e1
% 232.00/43.11    (21)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 232.00/43.11          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 232.00/43.11    (22)   ~ (e2 = e1)
% 232.00/43.11  
% 232.00/43.11  Begin of proof
% 232.00/43.11  | 
% 232.00/43.11  | BETA: splitting (14) gives:
% 232.00/43.11  | 
% 232.00/43.11  | Case 1:
% 232.00/43.11  | | 
% 232.00/43.11  | |   (23)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) =
% 232.00/43.11  | |           e3)
% 232.00/43.11  | | 
% 232.00/43.11  | | BETA: splitting (23) gives:
% 232.00/43.11  | | 
% 232.00/43.11  | | Case 1:
% 232.00/43.11  | | | 
% 232.00/43.11  | | |   (24)  all_57_4 = e3 & op(e3, e1) = e3
% 232.00/43.11  | | | 
% 232.00/43.11  | | | ALPHA: (24) implies:
% 232.00/43.11  | | |   (25)  all_57_4 = e3
% 232.00/43.11  | | | 
% 232.00/43.11  | | | REF_CLOSE: (2), (9), (25) are inconsistent by sub-proof #2426.
% 232.00/43.11  | | | 
% 232.00/43.11  | | Case 2:
% 232.00/43.11  | | | 
% 232.00/43.11  | | |   (26)  all_57_5 = e3 & op(e2, e1) = e3
% 232.00/43.11  | | | 
% 232.00/43.11  | | | ALPHA: (26) implies:
% 232.00/43.11  | | |   (27)  all_57_5 = e3
% 232.00/43.11  | | | 
% 232.00/43.11  | | | REF_CLOSE: (7), (13), (27) are inconsistent by sub-proof #2189.
% 232.00/43.11  | | | 
% 232.00/43.11  | | End of split
% 232.00/43.11  | | 
% 232.00/43.11  | Case 2:
% 232.00/43.11  | | 
% 232.00/43.11  | |   (28)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) =
% 232.00/43.11  | |           e3)
% 232.00/43.11  | | 
% 232.00/43.11  | | BETA: splitting (28) gives:
% 232.00/43.11  | | 
% 232.00/43.11  | | Case 1:
% 232.00/43.11  | | | 
% 232.00/43.11  | | |   (29)  all_57_8 = e3 & op(e1, e1) = e3
% 232.00/43.11  | | | 
% 232.00/43.11  | | | ALPHA: (29) implies:
% 232.00/43.11  | | |   (30)  op(e1, e1) = e3
% 232.00/43.11  | | | 
% 232.00/43.11  | | | REF_CLOSE: (3), (4), (5), (30) are inconsistent by sub-proof #2468.
% 232.00/43.11  | | | 
% 232.00/43.11  | | Case 2:
% 232.00/43.11  | | | 
% 232.00/43.11  | | |   (31)  all_57_14 = e3 & op(e0, e1) = e3
% 232.00/43.11  | | | 
% 232.00/43.11  | | | ALPHA: (31) implies:
% 232.00/43.11  | | |   (32)  all_57_14 = e3
% 232.00/43.11  | | | 
% 232.00/43.11  | | | BETA: splitting (21) gives:
% 232.00/43.11  | | | 
% 232.00/43.11  | | | Case 1:
% 232.00/43.11  | | | | 
% 232.00/43.11  | | | |   (33)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2)
% 232.00/43.11  | | | |           = e3)
% 232.00/43.11  | | | | 
% 232.00/43.11  | | | | BETA: splitting (33) gives:
% 232.00/43.11  | | | | 
% 232.00/43.11  | | | | Case 1:
% 232.00/43.11  | | | | | 
% 232.00/43.11  | | | | |   (34)  all_57_2 = e3 & op(e2, e3) = e3
% 232.00/43.11  | | | | | 
% 232.00/43.11  | | | | | ALPHA: (34) implies:
% 232.00/43.11  | | | | |   (35)  all_57_2 = e3
% 232.00/43.11  | | | | | 
% 232.00/43.11  | | | | | COMBINE_EQS: (17), (35) imply:
% 232.00/43.11  | | | | |   (36)  e3 = e1
% 232.00/43.11  | | | | | 
% 232.00/43.11  | | | | | SIMP: (36) implies:
% 232.00/43.11  | | | | |   (37)  e3 = e1
% 232.00/43.11  | | | | | 
% 232.00/43.11  | | | | | COMBINE_EQS: (32), (37) imply:
% 232.00/43.11  | | | | |   (38)  all_57_14 = e1
% 232.00/43.11  | | | | | 
% 232.00/43.11  | | | | | REF_CLOSE: (2), (3), (6), (7), (8), (10), (12), (15), (16), (18),
% 232.00/43.11  | | | | |            (19), (20), (22), (38) are inconsistent by sub-proof #2175.
% 232.00/43.11  | | | | | 
% 232.00/43.11  | | | | Case 2:
% 232.00/43.11  | | | | | 
% 232.00/43.11  | | | | |   (39)  all_57_3 = e3 & op(e2, e2) = e3
% 232.00/43.11  | | | | | 
% 232.00/43.11  | | | | | ALPHA: (39) implies:
% 232.00/43.11  | | | | |   (40)  op(e2, e2) = e3
% 232.00/43.11  | | | | | 
% 232.00/43.11  | | | | | REF_CLOSE: (3), (7), (11), (40) are inconsistent by sub-proof #2298.
% 232.00/43.11  | | | | | 
% 232.00/43.11  | | | | End of split
% 232.00/43.11  | | | | 
% 232.00/43.11  | | | Case 2:
% 232.00/43.11  | | | | 
% 232.00/43.11  | | | |   (41)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0)
% 232.00/43.11  | | | |           = e3)
% 232.00/43.11  | | | | 
% 232.00/43.11  | | | | BETA: splitting (41) gives:
% 232.00/43.11  | | | | 
% 232.00/43.11  | | | | Case 1:
% 232.00/43.11  | | | | | 
% 232.00/43.11  | | | | |   (42)  all_57_5 = e3 & op(e2, e1) = e3
% 232.00/43.11  | | | | | 
% 232.00/43.11  | | | | | REF_CLOSE: (2), (3), (4), (5), (7), (9), (13), (14), (32), (42) are
% 232.00/43.11  | | | | |            inconsistent by sub-proof #1888.
% 232.00/43.11  | | | | | 
% 232.00/43.11  | | | | Case 2:
% 232.00/43.11  | | | | | 
% 232.00/43.11  | | | | |   (43)  all_57_10 = e3 & op(e2, e0) = e3
% 232.00/43.11  | | | | | 
% 232.00/43.11  | | | | | ALPHA: (43) implies:
% 232.00/43.11  | | | | |   (44)  all_57_10 = e3
% 232.00/43.11  | | | | | 
% 232.00/43.11  | | | | | REF_CLOSE: (1), (8), (44) are inconsistent by sub-proof #1989.
% 232.00/43.11  | | | | | 
% 232.00/43.11  | | | | End of split
% 232.00/43.11  | | | | 
% 232.00/43.11  | | | End of split
% 232.00/43.11  | | | 
% 232.00/43.11  | | End of split
% 232.00/43.11  | | 
% 232.00/43.11  | End of split
% 232.00/43.11  | 
% 232.00/43.11  End of proof
% 232.00/43.11  
% 232.00/43.11  Sub-proof #1888 shows that the following formulas are inconsistent:
% 232.00/43.11  ----------------------------------------------------------------
% 232.00/43.11    (1)  all_57_5 = e3 & op(e2, e1) = e3
% 232.00/43.11    (2)   ~ (e3 = e1)
% 232.00/43.11    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.00/43.11           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.00/43.11    (4)   ~ (all_6_2 = e3)
% 232.00/43.11    (5)  op(e1, e1) = all_6_2
% 232.00/43.11    (6)  all_57_14 = e3
% 232.00/43.11    (7)   ~ (e3 = e2)
% 232.00/43.11    (8)  all_57_4 = e1
% 232.00/43.11    (9)  all_57_5 = e2
% 232.00/43.11    (10)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 232.00/43.11          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 232.00/43.11  
% 232.00/43.11  Begin of proof
% 232.00/43.11  | 
% 232.00/43.11  | ALPHA: (1) implies:
% 232.00/43.11  |   (11)  all_57_5 = e3
% 232.00/43.11  | 
% 232.00/43.11  | COMBINE_EQS: (9), (11) imply:
% 232.00/43.11  |   (12)  e3 = e2
% 232.00/43.11  | 
% 232.00/43.11  | SIMP: (12) implies:
% 232.00/43.11  |   (13)  e3 = e2
% 232.00/43.11  | 
% 232.00/43.11  | COMBINE_EQS: (6), (13) imply:
% 232.00/43.11  |   (14)  all_57_14 = e2
% 232.00/43.11  | 
% 232.00/43.11  | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (10), (14) are inconsistent by
% 232.00/43.11  |            sub-proof #1889.
% 232.00/43.11  | 
% 232.00/43.11  End of proof
% 232.00/43.11  
% 232.00/43.11  Sub-proof #1889 shows that the following formulas are inconsistent:
% 232.00/43.11  ----------------------------------------------------------------
% 232.00/43.11    (1)   ~ (e3 = e1)
% 232.00/43.11    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.00/43.11           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.00/43.11    (3)   ~ (all_6_2 = e3)
% 232.00/43.11    (4)  op(e1, e1) = all_6_2
% 232.00/43.11    (5)   ~ (e3 = e2)
% 232.00/43.11    (6)  all_57_4 = e1
% 232.00/43.11    (7)  all_57_14 = e2
% 232.00/43.11    (8)  all_57_5 = e2
% 232.00/43.11    (9)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 232.00/43.11         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 232.00/43.11  
% 232.00/43.11  Begin of proof
% 232.00/43.11  | 
% 232.00/43.11  | BETA: splitting (9) gives:
% 232.00/43.11  | 
% 232.00/43.11  | Case 1:
% 232.00/43.11  | | 
% 232.00/43.11  | |   (10)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) =
% 232.00/43.11  | |           e3)
% 232.00/43.11  | | 
% 232.00/43.11  | | REF_CLOSE: (1), (5), (6), (8), (10) are inconsistent by sub-proof #1892.
% 232.00/43.11  | | 
% 232.00/43.11  | Case 2:
% 232.00/43.11  | | 
% 232.00/43.11  | |   (11)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) =
% 232.00/43.11  | |           e3)
% 232.00/43.11  | | 
% 232.00/43.11  | | REF_CLOSE: (2), (3), (4), (5), (7), (11) are inconsistent by sub-proof
% 232.00/43.11  | |            #1890.
% 232.00/43.11  | | 
% 232.00/43.11  | End of split
% 232.00/43.11  | 
% 232.00/43.11  End of proof
% 232.00/43.11  
% 232.00/43.11  Sub-proof #1890 shows that the following formulas are inconsistent:
% 232.00/43.11  ----------------------------------------------------------------
% 232.00/43.11    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.00/43.11           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.00/43.11    (2)   ~ (all_6_2 = e3)
% 232.00/43.11    (3)  op(e1, e1) = all_6_2
% 232.00/43.11    (4)   ~ (e3 = e2)
% 232.00/43.11    (5)  all_57_14 = e2
% 232.00/43.11    (6)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 232.00/43.11  
% 232.00/43.11  Begin of proof
% 232.00/43.11  | 
% 232.00/43.11  | BETA: splitting (6) gives:
% 232.00/43.11  | 
% 232.00/43.11  | Case 1:
% 232.00/43.11  | | 
% 232.00/43.11  | |   (7)  all_57_8 = e3 & op(e1, e1) = e3
% 232.00/43.11  | | 
% 232.00/43.11  | | ALPHA: (7) implies:
% 232.00/43.11  | |   (8)  op(e1, e1) = e3
% 232.00/43.11  | | 
% 232.00/43.11  | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #2468.
% 232.00/43.11  | | 
% 232.00/43.11  | Case 2:
% 232.00/43.11  | | 
% 232.00/43.11  | |   (9)  all_57_14 = e3 & op(e0, e1) = e3
% 232.00/43.11  | | 
% 232.00/43.11  | | REF_CLOSE: (4), (5), (9) are inconsistent by sub-proof #1891.
% 232.00/43.11  | | 
% 232.00/43.11  | End of split
% 232.00/43.11  | 
% 232.00/43.11  End of proof
% 232.00/43.11  
% 232.00/43.11  Sub-proof #1891 shows that the following formulas are inconsistent:
% 232.00/43.11  ----------------------------------------------------------------
% 232.00/43.11    (1)  all_57_14 = e3 & op(e0, e1) = e3
% 232.00/43.11    (2)  all_57_14 = e2
% 232.00/43.11    (3)   ~ (e3 = e2)
% 232.00/43.11  
% 232.00/43.11  Begin of proof
% 232.00/43.11  | 
% 232.00/43.11  | ALPHA: (1) implies:
% 232.00/43.11  |   (4)  all_57_14 = e3
% 232.00/43.11  | 
% 232.00/43.11  | COMBINE_EQS: (2), (4) imply:
% 232.00/43.11  |   (5)  e3 = e2
% 232.00/43.11  | 
% 232.00/43.11  | REDUCE: (3), (5) imply:
% 232.00/43.11  |   (6)  $false
% 232.00/43.11  | 
% 232.00/43.11  | CLOSE: (6) is inconsistent.
% 232.00/43.11  | 
% 232.00/43.11  End of proof
% 232.00/43.11  
% 232.00/43.11  Sub-proof #1892 shows that the following formulas are inconsistent:
% 232.00/43.11  ----------------------------------------------------------------
% 232.00/43.11    (1)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3)
% 232.00/43.11    (2)   ~ (e3 = e1)
% 232.00/43.11    (3)   ~ (e3 = e2)
% 232.00/43.11    (4)  all_57_4 = e1
% 232.00/43.11    (5)  all_57_5 = e2
% 232.00/43.11  
% 232.00/43.11  Begin of proof
% 232.00/43.11  | 
% 232.00/43.11  | BETA: splitting (1) gives:
% 232.00/43.11  | 
% 232.00/43.11  | Case 1:
% 232.00/43.11  | | 
% 232.00/43.11  | |   (6)  all_57_4 = e3 & op(e3, e1) = e3
% 232.00/43.11  | | 
% 232.00/43.11  | | ALPHA: (6) implies:
% 232.00/43.11  | |   (7)  all_57_4 = e3
% 232.00/43.11  | | 
% 232.00/43.11  | | REF_CLOSE: (2), (4), (7) are inconsistent by sub-proof #2426.
% 232.00/43.11  | | 
% 232.00/43.11  | Case 2:
% 232.00/43.11  | | 
% 232.00/43.11  | |   (8)  all_57_5 = e3 & op(e2, e1) = e3
% 232.00/43.11  | | 
% 232.00/43.11  | | REF_CLOSE: (3), (5), (8) are inconsistent by sub-proof #1893.
% 232.00/43.11  | | 
% 232.00/43.11  | End of split
% 232.00/43.11  | 
% 232.00/43.11  End of proof
% 232.00/43.11  
% 232.00/43.11  Sub-proof #1893 shows that the following formulas are inconsistent:
% 232.00/43.11  ----------------------------------------------------------------
% 232.00/43.11    (1)  all_57_5 = e3 & op(e2, e1) = e3
% 232.00/43.11    (2)  all_57_5 = e2
% 232.00/43.11    (3)   ~ (e3 = e2)
% 232.00/43.11  
% 232.00/43.11  Begin of proof
% 232.00/43.11  | 
% 232.00/43.11  | ALPHA: (1) implies:
% 232.00/43.11  |   (4)  all_57_5 = e3
% 232.00/43.11  | 
% 232.00/43.11  | COMBINE_EQS: (2), (4) imply:
% 232.00/43.11  |   (5)  e3 = e2
% 232.00/43.11  | 
% 232.00/43.11  | REDUCE: (3), (5) imply:
% 232.00/43.11  |   (6)  $false
% 232.00/43.11  | 
% 232.00/43.11  | CLOSE: (6) is inconsistent.
% 232.00/43.11  | 
% 232.00/43.11  End of proof
% 232.00/43.11  
% 232.00/43.11  Sub-proof #1894 shows that the following formulas are inconsistent:
% 232.00/43.11  ----------------------------------------------------------------
% 232.00/43.11    (1)   ~ (all_48_2 = e0) | ( ~ (all_48_0 = e2) & op(all_48_1, e3) = all_48_0 &
% 232.00/43.11           op(e3, e0) = all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 =
% 232.00/43.11             e1) & op(e3, e0) = all_48_1 & $i(all_48_1))
% 232.00/43.11    (2)  all_48_2 = e0
% 232.00/43.11    (3)  op(e2, e3) = all_53_1
% 232.00/43.11    (4)   ~ (e3 = e1)
% 232.00/43.11    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.00/43.11           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.00/43.11    (6)  ( ~ (all_18_0 = e1) & op(all_18_1, e3) = all_18_0 & op(e3, e0) = all_18_1
% 232.00/43.11           & $i(all_18_0) & $i(all_18_1)) | ( ~ (all_18_1 = e2) & op(e3, e0) =
% 232.00/43.11           all_18_1 & $i(all_18_1))
% 232.00/43.11    (7)  op(e2, e3) = all_52_9
% 232.00/43.11    (8)   ~ (all_53_13 = e2)
% 232.00/43.11    (9)   ~ (all_53_7 = e2)
% 232.00/43.11    (10)  op(e2, e0) = all_52_15
% 232.00/43.11    (11)  all_55_4 = all_53_1
% 232.00/43.11    (12)   ~ (e3 = e2)
% 232.00/43.11    (13)   ~ (e3 = e0)
% 232.00/43.11    (14)  op(e0, e3) = all_53_3
% 232.00/43.11    (15)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 232.00/43.11    (16)  op(e3, e3) = e0
% 232.00/43.11    (17)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 232.00/43.11          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 232.00/43.11            e1)
% 232.00/43.11    (18)   ~ (e2 = e0)
% 232.00/43.11    (19)   ~ (all_53_1 = e0)
% 232.00/43.11    (20)   ~ (e1 = e0)
% 232.00/43.11    (21)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 232.00/43.11          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 232.00/43.11            e3)
% 232.00/43.11    (22)  op(e0, e2) = all_53_7
% 232.00/43.11    (23)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 232.00/43.11          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 232.00/43.11            e2)
% 232.00/43.11    (24)   ~ (all_53_3 = e0)
% 232.00/43.11    (25)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 232.00/43.11              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 232.00/43.11                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 232.00/43.11                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 232.00/43.11    (26)  op(all_52_9, all_52_9) = e3
% 232.00/43.11    (27)   ~ (all_53_3 = e1)
% 232.00/43.11    (28)  op(e0, e0) = e1
% 232.00/43.11    (29)  op(e2, e0) = all_53_13
% 232.00/43.11    (30)  op(all_52_15, all_52_15) = e0
% 232.00/43.11    (31)   ~ (all_53_12 = e0)
% 232.00/43.11    (32)   ~ (all_53_1 = e2)
% 232.00/43.11    (33)   ~ (e2 = e1)
% 232.00/43.11    (34)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 232.00/43.11          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 232.00/43.11    (35)  op(e3, e0) = all_53_12
% 232.00/43.11  
% 232.00/43.11  Begin of proof
% 232.00/43.11  | 
% 232.00/43.11  | BETA: splitting (34) gives:
% 232.00/43.11  | 
% 232.00/43.11  | Case 1:
% 232.00/43.11  | | 
% 232.00/43.11  | |   (36)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 232.00/43.11  | |           e2)
% 232.00/43.11  | | 
% 232.00/43.11  | | BETA: splitting (36) gives:
% 232.00/43.11  | | 
% 232.00/43.11  | | Case 1:
% 232.00/43.11  | | | 
% 232.00/43.11  | | |   (37)  all_57_9 = e2 & op(e3, e0) = e2
% 232.00/43.11  | | | 
% 232.00/43.11  | | | ALPHA: (37) implies:
% 232.00/43.11  | | |   (38)  op(e3, e0) = e2
% 232.00/43.11  | | | 
% 232.00/43.11  | | | GROUND_INST: instantiating (5) with all_53_1, all_52_9, e3, e2,
% 232.00/43.11  | | |              simplifying with (3), (7) gives:
% 232.00/43.11  | | |   (39)  all_53_1 = all_52_9
% 232.00/43.11  | | | 
% 232.00/43.11  | | | GROUND_INST: instantiating (5) with all_53_12, e2, e0, e3, simplifying
% 232.00/43.11  | | |              with (35), (38) gives:
% 232.00/43.11  | | |   (40)  all_53_12 = e2
% 232.00/43.11  | | | 
% 232.00/43.11  | | | BETA: splitting (1) gives:
% 232.00/43.11  | | | 
% 232.00/43.11  | | | Case 1:
% 232.00/43.11  | | | | 
% 232.00/43.11  | | | |   (41)   ~ (all_48_2 = e0)
% 232.00/43.11  | | | | 
% 232.00/43.11  | | | | REDUCE: (2), (41) imply:
% 232.00/43.11  | | | |   (42)  $false
% 232.00/43.11  | | | | 
% 232.00/43.11  | | | | CLOSE: (42) is inconsistent.
% 232.00/43.11  | | | | 
% 232.00/43.11  | | | Case 2:
% 232.00/43.11  | | | | 
% 232.00/43.11  | | | |   (43)  ( ~ (all_48_0 = e2) & op(all_48_1, e3) = all_48_0 & op(e3, e0) =
% 232.00/43.11  | | | |           all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 = e1)
% 232.00/43.11  | | | |           & op(e3, e0) = all_48_1 & $i(all_48_1))
% 232.00/43.11  | | | | 
% 232.00/43.11  | | | | REF_CLOSE: (3), (5), (6), (7), (11), (15), (16), (19), (26), (32), (38),
% 232.00/43.11  | | | |            (43) are inconsistent by sub-proof #1898.
% 232.00/43.11  | | | | 
% 232.00/43.11  | | | End of split
% 232.00/43.11  | | | 
% 232.00/43.11  | | Case 2:
% 232.00/43.11  | | | 
% 232.00/43.11  | | |   (44)  all_57_10 = e2 & op(e2, e0) = e2
% 232.00/43.11  | | | 
% 232.00/43.11  | | | REF_CLOSE: (5), (8), (29), (44) are inconsistent by sub-proof #2432.
% 232.00/43.11  | | | 
% 232.00/43.11  | | End of split
% 232.00/43.11  | | 
% 232.00/43.11  | Case 2:
% 232.00/43.11  | | 
% 232.00/43.11  | |   (45)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 232.00/43.11  | |           e2)
% 232.00/43.11  | | 
% 232.00/43.11  | | BETA: splitting (45) gives:
% 232.00/43.11  | | 
% 232.00/43.11  | | Case 1:
% 232.00/43.11  | | | 
% 232.00/43.11  | | |   (46)  all_57_11 = e2 & op(e1, e0) = e2
% 232.00/43.11  | | | 
% 232.00/43.11  | | | ALPHA: (46) implies:
% 232.00/43.11  | | |   (47)  all_57_11 = e2
% 232.00/43.11  | | | 
% 232.00/43.11  | | | REF_CLOSE: (4), (5), (9), (10), (12), (13), (14), (17), (18), (20), (21),
% 232.00/43.11  | | |            (22), (23), (24), (25), (27), (28), (30), (31), (33), (35),
% 232.00/43.11  | | |            (47) are inconsistent by sub-proof #1895.
% 232.00/43.11  | | | 
% 232.00/43.11  | | Case 2:
% 232.00/43.11  | | | 
% 232.00/43.11  | | |   (48)  all_57_15 = e2 & op(e0, e0) = e2
% 232.00/43.11  | | | 
% 232.00/43.11  | | | ALPHA: (48) implies:
% 232.00/43.11  | | |   (49)  op(e0, e0) = e2
% 232.00/43.11  | | | 
% 232.00/43.11  | | | REF_CLOSE: (5), (28), (33), (49) are inconsistent by sub-proof #2177.
% 232.00/43.11  | | | 
% 232.00/43.11  | | End of split
% 232.00/43.11  | | 
% 232.00/43.11  | End of split
% 232.00/43.11  | 
% 232.00/43.11  End of proof
% 232.00/43.11  
% 232.00/43.11  Sub-proof #1895 shows that the following formulas are inconsistent:
% 232.00/43.11  ----------------------------------------------------------------
% 232.00/43.11    (1)   ~ (e3 = e1)
% 232.00/43.11    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.00/43.11           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.00/43.11    (3)   ~ (all_53_7 = e2)
% 232.00/43.11    (4)  op(e2, e0) = all_52_15
% 232.00/43.11    (5)   ~ (e3 = e2)
% 232.00/43.11    (6)   ~ (e3 = e0)
% 232.00/43.11    (7)  op(e0, e3) = all_53_3
% 232.00/43.11    (8)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 232.00/43.11         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 232.00/43.11    (9)  all_57_11 = e2
% 232.00/43.11    (10)   ~ (e2 = e0)
% 232.00/43.11    (11)   ~ (e1 = e0)
% 232.00/43.11    (12)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 232.00/43.11          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 232.00/43.11            e3)
% 232.00/43.11    (13)  op(e0, e2) = all_53_7
% 232.00/43.11    (14)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 232.00/43.11          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 232.00/43.11            e2)
% 232.00/43.11    (15)   ~ (all_53_3 = e0)
% 232.00/43.11    (16)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 232.00/43.11              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 232.00/43.11                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 232.00/43.11                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 232.00/43.11    (17)   ~ (all_53_3 = e1)
% 232.00/43.11    (18)  op(e0, e0) = e1
% 232.00/43.11    (19)  op(all_52_15, all_52_15) = e0
% 232.00/43.11    (20)   ~ (all_53_12 = e0)
% 232.00/43.11    (21)   ~ (e2 = e1)
% 232.00/43.11    (22)  op(e3, e0) = all_53_12
% 232.00/43.11  
% 232.00/43.11  Begin of proof
% 232.00/43.11  | 
% 232.00/43.11  | BETA: splitting (16) gives:
% 232.00/43.11  | 
% 232.00/43.11  | Case 1:
% 232.00/43.11  | | 
% 232.00/43.11  | |   (23)  all_57_15 = e0 & op(e0, e0) = e0
% 232.00/43.11  | | 
% 232.00/43.11  | | ALPHA: (23) implies:
% 232.00/43.11  | |   (24)  op(e0, e0) = e0
% 232.00/43.11  | | 
% 232.00/43.11  | | REF_CLOSE: (2), (11), (18), (24) are inconsistent by sub-proof #2290.
% 232.00/43.11  | | 
% 232.00/43.11  | Case 2:
% 232.00/43.11  | | 
% 232.00/43.11  | |   (25)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 232.00/43.11  | |             e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0 &
% 232.00/43.11  | |             op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 232.00/43.11  | |           (all_57_14 = e0 & op(e0, e1) = e0))
% 232.00/43.11  | | 
% 232.00/43.11  | | ALPHA: (25) implies:
% 232.00/43.11  | |   (26)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 232.00/43.11  | |           e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 232.00/43.11  | | 
% 232.00/43.11  | | BETA: splitting (26) gives:
% 232.00/43.11  | | 
% 232.00/43.11  | | Case 1:
% 232.00/43.11  | | | 
% 232.00/43.11  | | |   (27)  all_57_9 = e0 & op(e3, e0) = e0
% 232.00/43.11  | | | 
% 232.00/43.11  | | | REF_CLOSE: (2), (20), (22), (27) are inconsistent by sub-proof #2434.
% 232.00/43.11  | | | 
% 232.00/43.11  | | Case 2:
% 232.00/43.11  | | | 
% 232.00/43.11  | | |   (28)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 232.00/43.11  | | |           = e0)
% 232.00/43.11  | | | 
% 232.00/43.11  | | | BETA: splitting (28) gives:
% 232.00/43.11  | | | 
% 232.00/43.11  | | | Case 1:
% 232.00/43.11  | | | | 
% 232.00/43.11  | | | |   (29)  all_57_10 = e0 & op(e2, e0) = e0
% 232.00/43.11  | | | | 
% 232.00/43.11  | | | | ALPHA: (29) implies:
% 232.00/43.11  | | | |   (30)  op(e2, e0) = e0
% 232.00/43.11  | | | | 
% 232.00/43.11  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12),
% 232.00/43.11  | | | |            (13), (14), (15), (16), (17), (18), (19), (21), (30) are
% 232.00/43.11  | | | |            inconsistent by sub-proof #1896.
% 232.00/43.11  | | | | 
% 232.00/43.11  | | | Case 2:
% 232.00/43.11  | | | | 
% 232.00/43.11  | | | |   (31)  all_57_11 = e0 & op(e1, e0) = e0
% 232.00/43.11  | | | | 
% 232.00/43.11  | | | | REF_CLOSE: (9), (10), (31) are inconsistent by sub-proof #2041.
% 232.00/43.11  | | | | 
% 232.00/43.11  | | | End of split
% 232.00/43.11  | | | 
% 232.00/43.11  | | End of split
% 232.00/43.11  | | 
% 232.00/43.11  | End of split
% 232.00/43.11  | 
% 232.00/43.11  End of proof
% 232.00/43.11  
% 232.00/43.11  Sub-proof #1896 shows that the following formulas are inconsistent:
% 232.00/43.11  ----------------------------------------------------------------
% 232.00/43.11    (1)  op(e2, e0) = e0
% 232.00/43.11    (2)   ~ (e3 = e1)
% 232.00/43.11    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.00/43.11           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.00/43.11    (4)   ~ (all_53_7 = e2)
% 232.00/43.11    (5)  op(e2, e0) = all_52_15
% 232.00/43.11    (6)   ~ (e3 = e2)
% 232.00/43.11    (7)   ~ (e3 = e0)
% 232.00/43.11    (8)  op(e0, e3) = all_53_3
% 232.00/43.11    (9)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 232.00/43.11         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 232.00/43.11    (10)   ~ (e2 = e0)
% 232.00/43.11    (11)   ~ (e1 = e0)
% 232.00/43.11    (12)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 232.00/43.11          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 232.00/43.11            e3)
% 232.00/43.11    (13)  op(e0, e2) = all_53_7
% 232.00/43.11    (14)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 232.00/43.11          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 232.00/43.11            e2)
% 232.00/43.11    (15)   ~ (all_53_3 = e0)
% 232.00/43.11    (16)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 232.00/43.11              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 232.00/43.11                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 232.00/43.11                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 232.00/43.11    (17)   ~ (all_53_3 = e1)
% 232.00/43.11    (18)  op(e0, e0) = e1
% 232.00/43.11    (19)  op(all_52_15, all_52_15) = e0
% 232.00/43.11    (20)   ~ (e2 = e1)
% 232.00/43.11  
% 232.00/43.11  Begin of proof
% 232.00/43.11  | 
% 232.00/43.11  | BETA: splitting (9) gives:
% 232.00/43.11  | 
% 232.00/43.11  | Case 1:
% 232.00/43.11  | | 
% 232.00/43.11  | |   (21)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 232.00/43.11  | |           e1)
% 232.00/43.11  | | 
% 232.00/43.11  | | REF_CLOSE: (2), (3), (6), (7), (8), (10), (11), (12), (14), (15), (16),
% 232.00/43.11  | |            (17), (18), (20), (21) are inconsistent by sub-proof #1917.
% 232.00/43.11  | | 
% 232.00/43.11  | Case 2:
% 232.00/43.11  | | 
% 232.00/43.11  | |   (22)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 232.00/43.11  | |           e1)
% 232.00/43.11  | | 
% 232.00/43.11  | | BETA: splitting (22) gives:
% 232.00/43.11  | | 
% 232.00/43.11  | | Case 1:
% 232.00/43.11  | | | 
% 232.00/43.11  | | |   (23)  all_57_14 = e1 & op(e0, e1) = e1
% 232.00/43.11  | | | 
% 232.00/43.11  | | | ALPHA: (23) implies:
% 232.00/43.11  | | |   (24)  all_57_14 = e1
% 232.00/43.11  | | | 
% 232.00/43.11  | | | REF_CLOSE: (2), (3), (4), (6), (7), (10), (11), (12), (13), (14), (16),
% 232.00/43.11  | | |            (18), (20), (24) are inconsistent by sub-proof #2175.
% 232.00/43.11  | | | 
% 232.00/43.11  | | Case 2:
% 232.00/43.11  | | | 
% 232.00/43.11  | | |   (25)  all_57_15 = e1 & op(e0, e0) = e1
% 232.00/43.11  | | | 
% 232.00/43.11  | | | REF_CLOSE: (1), (3), (5), (11), (19), (25) are inconsistent by sub-proof
% 232.00/43.11  | | |            #1897.
% 232.00/43.11  | | | 
% 232.00/43.11  | | End of split
% 232.00/43.11  | | 
% 232.00/43.11  | End of split
% 232.00/43.11  | 
% 232.00/43.11  End of proof
% 232.00/43.11  
% 232.00/43.11  Sub-proof #1897 shows that the following formulas are inconsistent:
% 232.00/43.11  ----------------------------------------------------------------
% 232.00/43.11    (1)  op(e2, e0) = e0
% 232.00/43.11    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.00/43.11           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.00/43.11    (3)  all_57_15 = e1 & op(e0, e0) = e1
% 232.00/43.11    (4)  op(e2, e0) = all_52_15
% 232.00/43.11    (5)   ~ (e1 = e0)
% 232.00/43.11    (6)  op(all_52_15, all_52_15) = e0
% 232.00/43.11  
% 232.00/43.11  Begin of proof
% 232.00/43.11  | 
% 232.00/43.11  | ALPHA: (3) implies:
% 232.00/43.11  |   (7)  op(e0, e0) = e1
% 232.00/43.11  | 
% 232.00/43.11  | GROUND_INST: instantiating (2) with e0, all_52_15, e0, e2, simplifying with
% 232.00/43.11  |              (1), (4) gives:
% 232.00/43.11  |   (8)  all_52_15 = e0
% 232.00/43.11  | 
% 232.00/43.11  | REDUCE: (6), (8) imply:
% 232.00/43.11  |   (9)  op(e0, e0) = e0
% 232.00/43.11  | 
% 232.00/43.11  | REF_CLOSE: (2), (5), (7), (9) are inconsistent by sub-proof #2290.
% 232.00/43.11  | 
% 232.00/43.11  End of proof
% 232.00/43.11  
% 232.00/43.11  Sub-proof #1898 shows that the following formulas are inconsistent:
% 232.00/43.11  ----------------------------------------------------------------
% 232.00/43.11    (1)  ( ~ (all_48_0 = e2) & op(all_48_1, e3) = all_48_0 & op(e3, e0) = all_48_1
% 232.00/43.11           & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 = e1) & op(e3, e0) =
% 232.00/43.11           all_48_1 & $i(all_48_1))
% 232.00/43.11    (2)  op(e2, e3) = all_53_1
% 232.00/43.11    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.00/43.11           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.00/43.11    (4)  ( ~ (all_18_0 = e1) & op(all_18_1, e3) = all_18_0 & op(e3, e0) = all_18_1
% 232.00/43.11           & $i(all_18_0) & $i(all_18_1)) | ( ~ (all_18_1 = e2) & op(e3, e0) =
% 232.00/43.11           all_18_1 & $i(all_18_1))
% 232.00/43.11    (5)  op(e2, e3) = all_52_9
% 232.00/43.11    (6)  all_55_4 = all_53_1
% 232.00/43.11    (7)  op(e3, e0) = e2
% 232.00/43.11    (8)  all_55_4 = e3 | all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 232.00/43.11    (9)  op(e3, e3) = e0
% 232.00/43.11    (10)   ~ (all_53_1 = e0)
% 232.00/43.11    (11)  op(all_52_9, all_52_9) = e3
% 232.00/43.11    (12)   ~ (all_53_1 = e2)
% 232.00/43.11  
% 232.00/43.11  Begin of proof
% 232.00/43.11  | 
% 232.00/43.11  | BETA: splitting (4) gives:
% 232.00/43.11  | 
% 232.00/43.11  | Case 1:
% 232.00/43.11  | | 
% 232.00/43.11  | |   (13)   ~ (all_18_0 = e1) & op(all_18_1, e3) = all_18_0 & op(e3, e0) =
% 232.00/43.11  | |         all_18_1 & $i(all_18_0) & $i(all_18_1)
% 232.00/43.11  | | 
% 232.00/43.11  | | ALPHA: (13) implies:
% 232.00/43.12  | |   (14)   ~ (all_18_0 = e1)
% 232.00/43.12  | |   (15)  op(e3, e0) = all_18_1
% 232.00/43.12  | |   (16)  op(all_18_1, e3) = all_18_0
% 232.00/43.12  | | 
% 232.00/43.12  | | GROUND_INST: instantiating (3) with all_53_1, all_52_9, e3, e2, simplifying
% 232.00/43.12  | |              with (2), (5) gives:
% 232.00/43.12  | |   (17)  all_53_1 = all_52_9
% 232.00/43.12  | | 
% 232.00/43.12  | | GROUND_INST: instantiating (3) with e2, all_18_1, e0, e3, simplifying with
% 232.00/43.12  | |              (7), (15) gives:
% 232.00/43.12  | |   (18)  all_18_1 = e2
% 232.00/43.12  | | 
% 232.00/43.12  | | COMBINE_EQS: (6), (17) imply:
% 232.00/43.12  | |   (19)  all_55_4 = all_52_9
% 232.00/43.12  | | 
% 232.00/43.12  | | REDUCE: (12), (17) imply:
% 232.00/43.12  | |   (20)   ~ (all_52_9 = e2)
% 232.00/43.12  | | 
% 232.00/43.12  | | REDUCE: (10), (17) imply:
% 232.00/43.12  | |   (21)   ~ (all_52_9 = e0)
% 232.00/43.12  | | 
% 232.00/43.12  | | REDUCE: (16), (18) imply:
% 232.00/43.12  | |   (22)  op(e2, e3) = all_18_0
% 232.00/43.12  | | 
% 232.00/43.12  | | GROUND_INST: instantiating (3) with all_52_9, all_18_0, e3, e2, simplifying
% 232.00/43.12  | |              with (5), (22) gives:
% 232.00/43.12  | |   (23)  all_52_9 = all_18_0
% 232.00/43.12  | | 
% 232.00/43.12  | | COMBINE_EQS: (19), (23) imply:
% 232.00/43.12  | |   (24)  all_55_4 = all_18_0
% 232.00/43.12  | | 
% 232.00/43.12  | | REDUCE: (20), (23) imply:
% 232.00/43.12  | |   (25)   ~ (all_18_0 = e2)
% 232.00/43.12  | | 
% 232.00/43.12  | | REDUCE: (21), (23) imply:
% 232.00/43.12  | |   (26)   ~ (all_18_0 = e0)
% 232.00/43.12  | | 
% 232.00/43.12  | | REDUCE: (11), (23) imply:
% 232.00/43.12  | |   (27)  op(all_18_0, all_18_0) = e3
% 232.00/43.12  | | 
% 232.00/43.12  | | BETA: splitting (8) gives:
% 232.00/43.12  | | 
% 232.00/43.12  | | Case 1:
% 232.00/43.12  | | | 
% 232.00/43.12  | | |   (28)  all_55_4 = e3
% 232.00/43.12  | | | 
% 232.00/43.12  | | | COMBINE_EQS: (24), (28) imply:
% 232.00/43.12  | | |   (29)  all_18_0 = e3
% 232.00/43.12  | | | 
% 232.00/43.12  | | | REDUCE: (26), (29) imply:
% 232.00/43.12  | | |   (30)   ~ (e3 = e0)
% 232.00/43.12  | | | 
% 232.00/43.12  | | | REDUCE: (27), (29) imply:
% 232.00/43.12  | | |   (31)  op(e3, e3) = e3
% 232.00/43.12  | | | 
% 232.00/43.12  | | | REF_CLOSE: (3), (9), (30), (31) are inconsistent by sub-proof #2494.
% 232.00/43.12  | | | 
% 232.00/43.12  | | Case 2:
% 232.00/43.12  | | | 
% 232.00/43.12  | | |   (32)  all_55_4 = e2 | all_55_4 = e1 | all_55_4 = e0
% 232.00/43.12  | | | 
% 232.00/43.12  | | | BETA: splitting (32) gives:
% 232.00/43.12  | | | 
% 232.00/43.12  | | | Case 1:
% 232.00/43.12  | | | | 
% 232.00/43.12  | | | |   (33)  all_55_4 = e2
% 232.00/43.12  | | | | 
% 232.00/43.12  | | | | COMBINE_EQS: (24), (33) imply:
% 232.00/43.12  | | | |   (34)  all_18_0 = e2
% 232.00/43.12  | | | | 
% 232.00/43.12  | | | | REDUCE: (25), (34) imply:
% 232.00/43.12  | | | |   (35)  $false
% 232.00/43.12  | | | | 
% 232.00/43.12  | | | | CLOSE: (35) is inconsistent.
% 232.00/43.12  | | | | 
% 232.00/43.12  | | | Case 2:
% 232.00/43.12  | | | | 
% 232.00/43.12  | | | |   (36)  all_55_4 = e1 | all_55_4 = e0
% 232.00/43.12  | | | | 
% 232.00/43.12  | | | | BETA: splitting (36) gives:
% 232.00/43.12  | | | | 
% 232.00/43.12  | | | | Case 1:
% 232.00/43.12  | | | | | 
% 232.00/43.12  | | | | |   (37)  all_55_4 = e1
% 232.00/43.12  | | | | | 
% 232.00/43.12  | | | | | COMBINE_EQS: (24), (37) imply:
% 232.00/43.12  | | | | |   (38)  all_18_0 = e1
% 232.00/43.12  | | | | | 
% 232.00/43.12  | | | | | REDUCE: (14), (38) imply:
% 232.00/43.12  | | | | |   (39)  $false
% 232.00/43.12  | | | | | 
% 232.00/43.12  | | | | | CLOSE: (39) is inconsistent.
% 232.00/43.12  | | | | | 
% 232.00/43.12  | | | | Case 2:
% 232.00/43.12  | | | | | 
% 232.00/43.12  | | | | |   (40)  all_55_4 = e0
% 232.00/43.12  | | | | | 
% 232.00/43.12  | | | | | COMBINE_EQS: (24), (40) imply:
% 232.00/43.12  | | | | |   (41)  all_18_0 = e0
% 232.00/43.12  | | | | | 
% 232.00/43.12  | | | | | REDUCE: (26), (41) imply:
% 232.00/43.12  | | | | |   (42)  $false
% 232.00/43.12  | | | | | 
% 232.00/43.12  | | | | | CLOSE: (42) is inconsistent.
% 232.00/43.12  | | | | | 
% 232.00/43.12  | | | | End of split
% 232.00/43.12  | | | | 
% 232.00/43.12  | | | End of split
% 232.00/43.12  | | | 
% 232.00/43.12  | | End of split
% 232.00/43.12  | | 
% 232.00/43.12  | Case 2:
% 232.00/43.12  | | 
% 232.00/43.12  | |   (43)   ~ (all_18_1 = e2) & op(e3, e0) = all_18_1 & $i(all_18_1)
% 232.00/43.12  | | 
% 232.00/43.12  | | ALPHA: (43) implies:
% 232.00/43.12  | |   (44)   ~ (all_18_1 = e2)
% 232.00/43.12  | |   (45)  op(e3, e0) = all_18_1
% 232.00/43.12  | | 
% 232.00/43.12  | | REF_CLOSE: (1), (3), (7), (44), (45) are inconsistent by sub-proof #1899.
% 232.00/43.12  | | 
% 232.00/43.12  | End of split
% 232.00/43.12  | 
% 232.00/43.12  End of proof
% 232.00/43.12  
% 232.00/43.12  Sub-proof #1899 shows that the following formulas are inconsistent:
% 232.00/43.12  ----------------------------------------------------------------
% 232.00/43.12    (1)  ( ~ (all_48_0 = e2) & op(all_48_1, e3) = all_48_0 & op(e3, e0) = all_48_1
% 232.00/43.12           & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 = e1) & op(e3, e0) =
% 232.00/43.12           all_48_1 & $i(all_48_1))
% 232.00/43.12    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.00/43.12           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.00/43.12    (3)  op(e3, e0) = e2
% 232.00/43.12    (4)   ~ (all_18_1 = e2)
% 232.00/43.12    (5)  op(e3, e0) = all_18_1
% 232.00/43.12  
% 232.00/43.12  Begin of proof
% 232.00/43.12  | 
% 232.00/43.12  | BETA: splitting (1) gives:
% 232.00/43.12  | 
% 232.00/43.12  | Case 1:
% 232.00/43.12  | | 
% 232.00/43.12  | |   (6)   ~ (all_48_0 = e2) & op(all_48_1, e3) = all_48_0 & op(e3, e0) =
% 232.00/43.12  | |        all_48_1 & $i(all_48_0) & $i(all_48_1)
% 232.00/43.12  | | 
% 232.00/43.12  | | ALPHA: (6) implies:
% 232.00/43.12  | |   (7)  op(e3, e0) = all_48_1
% 232.00/43.12  | | 
% 232.00/43.12  | | REF_CLOSE: (2), (3), (4), (5), (7) are inconsistent by sub-proof #1900.
% 232.00/43.12  | | 
% 232.00/43.12  | Case 2:
% 232.00/43.12  | | 
% 232.00/43.12  | |   (8)   ~ (all_48_1 = e1) & op(e3, e0) = all_48_1 & $i(all_48_1)
% 232.00/43.12  | | 
% 232.00/43.12  | | ALPHA: (8) implies:
% 232.00/43.12  | |   (9)  op(e3, e0) = all_48_1
% 232.00/43.12  | | 
% 232.00/43.12  | | REF_CLOSE: (2), (3), (4), (5), (9) are inconsistent by sub-proof #1900.
% 232.00/43.12  | | 
% 232.00/43.12  | End of split
% 232.00/43.12  | 
% 232.00/43.12  End of proof
% 232.00/43.12  
% 232.00/43.12  Sub-proof #1900 shows that the following formulas are inconsistent:
% 232.00/43.12  ----------------------------------------------------------------
% 232.00/43.12    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.00/43.12           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.00/43.12    (2)  op(e3, e0) = e2
% 232.00/43.12    (3)   ~ (all_18_1 = e2)
% 232.00/43.12    (4)  op(e3, e0) = all_18_1
% 232.00/43.12    (5)  op(e3, e0) = all_48_1
% 232.00/43.12  
% 232.00/43.12  Begin of proof
% 232.00/43.12  | 
% 232.00/43.12  | GROUND_INST: instantiating (1) with all_18_1, all_48_1, e0, e3, simplifying
% 232.00/43.12  |              with (4), (5) gives:
% 232.00/43.12  |   (6)  all_48_1 = all_18_1
% 232.00/43.12  | 
% 232.00/43.12  | GROUND_INST: instantiating (1) with e2, all_48_1, e0, e3, simplifying with
% 232.00/43.12  |              (2), (5) gives:
% 232.00/43.12  |   (7)  all_48_1 = e2
% 232.00/43.12  | 
% 232.00/43.12  | COMBINE_EQS: (6), (7) imply:
% 232.00/43.12  |   (8)  all_18_1 = e2
% 232.00/43.12  | 
% 232.00/43.12  | SIMP: (8) implies:
% 232.00/43.12  |   (9)  all_18_1 = e2
% 232.00/43.12  | 
% 232.00/43.12  | REDUCE: (3), (9) imply:
% 232.00/43.12  |   (10)  $false
% 232.00/43.12  | 
% 232.00/43.12  | CLOSE: (10) is inconsistent.
% 232.00/43.12  | 
% 232.00/43.12  End of proof
% 232.00/43.12  
% 232.00/43.12  Sub-proof #1901 shows that the following formulas are inconsistent:
% 232.00/43.12  ----------------------------------------------------------------
% 232.00/43.12    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.00/43.12           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.00/43.12    (2)  all_57_9 = e3 & op(e3, e0) = e3
% 232.00/43.12    (3)   ~ (all_53_13 = e2)
% 232.00/43.12    (4)   ~ (e3 = e2)
% 232.00/43.12    (5)  op(e1, e0) = all_52_23
% 232.00/43.12    (6)   ~ (e2 = e0)
% 232.00/43.12    (7)  op(e2, e2) = e2
% 232.00/43.12    (8)  op(all_52_23, all_52_23) = e0
% 232.00/43.12    (9)  op(e0, e0) = e1
% 232.00/43.12    (10)  op(e2, e0) = all_53_13
% 232.00/43.12    (11)   ~ (e2 = e1)
% 232.00/43.12    (12)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 232.00/43.12          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 232.00/43.12  
% 232.00/43.12  Begin of proof
% 232.00/43.12  | 
% 232.00/43.12  | ALPHA: (2) implies:
% 232.00/43.12  |   (13)  all_57_9 = e3
% 232.00/43.12  | 
% 232.00/43.12  | BETA: splitting (12) gives:
% 232.00/43.12  | 
% 232.00/43.12  | Case 1:
% 232.00/43.12  | | 
% 232.00/43.12  | |   (14)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 232.00/43.12  | |           e2)
% 232.00/43.12  | | 
% 232.00/43.12  | | BETA: splitting (14) gives:
% 232.00/43.12  | | 
% 232.00/43.12  | | Case 1:
% 232.00/43.12  | | | 
% 232.00/43.12  | | |   (15)  all_57_9 = e2 & op(e3, e0) = e2
% 232.00/43.12  | | | 
% 232.00/43.12  | | | ALPHA: (15) implies:
% 232.00/43.12  | | |   (16)  all_57_9 = e2
% 232.00/43.12  | | | 
% 232.00/43.12  | | | COMBINE_EQS: (13), (16) imply:
% 232.00/43.12  | | |   (17)  e3 = e2
% 232.00/43.12  | | | 
% 232.00/43.12  | | | REDUCE: (4), (17) imply:
% 232.00/43.12  | | |   (18)  $false
% 232.00/43.12  | | | 
% 232.00/43.12  | | | CLOSE: (18) is inconsistent.
% 232.00/43.12  | | | 
% 232.00/43.12  | | Case 2:
% 232.00/43.12  | | | 
% 232.00/43.12  | | |   (19)  all_57_10 = e2 & op(e2, e0) = e2
% 232.00/43.12  | | | 
% 232.00/43.12  | | | REF_CLOSE: (1), (3), (10), (19) are inconsistent by sub-proof #2432.
% 232.00/43.12  | | | 
% 232.00/43.12  | | End of split
% 232.00/43.12  | | 
% 232.00/43.12  | Case 2:
% 232.00/43.12  | | 
% 232.00/43.12  | |   (20)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 232.00/43.12  | |           e2)
% 232.00/43.12  | | 
% 232.00/43.12  | | REF_CLOSE: (1), (5), (6), (7), (8), (9), (11), (20) are inconsistent by
% 232.00/43.12  | |            sub-proof #1902.
% 232.00/43.12  | | 
% 232.00/43.12  | End of split
% 232.00/43.12  | 
% 232.00/43.12  End of proof
% 232.00/43.12  
% 232.00/43.12  Sub-proof #1902 shows that the following formulas are inconsistent:
% 232.00/43.12  ----------------------------------------------------------------
% 232.00/43.12    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.00/43.12           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.00/43.12    (2)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 232.00/43.12    (3)  op(e1, e0) = all_52_23
% 232.00/43.12    (4)   ~ (e2 = e0)
% 232.00/43.12    (5)  op(e2, e2) = e2
% 232.00/43.12    (6)  op(all_52_23, all_52_23) = e0
% 232.00/43.12    (7)  op(e0, e0) = e1
% 232.00/43.12    (8)   ~ (e2 = e1)
% 232.00/43.12  
% 232.00/43.12  Begin of proof
% 232.00/43.12  | 
% 232.00/43.12  | BETA: splitting (2) gives:
% 232.00/43.12  | 
% 232.00/43.12  | Case 1:
% 232.00/43.12  | | 
% 232.00/43.12  | |   (9)  all_57_11 = e2 & op(e1, e0) = e2
% 232.00/43.12  | | 
% 232.00/43.12  | | ALPHA: (9) implies:
% 232.00/43.12  | |   (10)  op(e1, e0) = e2
% 232.00/43.12  | | 
% 232.00/43.12  | | REF_CLOSE: (1), (3), (4), (5), (6), (10) are inconsistent by sub-proof
% 232.00/43.12  | |            #2369.
% 232.00/43.12  | | 
% 232.00/43.12  | Case 2:
% 232.00/43.12  | | 
% 232.00/43.12  | |   (11)  all_57_15 = e2 & op(e0, e0) = e2
% 232.00/43.12  | | 
% 232.00/43.12  | | ALPHA: (11) implies:
% 232.00/43.12  | |   (12)  op(e0, e0) = e2
% 232.00/43.12  | | 
% 232.00/43.12  | | REF_CLOSE: (1), (7), (8), (12) are inconsistent by sub-proof #2177.
% 232.00/43.12  | | 
% 232.00/43.12  | End of split
% 232.00/43.12  | 
% 232.00/43.12  End of proof
% 232.00/43.12  
% 232.00/43.12  Sub-proof #1903 shows that the following formulas are inconsistent:
% 232.00/43.12  ----------------------------------------------------------------
% 232.00/43.12    (1)   ~ (e3 = e1)
% 232.00/43.12    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.00/43.12           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.00/43.12    (3)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 232.00/43.12         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 232.00/43.12    (4)   ~ (e3 = e2)
% 232.00/43.12    (5)   ~ (e3 = e0)
% 232.00/43.12    (6)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 232.00/43.12         (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 232.00/43.12    (7)  all_57_5 = e3
% 232.00/43.12    (8)  op(e1, e1) = e1
% 232.00/43.12    (9)   ~ (e2 = e0)
% 232.00/43.12    (10)   ~ (e1 = e0)
% 232.00/43.12    (11)   ~ (all_53_8 = e0)
% 232.00/43.12    (12)   ~ (e2 = e1)
% 232.00/43.12    (13)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 232.00/43.12          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 232.00/43.12    (14)  op(e3, e1) = all_53_8
% 232.00/43.12    (15)  all_57_4 = e3 & op(e3, e1) = e3
% 232.00/43.12  
% 232.00/43.12  Begin of proof
% 232.00/43.12  | 
% 232.00/43.12  | ALPHA: (15) implies:
% 232.00/43.12  |   (16)  all_57_4 = e3
% 232.00/43.12  | 
% 232.00/43.12  | BETA: splitting (13) gives:
% 232.00/43.12  | 
% 232.00/43.12  | Case 1:
% 232.00/43.12  | | 
% 232.00/43.12  | |   (17)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) =
% 232.00/43.12  | |           e2)
% 232.00/43.12  | | 
% 232.00/43.12  | | BETA: splitting (17) gives:
% 232.00/43.12  | | 
% 232.00/43.12  | | Case 1:
% 232.00/43.12  | | | 
% 232.00/43.12  | | |   (18)  all_57_4 = e2 & op(e3, e1) = e2
% 232.00/43.12  | | | 
% 232.00/43.12  | | | REF_CLOSE: (4), (16), (18) are inconsistent by sub-proof #2487.
% 232.00/43.12  | | | 
% 232.00/43.12  | | Case 2:
% 232.00/43.12  | | | 
% 232.00/43.12  | | |   (19)  all_57_5 = e2 & op(e2, e1) = e2
% 232.00/43.12  | | | 
% 232.00/43.12  | | | ALPHA: (19) implies:
% 232.00/43.12  | | |   (20)  all_57_5 = e2
% 232.00/43.12  | | | 
% 232.00/43.12  | | | REF_CLOSE: (4), (7), (20) are inconsistent by sub-proof #2189.
% 232.00/43.12  | | | 
% 232.00/43.12  | | End of split
% 232.00/43.12  | | 
% 232.00/43.12  | Case 2:
% 232.00/43.12  | | 
% 232.00/43.12  | |   (21)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) =
% 232.00/43.12  | |           e2)
% 232.00/43.12  | | 
% 232.00/43.12  | | BETA: splitting (21) gives:
% 232.00/43.12  | | 
% 232.00/43.12  | | Case 1:
% 232.00/43.12  | | | 
% 232.00/43.12  | | |   (22)  all_57_8 = e2 & op(e1, e1) = e2
% 232.00/43.12  | | | 
% 232.00/43.12  | | | ALPHA: (22) implies:
% 232.00/43.12  | | |   (23)  op(e1, e1) = e2
% 232.00/43.12  | | | 
% 232.00/43.12  | | | REF_CLOSE: (2), (8), (12), (23) are inconsistent by sub-proof #2423.
% 232.00/43.12  | | | 
% 232.00/43.12  | | Case 2:
% 232.00/43.12  | | | 
% 232.00/43.12  | | |   (24)  all_57_14 = e2 & op(e0, e1) = e2
% 232.00/43.12  | | | 
% 232.00/43.12  | | | ALPHA: (24) implies:
% 232.00/43.12  | | |   (25)  all_57_14 = e2
% 232.00/43.12  | | | 
% 232.00/43.12  | | | BETA: splitting (3) gives:
% 232.00/43.12  | | | 
% 232.00/43.12  | | | Case 1:
% 232.00/43.12  | | | | 
% 232.00/43.12  | | | |   (26)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1)
% 232.00/43.12  | | | |           = e0)
% 232.00/43.12  | | | | 
% 232.00/43.12  | | | | REF_CLOSE: (2), (5), (7), (11), (14), (26) are inconsistent by sub-proof
% 232.00/43.12  | | | |            #1906.
% 232.00/43.12  | | | | 
% 232.00/43.12  | | | Case 2:
% 232.00/43.12  | | | | 
% 232.00/43.12  | | | |   (27)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1)
% 232.00/43.12  | | | |           = e0)
% 232.00/43.12  | | | | 
% 232.00/43.12  | | | | BETA: splitting (27) gives:
% 232.00/43.12  | | | | 
% 232.00/43.12  | | | | Case 1:
% 232.00/43.12  | | | | | 
% 232.00/43.12  | | | | |   (28)  all_57_8 = e0 & op(e1, e1) = e0
% 232.00/43.12  | | | | | 
% 232.00/43.12  | | | | | ALPHA: (28) implies:
% 232.00/43.12  | | | | |   (29)  op(e1, e1) = e0
% 232.00/43.12  | | | | | 
% 232.00/43.12  | | | | | REF_CLOSE: (1), (2), (6), (7), (10), (12), (16), (25), (29) are
% 232.00/43.12  | | | | |            inconsistent by sub-proof #1904.
% 232.00/43.12  | | | | | 
% 232.00/43.12  | | | | Case 2:
% 232.00/43.12  | | | | | 
% 232.00/43.12  | | | | |   (30)  all_57_14 = e0 & op(e0, e1) = e0
% 232.00/43.12  | | | | | 
% 232.00/43.12  | | | | | REF_CLOSE: (9), (25), (30) are inconsistent by sub-proof #2173.
% 232.00/43.12  | | | | | 
% 232.00/43.12  | | | | End of split
% 232.00/43.12  | | | | 
% 232.00/43.12  | | | End of split
% 232.00/43.12  | | | 
% 232.00/43.12  | | End of split
% 232.00/43.12  | | 
% 232.00/43.12  | End of split
% 232.00/43.12  | 
% 232.00/43.12  End of proof
% 232.00/43.12  
% 232.00/43.12  Sub-proof #1904 shows that the following formulas are inconsistent:
% 232.00/43.12  ----------------------------------------------------------------
% 232.00/43.12    (1)   ~ (e3 = e1)
% 232.00/43.12    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.00/43.12           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.00/43.12    (3)  all_57_4 = e3
% 232.00/43.12    (4)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 232.00/43.12         (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 232.00/43.12    (5)  all_57_5 = e3
% 232.00/43.12    (6)   ~ (e1 = e0)
% 232.00/43.12    (7)  all_57_14 = e2
% 232.00/43.12    (8)  op(e1, e1) = e0
% 232.00/43.12    (9)   ~ (e2 = e1)
% 232.00/43.12  
% 232.00/43.12  Begin of proof
% 232.00/43.12  | 
% 232.00/43.12  | BETA: splitting (4) gives:
% 232.00/43.12  | 
% 232.00/43.12  | Case 1:
% 232.00/43.12  | | 
% 232.00/43.12  | |   (10)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) =
% 232.00/43.12  | |           e1)
% 232.00/43.12  | | 
% 232.00/43.12  | | BETA: splitting (10) gives:
% 232.00/43.12  | | 
% 232.00/43.12  | | Case 1:
% 232.00/43.12  | | | 
% 232.00/43.12  | | |   (11)  all_57_4 = e1 & op(e3, e1) = e1
% 232.00/43.12  | | | 
% 232.00/43.12  | | | ALPHA: (11) implies:
% 232.00/43.12  | | |   (12)  all_57_4 = e1
% 232.00/43.12  | | | 
% 232.00/43.12  | | | REF_CLOSE: (1), (3), (12) are inconsistent by sub-proof #2426.
% 232.00/43.12  | | | 
% 232.00/43.12  | | Case 2:
% 232.00/43.12  | | | 
% 232.00/43.12  | | |   (13)  all_57_5 = e1 & op(e2, e1) = e1
% 232.00/43.12  | | | 
% 232.00/43.12  | | | REF_CLOSE: (1), (5), (13) are inconsistent by sub-proof #2376.
% 232.00/43.12  | | | 
% 232.00/43.12  | | End of split
% 232.00/43.12  | | 
% 232.00/43.12  | Case 2:
% 232.00/43.12  | | 
% 232.00/43.12  | |   (14)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) =
% 232.00/43.12  | |           e1)
% 232.00/43.12  | | 
% 232.00/43.12  | | REF_CLOSE: (2), (6), (7), (8), (9), (14) are inconsistent by sub-proof
% 232.00/43.12  | |            #1905.
% 232.00/43.12  | | 
% 232.00/43.12  | End of split
% 232.00/43.12  | 
% 232.00/43.12  End of proof
% 232.00/43.12  
% 232.00/43.12  Sub-proof #1905 shows that the following formulas are inconsistent:
% 232.00/43.12  ----------------------------------------------------------------
% 232.00/43.12    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.00/43.12           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.00/43.12    (2)   ~ (e1 = e0)
% 232.00/43.12    (3)  all_57_14 = e2
% 232.00/43.12    (4)  op(e1, e1) = e0
% 232.00/43.12    (5)   ~ (e2 = e1)
% 232.00/43.12    (6)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 232.00/43.12  
% 232.00/43.12  Begin of proof
% 232.00/43.12  | 
% 232.00/43.12  | BETA: splitting (6) gives:
% 232.00/43.12  | 
% 232.00/43.12  | Case 1:
% 232.00/43.12  | | 
% 232.00/43.12  | |   (7)  all_57_8 = e1 & op(e1, e1) = e1
% 232.00/43.12  | | 
% 232.00/43.12  | | ALPHA: (7) implies:
% 232.00/43.12  | |   (8)  op(e1, e1) = e1
% 232.00/43.12  | | 
% 232.00/43.12  | | REF_CLOSE: (1), (2), (4), (8) are inconsistent by sub-proof #2427.
% 232.00/43.12  | | 
% 232.00/43.12  | Case 2:
% 232.00/43.12  | | 
% 232.00/43.12  | |   (9)  all_57_14 = e1 & op(e0, e1) = e1
% 232.00/43.12  | | 
% 232.00/43.12  | | ALPHA: (9) implies:
% 232.00/43.12  | |   (10)  all_57_14 = e1
% 232.00/43.12  | | 
% 232.00/43.12  | | REF_CLOSE: (3), (5), (10) are inconsistent by sub-proof #2178.
% 232.00/43.12  | | 
% 232.00/43.12  | End of split
% 232.00/43.12  | 
% 232.00/43.12  End of proof
% 232.00/43.12  
% 232.00/43.12  Sub-proof #1906 shows that the following formulas are inconsistent:
% 232.00/43.12  ----------------------------------------------------------------
% 232.00/43.12    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.00/43.12           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.00/43.12    (2)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0)
% 232.00/43.12    (3)   ~ (e3 = e0)
% 232.00/43.12    (4)  all_57_5 = e3
% 232.00/43.12    (5)   ~ (all_53_8 = e0)
% 232.00/43.12    (6)  op(e3, e1) = all_53_8
% 232.00/43.12  
% 232.00/43.12  Begin of proof
% 232.00/43.12  | 
% 232.00/43.12  | BETA: splitting (2) gives:
% 232.00/43.12  | 
% 232.00/43.12  | Case 1:
% 232.00/43.12  | | 
% 232.00/43.12  | |   (7)  all_57_4 = e0 & op(e3, e1) = e0
% 232.00/43.12  | | 
% 232.00/43.12  | | ALPHA: (7) implies:
% 232.00/43.12  | |   (8)  op(e3, e1) = e0
% 232.00/43.12  | | 
% 232.00/43.12  | | REF_CLOSE: (1), (5), (6), (8) are inconsistent by sub-proof #2267.
% 232.00/43.12  | | 
% 232.00/43.12  | Case 2:
% 232.00/43.12  | | 
% 232.00/43.12  | |   (9)  all_57_5 = e0 & op(e2, e1) = e0
% 232.00/43.12  | | 
% 232.00/43.12  | | ALPHA: (9) implies:
% 232.00/43.12  | |   (10)  all_57_5 = e0
% 232.00/43.12  | | 
% 232.00/43.12  | | REF_CLOSE: (3), (4), (10) are inconsistent by sub-proof #2471.
% 232.00/43.12  | | 
% 232.00/43.12  | End of split
% 232.00/43.12  | 
% 232.00/43.12  End of proof
% 232.00/43.12  
% 232.00/43.12  Sub-proof #1907 shows that the following formulas are inconsistent:
% 232.00/43.12  ----------------------------------------------------------------
% 232.00/43.12    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 232.00/43.12         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 232.00/43.12    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 232.00/43.12         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 232.00/43.12    (3)   ~ (e3 = e1)
% 232.00/43.12    (4)   ~ (all_53_13 = e1)
% 232.00/43.12    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.00/43.12           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.00/43.12    (6)   ~ (all_53_9 = e1)
% 232.00/43.12    (7)   ~ (e3 = e2)
% 232.00/43.12    (8)   ~ (e3 = e0)
% 232.00/43.12    (9)  all_57_1 = e1
% 232.00/43.12    (10)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 232.00/43.12          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 232.00/43.12    (11)   ~ (e2 = e0)
% 232.00/43.12    (12)  all_57_2 = e3
% 232.00/43.12    (13)   ~ (e1 = e0)
% 232.00/43.12    (14)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 232.00/43.12          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 232.00/43.12    (15)  op(e2, e0) = all_53_13
% 232.00/43.12    (16)   ~ (e2 = e1)
% 232.00/43.12    (17)  op(e2, e1) = all_53_9
% 232.00/43.12  
% 232.00/43.12  Begin of proof
% 232.00/43.12  | 
% 232.00/43.12  | BETA: splitting (1) gives:
% 232.00/43.12  | 
% 232.00/43.12  | Case 1:
% 232.00/43.12  | | 
% 232.00/43.12  | |   (18)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) =
% 232.00/43.12  | |           e1)
% 232.00/43.12  | | 
% 232.00/43.12  | | BETA: splitting (18) gives:
% 232.00/43.12  | | 
% 232.00/43.12  | | Case 1:
% 232.00/43.12  | | | 
% 232.00/43.12  | | |   (19)  all_57_2 = e1 & op(e2, e3) = e1
% 232.00/43.12  | | | 
% 232.00/43.12  | | | REF_CLOSE: (3), (12), (19) are inconsistent by sub-proof #1928.
% 232.00/43.12  | | | 
% 232.00/43.12  | | Case 2:
% 232.00/43.12  | | | 
% 232.00/43.12  | | |   (20)  all_57_3 = e1 & op(e2, e2) = e1
% 232.00/43.12  | | | 
% 232.00/43.12  | | | ALPHA: (20) implies:
% 232.00/43.12  | | |   (21)  op(e2, e2) = e1
% 232.00/43.12  | | | 
% 232.00/43.12  | | | REF_CLOSE: (2), (3), (5), (7), (8), (9), (10), (11), (13), (14), (16),
% 232.00/43.12  | | |            (21) are inconsistent by sub-proof #1908.
% 232.00/43.12  | | | 
% 232.00/43.12  | | End of split
% 232.00/43.12  | | 
% 232.00/43.12  | Case 2:
% 232.00/43.12  | | 
% 232.00/43.12  | |   (22)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) =
% 232.00/43.12  | |           e1)
% 232.00/43.12  | | 
% 232.00/43.12  | | BETA: splitting (22) gives:
% 232.00/43.12  | | 
% 232.00/43.12  | | Case 1:
% 232.00/43.12  | | | 
% 232.00/43.12  | | |   (23)  all_57_5 = e1 & op(e2, e1) = e1
% 232.00/43.12  | | | 
% 232.00/43.12  | | | REF_CLOSE: (5), (6), (17), (23) are inconsistent by sub-proof #2305.
% 232.00/43.12  | | | 
% 232.00/43.12  | | Case 2:
% 232.00/43.12  | | | 
% 232.00/43.12  | | |   (24)  all_57_10 = e1 & op(e2, e0) = e1
% 232.00/43.12  | | | 
% 232.00/43.12  | | | REF_CLOSE: (4), (5), (15), (24) are inconsistent by sub-proof #2084.
% 232.00/43.12  | | | 
% 232.00/43.12  | | End of split
% 232.00/43.12  | | 
% 232.00/43.12  | End of split
% 232.00/43.12  | 
% 232.00/43.12  End of proof
% 232.00/43.12  
% 232.00/43.12  Sub-proof #1908 shows that the following formulas are inconsistent:
% 232.00/43.12  ----------------------------------------------------------------
% 232.00/43.12    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 232.00/43.12         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 232.00/43.12    (2)   ~ (e3 = e1)
% 232.00/43.12    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.00/43.12           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.00/43.12    (4)  op(e2, e2) = e1
% 232.00/43.12    (5)   ~ (e3 = e2)
% 232.00/43.12    (6)   ~ (e3 = e0)
% 232.00/43.12    (7)  all_57_1 = e1
% 232.00/43.12    (8)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 232.00/43.12         (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 232.00/43.12    (9)   ~ (e2 = e0)
% 232.00/43.12    (10)   ~ (e1 = e0)
% 232.00/43.12    (11)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 232.00/43.12          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 232.00/43.12    (12)   ~ (e2 = e1)
% 232.00/43.12  
% 232.00/43.12  Begin of proof
% 232.00/43.12  | 
% 232.00/43.12  | BETA: splitting (11) gives:
% 232.00/43.12  | 
% 232.00/43.12  | Case 1:
% 232.00/43.12  | | 
% 232.00/43.12  | |   (13)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 232.00/43.12  | |           e3)
% 232.00/43.12  | | 
% 232.00/43.12  | | BETA: splitting (13) gives:
% 232.00/43.12  | | 
% 232.00/43.12  | | Case 1:
% 232.00/43.12  | | | 
% 232.00/43.12  | | |   (14)  all_57_1 = e3 & op(e3, e2) = e3
% 232.00/43.12  | | | 
% 232.00/43.12  | | | REF_CLOSE: (2), (7), (14) are inconsistent by sub-proof #2196.
% 232.00/43.12  | | | 
% 232.00/43.12  | | Case 2:
% 232.00/43.12  | | | 
% 232.00/43.12  | | |   (15)  all_57_3 = e3 & op(e2, e2) = e3
% 232.00/43.12  | | | 
% 232.00/43.12  | | | ALPHA: (15) implies:
% 232.00/43.12  | | |   (16)  op(e2, e2) = e3
% 232.00/43.12  | | | 
% 232.00/43.12  | | | REF_CLOSE: (2), (3), (4), (16) are inconsistent by sub-proof #1912.
% 232.00/43.12  | | | 
% 232.00/43.12  | | End of split
% 232.00/43.12  | | 
% 232.00/43.12  | Case 2:
% 232.00/43.12  | | 
% 232.00/43.12  | |   (17)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 232.00/43.12  | |           e3)
% 232.00/43.12  | | 
% 232.00/43.12  | | BETA: splitting (17) gives:
% 232.00/43.12  | | 
% 232.00/43.12  | | Case 1:
% 232.00/43.12  | | | 
% 232.00/43.12  | | |   (18)  all_57_7 = e3 & op(e1, e2) = e3
% 232.00/43.12  | | | 
% 232.00/43.12  | | | ALPHA: (18) implies:
% 232.00/43.12  | | |   (19)  all_57_7 = e3
% 232.00/43.12  | | | 
% 232.00/43.12  | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (12), (19) are
% 232.00/43.12  | | |            inconsistent by sub-proof #1909.
% 232.00/43.12  | | | 
% 232.00/43.12  | | Case 2:
% 232.00/43.12  | | | 
% 232.00/43.12  | | |   (20)  all_57_13 = e3 & op(e0, e2) = e3
% 232.00/43.12  | | | 
% 232.00/43.12  | | | ALPHA: (20) implies:
% 232.00/43.12  | | |   (21)  all_57_13 = e3
% 232.00/43.12  | | | 
% 232.00/43.12  | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (12), (21) are
% 232.00/43.12  | | |            inconsistent by sub-proof #2145.
% 232.00/43.12  | | | 
% 232.00/43.12  | | End of split
% 232.00/43.12  | | 
% 232.00/43.12  | End of split
% 232.00/43.12  | 
% 232.00/43.12  End of proof
% 232.00/43.12  
% 232.00/43.12  Sub-proof #1909 shows that the following formulas are inconsistent:
% 232.00/43.12  ----------------------------------------------------------------
% 232.00/43.12    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 232.00/43.12         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 232.00/43.12    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.00/43.12           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.00/43.12    (3)  op(e2, e2) = e1
% 232.00/43.12    (4)   ~ (e3 = e2)
% 232.00/43.12    (5)   ~ (e3 = e0)
% 232.00/43.12    (6)  all_57_1 = e1
% 232.00/43.12    (7)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 232.00/43.12         (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 232.00/43.12    (8)   ~ (e2 = e0)
% 232.00/43.12    (9)   ~ (e1 = e0)
% 232.00/43.12    (10)  all_57_7 = e3
% 232.00/43.12    (11)   ~ (e2 = e1)
% 232.00/43.12  
% 232.00/43.12  Begin of proof
% 232.00/43.12  | 
% 232.00/43.12  | BETA: splitting (1) gives:
% 232.00/43.12  | 
% 232.00/43.12  | Case 1:
% 232.00/43.12  | | 
% 232.00/43.12  | |   (12)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 232.00/43.12  | |           e2)
% 232.00/43.12  | | 
% 232.00/43.12  | | REF_CLOSE: (2), (3), (6), (11), (12) are inconsistent by sub-proof #2150.
% 232.00/43.12  | | 
% 232.00/43.12  | Case 2:
% 232.00/43.12  | | 
% 232.00/43.12  | |   (13)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 232.00/43.12  | |           e2)
% 232.00/43.12  | | 
% 232.00/43.12  | | BETA: splitting (13) gives:
% 232.00/43.12  | | 
% 232.00/43.12  | | Case 1:
% 232.00/43.12  | | | 
% 232.00/43.12  | | |   (14)  all_57_7 = e2 & op(e1, e2) = e2
% 232.00/43.12  | | | 
% 232.00/43.12  | | | REF_CLOSE: (4), (10), (14) are inconsistent by sub-proof #2092.
% 232.00/43.12  | | | 
% 232.00/43.12  | | Case 2:
% 232.00/43.12  | | | 
% 232.00/43.12  | | |   (15)  all_57_13 = e2 & op(e0, e2) = e2
% 232.00/43.12  | | | 
% 232.00/43.12  | | | ALPHA: (15) implies:
% 232.00/43.12  | | |   (16)  all_57_13 = e2
% 232.00/43.12  | | | 
% 232.00/43.12  | | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (9), (10), (16) are inconsistent
% 232.00/43.12  | | |            by sub-proof #1910.
% 232.00/43.12  | | | 
% 232.00/43.12  | | End of split
% 232.00/43.12  | | 
% 232.00/43.12  | End of split
% 232.00/43.12  | 
% 232.00/43.12  End of proof
% 232.00/43.12  
% 232.00/43.12  Sub-proof #1910 shows that the following formulas are inconsistent:
% 232.00/43.12  ----------------------------------------------------------------
% 232.00/43.12    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.00/43.12           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.00/43.12    (2)  op(e2, e2) = e1
% 232.00/43.12    (3)   ~ (e3 = e0)
% 232.00/43.12    (4)  all_57_1 = e1
% 232.00/43.12    (5)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 232.00/43.12         (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 232.00/43.12    (6)   ~ (e2 = e0)
% 232.00/43.12    (7)  all_57_13 = e2
% 232.00/43.12    (8)   ~ (e1 = e0)
% 232.00/43.12    (9)  all_57_7 = e3
% 232.00/43.12  
% 232.00/43.12  Begin of proof
% 232.00/43.12  | 
% 232.00/43.12  | BETA: splitting (5) gives:
% 232.00/43.12  | 
% 232.00/43.12  | Case 1:
% 232.00/43.12  | | 
% 232.00/43.12  | |   (10)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) =
% 232.00/43.12  | |           e0)
% 232.00/43.12  | | 
% 232.00/43.12  | | REF_CLOSE: (1), (2), (4), (8), (10) are inconsistent by sub-proof #2149.
% 232.00/43.12  | | 
% 232.00/43.12  | Case 2:
% 232.00/43.12  | | 
% 232.00/43.12  | |   (11)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 232.00/43.12  | |           e0)
% 232.00/43.12  | | 
% 232.00/43.12  | | BETA: splitting (11) gives:
% 232.00/43.12  | | 
% 232.00/43.12  | | Case 1:
% 232.00/43.12  | | | 
% 232.00/43.12  | | |   (12)  all_57_7 = e0 & op(e1, e2) = e0
% 232.00/43.12  | | | 
% 232.00/43.12  | | | REF_CLOSE: (3), (9), (12) are inconsistent by sub-proof #2042.
% 232.00/43.12  | | | 
% 232.00/43.12  | | Case 2:
% 232.00/43.12  | | | 
% 232.00/43.12  | | |   (13)  all_57_13 = e0 & op(e0, e2) = e0
% 232.00/43.12  | | | 
% 232.00/43.12  | | | ALPHA: (13) implies:
% 232.00/43.13  | | |   (14)  all_57_13 = e0
% 232.00/43.13  | | | 
% 232.00/43.13  | | | REF_CLOSE: (6), (7), (14) are inconsistent by sub-proof #1911.
% 232.00/43.13  | | | 
% 232.00/43.13  | | End of split
% 232.00/43.13  | | 
% 232.00/43.13  | End of split
% 232.00/43.13  | 
% 232.00/43.13  End of proof
% 232.00/43.13  
% 232.00/43.13  Sub-proof #1911 shows that the following formulas are inconsistent:
% 232.00/43.13  ----------------------------------------------------------------
% 232.00/43.13    (1)  all_57_13 = e2
% 232.00/43.13    (2)  all_57_13 = e0
% 232.00/43.13    (3)   ~ (e2 = e0)
% 232.00/43.13  
% 232.00/43.13  Begin of proof
% 232.00/43.13  | 
% 232.00/43.13  | COMBINE_EQS: (1), (2) imply:
% 232.00/43.13  |   (4)  e2 = e0
% 232.00/43.13  | 
% 232.00/43.13  | SIMP: (4) implies:
% 232.00/43.13  |   (5)  e2 = e0
% 232.00/43.13  | 
% 232.00/43.13  | REDUCE: (3), (5) imply:
% 232.00/43.13  |   (6)  $false
% 232.00/43.13  | 
% 232.00/43.13  | CLOSE: (6) is inconsistent.
% 232.00/43.13  | 
% 232.00/43.13  End of proof
% 232.00/43.13  
% 232.00/43.13  Sub-proof #1912 shows that the following formulas are inconsistent:
% 232.00/43.13  ----------------------------------------------------------------
% 232.00/43.13    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.00/43.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.00/43.13    (2)  op(e2, e2) = e3
% 232.00/43.13    (3)  op(e2, e2) = e1
% 232.00/43.13    (4)   ~ (e3 = e1)
% 232.00/43.13  
% 232.00/43.13  Begin of proof
% 232.00/43.13  | 
% 232.00/43.13  | GROUND_INST: instantiating (1) with e1, e3, e2, e2, simplifying with (2), (3)
% 232.00/43.13  |              gives:
% 232.00/43.13  |   (5)  e3 = e1
% 232.00/43.13  | 
% 232.00/43.13  | REDUCE: (4), (5) imply:
% 232.00/43.13  |   (6)  $false
% 232.00/43.13  | 
% 232.00/43.13  | CLOSE: (6) is inconsistent.
% 232.00/43.13  | 
% 232.00/43.13  End of proof
% 232.00/43.13  
% 232.00/43.13  Sub-proof #1913 shows that the following formulas are inconsistent:
% 232.00/43.13  ----------------------------------------------------------------
% 232.00/43.13    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.00/43.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.00/43.13    (2)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 232.00/43.13    (3)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 232.00/43.13    (4)  all_55_11 = all_52_23
% 232.00/43.13    (5)   ~ (all_53_12 = all_52_23)
% 232.00/43.13    (6)   ~ (all_52_23 = e3)
% 232.00/43.13    (7)  op(all_52_23, all_52_23) = e0
% 232.00/43.13    (8)   ~ (all_53_12 = e1)
% 232.00/43.13    (9)  op(e0, e0) = e1
% 232.00/43.13    (10)  all_55_3 = all_53_12
% 232.00/43.13    (11)   ~ (all_53_12 = e3)
% 232.00/43.13    (12)   ~ (all_53_12 = e0)
% 232.00/43.13    (13)   ~ (all_52_23 = e1)
% 232.00/43.13  
% 232.00/43.13  Begin of proof
% 232.00/43.13  | 
% 232.00/43.13  | BETA: splitting (2) gives:
% 232.00/43.13  | 
% 232.00/43.13  | Case 1:
% 232.00/43.13  | | 
% 232.00/43.13  | |   (14)  all_55_3 = e3
% 232.00/43.13  | | 
% 232.00/43.13  | | COMBINE_EQS: (10), (14) imply:
% 232.00/43.13  | |   (15)  all_53_12 = e3
% 232.00/43.13  | | 
% 232.00/43.13  | | REDUCE: (11), (15) imply:
% 232.00/43.13  | |   (16)  $false
% 232.00/43.13  | | 
% 232.00/43.13  | | CLOSE: (16) is inconsistent.
% 232.00/43.13  | | 
% 232.00/43.13  | Case 2:
% 232.00/43.13  | | 
% 232.00/43.13  | |   (17)  all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 232.00/43.13  | | 
% 232.00/43.13  | | BETA: splitting (17) gives:
% 232.00/43.13  | | 
% 232.00/43.13  | | Case 1:
% 232.00/43.13  | | | 
% 232.00/43.13  | | |   (18)  all_55_3 = e2
% 232.00/43.13  | | | 
% 232.00/43.13  | | | COMBINE_EQS: (10), (18) imply:
% 232.00/43.13  | | |   (19)  all_53_12 = e2
% 232.00/43.13  | | | 
% 232.00/43.13  | | | SIMP: (19) implies:
% 232.00/43.13  | | |   (20)  all_53_12 = e2
% 232.00/43.13  | | | 
% 232.00/43.13  | | | REDUCE: (5), (20) imply:
% 232.00/43.13  | | |   (21)   ~ (all_52_23 = e2)
% 232.00/43.13  | | | 
% 232.00/43.13  | | | SIMP: (21) implies:
% 232.00/43.13  | | |   (22)   ~ (all_52_23 = e2)
% 232.00/43.13  | | | 
% 232.00/43.13  | | | BETA: splitting (3) gives:
% 232.00/43.13  | | | 
% 232.00/43.13  | | | Case 1:
% 232.00/43.13  | | | | 
% 232.00/43.13  | | | |   (23)  all_55_11 = e3
% 232.00/43.13  | | | | 
% 232.00/43.13  | | | | REF_CLOSE: (4), (6), (23) are inconsistent by sub-proof #1914.
% 232.00/43.13  | | | | 
% 232.00/43.13  | | | Case 2:
% 232.00/43.13  | | | | 
% 232.00/43.13  | | | |   (24)  all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 232.00/43.13  | | | | 
% 232.00/43.13  | | | | BETA: splitting (24) gives:
% 232.00/43.13  | | | | 
% 232.00/43.13  | | | | Case 1:
% 232.00/43.13  | | | | | 
% 232.00/43.13  | | | | |   (25)  all_55_11 = e2
% 232.00/43.13  | | | | | 
% 232.00/43.13  | | | | | COMBINE_EQS: (4), (25) imply:
% 232.00/43.13  | | | | |   (26)  all_52_23 = e2
% 232.00/43.13  | | | | | 
% 232.00/43.13  | | | | | REDUCE: (22), (26) imply:
% 232.00/43.13  | | | | |   (27)  $false
% 232.00/43.13  | | | | | 
% 232.00/43.13  | | | | | CLOSE: (27) is inconsistent.
% 232.00/43.13  | | | | | 
% 232.00/43.13  | | | | Case 2:
% 232.00/43.13  | | | | | 
% 232.00/43.13  | | | | |   (28)  all_55_11 = e1 | all_55_11 = e0
% 232.00/43.13  | | | | | 
% 232.00/43.13  | | | | | BETA: splitting (28) gives:
% 232.00/43.13  | | | | | 
% 232.00/43.13  | | | | | Case 1:
% 232.00/43.13  | | | | | | 
% 232.00/43.13  | | | | | |   (29)  all_55_11 = e1
% 232.00/43.13  | | | | | | 
% 232.00/43.13  | | | | | | COMBINE_EQS: (4), (29) imply:
% 232.00/43.13  | | | | | |   (30)  all_52_23 = e1
% 232.00/43.13  | | | | | | 
% 232.00/43.13  | | | | | | REDUCE: (13), (30) imply:
% 232.00/43.13  | | | | | |   (31)  $false
% 232.00/43.13  | | | | | | 
% 232.00/43.13  | | | | | | CLOSE: (31) is inconsistent.
% 232.00/43.13  | | | | | | 
% 232.00/43.13  | | | | | Case 2:
% 232.00/43.13  | | | | | | 
% 232.00/43.13  | | | | | |   (32)  all_55_11 = e0
% 232.00/43.13  | | | | | | 
% 232.00/43.13  | | | | | | COMBINE_EQS: (4), (32) imply:
% 232.00/43.13  | | | | | |   (33)  all_52_23 = e0
% 232.00/43.13  | | | | | | 
% 232.00/43.13  | | | | | | REDUCE: (13), (33) imply:
% 232.00/43.13  | | | | | |   (34)   ~ (e1 = e0)
% 232.00/43.13  | | | | | | 
% 232.00/43.13  | | | | | | SIMP: (34) implies:
% 232.00/43.13  | | | | | |   (35)   ~ (e1 = e0)
% 232.00/43.13  | | | | | | 
% 232.00/43.13  | | | | | | REDUCE: (7), (33) imply:
% 232.00/43.13  | | | | | |   (36)  op(e0, e0) = e0
% 232.00/43.13  | | | | | | 
% 232.00/43.13  | | | | | | REF_CLOSE: (1), (9), (35), (36) are inconsistent by sub-proof #2290.
% 232.00/43.13  | | | | | | 
% 232.00/43.13  | | | | | End of split
% 232.00/43.13  | | | | | 
% 232.00/43.13  | | | | End of split
% 232.00/43.13  | | | | 
% 232.00/43.13  | | | End of split
% 232.00/43.13  | | | 
% 232.00/43.13  | | Case 2:
% 232.00/43.13  | | | 
% 232.00/43.13  | | |   (37)  all_55_3 = e1 | all_55_3 = e0
% 232.00/43.13  | | | 
% 232.00/43.13  | | | REF_CLOSE: (8), (10), (12), (37) are inconsistent by sub-proof #2132.
% 232.00/43.13  | | | 
% 232.00/43.13  | | End of split
% 232.00/43.13  | | 
% 232.00/43.13  | End of split
% 232.00/43.13  | 
% 232.00/43.13  End of proof
% 232.00/43.13  
% 232.00/43.13  Sub-proof #1914 shows that the following formulas are inconsistent:
% 232.00/43.13  ----------------------------------------------------------------
% 232.00/43.13    (1)  all_55_11 = all_52_23
% 232.00/43.13    (2)  all_55_11 = e3
% 232.00/43.13    (3)   ~ (all_52_23 = e3)
% 232.00/43.13  
% 232.00/43.13  Begin of proof
% 232.00/43.13  | 
% 232.00/43.13  | COMBINE_EQS: (1), (2) imply:
% 232.00/43.13  |   (4)  all_52_23 = e3
% 232.00/43.13  | 
% 232.00/43.13  | SIMP: (4) implies:
% 232.00/43.13  |   (5)  all_52_23 = e3
% 232.00/43.13  | 
% 232.00/43.13  | REDUCE: (3), (5) imply:
% 232.00/43.13  |   (6)  $false
% 232.00/43.13  | 
% 232.00/43.13  | CLOSE: (6) is inconsistent.
% 232.00/43.13  | 
% 232.00/43.13  End of proof
% 232.00/43.13  
% 232.00/43.13  Sub-proof #1915 shows that the following formulas are inconsistent:
% 232.00/43.13  ----------------------------------------------------------------
% 232.00/43.13    (1)   ~ (e3 = e1)
% 232.00/43.13    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.00/43.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.00/43.13    (3)   ~ (all_53_7 = e2)
% 232.00/43.13    (4)   ~ (e3 = e2)
% 232.00/43.13    (5)   ~ (e3 = e0)
% 232.00/43.13    (6)  op(e0, e3) = all_53_3
% 232.00/43.13    (7)  op(e3, e3) = e0
% 232.00/43.13    (8)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 232.00/43.13         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 232.00/43.13    (9)  op(e3, e3) = all_52_1
% 232.00/43.13    (10)  op(all_52_1, all_52_1) = e3
% 232.00/43.13    (11)   ~ (e2 = e0)
% 232.00/43.13    (12)   ~ (e1 = e0)
% 232.00/43.13    (13)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 232.00/43.13          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 232.00/43.13            e3)
% 232.00/43.13    (14)  op(e0, e2) = all_53_7
% 232.00/43.13    (15)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 232.00/43.13          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 232.00/43.13            e2)
% 232.00/43.13    (16)   ~ (all_53_3 = e0)
% 232.00/43.13    (17)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 232.00/43.13              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 232.00/43.13                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 232.00/43.13                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 232.00/43.13    (18)   ~ (all_53_3 = e1)
% 232.00/43.13    (19)  op(e0, e0) = e1
% 232.00/43.13    (20)   ~ (e2 = e1)
% 232.00/43.13  
% 232.00/43.13  Begin of proof
% 232.00/43.13  | 
% 232.00/43.13  | BETA: splitting (8) gives:
% 232.00/43.13  | 
% 232.00/43.13  | Case 1:
% 232.00/43.13  | | 
% 232.00/43.13  | |   (21)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 232.00/43.13  | |           e1)
% 232.00/43.13  | | 
% 232.00/43.13  | | REF_CLOSE: (1), (2), (4), (5), (6), (11), (12), (13), (15), (16), (17),
% 232.00/43.13  | |            (18), (19), (20), (21) are inconsistent by sub-proof #1917.
% 232.00/43.13  | | 
% 232.00/43.13  | Case 2:
% 232.00/43.13  | | 
% 232.00/43.13  | |   (22)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 232.00/43.13  | |           e1)
% 232.00/43.13  | | 
% 232.00/43.13  | | BETA: splitting (22) gives:
% 232.00/43.13  | | 
% 232.00/43.13  | | Case 1:
% 232.00/43.13  | | | 
% 232.00/43.13  | | |   (23)  all_57_14 = e1 & op(e0, e1) = e1
% 232.00/43.13  | | | 
% 232.00/43.13  | | | ALPHA: (23) implies:
% 232.00/43.13  | | |   (24)  all_57_14 = e1
% 232.00/43.13  | | | 
% 232.00/43.13  | | | REF_CLOSE: (1), (2), (3), (4), (5), (11), (12), (13), (14), (15), (17),
% 232.00/43.13  | | |            (19), (20), (24) are inconsistent by sub-proof #2175.
% 232.00/43.13  | | | 
% 232.00/43.13  | | Case 2:
% 232.00/43.13  | | | 
% 232.00/43.13  | | |   (25)  all_57_15 = e1 & op(e0, e0) = e1
% 232.00/43.13  | | | 
% 232.00/43.13  | | | REF_CLOSE: (1), (2), (7), (9), (10), (25) are inconsistent by sub-proof
% 232.00/43.13  | | |            #1916.
% 232.00/43.13  | | | 
% 232.00/43.13  | | End of split
% 232.00/43.13  | | 
% 232.00/43.13  | End of split
% 232.00/43.13  | 
% 232.00/43.13  End of proof
% 232.00/43.13  
% 232.00/43.13  Sub-proof #1916 shows that the following formulas are inconsistent:
% 232.00/43.13  ----------------------------------------------------------------
% 232.00/43.13    (1)   ~ (e3 = e1)
% 232.00/43.13    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.00/43.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.00/43.13    (3)  all_57_15 = e1 & op(e0, e0) = e1
% 232.00/43.13    (4)  op(e3, e3) = e0
% 232.00/43.13    (5)  op(e3, e3) = all_52_1
% 232.00/43.13    (6)  op(all_52_1, all_52_1) = e3
% 232.00/43.13  
% 232.00/43.13  Begin of proof
% 232.00/43.13  | 
% 232.00/43.13  | ALPHA: (3) implies:
% 232.00/43.13  |   (7)  op(e0, e0) = e1
% 232.00/43.13  | 
% 232.00/43.13  | GROUND_INST: instantiating (2) with e0, all_52_1, e3, e3, simplifying with
% 232.00/43.13  |              (4), (5) gives:
% 232.00/43.13  |   (8)  all_52_1 = e0
% 232.00/43.13  | 
% 232.00/43.13  | REDUCE: (6), (8) imply:
% 232.00/43.13  |   (9)  op(e0, e0) = e3
% 232.00/43.13  | 
% 232.00/43.13  | REF_CLOSE: (1), (2), (7), (9) are inconsistent by sub-proof #2183.
% 232.00/43.13  | 
% 232.00/43.13  End of proof
% 232.00/43.13  
% 232.00/43.13  Sub-proof #1917 shows that the following formulas are inconsistent:
% 232.00/43.13  ----------------------------------------------------------------
% 232.00/43.13    (1)   ~ (e3 = e1)
% 232.00/43.13    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.00/43.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.00/43.13    (3)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 232.00/43.13    (4)   ~ (e3 = e2)
% 232.00/43.13    (5)   ~ (e3 = e0)
% 232.00/43.13    (6)  op(e0, e3) = all_53_3
% 232.00/43.13    (7)   ~ (e2 = e0)
% 232.00/43.13    (8)   ~ (e1 = e0)
% 232.00/43.13    (9)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 232.00/43.13         (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 232.00/43.13    (10)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 232.00/43.13          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 232.00/43.13            e2)
% 232.00/43.13    (11)   ~ (all_53_3 = e0)
% 232.00/43.13    (12)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 232.00/43.13              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 232.00/43.13                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 232.00/43.13                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 232.00/43.13    (13)   ~ (all_53_3 = e1)
% 232.00/43.13    (14)  op(e0, e0) = e1
% 232.00/43.13    (15)   ~ (e2 = e1)
% 232.00/43.13  
% 232.00/43.13  Begin of proof
% 232.00/43.13  | 
% 232.00/43.13  | BETA: splitting (3) gives:
% 232.00/43.13  | 
% 232.00/43.13  | Case 1:
% 232.00/43.13  | | 
% 232.00/43.13  | |   (16)  all_57_12 = e1 & op(e0, e3) = e1
% 232.00/43.13  | | 
% 232.00/43.13  | | REF_CLOSE: (2), (6), (13), (16) are inconsistent by sub-proof #1947.
% 232.00/43.13  | | 
% 232.00/43.13  | Case 2:
% 232.00/43.13  | | 
% 232.00/43.13  | |   (17)  all_57_13 = e1 & op(e0, e2) = e1
% 232.00/43.13  | | 
% 232.00/43.13  | | ALPHA: (17) implies:
% 232.00/43.13  | |   (18)  all_57_13 = e1
% 232.00/43.13  | | 
% 232.00/43.13  | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (14),
% 232.00/43.13  | |            (15), (18) are inconsistent by sub-proof #1918.
% 232.00/43.13  | | 
% 232.00/43.13  | End of split
% 232.00/43.13  | 
% 232.00/43.13  End of proof
% 232.00/43.13  
% 232.00/43.13  Sub-proof #1918 shows that the following formulas are inconsistent:
% 232.00/43.13  ----------------------------------------------------------------
% 232.00/43.13    (1)  all_57_13 = e1
% 232.00/43.13    (2)   ~ (e3 = e1)
% 232.00/43.13    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.00/43.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.00/43.13    (4)   ~ (e3 = e2)
% 232.00/43.13    (5)   ~ (e3 = e0)
% 232.00/43.13    (6)  op(e0, e3) = all_53_3
% 232.00/43.13    (7)   ~ (e2 = e0)
% 232.00/43.13    (8)   ~ (e1 = e0)
% 232.00/43.13    (9)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 232.00/43.13         (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 232.00/43.13    (10)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 232.00/43.13          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 232.00/43.13            e2)
% 232.00/43.13    (11)   ~ (all_53_3 = e0)
% 232.00/43.13    (12)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 232.00/43.13              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 232.00/43.13                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 232.00/43.13                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 232.00/43.13    (13)  op(e0, e0) = e1
% 232.00/43.13    (14)   ~ (e2 = e1)
% 232.00/43.13  
% 232.00/43.13  Begin of proof
% 232.00/43.13  | 
% 232.00/43.13  | BETA: splitting (12) gives:
% 232.00/43.13  | 
% 232.00/43.13  | Case 1:
% 232.00/43.13  | | 
% 232.00/43.13  | |   (15)  all_57_15 = e0 & op(e0, e0) = e0
% 232.00/43.13  | | 
% 232.00/43.13  | | ALPHA: (15) implies:
% 232.00/43.13  | |   (16)  op(e0, e0) = e0
% 232.00/43.13  | | 
% 232.00/43.13  | | REF_CLOSE: (3), (8), (13), (16) are inconsistent by sub-proof #2290.
% 232.00/43.13  | | 
% 232.00/43.13  | Case 2:
% 232.00/43.13  | | 
% 232.00/43.13  | |   (17)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 232.00/43.13  | |             e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0 &
% 232.00/43.13  | |             op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 232.00/43.13  | |           (all_57_14 = e0 & op(e0, e1) = e0))
% 232.00/43.13  | | 
% 232.00/43.13  | | ALPHA: (17) implies:
% 232.00/43.13  | |   (18)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 232.00/43.13  | |           e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 232.00/43.13  | | 
% 232.00/43.13  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 232.00/43.13  | |            (14), (18) are inconsistent by sub-proof #1919.
% 232.00/43.13  | | 
% 232.00/43.13  | End of split
% 232.00/43.13  | 
% 232.00/43.13  End of proof
% 232.00/43.13  
% 232.00/43.13  Sub-proof #1919 shows that the following formulas are inconsistent:
% 232.00/43.13  ----------------------------------------------------------------
% 232.00/43.13    (1)  all_57_13 = e1
% 232.00/43.13    (2)   ~ (e3 = e1)
% 232.00/43.13    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.00/43.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.00/43.13    (4)   ~ (e3 = e2)
% 232.00/43.13    (5)   ~ (e3 = e0)
% 232.00/43.13    (6)  op(e0, e3) = all_53_3
% 232.00/43.13    (7)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 232.00/43.13         (all_57_14 = e0 & op(e0, e1) = e0)
% 232.00/43.13    (8)   ~ (e2 = e0)
% 232.00/43.13    (9)   ~ (e1 = e0)
% 232.00/43.13    (10)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 232.00/43.13          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 232.00/43.13            e3)
% 232.00/43.13    (11)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 232.00/43.13          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 232.00/43.13            e2)
% 232.00/43.13    (12)   ~ (all_53_3 = e0)
% 232.00/43.13    (13)  op(e0, e0) = e1
% 232.00/43.13    (14)   ~ (e2 = e1)
% 232.00/43.13  
% 232.00/43.13  Begin of proof
% 232.00/43.13  | 
% 232.00/43.13  | BETA: splitting (7) gives:
% 232.00/43.13  | 
% 232.00/43.13  | Case 1:
% 232.00/43.13  | | 
% 232.00/43.13  | |   (15)  all_57_12 = e0 & op(e0, e3) = e0
% 232.00/43.13  | | 
% 232.00/43.13  | | ALPHA: (15) implies:
% 232.00/43.13  | |   (16)  op(e0, e3) = e0
% 232.00/43.13  | | 
% 232.00/43.13  | | REF_CLOSE: (3), (6), (12), (16) are inconsistent by sub-proof #2366.
% 232.00/43.13  | | 
% 232.00/43.13  | Case 2:
% 232.00/43.13  | | 
% 232.00/43.13  | |   (17)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 232.00/43.13  | |           e0)
% 232.00/43.13  | | 
% 232.00/43.13  | | BETA: splitting (17) gives:
% 232.00/43.13  | | 
% 232.00/43.13  | | Case 1:
% 232.00/43.13  | | | 
% 232.00/43.13  | | |   (18)  all_57_13 = e0 & op(e0, e2) = e0
% 232.00/43.13  | | | 
% 232.00/43.13  | | | REF_CLOSE: (1), (9), (18) are inconsistent by sub-proof #1920.
% 232.00/43.13  | | | 
% 232.00/43.13  | | Case 2:
% 232.00/43.13  | | | 
% 232.00/43.13  | | |   (19)  all_57_14 = e0 & op(e0, e1) = e0
% 232.00/43.13  | | | 
% 232.00/43.13  | | | ALPHA: (19) implies:
% 232.00/43.13  | | |   (20)  all_57_14 = e0
% 232.00/43.13  | | | 
% 232.00/43.13  | | | REF_CLOSE: (1), (2), (3), (4), (5), (8), (10), (11), (13), (14), (20) are
% 232.00/43.13  | | |            inconsistent by sub-proof #2068.
% 232.00/43.13  | | | 
% 232.00/43.13  | | End of split
% 232.00/43.13  | | 
% 232.00/43.13  | End of split
% 232.00/43.13  | 
% 232.00/43.13  End of proof
% 232.00/43.13  
% 232.00/43.13  Sub-proof #1920 shows that the following formulas are inconsistent:
% 232.00/43.13  ----------------------------------------------------------------
% 232.00/43.13    (1)  all_57_13 = e0 & op(e0, e2) = e0
% 232.00/43.13    (2)  all_57_13 = e1
% 232.00/43.13    (3)   ~ (e1 = e0)
% 232.00/43.13  
% 232.00/43.13  Begin of proof
% 232.00/43.13  | 
% 232.00/43.13  | ALPHA: (1) implies:
% 232.00/43.13  |   (4)  all_57_13 = e0
% 232.00/43.13  | 
% 232.00/43.13  | COMBINE_EQS: (2), (4) imply:
% 232.00/43.13  |   (5)  e1 = e0
% 232.00/43.13  | 
% 232.00/43.13  | REDUCE: (3), (5) imply:
% 232.00/43.13  |   (6)  $false
% 232.00/43.13  | 
% 232.00/43.13  | CLOSE: (6) is inconsistent.
% 232.00/43.13  | 
% 232.00/43.13  End of proof
% 232.00/43.13  
% 232.00/43.13  Sub-proof #1921 shows that the following formulas are inconsistent:
% 232.00/43.13  ----------------------------------------------------------------
% 232.00/43.13    (1)  op(e2, e3) = all_53_1
% 232.00/43.13    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.00/43.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.00/43.13    (3)   ~ (e3 = e2)
% 232.00/43.13    (4)  op(e3, e3) = e0
% 232.00/43.13    (5)  all_57_12 = e1
% 232.00/43.13    (6)   ~ (e2 = e0)
% 232.00/43.13    (7)  all_57_6 = e3
% 232.00/43.13    (8)   ~ (all_53_1 = e2)
% 232.00/43.13    (9)   ~ (e2 = e1)
% 232.00/43.13    (10)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 232.00/43.13          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 232.00/43.13  
% 232.00/43.13  Begin of proof
% 232.00/43.13  | 
% 232.00/43.13  | BETA: splitting (10) gives:
% 232.00/43.13  | 
% 232.00/43.13  | Case 1:
% 232.00/43.13  | | 
% 232.00/43.13  | |   (11)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) =
% 232.00/43.13  | |           e2)
% 232.00/43.13  | | 
% 232.00/43.13  | | REF_CLOSE: (1), (2), (4), (6), (8), (11) are inconsistent by sub-proof
% 232.00/43.13  | |            #1929.
% 232.00/43.13  | | 
% 232.00/43.13  | Case 2:
% 232.00/43.13  | | 
% 232.00/43.13  | |   (12)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) =
% 232.00/43.13  | |           e2)
% 232.00/43.13  | | 
% 232.00/43.13  | | BETA: splitting (12) gives:
% 232.00/43.13  | | 
% 232.00/43.13  | | Case 1:
% 232.00/43.13  | | | 
% 232.00/43.13  | | |   (13)  all_57_6 = e2 & op(e1, e3) = e2
% 232.00/43.13  | | | 
% 232.00/43.13  | | | REF_CLOSE: (3), (7), (13) are inconsistent by sub-proof #2012.
% 232.00/43.13  | | | 
% 232.00/43.13  | | Case 2:
% 232.00/43.13  | | | 
% 232.00/43.13  | | |   (14)  all_57_12 = e2 & op(e0, e3) = e2
% 232.00/43.13  | | | 
% 232.00/43.13  | | | REF_CLOSE: (5), (9), (14) are inconsistent by sub-proof #1922.
% 232.00/43.13  | | | 
% 232.00/43.13  | | End of split
% 232.00/43.13  | | 
% 232.00/43.13  | End of split
% 232.00/43.13  | 
% 232.00/43.13  End of proof
% 232.00/43.13  
% 232.00/43.13  Sub-proof #1922 shows that the following formulas are inconsistent:
% 232.00/43.13  ----------------------------------------------------------------
% 232.00/43.13    (1)  all_57_12 = e2 & op(e0, e3) = e2
% 232.00/43.13    (2)  all_57_12 = e1
% 232.00/43.13    (3)   ~ (e2 = e1)
% 232.00/43.13  
% 232.00/43.13  Begin of proof
% 232.00/43.13  | 
% 232.00/43.13  | ALPHA: (1) implies:
% 232.00/43.13  |   (4)  all_57_12 = e2
% 232.00/43.13  | 
% 232.00/43.13  | COMBINE_EQS: (2), (4) imply:
% 232.00/43.13  |   (5)  e2 = e1
% 232.00/43.13  | 
% 232.00/43.13  | REDUCE: (3), (5) imply:
% 232.00/43.13  |   (6)  $false
% 232.00/43.13  | 
% 232.00/43.13  | CLOSE: (6) is inconsistent.
% 232.00/43.13  | 
% 232.00/43.13  End of proof
% 232.00/43.13  
% 232.00/43.13  Sub-proof #1923 shows that the following formulas are inconsistent:
% 232.00/43.13  ----------------------------------------------------------------
% 232.00/43.13    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.00/43.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.00/43.13    (2)  all_57_6 = e1
% 232.00/43.13    (3)   ~ (e3 = e2)
% 232.00/43.13    (4)  op(e3, e3) = e0
% 232.00/43.13    (5)  all_57_12 = e1
% 232.00/43.13    (6)   ~ (e2 = e0)
% 232.00/43.13    (7)  all_57_2 = e3
% 232.00/43.13    (8)   ~ (e2 = e1)
% 232.00/43.13    (9)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 232.00/43.13         (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 232.00/43.13  
% 232.00/43.13  Begin of proof
% 232.00/43.13  | 
% 232.00/43.13  | BETA: splitting (9) gives:
% 232.00/43.13  | 
% 232.00/43.13  | Case 1:
% 232.00/43.13  | | 
% 232.00/43.13  | |   (10)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) =
% 232.00/43.13  | |           e2)
% 232.00/43.13  | | 
% 232.00/43.13  | | REF_CLOSE: (1), (3), (4), (6), (7), (10) are inconsistent by sub-proof
% 232.00/43.13  | |            #1924.
% 232.00/43.13  | | 
% 232.00/43.13  | Case 2:
% 232.00/43.13  | | 
% 232.00/43.13  | |   (11)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) =
% 232.00/43.13  | |           e2)
% 232.00/43.13  | | 
% 232.00/43.13  | | BETA: splitting (11) gives:
% 232.00/43.13  | | 
% 232.00/43.13  | | Case 1:
% 232.00/43.13  | | | 
% 232.00/43.13  | | |   (12)  all_57_6 = e2 & op(e1, e3) = e2
% 232.00/43.13  | | | 
% 232.00/43.13  | | | ALPHA: (12) implies:
% 232.00/43.13  | | |   (13)  all_57_6 = e2
% 232.00/43.13  | | | 
% 232.00/43.13  | | | REF_CLOSE: (2), (8), (13) are inconsistent by sub-proof #2233.
% 232.00/43.13  | | | 
% 232.00/43.13  | | Case 2:
% 232.00/43.13  | | | 
% 232.00/43.13  | | |   (14)  all_57_12 = e2 & op(e0, e3) = e2
% 232.00/43.13  | | | 
% 232.00/43.13  | | | ALPHA: (14) implies:
% 232.00/43.13  | | |   (15)  all_57_12 = e2
% 232.00/43.13  | | | 
% 232.00/43.13  | | | REF_CLOSE: (5), (8), (15) are inconsistent by sub-proof #2321.
% 232.00/43.13  | | | 
% 232.00/43.13  | | End of split
% 232.00/43.13  | | 
% 232.00/43.13  | End of split
% 232.00/43.13  | 
% 232.00/43.13  End of proof
% 232.00/43.13  
% 232.00/43.13  Sub-proof #1924 shows that the following formulas are inconsistent:
% 232.00/43.13  ----------------------------------------------------------------
% 232.00/43.13    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.00/43.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.00/43.13    (2)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2)
% 232.00/43.13    (3)   ~ (e3 = e2)
% 232.00/43.13    (4)  op(e3, e3) = e0
% 232.00/43.13    (5)   ~ (e2 = e0)
% 232.00/43.13    (6)  all_57_2 = e3
% 232.00/43.13  
% 232.00/43.13  Begin of proof
% 232.00/43.13  | 
% 232.00/43.13  | BETA: splitting (2) gives:
% 232.00/43.13  | 
% 232.00/43.13  | Case 1:
% 232.00/43.13  | | 
% 232.00/43.13  | |   (7)  all_57_0 = e2 & op(e3, e3) = e2
% 232.00/43.13  | | 
% 232.00/43.13  | | ALPHA: (7) implies:
% 232.00/43.13  | |   (8)  op(e3, e3) = e2
% 232.00/43.13  | | 
% 232.00/43.13  | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #2403.
% 232.00/43.13  | | 
% 232.00/43.13  | Case 2:
% 232.00/43.13  | | 
% 232.00/43.13  | |   (9)  all_57_2 = e2 & op(e2, e3) = e2
% 232.00/43.13  | | 
% 232.00/43.13  | | REF_CLOSE: (3), (6), (9) are inconsistent by sub-proof #1925.
% 232.00/43.13  | | 
% 232.00/43.13  | End of split
% 232.00/43.13  | 
% 232.00/43.13  End of proof
% 232.00/43.13  
% 232.00/43.13  Sub-proof #1925 shows that the following formulas are inconsistent:
% 232.00/43.13  ----------------------------------------------------------------
% 232.00/43.13    (1)  all_57_2 = e2 & op(e2, e3) = e2
% 232.00/43.13    (2)  all_57_2 = e3
% 232.00/43.13    (3)   ~ (e3 = e2)
% 232.00/43.13  
% 232.00/43.13  Begin of proof
% 232.00/43.13  | 
% 232.00/43.13  | ALPHA: (1) implies:
% 232.00/43.13  |   (4)  all_57_2 = e2
% 232.00/43.13  | 
% 232.00/43.13  | COMBINE_EQS: (2), (4) imply:
% 232.00/43.13  |   (5)  e3 = e2
% 232.00/43.13  | 
% 232.00/43.13  | REDUCE: (3), (5) imply:
% 232.00/43.13  |   (6)  $false
% 232.00/43.13  | 
% 232.00/43.13  | CLOSE: (6) is inconsistent.
% 232.00/43.13  | 
% 232.00/43.13  End of proof
% 232.00/43.13  
% 232.00/43.13  Sub-proof #1926 shows that the following formulas are inconsistent:
% 232.00/43.13  ----------------------------------------------------------------
% 232.00/43.13    (1)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 232.00/43.13         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 232.00/43.13    (2)   ~ (e3 = e1)
% 232.00/43.13    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.00/43.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.00/43.13    (4)  all_57_12 = e2
% 232.00/43.13    (5)   ~ (e3 = e2)
% 232.00/43.13    (6)   ~ (e3 = e0)
% 232.00/43.13    (7)  all_57_0 = e0
% 232.00/43.13    (8)  all_57_6 = e2
% 232.00/43.13    (9)   ~ (e2 = e0)
% 232.00/43.13    (10)   ~ (e1 = e0)
% 232.00/43.13    (11)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 232.00/43.13          (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 232.00/43.13    (12)   ~ (e2 = e1)
% 232.00/43.13    (13)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 232.00/43.13          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 232.00/43.13  
% 232.00/43.13  Begin of proof
% 232.00/43.13  | 
% 232.00/43.13  | BETA: splitting (11) gives:
% 232.00/43.13  | 
% 232.00/43.13  | Case 1:
% 232.00/43.13  | | 
% 232.00/43.13  | |   (14)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) =
% 232.00/43.13  | |           e3)
% 232.00/43.13  | | 
% 232.00/43.13  | | BETA: splitting (14) gives:
% 232.00/43.13  | | 
% 232.00/43.13  | | Case 1:
% 232.00/43.13  | | | 
% 232.00/43.13  | | |   (15)  all_57_0 = e3 & op(e3, e3) = e3
% 232.00/43.13  | | | 
% 232.00/43.13  | | | ALPHA: (15) implies:
% 232.00/43.13  | | |   (16)  op(e3, e3) = e3
% 232.00/43.13  | | | 
% 232.00/43.13  | | | REF_CLOSE: (1), (2), (3), (4), (6), (8), (9), (10), (12), (13), (16) are
% 232.00/43.13  | | |            inconsistent by sub-proof #2384.
% 232.00/43.13  | | | 
% 232.00/43.13  | | Case 2:
% 232.00/43.13  | | | 
% 232.00/43.13  | | |   (17)  all_57_2 = e3 & op(e2, e3) = e3
% 232.00/43.13  | | | 
% 232.00/43.13  | | | ALPHA: (17) implies:
% 232.00/43.13  | | |   (18)  all_57_2 = e3
% 232.00/43.13  | | | 
% 232.00/43.13  | | | REF_CLOSE: (1), (2), (4), (7), (8), (10), (12), (18) are inconsistent by
% 232.00/43.13  | | |            sub-proof #1927.
% 232.00/43.13  | | | 
% 232.00/43.13  | | End of split
% 232.00/43.13  | | 
% 232.00/43.13  | Case 2:
% 232.00/43.13  | | 
% 232.00/43.13  | |   (19)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) =
% 232.00/43.13  | |           e3)
% 232.00/43.13  | | 
% 232.00/43.13  | | BETA: splitting (19) gives:
% 232.00/43.13  | | 
% 232.00/43.13  | | Case 1:
% 232.00/43.13  | | | 
% 232.00/43.13  | | |   (20)  all_57_6 = e3 & op(e1, e3) = e3
% 232.00/43.13  | | | 
% 232.00/43.13  | | | ALPHA: (20) implies:
% 232.00/43.13  | | |   (21)  all_57_6 = e3
% 232.00/43.13  | | | 
% 232.00/43.13  | | | REF_CLOSE: (5), (8), (21) are inconsistent by sub-proof #2463.
% 232.00/43.13  | | | 
% 232.00/43.13  | | Case 2:
% 232.00/43.13  | | | 
% 232.00/43.13  | | |   (22)  all_57_12 = e3 & op(e0, e3) = e3
% 232.00/43.13  | | | 
% 232.00/43.13  | | | ALPHA: (22) implies:
% 232.00/43.13  | | |   (23)  all_57_12 = e3
% 232.00/43.13  | | | 
% 232.00/43.13  | | | REF_CLOSE: (4), (5), (23) are inconsistent by sub-proof #2392.
% 232.00/43.13  | | | 
% 232.00/43.13  | | End of split
% 232.00/43.13  | | 
% 232.00/43.13  | End of split
% 232.00/43.13  | 
% 232.00/43.13  End of proof
% 232.00/43.13  
% 232.00/43.13  Sub-proof #1927 shows that the following formulas are inconsistent:
% 232.00/43.13  ----------------------------------------------------------------
% 232.00/43.13    (1)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 232.00/43.13         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 232.00/43.13    (2)   ~ (e3 = e1)
% 232.00/43.13    (3)  all_57_12 = e2
% 232.00/43.13    (4)  all_57_0 = e0
% 232.00/43.13    (5)  all_57_6 = e2
% 232.00/43.13    (6)  all_57_2 = e3
% 232.00/43.13    (7)   ~ (e1 = e0)
% 232.00/43.13    (8)   ~ (e2 = e1)
% 232.00/43.13  
% 232.00/43.13  Begin of proof
% 232.00/43.13  | 
% 232.00/43.13  | BETA: splitting (1) gives:
% 232.00/43.13  | 
% 232.00/43.13  | Case 1:
% 232.00/43.13  | | 
% 232.00/43.13  | |   (9)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1)
% 232.00/43.13  | | 
% 232.00/43.13  | | BETA: splitting (9) gives:
% 232.00/43.13  | | 
% 232.00/43.13  | | Case 1:
% 232.00/43.13  | | | 
% 232.00/43.13  | | |   (10)  all_57_0 = e1 & op(e3, e3) = e1
% 232.00/43.13  | | | 
% 232.00/43.13  | | | REF_CLOSE: (4), (7), (10) are inconsistent by sub-proof #2454.
% 232.00/43.13  | | | 
% 232.00/43.13  | | Case 2:
% 232.00/43.13  | | | 
% 232.00/43.13  | | |   (11)  all_57_2 = e1 & op(e2, e3) = e1
% 232.00/43.13  | | | 
% 232.00/43.13  | | | REF_CLOSE: (2), (6), (11) are inconsistent by sub-proof #1928.
% 232.00/43.13  | | | 
% 232.00/43.13  | | End of split
% 232.00/43.13  | | 
% 232.00/43.13  | Case 2:
% 232.00/43.13  | | 
% 232.00/43.13  | |   (12)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) =
% 232.00/43.13  | |           e1)
% 232.00/43.13  | | 
% 232.00/43.13  | | BETA: splitting (12) gives:
% 232.00/43.13  | | 
% 232.00/43.13  | | Case 1:
% 232.00/43.13  | | | 
% 232.00/43.14  | | |   (13)  all_57_6 = e1 & op(e1, e3) = e1
% 232.00/43.14  | | | 
% 232.00/43.14  | | | REF_CLOSE: (5), (8), (13) are inconsistent by sub-proof #2389.
% 232.00/43.14  | | | 
% 232.00/43.14  | | Case 2:
% 232.00/43.14  | | | 
% 232.00/43.14  | | |   (14)  all_57_12 = e1 & op(e0, e3) = e1
% 232.00/43.14  | | | 
% 232.00/43.14  | | | REF_CLOSE: (3), (8), (14) are inconsistent by sub-proof #2388.
% 232.00/43.14  | | | 
% 232.00/43.14  | | End of split
% 232.00/43.14  | | 
% 232.00/43.14  | End of split
% 232.00/43.14  | 
% 232.00/43.14  End of proof
% 232.00/43.14  
% 232.00/43.14  Sub-proof #1928 shows that the following formulas are inconsistent:
% 232.00/43.14  ----------------------------------------------------------------
% 232.00/43.14    (1)  all_57_2 = e1 & op(e2, e3) = e1
% 232.00/43.14    (2)  all_57_2 = e3
% 232.00/43.14    (3)   ~ (e3 = e1)
% 232.00/43.14  
% 232.00/43.14  Begin of proof
% 232.00/43.14  | 
% 232.00/43.14  | ALPHA: (1) implies:
% 232.00/43.14  |   (4)  all_57_2 = e1
% 232.00/43.14  | 
% 232.00/43.14  | COMBINE_EQS: (2), (4) imply:
% 232.00/43.14  |   (5)  e3 = e1
% 232.00/43.14  | 
% 232.00/43.14  | REDUCE: (3), (5) imply:
% 232.00/43.14  |   (6)  $false
% 232.00/43.14  | 
% 232.00/43.14  | CLOSE: (6) is inconsistent.
% 232.00/43.14  | 
% 232.00/43.14  End of proof
% 232.00/43.14  
% 232.00/43.14  Sub-proof #1929 shows that the following formulas are inconsistent:
% 232.00/43.14  ----------------------------------------------------------------
% 232.00/43.14    (1)  op(e2, e3) = all_53_1
% 232.00/43.14    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.00/43.14           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.00/43.14    (3)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2)
% 232.00/43.14    (4)  op(e3, e3) = e0
% 232.00/43.14    (5)   ~ (e2 = e0)
% 232.00/43.14    (6)   ~ (all_53_1 = e2)
% 232.00/43.14  
% 232.00/43.14  Begin of proof
% 232.00/43.14  | 
% 232.00/43.14  | BETA: splitting (3) gives:
% 232.00/43.14  | 
% 232.00/43.14  | Case 1:
% 232.00/43.14  | | 
% 232.00/43.14  | |   (7)  all_57_0 = e2 & op(e3, e3) = e2
% 232.00/43.14  | | 
% 232.00/43.14  | | ALPHA: (7) implies:
% 232.00/43.14  | |   (8)  op(e3, e3) = e2
% 232.00/43.14  | | 
% 232.00/43.14  | | REF_CLOSE: (2), (4), (5), (8) are inconsistent by sub-proof #2403.
% 232.00/43.14  | | 
% 232.00/43.14  | Case 2:
% 232.00/43.14  | | 
% 232.00/43.14  | |   (9)  all_57_2 = e2 & op(e2, e3) = e2
% 232.00/43.14  | | 
% 232.00/43.14  | | REF_CLOSE: (1), (2), (6), (9) are inconsistent by sub-proof #2504.
% 232.00/43.14  | | 
% 232.00/43.14  | End of split
% 232.00/43.14  | 
% 232.00/43.14  End of proof
% 232.00/43.14  
% 232.00/43.14  Sub-proof #1930 shows that the following formulas are inconsistent:
% 232.00/43.14  ----------------------------------------------------------------
% 232.00/43.14    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.00/43.14           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.00/43.14    (2)   ~ (all_6_2 = e3)
% 232.00/43.14    (3)  op(e1, e1) = all_6_2
% 232.00/43.14    (4)   ~ (e3 = e2)
% 232.00/43.14    (5)   ~ (e3 = e0)
% 232.00/43.14    (6)  op(e3, e3) = e0
% 232.00/43.14    (7)   ~ (e1 = e0)
% 232.00/43.14    (8)  op(e0, e1) = all_52_29
% 232.00/43.14    (9)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 232.00/43.14         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 232.00/43.14    (10)  all_57_4 = e2 & op(e3, e1) = e2
% 232.00/43.14    (11)  op(all_52_29, all_52_29) = e1
% 232.00/43.14    (12)  all_57_5 = e0
% 232.00/43.14  
% 232.00/43.14  Begin of proof
% 232.00/43.14  | 
% 232.00/43.14  | ALPHA: (10) implies:
% 232.00/43.14  |   (13)  all_57_4 = e2
% 232.00/43.14  | 
% 232.00/43.14  | BETA: splitting (9) gives:
% 232.00/43.14  | 
% 232.00/43.14  | Case 1:
% 232.00/43.14  | | 
% 232.00/43.14  | |   (14)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) =
% 232.00/43.14  | |           e3)
% 232.00/43.14  | | 
% 232.00/43.14  | | BETA: splitting (14) gives:
% 232.00/43.14  | | 
% 232.00/43.14  | | Case 1:
% 232.00/43.14  | | | 
% 232.00/43.14  | | |   (15)  all_57_4 = e3 & op(e3, e1) = e3
% 232.00/43.14  | | | 
% 232.00/43.14  | | | ALPHA: (15) implies:
% 232.00/43.14  | | |   (16)  all_57_4 = e3
% 232.00/43.14  | | | 
% 232.00/43.14  | | | REF_CLOSE: (4), (13), (16) are inconsistent by sub-proof #2482.
% 232.00/43.14  | | | 
% 232.00/43.14  | | Case 2:
% 232.00/43.14  | | | 
% 232.00/43.14  | | |   (17)  all_57_5 = e3 & op(e2, e1) = e3
% 232.00/43.14  | | | 
% 232.00/43.14  | | | ALPHA: (17) implies:
% 232.00/43.14  | | |   (18)  all_57_5 = e3
% 232.00/43.14  | | | 
% 232.00/43.14  | | | REF_CLOSE: (5), (12), (18) are inconsistent by sub-proof #2471.
% 232.00/43.14  | | | 
% 232.00/43.14  | | End of split
% 232.00/43.14  | | 
% 232.00/43.14  | Case 2:
% 232.00/43.14  | | 
% 232.00/43.14  | |   (19)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) =
% 232.00/43.14  | |           e3)
% 232.00/43.14  | | 
% 232.00/43.14  | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (11), (19) are inconsistent by
% 232.00/43.14  | |            sub-proof #1933.
% 232.00/43.14  | | 
% 232.00/43.14  | End of split
% 232.00/43.14  | 
% 232.00/43.14  End of proof
% 232.00/43.14  
% 232.00/43.14  Sub-proof #1931 shows that the following formulas are inconsistent:
% 232.00/43.14  ----------------------------------------------------------------
% 232.00/43.14    (1)   ~ (e3 = e1)
% 232.00/43.14    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.00/43.14           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.00/43.14    (3)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 232.00/43.14         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 232.00/43.14    (4)   ~ (all_6_2 = e3)
% 232.00/43.14    (5)  op(e1, e1) = all_6_2
% 232.00/43.14    (6)   ~ (e3 = e2)
% 232.00/43.14    (7)   ~ (e3 = e0)
% 232.00/43.14    (8)  op(e1, e1) = e1
% 232.00/43.14    (9)   ~ (e2 = e0)
% 232.00/43.14    (10)  all_57_11 = e1
% 232.00/43.14    (11)   ~ (e2 = e1)
% 232.00/43.14    (12)  all_57_7 = e0
% 232.00/43.14    (13)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 232.00/43.14          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 232.00/43.14  
% 232.00/43.14  Begin of proof
% 232.00/43.14  | 
% 232.00/43.14  | BETA: splitting (3) gives:
% 232.00/43.14  | 
% 232.00/43.14  | Case 1:
% 232.00/43.14  | | 
% 232.00/43.14  | |   (14)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 232.00/43.14  | |           e3)
% 232.00/43.14  | | 
% 232.00/43.14  | | BETA: splitting (14) gives:
% 232.00/43.14  | | 
% 232.00/43.14  | | Case 1:
% 232.00/43.14  | | | 
% 232.00/43.14  | | |   (15)  all_57_6 = e3 & op(e1, e3) = e3
% 232.00/43.14  | | | 
% 232.00/43.14  | | | ALPHA: (15) implies:
% 232.00/43.14  | | |   (16)  all_57_6 = e3
% 232.00/43.14  | | | 
% 232.00/43.14  | | | BETA: splitting (13) gives:
% 232.00/43.14  | | | 
% 232.00/43.14  | | | Case 1:
% 232.00/43.14  | | | | 
% 232.00/43.14  | | | |   (17)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2)
% 232.00/43.14  | | | |           = e2)
% 232.00/43.14  | | | | 
% 232.00/43.14  | | | | BETA: splitting (17) gives:
% 232.00/43.14  | | | | 
% 232.00/43.14  | | | | Case 1:
% 232.00/43.14  | | | | | 
% 232.00/43.14  | | | | |   (18)  all_57_6 = e2 & op(e1, e3) = e2
% 232.00/43.14  | | | | | 
% 232.00/43.14  | | | | | REF_CLOSE: (6), (16), (18) are inconsistent by sub-proof #2012.
% 232.00/43.14  | | | | | 
% 232.00/43.14  | | | | Case 2:
% 232.00/43.14  | | | | | 
% 232.00/43.14  | | | | |   (19)  all_57_7 = e2 & op(e1, e2) = e2
% 232.00/43.14  | | | | | 
% 232.00/43.14  | | | | | ALPHA: (19) implies:
% 232.00/43.14  | | | | |   (20)  all_57_7 = e2
% 232.00/43.14  | | | | | 
% 232.00/43.14  | | | | | REF_CLOSE: (9), (12), (20) are inconsistent by sub-proof #2207.
% 232.00/43.14  | | | | | 
% 232.00/43.14  | | | | End of split
% 232.00/43.14  | | | | 
% 232.00/43.14  | | | Case 2:
% 232.00/43.14  | | | | 
% 232.00/43.14  | | | |   (21)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0)
% 232.00/43.14  | | | |           = e2)
% 232.00/43.14  | | | | 
% 232.00/43.14  | | | | REF_CLOSE: (2), (8), (10), (11), (21) are inconsistent by sub-proof
% 232.00/43.14  | | | |            #1932.
% 232.00/43.14  | | | | 
% 232.00/43.14  | | | End of split
% 232.00/43.14  | | | 
% 232.00/43.14  | | Case 2:
% 232.00/43.14  | | | 
% 232.00/43.14  | | |   (22)  all_57_7 = e3 & op(e1, e2) = e3
% 232.00/43.14  | | | 
% 232.00/43.14  | | | ALPHA: (22) implies:
% 232.00/43.14  | | |   (23)  all_57_7 = e3
% 232.00/43.14  | | | 
% 232.00/43.14  | | | REF_CLOSE: (7), (12), (23) are inconsistent by sub-proof #2269.
% 232.00/43.14  | | | 
% 232.00/43.14  | | End of split
% 232.00/43.14  | | 
% 232.00/43.14  | Case 2:
% 232.00/43.14  | | 
% 232.00/43.14  | |   (24)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 232.00/43.14  | |           e3)
% 232.00/43.14  | | 
% 232.00/43.14  | | REF_CLOSE: (1), (2), (4), (5), (10), (24) are inconsistent by sub-proof
% 232.00/43.14  | |            #2004.
% 232.00/43.14  | | 
% 232.00/43.14  | End of split
% 232.00/43.14  | 
% 232.00/43.14  End of proof
% 232.00/43.14  
% 232.00/43.14  Sub-proof #1932 shows that the following formulas are inconsistent:
% 232.00/43.14  ----------------------------------------------------------------
% 232.00/43.14    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.00/43.14           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.00/43.14    (2)  op(e1, e1) = e1
% 232.00/43.14    (3)  all_57_11 = e1
% 232.00/43.14    (4)   ~ (e2 = e1)
% 232.00/43.14    (5)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 232.00/43.14  
% 232.00/43.14  Begin of proof
% 232.00/43.14  | 
% 232.00/43.14  | BETA: splitting (5) gives:
% 232.00/43.14  | 
% 232.00/43.14  | Case 1:
% 232.00/43.14  | | 
% 232.00/43.14  | |   (6)  all_57_8 = e2 & op(e1, e1) = e2
% 232.00/43.14  | | 
% 232.00/43.14  | | ALPHA: (6) implies:
% 232.00/43.14  | |   (7)  op(e1, e1) = e2
% 232.00/43.14  | | 
% 232.00/43.14  | | REF_CLOSE: (1), (2), (4), (7) are inconsistent by sub-proof #2423.
% 232.00/43.14  | | 
% 232.00/43.14  | Case 2:
% 232.00/43.14  | | 
% 232.00/43.14  | |   (8)  all_57_11 = e2 & op(e1, e0) = e2
% 232.00/43.14  | | 
% 232.00/43.14  | | REF_CLOSE: (3), (4), (8) are inconsistent by sub-proof #2048.
% 232.00/43.14  | | 
% 232.00/43.14  | End of split
% 232.00/43.14  | 
% 232.00/43.14  End of proof
% 232.00/43.14  
% 232.00/43.14  Sub-proof #1933 shows that the following formulas are inconsistent:
% 232.00/43.14  ----------------------------------------------------------------
% 232.00/43.14    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.00/43.14           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.00/43.14    (2)   ~ (all_6_2 = e3)
% 232.00/43.14    (3)  op(e1, e1) = all_6_2
% 232.00/43.14    (4)  op(e3, e3) = e0
% 232.00/43.14    (5)   ~ (e1 = e0)
% 232.00/43.14    (6)  op(e0, e1) = all_52_29
% 232.00/43.14    (7)  op(all_52_29, all_52_29) = e1
% 232.00/43.14    (8)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 232.00/43.14  
% 232.00/43.14  Begin of proof
% 232.00/43.14  | 
% 232.00/43.14  | BETA: splitting (8) gives:
% 232.00/43.14  | 
% 232.00/43.14  | Case 1:
% 232.00/43.14  | | 
% 232.00/43.14  | |   (9)  all_57_8 = e3 & op(e1, e1) = e3
% 232.00/43.14  | | 
% 232.00/43.14  | | ALPHA: (9) implies:
% 232.00/43.14  | |   (10)  op(e1, e1) = e3
% 232.00/43.14  | | 
% 232.00/43.14  | | REF_CLOSE: (1), (2), (3), (10) are inconsistent by sub-proof #2468.
% 232.00/43.14  | | 
% 232.00/43.14  | Case 2:
% 232.00/43.14  | | 
% 232.00/43.14  | |   (11)  all_57_14 = e3 & op(e0, e1) = e3
% 232.00/43.14  | | 
% 232.00/43.14  | | ALPHA: (11) implies:
% 232.00/43.14  | |   (12)  op(e0, e1) = e3
% 232.00/43.14  | | 
% 232.00/43.14  | | REF_CLOSE: (1), (4), (5), (6), (7), (12) are inconsistent by sub-proof
% 232.00/43.14  | |            #1934.
% 232.00/43.14  | | 
% 232.00/43.14  | End of split
% 232.00/43.14  | 
% 232.00/43.14  End of proof
% 232.00/43.14  
% 232.00/43.14  Sub-proof #1934 shows that the following formulas are inconsistent:
% 232.00/43.14  ----------------------------------------------------------------
% 232.00/43.14    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.00/43.14           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.00/43.14    (2)  op(e0, e1) = e3
% 232.00/43.14    (3)  op(e3, e3) = e0
% 232.00/43.14    (4)   ~ (e1 = e0)
% 232.00/43.14    (5)  op(e0, e1) = all_52_29
% 232.00/43.14    (6)  op(all_52_29, all_52_29) = e1
% 232.00/43.14  
% 232.00/43.14  Begin of proof
% 232.00/43.14  | 
% 232.00/43.14  | GROUND_INST: instantiating (1) with all_52_29, e3, e1, e0, simplifying with
% 232.00/43.14  |              (2), (5) gives:
% 232.00/43.14  |   (7)  all_52_29 = e3
% 232.00/43.14  | 
% 232.00/43.14  | REDUCE: (6), (7) imply:
% 232.00/43.14  |   (8)  op(e3, e3) = e1
% 232.00/43.14  | 
% 232.00/43.14  | GROUND_INST: instantiating (1) with e0, e1, e3, e3, simplifying with (3), (8)
% 232.00/43.14  |              gives:
% 232.00/43.14  |   (9)  e1 = e0
% 232.00/43.14  | 
% 232.00/43.14  | REDUCE: (4), (9) imply:
% 232.00/43.14  |   (10)  $false
% 232.00/43.14  | 
% 232.00/43.14  | CLOSE: (10) is inconsistent.
% 232.00/43.14  | 
% 232.00/43.14  End of proof
% 232.00/43.14  
% 232.00/43.14  Sub-proof #1935 shows that the following formulas are inconsistent:
% 232.00/43.14  ----------------------------------------------------------------
% 232.00/43.14    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.00/43.14           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.00/43.14    (2)  op(e3, e3) = e0
% 232.00/43.14    (3)  op(e3, e2) = all_53_4
% 232.00/43.14    (4)   ~ (e2 = e0)
% 232.00/43.14    (5)   ~ (all_53_4 = e2)
% 232.00/43.14    (6)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2)
% 232.00/43.14  
% 232.00/43.14  Begin of proof
% 232.00/43.14  | 
% 232.00/43.14  | BETA: splitting (6) gives:
% 232.00/43.14  | 
% 232.00/43.14  | Case 1:
% 232.00/43.14  | | 
% 232.00/43.14  | |   (7)  all_57_0 = e2 & op(e3, e3) = e2
% 232.00/43.14  | | 
% 232.00/43.14  | | ALPHA: (7) implies:
% 232.00/43.14  | |   (8)  op(e3, e3) = e2
% 232.00/43.14  | | 
% 232.00/43.14  | | REF_CLOSE: (1), (2), (4), (8) are inconsistent by sub-proof #2403.
% 232.00/43.14  | | 
% 232.00/43.14  | Case 2:
% 232.00/43.14  | | 
% 232.00/43.14  | |   (9)  all_57_1 = e2 & op(e3, e2) = e2
% 232.00/43.14  | | 
% 232.00/43.14  | | REF_CLOSE: (1), (3), (5), (9) are inconsistent by sub-proof #2456.
% 232.00/43.14  | | 
% 232.00/43.14  | End of split
% 232.00/43.14  | 
% 232.00/43.14  End of proof
% 232.00/43.14  
% 232.00/43.14  Sub-proof #1936 shows that the following formulas are inconsistent:
% 232.00/43.14  ----------------------------------------------------------------
% 232.00/43.14    (1)  all_57_5 = e3 & op(e2, e1) = e3
% 232.00/43.14    (2)  all_57_5 = e0
% 232.00/43.14    (3)   ~ (e3 = e0)
% 232.00/43.14  
% 232.00/43.14  Begin of proof
% 232.00/43.14  | 
% 232.00/43.14  | ALPHA: (1) implies:
% 232.00/43.14  |   (4)  all_57_5 = e3
% 232.00/43.14  | 
% 232.00/43.14  | COMBINE_EQS: (2), (4) imply:
% 232.00/43.14  |   (5)  e3 = e0
% 232.00/43.14  | 
% 232.00/43.14  | REDUCE: (3), (5) imply:
% 232.00/43.14  |   (6)  $false
% 232.00/43.14  | 
% 232.00/43.14  | CLOSE: (6) is inconsistent.
% 232.00/43.14  | 
% 232.00/43.14  End of proof
% 232.00/43.14  
% 232.00/43.14  Sub-proof #1937 shows that the following formulas are inconsistent:
% 232.00/43.14  ----------------------------------------------------------------
% 232.00/43.14    (1)   ~ (all_53_8 = e1)
% 232.00/43.14    (2)  all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 232.00/43.14    (3)  all_55_2 = all_53_8
% 232.00/43.14    (4)   ~ (all_53_8 = e2)
% 232.00/43.14    (5)   ~ (all_53_8 = e0)
% 232.00/43.14  
% 232.00/43.14  Begin of proof
% 232.00/43.14  | 
% 232.00/43.14  | BETA: splitting (2) gives:
% 232.00/43.14  | 
% 232.00/43.14  | Case 1:
% 232.00/43.14  | | 
% 232.00/43.14  | |   (6)  all_55_2 = e2
% 232.00/43.14  | | 
% 232.00/43.14  | | REF_CLOSE: (3), (4), (6) are inconsistent by sub-proof #2027.
% 232.00/43.14  | | 
% 232.00/43.14  | Case 2:
% 232.00/43.14  | | 
% 232.00/43.14  | |   (7)  all_55_2 = e1 | all_55_2 = e0
% 232.00/43.14  | | 
% 232.00/43.14  | | REF_CLOSE: (1), (3), (5), (7) are inconsistent by sub-proof #2030.
% 232.00/43.14  | | 
% 232.00/43.14  | End of split
% 232.00/43.14  | 
% 232.00/43.14  End of proof
% 232.00/43.14  
% 232.00/43.14  Sub-proof #1938 shows that the following formulas are inconsistent:
% 232.00/43.14  ----------------------------------------------------------------
% 232.00/43.14    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.00/43.14           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.00/43.14    (2)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 232.00/43.14           op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 232.00/43.14           op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 232.00/43.14           = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3, e0)
% 232.00/43.14           = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) & $i(all_52_7))
% 232.00/43.14         | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0 &
% 232.00/43.14           op(all_52_9, all_52_9) = e3 & op(all_52_11, all_52_11) = e2 &
% 232.00/43.14           op(all_52_13, all_52_13) = e1 & op(all_52_15, all_52_15) = e0 & op(e2,
% 232.00/43.14             e3) = all_52_9 & op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13 &
% 232.00/43.14           op(e2, e0) = all_52_15 & $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 232.00/43.14           $i(all_52_15))
% 232.00/43.14    (3)   ~ (e3 = e0)
% 232.00/43.14    (4)  op(e3, e3) = e0
% 232.00/43.14    (5)   ~ (e1 = e0)
% 232.00/43.14    (6)  op(e0, e0) = e0
% 232.00/43.14    (7)  op(e2, e1) = e0
% 232.00/43.14  
% 232.00/43.14  Begin of proof
% 232.00/43.14  | 
% 232.00/43.14  | BETA: splitting (2) gives:
% 232.00/43.14  | 
% 232.00/43.14  | Case 1:
% 232.00/43.14  | | 
% 232.00/43.14  | |   (8)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 232.00/43.14  | |        op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 232.00/43.14  | |        op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3,
% 232.00/43.14  | |          e3) = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 &
% 232.00/43.14  | |        op(e3, e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 232.00/43.14  | |        $i(all_52_7)
% 232.00/43.14  | | 
% 232.00/43.14  | | REF_CLOSE: (1), (3), (4), (6), (8) are inconsistent by sub-proof #1939.
% 232.00/43.14  | | 
% 232.00/43.14  | Case 2:
% 232.00/43.14  | | 
% 232.00/43.14  | |   (9)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0 &
% 232.00/43.14  | |        op(all_52_9, all_52_9) = e3 & op(all_52_11, all_52_11) = e2 &
% 232.00/43.14  | |        op(all_52_13, all_52_13) = e1 & op(all_52_15, all_52_15) = e0 &
% 232.00/43.14  | |        op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 & op(e2, e1) =
% 232.00/43.14  | |        all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) & $i(all_52_11) &
% 232.00/43.14  | |        $i(all_52_13) & $i(all_52_15)
% 232.00/43.14  | | 
% 232.00/43.14  | | ALPHA: (9) implies:
% 232.00/43.14  | |   (10)  op(e2, e1) = all_52_13
% 232.00/43.14  | |   (11)  op(all_52_13, all_52_13) = e1
% 232.00/43.14  | | 
% 232.00/43.14  | | GROUND_INST: instantiating (1) with e0, all_52_13, e1, e2, simplifying with
% 232.00/43.14  | |              (7), (10) gives:
% 232.00/43.14  | |   (12)  all_52_13 = e0
% 232.00/43.14  | | 
% 232.00/43.14  | | REDUCE: (11), (12) imply:
% 232.00/43.14  | |   (13)  op(e0, e0) = e1
% 232.00/43.14  | | 
% 232.00/43.14  | | REF_CLOSE: (1), (5), (6), (13) are inconsistent by sub-proof #2290.
% 232.00/43.14  | | 
% 232.00/43.14  | End of split
% 232.00/43.14  | 
% 232.00/43.14  End of proof
% 232.00/43.14  
% 232.00/43.14  Sub-proof #1939 shows that the following formulas are inconsistent:
% 232.00/43.14  ----------------------------------------------------------------
% 232.00/43.14    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.00/43.14           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.00/43.14    (2)   ~ (e3 = e0)
% 232.00/43.14    (3)  op(e3, e3) = e0
% 232.00/43.14    (4)  op(e0, e0) = e0
% 232.00/43.14    (5)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 232.00/43.14         op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 232.00/43.14           all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3) = all_52_1 &
% 232.00/43.14         op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 232.00/43.14         $i(all_52_1) & $i(all_52_3) & $i(all_52_5) & $i(all_52_7)
% 232.00/43.14  
% 232.00/43.14  Begin of proof
% 232.00/43.14  | 
% 232.00/43.14  | ALPHA: (5) implies:
% 232.00/43.14  |   (6)  op(e3, e3) = all_52_1
% 232.00/43.14  |   (7)  op(all_52_1, all_52_1) = e3
% 232.00/43.14  | 
% 232.00/43.14  | GROUND_INST: instantiating (1) with e0, all_52_1, e3, e3, simplifying with
% 232.00/43.14  |              (3), (6) gives:
% 232.00/43.14  |   (8)  all_52_1 = e0
% 232.00/43.14  | 
% 232.00/43.14  | REDUCE: (7), (8) imply:
% 232.00/43.14  |   (9)  op(e0, e0) = e3
% 232.00/43.14  | 
% 232.00/43.14  | REF_CLOSE: (1), (2), (4), (9) are inconsistent by sub-proof #2304.
% 232.00/43.14  | 
% 232.00/43.14  End of proof
% 232.00/43.14  
% 232.00/43.14  Sub-proof #1940 shows that the following formulas are inconsistent:
% 232.00/43.14  ----------------------------------------------------------------
% 232.00/43.14    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.00/43.14           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.00/43.14    (2)  op(e3, e2) = all_53_4
% 232.00/43.14    (3)   ~ (e2 = e0)
% 232.00/43.14    (4)  op(e2, e2) = e2
% 232.00/43.14    (5)   ~ (all_53_4 = e0)
% 232.00/43.14    (6)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0)
% 232.00/43.14  
% 232.00/43.14  Begin of proof
% 232.00/43.14  | 
% 232.00/43.14  | BETA: splitting (6) gives:
% 232.00/43.14  | 
% 232.00/43.14  | Case 1:
% 232.00/43.14  | | 
% 232.00/43.14  | |   (7)  all_57_1 = e0 & op(e3, e2) = e0
% 232.00/43.14  | | 
% 232.00/43.14  | | ALPHA: (7) implies:
% 232.00/43.14  | |   (8)  op(e3, e2) = e0
% 232.00/43.14  | | 
% 232.00/43.14  | | REF_CLOSE: (1), (2), (5), (8) are inconsistent by sub-proof #1941.
% 232.00/43.14  | | 
% 232.00/43.14  | Case 2:
% 232.00/43.14  | | 
% 232.00/43.14  | |   (9)  all_57_3 = e0 & op(e2, e2) = e0
% 232.00/43.14  | | 
% 232.00/43.14  | | ALPHA: (9) implies:
% 232.00/43.14  | |   (10)  op(e2, e2) = e0
% 232.00/43.14  | | 
% 232.00/43.14  | | REF_CLOSE: (1), (3), (4), (10) are inconsistent by sub-proof #2472.
% 232.00/43.14  | | 
% 232.00/43.14  | End of split
% 232.00/43.14  | 
% 232.00/43.14  End of proof
% 232.00/43.14  
% 232.00/43.14  Sub-proof #1941 shows that the following formulas are inconsistent:
% 232.00/43.14  ----------------------------------------------------------------
% 232.00/43.14    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.00/43.14           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.00/43.14    (2)  op(e3, e2) = all_53_4
% 232.00/43.14    (3)  op(e3, e2) = e0
% 232.00/43.14    (4)   ~ (all_53_4 = e0)
% 232.00/43.14  
% 232.00/43.14  Begin of proof
% 232.00/43.14  | 
% 232.00/43.14  | GROUND_INST: instantiating (1) with all_53_4, e0, e2, e3, simplifying with
% 232.00/43.14  |              (2), (3) gives:
% 232.00/43.14  |   (5)  all_53_4 = e0
% 232.00/43.14  | 
% 232.00/43.14  | REDUCE: (4), (5) imply:
% 232.00/43.14  |   (6)  $false
% 232.00/43.14  | 
% 232.00/43.14  | CLOSE: (6) is inconsistent.
% 232.00/43.14  | 
% 232.00/43.14  End of proof
% 232.00/43.14  
% 232.00/43.14  Sub-proof #1942 shows that the following formulas are inconsistent:
% 232.00/43.14  ----------------------------------------------------------------
% 232.00/43.14    (1)  op(e2, e3) = all_53_1
% 232.00/43.14    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.00/43.14           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.00/43.14    (3)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0)
% 232.00/43.14    (4)   ~ (e2 = e0)
% 232.00/43.14    (5)   ~ (all_53_1 = e0)
% 232.00/43.14    (6)  op(e2, e2) = e2
% 232.00/43.14  
% 232.00/43.14  Begin of proof
% 232.00/43.14  | 
% 232.00/43.14  | BETA: splitting (3) gives:
% 232.00/43.14  | 
% 232.00/43.14  | Case 1:
% 232.00/43.14  | | 
% 232.00/43.14  | |   (7)  all_57_2 = e0 & op(e2, e3) = e0
% 232.00/43.14  | | 
% 232.00/43.14  | | ALPHA: (7) implies:
% 232.00/43.14  | |   (8)  op(e2, e3) = e0
% 232.00/43.14  | | 
% 232.00/43.14  | | REF_CLOSE: (1), (2), (5), (8) are inconsistent by sub-proof #1943.
% 232.00/43.14  | | 
% 232.00/43.14  | Case 2:
% 232.00/43.14  | | 
% 232.00/43.14  | |   (9)  all_57_3 = e0 & op(e2, e2) = e0
% 232.00/43.14  | | 
% 232.00/43.14  | | ALPHA: (9) implies:
% 232.00/43.14  | |   (10)  op(e2, e2) = e0
% 232.00/43.14  | | 
% 232.00/43.14  | | REF_CLOSE: (2), (4), (6), (10) are inconsistent by sub-proof #2472.
% 232.00/43.14  | | 
% 232.00/43.14  | End of split
% 232.00/43.14  | 
% 232.00/43.14  End of proof
% 232.00/43.14  
% 232.00/43.14  Sub-proof #1943 shows that the following formulas are inconsistent:
% 232.00/43.14  ----------------------------------------------------------------
% 232.00/43.14    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.00/43.14           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.00/43.14    (2)  op(e2, e3) = all_53_1
% 232.00/43.14    (3)  op(e2, e3) = e0
% 232.00/43.14    (4)   ~ (all_53_1 = e0)
% 232.00/43.14  
% 232.00/43.14  Begin of proof
% 232.00/43.14  | 
% 232.00/43.14  | GROUND_INST: instantiating (1) with all_53_1, e0, e3, e2, simplifying with
% 232.00/43.14  |              (2), (3) gives:
% 232.00/43.14  |   (5)  all_53_1 = e0
% 232.00/43.14  | 
% 232.00/43.14  | REDUCE: (4), (5) imply:
% 232.00/43.14  |   (6)  $false
% 232.00/43.14  | 
% 232.00/43.14  | CLOSE: (6) is inconsistent.
% 232.00/43.14  | 
% 232.00/43.14  End of proof
% 232.00/43.14  
% 232.00/43.14  Sub-proof #1944 shows that the following formulas are inconsistent:
% 232.00/43.14  ----------------------------------------------------------------
% 232.00/43.14    (1)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 &
% 232.00/43.14           op(all_52_17, all_52_17) = e3 & op(all_52_19, all_52_19) = e2 &
% 232.00/43.14           op(all_52_21, all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1,
% 232.00/43.14             e3) = all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 &
% 232.00/43.14           op(e1, e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21)
% 232.00/43.14           & $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 232.00/43.14           all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 232.00/43.14             all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 232.00/43.14             all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 232.00/43.14           op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 232.00/43.14           $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 232.00/43.14    (2)  op(e1, e0) = e2
% 232.00/43.14    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.00/43.14           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.00/43.14    (4)   ~ (e2 = e0)
% 232.00/43.14    (5)  op(e2, e2) = e2
% 232.00/43.14    (6)   ~ (e2 = e1)
% 232.00/43.14    (7)  op(e0, e1) = e2
% 232.00/43.14  
% 232.00/43.14  Begin of proof
% 232.00/43.14  | 
% 232.00/43.14  | BETA: splitting (1) gives:
% 232.00/43.14  | 
% 232.00/43.14  | Case 1:
% 232.00/43.14  | | 
% 232.00/43.14  | |   (8)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 &
% 232.00/43.14  | |        op(all_52_17, all_52_17) = e3 & op(all_52_19, all_52_19) = e2 &
% 232.00/43.14  | |        op(all_52_21, all_52_21) = e1 & op(all_52_23, all_52_23) = e0 &
% 232.00/43.14  | |        op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) =
% 232.00/43.14  | |        all_52_21 & op(e1, e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 232.00/43.14  | |        $i(all_52_21) & $i(all_52_23)
% 232.00/43.14  | | 
% 232.00/43.14  | | ALPHA: (8) implies:
% 232.00/43.14  | |   (9)  op(e1, e0) = all_52_23
% 232.00/43.14  | |   (10)  op(all_52_23, all_52_23) = e0
% 232.00/43.14  | | 
% 232.00/43.14  | | REF_CLOSE: (2), (3), (4), (5), (9), (10) are inconsistent by sub-proof
% 232.00/43.14  | |            #2369.
% 232.00/43.14  | | 
% 232.00/43.14  | Case 2:
% 232.00/43.14  | | 
% 232.00/43.14  | |   (11)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0 &
% 232.00/43.14  | |         op(all_52_25, all_52_25) = e3 & op(all_52_27, all_52_27) = e2 &
% 232.00/43.14  | |         op(all_52_29, all_52_29) = e1 & op(all_52_31, all_52_31) = e0 &
% 232.00/43.14  | |         op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 & op(e0, e1) =
% 232.00/43.14  | |         all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 232.00/43.14  | |         $i(all_52_29) & $i(all_52_31)
% 232.00/43.14  | | 
% 232.00/43.14  | | ALPHA: (11) implies:
% 232.00/43.14  | |   (12)  op(e0, e1) = all_52_29
% 232.00/43.14  | |   (13)  op(all_52_29, all_52_29) = e1
% 232.00/43.14  | | 
% 232.00/43.14  | | GROUND_INST: instantiating (3) with e2, all_52_29, e1, e0, simplifying with
% 232.00/43.14  | |              (7), (12) gives:
% 232.00/43.14  | |   (14)  all_52_29 = e2
% 232.00/43.14  | | 
% 232.00/43.14  | | REDUCE: (13), (14) imply:
% 232.00/43.14  | |   (15)  op(e2, e2) = e1
% 232.00/43.14  | | 
% 232.00/43.14  | | REF_CLOSE: (3), (5), (6), (15) are inconsistent by sub-proof #2306.
% 232.00/43.14  | | 
% 232.00/43.14  | End of split
% 232.00/43.14  | 
% 232.00/43.14  End of proof
% 232.00/43.14  
% 232.00/43.14  Sub-proof #1945 shows that the following formulas are inconsistent:
% 232.00/43.14  ----------------------------------------------------------------
% 232.00/43.14    (1)  op(e1, e0) = e2
% 232.00/43.14    (2)  op(e2, e1) = all_52_13
% 232.00/43.14    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.00/43.14           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.00/43.14    (4)   ~ (all_52_13 = e0)
% 232.00/43.14    (5)  ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 & op(e1, e0) = all_24_1
% 232.00/43.14           & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 = e3) & op(e1, e0) =
% 232.00/43.14           all_24_1 & $i(all_24_1))
% 232.00/43.14    (6)  all_55_6 = all_52_13
% 232.00/43.14    (7)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 232.00/43.14    (8)   ~ (all_52_13 = e2)
% 232.00/43.14    (9)  op(all_52_13, all_52_13) = e1
% 232.00/43.14    (10)  op(e1, e1) = e0
% 232.00/43.14    (11)  all_34_2 = e0
% 232.00/43.14    (12)   ~ (all_34_2 = e0) | ( ~ (all_34_0 = e3) & op(all_34_1, e1) = all_34_0 &
% 232.00/43.14            op(e1, e0) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 232.00/43.14              e2) & op(e1, e0) = all_34_1 & $i(all_34_1))
% 232.00/43.14  
% 232.00/43.14  Begin of proof
% 232.00/43.14  | 
% 232.00/43.14  | BETA: splitting (5) gives:
% 232.00/43.14  | 
% 232.00/43.14  | Case 1:
% 232.00/43.14  | | 
% 232.00/43.14  | |   (13)   ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 & op(e1, e0) =
% 232.00/43.14  | |         all_24_1 & $i(all_24_0) & $i(all_24_1)
% 232.00/43.14  | | 
% 232.00/43.14  | | ALPHA: (13) implies:
% 232.00/43.14  | |   (14)  op(e1, e0) = all_24_1
% 232.00/43.14  | | 
% 232.00/43.14  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (14)
% 232.00/43.14  | |            are inconsistent by sub-proof #1946.
% 232.00/43.14  | | 
% 232.00/43.14  | Case 2:
% 232.00/43.14  | | 
% 232.00/43.14  | |   (15)   ~ (all_24_1 = e3) & op(e1, e0) = all_24_1 & $i(all_24_1)
% 232.00/43.14  | | 
% 232.00/43.14  | | ALPHA: (15) implies:
% 232.00/43.14  | |   (16)  op(e1, e0) = all_24_1
% 232.00/43.14  | | 
% 232.00/43.14  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (16)
% 232.00/43.14  | |            are inconsistent by sub-proof #1946.
% 232.00/43.14  | | 
% 232.00/43.14  | End of split
% 232.00/43.14  | 
% 232.00/43.14  End of proof
% 232.00/43.14  
% 232.00/43.14  Sub-proof #1946 shows that the following formulas are inconsistent:
% 232.00/43.14  ----------------------------------------------------------------
% 232.00/43.14    (1)  op(e1, e0) = e2
% 232.00/43.14    (2)  op(e2, e1) = all_52_13
% 232.00/43.14    (3)  op(e1, e0) = all_24_1
% 232.00/43.14    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.00/43.14           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.00/43.14    (5)   ~ (all_52_13 = e0)
% 232.00/43.14    (6)  all_55_6 = all_52_13
% 232.00/43.14    (7)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 232.00/43.14    (8)   ~ (all_52_13 = e2)
% 232.00/43.14    (9)  op(all_52_13, all_52_13) = e1
% 232.00/43.14    (10)  op(e1, e1) = e0
% 232.00/43.14    (11)  all_34_2 = e0
% 232.00/43.14    (12)   ~ (all_34_2 = e0) | ( ~ (all_34_0 = e3) & op(all_34_1, e1) = all_34_0 &
% 232.00/43.14            op(e1, e0) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 232.00/43.14              e2) & op(e1, e0) = all_34_1 & $i(all_34_1))
% 232.00/43.14  
% 232.00/43.14  Begin of proof
% 232.00/43.14  | 
% 232.00/43.14  | BETA: splitting (12) gives:
% 232.00/43.14  | 
% 232.00/43.14  | Case 1:
% 232.00/43.14  | | 
% 232.00/43.14  | |   (13)   ~ (all_34_2 = e0)
% 232.00/43.14  | | 
% 232.00/43.14  | | REDUCE: (11), (13) imply:
% 232.00/43.15  | |   (14)  $false
% 232.00/43.15  | | 
% 232.00/43.15  | | CLOSE: (14) is inconsistent.
% 232.00/43.15  | | 
% 232.00/43.15  | Case 2:
% 232.00/43.15  | | 
% 232.00/43.15  | |   (15)  ( ~ (all_34_0 = e3) & op(all_34_1, e1) = all_34_0 & op(e1, e0) =
% 232.00/43.15  | |           all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 = e2) &
% 232.00/43.15  | |           op(e1, e0) = all_34_1 & $i(all_34_1))
% 232.00/43.15  | | 
% 232.00/43.15  | | GROUND_INST: instantiating (4) with e2, all_24_1, e0, e1, simplifying with
% 232.00/43.15  | |              (1), (3) gives:
% 232.00/43.15  | |   (16)  all_24_1 = e2
% 232.00/43.15  | | 
% 232.00/43.15  | | BETA: splitting (15) gives:
% 232.00/43.15  | | 
% 232.00/43.15  | | Case 1:
% 232.00/43.15  | | | 
% 232.00/43.15  | | |   (17)   ~ (all_34_0 = e3) & op(all_34_1, e1) = all_34_0 & op(e1, e0) =
% 232.00/43.15  | | |         all_34_1 & $i(all_34_0) & $i(all_34_1)
% 232.00/43.15  | | | 
% 232.00/43.15  | | | ALPHA: (17) implies:
% 232.00/43.15  | | |   (18)   ~ (all_34_0 = e3)
% 232.00/43.15  | | |   (19)  op(e1, e0) = all_34_1
% 232.00/43.15  | | |   (20)  op(all_34_1, e1) = all_34_0
% 232.00/43.15  | | | 
% 232.00/43.15  | | | GROUND_INST: instantiating (4) with e2, all_34_1, e0, e1, simplifying with
% 232.00/43.15  | | |              (1), (19) gives:
% 232.00/43.15  | | |   (21)  all_34_1 = e2
% 232.00/43.15  | | | 
% 232.00/43.15  | | | REDUCE: (20), (21) imply:
% 232.00/43.15  | | |   (22)  op(e2, e1) = all_34_0
% 232.00/43.15  | | | 
% 232.00/43.15  | | | GROUND_INST: instantiating (4) with all_52_13, all_34_0, e1, e2,
% 232.00/43.15  | | |              simplifying with (2), (22) gives:
% 232.00/43.15  | | |   (23)  all_52_13 = all_34_0
% 232.00/43.15  | | | 
% 232.00/43.15  | | | COMBINE_EQS: (6), (23) imply:
% 232.00/43.15  | | |   (24)  all_55_6 = all_34_0
% 232.00/43.15  | | | 
% 232.00/43.15  | | | REDUCE: (8), (23) imply:
% 232.00/43.15  | | |   (25)   ~ (all_34_0 = e2)
% 232.00/43.15  | | | 
% 232.00/43.15  | | | REDUCE: (5), (23) imply:
% 232.00/43.15  | | |   (26)   ~ (all_34_0 = e0)
% 232.00/43.15  | | | 
% 232.00/43.15  | | | REDUCE: (9), (23) imply:
% 232.00/43.15  | | |   (27)  op(all_34_0, all_34_0) = e1
% 232.00/43.15  | | | 
% 232.00/43.15  | | | BETA: splitting (7) gives:
% 232.00/43.15  | | | 
% 232.00/43.15  | | | Case 1:
% 232.00/43.15  | | | | 
% 232.00/43.15  | | | |   (28)  all_55_6 = e3
% 232.00/43.15  | | | | 
% 232.00/43.15  | | | | COMBINE_EQS: (24), (28) imply:
% 232.00/43.15  | | | |   (29)  all_34_0 = e3
% 232.00/43.15  | | | | 
% 232.00/43.15  | | | | SIMP: (29) implies:
% 232.00/43.15  | | | |   (30)  all_34_0 = e3
% 232.00/43.15  | | | | 
% 232.00/43.15  | | | | REDUCE: (18), (30) imply:
% 232.00/43.15  | | | |   (31)  $false
% 232.00/43.15  | | | | 
% 232.00/43.15  | | | | CLOSE: (31) is inconsistent.
% 232.00/43.15  | | | | 
% 232.00/43.15  | | | Case 2:
% 232.00/43.15  | | | | 
% 232.00/43.15  | | | |   (32)  all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 232.00/43.15  | | | | 
% 232.00/43.15  | | | | BETA: splitting (32) gives:
% 232.00/43.15  | | | | 
% 232.00/43.15  | | | | Case 1:
% 232.00/43.15  | | | | | 
% 232.00/43.15  | | | | |   (33)  all_55_6 = e2
% 232.00/43.15  | | | | | 
% 232.00/43.15  | | | | | COMBINE_EQS: (24), (33) imply:
% 232.00/43.15  | | | | |   (34)  all_34_0 = e2
% 232.00/43.15  | | | | | 
% 232.00/43.15  | | | | | SIMP: (34) implies:
% 232.00/43.15  | | | | |   (35)  all_34_0 = e2
% 232.00/43.15  | | | | | 
% 232.00/43.15  | | | | | REDUCE: (25), (35) imply:
% 232.00/43.15  | | | | |   (36)  $false
% 232.00/43.15  | | | | | 
% 232.00/43.15  | | | | | CLOSE: (36) is inconsistent.
% 232.00/43.15  | | | | | 
% 232.00/43.15  | | | | Case 2:
% 232.00/43.15  | | | | | 
% 232.00/43.15  | | | | |   (37)  all_55_6 = e1 | all_55_6 = e0
% 232.00/43.15  | | | | | 
% 232.00/43.15  | | | | | BETA: splitting (37) gives:
% 232.00/43.15  | | | | | 
% 232.00/43.15  | | | | | Case 1:
% 232.00/43.15  | | | | | | 
% 232.00/43.15  | | | | | |   (38)  all_55_6 = e1
% 232.00/43.15  | | | | | | 
% 232.00/43.15  | | | | | | COMBINE_EQS: (24), (38) imply:
% 232.00/43.15  | | | | | |   (39)  all_34_0 = e1
% 232.00/43.15  | | | | | | 
% 232.00/43.15  | | | | | | SIMP: (39) implies:
% 232.00/43.15  | | | | | |   (40)  all_34_0 = e1
% 232.00/43.15  | | | | | | 
% 232.00/43.15  | | | | | | REDUCE: (26), (40) imply:
% 232.00/43.15  | | | | | |   (41)   ~ (e1 = e0)
% 232.00/43.15  | | | | | | 
% 232.00/43.15  | | | | | | REDUCE: (27), (40) imply:
% 232.00/43.15  | | | | | |   (42)  op(e1, e1) = e1
% 232.00/43.15  | | | | | | 
% 232.00/43.15  | | | | | | REF_CLOSE: (4), (10), (41), (42) are inconsistent by sub-proof
% 232.00/43.15  | | | | | |            #2427.
% 232.00/43.15  | | | | | | 
% 232.00/43.15  | | | | | Case 2:
% 232.00/43.15  | | | | | | 
% 232.00/43.15  | | | | | |   (43)  all_55_6 = e0
% 232.00/43.15  | | | | | | 
% 232.00/43.15  | | | | | | COMBINE_EQS: (24), (43) imply:
% 232.00/43.15  | | | | | |   (44)  all_34_0 = e0
% 232.00/43.15  | | | | | | 
% 232.00/43.15  | | | | | | SIMP: (44) implies:
% 232.00/43.15  | | | | | |   (45)  all_34_0 = e0
% 232.00/43.15  | | | | | | 
% 232.00/43.15  | | | | | | REDUCE: (26), (45) imply:
% 232.00/43.15  | | | | | |   (46)  $false
% 232.00/43.15  | | | | | | 
% 232.00/43.15  | | | | | | CLOSE: (46) is inconsistent.
% 232.00/43.15  | | | | | | 
% 232.00/43.15  | | | | | End of split
% 232.00/43.15  | | | | | 
% 232.00/43.15  | | | | End of split
% 232.00/43.15  | | | | 
% 232.00/43.15  | | | End of split
% 232.00/43.15  | | | 
% 232.00/43.15  | | Case 2:
% 232.00/43.15  | | | 
% 232.00/43.15  | | |   (47)   ~ (all_34_1 = e2) & op(e1, e0) = all_34_1 & $i(all_34_1)
% 232.00/43.15  | | | 
% 232.00/43.15  | | | ALPHA: (47) implies:
% 232.00/43.15  | | |   (48)   ~ (all_34_1 = e2)
% 232.00/43.15  | | |   (49)  op(e1, e0) = all_34_1
% 232.00/43.15  | | | 
% 232.00/43.15  | | | GROUND_INST: instantiating (4) with e2, all_34_1, e0, e1, simplifying with
% 232.00/43.15  | | |              (1), (49) gives:
% 232.00/43.15  | | |   (50)  all_34_1 = e2
% 232.00/43.15  | | | 
% 232.00/43.15  | | | REDUCE: (48), (50) imply:
% 232.00/43.15  | | |   (51)  $false
% 232.00/43.15  | | | 
% 232.00/43.15  | | | CLOSE: (51) is inconsistent.
% 232.00/43.15  | | | 
% 232.00/43.15  | | End of split
% 232.00/43.15  | | 
% 232.00/43.15  | End of split
% 232.00/43.15  | 
% 232.00/43.15  End of proof
% 232.00/43.15  
% 232.00/43.15  Sub-proof #1947 shows that the following formulas are inconsistent:
% 232.00/43.15  ----------------------------------------------------------------
% 232.00/43.15    (1)  all_57_12 = e1 & op(e0, e3) = e1
% 232.00/43.15    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.00/43.15           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.00/43.15    (3)  op(e0, e3) = all_53_3
% 232.00/43.15    (4)   ~ (all_53_3 = e1)
% 232.00/43.15  
% 232.00/43.15  Begin of proof
% 232.00/43.15  | 
% 232.00/43.15  | ALPHA: (1) implies:
% 232.00/43.15  |   (5)  op(e0, e3) = e1
% 232.00/43.15  | 
% 232.00/43.15  | GROUND_INST: instantiating (2) with all_53_3, e1, e3, e0, simplifying with
% 232.00/43.15  |              (3), (5) gives:
% 232.00/43.15  |   (6)  all_53_3 = e1
% 232.00/43.15  | 
% 232.00/43.15  | REDUCE: (4), (6) imply:
% 232.00/43.15  |   (7)  $false
% 232.00/43.15  | 
% 232.00/43.15  | CLOSE: (7) is inconsistent.
% 232.00/43.15  | 
% 232.00/43.15  End of proof
% 232.00/43.15  
% 232.00/43.15  Sub-proof #1948 shows that the following formulas are inconsistent:
% 232.00/43.15  ----------------------------------------------------------------
% 232.00/43.15    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.00/43.15           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.00/43.15    (2)  all_57_6 = e1
% 232.00/43.15    (3)   ~ (e3 = e2)
% 232.00/43.15    (4)  all_57_11 = e0
% 232.00/43.15    (5)  op(e1, e1) = e1
% 232.00/43.15    (6)   ~ (e2 = e0)
% 232.00/43.15    (7)  all_57_7 = e3
% 232.00/43.15    (8)   ~ (e2 = e1)
% 232.00/43.15    (9)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 232.00/43.15         (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 232.00/43.15  
% 232.00/43.15  Begin of proof
% 232.00/43.15  | 
% 232.00/43.15  | BETA: splitting (9) gives:
% 232.00/43.15  | 
% 232.00/43.15  | Case 1:
% 232.00/43.15  | | 
% 232.00/43.15  | |   (10)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) =
% 232.00/43.15  | |           e2)
% 232.00/43.15  | | 
% 232.00/43.15  | | REF_CLOSE: (2), (3), (7), (8), (10) are inconsistent by sub-proof #2006.
% 232.00/43.15  | | 
% 232.00/43.15  | Case 2:
% 232.00/43.15  | | 
% 232.00/43.15  | |   (11)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) =
% 232.00/43.15  | |           e2)
% 232.00/43.15  | | 
% 232.00/43.15  | | BETA: splitting (11) gives:
% 232.00/43.15  | | 
% 232.00/43.15  | | Case 1:
% 232.00/43.15  | | | 
% 232.00/43.15  | | |   (12)  all_57_8 = e2 & op(e1, e1) = e2
% 232.00/43.15  | | | 
% 232.00/43.15  | | | ALPHA: (12) implies:
% 232.00/43.15  | | |   (13)  op(e1, e1) = e2
% 232.00/43.15  | | | 
% 232.00/43.15  | | | REF_CLOSE: (1), (5), (8), (13) are inconsistent by sub-proof #2423.
% 232.00/43.15  | | | 
% 232.00/43.15  | | Case 2:
% 232.00/43.15  | | | 
% 232.00/43.15  | | |   (14)  all_57_11 = e2 & op(e1, e0) = e2
% 232.00/43.15  | | | 
% 232.00/43.15  | | | ALPHA: (14) implies:
% 232.00/43.15  | | |   (15)  all_57_11 = e2
% 232.00/43.15  | | | 
% 232.00/43.15  | | | REF_CLOSE: (4), (6), (15) are inconsistent by sub-proof #1949.
% 232.00/43.15  | | | 
% 232.00/43.15  | | End of split
% 232.00/43.15  | | 
% 232.00/43.15  | End of split
% 232.00/43.15  | 
% 232.00/43.15  End of proof
% 232.00/43.15  
% 232.00/43.15  Sub-proof #1949 shows that the following formulas are inconsistent:
% 232.00/43.15  ----------------------------------------------------------------
% 232.00/43.15    (1)  all_57_11 = e2
% 232.00/43.15    (2)  all_57_11 = e0
% 232.00/43.15    (3)   ~ (e2 = e0)
% 232.00/43.15  
% 232.00/43.15  Begin of proof
% 232.00/43.15  | 
% 232.00/43.15  | COMBINE_EQS: (1), (2) imply:
% 232.00/43.15  |   (4)  e2 = e0
% 232.00/43.15  | 
% 232.00/43.15  | SIMP: (4) implies:
% 232.00/43.15  |   (5)  e2 = e0
% 232.00/43.15  | 
% 232.00/43.15  | REDUCE: (3), (5) imply:
% 232.00/43.15  |   (6)  $false
% 232.00/43.15  | 
% 232.00/43.15  | CLOSE: (6) is inconsistent.
% 232.00/43.15  | 
% 232.00/43.15  End of proof
% 232.00/43.15  
% 232.00/43.15  Sub-proof #1950 shows that the following formulas are inconsistent:
% 232.00/43.15  ----------------------------------------------------------------
% 232.00/43.15    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.00/43.15           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.00/43.15    (2)  op(e3, e3) = e2
% 232.00/43.15    (3)  op(e3, e3) = e1
% 232.00/43.15    (4)   ~ (e2 = e1)
% 232.00/43.15  
% 232.00/43.15  Begin of proof
% 232.00/43.15  | 
% 232.00/43.15  | GROUND_INST: instantiating (1) with e1, e2, e3, e3, simplifying with (2), (3)
% 232.00/43.15  |              gives:
% 232.00/43.15  |   (5)  e2 = e1
% 232.00/43.15  | 
% 232.00/43.15  | REDUCE: (4), (5) imply:
% 232.00/43.15  |   (6)  $false
% 232.00/43.15  | 
% 232.00/43.15  | CLOSE: (6) is inconsistent.
% 232.00/43.15  | 
% 232.00/43.15  End of proof
% 232.00/43.15  
% 232.00/43.15  Sub-proof #1951 shows that the following formulas are inconsistent:
% 232.00/43.15  ----------------------------------------------------------------
% 232.00/43.15    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.00/43.15           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.00/43.15    (2)   ~ (e3 = e2)
% 232.00/43.15    (3)  op(e3, e3) = e2
% 232.00/43.15    (4)  op(e3, e3) = all_52_1
% 232.00/43.15    (5)  op(all_52_1, all_52_1) = e3
% 232.00/43.15    (6)  op(e2, e2) = e2
% 232.00/43.15  
% 232.00/43.15  Begin of proof
% 232.00/43.15  | 
% 232.00/43.15  | GROUND_INST: instantiating (1) with e2, all_52_1, e3, e3, simplifying with
% 232.00/43.15  |              (3), (4) gives:
% 232.00/43.15  |   (7)  all_52_1 = e2
% 232.00/43.15  | 
% 232.00/43.15  | REDUCE: (5), (7) imply:
% 232.00/43.15  |   (8)  op(e2, e2) = e3
% 232.00/43.15  | 
% 232.00/43.15  | GROUND_INST: instantiating (1) with e2, e3, e2, e2, simplifying with (6), (8)
% 232.00/43.15  |              gives:
% 232.00/43.15  |   (9)  e3 = e2
% 232.00/43.15  | 
% 232.00/43.15  | REDUCE: (2), (9) imply:
% 232.00/43.15  |   (10)  $false
% 232.00/43.15  | 
% 232.00/43.15  | CLOSE: (10) is inconsistent.
% 232.00/43.15  | 
% 232.00/43.15  End of proof
% 232.00/43.15  
% 232.00/43.15  Sub-proof #1952 shows that the following formulas are inconsistent:
% 232.00/43.15  ----------------------------------------------------------------
% 232.00/43.15    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.00/43.15           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.00/43.15    (2)   ~ (all_53_13 = e2)
% 232.00/43.15    (3)  op(e2, e0) = all_53_13
% 232.00/43.15    (4)   ~ (all_53_12 = e2)
% 232.00/43.15    (5)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 232.00/43.15    (6)  op(e3, e0) = all_53_12
% 232.00/43.15  
% 232.00/43.15  Begin of proof
% 232.00/43.15  | 
% 232.00/43.15  | BETA: splitting (5) gives:
% 232.00/43.15  | 
% 232.00/43.15  | Case 1:
% 232.00/43.15  | | 
% 232.00/43.15  | |   (7)  all_57_9 = e2 & op(e3, e0) = e2
% 232.00/43.15  | | 
% 232.00/43.15  | | ALPHA: (7) implies:
% 232.00/43.15  | |   (8)  op(e3, e0) = e2
% 232.00/43.15  | | 
% 232.00/43.15  | | REF_CLOSE: (1), (4), (6), (8) are inconsistent by sub-proof #2331.
% 232.00/43.15  | | 
% 232.00/43.15  | Case 2:
% 232.00/43.15  | | 
% 232.00/43.15  | |   (9)  all_57_10 = e2 & op(e2, e0) = e2
% 232.00/43.15  | | 
% 232.00/43.15  | | REF_CLOSE: (1), (2), (3), (9) are inconsistent by sub-proof #2432.
% 232.00/43.15  | | 
% 232.00/43.15  | End of split
% 232.00/43.15  | 
% 232.00/43.15  End of proof
% 232.00/43.15  
% 232.00/43.15  Sub-proof #1953 shows that the following formulas are inconsistent:
% 232.00/43.15  ----------------------------------------------------------------
% 232.00/43.15    (1)   ~ (all_10_2 = e2)
% 232.00/43.15    (2)  all_55_0 = all_10_2
% 232.00/43.15    (3)   ~ (all_10_2 = e0)
% 232.00/43.15    (4)   ~ (all_10_2 = e1)
% 232.00/43.15    (5)  all_55_0 = e2 | all_55_0 = e1 | all_55_0 = e0
% 232.00/43.15  
% 232.00/43.15  Begin of proof
% 232.00/43.15  | 
% 232.00/43.15  | BETA: splitting (5) gives:
% 232.00/43.15  | 
% 232.00/43.15  | Case 1:
% 232.00/43.15  | | 
% 232.00/43.15  | |   (6)  all_55_0 = e2
% 232.00/43.15  | | 
% 232.00/43.15  | | COMBINE_EQS: (2), (6) imply:
% 232.00/43.15  | |   (7)  all_10_2 = e2
% 232.00/43.15  | | 
% 232.00/43.15  | | REDUCE: (1), (7) imply:
% 232.00/43.15  | |   (8)  $false
% 232.00/43.15  | | 
% 232.00/43.15  | | CLOSE: (8) is inconsistent.
% 232.00/43.15  | | 
% 232.00/43.15  | Case 2:
% 232.00/43.15  | | 
% 232.00/43.15  | |   (9)  all_55_0 = e1 | all_55_0 = e0
% 232.00/43.15  | | 
% 232.00/43.15  | | REF_CLOSE: (2), (3), (4), (9) are inconsistent by sub-proof #1954.
% 232.00/43.15  | | 
% 232.00/43.15  | End of split
% 232.00/43.15  | 
% 232.00/43.15  End of proof
% 232.00/43.15  
% 232.00/43.15  Sub-proof #1954 shows that the following formulas are inconsistent:
% 232.00/43.15  ----------------------------------------------------------------
% 232.00/43.15    (1)  all_55_0 = e1 | all_55_0 = e0
% 232.00/43.15    (2)  all_55_0 = all_10_2
% 232.00/43.15    (3)   ~ (all_10_2 = e1)
% 232.00/43.15    (4)   ~ (all_10_2 = e0)
% 232.00/43.15  
% 232.00/43.15  Begin of proof
% 232.00/43.15  | 
% 232.00/43.15  | BETA: splitting (1) gives:
% 232.00/43.15  | 
% 232.00/43.15  | Case 1:
% 232.00/43.15  | | 
% 232.00/43.15  | |   (5)  all_55_0 = e1
% 232.00/43.15  | | 
% 232.00/43.15  | | COMBINE_EQS: (2), (5) imply:
% 232.00/43.15  | |   (6)  all_10_2 = e1
% 232.00/43.15  | | 
% 232.00/43.15  | | REDUCE: (3), (6) imply:
% 232.00/43.15  | |   (7)  $false
% 232.00/43.15  | | 
% 232.00/43.15  | | CLOSE: (7) is inconsistent.
% 232.00/43.15  | | 
% 232.00/43.15  | Case 2:
% 232.00/43.15  | | 
% 232.00/43.15  | |   (8)  all_55_0 = e0
% 232.00/43.15  | | 
% 232.00/43.15  | | COMBINE_EQS: (2), (8) imply:
% 232.00/43.15  | |   (9)  all_10_2 = e0
% 232.00/43.15  | | 
% 232.00/43.15  | | REDUCE: (4), (9) imply:
% 232.00/43.15  | |   (10)  $false
% 232.00/43.15  | | 
% 232.00/43.15  | | CLOSE: (10) is inconsistent.
% 232.00/43.15  | | 
% 232.00/43.15  | End of split
% 232.00/43.15  | 
% 232.00/43.15  End of proof
% 232.00/43.15  
% 232.00/43.15  Sub-proof #1955 shows that the following formulas are inconsistent:
% 232.00/43.15  ----------------------------------------------------------------
% 232.00/43.15    (1)   ~ (e3 = e1)
% 232.00/43.15    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.00/43.15           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.00/43.15    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 232.00/43.15         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 232.00/43.15    (4)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 232.00/43.15         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 232.00/43.15    (5)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 232.00/43.15         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 232.00/43.15    (6)   ~ (e3 = e2)
% 232.00/43.15    (7)   ~ (e3 = e0)
% 232.00/43.15    (8)  op(e3, e3) = e3
% 232.00/43.15    (9)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 232.00/43.15    (10)   ~ (e2 = e0)
% 232.00/43.15    (11)   ~ (e1 = e0)
% 232.00/43.15    (12)   ~ (all_53_12 = e3)
% 232.00/43.15    (13)   ~ (e2 = e1)
% 232.00/43.15    (14)  op(e3, e0) = all_53_12
% 232.00/43.15  
% 232.00/43.15  Begin of proof
% 232.00/43.15  | 
% 232.00/43.15  | BETA: splitting (9) gives:
% 232.00/43.15  | 
% 232.00/43.15  | Case 1:
% 232.00/43.15  | | 
% 232.00/43.15  | |   (15)  all_57_4 = e3 & op(e3, e1) = e3
% 232.00/43.15  | | 
% 232.00/43.15  | | ALPHA: (15) implies:
% 232.00/43.15  | |   (16)  all_57_4 = e3
% 232.00/43.15  | | 
% 232.00/43.15  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (13), (16)
% 232.00/43.15  | |            are inconsistent by sub-proof #2474.
% 232.00/43.15  | | 
% 232.00/43.15  | Case 2:
% 232.00/43.15  | | 
% 232.00/43.15  | |   (17)  all_57_9 = e3 & op(e3, e0) = e3
% 232.00/43.15  | | 
% 232.00/43.15  | | ALPHA: (17) implies:
% 232.00/43.15  | |   (18)  op(e3, e0) = e3
% 232.00/43.15  | | 
% 232.00/43.15  | | REF_CLOSE: (2), (12), (14), (18) are inconsistent by sub-proof #2458.
% 232.00/43.15  | | 
% 232.00/43.15  | End of split
% 232.00/43.15  | 
% 232.00/43.15  End of proof
% 232.00/43.15  
% 232.00/43.15  Sub-proof #1956 shows that the following formulas are inconsistent:
% 232.00/43.15  ----------------------------------------------------------------
% 232.00/43.15    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.00/43.15           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.00/43.15    (2)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 232.00/43.15    (3)   ~ (e3 = e2)
% 232.00/43.15    (4)  all_57_11 = e3
% 232.00/43.15    (5)  op(e0, e0) = e1
% 232.00/43.15    (6)   ~ (e2 = e1)
% 232.00/43.15  
% 232.00/43.15  Begin of proof
% 232.00/43.15  | 
% 232.00/43.15  | BETA: splitting (2) gives:
% 232.00/43.15  | 
% 232.00/43.15  | Case 1:
% 232.00/43.15  | | 
% 232.00/43.15  | |   (7)  all_57_11 = e2 & op(e1, e0) = e2
% 232.00/43.15  | | 
% 232.00/43.15  | | REF_CLOSE: (3), (4), (7) are inconsistent by sub-proof #2141.
% 232.00/43.15  | | 
% 232.00/43.15  | Case 2:
% 232.00/43.15  | | 
% 232.00/43.15  | |   (8)  all_57_15 = e2 & op(e0, e0) = e2
% 232.00/43.15  | | 
% 232.00/43.15  | | ALPHA: (8) implies:
% 232.00/43.15  | |   (9)  op(e0, e0) = e2
% 232.00/43.15  | | 
% 232.00/43.15  | | REF_CLOSE: (1), (5), (6), (9) are inconsistent by sub-proof #2177.
% 232.00/43.15  | | 
% 232.00/43.15  | End of split
% 232.00/43.15  | 
% 232.00/43.15  End of proof
% 232.00/43.15  
% 232.00/43.15  Sub-proof #1957 shows that the following formulas are inconsistent:
% 232.00/43.15  ----------------------------------------------------------------
% 232.00/43.15    (1)  all_57_8 = e2
% 232.00/43.15    (2)  all_57_8 = e0
% 232.00/43.15    (3)   ~ (e2 = e0)
% 232.00/43.15  
% 232.00/43.15  Begin of proof
% 232.00/43.15  | 
% 232.00/43.15  | COMBINE_EQS: (1), (2) imply:
% 232.00/43.15  |   (4)  e2 = e0
% 232.00/43.15  | 
% 232.00/43.15  | SIMP: (4) implies:
% 232.00/43.15  |   (5)  e2 = e0
% 232.00/43.15  | 
% 232.00/43.15  | REDUCE: (3), (5) imply:
% 232.00/43.15  |   (6)  $false
% 232.00/43.15  | 
% 232.00/43.15  | CLOSE: (6) is inconsistent.
% 232.00/43.15  | 
% 232.00/43.15  End of proof
% 232.00/43.15  
% 232.00/43.15  Sub-proof #1958 shows that the following formulas are inconsistent:
% 232.00/43.15  ----------------------------------------------------------------
% 232.00/43.15    (1)   ~ (e3 = e1)
% 232.00/43.15    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.00/43.15           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.00/43.15    (3)  all_57_7 = e2
% 232.00/43.15    (4)  all_57_1 = e0
% 232.00/43.15    (5)  op(e2, e2) = e2
% 232.00/43.15    (6)   ~ (e1 = e0)
% 232.00/43.15    (7)  all_57_13 = e3
% 232.00/43.15    (8)   ~ (e2 = e1)
% 232.00/43.15    (9)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 232.00/43.15         (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 232.00/43.15  
% 232.00/43.15  Begin of proof
% 232.00/43.15  | 
% 232.00/43.15  | BETA: splitting (9) gives:
% 232.00/43.15  | 
% 232.00/43.15  | Case 1:
% 232.00/43.15  | | 
% 232.00/43.15  | |   (10)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) =
% 232.00/43.15  | |           e1)
% 232.00/43.15  | | 
% 232.00/43.15  | | REF_CLOSE: (2), (4), (5), (6), (8), (10) are inconsistent by sub-proof
% 232.00/43.15  | |            #2266.
% 232.00/43.15  | | 
% 232.00/43.15  | Case 2:
% 232.00/43.15  | | 
% 232.00/43.15  | |   (11)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 232.00/43.15  | |           e1)
% 232.00/43.15  | | 
% 232.00/43.15  | | BETA: splitting (11) gives:
% 232.00/43.15  | | 
% 232.00/43.15  | | Case 1:
% 232.00/43.15  | | | 
% 232.00/43.15  | | |   (12)  all_57_7 = e1 & op(e1, e2) = e1
% 232.00/43.15  | | | 
% 232.00/43.15  | | | REF_CLOSE: (3), (8), (12) are inconsistent by sub-proof #2190.
% 232.00/43.15  | | | 
% 232.00/43.15  | | Case 2:
% 232.00/43.15  | | | 
% 232.00/43.15  | | |   (13)  all_57_13 = e1 & op(e0, e2) = e1
% 232.00/43.15  | | | 
% 232.00/43.15  | | | REF_CLOSE: (1), (7), (13) are inconsistent by sub-proof #2264.
% 232.00/43.15  | | | 
% 232.00/43.15  | | End of split
% 232.00/43.15  | | 
% 232.00/43.15  | End of split
% 232.00/43.15  | 
% 232.00/43.15  End of proof
% 232.00/43.15  
% 232.00/43.15  Sub-proof #1959 shows that the following formulas are inconsistent:
% 232.00/43.15  ----------------------------------------------------------------
% 232.00/43.15    (1)  op(e2, e3) = all_53_1
% 232.00/43.15    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 232.00/43.15         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 232.00/43.15    (3)   ~ (e3 = e1)
% 232.00/43.15    (4)   ~ (all_53_13 = e1)
% 232.00/43.15    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.00/43.15           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.00/43.15    (6)  all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 232.00/43.15    (7)  ( ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 & op(e1, e0) = all_24_1
% 232.00/43.15           & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 = e3) & op(e1, e0) =
% 232.00/43.15           all_24_1 & $i(all_24_1))
% 232.00/43.15    (8)   ~ (all_53_13 = e2)
% 232.00/43.15    (9)   ~ (all_53_7 = e2)
% 232.00/43.15    (10)   ~ (all_53_13 = e3)
% 232.00/43.15    (11)   ~ (e3 = e2)
% 232.00/43.15    (12)   ~ (e3 = e0)
% 232.00/43.15    (13)  op(e3, e3) = e3
% 232.00/43.15    (14)  op(e3, e0) = e2
% 232.00/43.15    (15)  all_57_1 = e0
% 232.00/43.15    (16)  op(e0, e3) = all_53_3
% 232.00/43.15    (17)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 232.00/43.15          | (all_57_14 = e0 & op(e0, e1) = e0)
% 232.00/43.15    (18)  op(e1, e0) = all_34_1
% 232.00/43.15    (19)   ~ (all_53_3 = e2)
% 232.00/43.15    (20)  all_57_4 = e1
% 232.00/43.15    (21)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 232.00/43.15          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 232.00/43.15            e1)
% 232.00/43.15    (22)  all_57_6 = e2
% 232.00/43.15    (23)   ~ (e2 = e0)
% 232.00/43.15    (24)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 232.00/43.15            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 232.00/43.15            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 232.00/43.15            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 232.00/43.15              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 232.00/43.15            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 232.00/43.15            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 232.00/43.15              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 232.00/43.15              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 232.00/43.15            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 232.00/43.15            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 232.00/43.15            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 232.00/43.15              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 232.00/43.15              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 232.00/43.15            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 232.00/43.15              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 232.00/43.15            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 232.00/43.15            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 232.00/43.15              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 232.00/43.15              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 232.00/43.15            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 232.00/43.15            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 232.00/43.15    (25)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 232.00/43.15          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 232.00/43.15    (26)  op(e2, e2) = e2
% 232.00/43.15    (27)   ~ (e1 = e0)
% 232.00/43.15    (28)  all_57_13 = e3
% 232.00/43.15    (29)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 232.00/43.15          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 232.00/43.15            e3)
% 232.00/43.15    (30)  op(e0, e2) = all_53_7
% 232.00/43.15    (31)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 232.00/43.15          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 232.00/43.15            e2)
% 232.00/43.15    (32)  op(e0, e0) = e1
% 232.00/43.15    (33)  op(e2, e0) = all_53_13
% 232.00/43.15    (34)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 232.00/43.15          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 232.00/43.15    (35)   ~ (all_53_12 = e3)
% 232.00/43.15    (36)   ~ (all_53_1 = e3)
% 232.00/43.15    (37)   ~ (e2 = e1)
% 232.00/43.15    (38)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 232.00/43.15          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 232.00/43.15    (39)  op(e1, e0) = e3
% 232.00/43.15    (40)  all_55_7 = all_53_13
% 232.00/43.15    (41)  op(e3, e0) = all_53_12
% 232.00/43.15  
% 232.00/43.15  Begin of proof
% 232.00/43.15  | 
% 232.00/43.15  | BETA: splitting (34) gives:
% 232.00/43.15  | 
% 232.00/43.15  | Case 1:
% 232.00/43.15  | | 
% 232.00/43.15  | |   (42)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 232.00/43.15  | |           e3)
% 232.00/43.15  | | 
% 232.00/43.15  | | REF_CLOSE: (1), (5), (11), (26), (36), (42) are inconsistent by sub-proof
% 232.00/43.15  | |            #2297.
% 232.00/43.15  | | 
% 232.00/43.15  | Case 2:
% 232.00/43.15  | | 
% 232.00/43.15  | |   (43)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 232.00/43.15  | |           e3)
% 232.00/43.15  | | 
% 232.00/43.15  | | BETA: splitting (43) gives:
% 232.00/43.15  | | 
% 232.00/43.15  | | Case 1:
% 232.00/43.15  | | | 
% 232.00/43.15  | | |   (44)  all_57_5 = e3 & op(e2, e1) = e3
% 232.00/43.15  | | | 
% 232.00/43.15  | | | ALPHA: (44) implies:
% 232.00/43.15  | | |   (45)  all_57_5 = e3
% 232.00/43.15  | | | 
% 232.00/43.15  | | | BETA: splitting (17) gives:
% 232.00/43.15  | | | 
% 232.00/43.15  | | | Case 1:
% 232.00/43.15  | | | | 
% 232.00/43.15  | | | |   (46)  all_57_12 = e0 & op(e0, e3) = e0
% 232.00/43.15  | | | | 
% 232.00/43.15  | | | | ALPHA: (46) implies:
% 232.00/43.15  | | | |   (47)  all_57_12 = e0
% 232.00/43.15  | | | |   (48)  op(e0, e3) = e0
% 232.00/43.15  | | | | 
% 232.00/43.15  | | | | BETA: splitting (7) gives:
% 232.00/43.15  | | | | 
% 232.00/43.15  | | | | Case 1:
% 232.00/43.15  | | | | | 
% 232.00/43.15  | | | | |   (49)   ~ (all_24_0 = e2) & op(all_24_1, e1) = all_24_0 & op(e1, e0)
% 232.00/43.15  | | | | |         = all_24_1 & $i(all_24_0) & $i(all_24_1)
% 232.00/43.15  | | | | | 
% 232.00/43.15  | | | | | ALPHA: (49) implies:
% 232.00/43.15  | | | | |   (50)  op(e1, e0) = all_24_1
% 232.00/43.15  | | | | | 
% 232.00/43.15  | | | | | BETA: splitting (6) gives:
% 232.00/43.15  | | | | | 
% 232.00/43.15  | | | | | Case 1:
% 232.00/43.15  | | | | | | 
% 232.00/43.15  | | | | | |   (51)  all_55_7 = e2
% 232.00/43.15  | | | | | | 
% 232.00/43.15  | | | | | | REF_CLOSE: (8), (40), (51) are inconsistent by sub-proof #2171.
% 232.00/43.15  | | | | | | 
% 232.00/43.15  | | | | | Case 2:
% 232.00/43.15  | | | | | | 
% 232.00/43.15  | | | | | |   (52)   ~ (all_55_7 = e2)
% 232.00/43.15  | | | | | |   (53)  all_55_7 = e1 | all_55_7 = e0
% 232.00/43.15  | | | | | | 
% 232.00/43.15  | | | | | | BETA: splitting (24) gives:
% 232.00/43.15  | | | | | | 
% 232.00/43.15  | | | | | | Case 1:
% 232.00/43.15  | | | | | | | 
% 232.00/43.15  | | | | | | |   (54)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6
% 232.00/43.15  | | | | | | |           = e0 & op(all_52_1, all_52_1) = e3 & op(all_52_3,
% 232.00/43.15  | | | | | | |             all_52_3) = e2 & op(all_52_5, all_52_5) = e1 &
% 232.00/43.15  | | | | | | |           op(all_52_7, all_52_7) = e0 & op(e3, e3) = all_52_1 &
% 232.00/43.15  | | | | | | |           op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 232.00/43.15  | | | | | | |             e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) &
% 232.00/43.15  | | | | | | |           $i(all_52_5) & $i(all_52_7)) | (all_52_8 = e3 &
% 232.00/43.15  | | | | | | |           all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0 &
% 232.00/43.15  | | | | | | |           op(all_52_9, all_52_9) = e3 & op(all_52_11, all_52_11) =
% 232.00/43.15  | | | | | | |           e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 232.00/43.15  | | | | | | |             all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) =
% 232.00/43.15  | | | | | | |           all_52_11 & op(e2, e1) = all_52_13 & op(e2, e0) =
% 232.00/43.15  | | | | | | |           all_52_15 & $i(all_52_9) & $i(all_52_11) & $i(all_52_13)
% 232.00/43.15  | | | | | | |           & $i(all_52_15))
% 232.00/43.15  | | | | | | | 
% 232.00/43.15  | | | | | | | BETA: splitting (54) gives:
% 232.00/43.15  | | | | | | | 
% 232.00/43.15  | | | | | | | Case 1:
% 232.00/43.15  | | | | | | | | 
% 232.00/43.15  | | | | | | | |   (55)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6
% 232.00/43.15  | | | | | | | |         = e0 & op(all_52_1, all_52_1) = e3 & op(all_52_3,
% 232.00/43.15  | | | | | | | |           all_52_3) = e2 & op(all_52_5, all_52_5) = e1 &
% 232.00/43.15  | | | | | | | |         op(all_52_7, all_52_7) = e0 & op(e3, e3) = all_52_1 &
% 232.00/43.15  | | | | | | | |         op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 232.00/43.15  | | | | | | | |           e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) &
% 232.00/43.15  | | | | | | | |         $i(all_52_5) & $i(all_52_7)
% 232.00/43.15  | | | | | | | | 
% 232.00/43.15  | | | | | | | | ALPHA: (55) implies:
% 232.00/43.15  | | | | | | | |   (56)  op(e3, e0) = all_52_7
% 232.00/43.15  | | | | | | | |   (57)  op(all_52_7, all_52_7) = e0
% 232.00/43.15  | | | | | | | | 
% 232.00/43.15  | | | | | | | | BETA: splitting (53) gives:
% 232.00/43.15  | | | | | | | | 
% 232.00/43.15  | | | | | | | | Case 1:
% 232.00/43.15  | | | | | | | | | 
% 232.00/43.15  | | | | | | | | |   (58)  all_55_7 = e1
% 232.00/43.15  | | | | | | | | | 
% 232.00/43.15  | | | | | | | | | REF_CLOSE: (4), (40), (58) are inconsistent by sub-proof
% 232.00/43.15  | | | | | | | | |            #1970.
% 232.00/43.15  | | | | | | | | | 
% 232.00/43.15  | | | | | | | | Case 2:
% 232.00/43.15  | | | | | | | | | 
% 232.00/43.15  | | | | | | | | |   (59)  all_55_7 = e0
% 232.00/43.15  | | | | | | | | | 
% 232.00/43.15  | | | | | | | | | COMBINE_EQS: (40), (59) imply:
% 232.00/43.15  | | | | | | | | |   (60)  all_53_13 = e0
% 232.00/43.15  | | | | | | | | | 
% 232.00/43.15  | | | | | | | | | SIMP: (60) implies:
% 232.00/43.15  | | | | | | | | |   (61)  all_53_13 = e0
% 232.00/43.15  | | | | | | | | | 
% 232.00/43.15  | | | | | | | | | REDUCE: (8), (61) imply:
% 232.00/43.15  | | | | | | | | |   (62)   ~ (e2 = e0)
% 232.00/43.15  | | | | | | | | | 
% 232.00/43.15  | | | | | | | | | GROUND_INST: instantiating (5) with e2, all_52_7, e0, e3,
% 232.00/43.15  | | | | | | | | |              simplifying with (14), (56) gives:
% 232.00/43.15  | | | | | | | | |   (63)  all_52_7 = e2
% 232.00/43.15  | | | | | | | | | 
% 232.00/43.15  | | | | | | | | | REDUCE: (57), (63) imply:
% 232.00/43.15  | | | | | | | | |   (64)  op(e2, e2) = e0
% 232.00/43.15  | | | | | | | | | 
% 232.00/43.15  | | | | | | | | | REF_CLOSE: (5), (23), (26), (64) are inconsistent by sub-proof
% 232.00/43.15  | | | | | | | | |            #2472.
% 232.00/43.15  | | | | | | | | | 
% 232.00/43.15  | | | | | | | | End of split
% 232.00/43.15  | | | | | | | | 
% 232.00/43.15  | | | | | | | Case 2:
% 232.00/43.15  | | | | | | | | 
% 232.00/43.15  | | | | | | | |   (65)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 232.00/43.15  | | | | | | | |         all_52_14 = e0 & op(all_52_9, all_52_9) = e3 &
% 232.00/43.15  | | | | | | | |         op(all_52_11, all_52_11) = e2 & op(all_52_13, all_52_13)
% 232.00/43.15  | | | | | | | |         = e1 & op(all_52_15, all_52_15) = e0 & op(e2, e3) =
% 232.00/43.15  | | | | | | | |         all_52_9 & op(e2, e2) = all_52_11 & op(e2, e1) =
% 232.00/43.15  | | | | | | | |         all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 232.00/43.15  | | | | | | | |         $i(all_52_11) & $i(all_52_13) & $i(all_52_15)
% 232.00/43.15  | | | | | | | | 
% 232.00/43.15  | | | | | | | | ALPHA: (65) implies:
% 232.00/43.15  | | | | | | | |   (66)  op(e2, e0) = all_52_15
% 232.00/43.15  | | | | | | | |   (67)  op(all_52_15, all_52_15) = e0
% 232.00/43.15  | | | | | | | | 
% 232.00/43.15  | | | | | | | | BETA: splitting (53) gives:
% 232.00/43.15  | | | | | | | | 
% 232.00/43.15  | | | | | | | | Case 1:
% 232.00/43.15  | | | | | | | | | 
% 232.00/43.15  | | | | | | | | |   (68)  all_55_7 = e1
% 232.00/43.15  | | | | | | | | | 
% 232.00/43.15  | | | | | | | | | REF_CLOSE: (4), (40), (68) are inconsistent by sub-proof
% 232.00/43.15  | | | | | | | | |            #1970.
% 232.00/43.15  | | | | | | | | | 
% 232.00/43.15  | | | | | | | | Case 2:
% 232.00/43.15  | | | | | | | | | 
% 232.00/43.15  | | | | | | | | |   (69)  all_55_7 = e0
% 232.00/43.15  | | | | | | | | | 
% 232.00/43.15  | | | | | | | | | COMBINE_EQS: (40), (69) imply:
% 232.00/43.16  | | | | | | | | |   (70)  all_53_13 = e0
% 232.00/43.16  | | | | | | | | | 
% 232.00/43.16  | | | | | | | | | SIMP: (70) implies:
% 232.00/43.16  | | | | | | | | |   (71)  all_53_13 = e0
% 232.00/43.16  | | | | | | | | | 
% 232.00/43.16  | | | | | | | | | REDUCE: (4), (71) imply:
% 232.00/43.16  | | | | | | | | |   (72)   ~ (e1 = e0)
% 232.00/43.16  | | | | | | | | | 
% 232.00/43.16  | | | | | | | | | REDUCE: (33), (71) imply:
% 232.00/43.16  | | | | | | | | |   (73)  op(e2, e0) = e0
% 232.00/43.16  | | | | | | | | | 
% 232.00/43.16  | | | | | | | | | GROUND_INST: instantiating (5) with e0, all_52_15, e0, e2,
% 232.00/43.16  | | | | | | | | |              simplifying with (66), (73) gives:
% 232.00/43.16  | | | | | | | | |   (74)  all_52_15 = e0
% 232.00/43.16  | | | | | | | | | 
% 232.00/43.16  | | | | | | | | | REDUCE: (67), (74) imply:
% 232.00/43.16  | | | | | | | | |   (75)  op(e0, e0) = e0
% 232.00/43.16  | | | | | | | | | 
% 232.00/43.16  | | | | | | | | | REF_CLOSE: (5), (27), (32), (75) are inconsistent by sub-proof
% 232.00/43.16  | | | | | | | | |            #2290.
% 232.00/43.16  | | | | | | | | | 
% 232.00/43.16  | | | | | | | | End of split
% 232.00/43.16  | | | | | | | | 
% 232.00/43.16  | | | | | | | End of split
% 232.00/43.16  | | | | | | | 
% 232.00/43.16  | | | | | | Case 2:
% 232.00/43.16  | | | | | | | 
% 232.00/43.16  | | | | | | |   (76)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 232.00/43.16  | | | | | | |           all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 232.00/43.16  | | | | | | |           op(all_52_19, all_52_19) = e2 & op(all_52_21, all_52_21)
% 232.00/43.16  | | | | | | |           = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 232.00/43.16  | | | | | | |           all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) =
% 232.00/43.16  | | | | | | |           all_52_21 & op(e1, e0) = all_52_23 & $i(all_52_17) &
% 232.00/43.16  | | | | | | |           $i(all_52_19) & $i(all_52_21) & $i(all_52_23)) |
% 232.00/43.16  | | | | | | |         (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 232.00/43.16  | | | | | | |           all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 232.00/43.16  | | | | | | |           op(all_52_27, all_52_27) = e2 & op(all_52_29, all_52_29)
% 232.00/43.16  | | | | | | |           = e1 & op(all_52_31, all_52_31) = e0 & op(e0, e3) =
% 232.00/43.16  | | | | | | |           all_52_25 & op(e0, e2) = all_52_27 & op(e0, e1) =
% 232.00/43.16  | | | | | | |           all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 232.00/43.16  | | | | | | |           $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 232.00/43.16  | | | | | | | 
% 232.00/43.16  | | | | | | | BETA: splitting (76) gives:
% 232.00/43.16  | | | | | | | 
% 232.00/43.16  | | | | | | | Case 1:
% 232.00/43.16  | | | | | | | | 
% 232.00/43.16  | | | | | | | |   (77)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 &
% 232.00/43.16  | | | | | | | |         all_52_22 = e0 & op(all_52_17, all_52_17) = e3 &
% 232.00/43.16  | | | | | | | |         op(all_52_19, all_52_19) = e2 & op(all_52_21, all_52_21)
% 232.00/43.16  | | | | | | | |         = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 232.00/43.16  | | | | | | | |         all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) =
% 232.00/43.16  | | | | | | | |         all_52_21 & op(e1, e0) = all_52_23 & $i(all_52_17) &
% 232.00/43.16  | | | | | | | |         $i(all_52_19) & $i(all_52_21) & $i(all_52_23)
% 232.00/43.16  | | | | | | | | 
% 232.00/43.16  | | | | | | | | ALPHA: (77) implies:
% 232.00/43.16  | | | | | | | |   (78)  op(e1, e0) = all_52_23
% 232.00/43.16  | | | | | | | |   (79)  op(all_52_23, all_52_23) = e0
% 232.00/43.16  | | | | | | | | 
% 232.00/43.16  | | | | | | | | BETA: splitting (53) gives:
% 232.00/43.16  | | | | | | | | 
% 232.00/43.16  | | | | | | | | Case 1:
% 232.00/43.16  | | | | | | | | | 
% 232.00/43.16  | | | | | | | | |   (80)  all_55_7 = e1
% 232.00/43.16  | | | | | | | | | 
% 232.00/43.16  | | | | | | | | | REF_CLOSE: (4), (40), (80) are inconsistent by sub-proof
% 232.00/43.16  | | | | | | | | |            #1970.
% 232.00/43.16  | | | | | | | | | 
% 232.00/43.16  | | | | | | | | Case 2:
% 232.00/43.16  | | | | | | | | | 
% 232.00/43.16  | | | | | | | | |   (81)  all_55_7 = e0
% 232.00/43.16  | | | | | | | | | 
% 232.00/43.16  | | | | | | | | | COMBINE_EQS: (40), (81) imply:
% 232.00/43.16  | | | | | | | | |   (82)  all_53_13 = e0
% 232.00/43.16  | | | | | | | | | 
% 232.00/43.16  | | | | | | | | | SIMP: (82) implies:
% 232.00/43.16  | | | | | | | | |   (83)  all_53_13 = e0
% 232.00/43.16  | | | | | | | | | 
% 232.00/43.16  | | | | | | | | | REDUCE: (10), (83) imply:
% 232.00/43.16  | | | | | | | | |   (84)   ~ (e3 = e0)
% 232.00/43.16  | | | | | | | | | 
% 232.00/43.16  | | | | | | | | | GROUND_INST: instantiating (5) with e3, all_34_1, e0, e1,
% 232.00/43.16  | | | | | | | | |              simplifying with (18), (39) gives:
% 232.00/43.16  | | | | | | | | |   (85)  all_34_1 = e3
% 232.00/43.16  | | | | | | | | | 
% 232.00/43.16  | | | | | | | | | GROUND_INST: instantiating (5) with all_34_1, all_52_23, e0,
% 232.00/43.16  | | | | | | | | |              e1, simplifying with (18), (78) gives:
% 232.00/43.16  | | | | | | | | |   (86)  all_52_23 = all_34_1
% 232.00/43.16  | | | | | | | | | 
% 232.00/43.16  | | | | | | | | | GROUND_INST: instantiating (5) with all_24_1, all_52_23, e0,
% 232.00/43.16  | | | | | | | | |              e1, simplifying with (50), (78) gives:
% 232.00/43.16  | | | | | | | | |   (87)  all_52_23 = all_24_1
% 232.00/43.16  | | | | | | | | | 
% 232.00/43.16  | | | | | | | | | COMBINE_EQS: (86), (87) imply:
% 232.00/43.16  | | | | | | | | |   (88)  all_34_1 = all_24_1
% 232.00/43.16  | | | | | | | | | 
% 232.00/43.16  | | | | | | | | | SIMP: (88) implies:
% 232.00/43.16  | | | | | | | | |   (89)  all_34_1 = all_24_1
% 232.00/43.16  | | | | | | | | | 
% 232.00/43.16  | | | | | | | | | COMBINE_EQS: (85), (89) imply:
% 232.00/43.16  | | | | | | | | |   (90)  all_24_1 = e3
% 232.00/43.16  | | | | | | | | | 
% 232.00/43.16  | | | | | | | | | COMBINE_EQS: (87), (90) imply:
% 232.00/43.16  | | | | | | | | |   (91)  all_52_23 = e3
% 232.00/43.16  | | | | | | | | | 
% 232.00/43.16  | | | | | | | | | REDUCE: (79), (91) imply:
% 232.00/43.16  | | | | | | | | |   (92)  op(e3, e3) = e0
% 232.00/43.16  | | | | | | | | | 
% 232.00/43.16  | | | | | | | | | REF_CLOSE: (3), (5), (12), (15), (20), (25), (35), (41), (92)
% 232.00/43.16  | | | | | | | | |            are inconsistent by sub-proof #2280.
% 232.00/43.16  | | | | | | | | | 
% 232.00/43.16  | | | | | | | | End of split
% 232.00/43.16  | | | | | | | | 
% 232.00/43.16  | | | | | | | Case 2:
% 232.00/43.16  | | | | | | | | 
% 232.00/43.16  | | | | | | | |   (93)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 232.00/43.16  | | | | | | | |         all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 232.00/43.16  | | | | | | | |         op(all_52_27, all_52_27) = e2 & op(all_52_29, all_52_29)
% 232.00/43.16  | | | | | | | |         = e1 & op(all_52_31, all_52_31) = e0 & op(e0, e3) =
% 232.00/43.16  | | | | | | | |         all_52_25 & op(e0, e2) = all_52_27 & op(e0, e1) =
% 232.00/43.16  | | | | | | | |         all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 232.00/43.16  | | | | | | | |         $i(all_52_27) & $i(all_52_29) & $i(all_52_31)
% 232.00/43.16  | | | | | | | | 
% 232.00/43.16  | | | | | | | | ALPHA: (93) implies:
% 232.00/43.16  | | | | | | | |   (94)  op(e0, e0) = all_52_31
% 232.00/43.16  | | | | | | | |   (95)  op(e0, e3) = all_52_25
% 232.00/43.16  | | | | | | | |   (96)  op(all_52_25, all_52_25) = e3
% 232.00/43.16  | | | | | | | | 
% 232.00/43.16  | | | | | | | | REF_CLOSE: (3), (5), (11), (12), (16), (19), (21), (27), (29),
% 232.00/43.16  | | | | | | | |            (31), (32), (37), (47), (48), (94), (95), (96) are
% 232.00/43.16  | | | | | | | |            inconsistent by sub-proof #1962.
% 232.00/43.16  | | | | | | | | 
% 232.00/43.16  | | | | | | | End of split
% 232.00/43.16  | | | | | | | 
% 232.00/43.16  | | | | | | End of split
% 232.00/43.16  | | | | | | 
% 232.00/43.16  | | | | | End of split
% 232.00/43.16  | | | | | 
% 232.00/43.16  | | | | Case 2:
% 232.00/43.16  | | | | | 
% 232.00/43.16  | | | | |   (97)   ~ (all_24_1 = e3) & op(e1, e0) = all_24_1 & $i(all_24_1)
% 232.00/43.16  | | | | | 
% 232.00/43.16  | | | | | ALPHA: (97) implies:
% 232.00/43.16  | | | | |   (98)   ~ (all_24_1 = e3)
% 232.00/43.16  | | | | |   (99)  op(e1, e0) = all_24_1
% 232.00/43.16  | | | | | 
% 232.00/43.16  | | | | | REF_CLOSE: (5), (18), (39), (98), (99) are inconsistent by sub-proof
% 232.00/43.16  | | | | |            #1961.
% 232.00/43.16  | | | | | 
% 232.00/43.16  | | | | End of split
% 232.00/43.16  | | | | 
% 232.00/43.16  | | | Case 2:
% 232.00/43.16  | | | | 
% 232.00/43.16  | | | |   (100)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 232.00/43.16  | | | |              e1) = e0)
% 232.00/43.16  | | | | 
% 232.00/43.16  | | | | BETA: splitting (100) gives:
% 232.00/43.16  | | | | 
% 232.00/43.16  | | | | Case 1:
% 232.00/43.16  | | | | | 
% 232.00/43.16  | | | | |   (101)  all_57_13 = e0 & op(e0, e2) = e0
% 232.00/43.16  | | | | | 
% 232.00/43.16  | | | | | ALPHA: (101) implies:
% 232.00/43.16  | | | | |   (102)  all_57_13 = e0
% 232.00/43.16  | | | | | 
% 232.00/43.16  | | | | | COMBINE_EQS: (28), (102) imply:
% 232.00/43.16  | | | | |   (103)  e3 = e0
% 232.00/43.16  | | | | | 
% 232.00/43.16  | | | | | COMBINE_EQS: (45), (103) imply:
% 232.00/43.16  | | | | |   (104)  all_57_5 = e0
% 232.00/43.16  | | | | | 
% 232.00/43.16  | | | | | REF_CLOSE: (1), (5), (10), (11), (12), (26), (33), (34), (36), (104)
% 232.00/43.16  | | | | |            are inconsistent by sub-proof #2129.
% 232.00/43.16  | | | | | 
% 232.00/43.16  | | | | Case 2:
% 232.00/43.16  | | | | | 
% 232.00/43.16  | | | | |   (105)  all_57_14 = e0 & op(e0, e1) = e0
% 232.00/43.16  | | | | | 
% 232.00/43.16  | | | | | REF_CLOSE: (2), (3), (5), (9), (12), (13), (22), (23), (27), (30),
% 232.00/43.16  | | | | |            (31), (32), (37), (38), (105) are inconsistent by sub-proof
% 232.00/43.16  | | | | |            #1960.
% 232.00/43.16  | | | | | 
% 232.00/43.16  | | | | End of split
% 232.00/43.16  | | | | 
% 232.00/43.16  | | | End of split
% 232.00/43.16  | | | 
% 232.00/43.16  | | Case 2:
% 232.00/43.16  | | | 
% 232.00/43.16  | | |   (106)  all_57_10 = e3 & op(e2, e0) = e3
% 232.00/43.16  | | | 
% 232.00/43.16  | | | ALPHA: (106) implies:
% 232.00/43.16  | | |   (107)  op(e2, e0) = e3
% 232.00/43.16  | | | 
% 232.00/43.16  | | | REF_CLOSE: (5), (10), (33), (107) are inconsistent by sub-proof #2301.
% 232.00/43.16  | | | 
% 232.00/43.16  | | End of split
% 232.00/43.16  | | 
% 232.00/43.16  | End of split
% 232.00/43.16  | 
% 232.00/43.16  End of proof
% 232.00/43.16  
% 232.00/43.16  Sub-proof #1960 shows that the following formulas are inconsistent:
% 232.00/43.16  ----------------------------------------------------------------
% 232.00/43.16    (1)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 232.00/43.16         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 232.00/43.16    (2)   ~ (e3 = e1)
% 232.00/43.16    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.00/43.16           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.00/43.16    (4)   ~ (all_53_7 = e2)
% 232.00/43.16    (5)   ~ (e3 = e0)
% 232.00/43.16    (6)  op(e3, e3) = e3
% 232.00/43.16    (7)  all_57_6 = e2
% 232.00/43.16    (8)   ~ (e2 = e0)
% 232.00/43.16    (9)   ~ (e1 = e0)
% 232.00/43.16    (10)  op(e0, e2) = all_53_7
% 232.00/43.16    (11)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 232.00/43.16          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 232.00/43.16            e2)
% 232.00/43.16    (12)  op(e0, e0) = e1
% 232.00/43.16    (13)   ~ (e2 = e1)
% 232.00/43.16    (14)  all_57_14 = e0 & op(e0, e1) = e0
% 232.00/43.16    (15)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 232.00/43.16          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 232.00/43.16  
% 232.00/43.16  Begin of proof
% 232.00/43.16  | 
% 232.00/43.16  | ALPHA: (14) implies:
% 232.00/43.16  |   (16)  all_57_14 = e0
% 232.00/43.16  | 
% 232.00/43.16  | BETA: splitting (11) gives:
% 232.00/43.16  | 
% 232.00/43.16  | Case 1:
% 232.00/43.16  | | 
% 232.00/43.16  | |   (17)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 232.00/43.16  | |           e2)
% 232.00/43.16  | | 
% 232.00/43.16  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (13), (15),
% 232.00/43.16  | |            (17) are inconsistent by sub-proof #2082.
% 232.00/43.16  | | 
% 232.00/43.16  | Case 2:
% 232.00/43.16  | | 
% 232.00/43.16  | |   (18)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 232.00/43.16  | |           e2)
% 232.00/43.16  | | 
% 232.00/43.16  | | BETA: splitting (18) gives:
% 232.00/43.16  | | 
% 232.00/43.16  | | Case 1:
% 232.00/43.16  | | | 
% 232.00/43.16  | | |   (19)  all_57_14 = e2 & op(e0, e1) = e2
% 232.00/43.16  | | | 
% 232.00/43.16  | | | ALPHA: (19) implies:
% 232.00/43.16  | | |   (20)  all_57_14 = e2
% 232.00/43.16  | | | 
% 232.00/43.16  | | | REF_CLOSE: (8), (16), (20) are inconsistent by sub-proof #2422.
% 232.00/43.16  | | | 
% 232.00/43.16  | | Case 2:
% 232.00/43.16  | | | 
% 232.00/43.16  | | |   (21)  all_57_15 = e2 & op(e0, e0) = e2
% 232.00/43.16  | | | 
% 232.00/43.16  | | | ALPHA: (21) implies:
% 232.00/43.16  | | |   (22)  op(e0, e0) = e2
% 232.00/43.16  | | | 
% 232.00/43.16  | | | REF_CLOSE: (3), (12), (13), (22) are inconsistent by sub-proof #2177.
% 232.00/43.16  | | | 
% 232.00/43.16  | | End of split
% 232.00/43.16  | | 
% 232.00/43.16  | End of split
% 232.00/43.16  | 
% 232.00/43.16  End of proof
% 232.00/43.16  
% 232.00/43.16  Sub-proof #1961 shows that the following formulas are inconsistent:
% 232.00/43.16  ----------------------------------------------------------------
% 232.00/43.16    (1)  op(e1, e0) = all_24_1
% 232.00/43.16    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.00/43.16           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.00/43.16    (3)  op(e1, e0) = all_34_1
% 232.00/43.16    (4)  op(e1, e0) = e3
% 232.00/43.16    (5)   ~ (all_24_1 = e3)
% 232.00/43.16  
% 232.00/43.16  Begin of proof
% 232.00/43.16  | 
% 232.00/43.16  | GROUND_INST: instantiating (2) with e3, all_34_1, e0, e1, simplifying with
% 232.00/43.16  |              (3), (4) gives:
% 232.00/43.16  |   (6)  all_34_1 = e3
% 232.00/43.16  | 
% 232.00/43.16  | GROUND_INST: instantiating (2) with all_24_1, all_34_1, e0, e1, simplifying
% 232.00/43.16  |              with (1), (3) gives:
% 232.00/43.16  |   (7)  all_34_1 = all_24_1
% 232.00/43.16  | 
% 232.00/43.16  | COMBINE_EQS: (6), (7) imply:
% 232.08/43.16  |   (8)  all_24_1 = e3
% 232.08/43.16  | 
% 232.08/43.16  | SIMP: (8) implies:
% 232.08/43.16  |   (9)  all_24_1 = e3
% 232.08/43.16  | 
% 232.08/43.16  | REDUCE: (5), (9) imply:
% 232.08/43.16  |   (10)  $false
% 232.08/43.16  | 
% 232.08/43.16  | CLOSE: (10) is inconsistent.
% 232.08/43.16  | 
% 232.08/43.16  End of proof
% 232.08/43.16  
% 232.08/43.16  Sub-proof #1962 shows that the following formulas are inconsistent:
% 232.08/43.16  ----------------------------------------------------------------
% 232.08/43.16    (1)  all_57_12 = e0
% 232.08/43.16    (2)   ~ (e3 = e1)
% 232.08/43.16    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.08/43.16           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.08/43.16    (4)  op(e0, e3) = e0
% 232.08/43.16    (5)  op(e0, e3) = all_52_25
% 232.08/43.16    (6)   ~ (e3 = e2)
% 232.08/43.16    (7)   ~ (e3 = e0)
% 232.08/43.16    (8)  op(e0, e3) = all_53_3
% 232.08/43.16    (9)   ~ (all_53_3 = e2)
% 232.08/43.16    (10)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 232.08/43.16          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 232.08/43.16            e1)
% 232.08/43.16    (11)  op(e0, e0) = all_52_31
% 232.08/43.16    (12)  op(all_52_25, all_52_25) = e3
% 232.08/43.16    (13)   ~ (e1 = e0)
% 232.08/43.16    (14)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 232.08/43.16          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 232.08/43.16            e3)
% 232.08/43.16    (15)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 232.08/43.16          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 232.08/43.16            e2)
% 232.08/43.16    (16)  op(e0, e0) = e1
% 232.08/43.16    (17)   ~ (e2 = e1)
% 232.08/43.16  
% 232.08/43.16  Begin of proof
% 232.08/43.16  | 
% 232.08/43.16  | BETA: splitting (10) gives:
% 232.08/43.16  | 
% 232.08/43.16  | Case 1:
% 232.08/43.16  | | 
% 232.08/43.16  | |   (18)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 232.08/43.16  | |           e1)
% 232.08/43.16  | | 
% 232.08/43.16  | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (9), (13), (14), (15), (16), (17),
% 232.08/43.16  | |            (18) are inconsistent by sub-proof #1969.
% 232.08/43.16  | | 
% 232.08/43.16  | Case 2:
% 232.08/43.16  | | 
% 232.08/43.16  | |   (19)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 232.08/43.16  | |           e1)
% 232.08/43.16  | | 
% 232.08/43.16  | | BETA: splitting (19) gives:
% 232.08/43.16  | | 
% 232.08/43.16  | | Case 1:
% 232.08/43.16  | | | 
% 232.08/43.16  | | |   (20)  all_57_14 = e1 & op(e0, e1) = e1
% 232.08/43.16  | | | 
% 232.08/43.16  | | | ALPHA: (20) implies:
% 232.08/43.16  | | |   (21)  all_57_14 = e1
% 232.08/43.16  | | | 
% 232.08/43.16  | | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (9), (14), (15), (16), (17), (21)
% 232.08/43.16  | | |            are inconsistent by sub-proof #1964.
% 232.08/43.16  | | | 
% 232.08/43.16  | | Case 2:
% 232.08/43.16  | | | 
% 232.08/43.16  | | |   (22)  all_57_15 = e1 & op(e0, e0) = e1
% 232.08/43.16  | | | 
% 232.08/43.16  | | | REF_CLOSE: (2), (3), (4), (5), (11), (12), (22) are inconsistent by
% 232.08/43.16  | | |            sub-proof #1963.
% 232.08/43.16  | | | 
% 232.08/43.16  | | End of split
% 232.08/43.16  | | 
% 232.08/43.16  | End of split
% 232.08/43.16  | 
% 232.08/43.16  End of proof
% 232.08/43.16  
% 232.08/43.16  Sub-proof #1963 shows that the following formulas are inconsistent:
% 232.08/43.16  ----------------------------------------------------------------
% 232.08/43.16    (1)   ~ (e3 = e1)
% 232.08/43.16    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.08/43.16           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.08/43.16    (3)  op(e0, e3) = e0
% 232.08/43.16    (4)  all_57_15 = e1 & op(e0, e0) = e1
% 232.08/43.16    (5)  op(e0, e3) = all_52_25
% 232.08/43.16    (6)  op(e0, e0) = all_52_31
% 232.08/43.16    (7)  op(all_52_25, all_52_25) = e3
% 232.08/43.16  
% 232.08/43.16  Begin of proof
% 232.08/43.16  | 
% 232.08/43.16  | ALPHA: (4) implies:
% 232.08/43.16  |   (8)  op(e0, e0) = e1
% 232.08/43.16  | 
% 232.08/43.16  | GROUND_INST: instantiating (2) with e1, all_52_31, e0, e0, simplifying with
% 232.08/43.16  |              (6), (8) gives:
% 232.08/43.16  |   (9)  all_52_31 = e1
% 232.08/43.16  | 
% 232.08/43.16  | GROUND_INST: instantiating (2) with e0, all_52_25, e3, e0, simplifying with
% 232.08/43.16  |              (3), (5) gives:
% 232.08/43.16  |   (10)  all_52_25 = e0
% 232.08/43.16  | 
% 232.08/43.16  | REDUCE: (7), (10) imply:
% 232.08/43.16  |   (11)  op(e0, e0) = e3
% 232.08/43.16  | 
% 232.08/43.16  | REF_CLOSE: (1), (2), (8), (11) are inconsistent by sub-proof #2183.
% 232.08/43.16  | 
% 232.08/43.16  End of proof
% 232.08/43.16  
% 232.08/43.16  Sub-proof #1964 shows that the following formulas are inconsistent:
% 232.08/43.16  ----------------------------------------------------------------
% 232.08/43.16    (1)  all_57_12 = e0
% 232.08/43.16    (2)   ~ (e3 = e1)
% 232.08/43.16    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.08/43.16           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.08/43.16    (4)   ~ (e3 = e2)
% 232.08/43.16    (5)   ~ (e3 = e0)
% 232.08/43.16    (6)  op(e0, e3) = all_53_3
% 232.08/43.16    (7)   ~ (all_53_3 = e2)
% 232.08/43.16    (8)  all_57_14 = e1
% 232.08/43.16    (9)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 232.08/43.16         (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 232.08/43.16    (10)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 232.08/43.16          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 232.08/43.16            e2)
% 232.08/43.16    (11)  op(e0, e0) = e1
% 232.08/43.16    (12)   ~ (e2 = e1)
% 232.08/43.16  
% 232.08/43.16  Begin of proof
% 232.08/43.16  | 
% 232.08/43.16  | BETA: splitting (9) gives:
% 232.08/43.16  | 
% 232.08/43.16  | Case 1:
% 232.08/43.16  | | 
% 232.08/43.16  | |   (13)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 232.08/43.16  | |           e3)
% 232.08/43.16  | | 
% 232.08/43.16  | | BETA: splitting (13) gives:
% 232.08/43.16  | | 
% 232.08/43.16  | | Case 1:
% 232.08/43.16  | | | 
% 232.08/43.16  | | |   (14)  all_57_12 = e3 & op(e0, e3) = e3
% 232.08/43.16  | | | 
% 232.08/43.16  | | | REF_CLOSE: (1), (5), (14) are inconsistent by sub-proof #1978.
% 232.08/43.16  | | | 
% 232.08/43.16  | | Case 2:
% 232.08/43.16  | | | 
% 232.08/43.16  | | |   (15)  all_57_13 = e3 & op(e0, e2) = e3
% 232.08/43.16  | | | 
% 232.08/43.16  | | | ALPHA: (15) implies:
% 232.08/43.16  | | |   (16)  all_57_13 = e3
% 232.08/43.16  | | | 
% 232.08/43.16  | | | REF_CLOSE: (3), (4), (6), (7), (8), (10), (11), (12), (16) are
% 232.08/43.16  | | |            inconsistent by sub-proof #1967.
% 232.08/43.16  | | | 
% 232.08/43.16  | | End of split
% 232.08/43.16  | | 
% 232.08/43.16  | Case 2:
% 232.08/43.16  | | 
% 232.08/43.16  | |   (17)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 232.08/43.16  | |           e3)
% 232.08/43.16  | | 
% 232.08/43.16  | | REF_CLOSE: (2), (3), (8), (11), (17) are inconsistent by sub-proof #1965.
% 232.08/43.16  | | 
% 232.08/43.16  | End of split
% 232.08/43.16  | 
% 232.08/43.16  End of proof
% 232.08/43.16  
% 232.08/43.16  Sub-proof #1965 shows that the following formulas are inconsistent:
% 232.08/43.16  ----------------------------------------------------------------
% 232.08/43.16    (1)   ~ (e3 = e1)
% 232.08/43.16    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.08/43.16           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.08/43.16    (3)  all_57_14 = e1
% 232.08/43.16    (4)  op(e0, e0) = e1
% 232.08/43.16    (5)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 232.08/43.16  
% 232.08/43.16  Begin of proof
% 232.08/43.16  | 
% 232.08/43.16  | BETA: splitting (5) gives:
% 232.08/43.16  | 
% 232.08/43.16  | Case 1:
% 232.08/43.16  | | 
% 232.08/43.16  | |   (6)  all_57_14 = e3 & op(e0, e1) = e3
% 232.08/43.16  | | 
% 232.08/43.16  | | REF_CLOSE: (1), (3), (6) are inconsistent by sub-proof #1966.
% 232.08/43.16  | | 
% 232.08/43.16  | Case 2:
% 232.08/43.16  | | 
% 232.08/43.16  | |   (7)  all_57_15 = e3 & op(e0, e0) = e3
% 232.08/43.16  | | 
% 232.08/43.16  | | ALPHA: (7) implies:
% 232.08/43.16  | |   (8)  op(e0, e0) = e3
% 232.08/43.16  | | 
% 232.08/43.16  | | REF_CLOSE: (1), (2), (4), (8) are inconsistent by sub-proof #2183.
% 232.08/43.16  | | 
% 232.08/43.16  | End of split
% 232.08/43.16  | 
% 232.08/43.16  End of proof
% 232.08/43.16  
% 232.08/43.16  Sub-proof #1966 shows that the following formulas are inconsistent:
% 232.08/43.16  ----------------------------------------------------------------
% 232.08/43.16    (1)  all_57_14 = e3 & op(e0, e1) = e3
% 232.08/43.16    (2)  all_57_14 = e1
% 232.08/43.16    (3)   ~ (e3 = e1)
% 232.08/43.16  
% 232.08/43.16  Begin of proof
% 232.08/43.16  | 
% 232.08/43.16  | ALPHA: (1) implies:
% 232.08/43.16  |   (4)  all_57_14 = e3
% 232.08/43.16  | 
% 232.08/43.16  | COMBINE_EQS: (2), (4) imply:
% 232.08/43.16  |   (5)  e3 = e1
% 232.08/43.16  | 
% 232.08/43.16  | REDUCE: (3), (5) imply:
% 232.08/43.16  |   (6)  $false
% 232.08/43.16  | 
% 232.08/43.16  | CLOSE: (6) is inconsistent.
% 232.08/43.16  | 
% 232.08/43.16  End of proof
% 232.08/43.16  
% 232.08/43.16  Sub-proof #1967 shows that the following formulas are inconsistent:
% 232.08/43.16  ----------------------------------------------------------------
% 232.08/43.16    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.08/43.16           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.08/43.16    (2)   ~ (e3 = e2)
% 232.08/43.16    (3)  op(e0, e3) = all_53_3
% 232.08/43.16    (4)   ~ (all_53_3 = e2)
% 232.08/43.16    (5)  all_57_14 = e1
% 232.08/43.16    (6)  all_57_13 = e3
% 232.08/43.16    (7)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2) |
% 232.08/43.16         (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 232.08/43.16    (8)  op(e0, e0) = e1
% 232.08/43.16    (9)   ~ (e2 = e1)
% 232.08/43.16  
% 232.08/43.16  Begin of proof
% 232.08/43.16  | 
% 232.08/43.16  | BETA: splitting (7) gives:
% 232.08/43.16  | 
% 232.08/43.16  | Case 1:
% 232.08/43.16  | | 
% 232.08/43.16  | |   (10)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 232.08/43.16  | |           e2)
% 232.08/43.16  | | 
% 232.08/43.16  | | BETA: splitting (10) gives:
% 232.08/43.16  | | 
% 232.08/43.16  | | Case 1:
% 232.08/43.16  | | | 
% 232.08/43.16  | | |   (11)  all_57_12 = e2 & op(e0, e3) = e2
% 232.08/43.16  | | | 
% 232.08/43.16  | | | ALPHA: (11) implies:
% 232.08/43.16  | | |   (12)  op(e0, e3) = e2
% 232.08/43.16  | | | 
% 232.08/43.16  | | | REF_CLOSE: (1), (3), (4), (12) are inconsistent by sub-proof #1980.
% 232.08/43.16  | | | 
% 232.08/43.16  | | Case 2:
% 232.08/43.16  | | | 
% 232.08/43.16  | | |   (13)  all_57_13 = e2 & op(e0, e2) = e2
% 232.08/43.16  | | | 
% 232.08/43.16  | | | ALPHA: (13) implies:
% 232.08/43.16  | | |   (14)  all_57_13 = e2
% 232.08/43.16  | | | 
% 232.08/43.16  | | | REF_CLOSE: (2), (6), (14) are inconsistent by sub-proof #2203.
% 232.08/43.16  | | | 
% 232.08/43.16  | | End of split
% 232.08/43.16  | | 
% 232.08/43.16  | Case 2:
% 232.08/43.16  | | 
% 232.08/43.16  | |   (15)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 232.08/43.16  | |           e2)
% 232.08/43.16  | | 
% 232.08/43.16  | | BETA: splitting (15) gives:
% 232.08/43.16  | | 
% 232.08/43.16  | | Case 1:
% 232.08/43.16  | | | 
% 232.08/43.16  | | |   (16)  all_57_14 = e2 & op(e0, e1) = e2
% 232.08/43.16  | | | 
% 232.08/43.16  | | | REF_CLOSE: (5), (9), (16) are inconsistent by sub-proof #1968.
% 232.08/43.16  | | | 
% 232.08/43.16  | | Case 2:
% 232.08/43.16  | | | 
% 232.08/43.16  | | |   (17)  all_57_15 = e2 & op(e0, e0) = e2
% 232.08/43.16  | | | 
% 232.08/43.16  | | | ALPHA: (17) implies:
% 232.08/43.16  | | |   (18)  op(e0, e0) = e2
% 232.08/43.16  | | | 
% 232.08/43.16  | | | REF_CLOSE: (1), (8), (9), (18) are inconsistent by sub-proof #2177.
% 232.08/43.16  | | | 
% 232.08/43.16  | | End of split
% 232.08/43.16  | | 
% 232.08/43.16  | End of split
% 232.08/43.16  | 
% 232.08/43.16  End of proof
% 232.08/43.16  
% 232.08/43.16  Sub-proof #1968 shows that the following formulas are inconsistent:
% 232.08/43.16  ----------------------------------------------------------------
% 232.08/43.16    (1)  all_57_14 = e2 & op(e0, e1) = e2
% 232.08/43.16    (2)  all_57_14 = e1
% 232.08/43.16    (3)   ~ (e2 = e1)
% 232.08/43.16  
% 232.08/43.16  Begin of proof
% 232.08/43.16  | 
% 232.08/43.16  | ALPHA: (1) implies:
% 232.08/43.16  |   (4)  all_57_14 = e2
% 232.08/43.16  | 
% 232.08/43.16  | COMBINE_EQS: (2), (4) imply:
% 232.08/43.16  |   (5)  e2 = e1
% 232.08/43.16  | 
% 232.08/43.16  | REDUCE: (3), (5) imply:
% 232.08/43.16  |   (6)  $false
% 232.08/43.16  | 
% 232.08/43.16  | CLOSE: (6) is inconsistent.
% 232.08/43.16  | 
% 232.08/43.16  End of proof
% 232.08/43.16  
% 232.08/43.16  Sub-proof #1969 shows that the following formulas are inconsistent:
% 232.08/43.16  ----------------------------------------------------------------
% 232.08/43.16    (1)  all_57_12 = e0
% 232.08/43.16    (2)   ~ (e3 = e1)
% 232.08/43.16    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.08/43.16           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.08/43.16    (4)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 232.08/43.16    (5)   ~ (e3 = e2)
% 232.08/43.16    (6)   ~ (e3 = e0)
% 232.08/43.16    (7)  op(e0, e3) = all_53_3
% 232.08/43.16    (8)   ~ (all_53_3 = e2)
% 232.08/43.16    (9)   ~ (e1 = e0)
% 232.08/43.16    (10)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 232.08/43.16          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 232.08/43.16            e3)
% 232.08/43.16    (11)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 232.08/43.16          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 232.08/43.16            e2)
% 232.08/43.16    (12)  op(e0, e0) = e1
% 232.08/43.16    (13)   ~ (e2 = e1)
% 232.08/43.16  
% 232.08/43.16  Begin of proof
% 232.08/43.16  | 
% 232.08/43.16  | BETA: splitting (4) gives:
% 232.08/43.16  | 
% 232.08/43.16  | Case 1:
% 232.08/43.16  | | 
% 232.08/43.16  | |   (14)  all_57_12 = e1 & op(e0, e3) = e1
% 232.08/43.16  | | 
% 232.08/43.16  | | REF_CLOSE: (1), (9), (14) are inconsistent by sub-proof #2328.
% 232.08/43.16  | | 
% 232.08/43.16  | Case 2:
% 232.08/43.16  | | 
% 232.08/43.16  | |   (15)  all_57_13 = e1 & op(e0, e2) = e1
% 232.08/43.16  | | 
% 232.08/43.16  | | ALPHA: (15) implies:
% 232.08/43.16  | |   (16)  all_57_13 = e1
% 232.08/43.16  | | 
% 232.08/43.16  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (10), (11), (12), (13), (16)
% 232.08/43.16  | |            are inconsistent by sub-proof #1975.
% 232.08/43.16  | | 
% 232.08/43.16  | End of split
% 232.08/43.16  | 
% 232.08/43.16  End of proof
% 232.08/43.16  
% 232.08/43.16  Sub-proof #1970 shows that the following formulas are inconsistent:
% 232.08/43.16  ----------------------------------------------------------------
% 232.08/43.16    (1)  all_55_7 = all_53_13
% 232.08/43.16    (2)  all_55_7 = e1
% 232.08/43.16    (3)   ~ (all_53_13 = e1)
% 232.08/43.16  
% 232.08/43.16  Begin of proof
% 232.08/43.16  | 
% 232.08/43.16  | COMBINE_EQS: (1), (2) imply:
% 232.08/43.16  |   (4)  all_53_13 = e1
% 232.08/43.16  | 
% 232.08/43.16  | SIMP: (4) implies:
% 232.08/43.16  |   (5)  all_53_13 = e1
% 232.08/43.16  | 
% 232.08/43.16  | REDUCE: (3), (5) imply:
% 232.08/43.16  |   (6)  $false
% 232.08/43.16  | 
% 232.08/43.16  | CLOSE: (6) is inconsistent.
% 232.08/43.16  | 
% 232.08/43.16  End of proof
% 232.08/43.16  
% 232.08/43.16  Sub-proof #1971 shows that the following formulas are inconsistent:
% 232.08/43.16  ----------------------------------------------------------------
% 232.08/43.16    (1)  all_57_9 = e2
% 232.08/43.16    (2)   ~ (all_53_6 = e0)
% 232.08/43.16    (3)   ~ (e3 = e1)
% 232.08/43.16    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.08/43.16           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.08/43.16    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 232.08/43.16         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 232.08/43.16    (6)  all_55_9 = e1 | all_55_9 = e0
% 232.08/43.16    (7)  all_55_9 = all_53_6
% 232.08/43.16    (8)   ~ (all_53_2 = e3)
% 232.08/43.16    (9)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 232.08/43.16         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 232.08/43.16    (10)   ~ (e3 = e0)
% 232.08/43.16    (11)  op(e3, e3) = e3
% 232.08/43.16    (12)  all_55_8 = e3 | all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 232.08/43.16    (13)  op(e0, e3) = all_53_3
% 232.08/43.16    (14)   ~ (all_53_2 = e0)
% 232.08/43.16    (15)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 232.08/43.16          | (all_57_14 = e0 & op(e0, e1) = e0)
% 232.08/43.16    (16)   ~ (e2 = e0)
% 232.08/43.16    (17)  op(e2, e2) = e2
% 232.08/43.16    (18)   ~ (e1 = e0)
% 232.08/43.16    (19)   ~ (all_53_2 = all_53_3)
% 232.08/43.16    (20)   ~ (all_53_12 = e1)
% 232.08/43.16    (21)  all_55_8 = all_53_2
% 232.08/43.16    (22)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 232.08/43.16          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 232.08/43.16            e3)
% 232.08/43.16    (23)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 232.08/43.16          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 232.08/43.16            e2)
% 232.08/43.16    (24)  op(e0, e0) = e1
% 232.08/43.16    (25)  all_57_7 = e3
% 232.08/43.16    (26)   ~ (all_53_8 = e0)
% 232.08/43.16    (27)   ~ (all_53_6 = e3)
% 232.08/43.16    (28)   ~ (e2 = e1)
% 232.08/43.16    (29)   ~ (all_53_2 = all_53_6)
% 232.08/43.16    (30)  op(e3, e1) = all_53_8
% 232.08/43.16    (31)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 232.08/43.16          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 232.08/43.16    (32)  op(e3, e0) = all_53_12
% 232.08/43.16  
% 232.08/43.16  Begin of proof
% 232.08/43.16  | 
% 232.08/43.16  | BETA: splitting (9) gives:
% 232.08/43.16  | 
% 232.08/43.16  | Case 1:
% 232.08/43.16  | | 
% 232.08/43.16  | |   (33)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) =
% 232.08/43.16  | |           e0)
% 232.08/43.16  | | 
% 232.08/43.16  | | BETA: splitting (33) gives:
% 232.08/43.16  | | 
% 232.08/43.16  | | Case 1:
% 232.08/43.16  | | | 
% 232.08/43.16  | | |   (34)  all_57_0 = e0 & op(e3, e3) = e0
% 232.08/43.16  | | | 
% 232.08/43.16  | | | ALPHA: (34) implies:
% 232.08/43.16  | | |   (35)  op(e3, e3) = e0
% 232.08/43.16  | | | 
% 232.08/43.16  | | | REF_CLOSE: (4), (10), (11), (35) are inconsistent by sub-proof #2494.
% 232.08/43.16  | | | 
% 232.08/43.16  | | Case 2:
% 232.08/43.16  | | | 
% 232.08/43.16  | | |   (36)  all_57_1 = e0 & op(e3, e2) = e0
% 232.08/43.16  | | | 
% 232.08/43.16  | | | ALPHA: (36) implies:
% 232.08/43.16  | | |   (37)  all_57_1 = e0
% 232.08/43.16  | | | 
% 232.08/43.16  | | | BETA: splitting (31) gives:
% 232.08/43.16  | | | 
% 232.08/43.16  | | | Case 1:
% 232.08/43.16  | | | | 
% 232.08/43.16  | | | |   (38)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2)
% 232.08/43.16  | | | |           = e1)
% 232.08/43.16  | | | | 
% 232.08/43.16  | | | | REF_CLOSE: (4), (17), (18), (28), (37), (38) are inconsistent by
% 232.08/43.16  | | | |            sub-proof #2266.
% 232.08/43.16  | | | | 
% 232.08/43.16  | | | Case 2:
% 232.08/43.16  | | | | 
% 232.08/43.16  | | | |   (39)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2)
% 232.08/43.16  | | | |           = e1)
% 232.08/43.16  | | | | 
% 232.08/43.16  | | | | BETA: splitting (39) gives:
% 232.08/43.16  | | | | 
% 232.08/43.16  | | | | Case 1:
% 232.08/43.16  | | | | | 
% 232.08/43.16  | | | | |   (40)  all_57_7 = e1 & op(e1, e2) = e1
% 232.08/43.16  | | | | | 
% 232.08/43.16  | | | | | REF_CLOSE: (3), (25), (40) are inconsistent by sub-proof #2104.
% 232.08/43.16  | | | | | 
% 232.08/43.16  | | | | Case 2:
% 232.08/43.16  | | | | | 
% 232.08/43.16  | | | | |   (41)  all_57_13 = e1 & op(e0, e2) = e1
% 232.08/43.16  | | | | | 
% 232.08/43.16  | | | | | ALPHA: (41) implies:
% 232.08/43.16  | | | | |   (42)  all_57_13 = e1
% 232.08/43.16  | | | | | 
% 232.08/43.16  | | | | | BETA: splitting (6) gives:
% 232.08/43.16  | | | | | 
% 232.08/43.16  | | | | | Case 1:
% 232.08/43.16  | | | | | | 
% 232.08/43.16  | | | | | |   (43)  all_55_9 = e1
% 232.08/43.16  | | | | | | 
% 232.08/43.16  | | | | | | COMBINE_EQS: (7), (43) imply:
% 232.08/43.16  | | | | | |   (44)  all_53_6 = e1
% 232.08/43.16  | | | | | | 
% 232.08/43.16  | | | | | | REDUCE: (29), (44) imply:
% 232.08/43.16  | | | | | |   (45)   ~ (all_53_2 = e1)
% 232.08/43.16  | | | | | | 
% 232.08/43.16  | | | | | | REDUCE: (27), (44) imply:
% 232.08/43.17  | | | | | |   (46)   ~ (e3 = e1)
% 232.08/43.17  | | | | | | 
% 232.08/43.17  | | | | | | BETA: splitting (12) gives:
% 232.08/43.17  | | | | | | 
% 232.08/43.17  | | | | | | Case 1:
% 232.08/43.17  | | | | | | | 
% 232.08/43.17  | | | | | | |   (47)  all_55_8 = e3
% 232.08/43.17  | | | | | | | 
% 232.08/43.17  | | | | | | | REF_CLOSE: (8), (21), (47) are inconsistent by sub-proof #2496.
% 232.08/43.17  | | | | | | | 
% 232.08/43.17  | | | | | | Case 2:
% 232.08/43.17  | | | | | | | 
% 232.08/43.17  | | | | | | |   (48)   ~ (all_55_8 = e3)
% 232.08/43.17  | | | | | | |   (49)  all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 232.08/43.17  | | | | | | | 
% 232.08/43.17  | | | | | | | BETA: splitting (5) gives:
% 232.08/43.17  | | | | | | | 
% 232.08/43.17  | | | | | | | Case 1:
% 232.08/43.17  | | | | | | | | 
% 232.08/43.17  | | | | | | | |   (50)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 &
% 232.08/43.17  | | | | | | | |           op(e3, e2) = e1)
% 232.08/43.17  | | | | | | | | 
% 232.08/43.17  | | | | | | | | REF_CLOSE: (3), (4), (11), (18), (37), (50) are inconsistent by
% 232.08/43.17  | | | | | | | |            sub-proof #2445.
% 232.08/43.17  | | | | | | | | 
% 232.08/43.17  | | | | | | | Case 2:
% 232.08/43.17  | | | | | | | | 
% 232.08/43.17  | | | | | | | |   (51)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 &
% 232.08/43.17  | | | | | | | |           op(e3, e0) = e1)
% 232.08/43.17  | | | | | | | | 
% 232.08/43.17  | | | | | | | | BETA: splitting (51) gives:
% 232.08/43.17  | | | | | | | | 
% 232.08/43.17  | | | | | | | | Case 1:
% 232.08/43.17  | | | | | | | | | 
% 232.08/43.17  | | | | | | | | |   (52)  all_57_4 = e1 & op(e3, e1) = e1
% 232.08/43.17  | | | | | | | | | 
% 232.08/43.17  | | | | | | | | | ALPHA: (52) implies:
% 232.08/43.17  | | | | | | | | |   (53)  all_57_4 = e1
% 232.08/43.17  | | | | | | | | | 
% 232.08/43.17  | | | | | | | | | BETA: splitting (49) gives:
% 232.08/43.17  | | | | | | | | | 
% 232.08/43.17  | | | | | | | | | Case 1:
% 232.08/43.17  | | | | | | | | | | 
% 232.08/43.17  | | | | | | | | | |   (54)  all_55_8 = e2
% 232.08/43.17  | | | | | | | | | | 
% 232.08/43.17  | | | | | | | | | | COMBINE_EQS: (21), (54) imply:
% 232.08/43.17  | | | | | | | | | |   (55)  all_53_2 = e2
% 232.08/43.17  | | | | | | | | | | 
% 232.08/43.17  | | | | | | | | | | SIMP: (55) implies:
% 232.08/43.17  | | | | | | | | | |   (56)  all_53_2 = e2
% 232.08/43.17  | | | | | | | | | | 
% 232.08/43.17  | | | | | | | | | | REDUCE: (19), (56) imply:
% 232.08/43.17  | | | | | | | | | |   (57)   ~ (all_53_3 = e2)
% 232.08/43.17  | | | | | | | | | | 
% 232.08/43.17  | | | | | | | | | | SIMP: (57) implies:
% 232.08/43.17  | | | | | | | | | |   (58)   ~ (all_53_3 = e2)
% 232.08/43.17  | | | | | | | | | | 
% 232.08/43.17  | | | | | | | | | | REDUCE: (8), (56) imply:
% 232.08/43.17  | | | | | | | | | |   (59)   ~ (e3 = e2)
% 232.08/43.17  | | | | | | | | | | 
% 232.08/43.17  | | | | | | | | | | SIMP: (59) implies:
% 232.08/43.17  | | | | | | | | | |   (60)   ~ (e3 = e2)
% 232.08/43.17  | | | | | | | | | | 
% 232.08/43.17  | | | | | | | | | | BETA: splitting (15) gives:
% 232.08/43.17  | | | | | | | | | | 
% 232.08/43.17  | | | | | | | | | | Case 1:
% 232.08/43.17  | | | | | | | | | | | 
% 232.08/43.17  | | | | | | | | | | |   (61)  all_57_12 = e0 & op(e0, e3) = e0
% 232.08/43.17  | | | | | | | | | | | 
% 232.08/43.17  | | | | | | | | | | | ALPHA: (61) implies:
% 232.08/43.17  | | | | | | | | | | |   (62)  all_57_12 = e0
% 232.08/43.17  | | | | | | | | | | | 
% 232.08/43.17  | | | | | | | | | | | REF_CLOSE: (3), (4), (10), (13), (22), (23), (24), (28),
% 232.08/43.17  | | | | | | | | | | |            (42), (58), (60), (62) are inconsistent by
% 232.08/43.17  | | | | | | | | | | |            sub-proof #1975.
% 232.08/43.17  | | | | | | | | | | | 
% 232.08/43.17  | | | | | | | | | | Case 2:
% 232.08/43.17  | | | | | | | | | | | 
% 232.08/43.17  | | | | | | | | | | |   (63)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 232.08/43.17  | | | | | | | | | | |           e0 & op(e0, e1) = e0)
% 232.08/43.17  | | | | | | | | | | | 
% 232.08/43.17  | | | | | | | | | | | BETA: splitting (63) gives:
% 232.08/43.17  | | | | | | | | | | | 
% 232.08/43.17  | | | | | | | | | | | Case 1:
% 232.08/43.17  | | | | | | | | | | | | 
% 232.08/43.17  | | | | | | | | | | | |   (64)  all_57_13 = e0 & op(e0, e2) = e0
% 232.08/43.17  | | | | | | | | | | | | 
% 232.08/43.17  | | | | | | | | | | | | ALPHA: (64) implies:
% 232.08/43.17  | | | | | | | | | | | |   (65)  all_57_13 = e0
% 232.08/43.17  | | | | | | | | | | | | 
% 232.08/43.17  | | | | | | | | | | | | COMBINE_EQS: (42), (65) imply:
% 232.08/43.17  | | | | | | | | | | | |   (66)  e1 = e0
% 232.08/43.17  | | | | | | | | | | | | 
% 232.08/43.17  | | | | | | | | | | | | COMBINE_EQS: (53), (66) imply:
% 232.08/43.17  | | | | | | | | | | | |   (67)  all_57_4 = e0
% 232.08/43.17  | | | | | | | | | | | | 
% 232.08/43.17  | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (11), (18), (28), (37), (67)
% 232.08/43.17  | | | | | | | | | | | |            are inconsistent by sub-proof #2219.
% 232.08/43.17  | | | | | | | | | | | | 
% 232.08/43.17  | | | | | | | | | | | Case 2:
% 232.08/43.17  | | | | | | | | | | | | 
% 232.08/43.17  | | | | | | | | | | | |   (68)  all_57_14 = e0 & op(e0, e1) = e0
% 232.08/43.17  | | | | | | | | | | | | 
% 232.08/43.17  | | | | | | | | | | | | ALPHA: (68) implies:
% 232.08/43.17  | | | | | | | | | | | |   (69)  all_57_14 = e0
% 232.08/43.17  | | | | | | | | | | | | 
% 232.08/43.17  | | | | | | | | | | | | REF_CLOSE: (3), (4), (10), (16), (22), (23), (24), (28),
% 232.08/43.17  | | | | | | | | | | | |            (42), (60), (69) are inconsistent by sub-proof
% 232.08/43.17  | | | | | | | | | | | |            #2068.
% 232.08/43.17  | | | | | | | | | | | | 
% 232.08/43.17  | | | | | | | | | | | End of split
% 232.08/43.17  | | | | | | | | | | | 
% 232.08/43.17  | | | | | | | | | | End of split
% 232.08/43.17  | | | | | | | | | | 
% 232.08/43.17  | | | | | | | | | Case 2:
% 232.08/43.17  | | | | | | | | | | 
% 232.08/43.17  | | | | | | | | | |   (70)  all_55_8 = e1 | all_55_8 = e0
% 232.08/43.17  | | | | | | | | | | 
% 232.08/43.17  | | | | | | | | | | REF_CLOSE: (14), (21), (45), (70) are inconsistent by
% 232.08/43.17  | | | | | | | | | |            sub-proof #1974.
% 232.08/43.17  | | | | | | | | | | 
% 232.08/43.17  | | | | | | | | | End of split
% 232.08/43.17  | | | | | | | | | 
% 232.08/43.17  | | | | | | | | Case 2:
% 232.08/43.17  | | | | | | | | | 
% 232.08/43.17  | | | | | | | | |   (71)  all_57_9 = e1 & op(e3, e0) = e1
% 232.08/43.17  | | | | | | | | | 
% 232.08/43.17  | | | | | | | | | REF_CLOSE: (4), (20), (32), (71) are inconsistent by sub-proof
% 232.08/43.17  | | | | | | | | |            #2131.
% 232.08/43.17  | | | | | | | | | 
% 232.08/43.17  | | | | | | | | End of split
% 232.08/43.17  | | | | | | | | 
% 232.08/43.17  | | | | | | | End of split
% 232.08/43.17  | | | | | | | 
% 232.08/43.17  | | | | | | End of split
% 232.08/43.17  | | | | | | 
% 232.08/43.17  | | | | | Case 2:
% 232.08/43.17  | | | | | | 
% 232.08/43.17  | | | | | |   (72)  all_55_9 = e0
% 232.08/43.17  | | | | | | 
% 232.08/43.17  | | | | | | COMBINE_EQS: (7), (72) imply:
% 232.08/43.17  | | | | | |   (73)  all_53_6 = e0
% 232.08/43.17  | | | | | | 
% 232.08/43.17  | | | | | | REDUCE: (2), (73) imply:
% 232.08/43.17  | | | | | |   (74)  $false
% 232.08/43.17  | | | | | | 
% 232.08/43.17  | | | | | | CLOSE: (74) is inconsistent.
% 232.08/43.17  | | | | | | 
% 232.08/43.17  | | | | | End of split
% 232.08/43.17  | | | | | 
% 232.08/43.17  | | | | End of split
% 232.08/43.17  | | | | 
% 232.08/43.17  | | | End of split
% 232.08/43.17  | | | 
% 232.08/43.17  | | End of split
% 232.08/43.17  | | 
% 232.08/43.17  | Case 2:
% 232.08/43.17  | | 
% 232.08/43.17  | |   (75)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) =
% 232.08/43.17  | |           e0)
% 232.08/43.17  | | 
% 232.08/43.17  | | REF_CLOSE: (1), (4), (16), (26), (30), (75) are inconsistent by sub-proof
% 232.08/43.17  | |            #1972.
% 232.08/43.17  | | 
% 232.08/43.17  | End of split
% 232.08/43.17  | 
% 232.08/43.17  End of proof
% 232.08/43.17  
% 232.08/43.17  Sub-proof #1972 shows that the following formulas are inconsistent:
% 232.08/43.17  ----------------------------------------------------------------
% 232.08/43.17    (1)  all_57_9 = e2
% 232.08/43.17    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.08/43.17           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.08/43.17    (3)   ~ (e2 = e0)
% 232.08/43.17    (4)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 232.08/43.17    (5)   ~ (all_53_8 = e0)
% 232.08/43.17    (6)  op(e3, e1) = all_53_8
% 232.08/43.17  
% 232.08/43.17  Begin of proof
% 232.08/43.17  | 
% 232.08/43.17  | BETA: splitting (4) gives:
% 232.08/43.17  | 
% 232.08/43.17  | Case 1:
% 232.08/43.17  | | 
% 232.08/43.17  | |   (7)  all_57_4 = e0 & op(e3, e1) = e0
% 232.08/43.17  | | 
% 232.08/43.17  | | ALPHA: (7) implies:
% 232.08/43.17  | |   (8)  op(e3, e1) = e0
% 232.08/43.17  | | 
% 232.08/43.17  | | REF_CLOSE: (2), (5), (6), (8) are inconsistent by sub-proof #2267.
% 232.08/43.17  | | 
% 232.08/43.17  | Case 2:
% 232.08/43.17  | | 
% 232.08/43.17  | |   (9)  all_57_9 = e0 & op(e3, e0) = e0
% 232.08/43.17  | | 
% 232.08/43.17  | | REF_CLOSE: (1), (3), (9) are inconsistent by sub-proof #1973.
% 232.08/43.17  | | 
% 232.08/43.17  | End of split
% 232.08/43.17  | 
% 232.08/43.17  End of proof
% 232.08/43.17  
% 232.08/43.17  Sub-proof #1973 shows that the following formulas are inconsistent:
% 232.08/43.17  ----------------------------------------------------------------
% 232.08/43.17    (1)  all_57_9 = e0 & op(e3, e0) = e0
% 232.08/43.17    (2)  all_57_9 = e2
% 232.08/43.17    (3)   ~ (e2 = e0)
% 232.08/43.17  
% 232.08/43.17  Begin of proof
% 232.08/43.17  | 
% 232.08/43.17  | ALPHA: (1) implies:
% 232.08/43.17  |   (4)  all_57_9 = e0
% 232.08/43.17  | 
% 232.08/43.17  | COMBINE_EQS: (2), (4) imply:
% 232.08/43.17  |   (5)  e2 = e0
% 232.08/43.17  | 
% 232.08/43.17  | REDUCE: (3), (5) imply:
% 232.08/43.17  |   (6)  $false
% 232.08/43.17  | 
% 232.08/43.17  | CLOSE: (6) is inconsistent.
% 232.08/43.17  | 
% 232.08/43.17  End of proof
% 232.08/43.17  
% 232.08/43.17  Sub-proof #1974 shows that the following formulas are inconsistent:
% 232.08/43.17  ----------------------------------------------------------------
% 232.08/43.17    (1)  all_55_8 = e1 | all_55_8 = e0
% 232.08/43.17    (2)  all_55_8 = all_53_2
% 232.08/43.17    (3)   ~ (all_53_2 = e1)
% 232.08/43.17    (4)   ~ (all_53_2 = e0)
% 232.08/43.17  
% 232.08/43.17  Begin of proof
% 232.08/43.17  | 
% 232.08/43.17  | BETA: splitting (1) gives:
% 232.08/43.17  | 
% 232.08/43.17  | Case 1:
% 232.08/43.17  | | 
% 232.08/43.17  | |   (5)  all_55_8 = e1
% 232.08/43.17  | | 
% 232.08/43.17  | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #2367.
% 232.08/43.17  | | 
% 232.08/43.17  | Case 2:
% 232.08/43.17  | | 
% 232.08/43.17  | |   (6)  all_55_8 = e0
% 232.08/43.17  | | 
% 232.08/43.17  | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #1997.
% 232.08/43.17  | | 
% 232.08/43.17  | End of split
% 232.08/43.17  | 
% 232.08/43.17  End of proof
% 232.08/43.17  
% 232.08/43.17  Sub-proof #1975 shows that the following formulas are inconsistent:
% 232.08/43.17  ----------------------------------------------------------------
% 232.08/43.17    (1)  all_57_12 = e0
% 232.08/43.17    (2)  all_57_13 = e1
% 232.08/43.17    (3)   ~ (e3 = e1)
% 232.08/43.17    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.08/43.17           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.08/43.17    (5)   ~ (e3 = e2)
% 232.08/43.17    (6)   ~ (e3 = e0)
% 232.08/43.17    (7)  op(e0, e3) = all_53_3
% 232.08/43.17    (8)   ~ (all_53_3 = e2)
% 232.08/43.17    (9)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 232.08/43.17         (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 232.08/43.17    (10)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 232.08/43.17          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 232.08/43.17            e2)
% 232.08/43.17    (11)  op(e0, e0) = e1
% 232.08/43.17    (12)   ~ (e2 = e1)
% 232.08/43.17  
% 232.08/43.17  Begin of proof
% 232.08/43.17  | 
% 232.08/43.17  | BETA: splitting (9) gives:
% 232.08/43.17  | 
% 232.08/43.17  | Case 1:
% 232.08/43.17  | | 
% 232.08/43.17  | |   (13)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 232.08/43.17  | |           e3)
% 232.08/43.17  | | 
% 232.08/43.17  | | BETA: splitting (13) gives:
% 232.08/43.17  | | 
% 232.08/43.17  | | Case 1:
% 232.08/43.17  | | | 
% 232.08/43.17  | | |   (14)  all_57_12 = e3 & op(e0, e3) = e3
% 232.08/43.17  | | | 
% 232.08/43.17  | | | REF_CLOSE: (1), (6), (14) are inconsistent by sub-proof #1978.
% 232.08/43.17  | | | 
% 232.08/43.17  | | Case 2:
% 232.08/43.17  | | | 
% 232.08/43.17  | | |   (15)  all_57_13 = e3 & op(e0, e2) = e3
% 232.08/43.17  | | | 
% 232.08/43.17  | | | REF_CLOSE: (2), (3), (15) are inconsistent by sub-proof #1977.
% 232.08/43.17  | | | 
% 232.08/43.17  | | End of split
% 232.08/43.17  | | 
% 232.08/43.17  | Case 2:
% 232.08/43.17  | | 
% 232.08/43.17  | |   (16)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 232.08/43.17  | |           e3)
% 232.08/43.17  | | 
% 232.08/43.17  | | BETA: splitting (16) gives:
% 232.08/43.17  | | 
% 232.08/43.17  | | Case 1:
% 232.08/43.17  | | | 
% 232.08/43.17  | | |   (17)  all_57_14 = e3 & op(e0, e1) = e3
% 232.08/43.17  | | | 
% 232.08/43.17  | | | ALPHA: (17) implies:
% 232.08/43.17  | | |   (18)  all_57_14 = e3
% 232.08/43.17  | | | 
% 232.08/43.17  | | | REF_CLOSE: (2), (4), (5), (7), (8), (10), (11), (12), (18) are
% 232.08/43.17  | | |            inconsistent by sub-proof #1976.
% 232.08/43.17  | | | 
% 232.08/43.17  | | Case 2:
% 232.08/43.17  | | | 
% 232.08/43.17  | | |   (19)  all_57_15 = e3 & op(e0, e0) = e3
% 232.08/43.17  | | | 
% 232.08/43.17  | | | ALPHA: (19) implies:
% 232.08/43.17  | | |   (20)  op(e0, e0) = e3
% 232.08/43.17  | | | 
% 232.08/43.17  | | | REF_CLOSE: (3), (4), (11), (20) are inconsistent by sub-proof #2183.
% 232.08/43.17  | | | 
% 232.08/43.17  | | End of split
% 232.08/43.17  | | 
% 232.08/43.17  | End of split
% 232.08/43.17  | 
% 232.08/43.17  End of proof
% 232.08/43.17  
% 232.08/43.17  Sub-proof #1976 shows that the following formulas are inconsistent:
% 232.08/43.17  ----------------------------------------------------------------
% 232.08/43.17    (1)  all_57_13 = e1
% 232.08/43.17    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.08/43.17           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.08/43.17    (3)  all_57_14 = e3
% 232.08/43.17    (4)   ~ (e3 = e2)
% 232.08/43.17    (5)  op(e0, e3) = all_53_3
% 232.08/43.17    (6)   ~ (all_53_3 = e2)
% 232.08/43.17    (7)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2) |
% 232.08/43.17         (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 232.08/43.17    (8)  op(e0, e0) = e1
% 232.08/43.17    (9)   ~ (e2 = e1)
% 232.08/43.17  
% 232.08/43.17  Begin of proof
% 232.08/43.17  | 
% 232.08/43.17  | BETA: splitting (7) gives:
% 232.08/43.17  | 
% 232.08/43.17  | Case 1:
% 232.08/43.17  | | 
% 232.08/43.17  | |   (10)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 232.08/43.17  | |           e2)
% 232.08/43.17  | | 
% 232.08/43.17  | | BETA: splitting (10) gives:
% 232.08/43.17  | | 
% 232.08/43.17  | | Case 1:
% 232.08/43.17  | | | 
% 232.08/43.17  | | |   (11)  all_57_12 = e2 & op(e0, e3) = e2
% 232.08/43.17  | | | 
% 232.08/43.17  | | | ALPHA: (11) implies:
% 232.08/43.17  | | |   (12)  op(e0, e3) = e2
% 232.08/43.17  | | | 
% 232.08/43.17  | | | REF_CLOSE: (2), (5), (6), (12) are inconsistent by sub-proof #1980.
% 232.08/43.17  | | | 
% 232.08/43.17  | | Case 2:
% 232.08/43.17  | | | 
% 232.08/43.17  | | |   (13)  all_57_13 = e2 & op(e0, e2) = e2
% 232.08/43.17  | | | 
% 232.08/43.17  | | | REF_CLOSE: (1), (9), (13) are inconsistent by sub-proof #2101.
% 232.08/43.17  | | | 
% 232.08/43.17  | | End of split
% 232.08/43.17  | | 
% 232.08/43.17  | Case 2:
% 232.08/43.17  | | 
% 232.08/43.17  | |   (14)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 232.08/43.17  | |           e2)
% 232.08/43.17  | | 
% 232.08/43.17  | | REF_CLOSE: (2), (3), (4), (8), (9), (14) are inconsistent by sub-proof
% 232.08/43.17  | |            #2087.
% 232.08/43.17  | | 
% 232.08/43.17  | End of split
% 232.08/43.17  | 
% 232.08/43.17  End of proof
% 232.08/43.17  
% 232.08/43.17  Sub-proof #1977 shows that the following formulas are inconsistent:
% 232.08/43.17  ----------------------------------------------------------------
% 232.08/43.17    (1)  all_57_13 = e3 & op(e0, e2) = e3
% 232.08/43.17    (2)  all_57_13 = e1
% 232.08/43.17    (3)   ~ (e3 = e1)
% 232.08/43.17  
% 232.08/43.17  Begin of proof
% 232.08/43.17  | 
% 232.08/43.17  | ALPHA: (1) implies:
% 232.08/43.17  |   (4)  all_57_13 = e3
% 232.08/43.17  | 
% 232.08/43.17  | COMBINE_EQS: (2), (4) imply:
% 232.08/43.17  |   (5)  e3 = e1
% 232.08/43.17  | 
% 232.08/43.17  | REDUCE: (3), (5) imply:
% 232.08/43.17  |   (6)  $false
% 232.08/43.17  | 
% 232.08/43.17  | CLOSE: (6) is inconsistent.
% 232.08/43.17  | 
% 232.08/43.17  End of proof
% 232.08/43.17  
% 232.08/43.17  Sub-proof #1978 shows that the following formulas are inconsistent:
% 232.08/43.17  ----------------------------------------------------------------
% 232.08/43.17    (1)  all_57_12 = e3 & op(e0, e3) = e3
% 232.08/43.17    (2)  all_57_12 = e0
% 232.08/43.17    (3)   ~ (e3 = e0)
% 232.08/43.17  
% 232.08/43.17  Begin of proof
% 232.08/43.17  | 
% 232.08/43.17  | ALPHA: (1) implies:
% 232.08/43.17  |   (4)  all_57_12 = e3
% 232.08/43.17  | 
% 232.08/43.17  | COMBINE_EQS: (2), (4) imply:
% 232.08/43.17  |   (5)  e3 = e0
% 232.08/43.17  | 
% 232.08/43.17  | REDUCE: (3), (5) imply:
% 232.08/43.17  |   (6)  $false
% 232.08/43.17  | 
% 232.08/43.17  | CLOSE: (6) is inconsistent.
% 232.08/43.17  | 
% 232.08/43.17  End of proof
% 232.08/43.17  
% 232.08/43.17  Sub-proof #1979 shows that the following formulas are inconsistent:
% 232.08/43.17  ----------------------------------------------------------------
% 232.08/43.17    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.08/43.17           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.08/43.17    (2)   ~ (all_53_7 = e2)
% 232.08/43.17    (3)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 232.08/43.17    (4)  op(e0, e3) = all_53_3
% 232.08/43.17    (5)   ~ (all_53_3 = e2)
% 232.08/43.17    (6)  op(e0, e2) = all_53_7
% 232.08/43.17  
% 232.08/43.17  Begin of proof
% 232.08/43.17  | 
% 232.08/43.17  | BETA: splitting (3) gives:
% 232.08/43.17  | 
% 232.08/43.17  | Case 1:
% 232.08/43.17  | | 
% 232.08/43.17  | |   (7)  all_57_12 = e2 & op(e0, e3) = e2
% 232.08/43.17  | | 
% 232.08/43.17  | | ALPHA: (7) implies:
% 232.08/43.17  | |   (8)  op(e0, e3) = e2
% 232.08/43.17  | | 
% 232.08/43.17  | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #1980.
% 232.08/43.17  | | 
% 232.08/43.17  | Case 2:
% 232.08/43.17  | | 
% 232.08/43.17  | |   (9)  all_57_13 = e2 & op(e0, e2) = e2
% 232.08/43.17  | | 
% 232.08/43.17  | | ALPHA: (9) implies:
% 232.08/43.17  | |   (10)  op(e0, e2) = e2
% 232.08/43.17  | | 
% 232.08/43.17  | | REF_CLOSE: (1), (2), (6), (10) are inconsistent by sub-proof #2335.
% 232.08/43.17  | | 
% 232.08/43.17  | End of split
% 232.08/43.17  | 
% 232.08/43.17  End of proof
% 232.08/43.17  
% 232.08/43.17  Sub-proof #1980 shows that the following formulas are inconsistent:
% 232.08/43.17  ----------------------------------------------------------------
% 232.08/43.17    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.08/43.17           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.08/43.17    (2)  op(e0, e3) = all_53_3
% 232.08/43.17    (3)  op(e0, e3) = e2
% 232.08/43.17    (4)   ~ (all_53_3 = e2)
% 232.08/43.17  
% 232.08/43.17  Begin of proof
% 232.08/43.17  | 
% 232.08/43.17  | GROUND_INST: instantiating (1) with all_53_3, e2, e3, e0, simplifying with
% 232.08/43.17  |              (2), (3) gives:
% 232.08/43.17  |   (5)  all_53_3 = e2
% 232.08/43.17  | 
% 232.08/43.17  | REDUCE: (4), (5) imply:
% 232.08/43.17  |   (6)  $false
% 232.08/43.17  | 
% 232.08/43.17  | CLOSE: (6) is inconsistent.
% 232.08/43.17  | 
% 232.08/43.17  End of proof
% 232.08/43.17  
% 232.08/43.17  Sub-proof #1981 shows that the following formulas are inconsistent:
% 232.08/43.17  ----------------------------------------------------------------
% 232.08/43.17    (1)  all_57_10 = e0 & op(e2, e0) = e0
% 232.08/43.17    (2)  all_57_10 = e3
% 232.08/43.17    (3)   ~ (e3 = e0)
% 232.08/43.17  
% 232.08/43.17  Begin of proof
% 232.08/43.17  | 
% 232.08/43.17  | ALPHA: (1) implies:
% 232.08/43.17  |   (4)  all_57_10 = e0
% 232.08/43.17  | 
% 232.08/43.17  | COMBINE_EQS: (2), (4) imply:
% 232.08/43.17  |   (5)  e3 = e0
% 232.08/43.17  | 
% 232.08/43.17  | REDUCE: (3), (5) imply:
% 232.08/43.17  |   (6)  $false
% 232.08/43.17  | 
% 232.08/43.17  | CLOSE: (6) is inconsistent.
% 232.08/43.17  | 
% 232.08/43.17  End of proof
% 232.08/43.17  
% 232.08/43.17  Sub-proof #1982 shows that the following formulas are inconsistent:
% 232.08/43.17  ----------------------------------------------------------------
% 232.08/43.17    (1)   ~ (e3 = e1)
% 232.08/43.17    (2)   ~ (e3 = e2)
% 232.08/43.17    (3)   ~ (e3 = e0)
% 232.08/43.17    (4)  all_57_15 = e3
% 232.08/43.17    (5)  all_57_9 = e0
% 232.08/43.17    (6)   ~ (e2 = e0)
% 232.08/43.17    (7)   ~ (e1 = e0)
% 232.08/43.17    (8)  all_57_10 = e3
% 232.08/43.17    (9)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 232.08/43.17             | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 232.08/43.17               e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 232.08/43.17               op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 232.08/43.17    (10)   ~ (e2 = e1)
% 232.08/43.17    (11)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 232.08/43.17          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 232.08/43.17    (12)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 232.08/43.17          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 232.08/43.17  
% 232.08/43.17  Begin of proof
% 232.08/43.17  | 
% 232.08/43.17  | BETA: splitting (11) gives:
% 232.08/43.17  | 
% 232.08/43.17  | Case 1:
% 232.08/43.17  | | 
% 232.08/43.17  | |   (13)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 232.08/43.17  | |           e2)
% 232.08/43.17  | | 
% 232.08/43.17  | | REF_CLOSE: (2), (5), (6), (8), (13) are inconsistent by sub-proof #1991.
% 232.08/43.17  | | 
% 232.08/43.17  | Case 2:
% 232.08/43.17  | | 
% 232.08/43.17  | |   (14)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 232.08/43.17  | |           e2)
% 232.08/43.17  | | 
% 232.08/43.17  | | BETA: splitting (14) gives:
% 232.08/43.17  | | 
% 232.08/43.17  | | Case 1:
% 232.08/43.17  | | | 
% 232.08/43.17  | | |   (15)  all_57_11 = e2 & op(e1, e0) = e2
% 232.08/43.17  | | | 
% 232.08/43.17  | | | ALPHA: (15) implies:
% 232.08/43.17  | | |   (16)  all_57_11 = e2
% 232.08/43.17  | | | 
% 232.08/43.17  | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (16)
% 232.08/43.17  | | |            are inconsistent by sub-proof #1983.
% 232.08/43.17  | | | 
% 232.08/43.17  | | Case 2:
% 232.08/43.17  | | | 
% 232.08/43.17  | | |   (17)  all_57_15 = e2 & op(e0, e0) = e2
% 232.08/43.17  | | | 
% 232.08/43.17  | | | REF_CLOSE: (2), (4), (17) are inconsistent by sub-proof #2323.
% 232.08/43.17  | | | 
% 232.08/43.17  | | End of split
% 232.08/43.17  | | 
% 232.08/43.17  | End of split
% 232.08/43.17  | 
% 232.08/43.17  End of proof
% 232.08/43.17  
% 232.08/43.17  Sub-proof #1983 shows that the following formulas are inconsistent:
% 232.08/43.17  ----------------------------------------------------------------
% 232.08/43.17    (1)   ~ (e3 = e1)
% 232.08/43.17    (2)   ~ (e3 = e2)
% 232.08/43.17    (3)   ~ (e3 = e0)
% 232.08/43.17    (4)  all_57_15 = e3
% 232.08/43.17    (5)  all_57_11 = e2
% 232.08/43.17    (6)   ~ (e2 = e0)
% 232.08/43.17    (7)   ~ (e1 = e0)
% 232.08/43.17    (8)  all_57_10 = e3
% 232.08/43.17    (9)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 232.08/43.17             | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 232.08/43.17               e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 232.08/43.17               op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 232.08/43.17    (10)   ~ (e2 = e1)
% 232.08/43.17    (11)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 232.08/43.17          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 232.08/43.17    (12)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 232.08/43.17          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 232.08/43.17  
% 232.08/43.17  Begin of proof
% 232.08/43.17  | 
% 232.08/43.17  | BETA: splitting (12) gives:
% 232.08/43.17  | 
% 232.08/43.17  | Case 1:
% 232.08/43.17  | | 
% 232.08/43.17  | |   (13)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) =
% 232.08/43.17  | |           e1)
% 232.08/43.17  | | 
% 232.08/43.17  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (13) are
% 232.08/43.17  | |            inconsistent by sub-proof #1984.
% 232.08/43.17  | | 
% 232.08/43.17  | Case 2:
% 232.08/43.17  | | 
% 232.08/43.17  | |   (14)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 232.08/43.17  | |           e1)
% 232.08/43.17  | | 
% 232.08/43.17  | | BETA: splitting (14) gives:
% 232.08/43.17  | | 
% 232.08/43.17  | | Case 1:
% 232.08/43.17  | | | 
% 232.08/43.17  | | |   (15)  all_57_11 = e1 & op(e1, e0) = e1
% 232.08/43.17  | | | 
% 232.08/43.17  | | | ALPHA: (15) implies:
% 232.08/43.17  | | |   (16)  all_57_11 = e1
% 232.08/43.17  | | | 
% 232.08/43.17  | | | REF_CLOSE: (5), (10), (16) are inconsistent by sub-proof #2113.
% 232.08/43.17  | | | 
% 232.08/43.17  | | Case 2:
% 232.08/43.17  | | | 
% 232.08/43.17  | | |   (17)  all_57_15 = e1 & op(e0, e0) = e1
% 232.08/43.17  | | | 
% 232.08/43.17  | | | REF_CLOSE: (1), (4), (17) are inconsistent by sub-proof #2318.
% 232.08/43.17  | | | 
% 232.08/43.17  | | End of split
% 232.08/43.17  | | 
% 232.08/43.17  | End of split
% 232.08/43.17  | 
% 232.08/43.17  End of proof
% 232.08/43.17  
% 232.08/43.17  Sub-proof #1984 shows that the following formulas are inconsistent:
% 232.08/43.17  ----------------------------------------------------------------
% 232.08/43.17    (1)   ~ (e3 = e1)
% 232.08/43.17    (2)   ~ (e3 = e2)
% 232.08/43.17    (3)   ~ (e3 = e0)
% 232.08/43.17    (4)  all_57_15 = e3
% 232.08/43.17    (5)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 232.08/43.17    (6)   ~ (e2 = e0)
% 232.08/43.17    (7)   ~ (e1 = e0)
% 232.08/43.17    (8)  all_57_10 = e3
% 232.08/43.17    (9)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 232.08/43.17             | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 232.08/43.17               e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 232.08/43.17               op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 232.08/43.17    (10)   ~ (e2 = e1)
% 232.08/43.17    (11)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 232.08/43.17          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 232.08/43.17  
% 232.08/43.17  Begin of proof
% 232.08/43.17  | 
% 232.08/43.17  | BETA: splitting (5) gives:
% 232.08/43.17  | 
% 232.08/43.17  | Case 1:
% 232.08/43.17  | | 
% 232.08/43.17  | |   (12)  all_57_9 = e1 & op(e3, e0) = e1
% 232.08/43.17  | | 
% 232.08/43.17  | | ALPHA: (12) implies:
% 232.08/43.17  | |   (13)  all_57_9 = e1
% 232.08/43.17  | | 
% 232.08/43.17  | | REF_CLOSE: (2), (3), (4), (6), (7), (8), (9), (10), (11), (13) are
% 232.08/43.17  | |            inconsistent by sub-proof #1985.
% 232.08/43.17  | | 
% 232.08/43.17  | Case 2:
% 232.08/43.17  | | 
% 232.08/43.17  | |   (14)  all_57_10 = e1 & op(e2, e0) = e1
% 232.08/43.17  | | 
% 232.08/43.17  | | REF_CLOSE: (1), (8), (14) are inconsistent by sub-proof #2349.
% 232.08/43.17  | | 
% 232.08/43.17  | End of split
% 232.08/43.17  | 
% 232.08/43.17  End of proof
% 232.08/43.17  
% 232.08/43.17  Sub-proof #1985 shows that the following formulas are inconsistent:
% 232.08/43.17  ----------------------------------------------------------------
% 232.08/43.17    (1)  all_57_9 = e1
% 232.08/43.17    (2)   ~ (e3 = e2)
% 232.08/43.17    (3)   ~ (e3 = e0)
% 232.08/43.17    (4)  all_57_15 = e3
% 232.08/43.17    (5)   ~ (e2 = e0)
% 232.08/43.17    (6)   ~ (e1 = e0)
% 232.08/43.17    (7)  all_57_10 = e3
% 232.08/43.17    (8)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 232.08/43.17             | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 232.08/43.17               e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 232.08/43.17               op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 232.08/43.17    (9)   ~ (e2 = e1)
% 232.08/43.17    (10)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 232.08/43.17          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 232.08/43.17  
% 232.08/43.17  Begin of proof
% 232.08/43.17  | 
% 232.08/43.17  | BETA: splitting (8) gives:
% 232.08/43.17  | 
% 232.08/43.17  | Case 1:
% 232.08/43.17  | | 
% 232.08/43.17  | |   (11)  all_57_15 = e0 & op(e0, e0) = e0
% 232.08/43.17  | | 
% 232.08/43.17  | | REF_CLOSE: (3), (4), (11) are inconsistent by sub-proof #2329.
% 232.08/43.17  | | 
% 232.08/43.17  | Case 2:
% 232.08/43.17  | | 
% 232.08/43.17  | |   (12)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 232.08/43.17  | |             e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0 &
% 232.08/43.17  | |             op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 232.08/43.17  | |           (all_57_14 = e0 & op(e0, e1) = e0))
% 232.08/43.17  | | 
% 232.08/43.17  | | ALPHA: (12) implies:
% 232.08/43.17  | |   (13)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 232.08/43.17  | |           e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 232.08/43.17  | | 
% 232.08/43.17  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (13) are
% 232.08/43.17  | |            inconsistent by sub-proof #1986.
% 232.08/43.17  | | 
% 232.08/43.17  | End of split
% 232.08/43.17  | 
% 232.08/43.17  End of proof
% 232.08/43.17  
% 232.08/43.17  Sub-proof #1986 shows that the following formulas are inconsistent:
% 232.08/43.17  ----------------------------------------------------------------
% 232.08/43.17    (1)  all_57_9 = e1
% 232.08/43.17    (2)   ~ (e3 = e2)
% 232.08/43.17    (3)   ~ (e3 = e0)
% 232.08/43.17    (4)  all_57_15 = e3
% 232.08/43.17    (5)   ~ (e2 = e0)
% 232.08/43.17    (6)   ~ (e1 = e0)
% 232.08/43.17    (7)  all_57_10 = e3
% 232.08/43.17    (8)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) |
% 232.08/43.17         (all_57_11 = e0 & op(e1, e0) = e0)
% 232.08/43.17    (9)   ~ (e2 = e1)
% 232.08/43.17    (10)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 232.08/43.17          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 232.08/43.17  
% 232.08/43.17  Begin of proof
% 232.08/43.17  | 
% 232.08/43.17  | BETA: splitting (8) gives:
% 232.08/43.17  | 
% 232.08/43.17  | Case 1:
% 232.08/43.17  | | 
% 232.08/43.17  | |   (11)  all_57_9 = e0 & op(e3, e0) = e0
% 232.08/43.17  | | 
% 232.08/43.17  | | REF_CLOSE: (1), (6), (11) are inconsistent by sub-proof #1990.
% 232.08/43.17  | | 
% 232.08/43.17  | Case 2:
% 232.08/43.17  | | 
% 232.08/43.17  | |   (12)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 232.08/43.17  | |           e0)
% 232.08/43.17  | | 
% 232.08/43.17  | | BETA: splitting (12) gives:
% 232.08/43.17  | | 
% 232.08/43.17  | | Case 1:
% 232.08/43.17  | | | 
% 232.08/43.17  | | |   (13)  all_57_10 = e0 & op(e2, e0) = e0
% 232.08/43.17  | | | 
% 232.08/43.17  | | | ALPHA: (13) implies:
% 232.08/43.17  | | |   (14)  all_57_10 = e0
% 232.08/43.17  | | | 
% 232.08/43.17  | | | REF_CLOSE: (3), (7), (14) are inconsistent by sub-proof #1989.
% 232.08/43.17  | | | 
% 232.08/43.17  | | Case 2:
% 232.08/43.17  | | | 
% 232.08/43.17  | | |   (15)  all_57_11 = e0 & op(e1, e0) = e0
% 232.08/43.17  | | | 
% 232.08/43.17  | | | ALPHA: (15) implies:
% 232.08/43.17  | | |   (16)  all_57_11 = e0
% 232.08/43.17  | | | 
% 232.08/43.17  | | | REF_CLOSE: (1), (2), (4), (5), (7), (9), (10), (16) are inconsistent by
% 232.08/43.17  | | |            sub-proof #1987.
% 232.08/43.17  | | | 
% 232.08/43.17  | | End of split
% 232.08/43.17  | | 
% 232.08/43.17  | End of split
% 232.08/43.17  | 
% 232.08/43.17  End of proof
% 232.08/43.17  
% 232.08/43.17  Sub-proof #1987 shows that the following formulas are inconsistent:
% 232.08/43.17  ----------------------------------------------------------------
% 232.08/43.17    (1)  all_57_9 = e1
% 232.08/43.17    (2)   ~ (e3 = e2)
% 232.08/43.17    (3)  all_57_15 = e3
% 232.08/43.17    (4)  all_57_11 = e0
% 232.08/43.17    (5)   ~ (e2 = e0)
% 232.08/43.17    (6)  all_57_10 = e3
% 232.08/43.17    (7)   ~ (e2 = e1)
% 232.08/43.17    (8)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 232.08/43.17         (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 232.08/43.17  
% 232.08/43.17  Begin of proof
% 232.08/43.17  | 
% 232.08/43.17  | BETA: splitting (8) gives:
% 232.08/43.17  | 
% 232.08/43.17  | Case 1:
% 232.08/43.17  | | 
% 232.08/43.17  | |   (9)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 232.08/43.17  | |          e2)
% 232.08/43.17  | | 
% 232.08/43.17  | | BETA: splitting (9) gives:
% 232.08/43.17  | | 
% 232.08/43.17  | | Case 1:
% 232.08/43.17  | | | 
% 232.08/43.17  | | |   (10)  all_57_9 = e2 & op(e3, e0) = e2
% 232.08/43.17  | | | 
% 232.08/43.17  | | | REF_CLOSE: (1), (7), (10) are inconsistent by sub-proof #2481.
% 232.08/43.17  | | | 
% 232.08/43.17  | | Case 2:
% 232.08/43.17  | | | 
% 232.08/43.17  | | |   (11)  all_57_10 = e2 & op(e2, e0) = e2
% 232.08/43.17  | | | 
% 232.08/43.17  | | | ALPHA: (11) implies:
% 232.08/43.17  | | |   (12)  all_57_10 = e2
% 232.08/43.17  | | | 
% 232.08/43.17  | | | REF_CLOSE: (2), (6), (12) are inconsistent by sub-proof #2356.
% 232.08/43.17  | | | 
% 232.08/43.17  | | End of split
% 232.08/43.17  | | 
% 232.08/43.17  | Case 2:
% 232.08/43.17  | | 
% 232.08/43.17  | |   (13)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 232.08/43.17  | |           e2)
% 232.08/43.17  | | 
% 232.08/43.17  | | BETA: splitting (13) gives:
% 232.08/43.17  | | 
% 232.08/43.17  | | Case 1:
% 232.08/43.17  | | | 
% 232.08/43.17  | | |   (14)  all_57_11 = e2 & op(e1, e0) = e2
% 232.08/43.17  | | | 
% 232.08/43.17  | | | REF_CLOSE: (4), (5), (14) are inconsistent by sub-proof #1988.
% 232.08/43.17  | | | 
% 232.08/43.17  | | Case 2:
% 232.08/43.17  | | | 
% 232.08/43.17  | | |   (15)  all_57_15 = e2 & op(e0, e0) = e2
% 232.08/43.17  | | | 
% 232.08/43.17  | | | ALPHA: (15) implies:
% 232.08/43.17  | | |   (16)  all_57_15 = e2
% 232.08/43.17  | | | 
% 232.08/43.17  | | | REF_CLOSE: (2), (3), (16) are inconsistent by sub-proof #2058.
% 232.08/43.17  | | | 
% 232.08/43.17  | | End of split
% 232.08/43.17  | | 
% 232.08/43.17  | End of split
% 232.08/43.17  | 
% 232.08/43.17  End of proof
% 232.08/43.17  
% 232.08/43.17  Sub-proof #1988 shows that the following formulas are inconsistent:
% 232.08/43.17  ----------------------------------------------------------------
% 232.08/43.17    (1)  all_57_11 = e2 & op(e1, e0) = e2
% 232.08/43.17    (2)  all_57_11 = e0
% 232.08/43.17    (3)   ~ (e2 = e0)
% 232.08/43.17  
% 232.08/43.17  Begin of proof
% 232.08/43.17  | 
% 232.08/43.17  | ALPHA: (1) implies:
% 232.08/43.17  |   (4)  all_57_11 = e2
% 232.08/43.17  | 
% 232.08/43.17  | COMBINE_EQS: (2), (4) imply:
% 232.08/43.17  |   (5)  e2 = e0
% 232.08/43.17  | 
% 232.08/43.17  | REDUCE: (3), (5) imply:
% 232.08/43.17  |   (6)  $false
% 232.08/43.17  | 
% 232.08/43.17  | CLOSE: (6) is inconsistent.
% 232.08/43.17  | 
% 232.08/43.17  End of proof
% 232.08/43.17  
% 232.08/43.17  Sub-proof #1989 shows that the following formulas are inconsistent:
% 232.08/43.17  ----------------------------------------------------------------
% 232.08/43.17    (1)  all_57_10 = e3
% 232.08/43.17    (2)  all_57_10 = e0
% 232.08/43.17    (3)   ~ (e3 = e0)
% 232.08/43.17  
% 232.08/43.17  Begin of proof
% 232.08/43.17  | 
% 232.08/43.17  | COMBINE_EQS: (1), (2) imply:
% 232.08/43.17  |   (4)  e3 = e0
% 232.08/43.17  | 
% 232.08/43.17  | SIMP: (4) implies:
% 232.08/43.17  |   (5)  e3 = e0
% 232.08/43.17  | 
% 232.08/43.17  | REDUCE: (3), (5) imply:
% 232.08/43.17  |   (6)  $false
% 232.08/43.17  | 
% 232.08/43.17  | CLOSE: (6) is inconsistent.
% 232.08/43.17  | 
% 232.08/43.17  End of proof
% 232.08/43.17  
% 232.08/43.17  Sub-proof #1990 shows that the following formulas are inconsistent:
% 232.08/43.17  ----------------------------------------------------------------
% 232.08/43.17    (1)  all_57_9 = e0 & op(e3, e0) = e0
% 232.08/43.17    (2)  all_57_9 = e1
% 232.08/43.17    (3)   ~ (e1 = e0)
% 232.08/43.17  
% 232.08/43.17  Begin of proof
% 232.08/43.17  | 
% 232.08/43.17  | ALPHA: (1) implies:
% 232.08/43.17  |   (4)  all_57_9 = e0
% 232.08/43.17  | 
% 232.08/43.17  | COMBINE_EQS: (2), (4) imply:
% 232.08/43.17  |   (5)  e1 = e0
% 232.08/43.17  | 
% 232.08/43.17  | REDUCE: (3), (5) imply:
% 232.08/43.17  |   (6)  $false
% 232.08/43.17  | 
% 232.08/43.17  | CLOSE: (6) is inconsistent.
% 232.08/43.17  | 
% 232.08/43.17  End of proof
% 232.08/43.17  
% 232.08/43.17  Sub-proof #1991 shows that the following formulas are inconsistent:
% 232.08/43.17  ----------------------------------------------------------------
% 232.08/43.17    (1)   ~ (e3 = e2)
% 232.08/43.17    (2)  all_57_9 = e0
% 232.08/43.17    (3)   ~ (e2 = e0)
% 232.08/43.17    (4)  all_57_10 = e3
% 232.08/43.17    (5)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 232.08/43.17  
% 232.08/43.17  Begin of proof
% 232.08/43.17  | 
% 232.08/43.17  | BETA: splitting (5) gives:
% 232.08/43.17  | 
% 232.08/43.17  | Case 1:
% 232.08/43.17  | | 
% 232.08/43.17  | |   (6)  all_57_9 = e2 & op(e3, e0) = e2
% 232.08/43.17  | | 
% 232.08/43.17  | | ALPHA: (6) implies:
% 232.08/43.17  | |   (7)  all_57_9 = e2
% 232.08/43.17  | | 
% 232.08/43.17  | | REF_CLOSE: (2), (3), (7) are inconsistent by sub-proof #2440.
% 232.08/43.17  | | 
% 232.08/43.17  | Case 2:
% 232.08/43.17  | | 
% 232.08/43.17  | |   (8)  all_57_10 = e2 & op(e2, e0) = e2
% 232.08/43.17  | | 
% 232.08/43.18  | | REF_CLOSE: (1), (4), (8) are inconsistent by sub-proof #2250.
% 232.08/43.18  | | 
% 232.08/43.18  | End of split
% 232.08/43.18  | 
% 232.08/43.18  End of proof
% 232.08/43.18  
% 232.08/43.18  Sub-proof #1992 shows that the following formulas are inconsistent:
% 232.08/43.18  ----------------------------------------------------------------
% 232.08/43.18    (1)  all_55_12 = e1 | all_55_12 = e0
% 232.08/43.18    (2)  all_55_12 = all_53_3
% 232.08/43.18    (3)   ~ (all_53_3 = e1)
% 232.08/43.18    (4)   ~ (all_53_3 = e0)
% 232.08/43.18  
% 232.08/43.18  Begin of proof
% 232.08/43.18  | 
% 232.08/43.18  | BETA: splitting (1) gives:
% 232.08/43.18  | 
% 232.08/43.18  | Case 1:
% 232.08/43.18  | | 
% 232.08/43.18  | |   (5)  all_55_12 = e1
% 232.08/43.18  | | 
% 232.08/43.18  | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #1994.
% 232.08/43.18  | | 
% 232.08/43.18  | Case 2:
% 232.08/43.18  | | 
% 232.08/43.18  | |   (6)  all_55_12 = e0
% 232.08/43.18  | | 
% 232.08/43.18  | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #1993.
% 232.08/43.18  | | 
% 232.08/43.18  | End of split
% 232.08/43.18  | 
% 232.08/43.18  End of proof
% 232.08/43.18  
% 232.08/43.18  Sub-proof #1993 shows that the following formulas are inconsistent:
% 232.08/43.18  ----------------------------------------------------------------
% 232.08/43.18    (1)  all_55_12 = all_53_3
% 232.08/43.18    (2)  all_55_12 = e0
% 232.08/43.18    (3)   ~ (all_53_3 = e0)
% 232.08/43.18  
% 232.08/43.18  Begin of proof
% 232.08/43.18  | 
% 232.08/43.18  | COMBINE_EQS: (1), (2) imply:
% 232.08/43.18  |   (4)  all_53_3 = e0
% 232.08/43.18  | 
% 232.08/43.18  | SIMP: (4) implies:
% 232.08/43.18  |   (5)  all_53_3 = e0
% 232.08/43.18  | 
% 232.08/43.18  | REDUCE: (3), (5) imply:
% 232.08/43.18  |   (6)  $false
% 232.08/43.18  | 
% 232.08/43.18  | CLOSE: (6) is inconsistent.
% 232.08/43.18  | 
% 232.08/43.18  End of proof
% 232.08/43.18  
% 232.08/43.18  Sub-proof #1994 shows that the following formulas are inconsistent:
% 232.08/43.18  ----------------------------------------------------------------
% 232.08/43.18    (1)  all_55_12 = all_53_3
% 232.08/43.18    (2)  all_55_12 = e1
% 232.08/43.18    (3)   ~ (all_53_3 = e1)
% 232.08/43.18  
% 232.08/43.18  Begin of proof
% 232.08/43.18  | 
% 232.08/43.18  | COMBINE_EQS: (1), (2) imply:
% 232.08/43.18  |   (4)  all_53_3 = e1
% 232.08/43.18  | 
% 232.08/43.18  | SIMP: (4) implies:
% 232.08/43.18  |   (5)  all_53_3 = e1
% 232.08/43.18  | 
% 232.08/43.18  | REDUCE: (3), (5) imply:
% 232.08/43.18  |   (6)  $false
% 232.08/43.18  | 
% 232.08/43.18  | CLOSE: (6) is inconsistent.
% 232.08/43.18  | 
% 232.08/43.18  End of proof
% 232.08/43.18  
% 232.08/43.18  Sub-proof #1995 shows that the following formulas are inconsistent:
% 232.08/43.18  ----------------------------------------------------------------
% 232.08/43.18    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.08/43.18           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.08/43.18    (2)   ~ (all_30_1 = e3)
% 232.08/43.18    (3)  op(e0, e1) = e3
% 232.08/43.18    (4)  op(e0, e1) = all_40_1
% 232.08/43.18    (5)  op(e0, e1) = all_30_1
% 232.08/43.18  
% 232.08/43.18  Begin of proof
% 232.08/43.18  | 
% 232.08/43.18  | GROUND_INST: instantiating (1) with all_30_1, all_40_1, e1, e0, simplifying
% 232.08/43.18  |              with (4), (5) gives:
% 232.08/43.18  |   (6)  all_40_1 = all_30_1
% 232.08/43.18  | 
% 232.08/43.18  | GROUND_INST: instantiating (1) with e3, all_40_1, e1, e0, simplifying with
% 232.08/43.18  |              (3), (4) gives:
% 232.08/43.18  |   (7)  all_40_1 = e3
% 232.08/43.18  | 
% 232.08/43.18  | COMBINE_EQS: (6), (7) imply:
% 232.08/43.18  |   (8)  all_30_1 = e3
% 232.08/43.18  | 
% 232.08/43.18  | SIMP: (8) implies:
% 232.08/43.18  |   (9)  all_30_1 = e3
% 232.08/43.18  | 
% 232.08/43.18  | REDUCE: (2), (9) imply:
% 232.08/43.18  |   (10)  $false
% 232.08/43.18  | 
% 232.08/43.18  | CLOSE: (10) is inconsistent.
% 232.08/43.18  | 
% 232.08/43.18  End of proof
% 232.08/43.18  
% 232.08/43.18  Sub-proof #1996 shows that the following formulas are inconsistent:
% 232.08/43.18  ----------------------------------------------------------------
% 232.08/43.18    (1)   ~ (all_53_2 = e2)
% 232.08/43.18    (2)  all_55_8 = e2 | all_55_8 = e1 | all_55_8 = e0
% 232.08/43.18    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.08/43.18           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.08/43.18    (4)   ~ (all_53_2 = e3)
% 232.08/43.18    (5)  op(e0, e1) = e3
% 232.08/43.18    (6)  op(e3, e3) = e3
% 232.08/43.18    (7)   ~ (all_53_2 = e0)
% 232.08/43.18    (8)  op(e0, e1) = all_52_29
% 232.08/43.18    (9)  all_55_8 = all_53_2
% 232.08/43.18    (10)  op(all_52_29, all_52_29) = e1
% 232.08/43.18    (11)  op(e0, e1) = all_40_1
% 232.08/43.18    (12)  op(e0, e1) = all_30_1
% 232.08/43.18  
% 232.08/43.18  Begin of proof
% 232.08/43.18  | 
% 232.08/43.18  | BETA: splitting (2) gives:
% 232.08/43.18  | 
% 232.08/43.18  | Case 1:
% 232.08/43.18  | | 
% 232.08/43.18  | |   (13)  all_55_8 = e2
% 232.08/43.18  | | 
% 232.08/43.18  | | REF_CLOSE: (1), (9), (13) are inconsistent by sub-proof #2406.
% 232.08/43.18  | | 
% 232.08/43.18  | Case 2:
% 232.08/43.18  | | 
% 232.08/43.18  | |   (14)  all_55_8 = e1 | all_55_8 = e0
% 232.08/43.18  | | 
% 232.08/43.18  | | BETA: splitting (14) gives:
% 232.08/43.18  | | 
% 232.08/43.18  | | Case 1:
% 232.08/43.18  | | | 
% 232.08/43.18  | | |   (15)  all_55_8 = e1
% 232.08/43.18  | | | 
% 232.08/43.18  | | | COMBINE_EQS: (9), (15) imply:
% 232.08/43.18  | | |   (16)  all_53_2 = e1
% 232.08/43.18  | | | 
% 232.08/43.18  | | | SIMP: (16) implies:
% 232.08/43.18  | | |   (17)  all_53_2 = e1
% 232.08/43.18  | | | 
% 232.08/43.18  | | | REDUCE: (4), (17) imply:
% 232.08/43.18  | | |   (18)   ~ (e3 = e1)
% 232.08/43.18  | | | 
% 232.08/43.18  | | | SIMP: (18) implies:
% 232.08/43.18  | | |   (19)   ~ (e3 = e1)
% 232.08/43.18  | | | 
% 232.08/43.18  | | | GROUND_INST: instantiating (3) with all_40_1, all_52_29, e1, e0,
% 232.08/43.18  | | |              simplifying with (8), (11) gives:
% 232.08/43.18  | | |   (20)  all_52_29 = all_40_1
% 232.08/43.18  | | | 
% 232.08/43.18  | | | GROUND_INST: instantiating (3) with all_30_1, all_52_29, e1, e0,
% 232.08/43.18  | | |              simplifying with (8), (12) gives:
% 232.08/43.18  | | |   (21)  all_52_29 = all_30_1
% 232.08/43.18  | | | 
% 232.08/43.18  | | | GROUND_INST: instantiating (3) with e3, all_52_29, e1, e0, simplifying
% 232.08/43.18  | | |              with (5), (8) gives:
% 232.08/43.18  | | |   (22)  all_52_29 = e3
% 232.08/43.18  | | | 
% 232.08/43.18  | | | COMBINE_EQS: (20), (21) imply:
% 232.08/43.18  | | |   (23)  all_40_1 = all_30_1
% 232.08/43.18  | | | 
% 232.08/43.18  | | | COMBINE_EQS: (20), (22) imply:
% 232.08/43.18  | | |   (24)  all_40_1 = e3
% 232.08/43.18  | | | 
% 232.08/43.18  | | | COMBINE_EQS: (23), (24) imply:
% 232.08/43.18  | | |   (25)  all_30_1 = e3
% 232.08/43.18  | | | 
% 232.08/43.18  | | | REDUCE: (10), (22) imply:
% 232.08/43.18  | | |   (26)  op(e3, e3) = e1
% 232.08/43.18  | | | 
% 232.08/43.18  | | | REF_CLOSE: (3), (6), (19), (26) are inconsistent by sub-proof #2495.
% 232.08/43.18  | | | 
% 232.08/43.18  | | Case 2:
% 232.08/43.18  | | | 
% 232.08/43.18  | | |   (27)  all_55_8 = e0
% 232.08/43.18  | | | 
% 232.08/43.18  | | | REF_CLOSE: (7), (9), (27) are inconsistent by sub-proof #1997.
% 232.08/43.18  | | | 
% 232.08/43.18  | | End of split
% 232.08/43.18  | | 
% 232.08/43.18  | End of split
% 232.08/43.18  | 
% 232.08/43.18  End of proof
% 232.08/43.18  
% 232.08/43.18  Sub-proof #1997 shows that the following formulas are inconsistent:
% 232.08/43.18  ----------------------------------------------------------------
% 232.08/43.18    (1)  all_55_8 = all_53_2
% 232.08/43.18    (2)  all_55_8 = e0
% 232.08/43.18    (3)   ~ (all_53_2 = e0)
% 232.08/43.18  
% 232.08/43.18  Begin of proof
% 232.08/43.18  | 
% 232.08/43.18  | COMBINE_EQS: (1), (2) imply:
% 232.08/43.18  |   (4)  all_53_2 = e0
% 232.08/43.18  | 
% 232.08/43.18  | SIMP: (4) implies:
% 232.08/43.18  |   (5)  all_53_2 = e0
% 232.08/43.18  | 
% 232.08/43.18  | REDUCE: (3), (5) imply:
% 232.08/43.18  |   (6)  $false
% 232.08/43.18  | 
% 232.08/43.18  | CLOSE: (6) is inconsistent.
% 232.08/43.18  | 
% 232.08/43.18  End of proof
% 232.08/43.18  
% 232.08/43.18  Sub-proof #1998 shows that the following formulas are inconsistent:
% 232.08/43.18  ----------------------------------------------------------------
% 232.08/43.18    (1)  op(e1, e3) = all_52_17
% 232.08/43.18    (2)  all_55_10 = e3 | all_55_10 = e2 | all_55_10 = e1 | all_55_10 = e0
% 232.08/43.18    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.08/43.18           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.08/43.18    (4)   ~ (all_6_2 = e3)
% 232.08/43.18    (5)  op(e1, e1) = all_6_2
% 232.08/43.18    (6)  op(all_52_17, all_52_17) = e3
% 232.08/43.18    (7)  op(e1, e3) = e1
% 232.08/43.18    (8)  all_55_10 = all_6_2
% 232.08/43.18  
% 232.08/43.18  Begin of proof
% 232.08/43.18  | 
% 232.08/43.18  | BETA: splitting (2) gives:
% 232.08/43.18  | 
% 232.08/43.18  | Case 1:
% 232.08/43.18  | | 
% 232.08/43.18  | |   (9)  all_55_10 = e3
% 232.08/43.18  | | 
% 232.08/43.18  | | REF_CLOSE: (4), (8), (9) are inconsistent by sub-proof #2500.
% 232.08/43.18  | | 
% 232.08/43.18  | Case 2:
% 232.08/43.18  | | 
% 232.08/43.18  | |   (10)   ~ (all_55_10 = e3)
% 232.08/43.18  | | 
% 232.08/43.18  | | GROUND_INST: instantiating (3) with e1, all_52_17, e3, e1, simplifying with
% 232.08/43.18  | |              (1), (7) gives:
% 232.08/43.18  | |   (11)  all_52_17 = e1
% 232.08/43.18  | | 
% 232.08/43.18  | | REDUCE: (6), (11) imply:
% 232.08/43.18  | |   (12)  op(e1, e1) = e3
% 232.08/43.18  | | 
% 232.08/43.18  | | REF_CLOSE: (3), (4), (5), (12) are inconsistent by sub-proof #2468.
% 232.08/43.18  | | 
% 232.08/43.18  | End of split
% 232.08/43.18  | 
% 232.08/43.18  End of proof
% 232.08/43.18  
% 232.08/43.18  Sub-proof #1999 shows that the following formulas are inconsistent:
% 232.08/43.18  ----------------------------------------------------------------
% 232.08/43.18    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.08/43.18           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.08/43.18    (2)  op(e2, e0) = e3
% 232.08/43.18    (3)  all_55_3 = e3 | all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 232.08/43.18    (4)  op(e2, e0) = all_52_15
% 232.08/43.18    (5)  op(e3, e3) = e3
% 232.08/43.18    (6)   ~ (all_53_12 = e1)
% 232.08/43.18    (7)  all_55_3 = all_53_12
% 232.08/43.18    (8)   ~ (all_53_12 = e3)
% 232.08/43.18    (9)  op(all_52_15, all_52_15) = e0
% 232.08/43.18    (10)   ~ (all_53_12 = e2)
% 232.08/43.18  
% 232.08/43.18  Begin of proof
% 232.08/43.18  | 
% 232.08/43.18  | BETA: splitting (3) gives:
% 232.08/43.18  | 
% 232.08/43.18  | Case 1:
% 232.08/43.18  | | 
% 232.08/43.18  | |   (11)  all_55_3 = e3
% 232.08/43.18  | | 
% 232.08/43.18  | | COMBINE_EQS: (7), (11) imply:
% 232.08/43.18  | |   (12)  all_53_12 = e3
% 232.08/43.18  | | 
% 232.08/43.18  | | REDUCE: (8), (12) imply:
% 232.08/43.18  | |   (13)  $false
% 232.08/43.18  | | 
% 232.08/43.18  | | CLOSE: (13) is inconsistent.
% 232.08/43.18  | | 
% 232.08/43.18  | Case 2:
% 232.08/43.18  | | 
% 232.08/43.18  | |   (14)   ~ (all_55_3 = e3)
% 232.08/43.18  | |   (15)  all_55_3 = e2 | all_55_3 = e1 | all_55_3 = e0
% 232.08/43.18  | | 
% 232.08/43.18  | | BETA: splitting (15) gives:
% 232.08/43.18  | | 
% 232.08/43.18  | | Case 1:
% 232.08/43.18  | | | 
% 232.08/43.18  | | |   (16)  all_55_3 = e2
% 232.08/43.18  | | | 
% 232.08/43.18  | | | COMBINE_EQS: (7), (16) imply:
% 232.08/43.18  | | |   (17)  all_53_12 = e2
% 232.08/43.18  | | | 
% 232.08/43.18  | | | REDUCE: (10), (17) imply:
% 232.08/43.18  | | |   (18)  $false
% 232.08/43.18  | | | 
% 232.08/43.18  | | | CLOSE: (18) is inconsistent.
% 232.08/43.18  | | | 
% 232.08/43.18  | | Case 2:
% 232.08/43.18  | | | 
% 232.08/43.18  | | |   (19)  all_55_3 = e1 | all_55_3 = e0
% 232.08/43.18  | | | 
% 232.08/43.18  | | | BETA: splitting (19) gives:
% 232.08/43.18  | | | 
% 232.08/43.18  | | | Case 1:
% 232.08/43.18  | | | | 
% 232.08/43.18  | | | |   (20)  all_55_3 = e1
% 232.08/43.18  | | | | 
% 232.08/43.18  | | | | COMBINE_EQS: (7), (20) imply:
% 232.08/43.18  | | | |   (21)  all_53_12 = e1
% 232.08/43.18  | | | | 
% 232.08/43.18  | | | | REDUCE: (6), (21) imply:
% 232.08/43.18  | | | |   (22)  $false
% 232.08/43.18  | | | | 
% 232.08/43.18  | | | | CLOSE: (22) is inconsistent.
% 232.08/43.18  | | | | 
% 232.08/43.18  | | | Case 2:
% 232.08/43.18  | | | | 
% 232.08/43.18  | | | |   (23)  all_55_3 = e0
% 232.08/43.18  | | | | 
% 232.08/43.18  | | | | COMBINE_EQS: (7), (23) imply:
% 232.08/43.18  | | | |   (24)  all_53_12 = e0
% 232.08/43.18  | | | | 
% 232.08/43.18  | | | | REDUCE: (8), (24) imply:
% 232.08/43.18  | | | |   (25)   ~ (e3 = e0)
% 232.08/43.18  | | | | 
% 232.08/43.18  | | | | SIMP: (25) implies:
% 232.08/43.18  | | | |   (26)   ~ (e3 = e0)
% 232.08/43.18  | | | | 
% 232.08/43.18  | | | | GROUND_INST: instantiating (1) with e3, all_52_15, e0, e2, simplifying
% 232.08/43.18  | | | |              with (2), (4) gives:
% 232.08/43.18  | | | |   (27)  all_52_15 = e3
% 232.08/43.18  | | | | 
% 232.08/43.18  | | | | REDUCE: (9), (27) imply:
% 232.08/43.18  | | | |   (28)  op(e3, e3) = e0
% 232.08/43.18  | | | | 
% 232.08/43.18  | | | | REF_CLOSE: (1), (5), (26), (28) are inconsistent by sub-proof #2494.
% 232.08/43.18  | | | | 
% 232.08/43.18  | | | End of split
% 232.08/43.18  | | | 
% 232.08/43.18  | | End of split
% 232.08/43.18  | | 
% 232.08/43.18  | End of split
% 232.08/43.18  | 
% 232.08/43.18  End of proof
% 232.08/43.18  
% 232.08/43.18  Sub-proof #2000 shows that the following formulas are inconsistent:
% 232.08/43.18  ----------------------------------------------------------------
% 232.08/43.18    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.08/43.18           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.08/43.18    (2)  op(all_52_7, all_52_7) = e0
% 232.08/43.18    (3)  op(e3, e0) = e0
% 232.08/43.18    (4)   ~ (e1 = e0)
% 232.08/43.18    (5)  op(e0, e0) = e1
% 232.08/43.18    (6)  op(e3, e0) = all_52_7
% 232.08/43.18  
% 232.08/43.18  Begin of proof
% 232.08/43.18  | 
% 232.08/43.18  | GROUND_INST: instantiating (1) with e0, all_52_7, e0, e3, simplifying with
% 232.08/43.18  |              (3), (6) gives:
% 232.08/43.18  |   (7)  all_52_7 = e0
% 232.08/43.18  | 
% 232.08/43.18  | REDUCE: (2), (7) imply:
% 232.08/43.18  |   (8)  op(e0, e0) = e0
% 232.08/43.18  | 
% 232.08/43.18  | GROUND_INST: instantiating (1) with e1, e0, e0, e0, simplifying with (5), (8)
% 232.08/43.18  |              gives:
% 232.08/43.18  |   (9)  e1 = e0
% 232.08/43.18  | 
% 232.08/43.18  | REDUCE: (4), (9) imply:
% 232.08/43.18  |   (10)  $false
% 232.08/43.18  | 
% 232.08/43.18  | CLOSE: (10) is inconsistent.
% 232.08/43.18  | 
% 232.08/43.18  End of proof
% 232.08/43.18  
% 232.08/43.18  Sub-proof #2001 shows that the following formulas are inconsistent:
% 232.08/43.18  ----------------------------------------------------------------
% 232.08/43.18    (1)  all_55_12 = all_53_3
% 232.08/43.18    (2)  all_55_12 = e3
% 232.08/43.18    (3)   ~ (all_53_3 = e3)
% 232.08/43.18  
% 232.08/43.18  Begin of proof
% 232.08/43.18  | 
% 232.08/43.18  | COMBINE_EQS: (1), (2) imply:
% 232.08/43.18  |   (4)  all_53_3 = e3
% 232.08/43.18  | 
% 232.08/43.18  | SIMP: (4) implies:
% 232.08/43.18  |   (5)  all_53_3 = e3
% 232.08/43.18  | 
% 232.08/43.18  | REDUCE: (3), (5) imply:
% 232.08/43.18  |   (6)  $false
% 232.08/43.18  | 
% 232.08/43.18  | CLOSE: (6) is inconsistent.
% 232.08/43.18  | 
% 232.08/43.18  End of proof
% 232.08/43.18  
% 232.08/43.18  Sub-proof #2002 shows that the following formulas are inconsistent:
% 232.08/43.18  ----------------------------------------------------------------
% 232.08/43.18    (1)  all_55_13 = all_53_7
% 232.08/43.18    (2)  all_55_13 = e1
% 232.08/43.18    (3)   ~ (all_53_7 = e1)
% 232.08/43.18  
% 232.08/43.18  Begin of proof
% 232.08/43.18  | 
% 232.08/43.18  | COMBINE_EQS: (1), (2) imply:
% 232.08/43.18  |   (4)  all_53_7 = e1
% 232.08/43.18  | 
% 232.08/43.18  | SIMP: (4) implies:
% 232.08/43.18  |   (5)  all_53_7 = e1
% 232.08/43.18  | 
% 232.08/43.18  | REDUCE: (3), (5) imply:
% 232.08/43.18  |   (6)  $false
% 232.08/43.18  | 
% 232.08/43.18  | CLOSE: (6) is inconsistent.
% 232.08/43.18  | 
% 232.08/43.18  End of proof
% 232.08/43.18  
% 232.08/43.18  Sub-proof #2003 shows that the following formulas are inconsistent:
% 232.08/43.18  ----------------------------------------------------------------
% 232.08/43.18    (1)   ~ (e3 = e1)
% 232.08/43.18    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.08/43.18           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.08/43.18    (3)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 232.08/43.18         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 232.08/43.18    (4)   ~ (all_6_2 = e3)
% 232.08/43.18    (5)  op(e1, e1) = all_6_2
% 232.08/43.18    (6)  all_57_6 = e1
% 232.08/43.18    (7)   ~ (e3 = e2)
% 232.08/43.18    (8)   ~ (e2 = e0)
% 232.08/43.18    (9)  all_57_8 = e0
% 232.08/43.18    (10)  all_57_11 = e1
% 232.08/43.18    (11)   ~ (e2 = e1)
% 232.08/43.18    (12)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 232.08/43.18          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 232.08/43.18  
% 232.08/43.18  Begin of proof
% 232.08/43.18  | 
% 232.08/43.18  | BETA: splitting (3) gives:
% 232.08/43.18  | 
% 232.08/43.18  | Case 1:
% 232.08/43.18  | | 
% 232.08/43.18  | |   (13)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 232.08/43.18  | |           e3)
% 232.08/43.18  | | 
% 232.08/43.18  | | BETA: splitting (13) gives:
% 232.08/43.18  | | 
% 232.08/43.18  | | Case 1:
% 232.08/43.18  | | | 
% 232.08/43.18  | | |   (14)  all_57_6 = e3 & op(e1, e3) = e3
% 232.08/43.18  | | | 
% 232.08/43.18  | | | ALPHA: (14) implies:
% 232.08/43.18  | | |   (15)  all_57_6 = e3
% 232.08/43.18  | | | 
% 232.08/43.18  | | | REF_CLOSE: (1), (6), (15) are inconsistent by sub-proof #2017.
% 232.08/43.18  | | | 
% 232.08/43.18  | | Case 2:
% 232.08/43.18  | | | 
% 232.08/43.18  | | |   (16)  all_57_7 = e3 & op(e1, e2) = e3
% 232.08/43.18  | | | 
% 232.08/43.18  | | | ALPHA: (16) implies:
% 232.08/43.18  | | |   (17)  all_57_7 = e3
% 232.08/43.18  | | | 
% 232.08/43.18  | | | BETA: splitting (12) gives:
% 232.08/43.18  | | | 
% 232.08/43.18  | | | Case 1:
% 232.08/43.18  | | | | 
% 232.08/43.18  | | | |   (18)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2)
% 232.08/43.18  | | | |           = e2)
% 232.08/43.18  | | | | 
% 232.08/43.18  | | | | REF_CLOSE: (6), (7), (11), (17), (18) are inconsistent by sub-proof
% 232.08/43.18  | | | |            #2006.
% 232.08/43.18  | | | | 
% 232.08/43.18  | | | Case 2:
% 232.08/43.18  | | | | 
% 232.08/43.18  | | | |   (19)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0)
% 232.08/43.18  | | | |           = e2)
% 232.08/43.18  | | | | 
% 232.08/43.18  | | | | BETA: splitting (19) gives:
% 232.08/43.18  | | | | 
% 232.08/43.18  | | | | Case 1:
% 232.08/43.18  | | | | | 
% 232.08/43.18  | | | | |   (20)  all_57_8 = e2 & op(e1, e1) = e2
% 232.08/43.18  | | | | | 
% 232.08/43.18  | | | | | REF_CLOSE: (8), (9), (20) are inconsistent by sub-proof #2005.
% 232.08/43.18  | | | | | 
% 232.08/43.18  | | | | Case 2:
% 232.08/43.18  | | | | | 
% 232.08/43.18  | | | | |   (21)  all_57_11 = e2 & op(e1, e0) = e2
% 232.08/43.18  | | | | | 
% 232.08/43.18  | | | | | ALPHA: (21) implies:
% 232.08/43.18  | | | | |   (22)  all_57_11 = e2
% 232.08/43.18  | | | | | 
% 232.08/43.18  | | | | | REF_CLOSE: (10), (11), (22) are inconsistent by sub-proof #2113.
% 232.08/43.18  | | | | | 
% 232.08/43.18  | | | | End of split
% 232.08/43.18  | | | | 
% 232.08/43.18  | | | End of split
% 232.08/43.18  | | | 
% 232.08/43.18  | | End of split
% 232.08/43.18  | | 
% 232.08/43.18  | Case 2:
% 232.08/43.18  | | 
% 232.08/43.18  | |   (23)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 232.08/43.18  | |           e3)
% 232.08/43.18  | | 
% 232.08/43.18  | | REF_CLOSE: (1), (2), (4), (5), (10), (23) are inconsistent by sub-proof
% 232.08/43.18  | |            #2004.
% 232.08/43.18  | | 
% 232.08/43.18  | End of split
% 232.08/43.18  | 
% 232.08/43.18  End of proof
% 232.08/43.18  
% 232.08/43.18  Sub-proof #2004 shows that the following formulas are inconsistent:
% 232.08/43.18  ----------------------------------------------------------------
% 232.08/43.18    (1)   ~ (e3 = e1)
% 232.08/43.18    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.08/43.18           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.08/43.18    (3)   ~ (all_6_2 = e3)
% 232.08/43.18    (4)  op(e1, e1) = all_6_2
% 232.08/43.18    (5)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 232.08/43.18    (6)  all_57_11 = e1
% 232.08/43.18  
% 232.08/43.18  Begin of proof
% 232.08/43.18  | 
% 232.08/43.18  | BETA: splitting (5) gives:
% 232.08/43.18  | 
% 232.08/43.18  | Case 1:
% 232.08/43.18  | | 
% 232.08/43.18  | |   (7)  all_57_8 = e3 & op(e1, e1) = e3
% 232.08/43.18  | | 
% 232.08/43.18  | | ALPHA: (7) implies:
% 232.08/43.18  | |   (8)  op(e1, e1) = e3
% 232.08/43.18  | | 
% 232.08/43.18  | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #2468.
% 232.08/43.18  | | 
% 232.08/43.18  | Case 2:
% 232.08/43.18  | | 
% 232.08/43.18  | |   (9)  all_57_11 = e3 & op(e1, e0) = e3
% 232.08/43.18  | | 
% 232.08/43.18  | | ALPHA: (9) implies:
% 232.08/43.18  | |   (10)  all_57_11 = e3
% 232.08/43.18  | | 
% 232.08/43.18  | | REF_CLOSE: (1), (6), (10) are inconsistent by sub-proof #2218.
% 232.08/43.18  | | 
% 232.08/43.18  | End of split
% 232.08/43.18  | 
% 232.08/43.18  End of proof
% 232.08/43.18  
% 232.08/43.18  Sub-proof #2005 shows that the following formulas are inconsistent:
% 232.08/43.18  ----------------------------------------------------------------
% 232.08/43.18    (1)  all_57_8 = e2 & op(e1, e1) = e2
% 232.08/43.18    (2)  all_57_8 = e0
% 232.08/43.18    (3)   ~ (e2 = e0)
% 232.08/43.18  
% 232.08/43.18  Begin of proof
% 232.08/43.18  | 
% 232.08/43.18  | ALPHA: (1) implies:
% 232.08/43.18  |   (4)  all_57_8 = e2
% 232.08/43.18  | 
% 232.08/43.18  | COMBINE_EQS: (2), (4) imply:
% 232.08/43.18  |   (5)  e2 = e0
% 232.08/43.18  | 
% 232.08/43.18  | REDUCE: (3), (5) imply:
% 232.08/43.18  |   (6)  $false
% 232.08/43.18  | 
% 232.08/43.18  | CLOSE: (6) is inconsistent.
% 232.08/43.18  | 
% 232.08/43.18  End of proof
% 232.08/43.18  
% 232.08/43.18  Sub-proof #2006 shows that the following formulas are inconsistent:
% 232.08/43.18  ----------------------------------------------------------------
% 232.08/43.18    (1)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2)
% 232.08/43.18    (2)  all_57_6 = e1
% 232.08/43.18    (3)   ~ (e3 = e2)
% 232.08/43.18    (4)  all_57_7 = e3
% 232.08/43.18    (5)   ~ (e2 = e1)
% 232.08/43.18  
% 232.08/43.18  Begin of proof
% 232.08/43.18  | 
% 232.08/43.18  | BETA: splitting (1) gives:
% 232.08/43.18  | 
% 232.08/43.18  | Case 1:
% 232.08/43.18  | | 
% 232.08/43.18  | |   (6)  all_57_6 = e2 & op(e1, e3) = e2
% 232.08/43.18  | | 
% 232.08/43.18  | | ALPHA: (6) implies:
% 232.08/43.18  | |   (7)  all_57_6 = e2
% 232.08/43.18  | | 
% 232.08/43.18  | | REF_CLOSE: (2), (5), (7) are inconsistent by sub-proof #2233.
% 232.08/43.18  | | 
% 232.08/43.18  | Case 2:
% 232.08/43.18  | | 
% 232.08/43.18  | |   (8)  all_57_7 = e2 & op(e1, e2) = e2
% 232.08/43.18  | | 
% 232.08/43.18  | | REF_CLOSE: (3), (4), (8) are inconsistent by sub-proof #2092.
% 232.08/43.18  | | 
% 232.08/43.18  | End of split
% 232.08/43.18  | 
% 232.08/43.18  End of proof
% 232.08/43.18  
% 232.08/43.18  Sub-proof #2007 shows that the following formulas are inconsistent:
% 232.08/43.18  ----------------------------------------------------------------
% 232.08/43.18    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 232.08/43.18         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 232.08/43.18    (2)   ~ (e3 = e1)
% 232.08/43.18    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.08/43.18           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.08/43.18    (4)  op(e2, e2) = e0
% 232.08/43.18    (5)  all_57_3 = e0
% 232.08/43.18    (6)   ~ (e3 = e2)
% 232.08/43.18    (7)   ~ (e2 = e0)
% 232.08/43.18    (8)   ~ (e1 = e0)
% 232.08/43.18    (9)  all_57_13 = e3
% 232.08/43.18    (10)  all_57_7 = e3
% 232.08/43.18    (11)   ~ (e2 = e1)
% 232.08/43.18    (12)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 232.08/43.18          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 232.08/43.18  
% 232.08/43.18  Begin of proof
% 232.08/43.18  | 
% 232.08/43.18  | BETA: splitting (1) gives:
% 232.08/43.18  | 
% 232.08/43.18  | Case 1:
% 232.08/43.18  | | 
% 232.08/43.18  | |   (13)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 232.08/43.18  | |           e2)
% 232.08/43.18  | | 
% 232.08/43.18  | | BETA: splitting (13) gives:
% 232.08/43.18  | | 
% 232.08/43.18  | | Case 1:
% 232.08/43.18  | | | 
% 232.08/43.18  | | |   (14)  all_57_1 = e2 & op(e3, e2) = e2
% 232.08/43.18  | | | 
% 232.08/43.18  | | | ALPHA: (14) implies:
% 232.08/43.18  | | |   (15)  all_57_1 = e2
% 232.08/43.18  | | | 
% 232.08/43.18  | | | REF_CLOSE: (2), (5), (8), (9), (10), (11), (12), (15) are inconsistent by
% 232.08/43.18  | | |            sub-proof #2008.
% 232.08/43.18  | | | 
% 232.08/43.18  | | Case 2:
% 232.08/43.18  | | | 
% 232.08/43.18  | | |   (16)  all_57_3 = e2 & op(e2, e2) = e2
% 232.08/43.18  | | | 
% 232.08/43.18  | | | ALPHA: (16) implies:
% 232.08/43.18  | | |   (17)  op(e2, e2) = e2
% 232.08/43.18  | | | 
% 232.08/43.18  | | | REF_CLOSE: (3), (4), (7), (17) are inconsistent by sub-proof #2472.
% 232.08/43.18  | | | 
% 232.08/43.18  | | End of split
% 232.08/43.18  | | 
% 232.08/43.18  | Case 2:
% 232.08/43.18  | | 
% 232.08/43.18  | |   (18)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 232.08/43.18  | |           e2)
% 232.08/43.18  | | 
% 232.08/43.18  | | BETA: splitting (18) gives:
% 232.08/43.18  | | 
% 232.08/43.18  | | Case 1:
% 232.08/43.18  | | | 
% 232.08/43.18  | | |   (19)  all_57_7 = e2 & op(e1, e2) = e2
% 232.08/43.18  | | | 
% 232.08/43.18  | | | REF_CLOSE: (6), (10), (19) are inconsistent by sub-proof #2092.
% 232.08/43.18  | | | 
% 232.08/43.18  | | Case 2:
% 232.08/43.18  | | | 
% 232.08/43.18  | | |   (20)  all_57_13 = e2 & op(e0, e2) = e2
% 232.08/43.18  | | | 
% 232.08/43.18  | | | REF_CLOSE: (6), (9), (20) are inconsistent by sub-proof #2146.
% 232.08/43.18  | | | 
% 232.08/43.18  | | End of split
% 232.08/43.18  | | 
% 232.08/43.18  | End of split
% 232.08/43.18  | 
% 232.08/43.18  End of proof
% 232.08/43.18  
% 232.08/43.18  Sub-proof #2008 shows that the following formulas are inconsistent:
% 232.08/43.18  ----------------------------------------------------------------
% 232.08/43.18    (1)   ~ (e3 = e1)
% 232.08/43.18    (2)  all_57_3 = e0
% 232.08/43.18    (3)  all_57_1 = e2
% 232.08/43.18    (4)   ~ (e1 = e0)
% 232.08/43.18    (5)  all_57_13 = e3
% 232.08/43.18    (6)  all_57_7 = e3
% 232.08/43.18    (7)   ~ (e2 = e1)
% 232.08/43.18    (8)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 232.08/43.18         (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 232.08/43.18  
% 232.08/43.18  Begin of proof
% 232.08/43.18  | 
% 232.08/43.18  | BETA: splitting (8) gives:
% 232.08/43.18  | 
% 232.08/43.18  | Case 1:
% 232.08/43.18  | | 
% 232.08/43.18  | |   (9)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1)
% 232.08/43.18  | | 
% 232.08/43.18  | | BETA: splitting (9) gives:
% 232.08/43.18  | | 
% 232.08/43.18  | | Case 1:
% 232.08/43.18  | | | 
% 232.08/43.18  | | |   (10)  all_57_1 = e1 & op(e3, e2) = e1
% 232.08/43.18  | | | 
% 232.08/43.18  | | | REF_CLOSE: (3), (7), (10) are inconsistent by sub-proof #2210.
% 232.08/43.18  | | | 
% 232.08/43.18  | | Case 2:
% 232.08/43.18  | | | 
% 232.08/43.18  | | |   (11)  all_57_3 = e1 & op(e2, e2) = e1
% 232.08/43.18  | | | 
% 232.08/43.18  | | | REF_CLOSE: (2), (4), (11) are inconsistent by sub-proof #2362.
% 232.08/43.18  | | | 
% 232.08/43.18  | | End of split
% 232.08/43.18  | | 
% 232.08/43.18  | Case 2:
% 232.08/43.18  | | 
% 232.08/43.18  | |   (12)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 232.08/43.18  | |           e1)
% 232.08/43.18  | | 
% 232.08/43.18  | | BETA: splitting (12) gives:
% 232.08/43.18  | | 
% 232.08/43.18  | | Case 1:
% 232.08/43.18  | | | 
% 232.08/43.18  | | |   (13)  all_57_7 = e1 & op(e1, e2) = e1
% 232.08/43.18  | | | 
% 232.08/43.18  | | | ALPHA: (13) implies:
% 232.08/43.18  | | |   (14)  all_57_7 = e1
% 232.08/43.18  | | | 
% 232.08/43.18  | | | REF_CLOSE: (1), (6), (14) are inconsistent by sub-proof #2115.
% 232.08/43.18  | | | 
% 232.08/43.18  | | Case 2:
% 232.08/43.18  | | | 
% 232.08/43.18  | | |   (15)  all_57_13 = e1 & op(e0, e2) = e1
% 232.08/43.18  | | | 
% 232.08/43.18  | | | REF_CLOSE: (1), (5), (15) are inconsistent by sub-proof #2264.
% 232.08/43.18  | | | 
% 232.08/43.18  | | End of split
% 232.08/43.18  | | 
% 232.08/43.18  | End of split
% 232.08/43.18  | 
% 232.08/43.18  End of proof
% 232.08/43.18  
% 232.08/43.18  Sub-proof #2009 shows that the following formulas are inconsistent:
% 232.08/43.18  ----------------------------------------------------------------
% 232.08/43.18    (1)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 232.08/43.18    (2)   ~ (e3 = e1)
% 232.08/43.18    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.08/43.18           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.08/43.18    (4)   ~ (e3 = e2)
% 232.08/43.18    (5)   ~ (e3 = e0)
% 232.08/43.18    (6)  all_57_9 = e0
% 232.08/43.18    (7)   ~ (e2 = e0)
% 232.08/43.18    (8)   ~ (e1 = e0)
% 232.08/43.18    (9)  op(e1, e1) = e0
% 232.08/43.18    (10)  op(e0, e0) = e1
% 232.08/43.18    (11)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 232.08/43.18          (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 232.08/43.18    (12)   ~ (e2 = e1)
% 232.08/43.18    (13)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 232.08/43.18          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 232.08/43.18  
% 232.08/43.18  Begin of proof
% 232.08/43.18  | 
% 232.08/43.18  | BETA: splitting (1) gives:
% 232.08/43.18  | 
% 232.08/43.18  | Case 1:
% 232.08/43.18  | | 
% 232.08/43.18  | |   (14)  all_57_8 = e1 & op(e1, e1) = e1
% 232.08/43.18  | | 
% 232.08/43.18  | | ALPHA: (14) implies:
% 232.08/43.18  | |   (15)  op(e1, e1) = e1
% 232.08/43.18  | | 
% 232.08/43.18  | | REF_CLOSE: (3), (8), (9), (15) are inconsistent by sub-proof #2427.
% 232.08/43.18  | | 
% 232.08/43.18  | Case 2:
% 232.08/43.18  | | 
% 232.08/43.18  | |   (16)  all_57_11 = e1 & op(e1, e0) = e1
% 232.08/43.18  | | 
% 232.08/43.18  | | ALPHA: (16) implies:
% 232.08/43.18  | |   (17)  all_57_11 = e1
% 232.08/43.18  | | 
% 232.08/43.18  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (10), (11), (12), (13), (17) are
% 232.08/43.18  | |            inconsistent by sub-proof #2047.
% 232.08/43.18  | | 
% 232.08/43.18  | End of split
% 232.08/43.18  | 
% 232.08/43.18  End of proof
% 232.08/43.18  
% 232.08/43.18  Sub-proof #2010 shows that the following formulas are inconsistent:
% 232.08/43.18  ----------------------------------------------------------------
% 232.08/43.18    (1)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 232.08/43.18         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 232.08/43.18    (2)   ~ (e3 = e1)
% 232.08/43.18    (3)   ~ (e3 = e2)
% 232.08/43.18    (4)   ~ (e3 = e0)
% 232.08/43.18    (5)   ~ (e2 = e0)
% 232.08/43.18    (6)   ~ (e1 = e0)
% 232.08/43.18    (7)  all_57_6 = e3
% 232.08/43.18    (8)  all_57_0 = e3
% 232.08/43.18    (9)   ~ (e2 = e1)
% 232.08/43.18    (10)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 232.08/43.18          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 232.08/43.18    (11)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 232.08/43.18          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 232.08/43.18  
% 232.08/43.18  Begin of proof
% 232.08/43.18  | 
% 232.08/43.18  | BETA: splitting (11) gives:
% 232.08/43.18  | 
% 232.08/43.18  | Case 1:
% 232.08/43.18  | | 
% 232.08/43.18  | |   (12)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) =
% 232.08/43.18  | |           e0)
% 232.08/43.18  | | 
% 232.08/43.18  | | BETA: splitting (12) gives:
% 232.08/43.18  | | 
% 232.08/43.18  | | Case 1:
% 232.08/43.18  | | | 
% 232.08/43.18  | | |   (13)  all_57_0 = e0 & op(e3, e3) = e0
% 232.08/43.18  | | | 
% 232.08/43.18  | | | ALPHA: (13) implies:
% 232.08/43.18  | | |   (14)  all_57_0 = e0
% 232.08/43.18  | | | 
% 232.08/43.18  | | | COMBINE_EQS: (8), (14) imply:
% 232.08/43.18  | | |   (15)  e3 = e0
% 232.08/43.18  | | | 
% 232.08/43.18  | | | REDUCE: (4), (15) imply:
% 232.08/43.18  | | |   (16)  $false
% 232.08/43.18  | | | 
% 232.08/43.18  | | | CLOSE: (16) is inconsistent.
% 232.08/43.18  | | | 
% 232.08/43.18  | | Case 2:
% 232.08/43.18  | | | 
% 232.08/43.18  | | |   (17)  all_57_2 = e0 & op(e2, e3) = e0
% 232.08/43.18  | | | 
% 232.08/43.18  | | | ALPHA: (17) implies:
% 232.08/43.18  | | |   (18)  all_57_2 = e0
% 232.08/43.18  | | | 
% 232.08/43.18  | | | BETA: splitting (10) gives:
% 232.08/43.18  | | | 
% 232.08/43.18  | | | Case 1:
% 232.08/43.18  | | | | 
% 232.08/43.18  | | | |   (19)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3)
% 232.08/43.18  | | | |           = e2)
% 232.08/43.18  | | | | 
% 232.08/43.18  | | | | BETA: splitting (19) gives:
% 232.08/43.18  | | | | 
% 232.08/43.18  | | | | Case 1:
% 232.08/43.18  | | | | | 
% 232.08/43.18  | | | | |   (20)  all_57_0 = e2 & op(e3, e3) = e2
% 232.08/43.18  | | | | | 
% 232.08/43.18  | | | | | REF_CLOSE: (3), (8), (20) are inconsistent by sub-proof #2021.
% 232.08/43.18  | | | | | 
% 232.08/43.18  | | | | Case 2:
% 232.08/43.18  | | | | | 
% 232.08/43.18  | | | | |   (21)  all_57_2 = e2 & op(e2, e3) = e2
% 232.08/43.18  | | | | | 
% 232.08/43.18  | | | | | REF_CLOSE: (5), (18), (21) are inconsistent by sub-proof #2020.
% 232.08/43.18  | | | | | 
% 232.08/43.18  | | | | End of split
% 232.08/43.18  | | | | 
% 232.08/43.18  | | | Case 2:
% 232.08/43.18  | | | | 
% 232.08/43.18  | | | |   (22)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3)
% 232.08/43.18  | | | |           = e2)
% 232.08/43.18  | | | | 
% 232.08/43.18  | | | | BETA: splitting (22) gives:
% 232.08/43.18  | | | | 
% 232.08/43.18  | | | | Case 1:
% 232.08/43.18  | | | | | 
% 232.08/43.18  | | | | |   (23)  all_57_6 = e2 & op(e1, e3) = e2
% 232.08/43.18  | | | | | 
% 232.08/43.18  | | | | | ALPHA: (23) implies:
% 232.08/43.18  | | | | |   (24)  all_57_6 = e2
% 232.08/43.18  | | | | | 
% 232.08/43.18  | | | | | REF_CLOSE: (3), (7), (24) are inconsistent by sub-proof #2463.
% 232.08/43.18  | | | | | 
% 232.08/43.18  | | | | Case 2:
% 232.08/43.18  | | | | | 
% 232.08/43.18  | | | | |   (25)  all_57_12 = e2 & op(e0, e3) = e2
% 232.08/43.18  | | | | | 
% 232.08/43.18  | | | | | ALPHA: (25) implies:
% 232.08/43.18  | | | | |   (26)  all_57_12 = e2
% 232.08/43.18  | | | | | 
% 232.08/43.18  | | | | | REF_CLOSE: (1), (2), (6), (7), (8), (9), (18), (26) are inconsistent
% 232.08/43.18  | | | | |            by sub-proof #2015.
% 232.08/43.18  | | | | | 
% 232.08/43.18  | | | | End of split
% 232.08/43.18  | | | | 
% 232.08/43.18  | | | End of split
% 232.08/43.18  | | | 
% 232.08/43.18  | | End of split
% 232.08/43.18  | | 
% 232.08/43.18  | Case 2:
% 232.08/43.18  | | 
% 232.08/43.18  | |   (27)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) =
% 232.08/43.18  | |           e0)
% 232.08/43.18  | | 
% 232.08/43.18  | | BETA: splitting (27) gives:
% 232.08/43.18  | | 
% 232.08/43.18  | | Case 1:
% 232.08/43.18  | | | 
% 232.08/43.18  | | |   (28)  all_57_6 = e0 & op(e1, e3) = e0
% 232.08/43.18  | | | 
% 232.08/43.18  | | | REF_CLOSE: (4), (7), (28) are inconsistent by sub-proof #2465.
% 232.08/43.18  | | | 
% 232.08/43.18  | | Case 2:
% 232.08/43.18  | | | 
% 232.08/43.18  | | |   (29)  all_57_12 = e0 & op(e0, e3) = e0
% 232.08/43.18  | | | 
% 232.08/43.18  | | | ALPHA: (29) implies:
% 232.08/43.18  | | |   (30)  all_57_12 = e0
% 232.08/43.18  | | | 
% 232.08/43.18  | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (30) are
% 232.08/43.18  | | |            inconsistent by sub-proof #2011.
% 232.08/43.18  | | | 
% 232.08/43.18  | | End of split
% 232.08/43.18  | | 
% 232.08/43.18  | End of split
% 232.08/43.18  | 
% 232.08/43.18  End of proof
% 232.08/43.18  
% 232.08/43.18  Sub-proof #2011 shows that the following formulas are inconsistent:
% 232.08/43.18  ----------------------------------------------------------------
% 232.08/43.18    (1)  all_57_12 = e0
% 232.08/43.19    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 232.08/43.19         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 232.08/43.19    (3)   ~ (e3 = e1)
% 232.08/43.19    (4)   ~ (e3 = e2)
% 232.08/43.19    (5)   ~ (e2 = e0)
% 232.08/43.19    (6)   ~ (e1 = e0)
% 232.08/43.19    (7)  all_57_6 = e3
% 232.08/43.19    (8)  all_57_0 = e3
% 232.08/43.19    (9)   ~ (e2 = e1)
% 232.08/43.19    (10)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 232.08/43.19          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 232.08/43.19  
% 232.08/43.19  Begin of proof
% 232.08/43.19  | 
% 232.08/43.19  | BETA: splitting (10) gives:
% 232.08/43.19  | 
% 232.08/43.19  | Case 1:
% 232.08/43.19  | | 
% 232.08/43.19  | |   (11)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) =
% 232.08/43.19  | |           e2)
% 232.08/43.19  | | 
% 232.08/43.19  | | BETA: splitting (11) gives:
% 232.08/43.19  | | 
% 232.08/43.19  | | Case 1:
% 232.08/43.19  | | | 
% 232.08/43.19  | | |   (12)  all_57_0 = e2 & op(e3, e3) = e2
% 232.08/43.19  | | | 
% 232.08/43.19  | | | REF_CLOSE: (4), (8), (12) are inconsistent by sub-proof #2021.
% 232.08/43.19  | | | 
% 232.08/43.19  | | Case 2:
% 232.08/43.19  | | | 
% 232.08/43.19  | | |   (13)  all_57_2 = e2 & op(e2, e3) = e2
% 232.08/43.19  | | | 
% 232.08/43.19  | | | ALPHA: (13) implies:
% 232.08/43.19  | | |   (14)  all_57_2 = e2
% 232.08/43.19  | | | 
% 232.08/43.19  | | | BETA: splitting (2) gives:
% 232.08/43.19  | | | 
% 232.08/43.19  | | | Case 1:
% 232.08/43.19  | | | | 
% 232.08/43.19  | | | |   (15)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3)
% 232.08/43.19  | | | |           = e1)
% 232.08/43.19  | | | | 
% 232.08/43.19  | | | | BETA: splitting (15) gives:
% 232.08/43.19  | | | | 
% 232.08/43.19  | | | | Case 1:
% 232.08/43.19  | | | | | 
% 232.08/43.19  | | | | |   (16)  all_57_0 = e1 & op(e3, e3) = e1
% 232.08/43.19  | | | | | 
% 232.08/43.19  | | | | | REF_CLOSE: (3), (8), (16) are inconsistent by sub-proof #2019.
% 232.08/43.19  | | | | | 
% 232.08/43.19  | | | | Case 2:
% 232.08/43.19  | | | | | 
% 232.08/43.19  | | | | |   (17)  all_57_2 = e1 & op(e2, e3) = e1
% 232.08/43.19  | | | | | 
% 232.08/43.19  | | | | | ALPHA: (17) implies:
% 232.08/43.19  | | | | |   (18)  all_57_2 = e1
% 232.08/43.19  | | | | | 
% 232.08/43.19  | | | | | REF_CLOSE: (9), (14), (18) are inconsistent by sub-proof #2464.
% 232.08/43.19  | | | | | 
% 232.08/43.19  | | | | End of split
% 232.08/43.19  | | | | 
% 232.08/43.19  | | | Case 2:
% 232.08/43.19  | | | | 
% 232.08/43.19  | | | |   (19)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3)
% 232.08/43.19  | | | |           = e1)
% 232.08/43.19  | | | | 
% 232.08/43.19  | | | | REF_CLOSE: (1), (3), (6), (7), (19) are inconsistent by sub-proof #2013.
% 232.08/43.19  | | | | 
% 232.08/43.19  | | | End of split
% 232.08/43.19  | | | 
% 232.08/43.19  | | End of split
% 232.08/43.19  | | 
% 232.08/43.19  | Case 2:
% 232.08/43.19  | | 
% 232.08/43.19  | |   (20)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) =
% 232.08/43.19  | |           e2)
% 232.08/43.19  | | 
% 232.08/43.19  | | BETA: splitting (20) gives:
% 232.08/43.19  | | 
% 232.08/43.19  | | Case 1:
% 232.08/43.19  | | | 
% 232.08/43.19  | | |   (21)  all_57_6 = e2 & op(e1, e3) = e2
% 232.08/43.19  | | | 
% 232.08/43.19  | | | REF_CLOSE: (4), (7), (21) are inconsistent by sub-proof #2012.
% 232.08/43.19  | | | 
% 232.08/43.19  | | Case 2:
% 232.08/43.19  | | | 
% 232.08/43.19  | | |   (22)  all_57_12 = e2 & op(e0, e3) = e2
% 232.08/43.19  | | | 
% 232.08/43.19  | | | REF_CLOSE: (1), (5), (22) are inconsistent by sub-proof #2462.
% 232.08/43.19  | | | 
% 232.08/43.19  | | End of split
% 232.08/43.19  | | 
% 232.08/43.19  | End of split
% 232.08/43.19  | 
% 232.08/43.19  End of proof
% 232.08/43.19  
% 232.08/43.19  Sub-proof #2012 shows that the following formulas are inconsistent:
% 232.08/43.19  ----------------------------------------------------------------
% 232.08/43.19    (1)  all_57_6 = e2 & op(e1, e3) = e2
% 232.08/43.19    (2)  all_57_6 = e3
% 232.08/43.19    (3)   ~ (e3 = e2)
% 232.08/43.19  
% 232.08/43.19  Begin of proof
% 232.08/43.19  | 
% 232.08/43.19  | ALPHA: (1) implies:
% 232.08/43.19  |   (4)  all_57_6 = e2
% 232.08/43.19  | 
% 232.08/43.19  | COMBINE_EQS: (2), (4) imply:
% 232.08/43.19  |   (5)  e3 = e2
% 232.08/43.19  | 
% 232.08/43.19  | REDUCE: (3), (5) imply:
% 232.08/43.19  |   (6)  $false
% 232.08/43.19  | 
% 232.08/43.19  | CLOSE: (6) is inconsistent.
% 232.08/43.19  | 
% 232.08/43.19  End of proof
% 232.08/43.19  
% 232.08/43.19  Sub-proof #2013 shows that the following formulas are inconsistent:
% 232.08/43.19  ----------------------------------------------------------------
% 232.08/43.19    (1)  all_57_12 = e0
% 232.08/43.19    (2)   ~ (e3 = e1)
% 232.08/43.19    (3)   ~ (e1 = e0)
% 232.08/43.19    (4)  all_57_6 = e3
% 232.08/43.19    (5)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 232.08/43.19  
% 232.08/43.19  Begin of proof
% 232.08/43.19  | 
% 232.08/43.19  | BETA: splitting (5) gives:
% 232.08/43.19  | 
% 232.08/43.19  | Case 1:
% 232.08/43.19  | | 
% 232.08/43.19  | |   (6)  all_57_6 = e1 & op(e1, e3) = e1
% 232.08/43.19  | | 
% 232.08/43.19  | | ALPHA: (6) implies:
% 232.08/43.19  | |   (7)  all_57_6 = e1
% 232.08/43.19  | | 
% 232.08/43.19  | | REF_CLOSE: (2), (4), (7) are inconsistent by sub-proof #2017.
% 232.08/43.19  | | 
% 232.08/43.19  | Case 2:
% 232.08/43.19  | | 
% 232.08/43.19  | |   (8)  all_57_12 = e1 & op(e0, e3) = e1
% 232.08/43.19  | | 
% 232.08/43.19  | | ALPHA: (8) implies:
% 232.08/43.19  | |   (9)  all_57_12 = e1
% 232.08/43.19  | | 
% 232.08/43.19  | | REF_CLOSE: (1), (3), (9) are inconsistent by sub-proof #2014.
% 232.08/43.19  | | 
% 232.08/43.19  | End of split
% 232.08/43.19  | 
% 232.08/43.19  End of proof
% 232.08/43.19  
% 232.08/43.19  Sub-proof #2014 shows that the following formulas are inconsistent:
% 232.08/43.19  ----------------------------------------------------------------
% 232.08/43.19    (1)  all_57_12 = e1
% 232.08/43.19    (2)  all_57_12 = e0
% 232.08/43.19    (3)   ~ (e1 = e0)
% 232.08/43.19  
% 232.08/43.19  Begin of proof
% 232.08/43.19  | 
% 232.08/43.19  | COMBINE_EQS: (1), (2) imply:
% 232.08/43.19  |   (4)  e1 = e0
% 232.08/43.19  | 
% 232.08/43.19  | SIMP: (4) implies:
% 232.08/43.19  |   (5)  e1 = e0
% 232.08/43.19  | 
% 232.08/43.19  | REDUCE: (3), (5) imply:
% 232.08/43.19  |   (6)  $false
% 232.08/43.19  | 
% 232.08/43.19  | CLOSE: (6) is inconsistent.
% 232.08/43.19  | 
% 232.08/43.19  End of proof
% 232.08/43.19  
% 232.08/43.19  Sub-proof #2015 shows that the following formulas are inconsistent:
% 232.08/43.19  ----------------------------------------------------------------
% 232.08/43.19    (1)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 232.08/43.19         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 232.08/43.19    (2)   ~ (e3 = e1)
% 232.08/43.19    (3)  all_57_12 = e2
% 232.08/43.19    (4)   ~ (e1 = e0)
% 232.08/43.19    (5)  all_57_6 = e3
% 232.08/43.19    (6)  all_57_2 = e0
% 232.08/43.19    (7)  all_57_0 = e3
% 232.08/43.19    (8)   ~ (e2 = e1)
% 232.08/43.19  
% 232.08/43.19  Begin of proof
% 232.08/43.19  | 
% 232.08/43.19  | BETA: splitting (1) gives:
% 232.08/43.19  | 
% 232.08/43.19  | Case 1:
% 232.08/43.19  | | 
% 232.08/43.19  | |   (9)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1)
% 232.08/43.19  | | 
% 232.08/43.19  | | BETA: splitting (9) gives:
% 232.08/43.19  | | 
% 232.08/43.19  | | Case 1:
% 232.08/43.19  | | | 
% 232.08/43.19  | | |   (10)  all_57_0 = e1 & op(e3, e3) = e1
% 232.08/43.19  | | | 
% 232.08/43.19  | | | REF_CLOSE: (2), (7), (10) are inconsistent by sub-proof #2019.
% 232.08/43.19  | | | 
% 232.08/43.19  | | Case 2:
% 232.08/43.19  | | | 
% 232.08/43.19  | | |   (11)  all_57_2 = e1 & op(e2, e3) = e1
% 232.08/43.19  | | | 
% 232.08/43.19  | | | REF_CLOSE: (4), (6), (11) are inconsistent by sub-proof #2018.
% 232.08/43.19  | | | 
% 232.08/43.19  | | End of split
% 232.08/43.19  | | 
% 232.08/43.19  | Case 2:
% 232.08/43.19  | | 
% 232.08/43.19  | |   (12)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) =
% 232.08/43.19  | |           e1)
% 232.08/43.19  | | 
% 232.08/43.19  | | REF_CLOSE: (2), (3), (5), (8), (12) are inconsistent by sub-proof #2016.
% 232.08/43.19  | | 
% 232.08/43.19  | End of split
% 232.08/43.19  | 
% 232.08/43.19  End of proof
% 232.08/43.19  
% 232.08/43.19  Sub-proof #2016 shows that the following formulas are inconsistent:
% 232.08/43.19  ----------------------------------------------------------------
% 232.08/43.19    (1)   ~ (e3 = e1)
% 232.08/43.19    (2)  all_57_12 = e2
% 232.08/43.19    (3)  all_57_6 = e3
% 232.08/43.19    (4)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 232.08/43.19    (5)   ~ (e2 = e1)
% 232.08/43.19  
% 232.08/43.19  Begin of proof
% 232.08/43.19  | 
% 232.08/43.19  | BETA: splitting (4) gives:
% 232.08/43.19  | 
% 232.08/43.19  | Case 1:
% 232.08/43.19  | | 
% 232.08/43.19  | |   (6)  all_57_6 = e1 & op(e1, e3) = e1
% 232.08/43.19  | | 
% 232.08/43.19  | | ALPHA: (6) implies:
% 232.08/43.19  | |   (7)  all_57_6 = e1
% 232.08/43.19  | | 
% 232.08/43.19  | | REF_CLOSE: (1), (3), (7) are inconsistent by sub-proof #2017.
% 232.08/43.19  | | 
% 232.08/43.19  | Case 2:
% 232.08/43.19  | | 
% 232.08/43.19  | |   (8)  all_57_12 = e1 & op(e0, e3) = e1
% 232.08/43.19  | | 
% 232.08/43.19  | | ALPHA: (8) implies:
% 232.08/43.19  | |   (9)  all_57_12 = e1
% 232.08/43.19  | | 
% 232.08/43.19  | | REF_CLOSE: (2), (5), (9) are inconsistent by sub-proof #2321.
% 232.08/43.19  | | 
% 232.08/43.19  | End of split
% 232.08/43.19  | 
% 232.08/43.19  End of proof
% 232.08/43.19  
% 232.08/43.19  Sub-proof #2017 shows that the following formulas are inconsistent:
% 232.08/43.19  ----------------------------------------------------------------
% 232.08/43.19    (1)  all_57_6 = e3
% 232.08/43.19    (2)  all_57_6 = e1
% 232.08/43.19    (3)   ~ (e3 = e1)
% 232.08/43.19  
% 232.08/43.19  Begin of proof
% 232.08/43.19  | 
% 232.08/43.19  | COMBINE_EQS: (1), (2) imply:
% 232.08/43.19  |   (4)  e3 = e1
% 232.08/43.19  | 
% 232.08/43.19  | SIMP: (4) implies:
% 232.08/43.19  |   (5)  e3 = e1
% 232.08/43.19  | 
% 232.08/43.19  | REDUCE: (3), (5) imply:
% 232.08/43.19  |   (6)  $false
% 232.08/43.19  | 
% 232.08/43.19  | CLOSE: (6) is inconsistent.
% 232.08/43.19  | 
% 232.08/43.19  End of proof
% 232.08/43.19  
% 232.08/43.19  Sub-proof #2018 shows that the following formulas are inconsistent:
% 232.08/43.19  ----------------------------------------------------------------
% 232.08/43.19    (1)  all_57_2 = e1 & op(e2, e3) = e1
% 232.08/43.19    (2)  all_57_2 = e0
% 232.08/43.19    (3)   ~ (e1 = e0)
% 232.08/43.19  
% 232.08/43.19  Begin of proof
% 232.08/43.19  | 
% 232.08/43.19  | ALPHA: (1) implies:
% 232.08/43.19  |   (4)  all_57_2 = e1
% 232.08/43.19  | 
% 232.08/43.19  | COMBINE_EQS: (2), (4) imply:
% 232.08/43.19  |   (5)  e1 = e0
% 232.08/43.19  | 
% 232.08/43.19  | REDUCE: (3), (5) imply:
% 232.08/43.19  |   (6)  $false
% 232.08/43.19  | 
% 232.08/43.19  | CLOSE: (6) is inconsistent.
% 232.08/43.19  | 
% 232.08/43.19  End of proof
% 232.08/43.19  
% 232.08/43.19  Sub-proof #2019 shows that the following formulas are inconsistent:
% 232.08/43.19  ----------------------------------------------------------------
% 232.08/43.19    (1)  all_57_0 = e1 & op(e3, e3) = e1
% 232.08/43.19    (2)  all_57_0 = e3
% 232.08/43.19    (3)   ~ (e3 = e1)
% 232.08/43.19  
% 232.08/43.19  Begin of proof
% 232.08/43.19  | 
% 232.08/43.19  | ALPHA: (1) implies:
% 232.08/43.19  |   (4)  all_57_0 = e1
% 232.08/43.19  | 
% 232.08/43.19  | COMBINE_EQS: (2), (4) imply:
% 232.08/43.19  |   (5)  e3 = e1
% 232.08/43.19  | 
% 232.08/43.19  | REDUCE: (3), (5) imply:
% 232.08/43.19  |   (6)  $false
% 232.08/43.19  | 
% 232.08/43.19  | CLOSE: (6) is inconsistent.
% 232.08/43.19  | 
% 232.08/43.19  End of proof
% 232.08/43.19  
% 232.08/43.19  Sub-proof #2020 shows that the following formulas are inconsistent:
% 232.08/43.19  ----------------------------------------------------------------
% 232.08/43.19    (1)  all_57_2 = e2 & op(e2, e3) = e2
% 232.08/43.19    (2)  all_57_2 = e0
% 232.08/43.19    (3)   ~ (e2 = e0)
% 232.08/43.19  
% 232.08/43.19  Begin of proof
% 232.08/43.19  | 
% 232.08/43.19  | ALPHA: (1) implies:
% 232.08/43.19  |   (4)  all_57_2 = e2
% 232.08/43.19  | 
% 232.08/43.19  | COMBINE_EQS: (2), (4) imply:
% 232.08/43.19  |   (5)  e2 = e0
% 232.08/43.19  | 
% 232.08/43.19  | REDUCE: (3), (5) imply:
% 232.08/43.19  |   (6)  $false
% 232.08/43.19  | 
% 232.08/43.19  | CLOSE: (6) is inconsistent.
% 232.08/43.19  | 
% 232.08/43.19  End of proof
% 232.08/43.19  
% 232.08/43.19  Sub-proof #2021 shows that the following formulas are inconsistent:
% 232.08/43.19  ----------------------------------------------------------------
% 232.08/43.19    (1)  all_57_0 = e2 & op(e3, e3) = e2
% 232.08/43.19    (2)  all_57_0 = e3
% 232.08/43.19    (3)   ~ (e3 = e2)
% 232.08/43.19  
% 232.08/43.19  Begin of proof
% 232.08/43.19  | 
% 232.08/43.19  | ALPHA: (1) implies:
% 232.08/43.19  |   (4)  all_57_0 = e2
% 232.08/43.19  | 
% 232.08/43.19  | COMBINE_EQS: (2), (4) imply:
% 232.08/43.19  |   (5)  e3 = e2
% 232.08/43.19  | 
% 232.08/43.19  | REDUCE: (3), (5) imply:
% 232.08/43.19  |   (6)  $false
% 232.08/43.19  | 
% 232.08/43.19  | CLOSE: (6) is inconsistent.
% 232.08/43.19  | 
% 232.08/43.19  End of proof
% 232.08/43.19  
% 232.08/43.19  Sub-proof #2022 shows that the following formulas are inconsistent:
% 232.08/43.19  ----------------------------------------------------------------
% 232.08/43.19    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.08/43.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.08/43.19    (2)   ~ (all_53_9 = e0)
% 232.08/43.19    (3)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 232.08/43.19    (4)   ~ (all_53_13 = e0)
% 232.08/43.19    (5)  op(e2, e0) = all_53_13
% 232.08/43.19    (6)  op(e2, e1) = all_53_9
% 232.08/43.19  
% 232.08/43.19  Begin of proof
% 232.08/43.19  | 
% 232.08/43.19  | BETA: splitting (3) gives:
% 232.08/43.19  | 
% 232.08/43.19  | Case 1:
% 232.08/43.19  | | 
% 232.08/43.19  | |   (7)  all_57_5 = e0 & op(e2, e1) = e0
% 232.08/43.19  | | 
% 232.08/43.19  | | REF_CLOSE: (1), (2), (6), (7) are inconsistent by sub-proof #2023.
% 232.08/43.19  | | 
% 232.08/43.19  | Case 2:
% 232.08/43.19  | | 
% 232.08/43.19  | |   (8)  all_57_10 = e0 & op(e2, e0) = e0
% 232.08/43.19  | | 
% 232.08/43.19  | | ALPHA: (8) implies:
% 232.08/43.19  | |   (9)  op(e2, e0) = e0
% 232.08/43.19  | | 
% 232.08/43.19  | | REF_CLOSE: (1), (4), (5), (9) are inconsistent by sub-proof #2470.
% 232.08/43.19  | | 
% 232.08/43.19  | End of split
% 232.08/43.19  | 
% 232.08/43.19  End of proof
% 232.08/43.19  
% 232.08/43.19  Sub-proof #2023 shows that the following formulas are inconsistent:
% 232.08/43.19  ----------------------------------------------------------------
% 232.08/43.19    (1)  all_57_5 = e0 & op(e2, e1) = e0
% 232.08/43.19    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.08/43.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.08/43.19    (3)  op(e2, e1) = all_53_9
% 232.08/43.19    (4)   ~ (all_53_9 = e0)
% 232.08/43.19  
% 232.08/43.19  Begin of proof
% 232.08/43.19  | 
% 232.08/43.19  | ALPHA: (1) implies:
% 232.08/43.19  |   (5)  op(e2, e1) = e0
% 232.08/43.19  | 
% 232.08/43.19  | GROUND_INST: instantiating (2) with all_53_9, e0, e1, e2, simplifying with
% 232.08/43.19  |              (3), (5) gives:
% 232.08/43.19  |   (6)  all_53_9 = e0
% 232.08/43.19  | 
% 232.08/43.19  | REDUCE: (4), (6) imply:
% 232.08/43.19  |   (7)  $false
% 232.08/43.19  | 
% 232.08/43.19  | CLOSE: (7) is inconsistent.
% 232.08/43.19  | 
% 232.08/43.19  End of proof
% 232.08/43.19  
% 232.08/43.19  Sub-proof #2024 shows that the following formulas are inconsistent:
% 232.08/43.19  ----------------------------------------------------------------
% 232.08/43.19    (1)   ~ (all_53_6 = e0)
% 232.08/43.19    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.08/43.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.08/43.19    (3)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 232.08/43.19    (4)   ~ (all_53_7 = e0)
% 232.08/43.19    (5)  op(e0, e2) = all_53_7
% 232.08/43.19    (6)  op(e1, e2) = all_53_6
% 232.08/43.19  
% 232.08/43.19  Begin of proof
% 232.08/43.19  | 
% 232.08/43.19  | BETA: splitting (3) gives:
% 232.08/43.19  | 
% 232.08/43.19  | Case 1:
% 232.08/43.19  | | 
% 232.08/43.19  | |   (7)  all_57_7 = e0 & op(e1, e2) = e0
% 232.08/43.19  | | 
% 232.08/43.19  | | REF_CLOSE: (1), (2), (6), (7) are inconsistent by sub-proof #2039.
% 232.08/43.19  | | 
% 232.08/43.19  | Case 2:
% 232.08/43.19  | | 
% 232.08/43.19  | |   (8)  all_57_13 = e0 & op(e0, e2) = e0
% 232.08/43.19  | | 
% 232.08/43.19  | | ALPHA: (8) implies:
% 232.08/43.19  | |   (9)  op(e0, e2) = e0
% 232.08/43.19  | | 
% 232.08/43.19  | | REF_CLOSE: (2), (4), (5), (9) are inconsistent by sub-proof #2332.
% 232.08/43.19  | | 
% 232.08/43.19  | End of split
% 232.08/43.19  | 
% 232.08/43.19  End of proof
% 232.08/43.19  
% 232.08/43.19  Sub-proof #2025 shows that the following formulas are inconsistent:
% 232.08/43.19  ----------------------------------------------------------------
% 232.08/43.19    (1)   ~ (all_52_29 = e0)
% 232.08/43.19    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.08/43.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.08/43.19    (3)  all_55_14 = all_52_29
% 232.08/43.19    (4)   ~ (all_52_29 = e3)
% 232.08/43.19    (5)   ~ (all_52_29 = e1)
% 232.08/43.19    (6)  op(e2, e2) = e2
% 232.08/43.19    (7)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 232.08/43.19    (8)  op(all_52_29, all_52_29) = e1
% 232.08/43.19  
% 232.08/43.19  Begin of proof
% 232.08/43.19  | 
% 232.08/43.19  | BETA: splitting (7) gives:
% 232.08/43.19  | 
% 232.08/43.19  | Case 1:
% 232.08/43.19  | | 
% 232.08/43.19  | |   (9)  all_55_14 = e3
% 232.08/43.19  | | 
% 232.08/43.19  | | COMBINE_EQS: (3), (9) imply:
% 232.08/43.19  | |   (10)  all_52_29 = e3
% 232.08/43.19  | | 
% 232.08/43.19  | | SIMP: (10) implies:
% 232.08/43.19  | |   (11)  all_52_29 = e3
% 232.08/43.19  | | 
% 232.08/43.19  | | REDUCE: (4), (11) imply:
% 232.08/43.19  | |   (12)  $false
% 232.08/43.19  | | 
% 232.08/43.19  | | CLOSE: (12) is inconsistent.
% 232.08/43.19  | | 
% 232.08/43.19  | Case 2:
% 232.08/43.19  | | 
% 232.08/43.19  | |   (13)  all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 232.08/43.19  | | 
% 232.08/43.19  | | REF_CLOSE: (1), (2), (3), (5), (6), (8), (13) are inconsistent by sub-proof
% 232.08/43.19  | |            #2026.
% 232.08/43.19  | | 
% 232.08/43.19  | End of split
% 232.08/43.19  | 
% 232.08/43.19  End of proof
% 232.08/43.19  
% 232.08/43.19  Sub-proof #2026 shows that the following formulas are inconsistent:
% 232.08/43.19  ----------------------------------------------------------------
% 232.08/43.19    (1)   ~ (all_52_29 = e0)
% 232.08/43.19    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.08/43.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.08/43.19    (3)  all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 232.08/43.19    (4)  all_55_14 = all_52_29
% 232.08/43.19    (5)   ~ (all_52_29 = e1)
% 232.08/43.19    (6)  op(e2, e2) = e2
% 232.08/43.19    (7)  op(all_52_29, all_52_29) = e1
% 232.08/43.19  
% 232.08/43.19  Begin of proof
% 232.08/43.19  | 
% 232.08/43.19  | BETA: splitting (3) gives:
% 232.08/43.19  | 
% 232.08/43.19  | Case 1:
% 232.08/43.19  | | 
% 232.08/43.19  | |   (8)  all_55_14 = e2
% 232.08/43.19  | | 
% 232.08/43.19  | | COMBINE_EQS: (4), (8) imply:
% 232.08/43.19  | |   (9)  all_52_29 = e2
% 232.08/43.19  | | 
% 232.08/43.19  | | SIMP: (9) implies:
% 232.08/43.19  | |   (10)  all_52_29 = e2
% 232.08/43.19  | | 
% 232.08/43.19  | | REDUCE: (5), (10) imply:
% 232.08/43.19  | |   (11)   ~ (e2 = e1)
% 232.08/43.19  | | 
% 232.08/43.19  | | REDUCE: (7), (10) imply:
% 232.08/43.19  | |   (12)  op(e2, e2) = e1
% 232.08/43.19  | | 
% 232.08/43.19  | | REF_CLOSE: (2), (6), (11), (12) are inconsistent by sub-proof #2306.
% 232.08/43.19  | | 
% 232.08/43.19  | Case 2:
% 232.08/43.19  | | 
% 232.08/43.19  | |   (13)  all_55_14 = e1 | all_55_14 = e0
% 232.08/43.19  | | 
% 232.08/43.19  | | REF_CLOSE: (1), (4), (5), (13) are inconsistent by sub-proof #2035.
% 232.08/43.19  | | 
% 232.08/43.19  | End of split
% 232.08/43.19  | 
% 232.08/43.19  End of proof
% 232.08/43.19  
% 232.08/43.19  Sub-proof #2027 shows that the following formulas are inconsistent:
% 232.08/43.19  ----------------------------------------------------------------
% 232.08/43.19    (1)  all_55_2 = all_53_8
% 232.08/43.19    (2)  all_55_2 = e2
% 232.08/43.19    (3)   ~ (all_53_8 = e2)
% 232.08/43.19  
% 232.08/43.19  Begin of proof
% 232.08/43.19  | 
% 232.08/43.19  | COMBINE_EQS: (1), (2) imply:
% 232.08/43.19  |   (4)  all_53_8 = e2
% 232.08/43.19  | 
% 232.08/43.19  | SIMP: (4) implies:
% 232.08/43.19  |   (5)  all_53_8 = e2
% 232.08/43.19  | 
% 232.08/43.19  | REDUCE: (3), (5) imply:
% 232.08/43.19  |   (6)  $false
% 232.08/43.19  | 
% 232.08/43.19  | CLOSE: (6) is inconsistent.
% 232.08/43.19  | 
% 232.08/43.19  End of proof
% 232.08/43.19  
% 232.08/43.19  Sub-proof #2028 shows that the following formulas are inconsistent:
% 232.08/43.19  ----------------------------------------------------------------
% 232.08/43.19    (1)  all_55_2 = all_53_8
% 232.08/43.19    (2)  all_55_2 = e3
% 232.08/43.19    (3)   ~ (all_53_8 = e3)
% 232.08/43.19  
% 232.08/43.19  Begin of proof
% 232.08/43.19  | 
% 232.08/43.19  | COMBINE_EQS: (1), (2) imply:
% 232.08/43.19  |   (4)  all_53_8 = e3
% 232.08/43.19  | 
% 232.08/43.19  | SIMP: (4) implies:
% 232.08/43.19  |   (5)  all_53_8 = e3
% 232.08/43.19  | 
% 232.08/43.19  | REDUCE: (3), (5) imply:
% 232.08/43.19  |   (6)  $false
% 232.08/43.19  | 
% 232.08/43.19  | CLOSE: (6) is inconsistent.
% 232.08/43.19  | 
% 232.08/43.19  End of proof
% 232.08/43.19  
% 232.08/43.19  Sub-proof #2029 shows that the following formulas are inconsistent:
% 232.08/43.19  ----------------------------------------------------------------
% 232.08/43.19    (1)   ~ (all_52_29 = e0)
% 232.08/43.19    (2)   ~ (all_53_8 = all_52_29)
% 232.08/43.19    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.08/43.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.08/43.19    (4)   ~ (all_53_8 = e1)
% 232.08/43.19    (5)   ~ (all_53_8 = e3)
% 232.08/43.19    (6)  op(e3, e3) = e3
% 232.08/43.19    (7)  all_55_2 = all_53_8
% 232.08/43.19    (8)  all_55_2 = e3 | all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 232.08/43.19    (9)  all_55_14 = all_52_29
% 232.08/43.19    (10)   ~ (all_52_29 = e1)
% 232.08/43.19    (11)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 232.08/43.19    (12)  op(all_52_29, all_52_29) = e1
% 232.08/43.19    (13)   ~ (all_53_8 = e0)
% 232.08/43.19  
% 232.08/43.19  Begin of proof
% 232.08/43.19  | 
% 232.08/43.19  | BETA: splitting (8) gives:
% 232.08/43.19  | 
% 232.08/43.19  | Case 1:
% 232.08/43.19  | | 
% 232.08/43.19  | |   (14)  all_55_2 = e3
% 232.08/43.19  | | 
% 232.08/43.19  | | COMBINE_EQS: (7), (14) imply:
% 232.08/43.19  | |   (15)  all_53_8 = e3
% 232.08/43.19  | | 
% 232.08/43.19  | | REDUCE: (5), (15) imply:
% 232.08/43.19  | |   (16)  $false
% 232.08/43.19  | | 
% 232.08/43.19  | | CLOSE: (16) is inconsistent.
% 232.08/43.19  | | 
% 232.08/43.19  | Case 2:
% 232.08/43.19  | | 
% 232.08/43.19  | |   (17)  all_55_2 = e2 | all_55_2 = e1 | all_55_2 = e0
% 232.08/43.19  | | 
% 232.08/43.19  | | BETA: splitting (17) gives:
% 232.08/43.19  | | 
% 232.08/43.19  | | Case 1:
% 232.08/43.19  | | | 
% 232.08/43.19  | | |   (18)  all_55_2 = e2
% 232.08/43.19  | | | 
% 232.08/43.19  | | | COMBINE_EQS: (7), (18) imply:
% 232.08/43.19  | | |   (19)  all_53_8 = e2
% 232.08/43.19  | | | 
% 232.08/43.19  | | | REDUCE: (2), (19) imply:
% 232.08/43.19  | | |   (20)   ~ (all_52_29 = e2)
% 232.08/43.19  | | | 
% 232.08/43.19  | | | REF_CLOSE: (1), (3), (6), (9), (10), (11), (12), (20) are inconsistent by
% 232.08/43.19  | | |            sub-proof #2033.
% 232.08/43.19  | | | 
% 232.08/43.19  | | Case 2:
% 232.08/43.19  | | | 
% 232.08/43.19  | | |   (21)  all_55_2 = e1 | all_55_2 = e0
% 232.08/43.19  | | | 
% 232.08/43.19  | | | REF_CLOSE: (4), (7), (13), (21) are inconsistent by sub-proof #2030.
% 232.08/43.19  | | | 
% 232.08/43.19  | | End of split
% 232.08/43.19  | | 
% 232.08/43.19  | End of split
% 232.08/43.19  | 
% 232.08/43.19  End of proof
% 232.08/43.19  
% 232.08/43.19  Sub-proof #2030 shows that the following formulas are inconsistent:
% 232.08/43.19  ----------------------------------------------------------------
% 232.08/43.19    (1)  all_55_2 = e1 | all_55_2 = e0
% 232.08/43.19    (2)  all_55_2 = all_53_8
% 232.08/43.19    (3)   ~ (all_53_8 = e1)
% 232.08/43.19    (4)   ~ (all_53_8 = e0)
% 232.08/43.19  
% 232.08/43.19  Begin of proof
% 232.08/43.19  | 
% 232.08/43.19  | BETA: splitting (1) gives:
% 232.08/43.19  | 
% 232.08/43.19  | Case 1:
% 232.08/43.19  | | 
% 232.08/43.19  | |   (5)  all_55_2 = e1
% 232.08/43.19  | | 
% 232.08/43.19  | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #2032.
% 232.08/43.19  | | 
% 232.08/43.19  | Case 2:
% 232.08/43.19  | | 
% 232.08/43.19  | |   (6)  all_55_2 = e0
% 232.08/43.19  | | 
% 232.08/43.19  | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #2031.
% 232.08/43.19  | | 
% 232.08/43.19  | End of split
% 232.08/43.19  | 
% 232.08/43.19  End of proof
% 232.08/43.19  
% 232.08/43.19  Sub-proof #2031 shows that the following formulas are inconsistent:
% 232.08/43.19  ----------------------------------------------------------------
% 232.08/43.19    (1)  all_55_2 = all_53_8
% 232.08/43.19    (2)  all_55_2 = e0
% 232.08/43.19    (3)   ~ (all_53_8 = e0)
% 232.08/43.19  
% 232.08/43.19  Begin of proof
% 232.08/43.19  | 
% 232.08/43.19  | COMBINE_EQS: (1), (2) imply:
% 232.08/43.19  |   (4)  all_53_8 = e0
% 232.08/43.19  | 
% 232.08/43.19  | SIMP: (4) implies:
% 232.08/43.19  |   (5)  all_53_8 = e0
% 232.08/43.19  | 
% 232.08/43.19  | REDUCE: (3), (5) imply:
% 232.08/43.19  |   (6)  $false
% 232.08/43.19  | 
% 232.08/43.19  | CLOSE: (6) is inconsistent.
% 232.08/43.19  | 
% 232.08/43.19  End of proof
% 232.08/43.19  
% 232.08/43.19  Sub-proof #2032 shows that the following formulas are inconsistent:
% 232.08/43.19  ----------------------------------------------------------------
% 232.08/43.19    (1)  all_55_2 = all_53_8
% 232.08/43.19    (2)  all_55_2 = e1
% 232.08/43.19    (3)   ~ (all_53_8 = e1)
% 232.08/43.19  
% 232.08/43.19  Begin of proof
% 232.08/43.19  | 
% 232.08/43.19  | COMBINE_EQS: (1), (2) imply:
% 232.08/43.19  |   (4)  all_53_8 = e1
% 232.08/43.19  | 
% 232.08/43.19  | SIMP: (4) implies:
% 232.08/43.19  |   (5)  all_53_8 = e1
% 232.08/43.19  | 
% 232.08/43.19  | REDUCE: (3), (5) imply:
% 232.08/43.19  |   (6)  $false
% 232.08/43.19  | 
% 232.08/43.19  | CLOSE: (6) is inconsistent.
% 232.08/43.19  | 
% 232.08/43.19  End of proof
% 232.08/43.19  
% 232.08/43.19  Sub-proof #2033 shows that the following formulas are inconsistent:
% 232.08/43.19  ----------------------------------------------------------------
% 232.08/43.19    (1)   ~ (all_52_29 = e0)
% 232.08/43.19    (2)   ~ (all_52_29 = e2)
% 232.08/43.19    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.08/43.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.08/43.19    (4)  op(e3, e3) = e3
% 232.08/43.19    (5)  all_55_14 = all_52_29
% 232.08/43.19    (6)   ~ (all_52_29 = e1)
% 232.08/43.19    (7)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 232.08/43.19    (8)  op(all_52_29, all_52_29) = e1
% 232.08/43.19  
% 232.08/43.19  Begin of proof
% 232.08/43.19  | 
% 232.08/43.19  | SIMP: (2) implies:
% 232.08/43.19  |   (9)   ~ (all_52_29 = e2)
% 232.08/43.19  | 
% 232.08/43.19  | BETA: splitting (7) gives:
% 232.08/43.19  | 
% 232.08/43.19  | Case 1:
% 232.08/43.19  | | 
% 232.08/43.19  | |   (10)  all_55_14 = e3
% 232.08/43.19  | | 
% 232.08/43.19  | | COMBINE_EQS: (5), (10) imply:
% 232.08/43.19  | |   (11)  all_52_29 = e3
% 232.08/43.19  | | 
% 232.08/43.19  | | SIMP: (11) implies:
% 232.08/43.19  | |   (12)  all_52_29 = e3
% 232.08/43.19  | | 
% 232.08/43.19  | | REDUCE: (6), (12) imply:
% 232.08/43.19  | |   (13)   ~ (e3 = e1)
% 232.08/43.19  | | 
% 232.08/43.19  | | REDUCE: (8), (12) imply:
% 232.08/43.19  | |   (14)  op(e3, e3) = e1
% 232.08/43.19  | | 
% 232.08/43.19  | | REF_CLOSE: (3), (4), (13), (14) are inconsistent by sub-proof #2495.
% 232.08/43.19  | | 
% 232.08/43.19  | Case 2:
% 232.08/43.19  | | 
% 232.08/43.19  | |   (15)  all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 232.08/43.19  | | 
% 232.08/43.19  | | REF_CLOSE: (1), (5), (6), (9), (15) are inconsistent by sub-proof #2034.
% 232.08/43.19  | | 
% 232.08/43.19  | End of split
% 232.08/43.19  | 
% 232.08/43.19  End of proof
% 232.08/43.19  
% 232.08/43.19  Sub-proof #2034 shows that the following formulas are inconsistent:
% 232.08/43.19  ----------------------------------------------------------------
% 232.08/43.19    (1)   ~ (all_52_29 = e0)
% 232.08/43.19    (2)   ~ (all_52_29 = e2)
% 232.08/43.19    (3)  all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 232.08/43.19    (4)  all_55_14 = all_52_29
% 232.08/43.19    (5)   ~ (all_52_29 = e1)
% 232.08/43.19  
% 232.08/43.19  Begin of proof
% 232.08/43.19  | 
% 232.08/43.19  | BETA: splitting (3) gives:
% 232.08/43.19  | 
% 232.08/43.19  | Case 1:
% 232.08/43.19  | | 
% 232.08/43.19  | |   (6)  all_55_14 = e2
% 232.08/43.19  | | 
% 232.08/43.19  | | COMBINE_EQS: (4), (6) imply:
% 232.08/43.19  | |   (7)  all_52_29 = e2
% 232.08/43.19  | | 
% 232.08/43.19  | | REDUCE: (2), (7) imply:
% 232.08/43.19  | |   (8)  $false
% 232.08/43.19  | | 
% 232.08/43.19  | | CLOSE: (8) is inconsistent.
% 232.08/43.19  | | 
% 232.08/43.19  | Case 2:
% 232.08/43.19  | | 
% 232.08/43.19  | |   (9)  all_55_14 = e1 | all_55_14 = e0
% 232.08/43.19  | | 
% 232.08/43.19  | | REF_CLOSE: (1), (4), (5), (9) are inconsistent by sub-proof #2035.
% 232.08/43.19  | | 
% 232.08/43.19  | End of split
% 232.08/43.19  | 
% 232.08/43.19  End of proof
% 232.08/43.19  
% 232.08/43.19  Sub-proof #2035 shows that the following formulas are inconsistent:
% 232.08/43.19  ----------------------------------------------------------------
% 232.08/43.19    (1)  all_55_14 = e1 | all_55_14 = e0
% 232.08/43.19    (2)  all_55_14 = all_52_29
% 232.08/43.19    (3)   ~ (all_52_29 = e1)
% 232.08/43.19    (4)   ~ (all_52_29 = e0)
% 232.08/43.19  
% 232.08/43.19  Begin of proof
% 232.08/43.19  | 
% 232.08/43.19  | BETA: splitting (1) gives:
% 232.08/43.19  | 
% 232.08/43.19  | Case 1:
% 232.08/43.19  | | 
% 232.08/43.19  | |   (5)  all_55_14 = e1
% 232.08/43.19  | | 
% 232.08/43.19  | | COMBINE_EQS: (2), (5) imply:
% 232.08/43.19  | |   (6)  all_52_29 = e1
% 232.08/43.19  | | 
% 232.08/43.19  | | REDUCE: (3), (6) imply:
% 232.08/43.19  | |   (7)  $false
% 232.08/43.19  | | 
% 232.08/43.19  | | CLOSE: (7) is inconsistent.
% 232.08/43.19  | | 
% 232.08/43.19  | Case 2:
% 232.08/43.19  | | 
% 232.08/43.19  | |   (8)  all_55_14 = e0
% 232.08/43.19  | | 
% 232.08/43.19  | | COMBINE_EQS: (2), (8) imply:
% 232.08/43.19  | |   (9)  all_52_29 = e0
% 232.08/43.19  | | 
% 232.08/43.19  | | REDUCE: (4), (9) imply:
% 232.08/43.19  | |   (10)  $false
% 232.08/43.19  | | 
% 232.08/43.19  | | CLOSE: (10) is inconsistent.
% 232.08/43.19  | | 
% 232.08/43.19  | End of split
% 232.08/43.19  | 
% 232.08/43.19  End of proof
% 232.08/43.19  
% 232.08/43.19  Sub-proof #2036 shows that the following formulas are inconsistent:
% 232.08/43.19  ----------------------------------------------------------------
% 232.08/43.19    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.08/43.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.08/43.19    (2)   ~ (e1 = e0)
% 232.08/43.19    (3)  op(e0, e0) = e0
% 232.08/43.19    (4)  op(e1, e1) = e0
% 232.08/43.19    (5)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 &
% 232.08/43.19         op(all_52_17, all_52_17) = e3 & op(all_52_19, all_52_19) = e2 &
% 232.08/43.19         op(all_52_21, all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1,
% 232.08/43.19           e3) = all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 &
% 232.08/43.19         op(e1, e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 232.08/43.19         $i(all_52_23)
% 232.08/43.19  
% 232.08/43.19  Begin of proof
% 232.08/43.19  | 
% 232.08/43.19  | ALPHA: (5) implies:
% 232.08/43.19  |   (6)  op(e1, e1) = all_52_21
% 232.08/43.19  |   (7)  op(all_52_21, all_52_21) = e1
% 232.08/43.19  | 
% 232.08/43.19  | GROUND_INST: instantiating (1) with e0, all_52_21, e1, e1, simplifying with
% 232.08/43.19  |              (4), (6) gives:
% 232.08/43.19  |   (8)  all_52_21 = e0
% 232.08/43.19  | 
% 232.08/43.19  | REDUCE: (7), (8) imply:
% 232.08/43.19  |   (9)  op(e0, e0) = e1
% 232.08/43.19  | 
% 232.08/43.19  | REF_CLOSE: (1), (2), (3), (9) are inconsistent by sub-proof #2290.
% 232.08/43.19  | 
% 232.08/43.19  End of proof
% 232.08/43.19  
% 232.08/43.19  Sub-proof #2037 shows that the following formulas are inconsistent:
% 232.08/43.19  ----------------------------------------------------------------
% 232.08/43.19    (1)  op(e2, e3) = e0
% 232.08/43.19    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.08/43.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.08/43.19    (3)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 232.08/43.19           op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 232.08/43.19           op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 232.08/43.19           = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3, e0)
% 232.08/43.19           = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) & $i(all_52_7))
% 232.08/43.19         | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0 &
% 232.08/43.19           op(all_52_9, all_52_9) = e3 & op(all_52_11, all_52_11) = e2 &
% 232.08/43.19           op(all_52_13, all_52_13) = e1 & op(all_52_15, all_52_15) = e0 & op(e2,
% 232.08/43.19             e3) = all_52_9 & op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13 &
% 232.08/43.19           op(e2, e0) = all_52_15 & $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 232.08/43.19           $i(all_52_15))
% 232.08/43.19    (4)   ~ (e3 = e0)
% 232.08/43.19    (5)   ~ (e2 = e0)
% 232.08/43.19    (6)  op(e0, e0) = e0
% 232.08/43.19    (7)  op(e3, e2) = e0
% 232.08/43.19  
% 232.08/43.19  Begin of proof
% 232.08/43.19  | 
% 232.08/43.19  | BETA: splitting (3) gives:
% 232.08/43.19  | 
% 232.08/43.19  | Case 1:
% 232.08/43.19  | | 
% 232.08/43.19  | |   (8)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 232.08/43.19  | |        op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 232.08/43.19  | |        op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3,
% 232.08/43.19  | |          e3) = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 &
% 232.08/43.19  | |        op(e3, e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 232.08/43.19  | |        $i(all_52_7)
% 232.08/43.19  | | 
% 232.08/43.19  | | ALPHA: (8) implies:
% 232.08/43.19  | |   (9)  op(e3, e2) = all_52_3
% 232.08/43.19  | |   (10)  op(all_52_3, all_52_3) = e2
% 232.08/43.19  | | 
% 232.08/43.19  | | REF_CLOSE: (2), (5), (6), (7), (9), (10) are inconsistent by sub-proof
% 232.08/43.19  | |            #2399.
% 232.08/43.19  | | 
% 232.08/43.19  | Case 2:
% 232.08/43.19  | | 
% 232.08/43.19  | |   (11)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0 &
% 232.08/43.19  | |         op(all_52_9, all_52_9) = e3 & op(all_52_11, all_52_11) = e2 &
% 232.08/43.19  | |         op(all_52_13, all_52_13) = e1 & op(all_52_15, all_52_15) = e0 &
% 232.08/43.19  | |         op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 & op(e2, e1) =
% 232.08/43.19  | |         all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) & $i(all_52_11) &
% 232.08/43.19  | |         $i(all_52_13) & $i(all_52_15)
% 232.08/43.19  | | 
% 232.08/43.19  | | ALPHA: (11) implies:
% 232.08/43.19  | |   (12)  op(e2, e3) = all_52_9
% 232.08/43.19  | |   (13)  op(all_52_9, all_52_9) = e3
% 232.08/43.19  | | 
% 232.08/43.19  | | GROUND_INST: instantiating (2) with e0, all_52_9, e3, e2, simplifying with
% 232.08/43.19  | |              (1), (12) gives:
% 232.08/43.19  | |   (14)  all_52_9 = e0
% 232.08/43.19  | | 
% 232.08/43.19  | | REDUCE: (13), (14) imply:
% 232.08/43.19  | |   (15)  op(e0, e0) = e3
% 232.08/43.19  | | 
% 232.08/43.19  | | REF_CLOSE: (2), (4), (6), (15) are inconsistent by sub-proof #2304.
% 232.08/43.19  | | 
% 232.08/43.19  | End of split
% 232.08/43.19  | 
% 232.08/43.19  End of proof
% 232.08/43.19  
% 232.08/43.19  Sub-proof #2038 shows that the following formulas are inconsistent:
% 232.08/43.19  ----------------------------------------------------------------
% 232.08/43.19    (1)   ~ (all_53_6 = e0)
% 232.08/43.19    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.08/43.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.08/43.19    (3)   ~ (all_53_2 = e0)
% 232.08/43.19    (4)  op(e1, e3) = all_53_2
% 232.08/43.19    (5)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0)
% 232.08/43.19    (6)  op(e1, e2) = all_53_6
% 232.08/43.19  
% 232.08/43.19  Begin of proof
% 232.08/43.19  | 
% 232.08/43.19  | BETA: splitting (5) gives:
% 232.08/43.19  | 
% 232.08/43.19  | Case 1:
% 232.08/43.19  | | 
% 232.08/43.19  | |   (7)  all_57_6 = e0 & op(e1, e3) = e0
% 232.08/43.19  | | 
% 232.08/43.19  | | ALPHA: (7) implies:
% 232.08/43.19  | |   (8)  op(e1, e3) = e0
% 232.08/43.19  | | 
% 232.08/43.19  | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #2154.
% 232.08/43.19  | | 
% 232.08/43.19  | Case 2:
% 232.08/43.19  | | 
% 232.08/43.19  | |   (9)  all_57_7 = e0 & op(e1, e2) = e0
% 232.08/43.19  | | 
% 232.08/43.19  | | REF_CLOSE: (1), (2), (6), (9) are inconsistent by sub-proof #2039.
% 232.08/43.19  | | 
% 232.08/43.19  | End of split
% 232.08/43.19  | 
% 232.08/43.19  End of proof
% 232.08/43.19  
% 232.08/43.19  Sub-proof #2039 shows that the following formulas are inconsistent:
% 232.08/43.19  ----------------------------------------------------------------
% 232.08/43.19    (1)  all_57_7 = e0 & op(e1, e2) = e0
% 232.08/43.19    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.08/43.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.08/43.19    (3)  op(e1, e2) = all_53_6
% 232.08/43.19    (4)   ~ (all_53_6 = e0)
% 232.08/43.19  
% 232.08/43.19  Begin of proof
% 232.08/43.19  | 
% 232.08/43.19  | ALPHA: (1) implies:
% 232.08/43.19  |   (5)  op(e1, e2) = e0
% 232.08/43.19  | 
% 232.08/43.19  | GROUND_INST: instantiating (2) with all_53_6, e0, e2, e1, simplifying with
% 232.08/43.19  |              (3), (5) gives:
% 232.08/43.19  |   (6)  all_53_6 = e0
% 232.08/43.19  | 
% 232.08/43.19  | REDUCE: (4), (6) imply:
% 232.08/43.19  |   (7)  $false
% 232.08/43.20  | 
% 232.08/43.20  | CLOSE: (7) is inconsistent.
% 232.08/43.20  | 
% 232.08/43.20  End of proof
% 232.08/43.20  
% 232.08/43.20  Sub-proof #2040 shows that the following formulas are inconsistent:
% 232.08/43.20  ----------------------------------------------------------------
% 232.08/43.20    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.08/43.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.08/43.20    (2)   ~ (all_6_2 = e3)
% 232.08/43.20    (3)  op(e1, e1) = all_6_2
% 232.08/43.20    (4)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 232.08/43.20    (5)   ~ (e3 = e2)
% 232.08/43.20    (6)  all_57_11 = e2
% 232.08/43.20  
% 232.08/43.20  Begin of proof
% 232.08/43.20  | 
% 232.08/43.20  | BETA: splitting (4) gives:
% 232.08/43.20  | 
% 232.08/43.20  | Case 1:
% 232.08/43.20  | | 
% 232.08/43.20  | |   (7)  all_57_8 = e3 & op(e1, e1) = e3
% 232.08/43.20  | | 
% 232.08/43.20  | | ALPHA: (7) implies:
% 232.08/43.20  | |   (8)  op(e1, e1) = e3
% 232.08/43.20  | | 
% 232.08/43.20  | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #2468.
% 232.08/43.20  | | 
% 232.08/43.20  | Case 2:
% 232.08/43.20  | | 
% 232.08/43.20  | |   (9)  all_57_11 = e3 & op(e1, e0) = e3
% 232.08/43.20  | | 
% 232.08/43.20  | | ALPHA: (9) implies:
% 232.08/43.20  | |   (10)  all_57_11 = e3
% 232.08/43.20  | | 
% 232.08/43.20  | | REF_CLOSE: (5), (6), (10) are inconsistent by sub-proof #2119.
% 232.08/43.20  | | 
% 232.08/43.20  | End of split
% 232.08/43.20  | 
% 232.08/43.20  End of proof
% 232.08/43.20  
% 232.08/43.20  Sub-proof #2041 shows that the following formulas are inconsistent:
% 232.08/43.20  ----------------------------------------------------------------
% 232.08/43.20    (1)  all_57_11 = e0 & op(e1, e0) = e0
% 232.08/43.20    (2)  all_57_11 = e2
% 232.08/43.20    (3)   ~ (e2 = e0)
% 232.08/43.20  
% 232.08/43.20  Begin of proof
% 232.08/43.20  | 
% 232.08/43.20  | ALPHA: (1) implies:
% 232.08/43.20  |   (4)  all_57_11 = e0
% 232.08/43.20  | 
% 232.08/43.20  | COMBINE_EQS: (2), (4) imply:
% 232.08/43.20  |   (5)  e2 = e0
% 232.08/43.20  | 
% 232.08/43.20  | REDUCE: (3), (5) imply:
% 232.08/43.20  |   (6)  $false
% 232.08/43.20  | 
% 232.08/43.20  | CLOSE: (6) is inconsistent.
% 232.08/43.20  | 
% 232.08/43.20  End of proof
% 232.08/43.20  
% 232.08/43.20  Sub-proof #2042 shows that the following formulas are inconsistent:
% 232.08/43.20  ----------------------------------------------------------------
% 232.08/43.20    (1)  all_57_7 = e0 & op(e1, e2) = e0
% 232.08/43.20    (2)  all_57_7 = e3
% 232.08/43.20    (3)   ~ (e3 = e0)
% 232.08/43.20  
% 232.08/43.20  Begin of proof
% 232.08/43.20  | 
% 232.08/43.20  | ALPHA: (1) implies:
% 232.08/43.20  |   (4)  all_57_7 = e0
% 232.08/43.20  | 
% 232.08/43.20  | COMBINE_EQS: (2), (4) imply:
% 232.08/43.20  |   (5)  e3 = e0
% 232.08/43.20  | 
% 232.08/43.20  | REDUCE: (3), (5) imply:
% 232.08/43.20  |   (6)  $false
% 232.08/43.20  | 
% 232.08/43.20  | CLOSE: (6) is inconsistent.
% 232.08/43.20  | 
% 232.08/43.20  End of proof
% 232.08/43.20  
% 232.08/43.20  Sub-proof #2043 shows that the following formulas are inconsistent:
% 232.08/43.20  ----------------------------------------------------------------
% 232.08/43.20    (1)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 232.08/43.20    (2)   ~ (e3 = e1)
% 232.08/43.20    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.08/43.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.08/43.20    (4)   ~ (e3 = e2)
% 232.08/43.20    (5)   ~ (e3 = e0)
% 232.08/43.20    (6)  all_57_9 = e0
% 232.08/43.20    (7)   ~ (e2 = e0)
% 232.08/43.20    (8)  op(e1, e1) = e2
% 232.08/43.20    (9)  op(e0, e0) = e1
% 232.08/43.20    (10)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 232.08/43.20          (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 232.08/43.20    (11)   ~ (e2 = e1)
% 232.08/43.20    (12)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 232.08/43.20          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 232.08/43.20  
% 232.08/43.20  Begin of proof
% 232.08/43.20  | 
% 232.08/43.20  | BETA: splitting (1) gives:
% 232.08/43.20  | 
% 232.08/43.20  | Case 1:
% 232.08/43.20  | | 
% 232.08/43.20  | |   (13)  all_57_8 = e1 & op(e1, e1) = e1
% 232.08/43.20  | | 
% 232.08/43.20  | | ALPHA: (13) implies:
% 232.08/43.20  | |   (14)  op(e1, e1) = e1
% 232.08/43.20  | | 
% 232.08/43.20  | | REF_CLOSE: (3), (8), (11), (14) are inconsistent by sub-proof #2423.
% 232.08/43.20  | | 
% 232.08/43.20  | Case 2:
% 232.08/43.20  | | 
% 232.08/43.20  | |   (15)  all_57_11 = e1 & op(e1, e0) = e1
% 232.08/43.20  | | 
% 232.08/43.20  | | ALPHA: (15) implies:
% 232.08/43.20  | |   (16)  all_57_11 = e1
% 232.08/43.20  | | 
% 232.08/43.20  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (16) are
% 232.08/43.20  | |            inconsistent by sub-proof #2047.
% 232.08/43.20  | | 
% 232.08/43.20  | End of split
% 232.08/43.20  | 
% 232.08/43.20  End of proof
% 232.08/43.20  
% 232.08/43.20  Sub-proof #2044 shows that the following formulas are inconsistent:
% 232.08/43.20  ----------------------------------------------------------------
% 232.08/43.20    (1)  all_57_6 = e1 & op(e1, e3) = e1
% 232.08/43.20    (2)  all_57_6 = e0
% 232.08/43.20    (3)   ~ (e1 = e0)
% 232.08/43.20  
% 232.08/43.20  Begin of proof
% 232.08/43.20  | 
% 232.08/43.20  | ALPHA: (1) implies:
% 232.08/43.20  |   (4)  all_57_6 = e1
% 232.08/43.20  | 
% 232.08/43.20  | COMBINE_EQS: (2), (4) imply:
% 232.08/43.20  |   (5)  e1 = e0
% 232.08/43.20  | 
% 232.08/43.20  | REDUCE: (3), (5) imply:
% 232.08/43.20  |   (6)  $false
% 232.08/43.20  | 
% 232.08/43.20  | CLOSE: (6) is inconsistent.
% 232.08/43.20  | 
% 232.08/43.20  End of proof
% 232.08/43.20  
% 232.08/43.20  Sub-proof #2045 shows that the following formulas are inconsistent:
% 232.08/43.20  ----------------------------------------------------------------
% 232.08/43.20    (1)  all_57_4 = e0 & op(e3, e1) = e0
% 232.08/43.20    (2)  all_57_4 = e2
% 232.08/43.20    (3)   ~ (e2 = e0)
% 232.08/43.20  
% 232.08/43.20  Begin of proof
% 232.08/43.20  | 
% 232.08/43.20  | ALPHA: (1) implies:
% 232.08/43.20  |   (4)  all_57_4 = e0
% 232.08/43.20  | 
% 232.08/43.20  | COMBINE_EQS: (2), (4) imply:
% 232.08/43.20  |   (5)  e2 = e0
% 232.08/43.20  | 
% 232.08/43.20  | REDUCE: (3), (5) imply:
% 232.08/43.20  |   (6)  $false
% 232.08/43.20  | 
% 232.08/43.20  | CLOSE: (6) is inconsistent.
% 232.08/43.20  | 
% 232.08/43.20  End of proof
% 232.08/43.20  
% 232.08/43.20  Sub-proof #2046 shows that the following formulas are inconsistent:
% 232.08/43.20  ----------------------------------------------------------------
% 232.08/43.20    (1)  all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 232.08/43.20    (2)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 232.08/43.20    (3)  all_57_9 = e2
% 232.08/43.20    (4)   ~ (all_53_6 = all_53_14)
% 232.08/43.20    (5)   ~ (all_53_6 = e2)
% 232.08/43.20    (6)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 232.08/43.20         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 232.08/43.20    (7)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 232.08/43.20         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 232.08/43.20    (8)   ~ (all_53_8 = all_53_11)
% 232.08/43.20    (9)   ~ (e3 = e1)
% 232.08/43.20    (10)   ~ (all_53_13 = e1)
% 232.08/43.20    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.08/43.20            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.08/43.20    (12)   ~ (all_53_7 = e1)
% 232.08/43.20    (13)   ~ (all_53_3 = all_53_7)
% 232.08/43.20    (14)   ~ (all_6_2 = e3)
% 232.08/43.20    (15)  op(e1, e1) = all_6_2
% 232.08/43.20    (16)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 232.08/43.20    (17)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 232.08/43.20          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 232.08/43.20    (18)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 232.08/43.20    (19)  all_55_9 = all_53_6
% 232.08/43.20    (20)   ~ (all_53_4 = all_53_12)
% 232.08/43.20    (21)  all_57_12 = e2
% 232.08/43.20    (22)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 232.08/43.20          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 232.08/43.20    (23)   ~ (all_53_12 = all_53_13)
% 232.08/43.20    (24)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 232.08/43.20          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 232.08/43.20    (25)  all_55_1 = all_53_4
% 232.08/43.20    (26)  op(e1, e0) = all_53_14
% 232.08/43.20    (27)   ~ (all_53_6 = all_53_7)
% 232.08/43.20    (28)  all_55_7 = e3 | all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 232.08/43.20    (29)   ~ (e3 = e0)
% 232.08/43.20    (30)  op(e3, e3) = e3
% 232.08/43.20    (31)  op(e3, e0) = e2
% 232.08/43.20    (32)  op(e0, e3) = all_53_3
% 232.08/43.20    (33)   ~ (all_53_4 = all_53_7)
% 232.08/43.20    (34)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 232.08/43.20          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 232.08/43.20            e1)
% 232.08/43.20    (35)  op(e3, e2) = all_53_4
% 232.08/43.20    (36)   ~ (e2 = e0)
% 232.08/43.20    (37)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 232.08/43.20            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 232.08/43.20            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 232.08/43.20            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 232.08/43.20              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 232.08/43.20            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 232.08/43.20            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 232.08/43.20              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 232.08/43.20              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 232.08/43.20            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 232.08/43.20            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 232.08/43.20            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 232.08/43.20              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 232.08/43.20              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 232.08/43.20            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 232.08/43.20              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 232.08/43.20            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 232.08/43.20            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 232.08/43.20              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 232.08/43.20              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 232.08/43.20            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 232.08/43.20            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 232.08/43.20    (38)  op(e2, e2) = e2
% 232.08/43.20    (39)   ~ (e1 = e0)
% 232.08/43.20    (40)   ~ (all_53_3 = all_53_11)
% 232.08/43.20    (41)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 232.08/43.20          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 232.08/43.20    (42)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 232.08/43.20          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 232.08/43.20    (43)   ~ (all_53_14 = e1)
% 232.08/43.20    (44)   ~ (all_53_12 = e1)
% 232.08/43.20    (45)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 232.08/43.20    (46)   ~ (all_53_7 = all_53_11)
% 232.08/43.20    (47)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 232.08/43.20          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 232.08/43.20            e3)
% 232.08/43.20    (48)   ~ (all_53_4 = all_53_6)
% 232.08/43.20    (49)  op(e0, e2) = all_53_7
% 232.08/43.20    (50)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 232.08/43.20          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 232.08/43.20            e2)
% 232.08/43.20    (51)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 232.08/43.20              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 232.08/43.20                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 232.08/43.20                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 232.08/43.20    (52)  op(e1, e1) = e2
% 232.08/43.20    (53)   ~ (all_53_11 = e1)
% 232.08/43.20    (54)  all_55_13 = all_53_7
% 232.08/43.20    (55)  op(e0, e0) = e1
% 232.08/43.20    (56)  op(e2, e0) = all_53_13
% 232.08/43.20    (57)  all_55_11 = all_53_14
% 232.08/43.20    (58)   ~ (all_53_12 = e3)
% 232.08/43.20    (59)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 232.08/43.20          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 232.08/43.20    (60)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 232.08/43.20          (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 232.08/43.20    (61)   ~ (all_53_13 = all_53_14)
% 232.08/43.20    (62)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 232.08/43.20          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 232.08/43.20    (63)  op(e0, e3) = e2
% 232.08/43.20    (64)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 232.08/43.20          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 232.08/43.20    (65)   ~ (all_6_2 = e0)
% 232.08/43.20    (66)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 232.08/43.20          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 232.08/43.20    (67)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 232.08/43.20          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 232.08/43.20    (68)   ~ (all_53_12 = all_53_14)
% 232.08/43.20    (69)  all_55_14 = all_53_11
% 232.08/43.20    (70)  all_57_3 = e2
% 232.11/43.20    (71)  op(e3, e1) = all_53_8
% 232.11/43.20    (72)  all_55_7 = all_53_13
% 232.11/43.20    (73)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 232.11/43.20          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 232.11/43.20    (74)   ~ (all_53_4 = e3)
% 232.11/43.20    (75)  op(e3, e0) = all_53_12
% 232.11/43.20  
% 232.11/43.20  Begin of proof
% 232.11/43.20  | 
% 232.11/43.20  | GROUND_INST: instantiating (11) with all_53_3, e2, e3, e0, simplifying with
% 232.11/43.20  |              (32), (63) gives:
% 232.11/43.20  |   (76)  all_53_3 = e2
% 232.11/43.20  | 
% 232.11/43.20  | GROUND_INST: instantiating (11) with all_53_12, e2, e0, e3, simplifying with
% 232.11/43.20  |              (31), (75) gives:
% 232.11/43.20  |   (77)  all_53_12 = e2
% 232.11/43.20  | 
% 232.11/43.20  | REDUCE: (13), (76) imply:
% 232.11/43.20  |   (78)   ~ (all_53_7 = e2)
% 232.11/43.20  | 
% 232.11/43.20  | SIMP: (78) implies:
% 232.11/43.20  |   (79)   ~ (all_53_7 = e2)
% 232.11/43.20  | 
% 232.11/43.20  | REDUCE: (40), (76) imply:
% 232.11/43.20  |   (80)   ~ (all_53_11 = e2)
% 232.11/43.20  | 
% 232.11/43.20  | SIMP: (80) implies:
% 232.11/43.20  |   (81)   ~ (all_53_11 = e2)
% 232.11/43.20  | 
% 232.11/43.20  | REDUCE: (20), (77) imply:
% 232.11/43.20  |   (82)   ~ (all_53_4 = e2)
% 232.11/43.20  | 
% 232.11/43.20  | REDUCE: (23), (77) imply:
% 232.11/43.20  |   (83)   ~ (all_53_13 = e2)
% 232.11/43.20  | 
% 232.11/43.20  | SIMP: (83) implies:
% 232.11/43.20  |   (84)   ~ (all_53_13 = e2)
% 232.11/43.20  | 
% 232.11/43.20  | REDUCE: (68), (77) imply:
% 232.11/43.20  |   (85)   ~ (all_53_14 = e2)
% 232.11/43.20  | 
% 232.11/43.20  | SIMP: (85) implies:
% 232.11/43.20  |   (86)   ~ (all_53_14 = e2)
% 232.11/43.20  | 
% 232.11/43.20  | REDUCE: (58), (77) imply:
% 232.11/43.20  |   (87)   ~ (e3 = e2)
% 232.11/43.20  | 
% 232.11/43.20  | SIMP: (87) implies:
% 232.11/43.20  |   (88)   ~ (e3 = e2)
% 232.11/43.20  | 
% 232.11/43.20  | REDUCE: (44), (77) imply:
% 232.11/43.20  |   (89)   ~ (e2 = e1)
% 232.11/43.20  | 
% 232.11/43.20  | BETA: splitting (37) gives:
% 232.11/43.20  | 
% 232.11/43.20  | Case 1:
% 232.11/43.20  | | 
% 232.11/43.20  | |   (90)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 232.11/43.20  | |           op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 232.11/43.20  | |           op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3,
% 232.11/43.20  | |             e3) = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 &
% 232.11/43.20  | |           op(e3, e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5)
% 232.11/43.20  | |           & $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1
% 232.11/43.20  | |           & all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 232.11/43.20  | |             all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 232.11/43.20  | |             all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11
% 232.11/43.20  | |           & op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 232.11/43.20  | |           $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 232.11/43.20  | | 
% 232.11/43.20  | | BETA: splitting (90) gives:
% 232.11/43.20  | | 
% 232.11/43.20  | | Case 1:
% 232.11/43.20  | | | 
% 232.11/43.20  | | |   (91)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 232.11/43.20  | | |         op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 232.11/43.20  | | |         op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3,
% 232.11/43.20  | | |           e3) = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 &
% 232.11/43.20  | | |         op(e3, e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5)
% 232.11/43.20  | | |         & $i(all_52_7)
% 232.11/43.20  | | | 
% 232.11/43.20  | | | REF_CLOSE: (11), (31), (36), (38), (91) are inconsistent by sub-proof
% 232.11/43.20  | | |            #2296.
% 232.11/43.20  | | | 
% 232.11/43.20  | | Case 2:
% 232.11/43.20  | | | 
% 232.11/43.20  | | |   (92)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0 &
% 232.11/43.20  | | |         op(all_52_9, all_52_9) = e3 & op(all_52_11, all_52_11) = e2 &
% 232.11/43.20  | | |         op(all_52_13, all_52_13) = e1 & op(all_52_15, all_52_15) = e0 &
% 232.11/43.20  | | |         op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 & op(e2, e1) =
% 232.11/43.20  | | |         all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) & $i(all_52_11)
% 232.11/43.20  | | |         & $i(all_52_13) & $i(all_52_15)
% 232.11/43.20  | | | 
% 232.11/43.20  | | | ALPHA: (92) implies:
% 232.11/43.20  | | |   (93)  op(e2, e0) = all_52_15
% 232.11/43.20  | | |   (94)  op(e2, e2) = all_52_11
% 232.11/43.20  | | |   (95)  op(all_52_15, all_52_15) = e0
% 232.11/43.20  | | |   (96)  op(all_52_11, all_52_11) = e2
% 232.11/43.20  | | | 
% 232.11/43.20  | | | GROUND_INST: instantiating (11) with all_53_13, all_52_15, e0, e2,
% 232.11/43.20  | | |              simplifying with (56), (93) gives:
% 232.11/43.20  | | |   (97)  all_53_13 = all_52_15
% 232.11/43.20  | | | 
% 232.11/43.20  | | | GROUND_INST: instantiating (11) with e2, all_52_11, e2, e2, simplifying
% 232.11/43.20  | | |              with (38), (94) gives:
% 232.11/43.20  | | |   (98)  all_52_11 = e2
% 232.11/43.20  | | | 
% 232.11/43.20  | | | COMBINE_EQS: (72), (97) imply:
% 232.11/43.20  | | |   (99)  all_55_7 = all_52_15
% 232.11/43.20  | | | 
% 232.11/43.20  | | | REDUCE: (61), (97) imply:
% 232.11/43.20  | | |   (100)   ~ (all_53_14 = all_52_15)
% 232.11/43.20  | | | 
% 232.11/43.20  | | | SIMP: (100) implies:
% 232.11/43.20  | | |   (101)   ~ (all_53_14 = all_52_15)
% 232.11/43.20  | | | 
% 232.11/43.20  | | | REDUCE: (84), (97) imply:
% 232.11/43.20  | | |   (102)   ~ (all_52_15 = e2)
% 232.11/43.20  | | | 
% 232.11/43.20  | | | REDUCE: (10), (97) imply:
% 232.11/43.20  | | |   (103)   ~ (all_52_15 = e1)
% 232.11/43.20  | | | 
% 232.11/43.20  | | | BETA: splitting (45) gives:
% 232.11/43.20  | | | 
% 232.11/43.20  | | | Case 1:
% 232.11/43.20  | | | | 
% 232.11/43.20  | | | |   (104)  all_55_14 = e3
% 232.11/43.20  | | | | 
% 232.11/43.20  | | | | COMBINE_EQS: (69), (104) imply:
% 232.11/43.20  | | | |   (105)  all_53_11 = e3
% 232.11/43.20  | | | | 
% 232.11/43.20  | | | | REDUCE: (46), (105) imply:
% 232.11/43.20  | | | |   (106)   ~ (all_53_7 = e3)
% 232.11/43.20  | | | | 
% 232.11/43.20  | | | | BETA: splitting (1) gives:
% 232.11/43.20  | | | | 
% 232.11/43.20  | | | | Case 1:
% 232.11/43.20  | | | | | 
% 232.11/43.20  | | | | |   (107)  all_55_13 = e3
% 232.11/43.20  | | | | | 
% 232.11/43.20  | | | | | REF_CLOSE: (54), (106), (107) are inconsistent by sub-proof #2080.
% 232.11/43.20  | | | | | 
% 232.11/43.20  | | | | Case 2:
% 232.11/43.20  | | | | | 
% 232.11/43.20  | | | | |   (108)  all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 232.11/43.20  | | | | | 
% 232.11/43.20  | | | | | BETA: splitting (108) gives:
% 232.11/43.20  | | | | | 
% 232.11/43.20  | | | | | Case 1:
% 232.11/43.20  | | | | | | 
% 232.11/43.20  | | | | | |   (109)  all_55_13 = e2
% 232.11/43.20  | | | | | | 
% 232.11/43.20  | | | | | | REF_CLOSE: (54), (79), (109) are inconsistent by sub-proof #2287.
% 232.11/43.20  | | | | | | 
% 232.11/43.20  | | | | | Case 2:
% 232.11/43.20  | | | | | | 
% 232.11/43.20  | | | | | |   (110)  all_55_13 = e1 | all_55_13 = e0
% 232.11/43.20  | | | | | | 
% 232.11/43.20  | | | | | | BETA: splitting (110) gives:
% 232.11/43.20  | | | | | | 
% 232.11/43.20  | | | | | | Case 1:
% 232.11/43.20  | | | | | | | 
% 232.11/43.20  | | | | | | |   (111)  all_55_13 = e1
% 232.11/43.20  | | | | | | | 
% 232.11/43.20  | | | | | | | COMBINE_EQS: (54), (111) imply:
% 232.11/43.20  | | | | | | |   (112)  all_53_7 = e1
% 232.11/43.20  | | | | | | | 
% 232.11/43.20  | | | | | | | REDUCE: (12), (112) imply:
% 232.11/43.20  | | | | | | |   (113)  $false
% 232.11/43.20  | | | | | | | 
% 232.11/43.20  | | | | | | | CLOSE: (113) is inconsistent.
% 232.11/43.20  | | | | | | | 
% 232.11/43.20  | | | | | | Case 2:
% 232.11/43.20  | | | | | | | 
% 232.11/43.20  | | | | | | |   (114)  all_55_13 = e0
% 232.11/43.20  | | | | | | | 
% 232.11/43.20  | | | | | | | COMBINE_EQS: (54), (114) imply:
% 232.11/43.20  | | | | | | |   (115)  all_53_7 = e0
% 232.11/43.20  | | | | | | | 
% 232.11/43.20  | | | | | | | REDUCE: (33), (115) imply:
% 232.11/43.20  | | | | | | |   (116)   ~ (all_53_4 = e0)
% 232.11/43.20  | | | | | | | 
% 232.11/43.20  | | | | | | | REDUCE: (49), (115) imply:
% 232.11/43.20  | | | | | | |   (117)  op(e0, e2) = e0
% 232.11/43.20  | | | | | | | 
% 232.11/43.20  | | | | | | | BETA: splitting (2) gives:
% 232.11/43.20  | | | | | | | 
% 232.11/43.20  | | | | | | | Case 1:
% 232.11/43.20  | | | | | | | | 
% 232.11/43.20  | | | | | | | |   (118)  all_55_1 = e3
% 232.11/43.20  | | | | | | | | 
% 232.11/43.20  | | | | | | | | REF_CLOSE: (25), (74), (118) are inconsistent by sub-proof
% 232.11/43.20  | | | | | | | |            #2295.
% 232.11/43.20  | | | | | | | | 
% 232.11/43.20  | | | | | | | Case 2:
% 232.11/43.20  | | | | | | | | 
% 232.11/43.20  | | | | | | | |   (119)  all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 232.11/43.20  | | | | | | | | 
% 232.11/43.20  | | | | | | | | BETA: splitting (119) gives:
% 232.11/43.20  | | | | | | | | 
% 232.11/43.20  | | | | | | | | Case 1:
% 232.11/43.20  | | | | | | | | | 
% 232.11/43.20  | | | | | | | | |   (120)  all_55_1 = e2
% 232.11/43.20  | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | REF_CLOSE: (25), (82), (120) are inconsistent by sub-proof
% 232.11/43.20  | | | | | | | | |            #2284.
% 232.11/43.20  | | | | | | | | | 
% 232.11/43.20  | | | | | | | | Case 2:
% 232.11/43.20  | | | | | | | | | 
% 232.11/43.20  | | | | | | | | |   (121)  all_55_1 = e1 | all_55_1 = e0
% 232.11/43.20  | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | BETA: splitting (121) gives:
% 232.11/43.20  | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | Case 1:
% 232.11/43.20  | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | |   (122)  all_55_1 = e1
% 232.11/43.20  | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | COMBINE_EQS: (25), (122) imply:
% 232.11/43.20  | | | | | | | | | |   (123)  all_53_4 = e1
% 232.11/43.20  | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | SIMP: (123) implies:
% 232.11/43.20  | | | | | | | | | |   (124)  all_53_4 = e1
% 232.11/43.20  | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | REDUCE: (48), (124) imply:
% 232.11/43.20  | | | | | | | | | |   (125)   ~ (all_53_6 = e1)
% 232.11/43.20  | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | SIMP: (125) implies:
% 232.11/43.20  | | | | | | | | | |   (126)   ~ (all_53_6 = e1)
% 232.11/43.20  | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | BETA: splitting (18) gives:
% 232.11/43.20  | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | Case 1:
% 232.11/43.20  | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | |   (127)  all_55_9 = e3
% 232.11/43.20  | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | COMBINE_EQS: (19), (127) imply:
% 232.11/43.20  | | | | | | | | | | |   (128)  all_53_6 = e3
% 232.11/43.20  | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | REDUCE: (4), (128) imply:
% 232.11/43.20  | | | | | | | | | | |   (129)   ~ (all_53_14 = e3)
% 232.11/43.20  | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | SIMP: (129) implies:
% 232.11/43.20  | | | | | | | | | | |   (130)   ~ (all_53_14 = e3)
% 232.11/43.20  | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | BETA: splitting (16) gives:
% 232.11/43.20  | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | Case 1:
% 232.11/43.20  | | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | |   (131)  all_55_11 = e3
% 232.11/43.20  | | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | | REF_CLOSE: (57), (130), (131) are inconsistent by sub-proof
% 232.11/43.20  | | | | | | | | | | | |            #2497.
% 232.11/43.20  | | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | Case 2:
% 232.11/43.20  | | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | |   (132)  all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 232.11/43.20  | | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | | BETA: splitting (132) gives:
% 232.11/43.20  | | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | | Case 1:
% 232.11/43.20  | | | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | | |   (133)  all_55_11 = e2
% 232.11/43.20  | | | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | | | REF_CLOSE: (57), (86), (133) are inconsistent by sub-proof
% 232.11/43.20  | | | | | | | | | | | | |            #2282.
% 232.11/43.20  | | | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | | Case 2:
% 232.11/43.20  | | | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | | |   (134)  all_55_11 = e1 | all_55_11 = e0
% 232.11/43.20  | | | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | | | BETA: splitting (134) gives:
% 232.11/43.20  | | | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | | | Case 1:
% 232.11/43.20  | | | | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | | | |   (135)  all_55_11 = e1
% 232.11/43.20  | | | | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | | | | REF_CLOSE: (43), (57), (135) are inconsistent by sub-proof
% 232.11/43.20  | | | | | | | | | | | | | |            #2309.
% 232.11/43.20  | | | | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | | | Case 2:
% 232.11/43.20  | | | | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | | | |   (136)  all_55_11 = e0
% 232.11/43.20  | | | | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | | | | COMBINE_EQS: (57), (136) imply:
% 232.11/43.20  | | | | | | | | | | | | | |   (137)  all_53_14 = e0
% 232.11/43.20  | | | | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | | | | SIMP: (137) implies:
% 232.11/43.20  | | | | | | | | | | | | | |   (138)  all_53_14 = e0
% 232.11/43.20  | | | | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | | | | REDUCE: (101), (138) imply:
% 232.11/43.20  | | | | | | | | | | | | | |   (139)   ~ (all_52_15 = e0)
% 232.11/43.20  | | | | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | | | | SIMP: (139) implies:
% 232.11/43.20  | | | | | | | | | | | | | |   (140)   ~ (all_52_15 = e0)
% 232.11/43.20  | | | | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | | | | BETA: splitting (28) gives:
% 232.11/43.20  | | | | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | | | | Case 1:
% 232.11/43.20  | | | | | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | | | | |   (141)  all_55_7 = e3
% 232.11/43.20  | | | | | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | | | | | COMBINE_EQS: (99), (141) imply:
% 232.11/43.20  | | | | | | | | | | | | | | |   (142)  all_52_15 = e3
% 232.11/43.20  | | | | | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | | | | | SIMP: (142) implies:
% 232.11/43.20  | | | | | | | | | | | | | | |   (143)  all_52_15 = e3
% 232.11/43.20  | | | | | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | | | | | REDUCE: (95), (143) imply:
% 232.11/43.20  | | | | | | | | | | | | | | |   (144)  op(e3, e3) = e0
% 232.11/43.20  | | | | | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | | | | | REF_CLOSE: (11), (29), (30), (144) are inconsistent by
% 232.11/43.20  | | | | | | | | | | | | | | |            sub-proof #2494.
% 232.11/43.20  | | | | | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | | | | Case 2:
% 232.11/43.20  | | | | | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | | | | |   (145)  all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 232.11/43.20  | | | | | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | | | | | REF_CLOSE: (11), (55), (95), (99), (102), (103), (145) are
% 232.11/43.20  | | | | | | | | | | | | | | |            inconsistent by sub-proof #2078.
% 232.11/43.20  | | | | | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | | | | End of split
% 232.11/43.20  | | | | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | | | End of split
% 232.11/43.20  | | | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | | End of split
% 232.11/43.20  | | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | End of split
% 232.11/43.20  | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | Case 2:
% 232.11/43.20  | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | |   (146)  all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 232.11/43.20  | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | REF_CLOSE: (5), (11), (19), (27), (49), (117), (126), (146)
% 232.11/43.20  | | | | | | | | | | |            are inconsistent by sub-proof #2077.
% 232.11/43.20  | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | End of split
% 232.11/43.20  | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | Case 2:
% 232.11/43.20  | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | |   (147)  all_55_1 = e0
% 232.11/43.20  | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | REF_CLOSE: (25), (116), (147) are inconsistent by sub-proof
% 232.11/43.20  | | | | | | | | | |            #2076.
% 232.11/43.20  | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | End of split
% 232.11/43.20  | | | | | | | | | 
% 232.11/43.20  | | | | | | | | End of split
% 232.11/43.20  | | | | | | | | 
% 232.11/43.20  | | | | | | | End of split
% 232.11/43.20  | | | | | | | 
% 232.11/43.20  | | | | | | End of split
% 232.11/43.20  | | | | | | 
% 232.11/43.20  | | | | | End of split
% 232.11/43.20  | | | | | 
% 232.11/43.20  | | | | End of split
% 232.11/43.20  | | | | 
% 232.11/43.20  | | | Case 2:
% 232.11/43.20  | | | | 
% 232.11/43.20  | | | |   (148)  all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 232.11/43.20  | | | | 
% 232.11/43.20  | | | | BETA: splitting (41) gives:
% 232.11/43.20  | | | | 
% 232.11/43.20  | | | | Case 1:
% 232.11/43.20  | | | | | 
% 232.11/43.20  | | | | |   (149)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2,
% 232.11/43.20  | | | | |              e1) = e3)
% 232.11/43.20  | | | | | 
% 232.11/43.20  | | | | | BETA: splitting (149) gives:
% 232.11/43.20  | | | | | 
% 232.11/43.20  | | | | | Case 1:
% 232.11/43.20  | | | | | | 
% 232.11/43.20  | | | | | |   (150)  all_57_4 = e3 & op(e3, e1) = e3
% 232.11/43.20  | | | | | | 
% 232.11/43.20  | | | | | | ALPHA: (150) implies:
% 232.11/43.20  | | | | | |   (151)  all_57_4 = e3
% 232.11/43.20  | | | | | | 
% 232.11/43.20  | | | | | | REF_CLOSE: (9), (11), (17), (22), (24), (29), (30), (36), (39),
% 232.11/43.20  | | | | | |            (88), (89), (151) are inconsistent by sub-proof #2474.
% 232.11/43.20  | | | | | | 
% 232.11/43.20  | | | | | Case 2:
% 232.11/43.20  | | | | | | 
% 232.11/43.20  | | | | | |   (152)  all_57_5 = e3 & op(e2, e1) = e3
% 232.11/43.20  | | | | | | 
% 232.11/43.20  | | | | | | ALPHA: (152) implies:
% 232.11/43.20  | | | | | |   (153)  all_57_5 = e3
% 232.11/43.20  | | | | | | 
% 232.11/43.20  | | | | | | BETA: splitting (47) gives:
% 232.11/43.20  | | | | | | 
% 232.11/43.20  | | | | | | Case 1:
% 232.11/43.20  | | | | | | | 
% 232.11/43.20  | | | | | | |   (154)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 &
% 232.11/43.20  | | | | | | |            op(e0, e2) = e3)
% 232.11/43.20  | | | | | | | 
% 232.11/43.20  | | | | | | | BETA: splitting (154) gives:
% 232.11/43.20  | | | | | | | 
% 232.11/43.20  | | | | | | | Case 1:
% 232.11/43.20  | | | | | | | | 
% 232.11/43.20  | | | | | | | |   (155)  all_57_12 = e3 & op(e0, e3) = e3
% 232.11/43.20  | | | | | | | | 
% 232.11/43.20  | | | | | | | | REF_CLOSE: (21), (88), (155) are inconsistent by sub-proof
% 232.11/43.20  | | | | | | | |            #2075.
% 232.11/43.20  | | | | | | | | 
% 232.11/43.20  | | | | | | | Case 2:
% 232.11/43.20  | | | | | | | | 
% 232.11/43.20  | | | | | | | |   (156)  all_57_13 = e3 & op(e0, e2) = e3
% 232.11/43.20  | | | | | | | | 
% 232.11/43.20  | | | | | | | | ALPHA: (156) implies:
% 232.11/43.20  | | | | | | | |   (157)  all_57_13 = e3
% 232.11/43.20  | | | | | | | | 
% 232.11/43.20  | | | | | | | | BETA: splitting (51) gives:
% 232.11/43.20  | | | | | | | | 
% 232.11/43.20  | | | | | | | | Case 1:
% 232.11/43.20  | | | | | | | | | 
% 232.11/43.20  | | | | | | | | |   (158)  all_57_15 = e0 & op(e0, e0) = e0
% 232.11/43.20  | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | ALPHA: (158) implies:
% 232.11/43.20  | | | | | | | | |   (159)  op(e0, e0) = e0
% 232.11/43.20  | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | REF_CLOSE: (11), (39), (55), (159) are inconsistent by
% 232.11/43.20  | | | | | | | | |            sub-proof #2290.
% 232.11/43.20  | | | | | | | | | 
% 232.11/43.20  | | | | | | | | Case 2:
% 232.11/43.20  | | | | | | | | | 
% 232.11/43.20  | | | | | | | | |   (160)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0
% 232.11/43.20  | | | | | | | | |              & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 232.11/43.20  | | | | | | | | |              = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) |
% 232.11/43.20  | | | | | | | | |            (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 232.11/43.20  | | | | | | | | |              e0 & op(e0, e1) = e0))
% 232.11/43.20  | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | ALPHA: (160) implies:
% 232.11/43.20  | | | | | | | | |   (161)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0
% 232.11/43.20  | | | | | | | | |            & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 232.11/43.20  | | | | | | | | |            e0)
% 232.11/43.20  | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | BETA: splitting (6) gives:
% 232.11/43.20  | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | Case 1:
% 232.11/43.20  | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | |   (162)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 232.11/43.20  | | | | | | | | | |            & op(e2, e2) = e1)
% 232.11/43.20  | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | BETA: splitting (162) gives:
% 232.11/43.20  | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | Case 1:
% 232.11/43.20  | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | |   (163)  all_57_2 = e1 & op(e2, e3) = e1
% 232.11/43.20  | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | ALPHA: (163) implies:
% 232.11/43.20  | | | | | | | | | | |   (164)  all_57_2 = e1
% 232.11/43.20  | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | BETA: splitting (161) gives:
% 232.11/43.20  | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | Case 1:
% 232.11/43.20  | | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | |   (165)  all_57_12 = e0 & op(e0, e3) = e0
% 232.11/43.20  | | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | | ALPHA: (165) implies:
% 232.11/43.20  | | | | | | | | | | | |   (166)  all_57_12 = e0
% 232.11/43.20  | | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | | REF_CLOSE: (21), (36), (166) are inconsistent by sub-proof
% 232.11/43.20  | | | | | | | | | | | |            #2385.
% 232.11/43.20  | | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | Case 2:
% 232.11/43.20  | | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | |   (167)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 232.11/43.20  | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 232.11/43.20  | | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | | BETA: splitting (167) gives:
% 232.11/43.20  | | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | | Case 1:
% 232.11/43.20  | | | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | | |   (168)  all_57_13 = e0 & op(e0, e2) = e0
% 232.11/43.20  | | | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | | | REF_CLOSE: (29), (157), (168) are inconsistent by sub-proof
% 232.11/43.20  | | | | | | | | | | | | |            #2214.
% 232.11/43.20  | | | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | | Case 2:
% 232.11/43.20  | | | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | | |   (169)  all_57_14 = e0 & op(e0, e1) = e0
% 232.11/43.20  | | | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | | | ALPHA: (169) implies:
% 232.11/43.20  | | | | | | | | | | | | |   (170)  all_57_14 = e0
% 232.11/43.20  | | | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | | | BETA: splitting (62) gives:
% 232.11/43.20  | | | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | | | Case 1:
% 232.11/43.20  | | | | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | | | |   (171)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 232.11/43.20  | | | | | | | | | | | | | |            & op(e2, e2) = e0)
% 232.11/43.20  | | | | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | | | | BETA: splitting (171) gives:
% 232.11/43.20  | | | | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | | | | Case 1:
% 232.11/43.20  | | | | | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | | | | |   (172)  all_57_2 = e0 & op(e2, e3) = e0
% 232.11/43.20  | | | | | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | | | | | REF_CLOSE: (39), (164), (172) are inconsistent by sub-proof
% 232.11/43.20  | | | | | | | | | | | | | | |            #2467.
% 232.11/43.20  | | | | | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | | | | Case 2:
% 232.11/43.20  | | | | | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | | | | |   (173)  all_57_3 = e0 & op(e2, e2) = e0
% 232.11/43.20  | | | | | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | | | | | ALPHA: (173) implies:
% 232.11/43.20  | | | | | | | | | | | | | | |   (174)  op(e2, e2) = e0
% 232.11/43.20  | | | | | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | | | | | REF_CLOSE: (9), (11), (29), (34), (36), (39), (47), (50),
% 232.11/43.20  | | | | | | | | | | | | | | |            (55), (88), (89), (94), (96), (170), (174) are
% 232.11/43.20  | | | | | | | | | | | | | | |            inconsistent by sub-proof #2065.
% 232.11/43.20  | | | | | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | | | | End of split
% 232.11/43.20  | | | | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | | | Case 2:
% 232.11/43.20  | | | | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | | | |   (175)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 232.11/43.20  | | | | | | | | | | | | | |            e0 & op(e2, e0) = e0)
% 232.11/43.20  | | | | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | | | | BETA: splitting (175) gives:
% 232.11/43.20  | | | | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | | | | Case 1:
% 232.11/43.20  | | | | | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | | | | |   (176)  all_57_5 = e0 & op(e2, e1) = e0
% 232.11/43.20  | | | | | | | | | | | | | | | 
% 232.11/43.20  | | | | | | | | | | | | | | | REF_CLOSE: (29), (153), (176) are inconsistent by sub-proof
% 232.11/43.20  | | | | | | | | | | | | | | |            #2414.
% 232.11/43.20  | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | Case 2:
% 232.11/43.21  | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | |   (177)  all_57_10 = e0 & op(e2, e0) = e0
% 232.11/43.21  | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | ALPHA: (177) implies:
% 232.11/43.21  | | | | | | | | | | | | | | |   (178)  all_57_10 = e0
% 232.11/43.21  | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | BETA: splitting (60) gives:
% 232.11/43.21  | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | Case 1:
% 232.11/43.21  | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | |   (179)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 232.11/43.21  | | | | | | | | | | | | | | | |            e3 & op(e2, e0) = e3)
% 232.11/43.21  | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | REF_CLOSE: (11), (29), (58), (75), (178), (179) are
% 232.11/43.21  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2064.
% 232.11/43.21  | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | Case 2:
% 232.11/43.21  | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | |   (180)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 232.11/43.21  | | | | | | | | | | | | | | | |            e3 & op(e0, e0) = e3)
% 232.11/43.21  | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | BETA: splitting (180) gives:
% 232.11/43.21  | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | Case 1:
% 232.11/43.21  | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | |   (181)  all_57_11 = e3 & op(e1, e0) = e3
% 232.11/43.21  | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (16), (26), (28), (55), (57), (95), (99),
% 232.11/43.21  | | | | | | | | | | | | | | | | |            (101), (102), (103), (181) are inconsistent by
% 232.11/43.21  | | | | | | | | | | | | | | | | |            sub-proof #2062.
% 232.11/43.21  | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | Case 2:
% 232.11/43.21  | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | |   (182)  all_57_15 = e3 & op(e0, e0) = e3
% 232.11/43.21  | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | | ALPHA: (182) implies:
% 232.11/43.21  | | | | | | | | | | | | | | | | |   (183)  all_57_15 = e3
% 232.11/43.21  | | | | | | | | | | | | | | | | |   (184)  op(e0, e0) = e3
% 232.11/43.21  | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11), (29), (34), (36), (39), (50), (88),
% 232.11/43.21  | | | | | | | | | | | | | | | | |            (89), (157), (161), (183), (184) are inconsistent
% 232.11/43.21  | | | | | | | | | | | | | | | | |            by sub-proof #2054.
% 232.11/43.21  | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | End of split
% 232.11/43.21  | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | End of split
% 232.11/43.21  | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | End of split
% 232.11/43.21  | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | End of split
% 232.11/43.21  | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | End of split
% 232.11/43.21  | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | End of split
% 232.11/43.21  | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | Case 2:
% 232.11/43.21  | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | |   (185)  all_57_3 = e1 & op(e2, e2) = e1
% 232.11/43.21  | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | ALPHA: (185) implies:
% 232.11/43.21  | | | | | | | | | | |   (186)  op(e2, e2) = e1
% 232.11/43.21  | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | REF_CLOSE: (11), (38), (89), (186) are inconsistent by
% 232.11/43.21  | | | | | | | | | | |            sub-proof #2306.
% 232.11/43.21  | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | End of split
% 232.11/43.21  | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | Case 2:
% 232.11/43.21  | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | |   (187)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1
% 232.11/43.21  | | | | | | | | | |            & op(e2, e0) = e1)
% 232.11/43.21  | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | BETA: splitting (187) gives:
% 232.11/43.21  | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | Case 1:
% 232.11/43.21  | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | |   (188)  all_57_5 = e1 & op(e2, e1) = e1
% 232.11/43.21  | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | ALPHA: (188) implies:
% 232.11/43.21  | | | | | | | | | | |   (189)  all_57_5 = e1
% 232.11/43.21  | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | REF_CLOSE: (9), (153), (189) are inconsistent by sub-proof
% 232.11/43.21  | | | | | | | | | | |            #2382.
% 232.11/43.21  | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | Case 2:
% 232.11/43.21  | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | |   (190)  all_57_10 = e1 & op(e2, e0) = e1
% 232.11/43.21  | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | REF_CLOSE: (10), (11), (56), (190) are inconsistent by
% 232.11/43.21  | | | | | | | | | | |            sub-proof #2084.
% 232.11/43.21  | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | End of split
% 232.11/43.21  | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | End of split
% 232.11/43.21  | | | | | | | | | 
% 232.11/43.21  | | | | | | | | End of split
% 232.11/43.21  | | | | | | | | 
% 232.11/43.21  | | | | | | | End of split
% 232.11/43.21  | | | | | | | 
% 232.11/43.21  | | | | | | Case 2:
% 232.11/43.21  | | | | | | | 
% 232.11/43.21  | | | | | | |   (191)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 &
% 232.11/43.21  | | | | | | |            op(e0, e0) = e3)
% 232.11/43.21  | | | | | | | 
% 232.11/43.21  | | | | | | | BETA: splitting (191) gives:
% 232.11/43.21  | | | | | | | 
% 232.11/43.21  | | | | | | | Case 1:
% 232.11/43.21  | | | | | | | | 
% 232.11/43.21  | | | | | | | |   (192)  all_57_14 = e3 & op(e0, e1) = e3
% 232.11/43.21  | | | | | | | | 
% 232.11/43.21  | | | | | | | | ALPHA: (192) implies:
% 232.11/43.21  | | | | | | | |   (193)  all_57_14 = e3
% 232.11/43.21  | | | | | | | | 
% 232.11/43.21  | | | | | | | | BETA: splitting (51) gives:
% 232.11/43.21  | | | | | | | | 
% 232.11/43.21  | | | | | | | | Case 1:
% 232.11/43.21  | | | | | | | | | 
% 232.11/43.21  | | | | | | | | |   (194)  all_57_15 = e0 & op(e0, e0) = e0
% 232.11/43.21  | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | ALPHA: (194) implies:
% 232.11/43.21  | | | | | | | | |   (195)  op(e0, e0) = e0
% 232.11/43.21  | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | REF_CLOSE: (11), (39), (55), (195) are inconsistent by
% 232.11/43.21  | | | | | | | | |            sub-proof #2290.
% 232.11/43.21  | | | | | | | | | 
% 232.11/43.21  | | | | | | | | Case 2:
% 232.11/43.21  | | | | | | | | | 
% 232.11/43.21  | | | | | | | | |   (196)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0
% 232.11/43.21  | | | | | | | | |              & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 232.11/43.21  | | | | | | | | |              = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) |
% 232.11/43.21  | | | | | | | | |            (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 232.11/43.21  | | | | | | | | |              e0 & op(e0, e1) = e0))
% 232.11/43.21  | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | ALPHA: (196) implies:
% 232.11/43.21  | | | | | | | | |   (197)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0
% 232.11/43.21  | | | | | | | | |            & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 232.11/43.21  | | | | | | | | |            e0)
% 232.11/43.21  | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | BETA: splitting (6) gives:
% 232.11/43.21  | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | Case 1:
% 232.11/43.21  | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | |   (198)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 232.11/43.21  | | | | | | | | | |            & op(e2, e2) = e1)
% 232.11/43.21  | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | BETA: splitting (198) gives:
% 232.11/43.21  | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | Case 1:
% 232.11/43.21  | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | |   (199)  all_57_2 = e1 & op(e2, e3) = e1
% 232.11/43.21  | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | ALPHA: (199) implies:
% 232.11/43.21  | | | | | | | | | | |   (200)  all_57_2 = e1
% 232.11/43.21  | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | BETA: splitting (197) gives:
% 232.11/43.21  | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | Case 1:
% 232.11/43.21  | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | |   (201)  all_57_12 = e0 & op(e0, e3) = e0
% 232.11/43.21  | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | ALPHA: (201) implies:
% 232.11/43.21  | | | | | | | | | | | |   (202)  all_57_12 = e0
% 232.11/43.21  | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | REF_CLOSE: (21), (36), (202) are inconsistent by sub-proof
% 232.11/43.21  | | | | | | | | | | | |            #2385.
% 232.11/43.21  | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | Case 2:
% 232.11/43.21  | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | |   (203)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 232.11/43.21  | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 232.11/43.21  | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | BETA: splitting (203) gives:
% 232.11/43.21  | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | Case 1:
% 232.11/43.21  | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | |   (204)  all_57_13 = e0 & op(e0, e2) = e0
% 232.11/43.21  | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | ALPHA: (204) implies:
% 232.11/43.21  | | | | | | | | | | | | |   (205)  all_57_13 = e0
% 232.11/43.21  | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | BETA: splitting (62) gives:
% 232.11/43.21  | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | Case 1:
% 232.11/43.21  | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | |   (206)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 232.11/43.21  | | | | | | | | | | | | | |            & op(e2, e2) = e0)
% 232.11/43.21  | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | REF_CLOSE: (11), (36), (38), (39), (200), (206) are
% 232.11/43.21  | | | | | | | | | | | | | |            inconsistent by sub-proof #2457.
% 232.11/43.21  | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | Case 2:
% 232.11/43.21  | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | |   (207)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 232.11/43.21  | | | | | | | | | | | | | |            e0 & op(e2, e0) = e0)
% 232.11/43.21  | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 232.11/43.21  | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | Case 1:
% 232.11/43.21  | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | |   (208)  all_57_5 = e0 & op(e2, e1) = e0
% 232.11/43.21  | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | REF_CLOSE: (29), (153), (208) are inconsistent by sub-proof
% 232.11/43.21  | | | | | | | | | | | | | | |            #2414.
% 232.11/43.21  | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | Case 2:
% 232.11/43.21  | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | |   (209)  all_57_10 = e0 & op(e2, e0) = e0
% 232.11/43.21  | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | ALPHA: (209) implies:
% 232.11/43.21  | | | | | | | | | | | | | | |   (210)  all_57_10 = e0
% 232.11/43.21  | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | BETA: splitting (60) gives:
% 232.11/43.21  | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | Case 1:
% 232.11/43.21  | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | |   (211)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 232.11/43.21  | | | | | | | | | | | | | | | |            e3 & op(e2, e0) = e3)
% 232.11/43.21  | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | REF_CLOSE: (11), (29), (58), (75), (210), (211) are
% 232.11/43.21  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2064.
% 232.11/43.21  | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | Case 2:
% 232.11/43.21  | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | |   (212)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 232.11/43.21  | | | | | | | | | | | | | | | |            e3 & op(e0, e0) = e3)
% 232.11/43.21  | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11), (16), (21), (26), (28), (34), (39),
% 232.11/43.21  | | | | | | | | | | | | | | | |            (55), (57), (89), (95), (99), (101), (102), (103),
% 232.11/43.21  | | | | | | | | | | | | | | | |            (193), (205), (212) are inconsistent by sub-proof
% 232.11/43.21  | | | | | | | | | | | | | | | |            #2053.
% 232.11/43.21  | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | End of split
% 232.11/43.21  | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | End of split
% 232.11/43.21  | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | End of split
% 232.11/43.21  | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | Case 2:
% 232.11/43.21  | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | |   (213)  all_57_14 = e0 & op(e0, e1) = e0
% 232.11/43.21  | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | REF_CLOSE: (29), (193), (213) are inconsistent by sub-proof
% 232.11/43.21  | | | | | | | | | | | | |            #2314.
% 232.11/43.21  | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | End of split
% 232.11/43.21  | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | End of split
% 232.11/43.21  | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | Case 2:
% 232.11/43.21  | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | |   (214)  all_57_3 = e1 & op(e2, e2) = e1
% 232.11/43.21  | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | ALPHA: (214) implies:
% 232.11/43.21  | | | | | | | | | | |   (215)  op(e2, e2) = e1
% 232.11/43.21  | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | REF_CLOSE: (11), (38), (89), (215) are inconsistent by
% 232.11/43.21  | | | | | | | | | | |            sub-proof #2306.
% 232.11/43.21  | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | End of split
% 232.11/43.21  | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | Case 2:
% 232.11/43.21  | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | |   (216)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1
% 232.11/43.21  | | | | | | | | | |            & op(e2, e0) = e1)
% 232.11/43.21  | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | BETA: splitting (216) gives:
% 232.11/43.21  | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | Case 1:
% 232.11/43.21  | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | |   (217)  all_57_5 = e1 & op(e2, e1) = e1
% 232.11/43.21  | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | ALPHA: (217) implies:
% 232.11/43.21  | | | | | | | | | | |   (218)  all_57_5 = e1
% 232.11/43.21  | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | COMBINE_EQS: (153), (218) imply:
% 232.11/43.21  | | | | | | | | | | |   (219)  e3 = e1
% 232.11/43.21  | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | SIMP: (219) implies:
% 232.11/43.21  | | | | | | | | | | |   (220)  e3 = e1
% 232.11/43.21  | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | COMBINE_EQS: (193), (220) imply:
% 232.11/43.21  | | | | | | | | | | |   (221)  all_57_14 = e1
% 232.11/43.21  | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | REF_CLOSE: (9), (11), (21), (29), (36), (39), (47), (55),
% 232.11/43.21  | | | | | | | | | | |            (88), (197), (221) are inconsistent by sub-proof
% 232.11/43.21  | | | | | | | | | | |            #2180.
% 232.11/43.21  | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | Case 2:
% 232.11/43.21  | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | |   (222)  all_57_10 = e1 & op(e2, e0) = e1
% 232.11/43.21  | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | REF_CLOSE: (10), (11), (56), (222) are inconsistent by
% 232.11/43.21  | | | | | | | | | | |            sub-proof #2084.
% 232.11/43.21  | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | End of split
% 232.11/43.21  | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | End of split
% 232.11/43.21  | | | | | | | | | 
% 232.11/43.21  | | | | | | | | End of split
% 232.11/43.21  | | | | | | | | 
% 232.11/43.21  | | | | | | | Case 2:
% 232.11/43.21  | | | | | | | | 
% 232.11/43.21  | | | | | | | |   (223)  all_57_15 = e3 & op(e0, e0) = e3
% 232.11/43.21  | | | | | | | | 
% 232.11/43.21  | | | | | | | | ALPHA: (223) implies:
% 232.11/43.21  | | | | | | | |   (224)  op(e0, e0) = e3
% 232.11/43.21  | | | | | | | | 
% 232.11/43.21  | | | | | | | | REF_CLOSE: (9), (11), (55), (224) are inconsistent by sub-proof
% 232.11/43.21  | | | | | | | |            #2183.
% 232.11/43.21  | | | | | | | | 
% 232.11/43.21  | | | | | | | End of split
% 232.11/43.21  | | | | | | | 
% 232.11/43.21  | | | | | | End of split
% 232.11/43.21  | | | | | | 
% 232.11/43.21  | | | | | End of split
% 232.11/43.21  | | | | | 
% 232.11/43.21  | | | | Case 2:
% 232.11/43.21  | | | | | 
% 232.11/43.21  | | | | |   (225)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0,
% 232.11/43.21  | | | | |              e1) = e3)
% 232.11/43.21  | | | | | 
% 232.11/43.21  | | | | | BETA: splitting (225) gives:
% 232.11/43.21  | | | | | 
% 232.11/43.21  | | | | | Case 1:
% 232.11/43.21  | | | | | | 
% 232.11/43.21  | | | | | |   (226)  all_57_8 = e3 & op(e1, e1) = e3
% 232.11/43.21  | | | | | | 
% 232.11/43.21  | | | | | | ALPHA: (226) implies:
% 232.11/43.21  | | | | | |   (227)  op(e1, e1) = e3
% 232.11/43.21  | | | | | | 
% 232.11/43.21  | | | | | | REF_CLOSE: (11), (14), (15), (227) are inconsistent by sub-proof
% 232.11/43.21  | | | | | |            #2468.
% 232.11/43.21  | | | | | | 
% 232.11/43.21  | | | | | Case 2:
% 232.11/43.21  | | | | | | 
% 232.11/43.21  | | | | | |   (228)  all_57_14 = e3 & op(e0, e1) = e3
% 232.11/43.21  | | | | | | 
% 232.11/43.21  | | | | | | ALPHA: (228) implies:
% 232.11/43.21  | | | | | |   (229)  all_57_14 = e3
% 232.11/43.21  | | | | | | 
% 232.11/43.21  | | | | | | BETA: splitting (51) gives:
% 232.11/43.21  | | | | | | 
% 232.11/43.21  | | | | | | Case 1:
% 232.11/43.21  | | | | | | | 
% 232.11/43.21  | | | | | | |   (230)  all_57_15 = e0 & op(e0, e0) = e0
% 232.11/43.21  | | | | | | | 
% 232.11/43.21  | | | | | | | ALPHA: (230) implies:
% 232.11/43.21  | | | | | | |   (231)  op(e0, e0) = e0
% 232.11/43.21  | | | | | | | 
% 232.11/43.21  | | | | | | | REF_CLOSE: (11), (39), (55), (231) are inconsistent by sub-proof
% 232.11/43.21  | | | | | | |            #2290.
% 232.11/43.21  | | | | | | | 
% 232.11/43.21  | | | | | | Case 2:
% 232.11/43.21  | | | | | | | 
% 232.11/43.21  | | | | | | |   (232)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 &
% 232.11/43.21  | | | | | | |              op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 232.11/43.21  | | | | | | |              e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) |
% 232.11/43.21  | | | | | | |            (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 &
% 232.11/43.21  | | | | | | |              op(e0, e1) = e0))
% 232.11/43.21  | | | | | | | 
% 232.11/43.21  | | | | | | | ALPHA: (232) implies:
% 232.11/43.21  | | | | | | |   (233)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 232.11/43.21  | | | | | | |            op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 232.11/43.21  | | | | | | | 
% 232.11/43.21  | | | | | | | BETA: splitting (233) gives:
% 232.11/43.21  | | | | | | | 
% 232.11/43.21  | | | | | | | Case 1:
% 232.11/43.21  | | | | | | | | 
% 232.11/43.21  | | | | | | | |   (234)  all_57_12 = e0 & op(e0, e3) = e0
% 232.11/43.21  | | | | | | | | 
% 232.11/43.21  | | | | | | | | ALPHA: (234) implies:
% 232.11/43.21  | | | | | | | |   (235)  all_57_12 = e0
% 232.11/43.21  | | | | | | | | 
% 232.11/43.21  | | | | | | | | REF_CLOSE: (21), (36), (235) are inconsistent by sub-proof
% 232.11/43.21  | | | | | | | |            #2385.
% 232.11/43.21  | | | | | | | | 
% 232.11/43.21  | | | | | | | Case 2:
% 232.11/43.21  | | | | | | | | 
% 232.11/43.21  | | | | | | | |   (236)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 &
% 232.11/43.21  | | | | | | | |            op(e0, e1) = e0)
% 232.11/43.21  | | | | | | | | 
% 232.11/43.21  | | | | | | | | BETA: splitting (236) gives:
% 232.11/43.21  | | | | | | | | 
% 232.11/43.21  | | | | | | | | Case 1:
% 232.11/43.21  | | | | | | | | | 
% 232.11/43.21  | | | | | | | | |   (237)  all_57_13 = e0 & op(e0, e2) = e0
% 232.11/43.21  | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | ALPHA: (237) implies:
% 232.11/43.21  | | | | | | | | |   (238)  all_57_13 = e0
% 232.11/43.21  | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | BETA: splitting (148) gives:
% 232.11/43.21  | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | Case 1:
% 232.11/43.21  | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | |   (239)  all_55_14 = e2
% 232.11/43.21  | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | COMBINE_EQS: (69), (239) imply:
% 232.11/43.21  | | | | | | | | | |   (240)  all_53_11 = e2
% 232.11/43.21  | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | REDUCE: (81), (240) imply:
% 232.11/43.21  | | | | | | | | | |   (241)  $false
% 232.11/43.21  | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | CLOSE: (241) is inconsistent.
% 232.11/43.21  | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | Case 2:
% 232.11/43.21  | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | |   (242)  all_55_14 = e1 | all_55_14 = e0
% 232.11/43.21  | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | BETA: splitting (42) gives:
% 232.11/43.21  | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | Case 1:
% 232.11/43.21  | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | |   (243)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 232.11/43.21  | | | | | | | | | | |            & op(e2, e2) = e3)
% 232.11/43.21  | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | REF_CLOSE: (11), (35), (38), (74), (88), (243) are
% 232.11/43.21  | | | | | | | | | | |            inconsistent by sub-proof #2285.
% 232.11/43.21  | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | Case 2:
% 232.11/43.21  | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | |   (244)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 232.11/43.21  | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 232.11/43.21  | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | BETA: splitting (244) gives:
% 232.11/43.21  | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | Case 1:
% 232.11/43.21  | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | |   (245)  all_57_7 = e3 & op(e1, e2) = e3
% 232.11/43.21  | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | ALPHA: (245) implies:
% 232.11/43.21  | | | | | | | | | | | |   (246)  all_57_7 = e3
% 232.11/43.21  | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | BETA: splitting (73) gives:
% 232.11/43.21  | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | Case 1:
% 232.11/43.21  | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | |   (247)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 232.11/43.21  | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 232.11/43.21  | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | BETA: splitting (247) gives:
% 232.11/43.21  | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | Case 1:
% 232.11/43.21  | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | |   (248)  all_57_1 = e1 & op(e3, e2) = e1
% 232.11/43.21  | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | ALPHA: (248) implies:
% 232.11/43.21  | | | | | | | | | | | | | |   (249)  all_57_1 = e1
% 232.11/43.21  | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 232.11/43.21  | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | Case 1:
% 232.11/43.21  | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | |   (250)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 232.11/43.21  | | | | | | | | | | | | | | |            & op(e1, e2) = e1)
% 232.11/43.21  | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | BETA: splitting (250) gives:
% 232.11/43.21  | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | Case 1:
% 232.11/43.21  | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | |   (251)  all_57_6 = e1 & op(e1, e3) = e1
% 232.11/43.21  | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | ALPHA: (251) implies:
% 232.11/43.21  | | | | | | | | | | | | | | | |   (252)  all_57_6 = e1
% 232.11/43.21  | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | BETA: splitting (66) gives:
% 232.11/43.21  | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | Case 1:
% 232.11/43.21  | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | |   (253)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 232.11/43.21  | | | | | | | | | | | | | | | | |            & op(e2, e3) = e0)
% 232.11/43.21  | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | | BETA: splitting (253) gives:
% 232.11/43.21  | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | | Case 1:
% 232.11/43.21  | | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | | |   (254)  all_57_0 = e0 & op(e3, e3) = e0
% 232.11/43.21  | | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | | | ALPHA: (254) implies:
% 232.11/43.21  | | | | | | | | | | | | | | | | | |   (255)  op(e3, e3) = e0
% 232.11/43.21  | | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (29), (30), (255) are inconsistent by
% 232.11/43.21  | | | | | | | | | | | | | | | | | |            sub-proof #2494.
% 232.11/43.21  | | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | | Case 2:
% 232.11/43.21  | | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | | |   (256)  all_57_2 = e0 & op(e2, e3) = e0
% 232.11/43.21  | | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | | | ALPHA: (256) implies:
% 232.11/43.21  | | | | | | | | | | | | | | | | | |   (257)  all_57_2 = e0
% 232.11/43.21  | | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | | | BETA: splitting (60) gives:
% 232.11/43.21  | | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | | | Case 1:
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | | | |   (258)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 232.11/43.21  | | | | | | | | | | | | | | | | | | |            e3 & op(e2, e0) = e3)
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | BETA: splitting (258) gives:
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | Case 1:
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | |   (259)  all_57_9 = e3 & op(e3, e0) = e3
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | | ALPHA: (259) implies:
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | |   (260)  op(e3, e0) = e3
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (58), (75), (260) are inconsistent by
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | |            sub-proof #2458.
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | Case 2:
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | |   (261)  all_57_10 = e3 & op(e2, e0) = e3
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | | ALPHA: (261) implies:
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | |   (262)  all_57_10 = e3
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | | BETA: splitting (24) gives:
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | | |   (263)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e0)
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (29), (30), (39), (249), (263) are
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2492.
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | | |   (264)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e0)
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (264) gives:
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | | | |   (265)  all_57_4 = e0 & op(e3, e1) = e0
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (265) implies:
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | | | |   (266)  op(e3, e1) = e0
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (11), (53), (69), (71), (242), (266) are
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2164.
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | | | |   (267)  all_57_9 = e0 & op(e3, e0) = e0
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (267) implies:
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | | | |   (268)  all_57_9 = e0
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3), (268) imply:
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | | | |   (269)  e2 = e0
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (70), (269) imply:
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | | | |   (270)  all_57_3 = e0
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (36), (39), (59), (88), (89), (257),
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | | | |            (262), (270) are inconsistent by sub-proof #2247.
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | | | End of split
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | | End of split
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | End of split
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | | | Case 2:
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | | | |   (271)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 232.11/43.21  | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e0) = e3)
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11), (16), (21), (26), (28), (34), (39),
% 232.11/43.21  | | | | | | | | | | | | | | | | | | |            (55), (57), (89), (95), (99), (101), (102), (103),
% 232.11/43.21  | | | | | | | | | | | | | | | | | | |            (229), (238), (271) are inconsistent by sub-proof
% 232.11/43.21  | | | | | | | | | | | | | | | | | | |            #2053.
% 232.11/43.21  | | | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | | | End of split
% 232.11/43.21  | | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | | End of split
% 232.11/43.21  | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | Case 2:
% 232.11/43.21  | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | |   (272)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 232.11/43.21  | | | | | | | | | | | | | | | | |            e0 & op(e0, e3) = e0)
% 232.11/43.21  | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | | BETA: splitting (272) gives:
% 232.11/43.21  | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | | Case 1:
% 232.11/43.21  | | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | | |   (273)  all_57_6 = e0 & op(e1, e3) = e0
% 232.11/43.21  | | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (252), (273) are inconsistent by sub-proof
% 232.11/43.21  | | | | | | | | | | | | | | | | | |            #2347.
% 232.11/43.21  | | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | | Case 2:
% 232.11/43.21  | | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | | |   (274)  all_57_12 = e0 & op(e0, e3) = e0
% 232.11/43.21  | | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | | | ALPHA: (274) implies:
% 232.11/43.21  | | | | | | | | | | | | | | | | | |   (275)  all_57_12 = e0
% 232.11/43.21  | | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (21), (275) imply:
% 232.11/43.21  | | | | | | | | | | | | | | | | | |   (276)  e2 = e0
% 232.11/43.21  | | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (70), (276) imply:
% 232.11/43.21  | | | | | | | | | | | | | | | | | |   (277)  all_57_3 = e0
% 232.11/43.21  | | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (11), (17), (22), (24), (29), (30),
% 232.11/43.21  | | | | | | | | | | | | | | | | | |            (36), (39), (73), (88), (89), (238), (246), (277)
% 232.11/43.21  | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2091.
% 232.11/43.21  | | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | | End of split
% 232.11/43.21  | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | End of split
% 232.11/43.21  | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | Case 2:
% 232.11/43.21  | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | |   (278)  all_57_7 = e1 & op(e1, e2) = e1
% 232.11/43.21  | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | ALPHA: (278) implies:
% 232.11/43.21  | | | | | | | | | | | | | | | |   (279)  all_57_7 = e1
% 232.11/43.21  | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (279) imply:
% 232.11/43.21  | | | | | | | | | | | | | | | |   (280)  e3 = e1
% 232.11/43.21  | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | COMBINE_EQS: (229), (280) imply:
% 232.11/43.21  | | | | | | | | | | | | | | | |   (281)  all_57_14 = e1
% 232.11/43.21  | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11), (21), (29), (47), (55), (88), (238),
% 232.11/43.21  | | | | | | | | | | | | | | | |            (281) are inconsistent by sub-proof #2182.
% 232.11/43.21  | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | End of split
% 232.11/43.21  | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | Case 2:
% 232.11/43.21  | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | |   (282)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 232.11/43.21  | | | | | | | | | | | | | | |            e1 & op(e1, e0) = e1)
% 232.11/43.21  | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | BETA: splitting (282) gives:
% 232.11/43.21  | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | Case 1:
% 232.11/43.21  | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | |   (283)  all_57_8 = e1 & op(e1, e1) = e1
% 232.11/43.21  | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | ALPHA: (283) implies:
% 232.11/43.21  | | | | | | | | | | | | | | | |   (284)  op(e1, e1) = e1
% 232.11/43.21  | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | REF_CLOSE: (11), (52), (89), (284) are inconsistent by
% 232.11/43.21  | | | | | | | | | | | | | | | |            sub-proof #2423.
% 232.11/43.21  | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | Case 2:
% 232.11/43.21  | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | |   (285)  all_57_11 = e1 & op(e1, e0) = e1
% 232.11/43.21  | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | ALPHA: (285) implies:
% 232.11/43.21  | | | | | | | | | | | | | | | |   (286)  all_57_11 = e1
% 232.11/43.21  | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | BETA: splitting (24) gives:
% 232.11/43.21  | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | Case 1:
% 232.11/43.21  | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | |   (287)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 232.11/43.21  | | | | | | | | | | | | | | | | |            & op(e3, e2) = e0)
% 232.11/43.21  | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (29), (30), (39), (249), (287) are
% 232.11/43.21  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2492.
% 232.11/43.21  | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | Case 2:
% 232.11/43.21  | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | |   (288)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 232.11/43.21  | | | | | | | | | | | | | | | | |            & op(e3, e0) = e0)
% 232.11/43.21  | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | | BETA: splitting (288) gives:
% 232.11/43.21  | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | | Case 1:
% 232.11/43.21  | | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | | |   (289)  all_57_4 = e0 & op(e3, e1) = e0
% 232.11/43.21  | | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | | | ALPHA: (289) implies:
% 232.11/43.21  | | | | | | | | | | | | | | | | | |   (290)  op(e3, e1) = e0
% 232.11/43.21  | | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (11), (53), (69), (71), (242), (290) are
% 232.11/43.21  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2164.
% 232.11/43.21  | | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | | Case 2:
% 232.11/43.21  | | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | | |   (291)  all_57_9 = e0 & op(e3, e0) = e0
% 232.11/43.21  | | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | | | ALPHA: (291) implies:
% 232.11/43.21  | | | | | | | | | | | | | | | | | |   (292)  all_57_9 = e0
% 232.11/43.21  | | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11), (29), (36), (55), (60), (64), (88),
% 232.11/43.21  | | | | | | | | | | | | | | | | | |            (89), (286), (292) are inconsistent by sub-proof
% 232.11/43.21  | | | | | | | | | | | | | | | | | |            #2047.
% 232.11/43.21  | | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | | End of split
% 232.11/43.21  | | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | | End of split
% 232.11/43.21  | | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | | End of split
% 232.11/43.21  | | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | End of split
% 232.11/43.21  | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | Case 2:
% 232.11/43.21  | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | |   (293)  all_57_3 = e1 & op(e2, e2) = e1
% 232.11/43.21  | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | ALPHA: (293) implies:
% 232.11/43.21  | | | | | | | | | | | | | |   (294)  op(e2, e2) = e1
% 232.11/43.21  | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | REF_CLOSE: (11), (38), (89), (294) are inconsistent by
% 232.11/43.21  | | | | | | | | | | | | | |            sub-proof #2306.
% 232.11/43.21  | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | End of split
% 232.11/43.21  | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | Case 2:
% 232.11/43.21  | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | |   (295)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 232.11/43.21  | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 232.11/43.21  | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | BETA: splitting (295) gives:
% 232.11/43.21  | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | Case 1:
% 232.11/43.21  | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | |   (296)  all_57_7 = e1 & op(e1, e2) = e1
% 232.11/43.21  | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | ALPHA: (296) implies:
% 232.11/43.21  | | | | | | | | | | | | | |   (297)  all_57_7 = e1
% 232.11/43.21  | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | COMBINE_EQS: (246), (297) imply:
% 232.11/43.21  | | | | | | | | | | | | | |   (298)  e3 = e1
% 232.11/43.21  | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | SIMP: (298) implies:
% 232.11/43.21  | | | | | | | | | | | | | |   (299)  e3 = e1
% 232.11/43.21  | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | COMBINE_EQS: (229), (299) imply:
% 232.11/43.21  | | | | | | | | | | | | | |   (300)  all_57_14 = e1
% 232.11/43.21  | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | REF_CLOSE: (9), (11), (21), (29), (47), (55), (88), (238),
% 232.11/43.21  | | | | | | | | | | | | | |            (300) are inconsistent by sub-proof #2182.
% 232.11/43.21  | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | Case 2:
% 232.11/43.21  | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | |   (301)  all_57_13 = e1 & op(e0, e2) = e1
% 232.11/43.21  | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | | REF_CLOSE: (39), (238), (301) are inconsistent by sub-proof
% 232.11/43.21  | | | | | | | | | | | | | |            #2320.
% 232.11/43.21  | | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | | End of split
% 232.11/43.21  | | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | End of split
% 232.11/43.21  | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | Case 2:
% 232.11/43.21  | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | |   (302)  all_57_13 = e3 & op(e0, e2) = e3
% 232.11/43.21  | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | ALPHA: (302) implies:
% 232.11/43.21  | | | | | | | | | | | |   (303)  all_57_13 = e3
% 232.11/43.21  | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | | REF_CLOSE: (21), (29), (36), (229), (233), (303) are
% 232.11/43.21  | | | | | | | | | | | |            inconsistent by sub-proof #2088.
% 232.11/43.21  | | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | | End of split
% 232.11/43.21  | | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | | End of split
% 232.11/43.21  | | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | End of split
% 232.11/43.21  | | | | | | | | | 
% 232.11/43.21  | | | | | | | | Case 2:
% 232.11/43.21  | | | | | | | | | 
% 232.11/43.21  | | | | | | | | |   (304)  all_57_14 = e0 & op(e0, e1) = e0
% 232.11/43.21  | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | ALPHA: (304) implies:
% 232.11/43.21  | | | | | | | | |   (305)  all_57_14 = e0
% 232.11/43.21  | | | | | | | | | 
% 232.11/43.21  | | | | | | | | | REF_CLOSE: (29), (229), (305) are inconsistent by sub-proof
% 232.11/43.21  | | | | | | | | |            #2420.
% 232.11/43.21  | | | | | | | | | 
% 232.11/43.21  | | | | | | | | End of split
% 232.11/43.21  | | | | | | | | 
% 232.11/43.21  | | | | | | | End of split
% 232.11/43.21  | | | | | | | 
% 232.11/43.21  | | | | | | End of split
% 232.11/43.21  | | | | | | 
% 232.11/43.21  | | | | | End of split
% 232.11/43.21  | | | | | 
% 232.11/43.21  | | | | End of split
% 232.11/43.21  | | | | 
% 232.11/43.21  | | | End of split
% 232.11/43.21  | | | 
% 232.11/43.21  | | End of split
% 232.11/43.21  | | 
% 232.11/43.21  | Case 2:
% 232.11/43.21  | | 
% 232.11/43.21  | |   (306)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 232.11/43.21  | |            & op(all_52_17, all_52_17) = e3 & op(all_52_19, all_52_19) = e2 &
% 232.11/43.21  | |            op(all_52_21, all_52_21) = e1 & op(all_52_23, all_52_23) = e0 &
% 232.11/43.21  | |            op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) =
% 232.11/43.21  | |            all_52_21 & op(e1, e0) = all_52_23 & $i(all_52_17) &
% 232.11/43.21  | |            $i(all_52_19) & $i(all_52_21) & $i(all_52_23)) | (all_52_24 = e3
% 232.11/43.21  | |            & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0 &
% 232.11/43.21  | |            op(all_52_25, all_52_25) = e3 & op(all_52_27, all_52_27) = e2 &
% 232.11/43.21  | |            op(all_52_29, all_52_29) = e1 & op(all_52_31, all_52_31) = e0 &
% 232.11/43.21  | |            op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 & op(e0, e1) =
% 232.11/43.21  | |            all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 232.11/43.21  | |            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 232.11/43.21  | | 
% 232.11/43.21  | | BETA: splitting (306) gives:
% 232.11/43.21  | | 
% 232.11/43.21  | | Case 1:
% 232.11/43.21  | | | 
% 232.11/43.21  | | |   (307)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0
% 232.11/43.21  | | |          & op(all_52_17, all_52_17) = e3 & op(all_52_19, all_52_19) = e2 &
% 232.11/43.21  | | |          op(all_52_21, all_52_21) = e1 & op(all_52_23, all_52_23) = e0 &
% 232.11/43.21  | | |          op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) =
% 232.11/43.21  | | |          all_52_21 & op(e1, e0) = all_52_23 & $i(all_52_17) &
% 232.11/43.21  | | |          $i(all_52_19) & $i(all_52_21) & $i(all_52_23)
% 232.11/43.21  | | | 
% 232.11/43.21  | | | REF_CLOSE: (11), (38), (52), (89), (307) are inconsistent by sub-proof
% 232.11/43.21  | | |            #2260.
% 232.11/43.21  | | | 
% 232.11/43.21  | | Case 2:
% 232.11/43.21  | | | 
% 232.11/43.21  | | |   (308)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0
% 232.11/43.21  | | |          & op(all_52_25, all_52_25) = e3 & op(all_52_27, all_52_27) = e2 &
% 232.11/43.21  | | |          op(all_52_29, all_52_29) = e1 & op(all_52_31, all_52_31) = e0 &
% 232.11/43.21  | | |          op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 & op(e0, e1) =
% 232.11/43.21  | | |          all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 232.11/43.21  | | |          $i(all_52_27) & $i(all_52_29) & $i(all_52_31)
% 232.11/43.21  | | | 
% 232.11/43.21  | | | ALPHA: (308) implies:
% 232.11/43.21  | | |   (309)  op(e0, e0) = all_52_31
% 232.11/43.21  | | |   (310)  op(all_52_31, all_52_31) = e0
% 232.11/43.21  | | | 
% 232.11/43.21  | | | REF_CLOSE: (11), (15), (55), (65), (309), (310) are inconsistent by
% 232.11/43.21  | | |            sub-proof #2086.
% 232.11/43.21  | | | 
% 232.11/43.21  | | End of split
% 232.11/43.21  | | 
% 232.11/43.21  | End of split
% 232.11/43.21  | 
% 232.11/43.21  End of proof
% 232.11/43.21  
% 232.11/43.21  Sub-proof #2047 shows that the following formulas are inconsistent:
% 232.11/43.21  ----------------------------------------------------------------
% 232.11/43.21    (1)   ~ (e3 = e1)
% 232.11/43.21    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.11/43.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.11/43.21    (3)   ~ (e3 = e2)
% 232.11/43.21    (4)   ~ (e3 = e0)
% 232.11/43.21    (5)  all_57_9 = e0
% 232.11/43.21    (6)   ~ (e2 = e0)
% 232.11/43.21    (7)  op(e0, e0) = e1
% 232.11/43.21    (8)  all_57_11 = e1
% 232.11/43.21    (9)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 232.11/43.21         (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 232.11/43.21    (10)   ~ (e2 = e1)
% 232.11/43.21    (11)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 232.11/43.21          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 232.11/43.21  
% 232.11/43.21  Begin of proof
% 232.11/43.21  | 
% 232.11/43.21  | BETA: splitting (11) gives:
% 232.11/43.21  | 
% 232.11/43.21  | Case 1:
% 232.11/43.21  | | 
% 232.11/43.21  | |   (12)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 232.11/43.21  | |           e2)
% 232.11/43.21  | | 
% 232.11/43.21  | | BETA: splitting (12) gives:
% 232.11/43.21  | | 
% 232.11/43.21  | | Case 1:
% 232.11/43.21  | | | 
% 232.11/43.21  | | |   (13)  all_57_9 = e2 & op(e3, e0) = e2
% 232.11/43.21  | | | 
% 232.11/43.21  | | | REF_CLOSE: (5), (6), (13) are inconsistent by sub-proof #2486.
% 232.11/43.21  | | | 
% 232.11/43.21  | | Case 2:
% 232.11/43.21  | | | 
% 232.11/43.21  | | |   (14)  all_57_10 = e2 & op(e2, e0) = e2
% 232.11/43.21  | | | 
% 232.11/43.21  | | | ALPHA: (14) implies:
% 232.11/43.21  | | |   (15)  all_57_10 = e2
% 232.11/43.21  | | | 
% 232.11/43.21  | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (15) are inconsistent
% 232.11/43.21  | | |            by sub-proof #2049.
% 232.11/43.21  | | | 
% 232.11/43.21  | | End of split
% 232.11/43.21  | | 
% 232.11/43.21  | Case 2:
% 232.11/43.21  | | 
% 232.11/43.21  | |   (16)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 232.11/43.21  | |           e2)
% 232.11/43.21  | | 
% 232.11/43.21  | | BETA: splitting (16) gives:
% 232.11/43.21  | | 
% 232.11/43.21  | | Case 1:
% 232.11/43.21  | | | 
% 232.11/43.21  | | |   (17)  all_57_11 = e2 & op(e1, e0) = e2
% 232.11/43.21  | | | 
% 232.11/43.21  | | | REF_CLOSE: (8), (10), (17) are inconsistent by sub-proof #2048.
% 232.11/43.21  | | | 
% 232.11/43.21  | | Case 2:
% 232.11/43.21  | | | 
% 232.11/43.21  | | |   (18)  all_57_15 = e2 & op(e0, e0) = e2
% 232.11/43.21  | | | 
% 232.11/43.21  | | | ALPHA: (18) implies:
% 232.11/43.21  | | |   (19)  op(e0, e0) = e2
% 232.11/43.21  | | | 
% 232.11/43.21  | | | REF_CLOSE: (2), (7), (10), (19) are inconsistent by sub-proof #2177.
% 232.11/43.21  | | | 
% 232.11/43.21  | | End of split
% 232.11/43.21  | | 
% 232.11/43.21  | End of split
% 232.11/43.21  | 
% 232.11/43.21  End of proof
% 232.11/43.21  
% 232.11/43.21  Sub-proof #2048 shows that the following formulas are inconsistent:
% 232.11/43.21  ----------------------------------------------------------------
% 232.11/43.21    (1)  all_57_11 = e2 & op(e1, e0) = e2
% 232.11/43.21    (2)  all_57_11 = e1
% 232.11/43.21    (3)   ~ (e2 = e1)
% 232.11/43.21  
% 232.11/43.21  Begin of proof
% 232.11/43.21  | 
% 232.11/43.21  | ALPHA: (1) implies:
% 232.11/43.21  |   (4)  all_57_11 = e2
% 232.11/43.21  | 
% 232.11/43.21  | COMBINE_EQS: (2), (4) imply:
% 232.11/43.21  |   (5)  e2 = e1
% 232.11/43.21  | 
% 232.11/43.21  | REDUCE: (3), (5) imply:
% 232.11/43.21  |   (6)  $false
% 232.11/43.21  | 
% 232.11/43.21  | CLOSE: (6) is inconsistent.
% 232.11/43.21  | 
% 232.11/43.21  End of proof
% 232.11/43.21  
% 232.11/43.21  Sub-proof #2049 shows that the following formulas are inconsistent:
% 232.11/43.21  ----------------------------------------------------------------
% 232.11/43.21    (1)   ~ (e3 = e1)
% 232.11/43.21    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.11/43.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.11/43.21    (3)   ~ (e3 = e2)
% 232.11/43.21    (4)   ~ (e3 = e0)
% 232.11/43.21    (5)  all_57_10 = e2
% 232.11/43.21    (6)  all_57_9 = e0
% 232.11/43.21    (7)  op(e0, e0) = e1
% 232.11/43.21    (8)  all_57_11 = e1
% 232.11/43.21    (9)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 232.11/43.21         (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 232.11/43.21  
% 232.11/43.21  Begin of proof
% 232.11/43.21  | 
% 232.11/43.21  | BETA: splitting (9) gives:
% 232.11/43.21  | 
% 232.11/43.21  | Case 1:
% 232.11/43.21  | | 
% 232.11/43.21  | |   (10)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 232.11/43.21  | |           e3)
% 232.11/43.21  | | 
% 232.11/43.21  | | BETA: splitting (10) gives:
% 232.11/43.21  | | 
% 232.11/43.21  | | Case 1:
% 232.11/43.21  | | | 
% 232.11/43.21  | | |   (11)  all_57_9 = e3 & op(e3, e0) = e3
% 232.11/43.21  | | | 
% 232.11/43.21  | | | REF_CLOSE: (4), (6), (11) are inconsistent by sub-proof #2052.
% 232.11/43.21  | | | 
% 232.11/43.21  | | Case 2:
% 232.11/43.21  | | | 
% 232.11/43.21  | | |   (12)  all_57_10 = e3 & op(e2, e0) = e3
% 232.11/43.21  | | | 
% 232.11/43.21  | | | REF_CLOSE: (3), (5), (12) are inconsistent by sub-proof #2051.
% 232.11/43.21  | | | 
% 232.11/43.21  | | End of split
% 232.11/43.21  | | 
% 232.11/43.21  | Case 2:
% 232.11/43.21  | | 
% 232.11/43.21  | |   (13)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 232.11/43.21  | |           e3)
% 232.11/43.21  | | 
% 232.11/43.21  | | REF_CLOSE: (1), (2), (7), (8), (13) are inconsistent by sub-proof #2050.
% 232.11/43.21  | | 
% 232.11/43.21  | End of split
% 232.11/43.21  | 
% 232.11/43.21  End of proof
% 232.11/43.21  
% 232.11/43.21  Sub-proof #2050 shows that the following formulas are inconsistent:
% 232.11/43.21  ----------------------------------------------------------------
% 232.11/43.21    (1)   ~ (e3 = e1)
% 232.11/43.21    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.11/43.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.11/43.21    (3)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 232.11/43.21    (4)  op(e0, e0) = e1
% 232.11/43.21    (5)  all_57_11 = e1
% 232.11/43.21  
% 232.11/43.21  Begin of proof
% 232.11/43.21  | 
% 232.11/43.21  | BETA: splitting (3) gives:
% 232.11/43.21  | 
% 232.11/43.21  | Case 1:
% 232.11/43.21  | | 
% 232.11/43.21  | |   (6)  all_57_11 = e3 & op(e1, e0) = e3
% 232.11/43.21  | | 
% 232.11/43.21  | | ALPHA: (6) implies:
% 232.11/43.21  | |   (7)  all_57_11 = e3
% 232.11/43.21  | | 
% 232.11/43.21  | | REF_CLOSE: (1), (5), (7) are inconsistent by sub-proof #2218.
% 232.11/43.21  | | 
% 232.11/43.21  | Case 2:
% 232.11/43.21  | | 
% 232.11/43.21  | |   (8)  all_57_15 = e3 & op(e0, e0) = e3
% 232.11/43.21  | | 
% 232.11/43.21  | | ALPHA: (8) implies:
% 232.11/43.22  | |   (9)  op(e0, e0) = e3
% 232.11/43.22  | | 
% 232.11/43.22  | | REF_CLOSE: (1), (2), (4), (9) are inconsistent by sub-proof #2183.
% 232.11/43.22  | | 
% 232.11/43.22  | End of split
% 232.11/43.22  | 
% 232.11/43.22  End of proof
% 232.11/43.22  
% 232.11/43.22  Sub-proof #2051 shows that the following formulas are inconsistent:
% 232.11/43.22  ----------------------------------------------------------------
% 232.11/43.22    (1)  all_57_10 = e3 & op(e2, e0) = e3
% 232.11/43.22    (2)  all_57_10 = e2
% 232.11/43.22    (3)   ~ (e3 = e2)
% 232.11/43.22  
% 232.11/43.22  Begin of proof
% 232.11/43.22  | 
% 232.11/43.22  | ALPHA: (1) implies:
% 232.11/43.22  |   (4)  all_57_10 = e3
% 232.11/43.22  | 
% 232.11/43.22  | COMBINE_EQS: (2), (4) imply:
% 232.11/43.22  |   (5)  e3 = e2
% 232.11/43.22  | 
% 232.11/43.22  | REDUCE: (3), (5) imply:
% 232.11/43.22  |   (6)  $false
% 232.11/43.22  | 
% 232.11/43.22  | CLOSE: (6) is inconsistent.
% 232.11/43.22  | 
% 232.11/43.22  End of proof
% 232.11/43.22  
% 232.11/43.22  Sub-proof #2052 shows that the following formulas are inconsistent:
% 232.11/43.22  ----------------------------------------------------------------
% 232.11/43.22    (1)  all_57_9 = e3 & op(e3, e0) = e3
% 232.11/43.22    (2)  all_57_9 = e0
% 232.11/43.22    (3)   ~ (e3 = e0)
% 232.11/43.22  
% 232.11/43.22  Begin of proof
% 232.11/43.22  | 
% 232.11/43.22  | ALPHA: (1) implies:
% 232.11/43.22  |   (4)  all_57_9 = e3
% 232.11/43.22  | 
% 232.11/43.22  | COMBINE_EQS: (2), (4) imply:
% 232.11/43.22  |   (5)  e3 = e0
% 232.11/43.22  | 
% 232.11/43.22  | REDUCE: (3), (5) imply:
% 232.11/43.22  |   (6)  $false
% 232.11/43.22  | 
% 232.11/43.22  | CLOSE: (6) is inconsistent.
% 232.11/43.22  | 
% 232.11/43.22  End of proof
% 232.11/43.22  
% 232.11/43.22  Sub-proof #2053 shows that the following formulas are inconsistent:
% 232.11/43.22  ----------------------------------------------------------------
% 232.11/43.22    (1)   ~ (e3 = e1)
% 232.11/43.22    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.11/43.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.11/43.22    (3)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 232.11/43.22    (4)  all_57_14 = e3
% 232.11/43.22    (5)  all_55_7 = all_52_15
% 232.11/43.22    (6)  all_57_12 = e2
% 232.11/43.22    (7)  op(e1, e0) = all_53_14
% 232.11/43.22    (8)   ~ (all_52_15 = e1)
% 232.11/43.22    (9)  all_55_7 = e3 | all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 232.11/43.22    (10)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 232.11/43.22          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 232.11/43.22            e1)
% 232.11/43.22    (11)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 232.11/43.22    (12)   ~ (e1 = e0)
% 232.11/43.22    (13)  op(e0, e0) = e1
% 232.11/43.22    (14)  all_57_13 = e0
% 232.11/43.22    (15)   ~ (all_53_14 = all_52_15)
% 232.11/43.22    (16)  all_55_11 = all_53_14
% 232.11/43.22    (17)  op(all_52_15, all_52_15) = e0
% 232.11/43.22    (18)   ~ (e2 = e1)
% 232.11/43.22    (19)   ~ (all_52_15 = e2)
% 232.11/43.22  
% 232.11/43.22  Begin of proof
% 232.11/43.22  | 
% 232.11/43.22  | BETA: splitting (11) gives:
% 232.11/43.22  | 
% 232.11/43.22  | Case 1:
% 232.11/43.22  | | 
% 232.11/43.22  | |   (20)  all_57_11 = e3 & op(e1, e0) = e3
% 232.11/43.22  | | 
% 232.11/43.22  | | REF_CLOSE: (2), (3), (5), (7), (8), (9), (13), (15), (16), (17), (19), (20)
% 232.11/43.22  | |            are inconsistent by sub-proof #2062.
% 232.11/43.22  | | 
% 232.11/43.22  | Case 2:
% 232.11/43.22  | | 
% 232.11/43.22  | |   (21)  all_57_15 = e3 & op(e0, e0) = e3
% 232.11/43.22  | | 
% 232.11/43.22  | | ALPHA: (21) implies:
% 232.11/43.22  | |   (22)  all_57_15 = e3
% 232.11/43.22  | | 
% 232.11/43.22  | | REF_CLOSE: (1), (4), (6), (10), (12), (14), (18), (22) are inconsistent by
% 232.11/43.22  | |            sub-proof #2317.
% 232.11/43.22  | | 
% 232.11/43.22  | End of split
% 232.11/43.22  | 
% 232.11/43.22  End of proof
% 232.11/43.22  
% 232.11/43.22  Sub-proof #2054 shows that the following formulas are inconsistent:
% 232.11/43.22  ----------------------------------------------------------------
% 232.11/43.22    (1)   ~ (e3 = e1)
% 232.11/43.22    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.11/43.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.11/43.22    (3)   ~ (e3 = e2)
% 232.11/43.22    (4)   ~ (e3 = e0)
% 232.11/43.22    (5)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 232.11/43.22         (all_57_14 = e0 & op(e0, e1) = e0)
% 232.11/43.22    (6)  all_57_15 = e3
% 232.11/43.22    (7)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 232.11/43.22         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 232.11/43.22    (8)   ~ (e2 = e0)
% 232.11/43.22    (9)   ~ (e1 = e0)
% 232.11/43.22    (10)  all_57_13 = e3
% 232.11/43.22    (11)  op(e0, e0) = e3
% 232.11/43.22    (12)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 232.11/43.22          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 232.11/43.22            e2)
% 232.11/43.22    (13)   ~ (e2 = e1)
% 232.11/43.22  
% 232.11/43.22  Begin of proof
% 232.11/43.22  | 
% 232.11/43.22  | BETA: splitting (5) gives:
% 232.11/43.22  | 
% 232.11/43.22  | Case 1:
% 232.11/43.22  | | 
% 232.11/43.22  | |   (14)  all_57_12 = e0 & op(e0, e3) = e0
% 232.11/43.22  | | 
% 232.11/43.22  | | ALPHA: (14) implies:
% 232.11/43.22  | |   (15)  all_57_12 = e0
% 232.11/43.22  | | 
% 232.11/43.22  | | REF_CLOSE: (1), (3), (6), (7), (8), (9), (10), (12), (13), (15) are
% 232.11/43.22  | |            inconsistent by sub-proof #2059.
% 232.11/43.22  | | 
% 232.11/43.22  | Case 2:
% 232.11/43.22  | | 
% 232.11/43.22  | |   (16)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 232.11/43.22  | |           e0)
% 232.11/43.22  | | 
% 232.11/43.22  | | BETA: splitting (16) gives:
% 232.11/43.22  | | 
% 232.11/43.22  | | Case 1:
% 232.11/43.22  | | | 
% 232.11/43.22  | | |   (17)  all_57_13 = e0 & op(e0, e2) = e0
% 232.11/43.22  | | | 
% 232.11/43.22  | | | ALPHA: (17) implies:
% 232.11/43.22  | | |   (18)  all_57_13 = e0
% 232.11/43.22  | | | 
% 232.11/43.22  | | | REF_CLOSE: (4), (10), (18) are inconsistent by sub-proof #2184.
% 232.11/43.22  | | | 
% 232.11/43.22  | | Case 2:
% 232.11/43.22  | | | 
% 232.11/43.22  | | |   (19)  all_57_14 = e0 & op(e0, e1) = e0
% 232.11/43.22  | | | 
% 232.11/43.22  | | | ALPHA: (19) implies:
% 232.11/43.22  | | |   (20)  all_57_14 = e0
% 232.11/43.22  | | | 
% 232.11/43.22  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 232.11/43.22  | | |            (13), (20) are inconsistent by sub-proof #2055.
% 232.11/43.22  | | | 
% 232.11/43.22  | | End of split
% 232.11/43.22  | | 
% 232.11/43.22  | End of split
% 232.11/43.22  | 
% 232.11/43.22  End of proof
% 232.11/43.22  
% 232.11/43.22  Sub-proof #2055 shows that the following formulas are inconsistent:
% 232.11/43.22  ----------------------------------------------------------------
% 232.11/43.22    (1)   ~ (e3 = e1)
% 232.11/43.22    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.11/43.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.11/43.22    (3)   ~ (e3 = e2)
% 232.11/43.22    (4)   ~ (e3 = e0)
% 232.11/43.22    (5)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 232.11/43.22         (all_57_14 = e0 & op(e0, e1) = e0)
% 232.11/43.22    (6)  all_57_15 = e3
% 232.11/43.22    (7)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 232.11/43.22         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 232.11/43.22    (8)   ~ (e2 = e0)
% 232.11/43.22    (9)   ~ (e1 = e0)
% 232.11/43.22    (10)  all_57_13 = e3
% 232.11/43.22    (11)  op(e0, e0) = e3
% 232.11/43.22    (12)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 232.11/43.22          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 232.11/43.22            e2)
% 232.11/43.22    (13)   ~ (e2 = e1)
% 232.11/43.22    (14)  all_57_14 = e0
% 232.11/43.22  
% 232.11/43.22  Begin of proof
% 232.11/43.22  | 
% 232.11/43.22  | BETA: splitting (7) gives:
% 232.11/43.22  | 
% 232.11/43.22  | Case 1:
% 232.11/43.22  | | 
% 232.11/43.22  | |   (15)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 232.11/43.22  | |           e1)
% 232.11/43.22  | | 
% 232.11/43.22  | | BETA: splitting (15) gives:
% 232.11/43.22  | | 
% 232.11/43.22  | | Case 1:
% 232.11/43.22  | | | 
% 232.11/43.22  | | |   (16)  all_57_12 = e1 & op(e0, e3) = e1
% 232.11/43.22  | | | 
% 232.11/43.22  | | | ALPHA: (16) implies:
% 232.11/43.22  | | |   (17)  all_57_12 = e1
% 232.11/43.22  | | | 
% 232.11/43.22  | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13), (17)
% 232.11/43.22  | | |            are inconsistent by sub-proof #2057.
% 232.11/43.22  | | | 
% 232.11/43.22  | | Case 2:
% 232.11/43.22  | | | 
% 232.11/43.22  | | |   (18)  all_57_13 = e1 & op(e0, e2) = e1
% 232.11/43.22  | | | 
% 232.11/43.22  | | | ALPHA: (18) implies:
% 232.11/43.22  | | |   (19)  all_57_13 = e1
% 232.11/43.22  | | | 
% 232.11/43.22  | | | REF_CLOSE: (1), (10), (19) are inconsistent by sub-proof #2268.
% 232.11/43.22  | | | 
% 232.11/43.22  | | End of split
% 232.11/43.22  | | 
% 232.11/43.22  | Case 2:
% 232.11/43.22  | | 
% 232.11/43.22  | |   (20)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 232.11/43.22  | |           e1)
% 232.11/43.22  | | 
% 232.11/43.22  | | REF_CLOSE: (1), (2), (9), (11), (14), (20) are inconsistent by sub-proof
% 232.11/43.22  | |            #2056.
% 232.11/43.22  | | 
% 232.11/43.22  | End of split
% 232.11/43.22  | 
% 232.11/43.22  End of proof
% 232.11/43.22  
% 232.11/43.22  Sub-proof #2056 shows that the following formulas are inconsistent:
% 232.11/43.22  ----------------------------------------------------------------
% 232.11/43.22    (1)   ~ (e3 = e1)
% 232.11/43.22    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.11/43.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.11/43.22    (3)   ~ (e1 = e0)
% 232.11/43.22    (4)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 232.11/43.22    (5)  op(e0, e0) = e3
% 232.11/43.22    (6)  all_57_14 = e0
% 232.11/43.22  
% 232.11/43.22  Begin of proof
% 232.11/43.22  | 
% 232.11/43.22  | BETA: splitting (4) gives:
% 232.11/43.22  | 
% 232.11/43.22  | Case 1:
% 232.11/43.22  | | 
% 232.11/43.22  | |   (7)  all_57_14 = e1 & op(e0, e1) = e1
% 232.11/43.22  | | 
% 232.11/43.22  | | ALPHA: (7) implies:
% 232.11/43.22  | |   (8)  all_57_14 = e1
% 232.11/43.22  | | 
% 232.11/43.22  | | REF_CLOSE: (3), (6), (8) are inconsistent by sub-proof #2122.
% 232.11/43.22  | | 
% 232.11/43.22  | Case 2:
% 232.11/43.22  | | 
% 232.11/43.22  | |   (9)  all_57_15 = e1 & op(e0, e0) = e1
% 232.11/43.22  | | 
% 232.11/43.22  | | ALPHA: (9) implies:
% 232.11/43.22  | |   (10)  op(e0, e0) = e1
% 232.11/43.22  | | 
% 232.11/43.22  | | REF_CLOSE: (1), (2), (5), (10) are inconsistent by sub-proof #2183.
% 232.11/43.22  | | 
% 232.11/43.22  | End of split
% 232.11/43.22  | 
% 232.11/43.22  End of proof
% 232.11/43.22  
% 232.11/43.22  Sub-proof #2057 shows that the following formulas are inconsistent:
% 232.11/43.22  ----------------------------------------------------------------
% 232.11/43.22    (1)   ~ (e3 = e1)
% 232.11/43.22    (2)   ~ (e3 = e2)
% 232.11/43.22    (3)   ~ (e3 = e0)
% 232.11/43.22    (4)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 232.11/43.22         (all_57_14 = e0 & op(e0, e1) = e0)
% 232.11/43.22    (5)  all_57_15 = e3
% 232.11/43.22    (6)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 232.11/43.22         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 232.11/43.22    (7)  all_57_12 = e1
% 232.11/43.22    (8)   ~ (e2 = e0)
% 232.11/43.22    (9)   ~ (e1 = e0)
% 232.11/43.22    (10)  all_57_13 = e3
% 232.11/43.22    (11)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 232.11/43.22          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 232.11/43.22            e2)
% 232.11/43.22    (12)   ~ (e2 = e1)
% 232.11/43.22  
% 232.11/43.22  Begin of proof
% 232.11/43.22  | 
% 232.11/43.22  | BETA: splitting (11) gives:
% 232.11/43.22  | 
% 232.11/43.22  | Case 1:
% 232.11/43.22  | | 
% 232.11/43.22  | |   (13)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 232.11/43.22  | |           e2)
% 232.11/43.22  | | 
% 232.11/43.22  | | BETA: splitting (13) gives:
% 232.11/43.22  | | 
% 232.11/43.22  | | Case 1:
% 232.11/43.22  | | | 
% 232.11/43.22  | | |   (14)  all_57_12 = e2 & op(e0, e3) = e2
% 232.11/43.22  | | | 
% 232.11/43.22  | | | ALPHA: (14) implies:
% 232.11/43.22  | | |   (15)  all_57_12 = e2
% 232.11/43.22  | | | 
% 232.11/43.22  | | | REF_CLOSE: (7), (12), (15) are inconsistent by sub-proof #2321.
% 232.11/43.22  | | | 
% 232.11/43.22  | | Case 2:
% 232.11/43.22  | | | 
% 232.11/43.22  | | |   (16)  all_57_13 = e2 & op(e0, e2) = e2
% 232.11/43.22  | | | 
% 232.11/43.22  | | | REF_CLOSE: (2), (10), (16) are inconsistent by sub-proof #2146.
% 232.11/43.22  | | | 
% 232.11/43.22  | | End of split
% 232.11/43.22  | | 
% 232.11/43.22  | Case 2:
% 232.11/43.22  | | 
% 232.11/43.22  | |   (17)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 232.11/43.22  | |           e2)
% 232.11/43.22  | | 
% 232.11/43.22  | | BETA: splitting (17) gives:
% 232.11/43.22  | | 
% 232.11/43.22  | | Case 1:
% 232.11/43.22  | | | 
% 232.11/43.22  | | |   (18)  all_57_14 = e2 & op(e0, e1) = e2
% 232.11/43.22  | | | 
% 232.11/43.22  | | | ALPHA: (18) implies:
% 232.11/43.22  | | |   (19)  all_57_14 = e2
% 232.11/43.22  | | | 
% 232.11/43.22  | | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (10), (12), (19) are
% 232.11/43.22  | | |            inconsistent by sub-proof #2213.
% 232.11/43.22  | | | 
% 232.11/43.22  | | Case 2:
% 232.11/43.22  | | | 
% 232.11/43.22  | | |   (20)  all_57_15 = e2 & op(e0, e0) = e2
% 232.11/43.22  | | | 
% 232.11/43.22  | | | ALPHA: (20) implies:
% 232.11/43.22  | | |   (21)  all_57_15 = e2
% 232.11/43.22  | | | 
% 232.11/43.22  | | | REF_CLOSE: (2), (5), (21) are inconsistent by sub-proof #2058.
% 232.11/43.22  | | | 
% 232.11/43.22  | | End of split
% 232.11/43.22  | | 
% 232.11/43.22  | End of split
% 232.11/43.22  | 
% 232.11/43.22  End of proof
% 232.11/43.22  
% 232.11/43.22  Sub-proof #2058 shows that the following formulas are inconsistent:
% 232.11/43.22  ----------------------------------------------------------------
% 232.11/43.22    (1)  all_57_15 = e3
% 232.11/43.22    (2)  all_57_15 = e2
% 232.11/43.22    (3)   ~ (e3 = e2)
% 232.11/43.22  
% 232.11/43.22  Begin of proof
% 232.11/43.22  | 
% 232.11/43.22  | COMBINE_EQS: (1), (2) imply:
% 232.11/43.22  |   (4)  e3 = e2
% 232.11/43.22  | 
% 232.11/43.22  | SIMP: (4) implies:
% 232.11/43.22  |   (5)  e3 = e2
% 232.11/43.22  | 
% 232.11/43.22  | REDUCE: (3), (5) imply:
% 232.11/43.22  |   (6)  $false
% 232.11/43.22  | 
% 232.11/43.22  | CLOSE: (6) is inconsistent.
% 232.11/43.22  | 
% 232.11/43.22  End of proof
% 232.11/43.22  
% 232.11/43.22  Sub-proof #2059 shows that the following formulas are inconsistent:
% 232.11/43.22  ----------------------------------------------------------------
% 232.11/43.22    (1)  all_57_12 = e0
% 232.11/43.22    (2)   ~ (e3 = e1)
% 232.11/43.22    (3)   ~ (e3 = e2)
% 232.11/43.22    (4)  all_57_15 = e3
% 232.11/43.22    (5)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 232.11/43.22         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 232.11/43.22    (6)   ~ (e2 = e0)
% 232.11/43.22    (7)   ~ (e1 = e0)
% 232.11/43.22    (8)  all_57_13 = e3
% 232.11/43.22    (9)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2) |
% 232.11/43.22         (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 232.11/43.22    (10)   ~ (e2 = e1)
% 232.11/43.22  
% 232.11/43.22  Begin of proof
% 232.11/43.22  | 
% 232.11/43.22  | BETA: splitting (9) gives:
% 232.11/43.22  | 
% 232.11/43.22  | Case 1:
% 232.11/43.22  | | 
% 232.11/43.22  | |   (11)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 232.11/43.22  | |           e2)
% 232.11/43.22  | | 
% 232.11/43.22  | | REF_CLOSE: (1), (3), (6), (8), (11) are inconsistent by sub-proof #2061.
% 232.11/43.22  | | 
% 232.11/43.22  | Case 2:
% 232.11/43.22  | | 
% 232.11/43.22  | |   (12)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 232.11/43.22  | |           e2)
% 232.11/43.22  | | 
% 232.11/43.22  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (10), (12) are inconsistent by
% 232.11/43.22  | |            sub-proof #2060.
% 232.11/43.22  | | 
% 232.11/43.22  | End of split
% 232.11/43.22  | 
% 232.11/43.22  End of proof
% 232.11/43.22  
% 232.11/43.22  Sub-proof #2060 shows that the following formulas are inconsistent:
% 232.11/43.22  ----------------------------------------------------------------
% 232.11/43.22    (1)  all_57_12 = e0
% 232.11/43.22    (2)   ~ (e3 = e1)
% 232.11/43.22    (3)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 232.11/43.22    (4)   ~ (e3 = e2)
% 232.11/43.22    (5)  all_57_15 = e3
% 232.11/43.22    (6)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 232.11/43.22         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 232.11/43.22    (7)   ~ (e1 = e0)
% 232.11/43.22    (8)  all_57_13 = e3
% 232.11/43.22    (9)   ~ (e2 = e1)
% 232.11/43.22  
% 232.11/43.22  Begin of proof
% 232.11/43.22  | 
% 232.11/43.22  | BETA: splitting (3) gives:
% 232.11/43.22  | 
% 232.11/43.22  | Case 1:
% 232.11/43.22  | | 
% 232.11/43.22  | |   (10)  all_57_14 = e2 & op(e0, e1) = e2
% 232.11/43.22  | | 
% 232.11/43.22  | | ALPHA: (10) implies:
% 232.11/43.22  | |   (11)  all_57_14 = e2
% 232.11/43.22  | | 
% 232.11/43.22  | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (9), (11) are inconsistent by
% 232.11/43.22  | |            sub-proof #2215.
% 232.11/43.22  | | 
% 232.11/43.22  | Case 2:
% 232.11/43.22  | | 
% 232.11/43.22  | |   (12)  all_57_15 = e2 & op(e0, e0) = e2
% 232.11/43.22  | | 
% 232.11/43.22  | | REF_CLOSE: (4), (5), (12) are inconsistent by sub-proof #2323.
% 232.11/43.22  | | 
% 232.11/43.22  | End of split
% 232.11/43.22  | 
% 232.11/43.22  End of proof
% 232.11/43.22  
% 232.11/43.22  Sub-proof #2061 shows that the following formulas are inconsistent:
% 232.11/43.22  ----------------------------------------------------------------
% 232.11/43.22    (1)  all_57_12 = e0
% 232.11/43.22    (2)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 232.11/43.22    (3)   ~ (e3 = e2)
% 232.11/43.22    (4)   ~ (e2 = e0)
% 232.11/43.22    (5)  all_57_13 = e3
% 232.11/43.22  
% 232.11/43.22  Begin of proof
% 232.11/43.22  | 
% 232.11/43.22  | BETA: splitting (2) gives:
% 232.11/43.22  | 
% 232.11/43.22  | Case 1:
% 232.11/43.22  | | 
% 232.11/43.22  | |   (6)  all_57_12 = e2 & op(e0, e3) = e2
% 232.11/43.22  | | 
% 232.11/43.22  | | ALPHA: (6) implies:
% 232.11/43.22  | |   (7)  all_57_12 = e2
% 232.11/43.22  | | 
% 232.11/43.22  | | REF_CLOSE: (1), (4), (7) are inconsistent by sub-proof #2385.
% 232.11/43.22  | | 
% 232.11/43.22  | Case 2:
% 232.11/43.22  | | 
% 232.11/43.22  | |   (8)  all_57_13 = e2 & op(e0, e2) = e2
% 232.11/43.22  | | 
% 232.11/43.22  | | REF_CLOSE: (3), (5), (8) are inconsistent by sub-proof #2146.
% 232.11/43.22  | | 
% 232.11/43.22  | End of split
% 232.11/43.22  | 
% 232.11/43.22  End of proof
% 232.11/43.22  
% 232.11/43.22  Sub-proof #2062 shows that the following formulas are inconsistent:
% 232.11/43.22  ----------------------------------------------------------------
% 232.11/43.22    (1)  all_57_11 = e3 & op(e1, e0) = e3
% 232.11/43.22    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.11/43.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.11/43.22    (3)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 232.11/43.22    (4)  all_55_7 = all_52_15
% 232.11/43.22    (5)  op(e1, e0) = all_53_14
% 232.11/43.22    (6)   ~ (all_52_15 = e1)
% 232.11/43.22    (7)  all_55_7 = e3 | all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 232.11/43.22    (8)  op(e0, e0) = e1
% 232.11/43.22    (9)   ~ (all_53_14 = all_52_15)
% 232.11/43.22    (10)  all_55_11 = all_53_14
% 232.11/43.22    (11)  op(all_52_15, all_52_15) = e0
% 232.11/43.22    (12)   ~ (all_52_15 = e2)
% 232.11/43.22  
% 232.11/43.22  Begin of proof
% 232.11/43.22  | 
% 232.11/43.22  | ALPHA: (1) implies:
% 232.11/43.22  |   (13)  op(e1, e0) = e3
% 232.11/43.22  | 
% 232.11/43.22  | BETA: splitting (3) gives:
% 232.11/43.22  | 
% 232.11/43.22  | Case 1:
% 232.11/43.22  | | 
% 232.11/43.22  | |   (14)  all_55_11 = e3
% 232.11/43.22  | | 
% 232.11/43.22  | | COMBINE_EQS: (10), (14) imply:
% 232.11/43.22  | |   (15)  all_53_14 = e3
% 232.11/43.22  | | 
% 232.11/43.22  | | REDUCE: (9), (15) imply:
% 232.11/43.22  | |   (16)   ~ (all_52_15 = e3)
% 232.11/43.22  | | 
% 232.11/43.22  | | SIMP: (16) implies:
% 232.11/43.22  | |   (17)   ~ (all_52_15 = e3)
% 232.11/43.22  | | 
% 232.11/43.22  | | BETA: splitting (7) gives:
% 232.11/43.22  | | 
% 232.11/43.22  | | Case 1:
% 232.11/43.22  | | | 
% 232.11/43.22  | | |   (18)  all_55_7 = e3
% 232.11/43.22  | | | 
% 232.11/43.22  | | | REF_CLOSE: (4), (17), (18) are inconsistent by sub-proof #2063.
% 232.11/43.22  | | | 
% 232.11/43.22  | | Case 2:
% 232.11/43.22  | | | 
% 232.11/43.22  | | |   (19)  all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 232.11/43.22  | | | 
% 232.11/43.22  | | | REF_CLOSE: (2), (4), (6), (8), (11), (12), (19) are inconsistent by
% 232.11/43.22  | | |            sub-proof #2078.
% 232.11/43.22  | | | 
% 232.11/43.22  | | End of split
% 232.11/43.22  | | 
% 232.11/43.22  | Case 2:
% 232.11/43.22  | | 
% 232.11/43.22  | |   (20)   ~ (all_55_11 = e3)
% 232.11/43.22  | | 
% 232.11/43.22  | | REDUCE: (10), (20) imply:
% 232.11/43.22  | |   (21)   ~ (all_53_14 = e3)
% 232.11/43.22  | | 
% 232.11/43.22  | | REF_CLOSE: (2), (5), (13), (21) are inconsistent by sub-proof #2330.
% 232.11/43.22  | | 
% 232.11/43.22  | End of split
% 232.11/43.22  | 
% 232.11/43.22  End of proof
% 232.11/43.22  
% 232.11/43.22  Sub-proof #2063 shows that the following formulas are inconsistent:
% 232.11/43.22  ----------------------------------------------------------------
% 232.11/43.22    (1)  all_55_7 = all_52_15
% 232.11/43.22    (2)  all_55_7 = e3
% 232.11/43.22    (3)   ~ (all_52_15 = e3)
% 232.11/43.22  
% 232.11/43.22  Begin of proof
% 232.11/43.22  | 
% 232.11/43.22  | COMBINE_EQS: (1), (2) imply:
% 232.11/43.22  |   (4)  all_52_15 = e3
% 232.11/43.22  | 
% 232.11/43.22  | SIMP: (4) implies:
% 232.11/43.22  |   (5)  all_52_15 = e3
% 232.11/43.22  | 
% 232.11/43.22  | REDUCE: (3), (5) imply:
% 232.11/43.22  |   (6)  $false
% 232.11/43.22  | 
% 232.11/43.22  | CLOSE: (6) is inconsistent.
% 232.11/43.22  | 
% 232.11/43.22  End of proof
% 232.11/43.22  
% 232.11/43.22  Sub-proof #2064 shows that the following formulas are inconsistent:
% 232.11/43.22  ----------------------------------------------------------------
% 232.11/43.22    (1)  all_57_10 = e0
% 232.11/43.22    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.11/43.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.11/43.22    (3)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 232.11/43.22    (4)   ~ (e3 = e0)
% 232.11/43.22    (5)   ~ (all_53_12 = e3)
% 232.11/43.22    (6)  op(e3, e0) = all_53_12
% 232.11/43.22  
% 232.11/43.22  Begin of proof
% 232.11/43.22  | 
% 232.11/43.22  | BETA: splitting (3) gives:
% 232.11/43.22  | 
% 232.11/43.22  | Case 1:
% 232.11/43.22  | | 
% 232.11/43.22  | |   (7)  all_57_9 = e3 & op(e3, e0) = e3
% 232.11/43.22  | | 
% 232.11/43.22  | | ALPHA: (7) implies:
% 232.11/43.22  | |   (8)  op(e3, e0) = e3
% 232.11/43.22  | | 
% 232.11/43.22  | | REF_CLOSE: (2), (5), (6), (8) are inconsistent by sub-proof #2458.
% 232.11/43.22  | | 
% 232.11/43.22  | Case 2:
% 232.11/43.22  | | 
% 232.11/43.22  | |   (9)  all_57_10 = e3 & op(e2, e0) = e3
% 232.11/43.22  | | 
% 232.11/43.22  | | ALPHA: (9) implies:
% 232.11/43.22  | |   (10)  all_57_10 = e3
% 232.11/43.22  | | 
% 232.11/43.22  | | COMBINE_EQS: (1), (10) imply:
% 232.11/43.22  | |   (11)  e3 = e0
% 232.11/43.22  | | 
% 232.11/43.22  | | REDUCE: (4), (11) imply:
% 232.11/43.22  | |   (12)  $false
% 232.11/43.22  | | 
% 232.11/43.22  | | CLOSE: (12) is inconsistent.
% 232.11/43.22  | | 
% 232.11/43.22  | End of split
% 232.11/43.22  | 
% 232.11/43.22  End of proof
% 232.11/43.22  
% 232.11/43.22  Sub-proof #2065 shows that the following formulas are inconsistent:
% 232.11/43.22  ----------------------------------------------------------------
% 232.11/43.22    (1)   ~ (e3 = e1)
% 232.11/43.22    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.11/43.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.11/43.22    (3)  op(e2, e2) = e0
% 232.11/43.22    (4)   ~ (e3 = e2)
% 232.11/43.22    (5)   ~ (e3 = e0)
% 232.11/43.22    (6)  op(e2, e2) = all_52_11
% 232.11/43.22    (7)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 232.11/43.22         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 232.11/43.22    (8)   ~ (e2 = e0)
% 232.11/43.22    (9)   ~ (e1 = e0)
% 232.11/43.22    (10)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 232.11/43.22          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 232.11/43.22            e3)
% 232.11/43.22    (11)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 232.11/43.22          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 232.11/43.22            e2)
% 232.11/43.22    (12)  op(e0, e0) = e1
% 232.11/43.22    (13)   ~ (e2 = e1)
% 232.11/43.22    (14)  all_57_14 = e0
% 232.11/43.22    (15)  op(all_52_11, all_52_11) = e2
% 232.11/43.22  
% 232.11/43.22  Begin of proof
% 232.11/43.22  | 
% 232.11/43.22  | BETA: splitting (7) gives:
% 232.11/43.22  | 
% 232.11/43.22  | Case 1:
% 232.11/43.22  | | 
% 232.11/43.22  | |   (16)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 232.11/43.22  | |           e1)
% 232.11/43.22  | | 
% 232.11/43.22  | | REF_CLOSE: (1), (2), (4), (5), (8), (10), (11), (12), (13), (14), (16) are
% 232.11/43.22  | |            inconsistent by sub-proof #2067.
% 232.11/43.22  | | 
% 232.11/43.22  | Case 2:
% 232.11/43.22  | | 
% 232.11/43.22  | |   (17)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 232.11/43.22  | |           e1)
% 232.11/43.22  | | 
% 232.11/43.22  | | BETA: splitting (17) gives:
% 232.11/43.22  | | 
% 232.11/43.22  | | Case 1:
% 232.11/43.22  | | | 
% 232.11/43.22  | | |   (18)  all_57_14 = e1 & op(e0, e1) = e1
% 232.11/43.22  | | | 
% 232.11/43.22  | | | ALPHA: (18) implies:
% 232.11/43.22  | | |   (19)  all_57_14 = e1
% 232.11/43.22  | | | 
% 232.11/43.22  | | | REF_CLOSE: (9), (14), (19) are inconsistent by sub-proof #2122.
% 232.11/43.22  | | | 
% 232.11/43.22  | | Case 2:
% 232.11/43.22  | | | 
% 232.11/43.22  | | |   (20)  all_57_15 = e1 & op(e0, e0) = e1
% 232.11/43.22  | | | 
% 232.11/43.22  | | | REF_CLOSE: (2), (3), (6), (13), (15), (20) are inconsistent by sub-proof
% 232.11/43.22  | | |            #2066.
% 232.11/43.22  | | | 
% 232.11/43.22  | | End of split
% 232.11/43.22  | | 
% 232.11/43.22  | End of split
% 232.11/43.22  | 
% 232.11/43.22  End of proof
% 232.11/43.22  
% 232.11/43.22  Sub-proof #2066 shows that the following formulas are inconsistent:
% 232.11/43.22  ----------------------------------------------------------------
% 232.11/43.22    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.11/43.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.11/43.22    (2)  all_57_15 = e1 & op(e0, e0) = e1
% 232.11/43.22    (3)  op(e2, e2) = e0
% 232.11/43.22    (4)  op(e2, e2) = all_52_11
% 232.11/43.22    (5)   ~ (e2 = e1)
% 232.11/43.22    (6)  op(all_52_11, all_52_11) = e2
% 232.11/43.22  
% 232.11/43.22  Begin of proof
% 232.11/43.22  | 
% 232.11/43.22  | ALPHA: (2) implies:
% 232.11/43.22  |   (7)  op(e0, e0) = e1
% 232.11/43.22  | 
% 232.11/43.22  | GROUND_INST: instantiating (1) with e0, all_52_11, e2, e2, simplifying with
% 232.11/43.22  |              (3), (4) gives:
% 232.11/43.22  |   (8)  all_52_11 = e0
% 232.11/43.22  | 
% 232.11/43.22  | REDUCE: (6), (8) imply:
% 232.11/43.22  |   (9)  op(e0, e0) = e2
% 232.11/43.22  | 
% 232.11/43.22  | REF_CLOSE: (1), (5), (7), (9) are inconsistent by sub-proof #2177.
% 232.11/43.22  | 
% 232.11/43.22  End of proof
% 232.11/43.22  
% 232.11/43.22  Sub-proof #2067 shows that the following formulas are inconsistent:
% 232.11/43.22  ----------------------------------------------------------------
% 232.11/43.22    (1)   ~ (e3 = e1)
% 232.11/43.22    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.11/43.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.11/43.22    (3)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 232.11/43.22    (4)   ~ (e3 = e2)
% 232.11/43.22    (5)   ~ (e3 = e0)
% 232.11/43.22    (6)   ~ (e2 = e0)
% 232.11/43.22    (7)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 232.11/43.22         (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 232.11/43.22    (8)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2) |
% 232.11/43.22         (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 232.11/43.22    (9)  op(e0, e0) = e1
% 232.11/43.22    (10)   ~ (e2 = e1)
% 232.11/43.22    (11)  all_57_14 = e0
% 232.11/43.22  
% 232.11/43.22  Begin of proof
% 232.11/43.22  | 
% 232.11/43.22  | BETA: splitting (3) gives:
% 232.11/43.22  | 
% 232.11/43.22  | Case 1:
% 232.11/43.22  | | 
% 232.11/43.22  | |   (12)  all_57_12 = e1 & op(e0, e3) = e1
% 232.11/43.22  | | 
% 232.11/43.22  | | ALPHA: (12) implies:
% 232.11/43.22  | |   (13)  all_57_12 = e1
% 232.11/43.22  | | 
% 232.11/43.22  | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (13) are
% 232.11/43.22  | |            inconsistent by sub-proof #2070.
% 232.11/43.22  | | 
% 232.11/43.22  | Case 2:
% 232.11/43.22  | | 
% 232.11/43.22  | |   (14)  all_57_13 = e1 & op(e0, e2) = e1
% 232.11/43.22  | | 
% 232.11/43.22  | | ALPHA: (14) implies:
% 232.11/43.22  | |   (15)  all_57_13 = e1
% 232.11/43.22  | | 
% 232.11/43.22  | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (15) are
% 232.11/43.22  | |            inconsistent by sub-proof #2068.
% 232.11/43.22  | | 
% 232.11/43.22  | End of split
% 232.11/43.22  | 
% 232.11/43.22  End of proof
% 232.11/43.22  
% 232.11/43.22  Sub-proof #2068 shows that the following formulas are inconsistent:
% 232.11/43.22  ----------------------------------------------------------------
% 232.11/43.22    (1)  all_57_13 = e1
% 232.11/43.22    (2)   ~ (e3 = e1)
% 232.11/43.22    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.11/43.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.11/43.22    (4)   ~ (e3 = e2)
% 232.11/43.22    (5)   ~ (e3 = e0)
% 232.11/43.22    (6)   ~ (e2 = e0)
% 232.11/43.22    (7)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 232.11/43.22         (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 232.11/43.22    (8)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2) |
% 232.11/43.22         (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 232.11/43.22    (9)  op(e0, e0) = e1
% 232.11/43.22    (10)   ~ (e2 = e1)
% 232.11/43.22    (11)  all_57_14 = e0
% 232.11/43.22  
% 232.11/43.22  Begin of proof
% 232.11/43.22  | 
% 232.11/43.22  | BETA: splitting (7) gives:
% 232.11/43.22  | 
% 232.11/43.22  | Case 1:
% 232.11/43.22  | | 
% 232.11/43.22  | |   (12)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 232.11/43.22  | |           e3)
% 232.11/43.22  | | 
% 232.11/43.22  | | BETA: splitting (12) gives:
% 232.11/43.22  | | 
% 232.11/43.22  | | Case 1:
% 232.11/43.22  | | | 
% 232.11/43.22  | | |   (13)  all_57_12 = e3 & op(e0, e3) = e3
% 232.11/43.22  | | | 
% 232.11/43.22  | | | ALPHA: (13) implies:
% 232.11/43.22  | | |   (14)  all_57_12 = e3
% 232.11/43.22  | | | 
% 232.11/43.22  | | | REF_CLOSE: (1), (3), (4), (6), (8), (9), (10), (11), (14) are inconsistent
% 232.11/43.22  | | |            by sub-proof #2069.
% 232.11/43.22  | | | 
% 232.11/43.22  | | Case 2:
% 232.11/43.22  | | | 
% 232.11/43.22  | | |   (15)  all_57_13 = e3 & op(e0, e2) = e3
% 232.11/43.22  | | | 
% 232.11/43.22  | | | ALPHA: (15) implies:
% 232.11/43.22  | | |   (16)  all_57_13 = e3
% 232.11/43.22  | | | 
% 232.11/43.22  | | | REF_CLOSE: (1), (2), (16) are inconsistent by sub-proof #2268.
% 232.11/43.22  | | | 
% 232.11/43.22  | | End of split
% 232.11/43.22  | | 
% 232.11/43.22  | Case 2:
% 232.11/43.22  | | 
% 232.11/43.22  | |   (17)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 232.11/43.22  | |           e3)
% 232.11/43.22  | | 
% 232.11/43.22  | | REF_CLOSE: (2), (3), (5), (9), (11), (17) are inconsistent by sub-proof
% 232.11/43.22  | |            #2071.
% 232.11/43.22  | | 
% 232.11/43.22  | End of split
% 232.11/43.22  | 
% 232.11/43.22  End of proof
% 232.11/43.22  
% 232.11/43.22  Sub-proof #2069 shows that the following formulas are inconsistent:
% 232.11/43.22  ----------------------------------------------------------------
% 232.11/43.22    (1)  all_57_13 = e1
% 232.11/43.22    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.11/43.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.11/43.22    (3)   ~ (e3 = e2)
% 232.11/43.22    (4)   ~ (e2 = e0)
% 232.11/43.22    (5)  all_57_12 = e3
% 232.11/43.22    (6)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2) |
% 232.11/43.22         (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 232.11/43.22    (7)  op(e0, e0) = e1
% 232.11/43.22    (8)   ~ (e2 = e1)
% 232.11/43.22    (9)  all_57_14 = e0
% 232.11/43.22  
% 232.11/43.22  Begin of proof
% 232.11/43.22  | 
% 232.11/43.22  | BETA: splitting (6) gives:
% 232.11/43.22  | 
% 232.11/43.22  | Case 1:
% 232.11/43.22  | | 
% 232.11/43.22  | |   (10)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 232.11/43.22  | |           e2)
% 232.11/43.22  | | 
% 232.11/43.22  | | BETA: splitting (10) gives:
% 232.11/43.22  | | 
% 232.11/43.22  | | Case 1:
% 232.11/43.22  | | | 
% 232.11/43.22  | | |   (11)  all_57_12 = e2 & op(e0, e3) = e2
% 232.11/43.22  | | | 
% 232.11/43.22  | | | REF_CLOSE: (3), (5), (11) are inconsistent by sub-proof #2232.
% 232.11/43.22  | | | 
% 232.11/43.22  | | Case 2:
% 232.11/43.22  | | | 
% 232.11/43.22  | | |   (12)  all_57_13 = e2 & op(e0, e2) = e2
% 232.11/43.22  | | | 
% 232.11/43.22  | | | REF_CLOSE: (1), (8), (12) are inconsistent by sub-proof #2101.
% 232.11/43.22  | | | 
% 232.11/43.22  | | End of split
% 232.11/43.22  | | 
% 232.11/43.22  | Case 2:
% 232.11/43.22  | | 
% 232.11/43.22  | |   (13)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 232.11/43.22  | |           e2)
% 232.11/43.22  | | 
% 232.11/43.22  | | REF_CLOSE: (2), (4), (7), (8), (9), (13) are inconsistent by sub-proof
% 232.11/43.22  | |            #2073.
% 232.11/43.22  | | 
% 232.11/43.22  | End of split
% 232.11/43.22  | 
% 232.11/43.22  End of proof
% 232.11/43.22  
% 232.11/43.22  Sub-proof #2070 shows that the following formulas are inconsistent:
% 232.11/43.22  ----------------------------------------------------------------
% 232.11/43.22    (1)   ~ (e3 = e1)
% 232.11/43.22    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.11/43.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.11/43.22    (3)   ~ (e3 = e2)
% 232.11/43.22    (4)   ~ (e3 = e0)
% 232.11/43.22    (5)  all_57_12 = e1
% 232.11/43.22    (6)   ~ (e2 = e0)
% 232.11/43.22    (7)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 232.11/43.22         (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 232.11/43.22    (8)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2) |
% 232.11/43.22         (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 232.11/43.22    (9)  op(e0, e0) = e1
% 232.11/43.23    (10)   ~ (e2 = e1)
% 232.11/43.23    (11)  all_57_14 = e0
% 232.11/43.23  
% 232.11/43.23  Begin of proof
% 232.11/43.23  | 
% 232.11/43.23  | BETA: splitting (7) gives:
% 232.11/43.23  | 
% 232.11/43.23  | Case 1:
% 232.11/43.23  | | 
% 232.11/43.23  | |   (12)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 232.11/43.23  | |           e3)
% 232.11/43.23  | | 
% 232.11/43.23  | | BETA: splitting (12) gives:
% 232.11/43.23  | | 
% 232.11/43.23  | | Case 1:
% 232.11/43.23  | | | 
% 232.11/43.23  | | |   (13)  all_57_12 = e3 & op(e0, e3) = e3
% 232.11/43.23  | | | 
% 232.11/43.23  | | | ALPHA: (13) implies:
% 232.11/43.23  | | |   (14)  all_57_12 = e3
% 232.11/43.23  | | | 
% 232.11/43.23  | | | REF_CLOSE: (1), (5), (14) are inconsistent by sub-proof #2151.
% 232.11/43.23  | | | 
% 232.11/43.23  | | Case 2:
% 232.11/43.23  | | | 
% 232.11/43.23  | | |   (15)  all_57_13 = e3 & op(e0, e2) = e3
% 232.11/43.23  | | | 
% 232.11/43.23  | | | ALPHA: (15) implies:
% 232.11/43.23  | | |   (16)  all_57_13 = e3
% 232.11/43.23  | | | 
% 232.11/43.23  | | | REF_CLOSE: (2), (3), (5), (6), (8), (9), (10), (11), (16) are inconsistent
% 232.11/43.23  | | |            by sub-proof #2072.
% 232.11/43.23  | | | 
% 232.11/43.23  | | End of split
% 232.11/43.23  | | 
% 232.11/43.23  | Case 2:
% 232.11/43.23  | | 
% 232.11/43.23  | |   (17)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 232.11/43.23  | |           e3)
% 232.11/43.23  | | 
% 232.11/43.23  | | REF_CLOSE: (1), (2), (4), (9), (11), (17) are inconsistent by sub-proof
% 232.11/43.23  | |            #2071.
% 232.11/43.23  | | 
% 232.11/43.23  | End of split
% 232.11/43.23  | 
% 232.11/43.23  End of proof
% 232.11/43.23  
% 232.11/43.23  Sub-proof #2071 shows that the following formulas are inconsistent:
% 232.11/43.23  ----------------------------------------------------------------
% 232.11/43.23    (1)   ~ (e3 = e1)
% 232.11/43.23    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.11/43.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.11/43.23    (3)   ~ (e3 = e0)
% 232.11/43.23    (4)  op(e0, e0) = e1
% 232.11/43.23    (5)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 232.11/43.23    (6)  all_57_14 = e0
% 232.11/43.23  
% 232.11/43.23  Begin of proof
% 232.11/43.23  | 
% 232.11/43.23  | BETA: splitting (5) gives:
% 232.11/43.23  | 
% 232.11/43.23  | Case 1:
% 232.11/43.23  | | 
% 232.11/43.23  | |   (7)  all_57_14 = e3 & op(e0, e1) = e3
% 232.11/43.23  | | 
% 232.11/43.23  | | REF_CLOSE: (3), (6), (7) are inconsistent by sub-proof #2338.
% 232.11/43.23  | | 
% 232.11/43.23  | Case 2:
% 232.11/43.23  | | 
% 232.11/43.23  | |   (8)  all_57_15 = e3 & op(e0, e0) = e3
% 232.11/43.23  | | 
% 232.11/43.23  | | ALPHA: (8) implies:
% 232.11/43.23  | |   (9)  op(e0, e0) = e3
% 232.11/43.23  | | 
% 232.11/43.23  | | REF_CLOSE: (1), (2), (4), (9) are inconsistent by sub-proof #2183.
% 232.11/43.23  | | 
% 232.11/43.23  | End of split
% 232.11/43.23  | 
% 232.11/43.23  End of proof
% 232.11/43.23  
% 232.11/43.23  Sub-proof #2072 shows that the following formulas are inconsistent:
% 232.11/43.23  ----------------------------------------------------------------
% 232.11/43.23    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.11/43.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.11/43.23    (2)   ~ (e3 = e2)
% 232.11/43.23    (3)  all_57_12 = e1
% 232.11/43.23    (4)   ~ (e2 = e0)
% 232.11/43.23    (5)  all_57_13 = e3
% 232.11/43.23    (6)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2) |
% 232.11/43.23         (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 232.11/43.23    (7)  op(e0, e0) = e1
% 232.11/43.23    (8)   ~ (e2 = e1)
% 232.11/43.23    (9)  all_57_14 = e0
% 232.11/43.23  
% 232.11/43.23  Begin of proof
% 232.11/43.23  | 
% 232.11/43.23  | BETA: splitting (6) gives:
% 232.11/43.23  | 
% 232.11/43.23  | Case 1:
% 232.11/43.23  | | 
% 232.11/43.23  | |   (10)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 232.11/43.23  | |           e2)
% 232.11/43.23  | | 
% 232.11/43.23  | | BETA: splitting (10) gives:
% 232.11/43.23  | | 
% 232.11/43.23  | | Case 1:
% 232.11/43.23  | | | 
% 232.11/43.23  | | |   (11)  all_57_12 = e2 & op(e0, e3) = e2
% 232.11/43.23  | | | 
% 232.11/43.23  | | | ALPHA: (11) implies:
% 232.11/43.23  | | |   (12)  all_57_12 = e2
% 232.11/43.23  | | | 
% 232.11/43.23  | | | REF_CLOSE: (3), (8), (12) are inconsistent by sub-proof #2321.
% 232.11/43.23  | | | 
% 232.11/43.23  | | Case 2:
% 232.11/43.23  | | | 
% 232.11/43.23  | | |   (13)  all_57_13 = e2 & op(e0, e2) = e2
% 232.11/43.23  | | | 
% 232.11/43.23  | | | ALPHA: (13) implies:
% 232.11/43.23  | | |   (14)  all_57_13 = e2
% 232.11/43.23  | | | 
% 232.11/43.23  | | | REF_CLOSE: (2), (5), (14) are inconsistent by sub-proof #2203.
% 232.11/43.23  | | | 
% 232.11/43.23  | | End of split
% 232.11/43.23  | | 
% 232.11/43.23  | Case 2:
% 232.11/43.23  | | 
% 232.11/43.23  | |   (15)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 232.11/43.23  | |           e2)
% 232.11/43.23  | | 
% 232.11/43.23  | | REF_CLOSE: (1), (4), (7), (8), (9), (15) are inconsistent by sub-proof
% 232.11/43.23  | |            #2073.
% 232.11/43.23  | | 
% 232.11/43.23  | End of split
% 232.11/43.23  | 
% 232.11/43.23  End of proof
% 232.11/43.23  
% 232.11/43.23  Sub-proof #2073 shows that the following formulas are inconsistent:
% 232.11/43.23  ----------------------------------------------------------------
% 232.11/43.23    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.11/43.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.11/43.23    (2)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 232.11/43.23    (3)   ~ (e2 = e0)
% 232.11/43.23    (4)  op(e0, e0) = e1
% 232.11/43.23    (5)   ~ (e2 = e1)
% 232.11/43.23    (6)  all_57_14 = e0
% 232.11/43.23  
% 232.11/43.23  Begin of proof
% 232.11/43.23  | 
% 232.11/43.23  | BETA: splitting (2) gives:
% 232.11/43.23  | 
% 232.11/43.23  | Case 1:
% 232.11/43.23  | | 
% 232.11/43.23  | |   (7)  all_57_14 = e2 & op(e0, e1) = e2
% 232.11/43.23  | | 
% 232.11/43.23  | | REF_CLOSE: (3), (6), (7) are inconsistent by sub-proof #2074.
% 232.11/43.23  | | 
% 232.11/43.23  | Case 2:
% 232.11/43.23  | | 
% 232.11/43.23  | |   (8)  all_57_15 = e2 & op(e0, e0) = e2
% 232.11/43.23  | | 
% 232.11/43.23  | | ALPHA: (8) implies:
% 232.11/43.23  | |   (9)  op(e0, e0) = e2
% 232.11/43.23  | | 
% 232.11/43.23  | | REF_CLOSE: (1), (4), (5), (9) are inconsistent by sub-proof #2177.
% 232.11/43.23  | | 
% 232.11/43.23  | End of split
% 232.11/43.23  | 
% 232.11/43.23  End of proof
% 232.11/43.23  
% 232.11/43.23  Sub-proof #2074 shows that the following formulas are inconsistent:
% 232.11/43.23  ----------------------------------------------------------------
% 232.11/43.23    (1)  all_57_14 = e2 & op(e0, e1) = e2
% 232.11/43.23    (2)  all_57_14 = e0
% 232.11/43.23    (3)   ~ (e2 = e0)
% 232.11/43.23  
% 232.11/43.23  Begin of proof
% 232.11/43.23  | 
% 232.11/43.23  | ALPHA: (1) implies:
% 232.11/43.23  |   (4)  all_57_14 = e2
% 232.11/43.23  | 
% 232.11/43.23  | COMBINE_EQS: (2), (4) imply:
% 232.11/43.23  |   (5)  e2 = e0
% 232.11/43.23  | 
% 232.11/43.23  | REDUCE: (3), (5) imply:
% 232.11/43.23  |   (6)  $false
% 232.11/43.23  | 
% 232.11/43.23  | CLOSE: (6) is inconsistent.
% 232.11/43.23  | 
% 232.11/43.23  End of proof
% 232.11/43.23  
% 232.11/43.23  Sub-proof #2075 shows that the following formulas are inconsistent:
% 232.11/43.23  ----------------------------------------------------------------
% 232.11/43.23    (1)  all_57_12 = e3 & op(e0, e3) = e3
% 232.11/43.23    (2)  all_57_12 = e2
% 232.11/43.23    (3)   ~ (e3 = e2)
% 232.11/43.23  
% 232.11/43.23  Begin of proof
% 232.11/43.23  | 
% 232.11/43.23  | ALPHA: (1) implies:
% 232.11/43.23  |   (4)  all_57_12 = e3
% 232.11/43.23  | 
% 232.11/43.23  | COMBINE_EQS: (2), (4) imply:
% 232.11/43.23  |   (5)  e3 = e2
% 232.11/43.23  | 
% 232.11/43.23  | REDUCE: (3), (5) imply:
% 232.11/43.23  |   (6)  $false
% 232.11/43.23  | 
% 232.11/43.23  | CLOSE: (6) is inconsistent.
% 232.11/43.23  | 
% 232.11/43.23  End of proof
% 232.11/43.23  
% 232.11/43.23  Sub-proof #2076 shows that the following formulas are inconsistent:
% 232.11/43.23  ----------------------------------------------------------------
% 232.11/43.23    (1)  all_55_1 = all_53_4
% 232.11/43.23    (2)  all_55_1 = e0
% 232.11/43.23    (3)   ~ (all_53_4 = e0)
% 232.11/43.23  
% 232.11/43.23  Begin of proof
% 232.11/43.23  | 
% 232.11/43.23  | COMBINE_EQS: (1), (2) imply:
% 232.11/43.23  |   (4)  all_53_4 = e0
% 232.11/43.23  | 
% 232.11/43.23  | SIMP: (4) implies:
% 232.11/43.23  |   (5)  all_53_4 = e0
% 232.11/43.23  | 
% 232.11/43.23  | REDUCE: (3), (5) imply:
% 232.11/43.23  |   (6)  $false
% 232.11/43.23  | 
% 232.11/43.23  | CLOSE: (6) is inconsistent.
% 232.11/43.23  | 
% 232.11/43.23  End of proof
% 232.11/43.23  
% 232.11/43.23  Sub-proof #2077 shows that the following formulas are inconsistent:
% 232.11/43.23  ----------------------------------------------------------------
% 232.11/43.23    (1)  op(e0, e2) = e0
% 232.11/43.23    (2)   ~ (all_53_6 = e2)
% 232.11/43.23    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.11/43.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.11/43.23    (4)  all_55_9 = all_53_6
% 232.11/43.23    (5)   ~ (all_53_6 = all_53_7)
% 232.11/43.23    (6)  all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 232.11/43.23    (7)   ~ (all_53_6 = e1)
% 232.11/43.23    (8)  op(e0, e2) = all_53_7
% 232.11/43.23  
% 232.11/43.23  Begin of proof
% 232.11/43.23  | 
% 232.11/43.23  | BETA: splitting (6) gives:
% 232.11/43.23  | 
% 232.11/43.23  | Case 1:
% 232.11/43.23  | | 
% 232.11/43.23  | |   (9)  all_55_9 = e2
% 232.11/43.23  | | 
% 232.11/43.23  | | REF_CLOSE: (2), (4), (9) are inconsistent by sub-proof #2274.
% 232.11/43.23  | | 
% 232.11/43.23  | Case 2:
% 232.11/43.23  | | 
% 232.11/43.23  | |   (10)  all_55_9 = e1 | all_55_9 = e0
% 232.11/43.23  | | 
% 232.11/43.23  | | BETA: splitting (10) gives:
% 232.11/43.23  | | 
% 232.11/43.23  | | Case 1:
% 232.11/43.23  | | | 
% 232.11/43.23  | | |   (11)  all_55_9 = e1
% 232.11/43.23  | | | 
% 232.11/43.23  | | | REF_CLOSE: (4), (7), (11) are inconsistent by sub-proof #2273.
% 232.11/43.23  | | | 
% 232.11/43.23  | | Case 2:
% 232.11/43.23  | | | 
% 232.11/43.23  | | |   (12)  all_55_9 = e0
% 232.11/43.23  | | | 
% 232.11/43.23  | | | COMBINE_EQS: (4), (12) imply:
% 232.11/43.23  | | |   (13)  all_53_6 = e0
% 232.11/43.23  | | | 
% 232.11/43.23  | | | SIMP: (13) implies:
% 232.11/43.23  | | |   (14)  all_53_6 = e0
% 232.11/43.23  | | | 
% 232.11/43.23  | | | REDUCE: (5), (14) imply:
% 232.11/43.23  | | |   (15)   ~ (all_53_7 = e0)
% 232.11/43.23  | | | 
% 232.11/43.23  | | | SIMP: (15) implies:
% 232.11/43.23  | | |   (16)   ~ (all_53_7 = e0)
% 232.11/43.23  | | | 
% 232.11/43.23  | | | REF_CLOSE: (1), (3), (8), (16) are inconsistent by sub-proof #2332.
% 232.11/43.23  | | | 
% 232.11/43.23  | | End of split
% 232.11/43.23  | | 
% 232.11/43.23  | End of split
% 232.11/43.23  | 
% 232.11/43.23  End of proof
% 232.11/43.23  
% 232.11/43.23  Sub-proof #2078 shows that the following formulas are inconsistent:
% 232.11/43.23  ----------------------------------------------------------------
% 232.11/43.23    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.11/43.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.11/43.23    (2)  all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 232.11/43.23    (3)  all_55_7 = all_52_15
% 232.11/43.23    (4)   ~ (all_52_15 = e1)
% 232.11/43.23    (5)  op(e0, e0) = e1
% 232.11/43.23    (6)  op(all_52_15, all_52_15) = e0
% 232.11/43.23    (7)   ~ (all_52_15 = e2)
% 232.11/43.23  
% 232.11/43.23  Begin of proof
% 232.11/43.23  | 
% 232.11/43.23  | BETA: splitting (2) gives:
% 232.11/43.23  | 
% 232.11/43.23  | Case 1:
% 232.11/43.23  | | 
% 232.11/43.23  | |   (8)  all_55_7 = e2
% 232.11/43.23  | | 
% 232.11/43.23  | | REF_CLOSE: (3), (7), (8) are inconsistent by sub-proof #2278.
% 232.11/43.23  | | 
% 232.11/43.23  | Case 2:
% 232.11/43.23  | | 
% 232.11/43.23  | |   (9)  all_55_7 = e1 | all_55_7 = e0
% 232.11/43.23  | | 
% 232.11/43.23  | | REF_CLOSE: (1), (3), (4), (5), (6), (9) are inconsistent by sub-proof #2079.
% 232.11/43.23  | | 
% 232.11/43.23  | End of split
% 232.11/43.23  | 
% 232.11/43.23  End of proof
% 232.11/43.23  
% 232.11/43.23  Sub-proof #2079 shows that the following formulas are inconsistent:
% 232.11/43.23  ----------------------------------------------------------------
% 232.11/43.23    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.11/43.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.11/43.23    (2)  all_55_7 = all_52_15
% 232.11/43.23    (3)   ~ (all_52_15 = e1)
% 232.11/43.23    (4)  all_55_7 = e1 | all_55_7 = e0
% 232.11/43.23    (5)  op(e0, e0) = e1
% 232.11/43.23    (6)  op(all_52_15, all_52_15) = e0
% 232.11/43.23  
% 232.11/43.23  Begin of proof
% 232.11/43.23  | 
% 232.11/43.23  | BETA: splitting (4) gives:
% 232.11/43.23  | 
% 232.11/43.23  | Case 1:
% 232.11/43.23  | | 
% 232.11/43.23  | |   (7)  all_55_7 = e1
% 232.11/43.23  | | 
% 232.11/43.23  | | REF_CLOSE: (2), (3), (7) are inconsistent by sub-proof #2277.
% 232.11/43.23  | | 
% 232.11/43.23  | Case 2:
% 232.11/43.23  | | 
% 232.11/43.23  | |   (8)  all_55_7 = e0
% 232.11/43.23  | | 
% 232.11/43.23  | | COMBINE_EQS: (2), (8) imply:
% 232.11/43.23  | |   (9)  all_52_15 = e0
% 232.11/43.23  | | 
% 232.11/43.23  | | SIMP: (9) implies:
% 232.11/43.23  | |   (10)  all_52_15 = e0
% 232.11/43.23  | | 
% 232.11/43.23  | | REDUCE: (3), (10) imply:
% 232.11/43.23  | |   (11)   ~ (e1 = e0)
% 232.11/43.23  | | 
% 232.11/43.23  | | SIMP: (11) implies:
% 232.11/43.23  | |   (12)   ~ (e1 = e0)
% 232.11/43.23  | | 
% 232.11/43.23  | | REDUCE: (6), (10) imply:
% 232.11/43.23  | |   (13)  op(e0, e0) = e0
% 232.11/43.23  | | 
% 232.11/43.23  | | REF_CLOSE: (1), (5), (12), (13) are inconsistent by sub-proof #2290.
% 232.11/43.23  | | 
% 232.11/43.23  | End of split
% 232.11/43.23  | 
% 232.11/43.23  End of proof
% 232.11/43.23  
% 232.11/43.23  Sub-proof #2080 shows that the following formulas are inconsistent:
% 232.11/43.23  ----------------------------------------------------------------
% 232.11/43.23    (1)  all_55_13 = all_53_7
% 232.11/43.23    (2)  all_55_13 = e3
% 232.11/43.23    (3)   ~ (all_53_7 = e3)
% 232.11/43.23  
% 232.11/43.23  Begin of proof
% 232.11/43.23  | 
% 232.11/43.23  | COMBINE_EQS: (1), (2) imply:
% 232.11/43.23  |   (4)  all_53_7 = e3
% 232.11/43.23  | 
% 232.11/43.23  | SIMP: (4) implies:
% 232.11/43.23  |   (5)  all_53_7 = e3
% 232.11/43.23  | 
% 232.11/43.23  | REDUCE: (3), (5) imply:
% 232.11/43.23  |   (6)  $false
% 232.11/43.23  | 
% 232.11/43.23  | CLOSE: (6) is inconsistent.
% 232.11/43.23  | 
% 232.11/43.23  End of proof
% 232.11/43.23  
% 232.11/43.23  Sub-proof #2081 shows that the following formulas are inconsistent:
% 232.11/43.23  ----------------------------------------------------------------
% 232.11/43.23    (1)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 232.11/43.23         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 232.11/43.23    (2)   ~ (e3 = e1)
% 232.11/43.23    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.11/43.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.11/43.23    (4)   ~ (all_6_2 = e3)
% 232.11/43.23    (5)  op(e1, e1) = all_6_2
% 232.11/43.23    (6)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 232.11/43.23         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 232.11/43.23    (7)   ~ (all_53_7 = e2)
% 232.11/43.23    (8)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 232.11/43.23         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 232.11/43.23    (9)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 232.11/43.23         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 232.11/43.23    (10)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 232.11/43.23          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 232.11/43.23    (11)   ~ (e3 = e2)
% 232.11/43.23    (12)   ~ (e3 = e0)
% 232.11/43.23    (13)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 232.11/43.23          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 232.11/43.23    (14)  op(e3, e3) = e3
% 232.11/43.23    (15)  all_57_6 = e2
% 232.11/43.23    (16)   ~ (e2 = e0)
% 232.11/43.23    (17)   ~ (e1 = e0)
% 232.11/43.23    (18)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 232.11/43.23          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 232.11/43.23    (19)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 232.11/43.23          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 232.11/43.23            e3)
% 232.11/43.23    (20)  op(e0, e2) = all_53_7
% 232.11/43.23    (21)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 232.11/43.23          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 232.11/43.23            e2)
% 232.11/43.23    (22)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 232.11/43.23              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 232.11/43.23                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 232.11/43.23                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 232.11/43.23    (23)  op(e1, e1) = e2
% 232.11/43.23    (24)  op(e0, e0) = e1
% 232.11/43.23    (25)   ~ (e2 = e1)
% 232.11/43.23    (26)   ~ (all_6_2 = e0)
% 232.11/43.23    (27)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 232.11/43.23          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 232.11/43.23  
% 232.11/43.23  Begin of proof
% 232.11/43.23  | 
% 232.11/43.23  | BETA: splitting (21) gives:
% 232.11/43.23  | 
% 232.11/43.23  | Case 1:
% 232.11/43.23  | | 
% 232.11/43.23  | |   (28)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 232.11/43.23  | |           e2)
% 232.11/43.23  | | 
% 232.11/43.23  | | REF_CLOSE: (1), (2), (3), (7), (12), (14), (15), (16), (17), (20), (25),
% 232.11/43.23  | |            (27), (28) are inconsistent by sub-proof #2082.
% 232.11/43.23  | | 
% 232.11/43.23  | Case 2:
% 232.11/43.23  | | 
% 232.11/43.23  | |   (29)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 232.11/43.23  | |           e2)
% 232.11/43.23  | | 
% 232.11/43.23  | | BETA: splitting (29) gives:
% 232.11/43.23  | | 
% 232.11/43.23  | | Case 1:
% 232.11/43.23  | | | 
% 232.11/43.23  | | |   (30)  all_57_14 = e2 & op(e0, e1) = e2
% 232.11/43.23  | | | 
% 232.11/43.23  | | | ALPHA: (30) implies:
% 232.11/43.23  | | |   (31)  all_57_14 = e2
% 232.11/43.23  | | | 
% 232.11/43.23  | | | BETA: splitting (18) gives:
% 232.11/43.23  | | | 
% 232.11/43.23  | | | Case 1:
% 232.11/43.23  | | | | 
% 232.11/43.23  | | | |   (32)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1)
% 232.11/43.23  | | | |           = e3)
% 232.11/43.23  | | | | 
% 232.11/43.23  | | | | BETA: splitting (32) gives:
% 232.11/43.23  | | | | 
% 232.11/43.23  | | | | Case 1:
% 232.11/43.23  | | | | | 
% 232.11/43.23  | | | | |   (33)  all_57_4 = e3 & op(e3, e1) = e3
% 232.11/43.23  | | | | | 
% 232.11/43.23  | | | | | ALPHA: (33) implies:
% 232.11/43.23  | | | | |   (34)  all_57_4 = e3
% 232.11/43.23  | | | | | 
% 232.11/43.23  | | | | | REF_CLOSE: (2), (3), (6), (8), (9), (11), (12), (14), (16), (17),
% 232.11/43.23  | | | | |            (25), (34) are inconsistent by sub-proof #2474.
% 232.11/43.23  | | | | | 
% 232.11/43.23  | | | | Case 2:
% 232.11/43.23  | | | | | 
% 232.11/43.23  | | | | |   (35)  all_57_5 = e3 & op(e2, e1) = e3
% 232.11/43.23  | | | | | 
% 232.11/43.23  | | | | | ALPHA: (35) implies:
% 232.11/43.23  | | | | |   (36)  all_57_5 = e3
% 232.11/43.23  | | | | | 
% 232.11/43.23  | | | | | REF_CLOSE: (2), (3), (5), (7), (10), (11), (12), (13), (16), (17),
% 232.11/43.23  | | | | |            (19), (20), (21), (22), (23), (24), (25), (26), (31), (36)
% 232.11/43.23  | | | | |            are inconsistent by sub-proof #2174.
% 232.11/43.23  | | | | | 
% 232.11/43.23  | | | | End of split
% 232.11/43.23  | | | | 
% 232.11/43.23  | | | Case 2:
% 232.11/43.23  | | | | 
% 232.11/43.23  | | | |   (37)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1)
% 232.11/43.23  | | | |           = e3)
% 232.11/43.23  | | | | 
% 232.11/43.23  | | | | REF_CLOSE: (3), (4), (5), (11), (31), (37) are inconsistent by sub-proof
% 232.11/43.23  | | | |            #2409.
% 232.11/43.23  | | | | 
% 232.11/43.23  | | | End of split
% 232.11/43.23  | | | 
% 232.11/43.23  | | Case 2:
% 232.11/43.23  | | | 
% 232.11/43.23  | | |   (38)  all_57_15 = e2 & op(e0, e0) = e2
% 232.11/43.23  | | | 
% 232.11/43.23  | | | ALPHA: (38) implies:
% 232.11/43.23  | | |   (39)  op(e0, e0) = e2
% 232.11/43.23  | | | 
% 232.11/43.23  | | | REF_CLOSE: (3), (24), (25), (39) are inconsistent by sub-proof #2177.
% 232.11/43.23  | | | 
% 232.11/43.23  | | End of split
% 232.11/43.23  | | 
% 232.11/43.23  | End of split
% 232.11/43.23  | 
% 232.11/43.23  End of proof
% 232.11/43.23  
% 232.11/43.23  Sub-proof #2082 shows that the following formulas are inconsistent:
% 232.11/43.23  ----------------------------------------------------------------
% 232.11/43.23    (1)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 232.11/43.23         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 232.11/43.23    (2)   ~ (e3 = e1)
% 232.11/43.23    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.11/43.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.11/43.23    (4)   ~ (all_53_7 = e2)
% 232.11/43.23    (5)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 232.11/43.23    (6)   ~ (e3 = e0)
% 232.11/43.23    (7)  op(e3, e3) = e3
% 232.11/43.23    (8)  all_57_6 = e2
% 232.11/43.23    (9)   ~ (e2 = e0)
% 232.11/43.23    (10)   ~ (e1 = e0)
% 232.11/43.23    (11)  op(e0, e2) = all_53_7
% 232.11/43.23    (12)   ~ (e2 = e1)
% 232.11/43.23    (13)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 232.11/43.23          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 232.11/43.23  
% 232.11/43.23  Begin of proof
% 232.11/43.23  | 
% 232.11/43.23  | BETA: splitting (5) gives:
% 232.11/43.23  | 
% 232.11/43.23  | Case 1:
% 232.11/43.23  | | 
% 232.11/43.23  | |   (14)  all_57_12 = e2 & op(e0, e3) = e2
% 232.11/43.23  | | 
% 232.11/43.23  | | ALPHA: (14) implies:
% 232.11/43.23  | |   (15)  all_57_12 = e2
% 232.11/43.23  | | 
% 232.11/43.23  | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (9), (10), (12), (13), (15) are
% 232.11/43.23  | |            inconsistent by sub-proof #2384.
% 232.11/43.23  | | 
% 232.11/43.23  | Case 2:
% 232.11/43.23  | | 
% 232.11/43.23  | |   (16)  all_57_13 = e2 & op(e0, e2) = e2
% 232.11/43.23  | | 
% 232.11/43.23  | | ALPHA: (16) implies:
% 232.11/43.23  | |   (17)  op(e0, e2) = e2
% 232.11/43.23  | | 
% 232.11/43.23  | | REF_CLOSE: (3), (4), (11), (17) are inconsistent by sub-proof #2335.
% 232.11/43.23  | | 
% 232.11/43.23  | End of split
% 232.11/43.23  | 
% 232.11/43.23  End of proof
% 232.11/43.23  
% 232.11/43.23  Sub-proof #2083 shows that the following formulas are inconsistent:
% 232.11/43.23  ----------------------------------------------------------------
% 232.11/43.23    (1)  op(e2, e3) = all_53_1
% 232.11/43.23    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.11/43.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.11/43.23    (3)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2)
% 232.11/43.23    (4)   ~ (e3 = e2)
% 232.11/43.23    (5)  op(e3, e3) = e3
% 232.11/43.23    (6)   ~ (all_53_1 = e2)
% 232.11/43.23  
% 232.11/43.23  Begin of proof
% 232.11/43.23  | 
% 232.11/43.23  | BETA: splitting (3) gives:
% 232.11/43.23  | 
% 232.11/43.23  | Case 1:
% 232.11/43.23  | | 
% 232.11/43.23  | |   (7)  all_57_0 = e2 & op(e3, e3) = e2
% 232.11/43.23  | | 
% 232.11/43.23  | | ALPHA: (7) implies:
% 232.11/43.23  | |   (8)  op(e3, e3) = e2
% 232.11/43.23  | | 
% 232.11/43.23  | | REF_CLOSE: (2), (4), (5), (8) are inconsistent by sub-proof #2490.
% 232.11/43.23  | | 
% 232.11/43.23  | Case 2:
% 232.11/43.23  | | 
% 232.11/43.23  | |   (9)  all_57_2 = e2 & op(e2, e3) = e2
% 232.11/43.23  | | 
% 232.11/43.23  | | REF_CLOSE: (1), (2), (6), (9) are inconsistent by sub-proof #2504.
% 232.11/43.23  | | 
% 232.11/43.23  | End of split
% 232.11/43.23  | 
% 232.11/43.23  End of proof
% 232.11/43.23  
% 232.11/43.23  Sub-proof #2084 shows that the following formulas are inconsistent:
% 232.11/43.23  ----------------------------------------------------------------
% 232.11/43.23    (1)  all_57_10 = e1 & op(e2, e0) = e1
% 232.11/43.23    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.11/43.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.11/43.23    (3)  op(e2, e0) = all_53_13
% 232.11/43.23    (4)   ~ (all_53_13 = e1)
% 232.11/43.23  
% 232.11/43.23  Begin of proof
% 232.11/43.23  | 
% 232.11/43.23  | ALPHA: (1) implies:
% 232.11/43.23  |   (5)  op(e2, e0) = e1
% 232.11/43.23  | 
% 232.11/43.23  | GROUND_INST: instantiating (2) with all_53_13, e1, e0, e2, simplifying with
% 232.11/43.23  |              (3), (5) gives:
% 232.11/43.23  |   (6)  all_53_13 = e1
% 232.11/43.23  | 
% 232.11/43.23  | REDUCE: (4), (6) imply:
% 232.11/43.23  |   (7)  $false
% 232.11/43.23  | 
% 232.11/43.23  | CLOSE: (7) is inconsistent.
% 232.11/43.23  | 
% 232.11/43.23  End of proof
% 232.11/43.23  
% 232.11/43.23  Sub-proof #2085 shows that the following formulas are inconsistent:
% 232.11/43.23  ----------------------------------------------------------------
% 232.11/43.23    (1)   ~ (e3 = e1)
% 232.11/43.23    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.11/43.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.11/43.23    (3)   ~ (all_6_2 = e3)
% 232.11/43.23    (4)  op(e1, e1) = all_6_2
% 232.11/43.23    (5)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 232.11/43.23    (6)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 232.11/43.23         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 232.11/43.23    (7)   ~ (e3 = e2)
% 232.11/43.23    (8)   ~ (e3 = e0)
% 232.11/43.23    (9)  op(e1, e1) = e1
% 232.11/43.23    (10)   ~ (e2 = e0)
% 232.11/43.23    (11)   ~ (e1 = e0)
% 232.11/43.23    (12)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 232.11/43.23          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 232.11/43.23    (13)   ~ (all_53_12 = e1)
% 232.11/43.23    (14)   ~ (e2 = e1)
% 232.11/43.23    (15)   ~ (all_6_2 = e0)
% 232.11/43.23    (16)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 232.11/43.23          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 232.11/43.23    (17)  op(e3, e0) = all_53_12
% 232.11/43.23  
% 232.11/43.23  Begin of proof
% 232.11/43.23  | 
% 232.11/43.23  | BETA: splitting (5) gives:
% 232.11/43.23  | 
% 232.11/43.23  | Case 1:
% 232.11/43.23  | | 
% 232.11/43.23  | |   (18)  all_57_4 = e1 & op(e3, e1) = e1
% 232.11/43.23  | | 
% 232.11/43.23  | | ALPHA: (18) implies:
% 232.11/43.23  | |   (19)  all_57_4 = e1
% 232.11/43.23  | | 
% 232.11/43.23  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (14),
% 232.11/43.23  | |            (15), (16), (19) are inconsistent by sub-proof #2407.
% 232.11/43.23  | | 
% 232.11/43.23  | Case 2:
% 232.11/43.23  | | 
% 232.11/43.23  | |   (20)  all_57_9 = e1 & op(e3, e0) = e1
% 232.11/43.23  | | 
% 232.11/43.23  | | REF_CLOSE: (2), (13), (17), (20) are inconsistent by sub-proof #2131.
% 232.11/43.23  | | 
% 232.11/43.23  | End of split
% 232.11/43.23  | 
% 232.11/43.23  End of proof
% 232.11/43.23  
% 232.11/43.23  Sub-proof #2086 shows that the following formulas are inconsistent:
% 232.11/43.23  ----------------------------------------------------------------
% 232.11/43.23    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.11/43.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.11/43.23    (2)  op(e1, e1) = all_6_2
% 232.11/43.23    (3)  op(e0, e0) = all_52_31
% 232.11/43.23    (4)  op(e0, e0) = e1
% 232.11/43.23    (5)   ~ (all_6_2 = e0)
% 232.11/43.23    (6)  op(all_52_31, all_52_31) = e0
% 232.11/43.23  
% 232.11/43.23  Begin of proof
% 232.11/43.23  | 
% 232.11/43.23  | GROUND_INST: instantiating (1) with e1, all_52_31, e0, e0, simplifying with
% 232.11/43.23  |              (3), (4) gives:
% 232.11/43.23  |   (7)  all_52_31 = e1
% 232.11/43.23  | 
% 232.11/43.23  | REDUCE: (6), (7) imply:
% 232.11/43.23  |   (8)  op(e1, e1) = e0
% 232.11/43.23  | 
% 232.11/43.23  | GROUND_INST: instantiating (1) with all_6_2, e0, e1, e1, simplifying with (2),
% 232.11/43.23  |              (8) gives:
% 232.11/43.23  |   (9)  all_6_2 = e0
% 232.11/43.23  | 
% 232.11/43.23  | REDUCE: (5), (9) imply:
% 232.11/43.23  |   (10)  $false
% 232.11/43.23  | 
% 232.11/43.23  | CLOSE: (10) is inconsistent.
% 232.11/43.23  | 
% 232.11/43.23  End of proof
% 232.11/43.23  
% 232.11/43.23  Sub-proof #2087 shows that the following formulas are inconsistent:
% 232.11/43.23  ----------------------------------------------------------------
% 232.11/43.23    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.11/43.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.11/43.23    (2)  all_57_14 = e3
% 232.11/43.23    (3)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 232.11/43.23    (4)   ~ (e3 = e2)
% 232.11/43.23    (5)  op(e0, e0) = e1
% 232.11/43.23    (6)   ~ (e2 = e1)
% 232.11/43.23  
% 232.11/43.23  Begin of proof
% 232.11/43.23  | 
% 232.11/43.23  | BETA: splitting (3) gives:
% 232.11/43.23  | 
% 232.11/43.23  | Case 1:
% 232.11/43.23  | | 
% 232.11/43.23  | |   (7)  all_57_14 = e2 & op(e0, e1) = e2
% 232.11/43.23  | | 
% 232.11/43.23  | | ALPHA: (7) implies:
% 232.11/43.23  | |   (8)  all_57_14 = e2
% 232.11/43.23  | | 
% 232.11/43.23  | | REF_CLOSE: (2), (4), (8) are inconsistent by sub-proof #2410.
% 232.11/43.23  | | 
% 232.11/43.23  | Case 2:
% 232.11/43.23  | | 
% 232.11/43.23  | |   (9)  all_57_15 = e2 & op(e0, e0) = e2
% 232.11/43.23  | | 
% 232.11/43.23  | | ALPHA: (9) implies:
% 232.11/43.23  | |   (10)  op(e0, e0) = e2
% 232.11/43.23  | | 
% 232.11/43.23  | | REF_CLOSE: (1), (5), (6), (10) are inconsistent by sub-proof #2177.
% 232.11/43.23  | | 
% 232.11/43.23  | End of split
% 232.11/43.23  | 
% 232.11/43.23  End of proof
% 232.11/43.23  
% 232.11/43.23  Sub-proof #2088 shows that the following formulas are inconsistent:
% 232.11/43.23  ----------------------------------------------------------------
% 232.11/43.23    (1)  all_57_14 = e3
% 232.11/43.23    (2)  all_57_12 = e2
% 232.11/43.23    (3)   ~ (e3 = e0)
% 232.15/43.23    (4)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 232.15/43.23         (all_57_14 = e0 & op(e0, e1) = e0)
% 232.15/43.23    (5)   ~ (e2 = e0)
% 232.15/43.23    (6)  all_57_13 = e3
% 232.15/43.23  
% 232.15/43.23  Begin of proof
% 232.15/43.23  | 
% 232.15/43.23  | BETA: splitting (4) gives:
% 232.15/43.23  | 
% 232.15/43.23  | Case 1:
% 232.15/43.23  | | 
% 232.15/43.23  | |   (7)  all_57_12 = e0 & op(e0, e3) = e0
% 232.15/43.23  | | 
% 232.15/43.23  | | ALPHA: (7) implies:
% 232.15/43.23  | |   (8)  all_57_12 = e0
% 232.15/43.23  | | 
% 232.15/43.23  | | REF_CLOSE: (2), (5), (8) are inconsistent by sub-proof #2385.
% 232.15/43.23  | | 
% 232.15/43.23  | Case 2:
% 232.15/43.23  | | 
% 232.15/43.23  | |   (9)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 232.15/43.23  | |          e0)
% 232.15/43.23  | | 
% 232.15/43.23  | | BETA: splitting (9) gives:
% 232.15/43.23  | | 
% 232.15/43.23  | | Case 1:
% 232.15/43.23  | | | 
% 232.15/43.23  | | |   (10)  all_57_13 = e0 & op(e0, e2) = e0
% 232.15/43.23  | | | 
% 232.15/43.23  | | | ALPHA: (10) implies:
% 232.15/43.23  | | |   (11)  all_57_13 = e0
% 232.15/43.23  | | | 
% 232.15/43.23  | | | REF_CLOSE: (3), (6), (11) are inconsistent by sub-proof #2184.
% 232.15/43.23  | | | 
% 232.15/43.23  | | Case 2:
% 232.15/43.23  | | | 
% 232.15/43.23  | | |   (12)  all_57_14 = e0 & op(e0, e1) = e0
% 232.15/43.23  | | | 
% 232.15/43.23  | | | REF_CLOSE: (1), (3), (12) are inconsistent by sub-proof #2314.
% 232.15/43.23  | | | 
% 232.15/43.23  | | End of split
% 232.15/43.23  | | 
% 232.15/43.23  | End of split
% 232.15/43.23  | 
% 232.15/43.23  End of proof
% 232.15/43.23  
% 232.15/43.23  Sub-proof #2089 shows that the following formulas are inconsistent:
% 232.15/43.23  ----------------------------------------------------------------
% 232.15/43.23    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.23    (2)  all_57_14 = e3
% 232.15/43.23    (3)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 232.15/43.23    (4)   ~ (e3 = e2)
% 232.15/43.23    (5)  op(e1, e1) = e1
% 232.15/43.23    (6)   ~ (e2 = e1)
% 232.15/43.23  
% 232.15/43.23  Begin of proof
% 232.15/43.23  | 
% 232.15/43.23  | BETA: splitting (3) gives:
% 232.15/43.23  | 
% 232.15/43.23  | Case 1:
% 232.15/43.23  | | 
% 232.15/43.23  | |   (7)  all_57_8 = e2 & op(e1, e1) = e2
% 232.15/43.23  | | 
% 232.15/43.23  | | ALPHA: (7) implies:
% 232.15/43.23  | |   (8)  op(e1, e1) = e2
% 232.15/43.23  | | 
% 232.15/43.23  | | REF_CLOSE: (1), (5), (6), (8) are inconsistent by sub-proof #2423.
% 232.15/43.23  | | 
% 232.15/43.23  | Case 2:
% 232.15/43.23  | | 
% 232.15/43.23  | |   (9)  all_57_14 = e2 & op(e0, e1) = e2
% 232.15/43.24  | | 
% 232.15/43.24  | | REF_CLOSE: (2), (4), (9) are inconsistent by sub-proof #2324.
% 232.15/43.24  | | 
% 232.15/43.24  | End of split
% 232.15/43.24  | 
% 232.15/43.24  End of proof
% 232.15/43.24  
% 232.15/43.24  Sub-proof #2090 shows that the following formulas are inconsistent:
% 232.15/43.24  ----------------------------------------------------------------
% 232.15/43.24    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.24           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.24    (2)   ~ (all_53_9 = e1)
% 232.15/43.24    (3)  all_57_10 = e0 & op(e2, e0) = e0
% 232.15/43.24    (4)   ~ (all_53_9 = all_53_13)
% 232.15/43.24    (5)  all_55_6 = all_53_9
% 232.15/43.24    (6)  op(e2, e0) = all_53_13
% 232.15/43.24    (7)  all_55_6 = e1 | all_55_6 = e0
% 232.15/43.24  
% 232.15/43.24  Begin of proof
% 232.15/43.24  | 
% 232.15/43.24  | ALPHA: (3) implies:
% 232.15/43.24  |   (8)  op(e2, e0) = e0
% 232.15/43.24  | 
% 232.15/43.24  | BETA: splitting (7) gives:
% 232.15/43.24  | 
% 232.15/43.24  | Case 1:
% 232.15/43.24  | | 
% 232.15/43.24  | |   (9)  all_55_6 = e1
% 232.15/43.24  | | 
% 232.15/43.24  | | REF_CLOSE: (2), (5), (9) are inconsistent by sub-proof #2163.
% 232.15/43.24  | | 
% 232.15/43.24  | Case 2:
% 232.15/43.24  | | 
% 232.15/43.24  | |   (10)  all_55_6 = e0
% 232.15/43.24  | | 
% 232.15/43.24  | | COMBINE_EQS: (5), (10) imply:
% 232.15/43.24  | |   (11)  all_53_9 = e0
% 232.15/43.24  | | 
% 232.15/43.24  | | SIMP: (11) implies:
% 232.15/43.24  | |   (12)  all_53_9 = e0
% 232.15/43.24  | | 
% 232.15/43.24  | | REDUCE: (4), (12) imply:
% 232.15/43.24  | |   (13)   ~ (all_53_13 = e0)
% 232.15/43.24  | | 
% 232.15/43.24  | | SIMP: (13) implies:
% 232.15/43.24  | |   (14)   ~ (all_53_13 = e0)
% 232.15/43.24  | | 
% 232.15/43.24  | | REF_CLOSE: (1), (6), (8), (14) are inconsistent by sub-proof #2470.
% 232.15/43.24  | | 
% 232.15/43.24  | End of split
% 232.15/43.24  | 
% 232.15/43.24  End of proof
% 232.15/43.24  
% 232.15/43.24  Sub-proof #2091 shows that the following formulas are inconsistent:
% 232.15/43.24  ----------------------------------------------------------------
% 232.15/43.24    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 232.15/43.24         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 232.15/43.24    (2)   ~ (e3 = e1)
% 232.15/43.24    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.24           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.24    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 232.15/43.24         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 232.15/43.24    (5)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 232.15/43.24         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 232.15/43.24    (6)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 232.15/43.24         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 232.15/43.24    (7)  all_57_3 = e0
% 232.15/43.24    (8)   ~ (e3 = e2)
% 232.15/43.24    (9)   ~ (e3 = e0)
% 232.15/43.24    (10)  op(e3, e3) = e3
% 232.15/43.24    (11)   ~ (e2 = e0)
% 232.15/43.24    (12)   ~ (e1 = e0)
% 232.15/43.24    (13)  all_57_13 = e0
% 232.15/43.24    (14)  all_57_7 = e3
% 232.15/43.24    (15)   ~ (e2 = e1)
% 232.15/43.24    (16)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 232.15/43.24          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 232.15/43.24  
% 232.15/43.24  Begin of proof
% 232.15/43.24  | 
% 232.15/43.24  | BETA: splitting (1) gives:
% 232.15/43.24  | 
% 232.15/43.24  | Case 1:
% 232.15/43.24  | | 
% 232.15/43.24  | |   (17)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 232.15/43.24  | |           e2)
% 232.15/43.24  | | 
% 232.15/43.24  | | BETA: splitting (17) gives:
% 232.15/43.24  | | 
% 232.15/43.24  | | Case 1:
% 232.15/43.24  | | | 
% 232.15/43.24  | | |   (18)  all_57_1 = e2 & op(e3, e2) = e2
% 232.15/43.24  | | | 
% 232.15/43.24  | | | ALPHA: (18) implies:
% 232.15/43.24  | | |   (19)  all_57_1 = e2
% 232.15/43.24  | | | 
% 232.15/43.24  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 232.15/43.24  | | |            (13), (14), (15), (16), (19) are inconsistent by sub-proof
% 232.15/43.24  | | |            #2093.
% 232.15/43.24  | | | 
% 232.15/43.24  | | Case 2:
% 232.15/43.24  | | | 
% 232.15/43.24  | | |   (20)  all_57_3 = e2 & op(e2, e2) = e2
% 232.15/43.24  | | | 
% 232.15/43.24  | | | REF_CLOSE: (7), (11), (20) are inconsistent by sub-proof #2103.
% 232.15/43.24  | | | 
% 232.15/43.24  | | End of split
% 232.15/43.24  | | 
% 232.15/43.24  | Case 2:
% 232.15/43.24  | | 
% 232.15/43.24  | |   (21)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 232.15/43.24  | |           e2)
% 232.15/43.24  | | 
% 232.15/43.24  | | BETA: splitting (21) gives:
% 232.15/43.24  | | 
% 232.15/43.24  | | Case 1:
% 232.15/43.24  | | | 
% 232.15/43.24  | | |   (22)  all_57_7 = e2 & op(e1, e2) = e2
% 232.15/43.24  | | | 
% 232.15/43.24  | | | REF_CLOSE: (8), (14), (22) are inconsistent by sub-proof #2092.
% 232.15/43.24  | | | 
% 232.15/43.24  | | Case 2:
% 232.15/43.24  | | | 
% 232.15/43.24  | | |   (23)  all_57_13 = e2 & op(e0, e2) = e2
% 232.15/43.24  | | | 
% 232.15/43.24  | | | REF_CLOSE: (11), (13), (23) are inconsistent by sub-proof #2316.
% 232.15/43.24  | | | 
% 232.15/43.24  | | End of split
% 232.15/43.24  | | 
% 232.15/43.24  | End of split
% 232.15/43.24  | 
% 232.15/43.24  End of proof
% 232.15/43.24  
% 232.15/43.24  Sub-proof #2092 shows that the following formulas are inconsistent:
% 232.15/43.24  ----------------------------------------------------------------
% 232.15/43.24    (1)  all_57_7 = e2 & op(e1, e2) = e2
% 232.15/43.24    (2)  all_57_7 = e3
% 232.15/43.24    (3)   ~ (e3 = e2)
% 232.15/43.24  
% 232.15/43.24  Begin of proof
% 232.15/43.24  | 
% 232.15/43.24  | ALPHA: (1) implies:
% 232.15/43.24  |   (4)  all_57_7 = e2
% 232.15/43.24  | 
% 232.15/43.24  | COMBINE_EQS: (2), (4) imply:
% 232.15/43.24  |   (5)  e3 = e2
% 232.15/43.24  | 
% 232.15/43.24  | REDUCE: (3), (5) imply:
% 232.15/43.24  |   (6)  $false
% 232.15/43.24  | 
% 232.15/43.24  | CLOSE: (6) is inconsistent.
% 232.15/43.24  | 
% 232.15/43.24  End of proof
% 232.15/43.24  
% 232.15/43.24  Sub-proof #2093 shows that the following formulas are inconsistent:
% 232.15/43.24  ----------------------------------------------------------------
% 232.15/43.24    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 232.15/43.24         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 232.15/43.24    (2)   ~ (e3 = e1)
% 232.15/43.24    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.24           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.24    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 232.15/43.24         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 232.15/43.24    (5)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 232.15/43.24         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 232.15/43.24    (6)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 232.15/43.24         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 232.15/43.24    (7)  all_57_3 = e0
% 232.15/43.24    (8)   ~ (e3 = e2)
% 232.15/43.24    (9)   ~ (e3 = e0)
% 232.15/43.24    (10)  all_57_1 = e2
% 232.15/43.24    (11)  op(e3, e3) = e3
% 232.15/43.24    (12)   ~ (e2 = e0)
% 232.15/43.24    (13)   ~ (e1 = e0)
% 232.15/43.24    (14)  all_57_13 = e0
% 232.15/43.24    (15)  all_57_7 = e3
% 232.15/43.24    (16)   ~ (e2 = e1)
% 232.15/43.24    (17)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 232.15/43.24          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 232.15/43.24  
% 232.15/43.24  Begin of proof
% 232.15/43.24  | 
% 232.15/43.24  | BETA: splitting (6) gives:
% 232.15/43.24  | 
% 232.15/43.24  | Case 1:
% 232.15/43.24  | | 
% 232.15/43.24  | |   (18)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) =
% 232.15/43.24  | |           e0)
% 232.15/43.24  | | 
% 232.15/43.24  | | REF_CLOSE: (1), (2), (3), (7), (8), (9), (11), (12), (13), (15), (16), (17),
% 232.15/43.24  | |            (18) are inconsistent by sub-proof #2097.
% 232.15/43.24  | | 
% 232.15/43.24  | Case 2:
% 232.15/43.24  | | 
% 232.15/43.24  | |   (19)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) =
% 232.15/43.24  | |           e0)
% 232.15/43.24  | | 
% 232.15/43.24  | | BETA: splitting (19) gives:
% 232.15/43.24  | | 
% 232.15/43.24  | | Case 1:
% 232.15/43.24  | | | 
% 232.15/43.24  | | |   (20)  all_57_4 = e0 & op(e3, e1) = e0
% 232.15/43.24  | | | 
% 232.15/43.24  | | | ALPHA: (20) implies:
% 232.15/43.24  | | |   (21)  all_57_4 = e0
% 232.15/43.24  | | | 
% 232.15/43.24  | | | BETA: splitting (4) gives:
% 232.15/43.24  | | | 
% 232.15/43.24  | | | Case 1:
% 232.15/43.24  | | | | 
% 232.15/43.24  | | | |   (22)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2)
% 232.15/43.24  | | | |           = e1)
% 232.15/43.24  | | | | 
% 232.15/43.24  | | | | REF_CLOSE: (2), (3), (10), (11), (16), (22) are inconsistent by
% 232.15/43.24  | | | |            sub-proof #2096.
% 232.15/43.24  | | | | 
% 232.15/43.24  | | | Case 2:
% 232.15/43.24  | | | | 
% 232.15/43.24  | | | |   (23)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0)
% 232.15/43.24  | | | |           = e1)
% 232.15/43.24  | | | | 
% 232.15/43.24  | | | | BETA: splitting (23) gives:
% 232.15/43.24  | | | | 
% 232.15/43.24  | | | | Case 1:
% 232.15/43.24  | | | | | 
% 232.15/43.24  | | | | |   (24)  all_57_4 = e1 & op(e3, e1) = e1
% 232.15/43.24  | | | | | 
% 232.15/43.24  | | | | | ALPHA: (24) implies:
% 232.15/43.24  | | | | |   (25)  all_57_4 = e1
% 232.15/43.24  | | | | | 
% 232.15/43.24  | | | | | REF_CLOSE: (13), (21), (25) are inconsistent by sub-proof #2438.
% 232.15/43.24  | | | | | 
% 232.15/43.24  | | | | Case 2:
% 232.15/43.24  | | | | | 
% 232.15/43.24  | | | | |   (26)  all_57_9 = e1 & op(e3, e0) = e1
% 232.15/43.24  | | | | | 
% 232.15/43.24  | | | | | ALPHA: (26) implies:
% 232.15/43.24  | | | | |   (27)  all_57_9 = e1
% 232.15/43.24  | | | | | 
% 232.15/43.24  | | | | | BETA: splitting (17) gives:
% 232.15/43.24  | | | | | 
% 232.15/43.24  | | | | | Case 1:
% 232.15/43.24  | | | | | | 
% 232.15/43.24  | | | | | |   (28)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2,
% 232.15/43.24  | | | | | |             e2) = e1)
% 232.15/43.24  | | | | | | 
% 232.15/43.24  | | | | | | BETA: splitting (28) gives:
% 232.15/43.24  | | | | | | 
% 232.15/43.24  | | | | | | Case 1:
% 232.15/43.24  | | | | | | | 
% 232.15/43.24  | | | | | | |   (29)  all_57_1 = e1 & op(e3, e2) = e1
% 232.15/43.24  | | | | | | | 
% 232.15/43.24  | | | | | | | REF_CLOSE: (10), (16), (29) are inconsistent by sub-proof #2210.
% 232.15/43.24  | | | | | | | 
% 232.15/43.24  | | | | | | Case 2:
% 232.15/43.24  | | | | | | | 
% 232.15/43.24  | | | | | | |   (30)  all_57_3 = e1 & op(e2, e2) = e1
% 232.15/43.24  | | | | | | | 
% 232.15/43.24  | | | | | | | ALPHA: (30) implies:
% 232.15/43.24  | | | | | | |   (31)  all_57_3 = e1
% 232.15/43.24  | | | | | | | 
% 232.15/43.24  | | | | | | | COMBINE_EQS: (7), (31) imply:
% 232.15/43.24  | | | | | | |   (32)  e1 = e0
% 232.15/43.24  | | | | | | | 
% 232.15/43.24  | | | | | | | SIMP: (32) implies:
% 232.15/43.24  | | | | | | |   (33)  e1 = e0
% 232.15/43.24  | | | | | | | 
% 232.15/43.24  | | | | | | | COMBINE_EQS: (27), (33) imply:
% 232.15/43.24  | | | | | | |   (34)  all_57_9 = e0
% 232.15/43.24  | | | | | | | 
% 232.15/43.24  | | | | | | | REF_CLOSE: (2), (3), (4), (5), (8), (11), (12), (13), (16), (21),
% 232.15/43.24  | | | | | | |            (34) are inconsistent by sub-proof #2436.
% 232.15/43.24  | | | | | | | 
% 232.15/43.24  | | | | | | End of split
% 232.15/43.24  | | | | | | 
% 232.15/43.24  | | | | | Case 2:
% 232.15/43.24  | | | | | | 
% 232.15/43.24  | | | | | |   (35)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0,
% 232.15/43.24  | | | | | |             e2) = e1)
% 232.15/43.24  | | | | | | 
% 232.15/43.24  | | | | | | BETA: splitting (35) gives:
% 232.15/43.24  | | | | | | 
% 232.15/43.24  | | | | | | Case 1:
% 232.15/43.24  | | | | | | | 
% 232.15/43.24  | | | | | | |   (36)  all_57_7 = e1 & op(e1, e2) = e1
% 232.15/43.24  | | | | | | | 
% 232.15/43.24  | | | | | | | REF_CLOSE: (2), (15), (36) are inconsistent by sub-proof #2104.
% 232.15/43.24  | | | | | | | 
% 232.15/43.24  | | | | | | Case 2:
% 232.15/43.24  | | | | | | | 
% 232.15/43.24  | | | | | | |   (37)  all_57_13 = e1 & op(e0, e2) = e1
% 232.15/43.24  | | | | | | | 
% 232.15/43.24  | | | | | | | ALPHA: (37) implies:
% 232.15/43.24  | | | | | | |   (38)  all_57_13 = e1
% 232.15/43.24  | | | | | | | 
% 232.15/43.24  | | | | | | | COMBINE_EQS: (14), (38) imply:
% 232.15/43.24  | | | | | | |   (39)  e1 = e0
% 232.15/43.24  | | | | | | | 
% 232.15/43.24  | | | | | | | SIMP: (39) implies:
% 232.15/43.24  | | | | | | |   (40)  e1 = e0
% 232.15/43.24  | | | | | | | 
% 232.15/43.24  | | | | | | | COMBINE_EQS: (27), (40) imply:
% 232.15/43.24  | | | | | | |   (41)  all_57_9 = e0
% 232.15/43.24  | | | | | | | 
% 232.15/43.24  | | | | | | | REF_CLOSE: (2), (3), (4), (5), (8), (11), (12), (13), (16), (21),
% 232.15/43.24  | | | | | | |            (41) are inconsistent by sub-proof #2436.
% 232.15/43.24  | | | | | | | 
% 232.15/43.24  | | | | | | End of split
% 232.15/43.24  | | | | | | 
% 232.15/43.24  | | | | | End of split
% 232.15/43.24  | | | | | 
% 232.15/43.24  | | | | End of split
% 232.15/43.24  | | | | 
% 232.15/43.24  | | | End of split
% 232.15/43.24  | | | 
% 232.15/43.24  | | Case 2:
% 232.15/43.24  | | | 
% 232.15/43.24  | | |   (42)  all_57_9 = e0 & op(e3, e0) = e0
% 232.15/43.24  | | | 
% 232.15/43.24  | | | ALPHA: (42) implies:
% 232.15/43.24  | | |   (43)  all_57_9 = e0
% 232.15/43.24  | | | 
% 232.15/43.24  | | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (10), (11), (12), (13), (14),
% 232.15/43.24  | | |            (15), (16), (17), (43) are inconsistent by sub-proof #2094.
% 232.15/43.24  | | | 
% 232.15/43.24  | | End of split
% 232.15/43.24  | | 
% 232.15/43.24  | End of split
% 232.15/43.24  | 
% 232.15/43.24  End of proof
% 232.15/43.24  
% 232.15/43.24  Sub-proof #2094 shows that the following formulas are inconsistent:
% 232.15/43.24  ----------------------------------------------------------------
% 232.15/43.24    (1)   ~ (e3 = e1)
% 232.15/43.24    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.24           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.24    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 232.15/43.24         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 232.15/43.24    (4)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 232.15/43.24         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 232.15/43.24    (5)  all_57_3 = e0
% 232.15/43.24    (6)   ~ (e3 = e2)
% 232.15/43.24    (7)  all_57_1 = e2
% 232.15/43.24    (8)  op(e3, e3) = e3
% 232.15/43.24    (9)  all_57_9 = e0
% 232.15/43.24    (10)   ~ (e2 = e0)
% 232.15/43.24    (11)   ~ (e1 = e0)
% 232.15/43.24    (12)  all_57_13 = e0
% 232.15/43.24    (13)  all_57_7 = e3
% 232.15/43.24    (14)   ~ (e2 = e1)
% 232.15/43.24    (15)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 232.15/43.24          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 232.15/43.24  
% 232.15/43.24  Begin of proof
% 232.15/43.24  | 
% 232.15/43.24  | BETA: splitting (3) gives:
% 232.15/43.24  | 
% 232.15/43.24  | Case 1:
% 232.15/43.24  | | 
% 232.15/43.24  | |   (16)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) =
% 232.15/43.24  | |           e1)
% 232.15/43.24  | | 
% 232.15/43.24  | | REF_CLOSE: (1), (2), (7), (8), (14), (16) are inconsistent by sub-proof
% 232.15/43.24  | |            #2096.
% 232.15/43.24  | | 
% 232.15/43.24  | Case 2:
% 232.15/43.24  | | 
% 232.15/43.24  | |   (17)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) =
% 232.15/43.24  | |           e1)
% 232.15/43.24  | | 
% 232.15/43.24  | | BETA: splitting (17) gives:
% 232.15/43.24  | | 
% 232.15/43.24  | | Case 1:
% 232.15/43.24  | | | 
% 232.15/43.24  | | |   (18)  all_57_4 = e1 & op(e3, e1) = e1
% 232.15/43.24  | | | 
% 232.15/43.24  | | | ALPHA: (18) implies:
% 232.15/43.24  | | |   (19)  all_57_4 = e1
% 232.15/43.24  | | | 
% 232.15/43.24  | | | BETA: splitting (15) gives:
% 232.15/43.24  | | | 
% 232.15/43.24  | | | Case 1:
% 232.15/43.24  | | | | 
% 232.15/43.24  | | | |   (20)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2)
% 232.15/43.24  | | | |           = e1)
% 232.15/43.24  | | | | 
% 232.15/43.24  | | | | BETA: splitting (20) gives:
% 232.15/43.24  | | | | 
% 232.15/43.24  | | | | Case 1:
% 232.15/43.24  | | | | | 
% 232.15/43.24  | | | | |   (21)  all_57_1 = e1 & op(e3, e2) = e1
% 232.15/43.24  | | | | | 
% 232.15/43.24  | | | | | REF_CLOSE: (7), (14), (21) are inconsistent by sub-proof #2210.
% 232.15/43.24  | | | | | 
% 232.15/43.24  | | | | Case 2:
% 232.15/43.24  | | | | | 
% 232.15/43.24  | | | | |   (22)  all_57_3 = e1 & op(e2, e2) = e1
% 232.15/43.24  | | | | | 
% 232.15/43.24  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (14),
% 232.15/43.24  | | | | |            (19), (22) are inconsistent by sub-proof #2095.
% 232.15/43.24  | | | | | 
% 232.15/43.24  | | | | End of split
% 232.15/43.24  | | | | 
% 232.15/43.24  | | | Case 2:
% 232.15/43.24  | | | | 
% 232.15/43.24  | | | |   (23)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2)
% 232.15/43.24  | | | |           = e1)
% 232.15/43.24  | | | | 
% 232.15/43.24  | | | | BETA: splitting (23) gives:
% 232.15/43.24  | | | | 
% 232.15/43.24  | | | | Case 1:
% 232.15/43.24  | | | | | 
% 232.15/43.24  | | | | |   (24)  all_57_7 = e1 & op(e1, e2) = e1
% 232.15/43.24  | | | | | 
% 232.15/43.24  | | | | | REF_CLOSE: (1), (13), (24) are inconsistent by sub-proof #2104.
% 232.15/43.24  | | | | | 
% 232.15/43.24  | | | | Case 2:
% 232.15/43.24  | | | | | 
% 232.15/43.24  | | | | |   (25)  all_57_13 = e1 & op(e0, e2) = e1
% 232.15/43.24  | | | | | 
% 232.15/43.24  | | | | | ALPHA: (25) implies:
% 232.15/43.24  | | | | |   (26)  all_57_13 = e1
% 232.15/43.24  | | | | | 
% 232.15/43.24  | | | | | COMBINE_EQS: (12), (26) imply:
% 232.15/43.24  | | | | |   (27)  e1 = e0
% 232.15/43.24  | | | | | 
% 232.15/43.24  | | | | | SIMP: (27) implies:
% 232.15/43.24  | | | | |   (28)  e1 = e0
% 232.15/43.24  | | | | | 
% 232.15/43.24  | | | | | COMBINE_EQS: (19), (28) imply:
% 232.15/43.24  | | | | |   (29)  all_57_4 = e0
% 232.15/43.24  | | | | | 
% 232.15/43.24  | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (8), (9), (10), (11), (14), (29)
% 232.15/43.24  | | | | |            are inconsistent by sub-proof #2436.
% 232.15/43.24  | | | | | 
% 232.15/43.24  | | | | End of split
% 232.15/43.24  | | | | 
% 232.15/43.24  | | | End of split
% 232.15/43.24  | | | 
% 232.15/43.24  | | Case 2:
% 232.15/43.24  | | | 
% 232.15/43.24  | | |   (30)  all_57_9 = e1 & op(e3, e0) = e1
% 232.15/43.24  | | | 
% 232.15/43.24  | | | ALPHA: (30) implies:
% 232.15/43.24  | | |   (31)  all_57_9 = e1
% 232.15/43.24  | | | 
% 232.15/43.24  | | | REF_CLOSE: (9), (11), (31) are inconsistent by sub-proof #2479.
% 232.15/43.24  | | | 
% 232.15/43.24  | | End of split
% 232.15/43.24  | | 
% 232.15/43.24  | End of split
% 232.15/43.24  | 
% 232.15/43.24  End of proof
% 232.15/43.24  
% 232.15/43.24  Sub-proof #2095 shows that the following formulas are inconsistent:
% 232.15/43.24  ----------------------------------------------------------------
% 232.15/43.24    (1)   ~ (e3 = e1)
% 232.15/43.24    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.24           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.24    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 232.15/43.24         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 232.15/43.24    (4)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 232.15/43.24         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 232.15/43.24    (5)  all_57_3 = e0
% 232.15/43.24    (6)   ~ (e3 = e2)
% 232.15/43.24    (7)  op(e3, e3) = e3
% 232.15/43.24    (8)  all_57_4 = e1
% 232.15/43.24    (9)  all_57_9 = e0
% 232.15/43.24    (10)   ~ (e2 = e0)
% 232.15/43.24    (11)   ~ (e1 = e0)
% 232.15/43.24    (12)  all_57_3 = e1 & op(e2, e2) = e1
% 232.15/43.24    (13)   ~ (e2 = e1)
% 232.15/43.24  
% 232.15/43.24  Begin of proof
% 232.15/43.24  | 
% 232.15/43.24  | ALPHA: (12) implies:
% 232.15/43.24  |   (14)  all_57_3 = e1
% 232.15/43.24  | 
% 232.15/43.24  | COMBINE_EQS: (5), (14) imply:
% 232.15/43.24  |   (15)  e1 = e0
% 232.15/43.24  | 
% 232.15/43.24  | SIMP: (15) implies:
% 232.15/43.24  |   (16)  e1 = e0
% 232.15/43.24  | 
% 232.15/43.24  | COMBINE_EQS: (8), (16) imply:
% 232.15/43.24  |   (17)  all_57_4 = e0
% 232.15/43.24  | 
% 232.15/43.24  | REF_CLOSE: (1), (2), (3), (4), (6), (7), (9), (10), (11), (13), (17) are
% 232.15/43.24  |            inconsistent by sub-proof #2436.
% 232.15/43.24  | 
% 232.15/43.24  End of proof
% 232.15/43.24  
% 232.15/43.24  Sub-proof #2096 shows that the following formulas are inconsistent:
% 232.15/43.24  ----------------------------------------------------------------
% 232.15/43.24    (1)   ~ (e3 = e1)
% 232.15/43.24    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.24           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.24    (3)  all_57_1 = e2
% 232.15/43.24    (4)  op(e3, e3) = e3
% 232.15/43.24    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1)
% 232.15/43.24    (6)   ~ (e2 = e1)
% 232.15/43.24  
% 232.15/43.24  Begin of proof
% 232.15/43.24  | 
% 232.15/43.24  | BETA: splitting (5) gives:
% 232.15/43.24  | 
% 232.15/43.24  | Case 1:
% 232.15/43.24  | | 
% 232.15/43.24  | |   (7)  all_57_0 = e1 & op(e3, e3) = e1
% 232.15/43.24  | | 
% 232.15/43.24  | | ALPHA: (7) implies:
% 232.15/43.24  | |   (8)  op(e3, e3) = e1
% 232.15/43.24  | | 
% 232.15/43.24  | | REF_CLOSE: (1), (2), (4), (8) are inconsistent by sub-proof #2495.
% 232.15/43.24  | | 
% 232.15/43.24  | Case 2:
% 232.15/43.24  | | 
% 232.15/43.24  | |   (9)  all_57_1 = e1 & op(e3, e2) = e1
% 232.15/43.24  | | 
% 232.15/43.24  | | REF_CLOSE: (3), (6), (9) are inconsistent by sub-proof #2210.
% 232.15/43.24  | | 
% 232.15/43.24  | End of split
% 232.15/43.24  | 
% 232.15/43.24  End of proof
% 232.15/43.24  
% 232.15/43.24  Sub-proof #2097 shows that the following formulas are inconsistent:
% 232.15/43.24  ----------------------------------------------------------------
% 232.15/43.24    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 232.15/43.24         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 232.15/43.24    (2)   ~ (e3 = e1)
% 232.15/43.24    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.24           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.24    (4)  all_57_3 = e0
% 232.15/43.24    (5)   ~ (e3 = e2)
% 232.15/43.24    (6)   ~ (e3 = e0)
% 232.15/43.24    (7)  op(e3, e3) = e3
% 232.15/43.24    (8)   ~ (e2 = e0)
% 232.15/43.24    (9)   ~ (e1 = e0)
% 232.15/43.24    (10)  all_57_7 = e3
% 232.15/43.24    (11)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0)
% 232.15/43.24    (12)   ~ (e2 = e1)
% 232.15/43.24    (13)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 232.15/43.24          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 232.15/43.24  
% 232.15/43.24  Begin of proof
% 232.15/43.24  | 
% 232.15/43.24  | BETA: splitting (11) gives:
% 232.15/43.24  | 
% 232.15/43.24  | Case 1:
% 232.15/43.24  | | 
% 232.15/43.24  | |   (14)  all_57_0 = e0 & op(e3, e3) = e0
% 232.15/43.24  | | 
% 232.15/43.24  | | ALPHA: (14) implies:
% 232.15/43.24  | |   (15)  op(e3, e3) = e0
% 232.15/43.24  | | 
% 232.15/43.24  | | REF_CLOSE: (3), (6), (7), (15) are inconsistent by sub-proof #2494.
% 232.15/43.24  | | 
% 232.15/43.24  | Case 2:
% 232.15/43.24  | | 
% 232.15/43.24  | |   (16)  all_57_1 = e0 & op(e3, e2) = e0
% 232.15/43.24  | | 
% 232.15/43.24  | | ALPHA: (16) implies:
% 232.15/43.24  | |   (17)  all_57_1 = e0
% 232.15/43.24  | | 
% 232.15/43.24  | | REF_CLOSE: (1), (2), (4), (5), (8), (9), (10), (12), (13), (17) are
% 232.15/43.24  | |            inconsistent by sub-proof #2098.
% 232.15/43.24  | | 
% 232.15/43.24  | End of split
% 232.15/43.24  | 
% 232.15/43.24  End of proof
% 232.15/43.24  
% 232.15/43.24  Sub-proof #2098 shows that the following formulas are inconsistent:
% 232.15/43.24  ----------------------------------------------------------------
% 232.15/43.24    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 232.15/43.24         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 232.15/43.24    (2)   ~ (e3 = e1)
% 232.15/43.24    (3)  all_57_3 = e0
% 232.15/43.24    (4)   ~ (e3 = e2)
% 232.15/43.24    (5)  all_57_1 = e0
% 232.15/43.24    (6)   ~ (e2 = e0)
% 232.15/43.24    (7)   ~ (e1 = e0)
% 232.15/43.24    (8)  all_57_7 = e3
% 232.15/43.24    (9)   ~ (e2 = e1)
% 232.15/43.24    (10)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 232.15/43.24          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 232.15/43.24  
% 232.15/43.24  Begin of proof
% 232.15/43.24  | 
% 232.15/43.24  | BETA: splitting (10) gives:
% 232.15/43.24  | 
% 232.15/43.24  | Case 1:
% 232.15/43.24  | | 
% 232.15/43.24  | |   (11)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) =
% 232.15/43.24  | |           e1)
% 232.15/43.24  | | 
% 232.15/43.24  | | BETA: splitting (11) gives:
% 232.15/43.24  | | 
% 232.15/43.24  | | Case 1:
% 232.15/43.24  | | | 
% 232.15/43.24  | | |   (12)  all_57_1 = e1 & op(e3, e2) = e1
% 232.15/43.24  | | | 
% 232.15/43.24  | | | REF_CLOSE: (5), (7), (12) are inconsistent by sub-proof #2446.
% 232.15/43.24  | | | 
% 232.15/43.24  | | Case 2:
% 232.15/43.24  | | | 
% 232.15/43.24  | | |   (13)  all_57_3 = e1 & op(e2, e2) = e1
% 232.15/43.24  | | | 
% 232.15/43.24  | | | REF_CLOSE: (3), (7), (13) are inconsistent by sub-proof #2362.
% 232.15/43.24  | | | 
% 232.15/43.24  | | End of split
% 232.15/43.24  | | 
% 232.15/43.24  | Case 2:
% 232.15/43.24  | | 
% 232.15/43.24  | |   (14)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 232.15/43.24  | |           e1)
% 232.15/43.24  | | 
% 232.15/43.24  | | BETA: splitting (14) gives:
% 232.15/43.24  | | 
% 232.15/43.24  | | Case 1:
% 232.15/43.24  | | | 
% 232.15/43.24  | | |   (15)  all_57_7 = e1 & op(e1, e2) = e1
% 232.15/43.24  | | | 
% 232.15/43.24  | | | REF_CLOSE: (2), (8), (15) are inconsistent by sub-proof #2104.
% 232.15/43.24  | | | 
% 232.15/43.24  | | Case 2:
% 232.15/43.24  | | | 
% 232.15/43.24  | | |   (16)  all_57_13 = e1 & op(e0, e2) = e1
% 232.15/43.24  | | | 
% 232.15/43.24  | | | ALPHA: (16) implies:
% 232.15/43.24  | | |   (17)  all_57_13 = e1
% 232.15/43.24  | | | 
% 232.15/43.24  | | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (17) are inconsistent by
% 232.15/43.24  | | |            sub-proof #2099.
% 232.15/43.24  | | | 
% 232.15/43.24  | | End of split
% 232.15/43.24  | | 
% 232.15/43.24  | End of split
% 232.15/43.24  | 
% 232.15/43.24  End of proof
% 232.15/43.24  
% 232.15/43.24  Sub-proof #2099 shows that the following formulas are inconsistent:
% 232.15/43.24  ----------------------------------------------------------------
% 232.15/43.24    (1)  all_57_13 = e1
% 232.15/43.24    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 232.15/43.24         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 232.15/43.24    (3)  all_57_3 = e0
% 232.15/43.24    (4)   ~ (e3 = e2)
% 232.15/43.24    (5)  all_57_1 = e0
% 232.15/43.24    (6)   ~ (e2 = e0)
% 232.15/43.24    (7)  all_57_7 = e3
% 232.15/43.24    (8)   ~ (e2 = e1)
% 232.15/43.24  
% 232.15/43.24  Begin of proof
% 232.15/43.24  | 
% 232.15/43.24  | BETA: splitting (2) gives:
% 232.15/43.24  | 
% 232.15/43.24  | Case 1:
% 232.15/43.24  | | 
% 232.15/43.24  | |   (9)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2)
% 232.15/43.24  | | 
% 232.15/43.24  | | BETA: splitting (9) gives:
% 232.15/43.24  | | 
% 232.15/43.24  | | Case 1:
% 232.15/43.24  | | | 
% 232.15/43.24  | | |   (10)  all_57_1 = e2 & op(e3, e2) = e2
% 232.15/43.24  | | | 
% 232.15/43.24  | | | REF_CLOSE: (5), (6), (10) are inconsistent by sub-proof #2483.
% 232.15/43.24  | | | 
% 232.15/43.24  | | Case 2:
% 232.15/43.24  | | | 
% 232.15/43.24  | | |   (11)  all_57_3 = e2 & op(e2, e2) = e2
% 232.15/43.24  | | | 
% 232.15/43.24  | | | REF_CLOSE: (3), (6), (11) are inconsistent by sub-proof #2103.
% 232.15/43.24  | | | 
% 232.15/43.24  | | End of split
% 232.15/43.24  | | 
% 232.15/43.24  | Case 2:
% 232.15/43.24  | | 
% 232.15/43.24  | |   (12)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 232.15/43.24  | |           e2)
% 232.15/43.24  | | 
% 232.15/43.24  | | REF_CLOSE: (1), (4), (7), (8), (12) are inconsistent by sub-proof #2100.
% 232.15/43.24  | | 
% 232.15/43.24  | End of split
% 232.15/43.24  | 
% 232.15/43.24  End of proof
% 232.15/43.24  
% 232.15/43.24  Sub-proof #2100 shows that the following formulas are inconsistent:
% 232.15/43.24  ----------------------------------------------------------------
% 232.15/43.24    (1)  all_57_13 = e1
% 232.15/43.24    (2)   ~ (e3 = e2)
% 232.15/43.24    (3)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 232.15/43.24    (4)  all_57_7 = e3
% 232.15/43.24    (5)   ~ (e2 = e1)
% 232.15/43.24  
% 232.15/43.24  Begin of proof
% 232.15/43.24  | 
% 232.15/43.24  | BETA: splitting (3) gives:
% 232.15/43.24  | 
% 232.15/43.24  | Case 1:
% 232.15/43.24  | | 
% 232.15/43.24  | |   (6)  all_57_7 = e2 & op(e1, e2) = e2
% 232.15/43.24  | | 
% 232.15/43.24  | | ALPHA: (6) implies:
% 232.15/43.24  | |   (7)  all_57_7 = e2
% 232.15/43.24  | | 
% 232.15/43.24  | | REF_CLOSE: (2), (4), (7) are inconsistent by sub-proof #2102.
% 232.15/43.24  | | 
% 232.15/43.24  | Case 2:
% 232.15/43.24  | | 
% 232.15/43.24  | |   (8)  all_57_13 = e2 & op(e0, e2) = e2
% 232.15/43.24  | | 
% 232.15/43.24  | | REF_CLOSE: (1), (5), (8) are inconsistent by sub-proof #2101.
% 232.15/43.24  | | 
% 232.15/43.24  | End of split
% 232.15/43.24  | 
% 232.15/43.24  End of proof
% 232.15/43.24  
% 232.15/43.24  Sub-proof #2101 shows that the following formulas are inconsistent:
% 232.15/43.24  ----------------------------------------------------------------
% 232.15/43.24    (1)  all_57_13 = e2 & op(e0, e2) = e2
% 232.15/43.24    (2)  all_57_13 = e1
% 232.15/43.24    (3)   ~ (e2 = e1)
% 232.15/43.24  
% 232.15/43.24  Begin of proof
% 232.15/43.24  | 
% 232.15/43.24  | ALPHA: (1) implies:
% 232.15/43.24  |   (4)  all_57_13 = e2
% 232.15/43.24  | 
% 232.15/43.24  | COMBINE_EQS: (2), (4) imply:
% 232.15/43.24  |   (5)  e2 = e1
% 232.15/43.24  | 
% 232.15/43.24  | REDUCE: (3), (5) imply:
% 232.15/43.24  |   (6)  $false
% 232.15/43.24  | 
% 232.15/43.24  | CLOSE: (6) is inconsistent.
% 232.15/43.24  | 
% 232.15/43.24  End of proof
% 232.15/43.24  
% 232.15/43.24  Sub-proof #2102 shows that the following formulas are inconsistent:
% 232.15/43.24  ----------------------------------------------------------------
% 232.15/43.24    (1)  all_57_7 = e3
% 232.15/43.24    (2)  all_57_7 = e2
% 232.15/43.24    (3)   ~ (e3 = e2)
% 232.15/43.24  
% 232.15/43.24  Begin of proof
% 232.15/43.24  | 
% 232.15/43.24  | COMBINE_EQS: (1), (2) imply:
% 232.15/43.24  |   (4)  e3 = e2
% 232.15/43.24  | 
% 232.15/43.24  | SIMP: (4) implies:
% 232.15/43.24  |   (5)  e3 = e2
% 232.15/43.24  | 
% 232.15/43.24  | REDUCE: (3), (5) imply:
% 232.15/43.24  |   (6)  $false
% 232.15/43.24  | 
% 232.15/43.24  | CLOSE: (6) is inconsistent.
% 232.15/43.24  | 
% 232.15/43.24  End of proof
% 232.15/43.24  
% 232.15/43.24  Sub-proof #2103 shows that the following formulas are inconsistent:
% 232.15/43.24  ----------------------------------------------------------------
% 232.15/43.24    (1)  all_57_3 = e2 & op(e2, e2) = e2
% 232.15/43.24    (2)  all_57_3 = e0
% 232.15/43.24    (3)   ~ (e2 = e0)
% 232.15/43.24  
% 232.15/43.24  Begin of proof
% 232.15/43.24  | 
% 232.15/43.24  | ALPHA: (1) implies:
% 232.15/43.24  |   (4)  all_57_3 = e2
% 232.15/43.24  | 
% 232.15/43.24  | COMBINE_EQS: (2), (4) imply:
% 232.15/43.24  |   (5)  e2 = e0
% 232.15/43.24  | 
% 232.15/43.24  | SIMP: (5) implies:
% 232.15/43.24  |   (6)  e2 = e0
% 232.15/43.24  | 
% 232.15/43.24  | REDUCE: (3), (6) imply:
% 232.15/43.24  |   (7)  $false
% 232.15/43.24  | 
% 232.15/43.24  | CLOSE: (7) is inconsistent.
% 232.15/43.24  | 
% 232.15/43.24  End of proof
% 232.15/43.24  
% 232.15/43.24  Sub-proof #2104 shows that the following formulas are inconsistent:
% 232.15/43.24  ----------------------------------------------------------------
% 232.15/43.24    (1)  all_57_7 = e1 & op(e1, e2) = e1
% 232.15/43.24    (2)  all_57_7 = e3
% 232.15/43.24    (3)   ~ (e3 = e1)
% 232.15/43.24  
% 232.15/43.24  Begin of proof
% 232.15/43.24  | 
% 232.15/43.24  | ALPHA: (1) implies:
% 232.15/43.24  |   (4)  all_57_7 = e1
% 232.15/43.24  | 
% 232.15/43.24  | COMBINE_EQS: (2), (4) imply:
% 232.15/43.24  |   (5)  e3 = e1
% 232.15/43.24  | 
% 232.15/43.24  | REDUCE: (3), (5) imply:
% 232.15/43.24  |   (6)  $false
% 232.15/43.24  | 
% 232.15/43.24  | CLOSE: (6) is inconsistent.
% 232.15/43.24  | 
% 232.15/43.24  End of proof
% 232.15/43.24  
% 232.15/43.24  Sub-proof #2105 shows that the following formulas are inconsistent:
% 232.15/43.24  ----------------------------------------------------------------
% 232.15/43.24    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.24           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.24    (2)   ~ (all_52_23 = e0)
% 232.15/43.24    (3)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 232.15/43.24    (4)  op(e3, e3) = e3
% 232.15/43.24    (5)  all_55_11 = all_52_23
% 232.15/43.24    (6)  op(all_52_23, all_52_23) = e0
% 232.15/43.24    (7)   ~ (all_52_23 = e1)
% 232.15/43.24    (8)   ~ (all_52_23 = e2)
% 232.15/43.24  
% 232.15/43.24  Begin of proof
% 232.15/43.24  | 
% 232.15/43.24  | BETA: splitting (3) gives:
% 232.15/43.24  | 
% 232.15/43.24  | Case 1:
% 232.15/43.24  | | 
% 232.15/43.24  | |   (9)  all_55_11 = e3
% 232.15/43.24  | | 
% 232.15/43.24  | | REF_CLOSE: (1), (2), (4), (5), (6), (9) are inconsistent by sub-proof #2108.
% 232.15/43.24  | | 
% 232.15/43.24  | Case 2:
% 232.15/43.24  | | 
% 232.15/43.24  | |   (10)  all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 232.15/43.24  | | 
% 232.15/43.24  | | REF_CLOSE: (2), (5), (7), (8), (10) are inconsistent by sub-proof #2106.
% 232.15/43.24  | | 
% 232.15/43.24  | End of split
% 232.15/43.24  | 
% 232.15/43.24  End of proof
% 232.15/43.24  
% 232.15/43.24  Sub-proof #2106 shows that the following formulas are inconsistent:
% 232.15/43.24  ----------------------------------------------------------------
% 232.15/43.24    (1)  all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 232.15/43.24    (2)   ~ (all_52_23 = e0)
% 232.15/43.24    (3)  all_55_11 = all_52_23
% 232.15/43.24    (4)   ~ (all_52_23 = e1)
% 232.15/43.24    (5)   ~ (all_52_23 = e2)
% 232.15/43.24  
% 232.15/43.24  Begin of proof
% 232.15/43.24  | 
% 232.15/43.24  | BETA: splitting (1) gives:
% 232.15/43.24  | 
% 232.15/43.24  | Case 1:
% 232.15/43.24  | | 
% 232.15/43.24  | |   (6)  all_55_11 = e2
% 232.15/43.24  | | 
% 232.15/43.24  | | COMBINE_EQS: (3), (6) imply:
% 232.15/43.24  | |   (7)  all_52_23 = e2
% 232.15/43.24  | | 
% 232.15/43.24  | | SIMP: (7) implies:
% 232.15/43.24  | |   (8)  all_52_23 = e2
% 232.15/43.24  | | 
% 232.15/43.24  | | REDUCE: (5), (8) imply:
% 232.15/43.24  | |   (9)  $false
% 232.15/43.24  | | 
% 232.15/43.24  | | CLOSE: (9) is inconsistent.
% 232.15/43.24  | | 
% 232.15/43.24  | Case 2:
% 232.15/43.24  | | 
% 232.15/43.24  | |   (10)  all_55_11 = e1 | all_55_11 = e0
% 232.15/43.24  | | 
% 232.15/43.24  | | REF_CLOSE: (2), (3), (4), (10) are inconsistent by sub-proof #2107.
% 232.15/43.24  | | 
% 232.15/43.24  | End of split
% 232.15/43.24  | 
% 232.15/43.24  End of proof
% 232.15/43.24  
% 232.15/43.24  Sub-proof #2107 shows that the following formulas are inconsistent:
% 232.15/43.24  ----------------------------------------------------------------
% 232.15/43.24    (1)  all_55_11 = e1 | all_55_11 = e0
% 232.15/43.24    (2)  all_55_11 = all_52_23
% 232.15/43.24    (3)   ~ (all_52_23 = e1)
% 232.15/43.24    (4)   ~ (all_52_23 = e0)
% 232.15/43.24  
% 232.15/43.24  Begin of proof
% 232.15/43.24  | 
% 232.15/43.24  | BETA: splitting (1) gives:
% 232.15/43.24  | 
% 232.15/43.24  | Case 1:
% 232.15/43.24  | | 
% 232.15/43.24  | |   (5)  all_55_11 = e1
% 232.15/43.24  | | 
% 232.15/43.24  | | COMBINE_EQS: (2), (5) imply:
% 232.15/43.24  | |   (6)  all_52_23 = e1
% 232.15/43.24  | | 
% 232.15/43.24  | | SIMP: (6) implies:
% 232.15/43.24  | |   (7)  all_52_23 = e1
% 232.15/43.24  | | 
% 232.15/43.24  | | REDUCE: (3), (7) imply:
% 232.15/43.24  | |   (8)  $false
% 232.15/43.24  | | 
% 232.15/43.24  | | CLOSE: (8) is inconsistent.
% 232.15/43.24  | | 
% 232.15/43.24  | Case 2:
% 232.15/43.24  | | 
% 232.15/43.24  | |   (9)  all_55_11 = e0
% 232.15/43.24  | | 
% 232.15/43.24  | | COMBINE_EQS: (2), (9) imply:
% 232.15/43.24  | |   (10)  all_52_23 = e0
% 232.15/43.24  | | 
% 232.15/43.24  | | SIMP: (10) implies:
% 232.15/43.24  | |   (11)  all_52_23 = e0
% 232.15/43.24  | | 
% 232.15/43.24  | | REDUCE: (4), (11) imply:
% 232.15/43.24  | |   (12)  $false
% 232.15/43.24  | | 
% 232.15/43.24  | | CLOSE: (12) is inconsistent.
% 232.15/43.24  | | 
% 232.15/43.24  | End of split
% 232.15/43.24  | 
% 232.15/43.25  End of proof
% 232.15/43.25  
% 232.15/43.25  Sub-proof #2108 shows that the following formulas are inconsistent:
% 232.15/43.25  ----------------------------------------------------------------
% 232.15/43.25    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.25           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.25    (2)   ~ (all_52_23 = e0)
% 232.15/43.25    (3)  all_55_11 = e3
% 232.15/43.25    (4)  op(e3, e3) = e3
% 232.15/43.25    (5)  all_55_11 = all_52_23
% 232.15/43.25    (6)  op(all_52_23, all_52_23) = e0
% 232.15/43.25  
% 232.15/43.25  Begin of proof
% 232.15/43.25  | 
% 232.15/43.25  | COMBINE_EQS: (3), (5) imply:
% 232.15/43.25  |   (7)  all_52_23 = e3
% 232.15/43.25  | 
% 232.15/43.25  | SIMP: (7) implies:
% 232.15/43.25  |   (8)  all_52_23 = e3
% 232.15/43.25  | 
% 232.15/43.25  | REDUCE: (2), (8) imply:
% 232.15/43.25  |   (9)   ~ (e3 = e0)
% 232.15/43.25  | 
% 232.15/43.25  | REDUCE: (6), (8) imply:
% 232.15/43.25  |   (10)  op(e3, e3) = e0
% 232.15/43.25  | 
% 232.15/43.25  | REF_CLOSE: (1), (4), (9), (10) are inconsistent by sub-proof #2494.
% 232.15/43.25  | 
% 232.15/43.25  End of proof
% 232.15/43.25  
% 232.15/43.25  Sub-proof #2109 shows that the following formulas are inconsistent:
% 232.15/43.25  ----------------------------------------------------------------
% 232.15/43.25    (1)  all_55_7 = all_53_13
% 232.15/43.25    (2)  all_55_7 = e3
% 232.15/43.25    (3)   ~ (all_53_13 = e3)
% 232.15/43.25  
% 232.15/43.25  Begin of proof
% 232.15/43.25  | 
% 232.15/43.25  | COMBINE_EQS: (1), (2) imply:
% 232.15/43.25  |   (4)  all_53_13 = e3
% 232.15/43.25  | 
% 232.15/43.25  | SIMP: (4) implies:
% 232.15/43.25  |   (5)  all_53_13 = e3
% 232.15/43.25  | 
% 232.15/43.25  | REDUCE: (3), (5) imply:
% 232.15/43.25  |   (6)  $false
% 232.15/43.25  | 
% 232.15/43.25  | CLOSE: (6) is inconsistent.
% 232.15/43.25  | 
% 232.15/43.25  End of proof
% 232.15/43.25  
% 232.15/43.25  Sub-proof #2110 shows that the following formulas are inconsistent:
% 232.15/43.25  ----------------------------------------------------------------
% 232.15/43.25    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.25           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.25    (2)   ~ (all_6_2 = e3)
% 232.15/43.25    (3)  op(e1, e1) = all_6_2
% 232.15/43.25    (4)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0 &
% 232.15/43.25         op(all_52_9, all_52_9) = e3 & op(all_52_11, all_52_11) = e2 &
% 232.15/43.25         op(all_52_13, all_52_13) = e1 & op(all_52_15, all_52_15) = e0 & op(e2,
% 232.15/43.25           e3) = all_52_9 & op(e2, e2) = all_52_11 & op(e2, e1) = all_52_13 &
% 232.15/43.25         op(e2, e0) = all_52_15 & $i(all_52_9) & $i(all_52_11) & $i(all_52_13) &
% 232.15/43.25         $i(all_52_15)
% 232.15/43.25    (5)  op(e2, e3) = e1
% 232.15/43.25  
% 232.15/43.25  Begin of proof
% 232.15/43.25  | 
% 232.15/43.25  | ALPHA: (4) implies:
% 232.15/43.25  |   (6)  op(e2, e3) = all_52_9
% 232.15/43.25  |   (7)  op(all_52_9, all_52_9) = e3
% 232.15/43.25  | 
% 232.15/43.25  | GROUND_INST: instantiating (1) with e1, all_52_9, e3, e2, simplifying with
% 232.15/43.25  |              (5), (6) gives:
% 232.15/43.25  |   (8)  all_52_9 = e1
% 232.15/43.25  | 
% 232.15/43.25  | REDUCE: (7), (8) imply:
% 232.15/43.25  |   (9)  op(e1, e1) = e3
% 232.15/43.25  | 
% 232.15/43.25  | REF_CLOSE: (1), (2), (3), (9) are inconsistent by sub-proof #2468.
% 232.15/43.25  | 
% 232.15/43.25  End of proof
% 232.15/43.25  
% 232.15/43.25  Sub-proof #2111 shows that the following formulas are inconsistent:
% 232.15/43.25  ----------------------------------------------------------------
% 232.15/43.25    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.25           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.25    (2)  op(e3, e2) = e1
% 232.15/43.25    (3)  op(e1, e1) = e1
% 232.15/43.25    (4)   ~ (e2 = e1)
% 232.15/43.25    (5)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 232.15/43.25         op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 232.15/43.25           all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3) = all_52_1 &
% 232.15/43.25         op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 232.15/43.25         $i(all_52_1) & $i(all_52_3) & $i(all_52_5) & $i(all_52_7)
% 232.15/43.25  
% 232.15/43.25  Begin of proof
% 232.15/43.25  | 
% 232.15/43.25  | ALPHA: (5) implies:
% 232.15/43.25  |   (6)  op(e3, e2) = all_52_3
% 232.15/43.25  |   (7)  op(all_52_3, all_52_3) = e2
% 232.15/43.25  | 
% 232.15/43.25  | GROUND_INST: instantiating (1) with e1, all_52_3, e2, e3, simplifying with
% 232.15/43.25  |              (2), (6) gives:
% 232.15/43.25  |   (8)  all_52_3 = e1
% 232.15/43.25  | 
% 232.15/43.25  | REDUCE: (7), (8) imply:
% 232.15/43.25  |   (9)  op(e1, e1) = e2
% 232.15/43.25  | 
% 232.15/43.25  | REF_CLOSE: (1), (3), (4), (9) are inconsistent by sub-proof #2423.
% 232.15/43.25  | 
% 232.15/43.25  End of proof
% 232.15/43.25  
% 232.15/43.25  Sub-proof #2112 shows that the following formulas are inconsistent:
% 232.15/43.25  ----------------------------------------------------------------
% 232.15/43.25    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.25           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.25    (2)  op(e1, e0) = all_53_14
% 232.15/43.25    (3)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) |
% 232.15/43.25           (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0, e3) =
% 232.15/43.25             e0) | (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 232.15/43.25               e1) = e0))
% 232.15/43.25    (4)   ~ (all_53_14 = e0)
% 232.15/43.25    (5)   ~ (all_53_13 = e0)
% 232.15/43.25    (6)  op(e2, e0) = all_53_13
% 232.15/43.25    (7)   ~ (all_53_12 = e0)
% 232.15/43.25    (8)  op(e3, e0) = all_53_12
% 232.15/43.25  
% 232.15/43.25  Begin of proof
% 232.15/43.25  | 
% 232.15/43.25  | ALPHA: (3) implies:
% 232.15/43.25  |   (9)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 232.15/43.25  |        | (all_57_11 = e0 & op(e1, e0) = e0)
% 232.15/43.25  | 
% 232.15/43.25  | BETA: splitting (9) gives:
% 232.15/43.25  | 
% 232.15/43.25  | Case 1:
% 232.15/43.25  | | 
% 232.15/43.25  | |   (10)  all_57_9 = e0 & op(e3, e0) = e0
% 232.15/43.25  | | 
% 232.15/43.25  | | REF_CLOSE: (1), (7), (8), (10) are inconsistent by sub-proof #2434.
% 232.15/43.25  | | 
% 232.15/43.25  | Case 2:
% 232.15/43.25  | | 
% 232.15/43.25  | |   (11)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 232.15/43.25  | |           e0)
% 232.15/43.25  | | 
% 232.15/43.25  | | BETA: splitting (11) gives:
% 232.15/43.25  | | 
% 232.15/43.25  | | Case 1:
% 232.15/43.25  | | | 
% 232.15/43.25  | | |   (12)  all_57_10 = e0 & op(e2, e0) = e0
% 232.15/43.25  | | | 
% 232.15/43.25  | | | ALPHA: (12) implies:
% 232.15/43.25  | | |   (13)  op(e2, e0) = e0
% 232.15/43.25  | | | 
% 232.15/43.25  | | | REF_CLOSE: (1), (5), (6), (13) are inconsistent by sub-proof #2470.
% 232.15/43.25  | | | 
% 232.15/43.25  | | Case 2:
% 232.15/43.25  | | | 
% 232.15/43.25  | | |   (14)  all_57_11 = e0 & op(e1, e0) = e0
% 232.15/43.25  | | | 
% 232.15/43.25  | | | REF_CLOSE: (1), (2), (4), (14) are inconsistent by sub-proof #2341.
% 232.15/43.25  | | | 
% 232.15/43.25  | | End of split
% 232.15/43.25  | | 
% 232.15/43.25  | End of split
% 232.15/43.25  | 
% 232.15/43.25  End of proof
% 232.15/43.25  
% 232.15/43.25  Sub-proof #2113 shows that the following formulas are inconsistent:
% 232.15/43.25  ----------------------------------------------------------------
% 232.15/43.25    (1)  all_57_11 = e2
% 232.15/43.25    (2)  all_57_11 = e1
% 232.15/43.25    (3)   ~ (e2 = e1)
% 232.15/43.25  
% 232.15/43.25  Begin of proof
% 232.15/43.25  | 
% 232.15/43.25  | COMBINE_EQS: (1), (2) imply:
% 232.15/43.25  |   (4)  e2 = e1
% 232.15/43.25  | 
% 232.15/43.25  | SIMP: (4) implies:
% 232.15/43.25  |   (5)  e2 = e1
% 232.15/43.25  | 
% 232.15/43.25  | REDUCE: (3), (5) imply:
% 232.15/43.25  |   (6)  $false
% 232.15/43.25  | 
% 232.15/43.25  | CLOSE: (6) is inconsistent.
% 232.15/43.25  | 
% 232.15/43.25  End of proof
% 232.15/43.25  
% 232.15/43.25  Sub-proof #2114 shows that the following formulas are inconsistent:
% 232.15/43.25  ----------------------------------------------------------------
% 232.15/43.25    (1)   ~ (e3 = e1)
% 232.15/43.25    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.25           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.25    (3)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 232.15/43.25         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 232.15/43.25    (4)   ~ (all_6_2 = e3)
% 232.15/43.25    (5)  op(e1, e1) = all_6_2
% 232.15/43.25    (6)  all_57_7 = e1
% 232.15/43.25    (7)   ~ (e3 = e2)
% 232.15/43.25    (8)   ~ (e3 = e0)
% 232.15/43.25    (9)  all_57_6 = e0
% 232.15/43.25    (10)  all_57_11 = e2
% 232.15/43.25  
% 232.15/43.25  Begin of proof
% 232.15/43.25  | 
% 232.15/43.25  | BETA: splitting (3) gives:
% 232.15/43.25  | 
% 232.15/43.25  | Case 1:
% 232.15/43.25  | | 
% 232.15/43.25  | |   (11)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 232.15/43.25  | |           e3)
% 232.15/43.25  | | 
% 232.15/43.25  | | BETA: splitting (11) gives:
% 232.15/43.25  | | 
% 232.15/43.25  | | Case 1:
% 232.15/43.25  | | | 
% 232.15/43.25  | | |   (12)  all_57_6 = e3 & op(e1, e3) = e3
% 232.15/43.25  | | | 
% 232.15/43.25  | | | REF_CLOSE: (8), (9), (12) are inconsistent by sub-proof #2395.
% 232.15/43.25  | | | 
% 232.15/43.25  | | Case 2:
% 232.15/43.25  | | | 
% 232.15/43.25  | | |   (13)  all_57_7 = e3 & op(e1, e2) = e3
% 232.15/43.25  | | | 
% 232.15/43.25  | | | ALPHA: (13) implies:
% 232.15/43.25  | | |   (14)  all_57_7 = e3
% 232.15/43.25  | | | 
% 232.15/43.25  | | | REF_CLOSE: (1), (6), (14) are inconsistent by sub-proof #2115.
% 232.15/43.25  | | | 
% 232.15/43.25  | | End of split
% 232.15/43.25  | | 
% 232.15/43.25  | Case 2:
% 232.15/43.25  | | 
% 232.15/43.25  | |   (15)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 232.15/43.25  | |           e3)
% 232.15/43.25  | | 
% 232.15/43.25  | | REF_CLOSE: (2), (4), (5), (7), (10), (15) are inconsistent by sub-proof
% 232.15/43.25  | |            #2344.
% 232.15/43.25  | | 
% 232.15/43.25  | End of split
% 232.15/43.25  | 
% 232.15/43.25  End of proof
% 232.15/43.25  
% 232.15/43.25  Sub-proof #2115 shows that the following formulas are inconsistent:
% 232.15/43.25  ----------------------------------------------------------------
% 232.15/43.25    (1)  all_57_7 = e3
% 232.15/43.25    (2)  all_57_7 = e1
% 232.15/43.25    (3)   ~ (e3 = e1)
% 232.15/43.25  
% 232.15/43.25  Begin of proof
% 232.15/43.25  | 
% 232.15/43.25  | COMBINE_EQS: (1), (2) imply:
% 232.15/43.25  |   (4)  e3 = e1
% 232.15/43.25  | 
% 232.15/43.25  | SIMP: (4) implies:
% 232.15/43.25  |   (5)  e3 = e1
% 232.15/43.25  | 
% 232.15/43.25  | REDUCE: (3), (5) imply:
% 232.15/43.25  |   (6)  $false
% 232.15/43.25  | 
% 232.15/43.25  | CLOSE: (6) is inconsistent.
% 232.15/43.25  | 
% 232.15/43.25  End of proof
% 232.15/43.25  
% 232.15/43.25  Sub-proof #2116 shows that the following formulas are inconsistent:
% 232.15/43.25  ----------------------------------------------------------------
% 232.15/43.25    (1)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 232.15/43.25         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 232.15/43.25    (2)   ~ (e3 = e1)
% 232.15/43.25    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.25           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.25    (4)  all_57_12 = e2
% 232.15/43.25    (5)   ~ (e3 = e2)
% 232.15/43.25    (6)   ~ (e3 = e0)
% 232.15/43.25    (7)  op(e3, e3) = e3
% 232.15/43.25    (8)   ~ (e2 = e0)
% 232.15/43.25    (9)   ~ (e1 = e0)
% 232.15/43.25    (10)  all_57_6 = e3
% 232.15/43.25    (11)   ~ (e2 = e1)
% 232.15/43.25    (12)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 232.15/43.25          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 232.15/43.25    (13)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 232.15/43.25          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 232.15/43.25  
% 232.15/43.25  Begin of proof
% 232.15/43.25  | 
% 232.15/43.25  | BETA: splitting (1) gives:
% 232.15/43.25  | 
% 232.15/43.25  | Case 1:
% 232.15/43.25  | | 
% 232.15/43.25  | |   (14)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) =
% 232.15/43.25  | |           e1)
% 232.15/43.25  | | 
% 232.15/43.25  | | BETA: splitting (14) gives:
% 232.15/43.25  | | 
% 232.15/43.25  | | Case 1:
% 232.15/43.25  | | | 
% 232.15/43.25  | | |   (15)  all_57_0 = e1 & op(e3, e3) = e1
% 232.15/43.25  | | | 
% 232.15/43.25  | | | ALPHA: (15) implies:
% 232.15/43.25  | | |   (16)  op(e3, e3) = e1
% 232.15/43.25  | | | 
% 232.15/43.25  | | | REF_CLOSE: (2), (3), (7), (16) are inconsistent by sub-proof #2495.
% 232.15/43.25  | | | 
% 232.15/43.25  | | Case 2:
% 232.15/43.25  | | | 
% 232.15/43.25  | | |   (17)  all_57_2 = e1 & op(e2, e3) = e1
% 232.15/43.25  | | | 
% 232.15/43.25  | | | ALPHA: (17) implies:
% 232.15/43.25  | | |   (18)  all_57_2 = e1
% 232.15/43.25  | | | 
% 232.15/43.25  | | | REF_CLOSE: (3), (5), (6), (7), (8), (9), (10), (11), (12), (13), (18) are
% 232.15/43.25  | | |            inconsistent by sub-proof #2459.
% 232.15/43.25  | | | 
% 232.15/43.25  | | End of split
% 232.15/43.25  | | 
% 232.15/43.25  | Case 2:
% 232.15/43.25  | | 
% 232.15/43.25  | |   (19)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) =
% 232.15/43.25  | |           e1)
% 232.15/43.25  | | 
% 232.15/43.25  | | BETA: splitting (19) gives:
% 232.15/43.25  | | 
% 232.15/43.25  | | Case 1:
% 232.15/43.25  | | | 
% 232.15/43.25  | | |   (20)  all_57_6 = e1 & op(e1, e3) = e1
% 232.15/43.25  | | | 
% 232.15/43.25  | | | REF_CLOSE: (2), (10), (20) are inconsistent by sub-proof #2117.
% 232.15/43.25  | | | 
% 232.15/43.25  | | Case 2:
% 232.15/43.25  | | | 
% 232.15/43.25  | | |   (21)  all_57_12 = e1 & op(e0, e3) = e1
% 232.15/43.25  | | | 
% 232.15/43.25  | | | REF_CLOSE: (4), (11), (21) are inconsistent by sub-proof #2388.
% 232.15/43.25  | | | 
% 232.15/43.25  | | End of split
% 232.15/43.25  | | 
% 232.15/43.25  | End of split
% 232.15/43.25  | 
% 232.15/43.25  End of proof
% 232.15/43.25  
% 232.15/43.25  Sub-proof #2117 shows that the following formulas are inconsistent:
% 232.15/43.25  ----------------------------------------------------------------
% 232.15/43.25    (1)  all_57_6 = e1 & op(e1, e3) = e1
% 232.15/43.25    (2)  all_57_6 = e3
% 232.15/43.25    (3)   ~ (e3 = e1)
% 232.15/43.25  
% 232.15/43.25  Begin of proof
% 232.15/43.25  | 
% 232.15/43.25  | ALPHA: (1) implies:
% 232.15/43.25  |   (4)  all_57_6 = e1
% 232.15/43.25  | 
% 232.15/43.25  | COMBINE_EQS: (2), (4) imply:
% 232.15/43.25  |   (5)  e3 = e1
% 232.15/43.25  | 
% 232.15/43.25  | REDUCE: (3), (5) imply:
% 232.15/43.25  |   (6)  $false
% 232.15/43.25  | 
% 232.15/43.25  | CLOSE: (6) is inconsistent.
% 232.15/43.25  | 
% 232.15/43.25  End of proof
% 232.15/43.25  
% 232.15/43.25  Sub-proof #2118 shows that the following formulas are inconsistent:
% 232.15/43.25  ----------------------------------------------------------------
% 232.15/43.25    (1)  all_55_10 = all_6_2
% 232.15/43.25    (2)  all_55_10 = e0
% 232.15/43.25    (3)   ~ (all_6_2 = e0)
% 232.15/43.25  
% 232.15/43.25  Begin of proof
% 232.15/43.25  | 
% 232.15/43.25  | COMBINE_EQS: (1), (2) imply:
% 232.15/43.25  |   (4)  all_6_2 = e0
% 232.15/43.25  | 
% 232.15/43.25  | SIMP: (4) implies:
% 232.15/43.25  |   (5)  all_6_2 = e0
% 232.15/43.25  | 
% 232.15/43.25  | REDUCE: (3), (5) imply:
% 232.15/43.25  |   (6)  $false
% 232.15/43.25  | 
% 232.15/43.25  | CLOSE: (6) is inconsistent.
% 232.15/43.25  | 
% 232.15/43.25  End of proof
% 232.15/43.25  
% 232.15/43.25  Sub-proof #2119 shows that the following formulas are inconsistent:
% 232.15/43.25  ----------------------------------------------------------------
% 232.15/43.25    (1)  all_57_11 = e3
% 232.15/43.25    (2)  all_57_11 = e2
% 232.15/43.25    (3)   ~ (e3 = e2)
% 232.15/43.25  
% 232.15/43.25  Begin of proof
% 232.15/43.25  | 
% 232.15/43.25  | COMBINE_EQS: (1), (2) imply:
% 232.15/43.25  |   (4)  e3 = e2
% 232.15/43.25  | 
% 232.15/43.25  | SIMP: (4) implies:
% 232.15/43.25  |   (5)  e3 = e2
% 232.15/43.25  | 
% 232.15/43.25  | REDUCE: (3), (5) imply:
% 232.15/43.25  |   (6)  $false
% 232.15/43.25  | 
% 232.15/43.25  | CLOSE: (6) is inconsistent.
% 232.15/43.25  | 
% 232.15/43.25  End of proof
% 232.15/43.25  
% 232.15/43.25  Sub-proof #2120 shows that the following formulas are inconsistent:
% 232.15/43.25  ----------------------------------------------------------------
% 232.15/43.25    (1)  op(e0, e0) = all_4_2
% 232.15/43.25    (2)  all_57_15 = e0
% 232.15/43.25    (3)   ~ (e3 = e1)
% 232.15/43.25    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.25           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.25    (5)   ~ (all_53_7 = e2)
% 232.15/43.25    (6)   ~ (e3 = e2)
% 232.15/43.25    (7)   ~ (e3 = e0)
% 232.15/43.25    (8)   ~ (all_4_2 = e2)
% 232.15/43.25    (9)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 232.15/43.25         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 232.15/43.25    (10)   ~ (e2 = e0)
% 232.15/43.25    (11)   ~ (e1 = e0)
% 232.15/43.25    (12)  op(e0, e0) = e0
% 232.15/43.25    (13)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 232.15/43.25          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 232.15/43.25            e3)
% 232.15/43.25    (14)  op(e0, e2) = all_53_7
% 232.15/43.25    (15)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 232.15/43.25          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 232.15/43.25            e2)
% 232.15/43.25    (16)   ~ (e2 = e1)
% 232.15/43.25    (17)  all_57_14 = e0
% 232.15/43.25  
% 232.15/43.25  Begin of proof
% 232.15/43.25  | 
% 232.15/43.25  | BETA: splitting (9) gives:
% 232.15/43.25  | 
% 232.15/43.25  | Case 1:
% 232.15/43.25  | | 
% 232.15/43.25  | |   (18)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 232.15/43.25  | |           e1)
% 232.15/43.25  | | 
% 232.15/43.25  | | BETA: splitting (18) gives:
% 232.15/43.25  | | 
% 232.15/43.25  | | Case 1:
% 232.15/43.25  | | | 
% 232.15/43.25  | | |   (19)  all_57_12 = e1 & op(e0, e3) = e1
% 232.15/43.25  | | | 
% 232.15/43.25  | | | ALPHA: (19) implies:
% 232.15/43.25  | | |   (20)  all_57_12 = e1
% 232.15/43.25  | | | 
% 232.15/43.25  | | | BETA: splitting (15) gives:
% 232.15/43.25  | | | 
% 232.15/43.25  | | | Case 1:
% 232.15/43.25  | | | | 
% 232.15/43.25  | | | |   (21)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0,
% 232.15/43.25  | | | |             e2) = e2)
% 232.15/43.25  | | | | 
% 232.15/43.25  | | | | REF_CLOSE: (4), (5), (14), (16), (20), (21) are inconsistent by
% 232.15/43.25  | | | |            sub-proof #2128.
% 232.15/43.25  | | | | 
% 232.15/43.25  | | | Case 2:
% 232.15/43.25  | | | | 
% 232.15/43.25  | | | |   (22)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0,
% 232.15/43.25  | | | |             e0) = e2)
% 232.15/43.25  | | | | 
% 232.15/43.25  | | | | REF_CLOSE: (1), (4), (8), (10), (17), (22) are inconsistent by sub-proof
% 232.15/43.25  | | | |            #2127.
% 232.15/43.25  | | | | 
% 232.15/43.25  | | | End of split
% 232.15/43.25  | | | 
% 232.15/43.25  | | Case 2:
% 232.15/43.25  | | | 
% 232.15/43.25  | | |   (23)  all_57_13 = e1 & op(e0, e2) = e1
% 232.15/43.25  | | | 
% 232.15/43.25  | | | ALPHA: (23) implies:
% 232.15/43.25  | | |   (24)  all_57_13 = e1
% 232.15/43.25  | | | 
% 232.15/43.25  | | | REF_CLOSE: (2), (3), (4), (6), (7), (10), (12), (13), (15), (16), (17),
% 232.15/43.25  | | |            (24) are inconsistent by sub-proof #2123.
% 232.15/43.25  | | | 
% 232.15/43.25  | | End of split
% 232.15/43.25  | | 
% 232.15/43.25  | Case 2:
% 232.15/43.25  | | 
% 232.15/43.25  | |   (25)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 232.15/43.25  | |           e1)
% 232.15/43.25  | | 
% 232.15/43.25  | | REF_CLOSE: (4), (11), (12), (17), (25) are inconsistent by sub-proof #2121.
% 232.15/43.25  | | 
% 232.15/43.25  | End of split
% 232.15/43.25  | 
% 232.15/43.25  End of proof
% 232.15/43.25  
% 232.15/43.25  Sub-proof #2121 shows that the following formulas are inconsistent:
% 232.15/43.25  ----------------------------------------------------------------
% 232.15/43.25    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.25           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.25    (2)   ~ (e1 = e0)
% 232.15/43.25    (3)  op(e0, e0) = e0
% 232.15/43.25    (4)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 232.15/43.25    (5)  all_57_14 = e0
% 232.15/43.25  
% 232.15/43.25  Begin of proof
% 232.15/43.25  | 
% 232.15/43.25  | BETA: splitting (4) gives:
% 232.15/43.25  | 
% 232.15/43.25  | Case 1:
% 232.15/43.25  | | 
% 232.15/43.25  | |   (6)  all_57_14 = e1 & op(e0, e1) = e1
% 232.15/43.25  | | 
% 232.15/43.25  | | ALPHA: (6) implies:
% 232.15/43.25  | |   (7)  all_57_14 = e1
% 232.15/43.25  | | 
% 232.15/43.25  | | REF_CLOSE: (2), (5), (7) are inconsistent by sub-proof #2122.
% 232.15/43.25  | | 
% 232.15/43.25  | Case 2:
% 232.15/43.25  | | 
% 232.15/43.25  | |   (8)  all_57_15 = e1 & op(e0, e0) = e1
% 232.15/43.25  | | 
% 232.15/43.25  | | ALPHA: (8) implies:
% 232.15/43.25  | |   (9)  op(e0, e0) = e1
% 232.15/43.25  | | 
% 232.15/43.25  | | REF_CLOSE: (1), (2), (3), (9) are inconsistent by sub-proof #2290.
% 232.15/43.25  | | 
% 232.15/43.25  | End of split
% 232.15/43.25  | 
% 232.15/43.25  End of proof
% 232.15/43.25  
% 232.15/43.25  Sub-proof #2122 shows that the following formulas are inconsistent:
% 232.15/43.25  ----------------------------------------------------------------
% 232.15/43.25    (1)  all_57_14 = e1
% 232.15/43.25    (2)  all_57_14 = e0
% 232.15/43.25    (3)   ~ (e1 = e0)
% 232.15/43.25  
% 232.15/43.25  Begin of proof
% 232.15/43.25  | 
% 232.15/43.25  | COMBINE_EQS: (1), (2) imply:
% 232.15/43.25  |   (4)  e1 = e0
% 232.15/43.25  | 
% 232.15/43.25  | SIMP: (4) implies:
% 232.15/43.25  |   (5)  e1 = e0
% 232.15/43.25  | 
% 232.15/43.25  | REDUCE: (3), (5) imply:
% 232.15/43.25  |   (6)  $false
% 232.15/43.25  | 
% 232.15/43.25  | CLOSE: (6) is inconsistent.
% 232.15/43.25  | 
% 232.15/43.25  End of proof
% 232.15/43.25  
% 232.15/43.25  Sub-proof #2123 shows that the following formulas are inconsistent:
% 232.15/43.25  ----------------------------------------------------------------
% 232.15/43.25    (1)  all_57_15 = e0
% 232.15/43.25    (2)  all_57_13 = e1
% 232.15/43.25    (3)   ~ (e3 = e1)
% 232.15/43.25    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.25           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.25    (5)   ~ (e3 = e2)
% 232.15/43.25    (6)   ~ (e3 = e0)
% 232.15/43.25    (7)   ~ (e2 = e0)
% 232.15/43.25    (8)  op(e0, e0) = e0
% 232.15/43.25    (9)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 232.15/43.25         (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 232.15/43.25    (10)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 232.15/43.25          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 232.15/43.25            e2)
% 232.15/43.25    (11)   ~ (e2 = e1)
% 232.15/43.25    (12)  all_57_14 = e0
% 232.15/43.25  
% 232.15/43.25  Begin of proof
% 232.15/43.25  | 
% 232.15/43.25  | BETA: splitting (9) gives:
% 232.15/43.25  | 
% 232.15/43.25  | Case 1:
% 232.15/43.25  | | 
% 232.15/43.25  | |   (13)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 232.15/43.25  | |           e3)
% 232.15/43.25  | | 
% 232.15/43.25  | | BETA: splitting (13) gives:
% 232.15/43.25  | | 
% 232.15/43.25  | | Case 1:
% 232.15/43.25  | | | 
% 232.15/43.25  | | |   (14)  all_57_12 = e3 & op(e0, e3) = e3
% 232.15/43.25  | | | 
% 232.15/43.25  | | | ALPHA: (14) implies:
% 232.15/43.25  | | |   (15)  all_57_12 = e3
% 232.15/43.25  | | | 
% 232.15/43.25  | | | REF_CLOSE: (1), (2), (5), (7), (10), (11), (12), (15) are inconsistent by
% 232.15/43.25  | | |            sub-proof #2124.
% 232.15/43.25  | | | 
% 232.15/43.25  | | Case 2:
% 232.15/43.25  | | | 
% 232.15/43.25  | | |   (16)  all_57_13 = e3 & op(e0, e2) = e3
% 232.15/43.25  | | | 
% 232.15/43.25  | | | ALPHA: (16) implies:
% 232.15/43.25  | | |   (17)  all_57_13 = e3
% 232.15/43.25  | | | 
% 232.15/43.25  | | | REF_CLOSE: (2), (3), (17) are inconsistent by sub-proof #2268.
% 232.15/43.25  | | | 
% 232.15/43.25  | | End of split
% 232.15/43.25  | | 
% 232.15/43.25  | Case 2:
% 232.15/43.25  | | 
% 232.15/43.25  | |   (18)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 232.15/43.25  | |           e3)
% 232.15/43.25  | | 
% 232.15/43.25  | | BETA: splitting (18) gives:
% 232.15/43.25  | | 
% 232.15/43.25  | | Case 1:
% 232.15/43.25  | | | 
% 232.15/43.25  | | |   (19)  all_57_14 = e3 & op(e0, e1) = e3
% 232.15/43.25  | | | 
% 232.15/43.25  | | | ALPHA: (19) implies:
% 232.15/43.25  | | |   (20)  all_57_14 = e3
% 232.15/43.25  | | | 
% 232.15/43.25  | | | REF_CLOSE: (6), (12), (20) are inconsistent by sub-proof #2420.
% 232.15/43.25  | | | 
% 232.15/43.25  | | Case 2:
% 232.15/43.25  | | | 
% 232.15/43.25  | | |   (21)  all_57_15 = e3 & op(e0, e0) = e3
% 232.15/43.25  | | | 
% 232.15/43.25  | | | ALPHA: (21) implies:
% 232.15/43.25  | | |   (22)  op(e0, e0) = e3
% 232.15/43.25  | | | 
% 232.15/43.25  | | | REF_CLOSE: (4), (6), (8), (22) are inconsistent by sub-proof #2304.
% 232.15/43.25  | | | 
% 232.15/43.25  | | End of split
% 232.15/43.25  | | 
% 232.15/43.25  | End of split
% 232.15/43.25  | 
% 232.15/43.25  End of proof
% 232.15/43.25  
% 232.15/43.25  Sub-proof #2124 shows that the following formulas are inconsistent:
% 232.15/43.25  ----------------------------------------------------------------
% 232.15/43.25    (1)  all_57_15 = e0
% 232.15/43.25    (2)  all_57_13 = e1
% 232.15/43.25    (3)   ~ (e3 = e2)
% 232.15/43.25    (4)   ~ (e2 = e0)
% 232.15/43.25    (5)  all_57_12 = e3
% 232.15/43.25    (6)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2) |
% 232.15/43.25         (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 232.15/43.25    (7)   ~ (e2 = e1)
% 232.15/43.25    (8)  all_57_14 = e0
% 232.15/43.25  
% 232.15/43.25  Begin of proof
% 232.15/43.25  | 
% 232.15/43.25  | BETA: splitting (6) gives:
% 232.15/43.25  | 
% 232.15/43.25  | Case 1:
% 232.15/43.25  | | 
% 232.15/43.25  | |   (9)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 232.15/43.25  | |          e2)
% 232.15/43.25  | | 
% 232.15/43.25  | | BETA: splitting (9) gives:
% 232.15/43.25  | | 
% 232.15/43.25  | | Case 1:
% 232.15/43.25  | | | 
% 232.15/43.25  | | |   (10)  all_57_12 = e2 & op(e0, e3) = e2
% 232.15/43.25  | | | 
% 232.15/43.25  | | | REF_CLOSE: (3), (5), (10) are inconsistent by sub-proof #2232.
% 232.15/43.25  | | | 
% 232.15/43.25  | | Case 2:
% 232.15/43.25  | | | 
% 232.15/43.25  | | |   (11)  all_57_13 = e2 & op(e0, e2) = e2
% 232.15/43.25  | | | 
% 232.15/43.25  | | | ALPHA: (11) implies:
% 232.15/43.25  | | |   (12)  all_57_13 = e2
% 232.15/43.25  | | | 
% 232.15/43.25  | | | REF_CLOSE: (2), (7), (12) are inconsistent by sub-proof #2327.
% 232.15/43.25  | | | 
% 232.15/43.25  | | End of split
% 232.15/43.25  | | 
% 232.15/43.25  | Case 2:
% 232.15/43.25  | | 
% 232.15/43.25  | |   (13)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 232.15/43.25  | |           e2)
% 232.15/43.25  | | 
% 232.15/43.25  | | REF_CLOSE: (1), (4), (8), (13) are inconsistent by sub-proof #2125.
% 232.15/43.25  | | 
% 232.15/43.25  | End of split
% 232.15/43.25  | 
% 232.15/43.25  End of proof
% 232.15/43.25  
% 232.15/43.25  Sub-proof #2125 shows that the following formulas are inconsistent:
% 232.15/43.25  ----------------------------------------------------------------
% 232.15/43.25    (1)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 232.15/43.25    (2)  all_57_14 = e0
% 232.15/43.25    (3)   ~ (e2 = e0)
% 232.15/43.25    (4)  all_57_15 = e0
% 232.15/43.25  
% 232.15/43.25  Begin of proof
% 232.15/43.25  | 
% 232.15/43.25  | BETA: splitting (1) gives:
% 232.15/43.25  | 
% 232.15/43.25  | Case 1:
% 232.15/43.25  | | 
% 232.15/43.25  | |   (5)  all_57_14 = e2 & op(e0, e1) = e2
% 232.15/43.25  | | 
% 232.15/43.25  | | ALPHA: (5) implies:
% 232.15/43.25  | |   (6)  all_57_14 = e2
% 232.15/43.25  | | 
% 232.15/43.25  | | REF_CLOSE: (2), (3), (6) are inconsistent by sub-proof #2422.
% 232.15/43.25  | | 
% 232.15/43.25  | Case 2:
% 232.15/43.25  | | 
% 232.15/43.25  | |   (7)  all_57_15 = e2 & op(e0, e0) = e2
% 232.15/43.25  | | 
% 232.15/43.25  | | ALPHA: (7) implies:
% 232.15/43.25  | |   (8)  all_57_15 = e2
% 232.15/43.25  | | 
% 232.15/43.25  | | REF_CLOSE: (3), (4), (8) are inconsistent by sub-proof #2126.
% 232.15/43.25  | | 
% 232.15/43.25  | End of split
% 232.15/43.25  | 
% 232.15/43.25  End of proof
% 232.15/43.25  
% 232.15/43.25  Sub-proof #2126 shows that the following formulas are inconsistent:
% 232.15/43.25  ----------------------------------------------------------------
% 232.15/43.25    (1)  all_57_15 = e2
% 232.15/43.25    (2)  all_57_15 = e0
% 232.15/43.25    (3)   ~ (e2 = e0)
% 232.15/43.25  
% 232.15/43.25  Begin of proof
% 232.15/43.25  | 
% 232.15/43.25  | COMBINE_EQS: (1), (2) imply:
% 232.15/43.25  |   (4)  e2 = e0
% 232.15/43.25  | 
% 232.15/43.25  | SIMP: (4) implies:
% 232.15/43.25  |   (5)  e2 = e0
% 232.15/43.25  | 
% 232.15/43.25  | REDUCE: (3), (5) imply:
% 232.15/43.25  |   (6)  $false
% 232.15/43.25  | 
% 232.15/43.25  | CLOSE: (6) is inconsistent.
% 232.15/43.25  | 
% 232.15/43.25  End of proof
% 232.15/43.25  
% 232.15/43.25  Sub-proof #2127 shows that the following formulas are inconsistent:
% 232.15/43.25  ----------------------------------------------------------------
% 232.15/43.25    (1)  op(e0, e0) = all_4_2
% 232.15/43.25    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.25           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.25    (3)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 232.15/43.25    (4)   ~ (all_4_2 = e2)
% 232.15/43.25    (5)   ~ (e2 = e0)
% 232.15/43.25    (6)  all_57_14 = e0
% 232.15/43.25  
% 232.15/43.25  Begin of proof
% 232.15/43.25  | 
% 232.15/43.25  | BETA: splitting (3) gives:
% 232.15/43.25  | 
% 232.15/43.25  | Case 1:
% 232.15/43.25  | | 
% 232.15/43.25  | |   (7)  all_57_14 = e2 & op(e0, e1) = e2
% 232.15/43.25  | | 
% 232.15/43.25  | | ALPHA: (7) implies:
% 232.15/43.25  | |   (8)  all_57_14 = e2
% 232.15/43.25  | | 
% 232.15/43.25  | | REF_CLOSE: (5), (6), (8) are inconsistent by sub-proof #2422.
% 232.15/43.25  | | 
% 232.15/43.25  | Case 2:
% 232.15/43.25  | | 
% 232.15/43.25  | |   (9)  all_57_15 = e2 & op(e0, e0) = e2
% 232.15/43.25  | | 
% 232.15/43.25  | | ALPHA: (9) implies:
% 232.15/43.25  | |   (10)  op(e0, e0) = e2
% 232.15/43.25  | | 
% 232.15/43.25  | | REF_CLOSE: (1), (2), (4), (10) are inconsistent by sub-proof #2334.
% 232.15/43.25  | | 
% 232.15/43.25  | End of split
% 232.15/43.25  | 
% 232.15/43.25  End of proof
% 232.15/43.25  
% 232.15/43.25  Sub-proof #2128 shows that the following formulas are inconsistent:
% 232.15/43.25  ----------------------------------------------------------------
% 232.15/43.25    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.25           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.25    (2)   ~ (all_53_7 = e2)
% 232.15/43.25    (3)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 232.15/43.25    (4)  all_57_12 = e1
% 232.15/43.25    (5)  op(e0, e2) = all_53_7
% 232.15/43.25    (6)   ~ (e2 = e1)
% 232.15/43.25  
% 232.15/43.25  Begin of proof
% 232.15/43.25  | 
% 232.15/43.25  | BETA: splitting (3) gives:
% 232.15/43.25  | 
% 232.15/43.25  | Case 1:
% 232.15/43.25  | | 
% 232.15/43.25  | |   (7)  all_57_12 = e2 & op(e0, e3) = e2
% 232.15/43.25  | | 
% 232.15/43.25  | | ALPHA: (7) implies:
% 232.15/43.25  | |   (8)  all_57_12 = e2
% 232.15/43.25  | | 
% 232.15/43.25  | | REF_CLOSE: (4), (6), (8) are inconsistent by sub-proof #2321.
% 232.15/43.25  | | 
% 232.15/43.25  | Case 2:
% 232.15/43.25  | | 
% 232.15/43.25  | |   (9)  all_57_13 = e2 & op(e0, e2) = e2
% 232.15/43.25  | | 
% 232.15/43.25  | | ALPHA: (9) implies:
% 232.15/43.25  | |   (10)  op(e0, e2) = e2
% 232.15/43.25  | | 
% 232.15/43.25  | | REF_CLOSE: (1), (2), (5), (10) are inconsistent by sub-proof #2335.
% 232.15/43.25  | | 
% 232.15/43.25  | End of split
% 232.15/43.25  | 
% 232.15/43.25  End of proof
% 232.15/43.25  
% 232.15/43.25  Sub-proof #2129 shows that the following formulas are inconsistent:
% 232.15/43.25  ----------------------------------------------------------------
% 232.15/43.25    (1)  op(e2, e3) = all_53_1
% 232.15/43.25    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.25           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.25    (3)   ~ (all_53_13 = e3)
% 232.15/43.25    (4)   ~ (e3 = e2)
% 232.15/43.25    (5)   ~ (e3 = e0)
% 232.15/43.25    (6)  op(e2, e2) = e2
% 232.15/43.25    (7)  op(e2, e0) = all_53_13
% 232.15/43.25    (8)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 232.15/43.25         (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 232.15/43.25    (9)   ~ (all_53_1 = e3)
% 232.15/43.25    (10)  all_57_5 = e0
% 232.15/43.25  
% 232.15/43.25  Begin of proof
% 232.15/43.25  | 
% 232.15/43.25  | BETA: splitting (8) gives:
% 232.15/43.25  | 
% 232.15/43.25  | Case 1:
% 232.15/43.25  | | 
% 232.15/43.25  | |   (11)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 232.15/43.25  | |           e3)
% 232.15/43.25  | | 
% 232.15/43.25  | | REF_CLOSE: (1), (2), (4), (6), (9), (11) are inconsistent by sub-proof
% 232.15/43.25  | |            #2297.
% 232.15/43.25  | | 
% 232.15/43.25  | Case 2:
% 232.15/43.25  | | 
% 232.15/43.25  | |   (12)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 232.15/43.25  | |           e3)
% 232.15/43.25  | | 
% 232.15/43.25  | | BETA: splitting (12) gives:
% 232.15/43.25  | | 
% 232.15/43.25  | | Case 1:
% 232.15/43.25  | | | 
% 232.15/43.25  | | |   (13)  all_57_5 = e3 & op(e2, e1) = e3
% 232.15/43.25  | | | 
% 232.15/43.25  | | | ALPHA: (13) implies:
% 232.15/43.25  | | |   (14)  all_57_5 = e3
% 232.15/43.25  | | | 
% 232.15/43.25  | | | REF_CLOSE: (5), (10), (14) are inconsistent by sub-proof #2471.
% 232.15/43.25  | | | 
% 232.15/43.25  | | Case 2:
% 232.15/43.25  | | | 
% 232.15/43.25  | | |   (15)  all_57_10 = e3 & op(e2, e0) = e3
% 232.15/43.25  | | | 
% 232.15/43.25  | | | ALPHA: (15) implies:
% 232.15/43.25  | | |   (16)  op(e2, e0) = e3
% 232.15/43.25  | | | 
% 232.15/43.25  | | | REF_CLOSE: (2), (3), (7), (16) are inconsistent by sub-proof #2301.
% 232.15/43.25  | | | 
% 232.15/43.25  | | End of split
% 232.15/43.25  | | 
% 232.15/43.25  | End of split
% 232.15/43.25  | 
% 232.15/43.25  End of proof
% 232.15/43.25  
% 232.15/43.25  Sub-proof #2130 shows that the following formulas are inconsistent:
% 232.15/43.25  ----------------------------------------------------------------
% 232.15/43.25    (1)  all_55_7 = all_53_13
% 232.15/43.25    (2)  all_55_7 = e0
% 232.15/43.25    (3)   ~ (all_53_13 = e0)
% 232.15/43.25  
% 232.15/43.25  Begin of proof
% 232.15/43.25  | 
% 232.15/43.25  | COMBINE_EQS: (1), (2) imply:
% 232.15/43.25  |   (4)  all_53_13 = e0
% 232.15/43.25  | 
% 232.15/43.25  | SIMP: (4) implies:
% 232.15/43.25  |   (5)  all_53_13 = e0
% 232.15/43.25  | 
% 232.15/43.25  | REDUCE: (3), (5) imply:
% 232.15/43.25  |   (6)  $false
% 232.15/43.25  | 
% 232.15/43.25  | CLOSE: (6) is inconsistent.
% 232.15/43.25  | 
% 232.15/43.25  End of proof
% 232.15/43.25  
% 232.15/43.25  Sub-proof #2131 shows that the following formulas are inconsistent:
% 232.15/43.25  ----------------------------------------------------------------
% 232.15/43.25    (1)  all_57_9 = e1 & op(e3, e0) = e1
% 232.15/43.25    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.25           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.25    (3)  op(e3, e0) = all_53_12
% 232.15/43.25    (4)   ~ (all_53_12 = e1)
% 232.15/43.25  
% 232.15/43.25  Begin of proof
% 232.15/43.25  | 
% 232.15/43.25  | ALPHA: (1) implies:
% 232.15/43.25  |   (5)  op(e3, e0) = e1
% 232.15/43.25  | 
% 232.15/43.25  | GROUND_INST: instantiating (2) with all_53_12, e1, e0, e3, simplifying with
% 232.15/43.25  |              (3), (5) gives:
% 232.15/43.25  |   (6)  all_53_12 = e1
% 232.15/43.25  | 
% 232.15/43.25  | REDUCE: (4), (6) imply:
% 232.15/43.25  |   (7)  $false
% 232.15/43.25  | 
% 232.15/43.25  | CLOSE: (7) is inconsistent.
% 232.15/43.25  | 
% 232.15/43.25  End of proof
% 232.15/43.25  
% 232.15/43.25  Sub-proof #2132 shows that the following formulas are inconsistent:
% 232.15/43.25  ----------------------------------------------------------------
% 232.15/43.26    (1)  all_55_3 = e1 | all_55_3 = e0
% 232.15/43.26    (2)  all_55_3 = all_53_12
% 232.15/43.26    (3)   ~ (all_53_12 = e1)
% 232.15/43.26    (4)   ~ (all_53_12 = e0)
% 232.15/43.26  
% 232.15/43.26  Begin of proof
% 232.15/43.26  | 
% 232.15/43.26  | BETA: splitting (1) gives:
% 232.15/43.26  | 
% 232.15/43.26  | Case 1:
% 232.15/43.26  | | 
% 232.15/43.26  | |   (5)  all_55_3 = e1
% 232.15/43.26  | | 
% 232.15/43.26  | | COMBINE_EQS: (2), (5) imply:
% 232.15/43.26  | |   (6)  all_53_12 = e1
% 232.15/43.26  | | 
% 232.15/43.26  | | REDUCE: (3), (6) imply:
% 232.15/43.26  | |   (7)  $false
% 232.15/43.26  | | 
% 232.15/43.26  | | CLOSE: (7) is inconsistent.
% 232.15/43.26  | | 
% 232.15/43.26  | Case 2:
% 232.15/43.26  | | 
% 232.15/43.26  | |   (8)  all_55_3 = e0
% 232.15/43.26  | | 
% 232.15/43.26  | | COMBINE_EQS: (2), (8) imply:
% 232.15/43.26  | |   (9)  all_53_12 = e0
% 232.15/43.26  | | 
% 232.15/43.26  | | REDUCE: (4), (9) imply:
% 232.15/43.26  | |   (10)  $false
% 232.15/43.26  | | 
% 232.15/43.26  | | CLOSE: (10) is inconsistent.
% 232.15/43.26  | | 
% 232.15/43.26  | End of split
% 232.15/43.26  | 
% 232.15/43.26  End of proof
% 232.15/43.26  
% 232.15/43.26  Sub-proof #2133 shows that the following formulas are inconsistent:
% 232.15/43.26  ----------------------------------------------------------------
% 232.15/43.26    (1)  all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 232.15/43.26    (2)   ~ (all_53_14 = e1)
% 232.15/43.26    (3)   ~ (all_53_14 = e0)
% 232.15/43.26    (4)  all_55_11 = all_53_14
% 232.15/43.26    (5)   ~ (all_53_14 = e2)
% 232.15/43.26  
% 232.15/43.26  Begin of proof
% 232.15/43.26  | 
% 232.15/43.26  | BETA: splitting (1) gives:
% 232.15/43.26  | 
% 232.15/43.26  | Case 1:
% 232.15/43.26  | | 
% 232.15/43.26  | |   (6)  all_55_11 = e2
% 232.15/43.26  | | 
% 232.15/43.26  | | REF_CLOSE: (4), (5), (6) are inconsistent by sub-proof #2282.
% 232.15/43.26  | | 
% 232.15/43.26  | Case 2:
% 232.15/43.26  | | 
% 232.15/43.26  | |   (7)  all_55_11 = e1 | all_55_11 = e0
% 232.15/43.26  | | 
% 232.15/43.26  | | REF_CLOSE: (2), (3), (4), (7) are inconsistent by sub-proof #2307.
% 232.15/43.26  | | 
% 232.15/43.26  | End of split
% 232.15/43.26  | 
% 232.15/43.26  End of proof
% 232.15/43.26  
% 232.15/43.26  Sub-proof #2134 shows that the following formulas are inconsistent:
% 232.15/43.26  ----------------------------------------------------------------
% 232.15/43.26    (1)   ~ (e3 = e1)
% 232.15/43.26    (2)   ~ (e3 = e2)
% 232.15/43.26    (3)   ~ (e3 = e0)
% 232.15/43.26    (4)  all_57_15 = e3
% 232.15/43.26    (5)   ~ (e2 = e0)
% 232.15/43.26    (6)   ~ (e1 = e0)
% 232.15/43.26    (7)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 232.15/43.26             | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 232.15/43.26               e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 232.15/43.26               op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 232.15/43.26    (8)  all_57_11 = e3
% 232.15/43.26    (9)   ~ (e2 = e1)
% 232.15/43.26    (10)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 232.15/43.26          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 232.15/43.26    (11)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 232.15/43.26          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 232.15/43.26  
% 232.15/43.26  Begin of proof
% 232.15/43.26  | 
% 232.15/43.26  | BETA: splitting (7) gives:
% 232.15/43.26  | 
% 232.15/43.26  | Case 1:
% 232.15/43.26  | | 
% 232.15/43.26  | |   (12)  all_57_15 = e0 & op(e0, e0) = e0
% 232.15/43.26  | | 
% 232.15/43.26  | | REF_CLOSE: (3), (4), (12) are inconsistent by sub-proof #2329.
% 232.15/43.26  | | 
% 232.15/43.26  | Case 2:
% 232.15/43.26  | | 
% 232.15/43.26  | |   (13)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 232.15/43.26  | |             e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0 &
% 232.15/43.26  | |             op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 232.15/43.26  | |           (all_57_14 = e0 & op(e0, e1) = e0))
% 232.15/43.26  | | 
% 232.15/43.26  | | ALPHA: (13) implies:
% 232.15/43.26  | |   (14)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 232.15/43.26  | |           e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 232.15/43.26  | | 
% 232.15/43.26  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (14) are
% 232.15/43.26  | |            inconsistent by sub-proof #2135.
% 232.15/43.26  | | 
% 232.15/43.26  | End of split
% 232.15/43.26  | 
% 232.15/43.26  End of proof
% 232.15/43.26  
% 232.15/43.26  Sub-proof #2135 shows that the following formulas are inconsistent:
% 232.15/43.26  ----------------------------------------------------------------
% 232.15/43.26    (1)   ~ (e3 = e1)
% 232.15/43.26    (2)   ~ (e3 = e2)
% 232.15/43.26    (3)   ~ (e3 = e0)
% 232.15/43.26    (4)  all_57_15 = e3
% 232.15/43.26    (5)   ~ (e2 = e0)
% 232.15/43.26    (6)   ~ (e1 = e0)
% 232.15/43.26    (7)  all_57_11 = e3
% 232.15/43.26    (8)  (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) |
% 232.15/43.26         (all_57_11 = e0 & op(e1, e0) = e0)
% 232.15/43.26    (9)   ~ (e2 = e1)
% 232.15/43.26    (10)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 232.15/43.26          (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 232.15/43.26    (11)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 232.15/43.26          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 232.15/43.26  
% 232.15/43.26  Begin of proof
% 232.15/43.26  | 
% 232.15/43.26  | BETA: splitting (8) gives:
% 232.15/43.26  | 
% 232.15/43.26  | Case 1:
% 232.15/43.26  | | 
% 232.15/43.26  | |   (12)  all_57_9 = e0 & op(e3, e0) = e0
% 232.15/43.26  | | 
% 232.15/43.26  | | ALPHA: (12) implies:
% 232.15/43.26  | |   (13)  all_57_9 = e0
% 232.15/43.26  | | 
% 232.15/43.26  | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (9), (10), (11), (13) are
% 232.15/43.26  | |            inconsistent by sub-proof #2140.
% 232.15/43.26  | | 
% 232.15/43.26  | Case 2:
% 232.15/43.26  | | 
% 232.15/43.26  | |   (14)  (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 232.15/43.26  | |           e0)
% 232.15/43.26  | | 
% 232.15/43.26  | | BETA: splitting (14) gives:
% 232.15/43.26  | | 
% 232.15/43.26  | | Case 1:
% 232.15/43.26  | | | 
% 232.15/43.26  | | |   (15)  all_57_10 = e0 & op(e2, e0) = e0
% 232.15/43.26  | | | 
% 232.15/43.26  | | | ALPHA: (15) implies:
% 232.15/43.26  | | |   (16)  all_57_10 = e0
% 232.15/43.26  | | | 
% 232.15/43.26  | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (9), (10), (11), (16) are
% 232.15/43.26  | | |            inconsistent by sub-proof #2137.
% 232.15/43.26  | | | 
% 232.15/43.26  | | Case 2:
% 232.15/43.26  | | | 
% 232.15/43.26  | | |   (17)  all_57_11 = e0 & op(e1, e0) = e0
% 232.15/43.26  | | | 
% 232.15/43.26  | | | REF_CLOSE: (3), (7), (17) are inconsistent by sub-proof #2136.
% 232.15/43.26  | | | 
% 232.15/43.26  | | End of split
% 232.15/43.26  | | 
% 232.15/43.26  | End of split
% 232.15/43.26  | 
% 232.15/43.26  End of proof
% 232.15/43.26  
% 232.15/43.26  Sub-proof #2136 shows that the following formulas are inconsistent:
% 232.15/43.26  ----------------------------------------------------------------
% 232.15/43.26    (1)  all_57_11 = e0 & op(e1, e0) = e0
% 232.15/43.26    (2)  all_57_11 = e3
% 232.15/43.26    (3)   ~ (e3 = e0)
% 232.15/43.26  
% 232.15/43.26  Begin of proof
% 232.15/43.26  | 
% 232.15/43.26  | ALPHA: (1) implies:
% 232.15/43.26  |   (4)  all_57_11 = e0
% 232.15/43.26  | 
% 232.15/43.26  | COMBINE_EQS: (2), (4) imply:
% 232.15/43.26  |   (5)  e3 = e0
% 232.15/43.26  | 
% 232.15/43.26  | REDUCE: (3), (5) imply:
% 232.15/43.26  |   (6)  $false
% 232.15/43.26  | 
% 232.15/43.26  | CLOSE: (6) is inconsistent.
% 232.15/43.26  | 
% 232.15/43.26  End of proof
% 232.15/43.26  
% 232.15/43.26  Sub-proof #2137 shows that the following formulas are inconsistent:
% 232.15/43.26  ----------------------------------------------------------------
% 232.15/43.26    (1)  all_57_10 = e0
% 232.15/43.26    (2)   ~ (e3 = e1)
% 232.15/43.26    (3)   ~ (e3 = e2)
% 232.15/43.26    (4)  all_57_15 = e3
% 232.15/43.26    (5)   ~ (e2 = e0)
% 232.15/43.26    (6)   ~ (e1 = e0)
% 232.15/43.26    (7)  all_57_11 = e3
% 232.15/43.26    (8)   ~ (e2 = e1)
% 232.15/43.26    (9)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 232.15/43.26         (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 232.15/43.26    (10)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 232.15/43.26          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 232.15/43.26  
% 232.15/43.26  Begin of proof
% 232.15/43.26  | 
% 232.15/43.26  | BETA: splitting (9) gives:
% 232.15/43.26  | 
% 232.15/43.26  | Case 1:
% 232.15/43.26  | | 
% 232.15/43.26  | |   (11)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 232.15/43.26  | |           e2)
% 232.15/43.26  | | 
% 232.15/43.26  | | BETA: splitting (11) gives:
% 232.15/43.26  | | 
% 232.15/43.26  | | Case 1:
% 232.15/43.26  | | | 
% 232.15/43.26  | | |   (12)  all_57_9 = e2 & op(e3, e0) = e2
% 232.15/43.26  | | | 
% 232.15/43.26  | | | ALPHA: (12) implies:
% 232.15/43.26  | | |   (13)  all_57_9 = e2
% 232.15/43.26  | | | 
% 232.15/43.26  | | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (10), (13) are inconsistent by
% 232.15/43.26  | | |            sub-proof #2139.
% 232.15/43.26  | | | 
% 232.15/43.26  | | Case 2:
% 232.15/43.26  | | | 
% 232.15/43.26  | | |   (14)  all_57_10 = e2 & op(e2, e0) = e2
% 232.15/43.26  | | | 
% 232.15/43.26  | | | ALPHA: (14) implies:
% 232.15/43.26  | | |   (15)  all_57_10 = e2
% 232.15/43.26  | | | 
% 232.15/43.26  | | | REF_CLOSE: (1), (5), (15) are inconsistent by sub-proof #2138.
% 232.15/43.26  | | | 
% 232.15/43.26  | | End of split
% 232.15/43.26  | | 
% 232.15/43.26  | Case 2:
% 232.15/43.26  | | 
% 232.15/43.26  | |   (16)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 232.15/43.26  | |           e2)
% 232.15/43.26  | | 
% 232.15/43.26  | | BETA: splitting (16) gives:
% 232.15/43.26  | | 
% 232.15/43.26  | | Case 1:
% 232.15/43.26  | | | 
% 232.15/43.26  | | |   (17)  all_57_11 = e2 & op(e1, e0) = e2
% 232.15/43.26  | | | 
% 232.15/43.26  | | | REF_CLOSE: (3), (7), (17) are inconsistent by sub-proof #2141.
% 232.15/43.26  | | | 
% 232.15/43.26  | | Case 2:
% 232.15/43.26  | | | 
% 232.15/43.26  | | |   (18)  all_57_15 = e2 & op(e0, e0) = e2
% 232.15/43.26  | | | 
% 232.15/43.26  | | | REF_CLOSE: (3), (4), (18) are inconsistent by sub-proof #2323.
% 232.15/43.26  | | | 
% 232.15/43.26  | | End of split
% 232.15/43.26  | | 
% 232.15/43.26  | End of split
% 232.15/43.26  | 
% 232.15/43.26  End of proof
% 232.15/43.26  
% 232.15/43.26  Sub-proof #2138 shows that the following formulas are inconsistent:
% 232.15/43.26  ----------------------------------------------------------------
% 232.15/43.26    (1)  all_57_10 = e2
% 232.15/43.26    (2)  all_57_10 = e0
% 232.15/43.26    (3)   ~ (e2 = e0)
% 232.15/43.26  
% 232.15/43.26  Begin of proof
% 232.15/43.26  | 
% 232.15/43.26  | COMBINE_EQS: (1), (2) imply:
% 232.15/43.26  |   (4)  e2 = e0
% 232.15/43.26  | 
% 232.15/43.26  | SIMP: (4) implies:
% 232.15/43.26  |   (5)  e2 = e0
% 232.15/43.26  | 
% 232.15/43.26  | REDUCE: (3), (5) imply:
% 232.15/43.26  |   (6)  $false
% 232.15/43.26  | 
% 232.15/43.26  | CLOSE: (6) is inconsistent.
% 232.15/43.26  | 
% 232.15/43.26  End of proof
% 232.15/43.26  
% 232.15/43.26  Sub-proof #2139 shows that the following formulas are inconsistent:
% 232.15/43.26  ----------------------------------------------------------------
% 232.15/43.26    (1)  all_57_9 = e2
% 232.15/43.26    (2)  all_57_10 = e0
% 232.15/43.26    (3)   ~ (e3 = e1)
% 232.15/43.26    (4)  all_57_15 = e3
% 232.15/43.26    (5)   ~ (e1 = e0)
% 232.15/43.26    (6)  all_57_11 = e3
% 232.15/43.26    (7)   ~ (e2 = e1)
% 232.15/43.26    (8)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 232.15/43.26         (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 232.15/43.26  
% 232.15/43.26  Begin of proof
% 232.15/43.26  | 
% 232.15/43.26  | BETA: splitting (8) gives:
% 232.15/43.26  | 
% 232.15/43.26  | Case 1:
% 232.15/43.26  | | 
% 232.15/43.26  | |   (9)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) =
% 232.15/43.26  | |          e1)
% 232.15/43.26  | | 
% 232.15/43.26  | | BETA: splitting (9) gives:
% 232.15/43.26  | | 
% 232.15/43.26  | | Case 1:
% 232.15/43.26  | | | 
% 232.15/43.26  | | |   (10)  all_57_9 = e1 & op(e3, e0) = e1
% 232.15/43.26  | | | 
% 232.15/43.26  | | | ALPHA: (10) implies:
% 232.15/43.26  | | |   (11)  all_57_9 = e1
% 232.15/43.26  | | | 
% 232.15/43.26  | | | REF_CLOSE: (1), (7), (11) are inconsistent by sub-proof #2444.
% 232.15/43.26  | | | 
% 232.15/43.26  | | Case 2:
% 232.15/43.26  | | | 
% 232.15/43.26  | | |   (12)  all_57_10 = e1 & op(e2, e0) = e1
% 232.15/43.26  | | | 
% 232.15/43.26  | | | REF_CLOSE: (2), (5), (12) are inconsistent by sub-proof #2242.
% 232.15/43.26  | | | 
% 232.15/43.26  | | End of split
% 232.15/43.26  | | 
% 232.15/43.26  | Case 2:
% 232.15/43.26  | | 
% 232.15/43.26  | |   (13)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 232.15/43.26  | |           e1)
% 232.15/43.26  | | 
% 232.15/43.26  | | BETA: splitting (13) gives:
% 232.15/43.26  | | 
% 232.15/43.26  | | Case 1:
% 232.15/43.26  | | | 
% 232.15/43.26  | | |   (14)  all_57_11 = e1 & op(e1, e0) = e1
% 232.15/43.26  | | | 
% 232.15/43.26  | | | REF_CLOSE: (3), (6), (14) are inconsistent by sub-proof #2143.
% 232.15/43.26  | | | 
% 232.15/43.26  | | Case 2:
% 232.15/43.26  | | | 
% 232.15/43.26  | | |   (15)  all_57_15 = e1 & op(e0, e0) = e1
% 232.15/43.26  | | | 
% 232.15/43.26  | | | REF_CLOSE: (3), (4), (15) are inconsistent by sub-proof #2318.
% 232.15/43.26  | | | 
% 232.15/43.26  | | End of split
% 232.15/43.26  | | 
% 232.15/43.26  | End of split
% 232.15/43.26  | 
% 232.15/43.26  End of proof
% 232.15/43.26  
% 232.15/43.26  Sub-proof #2140 shows that the following formulas are inconsistent:
% 232.15/43.26  ----------------------------------------------------------------
% 232.15/43.26    (1)   ~ (e3 = e1)
% 232.15/43.26    (2)   ~ (e3 = e2)
% 232.15/43.26    (3)  all_57_15 = e3
% 232.15/43.26    (4)  all_57_9 = e0
% 232.15/43.26    (5)   ~ (e2 = e0)
% 232.15/43.26    (6)   ~ (e1 = e0)
% 232.15/43.26    (7)  all_57_11 = e3
% 232.15/43.26    (8)   ~ (e2 = e1)
% 232.15/43.26    (9)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 232.15/43.26         (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 232.15/43.26    (10)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 232.15/43.26          (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 232.15/43.26  
% 232.15/43.26  Begin of proof
% 232.15/43.26  | 
% 232.15/43.26  | BETA: splitting (9) gives:
% 232.15/43.26  | 
% 232.15/43.26  | Case 1:
% 232.15/43.26  | | 
% 232.15/43.26  | |   (11)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 232.15/43.26  | |           e2)
% 232.15/43.26  | | 
% 232.15/43.26  | | BETA: splitting (11) gives:
% 232.15/43.26  | | 
% 232.15/43.26  | | Case 1:
% 232.15/43.26  | | | 
% 232.15/43.26  | | |   (12)  all_57_9 = e2 & op(e3, e0) = e2
% 232.15/43.26  | | | 
% 232.15/43.26  | | | ALPHA: (12) implies:
% 232.15/43.26  | | |   (13)  all_57_9 = e2
% 232.15/43.26  | | | 
% 232.15/43.26  | | | REF_CLOSE: (4), (5), (13) are inconsistent by sub-proof #2440.
% 232.15/43.26  | | | 
% 232.15/43.26  | | Case 2:
% 232.15/43.26  | | | 
% 232.15/43.26  | | |   (14)  all_57_10 = e2 & op(e2, e0) = e2
% 232.15/43.26  | | | 
% 232.15/43.26  | | | ALPHA: (14) implies:
% 232.15/43.26  | | |   (15)  all_57_10 = e2
% 232.15/43.26  | | | 
% 232.15/43.26  | | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (10), (15) are inconsistent by
% 232.15/43.26  | | |            sub-proof #2142.
% 232.15/43.26  | | | 
% 232.15/43.26  | | End of split
% 232.15/43.26  | | 
% 232.15/43.26  | Case 2:
% 232.15/43.26  | | 
% 232.15/43.26  | |   (16)  (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 232.15/43.26  | |           e2)
% 232.15/43.26  | | 
% 232.15/43.26  | | BETA: splitting (16) gives:
% 232.15/43.26  | | 
% 232.15/43.26  | | Case 1:
% 232.15/43.26  | | | 
% 232.15/43.26  | | |   (17)  all_57_11 = e2 & op(e1, e0) = e2
% 232.15/43.26  | | | 
% 232.15/43.26  | | | REF_CLOSE: (2), (7), (17) are inconsistent by sub-proof #2141.
% 232.15/43.26  | | | 
% 232.15/43.26  | | Case 2:
% 232.15/43.26  | | | 
% 232.15/43.26  | | |   (18)  all_57_15 = e2 & op(e0, e0) = e2
% 232.15/43.26  | | | 
% 232.15/43.26  | | | REF_CLOSE: (2), (3), (18) are inconsistent by sub-proof #2323.
% 232.15/43.26  | | | 
% 232.15/43.26  | | End of split
% 232.15/43.26  | | 
% 232.15/43.26  | End of split
% 232.15/43.26  | 
% 232.15/43.26  End of proof
% 232.15/43.26  
% 232.15/43.26  Sub-proof #2141 shows that the following formulas are inconsistent:
% 232.15/43.26  ----------------------------------------------------------------
% 232.15/43.26    (1)  all_57_11 = e2 & op(e1, e0) = e2
% 232.15/43.26    (2)  all_57_11 = e3
% 232.15/43.26    (3)   ~ (e3 = e2)
% 232.15/43.26  
% 232.15/43.26  Begin of proof
% 232.15/43.26  | 
% 232.15/43.26  | ALPHA: (1) implies:
% 232.15/43.26  |   (4)  all_57_11 = e2
% 232.15/43.26  | 
% 232.15/43.26  | COMBINE_EQS: (2), (4) imply:
% 232.15/43.26  |   (5)  e3 = e2
% 232.15/43.26  | 
% 232.15/43.26  | REDUCE: (3), (5) imply:
% 232.15/43.26  |   (6)  $false
% 232.15/43.26  | 
% 232.15/43.26  | CLOSE: (6) is inconsistent.
% 232.15/43.26  | 
% 232.15/43.26  End of proof
% 232.15/43.26  
% 232.15/43.26  Sub-proof #2142 shows that the following formulas are inconsistent:
% 232.15/43.26  ----------------------------------------------------------------
% 232.15/43.26    (1)   ~ (e3 = e1)
% 232.15/43.26    (2)  all_57_15 = e3
% 232.15/43.26    (3)  all_57_10 = e2
% 232.15/43.26    (4)  all_57_9 = e0
% 232.15/43.26    (5)   ~ (e1 = e0)
% 232.15/43.26    (6)  all_57_11 = e3
% 232.15/43.26    (7)   ~ (e2 = e1)
% 232.15/43.26    (8)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 232.15/43.26         (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 232.15/43.26  
% 232.15/43.26  Begin of proof
% 232.15/43.26  | 
% 232.15/43.26  | BETA: splitting (8) gives:
% 232.15/43.26  | 
% 232.15/43.26  | Case 1:
% 232.15/43.26  | | 
% 232.15/43.26  | |   (9)  (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) =
% 232.15/43.26  | |          e1)
% 232.15/43.26  | | 
% 232.15/43.26  | | BETA: splitting (9) gives:
% 232.15/43.26  | | 
% 232.15/43.26  | | Case 1:
% 232.15/43.26  | | | 
% 232.15/43.26  | | |   (10)  all_57_9 = e1 & op(e3, e0) = e1
% 232.15/43.26  | | | 
% 232.15/43.26  | | | REF_CLOSE: (4), (5), (10) are inconsistent by sub-proof #2437.
% 232.15/43.26  | | | 
% 232.15/43.26  | | Case 2:
% 232.15/43.26  | | | 
% 232.15/43.26  | | |   (11)  all_57_10 = e1 & op(e2, e0) = e1
% 232.15/43.26  | | | 
% 232.15/43.26  | | | ALPHA: (11) implies:
% 232.15/43.26  | | |   (12)  all_57_10 = e1
% 232.15/43.26  | | | 
% 232.15/43.26  | | | REF_CLOSE: (3), (7), (12) are inconsistent by sub-proof #2144.
% 232.15/43.26  | | | 
% 232.15/43.26  | | End of split
% 232.15/43.26  | | 
% 232.15/43.26  | Case 2:
% 232.15/43.26  | | 
% 232.15/43.26  | |   (13)  (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 232.15/43.26  | |           e1)
% 232.15/43.26  | | 
% 232.15/43.26  | | BETA: splitting (13) gives:
% 232.15/43.26  | | 
% 232.15/43.26  | | Case 1:
% 232.15/43.26  | | | 
% 232.15/43.26  | | |   (14)  all_57_11 = e1 & op(e1, e0) = e1
% 232.15/43.26  | | | 
% 232.15/43.26  | | | REF_CLOSE: (1), (6), (14) are inconsistent by sub-proof #2143.
% 232.15/43.26  | | | 
% 232.15/43.26  | | Case 2:
% 232.15/43.26  | | | 
% 232.15/43.26  | | |   (15)  all_57_15 = e1 & op(e0, e0) = e1
% 232.15/43.26  | | | 
% 232.15/43.26  | | | REF_CLOSE: (1), (2), (15) are inconsistent by sub-proof #2318.
% 232.15/43.26  | | | 
% 232.15/43.26  | | End of split
% 232.15/43.26  | | 
% 232.15/43.26  | End of split
% 232.15/43.26  | 
% 232.15/43.26  End of proof
% 232.15/43.26  
% 232.15/43.26  Sub-proof #2143 shows that the following formulas are inconsistent:
% 232.15/43.26  ----------------------------------------------------------------
% 232.15/43.26    (1)  all_57_11 = e1 & op(e1, e0) = e1
% 232.15/43.26    (2)  all_57_11 = e3
% 232.15/43.26    (3)   ~ (e3 = e1)
% 232.15/43.26  
% 232.15/43.26  Begin of proof
% 232.15/43.26  | 
% 232.15/43.26  | ALPHA: (1) implies:
% 232.15/43.26  |   (4)  all_57_11 = e1
% 232.15/43.26  | 
% 232.15/43.26  | COMBINE_EQS: (2), (4) imply:
% 232.15/43.26  |   (5)  e3 = e1
% 232.15/43.26  | 
% 232.15/43.26  | REDUCE: (3), (5) imply:
% 232.15/43.26  |   (6)  $false
% 232.15/43.26  | 
% 232.15/43.26  | CLOSE: (6) is inconsistent.
% 232.15/43.26  | 
% 232.15/43.26  End of proof
% 232.15/43.26  
% 232.15/43.26  Sub-proof #2144 shows that the following formulas are inconsistent:
% 232.15/43.26  ----------------------------------------------------------------
% 232.15/43.26    (1)  all_57_10 = e2
% 232.15/43.26    (2)  all_57_10 = e1
% 232.15/43.26    (3)   ~ (e2 = e1)
% 232.15/43.26  
% 232.15/43.26  Begin of proof
% 232.15/43.26  | 
% 232.15/43.26  | COMBINE_EQS: (1), (2) imply:
% 232.15/43.26  |   (4)  e2 = e1
% 232.15/43.26  | 
% 232.15/43.26  | SIMP: (4) implies:
% 232.15/43.26  |   (5)  e2 = e1
% 232.15/43.26  | 
% 232.15/43.26  | REDUCE: (3), (5) imply:
% 232.15/43.26  |   (6)  $false
% 232.15/43.26  | 
% 232.15/43.26  | CLOSE: (6) is inconsistent.
% 232.15/43.26  | 
% 232.15/43.26  End of proof
% 232.15/43.26  
% 232.15/43.26  Sub-proof #2145 shows that the following formulas are inconsistent:
% 232.15/43.26  ----------------------------------------------------------------
% 232.15/43.26    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 232.15/43.26         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 232.15/43.26    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.26           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.26    (3)  op(e2, e2) = e1
% 232.15/43.26    (4)   ~ (e3 = e2)
% 232.15/43.26    (5)   ~ (e3 = e0)
% 232.15/43.26    (6)  all_57_1 = e1
% 232.15/43.26    (7)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 232.15/43.26         (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 232.15/43.26    (8)   ~ (e2 = e0)
% 232.15/43.26    (9)   ~ (e1 = e0)
% 232.15/43.26    (10)  all_57_13 = e3
% 232.15/43.26    (11)   ~ (e2 = e1)
% 232.15/43.26  
% 232.15/43.26  Begin of proof
% 232.15/43.26  | 
% 232.15/43.26  | BETA: splitting (1) gives:
% 232.15/43.26  | 
% 232.15/43.26  | Case 1:
% 232.15/43.26  | | 
% 232.15/43.26  | |   (12)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 232.15/43.26  | |           e2)
% 232.15/43.26  | | 
% 232.15/43.26  | | REF_CLOSE: (2), (3), (6), (11), (12) are inconsistent by sub-proof #2150.
% 232.15/43.26  | | 
% 232.15/43.26  | Case 2:
% 232.15/43.26  | | 
% 232.15/43.26  | |   (13)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 232.15/43.26  | |           e2)
% 232.15/43.26  | | 
% 232.15/43.26  | | BETA: splitting (13) gives:
% 232.15/43.26  | | 
% 232.15/43.26  | | Case 1:
% 232.15/43.26  | | | 
% 232.15/43.26  | | |   (14)  all_57_7 = e2 & op(e1, e2) = e2
% 232.15/43.26  | | | 
% 232.15/43.26  | | | ALPHA: (14) implies:
% 232.15/43.26  | | |   (15)  all_57_7 = e2
% 232.15/43.26  | | | 
% 232.15/43.26  | | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (9), (10), (15) are inconsistent
% 232.15/43.26  | | |            by sub-proof #2147.
% 232.15/43.26  | | | 
% 232.15/43.26  | | Case 2:
% 232.15/43.26  | | | 
% 232.15/43.26  | | |   (16)  all_57_13 = e2 & op(e0, e2) = e2
% 232.15/43.26  | | | 
% 232.15/43.26  | | | REF_CLOSE: (4), (10), (16) are inconsistent by sub-proof #2146.
% 232.15/43.26  | | | 
% 232.15/43.26  | | End of split
% 232.15/43.26  | | 
% 232.15/43.26  | End of split
% 232.15/43.26  | 
% 232.15/43.26  End of proof
% 232.15/43.26  
% 232.15/43.26  Sub-proof #2146 shows that the following formulas are inconsistent:
% 232.15/43.26  ----------------------------------------------------------------
% 232.15/43.26    (1)  all_57_13 = e2 & op(e0, e2) = e2
% 232.15/43.26    (2)  all_57_13 = e3
% 232.15/43.26    (3)   ~ (e3 = e2)
% 232.15/43.26  
% 232.15/43.26  Begin of proof
% 232.15/43.26  | 
% 232.15/43.26  | ALPHA: (1) implies:
% 232.15/43.26  |   (4)  all_57_13 = e2
% 232.15/43.26  | 
% 232.15/43.26  | COMBINE_EQS: (2), (4) imply:
% 232.15/43.26  |   (5)  e3 = e2
% 232.15/43.26  | 
% 232.15/43.26  | REDUCE: (3), (5) imply:
% 232.15/43.26  |   (6)  $false
% 232.15/43.26  | 
% 232.15/43.26  | CLOSE: (6) is inconsistent.
% 232.15/43.26  | 
% 232.15/43.26  End of proof
% 232.15/43.26  
% 232.15/43.26  Sub-proof #2147 shows that the following formulas are inconsistent:
% 232.15/43.26  ----------------------------------------------------------------
% 232.15/43.26    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.26           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.26    (2)  op(e2, e2) = e1
% 232.15/43.26    (3)  all_57_7 = e2
% 232.15/43.26    (4)   ~ (e3 = e0)
% 232.15/43.26    (5)  all_57_1 = e1
% 232.15/43.26    (6)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 232.15/43.26         (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 232.15/43.26    (7)   ~ (e2 = e0)
% 232.15/43.26    (8)   ~ (e1 = e0)
% 232.15/43.26    (9)  all_57_13 = e3
% 232.15/43.26  
% 232.15/43.26  Begin of proof
% 232.15/43.26  | 
% 232.15/43.26  | BETA: splitting (6) gives:
% 232.15/43.26  | 
% 232.15/43.26  | Case 1:
% 232.15/43.26  | | 
% 232.15/43.26  | |   (10)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) =
% 232.15/43.26  | |           e0)
% 232.15/43.26  | | 
% 232.15/43.26  | | REF_CLOSE: (1), (2), (5), (8), (10) are inconsistent by sub-proof #2149.
% 232.15/43.26  | | 
% 232.15/43.26  | Case 2:
% 232.15/43.26  | | 
% 232.15/43.26  | |   (11)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 232.15/43.26  | |           e0)
% 232.15/43.26  | | 
% 232.15/43.26  | | BETA: splitting (11) gives:
% 232.15/43.26  | | 
% 232.15/43.26  | | Case 1:
% 232.15/43.26  | | | 
% 232.15/43.26  | | |   (12)  all_57_7 = e0 & op(e1, e2) = e0
% 232.15/43.26  | | | 
% 232.15/43.26  | | | REF_CLOSE: (3), (7), (12) are inconsistent by sub-proof #2148.
% 232.15/43.26  | | | 
% 232.15/43.26  | | Case 2:
% 232.15/43.26  | | | 
% 232.15/43.26  | | |   (13)  all_57_13 = e0 & op(e0, e2) = e0
% 232.15/43.26  | | | 
% 232.15/43.26  | | | ALPHA: (13) implies:
% 232.15/43.26  | | |   (14)  all_57_13 = e0
% 232.15/43.26  | | | 
% 232.15/43.26  | | | REF_CLOSE: (4), (9), (14) are inconsistent by sub-proof #2184.
% 232.15/43.26  | | | 
% 232.15/43.26  | | End of split
% 232.15/43.26  | | 
% 232.15/43.26  | End of split
% 232.15/43.26  | 
% 232.15/43.26  End of proof
% 232.15/43.26  
% 232.15/43.26  Sub-proof #2148 shows that the following formulas are inconsistent:
% 232.15/43.26  ----------------------------------------------------------------
% 232.15/43.26    (1)  all_57_7 = e0 & op(e1, e2) = e0
% 232.15/43.26    (2)  all_57_7 = e2
% 232.15/43.26    (3)   ~ (e2 = e0)
% 232.15/43.26  
% 232.15/43.26  Begin of proof
% 232.15/43.26  | 
% 232.15/43.26  | ALPHA: (1) implies:
% 232.15/43.26  |   (4)  all_57_7 = e0
% 232.15/43.26  | 
% 232.15/43.26  | COMBINE_EQS: (2), (4) imply:
% 232.15/43.26  |   (5)  e2 = e0
% 232.15/43.26  | 
% 232.15/43.26  | REDUCE: (3), (5) imply:
% 232.15/43.26  |   (6)  $false
% 232.15/43.26  | 
% 232.15/43.26  | CLOSE: (6) is inconsistent.
% 232.15/43.26  | 
% 232.15/43.26  End of proof
% 232.15/43.26  
% 232.15/43.26  Sub-proof #2149 shows that the following formulas are inconsistent:
% 232.15/43.26  ----------------------------------------------------------------
% 232.15/43.26    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.26           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.26    (2)  op(e2, e2) = e1
% 232.15/43.26    (3)  all_57_1 = e1
% 232.15/43.26    (4)   ~ (e1 = e0)
% 232.15/43.26    (5)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0)
% 232.15/43.26  
% 232.15/43.26  Begin of proof
% 232.15/43.26  | 
% 232.15/43.26  | BETA: splitting (5) gives:
% 232.15/43.26  | 
% 232.15/43.26  | Case 1:
% 232.15/43.26  | | 
% 232.15/43.26  | |   (6)  all_57_1 = e0 & op(e3, e2) = e0
% 232.15/43.26  | | 
% 232.15/43.26  | | REF_CLOSE: (3), (4), (6) are inconsistent by sub-proof #2493.
% 232.15/43.26  | | 
% 232.15/43.26  | Case 2:
% 232.15/43.26  | | 
% 232.15/43.26  | |   (7)  all_57_3 = e0 & op(e2, e2) = e0
% 232.15/43.26  | | 
% 232.15/43.26  | | ALPHA: (7) implies:
% 232.15/43.26  | |   (8)  op(e2, e2) = e0
% 232.15/43.26  | | 
% 232.15/43.26  | | REF_CLOSE: (1), (2), (4), (8) are inconsistent by sub-proof #2352.
% 232.15/43.26  | | 
% 232.15/43.26  | End of split
% 232.15/43.26  | 
% 232.15/43.26  End of proof
% 232.15/43.26  
% 232.15/43.26  Sub-proof #2150 shows that the following formulas are inconsistent:
% 232.15/43.26  ----------------------------------------------------------------
% 232.15/43.26    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.26           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.26    (2)  op(e2, e2) = e1
% 232.15/43.26    (3)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2)
% 232.15/43.26    (4)  all_57_1 = e1
% 232.15/43.26    (5)   ~ (e2 = e1)
% 232.15/43.26  
% 232.15/43.26  Begin of proof
% 232.15/43.26  | 
% 232.15/43.26  | BETA: splitting (3) gives:
% 232.15/43.26  | 
% 232.15/43.26  | Case 1:
% 232.15/43.26  | | 
% 232.15/43.26  | |   (6)  all_57_1 = e2 & op(e3, e2) = e2
% 232.15/43.26  | | 
% 232.15/43.26  | | REF_CLOSE: (4), (5), (6) are inconsistent by sub-proof #2489.
% 232.15/43.26  | | 
% 232.15/43.26  | Case 2:
% 232.15/43.26  | | 
% 232.15/43.26  | |   (7)  all_57_3 = e2 & op(e2, e2) = e2
% 232.15/43.26  | | 
% 232.15/43.26  | | ALPHA: (7) implies:
% 232.15/43.26  | |   (8)  op(e2, e2) = e2
% 232.15/43.26  | | 
% 232.15/43.26  | | REF_CLOSE: (1), (2), (5), (8) are inconsistent by sub-proof #2306.
% 232.15/43.26  | | 
% 232.15/43.26  | End of split
% 232.15/43.26  | 
% 232.15/43.26  End of proof
% 232.15/43.26  
% 232.15/43.26  Sub-proof #2151 shows that the following formulas are inconsistent:
% 232.15/43.26  ----------------------------------------------------------------
% 232.15/43.26    (1)  all_57_12 = e3
% 232.15/43.26    (2)  all_57_12 = e1
% 232.15/43.26    (3)   ~ (e3 = e1)
% 232.15/43.26  
% 232.15/43.26  Begin of proof
% 232.15/43.26  | 
% 232.15/43.26  | COMBINE_EQS: (1), (2) imply:
% 232.15/43.26  |   (4)  e3 = e1
% 232.15/43.26  | 
% 232.15/43.26  | SIMP: (4) implies:
% 232.15/43.26  |   (5)  e3 = e1
% 232.15/43.26  | 
% 232.15/43.26  | REDUCE: (3), (5) imply:
% 232.15/43.26  |   (6)  $false
% 232.15/43.26  | 
% 232.15/43.26  | CLOSE: (6) is inconsistent.
% 232.15/43.26  | 
% 232.15/43.26  End of proof
% 232.15/43.26  
% 232.15/43.26  Sub-proof #2152 shows that the following formulas are inconsistent:
% 232.15/43.26  ----------------------------------------------------------------
% 232.15/43.26    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.26           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.26    (2)  all_57_6 = e1
% 232.15/43.26    (3)   ~ (e3 = e2)
% 232.15/43.26    (4)   ~ (e3 = e0)
% 232.15/43.26    (5)  op(e3, e3) = e3
% 232.15/43.26    (6)   ~ (all_53_2 = e0)
% 232.15/43.26    (7)   ~ (e2 = e0)
% 232.15/43.26    (8)  all_57_12 = e3
% 232.15/43.26    (9)  op(e1, e3) = all_53_2
% 232.15/43.26    (10)   ~ (e2 = e1)
% 232.15/43.26    (11)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 232.15/43.26          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 232.15/43.26    (12)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 232.15/43.26          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 232.15/43.26  
% 232.15/43.26  Begin of proof
% 232.15/43.26  | 
% 232.15/43.26  | BETA: splitting (12) gives:
% 232.15/43.26  | 
% 232.15/43.26  | Case 1:
% 232.15/43.26  | | 
% 232.15/43.26  | |   (13)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) =
% 232.15/43.26  | |           e0)
% 232.15/43.26  | | 
% 232.15/43.26  | | BETA: splitting (13) gives:
% 232.15/43.26  | | 
% 232.15/43.26  | | Case 1:
% 232.15/43.26  | | | 
% 232.15/43.26  | | |   (14)  all_57_0 = e0 & op(e3, e3) = e0
% 232.15/43.26  | | | 
% 232.15/43.26  | | | ALPHA: (14) implies:
% 232.15/43.26  | | |   (15)  op(e3, e3) = e0
% 232.15/43.26  | | | 
% 232.15/43.26  | | | REF_CLOSE: (1), (4), (5), (15) are inconsistent by sub-proof #2494.
% 232.15/43.26  | | | 
% 232.15/43.26  | | Case 2:
% 232.15/43.26  | | | 
% 232.15/43.26  | | |   (16)  all_57_2 = e0 & op(e2, e3) = e0
% 232.15/43.26  | | | 
% 232.15/43.26  | | | ALPHA: (16) implies:
% 232.15/43.26  | | |   (17)  all_57_2 = e0
% 232.15/43.26  | | | 
% 232.15/43.26  | | | REF_CLOSE: (1), (2), (3), (5), (7), (8), (10), (11), (17) are inconsistent
% 232.15/43.26  | | |            by sub-proof #2231.
% 232.15/43.26  | | | 
% 232.15/43.26  | | End of split
% 232.15/43.26  | | 
% 232.15/43.26  | Case 2:
% 232.15/43.26  | | 
% 232.15/43.26  | |   (18)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) =
% 232.15/43.26  | |           e0)
% 232.15/43.26  | | 
% 232.15/43.26  | | BETA: splitting (18) gives:
% 232.15/43.26  | | 
% 232.15/43.26  | | Case 1:
% 232.15/43.26  | | | 
% 232.15/43.26  | | |   (19)  all_57_6 = e0 & op(e1, e3) = e0
% 232.15/43.26  | | | 
% 232.15/43.26  | | | ALPHA: (19) implies:
% 232.15/43.26  | | |   (20)  op(e1, e3) = e0
% 232.15/43.26  | | | 
% 232.15/43.26  | | | REF_CLOSE: (1), (6), (9), (20) are inconsistent by sub-proof #2154.
% 232.15/43.26  | | | 
% 232.15/43.26  | | Case 2:
% 232.15/43.26  | | | 
% 232.15/43.26  | | |   (21)  all_57_12 = e0 & op(e0, e3) = e0
% 232.15/43.26  | | | 
% 232.15/43.26  | | | ALPHA: (21) implies:
% 232.15/43.26  | | |   (22)  all_57_12 = e0
% 232.15/43.26  | | | 
% 232.15/43.26  | | | REF_CLOSE: (4), (8), (22) are inconsistent by sub-proof #2153.
% 232.15/43.26  | | | 
% 232.15/43.26  | | End of split
% 232.15/43.26  | | 
% 232.15/43.26  | End of split
% 232.15/43.26  | 
% 232.15/43.26  End of proof
% 232.15/43.26  
% 232.15/43.26  Sub-proof #2153 shows that the following formulas are inconsistent:
% 232.15/43.26  ----------------------------------------------------------------
% 232.15/43.26    (1)  all_57_12 = e3
% 232.15/43.26    (2)  all_57_12 = e0
% 232.15/43.26    (3)   ~ (e3 = e0)
% 232.15/43.26  
% 232.15/43.26  Begin of proof
% 232.15/43.26  | 
% 232.15/43.26  | COMBINE_EQS: (1), (2) imply:
% 232.15/43.26  |   (4)  e3 = e0
% 232.15/43.26  | 
% 232.15/43.26  | SIMP: (4) implies:
% 232.15/43.26  |   (5)  e3 = e0
% 232.15/43.26  | 
% 232.15/43.26  | REDUCE: (3), (5) imply:
% 232.15/43.26  |   (6)  $false
% 232.15/43.26  | 
% 232.15/43.26  | CLOSE: (6) is inconsistent.
% 232.15/43.26  | 
% 232.15/43.26  End of proof
% 232.15/43.26  
% 232.15/43.26  Sub-proof #2154 shows that the following formulas are inconsistent:
% 232.15/43.26  ----------------------------------------------------------------
% 232.15/43.26    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.26           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.26    (2)  op(e1, e3) = all_53_2
% 232.15/43.26    (3)  op(e1, e3) = e0
% 232.15/43.26    (4)   ~ (all_53_2 = e0)
% 232.15/43.26  
% 232.15/43.26  Begin of proof
% 232.15/43.26  | 
% 232.15/43.26  | GROUND_INST: instantiating (1) with all_53_2, e0, e3, e1, simplifying with
% 232.15/43.26  |              (2), (3) gives:
% 232.15/43.26  |   (5)  all_53_2 = e0
% 232.15/43.26  | 
% 232.15/43.26  | REDUCE: (4), (5) imply:
% 232.15/43.26  |   (6)  $false
% 232.15/43.26  | 
% 232.15/43.26  | CLOSE: (6) is inconsistent.
% 232.15/43.26  | 
% 232.15/43.26  End of proof
% 232.15/43.26  
% 232.15/43.26  Sub-proof #2155 shows that the following formulas are inconsistent:
% 232.15/43.26  ----------------------------------------------------------------
% 232.15/43.26    (1)  op(e2, e3) = all_53_1
% 232.15/43.26    (2)   ~ (e3 = e1)
% 232.15/43.26    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.26           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.26    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1)
% 232.15/43.26    (5)  op(e3, e3) = e3
% 232.15/43.26    (6)   ~ (all_53_1 = e1)
% 232.15/43.26  
% 232.15/43.26  Begin of proof
% 232.15/43.26  | 
% 232.15/43.26  | BETA: splitting (4) gives:
% 232.15/43.26  | 
% 232.15/43.26  | Case 1:
% 232.15/43.26  | | 
% 232.15/43.26  | |   (7)  all_57_0 = e1 & op(e3, e3) = e1
% 232.15/43.26  | | 
% 232.15/43.26  | | ALPHA: (7) implies:
% 232.15/43.26  | |   (8)  op(e3, e3) = e1
% 232.15/43.26  | | 
% 232.15/43.26  | | REF_CLOSE: (2), (3), (5), (8) are inconsistent by sub-proof #2495.
% 232.15/43.26  | | 
% 232.15/43.26  | Case 2:
% 232.15/43.26  | | 
% 232.15/43.26  | |   (9)  all_57_2 = e1 & op(e2, e3) = e1
% 232.15/43.26  | | 
% 232.15/43.26  | | REF_CLOSE: (1), (3), (6), (9) are inconsistent by sub-proof #2156.
% 232.15/43.26  | | 
% 232.15/43.26  | End of split
% 232.15/43.26  | 
% 232.15/43.26  End of proof
% 232.15/43.26  
% 232.15/43.26  Sub-proof #2156 shows that the following formulas are inconsistent:
% 232.15/43.26  ----------------------------------------------------------------
% 232.15/43.26    (1)  all_57_2 = e1 & op(e2, e3) = e1
% 232.15/43.26    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.26           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.26    (3)  op(e2, e3) = all_53_1
% 232.15/43.26    (4)   ~ (all_53_1 = e1)
% 232.15/43.26  
% 232.15/43.26  Begin of proof
% 232.15/43.26  | 
% 232.15/43.26  | ALPHA: (1) implies:
% 232.15/43.26  |   (5)  op(e2, e3) = e1
% 232.15/43.26  | 
% 232.15/43.26  | GROUND_INST: instantiating (2) with all_53_1, e1, e3, e2, simplifying with
% 232.15/43.26  |              (3), (5) gives:
% 232.15/43.26  |   (6)  all_53_1 = e1
% 232.15/43.26  | 
% 232.15/43.26  | REDUCE: (4), (6) imply:
% 232.15/43.26  |   (7)  $false
% 232.15/43.26  | 
% 232.15/43.26  | CLOSE: (7) is inconsistent.
% 232.15/43.26  | 
% 232.15/43.26  End of proof
% 232.15/43.26  
% 232.15/43.26  Sub-proof #2157 shows that the following formulas are inconsistent:
% 232.15/43.26  ----------------------------------------------------------------
% 232.15/43.26    (1)   ~ (all_53_6 = e2)
% 232.15/43.26    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.26           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.26    (3)  all_55_9 = all_53_6
% 232.15/43.26    (4)  all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 232.15/43.26    (5)   ~ (all_53_6 = e1)
% 232.15/43.26    (6)  op(e0, e0) = e0
% 232.15/43.26    (7)  op(e1, e2) = all_52_19
% 232.15/43.26    (8)  op(all_52_19, all_52_19) = e2
% 232.15/43.26    (9)  op(e1, e2) = all_53_6
% 232.15/43.26  
% 232.15/43.26  Begin of proof
% 232.15/43.26  | 
% 232.15/43.26  | BETA: splitting (4) gives:
% 232.15/43.26  | 
% 232.15/43.26  | Case 1:
% 232.15/43.26  | | 
% 232.15/43.26  | |   (10)  all_55_9 = e2
% 232.15/43.26  | | 
% 232.15/43.26  | | REF_CLOSE: (1), (3), (10) are inconsistent by sub-proof #2274.
% 232.15/43.26  | | 
% 232.15/43.26  | Case 2:
% 232.15/43.26  | | 
% 232.15/43.26  | |   (11)   ~ (all_55_9 = e2)
% 232.15/43.26  | |   (12)  all_55_9 = e1 | all_55_9 = e0
% 232.15/43.26  | | 
% 232.15/43.27  | | BETA: splitting (12) gives:
% 232.15/43.27  | | 
% 232.15/43.27  | | Case 1:
% 232.15/43.27  | | | 
% 232.15/43.27  | | |   (13)  all_55_9 = e1
% 232.15/43.27  | | | 
% 232.15/43.27  | | | REF_CLOSE: (3), (5), (13) are inconsistent by sub-proof #2273.
% 232.15/43.27  | | | 
% 232.15/43.27  | | Case 2:
% 232.15/43.27  | | | 
% 232.15/43.27  | | |   (14)  all_55_9 = e0
% 232.15/43.27  | | | 
% 232.15/43.27  | | | COMBINE_EQS: (3), (14) imply:
% 232.15/43.27  | | |   (15)  all_53_6 = e0
% 232.15/43.27  | | | 
% 232.15/43.27  | | | SIMP: (15) implies:
% 232.15/43.27  | | |   (16)  all_53_6 = e0
% 232.15/43.27  | | | 
% 232.15/43.27  | | | REDUCE: (1), (16) imply:
% 232.15/43.27  | | |   (17)   ~ (e2 = e0)
% 232.15/43.27  | | | 
% 232.15/43.27  | | | SIMP: (17) implies:
% 232.15/43.27  | | |   (18)   ~ (e2 = e0)
% 232.15/43.27  | | | 
% 232.15/43.27  | | | REDUCE: (9), (16) imply:
% 232.15/43.27  | | |   (19)  op(e1, e2) = e0
% 232.15/43.27  | | | 
% 232.15/43.27  | | | REF_CLOSE: (2), (6), (7), (8), (18), (19) are inconsistent by sub-proof
% 232.15/43.27  | | |            #2158.
% 232.15/43.27  | | | 
% 232.15/43.27  | | End of split
% 232.15/43.27  | | 
% 232.15/43.27  | End of split
% 232.15/43.27  | 
% 232.15/43.27  End of proof
% 232.15/43.27  
% 232.15/43.27  Sub-proof #2158 shows that the following formulas are inconsistent:
% 232.15/43.27  ----------------------------------------------------------------
% 232.15/43.27    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.27           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.27    (2)  op(e1, e2) = e0
% 232.15/43.27    (3)   ~ (e2 = e0)
% 232.15/43.27    (4)  op(e0, e0) = e0
% 232.15/43.27    (5)  op(e1, e2) = all_52_19
% 232.15/43.27    (6)  op(all_52_19, all_52_19) = e2
% 232.15/43.27  
% 232.15/43.27  Begin of proof
% 232.15/43.27  | 
% 232.15/43.27  | GROUND_INST: instantiating (1) with e0, all_52_19, e2, e1, simplifying with
% 232.15/43.27  |              (2), (5) gives:
% 232.15/43.27  |   (7)  all_52_19 = e0
% 232.15/43.27  | 
% 232.15/43.27  | REDUCE: (6), (7) imply:
% 232.15/43.27  |   (8)  op(e0, e0) = e2
% 232.15/43.27  | 
% 232.15/43.27  | GROUND_INST: instantiating (1) with e0, e2, e0, e0, simplifying with (4), (8)
% 232.15/43.27  |              gives:
% 232.15/43.27  |   (9)  e2 = e0
% 232.15/43.27  | 
% 232.15/43.27  | REDUCE: (3), (9) imply:
% 232.15/43.27  |   (10)  $false
% 232.15/43.27  | 
% 232.15/43.27  | CLOSE: (10) is inconsistent.
% 232.15/43.27  | 
% 232.15/43.27  End of proof
% 232.15/43.27  
% 232.15/43.27  Sub-proof #2159 shows that the following formulas are inconsistent:
% 232.15/43.27  ----------------------------------------------------------------
% 232.15/43.27    (1)  all_55_9 = all_53_6
% 232.15/43.27    (2)  all_55_9 = e3
% 232.15/43.27    (3)   ~ (all_53_6 = e3)
% 232.15/43.27  
% 232.15/43.27  Begin of proof
% 232.15/43.27  | 
% 232.15/43.27  | COMBINE_EQS: (1), (2) imply:
% 232.15/43.27  |   (4)  all_53_6 = e3
% 232.15/43.27  | 
% 232.15/43.27  | SIMP: (4) implies:
% 232.15/43.27  |   (5)  all_53_6 = e3
% 232.15/43.27  | 
% 232.15/43.27  | REDUCE: (3), (5) imply:
% 232.15/43.27  |   (6)  $false
% 232.15/43.27  | 
% 232.15/43.27  | CLOSE: (6) is inconsistent.
% 232.15/43.27  | 
% 232.15/43.27  End of proof
% 232.15/43.27  
% 232.15/43.27  Sub-proof #2160 shows that the following formulas are inconsistent:
% 232.15/43.27  ----------------------------------------------------------------
% 232.15/43.27    (1)   ~ (all_53_9 = e1)
% 232.15/43.27    (2)   ~ (all_53_9 = e0)
% 232.15/43.27    (3)  all_55_6 = all_53_9
% 232.15/43.27    (4)   ~ (all_53_9 = e2)
% 232.15/43.27    (5)  all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 232.15/43.27  
% 232.15/43.27  Begin of proof
% 232.15/43.27  | 
% 232.15/43.27  | BETA: splitting (5) gives:
% 232.15/43.27  | 
% 232.15/43.27  | Case 1:
% 232.15/43.27  | | 
% 232.15/43.27  | |   (6)  all_55_6 = e2
% 232.15/43.27  | | 
% 232.15/43.27  | | REF_CLOSE: (3), (4), (6) are inconsistent by sub-proof #2398.
% 232.15/43.27  | | 
% 232.15/43.27  | Case 2:
% 232.15/43.27  | | 
% 232.15/43.27  | |   (7)  all_55_6 = e1 | all_55_6 = e0
% 232.15/43.27  | | 
% 232.15/43.27  | | REF_CLOSE: (1), (2), (3), (7) are inconsistent by sub-proof #2161.
% 232.15/43.27  | | 
% 232.15/43.27  | End of split
% 232.15/43.27  | 
% 232.15/43.27  End of proof
% 232.15/43.27  
% 232.15/43.27  Sub-proof #2161 shows that the following formulas are inconsistent:
% 232.15/43.27  ----------------------------------------------------------------
% 232.15/43.27    (1)  all_55_6 = e1 | all_55_6 = e0
% 232.15/43.27    (2)  all_55_6 = all_53_9
% 232.15/43.27    (3)   ~ (all_53_9 = e1)
% 232.15/43.27    (4)   ~ (all_53_9 = e0)
% 232.15/43.27  
% 232.15/43.27  Begin of proof
% 232.15/43.27  | 
% 232.15/43.27  | BETA: splitting (1) gives:
% 232.15/43.27  | 
% 232.15/43.27  | Case 1:
% 232.15/43.27  | | 
% 232.15/43.27  | |   (5)  all_55_6 = e1
% 232.15/43.27  | | 
% 232.15/43.27  | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #2163.
% 232.15/43.27  | | 
% 232.15/43.27  | Case 2:
% 232.15/43.27  | | 
% 232.15/43.27  | |   (6)  all_55_6 = e0
% 232.15/43.27  | | 
% 232.15/43.27  | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #2162.
% 232.15/43.27  | | 
% 232.15/43.27  | End of split
% 232.15/43.27  | 
% 232.15/43.27  End of proof
% 232.15/43.27  
% 232.15/43.27  Sub-proof #2162 shows that the following formulas are inconsistent:
% 232.15/43.27  ----------------------------------------------------------------
% 232.15/43.27    (1)  all_55_6 = all_53_9
% 232.15/43.27    (2)  all_55_6 = e0
% 232.15/43.27    (3)   ~ (all_53_9 = e0)
% 232.15/43.27  
% 232.15/43.27  Begin of proof
% 232.15/43.27  | 
% 232.15/43.27  | COMBINE_EQS: (1), (2) imply:
% 232.15/43.27  |   (4)  all_53_9 = e0
% 232.15/43.27  | 
% 232.15/43.27  | SIMP: (4) implies:
% 232.15/43.27  |   (5)  all_53_9 = e0
% 232.15/43.27  | 
% 232.15/43.27  | REDUCE: (3), (5) imply:
% 232.15/43.27  |   (6)  $false
% 232.15/43.27  | 
% 232.15/43.27  | CLOSE: (6) is inconsistent.
% 232.15/43.27  | 
% 232.15/43.27  End of proof
% 232.15/43.27  
% 232.15/43.27  Sub-proof #2163 shows that the following formulas are inconsistent:
% 232.15/43.27  ----------------------------------------------------------------
% 232.15/43.27    (1)  all_55_6 = all_53_9
% 232.15/43.27    (2)  all_55_6 = e1
% 232.15/43.27    (3)   ~ (all_53_9 = e1)
% 232.15/43.27  
% 232.15/43.27  Begin of proof
% 232.15/43.27  | 
% 232.15/43.27  | COMBINE_EQS: (1), (2) imply:
% 232.15/43.27  |   (4)  all_53_9 = e1
% 232.15/43.27  | 
% 232.15/43.27  | SIMP: (4) implies:
% 232.15/43.27  |   (5)  all_53_9 = e1
% 232.15/43.27  | 
% 232.15/43.27  | REDUCE: (3), (5) imply:
% 232.15/43.27  |   (6)  $false
% 232.15/43.27  | 
% 232.15/43.27  | CLOSE: (6) is inconsistent.
% 232.15/43.27  | 
% 232.15/43.27  End of proof
% 232.15/43.27  
% 232.15/43.27  Sub-proof #2164 shows that the following formulas are inconsistent:
% 232.15/43.27  ----------------------------------------------------------------
% 232.15/43.27    (1)  op(e3, e1) = e0
% 232.15/43.27    (2)   ~ (all_53_8 = all_53_11)
% 232.15/43.27    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.27           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.27    (4)  all_55_14 = e1 | all_55_14 = e0
% 232.15/43.27    (5)   ~ (all_53_11 = e1)
% 232.15/43.27    (6)  all_55_14 = all_53_11
% 232.15/43.27    (7)  op(e3, e1) = all_53_8
% 232.15/43.27  
% 232.15/43.27  Begin of proof
% 232.15/43.27  | 
% 232.15/43.27  | BETA: splitting (4) gives:
% 232.15/43.27  | 
% 232.15/43.27  | Case 1:
% 232.15/43.27  | | 
% 232.15/43.27  | |   (8)  all_55_14 = e1
% 232.15/43.27  | | 
% 232.15/43.27  | | REF_CLOSE: (5), (6), (8) are inconsistent by sub-proof #2165.
% 232.15/43.27  | | 
% 232.15/43.27  | Case 2:
% 232.15/43.27  | | 
% 232.15/43.27  | |   (9)  all_55_14 = e0
% 232.15/43.27  | | 
% 232.15/43.27  | | COMBINE_EQS: (6), (9) imply:
% 232.15/43.27  | |   (10)  all_53_11 = e0
% 232.15/43.27  | | 
% 232.15/43.27  | | SIMP: (10) implies:
% 232.15/43.27  | |   (11)  all_53_11 = e0
% 232.15/43.27  | | 
% 232.15/43.27  | | REDUCE: (2), (11) imply:
% 232.15/43.27  | |   (12)   ~ (all_53_8 = e0)
% 232.15/43.27  | | 
% 232.15/43.27  | | REF_CLOSE: (1), (3), (7), (12) are inconsistent by sub-proof #2267.
% 232.15/43.27  | | 
% 232.15/43.27  | End of split
% 232.15/43.27  | 
% 232.15/43.27  End of proof
% 232.15/43.27  
% 232.15/43.27  Sub-proof #2165 shows that the following formulas are inconsistent:
% 232.15/43.27  ----------------------------------------------------------------
% 232.15/43.27    (1)  all_55_14 = all_53_11
% 232.15/43.27    (2)  all_55_14 = e1
% 232.15/43.27    (3)   ~ (all_53_11 = e1)
% 232.15/43.27  
% 232.15/43.27  Begin of proof
% 232.15/43.27  | 
% 232.15/43.27  | COMBINE_EQS: (1), (2) imply:
% 232.15/43.27  |   (4)  all_53_11 = e1
% 232.15/43.27  | 
% 232.15/43.27  | SIMP: (4) implies:
% 232.15/43.27  |   (5)  all_53_11 = e1
% 232.15/43.27  | 
% 232.15/43.27  | REDUCE: (3), (5) imply:
% 232.15/43.27  |   (6)  $false
% 232.15/43.27  | 
% 232.15/43.27  | CLOSE: (6) is inconsistent.
% 232.15/43.27  | 
% 232.15/43.27  End of proof
% 232.15/43.27  
% 232.15/43.27  Sub-proof #2166 shows that the following formulas are inconsistent:
% 232.15/43.27  ----------------------------------------------------------------
% 232.15/43.27    (1)  all_55_4 = all_53_1
% 232.15/43.27    (2)  all_55_4 = e1
% 232.15/43.27    (3)   ~ (all_53_1 = e1)
% 232.15/43.27  
% 232.15/43.27  Begin of proof
% 232.15/43.27  | 
% 232.15/43.27  | COMBINE_EQS: (1), (2) imply:
% 232.15/43.27  |   (4)  all_53_1 = e1
% 232.15/43.27  | 
% 232.15/43.27  | SIMP: (4) implies:
% 232.15/43.27  |   (5)  all_53_1 = e1
% 232.15/43.27  | 
% 232.15/43.27  | REDUCE: (3), (5) imply:
% 232.15/43.27  |   (6)  $false
% 232.15/43.27  | 
% 232.15/43.27  | CLOSE: (6) is inconsistent.
% 232.15/43.27  | 
% 232.15/43.27  End of proof
% 232.15/43.27  
% 232.15/43.27  Sub-proof #2167 shows that the following formulas are inconsistent:
% 232.15/43.27  ----------------------------------------------------------------
% 232.15/43.27    (1)  op(e3, e1) = e0
% 232.15/43.27    (2)  op(e3, e1) = all_52_5
% 232.15/43.27    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.27           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.27    (4)  op(all_52_5, all_52_5) = e1
% 232.15/43.27    (5)   ~ (e1 = e0)
% 232.15/43.27    (6)  op(e0, e0) = e0
% 232.15/43.27  
% 232.15/43.27  Begin of proof
% 232.15/43.27  | 
% 232.15/43.27  | GROUND_INST: instantiating (3) with e0, all_52_5, e1, e3, simplifying with
% 232.15/43.27  |              (1), (2) gives:
% 232.15/43.27  |   (7)  all_52_5 = e0
% 232.15/43.27  | 
% 232.15/43.27  | REDUCE: (4), (7) imply:
% 232.15/43.27  |   (8)  op(e0, e0) = e1
% 232.15/43.27  | 
% 232.15/43.27  | GROUND_INST: instantiating (3) with e0, e1, e0, e0, simplifying with (6), (8)
% 232.15/43.27  |              gives:
% 232.15/43.27  |   (9)  e1 = e0
% 232.15/43.27  | 
% 232.15/43.27  | REDUCE: (5), (9) imply:
% 232.15/43.27  |   (10)  $false
% 232.15/43.27  | 
% 232.15/43.27  | CLOSE: (10) is inconsistent.
% 232.15/43.27  | 
% 232.15/43.27  End of proof
% 232.15/43.27  
% 232.15/43.27  Sub-proof #2168 shows that the following formulas are inconsistent:
% 232.15/43.27  ----------------------------------------------------------------
% 232.15/43.27    (1)  all_55_4 = all_53_1
% 232.15/43.27    (2)  all_55_4 = e2
% 232.15/43.27    (3)   ~ (all_53_1 = e2)
% 232.15/43.27  
% 232.15/43.27  Begin of proof
% 232.15/43.27  | 
% 232.15/43.27  | COMBINE_EQS: (1), (2) imply:
% 232.15/43.27  |   (4)  all_53_1 = e2
% 232.15/43.27  | 
% 232.15/43.27  | SIMP: (4) implies:
% 232.15/43.27  |   (5)  all_53_1 = e2
% 232.15/43.27  | 
% 232.15/43.27  | REDUCE: (3), (5) imply:
% 232.15/43.27  |   (6)  $false
% 232.15/43.27  | 
% 232.15/43.27  | CLOSE: (6) is inconsistent.
% 232.15/43.27  | 
% 232.15/43.27  End of proof
% 232.15/43.27  
% 232.15/43.27  Sub-proof #2169 shows that the following formulas are inconsistent:
% 232.15/43.27  ----------------------------------------------------------------
% 232.15/43.27    (1)  all_55_3 = all_53_12
% 232.15/43.27    (2)  all_55_3 = e3
% 232.15/43.27    (3)   ~ (all_53_12 = e3)
% 232.15/43.27  
% 232.15/43.27  Begin of proof
% 232.15/43.27  | 
% 232.15/43.27  | COMBINE_EQS: (1), (2) imply:
% 232.15/43.27  |   (4)  all_53_12 = e3
% 232.15/43.27  | 
% 232.15/43.27  | SIMP: (4) implies:
% 232.15/43.27  |   (5)  all_53_12 = e3
% 232.15/43.27  | 
% 232.15/43.27  | REDUCE: (3), (5) imply:
% 232.15/43.27  |   (6)  $false
% 232.15/43.27  | 
% 232.15/43.27  | CLOSE: (6) is inconsistent.
% 232.15/43.27  | 
% 232.15/43.27  End of proof
% 232.15/43.27  
% 232.15/43.27  Sub-proof #2170 shows that the following formulas are inconsistent:
% 232.15/43.27  ----------------------------------------------------------------
% 232.15/43.27    (1)  all_55_4 = all_53_1
% 232.15/43.27    (2)  all_55_4 = e3
% 232.15/43.27    (3)   ~ (all_53_1 = e3)
% 232.15/43.27  
% 232.15/43.27  Begin of proof
% 232.15/43.27  | 
% 232.15/43.27  | COMBINE_EQS: (1), (2) imply:
% 232.15/43.27  |   (4)  all_53_1 = e3
% 232.15/43.27  | 
% 232.15/43.27  | SIMP: (4) implies:
% 232.15/43.27  |   (5)  all_53_1 = e3
% 232.15/43.27  | 
% 232.15/43.27  | REDUCE: (3), (5) imply:
% 232.15/43.27  |   (6)  $false
% 232.15/43.27  | 
% 232.15/43.27  | CLOSE: (6) is inconsistent.
% 232.15/43.27  | 
% 232.15/43.27  End of proof
% 232.15/43.27  
% 232.15/43.27  Sub-proof #2171 shows that the following formulas are inconsistent:
% 232.15/43.27  ----------------------------------------------------------------
% 232.15/43.27    (1)  all_55_7 = all_53_13
% 232.15/43.27    (2)  all_55_7 = e2
% 232.15/43.27    (3)   ~ (all_53_13 = e2)
% 232.15/43.27  
% 232.15/43.27  Begin of proof
% 232.15/43.27  | 
% 232.15/43.27  | COMBINE_EQS: (1), (2) imply:
% 232.15/43.27  |   (4)  all_53_13 = e2
% 232.15/43.27  | 
% 232.15/43.27  | SIMP: (4) implies:
% 232.15/43.27  |   (5)  all_53_13 = e2
% 232.15/43.27  | 
% 232.15/43.27  | REDUCE: (3), (5) imply:
% 232.15/43.27  |   (6)  $false
% 232.15/43.27  | 
% 232.15/43.27  | CLOSE: (6) is inconsistent.
% 232.15/43.27  | 
% 232.15/43.27  End of proof
% 232.15/43.27  
% 232.15/43.27  Sub-proof #2172 shows that the following formulas are inconsistent:
% 232.15/43.27  ----------------------------------------------------------------
% 232.15/43.27    (1)  all_55_13 = e3 | all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 232.15/43.27    (2)  op(e0, e0) = all_4_2
% 232.15/43.27    (3)  all_55_1 = e3 | all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 232.15/43.27    (4)  all_57_9 = e2
% 232.15/43.27    (5)   ~ (all_53_6 = all_53_14)
% 232.15/43.27    (6)   ~ (all_53_6 = e2)
% 232.15/43.27    (7)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 232.15/43.27         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 232.15/43.27    (8)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 232.15/43.27         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 232.15/43.27    (9)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 232.15/43.27         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 232.15/43.27    (10)   ~ (e3 = e1)
% 232.15/43.27    (11)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 232.15/43.27          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 232.15/43.27    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.27            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.27    (13)   ~ (all_53_3 = all_53_7)
% 232.15/43.27    (14)   ~ (all_6_2 = e3)
% 232.15/43.27    (15)  op(e1, e1) = all_6_2
% 232.15/43.27    (16)  all_55_11 = e3 | all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 232.15/43.27    (17)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 232.15/43.27          (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 232.15/43.27    (18)  all_55_9 = e3 | all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 232.15/43.27    (19)  all_55_9 = all_53_6
% 232.15/43.27    (20)   ~ (all_53_4 = all_53_12)
% 232.15/43.27    (21)   ~ (all_53_7 = e2)
% 232.15/43.27    (22)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 232.15/43.27          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 232.15/43.27    (23)   ~ (all_53_9 = all_53_11)
% 232.15/43.27    (24)   ~ (all_53_12 = all_53_13)
% 232.15/43.27    (25)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 232.15/43.27          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 232.15/43.27    (26)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 232.15/43.27          (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 232.15/43.27    (27)   ~ (e3 = e2)
% 232.15/43.27    (28)  all_55_6 = e3 | all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 232.15/43.27    (29)  all_55_1 = all_53_4
% 232.15/43.27    (30)  op(e1, e0) = all_53_14
% 232.15/43.27    (31)   ~ (all_53_6 = all_53_7)
% 232.15/43.27    (32)  all_55_7 = e3 | all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 232.15/43.27    (33)   ~ (e3 = e0)
% 232.15/43.27    (34)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 232.15/43.27          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 232.15/43.27    (35)  op(e3, e3) = e3
% 232.15/43.27    (36)  op(e3, e0) = e2
% 232.15/43.27    (37)   ~ (all_4_2 = e2)
% 232.15/43.27    (38)  op(e0, e3) = all_53_3
% 232.15/43.27    (39)   ~ (all_53_11 = e0)
% 232.15/43.27    (40)   ~ (all_53_4 = all_53_7)
% 232.15/43.27    (41)   ~ (all_53_7 = e0)
% 232.15/43.27    (42)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 232.15/43.27          | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 232.15/43.27            e1)
% 232.15/43.27    (43)   ~ (all_53_4 = all_53_8)
% 232.15/43.27    (44)  all_55_6 = all_53_9
% 232.15/43.27    (45)  op(e3, e2) = all_53_4
% 232.15/43.27    (46)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 232.15/43.27          (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 232.15/43.27    (47)   ~ (e2 = e0)
% 232.15/43.27    (48)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 232.15/43.27            op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 232.15/43.27            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3)
% 232.15/43.27            = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3,
% 232.15/43.27              e0) = all_52_7 & $i(all_52_1) & $i(all_52_3) & $i(all_52_5) &
% 232.15/43.27            $i(all_52_7)) | (all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 &
% 232.15/43.27            all_52_14 = e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11,
% 232.15/43.27              all_52_11) = e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15,
% 232.15/43.27              all_52_15) = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 232.15/43.27            op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 232.15/43.27            $i(all_52_11) & $i(all_52_13) & $i(all_52_15)) | (all_52_16 = e3 &
% 232.15/43.27            all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 & op(all_52_17,
% 232.15/43.27              all_52_17) = e3 & op(all_52_19, all_52_19) = e2 & op(all_52_21,
% 232.15/43.27              all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1, e3) =
% 232.15/43.27            all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 & op(e1,
% 232.15/43.27              e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 232.15/43.27            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 232.15/43.27            all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 232.15/43.27              all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 232.15/43.27              all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 232.15/43.27            op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 232.15/43.27            $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 232.15/43.27    (49)   ~ (all_53_9 = e2)
% 232.15/43.27    (50)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 232.15/43.27          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 232.15/43.27    (51)  op(e2, e2) = e2
% 232.15/43.27    (52)   ~ (e1 = e0)
% 232.15/43.27    (53)   ~ (all_53_3 = all_53_11)
% 232.15/43.27    (54)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 232.15/43.27          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 232.15/43.27    (55)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 232.15/43.27          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 232.15/43.27    (56)  all_55_14 = e3 | all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 232.15/43.27    (57)  op(e0, e0) = e0
% 232.15/43.27    (58)   ~ (all_53_7 = all_53_11)
% 232.15/43.27    (59)   ~ (all_53_14 = e0)
% 232.15/43.27    (60)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 232.15/43.27          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 232.15/43.27            e3)
% 232.15/43.27    (61)   ~ (all_53_4 = all_53_6)
% 232.15/43.27    (62)  op(e0, e2) = all_53_7
% 232.15/43.27    (63)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 232.15/43.27          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 232.15/43.27            e2)
% 232.15/43.27    (64)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 232.15/43.27              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 232.15/43.27                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 232.15/43.27                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 232.15/43.27    (65)   ~ (all_53_13 = e0)
% 232.15/43.27    (66)  op(e1, e1) = e2
% 232.15/43.27    (67)  all_55_13 = all_53_7
% 232.15/43.27    (68)  op(e2, e0) = all_53_13
% 232.15/43.27    (69)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 232.15/43.27          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 232.15/43.27    (70)  all_55_11 = all_53_14
% 232.15/43.27    (71)   ~ (all_53_12 = e3)
% 232.15/43.27    (72)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 232.15/43.27          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 232.15/43.27    (73)   ~ (all_53_12 = e0)
% 232.15/43.27    (74)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 232.15/43.27          (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 232.15/43.27    (75)   ~ (all_53_13 = all_53_14)
% 232.15/43.27    (76)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 232.15/43.27          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 232.15/43.27    (77)   ~ (e2 = e1)
% 232.15/43.27    (78)  op(e2, e1) = all_53_9
% 232.15/43.27    (79)  op(e1, e2) = all_53_6
% 232.15/43.27    (80)   ~ (all_6_2 = e0)
% 232.15/43.27    (81)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 232.15/43.27          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 232.15/43.27    (82)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 232.15/43.27          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 232.15/43.27    (83)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 232.15/43.27          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 232.15/43.27    (84)   ~ (all_53_12 = all_53_14)
% 232.15/43.27    (85)  all_55_14 = all_53_11
% 232.15/43.27    (86)  all_57_3 = e2
% 232.15/43.27    (87)  op(e3, e1) = all_53_8
% 232.15/43.27    (88)  all_55_7 = all_53_13
% 232.15/43.27    (89)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 232.15/43.27          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 232.15/43.27    (90)   ~ (all_53_4 = e3)
% 232.15/43.27    (91)  op(e3, e0) = all_53_12
% 232.15/43.27  
% 232.15/43.27  Begin of proof
% 232.15/43.27  | 
% 232.15/43.27  | BETA: splitting (63) gives:
% 232.15/43.27  | 
% 232.15/43.27  | Case 1:
% 232.15/43.27  | | 
% 232.15/43.27  | |   (92)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 232.15/43.27  | |           e2)
% 232.15/43.27  | | 
% 232.15/43.27  | | BETA: splitting (92) gives:
% 232.15/43.27  | | 
% 232.15/43.27  | | Case 1:
% 232.15/43.27  | | | 
% 232.15/43.27  | | |   (93)  all_57_12 = e2 & op(e0, e3) = e2
% 232.15/43.27  | | | 
% 232.15/43.27  | | | ALPHA: (93) implies:
% 232.15/43.27  | | |   (94)  all_57_12 = e2
% 232.15/43.27  | | |   (95)  op(e0, e3) = e2
% 232.15/43.27  | | | 
% 232.15/43.27  | | | GROUND_INST: instantiating (12) with all_53_3, e2, e3, e0, simplifying
% 232.15/43.27  | | |              with (38), (95) gives:
% 232.15/43.27  | | |   (96)  all_53_3 = e2
% 232.15/43.27  | | | 
% 232.15/43.27  | | | GROUND_INST: instantiating (12) with all_53_12, e2, e0, e3, simplifying
% 232.15/43.27  | | |              with (36), (91) gives:
% 232.15/43.27  | | |   (97)  all_53_12 = e2
% 232.15/43.27  | | | 
% 232.15/43.27  | | | REDUCE: (13), (96) imply:
% 232.15/43.27  | | |   (98)   ~ (all_53_7 = e2)
% 232.15/43.27  | | | 
% 232.15/43.27  | | | REDUCE: (53), (96) imply:
% 232.15/43.27  | | |   (99)   ~ (all_53_11 = e2)
% 232.15/43.27  | | | 
% 232.15/43.27  | | | SIMP: (99) implies:
% 232.15/43.27  | | |   (100)   ~ (all_53_11 = e2)
% 232.15/43.27  | | | 
% 232.15/43.27  | | | REDUCE: (20), (97) imply:
% 232.15/43.27  | | |   (101)   ~ (all_53_4 = e2)
% 232.15/43.27  | | | 
% 232.15/43.27  | | | REDUCE: (24), (97) imply:
% 232.15/43.27  | | |   (102)   ~ (all_53_13 = e2)
% 232.15/43.27  | | | 
% 232.15/43.27  | | | SIMP: (102) implies:
% 232.15/43.27  | | |   (103)   ~ (all_53_13 = e2)
% 232.15/43.27  | | | 
% 232.15/43.27  | | | REDUCE: (84), (97) imply:
% 232.15/43.27  | | |   (104)   ~ (all_53_14 = e2)
% 232.15/43.27  | | | 
% 232.15/43.27  | | | SIMP: (104) implies:
% 232.15/43.27  | | |   (105)   ~ (all_53_14 = e2)
% 232.15/43.27  | | | 
% 232.15/43.27  | | | REDUCE: (71), (97) imply:
% 232.15/43.27  | | |   (106)   ~ (e3 = e2)
% 232.15/43.27  | | | 
% 232.15/43.27  | | | BETA: splitting (48) gives:
% 232.15/43.27  | | | 
% 232.15/43.27  | | | Case 1:
% 232.15/43.27  | | | | 
% 232.15/43.27  | | | |   (107)  (all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 232.15/43.27  | | | |            & op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 232.15/43.27  | | | |            op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 232.15/43.27  | | | |            op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) =
% 232.15/43.27  | | | |            all_52_5 & op(e3, e0) = all_52_7 & $i(all_52_1) &
% 232.15/43.27  | | | |            $i(all_52_3) & $i(all_52_5) & $i(all_52_7)) | (all_52_8 = e3
% 232.15/43.27  | | | |            & all_52_10 = e2 & all_52_12 = e1 & all_52_14 = e0 &
% 232.15/43.27  | | | |            op(all_52_9, all_52_9) = e3 & op(all_52_11, all_52_11) = e2 &
% 232.15/43.27  | | | |            op(all_52_13, all_52_13) = e1 & op(all_52_15, all_52_15) = e0
% 232.15/43.27  | | | |            & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 & op(e2, e1)
% 232.15/43.27  | | | |            = all_52_13 & op(e2, e0) = all_52_15 & $i(all_52_9) &
% 232.15/43.27  | | | |            $i(all_52_11) & $i(all_52_13) & $i(all_52_15))
% 232.15/43.27  | | | | 
% 232.15/43.27  | | | | BETA: splitting (107) gives:
% 232.15/43.27  | | | | 
% 232.15/43.27  | | | | Case 1:
% 232.15/43.27  | | | | | 
% 232.15/43.27  | | | | |   (108)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0
% 232.15/43.27  | | | | |          & op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 &
% 232.15/43.27  | | | | |          op(all_52_5, all_52_5) = e1 & op(all_52_7, all_52_7) = e0 &
% 232.15/43.27  | | | | |          op(e3, e3) = all_52_1 & op(e3, e2) = all_52_3 & op(e3, e1) =
% 232.15/43.27  | | | | |          all_52_5 & op(e3, e0) = all_52_7 & $i(all_52_1) &
% 232.15/43.27  | | | | |          $i(all_52_3) & $i(all_52_5) & $i(all_52_7)
% 232.15/43.27  | | | | | 
% 232.15/43.27  | | | | | REF_CLOSE: (12), (36), (47), (51), (108) are inconsistent by sub-proof
% 232.15/43.27  | | | | |            #2296.
% 232.15/43.27  | | | | | 
% 232.15/43.27  | | | | Case 2:
% 232.15/43.27  | | | | | 
% 232.15/43.27  | | | | |   (109)  all_52_8 = e3 & all_52_10 = e2 & all_52_12 = e1 & all_52_14 =
% 232.15/43.27  | | | | |          e0 & op(all_52_9, all_52_9) = e3 & op(all_52_11, all_52_11) =
% 232.15/43.27  | | | | |          e2 & op(all_52_13, all_52_13) = e1 & op(all_52_15, all_52_15)
% 232.15/43.27  | | | | |          = e0 & op(e2, e3) = all_52_9 & op(e2, e2) = all_52_11 &
% 232.15/43.27  | | | | |          op(e2, e1) = all_52_13 & op(e2, e0) = all_52_15 &
% 232.15/43.27  | | | | |          $i(all_52_9) & $i(all_52_11) & $i(all_52_13) & $i(all_52_15)
% 232.15/43.27  | | | | | 
% 232.15/43.27  | | | | | ALPHA: (109) implies:
% 232.15/43.27  | | | | |   (110)  op(e2, e0) = all_52_15
% 232.15/43.27  | | | | |   (111)  op(e2, e1) = all_52_13
% 232.15/43.27  | | | | |   (112)  op(e2, e2) = all_52_11
% 232.15/43.27  | | | | |   (113)  op(all_52_15, all_52_15) = e0
% 232.15/43.27  | | | | |   (114)  op(all_52_13, all_52_13) = e1
% 232.15/43.27  | | | | |   (115)  op(all_52_11, all_52_11) = e2
% 232.15/43.27  | | | | | 
% 232.15/43.27  | | | | | GROUND_INST: instantiating (12) with all_53_13, all_52_15, e0, e2,
% 232.15/43.27  | | | | |              simplifying with (68), (110) gives:
% 232.15/43.27  | | | | |   (116)  all_53_13 = all_52_15
% 232.15/43.27  | | | | | 
% 232.15/43.27  | | | | | GROUND_INST: instantiating (12) with all_53_9, all_52_13, e1, e2,
% 232.15/43.27  | | | | |              simplifying with (78), (111) gives:
% 232.15/43.27  | | | | |   (117)  all_53_9 = all_52_13
% 232.15/43.27  | | | | | 
% 232.15/43.27  | | | | | GROUND_INST: instantiating (12) with e2, all_52_11, e2, e2,
% 232.15/43.27  | | | | |              simplifying with (51), (112) gives:
% 232.15/43.27  | | | | |   (118)  all_52_11 = e2
% 232.15/43.27  | | | | | 
% 232.15/43.27  | | | | | COMBINE_EQS: (88), (116) imply:
% 232.15/43.27  | | | | |   (119)  all_55_7 = all_52_15
% 232.15/43.27  | | | | | 
% 232.15/43.27  | | | | | COMBINE_EQS: (44), (117) imply:
% 232.15/43.27  | | | | |   (120)  all_55_6 = all_52_13
% 232.15/43.27  | | | | | 
% 232.15/43.27  | | | | | REDUCE: (23), (117) imply:
% 232.15/43.27  | | | | |   (121)   ~ (all_53_11 = all_52_13)
% 232.15/43.27  | | | | | 
% 232.15/43.27  | | | | | SIMP: (121) implies:
% 232.15/43.27  | | | | |   (122)   ~ (all_53_11 = all_52_13)
% 232.15/43.27  | | | | | 
% 232.15/43.27  | | | | | REDUCE: (49), (117) imply:
% 232.15/43.27  | | | | |   (123)   ~ (all_52_13 = e2)
% 232.15/43.27  | | | | | 
% 232.15/43.27  | | | | | REDUCE: (75), (116) imply:
% 232.15/43.27  | | | | |   (124)   ~ (all_53_14 = all_52_15)
% 232.15/43.27  | | | | | 
% 232.15/43.27  | | | | | SIMP: (124) implies:
% 232.15/43.27  | | | | |   (125)   ~ (all_53_14 = all_52_15)
% 232.15/43.27  | | | | | 
% 232.15/43.27  | | | | | REDUCE: (103), (116) imply:
% 232.15/43.27  | | | | |   (126)   ~ (all_52_15 = e2)
% 232.15/43.27  | | | | | 
% 232.15/43.27  | | | | | REDUCE: (65), (116) imply:
% 232.15/43.27  | | | | |   (127)   ~ (all_52_15 = e0)
% 232.15/43.27  | | | | | 
% 232.15/43.27  | | | | | BETA: splitting (3) gives:
% 232.15/43.27  | | | | | 
% 232.15/43.27  | | | | | Case 1:
% 232.15/43.27  | | | | | | 
% 232.15/43.27  | | | | | |   (128)  all_55_1 = e3
% 232.15/43.27  | | | | | | 
% 232.15/43.27  | | | | | | REF_CLOSE: (29), (90), (128) are inconsistent by sub-proof #2295.
% 232.15/43.27  | | | | | | 
% 232.15/43.27  | | | | | Case 2:
% 232.15/43.27  | | | | | | 
% 232.15/43.27  | | | | | |   (129)   ~ (all_55_1 = e3)
% 232.15/43.27  | | | | | |   (130)  all_55_1 = e2 | all_55_1 = e1 | all_55_1 = e0
% 232.15/43.27  | | | | | | 
% 232.15/43.27  | | | | | | BETA: splitting (1) gives:
% 232.15/43.27  | | | | | | 
% 232.15/43.27  | | | | | | Case 1:
% 232.15/43.27  | | | | | | | 
% 232.15/43.27  | | | | | | |   (131)  all_55_13 = e3
% 232.15/43.27  | | | | | | | 
% 232.15/43.27  | | | | | | | COMBINE_EQS: (67), (131) imply:
% 232.15/43.27  | | | | | | |   (132)  all_53_7 = e3
% 232.15/43.27  | | | | | | | 
% 232.15/43.27  | | | | | | | SIMP: (132) implies:
% 232.15/43.27  | | | | | | |   (133)  all_53_7 = e3
% 232.15/43.27  | | | | | | | 
% 232.15/43.27  | | | | | | | REDUCE: (58), (133) imply:
% 232.15/43.27  | | | | | | |   (134)   ~ (all_53_11 = e3)
% 232.15/43.27  | | | | | | | 
% 232.15/43.27  | | | | | | | SIMP: (134) implies:
% 232.15/43.27  | | | | | | |   (135)   ~ (all_53_11 = e3)
% 232.15/43.27  | | | | | | | 
% 232.15/43.27  | | | | | | | BETA: splitting (56) gives:
% 232.15/43.27  | | | | | | | 
% 232.15/43.27  | | | | | | | Case 1:
% 232.15/43.27  | | | | | | | | 
% 232.15/43.27  | | | | | | | |   (136)  all_55_14 = e3
% 232.15/43.27  | | | | | | | | 
% 232.15/43.27  | | | | | | | | REF_CLOSE: (85), (135), (136) are inconsistent by sub-proof
% 232.15/43.27  | | | | | | | |            #2294.
% 232.15/43.27  | | | | | | | | 
% 232.15/43.27  | | | | | | | Case 2:
% 232.15/43.27  | | | | | | | | 
% 232.15/43.27  | | | | | | | |   (137)  all_55_14 = e2 | all_55_14 = e1 | all_55_14 = e0
% 232.15/43.27  | | | | | | | | 
% 232.15/43.27  | | | | | | | | BETA: splitting (137) gives:
% 232.15/43.27  | | | | | | | | 
% 232.15/43.27  | | | | | | | | Case 1:
% 232.15/43.27  | | | | | | | | | 
% 232.15/43.27  | | | | | | | | |   (138)  all_55_14 = e2
% 232.15/43.27  | | | | | | | | | 
% 232.15/43.27  | | | | | | | | | REF_CLOSE: (85), (100), (138) are inconsistent by sub-proof
% 232.15/43.27  | | | | | | | | |            #2293.
% 232.15/43.27  | | | | | | | | | 
% 232.15/43.27  | | | | | | | | Case 2:
% 232.15/43.27  | | | | | | | | | 
% 232.15/43.27  | | | | | | | | |   (139)  all_55_14 = e1 | all_55_14 = e0
% 232.15/43.27  | | | | | | | | | 
% 232.15/43.27  | | | | | | | | | BETA: splitting (139) gives:
% 232.15/43.27  | | | | | | | | | 
% 232.15/43.27  | | | | | | | | | Case 1:
% 232.15/43.27  | | | | | | | | | | 
% 232.15/43.27  | | | | | | | | | |   (140)  all_55_14 = e1
% 232.15/43.27  | | | | | | | | | | 
% 232.15/43.27  | | | | | | | | | | COMBINE_EQS: (85), (140) imply:
% 232.15/43.27  | | | | | | | | | |   (141)  all_53_11 = e1
% 232.15/43.27  | | | | | | | | | | 
% 232.15/43.27  | | | | | | | | | | SIMP: (141) implies:
% 232.15/43.27  | | | | | | | | | |   (142)  all_53_11 = e1
% 232.15/43.27  | | | | | | | | | | 
% 232.15/43.27  | | | | | | | | | | REDUCE: (122), (142) imply:
% 232.15/43.27  | | | | | | | | | |   (143)   ~ (all_52_13 = e1)
% 232.15/43.27  | | | | | | | | | | 
% 232.15/43.27  | | | | | | | | | | SIMP: (143) implies:
% 232.15/43.27  | | | | | | | | | |   (144)   ~ (all_52_13 = e1)
% 232.15/43.27  | | | | | | | | | | 
% 232.15/43.27  | | | | | | | | | | BETA: splitting (28) gives:
% 232.15/43.27  | | | | | | | | | | 
% 232.15/43.27  | | | | | | | | | | Case 1:
% 232.15/43.27  | | | | | | | | | | | 
% 232.15/43.27  | | | | | | | | | | |   (145)  all_55_6 = e3
% 232.15/43.27  | | | | | | | | | | | 
% 232.15/43.27  | | | | | | | | | | | COMBINE_EQS: (120), (145) imply:
% 232.15/43.27  | | | | | | | | | | |   (146)  all_52_13 = e3
% 232.15/43.27  | | | | | | | | | | | 
% 232.15/43.27  | | | | | | | | | | | SIMP: (146) implies:
% 232.15/43.27  | | | | | | | | | | |   (147)  all_52_13 = e3
% 232.15/43.27  | | | | | | | | | | | 
% 232.15/43.27  | | | | | | | | | | | REDUCE: (114), (147) imply:
% 232.15/43.27  | | | | | | | | | | |   (148)  op(e3, e3) = e1
% 232.15/43.27  | | | | | | | | | | | 
% 232.15/43.27  | | | | | | | | | | | REF_CLOSE: (10), (12), (35), (148) are inconsistent by
% 232.15/43.27  | | | | | | | | | | |            sub-proof #2495.
% 232.15/43.27  | | | | | | | | | | | 
% 232.15/43.27  | | | | | | | | | | Case 2:
% 232.15/43.27  | | | | | | | | | | | 
% 232.15/43.27  | | | | | | | | | | |   (149)  all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 232.15/43.27  | | | | | | | | | | | 
% 232.15/43.27  | | | | | | | | | | | REF_CLOSE: (12), (57), (114), (120), (123), (144), (149) are
% 232.15/43.27  | | | | | | | | | | |            inconsistent by sub-proof #2289.
% 232.15/43.27  | | | | | | | | | | | 
% 232.15/43.27  | | | | | | | | | | End of split
% 232.15/43.27  | | | | | | | | | | 
% 232.15/43.27  | | | | | | | | | Case 2:
% 232.15/43.27  | | | | | | | | | | 
% 232.15/43.27  | | | | | | | | | |   (150)  all_55_14 = e0
% 232.15/43.27  | | | | | | | | | | 
% 232.15/43.27  | | | | | | | | | | REF_CLOSE: (39), (85), (150) are inconsistent by sub-proof
% 232.15/43.27  | | | | | | | | | |            #2288.
% 232.15/43.27  | | | | | | | | | | 
% 232.15/43.27  | | | | | | | | | End of split
% 232.15/43.27  | | | | | | | | | 
% 232.15/43.27  | | | | | | | | End of split
% 232.15/43.27  | | | | | | | | 
% 232.15/43.27  | | | | | | | End of split
% 232.15/43.27  | | | | | | | 
% 232.15/43.27  | | | | | | Case 2:
% 232.15/43.27  | | | | | | | 
% 232.15/43.27  | | | | | | |   (151)   ~ (all_55_13 = e3)
% 232.15/43.27  | | | | | | |   (152)  all_55_13 = e2 | all_55_13 = e1 | all_55_13 = e0
% 232.15/43.27  | | | | | | | 
% 232.15/43.27  | | | | | | | REDUCE: (67), (151) imply:
% 232.15/43.27  | | | | | | |   (153)   ~ (all_53_7 = e3)
% 232.15/43.27  | | | | | | | 
% 232.15/43.27  | | | | | | | BETA: splitting (152) gives:
% 232.15/43.27  | | | | | | | 
% 232.15/43.27  | | | | | | | Case 1:
% 232.15/43.27  | | | | | | | | 
% 232.15/43.27  | | | | | | | |   (154)  all_55_13 = e2
% 232.15/43.27  | | | | | | | | 
% 232.15/43.27  | | | | | | | | REF_CLOSE: (21), (67), (154) are inconsistent by sub-proof
% 232.15/43.27  | | | | | | | |            #2287.
% 232.15/43.27  | | | | | | | | 
% 232.15/43.27  | | | | | | | Case 2:
% 232.15/43.27  | | | | | | | | 
% 232.15/43.27  | | | | | | | |   (155)   ~ (all_55_13 = e2)
% 232.15/43.27  | | | | | | | |   (156)  all_55_13 = e1 | all_55_13 = e0
% 232.15/43.27  | | | | | | | | 
% 232.15/43.27  | | | | | | | | BETA: splitting (156) gives:
% 232.15/43.27  | | | | | | | | 
% 232.15/43.27  | | | | | | | | Case 1:
% 232.15/43.27  | | | | | | | | | 
% 232.15/43.27  | | | | | | | | |   (157)  all_55_13 = e1
% 232.15/43.27  | | | | | | | | | 
% 232.15/43.27  | | | | | | | | | COMBINE_EQS: (67), (157) imply:
% 232.15/43.27  | | | | | | | | |   (158)  all_53_7 = e1
% 232.15/43.27  | | | | | | | | | 
% 232.15/43.27  | | | | | | | | | SIMP: (158) implies:
% 232.15/43.27  | | | | | | | | |   (159)  all_53_7 = e1
% 232.15/43.27  | | | | | | | | | 
% 232.15/43.27  | | | | | | | | | REDUCE: (40), (159) imply:
% 232.15/43.27  | | | | | | | | |   (160)   ~ (all_53_4 = e1)
% 232.15/43.27  | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | REDUCE: (31), (159) imply:
% 232.15/43.28  | | | | | | | | |   (161)   ~ (all_53_6 = e1)
% 232.15/43.28  | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | REDUCE: (153), (159) imply:
% 232.15/43.28  | | | | | | | | |   (162)   ~ (e3 = e1)
% 232.15/43.28  | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | REDUCE: (21), (159) imply:
% 232.15/43.28  | | | | | | | | |   (163)   ~ (e2 = e1)
% 232.15/43.28  | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | BETA: splitting (55) gives:
% 232.15/43.28  | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | Case 1:
% 232.15/43.28  | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | |   (164)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 232.15/43.28  | | | | | | | | | |            & op(e2, e2) = e3)
% 232.15/43.28  | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | REF_CLOSE: (12), (27), (45), (51), (90), (164) are
% 232.15/43.28  | | | | | | | | | |            inconsistent by sub-proof #2285.
% 232.15/43.28  | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | Case 2:
% 232.15/43.28  | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | |   (165)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3
% 232.15/43.28  | | | | | | | | | |            & op(e0, e2) = e3)
% 232.15/43.28  | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | BETA: splitting (165) gives:
% 232.15/43.28  | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | Case 1:
% 232.15/43.28  | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | |   (166)  all_57_7 = e3 & op(e1, e2) = e3
% 232.15/43.28  | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | ALPHA: (166) implies:
% 232.15/43.28  | | | | | | | | | | |   (167)  all_57_7 = e3
% 232.15/43.28  | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | BETA: splitting (46) gives:
% 232.15/43.28  | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | Case 1:
% 232.15/43.28  | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | |   (168)  (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 232.15/43.28  | | | | | | | | | | | |            & op(e2, e2) = e0)
% 232.15/43.28  | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | BETA: splitting (168) gives:
% 232.15/43.28  | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | Case 1:
% 232.15/43.28  | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | |   (169)  all_57_1 = e0 & op(e3, e2) = e0
% 232.15/43.28  | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | ALPHA: (169) implies:
% 232.15/43.28  | | | | | | | | | | | | |   (170)  all_57_1 = e0
% 232.15/43.28  | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | BETA: splitting (130) gives:
% 232.15/43.28  | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | Case 1:
% 232.15/43.28  | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | |   (171)  all_55_1 = e2
% 232.15/43.28  | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | REF_CLOSE: (29), (101), (171) are inconsistent by sub-proof
% 232.15/43.28  | | | | | | | | | | | | | |            #2284.
% 232.15/43.28  | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | Case 2:
% 232.15/43.28  | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | |   (172)  all_55_1 = e1 | all_55_1 = e0
% 232.15/43.28  | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | BETA: splitting (172) gives:
% 232.15/43.28  | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | Case 1:
% 232.15/43.28  | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | |   (173)  all_55_1 = e1
% 232.15/43.28  | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | REF_CLOSE: (29), (160), (173) are inconsistent by sub-proof
% 232.15/43.28  | | | | | | | | | | | | | | |            #2283.
% 232.15/43.28  | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | Case 2:
% 232.15/43.28  | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | |   (174)  all_55_1 = e0
% 232.15/43.28  | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | COMBINE_EQS: (29), (174) imply:
% 232.15/43.28  | | | | | | | | | | | | | | |   (175)  all_53_4 = e0
% 232.15/43.28  | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | SIMP: (175) implies:
% 232.15/43.28  | | | | | | | | | | | | | | |   (176)  all_53_4 = e0
% 232.15/43.28  | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | REDUCE: (61), (176) imply:
% 232.15/43.28  | | | | | | | | | | | | | | |   (177)   ~ (all_53_6 = e0)
% 232.15/43.28  | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | SIMP: (177) implies:
% 232.15/43.28  | | | | | | | | | | | | | | |   (178)   ~ (all_53_6 = e0)
% 232.15/43.28  | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | REDUCE: (160), (176) imply:
% 232.15/43.28  | | | | | | | | | | | | | | |   (179)   ~ (e1 = e0)
% 232.15/43.28  | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | BETA: splitting (18) gives:
% 232.15/43.28  | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | Case 1:
% 232.15/43.28  | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | |   (180)  all_55_9 = e3
% 232.15/43.28  | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | COMBINE_EQS: (19), (180) imply:
% 232.15/43.28  | | | | | | | | | | | | | | | |   (181)  all_53_6 = e3
% 232.15/43.28  | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | SIMP: (181) implies:
% 232.15/43.28  | | | | | | | | | | | | | | | |   (182)  all_53_6 = e3
% 232.15/43.28  | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | REDUCE: (5), (182) imply:
% 232.15/43.28  | | | | | | | | | | | | | | | |   (183)   ~ (all_53_14 = e3)
% 232.15/43.28  | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | SIMP: (183) implies:
% 232.15/43.28  | | | | | | | | | | | | | | | |   (184)   ~ (all_53_14 = e3)
% 232.15/43.28  | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | BETA: splitting (17) gives:
% 232.15/43.28  | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | Case 1:
% 232.15/43.28  | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | |   (185)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 232.15/43.28  | | | | | | | | | | | | | | | | |            & op(e3, e2) = e1)
% 232.15/43.28  | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (12), (35), (52), (170), (185) are
% 232.15/43.28  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2445.
% 232.15/43.28  | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | Case 2:
% 232.15/43.28  | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | |   (186)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 232.15/43.28  | | | | | | | | | | | | | | | | |            & op(e3, e0) = e1)
% 232.15/43.28  | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | BETA: splitting (186) gives:
% 232.15/43.28  | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | Case 1:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | |   (187)  all_57_4 = e1 & op(e3, e1) = e1
% 232.15/43.28  | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | ALPHA: (187) implies:
% 232.15/43.28  | | | | | | | | | | | | | | | | | |   (188)  all_57_4 = e1
% 232.15/43.28  | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | BETA: splitting (16) gives:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | Case 1:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | |   (189)  all_55_11 = e3
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (70), (184), (189) are inconsistent by sub-proof
% 232.15/43.28  | | | | | | | | | | | | | | | | | | |            #2497.
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | Case 2:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | |   (190)  all_55_11 = e2 | all_55_11 = e1 | all_55_11 = e0
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | Case 1:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | |   (191)  all_55_11 = e2
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (70), (105), (191) are inconsistent by sub-proof
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | |            #2282.
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | Case 2:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | |   (192)  all_55_11 = e1 | all_55_11 = e0
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | |   (193)  all_55_11 = e1
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (70), (193) imply:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | |   (194)  all_53_14 = e1
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | SIMP: (194) implies:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | |   (195)  all_53_14 = e1
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (195) imply:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | |   (196)   ~ (all_52_15 = e1)
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | SIMP: (196) implies:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | |   (197)   ~ (all_52_15 = e1)
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (32) gives:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | |   (198)  all_55_7 = e3
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (50), (71), (91), (113), (119), (127),
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | |            (170), (188), (197), (198) are inconsistent by
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2279.
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | |   (199)  all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (119), (126), (127), (197), (199) are inconsistent
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #2275.
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | End of split
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | |   (200)  all_55_11 = e0
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (59), (70), (200) are inconsistent by sub-proof
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | |            #2308.
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | End of split
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | End of split
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | End of split
% 232.15/43.28  | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | Case 2:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | |   (201)  all_57_9 = e1 & op(e3, e0) = e1
% 232.15/43.28  | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (77), (201) are inconsistent by sub-proof
% 232.15/43.28  | | | | | | | | | | | | | | | | | |            #2451.
% 232.15/43.28  | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | End of split
% 232.15/43.28  | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | End of split
% 232.15/43.28  | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | Case 2:
% 232.15/43.28  | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | |   (202)  all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 232.15/43.28  | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (19), (161), (178), (202) are inconsistent by
% 232.15/43.28  | | | | | | | | | | | | | | | |            sub-proof #2271.
% 232.15/43.28  | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | End of split
% 232.15/43.28  | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | End of split
% 232.15/43.28  | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | End of split
% 232.15/43.28  | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | Case 2:
% 232.15/43.28  | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | |   (203)  all_57_3 = e0 & op(e2, e2) = e0
% 232.15/43.28  | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | ALPHA: (203) implies:
% 232.15/43.28  | | | | | | | | | | | | |   (204)  op(e2, e2) = e0
% 232.15/43.28  | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | REF_CLOSE: (12), (47), (57), (112), (115), (204) are
% 232.15/43.28  | | | | | | | | | | | | |            inconsistent by sub-proof #2270.
% 232.15/43.28  | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | End of split
% 232.15/43.28  | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | Case 2:
% 232.15/43.28  | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | |   (205)  (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 232.15/43.28  | | | | | | | | | | | |            e0 & op(e0, e2) = e0)
% 232.15/43.28  | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | BETA: splitting (205) gives:
% 232.15/43.28  | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | Case 1:
% 232.15/43.28  | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | |   (206)  all_57_7 = e0 & op(e1, e2) = e0
% 232.15/43.28  | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | ALPHA: (206) implies:
% 232.15/43.28  | | | | | | | | | | | | |   (207)  all_57_7 = e0
% 232.15/43.28  | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | REF_CLOSE: (33), (167), (207) are inconsistent by sub-proof
% 232.15/43.28  | | | | | | | | | | | | |            #2269.
% 232.15/43.28  | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | Case 2:
% 232.15/43.28  | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | |   (208)  all_57_13 = e0 & op(e0, e2) = e0
% 232.15/43.28  | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | ALPHA: (208) implies:
% 232.15/43.28  | | | | | | | | | | | | |   (209)  op(e0, e2) = e0
% 232.15/43.28  | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | REF_CLOSE: (12), (41), (62), (209) are inconsistent by
% 232.15/43.28  | | | | | | | | | | | | |            sub-proof #2332.
% 232.15/43.28  | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | End of split
% 232.15/43.28  | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | End of split
% 232.15/43.28  | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | Case 2:
% 232.15/43.28  | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | |   (210)  all_57_13 = e3 & op(e0, e2) = e3
% 232.15/43.28  | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | ALPHA: (210) implies:
% 232.15/43.28  | | | | | | | | | | |   (211)  all_57_13 = e3
% 232.15/43.28  | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | BETA: splitting (42) gives:
% 232.15/43.28  | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | Case 1:
% 232.15/43.28  | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | |   (212)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 232.15/43.28  | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 232.15/43.28  | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | BETA: splitting (212) gives:
% 232.15/43.28  | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | Case 1:
% 232.15/43.28  | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | |   (213)  all_57_12 = e1 & op(e0, e3) = e1
% 232.15/43.28  | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | REF_CLOSE: (77), (94), (213) are inconsistent by sub-proof
% 232.15/43.28  | | | | | | | | | | | | |            #2388.
% 232.15/43.28  | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | Case 2:
% 232.15/43.28  | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | |   (214)  all_57_13 = e1 & op(e0, e2) = e1
% 232.15/43.28  | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | ALPHA: (214) implies:
% 232.15/43.28  | | | | | | | | | | | | |   (215)  all_57_13 = e1
% 232.15/43.28  | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | REF_CLOSE: (10), (211), (215) are inconsistent by sub-proof
% 232.15/43.28  | | | | | | | | | | | | |            #2268.
% 232.15/43.28  | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | End of split
% 232.15/43.28  | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | Case 2:
% 232.15/43.28  | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | |   (216)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 232.15/43.28  | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 232.15/43.28  | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | BETA: splitting (216) gives:
% 232.15/43.28  | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | Case 1:
% 232.15/43.28  | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | |   (217)  all_57_14 = e1 & op(e0, e1) = e1
% 232.15/43.28  | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | ALPHA: (217) implies:
% 232.15/43.28  | | | | | | | | | | | | |   (218)  all_57_14 = e1
% 232.15/43.28  | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | BETA: splitting (89) gives:
% 232.15/43.28  | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | Case 1:
% 232.15/43.28  | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | |   (219)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 232.15/43.28  | | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 232.15/43.28  | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 232.15/43.28  | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | Case 1:
% 232.15/43.28  | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | |   (220)  all_57_1 = e1 & op(e3, e2) = e1
% 232.15/43.28  | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | ALPHA: (220) implies:
% 232.15/43.28  | | | | | | | | | | | | | | |   (221)  all_57_1 = e1
% 232.15/43.28  | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | BETA: splitting (54) gives:
% 232.15/43.28  | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | Case 1:
% 232.15/43.28  | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | |   (222)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 232.15/43.28  | | | | | | | | | | | | | | | |            & op(e2, e1) = e3)
% 232.15/43.28  | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 232.15/43.28  | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | Case 1:
% 232.15/43.28  | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | |   (223)  all_57_4 = e3 & op(e3, e1) = e3
% 232.15/43.28  | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | ALPHA: (223) implies:
% 232.15/43.28  | | | | | | | | | | | | | | | | |   (224)  all_57_4 = e3
% 232.15/43.28  | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (12), (17), (22), (25), (27), (33), (35),
% 232.15/43.28  | | | | | | | | | | | | | | | | |            (47), (52), (77), (224) are inconsistent by
% 232.15/43.28  | | | | | | | | | | | | | | | | |            sub-proof #2474.
% 232.15/43.28  | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | Case 2:
% 232.15/43.28  | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | |   (225)  all_57_5 = e3 & op(e2, e1) = e3
% 232.15/43.28  | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | ALPHA: (225) implies:
% 232.15/43.28  | | | | | | | | | | | | | | | | |   (226)  all_57_5 = e3
% 232.15/43.28  | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | BETA: splitting (26) gives:
% 232.15/43.28  | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | Case 1:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | |   (227)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 232.15/43.28  | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e0)
% 232.15/43.28  | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | Case 1:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | |   (228)  all_57_4 = e0 & op(e3, e1) = e0
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | ALPHA: (228) implies:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | |   (229)  op(e3, e1) = e0
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | BETA: splitting (130) gives:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | Case 1:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | |   (230)  all_55_1 = e2
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (29), (101), (230) are inconsistent by sub-proof
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | |            #2284.
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | Case 2:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | |   (231)  all_55_1 = e1 | all_55_1 = e0
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | |   (232)  all_55_1 = e1
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (29), (160), (232) are inconsistent by sub-proof
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | |            #2283.
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | |   (233)  all_55_1 = e0
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (29), (233) imply:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | |   (234)  all_53_4 = e0
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | SIMP: (234) implies:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | |   (235)  all_53_4 = e0
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | REDUCE: (43), (235) imply:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | |   (236)   ~ (all_53_8 = e0)
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | SIMP: (236) implies:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | |   (237)   ~ (all_53_8 = e0)
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (87), (229), (237) are inconsistent by
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | |            sub-proof #2267.
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | End of split
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | End of split
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | Case 2:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | |   (238)  all_57_5 = e0 & op(e2, e1) = e0
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (33), (226), (238) are inconsistent by sub-proof
% 232.15/43.28  | | | | | | | | | | | | | | | | | | |            #2414.
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | End of split
% 232.15/43.28  | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | Case 2:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | |   (239)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 232.15/43.28  | | | | | | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 232.15/43.28  | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | Case 1:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | |   (240)  all_57_8 = e0 & op(e1, e1) = e0
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (15), (80), (240) are inconsistent by
% 232.15/43.28  | | | | | | | | | | | | | | | | | | |            sub-proof #2412.
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | Case 2:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | |   (241)  all_57_14 = e0 & op(e0, e1) = e0
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | ALPHA: (241) implies:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | |   (242)  all_57_14 = e0
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (218), (242) imply:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | |   (243)  e1 = e0
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (221), (243) imply:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | |   (244)  all_57_1 = e0
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | BETA: splitting (89) gives:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | Case 1:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (51), (52), (77), (219), (244) are
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2266.
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | Case 2:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | |   (245)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | |   (246)  all_57_7 = e1 & op(e1, e2) = e1
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (79), (161), (246) are inconsistent by
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | |            sub-proof #2265.
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | |   (247)  all_57_13 = e1 & op(e0, e2) = e1
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (211), (247) are inconsistent by sub-proof
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | |            #2264.
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | End of split
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | End of split
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | End of split
% 232.15/43.28  | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | End of split
% 232.15/43.28  | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | End of split
% 232.15/43.28  | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | Case 2:
% 232.15/43.28  | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | |   (248)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 232.15/43.28  | | | | | | | | | | | | | | | |            e3 & op(e0, e1) = e3)
% 232.15/43.28  | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | REF_CLOSE: (10), (12), (14), (15), (218), (248) are
% 232.15/43.28  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2263.
% 232.15/43.28  | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | End of split
% 232.15/43.28  | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | Case 2:
% 232.15/43.28  | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | |   (249)  all_57_3 = e1 & op(e2, e2) = e1
% 232.15/43.28  | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | ALPHA: (249) implies:
% 232.15/43.28  | | | | | | | | | | | | | | |   (250)  op(e2, e2) = e1
% 232.15/43.28  | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | REF_CLOSE: (12), (51), (77), (250) are inconsistent by
% 232.15/43.28  | | | | | | | | | | | | | | |            sub-proof #2306.
% 232.15/43.28  | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | End of split
% 232.15/43.28  | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | Case 2:
% 232.15/43.28  | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | |   (251)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 232.15/43.28  | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 232.15/43.28  | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | REF_CLOSE: (10), (12), (79), (161), (211), (251) are
% 232.15/43.28  | | | | | | | | | | | | | |            inconsistent by sub-proof #2262.
% 232.15/43.28  | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | End of split
% 232.15/43.28  | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | Case 2:
% 232.15/43.28  | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | |   (252)  all_57_15 = e1 & op(e0, e0) = e1
% 232.15/43.28  | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | ALPHA: (252) implies:
% 232.15/43.28  | | | | | | | | | | | | |   (253)  op(e0, e0) = e1
% 232.15/43.28  | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | REF_CLOSE: (12), (52), (57), (253) are inconsistent by
% 232.15/43.28  | | | | | | | | | | | | |            sub-proof #2290.
% 232.15/43.28  | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | End of split
% 232.15/43.28  | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | End of split
% 232.15/43.28  | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | End of split
% 232.15/43.28  | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | End of split
% 232.15/43.28  | | | | | | | | | 
% 232.15/43.28  | | | | | | | | Case 2:
% 232.15/43.28  | | | | | | | | | 
% 232.15/43.28  | | | | | | | | |   (254)  all_55_13 = e0
% 232.15/43.28  | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | REF_CLOSE: (41), (67), (254) are inconsistent by sub-proof
% 232.15/43.28  | | | | | | | | |            #2261.
% 232.15/43.28  | | | | | | | | | 
% 232.15/43.28  | | | | | | | | End of split
% 232.15/43.28  | | | | | | | | 
% 232.15/43.28  | | | | | | | End of split
% 232.15/43.28  | | | | | | | 
% 232.15/43.28  | | | | | | End of split
% 232.15/43.28  | | | | | | 
% 232.15/43.28  | | | | | End of split
% 232.15/43.28  | | | | | 
% 232.15/43.28  | | | | End of split
% 232.15/43.28  | | | | 
% 232.15/43.28  | | | Case 2:
% 232.15/43.28  | | | | 
% 232.15/43.28  | | | |   (255)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 =
% 232.15/43.28  | | | |            e0 & op(all_52_17, all_52_17) = e3 & op(all_52_19, all_52_19)
% 232.15/43.28  | | | |            = e2 & op(all_52_21, all_52_21) = e1 & op(all_52_23,
% 232.15/43.28  | | | |              all_52_23) = e0 & op(e1, e3) = all_52_17 & op(e1, e2) =
% 232.15/43.28  | | | |            all_52_19 & op(e1, e1) = all_52_21 & op(e1, e0) = all_52_23 &
% 232.15/43.28  | | | |            $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 232.15/43.28  | | | |            $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28
% 232.15/43.28  | | | |            = e1 & all_52_30 = e0 & op(all_52_25, all_52_25) = e3 &
% 232.15/43.28  | | | |            op(all_52_27, all_52_27) = e2 & op(all_52_29, all_52_29) = e1
% 232.15/43.28  | | | |            & op(all_52_31, all_52_31) = e0 & op(e0, e3) = all_52_25 &
% 232.15/43.28  | | | |            op(e0, e2) = all_52_27 & op(e0, e1) = all_52_29 & op(e0, e0)
% 232.15/43.28  | | | |            = all_52_31 & $i(all_52_25) & $i(all_52_27) & $i(all_52_29) &
% 232.15/43.28  | | | |            $i(all_52_31))
% 232.15/43.28  | | | | 
% 232.15/43.28  | | | | REF_CLOSE: (12), (27), (51), (66), (77), (95), (255) are inconsistent by
% 232.15/43.28  | | | |            sub-proof #2259.
% 232.15/43.28  | | | | 
% 232.15/43.28  | | | End of split
% 232.15/43.28  | | | 
% 232.15/43.28  | | Case 2:
% 232.15/43.28  | | | 
% 232.15/43.28  | | |   (256)  all_57_13 = e2 & op(e0, e2) = e2
% 232.15/43.28  | | | 
% 232.15/43.28  | | | ALPHA: (256) implies:
% 232.15/43.28  | | |   (257)  op(e0, e2) = e2
% 232.15/43.28  | | | 
% 232.15/43.28  | | | REF_CLOSE: (12), (21), (62), (257) are inconsistent by sub-proof #2335.
% 232.15/43.28  | | | 
% 232.15/43.28  | | End of split
% 232.15/43.28  | | 
% 232.15/43.28  | Case 2:
% 232.15/43.28  | | 
% 232.15/43.28  | |   (258)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 232.15/43.28  | |            e2)
% 232.15/43.28  | | 
% 232.15/43.28  | | BETA: splitting (258) gives:
% 232.15/43.28  | | 
% 232.15/43.28  | | Case 1:
% 232.15/43.28  | | | 
% 232.15/43.28  | | |   (259)  all_57_14 = e2 & op(e0, e1) = e2
% 232.15/43.28  | | | 
% 232.15/43.28  | | | ALPHA: (259) implies:
% 232.15/43.28  | | |   (260)  all_57_14 = e2
% 232.15/43.28  | | | 
% 232.15/43.28  | | | BETA: splitting (54) gives:
% 232.15/43.28  | | | 
% 232.15/43.28  | | | Case 1:
% 232.15/43.28  | | | | 
% 232.15/43.28  | | | |   (261)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1)
% 232.15/43.28  | | | |            = e3)
% 232.15/43.28  | | | | 
% 232.15/43.28  | | | | BETA: splitting (261) gives:
% 232.15/43.28  | | | | 
% 232.15/43.28  | | | | Case 1:
% 232.15/43.28  | | | | | 
% 232.15/43.28  | | | | |   (262)  all_57_4 = e3 & op(e3, e1) = e3
% 232.15/43.28  | | | | | 
% 232.15/43.28  | | | | | ALPHA: (262) implies:
% 232.15/43.28  | | | | |   (263)  all_57_4 = e3
% 232.15/43.28  | | | | | 
% 232.15/43.28  | | | | | REF_CLOSE: (10), (12), (17), (22), (25), (27), (33), (35), (47), (52),
% 232.15/43.28  | | | | |            (77), (263) are inconsistent by sub-proof #2474.
% 232.15/43.28  | | | | | 
% 232.15/43.28  | | | | Case 2:
% 232.15/43.28  | | | | | 
% 232.15/43.28  | | | | |   (264)  all_57_5 = e3 & op(e2, e1) = e3
% 232.15/43.28  | | | | | 
% 232.15/43.28  | | | | | ALPHA: (264) implies:
% 232.15/43.28  | | | | |   (265)  all_57_5 = e3
% 232.15/43.28  | | | | | 
% 232.15/43.28  | | | | | BETA: splitting (60) gives:
% 232.15/43.28  | | | | | 
% 232.15/43.28  | | | | | Case 1:
% 232.15/43.28  | | | | | | 
% 232.15/43.28  | | | | | |   (266)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 &
% 232.15/43.28  | | | | | |            op(e0, e2) = e3)
% 232.15/43.28  | | | | | | 
% 232.15/43.28  | | | | | | BETA: splitting (266) gives:
% 232.15/43.28  | | | | | | 
% 232.15/43.28  | | | | | | Case 1:
% 232.15/43.28  | | | | | | | 
% 232.15/43.28  | | | | | | |   (267)  all_57_12 = e3 & op(e0, e3) = e3
% 232.15/43.28  | | | | | | | 
% 232.15/43.28  | | | | | | | ALPHA: (267) implies:
% 232.15/43.28  | | | | | | |   (268)  all_57_12 = e3
% 232.15/43.28  | | | | | | | 
% 232.15/43.28  | | | | | | | BETA: splitting (76) gives:
% 232.15/43.28  | | | | | | | 
% 232.15/43.28  | | | | | | | Case 1:
% 232.15/43.28  | | | | | | | | 
% 232.15/43.28  | | | | | | | |   (269)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 &
% 232.15/43.28  | | | | | | | |            op(e2, e2) = e0)
% 232.15/43.28  | | | | | | | | 
% 232.15/43.28  | | | | | | | | BETA: splitting (269) gives:
% 232.15/43.28  | | | | | | | | 
% 232.15/43.28  | | | | | | | | Case 1:
% 232.15/43.28  | | | | | | | | | 
% 232.15/43.28  | | | | | | | | |   (270)  all_57_2 = e0 & op(e2, e3) = e0
% 232.15/43.28  | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | ALPHA: (270) implies:
% 232.15/43.28  | | | | | | | | |   (271)  all_57_2 = e0
% 232.15/43.28  | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | BETA: splitting (8) gives:
% 232.15/43.28  | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | Case 1:
% 232.15/43.28  | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | |   (272)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 232.15/43.28  | | | | | | | | | |            & op(e2, e3) = e1)
% 232.15/43.28  | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | BETA: splitting (272) gives:
% 232.15/43.28  | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | Case 1:
% 232.15/43.28  | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | |   (273)  all_57_0 = e1 & op(e3, e3) = e1
% 232.15/43.28  | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | ALPHA: (273) implies:
% 232.15/43.28  | | | | | | | | | | |   (274)  op(e3, e3) = e1
% 232.15/43.28  | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | REF_CLOSE: (10), (12), (35), (274) are inconsistent by
% 232.15/43.28  | | | | | | | | | | |            sub-proof #2495.
% 232.15/43.28  | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | Case 2:
% 232.15/43.28  | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | |   (275)  all_57_2 = e1 & op(e2, e3) = e1
% 232.15/43.28  | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | ALPHA: (275) implies:
% 232.15/43.28  | | | | | | | | | | |   (276)  all_57_2 = e1
% 232.15/43.28  | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | REF_CLOSE: (7), (10), (12), (27), (33), (35), (47), (51),
% 232.15/43.28  | | | | | | | | | | |            (52), (69), (72), (76), (77), (81), (82), (86),
% 232.15/43.28  | | | | | | | | | | |            (265), (268), (276) are inconsistent by sub-proof
% 232.15/43.28  | | | | | | | | | | |            #2235.
% 232.15/43.28  | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | End of split
% 232.15/43.28  | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | Case 2:
% 232.15/43.28  | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | |   (277)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1
% 232.15/43.28  | | | | | | | | | |            & op(e0, e3) = e1)
% 232.15/43.28  | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | BETA: splitting (277) gives:
% 232.15/43.28  | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | Case 1:
% 232.15/43.28  | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | |   (278)  all_57_6 = e1 & op(e1, e3) = e1
% 232.15/43.28  | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | ALPHA: (278) implies:
% 232.15/43.28  | | | | | | | | | | |   (279)  all_57_6 = e1
% 232.15/43.28  | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | REF_CLOSE: (12), (27), (35), (47), (77), (81), (268), (271),
% 232.15/43.28  | | | | | | | | | | |            (279) are inconsistent by sub-proof #2231.
% 232.15/43.28  | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | Case 2:
% 232.15/43.28  | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | |   (280)  all_57_12 = e1 & op(e0, e3) = e1
% 232.15/43.28  | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | REF_CLOSE: (10), (268), (280) are inconsistent by sub-proof
% 232.15/43.28  | | | | | | | | | | |            #2230.
% 232.15/43.28  | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | End of split
% 232.15/43.28  | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | End of split
% 232.15/43.28  | | | | | | | | | 
% 232.15/43.28  | | | | | | | | Case 2:
% 232.15/43.28  | | | | | | | | | 
% 232.15/43.28  | | | | | | | | |   (281)  all_57_3 = e0 & op(e2, e2) = e0
% 232.15/43.28  | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | ALPHA: (281) implies:
% 232.15/43.28  | | | | | | | | |   (282)  all_57_3 = e0
% 232.15/43.28  | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | REF_CLOSE: (7), (8), (10), (12), (27), (33), (35), (47), (52),
% 232.15/43.28  | | | | | | | | |            (69), (72), (77), (81), (82), (268), (282) are
% 232.15/43.28  | | | | | | | | |            inconsistent by sub-proof #2223.
% 232.15/43.28  | | | | | | | | | 
% 232.15/43.28  | | | | | | | | End of split
% 232.15/43.28  | | | | | | | | 
% 232.15/43.28  | | | | | | | Case 2:
% 232.15/43.28  | | | | | | | | 
% 232.15/43.28  | | | | | | | |   (283)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 &
% 232.15/43.28  | | | | | | | |            op(e2, e0) = e0)
% 232.15/43.28  | | | | | | | | 
% 232.15/43.28  | | | | | | | | REF_CLOSE: (12), (33), (65), (68), (265), (283) are inconsistent
% 232.15/43.28  | | | | | | | |            by sub-proof #2222.
% 232.15/43.28  | | | | | | | | 
% 232.15/43.28  | | | | | | | End of split
% 232.15/43.28  | | | | | | | 
% 232.15/43.28  | | | | | | Case 2:
% 232.15/43.28  | | | | | | | 
% 232.15/43.28  | | | | | | |   (284)  all_57_13 = e3 & op(e0, e2) = e3
% 232.15/43.28  | | | | | | | 
% 232.15/43.28  | | | | | | | ALPHA: (284) implies:
% 232.15/43.28  | | | | | | |   (285)  all_57_13 = e3
% 232.15/43.28  | | | | | | | 
% 232.15/43.28  | | | | | | | BETA: splitting (26) gives:
% 232.15/43.28  | | | | | | | 
% 232.15/43.28  | | | | | | | Case 1:
% 232.15/43.28  | | | | | | | | 
% 232.15/43.28  | | | | | | | |   (286)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 &
% 232.15/43.28  | | | | | | | |            op(e2, e1) = e0)
% 232.15/43.28  | | | | | | | | 
% 232.15/43.28  | | | | | | | | BETA: splitting (286) gives:
% 232.15/43.28  | | | | | | | | 
% 232.15/43.28  | | | | | | | | Case 1:
% 232.15/43.28  | | | | | | | | | 
% 232.15/43.28  | | | | | | | | |   (287)  all_57_4 = e0 & op(e3, e1) = e0
% 232.15/43.28  | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | ALPHA: (287) implies:
% 232.15/43.28  | | | | | | | | |   (288)  all_57_4 = e0
% 232.15/43.28  | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | BETA: splitting (81) gives:
% 232.15/43.28  | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | Case 1:
% 232.15/43.28  | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | |   (289)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 232.15/43.28  | | | | | | | | | |            & op(e2, e3) = e2)
% 232.15/43.28  | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | REF_CLOSE: (7), (10), (12), (27), (33), (35), (47), (51),
% 232.15/43.28  | | | | | | | | | |            (52), (69), (72), (76), (77), (86), (265), (289)
% 232.15/43.28  | | | | | | | | | |            are inconsistent by sub-proof #2238.
% 232.15/43.28  | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | Case 2:
% 232.15/43.28  | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | |   (290)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2
% 232.15/43.28  | | | | | | | | | |            & op(e0, e3) = e2)
% 232.15/43.28  | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | BETA: splitting (290) gives:
% 232.15/43.28  | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | Case 1:
% 232.15/43.28  | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | |   (291)  all_57_6 = e2 & op(e1, e3) = e2
% 232.15/43.28  | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | ALPHA: (291) implies:
% 232.15/43.28  | | | | | | | | | | |   (292)  all_57_6 = e2
% 232.15/43.28  | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | BETA: splitting (76) gives:
% 232.15/43.28  | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | Case 1:
% 232.15/43.28  | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | |   (293)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 232.15/43.28  | | | | | | | | | | | |            & op(e2, e2) = e0)
% 232.15/43.28  | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | BETA: splitting (293) gives:
% 232.15/43.28  | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | Case 1:
% 232.15/43.28  | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | |   (294)  all_57_2 = e0 & op(e2, e3) = e0
% 232.15/43.28  | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | ALPHA: (294) implies:
% 232.15/43.28  | | | | | | | | | | | | |   (295)  all_57_2 = e0
% 232.15/43.28  | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | BETA: splitting (7) gives:
% 232.15/43.28  | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | Case 1:
% 232.15/43.28  | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | |   (296)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 232.15/43.28  | | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 232.15/43.28  | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | BETA: splitting (296) gives:
% 232.15/43.28  | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | Case 1:
% 232.15/43.28  | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | |   (297)  all_57_2 = e1 & op(e2, e3) = e1
% 232.15/43.28  | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | ALPHA: (297) implies:
% 232.15/43.28  | | | | | | | | | | | | | | |   (298)  all_57_2 = e1
% 232.15/43.28  | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | REF_CLOSE: (12), (33), (47), (51), (52), (65), (68), (76),
% 232.15/43.28  | | | | | | | | | | | | | | |            (265), (298) are inconsistent by sub-proof #2469.
% 232.15/43.28  | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | Case 2:
% 232.15/43.28  | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | |   (299)  all_57_3 = e1 & op(e2, e2) = e1
% 232.15/43.28  | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | ALPHA: (299) implies:
% 232.15/43.28  | | | | | | | | | | | | | | |   (300)  op(e2, e2) = e1
% 232.15/43.28  | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | REF_CLOSE: (12), (51), (77), (300) are inconsistent by
% 232.15/43.28  | | | | | | | | | | | | | | |            sub-proof #2306.
% 232.15/43.28  | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | End of split
% 232.15/43.28  | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | Case 2:
% 232.15/43.28  | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | |   (301)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 232.15/43.28  | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 232.15/43.28  | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | BETA: splitting (301) gives:
% 232.15/43.28  | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | Case 1:
% 232.15/43.28  | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | |   (302)  all_57_5 = e1 & op(e2, e1) = e1
% 232.15/43.28  | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | REF_CLOSE: (10), (265), (302) are inconsistent by sub-proof
% 232.15/43.28  | | | | | | | | | | | | | | |            #2376.
% 232.15/43.28  | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | Case 2:
% 232.15/43.28  | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | |   (303)  all_57_10 = e1 & op(e2, e0) = e1
% 232.15/43.28  | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | ALPHA: (303) implies:
% 232.15/43.28  | | | | | | | | | | | | | | |   (304)  all_57_10 = e1
% 232.15/43.28  | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | BETA: splitting (11) gives:
% 232.15/43.28  | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | Case 1:
% 232.15/43.28  | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | |   (305)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 232.15/43.28  | | | | | | | | | | | | | | | |            & op(e1, e2) = e0)
% 232.15/43.28  | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | BETA: splitting (305) gives:
% 232.15/43.28  | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | Case 1:
% 232.15/43.28  | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | |   (306)  all_57_6 = e0 & op(e1, e3) = e0
% 232.15/43.28  | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | ALPHA: (306) implies:
% 232.15/43.28  | | | | | | | | | | | | | | | | |   (307)  all_57_6 = e0
% 232.15/43.28  | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | COMBINE_EQS: (292), (307) imply:
% 232.15/43.28  | | | | | | | | | | | | | | | | |   (308)  e2 = e0
% 232.15/43.28  | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | COMBINE_EQS: (86), (308) imply:
% 232.15/43.28  | | | | | | | | | | | | | | | | |   (309)  all_57_3 = e0
% 232.15/43.28  | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (47), (72), (77), (265), (295), (304), (309)
% 232.15/43.28  | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #2254.
% 232.15/43.28  | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | Case 2:
% 232.15/43.28  | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | |   (310)  all_57_7 = e0 & op(e1, e2) = e0
% 232.15/43.28  | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | ALPHA: (310) implies:
% 232.15/43.28  | | | | | | | | | | | | | | | | |   (311)  all_57_7 = e0
% 232.15/43.28  | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | BETA: splitting (89) gives:
% 232.15/43.28  | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | Case 1:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | |   (312)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 232.15/43.28  | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 232.15/43.28  | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | BETA: splitting (312) gives:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | Case 1:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | |   (313)  all_57_1 = e1 & op(e3, e2) = e1
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | ALPHA: (313) implies:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | |   (314)  all_57_1 = e1
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | BETA: splitting (74) gives:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | Case 1:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | |   (315)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | |            e3 & op(e2, e0) = e3)
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | BETA: splitting (315) gives:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | |   (316)  all_57_9 = e3 & op(e3, e0) = e3
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | ALPHA: (316) implies:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | |   (317)  op(e3, e0) = e3
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (71), (91), (317) are inconsistent by
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | |            sub-proof #2458.
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | |   (318)  all_57_10 = e3 & op(e2, e0) = e3
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | ALPHA: (318) implies:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | |   (319)  all_57_10 = e3
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (304), (319) are inconsistent by sub-proof
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | |            #2248.
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | End of split
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | Case 2:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | |   (320)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e0) = e3)
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | BETA: splitting (320) gives:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | |   (321)  all_57_11 = e3 & op(e1, e0) = e3
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | ALPHA: (321) implies:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | |   (322)  all_57_11 = e3
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (83) gives:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | |   (323)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e1)
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (323) gives:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | | |   (324)  all_57_6 = e1 & op(e1, e3) = e1
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (324) implies:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | | |   (325)  all_57_6 = e1
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (292), (325) imply:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | | |   (326)  e2 = e1
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (326) implies:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | | |   (327)  e2 = e1
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4), (327) imply:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | | |   (328)  all_57_9 = e1
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (22), (27), (35), (47), (77), (288), (314),
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | | |            (328) are inconsistent by sub-proof #2220.
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | | |   (329)  all_57_7 = e1 & op(e1, e2) = e1
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (329) implies:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | | |   (330)  all_57_7 = e1
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (311), (330) imply:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | | |   (331)  e1 = e0
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (331) implies:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | | |   (332)  e1 = e0
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (314), (332) imply:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | | |   (333)  all_57_1 = e0
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (10), (12), (17), (35), (52), (77), (288),
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | | |            (333) are inconsistent by sub-proof #2219.
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | | End of split
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | |   (334)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e1, e0) = e1)
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (12), (66), (77), (322), (334) are
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #2217.
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | End of split
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | Case 2:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | |   (335)  all_57_15 = e3 & op(e0, e0) = e3
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | ALPHA: (335) implies:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | |   (336)  all_57_15 = e3
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | |   (337)  op(e0, e0) = e3
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (12), (33), (42), (47), (52), (64), (77),
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | |            (260), (285), (336), (337) are inconsistent by
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | |            sub-proof #2212.
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | End of split
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | End of split
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | Case 2:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | |   (338)  all_57_3 = e1 & op(e2, e2) = e1
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | ALPHA: (338) implies:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | |   (339)  op(e2, e2) = e1
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (51), (77), (339) are inconsistent by
% 232.15/43.28  | | | | | | | | | | | | | | | | | | |            sub-proof #2306.
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | End of split
% 232.15/43.28  | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | Case 2:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | |   (340)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 232.15/43.28  | | | | | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 232.15/43.28  | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | BETA: splitting (340) gives:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | Case 1:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | |   (341)  all_57_7 = e1 & op(e1, e2) = e1
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | ALPHA: (341) implies:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | |   (342)  all_57_7 = e1
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (52), (311), (342) are inconsistent by sub-proof
% 232.15/43.28  | | | | | | | | | | | | | | | | | | |            #2211.
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | Case 2:
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | |   (343)  all_57_13 = e1 & op(e0, e2) = e1
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (285), (343) are inconsistent by sub-proof
% 232.15/43.28  | | | | | | | | | | | | | | | | | | |            #2264.
% 232.15/43.28  | | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | | End of split
% 232.15/43.28  | | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | End of split
% 232.15/43.28  | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | End of split
% 232.15/43.28  | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | Case 2:
% 232.15/43.28  | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | |   (344)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 232.15/43.28  | | | | | | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 232.15/43.28  | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | BETA: splitting (344) gives:
% 232.15/43.28  | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | Case 1:
% 232.15/43.28  | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | |   (345)  all_57_8 = e0 & op(e1, e1) = e0
% 232.15/43.28  | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (15), (80), (345) are inconsistent by
% 232.15/43.28  | | | | | | | | | | | | | | | | |            sub-proof #2412.
% 232.15/43.28  | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | Case 2:
% 232.15/43.28  | | | | | | | | | | | | | | | | | 
% 232.15/43.28  | | | | | | | | | | | | | | | | |   (346)  all_57_11 = e0 & op(e1, e0) = e0
% 232.15/43.29  | | | | | | | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (30), (59), (346) are inconsistent by
% 232.15/43.29  | | | | | | | | | | | | | | | | |            sub-proof #2341.
% 232.15/43.29  | | | | | | | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | | | | | | End of split
% 232.15/43.29  | | | | | | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | | | | | End of split
% 232.15/43.29  | | | | | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | | | | End of split
% 232.15/43.29  | | | | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | | | End of split
% 232.15/43.29  | | | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | | Case 2:
% 232.15/43.29  | | | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | | |   (347)  all_57_3 = e0 & op(e2, e2) = e0
% 232.15/43.29  | | | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | | | ALPHA: (347) implies:
% 232.15/43.29  | | | | | | | | | | | | |   (348)  all_57_3 = e0
% 232.15/43.29  | | | | | | | | | | | | |   (349)  op(e2, e2) = e0
% 232.15/43.29  | | | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | | | REF_CLOSE: (9), (10), (12), (14), (15), (27), (33), (34),
% 232.15/43.29  | | | | | | | | | | | | |            (47), (52), (54), (55), (66), (77), (89), (260),
% 232.15/43.29  | | | | | | | | | | | | |            (265), (285), (288), (348), (349) are inconsistent
% 232.15/43.29  | | | | | | | | | | | | |            by sub-proof #2187.
% 232.15/43.29  | | | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | | End of split
% 232.15/43.29  | | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | Case 2:
% 232.15/43.29  | | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | |   (350)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 232.15/43.29  | | | | | | | | | | | |            e0 & op(e2, e0) = e0)
% 232.15/43.29  | | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | | REF_CLOSE: (12), (33), (65), (68), (265), (350) are
% 232.15/43.29  | | | | | | | | | | | |            inconsistent by sub-proof #2222.
% 232.15/43.29  | | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | End of split
% 232.15/43.29  | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | Case 2:
% 232.15/43.29  | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | |   (351)  all_57_12 = e2 & op(e0, e3) = e2
% 232.15/43.29  | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | ALPHA: (351) implies:
% 232.15/43.29  | | | | | | | | | | |   (352)  all_57_12 = e2
% 232.15/43.29  | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | BETA: splitting (17) gives:
% 232.15/43.29  | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | Case 1:
% 232.15/43.29  | | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | |   (353)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 232.15/43.29  | | | | | | | | | | | |            & op(e3, e2) = e1)
% 232.15/43.29  | | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | | BETA: splitting (353) gives:
% 232.15/43.29  | | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | | Case 1:
% 232.15/43.29  | | | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | | |   (354)  all_57_0 = e1 & op(e3, e3) = e1
% 232.15/43.29  | | | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | | | ALPHA: (354) implies:
% 232.15/43.29  | | | | | | | | | | | | |   (355)  op(e3, e3) = e1
% 232.15/43.29  | | | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | | | REF_CLOSE: (10), (12), (35), (355) are inconsistent by
% 232.15/43.29  | | | | | | | | | | | | |            sub-proof #2495.
% 232.15/43.29  | | | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | | Case 2:
% 232.15/43.29  | | | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | | |   (356)  all_57_1 = e1 & op(e3, e2) = e1
% 232.15/43.29  | | | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | | | ALPHA: (356) implies:
% 232.15/43.29  | | | | | | | | | | | | |   (357)  all_57_1 = e1
% 232.15/43.29  | | | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | | | BETA: splitting (42) gives:
% 232.15/43.29  | | | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | | | Case 1:
% 232.15/43.29  | | | | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | | | |   (358)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 232.15/43.29  | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 232.15/43.29  | | | | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | | | | BETA: splitting (358) gives:
% 232.15/43.29  | | | | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | | | | Case 1:
% 232.15/43.29  | | | | | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | | | | |   (359)  all_57_12 = e1 & op(e0, e3) = e1
% 232.15/43.29  | | | | | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | | | | | ALPHA: (359) implies:
% 232.15/43.29  | | | | | | | | | | | | | | |   (360)  all_57_12 = e1
% 232.15/43.29  | | | | | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | | | | | COMBINE_EQS: (352), (360) imply:
% 232.15/43.29  | | | | | | | | | | | | | | |   (361)  e2 = e1
% 232.15/43.29  | | | | | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | | | | | SIMP: (361) implies:
% 232.15/43.29  | | | | | | | | | | | | | | |   (362)  e2 = e1
% 232.15/43.29  | | | | | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | | | | | COMBINE_EQS: (4), (362) imply:
% 232.15/43.29  | | | | | | | | | | | | | | |   (363)  all_57_9 = e1
% 232.15/43.29  | | | | | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | | | | | REF_CLOSE: (12), (22), (27), (35), (47), (77), (288), (357),
% 232.15/43.29  | | | | | | | | | | | | | | |            (363) are inconsistent by sub-proof #2220.
% 232.15/43.29  | | | | | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | | | | Case 2:
% 232.15/43.29  | | | | | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | | | | |   (364)  all_57_13 = e1 & op(e0, e2) = e1
% 232.15/43.29  | | | | | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | | | | | ALPHA: (364) implies:
% 232.15/43.29  | | | | | | | | | | | | | | |   (365)  all_57_13 = e1
% 232.15/43.29  | | | | | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | | | | | REF_CLOSE: (10), (285), (365) are inconsistent by sub-proof
% 232.15/43.29  | | | | | | | | | | | | | | |            #2268.
% 232.15/43.29  | | | | | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | | | | End of split
% 232.15/43.29  | | | | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | | | Case 2:
% 232.15/43.29  | | | | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | | | |   (366)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 232.15/43.29  | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 232.15/43.29  | | | | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | | | | BETA: splitting (366) gives:
% 232.15/43.29  | | | | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | | | | Case 1:
% 232.15/43.29  | | | | | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | | | | |   (367)  all_57_14 = e1 & op(e0, e1) = e1
% 232.15/43.29  | | | | | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | | | | | ALPHA: (367) implies:
% 232.15/43.29  | | | | | | | | | | | | | | |   (368)  all_57_14 = e1
% 232.15/43.29  | | | | | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | | | | | COMBINE_EQS: (260), (368) imply:
% 232.15/43.29  | | | | | | | | | | | | | | |   (369)  e2 = e1
% 232.15/43.29  | | | | | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | | | | | SIMP: (369) implies:
% 232.15/43.29  | | | | | | | | | | | | | | |   (370)  e2 = e1
% 232.15/43.29  | | | | | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | | | | | COMBINE_EQS: (4), (370) imply:
% 232.15/43.29  | | | | | | | | | | | | | | |   (371)  all_57_9 = e1
% 232.15/43.29  | | | | | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | | | | | REF_CLOSE: (12), (22), (27), (35), (47), (77), (288), (357),
% 232.15/43.29  | | | | | | | | | | | | | | |            (371) are inconsistent by sub-proof #2220.
% 232.15/43.29  | | | | | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | | | | Case 2:
% 232.15/43.29  | | | | | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | | | | |   (372)  all_57_15 = e1 & op(e0, e0) = e1
% 232.15/43.29  | | | | | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | | | | | ALPHA: (372) implies:
% 232.15/43.29  | | | | | | | | | | | | | | |   (373)  op(e0, e0) = e1
% 232.15/43.29  | | | | | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | | | | | REF_CLOSE: (10), (12), (15), (21), (26), (27), (33), (34),
% 232.15/43.29  | | | | | | | | | | | | | | |            (47), (52), (60), (62), (63), (64), (66), (77),
% 232.15/43.29  | | | | | | | | | | | | | | |            (80), (260), (265), (373) are inconsistent by
% 232.15/43.29  | | | | | | | | | | | | | | |            sub-proof #2174.
% 232.15/43.29  | | | | | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | | | | End of split
% 232.15/43.29  | | | | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | | | End of split
% 232.15/43.29  | | | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | | End of split
% 232.15/43.29  | | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | Case 2:
% 232.15/43.29  | | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | |   (374)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 232.15/43.29  | | | | | | | | | | | |            & op(e3, e0) = e1)
% 232.15/43.29  | | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | | BETA: splitting (374) gives:
% 232.15/43.29  | | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | | Case 1:
% 232.15/43.29  | | | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | | |   (375)  all_57_4 = e1 & op(e3, e1) = e1
% 232.15/43.29  | | | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | | | REF_CLOSE: (12), (15), (26), (33), (47), (52), (80), (260),
% 232.15/43.29  | | | | | | | | | | | | |            (265), (375) are inconsistent by sub-proof #2186.
% 232.15/43.29  | | | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | | Case 2:
% 232.15/43.29  | | | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | | |   (376)  all_57_9 = e1 & op(e3, e0) = e1
% 232.15/43.29  | | | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | | | REF_CLOSE: (4), (77), (376) are inconsistent by sub-proof
% 232.15/43.29  | | | | | | | | | | | | |            #2451.
% 232.15/43.29  | | | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | | End of split
% 232.15/43.29  | | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | | End of split
% 232.15/43.29  | | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | | End of split
% 232.15/43.29  | | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | End of split
% 232.15/43.29  | | | | | | | | | 
% 232.15/43.29  | | | | | | | | Case 2:
% 232.15/43.29  | | | | | | | | | 
% 232.15/43.29  | | | | | | | | |   (377)  all_57_5 = e0 & op(e2, e1) = e0
% 232.15/43.29  | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | REF_CLOSE: (33), (265), (377) are inconsistent by sub-proof
% 232.15/43.29  | | | | | | | | |            #2414.
% 232.15/43.29  | | | | | | | | | 
% 232.15/43.29  | | | | | | | | End of split
% 232.15/43.29  | | | | | | | | 
% 232.15/43.29  | | | | | | | Case 2:
% 232.15/43.29  | | | | | | | | 
% 232.15/43.29  | | | | | | | |   (378)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 &
% 232.15/43.29  | | | | | | | |            op(e0, e1) = e0)
% 232.15/43.29  | | | | | | | | 
% 232.15/43.29  | | | | | | | | BETA: splitting (378) gives:
% 232.15/43.29  | | | | | | | | 
% 232.15/43.29  | | | | | | | | Case 1:
% 232.15/43.29  | | | | | | | | | 
% 232.15/43.29  | | | | | | | | |   (379)  all_57_8 = e0 & op(e1, e1) = e0
% 232.15/43.29  | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | REF_CLOSE: (12), (15), (80), (379) are inconsistent by
% 232.15/43.29  | | | | | | | | |            sub-proof #2412.
% 232.15/43.29  | | | | | | | | | 
% 232.15/43.29  | | | | | | | | Case 2:
% 232.15/43.29  | | | | | | | | | 
% 232.15/43.29  | | | | | | | | |   (380)  all_57_14 = e0 & op(e0, e1) = e0
% 232.15/43.29  | | | | | | | | | 
% 232.15/43.29  | | | | | | | | | REF_CLOSE: (47), (260), (380) are inconsistent by sub-proof
% 232.15/43.29  | | | | | | | | |            #2173.
% 232.15/43.29  | | | | | | | | | 
% 232.15/43.29  | | | | | | | | End of split
% 232.15/43.29  | | | | | | | | 
% 232.15/43.29  | | | | | | | End of split
% 232.15/43.29  | | | | | | | 
% 232.15/43.29  | | | | | | End of split
% 232.15/43.29  | | | | | | 
% 232.15/43.29  | | | | | Case 2:
% 232.15/43.29  | | | | | | 
% 232.15/43.29  | | | | | |   (381)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 &
% 232.15/43.29  | | | | | |            op(e0, e0) = e3)
% 232.15/43.29  | | | | | | 
% 232.15/43.29  | | | | | | BETA: splitting (381) gives:
% 232.15/43.29  | | | | | | 
% 232.15/43.29  | | | | | | Case 1:
% 232.15/43.29  | | | | | | | 
% 232.15/43.29  | | | | | | |   (382)  all_57_14 = e3 & op(e0, e1) = e3
% 232.15/43.29  | | | | | | | 
% 232.15/43.29  | | | | | | | ALPHA: (382) implies:
% 232.15/43.29  | | | | | | |   (383)  all_57_14 = e3
% 232.15/43.29  | | | | | | | 
% 232.15/43.29  | | | | | | | REF_CLOSE: (27), (260), (383) are inconsistent by sub-proof #2410.
% 232.15/43.29  | | | | | | | 
% 232.15/43.29  | | | | | | Case 2:
% 232.15/43.29  | | | | | | | 
% 232.15/43.29  | | | | | | |   (384)  all_57_15 = e3 & op(e0, e0) = e3
% 232.15/43.29  | | | | | | | 
% 232.15/43.29  | | | | | | | ALPHA: (384) implies:
% 232.15/43.29  | | | | | | |   (385)  op(e0, e0) = e3
% 232.15/43.29  | | | | | | | 
% 232.15/43.29  | | | | | | | REF_CLOSE: (12), (33), (57), (385) are inconsistent by sub-proof
% 232.15/43.29  | | | | | | |            #2304.
% 232.15/43.29  | | | | | | | 
% 232.15/43.29  | | | | | | End of split
% 232.15/43.29  | | | | | | 
% 232.15/43.29  | | | | | End of split
% 232.15/43.29  | | | | | 
% 232.15/43.29  | | | | End of split
% 232.15/43.29  | | | | 
% 232.15/43.29  | | | Case 2:
% 232.15/43.29  | | | | 
% 232.15/43.29  | | | |   (386)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0,
% 232.15/43.29  | | | |              e1) = e3)
% 232.15/43.29  | | | | 
% 232.15/43.29  | | | | REF_CLOSE: (12), (14), (15), (27), (260), (386) are inconsistent by
% 232.15/43.29  | | | |            sub-proof #2409.
% 232.15/43.29  | | | | 
% 232.15/43.29  | | | End of split
% 232.15/43.29  | | | 
% 232.15/43.29  | | Case 2:
% 232.15/43.29  | | | 
% 232.15/43.29  | | |   (387)  all_57_15 = e2 & op(e0, e0) = e2
% 232.15/43.29  | | | 
% 232.15/43.29  | | | ALPHA: (387) implies:
% 232.15/43.29  | | |   (388)  op(e0, e0) = e2
% 232.15/43.29  | | | 
% 232.15/43.29  | | | REF_CLOSE: (2), (12), (37), (388) are inconsistent by sub-proof #2334.
% 232.15/43.29  | | | 
% 232.15/43.29  | | End of split
% 232.15/43.29  | | 
% 232.15/43.29  | End of split
% 232.15/43.29  | 
% 232.15/43.29  End of proof
% 232.15/43.29  
% 232.15/43.29  Sub-proof #2173 shows that the following formulas are inconsistent:
% 232.15/43.29  ----------------------------------------------------------------
% 232.15/43.29    (1)  all_57_14 = e0 & op(e0, e1) = e0
% 232.15/43.29    (2)  all_57_14 = e2
% 232.15/43.29    (3)   ~ (e2 = e0)
% 232.15/43.29  
% 232.15/43.29  Begin of proof
% 232.15/43.29  | 
% 232.15/43.29  | ALPHA: (1) implies:
% 232.15/43.29  |   (4)  all_57_14 = e0
% 232.15/43.29  | 
% 232.15/43.29  | COMBINE_EQS: (2), (4) imply:
% 232.15/43.29  |   (5)  e2 = e0
% 232.15/43.29  | 
% 232.15/43.29  | REDUCE: (3), (5) imply:
% 232.15/43.29  |   (6)  $false
% 232.15/43.29  | 
% 232.15/43.29  | CLOSE: (6) is inconsistent.
% 232.15/43.29  | 
% 232.15/43.29  End of proof
% 232.15/43.29  
% 232.15/43.29  Sub-proof #2174 shows that the following formulas are inconsistent:
% 232.15/43.29  ----------------------------------------------------------------
% 232.15/43.29    (1)   ~ (e3 = e1)
% 232.15/43.29    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.29    (3)  op(e1, e1) = all_6_2
% 232.15/43.29    (4)   ~ (all_53_7 = e2)
% 232.15/43.29    (5)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 232.15/43.29         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 232.15/43.29    (6)   ~ (e3 = e2)
% 232.15/43.29    (7)   ~ (e3 = e0)
% 232.15/43.29    (8)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 232.15/43.29         (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 232.15/43.29    (9)  all_57_5 = e3
% 232.15/43.29    (10)   ~ (e2 = e0)
% 232.15/43.29    (11)   ~ (e1 = e0)
% 232.15/43.29    (12)  all_57_14 = e2
% 232.15/43.29    (13)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 232.15/43.29          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 232.15/43.29            e3)
% 232.15/43.29    (14)  op(e0, e2) = all_53_7
% 232.15/43.29    (15)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 232.15/43.29          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 232.15/43.29            e2)
% 232.15/43.29    (16)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 232.15/43.29              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 232.15/43.29                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 232.15/43.29                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 232.15/43.29    (17)  op(e1, e1) = e2
% 232.15/43.29    (18)  op(e0, e0) = e1
% 232.15/43.29    (19)   ~ (e2 = e1)
% 232.15/43.29    (20)   ~ (all_6_2 = e0)
% 232.15/43.29  
% 232.15/43.29  Begin of proof
% 232.15/43.29  | 
% 232.15/43.29  | BETA: splitting (8) gives:
% 232.15/43.29  | 
% 232.15/43.29  | Case 1:
% 232.15/43.29  | | 
% 232.15/43.29  | |   (21)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) =
% 232.15/43.29  | |           e1)
% 232.15/43.29  | | 
% 232.15/43.29  | | BETA: splitting (21) gives:
% 232.15/43.29  | | 
% 232.15/43.29  | | Case 1:
% 232.15/43.29  | | | 
% 232.15/43.29  | | |   (22)  all_57_4 = e1 & op(e3, e1) = e1
% 232.15/43.29  | | | 
% 232.15/43.29  | | | REF_CLOSE: (2), (3), (5), (7), (9), (10), (11), (12), (20), (22) are
% 232.15/43.29  | | |            inconsistent by sub-proof #2186.
% 232.15/43.29  | | | 
% 232.15/43.29  | | Case 2:
% 232.15/43.29  | | | 
% 232.15/43.29  | | |   (23)  all_57_5 = e1 & op(e2, e1) = e1
% 232.15/43.29  | | | 
% 232.15/43.29  | | | REF_CLOSE: (1), (9), (23) are inconsistent by sub-proof #2376.
% 232.15/43.29  | | | 
% 232.15/43.29  | | End of split
% 232.15/43.29  | | 
% 232.15/43.29  | Case 2:
% 232.15/43.29  | | 
% 232.15/43.29  | |   (24)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) =
% 232.15/43.29  | |           e1)
% 232.15/43.29  | | 
% 232.15/43.29  | | BETA: splitting (24) gives:
% 232.15/43.29  | | 
% 232.15/43.29  | | Case 1:
% 232.15/43.29  | | | 
% 232.15/43.29  | | |   (25)  all_57_8 = e1 & op(e1, e1) = e1
% 232.15/43.29  | | | 
% 232.15/43.29  | | | ALPHA: (25) implies:
% 232.15/43.29  | | |   (26)  op(e1, e1) = e1
% 232.15/43.29  | | | 
% 232.15/43.29  | | | REF_CLOSE: (2), (17), (19), (26) are inconsistent by sub-proof #2423.
% 232.15/43.29  | | | 
% 232.15/43.29  | | Case 2:
% 232.15/43.29  | | | 
% 232.15/43.29  | | |   (27)  all_57_14 = e1 & op(e0, e1) = e1
% 232.15/43.29  | | | 
% 232.15/43.29  | | | ALPHA: (27) implies:
% 232.15/43.29  | | |   (28)  all_57_14 = e1
% 232.15/43.29  | | | 
% 232.15/43.29  | | | REF_CLOSE: (1), (2), (4), (6), (7), (10), (11), (13), (14), (15), (16),
% 232.15/43.29  | | |            (18), (19), (28) are inconsistent by sub-proof #2175.
% 232.15/43.29  | | | 
% 232.15/43.29  | | End of split
% 232.15/43.29  | | 
% 232.15/43.29  | End of split
% 232.15/43.29  | 
% 232.15/43.29  End of proof
% 232.15/43.29  
% 232.15/43.29  Sub-proof #2175 shows that the following formulas are inconsistent:
% 232.15/43.29  ----------------------------------------------------------------
% 232.15/43.29    (1)   ~ (e3 = e1)
% 232.15/43.29    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.29    (3)   ~ (all_53_7 = e2)
% 232.15/43.29    (4)   ~ (e3 = e2)
% 232.15/43.29    (5)   ~ (e3 = e0)
% 232.15/43.29    (6)   ~ (e2 = e0)
% 232.15/43.29    (7)   ~ (e1 = e0)
% 232.15/43.29    (8)  all_57_14 = e1
% 232.15/43.29    (9)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 232.15/43.29         (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 232.15/43.29    (10)  op(e0, e2) = all_53_7
% 232.15/43.29    (11)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 232.15/43.29          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 232.15/43.29            e2)
% 232.15/43.29    (12)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 232.15/43.29              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 232.15/43.29                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 232.15/43.29                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 232.15/43.29    (13)  op(e0, e0) = e1
% 232.15/43.29    (14)   ~ (e2 = e1)
% 232.15/43.29  
% 232.15/43.29  Begin of proof
% 232.15/43.29  | 
% 232.15/43.29  | BETA: splitting (11) gives:
% 232.15/43.29  | 
% 232.15/43.29  | Case 1:
% 232.15/43.29  | | 
% 232.15/43.29  | |   (15)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 232.15/43.29  | |           e2)
% 232.15/43.29  | | 
% 232.15/43.29  | | BETA: splitting (15) gives:
% 232.15/43.29  | | 
% 232.15/43.29  | | Case 1:
% 232.15/43.29  | | | 
% 232.15/43.29  | | |   (16)  all_57_12 = e2 & op(e0, e3) = e2
% 232.15/43.29  | | | 
% 232.15/43.29  | | | ALPHA: (16) implies:
% 232.15/43.29  | | |   (17)  all_57_12 = e2
% 232.15/43.29  | | | 
% 232.15/43.29  | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (12), (13), (17) are
% 232.15/43.29  | | |            inconsistent by sub-proof #2179.
% 232.15/43.29  | | | 
% 232.15/43.29  | | Case 2:
% 232.15/43.29  | | | 
% 232.15/43.29  | | |   (18)  all_57_13 = e2 & op(e0, e2) = e2
% 232.15/43.29  | | | 
% 232.15/43.29  | | | ALPHA: (18) implies:
% 232.15/43.29  | | |   (19)  op(e0, e2) = e2
% 232.15/43.29  | | | 
% 232.15/43.29  | | | REF_CLOSE: (2), (3), (10), (19) are inconsistent by sub-proof #2335.
% 232.15/43.29  | | | 
% 232.15/43.29  | | End of split
% 232.15/43.29  | | 
% 232.15/43.29  | Case 2:
% 232.15/43.29  | | 
% 232.15/43.29  | |   (20)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 232.15/43.29  | |           e2)
% 232.15/43.29  | | 
% 232.15/43.29  | | REF_CLOSE: (2), (8), (13), (14), (20) are inconsistent by sub-proof #2176.
% 232.15/43.29  | | 
% 232.15/43.29  | End of split
% 232.15/43.29  | 
% 232.15/43.29  End of proof
% 232.15/43.29  
% 232.15/43.29  Sub-proof #2176 shows that the following formulas are inconsistent:
% 232.15/43.29  ----------------------------------------------------------------
% 232.15/43.29    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.29    (2)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 232.15/43.29    (3)  all_57_14 = e1
% 232.15/43.29    (4)  op(e0, e0) = e1
% 232.15/43.29    (5)   ~ (e2 = e1)
% 232.15/43.29  
% 232.15/43.29  Begin of proof
% 232.15/43.29  | 
% 232.15/43.29  | BETA: splitting (2) gives:
% 232.15/43.29  | 
% 232.15/43.29  | Case 1:
% 232.15/43.29  | | 
% 232.15/43.29  | |   (6)  all_57_14 = e2 & op(e0, e1) = e2
% 232.15/43.29  | | 
% 232.15/43.29  | | ALPHA: (6) implies:
% 232.15/43.29  | |   (7)  all_57_14 = e2
% 232.15/43.29  | | 
% 232.15/43.29  | | REF_CLOSE: (3), (5), (7) are inconsistent by sub-proof #2178.
% 232.15/43.29  | | 
% 232.15/43.29  | Case 2:
% 232.15/43.29  | | 
% 232.15/43.29  | |   (8)  all_57_15 = e2 & op(e0, e0) = e2
% 232.15/43.29  | | 
% 232.15/43.29  | | ALPHA: (8) implies:
% 232.15/43.29  | |   (9)  op(e0, e0) = e2
% 232.15/43.29  | | 
% 232.15/43.29  | | REF_CLOSE: (1), (4), (5), (9) are inconsistent by sub-proof #2177.
% 232.15/43.29  | | 
% 232.15/43.29  | End of split
% 232.15/43.29  | 
% 232.15/43.29  End of proof
% 232.15/43.29  
% 232.15/43.29  Sub-proof #2177 shows that the following formulas are inconsistent:
% 232.15/43.29  ----------------------------------------------------------------
% 232.15/43.29    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.29    (2)  op(e0, e0) = e2
% 232.15/43.29    (3)  op(e0, e0) = e1
% 232.15/43.29    (4)   ~ (e2 = e1)
% 232.15/43.29  
% 232.15/43.29  Begin of proof
% 232.15/43.29  | 
% 232.15/43.29  | GROUND_INST: instantiating (1) with e1, e2, e0, e0, simplifying with (2), (3)
% 232.15/43.29  |              gives:
% 232.15/43.29  |   (5)  e2 = e1
% 232.15/43.29  | 
% 232.15/43.29  | REDUCE: (4), (5) imply:
% 232.15/43.29  |   (6)  $false
% 232.15/43.29  | 
% 232.15/43.29  | CLOSE: (6) is inconsistent.
% 232.15/43.29  | 
% 232.15/43.29  End of proof
% 232.15/43.29  
% 232.15/43.29  Sub-proof #2178 shows that the following formulas are inconsistent:
% 232.15/43.29  ----------------------------------------------------------------
% 232.15/43.29    (1)  all_57_14 = e2
% 232.15/43.29    (2)  all_57_14 = e1
% 232.15/43.29    (3)   ~ (e2 = e1)
% 232.15/43.29  
% 232.15/43.29  Begin of proof
% 232.15/43.29  | 
% 232.15/43.29  | COMBINE_EQS: (1), (2) imply:
% 232.15/43.29  |   (4)  e2 = e1
% 232.15/43.29  | 
% 232.15/43.29  | SIMP: (4) implies:
% 232.15/43.29  |   (5)  e2 = e1
% 232.15/43.29  | 
% 232.15/43.29  | REDUCE: (3), (5) imply:
% 232.15/43.29  |   (6)  $false
% 232.15/43.29  | 
% 232.15/43.29  | CLOSE: (6) is inconsistent.
% 232.15/43.29  | 
% 232.15/43.29  End of proof
% 232.15/43.29  
% 232.15/43.29  Sub-proof #2179 shows that the following formulas are inconsistent:
% 232.15/43.29  ----------------------------------------------------------------
% 232.15/43.29    (1)   ~ (e3 = e1)
% 232.15/43.29    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.29    (3)  all_57_12 = e2
% 232.15/43.29    (4)   ~ (e3 = e2)
% 232.15/43.29    (5)   ~ (e3 = e0)
% 232.15/43.29    (6)   ~ (e2 = e0)
% 232.15/43.29    (7)   ~ (e1 = e0)
% 232.15/43.29    (8)  all_57_14 = e1
% 232.15/43.29    (9)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 232.15/43.29         (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 232.15/43.29    (10)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 232.15/43.29              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 232.15/43.29                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 232.15/43.29                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 232.15/43.29    (11)  op(e0, e0) = e1
% 232.15/43.29  
% 232.15/43.29  Begin of proof
% 232.15/43.29  | 
% 232.15/43.29  | BETA: splitting (10) gives:
% 232.15/43.29  | 
% 232.15/43.29  | Case 1:
% 232.15/43.29  | | 
% 232.15/43.29  | |   (12)  all_57_15 = e0 & op(e0, e0) = e0
% 232.15/43.29  | | 
% 232.15/43.29  | | ALPHA: (12) implies:
% 232.15/43.29  | |   (13)  op(e0, e0) = e0
% 232.15/43.29  | | 
% 232.15/43.29  | | REF_CLOSE: (2), (7), (11), (13) are inconsistent by sub-proof #2290.
% 232.15/43.29  | | 
% 232.15/43.29  | Case 2:
% 232.15/43.29  | | 
% 232.15/43.29  | |   (14)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 232.15/43.29  | |             e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0 &
% 232.15/43.29  | |             op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 232.15/43.29  | |           (all_57_14 = e0 & op(e0, e1) = e0))
% 232.15/43.29  | | 
% 232.15/43.29  | | ALPHA: (14) implies:
% 232.15/43.29  | |   (15)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 232.15/43.29  | |           e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 232.15/43.29  | | 
% 232.15/43.29  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (15) are
% 232.15/43.29  | |            inconsistent by sub-proof #2180.
% 232.15/43.29  | | 
% 232.15/43.29  | End of split
% 232.15/43.29  | 
% 232.15/43.29  End of proof
% 232.15/43.29  
% 232.15/43.29  Sub-proof #2180 shows that the following formulas are inconsistent:
% 232.15/43.29  ----------------------------------------------------------------
% 232.15/43.29    (1)   ~ (e3 = e1)
% 232.15/43.29    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.29    (3)  all_57_12 = e2
% 232.15/43.29    (4)   ~ (e3 = e2)
% 232.15/43.29    (5)   ~ (e3 = e0)
% 232.15/43.29    (6)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 232.15/43.29         (all_57_14 = e0 & op(e0, e1) = e0)
% 232.15/43.29    (7)   ~ (e2 = e0)
% 232.15/43.29    (8)   ~ (e1 = e0)
% 232.15/43.29    (9)  all_57_14 = e1
% 232.15/43.29    (10)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 232.15/43.29          | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 232.15/43.29            e3)
% 232.15/43.29    (11)  op(e0, e0) = e1
% 232.15/43.29  
% 232.15/43.29  Begin of proof
% 232.15/43.29  | 
% 232.15/43.29  | BETA: splitting (6) gives:
% 232.15/43.29  | 
% 232.15/43.29  | Case 1:
% 232.15/43.29  | | 
% 232.15/43.29  | |   (12)  all_57_12 = e0 & op(e0, e3) = e0
% 232.15/43.29  | | 
% 232.15/43.29  | | REF_CLOSE: (3), (7), (12) are inconsistent by sub-proof #2185.
% 232.15/43.29  | | 
% 232.15/43.29  | Case 2:
% 232.15/43.29  | | 
% 232.15/43.29  | |   (13)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 232.15/43.29  | |           e0)
% 232.15/43.29  | | 
% 232.15/43.29  | | BETA: splitting (13) gives:
% 232.15/43.29  | | 
% 232.15/43.29  | | Case 1:
% 232.15/43.29  | | | 
% 232.15/43.29  | | |   (14)  all_57_13 = e0 & op(e0, e2) = e0
% 232.15/43.29  | | | 
% 232.15/43.29  | | | ALPHA: (14) implies:
% 232.15/43.29  | | |   (15)  all_57_13 = e0
% 232.15/43.29  | | | 
% 232.15/43.29  | | | REF_CLOSE: (1), (2), (3), (4), (5), (9), (10), (11), (15) are inconsistent
% 232.15/43.29  | | |            by sub-proof #2182.
% 232.15/43.29  | | | 
% 232.15/43.29  | | Case 2:
% 232.15/43.29  | | | 
% 232.15/43.29  | | |   (16)  all_57_14 = e0 & op(e0, e1) = e0
% 232.15/43.29  | | | 
% 232.15/43.29  | | | REF_CLOSE: (8), (9), (16) are inconsistent by sub-proof #2181.
% 232.15/43.29  | | | 
% 232.15/43.29  | | End of split
% 232.15/43.29  | | 
% 232.15/43.29  | End of split
% 232.15/43.29  | 
% 232.15/43.29  End of proof
% 232.15/43.29  
% 232.15/43.29  Sub-proof #2181 shows that the following formulas are inconsistent:
% 232.15/43.29  ----------------------------------------------------------------
% 232.15/43.29    (1)  all_57_14 = e0 & op(e0, e1) = e0
% 232.15/43.29    (2)  all_57_14 = e1
% 232.15/43.29    (3)   ~ (e1 = e0)
% 232.15/43.29  
% 232.15/43.29  Begin of proof
% 232.15/43.29  | 
% 232.15/43.29  | ALPHA: (1) implies:
% 232.15/43.29  |   (4)  all_57_14 = e0
% 232.15/43.29  | 
% 232.15/43.29  | COMBINE_EQS: (2), (4) imply:
% 232.15/43.29  |   (5)  e1 = e0
% 232.15/43.29  | 
% 232.15/43.29  | REDUCE: (3), (5) imply:
% 232.15/43.29  |   (6)  $false
% 232.15/43.29  | 
% 232.15/43.29  | CLOSE: (6) is inconsistent.
% 232.15/43.29  | 
% 232.15/43.29  End of proof
% 232.15/43.29  
% 232.15/43.29  Sub-proof #2182 shows that the following formulas are inconsistent:
% 232.15/43.29  ----------------------------------------------------------------
% 232.15/43.29    (1)   ~ (e3 = e1)
% 232.15/43.29    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.29    (3)  all_57_12 = e2
% 232.15/43.29    (4)   ~ (e3 = e2)
% 232.15/43.29    (5)   ~ (e3 = e0)
% 232.15/43.29    (6)  all_57_14 = e1
% 232.15/43.29    (7)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 232.15/43.29         (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 232.15/43.29    (8)  op(e0, e0) = e1
% 232.15/43.29    (9)  all_57_13 = e0
% 232.15/43.29  
% 232.15/43.29  Begin of proof
% 232.15/43.29  | 
% 232.15/43.29  | BETA: splitting (7) gives:
% 232.15/43.29  | 
% 232.15/43.29  | Case 1:
% 232.15/43.29  | | 
% 232.15/43.29  | |   (10)  (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 232.15/43.29  | |           e3)
% 232.15/43.29  | | 
% 232.15/43.29  | | BETA: splitting (10) gives:
% 232.15/43.29  | | 
% 232.15/43.29  | | Case 1:
% 232.15/43.29  | | | 
% 232.15/43.29  | | |   (11)  all_57_12 = e3 & op(e0, e3) = e3
% 232.15/43.29  | | | 
% 232.15/43.29  | | | ALPHA: (11) implies:
% 232.15/43.29  | | |   (12)  all_57_12 = e3
% 232.15/43.29  | | | 
% 232.15/43.29  | | | REF_CLOSE: (3), (4), (12) are inconsistent by sub-proof #2392.
% 232.15/43.29  | | | 
% 232.15/43.29  | | Case 2:
% 232.15/43.29  | | | 
% 232.15/43.29  | | |   (13)  all_57_13 = e3 & op(e0, e2) = e3
% 232.15/43.29  | | | 
% 232.15/43.29  | | | ALPHA: (13) implies:
% 232.15/43.29  | | |   (14)  all_57_13 = e3
% 232.15/43.29  | | | 
% 232.15/43.29  | | | REF_CLOSE: (5), (9), (14) are inconsistent by sub-proof #2184.
% 232.15/43.29  | | | 
% 232.15/43.29  | | End of split
% 232.15/43.29  | | 
% 232.15/43.29  | Case 2:
% 232.15/43.29  | | 
% 232.15/43.29  | |   (15)  (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 232.15/43.29  | |           e3)
% 232.15/43.29  | | 
% 232.15/43.29  | | BETA: splitting (15) gives:
% 232.15/43.29  | | 
% 232.15/43.29  | | Case 1:
% 232.15/43.29  | | | 
% 232.15/43.29  | | |   (16)  all_57_14 = e3 & op(e0, e1) = e3
% 232.15/43.29  | | | 
% 232.15/43.29  | | | ALPHA: (16) implies:
% 232.15/43.29  | | |   (17)  all_57_14 = e3
% 232.15/43.29  | | | 
% 232.15/43.29  | | | REF_CLOSE: (1), (6), (17) are inconsistent by sub-proof #2326.
% 232.15/43.29  | | | 
% 232.15/43.29  | | Case 2:
% 232.15/43.29  | | | 
% 232.15/43.29  | | |   (18)  all_57_15 = e3 & op(e0, e0) = e3
% 232.15/43.29  | | | 
% 232.15/43.29  | | | ALPHA: (18) implies:
% 232.15/43.29  | | |   (19)  op(e0, e0) = e3
% 232.15/43.29  | | | 
% 232.15/43.29  | | | REF_CLOSE: (1), (2), (8), (19) are inconsistent by sub-proof #2183.
% 232.15/43.29  | | | 
% 232.15/43.29  | | End of split
% 232.15/43.29  | | 
% 232.15/43.29  | End of split
% 232.15/43.29  | 
% 232.15/43.29  End of proof
% 232.15/43.29  
% 232.15/43.29  Sub-proof #2183 shows that the following formulas are inconsistent:
% 232.15/43.29  ----------------------------------------------------------------
% 232.15/43.29    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.29    (2)  op(e0, e0) = e3
% 232.15/43.29    (3)  op(e0, e0) = e1
% 232.15/43.29    (4)   ~ (e3 = e1)
% 232.15/43.29  
% 232.15/43.29  Begin of proof
% 232.15/43.29  | 
% 232.15/43.29  | GROUND_INST: instantiating (1) with e3, e1, e0, e0, simplifying with (2), (3)
% 232.15/43.29  |              gives:
% 232.15/43.29  |   (5)  e3 = e1
% 232.15/43.29  | 
% 232.15/43.29  | REDUCE: (4), (5) imply:
% 232.15/43.29  |   (6)  $false
% 232.15/43.29  | 
% 232.15/43.29  | CLOSE: (6) is inconsistent.
% 232.15/43.29  | 
% 232.15/43.29  End of proof
% 232.15/43.29  
% 232.15/43.29  Sub-proof #2184 shows that the following formulas are inconsistent:
% 232.15/43.29  ----------------------------------------------------------------
% 232.15/43.29    (1)  all_57_13 = e3
% 232.15/43.29    (2)  all_57_13 = e0
% 232.15/43.29    (3)   ~ (e3 = e0)
% 232.15/43.29  
% 232.15/43.29  Begin of proof
% 232.15/43.29  | 
% 232.15/43.29  | COMBINE_EQS: (1), (2) imply:
% 232.15/43.29  |   (4)  e3 = e0
% 232.15/43.29  | 
% 232.15/43.29  | SIMP: (4) implies:
% 232.15/43.29  |   (5)  e3 = e0
% 232.15/43.29  | 
% 232.15/43.29  | REDUCE: (3), (5) imply:
% 232.15/43.29  |   (6)  $false
% 232.15/43.29  | 
% 232.15/43.29  | CLOSE: (6) is inconsistent.
% 232.15/43.29  | 
% 232.15/43.29  End of proof
% 232.15/43.29  
% 232.15/43.29  Sub-proof #2185 shows that the following formulas are inconsistent:
% 232.15/43.29  ----------------------------------------------------------------
% 232.15/43.29    (1)  all_57_12 = e0 & op(e0, e3) = e0
% 232.15/43.29    (2)  all_57_12 = e2
% 232.15/43.29    (3)   ~ (e2 = e0)
% 232.15/43.29  
% 232.15/43.29  Begin of proof
% 232.15/43.29  | 
% 232.15/43.29  | ALPHA: (1) implies:
% 232.15/43.29  |   (4)  all_57_12 = e0
% 232.15/43.29  | 
% 232.15/43.29  | COMBINE_EQS: (2), (4) imply:
% 232.15/43.29  |   (5)  e2 = e0
% 232.15/43.29  | 
% 232.15/43.29  | REDUCE: (3), (5) imply:
% 232.15/43.29  |   (6)  $false
% 232.15/43.29  | 
% 232.15/43.29  | CLOSE: (6) is inconsistent.
% 232.15/43.29  | 
% 232.15/43.29  End of proof
% 232.15/43.29  
% 232.15/43.29  Sub-proof #2186 shows that the following formulas are inconsistent:
% 232.15/43.29  ----------------------------------------------------------------
% 232.15/43.29    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.29    (2)  op(e1, e1) = all_6_2
% 232.15/43.29    (3)  all_57_4 = e1 & op(e3, e1) = e1
% 232.15/43.29    (4)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 232.15/43.29         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 232.15/43.29    (5)   ~ (e3 = e0)
% 232.15/43.29    (6)  all_57_5 = e3
% 232.15/43.29    (7)   ~ (e2 = e0)
% 232.15/43.29    (8)   ~ (e1 = e0)
% 232.15/43.29    (9)  all_57_14 = e2
% 232.15/43.29    (10)   ~ (all_6_2 = e0)
% 232.15/43.29  
% 232.15/43.29  Begin of proof
% 232.15/43.29  | 
% 232.15/43.29  | ALPHA: (3) implies:
% 232.15/43.29  |   (11)  all_57_4 = e1
% 232.15/43.29  | 
% 232.15/43.29  | BETA: splitting (4) gives:
% 232.15/43.29  | 
% 232.15/43.29  | Case 1:
% 232.15/43.29  | | 
% 232.15/43.29  | |   (12)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) =
% 232.15/43.29  | |           e0)
% 232.15/43.29  | | 
% 232.15/43.29  | | REF_CLOSE: (5), (6), (8), (11), (12) are inconsistent by sub-proof #2413.
% 232.15/43.29  | | 
% 232.15/43.29  | Case 2:
% 232.15/43.29  | | 
% 232.15/43.29  | |   (13)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 232.15/43.29  | |           e0)
% 232.15/43.29  | | 
% 232.15/43.29  | | REF_CLOSE: (1), (2), (7), (9), (10), (13) are inconsistent by sub-proof
% 232.15/43.29  | |            #2411.
% 232.15/43.29  | | 
% 232.15/43.29  | End of split
% 232.15/43.29  | 
% 232.15/43.29  End of proof
% 232.15/43.29  
% 232.15/43.29  Sub-proof #2187 shows that the following formulas are inconsistent:
% 232.15/43.29  ----------------------------------------------------------------
% 232.15/43.29    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 232.15/43.29         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 232.15/43.29    (2)   ~ (e3 = e1)
% 232.15/43.29    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.29    (4)   ~ (all_6_2 = e3)
% 232.15/43.29    (5)  op(e1, e1) = all_6_2
% 232.15/43.29    (6)  all_57_4 = e0
% 232.15/43.29    (7)  op(e2, e2) = e0
% 232.15/43.29    (8)  all_57_3 = e0
% 232.15/43.29    (9)   ~ (e3 = e2)
% 232.15/43.29    (10)   ~ (e3 = e0)
% 232.15/43.29    (11)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 232.15/43.29          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 232.15/43.29    (12)  all_57_5 = e3
% 232.15/43.29    (13)   ~ (e2 = e0)
% 232.15/43.29    (14)   ~ (e1 = e0)
% 232.15/43.29    (15)  all_57_14 = e2
% 232.15/43.29    (16)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 232.15/43.29          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 232.15/43.29    (17)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 232.15/43.29          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 232.15/43.29    (18)  all_57_13 = e3
% 232.15/43.29    (19)  op(e1, e1) = e2
% 232.15/43.29    (20)   ~ (e2 = e1)
% 232.15/43.29    (21)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 232.15/43.29          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 232.15/43.29  
% 232.15/43.29  Begin of proof
% 232.15/43.29  | 
% 232.15/43.29  | BETA: splitting (1) gives:
% 232.15/43.29  | 
% 232.15/43.29  | Case 1:
% 232.15/43.29  | | 
% 232.15/43.29  | |   (22)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 232.15/43.29  | |           e2)
% 232.15/43.29  | | 
% 232.15/43.29  | | BETA: splitting (22) gives:
% 232.15/43.29  | | 
% 232.15/43.29  | | Case 1:
% 232.15/43.29  | | | 
% 232.15/43.29  | | |   (23)  all_57_1 = e2 & op(e3, e2) = e2
% 232.15/43.29  | | | 
% 232.15/43.30  | | | ALPHA: (23) implies:
% 232.15/43.30  | | |   (24)  all_57_1 = e2
% 232.15/43.30  | | | 
% 232.15/43.30  | | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (9), (10), (11), (12), (13),
% 232.15/43.30  | | |            (14), (15), (17), (18), (19), (20), (21), (24) are inconsistent
% 232.15/43.30  | | |            by sub-proof #2197.
% 232.15/43.30  | | | 
% 232.15/43.30  | | Case 2:
% 232.15/43.30  | | | 
% 232.15/43.30  | | |   (25)  all_57_3 = e2 & op(e2, e2) = e2
% 232.15/43.30  | | | 
% 232.15/43.30  | | | ALPHA: (25) implies:
% 232.15/43.30  | | |   (26)  op(e2, e2) = e2
% 232.15/43.30  | | | 
% 232.15/43.30  | | | REF_CLOSE: (3), (7), (13), (26) are inconsistent by sub-proof #2472.
% 232.15/43.30  | | | 
% 232.15/43.30  | | End of split
% 232.15/43.30  | | 
% 232.15/43.30  | Case 2:
% 232.15/43.30  | | 
% 232.15/43.30  | |   (27)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 232.15/43.30  | |           e2)
% 232.15/43.30  | | 
% 232.15/43.30  | | BETA: splitting (27) gives:
% 232.15/43.30  | | 
% 232.15/43.30  | | Case 1:
% 232.15/43.30  | | | 
% 232.15/43.30  | | |   (28)  all_57_7 = e2 & op(e1, e2) = e2
% 232.15/43.30  | | | 
% 232.15/43.30  | | | ALPHA: (28) implies:
% 232.15/43.30  | | |   (29)  all_57_7 = e2
% 232.15/43.30  | | | 
% 232.15/43.30  | | | BETA: splitting (21) gives:
% 232.15/43.30  | | | 
% 232.15/43.30  | | | Case 1:
% 232.15/43.30  | | | | 
% 232.15/43.30  | | | |   (30)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2)
% 232.15/43.30  | | | |           = e1)
% 232.15/43.30  | | | | 
% 232.15/43.30  | | | | BETA: splitting (30) gives:
% 232.15/43.30  | | | | 
% 232.15/43.30  | | | | Case 1:
% 232.15/43.30  | | | | | 
% 232.15/43.30  | | | | |   (31)  all_57_1 = e1 & op(e3, e2) = e1
% 232.15/43.30  | | | | | 
% 232.15/43.30  | | | | | ALPHA: (31) implies:
% 232.15/43.30  | | | | |   (32)  all_57_1 = e1
% 232.15/43.30  | | | | | 
% 232.15/43.30  | | | | | REF_CLOSE: (2), (3), (6), (8), (9), (10), (11), (12), (14), (15),
% 232.15/43.30  | | | | |            (17), (18), (19), (20), (29), (32) are inconsistent by
% 232.15/43.30  | | | | |            sub-proof #2191.
% 232.15/43.30  | | | | | 
% 232.15/43.30  | | | | Case 2:
% 232.15/43.30  | | | | | 
% 232.15/43.30  | | | | |   (33)  all_57_3 = e1 & op(e2, e2) = e1
% 232.15/43.30  | | | | | 
% 232.15/43.30  | | | | | ALPHA: (33) implies:
% 232.15/43.30  | | | | |   (34)  op(e2, e2) = e1
% 232.15/43.30  | | | | | 
% 232.15/43.30  | | | | | REF_CLOSE: (3), (7), (14), (34) are inconsistent by sub-proof #2352.
% 232.15/43.30  | | | | | 
% 232.15/43.30  | | | | End of split
% 232.15/43.30  | | | | 
% 232.15/43.30  | | | Case 2:
% 232.15/43.30  | | | | 
% 232.15/43.30  | | | |   (35)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2)
% 232.15/43.30  | | | |           = e1)
% 232.15/43.30  | | | | 
% 232.15/43.30  | | | | BETA: splitting (35) gives:
% 232.15/43.30  | | | | 
% 232.15/43.30  | | | | Case 1:
% 232.15/43.30  | | | | | 
% 232.15/43.30  | | | | |   (36)  all_57_7 = e1 & op(e1, e2) = e1
% 232.15/43.30  | | | | | 
% 232.15/43.30  | | | | | REF_CLOSE: (20), (29), (36) are inconsistent by sub-proof #2190.
% 232.15/43.30  | | | | | 
% 232.15/43.30  | | | | Case 2:
% 232.15/43.30  | | | | | 
% 232.15/43.30  | | | | |   (37)  all_57_13 = e1 & op(e0, e2) = e1
% 232.15/43.30  | | | | | 
% 232.15/43.30  | | | | | REF_CLOSE: (2), (18), (37) are inconsistent by sub-proof #2264.
% 232.15/43.30  | | | | | 
% 232.15/43.30  | | | | End of split
% 232.15/43.30  | | | | 
% 232.15/43.30  | | | End of split
% 232.15/43.30  | | | 
% 232.15/43.30  | | Case 2:
% 232.15/43.30  | | | 
% 232.15/43.30  | | |   (38)  all_57_13 = e2 & op(e0, e2) = e2
% 232.15/43.30  | | | 
% 232.15/43.30  | | | ALPHA: (38) implies:
% 232.15/43.30  | | |   (39)  all_57_13 = e2
% 232.15/43.30  | | | 
% 232.15/43.30  | | | COMBINE_EQS: (18), (39) imply:
% 232.15/43.30  | | |   (40)  e3 = e2
% 232.15/43.30  | | | 
% 232.15/43.30  | | | SIMP: (40) implies:
% 232.15/43.30  | | |   (41)  e3 = e2
% 232.15/43.30  | | | 
% 232.15/43.30  | | | COMBINE_EQS: (12), (41) imply:
% 232.15/43.30  | | |   (42)  all_57_5 = e2
% 232.15/43.30  | | | 
% 232.15/43.30  | | | REF_CLOSE: (3), (4), (5), (6), (9), (10), (15), (16), (42) are
% 232.15/43.30  | | |            inconsistent by sub-proof #2188.
% 232.15/43.30  | | | 
% 232.15/43.30  | | End of split
% 232.15/43.30  | | 
% 232.15/43.30  | End of split
% 232.15/43.30  | 
% 232.15/43.30  End of proof
% 232.15/43.30  
% 232.15/43.30  Sub-proof #2188 shows that the following formulas are inconsistent:
% 232.15/43.30  ----------------------------------------------------------------
% 232.15/43.30    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.30    (2)   ~ (all_6_2 = e3)
% 232.15/43.30    (3)  op(e1, e1) = all_6_2
% 232.15/43.30    (4)  all_57_4 = e0
% 232.15/43.30    (5)   ~ (e3 = e2)
% 232.15/43.30    (6)   ~ (e3 = e0)
% 232.15/43.30    (7)  all_57_14 = e2
% 232.15/43.30    (8)  all_57_5 = e2
% 232.15/43.30    (9)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 232.15/43.30         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 232.15/43.30  
% 232.15/43.30  Begin of proof
% 232.15/43.30  | 
% 232.15/43.30  | BETA: splitting (9) gives:
% 232.15/43.30  | 
% 232.15/43.30  | Case 1:
% 232.15/43.30  | | 
% 232.15/43.30  | |   (10)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) =
% 232.15/43.30  | |           e3)
% 232.15/43.30  | | 
% 232.15/43.30  | | BETA: splitting (10) gives:
% 232.15/43.30  | | 
% 232.15/43.30  | | Case 1:
% 232.15/43.30  | | | 
% 232.15/43.30  | | |   (11)  all_57_4 = e3 & op(e3, e1) = e3
% 232.15/43.30  | | | 
% 232.15/43.30  | | | ALPHA: (11) implies:
% 232.15/43.30  | | |   (12)  all_57_4 = e3
% 232.15/43.30  | | | 
% 232.15/43.30  | | | REF_CLOSE: (4), (6), (12) are inconsistent by sub-proof #2372.
% 232.15/43.30  | | | 
% 232.15/43.30  | | Case 2:
% 232.15/43.30  | | | 
% 232.15/43.30  | | |   (13)  all_57_5 = e3 & op(e2, e1) = e3
% 232.15/43.30  | | | 
% 232.15/43.30  | | | ALPHA: (13) implies:
% 232.15/43.30  | | |   (14)  all_57_5 = e3
% 232.15/43.30  | | | 
% 232.15/43.30  | | | REF_CLOSE: (5), (8), (14) are inconsistent by sub-proof #2189.
% 232.15/43.30  | | | 
% 232.15/43.30  | | End of split
% 232.15/43.30  | | 
% 232.15/43.30  | Case 2:
% 232.15/43.30  | | 
% 232.15/43.30  | |   (15)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) =
% 232.15/43.30  | |           e3)
% 232.15/43.30  | | 
% 232.15/43.30  | | REF_CLOSE: (1), (2), (3), (5), (7), (15) are inconsistent by sub-proof
% 232.15/43.30  | |            #2409.
% 232.15/43.30  | | 
% 232.15/43.30  | End of split
% 232.15/43.30  | 
% 232.15/43.30  End of proof
% 232.15/43.30  
% 232.15/43.30  Sub-proof #2189 shows that the following formulas are inconsistent:
% 232.15/43.30  ----------------------------------------------------------------
% 232.15/43.30    (1)  all_57_5 = e3
% 232.15/43.30    (2)  all_57_5 = e2
% 232.15/43.30    (3)   ~ (e3 = e2)
% 232.15/43.30  
% 232.15/43.30  Begin of proof
% 232.15/43.30  | 
% 232.15/43.30  | COMBINE_EQS: (1), (2) imply:
% 232.15/43.30  |   (4)  e3 = e2
% 232.15/43.30  | 
% 232.15/43.30  | SIMP: (4) implies:
% 232.15/43.30  |   (5)  e3 = e2
% 232.15/43.30  | 
% 232.15/43.30  | REDUCE: (3), (5) imply:
% 232.15/43.30  |   (6)  $false
% 232.15/43.30  | 
% 232.15/43.30  | CLOSE: (6) is inconsistent.
% 232.15/43.30  | 
% 232.15/43.30  End of proof
% 232.15/43.30  
% 232.15/43.30  Sub-proof #2190 shows that the following formulas are inconsistent:
% 232.15/43.30  ----------------------------------------------------------------
% 232.15/43.30    (1)  all_57_7 = e1 & op(e1, e2) = e1
% 232.15/43.30    (2)  all_57_7 = e2
% 232.15/43.30    (3)   ~ (e2 = e1)
% 232.15/43.30  
% 232.15/43.30  Begin of proof
% 232.15/43.30  | 
% 232.15/43.30  | ALPHA: (1) implies:
% 232.15/43.30  |   (4)  all_57_7 = e1
% 232.15/43.30  | 
% 232.15/43.30  | COMBINE_EQS: (2), (4) imply:
% 232.15/43.30  |   (5)  e2 = e1
% 232.15/43.30  | 
% 232.15/43.30  | REDUCE: (3), (5) imply:
% 232.15/43.30  |   (6)  $false
% 232.15/43.30  | 
% 232.15/43.30  | CLOSE: (6) is inconsistent.
% 232.15/43.30  | 
% 232.15/43.30  End of proof
% 232.15/43.30  
% 232.15/43.30  Sub-proof #2191 shows that the following formulas are inconsistent:
% 232.15/43.30  ----------------------------------------------------------------
% 232.15/43.30    (1)   ~ (e3 = e1)
% 232.15/43.30    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.30    (3)  all_57_7 = e2
% 232.15/43.30    (4)  all_57_4 = e0
% 232.15/43.30    (5)  all_57_3 = e0
% 232.15/43.30    (6)   ~ (e3 = e2)
% 232.15/43.30    (7)   ~ (e3 = e0)
% 232.15/43.30    (8)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 232.15/43.30         (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 232.15/43.30    (9)  all_57_1 = e1
% 232.15/43.30    (10)  all_57_5 = e3
% 232.15/43.30    (11)   ~ (e1 = e0)
% 232.15/43.30    (12)  all_57_14 = e2
% 232.15/43.30    (13)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 232.15/43.30          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 232.15/43.30    (14)  all_57_13 = e3
% 232.15/43.30    (15)  op(e1, e1) = e2
% 232.15/43.30    (16)   ~ (e2 = e1)
% 232.15/43.30  
% 232.15/43.30  Begin of proof
% 232.15/43.30  | 
% 232.15/43.30  | BETA: splitting (8) gives:
% 232.15/43.30  | 
% 232.15/43.30  | Case 1:
% 232.15/43.30  | | 
% 232.15/43.30  | |   (17)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) =
% 232.15/43.30  | |           e1)
% 232.15/43.30  | | 
% 232.15/43.30  | | BETA: splitting (17) gives:
% 232.15/43.30  | | 
% 232.15/43.30  | | Case 1:
% 232.15/43.30  | | | 
% 232.15/43.30  | | |   (18)  all_57_4 = e1 & op(e3, e1) = e1
% 232.15/43.30  | | | 
% 232.15/43.30  | | | ALPHA: (18) implies:
% 232.15/43.30  | | |   (19)  all_57_4 = e1
% 232.15/43.30  | | | 
% 232.15/43.30  | | | REF_CLOSE: (4), (11), (19) are inconsistent by sub-proof #2438.
% 232.15/43.30  | | | 
% 232.15/43.30  | | Case 2:
% 232.15/43.30  | | | 
% 232.15/43.30  | | |   (20)  all_57_5 = e1 & op(e2, e1) = e1
% 232.15/43.30  | | | 
% 232.15/43.30  | | | REF_CLOSE: (1), (3), (5), (6), (7), (9), (10), (13), (14), (20) are
% 232.15/43.30  | | |            inconsistent by sub-proof #2192.
% 232.15/43.30  | | | 
% 232.15/43.30  | | End of split
% 232.15/43.30  | | 
% 232.15/43.30  | Case 2:
% 232.15/43.30  | | 
% 232.15/43.30  | |   (21)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) =
% 232.15/43.30  | |           e1)
% 232.15/43.30  | | 
% 232.15/43.30  | | REF_CLOSE: (2), (12), (15), (16), (21) are inconsistent by sub-proof #2198.
% 232.15/43.30  | | 
% 232.15/43.30  | End of split
% 232.15/43.30  | 
% 232.15/43.30  End of proof
% 232.15/43.30  
% 232.15/43.30  Sub-proof #2192 shows that the following formulas are inconsistent:
% 232.15/43.30  ----------------------------------------------------------------
% 232.15/43.30    (1)   ~ (e3 = e1)
% 232.15/43.30    (2)  all_57_7 = e2
% 232.15/43.30    (3)  all_57_3 = e0
% 232.15/43.30    (4)   ~ (e3 = e2)
% 232.15/43.30    (5)   ~ (e3 = e0)
% 232.15/43.30    (6)  all_57_1 = e1
% 232.15/43.30    (7)  all_57_5 = e1 & op(e2, e1) = e1
% 232.15/43.30    (8)  all_57_5 = e3
% 232.15/43.30    (9)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 232.15/43.30         (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 232.15/43.30    (10)  all_57_13 = e3
% 232.15/43.30  
% 232.15/43.30  Begin of proof
% 232.15/43.30  | 
% 232.15/43.30  | ALPHA: (7) implies:
% 232.15/43.30  |   (11)  all_57_5 = e1
% 232.15/43.30  | 
% 232.15/43.30  | COMBINE_EQS: (8), (11) imply:
% 232.15/43.30  |   (12)  e3 = e1
% 232.15/43.30  | 
% 232.15/43.30  | COMBINE_EQS: (10), (12) imply:
% 232.15/43.30  |   (13)  all_57_13 = e1
% 232.15/43.30  | 
% 232.15/43.30  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (9), (13) are inconsistent by
% 232.15/43.30  |            sub-proof #2193.
% 232.15/43.30  | 
% 232.15/43.30  End of proof
% 232.15/43.30  
% 232.15/43.30  Sub-proof #2193 shows that the following formulas are inconsistent:
% 232.15/43.30  ----------------------------------------------------------------
% 232.15/43.30    (1)  all_57_13 = e1
% 232.15/43.30    (2)   ~ (e3 = e1)
% 232.15/43.30    (3)  all_57_7 = e2
% 232.15/43.30    (4)  all_57_3 = e0
% 232.15/43.30    (5)   ~ (e3 = e2)
% 232.15/43.30    (6)   ~ (e3 = e0)
% 232.15/43.30    (7)  all_57_1 = e1
% 232.15/43.30    (8)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 232.15/43.30         (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 232.15/43.30  
% 232.15/43.30  Begin of proof
% 232.15/43.30  | 
% 232.15/43.30  | BETA: splitting (8) gives:
% 232.15/43.30  | 
% 232.15/43.30  | Case 1:
% 232.15/43.30  | | 
% 232.15/43.30  | |   (9)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3)
% 232.15/43.30  | | 
% 232.15/43.30  | | REF_CLOSE: (2), (4), (6), (7), (9) are inconsistent by sub-proof #2195.
% 232.15/43.30  | | 
% 232.15/43.30  | Case 2:
% 232.15/43.30  | | 
% 232.15/43.30  | |   (10)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 232.15/43.30  | |           e3)
% 232.15/43.30  | | 
% 232.15/43.30  | | BETA: splitting (10) gives:
% 232.15/43.30  | | 
% 232.15/43.30  | | Case 1:
% 232.15/43.30  | | | 
% 232.15/43.30  | | |   (11)  all_57_7 = e3 & op(e1, e2) = e3
% 232.15/43.30  | | | 
% 232.15/43.30  | | | REF_CLOSE: (3), (5), (11) are inconsistent by sub-proof #2194.
% 232.15/43.30  | | | 
% 232.15/43.30  | | Case 2:
% 232.15/43.30  | | | 
% 232.15/43.30  | | |   (12)  all_57_13 = e3 & op(e0, e2) = e3
% 232.15/43.30  | | | 
% 232.15/43.30  | | | ALPHA: (12) implies:
% 232.15/43.30  | | |   (13)  all_57_13 = e3
% 232.15/43.30  | | | 
% 232.15/43.30  | | | REF_CLOSE: (1), (2), (13) are inconsistent by sub-proof #2268.
% 232.15/43.30  | | | 
% 232.15/43.30  | | End of split
% 232.15/43.30  | | 
% 232.15/43.30  | End of split
% 232.15/43.30  | 
% 232.15/43.30  End of proof
% 232.15/43.30  
% 232.15/43.30  Sub-proof #2194 shows that the following formulas are inconsistent:
% 232.15/43.30  ----------------------------------------------------------------
% 232.15/43.30    (1)  all_57_7 = e3 & op(e1, e2) = e3
% 232.15/43.30    (2)  all_57_7 = e2
% 232.15/43.30    (3)   ~ (e3 = e2)
% 232.15/43.30  
% 232.15/43.30  Begin of proof
% 232.15/43.30  | 
% 232.15/43.30  | ALPHA: (1) implies:
% 232.15/43.30  |   (4)  all_57_7 = e3
% 232.15/43.30  | 
% 232.15/43.30  | COMBINE_EQS: (2), (4) imply:
% 232.15/43.30  |   (5)  e3 = e2
% 232.15/43.30  | 
% 232.15/43.30  | REDUCE: (3), (5) imply:
% 232.15/43.30  |   (6)  $false
% 232.15/43.30  | 
% 232.15/43.30  | CLOSE: (6) is inconsistent.
% 232.15/43.30  | 
% 232.15/43.30  End of proof
% 232.15/43.30  
% 232.15/43.30  Sub-proof #2195 shows that the following formulas are inconsistent:
% 232.15/43.30  ----------------------------------------------------------------
% 232.15/43.30    (1)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3)
% 232.15/43.30    (2)   ~ (e3 = e1)
% 232.15/43.30    (3)  all_57_3 = e0
% 232.15/43.30    (4)   ~ (e3 = e0)
% 232.15/43.30    (5)  all_57_1 = e1
% 232.15/43.30  
% 232.15/43.30  Begin of proof
% 232.15/43.30  | 
% 232.15/43.30  | BETA: splitting (1) gives:
% 232.15/43.30  | 
% 232.15/43.30  | Case 1:
% 232.15/43.30  | | 
% 232.15/43.30  | |   (6)  all_57_1 = e3 & op(e3, e2) = e3
% 232.15/43.30  | | 
% 232.15/43.30  | | REF_CLOSE: (2), (5), (6) are inconsistent by sub-proof #2196.
% 232.15/43.30  | | 
% 232.15/43.30  | Case 2:
% 232.15/43.30  | | 
% 232.15/43.30  | |   (7)  all_57_3 = e3 & op(e2, e2) = e3
% 232.15/43.30  | | 
% 232.15/43.30  | | ALPHA: (7) implies:
% 232.15/43.30  | |   (8)  all_57_3 = e3
% 232.15/43.30  | | 
% 232.15/43.30  | | REF_CLOSE: (3), (4), (8) are inconsistent by sub-proof #2358.
% 232.15/43.30  | | 
% 232.15/43.30  | End of split
% 232.15/43.30  | 
% 232.15/43.30  End of proof
% 232.15/43.30  
% 232.15/43.30  Sub-proof #2196 shows that the following formulas are inconsistent:
% 232.15/43.30  ----------------------------------------------------------------
% 232.15/43.30    (1)  all_57_1 = e3 & op(e3, e2) = e3
% 232.15/43.30    (2)  all_57_1 = e1
% 232.15/43.30    (3)   ~ (e3 = e1)
% 232.15/43.30  
% 232.15/43.30  Begin of proof
% 232.15/43.30  | 
% 232.15/43.30  | ALPHA: (1) implies:
% 232.15/43.30  |   (4)  all_57_1 = e3
% 232.15/43.30  | 
% 232.15/43.30  | COMBINE_EQS: (2), (4) imply:
% 232.15/43.30  |   (5)  e3 = e1
% 232.15/43.30  | 
% 232.15/43.30  | SIMP: (5) implies:
% 232.15/43.30  |   (6)  e3 = e1
% 232.15/43.30  | 
% 232.15/43.30  | REDUCE: (3), (6) imply:
% 232.15/43.30  |   (7)  $false
% 232.15/43.30  | 
% 232.15/43.30  | CLOSE: (7) is inconsistent.
% 232.15/43.30  | 
% 232.15/43.30  End of proof
% 232.15/43.30  
% 232.15/43.30  Sub-proof #2197 shows that the following formulas are inconsistent:
% 232.15/43.30  ----------------------------------------------------------------
% 232.15/43.30    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 232.15/43.30         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 232.15/43.30    (2)   ~ (e3 = e1)
% 232.15/43.30    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.30    (4)  all_57_4 = e0
% 232.15/43.30    (5)  op(e2, e2) = e0
% 232.15/43.30    (6)  all_57_3 = e0
% 232.15/43.30    (7)   ~ (e3 = e2)
% 232.15/43.30    (8)   ~ (e3 = e0)
% 232.15/43.30    (9)  all_57_1 = e2
% 232.15/43.30    (10)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 232.15/43.30          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 232.15/43.30    (11)  all_57_5 = e3
% 232.15/43.30    (12)   ~ (e2 = e0)
% 232.15/43.30    (13)   ~ (e1 = e0)
% 232.15/43.30    (14)  all_57_14 = e2
% 232.15/43.30    (15)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 232.15/43.30          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 232.15/43.30    (16)  all_57_13 = e3
% 232.15/43.30    (17)  op(e1, e1) = e2
% 232.15/43.30    (18)   ~ (e2 = e1)
% 232.15/43.30    (19)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 232.15/43.30          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 232.15/43.30  
% 232.15/43.30  Begin of proof
% 232.15/43.30  | 
% 232.15/43.30  | BETA: splitting (19) gives:
% 232.15/43.30  | 
% 232.15/43.30  | Case 1:
% 232.15/43.30  | | 
% 232.15/43.30  | |   (20)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) =
% 232.15/43.30  | |           e1)
% 232.15/43.30  | | 
% 232.15/43.30  | | REF_CLOSE: (3), (5), (9), (13), (18), (20) are inconsistent by sub-proof
% 232.15/43.30  | |            #2209.
% 232.15/43.30  | | 
% 232.15/43.30  | Case 2:
% 232.15/43.30  | | 
% 232.15/43.30  | |   (21)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 232.15/43.30  | |           e1)
% 232.15/43.30  | | 
% 232.15/43.30  | | BETA: splitting (21) gives:
% 232.15/43.30  | | 
% 232.15/43.30  | | Case 1:
% 232.15/43.30  | | | 
% 232.15/43.30  | | |   (22)  all_57_7 = e1 & op(e1, e2) = e1
% 232.15/43.30  | | | 
% 232.15/43.30  | | | ALPHA: (22) implies:
% 232.15/43.30  | | |   (23)  all_57_7 = e1
% 232.15/43.30  | | | 
% 232.15/43.30  | | | BETA: splitting (10) gives:
% 232.15/43.30  | | | 
% 232.15/43.30  | | | Case 1:
% 232.15/43.30  | | | | 
% 232.15/43.30  | | | |   (24)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1)
% 232.15/43.30  | | | |           = e1)
% 232.15/43.30  | | | | 
% 232.15/43.30  | | | | BETA: splitting (24) gives:
% 232.15/43.30  | | | | 
% 232.15/43.30  | | | | Case 1:
% 232.15/43.30  | | | | | 
% 232.15/43.30  | | | | |   (25)  all_57_4 = e1 & op(e3, e1) = e1
% 232.15/43.30  | | | | | 
% 232.15/43.30  | | | | | ALPHA: (25) implies:
% 232.15/43.30  | | | | |   (26)  all_57_4 = e1
% 232.15/43.30  | | | | | 
% 232.15/43.30  | | | | | COMBINE_EQS: (4), (26) imply:
% 232.15/43.30  | | | | |   (27)  e1 = e0
% 232.15/43.30  | | | | | 
% 232.15/43.30  | | | | | SIMP: (27) implies:
% 232.15/43.30  | | | | |   (28)  e1 = e0
% 232.15/43.30  | | | | | 
% 232.15/43.30  | | | | | COMBINE_EQS: (23), (28) imply:
% 232.15/43.30  | | | | |   (29)  all_57_7 = e0
% 232.15/43.30  | | | | | 
% 232.15/43.30  | | | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (12), (13), (15), (16),
% 232.15/43.30  | | | | |            (18), (19), (29) are inconsistent by sub-proof #2199.
% 232.15/43.30  | | | | | 
% 232.15/43.30  | | | | Case 2:
% 232.15/43.30  | | | | | 
% 232.15/43.30  | | | | |   (30)  all_57_5 = e1 & op(e2, e1) = e1
% 232.15/43.30  | | | | | 
% 232.15/43.30  | | | | | REF_CLOSE: (2), (11), (30) are inconsistent by sub-proof #2376.
% 232.15/43.30  | | | | | 
% 232.15/43.30  | | | | End of split
% 232.15/43.30  | | | | 
% 232.15/43.30  | | | Case 2:
% 232.15/43.30  | | | | 
% 232.15/43.30  | | | |   (31)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1)
% 232.15/43.30  | | | |           = e1)
% 232.15/43.30  | | | | 
% 232.15/43.30  | | | | REF_CLOSE: (3), (14), (17), (18), (31) are inconsistent by sub-proof
% 232.15/43.30  | | | |            #2198.
% 232.15/43.30  | | | | 
% 232.15/43.30  | | | End of split
% 232.15/43.30  | | | 
% 232.15/43.30  | | Case 2:
% 232.15/43.30  | | | 
% 232.15/43.30  | | |   (32)  all_57_13 = e1 & op(e0, e2) = e1
% 232.15/43.30  | | | 
% 232.15/43.30  | | | REF_CLOSE: (2), (16), (32) are inconsistent by sub-proof #2264.
% 232.15/43.30  | | | 
% 232.15/43.30  | | End of split
% 232.15/43.30  | | 
% 232.15/43.30  | End of split
% 232.15/43.30  | 
% 232.15/43.30  End of proof
% 232.15/43.30  
% 232.15/43.30  Sub-proof #2198 shows that the following formulas are inconsistent:
% 232.15/43.30  ----------------------------------------------------------------
% 232.15/43.30    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.30    (2)  all_57_14 = e2
% 232.15/43.30    (3)  op(e1, e1) = e2
% 232.15/43.30    (4)   ~ (e2 = e1)
% 232.15/43.30    (5)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 232.15/43.30  
% 232.15/43.30  Begin of proof
% 232.15/43.30  | 
% 232.15/43.30  | BETA: splitting (5) gives:
% 232.15/43.30  | 
% 232.15/43.30  | Case 1:
% 232.15/43.30  | | 
% 232.15/43.30  | |   (6)  all_57_8 = e1 & op(e1, e1) = e1
% 232.15/43.30  | | 
% 232.15/43.30  | | ALPHA: (6) implies:
% 232.15/43.30  | |   (7)  op(e1, e1) = e1
% 232.15/43.30  | | 
% 232.15/43.30  | | REF_CLOSE: (1), (3), (4), (7) are inconsistent by sub-proof #2423.
% 232.15/43.30  | | 
% 232.15/43.30  | Case 2:
% 232.15/43.30  | | 
% 232.15/43.30  | |   (8)  all_57_14 = e1 & op(e0, e1) = e1
% 232.15/43.30  | | 
% 232.15/43.30  | | REF_CLOSE: (2), (4), (8) are inconsistent by sub-proof #2375.
% 232.15/43.30  | | 
% 232.15/43.30  | End of split
% 232.15/43.30  | 
% 232.15/43.30  End of proof
% 232.15/43.30  
% 232.15/43.30  Sub-proof #2199 shows that the following formulas are inconsistent:
% 232.15/43.30  ----------------------------------------------------------------
% 232.15/43.30    (1)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 232.15/43.30         (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 232.15/43.30    (2)   ~ (e3 = e1)
% 232.15/43.30    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.30    (4)  op(e2, e2) = e0
% 232.15/43.30    (5)  all_57_3 = e0
% 232.15/43.30    (6)   ~ (e3 = e2)
% 232.15/43.30    (7)   ~ (e3 = e0)
% 232.15/43.30    (8)   ~ (e2 = e0)
% 232.15/43.30    (9)   ~ (e1 = e0)
% 232.15/43.30    (10)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 232.15/43.30          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 232.15/43.30    (11)  all_57_13 = e3
% 232.15/43.30    (12)   ~ (e2 = e1)
% 232.15/43.30    (13)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 232.15/43.30          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 232.15/43.30    (14)  all_57_7 = e0
% 232.15/43.30  
% 232.15/43.30  Begin of proof
% 232.15/43.30  | 
% 232.15/43.30  | BETA: splitting (13) gives:
% 232.15/43.30  | 
% 232.15/43.30  | Case 1:
% 232.15/43.30  | | 
% 232.15/43.30  | |   (15)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) =
% 232.15/43.30  | |           e1)
% 232.15/43.30  | | 
% 232.15/43.30  | | BETA: splitting (15) gives:
% 232.15/43.30  | | 
% 232.15/43.30  | | Case 1:
% 232.15/43.30  | | | 
% 232.15/43.30  | | |   (16)  all_57_1 = e1 & op(e3, e2) = e1
% 232.15/43.30  | | | 
% 232.15/43.30  | | | ALPHA: (16) implies:
% 232.15/43.30  | | |   (17)  all_57_1 = e1
% 232.15/43.30  | | | 
% 232.15/43.30  | | | BETA: splitting (1) gives:
% 232.15/43.30  | | | 
% 232.15/43.30  | | | Case 1:
% 232.15/43.30  | | | | 
% 232.15/43.30  | | | |   (18)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2)
% 232.15/43.30  | | | |           = e2)
% 232.15/43.30  | | | | 
% 232.15/43.30  | | | | REF_CLOSE: (3), (4), (8), (12), (17), (18) are inconsistent by sub-proof
% 232.15/43.30  | | | |            #2208.
% 232.15/43.30  | | | | 
% 232.15/43.30  | | | Case 2:
% 232.15/43.30  | | | | 
% 232.15/43.30  | | | |   (19)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2)
% 232.15/43.30  | | | |           = e2)
% 232.15/43.30  | | | | 
% 232.15/43.30  | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 232.15/43.30  | | | |            (14), (19) are inconsistent by sub-proof #2201.
% 232.15/43.30  | | | | 
% 232.15/43.30  | | | End of split
% 232.15/43.30  | | | 
% 232.15/43.30  | | Case 2:
% 232.15/43.30  | | | 
% 232.15/43.30  | | |   (20)  all_57_3 = e1 & op(e2, e2) = e1
% 232.15/43.30  | | | 
% 232.15/43.30  | | | ALPHA: (20) implies:
% 232.15/43.30  | | |   (21)  op(e2, e2) = e1
% 232.15/43.30  | | | 
% 232.15/43.30  | | | REF_CLOSE: (3), (4), (9), (21) are inconsistent by sub-proof #2352.
% 232.15/43.30  | | | 
% 232.15/43.30  | | End of split
% 232.15/43.30  | | 
% 232.15/43.30  | Case 2:
% 232.15/43.30  | | 
% 232.15/43.30  | |   (22)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 232.15/43.30  | |           e1)
% 232.15/43.30  | | 
% 232.15/43.30  | | BETA: splitting (22) gives:
% 232.15/43.30  | | 
% 232.15/43.30  | | Case 1:
% 232.15/43.30  | | | 
% 232.15/43.30  | | |   (23)  all_57_7 = e1 & op(e1, e2) = e1
% 232.15/43.30  | | | 
% 232.15/43.30  | | | REF_CLOSE: (9), (14), (23) are inconsistent by sub-proof #2200.
% 232.15/43.30  | | | 
% 232.15/43.30  | | Case 2:
% 232.15/43.30  | | | 
% 232.15/43.30  | | |   (24)  all_57_13 = e1 & op(e0, e2) = e1
% 232.15/43.30  | | | 
% 232.15/43.30  | | | ALPHA: (24) implies:
% 232.15/43.30  | | |   (25)  all_57_13 = e1
% 232.15/43.30  | | | 
% 232.15/43.30  | | | REF_CLOSE: (2), (11), (25) are inconsistent by sub-proof #2268.
% 232.15/43.30  | | | 
% 232.15/43.30  | | End of split
% 232.15/43.30  | | 
% 232.15/43.30  | End of split
% 232.15/43.30  | 
% 232.15/43.30  End of proof
% 232.15/43.30  
% 232.15/43.30  Sub-proof #2200 shows that the following formulas are inconsistent:
% 232.15/43.30  ----------------------------------------------------------------
% 232.15/43.30    (1)  all_57_7 = e1 & op(e1, e2) = e1
% 232.15/43.30    (2)  all_57_7 = e0
% 232.15/43.30    (3)   ~ (e1 = e0)
% 232.15/43.30  
% 232.15/43.30  Begin of proof
% 232.15/43.30  | 
% 232.15/43.30  | ALPHA: (1) implies:
% 232.15/43.30  |   (4)  all_57_7 = e1
% 232.15/43.30  | 
% 232.15/43.30  | COMBINE_EQS: (2), (4) imply:
% 232.15/43.30  |   (5)  e1 = e0
% 232.15/43.30  | 
% 232.15/43.30  | REDUCE: (3), (5) imply:
% 232.15/43.30  |   (6)  $false
% 232.15/43.30  | 
% 232.15/43.30  | CLOSE: (6) is inconsistent.
% 232.15/43.30  | 
% 232.15/43.30  End of proof
% 232.15/43.30  
% 232.15/43.30  Sub-proof #2201 shows that the following formulas are inconsistent:
% 232.15/43.30  ----------------------------------------------------------------
% 232.15/43.30    (1)   ~ (e3 = e1)
% 232.15/43.30    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.30    (3)  op(e2, e2) = e0
% 232.15/43.30    (4)  all_57_3 = e0
% 232.15/43.30    (5)   ~ (e3 = e2)
% 232.15/43.30    (6)   ~ (e3 = e0)
% 232.15/43.30    (7)  (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 232.15/43.30    (8)   ~ (e2 = e0)
% 232.15/43.30    (9)   ~ (e1 = e0)
% 232.15/43.30    (10)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 232.15/43.30          (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 232.15/43.30    (11)   ~ (e2 = e1)
% 232.15/43.30    (12)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 232.15/43.30          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 232.15/43.30    (13)  all_57_7 = e0
% 232.15/43.30  
% 232.15/43.30  Begin of proof
% 232.15/43.30  | 
% 232.15/43.30  | BETA: splitting (7) gives:
% 232.15/43.30  | 
% 232.15/43.30  | Case 1:
% 232.15/43.30  | | 
% 232.15/43.30  | |   (14)  all_57_7 = e2 & op(e1, e2) = e2
% 232.15/43.30  | | 
% 232.15/43.30  | | ALPHA: (14) implies:
% 232.15/43.30  | |   (15)  all_57_7 = e2
% 232.15/43.30  | | 
% 232.15/43.30  | | REF_CLOSE: (8), (13), (15) are inconsistent by sub-proof #2207.
% 232.15/43.30  | | 
% 232.15/43.30  | Case 2:
% 232.15/43.30  | | 
% 232.15/43.30  | |   (16)  all_57_13 = e2 & op(e0, e2) = e2
% 232.15/43.30  | | 
% 232.15/43.30  | | ALPHA: (16) implies:
% 232.15/43.30  | |   (17)  all_57_13 = e2
% 232.15/43.30  | | 
% 232.15/43.30  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (9), (10), (11), (12), (13), (17)
% 232.15/43.30  | |            are inconsistent by sub-proof #2202.
% 232.15/43.30  | | 
% 232.15/43.30  | End of split
% 232.15/43.30  | 
% 232.15/43.30  End of proof
% 232.15/43.30  
% 232.15/43.30  Sub-proof #2202 shows that the following formulas are inconsistent:
% 232.15/43.30  ----------------------------------------------------------------
% 232.15/43.30    (1)   ~ (e3 = e1)
% 232.15/43.30    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.30    (3)  op(e2, e2) = e0
% 232.15/43.30    (4)  all_57_3 = e0
% 232.15/43.30    (5)   ~ (e3 = e2)
% 232.15/43.30    (6)   ~ (e3 = e0)
% 232.15/43.30    (7)  all_57_13 = e2
% 232.15/43.30    (8)   ~ (e1 = e0)
% 232.15/43.30    (9)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 232.15/43.30         (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 232.15/43.30    (10)   ~ (e2 = e1)
% 232.15/43.30    (11)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 232.15/43.30          (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 232.15/43.30    (12)  all_57_7 = e0
% 232.15/43.30  
% 232.15/43.30  Begin of proof
% 232.15/43.30  | 
% 232.15/43.30  | BETA: splitting (9) gives:
% 232.15/43.30  | 
% 232.15/43.30  | Case 1:
% 232.15/43.30  | | 
% 232.15/43.30  | |   (13)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 232.15/43.30  | |           e3)
% 232.15/43.30  | | 
% 232.15/43.30  | | BETA: splitting (13) gives:
% 232.15/43.30  | | 
% 232.15/43.30  | | Case 1:
% 232.15/43.30  | | | 
% 232.15/43.30  | | |   (14)  all_57_1 = e3 & op(e3, e2) = e3
% 232.15/43.30  | | | 
% 232.15/43.30  | | | ALPHA: (14) implies:
% 232.15/43.30  | | |   (15)  all_57_1 = e3
% 232.15/43.30  | | | 
% 232.15/43.30  | | | REF_CLOSE: (1), (2), (3), (7), (8), (10), (11), (12), (15) are
% 232.15/43.30  | | |            inconsistent by sub-proof #2204.
% 232.15/43.30  | | | 
% 232.15/43.30  | | Case 2:
% 232.15/43.30  | | | 
% 232.15/43.30  | | |   (16)  all_57_3 = e3 & op(e2, e2) = e3
% 232.15/43.30  | | | 
% 232.15/43.30  | | | ALPHA: (16) implies:
% 232.15/43.30  | | |   (17)  all_57_3 = e3
% 232.15/43.30  | | | 
% 232.15/43.30  | | | REF_CLOSE: (4), (6), (17) are inconsistent by sub-proof #2358.
% 232.15/43.30  | | | 
% 232.15/43.30  | | End of split
% 232.15/43.30  | | 
% 232.15/43.30  | Case 2:
% 232.15/43.30  | | 
% 232.15/43.30  | |   (18)  (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 232.15/43.30  | |           e3)
% 232.15/43.30  | | 
% 232.15/43.30  | | BETA: splitting (18) gives:
% 232.15/43.30  | | 
% 232.15/43.30  | | Case 1:
% 232.15/43.30  | | | 
% 232.15/43.30  | | |   (19)  all_57_7 = e3 & op(e1, e2) = e3
% 232.15/43.30  | | | 
% 232.15/43.30  | | | ALPHA: (19) implies:
% 232.15/43.30  | | |   (20)  all_57_7 = e3
% 232.15/43.30  | | | 
% 232.15/43.30  | | | REF_CLOSE: (6), (12), (20) are inconsistent by sub-proof #2269.
% 232.15/43.30  | | | 
% 232.15/43.30  | | Case 2:
% 232.15/43.30  | | | 
% 232.15/43.30  | | |   (21)  all_57_13 = e3 & op(e0, e2) = e3
% 232.15/43.30  | | | 
% 232.15/43.30  | | | ALPHA: (21) implies:
% 232.15/43.30  | | |   (22)  all_57_13 = e3
% 232.15/43.30  | | | 
% 232.15/43.30  | | | REF_CLOSE: (5), (7), (22) are inconsistent by sub-proof #2203.
% 232.15/43.30  | | | 
% 232.15/43.30  | | End of split
% 232.15/43.30  | | 
% 232.15/43.30  | End of split
% 232.15/43.30  | 
% 232.15/43.30  End of proof
% 232.15/43.30  
% 232.15/43.30  Sub-proof #2203 shows that the following formulas are inconsistent:
% 232.15/43.30  ----------------------------------------------------------------
% 232.15/43.30    (1)  all_57_13 = e3
% 232.15/43.30    (2)  all_57_13 = e2
% 232.15/43.30    (3)   ~ (e3 = e2)
% 232.15/43.30  
% 232.15/43.30  Begin of proof
% 232.15/43.30  | 
% 232.15/43.30  | COMBINE_EQS: (1), (2) imply:
% 232.15/43.30  |   (4)  e3 = e2
% 232.15/43.30  | 
% 232.15/43.30  | SIMP: (4) implies:
% 232.15/43.30  |   (5)  e3 = e2
% 232.15/43.30  | 
% 232.15/43.30  | REDUCE: (3), (5) imply:
% 232.15/43.30  |   (6)  $false
% 232.15/43.30  | 
% 232.15/43.30  | CLOSE: (6) is inconsistent.
% 232.15/43.30  | 
% 232.15/43.30  End of proof
% 232.15/43.30  
% 232.15/43.30  Sub-proof #2204 shows that the following formulas are inconsistent:
% 232.15/43.30  ----------------------------------------------------------------
% 232.15/43.30    (1)   ~ (e3 = e1)
% 232.15/43.30    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.30    (3)  op(e2, e2) = e0
% 232.15/43.30    (4)  all_57_13 = e2
% 232.15/43.30    (5)   ~ (e1 = e0)
% 232.15/43.30    (6)  all_57_1 = e3
% 232.15/43.30    (7)   ~ (e2 = e1)
% 232.15/43.30    (8)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 232.15/43.30         (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 232.15/43.30    (9)  all_57_7 = e0
% 232.15/43.30  
% 232.15/43.30  Begin of proof
% 232.15/43.30  | 
% 232.15/43.30  | BETA: splitting (8) gives:
% 232.15/43.30  | 
% 232.15/43.30  | Case 1:
% 232.15/43.30  | | 
% 232.15/43.30  | |   (10)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) =
% 232.15/43.30  | |           e1)
% 232.15/43.30  | | 
% 232.15/43.30  | | REF_CLOSE: (1), (2), (3), (5), (6), (10) are inconsistent by sub-proof
% 232.15/43.30  | |            #2206.
% 232.15/43.30  | | 
% 232.15/43.30  | Case 2:
% 232.15/43.30  | | 
% 232.15/43.30  | |   (11)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 232.15/43.30  | |           e1)
% 232.15/43.30  | | 
% 232.15/43.30  | | BETA: splitting (11) gives:
% 232.15/43.30  | | 
% 232.15/43.30  | | Case 1:
% 232.15/43.30  | | | 
% 232.15/43.30  | | |   (12)  all_57_7 = e1 & op(e1, e2) = e1
% 232.15/43.30  | | | 
% 232.15/43.30  | | | ALPHA: (12) implies:
% 232.15/43.30  | | |   (13)  all_57_7 = e1
% 232.15/43.30  | | | 
% 232.15/43.30  | | | REF_CLOSE: (5), (9), (13) are inconsistent by sub-proof #2211.
% 232.15/43.30  | | | 
% 232.15/43.30  | | Case 2:
% 232.15/43.30  | | | 
% 232.15/43.30  | | |   (14)  all_57_13 = e1 & op(e0, e2) = e1
% 232.15/43.30  | | | 
% 232.15/43.30  | | | REF_CLOSE: (4), (7), (14) are inconsistent by sub-proof #2205.
% 232.15/43.30  | | | 
% 232.15/43.30  | | End of split
% 232.15/43.30  | | 
% 232.15/43.30  | End of split
% 232.15/43.30  | 
% 232.15/43.30  End of proof
% 232.15/43.30  
% 232.15/43.30  Sub-proof #2205 shows that the following formulas are inconsistent:
% 232.15/43.30  ----------------------------------------------------------------
% 232.15/43.30    (1)  all_57_13 = e1 & op(e0, e2) = e1
% 232.15/43.30    (2)  all_57_13 = e2
% 232.15/43.30    (3)   ~ (e2 = e1)
% 232.15/43.30  
% 232.15/43.30  Begin of proof
% 232.15/43.30  | 
% 232.15/43.30  | ALPHA: (1) implies:
% 232.15/43.30  |   (4)  all_57_13 = e1
% 232.15/43.30  | 
% 232.15/43.30  | COMBINE_EQS: (2), (4) imply:
% 232.15/43.30  |   (5)  e2 = e1
% 232.15/43.30  | 
% 232.15/43.30  | REDUCE: (3), (5) imply:
% 232.15/43.30  |   (6)  $false
% 232.15/43.30  | 
% 232.15/43.30  | CLOSE: (6) is inconsistent.
% 232.15/43.30  | 
% 232.15/43.30  End of proof
% 232.15/43.30  
% 232.15/43.30  Sub-proof #2206 shows that the following formulas are inconsistent:
% 232.15/43.30  ----------------------------------------------------------------
% 232.15/43.30    (1)   ~ (e3 = e1)
% 232.15/43.30    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.30    (3)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1)
% 232.15/43.30    (4)  op(e2, e2) = e0
% 232.15/43.30    (5)   ~ (e1 = e0)
% 232.15/43.30    (6)  all_57_1 = e3
% 232.15/43.30  
% 232.15/43.30  Begin of proof
% 232.15/43.30  | 
% 232.15/43.30  | BETA: splitting (3) gives:
% 232.15/43.30  | 
% 232.15/43.30  | Case 1:
% 232.15/43.30  | | 
% 232.15/43.30  | |   (7)  all_57_1 = e1 & op(e3, e2) = e1
% 232.15/43.30  | | 
% 232.15/43.30  | | REF_CLOSE: (1), (6), (7) are inconsistent by sub-proof #2453.
% 232.15/43.30  | | 
% 232.15/43.30  | Case 2:
% 232.15/43.30  | | 
% 232.15/43.30  | |   (8)  all_57_3 = e1 & op(e2, e2) = e1
% 232.15/43.30  | | 
% 232.15/43.30  | | ALPHA: (8) implies:
% 232.15/43.30  | |   (9)  op(e2, e2) = e1
% 232.15/43.30  | | 
% 232.15/43.30  | | REF_CLOSE: (2), (4), (5), (9) are inconsistent by sub-proof #2352.
% 232.15/43.30  | | 
% 232.15/43.30  | End of split
% 232.15/43.30  | 
% 232.15/43.30  End of proof
% 232.15/43.30  
% 232.15/43.30  Sub-proof #2207 shows that the following formulas are inconsistent:
% 232.15/43.30  ----------------------------------------------------------------
% 232.15/43.30    (1)  all_57_7 = e2
% 232.15/43.30    (2)  all_57_7 = e0
% 232.15/43.30    (3)   ~ (e2 = e0)
% 232.15/43.30  
% 232.15/43.30  Begin of proof
% 232.15/43.30  | 
% 232.15/43.30  | COMBINE_EQS: (1), (2) imply:
% 232.15/43.30  |   (4)  e2 = e0
% 232.15/43.30  | 
% 232.15/43.30  | SIMP: (4) implies:
% 232.15/43.30  |   (5)  e2 = e0
% 232.15/43.30  | 
% 232.15/43.30  | REDUCE: (3), (5) imply:
% 232.15/43.30  |   (6)  $false
% 232.15/43.30  | 
% 232.15/43.30  | CLOSE: (6) is inconsistent.
% 232.15/43.30  | 
% 232.15/43.30  End of proof
% 232.15/43.30  
% 232.15/43.30  Sub-proof #2208 shows that the following formulas are inconsistent:
% 232.15/43.30  ----------------------------------------------------------------
% 232.15/43.30    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.31    (2)  (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2)
% 232.15/43.31    (3)  op(e2, e2) = e0
% 232.15/43.31    (4)  all_57_1 = e1
% 232.15/43.31    (5)   ~ (e2 = e0)
% 232.15/43.31    (6)   ~ (e2 = e1)
% 232.15/43.31  
% 232.15/43.31  Begin of proof
% 232.15/43.31  | 
% 232.15/43.31  | BETA: splitting (2) gives:
% 232.15/43.31  | 
% 232.15/43.31  | Case 1:
% 232.15/43.31  | | 
% 232.15/43.31  | |   (7)  all_57_1 = e2 & op(e3, e2) = e2
% 232.15/43.31  | | 
% 232.15/43.31  | | REF_CLOSE: (4), (6), (7) are inconsistent by sub-proof #2489.
% 232.15/43.31  | | 
% 232.15/43.31  | Case 2:
% 232.15/43.31  | | 
% 232.15/43.31  | |   (8)  all_57_3 = e2 & op(e2, e2) = e2
% 232.15/43.31  | | 
% 232.15/43.31  | | ALPHA: (8) implies:
% 232.15/43.31  | |   (9)  op(e2, e2) = e2
% 232.15/43.31  | | 
% 232.15/43.31  | | REF_CLOSE: (1), (3), (5), (9) are inconsistent by sub-proof #2472.
% 232.15/43.31  | | 
% 232.15/43.31  | End of split
% 232.15/43.31  | 
% 232.15/43.31  End of proof
% 232.15/43.31  
% 232.15/43.31  Sub-proof #2209 shows that the following formulas are inconsistent:
% 232.15/43.31  ----------------------------------------------------------------
% 232.15/43.31    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.31    (2)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1)
% 232.15/43.31    (3)  op(e2, e2) = e0
% 232.15/43.31    (4)  all_57_1 = e2
% 232.15/43.31    (5)   ~ (e1 = e0)
% 232.15/43.31    (6)   ~ (e2 = e1)
% 232.15/43.31  
% 232.15/43.31  Begin of proof
% 232.15/43.31  | 
% 232.15/43.31  | BETA: splitting (2) gives:
% 232.15/43.31  | 
% 232.15/43.31  | Case 1:
% 232.15/43.31  | | 
% 232.15/43.31  | |   (7)  all_57_1 = e1 & op(e3, e2) = e1
% 232.15/43.31  | | 
% 232.15/43.31  | | REF_CLOSE: (4), (6), (7) are inconsistent by sub-proof #2210.
% 232.15/43.31  | | 
% 232.15/43.31  | Case 2:
% 232.15/43.31  | | 
% 232.15/43.31  | |   (8)  all_57_3 = e1 & op(e2, e2) = e1
% 232.15/43.31  | | 
% 232.15/43.31  | | ALPHA: (8) implies:
% 232.15/43.31  | |   (9)  op(e2, e2) = e1
% 232.15/43.31  | | 
% 232.15/43.31  | | REF_CLOSE: (1), (3), (5), (9) are inconsistent by sub-proof #2352.
% 232.15/43.31  | | 
% 232.15/43.31  | End of split
% 232.15/43.31  | 
% 232.15/43.31  End of proof
% 232.15/43.31  
% 232.15/43.31  Sub-proof #2210 shows that the following formulas are inconsistent:
% 232.15/43.31  ----------------------------------------------------------------
% 232.15/43.31    (1)  all_57_1 = e1 & op(e3, e2) = e1
% 232.15/43.31    (2)  all_57_1 = e2
% 232.15/43.31    (3)   ~ (e2 = e1)
% 232.15/43.31  
% 232.15/43.31  Begin of proof
% 232.15/43.31  | 
% 232.15/43.31  | ALPHA: (1) implies:
% 232.15/43.31  |   (4)  all_57_1 = e1
% 232.15/43.31  | 
% 232.15/43.31  | COMBINE_EQS: (2), (4) imply:
% 232.15/43.31  |   (5)  e2 = e1
% 232.15/43.31  | 
% 232.15/43.31  | REDUCE: (3), (5) imply:
% 232.15/43.31  |   (6)  $false
% 232.15/43.31  | 
% 232.15/43.31  | CLOSE: (6) is inconsistent.
% 232.15/43.31  | 
% 232.15/43.31  End of proof
% 232.15/43.31  
% 232.15/43.31  Sub-proof #2211 shows that the following formulas are inconsistent:
% 232.15/43.31  ----------------------------------------------------------------
% 232.15/43.31    (1)  all_57_7 = e1
% 232.15/43.31    (2)  all_57_7 = e0
% 232.15/43.31    (3)   ~ (e1 = e0)
% 232.15/43.31  
% 232.15/43.31  Begin of proof
% 232.15/43.31  | 
% 232.15/43.31  | COMBINE_EQS: (1), (2) imply:
% 232.15/43.31  |   (4)  e1 = e0
% 232.15/43.31  | 
% 232.15/43.31  | SIMP: (4) implies:
% 232.15/43.31  |   (5)  e1 = e0
% 232.15/43.31  | 
% 232.15/43.31  | REDUCE: (3), (5) imply:
% 232.15/43.31  |   (6)  $false
% 232.15/43.31  | 
% 232.15/43.31  | CLOSE: (6) is inconsistent.
% 232.15/43.31  | 
% 232.15/43.31  End of proof
% 232.15/43.31  
% 232.15/43.31  Sub-proof #2212 shows that the following formulas are inconsistent:
% 232.15/43.31  ----------------------------------------------------------------
% 232.15/43.31    (1)   ~ (e3 = e1)
% 232.15/43.31    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.31    (3)   ~ (e3 = e0)
% 232.15/43.31    (4)  all_57_15 = e3
% 232.15/43.31    (5)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 232.15/43.31         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 232.15/43.31    (6)   ~ (e2 = e0)
% 232.15/43.31    (7)   ~ (e1 = e0)
% 232.15/43.31    (8)  all_57_14 = e2
% 232.15/43.31    (9)  all_57_13 = e3
% 232.15/43.31    (10)  op(e0, e0) = e3
% 232.15/43.31    (11)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 232.15/43.31              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 232.15/43.31                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 232.15/43.31                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 232.15/43.31    (12)   ~ (e2 = e1)
% 232.15/43.31  
% 232.15/43.31  Begin of proof
% 232.15/43.31  | 
% 232.15/43.31  | BETA: splitting (11) gives:
% 232.15/43.31  | 
% 232.15/43.31  | Case 1:
% 232.15/43.31  | | 
% 232.15/43.31  | |   (13)  all_57_15 = e0 & op(e0, e0) = e0
% 232.15/43.31  | | 
% 232.15/43.31  | | ALPHA: (13) implies:
% 232.15/43.31  | |   (14)  op(e0, e0) = e0
% 232.15/43.31  | | 
% 232.15/43.31  | | REF_CLOSE: (2), (3), (10), (14) are inconsistent by sub-proof #2304.
% 232.15/43.31  | | 
% 232.15/43.31  | Case 2:
% 232.15/43.31  | | 
% 232.15/43.31  | |   (15)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 232.15/43.31  | |             e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0 &
% 232.15/43.31  | |             op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 232.15/43.31  | |           (all_57_14 = e0 & op(e0, e1) = e0))
% 232.15/43.31  | | 
% 232.15/43.31  | | ALPHA: (15) implies:
% 232.15/43.31  | |   (16)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 232.15/43.31  | |           e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 232.15/43.31  | | 
% 232.15/43.31  | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (12), (16) are
% 232.15/43.31  | |            inconsistent by sub-proof #2213.
% 232.15/43.31  | | 
% 232.15/43.31  | End of split
% 232.15/43.31  | 
% 232.15/43.31  End of proof
% 232.15/43.31  
% 232.15/43.31  Sub-proof #2213 shows that the following formulas are inconsistent:
% 232.15/43.31  ----------------------------------------------------------------
% 232.15/43.31    (1)   ~ (e3 = e1)
% 232.15/43.31    (2)   ~ (e3 = e0)
% 232.15/43.31    (3)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 232.15/43.31         (all_57_14 = e0 & op(e0, e1) = e0)
% 232.15/43.31    (4)  all_57_15 = e3
% 232.15/43.31    (5)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 232.15/43.31         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 232.15/43.31    (6)   ~ (e2 = e0)
% 232.15/43.31    (7)   ~ (e1 = e0)
% 232.15/43.31    (8)  all_57_14 = e2
% 232.15/43.31    (9)  all_57_13 = e3
% 232.15/43.31    (10)   ~ (e2 = e1)
% 232.15/43.31  
% 232.15/43.31  Begin of proof
% 232.15/43.31  | 
% 232.15/43.31  | BETA: splitting (3) gives:
% 232.15/43.31  | 
% 232.15/43.31  | Case 1:
% 232.15/43.31  | | 
% 232.15/43.31  | |   (11)  all_57_12 = e0 & op(e0, e3) = e0
% 232.15/43.31  | | 
% 232.15/43.31  | | ALPHA: (11) implies:
% 232.15/43.31  | |   (12)  all_57_12 = e0
% 232.15/43.31  | | 
% 232.15/43.31  | | REF_CLOSE: (1), (4), (5), (7), (8), (9), (10), (12) are inconsistent by
% 232.15/43.31  | |            sub-proof #2215.
% 232.15/43.31  | | 
% 232.15/43.31  | Case 2:
% 232.15/43.31  | | 
% 232.15/43.31  | |   (13)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 232.15/43.31  | |           e0)
% 232.15/43.31  | | 
% 232.15/43.31  | | BETA: splitting (13) gives:
% 232.15/43.31  | | 
% 232.15/43.31  | | Case 1:
% 232.15/43.31  | | | 
% 232.15/43.31  | | |   (14)  all_57_13 = e0 & op(e0, e2) = e0
% 232.15/43.31  | | | 
% 232.15/43.31  | | | REF_CLOSE: (2), (9), (14) are inconsistent by sub-proof #2214.
% 232.15/43.31  | | | 
% 232.15/43.31  | | Case 2:
% 232.15/43.31  | | | 
% 232.15/43.31  | | |   (15)  all_57_14 = e0 & op(e0, e1) = e0
% 232.15/43.31  | | | 
% 232.15/43.31  | | | ALPHA: (15) implies:
% 232.15/43.31  | | |   (16)  all_57_14 = e0
% 232.15/43.31  | | | 
% 232.15/43.31  | | | REF_CLOSE: (6), (8), (16) are inconsistent by sub-proof #2422.
% 232.15/43.31  | | | 
% 232.15/43.31  | | End of split
% 232.15/43.31  | | 
% 232.15/43.31  | End of split
% 232.15/43.31  | 
% 232.15/43.31  End of proof
% 232.15/43.31  
% 232.15/43.31  Sub-proof #2214 shows that the following formulas are inconsistent:
% 232.15/43.31  ----------------------------------------------------------------
% 232.15/43.31    (1)  all_57_13 = e0 & op(e0, e2) = e0
% 232.15/43.31    (2)  all_57_13 = e3
% 232.15/43.31    (3)   ~ (e3 = e0)
% 232.15/43.31  
% 232.15/43.31  Begin of proof
% 232.15/43.31  | 
% 232.15/43.31  | ALPHA: (1) implies:
% 232.15/43.31  |   (4)  all_57_13 = e0
% 232.15/43.31  | 
% 232.15/43.31  | COMBINE_EQS: (2), (4) imply:
% 232.15/43.31  |   (5)  e3 = e0
% 232.15/43.31  | 
% 232.15/43.31  | REDUCE: (3), (5) imply:
% 232.15/43.31  |   (6)  $false
% 232.15/43.31  | 
% 232.15/43.31  | CLOSE: (6) is inconsistent.
% 232.15/43.31  | 
% 232.15/43.31  End of proof
% 232.15/43.31  
% 232.15/43.31  Sub-proof #2215 shows that the following formulas are inconsistent:
% 232.15/43.31  ----------------------------------------------------------------
% 232.15/43.31    (1)  all_57_12 = e0
% 232.15/43.31    (2)   ~ (e3 = e1)
% 232.15/43.31    (3)  all_57_15 = e3
% 232.15/43.31    (4)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 232.15/43.31         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 232.15/43.31    (5)   ~ (e1 = e0)
% 232.15/43.31    (6)  all_57_14 = e2
% 232.15/43.31    (7)  all_57_13 = e3
% 232.15/43.31    (8)   ~ (e2 = e1)
% 232.15/43.31  
% 232.15/43.31  Begin of proof
% 232.15/43.31  | 
% 232.15/43.31  | BETA: splitting (4) gives:
% 232.15/43.31  | 
% 232.15/43.31  | Case 1:
% 232.15/43.31  | | 
% 232.15/43.31  | |   (9)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 232.15/43.31  | |          e1)
% 232.15/43.31  | | 
% 232.15/43.31  | | REF_CLOSE: (1), (2), (5), (7), (9) are inconsistent by sub-proof #2216.
% 232.15/43.31  | | 
% 232.15/43.31  | Case 2:
% 232.15/43.31  | | 
% 232.15/43.31  | |   (10)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 232.15/43.31  | |           e1)
% 232.15/43.31  | | 
% 232.15/43.31  | | BETA: splitting (10) gives:
% 232.15/43.31  | | 
% 232.15/43.31  | | Case 1:
% 232.15/43.31  | | | 
% 232.15/43.31  | | |   (11)  all_57_14 = e1 & op(e0, e1) = e1
% 232.15/43.31  | | | 
% 232.15/43.31  | | | REF_CLOSE: (6), (8), (11) are inconsistent by sub-proof #2375.
% 232.15/43.31  | | | 
% 232.15/43.31  | | Case 2:
% 232.15/43.31  | | | 
% 232.15/43.31  | | |   (12)  all_57_15 = e1 & op(e0, e0) = e1
% 232.15/43.31  | | | 
% 232.15/43.31  | | | REF_CLOSE: (2), (3), (12) are inconsistent by sub-proof #2318.
% 232.15/43.31  | | | 
% 232.15/43.31  | | End of split
% 232.15/43.31  | | 
% 232.15/43.31  | End of split
% 232.15/43.31  | 
% 232.15/43.31  End of proof
% 232.15/43.31  
% 232.15/43.31  Sub-proof #2216 shows that the following formulas are inconsistent:
% 232.15/43.31  ----------------------------------------------------------------
% 232.15/43.31    (1)  all_57_12 = e0
% 232.15/43.31    (2)   ~ (e3 = e1)
% 232.15/43.31    (3)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 232.15/43.31    (4)   ~ (e1 = e0)
% 232.15/43.31    (5)  all_57_13 = e3
% 232.15/43.31  
% 232.15/43.31  Begin of proof
% 232.15/43.31  | 
% 232.15/43.31  | BETA: splitting (3) gives:
% 232.15/43.31  | 
% 232.15/43.31  | Case 1:
% 232.15/43.31  | | 
% 232.15/43.31  | |   (6)  all_57_12 = e1 & op(e0, e3) = e1
% 232.15/43.31  | | 
% 232.15/43.31  | | REF_CLOSE: (1), (4), (6) are inconsistent by sub-proof #2328.
% 232.15/43.31  | | 
% 232.15/43.31  | Case 2:
% 232.15/43.31  | | 
% 232.15/43.31  | |   (7)  all_57_13 = e1 & op(e0, e2) = e1
% 232.15/43.31  | | 
% 232.15/43.31  | | ALPHA: (7) implies:
% 232.15/43.31  | |   (8)  all_57_13 = e1
% 232.15/43.31  | | 
% 232.15/43.31  | | REF_CLOSE: (2), (5), (8) are inconsistent by sub-proof #2268.
% 232.15/43.31  | | 
% 232.15/43.31  | End of split
% 232.15/43.31  | 
% 232.15/43.31  End of proof
% 232.15/43.31  
% 232.15/43.31  Sub-proof #2217 shows that the following formulas are inconsistent:
% 232.15/43.31  ----------------------------------------------------------------
% 232.15/43.31    (1)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 232.15/43.31    (2)   ~ (e3 = e1)
% 232.15/43.31    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.31    (4)  op(e1, e1) = e2
% 232.15/43.31    (5)  all_57_11 = e3
% 232.15/43.31    (6)   ~ (e2 = e1)
% 232.15/43.31  
% 232.15/43.31  Begin of proof
% 232.15/43.31  | 
% 232.15/43.31  | BETA: splitting (1) gives:
% 232.15/43.31  | 
% 232.15/43.31  | Case 1:
% 232.15/43.31  | | 
% 232.15/43.31  | |   (7)  all_57_8 = e1 & op(e1, e1) = e1
% 232.15/43.31  | | 
% 232.15/43.31  | | ALPHA: (7) implies:
% 232.15/43.31  | |   (8)  op(e1, e1) = e1
% 232.15/43.31  | | 
% 232.15/43.31  | | REF_CLOSE: (3), (4), (6), (8) are inconsistent by sub-proof #2423.
% 232.15/43.31  | | 
% 232.15/43.31  | Case 2:
% 232.15/43.31  | | 
% 232.15/43.31  | |   (9)  all_57_11 = e1 & op(e1, e0) = e1
% 232.15/43.31  | | 
% 232.15/43.31  | | ALPHA: (9) implies:
% 232.15/43.31  | |   (10)  all_57_11 = e1
% 232.15/43.31  | | 
% 232.15/43.31  | | REF_CLOSE: (2), (5), (10) are inconsistent by sub-proof #2218.
% 232.15/43.31  | | 
% 232.15/43.31  | End of split
% 232.15/43.31  | 
% 232.15/43.31  End of proof
% 232.15/43.31  
% 232.15/43.31  Sub-proof #2218 shows that the following formulas are inconsistent:
% 232.15/43.31  ----------------------------------------------------------------
% 232.15/43.31    (1)  all_57_11 = e3
% 232.15/43.31    (2)  all_57_11 = e1
% 232.15/43.31    (3)   ~ (e3 = e1)
% 232.15/43.31  
% 232.15/43.31  Begin of proof
% 232.15/43.31  | 
% 232.15/43.31  | COMBINE_EQS: (1), (2) imply:
% 232.15/43.31  |   (4)  e3 = e1
% 232.15/43.31  | 
% 232.15/43.31  | SIMP: (4) implies:
% 232.15/43.31  |   (5)  e3 = e1
% 232.15/43.31  | 
% 232.15/43.31  | REDUCE: (3), (5) imply:
% 232.15/43.31  |   (6)  $false
% 232.15/43.31  | 
% 232.15/43.31  | CLOSE: (6) is inconsistent.
% 232.15/43.31  | 
% 232.15/43.31  End of proof
% 232.15/43.31  
% 232.15/43.31  Sub-proof #2219 shows that the following formulas are inconsistent:
% 232.15/43.31  ----------------------------------------------------------------
% 232.15/43.31    (1)  all_57_9 = e2
% 232.15/43.31    (2)   ~ (e3 = e1)
% 232.15/43.31    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.31    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 232.15/43.31         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 232.15/43.31    (5)  all_57_4 = e0
% 232.15/43.31    (6)  op(e3, e3) = e3
% 232.15/43.31    (7)  all_57_1 = e0
% 232.15/43.31    (8)   ~ (e1 = e0)
% 232.15/43.31    (9)   ~ (e2 = e1)
% 232.15/43.31  
% 232.15/43.31  Begin of proof
% 232.15/43.31  | 
% 232.15/43.31  | BETA: splitting (4) gives:
% 232.15/43.31  | 
% 232.15/43.31  | Case 1:
% 232.15/43.31  | | 
% 232.15/43.31  | |   (10)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) =
% 232.15/43.31  | |           e1)
% 232.15/43.31  | | 
% 232.15/43.31  | | REF_CLOSE: (2), (3), (6), (7), (8), (10) are inconsistent by sub-proof
% 232.15/43.31  | |            #2445.
% 232.15/43.31  | | 
% 232.15/43.31  | Case 2:
% 232.15/43.31  | | 
% 232.15/43.31  | |   (11)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) =
% 232.15/43.31  | |           e1)
% 232.15/43.31  | | 
% 232.15/43.31  | | BETA: splitting (11) gives:
% 232.15/43.31  | | 
% 232.15/43.31  | | Case 1:
% 232.15/43.31  | | | 
% 232.15/43.31  | | |   (12)  all_57_4 = e1 & op(e3, e1) = e1
% 232.15/43.31  | | | 
% 232.15/43.31  | | | ALPHA: (12) implies:
% 232.15/43.31  | | |   (13)  all_57_4 = e1
% 232.15/43.31  | | | 
% 232.15/43.31  | | | REF_CLOSE: (5), (8), (13) are inconsistent by sub-proof #2438.
% 232.15/43.31  | | | 
% 232.15/43.31  | | Case 2:
% 232.15/43.31  | | | 
% 232.15/43.31  | | |   (14)  all_57_9 = e1 & op(e3, e0) = e1
% 232.15/43.31  | | | 
% 232.15/43.31  | | | REF_CLOSE: (1), (9), (14) are inconsistent by sub-proof #2451.
% 232.15/43.31  | | | 
% 232.15/43.31  | | End of split
% 232.15/43.31  | | 
% 232.15/43.31  | End of split
% 232.15/43.31  | 
% 232.15/43.31  End of proof
% 232.15/43.31  
% 232.15/43.31  Sub-proof #2220 shows that the following formulas are inconsistent:
% 232.15/43.31  ----------------------------------------------------------------
% 232.15/43.31    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.31    (2)  all_57_9 = e1
% 232.15/43.31    (3)  all_57_4 = e0
% 232.15/43.31    (4)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 232.15/43.31         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 232.15/43.31    (5)   ~ (e3 = e2)
% 232.15/43.31    (6)  op(e3, e3) = e3
% 232.15/43.31    (7)  all_57_1 = e1
% 232.15/43.31    (8)   ~ (e2 = e0)
% 232.15/43.31    (9)   ~ (e2 = e1)
% 232.15/43.31  
% 232.15/43.31  Begin of proof
% 232.15/43.31  | 
% 232.15/43.31  | BETA: splitting (4) gives:
% 232.15/43.31  | 
% 232.15/43.31  | Case 1:
% 232.15/43.31  | | 
% 232.15/43.31  | |   (10)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) =
% 232.15/43.31  | |           e2)
% 232.15/43.31  | | 
% 232.15/43.31  | | REF_CLOSE: (1), (5), (6), (7), (9), (10) are inconsistent by sub-proof
% 232.15/43.31  | |            #2488.
% 232.15/43.31  | | 
% 232.15/43.31  | Case 2:
% 232.15/43.31  | | 
% 232.15/43.31  | |   (11)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) =
% 232.15/43.31  | |           e2)
% 232.15/43.31  | | 
% 232.15/43.31  | | REF_CLOSE: (2), (3), (8), (9), (11) are inconsistent by sub-proof #2221.
% 232.15/43.31  | | 
% 232.15/43.31  | End of split
% 232.15/43.31  | 
% 232.15/43.31  End of proof
% 232.15/43.31  
% 232.15/43.31  Sub-proof #2221 shows that the following formulas are inconsistent:
% 232.15/43.31  ----------------------------------------------------------------
% 232.15/43.31    (1)  all_57_9 = e1
% 232.15/43.31    (2)  all_57_4 = e0
% 232.15/43.31    (3)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 232.15/43.31    (4)   ~ (e2 = e0)
% 232.15/43.31    (5)   ~ (e2 = e1)
% 232.15/43.31  
% 232.15/43.31  Begin of proof
% 232.15/43.31  | 
% 232.15/43.31  | BETA: splitting (3) gives:
% 232.15/43.31  | 
% 232.15/43.31  | Case 1:
% 232.15/43.31  | | 
% 232.15/43.31  | |   (6)  all_57_4 = e2 & op(e3, e1) = e2
% 232.15/43.31  | | 
% 232.15/43.31  | | ALPHA: (6) implies:
% 232.15/43.31  | |   (7)  all_57_4 = e2
% 232.15/43.31  | | 
% 232.15/43.31  | | REF_CLOSE: (2), (4), (7) are inconsistent by sub-proof #2441.
% 232.15/43.31  | | 
% 232.15/43.31  | Case 2:
% 232.15/43.31  | | 
% 232.15/43.31  | |   (8)  all_57_9 = e2 & op(e3, e0) = e2
% 232.15/43.31  | | 
% 232.15/43.31  | | ALPHA: (8) implies:
% 232.15/43.31  | |   (9)  all_57_9 = e2
% 232.15/43.31  | | 
% 232.15/43.31  | | REF_CLOSE: (1), (5), (9) are inconsistent by sub-proof #2444.
% 232.15/43.31  | | 
% 232.15/43.31  | End of split
% 232.15/43.31  | 
% 232.15/43.31  End of proof
% 232.15/43.31  
% 232.15/43.31  Sub-proof #2222 shows that the following formulas are inconsistent:
% 232.15/43.31  ----------------------------------------------------------------
% 232.15/43.31    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.31    (2)   ~ (e3 = e0)
% 232.15/43.31    (3)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 232.15/43.31    (4)  all_57_5 = e3
% 232.15/43.31    (5)   ~ (all_53_13 = e0)
% 232.15/43.31    (6)  op(e2, e0) = all_53_13
% 232.15/43.31  
% 232.15/43.31  Begin of proof
% 232.15/43.31  | 
% 232.15/43.31  | BETA: splitting (3) gives:
% 232.15/43.31  | 
% 232.15/43.31  | Case 1:
% 232.15/43.31  | | 
% 232.15/43.31  | |   (7)  all_57_5 = e0 & op(e2, e1) = e0
% 232.15/43.31  | | 
% 232.15/43.31  | | REF_CLOSE: (2), (4), (7) are inconsistent by sub-proof #2414.
% 232.15/43.31  | | 
% 232.15/43.31  | Case 2:
% 232.15/43.31  | | 
% 232.15/43.31  | |   (8)  all_57_10 = e0 & op(e2, e0) = e0
% 232.15/43.31  | | 
% 232.15/43.31  | | ALPHA: (8) implies:
% 232.15/43.31  | |   (9)  op(e2, e0) = e0
% 232.15/43.31  | | 
% 232.15/43.31  | | REF_CLOSE: (1), (5), (6), (9) are inconsistent by sub-proof #2470.
% 232.15/43.31  | | 
% 232.15/43.31  | End of split
% 232.15/43.31  | 
% 232.15/43.31  End of proof
% 232.15/43.31  
% 232.15/43.31  Sub-proof #2223 shows that the following formulas are inconsistent:
% 232.15/43.31  ----------------------------------------------------------------
% 232.15/43.31    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 232.15/43.31         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 232.15/43.31    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 232.15/43.31         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 232.15/43.31    (3)   ~ (e3 = e1)
% 232.15/43.31    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.31    (5)  all_57_3 = e0
% 232.15/43.31    (6)   ~ (e3 = e2)
% 232.15/43.31    (7)   ~ (e3 = e0)
% 232.15/43.31    (8)  op(e3, e3) = e3
% 232.15/43.31    (9)   ~ (e2 = e0)
% 232.15/43.31    (10)   ~ (e1 = e0)
% 232.15/43.31    (11)  all_57_12 = e3
% 232.15/43.31    (12)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 232.15/43.31          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 232.15/43.31    (13)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 232.15/43.31          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 232.15/43.31    (14)   ~ (e2 = e1)
% 232.15/43.31    (15)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 232.15/43.31          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 232.15/43.31    (16)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 232.15/43.31          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 232.15/43.31  
% 232.15/43.31  Begin of proof
% 232.15/43.31  | 
% 232.15/43.31  | BETA: splitting (15) gives:
% 232.15/43.31  | 
% 232.15/43.31  | Case 1:
% 232.15/43.31  | | 
% 232.15/43.31  | |   (17)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) =
% 232.15/43.31  | |           e2)
% 232.15/43.31  | | 
% 232.15/43.31  | | BETA: splitting (17) gives:
% 232.15/43.31  | | 
% 232.15/43.31  | | Case 1:
% 232.15/43.31  | | | 
% 232.15/43.31  | | |   (18)  all_57_0 = e2 & op(e3, e3) = e2
% 232.15/43.31  | | | 
% 232.15/43.31  | | | ALPHA: (18) implies:
% 232.15/43.31  | | |   (19)  op(e3, e3) = e2
% 232.15/43.31  | | | 
% 232.15/43.31  | | | REF_CLOSE: (4), (6), (8), (19) are inconsistent by sub-proof #2490.
% 232.15/43.31  | | | 
% 232.15/43.31  | | Case 2:
% 232.15/43.31  | | | 
% 232.15/43.31  | | |   (20)  all_57_2 = e2 & op(e2, e3) = e2
% 232.15/43.31  | | | 
% 232.15/43.31  | | | ALPHA: (20) implies:
% 232.15/43.31  | | |   (21)  all_57_2 = e2
% 232.15/43.31  | | | 
% 232.15/43.31  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 232.15/43.31  | | |            (13), (14), (16), (21) are inconsistent by sub-proof #2224.
% 232.15/43.31  | | | 
% 232.15/43.31  | | End of split
% 232.15/43.31  | | 
% 232.15/43.31  | Case 2:
% 232.15/43.31  | | 
% 232.15/43.31  | |   (22)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) =
% 232.15/43.31  | |           e2)
% 232.15/43.31  | | 
% 232.15/43.31  | | BETA: splitting (22) gives:
% 232.15/43.31  | | 
% 232.15/43.31  | | Case 1:
% 232.15/43.31  | | | 
% 232.15/43.31  | | |   (23)  all_57_6 = e2 & op(e1, e3) = e2
% 232.15/43.31  | | | 
% 232.15/43.31  | | | ALPHA: (23) implies:
% 232.15/43.31  | | |   (24)  all_57_6 = e2
% 232.15/43.31  | | | 
% 232.15/43.31  | | | BETA: splitting (16) gives:
% 232.15/43.31  | | | 
% 232.15/43.31  | | | Case 1:
% 232.15/43.31  | | | | 
% 232.15/43.31  | | | |   (25)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3)
% 232.15/43.31  | | | |           = e0)
% 232.15/43.31  | | | | 
% 232.15/43.31  | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 232.15/43.31  | | | |            (14), (25) are inconsistent by sub-proof #2229.
% 232.15/43.31  | | | | 
% 232.15/43.31  | | | Case 2:
% 232.15/43.31  | | | | 
% 232.15/43.31  | | | |   (26)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3)
% 232.15/43.31  | | | |           = e0)
% 232.15/43.31  | | | | 
% 232.15/43.31  | | | | BETA: splitting (26) gives:
% 232.15/43.31  | | | | 
% 232.15/43.31  | | | | Case 1:
% 232.15/43.31  | | | | | 
% 232.15/43.31  | | | | |   (27)  all_57_6 = e0 & op(e1, e3) = e0
% 232.15/43.31  | | | | | 
% 232.15/43.31  | | | | | REF_CLOSE: (9), (24), (27) are inconsistent by sub-proof #2386.
% 232.15/43.31  | | | | | 
% 232.15/43.31  | | | | Case 2:
% 232.15/43.31  | | | | | 
% 232.15/43.31  | | | | |   (28)  all_57_12 = e0 & op(e0, e3) = e0
% 232.15/43.31  | | | | | 
% 232.15/43.31  | | | | | REF_CLOSE: (7), (11), (28) are inconsistent by sub-proof #2237.
% 232.15/43.31  | | | | | 
% 232.15/43.31  | | | | End of split
% 232.15/43.31  | | | | 
% 232.15/43.31  | | | End of split
% 232.15/43.31  | | | 
% 232.15/43.31  | | Case 2:
% 232.15/43.31  | | | 
% 232.15/43.31  | | |   (29)  all_57_12 = e2 & op(e0, e3) = e2
% 232.15/43.31  | | | 
% 232.15/43.31  | | | REF_CLOSE: (6), (11), (29) are inconsistent by sub-proof #2232.
% 232.15/43.31  | | | 
% 232.15/43.31  | | End of split
% 232.15/43.31  | | 
% 232.15/43.31  | End of split
% 232.15/43.31  | 
% 232.15/43.31  End of proof
% 232.15/43.31  
% 232.15/43.31  Sub-proof #2224 shows that the following formulas are inconsistent:
% 232.15/43.31  ----------------------------------------------------------------
% 232.15/43.31    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 232.15/43.31         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 232.15/43.31    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 232.15/43.31         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 232.15/43.31    (3)   ~ (e3 = e1)
% 232.15/43.31    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.31    (5)  all_57_2 = e2
% 232.15/43.31    (6)  all_57_3 = e0
% 232.15/43.31    (7)   ~ (e3 = e2)
% 232.15/43.31    (8)   ~ (e3 = e0)
% 232.15/43.31    (9)  op(e3, e3) = e3
% 232.15/43.31    (10)   ~ (e2 = e0)
% 232.15/43.31    (11)   ~ (e1 = e0)
% 232.15/43.31    (12)  all_57_12 = e3
% 232.15/43.31    (13)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 232.15/43.31          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 232.15/43.31    (14)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 232.15/43.31          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 232.15/43.31    (15)   ~ (e2 = e1)
% 232.15/43.31    (16)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 232.15/43.31          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 232.15/43.31  
% 232.15/43.31  Begin of proof
% 232.15/43.31  | 
% 232.15/43.31  | BETA: splitting (16) gives:
% 232.15/43.31  | 
% 232.15/43.31  | Case 1:
% 232.15/43.31  | | 
% 232.15/43.31  | |   (17)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) =
% 232.15/43.31  | |           e0)
% 232.15/43.31  | | 
% 232.15/43.31  | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (10), (11), (13), (14), (15),
% 232.15/43.31  | |            (17) are inconsistent by sub-proof #2229.
% 232.15/43.31  | | 
% 232.15/43.31  | Case 2:
% 232.15/43.31  | | 
% 232.15/43.31  | |   (18)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) =
% 232.15/43.31  | |           e0)
% 232.15/43.31  | | 
% 232.15/43.31  | | BETA: splitting (18) gives:
% 232.15/43.31  | | 
% 232.15/43.31  | | Case 1:
% 232.15/43.31  | | | 
% 232.15/43.31  | | |   (19)  all_57_6 = e0 & op(e1, e3) = e0
% 232.15/43.31  | | | 
% 232.15/43.31  | | | REF_CLOSE: (2), (3), (4), (5), (9), (11), (12), (15), (19) are
% 232.15/43.31  | | |            inconsistent by sub-proof #2225.
% 232.15/43.31  | | | 
% 232.15/43.31  | | Case 2:
% 232.15/43.31  | | | 
% 232.15/43.31  | | |   (20)  all_57_12 = e0 & op(e0, e3) = e0
% 232.15/43.31  | | | 
% 232.15/43.31  | | | REF_CLOSE: (8), (12), (20) are inconsistent by sub-proof #2237.
% 232.15/43.31  | | | 
% 232.15/43.31  | | End of split
% 232.15/43.31  | | 
% 232.15/43.31  | End of split
% 232.15/43.31  | 
% 232.15/43.31  End of proof
% 232.15/43.31  
% 232.15/43.31  Sub-proof #2225 shows that the following formulas are inconsistent:
% 232.15/43.31  ----------------------------------------------------------------
% 232.15/43.31    (1)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 232.15/43.31         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 232.15/43.31    (2)   ~ (e3 = e1)
% 232.15/43.31    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.31    (4)  all_57_2 = e2
% 232.15/43.31    (5)  op(e3, e3) = e3
% 232.15/43.31    (6)   ~ (e1 = e0)
% 232.15/43.31    (7)  all_57_12 = e3
% 232.15/43.31    (8)  all_57_6 = e0 & op(e1, e3) = e0
% 232.15/43.31    (9)   ~ (e2 = e1)
% 232.15/43.31  
% 232.15/43.31  Begin of proof
% 232.15/43.31  | 
% 232.15/43.31  | ALPHA: (8) implies:
% 232.15/43.31  |   (10)  all_57_6 = e0
% 232.15/43.31  | 
% 232.15/43.31  | BETA: splitting (1) gives:
% 232.15/43.31  | 
% 232.15/43.31  | Case 1:
% 232.15/43.31  | | 
% 232.15/43.31  | |   (11)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) =
% 232.15/43.31  | |           e1)
% 232.15/43.31  | | 
% 232.15/43.31  | | REF_CLOSE: (2), (3), (4), (5), (9), (11) are inconsistent by sub-proof
% 232.15/43.31  | |            #2228.
% 232.15/43.31  | | 
% 232.15/43.31  | Case 2:
% 232.15/43.31  | | 
% 232.15/43.31  | |   (12)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) =
% 232.15/43.31  | |           e1)
% 232.15/43.31  | | 
% 232.15/43.31  | | REF_CLOSE: (2), (6), (7), (10), (12) are inconsistent by sub-proof #2226.
% 232.15/43.31  | | 
% 232.15/43.31  | End of split
% 232.15/43.31  | 
% 232.15/43.31  End of proof
% 232.15/43.31  
% 232.15/43.31  Sub-proof #2226 shows that the following formulas are inconsistent:
% 232.15/43.31  ----------------------------------------------------------------
% 232.15/43.31    (1)   ~ (e3 = e1)
% 232.15/43.31    (2)  all_57_6 = e0
% 232.15/43.31    (3)   ~ (e1 = e0)
% 232.15/43.31    (4)  all_57_12 = e3
% 232.15/43.31    (5)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 232.15/43.31  
% 232.15/43.31  Begin of proof
% 232.15/43.31  | 
% 232.15/43.31  | BETA: splitting (5) gives:
% 232.15/43.31  | 
% 232.15/43.31  | Case 1:
% 232.15/43.31  | | 
% 232.15/43.31  | |   (6)  all_57_6 = e1 & op(e1, e3) = e1
% 232.15/43.31  | | 
% 232.15/43.31  | | ALPHA: (6) implies:
% 232.15/43.31  | |   (7)  all_57_6 = e1
% 232.15/43.31  | | 
% 232.15/43.31  | | REF_CLOSE: (2), (3), (7) are inconsistent by sub-proof #2227.
% 232.15/43.31  | | 
% 232.15/43.31  | Case 2:
% 232.15/43.31  | | 
% 232.15/43.31  | |   (8)  all_57_12 = e1 & op(e0, e3) = e1
% 232.15/43.31  | | 
% 232.15/43.31  | | REF_CLOSE: (1), (4), (8) are inconsistent by sub-proof #2230.
% 232.15/43.31  | | 
% 232.15/43.31  | End of split
% 232.15/43.31  | 
% 232.15/43.31  End of proof
% 232.15/43.31  
% 232.15/43.31  Sub-proof #2227 shows that the following formulas are inconsistent:
% 232.15/43.31  ----------------------------------------------------------------
% 232.15/43.31    (1)  all_57_6 = e1
% 232.15/43.31    (2)  all_57_6 = e0
% 232.15/43.31    (3)   ~ (e1 = e0)
% 232.15/43.31  
% 232.15/43.31  Begin of proof
% 232.15/43.31  | 
% 232.15/43.31  | COMBINE_EQS: (1), (2) imply:
% 232.15/43.31  |   (4)  e1 = e0
% 232.15/43.31  | 
% 232.15/43.31  | SIMP: (4) implies:
% 232.15/43.31  |   (5)  e1 = e0
% 232.15/43.31  | 
% 232.15/43.31  | REDUCE: (3), (5) imply:
% 232.15/43.31  |   (6)  $false
% 232.15/43.31  | 
% 232.15/43.31  | CLOSE: (6) is inconsistent.
% 232.15/43.31  | 
% 232.15/43.31  End of proof
% 232.15/43.31  
% 232.15/43.31  Sub-proof #2228 shows that the following formulas are inconsistent:
% 232.15/43.31  ----------------------------------------------------------------
% 232.15/43.31    (1)   ~ (e3 = e1)
% 232.15/43.31    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.31    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1)
% 232.15/43.31    (4)  all_57_2 = e2
% 232.15/43.31    (5)  op(e3, e3) = e3
% 232.15/43.31    (6)   ~ (e2 = e1)
% 232.15/43.31  
% 232.15/43.31  Begin of proof
% 232.15/43.31  | 
% 232.15/43.31  | BETA: splitting (3) gives:
% 232.15/43.31  | 
% 232.15/43.31  | Case 1:
% 232.15/43.31  | | 
% 232.15/43.31  | |   (7)  all_57_0 = e1 & op(e3, e3) = e1
% 232.15/43.31  | | 
% 232.15/43.31  | | ALPHA: (7) implies:
% 232.15/43.31  | |   (8)  op(e3, e3) = e1
% 232.15/43.31  | | 
% 232.15/43.31  | | REF_CLOSE: (1), (2), (5), (8) are inconsistent by sub-proof #2495.
% 232.15/43.31  | | 
% 232.15/43.31  | Case 2:
% 232.15/43.31  | | 
% 232.15/43.31  | |   (9)  all_57_2 = e1 & op(e2, e3) = e1
% 232.15/43.31  | | 
% 232.15/43.31  | | REF_CLOSE: (4), (6), (9) are inconsistent by sub-proof #2244.
% 232.15/43.31  | | 
% 232.15/43.31  | End of split
% 232.15/43.31  | 
% 232.15/43.31  End of proof
% 232.15/43.31  
% 232.15/43.31  Sub-proof #2229 shows that the following formulas are inconsistent:
% 232.15/43.31  ----------------------------------------------------------------
% 232.15/43.31    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 232.15/43.31         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 232.15/43.31    (2)   ~ (e3 = e1)
% 232.15/43.31    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.31    (4)  all_57_3 = e0
% 232.15/43.31    (5)   ~ (e3 = e2)
% 232.15/43.31    (6)   ~ (e3 = e0)
% 232.15/43.31    (7)  op(e3, e3) = e3
% 232.15/43.31    (8)   ~ (e2 = e0)
% 232.15/43.31    (9)   ~ (e1 = e0)
% 232.15/43.31    (10)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 232.15/43.31          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 232.15/43.31    (11)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 232.15/43.31          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 232.15/43.31    (12)   ~ (e2 = e1)
% 232.15/43.31    (13)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0)
% 232.15/43.31  
% 232.15/43.31  Begin of proof
% 232.15/43.31  | 
% 232.15/43.31  | BETA: splitting (13) gives:
% 232.15/43.31  | 
% 232.15/43.31  | Case 1:
% 232.15/43.31  | | 
% 232.15/43.31  | |   (14)  all_57_0 = e0 & op(e3, e3) = e0
% 232.15/43.31  | | 
% 232.15/43.31  | | ALPHA: (14) implies:
% 232.15/43.31  | |   (15)  op(e3, e3) = e0
% 232.15/43.31  | | 
% 232.15/43.31  | | REF_CLOSE: (3), (6), (7), (15) are inconsistent by sub-proof #2494.
% 232.15/43.31  | | 
% 232.15/43.31  | Case 2:
% 232.15/43.31  | | 
% 232.15/43.31  | |   (16)  all_57_2 = e0 & op(e2, e3) = e0
% 232.15/43.31  | | 
% 232.15/43.31  | | ALPHA: (16) implies:
% 232.15/43.31  | |   (17)  all_57_2 = e0
% 232.15/43.31  | | 
% 232.15/43.31  | | REF_CLOSE: (1), (2), (4), (5), (6), (8), (9), (10), (11), (12), (17) are
% 232.15/43.31  | |            inconsistent by sub-proof #2246.
% 232.15/43.31  | | 
% 232.15/43.31  | End of split
% 232.15/43.31  | 
% 232.15/43.31  End of proof
% 232.15/43.31  
% 232.15/43.31  Sub-proof #2230 shows that the following formulas are inconsistent:
% 232.15/43.31  ----------------------------------------------------------------
% 232.15/43.31    (1)  all_57_12 = e1 & op(e0, e3) = e1
% 232.15/43.31    (2)  all_57_12 = e3
% 232.15/43.31    (3)   ~ (e3 = e1)
% 232.15/43.31  
% 232.15/43.31  Begin of proof
% 232.15/43.31  | 
% 232.15/43.31  | ALPHA: (1) implies:
% 232.15/43.31  |   (4)  all_57_12 = e1
% 232.15/43.31  | 
% 232.15/43.31  | COMBINE_EQS: (2), (4) imply:
% 232.15/43.31  |   (5)  e3 = e1
% 232.15/43.31  | 
% 232.15/43.31  | REDUCE: (3), (5) imply:
% 232.15/43.31  |   (6)  $false
% 232.15/43.31  | 
% 232.15/43.31  | CLOSE: (6) is inconsistent.
% 232.15/43.31  | 
% 232.15/43.31  End of proof
% 232.15/43.31  
% 232.15/43.31  Sub-proof #2231 shows that the following formulas are inconsistent:
% 232.15/43.31  ----------------------------------------------------------------
% 232.15/43.31    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.31    (2)  all_57_6 = e1
% 232.15/43.31    (3)   ~ (e3 = e2)
% 232.15/43.31    (4)  op(e3, e3) = e3
% 232.15/43.31    (5)   ~ (e2 = e0)
% 232.15/43.31    (6)  all_57_12 = e3
% 232.15/43.31    (7)  all_57_2 = e0
% 232.15/43.31    (8)   ~ (e2 = e1)
% 232.15/43.32    (9)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 232.15/43.32         (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 232.15/43.32  
% 232.15/43.32  Begin of proof
% 232.15/43.32  | 
% 232.15/43.32  | BETA: splitting (9) gives:
% 232.15/43.32  | 
% 232.15/43.32  | Case 1:
% 232.15/43.32  | | 
% 232.15/43.32  | |   (10)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) =
% 232.15/43.32  | |           e2)
% 232.15/43.32  | | 
% 232.15/43.32  | | REF_CLOSE: (1), (3), (4), (5), (7), (10) are inconsistent by sub-proof
% 232.15/43.32  | |            #2234.
% 232.15/43.32  | | 
% 232.15/43.32  | Case 2:
% 232.15/43.32  | | 
% 232.15/43.32  | |   (11)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) =
% 232.15/43.32  | |           e2)
% 232.15/43.32  | | 
% 232.15/43.32  | | BETA: splitting (11) gives:
% 232.15/43.32  | | 
% 232.15/43.32  | | Case 1:
% 232.15/43.32  | | | 
% 232.15/43.32  | | |   (12)  all_57_6 = e2 & op(e1, e3) = e2
% 232.15/43.32  | | | 
% 232.15/43.32  | | | ALPHA: (12) implies:
% 232.15/43.32  | | |   (13)  all_57_6 = e2
% 232.15/43.32  | | | 
% 232.15/43.32  | | | REF_CLOSE: (2), (8), (13) are inconsistent by sub-proof #2233.
% 232.15/43.32  | | | 
% 232.15/43.32  | | Case 2:
% 232.15/43.32  | | | 
% 232.15/43.32  | | |   (14)  all_57_12 = e2 & op(e0, e3) = e2
% 232.15/43.32  | | | 
% 232.15/43.32  | | | REF_CLOSE: (3), (6), (14) are inconsistent by sub-proof #2232.
% 232.15/43.32  | | | 
% 232.15/43.32  | | End of split
% 232.15/43.32  | | 
% 232.15/43.32  | End of split
% 232.15/43.32  | 
% 232.15/43.32  End of proof
% 232.15/43.32  
% 232.15/43.32  Sub-proof #2232 shows that the following formulas are inconsistent:
% 232.15/43.32  ----------------------------------------------------------------
% 232.15/43.32    (1)  all_57_12 = e2 & op(e0, e3) = e2
% 232.15/43.32    (2)  all_57_12 = e3
% 232.15/43.32    (3)   ~ (e3 = e2)
% 232.15/43.32  
% 232.15/43.32  Begin of proof
% 232.15/43.32  | 
% 232.15/43.32  | ALPHA: (1) implies:
% 232.15/43.32  |   (4)  all_57_12 = e2
% 232.15/43.32  | 
% 232.15/43.32  | COMBINE_EQS: (2), (4) imply:
% 232.15/43.32  |   (5)  e3 = e2
% 232.15/43.32  | 
% 232.15/43.32  | REDUCE: (3), (5) imply:
% 232.15/43.32  |   (6)  $false
% 232.15/43.32  | 
% 232.15/43.32  | CLOSE: (6) is inconsistent.
% 232.15/43.32  | 
% 232.15/43.32  End of proof
% 232.15/43.32  
% 232.15/43.32  Sub-proof #2233 shows that the following formulas are inconsistent:
% 232.15/43.32  ----------------------------------------------------------------
% 232.15/43.32    (1)  all_57_6 = e2
% 232.15/43.32    (2)  all_57_6 = e1
% 232.15/43.32    (3)   ~ (e2 = e1)
% 232.15/43.32  
% 232.15/43.32  Begin of proof
% 232.15/43.32  | 
% 232.15/43.32  | COMBINE_EQS: (1), (2) imply:
% 232.15/43.32  |   (4)  e2 = e1
% 232.15/43.32  | 
% 232.15/43.32  | SIMP: (4) implies:
% 232.15/43.32  |   (5)  e2 = e1
% 232.15/43.32  | 
% 232.15/43.32  | REDUCE: (3), (5) imply:
% 232.15/43.32  |   (6)  $false
% 232.15/43.32  | 
% 232.15/43.32  | CLOSE: (6) is inconsistent.
% 232.15/43.32  | 
% 232.15/43.32  End of proof
% 232.15/43.32  
% 232.15/43.32  Sub-proof #2234 shows that the following formulas are inconsistent:
% 232.15/43.32  ----------------------------------------------------------------
% 232.15/43.32    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.32           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.32    (2)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2)
% 232.15/43.32    (3)   ~ (e3 = e2)
% 232.15/43.32    (4)  op(e3, e3) = e3
% 232.15/43.32    (5)   ~ (e2 = e0)
% 232.15/43.32    (6)  all_57_2 = e0
% 232.15/43.32  
% 232.15/43.32  Begin of proof
% 232.15/43.32  | 
% 232.15/43.32  | BETA: splitting (2) gives:
% 232.15/43.32  | 
% 232.15/43.32  | Case 1:
% 232.15/43.32  | | 
% 232.15/43.32  | |   (7)  all_57_0 = e2 & op(e3, e3) = e2
% 232.15/43.32  | | 
% 232.15/43.32  | | ALPHA: (7) implies:
% 232.15/43.32  | |   (8)  op(e3, e3) = e2
% 232.15/43.32  | | 
% 232.15/43.32  | | REF_CLOSE: (1), (3), (4), (8) are inconsistent by sub-proof #2490.
% 232.15/43.32  | | 
% 232.15/43.32  | Case 2:
% 232.15/43.32  | | 
% 232.15/43.32  | |   (9)  all_57_2 = e2 & op(e2, e3) = e2
% 232.15/43.32  | | 
% 232.15/43.32  | | REF_CLOSE: (5), (6), (9) are inconsistent by sub-proof #2257.
% 232.15/43.32  | | 
% 232.15/43.32  | End of split
% 232.15/43.32  | 
% 232.15/43.32  End of proof
% 232.15/43.32  
% 232.15/43.32  Sub-proof #2235 shows that the following formulas are inconsistent:
% 232.15/43.32  ----------------------------------------------------------------
% 232.15/43.32    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 232.15/43.32         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 232.15/43.32    (2)   ~ (e3 = e1)
% 232.15/43.32    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.32           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.32    (4)   ~ (e3 = e2)
% 232.15/43.32    (5)   ~ (e3 = e0)
% 232.15/43.32    (6)  op(e3, e3) = e3
% 232.15/43.32    (7)  all_57_5 = e3
% 232.15/43.32    (8)   ~ (e2 = e0)
% 232.15/43.32    (9)  op(e2, e2) = e2
% 232.15/43.32    (10)   ~ (e1 = e0)
% 232.15/43.32    (11)  all_57_12 = e3
% 232.15/43.32    (12)  all_57_2 = e1
% 232.15/43.32    (13)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 232.15/43.32          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 232.15/43.32    (14)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 232.15/43.32          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 232.15/43.32    (15)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 232.15/43.32          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 232.15/43.32    (16)   ~ (e2 = e1)
% 232.15/43.32    (17)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 232.15/43.32          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 232.15/43.32    (18)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 232.15/43.32          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 232.15/43.32    (19)  all_57_3 = e2
% 232.15/43.32  
% 232.15/43.32  Begin of proof
% 232.15/43.32  | 
% 232.15/43.32  | BETA: splitting (17) gives:
% 232.15/43.32  | 
% 232.15/43.32  | Case 1:
% 232.15/43.32  | | 
% 232.15/43.32  | |   (20)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) =
% 232.15/43.32  | |           e2)
% 232.15/43.32  | | 
% 232.15/43.32  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (13), (14),
% 232.15/43.32  | |            (15), (16), (19), (20) are inconsistent by sub-proof #2238.
% 232.15/43.32  | | 
% 232.15/43.32  | Case 2:
% 232.15/43.32  | | 
% 232.15/43.32  | |   (21)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) =
% 232.15/43.32  | |           e2)
% 232.15/43.32  | | 
% 232.15/43.32  | | BETA: splitting (21) gives:
% 232.15/43.32  | | 
% 232.15/43.32  | | Case 1:
% 232.15/43.32  | | | 
% 232.15/43.32  | | |   (22)  all_57_6 = e2 & op(e1, e3) = e2
% 232.15/43.32  | | | 
% 232.15/43.32  | | | ALPHA: (22) implies:
% 232.15/43.32  | | |   (23)  all_57_6 = e2
% 232.15/43.32  | | | 
% 232.15/43.32  | | | REF_CLOSE: (3), (5), (6), (8), (10), (11), (12), (18), (23) are
% 232.15/43.32  | | |            inconsistent by sub-proof #2236.
% 232.15/43.32  | | | 
% 232.15/43.32  | | Case 2:
% 232.15/43.32  | | | 
% 232.15/43.32  | | |   (24)  all_57_12 = e2 & op(e0, e3) = e2
% 232.15/43.32  | | | 
% 232.15/43.32  | | | ALPHA: (24) implies:
% 232.15/43.32  | | |   (25)  all_57_12 = e2
% 232.15/43.32  | | | 
% 232.15/43.32  | | | REF_CLOSE: (4), (11), (25) are inconsistent by sub-proof #2392.
% 232.15/43.32  | | | 
% 232.15/43.32  | | End of split
% 232.15/43.32  | | 
% 232.15/43.32  | End of split
% 232.15/43.32  | 
% 232.15/43.32  End of proof
% 232.15/43.32  
% 232.15/43.32  Sub-proof #2236 shows that the following formulas are inconsistent:
% 232.15/43.32  ----------------------------------------------------------------
% 232.15/43.32    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.32           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.32    (2)   ~ (e3 = e0)
% 232.15/43.32    (3)  op(e3, e3) = e3
% 232.15/43.32    (4)  all_57_6 = e2
% 232.15/43.32    (5)   ~ (e2 = e0)
% 232.15/43.32    (6)   ~ (e1 = e0)
% 232.15/43.32    (7)  all_57_12 = e3
% 232.15/43.32    (8)  all_57_2 = e1
% 232.15/43.32    (9)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 232.15/43.32         (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 232.15/43.32  
% 232.15/43.32  Begin of proof
% 232.15/43.32  | 
% 232.15/43.32  | BETA: splitting (9) gives:
% 232.15/43.32  | 
% 232.15/43.32  | Case 1:
% 232.15/43.32  | | 
% 232.15/43.32  | |   (10)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) =
% 232.15/43.32  | |           e0)
% 232.15/43.32  | | 
% 232.15/43.32  | | REF_CLOSE: (1), (2), (3), (6), (8), (10) are inconsistent by sub-proof
% 232.15/43.32  | |            #2466.
% 232.15/43.32  | | 
% 232.15/43.32  | Case 2:
% 232.15/43.32  | | 
% 232.15/43.32  | |   (11)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) =
% 232.15/43.32  | |           e0)
% 232.15/43.32  | | 
% 232.15/43.32  | | BETA: splitting (11) gives:
% 232.15/43.32  | | 
% 232.15/43.32  | | Case 1:
% 232.15/43.32  | | | 
% 232.15/43.32  | | |   (12)  all_57_6 = e0 & op(e1, e3) = e0
% 232.15/43.32  | | | 
% 232.15/43.32  | | | REF_CLOSE: (4), (5), (12) are inconsistent by sub-proof #2386.
% 232.15/43.32  | | | 
% 232.15/43.32  | | Case 2:
% 232.15/43.32  | | | 
% 232.15/43.32  | | |   (13)  all_57_12 = e0 & op(e0, e3) = e0
% 232.15/43.32  | | | 
% 232.15/43.32  | | | REF_CLOSE: (2), (7), (13) are inconsistent by sub-proof #2237.
% 232.15/43.32  | | | 
% 232.15/43.32  | | End of split
% 232.15/43.32  | | 
% 232.15/43.32  | End of split
% 232.15/43.32  | 
% 232.15/43.32  End of proof
% 232.15/43.32  
% 232.15/43.32  Sub-proof #2237 shows that the following formulas are inconsistent:
% 232.15/43.32  ----------------------------------------------------------------
% 232.15/43.32    (1)  all_57_12 = e0 & op(e0, e3) = e0
% 232.15/43.32    (2)  all_57_12 = e3
% 232.15/43.32    (3)   ~ (e3 = e0)
% 232.15/43.32  
% 232.15/43.32  Begin of proof
% 232.15/43.32  | 
% 232.15/43.32  | ALPHA: (1) implies:
% 232.15/43.32  |   (4)  all_57_12 = e0
% 232.15/43.32  | 
% 232.15/43.32  | COMBINE_EQS: (2), (4) imply:
% 232.15/43.32  |   (5)  e3 = e0
% 232.15/43.32  | 
% 232.15/43.32  | REDUCE: (3), (5) imply:
% 232.15/43.32  |   (6)  $false
% 232.15/43.32  | 
% 232.15/43.32  | CLOSE: (6) is inconsistent.
% 232.15/43.32  | 
% 232.15/43.32  End of proof
% 232.15/43.32  
% 232.15/43.32  Sub-proof #2238 shows that the following formulas are inconsistent:
% 232.15/43.32  ----------------------------------------------------------------
% 232.15/43.32    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 232.15/43.32         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 232.15/43.32    (2)   ~ (e3 = e1)
% 232.15/43.32    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.32           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.32    (4)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2)
% 232.15/43.32    (5)   ~ (e3 = e2)
% 232.15/43.32    (6)   ~ (e3 = e0)
% 232.15/43.32    (7)  op(e3, e3) = e3
% 232.15/43.32    (8)  all_57_5 = e3
% 232.15/43.32    (9)   ~ (e2 = e0)
% 232.15/43.32    (10)  op(e2, e2) = e2
% 232.15/43.32    (11)   ~ (e1 = e0)
% 232.15/43.32    (12)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 232.15/43.32          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 232.15/43.32    (13)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 232.15/43.32          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 232.15/43.32    (14)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 232.15/43.32          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 232.15/43.32    (15)   ~ (e2 = e1)
% 232.15/43.32    (16)  all_57_3 = e2
% 232.15/43.32  
% 232.15/43.32  Begin of proof
% 232.15/43.32  | 
% 232.15/43.32  | BETA: splitting (4) gives:
% 232.15/43.32  | 
% 232.15/43.32  | Case 1:
% 232.15/43.32  | | 
% 232.15/43.32  | |   (17)  all_57_0 = e2 & op(e3, e3) = e2
% 232.15/43.32  | | 
% 232.15/43.32  | | ALPHA: (17) implies:
% 232.15/43.32  | |   (18)  op(e3, e3) = e2
% 232.15/43.32  | | 
% 232.15/43.32  | | REF_CLOSE: (3), (5), (7), (18) are inconsistent by sub-proof #2490.
% 232.15/43.32  | | 
% 232.15/43.32  | Case 2:
% 232.15/43.32  | | 
% 232.15/43.32  | |   (19)  all_57_2 = e2 & op(e2, e3) = e2
% 232.15/43.32  | | 
% 232.15/43.32  | | ALPHA: (19) implies:
% 232.15/43.32  | |   (20)  all_57_2 = e2
% 232.15/43.32  | | 
% 232.15/43.32  | | REF_CLOSE: (1), (2), (3), (5), (6), (8), (9), (10), (11), (12), (13), (14),
% 232.15/43.32  | |            (15), (16), (20) are inconsistent by sub-proof #2239.
% 232.15/43.32  | | 
% 232.15/43.32  | End of split
% 232.15/43.32  | 
% 232.15/43.32  End of proof
% 232.15/43.32  
% 232.15/43.32  Sub-proof #2239 shows that the following formulas are inconsistent:
% 232.15/43.32  ----------------------------------------------------------------
% 232.15/43.32    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 232.15/43.32         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 232.15/43.32    (2)   ~ (e3 = e1)
% 232.15/43.32    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.32           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.32    (4)  all_57_2 = e2
% 232.15/43.32    (5)   ~ (e3 = e2)
% 232.15/43.32    (6)   ~ (e3 = e0)
% 232.15/43.32    (7)  all_57_5 = e3
% 232.15/43.32    (8)   ~ (e2 = e0)
% 232.15/43.32    (9)  op(e2, e2) = e2
% 232.15/43.32    (10)   ~ (e1 = e0)
% 232.15/43.32    (11)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 232.15/43.32          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 232.15/43.32    (12)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 232.15/43.32          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 232.15/43.32    (13)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 232.15/43.32          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 232.15/43.32    (14)   ~ (e2 = e1)
% 232.15/43.32    (15)  all_57_3 = e2
% 232.15/43.32  
% 232.15/43.32  Begin of proof
% 232.15/43.32  | 
% 232.15/43.32  | BETA: splitting (13) gives:
% 232.15/43.32  | 
% 232.15/43.32  | Case 1:
% 232.15/43.32  | | 
% 232.15/43.32  | |   (16)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) =
% 232.15/43.32  | |           e0)
% 232.15/43.32  | | 
% 232.15/43.32  | | BETA: splitting (16) gives:
% 232.15/43.32  | | 
% 232.15/43.32  | | Case 1:
% 232.15/43.32  | | | 
% 232.15/43.32  | | |   (17)  all_57_2 = e0 & op(e2, e3) = e0
% 232.15/43.32  | | | 
% 232.15/43.32  | | | ALPHA: (17) implies:
% 232.15/43.32  | | |   (18)  all_57_2 = e0
% 232.15/43.32  | | | 
% 232.15/43.32  | | | COMBINE_EQS: (4), (18) imply:
% 232.15/43.32  | | |   (19)  e2 = e0
% 232.15/43.32  | | | 
% 232.15/43.32  | | | REF_CLOSE: (1), (2), (4), (5), (6), (8), (10), (11), (12), (14), (15),
% 232.15/43.32  | | |            (19) are inconsistent by sub-proof #2245.
% 232.15/43.32  | | | 
% 232.15/43.32  | | Case 2:
% 232.15/43.32  | | | 
% 232.15/43.32  | | |   (20)  all_57_3 = e0 & op(e2, e2) = e0
% 232.15/43.32  | | | 
% 232.15/43.32  | | | ALPHA: (20) implies:
% 232.15/43.32  | | |   (21)  op(e2, e2) = e0
% 232.15/43.32  | | | 
% 232.15/43.32  | | | REF_CLOSE: (3), (8), (9), (21) are inconsistent by sub-proof #2472.
% 232.15/43.32  | | | 
% 232.15/43.32  | | End of split
% 232.15/43.32  | | 
% 232.15/43.32  | Case 2:
% 232.15/43.32  | | 
% 232.15/43.32  | |   (22)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 232.15/43.32  | |           e0)
% 232.15/43.32  | | 
% 232.15/43.32  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (9), (10), (14), (22) are
% 232.15/43.32  | |            inconsistent by sub-proof #2240.
% 232.15/43.32  | | 
% 232.15/43.32  | End of split
% 232.15/43.32  | 
% 232.15/43.32  End of proof
% 232.15/43.32  
% 232.15/43.32  Sub-proof #2240 shows that the following formulas are inconsistent:
% 232.15/43.32  ----------------------------------------------------------------
% 232.15/43.32    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 232.15/43.32         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 232.15/43.32    (2)   ~ (e3 = e1)
% 232.15/43.32    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.32           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.32    (4)  all_57_2 = e2
% 232.15/43.32    (5)   ~ (e3 = e0)
% 232.15/43.32    (6)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 232.15/43.32    (7)  all_57_5 = e3
% 232.15/43.32    (8)  op(e2, e2) = e2
% 232.15/43.32    (9)   ~ (e1 = e0)
% 232.15/43.32    (10)   ~ (e2 = e1)
% 232.15/43.32  
% 232.15/43.32  Begin of proof
% 232.15/43.32  | 
% 232.15/43.32  | BETA: splitting (6) gives:
% 232.15/43.32  | 
% 232.15/43.32  | Case 1:
% 232.15/43.32  | | 
% 232.15/43.32  | |   (11)  all_57_5 = e0 & op(e2, e1) = e0
% 232.15/43.32  | | 
% 232.15/43.32  | | REF_CLOSE: (5), (7), (11) are inconsistent by sub-proof #2414.
% 232.15/43.32  | | 
% 232.15/43.32  | Case 2:
% 232.15/43.32  | | 
% 232.15/43.32  | |   (12)  all_57_10 = e0 & op(e2, e0) = e0
% 232.15/43.32  | | 
% 232.15/43.32  | | ALPHA: (12) implies:
% 232.15/43.32  | |   (13)  all_57_10 = e0
% 232.15/43.32  | | 
% 232.15/43.32  | | REF_CLOSE: (1), (2), (3), (4), (7), (8), (9), (10), (13) are inconsistent by
% 232.15/43.32  | |            sub-proof #2241.
% 232.15/43.32  | | 
% 232.15/43.32  | End of split
% 232.15/43.32  | 
% 232.15/43.32  End of proof
% 232.15/43.32  
% 232.15/43.32  Sub-proof #2241 shows that the following formulas are inconsistent:
% 232.15/43.32  ----------------------------------------------------------------
% 232.15/43.32    (1)  all_57_10 = e0
% 232.15/43.32    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 232.15/43.32         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 232.15/43.32    (3)   ~ (e3 = e1)
% 232.15/43.32    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.32           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.32    (5)  all_57_2 = e2
% 232.15/43.32    (6)  all_57_5 = e3
% 232.15/43.32    (7)  op(e2, e2) = e2
% 232.15/43.32    (8)   ~ (e1 = e0)
% 232.15/43.32    (9)   ~ (e2 = e1)
% 232.15/43.32  
% 232.15/43.32  Begin of proof
% 232.15/43.32  | 
% 232.15/43.32  | BETA: splitting (2) gives:
% 232.15/43.32  | 
% 232.15/43.32  | Case 1:
% 232.15/43.32  | | 
% 232.15/43.32  | |   (10)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) =
% 232.15/43.32  | |           e1)
% 232.15/43.32  | | 
% 232.15/43.32  | | REF_CLOSE: (4), (5), (7), (9), (10) are inconsistent by sub-proof #2243.
% 232.15/43.32  | | 
% 232.15/43.32  | Case 2:
% 232.15/43.32  | | 
% 232.15/43.32  | |   (11)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) =
% 232.15/43.32  | |           e1)
% 232.15/43.32  | | 
% 232.15/43.32  | | BETA: splitting (11) gives:
% 232.15/43.32  | | 
% 232.15/43.32  | | Case 1:
% 232.15/43.32  | | | 
% 232.15/43.32  | | |   (12)  all_57_5 = e1 & op(e2, e1) = e1
% 232.15/43.32  | | | 
% 232.15/43.32  | | | REF_CLOSE: (3), (6), (12) are inconsistent by sub-proof #2376.
% 232.15/43.32  | | | 
% 232.15/43.32  | | Case 2:
% 232.15/43.32  | | | 
% 232.15/43.32  | | |   (13)  all_57_10 = e1 & op(e2, e0) = e1
% 232.15/43.32  | | | 
% 232.15/43.32  | | | REF_CLOSE: (1), (8), (13) are inconsistent by sub-proof #2242.
% 232.15/43.32  | | | 
% 232.15/43.32  | | End of split
% 232.15/43.32  | | 
% 232.15/43.32  | End of split
% 232.15/43.32  | 
% 232.15/43.32  End of proof
% 232.15/43.32  
% 232.15/43.32  Sub-proof #2242 shows that the following formulas are inconsistent:
% 232.15/43.32  ----------------------------------------------------------------
% 232.15/43.32    (1)  all_57_10 = e1 & op(e2, e0) = e1
% 232.15/43.32    (2)  all_57_10 = e0
% 232.15/43.32    (3)   ~ (e1 = e0)
% 232.15/43.32  
% 232.15/43.32  Begin of proof
% 232.15/43.32  | 
% 232.15/43.32  | ALPHA: (1) implies:
% 232.15/43.32  |   (4)  all_57_10 = e1
% 232.15/43.32  | 
% 232.15/43.32  | COMBINE_EQS: (2), (4) imply:
% 232.15/43.32  |   (5)  e1 = e0
% 232.15/43.32  | 
% 232.15/43.32  | REDUCE: (3), (5) imply:
% 232.15/43.32  |   (6)  $false
% 232.15/43.32  | 
% 232.15/43.32  | CLOSE: (6) is inconsistent.
% 232.15/43.32  | 
% 232.15/43.32  End of proof
% 232.15/43.32  
% 232.15/43.32  Sub-proof #2243 shows that the following formulas are inconsistent:
% 232.15/43.32  ----------------------------------------------------------------
% 232.15/43.32    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.32           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.32    (2)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1)
% 232.15/43.32    (3)  all_57_2 = e2
% 232.15/43.32    (4)  op(e2, e2) = e2
% 232.15/43.32    (5)   ~ (e2 = e1)
% 232.15/43.32  
% 232.15/43.32  Begin of proof
% 232.15/43.32  | 
% 232.15/43.32  | BETA: splitting (2) gives:
% 232.15/43.32  | 
% 232.15/43.32  | Case 1:
% 232.15/43.32  | | 
% 232.15/43.32  | |   (6)  all_57_2 = e1 & op(e2, e3) = e1
% 232.15/43.32  | | 
% 232.15/43.32  | | REF_CLOSE: (3), (5), (6) are inconsistent by sub-proof #2244.
% 232.15/43.32  | | 
% 232.15/43.32  | Case 2:
% 232.15/43.32  | | 
% 232.15/43.32  | |   (7)  all_57_3 = e1 & op(e2, e2) = e1
% 232.15/43.32  | | 
% 232.15/43.32  | | ALPHA: (7) implies:
% 232.15/43.32  | |   (8)  op(e2, e2) = e1
% 232.15/43.32  | | 
% 232.15/43.32  | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #2306.
% 232.15/43.32  | | 
% 232.15/43.32  | End of split
% 232.15/43.32  | 
% 232.15/43.32  End of proof
% 232.15/43.32  
% 232.15/43.32  Sub-proof #2244 shows that the following formulas are inconsistent:
% 232.15/43.32  ----------------------------------------------------------------
% 232.15/43.32    (1)  all_57_2 = e1 & op(e2, e3) = e1
% 232.15/43.32    (2)  all_57_2 = e2
% 232.15/43.32    (3)   ~ (e2 = e1)
% 232.15/43.32  
% 232.15/43.32  Begin of proof
% 232.15/43.32  | 
% 232.15/43.32  | ALPHA: (1) implies:
% 232.15/43.32  |   (4)  all_57_2 = e1
% 232.15/43.32  | 
% 232.15/43.32  | COMBINE_EQS: (2), (4) imply:
% 232.15/43.32  |   (5)  e2 = e1
% 232.15/43.32  | 
% 232.15/43.32  | REDUCE: (3), (5) imply:
% 232.15/43.32  |   (6)  $false
% 232.15/43.32  | 
% 232.15/43.32  | CLOSE: (6) is inconsistent.
% 232.15/43.32  | 
% 232.15/43.32  End of proof
% 232.15/43.32  
% 232.15/43.32  Sub-proof #2245 shows that the following formulas are inconsistent:
% 232.15/43.32  ----------------------------------------------------------------
% 232.15/43.32    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 232.15/43.32         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 232.15/43.32    (2)   ~ (e3 = e1)
% 232.15/43.32    (3)  all_57_2 = e2
% 232.15/43.32    (4)   ~ (e3 = e2)
% 232.15/43.32    (5)   ~ (e3 = e0)
% 232.15/43.32    (6)   ~ (e2 = e0)
% 232.15/43.32    (7)  e2 = e0
% 232.15/43.32    (8)   ~ (e1 = e0)
% 232.15/43.32    (9)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 232.15/43.32         (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 232.15/43.32    (10)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 232.15/43.32          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 232.15/43.32    (11)   ~ (e2 = e1)
% 232.15/43.32    (12)  all_57_3 = e2
% 232.15/43.32  
% 232.15/43.32  Begin of proof
% 232.15/43.32  | 
% 232.15/43.32  | COMBINE_EQS: (7), (12) imply:
% 232.15/43.32  |   (13)  all_57_3 = e0
% 232.15/43.32  | 
% 232.15/43.32  | COMBINE_EQS: (3), (7) imply:
% 232.15/43.32  |   (14)  all_57_2 = e0
% 232.15/43.32  | 
% 232.15/43.32  | REF_CLOSE: (1), (2), (4), (5), (6), (8), (9), (10), (11), (13), (14) are
% 232.15/43.32  |            inconsistent by sub-proof #2246.
% 232.15/43.32  | 
% 232.15/43.32  End of proof
% 232.15/43.32  
% 232.15/43.32  Sub-proof #2246 shows that the following formulas are inconsistent:
% 232.15/43.32  ----------------------------------------------------------------
% 232.15/43.32    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 232.15/43.32         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 232.15/43.32    (2)   ~ (e3 = e1)
% 232.15/43.32    (3)  all_57_3 = e0
% 232.15/43.32    (4)   ~ (e3 = e2)
% 232.15/43.32    (5)   ~ (e3 = e0)
% 232.15/43.32    (6)   ~ (e2 = e0)
% 232.15/43.32    (7)   ~ (e1 = e0)
% 232.15/43.32    (8)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 232.15/43.32         (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 232.15/43.32    (9)  all_57_2 = e0
% 232.15/43.32    (10)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 232.15/43.32          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 232.15/43.32    (11)   ~ (e2 = e1)
% 232.15/43.32  
% 232.15/43.32  Begin of proof
% 232.15/43.32  | 
% 232.15/43.32  | BETA: splitting (8) gives:
% 232.15/43.32  | 
% 232.15/43.32  | Case 1:
% 232.15/43.32  | | 
% 232.15/43.32  | |   (12)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 232.15/43.32  | |           e3)
% 232.15/43.32  | | 
% 232.15/43.32  | | BETA: splitting (12) gives:
% 232.15/43.32  | | 
% 232.15/43.32  | | Case 1:
% 232.15/43.32  | | | 
% 232.15/43.32  | | |   (13)  all_57_2 = e3 & op(e2, e3) = e3
% 232.15/43.32  | | | 
% 232.15/43.32  | | | ALPHA: (13) implies:
% 232.15/43.32  | | |   (14)  all_57_2 = e3
% 232.15/43.32  | | | 
% 232.15/43.32  | | | REF_CLOSE: (5), (9), (14) are inconsistent by sub-proof #2258.
% 232.15/43.32  | | | 
% 232.15/43.32  | | Case 2:
% 232.15/43.32  | | | 
% 232.15/43.32  | | |   (15)  all_57_3 = e3 & op(e2, e2) = e3
% 232.15/43.32  | | | 
% 232.15/43.32  | | | ALPHA: (15) implies:
% 232.15/43.32  | | |   (16)  all_57_3 = e3
% 232.15/43.32  | | | 
% 232.15/43.32  | | | REF_CLOSE: (3), (5), (16) are inconsistent by sub-proof #2358.
% 232.15/43.32  | | | 
% 232.15/43.32  | | End of split
% 232.15/43.32  | | 
% 232.15/43.32  | Case 2:
% 232.15/43.32  | | 
% 232.15/43.32  | |   (17)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 232.15/43.32  | |           e3)
% 232.15/43.32  | | 
% 232.15/43.32  | | BETA: splitting (17) gives:
% 232.15/43.32  | | 
% 232.15/43.32  | | Case 1:
% 232.15/43.32  | | | 
% 232.15/43.32  | | |   (18)  all_57_5 = e3 & op(e2, e1) = e3
% 232.15/43.32  | | | 
% 232.15/43.32  | | | ALPHA: (18) implies:
% 232.15/43.32  | | |   (19)  all_57_5 = e3
% 232.15/43.32  | | | 
% 232.15/43.32  | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (9), (10), (11), (19) are
% 232.15/43.32  | | |            inconsistent by sub-proof #2253.
% 232.15/43.32  | | | 
% 232.15/43.32  | | Case 2:
% 232.15/43.32  | | | 
% 232.15/43.32  | | |   (20)  all_57_10 = e3 & op(e2, e0) = e3
% 232.15/43.32  | | | 
% 232.15/43.32  | | | ALPHA: (20) implies:
% 232.15/43.32  | | |   (21)  all_57_10 = e3
% 232.15/43.32  | | | 
% 232.15/43.32  | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (9), (10), (11), (21) are
% 232.15/43.32  | | |            inconsistent by sub-proof #2247.
% 232.15/43.32  | | | 
% 232.15/43.32  | | End of split
% 232.15/43.32  | | 
% 232.15/43.32  | End of split
% 232.15/43.32  | 
% 232.15/43.32  End of proof
% 232.15/43.32  
% 232.15/43.32  Sub-proof #2247 shows that the following formulas are inconsistent:
% 232.15/43.32  ----------------------------------------------------------------
% 232.15/43.32    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 232.15/43.32         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 232.15/43.32    (2)   ~ (e3 = e1)
% 232.15/43.32    (3)  all_57_3 = e0
% 232.15/43.32    (4)   ~ (e3 = e2)
% 232.15/43.32    (5)   ~ (e2 = e0)
% 232.15/43.32    (6)   ~ (e1 = e0)
% 232.15/43.32    (7)  all_57_10 = e3
% 232.15/43.32    (8)  all_57_2 = e0
% 232.15/43.32    (9)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 232.15/43.32         (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 232.15/43.32    (10)   ~ (e2 = e1)
% 232.15/43.32  
% 232.15/43.32  Begin of proof
% 232.15/43.32  | 
% 232.15/43.32  | BETA: splitting (1) gives:
% 232.15/43.32  | 
% 232.15/43.32  | Case 1:
% 232.15/43.32  | | 
% 232.15/43.32  | |   (11)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) =
% 232.15/43.32  | |           e1)
% 232.15/43.32  | | 
% 232.15/43.32  | | BETA: splitting (11) gives:
% 232.15/43.32  | | 
% 232.15/43.32  | | Case 1:
% 232.15/43.32  | | | 
% 232.15/43.32  | | |   (12)  all_57_2 = e1 & op(e2, e3) = e1
% 232.15/43.32  | | | 
% 232.15/43.32  | | | ALPHA: (12) implies:
% 232.15/43.32  | | |   (13)  all_57_2 = e1
% 232.15/43.32  | | | 
% 232.15/43.32  | | | REF_CLOSE: (6), (8), (13) are inconsistent by sub-proof #2473.
% 232.15/43.32  | | | 
% 232.15/43.32  | | Case 2:
% 232.15/43.32  | | | 
% 232.15/43.32  | | |   (14)  all_57_3 = e1 & op(e2, e2) = e1
% 232.15/43.32  | | | 
% 232.15/43.32  | | | REF_CLOSE: (3), (6), (14) are inconsistent by sub-proof #2252.
% 232.15/43.32  | | | 
% 232.15/43.32  | | End of split
% 232.15/43.32  | | 
% 232.15/43.32  | Case 2:
% 232.15/43.32  | | 
% 232.15/43.32  | |   (15)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) =
% 232.15/43.32  | |           e1)
% 232.15/43.32  | | 
% 232.15/43.32  | | BETA: splitting (15) gives:
% 232.15/43.32  | | 
% 232.15/43.32  | | Case 1:
% 232.15/43.32  | | | 
% 232.15/43.32  | | |   (16)  all_57_5 = e1 & op(e2, e1) = e1
% 232.15/43.32  | | | 
% 232.15/43.32  | | | ALPHA: (16) implies:
% 232.15/43.32  | | |   (17)  all_57_5 = e1
% 232.15/43.32  | | | 
% 232.15/43.32  | | | REF_CLOSE: (3), (4), (5), (7), (8), (9), (10), (17) are inconsistent by
% 232.15/43.32  | | |            sub-proof #2249.
% 232.15/43.32  | | | 
% 232.15/43.32  | | Case 2:
% 232.15/43.32  | | | 
% 232.15/43.32  | | |   (18)  all_57_10 = e1 & op(e2, e0) = e1
% 232.15/43.32  | | | 
% 232.15/43.32  | | | ALPHA: (18) implies:
% 232.15/43.32  | | |   (19)  all_57_10 = e1
% 232.15/43.32  | | | 
% 232.15/43.32  | | | REF_CLOSE: (2), (7), (19) are inconsistent by sub-proof #2248.
% 232.15/43.32  | | | 
% 232.15/43.32  | | End of split
% 232.15/43.32  | | 
% 232.15/43.32  | End of split
% 232.15/43.32  | 
% 232.15/43.32  End of proof
% 232.15/43.32  
% 232.15/43.32  Sub-proof #2248 shows that the following formulas are inconsistent:
% 232.15/43.32  ----------------------------------------------------------------
% 232.15/43.32    (1)  all_57_10 = e3
% 232.15/43.32    (2)  all_57_10 = e1
% 232.15/43.32    (3)   ~ (e3 = e1)
% 232.15/43.32  
% 232.15/43.32  Begin of proof
% 232.15/43.32  | 
% 232.15/43.32  | COMBINE_EQS: (1), (2) imply:
% 232.15/43.32  |   (4)  e3 = e1
% 232.15/43.32  | 
% 232.15/43.32  | SIMP: (4) implies:
% 232.15/43.32  |   (5)  e3 = e1
% 232.15/43.32  | 
% 232.15/43.32  | REDUCE: (3), (5) imply:
% 232.15/43.32  |   (6)  $false
% 232.15/43.32  | 
% 232.15/43.32  | CLOSE: (6) is inconsistent.
% 232.15/43.32  | 
% 232.15/43.32  End of proof
% 232.15/43.32  
% 232.15/43.32  Sub-proof #2249 shows that the following formulas are inconsistent:
% 232.15/43.32  ----------------------------------------------------------------
% 232.15/43.32    (1)  all_57_3 = e0
% 232.15/43.32    (2)   ~ (e3 = e2)
% 232.15/43.32    (3)   ~ (e2 = e0)
% 232.15/43.32    (4)  all_57_10 = e3
% 232.15/43.32    (5)  all_57_5 = e1
% 232.15/43.32    (6)  all_57_2 = e0
% 232.15/43.32    (7)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 232.15/43.32         (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 232.15/43.32    (8)   ~ (e2 = e1)
% 232.15/43.32  
% 232.15/43.32  Begin of proof
% 232.15/43.32  | 
% 232.15/43.32  | BETA: splitting (7) gives:
% 232.15/43.32  | 
% 232.15/43.32  | Case 1:
% 232.15/43.32  | | 
% 232.15/43.32  | |   (9)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2)
% 232.15/43.32  | | 
% 232.15/43.32  | | BETA: splitting (9) gives:
% 232.15/43.32  | | 
% 232.15/43.32  | | Case 1:
% 232.15/43.32  | | | 
% 232.15/43.32  | | |   (10)  all_57_2 = e2 & op(e2, e3) = e2
% 232.15/43.32  | | | 
% 232.15/43.32  | | | REF_CLOSE: (3), (6), (10) are inconsistent by sub-proof #2257.
% 232.15/43.32  | | | 
% 232.15/43.32  | | Case 2:
% 232.15/43.32  | | | 
% 232.15/43.32  | | |   (11)  all_57_3 = e2 & op(e2, e2) = e2
% 232.15/43.32  | | | 
% 232.15/43.32  | | | REF_CLOSE: (1), (3), (11) are inconsistent by sub-proof #2256.
% 232.15/43.32  | | | 
% 232.15/43.32  | | End of split
% 232.15/43.32  | | 
% 232.15/43.32  | Case 2:
% 232.15/43.32  | | 
% 232.15/43.32  | |   (12)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 232.15/43.32  | |           e2)
% 232.15/43.32  | | 
% 232.15/43.32  | | BETA: splitting (12) gives:
% 232.15/43.32  | | 
% 232.15/43.32  | | Case 1:
% 232.15/43.32  | | | 
% 232.15/43.32  | | |   (13)  all_57_5 = e2 & op(e2, e1) = e2
% 232.15/43.32  | | | 
% 232.15/43.32  | | | REF_CLOSE: (5), (8), (13) are inconsistent by sub-proof #2251.
% 232.15/43.32  | | | 
% 232.15/43.32  | | Case 2:
% 232.15/43.32  | | | 
% 232.15/43.32  | | |   (14)  all_57_10 = e2 & op(e2, e0) = e2
% 232.15/43.32  | | | 
% 232.15/43.32  | | | REF_CLOSE: (2), (4), (14) are inconsistent by sub-proof #2250.
% 232.15/43.32  | | | 
% 232.15/43.32  | | End of split
% 232.15/43.32  | | 
% 232.15/43.32  | End of split
% 232.15/43.32  | 
% 232.15/43.32  End of proof
% 232.15/43.32  
% 232.15/43.32  Sub-proof #2250 shows that the following formulas are inconsistent:
% 232.15/43.32  ----------------------------------------------------------------
% 232.15/43.32    (1)  all_57_10 = e2 & op(e2, e0) = e2
% 232.15/43.32    (2)  all_57_10 = e3
% 232.15/43.32    (3)   ~ (e3 = e2)
% 232.15/43.32  
% 232.15/43.32  Begin of proof
% 232.15/43.32  | 
% 232.15/43.32  | ALPHA: (1) implies:
% 232.15/43.32  |   (4)  all_57_10 = e2
% 232.15/43.32  | 
% 232.15/43.32  | COMBINE_EQS: (2), (4) imply:
% 232.15/43.32  |   (5)  e3 = e2
% 232.15/43.32  | 
% 232.15/43.32  | REDUCE: (3), (5) imply:
% 232.15/43.32  |   (6)  $false
% 232.15/43.32  | 
% 232.15/43.32  | CLOSE: (6) is inconsistent.
% 232.15/43.32  | 
% 232.15/43.32  End of proof
% 232.15/43.32  
% 232.15/43.32  Sub-proof #2251 shows that the following formulas are inconsistent:
% 232.15/43.32  ----------------------------------------------------------------
% 232.15/43.32    (1)  all_57_5 = e2 & op(e2, e1) = e2
% 232.15/43.32    (2)  all_57_5 = e1
% 232.15/43.32    (3)   ~ (e2 = e1)
% 232.15/43.32  
% 232.15/43.32  Begin of proof
% 232.15/43.32  | 
% 232.15/43.32  | ALPHA: (1) implies:
% 232.15/43.32  |   (4)  all_57_5 = e2
% 232.15/43.32  | 
% 232.15/43.32  | COMBINE_EQS: (2), (4) imply:
% 232.15/43.32  |   (5)  e2 = e1
% 232.15/43.32  | 
% 232.15/43.32  | REDUCE: (3), (5) imply:
% 232.15/43.32  |   (6)  $false
% 232.15/43.32  | 
% 232.15/43.32  | CLOSE: (6) is inconsistent.
% 232.15/43.32  | 
% 232.15/43.32  End of proof
% 232.15/43.32  
% 232.15/43.32  Sub-proof #2252 shows that the following formulas are inconsistent:
% 232.15/43.32  ----------------------------------------------------------------
% 232.15/43.32    (1)  all_57_3 = e1 & op(e2, e2) = e1
% 232.15/43.32    (2)  all_57_3 = e0
% 232.15/43.32    (3)   ~ (e1 = e0)
% 232.15/43.32  
% 232.15/43.32  Begin of proof
% 232.15/43.32  | 
% 232.15/43.32  | ALPHA: (1) implies:
% 232.15/43.32  |   (4)  all_57_3 = e1
% 232.15/43.32  | 
% 232.15/43.32  | COMBINE_EQS: (2), (4) imply:
% 232.15/43.32  |   (5)  e1 = e0
% 232.15/43.32  | 
% 232.15/43.32  | REDUCE: (3), (5) imply:
% 232.15/43.32  |   (6)  $false
% 232.15/43.32  | 
% 232.15/43.32  | CLOSE: (6) is inconsistent.
% 232.15/43.32  | 
% 232.15/43.32  End of proof
% 232.15/43.32  
% 232.15/43.32  Sub-proof #2253 shows that the following formulas are inconsistent:
% 232.15/43.32  ----------------------------------------------------------------
% 232.15/43.32    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 232.15/43.32         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 232.15/43.32    (2)   ~ (e3 = e1)
% 232.15/43.32    (3)  all_57_3 = e0
% 232.15/43.32    (4)   ~ (e3 = e2)
% 232.15/43.32    (5)  all_57_5 = e3
% 232.15/43.32    (6)   ~ (e2 = e0)
% 232.15/43.32    (7)   ~ (e1 = e0)
% 232.15/43.32    (8)  all_57_2 = e0
% 232.15/43.32    (9)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 232.15/43.32         (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 232.15/43.32    (10)   ~ (e2 = e1)
% 232.15/43.32  
% 232.15/43.32  Begin of proof
% 232.15/43.32  | 
% 232.15/43.32  | BETA: splitting (1) gives:
% 232.15/43.32  | 
% 232.15/43.32  | Case 1:
% 232.15/43.32  | | 
% 232.15/43.33  | |   (11)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) =
% 232.15/43.33  | |           e1)
% 232.15/43.33  | | 
% 232.15/43.33  | | BETA: splitting (11) gives:
% 232.15/43.33  | | 
% 232.15/43.33  | | Case 1:
% 232.15/43.33  | | | 
% 232.15/43.33  | | |   (12)  all_57_2 = e1 & op(e2, e3) = e1
% 232.15/43.33  | | | 
% 232.15/43.33  | | | ALPHA: (12) implies:
% 232.15/43.33  | | |   (13)  all_57_2 = e1
% 232.15/43.33  | | | 
% 232.15/43.33  | | | REF_CLOSE: (7), (8), (13) are inconsistent by sub-proof #2473.
% 232.15/43.33  | | | 
% 232.15/43.33  | | Case 2:
% 232.15/43.33  | | | 
% 232.15/43.33  | | |   (14)  all_57_3 = e1 & op(e2, e2) = e1
% 232.15/43.33  | | | 
% 232.15/43.33  | | | REF_CLOSE: (3), (7), (14) are inconsistent by sub-proof #2362.
% 232.15/43.33  | | | 
% 232.15/43.33  | | End of split
% 232.15/43.33  | | 
% 232.15/43.33  | Case 2:
% 232.15/43.33  | | 
% 232.15/43.33  | |   (15)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) =
% 232.15/43.33  | |           e1)
% 232.15/43.33  | | 
% 232.15/43.33  | | BETA: splitting (15) gives:
% 232.15/43.33  | | 
% 232.15/43.33  | | Case 1:
% 232.15/43.33  | | | 
% 232.15/43.33  | | |   (16)  all_57_5 = e1 & op(e2, e1) = e1
% 232.15/43.33  | | | 
% 232.15/43.33  | | | REF_CLOSE: (2), (5), (16) are inconsistent by sub-proof #2376.
% 232.15/43.33  | | | 
% 232.15/43.33  | | Case 2:
% 232.15/43.33  | | | 
% 232.15/43.33  | | |   (17)  all_57_10 = e1 & op(e2, e0) = e1
% 232.15/43.33  | | | 
% 232.15/43.33  | | | ALPHA: (17) implies:
% 232.15/43.33  | | |   (18)  all_57_10 = e1
% 232.15/43.33  | | | 
% 232.15/43.33  | | | REF_CLOSE: (3), (4), (5), (6), (8), (9), (10), (18) are inconsistent by
% 232.15/43.33  | | |            sub-proof #2254.
% 232.15/43.33  | | | 
% 232.15/43.33  | | End of split
% 232.15/43.33  | | 
% 232.15/43.33  | End of split
% 232.15/43.33  | 
% 232.15/43.33  End of proof
% 232.15/43.33  
% 232.15/43.33  Sub-proof #2254 shows that the following formulas are inconsistent:
% 232.15/43.33  ----------------------------------------------------------------
% 232.15/43.33    (1)  all_57_10 = e1
% 232.15/43.33    (2)  all_57_3 = e0
% 232.15/43.33    (3)   ~ (e3 = e2)
% 232.15/43.33    (4)  all_57_5 = e3
% 232.15/43.33    (5)   ~ (e2 = e0)
% 232.15/43.33    (6)  all_57_2 = e0
% 232.15/43.33    (7)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 232.15/43.33         (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 232.15/43.33    (8)   ~ (e2 = e1)
% 232.15/43.33  
% 232.15/43.33  Begin of proof
% 232.15/43.33  | 
% 232.15/43.33  | BETA: splitting (7) gives:
% 232.15/43.33  | 
% 232.15/43.33  | Case 1:
% 232.15/43.33  | | 
% 232.15/43.33  | |   (9)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2)
% 232.15/43.33  | | 
% 232.15/43.33  | | BETA: splitting (9) gives:
% 232.15/43.33  | | 
% 232.15/43.33  | | Case 1:
% 232.15/43.33  | | | 
% 232.15/43.33  | | |   (10)  all_57_2 = e2 & op(e2, e3) = e2
% 232.15/43.33  | | | 
% 232.15/43.33  | | | REF_CLOSE: (5), (6), (10) are inconsistent by sub-proof #2257.
% 232.15/43.33  | | | 
% 232.15/43.33  | | Case 2:
% 232.15/43.33  | | | 
% 232.15/43.33  | | |   (11)  all_57_3 = e2 & op(e2, e2) = e2
% 232.15/43.33  | | | 
% 232.15/43.33  | | | REF_CLOSE: (2), (5), (11) are inconsistent by sub-proof #2256.
% 232.15/43.33  | | | 
% 232.15/43.33  | | End of split
% 232.15/43.33  | | 
% 232.15/43.33  | Case 2:
% 232.15/43.33  | | 
% 232.15/43.33  | |   (12)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 232.15/43.33  | |           e2)
% 232.15/43.33  | | 
% 232.15/43.33  | | BETA: splitting (12) gives:
% 232.15/43.33  | | 
% 232.15/43.33  | | Case 1:
% 232.15/43.33  | | | 
% 232.15/43.33  | | |   (13)  all_57_5 = e2 & op(e2, e1) = e2
% 232.15/43.33  | | | 
% 232.15/43.33  | | | REF_CLOSE: (3), (4), (13) are inconsistent by sub-proof #2425.
% 232.15/43.33  | | | 
% 232.15/43.33  | | Case 2:
% 232.15/43.33  | | | 
% 232.15/43.33  | | |   (14)  all_57_10 = e2 & op(e2, e0) = e2
% 232.15/43.33  | | | 
% 232.15/43.33  | | | REF_CLOSE: (1), (8), (14) are inconsistent by sub-proof #2255.
% 232.15/43.33  | | | 
% 232.15/43.33  | | End of split
% 232.15/43.33  | | 
% 232.15/43.33  | End of split
% 232.15/43.33  | 
% 232.15/43.33  End of proof
% 232.15/43.33  
% 232.15/43.33  Sub-proof #2255 shows that the following formulas are inconsistent:
% 232.15/43.33  ----------------------------------------------------------------
% 232.15/43.33    (1)  all_57_10 = e2 & op(e2, e0) = e2
% 232.15/43.33    (2)  all_57_10 = e1
% 232.15/43.33    (3)   ~ (e2 = e1)
% 232.15/43.33  
% 232.15/43.33  Begin of proof
% 232.15/43.33  | 
% 232.15/43.33  | ALPHA: (1) implies:
% 232.15/43.33  |   (4)  all_57_10 = e2
% 232.15/43.33  | 
% 232.15/43.33  | COMBINE_EQS: (2), (4) imply:
% 232.15/43.33  |   (5)  e2 = e1
% 232.15/43.33  | 
% 232.15/43.33  | REDUCE: (3), (5) imply:
% 232.15/43.33  |   (6)  $false
% 232.15/43.33  | 
% 232.15/43.33  | CLOSE: (6) is inconsistent.
% 232.15/43.33  | 
% 232.15/43.33  End of proof
% 232.15/43.33  
% 232.15/43.33  Sub-proof #2256 shows that the following formulas are inconsistent:
% 232.15/43.33  ----------------------------------------------------------------
% 232.15/43.33    (1)  all_57_3 = e2 & op(e2, e2) = e2
% 232.15/43.33    (2)  all_57_3 = e0
% 232.15/43.33    (3)   ~ (e2 = e0)
% 232.15/43.33  
% 232.15/43.33  Begin of proof
% 232.15/43.33  | 
% 232.15/43.33  | ALPHA: (1) implies:
% 232.15/43.33  |   (4)  all_57_3 = e2
% 232.15/43.33  | 
% 232.15/43.33  | COMBINE_EQS: (2), (4) imply:
% 232.15/43.33  |   (5)  e2 = e0
% 232.15/43.33  | 
% 232.15/43.33  | REDUCE: (3), (5) imply:
% 232.15/43.33  |   (6)  $false
% 232.15/43.33  | 
% 232.15/43.33  | CLOSE: (6) is inconsistent.
% 232.15/43.33  | 
% 232.15/43.33  End of proof
% 232.15/43.33  
% 232.15/43.33  Sub-proof #2257 shows that the following formulas are inconsistent:
% 232.15/43.33  ----------------------------------------------------------------
% 232.15/43.33    (1)  all_57_2 = e2 & op(e2, e3) = e2
% 232.15/43.33    (2)  all_57_2 = e0
% 232.15/43.33    (3)   ~ (e2 = e0)
% 232.15/43.33  
% 232.15/43.33  Begin of proof
% 232.15/43.33  | 
% 232.15/43.33  | ALPHA: (1) implies:
% 232.15/43.33  |   (4)  all_57_2 = e2
% 232.15/43.33  | 
% 232.15/43.33  | COMBINE_EQS: (2), (4) imply:
% 232.15/43.33  |   (5)  e2 = e0
% 232.15/43.33  | 
% 232.15/43.33  | SIMP: (5) implies:
% 232.15/43.33  |   (6)  e2 = e0
% 232.15/43.33  | 
% 232.15/43.33  | REDUCE: (3), (6) imply:
% 232.15/43.33  |   (7)  $false
% 232.15/43.33  | 
% 232.15/43.33  | CLOSE: (7) is inconsistent.
% 232.15/43.33  | 
% 232.15/43.33  End of proof
% 232.15/43.33  
% 232.15/43.33  Sub-proof #2258 shows that the following formulas are inconsistent:
% 232.15/43.33  ----------------------------------------------------------------
% 232.15/43.33    (1)  all_57_2 = e3
% 232.15/43.33    (2)  all_57_2 = e0
% 232.15/43.33    (3)   ~ (e3 = e0)
% 232.15/43.33  
% 232.15/43.33  Begin of proof
% 232.15/43.33  | 
% 232.15/43.33  | COMBINE_EQS: (1), (2) imply:
% 232.15/43.33  |   (4)  e3 = e0
% 232.15/43.33  | 
% 232.15/43.33  | SIMP: (4) implies:
% 232.15/43.33  |   (5)  e3 = e0
% 232.15/43.33  | 
% 232.15/43.33  | REDUCE: (3), (5) imply:
% 232.15/43.33  |   (6)  $false
% 232.15/43.33  | 
% 232.15/43.33  | CLOSE: (6) is inconsistent.
% 232.15/43.33  | 
% 232.15/43.33  End of proof
% 232.15/43.33  
% 232.15/43.33  Sub-proof #2259 shows that the following formulas are inconsistent:
% 232.15/43.33  ----------------------------------------------------------------
% 232.15/43.33    (1)  (all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 &
% 232.15/43.33           op(all_52_17, all_52_17) = e3 & op(all_52_19, all_52_19) = e2 &
% 232.15/43.33           op(all_52_21, all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1,
% 232.15/43.33             e3) = all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 &
% 232.15/43.33           op(e1, e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21)
% 232.15/43.33           & $i(all_52_23)) | (all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 &
% 232.15/43.33           all_52_30 = e0 & op(all_52_25, all_52_25) = e3 & op(all_52_27,
% 232.15/43.33             all_52_27) = e2 & op(all_52_29, all_52_29) = e1 & op(all_52_31,
% 232.15/43.33             all_52_31) = e0 & op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 &
% 232.15/43.33           op(e0, e1) = all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) &
% 232.15/43.33           $i(all_52_27) & $i(all_52_29) & $i(all_52_31))
% 232.15/43.33    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.33           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.33    (3)   ~ (e3 = e2)
% 232.15/43.33    (4)  op(e2, e2) = e2
% 232.15/43.33    (5)  op(e1, e1) = e2
% 232.15/43.33    (6)   ~ (e2 = e1)
% 232.15/43.33    (7)  op(e0, e3) = e2
% 232.15/43.33  
% 232.15/43.33  Begin of proof
% 232.15/43.33  | 
% 232.15/43.33  | BETA: splitting (1) gives:
% 232.15/43.33  | 
% 232.15/43.33  | Case 1:
% 232.15/43.33  | | 
% 232.15/43.33  | |   (8)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 &
% 232.15/43.33  | |        op(all_52_17, all_52_17) = e3 & op(all_52_19, all_52_19) = e2 &
% 232.15/43.33  | |        op(all_52_21, all_52_21) = e1 & op(all_52_23, all_52_23) = e0 &
% 232.15/43.33  | |        op(e1, e3) = all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) =
% 232.15/43.33  | |        all_52_21 & op(e1, e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) &
% 232.15/43.33  | |        $i(all_52_21) & $i(all_52_23)
% 232.15/43.33  | | 
% 232.15/43.33  | | REF_CLOSE: (2), (4), (5), (6), (8) are inconsistent by sub-proof #2260.
% 232.15/43.33  | | 
% 232.15/43.33  | Case 2:
% 232.15/43.33  | | 
% 232.15/43.33  | |   (9)  all_52_24 = e3 & all_52_26 = e2 & all_52_28 = e1 & all_52_30 = e0 &
% 232.15/43.33  | |        op(all_52_25, all_52_25) = e3 & op(all_52_27, all_52_27) = e2 &
% 232.15/43.33  | |        op(all_52_29, all_52_29) = e1 & op(all_52_31, all_52_31) = e0 &
% 232.15/43.33  | |        op(e0, e3) = all_52_25 & op(e0, e2) = all_52_27 & op(e0, e1) =
% 232.15/43.33  | |        all_52_29 & op(e0, e0) = all_52_31 & $i(all_52_25) & $i(all_52_27) &
% 232.15/43.33  | |        $i(all_52_29) & $i(all_52_31)
% 232.15/43.33  | | 
% 232.15/43.33  | | ALPHA: (9) implies:
% 232.15/43.33  | |   (10)  op(e0, e3) = all_52_25
% 232.15/43.33  | |   (11)  op(all_52_25, all_52_25) = e3
% 232.15/43.33  | | 
% 232.15/43.33  | | GROUND_INST: instantiating (2) with e2, all_52_25, e3, e0, simplifying with
% 232.15/43.33  | |              (7), (10) gives:
% 232.15/43.33  | |   (12)  all_52_25 = e2
% 232.15/43.33  | | 
% 232.15/43.33  | | REDUCE: (11), (12) imply:
% 232.15/43.33  | |   (13)  op(e2, e2) = e3
% 232.15/43.33  | | 
% 232.15/43.33  | | REF_CLOSE: (2), (3), (4), (13) are inconsistent by sub-proof #2298.
% 232.15/43.33  | | 
% 232.15/43.33  | End of split
% 232.15/43.33  | 
% 232.15/43.33  End of proof
% 232.15/43.33  
% 232.15/43.33  Sub-proof #2260 shows that the following formulas are inconsistent:
% 232.15/43.33  ----------------------------------------------------------------
% 232.15/43.33    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.33           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.33    (2)  op(e2, e2) = e2
% 232.15/43.33    (3)  op(e1, e1) = e2
% 232.15/43.33    (4)   ~ (e2 = e1)
% 232.15/43.33    (5)  all_52_16 = e3 & all_52_18 = e2 & all_52_20 = e1 & all_52_22 = e0 &
% 232.15/43.33         op(all_52_17, all_52_17) = e3 & op(all_52_19, all_52_19) = e2 &
% 232.15/43.33         op(all_52_21, all_52_21) = e1 & op(all_52_23, all_52_23) = e0 & op(e1,
% 232.15/43.33           e3) = all_52_17 & op(e1, e2) = all_52_19 & op(e1, e1) = all_52_21 &
% 232.15/43.33         op(e1, e0) = all_52_23 & $i(all_52_17) & $i(all_52_19) & $i(all_52_21) &
% 232.15/43.33         $i(all_52_23)
% 232.15/43.33  
% 232.15/43.33  Begin of proof
% 232.15/43.33  | 
% 232.15/43.33  | ALPHA: (5) implies:
% 232.15/43.33  |   (6)  op(e1, e1) = all_52_21
% 232.15/43.33  |   (7)  op(all_52_21, all_52_21) = e1
% 232.15/43.33  | 
% 232.15/43.33  | GROUND_INST: instantiating (1) with e2, all_52_21, e1, e1, simplifying with
% 232.15/43.33  |              (3), (6) gives:
% 232.15/43.33  |   (8)  all_52_21 = e2
% 232.15/43.33  | 
% 232.15/43.33  | REDUCE: (7), (8) imply:
% 232.15/43.33  |   (9)  op(e2, e2) = e1
% 232.15/43.33  | 
% 232.15/43.33  | REF_CLOSE: (1), (2), (4), (9) are inconsistent by sub-proof #2306.
% 232.15/43.33  | 
% 232.15/43.33  End of proof
% 232.15/43.33  
% 232.15/43.33  Sub-proof #2261 shows that the following formulas are inconsistent:
% 232.15/43.33  ----------------------------------------------------------------
% 232.15/43.33    (1)  all_55_13 = all_53_7
% 232.15/43.33    (2)  all_55_13 = e0
% 232.15/43.33    (3)   ~ (all_53_7 = e0)
% 232.15/43.33  
% 232.15/43.33  Begin of proof
% 232.15/43.33  | 
% 232.15/43.33  | COMBINE_EQS: (1), (2) imply:
% 232.15/43.33  |   (4)  all_53_7 = e0
% 232.15/43.33  | 
% 232.15/43.33  | SIMP: (4) implies:
% 232.15/43.33  |   (5)  all_53_7 = e0
% 232.15/43.33  | 
% 232.15/43.33  | REDUCE: (3), (5) imply:
% 232.15/43.33  |   (6)  $false
% 232.15/43.33  | 
% 232.15/43.33  | CLOSE: (6) is inconsistent.
% 232.15/43.33  | 
% 232.15/43.33  End of proof
% 232.15/43.33  
% 232.15/43.33  Sub-proof #2262 shows that the following formulas are inconsistent:
% 232.15/43.33  ----------------------------------------------------------------
% 232.15/43.33    (1)   ~ (e3 = e1)
% 232.15/43.33    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.33           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.33    (3)   ~ (all_53_6 = e1)
% 232.15/43.33    (4)  (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 232.15/43.33    (5)  all_57_13 = e3
% 232.15/43.33    (6)  op(e1, e2) = all_53_6
% 232.15/43.33  
% 232.15/43.33  Begin of proof
% 232.15/43.33  | 
% 232.15/43.33  | BETA: splitting (4) gives:
% 232.15/43.33  | 
% 232.15/43.33  | Case 1:
% 232.15/43.33  | | 
% 232.15/43.33  | |   (7)  all_57_7 = e1 & op(e1, e2) = e1
% 232.15/43.33  | | 
% 232.15/43.33  | | REF_CLOSE: (2), (3), (6), (7) are inconsistent by sub-proof #2265.
% 232.15/43.33  | | 
% 232.15/43.33  | Case 2:
% 232.15/43.33  | | 
% 232.15/43.33  | |   (8)  all_57_13 = e1 & op(e0, e2) = e1
% 232.15/43.33  | | 
% 232.15/43.33  | | ALPHA: (8) implies:
% 232.15/43.33  | |   (9)  all_57_13 = e1
% 232.15/43.33  | | 
% 232.15/43.33  | | REF_CLOSE: (1), (5), (9) are inconsistent by sub-proof #2268.
% 232.15/43.33  | | 
% 232.15/43.33  | End of split
% 232.15/43.33  | 
% 232.15/43.33  End of proof
% 232.15/43.33  
% 232.15/43.33  Sub-proof #2263 shows that the following formulas are inconsistent:
% 232.15/43.33  ----------------------------------------------------------------
% 232.15/43.33    (1)   ~ (e3 = e1)
% 232.15/43.33    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.33           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.33    (3)   ~ (all_6_2 = e3)
% 232.15/43.33    (4)  op(e1, e1) = all_6_2
% 232.15/43.33    (5)  all_57_14 = e1
% 232.15/43.33    (6)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 232.15/43.33  
% 232.15/43.33  Begin of proof
% 232.15/43.33  | 
% 232.15/43.33  | BETA: splitting (6) gives:
% 232.15/43.33  | 
% 232.15/43.33  | Case 1:
% 232.15/43.33  | | 
% 232.15/43.33  | |   (7)  all_57_8 = e3 & op(e1, e1) = e3
% 232.15/43.33  | | 
% 232.15/43.33  | | ALPHA: (7) implies:
% 232.15/43.33  | |   (8)  op(e1, e1) = e3
% 232.15/43.33  | | 
% 232.15/43.33  | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #2468.
% 232.15/43.33  | | 
% 232.15/43.33  | Case 2:
% 232.15/43.33  | | 
% 232.15/43.33  | |   (9)  all_57_14 = e3 & op(e0, e1) = e3
% 232.15/43.33  | | 
% 232.15/43.33  | | ALPHA: (9) implies:
% 232.15/43.33  | |   (10)  all_57_14 = e3
% 232.15/43.33  | | 
% 232.15/43.33  | | REF_CLOSE: (1), (5), (10) are inconsistent by sub-proof #2326.
% 232.15/43.33  | | 
% 232.15/43.33  | End of split
% 232.15/43.33  | 
% 232.15/43.33  End of proof
% 232.15/43.33  
% 232.15/43.33  Sub-proof #2264 shows that the following formulas are inconsistent:
% 232.15/43.33  ----------------------------------------------------------------
% 232.15/43.33    (1)  all_57_13 = e1 & op(e0, e2) = e1
% 232.15/43.33    (2)  all_57_13 = e3
% 232.15/43.33    (3)   ~ (e3 = e1)
% 232.15/43.33  
% 232.15/43.33  Begin of proof
% 232.15/43.33  | 
% 232.15/43.33  | ALPHA: (1) implies:
% 232.15/43.33  |   (4)  all_57_13 = e1
% 232.15/43.33  | 
% 232.15/43.33  | COMBINE_EQS: (2), (4) imply:
% 232.15/43.33  |   (5)  e3 = e1
% 232.15/43.33  | 
% 232.15/43.33  | REDUCE: (3), (5) imply:
% 232.15/43.33  |   (6)  $false
% 232.15/43.33  | 
% 232.15/43.33  | CLOSE: (6) is inconsistent.
% 232.15/43.33  | 
% 232.15/43.33  End of proof
% 232.15/43.33  
% 232.15/43.33  Sub-proof #2265 shows that the following formulas are inconsistent:
% 232.15/43.33  ----------------------------------------------------------------
% 232.15/43.33    (1)  all_57_7 = e1 & op(e1, e2) = e1
% 232.15/43.33    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.33           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.33    (3)  op(e1, e2) = all_53_6
% 232.15/43.33    (4)   ~ (all_53_6 = e1)
% 232.15/43.33  
% 232.15/43.33  Begin of proof
% 232.15/43.33  | 
% 232.15/43.33  | ALPHA: (1) implies:
% 232.15/43.33  |   (5)  op(e1, e2) = e1
% 232.15/43.33  | 
% 232.15/43.33  | GROUND_INST: instantiating (2) with all_53_6, e1, e2, e1, simplifying with
% 232.15/43.33  |              (3), (5) gives:
% 232.15/43.33  |   (6)  all_53_6 = e1
% 232.15/43.33  | 
% 232.15/43.33  | REDUCE: (4), (6) imply:
% 232.15/43.33  |   (7)  $false
% 232.15/43.33  | 
% 232.15/43.33  | CLOSE: (7) is inconsistent.
% 232.15/43.33  | 
% 232.15/43.33  End of proof
% 232.15/43.33  
% 232.15/43.33  Sub-proof #2266 shows that the following formulas are inconsistent:
% 232.15/43.33  ----------------------------------------------------------------
% 232.15/43.33    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.33           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.33    (2)  (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1)
% 232.15/43.33    (3)  all_57_1 = e0
% 232.15/43.33    (4)  op(e2, e2) = e2
% 232.15/43.33    (5)   ~ (e1 = e0)
% 232.15/43.33    (6)   ~ (e2 = e1)
% 232.15/43.33  
% 232.15/43.33  Begin of proof
% 232.15/43.33  | 
% 232.15/43.33  | BETA: splitting (2) gives:
% 232.15/43.33  | 
% 232.15/43.33  | Case 1:
% 232.15/43.33  | | 
% 232.15/43.33  | |   (7)  all_57_1 = e1 & op(e3, e2) = e1
% 232.15/43.33  | | 
% 232.15/43.33  | | REF_CLOSE: (3), (5), (7) are inconsistent by sub-proof #2446.
% 232.15/43.33  | | 
% 232.15/43.33  | Case 2:
% 232.15/43.33  | | 
% 232.15/43.33  | |   (8)  all_57_3 = e1 & op(e2, e2) = e1
% 232.15/43.33  | | 
% 232.15/43.33  | | ALPHA: (8) implies:
% 232.15/43.33  | |   (9)  op(e2, e2) = e1
% 232.15/43.33  | | 
% 232.15/43.33  | | REF_CLOSE: (1), (4), (6), (9) are inconsistent by sub-proof #2306.
% 232.15/43.33  | | 
% 232.15/43.33  | End of split
% 232.15/43.33  | 
% 232.15/43.33  End of proof
% 232.15/43.33  
% 232.15/43.33  Sub-proof #2267 shows that the following formulas are inconsistent:
% 232.15/43.33  ----------------------------------------------------------------
% 232.15/43.33    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.33           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.33    (2)  op(e3, e1) = all_53_8
% 232.15/43.33    (3)  op(e3, e1) = e0
% 232.15/43.33    (4)   ~ (all_53_8 = e0)
% 232.15/43.33  
% 232.15/43.33  Begin of proof
% 232.15/43.33  | 
% 232.15/43.33  | GROUND_INST: instantiating (1) with all_53_8, e0, e1, e3, simplifying with
% 232.15/43.33  |              (2), (3) gives:
% 232.15/43.33  |   (5)  all_53_8 = e0
% 232.15/43.33  | 
% 232.15/43.33  | REDUCE: (4), (5) imply:
% 232.15/43.33  |   (6)  $false
% 232.15/43.33  | 
% 232.15/43.33  | CLOSE: (6) is inconsistent.
% 232.15/43.33  | 
% 232.15/43.33  End of proof
% 232.15/43.33  
% 232.15/43.33  Sub-proof #2268 shows that the following formulas are inconsistent:
% 232.15/43.33  ----------------------------------------------------------------
% 232.15/43.33    (1)  all_57_13 = e3
% 232.15/43.33    (2)  all_57_13 = e1
% 232.15/43.33    (3)   ~ (e3 = e1)
% 232.15/43.33  
% 232.15/43.33  Begin of proof
% 232.15/43.33  | 
% 232.15/43.33  | COMBINE_EQS: (1), (2) imply:
% 232.15/43.33  |   (4)  e3 = e1
% 232.15/43.33  | 
% 232.15/43.33  | SIMP: (4) implies:
% 232.15/43.33  |   (5)  e3 = e1
% 232.15/43.33  | 
% 232.15/43.33  | REDUCE: (3), (5) imply:
% 232.15/43.33  |   (6)  $false
% 232.15/43.33  | 
% 232.15/43.33  | CLOSE: (6) is inconsistent.
% 232.15/43.33  | 
% 232.15/43.33  End of proof
% 232.15/43.33  
% 232.15/43.33  Sub-proof #2269 shows that the following formulas are inconsistent:
% 232.15/43.33  ----------------------------------------------------------------
% 232.15/43.33    (1)  all_57_7 = e3
% 232.15/43.33    (2)  all_57_7 = e0
% 232.15/43.33    (3)   ~ (e3 = e0)
% 232.15/43.33  
% 232.15/43.33  Begin of proof
% 232.15/43.33  | 
% 232.15/43.33  | COMBINE_EQS: (1), (2) imply:
% 232.15/43.33  |   (4)  e3 = e0
% 232.15/43.33  | 
% 232.15/43.33  | SIMP: (4) implies:
% 232.15/43.33  |   (5)  e3 = e0
% 232.15/43.33  | 
% 232.15/43.33  | REDUCE: (3), (5) imply:
% 232.15/43.33  |   (6)  $false
% 232.15/43.33  | 
% 232.15/43.33  | CLOSE: (6) is inconsistent.
% 232.15/43.33  | 
% 232.15/43.33  End of proof
% 232.15/43.33  
% 232.15/43.33  Sub-proof #2270 shows that the following formulas are inconsistent:
% 232.15/43.33  ----------------------------------------------------------------
% 232.15/43.33    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.15/43.33           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.15/43.33    (2)  op(e2, e2) = e0
% 232.15/43.33    (3)  op(e2, e2) = all_52_11
% 232.15/43.33    (4)   ~ (e2 = e0)
% 232.15/43.33    (5)  op(e0, e0) = e0
% 232.15/43.33    (6)  op(all_52_11, all_52_11) = e2
% 232.15/43.33  
% 232.15/43.33  Begin of proof
% 232.15/43.33  | 
% 232.15/43.33  | GROUND_INST: instantiating (1) with e0, all_52_11, e2, e2, simplifying with
% 232.15/43.33  |              (2), (3) gives:
% 232.15/43.33  |   (7)  all_52_11 = e0
% 232.15/43.33  | 
% 232.15/43.33  | REDUCE: (6), (7) imply:
% 232.15/43.33  |   (8)  op(e0, e0) = e2
% 232.15/43.33  | 
% 232.15/43.33  | GROUND_INST: instantiating (1) with e0, e2, e0, e0, simplifying with (5), (8)
% 232.15/43.33  |              gives:
% 232.15/43.33  |   (9)  e2 = e0
% 232.15/43.33  | 
% 232.15/43.33  | REDUCE: (4), (9) imply:
% 232.15/43.33  |   (10)  $false
% 232.15/43.33  | 
% 232.15/43.33  | CLOSE: (10) is inconsistent.
% 232.15/43.33  | 
% 232.15/43.33  End of proof
% 232.15/43.33  
% 232.15/43.33  Sub-proof #2271 shows that the following formulas are inconsistent:
% 232.15/43.33  ----------------------------------------------------------------
% 232.15/43.33    (1)   ~ (all_53_6 = e2)
% 232.15/43.33    (2)   ~ (all_53_6 = e0)
% 232.15/43.33    (3)  all_55_9 = all_53_6
% 232.15/43.33    (4)  all_55_9 = e2 | all_55_9 = e1 | all_55_9 = e0
% 232.15/43.33    (5)   ~ (all_53_6 = e1)
% 232.15/43.33  
% 232.15/43.33  Begin of proof
% 232.15/43.33  | 
% 232.15/43.33  | BETA: splitting (4) gives:
% 232.15/43.33  | 
% 232.15/43.33  | Case 1:
% 232.15/43.33  | | 
% 232.15/43.33  | |   (6)  all_55_9 = e2
% 232.15/43.33  | | 
% 232.15/43.33  | | REF_CLOSE: (1), (3), (6) are inconsistent by sub-proof #2274.
% 232.15/43.33  | | 
% 232.15/43.33  | Case 2:
% 232.15/43.33  | | 
% 232.15/43.33  | |   (7)  all_55_9 = e1 | all_55_9 = e0
% 232.15/43.33  | | 
% 232.15/43.33  | | BETA: splitting (7) gives:
% 232.15/43.33  | | 
% 232.15/43.33  | | Case 1:
% 232.15/43.33  | | | 
% 232.15/43.33  | | |   (8)  all_55_9 = e1
% 232.15/43.33  | | | 
% 232.15/43.33  | | | REF_CLOSE: (3), (5), (8) are inconsistent by sub-proof #2273.
% 232.15/43.33  | | | 
% 232.15/43.33  | | Case 2:
% 232.15/43.33  | | | 
% 232.25/43.33  | | |   (9)  all_55_9 = e0
% 232.25/43.33  | | | 
% 232.25/43.33  | | | REF_CLOSE: (2), (3), (9) are inconsistent by sub-proof #2272.
% 232.25/43.33  | | | 
% 232.25/43.33  | | End of split
% 232.25/43.33  | | 
% 232.25/43.33  | End of split
% 232.25/43.33  | 
% 232.25/43.33  End of proof
% 232.25/43.33  
% 232.25/43.33  Sub-proof #2272 shows that the following formulas are inconsistent:
% 232.25/43.33  ----------------------------------------------------------------
% 232.25/43.33    (1)  all_55_9 = all_53_6
% 232.25/43.33    (2)  all_55_9 = e0
% 232.25/43.33    (3)   ~ (all_53_6 = e0)
% 232.25/43.33  
% 232.25/43.33  Begin of proof
% 232.25/43.33  | 
% 232.25/43.33  | COMBINE_EQS: (1), (2) imply:
% 232.25/43.33  |   (4)  all_53_6 = e0
% 232.25/43.33  | 
% 232.25/43.33  | SIMP: (4) implies:
% 232.25/43.33  |   (5)  all_53_6 = e0
% 232.25/43.33  | 
% 232.25/43.33  | REDUCE: (3), (5) imply:
% 232.25/43.33  |   (6)  $false
% 232.25/43.33  | 
% 232.25/43.33  | CLOSE: (6) is inconsistent.
% 232.25/43.33  | 
% 232.25/43.33  End of proof
% 232.25/43.33  
% 232.25/43.33  Sub-proof #2273 shows that the following formulas are inconsistent:
% 232.25/43.33  ----------------------------------------------------------------
% 232.25/43.33    (1)  all_55_9 = all_53_6
% 232.25/43.33    (2)  all_55_9 = e1
% 232.25/43.33    (3)   ~ (all_53_6 = e1)
% 232.25/43.33  
% 232.25/43.33  Begin of proof
% 232.25/43.33  | 
% 232.25/43.33  | COMBINE_EQS: (1), (2) imply:
% 232.25/43.33  |   (4)  all_53_6 = e1
% 232.25/43.33  | 
% 232.25/43.33  | SIMP: (4) implies:
% 232.25/43.33  |   (5)  all_53_6 = e1
% 232.25/43.33  | 
% 232.25/43.33  | REDUCE: (3), (5) imply:
% 232.25/43.33  |   (6)  $false
% 232.25/43.33  | 
% 232.25/43.33  | CLOSE: (6) is inconsistent.
% 232.25/43.33  | 
% 232.25/43.33  End of proof
% 232.25/43.33  
% 232.25/43.33  Sub-proof #2274 shows that the following formulas are inconsistent:
% 232.25/43.33  ----------------------------------------------------------------
% 232.25/43.33    (1)  all_55_9 = all_53_6
% 232.25/43.33    (2)  all_55_9 = e2
% 232.25/43.33    (3)   ~ (all_53_6 = e2)
% 232.25/43.33  
% 232.25/43.33  Begin of proof
% 232.25/43.33  | 
% 232.25/43.33  | COMBINE_EQS: (1), (2) imply:
% 232.25/43.33  |   (4)  all_53_6 = e2
% 232.25/43.33  | 
% 232.25/43.33  | SIMP: (4) implies:
% 232.25/43.33  |   (5)  all_53_6 = e2
% 232.25/43.33  | 
% 232.25/43.33  | REDUCE: (3), (5) imply:
% 232.25/43.33  |   (6)  $false
% 232.25/43.33  | 
% 232.25/43.33  | CLOSE: (6) is inconsistent.
% 232.25/43.33  | 
% 232.25/43.33  End of proof
% 232.25/43.33  
% 232.25/43.33  Sub-proof #2275 shows that the following formulas are inconsistent:
% 232.25/43.33  ----------------------------------------------------------------
% 232.25/43.33    (1)  all_55_7 = e2 | all_55_7 = e1 | all_55_7 = e0
% 232.25/43.33    (2)  all_55_7 = all_52_15
% 232.25/43.33    (3)   ~ (all_52_15 = e1)
% 232.25/43.33    (4)   ~ (all_52_15 = e0)
% 232.25/43.33    (5)   ~ (all_52_15 = e2)
% 232.25/43.33  
% 232.25/43.33  Begin of proof
% 232.25/43.33  | 
% 232.25/43.33  | BETA: splitting (1) gives:
% 232.25/43.33  | 
% 232.25/43.33  | Case 1:
% 232.25/43.33  | | 
% 232.25/43.33  | |   (6)  all_55_7 = e2
% 232.25/43.33  | | 
% 232.25/43.33  | | REF_CLOSE: (2), (5), (6) are inconsistent by sub-proof #2278.
% 232.25/43.33  | | 
% 232.25/43.33  | Case 2:
% 232.25/43.33  | | 
% 232.25/43.33  | |   (7)  all_55_7 = e1 | all_55_7 = e0
% 232.25/43.33  | | 
% 232.25/43.33  | | BETA: splitting (7) gives:
% 232.25/43.33  | | 
% 232.25/43.33  | | Case 1:
% 232.25/43.33  | | | 
% 232.25/43.33  | | |   (8)  all_55_7 = e1
% 232.25/43.33  | | | 
% 232.25/43.33  | | | REF_CLOSE: (2), (3), (8) are inconsistent by sub-proof #2277.
% 232.25/43.33  | | | 
% 232.25/43.33  | | Case 2:
% 232.25/43.33  | | | 
% 232.25/43.33  | | |   (9)  all_55_7 = e0
% 232.25/43.33  | | | 
% 232.25/43.33  | | | REF_CLOSE: (2), (4), (9) are inconsistent by sub-proof #2276.
% 232.25/43.33  | | | 
% 232.25/43.33  | | End of split
% 232.25/43.33  | | 
% 232.25/43.33  | End of split
% 232.25/43.33  | 
% 232.25/43.33  End of proof
% 232.25/43.33  
% 232.25/43.33  Sub-proof #2276 shows that the following formulas are inconsistent:
% 232.25/43.33  ----------------------------------------------------------------
% 232.25/43.33    (1)  all_55_7 = all_52_15
% 232.25/43.33    (2)  all_55_7 = e0
% 232.25/43.33    (3)   ~ (all_52_15 = e0)
% 232.25/43.33  
% 232.25/43.33  Begin of proof
% 232.25/43.33  | 
% 232.25/43.33  | COMBINE_EQS: (1), (2) imply:
% 232.25/43.33  |   (4)  all_52_15 = e0
% 232.25/43.33  | 
% 232.25/43.33  | SIMP: (4) implies:
% 232.25/43.33  |   (5)  all_52_15 = e0
% 232.25/43.33  | 
% 232.25/43.33  | REDUCE: (3), (5) imply:
% 232.25/43.33  |   (6)  $false
% 232.25/43.33  | 
% 232.25/43.33  | CLOSE: (6) is inconsistent.
% 232.25/43.33  | 
% 232.25/43.33  End of proof
% 232.25/43.33  
% 232.25/43.33  Sub-proof #2277 shows that the following formulas are inconsistent:
% 232.25/43.33  ----------------------------------------------------------------
% 232.25/43.33    (1)  all_55_7 = all_52_15
% 232.25/43.33    (2)  all_55_7 = e1
% 232.25/43.33    (3)   ~ (all_52_15 = e1)
% 232.25/43.33  
% 232.25/43.33  Begin of proof
% 232.25/43.33  | 
% 232.25/43.33  | COMBINE_EQS: (1), (2) imply:
% 232.25/43.33  |   (4)  all_52_15 = e1
% 232.25/43.33  | 
% 232.25/43.33  | SIMP: (4) implies:
% 232.25/43.33  |   (5)  all_52_15 = e1
% 232.25/43.33  | 
% 232.25/43.33  | REDUCE: (3), (5) imply:
% 232.25/43.33  |   (6)  $false
% 232.25/43.33  | 
% 232.25/43.33  | CLOSE: (6) is inconsistent.
% 232.25/43.33  | 
% 232.25/43.33  End of proof
% 232.25/43.33  
% 232.25/43.33  Sub-proof #2278 shows that the following formulas are inconsistent:
% 232.25/43.33  ----------------------------------------------------------------
% 232.25/43.33    (1)  all_55_7 = all_52_15
% 232.25/43.33    (2)  all_55_7 = e2
% 232.25/43.33    (3)   ~ (all_52_15 = e2)
% 232.25/43.33  
% 232.25/43.33  Begin of proof
% 232.25/43.33  | 
% 232.25/43.33  | COMBINE_EQS: (1), (2) imply:
% 232.25/43.33  |   (4)  all_52_15 = e2
% 232.25/43.33  | 
% 232.25/43.33  | SIMP: (4) implies:
% 232.25/43.33  |   (5)  all_52_15 = e2
% 232.25/43.33  | 
% 232.25/43.33  | REDUCE: (3), (5) imply:
% 232.25/43.33  |   (6)  $false
% 232.25/43.33  | 
% 232.25/43.33  | CLOSE: (6) is inconsistent.
% 232.25/43.33  | 
% 232.25/43.33  End of proof
% 232.25/43.33  
% 232.25/43.33  Sub-proof #2279 shows that the following formulas are inconsistent:
% 232.25/43.33  ----------------------------------------------------------------
% 232.25/43.33    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.33           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.33    (2)  all_55_7 = all_52_15
% 232.25/43.33    (3)   ~ (all_52_15 = e1)
% 232.25/43.33    (4)  all_57_1 = e0
% 232.25/43.33    (5)  all_57_4 = e1
% 232.25/43.33    (6)  all_55_7 = e3
% 232.25/43.33    (7)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 232.25/43.33         (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 232.25/43.33    (8)   ~ (all_53_12 = e3)
% 232.25/43.33    (9)  op(all_52_15, all_52_15) = e0
% 232.25/43.33    (10)   ~ (all_52_15 = e0)
% 232.25/43.33    (11)  op(e3, e0) = all_53_12
% 232.25/43.33  
% 232.25/43.33  Begin of proof
% 232.25/43.33  | 
% 232.25/43.33  | COMBINE_EQS: (2), (6) imply:
% 232.25/43.33  |   (12)  all_52_15 = e3
% 232.25/43.33  | 
% 232.25/43.33  | SIMP: (12) implies:
% 232.25/43.33  |   (13)  all_52_15 = e3
% 232.25/43.33  | 
% 232.25/43.33  | REDUCE: (3), (13) imply:
% 232.25/43.33  |   (14)   ~ (e3 = e1)
% 232.25/43.33  | 
% 232.25/43.33  | REDUCE: (10), (13) imply:
% 232.25/43.33  |   (15)   ~ (e3 = e0)
% 232.25/43.33  | 
% 232.25/43.33  | REDUCE: (9), (13) imply:
% 232.25/43.33  |   (16)  op(e3, e3) = e0
% 232.25/43.33  | 
% 232.25/43.33  | REF_CLOSE: (1), (4), (5), (7), (8), (11), (14), (15), (16) are inconsistent by
% 232.25/43.33  |            sub-proof #2280.
% 232.25/43.33  | 
% 232.25/43.33  End of proof
% 232.25/43.33  
% 232.25/43.33  Sub-proof #2280 shows that the following formulas are inconsistent:
% 232.25/43.33  ----------------------------------------------------------------
% 232.25/43.33    (1)   ~ (e3 = e1)
% 232.25/43.33    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.33           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.33    (3)   ~ (e3 = e0)
% 232.25/43.33    (4)  all_57_1 = e0
% 232.25/43.33    (5)  all_57_4 = e1
% 232.25/43.33    (6)  op(e3, e3) = e0
% 232.25/43.33    (7)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 232.25/43.33         (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 232.25/43.33    (8)   ~ (all_53_12 = e3)
% 232.25/43.33    (9)  op(e3, e0) = all_53_12
% 232.25/43.33  
% 232.25/43.33  Begin of proof
% 232.25/43.33  | 
% 232.25/43.33  | BETA: splitting (7) gives:
% 232.25/43.33  | 
% 232.25/43.33  | Case 1:
% 232.25/43.33  | | 
% 232.25/43.33  | |   (10)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) =
% 232.25/43.33  | |           e3)
% 232.25/43.33  | | 
% 232.25/43.33  | | REF_CLOSE: (2), (3), (4), (6), (10) are inconsistent by sub-proof #2404.
% 232.25/43.33  | | 
% 232.25/43.33  | Case 2:
% 232.25/43.33  | | 
% 232.25/43.33  | |   (11)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) =
% 232.25/43.33  | |           e3)
% 232.25/43.33  | | 
% 232.25/43.33  | | REF_CLOSE: (1), (2), (5), (8), (9), (11) are inconsistent by sub-proof
% 232.25/43.33  | |            #2281.
% 232.25/43.33  | | 
% 232.25/43.33  | End of split
% 232.25/43.33  | 
% 232.25/43.33  End of proof
% 232.25/43.33  
% 232.25/43.33  Sub-proof #2281 shows that the following formulas are inconsistent:
% 232.25/43.33  ----------------------------------------------------------------
% 232.25/43.33    (1)   ~ (e3 = e1)
% 232.25/43.33    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.33           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.33    (3)  all_57_4 = e1
% 232.25/43.33    (4)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 232.25/43.33    (5)   ~ (all_53_12 = e3)
% 232.25/43.33    (6)  op(e3, e0) = all_53_12
% 232.25/43.33  
% 232.25/43.33  Begin of proof
% 232.25/43.33  | 
% 232.25/43.33  | BETA: splitting (4) gives:
% 232.25/43.33  | 
% 232.25/43.33  | Case 1:
% 232.25/43.33  | | 
% 232.25/43.33  | |   (7)  all_57_4 = e3 & op(e3, e1) = e3
% 232.25/43.33  | | 
% 232.25/43.33  | | ALPHA: (7) implies:
% 232.25/43.33  | |   (8)  all_57_4 = e3
% 232.25/43.33  | | 
% 232.25/43.33  | | REF_CLOSE: (1), (3), (8) are inconsistent by sub-proof #2426.
% 232.25/43.33  | | 
% 232.25/43.33  | Case 2:
% 232.25/43.33  | | 
% 232.25/43.33  | |   (9)  all_57_9 = e3 & op(e3, e0) = e3
% 232.25/43.33  | | 
% 232.25/43.33  | | ALPHA: (9) implies:
% 232.25/43.33  | |   (10)  op(e3, e0) = e3
% 232.25/43.33  | | 
% 232.25/43.33  | | REF_CLOSE: (2), (5), (6), (10) are inconsistent by sub-proof #2458.
% 232.25/43.33  | | 
% 232.25/43.33  | End of split
% 232.25/43.33  | 
% 232.25/43.33  End of proof
% 232.25/43.33  
% 232.25/43.33  Sub-proof #2282 shows that the following formulas are inconsistent:
% 232.25/43.33  ----------------------------------------------------------------
% 232.25/43.33    (1)  all_55_11 = all_53_14
% 232.25/43.33    (2)  all_55_11 = e2
% 232.25/43.33    (3)   ~ (all_53_14 = e2)
% 232.25/43.33  
% 232.25/43.33  Begin of proof
% 232.25/43.33  | 
% 232.25/43.33  | COMBINE_EQS: (1), (2) imply:
% 232.25/43.33  |   (4)  all_53_14 = e2
% 232.25/43.33  | 
% 232.25/43.33  | SIMP: (4) implies:
% 232.25/43.33  |   (5)  all_53_14 = e2
% 232.25/43.33  | 
% 232.25/43.33  | REDUCE: (3), (5) imply:
% 232.25/43.33  |   (6)  $false
% 232.25/43.33  | 
% 232.25/43.33  | CLOSE: (6) is inconsistent.
% 232.25/43.33  | 
% 232.25/43.33  End of proof
% 232.25/43.33  
% 232.25/43.33  Sub-proof #2283 shows that the following formulas are inconsistent:
% 232.25/43.33  ----------------------------------------------------------------
% 232.25/43.33    (1)  all_55_1 = all_53_4
% 232.25/43.33    (2)  all_55_1 = e1
% 232.25/43.33    (3)   ~ (all_53_4 = e1)
% 232.25/43.33  
% 232.25/43.33  Begin of proof
% 232.25/43.33  | 
% 232.25/43.33  | COMBINE_EQS: (1), (2) imply:
% 232.25/43.33  |   (4)  all_53_4 = e1
% 232.25/43.33  | 
% 232.25/43.33  | SIMP: (4) implies:
% 232.25/43.33  |   (5)  all_53_4 = e1
% 232.25/43.33  | 
% 232.25/43.33  | REDUCE: (3), (5) imply:
% 232.25/43.33  |   (6)  $false
% 232.25/43.33  | 
% 232.25/43.33  | CLOSE: (6) is inconsistent.
% 232.25/43.33  | 
% 232.25/43.33  End of proof
% 232.25/43.33  
% 232.25/43.33  Sub-proof #2284 shows that the following formulas are inconsistent:
% 232.25/43.33  ----------------------------------------------------------------
% 232.25/43.33    (1)  all_55_1 = all_53_4
% 232.25/43.33    (2)  all_55_1 = e2
% 232.25/43.33    (3)   ~ (all_53_4 = e2)
% 232.25/43.33  
% 232.25/43.33  Begin of proof
% 232.25/43.33  | 
% 232.25/43.33  | COMBINE_EQS: (1), (2) imply:
% 232.25/43.33  |   (4)  all_53_4 = e2
% 232.25/43.33  | 
% 232.25/43.33  | SIMP: (4) implies:
% 232.25/43.33  |   (5)  all_53_4 = e2
% 232.25/43.33  | 
% 232.25/43.33  | REDUCE: (3), (5) imply:
% 232.25/43.33  |   (6)  $false
% 232.25/43.33  | 
% 232.25/43.33  | CLOSE: (6) is inconsistent.
% 232.25/43.33  | 
% 232.25/43.33  End of proof
% 232.25/43.33  
% 232.25/43.33  Sub-proof #2285 shows that the following formulas are inconsistent:
% 232.25/43.33  ----------------------------------------------------------------
% 232.25/43.33    (1)  (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3)
% 232.25/43.33    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.33           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.33    (3)   ~ (e3 = e2)
% 232.25/43.33    (4)  op(e3, e2) = all_53_4
% 232.25/43.33    (5)  op(e2, e2) = e2
% 232.25/43.33    (6)   ~ (all_53_4 = e3)
% 232.25/43.33  
% 232.25/43.33  Begin of proof
% 232.25/43.33  | 
% 232.25/43.33  | BETA: splitting (1) gives:
% 232.25/43.33  | 
% 232.25/43.33  | Case 1:
% 232.25/43.33  | | 
% 232.25/43.33  | |   (7)  all_57_1 = e3 & op(e3, e2) = e3
% 232.25/43.33  | | 
% 232.25/43.33  | | REF_CLOSE: (2), (4), (6), (7) are inconsistent by sub-proof #2286.
% 232.25/43.33  | | 
% 232.25/43.33  | Case 2:
% 232.25/43.33  | | 
% 232.25/43.33  | |   (8)  all_57_3 = e3 & op(e2, e2) = e3
% 232.25/43.33  | | 
% 232.25/43.33  | | ALPHA: (8) implies:
% 232.25/43.33  | |   (9)  op(e2, e2) = e3
% 232.25/43.33  | | 
% 232.25/43.33  | | REF_CLOSE: (2), (3), (5), (9) are inconsistent by sub-proof #2298.
% 232.25/43.33  | | 
% 232.25/43.33  | End of split
% 232.25/43.33  | 
% 232.25/43.33  End of proof
% 232.25/43.33  
% 232.25/43.33  Sub-proof #2286 shows that the following formulas are inconsistent:
% 232.25/43.33  ----------------------------------------------------------------
% 232.25/43.34    (1)  all_57_1 = e3 & op(e3, e2) = e3
% 232.25/43.34    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.34           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.34    (3)  op(e3, e2) = all_53_4
% 232.25/43.34    (4)   ~ (all_53_4 = e3)
% 232.25/43.34  
% 232.25/43.34  Begin of proof
% 232.25/43.34  | 
% 232.25/43.34  | ALPHA: (1) implies:
% 232.25/43.34  |   (5)  op(e3, e2) = e3
% 232.25/43.34  | 
% 232.25/43.34  | GROUND_INST: instantiating (2) with all_53_4, e3, e2, e3, simplifying with
% 232.25/43.34  |              (3), (5) gives:
% 232.25/43.34  |   (6)  all_53_4 = e3
% 232.25/43.34  | 
% 232.25/43.34  | REDUCE: (4), (6) imply:
% 232.25/43.34  |   (7)  $false
% 232.25/43.34  | 
% 232.25/43.34  | CLOSE: (7) is inconsistent.
% 232.25/43.34  | 
% 232.25/43.34  End of proof
% 232.25/43.34  
% 232.25/43.34  Sub-proof #2287 shows that the following formulas are inconsistent:
% 232.25/43.34  ----------------------------------------------------------------
% 232.25/43.34    (1)  all_55_13 = all_53_7
% 232.25/43.34    (2)  all_55_13 = e2
% 232.25/43.34    (3)   ~ (all_53_7 = e2)
% 232.25/43.34  
% 232.25/43.34  Begin of proof
% 232.25/43.34  | 
% 232.25/43.34  | COMBINE_EQS: (1), (2) imply:
% 232.25/43.34  |   (4)  all_53_7 = e2
% 232.25/43.34  | 
% 232.25/43.34  | SIMP: (4) implies:
% 232.25/43.34  |   (5)  all_53_7 = e2
% 232.25/43.34  | 
% 232.25/43.34  | REDUCE: (3), (5) imply:
% 232.25/43.34  |   (6)  $false
% 232.25/43.34  | 
% 232.25/43.34  | CLOSE: (6) is inconsistent.
% 232.25/43.34  | 
% 232.25/43.34  End of proof
% 232.25/43.34  
% 232.25/43.34  Sub-proof #2288 shows that the following formulas are inconsistent:
% 232.25/43.34  ----------------------------------------------------------------
% 232.25/43.34    (1)  all_55_14 = all_53_11
% 232.25/43.34    (2)  all_55_14 = e0
% 232.25/43.34    (3)   ~ (all_53_11 = e0)
% 232.25/43.34  
% 232.25/43.34  Begin of proof
% 232.25/43.34  | 
% 232.25/43.34  | COMBINE_EQS: (1), (2) imply:
% 232.25/43.34  |   (4)  all_53_11 = e0
% 232.25/43.34  | 
% 232.25/43.34  | SIMP: (4) implies:
% 232.25/43.34  |   (5)  all_53_11 = e0
% 232.25/43.34  | 
% 232.25/43.34  | REDUCE: (3), (5) imply:
% 232.25/43.34  |   (6)  $false
% 232.25/43.34  | 
% 232.25/43.34  | CLOSE: (6) is inconsistent.
% 232.25/43.34  | 
% 232.25/43.34  End of proof
% 232.25/43.34  
% 232.25/43.34  Sub-proof #2289 shows that the following formulas are inconsistent:
% 232.25/43.34  ----------------------------------------------------------------
% 232.25/43.34    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.34           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.34    (2)  all_55_6 = all_52_13
% 232.25/43.34    (3)   ~ (all_52_13 = e2)
% 232.25/43.34    (4)  op(all_52_13, all_52_13) = e1
% 232.25/43.34    (5)   ~ (all_52_13 = e1)
% 232.25/43.34    (6)  op(e0, e0) = e0
% 232.25/43.34    (7)  all_55_6 = e2 | all_55_6 = e1 | all_55_6 = e0
% 232.25/43.34  
% 232.25/43.34  Begin of proof
% 232.25/43.34  | 
% 232.25/43.34  | BETA: splitting (7) gives:
% 232.25/43.34  | 
% 232.25/43.34  | Case 1:
% 232.25/43.34  | | 
% 232.25/43.34  | |   (8)  all_55_6 = e2
% 232.25/43.34  | | 
% 232.25/43.34  | | REF_CLOSE: (2), (3), (8) are inconsistent by sub-proof #2292.
% 232.25/43.34  | | 
% 232.25/43.34  | Case 2:
% 232.25/43.34  | | 
% 232.25/43.34  | |   (9)  all_55_6 = e1 | all_55_6 = e0
% 232.25/43.34  | | 
% 232.25/43.34  | | BETA: splitting (9) gives:
% 232.25/43.34  | | 
% 232.25/43.34  | | Case 1:
% 232.25/43.34  | | | 
% 232.25/43.34  | | |   (10)  all_55_6 = e1
% 232.25/43.34  | | | 
% 232.25/43.34  | | | REF_CLOSE: (2), (5), (10) are inconsistent by sub-proof #2291.
% 232.25/43.34  | | | 
% 232.25/43.34  | | Case 2:
% 232.25/43.34  | | | 
% 232.25/43.34  | | |   (11)  all_55_6 = e0
% 232.25/43.34  | | | 
% 232.25/43.34  | | | COMBINE_EQS: (2), (11) imply:
% 232.25/43.34  | | |   (12)  all_52_13 = e0
% 232.25/43.34  | | | 
% 232.25/43.34  | | | SIMP: (12) implies:
% 232.25/43.34  | | |   (13)  all_52_13 = e0
% 232.25/43.34  | | | 
% 232.25/43.34  | | | REDUCE: (5), (13) imply:
% 232.25/43.34  | | |   (14)   ~ (e1 = e0)
% 232.25/43.34  | | | 
% 232.25/43.34  | | | SIMP: (14) implies:
% 232.25/43.34  | | |   (15)   ~ (e1 = e0)
% 232.25/43.34  | | | 
% 232.25/43.34  | | | REDUCE: (4), (13) imply:
% 232.25/43.34  | | |   (16)  op(e0, e0) = e1
% 232.25/43.34  | | | 
% 232.25/43.34  | | | REF_CLOSE: (1), (6), (15), (16) are inconsistent by sub-proof #2290.
% 232.25/43.34  | | | 
% 232.25/43.34  | | End of split
% 232.25/43.34  | | 
% 232.25/43.34  | End of split
% 232.25/43.34  | 
% 232.25/43.34  End of proof
% 232.25/43.34  
% 232.25/43.34  Sub-proof #2290 shows that the following formulas are inconsistent:
% 232.25/43.34  ----------------------------------------------------------------
% 232.25/43.34    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.34           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.34    (2)  op(e0, e0) = e1
% 232.25/43.34    (3)  op(e0, e0) = e0
% 232.25/43.34    (4)   ~ (e1 = e0)
% 232.25/43.34  
% 232.25/43.34  Begin of proof
% 232.25/43.34  | 
% 232.25/43.34  | GROUND_INST: instantiating (1) with e1, e0, e0, e0, simplifying with (2), (3)
% 232.25/43.34  |              gives:
% 232.25/43.34  |   (5)  e1 = e0
% 232.25/43.34  | 
% 232.25/43.34  | REDUCE: (4), (5) imply:
% 232.25/43.34  |   (6)  $false
% 232.25/43.34  | 
% 232.25/43.34  | CLOSE: (6) is inconsistent.
% 232.25/43.34  | 
% 232.25/43.34  End of proof
% 232.25/43.34  
% 232.25/43.34  Sub-proof #2291 shows that the following formulas are inconsistent:
% 232.25/43.34  ----------------------------------------------------------------
% 232.25/43.34    (1)  all_55_6 = all_52_13
% 232.25/43.34    (2)  all_55_6 = e1
% 232.25/43.34    (3)   ~ (all_52_13 = e1)
% 232.25/43.34  
% 232.25/43.34  Begin of proof
% 232.25/43.34  | 
% 232.25/43.34  | COMBINE_EQS: (1), (2) imply:
% 232.25/43.34  |   (4)  all_52_13 = e1
% 232.25/43.34  | 
% 232.25/43.34  | SIMP: (4) implies:
% 232.25/43.34  |   (5)  all_52_13 = e1
% 232.25/43.34  | 
% 232.25/43.34  | REDUCE: (3), (5) imply:
% 232.25/43.34  |   (6)  $false
% 232.25/43.34  | 
% 232.25/43.34  | CLOSE: (6) is inconsistent.
% 232.25/43.34  | 
% 232.25/43.34  End of proof
% 232.25/43.34  
% 232.25/43.34  Sub-proof #2292 shows that the following formulas are inconsistent:
% 232.25/43.34  ----------------------------------------------------------------
% 232.25/43.34    (1)  all_55_6 = all_52_13
% 232.25/43.34    (2)  all_55_6 = e2
% 232.25/43.34    (3)   ~ (all_52_13 = e2)
% 232.25/43.34  
% 232.25/43.34  Begin of proof
% 232.25/43.34  | 
% 232.25/43.34  | COMBINE_EQS: (1), (2) imply:
% 232.25/43.34  |   (4)  all_52_13 = e2
% 232.25/43.34  | 
% 232.25/43.34  | SIMP: (4) implies:
% 232.25/43.34  |   (5)  all_52_13 = e2
% 232.25/43.34  | 
% 232.25/43.34  | REDUCE: (3), (5) imply:
% 232.25/43.34  |   (6)  $false
% 232.25/43.34  | 
% 232.25/43.34  | CLOSE: (6) is inconsistent.
% 232.25/43.34  | 
% 232.25/43.34  End of proof
% 232.25/43.34  
% 232.25/43.34  Sub-proof #2293 shows that the following formulas are inconsistent:
% 232.25/43.34  ----------------------------------------------------------------
% 232.25/43.34    (1)  all_55_14 = all_53_11
% 232.25/43.34    (2)  all_55_14 = e2
% 232.25/43.34    (3)   ~ (all_53_11 = e2)
% 232.25/43.34  
% 232.25/43.34  Begin of proof
% 232.25/43.34  | 
% 232.25/43.34  | COMBINE_EQS: (1), (2) imply:
% 232.25/43.34  |   (4)  all_53_11 = e2
% 232.25/43.34  | 
% 232.25/43.34  | SIMP: (4) implies:
% 232.25/43.34  |   (5)  all_53_11 = e2
% 232.25/43.34  | 
% 232.25/43.34  | REDUCE: (3), (5) imply:
% 232.25/43.34  |   (6)  $false
% 232.25/43.34  | 
% 232.25/43.34  | CLOSE: (6) is inconsistent.
% 232.25/43.34  | 
% 232.25/43.34  End of proof
% 232.25/43.34  
% 232.25/43.34  Sub-proof #2294 shows that the following formulas are inconsistent:
% 232.25/43.34  ----------------------------------------------------------------
% 232.25/43.34    (1)  all_55_14 = all_53_11
% 232.25/43.34    (2)  all_55_14 = e3
% 232.25/43.34    (3)   ~ (all_53_11 = e3)
% 232.25/43.34  
% 232.25/43.34  Begin of proof
% 232.25/43.34  | 
% 232.25/43.34  | COMBINE_EQS: (1), (2) imply:
% 232.25/43.34  |   (4)  all_53_11 = e3
% 232.25/43.34  | 
% 232.25/43.34  | SIMP: (4) implies:
% 232.25/43.34  |   (5)  all_53_11 = e3
% 232.25/43.34  | 
% 232.25/43.34  | REDUCE: (3), (5) imply:
% 232.25/43.34  |   (6)  $false
% 232.25/43.34  | 
% 232.25/43.34  | CLOSE: (6) is inconsistent.
% 232.25/43.34  | 
% 232.25/43.34  End of proof
% 232.25/43.34  
% 232.25/43.34  Sub-proof #2295 shows that the following formulas are inconsistent:
% 232.25/43.34  ----------------------------------------------------------------
% 232.25/43.34    (1)  all_55_1 = all_53_4
% 232.25/43.34    (2)  all_55_1 = e3
% 232.25/43.34    (3)   ~ (all_53_4 = e3)
% 232.25/43.34  
% 232.25/43.34  Begin of proof
% 232.25/43.34  | 
% 232.25/43.34  | COMBINE_EQS: (1), (2) imply:
% 232.25/43.34  |   (4)  all_53_4 = e3
% 232.25/43.34  | 
% 232.25/43.34  | SIMP: (4) implies:
% 232.25/43.34  |   (5)  all_53_4 = e3
% 232.25/43.34  | 
% 232.25/43.34  | REDUCE: (3), (5) imply:
% 232.25/43.34  |   (6)  $false
% 232.25/43.34  | 
% 232.25/43.34  | CLOSE: (6) is inconsistent.
% 232.25/43.34  | 
% 232.25/43.34  End of proof
% 232.25/43.34  
% 232.25/43.34  Sub-proof #2296 shows that the following formulas are inconsistent:
% 232.25/43.34  ----------------------------------------------------------------
% 232.25/43.34    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.34           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.34    (2)  op(e3, e0) = e2
% 232.25/43.34    (3)   ~ (e2 = e0)
% 232.25/43.34    (4)  op(e2, e2) = e2
% 232.25/43.34    (5)  all_52_0 = e3 & all_52_2 = e2 & all_52_4 = e1 & all_52_6 = e0 &
% 232.25/43.34         op(all_52_1, all_52_1) = e3 & op(all_52_3, all_52_3) = e2 & op(all_52_5,
% 232.25/43.34           all_52_5) = e1 & op(all_52_7, all_52_7) = e0 & op(e3, e3) = all_52_1 &
% 232.25/43.34         op(e3, e2) = all_52_3 & op(e3, e1) = all_52_5 & op(e3, e0) = all_52_7 &
% 232.25/43.34         $i(all_52_1) & $i(all_52_3) & $i(all_52_5) & $i(all_52_7)
% 232.25/43.34  
% 232.25/43.34  Begin of proof
% 232.25/43.34  | 
% 232.25/43.34  | ALPHA: (5) implies:
% 232.25/43.34  |   (6)  op(e3, e0) = all_52_7
% 232.25/43.34  |   (7)  op(all_52_7, all_52_7) = e0
% 232.25/43.34  | 
% 232.25/43.34  | GROUND_INST: instantiating (1) with e2, all_52_7, e0, e3, simplifying with
% 232.25/43.34  |              (2), (6) gives:
% 232.25/43.34  |   (8)  all_52_7 = e2
% 232.25/43.34  | 
% 232.25/43.34  | REDUCE: (7), (8) imply:
% 232.25/43.34  |   (9)  op(e2, e2) = e0
% 232.25/43.34  | 
% 232.25/43.34  | REF_CLOSE: (1), (3), (4), (9) are inconsistent by sub-proof #2472.
% 232.25/43.34  | 
% 232.25/43.34  End of proof
% 232.25/43.34  
% 232.25/43.34  Sub-proof #2297 shows that the following formulas are inconsistent:
% 232.25/43.34  ----------------------------------------------------------------
% 232.25/43.34    (1)  op(e2, e3) = all_53_1
% 232.25/43.34    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.34           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.34    (3)   ~ (e3 = e2)
% 232.25/43.34    (4)  op(e2, e2) = e2
% 232.25/43.34    (5)   ~ (all_53_1 = e3)
% 232.25/43.34    (6)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3)
% 232.25/43.34  
% 232.25/43.34  Begin of proof
% 232.25/43.34  | 
% 232.25/43.34  | BETA: splitting (6) gives:
% 232.25/43.34  | 
% 232.25/43.34  | Case 1:
% 232.25/43.34  | | 
% 232.25/43.34  | |   (7)  all_57_2 = e3 & op(e2, e3) = e3
% 232.25/43.34  | | 
% 232.25/43.34  | | REF_CLOSE: (1), (2), (5), (7) are inconsistent by sub-proof #2299.
% 232.25/43.34  | | 
% 232.25/43.34  | Case 2:
% 232.25/43.34  | | 
% 232.25/43.34  | |   (8)  all_57_3 = e3 & op(e2, e2) = e3
% 232.25/43.34  | | 
% 232.25/43.34  | | ALPHA: (8) implies:
% 232.25/43.34  | |   (9)  op(e2, e2) = e3
% 232.25/43.34  | | 
% 232.25/43.34  | | REF_CLOSE: (2), (3), (4), (9) are inconsistent by sub-proof #2298.
% 232.25/43.34  | | 
% 232.25/43.34  | End of split
% 232.25/43.34  | 
% 232.25/43.34  End of proof
% 232.25/43.34  
% 232.25/43.34  Sub-proof #2298 shows that the following formulas are inconsistent:
% 232.25/43.34  ----------------------------------------------------------------
% 232.25/43.34    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.34           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.34    (2)  op(e2, e2) = e3
% 232.25/43.34    (3)  op(e2, e2) = e2
% 232.25/43.34    (4)   ~ (e3 = e2)
% 232.25/43.34  
% 232.25/43.34  Begin of proof
% 232.25/43.34  | 
% 232.25/43.34  | GROUND_INST: instantiating (1) with e2, e3, e2, e2, simplifying with (2), (3)
% 232.25/43.34  |              gives:
% 232.25/43.34  |   (5)  e3 = e2
% 232.25/43.34  | 
% 232.25/43.34  | REDUCE: (4), (5) imply:
% 232.25/43.34  |   (6)  $false
% 232.25/43.34  | 
% 232.25/43.34  | CLOSE: (6) is inconsistent.
% 232.25/43.34  | 
% 232.25/43.34  End of proof
% 232.25/43.34  
% 232.25/43.34  Sub-proof #2299 shows that the following formulas are inconsistent:
% 232.25/43.34  ----------------------------------------------------------------
% 232.25/43.34    (1)  all_57_2 = e3 & op(e2, e3) = e3
% 232.25/43.34    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.34           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.34    (3)  op(e2, e3) = all_53_1
% 232.25/43.34    (4)   ~ (all_53_1 = e3)
% 232.25/43.34  
% 232.25/43.34  Begin of proof
% 232.25/43.34  | 
% 232.25/43.34  | ALPHA: (1) implies:
% 232.25/43.34  |   (5)  op(e2, e3) = e3
% 232.25/43.34  | 
% 232.25/43.34  | GROUND_INST: instantiating (2) with all_53_1, e3, e3, e2, simplifying with
% 232.25/43.34  |              (3), (5) gives:
% 232.25/43.34  |   (6)  all_53_1 = e3
% 232.25/43.34  | 
% 232.25/43.34  | REDUCE: (4), (6) imply:
% 232.25/43.34  |   (7)  $false
% 232.25/43.34  | 
% 232.25/43.34  | CLOSE: (7) is inconsistent.
% 232.25/43.34  | 
% 232.25/43.34  End of proof
% 232.25/43.34  
% 232.25/43.34  Sub-proof #2300 shows that the following formulas are inconsistent:
% 232.25/43.34  ----------------------------------------------------------------
% 232.25/43.34    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.34           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.34    (2)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 232.25/43.34    (3)   ~ (all_53_13 = e3)
% 232.25/43.34    (4)  op(e2, e0) = all_53_13
% 232.25/43.34    (5)   ~ (all_53_12 = e3)
% 232.25/43.34    (6)  op(e3, e0) = all_53_12
% 232.25/43.34  
% 232.25/43.34  Begin of proof
% 232.25/43.34  | 
% 232.25/43.34  | BETA: splitting (2) gives:
% 232.25/43.34  | 
% 232.25/43.34  | Case 1:
% 232.25/43.34  | | 
% 232.25/43.34  | |   (7)  all_57_9 = e3 & op(e3, e0) = e3
% 232.25/43.34  | | 
% 232.25/43.34  | | ALPHA: (7) implies:
% 232.25/43.34  | |   (8)  op(e3, e0) = e3
% 232.25/43.34  | | 
% 232.25/43.34  | | REF_CLOSE: (1), (5), (6), (8) are inconsistent by sub-proof #2458.
% 232.25/43.34  | | 
% 232.25/43.34  | Case 2:
% 232.25/43.34  | | 
% 232.25/43.34  | |   (9)  all_57_10 = e3 & op(e2, e0) = e3
% 232.25/43.34  | | 
% 232.25/43.34  | | ALPHA: (9) implies:
% 232.25/43.34  | |   (10)  op(e2, e0) = e3
% 232.25/43.34  | | 
% 232.25/43.34  | | REF_CLOSE: (1), (3), (4), (10) are inconsistent by sub-proof #2301.
% 232.25/43.34  | | 
% 232.25/43.34  | End of split
% 232.25/43.34  | 
% 232.25/43.34  End of proof
% 232.25/43.34  
% 232.25/43.34  Sub-proof #2301 shows that the following formulas are inconsistent:
% 232.25/43.34  ----------------------------------------------------------------
% 232.25/43.34    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.34           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.34    (2)  op(e2, e0) = all_53_13
% 232.25/43.34    (3)  op(e2, e0) = e3
% 232.25/43.34    (4)   ~ (all_53_13 = e3)
% 232.25/43.34  
% 232.25/43.34  Begin of proof
% 232.25/43.34  | 
% 232.25/43.34  | GROUND_INST: instantiating (1) with all_53_13, e3, e0, e2, simplifying with
% 232.25/43.34  |              (2), (3) gives:
% 232.25/43.34  |   (5)  all_53_13 = e3
% 232.25/43.34  | 
% 232.25/43.34  | REDUCE: (4), (5) imply:
% 232.25/43.34  |   (6)  $false
% 232.25/43.34  | 
% 232.25/43.34  | CLOSE: (6) is inconsistent.
% 232.25/43.34  | 
% 232.25/43.34  End of proof
% 232.25/43.34  
% 232.25/43.34  Sub-proof #2302 shows that the following formulas are inconsistent:
% 232.25/43.34  ----------------------------------------------------------------
% 232.25/43.34    (1)   ~ (e3 = e1)
% 232.25/43.34    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.34           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.34    (3)  all_57_10 = e1
% 232.25/43.34    (4)  op(e1, e0) = all_53_14
% 232.25/43.34    (5)   ~ (e3 = e0)
% 232.25/43.34    (6)   ~ (all_53_14 = e3)
% 232.25/43.34    (7)  op(e0, e0) = e0
% 232.25/43.34    (8)   ~ (all_53_12 = e3)
% 232.25/43.34    (9)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 232.25/43.34         (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 232.25/43.34    (10)  op(e3, e0) = all_53_12
% 232.25/43.34  
% 232.25/43.34  Begin of proof
% 232.25/43.34  | 
% 232.25/43.34  | BETA: splitting (9) gives:
% 232.25/43.34  | 
% 232.25/43.34  | Case 1:
% 232.25/43.34  | | 
% 232.25/43.34  | |   (11)  (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 232.25/43.34  | |           e3)
% 232.25/43.34  | | 
% 232.25/43.34  | | BETA: splitting (11) gives:
% 232.25/43.34  | | 
% 232.25/43.34  | | Case 1:
% 232.25/43.34  | | | 
% 232.25/43.34  | | |   (12)  all_57_9 = e3 & op(e3, e0) = e3
% 232.25/43.34  | | | 
% 232.25/43.34  | | | ALPHA: (12) implies:
% 232.25/43.34  | | |   (13)  op(e3, e0) = e3
% 232.25/43.34  | | | 
% 232.25/43.34  | | | REF_CLOSE: (2), (8), (10), (13) are inconsistent by sub-proof #2458.
% 232.25/43.34  | | | 
% 232.25/43.34  | | Case 2:
% 232.25/43.34  | | | 
% 232.25/43.34  | | |   (14)  all_57_10 = e3 & op(e2, e0) = e3
% 232.25/43.34  | | | 
% 232.25/43.34  | | | ALPHA: (14) implies:
% 232.25/43.34  | | |   (15)  all_57_10 = e3
% 232.25/43.34  | | | 
% 232.25/43.34  | | | COMBINE_EQS: (3), (15) imply:
% 232.25/43.34  | | |   (16)  e3 = e1
% 232.25/43.34  | | | 
% 232.25/43.34  | | | REDUCE: (1), (16) imply:
% 232.25/43.34  | | |   (17)  $false
% 232.25/43.34  | | | 
% 232.25/43.34  | | | CLOSE: (17) is inconsistent.
% 232.25/43.34  | | | 
% 232.25/43.34  | | End of split
% 232.25/43.34  | | 
% 232.25/43.34  | Case 2:
% 232.25/43.34  | | 
% 232.25/43.34  | |   (18)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 232.25/43.34  | |           e3)
% 232.25/43.34  | | 
% 232.25/43.34  | | REF_CLOSE: (2), (4), (5), (6), (7), (18) are inconsistent by sub-proof
% 232.25/43.34  | |            #2303.
% 232.25/43.34  | | 
% 232.25/43.34  | End of split
% 232.25/43.34  | 
% 232.25/43.34  End of proof
% 232.25/43.34  
% 232.25/43.34  Sub-proof #2303 shows that the following formulas are inconsistent:
% 232.25/43.34  ----------------------------------------------------------------
% 232.25/43.34    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.34           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.34    (2)  op(e1, e0) = all_53_14
% 232.25/43.34    (3)   ~ (e3 = e0)
% 232.25/43.34    (4)   ~ (all_53_14 = e3)
% 232.25/43.34    (5)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 232.25/43.34    (6)  op(e0, e0) = e0
% 232.25/43.34  
% 232.25/43.34  Begin of proof
% 232.25/43.34  | 
% 232.25/43.34  | BETA: splitting (5) gives:
% 232.25/43.34  | 
% 232.25/43.34  | Case 1:
% 232.25/43.34  | | 
% 232.25/43.34  | |   (7)  all_57_11 = e3 & op(e1, e0) = e3
% 232.25/43.34  | | 
% 232.25/43.34  | | ALPHA: (7) implies:
% 232.25/43.34  | |   (8)  op(e1, e0) = e3
% 232.25/43.34  | | 
% 232.25/43.34  | | REF_CLOSE: (1), (2), (4), (8) are inconsistent by sub-proof #2330.
% 232.25/43.34  | | 
% 232.25/43.34  | Case 2:
% 232.25/43.34  | | 
% 232.25/43.34  | |   (9)  all_57_15 = e3 & op(e0, e0) = e3
% 232.25/43.34  | | 
% 232.25/43.34  | | ALPHA: (9) implies:
% 232.25/43.34  | |   (10)  op(e0, e0) = e3
% 232.25/43.34  | | 
% 232.25/43.34  | | REF_CLOSE: (1), (3), (6), (10) are inconsistent by sub-proof #2304.
% 232.25/43.34  | | 
% 232.25/43.34  | End of split
% 232.25/43.34  | 
% 232.25/43.34  End of proof
% 232.25/43.34  
% 232.25/43.34  Sub-proof #2304 shows that the following formulas are inconsistent:
% 232.25/43.34  ----------------------------------------------------------------
% 232.25/43.34    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.34           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.34    (2)  op(e0, e0) = e3
% 232.25/43.34    (3)  op(e0, e0) = e0
% 232.25/43.34    (4)   ~ (e3 = e0)
% 232.25/43.34  
% 232.25/43.34  Begin of proof
% 232.25/43.34  | 
% 232.25/43.34  | GROUND_INST: instantiating (1) with e3, e0, e0, e0, simplifying with (2), (3)
% 232.25/43.34  |              gives:
% 232.25/43.34  |   (5)  e3 = e0
% 232.25/43.34  | 
% 232.25/43.34  | REDUCE: (4), (5) imply:
% 232.25/43.34  |   (6)  $false
% 232.25/43.34  | 
% 232.25/43.34  | CLOSE: (6) is inconsistent.
% 232.25/43.34  | 
% 232.25/43.34  End of proof
% 232.25/43.34  
% 232.25/43.34  Sub-proof #2305 shows that the following formulas are inconsistent:
% 232.25/43.34  ----------------------------------------------------------------
% 232.25/43.34    (1)  all_57_5 = e1 & op(e2, e1) = e1
% 232.25/43.34    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.34           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.34    (3)  op(e2, e1) = all_53_9
% 232.25/43.34    (4)   ~ (all_53_9 = e1)
% 232.25/43.34  
% 232.25/43.34  Begin of proof
% 232.25/43.34  | 
% 232.25/43.34  | ALPHA: (1) implies:
% 232.25/43.34  |   (5)  op(e2, e1) = e1
% 232.25/43.34  | 
% 232.25/43.34  | GROUND_INST: instantiating (2) with all_53_9, e1, e1, e2, simplifying with
% 232.25/43.34  |              (3), (5) gives:
% 232.25/43.34  |   (6)  all_53_9 = e1
% 232.25/43.34  | 
% 232.25/43.34  | REDUCE: (4), (6) imply:
% 232.25/43.34  |   (7)  $false
% 232.25/43.34  | 
% 232.25/43.34  | CLOSE: (7) is inconsistent.
% 232.25/43.34  | 
% 232.25/43.34  End of proof
% 232.25/43.34  
% 232.25/43.34  Sub-proof #2306 shows that the following formulas are inconsistent:
% 232.25/43.34  ----------------------------------------------------------------
% 232.25/43.34    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.34           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.34    (2)  op(e2, e2) = e2
% 232.25/43.34    (3)  op(e2, e2) = e1
% 232.25/43.34    (4)   ~ (e2 = e1)
% 232.25/43.34  
% 232.25/43.34  Begin of proof
% 232.25/43.34  | 
% 232.25/43.34  | GROUND_INST: instantiating (1) with e1, e2, e2, e2, simplifying with (2), (3)
% 232.25/43.34  |              gives:
% 232.25/43.34  |   (5)  e2 = e1
% 232.25/43.34  | 
% 232.25/43.34  | REDUCE: (4), (5) imply:
% 232.25/43.34  |   (6)  $false
% 232.25/43.34  | 
% 232.25/43.34  | CLOSE: (6) is inconsistent.
% 232.25/43.34  | 
% 232.25/43.34  End of proof
% 232.25/43.34  
% 232.25/43.34  Sub-proof #2307 shows that the following formulas are inconsistent:
% 232.25/43.34  ----------------------------------------------------------------
% 232.25/43.34    (1)  all_55_11 = e1 | all_55_11 = e0
% 232.25/43.34    (2)  all_55_11 = all_53_14
% 232.25/43.34    (3)   ~ (all_53_14 = e1)
% 232.25/43.34    (4)   ~ (all_53_14 = e0)
% 232.25/43.34  
% 232.25/43.34  Begin of proof
% 232.25/43.34  | 
% 232.25/43.34  | BETA: splitting (1) gives:
% 232.25/43.34  | 
% 232.25/43.34  | Case 1:
% 232.25/43.34  | | 
% 232.25/43.34  | |   (5)  all_55_11 = e1
% 232.25/43.34  | | 
% 232.25/43.34  | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #2309.
% 232.25/43.34  | | 
% 232.25/43.34  | Case 2:
% 232.25/43.34  | | 
% 232.25/43.34  | |   (6)  all_55_11 = e0
% 232.25/43.34  | | 
% 232.25/43.34  | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #2308.
% 232.25/43.34  | | 
% 232.25/43.34  | End of split
% 232.25/43.34  | 
% 232.25/43.34  End of proof
% 232.25/43.34  
% 232.25/43.34  Sub-proof #2308 shows that the following formulas are inconsistent:
% 232.25/43.34  ----------------------------------------------------------------
% 232.25/43.34    (1)  all_55_11 = all_53_14
% 232.25/43.34    (2)  all_55_11 = e0
% 232.25/43.34    (3)   ~ (all_53_14 = e0)
% 232.25/43.34  
% 232.25/43.34  Begin of proof
% 232.25/43.34  | 
% 232.25/43.34  | COMBINE_EQS: (1), (2) imply:
% 232.25/43.34  |   (4)  all_53_14 = e0
% 232.25/43.34  | 
% 232.25/43.34  | SIMP: (4) implies:
% 232.25/43.34  |   (5)  all_53_14 = e0
% 232.25/43.34  | 
% 232.25/43.34  | REDUCE: (3), (5) imply:
% 232.25/43.34  |   (6)  $false
% 232.25/43.34  | 
% 232.25/43.34  | CLOSE: (6) is inconsistent.
% 232.25/43.34  | 
% 232.25/43.34  End of proof
% 232.25/43.34  
% 232.25/43.34  Sub-proof #2309 shows that the following formulas are inconsistent:
% 232.25/43.34  ----------------------------------------------------------------
% 232.25/43.34    (1)  all_55_11 = all_53_14
% 232.25/43.34    (2)  all_55_11 = e1
% 232.25/43.34    (3)   ~ (all_53_14 = e1)
% 232.25/43.34  
% 232.25/43.34  Begin of proof
% 232.25/43.34  | 
% 232.25/43.34  | COMBINE_EQS: (1), (2) imply:
% 232.25/43.34  |   (4)  all_53_14 = e1
% 232.25/43.34  | 
% 232.25/43.34  | SIMP: (4) implies:
% 232.25/43.34  |   (5)  all_53_14 = e1
% 232.25/43.34  | 
% 232.25/43.34  | REDUCE: (3), (5) imply:
% 232.25/43.34  |   (6)  $false
% 232.25/43.34  | 
% 232.25/43.34  | CLOSE: (6) is inconsistent.
% 232.25/43.34  | 
% 232.25/43.34  End of proof
% 232.25/43.34  
% 232.25/43.34  Sub-proof #2310 shows that the following formulas are inconsistent:
% 232.25/43.34  ----------------------------------------------------------------
% 232.25/43.34    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.34           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.34    (2)   ~ (all_6_2 = e3)
% 232.25/43.34    (3)  op(e1, e1) = all_6_2
% 232.25/43.34    (4)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 232.25/43.34    (5)  op(e1, e0) = all_53_14
% 232.25/43.34    (6)   ~ (all_53_14 = e3)
% 232.25/43.34  
% 232.25/43.34  Begin of proof
% 232.25/43.34  | 
% 232.25/43.34  | BETA: splitting (4) gives:
% 232.25/43.34  | 
% 232.25/43.34  | Case 1:
% 232.25/43.34  | | 
% 232.25/43.34  | |   (7)  all_57_8 = e3 & op(e1, e1) = e3
% 232.25/43.34  | | 
% 232.25/43.34  | | ALPHA: (7) implies:
% 232.25/43.34  | |   (8)  op(e1, e1) = e3
% 232.25/43.34  | | 
% 232.25/43.34  | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #2468.
% 232.25/43.34  | | 
% 232.25/43.34  | Case 2:
% 232.25/43.34  | | 
% 232.25/43.34  | |   (9)  all_57_11 = e3 & op(e1, e0) = e3
% 232.25/43.34  | | 
% 232.25/43.34  | | ALPHA: (9) implies:
% 232.25/43.34  | |   (10)  op(e1, e0) = e3
% 232.25/43.34  | | 
% 232.25/43.34  | | REF_CLOSE: (1), (5), (6), (10) are inconsistent by sub-proof #2330.
% 232.25/43.34  | | 
% 232.25/43.34  | End of split
% 232.25/43.34  | 
% 232.25/43.34  End of proof
% 232.25/43.34  
% 232.25/43.34  Sub-proof #2311 shows that the following formulas are inconsistent:
% 232.25/43.34  ----------------------------------------------------------------
% 232.25/43.34    (1)   ~ (e3 = e1)
% 232.25/43.34    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.34           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.34    (3)  all_57_14 = e3
% 232.25/43.34    (4)   ~ (e3 = e2)
% 232.25/43.34    (5)  op(e1, e0) = all_53_14
% 232.25/43.34    (6)   ~ (e3 = e0)
% 232.25/43.34    (7)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 232.25/43.34         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 232.25/43.34    (8)   ~ (all_53_14 = e3)
% 232.25/43.34    (9)  (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 232.25/43.34    (10)   ~ (e2 = e0)
% 232.25/43.34    (11)   ~ (e1 = e0)
% 232.25/43.34    (12)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 232.25/43.34          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 232.25/43.34            e2)
% 232.25/43.34    (13)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 232.25/43.34              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 232.25/43.34                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 232.25/43.34                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 232.25/43.34    (14)   ~ (e2 = e1)
% 232.25/43.34  
% 232.25/43.34  Begin of proof
% 232.25/43.34  | 
% 232.25/43.34  | BETA: splitting (9) gives:
% 232.25/43.34  | 
% 232.25/43.34  | Case 1:
% 232.25/43.34  | | 
% 232.25/43.34  | |   (15)  all_57_11 = e3 & op(e1, e0) = e3
% 232.25/43.34  | | 
% 232.25/43.34  | | ALPHA: (15) implies:
% 232.25/43.34  | |   (16)  op(e1, e0) = e3
% 232.25/43.34  | | 
% 232.25/43.34  | | REF_CLOSE: (2), (5), (8), (16) are inconsistent by sub-proof #2330.
% 232.25/43.34  | | 
% 232.25/43.34  | Case 2:
% 232.25/43.34  | | 
% 232.25/43.34  | |   (17)  all_57_15 = e3 & op(e0, e0) = e3
% 232.25/43.34  | | 
% 232.25/43.34  | | ALPHA: (17) implies:
% 232.25/43.34  | |   (18)  all_57_15 = e3
% 232.25/43.34  | | 
% 232.25/43.34  | | REF_CLOSE: (1), (3), (4), (6), (7), (10), (11), (12), (13), (14), (18) are
% 232.25/43.34  | |            inconsistent by sub-proof #2312.
% 232.25/43.34  | | 
% 232.25/43.34  | End of split
% 232.25/43.34  | 
% 232.25/43.34  End of proof
% 232.25/43.34  
% 232.25/43.34  Sub-proof #2312 shows that the following formulas are inconsistent:
% 232.25/43.34  ----------------------------------------------------------------
% 232.25/43.34    (1)   ~ (e3 = e1)
% 232.25/43.34    (2)  all_57_14 = e3
% 232.25/43.34    (3)   ~ (e3 = e2)
% 232.25/43.34    (4)   ~ (e3 = e0)
% 232.25/43.34    (5)  all_57_15 = e3
% 232.25/43.34    (6)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 232.25/43.34         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 232.25/43.34    (7)   ~ (e2 = e0)
% 232.25/43.34    (8)   ~ (e1 = e0)
% 232.25/43.34    (9)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2) |
% 232.25/43.34         (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 232.25/43.34    (10)  (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 232.25/43.34              | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 232.25/43.34                = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 232.25/43.34                op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 232.25/43.34    (11)   ~ (e2 = e1)
% 232.25/43.34  
% 232.25/43.34  Begin of proof
% 232.25/43.34  | 
% 232.25/43.34  | BETA: splitting (10) gives:
% 232.25/43.34  | 
% 232.25/43.34  | Case 1:
% 232.25/43.34  | | 
% 232.25/43.34  | |   (12)  all_57_15 = e0 & op(e0, e0) = e0
% 232.25/43.34  | | 
% 232.25/43.34  | | REF_CLOSE: (4), (5), (12) are inconsistent by sub-proof #2329.
% 232.25/43.34  | | 
% 232.25/43.34  | Case 2:
% 232.25/43.34  | | 
% 232.25/43.34  | |   (13)  ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 232.25/43.34  | |             e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0 &
% 232.25/43.34  | |             op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 232.25/43.34  | |           (all_57_14 = e0 & op(e0, e1) = e0))
% 232.25/43.34  | | 
% 232.25/43.34  | | ALPHA: (13) implies:
% 232.25/43.34  | |   (14)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 232.25/43.34  | |           e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 232.25/43.34  | | 
% 232.25/43.34  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (14) are
% 232.25/43.34  | |            inconsistent by sub-proof #2313.
% 232.25/43.34  | | 
% 232.25/43.34  | End of split
% 232.25/43.34  | 
% 232.25/43.34  End of proof
% 232.25/43.34  
% 232.25/43.34  Sub-proof #2313 shows that the following formulas are inconsistent:
% 232.25/43.34  ----------------------------------------------------------------
% 232.25/43.35    (1)   ~ (e3 = e1)
% 232.25/43.35    (2)  all_57_14 = e3
% 232.25/43.35    (3)   ~ (e3 = e2)
% 232.25/43.35    (4)   ~ (e3 = e0)
% 232.25/43.35    (5)  (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 232.25/43.35         (all_57_14 = e0 & op(e0, e1) = e0)
% 232.25/43.35    (6)  all_57_15 = e3
% 232.25/43.35    (7)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 232.25/43.35         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 232.25/43.35    (8)   ~ (e2 = e0)
% 232.25/43.35    (9)   ~ (e1 = e0)
% 232.25/43.35    (10)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 232.25/43.35          | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 232.25/43.35            e2)
% 232.25/43.35    (11)   ~ (e2 = e1)
% 232.25/43.35  
% 232.25/43.35  Begin of proof
% 232.25/43.35  | 
% 232.25/43.35  | BETA: splitting (5) gives:
% 232.25/43.35  | 
% 232.25/43.35  | Case 1:
% 232.25/43.35  | | 
% 232.25/43.35  | |   (12)  all_57_12 = e0 & op(e0, e3) = e0
% 232.25/43.35  | | 
% 232.25/43.35  | | ALPHA: (12) implies:
% 232.25/43.35  | |   (13)  all_57_12 = e0
% 232.25/43.35  | | 
% 232.25/43.35  | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (9), (10), (11), (13) are
% 232.25/43.35  | |            inconsistent by sub-proof #2322.
% 232.25/43.35  | | 
% 232.25/43.35  | Case 2:
% 232.25/43.35  | | 
% 232.25/43.35  | |   (14)  (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 232.25/43.35  | |           e0)
% 232.25/43.35  | | 
% 232.25/43.35  | | BETA: splitting (14) gives:
% 232.25/43.35  | | 
% 232.25/43.35  | | Case 1:
% 232.25/43.35  | | | 
% 232.25/43.35  | | |   (15)  all_57_13 = e0 & op(e0, e2) = e0
% 232.25/43.35  | | | 
% 232.25/43.35  | | | ALPHA: (15) implies:
% 232.25/43.35  | | |   (16)  all_57_13 = e0
% 232.25/43.35  | | | 
% 232.25/43.35  | | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (9), (10), (11), (16) are
% 232.25/43.35  | | |            inconsistent by sub-proof #2315.
% 232.25/43.35  | | | 
% 232.25/43.35  | | Case 2:
% 232.25/43.35  | | | 
% 232.25/43.35  | | |   (17)  all_57_14 = e0 & op(e0, e1) = e0
% 232.25/43.35  | | | 
% 232.25/43.35  | | | REF_CLOSE: (2), (4), (17) are inconsistent by sub-proof #2314.
% 232.25/43.35  | | | 
% 232.25/43.35  | | End of split
% 232.25/43.35  | | 
% 232.25/43.35  | End of split
% 232.25/43.35  | 
% 232.25/43.35  End of proof
% 232.25/43.35  
% 232.25/43.35  Sub-proof #2314 shows that the following formulas are inconsistent:
% 232.25/43.35  ----------------------------------------------------------------
% 232.25/43.35    (1)  all_57_14 = e0 & op(e0, e1) = e0
% 232.25/43.35    (2)  all_57_14 = e3
% 232.25/43.35    (3)   ~ (e3 = e0)
% 232.25/43.35  
% 232.25/43.35  Begin of proof
% 232.25/43.35  | 
% 232.25/43.35  | ALPHA: (1) implies:
% 232.25/43.35  |   (4)  all_57_14 = e0
% 232.25/43.35  | 
% 232.25/43.35  | COMBINE_EQS: (2), (4) imply:
% 232.25/43.35  |   (5)  e3 = e0
% 232.25/43.35  | 
% 232.25/43.35  | REDUCE: (3), (5) imply:
% 232.25/43.35  |   (6)  $false
% 232.25/43.35  | 
% 232.25/43.35  | CLOSE: (6) is inconsistent.
% 232.25/43.35  | 
% 232.25/43.35  End of proof
% 232.25/43.35  
% 232.25/43.35  Sub-proof #2315 shows that the following formulas are inconsistent:
% 232.25/43.35  ----------------------------------------------------------------
% 232.25/43.35    (1)   ~ (e3 = e1)
% 232.25/43.35    (2)  all_57_14 = e3
% 232.25/43.35    (3)   ~ (e3 = e2)
% 232.25/43.35    (4)  all_57_15 = e3
% 232.25/43.35    (5)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 232.25/43.35         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 232.25/43.35    (6)   ~ (e2 = e0)
% 232.25/43.35    (7)   ~ (e1 = e0)
% 232.25/43.35    (8)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2) |
% 232.25/43.35         (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 232.25/43.35    (9)  all_57_13 = e0
% 232.25/43.35    (10)   ~ (e2 = e1)
% 232.25/43.35  
% 232.25/43.35  Begin of proof
% 232.25/43.35  | 
% 232.25/43.35  | BETA: splitting (8) gives:
% 232.25/43.35  | 
% 232.25/43.35  | Case 1:
% 232.25/43.35  | | 
% 232.25/43.35  | |   (11)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 232.25/43.35  | |           e2)
% 232.25/43.35  | | 
% 232.25/43.35  | | BETA: splitting (11) gives:
% 232.25/43.35  | | 
% 232.25/43.35  | | Case 1:
% 232.25/43.35  | | | 
% 232.25/43.35  | | |   (12)  all_57_12 = e2 & op(e0, e3) = e2
% 232.25/43.35  | | | 
% 232.25/43.35  | | | ALPHA: (12) implies:
% 232.25/43.35  | | |   (13)  all_57_12 = e2
% 232.25/43.35  | | | 
% 232.25/43.35  | | | REF_CLOSE: (1), (2), (4), (5), (7), (9), (10), (13) are inconsistent by
% 232.25/43.35  | | |            sub-proof #2317.
% 232.25/43.35  | | | 
% 232.25/43.35  | | Case 2:
% 232.25/43.35  | | | 
% 232.25/43.35  | | |   (14)  all_57_13 = e2 & op(e0, e2) = e2
% 232.25/43.35  | | | 
% 232.25/43.35  | | | REF_CLOSE: (6), (9), (14) are inconsistent by sub-proof #2316.
% 232.25/43.35  | | | 
% 232.25/43.35  | | End of split
% 232.25/43.35  | | 
% 232.25/43.35  | Case 2:
% 232.25/43.35  | | 
% 232.25/43.35  | |   (15)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 232.25/43.35  | |           e2)
% 232.25/43.35  | | 
% 232.25/43.35  | | BETA: splitting (15) gives:
% 232.25/43.35  | | 
% 232.25/43.35  | | Case 1:
% 232.25/43.35  | | | 
% 232.25/43.35  | | |   (16)  all_57_14 = e2 & op(e0, e1) = e2
% 232.25/43.35  | | | 
% 232.25/43.35  | | | ALPHA: (16) implies:
% 232.25/43.35  | | |   (17)  all_57_14 = e2
% 232.25/43.35  | | | 
% 232.25/43.35  | | | REF_CLOSE: (2), (3), (17) are inconsistent by sub-proof #2410.
% 232.25/43.35  | | | 
% 232.25/43.35  | | Case 2:
% 232.25/43.35  | | | 
% 232.25/43.35  | | |   (18)  all_57_15 = e2 & op(e0, e0) = e2
% 232.25/43.35  | | | 
% 232.25/43.35  | | | REF_CLOSE: (3), (4), (18) are inconsistent by sub-proof #2323.
% 232.25/43.35  | | | 
% 232.25/43.35  | | End of split
% 232.25/43.35  | | 
% 232.25/43.35  | End of split
% 232.25/43.35  | 
% 232.25/43.35  End of proof
% 232.25/43.35  
% 232.25/43.35  Sub-proof #2316 shows that the following formulas are inconsistent:
% 232.25/43.35  ----------------------------------------------------------------
% 232.25/43.35    (1)  all_57_13 = e2 & op(e0, e2) = e2
% 232.25/43.35    (2)  all_57_13 = e0
% 232.25/43.35    (3)   ~ (e2 = e0)
% 232.25/43.35  
% 232.25/43.35  Begin of proof
% 232.25/43.35  | 
% 232.25/43.35  | ALPHA: (1) implies:
% 232.25/43.35  |   (4)  all_57_13 = e2
% 232.25/43.35  | 
% 232.25/43.35  | COMBINE_EQS: (2), (4) imply:
% 232.25/43.35  |   (5)  e2 = e0
% 232.25/43.35  | 
% 232.25/43.35  | REDUCE: (3), (5) imply:
% 232.25/43.35  |   (6)  $false
% 232.25/43.35  | 
% 232.25/43.35  | CLOSE: (6) is inconsistent.
% 232.25/43.35  | 
% 232.25/43.35  End of proof
% 232.25/43.35  
% 232.25/43.35  Sub-proof #2317 shows that the following formulas are inconsistent:
% 232.25/43.35  ----------------------------------------------------------------
% 232.25/43.35    (1)   ~ (e3 = e1)
% 232.25/43.35    (2)  all_57_14 = e3
% 232.25/43.35    (3)  all_57_12 = e2
% 232.25/43.35    (4)  all_57_15 = e3
% 232.25/43.35    (5)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 232.25/43.35         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 232.25/43.35    (6)   ~ (e1 = e0)
% 232.25/43.35    (7)  all_57_13 = e0
% 232.25/43.35    (8)   ~ (e2 = e1)
% 232.25/43.35  
% 232.25/43.35  Begin of proof
% 232.25/43.35  | 
% 232.25/43.35  | BETA: splitting (5) gives:
% 232.25/43.35  | 
% 232.25/43.35  | Case 1:
% 232.25/43.35  | | 
% 232.25/43.35  | |   (9)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 232.25/43.35  | |          e1)
% 232.25/43.35  | | 
% 232.25/43.35  | | BETA: splitting (9) gives:
% 232.25/43.35  | | 
% 232.25/43.35  | | Case 1:
% 232.25/43.35  | | | 
% 232.25/43.35  | | |   (10)  all_57_12 = e1 & op(e0, e3) = e1
% 232.25/43.35  | | | 
% 232.25/43.35  | | | ALPHA: (10) implies:
% 232.25/43.35  | | |   (11)  all_57_12 = e1
% 232.25/43.35  | | | 
% 232.25/43.35  | | | REF_CLOSE: (3), (8), (11) are inconsistent by sub-proof #2321.
% 232.25/43.35  | | | 
% 232.25/43.35  | | Case 2:
% 232.25/43.35  | | | 
% 232.25/43.35  | | |   (12)  all_57_13 = e1 & op(e0, e2) = e1
% 232.25/43.35  | | | 
% 232.25/43.35  | | | REF_CLOSE: (6), (7), (12) are inconsistent by sub-proof #2320.
% 232.25/43.35  | | | 
% 232.25/43.35  | | End of split
% 232.25/43.35  | | 
% 232.25/43.35  | Case 2:
% 232.25/43.35  | | 
% 232.25/43.35  | |   (13)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 232.25/43.35  | |           e1)
% 232.25/43.35  | | 
% 232.25/43.35  | | BETA: splitting (13) gives:
% 232.25/43.35  | | 
% 232.25/43.35  | | Case 1:
% 232.25/43.35  | | | 
% 232.25/43.35  | | |   (14)  all_57_14 = e1 & op(e0, e1) = e1
% 232.25/43.35  | | | 
% 232.25/43.35  | | | REF_CLOSE: (1), (2), (14) are inconsistent by sub-proof #2319.
% 232.25/43.35  | | | 
% 232.25/43.35  | | Case 2:
% 232.25/43.35  | | | 
% 232.25/43.35  | | |   (15)  all_57_15 = e1 & op(e0, e0) = e1
% 232.25/43.35  | | | 
% 232.25/43.35  | | | REF_CLOSE: (1), (4), (15) are inconsistent by sub-proof #2318.
% 232.25/43.35  | | | 
% 232.25/43.35  | | End of split
% 232.25/43.35  | | 
% 232.25/43.35  | End of split
% 232.25/43.35  | 
% 232.25/43.35  End of proof
% 232.25/43.35  
% 232.25/43.35  Sub-proof #2318 shows that the following formulas are inconsistent:
% 232.25/43.35  ----------------------------------------------------------------
% 232.25/43.35    (1)  all_57_15 = e1 & op(e0, e0) = e1
% 232.25/43.35    (2)  all_57_15 = e3
% 232.25/43.35    (3)   ~ (e3 = e1)
% 232.25/43.35  
% 232.25/43.35  Begin of proof
% 232.25/43.35  | 
% 232.25/43.35  | ALPHA: (1) implies:
% 232.25/43.35  |   (4)  all_57_15 = e1
% 232.25/43.35  | 
% 232.25/43.35  | COMBINE_EQS: (2), (4) imply:
% 232.25/43.35  |   (5)  e3 = e1
% 232.25/43.35  | 
% 232.25/43.35  | SIMP: (5) implies:
% 232.25/43.35  |   (6)  e3 = e1
% 232.25/43.35  | 
% 232.25/43.35  | REDUCE: (3), (6) imply:
% 232.25/43.35  |   (7)  $false
% 232.25/43.35  | 
% 232.25/43.35  | CLOSE: (7) is inconsistent.
% 232.25/43.35  | 
% 232.25/43.35  End of proof
% 232.25/43.35  
% 232.25/43.35  Sub-proof #2319 shows that the following formulas are inconsistent:
% 232.25/43.35  ----------------------------------------------------------------
% 232.25/43.35    (1)  all_57_14 = e1 & op(e0, e1) = e1
% 232.25/43.35    (2)  all_57_14 = e3
% 232.25/43.35    (3)   ~ (e3 = e1)
% 232.25/43.35  
% 232.25/43.35  Begin of proof
% 232.25/43.35  | 
% 232.25/43.35  | ALPHA: (1) implies:
% 232.25/43.35  |   (4)  all_57_14 = e1
% 232.25/43.35  | 
% 232.25/43.35  | COMBINE_EQS: (2), (4) imply:
% 232.25/43.35  |   (5)  e3 = e1
% 232.25/43.35  | 
% 232.25/43.35  | REDUCE: (3), (5) imply:
% 232.25/43.35  |   (6)  $false
% 232.25/43.35  | 
% 232.25/43.35  | CLOSE: (6) is inconsistent.
% 232.25/43.35  | 
% 232.25/43.35  End of proof
% 232.25/43.35  
% 232.25/43.35  Sub-proof #2320 shows that the following formulas are inconsistent:
% 232.25/43.35  ----------------------------------------------------------------
% 232.25/43.35    (1)  all_57_13 = e1 & op(e0, e2) = e1
% 232.25/43.35    (2)  all_57_13 = e0
% 232.25/43.35    (3)   ~ (e1 = e0)
% 232.25/43.35  
% 232.25/43.35  Begin of proof
% 232.25/43.35  | 
% 232.25/43.35  | ALPHA: (1) implies:
% 232.25/43.35  |   (4)  all_57_13 = e1
% 232.25/43.35  | 
% 232.25/43.35  | COMBINE_EQS: (2), (4) imply:
% 232.25/43.35  |   (5)  e1 = e0
% 232.25/43.35  | 
% 232.25/43.35  | REDUCE: (3), (5) imply:
% 232.25/43.35  |   (6)  $false
% 232.25/43.35  | 
% 232.25/43.35  | CLOSE: (6) is inconsistent.
% 232.25/43.35  | 
% 232.25/43.35  End of proof
% 232.25/43.35  
% 232.25/43.35  Sub-proof #2321 shows that the following formulas are inconsistent:
% 232.25/43.35  ----------------------------------------------------------------
% 232.25/43.35    (1)  all_57_12 = e2
% 232.25/43.35    (2)  all_57_12 = e1
% 232.25/43.35    (3)   ~ (e2 = e1)
% 232.25/43.35  
% 232.25/43.35  Begin of proof
% 232.25/43.35  | 
% 232.25/43.35  | COMBINE_EQS: (1), (2) imply:
% 232.25/43.35  |   (4)  e2 = e1
% 232.25/43.35  | 
% 232.25/43.35  | SIMP: (4) implies:
% 232.25/43.35  |   (5)  e2 = e1
% 232.25/43.35  | 
% 232.25/43.35  | REDUCE: (3), (5) imply:
% 232.25/43.35  |   (6)  $false
% 232.25/43.35  | 
% 232.25/43.35  | CLOSE: (6) is inconsistent.
% 232.25/43.35  | 
% 232.25/43.35  End of proof
% 232.25/43.35  
% 232.25/43.35  Sub-proof #2322 shows that the following formulas are inconsistent:
% 232.25/43.35  ----------------------------------------------------------------
% 232.25/43.35    (1)  all_57_12 = e0
% 232.25/43.35    (2)   ~ (e3 = e1)
% 232.25/43.35    (3)  all_57_14 = e3
% 232.25/43.35    (4)   ~ (e3 = e2)
% 232.25/43.35    (5)  all_57_15 = e3
% 232.25/43.35    (6)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 232.25/43.35         (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 232.25/43.35    (7)   ~ (e2 = e0)
% 232.25/43.35    (8)   ~ (e1 = e0)
% 232.25/43.35    (9)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2) |
% 232.25/43.35         (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 232.25/43.35    (10)   ~ (e2 = e1)
% 232.25/43.35  
% 232.25/43.35  Begin of proof
% 232.25/43.35  | 
% 232.25/43.35  | BETA: splitting (9) gives:
% 232.25/43.35  | 
% 232.25/43.35  | Case 1:
% 232.25/43.35  | | 
% 232.25/43.35  | |   (11)  (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 232.25/43.35  | |           e2)
% 232.25/43.35  | | 
% 232.25/43.35  | | BETA: splitting (11) gives:
% 232.25/43.35  | | 
% 232.25/43.35  | | Case 1:
% 232.25/43.35  | | | 
% 232.25/43.35  | | |   (12)  all_57_12 = e2 & op(e0, e3) = e2
% 232.25/43.35  | | | 
% 232.25/43.35  | | | ALPHA: (12) implies:
% 232.25/43.35  | | |   (13)  all_57_12 = e2
% 232.25/43.35  | | | 
% 232.25/43.35  | | | REF_CLOSE: (1), (7), (13) are inconsistent by sub-proof #2385.
% 232.25/43.35  | | | 
% 232.25/43.35  | | Case 2:
% 232.25/43.35  | | | 
% 232.25/43.35  | | |   (14)  all_57_13 = e2 & op(e0, e2) = e2
% 232.25/43.35  | | | 
% 232.25/43.35  | | | ALPHA: (14) implies:
% 232.25/43.35  | | |   (15)  all_57_13 = e2
% 232.25/43.35  | | | 
% 232.25/43.35  | | | BETA: splitting (6) gives:
% 232.25/43.35  | | | 
% 232.25/43.35  | | | Case 1:
% 232.25/43.35  | | | | 
% 232.25/43.35  | | | |   (16)  (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0,
% 232.25/43.35  | | | |             e2) = e1)
% 232.25/43.35  | | | | 
% 232.25/43.35  | | | | BETA: splitting (16) gives:
% 232.25/43.35  | | | | 
% 232.25/43.35  | | | | Case 1:
% 232.25/43.35  | | | | | 
% 232.25/43.35  | | | | |   (17)  all_57_12 = e1 & op(e0, e3) = e1
% 232.25/43.35  | | | | | 
% 232.25/43.35  | | | | | REF_CLOSE: (1), (8), (17) are inconsistent by sub-proof #2328.
% 232.25/43.35  | | | | | 
% 232.25/43.35  | | | | Case 2:
% 232.25/43.35  | | | | | 
% 232.25/43.35  | | | | |   (18)  all_57_13 = e1 & op(e0, e2) = e1
% 232.25/43.35  | | | | | 
% 232.25/43.35  | | | | | ALPHA: (18) implies:
% 232.25/43.35  | | | | |   (19)  all_57_13 = e1
% 232.25/43.35  | | | | | 
% 232.25/43.35  | | | | | REF_CLOSE: (10), (15), (19) are inconsistent by sub-proof #2327.
% 232.25/43.35  | | | | | 
% 232.25/43.35  | | | | End of split
% 232.25/43.35  | | | | 
% 232.25/43.35  | | | Case 2:
% 232.25/43.35  | | | | 
% 232.25/43.35  | | | |   (20)  (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0,
% 232.25/43.35  | | | |             e0) = e1)
% 232.25/43.35  | | | | 
% 232.25/43.35  | | | | BETA: splitting (20) gives:
% 232.25/43.35  | | | | 
% 232.25/43.35  | | | | Case 1:
% 232.25/43.35  | | | | | 
% 232.25/43.35  | | | | |   (21)  all_57_14 = e1 & op(e0, e1) = e1
% 232.25/43.35  | | | | | 
% 232.25/43.35  | | | | | ALPHA: (21) implies:
% 232.25/43.35  | | | | |   (22)  all_57_14 = e1
% 232.25/43.35  | | | | | 
% 232.25/43.35  | | | | | REF_CLOSE: (2), (3), (22) are inconsistent by sub-proof #2326.
% 232.25/43.35  | | | | | 
% 232.25/43.35  | | | | Case 2:
% 232.25/43.35  | | | | | 
% 232.25/43.35  | | | | |   (23)  all_57_15 = e1 & op(e0, e0) = e1
% 232.25/43.35  | | | | | 
% 232.25/43.35  | | | | | REF_CLOSE: (2), (5), (23) are inconsistent by sub-proof #2325.
% 232.25/43.35  | | | | | 
% 232.25/43.35  | | | | End of split
% 232.25/43.35  | | | | 
% 232.25/43.35  | | | End of split
% 232.25/43.35  | | | 
% 232.25/43.35  | | End of split
% 232.25/43.35  | | 
% 232.25/43.35  | Case 2:
% 232.25/43.35  | | 
% 232.25/43.35  | |   (24)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 232.25/43.35  | |           e2)
% 232.25/43.35  | | 
% 232.25/43.35  | | BETA: splitting (24) gives:
% 232.25/43.35  | | 
% 232.25/43.35  | | Case 1:
% 232.25/43.35  | | | 
% 232.25/43.35  | | |   (25)  all_57_14 = e2 & op(e0, e1) = e2
% 232.25/43.35  | | | 
% 232.25/43.35  | | | REF_CLOSE: (3), (4), (25) are inconsistent by sub-proof #2324.
% 232.25/43.35  | | | 
% 232.25/43.35  | | Case 2:
% 232.25/43.35  | | | 
% 232.25/43.35  | | |   (26)  all_57_15 = e2 & op(e0, e0) = e2
% 232.25/43.35  | | | 
% 232.25/43.35  | | | REF_CLOSE: (4), (5), (26) are inconsistent by sub-proof #2323.
% 232.25/43.35  | | | 
% 232.25/43.35  | | End of split
% 232.25/43.35  | | 
% 232.25/43.35  | End of split
% 232.25/43.35  | 
% 232.25/43.35  End of proof
% 232.25/43.35  
% 232.25/43.35  Sub-proof #2323 shows that the following formulas are inconsistent:
% 232.25/43.35  ----------------------------------------------------------------
% 232.25/43.35    (1)  all_57_15 = e2 & op(e0, e0) = e2
% 232.25/43.35    (2)  all_57_15 = e3
% 232.25/43.35    (3)   ~ (e3 = e2)
% 232.25/43.35  
% 232.25/43.35  Begin of proof
% 232.25/43.35  | 
% 232.25/43.35  | ALPHA: (1) implies:
% 232.25/43.35  |   (4)  all_57_15 = e2
% 232.25/43.35  | 
% 232.25/43.35  | COMBINE_EQS: (2), (4) imply:
% 232.25/43.35  |   (5)  e3 = e2
% 232.25/43.35  | 
% 232.25/43.35  | REDUCE: (3), (5) imply:
% 232.25/43.35  |   (6)  $false
% 232.25/43.35  | 
% 232.25/43.35  | CLOSE: (6) is inconsistent.
% 232.25/43.35  | 
% 232.25/43.35  End of proof
% 232.25/43.35  
% 232.25/43.35  Sub-proof #2324 shows that the following formulas are inconsistent:
% 232.25/43.35  ----------------------------------------------------------------
% 232.25/43.35    (1)  all_57_14 = e2 & op(e0, e1) = e2
% 232.25/43.35    (2)  all_57_14 = e3
% 232.25/43.35    (3)   ~ (e3 = e2)
% 232.25/43.35  
% 232.25/43.35  Begin of proof
% 232.25/43.35  | 
% 232.25/43.35  | ALPHA: (1) implies:
% 232.25/43.35  |   (4)  all_57_14 = e2
% 232.25/43.35  | 
% 232.25/43.35  | COMBINE_EQS: (2), (4) imply:
% 232.25/43.35  |   (5)  e3 = e2
% 232.25/43.35  | 
% 232.25/43.35  | REDUCE: (3), (5) imply:
% 232.25/43.35  |   (6)  $false
% 232.25/43.35  | 
% 232.25/43.35  | CLOSE: (6) is inconsistent.
% 232.25/43.35  | 
% 232.25/43.35  End of proof
% 232.25/43.35  
% 232.25/43.35  Sub-proof #2325 shows that the following formulas are inconsistent:
% 232.25/43.35  ----------------------------------------------------------------
% 232.25/43.35    (1)  all_57_15 = e1 & op(e0, e0) = e1
% 232.25/43.35    (2)  all_57_15 = e3
% 232.25/43.35    (3)   ~ (e3 = e1)
% 232.25/43.35  
% 232.25/43.35  Begin of proof
% 232.25/43.35  | 
% 232.25/43.35  | ALPHA: (1) implies:
% 232.25/43.35  |   (4)  all_57_15 = e1
% 232.25/43.35  | 
% 232.25/43.35  | COMBINE_EQS: (2), (4) imply:
% 232.25/43.35  |   (5)  e3 = e1
% 232.25/43.35  | 
% 232.25/43.35  | REDUCE: (3), (5) imply:
% 232.25/43.35  |   (6)  $false
% 232.25/43.35  | 
% 232.25/43.35  | CLOSE: (6) is inconsistent.
% 232.25/43.35  | 
% 232.25/43.35  End of proof
% 232.25/43.35  
% 232.25/43.35  Sub-proof #2326 shows that the following formulas are inconsistent:
% 232.25/43.35  ----------------------------------------------------------------
% 232.25/43.35    (1)  all_57_14 = e3
% 232.25/43.35    (2)  all_57_14 = e1
% 232.25/43.35    (3)   ~ (e3 = e1)
% 232.25/43.35  
% 232.25/43.35  Begin of proof
% 232.25/43.35  | 
% 232.25/43.35  | COMBINE_EQS: (1), (2) imply:
% 232.25/43.35  |   (4)  e3 = e1
% 232.25/43.35  | 
% 232.25/43.35  | SIMP: (4) implies:
% 232.25/43.35  |   (5)  e3 = e1
% 232.25/43.35  | 
% 232.25/43.35  | REDUCE: (3), (5) imply:
% 232.25/43.35  |   (6)  $false
% 232.25/43.35  | 
% 232.25/43.35  | CLOSE: (6) is inconsistent.
% 232.25/43.35  | 
% 232.25/43.35  End of proof
% 232.25/43.35  
% 232.25/43.35  Sub-proof #2327 shows that the following formulas are inconsistent:
% 232.25/43.35  ----------------------------------------------------------------
% 232.25/43.35    (1)  all_57_13 = e2
% 232.25/43.35    (2)  all_57_13 = e1
% 232.25/43.35    (3)   ~ (e2 = e1)
% 232.25/43.35  
% 232.25/43.35  Begin of proof
% 232.25/43.35  | 
% 232.25/43.35  | COMBINE_EQS: (1), (2) imply:
% 232.25/43.35  |   (4)  e2 = e1
% 232.25/43.35  | 
% 232.25/43.35  | SIMP: (4) implies:
% 232.25/43.35  |   (5)  e2 = e1
% 232.25/43.35  | 
% 232.25/43.35  | REDUCE: (3), (5) imply:
% 232.25/43.35  |   (6)  $false
% 232.25/43.35  | 
% 232.25/43.35  | CLOSE: (6) is inconsistent.
% 232.25/43.35  | 
% 232.25/43.35  End of proof
% 232.25/43.35  
% 232.25/43.35  Sub-proof #2328 shows that the following formulas are inconsistent:
% 232.25/43.35  ----------------------------------------------------------------
% 232.25/43.35    (1)  all_57_12 = e1 & op(e0, e3) = e1
% 232.25/43.35    (2)  all_57_12 = e0
% 232.25/43.35    (3)   ~ (e1 = e0)
% 232.25/43.35  
% 232.25/43.35  Begin of proof
% 232.25/43.35  | 
% 232.25/43.35  | ALPHA: (1) implies:
% 232.25/43.35  |   (4)  all_57_12 = e1
% 232.25/43.35  | 
% 232.25/43.35  | COMBINE_EQS: (2), (4) imply:
% 232.25/43.35  |   (5)  e1 = e0
% 232.25/43.35  | 
% 232.25/43.35  | REDUCE: (3), (5) imply:
% 232.25/43.35  |   (6)  $false
% 232.25/43.35  | 
% 232.25/43.35  | CLOSE: (6) is inconsistent.
% 232.25/43.35  | 
% 232.25/43.35  End of proof
% 232.25/43.35  
% 232.25/43.35  Sub-proof #2329 shows that the following formulas are inconsistent:
% 232.25/43.35  ----------------------------------------------------------------
% 232.25/43.35    (1)  all_57_15 = e0 & op(e0, e0) = e0
% 232.25/43.35    (2)  all_57_15 = e3
% 232.25/43.35    (3)   ~ (e3 = e0)
% 232.25/43.35  
% 232.25/43.35  Begin of proof
% 232.25/43.35  | 
% 232.25/43.35  | ALPHA: (1) implies:
% 232.25/43.35  |   (4)  all_57_15 = e0
% 232.25/43.35  | 
% 232.25/43.35  | COMBINE_EQS: (2), (4) imply:
% 232.25/43.35  |   (5)  e3 = e0
% 232.25/43.35  | 
% 232.25/43.35  | REDUCE: (3), (5) imply:
% 232.25/43.35  |   (6)  $false
% 232.25/43.35  | 
% 232.25/43.35  | CLOSE: (6) is inconsistent.
% 232.25/43.35  | 
% 232.25/43.35  End of proof
% 232.25/43.35  
% 232.25/43.35  Sub-proof #2330 shows that the following formulas are inconsistent:
% 232.25/43.35  ----------------------------------------------------------------
% 232.25/43.35    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.35    (2)  op(e1, e0) = all_53_14
% 232.25/43.35    (3)  op(e1, e0) = e3
% 232.25/43.35    (4)   ~ (all_53_14 = e3)
% 232.25/43.35  
% 232.25/43.35  Begin of proof
% 232.25/43.35  | 
% 232.25/43.35  | GROUND_INST: instantiating (1) with all_53_14, e3, e0, e1, simplifying with
% 232.25/43.35  |              (2), (3) gives:
% 232.25/43.35  |   (5)  all_53_14 = e3
% 232.25/43.35  | 
% 232.25/43.35  | REDUCE: (4), (5) imply:
% 232.25/43.35  |   (6)  $false
% 232.25/43.35  | 
% 232.25/43.35  | CLOSE: (6) is inconsistent.
% 232.25/43.35  | 
% 232.25/43.35  End of proof
% 232.25/43.35  
% 232.25/43.35  Sub-proof #2331 shows that the following formulas are inconsistent:
% 232.25/43.35  ----------------------------------------------------------------
% 232.25/43.35    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.35    (2)  op(e3, e0) = all_53_12
% 232.25/43.35    (3)  op(e3, e0) = e2
% 232.25/43.35    (4)   ~ (all_53_12 = e2)
% 232.25/43.35  
% 232.25/43.35  Begin of proof
% 232.25/43.35  | 
% 232.25/43.35  | GROUND_INST: instantiating (1) with all_53_12, e2, e0, e3, simplifying with
% 232.25/43.35  |              (2), (3) gives:
% 232.25/43.35  |   (5)  all_53_12 = e2
% 232.25/43.35  | 
% 232.25/43.35  | REDUCE: (4), (5) imply:
% 232.25/43.35  |   (6)  $false
% 232.25/43.35  | 
% 232.25/43.35  | CLOSE: (6) is inconsistent.
% 232.25/43.35  | 
% 232.25/43.35  End of proof
% 232.25/43.35  
% 232.25/43.35  Sub-proof #2332 shows that the following formulas are inconsistent:
% 232.25/43.35  ----------------------------------------------------------------
% 232.25/43.35    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.35    (2)  op(e0, e2) = all_53_7
% 232.25/43.35    (3)  op(e0, e2) = e0
% 232.25/43.35    (4)   ~ (all_53_7 = e0)
% 232.25/43.35  
% 232.25/43.35  Begin of proof
% 232.25/43.35  | 
% 232.25/43.35  | GROUND_INST: instantiating (1) with all_53_7, e0, e2, e0, simplifying with
% 232.25/43.35  |              (2), (3) gives:
% 232.25/43.35  |   (5)  all_53_7 = e0
% 232.25/43.35  | 
% 232.25/43.35  | REDUCE: (4), (5) imply:
% 232.25/43.35  |   (6)  $false
% 232.25/43.35  | 
% 232.25/43.35  | CLOSE: (6) is inconsistent.
% 232.25/43.35  | 
% 232.25/43.35  End of proof
% 232.25/43.35  
% 232.25/43.35  Sub-proof #2333 shows that the following formulas are inconsistent:
% 232.25/43.35  ----------------------------------------------------------------
% 232.25/43.35    (1)  op(e0, e0) = all_4_2
% 232.25/43.35    (2)   ~ (e3 = e1)
% 232.25/43.35    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.35    (4)   ~ (all_6_2 = e3)
% 232.25/43.35    (5)  op(e1, e1) = all_6_2
% 232.25/43.35    (6)  all_57_4 = e2
% 232.25/43.35    (7)  (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 232.25/43.35    (8)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 232.25/43.35         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 232.25/43.35    (9)   ~ (e3 = e2)
% 232.25/43.35    (10)   ~ (e3 = e0)
% 232.25/43.35    (11)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 232.25/43.35          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 232.25/43.35    (12)   ~ (all_4_2 = e2)
% 232.25/43.35    (13)   ~ (e2 = e0)
% 232.25/43.35    (14)   ~ (e1 = e0)
% 232.25/43.35    (15)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 232.25/43.35          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 232.25/43.35    (16)   ~ (e2 = e1)
% 232.25/43.35    (17)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 232.25/43.35          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 232.25/43.35  
% 232.25/43.35  Begin of proof
% 232.25/43.35  | 
% 232.25/43.35  | BETA: splitting (7) gives:
% 232.25/43.35  | 
% 232.25/43.35  | Case 1:
% 232.25/43.35  | | 
% 232.25/43.35  | |   (18)  all_57_14 = e2 & op(e0, e1) = e2
% 232.25/43.35  | | 
% 232.25/43.35  | | ALPHA: (18) implies:
% 232.25/43.35  | |   (19)  all_57_14 = e2
% 232.25/43.35  | | 
% 232.25/43.35  | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (9), (10), (11), (13), (14), (15),
% 232.25/43.35  | |            (16), (17), (19) are inconsistent by sub-proof #2370.
% 232.25/43.35  | | 
% 232.25/43.35  | Case 2:
% 232.25/43.35  | | 
% 232.25/43.35  | |   (20)  all_57_15 = e2 & op(e0, e0) = e2
% 232.25/43.35  | | 
% 232.25/43.35  | | ALPHA: (20) implies:
% 232.25/43.35  | |   (21)  op(e0, e0) = e2
% 232.25/43.35  | | 
% 232.25/43.35  | | REF_CLOSE: (1), (3), (12), (21) are inconsistent by sub-proof #2334.
% 232.25/43.35  | | 
% 232.25/43.35  | End of split
% 232.25/43.35  | 
% 232.25/43.35  End of proof
% 232.25/43.35  
% 232.25/43.35  Sub-proof #2334 shows that the following formulas are inconsistent:
% 232.25/43.35  ----------------------------------------------------------------
% 232.25/43.35    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.35    (2)  op(e0, e0) = all_4_2
% 232.25/43.35    (3)  op(e0, e0) = e2
% 232.25/43.35    (4)   ~ (all_4_2 = e2)
% 232.25/43.35  
% 232.25/43.35  Begin of proof
% 232.25/43.35  | 
% 232.25/43.35  | GROUND_INST: instantiating (1) with all_4_2, e2, e0, e0, simplifying with (2),
% 232.25/43.35  |              (3) gives:
% 232.25/43.35  |   (5)  all_4_2 = e2
% 232.25/43.35  | 
% 232.25/43.35  | REDUCE: (4), (5) imply:
% 232.25/43.35  |   (6)  $false
% 232.25/43.35  | 
% 232.25/43.35  | CLOSE: (6) is inconsistent.
% 232.25/43.35  | 
% 232.25/43.35  End of proof
% 232.25/43.35  
% 232.25/43.35  Sub-proof #2335 shows that the following formulas are inconsistent:
% 232.25/43.35  ----------------------------------------------------------------
% 232.25/43.35    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.35    (2)  op(e0, e2) = all_53_7
% 232.25/43.35    (3)  op(e0, e2) = e2
% 232.25/43.35    (4)   ~ (all_53_7 = e2)
% 232.25/43.35  
% 232.25/43.35  Begin of proof
% 232.25/43.35  | 
% 232.25/43.35  | GROUND_INST: instantiating (1) with all_53_7, e2, e2, e0, simplifying with
% 232.25/43.35  |              (2), (3) gives:
% 232.25/43.35  |   (5)  all_53_7 = e2
% 232.25/43.35  | 
% 232.25/43.35  | REDUCE: (4), (5) imply:
% 232.25/43.35  |   (6)  $false
% 232.25/43.35  | 
% 232.25/43.35  | CLOSE: (6) is inconsistent.
% 232.25/43.35  | 
% 232.25/43.35  End of proof
% 232.25/43.35  
% 232.25/43.35  Sub-proof #2336 shows that the following formulas are inconsistent:
% 232.25/43.35  ----------------------------------------------------------------
% 232.25/43.35    (1)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 232.25/43.35         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 232.25/43.35    (2)   ~ (e3 = e1)
% 232.25/43.35    (3)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 232.25/43.35         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 232.25/43.35    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.35    (5)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 232.25/43.35         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 232.25/43.35    (6)   ~ (all_6_2 = e3)
% 232.25/43.35    (7)  op(e1, e1) = all_6_2
% 232.25/43.35    (8)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 232.25/43.35         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 232.25/43.35    (9)  all_57_12 = e2
% 232.25/43.35    (10)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 232.25/43.35          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 232.25/43.35    (11)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 232.25/43.35          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 232.25/43.35    (12)   ~ (e3 = e2)
% 232.25/43.35    (13)  op(e1, e0) = all_53_14
% 232.25/43.35    (14)   ~ (e3 = e0)
% 232.25/43.35    (15)  op(e3, e3) = e3
% 232.25/43.35    (16)  all_57_11 = e2
% 232.25/43.35    (17)   ~ (e2 = e0)
% 232.25/43.35    (18)  op(e2, e2) = e2
% 232.25/43.35    (19)   ~ (e1 = e0)
% 232.25/43.35    (20)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 232.25/43.35          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 232.25/43.35    (21)   ~ (all_53_14 = e0)
% 232.25/43.35    (22)   ~ (all_53_13 = e0)
% 232.25/43.35    (23)  op(e2, e0) = all_53_13
% 232.25/43.35    (24)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 232.25/43.35          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 232.25/43.35    (25)   ~ (e2 = e1)
% 232.25/43.35    (26)   ~ (all_6_2 = e0)
% 232.25/43.35    (27)  all_57_14 = e0
% 232.25/43.35  
% 232.25/43.35  Begin of proof
% 232.25/43.35  | 
% 232.25/43.35  | BETA: splitting (20) gives:
% 232.25/43.35  | 
% 232.25/43.35  | Case 1:
% 232.25/43.35  | | 
% 232.25/43.35  | |   (28)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) =
% 232.25/43.35  | |           e3)
% 232.25/43.35  | | 
% 232.25/43.35  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 232.25/43.35  | |            (13), (14), (15), (16), (17), (18), (19), (21), (22), (23), (24),
% 232.25/43.35  | |            (25), (26), (28) are inconsistent by sub-proof #2339.
% 232.25/43.35  | | 
% 232.25/43.35  | Case 2:
% 232.25/43.35  | | 
% 232.25/43.35  | |   (29)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) =
% 232.25/43.35  | |           e3)
% 232.25/43.35  | | 
% 232.25/43.35  | | REF_CLOSE: (4), (6), (7), (14), (27), (29) are inconsistent by sub-proof
% 232.25/43.35  | |            #2337.
% 232.25/43.35  | | 
% 232.25/43.35  | End of split
% 232.25/43.35  | 
% 232.25/43.35  End of proof
% 232.25/43.35  
% 232.25/43.35  Sub-proof #2337 shows that the following formulas are inconsistent:
% 232.25/43.35  ----------------------------------------------------------------
% 232.25/43.35    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.35    (2)   ~ (all_6_2 = e3)
% 232.25/43.35    (3)  op(e1, e1) = all_6_2
% 232.25/43.35    (4)   ~ (e3 = e0)
% 232.25/43.35    (5)  all_57_14 = e0
% 232.25/43.35    (6)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 232.25/43.35  
% 232.25/43.35  Begin of proof
% 232.25/43.35  | 
% 232.25/43.35  | BETA: splitting (6) gives:
% 232.25/43.35  | 
% 232.25/43.35  | Case 1:
% 232.25/43.35  | | 
% 232.25/43.35  | |   (7)  all_57_8 = e3 & op(e1, e1) = e3
% 232.25/43.35  | | 
% 232.25/43.35  | | ALPHA: (7) implies:
% 232.25/43.35  | |   (8)  op(e1, e1) = e3
% 232.25/43.35  | | 
% 232.25/43.35  | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #2468.
% 232.25/43.35  | | 
% 232.25/43.35  | Case 2:
% 232.25/43.35  | | 
% 232.25/43.35  | |   (9)  all_57_14 = e3 & op(e0, e1) = e3
% 232.25/43.35  | | 
% 232.25/43.35  | | REF_CLOSE: (4), (5), (9) are inconsistent by sub-proof #2338.
% 232.25/43.35  | | 
% 232.25/43.35  | End of split
% 232.25/43.35  | 
% 232.25/43.35  End of proof
% 232.25/43.35  
% 232.25/43.35  Sub-proof #2338 shows that the following formulas are inconsistent:
% 232.25/43.35  ----------------------------------------------------------------
% 232.25/43.35    (1)  all_57_14 = e3 & op(e0, e1) = e3
% 232.25/43.35    (2)  all_57_14 = e0
% 232.25/43.35    (3)   ~ (e3 = e0)
% 232.25/43.35  
% 232.25/43.35  Begin of proof
% 232.25/43.35  | 
% 232.25/43.35  | ALPHA: (1) implies:
% 232.25/43.35  |   (4)  all_57_14 = e3
% 232.25/43.35  | 
% 232.25/43.35  | COMBINE_EQS: (2), (4) imply:
% 232.25/43.35  |   (5)  e3 = e0
% 232.25/43.35  | 
% 232.25/43.35  | REDUCE: (3), (5) imply:
% 232.25/43.35  |   (6)  $false
% 232.25/43.35  | 
% 232.25/43.35  | CLOSE: (6) is inconsistent.
% 232.25/43.35  | 
% 232.25/43.35  End of proof
% 232.25/43.35  
% 232.25/43.35  Sub-proof #2339 shows that the following formulas are inconsistent:
% 232.25/43.35  ----------------------------------------------------------------
% 232.25/43.35    (1)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3)
% 232.25/43.35    (2)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 232.25/43.35         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 232.25/43.35    (3)   ~ (e3 = e1)
% 232.25/43.35    (4)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 232.25/43.35         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 232.25/43.35    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.35    (6)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 232.25/43.35         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 232.25/43.35    (7)   ~ (all_6_2 = e3)
% 232.25/43.35    (8)  op(e1, e1) = all_6_2
% 232.25/43.35    (9)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 232.25/43.35         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 232.25/43.35    (10)  all_57_12 = e2
% 232.25/43.35    (11)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 232.25/43.35          (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 232.25/43.36    (12)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 232.25/43.36          (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 232.25/43.36    (13)   ~ (e3 = e2)
% 232.25/43.36    (14)  op(e1, e0) = all_53_14
% 232.25/43.36    (15)   ~ (e3 = e0)
% 232.25/43.36    (16)  op(e3, e3) = e3
% 232.25/43.36    (17)  all_57_11 = e2
% 232.25/43.36    (18)   ~ (e2 = e0)
% 232.25/43.36    (19)  op(e2, e2) = e2
% 232.25/43.36    (20)   ~ (e1 = e0)
% 232.25/43.36    (21)   ~ (all_53_14 = e0)
% 232.25/43.36    (22)   ~ (all_53_13 = e0)
% 232.25/43.36    (23)  op(e2, e0) = all_53_13
% 232.25/43.36    (24)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 232.25/43.36          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 232.25/43.36    (25)   ~ (e2 = e1)
% 232.25/43.36    (26)   ~ (all_6_2 = e0)
% 232.25/43.36  
% 232.25/43.36  Begin of proof
% 232.25/43.36  | 
% 232.25/43.36  | BETA: splitting (1) gives:
% 232.25/43.36  | 
% 232.25/43.36  | Case 1:
% 232.25/43.36  | | 
% 232.25/43.36  | |   (27)  all_57_4 = e3 & op(e3, e1) = e3
% 232.25/43.36  | | 
% 232.25/43.36  | | ALPHA: (27) implies:
% 232.25/43.36  | |   (28)  all_57_4 = e3
% 232.25/43.36  | | 
% 232.25/43.36  | | REF_CLOSE: (3), (5), (9), (11), (12), (13), (15), (16), (18), (20), (25),
% 232.25/43.36  | |            (28) are inconsistent by sub-proof #2474.
% 232.25/43.36  | | 
% 232.25/43.36  | Case 2:
% 232.25/43.36  | | 
% 232.25/43.36  | |   (29)  all_57_5 = e3 & op(e2, e1) = e3
% 232.25/43.36  | | 
% 232.25/43.36  | | ALPHA: (29) implies:
% 232.25/43.36  | |   (30)  all_57_5 = e3
% 232.25/43.36  | | 
% 232.25/43.36  | | BETA: splitting (2) gives:
% 232.25/43.36  | | 
% 232.25/43.36  | | Case 1:
% 232.25/43.36  | | | 
% 232.25/43.36  | | |   (31)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) =
% 232.25/43.36  | | |           e1)
% 232.25/43.36  | | | 
% 232.25/43.36  | | | BETA: splitting (31) gives:
% 232.25/43.36  | | | 
% 232.25/43.36  | | | Case 1:
% 232.25/43.36  | | | | 
% 232.25/43.36  | | | |   (32)  all_57_0 = e1 & op(e3, e3) = e1
% 232.25/43.36  | | | | 
% 232.25/43.36  | | | | ALPHA: (32) implies:
% 232.25/43.36  | | | |   (33)  op(e3, e3) = e1
% 232.25/43.36  | | | | 
% 232.25/43.36  | | | | REF_CLOSE: (3), (5), (16), (33) are inconsistent by sub-proof #2495.
% 232.25/43.36  | | | | 
% 232.25/43.36  | | | Case 2:
% 232.25/43.36  | | | | 
% 232.25/43.36  | | | |   (34)  all_57_2 = e1 & op(e2, e3) = e1
% 232.25/43.36  | | | | 
% 232.25/43.36  | | | | ALPHA: (34) implies:
% 232.25/43.36  | | | |   (35)  all_57_2 = e1
% 232.25/43.36  | | | | 
% 232.25/43.36  | | | | REF_CLOSE: (5), (15), (18), (19), (20), (22), (23), (24), (30), (35) are
% 232.25/43.36  | | | |            inconsistent by sub-proof #2469.
% 232.25/43.36  | | | | 
% 232.25/43.36  | | | End of split
% 232.25/43.36  | | | 
% 232.25/43.36  | | Case 2:
% 232.25/43.36  | | | 
% 232.25/43.36  | | |   (36)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) =
% 232.25/43.36  | | |           e1)
% 232.25/43.36  | | | 
% 232.25/43.36  | | | BETA: splitting (36) gives:
% 232.25/43.36  | | | 
% 232.25/43.36  | | | Case 1:
% 232.25/43.36  | | | | 
% 232.25/43.36  | | | |   (37)  all_57_6 = e1 & op(e1, e3) = e1
% 232.25/43.36  | | | | 
% 232.25/43.36  | | | | ALPHA: (37) implies:
% 232.25/43.36  | | | |   (38)  all_57_6 = e1
% 232.25/43.36  | | | | 
% 232.25/43.36  | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (13), (14), (15), (17), (20),
% 232.25/43.36  | | | |            (21), (26), (38) are inconsistent by sub-proof #2340.
% 232.25/43.36  | | | | 
% 232.25/43.36  | | | Case 2:
% 232.25/43.36  | | | | 
% 232.25/43.36  | | | |   (39)  all_57_12 = e1 & op(e0, e3) = e1
% 232.25/43.36  | | | | 
% 232.25/43.36  | | | | REF_CLOSE: (10), (25), (39) are inconsistent by sub-proof #2388.
% 232.25/43.36  | | | | 
% 232.25/43.36  | | | End of split
% 232.25/43.36  | | | 
% 232.25/43.36  | | End of split
% 232.25/43.36  | | 
% 232.25/43.36  | End of split
% 232.25/43.36  | 
% 232.25/43.36  End of proof
% 232.25/43.36  
% 232.25/43.36  Sub-proof #2340 shows that the following formulas are inconsistent:
% 232.25/43.36  ----------------------------------------------------------------
% 232.25/43.36    (1)   ~ (e3 = e1)
% 232.25/43.36    (2)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 232.25/43.36         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 232.25/43.36    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.36    (4)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 232.25/43.36         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 232.25/43.36    (5)   ~ (all_6_2 = e3)
% 232.25/43.36    (6)  op(e1, e1) = all_6_2
% 232.25/43.36    (7)  all_57_6 = e1
% 232.25/43.36    (8)   ~ (e3 = e2)
% 232.25/43.36    (9)  op(e1, e0) = all_53_14
% 232.25/43.36    (10)   ~ (e3 = e0)
% 232.25/43.36    (11)  all_57_11 = e2
% 232.25/43.36    (12)   ~ (e1 = e0)
% 232.25/43.36    (13)   ~ (all_53_14 = e0)
% 232.25/43.36    (14)   ~ (all_6_2 = e0)
% 232.25/43.36  
% 232.25/43.36  Begin of proof
% 232.25/43.36  | 
% 232.25/43.36  | BETA: splitting (2) gives:
% 232.25/43.36  | 
% 232.25/43.36  | Case 1:
% 232.25/43.36  | | 
% 232.25/43.36  | |   (15)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) =
% 232.25/43.36  | |           e0)
% 232.25/43.36  | | 
% 232.25/43.36  | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (10), (11), (12), (15) are
% 232.25/43.36  | |            inconsistent by sub-proof #2342.
% 232.25/43.36  | | 
% 232.25/43.36  | Case 2:
% 232.25/43.36  | | 
% 232.25/43.36  | |   (16)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 232.25/43.36  | |           e0)
% 232.25/43.36  | | 
% 232.25/43.36  | | BETA: splitting (16) gives:
% 232.25/43.36  | | 
% 232.25/43.36  | | Case 1:
% 232.25/43.36  | | | 
% 232.25/43.36  | | |   (17)  all_57_8 = e0 & op(e1, e1) = e0
% 232.25/43.36  | | | 
% 232.25/43.36  | | | REF_CLOSE: (3), (6), (14), (17) are inconsistent by sub-proof #2412.
% 232.25/43.36  | | | 
% 232.25/43.36  | | Case 2:
% 232.25/43.36  | | | 
% 232.25/43.36  | | |   (18)  all_57_11 = e0 & op(e1, e0) = e0
% 232.25/43.36  | | | 
% 232.25/43.36  | | | REF_CLOSE: (3), (9), (13), (18) are inconsistent by sub-proof #2341.
% 232.25/43.36  | | | 
% 232.25/43.36  | | End of split
% 232.25/43.36  | | 
% 232.25/43.36  | End of split
% 232.25/43.36  | 
% 232.25/43.36  End of proof
% 232.25/43.36  
% 232.25/43.36  Sub-proof #2341 shows that the following formulas are inconsistent:
% 232.25/43.36  ----------------------------------------------------------------
% 232.25/43.36    (1)  all_57_11 = e0 & op(e1, e0) = e0
% 232.25/43.36    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.36    (3)  op(e1, e0) = all_53_14
% 232.25/43.36    (4)   ~ (all_53_14 = e0)
% 232.25/43.36  
% 232.25/43.36  Begin of proof
% 232.25/43.36  | 
% 232.25/43.36  | ALPHA: (1) implies:
% 232.25/43.36  |   (5)  op(e1, e0) = e0
% 232.25/43.36  | 
% 232.25/43.36  | GROUND_INST: instantiating (2) with all_53_14, e0, e0, e1, simplifying with
% 232.25/43.36  |              (3), (5) gives:
% 232.25/43.36  |   (6)  all_53_14 = e0
% 232.25/43.36  | 
% 232.25/43.36  | REDUCE: (4), (6) imply:
% 232.25/43.36  |   (7)  $false
% 232.25/43.36  | 
% 232.25/43.36  | CLOSE: (7) is inconsistent.
% 232.25/43.36  | 
% 232.25/43.36  End of proof
% 232.25/43.36  
% 232.25/43.36  Sub-proof #2342 shows that the following formulas are inconsistent:
% 232.25/43.36  ----------------------------------------------------------------
% 232.25/43.36    (1)   ~ (e3 = e1)
% 232.25/43.36    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.36    (3)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 232.25/43.36         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 232.25/43.36    (4)   ~ (all_6_2 = e3)
% 232.25/43.36    (5)  op(e1, e1) = all_6_2
% 232.25/43.36    (6)  all_57_6 = e1
% 232.25/43.36    (7)   ~ (e3 = e2)
% 232.25/43.36    (8)   ~ (e3 = e0)
% 232.25/43.36    (9)  all_57_11 = e2
% 232.25/43.36    (10)   ~ (e1 = e0)
% 232.25/43.36    (11)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0)
% 232.25/43.36  
% 232.25/43.36  Begin of proof
% 232.25/43.36  | 
% 232.25/43.36  | BETA: splitting (11) gives:
% 232.25/43.36  | 
% 232.25/43.36  | Case 1:
% 232.25/43.36  | | 
% 232.25/43.36  | |   (12)  all_57_6 = e0 & op(e1, e3) = e0
% 232.25/43.36  | | 
% 232.25/43.36  | | REF_CLOSE: (6), (10), (12) are inconsistent by sub-proof #2347.
% 232.25/43.36  | | 
% 232.25/43.36  | Case 2:
% 232.25/43.36  | | 
% 232.25/43.36  | |   (13)  all_57_7 = e0 & op(e1, e2) = e0
% 232.25/43.36  | | 
% 232.25/43.36  | | ALPHA: (13) implies:
% 232.25/43.36  | |   (14)  all_57_7 = e0
% 232.25/43.36  | | 
% 232.25/43.36  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (14) are
% 232.25/43.36  | |            inconsistent by sub-proof #2343.
% 232.25/43.36  | | 
% 232.25/43.36  | End of split
% 232.25/43.36  | 
% 232.25/43.36  End of proof
% 232.25/43.36  
% 232.25/43.36  Sub-proof #2343 shows that the following formulas are inconsistent:
% 232.25/43.36  ----------------------------------------------------------------
% 232.25/43.36    (1)   ~ (e3 = e1)
% 232.25/43.36    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.36    (3)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 232.25/43.36         (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 232.25/43.36    (4)   ~ (all_6_2 = e3)
% 232.25/43.36    (5)  op(e1, e1) = all_6_2
% 232.25/43.36    (6)  all_57_6 = e1
% 232.25/43.36    (7)   ~ (e3 = e2)
% 232.25/43.36    (8)   ~ (e3 = e0)
% 232.25/43.36    (9)  all_57_11 = e2
% 232.25/43.36    (10)  all_57_7 = e0
% 232.25/43.36  
% 232.25/43.36  Begin of proof
% 232.25/43.36  | 
% 232.25/43.36  | BETA: splitting (3) gives:
% 232.25/43.36  | 
% 232.25/43.36  | Case 1:
% 232.25/43.36  | | 
% 232.25/43.36  | |   (11)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 232.25/43.36  | |           e3)
% 232.25/43.36  | | 
% 232.25/43.36  | | BETA: splitting (11) gives:
% 232.25/43.36  | | 
% 232.25/43.36  | | Case 1:
% 232.25/43.36  | | | 
% 232.25/43.36  | | |   (12)  all_57_6 = e3 & op(e1, e3) = e3
% 232.25/43.36  | | | 
% 232.25/43.36  | | | REF_CLOSE: (1), (6), (12) are inconsistent by sub-proof #2346.
% 232.25/43.36  | | | 
% 232.25/43.36  | | Case 2:
% 232.25/43.36  | | | 
% 232.25/43.36  | | |   (13)  all_57_7 = e3 & op(e1, e2) = e3
% 232.25/43.36  | | | 
% 232.25/43.36  | | | REF_CLOSE: (8), (10), (13) are inconsistent by sub-proof #2345.
% 232.25/43.36  | | | 
% 232.25/43.36  | | End of split
% 232.25/43.36  | | 
% 232.25/43.36  | Case 2:
% 232.25/43.36  | | 
% 232.25/43.36  | |   (14)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 232.25/43.36  | |           e3)
% 232.25/43.36  | | 
% 232.25/43.36  | | REF_CLOSE: (2), (4), (5), (7), (9), (14) are inconsistent by sub-proof
% 232.25/43.36  | |            #2344.
% 232.25/43.36  | | 
% 232.25/43.36  | End of split
% 232.25/43.36  | 
% 232.25/43.36  End of proof
% 232.25/43.36  
% 232.25/43.36  Sub-proof #2344 shows that the following formulas are inconsistent:
% 232.25/43.36  ----------------------------------------------------------------
% 232.25/43.36    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.36    (2)   ~ (all_6_2 = e3)
% 232.25/43.36    (3)  op(e1, e1) = all_6_2
% 232.25/43.36    (4)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 232.25/43.36    (5)   ~ (e3 = e2)
% 232.25/43.36    (6)  all_57_11 = e2
% 232.25/43.36  
% 232.25/43.36  Begin of proof
% 232.25/43.36  | 
% 232.25/43.36  | BETA: splitting (4) gives:
% 232.25/43.36  | 
% 232.25/43.36  | Case 1:
% 232.25/43.36  | | 
% 232.25/43.36  | |   (7)  all_57_8 = e3 & op(e1, e1) = e3
% 232.25/43.36  | | 
% 232.25/43.36  | | ALPHA: (7) implies:
% 232.25/43.36  | |   (8)  op(e1, e1) = e3
% 232.25/43.36  | | 
% 232.25/43.36  | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #2468.
% 232.25/43.36  | | 
% 232.25/43.36  | Case 2:
% 232.25/43.36  | | 
% 232.25/43.36  | |   (9)  all_57_11 = e3 & op(e1, e0) = e3
% 232.25/43.36  | | 
% 232.25/43.36  | | ALPHA: (9) implies:
% 232.25/43.36  | |   (10)  all_57_11 = e3
% 232.25/43.36  | | 
% 232.25/43.36  | | COMBINE_EQS: (6), (10) imply:
% 232.25/43.36  | |   (11)  e3 = e2
% 232.25/43.36  | | 
% 232.25/43.36  | | REDUCE: (5), (11) imply:
% 232.25/43.36  | |   (12)  $false
% 232.25/43.36  | | 
% 232.25/43.36  | | CLOSE: (12) is inconsistent.
% 232.25/43.36  | | 
% 232.25/43.36  | End of split
% 232.25/43.36  | 
% 232.25/43.36  End of proof
% 232.25/43.36  
% 232.25/43.36  Sub-proof #2345 shows that the following formulas are inconsistent:
% 232.25/43.36  ----------------------------------------------------------------
% 232.25/43.36    (1)  all_57_7 = e3 & op(e1, e2) = e3
% 232.25/43.36    (2)  all_57_7 = e0
% 232.25/43.36    (3)   ~ (e3 = e0)
% 232.25/43.36  
% 232.25/43.36  Begin of proof
% 232.25/43.36  | 
% 232.25/43.36  | ALPHA: (1) implies:
% 232.25/43.36  |   (4)  all_57_7 = e3
% 232.25/43.36  | 
% 232.25/43.36  | COMBINE_EQS: (2), (4) imply:
% 232.25/43.36  |   (5)  e3 = e0
% 232.25/43.36  | 
% 232.25/43.36  | REDUCE: (3), (5) imply:
% 232.25/43.36  |   (6)  $false
% 232.25/43.36  | 
% 232.25/43.36  | CLOSE: (6) is inconsistent.
% 232.25/43.36  | 
% 232.25/43.36  End of proof
% 232.25/43.36  
% 232.25/43.36  Sub-proof #2346 shows that the following formulas are inconsistent:
% 232.25/43.36  ----------------------------------------------------------------
% 232.25/43.36    (1)  all_57_6 = e3 & op(e1, e3) = e3
% 232.25/43.36    (2)  all_57_6 = e1
% 232.25/43.36    (3)   ~ (e3 = e1)
% 232.25/43.36  
% 232.25/43.36  Begin of proof
% 232.25/43.36  | 
% 232.25/43.36  | ALPHA: (1) implies:
% 232.25/43.36  |   (4)  all_57_6 = e3
% 232.25/43.36  | 
% 232.25/43.36  | COMBINE_EQS: (2), (4) imply:
% 232.25/43.36  |   (5)  e3 = e1
% 232.25/43.36  | 
% 232.25/43.36  | REDUCE: (3), (5) imply:
% 232.25/43.36  |   (6)  $false
% 232.25/43.36  | 
% 232.25/43.36  | CLOSE: (6) is inconsistent.
% 232.25/43.36  | 
% 232.25/43.36  End of proof
% 232.25/43.36  
% 232.25/43.36  Sub-proof #2347 shows that the following formulas are inconsistent:
% 232.25/43.36  ----------------------------------------------------------------
% 232.25/43.36    (1)  all_57_6 = e0 & op(e1, e3) = e0
% 232.25/43.36    (2)  all_57_6 = e1
% 232.25/43.36    (3)   ~ (e1 = e0)
% 232.25/43.36  
% 232.25/43.36  Begin of proof
% 232.25/43.36  | 
% 232.25/43.36  | ALPHA: (1) implies:
% 232.25/43.36  |   (4)  all_57_6 = e0
% 232.25/43.36  | 
% 232.25/43.36  | COMBINE_EQS: (2), (4) imply:
% 232.25/43.36  |   (5)  e1 = e0
% 232.25/43.36  | 
% 232.25/43.36  | REDUCE: (3), (5) imply:
% 232.25/43.36  |   (6)  $false
% 232.25/43.36  | 
% 232.25/43.36  | CLOSE: (6) is inconsistent.
% 232.25/43.36  | 
% 232.25/43.36  End of proof
% 232.25/43.36  
% 232.25/43.36  Sub-proof #2348 shows that the following formulas are inconsistent:
% 232.25/43.36  ----------------------------------------------------------------
% 232.25/43.36    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 232.25/43.36         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 232.25/43.36    (2)   ~ (e3 = e1)
% 232.25/43.36    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.36    (4)  op(e2, e2) = e0
% 232.25/43.36    (5)  all_57_3 = e0
% 232.25/43.36    (6)   ~ (e3 = e2)
% 232.25/43.36    (7)   ~ (e3 = e0)
% 232.25/43.36    (8)   ~ (e2 = e0)
% 232.25/43.36    (9)   ~ (e1 = e0)
% 232.25/43.36    (10)  all_57_10 = e3
% 232.25/43.36    (11)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 232.25/43.36          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 232.25/43.36    (12)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 232.25/43.36          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 232.25/43.36    (13)   ~ (e2 = e1)
% 232.25/43.36    (14)  all_57_5 = e0
% 232.25/43.36  
% 232.25/43.36  Begin of proof
% 232.25/43.36  | 
% 232.25/43.36  | BETA: splitting (1) gives:
% 232.25/43.36  | 
% 232.25/43.36  | Case 1:
% 232.25/43.36  | | 
% 232.25/43.36  | |   (15)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) =
% 232.25/43.36  | |           e1)
% 232.25/43.36  | | 
% 232.25/43.36  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13),
% 232.25/43.36  | |            (14), (15) are inconsistent by sub-proof #2351.
% 232.25/43.36  | | 
% 232.25/43.36  | Case 2:
% 232.25/43.36  | | 
% 232.25/43.36  | |   (16)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) =
% 232.25/43.36  | |           e1)
% 232.25/43.36  | | 
% 232.25/43.36  | | BETA: splitting (16) gives:
% 232.25/43.36  | | 
% 232.25/43.36  | | Case 1:
% 232.25/43.36  | | | 
% 232.25/43.36  | | |   (17)  all_57_5 = e1 & op(e2, e1) = e1
% 232.25/43.36  | | | 
% 232.25/43.36  | | | ALPHA: (17) implies:
% 232.25/43.36  | | |   (18)  all_57_5 = e1
% 232.25/43.36  | | | 
% 232.25/43.36  | | | REF_CLOSE: (9), (14), (18) are inconsistent by sub-proof #2350.
% 232.25/43.36  | | | 
% 232.25/43.36  | | Case 2:
% 232.25/43.36  | | | 
% 232.25/43.36  | | |   (19)  all_57_10 = e1 & op(e2, e0) = e1
% 232.25/43.36  | | | 
% 232.25/43.36  | | | REF_CLOSE: (2), (10), (19) are inconsistent by sub-proof #2349.
% 232.25/43.36  | | | 
% 232.25/43.36  | | End of split
% 232.25/43.36  | | 
% 232.25/43.36  | End of split
% 232.25/43.36  | 
% 232.25/43.36  End of proof
% 232.25/43.36  
% 232.25/43.36  Sub-proof #2349 shows that the following formulas are inconsistent:
% 232.25/43.36  ----------------------------------------------------------------
% 232.25/43.36    (1)  all_57_10 = e1 & op(e2, e0) = e1
% 232.25/43.36    (2)  all_57_10 = e3
% 232.25/43.36    (3)   ~ (e3 = e1)
% 232.25/43.36  
% 232.25/43.36  Begin of proof
% 232.25/43.36  | 
% 232.25/43.36  | ALPHA: (1) implies:
% 232.25/43.36  |   (4)  all_57_10 = e1
% 232.25/43.36  | 
% 232.25/43.36  | COMBINE_EQS: (2), (4) imply:
% 232.25/43.36  |   (5)  e3 = e1
% 232.25/43.36  | 
% 232.25/43.36  | REDUCE: (3), (5) imply:
% 232.25/43.36  |   (6)  $false
% 232.25/43.36  | 
% 232.25/43.36  | CLOSE: (6) is inconsistent.
% 232.25/43.36  | 
% 232.25/43.36  End of proof
% 232.25/43.36  
% 232.25/43.36  Sub-proof #2350 shows that the following formulas are inconsistent:
% 232.25/43.36  ----------------------------------------------------------------
% 232.25/43.36    (1)  all_57_5 = e1
% 232.25/43.36    (2)  all_57_5 = e0
% 232.25/43.36    (3)   ~ (e1 = e0)
% 232.25/43.36  
% 232.25/43.36  Begin of proof
% 232.25/43.36  | 
% 232.25/43.36  | COMBINE_EQS: (1), (2) imply:
% 232.25/43.36  |   (4)  e1 = e0
% 232.25/43.36  | 
% 232.25/43.36  | SIMP: (4) implies:
% 232.25/43.36  |   (5)  e1 = e0
% 232.25/43.36  | 
% 232.25/43.36  | REDUCE: (3), (5) imply:
% 232.25/43.36  |   (6)  $false
% 232.25/43.36  | 
% 232.25/43.36  | CLOSE: (6) is inconsistent.
% 232.25/43.36  | 
% 232.25/43.36  End of proof
% 232.25/43.36  
% 232.25/43.36  Sub-proof #2351 shows that the following formulas are inconsistent:
% 232.25/43.36  ----------------------------------------------------------------
% 232.25/43.36    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 232.25/43.36         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 232.25/43.36    (2)   ~ (e3 = e1)
% 232.25/43.36    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.36    (4)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1)
% 232.25/43.36    (5)  op(e2, e2) = e0
% 232.25/43.36    (6)  all_57_3 = e0
% 232.25/43.36    (7)   ~ (e3 = e2)
% 232.25/43.36    (8)   ~ (e3 = e0)
% 232.25/43.36    (9)   ~ (e2 = e0)
% 232.25/43.36    (10)   ~ (e1 = e0)
% 232.25/43.36    (11)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 232.25/43.36          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 232.25/43.36    (12)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 232.25/43.36          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 232.25/43.36    (13)   ~ (e2 = e1)
% 232.25/43.36    (14)  all_57_5 = e0
% 232.25/43.36  
% 232.25/43.36  Begin of proof
% 232.25/43.36  | 
% 232.25/43.36  | BETA: splitting (4) gives:
% 232.25/43.36  | 
% 232.25/43.36  | Case 1:
% 232.25/43.36  | | 
% 232.25/43.36  | |   (15)  all_57_2 = e1 & op(e2, e3) = e1
% 232.25/43.36  | | 
% 232.25/43.36  | | ALPHA: (15) implies:
% 232.25/43.36  | |   (16)  all_57_2 = e1
% 232.25/43.36  | | 
% 232.25/43.36  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 232.25/43.36  | |            (14), (16) are inconsistent by sub-proof #2353.
% 232.25/43.36  | | 
% 232.25/43.36  | Case 2:
% 232.25/43.36  | | 
% 232.25/43.36  | |   (17)  all_57_3 = e1 & op(e2, e2) = e1
% 232.25/43.36  | | 
% 232.25/43.36  | | ALPHA: (17) implies:
% 232.25/43.36  | |   (18)  op(e2, e2) = e1
% 232.25/43.36  | | 
% 232.25/43.36  | | REF_CLOSE: (3), (5), (10), (18) are inconsistent by sub-proof #2352.
% 232.25/43.36  | | 
% 232.25/43.36  | End of split
% 232.25/43.36  | 
% 232.25/43.36  End of proof
% 232.25/43.36  
% 232.25/43.36  Sub-proof #2352 shows that the following formulas are inconsistent:
% 232.25/43.36  ----------------------------------------------------------------
% 232.25/43.36    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.36    (2)  op(e2, e2) = e1
% 232.25/43.36    (3)  op(e2, e2) = e0
% 232.25/43.36    (4)   ~ (e1 = e0)
% 232.25/43.36  
% 232.25/43.36  Begin of proof
% 232.25/43.36  | 
% 232.25/43.36  | GROUND_INST: instantiating (1) with e0, e1, e2, e2, simplifying with (2), (3)
% 232.25/43.36  |              gives:
% 232.25/43.36  |   (5)  e1 = e0
% 232.25/43.36  | 
% 232.25/43.36  | REDUCE: (4), (5) imply:
% 232.25/43.36  |   (6)  $false
% 232.25/43.36  | 
% 232.25/43.36  | CLOSE: (6) is inconsistent.
% 232.25/43.36  | 
% 232.25/43.36  End of proof
% 232.25/43.36  
% 232.25/43.36  Sub-proof #2353 shows that the following formulas are inconsistent:
% 232.25/43.36  ----------------------------------------------------------------
% 232.25/43.36    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 232.25/43.36         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 232.25/43.36    (2)   ~ (e3 = e1)
% 232.25/43.36    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.36    (4)  op(e2, e2) = e0
% 232.25/43.36    (5)  all_57_3 = e0
% 232.25/43.36    (6)   ~ (e3 = e2)
% 232.25/43.36    (7)   ~ (e3 = e0)
% 232.25/43.36    (8)   ~ (e2 = e0)
% 232.25/43.36    (9)   ~ (e1 = e0)
% 232.25/43.36    (10)  all_57_2 = e1
% 232.25/43.36    (11)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 232.25/43.36          (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 232.25/43.36    (12)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 232.25/43.36          (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 232.25/43.36    (13)   ~ (e2 = e1)
% 232.25/43.36    (14)  all_57_5 = e0
% 232.25/43.36  
% 232.25/43.36  Begin of proof
% 232.25/43.36  | 
% 232.25/43.36  | BETA: splitting (12) gives:
% 232.25/43.36  | 
% 232.25/43.36  | Case 1:
% 232.25/43.36  | | 
% 232.25/43.36  | |   (15)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 232.25/43.36  | |           e2)
% 232.25/43.36  | | 
% 232.25/43.36  | | REF_CLOSE: (3), (4), (8), (10), (13), (15) are inconsistent by sub-proof
% 232.25/43.36  | |            #2364.
% 232.25/43.36  | | 
% 232.25/43.36  | Case 2:
% 232.25/43.36  | | 
% 232.25/43.36  | |   (16)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 232.25/43.36  | |           e2)
% 232.25/43.36  | | 
% 232.25/43.36  | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (9), (11), (13), (14), (16) are
% 232.25/43.36  | |            inconsistent by sub-proof #2354.
% 232.25/43.36  | | 
% 232.25/43.36  | End of split
% 232.25/43.36  | 
% 232.25/43.36  End of proof
% 232.25/43.36  
% 232.25/43.36  Sub-proof #2354 shows that the following formulas are inconsistent:
% 232.25/43.36  ----------------------------------------------------------------
% 232.25/43.36    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 232.25/43.36         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 232.25/43.36    (2)   ~ (e3 = e1)
% 232.25/43.36    (3)  all_57_3 = e0
% 232.25/43.36    (4)   ~ (e3 = e2)
% 232.25/43.36    (5)   ~ (e3 = e0)
% 232.25/43.36    (6)   ~ (e2 = e0)
% 232.25/43.36    (7)   ~ (e1 = e0)
% 232.25/43.36    (8)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 232.25/43.36         (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 232.25/43.36    (9)   ~ (e2 = e1)
% 232.25/43.36    (10)  (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 232.25/43.36    (11)  all_57_5 = e0
% 232.25/43.36  
% 232.25/43.36  Begin of proof
% 232.25/43.36  | 
% 232.25/43.36  | BETA: splitting (10) gives:
% 232.25/43.36  | 
% 232.25/43.36  | Case 1:
% 232.25/43.36  | | 
% 232.25/43.36  | |   (12)  all_57_5 = e2 & op(e2, e1) = e2
% 232.25/43.36  | | 
% 232.25/43.36  | | ALPHA: (12) implies:
% 232.25/43.36  | |   (13)  all_57_5 = e2
% 232.25/43.36  | | 
% 232.25/43.36  | | REF_CLOSE: (6), (11), (13) are inconsistent by sub-proof #2363.
% 232.25/43.36  | | 
% 232.25/43.36  | Case 2:
% 232.25/43.36  | | 
% 232.25/43.36  | |   (14)  all_57_10 = e2 & op(e2, e0) = e2
% 232.25/43.36  | | 
% 232.25/43.36  | | ALPHA: (14) implies:
% 232.25/43.36  | |   (15)  all_57_10 = e2
% 232.25/43.36  | | 
% 232.25/43.36  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (11), (15) are
% 232.25/43.36  | |            inconsistent by sub-proof #2355.
% 232.25/43.36  | | 
% 232.25/43.36  | End of split
% 232.25/43.36  | 
% 232.25/43.36  End of proof
% 232.25/43.36  
% 232.25/43.36  Sub-proof #2355 shows that the following formulas are inconsistent:
% 232.25/43.36  ----------------------------------------------------------------
% 232.25/43.36    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 232.25/43.36         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 232.25/43.36    (2)   ~ (e3 = e1)
% 232.25/43.36    (3)  all_57_3 = e0
% 232.25/43.36    (4)   ~ (e3 = e2)
% 232.25/43.36    (5)   ~ (e3 = e0)
% 232.25/43.36    (6)  all_57_10 = e2
% 232.25/43.36    (7)   ~ (e1 = e0)
% 232.25/43.36    (8)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 232.25/43.36         (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 232.25/43.36    (9)   ~ (e2 = e1)
% 232.25/43.37    (10)  all_57_5 = e0
% 232.25/43.37  
% 232.25/43.37  Begin of proof
% 232.25/43.37  | 
% 232.25/43.37  | BETA: splitting (8) gives:
% 232.25/43.37  | 
% 232.25/43.37  | Case 1:
% 232.25/43.37  | | 
% 232.25/43.37  | |   (11)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 232.25/43.37  | |           e3)
% 232.25/43.37  | | 
% 232.25/43.37  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (9), (10), (11) are inconsistent by
% 232.25/43.37  | |            sub-proof #2357.
% 232.25/43.37  | | 
% 232.25/43.37  | Case 2:
% 232.25/43.37  | | 
% 232.25/43.37  | |   (12)  (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 232.25/43.37  | |           e3)
% 232.25/43.37  | | 
% 232.25/43.37  | | BETA: splitting (12) gives:
% 232.25/43.37  | | 
% 232.25/43.37  | | Case 1:
% 232.25/43.37  | | | 
% 232.25/43.37  | | |   (13)  all_57_5 = e3 & op(e2, e1) = e3
% 232.25/43.37  | | | 
% 232.25/43.37  | | | ALPHA: (13) implies:
% 232.25/43.37  | | |   (14)  all_57_5 = e3
% 232.25/43.37  | | | 
% 232.25/43.37  | | | REF_CLOSE: (5), (10), (14) are inconsistent by sub-proof #2471.
% 232.25/43.37  | | | 
% 232.25/43.37  | | Case 2:
% 232.25/43.37  | | | 
% 232.25/43.37  | | |   (15)  all_57_10 = e3 & op(e2, e0) = e3
% 232.25/43.37  | | | 
% 232.25/43.37  | | | ALPHA: (15) implies:
% 232.25/43.37  | | |   (16)  all_57_10 = e3
% 232.25/43.37  | | | 
% 232.25/43.37  | | | REF_CLOSE: (4), (6), (16) are inconsistent by sub-proof #2356.
% 232.25/43.37  | | | 
% 232.25/43.37  | | End of split
% 232.25/43.37  | | 
% 232.25/43.37  | End of split
% 232.25/43.37  | 
% 232.25/43.37  End of proof
% 232.25/43.37  
% 232.25/43.37  Sub-proof #2356 shows that the following formulas are inconsistent:
% 232.25/43.37  ----------------------------------------------------------------
% 232.25/43.37    (1)  all_57_10 = e3
% 232.25/43.37    (2)  all_57_10 = e2
% 232.25/43.37    (3)   ~ (e3 = e2)
% 232.25/43.37  
% 232.25/43.37  Begin of proof
% 232.25/43.37  | 
% 232.25/43.37  | COMBINE_EQS: (1), (2) imply:
% 232.25/43.37  |   (4)  e3 = e2
% 232.25/43.37  | 
% 232.25/43.37  | SIMP: (4) implies:
% 232.25/43.37  |   (5)  e3 = e2
% 232.25/43.37  | 
% 232.25/43.37  | REDUCE: (3), (5) imply:
% 232.25/43.37  |   (6)  $false
% 232.25/43.37  | 
% 232.25/43.37  | CLOSE: (6) is inconsistent.
% 232.25/43.37  | 
% 232.25/43.37  End of proof
% 232.25/43.37  
% 232.25/43.37  Sub-proof #2357 shows that the following formulas are inconsistent:
% 232.25/43.37  ----------------------------------------------------------------
% 232.25/43.37    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 232.25/43.37         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 232.25/43.37    (2)   ~ (e3 = e1)
% 232.25/43.37    (3)  all_57_3 = e0
% 232.25/43.37    (4)   ~ (e3 = e0)
% 232.25/43.37    (5)  all_57_10 = e2
% 232.25/43.37    (6)   ~ (e1 = e0)
% 232.25/43.37    (7)   ~ (e2 = e1)
% 232.25/43.37    (8)  (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3)
% 232.25/43.37    (9)  all_57_5 = e0
% 232.25/43.37  
% 232.25/43.37  Begin of proof
% 232.25/43.37  | 
% 232.25/43.37  | BETA: splitting (8) gives:
% 232.25/43.37  | 
% 232.25/43.37  | Case 1:
% 232.25/43.37  | | 
% 232.25/43.37  | |   (10)  all_57_2 = e3 & op(e2, e3) = e3
% 232.25/43.37  | | 
% 232.25/43.37  | | ALPHA: (10) implies:
% 232.25/43.37  | |   (11)  all_57_2 = e3
% 232.25/43.37  | | 
% 232.25/43.37  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (9), (11) are inconsistent by
% 232.25/43.37  | |            sub-proof #2359.
% 232.25/43.37  | | 
% 232.25/43.37  | Case 2:
% 232.25/43.37  | | 
% 232.25/43.37  | |   (12)  all_57_3 = e3 & op(e2, e2) = e3
% 232.25/43.37  | | 
% 232.25/43.37  | | ALPHA: (12) implies:
% 232.25/43.37  | |   (13)  all_57_3 = e3
% 232.25/43.37  | | 
% 232.25/43.37  | | REF_CLOSE: (3), (4), (13) are inconsistent by sub-proof #2358.
% 232.25/43.37  | | 
% 232.25/43.37  | End of split
% 232.25/43.37  | 
% 232.25/43.37  End of proof
% 232.25/43.37  
% 232.25/43.37  Sub-proof #2358 shows that the following formulas are inconsistent:
% 232.25/43.37  ----------------------------------------------------------------
% 232.25/43.37    (1)  all_57_3 = e3
% 232.25/43.37    (2)  all_57_3 = e0
% 232.25/43.37    (3)   ~ (e3 = e0)
% 232.25/43.37  
% 232.25/43.37  Begin of proof
% 232.25/43.37  | 
% 232.25/43.37  | COMBINE_EQS: (1), (2) imply:
% 232.25/43.37  |   (4)  e3 = e0
% 232.25/43.37  | 
% 232.25/43.37  | SIMP: (4) implies:
% 232.25/43.37  |   (5)  e3 = e0
% 232.25/43.37  | 
% 232.25/43.37  | REDUCE: (3), (5) imply:
% 232.25/43.37  |   (6)  $false
% 232.25/43.37  | 
% 232.25/43.37  | CLOSE: (6) is inconsistent.
% 232.25/43.37  | 
% 232.25/43.37  End of proof
% 232.25/43.37  
% 232.25/43.37  Sub-proof #2359 shows that the following formulas are inconsistent:
% 232.25/43.37  ----------------------------------------------------------------
% 232.25/43.37    (1)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 232.25/43.37         (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 232.25/43.37    (2)   ~ (e3 = e1)
% 232.25/43.37    (3)  all_57_3 = e0
% 232.25/43.37    (4)  all_57_10 = e2
% 232.25/43.37    (5)  all_57_2 = e3
% 232.25/43.37    (6)   ~ (e1 = e0)
% 232.25/43.37    (7)   ~ (e2 = e1)
% 232.25/43.37    (8)  all_57_5 = e0
% 232.25/43.37  
% 232.25/43.37  Begin of proof
% 232.25/43.37  | 
% 232.25/43.37  | BETA: splitting (1) gives:
% 232.25/43.37  | 
% 232.25/43.37  | Case 1:
% 232.25/43.37  | | 
% 232.25/43.37  | |   (9)  (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1)
% 232.25/43.37  | | 
% 232.25/43.37  | | BETA: splitting (9) gives:
% 232.25/43.37  | | 
% 232.25/43.37  | | Case 1:
% 232.25/43.37  | | | 
% 232.25/43.37  | | |   (10)  all_57_2 = e1 & op(e2, e3) = e1
% 232.25/43.37  | | | 
% 232.25/43.37  | | | ALPHA: (10) implies:
% 232.25/43.37  | | |   (11)  all_57_2 = e1
% 232.25/43.37  | | | 
% 232.25/43.37  | | | REF_CLOSE: (2), (5), (11) are inconsistent by sub-proof #2397.
% 232.25/43.37  | | | 
% 232.25/43.37  | | Case 2:
% 232.25/43.37  | | | 
% 232.25/43.37  | | |   (12)  all_57_3 = e1 & op(e2, e2) = e1
% 232.25/43.37  | | | 
% 232.25/43.37  | | | REF_CLOSE: (3), (6), (12) are inconsistent by sub-proof #2362.
% 232.25/43.37  | | | 
% 232.25/43.37  | | End of split
% 232.25/43.37  | | 
% 232.25/43.37  | Case 2:
% 232.25/43.37  | | 
% 232.25/43.37  | |   (13)  (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) =
% 232.25/43.37  | |           e1)
% 232.25/43.37  | | 
% 232.25/43.37  | | BETA: splitting (13) gives:
% 232.25/43.37  | | 
% 232.25/43.37  | | Case 1:
% 232.25/43.37  | | | 
% 232.25/43.37  | | |   (14)  all_57_5 = e1 & op(e2, e1) = e1
% 232.25/43.37  | | | 
% 232.25/43.37  | | | REF_CLOSE: (6), (8), (14) are inconsistent by sub-proof #2361.
% 232.25/43.37  | | | 
% 232.25/43.37  | | Case 2:
% 232.25/43.37  | | | 
% 232.25/43.37  | | |   (15)  all_57_10 = e1 & op(e2, e0) = e1
% 232.25/43.37  | | | 
% 232.25/43.37  | | | REF_CLOSE: (4), (7), (15) are inconsistent by sub-proof #2360.
% 232.25/43.37  | | | 
% 232.25/43.37  | | End of split
% 232.25/43.37  | | 
% 232.25/43.37  | End of split
% 232.25/43.37  | 
% 232.25/43.37  End of proof
% 232.25/43.37  
% 232.25/43.37  Sub-proof #2360 shows that the following formulas are inconsistent:
% 232.25/43.37  ----------------------------------------------------------------
% 232.25/43.37    (1)  all_57_10 = e1 & op(e2, e0) = e1
% 232.25/43.37    (2)  all_57_10 = e2
% 232.25/43.37    (3)   ~ (e2 = e1)
% 232.25/43.37  
% 232.25/43.37  Begin of proof
% 232.25/43.37  | 
% 232.25/43.37  | ALPHA: (1) implies:
% 232.25/43.37  |   (4)  all_57_10 = e1
% 232.25/43.37  | 
% 232.25/43.37  | COMBINE_EQS: (2), (4) imply:
% 232.25/43.37  |   (5)  e2 = e1
% 232.25/43.37  | 
% 232.25/43.37  | REDUCE: (3), (5) imply:
% 232.25/43.37  |   (6)  $false
% 232.25/43.37  | 
% 232.25/43.37  | CLOSE: (6) is inconsistent.
% 232.25/43.37  | 
% 232.25/43.37  End of proof
% 232.25/43.37  
% 232.25/43.37  Sub-proof #2361 shows that the following formulas are inconsistent:
% 232.25/43.37  ----------------------------------------------------------------
% 232.25/43.37    (1)  all_57_5 = e1 & op(e2, e1) = e1
% 232.25/43.37    (2)  all_57_5 = e0
% 232.25/43.37    (3)   ~ (e1 = e0)
% 232.25/43.37  
% 232.25/43.37  Begin of proof
% 232.25/43.37  | 
% 232.25/43.37  | ALPHA: (1) implies:
% 232.25/43.37  |   (4)  all_57_5 = e1
% 232.25/43.37  | 
% 232.25/43.37  | COMBINE_EQS: (2), (4) imply:
% 232.25/43.37  |   (5)  e1 = e0
% 232.25/43.37  | 
% 232.25/43.37  | REDUCE: (3), (5) imply:
% 232.25/43.37  |   (6)  $false
% 232.25/43.37  | 
% 232.25/43.37  | CLOSE: (6) is inconsistent.
% 232.25/43.37  | 
% 232.25/43.37  End of proof
% 232.25/43.37  
% 232.25/43.37  Sub-proof #2362 shows that the following formulas are inconsistent:
% 232.25/43.37  ----------------------------------------------------------------
% 232.25/43.37    (1)  all_57_3 = e1 & op(e2, e2) = e1
% 232.25/43.37    (2)  all_57_3 = e0
% 232.25/43.37    (3)   ~ (e1 = e0)
% 232.25/43.37  
% 232.25/43.37  Begin of proof
% 232.25/43.37  | 
% 232.25/43.37  | ALPHA: (1) implies:
% 232.25/43.37  |   (4)  all_57_3 = e1
% 232.25/43.37  | 
% 232.25/43.37  | COMBINE_EQS: (2), (4) imply:
% 232.25/43.37  |   (5)  e1 = e0
% 232.25/43.37  | 
% 232.25/43.37  | SIMP: (5) implies:
% 232.25/43.37  |   (6)  e1 = e0
% 232.25/43.37  | 
% 232.25/43.37  | REDUCE: (3), (6) imply:
% 232.25/43.37  |   (7)  $false
% 232.25/43.37  | 
% 232.25/43.37  | CLOSE: (7) is inconsistent.
% 232.25/43.37  | 
% 232.25/43.37  End of proof
% 232.25/43.37  
% 232.25/43.37  Sub-proof #2363 shows that the following formulas are inconsistent:
% 232.25/43.37  ----------------------------------------------------------------
% 232.25/43.37    (1)  all_57_5 = e2
% 232.25/43.37    (2)  all_57_5 = e0
% 232.25/43.37    (3)   ~ (e2 = e0)
% 232.25/43.37  
% 232.25/43.37  Begin of proof
% 232.25/43.37  | 
% 232.25/43.37  | COMBINE_EQS: (1), (2) imply:
% 232.25/43.37  |   (4)  e2 = e0
% 232.25/43.37  | 
% 232.25/43.37  | SIMP: (4) implies:
% 232.25/43.37  |   (5)  e2 = e0
% 232.25/43.37  | 
% 232.25/43.37  | REDUCE: (3), (5) imply:
% 232.25/43.37  |   (6)  $false
% 232.25/43.37  | 
% 232.25/43.37  | CLOSE: (6) is inconsistent.
% 232.25/43.37  | 
% 232.25/43.37  End of proof
% 232.25/43.37  
% 232.25/43.37  Sub-proof #2364 shows that the following formulas are inconsistent:
% 232.25/43.37  ----------------------------------------------------------------
% 232.25/43.37    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.37           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.37    (2)  (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2)
% 232.25/43.37    (3)  op(e2, e2) = e0
% 232.25/43.37    (4)   ~ (e2 = e0)
% 232.25/43.37    (5)  all_57_2 = e1
% 232.25/43.37    (6)   ~ (e2 = e1)
% 232.25/43.37  
% 232.25/43.37  Begin of proof
% 232.25/43.37  | 
% 232.25/43.37  | BETA: splitting (2) gives:
% 232.25/43.37  | 
% 232.25/43.37  | Case 1:
% 232.25/43.37  | | 
% 232.25/43.37  | |   (7)  all_57_2 = e2 & op(e2, e3) = e2
% 232.25/43.37  | | 
% 232.25/43.37  | | ALPHA: (7) implies:
% 232.25/43.37  | |   (8)  all_57_2 = e2
% 232.25/43.37  | | 
% 232.25/43.37  | | REF_CLOSE: (5), (6), (8) are inconsistent by sub-proof #2464.
% 232.25/43.37  | | 
% 232.25/43.37  | Case 2:
% 232.25/43.37  | | 
% 232.25/43.37  | |   (9)  all_57_3 = e2 & op(e2, e2) = e2
% 232.25/43.37  | | 
% 232.25/43.37  | | ALPHA: (9) implies:
% 232.25/43.37  | |   (10)  op(e2, e2) = e2
% 232.25/43.37  | | 
% 232.25/43.37  | | REF_CLOSE: (1), (3), (4), (10) are inconsistent by sub-proof #2472.
% 232.25/43.37  | | 
% 232.25/43.37  | End of split
% 232.25/43.37  | 
% 232.25/43.37  End of proof
% 232.25/43.37  
% 232.25/43.37  Sub-proof #2365 shows that the following formulas are inconsistent:
% 232.25/43.37  ----------------------------------------------------------------
% 232.25/43.37    (1)   ~ (all_53_2 = e1)
% 232.25/43.37    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.37           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.37    (3)  op(e0, e3) = e0
% 232.25/43.37    (4)  op(e0, e3) = all_53_3
% 232.25/43.37    (5)  all_55_8 = e1 | all_55_8 = e0
% 232.25/43.37    (6)   ~ (all_53_2 = all_53_3)
% 232.25/43.37    (7)  all_55_8 = all_53_2
% 232.25/43.37  
% 232.25/43.37  Begin of proof
% 232.25/43.37  | 
% 232.25/43.37  | BETA: splitting (5) gives:
% 232.25/43.37  | 
% 232.25/43.37  | Case 1:
% 232.25/43.37  | | 
% 232.25/43.37  | |   (8)  all_55_8 = e1
% 232.25/43.37  | | 
% 232.25/43.37  | | REF_CLOSE: (1), (7), (8) are inconsistent by sub-proof #2367.
% 232.25/43.37  | | 
% 232.25/43.37  | Case 2:
% 232.25/43.37  | | 
% 232.25/43.37  | |   (9)  all_55_8 = e0
% 232.25/43.37  | | 
% 232.25/43.37  | | COMBINE_EQS: (7), (9) imply:
% 232.25/43.37  | |   (10)  all_53_2 = e0
% 232.25/43.37  | | 
% 232.25/43.37  | | SIMP: (10) implies:
% 232.25/43.37  | |   (11)  all_53_2 = e0
% 232.25/43.37  | | 
% 232.25/43.37  | | REDUCE: (6), (11) imply:
% 232.25/43.37  | |   (12)   ~ (all_53_3 = e0)
% 232.25/43.37  | | 
% 232.25/43.37  | | SIMP: (12) implies:
% 232.25/43.37  | |   (13)   ~ (all_53_3 = e0)
% 232.25/43.37  | | 
% 232.25/43.37  | | REF_CLOSE: (2), (3), (4), (13) are inconsistent by sub-proof #2366.
% 232.25/43.37  | | 
% 232.25/43.37  | End of split
% 232.25/43.37  | 
% 232.25/43.37  End of proof
% 232.25/43.37  
% 232.25/43.37  Sub-proof #2366 shows that the following formulas are inconsistent:
% 232.25/43.37  ----------------------------------------------------------------
% 232.25/43.37    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.37           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.37    (2)  op(e0, e3) = all_53_3
% 232.25/43.37    (3)  op(e0, e3) = e0
% 232.25/43.37    (4)   ~ (all_53_3 = e0)
% 232.25/43.37  
% 232.25/43.37  Begin of proof
% 232.25/43.37  | 
% 232.25/43.37  | GROUND_INST: instantiating (1) with all_53_3, e0, e3, e0, simplifying with
% 232.25/43.37  |              (2), (3) gives:
% 232.25/43.37  |   (5)  all_53_3 = e0
% 232.25/43.37  | 
% 232.25/43.37  | REDUCE: (4), (5) imply:
% 232.25/43.37  |   (6)  $false
% 232.25/43.37  | 
% 232.25/43.37  | CLOSE: (6) is inconsistent.
% 232.25/43.37  | 
% 232.25/43.37  End of proof
% 232.25/43.37  
% 232.25/43.37  Sub-proof #2367 shows that the following formulas are inconsistent:
% 232.25/43.37  ----------------------------------------------------------------
% 232.25/43.37    (1)  all_55_8 = all_53_2
% 232.25/43.37    (2)  all_55_8 = e1
% 232.25/43.37    (3)   ~ (all_53_2 = e1)
% 232.25/43.37  
% 232.25/43.37  Begin of proof
% 232.25/43.37  | 
% 232.25/43.37  | COMBINE_EQS: (1), (2) imply:
% 232.25/43.37  |   (4)  all_53_2 = e1
% 232.25/43.37  | 
% 232.25/43.37  | SIMP: (4) implies:
% 232.25/43.37  |   (5)  all_53_2 = e1
% 232.25/43.37  | 
% 232.25/43.37  | REDUCE: (3), (5) imply:
% 232.25/43.37  |   (6)  $false
% 232.25/43.37  | 
% 232.25/43.37  | CLOSE: (6) is inconsistent.
% 232.25/43.37  | 
% 232.25/43.37  End of proof
% 232.25/43.37  
% 232.25/43.37  Sub-proof #2368 shows that the following formulas are inconsistent:
% 232.25/43.37  ----------------------------------------------------------------
% 232.25/43.37    (1)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 232.25/43.37         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 232.25/43.37    (2)   ~ (e3 = e1)
% 232.25/43.37    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.37           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.37    (4)   ~ (all_6_2 = e3)
% 232.25/43.37    (5)  op(e1, e1) = all_6_2
% 232.25/43.37    (6)  all_57_4 = e2
% 232.25/43.37    (7)  all_57_14 = e3
% 232.25/43.37    (8)  all_57_12 = e2
% 232.25/43.37    (9)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 232.25/43.37         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 232.25/43.37    (10)   ~ (e3 = e2)
% 232.25/43.37    (11)   ~ (e3 = e0)
% 232.25/43.37    (12)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 232.25/43.37          (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 232.25/43.37    (13)  op(e3, e3) = e3
% 232.25/43.37    (14)  op(e1, e0) = all_52_23
% 232.25/43.37    (15)  op(e1, e1) = e1
% 232.25/43.37    (16)   ~ (e2 = e0)
% 232.25/43.37    (17)  op(e2, e2) = e2
% 232.25/43.37    (18)   ~ (e1 = e0)
% 232.25/43.37    (19)  op(all_52_23, all_52_23) = e0
% 232.25/43.37    (20)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 232.25/43.37          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 232.25/43.37    (21)  all_57_7 = e3
% 232.25/43.37    (22)   ~ (e2 = e1)
% 232.25/43.37    (23)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 232.25/43.37          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 232.25/43.37    (24)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 232.25/43.37          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 232.25/43.37    (25)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 232.25/43.37          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 232.25/43.37  
% 232.25/43.37  Begin of proof
% 232.25/43.37  | 
% 232.25/43.37  | BETA: splitting (25) gives:
% 232.25/43.37  | 
% 232.25/43.37  | Case 1:
% 232.25/43.37  | | 
% 232.25/43.37  | |   (26)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) =
% 232.25/43.37  | |           e2)
% 232.25/43.37  | | 
% 232.25/43.37  | | BETA: splitting (26) gives:
% 232.25/43.37  | | 
% 232.25/43.37  | | Case 1:
% 232.25/43.37  | | | 
% 232.25/43.37  | | |   (27)  all_57_6 = e2 & op(e1, e3) = e2
% 232.25/43.37  | | | 
% 232.25/43.37  | | | ALPHA: (27) implies:
% 232.25/43.37  | | |   (28)  all_57_6 = e2
% 232.25/43.37  | | | 
% 232.25/43.37  | | | REF_CLOSE: (1), (2), (3), (8), (11), (13), (16), (18), (22), (24), (28)
% 232.25/43.37  | | |            are inconsistent by sub-proof #2384.
% 232.25/43.37  | | | 
% 232.25/43.37  | | Case 2:
% 232.25/43.37  | | | 
% 232.25/43.37  | | |   (29)  all_57_7 = e2 & op(e1, e2) = e2
% 232.25/43.37  | | | 
% 232.25/43.37  | | | ALPHA: (29) implies:
% 232.25/43.37  | | |   (30)  all_57_7 = e2
% 232.25/43.37  | | | 
% 232.25/43.37  | | | COMBINE_EQS: (21), (30) imply:
% 232.25/43.37  | | |   (31)  e3 = e2
% 232.25/43.37  | | | 
% 232.25/43.37  | | | COMBINE_EQS: (7), (31) imply:
% 232.25/43.37  | | |   (32)  all_57_14 = e2
% 232.25/43.37  | | | 
% 232.25/43.37  | | | REF_CLOSE: (2), (3), (4), (5), (6), (9), (10), (11), (12), (16), (18),
% 232.25/43.37  | | |            (20), (22), (23), (32) are inconsistent by sub-proof #2370.
% 232.25/43.37  | | | 
% 232.25/43.37  | | End of split
% 232.25/43.37  | | 
% 232.25/43.37  | Case 2:
% 232.25/43.37  | | 
% 232.25/43.37  | |   (33)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) =
% 232.25/43.37  | |           e2)
% 232.25/43.37  | | 
% 232.25/43.37  | | BETA: splitting (33) gives:
% 232.25/43.37  | | 
% 232.25/43.37  | | Case 1:
% 232.25/43.37  | | | 
% 232.25/43.37  | | |   (34)  all_57_8 = e2 & op(e1, e1) = e2
% 232.25/43.37  | | | 
% 232.25/43.37  | | | ALPHA: (34) implies:
% 232.25/43.37  | | |   (35)  op(e1, e1) = e2
% 232.25/43.37  | | | 
% 232.25/43.37  | | | REF_CLOSE: (3), (15), (22), (35) are inconsistent by sub-proof #2423.
% 232.25/43.37  | | | 
% 232.25/43.37  | | Case 2:
% 232.25/43.37  | | | 
% 232.25/43.37  | | |   (36)  all_57_11 = e2 & op(e1, e0) = e2
% 232.25/43.37  | | | 
% 232.25/43.37  | | | ALPHA: (36) implies:
% 232.25/43.37  | | |   (37)  op(e1, e0) = e2
% 232.25/43.37  | | | 
% 232.25/43.37  | | | REF_CLOSE: (3), (14), (16), (17), (19), (37) are inconsistent by sub-proof
% 232.25/43.37  | | |            #2369.
% 232.25/43.37  | | | 
% 232.25/43.37  | | End of split
% 232.25/43.37  | | 
% 232.25/43.37  | End of split
% 232.25/43.37  | 
% 232.25/43.37  End of proof
% 232.25/43.37  
% 232.25/43.37  Sub-proof #2369 shows that the following formulas are inconsistent:
% 232.25/43.37  ----------------------------------------------------------------
% 232.25/43.37    (1)  op(e1, e0) = e2
% 232.25/43.37    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.37           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.37    (3)  op(e1, e0) = all_52_23
% 232.25/43.37    (4)   ~ (e2 = e0)
% 232.25/43.37    (5)  op(e2, e2) = e2
% 232.25/43.37    (6)  op(all_52_23, all_52_23) = e0
% 232.25/43.37  
% 232.25/43.37  Begin of proof
% 232.25/43.37  | 
% 232.25/43.37  | GROUND_INST: instantiating (2) with e2, all_52_23, e0, e1, simplifying with
% 232.25/43.37  |              (1), (3) gives:
% 232.25/43.37  |   (7)  all_52_23 = e2
% 232.25/43.37  | 
% 232.25/43.37  | REDUCE: (6), (7) imply:
% 232.25/43.37  |   (8)  op(e2, e2) = e0
% 232.25/43.37  | 
% 232.25/43.37  | GROUND_INST: instantiating (2) with e2, e0, e2, e2, simplifying with (5), (8)
% 232.25/43.37  |              gives:
% 232.25/43.37  |   (9)  e2 = e0
% 232.25/43.37  | 
% 232.25/43.37  | REDUCE: (4), (9) imply:
% 232.25/43.37  |   (10)  $false
% 232.25/43.37  | 
% 232.25/43.37  | CLOSE: (10) is inconsistent.
% 232.25/43.37  | 
% 232.25/43.37  End of proof
% 232.25/43.37  
% 232.25/43.37  Sub-proof #2370 shows that the following formulas are inconsistent:
% 232.25/43.37  ----------------------------------------------------------------
% 232.25/43.37    (1)   ~ (e3 = e1)
% 232.25/43.37    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.37           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.37    (3)   ~ (all_6_2 = e3)
% 232.25/43.37    (4)  op(e1, e1) = all_6_2
% 232.25/43.37    (5)  all_57_4 = e2
% 232.25/43.37    (6)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 232.25/43.37         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 232.25/43.37    (7)   ~ (e3 = e2)
% 232.25/43.37    (8)   ~ (e3 = e0)
% 232.25/43.37    (9)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 232.25/43.37         (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 232.25/43.37    (10)   ~ (e2 = e0)
% 232.25/43.37    (11)   ~ (e1 = e0)
% 232.25/43.37    (12)  all_57_14 = e2
% 232.25/43.37    (13)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 232.25/43.37          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 232.25/43.37    (14)   ~ (e2 = e1)
% 232.25/43.37    (15)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 232.25/43.37          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 232.25/43.37  
% 232.25/43.37  Begin of proof
% 232.25/43.37  | 
% 232.25/43.37  | BETA: splitting (13) gives:
% 232.25/43.37  | 
% 232.25/43.37  | Case 1:
% 232.25/43.37  | | 
% 232.25/43.37  | |   (16)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) =
% 232.25/43.37  | |           e3)
% 232.25/43.37  | | 
% 232.25/43.37  | | BETA: splitting (16) gives:
% 232.25/43.37  | | 
% 232.25/43.37  | | Case 1:
% 232.25/43.37  | | | 
% 232.25/43.37  | | |   (17)  all_57_4 = e3 & op(e3, e1) = e3
% 232.25/43.37  | | | 
% 232.25/43.37  | | | ALPHA: (17) implies:
% 232.25/43.37  | | |   (18)  all_57_4 = e3
% 232.25/43.37  | | | 
% 232.25/43.37  | | | REF_CLOSE: (5), (7), (18) are inconsistent by sub-proof #2482.
% 232.25/43.37  | | | 
% 232.25/43.37  | | Case 2:
% 232.25/43.37  | | | 
% 232.25/43.37  | | |   (19)  all_57_5 = e3 & op(e2, e1) = e3
% 232.25/43.37  | | | 
% 232.25/43.37  | | | ALPHA: (19) implies:
% 232.25/43.37  | | |   (20)  all_57_5 = e3
% 232.25/43.37  | | | 
% 232.25/43.37  | | | BETA: splitting (6) gives:
% 232.25/43.37  | | | 
% 232.25/43.37  | | | Case 1:
% 232.25/43.37  | | | | 
% 232.25/43.37  | | | |   (21)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1)
% 232.25/43.37  | | | |           = e0)
% 232.25/43.37  | | | | 
% 232.25/43.37  | | | | BETA: splitting (21) gives:
% 232.25/43.37  | | | | 
% 232.25/43.37  | | | | Case 1:
% 232.25/43.37  | | | | | 
% 232.25/43.37  | | | | |   (22)  all_57_4 = e0 & op(e3, e1) = e0
% 232.25/43.37  | | | | | 
% 232.25/43.37  | | | | | ALPHA: (22) implies:
% 232.25/43.37  | | | | |   (23)  all_57_4 = e0
% 232.25/43.37  | | | | | 
% 232.25/43.37  | | | | | COMBINE_EQS: (5), (23) imply:
% 232.25/43.37  | | | | |   (24)  e2 = e0
% 232.25/43.37  | | | | | 
% 232.25/43.37  | | | | | REF_CLOSE: (1), (2), (5), (7), (9), (10), (11), (12), (14), (15),
% 232.25/43.37  | | | | |            (20), (24) are inconsistent by sub-proof #2377.
% 232.25/43.37  | | | | | 
% 232.25/43.37  | | | | Case 2:
% 232.25/43.37  | | | | | 
% 232.25/43.37  | | | | |   (25)  all_57_5 = e0 & op(e2, e1) = e0
% 232.25/43.37  | | | | | 
% 232.25/43.37  | | | | | REF_CLOSE: (8), (20), (25) are inconsistent by sub-proof #2414.
% 232.25/43.37  | | | | | 
% 232.25/43.37  | | | | End of split
% 232.25/43.37  | | | | 
% 232.25/43.37  | | | Case 2:
% 232.25/43.37  | | | | 
% 232.25/43.37  | | | |   (26)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1)
% 232.25/43.37  | | | |           = e0)
% 232.25/43.37  | | | | 
% 232.25/43.37  | | | | BETA: splitting (26) gives:
% 232.25/43.37  | | | | 
% 232.25/43.37  | | | | Case 1:
% 232.25/43.37  | | | | | 
% 232.25/43.38  | | | | |   (27)  all_57_8 = e0 & op(e1, e1) = e0
% 232.25/43.38  | | | | | 
% 232.25/43.38  | | | | | REF_CLOSE: (1), (2), (5), (9), (11), (12), (14), (20), (27) are
% 232.25/43.38  | | | | |            inconsistent by sub-proof #2373.
% 232.25/43.38  | | | | | 
% 232.25/43.38  | | | | Case 2:
% 232.25/43.38  | | | | | 
% 232.25/43.38  | | | | |   (28)  all_57_14 = e0 & op(e0, e1) = e0
% 232.25/43.38  | | | | | 
% 232.25/43.38  | | | | | ALPHA: (28) implies:
% 232.25/43.38  | | | | |   (29)  all_57_14 = e0
% 232.25/43.38  | | | | | 
% 232.25/43.38  | | | | | COMBINE_EQS: (12), (29) imply:
% 232.25/43.38  | | | | |   (30)  e2 = e0
% 232.25/43.38  | | | | | 
% 232.25/43.38  | | | | | COMBINE_EQS: (5), (30) imply:
% 232.25/43.38  | | | | |   (31)  all_57_4 = e0
% 232.25/43.38  | | | | | 
% 232.25/43.38  | | | | | REF_CLOSE: (1), (2), (3), (4), (7), (8), (9), (10), (11), (13), (14),
% 232.25/43.38  | | | | |            (15), (29), (31) are inconsistent by sub-proof #2371.
% 232.25/43.38  | | | | | 
% 232.25/43.38  | | | | End of split
% 232.25/43.38  | | | | 
% 232.25/43.38  | | | End of split
% 232.25/43.38  | | | 
% 232.25/43.38  | | End of split
% 232.25/43.38  | | 
% 232.25/43.38  | Case 2:
% 232.25/43.38  | | 
% 232.25/43.38  | |   (32)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) =
% 232.25/43.38  | |           e3)
% 232.25/43.38  | | 
% 232.25/43.38  | | REF_CLOSE: (2), (3), (4), (7), (12), (32) are inconsistent by sub-proof
% 232.25/43.38  | |            #2409.
% 232.25/43.38  | | 
% 232.25/43.38  | End of split
% 232.25/43.38  | 
% 232.25/43.38  End of proof
% 232.25/43.38  
% 232.25/43.38  Sub-proof #2371 shows that the following formulas are inconsistent:
% 232.25/43.38  ----------------------------------------------------------------
% 232.25/43.38    (1)   ~ (e3 = e1)
% 232.25/43.38    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.38           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.38    (3)   ~ (all_6_2 = e3)
% 232.25/43.38    (4)  op(e1, e1) = all_6_2
% 232.25/43.38    (5)  all_57_4 = e0
% 232.25/43.38    (6)   ~ (e3 = e2)
% 232.25/43.38    (7)   ~ (e3 = e0)
% 232.25/43.38    (8)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 232.25/43.38         (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 232.25/43.38    (9)   ~ (e2 = e0)
% 232.25/43.38    (10)   ~ (e1 = e0)
% 232.25/43.38    (11)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 232.25/43.38          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 232.25/43.38    (12)   ~ (e2 = e1)
% 232.25/43.38    (13)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 232.25/43.38          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 232.25/43.38    (14)  all_57_14 = e0
% 232.25/43.38  
% 232.25/43.38  Begin of proof
% 232.25/43.38  | 
% 232.25/43.38  | BETA: splitting (11) gives:
% 232.25/43.38  | 
% 232.25/43.38  | Case 1:
% 232.25/43.38  | | 
% 232.25/43.38  | |   (15)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) =
% 232.25/43.38  | |           e3)
% 232.25/43.38  | | 
% 232.25/43.38  | | BETA: splitting (15) gives:
% 232.25/43.38  | | 
% 232.25/43.38  | | Case 1:
% 232.25/43.38  | | | 
% 232.25/43.38  | | |   (16)  all_57_4 = e3 & op(e3, e1) = e3
% 232.25/43.38  | | | 
% 232.25/43.38  | | | ALPHA: (16) implies:
% 232.25/43.38  | | |   (17)  all_57_4 = e3
% 232.25/43.38  | | | 
% 232.25/43.38  | | | REF_CLOSE: (5), (7), (17) are inconsistent by sub-proof #2372.
% 232.25/43.38  | | | 
% 232.25/43.38  | | Case 2:
% 232.25/43.38  | | | 
% 232.25/43.38  | | |   (18)  all_57_5 = e3 & op(e2, e1) = e3
% 232.25/43.38  | | | 
% 232.25/43.38  | | | ALPHA: (18) implies:
% 232.25/43.38  | | |   (19)  all_57_5 = e3
% 232.25/43.38  | | | 
% 232.25/43.38  | | | REF_CLOSE: (1), (2), (5), (6), (8), (9), (10), (12), (13), (14), (19) are
% 232.25/43.38  | | |            inconsistent by sub-proof #2378.
% 232.25/43.38  | | | 
% 232.25/43.38  | | End of split
% 232.25/43.38  | | 
% 232.25/43.38  | Case 2:
% 232.25/43.38  | | 
% 232.25/43.38  | |   (20)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) =
% 232.25/43.38  | |           e3)
% 232.25/43.38  | | 
% 232.25/43.38  | | REF_CLOSE: (2), (3), (4), (7), (14), (20) are inconsistent by sub-proof
% 232.25/43.38  | |            #2419.
% 232.25/43.38  | | 
% 232.25/43.38  | End of split
% 232.25/43.38  | 
% 232.25/43.38  End of proof
% 232.25/43.38  
% 232.25/43.38  Sub-proof #2372 shows that the following formulas are inconsistent:
% 232.25/43.38  ----------------------------------------------------------------
% 232.25/43.38    (1)  all_57_4 = e3
% 232.25/43.38    (2)  all_57_4 = e0
% 232.25/43.38    (3)   ~ (e3 = e0)
% 232.25/43.38  
% 232.25/43.38  Begin of proof
% 232.25/43.38  | 
% 232.25/43.38  | COMBINE_EQS: (1), (2) imply:
% 232.25/43.38  |   (4)  e3 = e0
% 232.25/43.38  | 
% 232.25/43.38  | SIMP: (4) implies:
% 232.25/43.38  |   (5)  e3 = e0
% 232.25/43.38  | 
% 232.25/43.38  | REDUCE: (3), (5) imply:
% 232.25/43.38  |   (6)  $false
% 232.25/43.38  | 
% 232.25/43.38  | CLOSE: (6) is inconsistent.
% 232.25/43.38  | 
% 232.25/43.38  End of proof
% 232.25/43.38  
% 232.25/43.38  Sub-proof #2373 shows that the following formulas are inconsistent:
% 232.25/43.38  ----------------------------------------------------------------
% 232.25/43.38    (1)   ~ (e3 = e1)
% 232.25/43.38    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.38           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.38    (3)  all_57_4 = e2
% 232.25/43.38    (4)  all_57_8 = e0 & op(e1, e1) = e0
% 232.25/43.38    (5)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 232.25/43.38         (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 232.25/43.38    (6)  all_57_5 = e3
% 232.25/43.38    (7)   ~ (e1 = e0)
% 232.25/43.38    (8)  all_57_14 = e2
% 232.25/43.38    (9)   ~ (e2 = e1)
% 232.25/43.38  
% 232.25/43.38  Begin of proof
% 232.25/43.38  | 
% 232.25/43.38  | ALPHA: (4) implies:
% 232.25/43.38  |   (10)  op(e1, e1) = e0
% 232.25/43.38  | 
% 232.25/43.38  | BETA: splitting (5) gives:
% 232.25/43.38  | 
% 232.25/43.38  | Case 1:
% 232.25/43.38  | | 
% 232.25/43.38  | |   (11)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) =
% 232.25/43.38  | |           e1)
% 232.25/43.38  | | 
% 232.25/43.38  | | BETA: splitting (11) gives:
% 232.25/43.38  | | 
% 232.25/43.38  | | Case 1:
% 232.25/43.38  | | | 
% 232.25/43.38  | | |   (12)  all_57_4 = e1 & op(e3, e1) = e1
% 232.25/43.38  | | | 
% 232.25/43.38  | | | REF_CLOSE: (3), (9), (12) are inconsistent by sub-proof #2452.
% 232.25/43.38  | | | 
% 232.25/43.38  | | Case 2:
% 232.25/43.38  | | | 
% 232.25/43.38  | | |   (13)  all_57_5 = e1 & op(e2, e1) = e1
% 232.25/43.38  | | | 
% 232.25/43.38  | | | REF_CLOSE: (1), (6), (13) are inconsistent by sub-proof #2376.
% 232.25/43.38  | | | 
% 232.25/43.38  | | End of split
% 232.25/43.38  | | 
% 232.25/43.38  | Case 2:
% 232.25/43.38  | | 
% 232.25/43.38  | |   (14)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) =
% 232.25/43.38  | |           e1)
% 232.25/43.38  | | 
% 232.25/43.38  | | REF_CLOSE: (2), (7), (8), (9), (10), (14) are inconsistent by sub-proof
% 232.25/43.38  | |            #2374.
% 232.25/43.38  | | 
% 232.25/43.38  | End of split
% 232.25/43.38  | 
% 232.25/43.38  End of proof
% 232.25/43.38  
% 232.25/43.38  Sub-proof #2374 shows that the following formulas are inconsistent:
% 232.25/43.38  ----------------------------------------------------------------
% 232.25/43.38    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.38           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.38    (2)   ~ (e1 = e0)
% 232.25/43.38    (3)  all_57_14 = e2
% 232.25/43.38    (4)  op(e1, e1) = e0
% 232.25/43.38    (5)   ~ (e2 = e1)
% 232.25/43.38    (6)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 232.25/43.38  
% 232.25/43.38  Begin of proof
% 232.25/43.38  | 
% 232.25/43.38  | BETA: splitting (6) gives:
% 232.25/43.38  | 
% 232.25/43.38  | Case 1:
% 232.25/43.38  | | 
% 232.25/43.38  | |   (7)  all_57_8 = e1 & op(e1, e1) = e1
% 232.25/43.38  | | 
% 232.25/43.38  | | ALPHA: (7) implies:
% 232.25/43.38  | |   (8)  op(e1, e1) = e1
% 232.25/43.38  | | 
% 232.25/43.38  | | REF_CLOSE: (1), (2), (4), (8) are inconsistent by sub-proof #2427.
% 232.25/43.38  | | 
% 232.25/43.38  | Case 2:
% 232.25/43.38  | | 
% 232.25/43.38  | |   (9)  all_57_14 = e1 & op(e0, e1) = e1
% 232.25/43.38  | | 
% 232.25/43.38  | | REF_CLOSE: (3), (5), (9) are inconsistent by sub-proof #2375.
% 232.25/43.38  | | 
% 232.25/43.38  | End of split
% 232.25/43.38  | 
% 232.25/43.38  End of proof
% 232.25/43.38  
% 232.25/43.38  Sub-proof #2375 shows that the following formulas are inconsistent:
% 232.25/43.38  ----------------------------------------------------------------
% 232.25/43.38    (1)  all_57_14 = e1 & op(e0, e1) = e1
% 232.25/43.38    (2)  all_57_14 = e2
% 232.25/43.38    (3)   ~ (e2 = e1)
% 232.25/43.38  
% 232.25/43.38  Begin of proof
% 232.25/43.38  | 
% 232.25/43.38  | ALPHA: (1) implies:
% 232.25/43.38  |   (4)  all_57_14 = e1
% 232.25/43.38  | 
% 232.25/43.38  | COMBINE_EQS: (2), (4) imply:
% 232.25/43.38  |   (5)  e2 = e1
% 232.25/43.38  | 
% 232.25/43.38  | REDUCE: (3), (5) imply:
% 232.25/43.38  |   (6)  $false
% 232.25/43.38  | 
% 232.25/43.38  | CLOSE: (6) is inconsistent.
% 232.25/43.38  | 
% 232.25/43.38  End of proof
% 232.25/43.38  
% 232.25/43.38  Sub-proof #2376 shows that the following formulas are inconsistent:
% 232.25/43.38  ----------------------------------------------------------------
% 232.25/43.38    (1)  all_57_5 = e1 & op(e2, e1) = e1
% 232.25/43.38    (2)  all_57_5 = e3
% 232.25/43.38    (3)   ~ (e3 = e1)
% 232.25/43.38  
% 232.25/43.38  Begin of proof
% 232.25/43.38  | 
% 232.25/43.38  | ALPHA: (1) implies:
% 232.25/43.38  |   (4)  all_57_5 = e1
% 232.25/43.38  | 
% 232.25/43.38  | COMBINE_EQS: (2), (4) imply:
% 232.25/43.38  |   (5)  e3 = e1
% 232.25/43.38  | 
% 232.25/43.38  | REDUCE: (3), (5) imply:
% 232.25/43.38  |   (6)  $false
% 232.25/43.38  | 
% 232.25/43.38  | CLOSE: (6) is inconsistent.
% 232.25/43.38  | 
% 232.25/43.38  End of proof
% 232.25/43.38  
% 232.25/43.38  Sub-proof #2377 shows that the following formulas are inconsistent:
% 232.25/43.38  ----------------------------------------------------------------
% 232.25/43.38    (1)   ~ (e3 = e1)
% 232.25/43.38    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.38           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.38    (3)  all_57_4 = e2
% 232.25/43.38    (4)   ~ (e3 = e2)
% 232.25/43.38    (5)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 232.25/43.38         (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 232.25/43.38    (6)  all_57_5 = e3
% 232.25/43.38    (7)   ~ (e2 = e0)
% 232.25/43.38    (8)  e2 = e0
% 232.25/43.38    (9)   ~ (e1 = e0)
% 232.25/43.38    (10)  all_57_14 = e2
% 232.25/43.38    (11)   ~ (e2 = e1)
% 232.25/43.38    (12)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 232.25/43.38          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 232.25/43.38  
% 232.25/43.38  Begin of proof
% 232.25/43.38  | 
% 232.25/43.38  | COMBINE_EQS: (8), (10) imply:
% 232.25/43.38  |   (13)  all_57_14 = e0
% 232.25/43.38  | 
% 232.25/43.38  | COMBINE_EQS: (3), (8) imply:
% 232.25/43.38  |   (14)  all_57_4 = e0
% 232.25/43.38  | 
% 232.25/43.38  | REF_CLOSE: (1), (2), (4), (5), (6), (7), (9), (11), (12), (13), (14) are
% 232.25/43.38  |            inconsistent by sub-proof #2378.
% 232.25/43.38  | 
% 232.25/43.38  End of proof
% 232.25/43.38  
% 232.25/43.38  Sub-proof #2378 shows that the following formulas are inconsistent:
% 232.25/43.38  ----------------------------------------------------------------
% 232.25/43.38    (1)   ~ (e3 = e1)
% 232.25/43.38    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.38           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.38    (3)  all_57_4 = e0
% 232.25/43.38    (4)   ~ (e3 = e2)
% 232.25/43.38    (5)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 232.25/43.38         (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 232.25/43.38    (6)  all_57_5 = e3
% 232.25/43.38    (7)   ~ (e2 = e0)
% 232.25/43.38    (8)   ~ (e1 = e0)
% 232.25/43.38    (9)   ~ (e2 = e1)
% 232.25/43.38    (10)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 232.25/43.38          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 232.25/43.38    (11)  all_57_14 = e0
% 232.25/43.38  
% 232.25/43.38  Begin of proof
% 232.25/43.38  | 
% 232.25/43.38  | BETA: splitting (10) gives:
% 232.25/43.38  | 
% 232.25/43.38  | Case 1:
% 232.25/43.38  | | 
% 232.25/43.38  | |   (12)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) =
% 232.25/43.38  | |           e2)
% 232.25/43.38  | | 
% 232.25/43.38  | | REF_CLOSE: (3), (4), (6), (7), (12) are inconsistent by sub-proof #2383.
% 232.25/43.38  | | 
% 232.25/43.38  | Case 2:
% 232.25/43.38  | | 
% 232.25/43.38  | |   (13)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) =
% 232.25/43.38  | |           e2)
% 232.25/43.38  | | 
% 232.25/43.38  | | BETA: splitting (13) gives:
% 232.25/43.38  | | 
% 232.25/43.38  | | Case 1:
% 232.25/43.38  | | | 
% 232.25/43.38  | | |   (14)  all_57_8 = e2 & op(e1, e1) = e2
% 232.25/43.38  | | | 
% 232.25/43.38  | | | ALPHA: (14) implies:
% 232.25/43.38  | | |   (15)  op(e1, e1) = e2
% 232.25/43.38  | | | 
% 232.25/43.38  | | | REF_CLOSE: (1), (2), (3), (5), (6), (8), (9), (11), (15) are inconsistent
% 232.25/43.38  | | |            by sub-proof #2379.
% 232.25/43.38  | | | 
% 232.25/43.38  | | Case 2:
% 232.25/43.38  | | | 
% 232.25/43.38  | | |   (16)  all_57_14 = e2 & op(e0, e1) = e2
% 232.25/43.38  | | | 
% 232.25/43.38  | | | ALPHA: (16) implies:
% 232.25/43.38  | | |   (17)  all_57_14 = e2
% 232.25/43.38  | | | 
% 232.25/43.38  | | | REF_CLOSE: (7), (11), (17) are inconsistent by sub-proof #2422.
% 232.25/43.38  | | | 
% 232.25/43.38  | | End of split
% 232.25/43.38  | | 
% 232.25/43.38  | End of split
% 232.25/43.38  | 
% 232.25/43.38  End of proof
% 232.25/43.38  
% 232.25/43.38  Sub-proof #2379 shows that the following formulas are inconsistent:
% 232.25/43.38  ----------------------------------------------------------------
% 232.25/43.38    (1)   ~ (e3 = e1)
% 232.25/43.38    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.38           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.38    (3)  all_57_4 = e0
% 232.25/43.38    (4)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 232.25/43.38         (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 232.25/43.38    (5)  all_57_5 = e3
% 232.25/43.38    (6)   ~ (e1 = e0)
% 232.25/43.38    (7)  op(e1, e1) = e2
% 232.25/43.38    (8)   ~ (e2 = e1)
% 232.25/43.38    (9)  all_57_14 = e0
% 232.25/43.38  
% 232.25/43.38  Begin of proof
% 232.25/43.38  | 
% 232.25/43.38  | BETA: splitting (4) gives:
% 232.25/43.38  | 
% 232.25/43.38  | Case 1:
% 232.25/43.38  | | 
% 232.25/43.38  | |   (10)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) =
% 232.25/43.38  | |           e1)
% 232.25/43.38  | | 
% 232.25/43.38  | | BETA: splitting (10) gives:
% 232.25/43.38  | | 
% 232.25/43.38  | | Case 1:
% 232.25/43.38  | | | 
% 232.25/43.38  | | |   (11)  all_57_4 = e1 & op(e3, e1) = e1
% 232.25/43.38  | | | 
% 232.25/43.38  | | | ALPHA: (11) implies:
% 232.25/43.38  | | |   (12)  all_57_4 = e1
% 232.25/43.38  | | | 
% 232.25/43.38  | | | REF_CLOSE: (3), (6), (12) are inconsistent by sub-proof #2438.
% 232.25/43.38  | | | 
% 232.25/43.38  | | Case 2:
% 232.25/43.38  | | | 
% 232.25/43.38  | | |   (13)  all_57_5 = e1 & op(e2, e1) = e1
% 232.25/43.38  | | | 
% 232.25/43.38  | | | ALPHA: (13) implies:
% 232.25/43.38  | | |   (14)  all_57_5 = e1
% 232.25/43.38  | | | 
% 232.25/43.38  | | | REF_CLOSE: (1), (5), (14) are inconsistent by sub-proof #2382.
% 232.25/43.38  | | | 
% 232.25/43.38  | | End of split
% 232.25/43.38  | | 
% 232.25/43.38  | Case 2:
% 232.25/43.38  | | 
% 232.25/43.38  | |   (15)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) =
% 232.25/43.38  | |           e1)
% 232.25/43.38  | | 
% 232.25/43.38  | | REF_CLOSE: (2), (6), (7), (8), (9), (15) are inconsistent by sub-proof
% 232.25/43.38  | |            #2380.
% 232.25/43.38  | | 
% 232.25/43.38  | End of split
% 232.25/43.38  | 
% 232.25/43.38  End of proof
% 232.25/43.38  
% 232.25/43.38  Sub-proof #2380 shows that the following formulas are inconsistent:
% 232.25/43.38  ----------------------------------------------------------------
% 232.25/43.38    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.38           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.38    (2)   ~ (e1 = e0)
% 232.25/43.38    (3)  op(e1, e1) = e2
% 232.25/43.38    (4)   ~ (e2 = e1)
% 232.25/43.38    (5)  all_57_14 = e0
% 232.25/43.38    (6)  (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 232.25/43.38  
% 232.25/43.38  Begin of proof
% 232.25/43.38  | 
% 232.25/43.38  | BETA: splitting (6) gives:
% 232.25/43.38  | 
% 232.25/43.38  | Case 1:
% 232.25/43.38  | | 
% 232.25/43.38  | |   (7)  all_57_8 = e1 & op(e1, e1) = e1
% 232.25/43.38  | | 
% 232.25/43.38  | | ALPHA: (7) implies:
% 232.25/43.38  | |   (8)  op(e1, e1) = e1
% 232.25/43.38  | | 
% 232.25/43.38  | | REF_CLOSE: (1), (3), (4), (8) are inconsistent by sub-proof #2423.
% 232.25/43.38  | | 
% 232.25/43.38  | Case 2:
% 232.25/43.38  | | 
% 232.25/43.38  | |   (9)  all_57_14 = e1 & op(e0, e1) = e1
% 232.25/43.38  | | 
% 232.25/43.38  | | REF_CLOSE: (2), (5), (9) are inconsistent by sub-proof #2381.
% 232.25/43.38  | | 
% 232.25/43.38  | End of split
% 232.25/43.38  | 
% 232.25/43.38  End of proof
% 232.25/43.38  
% 232.25/43.38  Sub-proof #2381 shows that the following formulas are inconsistent:
% 232.25/43.38  ----------------------------------------------------------------
% 232.25/43.38    (1)  all_57_14 = e1 & op(e0, e1) = e1
% 232.25/43.38    (2)  all_57_14 = e0
% 232.25/43.38    (3)   ~ (e1 = e0)
% 232.25/43.38  
% 232.25/43.38  Begin of proof
% 232.25/43.38  | 
% 232.25/43.38  | ALPHA: (1) implies:
% 232.25/43.38  |   (4)  all_57_14 = e1
% 232.25/43.38  | 
% 232.25/43.38  | COMBINE_EQS: (2), (4) imply:
% 232.25/43.38  |   (5)  e1 = e0
% 232.25/43.38  | 
% 232.25/43.38  | REDUCE: (3), (5) imply:
% 232.25/43.38  |   (6)  $false
% 232.25/43.38  | 
% 232.25/43.38  | CLOSE: (6) is inconsistent.
% 232.25/43.38  | 
% 232.25/43.38  End of proof
% 232.25/43.38  
% 232.25/43.38  Sub-proof #2382 shows that the following formulas are inconsistent:
% 232.25/43.38  ----------------------------------------------------------------
% 232.25/43.38    (1)  all_57_5 = e3
% 232.25/43.38    (2)  all_57_5 = e1
% 232.25/43.38    (3)   ~ (e3 = e1)
% 232.25/43.38  
% 232.25/43.38  Begin of proof
% 232.25/43.38  | 
% 232.25/43.38  | COMBINE_EQS: (1), (2) imply:
% 232.25/43.38  |   (4)  e3 = e1
% 232.25/43.38  | 
% 232.25/43.38  | SIMP: (4) implies:
% 232.25/43.38  |   (5)  e3 = e1
% 232.25/43.38  | 
% 232.25/43.38  | REDUCE: (3), (5) imply:
% 232.25/43.38  |   (6)  $false
% 232.25/43.38  | 
% 232.25/43.38  | CLOSE: (6) is inconsistent.
% 232.25/43.38  | 
% 232.25/43.38  End of proof
% 232.25/43.38  
% 232.25/43.38  Sub-proof #2383 shows that the following formulas are inconsistent:
% 232.25/43.38  ----------------------------------------------------------------
% 232.25/43.38    (1)  all_57_4 = e0
% 232.25/43.38    (2)   ~ (e3 = e2)
% 232.25/43.38    (3)  all_57_5 = e3
% 232.25/43.38    (4)   ~ (e2 = e0)
% 232.25/43.38    (5)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2)
% 232.25/43.38  
% 232.25/43.38  Begin of proof
% 232.25/43.38  | 
% 232.25/43.38  | BETA: splitting (5) gives:
% 232.25/43.38  | 
% 232.25/43.38  | Case 1:
% 232.25/43.38  | | 
% 232.25/43.38  | |   (6)  all_57_4 = e2 & op(e3, e1) = e2
% 232.25/43.38  | | 
% 232.25/43.38  | | ALPHA: (6) implies:
% 232.25/43.38  | |   (7)  all_57_4 = e2
% 232.25/43.38  | | 
% 232.25/43.38  | | REF_CLOSE: (1), (4), (7) are inconsistent by sub-proof #2441.
% 232.25/43.38  | | 
% 232.25/43.38  | Case 2:
% 232.25/43.38  | | 
% 232.25/43.38  | |   (8)  all_57_5 = e2 & op(e2, e1) = e2
% 232.25/43.38  | | 
% 232.25/43.38  | | REF_CLOSE: (2), (3), (8) are inconsistent by sub-proof #2425.
% 232.25/43.38  | | 
% 232.25/43.38  | End of split
% 232.25/43.38  | 
% 232.25/43.38  End of proof
% 232.25/43.38  
% 232.25/43.38  Sub-proof #2384 shows that the following formulas are inconsistent:
% 232.25/43.38  ----------------------------------------------------------------
% 232.25/43.38    (1)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 232.25/43.38         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 232.25/43.38    (2)   ~ (e3 = e1)
% 232.25/43.38    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.38           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.38    (4)  all_57_12 = e2
% 232.25/43.38    (5)   ~ (e3 = e0)
% 232.25/43.38    (6)  op(e3, e3) = e3
% 232.25/43.38    (7)  all_57_6 = e2
% 232.25/43.38    (8)   ~ (e2 = e0)
% 232.25/43.38    (9)   ~ (e1 = e0)
% 232.25/43.38    (10)   ~ (e2 = e1)
% 232.25/43.38    (11)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 232.25/43.38          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 232.25/43.38  
% 232.25/43.38  Begin of proof
% 232.25/43.38  | 
% 232.25/43.38  | BETA: splitting (11) gives:
% 232.25/43.38  | 
% 232.25/43.38  | Case 1:
% 232.25/43.38  | | 
% 232.25/43.38  | |   (12)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) =
% 232.25/43.38  | |           e0)
% 232.25/43.38  | | 
% 232.25/43.38  | | BETA: splitting (12) gives:
% 232.25/43.38  | | 
% 232.25/43.38  | | Case 1:
% 232.25/43.38  | | | 
% 232.25/43.38  | | |   (13)  all_57_0 = e0 & op(e3, e3) = e0
% 232.25/43.38  | | | 
% 232.25/43.38  | | | ALPHA: (13) implies:
% 232.25/43.38  | | |   (14)  op(e3, e3) = e0
% 232.25/43.38  | | | 
% 232.25/43.38  | | | REF_CLOSE: (3), (5), (6), (14) are inconsistent by sub-proof #2494.
% 232.25/43.38  | | | 
% 232.25/43.38  | | Case 2:
% 232.25/43.38  | | | 
% 232.25/43.38  | | |   (15)  all_57_2 = e0 & op(e2, e3) = e0
% 232.25/43.38  | | | 
% 232.25/43.38  | | | ALPHA: (15) implies:
% 232.25/43.38  | | |   (16)  all_57_2 = e0
% 232.25/43.38  | | | 
% 232.25/43.38  | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (9), (10), (16) are inconsistent
% 232.25/43.38  | | |            by sub-proof #2387.
% 232.25/43.38  | | | 
% 232.25/43.38  | | End of split
% 232.25/43.38  | | 
% 232.25/43.38  | Case 2:
% 232.25/43.38  | | 
% 232.25/43.38  | |   (17)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) =
% 232.25/43.38  | |           e0)
% 232.25/43.38  | | 
% 232.25/43.38  | | BETA: splitting (17) gives:
% 232.25/43.38  | | 
% 232.25/43.38  | | Case 1:
% 232.25/43.38  | | | 
% 232.25/43.38  | | |   (18)  all_57_6 = e0 & op(e1, e3) = e0
% 232.25/43.38  | | | 
% 232.25/43.38  | | | REF_CLOSE: (7), (8), (18) are inconsistent by sub-proof #2386.
% 232.25/43.38  | | | 
% 232.25/43.38  | | Case 2:
% 232.25/43.38  | | | 
% 232.25/43.38  | | |   (19)  all_57_12 = e0 & op(e0, e3) = e0
% 232.25/43.38  | | | 
% 232.25/43.38  | | | ALPHA: (19) implies:
% 232.25/43.38  | | |   (20)  all_57_12 = e0
% 232.25/43.38  | | | 
% 232.25/43.38  | | | REF_CLOSE: (4), (8), (20) are inconsistent by sub-proof #2385.
% 232.25/43.38  | | | 
% 232.25/43.38  | | End of split
% 232.25/43.38  | | 
% 232.25/43.38  | End of split
% 232.25/43.38  | 
% 232.25/43.38  End of proof
% 232.25/43.38  
% 232.25/43.38  Sub-proof #2385 shows that the following formulas are inconsistent:
% 232.25/43.38  ----------------------------------------------------------------
% 232.25/43.38    (1)  all_57_12 = e2
% 232.25/43.38    (2)  all_57_12 = e0
% 232.25/43.38    (3)   ~ (e2 = e0)
% 232.25/43.38  
% 232.25/43.38  Begin of proof
% 232.25/43.38  | 
% 232.25/43.38  | COMBINE_EQS: (1), (2) imply:
% 232.25/43.38  |   (4)  e2 = e0
% 232.25/43.38  | 
% 232.25/43.38  | SIMP: (4) implies:
% 232.25/43.38  |   (5)  e2 = e0
% 232.25/43.38  | 
% 232.25/43.38  | REDUCE: (3), (5) imply:
% 232.25/43.38  |   (6)  $false
% 232.25/43.38  | 
% 232.25/43.38  | CLOSE: (6) is inconsistent.
% 232.25/43.38  | 
% 232.25/43.38  End of proof
% 232.25/43.38  
% 232.25/43.38  Sub-proof #2386 shows that the following formulas are inconsistent:
% 232.25/43.38  ----------------------------------------------------------------
% 232.25/43.38    (1)  all_57_6 = e0 & op(e1, e3) = e0
% 232.25/43.38    (2)  all_57_6 = e2
% 232.25/43.38    (3)   ~ (e2 = e0)
% 232.25/43.38  
% 232.25/43.38  Begin of proof
% 232.25/43.38  | 
% 232.25/43.38  | ALPHA: (1) implies:
% 232.25/43.38  |   (4)  all_57_6 = e0
% 232.25/43.38  | 
% 232.25/43.38  | COMBINE_EQS: (2), (4) imply:
% 232.25/43.38  |   (5)  e2 = e0
% 232.25/43.38  | 
% 232.25/43.38  | REDUCE: (3), (5) imply:
% 232.25/43.38  |   (6)  $false
% 232.25/43.38  | 
% 232.25/43.38  | CLOSE: (6) is inconsistent.
% 232.25/43.38  | 
% 232.25/43.38  End of proof
% 232.25/43.38  
% 232.25/43.38  Sub-proof #2387 shows that the following formulas are inconsistent:
% 232.25/43.38  ----------------------------------------------------------------
% 232.25/43.38    (1)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 232.25/43.38         (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 232.25/43.38    (2)   ~ (e3 = e1)
% 232.25/43.38    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.38           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.38    (4)  all_57_12 = e2
% 232.25/43.38    (5)  op(e3, e3) = e3
% 232.25/43.38    (6)  all_57_6 = e2
% 232.25/43.38    (7)   ~ (e1 = e0)
% 232.25/43.38    (8)  all_57_2 = e0
% 232.25/43.38    (9)   ~ (e2 = e1)
% 232.25/43.38  
% 232.25/43.38  Begin of proof
% 232.25/43.38  | 
% 232.25/43.38  | BETA: splitting (1) gives:
% 232.25/43.38  | 
% 232.25/43.38  | Case 1:
% 232.25/43.38  | | 
% 232.25/43.38  | |   (10)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) =
% 232.25/43.38  | |           e1)
% 232.25/43.38  | | 
% 232.25/43.38  | | BETA: splitting (10) gives:
% 232.25/43.38  | | 
% 232.25/43.38  | | Case 1:
% 232.25/43.38  | | | 
% 232.25/43.38  | | |   (11)  all_57_0 = e1 & op(e3, e3) = e1
% 232.25/43.38  | | | 
% 232.25/43.38  | | | ALPHA: (11) implies:
% 232.25/43.38  | | |   (12)  op(e3, e3) = e1
% 232.25/43.38  | | | 
% 232.25/43.38  | | | REF_CLOSE: (2), (3), (5), (12) are inconsistent by sub-proof #2495.
% 232.25/43.38  | | | 
% 232.25/43.38  | | Case 2:
% 232.25/43.38  | | | 
% 232.25/43.38  | | |   (13)  all_57_2 = e1 & op(e2, e3) = e1
% 232.25/43.38  | | | 
% 232.25/43.38  | | | ALPHA: (13) implies:
% 232.25/43.38  | | |   (14)  all_57_2 = e1
% 232.25/43.38  | | | 
% 232.25/43.38  | | | REF_CLOSE: (7), (8), (14) are inconsistent by sub-proof #2473.
% 232.25/43.38  | | | 
% 232.25/43.38  | | End of split
% 232.25/43.38  | | 
% 232.25/43.38  | Case 2:
% 232.25/43.38  | | 
% 232.25/43.38  | |   (15)  (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) =
% 232.25/43.38  | |           e1)
% 232.25/43.38  | | 
% 232.25/43.38  | | BETA: splitting (15) gives:
% 232.25/43.38  | | 
% 232.25/43.38  | | Case 1:
% 232.25/43.38  | | | 
% 232.25/43.38  | | |   (16)  all_57_6 = e1 & op(e1, e3) = e1
% 232.25/43.38  | | | 
% 232.25/43.38  | | | REF_CLOSE: (6), (9), (16) are inconsistent by sub-proof #2389.
% 232.25/43.38  | | | 
% 232.25/43.38  | | Case 2:
% 232.25/43.38  | | | 
% 232.25/43.38  | | |   (17)  all_57_12 = e1 & op(e0, e3) = e1
% 232.25/43.38  | | | 
% 232.25/43.38  | | | REF_CLOSE: (4), (9), (17) are inconsistent by sub-proof #2388.
% 232.25/43.38  | | | 
% 232.25/43.38  | | End of split
% 232.25/43.38  | | 
% 232.25/43.38  | End of split
% 232.25/43.38  | 
% 232.25/43.38  End of proof
% 232.25/43.38  
% 232.25/43.38  Sub-proof #2388 shows that the following formulas are inconsistent:
% 232.25/43.38  ----------------------------------------------------------------
% 232.25/43.38    (1)  all_57_12 = e1 & op(e0, e3) = e1
% 232.25/43.38    (2)  all_57_12 = e2
% 232.25/43.38    (3)   ~ (e2 = e1)
% 232.25/43.38  
% 232.25/43.38  Begin of proof
% 232.25/43.38  | 
% 232.25/43.38  | ALPHA: (1) implies:
% 232.25/43.38  |   (4)  all_57_12 = e1
% 232.25/43.38  | 
% 232.25/43.38  | COMBINE_EQS: (2), (4) imply:
% 232.25/43.38  |   (5)  e2 = e1
% 232.25/43.38  | 
% 232.25/43.38  | REDUCE: (3), (5) imply:
% 232.25/43.38  |   (6)  $false
% 232.25/43.38  | 
% 232.25/43.38  | CLOSE: (6) is inconsistent.
% 232.25/43.38  | 
% 232.25/43.38  End of proof
% 232.25/43.38  
% 232.25/43.38  Sub-proof #2389 shows that the following formulas are inconsistent:
% 232.25/43.38  ----------------------------------------------------------------
% 232.25/43.38    (1)  all_57_6 = e1 & op(e1, e3) = e1
% 232.25/43.38    (2)  all_57_6 = e2
% 232.25/43.38    (3)   ~ (e2 = e1)
% 232.25/43.38  
% 232.25/43.38  Begin of proof
% 232.25/43.38  | 
% 232.25/43.38  | ALPHA: (1) implies:
% 232.25/43.38  |   (4)  all_57_6 = e1
% 232.25/43.38  | 
% 232.25/43.38  | COMBINE_EQS: (2), (4) imply:
% 232.25/43.38  |   (5)  e2 = e1
% 232.25/43.38  | 
% 232.25/43.38  | REDUCE: (3), (5) imply:
% 232.25/43.38  |   (6)  $false
% 232.25/43.38  | 
% 232.25/43.38  | CLOSE: (6) is inconsistent.
% 232.25/43.38  | 
% 232.25/43.38  End of proof
% 232.25/43.38  
% 232.25/43.38  Sub-proof #2390 shows that the following formulas are inconsistent:
% 232.25/43.38  ----------------------------------------------------------------
% 232.25/43.38    (1)   ~ (e3 = e1)
% 232.25/43.38    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.38           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.38    (3)   ~ (e3 = e2)
% 232.25/43.38    (4)   ~ (e3 = e0)
% 232.25/43.38    (5)  all_57_6 = e0
% 232.25/43.38    (6)  op(e3, e3) = e0
% 232.25/43.38    (7)   ~ (e2 = e0)
% 232.25/43.38    (8)  all_57_2 = e1
% 232.25/43.38    (9)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 232.25/43.38         (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 232.25/43.38    (10)   ~ (e2 = e1)
% 232.25/43.38    (11)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 232.25/43.38          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 232.25/43.38  
% 232.25/43.38  Begin of proof
% 232.25/43.38  | 
% 232.25/43.38  | BETA: splitting (9) gives:
% 232.25/43.38  | 
% 232.25/43.38  | Case 1:
% 232.25/43.38  | | 
% 232.25/43.38  | |   (12)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) =
% 232.25/43.38  | |           e3)
% 232.25/43.38  | | 
% 232.25/43.38  | | REF_CLOSE: (1), (2), (4), (6), (8), (12) are inconsistent by sub-proof
% 232.25/43.38  | |            #2396.
% 232.25/43.38  | | 
% 232.25/43.38  | Case 2:
% 232.25/43.38  | | 
% 232.25/43.38  | |   (13)  (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) =
% 232.25/43.38  | |           e3)
% 232.25/43.38  | | 
% 232.25/43.38  | | BETA: splitting (13) gives:
% 232.25/43.38  | | 
% 232.25/43.38  | | Case 1:
% 232.25/43.38  | | | 
% 232.25/43.38  | | |   (14)  all_57_6 = e3 & op(e1, e3) = e3
% 232.25/43.38  | | | 
% 232.25/43.38  | | | REF_CLOSE: (4), (5), (14) are inconsistent by sub-proof #2395.
% 232.25/43.38  | | | 
% 232.25/43.38  | | Case 2:
% 232.25/43.38  | | | 
% 232.25/43.38  | | |   (15)  all_57_12 = e3 & op(e0, e3) = e3
% 232.25/43.38  | | | 
% 232.25/43.38  | | | ALPHA: (15) implies:
% 232.25/43.38  | | |   (16)  all_57_12 = e3
% 232.25/43.38  | | | 
% 232.25/43.38  | | | BETA: splitting (11) gives:
% 232.25/43.38  | | | 
% 232.25/43.38  | | | Case 1:
% 232.25/43.38  | | | | 
% 232.25/43.38  | | | |   (17)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3)
% 232.25/43.38  | | | |           = e2)
% 232.25/43.38  | | | | 
% 232.25/43.38  | | | | REF_CLOSE: (2), (6), (7), (8), (10), (17) are inconsistent by sub-proof
% 232.25/43.38  | | | |            #2394.
% 232.25/43.38  | | | | 
% 232.25/43.38  | | | Case 2:
% 232.25/43.38  | | | | 
% 232.25/43.38  | | | |   (18)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3)
% 232.25/43.38  | | | |           = e2)
% 232.25/43.38  | | | | 
% 232.25/43.38  | | | | REF_CLOSE: (3), (5), (7), (16), (18) are inconsistent by sub-proof
% 232.25/43.38  | | | |            #2391.
% 232.25/43.38  | | | | 
% 232.25/43.38  | | | End of split
% 232.25/43.38  | | | 
% 232.25/43.38  | | End of split
% 232.25/43.38  | | 
% 232.25/43.38  | End of split
% 232.25/43.38  | 
% 232.25/43.38  End of proof
% 232.25/43.38  
% 232.25/43.38  Sub-proof #2391 shows that the following formulas are inconsistent:
% 232.25/43.38  ----------------------------------------------------------------
% 232.25/43.38    (1)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 232.25/43.38    (2)   ~ (e3 = e2)
% 232.25/43.38    (3)  all_57_6 = e0
% 232.25/43.38    (4)   ~ (e2 = e0)
% 232.25/43.38    (5)  all_57_12 = e3
% 232.25/43.38  
% 232.25/43.38  Begin of proof
% 232.25/43.38  | 
% 232.25/43.38  | BETA: splitting (1) gives:
% 232.25/43.38  | 
% 232.25/43.38  | Case 1:
% 232.25/43.38  | | 
% 232.25/43.38  | |   (6)  all_57_6 = e2 & op(e1, e3) = e2
% 232.25/43.38  | | 
% 232.25/43.38  | | REF_CLOSE: (3), (4), (6) are inconsistent by sub-proof #2393.
% 232.25/43.38  | | 
% 232.25/43.38  | Case 2:
% 232.25/43.38  | | 
% 232.25/43.38  | |   (7)  all_57_12 = e2 & op(e0, e3) = e2
% 232.25/43.38  | | 
% 232.25/43.38  | | ALPHA: (7) implies:
% 232.25/43.38  | |   (8)  all_57_12 = e2
% 232.25/43.38  | | 
% 232.25/43.38  | | REF_CLOSE: (2), (5), (8) are inconsistent by sub-proof #2392.
% 232.25/43.38  | | 
% 232.25/43.38  | End of split
% 232.25/43.38  | 
% 232.25/43.38  End of proof
% 232.25/43.38  
% 232.25/43.38  Sub-proof #2392 shows that the following formulas are inconsistent:
% 232.25/43.38  ----------------------------------------------------------------
% 232.25/43.38    (1)  all_57_12 = e3
% 232.25/43.38    (2)  all_57_12 = e2
% 232.25/43.38    (3)   ~ (e3 = e2)
% 232.25/43.38  
% 232.25/43.38  Begin of proof
% 232.25/43.38  | 
% 232.25/43.38  | COMBINE_EQS: (1), (2) imply:
% 232.25/43.38  |   (4)  e3 = e2
% 232.25/43.38  | 
% 232.25/43.38  | SIMP: (4) implies:
% 232.25/43.38  |   (5)  e3 = e2
% 232.25/43.38  | 
% 232.25/43.38  | REDUCE: (3), (5) imply:
% 232.25/43.38  |   (6)  $false
% 232.25/43.38  | 
% 232.25/43.38  | CLOSE: (6) is inconsistent.
% 232.25/43.38  | 
% 232.25/43.38  End of proof
% 232.25/43.38  
% 232.25/43.38  Sub-proof #2393 shows that the following formulas are inconsistent:
% 232.25/43.38  ----------------------------------------------------------------
% 232.25/43.38    (1)  all_57_6 = e2 & op(e1, e3) = e2
% 232.25/43.38    (2)  all_57_6 = e0
% 232.25/43.38    (3)   ~ (e2 = e0)
% 232.25/43.38  
% 232.25/43.38  Begin of proof
% 232.25/43.38  | 
% 232.25/43.38  | ALPHA: (1) implies:
% 232.25/43.38  |   (4)  all_57_6 = e2
% 232.25/43.38  | 
% 232.25/43.38  | COMBINE_EQS: (2), (4) imply:
% 232.25/43.38  |   (5)  e2 = e0
% 232.25/43.38  | 
% 232.25/43.38  | REDUCE: (3), (5) imply:
% 232.25/43.38  |   (6)  $false
% 232.25/43.38  | 
% 232.25/43.38  | CLOSE: (6) is inconsistent.
% 232.25/43.38  | 
% 232.25/43.38  End of proof
% 232.25/43.38  
% 232.25/43.38  Sub-proof #2394 shows that the following formulas are inconsistent:
% 232.25/43.38  ----------------------------------------------------------------
% 232.25/43.38    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.38           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.38    (2)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2)
% 232.25/43.38    (3)  op(e3, e3) = e0
% 232.25/43.38    (4)   ~ (e2 = e0)
% 232.25/43.38    (5)  all_57_2 = e1
% 232.25/43.38    (6)   ~ (e2 = e1)
% 232.25/43.38  
% 232.25/43.38  Begin of proof
% 232.25/43.38  | 
% 232.25/43.38  | BETA: splitting (2) gives:
% 232.25/43.38  | 
% 232.25/43.38  | Case 1:
% 232.25/43.38  | | 
% 232.25/43.38  | |   (7)  all_57_0 = e2 & op(e3, e3) = e2
% 232.25/43.38  | | 
% 232.25/43.38  | | ALPHA: (7) implies:
% 232.25/43.38  | |   (8)  op(e3, e3) = e2
% 232.25/43.38  | | 
% 232.25/43.38  | | REF_CLOSE: (1), (3), (4), (8) are inconsistent by sub-proof #2403.
% 232.25/43.38  | | 
% 232.25/43.38  | Case 2:
% 232.25/43.38  | | 
% 232.25/43.38  | |   (9)  all_57_2 = e2 & op(e2, e3) = e2
% 232.25/43.38  | | 
% 232.25/43.38  | | ALPHA: (9) implies:
% 232.25/43.38  | |   (10)  all_57_2 = e2
% 232.25/43.38  | | 
% 232.25/43.38  | | REF_CLOSE: (5), (6), (10) are inconsistent by sub-proof #2464.
% 232.25/43.38  | | 
% 232.25/43.38  | End of split
% 232.25/43.38  | 
% 232.25/43.38  End of proof
% 232.25/43.38  
% 232.25/43.38  Sub-proof #2395 shows that the following formulas are inconsistent:
% 232.25/43.38  ----------------------------------------------------------------
% 232.25/43.38    (1)  all_57_6 = e3 & op(e1, e3) = e3
% 232.25/43.38    (2)  all_57_6 = e0
% 232.25/43.38    (3)   ~ (e3 = e0)
% 232.25/43.38  
% 232.25/43.38  Begin of proof
% 232.25/43.38  | 
% 232.25/43.38  | ALPHA: (1) implies:
% 232.25/43.38  |   (4)  all_57_6 = e3
% 232.25/43.38  | 
% 232.25/43.38  | COMBINE_EQS: (2), (4) imply:
% 232.25/43.38  |   (5)  e3 = e0
% 232.25/43.38  | 
% 232.25/43.38  | REDUCE: (3), (5) imply:
% 232.25/43.38  |   (6)  $false
% 232.25/43.38  | 
% 232.25/43.38  | CLOSE: (6) is inconsistent.
% 232.25/43.38  | 
% 232.25/43.38  End of proof
% 232.25/43.38  
% 232.25/43.38  Sub-proof #2396 shows that the following formulas are inconsistent:
% 232.25/43.38  ----------------------------------------------------------------
% 232.25/43.38    (1)   ~ (e3 = e1)
% 232.25/43.38    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.38           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.38    (3)   ~ (e3 = e0)
% 232.25/43.38    (4)  op(e3, e3) = e0
% 232.25/43.38    (5)  all_57_2 = e1
% 232.25/43.38    (6)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3)
% 232.25/43.38  
% 232.25/43.38  Begin of proof
% 232.25/43.38  | 
% 232.25/43.38  | BETA: splitting (6) gives:
% 232.25/43.38  | 
% 232.25/43.38  | Case 1:
% 232.25/43.38  | | 
% 232.25/43.38  | |   (7)  all_57_0 = e3 & op(e3, e3) = e3
% 232.25/43.38  | | 
% 232.25/43.38  | | ALPHA: (7) implies:
% 232.25/43.38  | |   (8)  op(e3, e3) = e3
% 232.25/43.38  | | 
% 232.25/43.38  | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #2494.
% 232.25/43.38  | | 
% 232.25/43.38  | Case 2:
% 232.25/43.38  | | 
% 232.25/43.38  | |   (9)  all_57_2 = e3 & op(e2, e3) = e3
% 232.25/43.38  | | 
% 232.25/43.38  | | ALPHA: (9) implies:
% 232.25/43.38  | |   (10)  all_57_2 = e3
% 232.25/43.38  | | 
% 232.25/43.38  | | REF_CLOSE: (1), (5), (10) are inconsistent by sub-proof #2397.
% 232.25/43.38  | | 
% 232.25/43.38  | End of split
% 232.25/43.38  | 
% 232.25/43.38  End of proof
% 232.25/43.38  
% 232.25/43.38  Sub-proof #2397 shows that the following formulas are inconsistent:
% 232.25/43.38  ----------------------------------------------------------------
% 232.25/43.38    (1)  all_57_2 = e3
% 232.25/43.38    (2)  all_57_2 = e1
% 232.25/43.39    (3)   ~ (e3 = e1)
% 232.25/43.39  
% 232.25/43.39  Begin of proof
% 232.25/43.39  | 
% 232.25/43.39  | COMBINE_EQS: (1), (2) imply:
% 232.25/43.39  |   (4)  e3 = e1
% 232.25/43.39  | 
% 232.25/43.39  | SIMP: (4) implies:
% 232.25/43.39  |   (5)  e3 = e1
% 232.25/43.39  | 
% 232.25/43.39  | REDUCE: (3), (5) imply:
% 232.25/43.39  |   (6)  $false
% 232.25/43.39  | 
% 232.25/43.39  | CLOSE: (6) is inconsistent.
% 232.25/43.39  | 
% 232.25/43.39  End of proof
% 232.25/43.39  
% 232.25/43.39  Sub-proof #2398 shows that the following formulas are inconsistent:
% 232.25/43.39  ----------------------------------------------------------------
% 232.25/43.39    (1)  all_55_6 = all_53_9
% 232.25/43.39    (2)  all_55_6 = e2
% 232.25/43.39    (3)   ~ (all_53_9 = e2)
% 232.25/43.39  
% 232.25/43.39  Begin of proof
% 232.25/43.39  | 
% 232.25/43.39  | COMBINE_EQS: (1), (2) imply:
% 232.25/43.39  |   (4)  all_53_9 = e2
% 232.25/43.39  | 
% 232.25/43.39  | SIMP: (4) implies:
% 232.25/43.39  |   (5)  all_53_9 = e2
% 232.25/43.39  | 
% 232.25/43.39  | REDUCE: (3), (5) imply:
% 232.25/43.39  |   (6)  $false
% 232.25/43.39  | 
% 232.25/43.39  | CLOSE: (6) is inconsistent.
% 232.25/43.39  | 
% 232.25/43.39  End of proof
% 232.25/43.39  
% 232.25/43.39  Sub-proof #2399 shows that the following formulas are inconsistent:
% 232.25/43.39  ----------------------------------------------------------------
% 232.25/43.39    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.39    (2)  op(e3, e2) = all_52_3
% 232.25/43.39    (3)  op(all_52_3, all_52_3) = e2
% 232.25/43.39    (4)   ~ (e2 = e0)
% 232.25/43.39    (5)  op(e0, e0) = e0
% 232.25/43.39    (6)  op(e3, e2) = e0
% 232.25/43.39  
% 232.25/43.39  Begin of proof
% 232.25/43.39  | 
% 232.25/43.39  | GROUND_INST: instantiating (1) with e0, all_52_3, e2, e3, simplifying with
% 232.25/43.39  |              (2), (6) gives:
% 232.25/43.39  |   (7)  all_52_3 = e0
% 232.25/43.39  | 
% 232.25/43.39  | REDUCE: (3), (7) imply:
% 232.25/43.39  |   (8)  op(e0, e0) = e2
% 232.25/43.39  | 
% 232.25/43.39  | GROUND_INST: instantiating (1) with e0, e2, e0, e0, simplifying with (5), (8)
% 232.25/43.39  |              gives:
% 232.25/43.39  |   (9)  e2 = e0
% 232.25/43.39  | 
% 232.25/43.39  | REDUCE: (4), (9) imply:
% 232.25/43.39  |   (10)  $false
% 232.25/43.39  | 
% 232.25/43.39  | CLOSE: (10) is inconsistent.
% 232.25/43.39  | 
% 232.25/43.39  End of proof
% 232.25/43.39  
% 232.25/43.39  Sub-proof #2400 shows that the following formulas are inconsistent:
% 232.25/43.39  ----------------------------------------------------------------
% 232.25/43.39    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.39    (2)  all_57_9 = e1
% 232.25/43.39    (3)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 232.25/43.39         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 232.25/43.39    (4)   ~ (e3 = e2)
% 232.25/43.39    (5)   ~ (e3 = e0)
% 232.25/43.39    (6)  all_57_1 = e0
% 232.25/43.39    (7)  op(e3, e3) = e0
% 232.25/43.39    (8)   ~ (e2 = e0)
% 232.25/43.39    (9)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 232.25/43.39         (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 232.25/43.39    (10)   ~ (all_53_12 = e3)
% 232.25/43.39    (11)   ~ (e2 = e1)
% 232.25/43.39    (12)  op(e3, e0) = all_53_12
% 232.25/43.39  
% 232.25/43.39  Begin of proof
% 232.25/43.39  | 
% 232.25/43.39  | BETA: splitting (9) gives:
% 232.25/43.39  | 
% 232.25/43.39  | Case 1:
% 232.25/43.39  | | 
% 232.25/43.39  | |   (13)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) =
% 232.25/43.39  | |           e3)
% 232.25/43.39  | | 
% 232.25/43.39  | | REF_CLOSE: (1), (5), (6), (7), (13) are inconsistent by sub-proof #2404.
% 232.25/43.39  | | 
% 232.25/43.39  | Case 2:
% 232.25/43.39  | | 
% 232.25/43.39  | |   (14)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) =
% 232.25/43.39  | |           e3)
% 232.25/43.39  | | 
% 232.25/43.39  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (10), (11), (12), (14) are
% 232.25/43.39  | |            inconsistent by sub-proof #2401.
% 232.25/43.39  | | 
% 232.25/43.39  | End of split
% 232.25/43.39  | 
% 232.25/43.39  End of proof
% 232.25/43.39  
% 232.25/43.39  Sub-proof #2401 shows that the following formulas are inconsistent:
% 232.25/43.39  ----------------------------------------------------------------
% 232.25/43.39    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.39    (2)  all_57_9 = e1
% 232.25/43.39    (3)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 232.25/43.39         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 232.25/43.39    (4)   ~ (e3 = e2)
% 232.25/43.39    (5)  all_57_1 = e0
% 232.25/43.39    (6)  op(e3, e3) = e0
% 232.25/43.39    (7)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 232.25/43.39    (8)   ~ (e2 = e0)
% 232.25/43.39    (9)   ~ (all_53_12 = e3)
% 232.25/43.39    (10)   ~ (e2 = e1)
% 232.25/43.39    (11)  op(e3, e0) = all_53_12
% 232.25/43.39  
% 232.25/43.39  Begin of proof
% 232.25/43.39  | 
% 232.25/43.39  | BETA: splitting (7) gives:
% 232.25/43.39  | 
% 232.25/43.39  | Case 1:
% 232.25/43.39  | | 
% 232.25/43.39  | |   (12)  all_57_4 = e3 & op(e3, e1) = e3
% 232.25/43.39  | | 
% 232.25/43.39  | | ALPHA: (12) implies:
% 232.25/43.39  | |   (13)  all_57_4 = e3
% 232.25/43.39  | | 
% 232.25/43.39  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (10), (13) are inconsistent by
% 232.25/43.39  | |            sub-proof #2402.
% 232.25/43.39  | | 
% 232.25/43.39  | Case 2:
% 232.25/43.39  | | 
% 232.25/43.39  | |   (14)  all_57_9 = e3 & op(e3, e0) = e3
% 232.25/43.39  | | 
% 232.25/43.39  | | ALPHA: (14) implies:
% 232.25/43.39  | |   (15)  op(e3, e0) = e3
% 232.25/43.39  | | 
% 232.25/43.39  | | REF_CLOSE: (1), (9), (11), (15) are inconsistent by sub-proof #2458.
% 232.25/43.39  | | 
% 232.25/43.39  | End of split
% 232.25/43.39  | 
% 232.25/43.39  End of proof
% 232.25/43.39  
% 232.25/43.39  Sub-proof #2402 shows that the following formulas are inconsistent:
% 232.25/43.39  ----------------------------------------------------------------
% 232.25/43.39    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.39    (2)  all_57_9 = e1
% 232.25/43.39    (3)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 232.25/43.39         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 232.25/43.39    (4)  all_57_4 = e3
% 232.25/43.39    (5)   ~ (e3 = e2)
% 232.25/43.39    (6)  all_57_1 = e0
% 232.25/43.39    (7)  op(e3, e3) = e0
% 232.25/43.39    (8)   ~ (e2 = e0)
% 232.25/43.39    (9)   ~ (e2 = e1)
% 232.25/43.39  
% 232.25/43.39  Begin of proof
% 232.25/43.39  | 
% 232.25/43.39  | BETA: splitting (3) gives:
% 232.25/43.39  | 
% 232.25/43.39  | Case 1:
% 232.25/43.39  | | 
% 232.25/43.39  | |   (10)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) =
% 232.25/43.39  | |           e2)
% 232.25/43.39  | | 
% 232.25/43.39  | | BETA: splitting (10) gives:
% 232.25/43.39  | | 
% 232.25/43.39  | | Case 1:
% 232.25/43.39  | | | 
% 232.25/43.39  | | |   (11)  all_57_0 = e2 & op(e3, e3) = e2
% 232.25/43.39  | | | 
% 232.25/43.39  | | | ALPHA: (11) implies:
% 232.25/43.39  | | |   (12)  op(e3, e3) = e2
% 232.25/43.39  | | | 
% 232.25/43.39  | | | REF_CLOSE: (1), (7), (8), (12) are inconsistent by sub-proof #2403.
% 232.25/43.39  | | | 
% 232.25/43.39  | | Case 2:
% 232.25/43.39  | | | 
% 232.25/43.39  | | |   (13)  all_57_1 = e2 & op(e3, e2) = e2
% 232.25/43.39  | | | 
% 232.25/43.39  | | | REF_CLOSE: (6), (8), (13) are inconsistent by sub-proof #2483.
% 232.25/43.39  | | | 
% 232.25/43.39  | | End of split
% 232.25/43.39  | | 
% 232.25/43.39  | Case 2:
% 232.25/43.39  | | 
% 232.25/43.39  | |   (14)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) =
% 232.25/43.39  | |           e2)
% 232.25/43.39  | | 
% 232.25/43.39  | | BETA: splitting (14) gives:
% 232.25/43.39  | | 
% 232.25/43.39  | | Case 1:
% 232.25/43.39  | | | 
% 232.25/43.39  | | |   (15)  all_57_4 = e2 & op(e3, e1) = e2
% 232.25/43.39  | | | 
% 232.25/43.39  | | | REF_CLOSE: (4), (5), (15) are inconsistent by sub-proof #2487.
% 232.25/43.39  | | | 
% 232.25/43.39  | | Case 2:
% 232.25/43.39  | | | 
% 232.25/43.39  | | |   (16)  all_57_9 = e2 & op(e3, e0) = e2
% 232.25/43.39  | | | 
% 232.25/43.39  | | | ALPHA: (16) implies:
% 232.25/43.39  | | |   (17)  all_57_9 = e2
% 232.25/43.39  | | | 
% 232.25/43.39  | | | REF_CLOSE: (2), (9), (17) are inconsistent by sub-proof #2444.
% 232.25/43.39  | | | 
% 232.25/43.39  | | End of split
% 232.25/43.39  | | 
% 232.25/43.39  | End of split
% 232.25/43.39  | 
% 232.25/43.39  End of proof
% 232.25/43.39  
% 232.25/43.39  Sub-proof #2403 shows that the following formulas are inconsistent:
% 232.25/43.39  ----------------------------------------------------------------
% 232.25/43.39    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.39    (2)  op(e3, e3) = e2
% 232.25/43.39    (3)  op(e3, e3) = e0
% 232.25/43.39    (4)   ~ (e2 = e0)
% 232.25/43.39  
% 232.25/43.39  Begin of proof
% 232.25/43.39  | 
% 232.25/43.39  | GROUND_INST: instantiating (1) with e0, e2, e3, e3, simplifying with (2), (3)
% 232.25/43.39  |              gives:
% 232.25/43.39  |   (5)  e2 = e0
% 232.25/43.39  | 
% 232.25/43.39  | REDUCE: (4), (5) imply:
% 232.25/43.39  |   (6)  $false
% 232.25/43.39  | 
% 232.25/43.39  | CLOSE: (6) is inconsistent.
% 232.25/43.39  | 
% 232.25/43.39  End of proof
% 232.25/43.39  
% 232.25/43.39  Sub-proof #2404 shows that the following formulas are inconsistent:
% 232.25/43.39  ----------------------------------------------------------------
% 232.25/43.39    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.39    (2)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3)
% 232.25/43.39    (3)   ~ (e3 = e0)
% 232.25/43.39    (4)  all_57_1 = e0
% 232.25/43.39    (5)  op(e3, e3) = e0
% 232.25/43.39  
% 232.25/43.39  Begin of proof
% 232.25/43.39  | 
% 232.25/43.39  | BETA: splitting (2) gives:
% 232.25/43.39  | 
% 232.25/43.39  | Case 1:
% 232.25/43.39  | | 
% 232.25/43.39  | |   (6)  all_57_0 = e3 & op(e3, e3) = e3
% 232.25/43.39  | | 
% 232.25/43.39  | | ALPHA: (6) implies:
% 232.25/43.39  | |   (7)  op(e3, e3) = e3
% 232.25/43.39  | | 
% 232.25/43.39  | | REF_CLOSE: (1), (3), (5), (7) are inconsistent by sub-proof #2494.
% 232.25/43.39  | | 
% 232.25/43.39  | Case 2:
% 232.25/43.39  | | 
% 232.25/43.39  | |   (8)  all_57_1 = e3 & op(e3, e2) = e3
% 232.25/43.39  | | 
% 232.25/43.39  | | REF_CLOSE: (3), (4), (8) are inconsistent by sub-proof #2405.
% 232.25/43.39  | | 
% 232.25/43.39  | End of split
% 232.25/43.39  | 
% 232.25/43.39  End of proof
% 232.25/43.39  
% 232.25/43.39  Sub-proof #2405 shows that the following formulas are inconsistent:
% 232.25/43.39  ----------------------------------------------------------------
% 232.25/43.39    (1)  all_57_1 = e3 & op(e3, e2) = e3
% 232.25/43.39    (2)  all_57_1 = e0
% 232.25/43.39    (3)   ~ (e3 = e0)
% 232.25/43.39  
% 232.25/43.39  Begin of proof
% 232.25/43.39  | 
% 232.25/43.39  | ALPHA: (1) implies:
% 232.25/43.39  |   (4)  all_57_1 = e3
% 232.25/43.39  | 
% 232.25/43.39  | COMBINE_EQS: (2), (4) imply:
% 232.25/43.39  |   (5)  e3 = e0
% 232.25/43.39  | 
% 232.25/43.39  | SIMP: (5) implies:
% 232.25/43.39  |   (6)  e3 = e0
% 232.25/43.39  | 
% 232.25/43.39  | REDUCE: (3), (6) imply:
% 232.25/43.39  |   (7)  $false
% 232.25/43.39  | 
% 232.25/43.39  | CLOSE: (7) is inconsistent.
% 232.25/43.39  | 
% 232.25/43.39  End of proof
% 232.25/43.39  
% 232.25/43.39  Sub-proof #2406 shows that the following formulas are inconsistent:
% 232.25/43.39  ----------------------------------------------------------------
% 232.25/43.39    (1)  all_55_8 = all_53_2
% 232.25/43.39    (2)  all_55_8 = e2
% 232.25/43.39    (3)   ~ (all_53_2 = e2)
% 232.25/43.39  
% 232.25/43.39  Begin of proof
% 232.25/43.39  | 
% 232.25/43.39  | COMBINE_EQS: (1), (2) imply:
% 232.25/43.39  |   (4)  all_53_2 = e2
% 232.25/43.39  | 
% 232.25/43.39  | SIMP: (4) implies:
% 232.25/43.39  |   (5)  all_53_2 = e2
% 232.25/43.39  | 
% 232.25/43.39  | REDUCE: (3), (5) imply:
% 232.25/43.39  |   (6)  $false
% 232.25/43.39  | 
% 232.25/43.39  | CLOSE: (6) is inconsistent.
% 232.25/43.39  | 
% 232.25/43.39  End of proof
% 232.25/43.39  
% 232.25/43.39  Sub-proof #2407 shows that the following formulas are inconsistent:
% 232.25/43.39  ----------------------------------------------------------------
% 232.25/43.39    (1)   ~ (e3 = e1)
% 232.25/43.39    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.39    (3)   ~ (all_6_2 = e3)
% 232.25/43.39    (4)  op(e1, e1) = all_6_2
% 232.25/43.39    (5)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 232.25/43.39         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 232.25/43.39    (6)   ~ (e3 = e2)
% 232.25/43.39    (7)   ~ (e3 = e0)
% 232.25/43.39    (8)  all_57_4 = e1
% 232.25/43.39    (9)  op(e1, e1) = e1
% 232.25/43.39    (10)   ~ (e2 = e0)
% 232.25/43.39    (11)   ~ (e1 = e0)
% 232.25/43.39    (12)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 232.25/43.39          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 232.25/43.39    (13)   ~ (e2 = e1)
% 232.25/43.39    (14)   ~ (all_6_2 = e0)
% 232.25/43.39    (15)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 232.25/43.39          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 232.25/43.39  
% 232.25/43.39  Begin of proof
% 232.25/43.39  | 
% 232.25/43.39  | BETA: splitting (15) gives:
% 232.25/43.39  | 
% 232.25/43.39  | Case 1:
% 232.25/43.39  | | 
% 232.25/43.39  | |   (16)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) =
% 232.25/43.39  | |           e2)
% 232.25/43.39  | | 
% 232.25/43.39  | | BETA: splitting (16) gives:
% 232.25/43.39  | | 
% 232.25/43.39  | | Case 1:
% 232.25/43.39  | | | 
% 232.25/43.39  | | |   (17)  all_57_4 = e2 & op(e3, e1) = e2
% 232.25/43.39  | | | 
% 232.25/43.39  | | | ALPHA: (17) implies:
% 232.25/43.39  | | |   (18)  all_57_4 = e2
% 232.25/43.39  | | | 
% 232.25/43.39  | | | REF_CLOSE: (8), (13), (18) are inconsistent by sub-proof #2430.
% 232.25/43.39  | | | 
% 232.25/43.39  | | Case 2:
% 232.25/43.39  | | | 
% 232.25/43.39  | | |   (19)  all_57_5 = e2 & op(e2, e1) = e2
% 232.25/43.39  | | | 
% 232.25/43.39  | | | ALPHA: (19) implies:
% 232.25/43.39  | | |   (20)  all_57_5 = e2
% 232.25/43.39  | | | 
% 232.25/43.39  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 232.25/43.39  | | |            (13), (15), (20) are inconsistent by sub-proof #2416.
% 232.25/43.39  | | | 
% 232.25/43.39  | | End of split
% 232.25/43.39  | | 
% 232.25/43.39  | Case 2:
% 232.25/43.39  | | 
% 232.25/43.39  | |   (21)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) =
% 232.25/43.39  | |           e2)
% 232.25/43.39  | | 
% 232.25/43.39  | | BETA: splitting (21) gives:
% 232.25/43.39  | | 
% 232.25/43.39  | | Case 1:
% 232.25/43.39  | | | 
% 232.25/43.39  | | |   (22)  all_57_8 = e2 & op(e1, e1) = e2
% 232.25/43.39  | | | 
% 232.25/43.39  | | | ALPHA: (22) implies:
% 232.25/43.39  | | |   (23)  op(e1, e1) = e2
% 232.25/43.39  | | | 
% 232.25/43.39  | | | REF_CLOSE: (2), (9), (13), (23) are inconsistent by sub-proof #2423.
% 232.25/43.39  | | | 
% 232.25/43.39  | | Case 2:
% 232.25/43.39  | | | 
% 232.25/43.39  | | |   (24)  all_57_14 = e2 & op(e0, e1) = e2
% 232.25/43.39  | | | 
% 232.25/43.39  | | | ALPHA: (24) implies:
% 232.25/43.39  | | |   (25)  all_57_14 = e2
% 232.25/43.39  | | | 
% 232.25/43.39  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (14),
% 232.25/43.39  | | |            (25) are inconsistent by sub-proof #2408.
% 232.25/43.39  | | | 
% 232.25/43.39  | | End of split
% 232.25/43.39  | | 
% 232.25/43.39  | End of split
% 232.25/43.39  | 
% 232.25/43.39  End of proof
% 232.25/43.39  
% 232.25/43.39  Sub-proof #2408 shows that the following formulas are inconsistent:
% 232.25/43.39  ----------------------------------------------------------------
% 232.25/43.39    (1)   ~ (e3 = e1)
% 232.25/43.39    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.39    (3)   ~ (all_6_2 = e3)
% 232.25/43.39    (4)  op(e1, e1) = all_6_2
% 232.25/43.39    (5)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 232.25/43.39         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 232.25/43.39    (6)   ~ (e3 = e2)
% 232.25/43.39    (7)   ~ (e3 = e0)
% 232.25/43.39    (8)  all_57_4 = e1
% 232.25/43.39    (9)   ~ (e2 = e0)
% 232.25/43.39    (10)   ~ (e1 = e0)
% 232.25/43.39    (11)  all_57_14 = e2
% 232.25/43.39    (12)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 232.25/43.39          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 232.25/43.39    (13)   ~ (all_6_2 = e0)
% 232.25/43.39  
% 232.25/43.39  Begin of proof
% 232.25/43.39  | 
% 232.25/43.39  | BETA: splitting (12) gives:
% 232.25/43.39  | 
% 232.25/43.39  | Case 1:
% 232.25/43.39  | | 
% 232.25/43.39  | |   (14)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) =
% 232.25/43.39  | |           e3)
% 232.25/43.39  | | 
% 232.25/43.39  | | BETA: splitting (14) gives:
% 232.25/43.39  | | 
% 232.25/43.39  | | Case 1:
% 232.25/43.39  | | | 
% 232.25/43.39  | | |   (15)  all_57_4 = e3 & op(e3, e1) = e3
% 232.25/43.39  | | | 
% 232.25/43.39  | | | REF_CLOSE: (1), (8), (15) are inconsistent by sub-proof #2415.
% 232.25/43.39  | | | 
% 232.25/43.39  | | Case 2:
% 232.25/43.39  | | | 
% 232.25/43.39  | | |   (16)  all_57_5 = e3 & op(e2, e1) = e3
% 232.25/43.39  | | | 
% 232.25/43.39  | | | ALPHA: (16) implies:
% 232.25/43.39  | | |   (17)  all_57_5 = e3
% 232.25/43.39  | | | 
% 232.25/43.39  | | | BETA: splitting (5) gives:
% 232.25/43.39  | | | 
% 232.25/43.39  | | | Case 1:
% 232.25/43.39  | | | | 
% 232.25/43.39  | | | |   (18)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1)
% 232.25/43.39  | | | |           = e0)
% 232.25/43.39  | | | | 
% 232.25/43.39  | | | | REF_CLOSE: (7), (8), (10), (17), (18) are inconsistent by sub-proof
% 232.25/43.39  | | | |            #2413.
% 232.25/43.39  | | | | 
% 232.25/43.39  | | | Case 2:
% 232.25/43.39  | | | | 
% 232.25/43.39  | | | |   (19)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1)
% 232.25/43.39  | | | |           = e0)
% 232.25/43.39  | | | | 
% 232.25/43.39  | | | | REF_CLOSE: (2), (4), (9), (11), (13), (19) are inconsistent by sub-proof
% 232.25/43.39  | | | |            #2411.
% 232.25/43.39  | | | | 
% 232.25/43.39  | | | End of split
% 232.25/43.39  | | | 
% 232.25/43.39  | | End of split
% 232.25/43.39  | | 
% 232.25/43.39  | Case 2:
% 232.25/43.39  | | 
% 232.25/43.39  | |   (20)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) =
% 232.25/43.39  | |           e3)
% 232.25/43.39  | | 
% 232.25/43.39  | | REF_CLOSE: (2), (3), (4), (6), (11), (20) are inconsistent by sub-proof
% 232.25/43.39  | |            #2409.
% 232.25/43.39  | | 
% 232.25/43.39  | End of split
% 232.25/43.39  | 
% 232.25/43.39  End of proof
% 232.25/43.39  
% 232.25/43.39  Sub-proof #2409 shows that the following formulas are inconsistent:
% 232.25/43.39  ----------------------------------------------------------------
% 232.25/43.39    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.39    (2)   ~ (all_6_2 = e3)
% 232.25/43.39    (3)  op(e1, e1) = all_6_2
% 232.25/43.39    (4)   ~ (e3 = e2)
% 232.25/43.39    (5)  all_57_14 = e2
% 232.25/43.39    (6)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 232.25/43.39  
% 232.25/43.39  Begin of proof
% 232.25/43.39  | 
% 232.25/43.39  | BETA: splitting (6) gives:
% 232.25/43.39  | 
% 232.25/43.39  | Case 1:
% 232.25/43.39  | | 
% 232.25/43.39  | |   (7)  all_57_8 = e3 & op(e1, e1) = e3
% 232.25/43.39  | | 
% 232.25/43.39  | | ALPHA: (7) implies:
% 232.25/43.39  | |   (8)  op(e1, e1) = e3
% 232.25/43.39  | | 
% 232.25/43.39  | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #2468.
% 232.25/43.39  | | 
% 232.25/43.39  | Case 2:
% 232.25/43.39  | | 
% 232.25/43.39  | |   (9)  all_57_14 = e3 & op(e0, e1) = e3
% 232.25/43.39  | | 
% 232.25/43.39  | | ALPHA: (9) implies:
% 232.25/43.39  | |   (10)  all_57_14 = e3
% 232.25/43.39  | | 
% 232.25/43.39  | | REF_CLOSE: (4), (5), (10) are inconsistent by sub-proof #2410.
% 232.25/43.39  | | 
% 232.25/43.39  | End of split
% 232.25/43.39  | 
% 232.25/43.39  End of proof
% 232.25/43.39  
% 232.25/43.39  Sub-proof #2410 shows that the following formulas are inconsistent:
% 232.25/43.39  ----------------------------------------------------------------
% 232.25/43.39    (1)  all_57_14 = e3
% 232.25/43.39    (2)  all_57_14 = e2
% 232.25/43.39    (3)   ~ (e3 = e2)
% 232.25/43.39  
% 232.25/43.39  Begin of proof
% 232.25/43.39  | 
% 232.25/43.39  | COMBINE_EQS: (1), (2) imply:
% 232.25/43.39  |   (4)  e3 = e2
% 232.25/43.39  | 
% 232.25/43.39  | SIMP: (4) implies:
% 232.25/43.39  |   (5)  e3 = e2
% 232.25/43.39  | 
% 232.25/43.39  | REDUCE: (3), (5) imply:
% 232.25/43.39  |   (6)  $false
% 232.25/43.39  | 
% 232.25/43.39  | CLOSE: (6) is inconsistent.
% 232.25/43.39  | 
% 232.25/43.39  End of proof
% 232.25/43.39  
% 232.25/43.39  Sub-proof #2411 shows that the following formulas are inconsistent:
% 232.25/43.39  ----------------------------------------------------------------
% 232.25/43.39    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.39    (2)  op(e1, e1) = all_6_2
% 232.25/43.39    (3)   ~ (e2 = e0)
% 232.25/43.39    (4)  all_57_14 = e2
% 232.25/43.39    (5)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 232.25/43.39    (6)   ~ (all_6_2 = e0)
% 232.25/43.39  
% 232.25/43.39  Begin of proof
% 232.25/43.39  | 
% 232.25/43.39  | BETA: splitting (5) gives:
% 232.25/43.39  | 
% 232.25/43.39  | Case 1:
% 232.25/43.39  | | 
% 232.25/43.39  | |   (7)  all_57_8 = e0 & op(e1, e1) = e0
% 232.25/43.39  | | 
% 232.25/43.39  | | REF_CLOSE: (1), (2), (6), (7) are inconsistent by sub-proof #2412.
% 232.25/43.39  | | 
% 232.25/43.39  | Case 2:
% 232.25/43.39  | | 
% 232.25/43.39  | |   (8)  all_57_14 = e0 & op(e0, e1) = e0
% 232.25/43.39  | | 
% 232.25/43.39  | | ALPHA: (8) implies:
% 232.25/43.39  | |   (9)  all_57_14 = e0
% 232.25/43.39  | | 
% 232.25/43.39  | | REF_CLOSE: (3), (4), (9) are inconsistent by sub-proof #2422.
% 232.25/43.39  | | 
% 232.25/43.39  | End of split
% 232.25/43.39  | 
% 232.25/43.39  End of proof
% 232.25/43.39  
% 232.25/43.39  Sub-proof #2412 shows that the following formulas are inconsistent:
% 232.25/43.39  ----------------------------------------------------------------
% 232.25/43.39    (1)  all_57_8 = e0 & op(e1, e1) = e0
% 232.25/43.39    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.39    (3)  op(e1, e1) = all_6_2
% 232.25/43.39    (4)   ~ (all_6_2 = e0)
% 232.25/43.39  
% 232.25/43.39  Begin of proof
% 232.25/43.39  | 
% 232.25/43.39  | ALPHA: (1) implies:
% 232.25/43.39  |   (5)  op(e1, e1) = e0
% 232.25/43.39  | 
% 232.25/43.39  | GROUND_INST: instantiating (2) with all_6_2, e0, e1, e1, simplifying with (3),
% 232.25/43.39  |              (5) gives:
% 232.25/43.39  |   (6)  all_6_2 = e0
% 232.25/43.39  | 
% 232.25/43.39  | REDUCE: (4), (6) imply:
% 232.25/43.39  |   (7)  $false
% 232.25/43.39  | 
% 232.25/43.39  | CLOSE: (7) is inconsistent.
% 232.25/43.39  | 
% 232.25/43.39  End of proof
% 232.25/43.39  
% 232.25/43.39  Sub-proof #2413 shows that the following formulas are inconsistent:
% 232.25/43.39  ----------------------------------------------------------------
% 232.25/43.39    (1)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0)
% 232.25/43.39    (2)   ~ (e3 = e0)
% 232.25/43.39    (3)  all_57_4 = e1
% 232.25/43.39    (4)  all_57_5 = e3
% 232.25/43.39    (5)   ~ (e1 = e0)
% 232.25/43.39  
% 232.25/43.39  Begin of proof
% 232.25/43.39  | 
% 232.25/43.39  | BETA: splitting (1) gives:
% 232.25/43.39  | 
% 232.25/43.39  | Case 1:
% 232.25/43.39  | | 
% 232.25/43.39  | |   (6)  all_57_4 = e0 & op(e3, e1) = e0
% 232.25/43.39  | | 
% 232.25/43.39  | | ALPHA: (6) implies:
% 232.25/43.39  | |   (7)  all_57_4 = e0
% 232.25/43.39  | | 
% 232.25/43.39  | | REF_CLOSE: (3), (5), (7) are inconsistent by sub-proof #2438.
% 232.25/43.39  | | 
% 232.25/43.39  | Case 2:
% 232.25/43.39  | | 
% 232.25/43.39  | |   (8)  all_57_5 = e0 & op(e2, e1) = e0
% 232.25/43.39  | | 
% 232.25/43.39  | | REF_CLOSE: (2), (4), (8) are inconsistent by sub-proof #2414.
% 232.25/43.39  | | 
% 232.25/43.39  | End of split
% 232.25/43.39  | 
% 232.25/43.39  End of proof
% 232.25/43.39  
% 232.25/43.39  Sub-proof #2414 shows that the following formulas are inconsistent:
% 232.25/43.39  ----------------------------------------------------------------
% 232.25/43.39    (1)  all_57_5 = e0 & op(e2, e1) = e0
% 232.25/43.39    (2)  all_57_5 = e3
% 232.25/43.39    (3)   ~ (e3 = e0)
% 232.25/43.39  
% 232.25/43.39  Begin of proof
% 232.25/43.39  | 
% 232.25/43.39  | ALPHA: (1) implies:
% 232.25/43.39  |   (4)  all_57_5 = e0
% 232.25/43.39  | 
% 232.25/43.39  | COMBINE_EQS: (2), (4) imply:
% 232.25/43.39  |   (5)  e3 = e0
% 232.25/43.39  | 
% 232.25/43.39  | REDUCE: (3), (5) imply:
% 232.25/43.39  |   (6)  $false
% 232.25/43.39  | 
% 232.25/43.39  | CLOSE: (6) is inconsistent.
% 232.25/43.39  | 
% 232.25/43.39  End of proof
% 232.25/43.39  
% 232.25/43.39  Sub-proof #2415 shows that the following formulas are inconsistent:
% 232.25/43.39  ----------------------------------------------------------------
% 232.25/43.39    (1)  all_57_4 = e3 & op(e3, e1) = e3
% 232.25/43.39    (2)  all_57_4 = e1
% 232.25/43.39    (3)   ~ (e3 = e1)
% 232.25/43.39  
% 232.25/43.39  Begin of proof
% 232.25/43.39  | 
% 232.25/43.39  | ALPHA: (1) implies:
% 232.25/43.39  |   (4)  all_57_4 = e3
% 232.25/43.39  | 
% 232.25/43.39  | COMBINE_EQS: (2), (4) imply:
% 232.25/43.39  |   (5)  e3 = e1
% 232.25/43.39  | 
% 232.25/43.39  | REDUCE: (3), (5) imply:
% 232.25/43.39  |   (6)  $false
% 232.25/43.39  | 
% 232.25/43.39  | CLOSE: (6) is inconsistent.
% 232.25/43.39  | 
% 232.25/43.39  End of proof
% 232.25/43.39  
% 232.25/43.39  Sub-proof #2416 shows that the following formulas are inconsistent:
% 232.25/43.39  ----------------------------------------------------------------
% 232.25/43.39    (1)   ~ (e3 = e1)
% 232.25/43.39    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.39    (3)   ~ (all_6_2 = e3)
% 232.25/43.39    (4)  op(e1, e1) = all_6_2
% 232.25/43.39    (5)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 232.25/43.39         (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 232.25/43.39    (6)   ~ (e3 = e2)
% 232.25/43.39    (7)   ~ (e3 = e0)
% 232.25/43.39    (8)  all_57_4 = e1
% 232.25/43.39    (9)  op(e1, e1) = e1
% 232.25/43.39    (10)   ~ (e2 = e0)
% 232.25/43.39    (11)   ~ (e1 = e0)
% 232.25/43.39    (12)  all_57_5 = e2
% 232.25/43.39    (13)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 232.25/43.39          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 232.25/43.39    (14)   ~ (e2 = e1)
% 232.25/43.39    (15)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 232.25/43.39          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 232.25/43.39  
% 232.25/43.39  Begin of proof
% 232.25/43.39  | 
% 232.25/43.39  | BETA: splitting (5) gives:
% 232.25/43.39  | 
% 232.25/43.39  | Case 1:
% 232.25/43.39  | | 
% 232.25/43.39  | |   (16)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) =
% 232.25/43.39  | |           e0)
% 232.25/43.39  | | 
% 232.25/43.39  | | BETA: splitting (16) gives:
% 232.25/43.39  | | 
% 232.25/43.39  | | Case 1:
% 232.25/43.39  | | | 
% 232.25/43.39  | | |   (17)  all_57_4 = e0 & op(e3, e1) = e0
% 232.25/43.39  | | | 
% 232.25/43.39  | | | REF_CLOSE: (8), (11), (17) are inconsistent by sub-proof #2429.
% 232.25/43.39  | | | 
% 232.25/43.39  | | Case 2:
% 232.25/43.39  | | | 
% 232.25/43.39  | | |   (18)  all_57_5 = e0 & op(e2, e1) = e0
% 232.25/43.39  | | | 
% 232.25/43.39  | | | REF_CLOSE: (10), (12), (18) are inconsistent by sub-proof #2428.
% 232.25/43.39  | | | 
% 232.25/43.39  | | End of split
% 232.25/43.39  | | 
% 232.25/43.39  | Case 2:
% 232.25/43.39  | | 
% 232.25/43.39  | |   (19)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 232.25/43.39  | |           e0)
% 232.25/43.39  | | 
% 232.25/43.39  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (13), (14),
% 232.25/43.39  | |            (15), (19) are inconsistent by sub-proof #2417.
% 232.25/43.39  | | 
% 232.25/43.39  | End of split
% 232.25/43.39  | 
% 232.25/43.39  End of proof
% 232.25/43.39  
% 232.25/43.39  Sub-proof #2417 shows that the following formulas are inconsistent:
% 232.25/43.39  ----------------------------------------------------------------
% 232.25/43.39    (1)   ~ (e3 = e1)
% 232.25/43.39    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.39    (3)   ~ (all_6_2 = e3)
% 232.25/43.39    (4)  op(e1, e1) = all_6_2
% 232.25/43.39    (5)   ~ (e3 = e2)
% 232.25/43.39    (6)   ~ (e3 = e0)
% 232.25/43.39    (7)  all_57_4 = e1
% 232.25/43.39    (8)  op(e1, e1) = e1
% 232.25/43.39    (9)   ~ (e2 = e0)
% 232.25/43.39    (10)   ~ (e1 = e0)
% 232.25/43.39    (11)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 232.25/43.39          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 232.25/43.39    (12)  (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 232.25/43.39    (13)   ~ (e2 = e1)
% 232.25/43.39    (14)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 232.25/43.39          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 232.25/43.39  
% 232.25/43.39  Begin of proof
% 232.25/43.39  | 
% 232.25/43.39  | BETA: splitting (12) gives:
% 232.25/43.39  | 
% 232.25/43.39  | Case 1:
% 232.25/43.39  | | 
% 232.25/43.39  | |   (15)  all_57_8 = e0 & op(e1, e1) = e0
% 232.25/43.39  | | 
% 232.25/43.39  | | ALPHA: (15) implies:
% 232.25/43.39  | |   (16)  op(e1, e1) = e0
% 232.25/43.39  | | 
% 232.25/43.39  | | REF_CLOSE: (2), (8), (10), (16) are inconsistent by sub-proof #2427.
% 232.25/43.39  | | 
% 232.25/43.39  | Case 2:
% 232.25/43.39  | | 
% 232.25/43.39  | |   (17)  all_57_14 = e0 & op(e0, e1) = e0
% 232.25/43.39  | | 
% 232.25/43.39  | | ALPHA: (17) implies:
% 232.25/43.39  | |   (18)  all_57_14 = e0
% 232.25/43.39  | | 
% 232.25/43.39  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (13), (14),
% 232.25/43.39  | |            (18) are inconsistent by sub-proof #2418.
% 232.25/43.39  | | 
% 232.25/43.39  | End of split
% 232.25/43.39  | 
% 232.25/43.39  End of proof
% 232.25/43.39  
% 232.25/43.39  Sub-proof #2418 shows that the following formulas are inconsistent:
% 232.25/43.39  ----------------------------------------------------------------
% 232.25/43.39    (1)   ~ (e3 = e1)
% 232.25/43.39    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.25/43.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.25/43.39    (3)   ~ (all_6_2 = e3)
% 232.25/43.39    (4)  op(e1, e1) = all_6_2
% 232.25/43.39    (5)   ~ (e3 = e2)
% 232.25/43.39    (6)   ~ (e3 = e0)
% 232.25/43.39    (7)  all_57_4 = e1
% 232.25/43.39    (8)  op(e1, e1) = e1
% 232.25/43.39    (9)   ~ (e2 = e0)
% 232.25/43.39    (10)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 232.25/43.39          (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 232.25/43.39    (11)   ~ (e2 = e1)
% 232.25/43.39    (12)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 232.25/43.39          (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 232.25/43.39    (13)  all_57_14 = e0
% 232.25/43.39  
% 232.25/43.39  Begin of proof
% 232.25/43.39  | 
% 232.25/43.39  | BETA: splitting (10) gives:
% 232.25/43.39  | 
% 232.25/43.39  | Case 1:
% 232.25/43.39  | | 
% 232.25/43.39  | |   (14)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) =
% 232.25/43.39  | |           e3)
% 232.25/43.39  | | 
% 232.25/43.39  | | BETA: splitting (14) gives:
% 232.25/43.39  | | 
% 232.25/43.39  | | Case 1:
% 232.25/43.39  | | | 
% 232.25/43.39  | | |   (15)  all_57_4 = e3 & op(e3, e1) = e3
% 232.25/43.39  | | | 
% 232.25/43.39  | | | ALPHA: (15) implies:
% 232.25/43.39  | | |   (16)  all_57_4 = e3
% 232.32/43.39  | | | 
% 232.32/43.39  | | | REF_CLOSE: (1), (7), (16) are inconsistent by sub-proof #2426.
% 232.32/43.39  | | | 
% 232.32/43.39  | | Case 2:
% 232.32/43.39  | | | 
% 232.32/43.39  | | |   (17)  all_57_5 = e3 & op(e2, e1) = e3
% 232.32/43.39  | | | 
% 232.32/43.39  | | | ALPHA: (17) implies:
% 232.32/43.39  | | |   (18)  all_57_5 = e3
% 232.32/43.39  | | | 
% 232.32/43.39  | | | BETA: splitting (12) gives:
% 232.32/43.39  | | | 
% 232.32/43.39  | | | Case 1:
% 232.32/43.39  | | | | 
% 232.32/43.39  | | | |   (19)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1)
% 232.32/43.39  | | | |           = e2)
% 232.32/43.39  | | | | 
% 232.32/43.39  | | | | REF_CLOSE: (5), (7), (11), (18), (19) are inconsistent by sub-proof
% 232.32/43.39  | | | |            #2424.
% 232.32/43.39  | | | | 
% 232.32/43.39  | | | Case 2:
% 232.32/43.39  | | | | 
% 232.32/43.39  | | | |   (20)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1)
% 232.32/43.39  | | | |           = e2)
% 232.32/43.39  | | | | 
% 232.32/43.39  | | | | REF_CLOSE: (2), (8), (9), (11), (13), (20) are inconsistent by sub-proof
% 232.32/43.39  | | | |            #2421.
% 232.32/43.39  | | | | 
% 232.32/43.39  | | | End of split
% 232.32/43.39  | | | 
% 232.32/43.39  | | End of split
% 232.32/43.39  | | 
% 232.32/43.39  | Case 2:
% 232.32/43.39  | | 
% 232.32/43.39  | |   (21)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) =
% 232.32/43.39  | |           e3)
% 232.32/43.39  | | 
% 232.32/43.39  | | REF_CLOSE: (2), (3), (4), (6), (13), (21) are inconsistent by sub-proof
% 232.32/43.39  | |            #2419.
% 232.32/43.39  | | 
% 232.32/43.39  | End of split
% 232.32/43.39  | 
% 232.32/43.39  End of proof
% 232.32/43.39  
% 232.32/43.39  Sub-proof #2419 shows that the following formulas are inconsistent:
% 232.32/43.39  ----------------------------------------------------------------
% 232.32/43.39    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.32/43.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.32/43.39    (2)   ~ (all_6_2 = e3)
% 232.32/43.39    (3)  op(e1, e1) = all_6_2
% 232.32/43.39    (4)   ~ (e3 = e0)
% 232.32/43.39    (5)  all_57_14 = e0
% 232.32/43.39    (6)  (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 232.32/43.39  
% 232.32/43.39  Begin of proof
% 232.32/43.39  | 
% 232.32/43.39  | BETA: splitting (6) gives:
% 232.32/43.39  | 
% 232.32/43.39  | Case 1:
% 232.32/43.39  | | 
% 232.32/43.39  | |   (7)  all_57_8 = e3 & op(e1, e1) = e3
% 232.32/43.39  | | 
% 232.32/43.39  | | ALPHA: (7) implies:
% 232.32/43.39  | |   (8)  op(e1, e1) = e3
% 232.32/43.39  | | 
% 232.32/43.39  | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #2468.
% 232.32/43.39  | | 
% 232.32/43.39  | Case 2:
% 232.32/43.39  | | 
% 232.32/43.39  | |   (9)  all_57_14 = e3 & op(e0, e1) = e3
% 232.32/43.39  | | 
% 232.32/43.39  | | ALPHA: (9) implies:
% 232.32/43.39  | |   (10)  all_57_14 = e3
% 232.32/43.39  | | 
% 232.32/43.39  | | REF_CLOSE: (4), (5), (10) are inconsistent by sub-proof #2420.
% 232.32/43.39  | | 
% 232.32/43.39  | End of split
% 232.32/43.39  | 
% 232.32/43.39  End of proof
% 232.32/43.39  
% 232.32/43.39  Sub-proof #2420 shows that the following formulas are inconsistent:
% 232.32/43.39  ----------------------------------------------------------------
% 232.32/43.39    (1)  all_57_14 = e3
% 232.32/43.39    (2)  all_57_14 = e0
% 232.32/43.39    (3)   ~ (e3 = e0)
% 232.32/43.39  
% 232.32/43.39  Begin of proof
% 232.32/43.39  | 
% 232.32/43.39  | COMBINE_EQS: (1), (2) imply:
% 232.32/43.39  |   (4)  e3 = e0
% 232.32/43.39  | 
% 232.32/43.39  | SIMP: (4) implies:
% 232.32/43.39  |   (5)  e3 = e0
% 232.32/43.39  | 
% 232.32/43.39  | REDUCE: (3), (5) imply:
% 232.32/43.39  |   (6)  $false
% 232.32/43.39  | 
% 232.32/43.39  | CLOSE: (6) is inconsistent.
% 232.32/43.39  | 
% 232.32/43.39  End of proof
% 232.32/43.39  
% 232.32/43.39  Sub-proof #2421 shows that the following formulas are inconsistent:
% 232.32/43.39  ----------------------------------------------------------------
% 232.32/43.39    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.32/43.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.32/43.39    (2)  (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 232.32/43.39    (3)  op(e1, e1) = e1
% 232.32/43.39    (4)   ~ (e2 = e0)
% 232.32/43.39    (5)   ~ (e2 = e1)
% 232.32/43.39    (6)  all_57_14 = e0
% 232.32/43.39  
% 232.32/43.39  Begin of proof
% 232.32/43.39  | 
% 232.32/43.39  | BETA: splitting (2) gives:
% 232.32/43.39  | 
% 232.32/43.39  | Case 1:
% 232.32/43.39  | | 
% 232.32/43.39  | |   (7)  all_57_8 = e2 & op(e1, e1) = e2
% 232.32/43.40  | | 
% 232.32/43.40  | | ALPHA: (7) implies:
% 232.32/43.40  | |   (8)  op(e1, e1) = e2
% 232.32/43.40  | | 
% 232.32/43.40  | | REF_CLOSE: (1), (3), (5), (8) are inconsistent by sub-proof #2423.
% 232.32/43.40  | | 
% 232.32/43.40  | Case 2:
% 232.32/43.40  | | 
% 232.32/43.40  | |   (9)  all_57_14 = e2 & op(e0, e1) = e2
% 232.32/43.40  | | 
% 232.32/43.40  | | ALPHA: (9) implies:
% 232.32/43.40  | |   (10)  all_57_14 = e2
% 232.32/43.40  | | 
% 232.32/43.40  | | REF_CLOSE: (4), (6), (10) are inconsistent by sub-proof #2422.
% 232.32/43.40  | | 
% 232.32/43.40  | End of split
% 232.32/43.40  | 
% 232.32/43.40  End of proof
% 232.32/43.40  
% 232.32/43.40  Sub-proof #2422 shows that the following formulas are inconsistent:
% 232.32/43.40  ----------------------------------------------------------------
% 232.32/43.40    (1)  all_57_14 = e2
% 232.32/43.40    (2)  all_57_14 = e0
% 232.32/43.40    (3)   ~ (e2 = e0)
% 232.32/43.40  
% 232.32/43.40  Begin of proof
% 232.32/43.40  | 
% 232.32/43.40  | COMBINE_EQS: (1), (2) imply:
% 232.32/43.40  |   (4)  e2 = e0
% 232.32/43.40  | 
% 232.32/43.40  | SIMP: (4) implies:
% 232.32/43.40  |   (5)  e2 = e0
% 232.32/43.40  | 
% 232.32/43.40  | REDUCE: (3), (5) imply:
% 232.32/43.40  |   (6)  $false
% 232.32/43.40  | 
% 232.32/43.40  | CLOSE: (6) is inconsistent.
% 232.32/43.40  | 
% 232.32/43.40  End of proof
% 232.32/43.40  
% 232.32/43.40  Sub-proof #2423 shows that the following formulas are inconsistent:
% 232.32/43.40  ----------------------------------------------------------------
% 232.32/43.40    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.32/43.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.32/43.40    (2)  op(e1, e1) = e2
% 232.32/43.40    (3)  op(e1, e1) = e1
% 232.32/43.40    (4)   ~ (e2 = e1)
% 232.32/43.40  
% 232.32/43.40  Begin of proof
% 232.32/43.40  | 
% 232.32/43.40  | GROUND_INST: instantiating (1) with e1, e2, e1, e1, simplifying with (2), (3)
% 232.32/43.40  |              gives:
% 232.32/43.40  |   (5)  e2 = e1
% 232.32/43.40  | 
% 232.32/43.40  | REDUCE: (4), (5) imply:
% 232.32/43.40  |   (6)  $false
% 232.32/43.40  | 
% 232.32/43.40  | CLOSE: (6) is inconsistent.
% 232.32/43.40  | 
% 232.32/43.40  End of proof
% 232.32/43.40  
% 232.32/43.40  Sub-proof #2424 shows that the following formulas are inconsistent:
% 232.32/43.40  ----------------------------------------------------------------
% 232.32/43.40    (1)   ~ (e3 = e2)
% 232.32/43.40    (2)  all_57_4 = e1
% 232.32/43.40    (3)  all_57_5 = e3
% 232.32/43.40    (4)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2)
% 232.32/43.40    (5)   ~ (e2 = e1)
% 232.32/43.40  
% 232.32/43.40  Begin of proof
% 232.32/43.40  | 
% 232.32/43.40  | BETA: splitting (4) gives:
% 232.32/43.40  | 
% 232.32/43.40  | Case 1:
% 232.32/43.40  | | 
% 232.32/43.40  | |   (6)  all_57_4 = e2 & op(e3, e1) = e2
% 232.32/43.40  | | 
% 232.32/43.40  | | ALPHA: (6) implies:
% 232.32/43.40  | |   (7)  all_57_4 = e2
% 232.32/43.40  | | 
% 232.32/43.40  | | REF_CLOSE: (2), (5), (7) are inconsistent by sub-proof #2430.
% 232.32/43.40  | | 
% 232.32/43.40  | Case 2:
% 232.32/43.40  | | 
% 232.32/43.40  | |   (8)  all_57_5 = e2 & op(e2, e1) = e2
% 232.32/43.40  | | 
% 232.32/43.40  | | REF_CLOSE: (1), (3), (8) are inconsistent by sub-proof #2425.
% 232.32/43.40  | | 
% 232.32/43.40  | End of split
% 232.32/43.40  | 
% 232.32/43.40  End of proof
% 232.32/43.40  
% 232.32/43.40  Sub-proof #2425 shows that the following formulas are inconsistent:
% 232.32/43.40  ----------------------------------------------------------------
% 232.32/43.40    (1)  all_57_5 = e2 & op(e2, e1) = e2
% 232.32/43.40    (2)  all_57_5 = e3
% 232.32/43.40    (3)   ~ (e3 = e2)
% 232.32/43.40  
% 232.32/43.40  Begin of proof
% 232.32/43.40  | 
% 232.32/43.40  | ALPHA: (1) implies:
% 232.32/43.40  |   (4)  all_57_5 = e2
% 232.32/43.40  | 
% 232.32/43.40  | COMBINE_EQS: (2), (4) imply:
% 232.32/43.40  |   (5)  e3 = e2
% 232.32/43.40  | 
% 232.32/43.40  | REDUCE: (3), (5) imply:
% 232.32/43.40  |   (6)  $false
% 232.32/43.40  | 
% 232.32/43.40  | CLOSE: (6) is inconsistent.
% 232.32/43.40  | 
% 232.32/43.40  End of proof
% 232.32/43.40  
% 232.32/43.40  Sub-proof #2426 shows that the following formulas are inconsistent:
% 232.32/43.40  ----------------------------------------------------------------
% 232.32/43.40    (1)  all_57_4 = e3
% 232.32/43.40    (2)  all_57_4 = e1
% 232.32/43.40    (3)   ~ (e3 = e1)
% 232.32/43.40  
% 232.32/43.40  Begin of proof
% 232.32/43.40  | 
% 232.32/43.40  | COMBINE_EQS: (1), (2) imply:
% 232.32/43.40  |   (4)  e3 = e1
% 232.32/43.40  | 
% 232.32/43.40  | SIMP: (4) implies:
% 232.32/43.40  |   (5)  e3 = e1
% 232.32/43.40  | 
% 232.32/43.40  | REDUCE: (3), (5) imply:
% 232.32/43.40  |   (6)  $false
% 232.32/43.40  | 
% 232.32/43.40  | CLOSE: (6) is inconsistent.
% 232.32/43.40  | 
% 232.32/43.40  End of proof
% 232.32/43.40  
% 232.32/43.40  Sub-proof #2427 shows that the following formulas are inconsistent:
% 232.32/43.40  ----------------------------------------------------------------
% 232.32/43.40    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.32/43.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.32/43.40    (2)  op(e1, e1) = e1
% 232.32/43.40    (3)  op(e1, e1) = e0
% 232.32/43.40    (4)   ~ (e1 = e0)
% 232.32/43.40  
% 232.32/43.40  Begin of proof
% 232.32/43.40  | 
% 232.32/43.40  | GROUND_INST: instantiating (1) with e1, e0, e1, e1, simplifying with (2), (3)
% 232.32/43.40  |              gives:
% 232.32/43.40  |   (5)  e1 = e0
% 232.32/43.40  | 
% 232.32/43.40  | REDUCE: (4), (5) imply:
% 232.32/43.40  |   (6)  $false
% 232.32/43.40  | 
% 232.32/43.40  | CLOSE: (6) is inconsistent.
% 232.32/43.40  | 
% 232.32/43.40  End of proof
% 232.32/43.40  
% 232.32/43.40  Sub-proof #2428 shows that the following formulas are inconsistent:
% 232.32/43.40  ----------------------------------------------------------------
% 232.32/43.40    (1)  all_57_5 = e0 & op(e2, e1) = e0
% 232.32/43.40    (2)  all_57_5 = e2
% 232.32/43.40    (3)   ~ (e2 = e0)
% 232.32/43.40  
% 232.32/43.40  Begin of proof
% 232.32/43.40  | 
% 232.32/43.40  | ALPHA: (1) implies:
% 232.32/43.40  |   (4)  all_57_5 = e0
% 232.32/43.40  | 
% 232.32/43.40  | COMBINE_EQS: (2), (4) imply:
% 232.32/43.40  |   (5)  e2 = e0
% 232.32/43.40  | 
% 232.32/43.40  | REDUCE: (3), (5) imply:
% 232.32/43.40  |   (6)  $false
% 232.32/43.40  | 
% 232.32/43.40  | CLOSE: (6) is inconsistent.
% 232.32/43.40  | 
% 232.32/43.40  End of proof
% 232.32/43.40  
% 232.32/43.40  Sub-proof #2429 shows that the following formulas are inconsistent:
% 232.32/43.40  ----------------------------------------------------------------
% 232.32/43.40    (1)  all_57_4 = e0 & op(e3, e1) = e0
% 232.32/43.40    (2)  all_57_4 = e1
% 232.32/43.40    (3)   ~ (e1 = e0)
% 232.32/43.40  
% 232.32/43.40  Begin of proof
% 232.32/43.40  | 
% 232.32/43.40  | ALPHA: (1) implies:
% 232.32/43.40  |   (4)  all_57_4 = e0
% 232.32/43.40  | 
% 232.32/43.40  | COMBINE_EQS: (2), (4) imply:
% 232.32/43.40  |   (5)  e1 = e0
% 232.32/43.40  | 
% 232.32/43.40  | REDUCE: (3), (5) imply:
% 232.32/43.40  |   (6)  $false
% 232.32/43.40  | 
% 232.32/43.40  | CLOSE: (6) is inconsistent.
% 232.32/43.40  | 
% 232.32/43.40  End of proof
% 232.32/43.40  
% 232.32/43.40  Sub-proof #2430 shows that the following formulas are inconsistent:
% 232.32/43.40  ----------------------------------------------------------------
% 232.32/43.40    (1)  all_57_4 = e2
% 232.32/43.40    (2)  all_57_4 = e1
% 232.32/43.40    (3)   ~ (e2 = e1)
% 232.32/43.40  
% 232.32/43.40  Begin of proof
% 232.32/43.40  | 
% 232.32/43.40  | COMBINE_EQS: (1), (2) imply:
% 232.32/43.40  |   (4)  e2 = e1
% 232.32/43.40  | 
% 232.32/43.40  | SIMP: (4) implies:
% 232.32/43.40  |   (5)  e2 = e1
% 232.32/43.40  | 
% 232.32/43.40  | REDUCE: (3), (5) imply:
% 232.32/43.40  |   (6)  $false
% 232.32/43.40  | 
% 232.32/43.40  | CLOSE: (6) is inconsistent.
% 232.32/43.40  | 
% 232.32/43.40  End of proof
% 232.32/43.40  
% 232.32/43.40  Sub-proof #2431 shows that the following formulas are inconsistent:
% 232.32/43.40  ----------------------------------------------------------------
% 232.32/43.40    (1)   ~ (e3 = e1)
% 232.32/43.40    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.32/43.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.32/43.40    (3)  all_57_4 = e2
% 232.32/43.40    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 232.32/43.40         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 232.32/43.40    (5)   ~ (all_53_13 = e2)
% 232.32/43.40    (6)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 232.32/43.40         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 232.32/43.40    (7)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 232.32/43.40         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 232.32/43.40    (8)   ~ (e3 = e2)
% 232.32/43.40    (9)   ~ (e3 = e0)
% 232.32/43.40    (10)  op(e3, e3) = e3
% 232.32/43.40    (11)   ~ (e2 = e0)
% 232.32/43.40    (12)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 232.32/43.40          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 232.32/43.40    (13)   ~ (e1 = e0)
% 232.32/43.40    (14)  op(e2, e0) = all_53_13
% 232.32/43.40    (15)   ~ (all_53_12 = e3)
% 232.32/43.40    (16)   ~ (all_53_12 = e0)
% 232.32/43.40    (17)   ~ (e2 = e1)
% 232.32/43.40    (18)  (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 232.32/43.40    (19)  op(e3, e0) = all_53_12
% 232.32/43.40  
% 232.32/43.40  Begin of proof
% 232.32/43.40  | 
% 232.32/43.40  | BETA: splitting (18) gives:
% 232.32/43.40  | 
% 232.32/43.40  | Case 1:
% 232.32/43.40  | | 
% 232.32/43.40  | |   (20)  all_57_9 = e2 & op(e3, e0) = e2
% 232.32/43.40  | | 
% 232.32/43.40  | | ALPHA: (20) implies:
% 232.32/43.40  | |   (21)  all_57_9 = e2
% 232.32/43.40  | | 
% 232.32/43.40  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13),
% 232.32/43.40  | |            (15), (16), (17), (19), (21) are inconsistent by sub-proof #2433.
% 232.32/43.40  | | 
% 232.32/43.40  | Case 2:
% 232.32/43.40  | | 
% 232.32/43.40  | |   (22)  all_57_10 = e2 & op(e2, e0) = e2
% 232.32/43.40  | | 
% 232.32/43.40  | | REF_CLOSE: (2), (5), (14), (22) are inconsistent by sub-proof #2432.
% 232.32/43.40  | | 
% 232.32/43.40  | End of split
% 232.32/43.40  | 
% 232.32/43.40  End of proof
% 232.32/43.40  
% 232.32/43.40  Sub-proof #2432 shows that the following formulas are inconsistent:
% 232.32/43.40  ----------------------------------------------------------------
% 232.32/43.40    (1)  all_57_10 = e2 & op(e2, e0) = e2
% 232.32/43.40    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.32/43.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.32/43.40    (3)  op(e2, e0) = all_53_13
% 232.32/43.40    (4)   ~ (all_53_13 = e2)
% 232.32/43.40  
% 232.32/43.40  Begin of proof
% 232.32/43.40  | 
% 232.32/43.40  | ALPHA: (1) implies:
% 232.32/43.40  |   (5)  op(e2, e0) = e2
% 232.32/43.40  | 
% 232.32/43.40  | GROUND_INST: instantiating (2) with all_53_13, e2, e0, e2, simplifying with
% 232.32/43.40  |              (3), (5) gives:
% 232.32/43.40  |   (6)  all_53_13 = e2
% 232.32/43.40  | 
% 232.32/43.40  | REDUCE: (4), (6) imply:
% 232.32/43.40  |   (7)  $false
% 232.32/43.40  | 
% 232.32/43.40  | CLOSE: (7) is inconsistent.
% 232.32/43.40  | 
% 232.32/43.40  End of proof
% 232.32/43.40  
% 232.32/43.40  Sub-proof #2433 shows that the following formulas are inconsistent:
% 232.32/43.40  ----------------------------------------------------------------
% 232.32/43.40    (1)  all_57_9 = e2
% 232.32/43.40    (2)   ~ (e3 = e1)
% 232.32/43.40    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.32/43.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.32/43.40    (4)  all_57_4 = e2
% 232.32/43.40    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 232.32/43.40         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 232.32/43.40    (6)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 232.32/43.40         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 232.32/43.40    (7)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 232.32/43.40         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 232.32/43.40    (8)   ~ (e3 = e2)
% 232.32/43.40    (9)   ~ (e3 = e0)
% 232.32/43.40    (10)  op(e3, e3) = e3
% 232.32/43.40    (11)   ~ (e2 = e0)
% 232.32/43.40    (12)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 232.32/43.40          (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 232.32/43.40    (13)   ~ (e1 = e0)
% 232.32/43.40    (14)   ~ (all_53_12 = e3)
% 232.32/43.40    (15)   ~ (all_53_12 = e0)
% 232.32/43.40    (16)   ~ (e2 = e1)
% 232.32/43.40    (17)  op(e3, e0) = all_53_12
% 232.32/43.40  
% 232.32/43.40  Begin of proof
% 232.32/43.40  | 
% 232.32/43.40  | BETA: splitting (7) gives:
% 232.32/43.40  | 
% 232.32/43.40  | Case 1:
% 232.32/43.40  | | 
% 232.32/43.40  | |   (18)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) =
% 232.32/43.40  | |           e0)
% 232.32/43.40  | | 
% 232.32/43.40  | | BETA: splitting (18) gives:
% 232.32/43.40  | | 
% 232.32/43.40  | | Case 1:
% 232.32/43.40  | | | 
% 232.32/43.40  | | |   (19)  all_57_0 = e0 & op(e3, e3) = e0
% 232.32/43.40  | | | 
% 232.32/43.40  | | | REF_CLOSE: (1), (2), (3), (4), (5), (8), (9), (12), (13), (14), (16),
% 232.32/43.40  | | |            (17), (19) are inconsistent by sub-proof #2447.
% 232.32/43.40  | | | 
% 232.32/43.40  | | Case 2:
% 232.32/43.40  | | | 
% 232.32/43.40  | | |   (20)  all_57_1 = e0 & op(e3, e2) = e0
% 232.32/43.40  | | | 
% 232.32/43.40  | | | ALPHA: (20) implies:
% 232.32/43.40  | | |   (21)  all_57_1 = e0
% 232.32/43.40  | | | 
% 232.32/43.40  | | | REF_CLOSE: (1), (2), (3), (4), (5), (10), (13), (16), (21) are
% 232.32/43.40  | | |            inconsistent by sub-proof #2442.
% 232.32/43.40  | | | 
% 232.32/43.40  | | End of split
% 232.32/43.40  | | 
% 232.32/43.40  | Case 2:
% 232.32/43.40  | | 
% 232.32/43.40  | |   (22)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) =
% 232.32/43.40  | |           e0)
% 232.32/43.40  | | 
% 232.32/43.40  | | BETA: splitting (22) gives:
% 232.32/43.40  | | 
% 232.32/43.40  | | Case 1:
% 232.32/43.40  | | | 
% 232.32/43.40  | | |   (23)  all_57_4 = e0 & op(e3, e1) = e0
% 232.32/43.40  | | | 
% 232.32/43.40  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (10), (11), (13), (16), (23)
% 232.32/43.40  | | |            are inconsistent by sub-proof #2435.
% 232.32/43.40  | | | 
% 232.32/43.40  | | Case 2:
% 232.32/43.40  | | | 
% 232.32/43.40  | | |   (24)  all_57_9 = e0 & op(e3, e0) = e0
% 232.32/43.40  | | | 
% 232.32/43.40  | | | REF_CLOSE: (3), (15), (17), (24) are inconsistent by sub-proof #2434.
% 232.32/43.40  | | | 
% 232.32/43.40  | | End of split
% 232.32/43.40  | | 
% 232.32/43.40  | End of split
% 232.32/43.40  | 
% 232.32/43.40  End of proof
% 232.32/43.40  
% 232.32/43.40  Sub-proof #2434 shows that the following formulas are inconsistent:
% 232.32/43.40  ----------------------------------------------------------------
% 232.32/43.40    (1)  all_57_9 = e0 & op(e3, e0) = e0
% 232.32/43.40    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.32/43.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.32/43.40    (3)  op(e3, e0) = all_53_12
% 232.32/43.40    (4)   ~ (all_53_12 = e0)
% 232.32/43.40  
% 232.32/43.40  Begin of proof
% 232.32/43.40  | 
% 232.32/43.40  | ALPHA: (1) implies:
% 232.32/43.40  |   (5)  op(e3, e0) = e0
% 232.32/43.40  | 
% 232.32/43.40  | GROUND_INST: instantiating (2) with all_53_12, e0, e0, e3, simplifying with
% 232.32/43.40  |              (3), (5) gives:
% 232.32/43.40  |   (6)  all_53_12 = e0
% 232.32/43.40  | 
% 232.32/43.40  | REDUCE: (4), (6) imply:
% 232.32/43.40  |   (7)  $false
% 232.32/43.40  | 
% 232.32/43.40  | CLOSE: (7) is inconsistent.
% 232.32/43.40  | 
% 232.32/43.40  End of proof
% 232.32/43.40  
% 232.32/43.40  Sub-proof #2435 shows that the following formulas are inconsistent:
% 232.32/43.40  ----------------------------------------------------------------
% 232.32/43.40    (1)  all_57_9 = e2
% 232.32/43.40    (2)   ~ (e3 = e1)
% 232.32/43.40    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.32/43.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.32/43.40    (4)  all_57_4 = e2
% 232.32/43.40    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 232.32/43.40         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 232.32/43.40    (6)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 232.32/43.40         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 232.32/43.40    (7)   ~ (e3 = e2)
% 232.32/43.40    (8)  all_57_4 = e0 & op(e3, e1) = e0
% 232.32/43.40    (9)  op(e3, e3) = e3
% 232.32/43.40    (10)   ~ (e2 = e0)
% 232.32/43.40    (11)   ~ (e1 = e0)
% 232.32/43.40    (12)   ~ (e2 = e1)
% 232.32/43.40  
% 232.32/43.40  Begin of proof
% 232.32/43.40  | 
% 232.32/43.40  | ALPHA: (8) implies:
% 232.32/43.40  |   (13)  all_57_4 = e0
% 232.32/43.40  | 
% 232.32/43.40  | COMBINE_EQS: (4), (13) imply:
% 232.32/43.40  |   (14)  e2 = e0
% 232.32/43.40  | 
% 232.32/43.40  | COMBINE_EQS: (1), (14) imply:
% 232.32/43.40  |   (15)  all_57_9 = e0
% 232.32/43.40  | 
% 232.32/43.40  | REF_CLOSE: (2), (3), (5), (6), (7), (9), (10), (11), (12), (13), (15) are
% 232.32/43.40  |            inconsistent by sub-proof #2436.
% 232.32/43.40  | 
% 232.32/43.40  End of proof
% 232.32/43.40  
% 232.32/43.40  Sub-proof #2436 shows that the following formulas are inconsistent:
% 232.32/43.40  ----------------------------------------------------------------
% 232.32/43.40    (1)   ~ (e3 = e1)
% 232.32/43.40    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.32/43.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.32/43.40    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 232.32/43.40         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 232.32/43.40    (4)  all_57_4 = e0
% 232.32/43.40    (5)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 232.32/43.40         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 232.32/43.40    (6)   ~ (e3 = e2)
% 232.32/43.40    (7)  op(e3, e3) = e3
% 232.32/43.40    (8)  all_57_9 = e0
% 232.32/43.40    (9)   ~ (e2 = e0)
% 232.32/43.40    (10)   ~ (e1 = e0)
% 232.32/43.40    (11)   ~ (e2 = e1)
% 232.32/43.40  
% 232.32/43.40  Begin of proof
% 232.32/43.40  | 
% 232.32/43.40  | BETA: splitting (3) gives:
% 232.32/43.40  | 
% 232.32/43.40  | Case 1:
% 232.32/43.40  | | 
% 232.32/43.40  | |   (12)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) =
% 232.32/43.40  | |           e1)
% 232.32/43.40  | | 
% 232.32/43.40  | | BETA: splitting (12) gives:
% 232.32/43.40  | | 
% 232.32/43.40  | | Case 1:
% 232.32/43.40  | | | 
% 232.32/43.40  | | |   (13)  all_57_0 = e1 & op(e3, e3) = e1
% 232.32/43.40  | | | 
% 232.32/43.40  | | | ALPHA: (13) implies:
% 232.32/43.40  | | |   (14)  op(e3, e3) = e1
% 232.32/43.40  | | | 
% 232.32/43.40  | | | REF_CLOSE: (1), (2), (7), (14) are inconsistent by sub-proof #2495.
% 232.32/43.40  | | | 
% 232.32/43.40  | | Case 2:
% 232.32/43.40  | | | 
% 232.32/43.40  | | |   (15)  all_57_1 = e1 & op(e3, e2) = e1
% 232.32/43.40  | | | 
% 232.32/43.40  | | | ALPHA: (15) implies:
% 232.32/43.40  | | |   (16)  all_57_1 = e1
% 232.32/43.40  | | | 
% 232.32/43.40  | | | REF_CLOSE: (2), (4), (5), (6), (7), (8), (9), (11), (16) are inconsistent
% 232.32/43.40  | | |            by sub-proof #2439.
% 232.32/43.40  | | | 
% 232.32/43.40  | | End of split
% 232.32/43.40  | | 
% 232.32/43.40  | Case 2:
% 232.32/43.40  | | 
% 232.32/43.40  | |   (17)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) =
% 232.32/43.40  | |           e1)
% 232.32/43.40  | | 
% 232.32/43.40  | | BETA: splitting (17) gives:
% 232.32/43.40  | | 
% 232.32/43.40  | | Case 1:
% 232.32/43.40  | | | 
% 232.32/43.40  | | |   (18)  all_57_4 = e1 & op(e3, e1) = e1
% 232.32/43.40  | | | 
% 232.32/43.40  | | | ALPHA: (18) implies:
% 232.32/43.40  | | |   (19)  all_57_4 = e1
% 232.32/43.40  | | | 
% 232.32/43.40  | | | REF_CLOSE: (4), (10), (19) are inconsistent by sub-proof #2438.
% 232.32/43.40  | | | 
% 232.32/43.40  | | Case 2:
% 232.32/43.40  | | | 
% 232.32/43.40  | | |   (20)  all_57_9 = e1 & op(e3, e0) = e1
% 232.32/43.40  | | | 
% 232.32/43.40  | | | REF_CLOSE: (8), (10), (20) are inconsistent by sub-proof #2437.
% 232.32/43.40  | | | 
% 232.32/43.40  | | End of split
% 232.32/43.40  | | 
% 232.32/43.40  | End of split
% 232.32/43.40  | 
% 232.32/43.40  End of proof
% 232.32/43.40  
% 232.32/43.40  Sub-proof #2437 shows that the following formulas are inconsistent:
% 232.32/43.40  ----------------------------------------------------------------
% 232.32/43.40    (1)  all_57_9 = e1 & op(e3, e0) = e1
% 232.32/43.40    (2)  all_57_9 = e0
% 232.32/43.40    (3)   ~ (e1 = e0)
% 232.32/43.40  
% 232.32/43.40  Begin of proof
% 232.32/43.40  | 
% 232.32/43.40  | ALPHA: (1) implies:
% 232.32/43.40  |   (4)  all_57_9 = e1
% 232.32/43.40  | 
% 232.32/43.40  | COMBINE_EQS: (2), (4) imply:
% 232.32/43.40  |   (5)  e1 = e0
% 232.32/43.40  | 
% 232.32/43.40  | REDUCE: (3), (5) imply:
% 232.32/43.40  |   (6)  $false
% 232.32/43.40  | 
% 232.32/43.40  | CLOSE: (6) is inconsistent.
% 232.32/43.40  | 
% 232.32/43.40  End of proof
% 232.32/43.40  
% 232.32/43.40  Sub-proof #2438 shows that the following formulas are inconsistent:
% 232.32/43.40  ----------------------------------------------------------------
% 232.32/43.40    (1)  all_57_4 = e1
% 232.32/43.40    (2)  all_57_4 = e0
% 232.32/43.40    (3)   ~ (e1 = e0)
% 232.32/43.40  
% 232.32/43.40  Begin of proof
% 232.32/43.40  | 
% 232.32/43.40  | COMBINE_EQS: (1), (2) imply:
% 232.32/43.40  |   (4)  e1 = e0
% 232.32/43.40  | 
% 232.32/43.40  | SIMP: (4) implies:
% 232.32/43.40  |   (5)  e1 = e0
% 232.32/43.40  | 
% 232.32/43.40  | REDUCE: (3), (5) imply:
% 232.32/43.40  |   (6)  $false
% 232.32/43.40  | 
% 232.32/43.40  | CLOSE: (6) is inconsistent.
% 232.32/43.40  | 
% 232.32/43.40  End of proof
% 232.32/43.40  
% 232.32/43.40  Sub-proof #2439 shows that the following formulas are inconsistent:
% 232.32/43.40  ----------------------------------------------------------------
% 232.32/43.40    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.32/43.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.32/43.40    (2)  all_57_4 = e0
% 232.32/43.40    (3)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 232.32/43.40         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 232.32/43.40    (4)   ~ (e3 = e2)
% 232.32/43.40    (5)  op(e3, e3) = e3
% 232.32/43.40    (6)  all_57_1 = e1
% 232.32/43.40    (7)  all_57_9 = e0
% 232.32/43.40    (8)   ~ (e2 = e0)
% 232.32/43.40    (9)   ~ (e2 = e1)
% 232.32/43.40  
% 232.32/43.40  Begin of proof
% 232.32/43.40  | 
% 232.32/43.40  | BETA: splitting (3) gives:
% 232.32/43.40  | 
% 232.32/43.40  | Case 1:
% 232.32/43.40  | | 
% 232.32/43.40  | |   (10)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) =
% 232.32/43.40  | |           e2)
% 232.32/43.40  | | 
% 232.32/43.40  | | REF_CLOSE: (1), (4), (5), (6), (9), (10) are inconsistent by sub-proof
% 232.32/43.40  | |            #2488.
% 232.32/43.40  | | 
% 232.32/43.40  | Case 2:
% 232.32/43.40  | | 
% 232.32/43.40  | |   (11)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) =
% 232.32/43.40  | |           e2)
% 232.32/43.40  | | 
% 232.32/43.40  | | BETA: splitting (11) gives:
% 232.32/43.40  | | 
% 232.32/43.40  | | Case 1:
% 232.32/43.40  | | | 
% 232.32/43.40  | | |   (12)  all_57_4 = e2 & op(e3, e1) = e2
% 232.32/43.40  | | | 
% 232.32/43.40  | | | ALPHA: (12) implies:
% 232.32/43.40  | | |   (13)  all_57_4 = e2
% 232.32/43.40  | | | 
% 232.32/43.40  | | | REF_CLOSE: (2), (8), (13) are inconsistent by sub-proof #2441.
% 232.32/43.40  | | | 
% 232.32/43.40  | | Case 2:
% 232.32/43.40  | | | 
% 232.32/43.40  | | |   (14)  all_57_9 = e2 & op(e3, e0) = e2
% 232.32/43.40  | | | 
% 232.32/43.40  | | | ALPHA: (14) implies:
% 232.32/43.40  | | |   (15)  all_57_9 = e2
% 232.32/43.40  | | | 
% 232.32/43.40  | | | REF_CLOSE: (7), (8), (15) are inconsistent by sub-proof #2440.
% 232.32/43.40  | | | 
% 232.32/43.40  | | End of split
% 232.32/43.40  | | 
% 232.32/43.40  | End of split
% 232.32/43.40  | 
% 232.32/43.40  End of proof
% 232.32/43.40  
% 232.32/43.40  Sub-proof #2440 shows that the following formulas are inconsistent:
% 232.32/43.40  ----------------------------------------------------------------
% 232.32/43.40    (1)  all_57_9 = e2
% 232.32/43.40    (2)  all_57_9 = e0
% 232.32/43.40    (3)   ~ (e2 = e0)
% 232.32/43.40  
% 232.32/43.40  Begin of proof
% 232.32/43.40  | 
% 232.32/43.40  | COMBINE_EQS: (1), (2) imply:
% 232.32/43.40  |   (4)  e2 = e0
% 232.32/43.40  | 
% 232.32/43.40  | SIMP: (4) implies:
% 232.32/43.40  |   (5)  e2 = e0
% 232.32/43.40  | 
% 232.32/43.40  | REDUCE: (3), (5) imply:
% 232.32/43.40  |   (6)  $false
% 232.32/43.40  | 
% 232.32/43.40  | CLOSE: (6) is inconsistent.
% 232.32/43.40  | 
% 232.32/43.40  End of proof
% 232.32/43.40  
% 232.32/43.40  Sub-proof #2441 shows that the following formulas are inconsistent:
% 232.32/43.40  ----------------------------------------------------------------
% 232.32/43.40    (1)  all_57_4 = e2
% 232.32/43.40    (2)  all_57_4 = e0
% 232.32/43.40    (3)   ~ (e2 = e0)
% 232.32/43.40  
% 232.32/43.40  Begin of proof
% 232.32/43.40  | 
% 232.32/43.40  | COMBINE_EQS: (1), (2) imply:
% 232.32/43.40  |   (4)  e2 = e0
% 232.32/43.40  | 
% 232.32/43.40  | SIMP: (4) implies:
% 232.32/43.40  |   (5)  e2 = e0
% 232.32/43.40  | 
% 232.32/43.40  | REDUCE: (3), (5) imply:
% 232.32/43.40  |   (6)  $false
% 232.32/43.40  | 
% 232.32/43.40  | CLOSE: (6) is inconsistent.
% 232.32/43.40  | 
% 232.32/43.40  End of proof
% 232.32/43.40  
% 232.32/43.40  Sub-proof #2442 shows that the following formulas are inconsistent:
% 232.32/43.40  ----------------------------------------------------------------
% 232.32/43.40    (1)  all_57_9 = e2
% 232.32/43.40    (2)   ~ (e3 = e1)
% 232.32/43.40    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.32/43.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.32/43.40    (4)  all_57_4 = e2
% 232.32/43.40    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 232.32/43.40         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 232.32/43.40    (6)  op(e3, e3) = e3
% 232.32/43.40    (7)  all_57_1 = e0
% 232.32/43.40    (8)   ~ (e1 = e0)
% 232.32/43.40    (9)   ~ (e2 = e1)
% 232.32/43.40  
% 232.32/43.40  Begin of proof
% 232.32/43.40  | 
% 232.32/43.40  | BETA: splitting (5) gives:
% 232.32/43.40  | 
% 232.32/43.40  | Case 1:
% 232.32/43.40  | | 
% 232.32/43.40  | |   (10)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) =
% 232.32/43.40  | |           e1)
% 232.32/43.40  | | 
% 232.32/43.40  | | REF_CLOSE: (2), (3), (6), (7), (8), (10) are inconsistent by sub-proof
% 232.32/43.40  | |            #2445.
% 232.32/43.40  | | 
% 232.32/43.40  | Case 2:
% 232.32/43.40  | | 
% 232.32/43.40  | |   (11)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) =
% 232.32/43.40  | |           e1)
% 232.32/43.40  | | 
% 232.32/43.40  | | REF_CLOSE: (1), (4), (9), (11) are inconsistent by sub-proof #2443.
% 232.32/43.40  | | 
% 232.32/43.40  | End of split
% 232.32/43.40  | 
% 232.32/43.40  End of proof
% 232.32/43.40  
% 232.32/43.40  Sub-proof #2443 shows that the following formulas are inconsistent:
% 232.32/43.40  ----------------------------------------------------------------
% 232.32/43.40    (1)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 232.32/43.40    (2)  all_57_4 = e2
% 232.32/43.40    (3)   ~ (e2 = e1)
% 232.32/43.40    (4)  all_57_9 = e2
% 232.32/43.40  
% 232.32/43.40  Begin of proof
% 232.32/43.40  | 
% 232.32/43.40  | BETA: splitting (1) gives:
% 232.32/43.40  | 
% 232.32/43.40  | Case 1:
% 232.32/43.40  | | 
% 232.32/43.40  | |   (5)  all_57_4 = e1 & op(e3, e1) = e1
% 232.32/43.40  | | 
% 232.32/43.40  | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #2452.
% 232.32/43.40  | | 
% 232.32/43.40  | Case 2:
% 232.32/43.40  | | 
% 232.32/43.40  | |   (6)  all_57_9 = e1 & op(e3, e0) = e1
% 232.32/43.40  | | 
% 232.32/43.40  | | ALPHA: (6) implies:
% 232.32/43.40  | |   (7)  all_57_9 = e1
% 232.32/43.40  | | 
% 232.32/43.40  | | REF_CLOSE: (3), (4), (7) are inconsistent by sub-proof #2444.
% 232.32/43.40  | | 
% 232.32/43.40  | End of split
% 232.32/43.40  | 
% 232.32/43.40  End of proof
% 232.32/43.40  
% 232.32/43.40  Sub-proof #2444 shows that the following formulas are inconsistent:
% 232.32/43.40  ----------------------------------------------------------------
% 232.32/43.40    (1)  all_57_9 = e2
% 232.32/43.40    (2)  all_57_9 = e1
% 232.32/43.40    (3)   ~ (e2 = e1)
% 232.32/43.40  
% 232.32/43.40  Begin of proof
% 232.32/43.40  | 
% 232.32/43.40  | COMBINE_EQS: (1), (2) imply:
% 232.32/43.40  |   (4)  e2 = e1
% 232.32/43.40  | 
% 232.32/43.40  | SIMP: (4) implies:
% 232.32/43.40  |   (5)  e2 = e1
% 232.32/43.40  | 
% 232.32/43.40  | REDUCE: (3), (5) imply:
% 232.32/43.40  |   (6)  $false
% 232.32/43.40  | 
% 232.32/43.40  | CLOSE: (6) is inconsistent.
% 232.32/43.40  | 
% 232.32/43.40  End of proof
% 232.32/43.40  
% 232.32/43.40  Sub-proof #2445 shows that the following formulas are inconsistent:
% 232.32/43.40  ----------------------------------------------------------------
% 232.32/43.40    (1)   ~ (e3 = e1)
% 232.32/43.40    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.32/43.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.32/43.40    (3)  op(e3, e3) = e3
% 232.32/43.40    (4)  all_57_1 = e0
% 232.32/43.40    (5)   ~ (e1 = e0)
% 232.32/43.40    (6)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1)
% 232.32/43.40  
% 232.32/43.40  Begin of proof
% 232.32/43.40  | 
% 232.32/43.40  | BETA: splitting (6) gives:
% 232.32/43.40  | 
% 232.32/43.40  | Case 1:
% 232.32/43.40  | | 
% 232.32/43.40  | |   (7)  all_57_0 = e1 & op(e3, e3) = e1
% 232.32/43.40  | | 
% 232.32/43.40  | | ALPHA: (7) implies:
% 232.32/43.40  | |   (8)  op(e3, e3) = e1
% 232.32/43.40  | | 
% 232.32/43.40  | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #2495.
% 232.32/43.40  | | 
% 232.32/43.40  | Case 2:
% 232.32/43.40  | | 
% 232.32/43.40  | |   (9)  all_57_1 = e1 & op(e3, e2) = e1
% 232.32/43.40  | | 
% 232.32/43.40  | | REF_CLOSE: (4), (5), (9) are inconsistent by sub-proof #2446.
% 232.32/43.40  | | 
% 232.32/43.40  | End of split
% 232.32/43.40  | 
% 232.32/43.40  End of proof
% 232.32/43.40  
% 232.32/43.40  Sub-proof #2446 shows that the following formulas are inconsistent:
% 232.32/43.40  ----------------------------------------------------------------
% 232.32/43.40    (1)  all_57_1 = e1 & op(e3, e2) = e1
% 232.32/43.40    (2)  all_57_1 = e0
% 232.32/43.40    (3)   ~ (e1 = e0)
% 232.32/43.40  
% 232.32/43.40  Begin of proof
% 232.32/43.40  | 
% 232.32/43.40  | ALPHA: (1) implies:
% 232.32/43.40  |   (4)  all_57_1 = e1
% 232.32/43.40  | 
% 232.32/43.40  | COMBINE_EQS: (2), (4) imply:
% 232.32/43.40  |   (5)  e1 = e0
% 232.32/43.40  | 
% 232.32/43.40  | SIMP: (5) implies:
% 232.32/43.40  |   (6)  e1 = e0
% 232.32/43.40  | 
% 232.32/43.40  | REDUCE: (3), (6) imply:
% 232.32/43.40  |   (7)  $false
% 232.32/43.40  | 
% 232.32/43.40  | CLOSE: (7) is inconsistent.
% 232.32/43.40  | 
% 232.32/43.40  End of proof
% 232.32/43.40  
% 232.32/43.40  Sub-proof #2447 shows that the following formulas are inconsistent:
% 232.32/43.40  ----------------------------------------------------------------
% 232.32/43.40    (1)  all_57_9 = e2
% 232.32/43.40    (2)   ~ (e3 = e1)
% 232.32/43.40    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.32/43.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.32/43.40    (4)  all_57_4 = e2
% 232.32/43.40    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 232.32/43.40         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 232.32/43.40    (6)  all_57_0 = e0 & op(e3, e3) = e0
% 232.32/43.40    (7)   ~ (e3 = e2)
% 232.32/43.40    (8)   ~ (e3 = e0)
% 232.32/43.40    (9)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 232.32/43.40         (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 232.32/43.40    (10)   ~ (e1 = e0)
% 232.32/43.40    (11)   ~ (all_53_12 = e3)
% 232.32/43.40    (12)   ~ (e2 = e1)
% 232.32/43.40    (13)  op(e3, e0) = all_53_12
% 232.32/43.40  
% 232.32/43.40  Begin of proof
% 232.32/43.40  | 
% 232.32/43.40  | ALPHA: (6) implies:
% 232.32/43.40  |   (14)  all_57_0 = e0
% 232.32/43.40  |   (15)  op(e3, e3) = e0
% 232.32/43.40  | 
% 232.32/43.40  | BETA: splitting (9) gives:
% 232.32/43.40  | 
% 232.32/43.40  | Case 1:
% 232.32/43.40  | | 
% 232.32/43.40  | |   (16)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) =
% 232.32/43.40  | |           e3)
% 232.32/43.40  | | 
% 232.32/43.40  | | REF_CLOSE: (1), (2), (3), (4), (5), (8), (10), (12), (14), (15), (16) are
% 232.32/43.40  | |            inconsistent by sub-proof #2449.
% 232.32/43.40  | | 
% 232.32/43.40  | Case 2:
% 232.32/43.40  | | 
% 232.32/43.40  | |   (17)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) =
% 232.32/43.40  | |           e3)
% 232.32/43.40  | | 
% 232.32/43.40  | | REF_CLOSE: (3), (4), (7), (11), (13), (17) are inconsistent by sub-proof
% 232.32/43.40  | |            #2448.
% 232.32/43.40  | | 
% 232.32/43.40  | End of split
% 232.32/43.40  | 
% 232.32/43.40  End of proof
% 232.32/43.40  
% 232.32/43.40  Sub-proof #2448 shows that the following formulas are inconsistent:
% 232.32/43.40  ----------------------------------------------------------------
% 232.32/43.40    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.32/43.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.32/43.40    (2)  all_57_4 = e2
% 232.32/43.40    (3)   ~ (e3 = e2)
% 232.32/43.40    (4)  (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 232.32/43.40    (5)   ~ (all_53_12 = e3)
% 232.32/43.40    (6)  op(e3, e0) = all_53_12
% 232.32/43.40  
% 232.32/43.40  Begin of proof
% 232.32/43.40  | 
% 232.32/43.40  | BETA: splitting (4) gives:
% 232.32/43.40  | 
% 232.32/43.40  | Case 1:
% 232.32/43.40  | | 
% 232.32/43.40  | |   (7)  all_57_4 = e3 & op(e3, e1) = e3
% 232.32/43.40  | | 
% 232.32/43.40  | | ALPHA: (7) implies:
% 232.32/43.40  | |   (8)  all_57_4 = e3
% 232.32/43.40  | | 
% 232.32/43.40  | | REF_CLOSE: (2), (3), (8) are inconsistent by sub-proof #2482.
% 232.32/43.40  | | 
% 232.32/43.40  | Case 2:
% 232.32/43.40  | | 
% 232.32/43.40  | |   (9)  all_57_9 = e3 & op(e3, e0) = e3
% 232.32/43.40  | | 
% 232.32/43.40  | | ALPHA: (9) implies:
% 232.32/43.40  | |   (10)  op(e3, e0) = e3
% 232.32/43.40  | | 
% 232.32/43.40  | | REF_CLOSE: (1), (5), (6), (10) are inconsistent by sub-proof #2458.
% 232.32/43.40  | | 
% 232.32/43.40  | End of split
% 232.32/43.40  | 
% 232.32/43.40  End of proof
% 232.32/43.40  
% 232.32/43.40  Sub-proof #2449 shows that the following formulas are inconsistent:
% 232.32/43.40  ----------------------------------------------------------------
% 232.32/43.40    (1)  all_57_9 = e2
% 232.32/43.40    (2)   ~ (e3 = e1)
% 232.32/43.40    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.32/43.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.32/43.40    (4)  all_57_4 = e2
% 232.32/43.40    (5)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 232.32/43.40         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 232.32/43.40    (6)  (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3)
% 232.32/43.40    (7)   ~ (e3 = e0)
% 232.32/43.40    (8)  all_57_0 = e0
% 232.32/43.40    (9)  op(e3, e3) = e0
% 232.32/43.40    (10)   ~ (e1 = e0)
% 232.32/43.40    (11)   ~ (e2 = e1)
% 232.32/43.40  
% 232.32/43.40  Begin of proof
% 232.32/43.40  | 
% 232.32/43.40  | BETA: splitting (6) gives:
% 232.32/43.40  | 
% 232.32/43.40  | Case 1:
% 232.32/43.40  | | 
% 232.32/43.40  | |   (12)  all_57_0 = e3 & op(e3, e3) = e3
% 232.32/43.40  | | 
% 232.32/43.40  | | ALPHA: (12) implies:
% 232.32/43.40  | |   (13)  op(e3, e3) = e3
% 232.32/43.40  | | 
% 232.32/43.40  | | REF_CLOSE: (3), (7), (9), (13) are inconsistent by sub-proof #2494.
% 232.32/43.40  | | 
% 232.32/43.40  | Case 2:
% 232.32/43.40  | | 
% 232.32/43.41  | |   (14)  all_57_1 = e3 & op(e3, e2) = e3
% 232.32/43.41  | | 
% 232.32/43.41  | | ALPHA: (14) implies:
% 232.32/43.41  | |   (15)  all_57_1 = e3
% 232.32/43.41  | | 
% 232.32/43.41  | | REF_CLOSE: (1), (2), (4), (5), (8), (10), (11), (15) are inconsistent by
% 232.32/43.41  | |            sub-proof #2450.
% 232.32/43.41  | | 
% 232.32/43.41  | End of split
% 232.32/43.41  | 
% 232.32/43.41  End of proof
% 232.32/43.41  
% 232.32/43.41  Sub-proof #2450 shows that the following formulas are inconsistent:
% 232.32/43.41  ----------------------------------------------------------------
% 232.32/43.41    (1)  all_57_9 = e2
% 232.32/43.41    (2)   ~ (e3 = e1)
% 232.32/43.41    (3)  all_57_4 = e2
% 232.32/43.41    (4)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 232.32/43.41         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 232.32/43.41    (5)  all_57_0 = e0
% 232.32/43.41    (6)   ~ (e1 = e0)
% 232.32/43.41    (7)  all_57_1 = e3
% 232.32/43.41    (8)   ~ (e2 = e1)
% 232.32/43.41  
% 232.32/43.41  Begin of proof
% 232.32/43.41  | 
% 232.32/43.41  | BETA: splitting (4) gives:
% 232.32/43.41  | 
% 232.32/43.41  | Case 1:
% 232.32/43.41  | | 
% 232.32/43.41  | |   (9)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1)
% 232.32/43.41  | | 
% 232.32/43.41  | | BETA: splitting (9) gives:
% 232.32/43.41  | | 
% 232.32/43.41  | | Case 1:
% 232.32/43.41  | | | 
% 232.32/43.41  | | |   (10)  all_57_0 = e1 & op(e3, e3) = e1
% 232.32/43.41  | | | 
% 232.32/43.41  | | | REF_CLOSE: (5), (6), (10) are inconsistent by sub-proof #2454.
% 232.32/43.41  | | | 
% 232.32/43.41  | | Case 2:
% 232.32/43.41  | | | 
% 232.32/43.41  | | |   (11)  all_57_1 = e1 & op(e3, e2) = e1
% 232.32/43.41  | | | 
% 232.32/43.41  | | | REF_CLOSE: (2), (7), (11) are inconsistent by sub-proof #2453.
% 232.32/43.41  | | | 
% 232.32/43.41  | | End of split
% 232.32/43.41  | | 
% 232.32/43.41  | Case 2:
% 232.32/43.41  | | 
% 232.32/43.41  | |   (12)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) =
% 232.32/43.41  | |           e1)
% 232.32/43.41  | | 
% 232.32/43.41  | | BETA: splitting (12) gives:
% 232.32/43.41  | | 
% 232.32/43.41  | | Case 1:
% 232.32/43.41  | | | 
% 232.32/43.41  | | |   (13)  all_57_4 = e1 & op(e3, e1) = e1
% 232.32/43.41  | | | 
% 232.32/43.41  | | | REF_CLOSE: (3), (8), (13) are inconsistent by sub-proof #2452.
% 232.32/43.41  | | | 
% 232.32/43.41  | | Case 2:
% 232.32/43.41  | | | 
% 232.32/43.41  | | |   (14)  all_57_9 = e1 & op(e3, e0) = e1
% 232.32/43.41  | | | 
% 232.32/43.41  | | | REF_CLOSE: (1), (8), (14) are inconsistent by sub-proof #2451.
% 232.32/43.41  | | | 
% 232.32/43.41  | | End of split
% 232.32/43.41  | | 
% 232.32/43.41  | End of split
% 232.32/43.41  | 
% 232.32/43.41  End of proof
% 232.32/43.41  
% 232.32/43.41  Sub-proof #2451 shows that the following formulas are inconsistent:
% 232.32/43.41  ----------------------------------------------------------------
% 232.32/43.41    (1)  all_57_9 = e1 & op(e3, e0) = e1
% 232.32/43.41    (2)  all_57_9 = e2
% 232.32/43.41    (3)   ~ (e2 = e1)
% 232.32/43.41  
% 232.32/43.41  Begin of proof
% 232.32/43.41  | 
% 232.32/43.41  | ALPHA: (1) implies:
% 232.32/43.41  |   (4)  all_57_9 = e1
% 232.32/43.41  | 
% 232.32/43.41  | COMBINE_EQS: (2), (4) imply:
% 232.32/43.41  |   (5)  e2 = e1
% 232.32/43.41  | 
% 232.32/43.41  | REDUCE: (3), (5) imply:
% 232.32/43.41  |   (6)  $false
% 232.32/43.41  | 
% 232.32/43.41  | CLOSE: (6) is inconsistent.
% 232.32/43.41  | 
% 232.32/43.41  End of proof
% 232.32/43.41  
% 232.32/43.41  Sub-proof #2452 shows that the following formulas are inconsistent:
% 232.32/43.41  ----------------------------------------------------------------
% 232.32/43.41    (1)  all_57_4 = e1 & op(e3, e1) = e1
% 232.32/43.41    (2)  all_57_4 = e2
% 232.32/43.41    (3)   ~ (e2 = e1)
% 232.32/43.41  
% 232.32/43.41  Begin of proof
% 232.32/43.41  | 
% 232.32/43.41  | ALPHA: (1) implies:
% 232.32/43.41  |   (4)  all_57_4 = e1
% 232.32/43.41  | 
% 232.32/43.41  | COMBINE_EQS: (2), (4) imply:
% 232.32/43.41  |   (5)  e2 = e1
% 232.32/43.41  | 
% 232.32/43.41  | REDUCE: (3), (5) imply:
% 232.32/43.41  |   (6)  $false
% 232.32/43.41  | 
% 232.32/43.41  | CLOSE: (6) is inconsistent.
% 232.32/43.41  | 
% 232.32/43.41  End of proof
% 232.32/43.41  
% 232.32/43.41  Sub-proof #2453 shows that the following formulas are inconsistent:
% 232.32/43.41  ----------------------------------------------------------------
% 232.32/43.41    (1)  all_57_1 = e1 & op(e3, e2) = e1
% 232.32/43.41    (2)  all_57_1 = e3
% 232.32/43.41    (3)   ~ (e3 = e1)
% 232.32/43.41  
% 232.32/43.41  Begin of proof
% 232.32/43.41  | 
% 232.32/43.41  | ALPHA: (1) implies:
% 232.32/43.41  |   (4)  all_57_1 = e1
% 232.32/43.41  | 
% 232.32/43.41  | COMBINE_EQS: (2), (4) imply:
% 232.32/43.41  |   (5)  e3 = e1
% 232.32/43.41  | 
% 232.32/43.41  | REDUCE: (3), (5) imply:
% 232.32/43.41  |   (6)  $false
% 232.32/43.41  | 
% 232.32/43.41  | CLOSE: (6) is inconsistent.
% 232.32/43.41  | 
% 232.32/43.41  End of proof
% 232.32/43.41  
% 232.32/43.41  Sub-proof #2454 shows that the following formulas are inconsistent:
% 232.32/43.41  ----------------------------------------------------------------
% 232.32/43.41    (1)  all_57_0 = e1 & op(e3, e3) = e1
% 232.32/43.41    (2)  all_57_0 = e0
% 232.32/43.41    (3)   ~ (e1 = e0)
% 232.32/43.41  
% 232.32/43.41  Begin of proof
% 232.32/43.41  | 
% 232.32/43.41  | ALPHA: (1) implies:
% 232.32/43.41  |   (4)  all_57_0 = e1
% 232.32/43.41  | 
% 232.32/43.41  | COMBINE_EQS: (2), (4) imply:
% 232.32/43.41  |   (5)  e1 = e0
% 232.32/43.41  | 
% 232.32/43.41  | SIMP: (5) implies:
% 232.32/43.41  |   (6)  e1 = e0
% 232.32/43.41  | 
% 232.32/43.41  | REDUCE: (3), (6) imply:
% 232.32/43.41  |   (7)  $false
% 232.32/43.41  | 
% 232.32/43.41  | CLOSE: (7) is inconsistent.
% 232.32/43.41  | 
% 232.32/43.41  End of proof
% 232.32/43.41  
% 232.32/43.41  Sub-proof #2455 shows that the following formulas are inconsistent:
% 232.32/43.41  ----------------------------------------------------------------
% 232.32/43.41    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.32/43.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.32/43.41    (2)   ~ (e3 = e2)
% 232.32/43.41    (3)  op(e3, e3) = e3
% 232.32/43.41    (4)  op(e3, e2) = all_53_4
% 232.32/43.41    (5)   ~ (all_53_4 = e2)
% 232.32/43.41    (6)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2)
% 232.32/43.41  
% 232.32/43.41  Begin of proof
% 232.32/43.41  | 
% 232.32/43.41  | BETA: splitting (6) gives:
% 232.32/43.41  | 
% 232.32/43.41  | Case 1:
% 232.32/43.41  | | 
% 232.32/43.41  | |   (7)  all_57_0 = e2 & op(e3, e3) = e2
% 232.32/43.41  | | 
% 232.32/43.41  | | ALPHA: (7) implies:
% 232.32/43.41  | |   (8)  op(e3, e3) = e2
% 232.32/43.41  | | 
% 232.32/43.41  | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #2490.
% 232.32/43.41  | | 
% 232.32/43.41  | Case 2:
% 232.32/43.41  | | 
% 232.32/43.41  | |   (9)  all_57_1 = e2 & op(e3, e2) = e2
% 232.32/43.41  | | 
% 232.32/43.41  | | REF_CLOSE: (1), (4), (5), (9) are inconsistent by sub-proof #2456.
% 232.32/43.41  | | 
% 232.32/43.41  | End of split
% 232.32/43.41  | 
% 232.32/43.41  End of proof
% 232.32/43.41  
% 232.32/43.41  Sub-proof #2456 shows that the following formulas are inconsistent:
% 232.32/43.41  ----------------------------------------------------------------
% 232.32/43.41    (1)  all_57_1 = e2 & op(e3, e2) = e2
% 232.32/43.41    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.32/43.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.32/43.41    (3)  op(e3, e2) = all_53_4
% 232.32/43.41    (4)   ~ (all_53_4 = e2)
% 232.32/43.41  
% 232.32/43.41  Begin of proof
% 232.32/43.41  | 
% 232.32/43.41  | ALPHA: (1) implies:
% 232.32/43.41  |   (5)  op(e3, e2) = e2
% 232.32/43.41  | 
% 232.32/43.41  | GROUND_INST: instantiating (2) with all_53_4, e2, e2, e3, simplifying with
% 232.32/43.41  |              (3), (5) gives:
% 232.32/43.41  |   (6)  all_53_4 = e2
% 232.32/43.41  | 
% 232.32/43.41  | REDUCE: (4), (6) imply:
% 232.32/43.41  |   (7)  $false
% 232.32/43.41  | 
% 232.32/43.41  | CLOSE: (7) is inconsistent.
% 232.32/43.41  | 
% 232.32/43.41  End of proof
% 232.32/43.41  
% 232.32/43.41  Sub-proof #2457 shows that the following formulas are inconsistent:
% 232.32/43.41  ----------------------------------------------------------------
% 232.32/43.41    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.32/43.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.32/43.41    (2)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0)
% 232.32/43.41    (3)   ~ (e2 = e0)
% 232.32/43.41    (4)  op(e2, e2) = e2
% 232.32/43.41    (5)   ~ (e1 = e0)
% 232.32/43.41    (6)  all_57_2 = e1
% 232.32/43.41  
% 232.32/43.41  Begin of proof
% 232.32/43.41  | 
% 232.32/43.41  | BETA: splitting (2) gives:
% 232.32/43.41  | 
% 232.32/43.41  | Case 1:
% 232.32/43.41  | | 
% 232.32/43.41  | |   (7)  all_57_2 = e0 & op(e2, e3) = e0
% 232.32/43.41  | | 
% 232.32/43.41  | | REF_CLOSE: (5), (6), (7) are inconsistent by sub-proof #2467.
% 232.32/43.41  | | 
% 232.32/43.41  | Case 2:
% 232.32/43.41  | | 
% 232.32/43.41  | |   (8)  all_57_3 = e0 & op(e2, e2) = e0
% 232.32/43.41  | | 
% 232.32/43.41  | | ALPHA: (8) implies:
% 232.32/43.41  | |   (9)  op(e2, e2) = e0
% 232.32/43.41  | | 
% 232.32/43.41  | | REF_CLOSE: (1), (3), (4), (9) are inconsistent by sub-proof #2472.
% 232.32/43.41  | | 
% 232.32/43.41  | End of split
% 232.32/43.41  | 
% 232.32/43.41  End of proof
% 232.32/43.41  
% 232.32/43.41  Sub-proof #2458 shows that the following formulas are inconsistent:
% 232.32/43.41  ----------------------------------------------------------------
% 232.32/43.41    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.32/43.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.32/43.41    (2)  op(e3, e0) = all_53_12
% 232.32/43.41    (3)  op(e3, e0) = e3
% 232.32/43.41    (4)   ~ (all_53_12 = e3)
% 232.32/43.41  
% 232.32/43.41  Begin of proof
% 232.32/43.41  | 
% 232.32/43.41  | GROUND_INST: instantiating (1) with all_53_12, e3, e0, e3, simplifying with
% 232.32/43.41  |              (2), (3) gives:
% 232.32/43.41  |   (5)  all_53_12 = e3
% 232.32/43.41  | 
% 232.32/43.41  | REDUCE: (4), (5) imply:
% 232.32/43.41  |   (6)  $false
% 232.32/43.41  | 
% 232.32/43.41  | CLOSE: (6) is inconsistent.
% 232.32/43.41  | 
% 232.32/43.41  End of proof
% 232.32/43.41  
% 232.32/43.41  Sub-proof #2459 shows that the following formulas are inconsistent:
% 232.32/43.41  ----------------------------------------------------------------
% 232.32/43.41    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.32/43.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.32/43.41    (2)   ~ (e3 = e2)
% 232.32/43.41    (3)   ~ (e3 = e0)
% 232.32/43.41    (4)  op(e3, e3) = e3
% 232.32/43.41    (5)   ~ (e2 = e0)
% 232.32/43.41    (6)   ~ (e1 = e0)
% 232.32/43.41    (7)  all_57_6 = e3
% 232.32/43.41    (8)  all_57_2 = e1
% 232.32/43.41    (9)   ~ (e2 = e1)
% 232.32/43.41    (10)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 232.32/43.41          (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 232.32/43.41    (11)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 232.32/43.41          (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 232.32/43.41  
% 232.32/43.41  Begin of proof
% 232.32/43.41  | 
% 232.32/43.41  | BETA: splitting (11) gives:
% 232.32/43.41  | 
% 232.32/43.41  | Case 1:
% 232.32/43.41  | | 
% 232.32/43.41  | |   (12)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) =
% 232.32/43.41  | |           e0)
% 232.32/43.41  | | 
% 232.32/43.41  | | REF_CLOSE: (1), (3), (4), (6), (8), (12) are inconsistent by sub-proof
% 232.32/43.41  | |            #2466.
% 232.32/43.41  | | 
% 232.32/43.41  | Case 2:
% 232.32/43.41  | | 
% 232.32/43.41  | |   (13)  (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) =
% 232.32/43.41  | |           e0)
% 232.32/43.41  | | 
% 232.32/43.41  | | BETA: splitting (13) gives:
% 232.32/43.41  | | 
% 232.32/43.41  | | Case 1:
% 232.32/43.41  | | | 
% 232.32/43.41  | | |   (14)  all_57_6 = e0 & op(e1, e3) = e0
% 232.32/43.41  | | | 
% 232.32/43.41  | | | REF_CLOSE: (3), (7), (14) are inconsistent by sub-proof #2465.
% 232.32/43.41  | | | 
% 232.32/43.41  | | Case 2:
% 232.32/43.41  | | | 
% 232.32/43.41  | | |   (15)  all_57_12 = e0 & op(e0, e3) = e0
% 232.32/43.41  | | | 
% 232.32/43.41  | | | ALPHA: (15) implies:
% 232.32/43.41  | | |   (16)  all_57_12 = e0
% 232.32/43.41  | | | 
% 232.32/43.41  | | | REF_CLOSE: (1), (2), (4), (5), (7), (8), (9), (10), (16) are inconsistent
% 232.32/43.41  | | |            by sub-proof #2460.
% 232.32/43.41  | | | 
% 232.32/43.41  | | End of split
% 232.32/43.41  | | 
% 232.32/43.41  | End of split
% 232.32/43.41  | 
% 232.32/43.41  End of proof
% 232.32/43.41  
% 232.32/43.41  Sub-proof #2460 shows that the following formulas are inconsistent:
% 232.32/43.41  ----------------------------------------------------------------
% 232.32/43.41    (1)  all_57_12 = e0
% 232.32/43.41    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.32/43.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.32/43.41    (3)   ~ (e3 = e2)
% 232.32/43.41    (4)  op(e3, e3) = e3
% 232.32/43.41    (5)   ~ (e2 = e0)
% 232.32/43.41    (6)  all_57_6 = e3
% 232.32/43.41    (7)  all_57_2 = e1
% 232.32/43.41    (8)   ~ (e2 = e1)
% 232.32/43.41    (9)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 232.32/43.41         (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 232.32/43.41  
% 232.32/43.41  Begin of proof
% 232.32/43.41  | 
% 232.32/43.41  | BETA: splitting (9) gives:
% 232.32/43.41  | 
% 232.32/43.41  | Case 1:
% 232.32/43.41  | | 
% 232.32/43.41  | |   (10)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) =
% 232.32/43.41  | |           e2)
% 232.32/43.41  | | 
% 232.32/43.41  | | BETA: splitting (10) gives:
% 232.32/43.41  | | 
% 232.32/43.41  | | Case 1:
% 232.32/43.41  | | | 
% 232.32/43.41  | | |   (11)  all_57_0 = e2 & op(e3, e3) = e2
% 232.32/43.41  | | | 
% 232.32/43.41  | | | ALPHA: (11) implies:
% 232.32/43.41  | | |   (12)  op(e3, e3) = e2
% 232.32/43.41  | | | 
% 232.32/43.41  | | | GROUND_INST: instantiating (2) with e2, e3, e3, e3, simplifying with (4),
% 232.32/43.41  | | |              (12) gives:
% 232.32/43.41  | | |   (13)  e3 = e2
% 232.32/43.41  | | | 
% 232.32/43.41  | | | REDUCE: (3), (13) imply:
% 232.32/43.41  | | |   (14)  $false
% 232.32/43.41  | | | 
% 232.32/43.41  | | | CLOSE: (14) is inconsistent.
% 232.32/43.41  | | | 
% 232.32/43.41  | | Case 2:
% 232.32/43.41  | | | 
% 232.32/43.41  | | |   (15)  all_57_2 = e2 & op(e2, e3) = e2
% 232.32/43.41  | | | 
% 232.32/43.41  | | | ALPHA: (15) implies:
% 232.32/43.41  | | |   (16)  all_57_2 = e2
% 232.32/43.41  | | | 
% 232.32/43.41  | | | REF_CLOSE: (7), (8), (16) are inconsistent by sub-proof #2464.
% 232.32/43.41  | | | 
% 232.32/43.41  | | End of split
% 232.32/43.41  | | 
% 232.32/43.41  | Case 2:
% 232.32/43.41  | | 
% 232.32/43.41  | |   (17)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) =
% 232.32/43.41  | |           e2)
% 232.32/43.41  | | 
% 232.32/43.41  | | REF_CLOSE: (1), (3), (5), (6), (17) are inconsistent by sub-proof #2461.
% 232.32/43.41  | | 
% 232.32/43.41  | End of split
% 232.32/43.41  | 
% 232.32/43.41  End of proof
% 232.32/43.41  
% 232.32/43.41  Sub-proof #2461 shows that the following formulas are inconsistent:
% 232.32/43.41  ----------------------------------------------------------------
% 232.32/43.41    (1)  (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 232.32/43.41    (2)  all_57_12 = e0
% 232.32/43.41    (3)   ~ (e3 = e2)
% 232.32/43.41    (4)   ~ (e2 = e0)
% 232.32/43.41    (5)  all_57_6 = e3
% 232.32/43.41  
% 232.32/43.41  Begin of proof
% 232.32/43.41  | 
% 232.32/43.41  | BETA: splitting (1) gives:
% 232.32/43.41  | 
% 232.32/43.41  | Case 1:
% 232.32/43.41  | | 
% 232.32/43.41  | |   (6)  all_57_6 = e2 & op(e1, e3) = e2
% 232.32/43.41  | | 
% 232.32/43.41  | | ALPHA: (6) implies:
% 232.32/43.41  | |   (7)  all_57_6 = e2
% 232.32/43.41  | | 
% 232.32/43.41  | | REF_CLOSE: (3), (5), (7) are inconsistent by sub-proof #2463.
% 232.32/43.41  | | 
% 232.32/43.41  | Case 2:
% 232.32/43.41  | | 
% 232.32/43.41  | |   (8)  all_57_12 = e2 & op(e0, e3) = e2
% 232.32/43.41  | | 
% 232.32/43.41  | | REF_CLOSE: (2), (4), (8) are inconsistent by sub-proof #2462.
% 232.32/43.41  | | 
% 232.32/43.41  | End of split
% 232.32/43.41  | 
% 232.32/43.41  End of proof
% 232.32/43.41  
% 232.32/43.41  Sub-proof #2462 shows that the following formulas are inconsistent:
% 232.32/43.41  ----------------------------------------------------------------
% 232.32/43.41    (1)  all_57_12 = e2 & op(e0, e3) = e2
% 232.32/43.41    (2)  all_57_12 = e0
% 232.32/43.41    (3)   ~ (e2 = e0)
% 232.32/43.41  
% 232.32/43.41  Begin of proof
% 232.32/43.41  | 
% 232.32/43.41  | ALPHA: (1) implies:
% 232.32/43.41  |   (4)  all_57_12 = e2
% 232.32/43.41  | 
% 232.32/43.41  | COMBINE_EQS: (2), (4) imply:
% 232.32/43.41  |   (5)  e2 = e0
% 232.32/43.41  | 
% 232.32/43.41  | REDUCE: (3), (5) imply:
% 232.32/43.41  |   (6)  $false
% 232.32/43.41  | 
% 232.32/43.41  | CLOSE: (6) is inconsistent.
% 232.32/43.41  | 
% 232.32/43.41  End of proof
% 232.32/43.41  
% 232.32/43.41  Sub-proof #2463 shows that the following formulas are inconsistent:
% 232.32/43.41  ----------------------------------------------------------------
% 232.32/43.41    (1)  all_57_6 = e3
% 232.32/43.41    (2)  all_57_6 = e2
% 232.32/43.41    (3)   ~ (e3 = e2)
% 232.32/43.41  
% 232.32/43.41  Begin of proof
% 232.32/43.41  | 
% 232.32/43.41  | COMBINE_EQS: (1), (2) imply:
% 232.32/43.41  |   (4)  e3 = e2
% 232.32/43.41  | 
% 232.32/43.41  | SIMP: (4) implies:
% 232.32/43.41  |   (5)  e3 = e2
% 232.32/43.41  | 
% 232.32/43.41  | REDUCE: (3), (5) imply:
% 232.32/43.41  |   (6)  $false
% 232.32/43.41  | 
% 232.32/43.41  | CLOSE: (6) is inconsistent.
% 232.32/43.41  | 
% 232.32/43.41  End of proof
% 232.32/43.41  
% 232.32/43.41  Sub-proof #2464 shows that the following formulas are inconsistent:
% 232.32/43.41  ----------------------------------------------------------------
% 232.32/43.41    (1)  all_57_2 = e2
% 232.32/43.41    (2)  all_57_2 = e1
% 232.32/43.41    (3)   ~ (e2 = e1)
% 232.32/43.41  
% 232.32/43.41  Begin of proof
% 232.32/43.41  | 
% 232.32/43.41  | COMBINE_EQS: (1), (2) imply:
% 232.32/43.41  |   (4)  e2 = e1
% 232.32/43.41  | 
% 232.32/43.41  | SIMP: (4) implies:
% 232.32/43.41  |   (5)  e2 = e1
% 232.32/43.41  | 
% 232.32/43.41  | REDUCE: (3), (5) imply:
% 232.32/43.41  |   (6)  $false
% 232.32/43.41  | 
% 232.32/43.41  | CLOSE: (6) is inconsistent.
% 232.32/43.41  | 
% 232.32/43.41  End of proof
% 232.32/43.41  
% 232.32/43.41  Sub-proof #2465 shows that the following formulas are inconsistent:
% 232.32/43.41  ----------------------------------------------------------------
% 232.32/43.41    (1)  all_57_6 = e0 & op(e1, e3) = e0
% 232.32/43.41    (2)  all_57_6 = e3
% 232.32/43.41    (3)   ~ (e3 = e0)
% 232.32/43.41  
% 232.32/43.41  Begin of proof
% 232.32/43.41  | 
% 232.32/43.41  | ALPHA: (1) implies:
% 232.32/43.41  |   (4)  all_57_6 = e0
% 232.32/43.41  | 
% 232.32/43.41  | COMBINE_EQS: (2), (4) imply:
% 232.32/43.41  |   (5)  e3 = e0
% 232.32/43.41  | 
% 232.32/43.41  | REDUCE: (3), (5) imply:
% 232.32/43.41  |   (6)  $false
% 232.32/43.41  | 
% 232.32/43.41  | CLOSE: (6) is inconsistent.
% 232.32/43.41  | 
% 232.32/43.41  End of proof
% 232.32/43.41  
% 232.32/43.41  Sub-proof #2466 shows that the following formulas are inconsistent:
% 232.32/43.41  ----------------------------------------------------------------
% 232.32/43.41    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.32/43.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.32/43.41    (2)   ~ (e3 = e0)
% 232.32/43.41    (3)  op(e3, e3) = e3
% 232.32/43.41    (4)   ~ (e1 = e0)
% 232.32/43.41    (5)  all_57_2 = e1
% 232.32/43.41    (6)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0)
% 232.32/43.41  
% 232.32/43.41  Begin of proof
% 232.32/43.41  | 
% 232.32/43.41  | BETA: splitting (6) gives:
% 232.32/43.41  | 
% 232.32/43.41  | Case 1:
% 232.32/43.41  | | 
% 232.32/43.41  | |   (7)  all_57_0 = e0 & op(e3, e3) = e0
% 232.32/43.41  | | 
% 232.32/43.41  | | ALPHA: (7) implies:
% 232.32/43.41  | |   (8)  op(e3, e3) = e0
% 232.32/43.41  | | 
% 232.32/43.41  | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #2494.
% 232.32/43.41  | | 
% 232.32/43.41  | Case 2:
% 232.32/43.41  | | 
% 232.32/43.41  | |   (9)  all_57_2 = e0 & op(e2, e3) = e0
% 232.32/43.41  | | 
% 232.32/43.41  | | REF_CLOSE: (4), (5), (9) are inconsistent by sub-proof #2467.
% 232.32/43.41  | | 
% 232.32/43.41  | End of split
% 232.32/43.41  | 
% 232.32/43.41  End of proof
% 232.32/43.41  
% 232.32/43.41  Sub-proof #2467 shows that the following formulas are inconsistent:
% 232.32/43.41  ----------------------------------------------------------------
% 232.32/43.41    (1)  all_57_2 = e0 & op(e2, e3) = e0
% 232.32/43.41    (2)  all_57_2 = e1
% 232.32/43.41    (3)   ~ (e1 = e0)
% 232.32/43.41  
% 232.32/43.41  Begin of proof
% 232.32/43.41  | 
% 232.32/43.41  | ALPHA: (1) implies:
% 232.32/43.41  |   (4)  all_57_2 = e0
% 232.32/43.41  | 
% 232.32/43.41  | COMBINE_EQS: (2), (4) imply:
% 232.32/43.41  |   (5)  e1 = e0
% 232.32/43.41  | 
% 232.32/43.41  | REDUCE: (3), (5) imply:
% 232.32/43.41  |   (6)  $false
% 232.32/43.41  | 
% 232.32/43.41  | CLOSE: (6) is inconsistent.
% 232.32/43.41  | 
% 232.32/43.41  End of proof
% 232.32/43.41  
% 232.32/43.41  Sub-proof #2468 shows that the following formulas are inconsistent:
% 232.32/43.41  ----------------------------------------------------------------
% 232.32/43.41    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.32/43.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.32/43.41    (2)  op(e1, e1) = all_6_2
% 232.32/43.41    (3)  op(e1, e1) = e3
% 232.32/43.41    (4)   ~ (all_6_2 = e3)
% 232.32/43.41  
% 232.32/43.41  Begin of proof
% 232.32/43.41  | 
% 232.32/43.41  | GROUND_INST: instantiating (1) with all_6_2, e3, e1, e1, simplifying with (2),
% 232.32/43.41  |              (3) gives:
% 232.32/43.41  |   (5)  all_6_2 = e3
% 232.32/43.41  | 
% 232.32/43.41  | REDUCE: (4), (5) imply:
% 232.32/43.41  |   (6)  $false
% 232.32/43.41  | 
% 232.32/43.41  | CLOSE: (6) is inconsistent.
% 232.32/43.41  | 
% 232.32/43.41  End of proof
% 232.32/43.41  
% 232.32/43.41  Sub-proof #2469 shows that the following formulas are inconsistent:
% 232.32/43.41  ----------------------------------------------------------------
% 232.32/43.41    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.32/43.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.32/43.41    (2)   ~ (e3 = e0)
% 232.32/43.41    (3)  all_57_5 = e3
% 232.32/43.41    (4)   ~ (e2 = e0)
% 232.32/43.41    (5)  op(e2, e2) = e2
% 232.32/43.41    (6)   ~ (e1 = e0)
% 232.32/43.41    (7)  all_57_2 = e1
% 232.32/43.41    (8)   ~ (all_53_13 = e0)
% 232.32/43.41    (9)  op(e2, e0) = all_53_13
% 232.32/43.41    (10)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 232.32/43.41          (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 232.32/43.41  
% 232.32/43.41  Begin of proof
% 232.32/43.41  | 
% 232.32/43.41  | BETA: splitting (10) gives:
% 232.32/43.41  | 
% 232.32/43.41  | Case 1:
% 232.32/43.41  | | 
% 232.32/43.41  | |   (11)  (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) =
% 232.32/43.41  | |           e0)
% 232.32/43.41  | | 
% 232.32/43.41  | | BETA: splitting (11) gives:
% 232.32/43.41  | | 
% 232.32/43.41  | | Case 1:
% 232.32/43.41  | | | 
% 232.32/43.41  | | |   (12)  all_57_2 = e0 & op(e2, e3) = e0
% 232.32/43.41  | | | 
% 232.32/43.41  | | | ALPHA: (12) implies:
% 232.32/43.41  | | |   (13)  all_57_2 = e0
% 232.32/43.41  | | | 
% 232.32/43.41  | | | REF_CLOSE: (6), (7), (13) are inconsistent by sub-proof #2473.
% 232.32/43.41  | | | 
% 232.32/43.41  | | Case 2:
% 232.32/43.41  | | | 
% 232.32/43.41  | | |   (14)  all_57_3 = e0 & op(e2, e2) = e0
% 232.32/43.41  | | | 
% 232.32/43.41  | | | ALPHA: (14) implies:
% 232.32/43.41  | | |   (15)  op(e2, e2) = e0
% 232.32/43.41  | | | 
% 232.32/43.41  | | | REF_CLOSE: (1), (4), (5), (15) are inconsistent by sub-proof #2472.
% 232.32/43.41  | | | 
% 232.32/43.41  | | End of split
% 232.32/43.41  | | 
% 232.32/43.41  | Case 2:
% 232.32/43.41  | | 
% 232.32/43.41  | |   (16)  (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 232.32/43.41  | |           e0)
% 232.32/43.41  | | 
% 232.32/43.41  | | BETA: splitting (16) gives:
% 232.32/43.41  | | 
% 232.32/43.41  | | Case 1:
% 232.32/43.41  | | | 
% 232.32/43.41  | | |   (17)  all_57_5 = e0 & op(e2, e1) = e0
% 232.32/43.41  | | | 
% 232.32/43.41  | | | ALPHA: (17) implies:
% 232.32/43.41  | | |   (18)  all_57_5 = e0
% 232.32/43.41  | | | 
% 232.32/43.41  | | | REF_CLOSE: (2), (3), (18) are inconsistent by sub-proof #2471.
% 232.32/43.41  | | | 
% 232.32/43.41  | | Case 2:
% 232.32/43.41  | | | 
% 232.32/43.41  | | |   (19)  all_57_10 = e0 & op(e2, e0) = e0
% 232.32/43.41  | | | 
% 232.32/43.41  | | | ALPHA: (19) implies:
% 232.32/43.41  | | |   (20)  op(e2, e0) = e0
% 232.32/43.41  | | | 
% 232.32/43.41  | | | REF_CLOSE: (1), (8), (9), (20) are inconsistent by sub-proof #2470.
% 232.32/43.41  | | | 
% 232.32/43.41  | | End of split
% 232.32/43.41  | | 
% 232.32/43.41  | End of split
% 232.32/43.41  | 
% 232.32/43.41  End of proof
% 232.32/43.41  
% 232.32/43.41  Sub-proof #2470 shows that the following formulas are inconsistent:
% 232.32/43.41  ----------------------------------------------------------------
% 232.32/43.41    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.32/43.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.32/43.41    (2)  op(e2, e0) = all_53_13
% 232.32/43.41    (3)  op(e2, e0) = e0
% 232.32/43.41    (4)   ~ (all_53_13 = e0)
% 232.32/43.41  
% 232.32/43.41  Begin of proof
% 232.32/43.41  | 
% 232.32/43.41  | GROUND_INST: instantiating (1) with all_53_13, e0, e0, e2, simplifying with
% 232.32/43.41  |              (2), (3) gives:
% 232.32/43.41  |   (5)  all_53_13 = e0
% 232.32/43.41  | 
% 232.32/43.41  | REDUCE: (4), (5) imply:
% 232.32/43.41  |   (6)  $false
% 232.32/43.41  | 
% 232.32/43.41  | CLOSE: (6) is inconsistent.
% 232.32/43.41  | 
% 232.32/43.41  End of proof
% 232.32/43.41  
% 232.32/43.41  Sub-proof #2471 shows that the following formulas are inconsistent:
% 232.32/43.41  ----------------------------------------------------------------
% 232.32/43.41    (1)  all_57_5 = e3
% 232.32/43.41    (2)  all_57_5 = e0
% 232.32/43.41    (3)   ~ (e3 = e0)
% 232.32/43.41  
% 232.32/43.41  Begin of proof
% 232.32/43.41  | 
% 232.32/43.41  | COMBINE_EQS: (1), (2) imply:
% 232.32/43.41  |   (4)  e3 = e0
% 232.32/43.41  | 
% 232.32/43.41  | SIMP: (4) implies:
% 232.32/43.41  |   (5)  e3 = e0
% 232.32/43.41  | 
% 232.32/43.41  | REDUCE: (3), (5) imply:
% 232.32/43.41  |   (6)  $false
% 232.32/43.41  | 
% 232.32/43.41  | CLOSE: (6) is inconsistent.
% 232.32/43.41  | 
% 232.32/43.41  End of proof
% 232.32/43.41  
% 232.32/43.41  Sub-proof #2472 shows that the following formulas are inconsistent:
% 232.32/43.41  ----------------------------------------------------------------
% 232.32/43.41    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.32/43.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.32/43.41    (2)  op(e2, e2) = e2
% 232.32/43.41    (3)  op(e2, e2) = e0
% 232.32/43.41    (4)   ~ (e2 = e0)
% 232.32/43.41  
% 232.32/43.41  Begin of proof
% 232.32/43.41  | 
% 232.32/43.41  | GROUND_INST: instantiating (1) with e2, e0, e2, e2, simplifying with (2), (3)
% 232.32/43.41  |              gives:
% 232.32/43.41  |   (5)  e2 = e0
% 232.32/43.41  | 
% 232.32/43.41  | REDUCE: (4), (5) imply:
% 232.32/43.41  |   (6)  $false
% 232.32/43.41  | 
% 232.32/43.41  | CLOSE: (6) is inconsistent.
% 232.32/43.41  | 
% 232.32/43.41  End of proof
% 232.32/43.41  
% 232.32/43.41  Sub-proof #2473 shows that the following formulas are inconsistent:
% 232.32/43.41  ----------------------------------------------------------------
% 232.32/43.41    (1)  all_57_2 = e1
% 232.32/43.41    (2)  all_57_2 = e0
% 232.32/43.41    (3)   ~ (e1 = e0)
% 232.32/43.41  
% 232.32/43.41  Begin of proof
% 232.32/43.41  | 
% 232.32/43.41  | COMBINE_EQS: (1), (2) imply:
% 232.32/43.41  |   (4)  e1 = e0
% 232.32/43.41  | 
% 232.32/43.41  | SIMP: (4) implies:
% 232.32/43.41  |   (5)  e1 = e0
% 232.32/43.41  | 
% 232.32/43.41  | REDUCE: (3), (5) imply:
% 232.32/43.41  |   (6)  $false
% 232.32/43.41  | 
% 232.32/43.41  | CLOSE: (6) is inconsistent.
% 232.32/43.41  | 
% 232.32/43.41  End of proof
% 232.32/43.41  
% 232.32/43.41  Sub-proof #2474 shows that the following formulas are inconsistent:
% 232.32/43.41  ----------------------------------------------------------------
% 232.32/43.41    (1)   ~ (e3 = e1)
% 232.32/43.41    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.32/43.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.32/43.41    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 232.32/43.41         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 232.32/43.41    (4)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 232.32/43.41         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 232.32/43.41    (5)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 232.32/43.41         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 232.32/43.41    (6)  all_57_4 = e3
% 232.32/43.41    (7)   ~ (e3 = e2)
% 232.32/43.41    (8)   ~ (e3 = e0)
% 232.32/43.41    (9)  op(e3, e3) = e3
% 232.32/43.41    (10)   ~ (e2 = e0)
% 232.32/43.41    (11)   ~ (e1 = e0)
% 232.32/43.41    (12)   ~ (e2 = e1)
% 232.32/43.41  
% 232.32/43.41  Begin of proof
% 232.32/43.41  | 
% 232.32/43.41  | BETA: splitting (3) gives:
% 232.32/43.41  | 
% 232.32/43.41  | Case 1:
% 232.32/43.41  | | 
% 232.32/43.41  | |   (13)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) =
% 232.32/43.41  | |           e1)
% 232.32/43.41  | | 
% 232.32/43.41  | | BETA: splitting (13) gives:
% 232.32/43.41  | | 
% 232.32/43.41  | | Case 1:
% 232.32/43.41  | | | 
% 232.32/43.41  | | |   (14)  all_57_0 = e1 & op(e3, e3) = e1
% 232.32/43.41  | | | 
% 232.32/43.41  | | | ALPHA: (14) implies:
% 232.32/43.41  | | |   (15)  op(e3, e3) = e1
% 232.32/43.41  | | | 
% 232.32/43.41  | | | REF_CLOSE: (1), (2), (9), (15) are inconsistent by sub-proof #2495.
% 232.32/43.41  | | | 
% 232.32/43.41  | | Case 2:
% 232.32/43.41  | | | 
% 232.32/43.41  | | |   (16)  all_57_1 = e1 & op(e3, e2) = e1
% 232.32/43.41  | | | 
% 232.32/43.41  | | | ALPHA: (16) implies:
% 232.32/43.41  | | |   (17)  all_57_1 = e1
% 232.32/43.41  | | | 
% 232.32/43.41  | | | BETA: splitting (5) gives:
% 232.32/43.41  | | | 
% 232.32/43.41  | | | Case 1:
% 232.32/43.41  | | | | 
% 232.32/43.41  | | | |   (18)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2)
% 232.32/43.41  | | | |           = e0)
% 232.32/43.41  | | | | 
% 232.32/43.41  | | | | REF_CLOSE: (2), (8), (9), (11), (17), (18) are inconsistent by sub-proof
% 232.32/43.41  | | | |            #2492.
% 232.32/43.41  | | | | 
% 232.32/43.41  | | | Case 2:
% 232.32/43.41  | | | | 
% 232.32/43.41  | | | |   (19)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0)
% 232.32/43.41  | | | |           = e0)
% 232.32/43.41  | | | | 
% 232.32/43.41  | | | | BETA: splitting (19) gives:
% 232.32/43.41  | | | | 
% 232.32/43.41  | | | | Case 1:
% 232.32/43.41  | | | | | 
% 232.32/43.41  | | | | |   (20)  all_57_4 = e0 & op(e3, e1) = e0
% 232.32/43.41  | | | | | 
% 232.32/43.41  | | | | | REF_CLOSE: (6), (8), (20) are inconsistent by sub-proof #2491.
% 232.32/43.41  | | | | | 
% 232.32/43.41  | | | | Case 2:
% 232.32/43.41  | | | | | 
% 232.32/43.41  | | | | |   (21)  all_57_9 = e0 & op(e3, e0) = e0
% 232.32/43.41  | | | | | 
% 232.32/43.41  | | | | | ALPHA: (21) implies:
% 232.32/43.41  | | | | |   (22)  all_57_9 = e0
% 232.32/43.41  | | | | | 
% 232.32/43.41  | | | | | REF_CLOSE: (2), (4), (6), (7), (9), (10), (12), (17), (22) are
% 232.32/43.41  | | | | |            inconsistent by sub-proof #2485.
% 232.32/43.41  | | | | | 
% 232.32/43.41  | | | | End of split
% 232.32/43.41  | | | | 
% 232.32/43.41  | | | End of split
% 232.32/43.41  | | | 
% 232.32/43.41  | | End of split
% 232.32/43.41  | | 
% 232.32/43.41  | Case 2:
% 232.32/43.41  | | 
% 232.32/43.41  | |   (23)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) =
% 232.32/43.41  | |           e1)
% 232.32/43.41  | | 
% 232.32/43.41  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 232.32/43.41  | |            (23) are inconsistent by sub-proof #2475.
% 232.32/43.41  | | 
% 232.32/43.41  | End of split
% 232.32/43.41  | 
% 232.32/43.41  End of proof
% 232.32/43.41  
% 232.32/43.41  Sub-proof #2475 shows that the following formulas are inconsistent:
% 232.32/43.41  ----------------------------------------------------------------
% 232.32/43.41    (1)   ~ (e3 = e1)
% 232.32/43.41    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.32/43.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.32/43.41    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 232.32/43.41         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 232.32/43.41    (4)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 232.32/43.41         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 232.32/43.41    (5)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 232.32/43.41    (6)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 232.32/43.41         (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 232.32/43.41    (7)  all_57_4 = e3
% 232.32/43.41    (8)   ~ (e3 = e2)
% 232.32/43.41    (9)   ~ (e3 = e0)
% 232.32/43.41    (10)  op(e3, e3) = e3
% 232.32/43.41    (11)   ~ (e2 = e0)
% 232.32/43.41    (12)   ~ (e1 = e0)
% 232.32/43.41    (13)   ~ (e2 = e1)
% 232.32/43.41  
% 232.32/43.41  Begin of proof
% 232.32/43.41  | 
% 232.32/43.41  | BETA: splitting (5) gives:
% 232.32/43.41  | 
% 232.32/43.41  | Case 1:
% 232.32/43.41  | | 
% 232.32/43.41  | |   (14)  all_57_4 = e1 & op(e3, e1) = e1
% 232.32/43.41  | | 
% 232.32/43.41  | | REF_CLOSE: (1), (7), (14) are inconsistent by sub-proof #2484.
% 232.32/43.41  | | 
% 232.32/43.41  | Case 2:
% 232.32/43.41  | | 
% 232.32/43.41  | |   (15)  all_57_9 = e1 & op(e3, e0) = e1
% 232.32/43.41  | | 
% 232.32/43.41  | | ALPHA: (15) implies:
% 232.32/43.41  | |   (16)  all_57_9 = e1
% 232.32/43.41  | | 
% 232.32/43.41  | | BETA: splitting (6) gives:
% 232.32/43.41  | | 
% 232.32/43.41  | | Case 1:
% 232.32/43.41  | | | 
% 232.32/43.41  | | |   (17)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) =
% 232.32/43.41  | | |           e0)
% 232.32/43.41  | | | 
% 232.32/43.41  | | | BETA: splitting (17) gives:
% 232.32/43.41  | | | 
% 232.32/43.41  | | | Case 1:
% 232.32/43.41  | | | | 
% 232.32/43.41  | | | |   (18)  all_57_0 = e0 & op(e3, e3) = e0
% 232.32/43.41  | | | | 
% 232.32/43.41  | | | | ALPHA: (18) implies:
% 232.32/43.41  | | | |   (19)  op(e3, e3) = e0
% 232.32/43.41  | | | | 
% 232.32/43.41  | | | | REF_CLOSE: (2), (9), (10), (19) are inconsistent by sub-proof #2494.
% 232.32/43.41  | | | | 
% 232.32/43.41  | | | Case 2:
% 232.32/43.41  | | | | 
% 232.32/43.41  | | | |   (20)  all_57_1 = e0 & op(e3, e2) = e0
% 232.32/43.41  | | | | 
% 232.32/43.41  | | | | ALPHA: (20) implies:
% 232.32/43.41  | | | |   (21)  all_57_1 = e0
% 232.32/43.41  | | | | 
% 232.32/43.41  | | | | BETA: splitting (4) gives:
% 232.32/43.41  | | | | 
% 232.32/43.41  | | | | Case 1:
% 232.32/43.41  | | | | | 
% 232.32/43.41  | | | | |   (22)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3,
% 232.32/43.41  | | | | |             e2) = e2)
% 232.32/43.41  | | | | | 
% 232.32/43.41  | | | | | BETA: splitting (22) gives:
% 232.32/43.41  | | | | | 
% 232.32/43.41  | | | | | Case 1:
% 232.32/43.41  | | | | | | 
% 232.32/43.41  | | | | | |   (23)  all_57_0 = e2 & op(e3, e3) = e2
% 232.32/43.41  | | | | | | 
% 232.32/43.41  | | | | | | ALPHA: (23) implies:
% 232.32/43.41  | | | | | |   (24)  op(e3, e3) = e2
% 232.32/43.41  | | | | | | 
% 232.32/43.41  | | | | | | REF_CLOSE: (2), (8), (10), (24) are inconsistent by sub-proof #2490.
% 232.32/43.41  | | | | | | 
% 232.32/43.41  | | | | | Case 2:
% 232.32/43.41  | | | | | | 
% 232.32/43.41  | | | | | |   (25)  all_57_1 = e2 & op(e3, e2) = e2
% 232.32/43.41  | | | | | | 
% 232.32/43.41  | | | | | | REF_CLOSE: (11), (21), (25) are inconsistent by sub-proof #2483.
% 232.32/43.41  | | | | | | 
% 232.32/43.41  | | | | | End of split
% 232.32/43.41  | | | | | 
% 232.32/43.41  | | | | Case 2:
% 232.32/43.41  | | | | | 
% 232.32/43.41  | | | | |   (26)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3,
% 232.32/43.41  | | | | |             e0) = e2)
% 232.32/43.41  | | | | | 
% 232.32/43.41  | | | | | REF_CLOSE: (7), (8), (13), (16), (26) are inconsistent by sub-proof
% 232.32/43.41  | | | | |            #2480.
% 232.32/43.41  | | | | | 
% 232.32/43.41  | | | | End of split
% 232.32/43.41  | | | | 
% 232.32/43.41  | | | End of split
% 232.32/43.41  | | | 
% 232.32/43.41  | | Case 2:
% 232.32/43.41  | | | 
% 232.32/43.41  | | |   (27)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) =
% 232.32/43.41  | | |           e0)
% 232.32/43.41  | | | 
% 232.32/43.41  | | | REF_CLOSE: (1), (2), (3), (4), (7), (8), (9), (10), (11), (12), (13), (27)
% 232.32/43.41  | | |            are inconsistent by sub-proof #2476.
% 232.32/43.41  | | | 
% 232.32/43.41  | | End of split
% 232.32/43.41  | | 
% 232.32/43.41  | End of split
% 232.32/43.41  | 
% 232.32/43.41  End of proof
% 232.32/43.41  
% 232.32/43.41  Sub-proof #2476 shows that the following formulas are inconsistent:
% 232.32/43.41  ----------------------------------------------------------------
% 232.32/43.41    (1)   ~ (e3 = e1)
% 232.32/43.41    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.32/43.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.32/43.41    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 232.32/43.41         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 232.32/43.41    (4)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 232.32/43.41         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 232.32/43.41    (5)  all_57_4 = e3
% 232.32/43.41    (6)   ~ (e3 = e2)
% 232.32/43.41    (7)   ~ (e3 = e0)
% 232.32/43.41    (8)  op(e3, e3) = e3
% 232.32/43.41    (9)   ~ (e2 = e0)
% 232.32/43.41    (10)   ~ (e1 = e0)
% 232.32/43.41    (11)  (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 232.32/43.41    (12)   ~ (e2 = e1)
% 232.32/43.41  
% 232.32/43.41  Begin of proof
% 232.32/43.41  | 
% 232.32/43.41  | BETA: splitting (11) gives:
% 232.32/43.41  | 
% 232.32/43.41  | Case 1:
% 232.32/43.41  | | 
% 232.32/43.41  | |   (13)  all_57_4 = e0 & op(e3, e1) = e0
% 232.32/43.41  | | 
% 232.32/43.41  | | REF_CLOSE: (5), (7), (13) are inconsistent by sub-proof #2491.
% 232.32/43.41  | | 
% 232.32/43.41  | Case 2:
% 232.32/43.41  | | 
% 232.32/43.41  | |   (14)  all_57_9 = e0 & op(e3, e0) = e0
% 232.32/43.41  | | 
% 232.32/43.41  | | ALPHA: (14) implies:
% 232.32/43.41  | |   (15)  all_57_9 = e0
% 232.32/43.41  | | 
% 232.32/43.41  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (12), (15) are
% 232.32/43.41  | |            inconsistent by sub-proof #2477.
% 232.32/43.41  | | 
% 232.32/43.41  | End of split
% 232.32/43.41  | 
% 232.32/43.41  End of proof
% 232.32/43.41  
% 232.32/43.41  Sub-proof #2477 shows that the following formulas are inconsistent:
% 232.32/43.41  ----------------------------------------------------------------
% 232.32/43.41    (1)   ~ (e3 = e1)
% 232.32/43.41    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.32/43.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.32/43.42    (3)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 232.32/43.42         (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 232.32/43.42    (4)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 232.32/43.42         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 232.32/43.42    (5)  all_57_4 = e3
% 232.32/43.42    (6)   ~ (e3 = e2)
% 232.32/43.42    (7)  op(e3, e3) = e3
% 232.32/43.42    (8)  all_57_9 = e0
% 232.32/43.42    (9)   ~ (e2 = e0)
% 232.32/43.42    (10)   ~ (e1 = e0)
% 232.32/43.42    (11)   ~ (e2 = e1)
% 232.32/43.42  
% 232.32/43.42  Begin of proof
% 232.32/43.42  | 
% 232.32/43.42  | BETA: splitting (3) gives:
% 232.32/43.42  | 
% 232.32/43.42  | Case 1:
% 232.32/43.42  | | 
% 232.32/43.42  | |   (12)  (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) =
% 232.32/43.42  | |           e1)
% 232.32/43.42  | | 
% 232.32/43.42  | | BETA: splitting (12) gives:
% 232.32/43.42  | | 
% 232.32/43.42  | | Case 1:
% 232.32/43.42  | | | 
% 232.32/43.42  | | |   (13)  all_57_0 = e1 & op(e3, e3) = e1
% 232.32/43.42  | | | 
% 232.32/43.42  | | | ALPHA: (13) implies:
% 232.32/43.42  | | |   (14)  op(e3, e3) = e1
% 232.32/43.42  | | | 
% 232.32/43.42  | | | REF_CLOSE: (1), (2), (7), (14) are inconsistent by sub-proof #2495.
% 232.32/43.42  | | | 
% 232.32/43.42  | | Case 2:
% 232.32/43.42  | | | 
% 232.32/43.42  | | |   (15)  all_57_1 = e1 & op(e3, e2) = e1
% 232.32/43.42  | | | 
% 232.32/43.42  | | | ALPHA: (15) implies:
% 232.32/43.42  | | |   (16)  all_57_1 = e1
% 232.32/43.42  | | | 
% 232.32/43.42  | | | REF_CLOSE: (2), (4), (5), (6), (7), (8), (9), (11), (16) are inconsistent
% 232.32/43.42  | | |            by sub-proof #2485.
% 232.32/43.42  | | | 
% 232.32/43.42  | | End of split
% 232.32/43.42  | | 
% 232.32/43.42  | Case 2:
% 232.32/43.42  | | 
% 232.32/43.42  | |   (17)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) =
% 232.32/43.42  | |           e1)
% 232.32/43.42  | | 
% 232.32/43.42  | | REF_CLOSE: (1), (5), (8), (10), (17) are inconsistent by sub-proof #2478.
% 232.32/43.42  | | 
% 232.32/43.42  | End of split
% 232.32/43.42  | 
% 232.32/43.42  End of proof
% 232.32/43.42  
% 232.32/43.42  Sub-proof #2478 shows that the following formulas are inconsistent:
% 232.32/43.42  ----------------------------------------------------------------
% 232.32/43.42    (1)   ~ (e3 = e1)
% 232.32/43.42    (2)  (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 232.32/43.42    (3)  all_57_4 = e3
% 232.32/43.42    (4)  all_57_9 = e0
% 232.32/43.42    (5)   ~ (e1 = e0)
% 232.32/43.42  
% 232.32/43.42  Begin of proof
% 232.32/43.42  | 
% 232.32/43.42  | BETA: splitting (2) gives:
% 232.32/43.42  | 
% 232.32/43.42  | Case 1:
% 232.32/43.42  | | 
% 232.32/43.42  | |   (6)  all_57_4 = e1 & op(e3, e1) = e1
% 232.32/43.42  | | 
% 232.32/43.42  | | REF_CLOSE: (1), (3), (6) are inconsistent by sub-proof #2484.
% 232.32/43.42  | | 
% 232.32/43.42  | Case 2:
% 232.32/43.42  | | 
% 232.32/43.42  | |   (7)  all_57_9 = e1 & op(e3, e0) = e1
% 232.32/43.42  | | 
% 232.32/43.42  | | ALPHA: (7) implies:
% 232.32/43.42  | |   (8)  all_57_9 = e1
% 232.32/43.42  | | 
% 232.32/43.42  | | REF_CLOSE: (4), (5), (8) are inconsistent by sub-proof #2479.
% 232.32/43.42  | | 
% 232.32/43.42  | End of split
% 232.32/43.42  | 
% 232.32/43.42  End of proof
% 232.32/43.42  
% 232.32/43.42  Sub-proof #2479 shows that the following formulas are inconsistent:
% 232.32/43.42  ----------------------------------------------------------------
% 232.32/43.42    (1)  all_57_9 = e1
% 232.32/43.42    (2)  all_57_9 = e0
% 232.32/43.42    (3)   ~ (e1 = e0)
% 232.32/43.42  
% 232.32/43.42  Begin of proof
% 232.32/43.42  | 
% 232.32/43.42  | COMBINE_EQS: (1), (2) imply:
% 232.32/43.42  |   (4)  e1 = e0
% 232.32/43.42  | 
% 232.32/43.42  | SIMP: (4) implies:
% 232.32/43.42  |   (5)  e1 = e0
% 232.32/43.42  | 
% 232.32/43.42  | REDUCE: (3), (5) imply:
% 232.32/43.42  |   (6)  $false
% 232.32/43.42  | 
% 232.32/43.42  | CLOSE: (6) is inconsistent.
% 232.32/43.42  | 
% 232.32/43.42  End of proof
% 232.32/43.42  
% 232.32/43.42  Sub-proof #2480 shows that the following formulas are inconsistent:
% 232.32/43.42  ----------------------------------------------------------------
% 232.32/43.42    (1)  all_57_9 = e1
% 232.32/43.42    (2)  all_57_4 = e3
% 232.32/43.42    (3)   ~ (e3 = e2)
% 232.32/43.42    (4)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 232.32/43.42    (5)   ~ (e2 = e1)
% 232.32/43.42  
% 232.32/43.42  Begin of proof
% 232.32/43.42  | 
% 232.32/43.42  | BETA: splitting (4) gives:
% 232.32/43.42  | 
% 232.32/43.42  | Case 1:
% 232.32/43.42  | | 
% 232.32/43.42  | |   (6)  all_57_4 = e2 & op(e3, e1) = e2
% 232.32/43.42  | | 
% 232.32/43.42  | | ALPHA: (6) implies:
% 232.32/43.42  | |   (7)  all_57_4 = e2
% 232.32/43.42  | | 
% 232.32/43.42  | | REF_CLOSE: (2), (3), (7) are inconsistent by sub-proof #2482.
% 232.32/43.42  | | 
% 232.32/43.42  | Case 2:
% 232.32/43.42  | | 
% 232.32/43.42  | |   (8)  all_57_9 = e2 & op(e3, e0) = e2
% 232.32/43.42  | | 
% 232.32/43.42  | | REF_CLOSE: (1), (5), (8) are inconsistent by sub-proof #2481.
% 232.32/43.42  | | 
% 232.32/43.42  | End of split
% 232.32/43.42  | 
% 232.32/43.42  End of proof
% 232.32/43.42  
% 232.32/43.42  Sub-proof #2481 shows that the following formulas are inconsistent:
% 232.32/43.42  ----------------------------------------------------------------
% 232.32/43.42    (1)  all_57_9 = e2 & op(e3, e0) = e2
% 232.32/43.42    (2)  all_57_9 = e1
% 232.32/43.42    (3)   ~ (e2 = e1)
% 232.32/43.42  
% 232.32/43.42  Begin of proof
% 232.32/43.42  | 
% 232.32/43.42  | ALPHA: (1) implies:
% 232.32/43.42  |   (4)  all_57_9 = e2
% 232.32/43.42  | 
% 232.32/43.42  | COMBINE_EQS: (2), (4) imply:
% 232.32/43.42  |   (5)  e2 = e1
% 232.32/43.42  | 
% 232.32/43.42  | REDUCE: (3), (5) imply:
% 232.32/43.42  |   (6)  $false
% 232.32/43.42  | 
% 232.32/43.42  | CLOSE: (6) is inconsistent.
% 232.32/43.42  | 
% 232.32/43.42  End of proof
% 232.32/43.42  
% 232.32/43.42  Sub-proof #2482 shows that the following formulas are inconsistent:
% 232.32/43.42  ----------------------------------------------------------------
% 232.32/43.42    (1)  all_57_4 = e3
% 232.32/43.42    (2)  all_57_4 = e2
% 232.32/43.42    (3)   ~ (e3 = e2)
% 232.32/43.42  
% 232.32/43.42  Begin of proof
% 232.32/43.42  | 
% 232.32/43.42  | COMBINE_EQS: (1), (2) imply:
% 232.32/43.42  |   (4)  e3 = e2
% 232.32/43.42  | 
% 232.32/43.42  | SIMP: (4) implies:
% 232.32/43.42  |   (5)  e3 = e2
% 232.32/43.42  | 
% 232.32/43.42  | REDUCE: (3), (5) imply:
% 232.32/43.42  |   (6)  $false
% 232.32/43.42  | 
% 232.32/43.42  | CLOSE: (6) is inconsistent.
% 232.32/43.42  | 
% 232.32/43.42  End of proof
% 232.32/43.42  
% 232.32/43.42  Sub-proof #2483 shows that the following formulas are inconsistent:
% 232.32/43.42  ----------------------------------------------------------------
% 232.32/43.42    (1)  all_57_1 = e2 & op(e3, e2) = e2
% 232.32/43.42    (2)  all_57_1 = e0
% 232.32/43.42    (3)   ~ (e2 = e0)
% 232.32/43.42  
% 232.32/43.42  Begin of proof
% 232.32/43.42  | 
% 232.32/43.42  | ALPHA: (1) implies:
% 232.32/43.42  |   (4)  all_57_1 = e2
% 232.32/43.42  | 
% 232.32/43.42  | COMBINE_EQS: (2), (4) imply:
% 232.32/43.42  |   (5)  e2 = e0
% 232.32/43.42  | 
% 232.32/43.42  | SIMP: (5) implies:
% 232.32/43.42  |   (6)  e2 = e0
% 232.32/43.42  | 
% 232.32/43.42  | REDUCE: (3), (6) imply:
% 232.32/43.42  |   (7)  $false
% 232.32/43.42  | 
% 232.32/43.42  | CLOSE: (7) is inconsistent.
% 232.32/43.42  | 
% 232.32/43.42  End of proof
% 232.32/43.42  
% 232.32/43.42  Sub-proof #2484 shows that the following formulas are inconsistent:
% 232.32/43.42  ----------------------------------------------------------------
% 232.32/43.42    (1)  all_57_4 = e1 & op(e3, e1) = e1
% 232.32/43.42    (2)  all_57_4 = e3
% 232.32/43.42    (3)   ~ (e3 = e1)
% 232.32/43.42  
% 232.32/43.42  Begin of proof
% 232.32/43.42  | 
% 232.32/43.42  | ALPHA: (1) implies:
% 232.32/43.42  |   (4)  all_57_4 = e1
% 232.32/43.42  | 
% 232.32/43.42  | COMBINE_EQS: (2), (4) imply:
% 232.32/43.42  |   (5)  e3 = e1
% 232.32/43.42  | 
% 232.32/43.42  | REDUCE: (3), (5) imply:
% 232.32/43.42  |   (6)  $false
% 232.32/43.42  | 
% 232.32/43.42  | CLOSE: (6) is inconsistent.
% 232.32/43.42  | 
% 232.32/43.42  End of proof
% 232.32/43.42  
% 232.32/43.42  Sub-proof #2485 shows that the following formulas are inconsistent:
% 232.32/43.42  ----------------------------------------------------------------
% 232.32/43.42    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.32/43.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.32/43.42    (2)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 232.32/43.42         (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 232.32/43.42    (3)  all_57_4 = e3
% 232.32/43.42    (4)   ~ (e3 = e2)
% 232.32/43.42    (5)  op(e3, e3) = e3
% 232.32/43.42    (6)  all_57_1 = e1
% 232.32/43.42    (7)  all_57_9 = e0
% 232.32/43.42    (8)   ~ (e2 = e0)
% 232.32/43.42    (9)   ~ (e2 = e1)
% 232.32/43.42  
% 232.32/43.42  Begin of proof
% 232.32/43.42  | 
% 232.32/43.42  | BETA: splitting (2) gives:
% 232.32/43.42  | 
% 232.32/43.42  | Case 1:
% 232.32/43.42  | | 
% 232.32/43.42  | |   (10)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) =
% 232.32/43.42  | |           e2)
% 232.32/43.42  | | 
% 232.32/43.42  | | REF_CLOSE: (1), (4), (5), (6), (9), (10) are inconsistent by sub-proof
% 232.32/43.42  | |            #2488.
% 232.32/43.42  | | 
% 232.32/43.42  | Case 2:
% 232.32/43.42  | | 
% 232.32/43.42  | |   (11)  (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) =
% 232.32/43.42  | |           e2)
% 232.32/43.42  | | 
% 232.32/43.42  | | BETA: splitting (11) gives:
% 232.32/43.42  | | 
% 232.32/43.42  | | Case 1:
% 232.32/43.42  | | | 
% 232.32/43.42  | | |   (12)  all_57_4 = e2 & op(e3, e1) = e2
% 232.32/43.42  | | | 
% 232.32/43.42  | | | REF_CLOSE: (3), (4), (12) are inconsistent by sub-proof #2487.
% 232.32/43.42  | | | 
% 232.32/43.42  | | Case 2:
% 232.32/43.42  | | | 
% 232.32/43.42  | | |   (13)  all_57_9 = e2 & op(e3, e0) = e2
% 232.32/43.42  | | | 
% 232.32/43.42  | | | REF_CLOSE: (7), (8), (13) are inconsistent by sub-proof #2486.
% 232.32/43.42  | | | 
% 232.32/43.42  | | End of split
% 232.32/43.42  | | 
% 232.32/43.42  | End of split
% 232.32/43.42  | 
% 232.32/43.42  End of proof
% 232.32/43.42  
% 232.32/43.42  Sub-proof #2486 shows that the following formulas are inconsistent:
% 232.32/43.42  ----------------------------------------------------------------
% 232.32/43.42    (1)  all_57_9 = e2 & op(e3, e0) = e2
% 232.32/43.42    (2)  all_57_9 = e0
% 232.32/43.42    (3)   ~ (e2 = e0)
% 232.32/43.42  
% 232.32/43.42  Begin of proof
% 232.32/43.42  | 
% 232.32/43.42  | ALPHA: (1) implies:
% 232.32/43.42  |   (4)  all_57_9 = e2
% 232.32/43.42  | 
% 232.32/43.42  | COMBINE_EQS: (2), (4) imply:
% 232.32/43.42  |   (5)  e2 = e0
% 232.32/43.42  | 
% 232.32/43.42  | REDUCE: (3), (5) imply:
% 232.32/43.42  |   (6)  $false
% 232.32/43.42  | 
% 232.32/43.42  | CLOSE: (6) is inconsistent.
% 232.32/43.42  | 
% 232.32/43.42  End of proof
% 232.32/43.42  
% 232.32/43.42  Sub-proof #2487 shows that the following formulas are inconsistent:
% 232.32/43.42  ----------------------------------------------------------------
% 232.32/43.42    (1)  all_57_4 = e2 & op(e3, e1) = e2
% 232.32/43.42    (2)  all_57_4 = e3
% 232.32/43.42    (3)   ~ (e3 = e2)
% 232.32/43.42  
% 232.32/43.42  Begin of proof
% 232.32/43.42  | 
% 232.32/43.42  | ALPHA: (1) implies:
% 232.32/43.42  |   (4)  all_57_4 = e2
% 232.32/43.42  | 
% 232.32/43.42  | COMBINE_EQS: (2), (4) imply:
% 232.32/43.42  |   (5)  e3 = e2
% 232.32/43.42  | 
% 232.32/43.42  | REDUCE: (3), (5) imply:
% 232.32/43.42  |   (6)  $false
% 232.32/43.42  | 
% 232.32/43.42  | CLOSE: (6) is inconsistent.
% 232.32/43.42  | 
% 232.32/43.42  End of proof
% 232.32/43.42  
% 232.32/43.42  Sub-proof #2488 shows that the following formulas are inconsistent:
% 232.32/43.42  ----------------------------------------------------------------
% 232.32/43.42    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.32/43.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.32/43.42    (2)   ~ (e3 = e2)
% 232.32/43.42    (3)  op(e3, e3) = e3
% 232.32/43.42    (4)  all_57_1 = e1
% 232.32/43.42    (5)   ~ (e2 = e1)
% 232.32/43.42    (6)  (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2)
% 232.32/43.42  
% 232.32/43.42  Begin of proof
% 232.32/43.42  | 
% 232.32/43.42  | BETA: splitting (6) gives:
% 232.32/43.42  | 
% 232.32/43.42  | Case 1:
% 232.32/43.42  | | 
% 232.32/43.42  | |   (7)  all_57_0 = e2 & op(e3, e3) = e2
% 232.32/43.42  | | 
% 232.32/43.42  | | ALPHA: (7) implies:
% 232.32/43.42  | |   (8)  op(e3, e3) = e2
% 232.32/43.42  | | 
% 232.32/43.42  | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #2490.
% 232.32/43.42  | | 
% 232.32/43.42  | Case 2:
% 232.32/43.42  | | 
% 232.32/43.42  | |   (9)  all_57_1 = e2 & op(e3, e2) = e2
% 232.32/43.42  | | 
% 232.32/43.42  | | REF_CLOSE: (4), (5), (9) are inconsistent by sub-proof #2489.
% 232.32/43.42  | | 
% 232.32/43.42  | End of split
% 232.32/43.42  | 
% 232.32/43.42  End of proof
% 232.32/43.42  
% 232.32/43.42  Sub-proof #2489 shows that the following formulas are inconsistent:
% 232.32/43.42  ----------------------------------------------------------------
% 232.32/43.42    (1)  all_57_1 = e2 & op(e3, e2) = e2
% 232.32/43.42    (2)  all_57_1 = e1
% 232.32/43.42    (3)   ~ (e2 = e1)
% 232.32/43.42  
% 232.32/43.42  Begin of proof
% 232.32/43.42  | 
% 232.32/43.42  | ALPHA: (1) implies:
% 232.32/43.42  |   (4)  all_57_1 = e2
% 232.32/43.42  | 
% 232.32/43.42  | COMBINE_EQS: (2), (4) imply:
% 232.32/43.42  |   (5)  e2 = e1
% 232.32/43.42  | 
% 232.32/43.42  | SIMP: (5) implies:
% 232.32/43.42  |   (6)  e2 = e1
% 232.32/43.42  | 
% 232.32/43.42  | REDUCE: (3), (6) imply:
% 232.32/43.42  |   (7)  $false
% 232.32/43.42  | 
% 232.32/43.42  | CLOSE: (7) is inconsistent.
% 232.32/43.42  | 
% 232.32/43.42  End of proof
% 232.32/43.42  
% 232.32/43.42  Sub-proof #2490 shows that the following formulas are inconsistent:
% 232.32/43.42  ----------------------------------------------------------------
% 232.32/43.42    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.32/43.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.32/43.42    (2)  op(e3, e3) = e3
% 232.32/43.42    (3)  op(e3, e3) = e2
% 232.32/43.42    (4)   ~ (e3 = e2)
% 232.32/43.42  
% 232.32/43.42  Begin of proof
% 232.32/43.42  | 
% 232.32/43.42  | GROUND_INST: instantiating (1) with e2, e3, e3, e3, simplifying with (2), (3)
% 232.32/43.42  |              gives:
% 232.32/43.42  |   (5)  e3 = e2
% 232.32/43.42  | 
% 232.32/43.42  | REDUCE: (4), (5) imply:
% 232.32/43.42  |   (6)  $false
% 232.32/43.42  | 
% 232.32/43.42  | CLOSE: (6) is inconsistent.
% 232.32/43.42  | 
% 232.32/43.42  End of proof
% 232.32/43.42  
% 232.32/43.42  Sub-proof #2491 shows that the following formulas are inconsistent:
% 232.32/43.42  ----------------------------------------------------------------
% 232.32/43.42    (1)  all_57_4 = e0 & op(e3, e1) = e0
% 232.32/43.42    (2)  all_57_4 = e3
% 232.32/43.42    (3)   ~ (e3 = e0)
% 232.32/43.42  
% 232.32/43.42  Begin of proof
% 232.32/43.42  | 
% 232.32/43.42  | ALPHA: (1) implies:
% 232.32/43.42  |   (4)  all_57_4 = e0
% 232.32/43.42  | 
% 232.32/43.42  | COMBINE_EQS: (2), (4) imply:
% 232.32/43.42  |   (5)  e3 = e0
% 232.32/43.42  | 
% 232.32/43.42  | REDUCE: (3), (5) imply:
% 232.32/43.42  |   (6)  $false
% 232.32/43.42  | 
% 232.32/43.42  | CLOSE: (6) is inconsistent.
% 232.32/43.42  | 
% 232.32/43.42  End of proof
% 232.32/43.42  
% 232.32/43.42  Sub-proof #2492 shows that the following formulas are inconsistent:
% 232.32/43.42  ----------------------------------------------------------------
% 232.32/43.42    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.32/43.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.32/43.42    (2)   ~ (e3 = e0)
% 232.32/43.42    (3)  op(e3, e3) = e3
% 232.32/43.42    (4)  all_57_1 = e1
% 232.32/43.42    (5)   ~ (e1 = e0)
% 232.32/43.42    (6)  (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0)
% 232.32/43.42  
% 232.32/43.42  Begin of proof
% 232.32/43.42  | 
% 232.32/43.42  | BETA: splitting (6) gives:
% 232.32/43.42  | 
% 232.32/43.42  | Case 1:
% 232.32/43.42  | | 
% 232.32/43.42  | |   (7)  all_57_0 = e0 & op(e3, e3) = e0
% 232.32/43.42  | | 
% 232.32/43.42  | | ALPHA: (7) implies:
% 232.32/43.42  | |   (8)  op(e3, e3) = e0
% 232.32/43.42  | | 
% 232.32/43.42  | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #2494.
% 232.32/43.42  | | 
% 232.32/43.42  | Case 2:
% 232.32/43.42  | | 
% 232.32/43.42  | |   (9)  all_57_1 = e0 & op(e3, e2) = e0
% 232.32/43.42  | | 
% 232.32/43.42  | | REF_CLOSE: (4), (5), (9) are inconsistent by sub-proof #2493.
% 232.32/43.42  | | 
% 232.32/43.42  | End of split
% 232.32/43.42  | 
% 232.32/43.42  End of proof
% 232.32/43.42  
% 232.32/43.42  Sub-proof #2493 shows that the following formulas are inconsistent:
% 232.32/43.42  ----------------------------------------------------------------
% 232.32/43.42    (1)  all_57_1 = e0 & op(e3, e2) = e0
% 232.32/43.42    (2)  all_57_1 = e1
% 232.32/43.42    (3)   ~ (e1 = e0)
% 232.32/43.42  
% 232.32/43.42  Begin of proof
% 232.32/43.42  | 
% 232.32/43.42  | ALPHA: (1) implies:
% 232.32/43.42  |   (4)  all_57_1 = e0
% 232.32/43.42  | 
% 232.32/43.42  | COMBINE_EQS: (2), (4) imply:
% 232.32/43.42  |   (5)  e1 = e0
% 232.32/43.42  | 
% 232.32/43.42  | REDUCE: (3), (5) imply:
% 232.32/43.42  |   (6)  $false
% 232.32/43.42  | 
% 232.32/43.42  | CLOSE: (6) is inconsistent.
% 232.32/43.42  | 
% 232.32/43.42  End of proof
% 232.32/43.42  
% 232.32/43.42  Sub-proof #2494 shows that the following formulas are inconsistent:
% 232.32/43.42  ----------------------------------------------------------------
% 232.32/43.42    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.32/43.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.32/43.42    (2)  op(e3, e3) = e3
% 232.32/43.42    (3)  op(e3, e3) = e0
% 232.32/43.42    (4)   ~ (e3 = e0)
% 232.32/43.42  
% 232.32/43.42  Begin of proof
% 232.32/43.42  | 
% 232.32/43.42  | GROUND_INST: instantiating (1) with e0, e3, e3, e3, simplifying with (2), (3)
% 232.32/43.42  |              gives:
% 232.32/43.42  |   (5)  e3 = e0
% 232.32/43.42  | 
% 232.32/43.42  | REDUCE: (4), (5) imply:
% 232.32/43.42  |   (6)  $false
% 232.32/43.42  | 
% 232.32/43.42  | CLOSE: (6) is inconsistent.
% 232.32/43.42  | 
% 232.32/43.42  End of proof
% 232.32/43.42  
% 232.32/43.42  Sub-proof #2495 shows that the following formulas are inconsistent:
% 232.32/43.42  ----------------------------------------------------------------
% 232.32/43.42    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.32/43.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.32/43.42    (2)  op(e3, e3) = e3
% 232.32/43.42    (3)  op(e3, e3) = e1
% 232.32/43.42    (4)   ~ (e3 = e1)
% 232.32/43.42  
% 232.32/43.42  Begin of proof
% 232.32/43.42  | 
% 232.32/43.42  | GROUND_INST: instantiating (1) with e1, e3, e3, e3, simplifying with (2), (3)
% 232.32/43.42  |              gives:
% 232.32/43.42  |   (5)  e3 = e1
% 232.32/43.42  | 
% 232.32/43.42  | REDUCE: (4), (5) imply:
% 232.32/43.42  |   (6)  $false
% 232.32/43.42  | 
% 232.32/43.42  | CLOSE: (6) is inconsistent.
% 232.32/43.42  | 
% 232.32/43.42  End of proof
% 232.32/43.42  
% 232.32/43.42  Sub-proof #2496 shows that the following formulas are inconsistent:
% 232.32/43.42  ----------------------------------------------------------------
% 232.32/43.42    (1)  all_55_8 = all_53_2
% 232.32/43.42    (2)  all_55_8 = e3
% 232.32/43.42    (3)   ~ (all_53_2 = e3)
% 232.32/43.42  
% 232.32/43.42  Begin of proof
% 232.32/43.42  | 
% 232.32/43.42  | COMBINE_EQS: (1), (2) imply:
% 232.32/43.42  |   (4)  all_53_2 = e3
% 232.32/43.42  | 
% 232.32/43.42  | SIMP: (4) implies:
% 232.32/43.42  |   (5)  all_53_2 = e3
% 232.32/43.42  | 
% 232.32/43.42  | REDUCE: (3), (5) imply:
% 232.32/43.42  |   (6)  $false
% 232.32/43.42  | 
% 232.32/43.42  | CLOSE: (6) is inconsistent.
% 232.32/43.42  | 
% 232.32/43.42  End of proof
% 232.32/43.42  
% 232.32/43.42  Sub-proof #2497 shows that the following formulas are inconsistent:
% 232.32/43.42  ----------------------------------------------------------------
% 232.32/43.42    (1)  all_55_11 = all_53_14
% 232.32/43.42    (2)  all_55_11 = e3
% 232.32/43.42    (3)   ~ (all_53_14 = e3)
% 232.32/43.42  
% 232.32/43.42  Begin of proof
% 232.32/43.42  | 
% 232.32/43.42  | COMBINE_EQS: (1), (2) imply:
% 232.32/43.42  |   (4)  all_53_14 = e3
% 232.32/43.42  | 
% 232.32/43.42  | SIMP: (4) implies:
% 232.32/43.42  |   (5)  all_53_14 = e3
% 232.32/43.42  | 
% 232.32/43.42  | REDUCE: (3), (5) imply:
% 232.32/43.42  |   (6)  $false
% 232.32/43.42  | 
% 232.32/43.42  | CLOSE: (6) is inconsistent.
% 232.32/43.42  | 
% 232.32/43.42  End of proof
% 232.32/43.42  
% 232.32/43.42  Sub-proof #2498 shows that the following formulas are inconsistent:
% 232.32/43.42  ----------------------------------------------------------------
% 232.32/43.42    (1)  all_55_6 = all_53_9
% 232.32/43.42    (2)  all_55_6 = e3
% 232.32/43.42    (3)   ~ (all_53_9 = e3)
% 232.32/43.42  
% 232.32/43.42  Begin of proof
% 232.32/43.42  | 
% 232.32/43.42  | COMBINE_EQS: (1), (2) imply:
% 232.32/43.42  |   (4)  all_53_9 = e3
% 232.32/43.42  | 
% 232.32/43.42  | SIMP: (4) implies:
% 232.32/43.42  |   (5)  all_53_9 = e3
% 232.32/43.42  | 
% 232.32/43.42  | REDUCE: (3), (5) imply:
% 232.32/43.42  |   (6)  $false
% 232.32/43.42  | 
% 232.32/43.42  | CLOSE: (6) is inconsistent.
% 232.32/43.42  | 
% 232.32/43.42  End of proof
% 232.32/43.42  
% 232.32/43.42  Sub-proof #2499 shows that the following formulas are inconsistent:
% 232.32/43.42  ----------------------------------------------------------------
% 232.32/43.42    (1)  all_55_10 = all_6_2
% 232.32/43.42    (2)  all_55_10 = e2
% 232.32/43.42    (3)   ~ (all_6_2 = e2)
% 232.32/43.42  
% 232.32/43.42  Begin of proof
% 232.32/43.42  | 
% 232.32/43.42  | COMBINE_EQS: (1), (2) imply:
% 232.32/43.42  |   (4)  all_6_2 = e2
% 232.32/43.42  | 
% 232.32/43.42  | SIMP: (4) implies:
% 232.32/43.42  |   (5)  all_6_2 = e2
% 232.32/43.42  | 
% 232.32/43.42  | REDUCE: (3), (5) imply:
% 232.32/43.42  |   (6)  $false
% 232.32/43.42  | 
% 232.32/43.42  | CLOSE: (6) is inconsistent.
% 232.32/43.42  | 
% 232.32/43.42  End of proof
% 232.32/43.42  
% 232.32/43.42  Sub-proof #2500 shows that the following formulas are inconsistent:
% 232.32/43.42  ----------------------------------------------------------------
% 232.32/43.42    (1)  all_55_10 = all_6_2
% 232.32/43.42    (2)  all_55_10 = e3
% 232.32/43.42    (3)   ~ (all_6_2 = e3)
% 232.32/43.42  
% 232.32/43.42  Begin of proof
% 232.32/43.42  | 
% 232.32/43.42  | COMBINE_EQS: (1), (2) imply:
% 232.32/43.42  |   (4)  all_6_2 = e3
% 232.32/43.42  | 
% 232.32/43.42  | SIMP: (4) implies:
% 232.32/43.42  |   (5)  all_6_2 = e3
% 232.32/43.42  | 
% 232.32/43.42  | REDUCE: (3), (5) imply:
% 232.32/43.42  |   (6)  $false
% 232.32/43.42  | 
% 232.32/43.42  | CLOSE: (6) is inconsistent.
% 232.32/43.42  | 
% 232.32/43.42  End of proof
% 232.32/43.42  
% 232.32/43.42  Sub-proof #2501 shows that the following formulas are inconsistent:
% 232.32/43.42  ----------------------------------------------------------------
% 232.32/43.42    (1)  all_55_15 = all_4_2
% 232.32/43.42    (2)  all_55_15 = e1
% 232.32/43.42    (3)   ~ (all_4_2 = e1)
% 232.32/43.42  
% 232.32/43.42  Begin of proof
% 232.32/43.42  | 
% 232.32/43.42  | COMBINE_EQS: (1), (2) imply:
% 232.32/43.42  |   (4)  all_4_2 = e1
% 232.32/43.42  | 
% 232.32/43.42  | SIMP: (4) implies:
% 232.32/43.42  |   (5)  all_4_2 = e1
% 232.32/43.42  | 
% 232.32/43.42  | REDUCE: (3), (5) imply:
% 232.32/43.42  |   (6)  $false
% 232.32/43.42  | 
% 232.32/43.42  | CLOSE: (6) is inconsistent.
% 232.32/43.42  | 
% 232.32/43.42  End of proof
% 232.32/43.42  
% 232.32/43.42  Sub-proof #2502 shows that the following formulas are inconsistent:
% 232.32/43.42  ----------------------------------------------------------------
% 232.32/43.42    (1)  all_55_15 = all_4_2
% 232.32/43.42    (2)  all_55_15 = e2
% 232.32/43.42    (3)   ~ (all_4_2 = e2)
% 232.32/43.42  
% 232.32/43.42  Begin of proof
% 232.32/43.42  | 
% 232.32/43.42  | COMBINE_EQS: (1), (2) imply:
% 232.32/43.42  |   (4)  all_4_2 = e2
% 232.32/43.42  | 
% 232.32/43.42  | SIMP: (4) implies:
% 232.32/43.42  |   (5)  all_4_2 = e2
% 232.32/43.42  | 
% 232.32/43.42  | REDUCE: (3), (5) imply:
% 232.32/43.42  |   (6)  $false
% 232.32/43.42  | 
% 232.32/43.42  | CLOSE: (6) is inconsistent.
% 232.32/43.42  | 
% 232.32/43.42  End of proof
% 232.32/43.42  
% 232.32/43.42  Sub-proof #2503 shows that the following formulas are inconsistent:
% 232.32/43.42  ----------------------------------------------------------------
% 232.32/43.42    (1)  all_55_15 = all_4_2
% 232.32/43.42    (2)  all_55_15 = e3
% 232.32/43.42    (3)   ~ (all_4_2 = e3)
% 232.32/43.42  
% 232.32/43.42  Begin of proof
% 232.32/43.42  | 
% 232.32/43.42  | COMBINE_EQS: (1), (2) imply:
% 232.32/43.42  |   (4)  all_4_2 = e3
% 232.32/43.42  | 
% 232.32/43.42  | SIMP: (4) implies:
% 232.32/43.42  |   (5)  all_4_2 = e3
% 232.32/43.42  | 
% 232.32/43.42  | REDUCE: (3), (5) imply:
% 232.32/43.42  |   (6)  $false
% 232.32/43.42  | 
% 232.32/43.42  | CLOSE: (6) is inconsistent.
% 232.32/43.42  | 
% 232.32/43.42  End of proof
% 232.32/43.42  
% 232.32/43.42  Sub-proof #2504 shows that the following formulas are inconsistent:
% 232.32/43.42  ----------------------------------------------------------------
% 232.32/43.42    (1)  all_57_2 = e2 & op(e2, e3) = e2
% 232.32/43.42    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 232.32/43.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 232.32/43.42    (3)  op(e2, e3) = all_53_1
% 232.32/43.42    (4)   ~ (all_53_1 = e2)
% 232.32/43.42  
% 232.32/43.42  Begin of proof
% 232.32/43.42  | 
% 232.32/43.42  | ALPHA: (1) implies:
% 232.32/43.42  |   (5)  op(e2, e3) = e2
% 232.32/43.42  | 
% 232.32/43.42  | GROUND_INST: instantiating (2) with all_53_1, e2, e3, e2, simplifying with
% 232.32/43.42  |              (3), (5) gives:
% 232.32/43.42  |   (6)  all_53_1 = e2
% 232.32/43.42  | 
% 232.32/43.42  | REDUCE: (4), (6) imply:
% 232.32/43.42  |   (7)  $false
% 232.32/43.42  | 
% 232.32/43.42  | CLOSE: (7) is inconsistent.
% 232.32/43.42  | 
% 232.32/43.42  End of proof
% 232.32/43.42  % SZS output end Proof for theBenchmark
% 232.32/43.42  
% 232.32/43.42  42828ms
%------------------------------------------------------------------------------